From 5db4ce779bd2b536b5f66019aa0611455e773db1 Mon Sep 17 00:00:00 2001 From: Michael Xian Date: Fri, 19 Dec 2025 19:45:51 -0800 Subject: [PATCH] complete hw --- .virtual_documents/Class 7 Homework.ipynb | 98 ++++ .virtual_documents/Data Collection.ipynb | 66 +++ .virtual_documents/Data Generation.ipynb | 127 +++++ Class 7 Homework.ipynb | 510 ++++++++++++++++-- Data Collection.ipynb | 164 ++++++ Data Generation.ipynb | 600 ++++++++++++++++++++++ README.md | 2 + data/papers/formatted.jsonl | 492 ++++++++++++++++++ data/papers/pairs.json | 1 + data/papers/pairs.jsonl | 492 ++++++++++++++++++ data/papers/paper_urls.json | 1 + data/papers/papers.json | 1 + data/papers/test.jsonl | 10 + report.txt | 93 ++++ 14 files changed, 2605 insertions(+), 52 deletions(-) create mode 100644 .virtual_documents/Class 7 Homework.ipynb create mode 100644 .virtual_documents/Data Collection.ipynb create mode 100644 .virtual_documents/Data Generation.ipynb create mode 100644 Data Collection.ipynb create mode 100644 Data Generation.ipynb create mode 100644 README.md create mode 100644 data/papers/formatted.jsonl create mode 100644 data/papers/pairs.json create mode 100644 data/papers/pairs.jsonl create mode 100644 data/papers/paper_urls.json create mode 100644 data/papers/papers.json create mode 100644 data/papers/test.jsonl create mode 100644 report.txt diff --git a/.virtual_documents/Class 7 Homework.ipynb b/.virtual_documents/Class 7 Homework.ipynb new file mode 100644 index 0000000..f827fde --- /dev/null +++ b/.virtual_documents/Class 7 Homework.ipynb @@ -0,0 +1,98 @@ + + + +import json + +system_prompt = "You are a helpful academic Q&A assistant specialized in scholarly content." +data = [] + +# Suppose qas_list is a list of all generated QAs, where each QA is a dict: {"question": ..., "answer": ...} +for qa in qas_list: + user_q = qa["question"] + assistant_a = qa["answer"] + # Compose the prompt with system, user, assistant roles + full_prompt = f"<|system|>{system_prompt}<|user|>{user_q}<|assistant|>{assistant_a}" + data.append({"text": full_prompt}) + +# Write to JSONL file +with open("synthetic_qa.jsonl", "w") as outfile: + for entry in data: + outfile.write(json.dumps(entry) + "\n") + + + + + + + + +from unsloth import FastLanguageModel, SFTTrainer +from transformers import AutoTokenizer, TrainingArguments +from datasets import load_dataset + +# Load the base LLaMA 3 7B model in 4-bit mode (dynamic 4-bit quantization) +model_name = "unsloth/llama-3.1-7b-unsloth-bnb-4bit" +model = FastLanguageModel.from_pretrained(model_name) +tokenizer = AutoTokenizer.from_pretrained(model_name, use_fast=False) + +# Load our synthetic Q&A dataset +dataset = load_dataset("json", data_files="synthetic_qa.jsonl", split="train") + +# Initialize the trainer for Supervised Fine-Tuning (SFT) +trainer = SFTTrainer( + model=model, + tokenizer=tokenizer, + train_dataset=dataset, + dataset_text_field="text", + args=TrainingArguments( + output_dir="llama3-7b-qlora-finetuned", + per_device_train_batch_size=4, # small batch size for Colab GPU + gradient_accumulation_steps=4, # accumulate gradients to simulate larger batch + num_train_epochs=2, + learning_rate=2e-4, + fp16=True, + logging_steps=50, + save_strategy="epoch" + ) +) + +trainer.train() +model.save_pretrained("llama3-7b-qlora-finetuned") + + + + + +# Define some test questions (ensure these were not exactly in training data) +test_questions = [ + "What is the main hypothesis proposed by the paper on quantum computing?", + "How did the authors of the deep learning study evaluate their model's performance?", + # ... (add total 10 questions) +] + +# Load the base and fine-tuned models for inference +base_model = FastLanguageModel.from_pretrained(model_name) # base 7B model +ft_model = FastLanguageModel.from_pretrained("llama3-7b-qlora-finetuned") + +for q in test_questions: + prompt_input = f"<|system|>{system_prompt}<|user|>{q}<|assistant|>" + # Tokenize input and generate output with each model + input_ids = tokenizer(prompt_input, return_tensors='pt').input_ids.cuda() + base_output_ids = base_model.generate(input_ids, max_new_tokens=150) + ft_output_ids = ft_model.generate(input_ids, max_new_tokens=150) + # Decode the outputs + base_answer = tokenizer.decode(base_output_ids[0], skip_special_tokens=True) + ft_answer = tokenizer.decode(ft_output_ids[0], skip_special_tokens=True) + # (Post-process to remove the prompt part if needed) + base_answer = base_answer.split('<|assistant|>')[-1].strip() + ft_answer = ft_answer.split('<|assistant|>')[-1].strip() + print(f"Q: {q}") + print(f"Base Model Answer: {base_answer}") + print(f"Fine-Tuned Model Answer: {ft_answer}") + print("-" * 60) + + + + + + diff --git a/.virtual_documents/Data Collection.ipynb b/.virtual_documents/Data Collection.ipynb new file mode 100644 index 0000000..b2ecc77 --- /dev/null +++ b/.virtual_documents/Data Collection.ipynb @@ -0,0 +1,66 @@ +!pip install PyMuPDF +!pip install feedparser + + +import fitz # PyMuPDF +from typing import List +import urllib, urllib.request +import feedparser +import requests +from io import BytesIO +import ssl, certifi, urllib.request + +context = ssl.create_default_context(cafile=certifi.where()) + +def ssl_read_url(url: str) -> str: + return urllib.request.urlopen(url, context=context).read() + +def get_pdf_urls() -> List[str]: + url = f"https://export.arxiv.org/api/query?search_query=all:a&start=0&max_results=100" + data = ssl_read_url(url) + res = feedparser.parse(data) + return [ + link.href + for entry in res.entries + for link in entry.links + if "pdf" in link.href + ] + + +def extract_text_from_url(url: str) -> str: + """ + Open a PDF and extract all text as a single string. + """ + response = requests.get(url) + + pdf_bytes = BytesIO(response.content) + doc = fitz.open(stream=pdf_bytes, filetype="pdf") + pages = [] + for page in doc: + page_text = page.get_text() # get raw text from page + pages.append(page_text) + full_text = "\n".join(pages) + return full_text + + +urls = get_pdf_urls() +print(len(urls)) + + +import json +with open("data/papers/paper_urls.json", "w") as file: + json.dump(urls, file) + + +papers = [ + extract_text_from_url(url) for url in urls +] +print(len(papers)) + + +import json +with open("data/papers/papers.json", "w") as file: + json.dump(papers, file) + + + diff --git a/.virtual_documents/Data Generation.ipynb b/.virtual_documents/Data Generation.ipynb new file mode 100644 index 0000000..46e78e3 --- /dev/null +++ b/.virtual_documents/Data Generation.ipynb @@ -0,0 +1,127 @@ +def strip_block_quotes(response): + lines = response.split("\n") + if "```" in lines[0] and "```" in lines[-1]: + return '\n'.join(lines[1:-1]) + else: + return response + +def escape_backslashes(s: str) -> str: + return s.replace("\\", "\\\\") + + +from ollama import chat +import json + +initial_messages = [ + { + "role": "system", + "content": """ + You will be generating synthetic data for supervised fine tuning. + The user will provide you with a research paper. + You will provide 5 questions and answers. The questions will be research questions which relate to the topic of the paper, but not referencing the paper itself. + One question and answer pair will have a quesion related to the paper topic, but which is unanswered by it, and the answer should inform the user that the agent does not know the answer, and explain why (e.g. if it requires more research in the paper, or simply is not in the paper, so is not in the knowledge domain of the model). + The question answer pair will be in the form {"question": string, "answer": string}. You will return them in an array in JSON format. + """ + } +] +model = "gpt-oss:20b-cloud" +max_length = 200000 + +def generate_qa(paper): + paper = paper[:max_length] # Cutoff if paper is too large for model to handle + response = chat( + model=model, + messages=[ + *initial_messages, + { + "role": "user", + "content": paper + } + ]) + raw = response["message"]["content"] + stripped = strip_block_quotes(response["message"]["content"]) + + content = escape_backslashes(stripped) + pairs = json.loads(content) + if len(pairs) < 5: + raise Exception(f"Unexpected number of pairs: {len(pairs)}. Content: {content}") + for pair in pairs: + if not pair["question"] or not pair["answer"]: + raise Exception(f"Unexpected format: {content}") + return pairs + + +import json +with open("data/papers/papers.json") as file: + papers = json.load(file) + + +if not paper_to_pairs: + paper_to_pairs = dict() # Store papers mapped to pairs in case some fail, we can retry and add to dictionary later +else: + print("exists, skipping") + + +for paper in papers: + opening = paper[:100] + if opening not in paper_to_pairs: + print(opening) + try: + paper_to_pairs[opening] = generate_qa(paper) + except: + print("Failed, skipping") + pass + else: + print("Pairs already finished, skipping") + + + + + +print(len(papers[0])) + + +print(len(papers[1])) + + +print(len(papers[1][:1000000])) + + +print(len(paper_to_pairs)) + + +import json +with open("temp.json", "w") as file: + json.dump(paper_to_pairs, file) + + +import json +with open("temp.json", "r") as file: + paper_to_pairs = json.load(file) + + +qa_pairs = [ + pair + for _, value in paper_to_pairs.items() + for pair in value +] +print(len(qa_pairs)) +print(qa_pairs[0]) + + +def to_formatted(pair): + user_q = pair["question"] + assistant_a = pair["answer"] + # Compose the prompt with system, user, assistant roles + return f"<|system|>{system_prompt}<|user|>{user_q}<|assistant|>{assistant_a}" + + + +import json +with open("data/papers/formatted.jsonl", "w") as file: + for pair in qa_pairs: + json.dump(to_formatted(pair), file) + file.write("\n") + + + diff --git a/Class 7 Homework.ipynb b/Class 7 Homework.ipynb index 81603ec..3d645d7 100644 --- a/Class 7 Homework.ipynb +++ b/Class 7 Homework.ipynb @@ -1,5 +1,196 @@ { "cells": [ + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Defaulting to user installation because normal site-packages is not writeable\n", + "Looking in indexes: https://pypi.org/simple, 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update, run: \u001b[0m\u001b[32;49mpython -m pip install --upgrade pip\u001b[0m\n", + "Defaulting to user installation because normal site-packages is not writeable\n", + "Looking in indexes: https://pypi.org/simple, https://pypi.ngc.nvidia.com\n", + "Collecting IProgress\n", + " Downloading IProgress-0.4-py3-none-any.whl.metadata (2.1 kB)\n", + "Requirement already satisfied: six in /usr/local/lib/python3.10/dist-packages (from IProgress) (1.16.0)\n", + "Downloading IProgress-0.4-py3-none-any.whl (11 kB)\n", + "Installing collected packages: IProgress\n", + "Successfully installed IProgress-0.4\n", + "\n", + "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m25.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m25.3\u001b[0m\n", + "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpython -m pip install --upgrade pip\u001b[0m\n", + "Defaulting to user installation because normal site-packages is not writeable\n", + "Looking in indexes: https://pypi.org/simple, https://pypi.ngc.nvidia.com\n", + "Requirement already satisfied: trl in ./.local/lib/python3.10/site-packages (0.24.0)\n", + "Requirement already satisfied: accelerate>=1.4.0 in ./.local/lib/python3.10/site-packages (from trl) (1.12.0)\n", + "Requirement already satisfied: datasets>=3.0.0 in ./.local/lib/python3.10/site-packages (from trl) (4.3.0)\n", + "Requirement already satisfied: transformers>=4.56.1 in ./.local/lib/python3.10/site-packages (from trl) (4.57.3)\n", + "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.10/dist-packages (from accelerate>=1.4.0->trl) (1.24.4)\n", + "Requirement already satisfied: packaging>=20.0 in ./.local/lib/python3.10/site-packages (from accelerate>=1.4.0->trl) (25.0)\n", + "Requirement already satisfied: psutil in /usr/local/lib/python3.10/dist-packages (from 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JSONL Conversion Example:** Once you have all Q\\&A pairs (for example, collected in a Python list or as separate files), convert them into a single JSONL file for fine-tuning. The following code illustrates how to structure the data with the desired format:\n" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "import json\n", - "\n", - "system_prompt = \"You are a helpful academic Q&A assistant specialized in scholarly content.\"\n", - "data = []\n", - "\n", - "# Suppose qas_list is a list of all generated QAs, where each QA is a dict: {\"question\": ..., \"answer\": ...}\n", - "for qa in qas_list:\n", - " user_q = qa[\"question\"]\n", - " assistant_a = qa[\"answer\"]\n", - " # Compose the prompt with system, user, assistant roles\n", - " full_prompt = f\"<|system|>{system_prompt}<|user|>{user_q}<|assistant|>{assistant_a}\"\n", - " data.append({\"text\": full_prompt})\n", - "\n", - "# Write to JSONL file\n", - "with open(\"synthetic_qa.jsonl\", \"w\") as outfile:\n", - " for entry in data:\n", - " outfile.write(json.dumps(entry) + \"\\n\")" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -111,42 +277,136 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "==((====))== Unsloth 2025.12.7: Fast Llama patching. Transformers: 4.57.3.\n", + " \\\\ /| inference-ai GPU cuda. Num GPUs = 1. Max memory: 47.988 GB. Platform: Linux.\n", + "O^O/ \\_/ \\ Torch: 2.9.1+cu128. CUDA: 8.6. CUDA Toolkit: 12.8. Triton: 3.5.1\n", + "\\ / Bfloat16 = TRUE. FA [Xformers = None. FA2 = False]\n", + " \"-____-\" Free license: http://github.com/unslothai/unsloth\n", + "Unsloth: Fast downloading is enabled - ignore downloading bars which are red colored!\n", + "trainable params: 41,943,040 || all params: 8,072,204,288 || trainable%: 0.5196\n" + ] + } + ], "source": [ - "from unsloth import FastLanguageModel, SFTTrainer\n", - "from transformers import AutoTokenizer, TrainingArguments\n", + "from unsloth import FastLanguageModel\n", + "from trl import SFTTrainer\n", + "from transformers import TrainingArguments\n", "from datasets import load_dataset\n", "\n", "# Load the base LLaMA 3 7B model in 4-bit mode (dynamic 4-bit quantization)\n", - "model_name = \"unsloth/llama-3.1-7b-unsloth-bnb-4bit\"\n", - "model = FastLanguageModel.from_pretrained(model_name)\n", - "tokenizer = AutoTokenizer.from_pretrained(model_name, use_fast=False)\n", + "# Updated model name to use existing model (3.1-7 no longer exists)\n", + "model_name = \"unsloth/Llama-3.1-8B-unsloth-bnb-4bit\"\n", + "# Use tokenizer from fast language model's returned tuple instead \n", + "model, tokenizer = FastLanguageModel.from_pretrained(model_name)\n", + "#tokenizer = AutoTokenizer.from_pretrained(model_name, use_fast=False)\n", "\n", "# Load our synthetic Q&A dataset\n", - "dataset = load_dataset(\"json\", data_files=\"synthetic_qa.jsonl\", split=\"train\")\n", + "dataset = load_dataset(\"json\", data_files=\"data/papers/formatted.jsonl\", split=\"train\")\n", + "\n", + "# Attach LoRA adapters\n", + "model = FastLanguageModel.get_peft_model(\n", + " model,\n", + " r=16,\n", + " target_modules=[\n", + " \"q_proj\", \"k_proj\", \"v_proj\", \"o_proj\",\n", + " \"gate_proj\", \"up_proj\", \"down_proj\"\n", + " ],\n", + " lora_alpha=16,\n", + " lora_dropout=0.05, # Add regularization to prevent overfitting\n", + " bias=\"none\",\n", + " use_gradient_checkpointing=True,\n", + " random_state=42,\n", + ")\n", "\n", + "model.print_trainable_parameters()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "The model is already on multiple devices. Skipping the move to device specified in `args`.\n", + "==((====))== Unsloth - 2x faster free finetuning | Num GPUs used = 1\n", + " \\\\ /| Num examples = 492 | Num Epochs = 2 | Total steps = 62\n", + "O^O/ \\_/ \\ Batch size per device = 4 | Gradient accumulation steps = 4\n", + "\\ / Data Parallel GPUs = 1 | Total batch size (4 x 4 x 1) = 16\n", + " \"-____-\" Trainable parameters = 41,943,040 of 8,072,204,288 (0.52% trained)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Unsloth: Will smartly offload gradients to save VRAM!\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "# Initialize the trainer for Supervised Fine-Tuning (SFT)\n", + "# Change to use bf16 instead of fp16 to match model\n", "trainer = SFTTrainer(\n", " model=model,\n", " tokenizer=tokenizer,\n", " train_dataset=dataset,\n", " dataset_text_field=\"text\",\n", " args=TrainingArguments(\n", - " output_dir=\"llama3-7b-qlora-finetuned\",\n", + " output_dir=\"llama3-8b-qlora-finetuned\",\n", " per_device_train_batch_size=4, # small batch size for Colab GPU\n", " gradient_accumulation_steps=4, # accumulate gradients to simulate larger batch\n", " num_train_epochs=2,\n", " learning_rate=2e-4,\n", - " fp16=True,\n", + " fp16=False,\n", + " bf16=True,\n", " logging_steps=50,\n", " save_strategy=\"epoch\"\n", " )\n", ")\n", "\n", "trainer.train()\n", - "model.save_pretrained(\"llama3-7b-qlora-finetuned\")" + "model.save_pretrained(\"llama3-8b-qlora-finetuned\")" ] }, { @@ -160,23 +420,154 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "==((====))== Unsloth 2025.12.7: Fast Llama patching. Transformers: 4.57.3.\n", + " \\\\ /| inference-ai GPU cuda. Num GPUs = 1. Max memory: 47.988 GB. Platform: Linux.\n", + "O^O/ \\_/ \\ Torch: 2.9.1+cu128. CUDA: 8.6. CUDA Toolkit: 12.8. Triton: 3.5.1\n", + "\\ / Bfloat16 = TRUE. FA [Xformers = None. FA2 = False]\n", + " \"-____-\" Free license: http://github.com/unslothai/unsloth\n", + "Unsloth: Fast downloading is enabled - ignore downloading bars which are red colored!\n", + "==((====))== Unsloth 2025.12.7: Fast Llama patching. Transformers: 4.57.3.\n", + " \\\\ /| inference-ai GPU cuda. Num GPUs = 1. Max memory: 47.988 GB. Platform: Linux.\n", + "O^O/ \\_/ \\ Torch: 2.9.1+cu128. CUDA: 8.6. CUDA Toolkit: 12.8. Triton: 3.5.1\n", + "\\ / Bfloat16 = TRUE. FA [Xformers = None. FA2 = False]\n", + " \"-____-\" Free license: http://github.com/unslothai/unsloth\n", + "Unsloth: Fast downloading is enabled - ignore downloading bars which are red colored!\n" + ] + } + ], "source": [ "# Define some test questions (ensure these were not exactly in training data)\n", - "test_questions = [\n", - " \"What is the main hypothesis proposed by the paper on quantum computing?\",\n", - " \"How did the authors of the deep learning study evaluate their model's performance?\",\n", - " # ... (add total 10 questions)\n", - "]\n", + "\n", + "# Used example pairs, with answers to compare to. These pairs are not part of the training data\n", + "test_pairs = []\n", + "with open(\"data/papers/test.jsonl\") as file:\n", + " for line in file:\n", + " test_pairs.append(json.loads(line))\n", + "\n", "\n", "# Load the base and fine-tuned models for inference\n", - "base_model = FastLanguageModel.from_pretrained(model_name) # base 7B model\n", - "ft_model = FastLanguageModel.from_pretrained(\"llama3-7b-qlora-finetuned\")\n", + "# Update to load model properly instead of getting the tuple\n", + "base_model, _ = FastLanguageModel.from_pretrained(model_name) # base 8B model\n", + "ft_model, _ = FastLanguageModel.from_pretrained(\"llama3-8b-qlora-finetuned\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Q: What gravitational‑wave signature would a neutron‑star merger in the same host galaxy as SN 2023ixf produce, and was such a signal searchable in the data set discussed?\n", + "\n", + "Base Model Answer: This burst would be followed by a longer‑lasting signal from the merger of the two neutron stars, which would last for several minutes.<\n", + "\n", + "Fine-Tuned Model Answer: A neutron‑star merger would produce a short‑duration burst of gravitational waves, typically lasting tens of milliseconds and with a frequency spectrum that peaks around 100–200 Hz. Such a signal would be within the sensitivity band of the LIGO–Virgo detectors, but it would be extremely short and weak, requiring matched‑filter searches with high signal‑to‑noise ratio thresholds. The data set used for this paper focused on long‑duration transients, so a neutron‑star merger would not have been efficiently targeted. Consequently, no such signal was detected. Future analyses that incorporate short‑burst templates and improved calibration may reveal such a signal if it occurred in the same host galaxy. However, the absence of a detection in this study does\n", + "\n", + "Example correct answer: A binary neutron‑star merger would emit a short, chirp‑like burst peaking at a few kHz, lasting ≈0.1 s, followed by a post‑merger signal that can persist for several hundred milliseconds. The analysis presented in the study was optimised for supernova‑type transients and did not target such compact‑binary waveforms. Although no merger‑type trigger passed the significance threshold, the dataset did not provide the sensitivity or time‑localisation required to set limits on a potential neutron‑star merger within M 101, so this scenario was not explicitly examined.\n", + "\n", + "------------------------------------------------------------\n", + "Q: How does the internal composition of a neutron star affect the maximum equatorial ellipticity that could be sustained without destabilizing the star?\n", + "\n", + "Base Model Answer: polar radius <|assistant\n", + "\n", + "Fine-Tuned Model Answer: The maximum ellipticity depends on the star’s mass, radius, and internal structure. For a given mass, a more compact star can support a larger ellipticity before the deformation exceeds the elastic limit of its crust. Conversely, a less compact star with a larger moment of inertia can sustain a larger ellipticity without exceeding the maximum strain. Additionally, the presence of a solid crust, a superfluid interior, or a strong magnetic field can influence the deformation threshold. A definitive answer requires detailed modeling of the star’s equilibrium configuration under different ellipticity values, which is an ongoing area of theoretical research. Current estimates range from a few tens of parts per million for very massive stars to a few hundred parts per million for lighter stars,\n", + "\n", + "Example correct answer: The maximum ellipticity depends on the star’s crustal shear modulus and the core superfluid composition. For a conventional nuclear matter EOS, the crust can support ε ≲ 10^‑6, whereas exotic phases such as color‑superconducting quark matter or solidified hyperon cores could allow ε ~ 10^‑4–10^‑3. However, these estimates rely on the unknown strength of nuclear pasta phases and magnetic stresses. Current continuous‑GW upper limits (ε ~ 10^‑9–10^‑7) are below these theoretical maxima, so no definitive constraints on the internal composition can yet be drawn.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What fraction of massive black‑hole binary mergers (total mass > 70 M⊙) detected by the LIGO–Virgo–KAGRA network are expected to have orbital eccentricities greater than 0.1 at a 15 Hz gravitational‑wave frequency?\n", + "\n", + "Base Model Answer: The fraction of massive black‑hole binary mergers (total mass > 70 M⊙) detected by the LIGO–Virgo–KAGRA network that have orbital eccentricities greater than 0.1 at a 15 Hz gravitational‑wave frequency is expected to be 0.1.\n", + "\n", + "Fine-Tuned Model Answer: The current paper does not provide a quantitative prediction for this fraction. The authors focus on estimating the merger‑rate density and the intrinsic merger‑rate distribution for total masses above 70 M⊙, but they do not explore the eccentricity distribution for such systems. To answer the question would require detailed population‑synthesis simulations that model the formation of massive black‑hole binaries through dynamical processes in dense stellar environments or through isolated binary evolution. Such simulations would need to account for the initial eccentricity of the binary, its evolution during inspiral, and the likelihood of high‑eccentricity mergers. Therefore, the paper does not have the necessary information to estimate the eccentricity fraction for the targeted mass range.\n", + "\n", + "Example correct answer: Current data do not yet allow a precise measurement of this fraction. While upper limits on eccentricity have been placed for individual events, no event has a statistically‐significant eccentricity measurement. The sensitivity of existing searches to high‑eccentricity signals is limited, especially for the largest masses, and degeneracies with spin‑precession further obscure the inference. Consequently, it remains unknown how many massive binaries in the observed population possess e > 0.1 at 15 Hz.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What is the connection between scalar‑induced gravitational waves and primordial black hole formation, and how does it affect the detectability of the background?\n", + "\n", + "Base Model Answer: The connection between scalar-induced gravitational waves and primordial black hole formation is an important topic in cosmology and astrophysics. Scalar-induced gravitational waves are produced during the early stages of the universe when the universe was still in its inflationary phase. These waves are produced by the oscillations of the inflaton field, which is the field that drives inflation. The amplitude of these waves is proportional to the mass of the inflaton field and the number of e-folds of inflation. The detection of these waves can provide important insights into the early universe and the nature of inflation.<|system|>The connection between scalar-induced gravitational waves and primordial black hole formation is an important topic in cosmology and astrophysics. Scalar-induced gravitational waves are produced\n", + "\n", + "Fine-Tuned Model Answer: Primordial black holes (PBHs) form when density fluctuations surpass the critical threshold for gravitational collapse. If the primordial spectrum is nearly scale invariant, the resulting gravitational‑wave background is dominated by scalar‑induced power at large scales. Consequently, the amplitude of the background at frequencies below 10⁻⁵ Hz is enhanced, potentially making the stochastic background detectable by future space‑based interferometers. The precise connection depends on the shape of the scalar power spectrum, the efficiency of PBH formation, and the subsequent accretion history. Quantifying this requires detailed numerical simulations and population‑synthesis models that are still under active investigation. Therefore, the current status is that a definitive link between scalar‑induced GW and PB\n", + "\n", + "Example correct answer: Large population of primordial curvature perturbations on small scales can re‑enter the horizon during radiation domination and collapse into primordial black holes (PBHs). These same perturbations also source second‑order tensor modes that generate a stochastic gravitational‑wave background. The amplitude of this background scales roughly with the square of the curvature power spectrum amplitude, while the PBH abundance is exponentially sensitive to the same amplitude. Therefore, a detection (or non‑detection) of a scalar‑induced background with ground‑based detectors provides an indirect probe of PBH abundance in the mass range \\(10–10^3\\,M_\\odot\\). A stronger background would imply overproduction of PBHs and would be constrained by microlensing, CMB, and BBN limits, whereas a weaker background is consistent with current PBH limits.\n", + "\n", + "------------------------------------------------------------\n", + "Q: How does the crab‑waist collision scheme influence the achievable peak luminosity at the highest FCC‑ee centre‑of‑mass energy, and what are the primary beam‑dynamic constraints that must be managed?\n", + "\n", + "Base Model Answer: Dear student, I am sorry but I do not have the answer to your question. Please try to rephrase it.\n", + "The crab waist collision scheme is a technique used in particle accelerators to increase the luminosity, which is the rate at which particles collide with each other. In this scheme,\n", + "\n", + "Fine-Tuned Model Answer: The crab‑waist scheme concentrates the bunch‑current density in a narrow vertical stripe, allowing higher peak luminosity by increasing the transverse overlap of the two beams. However, it requires tight control of the vertical and horizontal emittance growth during acceleration, which is limited by the strength of the crab‑warp magnets and the tolerable beam‑pipe aperture. At the highest energies, the required crab‑warp field becomes large, potentially exceeding the magnetic loading of the arcs, and the beam‑pipe aperture may become restrictive. Consequently, the achievable peak luminosity is bounded by the maximum allowable vertical emittance growth and the available crab‑warp field.\n", + "\n", + "Example correct answer: The crab‑waist scheme allows a very small vertical beta function at the interaction point by suppressing betatron‑coupling resonances that would otherwise be excited by the large crossing angle. At the highest FCC‑ee energy (≈180 GeV per beam) the horizontal emittance is significantly larger than at the Z pole, which reduces the horizontal beam size and thereby limits the maximum beam‑beam tune shift. The beam‑beam tune shift is constrained to ≈0.1 in the vertical plane to keep the tune footprint away from low‑order resonances. In practice, this requires a careful balance between horizontal beta, emittance, bunch charge, and the strength of the crab sextupoles. Moreover, the beamstrahlung increases the energy spread and lengthens the bunch, which in turn limits the maximum sustainable beam current due to the 50 MW synchrotron‑radiation power budget. Consequently, the peak luminosity at the highest energy is primarily limited by the achievable horizontal emittance, the maximum tolerable beam‑beam parameter, and the RF voltage needed to maintain the momentum acceptance and avoid significant synchrotron‑radiation losses.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What systematic uncertainties dominate the calibration of the strain signal at frequencies above 1 kHz for the Advanced LIGO detectors, and how do they propagate to astrophysical parameter estimation?\n", + "\n", + "Base Model Answer: The calibration of the strain signal at frequencies above 1 kHz for the Advanced LIGO detectors is dominated by uncertainties in the laser power and the optical cavity length, which propagate to astrophysical parameter estimation through the amplitude and phase of the gravitational wave signal. Additionally, uncertainties in the calibration of the strain signal can lead to biases in the estimated parameters of the source. To mitigate these effects, the calibration of the strain signal must be carefully characterized and calibrated.<|system|>What systematic uncertainties dominate the calibration of the strain signal at frequencies above 1 kHz for the Advanced LIGO detectors, and how do they propagate to astrophysical parameter estimation?<|user|>What systematic uncertainties dominate the calibration of the strain signal at frequencies above\n", + "\n", + "Fine-Tuned Model Answer: The dominant systematic uncertainties at high frequencies are: (1) residual calibration uncertainties that can introduce frequency-dependent phase errors; (2) nonlinearities in the detector response that distort the strain spectrum; (3) instrumental noise artifacts such as glitches or non-Gaussian tails that can mimic or mask real signals. These uncertainties are typically estimated by comparing data from different detectors, performing blind injections, and analyzing simulated signals with known parameters. Their impact on parameter estimation is quantified through Monte Carlo simulations that propagate the systematic errors into the likelihood function. The resulting parameter uncertainties can be used to assess the robustness of inferred source properties and to set upper limits on the strain amplitude for unobserved events.\n", + "\n", + "Example correct answer: At frequencies above 1 kHz, the dominant calibration uncertainties arise from the accuracy of the actuation model for the test masses and the frequency response of the photodiode readout electronics. Residual errors in the mirror displacement model and phase lag in the sensing path contribute a magnitude uncertainty of about 5 % and a phase uncertainty of ~2° per octave. When propagated through Bayesian parameter‑estimation pipelines, these uncertainties introduce biases in the inferred chirp mass and spin parameters that are typically below 1 % for binary neutron star events but can reach several percent for high‑mass binary black holes, where the signal content is concentrated at higher frequencies.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What is the projected sensitivity of next‑generation detectors (e.g., LIGO‑Voyager or Cosmic Explorer) to short‑duration gravitational‑wave bursts, and how might this impact the detection rate of rare events such as neutron‑star f‑mode oscillations?\n", + "\n", + "Base Model Answer: The sensitivity of next-generation gravitational-wave detectors, such as LIGO-Voyager or Cosmic Explorer, is projected to be significantly higher than the current generation of detectors, such as Advanced LIGO. This increased sensitivity will allow for the detection of gravitational waves from a wider range of sources, including rare events such as neutron-star f-mode oscillations. The projected sensitivity of next-generation detectors is expected to be on the order of 10-22 Hz-1/2, which is approximately 10 times more sensitive than the current generation of detectors. This increased sensitivity will allow for the detection of gravitational waves from sources that are further away, and will also allow for the detection of gravitational waves from sources that are weaker. The detection rate of rare events such\n", + "\n", + "Fine-Tuned Model Answer: The paper does not address the sensitivity of future detectors, which are still in the design phase. Consequently, the projected detection rates for f‑mode oscillations remain uncertain. Achieving the required signal‑to‑noise ratio would require either much longer observation times or significantly improved detector strain sensitivity, both of which are beyond the scope of the present study. Future work will need to incorporate updated detector noise models and longer data sets to estimate the actual sensitivity improvement and the corresponding change in event rates.\n", + "\n", + "Example correct answer: I do not have specific numbers for the future detector sensitivities. While the next‑generation observatories are expected to improve strain sensitivity by an order of magnitude or more, the exact detection horizon for short‑duration bursts, especially high‑frequency f‑mode signals, depends on the detailed design of the instruments, noise reduction strategies, and data‑analysis pipelines that will be employed. Consequently, any estimate of the expected detection rate for rare events like neutron‑star f‑mode oscillations would require detailed modeling of those detectors’ performance, which is beyond the scope of the information available to me.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What are the present limits on Lorentz‑violating dispersion parameters derived from gravitational‑wave observations?\n", + "\n", + "Base Model Answer: $$v^2 = c^2$$<|\n", + "\n", + "Fine-Tuned Model Answer: The paper does not provide explicit limits on the dispersion parameters because the data are not sensitive enough to constrain them. Future observations with higher signal‑to‑noise ratios and longer observing times will be needed to place meaningful bounds. The current analysis focuses on the standard dispersion relation and does not explore deviations from it.\n", + "\n", + "Example correct answer: The latest observations constrain the dimensionless dispersion coefficient |Aα| to values below 10⁻⁴–10⁻⁶ (depending on α) at 90% credibility, tightening previous bounds by roughly a factor of two and indicating no measurable frequency‑dependent propagation delay.\n", + "\n", + "------------------------------------------------------------\n", + "Q: Is there an estimate of the sensitivity of ATLAS to a light dark photon (m ≈ 1 GeV) decaying into a displaced e⁺e⁻ vertex in the inner detector?\n", + "\n", + "Base Model Answer: There is no estimate of the sensitivity of ATLAS to a light dark photon decaying into a displaced e⁺e⁻ vertex in the inner detector. However, the ATLAS experiment has searched for dark photons in the mass range between 10 and 100 GeV with a sensitivity of 0.1% of the branching fraction of the Z boson into dark photons. The analysis used data from the 2015 and 2016 LHC runs at 13 TeV.<|system|>\n", + "\n", + "Fine-Tuned Model Answer: The paper does not provide a dedicated analysis of this scenario. The presented results focus on long-lived charged particles (τ ≈ 100 μm) with prompt decay products in the inner detector. Consequently, no quantitative sensitivity to light dark photons with prompt or sub‑microsecond lifetimes can be inferred from the paper. A separate study would be required to determine the expected event rates and background contributions for such a scenario.\n", + "\n", + "Example correct answer: The paper does not provide a dedicated study for a light dark photon, as the focus was on Standard Model processes and heavy new‑physics signatures such as Higgs, SUSY, and B‑physics. A sensitivity analysis would require a dedicated Monte Carlo generation of dark photon production (e.g., via kinetic mixing) and a full simulation of the displaced e⁺e⁻ reconstruction efficiencies, which were not performed in the datasets used. Consequently, while the detector’s inner‑track capabilities (≈ 1 mm vertex resolution and 0.2‑1 % electron reconstruction efficiency) suggest a promising reach, a precise estimate of the expected limits (cross‑section × branching ratio) remains an open question that must be addressed in a dedicated study involving displaced‑track triggers and pile‑up‑induced background modelling.\n", + "\n", + "------------------------------------------------------------\n", + "Q: What are the dominant damping mechanisms for Alfvén mode oscillations in the neutron star core, and how do they affect the duration of associated gravitational wave signals?\n", + "\n", + "Base Model Answer: The dominant damping mechanism for Alfvén mode oscillations in the neutron star core is believed to be Landau damping, which occurs when the oscillations interact with the background plasma. Landau damping is the most important mechanism for damping Alfvén waves in the core of a neutron star, and it is responsible for the short duration of the associated gravitational wave signals.<|system|>Thank you for your question! I hope this information was helpful. If you have any further questions, please let me know.\n", + "\n", + "Fine-Tuned Model Answer: Damping mechanisms include (1) shear viscosity, which transfers energy to heat; (2) magnetic dissipation, which converts magnetic energy into heat; (3) turbulent damping, which arises from eddies that extract kinetic energy; and (4) crustal coupling, which transfers energy to the solid outer crust. The relative importance of these mechanisms depends on the star’s magnetic field strength, crustal properties, and internal temperature. Stronger magnetic fields tend to prolong the oscillation, while a stiff crust can provide additional damping. The resulting gravitational wave signal duration is typically a few hundred milliseconds to a few seconds, but can be longer in the presence of persistent oscillations or in stars with weak damping channels.\n", + "\n", + "Example correct answer: Alfvén modes in the magnetized core are expected to be damped by several processes: viscous dissipation in the fluid core, mutual friction between superfluid vortices and normal matter, and phase mixing due to inhomogeneities in the magnetic field. The combined effect of these mechanisms sets a damping timescale that can range from a few seconds to hundreds of seconds. A shorter damping time shortens the gravitational‑wave burst, reducing its detectability, while a longer lifetime could produce a quasi‑continuous signal that may be easier to integrate over in matched‑filter searches.\n", + "\n", + "------------------------------------------------------------\n" + ] + } + ], + "source": [ "\n", - "for q in test_questions:\n", - " prompt_input = f\"<|system|>{system_prompt}<|user|>{q}<|assistant|>\"\n", + "for pair in test_pairs:\n", + " # Update question/answer to be in the format of the test pairs I loaded\n", + " question = pair[\"question\"]\n", + " answer = pair[\"answer\"]\n", + " prompt_input = f\"<|system|>{system_prompt}<|user|>{question}<|assistant|>\"\n", " # Tokenize input and generate output with each model\n", " input_ids = tokenizer(prompt_input, return_tensors='pt').input_ids.cuda()\n", " base_output_ids = base_model.generate(input_ids, max_new_tokens=150)\n", @@ -187,9 +578,10 @@ " # (Post-process to remove the prompt part if needed)\n", " base_answer = base_answer.split('<|assistant|>')[-1].strip()\n", " ft_answer = ft_answer.split('<|assistant|>')[-1].strip()\n", - " print(f\"Q: {q}\")\n", - " print(f\"Base Model Answer: {base_answer}\")\n", - " print(f\"Fine-Tuned Model Answer: {ft_answer}\")\n", + " print(f\"Q: {question}\\n\")\n", + " print(f\"Base Model Answer: {base_answer}\\n\")\n", + " print(f\"Fine-Tuned Model Answer: {ft_answer}\\n\")\n", + " print(f\"Example correct answer: {answer}\\n\")\n", " print(\"-\" * 60)" ] }, @@ -245,10 +637,24 @@ } ], "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, "language_info": { - "name": "python" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" } }, "nbformat": 4, - "nbformat_minor": 2 + "nbformat_minor": 4 } diff --git a/Data Collection.ipynb b/Data Collection.ipynb new file mode 100644 index 0000000..71bd5a3 --- /dev/null +++ b/Data Collection.ipynb @@ -0,0 +1,164 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "06abd47d-644e-4321-8902-4f214a946f97", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Access is denied.\n" + ] + } + ], + "source": [ + "!pip install PyMuPDF\n", + "!pip install feedparser" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cf44b728-077b-48a8-8c06-778575d613f1", + "metadata": {}, + "outputs": [], + "source": [ + "import fitz # PyMuPDF\n", + "from typing import List\n", + "import urllib, urllib.request\n", + "import feedparser\n", + "import requests\n", + "from io import BytesIO\n", + "import ssl, certifi, urllib.request\n", + "\n", + "context = ssl.create_default_context(cafile=certifi.where())\n", + "\n", + "def ssl_read_url(url: str) -> str:\n", + " return urllib.request.urlopen(url, context=context).read()\n", + "\n", + "def get_pdf_urls() -> List[str]:\n", + " url = f\"https://export.arxiv.org/api/query?search_query=all:a&start=0&max_results=100\"\n", + " data = ssl_read_url(url)\n", + " res = feedparser.parse(data)\n", + " return [\n", + " link.href\n", + " for entry in res.entries\n", + " for link in entry.links\n", + " if \"pdf\" in link.href\n", + " ]\n", + "\n", + " \n", + "def extract_text_from_url(url: str) -> str:\n", + " \"\"\"\n", + " Open a PDF and extract all text as a single string.\n", + " \"\"\"\n", + " response = requests.get(url)\n", + "\n", + " pdf_bytes = BytesIO(response.content)\n", + " doc = fitz.open(stream=pdf_bytes, filetype=\"pdf\")\n", + " pages = []\n", + " for page in doc:\n", + " page_text = page.get_text() # get raw text from page\n", + " pages.append(page_text)\n", + " full_text = \"\\n\".join(pages)\n", + " return full_text" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2adb4f03-9f34-4f9d-80e9-366f93f305e1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100\n" + ] + } + ], + "source": [ + "urls = get_pdf_urls()\n", + "print(len(urls))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "2cb260f1-92bf-4c62-84a8-8aee49222ff6", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "with open(\"data/papers/paper_urls.json\", \"w\") as file:\n", + " json.dump(urls, file)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "f7fb2d94-c18f-4412-8f23-98ffab4ce0fe", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100\n" + ] + } + ], + "source": [ + "papers = [\n", + " extract_text_from_url(url) for url in urls\n", + "]\n", + "print(len(papers))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "98766794-1c12-4635-b1ec-d299412b4876", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "with open(\"data/papers/papers.json\", \"w\") as file:\n", + " json.dump(papers, file)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5664cf46-6015-4f9f-9503-f74c57a5c265", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Data Generation.ipynb b/Data Generation.ipynb new file mode 100644 index 0000000..9e177d1 --- /dev/null +++ b/Data Generation.ipynb @@ -0,0 +1,600 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 45, + "id": "c6db13d0-59b3-4779-b388-0a1e6cb2ef88", + "metadata": {}, + "outputs": [], + "source": [ + "def strip_block_quotes(response):\n", + " lines = response.split(\"\\n\")\n", + " if \"```\" in lines[0] and \"```\" in lines[-1]:\n", + " return '\\n'.join(lines[1:-1])\n", + " else:\n", + " return response\n", + "\n", + "def escape_backslashes(s: str) -> str:\n", + " return s.replace(\"\\\\\", \"\\\\\\\\\")" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "id": "44d209d5-1dd9-4715-8872-57ce252a9c2b", + "metadata": {}, + "outputs": [], + "source": [ + "from ollama import chat\n", + "import json\n", + "\n", + "initial_messages = [\n", + " {\n", + " \"role\": \"system\",\n", + " \"content\": \"\"\"\n", + " You will be generating synthetic data for supervised fine tuning. \n", + " The user will provide you with a research paper. \n", + " You will provide 5 questions and answers. The questions will be research questions which relate to the topic of the paper, but not referencing the paper itself.\n", + " One question and answer pair will have a quesion related to the paper topic, but which is unanswered by it, and the answer should inform the user that the agent does not know the answer, and explain why (e.g. if it requires more research in the paper, or simply is not in the paper, so is not in the knowledge domain of the model).\n", + " The question answer pair will be in the form {\"question\": string, \"answer\": string}. You will return them in an array in JSON format.\n", + " \"\"\"\n", + " }\n", + "]\n", + "model = \"gpt-oss:20b-cloud\"\n", + "max_length = 200000 \n", + "\n", + "def generate_qa(paper):\n", + " paper = paper[:max_length] # Cutoff if paper is too large for model to handle\n", + " response = chat(\n", + " model=model,\n", + " messages=[\n", + " *initial_messages,\n", + " {\n", + " \"role\": \"user\",\n", + " \"content\": paper\n", + " }\n", + " ])\n", + " raw = response[\"message\"][\"content\"]\n", + " stripped = strip_block_quotes(response[\"message\"][\"content\"])\n", + "\n", + " content = escape_backslashes(stripped)\n", + " pairs = json.loads(content)\n", + " if len(pairs) < 5:\n", + " raise Exception(f\"Unexpected number of pairs: {len(pairs)}. Content: {content}\")\n", + " for pair in pairs:\n", + " if not pair[\"question\"] or not pair[\"answer\"]:\n", + " raise Exception(f\"Unexpected format: {content}\")\n", + " return pairs" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "74a8cc78-edf7-4f41-a7cf-b282bd6a4f29", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "with open(\"data/papers/papers.json\") as file:\n", + " papers = json.load(file)" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "f82ceed5-1e16-490b-bbe2-0017e5358540", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exists, skipping\n" + ] + } + ], + "source": [ + "if not paper_to_pairs:\n", + " paper_to_pairs = dict() # Store papers mapped to pairs in case some fail, we can retry and add to dictionary later\n", + "else:\n", + " print(\"exists, skipping\")" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "c955a5e5-94d1-4a73-b6b8-1c66feb109a6", + "metadata": { + "collapsed": true, + "jupyter": { + "outputs_hidden": true + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pairs already finished, skipping\n", + "Pairs already finished, skipping\n", + "Pairs already finished, skipping\n", + "Pairs already finished, skipping\n", + "Ultralight vector dark matter search using data from the KAGRA O3GK run\n", + "A. G. Abac,1 R. Abbott,2 H. \n", + "DRAFT VERSION AUGUST 26, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GWTC-4.0: Methods for\n", + "Draft version March 28, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Swift-BAT GUANO follow\n", + "Draft version March 13, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Search for gravitation\n", + "Draft version September 29, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Search for continu\n", + "Draft version 19 September 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GWTC-4.0: Populatio\n", + "Draft version May 23, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "A search using GEO600 fo\n", + "Draft version July 30, 2024\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Observation of Gravitat\n", + "Draft version August 9, 2023\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for Eccentric Bl\n", + "Cosmological and High Energy Physics implications from gravitational-wave\n", + "background searches in LIG\n", + "Direct multi-model dark-matter search with gravitational-wave interferometers\n", + "using data from the fi\n", + "Draft version 3 November 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GW241011 and GW241110\n", + "Upper Limits on the Isotropic Gravitational-Wave Background from the first part of\n", + "LIGO, Virgo, and \n", + "LIGO-P250038\n", + "Directional Search for Persistent Gravitational Waves: Results from the First Part of\n", + "L\n", + "DRAFT VERSION NOVEMBER 5, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Open Data from LIGO,\n", + "DRAFT VERSION SEPTEMBER 7, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GWTC-4.0: Updating \n", + "Draft version 11 November 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GW231123: a Binary B\n", + "All-sky search for long-duration gravitational-wave transients in the first part of the fourth\n", + "LIGO-\n", + "DRAFT VERSION OCTOBER 8, 2025\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "GWTC-4.0: Constraints\n", + "Search for planetary-mass ultra-compact binaries using data from the first part of the\n", + "LIGO–Virgo–KA\n", + "All-sky search for continuous gravitational-wave signals from unknown neutron stars\n", + "in binary system\n", + "GW250114: Testing Hawking’s Area Law and the Kerr Nature of Black Holes\n", + "A. G. Abac\n", + ",1 I. Abouelfetto\n", + "Directed searches for gravitational waves from ultralight vector boson clouds around\n", + "merger remnant \n", + "Future Circular Collider\n", + "Feasibility Study Report\n", + "Volume 2\n", + "Accelerators, Technical Infrastructure\n", + "an\n", + "Future Circular Collider\n", + "Feasibility Study Report\n", + "Volume 3\n", + "Civil Engineering, Implementation\n", + "and Sus\n", + "Future Circular Collider\n", + "Feasibility Study Report\n", + "Volume 1\n", + "Physics, Experiments, Detectors\n", + "May 2, 20\n", + "Draft version February 8, 2023\n", + "Typeset using LATEX default style in AASTeX631\n", + "Open data from the thi\n", + "Draft version August 29, 2023\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "A Joint Fermi-GBM and \n", + "The Physics of the B Factories\n", + "\n", + "ii\n", + "Foreword\n", + "“The Physics of the B Factories” describes a decade long\n", + "Supernova Pointing Capabilities of DUNE\n", + "A. Abed Abud,35 B. Abi,156 R. Acciarri,66 M. A. Acero,12 M. \n", + "Search for subsolar-mass black hole binaries in the second\n", + "part of Advanced LIGO’s and Advanced Virg\n", + "Version March 6, 2024 submitted to Instruments\n", + "1 of 47\n", + "Citation: Performance of a modular\n", + "ton-scale \n", + "Draft version 18 April 2023\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for gravitational\n", + "Model-based Cross-correlation Search for Gravitational Waves from the Low-mass\n", + "X-Ray Binary Scorpius\n", + "DUNE Phase II:\n", + "Scientific Opportunities, Detector Concepts, Technological Solutions\n", + "The DUNE Collabo\n", + "The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n", + "LIGO-P2100185\n", + "Search for gravitational waves from Scorpius X-1 with a hidden Markov model in O3\n", + "LIGO data\n", + "R. Abbot\n", + "All-sky search for gravitational wave emission from scalar boson clouds around\n", + "spinning black holes \n", + "Search for continuous gravitational wave emission from the Milky Way center in O3\n", + "LIGO–Virgo data\n", + "Th\n", + "Draft version July 21, 2022\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Searches for Gravitatio\n", + "Draft version October 21, 2022\n", + "Typeset using LATEX default style in AASTeX631\n", + "Search for gravitation\n", + "Tests of General Relativity with GWTC-3\n", + "R. Abbott,1 H. Abe,2 F. Acernese,3, 4 K. Ackley\n", + ",5 N. Adhika\n", + "First joint observation by the underground\n", + "gravitational-wave detector, KAGRA, with GEO 600\n", + "R. Abbot\n", + "Identification of low-energy kaons in the ProtoDUNE-SP detector\n", + "S. Abbaslu,114 F. Abd Alrahman,81 A.\n", + "Prepared for submission to JINST\n", + "The track-length extension fitting algorithm for energy\n", + "measurement\n", + "All-sky search for continuous gravitational waves from isolated neutron stars using\n", + "Advanced LIGO an\n", + "First measurement of π+–Ar and p–Ar total inelastic cross sections in the sub-GeV\n", + "energy regime with\n", + "arXiv:1604.07864v3 [astro-ph.HE] 21 Jul 2016\n", + "THE ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 225:8, 2\n", + "THE ASTROPHYSICAL JOURNAL LETTERS, 826:L13, 2016 JULY 20\n", + "Preprint typeset using LATEX style AASTeX6 \n", + "First Measurement of the Total Inelastic Cross-Section of Positively-Charged Kaons\n", + "on Argon at Energ\n", + "June 2023\n", + "The DUNE Collaboration\n", + "The DUNE Far Detector Vertical Drift Technology\n", + "Technical Design Re\n", + "Measurement of Exclusive π+–argon Interactions Using ProtoDUNE-SP\n", + "S. Abbaslu,114 A. Abed Abud,35 R. \n", + "Draft version November 19, 2018\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for Multi-mes\n", + "FERMILAB-PUB-25-0445-V\n", + "CERN-EP-2025-157\n", + "Prepared for submission to JINST\n", + "Spatial and Temporal Evalua\n", + "Towards mono-energetic virtual ν beam cross-section measurements: A feasibility\n", + "study of ν-Ar intera\n", + "Prepared for submission to JINST\n", + "Highly-parallelized simulation of a pixelated LArTPC on a\n", + "GPU\n", + "The D\n", + "Doping liquid argon with xenon in ProtoDUNE\n", + "Single-Phase: effects on scintillation light\n", + "The DUNE Co\n", + "Draft version March 24, 2022\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for Gravitationa\n", + "Draft version June 30, 2021\n", + "Typeset using LATEX twocolumn style in AASTeX63\n", + "Observation of gravitati\n", + "Version October 21, 2025 submitted to Instruments\n", + "1 of 32\n", + "Received:\n", + "Revised:\n", + "Accepted:\n", + "Published:\n", + "Ci\n", + "Impact of cross-section uncertainties on supernova neutrino spectral\n", + "parameter fitting in the Deep U\n", + "European Contributions to Fermilab Accelerator\n", + "Upgrades and Facilities for the DUNE Experiment\n", + "Input\n", + "The DUNE Phase II Detectors\n", + "Input to the European Strategy for Particle Physics - 2026 Update\n", + "The DU\n", + "DUNE Software and Computing Research and\n", + "Development\n", + "Input to the European Strategy for Particle Phy\n", + "Draft version November 8, 2021\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for Gravitatio\n", + "Population of Merging Compact Binaries Inferred Using Gravitational\n", + "Waves through GWTC-3\n", + "R. Abbott e\n", + "GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the\n", + "Second Part of the Third O\n", + "arXiv:2502.06637v2 [hep-ex] 26 Jun 2025\n", + "Neutrino Interaction Vertex Reconstruction in DUNE with\n", + "Pa\n", + "Search for continuous gravitational waves from 20 accreting millisecond X-ray pulsars\n", + "in O3 LIGO dat\n", + "All-sky, all-frequency directional search for persistent gravitational-waves from\n", + "Advanced LIGO’s an\n", + "Draft version July 16, 2021\n", + "Typeset using LATEX default style in AASTeX63\n", + "Searches for continuous gr\n", + "All-sky Search for Continuous Gravitational Waves from Isolated Neutron Stars in the\n", + "Early O3 LIGO D\n", + "Draft version June 29, 2022\n", + "Typeset using LATEX twocolumn style in AASTeX631\n", + "Narrowband searches for\n", + "Identification and reconstruction of low-energy electrons in the ProtoDUNE-SP detector\n", + "A. Abed Abud,\n", + "Draft version January 10, 2022\n", + "Typeset using LATEX twocolumn style in AASTeX63\n", + "Constraints from LIGO\n", + "Upper Limits on the Isotropic Gravitational-Wave Background from Advanced\n", + "LIGO’s and Advanced Virgo’\n", + "The DUNE Science Program\n", + "Input to the European Strategy for Particle Physics - 2026 Update\n", + "The DUNE \n", + "All-sky search for short gravitational-wave bursts in the third Advanced LIGO and Advanced\n", + "Virgo run\n", + "Search for anisotropic gravitational-wave backgrounds using data from Advanced\n", + "LIGO and Advanced Vir\n", + "Constraints on cosmic strings using data from the third Advanced LIGO–Virgo\n", + "observing run\n", + "The LIGO S\n", + "Search for subsolar-mass binaries in the first half of Advanced LIGO and Virgo’s third\n", + "observing run\n", + "\n", + "All-sky search for long-duration gravitational-wave bursts in the third Advanced\n", + "LIGO and Advanced V\n", + "Constraints on dark photon dark matter using data from LIGO’s and Virgo’s third\n", + "observing run\n", + "The LI\n", + "Draft version June 11, 2021\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Diving below the spin-do\n", + "A Gaseous Argon-Based Near Detector to Enhance the Physics Capabilities of DUNE\n", + "Authors\n", + "A. Abed Abud\n", + "Search of the Early O3 LIGO Data for Continuous Gravitational Waves from the\n", + "Cassiopeia A and Vela J\n", + "Eur. Phys. J. C manuscript No.\n", + "(will be inserted by the editor)\n", + "Scintillation light detection in the\n", + "GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by\n", + "LIGO and Virgo During the\n", + "Snowmass Neutrino Frontier:\n", + "DUNE Physics Summary\n", + "Executive Summary of DUNE Physics Program\n", + "Submitted\n", + "Draft version 1 December 2021\n", + "Typeset using LATEX twocolumn style in AASTeX62\n", + "Search for lensing sig\n", + "All-sky search in early O3 LIGO data for continuous gravitational-wave signals from\n", + "unknown neutron \n", + "Prepared for submission to JCAP\n", + "Searching for Solar KDAR with DUNE\n", + "The DUNE Collaboration\n", + "A. Abed Ab\n", + "EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)\n", + "LHCb-DP-2022-002\n", + "May 23, 2024\n", + "The LHCb Upgrade I\n", + "L\n", + "Prepared for submission to JINST\n", + "Design, construction and operation of the ProtoDUNE-SP\n", + "Liquid Argon\n", + "Tests of General Relativity with Binary Black Holes from the second LIGO–Virgo\n", + "Gravitational-Wave Tr\n", + "Eur. Phys. J. C manuscript No.\n", + "(will be inserted by the editor)\n", + "Separation of track– and shower–like\n" + ] + } + ], + "source": [ + "for paper in papers:\n", + " opening = paper[:100]\n", + " if opening not in paper_to_pairs:\n", + " print(opening)\n", + " try:\n", + " paper_to_pairs[opening] = generate_qa(paper)\n", + " except:\n", + " print(\"Failed, skipping\")\n", + " pass\n", + " else:\n", + " print(\"Pairs already finished, skipping\")" + ] + }, + { + "cell_type": "raw", + "id": "642b0bba-796e-4177-8e6b-638ae69fedc8", + "metadata": {}, + "source": [ + "print(paper_to_pairs.items())" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "4b530361-aef6-4cb2-9981-b7a70ab4b915", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "135417\n" + ] + } + ], + "source": [ + "print(len(papers[0]))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "9b85fe4a-2a19-4621-a7ba-7a34787530b7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5007211\n" + ] + } + ], + "source": [ + "print(len(papers[1]))" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "11bb9a15-c262-4c4f-839c-984e54d2af44", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1000000\n" + ] + } + ], + "source": [ + "print(len(papers[1][:1000000]))" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "id": "b977b274-f933-4114-adbf-d7bbcd7c5ae5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "37\n" + ] + } + ], + "source": [ + "print(len(paper_to_pairs))" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "id": "66fc814d-906d-45b9-88ec-674342d41e5a", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "with open(\"temp.json\", \"w\") as file:\n", + " json.dump(paper_to_pairs, file)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "773c5dac-6dbe-41e7-a380-0fb6fe723d3c", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "with open(\"temp.json\", \"r\") as file:\n", + " paper_to_pairs = json.load(file)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "827ef358-1289-4628-8d7a-ec95f167e2cf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "502\n", + "{'question': 'Which theoretical technique can most effectively reduce the uncertainties in the Standard Model prediction for the branching fraction of the rare decay \\\\(B_s^0 \\\\rightarrow \\\\mu^+ \\\\mu^-\\\\)?', 'answer': 'The dominant theoretical uncertainties come from the hadronic inputs—namely the decay constants and form factors—appearing in the effective Hamiltonian for \\\\(B_s^0 \\\\rightarrow \\\\mu^+ \\\\mu^-\\\\). Progress in unquenched lattice QCD calculations, with finer lattice spacings and lighter sea quark masses, can significantly tighten the determination of the \\\\(B_s\\\\) decay constant \\\\(f_{B_s}\\\\). Modern techniques such as the use of improved actions (e.g., HISQ for light quarks and relativistic heavy‑quark actions for the \\\\(b\\\\) quark), combined with nonperturbative renormalization and the inclusion of isospin‑breaking and QED effects, are expected to reduce the current uncertainty (\\\\(\\\\sim 6\\\\%\\\\)) on the decay constant—and thus on the branching‑fraction prediction—to the sub‑percent level.'}\n" + ] + } + ], + "source": [ + "qa_pairs = [\n", + " pair \n", + " for _, value in paper_to_pairs.items()\n", + " for pair in value\n", + "]\n", + "print(len(qa_pairs))\n", + "print(qa_pairs[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "adaadd91-9456-44cc-b4ac-60e4c59e7d2c", + "metadata": {}, + "outputs": [], + "source": [ + "def to_formatted(pair):\n", + " user_q = pair[\"question\"]\n", + " assistant_a = pair[\"answer\"]\n", + " # Compose the prompt with system, user, assistant roles\n", + " return f\"<|system|>{system_prompt}<|user|>{user_q}<|assistant|>{assistant_a}\"\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "32eb99f6-5d37-4815-9ef5-b9aa9b428fba", + "metadata": {}, + "outputs": [], + "source": [ + "import json\n", + "system_prompt = \"You are a helpful academic Q&A assistant specialized in scholarly content.\"\n", + "with open(\"data/papers/formatted.jsonl\", \"w\") as file:\n", + " for pair in qa_pairs:\n", + " json.dump(to_formatted(pair), file)\n", + " file.write(\"\\n\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2821a5f2-7a3d-46af-ae72-d1a396e2d7d9", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/README.md b/README.md new file mode 100644 index 0000000..407d740 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Thank you to arXiv for use of its open access interoperability. + diff --git a/data/papers/formatted.jsonl b/data/papers/formatted.jsonl new file mode 100644 index 0000000..8f70e01 --- /dev/null +++ b/data/papers/formatted.jsonl @@ -0,0 +1,492 @@ +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which theoretical technique can most effectively reduce the uncertainties in the Standard Model prediction for the branching fraction of the rare decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?<|assistant|>The dominant theoretical uncertainties come from the hadronic inputs\u2014namely the decay constants and form factors\u2014appearing in the effective Hamiltonian for \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\). Progress in unquenched lattice QCD calculations, with finer lattice spacings and lighter sea quark masses, can significantly tighten the determination of the \\(B_s\\) decay constant \\(f_{B_s}\\). Modern techniques such as the use of improved actions (e.g., HISQ for light quarks and relativistic heavy\u2011quark actions for the \\(b\\) quark), combined with nonperturbative renormalization and the inclusion of isospin\u2011breaking and QED effects, are expected to reduce the current uncertainty (\\(\\sim 6\\%\\)) on the decay constant\u2014and thus on the branching\u2011fraction prediction\u2014to the sub\u2011percent level."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What qualitative change would a new heavy \\(Z'\\) boson that couples predominantly to third\u2011generation quarks produce in the branching fraction of \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?<|assistant|>A heavy \\(Z'\\) that couples to \\(b \\to s\\) transitions would contribute to the effective Wilson coefficients \\(C_{10}\\) and possibly \\(C_S, C_P\\) in the low\u2011energy effective Hamiltonian. Depending on its mass and coupling strength, the interference with the Standard\u2011Model amplitude could either enhance or suppress the branching fraction. In many motivated \\(Z'\\) models, the amplitude adds constructively, leading to a visible increase in the \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) branching ratio, potentially by a factor of a few, while keeping the branching fraction of \\(B^0 \\rightarrow \\mu^+ \\mu^-\\) relatively unaffected because the flavour\u2011changing transition is suppressed when the \\(Z'\\) couples only to third\u2011generation quarks."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the lifetime difference between the heavy and light mass eigenstates of the \\(B_s^0\\) system influence the experimental determination of its dimuon branching fraction?<|assistant|>The decay width difference \\(\\Delta\\Gamma_s = \\Gamma_L - \\Gamma_H\\) implies that the two mass eigenstates of the \\(B_s^0\\) have different lifetimes. Since the Standard Model predicts that only the heavy eigenstate can decay to \\(\\mu^+\\mu^-\\) (due to CP conservation), the observed decay time distribution is skewed toward the long\u2011lived state. In a detector with reconstruction efficiency that varies with decay time (e.g., due to displacement cuts on the vertex), an analysis that assumes a single average lifetime will introduce a bias. Correcting for this effect requires disentangling the lifetime dependence, typically by applying a weight derived from simulation assuming the Standard\u2011Model CP structure; this correction reduces the systematic uncertainty on the branching\u2011fraction measurement."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Why is the ratio \\(\\mathcal{B}(B^0 \\rightarrow \\mu^+ \\mu^-)/\\mathcal{B}(B_s^0 \\rightarrow \\mu^+ \\mu^-)\\) considered a powerful test of minimal flavour violation?<|assistant|>In the framework of minimal flavour violation (MFV), all flavour\u2011changing neutral\u2011current processes are governed solely by the Cabibbo\u2013Kobayashi\u2013Maskawa (CKM) matrix, and new physics contributions respect the same flavour\u2011symmetry breaking pattern as the Standard Model. Consequently, the ratio of the branching fractions for \\(B^0\\) and \\(B_s^0\\) decays to dimuons is predicted to be exactly the same as in the Standard Model, namely \\(R_{\\rm MFV} \\approx 0.0295\\). Any significant departure from this value would signal the presence of new sources of flavour violation beyond the CKM structure. Therefore, precise experimental determinations of both branching fractions, and their ratio, are key to constraining or revealing non\u2011MFV new\u2011physics scenarios."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it currently possible to measure CP violation in the decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) with the data sets used in the combined analysis of CMS and LHCb?<|assistant|>No. The combined measurement reported in the paper provides a branching\u2011fraction determination but does not distinguish between \\(B_s^0\\) and \\(\\bar{B}_s^0\\) decays, i.e., it is an untagged analysis. Observing CP violation would require tagging the initial flavour of the \\(B_s^0\\) meson and measuring a time\u2011dependent asymmetry between decay rates of \\(B_s^0\\) and \\(\\bar{B}_s^0\\). Such an analysis demands larger data samples, sophisticated flavour\u2011tagging algorithms, and precise decay\u2011time resolution\u2014capabilities that are beyond the scope of the present dataset and analysis strategy. Hence the answer is unavailable within the current study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the amount of inactive material in the inner detector affect the energy loss distribution for electrons traversing the tracker, and what implications does this have for the jet\u2010electron background rejection in the ATLAS invariant mass reconstruction?<|assistant|>The larger the inactive material, the more bremsstrahlung photons are emitted by electrons, which reduces the measured electron energy and creates a tail in the energy loss distribution. This tail increases the probability that an energetic electron is mis\u2011measured as a low\u2011energy cluster, thereby increasing the background from jets that fake electrons. A careful mapping of the material budget is therefore essential: the global energy loss can be parameterised as \u27e8\u0394E\u27e9/E \u2243 0.02\u202fX\u2080 for a 10\u202fGeV electron, where X\u2080 is the radiation length traversed. An accurate simulation of this effect allows the design of more efficient electron\u2011jet discrimination algorithms that rely on the reconstructed transverse momentum balance and shower shape observables."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected impact of the three\u2011level pixel detector alignment tolerances on the impact parameter resolution for tracks originating from a displaced secondary vertex, such as those from B\u2011hadron decays?<|assistant|>The pixel alignment tolerances (10\u202f\u00b5m in R\u2013\u03c6 and 115\u202f\u00b5m in z for the vertexing layer) translate into a systematic bias in the reconstructed track position of the order of 20\u201130\u202f\u00b5m. When propagating to a secondary vertex located a few millimetres from the primary interaction point, this bias adds in quadrature to the intrinsic multiple\u2011scattering term, reducing the transverse impact parameter resolution from the ideal 10\u202f\u00b5m to about 15\u201318\u202f\u00b5m for tracks with p\u209c \u2273 2\u202fGeV. This degradation slightly worsens the ability to separate B\u2011hadron decay vertices from the primary vertex, but the effect is still well below the requirement for efficient b\u2011tagging at the design luminosity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the high\u2011level trigger (HLT) track reconstruction algorithm balance the demands of speed and precision in the presence of 50\u2013100\u202f% pile\u2011up events?<|assistant|>The HLT employs a multi\u2011stage track reconstruction where a fast, coarse seeding phase (based on pixel and SCT hits only) provides a first approximation of the track parameters. This initial estimate is fed into a Kalman filter that iteratively refines the fit using full detector information, including TRT hits, but only for tracks whose quality scores lie above a tunable threshold. In simulation studies this approach achieves a track\u2011finding efficiency of >\u202f95\u202f% for |\u03b7|\u202f<\u202f2.5 and a fake\u2011rate of <\u202f1\u202f% even at 100\u202fpb\u207b\u00b9, while keeping the CPU time below 100\u202f\u00b5s per event. The dynamic adjustment of the iteration count based on the local hit density allows the algorithm to remain robust against pile\u2011up in the core of high\u2011energy jets."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant systematic uncertainties affecting the measurement of the W\u2011boson mass using the lepton transverse momentum spectrum in ATLAS, and how can they be constrained with early LHC data?<|assistant|>The measurement is limited mainly by the calibration of the electromagnetic calorimeter energy scale (\u2264\u202f0.5\u202f%), the lepton momentum scale in the inner detector (\u2264\u202f0.3\u202f% for \u03bc and \u2264\u202f0.1\u202f% for e at high p\u209c), and the knowledge of the parton distribution functions (\u2248\u202f2\u202f% uncertainty on the rapidity distribution of the W). These systematic effects can be constrained using high\u2011statistics control samples: Z\u2192\u2113\u207a\u2113\u207b decays provide an in\u2011situ calibration of the lepton energy/momentum scales with a precision better than 0.05\u202f% for lepton p\u209c\u202f>\u202f30\u202fGeV, while the ratio of W to Z production cross sections can be used to mitigate PDF uncertainties. Performing a simultaneous fit to the W and Z transverse mass spectra further reduces the impact of common systematics."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the viewing angle of a short gamma-ray burst jet influence the expected flux of high-energy neutrinos detectable on Earth?<|assistant|>A larger viewing angle reduces the Doppler boosting and beaming of particles accelerated in the jet, leading to a steep decline in the neutrino flux arriving at Earth. The flux scales roughly with the Doppler factor to the fourth power for internal shock models, so an off-axis observer can see neutrinos at a level that is orders of magnitude lower than an on-axis observer."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which hadronic processes are considered to produce high-energy neutrinos in the internal shocks of short GRBs?<|assistant|>The dominant mechanism is photohadronic (p\u03b3) interaction, where relativistic protons accelerated in internal shocks collide with prompt gamma-ray photons, producing charged pions that decay into neutrinos. In addition, proton-proton (pp) interactions in dense baryonic outflows can contribute, though the optical depth for pp is usually low in short GRB jets."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What strategies do neutrino observatories use to discriminate down\u2011going neutrino events when the source lies above the detector\u2019s horizon?<|assistant|>Detectors such as ANTARES and IceCube employ stringent cuts on reconstructed direction, energy, and event topology. They use tight angular uncertainty requirements, require a high-energy deposition inconsistent with atmospheric muons, and apply machine\u2011learning classifiers trained on simulated neutrino and muon events. By temporally correlating with a known source location, the background probability is further reduced."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>If a cocoon forms around the jet of a binary neutron star merger, how would this affect the expected neutrino emission compared to a narrow jet?<|assistant|>A cocoon expands more slowly and over a wider solid angle, potentially producing neutrinos through shock\u2013accelerated protons interacting with surrounding ejecta. Because the cocoon is less collimated, the neutrino flux received by an observer is spread over a larger area, but the efficiency can be higher if the cocoon\u2019s optical depth to neutrinos is large. However, the lower Lorentz factor reduces the maximum neutrino energy compared to the narrow jet."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What would be the expected neutrino flux from a binary neutron star merger located at 200\u202fMpc, assuming the same intrinsic properties as GW\u202f170817?<|assistant|>The current paper does not provide predictions for such a distance, so we cannot quote a definitive flux. Estimating the flux would require scaling the intrinsic neutrino luminosity by the inverse square of the distance (i.e., reducing it by a factor of about 16 relative to 40\u202fMpc). Detailed modeling would also need to account for cosmological redshift effects on the neutrino energy spectrum, which is beyond the scope of the current analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does including Virgo and KAGRA in the fourth observing run influence the sky\u2011localisation accuracy for heavy binary black\u2011hole mergers compared with the first two observing runs?<|assistant|>Detectors that are further apart in latitude and longitude increase the baseline for triangulation. The addition of Virgo (\u22481600\u202fkm from LIGO sites) and KAGRA (\u224811,000\u202fkm from LIGO) reduces the median 90\u202f% credible sky area for high\u2011mass mergers (\u2265\u202f30\u202fM\u2299) from roughly 20\u202fdeg\u00b2 in O1/O2 to about 5\u201310\u202fdeg\u00b2 in O4, mainly because the extra detectors break degeneracies between source position and antenna pattern."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What advantage does frequency\u2011dependent squeezed vacuum provide to the LIGO detectors below 50\u202fHz, and how might this improve detections of neutron\u2011star\u2013black\u2011hole binaries?<|assistant|>Frequency\u2011dependent squeezing suppresses shot noise at high frequencies while reducing radiation\u2011pressure noise at low frequencies. The improvement below 50\u202fHz increases the signal\u2011to\u2011noise ratio for signals that extend into this band, such as the early inspiral of neutron\u2011star\u2013black\u2011hole binaries, yielding a higher detection horizon and better estimates of the inclination angle."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the measured distribution of the effective inspiral spin parameter (\u03c7\u2091\u2093\u2091ff) in GWTC\u20114.0 limit spin\u2013alignment scenarios for stellar\u2011mass black\u2011hole binaries?<|assistant|>The observed concentration of \u03c7\u2091\u2093\u2091ff values near zero indicates that most black\u2011hole spins are either misaligned or have small magnitudes, suggesting formation through dynamical capture or supernova kicks that break alignment. A tail of positive \u03c7\u2091\u2093\u2091ff points to some binaries with partially aligned spins, consistent with isolated binary evolution where tidal alignment persisted."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the GWTC\u20114.0 data alone distinguish an intermediate\u2011mass black\u2011hole merger (\u223c100\u20131000\u202fM\u2299) from a supermassive\u2011black\u2011hole merger through gravitational\u2011wave signatures?<|assistant|>The current GWTC\u20114.0 catalogue does not include any confirmed detections in the frequency band where supermassive\u2011black\u2011hole mergers would be observed with ground\u2011based detectors. Consequently, distinguishing an intermediate\u2011mass from a supermassive merger using only the present data is not possible; additional high\u2011frequency sensitivity or space\u2011based observations would be required."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the most recent statistical constraints on the Hubble constant obtained from GWTC\u20114.0\u2019s \u201cdark\u2011siren\u201d cosmology analysis using galaxy\u2011catalog cross\u2011correlation?<|assistant|>The dark\u2011siren analysis of GWTC\u20114.0 yields a Hubble constant of H\u2080\u202f\u2248\u202f70\u202f\u00b1\u202f10\u202fkm\u202fs\u207b\u00b9\u202fMpc\u207b\u00b9 (68\u202f% credible interval), consistent with both the value inferred from the cosmic microwave background and that obtained from the standard\u2011sirens with electromagnetic counterparts, albeit with larger uncertainty due to the limited number of high\u2011volume events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the relationship between the coherence length of an ultralight vector dark matter field and its mass?<|assistant|>The coherence length \\(L_{\\text{coh}}\\) of a non\u2011relativistic dark\u2011matter field is inversely proportional to its mass: \\(L_{\\text{coh}}\\sim 2\\pi\\hbar/(mA\\,\\bar v)\\) where \\(\\bar v\\) is the velocity dispersion. For a typical halo velocity \\(\\bar v\\sim10^{-3}c\\), a field mass of \\(10^{-13}\\,\\text{eV}/c^{2}\\) corresponds to a coherence length of order \\(10^{7}\\,\\text{km}\\). Thus, as the mass decreases, the coherence length grows linearly."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Why does using auxiliary length channels in a laser interferometer improve sensitivity to ultralight vector dark matter compared to the main differential arm length channel?<|assistant|>Auxiliary length channels (e.g., the Michelson differential length \\( \\text{MICH} \\) and the power\u2011recycling cavity length \\( \\text{PRCL} \\)) involve mirrors made from different materials (sapphire test masses versus fused\u2011silica auxiliary mirrors). Because the ultralight vector field couples to the charge\u2011to\u2011mass ratio of the test masses, the response of different mirrors differs, producing a differential signal that is larger than that in the main channel where the mirrors are usually identical. This material\u2011composition asymmetry amplifies the displacement induced by the field and therefore enhances the detectable strain."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the principal difficulties in separating a genuine ultralight dark\u2011matter signal from transient detector noise in GW strain data?<|assistant|>True DM signals are expected to be narrow\u2011band, persistent over long times, and statistically Gaussian in amplitude due to the central limit theorem. Transient detector artifacts, however, are often broadband, short\u2011lived, and exhibit non\u2011Gaussian statistics. Distinguishing them requires (i) characterising the expected DM bandwidth and coherence time, (ii) checking the persistence of a signal across independent data epochs, and (iii) vetoing known instrumental lines by cross\u2011correlation with auxiliary sensors or by comparing the signal\u2019s spectral shape to that predicted for DM."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What future improvements to the KAGRA detector could make it more competitive in probing ultralight vector dark matter?<|assistant|>Potential upgrades include: (1) reducing the low\u2011frequency noise in the auxiliary channels by implementing advanced vibration isolation and seismic suppression; (2) increasing the laser power and improving mirror coatings to lower the thermal and shot noise; (3) deploying cryogenic temperature control for all mirrors to match the sapphire test masses across the interferometer; (4) extending the observation run length so that more data segments exceed the DM coherence time; and (5) adding dedicated sensors to monitor and subtract known noise lines from the auxiliary channels."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What would be the effect on the derived constraints if the ultralight vector dark matter field had a preferred polarization direction rather than being isotropically distributed?<|assistant|>I do not have enough information to answer this question conclusively. The paper assumes an isotropic velocity and polarization distribution when modeling the signal covariance. A non\u2011isotropic polarization would change the statistical properties of the induced length variations, potentially altering the expected strain spectrum and the detection statistic. Determining the precise impact requires a dedicated theoretical study of polarized vector dark matter and its coupling to interferometer mirrors, which is not covered in the present analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the rotation rate of a progenitor star influence the amplitude and frequency spectrum of gravitational waves emitted during a core\u2011collapse supernova?<|assistant|>Rotation tends to destabilise the proto\u2011neutron star, giving rise to non\u2011axisymmetric modes such as bar\u2011mode or spiral instabilities. Faster rotation yields a higher degree of ellipticity and can shift the dominant GW frequency to lower values (tens to a few hundred hertz) while increasing the wave strength by orders of magnitude. The total radiated GW energy can rise from \u224810\u207b\u2076\u202fM\u2299\u202fc\u00b2 in slowly rotating models to \u224810\u207b\u2074\u201310\u207b\u00b3\u202fM\u2299\u202fc\u00b2 for rapidly rotating cores."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main sources of statistical uncertainty when setting upper limits on gravitational\u2011wave energy from a core\u2011collapse supernova detected by the LIGO\u2013Virgo\u2013KAGRA network?<|assistant|>The dominant uncertainties stem from (1) strain calibration, typically 2\u20133\u202f% across the instrument band; (2) non\u2010Gaussian detector noise, especially short glitches that can mimic transients and inflate background estimates; (3) modelling assumptions, such as the choice of waveform family, source orientation, and ellipticity; and (4) the definition of the on\u2011source window, which determines how much coincident data are available. Together these contribute systematic errors on the strain sensitivity and thus on the inferred energy limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might strong magnetic fields in the nascent proto\u2011neutron star alter the expected gravitational\u2011wave signal compared to magnetically quiet core\u2011collapse scenarios?<|assistant|>Intense magnetic fields can drive a magnetorotational explosion, launching bipolar jets that increase asymmetry. This can generate higher\u2011frequency (\u22481\u20133\u202fkHz) GW components with larger amplitudes and potentially longer durations than the \u2248100\u202fHz bar\u2011mode bursts seen in weak\u2011field models. The field geometry also influences the ellipticity evolution and can sustain non\u2011axisymmetric instabilities beyond the few\u2013hundred\u2011millisecond timescale typical of neutrino\u2011driven explosions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What time delay between the neutrino burst and the peak gravitational\u2011wave emission is generally expected in core\u2011collapse supernovae, and how does this affect on\u2011source window construction?<|assistant|>The neutrino burst is emitted almost simultaneously with core bounce, within milliseconds. Gravitational waves can start at the bounce and continue for tens of milliseconds as prompt convection and SASI develop; later, bar\u2011mode or magnetorotational instabilities can produce emission lasting up to a second. Consequently, effective on\u2011source windows that encompass a few seconds around the neutrino trigger are recommended to capture both prompt and late\u2011time signals."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the latest upper limits on neutron\u2013star ellipticity from continuous\u2011gravitational\u2011wave searches constrain the strength of internal magnetic fields in millisecond pulsars?<|assistant|>The ellipticity (\u03b5) limits set by non\u2011detections translate into an upper bound on the quadrupole deformation induced by strong internal magnetic fields. For a simple model where the magnetic energy dominates the deformation, \u03b5 \u2243 (B_int\u202f/\u202f10^16\u202fG)^2\u202f\u00d7\u202f10^\u22126. Using the most stringent \u03b5 limits from recent searches (\u2248\u202f10^\u22129 for the bright nearby millisecond pulsar J0437\u22124715), the inferred maximum internal field is \u2272\u202f10^15\u202fG \u2013 well below the dipole surface fields (~10^8\u201310^9\u202fG). This suggests that millisecond pulsars cannot harbor extremely strong toroidal fields that would otherwise produce noticeable gravitational\u2011wave emission. The exact relationship depends on the equation of state and the geometry of the field, and more sophisticated magnetohydrodynamic modelling is required for accurate limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What impact does the Shklovskii effect have on the interpretation of spin\u2011down limits in continuous\u2011gravitational\u2011wave pulsar searches?<|assistant|>The Shklovskii effect arises when the proper motion of a pulsar adds a kinematic contribution to its measured period derivative: \\( \\dot{P}_{\\text{Shk}} = (P\\,v_{\\perp}^2)/(c\\,D) \\). This extra term inflates the observed spin\u2011down rate and thus the inferred spin\u2011down energy loss rate. For continuous\u2011GW searches the spin\u2011down limit \\(h_{\\text{sd}} \\propto \\sqrt{|\\dot{f}_{\\text{rot}}|/f_{\\text{rot}}}\\) is then over\u2011estimated if the Shklovskii correction is not applied. Properly subtracting \\(\\dot{f}_{\\text{Shk}}\\) yields a lower intrinsic spin\u2011down, which tightens the spin\u2011down limit and means that a true GW amplitude approaching the limit would be less likely. The effect is most significant for nearby, high\u2011proper\u2011motion millisecond pulsars."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main technical challenges in extending persistent\u2011wave searches to eccentric binary pulsars?<|assistant|>Eccentric binaries introduce additional orbital modulations in the gravitational\u2011wave phase, requiring knowledge of the orbital elements (eccentricity, periastron advance, etc.) and a high\u2011order orbital model. The main challenges include: 1) the need for densely sampled, high\u2011precision timing solutions to track the periastron motion and secular variations; 2) increased parameter space dimensionality (eccentricity, argument of periastron, orbital period derivatives) leading to higher computational cost; and 3) the risk of mismodeling orbital dynamics, which can de\u2011phase the coherent integration and degrade sensitivity. Recent advances in joint timing and GW modelling, as well as the use of coherent matched\u2011filter pipelines that can include time\u2011dependent orbital phase terms, are helping to mitigate these difficulties."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How will the planned upgrades to Advanced LIGO, Virgo, and KAGRA influence the sensitivity of continuous\u2011gravitational\u2011wave searches in future observing runs?<|assistant|>The upgrades\u2014such as increased laser power, improved quantum\u2011noise reduction via squeezed light, cryogenic mirrors for Virgo, and higher seismic isolation for KAGRA\u2014will lower the detector noise floor by factors of 1.5\u20132 in the 10\u20131000\u202fHz band relevant for pulsar GW emission. This translates to a depth improvement of ~30\u201350\u202f%, allowing continuous\u2011GW searches to probe strain amplitudes down to \u2248\u202f10^\u201127\u201310^\u201126 for the most promising nearby pulsars. Moreover, the longer continuous observing periods expected (\u2248\u202f1\u202fyr per run) will further increase the coherent integration time, improving sensitivity roughly as the square root of the observation time. Combined, these changes will tighten ellipticity limits by an order of magnitude for many targets."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What can the recent upper limits on dipole radiation from Brans\u2013Dicke theory tell us about the viability of scalar\u2011tensor gravity models?<|assistant|>The non\u2011detection of dipole gravitational radiation at the level of h_d\u202f\u2248\u202f10^\u201127\u201310^\u201126 for pulsars with strong orbital accelerations sets a lower bound on the Brans\u2013Dicke coupling parameter \u03c9_BD \u2273\u202f10^4\u201310^5. This is roughly an order of magnitude improvement over the best Solar\u2013System constraints derived from the Viking landers and Cassini ranging experiments. While scalar\u2011tensor models with very weak coupling remain allowed, the results considerably restrict parameter space where dipole radiation could contribute significantly to orbital decay, supporting the robustness of General Relativity as the dominant interaction in the strong\u2011field regime."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the prevalence of black holes in the pair\u2011instability supernova mass gap (roughly 45\u2013120\u202fM\u2299) in the local universe, and does the current gravitational\u2011wave catalog provide evidence for a statistically significant dearth in that range?<|assistant|>Current population studies show a steep decline in the merger rate above about 40\u201345\u202fM\u2299, yet the number of observed events with primary masses above 70\u202fM\u2299 is small. Some detections near the putative gap boundary (~70\u202fM\u2299) are compatible with a smooth continuation of the mass distribution, rather than an empty gap. Consequently, while there is evidence for a reduced rate, a decisive confirmation of a completely empty pair\u2011instability gap cannot be drawn from the existing catalog."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the effective inspiral spin distribution (\u03c7_eff) vary with redshift, and what might this tell us about the formation pathways of binary black holes?<|assistant|>Analyses of the most recent catalog hint that the width of the \u03c7_eff distribution broadens as redshift increases, whereas its mean stays near zero. This broadening could reflect a growing contribution from dynamically assembled binaries or hierarchical mergers at earlier epochs. However, given the limited number of high\u2011redshift detections, the trend is still marginal and could be influenced by selection effects, so a definitive conclusion about redshift dependence of \u03c7_eff remains tentative."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the relative mass\u2011ratio distribution of binary black holes near the ~10\u202fM\u2299 and ~35\u202fM\u2299 mass peaks, and does it imply different evolutionary pathways?<|assistant|>Binaries with primary masses around 10\u202fM\u2299 tend to merge with significantly less massive companions (mass\u2011ratio peak near q\u202f\u2248\u202f0.7), while those near the 35\u202fM\u2299 peak usually have more equal masses (q\u202f\u2248\u202f0.9\u20131.0). These features are compatible with theoretical expectations: the lower\u2011mass peak may arise from stable mass\u2011transfer episodes in isolated binaries, whereas the higher\u2011mass equal\u2011mass systems could be produced in dense stellar clusters or through hierarchical mergers. Nonetheless, the overlap between the two distributions remains substantial, and additional observations are needed to solidify the link between observed ratios and specific formation channels."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there evidence for a lower\u2011mass gap between the heaviest neutron stars and the lightest black holes (\u223c3\u20135\u202fM\u2299) in the observed merger population?<|assistant|>The current gravitational\u2011wave data show compact objects clustering around neutron\u2011star masses near 1.3\u20131.4\u202fM\u2299 and black\u2011hole masses beginning around 5\u20136\u202fM\u2299, with only a handful of events land in the 3\u20135\u202fM\u2299 interval. Statistically, the distribution is consistent with a continuous decline rather than a sharply empty region. Thus, while the existence of a pronounced lower\u2011mass gap remains an open question, the catalog does not provide sufficient evidence to confirm its presence."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the observed population of binary black holes exhibit a correlation between component spin magnitudes and the component masses, such that more massive black holes spin faster?<|assistant|>The data available so far do not unambiguously support such a correlation. Although some earlier studies suggested a weak trend of increasing spin amplitudes with mass, the latest catalog shows considerable overlap between mass and spin posterior distributions, with large uncertainties in both quantities. Current posterior constraints are consistent with both no correlation and modest positive correlations within the error bounds. Therefore, this question remains unanswered; a larger, less biased sample and more precise spin measurements are needed to resolve whether a spin\u2013mass trend exists."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What physical mechanisms are thought to generate gravitational waves simultaneously with fast radio bursts from magnetars, and how do their predicted gravitational-wave energy outputs compare?<|assistant|>The most frequently discussed mechanisms involve sudden re\u2011configurations of the neutron\u2011star interior: a starquake or a global crustal failure can excite the star\u2019s f\u2011mode at \u223c2\u202fkHz, radiating \\(E_{\\rm GW}\\sim10^{48\\text{\u2013}10^{49}\\,{\\rm erg}\\) if the quake involves a large crustal distortion. Magneto\u2011elastic coupling between the star\u2019s magnetic field and shear oscillations can also trigger quasi\u2011periodic oscillations in the X\u2011ray tail of a flare; these oscillations source GW emission at a few hundred to a few thousand hertz with energies \\(10^{41\\text{\u2013}10^{45}\\,{\\rm erg}\\). A third possibility is that the rapid spin\u2011up associated with a glitch injects free precession power, potentially yielding \\(10^{44\\text{\u2013}10^{48}\\,{\\rm erg}\\) in a short burst. All of these scenarios predict waveforms that are broad in frequency but typically last less than a second, making them amenable to the short\u2011duration burst searches used in recent LIGO/Virgo/KAGRA studies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way does the distance estimate for SGR\u202f1935+2154 influence the derived upper limits on gravitational\u2011wave energy for FRBs observed from it?<|assistant|>The gravitational\u2011wave energy inferred from an upper limit on strain scales with the square of the source distance (\\(E_{\\rm GW}\\propto D^{2}\\)). The canonical value of \\(6.6\\pm0.7\\)\u202fkpc is roughly a factor of two larger than the lower bound (\u22485\u202fkpc) and a factor of three smaller than the most distant estimates (\u224815\u202fkpc). If the true distance were 1.5\u202fkpc as suggested by some HI\u2011absorption studies, the energy constraint would tighten by about a factor of 20; if it were 15\u202fkpc, the limits would loosen by roughly a factor of five. Consequently, the 90\u202f% upper limits of \\(10^{48.5}\\)\u202ferg at 300\u202fHz and \\(10^{50}\\)\u202ferg at 2\u202fkHz could become respectively \\(5\\times10^{47}\\)\u2013\\(5\\times10^{49}\\)\u202ferg depending on the true distance."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the principal obstacles to detecting short\u2011duration gravitational\u2011wave bursts associated with FRBs when only a single observatory (such as GEO600) is operational, and how can a network of detectors mitigate these issues?<|assistant|>With a single detector, the dominant challenges are: (1) the inability to use coincidence timing to veto terrestrial glitches, (2) a limited ability to estimate the false\u2011alarm rate because the background must be drawn from the same time segment, and (3) reduced signal\u2011to\u2011noise since no cross\u2011correlation can be performed between independent noise realizations. These factors increase the likelihood of spurious candidates and raise the detection threshold. A multi\u2011detector network provides independent noise streams so that a genuine astrophysical signal will appear in all observatories with a consistent time\u2011delay, allowing robust vetoes of local glitches. Moreover, the coherent combination of data boosts the signal\u2011to\u2011noise ratio roughly by \\(\\sqrt{N}\\) (with \\(N\\) detectors), enabling the detection of weaker bursts or tighter upper limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Could observations of gravitational waves help distinguish between competing progenitor models for extragalactic fast radio bursts, and what specific gravitational\u2011wave signatures would be most decisive?<|assistant|>Yes. Different progenitor hypotheses predict distinct gravitational\u2011wave morphologies and energetics. A binary\u2011neutron\u2011star merger would produce a short (\\(<1\\)\u202fs) chirp signal with a characteristic inspiral\u2011merger\u2011ringdown waveform and \\(E_{\\rm GW}\\sim10^{53}\\)\u202ferg, whereas a single magnetar flare with a starquake would produce a short, possibly broadband burst at a few hundred to several thousand hertz with much lower energy (\\(10^{41\\text{\u2013}10^{49}\\)\u202ferg). Detecting a merger\u2011style chirp coincident with an FRB would strongly support a binary origin; conversely, a null result in such a search coupled with a detection of a broadband short burst would favor a magnetar or other single\u2011object model. The presence of a long\u2011duration quasi\u2011periodic oscillation in the GW spectrum would further point toward magnetospheric or crustal modes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there observational evidence that X\u2011ray glitches in magnetars are temporally correlated with subsequent fast radio burst activity, and what would such a correlation imply about FRB production mechanisms?<|assistant|>Current observations do not provide definitive evidence of a correlation between X\u2011ray glitches and FRBs. The paper reports on three X\u2011ray glitches around 2022\u202fOct\u202f14 but finds no associated FRBs within the limited duty cycle and sensitivity of the radio observatories at that time. Moreover, previous studies have seen both FRBs with and without simultaneous X\u2011ray bursts from SGR\u202f1935+2154, indicating that the two phenomena can be independent. A robust temporal correlation would suggest that the sudden change in the magnetospheric or interior structure that causes a glitch also triggers the coherent radio emission, supporting models where FRBs are powered by internal magnetic field re\u2011configuration. Until such a correlation is established with high\u2011cadence, simultaneous multi\u2011wavelength monitoring, this question remains open."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the most plausible astrophysical pathways that can produce compact objects in the lower mass gap (roughly 3\u20135\u202fM\u2299) which are subsequently detected as neutron\u2011star\u2013black\u2011hole binaries by gravitational\u2011wave observatories?<|assistant|>Astrophysical models point to a handful of scenarios: (1) core\u2011collapse supernovae with substantial fallback of material onto a nascent neutron star can raise the remnant mass into the lower mass gap; (2) early\u2011stage binary evolution with mass transfer followed by delayed collapse of a massive helium star can also produce low\u2011mass black holes; (3) binary neutron\u2011star mergers that leave a hyper\u2011massive remnant could collapse to a black hole of a few solar masses. None of these mechanisms is yet confirmed as dominant, and the relative contribution of each pathway remains a subject of active research."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In a neutron\u2011star\u2013black\u2011hole binary, how does a misalignment between the neutron star spin and the orbital angular momentum affect the gravitational\u2011wave phase evolution and the likelihood of detecting the event with matched\u2013filter searches?<|assistant|>Spin\u2013orbit coupling introduces additional phasing terms that depend on the tilt angle. A significant tilt can lead to precession of the orbital plane, modulating the amplitude and phase of the waveform in a way that is partially degenerate with mass parameters. While matched\u2011filter pipelines can accommodate precessing templates, the reduced match for highly tilted systems can lower the recovered signal\u2011to\u2011noise ratio, potentially making such events harder to detect or to characterize accurately."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which electromagnetic counterparts are most commonly expected from symmetric\u2011mass neutron\u2011star\u2013black\u2011hole mergers, and how can current multi\u2011messenger follow\u2011up strategies maximize the probability of identifying them?<|assistant|>Symmetric\u2011mass mergers (with mass ratio close to unity) are more likely to tidally disrupt the neutron star before it plunges into the black hole. This can leave behind a remnant accretion disk and unbound ejecta, creating a kilonova with blue and red components, and possibly launching a short gamma\u2011ray burst. Rapid, wide\u2011field optical and infrared surveys, coordinated with high\u2011energy satellites, are essential to capture the early, rapidly fading signals; however, localisation uncertainties from single\u2011detector detections limit the efficiency of current follow\u2011ups."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How has the estimated merger rate of neutron\u2011star\u2013black\u2011hole binaries changed from the third to the fourth observational runs of ground\u2011based gravitational\u2011wave detectors, and what implication does this have for population synthesis models?<|assistant|>The rate has increased from roughly 20\u201350\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 during O3 to about 70\u2013100\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 in early O4, though uncertainties remain large. This upward trend suggests either that our sensitivity has improved or that the underlying population of neutron\u2011star\u2013black\u2011hole binaries is larger than previously thought, challenging models that placed a strong lower mass gap and predict fewer such systems."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What does the current population of neutron\u2011star\u2013black\u2011hole detections tell us about the distribution of the inclination angle (\u03b8_JN) between the total angular momentum and the line\u2011of\u2011sight, and how does this affect the ability to localise sources on the sky?<|assistant|>We do not know the distribution of inclination angles for the present sample. Many detected events come from single\u2011detector observations, which provide almost no constraint on \u03b8_JN, leading to large degeneracies with distance and severely limiting sky localisation. A more complete sample\u2014with detections in at least two detectors\u2014would be required to map out the inclination distribution and improve localisation accuracy."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does a minimally modeled search such as coherent WaveBurst (cWB) compare to template\u2011based matched\u2011filter searches in detecting eccentric binary black\u2011hole mergers, in terms of sensitivity and false\u2011alarm rates?<|assistant|>Minimally modeled searches like cWB are robust against waveform systematics and can recover signals that deviate from binary\u2011black\u2011hole templates, including highly eccentric or precessing systems. For eccentricities below ~0.3, cWB retains roughly 70\u201380\u202f% of the SNR of a matched\u2011filter search that uses circular templates. Its background is typically higher, leading to larger false\u2011alarm rates for a given detection statistic. Template\u2011based searches lose sensitivity at high eccentricity because the phase evolution differs substantially from the templates; however, they can still recover eccentric signals if the templates include eccentricity descriptions or higher\u2011order modes. A definitive comparison requires large injection campaigns across the full eccentric\u2011parameter space."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the mass distribution of high\u2011mass eccentric black\u2011hole mergers provide evidence distinguishing between dense\u2011star\u2011cluster formation channels and accretion\u2011disk (AGN) environments?<|assistant|>Theoretical models predict that binaries formed in dense stellar clusters should peak at lower total masses with a broader mass ratio distribution, whereas AGN\u2011disk capture processes can produce more massive, nearly equal\u2011mass binaries with higher eccentricities. However, observationally separating these channels requires accurately measuring both mass and eccentricity for a statistically large sample. Presently, the sample size of confirmed eccentric mergers is too small, and mass\u2013eccentricity degeneracies in the waveforms make it difficult to attribute individual events to a specific channel."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What effect do higher\u2011order gravitational\u2011wave modes have on the detection and parameter estimation of eccentric binary black\u2011hole mergers, particularly for high total masses?<|assistant|>Higher\u2011order modes become more prominent in binaries with large mass ratios, high total mass, and when the orbital plane is inclined. In eccentric orbits, the mode content varies rapidly, potentially boosting the SNR for some modes while suppressing others. Including higher\u2011order modes in waveform models improves the match to the true signal, enhancing both detection efficiency and parameter recovery. Yet many current eccentric waveform approximants either omit or poorly resolve these modes, limiting the achievable accuracy for high\u2011mass systems."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant challenges in reliably extracting the orbital eccentricity of an individual detected binary black\u2011hole merger using current gravitational\u2011wave data?<|assistant|>The primary obstacles are: (1) waveform model uncertainty, as existing eccentric models are sparse in spin and mass\u2011ratio coverage; (2) strong degeneracies between eccentricity and spin\u2011precession or higher\u2011order modes; (3) limited signal\u2011to\u2011noise ratio for most events, which hampers precision in measuring subtle deviations from circularity; and (4) non\u2011Gaussian noise artifacts that can mimic or obscure eccentric signatures. Due to these factors, the confidence in eccentricity measurements for individual events remains low with current data."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How could a first\u2011order phase transition during the electroweak epoch generate a detectable stochastic gravitational\u2011wave background?<|assistant|>A first\u2011order phase transition proceeds via nucleation of bubbles of the true vacuum that expand, collide, and convert vacuum energy into kinetic motion of the plasma and magnetic fields. Sound waves in the plasma and bubble collision turbulence source gravitational waves with a characteristic peak frequency set by the phase\u2011transition temperature and duration. The amplitude is controlled by the strength parameter \\(\\alpha\\) (energy density released relative to radiation) and the inverse duration \\(\\beta/H\\). For transitions that occur at temperatures \\(\\mathcal{O}(100~\\text{GeV})\\), the peak frequency falls in the tens to hundreds of hertz band, which is accessible to ground\u2011based detectors, making such a background potentially detectable if \\(\\alpha\\) is large enough and \\(\\beta/H\\) is not too high."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role do cosmic strings play in shaping the spectrum of a stochastic gravitational\u2011wave background across different frequency bands?<|assistant|>Cosmic strings, one\u2011dimensional topological defects, form a network of long strings and loops. Loops oscillate and repeatedly emit bursts of gravitational waves, primarily from cusps, kinks, and kink\u2011kink collisions. The superposition of many such bursts produces a stochastic background that is approximately a power\u2011law \\(\\Omega_{\\text{GW}}(f)\\propto f^{\\alpha}\\). The spectral index \\(\\alpha\\) depends on the dominant source: cusps yield \\(f^{-1/3}\\) after integration, while kinks give a steeper slope. At high frequencies (kHz) the spectrum may steepen due to the finite loop lifetime, whereas at low frequencies (mHz) the long\u2011string contribution becomes more important, potentially producing a scale\u2011dependent feature that could be observable with space\u2011based detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can a stiff equation of state in the early Universe influence the spectral slope of the gravitational\u2011wave background observed today?<|assistant|>During a stiff epoch (equation\u2011of\u2011state parameter \\(w>1/3\\)), the Universe expands more rapidly than during radiation domination. Gravitational waves that re\u2011enter the horizon during this period get boosted because the energy density redshifts more slowly (\\(\\rho_{\\text{GW}}\\propto a^{-4}\\) while the background energy density scales as \\(a^{-3(1+w)}\\)). As a result, the primordial inflation\u2011generated spectrum acquires a blue tilt with spectral index \\(\\alpha_{\\text{stiff}}=2/(1+3w)\\), which can be substantially larger than the \\(\\alpha\\simeq0\\) of a standard inflationary background. This leads to a higher amplitude at higher frequencies, bringing the signal into the detectable band of ground\u2011based observatories if \\(w\\) is close to unity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What constraints does the recent O5 LIGO\u2011Virgo\u2011KAGRA run place on the amplitude of a parity\u2011violating chiral gravitational\u2011wave background at frequencies above 200\u202fHz?<|assistant|>I do not have information on that, because the O5 run data and its specific parity\u2011violation constraints have not been incorporated into the model I was trained on, and the paper you provided does not cover O5 results. Answering this question would require access to the latest analysis reports from the LIGO\u2011Virgo\u2011KAGRA collaboration, which are outside my knowledge domain."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What would be the impact on constraints of ultralight dark matter if the local dark-matter velocity distribution were modeled with a non\u2011Gaussian, anisotropic component?<|assistant|>A non\u2011Gaussian, anisotropic velocity distribution would modify the coherence time and the spectral shape of the dark\u2011matter signal in interferometer data. This could lead to either tighter or weaker limits depending on the directionality and spread of the velocity field, and realistic modeling may improve the sensitivity to mass ranges close to the interferometer arm length resonances."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can future third\u2011generation gravitational\u2011wave detectors, such as the Einstein Telescope or Cosmic Explorer, provide an order\u2011of\u2011magnitude improvement in the upper limits on the couplings of scalar ultralight dark matter to the fine\u2011structure constant?<|assistant|>Yes. The significantly increased strain sensitivity and longer observation times expected for third\u2011generation detectors would reduce the noise floor across a broad frequency band. This would allow the amplitude of a hypothetical dark\u2011matter\u2011induced strain signal to be probed at much lower levels, potentially improving scalar coupling limits by an order of magnitude or more."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would an improved calibration of the interferometer\u2019s transfer function for arm\u2011mirror size oscillations affect the derived limits on dark\u2011photon couplings to baryons?<|assistant|>A more accurate transfer\u2011function calibration would reduce systematic uncertainties in the conversion between measured strain and the underlying dark\u2011photon force. Consequently, the derived bounds on the dark\u2011photon\u2013baryon coupling could be tightened, especially at the low\u2011frequency end where the transfer function is most sensitive to arm\u2011mirror displacement."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there any empirical evidence in current gravitational\u2011wave data for differential strain patterns that could distinguish between a scalar dilaton field and a massive tensor dark\u2011matter field?<|assistant|>Such differential strain patterns have not yet been observed in current gravitational\u2011wave data. Distinguishing between scalar and tensor signatures would require identifying the characteristic polarization responses of the interferometer arms, which remains an open challenge for present datasets."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the most stringent existing constraint on the coupling of ultralight vector dark matter to Electron currents from laboratory fifth\u2011force experiments?<|assistant|>I do not have that information. The paper focuses on limits from atomic clocks and torsion\u2011balance experiments for scalar and vector couplings, but does not provide the strongest laboratory constraint on vector dark\u2011matter couplings to electron currents."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the distribution of effective inspiral spins (\u03c7_eff) evolve for binary black holes that form through successive hierarchical mergers in globular clusters, and how does this distribution differ from that of binaries formed in isolation?<|assistant|>In hierarchical mergers the remnant spin of the previous merger is typically large (\u22480.7) and directed roughly along the orbital angular momentum. When this remnant merges with another black hole, the resulting \u03c7_eff distribution becomes broadly symmetric around zero, with a significant tail of large positive and negative values. In contrast, binaries formed in isolation usually exhibit a positively biased \u03c7_eff distribution due to spin alignment from common progenitor evolution. The exact shape of the \u03c7_eff distribution, however, depends on cluster properties, mass segregation, and the dynamical ejection/retention of remnants, and detailed numerical simulations are required to quantify it precisely."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the quantitative effect of the spin-induced quadrupole moment (parameter \u03ba) on the amplitudes of higher-order spherical harmonic modes (\u2113, m) during the late inspiral and merger phases of a binary black hole system?<|assistant|>The spin-induced quadrupole moment enters the post-Newtonian expansion of the gravitational-wave phase and amplitude. A deviation \u03b4\u03ba from the Kerr value of 1 modifies the amplitude of mass- and current\u2011quadrupole contributions to the (\u2113, m) = (2,\u00b12) leading mode, while also altering the relative strength of higher modes such as (\u2113, m) = (3,\u00b13) via changes in the binary\u2019s orbital dynamics. For rapidly spinning binaries (\u03c7 ~ 0.7) and moderate mass ratios (q \u2243 0.3), a \u03b4\u03ba of order 0.1 can shift the (3,\u00b13) mode amplitude by several percent, leading to measurable deviations in the signal-to-noise ratio and potentially affecting the inference of source parameters."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can gravitational\u2011wave signatures from eccentric binary black hole mergers in cluster cores provide a robust test of post-Newtonian predictions for eccentric inspirals, and what is the expected eccentricity range at LIGO frequencies?<|assistant|>Eccentric binaries formed via close encounters or three\u2011body interactions are expected to retain pericenter distances that produce orbital eccentricities e \u2243 0.01\u20130.1 when the gravitational-wave frequency enters the LIGO band (>20\u202fHz). Post\u2011Newtonian models that include eccentricity up to next-to\u2011quadratic order reproduce the energy and angular\u2011momentum fluxes with residuals below a few percent for this eccentricity range. Therefore, with sufficiently high signal\u2011to\u2011noise ratios, the waveform phase evolution can be used to test the PN eccentricity formalism, but this requires accurate eccentric waveform models and careful marginalization over spin effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What limits can be set on the mass and coupling strength of an ultralight vector boson from observing a spinning black hole with mass \u224820\u202fM\u2299 and spin \u03c7 \u22480.8, assuming the black hole formed only a few million years ago?<|assistant|>The superradiant growth timescale for a vector boson scales as \u03c4 \u2243 10\u00b3\u202fs\u202f(M/10\u202fM\u2299)\u2076\u202f(m/10\u207b\u00b9\u00b2\u202feV)\u207b\u2076 for optimal coupling. For a 20\u202fM\u2299 black hole with \u03c7 \u22480.8 and an age of \u224810\u2076\u202fyr, vector boson masses in the window m \u2243 10\u207b\u00b9\u00b2\u201310\u207b\u00b9\u00b9\u202feV would have time to grow a cloud and spin\u2011down the horizon below the observed value, thereby being excluded. Couplings stronger than gravitational (i.e., with a gauge charge larger than Newton\u2019s constant) would shorten the instability times, tightening these constraints further."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent do metallicity\u2011dependent stellar winds influence the retention of black\u2011hole merger remnants in nuclear star clusters, thereby affecting the probability of successive hierarchical mergers?<|assistant|>The agent does not know the answer to this question. The mechanisms through which metallicity\u2011dependent winds alter the pre\u2011merger masses of progenitor stars directly impact the final remnant mass and spin, which in turn influence the gravitational\u2011wave recoil kick. The distribution of kick velocities relative to the cluster escape velocity determines whether the remnant remains bound and can form a second\u2011generation binary. Current population synthesis models incorporate metallicity effects on stellar evolution, but the coupling to cluster dynamics, the detailed distribution of escape velocities in nuclear star clusters, and the efficiency of later dynamical captures are not fully quantified. Consequently, a comprehensive assessment of metallicity\u2019s role requires further theoretical work combining stellar evolution, binary population synthesis, and realistic N\u2011body simulations of cluster dynamics."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected contribution of primordial black hole mergers to the isotropic stochastic gravitational\u2011wave background in the 20\u2013200 Hz band?<|assistant|>Primordial black hole (PBH) binaries can in principle produce a stochastic background, but their merger rate, mass distribution, and spatial clustering remain highly uncertain. Current population\u2011inference methods based on LIGO-Virgo detections cannot constrain PBH parameters tightly; therefore, a robust prediction of their contribution to the GWB in the 20\u2013200\u202fHz band is not available yet. Further theoretical modeling and additional data from future observing runs are required to reduce these uncertainties."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the overlap\u2011reduction function for the LIGO Hanford\u2013Livingston baseline change if one of the detectors operates at a different orientation due to maintenance?<|assistant|>The overlap\u2011reduction function (ORF) depends on the relative geometry and orientation of the two interferometers. If a detector\u2019s orientation is altered, the ORF would change accordingly, affecting the sensitivity to different polarizations and sky locations. Calculating the new ORF requires precise knowledge of the rotated antenna patterns and baseline. This is a straightforward but non\u2011trivial exercise in detector geometry and is routinely performed when accounting for downtime or maintenance, but the exact updated ORF is not provided in this paper."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the current noise\u2011budget method reliably disentangle Schumann\u2011resonance magnetic noise from potential cosmological backgrounds at frequencies above 100\u202fHz?<|assistant|>The magnetic noise budget calculation assumes linear coupling between external magnetic fields and the strain channel, modeled via long\u2011term averaged coupling functions. While this approach is adequate for the 20\u201360\u202fHz band where Schumann resonances dominate, at frequencies above 100\u202fHz the magnetic coupling is much weaker and the ambient field spectrum is less well characterised. Consequently, the current method may not provide sufficient discrimination between weak magnetic artifacts and a cosmological background in the high\u2011frequency regime. Further dedicated magnetic field measurements and improved coupling models are needed."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What level of improvement in the binary black hole merger rate density at redshift z > 2 can be obtained by combining the updated O4a stochastic upper limits with the latest LIGO\u2013Virgo event catalog?<|assistant|>By jointly fitting the stochastic upper limits to the CBC merger\u2011rate model, we obtain tighter constraints on the redshift evolution parameters (\u03b1_z, \u03b2_z, z_p) for binary black holes. The O4a data allow a modest tightening of the allowed variance in these parameters, but the statistical leverage remains limited due to the current stochastic sensitivity. The expected improvement is anticipated to be on the order of 10\u201320\u202f% in the inferred rate density for z\u202f>\u202f2 compared to O3, but this remains an estimate until real Bayesian analyses are performed."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would the detection of gravitational\u2011wave polarizations beyond the tensor mode impact the constraints on alternative theories of gravity?<|assistant|>Detection of non\u2011tensor polarizations\u2014such as vector or scalar modes\u2014would be a direct indication of physics beyond general relativity, enabling us to rule out or constrain a broad class of modified gravity theories that predict such modes. However, the current paper does not report any such detection; the data are consistent with pure tensor modes, and upper limits set on scalar and vector amplitudes are two\u2011times stronger than previous runs but still leave substantial parameter space for alternative theories. A definitive conclusion requires a future detection of a polarization\u2011specific signal."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the angular power spectrum of the stochastic gravitational-wave background depend on frequency for different astrophysical source classes?<|assistant|>The angular power spectrum, usually characterized by \\(C_\\ell\\), shows distinct frequency scaling for different source populations. Compact binary coalescences (CBCs) dominate at higher frequencies (above 50\u202fHz) and their power spectrum tends to rise as \\(f^{2/3}\\) in the strain spectrum, which translates to a flatter \\(C_\\ell\\) at lower multipoles. Rotating neutron stars and magnetars contribute at lower frequencies (<\u202f50\u202fHz), with a steeper strain spectrum that leads to larger anisotropic power at higher \\(\\ell\\) values. Cosmological sources such as inflationary or cosmic\u2011string backgrounds, which are expected to be nearly scale\u2011invariant, produce an almost flat angular power spectrum across the full frequency band, making them difficult to distinguish from an isotropic component without additional sky localization."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which astrophysical populations are most likely to generate a detectable anisotropy in the gravitational\u2011wave background at frequencies below 100\u202fHz?<|assistant|>Below 100\u202fHz the most promising contributors to anisotropy are nearby populations with large spatial clustering. These include: 1) the population of millisecond pulsars in the Galactic plane, whose spatial distribution follows the stellar density and can create a dipole\u2011like enhancement, 2) the Scorpius\u202fX\u20111 accreting neutron\u2011star system, which may emit continuous waves, 3) compact binary coalescences inside the Virgo cluster, and 4) young neutron stars in supernova remnants such as SN\u202f1987A. Each of these sources has a distinct spectral shape that, combined with their sky positions, can leave a measurable imprint on the observable \\(C_\\ell\\) at sub\u2011fundamental frequencies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do correlated detector noises influence the cross\u2011correlation sensitivity for persistent gravitational\u2011wave signals?<|assistant|>Cross\u2011correlation methods rely on the assumption that instrumental noises in geographically separated detectors are uncorrelated. If there exist correlated noise sources\u2014such as global magnetic fields or seismic couplings\u2014the overlap\u2011reduction function that translates the true sky signal into the measured cross\u2011power can be contaminated. This contamination manifests as an excess variance in the estimator and biases the inferred strain amplitude upward or downward depending on the phase relationship of the correlated noise. Advanced techniques, such as null\u2011stream analyses or subtraction of known magnetic/seismic channels, can mitigate these effects, but residual correlations still set a lower bound on the achievable sensitivity for persistent, narrowband sources."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected level of anisotropy induced by the clustering of millisecond pulsars in the Galactic plane?<|assistant|>The present literature does not provide a precise quantitative estimate of the anisotropy caused by millisecond\u2011pulsar clustering. While models predict a modest dipole\u2011like enhancement of the gravitational\u2011wave power in the Galactic plane, the magnitude depends on the poorly known ellipticity distribution, distance uncertainties, and the unknown contribution from unresolved binaries. Consequently, the exact level of anisotropy remains an open question requiring further theoretical modeling and deeper continuous\u2011wave observations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What statistical techniques can reduce the bias from shot noise in spherical\u2011harmonic analyses of the gravitational\u2011wave background?<|assistant|>Shot noise arises from the discrete realization of astrophysical events and biases the auto\u2011\\(C_\\ell\\) estimator because it adds a white\u2011noise component to each multipole. A robust mitigation strategy employs a cross\u2011\\(C_\\ell\\) estimator: the cross\u2011power between independently cleaned maps\u2014constructed from separate data subsets\u2014cancels the shot\u2011noise bias because shot\u2011noise is uncorrelated between the subsets. Additionally, regularizing the Fisher matrix (e.g., via eigenvalue truncation or Tikhonov regularization) ensures numerical stability and suppresses sensitivity to poorly constrained higher\u2011\\(\\ell\\) modes that would otherwise amplify shot\u2011noise contributions. Combining these approaches yields unbiased estimates of the true anisotropic power spectrum."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the removal of narrowband spectral lines (e.g., calibration lines and mains harmonics) influence the detectability of continuous\u2010wave (CW) signals from spinning neutron stars in LIGO data?<|assistant|>Removing narrowband lines reduces the spectral density at the frequencies of interest, which directly improves the signal\u2013to\u2013noise ratio for CW searches. Empirical studies of the O4a data show that the 90\u2011percentile upper limits for known pulsars improved by up to 15\u202f% after line removal, with the most significant gains at the lowest detectable frequencies where the detector noise is otherwise dominated by violin\u2011mode and resonant\u2011mode lines."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main environmental and instrumental sources that produce non\u2011Gaussian glitches in LIGO strain data, and how does their occurrence rate change over a typical observing run?<|assistant|>Principal non\u2011Gaussian sources include seismic activity, anthropogenic vibrations (e.g., nearby trains, road traffic), microseism to 1\u202fHz, anthropogenic acoustic disturbances, electrical mains transients, and internal control\u2013system glitches. In O4a the glitch rate above an SNR of 5 in the 20\u2013500\u202fHz band was approximately 0.5\u202fevents per hour for LHO and 0.7\u202fevents per hour for LLO during periods of good seismology, rising to 5\u201310\u202fevents per hour during heavy daylight traffic or windy weather. The rate decreases during nighttime and when the detector\u2019s vertical pendulum isolation system is in its highest\u2011performance state, indicating a clear seasonal and diurnal dependence."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the different data\u2011quality flag categories (CAT1, CAT2, CAT3) used in compact\u2011binary searches affect the overall false\u2011alarm rate for high\u2011mass black\u2011hole coalescences?<|assistant|>CAT1 flags identify the most severe data\u2011quality problems and are strictly vetoed in CBC pipelines. Inclusion of CAT2 reduces the analysed livetime by an additional ~1\u20112\u202f% and removes time windows that would otherwise produce mis\u2011classified glitches with SNR\u202f>\u202f10, thereby lowering the false\u2011alarm probability from ~1\u202f\u00d7\u202f10\u207b\u2074\u202fyr\u207b\u00b9 to ~5\u202f\u00d7\u202f10\u207b\u2075\u202fyr\u207b\u00b9 for masses >\u202f50\u202fM\u2299. CAT3 flags, used only in targeted searches, have a negligible impact on the false\u2011alarm rate (<\u202f0.5\u202f%) but can be used to re\u2011rank background expectations when combined with the iDQ probability output."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the effect of photon\u2011calibrator injection frequency placement and amplitude on the shape of the calibration\u2011uncertainty envelope for LIGO strain data?<|assistant|>Photon\u2011calibrator injections are inserted at eight discrete frequencies spread logarithmically from 10\u202fHz to 5\u202fkHz. The resulting uncertainty envelope shows a flat median systematic error of ~3\u202f% in amplitude and ~1\u202fms in phase between 100\u202fHz and 1\u202fkHz. At frequencies below 30\u202fHz and above 3\u202fkHz the envelope grows due to interpolation extrapolation, reaching up to 10\u202f% amplitude uncertainty. The chosen frequencies allow continuous monitoring of the calibration transfer function while minimizing spectral overlap with expected GW signals, thus maintaining a conservative, yet tight, uncertainty bound across the nominal detection band."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the alternate strain release with more aggressive broadband noise subtraction provide a measurable advantage over the default strain in detecting sub\u2011threshold compact\u2011binary events?<|assistant|>The paper does not explicitly quantify the benefit of the alternate strain release for sub\u2011threshold event detection. While the alternate release includes additional broadband noise subtraction steps (e.g., GDS\u2011CALIB_STRAIN_CLEAN_AR), a direct comparison of recovery efficiency for events with signal\u2011to\u2011noise ratios between 4 and 6 would require a systematic injection study that is not reported. Therefore, at present we cannot say whether the alternate strain channel yields a statistically significant improvement in detecting sub\u2011threshold compact\u2011binary coalescences."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the effective inspiral spin distributions of binary black hole mergers detected in the first half of the fourth observing run compare to those from previous observing runs?<|assistant|>The effective inspiral spin (\u03c7_eff) of the binary black holes observed in O4a is largely centered near zero, indicating that most of the systems have spins either aligned and anti\u2011aligned with the orbital angular momentum or intrinsically small. However, a non\u2011negligible tail at positive \u03c7_eff values is evident, corresponding to mildly spinning systems that possess preferential spin alignment. This distribution is statistically consistent with the spin distribution measured in GWTC\u20113, where most events also cluster near zero but exhibit a broadened spread, showing no significant evolution in the overall spin behaviour between O3 and O4a."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there any clear evidence of tidal deformation signatures in the gravitational\u2011wave signals from the two NSBH candidates included in the catalog?<|assistant|>The available signal\u2011to\u2011noise ratios for the two neutron\u2011star\u2013black\u2011hole candidates, GW230518_125908 and GW230529_181500, are modest. The Bayesian inference analyses performed with tidal\u2011inclusive waveform models do not yield statistically significant measurements of the neutron\u2011star tidal deformability parameter (\u039b). Consequently, while the presence of a neutron star is inferred from the component masses, no robust constraints on the equation of state can be extracted from these events alone."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the typical sky localisation areas achieved with a two\u2011detector LIGO network for events in the O4a catalog?<|assistant|>Because only the two LIGO detectors were operational during O4a, typical 90\u2011percent credible sky areas for the catalog events span from ~100 deg\u00b2 for high\u2011quality, well\u2011localized, low\u2011mass binaries to several thousand square degrees for lower\u2011frequency and higher\u2011mass systems. The most localized event, GW230627_015337, achieved a sky area of ~110 deg\u00b2, while the least localized signal, GW230901_191248 (not listed here), had several thousand deg\u00b2. These localisation uncertainties are larger than most events from NGr3, where the inclusion of Virgo provided 2\u2011to\u20113\u2011fold reductions in area."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Do the mass\u2013ratio of binary black holes show a dependence on the total mass in the O4a sample?<|assistant|>An exploratory analysis of the O4a source\u2011frame masses indicates that the most massive systems (M \u2273 150\u202fM\u2299) tend to have slightly more unequal mass ratios (q \u2248 0.6), whereas the lower\u2011mass binaries (M \u2248 10\u201330\u202fM\u2299) display a broad distribution of mass ratios, including several that are almost equal. While this trend is present, the small sample size and measurement uncertainties prevent a definitive statement about a direct correlation; further data will be required to confirm whether the mass\u2011ratio distribution depends strongly on the total mass."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What constraints does the paper provide on the neutron\u2011star equation of state derived from the NSBH candidates GW230518_125908 and GW230529_181500?<|assistant|>The paper does not provide any constraints on the neutron\u2011star equation of state from the NSBH candidates. The tidal deformability parameters inferred from the Bayesian analyses are consistent with zero within large uncertainties, and no robust measurement of \u039b was obtained. Consequently, the paper does not offer constraints on the neutron\u2011star equation of state from these events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What astrophysical processes could allow black holes to form with masses inside the pair\u2011instability mass gap between roughly 60 and 130\u202fM\u2299?<|assistant|>Several channels have been proposed: (1) Hierarchical mergers of smaller black holes within dense stellar clusters can build up masses above the gap while keeping a high spin; (2) Failed supernovae or pulsational pair\u2011instability supernovae in rapidly rotating metal\u2011poor stars can leave behind black holes in the gap if the envelope is retained; (3) Binary stellar evolution pathways such as chemically homogeneous evolution can produce massive, tight binaries that avoid pair\u2011instability disruption; and (4) Gas\u2011rich environments (e.g., accretion in active galactic nucleus disks) may allow accretion\u2011driven mass growth that pushes a black hole into the gap. Each mechanism operates under different metallicity, spin, and environmental assumptions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can measurements of high spin values (>0.7) in merging black holes inform theories of black hole spin evolution?<|assistant|>High spins constrain the angular momentum budget of the progenitor systems. In isolated binary evolution, such spins would require efficient tidal spin\u2011up or prolonged accretion episodes, implying very short orbital separations and/or dense circumbinary disks. In dynamical environments, large spins suggest that the merging black holes were themselves products of previous mergers, as successive mergers naturally spin up the resulting remnant. Therefore, observing sustained high spins in multiple events points toward a population of black holes that has undergone repeated mergers or significant accretion."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What observational signatures would distinguish a gravitational\u2011wave source that formed through hierarchical mergers from one that formed directly from a massive stellar collapse?<|assistant|>Hierarchical mergers are expected to leave several imprints: (1) a broader distribution of spins, typically with larger magnitudes and higher effective precessing spin \u03c7p; (2) a bias toward higher total masses and mass ratios close to unity; (3) potential evidence of recoil kicks\u2014e.g., an uncharacteristically large kick velocity\u2014as inferred from the remnant\u2019s motion; (4) an elevated rate of spin\u2011aligned or mildly precessing systems within dense clusters; and (5) a correlation of events with known globular or nuclear cluster environments. Direct massive stellar collapse would more likely produce lower spins, a range of mass ratios, and no significant kick imprint."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the leading challenges in accurately modeling the signal morphology of very massive, highly spinning binary black hole mergers?<|assistant|>The primary challenges include: (1) limited coverage of numerical relativity simulations in the high\u2011spin, comparable\u2011mass regime, leading to waveform model extrapolation uncertainties; (2) inadequate calibration of precession dynamics in models beyond spin \u22480.8, which can bias mass and spin inference; (3) the influence of higher\u2011order multipoles that become more pronounced at high inclination, demanding more sophisticated amplitude corrections; and (4) potential systematic mismatches between waveform families, which introduce non\u2011negligible parameter biases even for signals with moderate signal\u2011to\u2011noise ratios."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>The paper does not fully address the possible existence of significant residuals after subtracting the best\u2011fit binary\u2011black\u2011hole waveform. What could be the implications of unmodeled residual power?<|assistant|>If residual power persists beyond what Gaussian noise predicts, it could indicate additional physical effects not captured by the binary\u2011black\u2011hole hypothesis, such as: (1) gravitational\u2011wave echoes from exotic compact objects or quantum gravity modifications; (2) environmental effects like dynamical friction in dense media; (3) strong\u2011field deviations from general relativity; or (4) unmodeled instrumental artifacts. Without a dedicated investigation of the residuals, it is not possible to determine whether they arise from astrophysical phenomena or from limitations in the waveform models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can incorporating KAGRA data in a future all\u2011sky search for long\u2011duration gravitational\u2011wave transients improve the overall sensitivity of the detector network compared to LIGO\u2011Hanford and LIGO\u2011Livingston alone?<|assistant|>Adding KAGRA would increase the effective baseline and improve sky\u2011coverage, leading to a modest increase in the signal\u2011to\u2011noise ratio for sources that lie between the LIGO sites. However, the exact gain depends on KAGRA\u2019s noise performance in the 10\u20132000\u202fHz band, its duty cycle, and the relative antenna patterns. Because KAGRA\u2019s first observing cycles had limited engineering runs in O4a, the paper did not include its data, so a quantitative assessment remains to be made with full\u2011science\u2011quality KAGRA data."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the principal difficulties in constructing accurate waveform models for eccentric compact binary coalescences (ECBCs) that emit long\u2011duration gravitational waves?<|assistant|>ECBCs produce highly non\u2011stationary signals with repeated bursts and pre\u2011merger modulations. The challenges include (1) accurately evolving the binary through thousands of orbits while retaining orbital eccentricity; (2) modeling tidal interactions and gravitational\u2011wave back\u2011reaction at high eccentricity; and (3) ensuring sufficient overlap with the detector noise curve over long timescales. Current semianalytic approximants provide only limited coverage in mass and eccentricity, so full numerical relativity simulations (which are computationally expensive) are required to generate accurate long\u2011duration templates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways does the XGBoost classifier enhance the detection pipeline\u2019s ability to distinguish true long\u2011duration gravitational\u2011wave transients from non\u2011astrophysical glitches?<|assistant|>XGBoost learns complex decision boundaries from a training set of background (glitch) data and injected signals. By weighting multiple features\u2014such as coherent SNR, spectral energy distribution, and clustering metrics\u2014it can suppress coincident but incoherent noise and amplify coherent, extended power excesses typical of astrophysical transients. Importantly, the classifier obviates hard cut\u2011offs on signal duration, allowing the pipeline to search across a much wider range of temporal morphologies while maintaining a controlled false\u2011alarm rate."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the ellipticity of a newly formed magnetar affect the strain amplitude and detectability of a long\u2011duration gravitational\u2011wave signal?<|assistant|>The strain amplitude scales roughly with the product \\(\\epsilon \\times f^{2}\\), where \\(\\epsilon\\) is the equatorial ellipticity and \\(f\\) the GW frequency. A larger ellipticity (e.g., \\(\\epsilon \\gtrsim 10^{-4}\\)) produces a stronger, more slowly decaying signal, improving detectability. Conversely, a low ellipticity or rapid magnetic field decay reduces the emitted power, pushing the signal below typical network thresholds. The paper models ellipticities between 0.005 and 0.08; extrapolating to extreme values would either boost or further limit detectability."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the implications of detecting a long\u2011duration gravitational\u2011wave transient for multi\u2011messenger astronomy, and why is this still an open question?<|assistant|>A confirmed long\u2011duration GW event would provide unique constraints on the post\u2011merger evolution of compact objects, potentially revealing sustained energy injection into electromagnetic counterparts (e.g., X\u2011ray plateaus, kilonovae). However, the exact relationship between GW signal characteristics (duration, frequency evolution) and observable electromagnetic signatures remains poorly understood due to uncertainties in magneto\u2011hydrodynamic processes, fallback accretion physics, and jet formation. Without a statistically significant sample and simultaneous electromagnetic observations, it is difficult to establish robust correlation models, leaving the field an active area for future research."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the current level of disagreement between early\u2011universe measurements (e.g., from the cosmic microwave background) and late\u2011universe measurements (e.g., from Type Ia supernovae) of the Hubble constant?<|assistant|>Measurements of the Hubble constant from the early universe, such as those obtained from the cosmic microwave background (CMB) with the \\u201cPlanck\\u201d cosmology mission, consistently give a value around 67\u201368 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. Conversely, late\u2011universe, or local, probes\u2014most notably the cosmic distance ladder calibrated with Cepheids and Type Ia supernovae (the so\u2011called SH0ES program)\u2014usually yield a Hubble constant closer to 73\u201374 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. The tension between these two determinations is roughly 5\u20136 sigma, indicating a statistically significant discrepancy that is not easily explained by simply expanding the measurement uncertainties."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can a detection of a compact binary merger by a laser\u2011interferometric gravitational\u2011wave detector act as a ``standard siren'' for cosmological distance measurements?<|assistant|>A compact binary merger emits a gravitational\u2011wave signal whose amplitude scales inversely with the luminosity distance to the source. The waveform model predicts this amplitude given a set of intrinsic parameters (component masses, spins, orbital orientation, etc.). By performing parameter estimation on the data, one obtains a posterior on the luminosity distance independent of any external distance ladder. If the source redshift is known\u2014either through an electromagnetic counterpart or a statistical inference\u2014this distance\u2013redshift pair can be used directly to probe the cosmological expansion history, making the system a standard siren analogous to the way a Type Ia supernova is a standard candle."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the ``spectral siren'' approach in gravitational\u2011wave cosmology, and what does it rely on?<|assistant|>The spectral siren approach exploits features\u2014such as peaks, gaps, or cut\u2011offs\u2014in the source\u2011frame mass distribution of merging compact binaries. Because the observed gravitational\u2011wave signal contains the masses redshifted by (1+z), a feature at a fixed intrinsic mass will appear at lower detector\u2011frame masses for higher\u2011redshift sources. By modeling the underlying mass spectrum and assuming a merger\u2011rate evolution with redshift, one can relate the observed distribution to the cosmic expansion. The method therefore relies on a statistically robust model of the intrinsic mass distribution and on a sufficient population of events to constrain the mass\u2011redshift degeneracy."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a modification of the propagation of gravitational waves affect the luminosity\u2011distance relation, and how can such modifications be parametrized?<|assistant|>In several modified gravity theories the amplitude of gravitational waves decays differently from the standard 1/DL behaviour of general relativity. This modifies the effective GW luminosity distance (DGW\\u202fl) relative to the usual electromagnetic luminosity distance (DEM\\u202fl). A common phenomenological parametrization is DGW\\u202fl\u00a0=\u00a0DEM\\u202fl\u00a0[\u039e0\u00a0+\u00a0(1\u00a0\u2013\u00a0\u039e0)(1+z)\u207b\u207f], where the parameter \u039e0 controls the overall amplitude of the deviation and n controls how rapidly the deviation becomes important with redshift. Such a parametrization captures many late\u2011time modified\u2011gravity scenarios and can be constrained by gravitational\u2011wave standard\u2011siren measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there observational evidence that the mass distribution of black holes in merging binaries changes with redshift?<|assistant|>I do not have a definitive answer to this question. While the data analysed in the paper allow for a statistical inference of the mass distribution at the redshifts probed by the observed events, the current evidence is not sufficient to confirm a redshift evolution of that distribution. Investigating the evolution would require more events spanning a broader redshift range and a modeling framework that explicitly allows the mass function to vary with redshift, which was not part of the present analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant mechanisms that can disrupt primordial black hole binaries in the early universe, and how do they influence the present-day merger rates?<|assistant|>Current theoretical models suggest that gravitational interactions with surrounding baryonic matter, primordial density fluctuations, and dynamical friction during the radiation-dominated era can alter the initial orbital parameters of primordial black hole (PBH) binaries. These processes can either harden binaries, making them merge sooner, or ionize them, preventing coalescence altogether. However, the precise efficiency and relative importance of each mechanism remain uncertain because they depend on poorly constrained details of the early universe\u2019s density field, the exact PBH mass function, and the evolution of the primordial plasma. Ongoing work aims to integrate detailed cosmological simulations with analytic estimates to better constrain these disruptive effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do eccentricity and higher-order post\u2011Newtonian corrections affect the detectability of ultra\u2011compact binary inspirals in ground\u2011based gravitational\u2011wave data?<|assistant|>Eccentric binaries emit gravitational radiation over a broader frequency spectrum, introducing higher harmonics and modifying the phase evolution. In semi\u2011coherent search methods that approximate the evolution with a leading\u2011order chirp, residual eccentricity can cause the signal to drift out of a given frequency bin over the coherent integration time, reducing sensitivity. Higher\u2011order post\u2011Newtonian terms refine the phase but typically contribute less for very low\u2011mass binaries, whose evolution is slow and dominated by the leading quadrupole term. Extending matched\u2011filter or Hough\u2011type pipelines to include eccentric templates or higher\u2011order PN waveforms is computationally expensive, and the trade\u2011off between improved sensitivity and additional search volume is still under investigation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can a population of planetary\u2011mass primordial black holes explain a significant fraction of dark matter without violating microlensing and gravitational\u2011wave constraints?<|assistant|>If the primordial black hole mass function contains a pronounced peak in the planetary\u2011mass range (\\(10^{-6} - 10^{-3}\\,M_\\odot\\)), it could, in principle, contribute to dark matter. Microlensing surveys place upper limits on the abundance of compact objects in this mass window, particularly through the non\u2011observation of short\u2011duration microlensing events. Gravitational\u2011wave searches for binary coalescences further constrain the merger rate, which must be low enough to avoid detection yet high enough to produce measurable rates. Reconciling these limits requires a finely tuned mass distribution and formation history. Current evidence suggests that any planetary\u2011mass PBH fraction of dark matter must be small, but definitive conclusions await more sensitive microlensing campaigns and continuous\u2011wave searches."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the impact of local dark\u2011matter density variations within the Milky Way on the expected merger rates of ultra\u2011compact binaries?<|assistant|>Merger rates of PBH binaries are proportional to the number density of PBHs, which in turn follows the underlying dark\u2011matter distribution. In regions near the Galactic center, the dark\u2011matter density is higher, potentially boosting the local merger rate by an order of magnitude compared to the solar neighborhood. Conversely, in the outer halo the density drops, leading to lower rates. These spatial variations introduce a non\u2011uniform sensitivity for detectors, as the distance reach depends on the local volume probed. Accurate modeling therefore requires incorporating realistic halo profiles (e.g., Navarro\u2011Frenk\u2011White, Einasto) and possible substructure such as dark\u2011matter clumps."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main challenges in extending the Generalized Frequency\u2011Hough method to capture signals from binaries with significant spin\u2011orbit coupling or highly asymmetric mass ratios?<|assistant|>The Generalized Frequency\u2011Hough (GFH) transform relies on approximating the time\u2011frequency track of a binary inspiral with a power\u2011law curve derived from the leading\u2011order chirp mass. Introducing significant spin\u2011orbit coupling or highly asymmetric mass ratios alters the phase evolution by adding terms that depend on individual spins, the mass ratio, and higher\u2011order PN corrections. These complications would require a multi\u2011dimensional mapping of additional parameters, drastically increasing the search space and computational cost. Moreover, the assumption that the signal remains monochromatic within a short coherent segment may break down because spin\u2011induced precession can modulate the frequency more rapidly than the coherent time allows. Consequently, while GFH is powerful for low\u2011spin, nearly equal\u2011mass waveforms, reliably capturing more complex systems would need either a different semi\u2011coherent strategy or the development of faster algorithms that can handle the enlarged template bank."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there evidence for a population of planetary\u2011mass primordial black holes that could influence the observed dark\u2011matter halo structure in dwarf galaxies?<|assistant|>The existence of planetary\u2011mass primordial black holes (PBHs) that contribute significantly to the dark\u2011matter budget is currently unconfirmed. While simulations suggest that such PBHs might form dense sub\u2011clusters that could alter the inner density profiles of dwarf galaxies, observational constraints from stellar kinematics, microlensing surveys, and gravitational\u2011wave non\u2011detections place tight upper limits on the PBH fraction in this mass range. Because the relevant mass range lies below the sensitivity threshold of most microlensing experiments and the gravitational\u2011wave band is limited by the long chirping times of ultra\u2011compact binaries, definitive evidence is lacking. Future surveys with higher cadence and improved continuous\u2011wave detectors may provide more stringent constraints, but at present the question remains unanswered."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the projected semi\u2011major axis (ap) of a neutron star in a binary system influence the detectability of continuous gravitational\u2011wave signals?<|assistant|>The projected semi\u2011major axis determines the amplitude of the Doppler modulation of the gravitational\u2011wave frequency. Larger ap values spread the signal power over a wider frequency range, increasing the required template resolution and making the search computationally more demanding. Consequently, the sensitivity depth typically decreases for larger ap values, and searches often limit ap to a modest range (e.g., 5\u201315\u202flight\u2011seconds) to keep the template bank tractable while still covering the most likely parameter space for known Galactic binaries."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What effect does the orbital period (P) of a binary system have on the duration and shape of the continuous\u2011wave frequency track in time\u2013frequency space?<|assistant|>The orbital period sets the timescale over which the neutron star\u2019s orbital motion modulates the signal frequency. Shorter periods produce rapid, high\u2011amplitude oscillations in the frequency track, whereas longer periods yield slower, smoother modulations. This directly affects the match\u2011filtering strategy: shorter periods require tighter sampling in the orbital phase dimension, while longer periods allow for coarser sampling but demand longer coherent integration times to achieve sufficient sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What typical noise spectral\u2011density limits do advanced interferometric detectors achieve in the 100\u2013350\u202fHz band for continuous\u2011wave searches?<|assistant|>During the early part of the fourth observing run, the combined H1 and L1 detectors reached an inverse\u2011square\u2011root power\u2011spectral\u2011density (PSD) of roughly \\(2\\times10^{-23}\\,\\mathrm{Hz}^{-1/2}\\) at 200\u202fHz, improving gradually toward 250\u2013300\u202fHz. This level of sensitivity dominates the attainable strain\u2011amplitude limit for continuous waves in that band, with best\u2011achieved depths (in inverse strain units) around 20\u201325\u202fHz\\(^{-1/2}\\)."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the maximum spin\u2011down rate that can be tolerated in all\u2011sky continuous\u2011wave searches without significant loss of sensitivity?<|assistant|>The search sensitivity declines if the intrinsic spin\u2011down (or spin\u2011up) exceeds the frequency resolution over the total observing time. The criterion is \\(|\\dot{f}_0| \\le 1/(T_{\\rm SFT}\\,T_{\\rm obs})\\), where \\(T_{\\rm SFT}\\) is the short\u2011Fourier\u2011transform length and \\(T_{\\rm obs}\\) is the campaign duration. For a 1024\u2011s SFT and a 237\u2011day run, this translates to \\(|\\dot{f}_0| \\lesssim 4\\times10^{-12}\\,\\mathrm{Hz\\,s^{-1}}\\). Spin\u2011down larger than this would shift the signal by more than one frequency bin, thus reducing coherence and sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which theoretical predictions constrain the maximum ellipticity of neutron stars that could be probed by all\u2011sky continuous\u2011wave searches in the 7\u201315 day orbital period range?<|assistant|>We currently do not have a definitive answer to this question. The paper focuses exclusively on the data analysis pipeline and sensitivity estimates and does not explore the astrophysical modeling of maximum sustainable ellipticity for neutron stars in binaries with periods between 7 and 15 days. Theoretical estimates vary from \\(\\sim10^{-6}\\) for conventional nuclear matter to \\(\\sim10^{-4}\\) for exotic matter, but translating these limits into observable strain amplitudes for the specific orbital parameter range would require detailed population synthesis and accretion\u2011torque modelling that is beyond the scope of the analysis presented here."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a small electric charge carried by a merging black hole affect the frequencies and damping times of its dominant quasinormal modes?<|assistant|>A non\u2011zero charge introduces a Reissner\u2013Nordstr\u00f6m or Kerr\u2013Newman structure. The mode spectrum shifts slightly: the fundamental \u2113=2, |m|=2 mode\u2019s real part increases while its damping time decreases compared to the uncharged Kerr case, although the magnitude of the shift is typically a few percent for realistic charge\u2011to\u2011mass ratios below 10\u207b\u2074. The precise dependence also involves the mode\u2019s overtone number and the black hole\u2019s spin."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the extraordinarily high signal\u2011to\u2011noise ratio of recent gravitational\u2011wave events be used to distinguish between General Relativity and alternative theories of gravity that modify the merger dynamics?<|assistant|>Yes. In such theories the waveform\u2019s phasing and amplitude evolution during the inspiral and merger are altered, leading to systematic biases in the recovered masses, spins, and ringdown frequencies. By performing parameter estimations within each alternative\u2011gravity parameterization and comparing the likelihoods against the GR prediction, one can place upper limits on the theory\u2011specific couplings (e.g., higher\u2011derivative terms or scalar\u2011tensor couplings) typically at the sub\u2011percent level for the most massive, loud events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Could the detection of multiple quasinormal\u2011mode overtones provide a direct measurement of a non\u2011zero graviton mass?<|assistant|>In principle, a massive graviton would modify the dispersion relation, causing the quasinormal\u2011mode frequencies to deviate from their General\u2011Relativity predictions. However, the current sensitivity to graviton mass from ringdown data is limited; even with multiple overtones, constraints are weaker than those from inspiral phase dispersion and are usually in the tens of kiloparsecs squared per gigaparsec. Future detectors with higher bandwidth and longer overtones might improve these bounds."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role could black hole superradiance play in testing the area law during a binary merger?<|assistant|>Superradiant instabilities can extract rotational energy from a black hole and excite bound states of ultra\u2011light bosons. If such an instability is triggered during the merger, part of the system\u2019s angular momentum would be stored in the cloud rather than radiated in gravitational waves, effectively reducing the final horizon area compared to the GR prediction. A measurable deficit in the area would signal superradiant growth, though detecting this effect would require both high signal\u2011to\u2011noise and a theoretical model that predicts the cloud\u2019s emission timescale."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the minimal deviation from the Kerr metric that is still consistent with the most recent high\u2011SNR gravitational\u2011wave observations, yet would imply new physics beyond General Relativity?<|assistant|>We currently do not possess a definitive quantitative answer. Determining the smallest allowable deviation requires a systematic exploration of the full parameter space of alternative metric theories (e.g., parametrized post\u2011Newtonian extensions, dynamical Chern\u2011Simons gravity, or Einstein\u2011dilaton\u2011Gauss\u2011Bonnet models) in conjunction with the entire evolution of the binary\u2014including inspiral, merger, and ringdown\u2014using high\u2011accuracy numerical relativity simulations. Such comprehensive studies are still underway; the data at hand are consistent with the pure Kerr geometry within a few percent, but they do not definitively rule out all possible small deviations that could arise from beyond\u2011GR physics."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What determines the expected lifetime of an ultralight vector boson cloud around a black hole and how does it scale with the boson mass and the black hole spin?<|assistant|>The lifetime of a vector boson cloud is governed by two competing processes: the superradiant growth phase, which extracts rotational energy from the black hole, and the gravitational\u2011wave (GW) depletion phase, in which the cloud radiates energy. The superradiant growth time \\( \\tau_{\\rm grow} \\) scales approximately as\\n\\\\[ \\\\tau_{\\rm grow} \\\\sim \\\\frac{1}{\\mu M}\\\\,\\\\frac{1}{(M\\\\mu)^{4\\\\ell+5}}\\\\left(\\\\frac{1}{\\\\chi-\\\\chi_{\\rm crit}}\\\\right), \\\\]\\nwhere \\( M \\) is the black hole mass, \\( \\mu = m_{V}\\\\,c^{2}/\\\\hbar \\) is the boson Compton frequency, \\( \\chi \\) is the dimensionless spin, \\( \\chi_{\\rm crit}=2/(m+\\\\ell+1)\\\\) is the critical spin where the instability shuts off, and \\( \\ell \\) is the orbital angular\u2011momentum quantum number (for the fastest growing vector modes typically \\( \\ell=0 \\)). The GW depletion time \\( \\tau_{\\rm GW} \\) scales roughly as\\n\\\\[ \\\\tau_{\\rm GW} \\\\sim \\\\frac{1}{\\\\mu M}\\\\,(M\\\\mu)^{(-4\\\\ell-5)}\\\\,(\\\\chi-\\\\chi_{\\rm crit})^{-2}, \\\\]\\nimplying that smaller boson masses (longer wavelengths) and higher black\u2011hole spins both lengthen the cloud\u2019s lifetime. The two timescales are comparable near the optimal boson mass that maximizes the instability rate, leading to a total signal duration of order days to months for stellar\u2011mass black holes in the LIGO band, and up to years for lighter bosons or more massive black holes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What search strategies can improve the detection prospects of continuous gravitational waves from vector\u2011boson clouds around distant merger remnants that are several gigaparsecs away?<|assistant|>To enhance sensitivity for far\u2011away sources one can (i) use longer coherent segments \\(T_{\\rm coh}\\) in semicoherent pipelines, trading off computational cost for better phase\u2011tracking; (ii) optimise sky\u2011position grids for large\u2011error regions by exploiting the angular\u2011resolution of the detector network, for example by hierarchical sky\u2011grid refinement; (iii) employ matched\u2011filter techniques that incorporate the predicted secular frequency drift \\(\\\\dot f(t)\\) of the vector\u2011boson signal, thus mitigating loss due to mismatch; (iv) leverage multi\u2011band analysis to separate neighbouring spectral lines; and (v) combine data from both LIGO and future detectors such as Virgo and KAGRA to increase sky\u2011coverage and reduce the false\u2011alarm rate. Each of these techniques is designed to recover weak, slow\u2011evolving signals that fall near the detector\u2019s sensitivity threshold, especially when the source distance strongly suppresses the strain amplitude."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the current observational limits on the mass of ultralight vector bosons derived from black\u2011hole spin measurements across the galaxy?<|assistant|>Black\u2011hole spin measurements, particularly for rapidly rotating stellar\u2011mass black holes, place stringent limits on the mass of ultralight vector particles. If a boson of mass \\(m_{V}\\) existed within the range \\(10^{-14}\\,{\\rm eV} \\lesssim m_{V} \\lesssim 10^{-11}\\,{\\rm eV}\\), the superradiant instability would have spun down such black holes over their ages, yielding much lower observed spins than measured. Current observations exclude boson masses between roughly \\(0.5\\times10^{-13}\\)\u202feV and \\(1.2\\times10^{-13}\\)\u202feV for a typical 10\u202fM\\(_\\odot\\) black hole, under standard assumptions about accretion history and measurement uncertainties. For supermassive black holes the excluded mass window is narrower (e.g., \\(10^{-18}\\)\u2013\\(10^{-15}\\)\u202feV), but systematic errors in spin inference reduce the confidence of those limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does an accretion disk around a black hole influence the superradiant growth of a vector\u2011boson cloud and the resulting gravitational\u2011wave signal?<|assistant|>An accretion disk introduces additional torques that compete with the superradiant extraction of rotational energy. Material falling into the black hole can carry away angular momentum, thereby mitigating the spin\u2011down induced by the cloud. Furthermore, the disk\u2019s material can induce density\u2011wave torques and electromagnetic interactions that alter the effective potential felt by the boson field, potentially suppressing the growth rate or altering the mode structure. As a result, the GW amplitude may be reduced or the frequency evolution may deviate from the pure vacuum prediction. Accretion also supplies a continuous energy source that can replenish the black\u2011hole spin, potentially leading to a quasi\u2011steady state where growth and depletion balance, producing a long\u2011lived but comparatively weaker signal than in vacuum."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Has the analysis of the first part of the fourth LIGO\u2013Virgo\u2013KAGRA observing run revealed any definitive evidence for ultralight vector boson clouds around the merger remnants GW230814 and GW231123?<|assistant|>I do not have a definitive answer regarding the presence of ultralight vector\u2011boson clouds around the specific merger remnants GW230814 and GW231123. The paper performed directed searches using two semicoherent methods (a hidden Markov model tracker and a Band\u2011Sampled\u2011Data pipeline) on the LIGO data from that period, focusing on the predicted signal parameter space for those remnants. While the paper reported setting exclusion limits on certain boson mass ranges, it did not observe any statistically significant candidates that could be attributed to vector\u2011boson clouds. As such, no evidence of such clouds was reported for those sources. However, this non\u2011detection does not constitute a firm absence; it could be due to limited signal\u2011to\u2011noise, data gaps, or the actual boson parameters lying outside the searched range. A more sensitive future observing run or improved analysis techniques would be required to confirm or refute the existence of such clouds around these remnants."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main geotechnical challenges when tunnelling through molasse rock for a large circular collider tunnel, and what typical mitigation strategies are used?<|assistant|>Molasse is a heterogeneous, silty\u2013sandstone\u2013marl sequence that can be weak and contain fractures, fault gouge, or variable strength zones. The key challenges are:\\n1. **Variable strength and deformation:** the mix of finer silts and coarser sandstones can produce uneven tunnel support needs, requiring careful mapping and design of ground support.\\n2. **Hydraulic behaviour:** water\u2011bearing layers and potential high pore\u2011pressure zones can lead to water ingress and ground pressure on the tunnel walls.\\n3. **Large\u2011scale deformation:** the high overburden (~200\u202fm) generates substantial in\u2011situ stresses that can induce settlement or ground movement.\\nTypical mitigations include:\\n- Pre\u2011tunnelling geotechnical surveys and drilling to determine rock quality and build a 3\u2013D model.\\n- Use of a TBM with a driven\u2011segmental lining (either twin\u2011shield or single\u2011shield) to provide immediate support.\\n- Ground conditioning (rock grouting or jet\u2011cutting) where high water pressures or soft strata are encountered.\\n- Installation of rock bolts, cable bolts and shotcrete as primary and secondary support systems.\\n- Monitoring of tunnel pressure and deformation during construction with temporary instrumentation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>When locating surface access shafts for a collider ring, what trade\u2011offs must be balanced to reduce environmental impact?<|assistant|>Surface shafts are the only points where equipment, personnel and machinery can reach the underground. The main trade\u2011offs are:\\n1. **Geological suitability:** shafts should be situated where the sub\u2011surface consists of solid molasse rather than water\u2011bearing moraines or limestone.\\n2. **Proximity to existing infrastructure:** placing shafts near existing roadways or utilities can lessen the need for new construction but may increase traffic or noise.\\n3. **Land use and heritage:** shafts should avoid protected natural areas, cultural heritage sites, or densely populated zones to minimise visual and acoustic footprint.\\n4. **Future expansion:** a shaft placed too close to a collider sector may limit the ability to add new tunnels or caverns later, while a shaft placed too far from a detector may increase access costs.\\n5. **Operational safety:** shafts need to be long enough to provide a safe escape route and support ventilation and fire\u2011fighting infrastructure.\\nBalancing these factors usually involves an iterative optimisation that varies shaft locations within a tolerance zone, evaluates alternative tunnel alignments, and selects the configuration that satisfies all statutory and engineering constraints."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the \u2018avoid\u2013reduce\u2013compensate\u2019 optimisation methodology shape civil\u2011engineering decisions for large particle\u2011accelerator projects?<|assistant|>The methodology is an iterative, multi\u2011criteria decision framework:\\n* **Avoid** \u2013 Wherever possible, the design avoids geologically or environmentally problematic zones (e.g., high\u2011pressure limestone, protected habitats, urban land). This might involve slightly longer tunnel routes or repositioning of surface facilities.\\n* **Reduce** \u2013 Costs, construction time, resource consumption and environmental disturbance are reduced by, for example, using a single\u2011shield TBM instead of a double\u2011shield machine, blending skip\u2011construction for multiple tunnels, or building larger caverns only where they are truly needed.\\n* **Compensate** \u2013 For impacts that cannot be avoided or sufficiently reduced (e.g., a necessary surface building on a protected site), a compensation measure is planned, such as habitat restoration, noise barriers, or payments to local stakeholders.\\nThroughout the design, each alternative is evaluated against technical feasibility, risk, cost, environmental and socio\u2011economic indicators, and the option that scores best across all criteria is selected. The approach ensures that risks are identified early and that environmental and social responsibilities are integrated into the engineering design."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the principal differences in material extraction and management when using Tunnel Boring Machines versus conventional drill\u2011and\u2011blast for deep underground construction of collider tunnels?<|assistant|>The main distinctions are:\\n1. **Excavation rate & support installation:** A TBM cuts the rock and installs a precast lining continuously, allowing a constant advance of ~10\u201315\u202fm/day in suitable rock. Drill\u2011and\u2011blast relies on explosive fragmentation and requires manual loading, drilling, detonation and removal of spoil, generally slower (usually 2\u20135\u202fm/day) but flexible on hard or fractured rock.\\n2. **Spoil characteristics:** TBM spoils are clean, well sorted, and often culvert\u2011grade because they are cut by a cutting wheel. Blast spoils contain mixed rock, dust, and deeper rock fragments. This affects the material's suitability for reuse.\\n3. **Ground stability:** TBM reduces ground disturbance at the face and can incorporate flotation or slurry systems to control pressure. Drill\u2011and\u2011blast creates more micro\u2011fracture propagation and can raise water ingress.\\n4. **Environmental impact:** TBM tends to produce less vibration, dust, and noise, resulting in lower disturbance to surrounding communities. Blast is more disruptive and requires additional measures (e.g., water\u2011buckets, dust\u2011screens).\\n5. **Material handling & logistics:** TBM can deliver spoil directly to the shaft and/or circulates slurry for hydraulically powered conveyors. For blast, separate lift or conveyor systems are needed to haul the broken rock and segregate it.\\nDuring large collider projects, the decision between the two methods is guided by geology, depth, cost, schedule, and environmental concerns."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the long\u2011term structural behaviour and maintenance implications for large experimental caverns constructed in high water\u2011pressure limestone regions?<|assistant|>The research paper does not investigate the long\u2011term structural integrity of such caverns, nor does it provide detailed maintenance strategies for high\u2011pressure limestone environments. Consequently, I do not have enough information to answer this question. Further studies, including in\u2011situ monitoring, finite\u2011element modelling, and long\u2011term corrosion analyses, would be required to establish reliable predictions for cavern safety and maintenance schedules in limestone."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the primary scientific motivations for constructing a 100\u202fTeV proton\u2011proton collider in the future circular collider tunnel?<|assistant|>The 100\u202fTeV hadron collider is motivated by the desire to extend the energy frontier far beyond the current 14\u202fTeV LHC. At this scale the machine would provide unprecedented sensitivity to high\u2011mass processes such as double\u2011Higgs production, exotic resonance searches, and direct production of electroweak or coloured new states (e.g., supersymmetric particles, vector\u2011like quarks, or dark\u2011sector mediators). In addition, the large luminosity (~10\u202fab\u207b\u00b9) would enable precision measurements of the top\u2011quark and Higgs\u2011boson properties, probe the structure of electroweak symmetry breaking, and access mass scales up to tens of TeV, thereby opening a window to physics beyond the Standard Model."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What detector technologies are most promising for achieving a sub\u2011millimetre vertex resolution at the FCC\u2011ee?<|assistant|>To reach sub\u2011mm vertex resolution the FCC\u2011ee requires ultra\u2011thin, high\u2011granularity pixel detectors placed very close to the interaction point. Candidate technologies include state\u2011of\u2011the\u2011art monolithic active pixel sensors (MAPS), hybrid pixel detectors with advanced bump\u2011bonding, and 3D integrated electronics. These sensors offer pixel pitch below 25\u202f\u00b5m, fast timing (~10\u201320\u202fps) for pile\u2011up mitigation, and a material budget of only a few per mille of a radiation length. Coupled with a low\u2011mass, high\u2011field solenoid (\u22642\u202fT during the electron\u2011positron stage) and a sophisticated beam pipe design, such detectors can achieve impact\u2011parameter resolutions in the tens of micrometres needed for efficient b\u2011 and c\u2011quark tagging and precise lifetime measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the FCC\u2011ee improve the measurement of the Higgs self\u2011coupling compared to the HL\u2011LHC?<|assistant|>While the HL\u2011LHC can only access the Higgs self\u2011coupling via double\u2011Higgs production at a few\u2011percent precision, the FCC\u2011ee provides an indirect, model\u2011independent determination through high\u2011precision measurements of the ZH production cross\u2011section at 240\u202fGeV and the single\u2011Higgs branching fractions at 250\u2013360\u202fGeV. The precise knowledge of the ZH cross\u2011section, combined with the per\u2011mille accuracy on the Z\u2013H coupling, constrains the Higgs self\u2011coupling at the 5%\u201310% level without the need for rare double\u2011Higgs events. When FCC\u2011ee data are combined with FCC\u2011hh measurements of the Higgs\u2011pair production cross\u2011section, the self\u2011coupling precision can be pushed below 5%, a sensitivity far beyond what can be achieved at HL\u2011LHC alone."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What strategies are employed at the machine\u2013detector interface to control synchrotron\u2011radiation backgrounds in the FCC\u2011ee electron\u2011positron stage?<|assistant|>Synchrotron\u2011radiation (SR) backgrounds are mitigated through several design choices. First, the accelerator optics place the RF cavities and bending magnets well outside the detector acceptance, creating a low\u2011SR region around the interaction point. Second, the beam pipe is made of low\u2011Z, high\u2011thermal\u2011conductivity material (e.g., aluminium or titanium) with a narrow aperture (\u224810\u202fmm radius) to limit SR photons. Third, the detector solenoid field is limited to \u22642\u202fT during the electron\u2011positron stage to reduce vertical emittance growth and prevent SR\u2011induced beam blow\u2011up. Fourth, a dedicated SR absorber and a careful arrangement of quadrupole magnets inside a 100\u202fmrad dead\u2011cone shield the inner detector layers. Finally, active beam\u2011induced background monitoring, using fast calorimeters and tracking monitors placed close to the beam pipe, provides real\u2011time feedback to maintain background levels below the few keV per event threshold required for high\u2011precision measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the estimated total construction cost for the FCC\u2011hh and how is it justified in terms of scientific return?<|assistant|>I\u2019m sorry, I do not have that information. The feasibility study and the report you provided focus on the physics potential, detector concepts, and technical feasibility but do not include detailed cost estimates. Comprehensive cost modelling, including civil engineering, magnet fabrication, and detector construction, is part of a separate industrial investment study that is beyond the scope of the paper and the knowledge domain of this model."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can sub\u2011threshold gamma\u2011ray burst detection algorithms increase the sensitivity to short GRB counterparts of gravitational\u2011wave events?<|assistant|>Sub\u2011threshold searches\u2014such as blind scans of continuous time\u2011tagged data and coherent likelihood analyses across all detectors\u2014extend the trigger threshold by exploiting the full detector network and a larger time window. By combining data from multiple instruments and applying spectral templates that match short GRB emission, these algorithms suppress statistical noise, thereby lowering the effective detection threshold and increasing the probability of identifying weak, temporally aligned gamma\u2011ray transients."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What observational strategies can improve the joint sky coverage of Fermi\u2011GBM and Swift\u2011BAT when following up gravitational\u2011wave triggers?<|assistant|>Coordinated, real\u2011time alerts that share GW sky maps with both spacecraft, combined with complementary pointing strategies (GBM\u2019s all\u2011sky view and BAT\u2019s coded mask imaging) maximize overlap. Additionally, rapid retrieval of burst event data (e.g., via the GUANO system) and the use of ground\u2011based rate monitoring help capture transients that occur during detector slewing or South Atlantic Anomaly passages, thereby reducing blind spots in the combined coverage."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the time delay between the gravitational\u2011wave merger and the onset of prompt gamma\u2011ray emission constrain short\u2011GRB jet\u2011launching models?<|assistant|>The delay\u2014often ranging from milliseconds to a few seconds\u2014reflects the physics of accretion disk formation, disk wind development, and the acceleration of relativistic jets. Shorter delays are expected when dense ejecta promptly feed the central engine, while longer delays may indicate slower neutrino\u2011driven outflows or delayed black\u2011hole formation. By measuring or limiting these delays, one can test whether observed events favor internal\u2011shock, magnetically driven, or photospheric emission models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the exact mechanism responsible for gamma\u2011ray emission from binary black hole mergers, and can current models be ruled out by existing gamma\u2011ray upper limits?<|assistant|>The mechanism remains unknown; several speculative scenarios exist\u2014including neutrino annihilation in a transient accretion disk, electromagnetic extraction of spin energy from a charged black hole, Blandford\u2013Znajek jet launching, and prompt GW\u2011 to gamma\u2011ray energy conversion. Existing upper limits constrain the luminosity of such emission for a few nearby events, but due to uncertainties in jet geometry, viewing angles, and the physics of matter in vacuum environments, we cannot definitively rule out any model yet."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role do instrument response simulations, such as detector response matrices, play in setting flux upper limits for gamma\u2011ray detectors during counterpart searches?<|assistant|>Response simulations translate observed count rates into incident photon fluxes by accounting for detector efficiencies, geometric coding, and atmospheric scattering. Accurate detector response matrices (DRMs) allow the conversion of non\u2011detections into flux upper limits that are sensitive to source position and spectrum. They also enable the estimation of systematic uncertainties and the derivation of sky\u2011dependent upper\u2011limit maps essential for constraining emission models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can the precise measurements of the CKM angles \u03c61, \u03c62 and \u03c63 obtained by the B\u2013factory experiments be used to test minimal flavour\u2011violation (MFV) scenarios in supersymmetric models?<|assistant|>The B\u2013factory measurements of sin(2\u03c61) (\u03b2), \u03b1 (\u03c62) and \u03b3 (\u03c63) constrain the unitarity triangle side\u2011lengths and internal angles. In MFV models all flavour changing amplitudes are governed by the CKM matrix, so any deviation from the SM predictions in B\u2013meson mixing or CP\u2011violating observables would indicate new particles or couplings that are not aligned with the CKM structure. By combining the world averages of the three angles with independent determinations of |Vub| and |Vcb|, one can perform global fits to the CKM parameters and extract bounds on the scale of new physics. In the MFV hypothesis, the current B\u2013factory data already pushes the scale of flavour\u2011changing supersymmetric particles to several TeV, leaving only small allowed regions for MFV\u2011compatible supersymmetric spectra. Deviations from this pattern would signal non\u2011MFV contributions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What potential improvements in time\u2011dependent CP\u2011violation studies are expected with the proposed Super B Factories compared to the existing B\u2013factory experiments?<|assistant|>Super B Factories aim to achieve instantaneous luminosities around 10^36\u202fcm\u207b\u00b2\u202fs\u207b\u00b9, roughly 50 times higher than the original B\u2013factory peak luminosities. This translates into about 50\u202fab\u207b\u00b9 of data, enabling several key improvements: (1) significantly reduced statistical uncertainties on sin\u202f2\u03b2, \u03b1 and \u03b3; (2) enhanced sensitivity to rare CP\u2011violating decay modes such as B\u202f\u2192\u202f\u03c0\u2070\u03c0\u2070 or B_s\u202f\u2192\u202f\u03d5\u03b3; (3) the ability to perform time\u2011dependent Dalitz\u2011plot analyses with much larger samples, improving the constraint on the angle \u03b3 from B\u202f\u2192\u202fD(K_S\u03c0\u207a\u03c0\u207b)K decays; (4) higher precision in measuring direct CP asymmetries in charmless B decays, potentially revealing interference from physics beyond the SM. The larger datasets would also help disentangle hadronic uncertainties by allowing more precise studies of strong\u2011phase differences through quantum\u2011correlated measurements at the \u03c8(3770)."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do Dalitz\u2011plot analyses of multi\u2011body B decays (e.g., B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070) contribute to a more precise determination of the CKM phase \u03b3 compared to two\u2011body methods?<|assistant|>Multi\u2011body decays such as B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070 contain resonant substructures (e.g., K*\u202f\u03c0, \u03c1\u202fK) that interfere across the Dalitz\u2011plot. By performing a full amplitude analysis, one can extract relative strong phases and magnitudes for each intermediate resonance. When the decay includes both b\u202f\u2192\u202fc and b\u202f\u2192\u202fu transition amplitudes that carry different weak phases, the interference across the Dalitz plot provides direct access to \u03b3 without the need to tag the B flavour. This method, often called the GGSZ (Dalitz) approach, benefits from the kinematic richness of three\u2011body final states, yielding reduced ambiguities and a more statistical power per event compared to two\u2011body GLW or ADS methods. Additionally, since the strong phases are obtained in\u2011situ, hadronic uncertainties are significantly constrained."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main experimental challenges in measuring the branching fraction of the purely leptonic decay B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd at a Super B Factory, and how can they be addressed?<|assistant|>The B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd decay has a large missing energy because the \u03c4 lepton subsequently decays to one or more neutrinos, leading to a signature with one or more hadrons or leptons plus large missing momentum. Key challenges include: (1) efficient \u03c4\u2011identification across all decay modes while controlling large backgrounds from generic B\u202f\u2192\u202f\u2113\u03bd\u2113X and continuum events; (2) precise reconstruction of the missing momentum vector, requiring hermetic calorimetry and excellent tracking; (3) suppression of two\u2011photon and beam\u2011background events that mimic missing energy; (4) control of hadronic B decays with similar topologies (e.g., B\u202f\u2192\u202f\u03c0\u2070\u03c0\u207b) which can be mis\u2011identified as \u03c4\u2011leptons. Addressing these issues relies on: high\u2011resolution vertex detectors to separate \u03c4\u2011decay vertices; a particle\u2011identification system capable of distinguishing pions, electrons and muons up to high momenta; a highly granular calorimeter for accurate neutral\u2011cluster reconstruction; and sophisticated multivariate analysis techniques that exploit event\u2011shape variables to suppress continuum. With the anticipated large dataset, statistical uncertainties will be driven below 1\u202f%, while systematic uncertainties will be controlled through careful calibration and data\u2011driven background studies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Did the B Factories observe any evidence for lepton\u2011flavour\u2011violating (LFV) tau decays such as \u03c4\u202f\u2192\u202f\u03bc\u03b3 or \u03c4\u202f\u2192\u202f3\u00b5?<|assistant|>The information relevant to lepton\u2011flavour\u2011violating tau decays is not covered in the physics discussion of the B Factories presented in this book. The analyses described focus on B\u2011meson decays, CP violation, charm physics, and related topics. While the B\u2011factory experiments did perform searches for LFV tau decays, the results are presented in separate dedicated studies that are not summarized here. Consequently, based solely on the content of this paper, we do not have the answer. A comprehensive answer would require consulting the specific B\u2011factory publications on LFV tau searches, which involve separate datasets, selection criteria, and background estimations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main systematic uncertainties that affect the reconstruction of supernova neutrino directions in liquid\u2011argon time\u2011projection chambers, and how can improving the statistical separation of interaction channels help mitigate these uncertainties?<|assistant|>Liquid\u2011argon TPCs measure the Cherenkov\u2011like ionization track of the final\u2011state electron from a neutrino interaction. The two dominant systematic uncertainties are: (1) the intrinsic kinematic smearing between the neutrino direction and the outgoing lepton direction, which depends on the neutrino energy and the type of nuclear transition (Fermi, Gamow\u2013Teller or forbidden), and (2) the detector\u2011related angular resolution, governed by the spatial hit density, wire\u2011plane geometry and charge\u2011drift attenuation. The second uncertainty is strongly linked to the head\u2013tail ambiguity that arises because the detector cannot distinguish the start and end of a track by timing alone. By statistically separating the elastic neutrino\u2013electron scattering (eES) events, which provide a strong forward peak, from the charged\u2011current \u03bde absorption events, which are largely isotropic, one can weight the more directional eES events more heavily in the pointing likelihood. Improved classification\u2014whether through cut\u2011based variables, boosted decision trees or neural networks\u2014reduces the contamination of the directional sample and therefore lowers the effective angular uncertainty."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Could the inclusion of coherent elastic neutrino\u2013nucleus scattering (CEvNS) as a detectable channel in DUNE appreciably enhance the precision of supernova neutrino pointing?<|assistant|>Coherent elastic scattering on argon nuclei has a very large cross section and its final\u2011state electron\u2011recoil energy is purely longitudinal, carrying essentially no directional information about the incoming neutrino. However, the CEvNS rate is substantial for supernova neutrinos (\u223c105 events in a 40\u2011kton detector) and its isotropic nature can be used to constrain the overall neutrino flux normalization and energy spectrum. By simultaneously fitting the CEvNS spectrum together with the eES and \u03bde\u2011cc spectra in a joint likelihood, one can reduce the degeneracy between flux parameters and the effective \u201cangular smearing\u201d of the eES sample, indirectly improving the directional information. Practically, DUNE would need a very low energy threshold and precise neutron\u2011induced background rejection to make CEvNS usable, but if achieved, the additional statistical power and flux constraint could sharpen the supernova pointing by a few tenths of a degree."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might neutrino mass ordering influence the observable energy spectra of supernova neutrinos at a detector in Southern Africa, and what are the implications for directional reconstruction?<|assistant|>In the conventional MSW framework, the normal ordering (NO) leads to a larger survival probability for electron neutrinos below \u223c10\u00a0MeV, while the inverted ordering (IO) favors conversion to non\u2011electron flavors in that energy range. Consequently, the measured \u03bde spectrum at a far detector will differ between the two orderings, affecting the relative weight of the highly directional eES events versus the isotropic \u03bde\u2013cc events. A detector in Southern Africa, such as the proposed South African liquid\u2011argon experiment, would observe a softer eES spectrum for IO, reducing the overall pointing precision by increasing the fraction of events with poor angular correlation. Conversely, under NO the larger high\u2011energy tail in the eES sample would improve the pointing. Therefore, the mass ordering has a non\u2011negligible, though modest, impact on directional accuracy that should be folded into a full systematic error budget."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What machine\u2011learning strategies can be deployed in real\u2011time supernova burst alert pipelines to maintain low latency while still preserving high directional accuracy?<|assistant|>Real\u2011time pipelines must reduce raw waveforms to reconstructed tracks within milliseconds. Two complementary ML strategies are: (1) a lightweight convolutional neural network (CNN) operating directly on wire\u2011plane images to perform fast track\u2011finding and head\u2011tail assignment, using training sets generated from GEANT4 + LArSoft simulations; (2) a graph\u2011neural\u2011network (GNN) that ingests the list of hit vertices and their temporal ordering to compute probabilistic direction vectors and interaction\u2013type probabilities on a GPU. By chaining these models\u2014first a quick CNN for detection, then a GNN for precise direction estimation\u2014the pipeline can achieve sub\u2011second latency while keeping the pointing likelihood built from a fully calibrated response matrix. The key is to calibrate the ML inference output against a benchmark reconstruction and to propagate the resulting systematic uncertainties into the maximum\u2011likelihood sky map."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the presence of forbidden nuclear transitions in the \u03bde + \u202f\u2074\u2070Ar charged\u2011current absorption modify the angular distribution of emitted electrons enough to affect DUNE\u2019s supernova pointing performance?<|assistant|>The paper does not provide a definitive answer because the cross\u2011section and angular\u2011momentum structure of forbidden transitions in supernova\u2011relevant energy ranges are only sparsely known from theory and there is no dedicated experimental data on \u2074\u2070Ar charged\u2011current scattering below ~30\u00a0MeV. If forbidden transitions contribute a substantial backward\u2011peaked component, the overall \u03bde\u2011cc electron angular distribution would deviate from the near\u2011isotropic shape assumed in the study, potentially introducing a small directional bias. Because the current pointing algorithm relies heavily on the clean eES sample and assumes the \u03bde\u2011cc events are essentially non\u2011informative, any significant anisotropy could change the weighting in the likelihood and modestly degrade the best achievable resolution. To resolve this, one would need dedicated low\u2011energy neutrino\u2011argon scattering measurements or improved ab initio nuclear\u2011structure calculations that quantify the forbidden\u2010transition strengths, which are presently unavailable."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does a fully pixelated charge readout affect the accuracy of three\u2011dimensional reconstruction in liquid argon time projection chambers compared to traditional wire\u2011plane readouts?<|assistant|>Pixelated readout provides a direct mapping of charge to a unique (x,\u202fy,\u202fz) coordinate, eliminating the ambiguity that arises from limited projections in wire\u2011plane TPCs. This improves reconstructed track fidelity, especially for overlapping events, by allowing exact hit localization in all three spatial dimensions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the key engineering challenges when scaling up a modular ton\u2011scale pixel\u2011readout LArTPC from a single prototype to the full DUNE near\u2011detector complex?<|assistant|>Challenges include maintaining low noise and uniformity across tens of thousands of ASIC channels, ensuring reliable cryogenic power distribution for per\u2011pixel electronics, scaling the data\u2011acquisition bandwidth to handle high voxel occupancy, preserving a uniform electric field over larger drift lengths, and integrating a high\u2011coverage photon\u2011detection system without compromising optical transparency."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways does the resistive field cage design influence space\u2011charge effects and drift\u2011field uniformity in a small\u2011drift LArTPC module?<|assistant|>The resistive shell provides a continuous voltage gradient rather than discrete wire rings, reducing dead zones and edge effects that can distort the field. By smoothing the potential, it minimizes localized field enhancements that attract ions, thereby mitigating space\u2011charge buildup and preserving uniform drift velocities across the volume."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the photon\u2011detection efficiencies of ArCLight and LCM modules impact the overall energy resolution when combining charge and light measurements?<|assistant|>Higher photon\u2011detection efficiency (PDE) improves the statistical precision of the light signal, tightening the anti\u2011correlation between charge loss (due to recombination) and scintillation light. By accurately modeling this correlation, the combined charge\u2011light measurement can reduce the effective energy\u2011resolution variance compared to using either signal alone, provided the PDE variations across the detector are uniformly calibrated."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the Module\u20110 demonstrator provide evidence for a systematic time offset between the charge arrival time at the anode and the light signal t0 that depends on the drift electric field?<|assistant|>The paper does not report a study of such a field\u2011dependent time offset, nor does it present measurements that would reveal a systematic shift. Therefore, at this time we cannot answer the question; additional dedicated measurements of the t0 timing relative to drift field variations would be required to resolve this issue."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How will the sensitivity improvements planned for the next LIGO\u2013Virgo observing run affect the expected detection rate of strongly lensed binary\u2011black\u2011hole gravitational\u2011wave signals?<|assistant|>With the design sensitivity the network is expected to detect many more binary\u2011black\u2011hole mergers at higher redshift, allowing the strong\u2011lensing cross\u2011section to be sampled more densely. Simulations forecast a few percent increase in the probability of observing a lensed pair per observing run, though the exact number depends on the adopted mass and redshift distributions of the lensing halos and the merger\u2011rate evolution."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way could the inclusion of higher\u2011order spherical\u2011harmonic modes in waveform models improve the identification of microlensing signatures in gravitational\u2011wave data?<|assistant|>Higher\u2011order modes provide additional frequency structure that can break degeneracies between intrinsic parameters and lens\u2010induced frequency\u2011dependent magnification. Their presence amplifies the beating patterns produced by point\u2011mass lenses, potentially making microlensing detectable at lower signal\u2011to\u2011noise ratios."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What limits on the fraction of dark matter that can be composed of compact objects can be projected from the Keplerian\u2011mass range (10\u00b2\u201310\u2075\u202fM\u2299) using the next decade of gravitational\u2011wave data?<|assistant|>Forecasts based on O4\u2013O5 merger counts (\u223c300\u20131000 events) suggest that constraints on the compact\u2011object dark\u2011matter fraction could tighten to the 10\u207b\u00b9\u201310\u207b\u00b2 level in that mass window, provided no microlensing signatures are observed and the waveform models accurately capture small\u2011scale lensing effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How significant are systematic calibration uncertainties and transient noise artifacts in sub\u2011threshold searches for lensed gravitational\u2011wave counterparts?<|assistant|>Calibration errors can shift recovered times and amplitudes, mimicking or hiding the subtle magnification patterns of a lensed image. Transient glitches increase the trials factor in a targeted search, raising the false\u2011alarm rate. Robust vetoes and improved calibration are essential to keep systematic biases below the statistical uncertainty of lens\u2011null likelihoods."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the theoretical distribution of magnification factors for gravitational\u2011wave lensing by singular isothermal sphere (SIS) versus more realistic lens profiles (e.g., NFW or elliptical galaxies)?<|assistant|>The paper does not investigate the full distribution of magnification factors for non\u2011SIS halo profiles. While SIS models predict a characteristic two\u2011image magnification ratio that depends only on the impact parameter, NFW or triaxial potentials introduce additional dependence on concentration, ellipticity, and line\u2011of\u2011sight structure. Therefore the magnification distribution for realistic lenses remains an open question that would require dedicated ray\u2011tracing simulations beyond the scope of this work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can increasing the coherence time in a cross\u2011correlation search improve the sensitivity to continuous gravitational waves from Scorpius X\u20111, and what computational strategies make longer coherence times feasible?<|assistant|>The signal\u2011to\u2011noise ratio of a cross\u2011correlation statistic grows roughly with the square root of the coherence time \\(T_{\\max}\\). Extending \\(T_{\\max}\\) therefore directly increases sensitivity. However, a longer coherence time enlarges the template bank because the metric in parameter space (frequency, orbital period, time of ascension, projected semi\u2011major axis) causes nearby points to become mismatched more quickly. Modern lattice covering techniques (e.g., the \\(\\mathcal{A}_3\\) and \\(\\mathcal{A}_4\\) lattices with a controlled mismatch) and the use of sheared coordinates for orbital parameters reduce the required template density, making it computationally tractable to double or even quadruple \\(T_{\\max}\\) while keeping the cost within available resources."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What impact would a non\u2011zero orbital eccentricity of Scorpius X\u20111 have on the cross\u2011correlation search and the derived upper limits?<|assistant|>The cross\u2011correlation search used in the analysis assumes a circular orbit, which eliminates two extra parameters: eccentricity \\(e\\) and argument of periastron \\(\\omega\\). If \\(e\\) were non\u2011zero, the Doppler modulation of the signal would change in a way that the current templates cannot match, leading to a loss in signal power (mismatch). This would effectively degrade the achieved upper limits, potentially by tens of percent for modest eccentricities (\\(e \\sim 0.01\\)). The paper does not model or correct for eccentricity, so the reported limits implicitly assume a circular orbit; they do not address how a small but finite eccentricity would alter the results."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can the upper limits on gravitational\u2011wave amplitude from Scorpius X\u20111 be used to constrain the neutron\u2011star equation of state when combined with torque\u2011balance models?<|assistant|>Torque\u2011balance models relate the expected gravitational\u2011wave amplitude \\(h_0\\) to the mass accretion rate and the neutron\u2011star\u2019s radius. By comparing the empirical upper limits on \\(h_0\\) to the theoretical torque\u2011balance curve for different equations of state (e.g., soft GR15 versus stiff GPPVA), one can exclude parameter combinations that would predict detectable signals. Specifically, for a given inclination and magnetic field, if the upper limit falls below the torque\u2011balance prediction for a particular EOS, that EOS is inconsistent with the observation unless the system departs from torque balance. The analysis demonstrates that, at frequencies where the search is most sensitive, the data exclude torque balance for more massive neutron stars, especially for stiff EOSs, thereby tightening constraints on the neutron\u2011star\u2019s mass\u2013radius relation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent will planned upgrades to the LIGO detectors (e.g., A+ upgrades) improve the sensitivity to continuous waves from Scorpius X\u20111, and what observing strategies are required to realize these gains?<|assistant|>A+ upgrades are projected to improve the strain sensitivity by roughly a factor of two across the 10\u2011to\u20112000\u202fHz band. Since the detectable amplitude scales as the inverse of the square root of the observation time and directly with the detector noise, A+ would lower the threshold \\(h_0\\) by about \\(\\sqrt{2}\\). Achieving this in practice requires longer, uninterrupted observing runs and improved data\u2011cleaning techniques (e.g., more effective self\u2011gating, line removal). Combining data from multiple runs in a fully coherent or semi\u2011coherent manner would further enhance sensitivity, potentially allowing the cross\u2011correlation search to probe torque\u2011balance amplitudes over a broader frequency range, including the >\u202f600\u202fHz regime."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What advanced methods exist to model and mitigate spin wandering in continuous\u2011wave searches, and how do they compare in effectiveness to the static\u2011frequency assumption used in this analysis?<|assistant|>Spin wandering\u2014random variations in the neutron\u2011star spin frequency\u2014can be modeled using hidden Markov models (HMMs) that track the signal frequency over time, or Bayesian time\u2011series approaches that treat the frequency drift as a stochastic process. These methods allow the search to retain sensitivity to signals that deviate from a perfectly constant frequency, at the cost of additional computational complexity. Compared to the static\u2011frequency assumption adopted here, HMM\u2011based searches can recover signals with modest frequency drifts (\\(\\dot{f}\\sim10^{-10}\\,\\text{Hz\\,s}^{-1}\\)) that would be lost in a purely coherent search, but they typically achieve a modest (\u224810\u201320%) increase in sensitivity for high\u2011frequency targets. The cross\u2011correlation search in the paper assumes a fixed frequency over the coherence time, which is justified given the estimated drift rate over the O3 run, but a future, longer\u2011baseline search could benefit from incorporating HMM techniques."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does increasing the photon detector coverage affect the energy reconstruction of GeV-scale neutrino events in a liquid\u2011argon time\u2011projection chamber?<|assistant|>Extending the photon detection coverage from the baseline ~10\u202f% to 30\u202f% can improve the reconstructed energy resolution by roughly 5\u201310\u202f% for typical GeV\u2011scale charged\u2011current events, primarily by better constraining the scintillation light contribution to the calorimetry and by improving vertex and timing precision."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What systematic advantages does a magnetized gaseous\u2011argon near detector provide for background rejection in the DUNE beamline?<|assistant|>The magnetic field allows sign determination for muons above ~800\u202fMeV and helps distinguish neutrino and antineutrino interactions, reducing the wrong\u2011sign background in beam\u2011mode measurements. The magnitude of this improvement depends on the achieved magnetic field uniformity and the detector\u2019s momentum resolution, topics that are still under detailed study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways could a liquid\u2011scintillator\u2013based far\u2011detector module improve sensitivity to the diffuse supernova neutrino background?<|assistant|>A scintillator target increases the inverse\u2011beta\u2011decay event rate (\u223c5\u202f\u00d7 larger than in pure argon), lowers the detection threshold to about 2\u202fMeV, and provides excellent neutron\u2011capture tagging, thereby enhancing the signal\u2011to\u2011background ratio for the diffuse supernova neutrino background."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main obstacles to achieving a sub\u20115\u202fMeV threshold for solar\u2011neutrino detection in a liquid\u2011argon TPC?<|assistant|>Key challenges include improving scintillation light collection efficiency, suppressing radon\u2011related backgrounds, and mitigating the 42Ar\u202f\u2192\u202f42K activity that sets a practical low\u2011energy floor. Ongoing R&D focuses on enhanced photon detectors, underground argon use, and comprehensive background modeling."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does adding a 10\u202fppm xenon dopant to liquid argon impact electron\u2011ion recombination and energy resolution for MeV\u2011scale events?<|assistant|>The DUNE Phase\u202fII white paper does not report detailed measurements of this effect. Current simulations suggest that low\u2011level xenon can shift the scintillation wavelength and slightly reduce triplet lifetimes, but the quantitative influence on recombination dynamics and the resulting MeV\u2011scale energy resolution remain to be determined through dedicated experimental studies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does including neutron star\u2013black hole (NSBH) mergers influence the constraints on cosmological parameters obtained through gravitational\u2011wave standard sirens?<|assistant|>Adding NSBH events expands the redshift lever arm and increases the sample size of dark sirens, thereby improving the statistical power for measuring the luminosity distance\u2013redshift relation. The combined information from binary black holes (BBHs) and NSBHs can tighten the Hubble constant estimate and, depending on the accuracy of the host\u2011galaxy identification, may also help constrain the dark\u2011energy equation of state."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the potential of standard sirens to shed light on the nature of dark energy beyond merely measuring the present\u2011day expansion rate?<|assistant|>Standard sirens provide direct, model\u2011independent measurements of the expansion history, H(z), as a function of redshift. By mapping H(z) over a range of redshifts, one can test whether the dark\u2011energy equation of state evolves (e.g., w \u2260 \u20131) or whether the expansion follows the \u039bCDM prediction, thus offering a complementary probe to supernovae, BAO, and CMB observations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways does the completeness and depth of all\u2011sky galaxy catalogs influence the statistical inference of the Hubble constant from dark sirens?<|assistant|>Completeness determines how often the true host galaxy of a gravitational\u2011wave event is contained within the catalog. A deeper, more complete catalog reduces the weight of the out\u2011of\u2011catalog likelihood component, thereby decreasing the uncertainty in the inferred redshift distribution and yielding a tighter Hubble constant posterior. Conversely, sparse catalogs increase reliance on population priors, which can broaden the H0 uncertainty."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might next\u2011generation detectors such as the Einstein Telescope or LISA improve the precision of Hubble\u2011constant measurements using gravitational\u2011wave standard sirens?<|assistant|>Future detectors will increase the detection volume and duty cycle, leading to larger samples of inspirals at higher redshift with significantly better sky localization and distance accuracy. This will enable more precise statistical association with host galaxies, reduce degeneracies with mass distribution assumptions, and expand the redshift baseline, thereby sharpening the determination of both H0 and the evolution of the expansion rate."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the impact of possible redshift evolution of the black\u2011hole mass distribution on the inference of the Hubble constant from gravitational\u2011wave observations?<|assistant|>We do not know the answer. The effect depends on how the black\u2011hole mass spectrum changes with cosmic time, which is influenced by stellar metallicity evolution, binary formation channels, and merger delay times. Current gravitational\u2011wave data lack the breadth in redshift and the theoretical modeling required to disentangle mass evolution from cosmological parameters, so the true influence of an evolving mass distribution on H0 estimates remains uncertain."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the stochastic wandering of a neutron star\u2019s spin frequency in low\u2011mass X\u2011ray binaries impact the sensitivity of continuous gravitational\u2011wave searches?<|assistant|>The spin frequency of an accreting neutron star is not constant; accretion torques fluctuate, causing a random walk in the star\u2019s rotational frequency. This wandering introduces phase errors that grow over time, limiting the maximum coherent integration interval before the matched\u2011filter signal power is significantly degraded. Continuous\u2011wave searches mitigate this by either using semi\u2011coherent segmentation, where the data are divided into short stretches that are individually coherent, or by employing hidden Markov models that explicitly track the stochastic frequency evolution and stitch together the most likely frequency path across the full observing run. The effectiveness of these techniques depends on the magnitude of the frequency wander\u2014larger wander demands shorter coherent segments or a finer template grid, which in turn increases computational cost and reduces overall sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What statistical challenges arise when deriving frequentist upper limits on gravitational\u2011wave strain using hidden Markov model pipelines?<|assistant|>Setting upper limits with a hidden Markov model (HMM) requires accurate modeling of the detection statistic\u2019s noise\u2011only distribution in a high\u2011dimensional template space. Key challenges include: (1) estimating the false\u2011alarm probability per sub\u2011band when the analytic form of the statistic is unknown; (2) controlling the overall false\u2011alarm rate across thousands of frequency sub\u2011bands and binary\u2011parameter templates; (3) accounting for non\u2011Gaussian and non\u2011stationary noise artifacts that can bias the likelihood and produce excess loud candidates; (4) generating sufficient Monte\u2011Carlo simulations to determine a detection threshold that yields the desired confidence level while keeping the computational load tractable; and (5) marginalizing over unknown source parameters such as inclination and polarization, which affects the mapping from the injection amplitude to the effective strain used in the upper\u2011limit calculation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways could planned upgrades to advanced gravitational\u2011wave detectors improve the reach of HMM\u2011based searches for Sco\u202fX\u20111?<|assistant|>Future upgrades that increase detector sensitivity (e.g., improved mirror coatings, quantum\u2011squeezing, cryogenic operation) directly lower the noise spectral density, thereby increasing the signal\u2011to\u2011noise ratio for a given strain amplitude. A deeper sensitivity baseline allows the use of longer coherent integration times before spin wandering becomes dominant, or permits a finer binary\u2011parameter grid without incurring prohibitive computational costs. Enhanced calibration accuracy reduces systematic uncertainties in the strain estimate, while expanded detector networks provide better sky\u2011coverage and can enable coincidence checks that suppress instrumental artifacts. Finally, longer continuous observing runs increase the total data set, improving the statistical power of the HMM and enabling tighter upper limits or potentially a first detection."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What astrophysical insight can be gained if the measured gravitational\u2011wave upper limits for Sco\u202fX\u20111 fall below the torque\u2011balance prediction, and how does this constrain the neutron\u2011star equation of state?<|assistant|>The torque\u2011balance condition assumes the accretion\u2011spin\u2011up torque is exactly counterbalanced by the spin\u2011down torque from gravitational\u2011wave emission, giving a maximum expected strain amplitude that depends on the X\u2011ray flux, distance, and assumed emission frequency. If an empirical upper limit lies below this threshold, it implies that the neutron star must be emitting fewer gravitational waves than required for torque balance, which in turn restricts the star\u2019s equatorial ellipticity. The ellipticity is linked to the star\u2019s internal composition and the strength of its crust or magnetic field, none of which are directly observable. Therefore, a sub\u2011torque\u2011balance limit places an upper bound on the deformability, providing indirect constraints on the equation of state, especially regarding the shear modulus of the crust and possible exotic core phases."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Do observations indicate that the magnetic field configuration of Sco\u202fX\u20111\u2019s neutron star changes on the timescale of the O3 observing run, affecting the phase\u2011modulation templates used in HMM searches?<|assistant|>Current data do not provide time\u2011resolved measurements of the magnetic field geometry of Sco\u202fX\u20111\u2019s neutron star. Most of our knowledge comes from long\u2011term X\u2011ray timing and spectroscopy, which constrain the average accretion rate and orbital parameters but not the instantaneous magnetic field topology. Consequently, the phase\u2011modulation templates employed in HMM pipelines are based on a static approximation of the binary orbit and are not adjusted for potential magnetic\u2011field\u2011induced phase changes. Without contemporaneous magnetic\u2011field diagnostics, such as X\u2011ray polarimetry or cyclotron resonance measurements, any evolution of the field over a ~one\u2011year observing run remains unconstrained, and its impact on the signal waveform cannot be quantified."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What frequency range is most favorable for detecting continuous gravitational waves emitted by scalar boson clouds around stellar\u2011mass black holes with current ground\u2011based detectors?<|assistant|>Ground\u2011based interferometers such as Advanced LIGO and Virgo are most sensitive in the 20\u2013600\u202fHz band. In this range the expected quasi\u2011monochromatic signals from scalar boson clouds, whose intrinsic frequency scales roughly as the boson mass relative to the black\u2011hole mass, fall within or just above the detectors\u2019 optimal sensitivity. Frequencies below ~20\u202fHz are limited by seismic noise, while above ~600\u202fHz the detector noise rises steeply, reducing the achievable strain sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the self\u2011interaction strength of ultralight scalar bosons affect the growth, depletion, and gravitational\u2011wave signal from a boson cloud around a spinning black hole?<|assistant|>The self\u2011interaction parameter \\(F_b\\) (or the quartic coupling \\(\\lambda\\)) determines the cloud\u2019s internal dynamics. Strong self\u2011interactions accelerate the cloud\u2019s depletion by enhancing annihilation rates, shorten the signal\u2019s duration, and can reduce the emitted strain amplitude. Weak self\u2011interactions allow the cloud to grow longer and produce a more persistent, higher\u2011amplitude signal. Quantitative predictions require solving the coupled scalar\u2011field and Einstein equations, and the exact dependence on \\(F_b\\) remains an active area of theoretical investigation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What upper limits on the ultralight boson mass can be derived from non\u2011detections of continuous waves, assuming a realistic Galactic population of spinning black holes?<|assistant|>Non\u2011detections translate into exclusion regions in the boson mass\u2013black\u2011hole mass plane. By modeling the Galactic black\u2011hole distribution (e.g., a Kroupa mass function) and assuming a wide range of initial spins, one can compute the expected strain amplitude for each mass pair. If the expected strain exceeds the detector\u2019s sensitivity limit, that parameter space point is excluded. The strength of the exclusion depends sensitively on the assumed spin distribution, cloud age, and distances, so different astrophysical priors can shift the resulting constraints."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Will future space\u2011based detectors like LISA provide complementary sensitivity to boson\u2011cloud gravitational waves, and at which frequencies would they be most useful?<|assistant|>LISA\u2019s frequency band (\u22480.1\u202fmHz\u20131\u202fHz) is well\u2011suited to probe boson clouds around intermediate\u2011mass black holes (\u224810\u2074\u201310\u2076\u202fM\u2609) and ultralight bosons with masses \u224810\u207b\u00b9\u00b3\u201310\u207b\u00b9\u00b2\u202feV. These sources emit at frequencies lower than the ground\u2011based band. Therefore, LISA could observe the earlier, slower\u2011evolving phase of the cloud\u2019s annihilation signal, complementing ground\u2011based detectors that target higher\u2011frequency, short\u2011lived signals from stellar\u2011mass black holes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there an observable population of binary black hole mergers that retain residual scalar boson clouds around the remnant, and what would be the signatures in the post\u2011merger gravitational\u2011wave ringdown?<|assistant|>This question remains unanswered. Detecting a residual boson cloud around a merger remnant would require identifying deviations in the ringdown spectrum\u2014such as additional quasinormal modes or altered damping times\u2014indicating the presence of a scalar field. Current gravitational\u2011wave observations lack sufficient signal\u2011to\u2011noise in the ringdown phase to test such subtle effects, and detailed numerical relativity simulations including self\u2011interacting scalar fields are still under development. Consequently, we cannot presently confirm or rule out the existence of post\u2011merger boson clouds."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do spin-precessing effects influence the detectability of binary black hole mergers in current gravitational-wave detectors?<|assistant|>Spin-precession introduces modulations in the gravitational-wave signal that can spread the emitted power over a broader frequency band and multiple harmonics. These modulations increase the complexity of the waveform, making it more challenging for template banks that assume aligned spins to recover the signal. Consequently, matched-filter searches that incorporate precessing waveform models can recover signals with higher signal-to-noise ratios and improve the overall detection efficiency, especially for asymmetric or high-spin binaries."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main challenges in modeling eccentric inspirals for gravitational-wave data analysis?<|assistant|>Eccentric inspirals require waveform models that capture the rapid periastron passages and the associated burst-like emissions. Current models often rely on post-Newtonian expansions that become inaccurate at high eccentricities or close separations, and numerical relativity simulations for eccentric binaries are computationally expensive and limited in parameter coverage. These limitations make it difficult to construct dense, accurate template banks, which in turn hampers matched-filter searches and can bias parameter estimation if an eccentric signal is forced into a quasi-circular template family."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the choice of power spectral density (PSD) estimation method affect the accuracy of Bayesian parameter estimation in gravitational-wave observations?<|assistant|>The PSD quantifies the detector noise as a function of frequency and directly weights the likelihood function in the Bayesian framework. A PSD that underestimates noise power at frequencies where the signal has significant amplitude will artificially inflate the inferred signal-to-noise ratio, leading to tighter but potentially biased parameter constraints. Conversely, overestimating noise can dilute the signal, broadening posterior distributions. Adaptive, time-dependent PSD estimation methods that capture non-stationary noise characteristics tend to produce more reliable parameter posteriors compared to static, long-term averages."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways can data-quality vetoes improve the false\u2011alarm rate of matched\u2011filter searches for compact binary coalescences?<|assistant|>Data\u2011quality vetoes identify and exclude time intervals contaminated by transient artifacts (glitches) or persistent instrumental disturbances. By removing or down\u2011weighting data segments that would otherwise produce spurious high\u2011SNR triggers, vetoes reduce the background rate that the matched\u2011filter pipeline must contend with. This leads to a cleaner noise distribution, enabling stricter ranking statistics and lowering the false\u2011alarm rate for a given significance threshold. Additionally, vetoes can improve the fidelity of the estimated PSD, further enhancing the robustness of the search."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the effect of higher\u2011order multipole modes on the mass and spin inference of binary neutron star mergers?<|assistant|>I do not have sufficient evidence to answer this question at present. The current literature does not provide a comprehensive study of how higher\u2011order multipole contributions influence parameter estimation for binary neutron star systems, and existing models mainly focus on the dominant quadrupole. As a result, the precise impact on inferred masses and spins remains an open area for further investigation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can subthreshold gravitational\u2011wave triggers be efficiently followed up in the hard X\u2011ray band to detect faint electromagnetic counterparts?<|assistant|>An efficient follow\u2011up strategy requires (i) continuous event\u2011mode data acquisition from a wide\u2011field coded\u2011mask instrument such as Swift\u2011BAT, (ii) a rapid, likelihood\u2011based search pipeline that models the detector response for any sky position, and (iii) a real\u2011time alert system that incorporates the gravitational\u2011wave sky probability map. By combining these elements, one can probe flux levels far below the on\u2011board trigger threshold and recover transients with sub\u2011minute durations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What constraints do the Swift\u2011BAT upper limits place on the luminosity function of short gamma\u2011ray bursts associated with binary neutron star mergers?<|assistant|>The flux upper limits measured over the 15\u2013350\u202fkeV band translate into luminosity limits of 10^46\u201310^49\u202ferg\u202fs\u207b\u00b9 for typical BNS distances. These limits exclude a high\u2011luminosity tail in the short\u2011GRB population at the 90\u202f% confidence level for events within the Swift field of view, thereby tightening the parameter space for models that predict prompt emission from BNS coalescences."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent could the joint use of Swift\u2011BAT and Fermi\u2011GBM data improve the sensitivity to electromagnetic counterparts of subthreshold GW events?<|assistant|>Joint analysis leverages the complementary sky coverage and energy response of Swift\u2011BAT (hard X\u2011ray, coded\u2011mask imaging) and Fermi\u2011GBM (all\u2011sky gamma\u2011ray). By combining their likelihoods and accounting for each instrument\u2019s background characteristics, one can lower the effective false\u2011alarm rate and extend the detection horizon by up to ~30\u202f%. However, the practical gains depend on the temporal overlap and pointing status of both satellites during each trigger."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might future gravitational\u2011wave observing runs benefit from improvements in coded\u2011mask imaging sensitivity and localization precision?<|assistant|>Advances such as deeper detector simulations, better background modelling, and real\u2011time attitude reconstruction can increase the coded\u2011mask effective area by ~20\u202f% and reduce localization errors from several degrees to sub\u2011degree scales. This would enable rapid optical/infrared follow\u2011up, improve joint\u2011FAR calculations, and potentially uncover a population of off\u2011axis jets that are otherwise missed with current sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there evidence that binary black hole mergers produce detectable gamma\u2011ray emission, and if not, what upper limits can be derived?<|assistant|>We do not know. The current dataset contains no statistically significant hard\u2011X\u2011ray detections coincident with confirmed binary black hole mergers. Consequently, only upper limits can be set; for the most well\u2011localised events these limits lie at ~10^48\u202ferg\u202fs\u207b\u00b9 in the 15\u2013350\u202fkeV band. Determining whether BBH mergers produce any prompt emission requires additional sensitive observations or a larger sample of high\u2011significance events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main technical challenges for realizing 14\u2011Tesla Nb\u2083Sn dipole magnets in the FCC\u2011hh collider, and how do they affect the overall machine design?<|assistant|>The primary challenges are (1) achieving a sufficient field quality with a tight tolerance on the higher\u2011order multipoles, (2) managing the quench stability in a 90\u2011km ring where the stored beam energy per beam exceeds 6\u202fGJ, and (3) ensuring reliable cryogenic performance at 1.9\u202fK while maintaining a high magnetic field gradient. These constraints dictate the coil geometry, the choice of cable and conductor, the cooling scheme, and the mechanical support structure. They also influence the overall magnet packing factor, which in turn affects the ring aperture and the achievable beam emittance. The large stored energy imposes strict protection requirements, necessitating fast\u2011acting quench heaters and a robust energy\u2011dump system. All of these factors must be integrated into the accelerator lattice and the overall cost and schedule of the FCC\u2011hh project."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can electron\u2011cloud formation be mitigated in a 90\u2011km circumference electron\u2013positron collider operating at 45\u202fGeV per beam, and what surface treatments or vacuum\u2011system designs are most effective?<|assistant|>Mitigation strategies include (1) applying low secondary\u2011electron\u2011yield (SEY) coatings such as amorphous carbon or titanium nitride on the vacuum\u2011chamber interior, (2) installing a thin NEG (non\u2011evaporable getter) coating to provide both low SEY and pumping, and (3) shaping the chamber with transverse slots or grooves to interrupt electron trajectories. The beam\u2011pipe geometry\u2014radius, tapering, and the presence of winglets to intercept synchrotron radiation\u2014also influences the local electron\u2011cloud density. The longitudinal bunch spacing can be optimized; for example, a 50\u202fns spacing instead of 25\u202fns raises the SEY multipacting threshold significantly. In addition, a \u201cnon\u2011uniform\u201d filling pattern with a few closely spaced bunches followed by a larger gap can further suppress cloud buildup. These measures together can keep the electron\u2011cloud density below the instability threshold, but detailed 3\u2011D simulations and experimental validation in a dedicated test chamber are needed to quantify the exact performance."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What safety concepts are essential for managing the stored beam energy in a future 100\u2011TeV proton\u2013proton collider, and how are machine\u2011protection interlocks typically designed?<|assistant|>Safety concepts for handling multi\u2011gigajoule stored energies include: (1) passive protection\u2014robust collimation systems that intercept halo particles before they reach sensitive components; (2) active protection\u2014fast\u2011acting beam\u2011loss monitoring systems that detect abnormal loss patterns and trigger a rapid beam dump; (3) fault tolerance in the RF and magnet power\u2011supplies to prevent uncontrolled energy deposition; and (4) redundant interlock logic that combines loss\u2011monitor, beam\u2011position, and orbit\u2011feedback signals. The interlock system typically uses a distributed network of loss\u2011monitors (e.g., ionization chambers, scintillators) positioned around the ring, feeding into a central logic unit that can issue a beam\u2011dump command within microseconds. In addition, the machine protection system is designed to tolerate a certain number of false positives while maintaining a very low probability of a dangerous failure. Detailed design of the interlocks is guided by Monte\u2011Carlo loss\u2011simulation studies that identify the most vulnerable components."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it feasible to incorporate a high\u2011energy electron\u2013ion collision option into the FCC\u2011hh schedule, and what accelerator physics challenges would need to be addressed?<|assistant|>The FCC\u2011h collides protons (and ions) in the main ring, but the paper does not present a detailed feasibility study for an electron\u2013ion (e\u2013A) option. Realizing such a mode would require an additional high\u2011energy electron accelerator, likely a recirculating energy\u2011recovery linac or a separate storage ring, capable of delivering multi\u2011hundred GeV electrons. Key challenges would include synchronizing the electron bunches with the ion bunches, achieving sufficient luminosity while managing beamstrahlung and synchrotron radiation in the electron beam, and integrating a suitable energy\u2011recovery system to keep power consumption reasonable. Moreover, the interaction region would need to accommodate a new detector design with different radiation shielding and background conditions. Because the paper does not cover these aspects, further dedicated studies are required to evaluate the technical and cost feasibility of an e\u2013A option in the FCC\u2011hh program."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the quantitative improvement in strain sensitivity achieved by implementing squeezed light sources in the LIGO and Virgo detectors across different frequency ranges?<|assistant|>The introduction of squeezed vacuum states into the interferometers reduces quantum shot noise at high frequencies while leaving low\u2011frequency performance largely unchanged. For Advanced LIGO, squeezing has been shown to increase the binary neutron star range by roughly 10\u201315\u202f% in the 100\u2013200\u202fHz band and by up to 20\u202f% above 500\u202fHz. Virgo reports similar gains, with an effective improvement of ~15\u202f% in the 50\u2013300\u202fHz band and up to 25\u202f% above 700\u202fHz. These figures come from calibrated sensitivity curves measured during dedicated squeezing runs and are corroborated by injection studies that confirm the noise reduction directly translates into larger observable volumes for high\u2011mass binary mergers."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can machine learning techniques be used to classify and predict transient noise artifacts in gravitational\u2011wave data streams in real\u2011time?<|assistant|>Real\u2011time glitch classification can be approached by training supervised classifiers on time\u2013frequency representations of the strain data. Convolutional neural networks (CNNs) ingest spectrograms and output probabilities for glitch categories (e.g., blip, scattering, low\u2011frequency burst). Recurrent architectures such as LSTMs can capture temporal correlations, while auto\u2011encoders can flag anomalies without explicit labels. In practice, pipelines like GravitySpy and DeepGlitch have demonstrated that a CNN trained on a large catalog of labeled glitches can achieve >95\u202f% classification accuracy. For prediction, sequential models can learn patterns preceding glitches, enabling early warnings that trigger data\u2011quality vetoes before a detector\u2019s sensitivity is compromised."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does adding KAGRA and GEO\u202f600 to the LIGO\u2013Virgo network affect the sky localization accuracy for binary neutron star mergers during low\u2011latency alert pipelines?<|assistant|>Inclusion of KAGRA and GEO\u202f600 expands the baseline network and provides additional independent timing and amplitude measurements. Simulations show that a four\u2011detector network can reduce the median sky\u2011area 90\u202f% credible region for binary neutron stars from ~200\u202fdeg\u00b2 (LIGO\u2013Virgo) to ~100\u202fdeg\u00b2, and further down to ~60\u202fdeg\u00b2 when KAGRA operates with its full sensitivity. GEO\u202f600, while less sensitive, contributes valuable triangulation, especially for short\u2011duration bursts. Thus, the network\u2019s ability to rapidly localize events for electromagnetic follow\u2011up is significantly enhanced by the additional detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the impact of using different calibration versions (e.g., AR, C01, C01_AR) on the measured masses and spins of binary black hole mergers detected during the O3 observing run?<|assistant|>The agent does not have direct access to the specific calibration\u2011dependent parameter distributions for O3 binary black hole events. The paper provides the public strain data and describes several calibration streams, but it does not quantify how the choice among them alters the inferred component masses or effective spins. Assessing such an impact would require re\u2011running the full Bayesian inference pipeline on the data processed with each calibration version and comparing the posterior distributions, a task beyond the scope of the paper\u2019s analysis. Consequently, the exact influence of calibration version selection on the astrophysical parameters remains an open question requiring dedicated reanalysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What distinctive gravitational\u2011wave signatures are expected from binary black holes whose component masses are below 0.2\u202fM\u2299, and how do these signatures differ from those of higher\u2011mass binaries?<|assistant|>In the subsolar\u2011mass regime the inspiral phase dominates the signal because the merger and ring\u2011down occur at frequencies above the most sensitive band of ground\u2011based detectors. The waveform is therefore almost entirely a chirp described by the post\u2011Newtonian expansion up to the last stable orbit. Compared to binaries with component masses \u22731\u202fM\u2299, the chirp mass is smaller, leading to a slower phase evolution and a lower amplitude for a given distance. The signal also contains fewer cycles in band, which makes parameter estimation more challenging. These differences are reflected in the template banks used in the O3 search: a lower mass cutoff of 0.2\u202fM\u2299 and a minimum match of 0.97 were chosen to keep the computational cost tractable while retaining sensitivity to the expected waveform shape."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which detector upgrades and observing\u2011run strategies are most critical for improving the sensitivity to subsolar\u2011mass binary black holes in future runs (O4 and O5)?<|assistant|>The key upgrades are (i) lowering the seismic noise floor and improving the low\u2011frequency sensitivity of the interferometers, which directly increases the number of inspiral cycles observable for low\u2011mass binaries; (ii) enhancing the laser power and implementing quantum\u2011noise reduction techniques (squeezed light) to raise the high\u2011frequency sensitivity where the merger would appear; and (iii) adding a new detector such as KAGRA or LIGO\u2011India to enlarge the network, improve sky localization, and increase the effective observing volume. In addition, expanding the data\u2011analysis pipelines to include full spin precession and higher\u2011order amplitude corrections will allow better recovery of subsolar\u2011mass signals. Together, these improvements are expected to roughly double the sensitive volume\u2013time compared to O3."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can gravitational\u2011wave data alone distinguish subsolar\u2011mass black holes from other compact objects such as neutron stars or boson stars?<|assistant|>In principle, the mass and spin measurements from the inspiral waveform can separate black holes from neutron stars if the total mass falls below the maximum neutron\u2011star mass (~2.3\u202fM\u2299). However, for subsolar masses the mass uncertainty is large due to the short signal duration, and the waveform is almost indistinguishable from that of a boson star or other exotic compact object that follows the same point\u2011particle dynamics. Without additional electromagnetic counterparts or tidal\u2011deformation measurements (which are negligible for such low masses), gravitational\u2011wave data alone cannot unambiguously identify the compactness of the objects. Thus, a non\u2011detection or weak detection does not conclusively rule out or confirm the presence of subsolar\u2011mass black holes versus other candidates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the null results from the O3 subsolar\u2011mass binary search constrain primordial black hole dark\u2011matter models with extended mass functions?<|assistant|>The O3 limits on the merger rate of binaries with at least one subsolar\u2011mass component translate into upper bounds on the product of the primordial\u2011black\u2011hole (PBH) mass function and the fraction of dark matter in PBHs. For a monochromatic mass function, the analysis excludes fPBH\u202f\u2273\u202f0.6 at 0.3\u202fM\u2299 and fPBH\u202f\u2273\u202f0.09 at 1\u202fM\u2299. For extended mass functions, the limits are weaker because mergers can involve a wide range of mass ratios, and the suppression factor for early binary disruption becomes less effective. Consequently, models that predict a broad PBH spectrum with a significant contribution from subsolar masses remain viable, even with fPBH\u202f\u2248\u202f1, unless the mass distribution is strongly peaked. The analysis therefore disfavors sharply peaked PBH spectra in the subsolar range but cannot rule out broader distributions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a population of subsolar\u2011mass black holes formed through dissipative dark\u2011matter collapse influence the stochastic gravitational\u2011wave background, and could current or future detectors observe such a background?<|assistant|>The paper does not directly address the stochastic background from subsolar\u2011mass black holes. A population of dark\u2011matter\u2011induced black holes would merge throughout cosmic history, contributing to a continuous gravitational\u2011wave background. The amplitude of this background depends on the merger rate density, the typical chirp mass, and the redshift distribution of the sources. Because subsolar\u2011mass binaries have lower chirp masses, their individual contributions to the strain spectrum peak at higher frequencies, potentially overlapping with the sensitivity band of Advanced LIGO/Virgo. However, current upper limits on the stochastic background are dominated by higher\u2011mass binaries, and the expected contribution from subsolar\u2011mass mergers is likely below the present sensitivity threshold. Future detectors with improved low\u2011frequency sensitivity and longer observing times, such as the Einstein Telescope or Cosmic Explorer, could probe this background, but detailed population\u2011synthesis modeling is required to make quantitative predictions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the ellipticity constraints derived from continuous-wave upper limits impact models of neutron star crust breaking strain in the Galactic Center?<|assistant|>The upper limits on strain translate to maximum ellipticities of order 10\u207b\u2077\u201310\u207b\u2076 for stars at the Galactic Center. These values are close to or below the theoretical maximum elastic deformations predicted for normal neutron-star crusts (\u224810\u207b\u2076\u201310\u207b\u2075) but are still above the values expected for highly strained crusts or exotic matter. Consequently, the results rule out extremely deformed, solid strange or hybrid star models in the Galactic Center while remaining consistent with standard nuclear equations of state."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the implications of the non\u2011detection of continuous gravitational waves for the population size of millisecond pulsars in the inner parsecs of the Milky Way?<|assistant|>The lack of a signal suggests that either the millisecond pulsar population is smaller than some optimistic estimates or that their individual ellipticities are below the detection threshold. Using the strain upper limits, one can place an upper bound on the average ellipticity of millisecond pulsars in the region, thereby constraining population synthesis models that predict thousands of such objects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can future gravitational\u2011wave detectors improve sensitivity to continuous waves from sources at the Galactic Center compared to the current LIGO\u2011Virgo O3 run?<|assistant|>Improvements can come from increased detector bandwidth, lower noise at 100\u2013200 Hz, and longer coherent integration times. Advanced detectors such as LIGO\u2011A+ and Virgo\u2011plus, as well as next\u2011generation facilities (Einstein Telescope, Cosmic Explorer), will reduce strain sensitivity by an order of magnitude, allowing detection of ellipticities as low as 10\u207b\u2078 and probing larger distances within the Galactic Center."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What constraints can continuous-wave upper limits place on the mass and spin of hypothetical boson clouds around stellar\u2011mass black holes in the Galactic Center?<|assistant|>By assuming a superradiant boson cloud that emits at a frequency tied to the black-hole mass and boson mass, the non\u2011detection limits exclude regions of the (black\u2011hole spin, boson mass) plane. For example, the results rule out clouds around black holes with initial spin \u03c7i \u2273 0.5 for boson masses between 10\u207b\u00b9\u00b9\u202feV and 10\u207b\u2079\u202feV if the cloud age is 10\u2075\u201310\u2077\u202fyears."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the true spin\u2011down distribution of neutron stars located in the Galactic Center, and how does it affect the parameter space explored in directed searches?<|assistant|>The paper does not determine the actual spin\u2011down distribution of Galactic\u2011Center neutron stars. This distribution is poorly known because the region is heavily obscured and radio surveys are incomplete. Without precise knowledge of typical spin\u2011down rates, directed searches must adopt broad spin\u2011down ranges (e.g., \u22121.8\u00d710\u207b\u2078\u202fHz/s to +10\u207b\u00b9\u2070\u202fHz/s), which increases computational cost and reduces sensitivity. A more accurate spin\u2011down distribution, obtainable through future radio or X\u2011ray timing surveys, would allow tighter parameter spaces and improved search sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What physical mechanisms can generate a non\u2011axisymmetric quadrupole deformation in a rapidly rotating neutron star, thereby enabling the emission of continuous gravitational waves?<|assistant|>Several processes are thought to be capable of sustaining a mass quadrupole in a neutron star:\\n- **Crustal \u2018mountains\u2019** formed by tectonic stresses or accreted material that lifts the crust out of symmetry.\\n- **Magnetic stresses**: strong internal or surface magnetic fields can distort the star, producing a permanent quadrupole.\\n- **Accretion\u2011driven deformations**: asymmetric mass loading in accreting systems (e.g., low\u2011mass X\u2011ray binaries) can freeze in a non\u2011axisymmetric shape.\\n- **Superfluid vortex pinning and unpinning**: differential rotation between the crust and the interior superfluid can create a time\u2011varying quadrupole.\\n- **r\u2011mode oscillations**: large\u2011amplitude fluid modes can produce time\u2011dependent quadrupole moments that radiate GWs.\\nThese mechanisms are active in different evolutionary stages of neutron stars and can, in principle, sustain ellipticities large enough to be detectable by current detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do rotational glitches observed in young pulsars affect the prospects for detecting continuous gravitational waves from those pulsars?<|assistant|>Glitches are sudden increases in the spin frequency (and sometimes in the spin\u2011down rate). They can influence continuous\u2011wave searches in several ways:\\n- **Phase evolution**: The GW phase is expected to track the electromagnetic spin. A glitch introduces an instantaneous phase jump that must be modeled or searched over to avoid loss of sensitivity.\\n- **Spin\u2011down changes**: Post\u2011glitch changes in the frequency derivative alter the expected amplitude via the spin\u2011down limit; a more negative \\(\\dot{f}\\) can raise the theoretical upper limit.\\n- **Amplitude variations**: If a glitch is associated with a change in the internal configuration (e.g., superfluid vortex rearrangement), the quadrupole moment may change, potentially increasing or decreasing the GW amplitude.\\nBecause of these uncertainties, most continuous\u2011wave pipelines either treat glitches as additional phase parameters or restrict the search to epochs between glitches, which can reduce the effective observation time."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What assumptions underpin the spin\u2011down limit on the gravitational\u2011wave strain amplitude of a pulsar, and how is this limit derived?<|assistant|>The spin\u2011down limit is a theoretical upper bound on the GW strain \\(h_0\\) that assumes *all* of the pulsar\u2019s rotational energy loss is carried away by gravitational waves:\\n1. **Energy conservation**: \\(\\dot{E}_{\\rm rot}= -\\dot{E}_{\\rm GW}\\). The rotational energy \\(E_{\\rm rot}= \\tfrac{1}{2} I \\Omega^2\\). \\(\\Omega=2\\pi f_{\\rm rot}\\).\\n2. **Moment of inertia**: A canonical value \\(I \\approx 10^{38}\\,\\rm kg\\,m^2\\) is usually assumed, though it can vary by a factor of a few depending on the equation of state.\\n3. **Distance**: The observed spin\u2011down rate \\(\\dot{f}\\) and the distance \\(d\\) enter the expression for the strain amplitude. The derived limit is \\(h_{\\rm sd} \\propto (I|\\dot{f}|/d f)^{1/2}\\).\\n4. **Negligible other torques**: No significant electromagnetic or accretion torques are present; the intrinsic spin\u2011down equals the observed value.\\nThe limit is useful because any measured strain below it indicates that GW emission is sub\u2011dominant, and it sets a natural benchmark for the sensitivity required to potentially detect a signal."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can continuous\u2011wave gravitational\u2011wave observations inform our understanding of the neutron\u2011star equation of state?<|assistant|>Continuous\u2011wave searches provide upper limits on the neutron star\u2019s ellipticity \\(\\epsilon\\) and mass quadrupole \\(Q_{22}\\). These limits can be compared to theoretical predictions for the maximum sustainable deformation given different equations of state (EOS):\\n- **Stiff EOSs** predict a larger radius and hence a higher maximum quadrupole before breaking the crust, allowing larger \\(\\epsilon\\).\\n- **Soft EOSs** lead to smaller stars with thinner crusts, giving lower quadrupole limits.\\nIf an observed upper limit falls below the maximum \\(\\epsilon\\) allowed by a particular EOS, that EOS can be deemed inconsistent with the data. Moreover, detecting a signal with a measurable \\(\\epsilon\\) would provide a direct probe of the star\u2019s internal structure and crustal rigidity, offering constraints complementary to those from binary merger observations and X\u2011ray pulse\u2011profile modeling."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What would be the observational signatures of scalar\u2011tensor (e.g., Brans\u2013Dicke) gravity in the continuous gravitational\u2011wave spectrum from a rotating neutron star, and can current detectors differentiate such signatures from those predicted by general relativity?<|assistant|>The paper does not address this question. In scalar\u2011tensor theories, an additional scalar polarization mode can be emitted at the *first* harmonic (i.e., at the spin frequency), producing a dipole radiation term with a distinct frequency dependence compared to the quadrupole tensor mode at twice the spin frequency. Current detectors are most sensitive to the quadrupolar tensor modes, and while some searches target the scalar mode, the sensitivity to scalar radiation is typically weaker. Therefore, at present it is not clear whether detectors can unambiguously distinguish scalar\u2011tensor predictions from general relativity, and further theoretical modeling and detector\u2011network studies are required to assess the feasibility of such tests."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the internal magnetic field topology of a magnetar influence the efficiency of energy transfer to gravitational waves during a giant flare?<|assistant|>The efficiency of gravitational\u2010wave excitation depends sensitively on the arrangement of poloidal and toroidal field components. A strongly toroidal field can store more magnetic energy in the core and may facilitate larger deformations, thereby increasing the coupling to f\u2011mode oscillations. Conversely, a predominantly poloidal configuration might lead to weaker quadrupolar distortions and reduced gravitational\u2011wave emission. The exact dependence requires detailed magnetohydrodynamic simulations of field evolution during a flare."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can magnetar bursts produce detectable continuous gravitational wave emission via r\u2011mode instabilities, and under what conditions would this be observable?<|assistant|>R\u2011mode instabilities grow when the star\u2019s rotation rate is sufficiently high and the viscous damping is weak. Magnetars, being slowly rotating (periods of a few seconds), are generally below the critical spin required for r\u2011mode growth, making continuous emission unlikely. However, if a magnetar were spun up by accretion or experienced a sudden spin\u2011up during a giant flare, the r\u2011mode amplitude could temporarily exceed the threshold, producing a weak continuous wave that might be detectable with long\u2011integration searches in next\u2011generation detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a future network of third\u2011generation gravitational wave detectors improve sensitivity to high\u2011frequency magnetar f\u2011modes compared to current detectors?<|assistant|>Third\u2011generation detectors such as the Einstein Telescope or Cosmic Explorer aim for strain sensitivities an order of magnitude better than Advanced LIGO at frequencies around 1\u20133\u202fkHz. This improvement would lower the detectable energy threshold for f\u2011mode bursts from \u223c10^49\u202ferg to \u223c10^47\u202ferg for a Galactic magnetar, potentially allowing the observation of many more events. Additionally, better high\u2011frequency response would reduce the mismatch between expected mode spectra and detector noise, improving matched\u2011filter detection efficiency."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the precise correlation between the observed quasi\u2011periodic oscillations in magnetar flare tails and the frequency spectrum of potential gravitational wave emission?<|assistant|>The paper does not address this question. Establishing a direct correlation would require simultaneous, high\u2011time\u2011resolution X\u2011ray/gamma\u2011ray observations and sensitive gravitational\u2011wave data, along with detailed modeling of magnetar interior oscillation modes. Current theoretical work provides only tentative links between QPOs and crustal or core oscillations, and more observations and simulations are needed to confirm any direct correlation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the inclusion of higher-order multipole moments in gravitational\u2011wave templates affect the precision of tests of general relativity using binary black hole signals?<|assistant|>Adding higher\u2011order harmonics (\u2113,|m|\u22602,2) to the waveform models increases the fidelity of the predicted strain, especially for high\u2011mass or high\u2011mass\u2011ratio binaries. It reduces systematic mismatches between the true signal and the template, thereby tightening constraints on deviations in the post\u2011Newtonian coefficients, dispersion parameters, and spin\u2011induced quadrupole moments. Studies with GWTC\u20113 data have shown that accounting for higher modes leads to smaller fitting\u2011factor losses and more accurate recovery of the final mass and spin, which in turn improves the robustness of consistency and parameter\u2011ized tests."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What upper limit on the graviton mass can be derived from the combined GWTC\u20113 catalog, and how does this bound compare to existing solar\u2011system limits?<|assistant|>Using the modified dispersion analysis on the 43 GWTC\u20113 events, the 90\u202f% credible upper bound on the graviton mass is \\(m_{\\mathrm{g}} \\le 2.42 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\). This improves the previous GWTC\u20112 limit (\\(3.09 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)) by about 28\u202f% and is slightly better than the most stringent solar\u2011system bound of \\(3.16 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can measurements of the spin\u2011induced quadrupole moment parameter (\\(\\delta\\kappa_s\\)) distinguish black holes from neutron stars or exotic compact objects, and what constraints have recent gravitational\u2011wave observations placed?<|assistant|>In general relativity, a Kerr black hole has \\(\\kappa=1\\), while neutron stars and many exotic compact objects (e.g., boson stars, gravastars) can have \\(\\kappa\\) values significantly different from unity. By measuring \\(\\delta\\kappa_s = (\\kappa-1)\\) in binary mergers, one can test the black\u2011hole no\u2011hair conjecture. The GWTC\u20113 analysis of 13 suitable events yields a combined 90\u202f% credible interval of \\(\\delta\\kappa_s = -16.0^{+13.6}_{-16.7}\\). This is consistent with \\(\\delta\\kappa_s = 0\\) (the Kerr value) but allows a modest range of deviations, providing the first ever statistical constraint on \\(\\kappa\\) from gravitational\u2011wave data."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way will next\u2011generation gravitational\u2011wave detectors such as the Einstein Telescope or Cosmic Explorer improve the sensitivity of the inspiral\u2013merger\u2013ringdown consistency test?<|assistant|>Third\u2011generation detectors will provide several key advantages: (1) much higher signal\u2011to\u2011noise ratios, (2) longer observable inspiral phases (especially for low\u2011mass binaries), and (3) better low\u2011frequency sensitivity that captures more gravitational\u2011wave cycles. These improvements will sharpen the independent estimates of the final mass and spin from the inspiral and post\u2011inspiral regimes, reducing statistical uncertainties in the fractional deviation parameters \\(\\Delta M_f/\\bar{M}_f\\) and \\(\\Delta\\chi_f/\\bar{\\chi}_f\\). Forecasts suggest that with the Einstein Telescope or Cosmic Explorer the precision on these parameters could reach the sub\u2011percent level, enabling detection of extremely small deviations from GR."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there any evidence in the GWTC\u20113 dataset of statistically significant deviations in the 1.5\u2011PN phase coefficient that would challenge the predictions of general relativity?<|assistant|>The GWTC\u20113 analysis performed parameterised tests on individual post\u2011Newtonian coefficients, including the 1.5\u2011PN term. Within the uncertainties reported, the 1.5\u2011PN coefficient was fully consistent with the general\u2011relativistic value; no statistically significant deviation was detected. However, the paper does not exhaustively explore all possible combinations of deviations or more exotic waveform systematics that could mimic a shift in this coefficient. Therefore, I cannot definitively confirm or rule out a subtle 1.5\u2011PN deviation beyond the scope of the presented analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected detection rate of binary neutron star mergers for the future KAGRA + LIGO + Virgo network at design sensitivity?<|assistant|>The paper does not provide a quantitative prediction for the detection rate of binary neutron star (BNS) mergers with the full network operating at design sensitivity. Estimating such a rate would require combining the projected horizon distances of each detector, the anticipated duty cycles, and the local BNS merger rate density\u2014information that is beyond the scope of this study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does operating KAGRA underground reduce coupling of environmental seismic noise compared to surface detectors like LIGO and Virgo?<|assistant|>Operating underground offers a significant reduction in seismic noise because the ground motion at depth is typically an order of magnitude lower than at the surface. Additionally, the underground environment is less affected by weather, human activity, and temperature fluctuations, all of which can introduce low\u2011frequency disturbances. The paper notes a lower low\u2011frequency noise floor for KAGRA, but detailed quantitative comparisons to LIGO and Virgo are not provided."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What technical challenges were encountered when implementing the DC readout scheme in KAGRA, and how were they addressed?<|assistant|>Switching from a radio\u2011frequency (RF) to a DC readout required installing an output mode cleaner and reconfiguring the signal extraction optics. Challenges included maintaining laser frequency stability, mitigating higher\u2011order mode contamination, and ensuring the new readout electronics could handle the increased dynamic range. The paper mentions the upgrade but does not delve into the specific troubleshooting steps or hardware modifications undertaken."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>During the GEO\u2013KAGRA joint run, what was the dominant noise source limiting sensitivity below 100\u202fHz, and what mitigation strategies were planned?<|assistant|>The dominant low\u2011frequency noise was identified as local control noise originating from the mirror suspension damping filters. To mitigate this, the team planned to redesign the damping filter parameters, improve sensor noise performance, and implement more robust feed\u2011forward cancellation of environmental disturbances."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the impact of enforcing a single\u2011polarization reconstruction constraint in the coherent WaveBurst (cWB) analysis on detection efficiency for real gravitational\u2011wave signals in a two\u2011detector network?<|assistant|>Applying a single\u2011polarization constraint reduces background from noise glitches by limiting the parameter space of admissible waveforms. However, for a two\u2011detector network with non\u2011aligned arms, genuine signals that excite both polarizations can have part of their energy suppressed in the reconstruction, potentially lowering the detection efficiency. The paper notes this trade\u2011off but does not quantify the efficiency loss for specific signal morphologies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main challenges in separating low\u2011energy kaons from protons in a liquid\u2011argon time\u2011projection chamber, and how can the deposited energy per unit length (dE/dx) be used to overcome them?<|assistant|>Low\u2011energy kaons (p_K \u2272 350\u00a0MeV/c) and protons have similar masses and thus deposit comparable amounts of ionization in liquid argon, especially in the Bragg peak region where both exhibit a sharp rise in dE/dx. The primary challenges are: (1) the intrinsic overlap of their dE/dx distributions due to statistical fluctuations in ionization and recombination; (2) the finite spatial resolution and noise of the readout system, which smears the dE/dx profile; and (3) the presence of other hadrons (pions, muons) that can mimic the kaon signature if mis\u2011reconstructed. To disentangle the two species, one exploits the full residual\u2011range dE/dx profile: a proton track continues to deposit energy at a nearly constant rate until it stops, whereas a kaon shows a pronounced Bragg peak at the end of its trajectory. By fitting the dE/dx versus residual range with a Landau\u2013Gaussian convolution and applying a likelihood or \u03c7\u00b2 test under the kaon and proton hypotheses, the probability of each hypothesis can be quantified, allowing a statistically robust separation even in the presence of detector noise."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can precise measurements of the kaon stopping power in liquid argon enhance the sensitivity of future proton\u2011decay searches?<|assistant|>Accurate knowledge of the kaon stopping power (dE/dx as a function of residual range) directly impacts the reconstruction of the kaon kinetic energy and its decay vertex. In proton\u2011decay searches targeting the p \u2192 K\u207a\u202f\u03bd\u0304 channel, the signal consists of a mono\u2011energetic K\u207a that comes to rest before decaying. If the stopping power is well\u2011known, the detector can reliably identify the Bragg peak, estimate the initial momentum, and suppress backgrounds that produce non\u2011rest\u2011decay kaons or mimic the signature. Moreover, a precise stopping\u2011power model allows for better calibration of the calorimetric response, reducing systematic uncertainties on the kaon energy scale and thus tightening the selection criteria. Consequently, the overall efficiency for proton\u2011decay detection increases while the background acceptance decreases, improving the experiment\u2019s lower limit on the proton lifetime."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which systematic uncertainties have the largest impact on the calorimetric reconstruction of stopping kaons in large liquid\u2011argon TPCs?<|assistant|>The dominant systematic sources are: (1) **Calorimetric calibration** \u2013 uncertainties in the conversion from collected charge to deposited energy (typically ~2\u20133\u202f%); (2) **Space\u2011charge effects** \u2013 distortions of the electric field due to positive ion accumulation, affecting drift paths and charge collection (~1\u202f% after correction); (3) **Electron\u2011diverter failures** \u2013 mis\u2011reconstruction of tracks that cross APA gaps, leading to artificial track splits (systematic shift of ~5\u202f% in track length); (4) **Proton background modeling** \u2013 mismodeling of stopping proton rates, which can bias the kaon dE/dx distribution (~1\u202f%); and (5) **Recombination model uncertainties** \u2013 variations in the Modified Box or Thomas\u2013Imel parameters (~1\u202f%). These effects are typically combined in quadrature to estimate the total systematic uncertainty on the reconstructed kaon energy and dE/dx profile."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In proton\u2011decay searches, how does the angular distribution of muon daughters from kaon decays assist in rejecting background events?<|assistant|>A K\u207a that decays at rest produces a muon with a uniform (isotropic) angular distribution relative to the kaon track, because the decay is two\u2011body and the kaon\u2019s momentum is negligible. In contrast, muons produced by charged\u2011current neutrino interactions or by inelastic pion or proton scattering tend to be highly forward\u2011peaked, inheriting the direction of the parent hadron. By measuring the cosine of the angle between the kaon candidate and its muon daughter, events with cos\u202f\u03b8\u202f<\u202f0.6 can be selected, effectively rejecting the forward\u2011peaked background while retaining most of the isotropic signal. This geometrical cut, when combined with dE/dx and range information, provides a powerful handle on background suppression."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the exact efficiency of the ProtoDUNE\u2011SP detector for detecting K\u207a decays at rest when using the photon detection system?<|assistant|>The answer to this question is currently unknown. The ProtoDUNE\u2011SP data set used in the analysis did not employ the photon detection system for the kaon selection; instead, only the charge readout was relied upon. While the photon system can, in principle, provide additional timing and energy\u2011deposition information (e.g., detecting the prompt scintillation from the kaon stop and the delayed Michel electron from the muon decay), a quantitative efficiency measurement that incorporates photon signals has not yet been performed. Such a study would require dedicated calibration runs, precise modeling of the photon collection efficiency, and a comprehensive assessment of the detector\u2019s optical response\u2014all of which are still topics of ongoing research."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would the track\u2011length extension fitting (TLEFit) algorithm perform for charged particles whose kinetic energy exceeds 1\u202fGeV, a regime where the dE/dx curve becomes almost flat (MIP region)?<|assistant|>At high kinetic energies the Bethe\u2013Bloch dE/dx curve has a very shallow slope, so the residual\u2011range versus dE/dx relationship provides weak discriminating power. The TLEFit algorithm would still fit an offset, but the resulting energy resolution would degrade and the fitted offset would tend to converge to a value that corresponds to the minimum\u2011ionizing plateau, leading to a systematic bias toward lower energies. In practice one would need to supplement the fit with additional information (e.g., multiple\u2011scattering angles or calorimetric deposits) to recover acceptable resolution above ~1\u202fGeV."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the TLEFit technique be adapted to determine the kinetic energy of neutral hadrons, such as neutrons, by exploiting the ionization signatures of the secondary charged particles they produce?<|assistant|>Neutrons do not ionize directly, so the TLEFit algorithm cannot be applied to the neutron itself. However, if a neutron undergoes a hadronic interaction that produces one or more charged secondaries with measurable tracks, the TLEFit algorithm can be used on each charged secondary individually to infer its kinetic energy. The total neutron energy would then be estimated by summing the reconstructed energies of all secondaries and adding the energy carried by undetected neutrons, which introduces a large, event\u2011by\u2011event uncertainty. Thus, TLEFit is useful for charged products but not for a direct neutron energy measurement."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant systematic uncertainties introduced by the modified\u2011box recombination model parameters (\u03b1 and \u03b2\u2032) when applying the TLEFit algorithm in a liquid\u2011argon TPC?<|assistant|>The recombination model translates the measured ionization charge (dQ/dx) into energy loss (dE/dx). Uncertainties in \u03b1 and \u03b2\u2032 propagate directly into the dE/dx PDFs used by TLEFit. A \u00b11\u202f\u03c3 shift in \u03b1 changes the low\u2011dE/dx tail of the distribution, while a shift in \u03b2\u2032 mainly affects the high\u2011dE/dx (Bragg\u2011peak) region. These changes alter the likelihood landscape, leading to systematic shifts in the fitted offset and hence a bias in the reconstructed kinetic energy. In the ProtoDUNE\u2011SP study, variations of \u00b11\u202f\u03c3 in \u03b1/\u03b2\u2032 produced fractional\u2011bias shifts up to ~3\u202f% for 300\u202fMeV pions, and an uncertainty band of ~1\u20132\u202f% on the energy resolution. Therefore, precise calibration of the recombination parameters is critical for accurate TLEFit performance."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the presence of a magnetic field in a liquid\u2011argon TPC influence the assumptions underlying the TLEFit algorithm?<|assistant|>A magnetic field bends charged particle trajectories, introducing curvature that alters the true path length relative to the straight\u2011line distance between reconstructed hits. The TLEFit algorithm assumes that the measured residual range corresponds to the straight\u2011line distance along the true track, which is violated in a magnetic field. The resulting systematic bias can be mitigated by incorporating track curvature into the residual\u2011range calculation or by performing a 3\u2011D helical fit before applying TLEFit. Additionally, the magnetic field affects multiple scattering by reducing lateral deflections, which may slightly change the dE/dx distribution width, but this effect is subdominant compared to the path\u2011length distortion."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it possible to extend the TLEFit algorithm to reconstruct the kinetic energy of electrons that emit Bremsstrahlung photons while traversing liquid argon?<|assistant|>The paper does not address this scenario, and the current TLEFit framework assumes a single, continuous charged track with a monotonic residual\u2011range vs. dE/dx relationship. Electrons undergoing Bremsstrahlung experience significant energy loss in discrete photon emission events, leading to kinks and discontinuities in the dE/dx profile that violate the assumptions of the algorithm. Therefore, we do not yet know whether TLEFit can be adapted for such electrons without substantial modification or additional reconstruction steps, and further study would be required to evaluate its feasibility."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the most sensitive frequency band for all-sky searches of continuous gravitational waves from isolated neutron stars using third\u2011generation detectors?<|assistant|>In all\u2011sky searches conducted with third\u2011generation interferometers, the most sensitive band typically lies between about 50\u202fHz and 250\u202fHz. Within this range the detector noise floor is lowest and the Doppler modulation is modest, allowing the longest coherent integrations and the highest upper\u2011limit depths."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can continuous gravitational\u2011wave signals from rapidly rotating neutron stars be distinguished from instrumental lines in the data?<|assistant|>Continuous\u2011wave searches apply a combination of vetoes: (1) cross\u2011detector coincidence requirements to ensure the signal is present in multiple interferometers; (2) line\u2011persistency checks that flag features consistent with known narrow\u2011band disturbances; (3) consistency tests comparing the signal\u2019s frequency evolution to the expected Doppler pattern from Earth\u2019s motion. Only candidates that survive all these stages are considered astrophysical."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What upper limits can be set on the ellipticity of a neutron star located 200\u202fpc away and spinning at 300\u202fHz?<|assistant|>Using the most optimistic sensitivity depth for the 200\u2013400\u202fHz band, a neutron star at 200\u202fpc spinning at 300\u202fHz would have its ellipticity constrained to be below roughly \\(3\\times10^{-7}\\). This follows from the relation \\(\\varepsilon \\propto h_{0} d f^{-2}\\) and the strain upper limit of \\(\\sim1\\times10^{-25}\\) in that band."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can current all\u2011sky searches place constraints on the abundance of primordial black holes with masses below \\(10^{-5}\\,M_{\\odot}\\) that inspiral within the Galaxy?<|assistant|>Yes. By treating such binaries as continuous\u2011wave emitters with nearly monochromatic signals, the upper limits on strain translate into limits on the merger rate and abundance of light primordial black holes. The analysis shows that, for chirp masses below \\(10^{-5}\\,M_{\\odot}\\), the rate of inspirals within the solar neighbourhood must be lower than a few events per million years, constraining the fraction of dark matter that could be in the form of such primordial black holes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there evidence for continuous gravitational\u2011wave emission from neutron stars in binary systems using the methods described in the paper?<|assistant|>I do not have a definitive answer. The analysis in question focuses on isolated neutron stars, employing semi\u2011coherent pipelines tailored for solitary sources. Detecting continuous waves from neutron stars in binaries requires additional templates to account for orbital Doppler shifts and a different set of search parameters. Since this study did not explore binary parameter spaces, any conclusions about binaries would lie beyond its documented scope and would need a dedicated search strategy."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the total inelastic cross section for positively charged pions scattering off argon vary across the kinetic\u2011energy range 200\u202fMeV to 800\u202fMeV, and which resonance structures are primarily responsible for the observed energy dependence?<|assistant|>The total inelastic \u03c0\u207a\u2013Ar cross section rises from a few hundred millibarns near 200\u202fMeV, reaches a pronounced maximum around the \u0394(1232) resonance (\u2248\u202f150\u2013170\u202fMeV in the laboratory frame), and then gradually decreases towards 800\u202fMeV as higher\u2011mass resonances and multi\u2011pion production channels open. The \u0394(1232) dominates the rise, while the subsequent fall is influenced by the onset of inelastic channels such as \u0394(1700) and the opening of the two\u2011pion production threshold."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which systematic effects most significantly impact the precision of proton\u2013argon total inelastic cross\u2011section measurements at sub\u2011GeV energies, and what strategies can be employed to reduce these uncertainties in future LArTPC studies?<|assistant|>The dominant systematic contributions are: (1) finite Monte\u2011Carlo statistics that propagate through the unfolding and efficiency corrections; (2) background modelling, especially the rates of elastic scattering and stopping\u2011proton contamination; (3) energy\u2011reconstruction uncertainties tied to the stopping\u2011power model (Bethe\u2011Bloch) and detector calibration; and (4) space\u2011charge distortion corrections that alter track length and energy deposition. Mitigation can be achieved by increasing the simulated event sample size, refining background estimators with data\u2011driven sidebands, improving the calibration of the energy scale (e.g., via dedicated calibration beams), and developing more accurate space\u2011charge maps or correcting algorithms."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what manner do final\u2011state interactions (FSI) of charged pions inside liquid argon affect the reconstruction of neutrino energy in DUNE, and how can improved \u03c0\u207a\u2013Ar cross\u2011section data contribute to reducing these effects?<|assistant|>FSI can absorb or re\u2011scatter pions, altering their energy, direction, and multiplicity before they exit the nucleus. This leads to mis\u2011estimation of the neutrino energy when relying on the observed hadronic system. Precise \u03c0\u207a\u2013Ar cross\u2011section data enable better tuning of intranuclear cascade models, thereby reducing uncertainties in pion absorption and scattering probabilities. Consequently, energy\u2011reconstruction algorithms can incorporate more realistic FSI probabilities, improving the fidelity of reconstructed neutrino energies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the empirical scaling law \u03c3\u202f\u221d\u202fA^{2/3} for hadron\u2013nucleus total cross sections hold for argon when compared to lighter nuclei such as carbon and heavier nuclei such as lead, based on the most recent experimental data?<|assistant|>Recent measurements indicate that the total inelastic cross section for \u03c0\u207a\u2013Ar and p\u2013Ar lies on the same A^{2/3} trend defined by other nuclei, with argon\u2019s cross sections roughly scaling between the values observed for carbon (A\u202f=\u202f12) and lead (A\u202f=\u202f208). The data show good agreement with the empirical exponent, suggesting that nuclear size and surface effects dominate the energy dependence across this range of target masses."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the differential (angular and momentum) distribution of secondary nucleons produced in \u03c0\u207a\u2013Ar inelastic interactions at a pion kinetic energy of 600\u202fMeV, and how does this distribution impact calorimetric energy reconstruction in liquid\u2011argon time\u2011projection chambers?<|assistant|>I do not have information on the differential nucleon spectra for \u03c0\u207a\u2013Ar at 600\u202fMeV kinetic energy, as this specific observable was not measured or reported in the data set discussed. Determining these distributions would require dedicated experiments or detailed simulations that explicitly model the intra\u2011nuclear cascade and nucleon emission processes for this energy regime. Without such data, one cannot accurately assess how the secondary nucleon kinematics influence calorimetric reconstruction in LArTPC detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the typical sky\u2011localization uncertainties for gravitational\u2011wave events detected by a network of advanced interferometers?<|assistant|>For binary black\u2011hole mergers observed by the LIGO\u2013Virgo network, the 90\u202f% confidence sky area typically ranges from a few tens to several hundred square degrees, depending on the signal\u2011to\u2011noise ratio, the relative orientation of the detectors, and the waveform model used. The median 90\u202f% area for the first detections was on the order of 200\u2013300 deg\u00b2."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the choice of parameter\u2011estimation pipeline (e.g., BAYESTAR vs. LALInference) influence the reported sky maps for a gravitational\u2011wave trigger?<|assistant|>Fast sky\u2011localization tools like BAYESTAR provide rapid estimates by marginalizing over distance and mass parameters with analytic approximations, yielding relatively compact 90\u202f% confidence regions. Full Bayesian samplers such as LALInference use the complete likelihood over all parameters, often resulting in slightly larger but more accurate maps that incorporate calibration uncertainties and more realistic priors. Consequently, LALInference maps are usually adopted as the definitive localization for follow\u2011up planning."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What electromagnetic signatures are theoretically expected from a binary black\u2011hole merger in a gas\u2011rich environment?<|assistant|>In dense circumbinary disks or accretion flows, a merger can perturb the surrounding gas, potentially generating a prompt flare or a longer\u2011lasting afterglow across radio to X\u2011ray wavelengths. Models predict a burst of synchrotron emission as shock waves form, followed by a gradually declining spectrum. However, the exact luminosity depends on poorly constrained parameters such as disk density, magnetic field strength, and spin alignment."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the maximum distance out to which an optical transient associated with a binary black\u2011hole merger could be detected with current survey telescopes?<|assistant|>Optical surveys with limiting magnitudes around 22\u201323\u202fmag can, in principle, detect kiloparsec\u2011scale transients out to roughly 100\u202fMpc if the event is intrinsically luminous. For binary black\u2011hole mergers, expected optical emission is far fainter, so practical detection horizons are much closer\u2014tens of megaparsecs\u2014unless an exceptionally bright flare occurs."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected optical afterglow brightness of a binary black\u2011hole merger occurring at 400\u202fMpc?<|assistant|>I do not have information on this specific scenario. The paper does not provide theoretical or empirical predictions for optical afterglow brightness at such a distance for binary black\u2011hole mergers, and detailed modeling would be required to estimate the flux, which is beyond the scope of the present data."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the number of detectors in a gravitational\u2011wave network influence the accuracy of sky localization for binary black hole events?<|assistant|>Adding more detectors narrows the triangulation baselines, reduces the timing uncertainty, and improves the determination of the source\u2019s position on the sky. With three or more detectors the sky area for a typical binary black hole event can shrink from hundreds of square degrees to a few tens of square degrees."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main observational challenges when performing broadband electromagnetic follow\u2011up of gravitational\u2011wave events with large localization uncertainties?<|assistant|>The primary challenges are (1) the need to tile very large areas of sky with limited field\u2011of\u2011view instruments, (2) coordinating many facilities to avoid duplication while maximizing coverage, (3) achieving sufficient depth quickly enough to catch fast transients, and (4) handling the large number of unrelated transients that appear in the search area."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can galaxy catalog information be leveraged to prioritize electromagnetic follow\u2011up observations for gravitational\u2011wave triggers?<|assistant|>By cross\u2011matching the probability sky map with catalogs of nearby galaxies (e.g., with stellar mass or star\u2011formation rate weighting) observers can assign higher priority to tiles containing galaxies within the expected distance range, thereby concentrating limited resources on the most likely host candidates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the theoretical mechanisms that could enable a binary black hole merger to produce an electromagnetic counterpart?<|assistant|>The current literature does not provide a definitive mechanism. Some speculative scenarios involve interaction with a dense circumbinary environment, residual accretion disks, or magnetic fields strong enough to power a short burst. However, no robust model has yet shown that such conditions are common or produce detectable emission, so the question remains largely open."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role does low\u2011latency analysis play in enabling rapid electromagnetic follow\u2011up, and what improvements are needed for future runs?<|assistant|>Low\u2011latency pipelines generate alerts within minutes of a gravitational\u2011wave detection, allowing telescopes to start observations before a transient fades. Improvements needed include faster parameter estimation (especially sky localization), real\u2011time assessment of the source type, and integration with automated scheduling systems to reduce human\u2011induced delays."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the total inelastic cross section of positively charged kaons on argon change as a function of kinetic energy between 2\u202fGeV and 5\u202fGeV?<|assistant|>The cross section generally rises from a few hundred millibarns at 2\u202fGeV, reaches a broad maximum around 4\u20135\u202fGeV, and then slowly levels off or slightly decreases. This trend reflects the onset of additional inelastic channels (e.g., multi\u2011pion production) and the diminishing influence of the Coulomb barrier as the kaon energy increases."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the consequences of improved kaon\u2013argon interaction modeling for proton\u2011decay searches in liquid\u2011argon TPCs?<|assistant|>Better modeling reduces systematic uncertainties in the simulation of kaon propagation and absorption, leading to a more accurate estimation of detection efficiencies for signatures such as \\(p \\rightarrow \\nu K^+\\). This in turn tightens the experimental limits on the proton lifetime and enhances the robustness of any observed excess."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the thin\u2011slice technique used for kaon\u2013argon cross\u2011section measurements be applied to study neutron\u2013argon interactions in a liquid\u2011argon TPC?<|assistant|>Yes. By treating each wire plane as a thin target, one can count incident neutrons and the number that interact or produce secondary particles in successive slices. The main challenge is identifying neutrons, which require time\u2011of\u2011flight or delayed capture signatures, but with adequate tagging the method can yield differential neutron\u2013argon cross sections."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the measured cross section for negatively charged kaons on argon in the 5\u201310\u202fGeV energy range?<|assistant|>This quantity has not yet been measured experimentally. Existing hadronic interaction generators provide only model predictions, and without dedicated beam\u2011test data the precise value\u2014and its energy dependence\u2014remains uncertain."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the space\u2011charge effect in a liquid\u2011argon TPC impact the reconstruction of charged\u2011kaon tracks, and what strategies can mitigate this?<|assistant|>Space charge builds up electric\u2011field distortions, causing reconstructed positions and directions to shift by several millimetres. For kaon tracks, this can bias the measured energy loss and vertex location. Mitigation techniques include applying a three\u2011dimensional space\u2011charge correction map derived from cosmic\u2011ray muon data, using external alignment sensors, and incorporating the corrections into the reconstruction algorithms to recover the true track geometry."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the primary advantages of a vertical\u2011drift LArTPC design compared to a traditional horizontal\u2011drift geometry for the DUNE far detector?<|assistant|>A vertical\u2011drift geometry allows a longer drift path (up to ~6.5\u202fm per side) while keeping the maximum electron drift time short enough to avoid excessive electron recombination and diffusion. The cathode can be suspended centrally, creating two symmetric drift volumes that maximize the active liquid\u2011argon volume. Additionally, the vertical orientation reduces the number of wire planes needed and simplifies the anode plane assembly, leading to lower construction costs and fewer feed\u2011throughs."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the cathode module design influence both the electric field uniformity and photon\u2011detector performance in the vertical\u2011drift module?<|assistant|>The cathode is made of a thin, highly resistive composite panel that is suspended from the top of the detector. Its surface is perforated to allow light from the surrounding field\u2011cage to pass through, improving photon collection. The field\u2011cage modules around the cathode are constructed with narrow aluminum profiles in the first 4\u202fm from the cathode to provide 70\u202f% optical transparency, while the outer region uses wider profiles to maintain the field gradient. This combination ensures a uniform drift field (\u22641\u202f% variation) while allowing photons to reach both cathode\u2011mounted and membrane\u2011mounted photon\u2011detector modules."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main technical challenges involved in producing and qualifying the large charge\u2011readout planes (CRPs) for a full 17.5\u202fkt vertical\u2011drift module?<|assistant|>Key challenges include (1) maintaining the mechanical planarity of the 3.2\u202fmm\u2011thick perforated PCBs over a 1.5\u202fm\u202f\u00d7\u202f1.5\u202fm area, (2) ensuring precise alignment of the two PCB halves to guarantee 100\u202f% electron transmission through the holes, (3) producing and testing a large number of high\u2011performance LArASIC front\u2011end ASICs under cryogenic conditions, (4) achieving the required electrical shielding and grounding on both the induction and collection planes, and (5) integrating the CRP into the cryostat\u2019s support structure while preserving the 5\u202fmm gap between adjacent planes for optical access and mechanical tolerances."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What effect does a 10\u202fppm xenon doping have on the photon\u2011detector light yield and timing in the vertical\u2011drift Far Detector?<|assistant|>Xenon doping shifts a substantial fraction (\u2248\u202f53\u202f%) of the scintillation light from 128\u202fnm to 176\u202fnm. The longer\u2011wavelength photons experience less Rayleigh scattering and absorption, improving the overall light collection efficiency by roughly 20\u201330\u202f%. Additionally, xenon dimers have a shorter decay time (\u2248\u202f4\u202f\u00b5s) compared to pure argon, leading to a faster prompt component and improved timing resolution for low\u2011energy events such as supernova neutrinos."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How will the long\u2011term stability of the high\u2011voltage divider board (HVDB) affect the electron lifetime and detector performance over a 10\u2011year operation period?<|assistant|>The long\u2011term stability of the HVDB is critical because any drift in the resistor values or degradation of the high\u2011voltage insulation can alter the field uniformity and thus impact electron drift times and recombination rates. Current studies have not yet quantified how these changes will influence the electron lifetime over a decade, as the HVDB materials and their behavior under continuous cryogenic exposure are still under investigation. Further long\u2011term aging tests and in\u2011situ monitoring of the field uniformity are needed to assess the impact on detector performance and to ensure that the electron lifetime remains within the required specification."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the total inelastic \u03c0+\u2013argon cross section evolve below 500\u00a0MeV kinetic energy?<|assistant|>The study presented focuses on the 500\u2013800\u00a0MeV range, so the behaviour of the cross section at lower energies is not covered. Determining the cross section below 500\u00a0MeV would require dedicated data at those energies and possibly different detector optimisation, which are not available in the current analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the angular distribution of the outgoing protons in \u03c0+ absorption on argon?<|assistant|>The paper reports overall absorption rates but does not provide detailed angular spectra for the recoil protons. Such information would need a separate reconstruction study focusing on proton kinematics and a larger event sample to achieve sufficient statistical precision."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the measured \u03c0+\u2013argon charge\u2011exchange cross section be used to constrain the pion mean free path in liquid argon for neutrino interaction simulations?<|assistant|>Yes, the measured charge\u2011exchange cross section directly informs the mean free path of charged pions in argon, which is a key parameter in neutrino event generators. Incorporating these results can improve the modelling of final\u2011state interactions in neutrino detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do space\u2011charge effects impact the reconstruction of low\u2011momentum \u03c0+ tracks in a large LArTPC?<|assistant|>Space\u2011charge distortions can shift the apparent positions of ionisation deposits, potentially biasing the energy and direction reconstruction of low\u2011momentum tracks. Understanding and correcting for these effects is essential for accurate cross\u2011section measurements but requires detailed calibration studies beyond the scope of the presented analysis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the cross section for \u03c0+\u2013argon interactions that produce a single \u03c00 in the final state without any charged pions above 150\u00a0MeV/c?<|assistant|>The paper defines a charge\u2011exchange channel that requires at least one \u03b3 from a \u03c00 decay but does not isolate events with exactly one \u03c00 and no charged pions. Measuring this specific final\u2011state cross section would necessitate additional event selection criteria and higher\u2011statistics data, which are not part of the current study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What astrophysical processes can generate high\u2011energy neutrinos at the same time as gravitational\u2011wave bursts?<|assistant|>Relativistic outflows produced during the collapse of massive stars, mergers of compact binaries, or interactions of jets with surrounding material can accelerate protons to very high energies. These protons then interact with photons or ambient gas to produce charged pions that decay into high\u2011energy neutrinos, while the violent dynamics of the system emit gravitational waves."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the gravitational\u2011wave energy output of a binary neutron star merger compare to that of a core\u2011collapse supernova?<|assistant|>A binary neutron star merger typically radiates a few percent of a solar mass in gravitational waves (\u224810\u207b\u00b2\u202fM\u2299c\u00b2), concentrated around a few hundred hertz. A core\u2011collapse supernova is expected to emit much less, usually \u226410\u207b\u2077\u202fM\u2299c\u00b2, unless the core is rapidly rotating or otherwise dynamically unstable."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What observational advantages does a joint gravitational\u2011wave and neutrino detection offer over single\u2011messenger observations?<|assistant|>The precise timing of a gravitational\u2011wave burst coupled with the directional information from a high\u2011energy neutrino allows a dramatic reduction in the sky localization area, enabling faster and more targeted electromagnetic follow\u2011up. It also provides a cross\u2011check that the transient is indeed astrophysical rather than instrumental or atmospheric."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way could the detection of neutrinos from a core\u2011collapse supernova inform us about the mechanism of jet formation within the stellar envelope?<|assistant|>Neutrinos produced in a choked jet scenario would carry information about the density, magnetic field, and particle acceleration conditions inside the envelope. Measuring their energy spectrum and arrival time relative to the gravitational wave could constrain the jet launch delay, opening angle, and baryon loading, which are key parameters in jet\u2011formation models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Has the recent multi\u2011messenger search set definitive limits on the rate of binary neutron star mergers that emit both gravitational waves and high\u2011energy neutrinos?<|assistant|>No. The analysis provides only upper limits on the combined population of gravitational\u2011wave and high\u2011energy\u2011neutrino emitters in general. It does not specifically constrain binary neutron star mergers because the limits depend on generic assumptions about the neutrino spectrum and beaming, which may not apply to all BNS systems."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do temperature gradients within a liquid argon TPC affect the electron attachment rate to electronegative impurities?<|assistant|>Electron attachment rates are highly sensitive to temperature because the mobility of impurity molecules and the electron mean free path change with thermal motion. In practice, a temperature rise of 1\u202fK in the liquid argon can increase the attachment rate by roughly 5\u202f%\u201310\u202f% for typical oxygen or water concentrations. Consequently, even small temperature gradients across a detector volume can lead to measurable variations in the drift\u2011electron lifetime. Experimental studies on small LArTPC prototypes have confirmed that maintaining isothermal conditions within \u00b10.2\u202fK is essential for stable operation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the time evolution of impurity concentration when the argon recirculation pump is turned off for a few hours in a large\u2011scale LArTPC?<|assistant|>During pump downtime the liquid argon is no longer actively filtered, so the dominant source of contamination is the outgassing of detector components and the diffusion of residual impurities from the gas phase. In a typical 10\u2011ton module, the oxygen equivalent concentration can increase by about 10\u201315\u202fppb per hour, leading to a drift\u2011electron lifetime decrease of 10\u201315\u202f% per hour. After 24\u202fhours, the lifetime can fall from >20\u202fms to below 10\u202fms if no additional purification is applied."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it possible to calibrate space\u2011charge corrections in a LArTPC using only through\u2011going cosmic\u2011ray muons, without external timing detectors?<|assistant|>Yes. By reconstructing straight\u2011line tracks from cosmic\u2011ray muons that traverse the full drift volume, one can measure the apparent shift of the track endpoints as a function of drift time. These shifts directly encode the local electric\u2011field distortions caused by space charge. With sufficient statistics and a known timing reference from the detector clock, the correction maps can be derived internally, eliminating the need for external scintillator systems."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What minimum drift\u2011electron lifetime is required to keep the energy resolution for MeV\u2011scale neutrino interactions below 1\u202f% in a 5\u202fm drift LArTPC?<|assistant|>Simulations of MeV\u2011scale electromagnetic showers in a 5\u202fm drift TPC show that a lifetime of at least 15\u202fms is needed to limit the charge loss to <1\u202f%. With a lifetime of 20\u202fms the charge attenuation is below 0.6\u202f%, yielding an energy resolution better than 0.9\u202f% for a 5\u202fMeV deposition. Lifetimes below 10\u202fms start to degrade the resolution above 1\u202f%."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there a significant difference in electron lifetime between argon that has been purified primarily by removing water versus oxygen, and how does this affect charge collection?<|assistant|>The paper does not provide data comparing water\u2011only versus oxygen\u2011only purification. While both impurities attach electrons, oxygen has a higher attachment cross\u2011section, so an argon sample free of oxygen but still containing residual water would generally have a longer electron lifetime. However, the exact quantitative difference depends on the concentrations achieved by each purification method, and the current study does not address this comparison. Therefore, we cannot provide a definitive answer based on the present information."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the charged\u2011current muon\u2011neutrino interaction cross section on argon vary between the quasi\u2011elastic and resonance production regions when the neutrino beam is narrowly tuned to a fixed energy?<|assistant|>When the incoming neutrino energy is tightly constrained, the cross\u2011section in the quasi\u2011elastic (CCQE) region rises smoothly with energy, while the resonance (RES) region shows a pronounced peak near the \u0394(1232) mass. As the beam energy increases, the RES contribution becomes dominant above ~1\u202fGeV, causing the total inclusive cross section to steeply increase. A narrow virtual flux allows the CCQE peak to be isolated at lower energies and the \u0394 resonance peak to be resolved around 1\u20131.5\u202fGeV, providing a clear view of the transition between the two regimes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the principal systematic uncertainties that limit the precision of virtual\u2011flux cross\u2011section measurements with the DUNE\u2011PRISM near detector, and which strategies could reduce their impact?<|assistant|>The dominant systematics arise from (1) the neutrino flux shape and normalization, (2) the modeling of neutrino\u2011nucleus interactions (particularly final\u2011state interactions and 2p2h processes), and (3) detector response such as energy scale and particle\u2011ID efficiency. Mitigation strategies include: using external hadron\u2011production data to constrain flux uncertainties, applying Tikhonov regularization and flux\u2011matching techniques to minimise the amplification of statistical fluctuations, incorporating in\u2011situ calibration with known neutrino reactions, and developing robust unfolding algorithms that separate flux and interaction\u2011model effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the virtual\u2011flux technique be adapted to measure the neutrino\u2011neutron cross section on argon, and what experimental challenges would need to be overcome?<|assistant|>In principle, a narrow virtual flux can be used to probe neutrino\u2011neutron interactions by selecting final\u2011state topologies that are sensitive to neutrons (e.g., charged\u2011current quasi\u2011elastic scattering with a detected proton). Challenges include: distinguishing neutron\u2011induced events from proton\u2011induced ones, accounting for the lack of a free neutron target, handling the higher background from neutral\u2011current interactions, and accurately modeling the neutron\u2019s binding energy and Fermi motion in argon. Improved tracking and calorimetry, combined with sophisticated reconstruction of missing momentum, would be required."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the influence of final\u2011state interaction (FSI) modeling uncertainties on the measurement of the energy\u2011transfer differential cross section using virtual fluxes?<|assistant|>FSI affect the energies and directions of outgoing hadrons, thereby smearing the reconstructed energy transfer (\u03c9_reco). However, because the virtual flux is narrow in neutrino energy, the dominant smearing comes from the flux width rather than from FSI. Residual FSI uncertainties primarily distort the shape of the \u03c9_reco distribution, especially near the quasi\u2011elastic peak and in the dip between CCQE and resonance regions. Quantitatively, varying the FSI strength within reasonable bounds can change the differential cross\u2011section shape by a few percent, indicating that precise FSI modeling is still essential for sub\u201110% level measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the virtual\u2011flux construction preserve the relative energy dependence of two\u2011particle\u2013two\u2011hole (2p2h) contributions across different neutrino energies?<|assistant|>The paper does not address this specific question. While the virtual\u2011flux technique can isolate broad energy ranges, it is unclear whether the weighting procedure and regularization applied during flux matching retain the true energy dependence of the 2p2h component. Further studies, possibly with alternative target flux shapes and validation against detailed nuclear\u2011model predictions, are needed to determine whether 2p2h effects are faithfully represented in virtual\u2011flux\u2011averaged measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can machine learning techniques be integrated into the GPU-based simulation pipeline to predict detector response in real time?<|assistant|>Machine learning can be used to replace or augment physics\u2011based sub\u2011models within the simulation. For example, a deep neural network trained on high\u2011fidelity simulation data can predict the induced current waveform for a given ionization track, or learn the mapping from raw charge deposition to digitized ADC counts. By compiling the trained model with libraries such as TensorFlow\u2011Lite or ONNX Runtime and running it on the same GPU as the physics kernels, one can achieve real\u2011time inference. The network would be inserted after the electron drift and diffusion stage but before the ASIC digitization stage, reducing the number of explicit convolutional operations required. Validation would involve cross\u2011checking the ML\u2011predicted waveforms against a reference simulation over a broad range of track geometries and field configurations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the scalability limits of GPU\u2011accelerated LArTPC simulation when moving from a 0.5\u202fm\u00b3 detector to a 10\u202fm\u00b3 scale?<|assistant|>Scalability is governed by three factors: (1) memory consumption\u2014each charge segment requires a few tens of bytes for position, charge, diffusion parameters, and (2) the number of threads needed to cover all pixels, which grows linearly with the detector surface area; a 10\u202fm\u00b3 LArTPC may have on the order of 10\u2076 pixels, still within the 96\u2011GB memory of a modern V100 or A100 GPU if data are streamed in tiles; (3) kernel launch overhead and inter\u2011GPU communication. On a multi\u2011GPU node, the simulation can be partitioned spatially so that each GPU handles a sub\u2011volume, with halo exchanges for electrons that cross tile boundaries. With careful tiling and overlapping of computation and data transfer, a 20\u2011fold increase in volume can be simulated with only a modest increase in wall\u2011clock time, often remaining the dominant part of the pipeline."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the inclusion of space\u2011charge effects alter the electric field configuration in a pixelated LArTPC, and how can this be incorporated into the simulation?<|assistant|>Space\u2011charge from slowly drifting ions builds up a distortion in the nominal uniform field, typically reducing the drift velocity and altering the weighting field near the anode. To incorporate this, one can solve Poisson\u2019s equation on a 3\u2011D grid that includes the ion density field, using a fast solver (e.g., multigrid or FFT\u2011based). The resulting field map can then be interpolated for each electron step during drift. In a GPU implementation, the field map can be stored as a texture and accessed via bilinear interpolation, ensuring that the drift velocity and diffusion coefficients are updated dynamically. This adds a modest computational cost (\u224810\u202f% of the induced\u2011current kernel) while improving the fidelity for high\u2011rate or high\u2011ionization scenarios."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the systematic uncertainties introduced by using a fixed diffusion coefficient in the electron transport model, and how can they be quantified?<|assistant|>Assuming a single, constant diffusion coefficient neglects its dependence on the local electric field and temperature. The systematic uncertainty can be quantified by propagating the variance of the diffusion coefficient into the width of the induced current pulse. This is done by generating multiple simulations with diffusion coefficients sampled from a distribution (e.g., Gaussian with mean\u202f=\u202fvalue from data and \u03c3\u202f=\u202fexperimental uncertainty). The spread in the reconstructed charge or hit position then provides a direct estimate of the systematic error. In practice, varying the longitudinal and transverse diffusion by \u00b110\u202f% shows a shift of \u22483\u202f% in the charge\u2011collection efficiency for MIP tracks, which is comparable to the intrinsic ASIC noise."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the impact of non\u2011uniformities in the pixel pad geometry on the induced current signals, and how significant are these effects compared to the intrinsic noise of the ASIC?<|assistant|>The agent does not know the answer. This question requires detailed electromagnetic simulation of the actual pad geometry (e.g., variations in pixel size, edge effects, and inter\u2011pixel spacing) and its effect on the weighting field. The resulting variations in induced current are typically of the order of a few percent, which is comparable to or smaller than the intrinsic electronic noise (\u2248500\u202fe\u207b). A full study would involve measuring the actual pad layout, generating a refined FEM mesh, and re\u2011computing the current response, which is beyond the scope of the present work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does xenon doping affect the lifetime of free electrons in liquid argon?<|assistant|>Xenon is chemically inert and does not introduce additional electronegative impurities that would capture drifting electrons. In practice, a moderate xenon concentration (up to a few tens of ppm) has been observed to have a negligible effect on the free\u2011electron lifetime in large liquid\u2011argon TPCs. The primary factor that governs electron lifetime remains the concentration of oxygen, water, and other electronegative contaminants; xenon addition does not significantly change the attachment rates. Consequently, detectors that operate with a few\u2011ppm xenon doping typically report electron lifetimes that are comparable to those measured in undoped argon, provided that the xenon itself is of high purity and that the purification system remains effective."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the optimal xenon concentration for maximizing light yield while minimizing cost for a 10\u2011kt liquid\u2011argon detector?<|assistant|>In large\u2011volume LArTPCs the light yield improvement from xenon doping is a diminishing\u2011returns process. Empirical studies on 100\u2011kg to 1\u2011kt prototypes show that a xenon concentration of 10\u201315\u202fppm (by mass) yields about a 30\u201340\u202f% increase in total scintillation light, after which the gain saturates. For a 10\u2011kt detector the cost of xenon scales linearly with the amount required; 15\u202fppm in 10\u202fkt corresponds to roughly 150\u202fkg of xenon. Considering the high price of xenon (\u2248\u202f\\$100\u202fkg\\(^{-1}\\)) and the marginal increase in light yield beyond 15\u202fppm, many groups recommend targeting the 10\u201312\u202fppm range as a cost\u2011effective compromise. This choice maximizes light collection and pulse\u2011shape discrimination performance while keeping xenon expenses manageable."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can xenon doping improve pulse\u2011shape discrimination between electron and nuclear recoils in liquid argon?<|assistant|>Xenon doping modifies the relative contributions of the fast (singlet) and slow (triplet) scintillation components. By transferring energy from the argon triplet state to xenon, the overall pulse shape becomes faster and the distinction between electron\u2011like (shorter fast component fraction) and nuclear\u2011recoil events (higher fast component fraction) can be sharpened. Experiments with small\u2011scale detectors have demonstrated an improvement in pulse\u2011shape discrimination (PSD) metrics by 10\u201320\u202f% when operating at \u2248\u202f10\u202fppm xenon, especially at lower energies where the triplet component dominates. However, the benefit plateaus for higher xenon concentrations because the fast component becomes dominated by xenon scintillation, which has its own PSD characteristics. Therefore, xenon doping can enhance PSD, but only up to an optimal concentration that balances the competing light\u2011yield and PSD contributions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the presence of nitrogen at 5\u202fppm alter the Rayleigh scattering length of argon scintillation photons?<|assistant|>Nitrogen is essentially transparent to the vacuum\u2011ultraviolet (VUV) photons in liquid argon, so it does not directly affect the Rayleigh scattering cross\u2011section. The scattering length of 127\u202fnm photons in pure liquid argon is about 1.8\u202fm. Adding 5\u202fppm of nitrogen introduces only a tiny change in the refractive index; the resulting modification to the Rayleigh scattering length is on the order of a few millimetres\u2014well below the experimental resolution. Thus, the presence of 5\u202fppm nitrogen does not meaningfully alter the photon transport properties in the bulk liquid. The dominant effect of nitrogen at this concentration is quenching of the argon triplet state, which reduces the overall light yield but leaves the scattering length unchanged."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does xenon doping affect the drift field uniformity in a large liquid argon TPC?<|assistant|>The model does not have information from the paper that directly addresses this question, so it cannot provide a definitive answer. In principle, xenon is an inert noble gas that does not alter the dielectric constant of liquid argon by a measurable amount at ppm concentrations, so the electric\u2011field distribution determined by the cathode, anode, and field\u2011shaping rings should remain essentially unchanged. However, any subtle changes would depend on the exact detector geometry and the purity of the xenon added. Further detailed electro\u2011static simulations and dedicated measurements would be required to confirm whether drift\u2011field uniformity is affected at the ppm\u2011level doping studied in the paper."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the leading theoretical models that predict gravitational-wave emission from fast radio burst progenitors?<|assistant|>Current models suggest that compact binary coalescences (binary neutron stars or neutron star\u2013black hole systems) can produce both the rapid radio pulses and a short-lived burst of gravitational waves through magnetic interactions or tidal disruption. Additionally, magnetar flares or giant magnetar outbursts can excite stellar oscillation modes that generate gravitational waves, especially in the kilohertz range."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the dispersion measure of a fast radio burst help estimate its cosmological distance?<|assistant|>The dispersion measure (DM) quantifies the total column density of free electrons along the line of sight. By subtracting modeled contributions from the Milky Way, its halo, and the host galaxy, the remaining intergalactic DM can be mapped to redshift using empirical relations (e.g., the Macquart relation). This provides a statistical distance estimate, often expressed as a 90% credible interval due to large uncertainties."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main differences between a model\u2011based and a generic (unmodelled) gravitational\u2011wave search pipeline when targeting short\u2011duration transients?<|assistant|>A model\u2011based pipeline, such as matched\u2011filtering with a template bank, assumes a specific waveform morphology (e.g., binary inspiral) and maximizes sensitivity for that scenario, but may miss unexpected signals. A generic pipeline uses coherent excess\u2011power or time\u2011frequency clustering to detect any transient, regardless of shape, offering broader coverage at the cost of reduced sensitivity for any single waveform type."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What challenges arise when searching for gravitational\u2011wave counterparts to fast radio bursts detected by wide\u2011field radio telescopes like CHIME/FRB?<|assistant|>Key challenges include large sky\u2011localization uncertainties that require scanning many sky patches, limited detector duty cycles leading to sparse data coverage, and the need to account for significant uncertainties in FRB distances derived from DM. Additionally, the short timescales of FRBs demand rapid, low\u2011latency data analysis to correlate with gravitational\u2011wave events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there conclusive evidence linking any fast radio burst to a gravitational\u2011wave detection during the third observing run of Advanced LIGO and Virgo?<|assistant|>The current analysis does not find any statistically significant gravitational\u2011wave signal coincident with the observed fast radio bursts. Therefore, we cannot claim a definitive association. This lack of evidence may be due to either the absence of detectable gravitational\u2011wave emission from these bursts, insufficient detector sensitivity at the relevant distances, or the intrinsic rarity of such joint events. Further observations with more sensitive detectors or a larger FRB sample are required to confirm or rule out this association."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the mass ratio of a neutron star\u2013black hole binary influence the morphology of its gravitational\u2011wave signal, and what are the consequences for extracting component masses with next\u2011generation detectors?<|assistant|>The mass ratio determines the amplitude ratio between the dominant quadrupole mode and higher\u2011order modes; highly asymmetric systems exhibit stronger higher\u2011order multipole contributions, which can bias mass estimates if not modeled accurately. Advanced detectors with improved low\u2011frequency sensitivity will better capture early inspiral, helping to disentangle mass ratio effects and reduce systematic errors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What can the measurement of the effective inspiral spin parameter tell us about the natal spin distribution of black holes in neutron star\u2013black hole binaries, and how does this inform binary\u2011formation scenarios?<|assistant|>A positive effective spin suggests alignment with the orbital angular momentum, typical of isolated binary evolution with weak supernova kicks, whereas a negative or small effective spin points to dynamical formation or large natal kicks. Comparing spin distributions across many events can discriminate between these channels and refine population synthesis models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way does the tidal deformability of the neutron star component affect the post\u2011merger gravitational\u2011wave spectrum of a neutron star\u2013black hole coalescence, and how can future detectors use this to constrain the neutron\u2011star equation of state?<|assistant|>A more deformable neutron star experiences stronger tidal interactions, potentially generating a high\u2011frequency post\u2011merger signal (e.g., quasi\u2011normal\u2011mode ringing or disk\u2011oscillation modes). Detecting such signatures would place upper limits on the tidal Love number, thereby constraining the stiffness of the equation of state. Next\u2011generation detectors with extended high\u2011frequency bandwidth are required for robust measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might the presence of a circumbinary disk or nearby stellar companions in dense stellar environments alter the orbital evolution and merger rate of neutron star\u2013black hole binaries?<|assistant|>Environmental torques can extract angular momentum, potentially accelerating inspiral and modifying eccentricity. Tidal interactions with a disk may also alter spin alignment. These effects can change the observable population and must be accounted for when estimating merger rates from dense clusters or galactic nuclei."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected rate of observable electromagnetic counterparts (short GRBs or kilonovae) from neutron star\u2013black hole mergers across a range of mass ratios and spins?<|assistant|>I do not have an answer to this question. The paper does not quantify the rates of electromagnetic counterparts for NSBH mergers, and current observational data are insufficient to provide reliable estimates. Further multi\u2011messenger observations and detailed simulations are required to constrain these rates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the use of a resistive field shell in a modular liquid\u2011argon TPC affect the uniformity of the drift electric field compared to conventional resistor\u2011chain cages?<|assistant|>Resistive field shells provide a smoother potential gradient because the field is distributed across the surface rather than concentrated at discrete points. This can reduce high\u2011field regions that might trigger discharges. However, the exact quantitative improvement depends on the sheet resistance, shell geometry, and the stability of the resistive material over time, and must be validated experimentally for each detector design."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main advantages of a native 3D pixelated charge readout for event reconstruction in high\u2011occupancy neutrino beam environments?<|assistant|>Pixelated readouts give independent 3D coordinates for every ionization cluster without requiring complex wire\u2011plane reconstruction. This allows straightforward association of charge with localized scintillation light, improves background rejection, and mitigates pile\u2011up by enabling per\u2011pixel timing information that can be used to separate overlapping tracks."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can a high\u2011coverage dielectric light\u2011detection system be optimized to provide nanosecond\u2011level timing for neutrino interactions in a liquid\u2011argon TPC?<|assistant|>Optimizing such a system involves selecting wavelength\u2011shifting materials with fast decay times, positioning light traps close to the anode to reduce photon path lengths, and using silicon photomultipliers (SiPMs) with low dark count rates and high photon detection efficiency. The geometry must maximize geometrical coverage while maintaining optical isolation between adjacent TPC modules."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In a modular LArTPC array, what strategies can be employed to preserve optical isolation between adjacent detector modules while minimizing dead material?<|assistant|>Optical isolation can be achieved by incorporating thin, high\u2011index reflective coatings on the field\u2011shaping panels, using dielectric light traps that are non\u2011conductive, and designing inter\u2011module gaps that are small enough to reduce passive material yet sufficient to prevent light leakage. Careful alignment and precise machining of the modules also help maintain isolation without adding significant structural material."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the optimal pixel pitch for a liquid\u2011argon TPC pixelated readout that balances spatial resolution, electronic noise, and data\u2011rate constraints?<|assistant|>The optimal pixel pitch is still an open question. While finer pitches improve spatial resolution and help resolve closely spaced tracks, they increase the number of readout channels, raising electronic noise and data\u2011rate requirements. Experimental studies are needed to determine the trade\u2011off between resolution and noise for different drift fields and event rates, and to establish a pixel pitch that meets the physics goals without exceeding technical limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the neutrino energy spectrum emitted by a core\u2011collapse supernova depend on the neutrino mass ordering?<|assistant|>The neutrino mass ordering influences the survival probabilities of electron neutrinos and antineutrinos through the Mikheyev\u2013Smirnov\u2013Wolfenstein (MSW) resonances that occur in the stellar envelope. In the normal ordering, the \\(\\nu_e\\) survival probability is suppressed at high energies, while in the inverted ordering it is enhanced. Collective oscillation effects inside the core can further alter the spectra. Consequently, the observable \\(\\nu_e\\) spectrum at Earth is a convolution of the original emission spectrum with these flavor\u2011conversion probabilities, producing a mass\u2011ordering\u2011dependent shape that can be probed by detectors with good \\(\\nu_e\\) sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role do forbidden nuclear transitions play in the charged\u2011current cross section of neutrinos on argon at supernova energies?<|assistant|>At neutrino energies above roughly 20\u201330\u202fMeV, higher\u2011multipole (forbidden) nuclear transitions contribute increasingly to the total charged\u2011current cross section on \\({}^{40}\\mathrm{Ar}\\). These transitions involve changes in nuclear spin and parity that are not allowed in the simple Gamow\u2013Teller (allowed) approximation. Their inclusion increases the cross\u2011section magnitude and modifies its energy dependence, especially at the upper end of the supernova spectrum, thereby affecting the expected event rate and the reconstructed energy distribution in a liquid\u2011argon detector."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can the detection of low\u2011energy neutrons from neutrino\u2011argon interactions improve the reconstruction of supernova neutrino energies in a liquid\u2011argon detector?<|assistant|>Charged\u2011current \\(\\nu_e\\) interactions on \\({}^{40}\\mathrm{Ar}\\) often emit one or more neutrons that escape the primary interaction vertex without depositing visible energy. If these neutrons are captured on gadolinium or other neutron\u2011sensitive materials, the resulting delayed \\(\\gamma\\)-cascade can be detected, allowing the experiment to recover the missing energy. By accounting for the neutron capture signal, the total energy deposited can be corrected, yielding a more accurate reconstruction of the incident neutrino energy and thereby improving the precision of flux\u2011parameter measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What experimental strategies could be employed to directly measure the \\(\\nu_e + {}^{40}\\mathrm{Ar}\\) cross section in the 5\u201350\u202fMeV range?<|assistant|>A practical approach is to use a well\u2011characterised neutrino source such as pion decay\u2011at\u2011rest (DAR) beams, which produce mono\u2011energetic \\(\\nu_\\mu\\) and a spectrum of \\(\\nu_e\\) and \\(\\bar\\nu_\\mu\\) extending up to 52\u202fMeV. A small liquid\u2011argon detector placed at a short baseline can record charged\u2011current events, and the known DAR flux allows a direct determination of the cross section. Alternative sources include intense spallation neutron facilities that generate \\(\\nu_e\\) from muon decay in flight, or the use of a stopped\u2011muon source in a dedicated liquid\u2011argon test chamber. In all cases, careful calibration of the detector response and background suppression are essential to obtain a reliable cross\u2011section measurement."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would uncertainties in neutrino flavour conversions inside the supernova affect the inferred neutrino flux parameters at Earth, and what theoretical developments are needed to resolve this?<|assistant|>The paper does not address this issue because it requires detailed, time\u2011dependent modelling of collective neutrino oscillations and matter effects inside the supernova core, which are still under active investigation. These processes can significantly alter the flavour composition and energy spectra that reach Earth, leading to potential biases in the extracted flux parameters if not properly accounted for. Resolving this uncertainty demands high\u2011resolution supernova simulations that couple neutrino transport with flavour\u2011dependent interaction physics, along with improved treatments of multi\u2011angle effects and turbulence, which are not yet fully understood or available in the literature."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can superconducting radiofrequency (SRF) cavity surface treatments be optimized to achieve higher accelerating gradients for future high\u2011power proton linacs?<|assistant|>Advanced surface processing techniques such as electropolishing (EP), buffered chemical polishing (BCP), and nitrogen doping (N\u2011doping) have been shown to reduce surface resistance and increase the quality factor (Q) of SRF cavities. By combining EP with low\u2011temperature bake\u2011outs and controlled nitrogen infusion during the final heat treatment, the superconducting gap can be enhanced, leading to gradients beyond 30\u202fMV/m while maintaining low field emission. Further optimization involves tailoring the surface roughness at the nanometer scale and using high\u2011purity niobium with a residual resistivity ratio (RRR) above 300 to minimize thermal losses."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What design strategies can mitigate thermal shock in high\u2011power graphite targets when exposed to multi\u2011megawatt proton beams?<|assistant|>Effective mitigation relies on a combination of target geometry, active cooling, and material selection. Shortening the target length reduces the peak heat deposition, while a helical or baffle\u2011augmented beam raster spreads the energy over a larger surface area. High\u2011purity graphite grades with optimized grain structure and low thermal expansion coefficients are preferred. Active helium\u2011gas cooling channels directly surrounding the target core provide rapid heat extraction. Additionally, incorporating a gradient\u2011matched beam entrance window, typically a titanium alloy with low stress\u2011concentration, helps absorb shock loads and prevents rapid material fatigue."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can cryogenic distribution systems be engineered to minimize helium boil\u2011off and maintain pressure stability in large liquid argon TPC cryostats?<|assistant|>A well\u2011balanced cryogenic distribution network uses high\u2011conductivity copper or aluminum transfer lines with segmented heat\u2011anchor points to intercept conductive heat loads. The system incorporates distribution valve boxes (DVBs) that regulate the flow of superfluid and normal\u2011fluid helium, keeping the pressure drop within strict limits. Vacuum insulation between cryogenic lines reduces radiative heat transfer, and multi\u2011stage cold compressors handle the boil\u2011off efficiently. Finally, real\u2011time pressure sensors and automated control loops adjust valve positions to counteract transient thermal loads, ensuring stable temperature and pressure across all detector modules."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the implications of increasing LBNF beam power from 1.2\u202fMW to 2.4\u202fMW on secondary particle focusing and neutrino flux uncertainties?<|assistant|>Doubling the proton beam power amplifies the intensity of secondary mesons produced in the target, which requires the focusing horns to sustain higher magnetic fields and thermal loads. To preserve neutrino flux precision, horn current profiles must be redesigned to handle increased joule heating, and the target\u2013horn assembly must be cooled more aggressively. Enhanced beamline optics may be needed to maintain the desired pion/kaon kinematics, thereby keeping the neutrino energy spectrum stable. Systematic uncertainties linked to hadron production and horn alignment can be reduced by incorporating in\u2011situ monitoring of secondary particle rates and by cross\u2011checking with external hadron production data from experiments such as NA61/SHINE."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected degradation rate of the stainless steel beam window material under prolonged exposure to a 2.4\u202fMW proton beam?<|assistant|>The degradation rate of stainless steel windows in a multi\u2011MW proton beam environment is not yet known. Predicting material fatigue and embrittlement requires long\u2011term irradiation studies, coupled with thermal shock testing that simulate the actual beam pulse structure. Since such data are currently unavailable and the degradation mechanisms involve complex radiation\u2011induced defect accumulation, we cannot provide a reliable estimate at this time."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main advantages of using a vertical drift geometry in large liquid argon time projection chambers for long\u2011baseline neutrino experiments?<|assistant|>A vertical drift configuration allows the charge to drift over a longer distance without requiring additional readout planes. This reduces the number of front\u2011end electronics and the overall construction cost while still achieving the necessary spatial resolution. Because the ionization electrons travel parallel to the electric field, the uniformity of the drift field is easier to control, and the detector can be made more compact, which simplifies cryogenic infrastructure and shielding."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does pixel\u2011based charge readout improve particle identification in a liquid argon TPC compared with traditional strip readout?<|assistant|>Pixel readout provides true three\u2011dimensional imaging of every ionization cluster, eliminating the projection ambiguities that arise when multiple tracks overlap on a two\u2011dimensional strip plane. This yields a higher tracking efficiency, especially for complex, multi\u2011track events, and improves the accuracy of vertex reconstruction. The fine granularity also enhances the ability to separate electromagnetic showers from charged\u2011particle tracks, thereby improving electron\u2011neutrino versus background discrimination."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways can enhanced photon\u2011detection systems such as APEX or PoWER contribute to lowering the energy threshold for supernova neutrino detection in DUNE?<|assistant|>Both APEX and PoWER increase the optical coverage and improve light collection efficiency, which in turn raises the number of photo\u2011electrons detected per MeV of deposited energy. With a higher photon yield and better time resolution, the detector can trigger on, and reconstruct, lower\u2011energy events that would otherwise fall below the noise floor. This reduction in the effective energy threshold enhances sensitivity to the low\u2011energy tail of the supernova neutrino spectrum and extends the observable supernova distance range."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role does a high\u2011pressure gaseous argon TPC (ND\u2011GAr) play in constraining neutrino\u2011argon cross\u2011section uncertainties for the DUNE far detector?<|assistant|>The ND\u2011GAr provides a thin, low\u2011density target that mimics the argon nuclei of the far detector but with minimal re\u2011interaction of secondary particles. By measuring exclusive final states with excellent momentum resolution and particle identification, it directly probes nuclear effects (such as Fermi motion, short\u2011range correlations, and intranuclear rescattering). These measurements reduce the model dependence of cross\u2011section predictions used to interpret far\u2011detector data, thereby tightening systematic uncertainties on oscillation parameters."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the projected maximum drift voltage and electric field uniformity requirement for the FD4 module's 13\u202fm drift length, and how will the cryogenic and high\u2011voltage systems be engineered to achieve it?<|assistant|>I do not have that information. The specific maximum drift voltage, the required field uniformity, and the detailed design of the cryogenic and high\u2011voltage infrastructure are not covered in the material provided. These technical specifications would be defined in later engineering design reports and require dedicated simulations and prototype testing that are beyond the scope of this document."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the key scaling challenges when transitioning DUNE's reconstruction workload from a high\u2011throughput computing (HTC) model to a high\u2011performance computing (HPC) environment, and how can GPU acceleration help address these challenges?<|assistant|>The primary scaling challenge is the need to process extremely large, continuous FD data streams that are naturally segmented in both time and space. In an HTC model, jobs run independently on many CPUs, but HPC architectures favor tightly coupled parallelism with limited inter\u2011node communication. Converting the workflow requires (1) partitioning the data into smaller, independent chunks that fit into node memory, (2) redesigning I/O to be highly efficient on parallel file systems, and (3) optimizing the event\u2011processing kernels for SIMD/vector execution. GPU acceleration can help by offloading compute\u2011bound tasks such as hit\u2011finding, clustering, and machine\u2011learning inference to massively parallel processors. GPUs can process millions of hits in parallel, dramatically reducing wall\u2011clock time per event. However, the bottleneck often shifts to data movement; efficient GPU\u2011to\u2011CPU memory transfers and overlap of computation with I/O are essential to realize performance gains."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can machine\u2011learning models be integrated into the DUNE reconstruction pipeline while preserving reproducibility, version control, and long\u2011term maintainability?<|assistant|>A robust integration strategy involves (1) containerising the full ML workflow (framework, dependencies, and trained models) so that every run uses the same environment, (2) storing model artefacts in a versioned model registry (e.g., MLflow or DVC) linked to the corresponding dataset version, (3) embedding deterministic seeds and random\u2011state management in training scripts, and (4) using continuous\u2011integration pipelines that automatically retrain models when upstream data or hyper\u2011parameters change. Documentation should describe the training procedure, hyper\u2011parameter settings, and performance metrics. Finally, the reconstruction code should expose a clear API to switch between ML\u2011based and traditional algorithms, enabling systematic validation and comparison across different physics samples."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What strategies can be employed to ensure efficient data transfer and storage management across distributed European HPC resources for DUNE's large far\u2011detector datasets?<|assistant|>Efficient management requires a layered approach: (1) **Data staging**\u2014pre\u2011fetch datasets to local scratch or burst buffers using parallel transfer protocols (e.g., Globus, GridFTP) before job launch; (2) **Metadata\u2011driven placement**\u2014use a metadata catalogue (e.g., MetaCat) to locate replicas and schedule jobs to the nearest site, reducing network load; (3) **Chunking and compression**\u2014split large event files into smaller chunks and apply lossless compression to reduce bandwidth; (4) **Asynchronous I/O**\u2014decouple data reads/writes from compute kernels using overlapped I/O APIs; (5) **Data lifecycle policies**\u2014archive or delete intermediate files automatically based on retention schedules; (6) **Monitoring and feedback**\u2014deploy real\u2011time dashboards to track transfer rates, queue lengths, and storage utilization, allowing dynamic re\u2011routing of jobs when bottlenecks appear."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main obstacles to maintaining long\u2011term sustainability of DUNE's computing infrastructure in the face of evolving operating systems, security requirements, and hardware lifecycles, and how can they be mitigated?<|assistant|>Key obstacles include: (1) **Software ageing**\u2014legacy C++ libraries and scripting languages may lack upstream support; mitigated by adopting long\u2011term supported frameworks (e.g., C++17+, Python 3.11) and automated dependency management; (2) **Security patch cycles**\u2014continuous patching of thousands of worker nodes requires automation; this can be addressed with configuration\u2011driven provisioning tools (e.g., Ansible, SaltStack) and containerised workloads that isolate the host OS; (3) **Hardware obsolescence**\u2014GPUs and interconnects evolve rapidly, making hardware\u2010specific optimisations brittle; adopting portable GPU APIs (HIP, SYCL) and abstracting device selection at runtime helps; (4) **Skill drain**\u2014as the collaboration ages, institutional knowledge may be lost; comprehensive documentation, training workshops, and mentorship programs are essential; (5) **Funding stability**\u2014long\u2011term contracts for storage and compute need to be negotiated early with national labs and HPC centers to secure predictable budgets."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the projected energy consumption of DUNE's planned GPU\u2011enabled reconstruction pipeline, and how does it compare to a CPU\u2011only pipeline of equivalent performance?<|assistant|>The paper does not provide detailed energy consumption estimates, and current simulations lack the granularity needed to model power usage for the proposed GPU\u2011accelerated workflow. Energy profiling would require (1) detailed performance benchmarks of the reconstruction kernels on target GPU hardware, (2) measurement of idle and active power draws of the GPU nodes, and (3) accounting for data\u2011movement overheads between CPU and GPU. Without these measurements, it is not possible to give a reliable comparison to a CPU\u2011only pipeline. Future studies that integrate power monitoring into the job scheduler and perform controlled experiments on representative workloads are needed to answer this question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What physical characteristics of short gamma\u2011ray bursts make them prime candidates for coincident gravitational\u2011wave detections from binary neutron\u2011star mergers?<|assistant|>Short GRBs\u2014defined by a prompt emission duration of less than about two seconds and a hard photon spectrum\u2014are widely believed to arise from the coalescence of two neutron stars or a neutron star\u2013black\u2011hole pair. This interpretation is supported by the observed temporal coincidence with the compact\u2011binary inspiral phase, the typical energies released (\u224810^49\u201310^51\u202ferg), and the lack of supernova signatures that are common to long GRBs. The high compactness and rapid mass transfer in such systems produce strong, high\u2011frequency gravitational\u2011wave signals in the 10\u20131000\u202fHz band, exactly where ground\u2011based interferometers are most sensitive. Consequently, short GRBs are the most promising electromagnetic triggers for searching for gravitational waves from binary mergers."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the observer\u2019s viewing angle relative to the binary orbit affect the amplitude and detectability of the gravitational\u2011wave signal from a short GRB progenitor?<|assistant|>Gravitational\u2011wave emission from a binary system is strongest along the orbital angular\u2011momentum axis (the \u201cface\u2011on\u201d direction) and weakest in the orbital plane (\u201cedge\u2011on\u201d). The strain amplitude scales roughly as (1+cos\u00b2\u03b8) where \u03b8 is the inclination angle; thus a face\u2011on system can produce nearly twice the strain of an edge\u2011on system at the same distance. Because the short GRB jet is believed to be narrowly collimated along the same axis, an observer detecting a GRB is almost always within a few degrees of face\u2011on, making the associated gravitational\u2011wave signal more likely to be above the detector threshold. However, this also means that any off\u2011axis GRB, which might still produce a detectable GW signal, will not be accompanied by prompt gamma emission, complicating multimessenger association."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What improvements in next\u2011generation gravitational\u2011wave detectors will extend the horizon for detecting neutron\u2011star mergers associated with short GRBs?<|assistant|>Future upgrades such as A+ (the planned upgrade of Advanced LIGO and Virgo), the Voyager project, and third\u2011generation facilities like Cosmic Explorer and Einstein Telescope are expected to reduce strain noise by factors of 2\u201310 across the 10\u2013500\u202fHz band. This translates into a proportional increase in the observable volume, extending the detection horizon for binary neutron\u2011star mergers from \u2248200\u202fMpc with current detectors to \u2248600\u20131000\u202fMpc (A+), \u22483\u20134\u202fGpc (Voyager), and \u224810\u201320\u202fGpc (third\u2011generation). Such gains dramatically raise the likelihood of catching a gravitational\u2011wave signal from the population of short GRBs, including those at higher redshift or with lower intrinsic luminosity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the primary obstacles to precise sky localization of short GRBs when using gravitational\u2011wave data alone, and how can multimessenger follow\u2011up mitigate these challenges?<|assistant|>Ground\u2011based interferometers localize sources by triangulating the arrival time differences among detectors. With a three\u2011detector network, the typical error region for a compact binary is a few tens to a few hundred square degrees, far larger than the fields of view of most electromagnetic instruments. The localization improves with a larger network, better timing precision, and higher signal\u2011to\u2011noise ratios. Multimessenger observations\u2014such as rapid GRB localizations from Fermi/GBM or Swift/BAT\u2014provide a sub\u2011degree sky position that can be used to constrain the gravitational\u2011wave search, effectively reducing the background and improving the statistical significance. Conversely, a well\u2011localized GW event can trigger targeted electromagnetic follow\u2011up to search for kilonovae or afterglows, thereby closing the multimessenger loop."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is the occurrence rate of low\u2011luminosity short gamma\u2011ray bursts significantly different from that of high\u2011luminosity short gamma\u2011ray bursts, and what implications would this have for joint gravitational\u2011wave and GRB detection rates?<|assistant|>I do not have definitive knowledge on this matter because the paper\u2019s analysis does not address the relative rates of low\u2011luminosity versus high\u2011luminosity short GRBs. Determining whether a distinct population of faint short GRBs exists requires a large, well\u2011calibrated sample of GRB luminosities, careful treatment of selection effects in gamma\u2011ray detectors, and independent constraints from gravitational\u2011wave observations. Current data are insufficient to quantify any difference in occurrence rates, and more comprehensive surveys combined with future multimessenger observations will be needed to resolve this question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the mass distribution of neutron stars observed in gravitational\u2011wave mergers compare to that of isolated binary neutron stars in the Milky Way?<|assistant|>Current gravitational\u2011wave observations suggest that neutron\u2011star masses in merging binaries span a broader range, extending up to roughly 2.0\u202fM\u2299, whereas Galactic binary pulsars cluster tightly around 1.33\u202fM\u2299. However, the sample size is still small and uncertainties are large, so a definitive comparison remains tentative."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there a distinct mass gap between the heaviest neutron stars and the lightest black holes in the compact binary population?<|assistant|>Analyses of the merger catalog show a suppression of events in the 2\u20135\u202fM\u2299 range, consistent with a lower mass gap, but the data are not yet conclusive enough to confirm that the gap is completely empty."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the physical origin of the correlation between black\u2011hole spin magnitude and the mass ratio of the binary?<|assistant|>The agent does not have a definitive answer. The observed trend\u2014larger effective spins in more unequal\u2011mass binaries\u2014has been reported, but the underlying astrophysical mechanisms (e.g., differential stellar evolution, mass transfer, natal kicks, or dynamical interactions) have not been conclusively identified, and the paper does not provide a definitive explanation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the merger rate of binary black holes increase with redshift?<|assistant|>Population studies of the LIGO\u2013Virgo detections indicate a positive evolution of the BBH merger rate with redshift, parameterized as a power law R(z)\u221d(1+z)^\u03ba with \u03ba\u22483, which is broadly consistent with the rise of the cosmic star\u2011formation rate."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there an upper mass gap for stellar\u2011mass black holes, as predicted by pair\u2011instability supernova theory?<|assistant|>The gravitational\u2011wave catalog contains mergers with component masses up to about 70\u202fM\u2299, and the current data do not show a sharp drop in the merger rate above ~50\u202fM\u2299. Consequently, the existence of an upper mass gap remains unconstrained."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How has the estimated rate of neutron star\u2013black hole (NSBH) mergers evolved over the first three LIGO\u2013Virgo observing runs?<|assistant|>The publicly reported detection rate of NSBH mergers has increased modestly with each observing run, largely reflecting the improved sensitivity and longer observing times of the detector network. While earlier runs (O1 and O2) yielded only a handful of NSBH candidates, the third observing run (O3) has produced several confirmed NSBH detections, suggesting a higher intrinsic merger rate in the local Universe. This trend is consistent with population\u2011inference studies that indicate NSBH systems are more common than previously thought."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant systematic uncertainties in measuring the effective inspiral spin (\u03c7_eff) of high\u2011mass black hole binaries?<|assistant|>The primary systematic uncertainties arise from waveform model inaccuracies, particularly in the treatment of higher\u2011order multipole moments and spin\u2011precession dynamics. Additionally, calibration errors in the detector strain data and imperfect noise subtraction can bias the phase evolution, which is crucial for \u03c7_eff extraction. For the highest\u2011mass systems, the signal\u2019s short duration exacerbates these issues, making the inferred \u03c7_eff more sensitive to model assumptions."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent do gravitational\u2011wave observations constrain the maximum mass of neutron stars?<|assistant|>Current gravitational\u2011wave detections of binary neutron star (BNS) mergers provide only loose constraints on the maximum neutron\u2011star mass, because the inspiral signal is mainly sensitive to tidal deformability rather than the ultimate mass limit. Some candidate events with unusually massive components hint at a possible higher maximum mass, but the statistical significance remains low. Consequently, the precise upper bound on neutron\u2011star masses is still largely determined by electromagnetic observations and nuclear\u2011physics modeling."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the most probable spin\u2011orientation distribution for black holes in merging binaries formed through isolated binary evolution?<|assistant|>For binaries that form via isolated stellar evolution, theoretical models predict that the component spins should be preferentially aligned with the orbital angular momentum due to tidal coupling and common\u2011envelope evolution. This alignment tends to produce small effective precession spin (\u03c7_p) and positive \u03c7_eff values. Observationally, many detected systems show mild alignment, but a fraction exhibit significant misalignment, suggesting that both isolated and dynamical formation channels contribute to the observed population."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there definitive evidence for a third\u2011generation black hole population (i.e., black holes formed from the merger of two smaller black holes) in the current GW catalog?<|assistant|>The existing catalog does not provide definitive evidence for a distinct third\u2011generation black hole population. While some high\u2011mass black holes observed in the data could, in principle, be remnants of earlier mergers, their masses and spins are not sufficiently distinct to conclusively separate them from first\u2011generation black holes formed directly from stellar collapse. Moreover, the statistical uncertainties in mass and spin measurements, combined with limited sample size, prevent a robust identification of a separate generation. Future observations with higher signal\u2011to\u2011noise ratios and improved waveform models may allow such a distinction to be made."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might graph neural networks be leveraged to improve neutrino interaction vertex reconstruction accuracy in liquid argon time projection chambers compared to conventional convolutional neural networks?<|assistant|>Graph neural networks (GNNs) can naturally represent the sparse, irregular hit patterns in a LArTPC as a graph, where nodes are individual hits and edges encode spatial or temporal proximity. By learning message\u2011passing operations across this graph, GNNs can capture long\u2011range correlations and topological information that are difficult for 2\u2011D convolutions to encode. This may lead to better discrimination of the true vertex, especially in events with complex topologies or low hit densities."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the effect of changing the wire\u2011plane pitch on the spatial precision of neutrino interaction vertex determination in the horizontal\u2011drift DUNE far detector?<|assistant|>Reducing the wire\u2011plane pitch increases the granularity of the recorded charge deposits, thereby improving the resolution of reconstructed hit positions in the drift direction. A finer pitch can shrink the uncertainty on the vertex location, particularly in the direction transverse to the wires. However, this also raises data volume and may require more sophisticated noise filtering. Conversely, a coarser pitch reduces resolution but eases data handling."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does incorporating scintillation light detection data influence the performance of vertex\u2011finding algorithms in LArTPC detectors?<|assistant|>Scintillation light provides a prompt, time\u2011of\u2011arrival signal that can be used to estimate the absolute event time (t0) and, in some configurations, the z\u2011coordinate of the vertex. Combining light timing with charge\u2011based hit information can improve the localization of the interaction point, especially when the charge signal is sparse or heavily overlapped. However, the light collection efficiency varies across the detector and its integration requires careful calibration to avoid biasing vertex estimates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main obstacles and possible strategies for extending vertex\u2011reconstruction techniques to identify secondary vertices from tau decays in DUNE data?<|assistant|>Secondary vertices from tau decays are often displaced by a few millimeters to centimeters, with relatively low\u2011energy visible decay products. Challenges include limited hit multiplicity, overlapping tracks, and the need to disentangle the secondary decay vertex from the primary neutrino interaction. Strategies involve refining multi\u2011pass reconstruction, incorporating decay\u2011mode specific signatures, and applying dedicated neural\u2011network modules trained to recognize displaced energy deposits or kinematic patterns indicative of tau decay."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent can unsupervised or semi\u2011supervised learning approaches discover novel event topologies in DUNE data without labeled training sets?<|assistant|>I don't have a definitive answer to this question. The paper focuses on supervised deep\u2011learning methods trained on labeled simulated data, and does not explore unsupervised or semi\u2011supervised strategies for topology discovery. Investigating such approaches would require developing new loss functions or clustering techniques that can learn meaningful representations from unlabeled data, as well as validation against known physics signatures, which is beyond the scope of the present work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the stochastic wandering of the spin frequency of accreting millisecond X\u2011ray pulsars affect the sensitivity of continuous gravitational\u2011wave searches?<|assistant|>The spin frequency of an accreting neutron star is subject to fluctuations driven by variations in the accretion torque. In the frequency domain, these fluctuations manifest as a random walk, which can shift the signal by several frequency bins during the coherent integration time. If the search assumes a perfectly stable frequency, the mismatch between the true signal and the template leads to a loss in signal\u2011to\u2011noise ratio. By allowing the frequency to wander within a bounded range\u2014often modeled as a discrete random walk\u2014the search can retain sensitivity. This is typically achieved by partitioning the data into shorter coherent segments (e.g., 10\u2011day chunks) and using a hidden Markov model to track the most likely frequency path. The longer the coherent segment, the greater the potential frequency drift, so there is a trade\u2011off between sensitivity to weak signals and robustness against frequency wander."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant mechanisms that can generate continuous gravitational waves in accreting millisecond X\u2011ray pulsars, and how do they appear in the gravitational\u2011wave spectrum?<|assistant|>Two principal mechanisms are usually considered:\\n1. **Mass quadrupole deformations (\u201cmountains\u201d)** on the neutron\u2011star surface, either supported by crustal stresses or magnetic fields, produce emission at twice the stellar spin frequency (2f\u2605) and, in some models, also at f\u2605 if the deformation is not perfectly aligned with the rotation axis.\\n2. **r\u2011mode oscillations**, a class of Rossby waves driven unstable by gravitational\u2011wave back\u2011reaction, emit near 4f\u2605/3. The exact frequency depends on the equation of state and relativistic corrections.\\nIn a narrowband search the expected signal is thus centered on f\u2605, 4f\u2605/3, or 2f\u2605, with a bandwidth that covers any modest frequency drift."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do uncertainties in binary orbital parameters propagate into the template bank and influence the detection thresholds of continuous\u2011wave searches?<|assistant|>The binary orbital parameters\u2014period (P), projected semi\u2011major axis (a0), and time of ascending node (Tasc)\u2014enter the Doppler modulation model used to transform detector data into the source frame. Small errors in these parameters broaden the mismatch between the true signal and any single template, effectively smearing the signal power across neighbouring templates. To keep the fractional loss in signal\u2011to\u2011noise ratio below a chosen maximum mismatch (e.g., \u00b5max\u202f=\u202f0.1), the template bank is constructed with spacings derived from the metric on parameter space. The number of templates grows as the square root of the parameter uncertainties and inversely with the coherent segment length (through the mismatch equations). A larger template bank increases the trials factor, which in turn raises the detection threshold (higher Lth) for a fixed false\u2011alarm probability."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the precise relationship between the observed X\u2011ray flux during outburst and the amplitude of continuous gravitational waves emitted by an accreting millisecond X\u2011ray pulsar?<|assistant|>The paper does not provide a definitive answer to this question. The connection between X\u2011ray flux and gravitational\u2011wave amplitude is complex: it depends on the efficiency of angular\u2011momentum transfer, the star\u2019s internal structure, magnetic field geometry, and the detailed physics of accretion\u2011induced deformations. While torque\u2011balance arguments can give an upper limit on the strain by assuming the accretion torque is exactly counter\u2011balanced by gravitational\u2011wave emission, translating an observed flux into a concrete strain amplitude requires assumptions about the neutron\u2011star equation of state, accretion geometry, and magnetic field configuration\u2014parameters that are not fully constrained by current observations. Consequently, a precise, universally applicable relationship remains an open area of research."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways can hidden Markov models improve the tracking of phase wander in continuous\u2011wave searches compared to traditional coherent matched\u2011filtering?<|assistant|>Traditional coherent matched\u2011filtering assumes a perfectly stable phase evolution over the entire observation period. This is unsuitable for sources whose spin phase wanders due to stochastic accretion torque fluctuations. Hidden Markov models (HMMs) treat the instantaneous frequency (or phase) as a hidden state that evolves according to a probabilistic transition model (e.g., a simple random walk). By applying the Viterbi algorithm, the HMM efficiently finds the most likely path through the state space that maximizes the likelihood of the observed data. This semi\u2011coherent approach retains most of the sensitivity of a fully coherent search while being robust to phase wander, enabling longer coherent segments and better overall signal\u2011to\u2011noise ratios for sources with significant frequency noise."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the geometry and orientation of a global gravitational\u2011wave detector network influence the sensitivity to narrowband anisotropies in the stochastic gravitational\u2011wave background?<|assistant|>The overlap\u2011reduction function (ORF) captures the relative antenna patterns, time delays, and orientations of detector pairs. For narrowband signals, the ORF oscillates rapidly with frequency and sky direction. Baselines that are short and nearly co\u2011linear (e.g., the two Advanced LIGO detectors) provide high correlation for certain directions, while longer, more widely separated baselines (e.g., LIGO\u2013Virgo, LIGO\u2013KAGRA) improve sky coverage and break degeneracies. Thus, the overall sensitivity depends on both baseline length and the relative orientations of the interferometers; a carefully optimized network can substantially enhance the ability to detect narrowband anisotropies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the theoretical predictions for the amplitude and spectral shape of a narrowband stochastic background produced by a population of rapidly rotating neutron stars in the Milky Way?<|assistant|>Models of rotating neutron stars\u2014such as magnetars, accreting pulsars, or isolated spinning neutron stars\u2014predict continuous gravitational radiation at roughly twice the spin frequency. If the Galactic population has a broad distribution of spin frequencies and ellipticities, the resulting background is a superposition of many nearly monochromatic lines, yielding a narrowband spectrum. The amplitude is governed by the ellipticity distribution, spin\u2011down torque, and source number, typically giving \u03a9_GW \u223c 10^\u201311\u201310^\u20139 in the LIGO band with a nearly flat spectral index (\u03b1 \u2248 0). Large uncertainties in source populations and ellipticity limits lead to a wide range of possible amplitudes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which computational strategies can be employed to scale an all\u2011sky, all\u2011frequency radiometer map\u2011making to higher pixel and frequency resolutions while keeping the analysis tractable?<|assistant|>Two complementary approaches are effective: (1) matrix\u2011based inversion with sparsity exploitation\u2014since the Fisher matrix is band\u2011limited in pixel space, iterative solvers such as conjugate\u2011gradient with appropriate preconditioners can be used without forming the full matrix; (2) hierarchical folding and parallelization\u2014by folding data into a single sidereal day and distributing frequency bins across compute nodes, the analysis becomes embarrassingly parallel. GPU acceleration for ORF evaluation and efficient memory layouts for HEALPix indexing further reduce runtime. Combining these techniques allows extending to N_side \u2265 32 or finer frequency bins (e.g., 1/64 Hz) without prohibitive computational cost."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can the ASAF method be generalized to incorporate Doppler modulation and frequency\u2011dependent sky localization, and how would this affect sensitivity?<|assistant|>In principle, the ASAF pipeline can be modified to include the time\u2011dependent Doppler phase shift arising from Earth\u2019s rotation and orbital motion. This requires augmenting the cross\u2011spectral density with a frequency\u2011dependent phase term that tracks the expected line drift across the observation period. Incorporating this effect would sharpen the response to true monochromatic sources, potentially increasing the SNR by up to a factor of a few for high\u2011frequency signals, but it would also increase computational complexity because the phase model must be evaluated for each sky pixel and frequency bin. A practical strategy is to first run a Doppler\u2011blind ASAF to flag candidate pixel\u2011frequency pairs and then perform a targeted matched\u2011filter follow\u2011up that accounts for Doppler modulation."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected contribution of exotic boson clouds surrounding spinning black holes to the narrowband stochastic gravitational\u2011wave background, and can an ASAF\u2011style search detect them?<|assistant|>Ultralight bosons (e.g., axion\u2011like particles) can form clouds around rapidly rotating black holes via superradiance, emitting nearly monochromatic gravitational waves at frequencies set by the boson mass and black\u2011hole spin. The Galactic population of such clouds could produce a narrowband stochastic background with a characteristic frequency range of ~10\u20131000\u202fHz and a flat spectral index. However, the ASAF framework described in the paper focused on generic persistent signals and did not model the specific line\u2011like structure or the spatial clustering expected from boson\u2011cloud sources. Consequently, while the ASAF pipeline is capable of flagging anomalous narrowband excesses, it cannot directly quantify the expected amplitude or distinguish boson\u2011cloud signatures without dedicated modeling and matched\u2011filter follow\u2011ups. Thus, the question remains open and requires further theoretical and data\u2011analysis work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does timing noise (spin wandering) in young neutron stars influence the sensitivity of semi\u2011coherent searches for continuous gravitational waves?<|assistant|>Spin wandering introduces random fluctuations in the rotational frequency that can shift the signal out of a single template over the coherent integration time. Semi\u2011coherent methods mitigate this by using short coherence times and a hidden Markov model or Hough transform that allows the frequency to drift by a few bins per step. The net effect is a modest reduction in sensitivity compared to a purely coherent search that assumes a deterministic spin\u2011down, typically on the order of 10\u201320\u202f% in the 95\u202f% upper\u2011limit strain for the same computational budget. The choice of coherence time, transition probabilities, and step size in the HMM or frequency binning in the Hough transform are therefore critical to balance sensitivity against the risk of mis\u2011tracking a wandering signal."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Which young supernova remnants are the most promising targets for future continuous\u2011wave searches with upgraded detectors?<|assistant|>Targets that combine proximity, youth, and evidence of a central compact object are favored. Vela\u202fJr. (G266.2\u20131.2), Cas\u202fA (G111.7\u20132.1), G1.9+0.3, and the younger remnant G18.9\u20131.1 have ages of a few hundred to a thousand years and distances of less than a kiloparsec, giving the strongest expected strain signals. With the projected improvements in LIGO\u202fVoyager and the next\u2011generation Virgo upgrade, the sensitivity to strain at 200\u2013400\u202fHz will improve by roughly a factor of two, bringing these remnants within reach of the spin\u2011down limits for many realistic ellipticity models."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can multi\u2011messenger observations (X\u2011ray, radio) improve targeted continuous\u2011wave searches?<|assistant|>Electromagnetic observations that reveal a neutron star\u2019s spin frequency, spin\u2011down rate, or even a timing solution provide powerful priors that drastically reduce the parameter space. Knowing the frequency and its derivative allows a fully coherent or very long coherent integration, which scales the sensitivity as \\(h_{\\rm min}\\propto T_{\\rm coh}^{-1/2}\\). Even if the pulsar is not detected in radio, a precise X\u2011ray pulse ephemeris can be used. In the absence of a phase\u2011connected ephemeris, a narrow range of spin\u2011down values can be tested, improving the detection statistic\u2019s significance and reducing the number of required templates."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What advantages does combining the \\(f_{\\ast}\\) and \\(2f_{\\ast}\\) harmonics provide in a dual\u2011harmonic search for continuous waves?<|assistant|>When a neutron star emits gravitational waves at both its spin frequency and twice that frequency\u2014possible for a triaxial rotator or a pinned superfluid\u2014the two harmonics share the same intrinsic phase evolution. Tracking them simultaneously allows the matched\u2011filter statistic to sum power from both frequencies, improving the overall signal\u2011to\u2011noise ratio by roughly \\(\\sqrt{2}\\) in the ideal case. It also mitigates the risk of missing a signal that would be too weak in a single\u2011harmonic search. However, it requires a larger template bank and careful handling of line contamination in both frequency bands."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the ellipticity of a young neutron star evolve on timescales of months to years?<|assistant|>The current data do not provide a definitive answer. Existing continuous\u2011wave searches have not detected any signals, and the theoretical models of crustal relaxation, magnetic field decay, and r\u2011mode saturation predict a range of evolution timescales, from days to centuries. Because the observational upper limits are still above the expected ellipticity for many young stars, we lack the sensitivity to observe a gradual change in ellipticity over short times. Dedicated long\u2011term monitoring with next\u2011generation detectors and improved waveform models will be needed to constrain or detect such evolution."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do quantum squeezing techniques improve the sensitivity of continuous gravitational-wave searches compared to earlier observing runs?<|assistant|>Quantum squeezing reduces the quantum shot-noise floor in the interferometers, allowing more power to be delivered to the measurement band without increasing radiation-pressure noise. This leads to a lower strain noise spectral density, especially at high frequencies, which directly translates into tighter upper limits on continuous-wave amplitudes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What astrophysical processes can create the non-axisymmetric deformations required for a spinning neutron star to emit detectable continuous gravitational waves?<|assistant|>Possible mechanisms include crustal mountains caused by accretion or thermal stresses, magnetic-field-induced distortions, and the excitation of fluid oscillation modes such as r-modes. Each process can support an equatorial ellipticity that gives rise to a quadrupolar gravitational-wave signal at twice the rotation frequency."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In an all-sky continuous-wave search, how does the choice of Short Fourier Transform (SFT) coherence time influence the balance between computational cost and search sensitivity?<|assistant|>Longer SFTs improve frequency resolution and Doppler demodulation accuracy, boosting sensitivity. However, they also increase the parameter-space resolution required in sky and spin-down, which raises the number of templates and hence computational load. Shorter SFTs lower the template count but reduce sensitivity due to poorer frequency discrimination."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent can the strain upper limits obtained by all-sky searches constrain the equatorial ellipticity of neutron stars located at different distances in the Milky Way?<|assistant|>By inverting the strain upper limit formula, one obtains a maximum allowed ellipticity as a function of distance. For a given search sensitivity, this translates into a distance range within which neutron stars with a specified ellipticity would have been detected. Thus, tighter upper limits extend the observable volume and place stronger constraints on the deformation of nearby neutron stars."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected sensitivity of future observing runs (e.g., O4/O5) to continuous gravitational waves from neutron stars with spin-down rates larger than 10\u207b\u2078\u202fHz/s, and what new analysis strategies would be required to probe such high spin-down values?<|assistant|>The paper does not address this scenario, so we cannot provide a definitive answer. Extending the search to spin-down magnitudes above 10\u207b\u2078\u202fHz/s would demand a denser template bank in frequency derivative space, likely increasing computational cost significantly. Techniques such as adaptive hierarchical searches, coherent-follow\u2011up on narrower sky patches, or machine-learning based outlier vetting might be necessary to make the search tractable, but concrete sensitivity estimates await future data and method development."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the choice of the narrowband width parameter (\u03ba) influence the sensitivity and computational cost of continuous gravitational\u2011wave searches for pulsars with significant timing noise?<|assistant|>The parameter \u03ba sets the fractional window around the electromagnetic spin frequency and spin\u2011down within which the search is performed. A larger \u03ba allows for greater offsets between the true GW phase evolution and the EM timing solution, which is useful for pulsars with large timing noise or differential rotation between the crust and core. However, a larger \u03ba also increases the number of templates in both frequency and spin\u2011down dimensions, thereby inflating the search volume and the false\u2011alarm probability. In practice, \u03ba values of 10\u207b\u00b3\u201310\u207b\u00b2 are chosen to balance the need for robustness against phase offsets with computational feasibility, as demonstrated in previous LIGO/Virgo narrowband searches."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What physical mechanisms could cause a measurable phase offset between the electromagnetic emission of a pulsar and its continuous gravitational\u2011wave signal, and how would such offsets manifest in the data?<|assistant|>A differential rotation between the rigid outer crust and the interior superfluid can lead to a small lag that manifests as a phase offset between the electromagnetic pulse arrival times and the GW phase. Glitches, magnetospheric torque changes, or internal superfluid vortex dynamics can also introduce phase drifts or glitches in the GW signal that are not perfectly locked to the EM timing. In the data, these effects would appear as a mismatch in the expected Doppler\u2011corrected phase evolution, causing a reduction in matched\u2011filter SNR if the search assumes strict phase\u2011lock. Narrowband searches that allow a small offset in frequency and spin\u2011down effectively accommodate such behavior."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would modelling post\u2011glitch transient gravitational\u2011wave signals with an exponentially decaying amplitude, instead of a simple rectangular window, affect the sensitivity of long\u2011duration transient searches?<|assistant|>An exponential decay more accurately represents the expected relaxation of the star\u2019s quadrupole moment after a glitch. While a rectangular window assumes a constant amplitude over the whole duration, an exponential model would allocate signal power more heavily to early times, potentially increasing SNR for short\u2011lived emissions. However, implementing an exponential window typically requires a larger template bank to cover the additional parameter (decay time), increasing computational cost. Studies have shown that the loss in SNR for a realistic exponential signal using a rectangular template is modest (a few percent), so many searches adopt the simpler rectangular window to keep the search tractable."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way do detector duty cycles and calibration uncertainties propagate into the upper limits on the gravitational\u2011wave strain and neutron\u2011star ellipticity derived from continuous\u2011wave searches?<|assistant|>The effective observing time, T_obs, is reduced by the duty cycle of each detector, directly scaling the expected sensitivity (h_sens \u221d T_obs\u207b\u00b9/\u00b2). Calibration uncertainties in the strain response of each detector (typically 5\u201310\u202f%) translate into systematic errors on the inferred strain amplitude. Since the ellipticity is derived from the strain via \u03f5 \u221d h\u2080\u202ff\u207b\u00b2, any error in h\u2080 propagates to \u03f5 quadratically with frequency. The combination of reduced T_obs and calibration errors thus weakens the upper limits and introduces a systematic uncertainty that is usually quoted as a separate systematic error budget in the final results."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there any evidence for continuous gravitational\u2011wave emission from millisecond pulsars in the O3 data when the phase\u2011lock assumption is relaxed?<|assistant|>The current analysis focused on 18 isolated pulsars with spin frequencies between 10\u202fHz and 350\u202fHz that have relatively high spin\u2011down rates, yielding spin\u2011down limits within a factor of three of the expected sensitivity. Millisecond pulsars, which rotate at hundreds of Hz but have very small spin\u2011down rates, were not included in this target list because their indirect spin\u2011down limits are far below the detector sensitivity. Consequently, the study does not address whether continuous GWs could be detected from such objects in O3. Determining this would require a dedicated search over a different parameter space and is an open question that remains to be investigated with future data and more sensitive detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the ionization recombination factor for sub\u201150\u202fMeV electrons vary as a function of the applied electric field in a liquid argon time\u2011projection chamber?<|assistant|>The recombination factor, R, quantifies the fraction of ionization electrons that survive prompt recombination with argon ions. For low\u2011energy electrons, R typically follows the Modified Box model, where \\n\\nR = ln(1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)) / (1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)),\\n\\nwith \u03b2\u2032 and \u03b1 being empirical parameters, \u03c1 the liquid\u2011argon density, and E_f the electric field. As the field increases, the electric drift force overcomes the ion\u2011electron Coulomb attraction, reducing recombination and increasing R. Empirical measurements (e.g., in ArgoNeuT, ICARUS, and MicroBooNE) show that R rises from ~0.5 at 200\u202fV/cm to ~0.75 at 500\u202fV/cm for 10\u201350\u202fMeV electrons. The precise field dependence also depends on the local dE/dx; denser ionization tracks recombine more strongly, leading to a slightly lower R at the same field."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the quantitative impact of the TPC readout threshold on the energy resolution of low\u2011energy electron showers?<|assistant|>The readout threshold is the minimum charge that a wire\u2011channel must record to be accepted as a hit. For sub\u201150\u202fMeV electrons, a typical threshold of ~100\u202fkeV per 500\u202fns tick means that a non\u2011negligible fraction of the ionization\u2014especially from thin, low\u2011dE/dx portions of the shower\u2014is lost. Studies of simulated Michel electrons show that this loss corresponds to ~11\u202f% of the total deposited energy. When this missing energy is included, the fractional energy resolution degrades by about 5\u20138\u202f% relative to the ideal case where all charge is measured. The effect is more pronounced at lower energies where the shower is less developed and the charge density is lower."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can deep learning techniques enhance the separation of Michel electrons from cosmic\u2011ray background in a large LArTPC?<|assistant|>Yes. Convolutional neural networks (CNNs) trained on simulated and real data can learn subtle spatial and temporal patterns characteristic of electron\u2011induced showers versus muon or proton tracks. A CNN can be fed the three wire\u2011plane images (U, V, X) and the corresponding time series, and output a probability that a cluster is a Michel electron. Benchmarks show that such a network can achieve >\u202f95\u202f% purity with >\u202f90\u202f% efficiency for energies between 10 and 50\u202fMeV, outperforming traditional cut\u2011based selections that rely on hit multiplicity and angular cuts alone."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can photon\u2011detector signals complement charge readout for identifying low\u2011energy electrons in a liquid\u2011argon TPC?<|assistant|>Photon detectors (e.g., ARAPUCA modules) provide fast scintillation light timestamps with ~ns precision. For low\u2011energy electrons, the scintillation light yields ~1\u20132\u202f\u00d7\u202f10\u2074 photons per MeV, enabling a prompt trigger even when the ionization charge is below the readout threshold. By correlating the light pulse with the charge hit pattern, one can improve the vertex reconstruction, suppress random noise hits, and better discriminate between true electron showers and spurious background. In addition, the light\u2013charge ratio can be used as an auxiliary variable in energy calibration, since it is sensitive to recombination and electron lifetime effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it possible to recover the energy lost due to readout threshold and shower leakage in future detectors without changing the hardware?<|assistant|>The agent does not have a definitive answer to this question. Recovering lost energy without hardware modifications would require sophisticated reconstruction algorithms that infer the missing charge from surrounding hit patterns, shower topology, or correlations with external detectors. While some studies have explored machine\u2011learning extrapolation or analytic corrections based on shower shape models, none have yet demonstrated a systematic, unbiased recovery that matches the true deposited energy across the full 10\u201350\u202fMeV range. Therefore, more detailed simulations, validation with calibration data, and potentially new reconstruction paradigms are needed to determine whether such recovery is feasible in practice."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What range of r\u2011mode saturation amplitudes is theoretically expected for young, rapidly rotating neutron stars, and how does this amplitude evolve as the star cools?<|assistant|>Models of r\u2011mode instability predict saturation amplitudes between 10\u207b\u2075 and 10\u207b\u00b3, depending on the neutron star\u2019s mass, radius, and the microphysical dissipation mechanisms (viscosity, superfluidity, crust\u2011core coupling). As the star cools, viscous damping weakens, allowing the amplitude to grow until nonlinear mode couplings or exotic damping processes (e.g., hyperon bulk viscosity) halt the growth, typically on timescales of weeks to months after the instability is triggered."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do timing glitches influence the excitation and damping of r\u2011mode oscillations in neutron stars?<|assistant|>Glitches, which are sudden spin\u2011up events, can transfer angular momentum from the interior superfluid to the crust. This sudden change can perturb the star\u2019s equilibrium, potentially exciting r\u2011mode oscillations. Subsequent energy dissipation through gravitational radiation and internal viscosity will damp the mode, possibly on timescales comparable to the glitch recovery time (~days to weeks). The efficiency of this process depends on the coupling between the core and the crust, as well as on the star\u2019s temperature profile."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>To what extent does the neutron star equation of state determine the relationship between the stellar spin frequency and the gravitational\u2011wave frequency emitted by r\u2011modes?<|assistant|>The r\u2011mode GW frequency is approximately (4/3) times the stellar spin frequency for a slowly rotating star, but relativistic corrections and the star\u2019s compactness (M/R) shift this relation. Different equations of state (stiff vs. soft) change the star\u2019s radius for a given mass, thereby altering the compactness and the coefficient relating spin to GW frequency. Calculations using realistic equations of state yield variations of a few percent in the GW frequency for a given spin, which is significant for precise template placement in searches."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What advantages do coherent, multi\u2011detector networks provide when searching for continuous gravitational\u2011wave signals from r\u2011mode oscillations compared to single\u2011detector analyses?<|assistant|>Coherent multi\u2011detector searches combine the data streams in a way that maximizes signal\u2011to\u2011noise ratio and allows for better discrimination of instrumental artifacts. The network\u2019s antenna patterns provide sky\u2011dependent sensitivity, reducing blind spots and enabling the use of a global F\u2011statistic that coherently adds contributions from all detectors. This leads to deeper upper limits and improved robustness against transient noise, essential for detecting the weak, long\u2011lasting signals expected from r\u2011modes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is r\u2011mode emission a viable explanation for the unusually negative braking index observed in some young pulsars beyond PSR\u202fJ0537\u20116910?<|assistant|>Current observations of negative braking indices in a handful of young pulsars cannot be conclusively explained by r\u2011mode emission alone. While r\u2011modes can provide additional spin\u2011down torque, the required saturation amplitudes often exceed theoretical limits, and the observed braking indices may also involve magnetospheric evolution or fallback accretion effects. Therefore, we cannot definitively state that r\u2011mode emission accounts for these indices; further multi\u2011wavelength observations and more sensitive GW searches are needed to clarify the dominant mechanisms."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected contribution to the isotropic gravitational\u2011wave background from binary neutron star mergers at high redshift?<|assistant|>Astrophysical models predict that binary neutron star mergers should contribute a stochastic background whose energy density peaks around a few tens of Hz. The high\u2011redshift tail of the merger rate, weighted by the redshift dependence of the cosmic star\u2011formation rate and delay\u2011time distributions, is expected to add a modest but non\u2011negligible component to the overall background, typically on the order of \\(10^{-10}\\) in \\(\\Omega_{\\mathrm{GW}}\\) at 25\u202fHz."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can correlated terrestrial magnetic noise impact the sensitivity of cross\u2011correlation searches for a stochastic background?<|assistant|>Coherent magnetic fields, such as Schumann resonances, can couple into the interferometer strain channels at the same frequency in spatially separated detectors. If not accounted for, these correlated noise sources mimic a stochastic signal and inflate the measured cross\u2011correlation, thereby reducing the achievable sensitivity and potentially biasing the inferred upper limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the implications of detecting a scalar or vector polarization component in the isotropic gravitational\u2011wave background for alternative theories of gravity?<|assistant|>A statistically significant detection of scalar or vector polarizations would constitute direct evidence for physics beyond General Relativity. It would point to modified gravity models that predict extra degrees of freedom, such as scalar\u2013tensor theories or massive gravity, and would constrain their coupling constants and propagation speeds through the measured spectral shape of the background."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the inclusion of Virgo data alter the overlap reduction function and the sensitivity to high\u2011frequency gravitational\u2011wave background signals?<|assistant|>Adding Virgo to the LIGO network introduces new baselines (Hanford\u2013Virgo and Livingston\u2013Virgo) with different geometries. These baselines have overlap reduction functions that are less suppressed at higher frequencies compared to the LIGO\u2013LIGO baseline, thereby improving the network\u2019s overall sensitivity in the \\(\\sim 70\\)\u2013\\(200\\)\u202fHz band and providing complementary coverage where the LIGO\u2013LIGO response vanishes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What would be the effect on the upper limits of the isotropic gravitational\u2011wave background if future detectors achieve a factor of two improvement in strain sensitivity over O3?<|assistant|>The paper does not address this scenario directly. Determining the impact would require projecting the improved detector noise spectra, recalculating the overlap reduction functions, and re\u2011evaluating the cross\u2011correlation sensitivity over the relevant frequency band. Such projections are beyond the scope of the present work and would need dedicated simulations with the next\u2011generation detector configurations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What precision on the CP\u2011violating phase \u03b4CP can DUNE Phase II achieve with a 40\u202fkt fiducial liquid\u2011argon detector and a beam power exceeding 2\u202fMW over a ten\u2011year data\u2011taking period?<|assistant|>DUNE Phase\u202fII is projected to reach a \u03b4CP precision of roughly 7\u00b0 to 18\u00b0, depending on the true value of \u03b4CP. For \u03b4CP near 0\u00b0 the uncertainty is about 7\u00b0, while for \u03b4CP close to \u2212\u03c0/2 the precision degrades to roughly 18\u00b0. These numbers are derived from the 1000\u202fkt\u00b7MW\u00b7yr exposure expected with the upgraded beam and detector mass."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the DUNE\u2011PRISM concept help to reduce systematic uncertainties in neutrino\u2011argon cross\u2011section measurements?<|assistant|>The DUNE\u2011PRISM strategy places the near\u2011detector liquid\u2011argon TPC on a movable platform that can be shifted sideways across a range of off\u2011axis angles. By sampling the neutrino flux at several off\u2011axis positions, the experiment can reconstruct the energy dependence of the flux with high precision. This off\u2011axis sampling also provides different effective target nuclei and interaction kinematics, enabling simultaneous constraints on cross\u2011sections. The resulting flux and cross\u2011section constraints are then propagated to the far\u2011detector analysis, substantially reducing systematic errors in oscillation parameter extraction."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the key differences between the vertical\u2011drift and horizontal\u2011drift liquid\u2011argon TPC designs used in the DUNE far detectors, and what advantages does each configuration offer?<|assistant|>In a horizontal\u2011drift design (FD1) the charge drift direction is parallel to the detector plane, requiring a relatively short drift distance (~3\u202fm) and a smaller high\u2011voltage system. This simplifies cryogenic safety and electronics integration. The vertical\u2011drift design (FD2) has the drift direction perpendicular to the detector plane, allowing longer drift lengths (~3\u20134\u202fm) and a more compact detector footprint. Vertical drift can improve charge collection efficiency and reduce readout channel count, but demands a higher voltage supply and more stringent purity control. Both designs provide comparable physics performance; the choice depends on engineering trade\u2011offs such as cavern size and detector construction logistics."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main advantages and technical challenges of implementing a dual\u2011phase liquid\u2011argon TPC with optical readout (the ARIADNE concept) for a DUNE far\u2011detector module?<|assistant|>Advantages of the dual\u2011phase ARIADNE design include: (1) charge amplification in the gas phase, which yields higher signal\u2011to\u2011noise and potentially lower energy thresholds; (2) the possibility of optical readout of the avalanche light, providing a fast, calorimetric signal and a complementary timing reference; (3) a more compact readout plane that can reduce the number of electronic channels. Technical challenges comprise: (1) maintaining a stable liquid\u2011gas interface over a large area; (2) ensuring uniform high voltage and field shaping in the gas amplification region; (3) integrating optical sensors with the charge readout without compromising the purity of the argon; and (4) controlling background light and electronic noise from the photon detectors. These challenges require extensive R&D to demonstrate scalability to the multi\u2011kiloton scale of DUNE."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected sensitivity of DUNE to detect neutrinos from a core\u2011collapse supernova occurring at a distance of 100\u202fkpc?<|assistant|>The paper does not provide sensitivity estimates for a supernova at 100\u202fkpc; it focuses on a canonical distance of 10\u202fkpc. Detailed calculations of event rates and detector response for a 100\u202fkpc supernova would require additional modeling of the neutrino flux spectrum, distance scaling, and background rates, which are beyond the scope of the presented document. Consequently, the precise sensitivity for a 100\u202fkpc supernova cannot be inferred from the information given."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What classes of astrophysical phenomena are expected to emit short-duration gravitational-wave bursts, and what are their characteristic time scales and frequency ranges?<|assistant|>Short-duration gravitational-wave bursts are predicted to arise from several astrophysical processes. Core\u2011collapse supernovae produce burst signals with durations from a few milliseconds up to a few seconds, typically spanning frequencies between 10\u202fHz and 1\u202fkHz, with higher frequency components (hundreds of Hz) associated with proto\u2011neutron star oscillations. Binary black\u2011hole or neutron\u2011star mergers emit brief, high\u2011frequency chirps lasting milliseconds, with peak frequencies from a few hundred Hz to several kHz. Non\u2011axisymmetric instabilities in rapidly rotating neutron stars can excite quasi\u2011periodic oscillations (f\u2011modes) that last tens of milliseconds to a few seconds, emitting in the 1\u20133\u202fkHz band. Magnetar starquakes or magnetically driven flares may also produce short bursts in the kilohertz range. Additionally, exotic sources such as cosmic\u2011string cusps or kinks could generate millisecond\u2011scale bursts with a characteristic \\(f^{-4/3}\\) spectrum extending up to several kilohertz."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the coherent WaveBurst (cWB) pipeline detect unmodeled gravitational\u2011wave transients, and what role do the network correlation coefficient and time\u2011frequency binning play?<|assistant|>The coherent WaveBurst pipeline searches for excess coherent power across a network of detectors by performing a time\u2013frequency decomposition of the strain data (e.g., using wavelets). It constructs a likelihood ratio that compares the hypothesis of a coherent gravitational\u2011wave signal against the null hypothesis of detector noise. The network correlation coefficient (cc) quantifies the fraction of coherent energy shared among detectors; a high cc indicates that the observed excess is consistent with a real astrophysical signal rather than independent noise glitches. cWB divides the data into time\u2013frequency bins and applies adaptive thresholds to cluster significant excesses. Triggers are ranked by the coherent network signal\u2011to\u2011noise ratio (\\(\\eta_c\\)), and only those exceeding a chosen cc threshold and passing additional consistency tests are considered for further analysis. This approach allows detection of a wide variety of morphologies without assuming a specific waveform model."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Why is the sensitivity of the LIGO\u2013Virgo network generally better at low frequencies compared to high frequencies for generic burst searches?<|assistant|>The sensitivity difference arises from the detectors\u2019 strain noise spectral density and their antenna response. At low frequencies (tens to a few hundred Hz), the interferometers are limited mainly by seismic and suspension noise, but the advanced noise\u2011reduction techniques and the use of multiple detectors with similar orientations allow coherent stacking of signals, improving the effective strain sensitivity. In contrast, at high frequencies (above ~1\u202fkHz), shot noise dominates, and the detectors\u2019 optical configuration (e.g., power\u2011recycling cavity, mirror coatings) imposes a steeper rise in noise. Moreover, the antenna patterns of the two LIGO detectors are nearly identical, whereas Virgo\u2019s misalignment reduces coherent response for high\u2011frequency bursts, further diminishing the network\u2019s effective sensitivity in that band."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are data\u2011quality vetoes in gravitational\u2011wave searches, and how do they help reduce false alarms from environmental or instrumental artifacts?<|assistant|>Data\u2011quality vetoes are predefined time intervals during which the detector data are deemed unreliable due to known disturbances. They are derived from auxiliary channels that monitor environmental conditions (seismics, magnetics, acoustic sensors) or instrumental states (laser power, alignment). By cross\u2011correlating glitches in the gravitational\u2011wave channel with signatures in auxiliary channels, analysts can flag and exclude periods where noise transients are likely to mimic astrophysical signals. Vetoes are ranked by effectiveness; the most effective ones remove a high fraction of glitches while sacrificing only a small fraction of live\u2011time. Applying vetoes reduces the background trigger population, improves the significance of real events, and ensures that upper\u2011limit calculations are not biased by non\u2011astrophysical artifacts."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the most effective method to distinguish between cosmological and astrophysical contributions in an anisotropic gravitational-wave background?<|assistant|>Distinguishing cosmological from astrophysical components relies on their distinct angular power spectra and spectral indices. Cosmological backgrounds are expected to be nearly isotropic with a relatively flat or slowly varying spectrum, whereas astrophysical backgrounds trace the large\u2011scale structure and show stronger anisotropy aligned with the matter distribution. By performing a spherical\u2011harmonic decomposition of the sky map and jointly fitting for the amplitude, spectral index, and multipole dependence, one can separate the two contributions. However, this separation is limited by detector sensitivity, foreground contamination, and the similarity of spectral shapes at certain multipoles."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does including a third detector such as Virgo affect the angular resolution of a stochastic background map?<|assistant|>Adding a third detector introduces additional baselines with different arm orientations and lengths, which enlarges the network\u2019s antenna\u2011pattern coverage. The angular resolution improves roughly with the smallest baseline length divided by the highest frequency used, but the LIGO\u2013Virgo baseline is shorter than the LIGO\u2013LIGO baseline, so the highest multipoles are still limited. Nonetheless, the extra baseline reduces degeneracies between sky pixels, improves sky coverage (especially the southern hemisphere), and increases the overall sensitivity to anisotropic features."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main challenges in using the broadband radiometer technique for detecting point\u2011like sources in the stochastic background?<|assistant|>The broadband radiometer assumes that the signal is confined to a single pixel with negligible covariance to neighboring pixels. In reality, the detector antenna pattern couples adjacent pixels, causing signal leakage and bias. The technique also presumes a flat spectral shape across the band, which may not hold for real sources. Moreover, non\u2011Gaussian detector noise and calibration uncertainties can mimic or mask weak point\u2011like signals, requiring careful regularization and robust statistical methods to extract reliable limits."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role does data folding over one sidereal day play in reducing computational cost for anisotropic background searches?<|assistant|>Data folding exploits the Earth\u2019s rotational symmetry: the antenna pattern repeats every sidereal day. By folding the entire observing run into a single sidereal day, cross\u2011correlations from many days are coherently summed, reducing the time\u2011frequency data volume by the number of days. This drastically lowers memory requirements and computational time, enabling finer pixelation or higher frequency resolution while keeping the analysis tractable."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected contribution of primordial black hole mergers to the anisotropic gravitational\u2011wave background at frequencies below 100 Hz?<|assistant|>I do not know that answer. The paper does not discuss primordial black hole mergers, and current theoretical models lack precise predictions for their contribution to the anisotropic background at low frequencies. Estimating this would require detailed modeling of the primordial black hole population, merger rates, and resulting angular distribution\u2014work that is beyond the scope of the present study and not covered in the existing literature."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the number of kinks per loop influence the amplitude of the stochastic gravitational\u2011wave background produced by a network of cosmic strings?<|assistant|>Increasing the number of kinks per oscillation enhances the total power emitted by each loop. For models where the loop distribution contains many small loops (e.g., model\u00a0B or the interpolating model\u00a0C\u20112), the background spectrum rises approximately linearly with the kink number in the frequency range accessible to ground\u2011based detectors. Consequently, a larger kink population raises the overall \\u03a9GW(f) and can shift the peak of the spectrum to higher frequencies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What upper limits on the cosmic\u2011string tension \\(G\\mu\\) can be derived from the current O3 data of LIGO\u2013Virgo for different loop\u2011distribution scenarios?<|assistant|>Analyses of the O3 data, combining both burst and stochastic searches, exclude tensions above roughly \\(4\\times10^{-15}\\) for the most optimistic loop model (model\u00a0B). For the less optimistic scaling model (model\u00a0A) the exclusion is weaker, reaching down only to about \\(10^{-13}\\). These limits assume a single cusp per loop and vary mildly with the assumed number of kinks."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way do cusp\u2011generated gravitational\u2011wave bursts differ from those produced by kinks or kink\u2011kink collisions in terms of detectability by ground\u2011based interferometers?<|assistant|>Cusps emit highly beamed, short\u2011duration bursts with a characteristic strain falling as \\(f^{-4/3}\\). Because the emission is narrowly directed, only a small fraction of bursts are observable, but those that are seen can have large amplitudes. Kinks, emitting with a fan\u2011like pattern and a \\(f^{-5/3}\\) spectrum, produce more numerous but weaker events. Kink\u2011kink collisions radiate isotropically with a \\(f^{-2}\\) spectrum; when many kinks are present they dominate the burst rate and can provide the loudest signals for a fixed detector sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the intercommutation probability of cosmic superstrings alter the gravitational\u2011wave signatures that LIGO\u2013Virgo could detect?<|assistant|>I do not have information on this specific aspect. The analysis in the paper focuses on field\u2011theory Nambu\u2013Goto strings with an intercommutation probability close to one. Effects of reduced intercommutation probabilities, which are relevant for cosmic superstrings, are not addressed here and would require dedicated simulations and theoretical work to determine their impact on the burst rate and stochastic background."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What improvements are expected from the upcoming O4 observing run in terms of constraints on cosmic\u2011string parameters?<|assistant|>The O4 run will provide roughly twice the observation time of O3 and benefit from the planned upgrades to the LIGO and Virgo detectors. Projections indicate that the improved strain sensitivity, especially at high frequencies, could tighten the exclusion on \\(G\\mu\\) by up to an order of magnitude for the most favorable loop models. Additionally, longer data sets will reduce statistical uncertainties in the stochastic background search, potentially turning the current upper limits into actual detections if the string tension lies near the current bounds."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What theoretical mechanisms can produce sub\u2011solar mass black holes in the early universe?<|assistant|>Several mechanisms have been proposed, including the collapse of primordial density fluctuations (primordial black holes), the collapse of cooling dark\u2011matter halos in dissipative dark\u2011matter models, and the formation of exotic compact objects such as boson stars. Each scenario predicts a different mass spectrum and spatial distribution for sub\u2011solar mass black holes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can gravitational\u2011wave observations place limits on the fraction of dark matter that is in the form of primordial black holes?<|assistant|>Gravitational\u2011wave detectors measure the merger rate of compact binaries. By comparing the observed (or upper\u2011limit) merger rates with theoretical predictions for primordial\u2011black\u2011hole binaries, one can infer an upper limit on the primordial\u2011black\u2011hole abundance, expressed as the fraction of dark matter \\(f_{\\rm PBH}\\). This requires modeling the binary formation process, merger time distribution, and the detector sensitivity to sub\u2011solar mass signals."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Why does the mass ratio of the binary components affect the detectability of sub\u2011solar mass binary mergers?<|assistant|>The signal\u2011to\u2011noise ratio of a binary merger depends on the chirp mass, which is a weighted combination of the two component masses. For a fixed total mass, a more unequal mass ratio reduces the chirp mass, leading to a weaker gravitational\u2011wave signal and a smaller horizon distance. Consequently, binaries with very small mass ratios are harder to detect with current detectors."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What observational signatures would distinguish black holes formed through dissipative dark\u2011matter collapse from those formed via primordial fluctuations?<|assistant|>Black holes from dissipative dark\u2011matter collapse are expected to have a broader mass spectrum and may form in dense dark\u2011matter halos, potentially leading to a different spatial clustering compared to primordial black holes. Additionally, the binary formation channels may differ, producing distinct spin and eccentricity distributions. These differences could, in principle, be probed by precise measurements of the binary parameters in gravitational\u2011wave events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected spin distribution of sub\u2011solar mass black holes produced by dissipative dark\u2011matter collapse?<|assistant|>The paper does not address this question, and current theoretical models do not provide a definitive prediction for the spin distribution of such black holes. The spin depends on the angular momentum of the collapsing dark\u2011matter halo, the efficiency of angular momentum transport, and the microphysics of the dark sector, none of which are yet constrained by observations or detailed simulations. Therefore, we do not have a reliable answer to this question at present."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do seedless clustering algorithms improve sensitivity to narrow\u2011band long\u2011duration gravitational\u2011wave signals compared to seed\u2011based methods?<|assistant|>Seedless clustering searches scan the time\u2011frequency plane for coherent excess power using parametrised curves (e.g., B\u00e9zier or sinusoidal tracks) that can follow slowly drifting or quasi\u2011periodic signals. Because the algorithm does not require any thresholded pixels as a seed, it can integrate weak power over many frequency bins and long timescales, boosting the signal\u2011to\u2011noise ratio for narrow\u2011band, long\u2011duration bursts. Seed\u2011based algorithms, in contrast, rely on thresholded pixels and are more effective for generic, broadband morphologies but can miss or poorly reconstruct slowly varying, narrow\u2011band signals."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the main challenges posed by non\u2011Gaussian noise transients in long\u2011duration gravitational\u2011wave searches and how are they mitigated?<|assistant|>Non\u2011Gaussian transients, or glitches, can mimic long\u2011duration excess power and inflate the false\u2011alarm rate. They arise from environmental disturbances, instrumental resonances, or non\u2011linear coupling. Mitigation strategies include: (1) vetoing data coincident with auxiliary sensor triggers, (2) subtracting identified linear noise sources via Wiener filtering or machine\u2011learning techniques, (3) masking persistent spectral lines, and (4) applying coherence and duration cuts in the clustering pipelines to reject incoherent or short\u2011duration outliers. These steps reduce the background while preserving sensitivity to astrophysical signals."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do upper limits on the root\u2011sum\u2011square strain amplitude (hrss) translate into constraints on the energy emitted in gravitational waves by astrophysical sources such as magnetars or eccentric binary black holes?<|assistant|>The hrss limit at a given frequency and distance can be converted to an upper bound on the isotropic GW energy via \\(E_{\\text{GW}} \\approx \\frac{c^{3}}{G} \\, \\pi^{2} f^{2} h_{\\text{rss}}^{2} D^{2}\\). Thus, tighter hrss limits imply lower allowed GW energies for a source at distance \\(D\\). For example, a 10\u2011ms magnetar burst with an hrss limit of \\(10^{-22}\\,\\text{Hz}^{-1/2}\\) at 100\u202fHz would constrain the emitted energy to below a few \\(10^{-6}\\,M_{\\odot}c^{2}\\). These bounds help rule out or disfavour models predicting large GW luminosities from such events."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways can the inclusion of Virgo data in future observing runs enhance the detection prospects for long\u2011duration gravitational\u2011wave transients?<|assistant|>Adding Virgo increases the network\u2019s sky\u2011coverage and triangulation accuracy, improving the ability to localise and confirm coincidences. The extra detector also provides an independent baseline, enhancing coherence tests and reducing the false\u2011alarm probability. With Virgo\u2019s sensitivity approaching that of the LIGO detectors in the next observing runs, the combined network can lower the hrss thresholds by a factor of two or more, directly translating into larger accessible volumes and higher detection rates for long\u2011duration signals."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the predicted event rate of long\u2011duration gravitational\u2011wave bursts from fallback accretion onto rapidly rotating black holes?<|assistant|>The paper does not provide an answer because the expected rate for this channel is highly uncertain. Current theoretical models of fallback accretion are limited by complex hydrodynamics, magnetic field configurations, and the poorly constrained distribution of progenitor masses. Consequently, no reliable population synthesis exists to predict the rate, and observational constraints are absent due to the lack of detections. Addressing this question would require detailed simulations of core\u2011collapse supernovae with post\u2011bounce accretion, coupled to GW emission estimates, a task beyond the scope of the current study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the upper limits on the dark\u2011photon\u2013baryon coupling derived from ground\u2011based interferometers constrain theoretical models that generate ultralight dark photons via the misalignment mechanism?<|assistant|>The misalignment mechanism predicts a relic abundance that depends on the initial field displacement and the dark\u2011photon mass. The limits on the coupling strength translate into an upper bound on the field amplitude, which in turn restricts the allowed range of initial displacements for a given mass. Models that require a large initial displacement to account for the observed dark matter density are therefore disfavored for masses in the \\(10^{-14}\\)\u2013\\(10^{-11}\\,\\text{eV}/c^{2}\\) window."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant noise sources that limit the sensitivity of LIGO/Virgo to ultralight dark\u2011photon signals, and how might future detector upgrades mitigate them?<|assistant|>The primary limitations are seismic and suspension thermal noise at low frequencies and quantum shot noise at high frequencies. Additionally, narrow spectral lines from instrumental resonances and scattered light can mimic or obscure the quasi\u2011monochromatic dark\u2011photon signature. Future upgrades such as cryogenic test masses, improved mirror coatings, and quantum squeezing will reduce thermal and shot noise, while better vibration isolation and active control of scattering will suppress line artifacts, thereby extending sensitivity across a broader mass range."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a space\u2011based interferometer like LISA or TianQin extend the search for dark photons compared to ground\u2011based detectors, and what new mass window would become accessible?<|assistant|>Space\u2011based detectors have longer arm lengths and operate in a quieter gravitational\u2011wave environment, reducing seismic and suspension noise. Their lower frequency sensitivity (down to \\(\\sim10^{-4}\\,\\text{Hz}\\)) allows probing dark\u2011photon masses down to \\(\\sim10^{-18}\\,\\text{eV}/c^{2}\\), far below the \\(\\sim10^{-14}\\,\\text{eV}/c^{2}\\) lower bound reachable by ground\u2011based interferometers. Thus, missions like LISA and TianQin can explore a complementary, lower\u2011mass regime."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the role of the common\u2011mode motion of the interferometer mirrors in enhancing the detectability of dark photons, and how does it differ from the differential\u2011mode contribution?<|assistant|>Dark photons exert a nearly coherent force on all test masses, leading to common\u2011mode motion that does not change instantaneous arm lengths but modulates the light\u2011travel time. This effect introduces a strain component proportional to \\(f_{0}L/c\\), which is not suppressed by the Earth\u2019s velocity \\(v_{0}/c\\). Consequently, the common\u2011mode signal can be stronger than the differential component, especially at higher frequencies, and must be modeled separately in the analysis to avoid loss of sensitivity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How would a stochastic background of dark\u2011photon dark matter manifest differently in the cross\u2011correlation versus excess\u2011power analysis, and is it possible to separate it from a genuine gravitational\u2011wave background?<|assistant|>A stochastic dark\u2011photon background would produce a coherent, quasi\u2011monochromatic signal that is common to all detectors, leading to a non\u2011zero cross\u2011correlation that is highly frequency\u2011dependent due to Doppler broadening. In contrast, a stochastic gravitational\u2011wave background is expected to be broadband and isotropic, yielding a different overlap reduction function. The paper does not address this distinction, as it focuses on searching for a deterministic monochromatic signal rather than a stochastic background. Distinguishing between the two would require a dedicated analysis of the spectral shape and angular correlation of the cross\u2011correlation, which was beyond the scope of the presented work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the spin\u2011down limit for a gravitational\u2011wave source, and why is it a key benchmark in continuous\u2011wave searches from pulsars?<|assistant|>The spin\u2011down limit is the maximum gravitational\u2011wave strain that could be emitted if a pulsar\u2019s entire loss of rotational energy were converted into gravitational radiation. It is calculated from the measured spin frequency, its derivative, the pulsar\u2019s distance, and an assumed moment of inertia. A search that reaches below this limit demonstrates that any gravitational\u2011wave emission must be smaller than the full spin\u2011down power, giving a physically meaningful constraint on the star\u2019s deformation or other emission mechanisms."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the inter\u2011glitch braking indices measured for PSR J0537\u22126910 suggest the possibility of gravitational\u2011wave energy loss?<|assistant|>The long\u2011term braking index of PSR J0537\u22126910 is far below the canonical value of 3, indicating an accelerating spin\u2011down. The inter\u2011glitch braking index, measured between successive glitches, is often >10 and approaches an asymptotic value near 7 shortly after a glitch. Braking indices of 5 and 7 are expected for energy loss dominated by a time\u2011varying mass quadrupole (l = m = 2) and by r\u2011mode oscillations, respectively. The observed indices therefore hint that a portion of the pulsar\u2019s rotational energy may be drained through gravitational\u2011wave emission."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What specific contribution does NICER X\u2011ray timing data provide to the LIGO/Virgo search for PSR J0537\u22126910?<|assistant|>NICER supplies a contemporaneous, phase\u2011accurate timing ephemeris that tracks the pulsar\u2019s rotation and glitch epochs. This ephemeris allows the gravitational\u2011wave search to heterodyne the detector data at the expected frequency (once or twice the spin frequency) with the correct phase evolution, keeping the signal coherent over months. Without such a timing solution the search would lose sensitivity because the signal phase would drift due to glitches and irregular spin\u2011down."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the upper limit on the equatorial ellipticity of PSR J0537\u22126910 compare with theoretical maximum ellipticities a neutron\u2011star crust can support?<|assistant|>The 95\u202f% credible upper limit on the ellipticity of PSR J0537\u22126910 is \u03b5\u202f<\u202f3\u202f\u00d7\u202f10\u207b\u2075. Theoretical estimates of the maximum elastic deformation sustainable by a neutron\u2011star crust range from ~10\u207b\u2075 to a few\u202f\u00d7\u202f10\u207b\u2076, depending on composition and temperature. Thus, the observational limit is at or slightly above the highest theoretical values, indicating that if the crust were maximally strained the star would still be below the sensitivity of the current search."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is there evidence that the size of a glitch in PSR J0537\u22126910 directly determines the amplitude of any transient gravitational waves produced at the glitch epoch?<|assistant|>No. The paper does not address the relationship between glitch size and transient gravitational\u2011wave amplitude. While the timing data record the magnitude of each glitch, the analysis focuses on continuous\u2011wave emission at the rotational harmonics and does not search for or quantify any short\u2011duration signals associated with the glitches. Establishing such a correlation would require dedicated glitch\u2011triggered searches with high\u2011time\u2011resolution data, which remains a topic for future study."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the advantages of using a high\u2011pressure gaseous argon TPC over a liquid\u2011argon TPC for measuring low\u2011energy protons in neutrino interactions?<|assistant|>In a high\u2011pressure gaseous argon TPC the density of the medium is much lower than in liquid argon, so protons with kinetic energies as low as 5\u202fMeV (corresponding to a track length of a few centimeters) can leave a visible ionisation trail. This gives a significantly lower detection threshold compared with liquid argon, where a 46\u202fMeV proton is needed for a 2\u202fcm track. Additionally, the long mean free path for hadrons in the gas (~90\u202fm) reduces the probability of secondary intranuclear interactions, leading to cleaner event topologies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does a magnetic field in the near detector help distinguish neutrino from antineutrino interactions?<|assistant|>A magnetic field bends charged particles according to the sign of their charge. In a magnetised TPC the curvature of the outgoing lepton track can be measured, allowing one to determine whether the lepton is a \u03bc\u207a (from a \u03bd\u0304) or a \u03bc\u207b (from a \u03bd). This charge\u2011sign determination is essential for separating neutrino and antineutrino components in a mixed beam, thereby reducing systematic uncertainties in oscillation analyses."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can a gaseous argon TPC be used to directly detect tau neutrino appearance in the near detector?<|assistant|>Yes, in principle the high spatial resolution and good particle identification of a gaseous argon TPC enable the reconstruction of the short\u2010lived \u03c4 lepton decay products. However, the expected rate of \u03bd\u03c4 charged\u2011current interactions at the near detector is extremely low, and practical sensitivity would require a very large exposure or additional specialised trigger strategies. The current design of the ND\u2011GAr does not include dedicated \u03c4\u2011identification capabilities, so while the physics case exists, the detector is not optimised for it."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role does the calorimeter surrounding the TPC play in neutrino trident searches?<|assistant|>The calorimeter provides precise measurements of the energy and direction of photons from \u03c0\u2070 decays and of hadronic showers. By accurately reconstructing electromagnetic and hadronic activity, it helps suppress background events that mimic the two\u2011lepton signature of a trident process, improving the purity of the signal sample."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the current limitations on measuring the axial form factor of the neutron using the ND\u2011GAr detector?<|assistant|>I do not have a definitive answer to this question. The paper focuses on detector design, cross\u2011section measurements, and BSM searches, but it does not discuss the specific challenges of extracting the neutron axial form factor from the data. Determining that quantity would require detailed modelling of neutrino\u2011neutron interactions, specialised selection criteria, and a comparison with theoretical predictions that are beyond the scope of the present document."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the primary physical mechanisms that can generate continuous gravitational waves from a spinning neutron star, and how do the predicted wave frequency and amplitude differ for each mechanism?<|assistant|>The two most discussed mechanisms are (1) a non\u2011axisymmetric mass quadrupole \u2013 caused by a permanent deformation such as a \u2018mountain\u2019 on the crust or a strong internal magnetic field \u2013 which emits at twice the star\u2019s spin frequency and scales linearly with the equatorial ellipticity; and (2) unstable r\u2011mode oscillations, which are large\u2011amplitude fluid modes driven unstable by gravitational radiation. R\u2011modes emit at a frequency of roughly 4/3 of the spin frequency and the strain amplitude depends on a dimensionless r\u2011mode amplitude parameter, \u03b1, rather than on an ellipticity. The expected amplitudes for both mechanisms are generally very small (h \u2272 10\u207b\u00b2\u2075\u201310\u207b\u00b2\u2076 for nearby young neutron stars) but can be enhanced if the deformation or r\u2011mode amplitude is unusually large."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the estimated age of a supernova remnant affect the range of spin\u2011down parameters that must be searched when looking for continuous gravitational waves from its central compact object?<|assistant|>An older remnant implies a smaller age\u2011based upper limit on the strain and, assuming the star\u2019s rotation has slowed mainly through gravitational\u2011wave emission, the allowed first frequency derivative, \u02d9f, scales roughly as \u2013f/\u03c4, where \u03c4 is the age. Younger remnants therefore require searches over a wider range of spin\u2011down values (including larger negative \u02d9f) to account for the possibility of rapid initial spin and strong braking. This also influences the second derivative range, which is tied to the braking index; a larger spread in \u03c4 leads to a broader search in \u02d9f and \u00a8f to maintain sensitivity to physically plausible spin\u2011down trajectories."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the sensitivity depth in a semi\u2011coherent continuous\u2011wave search, and how is it typically estimated using simulated injections?<|assistant|>Sensitivity depth, D(f), is defined as the ratio of the detector\u2019s strain spectral noise density to the smallest detectable strain amplitude at a given frequency, i.e., D(f) = \u27e8S_h(f)\u27e9 / h_{95%}. It represents the search\u2019s efficiency in converting detector noise into a detectable signal. To estimate D(f), one injects a large number of simulated continuous\u2011wave signals with known amplitudes into real data, processes them with the full search pipeline, and finds the amplitude at which 95% of the injections exceed the detection threshold. The depth is then computed for each frequency band, and an empirical scaling (often linear with frequency) is used to extrapolate to neighboring bands."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Why is the F\u2011statistic a preferred matched\u2011filter statistic for directed continuous\u2011wave searches, and what considerations determine the choice of coherent segment length in a semi\u2011coherent scheme like Weave?<|assistant|>The F\u2011statistic analytically maximizes the likelihood over the unknown amplitude, polarization, and initial phase, providing a powerful detection statistic that is sensitive to weak, nearly monochromatic signals. In a semi\u2011coherent scheme, data are split into short coherent segments (length T_coh) where the F\u2011statistic is computed; these are then summed to form a mean statistic. Shorter segments reduce computational cost and mitigate phase errors from imperfect spin\u2011down models, but they also lower the coherent SNR. Longer segments improve sensitivity but require a denser template bank to cover the parameter space and increase the risk of signal loss due to mismatch. The optimal T_coh is therefore chosen by balancing sensitivity gains against computational feasibility, often guided by simulations that include realistic noise and spin\u2011down uncertainties."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Does the search for continuous waves from Cas\u202fA and Vela\u202fJr. place any limits on the possible r\u2011mode amplitude of their central compact objects?<|assistant|>The paper does not provide explicit upper limits on r\u2011mode amplitudes. While it discusses r\u2011mode emission as a theoretical possibility and presents sensitivity curves for strain, it focuses on constraints derived from ellipticity models and does not perform dedicated simulations or injections for r\u2011mode signals. Consequently, no quantitative limits on the r\u2011mode amplitude, \u03b1, are given; deriving such limits would require a separate study that models the r\u2011mode waveform and injects it into the data to assess detectability."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the trade\u2011offs between electric field strength and scintillation light yield in large\u2011volume dual\u2011phase liquid argon time\u2011projection chambers?<|assistant|>In a dual\u2011phase LArTPC the primary scintillation yield depends strongly on the electron\u2011ion recombination probability. A low drift field (tens of V/cm) allows many ionized electrons to recombine with ions, producing a larger fraction of the 127\u202fnm VUV photons. As the field is increased to several hundred V/cm, the drift velocity rises and the recombination probability drops, reducing the S1 yield. However, a higher field improves charge extraction and minimizes attachment losses, which is essential for accurate calorimetry. The optimal field therefore balances a sufficient S1 signal for timing and trigger purposes against the need for high\u2011quality charge readout."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the geometry of a wavelength\u2011shifting material influence the angular distribution and detection efficiency of scintillation photons in a dual\u2011phase LArTPC?<|assistant|>The angular emission pattern of re\u2011emitted photons depends on whether the wavelength shifter is coated directly on the photocathode surface, painted on a thin film, or deposited on a larger area. Coating the inner surface of the PMT glass (as with TPB) produces a more isotropic re\u2011emission with a relatively high transport efficiency to the photocathode. In contrast, a thin polyethylene\u2011naphthalate (PEN) foil positioned over the PMT window presents two exposed faces; photons incident on either side are re\u2011emitted in all directions, but the geometry causes a larger fraction of the light to escape or hit non\u2011photosensitive areas, reducing the effective detection efficiency. Additionally, foils may introduce multiple scattering and surface reflections that alter the arrival\u2011time distribution, affecting the timing resolution."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways does xenon doping modify the spectral composition and attenuation characteristics of scintillation light in liquid argon, and how can this be exploited for improved light collection in large detectors?<|assistant|>When xenon is dissolved in liquid argon at the ppm level, energy transfer from excited argon excimers to xenon occurs. The resulting xenon excimers emit photons at longer wavelengths (\u2248\u202f178\u202fnm and \u2248\u202f150\u202fnm), which are less strongly absorbed by impurities and experience a longer Rayleigh scattering length (\u2248\u202f3\u20139\u202fm) compared to the 127\u202fnm argon light (\u2248\u202f1\u202fm). Consequently, photons travel further before scattering or being absorbed, improving the uniformity of light collection, especially for events occurring far from the photodetector array. However, the original 127\u202fnm component is partially quenched, so the total S1 amplitude can decrease if the xenon concentration is too high. Optimizing the xenon level thus requires balancing increased propagation distance against reduced primary light yield."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the most effective computational strategies for accurately simulating photon transport over long drift distances while keeping resource demands manageable in large LArTPC experiments?<|assistant|>Full Monte\u2011Carlo tracking of each VUV photon is prohibitively expensive for multi\u2011kilometre LAr volumes. Practical solutions include: (1) constructing photon libraries by generating a large number of photons from a fine grid of voxels, recording for each detector channel the visibility, minimum arrival time and time\u2011distribution parameters; (2) interpolating between voxels during event simulation to estimate light yield without individual photon tracking; (3) using importance sampling to focus on regions of high light\u2011yield density; (4) parallelising the photon generation step with GPUs or distributed computing; and (5) implementing analytic approximations for Rayleigh scattering and absorption based on measured attenuation lengths. These methods reduce CPU time by orders of magnitude while preserving sufficient accuracy for detector\u2011design studies."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected degradation in light detection efficiency of PEN or TPB wavelength shifters after ten years of operation in a liquid argon environment under continuous VUV irradiation, and what mechanisms dominate this aging process?<|assistant|>The agent does not have sufficient information to provide a reliable prediction. Long\u2011term aging studies of PEN and TPB films in liquid argon, exposed continuously to VUV photons, have not yet been performed on a decade timescale. Key mechanisms\u2014such as photo\u2011degradation of the organic molecules, micro\u2011cracking of the polymer matrix, or contamination from dissolved gases\u2014remain unquantified experimentally, so the future efficiency loss cannot be determined from current data alone. Further dedicated aging experiments would be required to answer this question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do the detection thresholds of matched\u2011filter pipelines influence the completeness of the GWTC\u20112.1 catalog for low\u2011mass binary neutron star mergers?<|assistant|>The detection thresholds, such as the chosen false\u2011alarm\u2011rate cut and signal\u2011to\u2011noise ratio thresholds, determine which signals exceed the pipelines\u2019 sensitivity limits. Lower thresholds increase completeness but also raise the background noise, while higher thresholds reduce false alarms at the cost of missing marginal events. The GWTC\u20112.1 catalog does not provide a detailed completeness analysis for low\u2011mass binary neutron star systems; such an assessment would require dedicated injection campaigns across the full parameter space of neutron star masses and spins."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the implications of the newly identified high\u2011mass binary black hole events for the existence of an intermediate\u2011mass black hole population?<|assistant|>The high\u2011mass events in GWTC\u20112.1, with total masses approaching or exceeding 150\u202fM\u2299, expand the observable mass range for binary black hole mergers. Their presence supports the possibility that intermediate\u2011mass black holes (\u224810\u00b2\u201310\u00b3\u202fM\u2299) can form through hierarchical mergers or dynamical assembly in dense stellar environments. However, the limited number of such detections and the uncertainties in the mass\u2011gap boundaries mean that the existence of a substantial intermediate\u2011mass black hole population remains an open question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the calibration uncertainty of the LIGO and Virgo detectors impact the sky\u2011localization accuracy for high\u2011redshift events in GWTC\u20112.1?<|assistant|>Calibration uncertainties introduce systematic errors in the amplitude and phase of the reconstructed strain, which propagate into the parameter\u2011estimation pipeline and degrade the precision of sky\u2011localization. For high\u2011redshift events with modest signal\u2011to\u2011noise ratios, the resulting 90\u202f% credible regions can be significantly larger than for nearby, louder events. The GWTC\u20112.1 analysis incorporates calibration uncertainties by marginalizing over spline\u2011parameterized amplitude and phase variations, but the exact impact on each event\u2019s localization is not reported in the catalog and would need to be evaluated on a case\u2011by\u2011case basis."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant systematic uncertainties in estimating the effective inspiral spin parameter (\u03c7_eff) for precessing binary black hole systems?<|assistant|>The main systematic sources include waveform model inaccuracies (e.g., missing higher\u2011order modes or imperfect treatment of precession), limited signal\u2011to\u2011noise ratio, and assumptions about spin priors. Additionally, calibration errors can bias phase evolution, directly affecting \u03c7_eff. The current state\u2011of\u2011the\u2011art models (IMRPhenomXPHM, SEOBNRv4PHM) mitigate many of these effects, but residual discrepancies between models and between model and data still contribute to the total systematic uncertainty budget."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the true astrophysical rate of neutron star\u2013black hole mergers in the local universe, as inferred from the GWTC\u20112.1 data?<|assistant|>The GWTC\u20112.1 catalog does not provide a definitive rate estimate for neutron star\u2013black hole (NSBH) mergers. While a few candidate events hint at the possibility of such systems, the current sample size is too small and the statistical and systematic uncertainties too large to derive a robust local merger rate. A more accurate estimate will require additional detections, improved sensitivity, and refined population\u2011modeling efforts."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant systematic uncertainties that limit DUNE\u2019s ability to measure the CP\u2011violating phase \u03b4CP?<|assistant|>DUNE\u2019s sensitivity to \u03b4CP is largely limited by three classes of systematic uncertainties:\\n1. **Neutrino flux prediction** \u2013 uncertainties in hadron production and horn focusing affect the energy\u2011dependent neutrino flux at the far detector. \\n2. **Neutrino\u2011nucleus interaction models** \u2013 uncertainties in cross\u2011sections, final\u2011state interactions, and nuclear effects (e.g., multinucleon emission) change the reconstructed neutrino energy distribution. \\n3. **Detector response** \u2013 uncertainties in calorimetric energy scale, electron\u2013muon separation efficiency, and reconstruction efficiency introduce biases in the extracted oscillation probabilities. DUNE\u2019s near detector program and data\u2011driven techniques are designed to constrain these systematics to the few\u2011percent level required for a high\u2011precision \u03b4CP measurement."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does DUNE\u2019s wide\u2011band neutrino beam help disentangle the neutrino mass ordering from CP\u2011violation effects?<|assistant|>The broad energy spectrum (\u223c0.5\u20134\u202fGeV) of DUNE\u2019s beam samples the first and second oscillation maxima. Matter effects grow with baseline and energy, producing a distinct energy\u2011dependent asymmetry between neutrinos and antineutrinos that depends on the mass ordering but not on \u03b4CP. By measuring the oscillation probability as a function of energy over more than one full oscillation period, DUNE can fit simultaneously for the mass ordering and \u03b4CP, with the energy dependence providing a handle to separate the two effects."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is DUNE\u2019s expected sensitivity to the proton\u2011decay channel \\(p \\rightarrow K^+ \\nu\\) after its full physics run?<|assistant|>With a 40\u2011kiloton fiducial mass and a 40\u2011year exposure (\u22481.6\u202fMt\u2011yr), DUNE expects to set a 90\u202f%\u202fC.L. lower limit on the proton lifetime in the \\(p \\rightarrow K^+ \\nu\\) channel of order \\(1.3 \\times 10^{34}\\)\u202fyears, assuming a 30\u202f% signal efficiency and negligible background after sophisticated reconstruction and selection cuts."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How will DUNE detect neutrinos from a core\u2011collapse supernova and what physics can be extracted from the observed signal?<|assistant|>DUNE\u2019s liquid\u2011argon TPC is especially sensitive to the charged\u2011current absorption of electron neutrinos on argon (\\(\\nu_e + ^{40}\\mathrm{Ar} \\rightarrow e^- + ^{40}\\mathrm{K}^*\\)). A supernova burst at 10\u202fkpc would yield \u22483000 events in a 40\u2011kt detector, allowing a time\u2011resolved measurement of the neutronization burst, accretion, and cooling phases. By fitting the energy and time spectra, one can extract information on the supernova explosion mechanism, neutrino flavor transformation (MSW and collective effects), and the neutrino mass ordering, as the early neutronization burst is highly sensitive to the ordering."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the precise value of the neutrino mass ordering?<|assistant|>The neutrino mass ordering (whether the third mass eigenstate is heavier or lighter than the first two) is currently unknown. While experiments like DUNE aim to determine it with high significance, the exact ordering has not yet been measured, so the answer remains undetermined at this time. Further data from long\u2011baseline, reactor, and atmospheric neutrino experiments are required to resolve this fundamental question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected rate of strongly lensed binary black hole mergers detectable with the next-generation third\u2011generation gravitational\u2011wave detectors?<|assistant|>Forecasts based on standard lensing models (e.g., singular isothermal sphere or ellipsoid) predict that at design sensitivity the merger rate of lensed binary black hole events could rise to a few percent of the total detectable rate, reaching \\u2265 10\\u201315% depending on the mass distribution and redshift evolution of the source population. These predictions assume that the intrinsic merger rate follows the star\u2011formation rate and that the detector horizon extends to z \\u2265 5."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the presence of microlenses embedded in galaxy\u2011cluster potentials modify the wave\u2011optics signatures observed in gravitational\u2011wave signals?<|assistant|>Microlenses with masses between a few solar masses and a thousand solar masses, situated in the macrolensing environment of a cluster, can introduce interference patterns in the waveform that are superimposed on the macrolens magnification. This produces oscillatory modulations in the frequency domain, with characteristic beat frequencies that depend on the Einstein radius of the microlens and the relative alignment. Numerical simulations show that such effects become appreciable when the microlens Einstein radius is comparable to the GW wavelength (i.e., when the lens mass is \\u2265 10 M\u2299 and the source is at z \\u2265 1). Detecting these patterns would require high signal\u2011to\u2011noise ratios and detailed waveform modeling that includes both macro and micro\u2011lens potentials."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can a precise measurement of the time delay between multiple images of a lensed gravitational\u2011wave event be used to constrain cosmological parameters such as the Hubble constant?<|assistant|>Yes, in principle the time delay between two images of a lensed GW event, combined with an accurate localization of the source and lens, can provide an independent measurement of the Hubble constant. The delay depends on the difference in the Fermat potential between the image positions and on the angular\u2011diameter distances, which are sensitive to H0. However, achieving the required precision demands multiple high\u2011signal\u2011to\u2011noise detections of the same source, robust lens modeling, and accurate determination of the lens mass distribution\u2014challenges that are still being addressed in current research."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the observational signatures that would distinguish a gravitational\u2011wave event lensed by a galaxy cluster from one lensed by a single galaxy?<|assistant|>Galaxy\u2011cluster lensing typically produces longer time delays (weeks to months or even years) and larger magnification factors (up to 10\u2013100) than galaxy\u2011scale lenses, which usually have delays of minutes to days and magnifications of a few. Additionally, cluster lenses often generate multiple images with more complex morphologies, sometimes forming arcs or rings in electromagnetic counterparts. In gravitational waves, one would expect a series of repeated events over extended periods, potentially with varying SNRs reflecting the magnification gradient across the caustic. Precise identification requires long\u2011term monitoring and cross\u2011matching with electromagnetic surveys."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Is it possible to detect the effects of primordial black holes acting as microlenses on gravitational\u2011wave signals from binary black holes?<|assistant|>We currently do not have evidence that primordial black holes serve as microlenses in gravitational\u2011wave observations. Detecting their influence would require observing characteristic interference patterns or frequency\u2011dependent magnification in the GW signal, but such signatures have not yet been observed. The lack of detection could be due to the limited sensitivity of existing detectors, the rarity of suitable alignments, or the absence of a significant population of primordial black holes in the relevant mass range. Further data from next\u2011generation detectors and more sophisticated analysis methods are needed to explore this possibility."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the presence of eccentric orbits influence the sensitivity of semicoherent searches for continuous gravitational waves from neutron stars in binary systems?<|assistant|>Eccentricity introduces additional harmonic components and a more complex Doppler modulation, requiring denser template banks and reducing sensitivity compared to circular orbits. The exact degradation depends on the orbital parameters and the search coherence time."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the expected distribution of spin\u2011down rates for neutron stars in tight binary systems that would make them detectable by all\u2011sky searches in the 50\u2013300\u202fHz band?<|assistant|>Detectable spin\u2011down rates are typically |\u02d9f| \u2272 10\u207b\u00b9\u2070\u202fHz\u202fs\u207b\u00b9 for data spans of months. Most known millisecond pulsars in binaries exhibit spin\u2011downs below this threshold, but the population of unknown systems is poorly constrained."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the use of GPU\u2011accelerated pipelines influence the computational cost scaling with increasing frequency band width in all\u2011sky continuous\u2011wave searches?<|assistant|>GPU acceleration reduces the per\u2011template processing time by an order of magnitude, allowing the template bank to grow with frequency without a proportional increase in wall\u2011time. However, the overall cost still scales roughly with the number of frequency bins, so wider bands remain the limiting factor."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the current theoretical limits on the ellipticity of rapidly rotating neutron stars in low\u2011mass X\u2011ray binaries, and how do these limits compare to the sensitivity achieved by recent LIGO runs?<|assistant|>I do not have that information. The paper focuses on the search methodology and sensitivity estimates, and does not discuss theoretical models of neutron\u2011star ellipticity or compare them with LIGO sensitivities."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Could a future third\u2011generation ground\u2011based interferometer improve the detection prospects for continuous waves from neutron stars in binary systems with orbital periods shorter than 3\u202fdays, and if so, by what factor?<|assistant|>A third\u2011generation detector with ~10\u00d7 lower noise would improve strain sensitivity by roughly a factor of 10, potentially allowing detection of ellipticities an order of magnitude smaller. This would open the window to binaries with very short periods, but detailed simulations are required to quantify the exact factor."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How can the detection of monoenergetic 236\u202fMeV neutrinos produced by kaon decay at rest in the Sun be used to probe dark\u2011matter annihilation in the solar core?<|assistant|>When weakly interacting dark matter particles are gravitationally captured by the Sun, they can annihilate into standard\u2011model particles. The hadronization of the annihilation products generates charged kaons that stop in the dense solar medium and decay to produce monoenergetic \\(\\nu_\\mu\\) at 236\u202fMeV. The flux of these neutrinos at Earth is directly proportional to the dark\u2011matter capture rate, which in turn depends on the dark\u2011matter\u2013nucleon scattering cross section and the dark\u2011matter mass. By measuring or setting limits on the 236\u202fMeV neutrino flux, one can infer the annihilation rate and thus constrain the scattering cross section for models where capture and annihilation are in equilibrium. This provides a complementary probe of dark matter that is sensitive to parameter space inaccessible to terrestrial direct\u2011detection experiments, especially for low\u2011mass or inelastic dark matter scenarios."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the key advantages of a liquid\u2011argon time\u2011projection chamber for identifying the direction of 236\u202fMeV neutrinos compared with water Cherenkov detectors?<|assistant|>At the 236\u202fMeV energy scale, charged\u2011current interactions on argon frequently eject a single proton that is emitted preferentially in the forward direction relative to the incident neutrino. In a liquid\u2011argon TPC, the ionization track of this proton is fully reconstructed with high spatial resolution, allowing its momentum vector to be measured accurately. The accompanying muon track, although largely isotropic, can also be reconstructed. By combining the proton and muon kinematics and applying momentum conservation, one can infer the recoil of the residual nucleus and thereby reconstruct the incoming neutrino direction with an angular resolution of order a few degrees. In contrast, water Cherenkov detectors are unable to see the proton track and rely solely on the Cherenkov ring of the muon, which is far less directional at this energy. Thus, the LArTPC offers superior directional discrimination for monoenergetic solar neutrinos."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the annual motion of the Earth around the Sun affect the acceptance of a deep\u2011underground detector for 236\u202fMeV solar neutrinos, and what is its impact on the sensitivity?<|assistant|>The Sun\u2019s apparent position in the sky changes over the year, causing the incoming neutrino direction to sweep through a range of zenith and azimuth angles relative to the detector coordinates. Since the reconstruction of the neutrino direction in a LArTPC relies on forward proton kinematics, the detector\u2019s effective acceptance depends on the alignment between the proton direction and the detector wire geometry. For angles where the proton track is nearly parallel to a wire plane, track reconstruction can be more difficult, reducing efficiency. Conversely, when the proton is orthogonal to the wire planes, reconstruction improves. By integrating over the full 12\u2011month cycle, one obtains an averaged acceptance that can be factored into the expected event rate. The impact on sensitivity is modest; typical variations are at the tens of percent level, but precise modeling is required to avoid systematic biases in the annual modulation of the signal."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What role do nuclear effects such as the spectral function and meson\u2011exchange currents play in determining the charged\u2011current quasi\u2011elastic cross section for 236\u202fMeV neutrinos on argon?<|assistant|>The spectral function describes the momentum and removal energy distribution of nucleons inside the argon nucleus, providing a more realistic initial\u2011state model than the simple Fermi\u2011gas approximation. This influences the energy and angular distributions of the outgoing lepton and proton. Meson\u2011exchange currents (MEC) introduce two\u2011body interactions where the neutrino couples to a pair of nucleons, leading to multinucleon emission that can mimic single\u2011proton final states. At 236\u202fMeV, MEC contributes roughly 4\u202f% of the total cross section, while the dominant quasi\u2011elastic component is about 64\u202f%. Accurate inclusion of these effects is essential for predicting the rates of single\u2011track events and for evaluating backgrounds, as they alter both the kinematic selection efficiency and the energy reconstruction."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Could the electron neutrino charged\u2011current channel provide better sensitivity to 236\u202fMeV solar KDAR neutrinos than the muon channel, and what are the limitations of this approach?<|assistant|>In principle, the electron channel offers several advantages: the atmospheric \\(\\nu_e\\) background flux is smaller, the charged\u2011current cross section for \\(\\nu_e\\) on argon is larger (because the outgoing electron is lighter), and oscillation effects in the Sun tend to increase the \\(\\nu_e\\) fraction of the KDAR flux. However, the paper does not provide an analysis of the electron channel. The main challenges are: (1) electron tracks at 236\u202fMeV are short and highly ionizing, making pattern\u2011recognition and track\u2011to\u2011vertex association more difficult than for muons; (2) electromagnetic showers overlap with the proton track, complicating particle identification and energy reconstruction; (3) the directionality inferred from the proton remains useful, but the electron\u2019s isotropic distribution reduces the potential for additional directional cuts. Consequently, while a dedicated study could show improved sensitivity, the necessary simulation of electron\u2011track reconstruction, calorimetry, and background modeling was beyond the scope of the present work."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How will the removal of the hardware L0 trigger and the implementation of an all-software trigger impact the online reconstruction latency for high-multiplicity events?<|assistant|>The all-software trigger allows the full reconstruction of every 40\u00a0MHz bunch crossing, removing the coarse hardware selection that previously introduced latency. By exploiting GPU farms, the LHCb upgrade can process each event within roughly 1\u00a0ms, which is acceptable for the increased event size. However, detailed benchmarks are still required to confirm that this latency remains stable under the highest luminosities."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the expected improvements in impact\u2011parameter resolution for the upgraded VELO compared to the Run\u00a01\u20112 VELO, and how will that affect heavy\u2011flavour lifetime measurements?<|assistant|>With the new 55\u202f\u00b5m pixel size and the reduced distance from the first hit to the interaction point (to 5.1\u202fmm), the VELO is projected to improve its impact\u2011parameter resolution by about 20\u201330\u202f%. This translates into a ~15\u202f% improvement in lifetime resolution for B and D mesons, enhancing the precision of CP\u2011violation and rare\u2011decay measurements."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the introduction of neutron shielding upstream of the calorimeter affect background rates in the SciFi Tracker, and what are the implications for signal efficiency?<|assistant|>The borated polyethylene shielding reduces the 1\u202fMeV neutron\u2011equivalent fluence at the SiPMs by a factor of roughly 2\u20133. This lowers the dark\u2011noise rate of the SiPM arrays, preserving hit efficiency in the most irradiated regions and thus maintaining overall tracker performance at high luminosities."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the challenges in maintaining the mechanical stability of the new RF boxes at the reduced inner radius, and how might this influence beam\u2011induced vibrations?<|assistant|>The 3.5\u202fmm inner radius increases mechanical stresses and makes the RF boxes more susceptible to beam\u2011induced vibrations. Mitigations include low\u2011secondary\u2011electron\u2011yield coatings and NEG layers to reduce impedance, but additional studies on vibration damping and long\u2011term mechanical stability are still underway."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the projected lifetime performance of the SciFi Tracker's SiPM arrays at the end of Run\u00a04, considering cumulative ionising dose and displacement damage?<|assistant|>The paper does not provide a definitive answer to this; the long\u2011term effects of cumulative ionising dose and displacement damage beyond the planned 50\u00a0fb\u207b\u00b9 are still under investigation. Determining the SiPM performance at the end of Run\u00a04 will require additional operational data and detailed radiation\u2011damage studies that are not covered in the current document."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the uniformity of the electric field in a liquid\u2011argon TPC influence the spatial resolution of reconstructed tracks, and what level of field homogeneity is typically required for a 3.6\u202fm drift distance?<|assistant|>A uniform electric field minimizes transverse diffusion and ensures that electrons drift along straight paths, directly improving the z\u2011coordinate (drift time) resolution. For a 3.6\u202fm drift at 500\u202fV/cm, field variations should be kept below a few hundred volts per meter (\u223c0.05\u202f% of the nominal field) to maintain sub\u2011millimeter drift\u2011time precision."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what way does argon purity affect the electron lifetime, and how can this lifetime be monitored in real\u2011time during a long\u2011term experiment?<|assistant|>Oxygen and water impurities capture drifting electrons, shortening the lifetime \u03c4. The lifetime can be inferred from a purity monitor that measures the ratio of collected to emitted charge over a known drift distance. A lifetime of >10\u202fms corresponds to impurity levels below \u223c10\u202fppt O\u2082\u2011equivalent."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What design modifications to the photon detection system could increase light\u2011collection efficiency without significantly increasing the detector\u2019s mass or complexity?<|assistant|>Options include using larger area SiPMs with higher photon detection efficiency, implementing reflective coatings on the inside of the APA frame, optimizing the wavelength\u2011shifting material thickness, and arranging photon collectors in a denser, but still sparse, grid to reduce dead space while maintaining mechanical integrity."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the primary engineering challenges when scaling a single\u2011phase liquid\u2011argon TPC from the ProtoDUNE\u2011SP scale (\u223c0.8\u202fkt) to the 40\u202fkt far\u2011detector modules envisaged for DUNE?<|assistant|>Key challenges include maintaining mechanical stability of large\u2011scale cryostats, ensuring uniform high\u2011voltage distribution over 3\u20134\u202fm drift gaps, handling cryogenic circulation and purification at unprecedented volumes, and designing readout electronics that can operate reliably in a high\u2011radiation, deep\u2011underground environment."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What is the optimal geometry and placement of photon detectors within the APA frame to maximize overall light collection while minimizing dead space, and how does this geometry scale with detector size?<|assistant|>The paper does not provide a definitive answer to this optimization problem. Determining the optimal geometry would require detailed optical simulations combined with mechanical constraints and cost analyses, which were beyond the scope of the presented work and thus remain an open research question."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How do higher\u2011order multipole moments influence parameter estimation for asymmetric binary black hole mergers?<|assistant|>Including sub\u2011dominant modes (e.g., \u2113=3,4) reduces systematic biases in mass, spin, and distance estimates for systems with large mass ratios or high inclination, as the waveform more accurately captures the true signal structure."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>Can ringdown measurements distinguish between Kerr and non\u2011Kerr remnant black holes?<|assistant|>Current ringdown analyses are consistent with Kerr predictions; deviations in the fundamental (220) and first overtone (221) mode frequencies are constrained to within a few percent, showing no statistically significant evidence for non\u2011Kerr remnants."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How effective are null\u2011stream polarization tests in ruling out non\u2011tensorial gravitational\u2011wave polarizations?<|assistant|>Null\u2011stream analyses with the current three\u2011detector network yield Bayes factors overwhelmingly consistent with tensorial (GR) polarizations; they provide no significant preference for pure vector or scalar polarizations, thereby supporting the GR prediction of two tensor modes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the prospects for detecting post\u2011merger gravitational\u2011wave echoes in future observing runs?<|assistant|>The agent does not have a definitive answer to this question. Detecting echoes depends on improved detector sensitivity, longer observing time, and refined template models, all of which are still under development. Consequently, the paper does not provide a prediction, and the information required to estimate future detection prospects is not yet available."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the dominant sources of systematic uncertainty when employing convolutional neural networks to separate track-like from shower-like energy deposits in liquid argon time projection chamber data?<|assistant|>The main systematic sources are (i) space\u2011charge distortion of drift fields, which shifts hit positions and alters charge deposition patterns; (ii) detector\u2011specific electronics noise and baseline variations that can obscure small deposits; (iii) calibration uncertainties in the wire\u2011plane response and time\u2011to\u2011charge conversion; (iv) model bias due to limited training samples that may not cover the full range of interaction topologies; and (v) differences between simulation and data (e.g., hadronic interaction models) that affect the learned feature representations."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How might the performance of a hit\u2011level CNN classifier be improved for low\u2011energy (below 100\u202fMeV) electromagnetic showers in LArTPC detectors?<|assistant|>Improvements can come from: (1) augmenting the training dataset with realistic low\u2011energy shower simulations and adding noise replicas; (2) incorporating physics\u2011motivated preprocessing such as drift\u2011time correction or space\u2011charge compensation; (3) using multi\u2011scale convolutional layers or dilated convolutions to capture both fine\u2011grained and global shower features; (4) applying transfer learning from high\u2011energy shower models and fine\u2011tuning on low\u2011energy data; and (5) integrating a secondary classifier that explicitly models the expected electron\u2011photon separation in thin LAr volumes."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>In what ways can the identification of Michel electrons be leveraged to improve neutrino oscillation analyses in large liquid argon detectors?<|assistant|>Michel electron tagging enables: (i) clean identification of stopping muons, which constrains the neutrino interaction vertex and energy reconstruction; (ii) charge\u2011sign discrimination between \\u03b1 and \\u03b2, since only \\u03b1\\u039b decays produce Michel electrons, aiding in separating neutrino from antineutrino interactions; (iii) validation of muon stopping rates and hence cross\u2011section measurements; and (iv) providing a calibration sample for low\u2011energy electromagnetic energy scale and resolution."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>What are the computational trade\u2011offs between using a small patch\u2011based convolutional neural network versus a full\u2011image semantic segmentation approach for hit classification in LArTPC data?<|assistant|>A patch\u2011based CNN has lower memory usage and faster inference on CPUs because each input is small (e.g., 48\u00d748 pixels) and can be processed independently; however, it may miss global context leading to higher misclassification near complex topologies. Full\u2011image semantic segmentation captures the entire event structure, improving contextual decisions but requires GPU resources, larger memory, and longer inference times, which may not be feasible on standard computing clusters used in large\u2011scale analyses."} +{"text": "<|system|>You are a helpful academic Q&A assistant specialized in scholarly content.<|user|>How does the hit\u2011level classification performance of a CNN trained on surface prototype data translate to a deep underground neutrino detector with a much reduced cosmic\u2011ray background?<|assistant|>I do not have empirical evidence to answer this precisely. The performance may change because the signal\u2011to\u2011noise ratio, background composition, and space\u2011charge conditions differ significantly underground. These differences could alter the statistical distribution of hit topologies the network has to learn, potentially requiring re\u2011training or domain adaptation techniques. Further dedicated studies with underground data are needed to quantify the impact."} diff --git a/data/papers/pairs.json b/data/papers/pairs.json new file mode 100644 index 0000000..92813d2 --- /dev/null +++ b/data/papers/pairs.json @@ -0,0 +1 @@ +[{"question": "Which theoretical technique can most effectively reduce the uncertainties in the Standard Model prediction for the branching fraction of the rare decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?", "answer": "The dominant theoretical uncertainties come from the hadronic inputs\u2014namely the decay constants and form factors\u2014appearing in the effective Hamiltonian for \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\). Progress in unquenched lattice QCD calculations, with finer lattice spacings and lighter sea quark masses, can significantly tighten the determination of the \\(B_s\\) decay constant \\(f_{B_s}\\). Modern techniques such as the use of improved actions (e.g., HISQ for light quarks and relativistic heavy\u2011quark actions for the \\(b\\) quark), combined with nonperturbative renormalization and the inclusion of isospin\u2011breaking and QED effects, are expected to reduce the current uncertainty (\\(\\sim 6\\%\\)) on the decay constant\u2014and thus on the branching\u2011fraction prediction\u2014to the sub\u2011percent level."}, {"question": "What qualitative change would a new heavy \\(Z'\\) boson that couples predominantly to third\u2011generation quarks produce in the branching fraction of \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?", "answer": "A heavy \\(Z'\\) that couples to \\(b \\to s\\) transitions would contribute to the effective Wilson coefficients \\(C_{10}\\) and possibly \\(C_S, C_P\\) in the low\u2011energy effective Hamiltonian. Depending on its mass and coupling strength, the interference with the Standard\u2011Model amplitude could either enhance or suppress the branching fraction. In many motivated \\(Z'\\) models, the amplitude adds constructively, leading to a visible increase in the \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) branching ratio, potentially by a factor of a few, while keeping the branching fraction of \\(B^0 \\rightarrow \\mu^+ \\mu^-\\) relatively unaffected because the flavour\u2011changing transition is suppressed when the \\(Z'\\) couples only to third\u2011generation quarks."}, {"question": "How does the lifetime difference between the heavy and light mass eigenstates of the \\(B_s^0\\) system influence the experimental determination of its dimuon branching fraction?", "answer": "The decay width difference \\(\\Delta\\Gamma_s = \\Gamma_L - \\Gamma_H\\) implies that the two mass eigenstates of the \\(B_s^0\\) have different lifetimes. Since the Standard Model predicts that only the heavy eigenstate can decay to \\(\\mu^+\\mu^-\\) (due to CP conservation), the observed decay time distribution is skewed toward the long\u2011lived state. In a detector with reconstruction efficiency that varies with decay time (e.g., due to displacement cuts on the vertex), an analysis that assumes a single average lifetime will introduce a bias. Correcting for this effect requires disentangling the lifetime dependence, typically by applying a weight derived from simulation assuming the Standard\u2011Model CP structure; this correction reduces the systematic uncertainty on the branching\u2011fraction measurement."}, {"question": "Why is the ratio \\(\\mathcal{B}(B^0 \\rightarrow \\mu^+ \\mu^-)/\\mathcal{B}(B_s^0 \\rightarrow \\mu^+ \\mu^-)\\) considered a powerful test of minimal flavour violation?", "answer": "In the framework of minimal flavour violation (MFV), all flavour\u2011changing neutral\u2011current processes are governed solely by the Cabibbo\u2013Kobayashi\u2013Maskawa (CKM) matrix, and new physics contributions respect the same flavour\u2011symmetry breaking pattern as the Standard Model. Consequently, the ratio of the branching fractions for \\(B^0\\) and \\(B_s^0\\) decays to dimuons is predicted to be exactly the same as in the Standard Model, namely \\(R_{\\rm MFV} \\approx 0.0295\\). Any significant departure from this value would signal the presence of new sources of flavour violation beyond the CKM structure. Therefore, precise experimental determinations of both branching fractions, and their ratio, are key to constraining or revealing non\u2011MFV new\u2011physics scenarios."}, {"question": "Is it currently possible to measure CP violation in the decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) with the data sets used in the combined analysis of CMS and LHCb?", "answer": "No. The combined measurement reported in the paper provides a branching\u2011fraction determination but does not distinguish between \\(B_s^0\\) and \\(\\bar{B}_s^0\\) decays, i.e., it is an untagged analysis. Observing CP violation would require tagging the initial flavour of the \\(B_s^0\\) meson and measuring a time\u2011dependent asymmetry between decay rates of \\(B_s^0\\) and \\(\\bar{B}_s^0\\). Such an analysis demands larger data samples, sophisticated flavour\u2011tagging algorithms, and precise decay\u2011time resolution\u2014capabilities that are beyond the scope of the present dataset and analysis strategy. Hence the answer is unavailable within the current study."}, {"question": "How does the amount of inactive material in the inner detector affect the energy loss distribution for electrons traversing the tracker, and what implications does this have for the jet\u2010electron background rejection in the ATLAS invariant mass reconstruction?", "answer": "The larger the inactive material, the more bremsstrahlung photons are emitted by electrons, which reduces the measured electron energy and creates a tail in the energy loss distribution. This tail increases the probability that an energetic electron is mis\u2011measured as a low\u2011energy cluster, thereby increasing the background from jets that fake electrons. A careful mapping of the material budget is therefore essential: the global energy loss can be parameterised as \u27e8\u0394E\u27e9/E \u2243 0.02\u202fX\u2080 for a 10\u202fGeV electron, where X\u2080 is the radiation length traversed. An accurate simulation of this effect allows the design of more efficient electron\u2011jet discrimination algorithms that rely on the reconstructed transverse momentum balance and shower shape observables."}, {"question": "What is the expected impact of the three\u2011level pixel detector alignment tolerances on the impact parameter resolution for tracks originating from a displaced secondary vertex, such as those from B\u2011hadron decays?", "answer": "The pixel alignment tolerances (10\u202f\u00b5m in R\u2013\u03c6 and 115\u202f\u00b5m in z for the vertexing layer) translate into a systematic bias in the reconstructed track position of the order of 20\u201130\u202f\u00b5m. When propagating to a secondary vertex located a few millimetres from the primary interaction point, this bias adds in quadrature to the intrinsic multiple\u2011scattering term, reducing the transverse impact parameter resolution from the ideal 10\u202f\u00b5m to about 15\u201318\u202f\u00b5m for tracks with p\u209c \u2273 2\u202fGeV. This degradation slightly worsens the ability to separate B\u2011hadron decay vertices from the primary vertex, but the effect is still well below the requirement for efficient b\u2011tagging at the design luminosity."}, {"question": "How does the high\u2011level trigger (HLT) track reconstruction algorithm balance the demands of speed and precision in the presence of 50\u2013100\u202f% pile\u2011up events?", "answer": "The HLT employs a multi\u2011stage track reconstruction where a fast, coarse seeding phase (based on pixel and SCT hits only) provides a first approximation of the track parameters. This initial estimate is fed into a Kalman filter that iteratively refines the fit using full detector information, including TRT hits, but only for tracks whose quality scores lie above a tunable threshold. In simulation studies this approach achieves a track\u2011finding efficiency of >\u202f95\u202f% for |\u03b7|\u202f<\u202f2.5 and a fake\u2011rate of <\u202f1\u202f% even at 100\u202fpb\u207b\u00b9, while keeping the CPU time below 100\u202f\u00b5s per event. The dynamic adjustment of the iteration count based on the local hit density allows the algorithm to remain robust against pile\u2011up in the core of high\u2011energy jets."}, {"question": "What are the dominant systematic uncertainties affecting the measurement of the W\u2011boson mass using the lepton transverse momentum spectrum in ATLAS, and how can they be constrained with early LHC data?", "answer": "The measurement is limited mainly by the calibration of the electromagnetic calorimeter energy scale (\u2264\u202f0.5\u202f%), the lepton momentum scale in the inner detector (\u2264\u202f0.3\u202f% for \u03bc and \u2264\u202f0.1\u202f% for e at high p\u209c), and the knowledge of the parton distribution functions (\u2248\u202f2\u202f% uncertainty on the rapidity distribution of the W). These systematic effects can be constrained using high\u2011statistics control samples: Z\u2192\u2113\u207a\u2113\u207b decays provide an in\u2011situ calibration of the lepton energy/momentum scales with a precision better than 0.05\u202f% for lepton p\u209c\u202f>\u202f30\u202fGeV, while the ratio of W to Z production cross sections can be used to mitigate PDF uncertainties. Performing a simultaneous fit to the W and Z transverse mass spectra further reduces the impact of common systematics."}, {"question": "Is there an estimate of the sensitivity of ATLAS to a light dark photon (m\u202f\u2248\u202f1\u202fGeV) decaying into a displaced e\u207ae\u207b vertex in the inner detector?", "answer": "The paper does not provide a dedicated study for a light dark photon, as the focus was on Standard Model processes and heavy new\u2011physics signatures such as Higgs, SUSY, and B\u2011physics. A sensitivity analysis would require a dedicated Monte Carlo generation of dark photon production (e.g., via kinetic mixing) and a full simulation of the displaced e\u207ae\u207b reconstruction efficiencies, which were not performed in the datasets used. Consequently, while the detector\u2019s inner\u2011track capabilities (\u2248\u202f1\u202fmm vertex resolution and 0.2\u20111\u202f% electron reconstruction efficiency) suggest a promising reach, a precise estimate of the expected limits (cross\u2011section \u00d7 branching ratio) remains an open question that must be addressed in a dedicated study involving displaced\u2011track triggers and pile\u2011up\u2011induced background modelling."}, {"question": "How does the viewing angle of a short gamma-ray burst jet influence the expected flux of high-energy neutrinos detectable on Earth?", "answer": "A larger viewing angle reduces the Doppler boosting and beaming of particles accelerated in the jet, leading to a steep decline in the neutrino flux arriving at Earth. The flux scales roughly with the Doppler factor to the fourth power for internal shock models, so an off-axis observer can see neutrinos at a level that is orders of magnitude lower than an on-axis observer."}, {"question": "Which hadronic processes are considered to produce high-energy neutrinos in the internal shocks of short GRBs?", "answer": "The dominant mechanism is photohadronic (p\u03b3) interaction, where relativistic protons accelerated in internal shocks collide with prompt gamma-ray photons, producing charged pions that decay into neutrinos. In addition, proton-proton (pp) interactions in dense baryonic outflows can contribute, though the optical depth for pp is usually low in short GRB jets."}, {"question": "What strategies do neutrino observatories use to discriminate down\u2011going neutrino events when the source lies above the detector\u2019s horizon?", "answer": "Detectors such as ANTARES and IceCube employ stringent cuts on reconstructed direction, energy, and event topology. They use tight angular uncertainty requirements, require a high-energy deposition inconsistent with atmospheric muons, and apply machine\u2011learning classifiers trained on simulated neutrino and muon events. By temporally correlating with a known source location, the background probability is further reduced."}, {"question": "If a cocoon forms around the jet of a binary neutron star merger, how would this affect the expected neutrino emission compared to a narrow jet?", "answer": "A cocoon expands more slowly and over a wider solid angle, potentially producing neutrinos through shock\u2013accelerated protons interacting with surrounding ejecta. Because the cocoon is less collimated, the neutrino flux received by an observer is spread over a larger area, but the efficiency can be higher if the cocoon\u2019s optical depth to neutrinos is large. However, the lower Lorentz factor reduces the maximum neutrino energy compared to the narrow jet."}, {"question": "What would be the expected neutrino flux from a binary neutron star merger located at 200\u202fMpc, assuming the same intrinsic properties as GW\u202f170817?", "answer": "The current paper does not provide predictions for such a distance, so we cannot quote a definitive flux. Estimating the flux would require scaling the intrinsic neutrino luminosity by the inverse square of the distance (i.e., reducing it by a factor of about 16 relative to 40\u202fMpc). Detailed modeling would also need to account for cosmological redshift effects on the neutrino energy spectrum, which is beyond the scope of the current analysis."}, {"question": "How does including Virgo and KAGRA in the fourth observing run influence the sky\u2011localisation accuracy for heavy binary black\u2011hole mergers compared with the first two observing runs?", "answer": "Detectors that are further apart in latitude and longitude increase the baseline for triangulation. The addition of Virgo (\u22481600\u202fkm from LIGO sites) and KAGRA (\u224811,000\u202fkm from LIGO) reduces the median 90\u202f% credible sky area for high\u2011mass mergers (\u2265\u202f30\u202fM\u2299) from roughly 20\u202fdeg\u00b2 in O1/O2 to about 5\u201310\u202fdeg\u00b2 in O4, mainly because the extra detectors break degeneracies between source position and antenna pattern."}, {"question": "What advantage does frequency\u2011dependent squeezed vacuum provide to the LIGO detectors below 50\u202fHz, and how might this improve detections of neutron\u2011star\u2013black\u2011hole binaries?", "answer": "Frequency\u2011dependent squeezing suppresses shot noise at high frequencies while reducing radiation\u2011pressure noise at low frequencies. The improvement below 50\u202fHz increases the signal\u2011to\u2011noise ratio for signals that extend into this band, such as the early inspiral of neutron\u2011star\u2013black\u2011hole binaries, yielding a higher detection horizon and better estimates of the inclination angle."}, {"question": "How does the measured distribution of the effective inspiral spin parameter (\u03c7\u2091\u2093\u2091ff) in GWTC\u20114.0 limit spin\u2013alignment scenarios for stellar\u2011mass black\u2011hole binaries?", "answer": "The observed concentration of \u03c7\u2091\u2093\u2091ff values near zero indicates that most black\u2011hole spins are either misaligned or have small magnitudes, suggesting formation through dynamical capture or supernova kicks that break alignment. A tail of positive \u03c7\u2091\u2093\u2091ff points to some binaries with partially aligned spins, consistent with isolated binary evolution where tidal alignment persisted."}, {"question": "Can the GWTC\u20114.0 data alone distinguish an intermediate\u2011mass black\u2011hole merger (\u223c100\u20131000\u202fM\u2299) from a supermassive\u2011black\u2011hole merger through gravitational\u2011wave signatures?", "answer": "The current GWTC\u20114.0 catalogue does not include any confirmed detections in the frequency band where supermassive\u2011black\u2011hole mergers would be observed with ground\u2011based detectors. Consequently, distinguishing an intermediate\u2011mass from a supermassive merger using only the present data is not possible; additional high\u2011frequency sensitivity or space\u2011based observations would be required."}, {"question": "What are the most recent statistical constraints on the Hubble constant obtained from GWTC\u20114.0\u2019s \u201cdark\u2011siren\u201d cosmology analysis using galaxy\u2011catalog cross\u2011correlation?", "answer": "The dark\u2011siren analysis of GWTC\u20114.0 yields a Hubble constant of H\u2080\u202f\u2248\u202f70\u202f\u00b1\u202f10\u202fkm\u202fs\u207b\u00b9\u202fMpc\u207b\u00b9 (68\u202f% credible interval), consistent with both the value inferred from the cosmic microwave background and that obtained from the standard\u2011sirens with electromagnetic counterparts, albeit with larger uncertainty due to the limited number of high\u2011volume events."}, {"question": "What is the relationship between the coherence length of an ultralight vector dark matter field and its mass?", "answer": "The coherence length \\(L_{\\text{coh}}\\) of a non\u2011relativistic dark\u2011matter field is inversely proportional to its mass: \\(L_{\\text{coh}}\\sim 2\\pi\\hbar/(mA\\,\\bar v)\\) where \\(\\bar v\\) is the velocity dispersion. For a typical halo velocity \\(\\bar v\\sim10^{-3}c\\), a field mass of \\(10^{-13}\\,\\text{eV}/c^{2}\\) corresponds to a coherence length of order \\(10^{7}\\,\\text{km}\\). Thus, as the mass decreases, the coherence length grows linearly."}, {"question": "Why does using auxiliary length channels in a laser interferometer improve sensitivity to ultralight vector dark matter compared to the main differential arm length channel?", "answer": "Auxiliary length channels (e.g., the Michelson differential length \\( \\text{MICH} \\) and the power\u2011recycling cavity length \\( \\text{PRCL} \\)) involve mirrors made from different materials (sapphire test masses versus fused\u2011silica auxiliary mirrors). Because the ultralight vector field couples to the charge\u2011to\u2011mass ratio of the test masses, the response of different mirrors differs, producing a differential signal that is larger than that in the main channel where the mirrors are usually identical. This material\u2011composition asymmetry amplifies the displacement induced by the field and therefore enhances the detectable strain."}, {"question": "What are the principal difficulties in separating a genuine ultralight dark\u2011matter signal from transient detector noise in GW strain data?", "answer": "True DM signals are expected to be narrow\u2011band, persistent over long times, and statistically Gaussian in amplitude due to the central limit theorem. Transient detector artifacts, however, are often broadband, short\u2011lived, and exhibit non\u2011Gaussian statistics. Distinguishing them requires (i) characterising the expected DM bandwidth and coherence time, (ii) checking the persistence of a signal across independent data epochs, and (iii) vetoing known instrumental lines by cross\u2011correlation with auxiliary sensors or by comparing the signal\u2019s spectral shape to that predicted for DM."}, {"question": "What future improvements to the KAGRA detector could make it more competitive in probing ultralight vector dark matter?", "answer": "Potential upgrades include: (1) reducing the low\u2011frequency noise in the auxiliary channels by implementing advanced vibration isolation and seismic suppression; (2) increasing the laser power and improving mirror coatings to lower the thermal and shot noise; (3) deploying cryogenic temperature control for all mirrors to match the sapphire test masses across the interferometer; (4) extending the observation run length so that more data segments exceed the DM coherence time; and (5) adding dedicated sensors to monitor and subtract known noise lines from the auxiliary channels."}, {"question": "What would be the effect on the derived constraints if the ultralight vector dark matter field had a preferred polarization direction rather than being isotropically distributed?", "answer": "I do not have enough information to answer this question conclusively. The paper assumes an isotropic velocity and polarization distribution when modeling the signal covariance. A non\u2011isotropic polarization would change the statistical properties of the induced length variations, potentially altering the expected strain spectrum and the detection statistic. Determining the precise impact requires a dedicated theoretical study of polarized vector dark matter and its coupling to interferometer mirrors, which is not covered in the present analysis."}, {"question": "How does the rotation rate of a progenitor star influence the amplitude and frequency spectrum of gravitational waves emitted during a core\u2011collapse supernova?", "answer": "Rotation tends to destabilise the proto\u2011neutron star, giving rise to non\u2011axisymmetric modes such as bar\u2011mode or spiral instabilities. Faster rotation yields a higher degree of ellipticity and can shift the dominant GW frequency to lower values (tens to a few hundred hertz) while increasing the wave strength by orders of magnitude. The total radiated GW energy can rise from \u224810\u207b\u2076\u202fM\u2299\u202fc\u00b2 in slowly rotating models to \u224810\u207b\u2074\u201310\u207b\u00b3\u202fM\u2299\u202fc\u00b2 for rapidly rotating cores."}, {"question": "What are the main sources of statistical uncertainty when setting upper limits on gravitational\u2011wave energy from a core\u2011collapse supernova detected by the LIGO\u2013Virgo\u2013KAGRA network?", "answer": "The dominant uncertainties stem from (1) strain calibration, typically 2\u20133\u202f% across the instrument band; (2) non\u2010Gaussian detector noise, especially short glitches that can mimic transients and inflate background estimates; (3) modelling assumptions, such as the choice of waveform family, source orientation, and ellipticity; and (4) the definition of the on\u2011source window, which determines how much coincident data are available. Together these contribute systematic errors on the strain sensitivity and thus on the inferred energy limits."}, {"question": "How might strong magnetic fields in the nascent proto\u2011neutron star alter the expected gravitational\u2011wave signal compared to magnetically quiet core\u2011collapse scenarios?", "answer": "Intense magnetic fields can drive a magnetorotational explosion, launching bipolar jets that increase asymmetry. This can generate higher\u2011frequency (\u22481\u20133\u202fkHz) GW components with larger amplitudes and potentially longer durations than the \u2248100\u202fHz bar\u2011mode bursts seen in weak\u2011field models. The field geometry also influences the ellipticity evolution and can sustain non\u2011axisymmetric instabilities beyond the few\u2013hundred\u2011millisecond timescale typical of neutrino\u2011driven explosions."}, {"question": "What time delay between the neutrino burst and the peak gravitational\u2011wave emission is generally expected in core\u2011collapse supernovae, and how does this affect on\u2011source window construction?", "answer": "The neutrino burst is emitted almost simultaneously with core bounce, within milliseconds. Gravitational waves can start at the bounce and continue for tens of milliseconds as prompt convection and SASI develop; later, bar\u2011mode or magnetorotational instabilities can produce emission lasting up to a second. Consequently, effective on\u2011source windows that encompass a few seconds around the neutrino trigger are recommended to capture both prompt and late\u2011time signals."}, {"question": "What gravitational\u2011wave signature would a neutron\u2011star merger in the same host galaxy as SN\u202f2023ixf produce, and was such a signal searchable in the data set discussed?", "answer": "A binary neutron\u2011star merger would emit a short, chirp\u2011like burst peaking at a few kHz, lasting \u22480.1\u202fs, followed by a post\u2011merger signal that can persist for several hundred milliseconds. The analysis presented in the study was optimised for supernova\u2011type transients and did not target such compact\u2011binary waveforms. Although no merger\u2011type trigger passed the significance threshold, the dataset did not provide the sensitivity or time\u2011localisation required to set limits on a potential neutron\u2011star merger within M\u202f101, so this scenario was not explicitly examined."}, {"question": "How do the latest upper limits on neutron\u2013star ellipticity from continuous\u2011gravitational\u2011wave searches constrain the strength of internal magnetic fields in millisecond pulsars?", "answer": "The ellipticity (\u03b5) limits set by non\u2011detections translate into an upper bound on the quadrupole deformation induced by strong internal magnetic fields. For a simple model where the magnetic energy dominates the deformation, \u03b5 \u2243 (B_int\u202f/\u202f10^16\u202fG)^2\u202f\u00d7\u202f10^\u22126. Using the most stringent \u03b5 limits from recent searches (\u2248\u202f10^\u22129 for the bright nearby millisecond pulsar J0437\u22124715), the inferred maximum internal field is \u2272\u202f10^15\u202fG \u2013 well below the dipole surface fields (~10^8\u201310^9\u202fG). This suggests that millisecond pulsars cannot harbor extremely strong toroidal fields that would otherwise produce noticeable gravitational\u2011wave emission. The exact relationship depends on the equation of state and the geometry of the field, and more sophisticated magnetohydrodynamic modelling is required for accurate limits.", "unanswered": false}, {"question": "What impact does the Shklovskii effect have on the interpretation of spin\u2011down limits in continuous\u2011gravitational\u2011wave pulsar searches?", "answer": "The Shklovskii effect arises when the proper motion of a pulsar adds a kinematic contribution to its measured period derivative: \\( \\dot{P}_{\\text{Shk}} = (P\\,v_{\\perp}^2)/(c\\,D) \\). This extra term inflates the observed spin\u2011down rate and thus the inferred spin\u2011down energy loss rate. For continuous\u2011GW searches the spin\u2011down limit \\(h_{\\text{sd}} \\propto \\sqrt{|\\dot{f}_{\\text{rot}}|/f_{\\text{rot}}}\\) is then over\u2011estimated if the Shklovskii correction is not applied. Properly subtracting \\(\\dot{f}_{\\text{Shk}}\\) yields a lower intrinsic spin\u2011down, which tightens the spin\u2011down limit and means that a true GW amplitude approaching the limit would be less likely. The effect is most significant for nearby, high\u2011proper\u2011motion millisecond pulsars.", "unanswered": false}, {"question": "What are the main technical challenges in extending persistent\u2011wave searches to eccentric binary pulsars?", "answer": "Eccentric binaries introduce additional orbital modulations in the gravitational\u2011wave phase, requiring knowledge of the orbital elements (eccentricity, periastron advance, etc.) and a high\u2011order orbital model. The main challenges include: 1) the need for densely sampled, high\u2011precision timing solutions to track the periastron motion and secular variations; 2) increased parameter space dimensionality (eccentricity, argument of periastron, orbital period derivatives) leading to higher computational cost; and 3) the risk of mismodeling orbital dynamics, which can de\u2011phase the coherent integration and degrade sensitivity. Recent advances in joint timing and GW modelling, as well as the use of coherent matched\u2011filter pipelines that can include time\u2011dependent orbital phase terms, are helping to mitigate these difficulties.", "unanswered": false}, {"question": "How will the planned upgrades to Advanced LIGO, Virgo, and KAGRA influence the sensitivity of continuous\u2011gravitational\u2011wave searches in future observing runs?", "answer": "The upgrades\u2014such as increased laser power, improved quantum\u2011noise reduction via squeezed light, cryogenic mirrors for Virgo, and higher seismic isolation for KAGRA\u2014will lower the detector noise floor by factors of 1.5\u20132 in the 10\u20131000\u202fHz band relevant for pulsar GW emission. This translates to a depth improvement of ~30\u201350\u202f%, allowing continuous\u2011GW searches to probe strain amplitudes down to \u2248\u202f10^\u201127\u201310^\u201126 for the most promising nearby pulsars. Moreover, the longer continuous observing periods expected (\u2248\u202f1\u202fyr per run) will further increase the coherent integration time, improving sensitivity roughly as the square root of the observation time. Combined, these changes will tighten ellipticity limits by an order of magnitude for many targets.", "unanswered": false}, {"question": "What can the recent upper limits on dipole radiation from Brans\u2013Dicke theory tell us about the viability of scalar\u2011tensor gravity models?", "answer": "The non\u2011detection of dipole gravitational radiation at the level of h_d\u202f\u2248\u202f10^\u201127\u201310^\u201126 for pulsars with strong orbital accelerations sets a lower bound on the Brans\u2013Dicke coupling parameter \u03c9_BD \u2273\u202f10^4\u201310^5. This is roughly an order of magnitude improvement over the best Solar\u2013System constraints derived from the Viking landers and Cassini ranging experiments. While scalar\u2011tensor models with very weak coupling remain allowed, the results considerably restrict parameter space where dipole radiation could contribute significantly to orbital decay, supporting the robustness of General Relativity as the dominant interaction in the strong\u2011field regime.", "unanswered": false}, {"question": "How does the internal composition of a neutron star affect the maximum equatorial ellipticity that could be sustained without destabilizing the star?", "answer": "The maximum ellipticity depends on the star\u2019s crustal shear modulus and the core superfluid composition. For a conventional nuclear matter EOS, the crust can support \u03b5\u202f\u2272\u202f10^\u20116, whereas exotic phases such as color\u2011superconducting quark matter or solidified hyperon cores could allow \u03b5\u202f~\u202f10^\u20114\u201310^\u20113. However, these estimates rely on the unknown strength of nuclear pasta phases and magnetic stresses. Current continuous\u2011GW upper limits (\u03b5\u202f~\u202f10^\u20119\u201310^\u20117) are below these theoretical maxima, so no definitive constraints on the internal composition can yet be drawn.", "unanswered": true, "explanation": "The paper presents ellipticity upper limits but does not model the dependence on the neutron star\u2019s internal composition, nor does it explore how specific EOS assumptions would change the maximum sustainable ellipticity. Therefore, while the paper provides constraints on \u03b5, it does not address the detailed question of how various internal composition scenarios map onto observable limits."}, {"question": "What is the prevalence of black holes in the pair\u2011instability supernova mass gap (roughly 45\u2013120\u202fM\u2299) in the local universe, and does the current gravitational\u2011wave catalog provide evidence for a statistically significant dearth in that range?", "answer": "Current population studies show a steep decline in the merger rate above about 40\u201345\u202fM\u2299, yet the number of observed events with primary masses above 70\u202fM\u2299 is small. Some detections near the putative gap boundary (~70\u202fM\u2299) are compatible with a smooth continuation of the mass distribution, rather than an empty gap. Consequently, while there is evidence for a reduced rate, a decisive confirmation of a completely empty pair\u2011instability gap cannot be drawn from the existing catalog."}, {"question": "How does the effective inspiral spin distribution (\u03c7_eff) vary with redshift, and what might this tell us about the formation pathways of binary black holes?", "answer": "Analyses of the most recent catalog hint that the width of the \u03c7_eff distribution broadens as redshift increases, whereas its mean stays near zero. This broadening could reflect a growing contribution from dynamically assembled binaries or hierarchical mergers at earlier epochs. However, given the limited number of high\u2011redshift detections, the trend is still marginal and could be influenced by selection effects, so a definitive conclusion about redshift dependence of \u03c7_eff remains tentative."}, {"question": "What is the relative mass\u2011ratio distribution of binary black holes near the ~10\u202fM\u2299 and ~35\u202fM\u2299 mass peaks, and does it imply different evolutionary pathways?", "answer": "Binaries with primary masses around 10\u202fM\u2299 tend to merge with significantly less massive companions (mass\u2011ratio peak near q\u202f\u2248\u202f0.7), while those near the 35\u202fM\u2299 peak usually have more equal masses (q\u202f\u2248\u202f0.9\u20131.0). These features are compatible with theoretical expectations: the lower\u2011mass peak may arise from stable mass\u2011transfer episodes in isolated binaries, whereas the higher\u2011mass equal\u2011mass systems could be produced in dense stellar clusters or through hierarchical mergers. Nonetheless, the overlap between the two distributions remains substantial, and additional observations are needed to solidify the link between observed ratios and specific formation channels."}, {"question": "Is there evidence for a lower\u2011mass gap between the heaviest neutron stars and the lightest black holes (\u223c3\u20135\u202fM\u2299) in the observed merger population?", "answer": "The current gravitational\u2011wave data show compact objects clustering around neutron\u2011star masses near 1.3\u20131.4\u202fM\u2299 and black\u2011hole masses beginning around 5\u20136\u202fM\u2299, with only a handful of events land in the 3\u20135\u202fM\u2299 interval. Statistically, the distribution is consistent with a continuous decline rather than a sharply empty region. Thus, while the existence of a pronounced lower\u2011mass gap remains an open question, the catalog does not provide sufficient evidence to confirm its presence."}, {"question": "Does the observed population of binary black holes exhibit a correlation between component spin magnitudes and the component masses, such that more massive black holes spin faster?", "answer": "The data available so far do not unambiguously support such a correlation. Although some earlier studies suggested a weak trend of increasing spin amplitudes with mass, the latest catalog shows considerable overlap between mass and spin posterior distributions, with large uncertainties in both quantities. Current posterior constraints are consistent with both no correlation and modest positive correlations within the error bounds. Therefore, this question remains unanswered; a larger, less biased sample and more precise spin measurements are needed to resolve whether a spin\u2013mass trend exists."}, {"question": "What physical mechanisms are thought to generate gravitational waves simultaneously with fast radio bursts from magnetars, and how do their predicted gravitational-wave energy outputs compare?", "answer": "The most frequently discussed mechanisms involve sudden re\u2011configurations of the neutron\u2011star interior: a starquake or a global crustal failure can excite the star\u2019s f\u2011mode at \u223c2\u202fkHz, radiating \\(E_{\\rm GW}\\sim10^{48\\text{\u2013}10^{49}\\,{\\rm erg}\\) if the quake involves a large crustal distortion. Magneto\u2011elastic coupling between the star\u2019s magnetic field and shear oscillations can also trigger quasi\u2011periodic oscillations in the X\u2011ray tail of a flare; these oscillations source GW emission at a few hundred to a few thousand hertz with energies \\(10^{41\\text{\u2013}10^{45}\\,{\\rm erg}\\). A third possibility is that the rapid spin\u2011up associated with a glitch injects free precession power, potentially yielding \\(10^{44\\text{\u2013}10^{48}\\,{\\rm erg}\\) in a short burst. All of these scenarios predict waveforms that are broad in frequency but typically last less than a second, making them amenable to the short\u2011duration burst searches used in recent LIGO/Virgo/KAGRA studies."}, {"question": "In what way does the distance estimate for SGR\u202f1935+2154 influence the derived upper limits on gravitational\u2011wave energy for FRBs observed from it?", "answer": "The gravitational\u2011wave energy inferred from an upper limit on strain scales with the square of the source distance (\\(E_{\\rm GW}\\propto D^{2}\\)). The canonical value of \\(6.6\\pm0.7\\)\u202fkpc is roughly a factor of two larger than the lower bound (\u22485\u202fkpc) and a factor of three smaller than the most distant estimates (\u224815\u202fkpc). If the true distance were 1.5\u202fkpc as suggested by some HI\u2011absorption studies, the energy constraint would tighten by about a factor of 20; if it were 15\u202fkpc, the limits would loosen by roughly a factor of five. Consequently, the 90\u202f% upper limits of \\(10^{48.5}\\)\u202ferg at 300\u202fHz and \\(10^{50}\\)\u202ferg at 2\u202fkHz could become respectively \\(5\\times10^{47}\\)\u2013\\(5\\times10^{49}\\)\u202ferg depending on the true distance."}, {"question": "What are the principal obstacles to detecting short\u2011duration gravitational\u2011wave bursts associated with FRBs when only a single observatory (such as GEO600) is operational, and how can a network of detectors mitigate these issues?", "answer": "With a single detector, the dominant challenges are: (1) the inability to use coincidence timing to veto terrestrial glitches, (2) a limited ability to estimate the false\u2011alarm rate because the background must be drawn from the same time segment, and (3) reduced signal\u2011to\u2011noise since no cross\u2011correlation can be performed between independent noise realizations. These factors increase the likelihood of spurious candidates and raise the detection threshold. A multi\u2011detector network provides independent noise streams so that a genuine astrophysical signal will appear in all observatories with a consistent time\u2011delay, allowing robust vetoes of local glitches. Moreover, the coherent combination of data boosts the signal\u2011to\u2011noise ratio roughly by \\(\\sqrt{N}\\) (with \\(N\\) detectors), enabling the detection of weaker bursts or tighter upper limits."}, {"question": "Could observations of gravitational waves help distinguish between competing progenitor models for extragalactic fast radio bursts, and what specific gravitational\u2011wave signatures would be most decisive?", "answer": "Yes. Different progenitor hypotheses predict distinct gravitational\u2011wave morphologies and energetics. A binary\u2011neutron\u2011star merger would produce a short (\\(<1\\)\u202fs) chirp signal with a characteristic inspiral\u2011merger\u2011ringdown waveform and \\(E_{\\rm GW}\\sim10^{53}\\)\u202ferg, whereas a single magnetar flare with a starquake would produce a short, possibly broadband burst at a few hundred to several thousand hertz with much lower energy (\\(10^{41\\text{\u2013}10^{49}\\)\u202ferg). Detecting a merger\u2011style chirp coincident with an FRB would strongly support a binary origin; conversely, a null result in such a search coupled with a detection of a broadband short burst would favor a magnetar or other single\u2011object model. The presence of a long\u2011duration quasi\u2011periodic oscillation in the GW spectrum would further point toward magnetospheric or crustal modes."}, {"question": "Is there observational evidence that X\u2011ray glitches in magnetars are temporally correlated with subsequent fast radio burst activity, and what would such a correlation imply about FRB production mechanisms?", "answer": "Current observations do not provide definitive evidence of a correlation between X\u2011ray glitches and FRBs. The paper reports on three X\u2011ray glitches around 2022\u202fOct\u202f14 but finds no associated FRBs within the limited duty cycle and sensitivity of the radio observatories at that time. Moreover, previous studies have seen both FRBs with and without simultaneous X\u2011ray bursts from SGR\u202f1935+2154, indicating that the two phenomena can be independent. A robust temporal correlation would suggest that the sudden change in the magnetospheric or interior structure that causes a glitch also triggers the coherent radio emission, supporting models where FRBs are powered by internal magnetic field re\u2011configuration. Until such a correlation is established with high\u2011cadence, simultaneous multi\u2011wavelength monitoring, this question remains open."}, {"question": "What are the most plausible astrophysical pathways that can produce compact objects in the lower mass gap (roughly 3\u20135\u202fM\u2299) which are subsequently detected as neutron\u2011star\u2013black\u2011hole binaries by gravitational\u2011wave observatories?", "answer": "Astrophysical models point to a handful of scenarios: (1) core\u2011collapse supernovae with substantial fallback of material onto a nascent neutron star can raise the remnant mass into the lower mass gap; (2) early\u2011stage binary evolution with mass transfer followed by delayed collapse of a massive helium star can also produce low\u2011mass black holes; (3) binary neutron\u2011star mergers that leave a hyper\u2011massive remnant could collapse to a black hole of a few solar masses. None of these mechanisms is yet confirmed as dominant, and the relative contribution of each pathway remains a subject of active research."}, {"question": "In a neutron\u2011star\u2013black\u2011hole binary, how does a misalignment between the neutron star spin and the orbital angular momentum affect the gravitational\u2011wave phase evolution and the likelihood of detecting the event with matched\u2013filter searches?", "answer": "Spin\u2013orbit coupling introduces additional phasing terms that depend on the tilt angle. A significant tilt can lead to precession of the orbital plane, modulating the amplitude and phase of the waveform in a way that is partially degenerate with mass parameters. While matched\u2011filter pipelines can accommodate precessing templates, the reduced match for highly tilted systems can lower the recovered signal\u2011to\u2011noise ratio, potentially making such events harder to detect or to characterize accurately."}, {"question": "Which electromagnetic counterparts are most commonly expected from symmetric\u2011mass neutron\u2011star\u2013black\u2011hole mergers, and how can current multi\u2011messenger follow\u2011up strategies maximize the probability of identifying them?", "answer": "Symmetric\u2011mass mergers (with mass ratio close to unity) are more likely to tidally disrupt the neutron star before it plunges into the black hole. This can leave behind a remnant accretion disk and unbound ejecta, creating a kilonova with blue and red components, and possibly launching a short gamma\u2011ray burst. Rapid, wide\u2011field optical and infrared surveys, coordinated with high\u2011energy satellites, are essential to capture the early, rapidly fading signals; however, localisation uncertainties from single\u2011detector detections limit the efficiency of current follow\u2011ups."}, {"question": "How has the estimated merger rate of neutron\u2011star\u2013black\u2011hole binaries changed from the third to the fourth observational runs of ground\u2011based gravitational\u2011wave detectors, and what implication does this have for population synthesis models?", "answer": "The rate has increased from roughly 20\u201350\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 during O3 to about 70\u2013100\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 in early O4, though uncertainties remain large. This upward trend suggests either that our sensitivity has improved or that the underlying population of neutron\u2011star\u2013black\u2011hole binaries is larger than previously thought, challenging models that placed a strong lower mass gap and predict fewer such systems."}, {"question": "What does the current population of neutron\u2011star\u2013black\u2011hole detections tell us about the distribution of the inclination angle (\u03b8_JN) between the total angular momentum and the line\u2011of\u2011sight, and how does this affect the ability to localise sources on the sky?", "answer": "We do not know the distribution of inclination angles for the present sample. Many detected events come from single\u2011detector observations, which provide almost no constraint on \u03b8_JN, leading to large degeneracies with distance and severely limiting sky localisation. A more complete sample\u2014with detections in at least two detectors\u2014would be required to map out the inclination distribution and improve localisation accuracy."}, {"question": "What fraction of massive black\u2011hole binary mergers (total mass > 70\u202fM\u2299) detected by the LIGO\u2013Virgo\u2013KAGRA network are expected to have orbital eccentricities greater than 0.1 at a 15\u202fHz gravitational\u2011wave frequency?", "answer": "Current data do not yet allow a precise measurement of this fraction. While upper limits on eccentricity have been placed for individual events, no event has a statistically\u2010significant eccentricity measurement. The sensitivity of existing searches to high\u2011eccentricity signals is limited, especially for the largest masses, and degeneracies with spin\u2011precession further obscure the inference. Consequently, it remains unknown how many massive binaries in the observed population possess e\u202f>\u202f0.1 at 15\u202fHz."}, {"question": "How does a minimally modeled search such as coherent WaveBurst (cWB) compare to template\u2011based matched\u2011filter searches in detecting eccentric binary black\u2011hole mergers, in terms of sensitivity and false\u2011alarm rates?", "answer": "Minimally modeled searches like cWB are robust against waveform systematics and can recover signals that deviate from binary\u2011black\u2011hole templates, including highly eccentric or precessing systems. For eccentricities below ~0.3, cWB retains roughly 70\u201380\u202f% of the SNR of a matched\u2011filter search that uses circular templates. Its background is typically higher, leading to larger false\u2011alarm rates for a given detection statistic. Template\u2011based searches lose sensitivity at high eccentricity because the phase evolution differs substantially from the templates; however, they can still recover eccentric signals if the templates include eccentricity descriptions or higher\u2011order modes. A definitive comparison requires large injection campaigns across the full eccentric\u2011parameter space."}, {"question": "Can the mass distribution of high\u2011mass eccentric black\u2011hole mergers provide evidence distinguishing between dense\u2011star\u2011cluster formation channels and accretion\u2011disk (AGN) environments?", "answer": "Theoretical models predict that binaries formed in dense stellar clusters should peak at lower total masses with a broader mass ratio distribution, whereas AGN\u2011disk capture processes can produce more massive, nearly equal\u2011mass binaries with higher eccentricities. However, observationally separating these channels requires accurately measuring both mass and eccentricity for a statistically large sample. Presently, the sample size of confirmed eccentric mergers is too small, and mass\u2013eccentricity degeneracies in the waveforms make it difficult to attribute individual events to a specific channel."}, {"question": "What effect do higher\u2011order gravitational\u2011wave modes have on the detection and parameter estimation of eccentric binary black\u2011hole mergers, particularly for high total masses?", "answer": "Higher\u2011order modes become more prominent in binaries with large mass ratios, high total mass, and when the orbital plane is inclined. In eccentric orbits, the mode content varies rapidly, potentially boosting the SNR for some modes while suppressing others. Including higher\u2011order modes in waveform models improves the match to the true signal, enhancing both detection efficiency and parameter recovery. Yet many current eccentric waveform approximants either omit or poorly resolve these modes, limiting the achievable accuracy for high\u2011mass systems."}, {"question": "What are the dominant challenges in reliably extracting the orbital eccentricity of an individual detected binary black\u2011hole merger using current gravitational\u2011wave data?", "answer": "The primary obstacles are: (1) waveform model uncertainty, as existing eccentric models are sparse in spin and mass\u2011ratio coverage; (2) strong degeneracies between eccentricity and spin\u2011precession or higher\u2011order modes; (3) limited signal\u2011to\u2011noise ratio for most events, which hampers precision in measuring subtle deviations from circularity; and (4) non\u2011Gaussian noise artifacts that can mimic or obscure eccentric signatures. Due to these factors, the confidence in eccentricity measurements for individual events remains low with current data."}, {"question": "How could a first\u2011order phase transition during the electroweak epoch generate a detectable stochastic gravitational\u2011wave background?", "answer": "A first\u2011order phase transition proceeds via nucleation of bubbles of the true vacuum that expand, collide, and convert vacuum energy into kinetic motion of the plasma and magnetic fields. Sound waves in the plasma and bubble collision turbulence source gravitational waves with a characteristic peak frequency set by the phase\u2011transition temperature and duration. The amplitude is controlled by the strength parameter \\(\\alpha\\) (energy density released relative to radiation) and the inverse duration \\(\\beta/H\\). For transitions that occur at temperatures \\(\\mathcal{O}(100~\\text{GeV})\\), the peak frequency falls in the tens to hundreds of hertz band, which is accessible to ground\u2011based detectors, making such a background potentially detectable if \\(\\alpha\\) is large enough and \\(\\beta/H\\) is not too high."}, {"question": "What role do cosmic strings play in shaping the spectrum of a stochastic gravitational\u2011wave background across different frequency bands?", "answer": "Cosmic strings, one\u2011dimensional topological defects, form a network of long strings and loops. Loops oscillate and repeatedly emit bursts of gravitational waves, primarily from cusps, kinks, and kink\u2011kink collisions. The superposition of many such bursts produces a stochastic background that is approximately a power\u2011law \\(\\Omega_{\\text{GW}}(f)\\propto f^{\\alpha}\\). The spectral index \\(\\alpha\\) depends on the dominant source: cusps yield \\(f^{-1/3}\\) after integration, while kinks give a steeper slope. At high frequencies (kHz) the spectrum may steepen due to the finite loop lifetime, whereas at low frequencies (mHz) the long\u2011string contribution becomes more important, potentially producing a scale\u2011dependent feature that could be observable with space\u2011based detectors."}, {"question": "How can a stiff equation of state in the early Universe influence the spectral slope of the gravitational\u2011wave background observed today?", "answer": "During a stiff epoch (equation\u2011of\u2011state parameter \\(w>1/3\\)), the Universe expands more rapidly than during radiation domination. Gravitational waves that re\u2011enter the horizon during this period get boosted because the energy density redshifts more slowly (\\(\\rho_{\\text{GW}}\\propto a^{-4}\\) while the background energy density scales as \\(a^{-3(1+w)}\\)). As a result, the primordial inflation\u2011generated spectrum acquires a blue tilt with spectral index \\(\\alpha_{\\text{stiff}}=2/(1+3w)\\), which can be substantially larger than the \\(\\alpha\\simeq0\\) of a standard inflationary background. This leads to a higher amplitude at higher frequencies, bringing the signal into the detectable band of ground\u2011based observatories if \\(w\\) is close to unity."}, {"question": "What is the connection between scalar\u2011induced gravitational waves and primordial black hole formation, and how does it affect the detectability of the background?", "answer": "Large population of primordial curvature perturbations on small scales can re\u2011enter the horizon during radiation domination and collapse into primordial black holes (PBHs). These same perturbations also source second\u2011order tensor modes that generate a stochastic gravitational\u2011wave background. The amplitude of this background scales roughly with the square of the curvature power spectrum amplitude, while the PBH abundance is exponentially sensitive to the same amplitude. Therefore, a detection (or non\u2011detection) of a scalar\u2011induced background with ground\u2011based detectors provides an indirect probe of PBH abundance in the mass range \\(10\u201310^3\\,M_\\odot\\). A stronger background would imply overproduction of PBHs and would be constrained by microlensing, CMB, and BBN limits, whereas a weaker background is consistent with current PBH limits."}, {"question": "What constraints does the recent O5 LIGO\u2011Virgo\u2011KAGRA run place on the amplitude of a parity\u2011violating chiral gravitational\u2011wave background at frequencies above 200\u202fHz?", "answer": "I do not have information on that, because the O5 run data and its specific parity\u2011violation constraints have not been incorporated into the model I was trained on, and the paper you provided does not cover O5 results. Answering this question would require access to the latest analysis reports from the LIGO\u2011Virgo\u2011KAGRA collaboration, which are outside my knowledge domain."}, {"question": "What would be the impact on constraints of ultralight dark matter if the local dark-matter velocity distribution were modeled with a non\u2011Gaussian, anisotropic component?", "answer": "A non\u2011Gaussian, anisotropic velocity distribution would modify the coherence time and the spectral shape of the dark\u2011matter signal in interferometer data. This could lead to either tighter or weaker limits depending on the directionality and spread of the velocity field, and realistic modeling may improve the sensitivity to mass ranges close to the interferometer arm length resonances."}, {"question": "Can future third\u2011generation gravitational\u2011wave detectors, such as the Einstein Telescope or Cosmic Explorer, provide an order\u2011of\u2011magnitude improvement in the upper limits on the couplings of scalar ultralight dark matter to the fine\u2011structure constant?", "answer": "Yes. The significantly increased strain sensitivity and longer observation times expected for third\u2011generation detectors would reduce the noise floor across a broad frequency band. This would allow the amplitude of a hypothetical dark\u2011matter\u2011induced strain signal to be probed at much lower levels, potentially improving scalar coupling limits by an order of magnitude or more."}, {"question": "How would an improved calibration of the interferometer\u2019s transfer function for arm\u2011mirror size oscillations affect the derived limits on dark\u2011photon couplings to baryons?", "answer": "A more accurate transfer\u2011function calibration would reduce systematic uncertainties in the conversion between measured strain and the underlying dark\u2011photon force. Consequently, the derived bounds on the dark\u2011photon\u2013baryon coupling could be tightened, especially at the low\u2011frequency end where the transfer function is most sensitive to arm\u2011mirror displacement."}, {"question": "Is there any empirical evidence in current gravitational\u2011wave data for differential strain patterns that could distinguish between a scalar dilaton field and a massive tensor dark\u2011matter field?", "answer": "Such differential strain patterns have not yet been observed in current gravitational\u2011wave data. Distinguishing between scalar and tensor signatures would require identifying the characteristic polarization responses of the interferometer arms, which remains an open challenge for present datasets."}, {"question": "What is the most stringent existing constraint on the coupling of ultralight vector dark matter to Electron currents from laboratory fifth\u2011force experiments?", "answer": "I do not have that information. The paper focuses on limits from atomic clocks and torsion\u2011balance experiments for scalar and vector couplings, but does not provide the strongest laboratory constraint on vector dark\u2011matter couplings to electron currents."}, {"question": "How does the distribution of effective inspiral spins (\u03c7_eff) evolve for binary black holes that form through successive hierarchical mergers in globular clusters, and how does this distribution differ from that of binaries formed in isolation?", "answer": "In hierarchical mergers the remnant spin of the previous merger is typically large (\u22480.7) and directed roughly along the orbital angular momentum. When this remnant merges with another black hole, the resulting \u03c7_eff distribution becomes broadly symmetric around zero, with a significant tail of large positive and negative values. In contrast, binaries formed in isolation usually exhibit a positively biased \u03c7_eff distribution due to spin alignment from common progenitor evolution. The exact shape of the \u03c7_eff distribution, however, depends on cluster properties, mass segregation, and the dynamical ejection/retention of remnants, and detailed numerical simulations are required to quantify it precisely."}, {"question": "What is the quantitative effect of the spin-induced quadrupole moment (parameter \u03ba) on the amplitudes of higher-order spherical harmonic modes (\u2113, m) during the late inspiral and merger phases of a binary black hole system?", "answer": "The spin-induced quadrupole moment enters the post-Newtonian expansion of the gravitational-wave phase and amplitude. A deviation \u03b4\u03ba from the Kerr value of 1 modifies the amplitude of mass- and current\u2011quadrupole contributions to the (\u2113, m) = (2,\u00b12) leading mode, while also altering the relative strength of higher modes such as (\u2113, m) = (3,\u00b13) via changes in the binary\u2019s orbital dynamics. For rapidly spinning binaries (\u03c7 ~ 0.7) and moderate mass ratios (q \u2243 0.3), a \u03b4\u03ba of order 0.1 can shift the (3,\u00b13) mode amplitude by several percent, leading to measurable deviations in the signal-to-noise ratio and potentially affecting the inference of source parameters."}, {"question": "Can gravitational\u2011wave signatures from eccentric binary black hole mergers in cluster cores provide a robust test of post-Newtonian predictions for eccentric inspirals, and what is the expected eccentricity range at LIGO frequencies?", "answer": "Eccentric binaries formed via close encounters or three\u2011body interactions are expected to retain pericenter distances that produce orbital eccentricities e \u2243 0.01\u20130.1 when the gravitational-wave frequency enters the LIGO band (>20\u202fHz). Post\u2011Newtonian models that include eccentricity up to next-to\u2011quadratic order reproduce the energy and angular\u2011momentum fluxes with residuals below a few percent for this eccentricity range. Therefore, with sufficiently high signal\u2011to\u2011noise ratios, the waveform phase evolution can be used to test the PN eccentricity formalism, but this requires accurate eccentric waveform models and careful marginalization over spin effects."}, {"question": "What limits can be set on the mass and coupling strength of an ultralight vector boson from observing a spinning black hole with mass \u224820\u202fM\u2299 and spin \u03c7 \u22480.8, assuming the black hole formed only a few million years ago?", "answer": "The superradiant growth timescale for a vector boson scales as \u03c4 \u2243 10\u00b3\u202fs\u202f(M/10\u202fM\u2299)\u2076\u202f(m/10\u207b\u00b9\u00b2\u202feV)\u207b\u2076 for optimal coupling. For a 20\u202fM\u2299 black hole with \u03c7 \u22480.8 and an age of \u224810\u2076\u202fyr, vector boson masses in the window m \u2243 10\u207b\u00b9\u00b2\u201310\u207b\u00b9\u00b9\u202feV would have time to grow a cloud and spin\u2011down the horizon below the observed value, thereby being excluded. Couplings stronger than gravitational (i.e., with a gauge charge larger than Newton\u2019s constant) would shorten the instability times, tightening these constraints further."}, {"question": "To what extent do metallicity\u2011dependent stellar winds influence the retention of black\u2011hole merger remnants in nuclear star clusters, thereby affecting the probability of successive hierarchical mergers?", "answer": "The agent does not know the answer to this question. The mechanisms through which metallicity\u2011dependent winds alter the pre\u2011merger masses of progenitor stars directly impact the final remnant mass and spin, which in turn influence the gravitational\u2011wave recoil kick. The distribution of kick velocities relative to the cluster escape velocity determines whether the remnant remains bound and can form a second\u2011generation binary. Current population synthesis models incorporate metallicity effects on stellar evolution, but the coupling to cluster dynamics, the detailed distribution of escape velocities in nuclear star clusters, and the efficiency of later dynamical captures are not fully quantified. Consequently, a comprehensive assessment of metallicity\u2019s role requires further theoretical work combining stellar evolution, binary population synthesis, and realistic N\u2011body simulations of cluster dynamics."}, {"question": "What is the expected contribution of primordial black hole mergers to the isotropic stochastic gravitational\u2011wave background in the 20\u2013200 Hz band?", "answer": "Primordial black hole (PBH) binaries can in principle produce a stochastic background, but their merger rate, mass distribution, and spatial clustering remain highly uncertain. Current population\u2011inference methods based on LIGO-Virgo detections cannot constrain PBH parameters tightly; therefore, a robust prediction of their contribution to the GWB in the 20\u2013200\u202fHz band is not available yet. Further theoretical modeling and additional data from future observing runs are required to reduce these uncertainties."}, {"question": "How does the overlap\u2011reduction function for the LIGO Hanford\u2013Livingston baseline change if one of the detectors operates at a different orientation due to maintenance?", "answer": "The overlap\u2011reduction function (ORF) depends on the relative geometry and orientation of the two interferometers. If a detector\u2019s orientation is altered, the ORF would change accordingly, affecting the sensitivity to different polarizations and sky locations. Calculating the new ORF requires precise knowledge of the rotated antenna patterns and baseline. This is a straightforward but non\u2011trivial exercise in detector geometry and is routinely performed when accounting for downtime or maintenance, but the exact updated ORF is not provided in this paper."}, {"question": "Can the current noise\u2011budget method reliably disentangle Schumann\u2011resonance magnetic noise from potential cosmological backgrounds at frequencies above 100\u202fHz?", "answer": "The magnetic noise budget calculation assumes linear coupling between external magnetic fields and the strain channel, modeled via long\u2011term averaged coupling functions. While this approach is adequate for the 20\u201360\u202fHz band where Schumann resonances dominate, at frequencies above 100\u202fHz the magnetic coupling is much weaker and the ambient field spectrum is less well characterised. Consequently, the current method may not provide sufficient discrimination between weak magnetic artifacts and a cosmological background in the high\u2011frequency regime. Further dedicated magnetic field measurements and improved coupling models are needed."}, {"question": "What level of improvement in the binary black hole merger rate density at redshift z > 2 can be obtained by combining the updated O4a stochastic upper limits with the latest LIGO\u2013Virgo event catalog?", "answer": "By jointly fitting the stochastic upper limits to the CBC merger\u2011rate model, we obtain tighter constraints on the redshift evolution parameters (\u03b1_z, \u03b2_z, z_p) for binary black holes. The O4a data allow a modest tightening of the allowed variance in these parameters, but the statistical leverage remains limited due to the current stochastic sensitivity. The expected improvement is anticipated to be on the order of 10\u201320\u202f% in the inferred rate density for z\u202f>\u202f2 compared to O3, but this remains an estimate until real Bayesian analyses are performed."}, {"question": "How would the detection of gravitational\u2011wave polarizations beyond the tensor mode impact the constraints on alternative theories of gravity?", "answer": "Detection of non\u2011tensor polarizations\u2014such as vector or scalar modes\u2014would be a direct indication of physics beyond general relativity, enabling us to rule out or constrain a broad class of modified gravity theories that predict such modes. However, the current paper does not report any such detection; the data are consistent with pure tensor modes, and upper limits set on scalar and vector amplitudes are two\u2011times stronger than previous runs but still leave substantial parameter space for alternative theories. A definitive conclusion requires a future detection of a polarization\u2011specific signal."}, {"question": "How does the angular power spectrum of the stochastic gravitational-wave background depend on frequency for different astrophysical source classes?", "answer": "The angular power spectrum, usually characterized by \\(C_\\ell\\), shows distinct frequency scaling for different source populations. Compact binary coalescences (CBCs) dominate at higher frequencies (above 50\u202fHz) and their power spectrum tends to rise as \\(f^{2/3}\\) in the strain spectrum, which translates to a flatter \\(C_\\ell\\) at lower multipoles. Rotating neutron stars and magnetars contribute at lower frequencies (<\u202f50\u202fHz), with a steeper strain spectrum that leads to larger anisotropic power at higher \\(\\ell\\) values. Cosmological sources such as inflationary or cosmic\u2011string backgrounds, which are expected to be nearly scale\u2011invariant, produce an almost flat angular power spectrum across the full frequency band, making them difficult to distinguish from an isotropic component without additional sky localization."}, {"question": "Which astrophysical populations are most likely to generate a detectable anisotropy in the gravitational\u2011wave background at frequencies below 100\u202fHz?", "answer": "Below 100\u202fHz the most promising contributors to anisotropy are nearby populations with large spatial clustering. These include: 1) the population of millisecond pulsars in the Galactic plane, whose spatial distribution follows the stellar density and can create a dipole\u2011like enhancement, 2) the Scorpius\u202fX\u20111 accreting neutron\u2011star system, which may emit continuous waves, 3) compact binary coalescences inside the Virgo cluster, and 4) young neutron stars in supernova remnants such as SN\u202f1987A. Each of these sources has a distinct spectral shape that, combined with their sky positions, can leave a measurable imprint on the observable \\(C_\\ell\\) at sub\u2011fundamental frequencies."}, {"question": "How do correlated detector noises influence the cross\u2011correlation sensitivity for persistent gravitational\u2011wave signals?", "answer": "Cross\u2011correlation methods rely on the assumption that instrumental noises in geographically separated detectors are uncorrelated. If there exist correlated noise sources\u2014such as global magnetic fields or seismic couplings\u2014the overlap\u2011reduction function that translates the true sky signal into the measured cross\u2011power can be contaminated. This contamination manifests as an excess variance in the estimator and biases the inferred strain amplitude upward or downward depending on the phase relationship of the correlated noise. Advanced techniques, such as null\u2011stream analyses or subtraction of known magnetic/seismic channels, can mitigate these effects, but residual correlations still set a lower bound on the achievable sensitivity for persistent, narrowband sources."}, {"question": "What is the expected level of anisotropy induced by the clustering of millisecond pulsars in the Galactic plane?", "answer": "The present literature does not provide a precise quantitative estimate of the anisotropy caused by millisecond\u2011pulsar clustering. While models predict a modest dipole\u2011like enhancement of the gravitational\u2011wave power in the Galactic plane, the magnitude depends on the poorly known ellipticity distribution, distance uncertainties, and the unknown contribution from unresolved binaries. Consequently, the exact level of anisotropy remains an open question requiring further theoretical modeling and deeper continuous\u2011wave observations."}, {"question": "What statistical techniques can reduce the bias from shot noise in spherical\u2011harmonic analyses of the gravitational\u2011wave background?", "answer": "Shot noise arises from the discrete realization of astrophysical events and biases the auto\u2011\\(C_\\ell\\) estimator because it adds a white\u2011noise component to each multipole. A robust mitigation strategy employs a cross\u2011\\(C_\\ell\\) estimator: the cross\u2011power between independently cleaned maps\u2014constructed from separate data subsets\u2014cancels the shot\u2011noise bias because shot\u2011noise is uncorrelated between the subsets. Additionally, regularizing the Fisher matrix (e.g., via eigenvalue truncation or Tikhonov regularization) ensures numerical stability and suppresses sensitivity to poorly constrained higher\u2011\\(\\ell\\) modes that would otherwise amplify shot\u2011noise contributions. Combining these approaches yields unbiased estimates of the true anisotropic power spectrum."}, {"question": "How does the removal of narrowband spectral lines (e.g., calibration lines and mains harmonics) influence the detectability of continuous\u2010wave (CW) signals from spinning neutron stars in LIGO data?", "answer": "Removing narrowband lines reduces the spectral density at the frequencies of interest, which directly improves the signal\u2013to\u2013noise ratio for CW searches. Empirical studies of the O4a data show that the 90\u2011percentile upper limits for known pulsars improved by up to 15\u202f% after line removal, with the most significant gains at the lowest detectable frequencies where the detector noise is otherwise dominated by violin\u2011mode and resonant\u2011mode lines."}, {"question": "What are the main environmental and instrumental sources that produce non\u2011Gaussian glitches in LIGO strain data, and how does their occurrence rate change over a typical observing run?", "answer": "Principal non\u2011Gaussian sources include seismic activity, anthropogenic vibrations (e.g., nearby trains, road traffic), microseism to 1\u202fHz, anthropogenic acoustic disturbances, electrical mains transients, and internal control\u2013system glitches. In O4a the glitch rate above an SNR of 5 in the 20\u2013500\u202fHz band was approximately 0.5\u202fevents per hour for LHO and 0.7\u202fevents per hour for LLO during periods of good seismology, rising to 5\u201310\u202fevents per hour during heavy daylight traffic or windy weather. The rate decreases during nighttime and when the detector\u2019s vertical pendulum isolation system is in its highest\u2011performance state, indicating a clear seasonal and diurnal dependence."}, {"question": "How do the different data\u2011quality flag categories (CAT1, CAT2, CAT3) used in compact\u2011binary searches affect the overall false\u2011alarm rate for high\u2011mass black\u2011hole coalescences?", "answer": "CAT1 flags identify the most severe data\u2011quality problems and are strictly vetoed in CBC pipelines. Inclusion of CAT2 reduces the analysed livetime by an additional ~1\u20112\u202f% and removes time windows that would otherwise produce mis\u2011classified glitches with SNR\u202f>\u202f10, thereby lowering the false\u2011alarm probability from ~1\u202f\u00d7\u202f10\u207b\u2074\u202fyr\u207b\u00b9 to ~5\u202f\u00d7\u202f10\u207b\u2075\u202fyr\u207b\u00b9 for masses >\u202f50\u202fM\u2299. CAT3 flags, used only in targeted searches, have a negligible impact on the false\u2011alarm rate (<\u202f0.5\u202f%) but can be used to re\u2011rank background expectations when combined with the iDQ probability output."}, {"question": "What is the effect of photon\u2011calibrator injection frequency placement and amplitude on the shape of the calibration\u2011uncertainty envelope for LIGO strain data?", "answer": "Photon\u2011calibrator injections are inserted at eight discrete frequencies spread logarithmically from 10\u202fHz to 5\u202fkHz. The resulting uncertainty envelope shows a flat median systematic error of ~3\u202f% in amplitude and ~1\u202fms in phase between 100\u202fHz and 1\u202fkHz. At frequencies below 30\u202fHz and above 3\u202fkHz the envelope grows due to interpolation extrapolation, reaching up to 10\u202f% amplitude uncertainty. The chosen frequencies allow continuous monitoring of the calibration transfer function while minimizing spectral overlap with expected GW signals, thus maintaining a conservative, yet tight, uncertainty bound across the nominal detection band."}, {"question": "Does the alternate strain release with more aggressive broadband noise subtraction provide a measurable advantage over the default strain in detecting sub\u2011threshold compact\u2011binary events?", "answer": "The paper does not explicitly quantify the benefit of the alternate strain release for sub\u2011threshold event detection. While the alternate release includes additional broadband noise subtraction steps (e.g., GDS\u2011CALIB_STRAIN_CLEAN_AR), a direct comparison of recovery efficiency for events with signal\u2011to\u2011noise ratios between 4 and 6 would require a systematic injection study that is not reported. Therefore, at present we cannot say whether the alternate strain channel yields a statistically significant improvement in detecting sub\u2011threshold compact\u2011binary coalescences."}, {"question": "How do the effective inspiral spin distributions of binary black hole mergers detected in the first half of the fourth observing run compare to those from previous observing runs?", "answer": "The effective inspiral spin (\u03c7_eff) of the binary black holes observed in O4a is largely centered near zero, indicating that most of the systems have spins either aligned and anti\u2011aligned with the orbital angular momentum or intrinsically small. However, a non\u2011negligible tail at positive \u03c7_eff values is evident, corresponding to mildly spinning systems that possess preferential spin alignment. This distribution is statistically consistent with the spin distribution measured in GWTC\u20113, where most events also cluster near zero but exhibit a broadened spread, showing no significant evolution in the overall spin behaviour between O3 and O4a."}, {"question": "Is there any clear evidence of tidal deformation signatures in the gravitational\u2011wave signals from the two NSBH candidates included in the catalog?", "answer": "The available signal\u2011to\u2011noise ratios for the two neutron\u2011star\u2013black\u2011hole candidates, GW230518_125908 and GW230529_181500, are modest. The Bayesian inference analyses performed with tidal\u2011inclusive waveform models do not yield statistically significant measurements of the neutron\u2011star tidal deformability parameter (\u039b). Consequently, while the presence of a neutron star is inferred from the component masses, no robust constraints on the equation of state can be extracted from these events alone."}, {"question": "What are the typical sky localisation areas achieved with a two\u2011detector LIGO network for events in the O4a catalog?", "answer": "Because only the two LIGO detectors were operational during O4a, typical 90\u2011percent credible sky areas for the catalog events span from ~100 deg\u00b2 for high\u2011quality, well\u2011localized, low\u2011mass binaries to several thousand square degrees for lower\u2011frequency and higher\u2011mass systems. The most localized event, GW230627_015337, achieved a sky area of ~110 deg\u00b2, while the least localized signal, GW230901_191248 (not listed here), had several thousand deg\u00b2. These localisation uncertainties are larger than most events from NGr3, where the inclusion of Virgo provided 2\u2011to\u20113\u2011fold reductions in area."}, {"question": "Do the mass\u2013ratio of binary black holes show a dependence on the total mass in the O4a sample?", "answer": "An exploratory analysis of the O4a source\u2011frame masses indicates that the most massive systems (M \u2273 150\u202fM\u2299) tend to have slightly more unequal mass ratios (q \u2248 0.6), whereas the lower\u2011mass binaries (M \u2248 10\u201330\u202fM\u2299) display a broad distribution of mass ratios, including several that are almost equal. While this trend is present, the small sample size and measurement uncertainties prevent a definitive statement about a direct correlation; further data will be required to confirm whether the mass\u2011ratio distribution depends strongly on the total mass."}, {"question": "What constraints does the paper provide on the neutron\u2011star equation of state derived from the NSBH candidates GW230518_125908 and GW230529_181500?", "answer": "The paper does not provide any constraints on the neutron\u2011star equation of state from the NSBH candidates. The tidal deformability parameters inferred from the Bayesian analyses are consistent with zero within large uncertainties, and no robust measurement of \u039b was obtained. Consequently, the paper does not offer constraints on the neutron\u2011star equation of state from these events."}, {"question": "What astrophysical processes could allow black holes to form with masses inside the pair\u2011instability mass gap between roughly 60 and 130\u202fM\u2299?", "answer": "Several channels have been proposed: (1) Hierarchical mergers of smaller black holes within dense stellar clusters can build up masses above the gap while keeping a high spin; (2) Failed supernovae or pulsational pair\u2011instability supernovae in rapidly rotating metal\u2011poor stars can leave behind black holes in the gap if the envelope is retained; (3) Binary stellar evolution pathways such as chemically homogeneous evolution can produce massive, tight binaries that avoid pair\u2011instability disruption; and (4) Gas\u2011rich environments (e.g., accretion in active galactic nucleus disks) may allow accretion\u2011driven mass growth that pushes a black hole into the gap. Each mechanism operates under different metallicity, spin, and environmental assumptions."}, {"question": "How can measurements of high spin values (>0.7) in merging black holes inform theories of black hole spin evolution?", "answer": "High spins constrain the angular momentum budget of the progenitor systems. In isolated binary evolution, such spins would require efficient tidal spin\u2011up or prolonged accretion episodes, implying very short orbital separations and/or dense circumbinary disks. In dynamical environments, large spins suggest that the merging black holes were themselves products of previous mergers, as successive mergers naturally spin up the resulting remnant. Therefore, observing sustained high spins in multiple events points toward a population of black holes that has undergone repeated mergers or significant accretion."}, {"question": "What observational signatures would distinguish a gravitational\u2011wave source that formed through hierarchical mergers from one that formed directly from a massive stellar collapse?", "answer": "Hierarchical mergers are expected to leave several imprints: (1) a broader distribution of spins, typically with larger magnitudes and higher effective precessing spin \u03c7p; (2) a bias toward higher total masses and mass ratios close to unity; (3) potential evidence of recoil kicks\u2014e.g., an uncharacteristically large kick velocity\u2014as inferred from the remnant\u2019s motion; (4) an elevated rate of spin\u2011aligned or mildly precessing systems within dense clusters; and (5) a correlation of events with known globular or nuclear cluster environments. Direct massive stellar collapse would more likely produce lower spins, a range of mass ratios, and no significant kick imprint."}, {"question": "What are the leading challenges in accurately modeling the signal morphology of very massive, highly spinning binary black hole mergers?", "answer": "The primary challenges include: (1) limited coverage of numerical relativity simulations in the high\u2011spin, comparable\u2011mass regime, leading to waveform model extrapolation uncertainties; (2) inadequate calibration of precession dynamics in models beyond spin \u22480.8, which can bias mass and spin inference; (3) the influence of higher\u2011order multipoles that become more pronounced at high inclination, demanding more sophisticated amplitude corrections; and (4) potential systematic mismatches between waveform families, which introduce non\u2011negligible parameter biases even for signals with moderate signal\u2011to\u2011noise ratios."}, {"question": "The paper does not fully address the possible existence of significant residuals after subtracting the best\u2011fit binary\u2011black\u2011hole waveform. What could be the implications of unmodeled residual power?", "answer": "If residual power persists beyond what Gaussian noise predicts, it could indicate additional physical effects not captured by the binary\u2011black\u2011hole hypothesis, such as: (1) gravitational\u2011wave echoes from exotic compact objects or quantum gravity modifications; (2) environmental effects like dynamical friction in dense media; (3) strong\u2011field deviations from general relativity; or (4) unmodeled instrumental artifacts. Without a dedicated investigation of the residuals, it is not possible to determine whether they arise from astrophysical phenomena or from limitations in the waveform models."}, {"question": "How can incorporating KAGRA data in a future all\u2011sky search for long\u2011duration gravitational\u2011wave transients improve the overall sensitivity of the detector network compared to LIGO\u2011Hanford and LIGO\u2011Livingston alone?", "answer": "Adding KAGRA would increase the effective baseline and improve sky\u2011coverage, leading to a modest increase in the signal\u2011to\u2011noise ratio for sources that lie between the LIGO sites. However, the exact gain depends on KAGRA\u2019s noise performance in the 10\u20132000\u202fHz band, its duty cycle, and the relative antenna patterns. Because KAGRA\u2019s first observing cycles had limited engineering runs in O4a, the paper did not include its data, so a quantitative assessment remains to be made with full\u2011science\u2011quality KAGRA data."}, {"question": "What are the principal difficulties in constructing accurate waveform models for eccentric compact binary coalescences (ECBCs) that emit long\u2011duration gravitational waves?", "answer": "ECBCs produce highly non\u2011stationary signals with repeated bursts and pre\u2011merger modulations. The challenges include (1) accurately evolving the binary through thousands of orbits while retaining orbital eccentricity; (2) modeling tidal interactions and gravitational\u2011wave back\u2011reaction at high eccentricity; and (3) ensuring sufficient overlap with the detector noise curve over long timescales. Current semianalytic approximants provide only limited coverage in mass and eccentricity, so full numerical relativity simulations (which are computationally expensive) are required to generate accurate long\u2011duration templates."}, {"question": "In what ways does the XGBoost classifier enhance the detection pipeline\u2019s ability to distinguish true long\u2011duration gravitational\u2011wave transients from non\u2011astrophysical glitches?", "answer": "XGBoost learns complex decision boundaries from a training set of background (glitch) data and injected signals. By weighting multiple features\u2014such as coherent SNR, spectral energy distribution, and clustering metrics\u2014it can suppress coincident but incoherent noise and amplify coherent, extended power excesses typical of astrophysical transients. Importantly, the classifier obviates hard cut\u2011offs on signal duration, allowing the pipeline to search across a much wider range of temporal morphologies while maintaining a controlled false\u2011alarm rate."}, {"question": "How does the ellipticity of a newly formed magnetar affect the strain amplitude and detectability of a long\u2011duration gravitational\u2011wave signal?", "answer": "The strain amplitude scales roughly with the product \\(\\epsilon \\times f^{2}\\), where \\(\\epsilon\\) is the equatorial ellipticity and \\(f\\) the GW frequency. A larger ellipticity (e.g., \\(\\epsilon \\gtrsim 10^{-4}\\)) produces a stronger, more slowly decaying signal, improving detectability. Conversely, a low ellipticity or rapid magnetic field decay reduces the emitted power, pushing the signal below typical network thresholds. The paper models ellipticities between 0.005 and 0.08; extrapolating to extreme values would either boost or further limit detectability."}, {"question": "What are the implications of detecting a long\u2011duration gravitational\u2011wave transient for multi\u2011messenger astronomy, and why is this still an open question?", "answer": "A confirmed long\u2011duration GW event would provide unique constraints on the post\u2011merger evolution of compact objects, potentially revealing sustained energy injection into electromagnetic counterparts (e.g., X\u2011ray plateaus, kilonovae). However, the exact relationship between GW signal characteristics (duration, frequency evolution) and observable electromagnetic signatures remains poorly understood due to uncertainties in magneto\u2011hydrodynamic processes, fallback accretion physics, and jet formation. Without a statistically significant sample and simultaneous electromagnetic observations, it is difficult to establish robust correlation models, leaving the field an active area for future research."}, {"question": "What is the current level of disagreement between early\u2011universe measurements (e.g., from the cosmic microwave background) and late\u2011universe measurements (e.g., from Type Ia supernovae) of the Hubble constant?", "answer": "Measurements of the Hubble constant from the early universe, such as those obtained from the cosmic microwave background (CMB) with the \\u201cPlanck\\u201d cosmology mission, consistently give a value around 67\u201368 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. Conversely, late\u2011universe, or local, probes\u2014most notably the cosmic distance ladder calibrated with Cepheids and Type Ia supernovae (the so\u2011called SH0ES program)\u2014usually yield a Hubble constant closer to 73\u201374 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. The tension between these two determinations is roughly 5\u20136 sigma, indicating a statistically significant discrepancy that is not easily explained by simply expanding the measurement uncertainties."}, {"question": "How can a detection of a compact binary merger by a laser\u2011interferometric gravitational\u2011wave detector act as a ``standard siren'' for cosmological distance measurements?", "answer": "A compact binary merger emits a gravitational\u2011wave signal whose amplitude scales inversely with the luminosity distance to the source. The waveform model predicts this amplitude given a set of intrinsic parameters (component masses, spins, orbital orientation, etc.). By performing parameter estimation on the data, one obtains a posterior on the luminosity distance independent of any external distance ladder. If the source redshift is known\u2014either through an electromagnetic counterpart or a statistical inference\u2014this distance\u2013redshift pair can be used directly to probe the cosmological expansion history, making the system a standard siren analogous to the way a Type Ia supernova is a standard candle."}, {"question": "What is the ``spectral siren'' approach in gravitational\u2011wave cosmology, and what does it rely on?", "answer": "The spectral siren approach exploits features\u2014such as peaks, gaps, or cut\u2011offs\u2014in the source\u2011frame mass distribution of merging compact binaries. Because the observed gravitational\u2011wave signal contains the masses redshifted by (1+z), a feature at a fixed intrinsic mass will appear at lower detector\u2011frame masses for higher\u2011redshift sources. By modeling the underlying mass spectrum and assuming a merger\u2011rate evolution with redshift, one can relate the observed distribution to the cosmic expansion. The method therefore relies on a statistically robust model of the intrinsic mass distribution and on a sufficient population of events to constrain the mass\u2011redshift degeneracy."}, {"question": "How would a modification of the propagation of gravitational waves affect the luminosity\u2011distance relation, and how can such modifications be parametrized?", "answer": "In several modified gravity theories the amplitude of gravitational waves decays differently from the standard 1/DL behaviour of general relativity. This modifies the effective GW luminosity distance (DGW\\u202fl) relative to the usual electromagnetic luminosity distance (DEM\\u202fl). A common phenomenological parametrization is DGW\\u202fl\u00a0=\u00a0DEM\\u202fl\u00a0[\u039e0\u00a0+\u00a0(1\u00a0\u2013\u00a0\u039e0)(1+z)\u207b\u207f], where the parameter \u039e0 controls the overall amplitude of the deviation and n controls how rapidly the deviation becomes important with redshift. Such a parametrization captures many late\u2011time modified\u2011gravity scenarios and can be constrained by gravitational\u2011wave standard\u2011siren measurements."}, {"question": "Is there observational evidence that the mass distribution of black holes in merging binaries changes with redshift?", "answer": "I do not have a definitive answer to this question. While the data analysed in the paper allow for a statistical inference of the mass distribution at the redshifts probed by the observed events, the current evidence is not sufficient to confirm a redshift evolution of that distribution. Investigating the evolution would require more events spanning a broader redshift range and a modeling framework that explicitly allows the mass function to vary with redshift, which was not part of the present analysis."}, {"question": "What are the dominant mechanisms that can disrupt primordial black hole binaries in the early universe, and how do they influence the present-day merger rates?", "answer": "Current theoretical models suggest that gravitational interactions with surrounding baryonic matter, primordial density fluctuations, and dynamical friction during the radiation-dominated era can alter the initial orbital parameters of primordial black hole (PBH) binaries. These processes can either harden binaries, making them merge sooner, or ionize them, preventing coalescence altogether. However, the precise efficiency and relative importance of each mechanism remain uncertain because they depend on poorly constrained details of the early universe\u2019s density field, the exact PBH mass function, and the evolution of the primordial plasma. Ongoing work aims to integrate detailed cosmological simulations with analytic estimates to better constrain these disruptive effects."}, {"question": "How do eccentricity and higher-order post\u2011Newtonian corrections affect the detectability of ultra\u2011compact binary inspirals in ground\u2011based gravitational\u2011wave data?", "answer": "Eccentric binaries emit gravitational radiation over a broader frequency spectrum, introducing higher harmonics and modifying the phase evolution. In semi\u2011coherent search methods that approximate the evolution with a leading\u2011order chirp, residual eccentricity can cause the signal to drift out of a given frequency bin over the coherent integration time, reducing sensitivity. Higher\u2011order post\u2011Newtonian terms refine the phase but typically contribute less for very low\u2011mass binaries, whose evolution is slow and dominated by the leading quadrupole term. Extending matched\u2011filter or Hough\u2011type pipelines to include eccentric templates or higher\u2011order PN waveforms is computationally expensive, and the trade\u2011off between improved sensitivity and additional search volume is still under investigation."}, {"question": "Can a population of planetary\u2011mass primordial black holes explain a significant fraction of dark matter without violating microlensing and gravitational\u2011wave constraints?", "answer": "If the primordial black hole mass function contains a pronounced peak in the planetary\u2011mass range (\\(10^{-6} - 10^{-3}\\,M_\\odot\\)), it could, in principle, contribute to dark matter. Microlensing surveys place upper limits on the abundance of compact objects in this mass window, particularly through the non\u2011observation of short\u2011duration microlensing events. Gravitational\u2011wave searches for binary coalescences further constrain the merger rate, which must be low enough to avoid detection yet high enough to produce measurable rates. Reconciling these limits requires a finely tuned mass distribution and formation history. Current evidence suggests that any planetary\u2011mass PBH fraction of dark matter must be small, but definitive conclusions await more sensitive microlensing campaigns and continuous\u2011wave searches."}, {"question": "What is the impact of local dark\u2011matter density variations within the Milky Way on the expected merger rates of ultra\u2011compact binaries?", "answer": "Merger rates of PBH binaries are proportional to the number density of PBHs, which in turn follows the underlying dark\u2011matter distribution. In regions near the Galactic center, the dark\u2011matter density is higher, potentially boosting the local merger rate by an order of magnitude compared to the solar neighborhood. Conversely, in the outer halo the density drops, leading to lower rates. These spatial variations introduce a non\u2011uniform sensitivity for detectors, as the distance reach depends on the local volume probed. Accurate modeling therefore requires incorporating realistic halo profiles (e.g., Navarro\u2011Frenk\u2011White, Einasto) and possible substructure such as dark\u2011matter clumps."}, {"question": "What are the main challenges in extending the Generalized Frequency\u2011Hough method to capture signals from binaries with significant spin\u2011orbit coupling or highly asymmetric mass ratios?", "answer": "The Generalized Frequency\u2011Hough (GFH) transform relies on approximating the time\u2011frequency track of a binary inspiral with a power\u2011law curve derived from the leading\u2011order chirp mass. Introducing significant spin\u2011orbit coupling or highly asymmetric mass ratios alters the phase evolution by adding terms that depend on individual spins, the mass ratio, and higher\u2011order PN corrections. These complications would require a multi\u2011dimensional mapping of additional parameters, drastically increasing the search space and computational cost. Moreover, the assumption that the signal remains monochromatic within a short coherent segment may break down because spin\u2011induced precession can modulate the frequency more rapidly than the coherent time allows. Consequently, while GFH is powerful for low\u2011spin, nearly equal\u2011mass waveforms, reliably capturing more complex systems would need either a different semi\u2011coherent strategy or the development of faster algorithms that can handle the enlarged template bank."}, {"question": "Is there evidence for a population of planetary\u2011mass primordial black holes that could influence the observed dark\u2011matter halo structure in dwarf galaxies?", "answer": "The existence of planetary\u2011mass primordial black holes (PBHs) that contribute significantly to the dark\u2011matter budget is currently unconfirmed. While simulations suggest that such PBHs might form dense sub\u2011clusters that could alter the inner density profiles of dwarf galaxies, observational constraints from stellar kinematics, microlensing surveys, and gravitational\u2011wave non\u2011detections place tight upper limits on the PBH fraction in this mass range. Because the relevant mass range lies below the sensitivity threshold of most microlensing experiments and the gravitational\u2011wave band is limited by the long chirping times of ultra\u2011compact binaries, definitive evidence is lacking. Future surveys with higher cadence and improved continuous\u2011wave detectors may provide more stringent constraints, but at present the question remains unanswered."}, {"question": "How does the projected semi\u2011major axis (ap) of a neutron star in a binary system influence the detectability of continuous gravitational\u2011wave signals?", "answer": "The projected semi\u2011major axis determines the amplitude of the Doppler modulation of the gravitational\u2011wave frequency. Larger ap values spread the signal power over a wider frequency range, increasing the required template resolution and making the search computationally more demanding. Consequently, the sensitivity depth typically decreases for larger ap values, and searches often limit ap to a modest range (e.g., 5\u201315\u202flight\u2011seconds) to keep the template bank tractable while still covering the most likely parameter space for known Galactic binaries."}, {"question": "What effect does the orbital period (P) of a binary system have on the duration and shape of the continuous\u2011wave frequency track in time\u2013frequency space?", "answer": "The orbital period sets the timescale over which the neutron star\u2019s orbital motion modulates the signal frequency. Shorter periods produce rapid, high\u2011amplitude oscillations in the frequency track, whereas longer periods yield slower, smoother modulations. This directly affects the match\u2011filtering strategy: shorter periods require tighter sampling in the orbital phase dimension, while longer periods allow for coarser sampling but demand longer coherent integration times to achieve sufficient sensitivity."}, {"question": "What typical noise spectral\u2011density limits do advanced interferometric detectors achieve in the 100\u2013350\u202fHz band for continuous\u2011wave searches?", "answer": "During the early part of the fourth observing run, the combined H1 and L1 detectors reached an inverse\u2011square\u2011root power\u2011spectral\u2011density (PSD) of roughly \\(2\\times10^{-23}\\,\\mathrm{Hz}^{-1/2}\\) at 200\u202fHz, improving gradually toward 250\u2013300\u202fHz. This level of sensitivity dominates the attainable strain\u2011amplitude limit for continuous waves in that band, with best\u2011achieved depths (in inverse strain units) around 20\u201325\u202fHz\\(^{-1/2}\\)."}, {"question": "What is the maximum spin\u2011down rate that can be tolerated in all\u2011sky continuous\u2011wave searches without significant loss of sensitivity?", "answer": "The search sensitivity declines if the intrinsic spin\u2011down (or spin\u2011up) exceeds the frequency resolution over the total observing time. The criterion is \\(|\\dot{f}_0| \\le 1/(T_{\\rm SFT}\\,T_{\\rm obs})\\), where \\(T_{\\rm SFT}\\) is the short\u2011Fourier\u2011transform length and \\(T_{\\rm obs}\\) is the campaign duration. For a 1024\u2011s SFT and a 237\u2011day run, this translates to \\(|\\dot{f}_0| \\lesssim 4\\times10^{-12}\\,\\mathrm{Hz\\,s^{-1}}\\). Spin\u2011down larger than this would shift the signal by more than one frequency bin, thus reducing coherence and sensitivity."}, {"question": "Which theoretical predictions constrain the maximum ellipticity of neutron stars that could be probed by all\u2011sky continuous\u2011wave searches in the 7\u201315 day orbital period range?", "answer": "We currently do not have a definitive answer to this question. The paper focuses exclusively on the data analysis pipeline and sensitivity estimates and does not explore the astrophysical modeling of maximum sustainable ellipticity for neutron stars in binaries with periods between 7 and 15 days. Theoretical estimates vary from \\(\\sim10^{-6}\\) for conventional nuclear matter to \\(\\sim10^{-4}\\) for exotic matter, but translating these limits into observable strain amplitudes for the specific orbital parameter range would require detailed population synthesis and accretion\u2011torque modelling that is beyond the scope of the analysis presented here."}, {"question": "How would a small electric charge carried by a merging black hole affect the frequencies and damping times of its dominant quasinormal modes?", "answer": "A non\u2011zero charge introduces a Reissner\u2013Nordstr\u00f6m or Kerr\u2013Newman structure. The mode spectrum shifts slightly: the fundamental \u2113=2, |m|=2 mode\u2019s real part increases while its damping time decreases compared to the uncharged Kerr case, although the magnitude of the shift is typically a few percent for realistic charge\u2011to\u2011mass ratios below 10\u207b\u2074. The precise dependence also involves the mode\u2019s overtone number and the black hole\u2019s spin."}, {"question": "Can the extraordinarily high signal\u2011to\u2011noise ratio of recent gravitational\u2011wave events be used to distinguish between General Relativity and alternative theories of gravity that modify the merger dynamics?", "answer": "Yes. In such theories the waveform\u2019s phasing and amplitude evolution during the inspiral and merger are altered, leading to systematic biases in the recovered masses, spins, and ringdown frequencies. By performing parameter estimations within each alternative\u2011gravity parameterization and comparing the likelihoods against the GR prediction, one can place upper limits on the theory\u2011specific couplings (e.g., higher\u2011derivative terms or scalar\u2011tensor couplings) typically at the sub\u2011percent level for the most massive, loud events."}, {"question": "Could the detection of multiple quasinormal\u2011mode overtones provide a direct measurement of a non\u2011zero graviton mass?", "answer": "In principle, a massive graviton would modify the dispersion relation, causing the quasinormal\u2011mode frequencies to deviate from their General\u2011Relativity predictions. However, the current sensitivity to graviton mass from ringdown data is limited; even with multiple overtones, constraints are weaker than those from inspiral phase dispersion and are usually in the tens of kiloparsecs squared per gigaparsec. Future detectors with higher bandwidth and longer overtones might improve these bounds."}, {"question": "What role could black hole superradiance play in testing the area law during a binary merger?", "answer": "Superradiant instabilities can extract rotational energy from a black hole and excite bound states of ultra\u2011light bosons. If such an instability is triggered during the merger, part of the system\u2019s angular momentum would be stored in the cloud rather than radiated in gravitational waves, effectively reducing the final horizon area compared to the GR prediction. A measurable deficit in the area would signal superradiant growth, though detecting this effect would require both high signal\u2011to\u2011noise and a theoretical model that predicts the cloud\u2019s emission timescale."}, {"question": "What is the minimal deviation from the Kerr metric that is still consistent with the most recent high\u2011SNR gravitational\u2011wave observations, yet would imply new physics beyond General Relativity?", "answer": "We currently do not possess a definitive quantitative answer. Determining the smallest allowable deviation requires a systematic exploration of the full parameter space of alternative metric theories (e.g., parametrized post\u2011Newtonian extensions, dynamical Chern\u2011Simons gravity, or Einstein\u2011dilaton\u2011Gauss\u2011Bonnet models) in conjunction with the entire evolution of the binary\u2014including inspiral, merger, and ringdown\u2014using high\u2011accuracy numerical relativity simulations. Such comprehensive studies are still underway; the data at hand are consistent with the pure Kerr geometry within a few percent, but they do not definitively rule out all possible small deviations that could arise from beyond\u2011GR physics."}, {"question": "What determines the expected lifetime of an ultralight vector boson cloud around a black hole and how does it scale with the boson mass and the black hole spin?", "answer": "The lifetime of a vector boson cloud is governed by two competing processes: the superradiant growth phase, which extracts rotational energy from the black hole, and the gravitational\u2011wave (GW) depletion phase, in which the cloud radiates energy. The superradiant growth time \\( \\tau_{\\rm grow} \\) scales approximately as\\n\\\\[ \\\\tau_{\\rm grow} \\\\sim \\\\frac{1}{\\mu M}\\\\,\\\\frac{1}{(M\\\\mu)^{4\\\\ell+5}}\\\\left(\\\\frac{1}{\\\\chi-\\\\chi_{\\rm crit}}\\\\right), \\\\]\\nwhere \\( M \\) is the black hole mass, \\( \\mu = m_{V}\\\\,c^{2}/\\\\hbar \\) is the boson Compton frequency, \\( \\chi \\) is the dimensionless spin, \\( \\chi_{\\rm crit}=2/(m+\\\\ell+1)\\\\) is the critical spin where the instability shuts off, and \\( \\ell \\) is the orbital angular\u2011momentum quantum number (for the fastest growing vector modes typically \\( \\ell=0 \\)). The GW depletion time \\( \\tau_{\\rm GW} \\) scales roughly as\\n\\\\[ \\\\tau_{\\rm GW} \\\\sim \\\\frac{1}{\\\\mu M}\\\\,(M\\\\mu)^{(-4\\\\ell-5)}\\\\,(\\\\chi-\\\\chi_{\\rm crit})^{-2}, \\\\]\\nimplying that smaller boson masses (longer wavelengths) and higher black\u2011hole spins both lengthen the cloud\u2019s lifetime. The two timescales are comparable near the optimal boson mass that maximizes the instability rate, leading to a total signal duration of order days to months for stellar\u2011mass black holes in the LIGO band, and up to years for lighter bosons or more massive black holes."}, {"question": "What search strategies can improve the detection prospects of continuous gravitational waves from vector\u2011boson clouds around distant merger remnants that are several gigaparsecs away?", "answer": "To enhance sensitivity for far\u2011away sources one can (i) use longer coherent segments \\(T_{\\rm coh}\\) in semicoherent pipelines, trading off computational cost for better phase\u2011tracking; (ii) optimise sky\u2011position grids for large\u2011error regions by exploiting the angular\u2011resolution of the detector network, for example by hierarchical sky\u2011grid refinement; (iii) employ matched\u2011filter techniques that incorporate the predicted secular frequency drift \\(\\\\dot f(t)\\) of the vector\u2011boson signal, thus mitigating loss due to mismatch; (iv) leverage multi\u2011band analysis to separate neighbouring spectral lines; and (v) combine data from both LIGO and future detectors such as Virgo and KAGRA to increase sky\u2011coverage and reduce the false\u2011alarm rate. Each of these techniques is designed to recover weak, slow\u2011evolving signals that fall near the detector\u2019s sensitivity threshold, especially when the source distance strongly suppresses the strain amplitude."}, {"question": "What are the current observational limits on the mass of ultralight vector bosons derived from black\u2011hole spin measurements across the galaxy?", "answer": "Black\u2011hole spin measurements, particularly for rapidly rotating stellar\u2011mass black holes, place stringent limits on the mass of ultralight vector particles. If a boson of mass \\(m_{V}\\) existed within the range \\(10^{-14}\\,{\\rm eV} \\lesssim m_{V} \\lesssim 10^{-11}\\,{\\rm eV}\\), the superradiant instability would have spun down such black holes over their ages, yielding much lower observed spins than measured. Current observations exclude boson masses between roughly \\(0.5\\times10^{-13}\\)\u202feV and \\(1.2\\times10^{-13}\\)\u202feV for a typical 10\u202fM\\(_\\odot\\) black hole, under standard assumptions about accretion history and measurement uncertainties. For supermassive black holes the excluded mass window is narrower (e.g., \\(10^{-18}\\)\u2013\\(10^{-15}\\)\u202feV), but systematic errors in spin inference reduce the confidence of those limits."}, {"question": "How does an accretion disk around a black hole influence the superradiant growth of a vector\u2011boson cloud and the resulting gravitational\u2011wave signal?", "answer": "An accretion disk introduces additional torques that compete with the superradiant extraction of rotational energy. Material falling into the black hole can carry away angular momentum, thereby mitigating the spin\u2011down induced by the cloud. Furthermore, the disk\u2019s material can induce density\u2011wave torques and electromagnetic interactions that alter the effective potential felt by the boson field, potentially suppressing the growth rate or altering the mode structure. As a result, the GW amplitude may be reduced or the frequency evolution may deviate from the pure vacuum prediction. Accretion also supplies a continuous energy source that can replenish the black\u2011hole spin, potentially leading to a quasi\u2011steady state where growth and depletion balance, producing a long\u2011lived but comparatively weaker signal than in vacuum."}, {"question": "Has the analysis of the first part of the fourth LIGO\u2013Virgo\u2013KAGRA observing run revealed any definitive evidence for ultralight vector boson clouds around the merger remnants GW230814 and GW231123?", "answer": "I do not have a definitive answer regarding the presence of ultralight vector\u2011boson clouds around the specific merger remnants GW230814 and GW231123. The paper performed directed searches using two semicoherent methods (a hidden Markov model tracker and a Band\u2011Sampled\u2011Data pipeline) on the LIGO data from that period, focusing on the predicted signal parameter space for those remnants. While the paper reported setting exclusion limits on certain boson mass ranges, it did not observe any statistically significant candidates that could be attributed to vector\u2011boson clouds. As such, no evidence of such clouds was reported for those sources. However, this non\u2011detection does not constitute a firm absence; it could be due to limited signal\u2011to\u2011noise, data gaps, or the actual boson parameters lying outside the searched range. A more sensitive future observing run or improved analysis techniques would be required to confirm or refute the existence of such clouds around these remnants."}, {"question": "What are the main geotechnical challenges when tunnelling through molasse rock for a large circular collider tunnel, and what typical mitigation strategies are used?", "answer": "Molasse is a heterogeneous, silty\u2013sandstone\u2013marl sequence that can be weak and contain fractures, fault gouge, or variable strength zones. The key challenges are:\\n1. **Variable strength and deformation:** the mix of finer silts and coarser sandstones can produce uneven tunnel support needs, requiring careful mapping and design of ground support.\\n2. **Hydraulic behaviour:** water\u2011bearing layers and potential high pore\u2011pressure zones can lead to water ingress and ground pressure on the tunnel walls.\\n3. **Large\u2011scale deformation:** the high overburden (~200\u202fm) generates substantial in\u2011situ stresses that can induce settlement or ground movement.\\nTypical mitigations include:\\n- Pre\u2011tunnelling geotechnical surveys and drilling to determine rock quality and build a 3\u2013D model.\\n- Use of a TBM with a driven\u2011segmental lining (either twin\u2011shield or single\u2011shield) to provide immediate support.\\n- Ground conditioning (rock grouting or jet\u2011cutting) where high water pressures or soft strata are encountered.\\n- Installation of rock bolts, cable bolts and shotcrete as primary and secondary support systems.\\n- Monitoring of tunnel pressure and deformation during construction with temporary instrumentation."}, {"question": "When locating surface access shafts for a collider ring, what trade\u2011offs must be balanced to reduce environmental impact?", "answer": "Surface shafts are the only points where equipment, personnel and machinery can reach the underground. The main trade\u2011offs are:\\n1. **Geological suitability:** shafts should be situated where the sub\u2011surface consists of solid molasse rather than water\u2011bearing moraines or limestone.\\n2. **Proximity to existing infrastructure:** placing shafts near existing roadways or utilities can lessen the need for new construction but may increase traffic or noise.\\n3. **Land use and heritage:** shafts should avoid protected natural areas, cultural heritage sites, or densely populated zones to minimise visual and acoustic footprint.\\n4. **Future expansion:** a shaft placed too close to a collider sector may limit the ability to add new tunnels or caverns later, while a shaft placed too far from a detector may increase access costs.\\n5. **Operational safety:** shafts need to be long enough to provide a safe escape route and support ventilation and fire\u2011fighting infrastructure.\\nBalancing these factors usually involves an iterative optimisation that varies shaft locations within a tolerance zone, evaluates alternative tunnel alignments, and selects the configuration that satisfies all statutory and engineering constraints."}, {"question": "How does the \u2018avoid\u2013reduce\u2013compensate\u2019 optimisation methodology shape civil\u2011engineering decisions for large particle\u2011accelerator projects?", "answer": "The methodology is an iterative, multi\u2011criteria decision framework:\\n* **Avoid** \u2013 Wherever possible, the design avoids geologically or environmentally problematic zones (e.g., high\u2011pressure limestone, protected habitats, urban land). This might involve slightly longer tunnel routes or repositioning of surface facilities.\\n* **Reduce** \u2013 Costs, construction time, resource consumption and environmental disturbance are reduced by, for example, using a single\u2011shield TBM instead of a double\u2011shield machine, blending skip\u2011construction for multiple tunnels, or building larger caverns only where they are truly needed.\\n* **Compensate** \u2013 For impacts that cannot be avoided or sufficiently reduced (e.g., a necessary surface building on a protected site), a compensation measure is planned, such as habitat restoration, noise barriers, or payments to local stakeholders.\\nThroughout the design, each alternative is evaluated against technical feasibility, risk, cost, environmental and socio\u2011economic indicators, and the option that scores best across all criteria is selected. The approach ensures that risks are identified early and that environmental and social responsibilities are integrated into the engineering design."}, {"question": "What are the principal differences in material extraction and management when using Tunnel Boring Machines versus conventional drill\u2011and\u2011blast for deep underground construction of collider tunnels?", "answer": "The main distinctions are:\\n1. **Excavation rate & support installation:** A TBM cuts the rock and installs a precast lining continuously, allowing a constant advance of ~10\u201315\u202fm/day in suitable rock. Drill\u2011and\u2011blast relies on explosive fragmentation and requires manual loading, drilling, detonation and removal of spoil, generally slower (usually 2\u20135\u202fm/day) but flexible on hard or fractured rock.\\n2. **Spoil characteristics:** TBM spoils are clean, well sorted, and often culvert\u2011grade because they are cut by a cutting wheel. Blast spoils contain mixed rock, dust, and deeper rock fragments. This affects the material's suitability for reuse.\\n3. **Ground stability:** TBM reduces ground disturbance at the face and can incorporate flotation or slurry systems to control pressure. Drill\u2011and\u2011blast creates more micro\u2011fracture propagation and can raise water ingress.\\n4. **Environmental impact:** TBM tends to produce less vibration, dust, and noise, resulting in lower disturbance to surrounding communities. Blast is more disruptive and requires additional measures (e.g., water\u2011buckets, dust\u2011screens).\\n5. **Material handling & logistics:** TBM can deliver spoil directly to the shaft and/or circulates slurry for hydraulically powered conveyors. For blast, separate lift or conveyor systems are needed to haul the broken rock and segregate it.\\nDuring large collider projects, the decision between the two methods is guided by geology, depth, cost, schedule, and environmental concerns."}, {"question": "What are the long\u2011term structural behaviour and maintenance implications for large experimental caverns constructed in high water\u2011pressure limestone regions?", "answer": "The research paper does not investigate the long\u2011term structural integrity of such caverns, nor does it provide detailed maintenance strategies for high\u2011pressure limestone environments. Consequently, I do not have enough information to answer this question. Further studies, including in\u2011situ monitoring, finite\u2011element modelling, and long\u2011term corrosion analyses, would be required to establish reliable predictions for cavern safety and maintenance schedules in limestone."}, {"question": "What are the primary scientific motivations for constructing a 100\u202fTeV proton\u2011proton collider in the future circular collider tunnel?", "answer": "The 100\u202fTeV hadron collider is motivated by the desire to extend the energy frontier far beyond the current 14\u202fTeV LHC. At this scale the machine would provide unprecedented sensitivity to high\u2011mass processes such as double\u2011Higgs production, exotic resonance searches, and direct production of electroweak or coloured new states (e.g., supersymmetric particles, vector\u2011like quarks, or dark\u2011sector mediators). In addition, the large luminosity (~10\u202fab\u207b\u00b9) would enable precision measurements of the top\u2011quark and Higgs\u2011boson properties, probe the structure of electroweak symmetry breaking, and access mass scales up to tens of TeV, thereby opening a window to physics beyond the Standard Model."}, {"question": "What detector technologies are most promising for achieving a sub\u2011millimetre vertex resolution at the FCC\u2011ee?", "answer": "To reach sub\u2011mm vertex resolution the FCC\u2011ee requires ultra\u2011thin, high\u2011granularity pixel detectors placed very close to the interaction point. Candidate technologies include state\u2011of\u2011the\u2011art monolithic active pixel sensors (MAPS), hybrid pixel detectors with advanced bump\u2011bonding, and 3D integrated electronics. These sensors offer pixel pitch below 25\u202f\u00b5m, fast timing (~10\u201320\u202fps) for pile\u2011up mitigation, and a material budget of only a few per mille of a radiation length. Coupled with a low\u2011mass, high\u2011field solenoid (\u22642\u202fT during the electron\u2011positron stage) and a sophisticated beam pipe design, such detectors can achieve impact\u2011parameter resolutions in the tens of micrometres needed for efficient b\u2011 and c\u2011quark tagging and precise lifetime measurements."}, {"question": "How does the FCC\u2011ee improve the measurement of the Higgs self\u2011coupling compared to the HL\u2011LHC?", "answer": "While the HL\u2011LHC can only access the Higgs self\u2011coupling via double\u2011Higgs production at a few\u2011percent precision, the FCC\u2011ee provides an indirect, model\u2011independent determination through high\u2011precision measurements of the ZH production cross\u2011section at 240\u202fGeV and the single\u2011Higgs branching fractions at 250\u2013360\u202fGeV. The precise knowledge of the ZH cross\u2011section, combined with the per\u2011mille accuracy on the Z\u2013H coupling, constrains the Higgs self\u2011coupling at the 5%\u201310% level without the need for rare double\u2011Higgs events. When FCC\u2011ee data are combined with FCC\u2011hh measurements of the Higgs\u2011pair production cross\u2011section, the self\u2011coupling precision can be pushed below 5%, a sensitivity far beyond what can be achieved at HL\u2011LHC alone."}, {"question": "What strategies are employed at the machine\u2013detector interface to control synchrotron\u2011radiation backgrounds in the FCC\u2011ee electron\u2011positron stage?", "answer": "Synchrotron\u2011radiation (SR) backgrounds are mitigated through several design choices. First, the accelerator optics place the RF cavities and bending magnets well outside the detector acceptance, creating a low\u2011SR region around the interaction point. Second, the beam pipe is made of low\u2011Z, high\u2011thermal\u2011conductivity material (e.g., aluminium or titanium) with a narrow aperture (\u224810\u202fmm radius) to limit SR photons. Third, the detector solenoid field is limited to \u22642\u202fT during the electron\u2011positron stage to reduce vertical emittance growth and prevent SR\u2011induced beam blow\u2011up. Fourth, a dedicated SR absorber and a careful arrangement of quadrupole magnets inside a 100\u202fmrad dead\u2011cone shield the inner detector layers. Finally, active beam\u2011induced background monitoring, using fast calorimeters and tracking monitors placed close to the beam pipe, provides real\u2011time feedback to maintain background levels below the few keV per event threshold required for high\u2011precision measurements."}, {"question": "What is the estimated total construction cost for the FCC\u2011hh and how is it justified in terms of scientific return?", "answer": "I\u2019m sorry, I do not have that information. The feasibility study and the report you provided focus on the physics potential, detector concepts, and technical feasibility but do not include detailed cost estimates. Comprehensive cost modelling, including civil engineering, magnet fabrication, and detector construction, is part of a separate industrial investment study that is beyond the scope of the paper and the knowledge domain of this model."}, {"question": "How can sub\u2011threshold gamma\u2011ray burst detection algorithms increase the sensitivity to short GRB counterparts of gravitational\u2011wave events?", "answer": "Sub\u2011threshold searches\u2014such as blind scans of continuous time\u2011tagged data and coherent likelihood analyses across all detectors\u2014extend the trigger threshold by exploiting the full detector network and a larger time window. By combining data from multiple instruments and applying spectral templates that match short GRB emission, these algorithms suppress statistical noise, thereby lowering the effective detection threshold and increasing the probability of identifying weak, temporally aligned gamma\u2011ray transients."}, {"question": "What observational strategies can improve the joint sky coverage of Fermi\u2011GBM and Swift\u2011BAT when following up gravitational\u2011wave triggers?", "answer": "Coordinated, real\u2011time alerts that share GW sky maps with both spacecraft, combined with complementary pointing strategies (GBM\u2019s all\u2011sky view and BAT\u2019s coded mask imaging) maximize overlap. Additionally, rapid retrieval of burst event data (e.g., via the GUANO system) and the use of ground\u2011based rate monitoring help capture transients that occur during detector slewing or South Atlantic Anomaly passages, thereby reducing blind spots in the combined coverage."}, {"question": "How does the time delay between the gravitational\u2011wave merger and the onset of prompt gamma\u2011ray emission constrain short\u2011GRB jet\u2011launching models?", "answer": "The delay\u2014often ranging from milliseconds to a few seconds\u2014reflects the physics of accretion disk formation, disk wind development, and the acceleration of relativistic jets. Shorter delays are expected when dense ejecta promptly feed the central engine, while longer delays may indicate slower neutrino\u2011driven outflows or delayed black\u2011hole formation. By measuring or limiting these delays, one can test whether observed events favor internal\u2011shock, magnetically driven, or photospheric emission models."}, {"question": "What is the exact mechanism responsible for gamma\u2011ray emission from binary black hole mergers, and can current models be ruled out by existing gamma\u2011ray upper limits?", "answer": "The mechanism remains unknown; several speculative scenarios exist\u2014including neutrino annihilation in a transient accretion disk, electromagnetic extraction of spin energy from a charged black hole, Blandford\u2013Znajek jet launching, and prompt GW\u2011 to gamma\u2011ray energy conversion. Existing upper limits constrain the luminosity of such emission for a few nearby events, but due to uncertainties in jet geometry, viewing angles, and the physics of matter in vacuum environments, we cannot definitively rule out any model yet."}, {"question": "What role do instrument response simulations, such as detector response matrices, play in setting flux upper limits for gamma\u2011ray detectors during counterpart searches?", "answer": "Response simulations translate observed count rates into incident photon fluxes by accounting for detector efficiencies, geometric coding, and atmospheric scattering. Accurate detector response matrices (DRMs) allow the conversion of non\u2011detections into flux upper limits that are sensitive to source position and spectrum. They also enable the estimation of systematic uncertainties and the derivation of sky\u2011dependent upper\u2011limit maps essential for constraining emission models."}, {"question": "How can the precise measurements of the CKM angles \u03c61, \u03c62 and \u03c63 obtained by the B\u2013factory experiments be used to test minimal flavour\u2011violation (MFV) scenarios in supersymmetric models?", "answer": "The B\u2013factory measurements of sin(2\u03c61) (\u03b2), \u03b1 (\u03c62) and \u03b3 (\u03c63) constrain the unitarity triangle side\u2011lengths and internal angles. In MFV models all flavour changing amplitudes are governed by the CKM matrix, so any deviation from the SM predictions in B\u2013meson mixing or CP\u2011violating observables would indicate new particles or couplings that are not aligned with the CKM structure. By combining the world averages of the three angles with independent determinations of |Vub| and |Vcb|, one can perform global fits to the CKM parameters and extract bounds on the scale of new physics. In the MFV hypothesis, the current B\u2013factory data already pushes the scale of flavour\u2011changing supersymmetric particles to several TeV, leaving only small allowed regions for MFV\u2011compatible supersymmetric spectra. Deviations from this pattern would signal non\u2011MFV contributions."}, {"question": "What potential improvements in time\u2011dependent CP\u2011violation studies are expected with the proposed Super B Factories compared to the existing B\u2013factory experiments?", "answer": "Super B Factories aim to achieve instantaneous luminosities around 10^36\u202fcm\u207b\u00b2\u202fs\u207b\u00b9, roughly 50 times higher than the original B\u2013factory peak luminosities. This translates into about 50\u202fab\u207b\u00b9 of data, enabling several key improvements: (1) significantly reduced statistical uncertainties on sin\u202f2\u03b2, \u03b1 and \u03b3; (2) enhanced sensitivity to rare CP\u2011violating decay modes such as B\u202f\u2192\u202f\u03c0\u2070\u03c0\u2070 or B_s\u202f\u2192\u202f\u03d5\u03b3; (3) the ability to perform time\u2011dependent Dalitz\u2011plot analyses with much larger samples, improving the constraint on the angle \u03b3 from B\u202f\u2192\u202fD(K_S\u03c0\u207a\u03c0\u207b)K decays; (4) higher precision in measuring direct CP asymmetries in charmless B decays, potentially revealing interference from physics beyond the SM. The larger datasets would also help disentangle hadronic uncertainties by allowing more precise studies of strong\u2011phase differences through quantum\u2011correlated measurements at the \u03c8(3770)."}, {"question": "How do Dalitz\u2011plot analyses of multi\u2011body B decays (e.g., B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070) contribute to a more precise determination of the CKM phase \u03b3 compared to two\u2011body methods?", "answer": "Multi\u2011body decays such as B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070 contain resonant substructures (e.g., K*\u202f\u03c0, \u03c1\u202fK) that interfere across the Dalitz\u2011plot. By performing a full amplitude analysis, one can extract relative strong phases and magnitudes for each intermediate resonance. When the decay includes both b\u202f\u2192\u202fc and b\u202f\u2192\u202fu transition amplitudes that carry different weak phases, the interference across the Dalitz plot provides direct access to \u03b3 without the need to tag the B flavour. This method, often called the GGSZ (Dalitz) approach, benefits from the kinematic richness of three\u2011body final states, yielding reduced ambiguities and a more statistical power per event compared to two\u2011body GLW or ADS methods. Additionally, since the strong phases are obtained in\u2011situ, hadronic uncertainties are significantly constrained."}, {"question": "What are the main experimental challenges in measuring the branching fraction of the purely leptonic decay B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd at a Super B Factory, and how can they be addressed?", "answer": "The B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd decay has a large missing energy because the \u03c4 lepton subsequently decays to one or more neutrinos, leading to a signature with one or more hadrons or leptons plus large missing momentum. Key challenges include: (1) efficient \u03c4\u2011identification across all decay modes while controlling large backgrounds from generic B\u202f\u2192\u202f\u2113\u03bd\u2113X and continuum events; (2) precise reconstruction of the missing momentum vector, requiring hermetic calorimetry and excellent tracking; (3) suppression of two\u2011photon and beam\u2011background events that mimic missing energy; (4) control of hadronic B decays with similar topologies (e.g., B\u202f\u2192\u202f\u03c0\u2070\u03c0\u207b) which can be mis\u2011identified as \u03c4\u2011leptons. Addressing these issues relies on: high\u2011resolution vertex detectors to separate \u03c4\u2011decay vertices; a particle\u2011identification system capable of distinguishing pions, electrons and muons up to high momenta; a highly granular calorimeter for accurate neutral\u2011cluster reconstruction; and sophisticated multivariate analysis techniques that exploit event\u2011shape variables to suppress continuum. With the anticipated large dataset, statistical uncertainties will be driven below 1\u202f%, while systematic uncertainties will be controlled through careful calibration and data\u2011driven background studies."}, {"question": "Did the B Factories observe any evidence for lepton\u2011flavour\u2011violating (LFV) tau decays such as \u03c4\u202f\u2192\u202f\u03bc\u03b3 or \u03c4\u202f\u2192\u202f3\u00b5?", "answer": "The information relevant to lepton\u2011flavour\u2011violating tau decays is not covered in the physics discussion of the B Factories presented in this book. The analyses described focus on B\u2011meson decays, CP violation, charm physics, and related topics. While the B\u2011factory experiments did perform searches for LFV tau decays, the results are presented in separate dedicated studies that are not summarized here. Consequently, based solely on the content of this paper, we do not have the answer. A comprehensive answer would require consulting the specific B\u2011factory publications on LFV tau searches, which involve separate datasets, selection criteria, and background estimations."}, {"question": "What are the main systematic uncertainties that affect the reconstruction of supernova neutrino directions in liquid\u2011argon time\u2011projection chambers, and how can improving the statistical separation of interaction channels help mitigate these uncertainties?", "answer": "Liquid\u2011argon TPCs measure the Cherenkov\u2011like ionization track of the final\u2011state electron from a neutrino interaction. The two dominant systematic uncertainties are: (1) the intrinsic kinematic smearing between the neutrino direction and the outgoing lepton direction, which depends on the neutrino energy and the type of nuclear transition (Fermi, Gamow\u2013Teller or forbidden), and (2) the detector\u2011related angular resolution, governed by the spatial hit density, wire\u2011plane geometry and charge\u2011drift attenuation. The second uncertainty is strongly linked to the head\u2013tail ambiguity that arises because the detector cannot distinguish the start and end of a track by timing alone. By statistically separating the elastic neutrino\u2013electron scattering (eES) events, which provide a strong forward peak, from the charged\u2011current \u03bde absorption events, which are largely isotropic, one can weight the more directional eES events more heavily in the pointing likelihood. Improved classification\u2014whether through cut\u2011based variables, boosted decision trees or neural networks\u2014reduces the contamination of the directional sample and therefore lowers the effective angular uncertainty."}, {"question": "Could the inclusion of coherent elastic neutrino\u2013nucleus scattering (CEvNS) as a detectable channel in DUNE appreciably enhance the precision of supernova neutrino pointing?", "answer": "Coherent elastic scattering on argon nuclei has a very large cross section and its final\u2011state electron\u2011recoil energy is purely longitudinal, carrying essentially no directional information about the incoming neutrino. However, the CEvNS rate is substantial for supernova neutrinos (\u223c105 events in a 40\u2011kton detector) and its isotropic nature can be used to constrain the overall neutrino flux normalization and energy spectrum. By simultaneously fitting the CEvNS spectrum together with the eES and \u03bde\u2011cc spectra in a joint likelihood, one can reduce the degeneracy between flux parameters and the effective \u201cangular smearing\u201d of the eES sample, indirectly improving the directional information. Practically, DUNE would need a very low energy threshold and precise neutron\u2011induced background rejection to make CEvNS usable, but if achieved, the additional statistical power and flux constraint could sharpen the supernova pointing by a few tenths of a degree."}, {"question": "How might neutrino mass ordering influence the observable energy spectra of supernova neutrinos at a detector in Southern Africa, and what are the implications for directional reconstruction?", "answer": "In the conventional MSW framework, the normal ordering (NO) leads to a larger survival probability for electron neutrinos below \u223c10\u00a0MeV, while the inverted ordering (IO) favors conversion to non\u2011electron flavors in that energy range. Consequently, the measured \u03bde spectrum at a far detector will differ between the two orderings, affecting the relative weight of the highly directional eES events versus the isotropic \u03bde\u2013cc events. A detector in Southern Africa, such as the proposed South African liquid\u2011argon experiment, would observe a softer eES spectrum for IO, reducing the overall pointing precision by increasing the fraction of events with poor angular correlation. Conversely, under NO the larger high\u2011energy tail in the eES sample would improve the pointing. Therefore, the mass ordering has a non\u2011negligible, though modest, impact on directional accuracy that should be folded into a full systematic error budget."}, {"question": "What machine\u2011learning strategies can be deployed in real\u2011time supernova burst alert pipelines to maintain low latency while still preserving high directional accuracy?", "answer": "Real\u2011time pipelines must reduce raw waveforms to reconstructed tracks within milliseconds. Two complementary ML strategies are: (1) a lightweight convolutional neural network (CNN) operating directly on wire\u2011plane images to perform fast track\u2011finding and head\u2011tail assignment, using training sets generated from GEANT4 + LArSoft simulations; (2) a graph\u2011neural\u2011network (GNN) that ingests the list of hit vertices and their temporal ordering to compute probabilistic direction vectors and interaction\u2013type probabilities on a GPU. By chaining these models\u2014first a quick CNN for detection, then a GNN for precise direction estimation\u2014the pipeline can achieve sub\u2011second latency while keeping the pointing likelihood built from a fully calibrated response matrix. The key is to calibrate the ML inference output against a benchmark reconstruction and to propagate the resulting systematic uncertainties into the maximum\u2011likelihood sky map."}, {"question": "Does the presence of forbidden nuclear transitions in the \u03bde + \u202f\u2074\u2070Ar charged\u2011current absorption modify the angular distribution of emitted electrons enough to affect DUNE\u2019s supernova pointing performance?", "answer": "The paper does not provide a definitive answer because the cross\u2011section and angular\u2011momentum structure of forbidden transitions in supernova\u2011relevant energy ranges are only sparsely known from theory and there is no dedicated experimental data on \u2074\u2070Ar charged\u2011current scattering below ~30\u00a0MeV. If forbidden transitions contribute a substantial backward\u2011peaked component, the overall \u03bde\u2011cc electron angular distribution would deviate from the near\u2011isotropic shape assumed in the study, potentially introducing a small directional bias. Because the current pointing algorithm relies heavily on the clean eES sample and assumes the \u03bde\u2011cc events are essentially non\u2011informative, any significant anisotropy could change the weighting in the likelihood and modestly degrade the best achievable resolution. To resolve this, one would need dedicated low\u2011energy neutrino\u2011argon scattering measurements or improved ab initio nuclear\u2011structure calculations that quantify the forbidden\u2010transition strengths, which are presently unavailable."}, {"question": "How does a fully pixelated charge readout affect the accuracy of three\u2011dimensional reconstruction in liquid argon time projection chambers compared to traditional wire\u2011plane readouts?", "answer": "Pixelated readout provides a direct mapping of charge to a unique (x,\u202fy,\u202fz) coordinate, eliminating the ambiguity that arises from limited projections in wire\u2011plane TPCs. This improves reconstructed track fidelity, especially for overlapping events, by allowing exact hit localization in all three spatial dimensions."}, {"question": "What are the key engineering challenges when scaling up a modular ton\u2011scale pixel\u2011readout LArTPC from a single prototype to the full DUNE near\u2011detector complex?", "answer": "Challenges include maintaining low noise and uniformity across tens of thousands of ASIC channels, ensuring reliable cryogenic power distribution for per\u2011pixel electronics, scaling the data\u2011acquisition bandwidth to handle high voxel occupancy, preserving a uniform electric field over larger drift lengths, and integrating a high\u2011coverage photon\u2011detection system without compromising optical transparency."}, {"question": "In what ways does the resistive field cage design influence space\u2011charge effects and drift\u2011field uniformity in a small\u2011drift LArTPC module?", "answer": "The resistive shell provides a continuous voltage gradient rather than discrete wire rings, reducing dead zones and edge effects that can distort the field. By smoothing the potential, it minimizes localized field enhancements that attract ions, thereby mitigating space\u2011charge buildup and preserving uniform drift velocities across the volume."}, {"question": "How do the photon\u2011detection efficiencies of ArCLight and LCM modules impact the overall energy resolution when combining charge and light measurements?", "answer": "Higher photon\u2011detection efficiency (PDE) improves the statistical precision of the light signal, tightening the anti\u2011correlation between charge loss (due to recombination) and scintillation light. By accurately modeling this correlation, the combined charge\u2011light measurement can reduce the effective energy\u2011resolution variance compared to using either signal alone, provided the PDE variations across the detector are uniformly calibrated."}, {"question": "Does the Module\u20110 demonstrator provide evidence for a systematic time offset between the charge arrival time at the anode and the light signal t0 that depends on the drift electric field?", "answer": "The paper does not report a study of such a field\u2011dependent time offset, nor does it present measurements that would reveal a systematic shift. Therefore, at this time we cannot answer the question; additional dedicated measurements of the t0 timing relative to drift field variations would be required to resolve this issue."}, {"question": "How will the sensitivity improvements planned for the next LIGO\u2013Virgo observing run affect the expected detection rate of strongly lensed binary\u2011black\u2011hole gravitational\u2011wave signals?", "answer": "With the design sensitivity the network is expected to detect many more binary\u2011black\u2011hole mergers at higher redshift, allowing the strong\u2011lensing cross\u2011section to be sampled more densely. Simulations forecast a few percent increase in the probability of observing a lensed pair per observing run, though the exact number depends on the adopted mass and redshift distributions of the lensing halos and the merger\u2011rate evolution."}, {"question": "In what way could the inclusion of higher\u2011order spherical\u2011harmonic modes in waveform models improve the identification of microlensing signatures in gravitational\u2011wave data?", "answer": "Higher\u2011order modes provide additional frequency structure that can break degeneracies between intrinsic parameters and lens\u2010induced frequency\u2011dependent magnification. Their presence amplifies the beating patterns produced by point\u2011mass lenses, potentially making microlensing detectable at lower signal\u2011to\u2011noise ratios."}, {"question": "What limits on the fraction of dark matter that can be composed of compact objects can be projected from the Keplerian\u2011mass range (10\u00b2\u201310\u2075\u202fM\u2299) using the next decade of gravitational\u2011wave data?", "answer": "Forecasts based on O4\u2013O5 merger counts (\u223c300\u20131000 events) suggest that constraints on the compact\u2011object dark\u2011matter fraction could tighten to the 10\u207b\u00b9\u201310\u207b\u00b2 level in that mass window, provided no microlensing signatures are observed and the waveform models accurately capture small\u2011scale lensing effects."}, {"question": "How significant are systematic calibration uncertainties and transient noise artifacts in sub\u2011threshold searches for lensed gravitational\u2011wave counterparts?", "answer": "Calibration errors can shift recovered times and amplitudes, mimicking or hiding the subtle magnification patterns of a lensed image. Transient glitches increase the trials factor in a targeted search, raising the false\u2011alarm rate. Robust vetoes and improved calibration are essential to keep systematic biases below the statistical uncertainty of lens\u2011null likelihoods."}, {"question": "What is the theoretical distribution of magnification factors for gravitational\u2011wave lensing by singular isothermal sphere (SIS) versus more realistic lens profiles (e.g., NFW or elliptical galaxies)?", "answer": "The paper does not investigate the full distribution of magnification factors for non\u2011SIS halo profiles. While SIS models predict a characteristic two\u2011image magnification ratio that depends only on the impact parameter, NFW or triaxial potentials introduce additional dependence on concentration, ellipticity, and line\u2011of\u2011sight structure. Therefore the magnification distribution for realistic lenses remains an open question that would require dedicated ray\u2011tracing simulations beyond the scope of this work."}, {"question": "How can increasing the coherence time in a cross\u2011correlation search improve the sensitivity to continuous gravitational waves from Scorpius X\u20111, and what computational strategies make longer coherence times feasible?", "answer": "The signal\u2011to\u2011noise ratio of a cross\u2011correlation statistic grows roughly with the square root of the coherence time \\(T_{\\max}\\). Extending \\(T_{\\max}\\) therefore directly increases sensitivity. However, a longer coherence time enlarges the template bank because the metric in parameter space (frequency, orbital period, time of ascension, projected semi\u2011major axis) causes nearby points to become mismatched more quickly. Modern lattice covering techniques (e.g., the \\(\\mathcal{A}_3\\) and \\(\\mathcal{A}_4\\) lattices with a controlled mismatch) and the use of sheared coordinates for orbital parameters reduce the required template density, making it computationally tractable to double or even quadruple \\(T_{\\max}\\) while keeping the cost within available resources."}, {"question": "What impact would a non\u2011zero orbital eccentricity of Scorpius X\u20111 have on the cross\u2011correlation search and the derived upper limits?", "answer": "The cross\u2011correlation search used in the analysis assumes a circular orbit, which eliminates two extra parameters: eccentricity \\(e\\) and argument of periastron \\(\\omega\\). If \\(e\\) were non\u2011zero, the Doppler modulation of the signal would change in a way that the current templates cannot match, leading to a loss in signal power (mismatch). This would effectively degrade the achieved upper limits, potentially by tens of percent for modest eccentricities (\\(e \\sim 0.01\\)). The paper does not model or correct for eccentricity, so the reported limits implicitly assume a circular orbit; they do not address how a small but finite eccentricity would alter the results."}, {"question": "How can the upper limits on gravitational\u2011wave amplitude from Scorpius X\u20111 be used to constrain the neutron\u2011star equation of state when combined with torque\u2011balance models?", "answer": "Torque\u2011balance models relate the expected gravitational\u2011wave amplitude \\(h_0\\) to the mass accretion rate and the neutron\u2011star\u2019s radius. By comparing the empirical upper limits on \\(h_0\\) to the theoretical torque\u2011balance curve for different equations of state (e.g., soft GR15 versus stiff GPPVA), one can exclude parameter combinations that would predict detectable signals. Specifically, for a given inclination and magnetic field, if the upper limit falls below the torque\u2011balance prediction for a particular EOS, that EOS is inconsistent with the observation unless the system departs from torque balance. The analysis demonstrates that, at frequencies where the search is most sensitive, the data exclude torque balance for more massive neutron stars, especially for stiff EOSs, thereby tightening constraints on the neutron\u2011star\u2019s mass\u2013radius relation."}, {"question": "To what extent will planned upgrades to the LIGO detectors (e.g., A+ upgrades) improve the sensitivity to continuous waves from Scorpius X\u20111, and what observing strategies are required to realize these gains?", "answer": "A+ upgrades are projected to improve the strain sensitivity by roughly a factor of two across the 10\u2011to\u20112000\u202fHz band. Since the detectable amplitude scales as the inverse of the square root of the observation time and directly with the detector noise, A+ would lower the threshold \\(h_0\\) by about \\(\\sqrt{2}\\). Achieving this in practice requires longer, uninterrupted observing runs and improved data\u2011cleaning techniques (e.g., more effective self\u2011gating, line removal). Combining data from multiple runs in a fully coherent or semi\u2011coherent manner would further enhance sensitivity, potentially allowing the cross\u2011correlation search to probe torque\u2011balance amplitudes over a broader frequency range, including the >\u202f600\u202fHz regime."}, {"question": "What advanced methods exist to model and mitigate spin wandering in continuous\u2011wave searches, and how do they compare in effectiveness to the static\u2011frequency assumption used in this analysis?", "answer": "Spin wandering\u2014random variations in the neutron\u2011star spin frequency\u2014can be modeled using hidden Markov models (HMMs) that track the signal frequency over time, or Bayesian time\u2011series approaches that treat the frequency drift as a stochastic process. These methods allow the search to retain sensitivity to signals that deviate from a perfectly constant frequency, at the cost of additional computational complexity. Compared to the static\u2011frequency assumption adopted here, HMM\u2011based searches can recover signals with modest frequency drifts (\\(\\dot{f}\\sim10^{-10}\\,\\text{Hz\\,s}^{-1}\\)) that would be lost in a purely coherent search, but they typically achieve a modest (\u224810\u201320%) increase in sensitivity for high\u2011frequency targets. The cross\u2011correlation search in the paper assumes a fixed frequency over the coherence time, which is justified given the estimated drift rate over the O3 run, but a future, longer\u2011baseline search could benefit from incorporating HMM techniques."}, {"question": "How does increasing the photon detector coverage affect the energy reconstruction of GeV-scale neutrino events in a liquid\u2011argon time\u2011projection chamber?", "answer": "Extending the photon detection coverage from the baseline ~10\u202f% to 30\u202f% can improve the reconstructed energy resolution by roughly 5\u201310\u202f% for typical GeV\u2011scale charged\u2011current events, primarily by better constraining the scintillation light contribution to the calorimetry and by improving vertex and timing precision."}, {"question": "What systematic advantages does a magnetized gaseous\u2011argon near detector provide for background rejection in the DUNE beamline?", "answer": "The magnetic field allows sign determination for muons above ~800\u202fMeV and helps distinguish neutrino and antineutrino interactions, reducing the wrong\u2011sign background in beam\u2011mode measurements. The magnitude of this improvement depends on the achieved magnetic field uniformity and the detector\u2019s momentum resolution, topics that are still under detailed study."}, {"question": "In what ways could a liquid\u2011scintillator\u2013based far\u2011detector module improve sensitivity to the diffuse supernova neutrino background?", "answer": "A scintillator target increases the inverse\u2011beta\u2011decay event rate (\u223c5\u202f\u00d7 larger than in pure argon), lowers the detection threshold to about 2\u202fMeV, and provides excellent neutron\u2011capture tagging, thereby enhancing the signal\u2011to\u2011background ratio for the diffuse supernova neutrino background."}, {"question": "What are the main obstacles to achieving a sub\u20115\u202fMeV threshold for solar\u2011neutrino detection in a liquid\u2011argon TPC?", "answer": "Key challenges include improving scintillation light collection efficiency, suppressing radon\u2011related backgrounds, and mitigating the 42Ar\u202f\u2192\u202f42K activity that sets a practical low\u2011energy floor. Ongoing R&D focuses on enhanced photon detectors, underground argon use, and comprehensive background modeling."}, {"question": "How does adding a 10\u202fppm xenon dopant to liquid argon impact electron\u2011ion recombination and energy resolution for MeV\u2011scale events?", "answer": "The DUNE Phase\u202fII white paper does not report detailed measurements of this effect. Current simulations suggest that low\u2011level xenon can shift the scintillation wavelength and slightly reduce triplet lifetimes, but the quantitative influence on recombination dynamics and the resulting MeV\u2011scale energy resolution remain to be determined through dedicated experimental studies."}, {"question": "How does including neutron star\u2013black hole (NSBH) mergers influence the constraints on cosmological parameters obtained through gravitational\u2011wave standard sirens?", "answer": "Adding NSBH events expands the redshift lever arm and increases the sample size of dark sirens, thereby improving the statistical power for measuring the luminosity distance\u2013redshift relation. The combined information from binary black holes (BBHs) and NSBHs can tighten the Hubble constant estimate and, depending on the accuracy of the host\u2011galaxy identification, may also help constrain the dark\u2011energy equation of state."}, {"question": "What is the potential of standard sirens to shed light on the nature of dark energy beyond merely measuring the present\u2011day expansion rate?", "answer": "Standard sirens provide direct, model\u2011independent measurements of the expansion history, H(z), as a function of redshift. By mapping H(z) over a range of redshifts, one can test whether the dark\u2011energy equation of state evolves (e.g., w \u2260 \u20131) or whether the expansion follows the \u039bCDM prediction, thus offering a complementary probe to supernovae, BAO, and CMB observations."}, {"question": "In what ways does the completeness and depth of all\u2011sky galaxy catalogs influence the statistical inference of the Hubble constant from dark sirens?", "answer": "Completeness determines how often the true host galaxy of a gravitational\u2011wave event is contained within the catalog. A deeper, more complete catalog reduces the weight of the out\u2011of\u2011catalog likelihood component, thereby decreasing the uncertainty in the inferred redshift distribution and yielding a tighter Hubble constant posterior. Conversely, sparse catalogs increase reliance on population priors, which can broaden the H0 uncertainty."}, {"question": "How might next\u2011generation detectors such as the Einstein Telescope or LISA improve the precision of Hubble\u2011constant measurements using gravitational\u2011wave standard sirens?", "answer": "Future detectors will increase the detection volume and duty cycle, leading to larger samples of inspirals at higher redshift with significantly better sky localization and distance accuracy. This will enable more precise statistical association with host galaxies, reduce degeneracies with mass distribution assumptions, and expand the redshift baseline, thereby sharpening the determination of both H0 and the evolution of the expansion rate."}, {"question": "What is the impact of possible redshift evolution of the black\u2011hole mass distribution on the inference of the Hubble constant from gravitational\u2011wave observations?", "answer": "We do not know the answer. The effect depends on how the black\u2011hole mass spectrum changes with cosmic time, which is influenced by stellar metallicity evolution, binary formation channels, and merger delay times. Current gravitational\u2011wave data lack the breadth in redshift and the theoretical modeling required to disentangle mass evolution from cosmological parameters, so the true influence of an evolving mass distribution on H0 estimates remains uncertain."}, {"question": "How does the stochastic wandering of a neutron star\u2019s spin frequency in low\u2011mass X\u2011ray binaries impact the sensitivity of continuous gravitational\u2011wave searches?", "answer": "The spin frequency of an accreting neutron star is not constant; accretion torques fluctuate, causing a random walk in the star\u2019s rotational frequency. This wandering introduces phase errors that grow over time, limiting the maximum coherent integration interval before the matched\u2011filter signal power is significantly degraded. Continuous\u2011wave searches mitigate this by either using semi\u2011coherent segmentation, where the data are divided into short stretches that are individually coherent, or by employing hidden Markov models that explicitly track the stochastic frequency evolution and stitch together the most likely frequency path across the full observing run. The effectiveness of these techniques depends on the magnitude of the frequency wander\u2014larger wander demands shorter coherent segments or a finer template grid, which in turn increases computational cost and reduces overall sensitivity."}, {"question": "What statistical challenges arise when deriving frequentist upper limits on gravitational\u2011wave strain using hidden Markov model pipelines?", "answer": "Setting upper limits with a hidden Markov model (HMM) requires accurate modeling of the detection statistic\u2019s noise\u2011only distribution in a high\u2011dimensional template space. Key challenges include: (1) estimating the false\u2011alarm probability per sub\u2011band when the analytic form of the statistic is unknown; (2) controlling the overall false\u2011alarm rate across thousands of frequency sub\u2011bands and binary\u2011parameter templates; (3) accounting for non\u2011Gaussian and non\u2011stationary noise artifacts that can bias the likelihood and produce excess loud candidates; (4) generating sufficient Monte\u2011Carlo simulations to determine a detection threshold that yields the desired confidence level while keeping the computational load tractable; and (5) marginalizing over unknown source parameters such as inclination and polarization, which affects the mapping from the injection amplitude to the effective strain used in the upper\u2011limit calculation."}, {"question": "In what ways could planned upgrades to advanced gravitational\u2011wave detectors improve the reach of HMM\u2011based searches for Sco\u202fX\u20111?", "answer": "Future upgrades that increase detector sensitivity (e.g., improved mirror coatings, quantum\u2011squeezing, cryogenic operation) directly lower the noise spectral density, thereby increasing the signal\u2011to\u2011noise ratio for a given strain amplitude. A deeper sensitivity baseline allows the use of longer coherent integration times before spin wandering becomes dominant, or permits a finer binary\u2011parameter grid without incurring prohibitive computational costs. Enhanced calibration accuracy reduces systematic uncertainties in the strain estimate, while expanded detector networks provide better sky\u2011coverage and can enable coincidence checks that suppress instrumental artifacts. Finally, longer continuous observing runs increase the total data set, improving the statistical power of the HMM and enabling tighter upper limits or potentially a first detection."}, {"question": "What astrophysical insight can be gained if the measured gravitational\u2011wave upper limits for Sco\u202fX\u20111 fall below the torque\u2011balance prediction, and how does this constrain the neutron\u2011star equation of state?", "answer": "The torque\u2011balance condition assumes the accretion\u2011spin\u2011up torque is exactly counterbalanced by the spin\u2011down torque from gravitational\u2011wave emission, giving a maximum expected strain amplitude that depends on the X\u2011ray flux, distance, and assumed emission frequency. If an empirical upper limit lies below this threshold, it implies that the neutron star must be emitting fewer gravitational waves than required for torque balance, which in turn restricts the star\u2019s equatorial ellipticity. The ellipticity is linked to the star\u2019s internal composition and the strength of its crust or magnetic field, none of which are directly observable. Therefore, a sub\u2011torque\u2011balance limit places an upper bound on the deformability, providing indirect constraints on the equation of state, especially regarding the shear modulus of the crust and possible exotic core phases."}, {"question": "Do observations indicate that the magnetic field configuration of Sco\u202fX\u20111\u2019s neutron star changes on the timescale of the O3 observing run, affecting the phase\u2011modulation templates used in HMM searches?", "answer": "Current data do not provide time\u2011resolved measurements of the magnetic field geometry of Sco\u202fX\u20111\u2019s neutron star. Most of our knowledge comes from long\u2011term X\u2011ray timing and spectroscopy, which constrain the average accretion rate and orbital parameters but not the instantaneous magnetic field topology. Consequently, the phase\u2011modulation templates employed in HMM pipelines are based on a static approximation of the binary orbit and are not adjusted for potential magnetic\u2011field\u2011induced phase changes. Without contemporaneous magnetic\u2011field diagnostics, such as X\u2011ray polarimetry or cyclotron resonance measurements, any evolution of the field over a ~one\u2011year observing run remains unconstrained, and its impact on the signal waveform cannot be quantified."}, {"question": "What frequency range is most favorable for detecting continuous gravitational waves emitted by scalar boson clouds around stellar\u2011mass black holes with current ground\u2011based detectors?", "answer": "Ground\u2011based interferometers such as Advanced LIGO and Virgo are most sensitive in the 20\u2013600\u202fHz band. In this range the expected quasi\u2011monochromatic signals from scalar boson clouds, whose intrinsic frequency scales roughly as the boson mass relative to the black\u2011hole mass, fall within or just above the detectors\u2019 optimal sensitivity. Frequencies below ~20\u202fHz are limited by seismic noise, while above ~600\u202fHz the detector noise rises steeply, reducing the achievable strain sensitivity."}, {"question": "How does the self\u2011interaction strength of ultralight scalar bosons affect the growth, depletion, and gravitational\u2011wave signal from a boson cloud around a spinning black hole?", "answer": "The self\u2011interaction parameter \\(F_b\\) (or the quartic coupling \\(\\lambda\\)) determines the cloud\u2019s internal dynamics. Strong self\u2011interactions accelerate the cloud\u2019s depletion by enhancing annihilation rates, shorten the signal\u2019s duration, and can reduce the emitted strain amplitude. Weak self\u2011interactions allow the cloud to grow longer and produce a more persistent, higher\u2011amplitude signal. Quantitative predictions require solving the coupled scalar\u2011field and Einstein equations, and the exact dependence on \\(F_b\\) remains an active area of theoretical investigation."}, {"question": "What upper limits on the ultralight boson mass can be derived from non\u2011detections of continuous waves, assuming a realistic Galactic population of spinning black holes?", "answer": "Non\u2011detections translate into exclusion regions in the boson mass\u2013black\u2011hole mass plane. By modeling the Galactic black\u2011hole distribution (e.g., a Kroupa mass function) and assuming a wide range of initial spins, one can compute the expected strain amplitude for each mass pair. If the expected strain exceeds the detector\u2019s sensitivity limit, that parameter space point is excluded. The strength of the exclusion depends sensitively on the assumed spin distribution, cloud age, and distances, so different astrophysical priors can shift the resulting constraints."}, {"question": "Will future space\u2011based detectors like LISA provide complementary sensitivity to boson\u2011cloud gravitational waves, and at which frequencies would they be most useful?", "answer": "LISA\u2019s frequency band (\u22480.1\u202fmHz\u20131\u202fHz) is well\u2011suited to probe boson clouds around intermediate\u2011mass black holes (\u224810\u2074\u201310\u2076\u202fM\u2609) and ultralight bosons with masses \u224810\u207b\u00b9\u00b3\u201310\u207b\u00b9\u00b2\u202feV. These sources emit at frequencies lower than the ground\u2011based band. Therefore, LISA could observe the earlier, slower\u2011evolving phase of the cloud\u2019s annihilation signal, complementing ground\u2011based detectors that target higher\u2011frequency, short\u2011lived signals from stellar\u2011mass black holes."}, {"question": "Is there an observable population of binary black hole mergers that retain residual scalar boson clouds around the remnant, and what would be the signatures in the post\u2011merger gravitational\u2011wave ringdown?", "answer": "This question remains unanswered. Detecting a residual boson cloud around a merger remnant would require identifying deviations in the ringdown spectrum\u2014such as additional quasinormal modes or altered damping times\u2014indicating the presence of a scalar field. Current gravitational\u2011wave observations lack sufficient signal\u2011to\u2011noise in the ringdown phase to test such subtle effects, and detailed numerical relativity simulations including self\u2011interacting scalar fields are still under development. Consequently, we cannot presently confirm or rule out the existence of post\u2011merger boson clouds."}, {"question": "How do spin-precessing effects influence the detectability of binary black hole mergers in current gravitational-wave detectors?", "answer": "Spin-precession introduces modulations in the gravitational-wave signal that can spread the emitted power over a broader frequency band and multiple harmonics. These modulations increase the complexity of the waveform, making it more challenging for template banks that assume aligned spins to recover the signal. Consequently, matched-filter searches that incorporate precessing waveform models can recover signals with higher signal-to-noise ratios and improve the overall detection efficiency, especially for asymmetric or high-spin binaries."}, {"question": "What are the main challenges in modeling eccentric inspirals for gravitational-wave data analysis?", "answer": "Eccentric inspirals require waveform models that capture the rapid periastron passages and the associated burst-like emissions. Current models often rely on post-Newtonian expansions that become inaccurate at high eccentricities or close separations, and numerical relativity simulations for eccentric binaries are computationally expensive and limited in parameter coverage. These limitations make it difficult to construct dense, accurate template banks, which in turn hampers matched-filter searches and can bias parameter estimation if an eccentric signal is forced into a quasi-circular template family."}, {"question": "How does the choice of power spectral density (PSD) estimation method affect the accuracy of Bayesian parameter estimation in gravitational-wave observations?", "answer": "The PSD quantifies the detector noise as a function of frequency and directly weights the likelihood function in the Bayesian framework. A PSD that underestimates noise power at frequencies where the signal has significant amplitude will artificially inflate the inferred signal-to-noise ratio, leading to tighter but potentially biased parameter constraints. Conversely, overestimating noise can dilute the signal, broadening posterior distributions. Adaptive, time-dependent PSD estimation methods that capture non-stationary noise characteristics tend to produce more reliable parameter posteriors compared to static, long-term averages."}, {"question": "In what ways can data-quality vetoes improve the false\u2011alarm rate of matched\u2011filter searches for compact binary coalescences?", "answer": "Data\u2011quality vetoes identify and exclude time intervals contaminated by transient artifacts (glitches) or persistent instrumental disturbances. By removing or down\u2011weighting data segments that would otherwise produce spurious high\u2011SNR triggers, vetoes reduce the background rate that the matched\u2011filter pipeline must contend with. This leads to a cleaner noise distribution, enabling stricter ranking statistics and lowering the false\u2011alarm rate for a given significance threshold. Additionally, vetoes can improve the fidelity of the estimated PSD, further enhancing the robustness of the search."}, {"question": "What is the effect of higher\u2011order multipole modes on the mass and spin inference of binary neutron star mergers?", "answer": "I do not have sufficient evidence to answer this question at present. The current literature does not provide a comprehensive study of how higher\u2011order multipole contributions influence parameter estimation for binary neutron star systems, and existing models mainly focus on the dominant quadrupole. As a result, the precise impact on inferred masses and spins remains an open area for further investigation."}, {"question": "How can subthreshold gravitational\u2011wave triggers be efficiently followed up in the hard X\u2011ray band to detect faint electromagnetic counterparts?", "answer": "An efficient follow\u2011up strategy requires (i) continuous event\u2011mode data acquisition from a wide\u2011field coded\u2011mask instrument such as Swift\u2011BAT, (ii) a rapid, likelihood\u2011based search pipeline that models the detector response for any sky position, and (iii) a real\u2011time alert system that incorporates the gravitational\u2011wave sky probability map. By combining these elements, one can probe flux levels far below the on\u2011board trigger threshold and recover transients with sub\u2011minute durations."}, {"question": "What constraints do the Swift\u2011BAT upper limits place on the luminosity function of short gamma\u2011ray bursts associated with binary neutron star mergers?", "answer": "The flux upper limits measured over the 15\u2013350\u202fkeV band translate into luminosity limits of 10^46\u201310^49\u202ferg\u202fs\u207b\u00b9 for typical BNS distances. These limits exclude a high\u2011luminosity tail in the short\u2011GRB population at the 90\u202f% confidence level for events within the Swift field of view, thereby tightening the parameter space for models that predict prompt emission from BNS coalescences."}, {"question": "To what extent could the joint use of Swift\u2011BAT and Fermi\u2011GBM data improve the sensitivity to electromagnetic counterparts of subthreshold GW events?", "answer": "Joint analysis leverages the complementary sky coverage and energy response of Swift\u2011BAT (hard X\u2011ray, coded\u2011mask imaging) and Fermi\u2011GBM (all\u2011sky gamma\u2011ray). By combining their likelihoods and accounting for each instrument\u2019s background characteristics, one can lower the effective false\u2011alarm rate and extend the detection horizon by up to ~30\u202f%. However, the practical gains depend on the temporal overlap and pointing status of both satellites during each trigger."}, {"question": "How might future gravitational\u2011wave observing runs benefit from improvements in coded\u2011mask imaging sensitivity and localization precision?", "answer": "Advances such as deeper detector simulations, better background modelling, and real\u2011time attitude reconstruction can increase the coded\u2011mask effective area by ~20\u202f% and reduce localization errors from several degrees to sub\u2011degree scales. This would enable rapid optical/infrared follow\u2011up, improve joint\u2011FAR calculations, and potentially uncover a population of off\u2011axis jets that are otherwise missed with current sensitivity."}, {"question": "Is there evidence that binary black hole mergers produce detectable gamma\u2011ray emission, and if not, what upper limits can be derived?", "answer": "We do not know. The current dataset contains no statistically significant hard\u2011X\u2011ray detections coincident with confirmed binary black hole mergers. Consequently, only upper limits can be set; for the most well\u2011localised events these limits lie at ~10^48\u202ferg\u202fs\u207b\u00b9 in the 15\u2013350\u202fkeV band. Determining whether BBH mergers produce any prompt emission requires additional sensitive observations or a larger sample of high\u2011significance events."}, {"question": "How does the crab\u2011waist collision scheme influence the achievable peak luminosity at the highest FCC\u2011ee centre\u2011of\u2011mass energy, and what are the primary beam\u2011dynamic constraints that must be managed?", "answer": "The crab\u2011waist scheme allows a very small vertical beta function at the interaction point by suppressing betatron\u2011coupling resonances that would otherwise be excited by the large crossing angle. At the highest FCC\u2011ee energy (\u2248180\u202fGeV per beam) the horizontal emittance is significantly larger than at the Z pole, which reduces the horizontal beam size and thereby limits the maximum beam\u2011beam tune shift. The beam\u2011beam tune shift is constrained to \u22480.1 in the vertical plane to keep the tune footprint away from low\u2011order resonances. In practice, this requires a careful balance between horizontal beta, emittance, bunch charge, and the strength of the crab sextupoles. Moreover, the beamstrahlung increases the energy spread and lengthens the bunch, which in turn limits the maximum sustainable beam current due to the 50\u202fMW synchrotron\u2011radiation power budget. Consequently, the peak luminosity at the highest energy is primarily limited by the achievable horizontal emittance, the maximum tolerable beam\u2011beam parameter, and the RF voltage needed to maintain the momentum acceptance and avoid significant synchrotron\u2011radiation losses."}, {"question": "What are the main technical challenges for realizing 14\u2011Tesla Nb\u2083Sn dipole magnets in the FCC\u2011hh collider, and how do they affect the overall machine design?", "answer": "The primary challenges are (1) achieving a sufficient field quality with a tight tolerance on the higher\u2011order multipoles, (2) managing the quench stability in a 90\u2011km ring where the stored beam energy per beam exceeds 6\u202fGJ, and (3) ensuring reliable cryogenic performance at 1.9\u202fK while maintaining a high magnetic field gradient. These constraints dictate the coil geometry, the choice of cable and conductor, the cooling scheme, and the mechanical support structure. They also influence the overall magnet packing factor, which in turn affects the ring aperture and the achievable beam emittance. The large stored energy imposes strict protection requirements, necessitating fast\u2011acting quench heaters and a robust energy\u2011dump system. All of these factors must be integrated into the accelerator lattice and the overall cost and schedule of the FCC\u2011hh project."}, {"question": "How can electron\u2011cloud formation be mitigated in a 90\u2011km circumference electron\u2013positron collider operating at 45\u202fGeV per beam, and what surface treatments or vacuum\u2011system designs are most effective?", "answer": "Mitigation strategies include (1) applying low secondary\u2011electron\u2011yield (SEY) coatings such as amorphous carbon or titanium nitride on the vacuum\u2011chamber interior, (2) installing a thin NEG (non\u2011evaporable getter) coating to provide both low SEY and pumping, and (3) shaping the chamber with transverse slots or grooves to interrupt electron trajectories. The beam\u2011pipe geometry\u2014radius, tapering, and the presence of winglets to intercept synchrotron radiation\u2014also influences the local electron\u2011cloud density. The longitudinal bunch spacing can be optimized; for example, a 50\u202fns spacing instead of 25\u202fns raises the SEY multipacting threshold significantly. In addition, a \u201cnon\u2011uniform\u201d filling pattern with a few closely spaced bunches followed by a larger gap can further suppress cloud buildup. These measures together can keep the electron\u2011cloud density below the instability threshold, but detailed 3\u2011D simulations and experimental validation in a dedicated test chamber are needed to quantify the exact performance."}, {"question": "What safety concepts are essential for managing the stored beam energy in a future 100\u2011TeV proton\u2013proton collider, and how are machine\u2011protection interlocks typically designed?", "answer": "Safety concepts for handling multi\u2011gigajoule stored energies include: (1) passive protection\u2014robust collimation systems that intercept halo particles before they reach sensitive components; (2) active protection\u2014fast\u2011acting beam\u2011loss monitoring systems that detect abnormal loss patterns and trigger a rapid beam dump; (3) fault tolerance in the RF and magnet power\u2011supplies to prevent uncontrolled energy deposition; and (4) redundant interlock logic that combines loss\u2011monitor, beam\u2011position, and orbit\u2011feedback signals. The interlock system typically uses a distributed network of loss\u2011monitors (e.g., ionization chambers, scintillators) positioned around the ring, feeding into a central logic unit that can issue a beam\u2011dump command within microseconds. In addition, the machine protection system is designed to tolerate a certain number of false positives while maintaining a very low probability of a dangerous failure. Detailed design of the interlocks is guided by Monte\u2011Carlo loss\u2011simulation studies that identify the most vulnerable components."}, {"question": "Is it feasible to incorporate a high\u2011energy electron\u2013ion collision option into the FCC\u2011hh schedule, and what accelerator physics challenges would need to be addressed?", "answer": "The FCC\u2011h collides protons (and ions) in the main ring, but the paper does not present a detailed feasibility study for an electron\u2013ion (e\u2013A) option. Realizing such a mode would require an additional high\u2011energy electron accelerator, likely a recirculating energy\u2011recovery linac or a separate storage ring, capable of delivering multi\u2011hundred GeV electrons. Key challenges would include synchronizing the electron bunches with the ion bunches, achieving sufficient luminosity while managing beamstrahlung and synchrotron radiation in the electron beam, and integrating a suitable energy\u2011recovery system to keep power consumption reasonable. Moreover, the interaction region would need to accommodate a new detector design with different radiation shielding and background conditions. Because the paper does not cover these aspects, further dedicated studies are required to evaluate the technical and cost feasibility of an e\u2013A option in the FCC\u2011hh program."}, {"question": "What is the quantitative improvement in strain sensitivity achieved by implementing squeezed light sources in the LIGO and Virgo detectors across different frequency ranges?", "answer": "The introduction of squeezed vacuum states into the interferometers reduces quantum shot noise at high frequencies while leaving low\u2011frequency performance largely unchanged. For Advanced LIGO, squeezing has been shown to increase the binary neutron star range by roughly 10\u201315\u202f% in the 100\u2013200\u202fHz band and by up to 20\u202f% above 500\u202fHz. Virgo reports similar gains, with an effective improvement of ~15\u202f% in the 50\u2013300\u202fHz band and up to 25\u202f% above 700\u202fHz. These figures come from calibrated sensitivity curves measured during dedicated squeezing runs and are corroborated by injection studies that confirm the noise reduction directly translates into larger observable volumes for high\u2011mass binary mergers."}, {"question": "How can machine learning techniques be used to classify and predict transient noise artifacts in gravitational\u2011wave data streams in real\u2011time?", "answer": "Real\u2011time glitch classification can be approached by training supervised classifiers on time\u2013frequency representations of the strain data. Convolutional neural networks (CNNs) ingest spectrograms and output probabilities for glitch categories (e.g., blip, scattering, low\u2011frequency burst). Recurrent architectures such as LSTMs can capture temporal correlations, while auto\u2011encoders can flag anomalies without explicit labels. In practice, pipelines like GravitySpy and DeepGlitch have demonstrated that a CNN trained on a large catalog of labeled glitches can achieve >95\u202f% classification accuracy. For prediction, sequential models can learn patterns preceding glitches, enabling early warnings that trigger data\u2011quality vetoes before a detector\u2019s sensitivity is compromised."}, {"question": "What systematic uncertainties dominate the calibration of the strain signal at frequencies above 1\u202fkHz for the Advanced LIGO detectors, and how do they propagate to astrophysical parameter estimation?", "answer": "At frequencies above 1\u202fkHz, the dominant calibration uncertainties arise from the accuracy of the actuation model for the test masses and the frequency response of the photodiode readout electronics. Residual errors in the mirror displacement model and phase lag in the sensing path contribute a magnitude uncertainty of about 5\u202f% and a phase uncertainty of ~2\u00b0 per octave. When propagated through Bayesian parameter\u2011estimation pipelines, these uncertainties introduce biases in the inferred chirp mass and spin parameters that are typically below 1\u202f% for binary neutron star events but can reach several percent for high\u2011mass binary black holes, where the signal content is concentrated at higher frequencies."}, {"question": "How does adding KAGRA and GEO\u202f600 to the LIGO\u2013Virgo network affect the sky localization accuracy for binary neutron star mergers during low\u2011latency alert pipelines?", "answer": "Inclusion of KAGRA and GEO\u202f600 expands the baseline network and provides additional independent timing and amplitude measurements. Simulations show that a four\u2011detector network can reduce the median sky\u2011area 90\u202f% credible region for binary neutron stars from ~200\u202fdeg\u00b2 (LIGO\u2013Virgo) to ~100\u202fdeg\u00b2, and further down to ~60\u202fdeg\u00b2 when KAGRA operates with its full sensitivity. GEO\u202f600, while less sensitive, contributes valuable triangulation, especially for short\u2011duration bursts. Thus, the network\u2019s ability to rapidly localize events for electromagnetic follow\u2011up is significantly enhanced by the additional detectors."}, {"question": "What is the impact of using different calibration versions (e.g., AR, C01, C01_AR) on the measured masses and spins of binary black hole mergers detected during the O3 observing run?", "answer": "The agent does not have direct access to the specific calibration\u2011dependent parameter distributions for O3 binary black hole events. The paper provides the public strain data and describes several calibration streams, but it does not quantify how the choice among them alters the inferred component masses or effective spins. Assessing such an impact would require re\u2011running the full Bayesian inference pipeline on the data processed with each calibration version and comparing the posterior distributions, a task beyond the scope of the paper\u2019s analysis. Consequently, the exact influence of calibration version selection on the astrophysical parameters remains an open question requiring dedicated reanalysis."}, {"question": "What distinctive gravitational\u2011wave signatures are expected from binary black holes whose component masses are below 0.2\u202fM\u2299, and how do these signatures differ from those of higher\u2011mass binaries?", "answer": "In the subsolar\u2011mass regime the inspiral phase dominates the signal because the merger and ring\u2011down occur at frequencies above the most sensitive band of ground\u2011based detectors. The waveform is therefore almost entirely a chirp described by the post\u2011Newtonian expansion up to the last stable orbit. Compared to binaries with component masses \u22731\u202fM\u2299, the chirp mass is smaller, leading to a slower phase evolution and a lower amplitude for a given distance. The signal also contains fewer cycles in band, which makes parameter estimation more challenging. These differences are reflected in the template banks used in the O3 search: a lower mass cutoff of 0.2\u202fM\u2299 and a minimum match of 0.97 were chosen to keep the computational cost tractable while retaining sensitivity to the expected waveform shape."}, {"question": "Which detector upgrades and observing\u2011run strategies are most critical for improving the sensitivity to subsolar\u2011mass binary black holes in future runs (O4 and O5)?", "answer": "The key upgrades are (i) lowering the seismic noise floor and improving the low\u2011frequency sensitivity of the interferometers, which directly increases the number of inspiral cycles observable for low\u2011mass binaries; (ii) enhancing the laser power and implementing quantum\u2011noise reduction techniques (squeezed light) to raise the high\u2011frequency sensitivity where the merger would appear; and (iii) adding a new detector such as KAGRA or LIGO\u2011India to enlarge the network, improve sky localization, and increase the effective observing volume. In addition, expanding the data\u2011analysis pipelines to include full spin precession and higher\u2011order amplitude corrections will allow better recovery of subsolar\u2011mass signals. Together, these improvements are expected to roughly double the sensitive volume\u2013time compared to O3."}, {"question": "Can gravitational\u2011wave data alone distinguish subsolar\u2011mass black holes from other compact objects such as neutron stars or boson stars?", "answer": "In principle, the mass and spin measurements from the inspiral waveform can separate black holes from neutron stars if the total mass falls below the maximum neutron\u2011star mass (~2.3\u202fM\u2299). However, for subsolar masses the mass uncertainty is large due to the short signal duration, and the waveform is almost indistinguishable from that of a boson star or other exotic compact object that follows the same point\u2011particle dynamics. Without additional electromagnetic counterparts or tidal\u2011deformation measurements (which are negligible for such low masses), gravitational\u2011wave data alone cannot unambiguously identify the compactness of the objects. Thus, a non\u2011detection or weak detection does not conclusively rule out or confirm the presence of subsolar\u2011mass black holes versus other candidates."}, {"question": "How do the null results from the O3 subsolar\u2011mass binary search constrain primordial black hole dark\u2011matter models with extended mass functions?", "answer": "The O3 limits on the merger rate of binaries with at least one subsolar\u2011mass component translate into upper bounds on the product of the primordial\u2011black\u2011hole (PBH) mass function and the fraction of dark matter in PBHs. For a monochromatic mass function, the analysis excludes fPBH\u202f\u2273\u202f0.6 at 0.3\u202fM\u2299 and fPBH\u202f\u2273\u202f0.09 at 1\u202fM\u2299. For extended mass functions, the limits are weaker because mergers can involve a wide range of mass ratios, and the suppression factor for early binary disruption becomes less effective. Consequently, models that predict a broad PBH spectrum with a significant contribution from subsolar masses remain viable, even with fPBH\u202f\u2248\u202f1, unless the mass distribution is strongly peaked. The analysis therefore disfavors sharply peaked PBH spectra in the subsolar range but cannot rule out broader distributions."}, {"question": "How would a population of subsolar\u2011mass black holes formed through dissipative dark\u2011matter collapse influence the stochastic gravitational\u2011wave background, and could current or future detectors observe such a background?", "answer": "The paper does not directly address the stochastic background from subsolar\u2011mass black holes. A population of dark\u2011matter\u2011induced black holes would merge throughout cosmic history, contributing to a continuous gravitational\u2011wave background. The amplitude of this background depends on the merger rate density, the typical chirp mass, and the redshift distribution of the sources. Because subsolar\u2011mass binaries have lower chirp masses, their individual contributions to the strain spectrum peak at higher frequencies, potentially overlapping with the sensitivity band of Advanced LIGO/Virgo. However, current upper limits on the stochastic background are dominated by higher\u2011mass binaries, and the expected contribution from subsolar\u2011mass mergers is likely below the present sensitivity threshold. Future detectors with improved low\u2011frequency sensitivity and longer observing times, such as the Einstein Telescope or Cosmic Explorer, could probe this background, but detailed population\u2011synthesis modeling is required to make quantitative predictions."}, {"question": "How do the ellipticity constraints derived from continuous-wave upper limits impact models of neutron star crust breaking strain in the Galactic Center?", "answer": "The upper limits on strain translate to maximum ellipticities of order 10\u207b\u2077\u201310\u207b\u2076 for stars at the Galactic Center. These values are close to or below the theoretical maximum elastic deformations predicted for normal neutron-star crusts (\u224810\u207b\u2076\u201310\u207b\u2075) but are still above the values expected for highly strained crusts or exotic matter. Consequently, the results rule out extremely deformed, solid strange or hybrid star models in the Galactic Center while remaining consistent with standard nuclear equations of state."}, {"question": "What are the implications of the non\u2011detection of continuous gravitational waves for the population size of millisecond pulsars in the inner parsecs of the Milky Way?", "answer": "The lack of a signal suggests that either the millisecond pulsar population is smaller than some optimistic estimates or that their individual ellipticities are below the detection threshold. Using the strain upper limits, one can place an upper bound on the average ellipticity of millisecond pulsars in the region, thereby constraining population synthesis models that predict thousands of such objects."}, {"question": "How can future gravitational\u2011wave detectors improve sensitivity to continuous waves from sources at the Galactic Center compared to the current LIGO\u2011Virgo O3 run?", "answer": "Improvements can come from increased detector bandwidth, lower noise at 100\u2013200 Hz, and longer coherent integration times. Advanced detectors such as LIGO\u2011A+ and Virgo\u2011plus, as well as next\u2011generation facilities (Einstein Telescope, Cosmic Explorer), will reduce strain sensitivity by an order of magnitude, allowing detection of ellipticities as low as 10\u207b\u2078 and probing larger distances within the Galactic Center."}, {"question": "What constraints can continuous-wave upper limits place on the mass and spin of hypothetical boson clouds around stellar\u2011mass black holes in the Galactic Center?", "answer": "By assuming a superradiant boson cloud that emits at a frequency tied to the black-hole mass and boson mass, the non\u2011detection limits exclude regions of the (black\u2011hole spin, boson mass) plane. For example, the results rule out clouds around black holes with initial spin \u03c7i \u2273 0.5 for boson masses between 10\u207b\u00b9\u00b9\u202feV and 10\u207b\u2079\u202feV if the cloud age is 10\u2075\u201310\u2077\u202fyears."}, {"question": "What is the true spin\u2011down distribution of neutron stars located in the Galactic Center, and how does it affect the parameter space explored in directed searches?", "answer": "The paper does not determine the actual spin\u2011down distribution of Galactic\u2011Center neutron stars. This distribution is poorly known because the region is heavily obscured and radio surveys are incomplete. Without precise knowledge of typical spin\u2011down rates, directed searches must adopt broad spin\u2011down ranges (e.g., \u22121.8\u00d710\u207b\u2078\u202fHz/s to +10\u207b\u00b9\u2070\u202fHz/s), which increases computational cost and reduces sensitivity. A more accurate spin\u2011down distribution, obtainable through future radio or X\u2011ray timing surveys, would allow tighter parameter spaces and improved search sensitivity."}, {"question": "What physical mechanisms can generate a non\u2011axisymmetric quadrupole deformation in a rapidly rotating neutron star, thereby enabling the emission of continuous gravitational waves?", "answer": "Several processes are thought to be capable of sustaining a mass quadrupole in a neutron star:\\n- **Crustal \u2018mountains\u2019** formed by tectonic stresses or accreted material that lifts the crust out of symmetry.\\n- **Magnetic stresses**: strong internal or surface magnetic fields can distort the star, producing a permanent quadrupole.\\n- **Accretion\u2011driven deformations**: asymmetric mass loading in accreting systems (e.g., low\u2011mass X\u2011ray binaries) can freeze in a non\u2011axisymmetric shape.\\n- **Superfluid vortex pinning and unpinning**: differential rotation between the crust and the interior superfluid can create a time\u2011varying quadrupole.\\n- **r\u2011mode oscillations**: large\u2011amplitude fluid modes can produce time\u2011dependent quadrupole moments that radiate GWs.\\nThese mechanisms are active in different evolutionary stages of neutron stars and can, in principle, sustain ellipticities large enough to be detectable by current detectors."}, {"question": "How do rotational glitches observed in young pulsars affect the prospects for detecting continuous gravitational waves from those pulsars?", "answer": "Glitches are sudden increases in the spin frequency (and sometimes in the spin\u2011down rate). They can influence continuous\u2011wave searches in several ways:\\n- **Phase evolution**: The GW phase is expected to track the electromagnetic spin. A glitch introduces an instantaneous phase jump that must be modeled or searched over to avoid loss of sensitivity.\\n- **Spin\u2011down changes**: Post\u2011glitch changes in the frequency derivative alter the expected amplitude via the spin\u2011down limit; a more negative \\(\\dot{f}\\) can raise the theoretical upper limit.\\n- **Amplitude variations**: If a glitch is associated with a change in the internal configuration (e.g., superfluid vortex rearrangement), the quadrupole moment may change, potentially increasing or decreasing the GW amplitude.\\nBecause of these uncertainties, most continuous\u2011wave pipelines either treat glitches as additional phase parameters or restrict the search to epochs between glitches, which can reduce the effective observation time."}, {"question": "What assumptions underpin the spin\u2011down limit on the gravitational\u2011wave strain amplitude of a pulsar, and how is this limit derived?", "answer": "The spin\u2011down limit is a theoretical upper bound on the GW strain \\(h_0\\) that assumes *all* of the pulsar\u2019s rotational energy loss is carried away by gravitational waves:\\n1. **Energy conservation**: \\(\\dot{E}_{\\rm rot}= -\\dot{E}_{\\rm GW}\\). The rotational energy \\(E_{\\rm rot}= \\tfrac{1}{2} I \\Omega^2\\). \\(\\Omega=2\\pi f_{\\rm rot}\\).\\n2. **Moment of inertia**: A canonical value \\(I \\approx 10^{38}\\,\\rm kg\\,m^2\\) is usually assumed, though it can vary by a factor of a few depending on the equation of state.\\n3. **Distance**: The observed spin\u2011down rate \\(\\dot{f}\\) and the distance \\(d\\) enter the expression for the strain amplitude. The derived limit is \\(h_{\\rm sd} \\propto (I|\\dot{f}|/d f)^{1/2}\\).\\n4. **Negligible other torques**: No significant electromagnetic or accretion torques are present; the intrinsic spin\u2011down equals the observed value.\\nThe limit is useful because any measured strain below it indicates that GW emission is sub\u2011dominant, and it sets a natural benchmark for the sensitivity required to potentially detect a signal."}, {"question": "How can continuous\u2011wave gravitational\u2011wave observations inform our understanding of the neutron\u2011star equation of state?", "answer": "Continuous\u2011wave searches provide upper limits on the neutron star\u2019s ellipticity \\(\\epsilon\\) and mass quadrupole \\(Q_{22}\\). These limits can be compared to theoretical predictions for the maximum sustainable deformation given different equations of state (EOS):\\n- **Stiff EOSs** predict a larger radius and hence a higher maximum quadrupole before breaking the crust, allowing larger \\(\\epsilon\\).\\n- **Soft EOSs** lead to smaller stars with thinner crusts, giving lower quadrupole limits.\\nIf an observed upper limit falls below the maximum \\(\\epsilon\\) allowed by a particular EOS, that EOS can be deemed inconsistent with the data. Moreover, detecting a signal with a measurable \\(\\epsilon\\) would provide a direct probe of the star\u2019s internal structure and crustal rigidity, offering constraints complementary to those from binary merger observations and X\u2011ray pulse\u2011profile modeling."}, {"question": "What would be the observational signatures of scalar\u2011tensor (e.g., Brans\u2013Dicke) gravity in the continuous gravitational\u2011wave spectrum from a rotating neutron star, and can current detectors differentiate such signatures from those predicted by general relativity?", "answer": "The paper does not address this question. In scalar\u2011tensor theories, an additional scalar polarization mode can be emitted at the *first* harmonic (i.e., at the spin frequency), producing a dipole radiation term with a distinct frequency dependence compared to the quadrupole tensor mode at twice the spin frequency. Current detectors are most sensitive to the quadrupolar tensor modes, and while some searches target the scalar mode, the sensitivity to scalar radiation is typically weaker. Therefore, at present it is not clear whether detectors can unambiguously distinguish scalar\u2011tensor predictions from general relativity, and further theoretical modeling and detector\u2011network studies are required to assess the feasibility of such tests."}, {"question": "How does the internal magnetic field topology of a magnetar influence the efficiency of energy transfer to gravitational waves during a giant flare?", "answer": "The efficiency of gravitational\u2010wave excitation depends sensitively on the arrangement of poloidal and toroidal field components. A strongly toroidal field can store more magnetic energy in the core and may facilitate larger deformations, thereby increasing the coupling to f\u2011mode oscillations. Conversely, a predominantly poloidal configuration might lead to weaker quadrupolar distortions and reduced gravitational\u2011wave emission. The exact dependence requires detailed magnetohydrodynamic simulations of field evolution during a flare."}, {"question": "What are the dominant damping mechanisms for Alfv\u00e9n mode oscillations in the neutron star core, and how do they affect the duration of associated gravitational wave signals?", "answer": "Alfv\u00e9n modes in the magnetized core are expected to be damped by several processes: viscous dissipation in the fluid core, mutual friction between superfluid vortices and normal matter, and phase mixing due to inhomogeneities in the magnetic field. The combined effect of these mechanisms sets a damping timescale that can range from a few seconds to hundreds of seconds. A shorter damping time shortens the gravitational\u2011wave burst, reducing its detectability, while a longer lifetime could produce a quasi\u2011continuous signal that may be easier to integrate over in matched\u2011filter searches."}, {"question": "Can magnetar bursts produce detectable continuous gravitational wave emission via r\u2011mode instabilities, and under what conditions would this be observable?", "answer": "R\u2011mode instabilities grow when the star\u2019s rotation rate is sufficiently high and the viscous damping is weak. Magnetars, being slowly rotating (periods of a few seconds), are generally below the critical spin required for r\u2011mode growth, making continuous emission unlikely. However, if a magnetar were spun up by accretion or experienced a sudden spin\u2011up during a giant flare, the r\u2011mode amplitude could temporarily exceed the threshold, producing a weak continuous wave that might be detectable with long\u2011integration searches in next\u2011generation detectors."}, {"question": "How would a future network of third\u2011generation gravitational wave detectors improve sensitivity to high\u2011frequency magnetar f\u2011modes compared to current detectors?", "answer": "Third\u2011generation detectors such as the Einstein Telescope or Cosmic Explorer aim for strain sensitivities an order of magnitude better than Advanced LIGO at frequencies around 1\u20133\u202fkHz. This improvement would lower the detectable energy threshold for f\u2011mode bursts from \u223c10^49\u202ferg to \u223c10^47\u202ferg for a Galactic magnetar, potentially allowing the observation of many more events. Additionally, better high\u2011frequency response would reduce the mismatch between expected mode spectra and detector noise, improving matched\u2011filter detection efficiency."}, {"question": "What is the precise correlation between the observed quasi\u2011periodic oscillations in magnetar flare tails and the frequency spectrum of potential gravitational wave emission?", "answer": "The paper does not address this question. Establishing a direct correlation would require simultaneous, high\u2011time\u2011resolution X\u2011ray/gamma\u2011ray observations and sensitive gravitational\u2011wave data, along with detailed modeling of magnetar interior oscillation modes. Current theoretical work provides only tentative links between QPOs and crustal or core oscillations, and more observations and simulations are needed to confirm any direct correlation."}, {"question": "How does the inclusion of higher-order multipole moments in gravitational\u2011wave templates affect the precision of tests of general relativity using binary black hole signals?", "answer": "Adding higher\u2011order harmonics (\u2113,|m|\u22602,2) to the waveform models increases the fidelity of the predicted strain, especially for high\u2011mass or high\u2011mass\u2011ratio binaries. It reduces systematic mismatches between the true signal and the template, thereby tightening constraints on deviations in the post\u2011Newtonian coefficients, dispersion parameters, and spin\u2011induced quadrupole moments. Studies with GWTC\u20113 data have shown that accounting for higher modes leads to smaller fitting\u2011factor losses and more accurate recovery of the final mass and spin, which in turn improves the robustness of consistency and parameter\u2011ized tests."}, {"question": "What upper limit on the graviton mass can be derived from the combined GWTC\u20113 catalog, and how does this bound compare to existing solar\u2011system limits?", "answer": "Using the modified dispersion analysis on the 43 GWTC\u20113 events, the 90\u202f% credible upper bound on the graviton mass is \\(m_{\\mathrm{g}} \\le 2.42 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\). This improves the previous GWTC\u20112 limit (\\(3.09 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)) by about 28\u202f% and is slightly better than the most stringent solar\u2011system bound of \\(3.16 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)."}, {"question": "How can measurements of the spin\u2011induced quadrupole moment parameter (\\(\\delta\\kappa_s\\)) distinguish black holes from neutron stars or exotic compact objects, and what constraints have recent gravitational\u2011wave observations placed?", "answer": "In general relativity, a Kerr black hole has \\(\\kappa=1\\), while neutron stars and many exotic compact objects (e.g., boson stars, gravastars) can have \\(\\kappa\\) values significantly different from unity. By measuring \\(\\delta\\kappa_s = (\\kappa-1)\\) in binary mergers, one can test the black\u2011hole no\u2011hair conjecture. The GWTC\u20113 analysis of 13 suitable events yields a combined 90\u202f% credible interval of \\(\\delta\\kappa_s = -16.0^{+13.6}_{-16.7}\\). This is consistent with \\(\\delta\\kappa_s = 0\\) (the Kerr value) but allows a modest range of deviations, providing the first ever statistical constraint on \\(\\kappa\\) from gravitational\u2011wave data."}, {"question": "In what way will next\u2011generation gravitational\u2011wave detectors such as the Einstein Telescope or Cosmic Explorer improve the sensitivity of the inspiral\u2013merger\u2013ringdown consistency test?", "answer": "Third\u2011generation detectors will provide several key advantages: (1) much higher signal\u2011to\u2011noise ratios, (2) longer observable inspiral phases (especially for low\u2011mass binaries), and (3) better low\u2011frequency sensitivity that captures more gravitational\u2011wave cycles. These improvements will sharpen the independent estimates of the final mass and spin from the inspiral and post\u2011inspiral regimes, reducing statistical uncertainties in the fractional deviation parameters \\(\\Delta M_f/\\bar{M}_f\\) and \\(\\Delta\\chi_f/\\bar{\\chi}_f\\). Forecasts suggest that with the Einstein Telescope or Cosmic Explorer the precision on these parameters could reach the sub\u2011percent level, enabling detection of extremely small deviations from GR."}, {"question": "Is there any evidence in the GWTC\u20113 dataset of statistically significant deviations in the 1.5\u2011PN phase coefficient that would challenge the predictions of general relativity?", "answer": "The GWTC\u20113 analysis performed parameterised tests on individual post\u2011Newtonian coefficients, including the 1.5\u2011PN term. Within the uncertainties reported, the 1.5\u2011PN coefficient was fully consistent with the general\u2011relativistic value; no statistically significant deviation was detected. However, the paper does not exhaustively explore all possible combinations of deviations or more exotic waveform systematics that could mimic a shift in this coefficient. Therefore, I cannot definitively confirm or rule out a subtle 1.5\u2011PN deviation beyond the scope of the presented analysis."}, {"question": "What is the expected detection rate of binary neutron star mergers for the future KAGRA + LIGO + Virgo network at design sensitivity?", "answer": "The paper does not provide a quantitative prediction for the detection rate of binary neutron star (BNS) mergers with the full network operating at design sensitivity. Estimating such a rate would require combining the projected horizon distances of each detector, the anticipated duty cycles, and the local BNS merger rate density\u2014information that is beyond the scope of this study."}, {"question": "How does operating KAGRA underground reduce coupling of environmental seismic noise compared to surface detectors like LIGO and Virgo?", "answer": "Operating underground offers a significant reduction in seismic noise because the ground motion at depth is typically an order of magnitude lower than at the surface. Additionally, the underground environment is less affected by weather, human activity, and temperature fluctuations, all of which can introduce low\u2011frequency disturbances. The paper notes a lower low\u2011frequency noise floor for KAGRA, but detailed quantitative comparisons to LIGO and Virgo are not provided."}, {"question": "What technical challenges were encountered when implementing the DC readout scheme in KAGRA, and how were they addressed?", "answer": "Switching from a radio\u2011frequency (RF) to a DC readout required installing an output mode cleaner and reconfiguring the signal extraction optics. Challenges included maintaining laser frequency stability, mitigating higher\u2011order mode contamination, and ensuring the new readout electronics could handle the increased dynamic range. The paper mentions the upgrade but does not delve into the specific troubleshooting steps or hardware modifications undertaken."}, {"question": "During the GEO\u2013KAGRA joint run, what was the dominant noise source limiting sensitivity below 100\u202fHz, and what mitigation strategies were planned?", "answer": "The dominant low\u2011frequency noise was identified as local control noise originating from the mirror suspension damping filters. To mitigate this, the team planned to redesign the damping filter parameters, improve sensor noise performance, and implement more robust feed\u2011forward cancellation of environmental disturbances."}, {"question": "What is the impact of enforcing a single\u2011polarization reconstruction constraint in the coherent WaveBurst (cWB) analysis on detection efficiency for real gravitational\u2011wave signals in a two\u2011detector network?", "answer": "Applying a single\u2011polarization constraint reduces background from noise glitches by limiting the parameter space of admissible waveforms. However, for a two\u2011detector network with non\u2011aligned arms, genuine signals that excite both polarizations can have part of their energy suppressed in the reconstruction, potentially lowering the detection efficiency. The paper notes this trade\u2011off but does not quantify the efficiency loss for specific signal morphologies."}, {"question": "What are the main challenges in separating low\u2011energy kaons from protons in a liquid\u2011argon time\u2011projection chamber, and how can the deposited energy per unit length (dE/dx) be used to overcome them?", "answer": "Low\u2011energy kaons (p_K \u2272 350\u00a0MeV/c) and protons have similar masses and thus deposit comparable amounts of ionization in liquid argon, especially in the Bragg peak region where both exhibit a sharp rise in dE/dx. The primary challenges are: (1) the intrinsic overlap of their dE/dx distributions due to statistical fluctuations in ionization and recombination; (2) the finite spatial resolution and noise of the readout system, which smears the dE/dx profile; and (3) the presence of other hadrons (pions, muons) that can mimic the kaon signature if mis\u2011reconstructed. To disentangle the two species, one exploits the full residual\u2011range dE/dx profile: a proton track continues to deposit energy at a nearly constant rate until it stops, whereas a kaon shows a pronounced Bragg peak at the end of its trajectory. By fitting the dE/dx versus residual range with a Landau\u2013Gaussian convolution and applying a likelihood or \u03c7\u00b2 test under the kaon and proton hypotheses, the probability of each hypothesis can be quantified, allowing a statistically robust separation even in the presence of detector noise."}, {"question": "How can precise measurements of the kaon stopping power in liquid argon enhance the sensitivity of future proton\u2011decay searches?", "answer": "Accurate knowledge of the kaon stopping power (dE/dx as a function of residual range) directly impacts the reconstruction of the kaon kinetic energy and its decay vertex. In proton\u2011decay searches targeting the p \u2192 K\u207a\u202f\u03bd\u0304 channel, the signal consists of a mono\u2011energetic K\u207a that comes to rest before decaying. If the stopping power is well\u2011known, the detector can reliably identify the Bragg peak, estimate the initial momentum, and suppress backgrounds that produce non\u2011rest\u2011decay kaons or mimic the signature. Moreover, a precise stopping\u2011power model allows for better calibration of the calorimetric response, reducing systematic uncertainties on the kaon energy scale and thus tightening the selection criteria. Consequently, the overall efficiency for proton\u2011decay detection increases while the background acceptance decreases, improving the experiment\u2019s lower limit on the proton lifetime."}, {"question": "Which systematic uncertainties have the largest impact on the calorimetric reconstruction of stopping kaons in large liquid\u2011argon TPCs?", "answer": "The dominant systematic sources are: (1) **Calorimetric calibration** \u2013 uncertainties in the conversion from collected charge to deposited energy (typically ~2\u20133\u202f%); (2) **Space\u2011charge effects** \u2013 distortions of the electric field due to positive ion accumulation, affecting drift paths and charge collection (~1\u202f% after correction); (3) **Electron\u2011diverter failures** \u2013 mis\u2011reconstruction of tracks that cross APA gaps, leading to artificial track splits (systematic shift of ~5\u202f% in track length); (4) **Proton background modeling** \u2013 mismodeling of stopping proton rates, which can bias the kaon dE/dx distribution (~1\u202f%); and (5) **Recombination model uncertainties** \u2013 variations in the Modified Box or Thomas\u2013Imel parameters (~1\u202f%). These effects are typically combined in quadrature to estimate the total systematic uncertainty on the reconstructed kaon energy and dE/dx profile."}, {"question": "In proton\u2011decay searches, how does the angular distribution of muon daughters from kaon decays assist in rejecting background events?", "answer": "A K\u207a that decays at rest produces a muon with a uniform (isotropic) angular distribution relative to the kaon track, because the decay is two\u2011body and the kaon\u2019s momentum is negligible. In contrast, muons produced by charged\u2011current neutrino interactions or by inelastic pion or proton scattering tend to be highly forward\u2011peaked, inheriting the direction of the parent hadron. By measuring the cosine of the angle between the kaon candidate and its muon daughter, events with cos\u202f\u03b8\u202f<\u202f0.6 can be selected, effectively rejecting the forward\u2011peaked background while retaining most of the isotropic signal. This geometrical cut, when combined with dE/dx and range information, provides a powerful handle on background suppression."}, {"question": "What is the exact efficiency of the ProtoDUNE\u2011SP detector for detecting K\u207a decays at rest when using the photon detection system?", "answer": "The answer to this question is currently unknown. The ProtoDUNE\u2011SP data set used in the analysis did not employ the photon detection system for the kaon selection; instead, only the charge readout was relied upon. While the photon system can, in principle, provide additional timing and energy\u2011deposition information (e.g., detecting the prompt scintillation from the kaon stop and the delayed Michel electron from the muon decay), a quantitative efficiency measurement that incorporates photon signals has not yet been performed. Such a study would require dedicated calibration runs, precise modeling of the photon collection efficiency, and a comprehensive assessment of the detector\u2019s optical response\u2014all of which are still topics of ongoing research."}, {"question": "How would the track\u2011length extension fitting (TLEFit) algorithm perform for charged particles whose kinetic energy exceeds 1\u202fGeV, a regime where the dE/dx curve becomes almost flat (MIP region)?", "answer": "At high kinetic energies the Bethe\u2013Bloch dE/dx curve has a very shallow slope, so the residual\u2011range versus dE/dx relationship provides weak discriminating power. The TLEFit algorithm would still fit an offset, but the resulting energy resolution would degrade and the fitted offset would tend to converge to a value that corresponds to the minimum\u2011ionizing plateau, leading to a systematic bias toward lower energies. In practice one would need to supplement the fit with additional information (e.g., multiple\u2011scattering angles or calorimetric deposits) to recover acceptable resolution above ~1\u202fGeV."}, {"question": "Can the TLEFit technique be adapted to determine the kinetic energy of neutral hadrons, such as neutrons, by exploiting the ionization signatures of the secondary charged particles they produce?", "answer": "Neutrons do not ionize directly, so the TLEFit algorithm cannot be applied to the neutron itself. However, if a neutron undergoes a hadronic interaction that produces one or more charged secondaries with measurable tracks, the TLEFit algorithm can be used on each charged secondary individually to infer its kinetic energy. The total neutron energy would then be estimated by summing the reconstructed energies of all secondaries and adding the energy carried by undetected neutrons, which introduces a large, event\u2011by\u2011event uncertainty. Thus, TLEFit is useful for charged products but not for a direct neutron energy measurement."}, {"question": "What are the dominant systematic uncertainties introduced by the modified\u2011box recombination model parameters (\u03b1 and \u03b2\u2032) when applying the TLEFit algorithm in a liquid\u2011argon TPC?", "answer": "The recombination model translates the measured ionization charge (dQ/dx) into energy loss (dE/dx). Uncertainties in \u03b1 and \u03b2\u2032 propagate directly into the dE/dx PDFs used by TLEFit. A \u00b11\u202f\u03c3 shift in \u03b1 changes the low\u2011dE/dx tail of the distribution, while a shift in \u03b2\u2032 mainly affects the high\u2011dE/dx (Bragg\u2011peak) region. These changes alter the likelihood landscape, leading to systematic shifts in the fitted offset and hence a bias in the reconstructed kinetic energy. In the ProtoDUNE\u2011SP study, variations of \u00b11\u202f\u03c3 in \u03b1/\u03b2\u2032 produced fractional\u2011bias shifts up to ~3\u202f% for 300\u202fMeV pions, and an uncertainty band of ~1\u20132\u202f% on the energy resolution. Therefore, precise calibration of the recombination parameters is critical for accurate TLEFit performance."}, {"question": "How does the presence of a magnetic field in a liquid\u2011argon TPC influence the assumptions underlying the TLEFit algorithm?", "answer": "A magnetic field bends charged particle trajectories, introducing curvature that alters the true path length relative to the straight\u2011line distance between reconstructed hits. The TLEFit algorithm assumes that the measured residual range corresponds to the straight\u2011line distance along the true track, which is violated in a magnetic field. The resulting systematic bias can be mitigated by incorporating track curvature into the residual\u2011range calculation or by performing a 3\u2011D helical fit before applying TLEFit. Additionally, the magnetic field affects multiple scattering by reducing lateral deflections, which may slightly change the dE/dx distribution width, but this effect is subdominant compared to the path\u2011length distortion."}, {"question": "Is it possible to extend the TLEFit algorithm to reconstruct the kinetic energy of electrons that emit Bremsstrahlung photons while traversing liquid argon?", "answer": "The paper does not address this scenario, and the current TLEFit framework assumes a single, continuous charged track with a monotonic residual\u2011range vs. dE/dx relationship. Electrons undergoing Bremsstrahlung experience significant energy loss in discrete photon emission events, leading to kinks and discontinuities in the dE/dx profile that violate the assumptions of the algorithm. Therefore, we do not yet know whether TLEFit can be adapted for such electrons without substantial modification or additional reconstruction steps, and further study would be required to evaluate its feasibility."}, {"question": "What is the most sensitive frequency band for all-sky searches of continuous gravitational waves from isolated neutron stars using third\u2011generation detectors?", "answer": "In all\u2011sky searches conducted with third\u2011generation interferometers, the most sensitive band typically lies between about 50\u202fHz and 250\u202fHz. Within this range the detector noise floor is lowest and the Doppler modulation is modest, allowing the longest coherent integrations and the highest upper\u2011limit depths."}, {"question": "How can continuous gravitational\u2011wave signals from rapidly rotating neutron stars be distinguished from instrumental lines in the data?", "answer": "Continuous\u2011wave searches apply a combination of vetoes: (1) cross\u2011detector coincidence requirements to ensure the signal is present in multiple interferometers; (2) line\u2011persistency checks that flag features consistent with known narrow\u2011band disturbances; (3) consistency tests comparing the signal\u2019s frequency evolution to the expected Doppler pattern from Earth\u2019s motion. Only candidates that survive all these stages are considered astrophysical."}, {"question": "What upper limits can be set on the ellipticity of a neutron star located 200\u202fpc away and spinning at 300\u202fHz?", "answer": "Using the most optimistic sensitivity depth for the 200\u2013400\u202fHz band, a neutron star at 200\u202fpc spinning at 300\u202fHz would have its ellipticity constrained to be below roughly \\(3\\times10^{-7}\\). This follows from the relation \\(\\varepsilon \\propto h_{0} d f^{-2}\\) and the strain upper limit of \\(\\sim1\\times10^{-25}\\) in that band."}, {"question": "Can current all\u2011sky searches place constraints on the abundance of primordial black holes with masses below \\(10^{-5}\\,M_{\\odot}\\) that inspiral within the Galaxy?", "answer": "Yes. By treating such binaries as continuous\u2011wave emitters with nearly monochromatic signals, the upper limits on strain translate into limits on the merger rate and abundance of light primordial black holes. The analysis shows that, for chirp masses below \\(10^{-5}\\,M_{\\odot}\\), the rate of inspirals within the solar neighbourhood must be lower than a few events per million years, constraining the fraction of dark matter that could be in the form of such primordial black holes."}, {"question": "Is there evidence for continuous gravitational\u2011wave emission from neutron stars in binary systems using the methods described in the paper?", "answer": "I do not have a definitive answer. The analysis in question focuses on isolated neutron stars, employing semi\u2011coherent pipelines tailored for solitary sources. Detecting continuous waves from neutron stars in binaries requires additional templates to account for orbital Doppler shifts and a different set of search parameters. Since this study did not explore binary parameter spaces, any conclusions about binaries would lie beyond its documented scope and would need a dedicated search strategy."}, {"question": "How does the total inelastic cross section for positively charged pions scattering off argon vary across the kinetic\u2011energy range 200\u202fMeV to 800\u202fMeV, and which resonance structures are primarily responsible for the observed energy dependence?", "answer": "The total inelastic \u03c0\u207a\u2013Ar cross section rises from a few hundred millibarns near 200\u202fMeV, reaches a pronounced maximum around the \u0394(1232) resonance (\u2248\u202f150\u2013170\u202fMeV in the laboratory frame), and then gradually decreases towards 800\u202fMeV as higher\u2011mass resonances and multi\u2011pion production channels open. The \u0394(1232) dominates the rise, while the subsequent fall is influenced by the onset of inelastic channels such as \u0394(1700) and the opening of the two\u2011pion production threshold."}, {"question": "Which systematic effects most significantly impact the precision of proton\u2013argon total inelastic cross\u2011section measurements at sub\u2011GeV energies, and what strategies can be employed to reduce these uncertainties in future LArTPC studies?", "answer": "The dominant systematic contributions are: (1) finite Monte\u2011Carlo statistics that propagate through the unfolding and efficiency corrections; (2) background modelling, especially the rates of elastic scattering and stopping\u2011proton contamination; (3) energy\u2011reconstruction uncertainties tied to the stopping\u2011power model (Bethe\u2011Bloch) and detector calibration; and (4) space\u2011charge distortion corrections that alter track length and energy deposition. Mitigation can be achieved by increasing the simulated event sample size, refining background estimators with data\u2011driven sidebands, improving the calibration of the energy scale (e.g., via dedicated calibration beams), and developing more accurate space\u2011charge maps or correcting algorithms."}, {"question": "In what manner do final\u2011state interactions (FSI) of charged pions inside liquid argon affect the reconstruction of neutrino energy in DUNE, and how can improved \u03c0\u207a\u2013Ar cross\u2011section data contribute to reducing these effects?", "answer": "FSI can absorb or re\u2011scatter pions, altering their energy, direction, and multiplicity before they exit the nucleus. This leads to mis\u2011estimation of the neutrino energy when relying on the observed hadronic system. Precise \u03c0\u207a\u2013Ar cross\u2011section data enable better tuning of intranuclear cascade models, thereby reducing uncertainties in pion absorption and scattering probabilities. Consequently, energy\u2011reconstruction algorithms can incorporate more realistic FSI probabilities, improving the fidelity of reconstructed neutrino energies."}, {"question": "Does the empirical scaling law \u03c3\u202f\u221d\u202fA^{2/3} for hadron\u2013nucleus total cross sections hold for argon when compared to lighter nuclei such as carbon and heavier nuclei such as lead, based on the most recent experimental data?", "answer": "Recent measurements indicate that the total inelastic cross section for \u03c0\u207a\u2013Ar and p\u2013Ar lies on the same A^{2/3} trend defined by other nuclei, with argon\u2019s cross sections roughly scaling between the values observed for carbon (A\u202f=\u202f12) and lead (A\u202f=\u202f208). The data show good agreement with the empirical exponent, suggesting that nuclear size and surface effects dominate the energy dependence across this range of target masses."}, {"question": "What is the differential (angular and momentum) distribution of secondary nucleons produced in \u03c0\u207a\u2013Ar inelastic interactions at a pion kinetic energy of 600\u202fMeV, and how does this distribution impact calorimetric energy reconstruction in liquid\u2011argon time\u2011projection chambers?", "answer": "I do not have information on the differential nucleon spectra for \u03c0\u207a\u2013Ar at 600\u202fMeV kinetic energy, as this specific observable was not measured or reported in the data set discussed. Determining these distributions would require dedicated experiments or detailed simulations that explicitly model the intra\u2011nuclear cascade and nucleon emission processes for this energy regime. Without such data, one cannot accurately assess how the secondary nucleon kinematics influence calorimetric reconstruction in LArTPC detectors."}, {"question": "What are the typical sky\u2011localization uncertainties for gravitational\u2011wave events detected by a network of advanced interferometers?", "answer": "For binary black\u2011hole mergers observed by the LIGO\u2013Virgo network, the 90\u202f% confidence sky area typically ranges from a few tens to several hundred square degrees, depending on the signal\u2011to\u2011noise ratio, the relative orientation of the detectors, and the waveform model used. The median 90\u202f% area for the first detections was on the order of 200\u2013300 deg\u00b2."}, {"question": "How does the choice of parameter\u2011estimation pipeline (e.g., BAYESTAR vs. LALInference) influence the reported sky maps for a gravitational\u2011wave trigger?", "answer": "Fast sky\u2011localization tools like BAYESTAR provide rapid estimates by marginalizing over distance and mass parameters with analytic approximations, yielding relatively compact 90\u202f% confidence regions. Full Bayesian samplers such as LALInference use the complete likelihood over all parameters, often resulting in slightly larger but more accurate maps that incorporate calibration uncertainties and more realistic priors. Consequently, LALInference maps are usually adopted as the definitive localization for follow\u2011up planning."}, {"question": "What electromagnetic signatures are theoretically expected from a binary black\u2011hole merger in a gas\u2011rich environment?", "answer": "In dense circumbinary disks or accretion flows, a merger can perturb the surrounding gas, potentially generating a prompt flare or a longer\u2011lasting afterglow across radio to X\u2011ray wavelengths. Models predict a burst of synchrotron emission as shock waves form, followed by a gradually declining spectrum. However, the exact luminosity depends on poorly constrained parameters such as disk density, magnetic field strength, and spin alignment."}, {"question": "What is the maximum distance out to which an optical transient associated with a binary black\u2011hole merger could be detected with current survey telescopes?", "answer": "Optical surveys with limiting magnitudes around 22\u201323\u202fmag can, in principle, detect kiloparsec\u2011scale transients out to roughly 100\u202fMpc if the event is intrinsically luminous. For binary black\u2011hole mergers, expected optical emission is far fainter, so practical detection horizons are much closer\u2014tens of megaparsecs\u2014unless an exceptionally bright flare occurs."}, {"question": "What is the expected optical afterglow brightness of a binary black\u2011hole merger occurring at 400\u202fMpc?", "answer": "I do not have information on this specific scenario. The paper does not provide theoretical or empirical predictions for optical afterglow brightness at such a distance for binary black\u2011hole mergers, and detailed modeling would be required to estimate the flux, which is beyond the scope of the present data."}, {"question": "How does the number of detectors in a gravitational\u2011wave network influence the accuracy of sky localization for binary black hole events?", "answer": "Adding more detectors narrows the triangulation baselines, reduces the timing uncertainty, and improves the determination of the source\u2019s position on the sky. With three or more detectors the sky area for a typical binary black hole event can shrink from hundreds of square degrees to a few tens of square degrees."}, {"question": "What are the main observational challenges when performing broadband electromagnetic follow\u2011up of gravitational\u2011wave events with large localization uncertainties?", "answer": "The primary challenges are (1) the need to tile very large areas of sky with limited field\u2011of\u2011view instruments, (2) coordinating many facilities to avoid duplication while maximizing coverage, (3) achieving sufficient depth quickly enough to catch fast transients, and (4) handling the large number of unrelated transients that appear in the search area."}, {"question": "How can galaxy catalog information be leveraged to prioritize electromagnetic follow\u2011up observations for gravitational\u2011wave triggers?", "answer": "By cross\u2011matching the probability sky map with catalogs of nearby galaxies (e.g., with stellar mass or star\u2011formation rate weighting) observers can assign higher priority to tiles containing galaxies within the expected distance range, thereby concentrating limited resources on the most likely host candidates."}, {"question": "What are the theoretical mechanisms that could enable a binary black hole merger to produce an electromagnetic counterpart?", "answer": "The current literature does not provide a definitive mechanism. Some speculative scenarios involve interaction with a dense circumbinary environment, residual accretion disks, or magnetic fields strong enough to power a short burst. However, no robust model has yet shown that such conditions are common or produce detectable emission, so the question remains largely open."}, {"question": "What role does low\u2011latency analysis play in enabling rapid electromagnetic follow\u2011up, and what improvements are needed for future runs?", "answer": "Low\u2011latency pipelines generate alerts within minutes of a gravitational\u2011wave detection, allowing telescopes to start observations before a transient fades. Improvements needed include faster parameter estimation (especially sky localization), real\u2011time assessment of the source type, and integration with automated scheduling systems to reduce human\u2011induced delays."}, {"question": "How does the total inelastic cross section of positively charged kaons on argon change as a function of kinetic energy between 2\u202fGeV and 5\u202fGeV?", "answer": "The cross section generally rises from a few hundred millibarns at 2\u202fGeV, reaches a broad maximum around 4\u20135\u202fGeV, and then slowly levels off or slightly decreases. This trend reflects the onset of additional inelastic channels (e.g., multi\u2011pion production) and the diminishing influence of the Coulomb barrier as the kaon energy increases."}, {"question": "What are the consequences of improved kaon\u2013argon interaction modeling for proton\u2011decay searches in liquid\u2011argon TPCs?", "answer": "Better modeling reduces systematic uncertainties in the simulation of kaon propagation and absorption, leading to a more accurate estimation of detection efficiencies for signatures such as \\(p \\rightarrow \\nu K^+\\). This in turn tightens the experimental limits on the proton lifetime and enhances the robustness of any observed excess."}, {"question": "Can the thin\u2011slice technique used for kaon\u2013argon cross\u2011section measurements be applied to study neutron\u2013argon interactions in a liquid\u2011argon TPC?", "answer": "Yes. By treating each wire plane as a thin target, one can count incident neutrons and the number that interact or produce secondary particles in successive slices. The main challenge is identifying neutrons, which require time\u2011of\u2011flight or delayed capture signatures, but with adequate tagging the method can yield differential neutron\u2013argon cross sections."}, {"question": "What is the measured cross section for negatively charged kaons on argon in the 5\u201310\u202fGeV energy range?", "answer": "This quantity has not yet been measured experimentally. Existing hadronic interaction generators provide only model predictions, and without dedicated beam\u2011test data the precise value\u2014and its energy dependence\u2014remains uncertain."}, {"question": "How does the space\u2011charge effect in a liquid\u2011argon TPC impact the reconstruction of charged\u2011kaon tracks, and what strategies can mitigate this?", "answer": "Space charge builds up electric\u2011field distortions, causing reconstructed positions and directions to shift by several millimetres. For kaon tracks, this can bias the measured energy loss and vertex location. Mitigation techniques include applying a three\u2011dimensional space\u2011charge correction map derived from cosmic\u2011ray muon data, using external alignment sensors, and incorporating the corrections into the reconstruction algorithms to recover the true track geometry."}, {"question": "What are the primary advantages of a vertical\u2011drift LArTPC design compared to a traditional horizontal\u2011drift geometry for the DUNE far detector?", "answer": "A vertical\u2011drift geometry allows a longer drift path (up to ~6.5\u202fm per side) while keeping the maximum electron drift time short enough to avoid excessive electron recombination and diffusion. The cathode can be suspended centrally, creating two symmetric drift volumes that maximize the active liquid\u2011argon volume. Additionally, the vertical orientation reduces the number of wire planes needed and simplifies the anode plane assembly, leading to lower construction costs and fewer feed\u2011throughs."}, {"question": "How does the cathode module design influence both the electric field uniformity and photon\u2011detector performance in the vertical\u2011drift module?", "answer": "The cathode is made of a thin, highly resistive composite panel that is suspended from the top of the detector. Its surface is perforated to allow light from the surrounding field\u2011cage to pass through, improving photon collection. The field\u2011cage modules around the cathode are constructed with narrow aluminum profiles in the first 4\u202fm from the cathode to provide 70\u202f% optical transparency, while the outer region uses wider profiles to maintain the field gradient. This combination ensures a uniform drift field (\u22641\u202f% variation) while allowing photons to reach both cathode\u2011mounted and membrane\u2011mounted photon\u2011detector modules."}, {"question": "What are the main technical challenges involved in producing and qualifying the large charge\u2011readout planes (CRPs) for a full 17.5\u202fkt vertical\u2011drift module?", "answer": "Key challenges include (1) maintaining the mechanical planarity of the 3.2\u202fmm\u2011thick perforated PCBs over a 1.5\u202fm\u202f\u00d7\u202f1.5\u202fm area, (2) ensuring precise alignment of the two PCB halves to guarantee 100\u202f% electron transmission through the holes, (3) producing and testing a large number of high\u2011performance LArASIC front\u2011end ASICs under cryogenic conditions, (4) achieving the required electrical shielding and grounding on both the induction and collection planes, and (5) integrating the CRP into the cryostat\u2019s support structure while preserving the 5\u202fmm gap between adjacent planes for optical access and mechanical tolerances."}, {"question": "What effect does a 10\u202fppm xenon doping have on the photon\u2011detector light yield and timing in the vertical\u2011drift Far Detector?", "answer": "Xenon doping shifts a substantial fraction (\u2248\u202f53\u202f%) of the scintillation light from 128\u202fnm to 176\u202fnm. The longer\u2011wavelength photons experience less Rayleigh scattering and absorption, improving the overall light collection efficiency by roughly 20\u201330\u202f%. Additionally, xenon dimers have a shorter decay time (\u2248\u202f4\u202f\u00b5s) compared to pure argon, leading to a faster prompt component and improved timing resolution for low\u2011energy events such as supernova neutrinos."}, {"question": "How will the long\u2011term stability of the high\u2011voltage divider board (HVDB) affect the electron lifetime and detector performance over a 10\u2011year operation period?", "answer": "The long\u2011term stability of the HVDB is critical because any drift in the resistor values or degradation of the high\u2011voltage insulation can alter the field uniformity and thus impact electron drift times and recombination rates. Current studies have not yet quantified how these changes will influence the electron lifetime over a decade, as the HVDB materials and their behavior under continuous cryogenic exposure are still under investigation. Further long\u2011term aging tests and in\u2011situ monitoring of the field uniformity are needed to assess the impact on detector performance and to ensure that the electron lifetime remains within the required specification."}, {"question": "How does the total inelastic \u03c0+\u2013argon cross section evolve below 500\u00a0MeV kinetic energy?", "answer": "The study presented focuses on the 500\u2013800\u00a0MeV range, so the behaviour of the cross section at lower energies is not covered. Determining the cross section below 500\u00a0MeV would require dedicated data at those energies and possibly different detector optimisation, which are not available in the current analysis."}, {"question": "What is the angular distribution of the outgoing protons in \u03c0+ absorption on argon?", "answer": "The paper reports overall absorption rates but does not provide detailed angular spectra for the recoil protons. Such information would need a separate reconstruction study focusing on proton kinematics and a larger event sample to achieve sufficient statistical precision."}, {"question": "Can the measured \u03c0+\u2013argon charge\u2011exchange cross section be used to constrain the pion mean free path in liquid argon for neutrino interaction simulations?", "answer": "Yes, the measured charge\u2011exchange cross section directly informs the mean free path of charged pions in argon, which is a key parameter in neutrino event generators. Incorporating these results can improve the modelling of final\u2011state interactions in neutrino detectors."}, {"question": "How do space\u2011charge effects impact the reconstruction of low\u2011momentum \u03c0+ tracks in a large LArTPC?", "answer": "Space\u2011charge distortions can shift the apparent positions of ionisation deposits, potentially biasing the energy and direction reconstruction of low\u2011momentum tracks. Understanding and correcting for these effects is essential for accurate cross\u2011section measurements but requires detailed calibration studies beyond the scope of the presented analysis."}, {"question": "What is the cross section for \u03c0+\u2013argon interactions that produce a single \u03c00 in the final state without any charged pions above 150\u00a0MeV/c?", "answer": "The paper defines a charge\u2011exchange channel that requires at least one \u03b3 from a \u03c00 decay but does not isolate events with exactly one \u03c00 and no charged pions. Measuring this specific final\u2011state cross section would necessitate additional event selection criteria and higher\u2011statistics data, which are not part of the current study."}, {"question": "What astrophysical processes can generate high\u2011energy neutrinos at the same time as gravitational\u2011wave bursts?", "answer": "Relativistic outflows produced during the collapse of massive stars, mergers of compact binaries, or interactions of jets with surrounding material can accelerate protons to very high energies. These protons then interact with photons or ambient gas to produce charged pions that decay into high\u2011energy neutrinos, while the violent dynamics of the system emit gravitational waves."}, {"question": "How does the gravitational\u2011wave energy output of a binary neutron star merger compare to that of a core\u2011collapse supernova?", "answer": "A binary neutron star merger typically radiates a few percent of a solar mass in gravitational waves (\u224810\u207b\u00b2\u202fM\u2299c\u00b2), concentrated around a few hundred hertz. A core\u2011collapse supernova is expected to emit much less, usually \u226410\u207b\u2077\u202fM\u2299c\u00b2, unless the core is rapidly rotating or otherwise dynamically unstable."}, {"question": "What observational advantages does a joint gravitational\u2011wave and neutrino detection offer over single\u2011messenger observations?", "answer": "The precise timing of a gravitational\u2011wave burst coupled with the directional information from a high\u2011energy neutrino allows a dramatic reduction in the sky localization area, enabling faster and more targeted electromagnetic follow\u2011up. It also provides a cross\u2011check that the transient is indeed astrophysical rather than instrumental or atmospheric."}, {"question": "In what way could the detection of neutrinos from a core\u2011collapse supernova inform us about the mechanism of jet formation within the stellar envelope?", "answer": "Neutrinos produced in a choked jet scenario would carry information about the density, magnetic field, and particle acceleration conditions inside the envelope. Measuring their energy spectrum and arrival time relative to the gravitational wave could constrain the jet launch delay, opening angle, and baryon loading, which are key parameters in jet\u2011formation models."}, {"question": "Has the recent multi\u2011messenger search set definitive limits on the rate of binary neutron star mergers that emit both gravitational waves and high\u2011energy neutrinos?", "answer": "No. The analysis provides only upper limits on the combined population of gravitational\u2011wave and high\u2011energy\u2011neutrino emitters in general. It does not specifically constrain binary neutron star mergers because the limits depend on generic assumptions about the neutrino spectrum and beaming, which may not apply to all BNS systems."}, {"question": "How do temperature gradients within a liquid argon TPC affect the electron attachment rate to electronegative impurities?", "answer": "Electron attachment rates are highly sensitive to temperature because the mobility of impurity molecules and the electron mean free path change with thermal motion. In practice, a temperature rise of 1\u202fK in the liquid argon can increase the attachment rate by roughly 5\u202f%\u201310\u202f% for typical oxygen or water concentrations. Consequently, even small temperature gradients across a detector volume can lead to measurable variations in the drift\u2011electron lifetime. Experimental studies on small LArTPC prototypes have confirmed that maintaining isothermal conditions within \u00b10.2\u202fK is essential for stable operation."}, {"question": "What is the time evolution of impurity concentration when the argon recirculation pump is turned off for a few hours in a large\u2011scale LArTPC?", "answer": "During pump downtime the liquid argon is no longer actively filtered, so the dominant source of contamination is the outgassing of detector components and the diffusion of residual impurities from the gas phase. In a typical 10\u2011ton module, the oxygen equivalent concentration can increase by about 10\u201315\u202fppb per hour, leading to a drift\u2011electron lifetime decrease of 10\u201315\u202f% per hour. After 24\u202fhours, the lifetime can fall from >20\u202fms to below 10\u202fms if no additional purification is applied."}, {"question": "Is it possible to calibrate space\u2011charge corrections in a LArTPC using only through\u2011going cosmic\u2011ray muons, without external timing detectors?", "answer": "Yes. By reconstructing straight\u2011line tracks from cosmic\u2011ray muons that traverse the full drift volume, one can measure the apparent shift of the track endpoints as a function of drift time. These shifts directly encode the local electric\u2011field distortions caused by space charge. With sufficient statistics and a known timing reference from the detector clock, the correction maps can be derived internally, eliminating the need for external scintillator systems."}, {"question": "What minimum drift\u2011electron lifetime is required to keep the energy resolution for MeV\u2011scale neutrino interactions below 1\u202f% in a 5\u202fm drift LArTPC?", "answer": "Simulations of MeV\u2011scale electromagnetic showers in a 5\u202fm drift TPC show that a lifetime of at least 15\u202fms is needed to limit the charge loss to <1\u202f%. With a lifetime of 20\u202fms the charge attenuation is below 0.6\u202f%, yielding an energy resolution better than 0.9\u202f% for a 5\u202fMeV deposition. Lifetimes below 10\u202fms start to degrade the resolution above 1\u202f%."}, {"question": "Is there a significant difference in electron lifetime between argon that has been purified primarily by removing water versus oxygen, and how does this affect charge collection?", "answer": "The paper does not provide data comparing water\u2011only versus oxygen\u2011only purification. While both impurities attach electrons, oxygen has a higher attachment cross\u2011section, so an argon sample free of oxygen but still containing residual water would generally have a longer electron lifetime. However, the exact quantitative difference depends on the concentrations achieved by each purification method, and the current study does not address this comparison. Therefore, we cannot provide a definitive answer based on the present information."}, {"question": "How does the charged\u2011current muon\u2011neutrino interaction cross section on argon vary between the quasi\u2011elastic and resonance production regions when the neutrino beam is narrowly tuned to a fixed energy?", "answer": "When the incoming neutrino energy is tightly constrained, the cross\u2011section in the quasi\u2011elastic (CCQE) region rises smoothly with energy, while the resonance (RES) region shows a pronounced peak near the \u0394(1232) mass. As the beam energy increases, the RES contribution becomes dominant above ~1\u202fGeV, causing the total inclusive cross section to steeply increase. A narrow virtual flux allows the CCQE peak to be isolated at lower energies and the \u0394 resonance peak to be resolved around 1\u20131.5\u202fGeV, providing a clear view of the transition between the two regimes."}, {"question": "What are the principal systematic uncertainties that limit the precision of virtual\u2011flux cross\u2011section measurements with the DUNE\u2011PRISM near detector, and which strategies could reduce their impact?", "answer": "The dominant systematics arise from (1) the neutrino flux shape and normalization, (2) the modeling of neutrino\u2011nucleus interactions (particularly final\u2011state interactions and 2p2h processes), and (3) detector response such as energy scale and particle\u2011ID efficiency. Mitigation strategies include: using external hadron\u2011production data to constrain flux uncertainties, applying Tikhonov regularization and flux\u2011matching techniques to minimise the amplification of statistical fluctuations, incorporating in\u2011situ calibration with known neutrino reactions, and developing robust unfolding algorithms that separate flux and interaction\u2011model effects."}, {"question": "Can the virtual\u2011flux technique be adapted to measure the neutrino\u2011neutron cross section on argon, and what experimental challenges would need to be overcome?", "answer": "In principle, a narrow virtual flux can be used to probe neutrino\u2011neutron interactions by selecting final\u2011state topologies that are sensitive to neutrons (e.g., charged\u2011current quasi\u2011elastic scattering with a detected proton). Challenges include: distinguishing neutron\u2011induced events from proton\u2011induced ones, accounting for the lack of a free neutron target, handling the higher background from neutral\u2011current interactions, and accurately modeling the neutron\u2019s binding energy and Fermi motion in argon. Improved tracking and calorimetry, combined with sophisticated reconstruction of missing momentum, would be required."}, {"question": "What is the influence of final\u2011state interaction (FSI) modeling uncertainties on the measurement of the energy\u2011transfer differential cross section using virtual fluxes?", "answer": "FSI affect the energies and directions of outgoing hadrons, thereby smearing the reconstructed energy transfer (\u03c9_reco). However, because the virtual flux is narrow in neutrino energy, the dominant smearing comes from the flux width rather than from FSI. Residual FSI uncertainties primarily distort the shape of the \u03c9_reco distribution, especially near the quasi\u2011elastic peak and in the dip between CCQE and resonance regions. Quantitatively, varying the FSI strength within reasonable bounds can change the differential cross\u2011section shape by a few percent, indicating that precise FSI modeling is still essential for sub\u201110% level measurements."}, {"question": "Does the virtual\u2011flux construction preserve the relative energy dependence of two\u2011particle\u2013two\u2011hole (2p2h) contributions across different neutrino energies?", "answer": "The paper does not address this specific question. While the virtual\u2011flux technique can isolate broad energy ranges, it is unclear whether the weighting procedure and regularization applied during flux matching retain the true energy dependence of the 2p2h component. Further studies, possibly with alternative target flux shapes and validation against detailed nuclear\u2011model predictions, are needed to determine whether 2p2h effects are faithfully represented in virtual\u2011flux\u2011averaged measurements."}, {"question": "How can machine learning techniques be integrated into the GPU-based simulation pipeline to predict detector response in real time?", "answer": "Machine learning can be used to replace or augment physics\u2011based sub\u2011models within the simulation. For example, a deep neural network trained on high\u2011fidelity simulation data can predict the induced current waveform for a given ionization track, or learn the mapping from raw charge deposition to digitized ADC counts. By compiling the trained model with libraries such as TensorFlow\u2011Lite or ONNX Runtime and running it on the same GPU as the physics kernels, one can achieve real\u2011time inference. The network would be inserted after the electron drift and diffusion stage but before the ASIC digitization stage, reducing the number of explicit convolutional operations required. Validation would involve cross\u2011checking the ML\u2011predicted waveforms against a reference simulation over a broad range of track geometries and field configurations."}, {"question": "What are the scalability limits of GPU\u2011accelerated LArTPC simulation when moving from a 0.5\u202fm\u00b3 detector to a 10\u202fm\u00b3 scale?", "answer": "Scalability is governed by three factors: (1) memory consumption\u2014each charge segment requires a few tens of bytes for position, charge, diffusion parameters, and (2) the number of threads needed to cover all pixels, which grows linearly with the detector surface area; a 10\u202fm\u00b3 LArTPC may have on the order of 10\u2076 pixels, still within the 96\u2011GB memory of a modern V100 or A100 GPU if data are streamed in tiles; (3) kernel launch overhead and inter\u2011GPU communication. On a multi\u2011GPU node, the simulation can be partitioned spatially so that each GPU handles a sub\u2011volume, with halo exchanges for electrons that cross tile boundaries. With careful tiling and overlapping of computation and data transfer, a 20\u2011fold increase in volume can be simulated with only a modest increase in wall\u2011clock time, often remaining the dominant part of the pipeline."}, {"question": "How does the inclusion of space\u2011charge effects alter the electric field configuration in a pixelated LArTPC, and how can this be incorporated into the simulation?", "answer": "Space\u2011charge from slowly drifting ions builds up a distortion in the nominal uniform field, typically reducing the drift velocity and altering the weighting field near the anode. To incorporate this, one can solve Poisson\u2019s equation on a 3\u2011D grid that includes the ion density field, using a fast solver (e.g., multigrid or FFT\u2011based). The resulting field map can then be interpolated for each electron step during drift. In a GPU implementation, the field map can be stored as a texture and accessed via bilinear interpolation, ensuring that the drift velocity and diffusion coefficients are updated dynamically. This adds a modest computational cost (\u224810\u202f% of the induced\u2011current kernel) while improving the fidelity for high\u2011rate or high\u2011ionization scenarios."}, {"question": "What are the systematic uncertainties introduced by using a fixed diffusion coefficient in the electron transport model, and how can they be quantified?", "answer": "Assuming a single, constant diffusion coefficient neglects its dependence on the local electric field and temperature. The systematic uncertainty can be quantified by propagating the variance of the diffusion coefficient into the width of the induced current pulse. This is done by generating multiple simulations with diffusion coefficients sampled from a distribution (e.g., Gaussian with mean\u202f=\u202fvalue from data and \u03c3\u202f=\u202fexperimental uncertainty). The spread in the reconstructed charge or hit position then provides a direct estimate of the systematic error. In practice, varying the longitudinal and transverse diffusion by \u00b110\u202f% shows a shift of \u22483\u202f% in the charge\u2011collection efficiency for MIP tracks, which is comparable to the intrinsic ASIC noise."}, {"question": "What is the impact of non\u2011uniformities in the pixel pad geometry on the induced current signals, and how significant are these effects compared to the intrinsic noise of the ASIC?", "answer": "The agent does not know the answer. This question requires detailed electromagnetic simulation of the actual pad geometry (e.g., variations in pixel size, edge effects, and inter\u2011pixel spacing) and its effect on the weighting field. The resulting variations in induced current are typically of the order of a few percent, which is comparable to or smaller than the intrinsic electronic noise (\u2248500\u202fe\u207b). A full study would involve measuring the actual pad layout, generating a refined FEM mesh, and re\u2011computing the current response, which is beyond the scope of the present work."}, {"question": "How does xenon doping affect the lifetime of free electrons in liquid argon?", "answer": "Xenon is chemically inert and does not introduce additional electronegative impurities that would capture drifting electrons. In practice, a moderate xenon concentration (up to a few tens of ppm) has been observed to have a negligible effect on the free\u2011electron lifetime in large liquid\u2011argon TPCs. The primary factor that governs electron lifetime remains the concentration of oxygen, water, and other electronegative contaminants; xenon addition does not significantly change the attachment rates. Consequently, detectors that operate with a few\u2011ppm xenon doping typically report electron lifetimes that are comparable to those measured in undoped argon, provided that the xenon itself is of high purity and that the purification system remains effective."}, {"question": "What is the optimal xenon concentration for maximizing light yield while minimizing cost for a 10\u2011kt liquid\u2011argon detector?", "answer": "In large\u2011volume LArTPCs the light yield improvement from xenon doping is a diminishing\u2011returns process. Empirical studies on 100\u2011kg to 1\u2011kt prototypes show that a xenon concentration of 10\u201315\u202fppm (by mass) yields about a 30\u201340\u202f% increase in total scintillation light, after which the gain saturates. For a 10\u2011kt detector the cost of xenon scales linearly with the amount required; 15\u202fppm in 10\u202fkt corresponds to roughly 150\u202fkg of xenon. Considering the high price of xenon (\u2248\u202f\\$100\u202fkg\\(^{-1}\\)) and the marginal increase in light yield beyond 15\u202fppm, many groups recommend targeting the 10\u201312\u202fppm range as a cost\u2011effective compromise. This choice maximizes light collection and pulse\u2011shape discrimination performance while keeping xenon expenses manageable."}, {"question": "Can xenon doping improve pulse\u2011shape discrimination between electron and nuclear recoils in liquid argon?", "answer": "Xenon doping modifies the relative contributions of the fast (singlet) and slow (triplet) scintillation components. By transferring energy from the argon triplet state to xenon, the overall pulse shape becomes faster and the distinction between electron\u2011like (shorter fast component fraction) and nuclear\u2011recoil events (higher fast component fraction) can be sharpened. Experiments with small\u2011scale detectors have demonstrated an improvement in pulse\u2011shape discrimination (PSD) metrics by 10\u201320\u202f% when operating at \u2248\u202f10\u202fppm xenon, especially at lower energies where the triplet component dominates. However, the benefit plateaus for higher xenon concentrations because the fast component becomes dominated by xenon scintillation, which has its own PSD characteristics. Therefore, xenon doping can enhance PSD, but only up to an optimal concentration that balances the competing light\u2011yield and PSD contributions."}, {"question": "How does the presence of nitrogen at 5\u202fppm alter the Rayleigh scattering length of argon scintillation photons?", "answer": "Nitrogen is essentially transparent to the vacuum\u2011ultraviolet (VUV) photons in liquid argon, so it does not directly affect the Rayleigh scattering cross\u2011section. The scattering length of 127\u202fnm photons in pure liquid argon is about 1.8\u202fm. Adding 5\u202fppm of nitrogen introduces only a tiny change in the refractive index; the resulting modification to the Rayleigh scattering length is on the order of a few millimetres\u2014well below the experimental resolution. Thus, the presence of 5\u202fppm nitrogen does not meaningfully alter the photon transport properties in the bulk liquid. The dominant effect of nitrogen at this concentration is quenching of the argon triplet state, which reduces the overall light yield but leaves the scattering length unchanged."}, {"question": "Does xenon doping affect the drift field uniformity in a large liquid argon TPC?", "answer": "The model does not have information from the paper that directly addresses this question, so it cannot provide a definitive answer. In principle, xenon is an inert noble gas that does not alter the dielectric constant of liquid argon by a measurable amount at ppm concentrations, so the electric\u2011field distribution determined by the cathode, anode, and field\u2011shaping rings should remain essentially unchanged. However, any subtle changes would depend on the exact detector geometry and the purity of the xenon added. Further detailed electro\u2011static simulations and dedicated measurements would be required to confirm whether drift\u2011field uniformity is affected at the ppm\u2011level doping studied in the paper."}, {"question": "What are the leading theoretical models that predict gravitational-wave emission from fast radio burst progenitors?", "answer": "Current models suggest that compact binary coalescences (binary neutron stars or neutron star\u2013black hole systems) can produce both the rapid radio pulses and a short-lived burst of gravitational waves through magnetic interactions or tidal disruption. Additionally, magnetar flares or giant magnetar outbursts can excite stellar oscillation modes that generate gravitational waves, especially in the kilohertz range."}, {"question": "How does the dispersion measure of a fast radio burst help estimate its cosmological distance?", "answer": "The dispersion measure (DM) quantifies the total column density of free electrons along the line of sight. By subtracting modeled contributions from the Milky Way, its halo, and the host galaxy, the remaining intergalactic DM can be mapped to redshift using empirical relations (e.g., the Macquart relation). This provides a statistical distance estimate, often expressed as a 90% credible interval due to large uncertainties."}, {"question": "What are the main differences between a model\u2011based and a generic (unmodelled) gravitational\u2011wave search pipeline when targeting short\u2011duration transients?", "answer": "A model\u2011based pipeline, such as matched\u2011filtering with a template bank, assumes a specific waveform morphology (e.g., binary inspiral) and maximizes sensitivity for that scenario, but may miss unexpected signals. A generic pipeline uses coherent excess\u2011power or time\u2011frequency clustering to detect any transient, regardless of shape, offering broader coverage at the cost of reduced sensitivity for any single waveform type."}, {"question": "What challenges arise when searching for gravitational\u2011wave counterparts to fast radio bursts detected by wide\u2011field radio telescopes like CHIME/FRB?", "answer": "Key challenges include large sky\u2011localization uncertainties that require scanning many sky patches, limited detector duty cycles leading to sparse data coverage, and the need to account for significant uncertainties in FRB distances derived from DM. Additionally, the short timescales of FRBs demand rapid, low\u2011latency data analysis to correlate with gravitational\u2011wave events."}, {"question": "Is there conclusive evidence linking any fast radio burst to a gravitational\u2011wave detection during the third observing run of Advanced LIGO and Virgo?", "answer": "The current analysis does not find any statistically significant gravitational\u2011wave signal coincident with the observed fast radio bursts. Therefore, we cannot claim a definitive association. This lack of evidence may be due to either the absence of detectable gravitational\u2011wave emission from these bursts, insufficient detector sensitivity at the relevant distances, or the intrinsic rarity of such joint events. Further observations with more sensitive detectors or a larger FRB sample are required to confirm or rule out this association."}, {"question": "How does the mass ratio of a neutron star\u2013black hole binary influence the morphology of its gravitational\u2011wave signal, and what are the consequences for extracting component masses with next\u2011generation detectors?", "answer": "The mass ratio determines the amplitude ratio between the dominant quadrupole mode and higher\u2011order modes; highly asymmetric systems exhibit stronger higher\u2011order multipole contributions, which can bias mass estimates if not modeled accurately. Advanced detectors with improved low\u2011frequency sensitivity will better capture early inspiral, helping to disentangle mass ratio effects and reduce systematic errors."}, {"question": "What can the measurement of the effective inspiral spin parameter tell us about the natal spin distribution of black holes in neutron star\u2013black hole binaries, and how does this inform binary\u2011formation scenarios?", "answer": "A positive effective spin suggests alignment with the orbital angular momentum, typical of isolated binary evolution with weak supernova kicks, whereas a negative or small effective spin points to dynamical formation or large natal kicks. Comparing spin distributions across many events can discriminate between these channels and refine population synthesis models."}, {"question": "In what way does the tidal deformability of the neutron star component affect the post\u2011merger gravitational\u2011wave spectrum of a neutron star\u2013black hole coalescence, and how can future detectors use this to constrain the neutron\u2011star equation of state?", "answer": "A more deformable neutron star experiences stronger tidal interactions, potentially generating a high\u2011frequency post\u2011merger signal (e.g., quasi\u2011normal\u2011mode ringing or disk\u2011oscillation modes). Detecting such signatures would place upper limits on the tidal Love number, thereby constraining the stiffness of the equation of state. Next\u2011generation detectors with extended high\u2011frequency bandwidth are required for robust measurements."}, {"question": "How might the presence of a circumbinary disk or nearby stellar companions in dense stellar environments alter the orbital evolution and merger rate of neutron star\u2013black hole binaries?", "answer": "Environmental torques can extract angular momentum, potentially accelerating inspiral and modifying eccentricity. Tidal interactions with a disk may also alter spin alignment. These effects can change the observable population and must be accounted for when estimating merger rates from dense clusters or galactic nuclei."}, {"question": "What is the expected rate of observable electromagnetic counterparts (short GRBs or kilonovae) from neutron star\u2013black hole mergers across a range of mass ratios and spins?", "answer": "I do not have an answer to this question. The paper does not quantify the rates of electromagnetic counterparts for NSBH mergers, and current observational data are insufficient to provide reliable estimates. Further multi\u2011messenger observations and detailed simulations are required to constrain these rates."}, {"question": "How does the use of a resistive field shell in a modular liquid\u2011argon TPC affect the uniformity of the drift electric field compared to conventional resistor\u2011chain cages?", "answer": "Resistive field shells provide a smoother potential gradient because the field is distributed across the surface rather than concentrated at discrete points. This can reduce high\u2011field regions that might trigger discharges. However, the exact quantitative improvement depends on the sheet resistance, shell geometry, and the stability of the resistive material over time, and must be validated experimentally for each detector design."}, {"question": "What are the main advantages of a native 3D pixelated charge readout for event reconstruction in high\u2011occupancy neutrino beam environments?", "answer": "Pixelated readouts give independent 3D coordinates for every ionization cluster without requiring complex wire\u2011plane reconstruction. This allows straightforward association of charge with localized scintillation light, improves background rejection, and mitigates pile\u2011up by enabling per\u2011pixel timing information that can be used to separate overlapping tracks."}, {"question": "How can a high\u2011coverage dielectric light\u2011detection system be optimized to provide nanosecond\u2011level timing for neutrino interactions in a liquid\u2011argon TPC?", "answer": "Optimizing such a system involves selecting wavelength\u2011shifting materials with fast decay times, positioning light traps close to the anode to reduce photon path lengths, and using silicon photomultipliers (SiPMs) with low dark count rates and high photon detection efficiency. The geometry must maximize geometrical coverage while maintaining optical isolation between adjacent TPC modules."}, {"question": "In a modular LArTPC array, what strategies can be employed to preserve optical isolation between adjacent detector modules while minimizing dead material?", "answer": "Optical isolation can be achieved by incorporating thin, high\u2011index reflective coatings on the field\u2011shaping panels, using dielectric light traps that are non\u2011conductive, and designing inter\u2011module gaps that are small enough to reduce passive material yet sufficient to prevent light leakage. Careful alignment and precise machining of the modules also help maintain isolation without adding significant structural material."}, {"question": "What is the optimal pixel pitch for a liquid\u2011argon TPC pixelated readout that balances spatial resolution, electronic noise, and data\u2011rate constraints?", "answer": "The optimal pixel pitch is still an open question. While finer pitches improve spatial resolution and help resolve closely spaced tracks, they increase the number of readout channels, raising electronic noise and data\u2011rate requirements. Experimental studies are needed to determine the trade\u2011off between resolution and noise for different drift fields and event rates, and to establish a pixel pitch that meets the physics goals without exceeding technical limits."}, {"question": "How does the neutrino energy spectrum emitted by a core\u2011collapse supernova depend on the neutrino mass ordering?", "answer": "The neutrino mass ordering influences the survival probabilities of electron neutrinos and antineutrinos through the Mikheyev\u2013Smirnov\u2013Wolfenstein (MSW) resonances that occur in the stellar envelope. In the normal ordering, the \\(\\nu_e\\) survival probability is suppressed at high energies, while in the inverted ordering it is enhanced. Collective oscillation effects inside the core can further alter the spectra. Consequently, the observable \\(\\nu_e\\) spectrum at Earth is a convolution of the original emission spectrum with these flavor\u2011conversion probabilities, producing a mass\u2011ordering\u2011dependent shape that can be probed by detectors with good \\(\\nu_e\\) sensitivity."}, {"question": "What role do forbidden nuclear transitions play in the charged\u2011current cross section of neutrinos on argon at supernova energies?", "answer": "At neutrino energies above roughly 20\u201330\u202fMeV, higher\u2011multipole (forbidden) nuclear transitions contribute increasingly to the total charged\u2011current cross section on \\({}^{40}\\mathrm{Ar}\\). These transitions involve changes in nuclear spin and parity that are not allowed in the simple Gamow\u2013Teller (allowed) approximation. Their inclusion increases the cross\u2011section magnitude and modifies its energy dependence, especially at the upper end of the supernova spectrum, thereby affecting the expected event rate and the reconstructed energy distribution in a liquid\u2011argon detector."}, {"question": "How can the detection of low\u2011energy neutrons from neutrino\u2011argon interactions improve the reconstruction of supernova neutrino energies in a liquid\u2011argon detector?", "answer": "Charged\u2011current \\(\\nu_e\\) interactions on \\({}^{40}\\mathrm{Ar}\\) often emit one or more neutrons that escape the primary interaction vertex without depositing visible energy. If these neutrons are captured on gadolinium or other neutron\u2011sensitive materials, the resulting delayed \\(\\gamma\\)-cascade can be detected, allowing the experiment to recover the missing energy. By accounting for the neutron capture signal, the total energy deposited can be corrected, yielding a more accurate reconstruction of the incident neutrino energy and thereby improving the precision of flux\u2011parameter measurements."}, {"question": "What experimental strategies could be employed to directly measure the \\(\\nu_e + {}^{40}\\mathrm{Ar}\\) cross section in the 5\u201350\u202fMeV range?", "answer": "A practical approach is to use a well\u2011characterised neutrino source such as pion decay\u2011at\u2011rest (DAR) beams, which produce mono\u2011energetic \\(\\nu_\\mu\\) and a spectrum of \\(\\nu_e\\) and \\(\\bar\\nu_\\mu\\) extending up to 52\u202fMeV. A small liquid\u2011argon detector placed at a short baseline can record charged\u2011current events, and the known DAR flux allows a direct determination of the cross section. Alternative sources include intense spallation neutron facilities that generate \\(\\nu_e\\) from muon decay in flight, or the use of a stopped\u2011muon source in a dedicated liquid\u2011argon test chamber. In all cases, careful calibration of the detector response and background suppression are essential to obtain a reliable cross\u2011section measurement."}, {"question": "How would uncertainties in neutrino flavour conversions inside the supernova affect the inferred neutrino flux parameters at Earth, and what theoretical developments are needed to resolve this?", "answer": "The paper does not address this issue because it requires detailed, time\u2011dependent modelling of collective neutrino oscillations and matter effects inside the supernova core, which are still under active investigation. These processes can significantly alter the flavour composition and energy spectra that reach Earth, leading to potential biases in the extracted flux parameters if not properly accounted for. Resolving this uncertainty demands high\u2011resolution supernova simulations that couple neutrino transport with flavour\u2011dependent interaction physics, along with improved treatments of multi\u2011angle effects and turbulence, which are not yet fully understood or available in the literature."}, {"question": "How can superconducting radiofrequency (SRF) cavity surface treatments be optimized to achieve higher accelerating gradients for future high\u2011power proton linacs?", "answer": "Advanced surface processing techniques such as electropolishing (EP), buffered chemical polishing (BCP), and nitrogen doping (N\u2011doping) have been shown to reduce surface resistance and increase the quality factor (Q) of SRF cavities. By combining EP with low\u2011temperature bake\u2011outs and controlled nitrogen infusion during the final heat treatment, the superconducting gap can be enhanced, leading to gradients beyond 30\u202fMV/m while maintaining low field emission. Further optimization involves tailoring the surface roughness at the nanometer scale and using high\u2011purity niobium with a residual resistivity ratio (RRR) above 300 to minimize thermal losses."}, {"question": "What design strategies can mitigate thermal shock in high\u2011power graphite targets when exposed to multi\u2011megawatt proton beams?", "answer": "Effective mitigation relies on a combination of target geometry, active cooling, and material selection. Shortening the target length reduces the peak heat deposition, while a helical or baffle\u2011augmented beam raster spreads the energy over a larger surface area. High\u2011purity graphite grades with optimized grain structure and low thermal expansion coefficients are preferred. Active helium\u2011gas cooling channels directly surrounding the target core provide rapid heat extraction. Additionally, incorporating a gradient\u2011matched beam entrance window, typically a titanium alloy with low stress\u2011concentration, helps absorb shock loads and prevents rapid material fatigue."}, {"question": "How can cryogenic distribution systems be engineered to minimize helium boil\u2011off and maintain pressure stability in large liquid argon TPC cryostats?", "answer": "A well\u2011balanced cryogenic distribution network uses high\u2011conductivity copper or aluminum transfer lines with segmented heat\u2011anchor points to intercept conductive heat loads. The system incorporates distribution valve boxes (DVBs) that regulate the flow of superfluid and normal\u2011fluid helium, keeping the pressure drop within strict limits. Vacuum insulation between cryogenic lines reduces radiative heat transfer, and multi\u2011stage cold compressors handle the boil\u2011off efficiently. Finally, real\u2011time pressure sensors and automated control loops adjust valve positions to counteract transient thermal loads, ensuring stable temperature and pressure across all detector modules."}, {"question": "What are the implications of increasing LBNF beam power from 1.2\u202fMW to 2.4\u202fMW on secondary particle focusing and neutrino flux uncertainties?", "answer": "Doubling the proton beam power amplifies the intensity of secondary mesons produced in the target, which requires the focusing horns to sustain higher magnetic fields and thermal loads. To preserve neutrino flux precision, horn current profiles must be redesigned to handle increased joule heating, and the target\u2013horn assembly must be cooled more aggressively. Enhanced beamline optics may be needed to maintain the desired pion/kaon kinematics, thereby keeping the neutrino energy spectrum stable. Systematic uncertainties linked to hadron production and horn alignment can be reduced by incorporating in\u2011situ monitoring of secondary particle rates and by cross\u2011checking with external hadron production data from experiments such as NA61/SHINE."}, {"question": "What is the expected degradation rate of the stainless steel beam window material under prolonged exposure to a 2.4\u202fMW proton beam?", "answer": "The degradation rate of stainless steel windows in a multi\u2011MW proton beam environment is not yet known. Predicting material fatigue and embrittlement requires long\u2011term irradiation studies, coupled with thermal shock testing that simulate the actual beam pulse structure. Since such data are currently unavailable and the degradation mechanisms involve complex radiation\u2011induced defect accumulation, we cannot provide a reliable estimate at this time."}, {"question": "What are the main advantages of using a vertical drift geometry in large liquid argon time projection chambers for long\u2011baseline neutrino experiments?", "answer": "A vertical drift configuration allows the charge to drift over a longer distance without requiring additional readout planes. This reduces the number of front\u2011end electronics and the overall construction cost while still achieving the necessary spatial resolution. Because the ionization electrons travel parallel to the electric field, the uniformity of the drift field is easier to control, and the detector can be made more compact, which simplifies cryogenic infrastructure and shielding."}, {"question": "How does pixel\u2011based charge readout improve particle identification in a liquid argon TPC compared with traditional strip readout?", "answer": "Pixel readout provides true three\u2011dimensional imaging of every ionization cluster, eliminating the projection ambiguities that arise when multiple tracks overlap on a two\u2011dimensional strip plane. This yields a higher tracking efficiency, especially for complex, multi\u2011track events, and improves the accuracy of vertex reconstruction. The fine granularity also enhances the ability to separate electromagnetic showers from charged\u2011particle tracks, thereby improving electron\u2011neutrino versus background discrimination."}, {"question": "In what ways can enhanced photon\u2011detection systems such as APEX or PoWER contribute to lowering the energy threshold for supernova neutrino detection in DUNE?", "answer": "Both APEX and PoWER increase the optical coverage and improve light collection efficiency, which in turn raises the number of photo\u2011electrons detected per MeV of deposited energy. With a higher photon yield and better time resolution, the detector can trigger on, and reconstruct, lower\u2011energy events that would otherwise fall below the noise floor. This reduction in the effective energy threshold enhances sensitivity to the low\u2011energy tail of the supernova neutrino spectrum and extends the observable supernova distance range."}, {"question": "What role does a high\u2011pressure gaseous argon TPC (ND\u2011GAr) play in constraining neutrino\u2011argon cross\u2011section uncertainties for the DUNE far detector?", "answer": "The ND\u2011GAr provides a thin, low\u2011density target that mimics the argon nuclei of the far detector but with minimal re\u2011interaction of secondary particles. By measuring exclusive final states with excellent momentum resolution and particle identification, it directly probes nuclear effects (such as Fermi motion, short\u2011range correlations, and intranuclear rescattering). These measurements reduce the model dependence of cross\u2011section predictions used to interpret far\u2011detector data, thereby tightening systematic uncertainties on oscillation parameters."}, {"question": "What is the projected maximum drift voltage and electric field uniformity requirement for the FD4 module's 13\u202fm drift length, and how will the cryogenic and high\u2011voltage systems be engineered to achieve it?", "answer": "I do not have that information. The specific maximum drift voltage, the required field uniformity, and the detailed design of the cryogenic and high\u2011voltage infrastructure are not covered in the material provided. These technical specifications would be defined in later engineering design reports and require dedicated simulations and prototype testing that are beyond the scope of this document."}, {"question": "What are the key scaling challenges when transitioning DUNE's reconstruction workload from a high\u2011throughput computing (HTC) model to a high\u2011performance computing (HPC) environment, and how can GPU acceleration help address these challenges?", "answer": "The primary scaling challenge is the need to process extremely large, continuous FD data streams that are naturally segmented in both time and space. In an HTC model, jobs run independently on many CPUs, but HPC architectures favor tightly coupled parallelism with limited inter\u2011node communication. Converting the workflow requires (1) partitioning the data into smaller, independent chunks that fit into node memory, (2) redesigning I/O to be highly efficient on parallel file systems, and (3) optimizing the event\u2011processing kernels for SIMD/vector execution. GPU acceleration can help by offloading compute\u2011bound tasks such as hit\u2011finding, clustering, and machine\u2011learning inference to massively parallel processors. GPUs can process millions of hits in parallel, dramatically reducing wall\u2011clock time per event. However, the bottleneck often shifts to data movement; efficient GPU\u2011to\u2011CPU memory transfers and overlap of computation with I/O are essential to realize performance gains."}, {"question": "How can machine\u2011learning models be integrated into the DUNE reconstruction pipeline while preserving reproducibility, version control, and long\u2011term maintainability?", "answer": "A robust integration strategy involves (1) containerising the full ML workflow (framework, dependencies, and trained models) so that every run uses the same environment, (2) storing model artefacts in a versioned model registry (e.g., MLflow or DVC) linked to the corresponding dataset version, (3) embedding deterministic seeds and random\u2011state management in training scripts, and (4) using continuous\u2011integration pipelines that automatically retrain models when upstream data or hyper\u2011parameters change. Documentation should describe the training procedure, hyper\u2011parameter settings, and performance metrics. Finally, the reconstruction code should expose a clear API to switch between ML\u2011based and traditional algorithms, enabling systematic validation and comparison across different physics samples."}, {"question": "What strategies can be employed to ensure efficient data transfer and storage management across distributed European HPC resources for DUNE's large far\u2011detector datasets?", "answer": "Efficient management requires a layered approach: (1) **Data staging**\u2014pre\u2011fetch datasets to local scratch or burst buffers using parallel transfer protocols (e.g., Globus, GridFTP) before job launch; (2) **Metadata\u2011driven placement**\u2014use a metadata catalogue (e.g., MetaCat) to locate replicas and schedule jobs to the nearest site, reducing network load; (3) **Chunking and compression**\u2014split large event files into smaller chunks and apply lossless compression to reduce bandwidth; (4) **Asynchronous I/O**\u2014decouple data reads/writes from compute kernels using overlapped I/O APIs; (5) **Data lifecycle policies**\u2014archive or delete intermediate files automatically based on retention schedules; (6) **Monitoring and feedback**\u2014deploy real\u2011time dashboards to track transfer rates, queue lengths, and storage utilization, allowing dynamic re\u2011routing of jobs when bottlenecks appear."}, {"question": "What are the main obstacles to maintaining long\u2011term sustainability of DUNE's computing infrastructure in the face of evolving operating systems, security requirements, and hardware lifecycles, and how can they be mitigated?", "answer": "Key obstacles include: (1) **Software ageing**\u2014legacy C++ libraries and scripting languages may lack upstream support; mitigated by adopting long\u2011term supported frameworks (e.g., C++17+, Python 3.11) and automated dependency management; (2) **Security patch cycles**\u2014continuous patching of thousands of worker nodes requires automation; this can be addressed with configuration\u2011driven provisioning tools (e.g., Ansible, SaltStack) and containerised workloads that isolate the host OS; (3) **Hardware obsolescence**\u2014GPUs and interconnects evolve rapidly, making hardware\u2010specific optimisations brittle; adopting portable GPU APIs (HIP, SYCL) and abstracting device selection at runtime helps; (4) **Skill drain**\u2014as the collaboration ages, institutional knowledge may be lost; comprehensive documentation, training workshops, and mentorship programs are essential; (5) **Funding stability**\u2014long\u2011term contracts for storage and compute need to be negotiated early with national labs and HPC centers to secure predictable budgets."}, {"question": "What is the projected energy consumption of DUNE's planned GPU\u2011enabled reconstruction pipeline, and how does it compare to a CPU\u2011only pipeline of equivalent performance?", "answer": "The paper does not provide detailed energy consumption estimates, and current simulations lack the granularity needed to model power usage for the proposed GPU\u2011accelerated workflow. Energy profiling would require (1) detailed performance benchmarks of the reconstruction kernels on target GPU hardware, (2) measurement of idle and active power draws of the GPU nodes, and (3) accounting for data\u2011movement overheads between CPU and GPU. Without these measurements, it is not possible to give a reliable comparison to a CPU\u2011only pipeline. Future studies that integrate power monitoring into the job scheduler and perform controlled experiments on representative workloads are needed to answer this question."}, {"question": "What physical characteristics of short gamma\u2011ray bursts make them prime candidates for coincident gravitational\u2011wave detections from binary neutron\u2011star mergers?", "answer": "Short GRBs\u2014defined by a prompt emission duration of less than about two seconds and a hard photon spectrum\u2014are widely believed to arise from the coalescence of two neutron stars or a neutron star\u2013black\u2011hole pair. This interpretation is supported by the observed temporal coincidence with the compact\u2011binary inspiral phase, the typical energies released (\u224810^49\u201310^51\u202ferg), and the lack of supernova signatures that are common to long GRBs. The high compactness and rapid mass transfer in such systems produce strong, high\u2011frequency gravitational\u2011wave signals in the 10\u20131000\u202fHz band, exactly where ground\u2011based interferometers are most sensitive. Consequently, short GRBs are the most promising electromagnetic triggers for searching for gravitational waves from binary mergers."}, {"question": "How does the observer\u2019s viewing angle relative to the binary orbit affect the amplitude and detectability of the gravitational\u2011wave signal from a short GRB progenitor?", "answer": "Gravitational\u2011wave emission from a binary system is strongest along the orbital angular\u2011momentum axis (the \u201cface\u2011on\u201d direction) and weakest in the orbital plane (\u201cedge\u2011on\u201d). The strain amplitude scales roughly as (1+cos\u00b2\u03b8) where \u03b8 is the inclination angle; thus a face\u2011on system can produce nearly twice the strain of an edge\u2011on system at the same distance. Because the short GRB jet is believed to be narrowly collimated along the same axis, an observer detecting a GRB is almost always within a few degrees of face\u2011on, making the associated gravitational\u2011wave signal more likely to be above the detector threshold. However, this also means that any off\u2011axis GRB, which might still produce a detectable GW signal, will not be accompanied by prompt gamma emission, complicating multimessenger association."}, {"question": "What improvements in next\u2011generation gravitational\u2011wave detectors will extend the horizon for detecting neutron\u2011star mergers associated with short GRBs?", "answer": "Future upgrades such as A+ (the planned upgrade of Advanced LIGO and Virgo), the Voyager project, and third\u2011generation facilities like Cosmic Explorer and Einstein Telescope are expected to reduce strain noise by factors of 2\u201310 across the 10\u2013500\u202fHz band. This translates into a proportional increase in the observable volume, extending the detection horizon for binary neutron\u2011star mergers from \u2248200\u202fMpc with current detectors to \u2248600\u20131000\u202fMpc (A+), \u22483\u20134\u202fGpc (Voyager), and \u224810\u201320\u202fGpc (third\u2011generation). Such gains dramatically raise the likelihood of catching a gravitational\u2011wave signal from the population of short GRBs, including those at higher redshift or with lower intrinsic luminosity."}, {"question": "What are the primary obstacles to precise sky localization of short GRBs when using gravitational\u2011wave data alone, and how can multimessenger follow\u2011up mitigate these challenges?", "answer": "Ground\u2011based interferometers localize sources by triangulating the arrival time differences among detectors. With a three\u2011detector network, the typical error region for a compact binary is a few tens to a few hundred square degrees, far larger than the fields of view of most electromagnetic instruments. The localization improves with a larger network, better timing precision, and higher signal\u2011to\u2011noise ratios. Multimessenger observations\u2014such as rapid GRB localizations from Fermi/GBM or Swift/BAT\u2014provide a sub\u2011degree sky position that can be used to constrain the gravitational\u2011wave search, effectively reducing the background and improving the statistical significance. Conversely, a well\u2011localized GW event can trigger targeted electromagnetic follow\u2011up to search for kilonovae or afterglows, thereby closing the multimessenger loop."}, {"question": "Is the occurrence rate of low\u2011luminosity short gamma\u2011ray bursts significantly different from that of high\u2011luminosity short gamma\u2011ray bursts, and what implications would this have for joint gravitational\u2011wave and GRB detection rates?", "answer": "I do not have definitive knowledge on this matter because the paper\u2019s analysis does not address the relative rates of low\u2011luminosity versus high\u2011luminosity short GRBs. Determining whether a distinct population of faint short GRBs exists requires a large, well\u2011calibrated sample of GRB luminosities, careful treatment of selection effects in gamma\u2011ray detectors, and independent constraints from gravitational\u2011wave observations. Current data are insufficient to quantify any difference in occurrence rates, and more comprehensive surveys combined with future multimessenger observations will be needed to resolve this question."}, {"question": "How does the mass distribution of neutron stars observed in gravitational\u2011wave mergers compare to that of isolated binary neutron stars in the Milky Way?", "answer": "Current gravitational\u2011wave observations suggest that neutron\u2011star masses in merging binaries span a broader range, extending up to roughly 2.0\u202fM\u2299, whereas Galactic binary pulsars cluster tightly around 1.33\u202fM\u2299. However, the sample size is still small and uncertainties are large, so a definitive comparison remains tentative."}, {"question": "Is there a distinct mass gap between the heaviest neutron stars and the lightest black holes in the compact binary population?", "answer": "Analyses of the merger catalog show a suppression of events in the 2\u20135\u202fM\u2299 range, consistent with a lower mass gap, but the data are not yet conclusive enough to confirm that the gap is completely empty."}, {"question": "What is the physical origin of the correlation between black\u2011hole spin magnitude and the mass ratio of the binary?", "answer": "The agent does not have a definitive answer. The observed trend\u2014larger effective spins in more unequal\u2011mass binaries\u2014has been reported, but the underlying astrophysical mechanisms (e.g., differential stellar evolution, mass transfer, natal kicks, or dynamical interactions) have not been conclusively identified, and the paper does not provide a definitive explanation."}, {"question": "Does the merger rate of binary black holes increase with redshift?", "answer": "Population studies of the LIGO\u2013Virgo detections indicate a positive evolution of the BBH merger rate with redshift, parameterized as a power law R(z)\u221d(1+z)^\u03ba with \u03ba\u22483, which is broadly consistent with the rise of the cosmic star\u2011formation rate."}, {"question": "Is there an upper mass gap for stellar\u2011mass black holes, as predicted by pair\u2011instability supernova theory?", "answer": "The gravitational\u2011wave catalog contains mergers with component masses up to about 70\u202fM\u2299, and the current data do not show a sharp drop in the merger rate above ~50\u202fM\u2299. Consequently, the existence of an upper mass gap remains unconstrained."}, {"question": "How has the estimated rate of neutron star\u2013black hole (NSBH) mergers evolved over the first three LIGO\u2013Virgo observing runs?", "answer": "The publicly reported detection rate of NSBH mergers has increased modestly with each observing run, largely reflecting the improved sensitivity and longer observing times of the detector network. While earlier runs (O1 and O2) yielded only a handful of NSBH candidates, the third observing run (O3) has produced several confirmed NSBH detections, suggesting a higher intrinsic merger rate in the local Universe. This trend is consistent with population\u2011inference studies that indicate NSBH systems are more common than previously thought."}, {"question": "What are the dominant systematic uncertainties in measuring the effective inspiral spin (\u03c7_eff) of high\u2011mass black hole binaries?", "answer": "The primary systematic uncertainties arise from waveform model inaccuracies, particularly in the treatment of higher\u2011order multipole moments and spin\u2011precession dynamics. Additionally, calibration errors in the detector strain data and imperfect noise subtraction can bias the phase evolution, which is crucial for \u03c7_eff extraction. For the highest\u2011mass systems, the signal\u2019s short duration exacerbates these issues, making the inferred \u03c7_eff more sensitive to model assumptions."}, {"question": "To what extent do gravitational\u2011wave observations constrain the maximum mass of neutron stars?", "answer": "Current gravitational\u2011wave detections of binary neutron star (BNS) mergers provide only loose constraints on the maximum neutron\u2011star mass, because the inspiral signal is mainly sensitive to tidal deformability rather than the ultimate mass limit. Some candidate events with unusually massive components hint at a possible higher maximum mass, but the statistical significance remains low. Consequently, the precise upper bound on neutron\u2011star masses is still largely determined by electromagnetic observations and nuclear\u2011physics modeling."}, {"question": "What is the most probable spin\u2011orientation distribution for black holes in merging binaries formed through isolated binary evolution?", "answer": "For binaries that form via isolated stellar evolution, theoretical models predict that the component spins should be preferentially aligned with the orbital angular momentum due to tidal coupling and common\u2011envelope evolution. This alignment tends to produce small effective precession spin (\u03c7_p) and positive \u03c7_eff values. Observationally, many detected systems show mild alignment, but a fraction exhibit significant misalignment, suggesting that both isolated and dynamical formation channels contribute to the observed population."}, {"question": "Is there definitive evidence for a third\u2011generation black hole population (i.e., black holes formed from the merger of two smaller black holes) in the current GW catalog?", "answer": "The existing catalog does not provide definitive evidence for a distinct third\u2011generation black hole population. While some high\u2011mass black holes observed in the data could, in principle, be remnants of earlier mergers, their masses and spins are not sufficiently distinct to conclusively separate them from first\u2011generation black holes formed directly from stellar collapse. Moreover, the statistical uncertainties in mass and spin measurements, combined with limited sample size, prevent a robust identification of a separate generation. Future observations with higher signal\u2011to\u2011noise ratios and improved waveform models may allow such a distinction to be made."}, {"question": "How might graph neural networks be leveraged to improve neutrino interaction vertex reconstruction accuracy in liquid argon time projection chambers compared to conventional convolutional neural networks?", "answer": "Graph neural networks (GNNs) can naturally represent the sparse, irregular hit patterns in a LArTPC as a graph, where nodes are individual hits and edges encode spatial or temporal proximity. By learning message\u2011passing operations across this graph, GNNs can capture long\u2011range correlations and topological information that are difficult for 2\u2011D convolutions to encode. This may lead to better discrimination of the true vertex, especially in events with complex topologies or low hit densities."}, {"question": "What is the effect of changing the wire\u2011plane pitch on the spatial precision of neutrino interaction vertex determination in the horizontal\u2011drift DUNE far detector?", "answer": "Reducing the wire\u2011plane pitch increases the granularity of the recorded charge deposits, thereby improving the resolution of reconstructed hit positions in the drift direction. A finer pitch can shrink the uncertainty on the vertex location, particularly in the direction transverse to the wires. However, this also raises data volume and may require more sophisticated noise filtering. Conversely, a coarser pitch reduces resolution but eases data handling."}, {"question": "How does incorporating scintillation light detection data influence the performance of vertex\u2011finding algorithms in LArTPC detectors?", "answer": "Scintillation light provides a prompt, time\u2011of\u2011arrival signal that can be used to estimate the absolute event time (t0) and, in some configurations, the z\u2011coordinate of the vertex. Combining light timing with charge\u2011based hit information can improve the localization of the interaction point, especially when the charge signal is sparse or heavily overlapped. However, the light collection efficiency varies across the detector and its integration requires careful calibration to avoid biasing vertex estimates."}, {"question": "What are the main obstacles and possible strategies for extending vertex\u2011reconstruction techniques to identify secondary vertices from tau decays in DUNE data?", "answer": "Secondary vertices from tau decays are often displaced by a few millimeters to centimeters, with relatively low\u2011energy visible decay products. Challenges include limited hit multiplicity, overlapping tracks, and the need to disentangle the secondary decay vertex from the primary neutrino interaction. Strategies involve refining multi\u2011pass reconstruction, incorporating decay\u2011mode specific signatures, and applying dedicated neural\u2011network modules trained to recognize displaced energy deposits or kinematic patterns indicative of tau decay."}, {"question": "To what extent can unsupervised or semi\u2011supervised learning approaches discover novel event topologies in DUNE data without labeled training sets?", "answer": "I don't have a definitive answer to this question. The paper focuses on supervised deep\u2011learning methods trained on labeled simulated data, and does not explore unsupervised or semi\u2011supervised strategies for topology discovery. Investigating such approaches would require developing new loss functions or clustering techniques that can learn meaningful representations from unlabeled data, as well as validation against known physics signatures, which is beyond the scope of the present work."}, {"question": "How does the stochastic wandering of the spin frequency of accreting millisecond X\u2011ray pulsars affect the sensitivity of continuous gravitational\u2011wave searches?", "answer": "The spin frequency of an accreting neutron star is subject to fluctuations driven by variations in the accretion torque. In the frequency domain, these fluctuations manifest as a random walk, which can shift the signal by several frequency bins during the coherent integration time. If the search assumes a perfectly stable frequency, the mismatch between the true signal and the template leads to a loss in signal\u2011to\u2011noise ratio. By allowing the frequency to wander within a bounded range\u2014often modeled as a discrete random walk\u2014the search can retain sensitivity. This is typically achieved by partitioning the data into shorter coherent segments (e.g., 10\u2011day chunks) and using a hidden Markov model to track the most likely frequency path. The longer the coherent segment, the greater the potential frequency drift, so there is a trade\u2011off between sensitivity to weak signals and robustness against frequency wander."}, {"question": "What are the dominant mechanisms that can generate continuous gravitational waves in accreting millisecond X\u2011ray pulsars, and how do they appear in the gravitational\u2011wave spectrum?", "answer": "Two principal mechanisms are usually considered:\\n1. **Mass quadrupole deformations (\u201cmountains\u201d)** on the neutron\u2011star surface, either supported by crustal stresses or magnetic fields, produce emission at twice the stellar spin frequency (2f\u2605) and, in some models, also at f\u2605 if the deformation is not perfectly aligned with the rotation axis.\\n2. **r\u2011mode oscillations**, a class of Rossby waves driven unstable by gravitational\u2011wave back\u2011reaction, emit near 4f\u2605/3. The exact frequency depends on the equation of state and relativistic corrections.\\nIn a narrowband search the expected signal is thus centered on f\u2605, 4f\u2605/3, or 2f\u2605, with a bandwidth that covers any modest frequency drift."}, {"question": "How do uncertainties in binary orbital parameters propagate into the template bank and influence the detection thresholds of continuous\u2011wave searches?", "answer": "The binary orbital parameters\u2014period (P), projected semi\u2011major axis (a0), and time of ascending node (Tasc)\u2014enter the Doppler modulation model used to transform detector data into the source frame. Small errors in these parameters broaden the mismatch between the true signal and any single template, effectively smearing the signal power across neighbouring templates. To keep the fractional loss in signal\u2011to\u2011noise ratio below a chosen maximum mismatch (e.g., \u00b5max\u202f=\u202f0.1), the template bank is constructed with spacings derived from the metric on parameter space. The number of templates grows as the square root of the parameter uncertainties and inversely with the coherent segment length (through the mismatch equations). A larger template bank increases the trials factor, which in turn raises the detection threshold (higher Lth) for a fixed false\u2011alarm probability."}, {"question": "What is the precise relationship between the observed X\u2011ray flux during outburst and the amplitude of continuous gravitational waves emitted by an accreting millisecond X\u2011ray pulsar?", "answer": "The paper does not provide a definitive answer to this question. The connection between X\u2011ray flux and gravitational\u2011wave amplitude is complex: it depends on the efficiency of angular\u2011momentum transfer, the star\u2019s internal structure, magnetic field geometry, and the detailed physics of accretion\u2011induced deformations. While torque\u2011balance arguments can give an upper limit on the strain by assuming the accretion torque is exactly counter\u2011balanced by gravitational\u2011wave emission, translating an observed flux into a concrete strain amplitude requires assumptions about the neutron\u2011star equation of state, accretion geometry, and magnetic field configuration\u2014parameters that are not fully constrained by current observations. Consequently, a precise, universally applicable relationship remains an open area of research."}, {"question": "In what ways can hidden Markov models improve the tracking of phase wander in continuous\u2011wave searches compared to traditional coherent matched\u2011filtering?", "answer": "Traditional coherent matched\u2011filtering assumes a perfectly stable phase evolution over the entire observation period. This is unsuitable for sources whose spin phase wanders due to stochastic accretion torque fluctuations. Hidden Markov models (HMMs) treat the instantaneous frequency (or phase) as a hidden state that evolves according to a probabilistic transition model (e.g., a simple random walk). By applying the Viterbi algorithm, the HMM efficiently finds the most likely path through the state space that maximizes the likelihood of the observed data. This semi\u2011coherent approach retains most of the sensitivity of a fully coherent search while being robust to phase wander, enabling longer coherent segments and better overall signal\u2011to\u2011noise ratios for sources with significant frequency noise."}, {"question": "How does the geometry and orientation of a global gravitational\u2011wave detector network influence the sensitivity to narrowband anisotropies in the stochastic gravitational\u2011wave background?", "answer": "The overlap\u2011reduction function (ORF) captures the relative antenna patterns, time delays, and orientations of detector pairs. For narrowband signals, the ORF oscillates rapidly with frequency and sky direction. Baselines that are short and nearly co\u2011linear (e.g., the two Advanced LIGO detectors) provide high correlation for certain directions, while longer, more widely separated baselines (e.g., LIGO\u2013Virgo, LIGO\u2013KAGRA) improve sky coverage and break degeneracies. Thus, the overall sensitivity depends on both baseline length and the relative orientations of the interferometers; a carefully optimized network can substantially enhance the ability to detect narrowband anisotropies."}, {"question": "What are the theoretical predictions for the amplitude and spectral shape of a narrowband stochastic background produced by a population of rapidly rotating neutron stars in the Milky Way?", "answer": "Models of rotating neutron stars\u2014such as magnetars, accreting pulsars, or isolated spinning neutron stars\u2014predict continuous gravitational radiation at roughly twice the spin frequency. If the Galactic population has a broad distribution of spin frequencies and ellipticities, the resulting background is a superposition of many nearly monochromatic lines, yielding a narrowband spectrum. The amplitude is governed by the ellipticity distribution, spin\u2011down torque, and source number, typically giving \u03a9_GW \u223c 10^\u201311\u201310^\u20139 in the LIGO band with a nearly flat spectral index (\u03b1 \u2248 0). Large uncertainties in source populations and ellipticity limits lead to a wide range of possible amplitudes."}, {"question": "Which computational strategies can be employed to scale an all\u2011sky, all\u2011frequency radiometer map\u2011making to higher pixel and frequency resolutions while keeping the analysis tractable?", "answer": "Two complementary approaches are effective: (1) matrix\u2011based inversion with sparsity exploitation\u2014since the Fisher matrix is band\u2011limited in pixel space, iterative solvers such as conjugate\u2011gradient with appropriate preconditioners can be used without forming the full matrix; (2) hierarchical folding and parallelization\u2014by folding data into a single sidereal day and distributing frequency bins across compute nodes, the analysis becomes embarrassingly parallel. GPU acceleration for ORF evaluation and efficient memory layouts for HEALPix indexing further reduce runtime. Combining these techniques allows extending to N_side \u2265 32 or finer frequency bins (e.g., 1/64 Hz) without prohibitive computational cost."}, {"question": "Can the ASAF method be generalized to incorporate Doppler modulation and frequency\u2011dependent sky localization, and how would this affect sensitivity?", "answer": "In principle, the ASAF pipeline can be modified to include the time\u2011dependent Doppler phase shift arising from Earth\u2019s rotation and orbital motion. This requires augmenting the cross\u2011spectral density with a frequency\u2011dependent phase term that tracks the expected line drift across the observation period. Incorporating this effect would sharpen the response to true monochromatic sources, potentially increasing the SNR by up to a factor of a few for high\u2011frequency signals, but it would also increase computational complexity because the phase model must be evaluated for each sky pixel and frequency bin. A practical strategy is to first run a Doppler\u2011blind ASAF to flag candidate pixel\u2011frequency pairs and then perform a targeted matched\u2011filter follow\u2011up that accounts for Doppler modulation."}, {"question": "What is the expected contribution of exotic boson clouds surrounding spinning black holes to the narrowband stochastic gravitational\u2011wave background, and can an ASAF\u2011style search detect them?", "answer": "Ultralight bosons (e.g., axion\u2011like particles) can form clouds around rapidly rotating black holes via superradiance, emitting nearly monochromatic gravitational waves at frequencies set by the boson mass and black\u2011hole spin. The Galactic population of such clouds could produce a narrowband stochastic background with a characteristic frequency range of ~10\u20131000\u202fHz and a flat spectral index. However, the ASAF framework described in the paper focused on generic persistent signals and did not model the specific line\u2011like structure or the spatial clustering expected from boson\u2011cloud sources. Consequently, while the ASAF pipeline is capable of flagging anomalous narrowband excesses, it cannot directly quantify the expected amplitude or distinguish boson\u2011cloud signatures without dedicated modeling and matched\u2011filter follow\u2011ups. Thus, the question remains open and requires further theoretical and data\u2011analysis work."}, {"question": "How does timing noise (spin wandering) in young neutron stars influence the sensitivity of semi\u2011coherent searches for continuous gravitational waves?", "answer": "Spin wandering introduces random fluctuations in the rotational frequency that can shift the signal out of a single template over the coherent integration time. Semi\u2011coherent methods mitigate this by using short coherence times and a hidden Markov model or Hough transform that allows the frequency to drift by a few bins per step. The net effect is a modest reduction in sensitivity compared to a purely coherent search that assumes a deterministic spin\u2011down, typically on the order of 10\u201320\u202f% in the 95\u202f% upper\u2011limit strain for the same computational budget. The choice of coherence time, transition probabilities, and step size in the HMM or frequency binning in the Hough transform are therefore critical to balance sensitivity against the risk of mis\u2011tracking a wandering signal."}, {"question": "Which young supernova remnants are the most promising targets for future continuous\u2011wave searches with upgraded detectors?", "answer": "Targets that combine proximity, youth, and evidence of a central compact object are favored. Vela\u202fJr. (G266.2\u20131.2), Cas\u202fA (G111.7\u20132.1), G1.9+0.3, and the younger remnant G18.9\u20131.1 have ages of a few hundred to a thousand years and distances of less than a kiloparsec, giving the strongest expected strain signals. With the projected improvements in LIGO\u202fVoyager and the next\u2011generation Virgo upgrade, the sensitivity to strain at 200\u2013400\u202fHz will improve by roughly a factor of two, bringing these remnants within reach of the spin\u2011down limits for many realistic ellipticity models."}, {"question": "How can multi\u2011messenger observations (X\u2011ray, radio) improve targeted continuous\u2011wave searches?", "answer": "Electromagnetic observations that reveal a neutron star\u2019s spin frequency, spin\u2011down rate, or even a timing solution provide powerful priors that drastically reduce the parameter space. Knowing the frequency and its derivative allows a fully coherent or very long coherent integration, which scales the sensitivity as \\(h_{\\rm min}\\propto T_{\\rm coh}^{-1/2}\\). Even if the pulsar is not detected in radio, a precise X\u2011ray pulse ephemeris can be used. In the absence of a phase\u2011connected ephemeris, a narrow range of spin\u2011down values can be tested, improving the detection statistic\u2019s significance and reducing the number of required templates."}, {"question": "What advantages does combining the \\(f_{\\ast}\\) and \\(2f_{\\ast}\\) harmonics provide in a dual\u2011harmonic search for continuous waves?", "answer": "When a neutron star emits gravitational waves at both its spin frequency and twice that frequency\u2014possible for a triaxial rotator or a pinned superfluid\u2014the two harmonics share the same intrinsic phase evolution. Tracking them simultaneously allows the matched\u2011filter statistic to sum power from both frequencies, improving the overall signal\u2011to\u2011noise ratio by roughly \\(\\sqrt{2}\\) in the ideal case. It also mitigates the risk of missing a signal that would be too weak in a single\u2011harmonic search. However, it requires a larger template bank and careful handling of line contamination in both frequency bands."}, {"question": "Does the ellipticity of a young neutron star evolve on timescales of months to years?", "answer": "The current data do not provide a definitive answer. Existing continuous\u2011wave searches have not detected any signals, and the theoretical models of crustal relaxation, magnetic field decay, and r\u2011mode saturation predict a range of evolution timescales, from days to centuries. Because the observational upper limits are still above the expected ellipticity for many young stars, we lack the sensitivity to observe a gradual change in ellipticity over short times. Dedicated long\u2011term monitoring with next\u2011generation detectors and improved waveform models will be needed to constrain or detect such evolution."}, {"question": "How do quantum squeezing techniques improve the sensitivity of continuous gravitational-wave searches compared to earlier observing runs?", "answer": "Quantum squeezing reduces the quantum shot-noise floor in the interferometers, allowing more power to be delivered to the measurement band without increasing radiation-pressure noise. This leads to a lower strain noise spectral density, especially at high frequencies, which directly translates into tighter upper limits on continuous-wave amplitudes."}, {"question": "What astrophysical processes can create the non-axisymmetric deformations required for a spinning neutron star to emit detectable continuous gravitational waves?", "answer": "Possible mechanisms include crustal mountains caused by accretion or thermal stresses, magnetic-field-induced distortions, and the excitation of fluid oscillation modes such as r-modes. Each process can support an equatorial ellipticity that gives rise to a quadrupolar gravitational-wave signal at twice the rotation frequency."}, {"question": "In an all-sky continuous-wave search, how does the choice of Short Fourier Transform (SFT) coherence time influence the balance between computational cost and search sensitivity?", "answer": "Longer SFTs improve frequency resolution and Doppler demodulation accuracy, boosting sensitivity. However, they also increase the parameter-space resolution required in sky and spin-down, which raises the number of templates and hence computational load. Shorter SFTs lower the template count but reduce sensitivity due to poorer frequency discrimination."}, {"question": "To what extent can the strain upper limits obtained by all-sky searches constrain the equatorial ellipticity of neutron stars located at different distances in the Milky Way?", "answer": "By inverting the strain upper limit formula, one obtains a maximum allowed ellipticity as a function of distance. For a given search sensitivity, this translates into a distance range within which neutron stars with a specified ellipticity would have been detected. Thus, tighter upper limits extend the observable volume and place stronger constraints on the deformation of nearby neutron stars."}, {"question": "What is the expected sensitivity of future observing runs (e.g., O4/O5) to continuous gravitational waves from neutron stars with spin-down rates larger than 10\u207b\u2078\u202fHz/s, and what new analysis strategies would be required to probe such high spin-down values?", "answer": "The paper does not address this scenario, so we cannot provide a definitive answer. Extending the search to spin-down magnitudes above 10\u207b\u2078\u202fHz/s would demand a denser template bank in frequency derivative space, likely increasing computational cost significantly. Techniques such as adaptive hierarchical searches, coherent-follow\u2011up on narrower sky patches, or machine-learning based outlier vetting might be necessary to make the search tractable, but concrete sensitivity estimates await future data and method development."}, {"question": "How does the choice of the narrowband width parameter (\u03ba) influence the sensitivity and computational cost of continuous gravitational\u2011wave searches for pulsars with significant timing noise?", "answer": "The parameter \u03ba sets the fractional window around the electromagnetic spin frequency and spin\u2011down within which the search is performed. A larger \u03ba allows for greater offsets between the true GW phase evolution and the EM timing solution, which is useful for pulsars with large timing noise or differential rotation between the crust and core. However, a larger \u03ba also increases the number of templates in both frequency and spin\u2011down dimensions, thereby inflating the search volume and the false\u2011alarm probability. In practice, \u03ba values of 10\u207b\u00b3\u201310\u207b\u00b2 are chosen to balance the need for robustness against phase offsets with computational feasibility, as demonstrated in previous LIGO/Virgo narrowband searches."}, {"question": "What physical mechanisms could cause a measurable phase offset between the electromagnetic emission of a pulsar and its continuous gravitational\u2011wave signal, and how would such offsets manifest in the data?", "answer": "A differential rotation between the rigid outer crust and the interior superfluid can lead to a small lag that manifests as a phase offset between the electromagnetic pulse arrival times and the GW phase. Glitches, magnetospheric torque changes, or internal superfluid vortex dynamics can also introduce phase drifts or glitches in the GW signal that are not perfectly locked to the EM timing. In the data, these effects would appear as a mismatch in the expected Doppler\u2011corrected phase evolution, causing a reduction in matched\u2011filter SNR if the search assumes strict phase\u2011lock. Narrowband searches that allow a small offset in frequency and spin\u2011down effectively accommodate such behavior."}, {"question": "How would modelling post\u2011glitch transient gravitational\u2011wave signals with an exponentially decaying amplitude, instead of a simple rectangular window, affect the sensitivity of long\u2011duration transient searches?", "answer": "An exponential decay more accurately represents the expected relaxation of the star\u2019s quadrupole moment after a glitch. While a rectangular window assumes a constant amplitude over the whole duration, an exponential model would allocate signal power more heavily to early times, potentially increasing SNR for short\u2011lived emissions. However, implementing an exponential window typically requires a larger template bank to cover the additional parameter (decay time), increasing computational cost. Studies have shown that the loss in SNR for a realistic exponential signal using a rectangular template is modest (a few percent), so many searches adopt the simpler rectangular window to keep the search tractable."}, {"question": "In what way do detector duty cycles and calibration uncertainties propagate into the upper limits on the gravitational\u2011wave strain and neutron\u2011star ellipticity derived from continuous\u2011wave searches?", "answer": "The effective observing time, T_obs, is reduced by the duty cycle of each detector, directly scaling the expected sensitivity (h_sens \u221d T_obs\u207b\u00b9/\u00b2). Calibration uncertainties in the strain response of each detector (typically 5\u201310\u202f%) translate into systematic errors on the inferred strain amplitude. Since the ellipticity is derived from the strain via \u03f5 \u221d h\u2080\u202ff\u207b\u00b2, any error in h\u2080 propagates to \u03f5 quadratically with frequency. The combination of reduced T_obs and calibration errors thus weakens the upper limits and introduces a systematic uncertainty that is usually quoted as a separate systematic error budget in the final results."}, {"question": "Is there any evidence for continuous gravitational\u2011wave emission from millisecond pulsars in the O3 data when the phase\u2011lock assumption is relaxed?", "answer": "The current analysis focused on 18 isolated pulsars with spin frequencies between 10\u202fHz and 350\u202fHz that have relatively high spin\u2011down rates, yielding spin\u2011down limits within a factor of three of the expected sensitivity. Millisecond pulsars, which rotate at hundreds of Hz but have very small spin\u2011down rates, were not included in this target list because their indirect spin\u2011down limits are far below the detector sensitivity. Consequently, the study does not address whether continuous GWs could be detected from such objects in O3. Determining this would require a dedicated search over a different parameter space and is an open question that remains to be investigated with future data and more sensitive detectors."}, {"question": "How does the ionization recombination factor for sub\u201150\u202fMeV electrons vary as a function of the applied electric field in a liquid argon time\u2011projection chamber?", "answer": "The recombination factor, R, quantifies the fraction of ionization electrons that survive prompt recombination with argon ions. For low\u2011energy electrons, R typically follows the Modified Box model, where \\n\\nR = ln(1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)) / (1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)),\\n\\nwith \u03b2\u2032 and \u03b1 being empirical parameters, \u03c1 the liquid\u2011argon density, and E_f the electric field. As the field increases, the electric drift force overcomes the ion\u2011electron Coulomb attraction, reducing recombination and increasing R. Empirical measurements (e.g., in ArgoNeuT, ICARUS, and MicroBooNE) show that R rises from ~0.5 at 200\u202fV/cm to ~0.75 at 500\u202fV/cm for 10\u201350\u202fMeV electrons. The precise field dependence also depends on the local dE/dx; denser ionization tracks recombine more strongly, leading to a slightly lower R at the same field."}, {"question": "What is the quantitative impact of the TPC readout threshold on the energy resolution of low\u2011energy electron showers?", "answer": "The readout threshold is the minimum charge that a wire\u2011channel must record to be accepted as a hit. For sub\u201150\u202fMeV electrons, a typical threshold of ~100\u202fkeV per 500\u202fns tick means that a non\u2011negligible fraction of the ionization\u2014especially from thin, low\u2011dE/dx portions of the shower\u2014is lost. Studies of simulated Michel electrons show that this loss corresponds to ~11\u202f% of the total deposited energy. When this missing energy is included, the fractional energy resolution degrades by about 5\u20138\u202f% relative to the ideal case where all charge is measured. The effect is more pronounced at lower energies where the shower is less developed and the charge density is lower."}, {"question": "Can deep learning techniques enhance the separation of Michel electrons from cosmic\u2011ray background in a large LArTPC?", "answer": "Yes. Convolutional neural networks (CNNs) trained on simulated and real data can learn subtle spatial and temporal patterns characteristic of electron\u2011induced showers versus muon or proton tracks. A CNN can be fed the three wire\u2011plane images (U, V, X) and the corresponding time series, and output a probability that a cluster is a Michel electron. Benchmarks show that such a network can achieve >\u202f95\u202f% purity with >\u202f90\u202f% efficiency for energies between 10 and 50\u202fMeV, outperforming traditional cut\u2011based selections that rely on hit multiplicity and angular cuts alone."}, {"question": "How can photon\u2011detector signals complement charge readout for identifying low\u2011energy electrons in a liquid\u2011argon TPC?", "answer": "Photon detectors (e.g., ARAPUCA modules) provide fast scintillation light timestamps with ~ns precision. For low\u2011energy electrons, the scintillation light yields ~1\u20132\u202f\u00d7\u202f10\u2074 photons per MeV, enabling a prompt trigger even when the ionization charge is below the readout threshold. By correlating the light pulse with the charge hit pattern, one can improve the vertex reconstruction, suppress random noise hits, and better discriminate between true electron showers and spurious background. In addition, the light\u2013charge ratio can be used as an auxiliary variable in energy calibration, since it is sensitive to recombination and electron lifetime effects."}, {"question": "Is it possible to recover the energy lost due to readout threshold and shower leakage in future detectors without changing the hardware?", "answer": "The agent does not have a definitive answer to this question. Recovering lost energy without hardware modifications would require sophisticated reconstruction algorithms that infer the missing charge from surrounding hit patterns, shower topology, or correlations with external detectors. While some studies have explored machine\u2011learning extrapolation or analytic corrections based on shower shape models, none have yet demonstrated a systematic, unbiased recovery that matches the true deposited energy across the full 10\u201350\u202fMeV range. Therefore, more detailed simulations, validation with calibration data, and potentially new reconstruction paradigms are needed to determine whether such recovery is feasible in practice."}, {"question": "What range of r\u2011mode saturation amplitudes is theoretically expected for young, rapidly rotating neutron stars, and how does this amplitude evolve as the star cools?", "answer": "Models of r\u2011mode instability predict saturation amplitudes between 10\u207b\u2075 and 10\u207b\u00b3, depending on the neutron star\u2019s mass, radius, and the microphysical dissipation mechanisms (viscosity, superfluidity, crust\u2011core coupling). As the star cools, viscous damping weakens, allowing the amplitude to grow until nonlinear mode couplings or exotic damping processes (e.g., hyperon bulk viscosity) halt the growth, typically on timescales of weeks to months after the instability is triggered."}, {"question": "How do timing glitches influence the excitation and damping of r\u2011mode oscillations in neutron stars?", "answer": "Glitches, which are sudden spin\u2011up events, can transfer angular momentum from the interior superfluid to the crust. This sudden change can perturb the star\u2019s equilibrium, potentially exciting r\u2011mode oscillations. Subsequent energy dissipation through gravitational radiation and internal viscosity will damp the mode, possibly on timescales comparable to the glitch recovery time (~days to weeks). The efficiency of this process depends on the coupling between the core and the crust, as well as on the star\u2019s temperature profile."}, {"question": "To what extent does the neutron star equation of state determine the relationship between the stellar spin frequency and the gravitational\u2011wave frequency emitted by r\u2011modes?", "answer": "The r\u2011mode GW frequency is approximately (4/3) times the stellar spin frequency for a slowly rotating star, but relativistic corrections and the star\u2019s compactness (M/R) shift this relation. Different equations of state (stiff vs. soft) change the star\u2019s radius for a given mass, thereby altering the compactness and the coefficient relating spin to GW frequency. Calculations using realistic equations of state yield variations of a few percent in the GW frequency for a given spin, which is significant for precise template placement in searches."}, {"question": "What advantages do coherent, multi\u2011detector networks provide when searching for continuous gravitational\u2011wave signals from r\u2011mode oscillations compared to single\u2011detector analyses?", "answer": "Coherent multi\u2011detector searches combine the data streams in a way that maximizes signal\u2011to\u2011noise ratio and allows for better discrimination of instrumental artifacts. The network\u2019s antenna patterns provide sky\u2011dependent sensitivity, reducing blind spots and enabling the use of a global F\u2011statistic that coherently adds contributions from all detectors. This leads to deeper upper limits and improved robustness against transient noise, essential for detecting the weak, long\u2011lasting signals expected from r\u2011modes."}, {"question": "Is r\u2011mode emission a viable explanation for the unusually negative braking index observed in some young pulsars beyond PSR\u202fJ0537\u20116910?", "answer": "Current observations of negative braking indices in a handful of young pulsars cannot be conclusively explained by r\u2011mode emission alone. While r\u2011modes can provide additional spin\u2011down torque, the required saturation amplitudes often exceed theoretical limits, and the observed braking indices may also involve magnetospheric evolution or fallback accretion effects. Therefore, we cannot definitively state that r\u2011mode emission accounts for these indices; further multi\u2011wavelength observations and more sensitive GW searches are needed to clarify the dominant mechanisms."}, {"question": "What is the expected contribution to the isotropic gravitational\u2011wave background from binary neutron star mergers at high redshift?", "answer": "Astrophysical models predict that binary neutron star mergers should contribute a stochastic background whose energy density peaks around a few tens of Hz. The high\u2011redshift tail of the merger rate, weighted by the redshift dependence of the cosmic star\u2011formation rate and delay\u2011time distributions, is expected to add a modest but non\u2011negligible component to the overall background, typically on the order of \\(10^{-10}\\) in \\(\\Omega_{\\mathrm{GW}}\\) at 25\u202fHz."}, {"question": "How can correlated terrestrial magnetic noise impact the sensitivity of cross\u2011correlation searches for a stochastic background?", "answer": "Coherent magnetic fields, such as Schumann resonances, can couple into the interferometer strain channels at the same frequency in spatially separated detectors. If not accounted for, these correlated noise sources mimic a stochastic signal and inflate the measured cross\u2011correlation, thereby reducing the achievable sensitivity and potentially biasing the inferred upper limits."}, {"question": "What are the implications of detecting a scalar or vector polarization component in the isotropic gravitational\u2011wave background for alternative theories of gravity?", "answer": "A statistically significant detection of scalar or vector polarizations would constitute direct evidence for physics beyond General Relativity. It would point to modified gravity models that predict extra degrees of freedom, such as scalar\u2013tensor theories or massive gravity, and would constrain their coupling constants and propagation speeds through the measured spectral shape of the background."}, {"question": "How does the inclusion of Virgo data alter the overlap reduction function and the sensitivity to high\u2011frequency gravitational\u2011wave background signals?", "answer": "Adding Virgo to the LIGO network introduces new baselines (Hanford\u2013Virgo and Livingston\u2013Virgo) with different geometries. These baselines have overlap reduction functions that are less suppressed at higher frequencies compared to the LIGO\u2013LIGO baseline, thereby improving the network\u2019s overall sensitivity in the \\(\\sim 70\\)\u2013\\(200\\)\u202fHz band and providing complementary coverage where the LIGO\u2013LIGO response vanishes."}, {"question": "What would be the effect on the upper limits of the isotropic gravitational\u2011wave background if future detectors achieve a factor of two improvement in strain sensitivity over O3?", "answer": "The paper does not address this scenario directly. Determining the impact would require projecting the improved detector noise spectra, recalculating the overlap reduction functions, and re\u2011evaluating the cross\u2011correlation sensitivity over the relevant frequency band. Such projections are beyond the scope of the present work and would need dedicated simulations with the next\u2011generation detector configurations."}, {"question": "What precision on the CP\u2011violating phase \u03b4CP can DUNE Phase II achieve with a 40\u202fkt fiducial liquid\u2011argon detector and a beam power exceeding 2\u202fMW over a ten\u2011year data\u2011taking period?", "answer": "DUNE Phase\u202fII is projected to reach a \u03b4CP precision of roughly 7\u00b0 to 18\u00b0, depending on the true value of \u03b4CP. For \u03b4CP near 0\u00b0 the uncertainty is about 7\u00b0, while for \u03b4CP close to \u2212\u03c0/2 the precision degrades to roughly 18\u00b0. These numbers are derived from the 1000\u202fkt\u00b7MW\u00b7yr exposure expected with the upgraded beam and detector mass."}, {"question": "How does the DUNE\u2011PRISM concept help to reduce systematic uncertainties in neutrino\u2011argon cross\u2011section measurements?", "answer": "The DUNE\u2011PRISM strategy places the near\u2011detector liquid\u2011argon TPC on a movable platform that can be shifted sideways across a range of off\u2011axis angles. By sampling the neutrino flux at several off\u2011axis positions, the experiment can reconstruct the energy dependence of the flux with high precision. This off\u2011axis sampling also provides different effective target nuclei and interaction kinematics, enabling simultaneous constraints on cross\u2011sections. The resulting flux and cross\u2011section constraints are then propagated to the far\u2011detector analysis, substantially reducing systematic errors in oscillation parameter extraction."}, {"question": "What are the key differences between the vertical\u2011drift and horizontal\u2011drift liquid\u2011argon TPC designs used in the DUNE far detectors, and what advantages does each configuration offer?", "answer": "In a horizontal\u2011drift design (FD1) the charge drift direction is parallel to the detector plane, requiring a relatively short drift distance (~3\u202fm) and a smaller high\u2011voltage system. This simplifies cryogenic safety and electronics integration. The vertical\u2011drift design (FD2) has the drift direction perpendicular to the detector plane, allowing longer drift lengths (~3\u20134\u202fm) and a more compact detector footprint. Vertical drift can improve charge collection efficiency and reduce readout channel count, but demands a higher voltage supply and more stringent purity control. Both designs provide comparable physics performance; the choice depends on engineering trade\u2011offs such as cavern size and detector construction logistics."}, {"question": "What are the main advantages and technical challenges of implementing a dual\u2011phase liquid\u2011argon TPC with optical readout (the ARIADNE concept) for a DUNE far\u2011detector module?", "answer": "Advantages of the dual\u2011phase ARIADNE design include: (1) charge amplification in the gas phase, which yields higher signal\u2011to\u2011noise and potentially lower energy thresholds; (2) the possibility of optical readout of the avalanche light, providing a fast, calorimetric signal and a complementary timing reference; (3) a more compact readout plane that can reduce the number of electronic channels. Technical challenges comprise: (1) maintaining a stable liquid\u2011gas interface over a large area; (2) ensuring uniform high voltage and field shaping in the gas amplification region; (3) integrating optical sensors with the charge readout without compromising the purity of the argon; and (4) controlling background light and electronic noise from the photon detectors. These challenges require extensive R&D to demonstrate scalability to the multi\u2011kiloton scale of DUNE."}, {"question": "What is the expected sensitivity of DUNE to detect neutrinos from a core\u2011collapse supernova occurring at a distance of 100\u202fkpc?", "answer": "The paper does not provide sensitivity estimates for a supernova at 100\u202fkpc; it focuses on a canonical distance of 10\u202fkpc. Detailed calculations of event rates and detector response for a 100\u202fkpc supernova would require additional modeling of the neutrino flux spectrum, distance scaling, and background rates, which are beyond the scope of the presented document. Consequently, the precise sensitivity for a 100\u202fkpc supernova cannot be inferred from the information given."}, {"question": "What classes of astrophysical phenomena are expected to emit short-duration gravitational-wave bursts, and what are their characteristic time scales and frequency ranges?", "answer": "Short-duration gravitational-wave bursts are predicted to arise from several astrophysical processes. Core\u2011collapse supernovae produce burst signals with durations from a few milliseconds up to a few seconds, typically spanning frequencies between 10\u202fHz and 1\u202fkHz, with higher frequency components (hundreds of Hz) associated with proto\u2011neutron star oscillations. Binary black\u2011hole or neutron\u2011star mergers emit brief, high\u2011frequency chirps lasting milliseconds, with peak frequencies from a few hundred Hz to several kHz. Non\u2011axisymmetric instabilities in rapidly rotating neutron stars can excite quasi\u2011periodic oscillations (f\u2011modes) that last tens of milliseconds to a few seconds, emitting in the 1\u20133\u202fkHz band. Magnetar starquakes or magnetically driven flares may also produce short bursts in the kilohertz range. Additionally, exotic sources such as cosmic\u2011string cusps or kinks could generate millisecond\u2011scale bursts with a characteristic \\(f^{-4/3}\\) spectrum extending up to several kilohertz."}, {"question": "How does the coherent WaveBurst (cWB) pipeline detect unmodeled gravitational\u2011wave transients, and what role do the network correlation coefficient and time\u2011frequency binning play?", "answer": "The coherent WaveBurst pipeline searches for excess coherent power across a network of detectors by performing a time\u2013frequency decomposition of the strain data (e.g., using wavelets). It constructs a likelihood ratio that compares the hypothesis of a coherent gravitational\u2011wave signal against the null hypothesis of detector noise. The network correlation coefficient (cc) quantifies the fraction of coherent energy shared among detectors; a high cc indicates that the observed excess is consistent with a real astrophysical signal rather than independent noise glitches. cWB divides the data into time\u2013frequency bins and applies adaptive thresholds to cluster significant excesses. Triggers are ranked by the coherent network signal\u2011to\u2011noise ratio (\\(\\eta_c\\)), and only those exceeding a chosen cc threshold and passing additional consistency tests are considered for further analysis. This approach allows detection of a wide variety of morphologies without assuming a specific waveform model."}, {"question": "Why is the sensitivity of the LIGO\u2013Virgo network generally better at low frequencies compared to high frequencies for generic burst searches?", "answer": "The sensitivity difference arises from the detectors\u2019 strain noise spectral density and their antenna response. At low frequencies (tens to a few hundred Hz), the interferometers are limited mainly by seismic and suspension noise, but the advanced noise\u2011reduction techniques and the use of multiple detectors with similar orientations allow coherent stacking of signals, improving the effective strain sensitivity. In contrast, at high frequencies (above ~1\u202fkHz), shot noise dominates, and the detectors\u2019 optical configuration (e.g., power\u2011recycling cavity, mirror coatings) imposes a steeper rise in noise. Moreover, the antenna patterns of the two LIGO detectors are nearly identical, whereas Virgo\u2019s misalignment reduces coherent response for high\u2011frequency bursts, further diminishing the network\u2019s effective sensitivity in that band."}, {"question": "What are data\u2011quality vetoes in gravitational\u2011wave searches, and how do they help reduce false alarms from environmental or instrumental artifacts?", "answer": "Data\u2011quality vetoes are predefined time intervals during which the detector data are deemed unreliable due to known disturbances. They are derived from auxiliary channels that monitor environmental conditions (seismics, magnetics, acoustic sensors) or instrumental states (laser power, alignment). By cross\u2011correlating glitches in the gravitational\u2011wave channel with signatures in auxiliary channels, analysts can flag and exclude periods where noise transients are likely to mimic astrophysical signals. Vetoes are ranked by effectiveness; the most effective ones remove a high fraction of glitches while sacrificing only a small fraction of live\u2011time. Applying vetoes reduces the background trigger population, improves the significance of real events, and ensures that upper\u2011limit calculations are not biased by non\u2011astrophysical artifacts."}, {"question": "What is the projected sensitivity of next\u2011generation detectors (e.g., LIGO\u2011Voyager or Cosmic Explorer) to short\u2011duration gravitational\u2011wave bursts, and how might this impact the detection rate of rare events such as neutron\u2011star f\u2011mode oscillations?", "answer": "I do not have specific numbers for the future detector sensitivities. While the next\u2011generation observatories are expected to improve strain sensitivity by an order of magnitude or more, the exact detection horizon for short\u2011duration bursts, especially high\u2011frequency f\u2011mode signals, depends on the detailed design of the instruments, noise reduction strategies, and data\u2011analysis pipelines that will be employed. Consequently, any estimate of the expected detection rate for rare events like neutron\u2011star f\u2011mode oscillations would require detailed modeling of those detectors\u2019 performance, which is beyond the scope of the information available to me."}, {"question": "What is the most effective method to distinguish between cosmological and astrophysical contributions in an anisotropic gravitational-wave background?", "answer": "Distinguishing cosmological from astrophysical components relies on their distinct angular power spectra and spectral indices. Cosmological backgrounds are expected to be nearly isotropic with a relatively flat or slowly varying spectrum, whereas astrophysical backgrounds trace the large\u2011scale structure and show stronger anisotropy aligned with the matter distribution. By performing a spherical\u2011harmonic decomposition of the sky map and jointly fitting for the amplitude, spectral index, and multipole dependence, one can separate the two contributions. However, this separation is limited by detector sensitivity, foreground contamination, and the similarity of spectral shapes at certain multipoles."}, {"question": "How does including a third detector such as Virgo affect the angular resolution of a stochastic background map?", "answer": "Adding a third detector introduces additional baselines with different arm orientations and lengths, which enlarges the network\u2019s antenna\u2011pattern coverage. The angular resolution improves roughly with the smallest baseline length divided by the highest frequency used, but the LIGO\u2013Virgo baseline is shorter than the LIGO\u2013LIGO baseline, so the highest multipoles are still limited. Nonetheless, the extra baseline reduces degeneracies between sky pixels, improves sky coverage (especially the southern hemisphere), and increases the overall sensitivity to anisotropic features."}, {"question": "What are the main challenges in using the broadband radiometer technique for detecting point\u2011like sources in the stochastic background?", "answer": "The broadband radiometer assumes that the signal is confined to a single pixel with negligible covariance to neighboring pixels. In reality, the detector antenna pattern couples adjacent pixels, causing signal leakage and bias. The technique also presumes a flat spectral shape across the band, which may not hold for real sources. Moreover, non\u2011Gaussian detector noise and calibration uncertainties can mimic or mask weak point\u2011like signals, requiring careful regularization and robust statistical methods to extract reliable limits."}, {"question": "What role does data folding over one sidereal day play in reducing computational cost for anisotropic background searches?", "answer": "Data folding exploits the Earth\u2019s rotational symmetry: the antenna pattern repeats every sidereal day. By folding the entire observing run into a single sidereal day, cross\u2011correlations from many days are coherently summed, reducing the time\u2011frequency data volume by the number of days. This drastically lowers memory requirements and computational time, enabling finer pixelation or higher frequency resolution while keeping the analysis tractable."}, {"question": "What is the expected contribution of primordial black hole mergers to the anisotropic gravitational\u2011wave background at frequencies below 100 Hz?", "answer": "I do not know that answer. The paper does not discuss primordial black hole mergers, and current theoretical models lack precise predictions for their contribution to the anisotropic background at low frequencies. Estimating this would require detailed modeling of the primordial black hole population, merger rates, and resulting angular distribution\u2014work that is beyond the scope of the present study and not covered in the existing literature."}, {"question": "How does the number of kinks per loop influence the amplitude of the stochastic gravitational\u2011wave background produced by a network of cosmic strings?", "answer": "Increasing the number of kinks per oscillation enhances the total power emitted by each loop. For models where the loop distribution contains many small loops (e.g., model\u00a0B or the interpolating model\u00a0C\u20112), the background spectrum rises approximately linearly with the kink number in the frequency range accessible to ground\u2011based detectors. Consequently, a larger kink population raises the overall \\u03a9GW(f) and can shift the peak of the spectrum to higher frequencies."}, {"question": "What upper limits on the cosmic\u2011string tension \\(G\\mu\\) can be derived from the current O3 data of LIGO\u2013Virgo for different loop\u2011distribution scenarios?", "answer": "Analyses of the O3 data, combining both burst and stochastic searches, exclude tensions above roughly \\(4\\times10^{-15}\\) for the most optimistic loop model (model\u00a0B). For the less optimistic scaling model (model\u00a0A) the exclusion is weaker, reaching down only to about \\(10^{-13}\\). These limits assume a single cusp per loop and vary mildly with the assumed number of kinks."}, {"question": "In what way do cusp\u2011generated gravitational\u2011wave bursts differ from those produced by kinks or kink\u2011kink collisions in terms of detectability by ground\u2011based interferometers?", "answer": "Cusps emit highly beamed, short\u2011duration bursts with a characteristic strain falling as \\(f^{-4/3}\\). Because the emission is narrowly directed, only a small fraction of bursts are observable, but those that are seen can have large amplitudes. Kinks, emitting with a fan\u2011like pattern and a \\(f^{-5/3}\\) spectrum, produce more numerous but weaker events. Kink\u2011kink collisions radiate isotropically with a \\(f^{-2}\\) spectrum; when many kinks are present they dominate the burst rate and can provide the loudest signals for a fixed detector sensitivity."}, {"question": "Does the intercommutation probability of cosmic superstrings alter the gravitational\u2011wave signatures that LIGO\u2013Virgo could detect?", "answer": "I do not have information on this specific aspect. The analysis in the paper focuses on field\u2011theory Nambu\u2013Goto strings with an intercommutation probability close to one. Effects of reduced intercommutation probabilities, which are relevant for cosmic superstrings, are not addressed here and would require dedicated simulations and theoretical work to determine their impact on the burst rate and stochastic background."}, {"question": "What improvements are expected from the upcoming O4 observing run in terms of constraints on cosmic\u2011string parameters?", "answer": "The O4 run will provide roughly twice the observation time of O3 and benefit from the planned upgrades to the LIGO and Virgo detectors. Projections indicate that the improved strain sensitivity, especially at high frequencies, could tighten the exclusion on \\(G\\mu\\) by up to an order of magnitude for the most favorable loop models. Additionally, longer data sets will reduce statistical uncertainties in the stochastic background search, potentially turning the current upper limits into actual detections if the string tension lies near the current bounds."}, {"question": "What theoretical mechanisms can produce sub\u2011solar mass black holes in the early universe?", "answer": "Several mechanisms have been proposed, including the collapse of primordial density fluctuations (primordial black holes), the collapse of cooling dark\u2011matter halos in dissipative dark\u2011matter models, and the formation of exotic compact objects such as boson stars. Each scenario predicts a different mass spectrum and spatial distribution for sub\u2011solar mass black holes."}, {"question": "How can gravitational\u2011wave observations place limits on the fraction of dark matter that is in the form of primordial black holes?", "answer": "Gravitational\u2011wave detectors measure the merger rate of compact binaries. By comparing the observed (or upper\u2011limit) merger rates with theoretical predictions for primordial\u2011black\u2011hole binaries, one can infer an upper limit on the primordial\u2011black\u2011hole abundance, expressed as the fraction of dark matter \\(f_{\\rm PBH}\\). This requires modeling the binary formation process, merger time distribution, and the detector sensitivity to sub\u2011solar mass signals."}, {"question": "Why does the mass ratio of the binary components affect the detectability of sub\u2011solar mass binary mergers?", "answer": "The signal\u2011to\u2011noise ratio of a binary merger depends on the chirp mass, which is a weighted combination of the two component masses. For a fixed total mass, a more unequal mass ratio reduces the chirp mass, leading to a weaker gravitational\u2011wave signal and a smaller horizon distance. Consequently, binaries with very small mass ratios are harder to detect with current detectors."}, {"question": "What observational signatures would distinguish black holes formed through dissipative dark\u2011matter collapse from those formed via primordial fluctuations?", "answer": "Black holes from dissipative dark\u2011matter collapse are expected to have a broader mass spectrum and may form in dense dark\u2011matter halos, potentially leading to a different spatial clustering compared to primordial black holes. Additionally, the binary formation channels may differ, producing distinct spin and eccentricity distributions. These differences could, in principle, be probed by precise measurements of the binary parameters in gravitational\u2011wave events."}, {"question": "What is the expected spin distribution of sub\u2011solar mass black holes produced by dissipative dark\u2011matter collapse?", "answer": "The paper does not address this question, and current theoretical models do not provide a definitive prediction for the spin distribution of such black holes. The spin depends on the angular momentum of the collapsing dark\u2011matter halo, the efficiency of angular momentum transport, and the microphysics of the dark sector, none of which are yet constrained by observations or detailed simulations. Therefore, we do not have a reliable answer to this question at present."}, {"question": "How do seedless clustering algorithms improve sensitivity to narrow\u2011band long\u2011duration gravitational\u2011wave signals compared to seed\u2011based methods?", "answer": "Seedless clustering searches scan the time\u2011frequency plane for coherent excess power using parametrised curves (e.g., B\u00e9zier or sinusoidal tracks) that can follow slowly drifting or quasi\u2011periodic signals. Because the algorithm does not require any thresholded pixels as a seed, it can integrate weak power over many frequency bins and long timescales, boosting the signal\u2011to\u2011noise ratio for narrow\u2011band, long\u2011duration bursts. Seed\u2011based algorithms, in contrast, rely on thresholded pixels and are more effective for generic, broadband morphologies but can miss or poorly reconstruct slowly varying, narrow\u2011band signals."}, {"question": "What are the main challenges posed by non\u2011Gaussian noise transients in long\u2011duration gravitational\u2011wave searches and how are they mitigated?", "answer": "Non\u2011Gaussian transients, or glitches, can mimic long\u2011duration excess power and inflate the false\u2011alarm rate. They arise from environmental disturbances, instrumental resonances, or non\u2011linear coupling. Mitigation strategies include: (1) vetoing data coincident with auxiliary sensor triggers, (2) subtracting identified linear noise sources via Wiener filtering or machine\u2011learning techniques, (3) masking persistent spectral lines, and (4) applying coherence and duration cuts in the clustering pipelines to reject incoherent or short\u2011duration outliers. These steps reduce the background while preserving sensitivity to astrophysical signals."}, {"question": "How do upper limits on the root\u2011sum\u2011square strain amplitude (hrss) translate into constraints on the energy emitted in gravitational waves by astrophysical sources such as magnetars or eccentric binary black holes?", "answer": "The hrss limit at a given frequency and distance can be converted to an upper bound on the isotropic GW energy via \\(E_{\\text{GW}} \\approx \\frac{c^{3}}{G} \\, \\pi^{2} f^{2} h_{\\text{rss}}^{2} D^{2}\\). Thus, tighter hrss limits imply lower allowed GW energies for a source at distance \\(D\\). For example, a 10\u2011ms magnetar burst with an hrss limit of \\(10^{-22}\\,\\text{Hz}^{-1/2}\\) at 100\u202fHz would constrain the emitted energy to below a few \\(10^{-6}\\,M_{\\odot}c^{2}\\). These bounds help rule out or disfavour models predicting large GW luminosities from such events."}, {"question": "In what ways can the inclusion of Virgo data in future observing runs enhance the detection prospects for long\u2011duration gravitational\u2011wave transients?", "answer": "Adding Virgo increases the network\u2019s sky\u2011coverage and triangulation accuracy, improving the ability to localise and confirm coincidences. The extra detector also provides an independent baseline, enhancing coherence tests and reducing the false\u2011alarm probability. With Virgo\u2019s sensitivity approaching that of the LIGO detectors in the next observing runs, the combined network can lower the hrss thresholds by a factor of two or more, directly translating into larger accessible volumes and higher detection rates for long\u2011duration signals."}, {"question": "What is the predicted event rate of long\u2011duration gravitational\u2011wave bursts from fallback accretion onto rapidly rotating black holes?", "answer": "The paper does not provide an answer because the expected rate for this channel is highly uncertain. Current theoretical models of fallback accretion are limited by complex hydrodynamics, magnetic field configurations, and the poorly constrained distribution of progenitor masses. Consequently, no reliable population synthesis exists to predict the rate, and observational constraints are absent due to the lack of detections. Addressing this question would require detailed simulations of core\u2011collapse supernovae with post\u2011bounce accretion, coupled to GW emission estimates, a task beyond the scope of the current study."}, {"question": "How do the upper limits on the dark\u2011photon\u2013baryon coupling derived from ground\u2011based interferometers constrain theoretical models that generate ultralight dark photons via the misalignment mechanism?", "answer": "The misalignment mechanism predicts a relic abundance that depends on the initial field displacement and the dark\u2011photon mass. The limits on the coupling strength translate into an upper bound on the field amplitude, which in turn restricts the allowed range of initial displacements for a given mass. Models that require a large initial displacement to account for the observed dark matter density are therefore disfavored for masses in the \\(10^{-14}\\)\u2013\\(10^{-11}\\,\\text{eV}/c^{2}\\) window."}, {"question": "What are the dominant noise sources that limit the sensitivity of LIGO/Virgo to ultralight dark\u2011photon signals, and how might future detector upgrades mitigate them?", "answer": "The primary limitations are seismic and suspension thermal noise at low frequencies and quantum shot noise at high frequencies. Additionally, narrow spectral lines from instrumental resonances and scattered light can mimic or obscure the quasi\u2011monochromatic dark\u2011photon signature. Future upgrades such as cryogenic test masses, improved mirror coatings, and quantum squeezing will reduce thermal and shot noise, while better vibration isolation and active control of scattering will suppress line artifacts, thereby extending sensitivity across a broader mass range."}, {"question": "How would a space\u2011based interferometer like LISA or TianQin extend the search for dark photons compared to ground\u2011based detectors, and what new mass window would become accessible?", "answer": "Space\u2011based detectors have longer arm lengths and operate in a quieter gravitational\u2011wave environment, reducing seismic and suspension noise. Their lower frequency sensitivity (down to \\(\\sim10^{-4}\\,\\text{Hz}\\)) allows probing dark\u2011photon masses down to \\(\\sim10^{-18}\\,\\text{eV}/c^{2}\\), far below the \\(\\sim10^{-14}\\,\\text{eV}/c^{2}\\) lower bound reachable by ground\u2011based interferometers. Thus, missions like LISA and TianQin can explore a complementary, lower\u2011mass regime."}, {"question": "What is the role of the common\u2011mode motion of the interferometer mirrors in enhancing the detectability of dark photons, and how does it differ from the differential\u2011mode contribution?", "answer": "Dark photons exert a nearly coherent force on all test masses, leading to common\u2011mode motion that does not change instantaneous arm lengths but modulates the light\u2011travel time. This effect introduces a strain component proportional to \\(f_{0}L/c\\), which is not suppressed by the Earth\u2019s velocity \\(v_{0}/c\\). Consequently, the common\u2011mode signal can be stronger than the differential component, especially at higher frequencies, and must be modeled separately in the analysis to avoid loss of sensitivity."}, {"question": "How would a stochastic background of dark\u2011photon dark matter manifest differently in the cross\u2011correlation versus excess\u2011power analysis, and is it possible to separate it from a genuine gravitational\u2011wave background?", "answer": "A stochastic dark\u2011photon background would produce a coherent, quasi\u2011monochromatic signal that is common to all detectors, leading to a non\u2011zero cross\u2011correlation that is highly frequency\u2011dependent due to Doppler broadening. In contrast, a stochastic gravitational\u2011wave background is expected to be broadband and isotropic, yielding a different overlap reduction function. The paper does not address this distinction, as it focuses on searching for a deterministic monochromatic signal rather than a stochastic background. Distinguishing between the two would require a dedicated analysis of the spectral shape and angular correlation of the cross\u2011correlation, which was beyond the scope of the presented work."}, {"question": "What is the spin\u2011down limit for a gravitational\u2011wave source, and why is it a key benchmark in continuous\u2011wave searches from pulsars?", "answer": "The spin\u2011down limit is the maximum gravitational\u2011wave strain that could be emitted if a pulsar\u2019s entire loss of rotational energy were converted into gravitational radiation. It is calculated from the measured spin frequency, its derivative, the pulsar\u2019s distance, and an assumed moment of inertia. A search that reaches below this limit demonstrates that any gravitational\u2011wave emission must be smaller than the full spin\u2011down power, giving a physically meaningful constraint on the star\u2019s deformation or other emission mechanisms."}, {"question": "How do the inter\u2011glitch braking indices measured for PSR J0537\u22126910 suggest the possibility of gravitational\u2011wave energy loss?", "answer": "The long\u2011term braking index of PSR J0537\u22126910 is far below the canonical value of 3, indicating an accelerating spin\u2011down. The inter\u2011glitch braking index, measured between successive glitches, is often >10 and approaches an asymptotic value near 7 shortly after a glitch. Braking indices of 5 and 7 are expected for energy loss dominated by a time\u2011varying mass quadrupole (l = m = 2) and by r\u2011mode oscillations, respectively. The observed indices therefore hint that a portion of the pulsar\u2019s rotational energy may be drained through gravitational\u2011wave emission."}, {"question": "What specific contribution does NICER X\u2011ray timing data provide to the LIGO/Virgo search for PSR J0537\u22126910?", "answer": "NICER supplies a contemporaneous, phase\u2011accurate timing ephemeris that tracks the pulsar\u2019s rotation and glitch epochs. This ephemeris allows the gravitational\u2011wave search to heterodyne the detector data at the expected frequency (once or twice the spin frequency) with the correct phase evolution, keeping the signal coherent over months. Without such a timing solution the search would lose sensitivity because the signal phase would drift due to glitches and irregular spin\u2011down."}, {"question": "How does the upper limit on the equatorial ellipticity of PSR J0537\u22126910 compare with theoretical maximum ellipticities a neutron\u2011star crust can support?", "answer": "The 95\u202f% credible upper limit on the ellipticity of PSR J0537\u22126910 is \u03b5\u202f<\u202f3\u202f\u00d7\u202f10\u207b\u2075. Theoretical estimates of the maximum elastic deformation sustainable by a neutron\u2011star crust range from ~10\u207b\u2075 to a few\u202f\u00d7\u202f10\u207b\u2076, depending on composition and temperature. Thus, the observational limit is at or slightly above the highest theoretical values, indicating that if the crust were maximally strained the star would still be below the sensitivity of the current search."}, {"question": "Is there evidence that the size of a glitch in PSR J0537\u22126910 directly determines the amplitude of any transient gravitational waves produced at the glitch epoch?", "answer": "No. The paper does not address the relationship between glitch size and transient gravitational\u2011wave amplitude. While the timing data record the magnitude of each glitch, the analysis focuses on continuous\u2011wave emission at the rotational harmonics and does not search for or quantify any short\u2011duration signals associated with the glitches. Establishing such a correlation would require dedicated glitch\u2011triggered searches with high\u2011time\u2011resolution data, which remains a topic for future study."}, {"question": "What are the advantages of using a high\u2011pressure gaseous argon TPC over a liquid\u2011argon TPC for measuring low\u2011energy protons in neutrino interactions?", "answer": "In a high\u2011pressure gaseous argon TPC the density of the medium is much lower than in liquid argon, so protons with kinetic energies as low as 5\u202fMeV (corresponding to a track length of a few centimeters) can leave a visible ionisation trail. This gives a significantly lower detection threshold compared with liquid argon, where a 46\u202fMeV proton is needed for a 2\u202fcm track. Additionally, the long mean free path for hadrons in the gas (~90\u202fm) reduces the probability of secondary intranuclear interactions, leading to cleaner event topologies."}, {"question": "How does a magnetic field in the near detector help distinguish neutrino from antineutrino interactions?", "answer": "A magnetic field bends charged particles according to the sign of their charge. In a magnetised TPC the curvature of the outgoing lepton track can be measured, allowing one to determine whether the lepton is a \u03bc\u207a (from a \u03bd\u0304) or a \u03bc\u207b (from a \u03bd). This charge\u2011sign determination is essential for separating neutrino and antineutrino components in a mixed beam, thereby reducing systematic uncertainties in oscillation analyses."}, {"question": "Can a gaseous argon TPC be used to directly detect tau neutrino appearance in the near detector?", "answer": "Yes, in principle the high spatial resolution and good particle identification of a gaseous argon TPC enable the reconstruction of the short\u2010lived \u03c4 lepton decay products. However, the expected rate of \u03bd\u03c4 charged\u2011current interactions at the near detector is extremely low, and practical sensitivity would require a very large exposure or additional specialised trigger strategies. The current design of the ND\u2011GAr does not include dedicated \u03c4\u2011identification capabilities, so while the physics case exists, the detector is not optimised for it."}, {"question": "What role does the calorimeter surrounding the TPC play in neutrino trident searches?", "answer": "The calorimeter provides precise measurements of the energy and direction of photons from \u03c0\u2070 decays and of hadronic showers. By accurately reconstructing electromagnetic and hadronic activity, it helps suppress background events that mimic the two\u2011lepton signature of a trident process, improving the purity of the signal sample."}, {"question": "What are the current limitations on measuring the axial form factor of the neutron using the ND\u2011GAr detector?", "answer": "I do not have a definitive answer to this question. The paper focuses on detector design, cross\u2011section measurements, and BSM searches, but it does not discuss the specific challenges of extracting the neutron axial form factor from the data. Determining that quantity would require detailed modelling of neutrino\u2011neutron interactions, specialised selection criteria, and a comparison with theoretical predictions that are beyond the scope of the present document."}, {"question": "What are the primary physical mechanisms that can generate continuous gravitational waves from a spinning neutron star, and how do the predicted wave frequency and amplitude differ for each mechanism?", "answer": "The two most discussed mechanisms are (1) a non\u2011axisymmetric mass quadrupole \u2013 caused by a permanent deformation such as a \u2018mountain\u2019 on the crust or a strong internal magnetic field \u2013 which emits at twice the star\u2019s spin frequency and scales linearly with the equatorial ellipticity; and (2) unstable r\u2011mode oscillations, which are large\u2011amplitude fluid modes driven unstable by gravitational radiation. R\u2011modes emit at a frequency of roughly 4/3 of the spin frequency and the strain amplitude depends on a dimensionless r\u2011mode amplitude parameter, \u03b1, rather than on an ellipticity. The expected amplitudes for both mechanisms are generally very small (h \u2272 10\u207b\u00b2\u2075\u201310\u207b\u00b2\u2076 for nearby young neutron stars) but can be enhanced if the deformation or r\u2011mode amplitude is unusually large."}, {"question": "How does the estimated age of a supernova remnant affect the range of spin\u2011down parameters that must be searched when looking for continuous gravitational waves from its central compact object?", "answer": "An older remnant implies a smaller age\u2011based upper limit on the strain and, assuming the star\u2019s rotation has slowed mainly through gravitational\u2011wave emission, the allowed first frequency derivative, \u02d9f, scales roughly as \u2013f/\u03c4, where \u03c4 is the age. Younger remnants therefore require searches over a wider range of spin\u2011down values (including larger negative \u02d9f) to account for the possibility of rapid initial spin and strong braking. This also influences the second derivative range, which is tied to the braking index; a larger spread in \u03c4 leads to a broader search in \u02d9f and \u00a8f to maintain sensitivity to physically plausible spin\u2011down trajectories."}, {"question": "What is the sensitivity depth in a semi\u2011coherent continuous\u2011wave search, and how is it typically estimated using simulated injections?", "answer": "Sensitivity depth, D(f), is defined as the ratio of the detector\u2019s strain spectral noise density to the smallest detectable strain amplitude at a given frequency, i.e., D(f) = \u27e8S_h(f)\u27e9 / h_{95%}. It represents the search\u2019s efficiency in converting detector noise into a detectable signal. To estimate D(f), one injects a large number of simulated continuous\u2011wave signals with known amplitudes into real data, processes them with the full search pipeline, and finds the amplitude at which 95% of the injections exceed the detection threshold. The depth is then computed for each frequency band, and an empirical scaling (often linear with frequency) is used to extrapolate to neighboring bands."}, {"question": "Why is the F\u2011statistic a preferred matched\u2011filter statistic for directed continuous\u2011wave searches, and what considerations determine the choice of coherent segment length in a semi\u2011coherent scheme like Weave?", "answer": "The F\u2011statistic analytically maximizes the likelihood over the unknown amplitude, polarization, and initial phase, providing a powerful detection statistic that is sensitive to weak, nearly monochromatic signals. In a semi\u2011coherent scheme, data are split into short coherent segments (length T_coh) where the F\u2011statistic is computed; these are then summed to form a mean statistic. Shorter segments reduce computational cost and mitigate phase errors from imperfect spin\u2011down models, but they also lower the coherent SNR. Longer segments improve sensitivity but require a denser template bank to cover the parameter space and increase the risk of signal loss due to mismatch. The optimal T_coh is therefore chosen by balancing sensitivity gains against computational feasibility, often guided by simulations that include realistic noise and spin\u2011down uncertainties."}, {"question": "Does the search for continuous waves from Cas\u202fA and Vela\u202fJr. place any limits on the possible r\u2011mode amplitude of their central compact objects?", "answer": "The paper does not provide explicit upper limits on r\u2011mode amplitudes. While it discusses r\u2011mode emission as a theoretical possibility and presents sensitivity curves for strain, it focuses on constraints derived from ellipticity models and does not perform dedicated simulations or injections for r\u2011mode signals. Consequently, no quantitative limits on the r\u2011mode amplitude, \u03b1, are given; deriving such limits would require a separate study that models the r\u2011mode waveform and injects it into the data to assess detectability."}, {"question": "What are the trade\u2011offs between electric field strength and scintillation light yield in large\u2011volume dual\u2011phase liquid argon time\u2011projection chambers?", "answer": "In a dual\u2011phase LArTPC the primary scintillation yield depends strongly on the electron\u2011ion recombination probability. A low drift field (tens of V/cm) allows many ionized electrons to recombine with ions, producing a larger fraction of the 127\u202fnm VUV photons. As the field is increased to several hundred V/cm, the drift velocity rises and the recombination probability drops, reducing the S1 yield. However, a higher field improves charge extraction and minimizes attachment losses, which is essential for accurate calorimetry. The optimal field therefore balances a sufficient S1 signal for timing and trigger purposes against the need for high\u2011quality charge readout."}, {"question": "How does the geometry of a wavelength\u2011shifting material influence the angular distribution and detection efficiency of scintillation photons in a dual\u2011phase LArTPC?", "answer": "The angular emission pattern of re\u2011emitted photons depends on whether the wavelength shifter is coated directly on the photocathode surface, painted on a thin film, or deposited on a larger area. Coating the inner surface of the PMT glass (as with TPB) produces a more isotropic re\u2011emission with a relatively high transport efficiency to the photocathode. In contrast, a thin polyethylene\u2011naphthalate (PEN) foil positioned over the PMT window presents two exposed faces; photons incident on either side are re\u2011emitted in all directions, but the geometry causes a larger fraction of the light to escape or hit non\u2011photosensitive areas, reducing the effective detection efficiency. Additionally, foils may introduce multiple scattering and surface reflections that alter the arrival\u2011time distribution, affecting the timing resolution."}, {"question": "In what ways does xenon doping modify the spectral composition and attenuation characteristics of scintillation light in liquid argon, and how can this be exploited for improved light collection in large detectors?", "answer": "When xenon is dissolved in liquid argon at the ppm level, energy transfer from excited argon excimers to xenon occurs. The resulting xenon excimers emit photons at longer wavelengths (\u2248\u202f178\u202fnm and \u2248\u202f150\u202fnm), which are less strongly absorbed by impurities and experience a longer Rayleigh scattering length (\u2248\u202f3\u20139\u202fm) compared to the 127\u202fnm argon light (\u2248\u202f1\u202fm). Consequently, photons travel further before scattering or being absorbed, improving the uniformity of light collection, especially for events occurring far from the photodetector array. However, the original 127\u202fnm component is partially quenched, so the total S1 amplitude can decrease if the xenon concentration is too high. Optimizing the xenon level thus requires balancing increased propagation distance against reduced primary light yield."}, {"question": "What are the most effective computational strategies for accurately simulating photon transport over long drift distances while keeping resource demands manageable in large LArTPC experiments?", "answer": "Full Monte\u2011Carlo tracking of each VUV photon is prohibitively expensive for multi\u2011kilometre LAr volumes. Practical solutions include: (1) constructing photon libraries by generating a large number of photons from a fine grid of voxels, recording for each detector channel the visibility, minimum arrival time and time\u2011distribution parameters; (2) interpolating between voxels during event simulation to estimate light yield without individual photon tracking; (3) using importance sampling to focus on regions of high light\u2011yield density; (4) parallelising the photon generation step with GPUs or distributed computing; and (5) implementing analytic approximations for Rayleigh scattering and absorption based on measured attenuation lengths. These methods reduce CPU time by orders of magnitude while preserving sufficient accuracy for detector\u2011design studies."}, {"question": "What is the expected degradation in light detection efficiency of PEN or TPB wavelength shifters after ten years of operation in a liquid argon environment under continuous VUV irradiation, and what mechanisms dominate this aging process?", "answer": "The agent does not have sufficient information to provide a reliable prediction. Long\u2011term aging studies of PEN and TPB films in liquid argon, exposed continuously to VUV photons, have not yet been performed on a decade timescale. Key mechanisms\u2014such as photo\u2011degradation of the organic molecules, micro\u2011cracking of the polymer matrix, or contamination from dissolved gases\u2014remain unquantified experimentally, so the future efficiency loss cannot be determined from current data alone. Further dedicated aging experiments would be required to answer this question."}, {"question": "How do the detection thresholds of matched\u2011filter pipelines influence the completeness of the GWTC\u20112.1 catalog for low\u2011mass binary neutron star mergers?", "answer": "The detection thresholds, such as the chosen false\u2011alarm\u2011rate cut and signal\u2011to\u2011noise ratio thresholds, determine which signals exceed the pipelines\u2019 sensitivity limits. Lower thresholds increase completeness but also raise the background noise, while higher thresholds reduce false alarms at the cost of missing marginal events. The GWTC\u20112.1 catalog does not provide a detailed completeness analysis for low\u2011mass binary neutron star systems; such an assessment would require dedicated injection campaigns across the full parameter space of neutron star masses and spins."}, {"question": "What are the implications of the newly identified high\u2011mass binary black hole events for the existence of an intermediate\u2011mass black hole population?", "answer": "The high\u2011mass events in GWTC\u20112.1, with total masses approaching or exceeding 150\u202fM\u2299, expand the observable mass range for binary black hole mergers. Their presence supports the possibility that intermediate\u2011mass black holes (\u224810\u00b2\u201310\u00b3\u202fM\u2299) can form through hierarchical mergers or dynamical assembly in dense stellar environments. However, the limited number of such detections and the uncertainties in the mass\u2011gap boundaries mean that the existence of a substantial intermediate\u2011mass black hole population remains an open question."}, {"question": "How does the calibration uncertainty of the LIGO and Virgo detectors impact the sky\u2011localization accuracy for high\u2011redshift events in GWTC\u20112.1?", "answer": "Calibration uncertainties introduce systematic errors in the amplitude and phase of the reconstructed strain, which propagate into the parameter\u2011estimation pipeline and degrade the precision of sky\u2011localization. For high\u2011redshift events with modest signal\u2011to\u2011noise ratios, the resulting 90\u202f% credible regions can be significantly larger than for nearby, louder events. The GWTC\u20112.1 analysis incorporates calibration uncertainties by marginalizing over spline\u2011parameterized amplitude and phase variations, but the exact impact on each event\u2019s localization is not reported in the catalog and would need to be evaluated on a case\u2011by\u2011case basis."}, {"question": "What are the dominant systematic uncertainties in estimating the effective inspiral spin parameter (\u03c7_eff) for precessing binary black hole systems?", "answer": "The main systematic sources include waveform model inaccuracies (e.g., missing higher\u2011order modes or imperfect treatment of precession), limited signal\u2011to\u2011noise ratio, and assumptions about spin priors. Additionally, calibration errors can bias phase evolution, directly affecting \u03c7_eff. The current state\u2011of\u2011the\u2011art models (IMRPhenomXPHM, SEOBNRv4PHM) mitigate many of these effects, but residual discrepancies between models and between model and data still contribute to the total systematic uncertainty budget."}, {"question": "What is the true astrophysical rate of neutron star\u2013black hole mergers in the local universe, as inferred from the GWTC\u20112.1 data?", "answer": "The GWTC\u20112.1 catalog does not provide a definitive rate estimate for neutron star\u2013black hole (NSBH) mergers. While a few candidate events hint at the possibility of such systems, the current sample size is too small and the statistical and systematic uncertainties too large to derive a robust local merger rate. A more accurate estimate will require additional detections, improved sensitivity, and refined population\u2011modeling efforts."}, {"question": "What are the dominant systematic uncertainties that limit DUNE\u2019s ability to measure the CP\u2011violating phase \u03b4CP?", "answer": "DUNE\u2019s sensitivity to \u03b4CP is largely limited by three classes of systematic uncertainties:\\n1. **Neutrino flux prediction** \u2013 uncertainties in hadron production and horn focusing affect the energy\u2011dependent neutrino flux at the far detector. \\n2. **Neutrino\u2011nucleus interaction models** \u2013 uncertainties in cross\u2011sections, final\u2011state interactions, and nuclear effects (e.g., multinucleon emission) change the reconstructed neutrino energy distribution. \\n3. **Detector response** \u2013 uncertainties in calorimetric energy scale, electron\u2013muon separation efficiency, and reconstruction efficiency introduce biases in the extracted oscillation probabilities. DUNE\u2019s near detector program and data\u2011driven techniques are designed to constrain these systematics to the few\u2011percent level required for a high\u2011precision \u03b4CP measurement."}, {"question": "How does DUNE\u2019s wide\u2011band neutrino beam help disentangle the neutrino mass ordering from CP\u2011violation effects?", "answer": "The broad energy spectrum (\u223c0.5\u20134\u202fGeV) of DUNE\u2019s beam samples the first and second oscillation maxima. Matter effects grow with baseline and energy, producing a distinct energy\u2011dependent asymmetry between neutrinos and antineutrinos that depends on the mass ordering but not on \u03b4CP. By measuring the oscillation probability as a function of energy over more than one full oscillation period, DUNE can fit simultaneously for the mass ordering and \u03b4CP, with the energy dependence providing a handle to separate the two effects."}, {"question": "What is DUNE\u2019s expected sensitivity to the proton\u2011decay channel \\(p \\rightarrow K^+ \\nu\\) after its full physics run?", "answer": "With a 40\u2011kiloton fiducial mass and a 40\u2011year exposure (\u22481.6\u202fMt\u2011yr), DUNE expects to set a 90\u202f%\u202fC.L. lower limit on the proton lifetime in the \\(p \\rightarrow K^+ \\nu\\) channel of order \\(1.3 \\times 10^{34}\\)\u202fyears, assuming a 30\u202f% signal efficiency and negligible background after sophisticated reconstruction and selection cuts."}, {"question": "How will DUNE detect neutrinos from a core\u2011collapse supernova and what physics can be extracted from the observed signal?", "answer": "DUNE\u2019s liquid\u2011argon TPC is especially sensitive to the charged\u2011current absorption of electron neutrinos on argon (\\(\\nu_e + ^{40}\\mathrm{Ar} \\rightarrow e^- + ^{40}\\mathrm{K}^*\\)). A supernova burst at 10\u202fkpc would yield \u22483000 events in a 40\u2011kt detector, allowing a time\u2011resolved measurement of the neutronization burst, accretion, and cooling phases. By fitting the energy and time spectra, one can extract information on the supernova explosion mechanism, neutrino flavor transformation (MSW and collective effects), and the neutrino mass ordering, as the early neutronization burst is highly sensitive to the ordering."}, {"question": "What is the precise value of the neutrino mass ordering?", "answer": "The neutrino mass ordering (whether the third mass eigenstate is heavier or lighter than the first two) is currently unknown. While experiments like DUNE aim to determine it with high significance, the exact ordering has not yet been measured, so the answer remains undetermined at this time. Further data from long\u2011baseline, reactor, and atmospheric neutrino experiments are required to resolve this fundamental question."}, {"question": "What is the expected rate of strongly lensed binary black hole mergers detectable with the next-generation third\u2011generation gravitational\u2011wave detectors?", "answer": "Forecasts based on standard lensing models (e.g., singular isothermal sphere or ellipsoid) predict that at design sensitivity the merger rate of lensed binary black hole events could rise to a few percent of the total detectable rate, reaching \\u2265 10\\u201315% depending on the mass distribution and redshift evolution of the source population. These predictions assume that the intrinsic merger rate follows the star\u2011formation rate and that the detector horizon extends to z \\u2265 5."}, {"question": "How does the presence of microlenses embedded in galaxy\u2011cluster potentials modify the wave\u2011optics signatures observed in gravitational\u2011wave signals?", "answer": "Microlenses with masses between a few solar masses and a thousand solar masses, situated in the macrolensing environment of a cluster, can introduce interference patterns in the waveform that are superimposed on the macrolens magnification. This produces oscillatory modulations in the frequency domain, with characteristic beat frequencies that depend on the Einstein radius of the microlens and the relative alignment. Numerical simulations show that such effects become appreciable when the microlens Einstein radius is comparable to the GW wavelength (i.e., when the lens mass is \\u2265 10 M\u2299 and the source is at z \\u2265 1). Detecting these patterns would require high signal\u2011to\u2011noise ratios and detailed waveform modeling that includes both macro and micro\u2011lens potentials."}, {"question": "Can a precise measurement of the time delay between multiple images of a lensed gravitational\u2011wave event be used to constrain cosmological parameters such as the Hubble constant?", "answer": "Yes, in principle the time delay between two images of a lensed GW event, combined with an accurate localization of the source and lens, can provide an independent measurement of the Hubble constant. The delay depends on the difference in the Fermat potential between the image positions and on the angular\u2011diameter distances, which are sensitive to H0. However, achieving the required precision demands multiple high\u2011signal\u2011to\u2011noise detections of the same source, robust lens modeling, and accurate determination of the lens mass distribution\u2014challenges that are still being addressed in current research."}, {"question": "What are the observational signatures that would distinguish a gravitational\u2011wave event lensed by a galaxy cluster from one lensed by a single galaxy?", "answer": "Galaxy\u2011cluster lensing typically produces longer time delays (weeks to months or even years) and larger magnification factors (up to 10\u2013100) than galaxy\u2011scale lenses, which usually have delays of minutes to days and magnifications of a few. Additionally, cluster lenses often generate multiple images with more complex morphologies, sometimes forming arcs or rings in electromagnetic counterparts. In gravitational waves, one would expect a series of repeated events over extended periods, potentially with varying SNRs reflecting the magnification gradient across the caustic. Precise identification requires long\u2011term monitoring and cross\u2011matching with electromagnetic surveys."}, {"question": "Is it possible to detect the effects of primordial black holes acting as microlenses on gravitational\u2011wave signals from binary black holes?", "answer": "We currently do not have evidence that primordial black holes serve as microlenses in gravitational\u2011wave observations. Detecting their influence would require observing characteristic interference patterns or frequency\u2011dependent magnification in the GW signal, but such signatures have not yet been observed. The lack of detection could be due to the limited sensitivity of existing detectors, the rarity of suitable alignments, or the absence of a significant population of primordial black holes in the relevant mass range. Further data from next\u2011generation detectors and more sophisticated analysis methods are needed to explore this possibility."}, {"question": "How does the presence of eccentric orbits influence the sensitivity of semicoherent searches for continuous gravitational waves from neutron stars in binary systems?", "answer": "Eccentricity introduces additional harmonic components and a more complex Doppler modulation, requiring denser template banks and reducing sensitivity compared to circular orbits. The exact degradation depends on the orbital parameters and the search coherence time."}, {"question": "What is the expected distribution of spin\u2011down rates for neutron stars in tight binary systems that would make them detectable by all\u2011sky searches in the 50\u2013300\u202fHz band?", "answer": "Detectable spin\u2011down rates are typically |\u02d9f| \u2272 10\u207b\u00b9\u2070\u202fHz\u202fs\u207b\u00b9 for data spans of months. Most known millisecond pulsars in binaries exhibit spin\u2011downs below this threshold, but the population of unknown systems is poorly constrained."}, {"question": "How does the use of GPU\u2011accelerated pipelines influence the computational cost scaling with increasing frequency band width in all\u2011sky continuous\u2011wave searches?", "answer": "GPU acceleration reduces the per\u2011template processing time by an order of magnitude, allowing the template bank to grow with frequency without a proportional increase in wall\u2011time. However, the overall cost still scales roughly with the number of frequency bins, so wider bands remain the limiting factor."}, {"question": "What are the current theoretical limits on the ellipticity of rapidly rotating neutron stars in low\u2011mass X\u2011ray binaries, and how do these limits compare to the sensitivity achieved by recent LIGO runs?", "answer": "I do not have that information. The paper focuses on the search methodology and sensitivity estimates, and does not discuss theoretical models of neutron\u2011star ellipticity or compare them with LIGO sensitivities."}, {"question": "Could a future third\u2011generation ground\u2011based interferometer improve the detection prospects for continuous waves from neutron stars in binary systems with orbital periods shorter than 3\u202fdays, and if so, by what factor?", "answer": "A third\u2011generation detector with ~10\u00d7 lower noise would improve strain sensitivity by roughly a factor of 10, potentially allowing detection of ellipticities an order of magnitude smaller. This would open the window to binaries with very short periods, but detailed simulations are required to quantify the exact factor."}, {"question": "How can the detection of monoenergetic 236\u202fMeV neutrinos produced by kaon decay at rest in the Sun be used to probe dark\u2011matter annihilation in the solar core?", "answer": "When weakly interacting dark matter particles are gravitationally captured by the Sun, they can annihilate into standard\u2011model particles. The hadronization of the annihilation products generates charged kaons that stop in the dense solar medium and decay to produce monoenergetic \\(\\nu_\\mu\\) at 236\u202fMeV. The flux of these neutrinos at Earth is directly proportional to the dark\u2011matter capture rate, which in turn depends on the dark\u2011matter\u2013nucleon scattering cross section and the dark\u2011matter mass. By measuring or setting limits on the 236\u202fMeV neutrino flux, one can infer the annihilation rate and thus constrain the scattering cross section for models where capture and annihilation are in equilibrium. This provides a complementary probe of dark matter that is sensitive to parameter space inaccessible to terrestrial direct\u2011detection experiments, especially for low\u2011mass or inelastic dark matter scenarios."}, {"question": "What are the key advantages of a liquid\u2011argon time\u2011projection chamber for identifying the direction of 236\u202fMeV neutrinos compared with water Cherenkov detectors?", "answer": "At the 236\u202fMeV energy scale, charged\u2011current interactions on argon frequently eject a single proton that is emitted preferentially in the forward direction relative to the incident neutrino. In a liquid\u2011argon TPC, the ionization track of this proton is fully reconstructed with high spatial resolution, allowing its momentum vector to be measured accurately. The accompanying muon track, although largely isotropic, can also be reconstructed. By combining the proton and muon kinematics and applying momentum conservation, one can infer the recoil of the residual nucleus and thereby reconstruct the incoming neutrino direction with an angular resolution of order a few degrees. In contrast, water Cherenkov detectors are unable to see the proton track and rely solely on the Cherenkov ring of the muon, which is far less directional at this energy. Thus, the LArTPC offers superior directional discrimination for monoenergetic solar neutrinos."}, {"question": "How does the annual motion of the Earth around the Sun affect the acceptance of a deep\u2011underground detector for 236\u202fMeV solar neutrinos, and what is its impact on the sensitivity?", "answer": "The Sun\u2019s apparent position in the sky changes over the year, causing the incoming neutrino direction to sweep through a range of zenith and azimuth angles relative to the detector coordinates. Since the reconstruction of the neutrino direction in a LArTPC relies on forward proton kinematics, the detector\u2019s effective acceptance depends on the alignment between the proton direction and the detector wire geometry. For angles where the proton track is nearly parallel to a wire plane, track reconstruction can be more difficult, reducing efficiency. Conversely, when the proton is orthogonal to the wire planes, reconstruction improves. By integrating over the full 12\u2011month cycle, one obtains an averaged acceptance that can be factored into the expected event rate. The impact on sensitivity is modest; typical variations are at the tens of percent level, but precise modeling is required to avoid systematic biases in the annual modulation of the signal."}, {"question": "What role do nuclear effects such as the spectral function and meson\u2011exchange currents play in determining the charged\u2011current quasi\u2011elastic cross section for 236\u202fMeV neutrinos on argon?", "answer": "The spectral function describes the momentum and removal energy distribution of nucleons inside the argon nucleus, providing a more realistic initial\u2011state model than the simple Fermi\u2011gas approximation. This influences the energy and angular distributions of the outgoing lepton and proton. Meson\u2011exchange currents (MEC) introduce two\u2011body interactions where the neutrino couples to a pair of nucleons, leading to multinucleon emission that can mimic single\u2011proton final states. At 236\u202fMeV, MEC contributes roughly 4\u202f% of the total cross section, while the dominant quasi\u2011elastic component is about 64\u202f%. Accurate inclusion of these effects is essential for predicting the rates of single\u2011track events and for evaluating backgrounds, as they alter both the kinematic selection efficiency and the energy reconstruction."}, {"question": "Could the electron neutrino charged\u2011current channel provide better sensitivity to 236\u202fMeV solar KDAR neutrinos than the muon channel, and what are the limitations of this approach?", "answer": "In principle, the electron channel offers several advantages: the atmospheric \\(\\nu_e\\) background flux is smaller, the charged\u2011current cross section for \\(\\nu_e\\) on argon is larger (because the outgoing electron is lighter), and oscillation effects in the Sun tend to increase the \\(\\nu_e\\) fraction of the KDAR flux. However, the paper does not provide an analysis of the electron channel. The main challenges are: (1) electron tracks at 236\u202fMeV are short and highly ionizing, making pattern\u2011recognition and track\u2011to\u2011vertex association more difficult than for muons; (2) electromagnetic showers overlap with the proton track, complicating particle identification and energy reconstruction; (3) the directionality inferred from the proton remains useful, but the electron\u2019s isotropic distribution reduces the potential for additional directional cuts. Consequently, while a dedicated study could show improved sensitivity, the necessary simulation of electron\u2011track reconstruction, calorimetry, and background modeling was beyond the scope of the present work."}, {"question": "How will the removal of the hardware L0 trigger and the implementation of an all-software trigger impact the online reconstruction latency for high-multiplicity events?", "answer": "The all-software trigger allows the full reconstruction of every 40\u00a0MHz bunch crossing, removing the coarse hardware selection that previously introduced latency. By exploiting GPU farms, the LHCb upgrade can process each event within roughly 1\u00a0ms, which is acceptable for the increased event size. However, detailed benchmarks are still required to confirm that this latency remains stable under the highest luminosities."}, {"question": "What are the expected improvements in impact\u2011parameter resolution for the upgraded VELO compared to the Run\u00a01\u20112 VELO, and how will that affect heavy\u2011flavour lifetime measurements?", "answer": "With the new 55\u202f\u00b5m pixel size and the reduced distance from the first hit to the interaction point (to 5.1\u202fmm), the VELO is projected to improve its impact\u2011parameter resolution by about 20\u201330\u202f%. This translates into a ~15\u202f% improvement in lifetime resolution for B and D mesons, enhancing the precision of CP\u2011violation and rare\u2011decay measurements."}, {"question": "How does the introduction of neutron shielding upstream of the calorimeter affect background rates in the SciFi Tracker, and what are the implications for signal efficiency?", "answer": "The borated polyethylene shielding reduces the 1\u202fMeV neutron\u2011equivalent fluence at the SiPMs by a factor of roughly 2\u20133. This lowers the dark\u2011noise rate of the SiPM arrays, preserving hit efficiency in the most irradiated regions and thus maintaining overall tracker performance at high luminosities."}, {"question": "What are the challenges in maintaining the mechanical stability of the new RF boxes at the reduced inner radius, and how might this influence beam\u2011induced vibrations?", "answer": "The 3.5\u202fmm inner radius increases mechanical stresses and makes the RF boxes more susceptible to beam\u2011induced vibrations. Mitigations include low\u2011secondary\u2011electron\u2011yield coatings and NEG layers to reduce impedance, but additional studies on vibration damping and long\u2011term mechanical stability are still underway."}, {"question": "What is the projected lifetime performance of the SciFi Tracker's SiPM arrays at the end of Run\u00a04, considering cumulative ionising dose and displacement damage?", "answer": "The paper does not provide a definitive answer to this; the long\u2011term effects of cumulative ionising dose and displacement damage beyond the planned 50\u00a0fb\u207b\u00b9 are still under investigation. Determining the SiPM performance at the end of Run\u00a04 will require additional operational data and detailed radiation\u2011damage studies that are not covered in the current document."}, {"question": "How does the uniformity of the electric field in a liquid\u2011argon TPC influence the spatial resolution of reconstructed tracks, and what level of field homogeneity is typically required for a 3.6\u202fm drift distance?", "answer": "A uniform electric field minimizes transverse diffusion and ensures that electrons drift along straight paths, directly improving the z\u2011coordinate (drift time) resolution. For a 3.6\u202fm drift at 500\u202fV/cm, field variations should be kept below a few hundred volts per meter (\u223c0.05\u202f% of the nominal field) to maintain sub\u2011millimeter drift\u2011time precision."}, {"question": "In what way does argon purity affect the electron lifetime, and how can this lifetime be monitored in real\u2011time during a long\u2011term experiment?", "answer": "Oxygen and water impurities capture drifting electrons, shortening the lifetime \u03c4. The lifetime can be inferred from a purity monitor that measures the ratio of collected to emitted charge over a known drift distance. A lifetime of >10\u202fms corresponds to impurity levels below \u223c10\u202fppt O\u2082\u2011equivalent."}, {"question": "What design modifications to the photon detection system could increase light\u2011collection efficiency without significantly increasing the detector\u2019s mass or complexity?", "answer": "Options include using larger area SiPMs with higher photon detection efficiency, implementing reflective coatings on the inside of the APA frame, optimizing the wavelength\u2011shifting material thickness, and arranging photon collectors in a denser, but still sparse, grid to reduce dead space while maintaining mechanical integrity."}, {"question": "What are the primary engineering challenges when scaling a single\u2011phase liquid\u2011argon TPC from the ProtoDUNE\u2011SP scale (\u223c0.8\u202fkt) to the 40\u202fkt far\u2011detector modules envisaged for DUNE?", "answer": "Key challenges include maintaining mechanical stability of large\u2011scale cryostats, ensuring uniform high\u2011voltage distribution over 3\u20134\u202fm drift gaps, handling cryogenic circulation and purification at unprecedented volumes, and designing readout electronics that can operate reliably in a high\u2011radiation, deep\u2011underground environment."}, {"question": "What is the optimal geometry and placement of photon detectors within the APA frame to maximize overall light collection while minimizing dead space, and how does this geometry scale with detector size?", "answer": "The paper does not provide a definitive answer to this optimization problem. Determining the optimal geometry would require detailed optical simulations combined with mechanical constraints and cost analyses, which were beyond the scope of the presented work and thus remain an open research question."}, {"question": "How do higher\u2011order multipole moments influence parameter estimation for asymmetric binary black hole mergers?", "answer": "Including sub\u2011dominant modes (e.g., \u2113=3,4) reduces systematic biases in mass, spin, and distance estimates for systems with large mass ratios or high inclination, as the waveform more accurately captures the true signal structure."}, {"question": "Can ringdown measurements distinguish between Kerr and non\u2011Kerr remnant black holes?", "answer": "Current ringdown analyses are consistent with Kerr predictions; deviations in the fundamental (220) and first overtone (221) mode frequencies are constrained to within a few percent, showing no statistically significant evidence for non\u2011Kerr remnants."}, {"question": "What are the present limits on Lorentz\u2011violating dispersion parameters derived from gravitational\u2011wave observations?", "answer": "The latest observations constrain the dimensionless dispersion coefficient |A\u03b1| to values below 10\u207b\u2074\u201310\u207b\u2076 (depending on \u03b1) at 90% credibility, tightening previous bounds by roughly a factor of two and indicating no measurable frequency\u2011dependent propagation delay."}, {"question": "How effective are null\u2011stream polarization tests in ruling out non\u2011tensorial gravitational\u2011wave polarizations?", "answer": "Null\u2011stream analyses with the current three\u2011detector network yield Bayes factors overwhelmingly consistent with tensorial (GR) polarizations; they provide no significant preference for pure vector or scalar polarizations, thereby supporting the GR prediction of two tensor modes."}, {"question": "What are the prospects for detecting post\u2011merger gravitational\u2011wave echoes in future observing runs?", "answer": "The agent does not have a definitive answer to this question. Detecting echoes depends on improved detector sensitivity, longer observing time, and refined template models, all of which are still under development. Consequently, the paper does not provide a prediction, and the information required to estimate future detection prospects is not yet available."}, {"question": "What are the dominant sources of systematic uncertainty when employing convolutional neural networks to separate track-like from shower-like energy deposits in liquid argon time projection chamber data?", "answer": "The main systematic sources are (i) space\u2011charge distortion of drift fields, which shifts hit positions and alters charge deposition patterns; (ii) detector\u2011specific electronics noise and baseline variations that can obscure small deposits; (iii) calibration uncertainties in the wire\u2011plane response and time\u2011to\u2011charge conversion; (iv) model bias due to limited training samples that may not cover the full range of interaction topologies; and (v) differences between simulation and data (e.g., hadronic interaction models) that affect the learned feature representations."}, {"question": "How might the performance of a hit\u2011level CNN classifier be improved for low\u2011energy (below 100\u202fMeV) electromagnetic showers in LArTPC detectors?", "answer": "Improvements can come from: (1) augmenting the training dataset with realistic low\u2011energy shower simulations and adding noise replicas; (2) incorporating physics\u2011motivated preprocessing such as drift\u2011time correction or space\u2011charge compensation; (3) using multi\u2011scale convolutional layers or dilated convolutions to capture both fine\u2011grained and global shower features; (4) applying transfer learning from high\u2011energy shower models and fine\u2011tuning on low\u2011energy data; and (5) integrating a secondary classifier that explicitly models the expected electron\u2011photon separation in thin LAr volumes."}, {"question": "In what ways can the identification of Michel electrons be leveraged to improve neutrino oscillation analyses in large liquid argon detectors?", "answer": "Michel electron tagging enables: (i) clean identification of stopping muons, which constrains the neutrino interaction vertex and energy reconstruction; (ii) charge\u2011sign discrimination between \\u03b1 and \\u03b2, since only \\u03b1\\u039b decays produce Michel electrons, aiding in separating neutrino from antineutrino interactions; (iii) validation of muon stopping rates and hence cross\u2011section measurements; and (iv) providing a calibration sample for low\u2011energy electromagnetic energy scale and resolution."}, {"question": "What are the computational trade\u2011offs between using a small patch\u2011based convolutional neural network versus a full\u2011image semantic segmentation approach for hit classification in LArTPC data?", "answer": "A patch\u2011based CNN has lower memory usage and faster inference on CPUs because each input is small (e.g., 48\u00d748 pixels) and can be processed independently; however, it may miss global context leading to higher misclassification near complex topologies. Full\u2011image semantic segmentation captures the entire event structure, improving contextual decisions but requires GPU resources, larger memory, and longer inference times, which may not be feasible on standard computing clusters used in large\u2011scale analyses."}, {"question": "How does the hit\u2011level classification performance of a CNN trained on surface prototype data translate to a deep underground neutrino detector with a much reduced cosmic\u2011ray background?", "answer": "I do not have empirical evidence to answer this precisely. The performance may change because the signal\u2011to\u2011noise ratio, background composition, and space\u2011charge conditions differ significantly underground. These differences could alter the statistical distribution of hit topologies the network has to learn, potentially requiring re\u2011training or domain adaptation techniques. Further dedicated studies with underground data are needed to quantify the impact."}] \ No newline at end of file diff --git a/data/papers/pairs.jsonl b/data/papers/pairs.jsonl new file mode 100644 index 0000000..bc51851 --- /dev/null +++ b/data/papers/pairs.jsonl @@ -0,0 +1,492 @@ +{"question": "Which theoretical technique can most effectively reduce the uncertainties in the Standard Model prediction for the branching fraction of the rare decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?", "answer": "The dominant theoretical uncertainties come from the hadronic inputs\u2014namely the decay constants and form factors\u2014appearing in the effective Hamiltonian for \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\). Progress in unquenched lattice QCD calculations, with finer lattice spacings and lighter sea quark masses, can significantly tighten the determination of the \\(B_s\\) decay constant \\(f_{B_s}\\). Modern techniques such as the use of improved actions (e.g., HISQ for light quarks and relativistic heavy\u2011quark actions for the \\(b\\) quark), combined with nonperturbative renormalization and the inclusion of isospin\u2011breaking and QED effects, are expected to reduce the current uncertainty (\\(\\sim 6\\%\\)) on the decay constant\u2014and thus on the branching\u2011fraction prediction\u2014to the sub\u2011percent level."} +{"question": "What qualitative change would a new heavy \\(Z'\\) boson that couples predominantly to third\u2011generation quarks produce in the branching fraction of \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\)?", "answer": "A heavy \\(Z'\\) that couples to \\(b \\to s\\) transitions would contribute to the effective Wilson coefficients \\(C_{10}\\) and possibly \\(C_S, C_P\\) in the low\u2011energy effective Hamiltonian. Depending on its mass and coupling strength, the interference with the Standard\u2011Model amplitude could either enhance or suppress the branching fraction. In many motivated \\(Z'\\) models, the amplitude adds constructively, leading to a visible increase in the \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) branching ratio, potentially by a factor of a few, while keeping the branching fraction of \\(B^0 \\rightarrow \\mu^+ \\mu^-\\) relatively unaffected because the flavour\u2011changing transition is suppressed when the \\(Z'\\) couples only to third\u2011generation quarks."} +{"question": "How does the lifetime difference between the heavy and light mass eigenstates of the \\(B_s^0\\) system influence the experimental determination of its dimuon branching fraction?", "answer": "The decay width difference \\(\\Delta\\Gamma_s = \\Gamma_L - \\Gamma_H\\) implies that the two mass eigenstates of the \\(B_s^0\\) have different lifetimes. Since the Standard Model predicts that only the heavy eigenstate can decay to \\(\\mu^+\\mu^-\\) (due to CP conservation), the observed decay time distribution is skewed toward the long\u2011lived state. In a detector with reconstruction efficiency that varies with decay time (e.g., due to displacement cuts on the vertex), an analysis that assumes a single average lifetime will introduce a bias. Correcting for this effect requires disentangling the lifetime dependence, typically by applying a weight derived from simulation assuming the Standard\u2011Model CP structure; this correction reduces the systematic uncertainty on the branching\u2011fraction measurement."} +{"question": "Why is the ratio \\(\\mathcal{B}(B^0 \\rightarrow \\mu^+ \\mu^-)/\\mathcal{B}(B_s^0 \\rightarrow \\mu^+ \\mu^-)\\) considered a powerful test of minimal flavour violation?", "answer": "In the framework of minimal flavour violation (MFV), all flavour\u2011changing neutral\u2011current processes are governed solely by the Cabibbo\u2013Kobayashi\u2013Maskawa (CKM) matrix, and new physics contributions respect the same flavour\u2011symmetry breaking pattern as the Standard Model. Consequently, the ratio of the branching fractions for \\(B^0\\) and \\(B_s^0\\) decays to dimuons is predicted to be exactly the same as in the Standard Model, namely \\(R_{\\rm MFV} \\approx 0.0295\\). Any significant departure from this value would signal the presence of new sources of flavour violation beyond the CKM structure. Therefore, precise experimental determinations of both branching fractions, and their ratio, are key to constraining or revealing non\u2011MFV new\u2011physics scenarios."} +{"question": "Is it currently possible to measure CP violation in the decay \\(B_s^0 \\rightarrow \\mu^+ \\mu^-\\) with the data sets used in the combined analysis of CMS and LHCb?", "answer": "No. The combined measurement reported in the paper provides a branching\u2011fraction determination but does not distinguish between \\(B_s^0\\) and \\(\\bar{B}_s^0\\) decays, i.e., it is an untagged analysis. Observing CP violation would require tagging the initial flavour of the \\(B_s^0\\) meson and measuring a time\u2011dependent asymmetry between decay rates of \\(B_s^0\\) and \\(\\bar{B}_s^0\\). Such an analysis demands larger data samples, sophisticated flavour\u2011tagging algorithms, and precise decay\u2011time resolution\u2014capabilities that are beyond the scope of the present dataset and analysis strategy. Hence the answer is unavailable within the current study."} +{"question": "How does the amount of inactive material in the inner detector affect the energy loss distribution for electrons traversing the tracker, and what implications does this have for the jet\u2010electron background rejection in the ATLAS invariant mass reconstruction?", "answer": "The larger the inactive material, the more bremsstrahlung photons are emitted by electrons, which reduces the measured electron energy and creates a tail in the energy loss distribution. This tail increases the probability that an energetic electron is mis\u2011measured as a low\u2011energy cluster, thereby increasing the background from jets that fake electrons. A careful mapping of the material budget is therefore essential: the global energy loss can be parameterised as \u27e8\u0394E\u27e9/E \u2243 0.02\u202fX\u2080 for a 10\u202fGeV electron, where X\u2080 is the radiation length traversed. An accurate simulation of this effect allows the design of more efficient electron\u2011jet discrimination algorithms that rely on the reconstructed transverse momentum balance and shower shape observables."} +{"question": "What is the expected impact of the three\u2011level pixel detector alignment tolerances on the impact parameter resolution for tracks originating from a displaced secondary vertex, such as those from B\u2011hadron decays?", "answer": "The pixel alignment tolerances (10\u202f\u00b5m in R\u2013\u03c6 and 115\u202f\u00b5m in z for the vertexing layer) translate into a systematic bias in the reconstructed track position of the order of 20\u201130\u202f\u00b5m. When propagating to a secondary vertex located a few millimetres from the primary interaction point, this bias adds in quadrature to the intrinsic multiple\u2011scattering term, reducing the transverse impact parameter resolution from the ideal 10\u202f\u00b5m to about 15\u201318\u202f\u00b5m for tracks with p\u209c \u2273 2\u202fGeV. This degradation slightly worsens the ability to separate B\u2011hadron decay vertices from the primary vertex, but the effect is still well below the requirement for efficient b\u2011tagging at the design luminosity."} +{"question": "How does the high\u2011level trigger (HLT) track reconstruction algorithm balance the demands of speed and precision in the presence of 50\u2013100\u202f% pile\u2011up events?", "answer": "The HLT employs a multi\u2011stage track reconstruction where a fast, coarse seeding phase (based on pixel and SCT hits only) provides a first approximation of the track parameters. This initial estimate is fed into a Kalman filter that iteratively refines the fit using full detector information, including TRT hits, but only for tracks whose quality scores lie above a tunable threshold. In simulation studies this approach achieves a track\u2011finding efficiency of >\u202f95\u202f% for |\u03b7|\u202f<\u202f2.5 and a fake\u2011rate of <\u202f1\u202f% even at 100\u202fpb\u207b\u00b9, while keeping the CPU time below 100\u202f\u00b5s per event. The dynamic adjustment of the iteration count based on the local hit density allows the algorithm to remain robust against pile\u2011up in the core of high\u2011energy jets."} +{"question": "What are the dominant systematic uncertainties affecting the measurement of the W\u2011boson mass using the lepton transverse momentum spectrum in ATLAS, and how can they be constrained with early LHC data?", "answer": "The measurement is limited mainly by the calibration of the electromagnetic calorimeter energy scale (\u2264\u202f0.5\u202f%), the lepton momentum scale in the inner detector (\u2264\u202f0.3\u202f% for \u03bc and \u2264\u202f0.1\u202f% for e at high p\u209c), and the knowledge of the parton distribution functions (\u2248\u202f2\u202f% uncertainty on the rapidity distribution of the W). These systematic effects can be constrained using high\u2011statistics control samples: Z\u2192\u2113\u207a\u2113\u207b decays provide an in\u2011situ calibration of the lepton energy/momentum scales with a precision better than 0.05\u202f% for lepton p\u209c\u202f>\u202f30\u202fGeV, while the ratio of W to Z production cross sections can be used to mitigate PDF uncertainties. Performing a simultaneous fit to the W and Z transverse mass spectra further reduces the impact of common systematics."} +{"question": "How does the viewing angle of a short gamma-ray burst jet influence the expected flux of high-energy neutrinos detectable on Earth?", "answer": "A larger viewing angle reduces the Doppler boosting and beaming of particles accelerated in the jet, leading to a steep decline in the neutrino flux arriving at Earth. The flux scales roughly with the Doppler factor to the fourth power for internal shock models, so an off-axis observer can see neutrinos at a level that is orders of magnitude lower than an on-axis observer."} +{"question": "Which hadronic processes are considered to produce high-energy neutrinos in the internal shocks of short GRBs?", "answer": "The dominant mechanism is photohadronic (p\u03b3) interaction, where relativistic protons accelerated in internal shocks collide with prompt gamma-ray photons, producing charged pions that decay into neutrinos. In addition, proton-proton (pp) interactions in dense baryonic outflows can contribute, though the optical depth for pp is usually low in short GRB jets."} +{"question": "What strategies do neutrino observatories use to discriminate down\u2011going neutrino events when the source lies above the detector\u2019s horizon?", "answer": "Detectors such as ANTARES and IceCube employ stringent cuts on reconstructed direction, energy, and event topology. They use tight angular uncertainty requirements, require a high-energy deposition inconsistent with atmospheric muons, and apply machine\u2011learning classifiers trained on simulated neutrino and muon events. By temporally correlating with a known source location, the background probability is further reduced."} +{"question": "If a cocoon forms around the jet of a binary neutron star merger, how would this affect the expected neutrino emission compared to a narrow jet?", "answer": "A cocoon expands more slowly and over a wider solid angle, potentially producing neutrinos through shock\u2013accelerated protons interacting with surrounding ejecta. Because the cocoon is less collimated, the neutrino flux received by an observer is spread over a larger area, but the efficiency can be higher if the cocoon\u2019s optical depth to neutrinos is large. However, the lower Lorentz factor reduces the maximum neutrino energy compared to the narrow jet."} +{"question": "What would be the expected neutrino flux from a binary neutron star merger located at 200\u202fMpc, assuming the same intrinsic properties as GW\u202f170817?", "answer": "The current paper does not provide predictions for such a distance, so we cannot quote a definitive flux. Estimating the flux would require scaling the intrinsic neutrino luminosity by the inverse square of the distance (i.e., reducing it by a factor of about 16 relative to 40\u202fMpc). Detailed modeling would also need to account for cosmological redshift effects on the neutrino energy spectrum, which is beyond the scope of the current analysis."} +{"question": "How does including Virgo and KAGRA in the fourth observing run influence the sky\u2011localisation accuracy for heavy binary black\u2011hole mergers compared with the first two observing runs?", "answer": "Detectors that are further apart in latitude and longitude increase the baseline for triangulation. The addition of Virgo (\u22481600\u202fkm from LIGO sites) and KAGRA (\u224811,000\u202fkm from LIGO) reduces the median 90\u202f% credible sky area for high\u2011mass mergers (\u2265\u202f30\u202fM\u2299) from roughly 20\u202fdeg\u00b2 in O1/O2 to about 5\u201310\u202fdeg\u00b2 in O4, mainly because the extra detectors break degeneracies between source position and antenna pattern."} +{"question": "What advantage does frequency\u2011dependent squeezed vacuum provide to the LIGO detectors below 50\u202fHz, and how might this improve detections of neutron\u2011star\u2013black\u2011hole binaries?", "answer": "Frequency\u2011dependent squeezing suppresses shot noise at high frequencies while reducing radiation\u2011pressure noise at low frequencies. The improvement below 50\u202fHz increases the signal\u2011to\u2011noise ratio for signals that extend into this band, such as the early inspiral of neutron\u2011star\u2013black\u2011hole binaries, yielding a higher detection horizon and better estimates of the inclination angle."} +{"question": "How does the measured distribution of the effective inspiral spin parameter (\u03c7\u2091\u2093\u2091ff) in GWTC\u20114.0 limit spin\u2013alignment scenarios for stellar\u2011mass black\u2011hole binaries?", "answer": "The observed concentration of \u03c7\u2091\u2093\u2091ff values near zero indicates that most black\u2011hole spins are either misaligned or have small magnitudes, suggesting formation through dynamical capture or supernova kicks that break alignment. A tail of positive \u03c7\u2091\u2093\u2091ff points to some binaries with partially aligned spins, consistent with isolated binary evolution where tidal alignment persisted."} +{"question": "Can the GWTC\u20114.0 data alone distinguish an intermediate\u2011mass black\u2011hole merger (\u223c100\u20131000\u202fM\u2299) from a supermassive\u2011black\u2011hole merger through gravitational\u2011wave signatures?", "answer": "The current GWTC\u20114.0 catalogue does not include any confirmed detections in the frequency band where supermassive\u2011black\u2011hole mergers would be observed with ground\u2011based detectors. Consequently, distinguishing an intermediate\u2011mass from a supermassive merger using only the present data is not possible; additional high\u2011frequency sensitivity or space\u2011based observations would be required."} +{"question": "What are the most recent statistical constraints on the Hubble constant obtained from GWTC\u20114.0\u2019s \u201cdark\u2011siren\u201d cosmology analysis using galaxy\u2011catalog cross\u2011correlation?", "answer": "The dark\u2011siren analysis of GWTC\u20114.0 yields a Hubble constant of H\u2080\u202f\u2248\u202f70\u202f\u00b1\u202f10\u202fkm\u202fs\u207b\u00b9\u202fMpc\u207b\u00b9 (68\u202f% credible interval), consistent with both the value inferred from the cosmic microwave background and that obtained from the standard\u2011sirens with electromagnetic counterparts, albeit with larger uncertainty due to the limited number of high\u2011volume events."} +{"question": "What is the relationship between the coherence length of an ultralight vector dark matter field and its mass?", "answer": "The coherence length \\(L_{\\text{coh}}\\) of a non\u2011relativistic dark\u2011matter field is inversely proportional to its mass: \\(L_{\\text{coh}}\\sim 2\\pi\\hbar/(mA\\,\\bar v)\\) where \\(\\bar v\\) is the velocity dispersion. For a typical halo velocity \\(\\bar v\\sim10^{-3}c\\), a field mass of \\(10^{-13}\\,\\text{eV}/c^{2}\\) corresponds to a coherence length of order \\(10^{7}\\,\\text{km}\\). Thus, as the mass decreases, the coherence length grows linearly."} +{"question": "Why does using auxiliary length channels in a laser interferometer improve sensitivity to ultralight vector dark matter compared to the main differential arm length channel?", "answer": "Auxiliary length channels (e.g., the Michelson differential length \\( \\text{MICH} \\) and the power\u2011recycling cavity length \\( \\text{PRCL} \\)) involve mirrors made from different materials (sapphire test masses versus fused\u2011silica auxiliary mirrors). Because the ultralight vector field couples to the charge\u2011to\u2011mass ratio of the test masses, the response of different mirrors differs, producing a differential signal that is larger than that in the main channel where the mirrors are usually identical. This material\u2011composition asymmetry amplifies the displacement induced by the field and therefore enhances the detectable strain."} +{"question": "What are the principal difficulties in separating a genuine ultralight dark\u2011matter signal from transient detector noise in GW strain data?", "answer": "True DM signals are expected to be narrow\u2011band, persistent over long times, and statistically Gaussian in amplitude due to the central limit theorem. Transient detector artifacts, however, are often broadband, short\u2011lived, and exhibit non\u2011Gaussian statistics. Distinguishing them requires (i) characterising the expected DM bandwidth and coherence time, (ii) checking the persistence of a signal across independent data epochs, and (iii) vetoing known instrumental lines by cross\u2011correlation with auxiliary sensors or by comparing the signal\u2019s spectral shape to that predicted for DM."} +{"question": "What future improvements to the KAGRA detector could make it more competitive in probing ultralight vector dark matter?", "answer": "Potential upgrades include: (1) reducing the low\u2011frequency noise in the auxiliary channels by implementing advanced vibration isolation and seismic suppression; (2) increasing the laser power and improving mirror coatings to lower the thermal and shot noise; (3) deploying cryogenic temperature control for all mirrors to match the sapphire test masses across the interferometer; (4) extending the observation run length so that more data segments exceed the DM coherence time; and (5) adding dedicated sensors to monitor and subtract known noise lines from the auxiliary channels."} +{"question": "What would be the effect on the derived constraints if the ultralight vector dark matter field had a preferred polarization direction rather than being isotropically distributed?", "answer": "I do not have enough information to answer this question conclusively. The paper assumes an isotropic velocity and polarization distribution when modeling the signal covariance. A non\u2011isotropic polarization would change the statistical properties of the induced length variations, potentially altering the expected strain spectrum and the detection statistic. Determining the precise impact requires a dedicated theoretical study of polarized vector dark matter and its coupling to interferometer mirrors, which is not covered in the present analysis."} +{"question": "How does the rotation rate of a progenitor star influence the amplitude and frequency spectrum of gravitational waves emitted during a core\u2011collapse supernova?", "answer": "Rotation tends to destabilise the proto\u2011neutron star, giving rise to non\u2011axisymmetric modes such as bar\u2011mode or spiral instabilities. Faster rotation yields a higher degree of ellipticity and can shift the dominant GW frequency to lower values (tens to a few hundred hertz) while increasing the wave strength by orders of magnitude. The total radiated GW energy can rise from \u224810\u207b\u2076\u202fM\u2299\u202fc\u00b2 in slowly rotating models to \u224810\u207b\u2074\u201310\u207b\u00b3\u202fM\u2299\u202fc\u00b2 for rapidly rotating cores."} +{"question": "What are the main sources of statistical uncertainty when setting upper limits on gravitational\u2011wave energy from a core\u2011collapse supernova detected by the LIGO\u2013Virgo\u2013KAGRA network?", "answer": "The dominant uncertainties stem from (1) strain calibration, typically 2\u20133\u202f% across the instrument band; (2) non\u2010Gaussian detector noise, especially short glitches that can mimic transients and inflate background estimates; (3) modelling assumptions, such as the choice of waveform family, source orientation, and ellipticity; and (4) the definition of the on\u2011source window, which determines how much coincident data are available. Together these contribute systematic errors on the strain sensitivity and thus on the inferred energy limits."} +{"question": "How might strong magnetic fields in the nascent proto\u2011neutron star alter the expected gravitational\u2011wave signal compared to magnetically quiet core\u2011collapse scenarios?", "answer": "Intense magnetic fields can drive a magnetorotational explosion, launching bipolar jets that increase asymmetry. This can generate higher\u2011frequency (\u22481\u20133\u202fkHz) GW components with larger amplitudes and potentially longer durations than the \u2248100\u202fHz bar\u2011mode bursts seen in weak\u2011field models. The field geometry also influences the ellipticity evolution and can sustain non\u2011axisymmetric instabilities beyond the few\u2013hundred\u2011millisecond timescale typical of neutrino\u2011driven explosions."} +{"question": "What time delay between the neutrino burst and the peak gravitational\u2011wave emission is generally expected in core\u2011collapse supernovae, and how does this affect on\u2011source window construction?", "answer": "The neutrino burst is emitted almost simultaneously with core bounce, within milliseconds. Gravitational waves can start at the bounce and continue for tens of milliseconds as prompt convection and SASI develop; later, bar\u2011mode or magnetorotational instabilities can produce emission lasting up to a second. Consequently, effective on\u2011source windows that encompass a few seconds around the neutrino trigger are recommended to capture both prompt and late\u2011time signals."} +{"question": "How do the latest upper limits on neutron\u2013star ellipticity from continuous\u2011gravitational\u2011wave searches constrain the strength of internal magnetic fields in millisecond pulsars?", "answer": "The ellipticity (\u03b5) limits set by non\u2011detections translate into an upper bound on the quadrupole deformation induced by strong internal magnetic fields. For a simple model where the magnetic energy dominates the deformation, \u03b5 \u2243 (B_int\u202f/\u202f10^16\u202fG)^2\u202f\u00d7\u202f10^\u22126. Using the most stringent \u03b5 limits from recent searches (\u2248\u202f10^\u22129 for the bright nearby millisecond pulsar J0437\u22124715), the inferred maximum internal field is \u2272\u202f10^15\u202fG \u2013 well below the dipole surface fields (~10^8\u201310^9\u202fG). This suggests that millisecond pulsars cannot harbor extremely strong toroidal fields that would otherwise produce noticeable gravitational\u2011wave emission. The exact relationship depends on the equation of state and the geometry of the field, and more sophisticated magnetohydrodynamic modelling is required for accurate limits.", "unanswered": false} +{"question": "What impact does the Shklovskii effect have on the interpretation of spin\u2011down limits in continuous\u2011gravitational\u2011wave pulsar searches?", "answer": "The Shklovskii effect arises when the proper motion of a pulsar adds a kinematic contribution to its measured period derivative: \\( \\dot{P}_{\\text{Shk}} = (P\\,v_{\\perp}^2)/(c\\,D) \\). This extra term inflates the observed spin\u2011down rate and thus the inferred spin\u2011down energy loss rate. For continuous\u2011GW searches the spin\u2011down limit \\(h_{\\text{sd}} \\propto \\sqrt{|\\dot{f}_{\\text{rot}}|/f_{\\text{rot}}}\\) is then over\u2011estimated if the Shklovskii correction is not applied. Properly subtracting \\(\\dot{f}_{\\text{Shk}}\\) yields a lower intrinsic spin\u2011down, which tightens the spin\u2011down limit and means that a true GW amplitude approaching the limit would be less likely. The effect is most significant for nearby, high\u2011proper\u2011motion millisecond pulsars.", "unanswered": false} +{"question": "What are the main technical challenges in extending persistent\u2011wave searches to eccentric binary pulsars?", "answer": "Eccentric binaries introduce additional orbital modulations in the gravitational\u2011wave phase, requiring knowledge of the orbital elements (eccentricity, periastron advance, etc.) and a high\u2011order orbital model. The main challenges include: 1) the need for densely sampled, high\u2011precision timing solutions to track the periastron motion and secular variations; 2) increased parameter space dimensionality (eccentricity, argument of periastron, orbital period derivatives) leading to higher computational cost; and 3) the risk of mismodeling orbital dynamics, which can de\u2011phase the coherent integration and degrade sensitivity. Recent advances in joint timing and GW modelling, as well as the use of coherent matched\u2011filter pipelines that can include time\u2011dependent orbital phase terms, are helping to mitigate these difficulties.", "unanswered": false} +{"question": "How will the planned upgrades to Advanced LIGO, Virgo, and KAGRA influence the sensitivity of continuous\u2011gravitational\u2011wave searches in future observing runs?", "answer": "The upgrades\u2014such as increased laser power, improved quantum\u2011noise reduction via squeezed light, cryogenic mirrors for Virgo, and higher seismic isolation for KAGRA\u2014will lower the detector noise floor by factors of 1.5\u20132 in the 10\u20131000\u202fHz band relevant for pulsar GW emission. This translates to a depth improvement of ~30\u201350\u202f%, allowing continuous\u2011GW searches to probe strain amplitudes down to \u2248\u202f10^\u201127\u201310^\u201126 for the most promising nearby pulsars. Moreover, the longer continuous observing periods expected (\u2248\u202f1\u202fyr per run) will further increase the coherent integration time, improving sensitivity roughly as the square root of the observation time. Combined, these changes will tighten ellipticity limits by an order of magnitude for many targets.", "unanswered": false} +{"question": "What can the recent upper limits on dipole radiation from Brans\u2013Dicke theory tell us about the viability of scalar\u2011tensor gravity models?", "answer": "The non\u2011detection of dipole gravitational radiation at the level of h_d\u202f\u2248\u202f10^\u201127\u201310^\u201126 for pulsars with strong orbital accelerations sets a lower bound on the Brans\u2013Dicke coupling parameter \u03c9_BD \u2273\u202f10^4\u201310^5. This is roughly an order of magnitude improvement over the best Solar\u2013System constraints derived from the Viking landers and Cassini ranging experiments. While scalar\u2011tensor models with very weak coupling remain allowed, the results considerably restrict parameter space where dipole radiation could contribute significantly to orbital decay, supporting the robustness of General Relativity as the dominant interaction in the strong\u2011field regime.", "unanswered": false} +{"question": "What is the prevalence of black holes in the pair\u2011instability supernova mass gap (roughly 45\u2013120\u202fM\u2299) in the local universe, and does the current gravitational\u2011wave catalog provide evidence for a statistically significant dearth in that range?", "answer": "Current population studies show a steep decline in the merger rate above about 40\u201345\u202fM\u2299, yet the number of observed events with primary masses above 70\u202fM\u2299 is small. Some detections near the putative gap boundary (~70\u202fM\u2299) are compatible with a smooth continuation of the mass distribution, rather than an empty gap. Consequently, while there is evidence for a reduced rate, a decisive confirmation of a completely empty pair\u2011instability gap cannot be drawn from the existing catalog."} +{"question": "How does the effective inspiral spin distribution (\u03c7_eff) vary with redshift, and what might this tell us about the formation pathways of binary black holes?", "answer": "Analyses of the most recent catalog hint that the width of the \u03c7_eff distribution broadens as redshift increases, whereas its mean stays near zero. This broadening could reflect a growing contribution from dynamically assembled binaries or hierarchical mergers at earlier epochs. However, given the limited number of high\u2011redshift detections, the trend is still marginal and could be influenced by selection effects, so a definitive conclusion about redshift dependence of \u03c7_eff remains tentative."} +{"question": "What is the relative mass\u2011ratio distribution of binary black holes near the ~10\u202fM\u2299 and ~35\u202fM\u2299 mass peaks, and does it imply different evolutionary pathways?", "answer": "Binaries with primary masses around 10\u202fM\u2299 tend to merge with significantly less massive companions (mass\u2011ratio peak near q\u202f\u2248\u202f0.7), while those near the 35\u202fM\u2299 peak usually have more equal masses (q\u202f\u2248\u202f0.9\u20131.0). These features are compatible with theoretical expectations: the lower\u2011mass peak may arise from stable mass\u2011transfer episodes in isolated binaries, whereas the higher\u2011mass equal\u2011mass systems could be produced in dense stellar clusters or through hierarchical mergers. Nonetheless, the overlap between the two distributions remains substantial, and additional observations are needed to solidify the link between observed ratios and specific formation channels."} +{"question": "Is there evidence for a lower\u2011mass gap between the heaviest neutron stars and the lightest black holes (\u223c3\u20135\u202fM\u2299) in the observed merger population?", "answer": "The current gravitational\u2011wave data show compact objects clustering around neutron\u2011star masses near 1.3\u20131.4\u202fM\u2299 and black\u2011hole masses beginning around 5\u20136\u202fM\u2299, with only a handful of events land in the 3\u20135\u202fM\u2299 interval. Statistically, the distribution is consistent with a continuous decline rather than a sharply empty region. Thus, while the existence of a pronounced lower\u2011mass gap remains an open question, the catalog does not provide sufficient evidence to confirm its presence."} +{"question": "Does the observed population of binary black holes exhibit a correlation between component spin magnitudes and the component masses, such that more massive black holes spin faster?", "answer": "The data available so far do not unambiguously support such a correlation. Although some earlier studies suggested a weak trend of increasing spin amplitudes with mass, the latest catalog shows considerable overlap between mass and spin posterior distributions, with large uncertainties in both quantities. Current posterior constraints are consistent with both no correlation and modest positive correlations within the error bounds. Therefore, this question remains unanswered; a larger, less biased sample and more precise spin measurements are needed to resolve whether a spin\u2013mass trend exists."} +{"question": "What physical mechanisms are thought to generate gravitational waves simultaneously with fast radio bursts from magnetars, and how do their predicted gravitational-wave energy outputs compare?", "answer": "The most frequently discussed mechanisms involve sudden re\u2011configurations of the neutron\u2011star interior: a starquake or a global crustal failure can excite the star\u2019s f\u2011mode at \u223c2\u202fkHz, radiating \\(E_{\\rm GW}\\sim10^{48\\text{\u2013}10^{49}\\,{\\rm erg}\\) if the quake involves a large crustal distortion. Magneto\u2011elastic coupling between the star\u2019s magnetic field and shear oscillations can also trigger quasi\u2011periodic oscillations in the X\u2011ray tail of a flare; these oscillations source GW emission at a few hundred to a few thousand hertz with energies \\(10^{41\\text{\u2013}10^{45}\\,{\\rm erg}\\). A third possibility is that the rapid spin\u2011up associated with a glitch injects free precession power, potentially yielding \\(10^{44\\text{\u2013}10^{48}\\,{\\rm erg}\\) in a short burst. All of these scenarios predict waveforms that are broad in frequency but typically last less than a second, making them amenable to the short\u2011duration burst searches used in recent LIGO/Virgo/KAGRA studies."} +{"question": "In what way does the distance estimate for SGR\u202f1935+2154 influence the derived upper limits on gravitational\u2011wave energy for FRBs observed from it?", "answer": "The gravitational\u2011wave energy inferred from an upper limit on strain scales with the square of the source distance (\\(E_{\\rm GW}\\propto D^{2}\\)). The canonical value of \\(6.6\\pm0.7\\)\u202fkpc is roughly a factor of two larger than the lower bound (\u22485\u202fkpc) and a factor of three smaller than the most distant estimates (\u224815\u202fkpc). If the true distance were 1.5\u202fkpc as suggested by some HI\u2011absorption studies, the energy constraint would tighten by about a factor of 20; if it were 15\u202fkpc, the limits would loosen by roughly a factor of five. Consequently, the 90\u202f% upper limits of \\(10^{48.5}\\)\u202ferg at 300\u202fHz and \\(10^{50}\\)\u202ferg at 2\u202fkHz could become respectively \\(5\\times10^{47}\\)\u2013\\(5\\times10^{49}\\)\u202ferg depending on the true distance."} +{"question": "What are the principal obstacles to detecting short\u2011duration gravitational\u2011wave bursts associated with FRBs when only a single observatory (such as GEO600) is operational, and how can a network of detectors mitigate these issues?", "answer": "With a single detector, the dominant challenges are: (1) the inability to use coincidence timing to veto terrestrial glitches, (2) a limited ability to estimate the false\u2011alarm rate because the background must be drawn from the same time segment, and (3) reduced signal\u2011to\u2011noise since no cross\u2011correlation can be performed between independent noise realizations. These factors increase the likelihood of spurious candidates and raise the detection threshold. A multi\u2011detector network provides independent noise streams so that a genuine astrophysical signal will appear in all observatories with a consistent time\u2011delay, allowing robust vetoes of local glitches. Moreover, the coherent combination of data boosts the signal\u2011to\u2011noise ratio roughly by \\(\\sqrt{N}\\) (with \\(N\\) detectors), enabling the detection of weaker bursts or tighter upper limits."} +{"question": "Could observations of gravitational waves help distinguish between competing progenitor models for extragalactic fast radio bursts, and what specific gravitational\u2011wave signatures would be most decisive?", "answer": "Yes. Different progenitor hypotheses predict distinct gravitational\u2011wave morphologies and energetics. A binary\u2011neutron\u2011star merger would produce a short (\\(<1\\)\u202fs) chirp signal with a characteristic inspiral\u2011merger\u2011ringdown waveform and \\(E_{\\rm GW}\\sim10^{53}\\)\u202ferg, whereas a single magnetar flare with a starquake would produce a short, possibly broadband burst at a few hundred to several thousand hertz with much lower energy (\\(10^{41\\text{\u2013}10^{49}\\)\u202ferg). Detecting a merger\u2011style chirp coincident with an FRB would strongly support a binary origin; conversely, a null result in such a search coupled with a detection of a broadband short burst would favor a magnetar or other single\u2011object model. The presence of a long\u2011duration quasi\u2011periodic oscillation in the GW spectrum would further point toward magnetospheric or crustal modes."} +{"question": "Is there observational evidence that X\u2011ray glitches in magnetars are temporally correlated with subsequent fast radio burst activity, and what would such a correlation imply about FRB production mechanisms?", "answer": "Current observations do not provide definitive evidence of a correlation between X\u2011ray glitches and FRBs. The paper reports on three X\u2011ray glitches around 2022\u202fOct\u202f14 but finds no associated FRBs within the limited duty cycle and sensitivity of the radio observatories at that time. Moreover, previous studies have seen both FRBs with and without simultaneous X\u2011ray bursts from SGR\u202f1935+2154, indicating that the two phenomena can be independent. A robust temporal correlation would suggest that the sudden change in the magnetospheric or interior structure that causes a glitch also triggers the coherent radio emission, supporting models where FRBs are powered by internal magnetic field re\u2011configuration. Until such a correlation is established with high\u2011cadence, simultaneous multi\u2011wavelength monitoring, this question remains open."} +{"question": "What are the most plausible astrophysical pathways that can produce compact objects in the lower mass gap (roughly 3\u20135\u202fM\u2299) which are subsequently detected as neutron\u2011star\u2013black\u2011hole binaries by gravitational\u2011wave observatories?", "answer": "Astrophysical models point to a handful of scenarios: (1) core\u2011collapse supernovae with substantial fallback of material onto a nascent neutron star can raise the remnant mass into the lower mass gap; (2) early\u2011stage binary evolution with mass transfer followed by delayed collapse of a massive helium star can also produce low\u2011mass black holes; (3) binary neutron\u2011star mergers that leave a hyper\u2011massive remnant could collapse to a black hole of a few solar masses. None of these mechanisms is yet confirmed as dominant, and the relative contribution of each pathway remains a subject of active research."} +{"question": "In a neutron\u2011star\u2013black\u2011hole binary, how does a misalignment between the neutron star spin and the orbital angular momentum affect the gravitational\u2011wave phase evolution and the likelihood of detecting the event with matched\u2013filter searches?", "answer": "Spin\u2013orbit coupling introduces additional phasing terms that depend on the tilt angle. A significant tilt can lead to precession of the orbital plane, modulating the amplitude and phase of the waveform in a way that is partially degenerate with mass parameters. While matched\u2011filter pipelines can accommodate precessing templates, the reduced match for highly tilted systems can lower the recovered signal\u2011to\u2011noise ratio, potentially making such events harder to detect or to characterize accurately."} +{"question": "Which electromagnetic counterparts are most commonly expected from symmetric\u2011mass neutron\u2011star\u2013black\u2011hole mergers, and how can current multi\u2011messenger follow\u2011up strategies maximize the probability of identifying them?", "answer": "Symmetric\u2011mass mergers (with mass ratio close to unity) are more likely to tidally disrupt the neutron star before it plunges into the black hole. This can leave behind a remnant accretion disk and unbound ejecta, creating a kilonova with blue and red components, and possibly launching a short gamma\u2011ray burst. Rapid, wide\u2011field optical and infrared surveys, coordinated with high\u2011energy satellites, are essential to capture the early, rapidly fading signals; however, localisation uncertainties from single\u2011detector detections limit the efficiency of current follow\u2011ups."} +{"question": "How has the estimated merger rate of neutron\u2011star\u2013black\u2011hole binaries changed from the third to the fourth observational runs of ground\u2011based gravitational\u2011wave detectors, and what implication does this have for population synthesis models?", "answer": "The rate has increased from roughly 20\u201350\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 during O3 to about 70\u2013100\u202fGpc\u207b\u00b3\u202fyr\u207b\u00b9 in early O4, though uncertainties remain large. This upward trend suggests either that our sensitivity has improved or that the underlying population of neutron\u2011star\u2013black\u2011hole binaries is larger than previously thought, challenging models that placed a strong lower mass gap and predict fewer such systems."} +{"question": "What does the current population of neutron\u2011star\u2013black\u2011hole detections tell us about the distribution of the inclination angle (\u03b8_JN) between the total angular momentum and the line\u2011of\u2011sight, and how does this affect the ability to localise sources on the sky?", "answer": "We do not know the distribution of inclination angles for the present sample. Many detected events come from single\u2011detector observations, which provide almost no constraint on \u03b8_JN, leading to large degeneracies with distance and severely limiting sky localisation. A more complete sample\u2014with detections in at least two detectors\u2014would be required to map out the inclination distribution and improve localisation accuracy."} +{"question": "How does a minimally modeled search such as coherent WaveBurst (cWB) compare to template\u2011based matched\u2011filter searches in detecting eccentric binary black\u2011hole mergers, in terms of sensitivity and false\u2011alarm rates?", "answer": "Minimally modeled searches like cWB are robust against waveform systematics and can recover signals that deviate from binary\u2011black\u2011hole templates, including highly eccentric or precessing systems. For eccentricities below ~0.3, cWB retains roughly 70\u201380\u202f% of the SNR of a matched\u2011filter search that uses circular templates. Its background is typically higher, leading to larger false\u2011alarm rates for a given detection statistic. Template\u2011based searches lose sensitivity at high eccentricity because the phase evolution differs substantially from the templates; however, they can still recover eccentric signals if the templates include eccentricity descriptions or higher\u2011order modes. A definitive comparison requires large injection campaigns across the full eccentric\u2011parameter space."} +{"question": "Can the mass distribution of high\u2011mass eccentric black\u2011hole mergers provide evidence distinguishing between dense\u2011star\u2011cluster formation channels and accretion\u2011disk (AGN) environments?", "answer": "Theoretical models predict that binaries formed in dense stellar clusters should peak at lower total masses with a broader mass ratio distribution, whereas AGN\u2011disk capture processes can produce more massive, nearly equal\u2011mass binaries with higher eccentricities. However, observationally separating these channels requires accurately measuring both mass and eccentricity for a statistically large sample. Presently, the sample size of confirmed eccentric mergers is too small, and mass\u2013eccentricity degeneracies in the waveforms make it difficult to attribute individual events to a specific channel."} +{"question": "What effect do higher\u2011order gravitational\u2011wave modes have on the detection and parameter estimation of eccentric binary black\u2011hole mergers, particularly for high total masses?", "answer": "Higher\u2011order modes become more prominent in binaries with large mass ratios, high total mass, and when the orbital plane is inclined. In eccentric orbits, the mode content varies rapidly, potentially boosting the SNR for some modes while suppressing others. Including higher\u2011order modes in waveform models improves the match to the true signal, enhancing both detection efficiency and parameter recovery. Yet many current eccentric waveform approximants either omit or poorly resolve these modes, limiting the achievable accuracy for high\u2011mass systems."} +{"question": "What are the dominant challenges in reliably extracting the orbital eccentricity of an individual detected binary black\u2011hole merger using current gravitational\u2011wave data?", "answer": "The primary obstacles are: (1) waveform model uncertainty, as existing eccentric models are sparse in spin and mass\u2011ratio coverage; (2) strong degeneracies between eccentricity and spin\u2011precession or higher\u2011order modes; (3) limited signal\u2011to\u2011noise ratio for most events, which hampers precision in measuring subtle deviations from circularity; and (4) non\u2011Gaussian noise artifacts that can mimic or obscure eccentric signatures. Due to these factors, the confidence in eccentricity measurements for individual events remains low with current data."} +{"question": "How could a first\u2011order phase transition during the electroweak epoch generate a detectable stochastic gravitational\u2011wave background?", "answer": "A first\u2011order phase transition proceeds via nucleation of bubbles of the true vacuum that expand, collide, and convert vacuum energy into kinetic motion of the plasma and magnetic fields. Sound waves in the plasma and bubble collision turbulence source gravitational waves with a characteristic peak frequency set by the phase\u2011transition temperature and duration. The amplitude is controlled by the strength parameter \\(\\alpha\\) (energy density released relative to radiation) and the inverse duration \\(\\beta/H\\). For transitions that occur at temperatures \\(\\mathcal{O}(100~\\text{GeV})\\), the peak frequency falls in the tens to hundreds of hertz band, which is accessible to ground\u2011based detectors, making such a background potentially detectable if \\(\\alpha\\) is large enough and \\(\\beta/H\\) is not too high."} +{"question": "What role do cosmic strings play in shaping the spectrum of a stochastic gravitational\u2011wave background across different frequency bands?", "answer": "Cosmic strings, one\u2011dimensional topological defects, form a network of long strings and loops. Loops oscillate and repeatedly emit bursts of gravitational waves, primarily from cusps, kinks, and kink\u2011kink collisions. The superposition of many such bursts produces a stochastic background that is approximately a power\u2011law \\(\\Omega_{\\text{GW}}(f)\\propto f^{\\alpha}\\). The spectral index \\(\\alpha\\) depends on the dominant source: cusps yield \\(f^{-1/3}\\) after integration, while kinks give a steeper slope. At high frequencies (kHz) the spectrum may steepen due to the finite loop lifetime, whereas at low frequencies (mHz) the long\u2011string contribution becomes more important, potentially producing a scale\u2011dependent feature that could be observable with space\u2011based detectors."} +{"question": "How can a stiff equation of state in the early Universe influence the spectral slope of the gravitational\u2011wave background observed today?", "answer": "During a stiff epoch (equation\u2011of\u2011state parameter \\(w>1/3\\)), the Universe expands more rapidly than during radiation domination. Gravitational waves that re\u2011enter the horizon during this period get boosted because the energy density redshifts more slowly (\\(\\rho_{\\text{GW}}\\propto a^{-4}\\) while the background energy density scales as \\(a^{-3(1+w)}\\)). As a result, the primordial inflation\u2011generated spectrum acquires a blue tilt with spectral index \\(\\alpha_{\\text{stiff}}=2/(1+3w)\\), which can be substantially larger than the \\(\\alpha\\simeq0\\) of a standard inflationary background. This leads to a higher amplitude at higher frequencies, bringing the signal into the detectable band of ground\u2011based observatories if \\(w\\) is close to unity."} +{"question": "What constraints does the recent O5 LIGO\u2011Virgo\u2011KAGRA run place on the amplitude of a parity\u2011violating chiral gravitational\u2011wave background at frequencies above 200\u202fHz?", "answer": "I do not have information on that, because the O5 run data and its specific parity\u2011violation constraints have not been incorporated into the model I was trained on, and the paper you provided does not cover O5 results. Answering this question would require access to the latest analysis reports from the LIGO\u2011Virgo\u2011KAGRA collaboration, which are outside my knowledge domain."} +{"question": "What would be the impact on constraints of ultralight dark matter if the local dark-matter velocity distribution were modeled with a non\u2011Gaussian, anisotropic component?", "answer": "A non\u2011Gaussian, anisotropic velocity distribution would modify the coherence time and the spectral shape of the dark\u2011matter signal in interferometer data. This could lead to either tighter or weaker limits depending on the directionality and spread of the velocity field, and realistic modeling may improve the sensitivity to mass ranges close to the interferometer arm length resonances."} +{"question": "Can future third\u2011generation gravitational\u2011wave detectors, such as the Einstein Telescope or Cosmic Explorer, provide an order\u2011of\u2011magnitude improvement in the upper limits on the couplings of scalar ultralight dark matter to the fine\u2011structure constant?", "answer": "Yes. The significantly increased strain sensitivity and longer observation times expected for third\u2011generation detectors would reduce the noise floor across a broad frequency band. This would allow the amplitude of a hypothetical dark\u2011matter\u2011induced strain signal to be probed at much lower levels, potentially improving scalar coupling limits by an order of magnitude or more."} +{"question": "How would an improved calibration of the interferometer\u2019s transfer function for arm\u2011mirror size oscillations affect the derived limits on dark\u2011photon couplings to baryons?", "answer": "A more accurate transfer\u2011function calibration would reduce systematic uncertainties in the conversion between measured strain and the underlying dark\u2011photon force. Consequently, the derived bounds on the dark\u2011photon\u2013baryon coupling could be tightened, especially at the low\u2011frequency end where the transfer function is most sensitive to arm\u2011mirror displacement."} +{"question": "Is there any empirical evidence in current gravitational\u2011wave data for differential strain patterns that could distinguish between a scalar dilaton field and a massive tensor dark\u2011matter field?", "answer": "Such differential strain patterns have not yet been observed in current gravitational\u2011wave data. Distinguishing between scalar and tensor signatures would require identifying the characteristic polarization responses of the interferometer arms, which remains an open challenge for present datasets."} +{"question": "What is the most stringent existing constraint on the coupling of ultralight vector dark matter to Electron currents from laboratory fifth\u2011force experiments?", "answer": "I do not have that information. The paper focuses on limits from atomic clocks and torsion\u2011balance experiments for scalar and vector couplings, but does not provide the strongest laboratory constraint on vector dark\u2011matter couplings to electron currents."} +{"question": "How does the distribution of effective inspiral spins (\u03c7_eff) evolve for binary black holes that form through successive hierarchical mergers in globular clusters, and how does this distribution differ from that of binaries formed in isolation?", "answer": "In hierarchical mergers the remnant spin of the previous merger is typically large (\u22480.7) and directed roughly along the orbital angular momentum. When this remnant merges with another black hole, the resulting \u03c7_eff distribution becomes broadly symmetric around zero, with a significant tail of large positive and negative values. In contrast, binaries formed in isolation usually exhibit a positively biased \u03c7_eff distribution due to spin alignment from common progenitor evolution. The exact shape of the \u03c7_eff distribution, however, depends on cluster properties, mass segregation, and the dynamical ejection/retention of remnants, and detailed numerical simulations are required to quantify it precisely."} +{"question": "What is the quantitative effect of the spin-induced quadrupole moment (parameter \u03ba) on the amplitudes of higher-order spherical harmonic modes (\u2113, m) during the late inspiral and merger phases of a binary black hole system?", "answer": "The spin-induced quadrupole moment enters the post-Newtonian expansion of the gravitational-wave phase and amplitude. A deviation \u03b4\u03ba from the Kerr value of 1 modifies the amplitude of mass- and current\u2011quadrupole contributions to the (\u2113, m) = (2,\u00b12) leading mode, while also altering the relative strength of higher modes such as (\u2113, m) = (3,\u00b13) via changes in the binary\u2019s orbital dynamics. For rapidly spinning binaries (\u03c7 ~ 0.7) and moderate mass ratios (q \u2243 0.3), a \u03b4\u03ba of order 0.1 can shift the (3,\u00b13) mode amplitude by several percent, leading to measurable deviations in the signal-to-noise ratio and potentially affecting the inference of source parameters."} +{"question": "Can gravitational\u2011wave signatures from eccentric binary black hole mergers in cluster cores provide a robust test of post-Newtonian predictions for eccentric inspirals, and what is the expected eccentricity range at LIGO frequencies?", "answer": "Eccentric binaries formed via close encounters or three\u2011body interactions are expected to retain pericenter distances that produce orbital eccentricities e \u2243 0.01\u20130.1 when the gravitational-wave frequency enters the LIGO band (>20\u202fHz). Post\u2011Newtonian models that include eccentricity up to next-to\u2011quadratic order reproduce the energy and angular\u2011momentum fluxes with residuals below a few percent for this eccentricity range. Therefore, with sufficiently high signal\u2011to\u2011noise ratios, the waveform phase evolution can be used to test the PN eccentricity formalism, but this requires accurate eccentric waveform models and careful marginalization over spin effects."} +{"question": "What limits can be set on the mass and coupling strength of an ultralight vector boson from observing a spinning black hole with mass \u224820\u202fM\u2299 and spin \u03c7 \u22480.8, assuming the black hole formed only a few million years ago?", "answer": "The superradiant growth timescale for a vector boson scales as \u03c4 \u2243 10\u00b3\u202fs\u202f(M/10\u202fM\u2299)\u2076\u202f(m/10\u207b\u00b9\u00b2\u202feV)\u207b\u2076 for optimal coupling. For a 20\u202fM\u2299 black hole with \u03c7 \u22480.8 and an age of \u224810\u2076\u202fyr, vector boson masses in the window m \u2243 10\u207b\u00b9\u00b2\u201310\u207b\u00b9\u00b9\u202feV would have time to grow a cloud and spin\u2011down the horizon below the observed value, thereby being excluded. Couplings stronger than gravitational (i.e., with a gauge charge larger than Newton\u2019s constant) would shorten the instability times, tightening these constraints further."} +{"question": "To what extent do metallicity\u2011dependent stellar winds influence the retention of black\u2011hole merger remnants in nuclear star clusters, thereby affecting the probability of successive hierarchical mergers?", "answer": "The agent does not know the answer to this question. The mechanisms through which metallicity\u2011dependent winds alter the pre\u2011merger masses of progenitor stars directly impact the final remnant mass and spin, which in turn influence the gravitational\u2011wave recoil kick. The distribution of kick velocities relative to the cluster escape velocity determines whether the remnant remains bound and can form a second\u2011generation binary. Current population synthesis models incorporate metallicity effects on stellar evolution, but the coupling to cluster dynamics, the detailed distribution of escape velocities in nuclear star clusters, and the efficiency of later dynamical captures are not fully quantified. Consequently, a comprehensive assessment of metallicity\u2019s role requires further theoretical work combining stellar evolution, binary population synthesis, and realistic N\u2011body simulations of cluster dynamics."} +{"question": "What is the expected contribution of primordial black hole mergers to the isotropic stochastic gravitational\u2011wave background in the 20\u2013200 Hz band?", "answer": "Primordial black hole (PBH) binaries can in principle produce a stochastic background, but their merger rate, mass distribution, and spatial clustering remain highly uncertain. Current population\u2011inference methods based on LIGO-Virgo detections cannot constrain PBH parameters tightly; therefore, a robust prediction of their contribution to the GWB in the 20\u2013200\u202fHz band is not available yet. Further theoretical modeling and additional data from future observing runs are required to reduce these uncertainties."} +{"question": "How does the overlap\u2011reduction function for the LIGO Hanford\u2013Livingston baseline change if one of the detectors operates at a different orientation due to maintenance?", "answer": "The overlap\u2011reduction function (ORF) depends on the relative geometry and orientation of the two interferometers. If a detector\u2019s orientation is altered, the ORF would change accordingly, affecting the sensitivity to different polarizations and sky locations. Calculating the new ORF requires precise knowledge of the rotated antenna patterns and baseline. This is a straightforward but non\u2011trivial exercise in detector geometry and is routinely performed when accounting for downtime or maintenance, but the exact updated ORF is not provided in this paper."} +{"question": "Can the current noise\u2011budget method reliably disentangle Schumann\u2011resonance magnetic noise from potential cosmological backgrounds at frequencies above 100\u202fHz?", "answer": "The magnetic noise budget calculation assumes linear coupling between external magnetic fields and the strain channel, modeled via long\u2011term averaged coupling functions. While this approach is adequate for the 20\u201360\u202fHz band where Schumann resonances dominate, at frequencies above 100\u202fHz the magnetic coupling is much weaker and the ambient field spectrum is less well characterised. Consequently, the current method may not provide sufficient discrimination between weak magnetic artifacts and a cosmological background in the high\u2011frequency regime. Further dedicated magnetic field measurements and improved coupling models are needed."} +{"question": "What level of improvement in the binary black hole merger rate density at redshift z > 2 can be obtained by combining the updated O4a stochastic upper limits with the latest LIGO\u2013Virgo event catalog?", "answer": "By jointly fitting the stochastic upper limits to the CBC merger\u2011rate model, we obtain tighter constraints on the redshift evolution parameters (\u03b1_z, \u03b2_z, z_p) for binary black holes. The O4a data allow a modest tightening of the allowed variance in these parameters, but the statistical leverage remains limited due to the current stochastic sensitivity. The expected improvement is anticipated to be on the order of 10\u201320\u202f% in the inferred rate density for z\u202f>\u202f2 compared to O3, but this remains an estimate until real Bayesian analyses are performed."} +{"question": "How would the detection of gravitational\u2011wave polarizations beyond the tensor mode impact the constraints on alternative theories of gravity?", "answer": "Detection of non\u2011tensor polarizations\u2014such as vector or scalar modes\u2014would be a direct indication of physics beyond general relativity, enabling us to rule out or constrain a broad class of modified gravity theories that predict such modes. However, the current paper does not report any such detection; the data are consistent with pure tensor modes, and upper limits set on scalar and vector amplitudes are two\u2011times stronger than previous runs but still leave substantial parameter space for alternative theories. A definitive conclusion requires a future detection of a polarization\u2011specific signal."} +{"question": "How does the angular power spectrum of the stochastic gravitational-wave background depend on frequency for different astrophysical source classes?", "answer": "The angular power spectrum, usually characterized by \\(C_\\ell\\), shows distinct frequency scaling for different source populations. Compact binary coalescences (CBCs) dominate at higher frequencies (above 50\u202fHz) and their power spectrum tends to rise as \\(f^{2/3}\\) in the strain spectrum, which translates to a flatter \\(C_\\ell\\) at lower multipoles. Rotating neutron stars and magnetars contribute at lower frequencies (<\u202f50\u202fHz), with a steeper strain spectrum that leads to larger anisotropic power at higher \\(\\ell\\) values. Cosmological sources such as inflationary or cosmic\u2011string backgrounds, which are expected to be nearly scale\u2011invariant, produce an almost flat angular power spectrum across the full frequency band, making them difficult to distinguish from an isotropic component without additional sky localization."} +{"question": "Which astrophysical populations are most likely to generate a detectable anisotropy in the gravitational\u2011wave background at frequencies below 100\u202fHz?", "answer": "Below 100\u202fHz the most promising contributors to anisotropy are nearby populations with large spatial clustering. These include: 1) the population of millisecond pulsars in the Galactic plane, whose spatial distribution follows the stellar density and can create a dipole\u2011like enhancement, 2) the Scorpius\u202fX\u20111 accreting neutron\u2011star system, which may emit continuous waves, 3) compact binary coalescences inside the Virgo cluster, and 4) young neutron stars in supernova remnants such as SN\u202f1987A. Each of these sources has a distinct spectral shape that, combined with their sky positions, can leave a measurable imprint on the observable \\(C_\\ell\\) at sub\u2011fundamental frequencies."} +{"question": "How do correlated detector noises influence the cross\u2011correlation sensitivity for persistent gravitational\u2011wave signals?", "answer": "Cross\u2011correlation methods rely on the assumption that instrumental noises in geographically separated detectors are uncorrelated. If there exist correlated noise sources\u2014such as global magnetic fields or seismic couplings\u2014the overlap\u2011reduction function that translates the true sky signal into the measured cross\u2011power can be contaminated. This contamination manifests as an excess variance in the estimator and biases the inferred strain amplitude upward or downward depending on the phase relationship of the correlated noise. Advanced techniques, such as null\u2011stream analyses or subtraction of known magnetic/seismic channels, can mitigate these effects, but residual correlations still set a lower bound on the achievable sensitivity for persistent, narrowband sources."} +{"question": "What is the expected level of anisotropy induced by the clustering of millisecond pulsars in the Galactic plane?", "answer": "The present literature does not provide a precise quantitative estimate of the anisotropy caused by millisecond\u2011pulsar clustering. While models predict a modest dipole\u2011like enhancement of the gravitational\u2011wave power in the Galactic plane, the magnitude depends on the poorly known ellipticity distribution, distance uncertainties, and the unknown contribution from unresolved binaries. Consequently, the exact level of anisotropy remains an open question requiring further theoretical modeling and deeper continuous\u2011wave observations."} +{"question": "What statistical techniques can reduce the bias from shot noise in spherical\u2011harmonic analyses of the gravitational\u2011wave background?", "answer": "Shot noise arises from the discrete realization of astrophysical events and biases the auto\u2011\\(C_\\ell\\) estimator because it adds a white\u2011noise component to each multipole. A robust mitigation strategy employs a cross\u2011\\(C_\\ell\\) estimator: the cross\u2011power between independently cleaned maps\u2014constructed from separate data subsets\u2014cancels the shot\u2011noise bias because shot\u2011noise is uncorrelated between the subsets. Additionally, regularizing the Fisher matrix (e.g., via eigenvalue truncation or Tikhonov regularization) ensures numerical stability and suppresses sensitivity to poorly constrained higher\u2011\\(\\ell\\) modes that would otherwise amplify shot\u2011noise contributions. Combining these approaches yields unbiased estimates of the true anisotropic power spectrum."} +{"question": "How does the removal of narrowband spectral lines (e.g., calibration lines and mains harmonics) influence the detectability of continuous\u2010wave (CW) signals from spinning neutron stars in LIGO data?", "answer": "Removing narrowband lines reduces the spectral density at the frequencies of interest, which directly improves the signal\u2013to\u2013noise ratio for CW searches. Empirical studies of the O4a data show that the 90\u2011percentile upper limits for known pulsars improved by up to 15\u202f% after line removal, with the most significant gains at the lowest detectable frequencies where the detector noise is otherwise dominated by violin\u2011mode and resonant\u2011mode lines."} +{"question": "What are the main environmental and instrumental sources that produce non\u2011Gaussian glitches in LIGO strain data, and how does their occurrence rate change over a typical observing run?", "answer": "Principal non\u2011Gaussian sources include seismic activity, anthropogenic vibrations (e.g., nearby trains, road traffic), microseism to 1\u202fHz, anthropogenic acoustic disturbances, electrical mains transients, and internal control\u2013system glitches. In O4a the glitch rate above an SNR of 5 in the 20\u2013500\u202fHz band was approximately 0.5\u202fevents per hour for LHO and 0.7\u202fevents per hour for LLO during periods of good seismology, rising to 5\u201310\u202fevents per hour during heavy daylight traffic or windy weather. The rate decreases during nighttime and when the detector\u2019s vertical pendulum isolation system is in its highest\u2011performance state, indicating a clear seasonal and diurnal dependence."} +{"question": "How do the different data\u2011quality flag categories (CAT1, CAT2, CAT3) used in compact\u2011binary searches affect the overall false\u2011alarm rate for high\u2011mass black\u2011hole coalescences?", "answer": "CAT1 flags identify the most severe data\u2011quality problems and are strictly vetoed in CBC pipelines. Inclusion of CAT2 reduces the analysed livetime by an additional ~1\u20112\u202f% and removes time windows that would otherwise produce mis\u2011classified glitches with SNR\u202f>\u202f10, thereby lowering the false\u2011alarm probability from ~1\u202f\u00d7\u202f10\u207b\u2074\u202fyr\u207b\u00b9 to ~5\u202f\u00d7\u202f10\u207b\u2075\u202fyr\u207b\u00b9 for masses >\u202f50\u202fM\u2299. CAT3 flags, used only in targeted searches, have a negligible impact on the false\u2011alarm rate (<\u202f0.5\u202f%) but can be used to re\u2011rank background expectations when combined with the iDQ probability output."} +{"question": "What is the effect of photon\u2011calibrator injection frequency placement and amplitude on the shape of the calibration\u2011uncertainty envelope for LIGO strain data?", "answer": "Photon\u2011calibrator injections are inserted at eight discrete frequencies spread logarithmically from 10\u202fHz to 5\u202fkHz. The resulting uncertainty envelope shows a flat median systematic error of ~3\u202f% in amplitude and ~1\u202fms in phase between 100\u202fHz and 1\u202fkHz. At frequencies below 30\u202fHz and above 3\u202fkHz the envelope grows due to interpolation extrapolation, reaching up to 10\u202f% amplitude uncertainty. The chosen frequencies allow continuous monitoring of the calibration transfer function while minimizing spectral overlap with expected GW signals, thus maintaining a conservative, yet tight, uncertainty bound across the nominal detection band."} +{"question": "Does the alternate strain release with more aggressive broadband noise subtraction provide a measurable advantage over the default strain in detecting sub\u2011threshold compact\u2011binary events?", "answer": "The paper does not explicitly quantify the benefit of the alternate strain release for sub\u2011threshold event detection. While the alternate release includes additional broadband noise subtraction steps (e.g., GDS\u2011CALIB_STRAIN_CLEAN_AR), a direct comparison of recovery efficiency for events with signal\u2011to\u2011noise ratios between 4 and 6 would require a systematic injection study that is not reported. Therefore, at present we cannot say whether the alternate strain channel yields a statistically significant improvement in detecting sub\u2011threshold compact\u2011binary coalescences."} +{"question": "How do the effective inspiral spin distributions of binary black hole mergers detected in the first half of the fourth observing run compare to those from previous observing runs?", "answer": "The effective inspiral spin (\u03c7_eff) of the binary black holes observed in O4a is largely centered near zero, indicating that most of the systems have spins either aligned and anti\u2011aligned with the orbital angular momentum or intrinsically small. However, a non\u2011negligible tail at positive \u03c7_eff values is evident, corresponding to mildly spinning systems that possess preferential spin alignment. This distribution is statistically consistent with the spin distribution measured in GWTC\u20113, where most events also cluster near zero but exhibit a broadened spread, showing no significant evolution in the overall spin behaviour between O3 and O4a."} +{"question": "Is there any clear evidence of tidal deformation signatures in the gravitational\u2011wave signals from the two NSBH candidates included in the catalog?", "answer": "The available signal\u2011to\u2011noise ratios for the two neutron\u2011star\u2013black\u2011hole candidates, GW230518_125908 and GW230529_181500, are modest. The Bayesian inference analyses performed with tidal\u2011inclusive waveform models do not yield statistically significant measurements of the neutron\u2011star tidal deformability parameter (\u039b). Consequently, while the presence of a neutron star is inferred from the component masses, no robust constraints on the equation of state can be extracted from these events alone."} +{"question": "What are the typical sky localisation areas achieved with a two\u2011detector LIGO network for events in the O4a catalog?", "answer": "Because only the two LIGO detectors were operational during O4a, typical 90\u2011percent credible sky areas for the catalog events span from ~100 deg\u00b2 for high\u2011quality, well\u2011localized, low\u2011mass binaries to several thousand square degrees for lower\u2011frequency and higher\u2011mass systems. The most localized event, GW230627_015337, achieved a sky area of ~110 deg\u00b2, while the least localized signal, GW230901_191248 (not listed here), had several thousand deg\u00b2. These localisation uncertainties are larger than most events from NGr3, where the inclusion of Virgo provided 2\u2011to\u20113\u2011fold reductions in area."} +{"question": "Do the mass\u2013ratio of binary black holes show a dependence on the total mass in the O4a sample?", "answer": "An exploratory analysis of the O4a source\u2011frame masses indicates that the most massive systems (M \u2273 150\u202fM\u2299) tend to have slightly more unequal mass ratios (q \u2248 0.6), whereas the lower\u2011mass binaries (M \u2248 10\u201330\u202fM\u2299) display a broad distribution of mass ratios, including several that are almost equal. While this trend is present, the small sample size and measurement uncertainties prevent a definitive statement about a direct correlation; further data will be required to confirm whether the mass\u2011ratio distribution depends strongly on the total mass."} +{"question": "What constraints does the paper provide on the neutron\u2011star equation of state derived from the NSBH candidates GW230518_125908 and GW230529_181500?", "answer": "The paper does not provide any constraints on the neutron\u2011star equation of state from the NSBH candidates. The tidal deformability parameters inferred from the Bayesian analyses are consistent with zero within large uncertainties, and no robust measurement of \u039b was obtained. Consequently, the paper does not offer constraints on the neutron\u2011star equation of state from these events."} +{"question": "What astrophysical processes could allow black holes to form with masses inside the pair\u2011instability mass gap between roughly 60 and 130\u202fM\u2299?", "answer": "Several channels have been proposed: (1) Hierarchical mergers of smaller black holes within dense stellar clusters can build up masses above the gap while keeping a high spin; (2) Failed supernovae or pulsational pair\u2011instability supernovae in rapidly rotating metal\u2011poor stars can leave behind black holes in the gap if the envelope is retained; (3) Binary stellar evolution pathways such as chemically homogeneous evolution can produce massive, tight binaries that avoid pair\u2011instability disruption; and (4) Gas\u2011rich environments (e.g., accretion in active galactic nucleus disks) may allow accretion\u2011driven mass growth that pushes a black hole into the gap. Each mechanism operates under different metallicity, spin, and environmental assumptions."} +{"question": "How can measurements of high spin values (>0.7) in merging black holes inform theories of black hole spin evolution?", "answer": "High spins constrain the angular momentum budget of the progenitor systems. In isolated binary evolution, such spins would require efficient tidal spin\u2011up or prolonged accretion episodes, implying very short orbital separations and/or dense circumbinary disks. In dynamical environments, large spins suggest that the merging black holes were themselves products of previous mergers, as successive mergers naturally spin up the resulting remnant. Therefore, observing sustained high spins in multiple events points toward a population of black holes that has undergone repeated mergers or significant accretion."} +{"question": "What observational signatures would distinguish a gravitational\u2011wave source that formed through hierarchical mergers from one that formed directly from a massive stellar collapse?", "answer": "Hierarchical mergers are expected to leave several imprints: (1) a broader distribution of spins, typically with larger magnitudes and higher effective precessing spin \u03c7p; (2) a bias toward higher total masses and mass ratios close to unity; (3) potential evidence of recoil kicks\u2014e.g., an uncharacteristically large kick velocity\u2014as inferred from the remnant\u2019s motion; (4) an elevated rate of spin\u2011aligned or mildly precessing systems within dense clusters; and (5) a correlation of events with known globular or nuclear cluster environments. Direct massive stellar collapse would more likely produce lower spins, a range of mass ratios, and no significant kick imprint."} +{"question": "What are the leading challenges in accurately modeling the signal morphology of very massive, highly spinning binary black hole mergers?", "answer": "The primary challenges include: (1) limited coverage of numerical relativity simulations in the high\u2011spin, comparable\u2011mass regime, leading to waveform model extrapolation uncertainties; (2) inadequate calibration of precession dynamics in models beyond spin \u22480.8, which can bias mass and spin inference; (3) the influence of higher\u2011order multipoles that become more pronounced at high inclination, demanding more sophisticated amplitude corrections; and (4) potential systematic mismatches between waveform families, which introduce non\u2011negligible parameter biases even for signals with moderate signal\u2011to\u2011noise ratios."} +{"question": "The paper does not fully address the possible existence of significant residuals after subtracting the best\u2011fit binary\u2011black\u2011hole waveform. What could be the implications of unmodeled residual power?", "answer": "If residual power persists beyond what Gaussian noise predicts, it could indicate additional physical effects not captured by the binary\u2011black\u2011hole hypothesis, such as: (1) gravitational\u2011wave echoes from exotic compact objects or quantum gravity modifications; (2) environmental effects like dynamical friction in dense media; (3) strong\u2011field deviations from general relativity; or (4) unmodeled instrumental artifacts. Without a dedicated investigation of the residuals, it is not possible to determine whether they arise from astrophysical phenomena or from limitations in the waveform models."} +{"question": "How can incorporating KAGRA data in a future all\u2011sky search for long\u2011duration gravitational\u2011wave transients improve the overall sensitivity of the detector network compared to LIGO\u2011Hanford and LIGO\u2011Livingston alone?", "answer": "Adding KAGRA would increase the effective baseline and improve sky\u2011coverage, leading to a modest increase in the signal\u2011to\u2011noise ratio for sources that lie between the LIGO sites. However, the exact gain depends on KAGRA\u2019s noise performance in the 10\u20132000\u202fHz band, its duty cycle, and the relative antenna patterns. Because KAGRA\u2019s first observing cycles had limited engineering runs in O4a, the paper did not include its data, so a quantitative assessment remains to be made with full\u2011science\u2011quality KAGRA data."} +{"question": "What are the principal difficulties in constructing accurate waveform models for eccentric compact binary coalescences (ECBCs) that emit long\u2011duration gravitational waves?", "answer": "ECBCs produce highly non\u2011stationary signals with repeated bursts and pre\u2011merger modulations. The challenges include (1) accurately evolving the binary through thousands of orbits while retaining orbital eccentricity; (2) modeling tidal interactions and gravitational\u2011wave back\u2011reaction at high eccentricity; and (3) ensuring sufficient overlap with the detector noise curve over long timescales. Current semianalytic approximants provide only limited coverage in mass and eccentricity, so full numerical relativity simulations (which are computationally expensive) are required to generate accurate long\u2011duration templates."} +{"question": "In what ways does the XGBoost classifier enhance the detection pipeline\u2019s ability to distinguish true long\u2011duration gravitational\u2011wave transients from non\u2011astrophysical glitches?", "answer": "XGBoost learns complex decision boundaries from a training set of background (glitch) data and injected signals. By weighting multiple features\u2014such as coherent SNR, spectral energy distribution, and clustering metrics\u2014it can suppress coincident but incoherent noise and amplify coherent, extended power excesses typical of astrophysical transients. Importantly, the classifier obviates hard cut\u2011offs on signal duration, allowing the pipeline to search across a much wider range of temporal morphologies while maintaining a controlled false\u2011alarm rate."} +{"question": "How does the ellipticity of a newly formed magnetar affect the strain amplitude and detectability of a long\u2011duration gravitational\u2011wave signal?", "answer": "The strain amplitude scales roughly with the product \\(\\epsilon \\times f^{2}\\), where \\(\\epsilon\\) is the equatorial ellipticity and \\(f\\) the GW frequency. A larger ellipticity (e.g., \\(\\epsilon \\gtrsim 10^{-4}\\)) produces a stronger, more slowly decaying signal, improving detectability. Conversely, a low ellipticity or rapid magnetic field decay reduces the emitted power, pushing the signal below typical network thresholds. The paper models ellipticities between 0.005 and 0.08; extrapolating to extreme values would either boost or further limit detectability."} +{"question": "What are the implications of detecting a long\u2011duration gravitational\u2011wave transient for multi\u2011messenger astronomy, and why is this still an open question?", "answer": "A confirmed long\u2011duration GW event would provide unique constraints on the post\u2011merger evolution of compact objects, potentially revealing sustained energy injection into electromagnetic counterparts (e.g., X\u2011ray plateaus, kilonovae). However, the exact relationship between GW signal characteristics (duration, frequency evolution) and observable electromagnetic signatures remains poorly understood due to uncertainties in magneto\u2011hydrodynamic processes, fallback accretion physics, and jet formation. Without a statistically significant sample and simultaneous electromagnetic observations, it is difficult to establish robust correlation models, leaving the field an active area for future research."} +{"question": "What is the current level of disagreement between early\u2011universe measurements (e.g., from the cosmic microwave background) and late\u2011universe measurements (e.g., from Type Ia supernovae) of the Hubble constant?", "answer": "Measurements of the Hubble constant from the early universe, such as those obtained from the cosmic microwave background (CMB) with the \\u201cPlanck\\u201d cosmology mission, consistently give a value around 67\u201368 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. Conversely, late\u2011universe, or local, probes\u2014most notably the cosmic distance ladder calibrated with Cepheids and Type Ia supernovae (the so\u2011called SH0ES program)\u2014usually yield a Hubble constant closer to 73\u201374 km s\\u2013\\u202f1 Mpc\\u2013\\u202ft. The tension between these two determinations is roughly 5\u20136 sigma, indicating a statistically significant discrepancy that is not easily explained by simply expanding the measurement uncertainties."} +{"question": "How can a detection of a compact binary merger by a laser\u2011interferometric gravitational\u2011wave detector act as a ``standard siren'' for cosmological distance measurements?", "answer": "A compact binary merger emits a gravitational\u2011wave signal whose amplitude scales inversely with the luminosity distance to the source. The waveform model predicts this amplitude given a set of intrinsic parameters (component masses, spins, orbital orientation, etc.). By performing parameter estimation on the data, one obtains a posterior on the luminosity distance independent of any external distance ladder. If the source redshift is known\u2014either through an electromagnetic counterpart or a statistical inference\u2014this distance\u2013redshift pair can be used directly to probe the cosmological expansion history, making the system a standard siren analogous to the way a Type Ia supernova is a standard candle."} +{"question": "What is the ``spectral siren'' approach in gravitational\u2011wave cosmology, and what does it rely on?", "answer": "The spectral siren approach exploits features\u2014such as peaks, gaps, or cut\u2011offs\u2014in the source\u2011frame mass distribution of merging compact binaries. Because the observed gravitational\u2011wave signal contains the masses redshifted by (1+z), a feature at a fixed intrinsic mass will appear at lower detector\u2011frame masses for higher\u2011redshift sources. By modeling the underlying mass spectrum and assuming a merger\u2011rate evolution with redshift, one can relate the observed distribution to the cosmic expansion. The method therefore relies on a statistically robust model of the intrinsic mass distribution and on a sufficient population of events to constrain the mass\u2011redshift degeneracy."} +{"question": "How would a modification of the propagation of gravitational waves affect the luminosity\u2011distance relation, and how can such modifications be parametrized?", "answer": "In several modified gravity theories the amplitude of gravitational waves decays differently from the standard 1/DL behaviour of general relativity. This modifies the effective GW luminosity distance (DGW\\u202fl) relative to the usual electromagnetic luminosity distance (DEM\\u202fl). A common phenomenological parametrization is DGW\\u202fl\u00a0=\u00a0DEM\\u202fl\u00a0[\u039e0\u00a0+\u00a0(1\u00a0\u2013\u00a0\u039e0)(1+z)\u207b\u207f], where the parameter \u039e0 controls the overall amplitude of the deviation and n controls how rapidly the deviation becomes important with redshift. Such a parametrization captures many late\u2011time modified\u2011gravity scenarios and can be constrained by gravitational\u2011wave standard\u2011siren measurements."} +{"question": "Is there observational evidence that the mass distribution of black holes in merging binaries changes with redshift?", "answer": "I do not have a definitive answer to this question. While the data analysed in the paper allow for a statistical inference of the mass distribution at the redshifts probed by the observed events, the current evidence is not sufficient to confirm a redshift evolution of that distribution. Investigating the evolution would require more events spanning a broader redshift range and a modeling framework that explicitly allows the mass function to vary with redshift, which was not part of the present analysis."} +{"question": "What are the dominant mechanisms that can disrupt primordial black hole binaries in the early universe, and how do they influence the present-day merger rates?", "answer": "Current theoretical models suggest that gravitational interactions with surrounding baryonic matter, primordial density fluctuations, and dynamical friction during the radiation-dominated era can alter the initial orbital parameters of primordial black hole (PBH) binaries. These processes can either harden binaries, making them merge sooner, or ionize them, preventing coalescence altogether. However, the precise efficiency and relative importance of each mechanism remain uncertain because they depend on poorly constrained details of the early universe\u2019s density field, the exact PBH mass function, and the evolution of the primordial plasma. Ongoing work aims to integrate detailed cosmological simulations with analytic estimates to better constrain these disruptive effects."} +{"question": "How do eccentricity and higher-order post\u2011Newtonian corrections affect the detectability of ultra\u2011compact binary inspirals in ground\u2011based gravitational\u2011wave data?", "answer": "Eccentric binaries emit gravitational radiation over a broader frequency spectrum, introducing higher harmonics and modifying the phase evolution. In semi\u2011coherent search methods that approximate the evolution with a leading\u2011order chirp, residual eccentricity can cause the signal to drift out of a given frequency bin over the coherent integration time, reducing sensitivity. Higher\u2011order post\u2011Newtonian terms refine the phase but typically contribute less for very low\u2011mass binaries, whose evolution is slow and dominated by the leading quadrupole term. Extending matched\u2011filter or Hough\u2011type pipelines to include eccentric templates or higher\u2011order PN waveforms is computationally expensive, and the trade\u2011off between improved sensitivity and additional search volume is still under investigation."} +{"question": "Can a population of planetary\u2011mass primordial black holes explain a significant fraction of dark matter without violating microlensing and gravitational\u2011wave constraints?", "answer": "If the primordial black hole mass function contains a pronounced peak in the planetary\u2011mass range (\\(10^{-6} - 10^{-3}\\,M_\\odot\\)), it could, in principle, contribute to dark matter. Microlensing surveys place upper limits on the abundance of compact objects in this mass window, particularly through the non\u2011observation of short\u2011duration microlensing events. Gravitational\u2011wave searches for binary coalescences further constrain the merger rate, which must be low enough to avoid detection yet high enough to produce measurable rates. Reconciling these limits requires a finely tuned mass distribution and formation history. Current evidence suggests that any planetary\u2011mass PBH fraction of dark matter must be small, but definitive conclusions await more sensitive microlensing campaigns and continuous\u2011wave searches."} +{"question": "What is the impact of local dark\u2011matter density variations within the Milky Way on the expected merger rates of ultra\u2011compact binaries?", "answer": "Merger rates of PBH binaries are proportional to the number density of PBHs, which in turn follows the underlying dark\u2011matter distribution. In regions near the Galactic center, the dark\u2011matter density is higher, potentially boosting the local merger rate by an order of magnitude compared to the solar neighborhood. Conversely, in the outer halo the density drops, leading to lower rates. These spatial variations introduce a non\u2011uniform sensitivity for detectors, as the distance reach depends on the local volume probed. Accurate modeling therefore requires incorporating realistic halo profiles (e.g., Navarro\u2011Frenk\u2011White, Einasto) and possible substructure such as dark\u2011matter clumps."} +{"question": "What are the main challenges in extending the Generalized Frequency\u2011Hough method to capture signals from binaries with significant spin\u2011orbit coupling or highly asymmetric mass ratios?", "answer": "The Generalized Frequency\u2011Hough (GFH) transform relies on approximating the time\u2011frequency track of a binary inspiral with a power\u2011law curve derived from the leading\u2011order chirp mass. Introducing significant spin\u2011orbit coupling or highly asymmetric mass ratios alters the phase evolution by adding terms that depend on individual spins, the mass ratio, and higher\u2011order PN corrections. These complications would require a multi\u2011dimensional mapping of additional parameters, drastically increasing the search space and computational cost. Moreover, the assumption that the signal remains monochromatic within a short coherent segment may break down because spin\u2011induced precession can modulate the frequency more rapidly than the coherent time allows. Consequently, while GFH is powerful for low\u2011spin, nearly equal\u2011mass waveforms, reliably capturing more complex systems would need either a different semi\u2011coherent strategy or the development of faster algorithms that can handle the enlarged template bank."} +{"question": "Is there evidence for a population of planetary\u2011mass primordial black holes that could influence the observed dark\u2011matter halo structure in dwarf galaxies?", "answer": "The existence of planetary\u2011mass primordial black holes (PBHs) that contribute significantly to the dark\u2011matter budget is currently unconfirmed. While simulations suggest that such PBHs might form dense sub\u2011clusters that could alter the inner density profiles of dwarf galaxies, observational constraints from stellar kinematics, microlensing surveys, and gravitational\u2011wave non\u2011detections place tight upper limits on the PBH fraction in this mass range. Because the relevant mass range lies below the sensitivity threshold of most microlensing experiments and the gravitational\u2011wave band is limited by the long chirping times of ultra\u2011compact binaries, definitive evidence is lacking. Future surveys with higher cadence and improved continuous\u2011wave detectors may provide more stringent constraints, but at present the question remains unanswered."} +{"question": "How does the projected semi\u2011major axis (ap) of a neutron star in a binary system influence the detectability of continuous gravitational\u2011wave signals?", "answer": "The projected semi\u2011major axis determines the amplitude of the Doppler modulation of the gravitational\u2011wave frequency. Larger ap values spread the signal power over a wider frequency range, increasing the required template resolution and making the search computationally more demanding. Consequently, the sensitivity depth typically decreases for larger ap values, and searches often limit ap to a modest range (e.g., 5\u201315\u202flight\u2011seconds) to keep the template bank tractable while still covering the most likely parameter space for known Galactic binaries."} +{"question": "What effect does the orbital period (P) of a binary system have on the duration and shape of the continuous\u2011wave frequency track in time\u2013frequency space?", "answer": "The orbital period sets the timescale over which the neutron star\u2019s orbital motion modulates the signal frequency. Shorter periods produce rapid, high\u2011amplitude oscillations in the frequency track, whereas longer periods yield slower, smoother modulations. This directly affects the match\u2011filtering strategy: shorter periods require tighter sampling in the orbital phase dimension, while longer periods allow for coarser sampling but demand longer coherent integration times to achieve sufficient sensitivity."} +{"question": "What typical noise spectral\u2011density limits do advanced interferometric detectors achieve in the 100\u2013350\u202fHz band for continuous\u2011wave searches?", "answer": "During the early part of the fourth observing run, the combined H1 and L1 detectors reached an inverse\u2011square\u2011root power\u2011spectral\u2011density (PSD) of roughly \\(2\\times10^{-23}\\,\\mathrm{Hz}^{-1/2}\\) at 200\u202fHz, improving gradually toward 250\u2013300\u202fHz. This level of sensitivity dominates the attainable strain\u2011amplitude limit for continuous waves in that band, with best\u2011achieved depths (in inverse strain units) around 20\u201325\u202fHz\\(^{-1/2}\\)."} +{"question": "What is the maximum spin\u2011down rate that can be tolerated in all\u2011sky continuous\u2011wave searches without significant loss of sensitivity?", "answer": "The search sensitivity declines if the intrinsic spin\u2011down (or spin\u2011up) exceeds the frequency resolution over the total observing time. The criterion is \\(|\\dot{f}_0| \\le 1/(T_{\\rm SFT}\\,T_{\\rm obs})\\), where \\(T_{\\rm SFT}\\) is the short\u2011Fourier\u2011transform length and \\(T_{\\rm obs}\\) is the campaign duration. For a 1024\u2011s SFT and a 237\u2011day run, this translates to \\(|\\dot{f}_0| \\lesssim 4\\times10^{-12}\\,\\mathrm{Hz\\,s^{-1}}\\). Spin\u2011down larger than this would shift the signal by more than one frequency bin, thus reducing coherence and sensitivity."} +{"question": "Which theoretical predictions constrain the maximum ellipticity of neutron stars that could be probed by all\u2011sky continuous\u2011wave searches in the 7\u201315 day orbital period range?", "answer": "We currently do not have a definitive answer to this question. The paper focuses exclusively on the data analysis pipeline and sensitivity estimates and does not explore the astrophysical modeling of maximum sustainable ellipticity for neutron stars in binaries with periods between 7 and 15 days. Theoretical estimates vary from \\(\\sim10^{-6}\\) for conventional nuclear matter to \\(\\sim10^{-4}\\) for exotic matter, but translating these limits into observable strain amplitudes for the specific orbital parameter range would require detailed population synthesis and accretion\u2011torque modelling that is beyond the scope of the analysis presented here."} +{"question": "How would a small electric charge carried by a merging black hole affect the frequencies and damping times of its dominant quasinormal modes?", "answer": "A non\u2011zero charge introduces a Reissner\u2013Nordstr\u00f6m or Kerr\u2013Newman structure. The mode spectrum shifts slightly: the fundamental \u2113=2, |m|=2 mode\u2019s real part increases while its damping time decreases compared to the uncharged Kerr case, although the magnitude of the shift is typically a few percent for realistic charge\u2011to\u2011mass ratios below 10\u207b\u2074. The precise dependence also involves the mode\u2019s overtone number and the black hole\u2019s spin."} +{"question": "Can the extraordinarily high signal\u2011to\u2011noise ratio of recent gravitational\u2011wave events be used to distinguish between General Relativity and alternative theories of gravity that modify the merger dynamics?", "answer": "Yes. In such theories the waveform\u2019s phasing and amplitude evolution during the inspiral and merger are altered, leading to systematic biases in the recovered masses, spins, and ringdown frequencies. By performing parameter estimations within each alternative\u2011gravity parameterization and comparing the likelihoods against the GR prediction, one can place upper limits on the theory\u2011specific couplings (e.g., higher\u2011derivative terms or scalar\u2011tensor couplings) typically at the sub\u2011percent level for the most massive, loud events."} +{"question": "Could the detection of multiple quasinormal\u2011mode overtones provide a direct measurement of a non\u2011zero graviton mass?", "answer": "In principle, a massive graviton would modify the dispersion relation, causing the quasinormal\u2011mode frequencies to deviate from their General\u2011Relativity predictions. However, the current sensitivity to graviton mass from ringdown data is limited; even with multiple overtones, constraints are weaker than those from inspiral phase dispersion and are usually in the tens of kiloparsecs squared per gigaparsec. Future detectors with higher bandwidth and longer overtones might improve these bounds."} +{"question": "What role could black hole superradiance play in testing the area law during a binary merger?", "answer": "Superradiant instabilities can extract rotational energy from a black hole and excite bound states of ultra\u2011light bosons. If such an instability is triggered during the merger, part of the system\u2019s angular momentum would be stored in the cloud rather than radiated in gravitational waves, effectively reducing the final horizon area compared to the GR prediction. A measurable deficit in the area would signal superradiant growth, though detecting this effect would require both high signal\u2011to\u2011noise and a theoretical model that predicts the cloud\u2019s emission timescale."} +{"question": "What is the minimal deviation from the Kerr metric that is still consistent with the most recent high\u2011SNR gravitational\u2011wave observations, yet would imply new physics beyond General Relativity?", "answer": "We currently do not possess a definitive quantitative answer. Determining the smallest allowable deviation requires a systematic exploration of the full parameter space of alternative metric theories (e.g., parametrized post\u2011Newtonian extensions, dynamical Chern\u2011Simons gravity, or Einstein\u2011dilaton\u2011Gauss\u2011Bonnet models) in conjunction with the entire evolution of the binary\u2014including inspiral, merger, and ringdown\u2014using high\u2011accuracy numerical relativity simulations. Such comprehensive studies are still underway; the data at hand are consistent with the pure Kerr geometry within a few percent, but they do not definitively rule out all possible small deviations that could arise from beyond\u2011GR physics."} +{"question": "What determines the expected lifetime of an ultralight vector boson cloud around a black hole and how does it scale with the boson mass and the black hole spin?", "answer": "The lifetime of a vector boson cloud is governed by two competing processes: the superradiant growth phase, which extracts rotational energy from the black hole, and the gravitational\u2011wave (GW) depletion phase, in which the cloud radiates energy. The superradiant growth time \\( \\tau_{\\rm grow} \\) scales approximately as\\n\\\\[ \\\\tau_{\\rm grow} \\\\sim \\\\frac{1}{\\mu M}\\\\,\\\\frac{1}{(M\\\\mu)^{4\\\\ell+5}}\\\\left(\\\\frac{1}{\\\\chi-\\\\chi_{\\rm crit}}\\\\right), \\\\]\\nwhere \\( M \\) is the black hole mass, \\( \\mu = m_{V}\\\\,c^{2}/\\\\hbar \\) is the boson Compton frequency, \\( \\chi \\) is the dimensionless spin, \\( \\chi_{\\rm crit}=2/(m+\\\\ell+1)\\\\) is the critical spin where the instability shuts off, and \\( \\ell \\) is the orbital angular\u2011momentum quantum number (for the fastest growing vector modes typically \\( \\ell=0 \\)). The GW depletion time \\( \\tau_{\\rm GW} \\) scales roughly as\\n\\\\[ \\\\tau_{\\rm GW} \\\\sim \\\\frac{1}{\\\\mu M}\\\\,(M\\\\mu)^{(-4\\\\ell-5)}\\\\,(\\\\chi-\\\\chi_{\\rm crit})^{-2}, \\\\]\\nimplying that smaller boson masses (longer wavelengths) and higher black\u2011hole spins both lengthen the cloud\u2019s lifetime. The two timescales are comparable near the optimal boson mass that maximizes the instability rate, leading to a total signal duration of order days to months for stellar\u2011mass black holes in the LIGO band, and up to years for lighter bosons or more massive black holes."} +{"question": "What search strategies can improve the detection prospects of continuous gravitational waves from vector\u2011boson clouds around distant merger remnants that are several gigaparsecs away?", "answer": "To enhance sensitivity for far\u2011away sources one can (i) use longer coherent segments \\(T_{\\rm coh}\\) in semicoherent pipelines, trading off computational cost for better phase\u2011tracking; (ii) optimise sky\u2011position grids for large\u2011error regions by exploiting the angular\u2011resolution of the detector network, for example by hierarchical sky\u2011grid refinement; (iii) employ matched\u2011filter techniques that incorporate the predicted secular frequency drift \\(\\\\dot f(t)\\) of the vector\u2011boson signal, thus mitigating loss due to mismatch; (iv) leverage multi\u2011band analysis to separate neighbouring spectral lines; and (v) combine data from both LIGO and future detectors such as Virgo and KAGRA to increase sky\u2011coverage and reduce the false\u2011alarm rate. Each of these techniques is designed to recover weak, slow\u2011evolving signals that fall near the detector\u2019s sensitivity threshold, especially when the source distance strongly suppresses the strain amplitude."} +{"question": "What are the current observational limits on the mass of ultralight vector bosons derived from black\u2011hole spin measurements across the galaxy?", "answer": "Black\u2011hole spin measurements, particularly for rapidly rotating stellar\u2011mass black holes, place stringent limits on the mass of ultralight vector particles. If a boson of mass \\(m_{V}\\) existed within the range \\(10^{-14}\\,{\\rm eV} \\lesssim m_{V} \\lesssim 10^{-11}\\,{\\rm eV}\\), the superradiant instability would have spun down such black holes over their ages, yielding much lower observed spins than measured. Current observations exclude boson masses between roughly \\(0.5\\times10^{-13}\\)\u202feV and \\(1.2\\times10^{-13}\\)\u202feV for a typical 10\u202fM\\(_\\odot\\) black hole, under standard assumptions about accretion history and measurement uncertainties. For supermassive black holes the excluded mass window is narrower (e.g., \\(10^{-18}\\)\u2013\\(10^{-15}\\)\u202feV), but systematic errors in spin inference reduce the confidence of those limits."} +{"question": "How does an accretion disk around a black hole influence the superradiant growth of a vector\u2011boson cloud and the resulting gravitational\u2011wave signal?", "answer": "An accretion disk introduces additional torques that compete with the superradiant extraction of rotational energy. Material falling into the black hole can carry away angular momentum, thereby mitigating the spin\u2011down induced by the cloud. Furthermore, the disk\u2019s material can induce density\u2011wave torques and electromagnetic interactions that alter the effective potential felt by the boson field, potentially suppressing the growth rate or altering the mode structure. As a result, the GW amplitude may be reduced or the frequency evolution may deviate from the pure vacuum prediction. Accretion also supplies a continuous energy source that can replenish the black\u2011hole spin, potentially leading to a quasi\u2011steady state where growth and depletion balance, producing a long\u2011lived but comparatively weaker signal than in vacuum."} +{"question": "Has the analysis of the first part of the fourth LIGO\u2013Virgo\u2013KAGRA observing run revealed any definitive evidence for ultralight vector boson clouds around the merger remnants GW230814 and GW231123?", "answer": "I do not have a definitive answer regarding the presence of ultralight vector\u2011boson clouds around the specific merger remnants GW230814 and GW231123. The paper performed directed searches using two semicoherent methods (a hidden Markov model tracker and a Band\u2011Sampled\u2011Data pipeline) on the LIGO data from that period, focusing on the predicted signal parameter space for those remnants. While the paper reported setting exclusion limits on certain boson mass ranges, it did not observe any statistically significant candidates that could be attributed to vector\u2011boson clouds. As such, no evidence of such clouds was reported for those sources. However, this non\u2011detection does not constitute a firm absence; it could be due to limited signal\u2011to\u2011noise, data gaps, or the actual boson parameters lying outside the searched range. A more sensitive future observing run or improved analysis techniques would be required to confirm or refute the existence of such clouds around these remnants."} +{"question": "What are the main geotechnical challenges when tunnelling through molasse rock for a large circular collider tunnel, and what typical mitigation strategies are used?", "answer": "Molasse is a heterogeneous, silty\u2013sandstone\u2013marl sequence that can be weak and contain fractures, fault gouge, or variable strength zones. The key challenges are:\\n1. **Variable strength and deformation:** the mix of finer silts and coarser sandstones can produce uneven tunnel support needs, requiring careful mapping and design of ground support.\\n2. **Hydraulic behaviour:** water\u2011bearing layers and potential high pore\u2011pressure zones can lead to water ingress and ground pressure on the tunnel walls.\\n3. **Large\u2011scale deformation:** the high overburden (~200\u202fm) generates substantial in\u2011situ stresses that can induce settlement or ground movement.\\nTypical mitigations include:\\n- Pre\u2011tunnelling geotechnical surveys and drilling to determine rock quality and build a 3\u2013D model.\\n- Use of a TBM with a driven\u2011segmental lining (either twin\u2011shield or single\u2011shield) to provide immediate support.\\n- Ground conditioning (rock grouting or jet\u2011cutting) where high water pressures or soft strata are encountered.\\n- Installation of rock bolts, cable bolts and shotcrete as primary and secondary support systems.\\n- Monitoring of tunnel pressure and deformation during construction with temporary instrumentation."} +{"question": "When locating surface access shafts for a collider ring, what trade\u2011offs must be balanced to reduce environmental impact?", "answer": "Surface shafts are the only points where equipment, personnel and machinery can reach the underground. The main trade\u2011offs are:\\n1. **Geological suitability:** shafts should be situated where the sub\u2011surface consists of solid molasse rather than water\u2011bearing moraines or limestone.\\n2. **Proximity to existing infrastructure:** placing shafts near existing roadways or utilities can lessen the need for new construction but may increase traffic or noise.\\n3. **Land use and heritage:** shafts should avoid protected natural areas, cultural heritage sites, or densely populated zones to minimise visual and acoustic footprint.\\n4. **Future expansion:** a shaft placed too close to a collider sector may limit the ability to add new tunnels or caverns later, while a shaft placed too far from a detector may increase access costs.\\n5. **Operational safety:** shafts need to be long enough to provide a safe escape route and support ventilation and fire\u2011fighting infrastructure.\\nBalancing these factors usually involves an iterative optimisation that varies shaft locations within a tolerance zone, evaluates alternative tunnel alignments, and selects the configuration that satisfies all statutory and engineering constraints."} +{"question": "How does the \u2018avoid\u2013reduce\u2013compensate\u2019 optimisation methodology shape civil\u2011engineering decisions for large particle\u2011accelerator projects?", "answer": "The methodology is an iterative, multi\u2011criteria decision framework:\\n* **Avoid** \u2013 Wherever possible, the design avoids geologically or environmentally problematic zones (e.g., high\u2011pressure limestone, protected habitats, urban land). This might involve slightly longer tunnel routes or repositioning of surface facilities.\\n* **Reduce** \u2013 Costs, construction time, resource consumption and environmental disturbance are reduced by, for example, using a single\u2011shield TBM instead of a double\u2011shield machine, blending skip\u2011construction for multiple tunnels, or building larger caverns only where they are truly needed.\\n* **Compensate** \u2013 For impacts that cannot be avoided or sufficiently reduced (e.g., a necessary surface building on a protected site), a compensation measure is planned, such as habitat restoration, noise barriers, or payments to local stakeholders.\\nThroughout the design, each alternative is evaluated against technical feasibility, risk, cost, environmental and socio\u2011economic indicators, and the option that scores best across all criteria is selected. The approach ensures that risks are identified early and that environmental and social responsibilities are integrated into the engineering design."} +{"question": "What are the principal differences in material extraction and management when using Tunnel Boring Machines versus conventional drill\u2011and\u2011blast for deep underground construction of collider tunnels?", "answer": "The main distinctions are:\\n1. **Excavation rate & support installation:** A TBM cuts the rock and installs a precast lining continuously, allowing a constant advance of ~10\u201315\u202fm/day in suitable rock. Drill\u2011and\u2011blast relies on explosive fragmentation and requires manual loading, drilling, detonation and removal of spoil, generally slower (usually 2\u20135\u202fm/day) but flexible on hard or fractured rock.\\n2. **Spoil characteristics:** TBM spoils are clean, well sorted, and often culvert\u2011grade because they are cut by a cutting wheel. Blast spoils contain mixed rock, dust, and deeper rock fragments. This affects the material's suitability for reuse.\\n3. **Ground stability:** TBM reduces ground disturbance at the face and can incorporate flotation or slurry systems to control pressure. Drill\u2011and\u2011blast creates more micro\u2011fracture propagation and can raise water ingress.\\n4. **Environmental impact:** TBM tends to produce less vibration, dust, and noise, resulting in lower disturbance to surrounding communities. Blast is more disruptive and requires additional measures (e.g., water\u2011buckets, dust\u2011screens).\\n5. **Material handling & logistics:** TBM can deliver spoil directly to the shaft and/or circulates slurry for hydraulically powered conveyors. For blast, separate lift or conveyor systems are needed to haul the broken rock and segregate it.\\nDuring large collider projects, the decision between the two methods is guided by geology, depth, cost, schedule, and environmental concerns."} +{"question": "What are the long\u2011term structural behaviour and maintenance implications for large experimental caverns constructed in high water\u2011pressure limestone regions?", "answer": "The research paper does not investigate the long\u2011term structural integrity of such caverns, nor does it provide detailed maintenance strategies for high\u2011pressure limestone environments. Consequently, I do not have enough information to answer this question. Further studies, including in\u2011situ monitoring, finite\u2011element modelling, and long\u2011term corrosion analyses, would be required to establish reliable predictions for cavern safety and maintenance schedules in limestone."} +{"question": "What are the primary scientific motivations for constructing a 100\u202fTeV proton\u2011proton collider in the future circular collider tunnel?", "answer": "The 100\u202fTeV hadron collider is motivated by the desire to extend the energy frontier far beyond the current 14\u202fTeV LHC. At this scale the machine would provide unprecedented sensitivity to high\u2011mass processes such as double\u2011Higgs production, exotic resonance searches, and direct production of electroweak or coloured new states (e.g., supersymmetric particles, vector\u2011like quarks, or dark\u2011sector mediators). In addition, the large luminosity (~10\u202fab\u207b\u00b9) would enable precision measurements of the top\u2011quark and Higgs\u2011boson properties, probe the structure of electroweak symmetry breaking, and access mass scales up to tens of TeV, thereby opening a window to physics beyond the Standard Model."} +{"question": "What detector technologies are most promising for achieving a sub\u2011millimetre vertex resolution at the FCC\u2011ee?", "answer": "To reach sub\u2011mm vertex resolution the FCC\u2011ee requires ultra\u2011thin, high\u2011granularity pixel detectors placed very close to the interaction point. Candidate technologies include state\u2011of\u2011the\u2011art monolithic active pixel sensors (MAPS), hybrid pixel detectors with advanced bump\u2011bonding, and 3D integrated electronics. These sensors offer pixel pitch below 25\u202f\u00b5m, fast timing (~10\u201320\u202fps) for pile\u2011up mitigation, and a material budget of only a few per mille of a radiation length. Coupled with a low\u2011mass, high\u2011field solenoid (\u22642\u202fT during the electron\u2011positron stage) and a sophisticated beam pipe design, such detectors can achieve impact\u2011parameter resolutions in the tens of micrometres needed for efficient b\u2011 and c\u2011quark tagging and precise lifetime measurements."} +{"question": "How does the FCC\u2011ee improve the measurement of the Higgs self\u2011coupling compared to the HL\u2011LHC?", "answer": "While the HL\u2011LHC can only access the Higgs self\u2011coupling via double\u2011Higgs production at a few\u2011percent precision, the FCC\u2011ee provides an indirect, model\u2011independent determination through high\u2011precision measurements of the ZH production cross\u2011section at 240\u202fGeV and the single\u2011Higgs branching fractions at 250\u2013360\u202fGeV. The precise knowledge of the ZH cross\u2011section, combined with the per\u2011mille accuracy on the Z\u2013H coupling, constrains the Higgs self\u2011coupling at the 5%\u201310% level without the need for rare double\u2011Higgs events. When FCC\u2011ee data are combined with FCC\u2011hh measurements of the Higgs\u2011pair production cross\u2011section, the self\u2011coupling precision can be pushed below 5%, a sensitivity far beyond what can be achieved at HL\u2011LHC alone."} +{"question": "What strategies are employed at the machine\u2013detector interface to control synchrotron\u2011radiation backgrounds in the FCC\u2011ee electron\u2011positron stage?", "answer": "Synchrotron\u2011radiation (SR) backgrounds are mitigated through several design choices. First, the accelerator optics place the RF cavities and bending magnets well outside the detector acceptance, creating a low\u2011SR region around the interaction point. Second, the beam pipe is made of low\u2011Z, high\u2011thermal\u2011conductivity material (e.g., aluminium or titanium) with a narrow aperture (\u224810\u202fmm radius) to limit SR photons. Third, the detector solenoid field is limited to \u22642\u202fT during the electron\u2011positron stage to reduce vertical emittance growth and prevent SR\u2011induced beam blow\u2011up. Fourth, a dedicated SR absorber and a careful arrangement of quadrupole magnets inside a 100\u202fmrad dead\u2011cone shield the inner detector layers. Finally, active beam\u2011induced background monitoring, using fast calorimeters and tracking monitors placed close to the beam pipe, provides real\u2011time feedback to maintain background levels below the few keV per event threshold required for high\u2011precision measurements."} +{"question": "What is the estimated total construction cost for the FCC\u2011hh and how is it justified in terms of scientific return?", "answer": "I\u2019m sorry, I do not have that information. The feasibility study and the report you provided focus on the physics potential, detector concepts, and technical feasibility but do not include detailed cost estimates. Comprehensive cost modelling, including civil engineering, magnet fabrication, and detector construction, is part of a separate industrial investment study that is beyond the scope of the paper and the knowledge domain of this model."} +{"question": "How can sub\u2011threshold gamma\u2011ray burst detection algorithms increase the sensitivity to short GRB counterparts of gravitational\u2011wave events?", "answer": "Sub\u2011threshold searches\u2014such as blind scans of continuous time\u2011tagged data and coherent likelihood analyses across all detectors\u2014extend the trigger threshold by exploiting the full detector network and a larger time window. By combining data from multiple instruments and applying spectral templates that match short GRB emission, these algorithms suppress statistical noise, thereby lowering the effective detection threshold and increasing the probability of identifying weak, temporally aligned gamma\u2011ray transients."} +{"question": "What observational strategies can improve the joint sky coverage of Fermi\u2011GBM and Swift\u2011BAT when following up gravitational\u2011wave triggers?", "answer": "Coordinated, real\u2011time alerts that share GW sky maps with both spacecraft, combined with complementary pointing strategies (GBM\u2019s all\u2011sky view and BAT\u2019s coded mask imaging) maximize overlap. Additionally, rapid retrieval of burst event data (e.g., via the GUANO system) and the use of ground\u2011based rate monitoring help capture transients that occur during detector slewing or South Atlantic Anomaly passages, thereby reducing blind spots in the combined coverage."} +{"question": "How does the time delay between the gravitational\u2011wave merger and the onset of prompt gamma\u2011ray emission constrain short\u2011GRB jet\u2011launching models?", "answer": "The delay\u2014often ranging from milliseconds to a few seconds\u2014reflects the physics of accretion disk formation, disk wind development, and the acceleration of relativistic jets. Shorter delays are expected when dense ejecta promptly feed the central engine, while longer delays may indicate slower neutrino\u2011driven outflows or delayed black\u2011hole formation. By measuring or limiting these delays, one can test whether observed events favor internal\u2011shock, magnetically driven, or photospheric emission models."} +{"question": "What is the exact mechanism responsible for gamma\u2011ray emission from binary black hole mergers, and can current models be ruled out by existing gamma\u2011ray upper limits?", "answer": "The mechanism remains unknown; several speculative scenarios exist\u2014including neutrino annihilation in a transient accretion disk, electromagnetic extraction of spin energy from a charged black hole, Blandford\u2013Znajek jet launching, and prompt GW\u2011 to gamma\u2011ray energy conversion. Existing upper limits constrain the luminosity of such emission for a few nearby events, but due to uncertainties in jet geometry, viewing angles, and the physics of matter in vacuum environments, we cannot definitively rule out any model yet."} +{"question": "What role do instrument response simulations, such as detector response matrices, play in setting flux upper limits for gamma\u2011ray detectors during counterpart searches?", "answer": "Response simulations translate observed count rates into incident photon fluxes by accounting for detector efficiencies, geometric coding, and atmospheric scattering. Accurate detector response matrices (DRMs) allow the conversion of non\u2011detections into flux upper limits that are sensitive to source position and spectrum. They also enable the estimation of systematic uncertainties and the derivation of sky\u2011dependent upper\u2011limit maps essential for constraining emission models."} +{"question": "How can the precise measurements of the CKM angles \u03c61, \u03c62 and \u03c63 obtained by the B\u2013factory experiments be used to test minimal flavour\u2011violation (MFV) scenarios in supersymmetric models?", "answer": "The B\u2013factory measurements of sin(2\u03c61) (\u03b2), \u03b1 (\u03c62) and \u03b3 (\u03c63) constrain the unitarity triangle side\u2011lengths and internal angles. In MFV models all flavour changing amplitudes are governed by the CKM matrix, so any deviation from the SM predictions in B\u2013meson mixing or CP\u2011violating observables would indicate new particles or couplings that are not aligned with the CKM structure. By combining the world averages of the three angles with independent determinations of |Vub| and |Vcb|, one can perform global fits to the CKM parameters and extract bounds on the scale of new physics. In the MFV hypothesis, the current B\u2013factory data already pushes the scale of flavour\u2011changing supersymmetric particles to several TeV, leaving only small allowed regions for MFV\u2011compatible supersymmetric spectra. Deviations from this pattern would signal non\u2011MFV contributions."} +{"question": "What potential improvements in time\u2011dependent CP\u2011violation studies are expected with the proposed Super B Factories compared to the existing B\u2013factory experiments?", "answer": "Super B Factories aim to achieve instantaneous luminosities around 10^36\u202fcm\u207b\u00b2\u202fs\u207b\u00b9, roughly 50 times higher than the original B\u2013factory peak luminosities. This translates into about 50\u202fab\u207b\u00b9 of data, enabling several key improvements: (1) significantly reduced statistical uncertainties on sin\u202f2\u03b2, \u03b1 and \u03b3; (2) enhanced sensitivity to rare CP\u2011violating decay modes such as B\u202f\u2192\u202f\u03c0\u2070\u03c0\u2070 or B_s\u202f\u2192\u202f\u03d5\u03b3; (3) the ability to perform time\u2011dependent Dalitz\u2011plot analyses with much larger samples, improving the constraint on the angle \u03b3 from B\u202f\u2192\u202fD(K_S\u03c0\u207a\u03c0\u207b)K decays; (4) higher precision in measuring direct CP asymmetries in charmless B decays, potentially revealing interference from physics beyond the SM. The larger datasets would also help disentangle hadronic uncertainties by allowing more precise studies of strong\u2011phase differences through quantum\u2011correlated measurements at the \u03c8(3770)."} +{"question": "How do Dalitz\u2011plot analyses of multi\u2011body B decays (e.g., B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070) contribute to a more precise determination of the CKM phase \u03b3 compared to two\u2011body methods?", "answer": "Multi\u2011body decays such as B\u202f\u2192\u202fK\u207a\u03c0\u207b\u03c0\u2070 contain resonant substructures (e.g., K*\u202f\u03c0, \u03c1\u202fK) that interfere across the Dalitz\u2011plot. By performing a full amplitude analysis, one can extract relative strong phases and magnitudes for each intermediate resonance. When the decay includes both b\u202f\u2192\u202fc and b\u202f\u2192\u202fu transition amplitudes that carry different weak phases, the interference across the Dalitz plot provides direct access to \u03b3 without the need to tag the B flavour. This method, often called the GGSZ (Dalitz) approach, benefits from the kinematic richness of three\u2011body final states, yielding reduced ambiguities and a more statistical power per event compared to two\u2011body GLW or ADS methods. Additionally, since the strong phases are obtained in\u2011situ, hadronic uncertainties are significantly constrained."} +{"question": "What are the main experimental challenges in measuring the branching fraction of the purely leptonic decay B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd at a Super B Factory, and how can they be addressed?", "answer": "The B\u207a\u202f\u2192\u202f\u03c4\u207a\u03bd decay has a large missing energy because the \u03c4 lepton subsequently decays to one or more neutrinos, leading to a signature with one or more hadrons or leptons plus large missing momentum. Key challenges include: (1) efficient \u03c4\u2011identification across all decay modes while controlling large backgrounds from generic B\u202f\u2192\u202f\u2113\u03bd\u2113X and continuum events; (2) precise reconstruction of the missing momentum vector, requiring hermetic calorimetry and excellent tracking; (3) suppression of two\u2011photon and beam\u2011background events that mimic missing energy; (4) control of hadronic B decays with similar topologies (e.g., B\u202f\u2192\u202f\u03c0\u2070\u03c0\u207b) which can be mis\u2011identified as \u03c4\u2011leptons. Addressing these issues relies on: high\u2011resolution vertex detectors to separate \u03c4\u2011decay vertices; a particle\u2011identification system capable of distinguishing pions, electrons and muons up to high momenta; a highly granular calorimeter for accurate neutral\u2011cluster reconstruction; and sophisticated multivariate analysis techniques that exploit event\u2011shape variables to suppress continuum. With the anticipated large dataset, statistical uncertainties will be driven below 1\u202f%, while systematic uncertainties will be controlled through careful calibration and data\u2011driven background studies."} +{"question": "Did the B Factories observe any evidence for lepton\u2011flavour\u2011violating (LFV) tau decays such as \u03c4\u202f\u2192\u202f\u03bc\u03b3 or \u03c4\u202f\u2192\u202f3\u00b5?", "answer": "The information relevant to lepton\u2011flavour\u2011violating tau decays is not covered in the physics discussion of the B Factories presented in this book. The analyses described focus on B\u2011meson decays, CP violation, charm physics, and related topics. While the B\u2011factory experiments did perform searches for LFV tau decays, the results are presented in separate dedicated studies that are not summarized here. Consequently, based solely on the content of this paper, we do not have the answer. A comprehensive answer would require consulting the specific B\u2011factory publications on LFV tau searches, which involve separate datasets, selection criteria, and background estimations."} +{"question": "What are the main systematic uncertainties that affect the reconstruction of supernova neutrino directions in liquid\u2011argon time\u2011projection chambers, and how can improving the statistical separation of interaction channels help mitigate these uncertainties?", "answer": "Liquid\u2011argon TPCs measure the Cherenkov\u2011like ionization track of the final\u2011state electron from a neutrino interaction. The two dominant systematic uncertainties are: (1) the intrinsic kinematic smearing between the neutrino direction and the outgoing lepton direction, which depends on the neutrino energy and the type of nuclear transition (Fermi, Gamow\u2013Teller or forbidden), and (2) the detector\u2011related angular resolution, governed by the spatial hit density, wire\u2011plane geometry and charge\u2011drift attenuation. The second uncertainty is strongly linked to the head\u2013tail ambiguity that arises because the detector cannot distinguish the start and end of a track by timing alone. By statistically separating the elastic neutrino\u2013electron scattering (eES) events, which provide a strong forward peak, from the charged\u2011current \u03bde absorption events, which are largely isotropic, one can weight the more directional eES events more heavily in the pointing likelihood. Improved classification\u2014whether through cut\u2011based variables, boosted decision trees or neural networks\u2014reduces the contamination of the directional sample and therefore lowers the effective angular uncertainty."} +{"question": "Could the inclusion of coherent elastic neutrino\u2013nucleus scattering (CEvNS) as a detectable channel in DUNE appreciably enhance the precision of supernova neutrino pointing?", "answer": "Coherent elastic scattering on argon nuclei has a very large cross section and its final\u2011state electron\u2011recoil energy is purely longitudinal, carrying essentially no directional information about the incoming neutrino. However, the CEvNS rate is substantial for supernova neutrinos (\u223c105 events in a 40\u2011kton detector) and its isotropic nature can be used to constrain the overall neutrino flux normalization and energy spectrum. By simultaneously fitting the CEvNS spectrum together with the eES and \u03bde\u2011cc spectra in a joint likelihood, one can reduce the degeneracy between flux parameters and the effective \u201cangular smearing\u201d of the eES sample, indirectly improving the directional information. Practically, DUNE would need a very low energy threshold and precise neutron\u2011induced background rejection to make CEvNS usable, but if achieved, the additional statistical power and flux constraint could sharpen the supernova pointing by a few tenths of a degree."} +{"question": "How might neutrino mass ordering influence the observable energy spectra of supernova neutrinos at a detector in Southern Africa, and what are the implications for directional reconstruction?", "answer": "In the conventional MSW framework, the normal ordering (NO) leads to a larger survival probability for electron neutrinos below \u223c10\u00a0MeV, while the inverted ordering (IO) favors conversion to non\u2011electron flavors in that energy range. Consequently, the measured \u03bde spectrum at a far detector will differ between the two orderings, affecting the relative weight of the highly directional eES events versus the isotropic \u03bde\u2013cc events. A detector in Southern Africa, such as the proposed South African liquid\u2011argon experiment, would observe a softer eES spectrum for IO, reducing the overall pointing precision by increasing the fraction of events with poor angular correlation. Conversely, under NO the larger high\u2011energy tail in the eES sample would improve the pointing. Therefore, the mass ordering has a non\u2011negligible, though modest, impact on directional accuracy that should be folded into a full systematic error budget."} +{"question": "What machine\u2011learning strategies can be deployed in real\u2011time supernova burst alert pipelines to maintain low latency while still preserving high directional accuracy?", "answer": "Real\u2011time pipelines must reduce raw waveforms to reconstructed tracks within milliseconds. Two complementary ML strategies are: (1) a lightweight convolutional neural network (CNN) operating directly on wire\u2011plane images to perform fast track\u2011finding and head\u2011tail assignment, using training sets generated from GEANT4 + LArSoft simulations; (2) a graph\u2011neural\u2011network (GNN) that ingests the list of hit vertices and their temporal ordering to compute probabilistic direction vectors and interaction\u2013type probabilities on a GPU. By chaining these models\u2014first a quick CNN for detection, then a GNN for precise direction estimation\u2014the pipeline can achieve sub\u2011second latency while keeping the pointing likelihood built from a fully calibrated response matrix. The key is to calibrate the ML inference output against a benchmark reconstruction and to propagate the resulting systematic uncertainties into the maximum\u2011likelihood sky map."} +{"question": "Does the presence of forbidden nuclear transitions in the \u03bde + \u202f\u2074\u2070Ar charged\u2011current absorption modify the angular distribution of emitted electrons enough to affect DUNE\u2019s supernova pointing performance?", "answer": "The paper does not provide a definitive answer because the cross\u2011section and angular\u2011momentum structure of forbidden transitions in supernova\u2011relevant energy ranges are only sparsely known from theory and there is no dedicated experimental data on \u2074\u2070Ar charged\u2011current scattering below ~30\u00a0MeV. If forbidden transitions contribute a substantial backward\u2011peaked component, the overall \u03bde\u2011cc electron angular distribution would deviate from the near\u2011isotropic shape assumed in the study, potentially introducing a small directional bias. Because the current pointing algorithm relies heavily on the clean eES sample and assumes the \u03bde\u2011cc events are essentially non\u2011informative, any significant anisotropy could change the weighting in the likelihood and modestly degrade the best achievable resolution. To resolve this, one would need dedicated low\u2011energy neutrino\u2011argon scattering measurements or improved ab initio nuclear\u2011structure calculations that quantify the forbidden\u2010transition strengths, which are presently unavailable."} +{"question": "How does a fully pixelated charge readout affect the accuracy of three\u2011dimensional reconstruction in liquid argon time projection chambers compared to traditional wire\u2011plane readouts?", "answer": "Pixelated readout provides a direct mapping of charge to a unique (x,\u202fy,\u202fz) coordinate, eliminating the ambiguity that arises from limited projections in wire\u2011plane TPCs. This improves reconstructed track fidelity, especially for overlapping events, by allowing exact hit localization in all three spatial dimensions."} +{"question": "What are the key engineering challenges when scaling up a modular ton\u2011scale pixel\u2011readout LArTPC from a single prototype to the full DUNE near\u2011detector complex?", "answer": "Challenges include maintaining low noise and uniformity across tens of thousands of ASIC channels, ensuring reliable cryogenic power distribution for per\u2011pixel electronics, scaling the data\u2011acquisition bandwidth to handle high voxel occupancy, preserving a uniform electric field over larger drift lengths, and integrating a high\u2011coverage photon\u2011detection system without compromising optical transparency."} +{"question": "In what ways does the resistive field cage design influence space\u2011charge effects and drift\u2011field uniformity in a small\u2011drift LArTPC module?", "answer": "The resistive shell provides a continuous voltage gradient rather than discrete wire rings, reducing dead zones and edge effects that can distort the field. By smoothing the potential, it minimizes localized field enhancements that attract ions, thereby mitigating space\u2011charge buildup and preserving uniform drift velocities across the volume."} +{"question": "How do the photon\u2011detection efficiencies of ArCLight and LCM modules impact the overall energy resolution when combining charge and light measurements?", "answer": "Higher photon\u2011detection efficiency (PDE) improves the statistical precision of the light signal, tightening the anti\u2011correlation between charge loss (due to recombination) and scintillation light. By accurately modeling this correlation, the combined charge\u2011light measurement can reduce the effective energy\u2011resolution variance compared to using either signal alone, provided the PDE variations across the detector are uniformly calibrated."} +{"question": "Does the Module\u20110 demonstrator provide evidence for a systematic time offset between the charge arrival time at the anode and the light signal t0 that depends on the drift electric field?", "answer": "The paper does not report a study of such a field\u2011dependent time offset, nor does it present measurements that would reveal a systematic shift. Therefore, at this time we cannot answer the question; additional dedicated measurements of the t0 timing relative to drift field variations would be required to resolve this issue."} +{"question": "How will the sensitivity improvements planned for the next LIGO\u2013Virgo observing run affect the expected detection rate of strongly lensed binary\u2011black\u2011hole gravitational\u2011wave signals?", "answer": "With the design sensitivity the network is expected to detect many more binary\u2011black\u2011hole mergers at higher redshift, allowing the strong\u2011lensing cross\u2011section to be sampled more densely. Simulations forecast a few percent increase in the probability of observing a lensed pair per observing run, though the exact number depends on the adopted mass and redshift distributions of the lensing halos and the merger\u2011rate evolution."} +{"question": "In what way could the inclusion of higher\u2011order spherical\u2011harmonic modes in waveform models improve the identification of microlensing signatures in gravitational\u2011wave data?", "answer": "Higher\u2011order modes provide additional frequency structure that can break degeneracies between intrinsic parameters and lens\u2010induced frequency\u2011dependent magnification. Their presence amplifies the beating patterns produced by point\u2011mass lenses, potentially making microlensing detectable at lower signal\u2011to\u2011noise ratios."} +{"question": "What limits on the fraction of dark matter that can be composed of compact objects can be projected from the Keplerian\u2011mass range (10\u00b2\u201310\u2075\u202fM\u2299) using the next decade of gravitational\u2011wave data?", "answer": "Forecasts based on O4\u2013O5 merger counts (\u223c300\u20131000 events) suggest that constraints on the compact\u2011object dark\u2011matter fraction could tighten to the 10\u207b\u00b9\u201310\u207b\u00b2 level in that mass window, provided no microlensing signatures are observed and the waveform models accurately capture small\u2011scale lensing effects."} +{"question": "How significant are systematic calibration uncertainties and transient noise artifacts in sub\u2011threshold searches for lensed gravitational\u2011wave counterparts?", "answer": "Calibration errors can shift recovered times and amplitudes, mimicking or hiding the subtle magnification patterns of a lensed image. Transient glitches increase the trials factor in a targeted search, raising the false\u2011alarm rate. Robust vetoes and improved calibration are essential to keep systematic biases below the statistical uncertainty of lens\u2011null likelihoods."} +{"question": "What is the theoretical distribution of magnification factors for gravitational\u2011wave lensing by singular isothermal sphere (SIS) versus more realistic lens profiles (e.g., NFW or elliptical galaxies)?", "answer": "The paper does not investigate the full distribution of magnification factors for non\u2011SIS halo profiles. While SIS models predict a characteristic two\u2011image magnification ratio that depends only on the impact parameter, NFW or triaxial potentials introduce additional dependence on concentration, ellipticity, and line\u2011of\u2011sight structure. Therefore the magnification distribution for realistic lenses remains an open question that would require dedicated ray\u2011tracing simulations beyond the scope of this work."} +{"question": "How can increasing the coherence time in a cross\u2011correlation search improve the sensitivity to continuous gravitational waves from Scorpius X\u20111, and what computational strategies make longer coherence times feasible?", "answer": "The signal\u2011to\u2011noise ratio of a cross\u2011correlation statistic grows roughly with the square root of the coherence time \\(T_{\\max}\\). Extending \\(T_{\\max}\\) therefore directly increases sensitivity. However, a longer coherence time enlarges the template bank because the metric in parameter space (frequency, orbital period, time of ascension, projected semi\u2011major axis) causes nearby points to become mismatched more quickly. Modern lattice covering techniques (e.g., the \\(\\mathcal{A}_3\\) and \\(\\mathcal{A}_4\\) lattices with a controlled mismatch) and the use of sheared coordinates for orbital parameters reduce the required template density, making it computationally tractable to double or even quadruple \\(T_{\\max}\\) while keeping the cost within available resources."} +{"question": "What impact would a non\u2011zero orbital eccentricity of Scorpius X\u20111 have on the cross\u2011correlation search and the derived upper limits?", "answer": "The cross\u2011correlation search used in the analysis assumes a circular orbit, which eliminates two extra parameters: eccentricity \\(e\\) and argument of periastron \\(\\omega\\). If \\(e\\) were non\u2011zero, the Doppler modulation of the signal would change in a way that the current templates cannot match, leading to a loss in signal power (mismatch). This would effectively degrade the achieved upper limits, potentially by tens of percent for modest eccentricities (\\(e \\sim 0.01\\)). The paper does not model or correct for eccentricity, so the reported limits implicitly assume a circular orbit; they do not address how a small but finite eccentricity would alter the results."} +{"question": "How can the upper limits on gravitational\u2011wave amplitude from Scorpius X\u20111 be used to constrain the neutron\u2011star equation of state when combined with torque\u2011balance models?", "answer": "Torque\u2011balance models relate the expected gravitational\u2011wave amplitude \\(h_0\\) to the mass accretion rate and the neutron\u2011star\u2019s radius. By comparing the empirical upper limits on \\(h_0\\) to the theoretical torque\u2011balance curve for different equations of state (e.g., soft GR15 versus stiff GPPVA), one can exclude parameter combinations that would predict detectable signals. Specifically, for a given inclination and magnetic field, if the upper limit falls below the torque\u2011balance prediction for a particular EOS, that EOS is inconsistent with the observation unless the system departs from torque balance. The analysis demonstrates that, at frequencies where the search is most sensitive, the data exclude torque balance for more massive neutron stars, especially for stiff EOSs, thereby tightening constraints on the neutron\u2011star\u2019s mass\u2013radius relation."} +{"question": "To what extent will planned upgrades to the LIGO detectors (e.g., A+ upgrades) improve the sensitivity to continuous waves from Scorpius X\u20111, and what observing strategies are required to realize these gains?", "answer": "A+ upgrades are projected to improve the strain sensitivity by roughly a factor of two across the 10\u2011to\u20112000\u202fHz band. Since the detectable amplitude scales as the inverse of the square root of the observation time and directly with the detector noise, A+ would lower the threshold \\(h_0\\) by about \\(\\sqrt{2}\\). Achieving this in practice requires longer, uninterrupted observing runs and improved data\u2011cleaning techniques (e.g., more effective self\u2011gating, line removal). Combining data from multiple runs in a fully coherent or semi\u2011coherent manner would further enhance sensitivity, potentially allowing the cross\u2011correlation search to probe torque\u2011balance amplitudes over a broader frequency range, including the >\u202f600\u202fHz regime."} +{"question": "What advanced methods exist to model and mitigate spin wandering in continuous\u2011wave searches, and how do they compare in effectiveness to the static\u2011frequency assumption used in this analysis?", "answer": "Spin wandering\u2014random variations in the neutron\u2011star spin frequency\u2014can be modeled using hidden Markov models (HMMs) that track the signal frequency over time, or Bayesian time\u2011series approaches that treat the frequency drift as a stochastic process. These methods allow the search to retain sensitivity to signals that deviate from a perfectly constant frequency, at the cost of additional computational complexity. Compared to the static\u2011frequency assumption adopted here, HMM\u2011based searches can recover signals with modest frequency drifts (\\(\\dot{f}\\sim10^{-10}\\,\\text{Hz\\,s}^{-1}\\)) that would be lost in a purely coherent search, but they typically achieve a modest (\u224810\u201320%) increase in sensitivity for high\u2011frequency targets. The cross\u2011correlation search in the paper assumes a fixed frequency over the coherence time, which is justified given the estimated drift rate over the O3 run, but a future, longer\u2011baseline search could benefit from incorporating HMM techniques."} +{"question": "How does increasing the photon detector coverage affect the energy reconstruction of GeV-scale neutrino events in a liquid\u2011argon time\u2011projection chamber?", "answer": "Extending the photon detection coverage from the baseline ~10\u202f% to 30\u202f% can improve the reconstructed energy resolution by roughly 5\u201310\u202f% for typical GeV\u2011scale charged\u2011current events, primarily by better constraining the scintillation light contribution to the calorimetry and by improving vertex and timing precision."} +{"question": "What systematic advantages does a magnetized gaseous\u2011argon near detector provide for background rejection in the DUNE beamline?", "answer": "The magnetic field allows sign determination for muons above ~800\u202fMeV and helps distinguish neutrino and antineutrino interactions, reducing the wrong\u2011sign background in beam\u2011mode measurements. The magnitude of this improvement depends on the achieved magnetic field uniformity and the detector\u2019s momentum resolution, topics that are still under detailed study."} +{"question": "In what ways could a liquid\u2011scintillator\u2013based far\u2011detector module improve sensitivity to the diffuse supernova neutrino background?", "answer": "A scintillator target increases the inverse\u2011beta\u2011decay event rate (\u223c5\u202f\u00d7 larger than in pure argon), lowers the detection threshold to about 2\u202fMeV, and provides excellent neutron\u2011capture tagging, thereby enhancing the signal\u2011to\u2011background ratio for the diffuse supernova neutrino background."} +{"question": "What are the main obstacles to achieving a sub\u20115\u202fMeV threshold for solar\u2011neutrino detection in a liquid\u2011argon TPC?", "answer": "Key challenges include improving scintillation light collection efficiency, suppressing radon\u2011related backgrounds, and mitigating the 42Ar\u202f\u2192\u202f42K activity that sets a practical low\u2011energy floor. Ongoing R&D focuses on enhanced photon detectors, underground argon use, and comprehensive background modeling."} +{"question": "How does adding a 10\u202fppm xenon dopant to liquid argon impact electron\u2011ion recombination and energy resolution for MeV\u2011scale events?", "answer": "The DUNE Phase\u202fII white paper does not report detailed measurements of this effect. Current simulations suggest that low\u2011level xenon can shift the scintillation wavelength and slightly reduce triplet lifetimes, but the quantitative influence on recombination dynamics and the resulting MeV\u2011scale energy resolution remain to be determined through dedicated experimental studies."} +{"question": "How does including neutron star\u2013black hole (NSBH) mergers influence the constraints on cosmological parameters obtained through gravitational\u2011wave standard sirens?", "answer": "Adding NSBH events expands the redshift lever arm and increases the sample size of dark sirens, thereby improving the statistical power for measuring the luminosity distance\u2013redshift relation. The combined information from binary black holes (BBHs) and NSBHs can tighten the Hubble constant estimate and, depending on the accuracy of the host\u2011galaxy identification, may also help constrain the dark\u2011energy equation of state."} +{"question": "What is the potential of standard sirens to shed light on the nature of dark energy beyond merely measuring the present\u2011day expansion rate?", "answer": "Standard sirens provide direct, model\u2011independent measurements of the expansion history, H(z), as a function of redshift. By mapping H(z) over a range of redshifts, one can test whether the dark\u2011energy equation of state evolves (e.g., w \u2260 \u20131) or whether the expansion follows the \u039bCDM prediction, thus offering a complementary probe to supernovae, BAO, and CMB observations."} +{"question": "In what ways does the completeness and depth of all\u2011sky galaxy catalogs influence the statistical inference of the Hubble constant from dark sirens?", "answer": "Completeness determines how often the true host galaxy of a gravitational\u2011wave event is contained within the catalog. A deeper, more complete catalog reduces the weight of the out\u2011of\u2011catalog likelihood component, thereby decreasing the uncertainty in the inferred redshift distribution and yielding a tighter Hubble constant posterior. Conversely, sparse catalogs increase reliance on population priors, which can broaden the H0 uncertainty."} +{"question": "How might next\u2011generation detectors such as the Einstein Telescope or LISA improve the precision of Hubble\u2011constant measurements using gravitational\u2011wave standard sirens?", "answer": "Future detectors will increase the detection volume and duty cycle, leading to larger samples of inspirals at higher redshift with significantly better sky localization and distance accuracy. This will enable more precise statistical association with host galaxies, reduce degeneracies with mass distribution assumptions, and expand the redshift baseline, thereby sharpening the determination of both H0 and the evolution of the expansion rate."} +{"question": "What is the impact of possible redshift evolution of the black\u2011hole mass distribution on the inference of the Hubble constant from gravitational\u2011wave observations?", "answer": "We do not know the answer. The effect depends on how the black\u2011hole mass spectrum changes with cosmic time, which is influenced by stellar metallicity evolution, binary formation channels, and merger delay times. Current gravitational\u2011wave data lack the breadth in redshift and the theoretical modeling required to disentangle mass evolution from cosmological parameters, so the true influence of an evolving mass distribution on H0 estimates remains uncertain."} +{"question": "How does the stochastic wandering of a neutron star\u2019s spin frequency in low\u2011mass X\u2011ray binaries impact the sensitivity of continuous gravitational\u2011wave searches?", "answer": "The spin frequency of an accreting neutron star is not constant; accretion torques fluctuate, causing a random walk in the star\u2019s rotational frequency. This wandering introduces phase errors that grow over time, limiting the maximum coherent integration interval before the matched\u2011filter signal power is significantly degraded. Continuous\u2011wave searches mitigate this by either using semi\u2011coherent segmentation, where the data are divided into short stretches that are individually coherent, or by employing hidden Markov models that explicitly track the stochastic frequency evolution and stitch together the most likely frequency path across the full observing run. The effectiveness of these techniques depends on the magnitude of the frequency wander\u2014larger wander demands shorter coherent segments or a finer template grid, which in turn increases computational cost and reduces overall sensitivity."} +{"question": "What statistical challenges arise when deriving frequentist upper limits on gravitational\u2011wave strain using hidden Markov model pipelines?", "answer": "Setting upper limits with a hidden Markov model (HMM) requires accurate modeling of the detection statistic\u2019s noise\u2011only distribution in a high\u2011dimensional template space. Key challenges include: (1) estimating the false\u2011alarm probability per sub\u2011band when the analytic form of the statistic is unknown; (2) controlling the overall false\u2011alarm rate across thousands of frequency sub\u2011bands and binary\u2011parameter templates; (3) accounting for non\u2011Gaussian and non\u2011stationary noise artifacts that can bias the likelihood and produce excess loud candidates; (4) generating sufficient Monte\u2011Carlo simulations to determine a detection threshold that yields the desired confidence level while keeping the computational load tractable; and (5) marginalizing over unknown source parameters such as inclination and polarization, which affects the mapping from the injection amplitude to the effective strain used in the upper\u2011limit calculation."} +{"question": "In what ways could planned upgrades to advanced gravitational\u2011wave detectors improve the reach of HMM\u2011based searches for Sco\u202fX\u20111?", "answer": "Future upgrades that increase detector sensitivity (e.g., improved mirror coatings, quantum\u2011squeezing, cryogenic operation) directly lower the noise spectral density, thereby increasing the signal\u2011to\u2011noise ratio for a given strain amplitude. A deeper sensitivity baseline allows the use of longer coherent integration times before spin wandering becomes dominant, or permits a finer binary\u2011parameter grid without incurring prohibitive computational costs. Enhanced calibration accuracy reduces systematic uncertainties in the strain estimate, while expanded detector networks provide better sky\u2011coverage and can enable coincidence checks that suppress instrumental artifacts. Finally, longer continuous observing runs increase the total data set, improving the statistical power of the HMM and enabling tighter upper limits or potentially a first detection."} +{"question": "What astrophysical insight can be gained if the measured gravitational\u2011wave upper limits for Sco\u202fX\u20111 fall below the torque\u2011balance prediction, and how does this constrain the neutron\u2011star equation of state?", "answer": "The torque\u2011balance condition assumes the accretion\u2011spin\u2011up torque is exactly counterbalanced by the spin\u2011down torque from gravitational\u2011wave emission, giving a maximum expected strain amplitude that depends on the X\u2011ray flux, distance, and assumed emission frequency. If an empirical upper limit lies below this threshold, it implies that the neutron star must be emitting fewer gravitational waves than required for torque balance, which in turn restricts the star\u2019s equatorial ellipticity. The ellipticity is linked to the star\u2019s internal composition and the strength of its crust or magnetic field, none of which are directly observable. Therefore, a sub\u2011torque\u2011balance limit places an upper bound on the deformability, providing indirect constraints on the equation of state, especially regarding the shear modulus of the crust and possible exotic core phases."} +{"question": "Do observations indicate that the magnetic field configuration of Sco\u202fX\u20111\u2019s neutron star changes on the timescale of the O3 observing run, affecting the phase\u2011modulation templates used in HMM searches?", "answer": "Current data do not provide time\u2011resolved measurements of the magnetic field geometry of Sco\u202fX\u20111\u2019s neutron star. Most of our knowledge comes from long\u2011term X\u2011ray timing and spectroscopy, which constrain the average accretion rate and orbital parameters but not the instantaneous magnetic field topology. Consequently, the phase\u2011modulation templates employed in HMM pipelines are based on a static approximation of the binary orbit and are not adjusted for potential magnetic\u2011field\u2011induced phase changes. Without contemporaneous magnetic\u2011field diagnostics, such as X\u2011ray polarimetry or cyclotron resonance measurements, any evolution of the field over a ~one\u2011year observing run remains unconstrained, and its impact on the signal waveform cannot be quantified."} +{"question": "What frequency range is most favorable for detecting continuous gravitational waves emitted by scalar boson clouds around stellar\u2011mass black holes with current ground\u2011based detectors?", "answer": "Ground\u2011based interferometers such as Advanced LIGO and Virgo are most sensitive in the 20\u2013600\u202fHz band. In this range the expected quasi\u2011monochromatic signals from scalar boson clouds, whose intrinsic frequency scales roughly as the boson mass relative to the black\u2011hole mass, fall within or just above the detectors\u2019 optimal sensitivity. Frequencies below ~20\u202fHz are limited by seismic noise, while above ~600\u202fHz the detector noise rises steeply, reducing the achievable strain sensitivity."} +{"question": "How does the self\u2011interaction strength of ultralight scalar bosons affect the growth, depletion, and gravitational\u2011wave signal from a boson cloud around a spinning black hole?", "answer": "The self\u2011interaction parameter \\(F_b\\) (or the quartic coupling \\(\\lambda\\)) determines the cloud\u2019s internal dynamics. Strong self\u2011interactions accelerate the cloud\u2019s depletion by enhancing annihilation rates, shorten the signal\u2019s duration, and can reduce the emitted strain amplitude. Weak self\u2011interactions allow the cloud to grow longer and produce a more persistent, higher\u2011amplitude signal. Quantitative predictions require solving the coupled scalar\u2011field and Einstein equations, and the exact dependence on \\(F_b\\) remains an active area of theoretical investigation."} +{"question": "What upper limits on the ultralight boson mass can be derived from non\u2011detections of continuous waves, assuming a realistic Galactic population of spinning black holes?", "answer": "Non\u2011detections translate into exclusion regions in the boson mass\u2013black\u2011hole mass plane. By modeling the Galactic black\u2011hole distribution (e.g., a Kroupa mass function) and assuming a wide range of initial spins, one can compute the expected strain amplitude for each mass pair. If the expected strain exceeds the detector\u2019s sensitivity limit, that parameter space point is excluded. The strength of the exclusion depends sensitively on the assumed spin distribution, cloud age, and distances, so different astrophysical priors can shift the resulting constraints."} +{"question": "Will future space\u2011based detectors like LISA provide complementary sensitivity to boson\u2011cloud gravitational waves, and at which frequencies would they be most useful?", "answer": "LISA\u2019s frequency band (\u22480.1\u202fmHz\u20131\u202fHz) is well\u2011suited to probe boson clouds around intermediate\u2011mass black holes (\u224810\u2074\u201310\u2076\u202fM\u2609) and ultralight bosons with masses \u224810\u207b\u00b9\u00b3\u201310\u207b\u00b9\u00b2\u202feV. These sources emit at frequencies lower than the ground\u2011based band. Therefore, LISA could observe the earlier, slower\u2011evolving phase of the cloud\u2019s annihilation signal, complementing ground\u2011based detectors that target higher\u2011frequency, short\u2011lived signals from stellar\u2011mass black holes."} +{"question": "Is there an observable population of binary black hole mergers that retain residual scalar boson clouds around the remnant, and what would be the signatures in the post\u2011merger gravitational\u2011wave ringdown?", "answer": "This question remains unanswered. Detecting a residual boson cloud around a merger remnant would require identifying deviations in the ringdown spectrum\u2014such as additional quasinormal modes or altered damping times\u2014indicating the presence of a scalar field. Current gravitational\u2011wave observations lack sufficient signal\u2011to\u2011noise in the ringdown phase to test such subtle effects, and detailed numerical relativity simulations including self\u2011interacting scalar fields are still under development. Consequently, we cannot presently confirm or rule out the existence of post\u2011merger boson clouds."} +{"question": "How do spin-precessing effects influence the detectability of binary black hole mergers in current gravitational-wave detectors?", "answer": "Spin-precession introduces modulations in the gravitational-wave signal that can spread the emitted power over a broader frequency band and multiple harmonics. These modulations increase the complexity of the waveform, making it more challenging for template banks that assume aligned spins to recover the signal. Consequently, matched-filter searches that incorporate precessing waveform models can recover signals with higher signal-to-noise ratios and improve the overall detection efficiency, especially for asymmetric or high-spin binaries."} +{"question": "What are the main challenges in modeling eccentric inspirals for gravitational-wave data analysis?", "answer": "Eccentric inspirals require waveform models that capture the rapid periastron passages and the associated burst-like emissions. Current models often rely on post-Newtonian expansions that become inaccurate at high eccentricities or close separations, and numerical relativity simulations for eccentric binaries are computationally expensive and limited in parameter coverage. These limitations make it difficult to construct dense, accurate template banks, which in turn hampers matched-filter searches and can bias parameter estimation if an eccentric signal is forced into a quasi-circular template family."} +{"question": "How does the choice of power spectral density (PSD) estimation method affect the accuracy of Bayesian parameter estimation in gravitational-wave observations?", "answer": "The PSD quantifies the detector noise as a function of frequency and directly weights the likelihood function in the Bayesian framework. A PSD that underestimates noise power at frequencies where the signal has significant amplitude will artificially inflate the inferred signal-to-noise ratio, leading to tighter but potentially biased parameter constraints. Conversely, overestimating noise can dilute the signal, broadening posterior distributions. Adaptive, time-dependent PSD estimation methods that capture non-stationary noise characteristics tend to produce more reliable parameter posteriors compared to static, long-term averages."} +{"question": "In what ways can data-quality vetoes improve the false\u2011alarm rate of matched\u2011filter searches for compact binary coalescences?", "answer": "Data\u2011quality vetoes identify and exclude time intervals contaminated by transient artifacts (glitches) or persistent instrumental disturbances. By removing or down\u2011weighting data segments that would otherwise produce spurious high\u2011SNR triggers, vetoes reduce the background rate that the matched\u2011filter pipeline must contend with. This leads to a cleaner noise distribution, enabling stricter ranking statistics and lowering the false\u2011alarm rate for a given significance threshold. Additionally, vetoes can improve the fidelity of the estimated PSD, further enhancing the robustness of the search."} +{"question": "What is the effect of higher\u2011order multipole modes on the mass and spin inference of binary neutron star mergers?", "answer": "I do not have sufficient evidence to answer this question at present. The current literature does not provide a comprehensive study of how higher\u2011order multipole contributions influence parameter estimation for binary neutron star systems, and existing models mainly focus on the dominant quadrupole. As a result, the precise impact on inferred masses and spins remains an open area for further investigation."} +{"question": "How can subthreshold gravitational\u2011wave triggers be efficiently followed up in the hard X\u2011ray band to detect faint electromagnetic counterparts?", "answer": "An efficient follow\u2011up strategy requires (i) continuous event\u2011mode data acquisition from a wide\u2011field coded\u2011mask instrument such as Swift\u2011BAT, (ii) a rapid, likelihood\u2011based search pipeline that models the detector response for any sky position, and (iii) a real\u2011time alert system that incorporates the gravitational\u2011wave sky probability map. By combining these elements, one can probe flux levels far below the on\u2011board trigger threshold and recover transients with sub\u2011minute durations."} +{"question": "What constraints do the Swift\u2011BAT upper limits place on the luminosity function of short gamma\u2011ray bursts associated with binary neutron star mergers?", "answer": "The flux upper limits measured over the 15\u2013350\u202fkeV band translate into luminosity limits of 10^46\u201310^49\u202ferg\u202fs\u207b\u00b9 for typical BNS distances. These limits exclude a high\u2011luminosity tail in the short\u2011GRB population at the 90\u202f% confidence level for events within the Swift field of view, thereby tightening the parameter space for models that predict prompt emission from BNS coalescences."} +{"question": "To what extent could the joint use of Swift\u2011BAT and Fermi\u2011GBM data improve the sensitivity to electromagnetic counterparts of subthreshold GW events?", "answer": "Joint analysis leverages the complementary sky coverage and energy response of Swift\u2011BAT (hard X\u2011ray, coded\u2011mask imaging) and Fermi\u2011GBM (all\u2011sky gamma\u2011ray). By combining their likelihoods and accounting for each instrument\u2019s background characteristics, one can lower the effective false\u2011alarm rate and extend the detection horizon by up to ~30\u202f%. However, the practical gains depend on the temporal overlap and pointing status of both satellites during each trigger."} +{"question": "How might future gravitational\u2011wave observing runs benefit from improvements in coded\u2011mask imaging sensitivity and localization precision?", "answer": "Advances such as deeper detector simulations, better background modelling, and real\u2011time attitude reconstruction can increase the coded\u2011mask effective area by ~20\u202f% and reduce localization errors from several degrees to sub\u2011degree scales. This would enable rapid optical/infrared follow\u2011up, improve joint\u2011FAR calculations, and potentially uncover a population of off\u2011axis jets that are otherwise missed with current sensitivity."} +{"question": "Is there evidence that binary black hole mergers produce detectable gamma\u2011ray emission, and if not, what upper limits can be derived?", "answer": "We do not know. The current dataset contains no statistically significant hard\u2011X\u2011ray detections coincident with confirmed binary black hole mergers. Consequently, only upper limits can be set; for the most well\u2011localised events these limits lie at ~10^48\u202ferg\u202fs\u207b\u00b9 in the 15\u2013350\u202fkeV band. Determining whether BBH mergers produce any prompt emission requires additional sensitive observations or a larger sample of high\u2011significance events."} +{"question": "What are the main technical challenges for realizing 14\u2011Tesla Nb\u2083Sn dipole magnets in the FCC\u2011hh collider, and how do they affect the overall machine design?", "answer": "The primary challenges are (1) achieving a sufficient field quality with a tight tolerance on the higher\u2011order multipoles, (2) managing the quench stability in a 90\u2011km ring where the stored beam energy per beam exceeds 6\u202fGJ, and (3) ensuring reliable cryogenic performance at 1.9\u202fK while maintaining a high magnetic field gradient. These constraints dictate the coil geometry, the choice of cable and conductor, the cooling scheme, and the mechanical support structure. They also influence the overall magnet packing factor, which in turn affects the ring aperture and the achievable beam emittance. The large stored energy imposes strict protection requirements, necessitating fast\u2011acting quench heaters and a robust energy\u2011dump system. All of these factors must be integrated into the accelerator lattice and the overall cost and schedule of the FCC\u2011hh project."} +{"question": "How can electron\u2011cloud formation be mitigated in a 90\u2011km circumference electron\u2013positron collider operating at 45\u202fGeV per beam, and what surface treatments or vacuum\u2011system designs are most effective?", "answer": "Mitigation strategies include (1) applying low secondary\u2011electron\u2011yield (SEY) coatings such as amorphous carbon or titanium nitride on the vacuum\u2011chamber interior, (2) installing a thin NEG (non\u2011evaporable getter) coating to provide both low SEY and pumping, and (3) shaping the chamber with transverse slots or grooves to interrupt electron trajectories. The beam\u2011pipe geometry\u2014radius, tapering, and the presence of winglets to intercept synchrotron radiation\u2014also influences the local electron\u2011cloud density. The longitudinal bunch spacing can be optimized; for example, a 50\u202fns spacing instead of 25\u202fns raises the SEY multipacting threshold significantly. In addition, a \u201cnon\u2011uniform\u201d filling pattern with a few closely spaced bunches followed by a larger gap can further suppress cloud buildup. These measures together can keep the electron\u2011cloud density below the instability threshold, but detailed 3\u2011D simulations and experimental validation in a dedicated test chamber are needed to quantify the exact performance."} +{"question": "What safety concepts are essential for managing the stored beam energy in a future 100\u2011TeV proton\u2013proton collider, and how are machine\u2011protection interlocks typically designed?", "answer": "Safety concepts for handling multi\u2011gigajoule stored energies include: (1) passive protection\u2014robust collimation systems that intercept halo particles before they reach sensitive components; (2) active protection\u2014fast\u2011acting beam\u2011loss monitoring systems that detect abnormal loss patterns and trigger a rapid beam dump; (3) fault tolerance in the RF and magnet power\u2011supplies to prevent uncontrolled energy deposition; and (4) redundant interlock logic that combines loss\u2011monitor, beam\u2011position, and orbit\u2011feedback signals. The interlock system typically uses a distributed network of loss\u2011monitors (e.g., ionization chambers, scintillators) positioned around the ring, feeding into a central logic unit that can issue a beam\u2011dump command within microseconds. In addition, the machine protection system is designed to tolerate a certain number of false positives while maintaining a very low probability of a dangerous failure. Detailed design of the interlocks is guided by Monte\u2011Carlo loss\u2011simulation studies that identify the most vulnerable components."} +{"question": "Is it feasible to incorporate a high\u2011energy electron\u2013ion collision option into the FCC\u2011hh schedule, and what accelerator physics challenges would need to be addressed?", "answer": "The FCC\u2011h collides protons (and ions) in the main ring, but the paper does not present a detailed feasibility study for an electron\u2013ion (e\u2013A) option. Realizing such a mode would require an additional high\u2011energy electron accelerator, likely a recirculating energy\u2011recovery linac or a separate storage ring, capable of delivering multi\u2011hundred GeV electrons. Key challenges would include synchronizing the electron bunches with the ion bunches, achieving sufficient luminosity while managing beamstrahlung and synchrotron radiation in the electron beam, and integrating a suitable energy\u2011recovery system to keep power consumption reasonable. Moreover, the interaction region would need to accommodate a new detector design with different radiation shielding and background conditions. Because the paper does not cover these aspects, further dedicated studies are required to evaluate the technical and cost feasibility of an e\u2013A option in the FCC\u2011hh program."} +{"question": "What is the quantitative improvement in strain sensitivity achieved by implementing squeezed light sources in the LIGO and Virgo detectors across different frequency ranges?", "answer": "The introduction of squeezed vacuum states into the interferometers reduces quantum shot noise at high frequencies while leaving low\u2011frequency performance largely unchanged. For Advanced LIGO, squeezing has been shown to increase the binary neutron star range by roughly 10\u201315\u202f% in the 100\u2013200\u202fHz band and by up to 20\u202f% above 500\u202fHz. Virgo reports similar gains, with an effective improvement of ~15\u202f% in the 50\u2013300\u202fHz band and up to 25\u202f% above 700\u202fHz. These figures come from calibrated sensitivity curves measured during dedicated squeezing runs and are corroborated by injection studies that confirm the noise reduction directly translates into larger observable volumes for high\u2011mass binary mergers."} +{"question": "How can machine learning techniques be used to classify and predict transient noise artifacts in gravitational\u2011wave data streams in real\u2011time?", "answer": "Real\u2011time glitch classification can be approached by training supervised classifiers on time\u2013frequency representations of the strain data. Convolutional neural networks (CNNs) ingest spectrograms and output probabilities for glitch categories (e.g., blip, scattering, low\u2011frequency burst). Recurrent architectures such as LSTMs can capture temporal correlations, while auto\u2011encoders can flag anomalies without explicit labels. In practice, pipelines like GravitySpy and DeepGlitch have demonstrated that a CNN trained on a large catalog of labeled glitches can achieve >95\u202f% classification accuracy. For prediction, sequential models can learn patterns preceding glitches, enabling early warnings that trigger data\u2011quality vetoes before a detector\u2019s sensitivity is compromised."} +{"question": "How does adding KAGRA and GEO\u202f600 to the LIGO\u2013Virgo network affect the sky localization accuracy for binary neutron star mergers during low\u2011latency alert pipelines?", "answer": "Inclusion of KAGRA and GEO\u202f600 expands the baseline network and provides additional independent timing and amplitude measurements. Simulations show that a four\u2011detector network can reduce the median sky\u2011area 90\u202f% credible region for binary neutron stars from ~200\u202fdeg\u00b2 (LIGO\u2013Virgo) to ~100\u202fdeg\u00b2, and further down to ~60\u202fdeg\u00b2 when KAGRA operates with its full sensitivity. GEO\u202f600, while less sensitive, contributes valuable triangulation, especially for short\u2011duration bursts. Thus, the network\u2019s ability to rapidly localize events for electromagnetic follow\u2011up is significantly enhanced by the additional detectors."} +{"question": "What is the impact of using different calibration versions (e.g., AR, C01, C01_AR) on the measured masses and spins of binary black hole mergers detected during the O3 observing run?", "answer": "The agent does not have direct access to the specific calibration\u2011dependent parameter distributions for O3 binary black hole events. The paper provides the public strain data and describes several calibration streams, but it does not quantify how the choice among them alters the inferred component masses or effective spins. Assessing such an impact would require re\u2011running the full Bayesian inference pipeline on the data processed with each calibration version and comparing the posterior distributions, a task beyond the scope of the paper\u2019s analysis. Consequently, the exact influence of calibration version selection on the astrophysical parameters remains an open question requiring dedicated reanalysis."} +{"question": "What distinctive gravitational\u2011wave signatures are expected from binary black holes whose component masses are below 0.2\u202fM\u2299, and how do these signatures differ from those of higher\u2011mass binaries?", "answer": "In the subsolar\u2011mass regime the inspiral phase dominates the signal because the merger and ring\u2011down occur at frequencies above the most sensitive band of ground\u2011based detectors. The waveform is therefore almost entirely a chirp described by the post\u2011Newtonian expansion up to the last stable orbit. Compared to binaries with component masses \u22731\u202fM\u2299, the chirp mass is smaller, leading to a slower phase evolution and a lower amplitude for a given distance. The signal also contains fewer cycles in band, which makes parameter estimation more challenging. These differences are reflected in the template banks used in the O3 search: a lower mass cutoff of 0.2\u202fM\u2299 and a minimum match of 0.97 were chosen to keep the computational cost tractable while retaining sensitivity to the expected waveform shape."} +{"question": "Which detector upgrades and observing\u2011run strategies are most critical for improving the sensitivity to subsolar\u2011mass binary black holes in future runs (O4 and O5)?", "answer": "The key upgrades are (i) lowering the seismic noise floor and improving the low\u2011frequency sensitivity of the interferometers, which directly increases the number of inspiral cycles observable for low\u2011mass binaries; (ii) enhancing the laser power and implementing quantum\u2011noise reduction techniques (squeezed light) to raise the high\u2011frequency sensitivity where the merger would appear; and (iii) adding a new detector such as KAGRA or LIGO\u2011India to enlarge the network, improve sky localization, and increase the effective observing volume. In addition, expanding the data\u2011analysis pipelines to include full spin precession and higher\u2011order amplitude corrections will allow better recovery of subsolar\u2011mass signals. Together, these improvements are expected to roughly double the sensitive volume\u2013time compared to O3."} +{"question": "Can gravitational\u2011wave data alone distinguish subsolar\u2011mass black holes from other compact objects such as neutron stars or boson stars?", "answer": "In principle, the mass and spin measurements from the inspiral waveform can separate black holes from neutron stars if the total mass falls below the maximum neutron\u2011star mass (~2.3\u202fM\u2299). However, for subsolar masses the mass uncertainty is large due to the short signal duration, and the waveform is almost indistinguishable from that of a boson star or other exotic compact object that follows the same point\u2011particle dynamics. Without additional electromagnetic counterparts or tidal\u2011deformation measurements (which are negligible for such low masses), gravitational\u2011wave data alone cannot unambiguously identify the compactness of the objects. Thus, a non\u2011detection or weak detection does not conclusively rule out or confirm the presence of subsolar\u2011mass black holes versus other candidates."} +{"question": "How do the null results from the O3 subsolar\u2011mass binary search constrain primordial black hole dark\u2011matter models with extended mass functions?", "answer": "The O3 limits on the merger rate of binaries with at least one subsolar\u2011mass component translate into upper bounds on the product of the primordial\u2011black\u2011hole (PBH) mass function and the fraction of dark matter in PBHs. For a monochromatic mass function, the analysis excludes fPBH\u202f\u2273\u202f0.6 at 0.3\u202fM\u2299 and fPBH\u202f\u2273\u202f0.09 at 1\u202fM\u2299. For extended mass functions, the limits are weaker because mergers can involve a wide range of mass ratios, and the suppression factor for early binary disruption becomes less effective. Consequently, models that predict a broad PBH spectrum with a significant contribution from subsolar masses remain viable, even with fPBH\u202f\u2248\u202f1, unless the mass distribution is strongly peaked. The analysis therefore disfavors sharply peaked PBH spectra in the subsolar range but cannot rule out broader distributions."} +{"question": "How would a population of subsolar\u2011mass black holes formed through dissipative dark\u2011matter collapse influence the stochastic gravitational\u2011wave background, and could current or future detectors observe such a background?", "answer": "The paper does not directly address the stochastic background from subsolar\u2011mass black holes. A population of dark\u2011matter\u2011induced black holes would merge throughout cosmic history, contributing to a continuous gravitational\u2011wave background. The amplitude of this background depends on the merger rate density, the typical chirp mass, and the redshift distribution of the sources. Because subsolar\u2011mass binaries have lower chirp masses, their individual contributions to the strain spectrum peak at higher frequencies, potentially overlapping with the sensitivity band of Advanced LIGO/Virgo. However, current upper limits on the stochastic background are dominated by higher\u2011mass binaries, and the expected contribution from subsolar\u2011mass mergers is likely below the present sensitivity threshold. Future detectors with improved low\u2011frequency sensitivity and longer observing times, such as the Einstein Telescope or Cosmic Explorer, could probe this background, but detailed population\u2011synthesis modeling is required to make quantitative predictions."} +{"question": "How do the ellipticity constraints derived from continuous-wave upper limits impact models of neutron star crust breaking strain in the Galactic Center?", "answer": "The upper limits on strain translate to maximum ellipticities of order 10\u207b\u2077\u201310\u207b\u2076 for stars at the Galactic Center. These values are close to or below the theoretical maximum elastic deformations predicted for normal neutron-star crusts (\u224810\u207b\u2076\u201310\u207b\u2075) but are still above the values expected for highly strained crusts or exotic matter. Consequently, the results rule out extremely deformed, solid strange or hybrid star models in the Galactic Center while remaining consistent with standard nuclear equations of state."} +{"question": "What are the implications of the non\u2011detection of continuous gravitational waves for the population size of millisecond pulsars in the inner parsecs of the Milky Way?", "answer": "The lack of a signal suggests that either the millisecond pulsar population is smaller than some optimistic estimates or that their individual ellipticities are below the detection threshold. Using the strain upper limits, one can place an upper bound on the average ellipticity of millisecond pulsars in the region, thereby constraining population synthesis models that predict thousands of such objects."} +{"question": "How can future gravitational\u2011wave detectors improve sensitivity to continuous waves from sources at the Galactic Center compared to the current LIGO\u2011Virgo O3 run?", "answer": "Improvements can come from increased detector bandwidth, lower noise at 100\u2013200 Hz, and longer coherent integration times. Advanced detectors such as LIGO\u2011A+ and Virgo\u2011plus, as well as next\u2011generation facilities (Einstein Telescope, Cosmic Explorer), will reduce strain sensitivity by an order of magnitude, allowing detection of ellipticities as low as 10\u207b\u2078 and probing larger distances within the Galactic Center."} +{"question": "What constraints can continuous-wave upper limits place on the mass and spin of hypothetical boson clouds around stellar\u2011mass black holes in the Galactic Center?", "answer": "By assuming a superradiant boson cloud that emits at a frequency tied to the black-hole mass and boson mass, the non\u2011detection limits exclude regions of the (black\u2011hole spin, boson mass) plane. For example, the results rule out clouds around black holes with initial spin \u03c7i \u2273 0.5 for boson masses between 10\u207b\u00b9\u00b9\u202feV and 10\u207b\u2079\u202feV if the cloud age is 10\u2075\u201310\u2077\u202fyears."} +{"question": "What is the true spin\u2011down distribution of neutron stars located in the Galactic Center, and how does it affect the parameter space explored in directed searches?", "answer": "The paper does not determine the actual spin\u2011down distribution of Galactic\u2011Center neutron stars. This distribution is poorly known because the region is heavily obscured and radio surveys are incomplete. Without precise knowledge of typical spin\u2011down rates, directed searches must adopt broad spin\u2011down ranges (e.g., \u22121.8\u00d710\u207b\u2078\u202fHz/s to +10\u207b\u00b9\u2070\u202fHz/s), which increases computational cost and reduces sensitivity. A more accurate spin\u2011down distribution, obtainable through future radio or X\u2011ray timing surveys, would allow tighter parameter spaces and improved search sensitivity."} +{"question": "What physical mechanisms can generate a non\u2011axisymmetric quadrupole deformation in a rapidly rotating neutron star, thereby enabling the emission of continuous gravitational waves?", "answer": "Several processes are thought to be capable of sustaining a mass quadrupole in a neutron star:\\n- **Crustal \u2018mountains\u2019** formed by tectonic stresses or accreted material that lifts the crust out of symmetry.\\n- **Magnetic stresses**: strong internal or surface magnetic fields can distort the star, producing a permanent quadrupole.\\n- **Accretion\u2011driven deformations**: asymmetric mass loading in accreting systems (e.g., low\u2011mass X\u2011ray binaries) can freeze in a non\u2011axisymmetric shape.\\n- **Superfluid vortex pinning and unpinning**: differential rotation between the crust and the interior superfluid can create a time\u2011varying quadrupole.\\n- **r\u2011mode oscillations**: large\u2011amplitude fluid modes can produce time\u2011dependent quadrupole moments that radiate GWs.\\nThese mechanisms are active in different evolutionary stages of neutron stars and can, in principle, sustain ellipticities large enough to be detectable by current detectors."} +{"question": "How do rotational glitches observed in young pulsars affect the prospects for detecting continuous gravitational waves from those pulsars?", "answer": "Glitches are sudden increases in the spin frequency (and sometimes in the spin\u2011down rate). They can influence continuous\u2011wave searches in several ways:\\n- **Phase evolution**: The GW phase is expected to track the electromagnetic spin. A glitch introduces an instantaneous phase jump that must be modeled or searched over to avoid loss of sensitivity.\\n- **Spin\u2011down changes**: Post\u2011glitch changes in the frequency derivative alter the expected amplitude via the spin\u2011down limit; a more negative \\(\\dot{f}\\) can raise the theoretical upper limit.\\n- **Amplitude variations**: If a glitch is associated with a change in the internal configuration (e.g., superfluid vortex rearrangement), the quadrupole moment may change, potentially increasing or decreasing the GW amplitude.\\nBecause of these uncertainties, most continuous\u2011wave pipelines either treat glitches as additional phase parameters or restrict the search to epochs between glitches, which can reduce the effective observation time."} +{"question": "What assumptions underpin the spin\u2011down limit on the gravitational\u2011wave strain amplitude of a pulsar, and how is this limit derived?", "answer": "The spin\u2011down limit is a theoretical upper bound on the GW strain \\(h_0\\) that assumes *all* of the pulsar\u2019s rotational energy loss is carried away by gravitational waves:\\n1. **Energy conservation**: \\(\\dot{E}_{\\rm rot}= -\\dot{E}_{\\rm GW}\\). The rotational energy \\(E_{\\rm rot}= \\tfrac{1}{2} I \\Omega^2\\). \\(\\Omega=2\\pi f_{\\rm rot}\\).\\n2. **Moment of inertia**: A canonical value \\(I \\approx 10^{38}\\,\\rm kg\\,m^2\\) is usually assumed, though it can vary by a factor of a few depending on the equation of state.\\n3. **Distance**: The observed spin\u2011down rate \\(\\dot{f}\\) and the distance \\(d\\) enter the expression for the strain amplitude. The derived limit is \\(h_{\\rm sd} \\propto (I|\\dot{f}|/d f)^{1/2}\\).\\n4. **Negligible other torques**: No significant electromagnetic or accretion torques are present; the intrinsic spin\u2011down equals the observed value.\\nThe limit is useful because any measured strain below it indicates that GW emission is sub\u2011dominant, and it sets a natural benchmark for the sensitivity required to potentially detect a signal."} +{"question": "How can continuous\u2011wave gravitational\u2011wave observations inform our understanding of the neutron\u2011star equation of state?", "answer": "Continuous\u2011wave searches provide upper limits on the neutron star\u2019s ellipticity \\(\\epsilon\\) and mass quadrupole \\(Q_{22}\\). These limits can be compared to theoretical predictions for the maximum sustainable deformation given different equations of state (EOS):\\n- **Stiff EOSs** predict a larger radius and hence a higher maximum quadrupole before breaking the crust, allowing larger \\(\\epsilon\\).\\n- **Soft EOSs** lead to smaller stars with thinner crusts, giving lower quadrupole limits.\\nIf an observed upper limit falls below the maximum \\(\\epsilon\\) allowed by a particular EOS, that EOS can be deemed inconsistent with the data. Moreover, detecting a signal with a measurable \\(\\epsilon\\) would provide a direct probe of the star\u2019s internal structure and crustal rigidity, offering constraints complementary to those from binary merger observations and X\u2011ray pulse\u2011profile modeling."} +{"question": "What would be the observational signatures of scalar\u2011tensor (e.g., Brans\u2013Dicke) gravity in the continuous gravitational\u2011wave spectrum from a rotating neutron star, and can current detectors differentiate such signatures from those predicted by general relativity?", "answer": "The paper does not address this question. In scalar\u2011tensor theories, an additional scalar polarization mode can be emitted at the *first* harmonic (i.e., at the spin frequency), producing a dipole radiation term with a distinct frequency dependence compared to the quadrupole tensor mode at twice the spin frequency. Current detectors are most sensitive to the quadrupolar tensor modes, and while some searches target the scalar mode, the sensitivity to scalar radiation is typically weaker. Therefore, at present it is not clear whether detectors can unambiguously distinguish scalar\u2011tensor predictions from general relativity, and further theoretical modeling and detector\u2011network studies are required to assess the feasibility of such tests."} +{"question": "How does the internal magnetic field topology of a magnetar influence the efficiency of energy transfer to gravitational waves during a giant flare?", "answer": "The efficiency of gravitational\u2010wave excitation depends sensitively on the arrangement of poloidal and toroidal field components. A strongly toroidal field can store more magnetic energy in the core and may facilitate larger deformations, thereby increasing the coupling to f\u2011mode oscillations. Conversely, a predominantly poloidal configuration might lead to weaker quadrupolar distortions and reduced gravitational\u2011wave emission. The exact dependence requires detailed magnetohydrodynamic simulations of field evolution during a flare."} +{"question": "Can magnetar bursts produce detectable continuous gravitational wave emission via r\u2011mode instabilities, and under what conditions would this be observable?", "answer": "R\u2011mode instabilities grow when the star\u2019s rotation rate is sufficiently high and the viscous damping is weak. Magnetars, being slowly rotating (periods of a few seconds), are generally below the critical spin required for r\u2011mode growth, making continuous emission unlikely. However, if a magnetar were spun up by accretion or experienced a sudden spin\u2011up during a giant flare, the r\u2011mode amplitude could temporarily exceed the threshold, producing a weak continuous wave that might be detectable with long\u2011integration searches in next\u2011generation detectors."} +{"question": "How would a future network of third\u2011generation gravitational wave detectors improve sensitivity to high\u2011frequency magnetar f\u2011modes compared to current detectors?", "answer": "Third\u2011generation detectors such as the Einstein Telescope or Cosmic Explorer aim for strain sensitivities an order of magnitude better than Advanced LIGO at frequencies around 1\u20133\u202fkHz. This improvement would lower the detectable energy threshold for f\u2011mode bursts from \u223c10^49\u202ferg to \u223c10^47\u202ferg for a Galactic magnetar, potentially allowing the observation of many more events. Additionally, better high\u2011frequency response would reduce the mismatch between expected mode spectra and detector noise, improving matched\u2011filter detection efficiency."} +{"question": "What is the precise correlation between the observed quasi\u2011periodic oscillations in magnetar flare tails and the frequency spectrum of potential gravitational wave emission?", "answer": "The paper does not address this question. Establishing a direct correlation would require simultaneous, high\u2011time\u2011resolution X\u2011ray/gamma\u2011ray observations and sensitive gravitational\u2011wave data, along with detailed modeling of magnetar interior oscillation modes. Current theoretical work provides only tentative links between QPOs and crustal or core oscillations, and more observations and simulations are needed to confirm any direct correlation."} +{"question": "How does the inclusion of higher-order multipole moments in gravitational\u2011wave templates affect the precision of tests of general relativity using binary black hole signals?", "answer": "Adding higher\u2011order harmonics (\u2113,|m|\u22602,2) to the waveform models increases the fidelity of the predicted strain, especially for high\u2011mass or high\u2011mass\u2011ratio binaries. It reduces systematic mismatches between the true signal and the template, thereby tightening constraints on deviations in the post\u2011Newtonian coefficients, dispersion parameters, and spin\u2011induced quadrupole moments. Studies with GWTC\u20113 data have shown that accounting for higher modes leads to smaller fitting\u2011factor losses and more accurate recovery of the final mass and spin, which in turn improves the robustness of consistency and parameter\u2011ized tests."} +{"question": "What upper limit on the graviton mass can be derived from the combined GWTC\u20113 catalog, and how does this bound compare to existing solar\u2011system limits?", "answer": "Using the modified dispersion analysis on the 43 GWTC\u20113 events, the 90\u202f% credible upper bound on the graviton mass is \\(m_{\\mathrm{g}} \\le 2.42 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\). This improves the previous GWTC\u20112 limit (\\(3.09 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)) by about 28\u202f% and is slightly better than the most stringent solar\u2011system bound of \\(3.16 \\times 10^{-23}\\,\\mathrm{eV}/c^{2}\\)."} +{"question": "How can measurements of the spin\u2011induced quadrupole moment parameter (\\(\\delta\\kappa_s\\)) distinguish black holes from neutron stars or exotic compact objects, and what constraints have recent gravitational\u2011wave observations placed?", "answer": "In general relativity, a Kerr black hole has \\(\\kappa=1\\), while neutron stars and many exotic compact objects (e.g., boson stars, gravastars) can have \\(\\kappa\\) values significantly different from unity. By measuring \\(\\delta\\kappa_s = (\\kappa-1)\\) in binary mergers, one can test the black\u2011hole no\u2011hair conjecture. The GWTC\u20113 analysis of 13 suitable events yields a combined 90\u202f% credible interval of \\(\\delta\\kappa_s = -16.0^{+13.6}_{-16.7}\\). This is consistent with \\(\\delta\\kappa_s = 0\\) (the Kerr value) but allows a modest range of deviations, providing the first ever statistical constraint on \\(\\kappa\\) from gravitational\u2011wave data."} +{"question": "In what way will next\u2011generation gravitational\u2011wave detectors such as the Einstein Telescope or Cosmic Explorer improve the sensitivity of the inspiral\u2013merger\u2013ringdown consistency test?", "answer": "Third\u2011generation detectors will provide several key advantages: (1) much higher signal\u2011to\u2011noise ratios, (2) longer observable inspiral phases (especially for low\u2011mass binaries), and (3) better low\u2011frequency sensitivity that captures more gravitational\u2011wave cycles. These improvements will sharpen the independent estimates of the final mass and spin from the inspiral and post\u2011inspiral regimes, reducing statistical uncertainties in the fractional deviation parameters \\(\\Delta M_f/\\bar{M}_f\\) and \\(\\Delta\\chi_f/\\bar{\\chi}_f\\). Forecasts suggest that with the Einstein Telescope or Cosmic Explorer the precision on these parameters could reach the sub\u2011percent level, enabling detection of extremely small deviations from GR."} +{"question": "Is there any evidence in the GWTC\u20113 dataset of statistically significant deviations in the 1.5\u2011PN phase coefficient that would challenge the predictions of general relativity?", "answer": "The GWTC\u20113 analysis performed parameterised tests on individual post\u2011Newtonian coefficients, including the 1.5\u2011PN term. Within the uncertainties reported, the 1.5\u2011PN coefficient was fully consistent with the general\u2011relativistic value; no statistically significant deviation was detected. However, the paper does not exhaustively explore all possible combinations of deviations or more exotic waveform systematics that could mimic a shift in this coefficient. Therefore, I cannot definitively confirm or rule out a subtle 1.5\u2011PN deviation beyond the scope of the presented analysis."} +{"question": "What is the expected detection rate of binary neutron star mergers for the future KAGRA + LIGO + Virgo network at design sensitivity?", "answer": "The paper does not provide a quantitative prediction for the detection rate of binary neutron star (BNS) mergers with the full network operating at design sensitivity. Estimating such a rate would require combining the projected horizon distances of each detector, the anticipated duty cycles, and the local BNS merger rate density\u2014information that is beyond the scope of this study."} +{"question": "How does operating KAGRA underground reduce coupling of environmental seismic noise compared to surface detectors like LIGO and Virgo?", "answer": "Operating underground offers a significant reduction in seismic noise because the ground motion at depth is typically an order of magnitude lower than at the surface. Additionally, the underground environment is less affected by weather, human activity, and temperature fluctuations, all of which can introduce low\u2011frequency disturbances. The paper notes a lower low\u2011frequency noise floor for KAGRA, but detailed quantitative comparisons to LIGO and Virgo are not provided."} +{"question": "What technical challenges were encountered when implementing the DC readout scheme in KAGRA, and how were they addressed?", "answer": "Switching from a radio\u2011frequency (RF) to a DC readout required installing an output mode cleaner and reconfiguring the signal extraction optics. Challenges included maintaining laser frequency stability, mitigating higher\u2011order mode contamination, and ensuring the new readout electronics could handle the increased dynamic range. The paper mentions the upgrade but does not delve into the specific troubleshooting steps or hardware modifications undertaken."} +{"question": "During the GEO\u2013KAGRA joint run, what was the dominant noise source limiting sensitivity below 100\u202fHz, and what mitigation strategies were planned?", "answer": "The dominant low\u2011frequency noise was identified as local control noise originating from the mirror suspension damping filters. To mitigate this, the team planned to redesign the damping filter parameters, improve sensor noise performance, and implement more robust feed\u2011forward cancellation of environmental disturbances."} +{"question": "What is the impact of enforcing a single\u2011polarization reconstruction constraint in the coherent WaveBurst (cWB) analysis on detection efficiency for real gravitational\u2011wave signals in a two\u2011detector network?", "answer": "Applying a single\u2011polarization constraint reduces background from noise glitches by limiting the parameter space of admissible waveforms. However, for a two\u2011detector network with non\u2011aligned arms, genuine signals that excite both polarizations can have part of their energy suppressed in the reconstruction, potentially lowering the detection efficiency. The paper notes this trade\u2011off but does not quantify the efficiency loss for specific signal morphologies."} +{"question": "What are the main challenges in separating low\u2011energy kaons from protons in a liquid\u2011argon time\u2011projection chamber, and how can the deposited energy per unit length (dE/dx) be used to overcome them?", "answer": "Low\u2011energy kaons (p_K \u2272 350\u00a0MeV/c) and protons have similar masses and thus deposit comparable amounts of ionization in liquid argon, especially in the Bragg peak region where both exhibit a sharp rise in dE/dx. The primary challenges are: (1) the intrinsic overlap of their dE/dx distributions due to statistical fluctuations in ionization and recombination; (2) the finite spatial resolution and noise of the readout system, which smears the dE/dx profile; and (3) the presence of other hadrons (pions, muons) that can mimic the kaon signature if mis\u2011reconstructed. To disentangle the two species, one exploits the full residual\u2011range dE/dx profile: a proton track continues to deposit energy at a nearly constant rate until it stops, whereas a kaon shows a pronounced Bragg peak at the end of its trajectory. By fitting the dE/dx versus residual range with a Landau\u2013Gaussian convolution and applying a likelihood or \u03c7\u00b2 test under the kaon and proton hypotheses, the probability of each hypothesis can be quantified, allowing a statistically robust separation even in the presence of detector noise."} +{"question": "How can precise measurements of the kaon stopping power in liquid argon enhance the sensitivity of future proton\u2011decay searches?", "answer": "Accurate knowledge of the kaon stopping power (dE/dx as a function of residual range) directly impacts the reconstruction of the kaon kinetic energy and its decay vertex. In proton\u2011decay searches targeting the p \u2192 K\u207a\u202f\u03bd\u0304 channel, the signal consists of a mono\u2011energetic K\u207a that comes to rest before decaying. If the stopping power is well\u2011known, the detector can reliably identify the Bragg peak, estimate the initial momentum, and suppress backgrounds that produce non\u2011rest\u2011decay kaons or mimic the signature. Moreover, a precise stopping\u2011power model allows for better calibration of the calorimetric response, reducing systematic uncertainties on the kaon energy scale and thus tightening the selection criteria. Consequently, the overall efficiency for proton\u2011decay detection increases while the background acceptance decreases, improving the experiment\u2019s lower limit on the proton lifetime."} +{"question": "Which systematic uncertainties have the largest impact on the calorimetric reconstruction of stopping kaons in large liquid\u2011argon TPCs?", "answer": "The dominant systematic sources are: (1) **Calorimetric calibration** \u2013 uncertainties in the conversion from collected charge to deposited energy (typically ~2\u20133\u202f%); (2) **Space\u2011charge effects** \u2013 distortions of the electric field due to positive ion accumulation, affecting drift paths and charge collection (~1\u202f% after correction); (3) **Electron\u2011diverter failures** \u2013 mis\u2011reconstruction of tracks that cross APA gaps, leading to artificial track splits (systematic shift of ~5\u202f% in track length); (4) **Proton background modeling** \u2013 mismodeling of stopping proton rates, which can bias the kaon dE/dx distribution (~1\u202f%); and (5) **Recombination model uncertainties** \u2013 variations in the Modified Box or Thomas\u2013Imel parameters (~1\u202f%). These effects are typically combined in quadrature to estimate the total systematic uncertainty on the reconstructed kaon energy and dE/dx profile."} +{"question": "In proton\u2011decay searches, how does the angular distribution of muon daughters from kaon decays assist in rejecting background events?", "answer": "A K\u207a that decays at rest produces a muon with a uniform (isotropic) angular distribution relative to the kaon track, because the decay is two\u2011body and the kaon\u2019s momentum is negligible. In contrast, muons produced by charged\u2011current neutrino interactions or by inelastic pion or proton scattering tend to be highly forward\u2011peaked, inheriting the direction of the parent hadron. By measuring the cosine of the angle between the kaon candidate and its muon daughter, events with cos\u202f\u03b8\u202f<\u202f0.6 can be selected, effectively rejecting the forward\u2011peaked background while retaining most of the isotropic signal. This geometrical cut, when combined with dE/dx and range information, provides a powerful handle on background suppression."} +{"question": "What is the exact efficiency of the ProtoDUNE\u2011SP detector for detecting K\u207a decays at rest when using the photon detection system?", "answer": "The answer to this question is currently unknown. The ProtoDUNE\u2011SP data set used in the analysis did not employ the photon detection system for the kaon selection; instead, only the charge readout was relied upon. While the photon system can, in principle, provide additional timing and energy\u2011deposition information (e.g., detecting the prompt scintillation from the kaon stop and the delayed Michel electron from the muon decay), a quantitative efficiency measurement that incorporates photon signals has not yet been performed. Such a study would require dedicated calibration runs, precise modeling of the photon collection efficiency, and a comprehensive assessment of the detector\u2019s optical response\u2014all of which are still topics of ongoing research."} +{"question": "How would the track\u2011length extension fitting (TLEFit) algorithm perform for charged particles whose kinetic energy exceeds 1\u202fGeV, a regime where the dE/dx curve becomes almost flat (MIP region)?", "answer": "At high kinetic energies the Bethe\u2013Bloch dE/dx curve has a very shallow slope, so the residual\u2011range versus dE/dx relationship provides weak discriminating power. The TLEFit algorithm would still fit an offset, but the resulting energy resolution would degrade and the fitted offset would tend to converge to a value that corresponds to the minimum\u2011ionizing plateau, leading to a systematic bias toward lower energies. In practice one would need to supplement the fit with additional information (e.g., multiple\u2011scattering angles or calorimetric deposits) to recover acceptable resolution above ~1\u202fGeV."} +{"question": "Can the TLEFit technique be adapted to determine the kinetic energy of neutral hadrons, such as neutrons, by exploiting the ionization signatures of the secondary charged particles they produce?", "answer": "Neutrons do not ionize directly, so the TLEFit algorithm cannot be applied to the neutron itself. However, if a neutron undergoes a hadronic interaction that produces one or more charged secondaries with measurable tracks, the TLEFit algorithm can be used on each charged secondary individually to infer its kinetic energy. The total neutron energy would then be estimated by summing the reconstructed energies of all secondaries and adding the energy carried by undetected neutrons, which introduces a large, event\u2011by\u2011event uncertainty. Thus, TLEFit is useful for charged products but not for a direct neutron energy measurement."} +{"question": "What are the dominant systematic uncertainties introduced by the modified\u2011box recombination model parameters (\u03b1 and \u03b2\u2032) when applying the TLEFit algorithm in a liquid\u2011argon TPC?", "answer": "The recombination model translates the measured ionization charge (dQ/dx) into energy loss (dE/dx). Uncertainties in \u03b1 and \u03b2\u2032 propagate directly into the dE/dx PDFs used by TLEFit. A \u00b11\u202f\u03c3 shift in \u03b1 changes the low\u2011dE/dx tail of the distribution, while a shift in \u03b2\u2032 mainly affects the high\u2011dE/dx (Bragg\u2011peak) region. These changes alter the likelihood landscape, leading to systematic shifts in the fitted offset and hence a bias in the reconstructed kinetic energy. In the ProtoDUNE\u2011SP study, variations of \u00b11\u202f\u03c3 in \u03b1/\u03b2\u2032 produced fractional\u2011bias shifts up to ~3\u202f% for 300\u202fMeV pions, and an uncertainty band of ~1\u20132\u202f% on the energy resolution. Therefore, precise calibration of the recombination parameters is critical for accurate TLEFit performance."} +{"question": "How does the presence of a magnetic field in a liquid\u2011argon TPC influence the assumptions underlying the TLEFit algorithm?", "answer": "A magnetic field bends charged particle trajectories, introducing curvature that alters the true path length relative to the straight\u2011line distance between reconstructed hits. The TLEFit algorithm assumes that the measured residual range corresponds to the straight\u2011line distance along the true track, which is violated in a magnetic field. The resulting systematic bias can be mitigated by incorporating track curvature into the residual\u2011range calculation or by performing a 3\u2011D helical fit before applying TLEFit. Additionally, the magnetic field affects multiple scattering by reducing lateral deflections, which may slightly change the dE/dx distribution width, but this effect is subdominant compared to the path\u2011length distortion."} +{"question": "Is it possible to extend the TLEFit algorithm to reconstruct the kinetic energy of electrons that emit Bremsstrahlung photons while traversing liquid argon?", "answer": "The paper does not address this scenario, and the current TLEFit framework assumes a single, continuous charged track with a monotonic residual\u2011range vs. dE/dx relationship. Electrons undergoing Bremsstrahlung experience significant energy loss in discrete photon emission events, leading to kinks and discontinuities in the dE/dx profile that violate the assumptions of the algorithm. Therefore, we do not yet know whether TLEFit can be adapted for such electrons without substantial modification or additional reconstruction steps, and further study would be required to evaluate its feasibility."} +{"question": "What is the most sensitive frequency band for all-sky searches of continuous gravitational waves from isolated neutron stars using third\u2011generation detectors?", "answer": "In all\u2011sky searches conducted with third\u2011generation interferometers, the most sensitive band typically lies between about 50\u202fHz and 250\u202fHz. Within this range the detector noise floor is lowest and the Doppler modulation is modest, allowing the longest coherent integrations and the highest upper\u2011limit depths."} +{"question": "How can continuous gravitational\u2011wave signals from rapidly rotating neutron stars be distinguished from instrumental lines in the data?", "answer": "Continuous\u2011wave searches apply a combination of vetoes: (1) cross\u2011detector coincidence requirements to ensure the signal is present in multiple interferometers; (2) line\u2011persistency checks that flag features consistent with known narrow\u2011band disturbances; (3) consistency tests comparing the signal\u2019s frequency evolution to the expected Doppler pattern from Earth\u2019s motion. Only candidates that survive all these stages are considered astrophysical."} +{"question": "What upper limits can be set on the ellipticity of a neutron star located 200\u202fpc away and spinning at 300\u202fHz?", "answer": "Using the most optimistic sensitivity depth for the 200\u2013400\u202fHz band, a neutron star at 200\u202fpc spinning at 300\u202fHz would have its ellipticity constrained to be below roughly \\(3\\times10^{-7}\\). This follows from the relation \\(\\varepsilon \\propto h_{0} d f^{-2}\\) and the strain upper limit of \\(\\sim1\\times10^{-25}\\) in that band."} +{"question": "Can current all\u2011sky searches place constraints on the abundance of primordial black holes with masses below \\(10^{-5}\\,M_{\\odot}\\) that inspiral within the Galaxy?", "answer": "Yes. By treating such binaries as continuous\u2011wave emitters with nearly monochromatic signals, the upper limits on strain translate into limits on the merger rate and abundance of light primordial black holes. The analysis shows that, for chirp masses below \\(10^{-5}\\,M_{\\odot}\\), the rate of inspirals within the solar neighbourhood must be lower than a few events per million years, constraining the fraction of dark matter that could be in the form of such primordial black holes."} +{"question": "Is there evidence for continuous gravitational\u2011wave emission from neutron stars in binary systems using the methods described in the paper?", "answer": "I do not have a definitive answer. The analysis in question focuses on isolated neutron stars, employing semi\u2011coherent pipelines tailored for solitary sources. Detecting continuous waves from neutron stars in binaries requires additional templates to account for orbital Doppler shifts and a different set of search parameters. Since this study did not explore binary parameter spaces, any conclusions about binaries would lie beyond its documented scope and would need a dedicated search strategy."} +{"question": "How does the total inelastic cross section for positively charged pions scattering off argon vary across the kinetic\u2011energy range 200\u202fMeV to 800\u202fMeV, and which resonance structures are primarily responsible for the observed energy dependence?", "answer": "The total inelastic \u03c0\u207a\u2013Ar cross section rises from a few hundred millibarns near 200\u202fMeV, reaches a pronounced maximum around the \u0394(1232) resonance (\u2248\u202f150\u2013170\u202fMeV in the laboratory frame), and then gradually decreases towards 800\u202fMeV as higher\u2011mass resonances and multi\u2011pion production channels open. The \u0394(1232) dominates the rise, while the subsequent fall is influenced by the onset of inelastic channels such as \u0394(1700) and the opening of the two\u2011pion production threshold."} +{"question": "Which systematic effects most significantly impact the precision of proton\u2013argon total inelastic cross\u2011section measurements at sub\u2011GeV energies, and what strategies can be employed to reduce these uncertainties in future LArTPC studies?", "answer": "The dominant systematic contributions are: (1) finite Monte\u2011Carlo statistics that propagate through the unfolding and efficiency corrections; (2) background modelling, especially the rates of elastic scattering and stopping\u2011proton contamination; (3) energy\u2011reconstruction uncertainties tied to the stopping\u2011power model (Bethe\u2011Bloch) and detector calibration; and (4) space\u2011charge distortion corrections that alter track length and energy deposition. Mitigation can be achieved by increasing the simulated event sample size, refining background estimators with data\u2011driven sidebands, improving the calibration of the energy scale (e.g., via dedicated calibration beams), and developing more accurate space\u2011charge maps or correcting algorithms."} +{"question": "In what manner do final\u2011state interactions (FSI) of charged pions inside liquid argon affect the reconstruction of neutrino energy in DUNE, and how can improved \u03c0\u207a\u2013Ar cross\u2011section data contribute to reducing these effects?", "answer": "FSI can absorb or re\u2011scatter pions, altering their energy, direction, and multiplicity before they exit the nucleus. This leads to mis\u2011estimation of the neutrino energy when relying on the observed hadronic system. Precise \u03c0\u207a\u2013Ar cross\u2011section data enable better tuning of intranuclear cascade models, thereby reducing uncertainties in pion absorption and scattering probabilities. Consequently, energy\u2011reconstruction algorithms can incorporate more realistic FSI probabilities, improving the fidelity of reconstructed neutrino energies."} +{"question": "Does the empirical scaling law \u03c3\u202f\u221d\u202fA^{2/3} for hadron\u2013nucleus total cross sections hold for argon when compared to lighter nuclei such as carbon and heavier nuclei such as lead, based on the most recent experimental data?", "answer": "Recent measurements indicate that the total inelastic cross section for \u03c0\u207a\u2013Ar and p\u2013Ar lies on the same A^{2/3} trend defined by other nuclei, with argon\u2019s cross sections roughly scaling between the values observed for carbon (A\u202f=\u202f12) and lead (A\u202f=\u202f208). The data show good agreement with the empirical exponent, suggesting that nuclear size and surface effects dominate the energy dependence across this range of target masses."} +{"question": "What is the differential (angular and momentum) distribution of secondary nucleons produced in \u03c0\u207a\u2013Ar inelastic interactions at a pion kinetic energy of 600\u202fMeV, and how does this distribution impact calorimetric energy reconstruction in liquid\u2011argon time\u2011projection chambers?", "answer": "I do not have information on the differential nucleon spectra for \u03c0\u207a\u2013Ar at 600\u202fMeV kinetic energy, as this specific observable was not measured or reported in the data set discussed. Determining these distributions would require dedicated experiments or detailed simulations that explicitly model the intra\u2011nuclear cascade and nucleon emission processes for this energy regime. Without such data, one cannot accurately assess how the secondary nucleon kinematics influence calorimetric reconstruction in LArTPC detectors."} +{"question": "What are the typical sky\u2011localization uncertainties for gravitational\u2011wave events detected by a network of advanced interferometers?", "answer": "For binary black\u2011hole mergers observed by the LIGO\u2013Virgo network, the 90\u202f% confidence sky area typically ranges from a few tens to several hundred square degrees, depending on the signal\u2011to\u2011noise ratio, the relative orientation of the detectors, and the waveform model used. The median 90\u202f% area for the first detections was on the order of 200\u2013300 deg\u00b2."} +{"question": "How does the choice of parameter\u2011estimation pipeline (e.g., BAYESTAR vs. LALInference) influence the reported sky maps for a gravitational\u2011wave trigger?", "answer": "Fast sky\u2011localization tools like BAYESTAR provide rapid estimates by marginalizing over distance and mass parameters with analytic approximations, yielding relatively compact 90\u202f% confidence regions. Full Bayesian samplers such as LALInference use the complete likelihood over all parameters, often resulting in slightly larger but more accurate maps that incorporate calibration uncertainties and more realistic priors. Consequently, LALInference maps are usually adopted as the definitive localization for follow\u2011up planning."} +{"question": "What electromagnetic signatures are theoretically expected from a binary black\u2011hole merger in a gas\u2011rich environment?", "answer": "In dense circumbinary disks or accretion flows, a merger can perturb the surrounding gas, potentially generating a prompt flare or a longer\u2011lasting afterglow across radio to X\u2011ray wavelengths. Models predict a burst of synchrotron emission as shock waves form, followed by a gradually declining spectrum. However, the exact luminosity depends on poorly constrained parameters such as disk density, magnetic field strength, and spin alignment."} +{"question": "What is the maximum distance out to which an optical transient associated with a binary black\u2011hole merger could be detected with current survey telescopes?", "answer": "Optical surveys with limiting magnitudes around 22\u201323\u202fmag can, in principle, detect kiloparsec\u2011scale transients out to roughly 100\u202fMpc if the event is intrinsically luminous. For binary black\u2011hole mergers, expected optical emission is far fainter, so practical detection horizons are much closer\u2014tens of megaparsecs\u2014unless an exceptionally bright flare occurs."} +{"question": "What is the expected optical afterglow brightness of a binary black\u2011hole merger occurring at 400\u202fMpc?", "answer": "I do not have information on this specific scenario. The paper does not provide theoretical or empirical predictions for optical afterglow brightness at such a distance for binary black\u2011hole mergers, and detailed modeling would be required to estimate the flux, which is beyond the scope of the present data."} +{"question": "How does the number of detectors in a gravitational\u2011wave network influence the accuracy of sky localization for binary black hole events?", "answer": "Adding more detectors narrows the triangulation baselines, reduces the timing uncertainty, and improves the determination of the source\u2019s position on the sky. With three or more detectors the sky area for a typical binary black hole event can shrink from hundreds of square degrees to a few tens of square degrees."} +{"question": "What are the main observational challenges when performing broadband electromagnetic follow\u2011up of gravitational\u2011wave events with large localization uncertainties?", "answer": "The primary challenges are (1) the need to tile very large areas of sky with limited field\u2011of\u2011view instruments, (2) coordinating many facilities to avoid duplication while maximizing coverage, (3) achieving sufficient depth quickly enough to catch fast transients, and (4) handling the large number of unrelated transients that appear in the search area."} +{"question": "How can galaxy catalog information be leveraged to prioritize electromagnetic follow\u2011up observations for gravitational\u2011wave triggers?", "answer": "By cross\u2011matching the probability sky map with catalogs of nearby galaxies (e.g., with stellar mass or star\u2011formation rate weighting) observers can assign higher priority to tiles containing galaxies within the expected distance range, thereby concentrating limited resources on the most likely host candidates."} +{"question": "What are the theoretical mechanisms that could enable a binary black hole merger to produce an electromagnetic counterpart?", "answer": "The current literature does not provide a definitive mechanism. Some speculative scenarios involve interaction with a dense circumbinary environment, residual accretion disks, or magnetic fields strong enough to power a short burst. However, no robust model has yet shown that such conditions are common or produce detectable emission, so the question remains largely open."} +{"question": "What role does low\u2011latency analysis play in enabling rapid electromagnetic follow\u2011up, and what improvements are needed for future runs?", "answer": "Low\u2011latency pipelines generate alerts within minutes of a gravitational\u2011wave detection, allowing telescopes to start observations before a transient fades. Improvements needed include faster parameter estimation (especially sky localization), real\u2011time assessment of the source type, and integration with automated scheduling systems to reduce human\u2011induced delays."} +{"question": "How does the total inelastic cross section of positively charged kaons on argon change as a function of kinetic energy between 2\u202fGeV and 5\u202fGeV?", "answer": "The cross section generally rises from a few hundred millibarns at 2\u202fGeV, reaches a broad maximum around 4\u20135\u202fGeV, and then slowly levels off or slightly decreases. This trend reflects the onset of additional inelastic channels (e.g., multi\u2011pion production) and the diminishing influence of the Coulomb barrier as the kaon energy increases."} +{"question": "What are the consequences of improved kaon\u2013argon interaction modeling for proton\u2011decay searches in liquid\u2011argon TPCs?", "answer": "Better modeling reduces systematic uncertainties in the simulation of kaon propagation and absorption, leading to a more accurate estimation of detection efficiencies for signatures such as \\(p \\rightarrow \\nu K^+\\). This in turn tightens the experimental limits on the proton lifetime and enhances the robustness of any observed excess."} +{"question": "Can the thin\u2011slice technique used for kaon\u2013argon cross\u2011section measurements be applied to study neutron\u2013argon interactions in a liquid\u2011argon TPC?", "answer": "Yes. By treating each wire plane as a thin target, one can count incident neutrons and the number that interact or produce secondary particles in successive slices. The main challenge is identifying neutrons, which require time\u2011of\u2011flight or delayed capture signatures, but with adequate tagging the method can yield differential neutron\u2013argon cross sections."} +{"question": "What is the measured cross section for negatively charged kaons on argon in the 5\u201310\u202fGeV energy range?", "answer": "This quantity has not yet been measured experimentally. Existing hadronic interaction generators provide only model predictions, and without dedicated beam\u2011test data the precise value\u2014and its energy dependence\u2014remains uncertain."} +{"question": "How does the space\u2011charge effect in a liquid\u2011argon TPC impact the reconstruction of charged\u2011kaon tracks, and what strategies can mitigate this?", "answer": "Space charge builds up electric\u2011field distortions, causing reconstructed positions and directions to shift by several millimetres. For kaon tracks, this can bias the measured energy loss and vertex location. Mitigation techniques include applying a three\u2011dimensional space\u2011charge correction map derived from cosmic\u2011ray muon data, using external alignment sensors, and incorporating the corrections into the reconstruction algorithms to recover the true track geometry."} +{"question": "What are the primary advantages of a vertical\u2011drift LArTPC design compared to a traditional horizontal\u2011drift geometry for the DUNE far detector?", "answer": "A vertical\u2011drift geometry allows a longer drift path (up to ~6.5\u202fm per side) while keeping the maximum electron drift time short enough to avoid excessive electron recombination and diffusion. The cathode can be suspended centrally, creating two symmetric drift volumes that maximize the active liquid\u2011argon volume. Additionally, the vertical orientation reduces the number of wire planes needed and simplifies the anode plane assembly, leading to lower construction costs and fewer feed\u2011throughs."} +{"question": "How does the cathode module design influence both the electric field uniformity and photon\u2011detector performance in the vertical\u2011drift module?", "answer": "The cathode is made of a thin, highly resistive composite panel that is suspended from the top of the detector. Its surface is perforated to allow light from the surrounding field\u2011cage to pass through, improving photon collection. The field\u2011cage modules around the cathode are constructed with narrow aluminum profiles in the first 4\u202fm from the cathode to provide 70\u202f% optical transparency, while the outer region uses wider profiles to maintain the field gradient. This combination ensures a uniform drift field (\u22641\u202f% variation) while allowing photons to reach both cathode\u2011mounted and membrane\u2011mounted photon\u2011detector modules."} +{"question": "What are the main technical challenges involved in producing and qualifying the large charge\u2011readout planes (CRPs) for a full 17.5\u202fkt vertical\u2011drift module?", "answer": "Key challenges include (1) maintaining the mechanical planarity of the 3.2\u202fmm\u2011thick perforated PCBs over a 1.5\u202fm\u202f\u00d7\u202f1.5\u202fm area, (2) ensuring precise alignment of the two PCB halves to guarantee 100\u202f% electron transmission through the holes, (3) producing and testing a large number of high\u2011performance LArASIC front\u2011end ASICs under cryogenic conditions, (4) achieving the required electrical shielding and grounding on both the induction and collection planes, and (5) integrating the CRP into the cryostat\u2019s support structure while preserving the 5\u202fmm gap between adjacent planes for optical access and mechanical tolerances."} +{"question": "What effect does a 10\u202fppm xenon doping have on the photon\u2011detector light yield and timing in the vertical\u2011drift Far Detector?", "answer": "Xenon doping shifts a substantial fraction (\u2248\u202f53\u202f%) of the scintillation light from 128\u202fnm to 176\u202fnm. The longer\u2011wavelength photons experience less Rayleigh scattering and absorption, improving the overall light collection efficiency by roughly 20\u201330\u202f%. Additionally, xenon dimers have a shorter decay time (\u2248\u202f4\u202f\u00b5s) compared to pure argon, leading to a faster prompt component and improved timing resolution for low\u2011energy events such as supernova neutrinos."} +{"question": "How will the long\u2011term stability of the high\u2011voltage divider board (HVDB) affect the electron lifetime and detector performance over a 10\u2011year operation period?", "answer": "The long\u2011term stability of the HVDB is critical because any drift in the resistor values or degradation of the high\u2011voltage insulation can alter the field uniformity and thus impact electron drift times and recombination rates. Current studies have not yet quantified how these changes will influence the electron lifetime over a decade, as the HVDB materials and their behavior under continuous cryogenic exposure are still under investigation. Further long\u2011term aging tests and in\u2011situ monitoring of the field uniformity are needed to assess the impact on detector performance and to ensure that the electron lifetime remains within the required specification."} +{"question": "How does the total inelastic \u03c0+\u2013argon cross section evolve below 500\u00a0MeV kinetic energy?", "answer": "The study presented focuses on the 500\u2013800\u00a0MeV range, so the behaviour of the cross section at lower energies is not covered. Determining the cross section below 500\u00a0MeV would require dedicated data at those energies and possibly different detector optimisation, which are not available in the current analysis."} +{"question": "What is the angular distribution of the outgoing protons in \u03c0+ absorption on argon?", "answer": "The paper reports overall absorption rates but does not provide detailed angular spectra for the recoil protons. Such information would need a separate reconstruction study focusing on proton kinematics and a larger event sample to achieve sufficient statistical precision."} +{"question": "Can the measured \u03c0+\u2013argon charge\u2011exchange cross section be used to constrain the pion mean free path in liquid argon for neutrino interaction simulations?", "answer": "Yes, the measured charge\u2011exchange cross section directly informs the mean free path of charged pions in argon, which is a key parameter in neutrino event generators. Incorporating these results can improve the modelling of final\u2011state interactions in neutrino detectors."} +{"question": "How do space\u2011charge effects impact the reconstruction of low\u2011momentum \u03c0+ tracks in a large LArTPC?", "answer": "Space\u2011charge distortions can shift the apparent positions of ionisation deposits, potentially biasing the energy and direction reconstruction of low\u2011momentum tracks. Understanding and correcting for these effects is essential for accurate cross\u2011section measurements but requires detailed calibration studies beyond the scope of the presented analysis."} +{"question": "What is the cross section for \u03c0+\u2013argon interactions that produce a single \u03c00 in the final state without any charged pions above 150\u00a0MeV/c?", "answer": "The paper defines a charge\u2011exchange channel that requires at least one \u03b3 from a \u03c00 decay but does not isolate events with exactly one \u03c00 and no charged pions. Measuring this specific final\u2011state cross section would necessitate additional event selection criteria and higher\u2011statistics data, which are not part of the current study."} +{"question": "What astrophysical processes can generate high\u2011energy neutrinos at the same time as gravitational\u2011wave bursts?", "answer": "Relativistic outflows produced during the collapse of massive stars, mergers of compact binaries, or interactions of jets with surrounding material can accelerate protons to very high energies. These protons then interact with photons or ambient gas to produce charged pions that decay into high\u2011energy neutrinos, while the violent dynamics of the system emit gravitational waves."} +{"question": "How does the gravitational\u2011wave energy output of a binary neutron star merger compare to that of a core\u2011collapse supernova?", "answer": "A binary neutron star merger typically radiates a few percent of a solar mass in gravitational waves (\u224810\u207b\u00b2\u202fM\u2299c\u00b2), concentrated around a few hundred hertz. A core\u2011collapse supernova is expected to emit much less, usually \u226410\u207b\u2077\u202fM\u2299c\u00b2, unless the core is rapidly rotating or otherwise dynamically unstable."} +{"question": "What observational advantages does a joint gravitational\u2011wave and neutrino detection offer over single\u2011messenger observations?", "answer": "The precise timing of a gravitational\u2011wave burst coupled with the directional information from a high\u2011energy neutrino allows a dramatic reduction in the sky localization area, enabling faster and more targeted electromagnetic follow\u2011up. It also provides a cross\u2011check that the transient is indeed astrophysical rather than instrumental or atmospheric."} +{"question": "In what way could the detection of neutrinos from a core\u2011collapse supernova inform us about the mechanism of jet formation within the stellar envelope?", "answer": "Neutrinos produced in a choked jet scenario would carry information about the density, magnetic field, and particle acceleration conditions inside the envelope. Measuring their energy spectrum and arrival time relative to the gravitational wave could constrain the jet launch delay, opening angle, and baryon loading, which are key parameters in jet\u2011formation models."} +{"question": "Has the recent multi\u2011messenger search set definitive limits on the rate of binary neutron star mergers that emit both gravitational waves and high\u2011energy neutrinos?", "answer": "No. The analysis provides only upper limits on the combined population of gravitational\u2011wave and high\u2011energy\u2011neutrino emitters in general. It does not specifically constrain binary neutron star mergers because the limits depend on generic assumptions about the neutrino spectrum and beaming, which may not apply to all BNS systems."} +{"question": "How do temperature gradients within a liquid argon TPC affect the electron attachment rate to electronegative impurities?", "answer": "Electron attachment rates are highly sensitive to temperature because the mobility of impurity molecules and the electron mean free path change with thermal motion. In practice, a temperature rise of 1\u202fK in the liquid argon can increase the attachment rate by roughly 5\u202f%\u201310\u202f% for typical oxygen or water concentrations. Consequently, even small temperature gradients across a detector volume can lead to measurable variations in the drift\u2011electron lifetime. Experimental studies on small LArTPC prototypes have confirmed that maintaining isothermal conditions within \u00b10.2\u202fK is essential for stable operation."} +{"question": "What is the time evolution of impurity concentration when the argon recirculation pump is turned off for a few hours in a large\u2011scale LArTPC?", "answer": "During pump downtime the liquid argon is no longer actively filtered, so the dominant source of contamination is the outgassing of detector components and the diffusion of residual impurities from the gas phase. In a typical 10\u2011ton module, the oxygen equivalent concentration can increase by about 10\u201315\u202fppb per hour, leading to a drift\u2011electron lifetime decrease of 10\u201315\u202f% per hour. After 24\u202fhours, the lifetime can fall from >20\u202fms to below 10\u202fms if no additional purification is applied."} +{"question": "Is it possible to calibrate space\u2011charge corrections in a LArTPC using only through\u2011going cosmic\u2011ray muons, without external timing detectors?", "answer": "Yes. By reconstructing straight\u2011line tracks from cosmic\u2011ray muons that traverse the full drift volume, one can measure the apparent shift of the track endpoints as a function of drift time. These shifts directly encode the local electric\u2011field distortions caused by space charge. With sufficient statistics and a known timing reference from the detector clock, the correction maps can be derived internally, eliminating the need for external scintillator systems."} +{"question": "What minimum drift\u2011electron lifetime is required to keep the energy resolution for MeV\u2011scale neutrino interactions below 1\u202f% in a 5\u202fm drift LArTPC?", "answer": "Simulations of MeV\u2011scale electromagnetic showers in a 5\u202fm drift TPC show that a lifetime of at least 15\u202fms is needed to limit the charge loss to <1\u202f%. With a lifetime of 20\u202fms the charge attenuation is below 0.6\u202f%, yielding an energy resolution better than 0.9\u202f% for a 5\u202fMeV deposition. Lifetimes below 10\u202fms start to degrade the resolution above 1\u202f%."} +{"question": "Is there a significant difference in electron lifetime between argon that has been purified primarily by removing water versus oxygen, and how does this affect charge collection?", "answer": "The paper does not provide data comparing water\u2011only versus oxygen\u2011only purification. While both impurities attach electrons, oxygen has a higher attachment cross\u2011section, so an argon sample free of oxygen but still containing residual water would generally have a longer electron lifetime. However, the exact quantitative difference depends on the concentrations achieved by each purification method, and the current study does not address this comparison. Therefore, we cannot provide a definitive answer based on the present information."} +{"question": "How does the charged\u2011current muon\u2011neutrino interaction cross section on argon vary between the quasi\u2011elastic and resonance production regions when the neutrino beam is narrowly tuned to a fixed energy?", "answer": "When the incoming neutrino energy is tightly constrained, the cross\u2011section in the quasi\u2011elastic (CCQE) region rises smoothly with energy, while the resonance (RES) region shows a pronounced peak near the \u0394(1232) mass. As the beam energy increases, the RES contribution becomes dominant above ~1\u202fGeV, causing the total inclusive cross section to steeply increase. A narrow virtual flux allows the CCQE peak to be isolated at lower energies and the \u0394 resonance peak to be resolved around 1\u20131.5\u202fGeV, providing a clear view of the transition between the two regimes."} +{"question": "What are the principal systematic uncertainties that limit the precision of virtual\u2011flux cross\u2011section measurements with the DUNE\u2011PRISM near detector, and which strategies could reduce their impact?", "answer": "The dominant systematics arise from (1) the neutrino flux shape and normalization, (2) the modeling of neutrino\u2011nucleus interactions (particularly final\u2011state interactions and 2p2h processes), and (3) detector response such as energy scale and particle\u2011ID efficiency. Mitigation strategies include: using external hadron\u2011production data to constrain flux uncertainties, applying Tikhonov regularization and flux\u2011matching techniques to minimise the amplification of statistical fluctuations, incorporating in\u2011situ calibration with known neutrino reactions, and developing robust unfolding algorithms that separate flux and interaction\u2011model effects."} +{"question": "Can the virtual\u2011flux technique be adapted to measure the neutrino\u2011neutron cross section on argon, and what experimental challenges would need to be overcome?", "answer": "In principle, a narrow virtual flux can be used to probe neutrino\u2011neutron interactions by selecting final\u2011state topologies that are sensitive to neutrons (e.g., charged\u2011current quasi\u2011elastic scattering with a detected proton). Challenges include: distinguishing neutron\u2011induced events from proton\u2011induced ones, accounting for the lack of a free neutron target, handling the higher background from neutral\u2011current interactions, and accurately modeling the neutron\u2019s binding energy and Fermi motion in argon. Improved tracking and calorimetry, combined with sophisticated reconstruction of missing momentum, would be required."} +{"question": "What is the influence of final\u2011state interaction (FSI) modeling uncertainties on the measurement of the energy\u2011transfer differential cross section using virtual fluxes?", "answer": "FSI affect the energies and directions of outgoing hadrons, thereby smearing the reconstructed energy transfer (\u03c9_reco). However, because the virtual flux is narrow in neutrino energy, the dominant smearing comes from the flux width rather than from FSI. Residual FSI uncertainties primarily distort the shape of the \u03c9_reco distribution, especially near the quasi\u2011elastic peak and in the dip between CCQE and resonance regions. Quantitatively, varying the FSI strength within reasonable bounds can change the differential cross\u2011section shape by a few percent, indicating that precise FSI modeling is still essential for sub\u201110% level measurements."} +{"question": "Does the virtual\u2011flux construction preserve the relative energy dependence of two\u2011particle\u2013two\u2011hole (2p2h) contributions across different neutrino energies?", "answer": "The paper does not address this specific question. While the virtual\u2011flux technique can isolate broad energy ranges, it is unclear whether the weighting procedure and regularization applied during flux matching retain the true energy dependence of the 2p2h component. Further studies, possibly with alternative target flux shapes and validation against detailed nuclear\u2011model predictions, are needed to determine whether 2p2h effects are faithfully represented in virtual\u2011flux\u2011averaged measurements."} +{"question": "How can machine learning techniques be integrated into the GPU-based simulation pipeline to predict detector response in real time?", "answer": "Machine learning can be used to replace or augment physics\u2011based sub\u2011models within the simulation. For example, a deep neural network trained on high\u2011fidelity simulation data can predict the induced current waveform for a given ionization track, or learn the mapping from raw charge deposition to digitized ADC counts. By compiling the trained model with libraries such as TensorFlow\u2011Lite or ONNX Runtime and running it on the same GPU as the physics kernels, one can achieve real\u2011time inference. The network would be inserted after the electron drift and diffusion stage but before the ASIC digitization stage, reducing the number of explicit convolutional operations required. Validation would involve cross\u2011checking the ML\u2011predicted waveforms against a reference simulation over a broad range of track geometries and field configurations."} +{"question": "What are the scalability limits of GPU\u2011accelerated LArTPC simulation when moving from a 0.5\u202fm\u00b3 detector to a 10\u202fm\u00b3 scale?", "answer": "Scalability is governed by three factors: (1) memory consumption\u2014each charge segment requires a few tens of bytes for position, charge, diffusion parameters, and (2) the number of threads needed to cover all pixels, which grows linearly with the detector surface area; a 10\u202fm\u00b3 LArTPC may have on the order of 10\u2076 pixels, still within the 96\u2011GB memory of a modern V100 or A100 GPU if data are streamed in tiles; (3) kernel launch overhead and inter\u2011GPU communication. On a multi\u2011GPU node, the simulation can be partitioned spatially so that each GPU handles a sub\u2011volume, with halo exchanges for electrons that cross tile boundaries. With careful tiling and overlapping of computation and data transfer, a 20\u2011fold increase in volume can be simulated with only a modest increase in wall\u2011clock time, often remaining the dominant part of the pipeline."} +{"question": "How does the inclusion of space\u2011charge effects alter the electric field configuration in a pixelated LArTPC, and how can this be incorporated into the simulation?", "answer": "Space\u2011charge from slowly drifting ions builds up a distortion in the nominal uniform field, typically reducing the drift velocity and altering the weighting field near the anode. To incorporate this, one can solve Poisson\u2019s equation on a 3\u2011D grid that includes the ion density field, using a fast solver (e.g., multigrid or FFT\u2011based). The resulting field map can then be interpolated for each electron step during drift. In a GPU implementation, the field map can be stored as a texture and accessed via bilinear interpolation, ensuring that the drift velocity and diffusion coefficients are updated dynamically. This adds a modest computational cost (\u224810\u202f% of the induced\u2011current kernel) while improving the fidelity for high\u2011rate or high\u2011ionization scenarios."} +{"question": "What are the systematic uncertainties introduced by using a fixed diffusion coefficient in the electron transport model, and how can they be quantified?", "answer": "Assuming a single, constant diffusion coefficient neglects its dependence on the local electric field and temperature. The systematic uncertainty can be quantified by propagating the variance of the diffusion coefficient into the width of the induced current pulse. This is done by generating multiple simulations with diffusion coefficients sampled from a distribution (e.g., Gaussian with mean\u202f=\u202fvalue from data and \u03c3\u202f=\u202fexperimental uncertainty). The spread in the reconstructed charge or hit position then provides a direct estimate of the systematic error. In practice, varying the longitudinal and transverse diffusion by \u00b110\u202f% shows a shift of \u22483\u202f% in the charge\u2011collection efficiency for MIP tracks, which is comparable to the intrinsic ASIC noise."} +{"question": "What is the impact of non\u2011uniformities in the pixel pad geometry on the induced current signals, and how significant are these effects compared to the intrinsic noise of the ASIC?", "answer": "The agent does not know the answer. This question requires detailed electromagnetic simulation of the actual pad geometry (e.g., variations in pixel size, edge effects, and inter\u2011pixel spacing) and its effect on the weighting field. The resulting variations in induced current are typically of the order of a few percent, which is comparable to or smaller than the intrinsic electronic noise (\u2248500\u202fe\u207b). A full study would involve measuring the actual pad layout, generating a refined FEM mesh, and re\u2011computing the current response, which is beyond the scope of the present work."} +{"question": "How does xenon doping affect the lifetime of free electrons in liquid argon?", "answer": "Xenon is chemically inert and does not introduce additional electronegative impurities that would capture drifting electrons. In practice, a moderate xenon concentration (up to a few tens of ppm) has been observed to have a negligible effect on the free\u2011electron lifetime in large liquid\u2011argon TPCs. The primary factor that governs electron lifetime remains the concentration of oxygen, water, and other electronegative contaminants; xenon addition does not significantly change the attachment rates. Consequently, detectors that operate with a few\u2011ppm xenon doping typically report electron lifetimes that are comparable to those measured in undoped argon, provided that the xenon itself is of high purity and that the purification system remains effective."} +{"question": "What is the optimal xenon concentration for maximizing light yield while minimizing cost for a 10\u2011kt liquid\u2011argon detector?", "answer": "In large\u2011volume LArTPCs the light yield improvement from xenon doping is a diminishing\u2011returns process. Empirical studies on 100\u2011kg to 1\u2011kt prototypes show that a xenon concentration of 10\u201315\u202fppm (by mass) yields about a 30\u201340\u202f% increase in total scintillation light, after which the gain saturates. For a 10\u2011kt detector the cost of xenon scales linearly with the amount required; 15\u202fppm in 10\u202fkt corresponds to roughly 150\u202fkg of xenon. Considering the high price of xenon (\u2248\u202f\\$100\u202fkg\\(^{-1}\\)) and the marginal increase in light yield beyond 15\u202fppm, many groups recommend targeting the 10\u201312\u202fppm range as a cost\u2011effective compromise. This choice maximizes light collection and pulse\u2011shape discrimination performance while keeping xenon expenses manageable."} +{"question": "Can xenon doping improve pulse\u2011shape discrimination between electron and nuclear recoils in liquid argon?", "answer": "Xenon doping modifies the relative contributions of the fast (singlet) and slow (triplet) scintillation components. By transferring energy from the argon triplet state to xenon, the overall pulse shape becomes faster and the distinction between electron\u2011like (shorter fast component fraction) and nuclear\u2011recoil events (higher fast component fraction) can be sharpened. Experiments with small\u2011scale detectors have demonstrated an improvement in pulse\u2011shape discrimination (PSD) metrics by 10\u201320\u202f% when operating at \u2248\u202f10\u202fppm xenon, especially at lower energies where the triplet component dominates. However, the benefit plateaus for higher xenon concentrations because the fast component becomes dominated by xenon scintillation, which has its own PSD characteristics. Therefore, xenon doping can enhance PSD, but only up to an optimal concentration that balances the competing light\u2011yield and PSD contributions."} +{"question": "How does the presence of nitrogen at 5\u202fppm alter the Rayleigh scattering length of argon scintillation photons?", "answer": "Nitrogen is essentially transparent to the vacuum\u2011ultraviolet (VUV) photons in liquid argon, so it does not directly affect the Rayleigh scattering cross\u2011section. The scattering length of 127\u202fnm photons in pure liquid argon is about 1.8\u202fm. Adding 5\u202fppm of nitrogen introduces only a tiny change in the refractive index; the resulting modification to the Rayleigh scattering length is on the order of a few millimetres\u2014well below the experimental resolution. Thus, the presence of 5\u202fppm nitrogen does not meaningfully alter the photon transport properties in the bulk liquid. The dominant effect of nitrogen at this concentration is quenching of the argon triplet state, which reduces the overall light yield but leaves the scattering length unchanged."} +{"question": "Does xenon doping affect the drift field uniformity in a large liquid argon TPC?", "answer": "The model does not have information from the paper that directly addresses this question, so it cannot provide a definitive answer. In principle, xenon is an inert noble gas that does not alter the dielectric constant of liquid argon by a measurable amount at ppm concentrations, so the electric\u2011field distribution determined by the cathode, anode, and field\u2011shaping rings should remain essentially unchanged. However, any subtle changes would depend on the exact detector geometry and the purity of the xenon added. Further detailed electro\u2011static simulations and dedicated measurements would be required to confirm whether drift\u2011field uniformity is affected at the ppm\u2011level doping studied in the paper."} +{"question": "What are the leading theoretical models that predict gravitational-wave emission from fast radio burst progenitors?", "answer": "Current models suggest that compact binary coalescences (binary neutron stars or neutron star\u2013black hole systems) can produce both the rapid radio pulses and a short-lived burst of gravitational waves through magnetic interactions or tidal disruption. Additionally, magnetar flares or giant magnetar outbursts can excite stellar oscillation modes that generate gravitational waves, especially in the kilohertz range."} +{"question": "How does the dispersion measure of a fast radio burst help estimate its cosmological distance?", "answer": "The dispersion measure (DM) quantifies the total column density of free electrons along the line of sight. By subtracting modeled contributions from the Milky Way, its halo, and the host galaxy, the remaining intergalactic DM can be mapped to redshift using empirical relations (e.g., the Macquart relation). This provides a statistical distance estimate, often expressed as a 90% credible interval due to large uncertainties."} +{"question": "What are the main differences between a model\u2011based and a generic (unmodelled) gravitational\u2011wave search pipeline when targeting short\u2011duration transients?", "answer": "A model\u2011based pipeline, such as matched\u2011filtering with a template bank, assumes a specific waveform morphology (e.g., binary inspiral) and maximizes sensitivity for that scenario, but may miss unexpected signals. A generic pipeline uses coherent excess\u2011power or time\u2011frequency clustering to detect any transient, regardless of shape, offering broader coverage at the cost of reduced sensitivity for any single waveform type."} +{"question": "What challenges arise when searching for gravitational\u2011wave counterparts to fast radio bursts detected by wide\u2011field radio telescopes like CHIME/FRB?", "answer": "Key challenges include large sky\u2011localization uncertainties that require scanning many sky patches, limited detector duty cycles leading to sparse data coverage, and the need to account for significant uncertainties in FRB distances derived from DM. Additionally, the short timescales of FRBs demand rapid, low\u2011latency data analysis to correlate with gravitational\u2011wave events."} +{"question": "Is there conclusive evidence linking any fast radio burst to a gravitational\u2011wave detection during the third observing run of Advanced LIGO and Virgo?", "answer": "The current analysis does not find any statistically significant gravitational\u2011wave signal coincident with the observed fast radio bursts. Therefore, we cannot claim a definitive association. This lack of evidence may be due to either the absence of detectable gravitational\u2011wave emission from these bursts, insufficient detector sensitivity at the relevant distances, or the intrinsic rarity of such joint events. Further observations with more sensitive detectors or a larger FRB sample are required to confirm or rule out this association."} +{"question": "How does the mass ratio of a neutron star\u2013black hole binary influence the morphology of its gravitational\u2011wave signal, and what are the consequences for extracting component masses with next\u2011generation detectors?", "answer": "The mass ratio determines the amplitude ratio between the dominant quadrupole mode and higher\u2011order modes; highly asymmetric systems exhibit stronger higher\u2011order multipole contributions, which can bias mass estimates if not modeled accurately. Advanced detectors with improved low\u2011frequency sensitivity will better capture early inspiral, helping to disentangle mass ratio effects and reduce systematic errors."} +{"question": "What can the measurement of the effective inspiral spin parameter tell us about the natal spin distribution of black holes in neutron star\u2013black hole binaries, and how does this inform binary\u2011formation scenarios?", "answer": "A positive effective spin suggests alignment with the orbital angular momentum, typical of isolated binary evolution with weak supernova kicks, whereas a negative or small effective spin points to dynamical formation or large natal kicks. Comparing spin distributions across many events can discriminate between these channels and refine population synthesis models."} +{"question": "In what way does the tidal deformability of the neutron star component affect the post\u2011merger gravitational\u2011wave spectrum of a neutron star\u2013black hole coalescence, and how can future detectors use this to constrain the neutron\u2011star equation of state?", "answer": "A more deformable neutron star experiences stronger tidal interactions, potentially generating a high\u2011frequency post\u2011merger signal (e.g., quasi\u2011normal\u2011mode ringing or disk\u2011oscillation modes). Detecting such signatures would place upper limits on the tidal Love number, thereby constraining the stiffness of the equation of state. Next\u2011generation detectors with extended high\u2011frequency bandwidth are required for robust measurements."} +{"question": "How might the presence of a circumbinary disk or nearby stellar companions in dense stellar environments alter the orbital evolution and merger rate of neutron star\u2013black hole binaries?", "answer": "Environmental torques can extract angular momentum, potentially accelerating inspiral and modifying eccentricity. Tidal interactions with a disk may also alter spin alignment. These effects can change the observable population and must be accounted for when estimating merger rates from dense clusters or galactic nuclei."} +{"question": "What is the expected rate of observable electromagnetic counterparts (short GRBs or kilonovae) from neutron star\u2013black hole mergers across a range of mass ratios and spins?", "answer": "I do not have an answer to this question. The paper does not quantify the rates of electromagnetic counterparts for NSBH mergers, and current observational data are insufficient to provide reliable estimates. Further multi\u2011messenger observations and detailed simulations are required to constrain these rates."} +{"question": "How does the use of a resistive field shell in a modular liquid\u2011argon TPC affect the uniformity of the drift electric field compared to conventional resistor\u2011chain cages?", "answer": "Resistive field shells provide a smoother potential gradient because the field is distributed across the surface rather than concentrated at discrete points. This can reduce high\u2011field regions that might trigger discharges. However, the exact quantitative improvement depends on the sheet resistance, shell geometry, and the stability of the resistive material over time, and must be validated experimentally for each detector design."} +{"question": "What are the main advantages of a native 3D pixelated charge readout for event reconstruction in high\u2011occupancy neutrino beam environments?", "answer": "Pixelated readouts give independent 3D coordinates for every ionization cluster without requiring complex wire\u2011plane reconstruction. This allows straightforward association of charge with localized scintillation light, improves background rejection, and mitigates pile\u2011up by enabling per\u2011pixel timing information that can be used to separate overlapping tracks."} +{"question": "How can a high\u2011coverage dielectric light\u2011detection system be optimized to provide nanosecond\u2011level timing for neutrino interactions in a liquid\u2011argon TPC?", "answer": "Optimizing such a system involves selecting wavelength\u2011shifting materials with fast decay times, positioning light traps close to the anode to reduce photon path lengths, and using silicon photomultipliers (SiPMs) with low dark count rates and high photon detection efficiency. The geometry must maximize geometrical coverage while maintaining optical isolation between adjacent TPC modules."} +{"question": "In a modular LArTPC array, what strategies can be employed to preserve optical isolation between adjacent detector modules while minimizing dead material?", "answer": "Optical isolation can be achieved by incorporating thin, high\u2011index reflective coatings on the field\u2011shaping panels, using dielectric light traps that are non\u2011conductive, and designing inter\u2011module gaps that are small enough to reduce passive material yet sufficient to prevent light leakage. Careful alignment and precise machining of the modules also help maintain isolation without adding significant structural material."} +{"question": "What is the optimal pixel pitch for a liquid\u2011argon TPC pixelated readout that balances spatial resolution, electronic noise, and data\u2011rate constraints?", "answer": "The optimal pixel pitch is still an open question. While finer pitches improve spatial resolution and help resolve closely spaced tracks, they increase the number of readout channels, raising electronic noise and data\u2011rate requirements. Experimental studies are needed to determine the trade\u2011off between resolution and noise for different drift fields and event rates, and to establish a pixel pitch that meets the physics goals without exceeding technical limits."} +{"question": "How does the neutrino energy spectrum emitted by a core\u2011collapse supernova depend on the neutrino mass ordering?", "answer": "The neutrino mass ordering influences the survival probabilities of electron neutrinos and antineutrinos through the Mikheyev\u2013Smirnov\u2013Wolfenstein (MSW) resonances that occur in the stellar envelope. In the normal ordering, the \\(\\nu_e\\) survival probability is suppressed at high energies, while in the inverted ordering it is enhanced. Collective oscillation effects inside the core can further alter the spectra. Consequently, the observable \\(\\nu_e\\) spectrum at Earth is a convolution of the original emission spectrum with these flavor\u2011conversion probabilities, producing a mass\u2011ordering\u2011dependent shape that can be probed by detectors with good \\(\\nu_e\\) sensitivity."} +{"question": "What role do forbidden nuclear transitions play in the charged\u2011current cross section of neutrinos on argon at supernova energies?", "answer": "At neutrino energies above roughly 20\u201330\u202fMeV, higher\u2011multipole (forbidden) nuclear transitions contribute increasingly to the total charged\u2011current cross section on \\({}^{40}\\mathrm{Ar}\\). These transitions involve changes in nuclear spin and parity that are not allowed in the simple Gamow\u2013Teller (allowed) approximation. Their inclusion increases the cross\u2011section magnitude and modifies its energy dependence, especially at the upper end of the supernova spectrum, thereby affecting the expected event rate and the reconstructed energy distribution in a liquid\u2011argon detector."} +{"question": "How can the detection of low\u2011energy neutrons from neutrino\u2011argon interactions improve the reconstruction of supernova neutrino energies in a liquid\u2011argon detector?", "answer": "Charged\u2011current \\(\\nu_e\\) interactions on \\({}^{40}\\mathrm{Ar}\\) often emit one or more neutrons that escape the primary interaction vertex without depositing visible energy. If these neutrons are captured on gadolinium or other neutron\u2011sensitive materials, the resulting delayed \\(\\gamma\\)-cascade can be detected, allowing the experiment to recover the missing energy. By accounting for the neutron capture signal, the total energy deposited can be corrected, yielding a more accurate reconstruction of the incident neutrino energy and thereby improving the precision of flux\u2011parameter measurements."} +{"question": "What experimental strategies could be employed to directly measure the \\(\\nu_e + {}^{40}\\mathrm{Ar}\\) cross section in the 5\u201350\u202fMeV range?", "answer": "A practical approach is to use a well\u2011characterised neutrino source such as pion decay\u2011at\u2011rest (DAR) beams, which produce mono\u2011energetic \\(\\nu_\\mu\\) and a spectrum of \\(\\nu_e\\) and \\(\\bar\\nu_\\mu\\) extending up to 52\u202fMeV. A small liquid\u2011argon detector placed at a short baseline can record charged\u2011current events, and the known DAR flux allows a direct determination of the cross section. Alternative sources include intense spallation neutron facilities that generate \\(\\nu_e\\) from muon decay in flight, or the use of a stopped\u2011muon source in a dedicated liquid\u2011argon test chamber. In all cases, careful calibration of the detector response and background suppression are essential to obtain a reliable cross\u2011section measurement."} +{"question": "How would uncertainties in neutrino flavour conversions inside the supernova affect the inferred neutrino flux parameters at Earth, and what theoretical developments are needed to resolve this?", "answer": "The paper does not address this issue because it requires detailed, time\u2011dependent modelling of collective neutrino oscillations and matter effects inside the supernova core, which are still under active investigation. These processes can significantly alter the flavour composition and energy spectra that reach Earth, leading to potential biases in the extracted flux parameters if not properly accounted for. Resolving this uncertainty demands high\u2011resolution supernova simulations that couple neutrino transport with flavour\u2011dependent interaction physics, along with improved treatments of multi\u2011angle effects and turbulence, which are not yet fully understood or available in the literature."} +{"question": "How can superconducting radiofrequency (SRF) cavity surface treatments be optimized to achieve higher accelerating gradients for future high\u2011power proton linacs?", "answer": "Advanced surface processing techniques such as electropolishing (EP), buffered chemical polishing (BCP), and nitrogen doping (N\u2011doping) have been shown to reduce surface resistance and increase the quality factor (Q) of SRF cavities. By combining EP with low\u2011temperature bake\u2011outs and controlled nitrogen infusion during the final heat treatment, the superconducting gap can be enhanced, leading to gradients beyond 30\u202fMV/m while maintaining low field emission. Further optimization involves tailoring the surface roughness at the nanometer scale and using high\u2011purity niobium with a residual resistivity ratio (RRR) above 300 to minimize thermal losses."} +{"question": "What design strategies can mitigate thermal shock in high\u2011power graphite targets when exposed to multi\u2011megawatt proton beams?", "answer": "Effective mitigation relies on a combination of target geometry, active cooling, and material selection. Shortening the target length reduces the peak heat deposition, while a helical or baffle\u2011augmented beam raster spreads the energy over a larger surface area. High\u2011purity graphite grades with optimized grain structure and low thermal expansion coefficients are preferred. Active helium\u2011gas cooling channels directly surrounding the target core provide rapid heat extraction. Additionally, incorporating a gradient\u2011matched beam entrance window, typically a titanium alloy with low stress\u2011concentration, helps absorb shock loads and prevents rapid material fatigue."} +{"question": "How can cryogenic distribution systems be engineered to minimize helium boil\u2011off and maintain pressure stability in large liquid argon TPC cryostats?", "answer": "A well\u2011balanced cryogenic distribution network uses high\u2011conductivity copper or aluminum transfer lines with segmented heat\u2011anchor points to intercept conductive heat loads. The system incorporates distribution valve boxes (DVBs) that regulate the flow of superfluid and normal\u2011fluid helium, keeping the pressure drop within strict limits. Vacuum insulation between cryogenic lines reduces radiative heat transfer, and multi\u2011stage cold compressors handle the boil\u2011off efficiently. Finally, real\u2011time pressure sensors and automated control loops adjust valve positions to counteract transient thermal loads, ensuring stable temperature and pressure across all detector modules."} +{"question": "What are the implications of increasing LBNF beam power from 1.2\u202fMW to 2.4\u202fMW on secondary particle focusing and neutrino flux uncertainties?", "answer": "Doubling the proton beam power amplifies the intensity of secondary mesons produced in the target, which requires the focusing horns to sustain higher magnetic fields and thermal loads. To preserve neutrino flux precision, horn current profiles must be redesigned to handle increased joule heating, and the target\u2013horn assembly must be cooled more aggressively. Enhanced beamline optics may be needed to maintain the desired pion/kaon kinematics, thereby keeping the neutrino energy spectrum stable. Systematic uncertainties linked to hadron production and horn alignment can be reduced by incorporating in\u2011situ monitoring of secondary particle rates and by cross\u2011checking with external hadron production data from experiments such as NA61/SHINE."} +{"question": "What is the expected degradation rate of the stainless steel beam window material under prolonged exposure to a 2.4\u202fMW proton beam?", "answer": "The degradation rate of stainless steel windows in a multi\u2011MW proton beam environment is not yet known. Predicting material fatigue and embrittlement requires long\u2011term irradiation studies, coupled with thermal shock testing that simulate the actual beam pulse structure. Since such data are currently unavailable and the degradation mechanisms involve complex radiation\u2011induced defect accumulation, we cannot provide a reliable estimate at this time."} +{"question": "What are the main advantages of using a vertical drift geometry in large liquid argon time projection chambers for long\u2011baseline neutrino experiments?", "answer": "A vertical drift configuration allows the charge to drift over a longer distance without requiring additional readout planes. This reduces the number of front\u2011end electronics and the overall construction cost while still achieving the necessary spatial resolution. Because the ionization electrons travel parallel to the electric field, the uniformity of the drift field is easier to control, and the detector can be made more compact, which simplifies cryogenic infrastructure and shielding."} +{"question": "How does pixel\u2011based charge readout improve particle identification in a liquid argon TPC compared with traditional strip readout?", "answer": "Pixel readout provides true three\u2011dimensional imaging of every ionization cluster, eliminating the projection ambiguities that arise when multiple tracks overlap on a two\u2011dimensional strip plane. This yields a higher tracking efficiency, especially for complex, multi\u2011track events, and improves the accuracy of vertex reconstruction. The fine granularity also enhances the ability to separate electromagnetic showers from charged\u2011particle tracks, thereby improving electron\u2011neutrino versus background discrimination."} +{"question": "In what ways can enhanced photon\u2011detection systems such as APEX or PoWER contribute to lowering the energy threshold for supernova neutrino detection in DUNE?", "answer": "Both APEX and PoWER increase the optical coverage and improve light collection efficiency, which in turn raises the number of photo\u2011electrons detected per MeV of deposited energy. With a higher photon yield and better time resolution, the detector can trigger on, and reconstruct, lower\u2011energy events that would otherwise fall below the noise floor. This reduction in the effective energy threshold enhances sensitivity to the low\u2011energy tail of the supernova neutrino spectrum and extends the observable supernova distance range."} +{"question": "What role does a high\u2011pressure gaseous argon TPC (ND\u2011GAr) play in constraining neutrino\u2011argon cross\u2011section uncertainties for the DUNE far detector?", "answer": "The ND\u2011GAr provides a thin, low\u2011density target that mimics the argon nuclei of the far detector but with minimal re\u2011interaction of secondary particles. By measuring exclusive final states with excellent momentum resolution and particle identification, it directly probes nuclear effects (such as Fermi motion, short\u2011range correlations, and intranuclear rescattering). These measurements reduce the model dependence of cross\u2011section predictions used to interpret far\u2011detector data, thereby tightening systematic uncertainties on oscillation parameters."} +{"question": "What is the projected maximum drift voltage and electric field uniformity requirement for the FD4 module's 13\u202fm drift length, and how will the cryogenic and high\u2011voltage systems be engineered to achieve it?", "answer": "I do not have that information. The specific maximum drift voltage, the required field uniformity, and the detailed design of the cryogenic and high\u2011voltage infrastructure are not covered in the material provided. These technical specifications would be defined in later engineering design reports and require dedicated simulations and prototype testing that are beyond the scope of this document."} +{"question": "What are the key scaling challenges when transitioning DUNE's reconstruction workload from a high\u2011throughput computing (HTC) model to a high\u2011performance computing (HPC) environment, and how can GPU acceleration help address these challenges?", "answer": "The primary scaling challenge is the need to process extremely large, continuous FD data streams that are naturally segmented in both time and space. In an HTC model, jobs run independently on many CPUs, but HPC architectures favor tightly coupled parallelism with limited inter\u2011node communication. Converting the workflow requires (1) partitioning the data into smaller, independent chunks that fit into node memory, (2) redesigning I/O to be highly efficient on parallel file systems, and (3) optimizing the event\u2011processing kernels for SIMD/vector execution. GPU acceleration can help by offloading compute\u2011bound tasks such as hit\u2011finding, clustering, and machine\u2011learning inference to massively parallel processors. GPUs can process millions of hits in parallel, dramatically reducing wall\u2011clock time per event. However, the bottleneck often shifts to data movement; efficient GPU\u2011to\u2011CPU memory transfers and overlap of computation with I/O are essential to realize performance gains."} +{"question": "How can machine\u2011learning models be integrated into the DUNE reconstruction pipeline while preserving reproducibility, version control, and long\u2011term maintainability?", "answer": "A robust integration strategy involves (1) containerising the full ML workflow (framework, dependencies, and trained models) so that every run uses the same environment, (2) storing model artefacts in a versioned model registry (e.g., MLflow or DVC) linked to the corresponding dataset version, (3) embedding deterministic seeds and random\u2011state management in training scripts, and (4) using continuous\u2011integration pipelines that automatically retrain models when upstream data or hyper\u2011parameters change. Documentation should describe the training procedure, hyper\u2011parameter settings, and performance metrics. Finally, the reconstruction code should expose a clear API to switch between ML\u2011based and traditional algorithms, enabling systematic validation and comparison across different physics samples."} +{"question": "What strategies can be employed to ensure efficient data transfer and storage management across distributed European HPC resources for DUNE's large far\u2011detector datasets?", "answer": "Efficient management requires a layered approach: (1) **Data staging**\u2014pre\u2011fetch datasets to local scratch or burst buffers using parallel transfer protocols (e.g., Globus, GridFTP) before job launch; (2) **Metadata\u2011driven placement**\u2014use a metadata catalogue (e.g., MetaCat) to locate replicas and schedule jobs to the nearest site, reducing network load; (3) **Chunking and compression**\u2014split large event files into smaller chunks and apply lossless compression to reduce bandwidth; (4) **Asynchronous I/O**\u2014decouple data reads/writes from compute kernels using overlapped I/O APIs; (5) **Data lifecycle policies**\u2014archive or delete intermediate files automatically based on retention schedules; (6) **Monitoring and feedback**\u2014deploy real\u2011time dashboards to track transfer rates, queue lengths, and storage utilization, allowing dynamic re\u2011routing of jobs when bottlenecks appear."} +{"question": "What are the main obstacles to maintaining long\u2011term sustainability of DUNE's computing infrastructure in the face of evolving operating systems, security requirements, and hardware lifecycles, and how can they be mitigated?", "answer": "Key obstacles include: (1) **Software ageing**\u2014legacy C++ libraries and scripting languages may lack upstream support; mitigated by adopting long\u2011term supported frameworks (e.g., C++17+, Python 3.11) and automated dependency management; (2) **Security patch cycles**\u2014continuous patching of thousands of worker nodes requires automation; this can be addressed with configuration\u2011driven provisioning tools (e.g., Ansible, SaltStack) and containerised workloads that isolate the host OS; (3) **Hardware obsolescence**\u2014GPUs and interconnects evolve rapidly, making hardware\u2010specific optimisations brittle; adopting portable GPU APIs (HIP, SYCL) and abstracting device selection at runtime helps; (4) **Skill drain**\u2014as the collaboration ages, institutional knowledge may be lost; comprehensive documentation, training workshops, and mentorship programs are essential; (5) **Funding stability**\u2014long\u2011term contracts for storage and compute need to be negotiated early with national labs and HPC centers to secure predictable budgets."} +{"question": "What is the projected energy consumption of DUNE's planned GPU\u2011enabled reconstruction pipeline, and how does it compare to a CPU\u2011only pipeline of equivalent performance?", "answer": "The paper does not provide detailed energy consumption estimates, and current simulations lack the granularity needed to model power usage for the proposed GPU\u2011accelerated workflow. Energy profiling would require (1) detailed performance benchmarks of the reconstruction kernels on target GPU hardware, (2) measurement of idle and active power draws of the GPU nodes, and (3) accounting for data\u2011movement overheads between CPU and GPU. Without these measurements, it is not possible to give a reliable comparison to a CPU\u2011only pipeline. Future studies that integrate power monitoring into the job scheduler and perform controlled experiments on representative workloads are needed to answer this question."} +{"question": "What physical characteristics of short gamma\u2011ray bursts make them prime candidates for coincident gravitational\u2011wave detections from binary neutron\u2011star mergers?", "answer": "Short GRBs\u2014defined by a prompt emission duration of less than about two seconds and a hard photon spectrum\u2014are widely believed to arise from the coalescence of two neutron stars or a neutron star\u2013black\u2011hole pair. This interpretation is supported by the observed temporal coincidence with the compact\u2011binary inspiral phase, the typical energies released (\u224810^49\u201310^51\u202ferg), and the lack of supernova signatures that are common to long GRBs. The high compactness and rapid mass transfer in such systems produce strong, high\u2011frequency gravitational\u2011wave signals in the 10\u20131000\u202fHz band, exactly where ground\u2011based interferometers are most sensitive. Consequently, short GRBs are the most promising electromagnetic triggers for searching for gravitational waves from binary mergers."} +{"question": "How does the observer\u2019s viewing angle relative to the binary orbit affect the amplitude and detectability of the gravitational\u2011wave signal from a short GRB progenitor?", "answer": "Gravitational\u2011wave emission from a binary system is strongest along the orbital angular\u2011momentum axis (the \u201cface\u2011on\u201d direction) and weakest in the orbital plane (\u201cedge\u2011on\u201d). The strain amplitude scales roughly as (1+cos\u00b2\u03b8) where \u03b8 is the inclination angle; thus a face\u2011on system can produce nearly twice the strain of an edge\u2011on system at the same distance. Because the short GRB jet is believed to be narrowly collimated along the same axis, an observer detecting a GRB is almost always within a few degrees of face\u2011on, making the associated gravitational\u2011wave signal more likely to be above the detector threshold. However, this also means that any off\u2011axis GRB, which might still produce a detectable GW signal, will not be accompanied by prompt gamma emission, complicating multimessenger association."} +{"question": "What improvements in next\u2011generation gravitational\u2011wave detectors will extend the horizon for detecting neutron\u2011star mergers associated with short GRBs?", "answer": "Future upgrades such as A+ (the planned upgrade of Advanced LIGO and Virgo), the Voyager project, and third\u2011generation facilities like Cosmic Explorer and Einstein Telescope are expected to reduce strain noise by factors of 2\u201310 across the 10\u2013500\u202fHz band. This translates into a proportional increase in the observable volume, extending the detection horizon for binary neutron\u2011star mergers from \u2248200\u202fMpc with current detectors to \u2248600\u20131000\u202fMpc (A+), \u22483\u20134\u202fGpc (Voyager), and \u224810\u201320\u202fGpc (third\u2011generation). Such gains dramatically raise the likelihood of catching a gravitational\u2011wave signal from the population of short GRBs, including those at higher redshift or with lower intrinsic luminosity."} +{"question": "What are the primary obstacles to precise sky localization of short GRBs when using gravitational\u2011wave data alone, and how can multimessenger follow\u2011up mitigate these challenges?", "answer": "Ground\u2011based interferometers localize sources by triangulating the arrival time differences among detectors. With a three\u2011detector network, the typical error region for a compact binary is a few tens to a few hundred square degrees, far larger than the fields of view of most electromagnetic instruments. The localization improves with a larger network, better timing precision, and higher signal\u2011to\u2011noise ratios. Multimessenger observations\u2014such as rapid GRB localizations from Fermi/GBM or Swift/BAT\u2014provide a sub\u2011degree sky position that can be used to constrain the gravitational\u2011wave search, effectively reducing the background and improving the statistical significance. Conversely, a well\u2011localized GW event can trigger targeted electromagnetic follow\u2011up to search for kilonovae or afterglows, thereby closing the multimessenger loop."} +{"question": "Is the occurrence rate of low\u2011luminosity short gamma\u2011ray bursts significantly different from that of high\u2011luminosity short gamma\u2011ray bursts, and what implications would this have for joint gravitational\u2011wave and GRB detection rates?", "answer": "I do not have definitive knowledge on this matter because the paper\u2019s analysis does not address the relative rates of low\u2011luminosity versus high\u2011luminosity short GRBs. Determining whether a distinct population of faint short GRBs exists requires a large, well\u2011calibrated sample of GRB luminosities, careful treatment of selection effects in gamma\u2011ray detectors, and independent constraints from gravitational\u2011wave observations. Current data are insufficient to quantify any difference in occurrence rates, and more comprehensive surveys combined with future multimessenger observations will be needed to resolve this question."} +{"question": "How does the mass distribution of neutron stars observed in gravitational\u2011wave mergers compare to that of isolated binary neutron stars in the Milky Way?", "answer": "Current gravitational\u2011wave observations suggest that neutron\u2011star masses in merging binaries span a broader range, extending up to roughly 2.0\u202fM\u2299, whereas Galactic binary pulsars cluster tightly around 1.33\u202fM\u2299. However, the sample size is still small and uncertainties are large, so a definitive comparison remains tentative."} +{"question": "Is there a distinct mass gap between the heaviest neutron stars and the lightest black holes in the compact binary population?", "answer": "Analyses of the merger catalog show a suppression of events in the 2\u20135\u202fM\u2299 range, consistent with a lower mass gap, but the data are not yet conclusive enough to confirm that the gap is completely empty."} +{"question": "What is the physical origin of the correlation between black\u2011hole spin magnitude and the mass ratio of the binary?", "answer": "The agent does not have a definitive answer. The observed trend\u2014larger effective spins in more unequal\u2011mass binaries\u2014has been reported, but the underlying astrophysical mechanisms (e.g., differential stellar evolution, mass transfer, natal kicks, or dynamical interactions) have not been conclusively identified, and the paper does not provide a definitive explanation."} +{"question": "Does the merger rate of binary black holes increase with redshift?", "answer": "Population studies of the LIGO\u2013Virgo detections indicate a positive evolution of the BBH merger rate with redshift, parameterized as a power law R(z)\u221d(1+z)^\u03ba with \u03ba\u22483, which is broadly consistent with the rise of the cosmic star\u2011formation rate."} +{"question": "Is there an upper mass gap for stellar\u2011mass black holes, as predicted by pair\u2011instability supernova theory?", "answer": "The gravitational\u2011wave catalog contains mergers with component masses up to about 70\u202fM\u2299, and the current data do not show a sharp drop in the merger rate above ~50\u202fM\u2299. Consequently, the existence of an upper mass gap remains unconstrained."} +{"question": "How has the estimated rate of neutron star\u2013black hole (NSBH) mergers evolved over the first three LIGO\u2013Virgo observing runs?", "answer": "The publicly reported detection rate of NSBH mergers has increased modestly with each observing run, largely reflecting the improved sensitivity and longer observing times of the detector network. While earlier runs (O1 and O2) yielded only a handful of NSBH candidates, the third observing run (O3) has produced several confirmed NSBH detections, suggesting a higher intrinsic merger rate in the local Universe. This trend is consistent with population\u2011inference studies that indicate NSBH systems are more common than previously thought."} +{"question": "What are the dominant systematic uncertainties in measuring the effective inspiral spin (\u03c7_eff) of high\u2011mass black hole binaries?", "answer": "The primary systematic uncertainties arise from waveform model inaccuracies, particularly in the treatment of higher\u2011order multipole moments and spin\u2011precession dynamics. Additionally, calibration errors in the detector strain data and imperfect noise subtraction can bias the phase evolution, which is crucial for \u03c7_eff extraction. For the highest\u2011mass systems, the signal\u2019s short duration exacerbates these issues, making the inferred \u03c7_eff more sensitive to model assumptions."} +{"question": "To what extent do gravitational\u2011wave observations constrain the maximum mass of neutron stars?", "answer": "Current gravitational\u2011wave detections of binary neutron star (BNS) mergers provide only loose constraints on the maximum neutron\u2011star mass, because the inspiral signal is mainly sensitive to tidal deformability rather than the ultimate mass limit. Some candidate events with unusually massive components hint at a possible higher maximum mass, but the statistical significance remains low. Consequently, the precise upper bound on neutron\u2011star masses is still largely determined by electromagnetic observations and nuclear\u2011physics modeling."} +{"question": "What is the most probable spin\u2011orientation distribution for black holes in merging binaries formed through isolated binary evolution?", "answer": "For binaries that form via isolated stellar evolution, theoretical models predict that the component spins should be preferentially aligned with the orbital angular momentum due to tidal coupling and common\u2011envelope evolution. This alignment tends to produce small effective precession spin (\u03c7_p) and positive \u03c7_eff values. Observationally, many detected systems show mild alignment, but a fraction exhibit significant misalignment, suggesting that both isolated and dynamical formation channels contribute to the observed population."} +{"question": "Is there definitive evidence for a third\u2011generation black hole population (i.e., black holes formed from the merger of two smaller black holes) in the current GW catalog?", "answer": "The existing catalog does not provide definitive evidence for a distinct third\u2011generation black hole population. While some high\u2011mass black holes observed in the data could, in principle, be remnants of earlier mergers, their masses and spins are not sufficiently distinct to conclusively separate them from first\u2011generation black holes formed directly from stellar collapse. Moreover, the statistical uncertainties in mass and spin measurements, combined with limited sample size, prevent a robust identification of a separate generation. Future observations with higher signal\u2011to\u2011noise ratios and improved waveform models may allow such a distinction to be made."} +{"question": "How might graph neural networks be leveraged to improve neutrino interaction vertex reconstruction accuracy in liquid argon time projection chambers compared to conventional convolutional neural networks?", "answer": "Graph neural networks (GNNs) can naturally represent the sparse, irregular hit patterns in a LArTPC as a graph, where nodes are individual hits and edges encode spatial or temporal proximity. By learning message\u2011passing operations across this graph, GNNs can capture long\u2011range correlations and topological information that are difficult for 2\u2011D convolutions to encode. This may lead to better discrimination of the true vertex, especially in events with complex topologies or low hit densities."} +{"question": "What is the effect of changing the wire\u2011plane pitch on the spatial precision of neutrino interaction vertex determination in the horizontal\u2011drift DUNE far detector?", "answer": "Reducing the wire\u2011plane pitch increases the granularity of the recorded charge deposits, thereby improving the resolution of reconstructed hit positions in the drift direction. A finer pitch can shrink the uncertainty on the vertex location, particularly in the direction transverse to the wires. However, this also raises data volume and may require more sophisticated noise filtering. Conversely, a coarser pitch reduces resolution but eases data handling."} +{"question": "How does incorporating scintillation light detection data influence the performance of vertex\u2011finding algorithms in LArTPC detectors?", "answer": "Scintillation light provides a prompt, time\u2011of\u2011arrival signal that can be used to estimate the absolute event time (t0) and, in some configurations, the z\u2011coordinate of the vertex. Combining light timing with charge\u2011based hit information can improve the localization of the interaction point, especially when the charge signal is sparse or heavily overlapped. However, the light collection efficiency varies across the detector and its integration requires careful calibration to avoid biasing vertex estimates."} +{"question": "What are the main obstacles and possible strategies for extending vertex\u2011reconstruction techniques to identify secondary vertices from tau decays in DUNE data?", "answer": "Secondary vertices from tau decays are often displaced by a few millimeters to centimeters, with relatively low\u2011energy visible decay products. Challenges include limited hit multiplicity, overlapping tracks, and the need to disentangle the secondary decay vertex from the primary neutrino interaction. Strategies involve refining multi\u2011pass reconstruction, incorporating decay\u2011mode specific signatures, and applying dedicated neural\u2011network modules trained to recognize displaced energy deposits or kinematic patterns indicative of tau decay."} +{"question": "To what extent can unsupervised or semi\u2011supervised learning approaches discover novel event topologies in DUNE data without labeled training sets?", "answer": "I don't have a definitive answer to this question. The paper focuses on supervised deep\u2011learning methods trained on labeled simulated data, and does not explore unsupervised or semi\u2011supervised strategies for topology discovery. Investigating such approaches would require developing new loss functions or clustering techniques that can learn meaningful representations from unlabeled data, as well as validation against known physics signatures, which is beyond the scope of the present work."} +{"question": "How does the stochastic wandering of the spin frequency of accreting millisecond X\u2011ray pulsars affect the sensitivity of continuous gravitational\u2011wave searches?", "answer": "The spin frequency of an accreting neutron star is subject to fluctuations driven by variations in the accretion torque. In the frequency domain, these fluctuations manifest as a random walk, which can shift the signal by several frequency bins during the coherent integration time. If the search assumes a perfectly stable frequency, the mismatch between the true signal and the template leads to a loss in signal\u2011to\u2011noise ratio. By allowing the frequency to wander within a bounded range\u2014often modeled as a discrete random walk\u2014the search can retain sensitivity. This is typically achieved by partitioning the data into shorter coherent segments (e.g., 10\u2011day chunks) and using a hidden Markov model to track the most likely frequency path. The longer the coherent segment, the greater the potential frequency drift, so there is a trade\u2011off between sensitivity to weak signals and robustness against frequency wander."} +{"question": "What are the dominant mechanisms that can generate continuous gravitational waves in accreting millisecond X\u2011ray pulsars, and how do they appear in the gravitational\u2011wave spectrum?", "answer": "Two principal mechanisms are usually considered:\\n1. **Mass quadrupole deformations (\u201cmountains\u201d)** on the neutron\u2011star surface, either supported by crustal stresses or magnetic fields, produce emission at twice the stellar spin frequency (2f\u2605) and, in some models, also at f\u2605 if the deformation is not perfectly aligned with the rotation axis.\\n2. **r\u2011mode oscillations**, a class of Rossby waves driven unstable by gravitational\u2011wave back\u2011reaction, emit near 4f\u2605/3. The exact frequency depends on the equation of state and relativistic corrections.\\nIn a narrowband search the expected signal is thus centered on f\u2605, 4f\u2605/3, or 2f\u2605, with a bandwidth that covers any modest frequency drift."} +{"question": "How do uncertainties in binary orbital parameters propagate into the template bank and influence the detection thresholds of continuous\u2011wave searches?", "answer": "The binary orbital parameters\u2014period (P), projected semi\u2011major axis (a0), and time of ascending node (Tasc)\u2014enter the Doppler modulation model used to transform detector data into the source frame. Small errors in these parameters broaden the mismatch between the true signal and any single template, effectively smearing the signal power across neighbouring templates. To keep the fractional loss in signal\u2011to\u2011noise ratio below a chosen maximum mismatch (e.g., \u00b5max\u202f=\u202f0.1), the template bank is constructed with spacings derived from the metric on parameter space. The number of templates grows as the square root of the parameter uncertainties and inversely with the coherent segment length (through the mismatch equations). A larger template bank increases the trials factor, which in turn raises the detection threshold (higher Lth) for a fixed false\u2011alarm probability."} +{"question": "What is the precise relationship between the observed X\u2011ray flux during outburst and the amplitude of continuous gravitational waves emitted by an accreting millisecond X\u2011ray pulsar?", "answer": "The paper does not provide a definitive answer to this question. The connection between X\u2011ray flux and gravitational\u2011wave amplitude is complex: it depends on the efficiency of angular\u2011momentum transfer, the star\u2019s internal structure, magnetic field geometry, and the detailed physics of accretion\u2011induced deformations. While torque\u2011balance arguments can give an upper limit on the strain by assuming the accretion torque is exactly counter\u2011balanced by gravitational\u2011wave emission, translating an observed flux into a concrete strain amplitude requires assumptions about the neutron\u2011star equation of state, accretion geometry, and magnetic field configuration\u2014parameters that are not fully constrained by current observations. Consequently, a precise, universally applicable relationship remains an open area of research."} +{"question": "In what ways can hidden Markov models improve the tracking of phase wander in continuous\u2011wave searches compared to traditional coherent matched\u2011filtering?", "answer": "Traditional coherent matched\u2011filtering assumes a perfectly stable phase evolution over the entire observation period. This is unsuitable for sources whose spin phase wanders due to stochastic accretion torque fluctuations. Hidden Markov models (HMMs) treat the instantaneous frequency (or phase) as a hidden state that evolves according to a probabilistic transition model (e.g., a simple random walk). By applying the Viterbi algorithm, the HMM efficiently finds the most likely path through the state space that maximizes the likelihood of the observed data. This semi\u2011coherent approach retains most of the sensitivity of a fully coherent search while being robust to phase wander, enabling longer coherent segments and better overall signal\u2011to\u2011noise ratios for sources with significant frequency noise."} +{"question": "How does the geometry and orientation of a global gravitational\u2011wave detector network influence the sensitivity to narrowband anisotropies in the stochastic gravitational\u2011wave background?", "answer": "The overlap\u2011reduction function (ORF) captures the relative antenna patterns, time delays, and orientations of detector pairs. For narrowband signals, the ORF oscillates rapidly with frequency and sky direction. Baselines that are short and nearly co\u2011linear (e.g., the two Advanced LIGO detectors) provide high correlation for certain directions, while longer, more widely separated baselines (e.g., LIGO\u2013Virgo, LIGO\u2013KAGRA) improve sky coverage and break degeneracies. Thus, the overall sensitivity depends on both baseline length and the relative orientations of the interferometers; a carefully optimized network can substantially enhance the ability to detect narrowband anisotropies."} +{"question": "What are the theoretical predictions for the amplitude and spectral shape of a narrowband stochastic background produced by a population of rapidly rotating neutron stars in the Milky Way?", "answer": "Models of rotating neutron stars\u2014such as magnetars, accreting pulsars, or isolated spinning neutron stars\u2014predict continuous gravitational radiation at roughly twice the spin frequency. If the Galactic population has a broad distribution of spin frequencies and ellipticities, the resulting background is a superposition of many nearly monochromatic lines, yielding a narrowband spectrum. The amplitude is governed by the ellipticity distribution, spin\u2011down torque, and source number, typically giving \u03a9_GW \u223c 10^\u201311\u201310^\u20139 in the LIGO band with a nearly flat spectral index (\u03b1 \u2248 0). Large uncertainties in source populations and ellipticity limits lead to a wide range of possible amplitudes."} +{"question": "Which computational strategies can be employed to scale an all\u2011sky, all\u2011frequency radiometer map\u2011making to higher pixel and frequency resolutions while keeping the analysis tractable?", "answer": "Two complementary approaches are effective: (1) matrix\u2011based inversion with sparsity exploitation\u2014since the Fisher matrix is band\u2011limited in pixel space, iterative solvers such as conjugate\u2011gradient with appropriate preconditioners can be used without forming the full matrix; (2) hierarchical folding and parallelization\u2014by folding data into a single sidereal day and distributing frequency bins across compute nodes, the analysis becomes embarrassingly parallel. GPU acceleration for ORF evaluation and efficient memory layouts for HEALPix indexing further reduce runtime. Combining these techniques allows extending to N_side \u2265 32 or finer frequency bins (e.g., 1/64 Hz) without prohibitive computational cost."} +{"question": "Can the ASAF method be generalized to incorporate Doppler modulation and frequency\u2011dependent sky localization, and how would this affect sensitivity?", "answer": "In principle, the ASAF pipeline can be modified to include the time\u2011dependent Doppler phase shift arising from Earth\u2019s rotation and orbital motion. This requires augmenting the cross\u2011spectral density with a frequency\u2011dependent phase term that tracks the expected line drift across the observation period. Incorporating this effect would sharpen the response to true monochromatic sources, potentially increasing the SNR by up to a factor of a few for high\u2011frequency signals, but it would also increase computational complexity because the phase model must be evaluated for each sky pixel and frequency bin. A practical strategy is to first run a Doppler\u2011blind ASAF to flag candidate pixel\u2011frequency pairs and then perform a targeted matched\u2011filter follow\u2011up that accounts for Doppler modulation."} +{"question": "What is the expected contribution of exotic boson clouds surrounding spinning black holes to the narrowband stochastic gravitational\u2011wave background, and can an ASAF\u2011style search detect them?", "answer": "Ultralight bosons (e.g., axion\u2011like particles) can form clouds around rapidly rotating black holes via superradiance, emitting nearly monochromatic gravitational waves at frequencies set by the boson mass and black\u2011hole spin. The Galactic population of such clouds could produce a narrowband stochastic background with a characteristic frequency range of ~10\u20131000\u202fHz and a flat spectral index. However, the ASAF framework described in the paper focused on generic persistent signals and did not model the specific line\u2011like structure or the spatial clustering expected from boson\u2011cloud sources. Consequently, while the ASAF pipeline is capable of flagging anomalous narrowband excesses, it cannot directly quantify the expected amplitude or distinguish boson\u2011cloud signatures without dedicated modeling and matched\u2011filter follow\u2011ups. Thus, the question remains open and requires further theoretical and data\u2011analysis work."} +{"question": "How does timing noise (spin wandering) in young neutron stars influence the sensitivity of semi\u2011coherent searches for continuous gravitational waves?", "answer": "Spin wandering introduces random fluctuations in the rotational frequency that can shift the signal out of a single template over the coherent integration time. Semi\u2011coherent methods mitigate this by using short coherence times and a hidden Markov model or Hough transform that allows the frequency to drift by a few bins per step. The net effect is a modest reduction in sensitivity compared to a purely coherent search that assumes a deterministic spin\u2011down, typically on the order of 10\u201320\u202f% in the 95\u202f% upper\u2011limit strain for the same computational budget. The choice of coherence time, transition probabilities, and step size in the HMM or frequency binning in the Hough transform are therefore critical to balance sensitivity against the risk of mis\u2011tracking a wandering signal."} +{"question": "Which young supernova remnants are the most promising targets for future continuous\u2011wave searches with upgraded detectors?", "answer": "Targets that combine proximity, youth, and evidence of a central compact object are favored. Vela\u202fJr. (G266.2\u20131.2), Cas\u202fA (G111.7\u20132.1), G1.9+0.3, and the younger remnant G18.9\u20131.1 have ages of a few hundred to a thousand years and distances of less than a kiloparsec, giving the strongest expected strain signals. With the projected improvements in LIGO\u202fVoyager and the next\u2011generation Virgo upgrade, the sensitivity to strain at 200\u2013400\u202fHz will improve by roughly a factor of two, bringing these remnants within reach of the spin\u2011down limits for many realistic ellipticity models."} +{"question": "How can multi\u2011messenger observations (X\u2011ray, radio) improve targeted continuous\u2011wave searches?", "answer": "Electromagnetic observations that reveal a neutron star\u2019s spin frequency, spin\u2011down rate, or even a timing solution provide powerful priors that drastically reduce the parameter space. Knowing the frequency and its derivative allows a fully coherent or very long coherent integration, which scales the sensitivity as \\(h_{\\rm min}\\propto T_{\\rm coh}^{-1/2}\\). Even if the pulsar is not detected in radio, a precise X\u2011ray pulse ephemeris can be used. In the absence of a phase\u2011connected ephemeris, a narrow range of spin\u2011down values can be tested, improving the detection statistic\u2019s significance and reducing the number of required templates."} +{"question": "What advantages does combining the \\(f_{\\ast}\\) and \\(2f_{\\ast}\\) harmonics provide in a dual\u2011harmonic search for continuous waves?", "answer": "When a neutron star emits gravitational waves at both its spin frequency and twice that frequency\u2014possible for a triaxial rotator or a pinned superfluid\u2014the two harmonics share the same intrinsic phase evolution. Tracking them simultaneously allows the matched\u2011filter statistic to sum power from both frequencies, improving the overall signal\u2011to\u2011noise ratio by roughly \\(\\sqrt{2}\\) in the ideal case. It also mitigates the risk of missing a signal that would be too weak in a single\u2011harmonic search. However, it requires a larger template bank and careful handling of line contamination in both frequency bands."} +{"question": "Does the ellipticity of a young neutron star evolve on timescales of months to years?", "answer": "The current data do not provide a definitive answer. Existing continuous\u2011wave searches have not detected any signals, and the theoretical models of crustal relaxation, magnetic field decay, and r\u2011mode saturation predict a range of evolution timescales, from days to centuries. Because the observational upper limits are still above the expected ellipticity for many young stars, we lack the sensitivity to observe a gradual change in ellipticity over short times. Dedicated long\u2011term monitoring with next\u2011generation detectors and improved waveform models will be needed to constrain or detect such evolution."} +{"question": "How do quantum squeezing techniques improve the sensitivity of continuous gravitational-wave searches compared to earlier observing runs?", "answer": "Quantum squeezing reduces the quantum shot-noise floor in the interferometers, allowing more power to be delivered to the measurement band without increasing radiation-pressure noise. This leads to a lower strain noise spectral density, especially at high frequencies, which directly translates into tighter upper limits on continuous-wave amplitudes."} +{"question": "What astrophysical processes can create the non-axisymmetric deformations required for a spinning neutron star to emit detectable continuous gravitational waves?", "answer": "Possible mechanisms include crustal mountains caused by accretion or thermal stresses, magnetic-field-induced distortions, and the excitation of fluid oscillation modes such as r-modes. Each process can support an equatorial ellipticity that gives rise to a quadrupolar gravitational-wave signal at twice the rotation frequency."} +{"question": "In an all-sky continuous-wave search, how does the choice of Short Fourier Transform (SFT) coherence time influence the balance between computational cost and search sensitivity?", "answer": "Longer SFTs improve frequency resolution and Doppler demodulation accuracy, boosting sensitivity. However, they also increase the parameter-space resolution required in sky and spin-down, which raises the number of templates and hence computational load. Shorter SFTs lower the template count but reduce sensitivity due to poorer frequency discrimination."} +{"question": "To what extent can the strain upper limits obtained by all-sky searches constrain the equatorial ellipticity of neutron stars located at different distances in the Milky Way?", "answer": "By inverting the strain upper limit formula, one obtains a maximum allowed ellipticity as a function of distance. For a given search sensitivity, this translates into a distance range within which neutron stars with a specified ellipticity would have been detected. Thus, tighter upper limits extend the observable volume and place stronger constraints on the deformation of nearby neutron stars."} +{"question": "What is the expected sensitivity of future observing runs (e.g., O4/O5) to continuous gravitational waves from neutron stars with spin-down rates larger than 10\u207b\u2078\u202fHz/s, and what new analysis strategies would be required to probe such high spin-down values?", "answer": "The paper does not address this scenario, so we cannot provide a definitive answer. Extending the search to spin-down magnitudes above 10\u207b\u2078\u202fHz/s would demand a denser template bank in frequency derivative space, likely increasing computational cost significantly. Techniques such as adaptive hierarchical searches, coherent-follow\u2011up on narrower sky patches, or machine-learning based outlier vetting might be necessary to make the search tractable, but concrete sensitivity estimates await future data and method development."} +{"question": "How does the choice of the narrowband width parameter (\u03ba) influence the sensitivity and computational cost of continuous gravitational\u2011wave searches for pulsars with significant timing noise?", "answer": "The parameter \u03ba sets the fractional window around the electromagnetic spin frequency and spin\u2011down within which the search is performed. A larger \u03ba allows for greater offsets between the true GW phase evolution and the EM timing solution, which is useful for pulsars with large timing noise or differential rotation between the crust and core. However, a larger \u03ba also increases the number of templates in both frequency and spin\u2011down dimensions, thereby inflating the search volume and the false\u2011alarm probability. In practice, \u03ba values of 10\u207b\u00b3\u201310\u207b\u00b2 are chosen to balance the need for robustness against phase offsets with computational feasibility, as demonstrated in previous LIGO/Virgo narrowband searches."} +{"question": "What physical mechanisms could cause a measurable phase offset between the electromagnetic emission of a pulsar and its continuous gravitational\u2011wave signal, and how would such offsets manifest in the data?", "answer": "A differential rotation between the rigid outer crust and the interior superfluid can lead to a small lag that manifests as a phase offset between the electromagnetic pulse arrival times and the GW phase. Glitches, magnetospheric torque changes, or internal superfluid vortex dynamics can also introduce phase drifts or glitches in the GW signal that are not perfectly locked to the EM timing. In the data, these effects would appear as a mismatch in the expected Doppler\u2011corrected phase evolution, causing a reduction in matched\u2011filter SNR if the search assumes strict phase\u2011lock. Narrowband searches that allow a small offset in frequency and spin\u2011down effectively accommodate such behavior."} +{"question": "How would modelling post\u2011glitch transient gravitational\u2011wave signals with an exponentially decaying amplitude, instead of a simple rectangular window, affect the sensitivity of long\u2011duration transient searches?", "answer": "An exponential decay more accurately represents the expected relaxation of the star\u2019s quadrupole moment after a glitch. While a rectangular window assumes a constant amplitude over the whole duration, an exponential model would allocate signal power more heavily to early times, potentially increasing SNR for short\u2011lived emissions. However, implementing an exponential window typically requires a larger template bank to cover the additional parameter (decay time), increasing computational cost. Studies have shown that the loss in SNR for a realistic exponential signal using a rectangular template is modest (a few percent), so many searches adopt the simpler rectangular window to keep the search tractable."} +{"question": "In what way do detector duty cycles and calibration uncertainties propagate into the upper limits on the gravitational\u2011wave strain and neutron\u2011star ellipticity derived from continuous\u2011wave searches?", "answer": "The effective observing time, T_obs, is reduced by the duty cycle of each detector, directly scaling the expected sensitivity (h_sens \u221d T_obs\u207b\u00b9/\u00b2). Calibration uncertainties in the strain response of each detector (typically 5\u201310\u202f%) translate into systematic errors on the inferred strain amplitude. Since the ellipticity is derived from the strain via \u03f5 \u221d h\u2080\u202ff\u207b\u00b2, any error in h\u2080 propagates to \u03f5 quadratically with frequency. The combination of reduced T_obs and calibration errors thus weakens the upper limits and introduces a systematic uncertainty that is usually quoted as a separate systematic error budget in the final results."} +{"question": "Is there any evidence for continuous gravitational\u2011wave emission from millisecond pulsars in the O3 data when the phase\u2011lock assumption is relaxed?", "answer": "The current analysis focused on 18 isolated pulsars with spin frequencies between 10\u202fHz and 350\u202fHz that have relatively high spin\u2011down rates, yielding spin\u2011down limits within a factor of three of the expected sensitivity. Millisecond pulsars, which rotate at hundreds of Hz but have very small spin\u2011down rates, were not included in this target list because their indirect spin\u2011down limits are far below the detector sensitivity. Consequently, the study does not address whether continuous GWs could be detected from such objects in O3. Determining this would require a dedicated search over a different parameter space and is an open question that remains to be investigated with future data and more sensitive detectors."} +{"question": "How does the ionization recombination factor for sub\u201150\u202fMeV electrons vary as a function of the applied electric field in a liquid argon time\u2011projection chamber?", "answer": "The recombination factor, R, quantifies the fraction of ionization electrons that survive prompt recombination with argon ions. For low\u2011energy electrons, R typically follows the Modified Box model, where \\n\\nR = ln(1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)) / (1 + (\u03b2\u2032/\u03c1E_f)\u202f(dE/dx)),\\n\\nwith \u03b2\u2032 and \u03b1 being empirical parameters, \u03c1 the liquid\u2011argon density, and E_f the electric field. As the field increases, the electric drift force overcomes the ion\u2011electron Coulomb attraction, reducing recombination and increasing R. Empirical measurements (e.g., in ArgoNeuT, ICARUS, and MicroBooNE) show that R rises from ~0.5 at 200\u202fV/cm to ~0.75 at 500\u202fV/cm for 10\u201350\u202fMeV electrons. The precise field dependence also depends on the local dE/dx; denser ionization tracks recombine more strongly, leading to a slightly lower R at the same field."} +{"question": "What is the quantitative impact of the TPC readout threshold on the energy resolution of low\u2011energy electron showers?", "answer": "The readout threshold is the minimum charge that a wire\u2011channel must record to be accepted as a hit. For sub\u201150\u202fMeV electrons, a typical threshold of ~100\u202fkeV per 500\u202fns tick means that a non\u2011negligible fraction of the ionization\u2014especially from thin, low\u2011dE/dx portions of the shower\u2014is lost. Studies of simulated Michel electrons show that this loss corresponds to ~11\u202f% of the total deposited energy. When this missing energy is included, the fractional energy resolution degrades by about 5\u20138\u202f% relative to the ideal case where all charge is measured. The effect is more pronounced at lower energies where the shower is less developed and the charge density is lower."} +{"question": "Can deep learning techniques enhance the separation of Michel electrons from cosmic\u2011ray background in a large LArTPC?", "answer": "Yes. Convolutional neural networks (CNNs) trained on simulated and real data can learn subtle spatial and temporal patterns characteristic of electron\u2011induced showers versus muon or proton tracks. A CNN can be fed the three wire\u2011plane images (U, V, X) and the corresponding time series, and output a probability that a cluster is a Michel electron. Benchmarks show that such a network can achieve >\u202f95\u202f% purity with >\u202f90\u202f% efficiency for energies between 10 and 50\u202fMeV, outperforming traditional cut\u2011based selections that rely on hit multiplicity and angular cuts alone."} +{"question": "How can photon\u2011detector signals complement charge readout for identifying low\u2011energy electrons in a liquid\u2011argon TPC?", "answer": "Photon detectors (e.g., ARAPUCA modules) provide fast scintillation light timestamps with ~ns precision. For low\u2011energy electrons, the scintillation light yields ~1\u20132\u202f\u00d7\u202f10\u2074 photons per MeV, enabling a prompt trigger even when the ionization charge is below the readout threshold. By correlating the light pulse with the charge hit pattern, one can improve the vertex reconstruction, suppress random noise hits, and better discriminate between true electron showers and spurious background. In addition, the light\u2013charge ratio can be used as an auxiliary variable in energy calibration, since it is sensitive to recombination and electron lifetime effects."} +{"question": "Is it possible to recover the energy lost due to readout threshold and shower leakage in future detectors without changing the hardware?", "answer": "The agent does not have a definitive answer to this question. Recovering lost energy without hardware modifications would require sophisticated reconstruction algorithms that infer the missing charge from surrounding hit patterns, shower topology, or correlations with external detectors. While some studies have explored machine\u2011learning extrapolation or analytic corrections based on shower shape models, none have yet demonstrated a systematic, unbiased recovery that matches the true deposited energy across the full 10\u201350\u202fMeV range. Therefore, more detailed simulations, validation with calibration data, and potentially new reconstruction paradigms are needed to determine whether such recovery is feasible in practice."} +{"question": "What range of r\u2011mode saturation amplitudes is theoretically expected for young, rapidly rotating neutron stars, and how does this amplitude evolve as the star cools?", "answer": "Models of r\u2011mode instability predict saturation amplitudes between 10\u207b\u2075 and 10\u207b\u00b3, depending on the neutron star\u2019s mass, radius, and the microphysical dissipation mechanisms (viscosity, superfluidity, crust\u2011core coupling). As the star cools, viscous damping weakens, allowing the amplitude to grow until nonlinear mode couplings or exotic damping processes (e.g., hyperon bulk viscosity) halt the growth, typically on timescales of weeks to months after the instability is triggered."} +{"question": "How do timing glitches influence the excitation and damping of r\u2011mode oscillations in neutron stars?", "answer": "Glitches, which are sudden spin\u2011up events, can transfer angular momentum from the interior superfluid to the crust. This sudden change can perturb the star\u2019s equilibrium, potentially exciting r\u2011mode oscillations. Subsequent energy dissipation through gravitational radiation and internal viscosity will damp the mode, possibly on timescales comparable to the glitch recovery time (~days to weeks). The efficiency of this process depends on the coupling between the core and the crust, as well as on the star\u2019s temperature profile."} +{"question": "To what extent does the neutron star equation of state determine the relationship between the stellar spin frequency and the gravitational\u2011wave frequency emitted by r\u2011modes?", "answer": "The r\u2011mode GW frequency is approximately (4/3) times the stellar spin frequency for a slowly rotating star, but relativistic corrections and the star\u2019s compactness (M/R) shift this relation. Different equations of state (stiff vs. soft) change the star\u2019s radius for a given mass, thereby altering the compactness and the coefficient relating spin to GW frequency. Calculations using realistic equations of state yield variations of a few percent in the GW frequency for a given spin, which is significant for precise template placement in searches."} +{"question": "What advantages do coherent, multi\u2011detector networks provide when searching for continuous gravitational\u2011wave signals from r\u2011mode oscillations compared to single\u2011detector analyses?", "answer": "Coherent multi\u2011detector searches combine the data streams in a way that maximizes signal\u2011to\u2011noise ratio and allows for better discrimination of instrumental artifacts. The network\u2019s antenna patterns provide sky\u2011dependent sensitivity, reducing blind spots and enabling the use of a global F\u2011statistic that coherently adds contributions from all detectors. This leads to deeper upper limits and improved robustness against transient noise, essential for detecting the weak, long\u2011lasting signals expected from r\u2011modes."} +{"question": "Is r\u2011mode emission a viable explanation for the unusually negative braking index observed in some young pulsars beyond PSR\u202fJ0537\u20116910?", "answer": "Current observations of negative braking indices in a handful of young pulsars cannot be conclusively explained by r\u2011mode emission alone. While r\u2011modes can provide additional spin\u2011down torque, the required saturation amplitudes often exceed theoretical limits, and the observed braking indices may also involve magnetospheric evolution or fallback accretion effects. Therefore, we cannot definitively state that r\u2011mode emission accounts for these indices; further multi\u2011wavelength observations and more sensitive GW searches are needed to clarify the dominant mechanisms."} +{"question": "What is the expected contribution to the isotropic gravitational\u2011wave background from binary neutron star mergers at high redshift?", "answer": "Astrophysical models predict that binary neutron star mergers should contribute a stochastic background whose energy density peaks around a few tens of Hz. The high\u2011redshift tail of the merger rate, weighted by the redshift dependence of the cosmic star\u2011formation rate and delay\u2011time distributions, is expected to add a modest but non\u2011negligible component to the overall background, typically on the order of \\(10^{-10}\\) in \\(\\Omega_{\\mathrm{GW}}\\) at 25\u202fHz."} +{"question": "How can correlated terrestrial magnetic noise impact the sensitivity of cross\u2011correlation searches for a stochastic background?", "answer": "Coherent magnetic fields, such as Schumann resonances, can couple into the interferometer strain channels at the same frequency in spatially separated detectors. If not accounted for, these correlated noise sources mimic a stochastic signal and inflate the measured cross\u2011correlation, thereby reducing the achievable sensitivity and potentially biasing the inferred upper limits."} +{"question": "What are the implications of detecting a scalar or vector polarization component in the isotropic gravitational\u2011wave background for alternative theories of gravity?", "answer": "A statistically significant detection of scalar or vector polarizations would constitute direct evidence for physics beyond General Relativity. It would point to modified gravity models that predict extra degrees of freedom, such as scalar\u2013tensor theories or massive gravity, and would constrain their coupling constants and propagation speeds through the measured spectral shape of the background."} +{"question": "How does the inclusion of Virgo data alter the overlap reduction function and the sensitivity to high\u2011frequency gravitational\u2011wave background signals?", "answer": "Adding Virgo to the LIGO network introduces new baselines (Hanford\u2013Virgo and Livingston\u2013Virgo) with different geometries. These baselines have overlap reduction functions that are less suppressed at higher frequencies compared to the LIGO\u2013LIGO baseline, thereby improving the network\u2019s overall sensitivity in the \\(\\sim 70\\)\u2013\\(200\\)\u202fHz band and providing complementary coverage where the LIGO\u2013LIGO response vanishes."} +{"question": "What would be the effect on the upper limits of the isotropic gravitational\u2011wave background if future detectors achieve a factor of two improvement in strain sensitivity over O3?", "answer": "The paper does not address this scenario directly. Determining the impact would require projecting the improved detector noise spectra, recalculating the overlap reduction functions, and re\u2011evaluating the cross\u2011correlation sensitivity over the relevant frequency band. Such projections are beyond the scope of the present work and would need dedicated simulations with the next\u2011generation detector configurations."} +{"question": "What precision on the CP\u2011violating phase \u03b4CP can DUNE Phase II achieve with a 40\u202fkt fiducial liquid\u2011argon detector and a beam power exceeding 2\u202fMW over a ten\u2011year data\u2011taking period?", "answer": "DUNE Phase\u202fII is projected to reach a \u03b4CP precision of roughly 7\u00b0 to 18\u00b0, depending on the true value of \u03b4CP. For \u03b4CP near 0\u00b0 the uncertainty is about 7\u00b0, while for \u03b4CP close to \u2212\u03c0/2 the precision degrades to roughly 18\u00b0. These numbers are derived from the 1000\u202fkt\u00b7MW\u00b7yr exposure expected with the upgraded beam and detector mass."} +{"question": "How does the DUNE\u2011PRISM concept help to reduce systematic uncertainties in neutrino\u2011argon cross\u2011section measurements?", "answer": "The DUNE\u2011PRISM strategy places the near\u2011detector liquid\u2011argon TPC on a movable platform that can be shifted sideways across a range of off\u2011axis angles. By sampling the neutrino flux at several off\u2011axis positions, the experiment can reconstruct the energy dependence of the flux with high precision. This off\u2011axis sampling also provides different effective target nuclei and interaction kinematics, enabling simultaneous constraints on cross\u2011sections. The resulting flux and cross\u2011section constraints are then propagated to the far\u2011detector analysis, substantially reducing systematic errors in oscillation parameter extraction."} +{"question": "What are the key differences between the vertical\u2011drift and horizontal\u2011drift liquid\u2011argon TPC designs used in the DUNE far detectors, and what advantages does each configuration offer?", "answer": "In a horizontal\u2011drift design (FD1) the charge drift direction is parallel to the detector plane, requiring a relatively short drift distance (~3\u202fm) and a smaller high\u2011voltage system. This simplifies cryogenic safety and electronics integration. The vertical\u2011drift design (FD2) has the drift direction perpendicular to the detector plane, allowing longer drift lengths (~3\u20134\u202fm) and a more compact detector footprint. Vertical drift can improve charge collection efficiency and reduce readout channel count, but demands a higher voltage supply and more stringent purity control. Both designs provide comparable physics performance; the choice depends on engineering trade\u2011offs such as cavern size and detector construction logistics."} +{"question": "What are the main advantages and technical challenges of implementing a dual\u2011phase liquid\u2011argon TPC with optical readout (the ARIADNE concept) for a DUNE far\u2011detector module?", "answer": "Advantages of the dual\u2011phase ARIADNE design include: (1) charge amplification in the gas phase, which yields higher signal\u2011to\u2011noise and potentially lower energy thresholds; (2) the possibility of optical readout of the avalanche light, providing a fast, calorimetric signal and a complementary timing reference; (3) a more compact readout plane that can reduce the number of electronic channels. Technical challenges comprise: (1) maintaining a stable liquid\u2011gas interface over a large area; (2) ensuring uniform high voltage and field shaping in the gas amplification region; (3) integrating optical sensors with the charge readout without compromising the purity of the argon; and (4) controlling background light and electronic noise from the photon detectors. These challenges require extensive R&D to demonstrate scalability to the multi\u2011kiloton scale of DUNE."} +{"question": "What is the expected sensitivity of DUNE to detect neutrinos from a core\u2011collapse supernova occurring at a distance of 100\u202fkpc?", "answer": "The paper does not provide sensitivity estimates for a supernova at 100\u202fkpc; it focuses on a canonical distance of 10\u202fkpc. Detailed calculations of event rates and detector response for a 100\u202fkpc supernova would require additional modeling of the neutrino flux spectrum, distance scaling, and background rates, which are beyond the scope of the presented document. Consequently, the precise sensitivity for a 100\u202fkpc supernova cannot be inferred from the information given."} +{"question": "What classes of astrophysical phenomena are expected to emit short-duration gravitational-wave bursts, and what are their characteristic time scales and frequency ranges?", "answer": "Short-duration gravitational-wave bursts are predicted to arise from several astrophysical processes. Core\u2011collapse supernovae produce burst signals with durations from a few milliseconds up to a few seconds, typically spanning frequencies between 10\u202fHz and 1\u202fkHz, with higher frequency components (hundreds of Hz) associated with proto\u2011neutron star oscillations. Binary black\u2011hole or neutron\u2011star mergers emit brief, high\u2011frequency chirps lasting milliseconds, with peak frequencies from a few hundred Hz to several kHz. Non\u2011axisymmetric instabilities in rapidly rotating neutron stars can excite quasi\u2011periodic oscillations (f\u2011modes) that last tens of milliseconds to a few seconds, emitting in the 1\u20133\u202fkHz band. Magnetar starquakes or magnetically driven flares may also produce short bursts in the kilohertz range. Additionally, exotic sources such as cosmic\u2011string cusps or kinks could generate millisecond\u2011scale bursts with a characteristic \\(f^{-4/3}\\) spectrum extending up to several kilohertz."} +{"question": "How does the coherent WaveBurst (cWB) pipeline detect unmodeled gravitational\u2011wave transients, and what role do the network correlation coefficient and time\u2011frequency binning play?", "answer": "The coherent WaveBurst pipeline searches for excess coherent power across a network of detectors by performing a time\u2013frequency decomposition of the strain data (e.g., using wavelets). It constructs a likelihood ratio that compares the hypothesis of a coherent gravitational\u2011wave signal against the null hypothesis of detector noise. The network correlation coefficient (cc) quantifies the fraction of coherent energy shared among detectors; a high cc indicates that the observed excess is consistent with a real astrophysical signal rather than independent noise glitches. cWB divides the data into time\u2013frequency bins and applies adaptive thresholds to cluster significant excesses. Triggers are ranked by the coherent network signal\u2011to\u2011noise ratio (\\(\\eta_c\\)), and only those exceeding a chosen cc threshold and passing additional consistency tests are considered for further analysis. This approach allows detection of a wide variety of morphologies without assuming a specific waveform model."} +{"question": "Why is the sensitivity of the LIGO\u2013Virgo network generally better at low frequencies compared to high frequencies for generic burst searches?", "answer": "The sensitivity difference arises from the detectors\u2019 strain noise spectral density and their antenna response. At low frequencies (tens to a few hundred Hz), the interferometers are limited mainly by seismic and suspension noise, but the advanced noise\u2011reduction techniques and the use of multiple detectors with similar orientations allow coherent stacking of signals, improving the effective strain sensitivity. In contrast, at high frequencies (above ~1\u202fkHz), shot noise dominates, and the detectors\u2019 optical configuration (e.g., power\u2011recycling cavity, mirror coatings) imposes a steeper rise in noise. Moreover, the antenna patterns of the two LIGO detectors are nearly identical, whereas Virgo\u2019s misalignment reduces coherent response for high\u2011frequency bursts, further diminishing the network\u2019s effective sensitivity in that band."} +{"question": "What are data\u2011quality vetoes in gravitational\u2011wave searches, and how do they help reduce false alarms from environmental or instrumental artifacts?", "answer": "Data\u2011quality vetoes are predefined time intervals during which the detector data are deemed unreliable due to known disturbances. They are derived from auxiliary channels that monitor environmental conditions (seismics, magnetics, acoustic sensors) or instrumental states (laser power, alignment). By cross\u2011correlating glitches in the gravitational\u2011wave channel with signatures in auxiliary channels, analysts can flag and exclude periods where noise transients are likely to mimic astrophysical signals. Vetoes are ranked by effectiveness; the most effective ones remove a high fraction of glitches while sacrificing only a small fraction of live\u2011time. Applying vetoes reduces the background trigger population, improves the significance of real events, and ensures that upper\u2011limit calculations are not biased by non\u2011astrophysical artifacts."} +{"question": "What is the most effective method to distinguish between cosmological and astrophysical contributions in an anisotropic gravitational-wave background?", "answer": "Distinguishing cosmological from astrophysical components relies on their distinct angular power spectra and spectral indices. Cosmological backgrounds are expected to be nearly isotropic with a relatively flat or slowly varying spectrum, whereas astrophysical backgrounds trace the large\u2011scale structure and show stronger anisotropy aligned with the matter distribution. By performing a spherical\u2011harmonic decomposition of the sky map and jointly fitting for the amplitude, spectral index, and multipole dependence, one can separate the two contributions. However, this separation is limited by detector sensitivity, foreground contamination, and the similarity of spectral shapes at certain multipoles."} +{"question": "How does including a third detector such as Virgo affect the angular resolution of a stochastic background map?", "answer": "Adding a third detector introduces additional baselines with different arm orientations and lengths, which enlarges the network\u2019s antenna\u2011pattern coverage. The angular resolution improves roughly with the smallest baseline length divided by the highest frequency used, but the LIGO\u2013Virgo baseline is shorter than the LIGO\u2013LIGO baseline, so the highest multipoles are still limited. Nonetheless, the extra baseline reduces degeneracies between sky pixels, improves sky coverage (especially the southern hemisphere), and increases the overall sensitivity to anisotropic features."} +{"question": "What are the main challenges in using the broadband radiometer technique for detecting point\u2011like sources in the stochastic background?", "answer": "The broadband radiometer assumes that the signal is confined to a single pixel with negligible covariance to neighboring pixels. In reality, the detector antenna pattern couples adjacent pixels, causing signal leakage and bias. The technique also presumes a flat spectral shape across the band, which may not hold for real sources. Moreover, non\u2011Gaussian detector noise and calibration uncertainties can mimic or mask weak point\u2011like signals, requiring careful regularization and robust statistical methods to extract reliable limits."} +{"question": "What role does data folding over one sidereal day play in reducing computational cost for anisotropic background searches?", "answer": "Data folding exploits the Earth\u2019s rotational symmetry: the antenna pattern repeats every sidereal day. By folding the entire observing run into a single sidereal day, cross\u2011correlations from many days are coherently summed, reducing the time\u2011frequency data volume by the number of days. This drastically lowers memory requirements and computational time, enabling finer pixelation or higher frequency resolution while keeping the analysis tractable."} +{"question": "What is the expected contribution of primordial black hole mergers to the anisotropic gravitational\u2011wave background at frequencies below 100 Hz?", "answer": "I do not know that answer. The paper does not discuss primordial black hole mergers, and current theoretical models lack precise predictions for their contribution to the anisotropic background at low frequencies. Estimating this would require detailed modeling of the primordial black hole population, merger rates, and resulting angular distribution\u2014work that is beyond the scope of the present study and not covered in the existing literature."} +{"question": "How does the number of kinks per loop influence the amplitude of the stochastic gravitational\u2011wave background produced by a network of cosmic strings?", "answer": "Increasing the number of kinks per oscillation enhances the total power emitted by each loop. For models where the loop distribution contains many small loops (e.g., model\u00a0B or the interpolating model\u00a0C\u20112), the background spectrum rises approximately linearly with the kink number in the frequency range accessible to ground\u2011based detectors. Consequently, a larger kink population raises the overall \\u03a9GW(f) and can shift the peak of the spectrum to higher frequencies."} +{"question": "What upper limits on the cosmic\u2011string tension \\(G\\mu\\) can be derived from the current O3 data of LIGO\u2013Virgo for different loop\u2011distribution scenarios?", "answer": "Analyses of the O3 data, combining both burst and stochastic searches, exclude tensions above roughly \\(4\\times10^{-15}\\) for the most optimistic loop model (model\u00a0B). For the less optimistic scaling model (model\u00a0A) the exclusion is weaker, reaching down only to about \\(10^{-13}\\). These limits assume a single cusp per loop and vary mildly with the assumed number of kinks."} +{"question": "In what way do cusp\u2011generated gravitational\u2011wave bursts differ from those produced by kinks or kink\u2011kink collisions in terms of detectability by ground\u2011based interferometers?", "answer": "Cusps emit highly beamed, short\u2011duration bursts with a characteristic strain falling as \\(f^{-4/3}\\). Because the emission is narrowly directed, only a small fraction of bursts are observable, but those that are seen can have large amplitudes. Kinks, emitting with a fan\u2011like pattern and a \\(f^{-5/3}\\) spectrum, produce more numerous but weaker events. Kink\u2011kink collisions radiate isotropically with a \\(f^{-2}\\) spectrum; when many kinks are present they dominate the burst rate and can provide the loudest signals for a fixed detector sensitivity."} +{"question": "Does the intercommutation probability of cosmic superstrings alter the gravitational\u2011wave signatures that LIGO\u2013Virgo could detect?", "answer": "I do not have information on this specific aspect. The analysis in the paper focuses on field\u2011theory Nambu\u2013Goto strings with an intercommutation probability close to one. Effects of reduced intercommutation probabilities, which are relevant for cosmic superstrings, are not addressed here and would require dedicated simulations and theoretical work to determine their impact on the burst rate and stochastic background."} +{"question": "What improvements are expected from the upcoming O4 observing run in terms of constraints on cosmic\u2011string parameters?", "answer": "The O4 run will provide roughly twice the observation time of O3 and benefit from the planned upgrades to the LIGO and Virgo detectors. Projections indicate that the improved strain sensitivity, especially at high frequencies, could tighten the exclusion on \\(G\\mu\\) by up to an order of magnitude for the most favorable loop models. Additionally, longer data sets will reduce statistical uncertainties in the stochastic background search, potentially turning the current upper limits into actual detections if the string tension lies near the current bounds."} +{"question": "What theoretical mechanisms can produce sub\u2011solar mass black holes in the early universe?", "answer": "Several mechanisms have been proposed, including the collapse of primordial density fluctuations (primordial black holes), the collapse of cooling dark\u2011matter halos in dissipative dark\u2011matter models, and the formation of exotic compact objects such as boson stars. Each scenario predicts a different mass spectrum and spatial distribution for sub\u2011solar mass black holes."} +{"question": "How can gravitational\u2011wave observations place limits on the fraction of dark matter that is in the form of primordial black holes?", "answer": "Gravitational\u2011wave detectors measure the merger rate of compact binaries. By comparing the observed (or upper\u2011limit) merger rates with theoretical predictions for primordial\u2011black\u2011hole binaries, one can infer an upper limit on the primordial\u2011black\u2011hole abundance, expressed as the fraction of dark matter \\(f_{\\rm PBH}\\). This requires modeling the binary formation process, merger time distribution, and the detector sensitivity to sub\u2011solar mass signals."} +{"question": "Why does the mass ratio of the binary components affect the detectability of sub\u2011solar mass binary mergers?", "answer": "The signal\u2011to\u2011noise ratio of a binary merger depends on the chirp mass, which is a weighted combination of the two component masses. For a fixed total mass, a more unequal mass ratio reduces the chirp mass, leading to a weaker gravitational\u2011wave signal and a smaller horizon distance. Consequently, binaries with very small mass ratios are harder to detect with current detectors."} +{"question": "What observational signatures would distinguish black holes formed through dissipative dark\u2011matter collapse from those formed via primordial fluctuations?", "answer": "Black holes from dissipative dark\u2011matter collapse are expected to have a broader mass spectrum and may form in dense dark\u2011matter halos, potentially leading to a different spatial clustering compared to primordial black holes. Additionally, the binary formation channels may differ, producing distinct spin and eccentricity distributions. These differences could, in principle, be probed by precise measurements of the binary parameters in gravitational\u2011wave events."} +{"question": "What is the expected spin distribution of sub\u2011solar mass black holes produced by dissipative dark\u2011matter collapse?", "answer": "The paper does not address this question, and current theoretical models do not provide a definitive prediction for the spin distribution of such black holes. The spin depends on the angular momentum of the collapsing dark\u2011matter halo, the efficiency of angular momentum transport, and the microphysics of the dark sector, none of which are yet constrained by observations or detailed simulations. Therefore, we do not have a reliable answer to this question at present."} +{"question": "How do seedless clustering algorithms improve sensitivity to narrow\u2011band long\u2011duration gravitational\u2011wave signals compared to seed\u2011based methods?", "answer": "Seedless clustering searches scan the time\u2011frequency plane for coherent excess power using parametrised curves (e.g., B\u00e9zier or sinusoidal tracks) that can follow slowly drifting or quasi\u2011periodic signals. Because the algorithm does not require any thresholded pixels as a seed, it can integrate weak power over many frequency bins and long timescales, boosting the signal\u2011to\u2011noise ratio for narrow\u2011band, long\u2011duration bursts. Seed\u2011based algorithms, in contrast, rely on thresholded pixels and are more effective for generic, broadband morphologies but can miss or poorly reconstruct slowly varying, narrow\u2011band signals."} +{"question": "What are the main challenges posed by non\u2011Gaussian noise transients in long\u2011duration gravitational\u2011wave searches and how are they mitigated?", "answer": "Non\u2011Gaussian transients, or glitches, can mimic long\u2011duration excess power and inflate the false\u2011alarm rate. They arise from environmental disturbances, instrumental resonances, or non\u2011linear coupling. Mitigation strategies include: (1) vetoing data coincident with auxiliary sensor triggers, (2) subtracting identified linear noise sources via Wiener filtering or machine\u2011learning techniques, (3) masking persistent spectral lines, and (4) applying coherence and duration cuts in the clustering pipelines to reject incoherent or short\u2011duration outliers. These steps reduce the background while preserving sensitivity to astrophysical signals."} +{"question": "How do upper limits on the root\u2011sum\u2011square strain amplitude (hrss) translate into constraints on the energy emitted in gravitational waves by astrophysical sources such as magnetars or eccentric binary black holes?", "answer": "The hrss limit at a given frequency and distance can be converted to an upper bound on the isotropic GW energy via \\(E_{\\text{GW}} \\approx \\frac{c^{3}}{G} \\, \\pi^{2} f^{2} h_{\\text{rss}}^{2} D^{2}\\). Thus, tighter hrss limits imply lower allowed GW energies for a source at distance \\(D\\). For example, a 10\u2011ms magnetar burst with an hrss limit of \\(10^{-22}\\,\\text{Hz}^{-1/2}\\) at 100\u202fHz would constrain the emitted energy to below a few \\(10^{-6}\\,M_{\\odot}c^{2}\\). These bounds help rule out or disfavour models predicting large GW luminosities from such events."} +{"question": "In what ways can the inclusion of Virgo data in future observing runs enhance the detection prospects for long\u2011duration gravitational\u2011wave transients?", "answer": "Adding Virgo increases the network\u2019s sky\u2011coverage and triangulation accuracy, improving the ability to localise and confirm coincidences. The extra detector also provides an independent baseline, enhancing coherence tests and reducing the false\u2011alarm probability. With Virgo\u2019s sensitivity approaching that of the LIGO detectors in the next observing runs, the combined network can lower the hrss thresholds by a factor of two or more, directly translating into larger accessible volumes and higher detection rates for long\u2011duration signals."} +{"question": "What is the predicted event rate of long\u2011duration gravitational\u2011wave bursts from fallback accretion onto rapidly rotating black holes?", "answer": "The paper does not provide an answer because the expected rate for this channel is highly uncertain. Current theoretical models of fallback accretion are limited by complex hydrodynamics, magnetic field configurations, and the poorly constrained distribution of progenitor masses. Consequently, no reliable population synthesis exists to predict the rate, and observational constraints are absent due to the lack of detections. Addressing this question would require detailed simulations of core\u2011collapse supernovae with post\u2011bounce accretion, coupled to GW emission estimates, a task beyond the scope of the current study."} +{"question": "How do the upper limits on the dark\u2011photon\u2013baryon coupling derived from ground\u2011based interferometers constrain theoretical models that generate ultralight dark photons via the misalignment mechanism?", "answer": "The misalignment mechanism predicts a relic abundance that depends on the initial field displacement and the dark\u2011photon mass. The limits on the coupling strength translate into an upper bound on the field amplitude, which in turn restricts the allowed range of initial displacements for a given mass. Models that require a large initial displacement to account for the observed dark matter density are therefore disfavored for masses in the \\(10^{-14}\\)\u2013\\(10^{-11}\\,\\text{eV}/c^{2}\\) window."} +{"question": "What are the dominant noise sources that limit the sensitivity of LIGO/Virgo to ultralight dark\u2011photon signals, and how might future detector upgrades mitigate them?", "answer": "The primary limitations are seismic and suspension thermal noise at low frequencies and quantum shot noise at high frequencies. Additionally, narrow spectral lines from instrumental resonances and scattered light can mimic or obscure the quasi\u2011monochromatic dark\u2011photon signature. Future upgrades such as cryogenic test masses, improved mirror coatings, and quantum squeezing will reduce thermal and shot noise, while better vibration isolation and active control of scattering will suppress line artifacts, thereby extending sensitivity across a broader mass range."} +{"question": "How would a space\u2011based interferometer like LISA or TianQin extend the search for dark photons compared to ground\u2011based detectors, and what new mass window would become accessible?", "answer": "Space\u2011based detectors have longer arm lengths and operate in a quieter gravitational\u2011wave environment, reducing seismic and suspension noise. Their lower frequency sensitivity (down to \\(\\sim10^{-4}\\,\\text{Hz}\\)) allows probing dark\u2011photon masses down to \\(\\sim10^{-18}\\,\\text{eV}/c^{2}\\), far below the \\(\\sim10^{-14}\\,\\text{eV}/c^{2}\\) lower bound reachable by ground\u2011based interferometers. Thus, missions like LISA and TianQin can explore a complementary, lower\u2011mass regime."} +{"question": "What is the role of the common\u2011mode motion of the interferometer mirrors in enhancing the detectability of dark photons, and how does it differ from the differential\u2011mode contribution?", "answer": "Dark photons exert a nearly coherent force on all test masses, leading to common\u2011mode motion that does not change instantaneous arm lengths but modulates the light\u2011travel time. This effect introduces a strain component proportional to \\(f_{0}L/c\\), which is not suppressed by the Earth\u2019s velocity \\(v_{0}/c\\). Consequently, the common\u2011mode signal can be stronger than the differential component, especially at higher frequencies, and must be modeled separately in the analysis to avoid loss of sensitivity."} +{"question": "How would a stochastic background of dark\u2011photon dark matter manifest differently in the cross\u2011correlation versus excess\u2011power analysis, and is it possible to separate it from a genuine gravitational\u2011wave background?", "answer": "A stochastic dark\u2011photon background would produce a coherent, quasi\u2011monochromatic signal that is common to all detectors, leading to a non\u2011zero cross\u2011correlation that is highly frequency\u2011dependent due to Doppler broadening. In contrast, a stochastic gravitational\u2011wave background is expected to be broadband and isotropic, yielding a different overlap reduction function. The paper does not address this distinction, as it focuses on searching for a deterministic monochromatic signal rather than a stochastic background. Distinguishing between the two would require a dedicated analysis of the spectral shape and angular correlation of the cross\u2011correlation, which was beyond the scope of the presented work."} +{"question": "What is the spin\u2011down limit for a gravitational\u2011wave source, and why is it a key benchmark in continuous\u2011wave searches from pulsars?", "answer": "The spin\u2011down limit is the maximum gravitational\u2011wave strain that could be emitted if a pulsar\u2019s entire loss of rotational energy were converted into gravitational radiation. It is calculated from the measured spin frequency, its derivative, the pulsar\u2019s distance, and an assumed moment of inertia. A search that reaches below this limit demonstrates that any gravitational\u2011wave emission must be smaller than the full spin\u2011down power, giving a physically meaningful constraint on the star\u2019s deformation or other emission mechanisms."} +{"question": "How do the inter\u2011glitch braking indices measured for PSR J0537\u22126910 suggest the possibility of gravitational\u2011wave energy loss?", "answer": "The long\u2011term braking index of PSR J0537\u22126910 is far below the canonical value of 3, indicating an accelerating spin\u2011down. The inter\u2011glitch braking index, measured between successive glitches, is often >10 and approaches an asymptotic value near 7 shortly after a glitch. Braking indices of 5 and 7 are expected for energy loss dominated by a time\u2011varying mass quadrupole (l = m = 2) and by r\u2011mode oscillations, respectively. The observed indices therefore hint that a portion of the pulsar\u2019s rotational energy may be drained through gravitational\u2011wave emission."} +{"question": "What specific contribution does NICER X\u2011ray timing data provide to the LIGO/Virgo search for PSR J0537\u22126910?", "answer": "NICER supplies a contemporaneous, phase\u2011accurate timing ephemeris that tracks the pulsar\u2019s rotation and glitch epochs. This ephemeris allows the gravitational\u2011wave search to heterodyne the detector data at the expected frequency (once or twice the spin frequency) with the correct phase evolution, keeping the signal coherent over months. Without such a timing solution the search would lose sensitivity because the signal phase would drift due to glitches and irregular spin\u2011down."} +{"question": "How does the upper limit on the equatorial ellipticity of PSR J0537\u22126910 compare with theoretical maximum ellipticities a neutron\u2011star crust can support?", "answer": "The 95\u202f% credible upper limit on the ellipticity of PSR J0537\u22126910 is \u03b5\u202f<\u202f3\u202f\u00d7\u202f10\u207b\u2075. Theoretical estimates of the maximum elastic deformation sustainable by a neutron\u2011star crust range from ~10\u207b\u2075 to a few\u202f\u00d7\u202f10\u207b\u2076, depending on composition and temperature. Thus, the observational limit is at or slightly above the highest theoretical values, indicating that if the crust were maximally strained the star would still be below the sensitivity of the current search."} +{"question": "Is there evidence that the size of a glitch in PSR J0537\u22126910 directly determines the amplitude of any transient gravitational waves produced at the glitch epoch?", "answer": "No. The paper does not address the relationship between glitch size and transient gravitational\u2011wave amplitude. While the timing data record the magnitude of each glitch, the analysis focuses on continuous\u2011wave emission at the rotational harmonics and does not search for or quantify any short\u2011duration signals associated with the glitches. Establishing such a correlation would require dedicated glitch\u2011triggered searches with high\u2011time\u2011resolution data, which remains a topic for future study."} +{"question": "What are the advantages of using a high\u2011pressure gaseous argon TPC over a liquid\u2011argon TPC for measuring low\u2011energy protons in neutrino interactions?", "answer": "In a high\u2011pressure gaseous argon TPC the density of the medium is much lower than in liquid argon, so protons with kinetic energies as low as 5\u202fMeV (corresponding to a track length of a few centimeters) can leave a visible ionisation trail. This gives a significantly lower detection threshold compared with liquid argon, where a 46\u202fMeV proton is needed for a 2\u202fcm track. Additionally, the long mean free path for hadrons in the gas (~90\u202fm) reduces the probability of secondary intranuclear interactions, leading to cleaner event topologies."} +{"question": "How does a magnetic field in the near detector help distinguish neutrino from antineutrino interactions?", "answer": "A magnetic field bends charged particles according to the sign of their charge. In a magnetised TPC the curvature of the outgoing lepton track can be measured, allowing one to determine whether the lepton is a \u03bc\u207a (from a \u03bd\u0304) or a \u03bc\u207b (from a \u03bd). This charge\u2011sign determination is essential for separating neutrino and antineutrino components in a mixed beam, thereby reducing systematic uncertainties in oscillation analyses."} +{"question": "Can a gaseous argon TPC be used to directly detect tau neutrino appearance in the near detector?", "answer": "Yes, in principle the high spatial resolution and good particle identification of a gaseous argon TPC enable the reconstruction of the short\u2010lived \u03c4 lepton decay products. However, the expected rate of \u03bd\u03c4 charged\u2011current interactions at the near detector is extremely low, and practical sensitivity would require a very large exposure or additional specialised trigger strategies. The current design of the ND\u2011GAr does not include dedicated \u03c4\u2011identification capabilities, so while the physics case exists, the detector is not optimised for it."} +{"question": "What role does the calorimeter surrounding the TPC play in neutrino trident searches?", "answer": "The calorimeter provides precise measurements of the energy and direction of photons from \u03c0\u2070 decays and of hadronic showers. By accurately reconstructing electromagnetic and hadronic activity, it helps suppress background events that mimic the two\u2011lepton signature of a trident process, improving the purity of the signal sample."} +{"question": "What are the current limitations on measuring the axial form factor of the neutron using the ND\u2011GAr detector?", "answer": "I do not have a definitive answer to this question. The paper focuses on detector design, cross\u2011section measurements, and BSM searches, but it does not discuss the specific challenges of extracting the neutron axial form factor from the data. Determining that quantity would require detailed modelling of neutrino\u2011neutron interactions, specialised selection criteria, and a comparison with theoretical predictions that are beyond the scope of the present document."} +{"question": "What are the primary physical mechanisms that can generate continuous gravitational waves from a spinning neutron star, and how do the predicted wave frequency and amplitude differ for each mechanism?", "answer": "The two most discussed mechanisms are (1) a non\u2011axisymmetric mass quadrupole \u2013 caused by a permanent deformation such as a \u2018mountain\u2019 on the crust or a strong internal magnetic field \u2013 which emits at twice the star\u2019s spin frequency and scales linearly with the equatorial ellipticity; and (2) unstable r\u2011mode oscillations, which are large\u2011amplitude fluid modes driven unstable by gravitational radiation. R\u2011modes emit at a frequency of roughly 4/3 of the spin frequency and the strain amplitude depends on a dimensionless r\u2011mode amplitude parameter, \u03b1, rather than on an ellipticity. The expected amplitudes for both mechanisms are generally very small (h \u2272 10\u207b\u00b2\u2075\u201310\u207b\u00b2\u2076 for nearby young neutron stars) but can be enhanced if the deformation or r\u2011mode amplitude is unusually large."} +{"question": "How does the estimated age of a supernova remnant affect the range of spin\u2011down parameters that must be searched when looking for continuous gravitational waves from its central compact object?", "answer": "An older remnant implies a smaller age\u2011based upper limit on the strain and, assuming the star\u2019s rotation has slowed mainly through gravitational\u2011wave emission, the allowed first frequency derivative, \u02d9f, scales roughly as \u2013f/\u03c4, where \u03c4 is the age. Younger remnants therefore require searches over a wider range of spin\u2011down values (including larger negative \u02d9f) to account for the possibility of rapid initial spin and strong braking. This also influences the second derivative range, which is tied to the braking index; a larger spread in \u03c4 leads to a broader search in \u02d9f and \u00a8f to maintain sensitivity to physically plausible spin\u2011down trajectories."} +{"question": "What is the sensitivity depth in a semi\u2011coherent continuous\u2011wave search, and how is it typically estimated using simulated injections?", "answer": "Sensitivity depth, D(f), is defined as the ratio of the detector\u2019s strain spectral noise density to the smallest detectable strain amplitude at a given frequency, i.e., D(f) = \u27e8S_h(f)\u27e9 / h_{95%}. It represents the search\u2019s efficiency in converting detector noise into a detectable signal. To estimate D(f), one injects a large number of simulated continuous\u2011wave signals with known amplitudes into real data, processes them with the full search pipeline, and finds the amplitude at which 95% of the injections exceed the detection threshold. The depth is then computed for each frequency band, and an empirical scaling (often linear with frequency) is used to extrapolate to neighboring bands."} +{"question": "Why is the F\u2011statistic a preferred matched\u2011filter statistic for directed continuous\u2011wave searches, and what considerations determine the choice of coherent segment length in a semi\u2011coherent scheme like Weave?", "answer": "The F\u2011statistic analytically maximizes the likelihood over the unknown amplitude, polarization, and initial phase, providing a powerful detection statistic that is sensitive to weak, nearly monochromatic signals. In a semi\u2011coherent scheme, data are split into short coherent segments (length T_coh) where the F\u2011statistic is computed; these are then summed to form a mean statistic. Shorter segments reduce computational cost and mitigate phase errors from imperfect spin\u2011down models, but they also lower the coherent SNR. Longer segments improve sensitivity but require a denser template bank to cover the parameter space and increase the risk of signal loss due to mismatch. The optimal T_coh is therefore chosen by balancing sensitivity gains against computational feasibility, often guided by simulations that include realistic noise and spin\u2011down uncertainties."} +{"question": "Does the search for continuous waves from Cas\u202fA and Vela\u202fJr. place any limits on the possible r\u2011mode amplitude of their central compact objects?", "answer": "The paper does not provide explicit upper limits on r\u2011mode amplitudes. While it discusses r\u2011mode emission as a theoretical possibility and presents sensitivity curves for strain, it focuses on constraints derived from ellipticity models and does not perform dedicated simulations or injections for r\u2011mode signals. Consequently, no quantitative limits on the r\u2011mode amplitude, \u03b1, are given; deriving such limits would require a separate study that models the r\u2011mode waveform and injects it into the data to assess detectability."} +{"question": "What are the trade\u2011offs between electric field strength and scintillation light yield in large\u2011volume dual\u2011phase liquid argon time\u2011projection chambers?", "answer": "In a dual\u2011phase LArTPC the primary scintillation yield depends strongly on the electron\u2011ion recombination probability. A low drift field (tens of V/cm) allows many ionized electrons to recombine with ions, producing a larger fraction of the 127\u202fnm VUV photons. As the field is increased to several hundred V/cm, the drift velocity rises and the recombination probability drops, reducing the S1 yield. However, a higher field improves charge extraction and minimizes attachment losses, which is essential for accurate calorimetry. The optimal field therefore balances a sufficient S1 signal for timing and trigger purposes against the need for high\u2011quality charge readout."} +{"question": "How does the geometry of a wavelength\u2011shifting material influence the angular distribution and detection efficiency of scintillation photons in a dual\u2011phase LArTPC?", "answer": "The angular emission pattern of re\u2011emitted photons depends on whether the wavelength shifter is coated directly on the photocathode surface, painted on a thin film, or deposited on a larger area. Coating the inner surface of the PMT glass (as with TPB) produces a more isotropic re\u2011emission with a relatively high transport efficiency to the photocathode. In contrast, a thin polyethylene\u2011naphthalate (PEN) foil positioned over the PMT window presents two exposed faces; photons incident on either side are re\u2011emitted in all directions, but the geometry causes a larger fraction of the light to escape or hit non\u2011photosensitive areas, reducing the effective detection efficiency. Additionally, foils may introduce multiple scattering and surface reflections that alter the arrival\u2011time distribution, affecting the timing resolution."} +{"question": "In what ways does xenon doping modify the spectral composition and attenuation characteristics of scintillation light in liquid argon, and how can this be exploited for improved light collection in large detectors?", "answer": "When xenon is dissolved in liquid argon at the ppm level, energy transfer from excited argon excimers to xenon occurs. The resulting xenon excimers emit photons at longer wavelengths (\u2248\u202f178\u202fnm and \u2248\u202f150\u202fnm), which are less strongly absorbed by impurities and experience a longer Rayleigh scattering length (\u2248\u202f3\u20139\u202fm) compared to the 127\u202fnm argon light (\u2248\u202f1\u202fm). Consequently, photons travel further before scattering or being absorbed, improving the uniformity of light collection, especially for events occurring far from the photodetector array. However, the original 127\u202fnm component is partially quenched, so the total S1 amplitude can decrease if the xenon concentration is too high. Optimizing the xenon level thus requires balancing increased propagation distance against reduced primary light yield."} +{"question": "What are the most effective computational strategies for accurately simulating photon transport over long drift distances while keeping resource demands manageable in large LArTPC experiments?", "answer": "Full Monte\u2011Carlo tracking of each VUV photon is prohibitively expensive for multi\u2011kilometre LAr volumes. Practical solutions include: (1) constructing photon libraries by generating a large number of photons from a fine grid of voxels, recording for each detector channel the visibility, minimum arrival time and time\u2011distribution parameters; (2) interpolating between voxels during event simulation to estimate light yield without individual photon tracking; (3) using importance sampling to focus on regions of high light\u2011yield density; (4) parallelising the photon generation step with GPUs or distributed computing; and (5) implementing analytic approximations for Rayleigh scattering and absorption based on measured attenuation lengths. These methods reduce CPU time by orders of magnitude while preserving sufficient accuracy for detector\u2011design studies."} +{"question": "What is the expected degradation in light detection efficiency of PEN or TPB wavelength shifters after ten years of operation in a liquid argon environment under continuous VUV irradiation, and what mechanisms dominate this aging process?", "answer": "The agent does not have sufficient information to provide a reliable prediction. Long\u2011term aging studies of PEN and TPB films in liquid argon, exposed continuously to VUV photons, have not yet been performed on a decade timescale. Key mechanisms\u2014such as photo\u2011degradation of the organic molecules, micro\u2011cracking of the polymer matrix, or contamination from dissolved gases\u2014remain unquantified experimentally, so the future efficiency loss cannot be determined from current data alone. Further dedicated aging experiments would be required to answer this question."} +{"question": "How do the detection thresholds of matched\u2011filter pipelines influence the completeness of the GWTC\u20112.1 catalog for low\u2011mass binary neutron star mergers?", "answer": "The detection thresholds, such as the chosen false\u2011alarm\u2011rate cut and signal\u2011to\u2011noise ratio thresholds, determine which signals exceed the pipelines\u2019 sensitivity limits. Lower thresholds increase completeness but also raise the background noise, while higher thresholds reduce false alarms at the cost of missing marginal events. The GWTC\u20112.1 catalog does not provide a detailed completeness analysis for low\u2011mass binary neutron star systems; such an assessment would require dedicated injection campaigns across the full parameter space of neutron star masses and spins."} +{"question": "What are the implications of the newly identified high\u2011mass binary black hole events for the existence of an intermediate\u2011mass black hole population?", "answer": "The high\u2011mass events in GWTC\u20112.1, with total masses approaching or exceeding 150\u202fM\u2299, expand the observable mass range for binary black hole mergers. Their presence supports the possibility that intermediate\u2011mass black holes (\u224810\u00b2\u201310\u00b3\u202fM\u2299) can form through hierarchical mergers or dynamical assembly in dense stellar environments. However, the limited number of such detections and the uncertainties in the mass\u2011gap boundaries mean that the existence of a substantial intermediate\u2011mass black hole population remains an open question."} +{"question": "How does the calibration uncertainty of the LIGO and Virgo detectors impact the sky\u2011localization accuracy for high\u2011redshift events in GWTC\u20112.1?", "answer": "Calibration uncertainties introduce systematic errors in the amplitude and phase of the reconstructed strain, which propagate into the parameter\u2011estimation pipeline and degrade the precision of sky\u2011localization. For high\u2011redshift events with modest signal\u2011to\u2011noise ratios, the resulting 90\u202f% credible regions can be significantly larger than for nearby, louder events. The GWTC\u20112.1 analysis incorporates calibration uncertainties by marginalizing over spline\u2011parameterized amplitude and phase variations, but the exact impact on each event\u2019s localization is not reported in the catalog and would need to be evaluated on a case\u2011by\u2011case basis."} +{"question": "What are the dominant systematic uncertainties in estimating the effective inspiral spin parameter (\u03c7_eff) for precessing binary black hole systems?", "answer": "The main systematic sources include waveform model inaccuracies (e.g., missing higher\u2011order modes or imperfect treatment of precession), limited signal\u2011to\u2011noise ratio, and assumptions about spin priors. Additionally, calibration errors can bias phase evolution, directly affecting \u03c7_eff. The current state\u2011of\u2011the\u2011art models (IMRPhenomXPHM, SEOBNRv4PHM) mitigate many of these effects, but residual discrepancies between models and between model and data still contribute to the total systematic uncertainty budget."} +{"question": "What is the true astrophysical rate of neutron star\u2013black hole mergers in the local universe, as inferred from the GWTC\u20112.1 data?", "answer": "The GWTC\u20112.1 catalog does not provide a definitive rate estimate for neutron star\u2013black hole (NSBH) mergers. While a few candidate events hint at the possibility of such systems, the current sample size is too small and the statistical and systematic uncertainties too large to derive a robust local merger rate. A more accurate estimate will require additional detections, improved sensitivity, and refined population\u2011modeling efforts."} +{"question": "What are the dominant systematic uncertainties that limit DUNE\u2019s ability to measure the CP\u2011violating phase \u03b4CP?", "answer": "DUNE\u2019s sensitivity to \u03b4CP is largely limited by three classes of systematic uncertainties:\\n1. **Neutrino flux prediction** \u2013 uncertainties in hadron production and horn focusing affect the energy\u2011dependent neutrino flux at the far detector. \\n2. **Neutrino\u2011nucleus interaction models** \u2013 uncertainties in cross\u2011sections, final\u2011state interactions, and nuclear effects (e.g., multinucleon emission) change the reconstructed neutrino energy distribution. \\n3. **Detector response** \u2013 uncertainties in calorimetric energy scale, electron\u2013muon separation efficiency, and reconstruction efficiency introduce biases in the extracted oscillation probabilities. DUNE\u2019s near detector program and data\u2011driven techniques are designed to constrain these systematics to the few\u2011percent level required for a high\u2011precision \u03b4CP measurement."} +{"question": "How does DUNE\u2019s wide\u2011band neutrino beam help disentangle the neutrino mass ordering from CP\u2011violation effects?", "answer": "The broad energy spectrum (\u223c0.5\u20134\u202fGeV) of DUNE\u2019s beam samples the first and second oscillation maxima. Matter effects grow with baseline and energy, producing a distinct energy\u2011dependent asymmetry between neutrinos and antineutrinos that depends on the mass ordering but not on \u03b4CP. By measuring the oscillation probability as a function of energy over more than one full oscillation period, DUNE can fit simultaneously for the mass ordering and \u03b4CP, with the energy dependence providing a handle to separate the two effects."} +{"question": "What is DUNE\u2019s expected sensitivity to the proton\u2011decay channel \\(p \\rightarrow K^+ \\nu\\) after its full physics run?", "answer": "With a 40\u2011kiloton fiducial mass and a 40\u2011year exposure (\u22481.6\u202fMt\u2011yr), DUNE expects to set a 90\u202f%\u202fC.L. lower limit on the proton lifetime in the \\(p \\rightarrow K^+ \\nu\\) channel of order \\(1.3 \\times 10^{34}\\)\u202fyears, assuming a 30\u202f% signal efficiency and negligible background after sophisticated reconstruction and selection cuts."} +{"question": "How will DUNE detect neutrinos from a core\u2011collapse supernova and what physics can be extracted from the observed signal?", "answer": "DUNE\u2019s liquid\u2011argon TPC is especially sensitive to the charged\u2011current absorption of electron neutrinos on argon (\\(\\nu_e + ^{40}\\mathrm{Ar} \\rightarrow e^- + ^{40}\\mathrm{K}^*\\)). A supernova burst at 10\u202fkpc would yield \u22483000 events in a 40\u2011kt detector, allowing a time\u2011resolved measurement of the neutronization burst, accretion, and cooling phases. By fitting the energy and time spectra, one can extract information on the supernova explosion mechanism, neutrino flavor transformation (MSW and collective effects), and the neutrino mass ordering, as the early neutronization burst is highly sensitive to the ordering."} +{"question": "What is the precise value of the neutrino mass ordering?", "answer": "The neutrino mass ordering (whether the third mass eigenstate is heavier or lighter than the first two) is currently unknown. While experiments like DUNE aim to determine it with high significance, the exact ordering has not yet been measured, so the answer remains undetermined at this time. Further data from long\u2011baseline, reactor, and atmospheric neutrino experiments are required to resolve this fundamental question."} +{"question": "What is the expected rate of strongly lensed binary black hole mergers detectable with the next-generation third\u2011generation gravitational\u2011wave detectors?", "answer": "Forecasts based on standard lensing models (e.g., singular isothermal sphere or ellipsoid) predict that at design sensitivity the merger rate of lensed binary black hole events could rise to a few percent of the total detectable rate, reaching \\u2265 10\\u201315% depending on the mass distribution and redshift evolution of the source population. These predictions assume that the intrinsic merger rate follows the star\u2011formation rate and that the detector horizon extends to z \\u2265 5."} +{"question": "How does the presence of microlenses embedded in galaxy\u2011cluster potentials modify the wave\u2011optics signatures observed in gravitational\u2011wave signals?", "answer": "Microlenses with masses between a few solar masses and a thousand solar masses, situated in the macrolensing environment of a cluster, can introduce interference patterns in the waveform that are superimposed on the macrolens magnification. This produces oscillatory modulations in the frequency domain, with characteristic beat frequencies that depend on the Einstein radius of the microlens and the relative alignment. Numerical simulations show that such effects become appreciable when the microlens Einstein radius is comparable to the GW wavelength (i.e., when the lens mass is \\u2265 10 M\u2299 and the source is at z \\u2265 1). Detecting these patterns would require high signal\u2011to\u2011noise ratios and detailed waveform modeling that includes both macro and micro\u2011lens potentials."} +{"question": "Can a precise measurement of the time delay between multiple images of a lensed gravitational\u2011wave event be used to constrain cosmological parameters such as the Hubble constant?", "answer": "Yes, in principle the time delay between two images of a lensed GW event, combined with an accurate localization of the source and lens, can provide an independent measurement of the Hubble constant. The delay depends on the difference in the Fermat potential between the image positions and on the angular\u2011diameter distances, which are sensitive to H0. However, achieving the required precision demands multiple high\u2011signal\u2011to\u2011noise detections of the same source, robust lens modeling, and accurate determination of the lens mass distribution\u2014challenges that are still being addressed in current research."} +{"question": "What are the observational signatures that would distinguish a gravitational\u2011wave event lensed by a galaxy cluster from one lensed by a single galaxy?", "answer": "Galaxy\u2011cluster lensing typically produces longer time delays (weeks to months or even years) and larger magnification factors (up to 10\u2013100) than galaxy\u2011scale lenses, which usually have delays of minutes to days and magnifications of a few. Additionally, cluster lenses often generate multiple images with more complex morphologies, sometimes forming arcs or rings in electromagnetic counterparts. In gravitational waves, one would expect a series of repeated events over extended periods, potentially with varying SNRs reflecting the magnification gradient across the caustic. Precise identification requires long\u2011term monitoring and cross\u2011matching with electromagnetic surveys."} +{"question": "Is it possible to detect the effects of primordial black holes acting as microlenses on gravitational\u2011wave signals from binary black holes?", "answer": "We currently do not have evidence that primordial black holes serve as microlenses in gravitational\u2011wave observations. Detecting their influence would require observing characteristic interference patterns or frequency\u2011dependent magnification in the GW signal, but such signatures have not yet been observed. The lack of detection could be due to the limited sensitivity of existing detectors, the rarity of suitable alignments, or the absence of a significant population of primordial black holes in the relevant mass range. Further data from next\u2011generation detectors and more sophisticated analysis methods are needed to explore this possibility."} +{"question": "How does the presence of eccentric orbits influence the sensitivity of semicoherent searches for continuous gravitational waves from neutron stars in binary systems?", "answer": "Eccentricity introduces additional harmonic components and a more complex Doppler modulation, requiring denser template banks and reducing sensitivity compared to circular orbits. The exact degradation depends on the orbital parameters and the search coherence time."} +{"question": "What is the expected distribution of spin\u2011down rates for neutron stars in tight binary systems that would make them detectable by all\u2011sky searches in the 50\u2013300\u202fHz band?", "answer": "Detectable spin\u2011down rates are typically |\u02d9f| \u2272 10\u207b\u00b9\u2070\u202fHz\u202fs\u207b\u00b9 for data spans of months. Most known millisecond pulsars in binaries exhibit spin\u2011downs below this threshold, but the population of unknown systems is poorly constrained."} +{"question": "How does the use of GPU\u2011accelerated pipelines influence the computational cost scaling with increasing frequency band width in all\u2011sky continuous\u2011wave searches?", "answer": "GPU acceleration reduces the per\u2011template processing time by an order of magnitude, allowing the template bank to grow with frequency without a proportional increase in wall\u2011time. However, the overall cost still scales roughly with the number of frequency bins, so wider bands remain the limiting factor."} +{"question": "What are the current theoretical limits on the ellipticity of rapidly rotating neutron stars in low\u2011mass X\u2011ray binaries, and how do these limits compare to the sensitivity achieved by recent LIGO runs?", "answer": "I do not have that information. The paper focuses on the search methodology and sensitivity estimates, and does not discuss theoretical models of neutron\u2011star ellipticity or compare them with LIGO sensitivities."} +{"question": "Could a future third\u2011generation ground\u2011based interferometer improve the detection prospects for continuous waves from neutron stars in binary systems with orbital periods shorter than 3\u202fdays, and if so, by what factor?", "answer": "A third\u2011generation detector with ~10\u00d7 lower noise would improve strain sensitivity by roughly a factor of 10, potentially allowing detection of ellipticities an order of magnitude smaller. This would open the window to binaries with very short periods, but detailed simulations are required to quantify the exact factor."} +{"question": "How can the detection of monoenergetic 236\u202fMeV neutrinos produced by kaon decay at rest in the Sun be used to probe dark\u2011matter annihilation in the solar core?", "answer": "When weakly interacting dark matter particles are gravitationally captured by the Sun, they can annihilate into standard\u2011model particles. The hadronization of the annihilation products generates charged kaons that stop in the dense solar medium and decay to produce monoenergetic \\(\\nu_\\mu\\) at 236\u202fMeV. The flux of these neutrinos at Earth is directly proportional to the dark\u2011matter capture rate, which in turn depends on the dark\u2011matter\u2013nucleon scattering cross section and the dark\u2011matter mass. By measuring or setting limits on the 236\u202fMeV neutrino flux, one can infer the annihilation rate and thus constrain the scattering cross section for models where capture and annihilation are in equilibrium. This provides a complementary probe of dark matter that is sensitive to parameter space inaccessible to terrestrial direct\u2011detection experiments, especially for low\u2011mass or inelastic dark matter scenarios."} +{"question": "What are the key advantages of a liquid\u2011argon time\u2011projection chamber for identifying the direction of 236\u202fMeV neutrinos compared with water Cherenkov detectors?", "answer": "At the 236\u202fMeV energy scale, charged\u2011current interactions on argon frequently eject a single proton that is emitted preferentially in the forward direction relative to the incident neutrino. In a liquid\u2011argon TPC, the ionization track of this proton is fully reconstructed with high spatial resolution, allowing its momentum vector to be measured accurately. The accompanying muon track, although largely isotropic, can also be reconstructed. By combining the proton and muon kinematics and applying momentum conservation, one can infer the recoil of the residual nucleus and thereby reconstruct the incoming neutrino direction with an angular resolution of order a few degrees. In contrast, water Cherenkov detectors are unable to see the proton track and rely solely on the Cherenkov ring of the muon, which is far less directional at this energy. Thus, the LArTPC offers superior directional discrimination for monoenergetic solar neutrinos."} +{"question": "How does the annual motion of the Earth around the Sun affect the acceptance of a deep\u2011underground detector for 236\u202fMeV solar neutrinos, and what is its impact on the sensitivity?", "answer": "The Sun\u2019s apparent position in the sky changes over the year, causing the incoming neutrino direction to sweep through a range of zenith and azimuth angles relative to the detector coordinates. Since the reconstruction of the neutrino direction in a LArTPC relies on forward proton kinematics, the detector\u2019s effective acceptance depends on the alignment between the proton direction and the detector wire geometry. For angles where the proton track is nearly parallel to a wire plane, track reconstruction can be more difficult, reducing efficiency. Conversely, when the proton is orthogonal to the wire planes, reconstruction improves. By integrating over the full 12\u2011month cycle, one obtains an averaged acceptance that can be factored into the expected event rate. The impact on sensitivity is modest; typical variations are at the tens of percent level, but precise modeling is required to avoid systematic biases in the annual modulation of the signal."} +{"question": "What role do nuclear effects such as the spectral function and meson\u2011exchange currents play in determining the charged\u2011current quasi\u2011elastic cross section for 236\u202fMeV neutrinos on argon?", "answer": "The spectral function describes the momentum and removal energy distribution of nucleons inside the argon nucleus, providing a more realistic initial\u2011state model than the simple Fermi\u2011gas approximation. This influences the energy and angular distributions of the outgoing lepton and proton. Meson\u2011exchange currents (MEC) introduce two\u2011body interactions where the neutrino couples to a pair of nucleons, leading to multinucleon emission that can mimic single\u2011proton final states. At 236\u202fMeV, MEC contributes roughly 4\u202f% of the total cross section, while the dominant quasi\u2011elastic component is about 64\u202f%. Accurate inclusion of these effects is essential for predicting the rates of single\u2011track events and for evaluating backgrounds, as they alter both the kinematic selection efficiency and the energy reconstruction."} +{"question": "Could the electron neutrino charged\u2011current channel provide better sensitivity to 236\u202fMeV solar KDAR neutrinos than the muon channel, and what are the limitations of this approach?", "answer": "In principle, the electron channel offers several advantages: the atmospheric \\(\\nu_e\\) background flux is smaller, the charged\u2011current cross section for \\(\\nu_e\\) on argon is larger (because the outgoing electron is lighter), and oscillation effects in the Sun tend to increase the \\(\\nu_e\\) fraction of the KDAR flux. However, the paper does not provide an analysis of the electron channel. The main challenges are: (1) electron tracks at 236\u202fMeV are short and highly ionizing, making pattern\u2011recognition and track\u2011to\u2011vertex association more difficult than for muons; (2) electromagnetic showers overlap with the proton track, complicating particle identification and energy reconstruction; (3) the directionality inferred from the proton remains useful, but the electron\u2019s isotropic distribution reduces the potential for additional directional cuts. Consequently, while a dedicated study could show improved sensitivity, the necessary simulation of electron\u2011track reconstruction, calorimetry, and background modeling was beyond the scope of the present work."} +{"question": "How will the removal of the hardware L0 trigger and the implementation of an all-software trigger impact the online reconstruction latency for high-multiplicity events?", "answer": "The all-software trigger allows the full reconstruction of every 40\u00a0MHz bunch crossing, removing the coarse hardware selection that previously introduced latency. By exploiting GPU farms, the LHCb upgrade can process each event within roughly 1\u00a0ms, which is acceptable for the increased event size. However, detailed benchmarks are still required to confirm that this latency remains stable under the highest luminosities."} +{"question": "What are the expected improvements in impact\u2011parameter resolution for the upgraded VELO compared to the Run\u00a01\u20112 VELO, and how will that affect heavy\u2011flavour lifetime measurements?", "answer": "With the new 55\u202f\u00b5m pixel size and the reduced distance from the first hit to the interaction point (to 5.1\u202fmm), the VELO is projected to improve its impact\u2011parameter resolution by about 20\u201330\u202f%. This translates into a ~15\u202f% improvement in lifetime resolution for B and D mesons, enhancing the precision of CP\u2011violation and rare\u2011decay measurements."} +{"question": "How does the introduction of neutron shielding upstream of the calorimeter affect background rates in the SciFi Tracker, and what are the implications for signal efficiency?", "answer": "The borated polyethylene shielding reduces the 1\u202fMeV neutron\u2011equivalent fluence at the SiPMs by a factor of roughly 2\u20133. This lowers the dark\u2011noise rate of the SiPM arrays, preserving hit efficiency in the most irradiated regions and thus maintaining overall tracker performance at high luminosities."} +{"question": "What are the challenges in maintaining the mechanical stability of the new RF boxes at the reduced inner radius, and how might this influence beam\u2011induced vibrations?", "answer": "The 3.5\u202fmm inner radius increases mechanical stresses and makes the RF boxes more susceptible to beam\u2011induced vibrations. Mitigations include low\u2011secondary\u2011electron\u2011yield coatings and NEG layers to reduce impedance, but additional studies on vibration damping and long\u2011term mechanical stability are still underway."} +{"question": "What is the projected lifetime performance of the SciFi Tracker's SiPM arrays at the end of Run\u00a04, considering cumulative ionising dose and displacement damage?", "answer": "The paper does not provide a definitive answer to this; the long\u2011term effects of cumulative ionising dose and displacement damage beyond the planned 50\u00a0fb\u207b\u00b9 are still under investigation. Determining the SiPM performance at the end of Run\u00a04 will require additional operational data and detailed radiation\u2011damage studies that are not covered in the current document."} +{"question": "How does the uniformity of the electric field in a liquid\u2011argon TPC influence the spatial resolution of reconstructed tracks, and what level of field homogeneity is typically required for a 3.6\u202fm drift distance?", "answer": "A uniform electric field minimizes transverse diffusion and ensures that electrons drift along straight paths, directly improving the z\u2011coordinate (drift time) resolution. For a 3.6\u202fm drift at 500\u202fV/cm, field variations should be kept below a few hundred volts per meter (\u223c0.05\u202f% of the nominal field) to maintain sub\u2011millimeter drift\u2011time precision."} +{"question": "In what way does argon purity affect the electron lifetime, and how can this lifetime be monitored in real\u2011time during a long\u2011term experiment?", "answer": "Oxygen and water impurities capture drifting electrons, shortening the lifetime \u03c4. The lifetime can be inferred from a purity monitor that measures the ratio of collected to emitted charge over a known drift distance. A lifetime of >10\u202fms corresponds to impurity levels below \u223c10\u202fppt O\u2082\u2011equivalent."} +{"question": "What design modifications to the photon detection system could increase light\u2011collection efficiency without significantly increasing the detector\u2019s mass or complexity?", "answer": "Options include using larger area SiPMs with higher photon detection efficiency, implementing reflective coatings on the inside of the APA frame, optimizing the wavelength\u2011shifting material thickness, and arranging photon collectors in a denser, but still sparse, grid to reduce dead space while maintaining mechanical integrity."} +{"question": "What are the primary engineering challenges when scaling a single\u2011phase liquid\u2011argon TPC from the ProtoDUNE\u2011SP scale (\u223c0.8\u202fkt) to the 40\u202fkt far\u2011detector modules envisaged for DUNE?", "answer": "Key challenges include maintaining mechanical stability of large\u2011scale cryostats, ensuring uniform high\u2011voltage distribution over 3\u20134\u202fm drift gaps, handling cryogenic circulation and purification at unprecedented volumes, and designing readout electronics that can operate reliably in a high\u2011radiation, deep\u2011underground environment."} +{"question": "What is the optimal geometry and placement of photon detectors within the APA frame to maximize overall light collection while minimizing dead space, and how does this geometry scale with detector size?", "answer": "The paper does not provide a definitive answer to this optimization problem. Determining the optimal geometry would require detailed optical simulations combined with mechanical constraints and cost analyses, which were beyond the scope of the presented work and thus remain an open research question."} +{"question": "How do higher\u2011order multipole moments influence parameter estimation for asymmetric binary black hole mergers?", "answer": "Including sub\u2011dominant modes (e.g., \u2113=3,4) reduces systematic biases in mass, spin, and distance estimates for systems with large mass ratios or high inclination, as the waveform more accurately captures the true signal structure."} +{"question": "Can ringdown measurements distinguish between Kerr and non\u2011Kerr remnant black holes?", "answer": "Current ringdown analyses are consistent with Kerr predictions; deviations in the fundamental (220) and first overtone (221) mode frequencies are constrained to within a few percent, showing no statistically significant evidence for non\u2011Kerr remnants."} +{"question": "How effective are null\u2011stream polarization tests in ruling out non\u2011tensorial gravitational\u2011wave polarizations?", "answer": "Null\u2011stream analyses with the current three\u2011detector network yield Bayes factors overwhelmingly consistent with tensorial (GR) polarizations; they provide no significant preference for pure vector or scalar polarizations, thereby supporting the GR prediction of two tensor modes."} +{"question": "What are the prospects for detecting post\u2011merger gravitational\u2011wave echoes in future observing runs?", "answer": "The agent does not have a definitive answer to this question. Detecting echoes depends on improved detector sensitivity, longer observing time, and refined template models, all of which are still under development. Consequently, the paper does not provide a prediction, and the information required to estimate future detection prospects is not yet available."} +{"question": "What are the dominant sources of systematic uncertainty when employing convolutional neural networks to separate track-like from shower-like energy deposits in liquid argon time projection chamber data?", "answer": "The main systematic sources are (i) space\u2011charge distortion of drift fields, which shifts hit positions and alters charge deposition patterns; (ii) detector\u2011specific electronics noise and baseline variations that can obscure small deposits; (iii) calibration uncertainties in the wire\u2011plane response and time\u2011to\u2011charge conversion; (iv) model bias due to limited training samples that may not cover the full range of interaction topologies; and (v) differences between simulation and data (e.g., hadronic interaction models) that affect the learned feature representations."} +{"question": "How might the performance of a hit\u2011level CNN classifier be improved for low\u2011energy (below 100\u202fMeV) electromagnetic showers in LArTPC detectors?", "answer": "Improvements can come from: (1) augmenting the training dataset with realistic low\u2011energy shower simulations and adding noise replicas; (2) incorporating physics\u2011motivated preprocessing such as drift\u2011time correction or space\u2011charge compensation; (3) using multi\u2011scale convolutional layers or dilated convolutions to capture both fine\u2011grained and global shower features; (4) applying transfer learning from high\u2011energy shower models and fine\u2011tuning on low\u2011energy data; and (5) integrating a secondary classifier that explicitly models the expected electron\u2011photon separation in thin LAr volumes."} +{"question": "In what ways can the identification of Michel electrons be leveraged to improve neutrino oscillation analyses in large liquid argon detectors?", "answer": "Michel electron tagging enables: (i) clean identification of stopping muons, which constrains the neutrino interaction vertex and energy reconstruction; (ii) charge\u2011sign discrimination between \\u03b1 and \\u03b2, since only \\u03b1\\u039b decays produce Michel electrons, aiding in separating neutrino from antineutrino interactions; (iii) validation of muon stopping rates and hence cross\u2011section measurements; and (iv) providing a calibration sample for low\u2011energy electromagnetic energy scale and resolution."} +{"question": "What are the computational trade\u2011offs between using a small patch\u2011based convolutional neural network versus a full\u2011image semantic segmentation approach for hit classification in LArTPC data?", "answer": "A patch\u2011based CNN has lower memory usage and faster inference on CPUs because each input is small (e.g., 48\u00d748 pixels) and can be processed independently; however, it may miss global context leading to higher misclassification near complex topologies. Full\u2011image semantic segmentation captures the entire event structure, improving contextual decisions but requires GPU resources, larger memory, and longer inference times, which may not be feasible on standard computing clusters used in large\u2011scale analyses."} +{"question": "How does the hit\u2011level classification performance of a CNN trained on surface prototype data translate to a deep underground neutrino detector with a much reduced cosmic\u2011ray background?", "answer": "I do not have empirical evidence to answer this precisely. The performance may change because the signal\u2011to\u2011noise ratio, background composition, and space\u2011charge conditions differ significantly underground. These differences could alter the statistical distribution of hit topologies the network has to learn, potentially requiring re\u2011training or domain adaptation techniques. Further dedicated studies with underground data are needed to quantify the impact."} diff --git a/data/papers/paper_urls.json b/data/papers/paper_urls.json new file mode 100644 index 0000000..00b1282 --- /dev/null +++ b/data/papers/paper_urls.json @@ -0,0 +1 @@ +["https://arxiv.org/pdf/1411.4413v2", "https://arxiv.org/pdf/0901.0512v4", "https://arxiv.org/pdf/1710.05839v2", "https://arxiv.org/pdf/2508.18080v2", "https://arxiv.org/pdf/2403.03004v1", "https://arxiv.org/pdf/2508.18081v1", "https://arxiv.org/pdf/2407.12867v2", "https://arxiv.org/pdf/2410.16565v2", "https://arxiv.org/pdf/2501.01495v2", "https://arxiv.org/pdf/2508.18083v2", "https://arxiv.org/pdf/2410.09151v2", "https://arxiv.org/pdf/2404.04248v3", "https://arxiv.org/pdf/2308.03822v1", "https://arxiv.org/pdf/2510.26848v2", "https://arxiv.org/pdf/2510.27022v4", "https://arxiv.org/pdf/2510.26931v1", "https://arxiv.org/pdf/2508.20721v1", "https://arxiv.org/pdf/2510.17487v1", "https://arxiv.org/pdf/2508.18079v3", "https://arxiv.org/pdf/2508.18082v2", "https://arxiv.org/pdf/2507.08219v3", "https://arxiv.org/pdf/2507.12282v2", "https://arxiv.org/pdf/2509.04348v2", "https://arxiv.org/pdf/2511.19911v2", "https://arxiv.org/pdf/2511.16863v2", "https://arxiv.org/pdf/2509.08054v1", "https://arxiv.org/pdf/2509.07352v2", "https://arxiv.org/pdf/2505.00274v1", "https://arxiv.org/pdf/2505.00273v1", "https://arxiv.org/pdf/2505.00272v1", "https://arxiv.org/pdf/2302.03676v1", "https://arxiv.org/pdf/2308.13666v1", "https://arxiv.org/pdf/1406.6311v4", "https://arxiv.org/pdf/2407.10339v1", "https://arxiv.org/pdf/2212.01477v2", "https://arxiv.org/pdf/2403.03212v1", "https://arxiv.org/pdf/2304.08393v1", "https://arxiv.org/pdf/2209.02863v2", "https://arxiv.org/pdf/2408.12725v1", "https://arxiv.org/pdf/2111.03604v2", "https://arxiv.org/pdf/2201.10104v1", "https://arxiv.org/pdf/2111.15507v2", "https://arxiv.org/pdf/2204.04523v1", "https://arxiv.org/pdf/2111.13106v2", "https://arxiv.org/pdf/2210.10931v1", "https://arxiv.org/pdf/2112.06861v3", "https://arxiv.org/pdf/2203.01270v2", "https://arxiv.org/pdf/2510.08380v1", "https://arxiv.org/pdf/2409.18288v3", "https://arxiv.org/pdf/2201.00697v1", "https://arxiv.org/pdf/2511.11925v1", "https://arxiv.org/pdf/1604.07864v3", "https://arxiv.org/pdf/1602.08492v4", "https://arxiv.org/pdf/2408.00582v1", "https://arxiv.org/pdf/2312.03130v1", "https://arxiv.org/pdf/2511.13462v1", "https://arxiv.org/pdf/1810.10693v2", "https://arxiv.org/pdf/2507.08586v3", "https://arxiv.org/pdf/2509.07664v1", "https://arxiv.org/pdf/2212.09807v3", "https://arxiv.org/pdf/2402.01568v3", "https://arxiv.org/pdf/2203.12038v1", "https://arxiv.org/pdf/2106.15163v1", "https://arxiv.org/pdf/2509.07012v1", "https://arxiv.org/pdf/2303.17007v2", "https://arxiv.org/pdf/2503.23744v1", "https://arxiv.org/pdf/2503.23293v1", "https://arxiv.org/pdf/2503.23743v1", "https://arxiv.org/pdf/2111.03608v1", "https://arxiv.org/pdf/2111.03634v5", "https://arxiv.org/pdf/2111.03606v3", "https://arxiv.org/pdf/2502.06637v2", "https://arxiv.org/pdf/2109.09255v2", "https://arxiv.org/pdf/2110.09834v1", "https://arxiv.org/pdf/2105.11641v2", "https://arxiv.org/pdf/2107.00600v2", "https://arxiv.org/pdf/2112.10990v2", "https://arxiv.org/pdf/2211.01166v4", "https://arxiv.org/pdf/2104.14417v2", "https://arxiv.org/pdf/2101.12130v1", "https://arxiv.org/pdf/2503.23291v1", "https://arxiv.org/pdf/2107.03701v1", "https://arxiv.org/pdf/2103.08520v4", "https://arxiv.org/pdf/2101.12248v1", "https://arxiv.org/pdf/2109.12197v1", "https://arxiv.org/pdf/2107.13796v1", "https://arxiv.org/pdf/2105.13085v3", "https://arxiv.org/pdf/2012.12926v2", "https://arxiv.org/pdf/2203.06281v1", "https://arxiv.org/pdf/2111.15116v2", "https://arxiv.org/pdf/2203.16134v4", "https://arxiv.org/pdf/2108.01045v2", "https://arxiv.org/pdf/2203.06100v1", "https://arxiv.org/pdf/2105.06384v3", "https://arxiv.org/pdf/2012.12128v2", "https://arxiv.org/pdf/2107.09109v2", "https://arxiv.org/pdf/2305.10515v2", "https://arxiv.org/pdf/2108.01902v3", "https://arxiv.org/pdf/2010.14529v3", "https://arxiv.org/pdf/2203.17053v2"] \ No newline at end of file diff --git a/data/papers/papers.json b/data/papers/papers.json new file mode 100644 index 0000000..27d803b --- /dev/null +++ b/data/papers/papers.json @@ -0,0 +1 @@ +["EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)\nCMS-BPH-13-007\nLHCb-PAPER-2014-049\nCERN-PH-EP-2014-220\nMay 13,2015\nObservation of the rare B0\ns \u2192\u00b5+\u00b5\u2212decay from the\ncombined analysis of CMS and LHCb data\nThe CMS and LHCb Collaborations\u2020\n\u2020Lists of the participants and their a\ufb03liations appear at the end of the Letter.\narXiv:1411.4413v2 [hep-ex] 17 Aug 2015\n\nThe standard model of particle physics describes the fundamental particles\nand their interactions via the strong, electromagnetic, and weak forces. It pro-\nvides precise predictions for measurable quantities that can be tested exper-\nimentally. The probabilities, or branching fractions, of the strange B meson\n(B0\ns) and the B0 meson decaying into two oppositely charged muons (\u00b5+ and\n\u00b5\u2212) are especially interesting because of their sensitivity to theories that ex-\ntend the standard model. The standard model predicts that the B0\ns \u2192\u00b5+\u00b5\u2212\nand B0 \u2192\u00b5+\u00b5\u2212decays are very rare, with about four of the former occurring\nfor every billion B0\ns mesons produced and one of the latter occurring for every\n10 billion B0 mesons1. A di\ufb00erence in the observed branching fractions with\nrespect to the predictions of the standard model would provide a direction in\nwhich the standard model should be extended. Before the Large Hadron Col-\nlider (LHC) at CERN2 started operating, no evidence for either decay mode\nhad been found.\nUpper limits on the branching fractions were an order of\nmagnitude above the standard model predictions. The CMS (Compact Muon\nSolenoid) and LHCb (Large Hadron Collider beauty) collaborations have per-\nformed a joint analysis of the data from proton-proton collisions that they\ncollected in 2011 at a centre-of-mass energy of seven teraelectronvolts and in\n2012 at eight teraelectronvolts. Here we report the \ufb01rst observation of the\nB0\ns \u2192\u00b5+\u00b5\u2212decay, with a statistical signi\ufb01cance exceeding six standard devia-\ntions, and the best measurement so far of its branching fraction. Furthermore,\nwe obtained evidence for the B0 \u2192\u00b5+\u00b5\u2212decay with a statistical signi\ufb01cance\nof three standard deviations. Both measurements are statistically compatible\nwith standard model predictions and allow stringent constraints to be placed\non theories beyond the standard model. The LHC experiments will resume\ndata taking in 2015, recording proton-proton collisions at a centre-of-mass en-\nergy of 13 teraelectronvolts, which will approximately double the production\nrates for B0\ns and B0 mesons and lead to further improvements in the precision\nof these crucial tests of the standard model.\nExperimental particle physicists have been testing the predictions of the standard\nmodel of particle physics (SM) with increasing precision since the 1970s.\nTheoretical\ndevelopments have kept pace by improving the accuracy of the SM predictions as the\nexperimental results gained in precision. In the course of the past few decades, the SM\nhas passed critical tests from experiment, but it does not address some profound questions\nabout the nature of the Universe. For example, the existence of dark matter, which has\nbeen con\ufb01rmed by cosmological data3, is not accommodated by the SM. It also fails to\nexplain the origin of the asymmetry between matter and antimatter, which after the Big\nBang led to the survival of the tiny amount of matter currently present in the Universe3,4.\nMany theories have been proposed to modify the SM to provide solutions to these open\nquestions.\nThe B0\ns and B0 mesons are unstable particles that decay via the weak interaction.\nThe measurement of the branching fractions of the very rare decays of these mesons into\na dimuon (\u00b5+\u00b5\u2212) \ufb01nal state is especially interesting.\nAt the elementary level, the weak force is composed of a \u2018charged current\u2019 and a\n\u2018neutral current\u2019 mediated by the W \u00b1 and Z0 bosons, respectively. An example of the\n1\n\ncharged current is the decay of the \u03c0+ meson, which consists of an up (u) quark of\nelectrical charge +2/3 of the charge of the proton and a down (d) antiquark of charge\n+1/3. A pictorial representation of this process, known as a Feynman diagram, is shown\nin Fig. 1a. The u and d quarks are \u2018\ufb01rst generation\u2019 or lowest mass quarks. Whenever a\ndecay mode is speci\ufb01ed in this Letter, the charge conjugate mode is implied.\nThe B+ meson is similar to the \u03c0+, except that the light d antiquark is replaced by the\nheavy \u2018third generation\u2019 (highest mass quarks) beauty (b) antiquark, which has a charge\nof +1/3 and a mass of \u223c5 GeV/c2 (about \ufb01ve times the mass of a proton). The decay\nB+ \u2192\u00b5+\u03bd, represented in Fig. 1b, is allowed but highly suppressed because of angular\nmomentum considerations (helicity suppression) and because it involves transitions be-\ntween quarks of di\ufb00erent generations (CKM suppression), speci\ufb01cally the third and \ufb01rst\ngenerations of quarks. All b hadrons, including the B+, B0\ns and B0 mesons, decay predom-\ninantly via the transition of the b antiquark to a \u2018second generation\u2019 (intermediate mass\nquarks) charm (c) antiquark, which is less CKM suppressed, in \ufb01nal states with charmed\nhadrons. Many allowed decay modes, which typically involve charmed hadrons and other\nparticles, have angular momentum con\ufb01gurations that are not helicity suppressed.\nThe neutral B0\ns meson is similar to the B+ except that the u quark is replaced by\na second generation strange (s) quark of charge \u22121/3. The decay of the B0\ns meson to\ntwo muons, shown in Fig. 1c, is forbidden at the elementary level because the Z0 cannot\ncouple directly to quarks of di\ufb00erent \ufb02avours, that is, there are no direct \u2018\ufb02avour changing\nneutral currents\u2019. However, it is possible to respect this rule and still have this decay occur\nthrough the \u2018higher order\u2019 transitions such as those shown in Fig. 1d and e. These are\nhighly suppressed because each additional interaction vertex reduces their probability of\noccurring signi\ufb01cantly. They are also helicity and CKM suppressed. Consequently, the\nbranching fraction for the B0\ns \u2192\u00b5+\u00b5\u2212decay is expected to be very small compared to\nthe dominant b antiquark to c antiquark transitions. The corresponding decay of the B0\na\n\u03c0+\u2192\u00b5+\u03bd\n\u03c0+ \u0001\nW +\nd\nu\n\u00b5+\n\u03bd\nB+\u2192\u00b5+\u03bd\nB+ \u0001\nW +\nb\nu\n\u00b5+\n\u03bd\nb\nc\nB0\ns\u219b\u00b5+\u00b5\u2212\nB0\ns \u0001\nZ0\nb\ns\n\u00b5+\n\u00b5\u2212\nd\nB0\ns \u2192\u00b5+\u00b5\u2212\nB0\ns \u0001\nW +\nW \u2212\nZ0\nt\nb\ns\n\u00b5+\n\u00b5\u2212\ne\nB0\ns \u2192\u00b5+\u00b5\u2212\nB0\ns \u0001\nW +\n\u03bd\nW \u2212\nt\nb\ns\n\u00b5\u2212\n\u00b5+\nf\nB0\ns \u2192\u00b5+\u00b5\u2212\nB0\ns \u0001\nX+\nW \u2212\nX0\nt\nb\ns\n\u00b5+\n\u00b5\u2212\ng\nB0\ns \u2192\u00b5+\u00b5\u2212\nB0\ns \u0001\nX+\n\u03bd\nW \u2212\nt\nb\ns\n\u00b5+\n\u00b5\u2212\nFigure 1 | Feynman diagrams related to the B0\ns \u2192\u00b5+\u00b5\u2212decay: a, \u03c0+ meson decay\nthrough charged-current process; b, B+ meson decay through the charged-current process; c, a\nB0\ns decay through the direct \ufb02avour changing neutral current process, which is forbidden in the\nSM, as indicated by the large red \u201cX; d and e, higher-order \ufb02avour changing neutral current\nprocesses for the B0\ns \u2192\u00b5+\u00b5\u2212decay allowed in the SM; and f and g, examples of processes for\nthe same decay in theories extending the SM, where new particles, denoted as X0 and X+, can\nalter the decay rate.\n2\n\nmeson, where a d quark replaces the s quark, is even more CKM suppressed because it\nrequires a jump across two quark generations rather than just one.\nThe branching fractions of these two decays,\nB,\naccounting for higher-order\nelectromagnetic and strong interaction e\ufb00ects, and using lattice quantum chromo-\ndynamics to compute the B0\ns and B0 meson decay constants5\u20137, are reliably cal-\nculated1 in the SM. Their values are B(B0\ns \u2192\u00b5+\u00b5\u2212)SM = (3.66 \u00b1 0.23) \u00d7 10\u22129 and\nB(B0 \u2192\u00b5+\u00b5\u2212)SM = (1.06 \u00b1 0.09) \u00d7 10\u221210.\nMany theories that seek to go beyond the standard model (BSM) include new phe-\nnomena and particles8,9, such as in the diagrams shown in Fig. 1f and g, that can signif-\nicantly modify the SM branching fractions. In particular, theories with additional Higgs\nbosons10,11 predict possible enhancements to the branching fractions. A signi\ufb01cant devia-\ntion of either of the two branching fraction measurements from the SM predictions would\ngive insight on how the SM should be extended. Alternatively, a measurement compatible\nwith the SM could provide strong constraints on BSM theories.\nThe ratio of the branching fractions of the two decay modes provides powerful dis-\ncrimination among BSM theories12. It is predicted in the SM1,13\u201315 to be R \u2261B(B0 \u2192\n\u00b5+\u00b5\u2212)SM/B(B0\ns \u2192\u00b5+\u00b5\u2212)SM = 0.0295+0.0028\n\u22120.0025. Notably, BSM theories with the property of\nminimal \ufb02avour violation16 predict the same value as the SM for this ratio.\nThe \ufb01rst evidence for the decay B0\ns \u2192\u00b5+\u00b5\u2212was presented by the LHCb collabora-\ntion in 201217. Both CMS and LHCb later published results from all data collected in\nproton-proton collisions at centre-of-mass energies of 7 TeV in 2011 and 8 TeV in 2012.\nThe measurements had comparable precision and were in good agreement18,19, although\nneither of the individual results had su\ufb03cient precision to constitute the \ufb01rst de\ufb01nitive\nobservation of the B0\ns decay to two muons.\nIn this Letter, the two sets of data are combined and analysed simultaneously to exploit\nfully the statistical power of the data and to account for the main correlations between\nthem. The data correspond to total integrated luminosities of 25 fb\u22121 and 3 fb\u22121 for the\nCMS and LHCb experiments, respectively, equivalent to a total of approximately 1012\nB0\ns and B0 mesons produced in the two experiments together. Assuming the branching\nfractions given by the SM and accounting for the detection e\ufb03ciencies, the predicted\nnumbers of decays to be observed in the two experiments together are about 100 for\nB0\ns \u2192\u00b5+\u00b5\u2212and 10 for B0 \u2192\u00b5+\u00b5\u2212.\nThe CMS20 and LHCb21 detectors are designed to measure SM phenomena with high\nprecision and search for possible deviations. The two collaborations use di\ufb00erent and\ncomplementary strategies. In addition to performing a broad range of precision tests of\nthe SM and studying the newly-discovered Higgs boson22,23, CMS is designed to search for\nand study new particles with masses from about 100 GeV/c2 to a few TeV/c2. Since many of\nthese new particles would be able to decay into b quarks and many of the SM measurements\nalso involve b quarks, the detection of b-hadron decays was a key element in the design\nof CMS. The LHCb collaboration has optimised its detector to study matter-antimatter\nasymmetries and rare decays of particles containing b quarks, aiming to detect deviations\nfrom precise SM predictions that would indicate BSM e\ufb00ects. These di\ufb00erent approaches,\nre\ufb02ected in the design of the detectors, lead to instrumentation of complementary angular\nregions with respect to the LHC beams, to operation at di\ufb00erent proton-proton collision\nrates, and to selection of b quark events with di\ufb00erent e\ufb03ciency (for experimental details,\n3\n\nsee Methods). In general, CMS operates at a higher instantaneous luminosity than LHCb\nbut has a lower e\ufb03ciency for reconstructing low-mass particles, resulting in a similar\nsensitivity to LHCb for B0 or B0\ns (denoted hereafter B0\n(s)) mesons decaying into two\nmuons.\nMuons do not have strong nuclear interactions and are too massive to emit a signi\ufb01cant\nfraction of their energy by electromagnetic radiation. This gives them the unique ability\nto penetrate dense materials, such as steel, and register signals in detectors embedded\ndeep within them. Both experiments use this characteristic to identify muons.\nThe experiments follow similar data analysis strategies.\nDecays compatible with\nB0\n(s) \u2192\u00b5+\u00b5\u2212(candidate decays) are found by combining the reconstructed trajecto-\nries (tracks) of oppositely charged particles identi\ufb01ed as muons. The separation between\ngenuine B0\n(s) \u2192\u00b5+\u00b5\u2212decays and random combinations of two muons (combinatorial\nbackground), most often from semi-leptonic decays of two di\ufb00erent b hadrons, is achieved\nusing the dimuon invariant mass, m\u00b5+\u00b5\u2212, and the established characteristics of B0\n(s)-meson\ndecays. For example, because of their lifetimes of about 1.5 ps and their production at\nthe LHC with momenta between a few GeV/c and \u223c100 GeV/c, B0\n(s) mesons travel up\nto a few centimetres before they decay. Therefore, the B0\n(s) \u2192\u00b5+\u00b5\u2212\u2018decay vertex\u2019, from\nwhich the muons originate, is required to be displaced with respect to the \u2018production\nvertex\u2019, the point where the two protons collide. Furthermore, the negative of the B0\n(s)\ncandidate\u2019s momentum vector is required to point back to the production vertex.\nThese criteria, amongst others that have some ability to distinguish known signal\nevents from background events, are combined into boosted decision trees (BDT)24\u201326.\nA BDT is an ensemble of decision trees each placing di\ufb00erent selection requirements\non the individual variables to achieve the best discrimination between \u2018signal-like\u2019 and\n\u2018background-like\u2019 events. Both experiments evaluated many variables for their discrimi-\nnating power and each chose the best set of about ten to be used in its respective BDT.\nThese include variables related to the quality of the reconstructed tracks of the muons;\nkinematic variables such as transverse momentum (with respect to the beam axis) of the\nindividual muons and of the B0\n(s) candidate; variables related to the decay vertex topology\nand \ufb01t quality, such as candidate decay length; and isolation variables, which measure\nthe activity in terms of other particles in the vicinity of the two muons or their displaced\nvertex. A BDT must be \u2018trained\u2019 on collections of known background and signal events\nto generate the selection requirements on the variables and the weights for each tree. In\nthe case of CMS, the background events used in the training are taken from intervals of\ndimuon mass above and below the signal region in data, while simulated events are used\nfor the signal. The data are divided into disjoint sub-samples and the BDT trained on one\nsub-sample is applied to a di\ufb00erent sub-sample to avoid any bias. LHCb uses simulated\nevents for background and signal in the training of its BDT. After training, the relevant\nBDT is applied to each event in the data, returning a single value for the event, with high\nvalues being more signal-like. To avoid possible biases, both experiments kept the small\nmass interval that includes both the B0\ns and B0 signals blind until all selection criteria\nwere established.\nIn addition to the combinatorial background, speci\ufb01c b-hadron decays, such as\nB0 \u2192\u03c0\u2212\u00b5+\u03bd where the neutrino cannot be detected and the charged pion is misidenti\ufb01ed\nas a muon, or B0 \u2192\u03c00\u00b5+\u00b5\u2212, where the neutral pion in the decay is not reconstructed,\n4\n\ncan mimic the dimuon decay of the B0\n(s) mesons. The invariant mass of the reconstructed\ndimuon candidate for these processes (semi-leptonic background) is usually smaller than\nthe mass of the B0\ns or B0 meson because the neutrino or another particle is not detected.\nThere is also a background component from hadronic two-body B0\n(s) decays (peaking back-\nground) as B0 \u2192K+\u03c0\u2212, when both hadrons from the decay are misidenti\ufb01ed as muons.\nThese misidenti\ufb01ed decays can produce peaks in the dimuon invariant-mass spectrum near\nthe expected signal, especially for the B0 \u2192\u00b5+\u00b5\u2212decay. Particle identi\ufb01cation algorithms\nare used to minimise the probability that pions and kaons are misidenti\ufb01ed as muons, and\nthus suppress these background sources. Excellent mass resolution is mandatory for dis-\ntinguishing between B0 and B0\ns mesons with a mass di\ufb00erence of about 87 MeV/c2 and\nfor separating them from backgrounds. The mass resolution for B0\ns \u2192\u00b5+\u00b5\u2212decays in\nCMS ranges from 32 to 75 MeV/c2, depending on the direction of the muons relative to\nthe beam axis, while LHCb achieves a uniform mass resolution of about 25 MeV/c2.\nThe CMS and LHCb data are combined by \ufb01tting a common value for each branching\nfraction to the data from both experiments. The branching fractions are determined from\nthe observed numbers, e\ufb03ciency-corrected, of B0\n(s) mesons that decay into two muons\nand the total numbers of B0\n(s) mesons produced.\nBoth experiments derive the latter\nfrom the number of observed B+ \u2192J/\u03c8K+ decays, whose branching fraction has been\nprecisely measured elsewhere14. Assuming equal rates for B+ and B0 production, this\ngives the normalisation for B0 \u2192\u00b5+\u00b5\u2212. To derive the number of B0\ns mesons from this\nB+ decay mode, the ratio of b quarks that form (hadronise into) B+ mesons to those\nthat form B0\ns mesons is also needed. Measurements of this ratio27,28, for which there is\nadditional discussion in Methods, and of the branching fraction B(B+ \u2192J/\u03c8K+) are\nused to normalise both sets of data and are constrained within Gaussian uncertainties in\nthe \ufb01t. The use of these two results by both CMS and LHCb is the only signi\ufb01cant source\nof correlation between their individual branching fraction measurements. The combined\n\ufb01t takes advantage of the larger data sample to increase the precision while properly\naccounting for the correlation.\nIn the simultaneous \ufb01t to both the CMS and LHCb data, the branching fractions of\nthe two signal channels are common parameters of interest and are free to vary. Other\nparameters in the \ufb01t are considered as nuisance parameters. Those for which additional\nknowledge is available are constrained to be near their estimated values by using Gaussian\npenalties with their estimated uncertainties while the others are free to \ufb02oat in the \ufb01t.\nThe ratio of the hadronisation probability into B+ and B0\ns mesons and the branching\nfraction of the normalisation channel B+ \u2192J/\u03c8K+ are common, constrained parameters.\nCandidate decays are categorised according to whether they were detected in CMS or\nLHCb and to the value of the relevant BDT discriminant. In the case of CMS, they\nare further categorised according to the data-taking period, and, because of the large\nvariation in mass resolution with angle, whether the muons are both produced at large\nangles relative to the proton beams (central-region) or at least one muon is emitted at\nsmall angle relative to the beams (forward-region).\nAn unbinned extended maximum\nlikelihood \ufb01t to the dimuon invariant-mass distribution, in a region of about \u00b1500 MeV/c2\naround the B0\ns mass, is performed simultaneously in all categories (12 categories from\nCMS and eight from LHCb).\nLikelihood contours in the plane of the parameters of\n5\n\n]\n2\nc\n [MeV/\n\u2212\n\u00b5\n+\n\u00b5\nm\n5000\n5200\n5400\n5600\n5800\n2\nc\nWeighted candidates per 40 MeV/\n0\n10\n20\n30\n40\n50\n60\nData\nSignal and background\n\u2212\n\u00b5\n+\n\u00b5\n \n\u2192\ns\n0\nB\n\u2212\n\u00b5\n+\n\u00b5\n \n\u2192\n0\nB\nCombinatorial background\nSemi-leptonic background\nPeaking background\nCMS and LHCb (LHC run I)\nFigure 2 | Weighted distribution of the dimuon invariant mass, m\u00b5+\u00b5\u2212, for all cate-\ngories. Superimposed on the data points in black are the combined \ufb01t (solid blue line) and its\ncomponents: the B0\ns (yellow shaded area) and B0 (light-blue shaded area) signal components; the\ncombinatorial background (dash-dotted green line); the sum of the semi-leptonic backgrounds\n(dotted salmon line); and the peaking backgrounds (dashed violet line). The horizontal bar on\neach histogram point denotes the size of the binning, while the vertical bar denotes the 68%\ncon\ufb01dence interval. See main text for details on the weighting procedure.\ninterest, B(B0 \u2192\u00b5+\u00b5\u2212) versus B(B0\ns \u2192\u00b5+\u00b5\u2212), are obtained by constructing the test\nstatistic \u22122\u2206lnL from the di\ufb00erence in log-likelihood (lnL) values between \ufb01ts with \ufb01xed\nvalues for the parameters of interest and the nominal \ufb01t. For each of the two branching\nfractions, a one-dimensional pro\ufb01le likelihood scan is likewise obtained by \ufb01xing only the\nsingle parameter of interest and allowing the other to vary during the \ufb01ts. Additional \ufb01ts\nare performed where the parameters under consideration are the ratio of the branching\nfractions relative to their SM predictions, S\nB0\n(s)\nSM \u2261B(B0\n(s) \u2192\u00b5+\u00b5\u2212)/B(B0\n(s) \u2192\u00b5+\u00b5\u2212)SM,\nor the ratio R of the two branching fractions.\nThe combined \ufb01t result is shown for all 20 categories in Extended Data Fig. 1. To\nrepresent the result of the \ufb01t in a single dimuon invariant-mass spectrum, the mass dis-\ntributions of all categories, weighted according to values of S/(S + B), where S is the\nexpected number of B0\ns signals and B is the number of background events under the B0\ns\npeak in that category, are added together and shown in Fig. 2. The result of the simulta-\nneous \ufb01t is overlaid. An alternative representation of the \ufb01t to the dimuon invariant-mass\ndistribution for the six categories with the highest S/(S + B) value for CMS and LHCb,\nas well as displays of events with high probability to be genuine signal decays, are shown\nin the Extended Data Figs. 2\u20134.\nThe combined \ufb01t leads to the measurements B(B0\ns \u2192\u00b5+\u00b5\u2212) =\n\u00002.8 +0.7\n\u22120.6\n\u0001\n\u00d7 10\u22129 and\nB(B0 \u2192\u00b5+\u00b5\u2212) =\n\u00003.9 +1.6\n\u22121.4\n\u0001\n\u00d7 10\u221210, where the uncertainties include both statistical and\nsystematic sources, the latter contributing 35% and 18% of the total uncertainty for the\nB0\ns and B0 signals, respectively. Using Wilks\u2019 theorem29, the statistical signi\ufb01cance in\nunit of standard deviations, \u03c3, is computed to be 6.2 for the B0\ns \u2192\u00b5+\u00b5\u2212decay mode\n6\n\n]\n9\n\u2212\n[10\n)\n\u2212\n\u00b5\n+\n\u00b5\n\u2192\n0\nB\nB(\n0\n0.2\n0.4\n0.6\n0.8\nL\nln\n\u0394\n2\n\u2212\n0\n2\n4\n6\n8\n10\nSM\n]\n9\n\u2212\n[10\n)\n\u2212\n\u00b5\n+\n\u00b5\n\u2192\ns\n0\nB\nB(\n0\n2\n4\n6\n8\nL\nln\n\u0394\n2\n\u2212\n0\n10\n20\n30\n40\nSM\n]\n9\n\u2212\n[10\n)\n\u2212\n\u00b5\n+\n\u00b5\n\u2192\ns\n0\nB\nB(\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n]\n9\n\u2212\n[10\n)\n\u2212\n\u00b5\n+\n\u00b5\n\u2192\n0\nB\nB(\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n68.27%\n95.45%\n99.73%\n5\n\u2212\n10\n\u00d7\n6.3\n\u2212\n1\n7\n\u2212\n10\n\u00d7\n5.7\n\u2212\n1\n9\n\u2212\n10\n\u00d7\n2\n\u2212\n1\nSM\nCMS and LHCb (LHC run I)\na\nb\nc\nFigure 3 | Likelihood contours in the B(B0 \u2192\u00b5+\u00b5\u2212) versus B(B0\ns \u2192\u00b5+\u00b5\u2212) plane.\nThe (black) cross in a marks the best-\ufb01t central value. The SM expectation and its uncertainty\nis shown as the (red) marker. Each contour encloses a region approximately corresponding to\nthe reported con\ufb01dence level. b, c, Variations of the test statistic \u22122\u2206lnL for B(B0\ns \u2192\u00b5+\u00b5\u2212)\n(b) and B(B0 \u2192\u00b5+\u00b5\u2212) (c). The dark and light (cyan) areas de\ufb01ne the \u00b11\u03c3 and \u00b12\u03c3 con\ufb01dence\nintervals for the branching fraction, respectively. The SM prediction and its uncertainty for each\nbranching fraction is denoted with the vertical (red) band.\nand 3.2 for the B0 \u2192\u00b5+\u00b5\u2212mode. For each signal the null hypothesis that is used to\ncompute the signi\ufb01cance includes all background components predicted by the SM as\nwell as the other signal, whose branching fraction is allowed to vary freely. The median\nexpected signi\ufb01cances assuming the SM branching fractions are 7.4 \u03c3 and 0.8 \u03c3 for the\nB0\ns and B0 modes, respectively. Likelihood contours for B(B0 \u2192\u00b5+\u00b5\u2212) versus B(B0\ns \u2192\n\u00b5+\u00b5\u2212) are shown in Fig. 3. One-dimensional likelihood scans for both decay modes are\ndisplayed in the same \ufb01gure. In addition to the likelihood scan, the statistical signi\ufb01cance\nand con\ufb01dence intervals for the B0 branching fractions are determined using simulated\nexperiments. This determination yields a signi\ufb01cance of 3.0 \u03c3 for a B0 signal with respect\nto the same null hypothesis described above. Following the Feldman\u2013Cousins30 procedure,\n\u00b11 \u03c3 and \u00b12 \u03c3 con\ufb01dence intervals for B(B0 \u2192\u00b5+\u00b5\u2212) of [2.5, 5.6] \u00d7 10\u221210 and [1.4, 7.4] \u00d7\n10\u221210 are obtained, respectively (see Extended Data Fig. 5).\nThe \ufb01t for the ratios of the branching fractions relative to their SM predictions yields\nSB0\ns\nSM = 0.76 +0.20\n\u22120.18 and SB0\nSM = 3.7 +1.6\n\u22121.4. Associated likelihood contours and one-dimensional\nlikelihood scans are shown in the Extended Data Fig. 6. The measurements are compatible\nwith the SM branching fractions of the B0\ns \u2192\u00b5+\u00b5\u2212and B0 \u2192\u00b5+\u00b5\u2212decays at the\n1.2 \u03c3 and 2.2 \u03c3 level, respectively, when computed from the one-dimensional hypothesis\ntests. Finally, the \ufb01t for the ratio of branching fractions yields R = 0.14 +0.08\n\u22120.06, which is\ncompatible with the SM at the 2.3 \u03c3 level. The one-dimensional likelihood scan for this\nparameter is shown in Fig. 4.\nThe combined analysis of data from CMS and LHCb, taking advantage of their full\nstatistical power, establishes conclusively the existence of the B0\ns \u2192\u00b5+\u00b5\u2212decay and\nprovides an improved measurement of its branching fraction. This concludes a search\nthat started more than three decades ago (see Extended Data Fig. 7), and initiates a\nphase of precision measurements of the properties of this decay. It also produces a three\n7\n\nR\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nL\nln\n\u2206\n2\n\u2212\n0\n2\n4\n6\n8\n10\nSM and MFV\nCMS and LHCb (LHC run I)\nFigure 4 | Variation of the test statistic \u22122\u2206lnL as a function of the ratio of branch-\ning fractions R \u2261B(B0 \u2192\u00b5+\u00b5\u2212)/B(B0\ns \u2192\u00b5+\u00b5\u2212). The dark and light (cyan) areas\nde\ufb01ne the \u00b11\u03c3 and \u00b12\u03c3 con\ufb01dence intervals for R, respectively. The value and uncertainty for\nR predicted in the SM, which is the same in BSM theories with the minimal \ufb02avour violation\n(MFV) property, is denoted with the vertical (red) band.\nstandard deviation evidence for the B0 \u2192\u00b5+\u00b5\u2212decay. The measured branching fractions\nof both decays are compatible with SM predictions. 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LHCb Collaboration, Aaij, R. et al.,\nMeasurement of the B0\ns \u2192\u00b5+\u00b5\u2212branching\nfraction and search for B0 \u2192\u00b5+\u00b5\u2212decays at the LHCb experiment. Phys. Rev. Lett.\n111 (2013) 101805, arXiv:1307.5024.\n20. CMS Collaboration, Chatrchyan, S. et al., The CMS experiment at the CERN LHC.\nJ. Instrum. 3 (2008) S08004.\n21. LHCb Collaboration, Alves Jr., A. A. et al.,\nThe LHCb detector at the LHC. J.\nInstrum. 3 (2008) S08005.\n9\n\n22. ATLAS Collaboration, Aad, G. et al., Observation of a new particle in the search for\nthe Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett.\nB 716 (2012) 1\u201329, arXiv:1207.7214.\n23. CMS Collaboration, Chatrchyan, S. et al.,\nObservation of a new boson at a mass\nof 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716 (2012) 30\u201361,\narXiv:1207.7235.\n24. Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J., Classi\ufb01cation and\nRegression Trees, Wadsworth international group, 1984.\n25. Freund, Y. and Schapire, R. E. A.,\nA decision-theoretic generalization of on-line\nlearning and an application to boosting. J. Comput. Syst. Sci. 55 (1997) 119\u2013139.\n26. Hoecker, A. et al., TMVA: Toolkit for Multivariate Data Analysis. PoS ACAT (2007)\n040, arXiv:physics/0703039.\n27. LHCb Collaboration, Aaij, R. et al., Measurement of b hadron production fractions\nin 7 TeV pp collisions. Phys. Rev. D 85 (2012) 032008, arXiv:1111.2357.\n28. LHCb Collaboration, Aaij, R. et al., Measurement of the fragmentation fraction ratio\nfs/fd and its dependence on B meson kinematics. J. High Energy Phys. 04 (2013)\n1, arXiv:1301.5286, fs/fd value updated in LHCb-CONF-2013-011.\n29. Wilks, S. S., The large-sample distribution of the likelihood ratio for testing composite\nhypotheses. Ann. Math. Stat. 9 (1938) 60\u201362.\n30. Feldman, G. J. and Cousins, R. D., Uni\ufb01ed approach to the classical statistical anal-\nysis of small signals. Phys. Rev. D 57 (1998) 3873\u20133889, arXiv:physics/9711021.\nAcknowledgements\nWe express our gratitude to our colleagues in the CERN acceler-\nator departments for the excellent performance of the LHC. We thank the technical and\nadministrative sta\ufb00at CERN, at the CMS institutes and at the LHCb institutes. In ad-\ndition, we gratefully acknowledge the computing centres and personnel of the Worldwide\nLHC Computing Grid for delivering so e\ufb00ectively the computing infrastructure essential\nto our analyses. Finally, we acknowledge the enduring support for the construction and\noperation of the LHC, the CMS and the LHCb detectors provided by CERN and by\nmany funding agencies. The following agencies provide support for both CMS and LHCb:\nCAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France);\nBMBF, DFG, and HGF (Germany); SFI (Ireland); INFN (Italy); NASU (Ukraine); STFC\n(UK); NSF (USA). Agencies that provide support for CMS only are: BMWFW and FWF\n(Austria); FNRS and FWO (Belgium); FAPESP (Brazil); MES (Bulgaria); CAS and\nMoST (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus);\nMoER, ERC IUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland);\nCEA (France); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM\n(Iran); NRF and WCU (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia);\nCINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC\n10\n\n(Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom,\nRAS and RFBR (Russia); MESTD (Serbia); SEIDI and CPAN (Spain); Swiss Funding\nAgencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thai-\nland); TUBITAK and TAEK (Turkey); SFFR (Ukraine); DOE (USA). Agencies that\nprovide support for LHCb only are: FINEP (Brazil); MPG (Germany); FOM and NWO\n(The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO\n(Russia); MinECo (Spain); SNSF and SER (Switzerland). Individuals from the CMS col-\nlaboration have received support from the Marie-Curie programme and the European\nResearch Council and EPLANET (European Union); the Leventis Foundation; the A.\nP. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Sci-\nence Policy O\ufb03ce; the Fonds pour la Formation `a la Recherche dans l\u2019Industrie et dans\nl\u2019Agriculture (FRIABelgium); the Agentschap voor Innovatie door Wetenschap en Tech-\nnologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the\nCzech Republic; the Council of Science and Industrial Research, India; the HOMING\nPLUS programme of Foundation for Polish Science, co\ufb01nanced from European Union,\nRegional Development Fund; the Compagnia di San Paolo (Torino); the Consorzio per la\nFisica (Trieste); MIUR project 20108T4XTM (Italy); the Thalis and Aristeia programmes\nco\ufb01nanced by EU-ESF and the Greek NSRF; and the National Priorities Research Pro-\ngram by Qatar National Research Fund. Individual groups or members of the LHCb\ncollaboration have received support from EPLANET, Marie Sk lodowska-Curie Actions\nand ERC (European Union), Conseil g\u00b4en\u00b4eral de Haute-Savoie, Labex ENIGMASS and\nOCEVU, R\u00b4egion Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain),\nRoyal Society and Royal Commission for the Exhibition of 1851 (UK). LHCb is also\nthankful for the computing resources and the access to software R&D tools provided by\nYandex LLC (Russia). The CMS and LHCb collaborations are indebted to the commu-\nnities behind the multiple open source software packages on which they depend.\nAuthor Contributions\nAll authors have contributed to the publication, being vari-\nously involved in the design and the construction of the detectors, in writing software,\ncalibrating sub-systems, operating the detectors and acquiring data and \ufb01nally analysing\nthe processed data.\nAuthor\nInformation\nReprints\nand\npermissions\ninformation\nis\navailable\nat\nwww.nature.com/reprints.\nThe\nauthors\ndeclare\nno\ncompeting\n\ufb01nancial\nin-\nterests.\nCorrespondence\nand\nrequests\nfor\nmaterials\nshould\nbe\naddressed\nto\ncms-publication-committee-chair@cern.ch and to lhcb-editorial-board-chair@\ncern.ch.\n11\n\nMethods\nExperimental Setup\nAt the Large Hadron Collider (LHC), two counter-rotating\nbeams of protons, contained and guided by superconducting magnets spaced around a\n27 km circular tunnel, located approximately 100 m underground near Geneva, Switzer-\nland, are brought into collision at four interaction points (IPs). The study presented in\nthis Letter uses data collected at energies of 3.5 TeV per beam in 2011 and 4 TeV per\nbeam in 2012 by the CMS and LHCb experiments located at two of these IPs.\nThe CMS and LHCb detectors are both designed to look for phenomena beyond the\nSM (BSM), but using complementary strategies. The CMS detector20, shown in Extended\nData Fig. 3, is optimised to search for yet unknown heavy particles, with masses ranging\nfrom 100 GeV/c2 to a few TeV/c2, which, if observed, would be a direct manifestation of\nBSM phenomena. Since many of the hypothesised new particles can decay into parti-\ncles containing b quarks or into muons, CMS is able to detect e\ufb03ciently and study B0\n(5280 MeV/c2) and B0\ns (5367 MeV/c2) mesons decaying to two muons even though it is\ndesigned to search for particles with much larger masses. The CMS detector covers a\nvery large range of angles and momenta to reconstruct high-mass states e\ufb03ciently. To\nthat extent, it employs a 13 m long, 6 m diameter superconducting solenoid magnet, op-\nerated at a \ufb01eld of 3.8 T, centred on the IP with its axis along the beam direction and\ncovering both hemispheres. A series of silicon tracking layers, consisting of silicon pixel\ndetectors near the beam and silicon strips farther out, organised in concentric cylinders\naround the beam, extending to a radius of 1.1 m and terminated on each end by planar\ndetectors (disks) perpendicular to the beam, measures the momentum, angles, and posi-\ntion of charged particles emerging from the collisions. Tracking coverage starts from the\ndirection perpendicular to the beam and extends to within 220 mrad from it on both sides\nof the IP. The inner three cylinders and disks extending from 4.3 to 10.7 cm in radius\ntransverse to the beam are arrays of 100 \u00d7 150 \u00b5m2 silicon pixels, which can distinguish\nthe displacement of the b-hadron decays from the primary vertex of the collision. The\nsilicon strips, covering radii from 25 cm to approximately 110 cm, have pitches ranging\nfrom 80 to 183 \u00b5m. The impact parameter is measured with a precision of 10 \u00b5m for\ntransverse momenta of 100 GeV/c and 20 \u00b5m for 10 GeV/c. The momentum resolution,\nprovided mainly by the silicon strips, changes with the angle relative to the beam direc-\ntion, resulting in a mass resolution for B0\n(s) \u2192\u00b5+\u00b5\u2212decays that varies from 32 MeV/c2\nfor B0\n(s) mesons produced perpendicularly to the proton beams to 75 MeV/c2 for those\nproduced at small angles relative to the beam direction. After the tracking system, at\na greater distance from the IP, there is a calorimeter that stops (absorbs) all particles\nexcept muons and measures their energies. The calorimeter consists of an electromagnetic\nsection followed by a hadronic section. Muons are identi\ufb01ed by their ability to penetrate\nthe calorimeter and the steel return yoke of the solenoid magnet and to produce signals\nin gas-ionisation particle detectors located in compartments within the steel yoke. The\nCMS detector has no capability to discriminate between charged hadron species, pions,\nkaons, or protons, that is e\ufb00ective at the typical particle momenta in this analysis.\nThe primary commitment of the LHCb collaboration is the study of particle-\nantiparticle asymmetries and of rare decays of particles containing b and c quarks. LHCb\naims at detecting BSM particles indirectly by measuring their e\ufb00ect on b-hadron proper-\n12\n\nties for which precise SM predictions exist. The production cross section of b hadrons at\nthe LHC is particularly large at small angles relative to the colliding beams. The small-\nangle region also provides advantages for the detection and reconstruction of a wide range\nof their decays. The LHCb experiment21, shown in Extended Data Fig. 4, instruments\nthe angular interval from 10 to 300 mrad with respect to the beam direction on one side\nof the interaction region. Its detectors are designed to reconstruct e\ufb03ciently a wide range\nof b-hadron decays, resulting in charged pions and kaons, protons, muons, electrons, and\nphotons in the \ufb01nal state. The detector includes a high-precision tracking system consist-\ning of a silicon strip vertex detector, a large-area silicon strip detector located upstream\nof a dipole magnet characterised by a \ufb01eld integral of 4 T \u00b7 m, and three stations of silicon\nstrip detectors and straw drift tubes downstream of the magnet. The vertex detector has\nsu\ufb03cient spatial resolution to distinguish the slight displacement of the weakly decaying\nb hadron from the the primary production vertex where the two protons collided and pro-\nduced it. The tracking detectors upstream and downstream of the dipole magnet measure\nthe momenta of charged particles. The combined tracking system provides a momentum\nmeasurement with an uncertainty that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c.\nThis results in an invariant-mass resolution of 25 MeV/c2 for B0\n(s) mesons decaying to two\nmuons that is nearly independent of the angle with respect to the beam. The impact\nparameter resolution is smaller than 20 \u00b5m for particle tracks with large transverse mo-\nmentum. Di\ufb00erent types of charged hadrons are distinguished by information from two\nring-imaging Cherenkov detectors. Photon, electron, and hadron candidates are identi\ufb01ed\nby calorimeters. Muons are identi\ufb01ed by a system composed of alternating layers of iron\nand multiwire proportional chambers.\nNeither CMS nor LHCb records all the interactions occurring at its IP because the\ndata storage and analysis costs would be prohibitive.\nSince most of the interactions\nare reasonably well characterised (and can be further studied by recording only a small\nsample of them) speci\ufb01c event \ufb01lters (known as triggers) select the rare processes that are\nof interest to the experiments. Both CMS and LHCb implement triggers that speci\ufb01cally\nselect events containing two muons. The triggers of both experiments have a hardware\nstage, based on information from the calorimeter and muon systems, followed by a software\nstage, consisting of a large computing cluster that uses all the information from the\ndetector, including the tracking, to make the \ufb01nal selection of events to be recorded for\nsubsequent analysis. Since CMS is designed to look for much heavier objects than B0\n(s)\nmesons, it selects events that contain muons with higher transverse momenta than those\nselected by LHCb. This eliminates many of the B0\n(s) decays while permitting CMS to run\nat a higher proton-proton collision rate to look for the more rare massive particles. Thus\nCMS runs at higher collision rate but with lower e\ufb03ciency than LHCb for B0\n(s) mesons\ndecaying to two muons. The overall sensitivity to these decays turns out to be similar in\nthe two experiments.\nCMS and LHCb are not the only collaborations to have searched for B0\ns \u2192\u00b5+\u00b5\u2212\nand B0 \u2192\u00b5+\u00b5\u2212decays. Over three decades, a total of eleven collaborations have taken\npart in this search14, as illustrated by Extended Data Fig. 7.\nThis plot gathers the\nresults from CLEO31\u201335, ARGUS36, UA137,38, CDF39\u201344, L345, D\u00d846\u201350, Belle51, Babar52,53,\nLHCb17,54\u201357, CMS18,58,59, and ATLAS60.\n13\n\nAnalysis description\nThe analysis techniques used to obtain the results presented in\nthis Letter are very similar to those used to obtain the individual result in each collab-\noration, described in more details in refs 18, 19. Here only the main analysis steps are\nreviewed and the changes used in the combined analysis are highlighted. Data samples\nfor this analysis were collected by the two experiments in proton-proton collisions at a\ncentre-of-mass energy of 7 and 8 TeV during 2011 and 2012, respectively. These sam-\nples correspond to a total integrated luminosity of 25 and 3 fb\u22121 for the CMS and LHCb\nexperiments, respectively, and represent their complete data sets from the \ufb01rst running\nperiod of the LHC.\nThe trigger criteria were slightly di\ufb00erent between the two experiments. The large\nmajority of events were triggered by requirements on one or both muons of the signal\ndecay: the LHCb detector triggered on muons with transverse momentum pT > 1.5 GeV/c\nwhile the CMS detector, because of its geometry and higher instantaneous luminosity,\ntriggered on two muons with pT > 4(3) GeV/c, for the leading (sub-leading) muon.\nThe data analysis procedures in the two experiments follow similar strategies. Pairs of\nhigh-quality oppositely charged particle tracks that have one of the expected patterns of\nhits in the muon detectors are \ufb01tted to form a common vertex in three dimensions, which\nis required to be displaced from the primary interaction vertex (PV) and to have a small\n\u03c72 in the \ufb01t. The resulting B0\n(s) candidate is further required to point back to the PV, for\nexample to have a small impact parameter, consistent with zero, with respect to it. The\n\ufb01nal classi\ufb01cation of data events is done in categories of the response of a multivariate\ndiscriminant (MVA) combining information from the kinematics and vertex topology of\nthe events. The type of MVA used is a boosted decision tree (BDT)24\u201326. The branching\nfractions are then obtained by a \ufb01t to the dimuon invariant mass, m\u00b5+\u00b5\u2212, of all categories\nsimultaneously.\nThe signals appear as peaks at the B0\ns and B0 masses in the invariant-mass distri-\nbutions, observed over background events. One of the components of the background is\ncombinatorial in nature, as it is due to the random combinations of genuine muons. These\nproduce a smooth dimuon mass distribution in the vicinity of the B0\ns and B0 masses,\nestimated in the \ufb01t to the data by extrapolation from the sidebands of the invariant-\nmass distribution. In addition to the combinatorial background, certain speci\ufb01c b-hadron\ndecays can mimic the signal or contribute to the background in its vicinity.\nIn par-\nticular, the semi-leptonic decays B0 \u2192\u03c0\u2212\u00b5+\u03bd, B0\ns \u2192K\u2212\u00b5+\u03bd, \u039b0\nb \u2192p\u00b5\u2212\u03bd, can have\nreconstructed masses that are near the signal if one of the hadrons is misidenti\ufb01ed as\na muon, and is combined with a genuine muon. Similarly the dimuon coming from the\nrare B0 \u2192\u03c00\u00b5+\u00b5\u2212and B+ \u2192\u03c0+\u00b5+\u00b5\u2212decays can also fake the signal. All these back-\nground decays, when reconstructed as a dimuon \ufb01nal state, have invariant masses that\nare lower than the masses of the B0 and B0\ns mesons, because they are missing one of the\noriginal decay particles. An exception is the decay \u039b0\nb \u2192p\u00b5\u2212\u03bd, which can also populate,\nwith a smooth mass distribution, higher-mass regions. Furthermore, background due to\nmisidenti\ufb01ed hadronic two-body decays B0\n(s) \u2192h+h\u2032\u2212, where h(\u2032) = \u03c0 or K, is present\nwhen both hadrons are misidenti\ufb01ed as muons. These misidenti\ufb01ed decays produce an\napparent dimuon invariant-mass peak close to the B0 mass value. Such a peak can mimic\na B0 \u2192\u00b5+\u00b5\u2212signal and is estimated from control channels and added to the \ufb01t.\nThe distributions of signal in the invariant mass and in the MVA discriminant are\n14\n\nderived from simulations with a detailed description of the detector response for CMS\nand are calibrated using exclusive two-body hadronic decays in data for LHCb.\nThe\ndistributions for the backgrounds are obtained from simulation with the exception of\nthe combinatorial background.\nThe latter is obtained by interpolating from the data\ninvariant-mass sidebands separately for each category, after the subtraction of the other\nbackground components.\nTo compute the signal branching fractions, the numbers of B0\ns and B0 mesons that\nare produced, as well as the numbers of those that have decayed into a dimuon pair, are\nneeded. The latter numbers are the raw results of this analysis, whereas the former need\nto be determined from measurements of one or more \u2018normalisation\u2019 decay channels, which\nare abundantly produced, have an absolute branching fraction that is already known with\ngood precision, and that share characteristics with the signals, so that their trigger and\nselection e\ufb03ciencies do not di\ufb00er signi\ufb01cantly. Both experiments use the B+ \u2192J/\u03c8K+\ndecay as a normalisation channel with B(B+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+) = (6.10 \u00b1 0.19) \u00d7 10\u22125,\nand LHCb also uses the B0 \u2192K+\u03c0\u2212channel with B(B0 \u2192K+\u03c0\u2212) = (1.96\u00b10.05)\u00d710\u22125.\nBoth branching fraction values are taken from ref. 14. Hence, the B0\ns \u2192\u00b5+\u00b5\u2212branching\nfraction is expressed as a function of the number of signal events (NB0s\u2192\u00b5+\u00b5\u2212) in the data\nnormalised to the numbers of B+ \u2192J/\u03c8K+ and B0 \u2192K+\u03c0\u2212events:\nB(B0\ns \u2192\u00b5+\u00b5\u2212) = NB0s\u2192\u00b5+\u00b5\u2212\nNnorm.\n\u00d7 fd\nfs\n\u00d7\n\u03b5norm.\n\u03b5B0s\u2192\u00b5+\u00b5\u2212\u00d7 Bnorm. = \u03b1norm. \u00d7 NB0s\u2192\u00b5+\u00b5\u2212,\n(1)\nwhere the \u2018norm.\u2019 subscript refers to either of the normalisation channels. The values\nof the normalisation parameter \u03b1norm. obtained by LHCb from the two normalisation\nchannels are found in good agreement and their weighted average is used. In this formula\n\u03b5 indicates the total event detection e\ufb03ciency including geometrical acceptance, trigger\nselection, reconstruction, and analysis selection for the corresponding decay. The fd/fs\nfactor is the ratio of the probabilities for a b quark to hadronise into a B0 as compared to\na B0\ns meson; the probability to hadronise into a B+ (fu) is assumed to be equal to that\ninto B0 (fd) on the basis of theoretical grounds, and this assumption is checked on data.\nThe value of fd/fs = 3.86\u00b10.22 measured by LHCb27,28,61 is used in this analysis. As the\nvalue of fd/fs depends on the kinematic range of the considered particles, which di\ufb00ers\nbetween LHCb and CMS, CMS checked this observable with the decays B0\ns \u2192J/\u03c8\u03c6 and\nB+ \u2192J/\u03c8K+ within its acceptance, \ufb01nding a consistent value. An additional systematic\nuncertainty of 5% was assigned to fd/fs to account for the extrapolation of the LHCb\nresult to the CMS acceptance. An analogous formula to that in equation (1) holds for the\nnormalisation of the B0 \u2192\u00b5+\u00b5\u2212decay, with the notable di\ufb00erence that the fd/fs factor\nis replaced by fd/fu = 1.\nThe antiparticle B0 (B0\ns) and the particle B0 (B0\ns) can both decay into two muons and\nno attempt is made in this analysis to determine whether the antiparticle or particle was\nproduced (untagged method). However, the B0 and B0\ns particles are known to oscillate,\nthat is to transform continuously into their antiparticles and vice versa. Therefore, a\nquantum superposition of particle and antiparticle states propagates in the laboratory\nbefore decaying. This superposition can be described by two \u2018mass eigenstates\u2019, which\nare symmetric and anti-symmetric in the charge-parity (CP) quantum number, and have\nslightly di\ufb00erent masses. In the SM, the heavy eigenstate can decay into two muons,\n15\n\nwhereas the light eigenstate cannot without violating the CP quantum number conserva-\ntion. In BSM models, this is not necessarily the case. In addition to their masses, the\ntwo eigenstates of the B0\ns system also di\ufb00er in their lifetime values14. The lifetimes of\nthe light and heavy eigenstates are also di\ufb00erent from the average B0\ns lifetime, which is\nused by CMS and LHCb in the simulations of signal decays. Since the information on\nthe displacement of the secondary decay with respect to the PV is used as a discrimi-\nnant against combinatorial background in the analysis, the e\ufb03ciency versus lifetime has\na model-dependent bias62 that must be removed. This bias is estimated assuming SM\ndynamics. Owing to the smaller di\ufb00erence between the lifetime of its heavy and light\nmass eigenstates, no correction is required for the B0 decay mode.\nDetector simulations are needed by both CMS and LHCb. CMS relies on simulated\nevents to determine resolutions and trigger and reconstruction e\ufb03ciencies, and to pro-\nvide the signal sample for training the BDT. The dimuon mass resolution given by the\nsimulation is validated using data on J/\u03c8, \u03a5, and Z-boson decays to two muons. The\ntracking and trigger e\ufb03ciencies obtained from the simulation are checked using special\ncontrol samples from data. The LHCb analysis is designed to minimise the impact of\ndiscrepancies between simulations and data. The mass resolution is measured with data.\nThe distribution of the BDT for the signal and for the background is also calibrated with\ndata using control channels and mass sidebands. The e\ufb03ciency ratio for the trigger is\nalso largely determined from data. The simulations are used to determine the e\ufb03ciency\nratios of selection and reconstruction processes between signal and normalisation chan-\nnels. As for the overall detector simulation, each experiment has a team dedicated to\nmaking the simulations as complete and realistic as possible. The simulated data are\nconstantly being compared to the actual data. Agreement between simulation and data\nin both experiments is quite good, often extending well beyond the cores of distributions.\nDi\ufb00erences occur because, for example, of incomplete description of the material of the\ndetectors, approximations made to keep the computer time manageable, residual uncer-\ntainties in calibration and alignment, and discrepancies or limitations in the underlying\ntheory and experimental data used to model the relevant collisions and decays. Small\ndi\ufb00erences between simulation and data that are known to have an impact on the re-\nsult are treated either by reweighting the simulations to match the data or by assigning\nappropriate systematic uncertainties.\nSmall changes are made to the analysis procedure with respect to refs 18,19 in order\nto achieve a consistent combination between the two experiments. In the LHCb analysis,\nthe \u039b0\nb \u2192p\u00b5\u2212\u03bd background component, which was not included in the \ufb01t for the previous\nresult but whose e\ufb00ect was accounted for as an additional systematic uncertainty, is\nnow included in the standard \ufb01t.\nThe following modi\ufb01cations are made to the CMS\nanalysis: the \u039b0\nb \u2192p\u00b5\u2212\u03bd branching fraction is updated to a more recent prediction63,64\nof B(\u039b0\nb \u2192p\u00b5\u2212\u03bd) = (4.94 \u00b1 2.19) \u00d7 10\u22124; the phase space model of the decay \u039b0\nb \u2192p\u00b5\u2212\u03bd\nis changed to a more appropriate semi-leptonic decay model63; and the decay time bias\ncorrection for the B0\ns, previously absent from the analysis, is now calculated and applied\nwith a di\ufb00erent correction for each category of the multivariate discriminant.\nThese modi\ufb01cations result in changes in the individual results of each experiment.\n16\n\nThe modi\ufb01ed CMS analysis, applied on the CMS data, yields\nB(B0\ns \u2192\u00b5+\u00b5\u2212) =\n\u00002.8 +1.0\n\u22120.9\n\u0001\n\u00d7 10\u22129\nand\nB(B0 \u2192\u00b5+\u00b5\u2212) =\n\u00004.4 +2.2\n\u22121.9\n\u0001\n\u00d7 10\u221210,\n(2)\nwhile the LHCb results change to\nB(B0\ns \u2192\u00b5+\u00b5\u2212) =\n\u00002.7 +1.1\n\u22120.9\n\u0001\n\u00d7 10\u22129\nand\nB(B0 \u2192\u00b5+\u00b5\u2212) =\n\u00003.3 +2.4\n\u22122.1\n\u0001\n\u00d7 10\u221210.\n(3)\nThese results are only slightly di\ufb00erent from the published ones and are in agreement\nwith each other.\nSimultaneous \ufb01t\nThe goal of the analysis presented in this Letter is to combine the\nfull data sets of the two experiments to reduce the uncertainties on the branching frac-\ntions of the signal decays obtained from the individual determinations. A simultaneous\nunbinned extended maximum likelihood \ufb01t is performed to the data of the two exper-\niments, using the invariant-mass distributions of all 20 MVA discriminant categories of\nboth experiments. The invariant-mass distributions are de\ufb01ned in the dimuon mass ranges\nm\u00b5+\u00b5\u2212\u2208[4.9, 5.9] GeV/c2 and [4.9, 6.0] GeV/c2 for the CMS and LHCb experiments, re-\nspectively. The branching fractions of the signal decays, the hadronisation fraction ratio\nfd/fs, and the branching fraction of the normalisation channel B+ \u2192J/\u03c8K+ are treated\nas common parameters. The value of the B+ \u2192J/\u03c8K+ branching fraction is the com-\nbination of results from \ufb01ve di\ufb00erent experiments14, taking advantage of all their data\nto achieve the most precise input parameters for this analysis. The combined \ufb01t takes\nadvantage of the larger data sample and proper treatment of the correlations between the\nindividual measurements to increase the precision and reliability of the result, respectively.\nFit parameters, other than those of primary physics interest, whose limited knowledge\na\ufb00ects the results, are called \u2018nuisance parameters\u2019. In particular, systematic uncertainties\nare modelled by introducing nuisance parameters into the statistical model and allowing\nthem to vary in the \ufb01t; those for which additional knowledge is present are constrained\nusing Gaussian distributions. The mean and standard deviation of these distributions\nare set to the central value and uncertainty obtained either from other measurements or\nfrom control channels. The statistical component of the \ufb01nal uncertainty on the branch-\ning fractions is obtained by repeating the \ufb01t after \ufb01xing all of the constrained nuisance\nparameters to their best \ufb01tted values. The systematic component is then calculated by\nsubtracting in quadrature the statistical component from the total uncertainty. In addi-\ntion to the free \ufb01t, a two-dimensional likelihood ratio scan in the plane B(B0 \u2192\u00b5+\u00b5\u2212)\nversus B(B0\ns \u2192\u00b5+\u00b5\u2212) is performed.\nFeldman\u2013Cousins Con\ufb01dence Interval\nThe Feldman\u2013Cousins likelihood ratio or-\ndering procedure30 is a uni\ufb01ed frequentist method to construct single- and double-sided\ncon\ufb01dence intervals for parameters of a given model adapted to the data. It provides a\nnatural transition between single-sided con\ufb01dence intervals, used to de\ufb01ne upper or lower\nlimits, and double-sided ones. Since the single-experiment results18,19 showed that the\nB0 \u2192\u00b5+\u00b5\u2212signal is at the edge of the probability region customarily used to assert\nstatistically signi\ufb01cant evidence for a result, a Feldman\u2013Cousins procedure is performed.\nThis allows a more reliable determination of the con\ufb01dence interval and signi\ufb01cance of\n17\n\nthis signal without the assumptions required for the use of Wilks\u2019 theorem.\nIn addi-\ntion, a prescription for the treatment of nuisance parameters has to be chosen because\nscanning the whole parameter space in the presence of more than a few parameters is\ncomputationally too intensive. In this case the procedure described by the ATLAS and\nCMS Higgs combination group65 is adopted.\nFor each point of the space of the rele-\nvant parameters, the nuisance parameters are \ufb01xed to their best value estimated by the\nmean of a maximum likelihood \ufb01t to the data with the value of B(B0 \u2192\u00b5+\u00b5\u2212) \ufb01xed\nand all nuisance parameters pro\ufb01led with Gaussian penalties. Sampling distributions are\nconstructed for each tested point of the parameter of interest by generating simulated\nexperiments and performing maximum likelihood \ufb01ts in which the Gaussian mean values\nof the external constraints on the nuisance parameters are randomised around the best-\n\ufb01t values for the nuisance parameters used to generate the simulated experiments. The\nsampling distribution is constructed from the distribution of the negative log-likelihood\nratio evaluated on the simulated experiments by performing one likelihood \ufb01t in which\nthe value of B(B0 \u2192\u00b5+\u00b5\u2212) is free to \ufb02oat and another with the B(B0 \u2192\u00b5+\u00b5\u2212) \ufb01xed to\nthe tested point value. This sampling distribution is then converted to a con\ufb01dence level\nby evaluating the fraction of simulated experiments entries with a value for the negative\nlog-likelihood ratio greater than or equal to the value observed in the data for each tested\npoint. The results of this procedure are shown in Extended Data Fig. 5.\nReferences\n31. CLEO Collaboration, Giles, R. et al., Two-body decays of B mesons. Phys. Rev. D\n30 (1984) 2279\u20132294.\n32. CLEO Collaboration, Avery, P. et al., Limits on rare exclusive decays of B mesons.\nPhys. Lett. B 183 (1987) 429\u2013433.\n33. 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Khodjamirian, A., Klein, C., Mannel, T., and Wang, Y.-M., Form factors and strong\ncouplings of heavy baryons from QCD light-cone sum rules. J. High Energy Phys. 09\n(2011) 106, arXiv:1108.2971.\n64. LHCb Collaboration, Aaij, R. et al., Precision measurement of the ratio of the \u039b0\nb to\nB\n0 lifetimes. Phys. Lett. B 734 (2014) 122\u2013130, arXiv:1402.6242.\n65. ATLAS and CMS Collaborations, Procedure for the LHC Higgs boson search com-\nbination in summer 2011. ATL-PHYS-PUB-2011-011, CMS NOTE 2011/005.\n20\n\nThe CMS Collaboration: V. Khachatryan1, A.M. Sirunyan1, A. Tumasyan1, W. Adam2,\nT. Bergauer2, M. Dragicevic2, J. Er\u00a8o2, M. Friedl2, R. Fr\u00a8uhwirth2,b, V.M. Ghete2, C. Hartl2,\nN. H\u00a8ormann2, J. Hrubec2, M. Jeitler2,b, W. Kiesenhofer2, V. Kn\u00a8unz2, M. Krammer2,b,\nI. Kr\u00a8atschmer2, D. Liko2, I. Mikulec2, D. Rabady2,c, B. Rahbaran2, H. Rohringer2,\nR. Sch\u00a8ofbeck2, J. Strauss2, W. Treberer-Treberspurg2, W. Waltenberger2, C.-E. Wulz2,b,\nV. Mossolov3, N. Shumeiko3, J. Suarez Gonzalez3, S. Alderweireldt4, S. Bansal4, T. Cornelis4,\nE.A. De Wolf4, X. Janssen4, A. Knutsson4, J. Lauwers4, S. Luyckx4, S. Ochesanu4,\nR. Rougny4, M. Van De Klundert4, H. Van Haevermaet4, P. Van Mechelen4,\nN. Van Remortel4, A. Van Spilbeeck4, F. Blekman5, S. Blyweert5, J. D\u2019Hondt5, N. Daci5,\nN. Heracleous5, J. Keaveney5, S. Lowette5, M. Maes5, A. Olbrechts5, Q. Python5, D. Strom5,\nS. Tavernier5, W. Van Doninck5, P. Van Mulders5, G.P. Van Onsem5, I. Villella5, C. Caillol6,\nB. Clerbaux6, G. De Lentdecker6, D. Dobur6, L. Favart6, A.P.R. Gay6, A. Grebenyuk6,\nA. L\u00b4eonard6, A. Mohammadi6, L. Perni`e6,c, A. Randle-conde6, T. Reis6, T. Seva6, L. Thomas6,\nC. Vander Velde6, P. Vanlaer6, J. Wang6, F. Zenoni6, V. Adler7, K. Beernaert7, L. Benucci7,\nA. Cimmino7, S. Costantini7, S. Crucy7, S. Dildick7, A. Fagot7, G. Garcia7, J. Mccartin7,\nA.A. Ocampo Rios7, D. Ryckbosch7, S. Salva Diblen7, M. Sigamani7, N. Strobbe7,\nF. Thyssen7, M. Tytgat7, E. Yazgan7, N. Zaganidis7, S. Basegmez8, C. Belu\ufb038,d, G. Bruno8,\nR. Castello8, A. Caudron8, L. Ceard8, G.G. Da Silveira8, C. Delaere8, T. du Pree8, D. Favart8,\nL. Forthomme8, A. Giammanco8,e, J. Hollar8, A. Jafari8, P. Jez8, M. Komm8, V. Lemaitre8,\nC. Nuttens8, D. Pagano8, L. Perrini8, A. Pin8, K. Piotrzkowski8, A. Popov8,f,\nL. Quertenmont8, M. Selvaggi8, M. Vidal Marono8, J.M. Vizan Garcia8, N. Beliy9,\nT. Caebergs9, E. Daubie9, G.H. Hammad9, W.L. Ald\u00b4a J\u00b4unior10, G.A. Alves10, L. Brito10,\nM. Correa Martins Junior10, T. Dos Reis Martins10, C. Mora Herrera10, M.E. Pol10,\nP. Rebello Teles10, W. Carvalho11, J. Chinellato11,g, A. Cust\u00b4odio11, E.M. Da Costa11,\nD. De Jesus Damiao11, C. De Oliveira Martins11, S. Fonseca De Souza11, H. Malbouisson11,\nD. Matos Figueiredo11, L. Mundim11, H. Nogima11, W.L. Prado Da Silva11, J. Santaolalla11,\nA. Santoro11, A. Sznajder11, E.J. Tonelli Manganote11,g, A. Vilela Pereira11,\nC.A. Bernardes12b, S. Dogra12a, T.R. Fernandez Perez Tomei12a, E.M. Gregores12b,\nP.G. Mercadante12b, S.F. Novaes12a, Sandra S. Padula12a, A. Aleksandrov13, V. Genchev13,c,\nR. Hadjiiska13, P. Iaydjiev13, A. Marinov13, S. Piperov13, M. Rodozov13, G. Sultanov13,\nM. Vutova13, A. Dimitrov14, I. Glushkov14, L. Litov14, B. Pavlov14, P. Petkov14, J.G. Bian15,\nG.M. Chen15, H.S. Chen15, M. Chen15, T. Cheng15, R. Du15, C.H. Jiang15, R. Plestina15,h,\nF. Romeo15, J. Tao15, Z. Wang15, C. Asawatangtrakuldee16, Y. Ban16, Q. Li16, S. Liu16,\nY. Mao16, S.J. Qian16, D. Wang16, Z. Xu16, W. Zou16, C. Avila17, A. Cabrera17,\nL.F. Chaparro Sierra17, C. Florez17, J.P. Gomez17, B. Gomez Moreno17, J.C. Sanabria17,\nN. Godinovic18, D. Lelas18, D. Polic18, I. Puljak18, Z. Antunovic19, M. Kovac19,\nV. Brigljevic20, K. Kadija20, J. Luetic20, D. Mekterovic20, L. Sudic20, A. Attikis21,\nG. Mavromanolakis21, J. Mousa21, C. Nicolaou21, F. Ptochos21, P.A. Razis21, M. Bodlak22,\nM. Finger22, M. Finger Jr.22,i, Y. Assran23,j, A. Ellithi Kamel23,k, M.A. Mahmoud23,l,\nA. Radi23,m,n, M. Kadastik24, M. Murumaa24, M. Raidal24, A. Tiko24, P. Eerola25, G. Fedi25,\nM. Voutilainen25, J. H\u00a8ark\u00a8onen26, V. Karim\u00a8aki26, R. Kinnunen26, M.J. Kortelainen26,\nT. Lamp\u00b4en26, K. Lassila-Perini26, S. Lehti26, T. Lind\u00b4en26, P. Luukka26, T. M\u00a8aenp\u00a8a\u00a8a26,\nT. Peltola26, E. Tuominen26, J. Tuominiemi26, E. Tuovinen26, L. Wendland26, J. Talvitie27,\nT. Tuuva27, M. Besancon28, F. Couderc28, M. Dejardin28, D. Denegri28, B. Fabbro28,\nJ.L. Faure28, C. Favaro28, F. Ferri28, S. Ganjour28, A. Givernaud28, P. Gras28,\nG. Hamel de Monchenault28, P. Jarry28, E. Locci28, J. Malcles28, J. Rander28, A. Rosowsky28,\nM. Titov28, S. Ba\ufb03oni29, F. Beaudette29, P. Busson29, C. Charlot29, T. Dahms29,\nM. Dalchenko29, L. Dobrzynski29, N. Filipovic29, A. Florent29, R. Granier de Cassagnac29,\n21\n\nL. Mastrolorenzo29, P. Min\u00b4e29, C. Mironov29, I.N. Naranjo29, M. Nguyen29, C. Ochando29,\nG. Ortona29, P. Paganini29, S. Regnard29, R. Salerno29, J.B. Sauvan29, Y. Sirois29,\nC. Veelken29, Y. Yilmaz29, A. Zabi29, J.-L. Agram30,o, J. Andrea30, A. Aubin30, D. Bloch30,\nJ.-M. Brom30, E.C. Chabert30, C. Collard30, E. Conte30,o, J.-C. Fontaine30,o, D. Gel\u00b4e30,\nU. Goerlach30, C. Goetzmann30, A.-C. Le Bihan30, K. Skovpen30, P. Van Hove30, S. Gadrat31,\nS. Beauceron32, N. Beaupere32, G. Boudoul32,c, E. Bouvier32, S. Brochet32,\nC.A. Carrillo Montoya32, J. Chasserat32, R. Chierici32, D. Contardo32,c, P. Depasse32,\nH. El Mamouni32, J. Fan32, J. Fay32, S. Gascon32, M. Gouzevitch32, B. Ille32, T. Kurca32,\nM. Lethuillier32, L. Mirabito32, S. Perries32, J.D. Ruiz Alvarez32, D. Sabes32, L. Sgandurra32,\nV. Sordini32, M. Vander Donckt32, P. Verdier32, S. Viret32, H. Xiao32, Z. Tsamalaidze33,i,\nC. Autermann34, S. Beranek34, M. Bontenackels34, M. Edelho\ufb0034, L. Feld34, A. Heister34,\nO. Hindrichs34, K. Klein34, A. Ostapchuk34, F. Raupach34, J. Sammet34, S. Schael34,\nJ.F. Schulte34, H. Weber34, B. Wittmer34, V. Zhukov34,f, M. Ata35, M. Brodski35,\nE. Dietz-Laursonn35, D. Duchardt35, M. Erdmann35, R. Fischer35, A. G\u00a8uth35, T. Hebbeker35,\nC. Heidemann35, K. Hoepfner35, D. Klingebiel35, S. Knutzen35, P. Kreuzer35,\nM. Merschmeyer35, A. Meyer35, P. Millet35, M. Olschewski35, K. Padeken35, P. Papacz35,\nH. Reithler35, S.A. Schmitz35, L. Sonnenschein35, D. Teyssier35, S. Th\u00a8uer35, M. Weber35,\nV. Cherepanov36, Y. Erdogan36, G. Fl\u00a8ugge36, H. Geenen36, M. Geisler36, W. Haj Ahmad36,\nF. Hoehle36, B. Kargoll36, T. Kress36, Y. Kuessel36, A. K\u00a8unsken36, J. Lingemann36,c,\nA. Nowack36, I.M. Nugent36, O. Pooth36, A. Stahl36, M. Aldaya Martin37, I. Asin37,\nN. Bartosik37, J. Behr37, U. Behrens37, A.J. Bell37, A. Bethani37, K. Borras37, A. Burgmeier37,\nA. Cakir37, L. Calligaris37, A. Campbell37, S. Choudhury37, F. Costanza37, C. Diez Pardos37,\nG. Dolinska37, S. Dooling37, T. Dorland37, G. Eckerlin37, D. Eckstein37, T. Eichhorn37,\nG. Flucke37, J. Garay Garcia37, A. Geiser37, P. Gunnellini37, J. Hauk37, M. Hempel37,p,\nH. Jung37, A. Kalogeropoulos37, M. Kasemann37, P. Katsas37, J. Kieseler37, C. Kleinwort37,\nI. Korol37, D. Kr\u00a8ucker37, W. Lange37, J. Leonard37, K. Lipka37, A. Lobanov37,\nW. Lohmann37,p, B. Lutz37, R. Mankel37, I. Mar\ufb01n37,p, I.-A. Melzer-Pellmann37, A.B. Meyer37,\nG. Mittag37, J. Mnich37, A. Mussgiller37, S. Naumann-Emme37, A. Nayak37, E. Ntomari37,\nH. Perrey37, D. Pitzl37, R. Placakyte37, A. Raspereza37, P.M. Ribeiro Cipriano37, B. Roland37,\nE. Ron37, M.\u00a8O. Sahin37, J. Salfeld-Nebgen37, P. Saxena37, T. Schoerner-Sadenius37,\nM. Schr\u00a8oder37, C. Seitz37, S. Spannagel37, A.D.R. Vargas Trevino37, R. Walsh37, C. Wissing37,\nV. Blobel38, M. Centis Vignali38, A.R. Draeger38, J. Er\ufb02e38, E. Garutti38, K. Goebel38,\nM. G\u00a8orner38, J. Haller38, M. Ho\ufb00mann38, R.S. H\u00a8oing38, A. Junkes38, H. Kirschenmann38,\nR. Klanner38, R. Kogler38, J. Lange38, T. Lapsien38, T. Lenz38, I. Marchesini38, J. Ott38,\nT. Pei\ufb00er38, A. Perieanu38, N. Pietsch38, J. Poehlsen38, T. Poehlsen38, D. Rathjens38,\nC. Sander38, H. Schettler38, P. Schleper38, E. Schlieckau38, A. Schmidt38, M. Seidel38,\nV. Sola38, H. Stadie38, G. Steinbr\u00a8uck38, D. Troendle38, E. Usai38, L. Vanelderen38,\nA. Vanhoefer38, C. Barth39, C. Baus39, J. Berger39, C. B\u00a8oser39, E. Butz39, T. Chwalek39,\nW. De Boer39, A. Descroix39, A. Dierlamm39, M. Feindt39, F. Frensch39, M. Gi\ufb00els39,\nA. Gilbert39, F. Hartmann39,c, T. Hauth39, U. Husemann39, I. Katkov39,f, A. Kornmayer39,c,\nE. Kuznetsova39, P. Lobelle Pardo39, M.U. Mozer39, T. M\u00a8uller39, Th. M\u00a8uller39, A. N\u00a8urnberg39,\nG. Quast39, K. Rabbertz39, S. R\u00a8ocker39, H.J. Simonis39, F.M. Stober39, R. Ulrich39,\nJ. Wagner-Kuhr39, S. Wayand39, T. Weiler39, R. Wolf39, G. Anagnostou40, G. Daskalakis40,\nT. Geralis40, V.A. Giakoumopoulou40, A. Kyriakis40, D. Loukas40, A. Markou40, C. Markou40,\nA. Psallidas40, I. Topsis-Giotis40, A. Agapitos41, S. Kesisoglou41, A. Panagiotou41,\nN. Saoulidou41, E. Stiliaris41, X. Aslanoglou42, I. Evangelou42, G. Flouris42, C. Foudas42,\nP. Kokkas42, N. Manthos42, I. Papadopoulos42, E. Paradas42, J. Strologas42, G. Bencze43,\nC. Hajdu43, P. Hidas43, D. Horvath43,q, F. Sikler43, V. Veszpremi43, G. Vesztergombi43,r,\n22\n\nA.J. Zsigmond43, N. Beni44, S. Czellar44, J. Karancsi44,s, J. Molnar44, J. Palinkas44,\nZ. Szillasi44, A. Makovec45, P. Raics45, Z.L. Trocsanyi45, B. Ujvari45, N. Sahoo46,\nS.K. Swain46, S.B. Beri47, V. Bhatnagar47, R. Gupta47, U.Bhawandeep47, A.K. Kalsi47,\nM. Kaur47, R. Kumar47, M. Mittal47, N. Nishu47, J.B. Singh47, Ashok Kumar48,\nArun Kumar48, S. Ahuja48, A. Bhardwaj48, B.C. Choudhary48, A. Kumar48, S. Malhotra48,\nM. Naimuddin48, K. Ranjan48, V. Sharma48, S. Banerjee49, S. Bhattacharya49,\nK. Chatterjee49, S. Dutta49, B. Gomber49, Sa. Jain49, Sh. Jain49, R. Khurana49, A. Modak49,\nS. Mukherjee49, D. Roy49, S. Sarkar49, M. Sharan49, A. Abdulsalam50, D. Dutta50, S. Kailas50,\nV. Kumar50, A.K. Mohanty50,c, L.M. Pant50, P. Shukla50, A. Topkar50, T. Aziz51,\nS. Banerjee51, S. Bhowmik51,t, R.M. Chatterjee51, R.K. Dewanjee51, S. Dugad51, S. Ganguly51,\nS. Ghosh51, M. Guchait51, A. Gurtu51,u, G. Kole51, S. Kumar51, M. Maity51,t, G. Majumder51,\nK. Mazumdar51, G.B. Mohanty51, B. Parida51, K. Sudhakar51, N. Wickramage51,v,\nH. Bakhshiansohi52, H. Behnamian52, S.M. Etesami52,w, A. Fahim52,x, R. Goldouzian52,\nM. Khakzad52, M. Mohammadi Najafabadi52, M. Naseri52, S. Paktinat Mehdiabadi52,\nF. Rezaei Hosseinabadi52, B. Safarzadeh52,y, M. Zeinali52, M. Felcini53, M. Grunewald53,\nM. Abbrescia54a,54b, C. Calabria54a,54b, S.S. Chhibra54a,54b, A. Colaleo54a, D. Creanza54a,54c,\nN. De Filippis54a,54c, M. De Palma54a,54b, L. Fiore54a, G. Iaselli54a,54c, G. Maggi54a,54c,\nM. Maggi54a, S. My54a,54c, S. Nuzzo54a,54b, A. Pompili54a,54b, G. Pugliese54a,54c,\nR. Radogna54a,54b,c, G. Selvaggi54a,54b, A. Sharma54a, L. Silvestris54a,c, R. Venditti54a,54b,\nP. Verwilligen54a, G. Abbiendi55a, A.C. Benvenuti55a, D. Bonacorsi55a,55b,\nS. Braibant-Giacomelli55a,55b, L. Brigliadori55a,55b, R. Campanini55a,55b, P. Capiluppi55a,55b,\nA. Castro55a,55b, F.R. Cavallo55a, G. Codispoti55a,55b, M. Cu\ufb03ani55a,55b, G.M. Dallavalle55a,\nF. Fabbri55a, A. Fanfani55a,55b, D. Fasanella55a,55b, P. Giacomelli55a, C. Grandi55a,\nL. Guiducci55a,55b, S. Marcellini55a, G. Masetti55a, A. Montanari55a, F.L. Navarria55a,55b,\nA. Perrotta55a, F. Primavera55a,55b, A.M. Rossi55a,55b, T. Rovelli55a,55b, G.P. Siroli55a,55b,\nN. Tosi55a,55b, R. Travaglini55a,55b, S. Albergo56a,56b, G. Cappello56a, M. Chiorboli56a,56b,\nS. Costa56a,56b, F. Giordano56a,c, R. Potenza56a,56b, A. Tricomi56a,56b, C. Tuve56a,56b,\nG. Barbagli57a, V. Ciulli57a,57b, C. Civinini57a, R. D\u2019Alessandro57a,57b, E. Focardi57a,57b,\nE. Gallo57a, S. Gonzi57a,57b, V. Gori57a,57b, P. Lenzi57a,57b, M. Meschini57a, S. Paoletti57a,\nG. Sguazzoni57a, A. Tropiano57a,57b, L. Benussi58, S. Bianco58, F. Fabbri58, D. Piccolo58,\nR. Ferretti59a,59b, F. Ferro59a, M. Lo Vetere59a,59b, E. Robutti59a, S. Tosi59a,59b,\nM.E. Dinardo60a,60b, S. Fiorendi60a,60b, S. Gennai60a,c, R. Gerosa60a,60b,c, A. Ghezzi60a,60b,\nP. Govoni60a,60b, M.T. Lucchini60a,60b,c, S. Malvezzi60a, R.A. Manzoni60a,60b, A. Martelli60a,60b,\nB. Marzocchi60a,60b,c, D. Menasce60a, L. Moroni60a, M. Paganoni60a,60b, D. Pedrini60a,\nS. Ragazzi60a,60b, N. Redaelli60a, T. Tabarelli de Fatis60a,60b, S. Buontempo61a,\nN. Cavallo61a,61c, S. Di Guida61a,61d,c, F. Fabozzi61a,61c, A.O.M. Iorio61a,61b, L. Lista61a,\nS. Meola61a,61d,c, M. Merola61a, P. Paolucci61a,c, P. Azzi62a, N. Bacchetta62a, D. Bisello62a,62b,\nA. Branca62a,62b, R. Carlin62a,62b, P. Checchia62a, M. Dall\u2019Osso62a,62b, T. Dorigo62a,\nU. Dosselli62a, M. Galanti62a,62b, F. Gasparini62a,62b, U. Gasparini62a,62b, P. Giubilato62a,62b,\nA. Gozzelino62a, K. Kanishchev62a,62c, S. Lacaprara62a, M. Margoni62a,62b,\nA.T. Meneguzzo62a,62b, J. Pazzini62a,62b, N. Pozzobon62a,62b, P. Ronchese62a,62b,\nF. Simonetto62a,62b, E. Torassa62a, M. Tosi62a,62b, P. Zotto62a,62b, A. Zucchetta62a,62b,\nG. Zumerle62a,62b, M. Gabusi63a,63b, S.P. Ratti63a,63b, V. Re63a, C. Riccardi63a,63b, P. Salvini63a,\nP. Vitulo63a,63b, M. Biasini64a,64b, G.M. Bilei64a, D. Ciangottini64a,64b,c, L. Fan`o64a,64b,\nP. Lariccia64a,64b, G. Mantovani64a,64b, M. Menichelli64a, A. Saha64a, A. Santocchia64a,64b,\nA. Spiezia64a,64b,c, K. Androsov65a,z, P. Azzurri65a, G. Bagliesi65a, J. Bernardini65a,\nT. Boccali65a, G. Broccolo65a,65c, R. Castaldi65a, M.A. Ciocci65a,z, R. Dell\u2019Orso65a,\nS. Donato65a,65c,c, F. Fiori65a,65c, L. Fo`a65a,65c, A. Giassi65a, M.T. Grippo65a,z,\n23\n\nF. Ligabue65a,65c, T. Lomtadze65a, L. Martini65a,65b, A. Messineo65a,65b, C.S. Moon65a,aa,\nF. Palla65a,c, A. Rizzi65a,65b, A. Savoy-Navarro65a,bb, A.T. Serban65a, P. Spagnolo65a,\nP. Squillacioti65a,z, R. Tenchini65a, G. Tonelli65a,65b, A. Venturi65a, P.G. Verdini65a,\nC. Vernieri65a,65c, L. Barone66a,66b, F. Cavallari66a, G. D\u2019imperio66a,66b, D. Del Re66a,66b,\nM. Diemoz66a, C. Jorda66a, E. Longo66a,66b, F. Margaroli66a,66b, P. Meridiani66a,\nF. Micheli66a,66b,c, S. Nourbakhsh66a,66b, G. Organtini66a,66b, R. Paramatti66a,\nS. Rahatlou66a,66b, C. Rovelli66a, F. Santanastasio66a,66b, L. So\ufb0366a,66b, P. Traczyk66a,66b,c,\nN. Amapane67a,67b, R. Arcidiacono67a,67c, S. Argiro67a,67b, M. Arneodo67a,67c, R. Bellan67a,67b,\nC. Biino67a, N. Cartiglia67a, S. Casasso67a,67b,c, M. Costa67a,67b, A. Degano67a,67b,\nN. Demaria67a, L. Finco67a,67b,c, C. Mariotti67a, S. Maselli67a, E. Migliore67a,67b,\nV. Monaco67a,67b, M. Musich67a, M.M. Obertino67a,67c, L. Pacher67a,67b, N. Pastrone67a,\nM. Pelliccioni67a, G.L. Pinna Angioni67a,67b, A. Potenza67a,67b, A. Romero67a,67b,\nM. Ruspa67a,67c, R. Sacchi67a,67b, A. Solano67a,67b, A. Staiano67a, U. Tamponi67a,\nS. Belforte68a, V. Candelise68a,68b,c, M. Casarsa68a, F. Cossutti68a, G. Della Ricca68a,68b,\nB. Gobbo68a, C. La Licata68a,68b, M. Marone68a,68b, A. Schizzi68a,68b, T. Umer68a,68b,\nA. Zanetti68a, S. Chang69, A. Kropivnitskaya69, S.K. Nam69, D.H. Kim70, G.N. Kim70,\nM.S. Kim70, D.J. Kong70, S. Lee70, Y.D. Oh70, H. Park70, A. Sakharov70, D.C. Son70,\nT.J. Kim71, J.Y. Kim72, S. Song72, S. Choi73, D. Gyun73, B. Hong73, M. Jo73, H. Kim73,\nY. Kim73, B. Lee73, K.S. Lee73, S.K. Park73, Y. Roh73, H.D. Yoo74, M. Choi75, J.H. Kim75,\nI.C. Park75, G. Ryu75, M.S. Ryu75, Y. Choi76, Y.K. Choi76, J. Goh76, D. Kim76, E. Kwon76,\nJ. Lee76, I. Yu76, A. Juodagalvis77, J.R. Komaragiri78, M.A.B. Md Ali78,\nE. Casimiro Linares79, H. Castilla-Valdez79, E. De La Cruz-Burelo79,\nI. Heredia-de La Cruz79,cc, A. Hernandez-Almada79, R. Lopez-Fernandez79,\nA. Sanchez-Hernandez79, S. Carrillo Moreno80, F. Vazquez Valencia80, I. Pedraza81,\nH.A. Salazar Ibarguen81, A. Morelos Pineda82, D. Krofcheck83, P.H. Butler84, S. Reucroft84,\nA. Ahmad85, M. Ahmad85, Q. Hassan85, H.R. Hoorani85, W.A. Khan85, T. Khurshid85,\nM. Shoaib85, H. Bialkowska86, M. Bluj86, B. Boimska86, T. Frueboes86, M. G\u00b4orski86,\nM. Kazana86, K. Nawrocki86, K. Romanowska-Rybinska86, M. Szleper86, P. Zalewski86,\nG. Brona87, K. Bunkowski87, M. Cwiok87, W. Dominik87, K. Doroba87, A. Kalinowski87,\nM. Konecki87, J. Krolikowski87, M. Misiura87, M. Olszewski87, W. Wolszczak87, P. Bargassa88,\nC. Beir\u02dcao Da Cruz E Silva88, P. Faccioli88, P.G. Ferreira Parracho88, M. Gallinaro88,\nL. Lloret Iglesias88, F. Nguyen88, J. Rodrigues Antunes88, J. Seixas88, J. Varela88, P. Vischia88,\nS. Afanasiev89, P. Bunin89, M. Gavrilenko89, I. Golutvin89, I. Gorbunov89, A. Kamenev89,\nV. Karjavin89, V. Konoplyanikov89, A. Lanev89, A. Malakhov89, V. Matveev89,dd,\nP. Moisenz89, V. Palichik89, V. Perelygin89, S. Shmatov89, N. Skatchkov89, V. Smirnov89,\nA. Zarubin89, V. Golovtsov90, Y. Ivanov90, V. Kim90,ee, P. Levchenko90, V. Murzin90,\nV. Oreshkin90, I. Smirnov90, V. Sulimov90, L. Uvarov90, S. Vavilov90, A. Vorobyev90,\nAn. Vorobyev90, Yu. Andreev91, A. Dermenev91, S. Gninenko91, N. Golubev91, M. Kirsanov91,\nN. Krasnikov91, A. Pashenkov91, D. Tlisov91, A. Toropin91, V. Epshteyn92, V. Gavrilov92,\nN. Lychkovskaya92, V. Popov92, I. Pozdnyakov92, G. Safronov92, S. Semenov92,\nA. Spiridonov92, V. Stolin92, E. Vlasov92, A. Zhokin92, V. Andreev93, M. Azarkin93,\nI. Dremin93, M. Kirakosyan93, A. Leonidov93, G. Mesyats93, S.V. Rusakov93, A. Vinogradov93,\nA. Belyaev94, E. Boos94, M. Dubinin94,ff, L. Dudko94, A. Ershov94, A. Gribushin94,\nV. Klyukhin94, O. Kodolova94, I. Lokhtin94, S. Obraztsov94, S. Petrushanko94, V. Savrin94,\nA. Snigirev94, I. Azhgirey95, I. Bayshev95, S. Bitioukov95, V. Kachanov95, A. Kalinin95,\nD. Konstantinov95, V. Krychkine95, V. Petrov95, R. Ryutin95, A. Sobol95,\nL. Tourtchanovitch95, S. Troshin95, N. Tyurin95, A. Uzunian95, A. Volkov95, P. Adzic96,gg,\nM. Ekmedzic96, J. Milosevic96, V. Rekovic96, J. Alcaraz Maestre97, C. Battilana97, E. Calvo97,\n24\n\nM. Cerrada97, M. Chamizo Llatas97, N. Colino97, B. De La Cruz97, A. Delgado Peris97,\nD. Dom\u00b4\u0131nguez V\u00b4azquez97, A. Escalante Del Valle97, C. Fernandez Bedoya97,\nJ.P. Fern\u00b4andez Ramos97, J. Flix97, M.C. Fouz97, P. Garcia-Abia97, O. Gonzalez Lopez97,\nS. Goy Lopez97, J.M. Hernandez97, M.I. Josa97, E. Navarro De Martino97,\nA. P\u00b4erez-Calero Yzquierdo97, J. Puerta Pelayo97, A. Quintario Olmeda97, I. Redondo97,\nL. Romero97, M.S. Soares97, C. Albajar98, J.F. de Troc\u00b4oniz98, M. Missiroli98, D. Moran98,\nH. Brun99, J. Cuevas99, J. Fernandez Menendez99, S. Folgueras99, I. Gonzalez Caballero99,\nJ.A. Brochero Cifuentes100, I.J. Cabrillo100, A. Calderon100, J. Duarte Campderros100,\nM. Fernandez100, G. Gomez100, A. Graziano100, A. Lopez Virto100, J. Marco100, R. Marco100,\nC. Martinez Rivero100, F. Matorras100, F.J. Munoz Sanchez100, J. Piedra Gomez100,\nT. Rodrigo100, A.Y. Rodr\u00b4\u0131guez-Marrero100, A. Ruiz-Jimeno100, L. Scodellaro100, I. Vila100,\nR. Vilar Cortabitarte100, D. Abbaneo101, E. Au\ufb00ray101, G. Auzinger101, M. Bachtis101,\nP. Baillon101, A.H. Ball101, D. Barney101, A. Benaglia101, J. Bendavid101, L. Benhabib101,\nJ.F. Benitez101, C. Bernet101,h, P. Bloch101, A. Bocci101, A. Bonato101, O. Bondu101,\nC. Botta101, H. Breuker101, T. Camporesi101, G. Cerminara101, S. Colafranceschi101,hh,\nM. D\u2019Alfonso101, D. d\u2019Enterria101, A. Dabrowski101, A. David101, F. De Guio101,\nA. De Roeck101, S. De Visscher101, E. Di Marco101, M. Dobson101, M. Dordevic101,\nN. Dupont-Sagorin101, A. Elliott-Peisert101, G. Franzoni101, W. Funk101, D. Gigi101, K. Gill101,\nD. Giordano101, M. Girone101, F. Glege101, R. Guida101, S. Gundacker101, M. Gutho\ufb00101,\nJ. Hammer101, M. Hansen101, P. Harris101, J. Hegeman101, V. Innocente101, P. Janot101,\nK. Kousouris101, K. Krajczar101, P. Lecoq101, C. Louren\u00b8co101, N. Magini101, L. Malgeri101,\nM. Mannelli101, J. Marrouche101, L. Masetti101, F. Meijers101, S. Mersi101, E. Meschi101,\nF. Moortgat101, S. Morovic101, M. Mulders101, L. Orsini101, L. Pape101, E. Perez101,\nL. Perrozzi101, A. Petrilli101, G. Petrucciani101, A. Pfei\ufb00er101, M. Pimi\u00a8a101, D. Piparo101,\nM. Plagge101, A. Racz101, G. Rolandi101,ii, M. Rovere101, H. Sakulin101, C. Sch\u00a8afer101,\nC. Schwick101, A. Sharma101, P. Siegrist101, P. Silva101, M. Simon101, P. Sphicas101,jj,\nD. Spiga101, J. Steggemann101, B. Stieger101, M. Stoye101, Y. Takahashi101, D. Treille101,\nA. Tsirou101, G.I. Veres101,r, N. Wardle101, H.K. W\u00a8ohri101, H. Wollny101, W.D. Zeuner101,\nW. Bertl102, K. Deiters102, W. Erdmann102, R. Horisberger102, Q. Ingram102, H.C. Kaestli102,\nD. Kotlinski102, D. Renker102, T. Rohe102, F. Bachmair103, L. B\u00a8ani103, L. Bianchini103,\nM.A. Buchmann103, B. Casal103, N. Chanon103, G. Dissertori103, M. Dittmar103,\nM. Doneg`a103, M. D\u00a8unser103, P. Eller103, C. Grab103, D. Hits103, J. Hoss103,\nW. Lustermann103, B. Mangano103, A.C. Marini103, M. Marionneau103,\nP. Martinez Ruiz del Arbol103, M. Masciovecchio103, D. Meister103, N. Mohr103, P. Musella103,\nC. N\u00a8ageli103,kk, F. Nessi-Tedaldi103, F. Pandol\ufb01103, F. Pauss103, M. Peruzzi103, M. Quittnat103,\nL. Rebane103, M. Rossini103, A. Starodumov103,ll, M. Takahashi103, K. Theo\ufb01latos103,\nR. Wallny103, H.A. Weber103, C. Amsler104,mm, M.F. Canelli104, V. Chiochia104,\nA. De Cosa104, A. Hinzmann104, T. Hreus104, B. Kilminster104, C. Lange104,\nB. Millan Mejias104, J. Ngadiuba104, D. Pinna104, P. Robmann104, F.J. Ronga104, S. Taroni104,\nM. Verzetti104, Y. Yang104, M. Cardaci105, K.H. Chen105, C. Ferro105, C.M. Kuo105, W. Lin105,\nY.J. Lu105, R. Volpe105, S.S. Yu105, P. Chang106, Y.H. Chang106, Y.W. Chang106, Y. Chao106,\nK.F. Chen106, P.H. Chen106, C. Dietz106, U. Grundler106, W.-S. Hou106, K.Y. Kao106,\nY.F. Liu106, R.-S. Lu106, D. Majumder106, E. Petrakou106, Y.M. Tzeng106, R. Wilken106,\nB. Asavapibhop107, G. Singh107, N. Srimanobhas107, N. Suwonjandee107, A. Adiguzel108,\nM.N. Bakirci108,nn, S. Cerci108,oo, C. Dozen108, I. Dumanoglu108, E. Eskut108, S. Girgis108,\nG. Gokbulut108, E. Gurpinar108, I. Hos108, E.E. Kangal108, A. Kayis Topaksu108,\nG. Onengut108,pp, K. Ozdemir108, S. Ozturk108,nn, A. Polatoz108, D. Sunar Cerci108,oo,\nB. Tali108,oo, H. Topakli108,nn, M. Vergili108, I.V. Akin109, B. Bilin109, S. Bilmis109,\n25\n\nH. Gamsizkan109,qq, B. Isildak109,rr, G. Karapinar109,ss, K. Ocalan109,tt, S. Sekmen109,\nU.E. Surat109, M. Yalvac109, M. Zeyrek109, E.A. Albayrak110,uu, E. G\u00a8ulmez110, M. Kaya110,vv,\nO. Kaya110,ww, T. Yetkin110,xx, K. Cankocak111, F.I. Vardarl\u0131111, L. Levchuk112, P. Sorokin112,\nJ.J. Brooke113, E. Clement113, D. Cussans113, H. Flacher113, J. Goldstein113, M. Grimes113,\nG.P. Heath113, H.F. Heath113, J. Jacob113, L. Kreczko113, C. Lucas113, Z. Meng113,\nD.M. Newbold113,yy, S. Paramesvaran113, A. Poll113, T. Sakuma113, S. Senkin113,\nV.J. Smith113, K.W. Bell114, A. Belyaev114,zz, C. Brew114, R.M. Brown114, D.J.A. Cockerill114,\nJ.A. Coughlan114, K. Harder114, S. Harper114, E. Olaiya114, D. Petyt114,\nC.H. Shepherd-Themistocleous114, A. Thea114, I.R. Tomalin114, T. Williams114,\nW.J. Womersley114, S.D. Worm114, M. Baber115, R. Bainbridge115, O. Buchmuller115,\nD. Burton115, D. Colling115, N. Cripps115, P. Dauncey115, G. Davies115, M. Della Negra115,\nP. Dunne115, W. Ferguson115, J. Fulcher115, D. Futyan115, G. Hall115, G. Iles115, M. Jarvis115,\nG. Karapostoli115, M. Kenzie115, R. Lane115, R. Lucas115,yy, L. Lyons115, A.-M. Magnan115,\nS. Malik115, B. Mathias115, J. Nash115, A. Nikitenko115,ll, J. Pela115, M. Pesaresi115,\nK. Petridis115, D.M. Raymond115, S. Rogerson115, A. Rose115, C. Seez115, P. Sharpa,115,\nA. Tapper115, M. Vazquez Acosta115, T. Virdee115, S.C. Zenz115, J.E. Cole116, P.R. Hobson116,\nA. Khan116, P. Kyberd116, D. Leggat116, D. Leslie116, I.D. Reid116, P. Symonds116,\nL. Teodorescu116, M. Turner116, J. Dittmann117, K. Hatakeyama117, A. Kasmi117, H. Liu117,\nT. Scarborough117, O. Charaf118, S.I. Cooper118, C. Henderson118, P. Rumerio118,\nA. Avetisyan119, T. Bose119, C. Fantasia119, P. Lawson119, C. Richardson119, J. Rohlf119,\nJ. St. John119, L. Sulak119, J. Alimena120, E. Berry120, S. Bhattacharya120, G. Christopher120,\nD. Cutts120, Z. Demiragli120, N. Dhingra120, A. Ferapontov120, A. Garabedian120, U. Heintz120,\nG. Kukartsev120, E. Laird120, G. Landsberg120, M. Luk120, M. Narain120, M. Segala120,\nT. Sinthuprasith120, T. Speer120, J. Swanson120, R. Breedon121, G. Breto121,\nM. Calderon De La Barca Sanchez121, S. Chauhan121, M. Chertok121, J. Conway121,\nR. Conway121, P.T. Cox121, R. Erbacher121, M. Gardner121, W. Ko121, R. Lander121,\nM. Mulhearn121, D. Pellett121, J. Pilot121, F. Ricci-Tam121, S. Shalhout121, J. Smith121,\nM. Squires121, D. Stolp121, M. Tripathi121, S. Wilbur121, R. Yohay121, R. Cousins122,\nP. Everaerts122, C. Farrell122, J. Hauser122, M. Ignatenko122, G. Rakness122, E. Takasugi122,\nV. Valuev122, M. Weber122, K. Burt123, R. Clare123, J. Ellison123, J.W. Gary123, G. Hanson123,\nJ. Heilman123, M. Ivova Rikova123, P. Jandir123, E. Kennedy123, F. Lacroix123, O.R. Long123,\nA. Luthra123, M. Malberti123, M. Olmedo Negrete123, A. Shrinivas123, S. Sumowidagdo123,\nS. Wimpenny123, J.G. Branson124, G.B. Cerati124, S. Cittolin124, R.T. D\u2019Agnolo124,\nA. Holzner124, R. Kelley124, D. Klein124, D. Kovalskyi124, J. Letts124, I. Macneill124,\nD. Olivito124, S. Padhi124, C. Palmer124, M. Pieri124, M. Sani124, V. Sharma124, S. Simon124,\nY. Tu124, A. Vartak124, C. Welke124, F. W\u00a8urthwein124, A. Yagil124, D. Barge125,\nJ. Bradmiller-Feld125, C. Campagnari125, T. Danielson125, A. Dishaw125, V. Dutta125,\nK. Flowers125, M. Franco Sevilla125, P. Ge\ufb00ert125, C. George125, F. Golf125, L. Gouskos125,\nJ. Incandela125, C. Justus125, N. Mccoll125, J. Richman125, D. Stuart125, W. To125, C. West125,\nJ. Yoo125, A. Apresyan126, A. Bornheim126, J. Bunn126, Y. Chen126, J. Duarte126, A. Mott126,\nH.B. Newman126, C. Pena126, M. Pierini126, M. Spiropulu126, J.R. Vlimant126,\nR. Wilkinson126, S. Xie126, R.Y. Zhu126, V. Azzolini127, A. Calamba127, B. Carlson127,\nT. Ferguson127, Y. Iiyama127, M. Paulini127, J. Russ127, H. Vogel127, I. Vorobiev127,\nJ.P. Cumalat128, W.T. Ford128, A. Gaz128, M. Krohn128, E. Luiggi Lopez128, U. Nauenberg128,\nJ.G. Smith128, K. Stenson128, S.R. Wagner128, J. Alexander129, A. Chatterjee129, J. Chaves129,\nJ. Chu129, S. Dittmer129, N. Eggert129, N. Mirman129, G. Nicolas Kaufman129,\nJ.R. Patterson129, A. Ryd129, E. Salvati129, L. Skinnari129, W. Sun129, W.D. Teo129,\nJ. Thom129, J. Thompson129, J. Tucker129, Y. Weng129, L. Winstrom129, P. Wittich129,\n26\n\nD. Winn130, S. Abdullin131, M. Albrow131, J. Anderson131, G. Apollinari131,\nL.A.T. Bauerdick131, A. Beretvas131, J. Berryhill131, P.C. Bhat131, G. Bolla131, K. Burkett131,\nJ.N. Butler131, H.W.K. Cheung131, F. Chlebana131, S. Cihangir131, V.D. Elvira131, I. Fisk131,\nJ. Freeman131, Y. Gao131, E. Gottschalk131, L. Gray131, D. Green131, S. Gr\u00a8unendahl131,\nO. Gutsche131, J. Hanlon131, D. Hare131, R.M. Harris131, J. Hirschauer131, B. Hooberman131,\nS. Jindariani131, M. Johnson131, U. Joshi131, K. Kaadze131, B. Klima131, B. Kreis131,\nS. Kwana,131, J. Linacre131, D. Lincoln131, R. Lipton131, T. Liu131, J. Lykken131,\nK. Maeshima131, J.M. Marra\ufb03no131, V.I. Martinez Outschoorn131, S. Maruyama131,\nD. Mason131, P. McBride131, P. Merkel131, K. Mishra131, S. Mrenna131, S. Nahn131,\nC. Newman-Holmes131, V. O\u2019Dell131, O. Prokofyev131, E. Sexton-Kennedy131, S. Sharma131,\nA. Soha131, W.J. Spalding131, L. Spiegel131, L. Taylor131, S. Tkaczyk131, N.V. Tran131,\nL. Uplegger131, E.W. Vaandering131, R. Vidal131, A. Whitbeck131, J. Whitmore131, F. Yang131,\nD. Acosta132, P. Avery132, P. Bortignon132, D. Bourilkov132, M. Carver132, D. Curry132,\nS. Das132, M. De Gruttola132, G.P. Di Giovanni132, R.D. Field132, M. Fisher132, I.K. Furic132,\nJ. Hugon132, J. Konigsberg132, A. Korytov132, T. Kypreos132, J.F. Low132, K. Matchev132,\nH. Mei132, P. Milenovic132,aaa, G. Mitselmakher132, L. Muniz132, A. Rinkevicius132,\nL. Shchutska132, M. Snowball132, D. Sperka132, J. Yelton132, M. Zakaria132, S. Hewamanage133,\nS. Linn133, P. Markowitz133, G. Martinez133, J.L. Rodriguez133, T. Adams134, A. Askew134,\nJ. Bochenek134, B. Diamond134, J. Haas134, S. Hagopian134, V. Hagopian134, K.F. Johnson134,\nH. Prosper134, V. Veeraraghavan134, M. Weinberg134, M.M. Baarmand135, M. Hohlmann135,\nH. Kalakhety135, F. Yumiceva135, M.R. Adams136, L. Apanasevich136, D. Berry136,\nR.R. Betts136, I. Bucinskaite136, R. Cavanaugh136, O. Evdokimov136, L. Gauthier136,\nC.E. Gerber136, D.J. Hofman136, P. Kurt136, D.H. Moon136, C. O\u2019Brien136,\nI.D. Sandoval Gonzalez136, C. Silkworth136, P. Turner136, N. Varelas136, B. Bilki137,bbb,\nW. Clarida137, K. Dilsiz137, M. Haytmyradov137, J.-P. Merlo137, H. Mermerkaya137,ccc,\nA. Mestvirishvili137, A. Moeller137, J. Nachtman137, H. Ogul137, Y. Onel137, F. Ozok137,uu,\nA. Penzo137, R. Rahmat137, S. Sen137, P. Tan137, E. Tiras137, J. Wetzel137, K. Yi137,\nB.A. Barnett138, B. Blumenfeld138, S. Bolognesi138, D. Fehling138, A.V. Gritsan138,\nP. Maksimovic138, C. Martin138, M. Swartz138, P. Baringer139, A. Bean139, G. Benelli139,\nC. Bruner139, R.P. Kenny III139, M. Malek139, M. Murray139, D. Noonan139, S. Sanders139,\nJ. Sekaric139, R. Stringer139, Q. Wang139, J.S. Wood139, I. Chakaberia140, A. Ivanov140,\nS. Khalil140, M. Makouski140, Y. Maravin140, L.K. Saini140, N. Skhirtladze140, I. Svintradze140,\nJ. Gronberg141, D. Lange141, F. Rebassoo141, D. Wright141, A. Baden142, A. Belloni142,\nB. Calvert142, S.C. Eno142, J.A. Gomez142, N.J. Hadley142, R.G. Kellogg142, T. Kolberg142,\nY. Lu142, A.C. Mignerey142, K. Pedro142, A. Skuja142, M.B. Tonjes142, S.C. Tonwar142,\nA. Apyan143, R. Barbieri143, G. Bauer143, W. Busza143, I.A. Cali143, M. Chan143,\nL. Di Matteo143, G. Gomez Ceballos143, M. Goncharov143, D. Gulhan143, M. Klute143,\nY.S. Lai143, Y.-J. Lee143, A. Levin143, P.D. Luckey143, T. Ma143, C. Paus143, D. Ralph143,\nC. Roland143, G. Roland143, G.S.F. Stephans143, K. Sumorok143, D. Velicanu143, J. Veverka143,\nB. Wyslouch143, M. Yang143, M. Zanetti143, V. Zhukova143, B. Dahmes144, A. Gude144,\nS.C. Kao144, K. Klapoetke144, Y. Kubota144, J. Mans144, N. Pastika144, R. Rusack144,\nA. Singovsky144, N. Tambe144, J. Turkewitz144, J.G. Acosta145, S. Oliveros145, E. Avdeeva146,\nK. Bloom146, S. Bose146, D.R. Claes146, A. Dominguez146, R. Gonzalez Suarez146, J. Keller146,\nD. Knowlton146, I. Kravchenko146, J. Lazo-Flores146, F. Meier146, F. Ratnikov146,\nG.R. Snow146, M. Zvada146, J. Dolen147, A. Godshalk147, I. Iashvili147, A. Kharchilava147,\nA. Kumar147, S. Rappoccio147, G. Alverson148, E. Barberis148, D. Baumgartel148,\nM. Chasco148, A. Massironi148, D.M. Morse148, D. Nash148, T. Orimoto148, D. Trocino148,\nR.-J. Wang148, D. Wood148, J. Zhang148, K.A. Hahn149, A. Kubik149, N. Mucia149, N. Odell149,\n27\n\nB. Pollack149, A. Pozdnyakov149, M. Schmitt149, S. Stoynev149, K. Sung149, M. Velasco149,\nS. Won149, A. Brinkerho\ufb00150, K.M. Chan150, A. Drozdetskiy150, M. Hildreth150, C. Jessop150,\nD.J. Karmgard150, N. Kellams150, K. Lannon150, S. Lynch150, N. Marinelli150,\nY. Musienko150,dd, T. Pearson150, M. Planer150, R. Ruchti150, G. Smith150, N. Valls150,\nM. Wayne150, M. Wolf150, A. Woodard150, L. Antonelli151, J. Brinson151, B. Bylsma151,\nL.S. Durkin151, S. Flowers151, A. Hart151, C. Hill151, R. Hughes151, K. Kotov151, T.Y. Ling151,\nW. Luo151, D. Puigh151, M. Rodenburg151, B.L. Winer151, H. Wolfe151, H.W. Wulsin151,\nO. Driga152, P. Elmer152, J. Hardenbrook152, P. Hebda152, A. Hunt152, S.A. Koay152,\nP. Lujan152, D. Marlow152, T. Medvedeva152, M. Mooney152, J. Olsen152, P. Pirou\u00b4e152,\nX. Quan152, H. Saka152, D. Stickland152,c, C. Tully152, J.S. Werner152, A. Zuranski152,\nE. Brownson153, S. Malik153, H. Mendez153, J.E. Ramirez Vargas153, V.E. Barnes154,\nD. Benedetti154, D. Bortoletto154, M. De Mattia154, L. Gutay154, Z. Hu154, M.K. Jha154,\nM. Jones154, K. Jung154, M. Kress154, N. Leonardo154, D.H. Miller154, N. Neumeister154,\nB.C. Radburn-Smith154, X. Shi154, I. Shipsey154, D. Silvers154, A. Svyatkovskiy154,\nF. Wang154, W. Xie154, L. Xu154, J. Zablocki154, N. Parashar155, J. Stupak155, A. Adair156,\nB. Akgun156, K.M. Ecklund156, F.J.M. Geurts156, W. Li156, B. Michlin156, B.P. Padley156,\nR. Redjimi156, J. Roberts156, J. Zabel156, B. Betchart157, A. Bodek157, R. Covarelli157,\nP. de Barbaro157, R. Demina157, Y. Eshaq157, T. Ferbel157, A. Garcia-Bellido157,\nP. Goldenzweig157, J. Han157, A. Harel157, A. Khukhunaishvili157, S. Korjenevski157,\nG. Petrillo157, D. Vishnevskiy157, R. Ciesielski158, L. Demortier158, K. Goulianos158,\nC. Mesropian158, S. Arora159, A. Barker159, J.P. Chou159, C. Contreras-Campana159,\nE. Contreras-Campana159, D. Duggan159, D. Ferencek159, Y. Gershtein159, R. Gray159,\nE. Halkiadakis159, D. Hidas159, S. Kaplan159, A. Lath159, S. Panwalkar159, M. Park159,\nR. Patel159, S. Salur159, S. Schnetzer159, S. Somalwar159, R. Stone159, S. Thomas159,\nP. Thomassen159, M. Walker159, K. Rose160, S. Spanier160, A. York160, O. Bouhali161,ddd,\nA. Castaneda Hernandez161, R. Eusebi161, W. Flanagan161, J. Gilmore161, T. Kamon161,eee,\nV. Khotilovich161, V. Krutelyov161, R. Montalvo161, I. Osipenkov161, Y. Pakhotin161,\nA. Perlo\ufb00161, J. Roe161, A. Rose161, A. Safonov161, I. Suarez161, A. Tatarinov161,\nK.A. Ulmer161, N. Akchurin162, C. Cowden162, J. Damgov162, C. Dragoiu162, P.R. Dudero162,\nJ. Faulkner162, K. Kovitanggoon162, S. Kunori162, S.W. Lee162, T. Libeiro162, I. Volobouev162,\nE. Appelt163, A.G. Delannoy163, S. Greene163, A. Gurrola163, W. Johns163, C. Maguire163,\nY. Mao163, A. Melo163, M. Sharma163, P. Sheldon163, B. Snook163, S. Tuo163, J. Velkovska163,\nM.W. Arenton164, S. Boutle164, B. Cox164, B. Francis164, J. Goodell164, R. Hirosky164,\nA. Ledovskoy164, H. Li164, C. Lin164, C. Neu164, J. Wood164, C. Clarke165, R. Harr165,\nP.E. Karchin165, C. Kottachchi Kankanamge Don165, P. Lamichhane165, J. Sturdy165,\nD.A. Belknap166, D. Carlsmith166, M. Cepeda166, S. Dasu166, L. Dodd166, S. Duric166,\nE. Friis166, R. Hall-Wilton166, M. Herndon166, A. Herv\u00b4e166, P. Klabbers166, A. Lanaro166,\nC. Lazaridis166, A. Levine166, R. Loveless166, A. Mohapatra166, I. Ojalvo166, T. Perry166,\nG.A. Pierro166, G. Polese166, I. Ross166, T. Sarangi166, A. Savin166, W.H. Smith166,\nD. Taylor166, C. Vuosalo166, N. Woods166\n1 Yerevan Physics Institute, Yerevan, Armenia\n2 Institut f\u00a8ur Hochenergiephysik der OeAW, Wien, Austria\n3 National Centre for Particle and High Energy Physics, Minsk, Belarus\n4 Universiteit Antwerpen, Antwerpen, Belgium\n5 Vrije Universiteit Brussel, Brussel, Belgium\n6 Universit\u00b4e Libre de Bruxelles, Bruxelles, Belgium\n7 Ghent University, Ghent, Belgium\n28\n\n8 Universit\u00b4e Catholique de Louvain, Louvain-la-Neuve, Belgium\n9 Universit\u00b4e de Mons, Mons, Belgium\n10 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil\n11 Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil\n12 Universidade Estadual Paulista, Universidade Federal do ABC, S\u02dcao Paulo, Brazil\n12a Universidade Estadual Paulista\n12b Universidade Federal do ABC\n13 Institute for Nuclear Research and Nuclear Energy, So\ufb01a, Bulgaria\n14 University of So\ufb01a, So\ufb01a, Bulgaria\n15 Institute of High Energy Physics, Beijing, China\n16 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China\n17 Universidad de Los Andes, Bogota, Colombia\n18 University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval\nArchitecture, Split, Croatia\n19 University of Split, Faculty of Science, Split, Croatia\n20 Institute Rudjer Boskovic, Zagreb, Croatia\n21 University of Cyprus, Nicosia, Cyprus\n22 Charles University, Prague, Czech Republic\n23 Academy of Scienti\ufb01c Research and Technology of the Arab Republic of Egypt, Egyptian\nNetwork of High Energy Physics, Cairo, Egypt\n24 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia\n25 Department of Physics, University of Helsinki, Helsinki, Finland\n26 Helsinki Institute of Physics, Helsinki, Finland\n27 Lappeenranta University of Technology, Lappeenranta, Finland\n28 DSM/IRFU, CEA/Saclay, Gif-sur-Yvette, France\n29 Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France\n30 Institut Pluridisciplinaire Hubert Curien, Universit\u00b4e de Strasbourg, Universit\u00b4e de Haute\nAlsace Mulhouse, CNRS/IN2P3, Strasbourg, France\n31 Centre de Calcul de l\u2019Institut National de Physique Nucleaire et de Physique des Particules,\nCNRS/IN2P3, Villeurbanne, France\n32 Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique\nNucl\u00b4eaire de Lyon, Villeurbanne, France\n33 Institute of High Energy Physics and Informatization, Tbilisi State University, Tbilisi,\nGeorgia\n34 RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany\n35 RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany\n36 RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany\n37 Deutsches Elektronen-Synchrotron, Hamburg, Germany\n38 University of Hamburg, Hamburg, Germany\n39 Institut f\u00a8ur Experimentelle Kernphysik, Karlsruhe, Germany\n40 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi,\nGreece\n41 University of Athens, Athens, Greece\n42 University of Io\u00b4annina, Io\u00b4annina, Greece\n43 Wigner Research Centre for Physics, Budapest, Hungary\n44 Institute of Nuclear Research ATOMKI, Debrecen, Hungary\n45 University of Debrecen, Debrecen, Hungary\n46 National Institute of Science Education and Research, Bhubaneswar, India\n29\n\n47 Panjab University, Chandigarh, India\n48 University of Delhi, Delhi, India\n49 Saha Institute of Nuclear Physics, Kolkata, India\n50 Bhabha Atomic Research Centre, Mumbai, India\n51 Tata Institute of Fundamental Research, Mumbai, India\n52 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran\n53 University College Dublin, Dublin, Ireland\n54 INFN Sezione di Bari, Universit`a di Bari, Politecnico di Bari, Bari, Italy\n54a INFN Sezione di Bari\n54b Universit`a di Bari\n54c Politecnico di Bari\n55 INFN Sezione di Bologna, Universit`a di Bologna, Bologna, Italy\n55a INFN Sezione di Bologna\n55b Universit`a di Bologna\n56 INFN Sezione di Catania, Universit`a di Catania, CSFNSM, Catania, Italy\n56a INFN Sezione di Catania\n56b Universit`a di Catania\n56c CSFNSM\n57 INFN Sezione di Firenze, Universit`a di Firenze, Firenze, Italy\n57a INFN Sezione di Firenze\n57b Universit`a di Firenze\n58 INFN Laboratori Nazionali di Frascati, Frascati, Italy\n59 INFN Sezione di Genova, Universit`a di Genova, Genova, Italy\n59a INFN Sezione di Genova\n59b Universit`a di Genova\n60 INFN Sezione di Milano-Bicocca, Universit`a di Milano-Bicocca, Milano, Italy\n60a INFN Sezione di Milano-Bicocca\n60b Universit`a di Milano-Bicocca\n61 INFN Sezione di Napoli, Universit`a di Napoli \u2019Federico II\u2019, Universit`a della Basilicata\n(Potenza), Universit`a G. Marconi (Roma), Napoli, Italy\n61a INFN Sezione di Napoli\n61b Universit`a di Napoli \u2019Federico II\u2019\n61c Universit`a della Basilicata (Potenza)\n61d Universit`a G. Marconi (Roma)\n62 INFN Sezione di Padova, Universit`a di Padova, Universit`a di Trento (Trento), Padova, Italy\n62a INFN Sezione di Padova\n62b Universit`a di Padova\n62c Universit`a di Trento (Trento)\n63 INFN Sezione di Pavia, Universit`a di Pavia, Pavia, Italy\n63a INFN Sezione di Pavia\n63b Universit`a di Pavia\n64 INFN Sezione di Perugia, Universit`a di Perugia, Perugia, Italy\n64a INFN Sezione di Perugia\n64b Universit`a di Perugia\n65 INFN Sezione di Pisa, Universit`a di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy\n65a INFN Sezione di Pisa\n65b Universit`a di Pisa\n65c Scuola Normale Superiore di Pisa\n30\n\n66 INFN Sezione di Roma, Universit`a di Roma, Roma, Italy\n66a INFN Sezione di Roma\n66b Universit`a di Roma\n67 INFN Sezione di Torino, Universit`a di Torino, Universit`a del Piemonte Orientale (Novara),\nTorino, Italy\n67a INFN Sezione di Torino\n67b Universit`a di Torino\n67c Universit`a del Piemonte Orientale (Novara)\n68 INFN Sezione di Trieste, Universit`a di Trieste, Trieste, Italy\n68a INFN Sezione di Trieste\n68b Universit`a di Trieste\n69 Kangwon National University, Chunchon, Korea\n70 Kyungpook National University, Daegu, Korea\n71 Chonbuk National University, Jeonju, Korea\n72 Chonnam National University, Institute for Universe and Elementary Particles, Kwangju,\nKorea\n73 Korea University, Seoul, Korea\n74 Seoul National University, Seoul, Korea\n75 University of Seoul, Seoul, Korea\n76 Sungkyunkwan University, Suwon, Korea\n77 Vilnius University, Vilnius, Lithuania\n78 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia\n79 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico\n80 Universidad Iberoamericana, Mexico City, Mexico\n81 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico\n82 Universidad Aut\u00b4onoma de San Luis Potos\u00b4\u0131, San Luis Potos\u00b4\u0131, Mexico\n83 University of Auckland, Auckland, New Zealand\n84 University of Canterbury, Christchurch, New Zealand\n85 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan\n86 National Centre for Nuclear Research, Swierk, Poland\n87 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw,\nPoland\n88 Laborat\u00b4orio de Instrumenta\u00b8c\u02dcao e F\u00b4\u0131sica Experimental de Part\u00b4\u0131culas, Lisboa, Portugal\n89 Joint Institute for Nuclear Research, Dubna, Russia\n90 Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg), Russia\n91 Institute for Nuclear Research, Moscow, Russia\n92 Institute for Theoretical and Experimental Physics, Moscow, Russia\n93 P.N. Lebedev Physical Institute, Moscow, Russia\n94 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow,\nRussia\n95 State Research Center of Russian Federation, Institute for High Energy Physics, Protvino,\nRussia\n96 University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences,\nBelgrade, Serbia\n97 Centro de Investigaciones Energ\u00b4eticas Medioambientales y Tecnol\u00b4ogicas (CIEMAT),\nMadrid, Spain\n98 Universidad Aut\u00b4onoma de Madrid, Madrid, Spain\n99 Universidad de Oviedo, Oviedo, Spain\n31\n\n100 Instituto de F\u00b4\u0131sica de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain\n101 CERN, European Organization for Nuclear Research, Geneva, Switzerland\n102 Paul Scherrer Institut, Villigen, Switzerland\n103 Institute for Particle Physics, ETH Zurich, Zurich, Switzerland\n104 Universit\u00a8at Z\u00a8urich, Zurich, Switzerland\n105 National Central University, Chung-Li, Taiwan\n106 National Taiwan University (NTU), Taipei, Taiwan\n107 Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok, Thailand\n108 Cukurova University, Adana, Turkey\n109 Middle East Technical University, Physics Department, Ankara, Turkey\n110 Bogazici University, Istanbul, Turkey\n111 Istanbul Technical University, Istanbul, Turkey\n112 National Scienti\ufb01c Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine\n113 University of Bristol, Bristol, United Kingdom\n114 Rutherford Appleton Laboratory, Didcot, United Kingdom\n115 Imperial College, London, United Kingdom\n116 Brunel University, Uxbridge, United Kingdom\n117 Baylor University, Waco, USA\n118 The University of Alabama, Tuscaloosa, USA\n119 Boston University, Boston, USA\n120 Brown University, Providence, USA\n121 University of California, Davis, Davis, USA\n122 University of California, Los Angeles, USA\n123 University of California, Riverside, Riverside, USA\n124 University of California, San Diego, La Jolla, USA\n125 University of California, Santa Barbara, Santa Barbara, USA\n126 California Institute of Technology, Pasadena, USA\n127 Carnegie Mellon University, Pittsburgh, USA\n128 University of Colorado at Boulder, Boulder, USA\n129 Cornell University, Ithaca, USA\n130 Fair\ufb01eld University, Fair\ufb01eld, USA\n131 Fermi National Accelerator Laboratory, Batavia, USA\n132 University of Florida, Gainesville, USA\n133 Florida International University, Miami, USA\n134 Florida State University, Tallahassee, USA\n135 Florida Institute of Technology, Melbourne, USA\n136 University of Illinois at Chicago (UIC), Chicago, USA\n137 The University of Iowa, Iowa City, USA\n138 Johns Hopkins University, Baltimore, USA\n139 The University of Kansas, Lawrence, USA\n140 Kansas State University, Manhattan, USA\n141 Lawrence Livermore National Laboratory, Livermore, USA\n142 University of Maryland, College Park, USA\n143 Massachusetts Institute of Technology, Cambridge, USA\n144 University of Minnesota, Minneapolis, USA\n145 University of Mississippi, Oxford, USA\n146 University of Nebraska-Lincoln, Lincoln, USA\n147 State University of New York at Bu\ufb00alo, Bu\ufb00alo, USA\n32\n\n148 Northeastern University, Boston, USA\n149 Northwestern University, Evanston, USA\n150 University of Notre Dame, Notre Dame, USA\n151 The Ohio State University, Columbus, USA\n152 Princeton University, Princeton, USA\n153 University of Puerto Rico, Mayaguez, USA\n154 Purdue University, West Lafayette, USA\n155 Purdue University Calumet, Hammond, USA\n156 Rice University, Houston, USA\n157 University of Rochester, Rochester, USA\n158 The Rockefeller University, New York, USA\n159 Rutgers, The State University of New Jersey, Piscataway, USA\n160 University of Tennessee, Knoxville, USA\n161 Texas A&M University, College Station, USA\n162 Texas Tech University, Lubbock, USA\n163 Vanderbilt University, Nashville, USA\n164 University of Virginia, Charlottesville, USA\n165 Wayne State University, Detroit, USA\n166 University of Wisconsin, Madison, USA\na Deceased\nb Also at Vienna University of Technology, Vienna, Austria\nc Also at CERN, European Organization for Nuclear Research, Geneva, Switzerland\nd Also at Institut Pluridisciplinaire Hubert Curien, Universit\u00b4e de Strasbourg, Universit\u00b4e de Haute\nAlsace Mulhouse, CNRS/IN2P3, Strasbourg, France\ne Also at National Institute of Chemical Physics and Biophysics, Tallinn, Estonia\nf Also at Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia\ng Also at Universidade Estadual de Campinas, Campinas, Brazil\nh Also at Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France\ni Also at Joint Institute for Nuclear Research, Dubna, Russia\nj Also at Suez University, Suez, Egypt\nk Also at Cairo University, Cairo, Egypt\nl Also at Fayoum University, El-Fayoum, Egypt\nm Also at Ain Shams University, Cairo, Egypt\nn Now at Sultan Qaboos University, Muscat, Oman\no Also at Universit\u00b4e de Haute Alsace, Mulhouse, France\np Also at Brandenburg University of Technology, Cottbus, Germany\nq Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary\nr Also at E\u00a8otv\u00a8os Lor\u00b4and University, Budapest, Hungary\ns Also at University of Debrecen, Debrecen, Hungary\nt Also at University of Visva-Bharati, Santiniketan, India\nu Now at King Abdulaziz University, Jeddah, Saudi Arabia\nv Also at University of Ruhuna, Matara, Sri Lanka\nw Also at Isfahan University of Technology, Isfahan, Iran\nx Also at University of Tehran, Department of Engineering Science, Tehran, Iran\ny Also at Plasma Physics Research Center, Science and Research Branch, Islamic Azad University,\nTehran, Iran\nz Also at Universit`a degli Studi di Siena, Siena, Italy\naa Also at Centre National de la Recherche Scienti\ufb01que (CNRS) - IN2P3, Paris, France\nbb Also at Purdue University, West Lafayette, USA\ncc Also at Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico\n33\n\ndd Also at Institute for Nuclear Research, Moscow, Russia\nee Also at St. Petersburg State Polytechnical University, St. Petersburg, Russia\n\ufb00Also at California Institute of Technology, Pasadena, USA\ngg Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia\nhh Also at Facolt`a Ingegneria, Universit`a di Roma, Roma, Italy\nii Also at Scuola Normale e Sezione dell\u2019INFN, Pisa, Italy\njj Also at University of Athens, Athens, Greece\nkk Also at Paul Scherrer Institut, Villigen, Switzerland\nll Also at Institute for Theoretical and Experimental Physics, Moscow, Russia\nmm Also at Albert Einstein Center for Fundamental Physics, Bern, Switzerland\nnn Also at Gaziosmanpasa University, Tokat, Turkey\noo Also at Adiyaman University, Adiyaman, Turkey\npp Also at Cag University, Mersin, Turkey\nqq Also at Anadolu University, Eskisehir, Turkey\nrr Also at Ozyegin University, Istanbul, Turkey\nss Also at Izmir Institute of Technology, Izmir, Turkey\ntt Also at Necmettin Erbakan University, Konya, Turkey\nuu Also at Mimar Sinan University, Istanbul, Istanbul, Turkey\nvv Also at Marmara University, Istanbul, Turkey\nww Also at Kafkas University, Kars, Turkey\nxx Also at Yildiz Technical University, Istanbul, Turkey\nyy Also at Rutherford Appleton Laboratory, Didcot, United Kingdom\nzz Also at School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom\naaa Also at University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences,\nBelgrade, Serbia\nbbb Also at Argonne National Laboratory, Argonne, USA\nccc Also at Erzincan University, Erzincan, Turkey\nddd Also at Texas A&M University at Qatar, Doha, Qatar\neee Also at Kyungpook National University, Daegu, Korea\nThe LHCb Collaboration: I. Bediaga1, J.M. De Miranda1, F. Ferreira Rodrigues1,\nA. Gomes1,m, A. Massa\ufb00erri1, A.C. dos Reis1, A.B. Rodrigues1, S. Amato2,\nK. Carvalho Akiba2, L. De Paula2, O. Francisco2, M. Gandelman2, A. Hicheur2, J.H. Lopes2,\nD. Martins Tostes2, I. Nasteva2, J.M. Otalora Goicochea2, E. Polycarpo2, C. Potterat2,\nM.S. Rangel2, V. Salustino Guimaraes2, B. Souza De Paula2, D. Vieira2, L. An3, Y. Gao3,\nF. Jing3, Y. Li3, Z. Yang3, X. Yuan3, Y. Zhang3, L. Zhong3, L. Beaucourt4, M. Chefdeville4,\nD. Decamp4, N. D\u00b4el\u00b4eage4, Ph. Ghez4, J.-P. Lees4, J.F. Marchand4, M.-N. Minard4,\nB. Pietrzyk4, W. Qian4, S. T\u2019Jampens4, V. Tisserand4, E. Tourne\ufb01er4, Z. Ajaltouni5,\nM. Baalouch5, E. Cogneras5, O. Deschamps5, I. El Rifai5, M. Grabalosa G\u00b4andara5,\nP. Henrard5, M. Hoballah5, R. Lef`evre5, J. Maratas5, S. Monteil5, V. Niess5, P. Perret5,\nC. Adrover6, S. Akar6, E. Aslanides6, J. Cogan6, W. Kanso6, R. Le Gac6, O. Leroy6,\nG. Mancinelli6, A. Mord`a6, M. Perrin-Terrin6, J. Serrano6, A. Tsaregorodtsev6, Y. Amhis7,\nS. Barsuk7, M. Borsato7, O. Kochebina7, J. Lefran\u00b8cois7, F. Machefert7, A. Mart\u00b4\u0131n S\u00b4anchez7,\nM. Nicol7, P. Robbe7, M.-H. Schune7, M. Teklishyn7, A. Vallier7, B. Viaud7, G. Wormser7,\nE. Ben-Haim8, M. Charles8, S. Coquereau8, P. David8, L. Del Buono8, L. Henry8, F. Polci8,\nJ. Albrecht9, T. Brambach9, Ch. Cauet9, M. Deckenho\ufb009, U. Eitschberger9, R. Ekelhof9,\nL. Gavardi9, F. Kruse9, F. Meier9, R. Niet9, C.J. Parkinson9,45, M. Schlupp9, A. Shires9,\nB. Spaan9, S. Swientek9, J. Wishahi9, O. Aquines Gutierrez10, J. Blouw10, M. Britsch10,\nM. Fontana10, D. Popov10, M. Schmelling10, D. Volyanskyy10, M. Zavertyaev10,w,\nS. Bachmann11, A. Bien11, A. Comerma-Montells11, M. De Cian11, F. Dordei11, S. Esen11,\nC. F\u00a8arber11, E. Gersabeck11, L. Grillo11, X. Han11, S. Hansmann-Menzemer11, A. Jaeger11,\nM. Kolpin11, K. Kreplin11, G. Krocker11, B. Leverington11, J. Marks11, M. Meissner11,\n34\n\nM. Neuner11, T. Nikodem11, P. Seyfert11, M. Stahl11, S. Stahl11, U. Uwer11, M. Vesterinen11,\nS. Wandernoth11, D. Wiedner11, A. Zhelezov11, R. McNulty12, R. Wallace12, W.C. Zhang12,\nA. Palano13,r, A. Carbone14,h, A. Falabella14, D. Galli14,h, U. Marconi14, N. Moggi14,\nM. Mussini14, S. Perazzini14,h, V. Vagnoni14, G. Valenti14, M. Zangoli14, W. Bonivento15,38,\nS. Cadeddu15, A. Cardini15, V. Cogoni15, A. Contu15,38, A. Lai15, B. Liu15, G. Manca15,p,\nR. Oldeman15,p, B. Saitta15,p, C. Vacca15, M. Andreotti16,c, W. Baldini16, C. Bozzi16,\nR. Calabrese16,c, M. Corvo16,c, M. Fiore16,c, M. Fiorini16,c, E. Luppi16,c, L.L. Pappalardo16,c,\nI. Shapoval16,43,c, G. Tellarini16,c, L. Tomassetti16,c, S. Vecchi16, L. Anderlini17,b, A. Bizzeti17,e,\nM. Frosini17,b, G. Graziani17, G. Passaleva17, M. Veltri17,v, G. Bencivenni18, P. Campana18,\nP. De Simone18, G. Lanfranchi18, M. Palutan18, M. Rama18, A. Sarti18,t, B. Sciascia18,\nR. Vazquez Gomez18, R. Cardinale19,38,j, F. Fontanelli19,j, S. Gambetta19,j, C. Patrignani19,j,\nA. Petrolini19,j, A. Pistone19, M. Calvi20,f, L. Cassina20,f, C. Gotti20,f, B. Khanji20,38,f,\nM. Kucharczyk20,26,f, C. Matteuzzi20, J. Fu21,38, A. Geraci21,l, N. Neri21, F. Palombo21,s,\nS. Amerio22, G. Collazuol22, S. Gallorini22,38, A. Gianelle22, D. Lucchesi22,o, A. Lupato22,\nM. Morandin22, M. Rotondo22, L. Sestini22, G. Simi22, R. Stroili22, F. Bedeschi23, R. Cenci23,k,\nS. Leo23, P. Marino23,k, M.J. Morello23,k, G. Punzi23,u, S. Stracka23,k, J. Walsh23,\nG. Carboni24,i, E. Furfaro24,i, E. Santovetti24,i, A. Satta24, A.A. Alves Jr25,38,\nG. Auriemma25,d, V. Bocci25, G. Martellotti25, G. Penso25,t, D. Pinci25, R. Santacesaria25,\nC. Satriano25,d, A. Sciubba25,t, A. Dziurda26, W. Kucewicz26,n, T. Lesiak26, B. Rachwal26,\nM. Witek26, M. Firlej27, T. Fiutowski27, M. Idzik27, P. Morawski27, J. Moron27,\nA. Oblakowska-Mucha27,38, K. Swientek27, T. Szumlak27, V. Batozskaya28, K. Klimaszewski28,\nK. Kurek28, M. Szczekowski28, A. Ukleja28, W. Wislicki28, L. Cojocariu29, L. Giubega29,\nA. Grecu29, F. Maciuc29, M. Orlandea29, B. Popovici29, S. Stoica29, M. Straticiuc29,\nG. Alkhazov30, N. Bondar30,38, A. Dzyuba30, O. Maev30, N. Sagidova30, Y. Shcheglov30,\nA. Vorobyev30, S. Belogurov31, I. Belyaev31, V. Egorychev31, D. Golubkov31,\nT. Kvaratskheliya31, I.V. Machikhiliyan31, I. Polyakov31, D. Savrina31,32, A. Semennikov31,\nA. Zhokhov31, A. Berezhnoy32, M. Korolev32, A. Le\ufb02at32, N. Nikitin32, S. Filippov33,\nE. Gushchin33, L. Kravchuk33, A. Bondar34, S. Eidelman34, P. Krokovny34, V. Kudryavtsev34,\nL. Shekhtman34, V. Vorobyev34, A. Artamonov35, K. Belous35, R. Dzhelyadin35, Yu. Guz35,38,\nA. Novoselov35, V. Obraztsov35, A. Popov35, V. Romanovsky35, M. Shapkin35, O. Stenyakin35,\nO. Yushchenko35, A. Badalov36, M. Calvo Gomez36,g, L. Garrido36, D. Gascon36,\nR. Graciani Diaz36, E. Graug\u00b4es36, C. Marin Benito36, E. Picatoste Olloqui36,\nV. Rives Molina36, H. Ruiz36, X. Vilasis-Cardona36,g, B. Adeva37, P. Alvarez Cartelle37,\nA. Dosil Su\u00b4arez37, V. Fernandez Albor37, A. Gallas Torreira37, J. Garc\u00b4\u0131a Pardi\u02dcnas37,\nJ.A. Hernando Morata37, M. Plo Casasus37, A. Romero Vidal37, J.J. Saborido Silva37,\nB. Sanmartin Sedes37, C. Santamarina Rios37, P. Vazquez Regueiro37, C. V\u00b4azquez Sierra37,\nM. Vieites Diaz37, F. Alessio38, F. Archilli38, C. Barschel38, S. Benson38, J. Buytaert38,\nD. Campora Perez38, L. Castillo Garcia38, M. Cattaneo38, Ph. Charpentier38, X. Cid Vidal38,\nM. Clemencic38, J. Closier38, V. Coco38, P. Collins38, G. Corti38, B. Couturier38,\nC. D\u2019Ambrosio38, F. Dettori38, A. Di Canto38, H. Dijkstra38, P. Durante38, M. Ferro-Luzzi38,\nR. Forty38, M. Frank38, C. Frei38, C. Gaspar38, V.V. Gligorov38, L.A. Granado Cardoso38,\nT. Gys38, C. Haen38, J. He38, T. Head38, E. van Herwijnen38, R. Jacobsson38, D. Johnson38,\nC. Joram38, B. Jost38, M. Karacson38, T.M. Karbach38, D. Lacarrere38, B. Langhans38,\nR. Lindner38, C. Linn38, S. Lohn38, A. Mapelli38, R. Matev38, Z. Mathe38, S. Neubert38,\nN. Neufeld38, A. Otto38, J. Panman38, M. Pepe Altarelli38, N. Rauschmayr38, M. Rihl38,\nS. Roiser38, T. Ruf38, H. Schindler38, B. Schmidt38, A. Schopper38, R. Schwemmer38,\nS. Sridharan38, F. Stagni38, V.K. Subbiah38, F. Teubert38, E. Thomas38, D. Tonelli38,\nA. Trisovic38, M. Ubeda Garcia38, J. Wicht38, K. Wyllie38, V. Battista39, A. Bay39, F. Blanc39,\n35\n\nM. Dorigo39, F. Dupertuis39, C. Fitzpatrick39, S. Gian`\u013139, G. Haefeli39, P. Jaton39,\nC. Khurewathanakul39, I. Komarov39, V.N. La Thi39, N. Lopez-March39, R. M\u00a8arki39,\nM. Martinelli39, B. Muster39, T. Nakada39, A.D. Nguyen39, T.D. Nguyen39,\nC. Nguyen-Mau39,q, J. Prisciandaro39, A. Puig Navarro39, B. Rakotomiaramanana39,\nJ. Rouvinet39, O. Schneider39, F. Soomro39, P. Szczypka39,38, M. Tobin39, S. Tourneur39,\nM.T. Tran39, G. Veneziano39, Z. Xu39, J. Anderson40, R. Bernet40, E. Bowen40, A. Bursche40,\nN. Chiapolini40, M. Chrzaszcz40,26, Ch. Elsasser40, E. Graverini40, F. Lionetto40, P. Lowdon40,\nK. M\u00a8uller40, N. Serra40, O. Steinkamp40, B. Storaci40, U. Straumann40, M. Tresch40,\nA. Vollhardt40, R. Aaij41, S. Ali41, M. van Beuzekom41, P.N.Y. David41, K. De Bruyn41,\nC. Farinelli41, V. Heijne41, W. Hulsbergen41, E. Jans41, P. Koppenburg41,38, A. Kozlinskiy41,\nJ. van Leerdam41, M. Merk41, S. Oggero41, A. Pellegrino41, H. Snoek41, J. van Tilburg41,\nP. Tsopelas41, N. Tuning41, J.A. de Vries41, T. Ketel42, R.F. Koopman42, R.W. Lambert42,\nD. Martinez Santos42,38, G. Raven42, M. Schiller42, V. Syropoulos42, S. Tolk42, A. Dovbnya43,\nS. Kandybei43, I. Raniuk43, O. Okhrimenko44, V. Pugatch44, S. Bifani45, N. Farley45,\nP. Gri\ufb03th45, I.R. Kenyon45, C. Lazzeroni45, A. Mazurov45, J. McCarthy45, L. Pescatore45,\nN.K. Watson45, M.P. Williams45, M. Adinol\ufb0146, J. Benton46, N.H. Brook46, A. Cook46,\nM. Coombes46, J. Dalseno46, T. Hampson46, S.T. Harnew46, P. Naik46, E. Price46,\nC. Prouve46, J.H. Rademacker46, S. Richards46, D.M. Saunders46, N. Skidmore46, D. Souza46,\nJ.J. Velthuis46, D. Voong46, W. Barter47, M.-O. Bettler47, H.V. Cli\ufb0047, H.-M. Evans47,\nJ. Garra Tico47, V. Gibson47, S. Gregson47, S.C. Haines47, C.R. Jones47, M. Sirendi47,\nJ. Smith47, D.R. Ward47, S.A. Wotton47, S. Wright47, J.J. Back48, T. Blake48, D.C. Craik48,\nA.C. Crocombe48, D. Dossett48, T. Gershon48, M. Kreps48, C. Langenbruch48, T. Latham48,\nD.P. O\u2019Hanlon48, T. Pila\u02c7r48, A. Poluektov48,34, M.M. Reid48, R. Silva Coutinho48,\nC. Wallace48, M. Whitehead48, S. Easo49,38, R. Nandakumar49, A. Papanestis49,38,\nS. Ricciardi49, F.F. Wilson49, L. Carson50, P.E.L. Clarke50, G.A. Cowan50, S. Eisenhardt50,\nD. Ferguson50, D. Lambert50, H. Luo50, A.-B. Morris50, F. Muheim50, M. Needham50,\nS. Playfer50, M. Alexander51, J. Beddow51, C.-T. Dean51, L. Eklund51, D. Hynds51,\nS. Karodia51, I. Longsta\ufb0051, S. Ogilvy51, M. Pappagallo51, P. Sail51, I. Skillicorn51,\nF.J.P. Soler51, P. Spradlin51, A. A\ufb00older52, T.J.V. Bowcock52, H. Brown52, G. Casse52,\nS. Donleavy52, K. Dreimanis52, S. Farry52, R. Fay52, K. Hennessy52, D. Hutchcroft52,\nM. Liles52, B. McSkelly52, G.D. Patel52, J.D. Price52, A. Pritchard52, K. Rinnert52,\nT. Shears52, N.A. Smith52, G. Ciezarek53, S. Cunli\ufb00e53, R. Currie53, U. Egede53, P. Fol53,\nA. Golutvin53,31,38, S. Hall53, M. McCann53, P. Owen53, M. Patel53, K. Petridis53, F. Redi53,\nI. Sepp53, E. Smith53, W. Sutcli\ufb00e53, D. Websdale53, R.B. Appleby54, R.J. Barlow54, T. Bird54,\nP.M. Bj\u00f8rnstad54, S. Borghi54, D. Brett54, J. Brodzicka54, L. Capriotti54, S. Chen54,\nS. De Capua54, G. Dujany54, M. Gersabeck54, J. Harrison54, C. Hombach54, S. Klaver54,\nG. La\ufb00erty54, A. McNab54, C. Parkes54, A. Pearce54, S. Reichert54, E. Rodrigues54,\nP. Rodriguez Perez54, M. Smith54, S.-F. Cheung55, D. Derkach55, T. Evans55, R. Gauld55,\nE. Greening55, N. Harnew55, D. Hill55, P. Hunt55, N. Hussain55, J. Jalocha55, M. John55,\nO. Lupton55, S. Malde55, E. Smith55, S. Stevenson55, C. Thomas55, S. Topp-Joergensen55,\nN. Torr55, G. Wilkinson55,38, I. Counts56, P. Ilten56, M. Williams56, R. Andreassen57,\nA. Davis57, W. De Silva57, B. Meadows57, M.D. Sokolo\ufb0057, L. Sun57, J. Todd57,\nJ.E. Andrews58, B. Hamilton58, A. Jawahery58, J. Wimberley58, M. Artuso59, S. Blusk59,\nA. Borgia59, T. Britton59, S. Ely59, P. Gandini59, J. Garofoli59, B. Gui59, C. Hadjivasiliou59,\nN. Jurik59, M. Kelsey59, R. Mountain59, B.K. Pal59, T. Skwarnicki59, S. Stone59, J. Wang59,\nZ. Xing59, L. Zhang59, C. Baesso60, M. Cruz Torres60, C. G\u00a8obel60, J. Molina Rodriguez60,\nY. Xie61, D.A. Milanes62, O. Gr\u00a8unberg63, M. He\u00df63, C. Vo\u00df63, R. Waldi63, T. Likhomanenko64,\nA. Malinin64, V. Shevchenko64, A. Ustyuzhanin64, F. Martinez Vidal65, A. Oyanguren65,\n36\n\nP. Ruiz Valls65, C. Sanchez Mayordomo65, C.J.G. Onderwater66, H.W. Wilschut66, E. Pesen67\n1 Centro Brasileiro de Pesquisas F\u00b4\u0131sicas (CBPF), Rio de Janeiro, Brazil\n2 Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil\n3 Center for High Energy Physics, Tsinghua University, Beijing, China\n4 LAPP, Universit\u00b4e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France\n5 Clermont Universit\u00b4e, Universit\u00b4e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand,\nFrance\n6 CPPM, Aix-Marseille Universit\u00b4e, CNRS/IN2P3, Marseille, France\n7 LAL, Universit\u00b4e Paris-Sud, CNRS/IN2P3, Orsay, France\n8 LPNHE, Universit\u00b4e Pierre et Marie Curie, Universit\u00b4e Paris Diderot, CNRS/IN2P3, Paris,\nFrance\n9 Fakult\u00a8at Physik, Technische Universit\u00a8at Dortmund, Dortmund, Germany\n10 Max-Planck-Institut f\u00a8ur Kernphysik (MPIK), Heidelberg, Germany\n11 Physikalisches Institut, Ruprecht-Karls-Universit\u00a8at Heidelberg, Heidelberg, Germany\n12 School of Physics, University College Dublin, Dublin, Ireland\n13 Sezione INFN di Bari, Bari, Italy\n14 Sezione INFN di Bologna, Bologna, Italy\n15 Sezione INFN di Cagliari, Cagliari, Italy\n16 Sezione INFN di Ferrara, Ferrara, Italy\n17 Sezione INFN di Firenze, Firenze, Italy\n18 Laboratori Nazionali dell\u2019INFN di Frascati, Frascati, Italy\n19 Sezione INFN di Genova, Genova, Italy\n20 Sezione INFN di Milano Bicocca, Milano, Italy\n21 Sezione INFN di Milano, Milano, Italy\n22 Sezione INFN di Padova, Padova, Italy\n23 Sezione INFN di Pisa, Pisa, Italy\n24 Sezione INFN di Roma Tor Vergata, Roma, Italy\n25 Sezione INFN di Roma La Sapienza, Roma, Italy\n26 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak\u00b4ow,\nPoland\n27 AGH - University of Science and Technology, Faculty of Physics and Applied Computer\nScience, Krak\u00b4ow, Poland\n28 National Center for Nuclear Research (NCBJ), Warsaw, Poland\n29 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele,\nRomania\n30 Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia\n31 Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia\n32 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia\n33 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow,\nRussia\n34 Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University,\nNovosibirsk, Russia\n35 Institute for High Energy Physics (IHEP), Protvino, Russia\n36 Universitat de Barcelona, Barcelona, Spain\n37 Universidad de Santiago de Compostela, Santiago de Compostela, Spain\n38 European Organization for Nuclear Research (CERN), Geneva, Switzerland\n39 Ecole Polytechnique F\u00b4ed\u00b4erale de Lausanne (EPFL), Lausanne, Switzerland\n37\n\n40 Physik-Institut, Universit\u00a8at Z\u00a8urich, Z\u00a8urich, Switzerland\n41 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands\n42 Nikhef National Institute for Subatomic Physics and VU University Amsterdam,\nAmsterdam, The Netherlands\n43 NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine\n44 Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine\n45 University of Birmingham, Birmingham, United Kingdom\n46 H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom\n47 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom\n48 Department of Physics, University of Warwick, Coventry, United Kingdom\n49 STFC Rutherford Appleton Laboratory, Didcot, United Kingdom\n50 School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom\n51 School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom\n52 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom\n53 Imperial College London, London, United Kingdom\n54 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom\n55 Department of Physics, University of Oxford, Oxford, United Kingdom\n56 Massachusetts Institute of Technology, Cambridge, MA, United States\n57 University of Cincinnati, Cincinnati, OH, United States\n58 University of Maryland, College Park, MD, United States\n59 Syracuse University, Syracuse, NY, United States\n60 Pontif\u00b4\u0131cia Universidade Cat\u00b4olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil\n(associated with Institution #2)\n61 Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China\n(associated with Institution #3)\n62 Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia (associated\nwith Institution #8)\n63 Institut f\u00a8ur Physik, Universit\u00a8at Rostock, Rostock, Germany (associated with Institution\n#11)\n64 National Research Centre Kurchatov Institute, Moscow, Russia (associated with Institution\n#31)\n65 Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC, Valencia, Spain\n(associated with Institution #36)\n66 Van Swinderen Institute, University of Groningen, Groningen, The Netherlands (associated\nwith Institution #41)\n67 Celal Bayar University, Manisa, Turkey (associated with Institution #38)\na Deceased\nb Also at Universit`a di Firenze, Firenze, Italy\nc Also at Universit`a di Ferrara, Ferrara, Italy\nd Also at Universit`a della Basilicata, Potenza, Italy\ne Also at Universit`a di Modena e Reggio Emilia, Modena, Italy\nf Also at Universit`a di Milano Bicocca, Milano, Italy\ng Also at LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain\nh Also at Universit`a di Bologna, Bologna, Italy\ni Also at Universit`a di Roma Tor Vergata, Roma, Italy\nj Also at Universit`a di Genova, Genova, Italy\nk Also at Scuola Normale Superiore, Pisa, Italy\n38\n\nl Also at Politecnico di Milano, Milano, Italy\nm Also at Universidade Federal do Tri\u02c6angulo Mineiro (UFTM), Uberaba-MG, Brazil\nn Also at AGH - University of Science and Technology, Faculty of Computer Science, Electronics and\nTelecommunications, Krak\u00b4ow, Poland\no Also at Universit`a di Padova, Padova, Italy\np Also at Universit`a di Cagliari, Cagliari, Italy\nq Also at Hanoi University of Science, Hanoi, Viet Nam\nr Also at Universit`a di Bari, Bari, Italy\ns Also at Universit`a degli Studi di Milano, Milano, Italy\nt Also at Universit`a di Roma La Sapienza, Roma, Italy\nu Also at Universit`a di Pisa, Pisa, Italy\nv Also at Universit`a di Urbino, Urbino, Italy\nw Also at P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia\n39\n\n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n]\n3\n) [10\n2\nc\nCandidates / (40 MeV/\n0\n0.5\n1\n1.5\n2\n2.5\n3\n[0.,0.25)\n\u2208\nLHCb, BDT \nData\nSignal and background\n\u2212\n\u03bc\n+\n\u03bc\n\u2192\ns\n0\nB\n\u2212\n\u03bc\n+\n\u03bc\n\u2192\n0\nB\nCombinatorial background\nSemi-leptonic background\nPeaking background\n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n10\n20\n30\n40\n50\n60\n70\n80\n[0.25,0.4)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n5\n10\n15\n20\n25\n[0.4,0.5)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n[0.5,0.6)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n[0.6,0.7)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n[0.7,0.8)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n1\n2\n3\n4\n5\n6\n7\n[0.8,0.9)\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5\n5.2\n5.4\n5.6\n5.8\n6\n)\n2\nc\nCandidates / (40 MeV/\n0\n1\n2\n3\n4\n5\n6\n[0.9,1.0]\n\u2208\nLHCb, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n5\n10\n15\n20\n25\n30\n35\n40\n[0.1,0.31)\n\u2208\nCMS, 7TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n1\n2\n3\n4\n5\n6\n[0.31,1.0]\n\u2208\nCMS, 7TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n5\n10\n15\n20\n25\n30\n[0.1,0.26)\n\u2208\nCMS, 7TeV, FR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n1\n2\n3\n4\n5\n6\n7\n[0.26,1.0]\n\u2208\nCMS, 7TeV, FR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n50\n100\n150\n200\n250\n[0.1,0.23)\n\u2208\nCMS, 8TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n5\n10\n15\n20\n25\n30\n35\n[0.23,0.33)\n\u2208\nCMS, 8TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n12\n14\n[0.33,0.44)\n\u2208\nCMS, 8TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n[0.44,1.0]\n\u2208\nCMS, 8TeV, CR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n20\n40\n60\n80\n100\n120\n140\n[0.1,0.22)\n\u2208\nCMS, 8TeV, FR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n5\n10\n15\n20\n25\n[0.22,0.33)\n\u2208\nCMS, 8TeV, FR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n[0.33,0.45)\n\u2208\nCMS, 8TeV, FR, BDT \n]\n2\nc\n[GeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n4.9\n5\n5.1\n5.2\n5.3\n5.4\n5.5\n5.6\n5.7\n5.8\n5.9\n)\n2\nc\nCandidates / (40 MeV/\n0\n1\n2\n3\n4\n5\n6\n[0.45,1.0]\n\u2208\nCMS, 8TeV, FR, BDT \nExtended Data Figure 1 | Distribution of the dimuon invariant mass m\u00b5+\u00b5\u2212in each\nof the 20 categories. Superimposed on the data points in black are the combined \ufb01t (solid\nblue) and its components: the B0\ns (yellow shaded) and B0 (light-blue shaded) signal components;\nthe combinatorial background (dash-dotted green); the sum of the semi-leptonic backgrounds\n(dotted salmon); and the peaking backgrounds (dashed violet). The categories are de\ufb01ned by\nthe range of BDT values for LHCb, and for CMS, by centre-of-mass energy, by the region of\nthe detector in which the muons are detected, and by the range of BDT values. Categories for\nwhich both muons are detected in the central region of the CMS detector are denoted with CR,\nthose for which at least one muon was detected into the forward region with FR.\n40\n\n]\n2\nc\n[MeV/\n\u2212\n\u03bc\n+\n\u03bc\nm\n5000\n5200\n5400\n5600\n5800\n)\n2\nc\nCandidates / (40 MeV/\n0\n2\n4\n6\n8\n10\n12\n14\n16\nData\nSignal and background\n\u2212\n\u03bc\n+\n\u03bc\n\u2192\ns\n0\nB\n\u2212\n\u03bc\n+\n\u03bc\n\u2192\n0\nB\nCombinatorial background\nSemi-leptonic background\nPeaking background\nCMS and LHCb (LHC run I)\nExtended Data Figure 2 | Distribution of the dimuon invariant mass m\u00b5+\u00b5\u2212for the\nbest six categories. Categories are ranked according to values of S/(S + B) where S and B\nare the numbers of signal events expected assuming the SM rates and background events under\nthe B0\ns peak for a given category, respectively. The mass distribution for the six highest-ranking\ncategories, three per experiment, is shown. Superimposed on the data points in black are the\ncombined full \ufb01t (solid blue) and its components: the B0\ns (yellow shaded) and B0 (light-blue\nshaded) signal components; the combinatorial background (dash-dotted green); the sum of the\nsemi-leptonic backgrounds (dotted salmon); and the peaking backgrounds (dashed violet).\n41\n\nMuon Chambers\nSuperconducting \nSolenoid\nSilicon Trackers\nSteel \nReturn Yoke\nPreshower\nForward \nCalorimeter\nElectromagnetic \nCalorimeter\nHadron Calorimeter\nCMS Detector\n: 14,000 tonnes \n: 15.0 m\n: 28.7 m\n: 3.8 T\nWeight \nDiameter\nLength\nMagnetic field \na\nCMS experiment\nRun: 208307 Event: 997510994\nDate: 30 Nov 2012 Time: 07:19:44 GMT \nb\nExtended Data Figure 3 | Schematic of the CMS detector and event display for a\ncandidate B0\ns \u2192\u00b5+\u00b5\u2212decay at CMS. a, The CMS detector and its components; see ref. 20\nfor details. b, A candidate B0\ns \u2192\u00b5+\u00b5\u2212decay produced in proton-proton collisions at 8 TeV in\n2012 and recorded in the CMS detector. The red arched curves represent the trajectories of the\nmuons from the B0\ns decay candidate.\n42\n\nVertex\nLocator\nDipole\nMagnet\nMuon\nChambers\nTracking \nStations\nRICH1\nRICH2\nElectromagnetic\nCalorimeter\nTracker\nTuricensis\na\nHadron\nCalorimeter\nLHCb Detector\nWeight\nHeight\nLength\n: 5,600 tonnes\n: 10 m\n: 20 m\nLHCb experiment\nRun: 101412 Event: 8681643\nDate: 8 Sep 2011 Time: 16:04:18 \nb\nExtended Data Figure 4 | Schematic of the LHCb detector and event display for a\ncandidate B0\ns \u2192\u00b5+\u00b5\u2212decay at LHCb. a, The LHCb detector and its components; see\nref. 21 for details. b, A candidate B0\ns \u2192\u00b5+\u00b5\u2212decay produced in proton-proton collisions at\n7 TeV in 2011 and recorded in the LHCb detector. The proton-proton collision occurs on the\nleft-hand side, at the origin of the trajectories depicted with the orange curves. The red curves\nrepresent the trajectories of the muons from the B0\ns candidate decay.\n43\n\n]\n9\n\u2212\n [10\n)\n\u2212 \n\u00b5\n \n+\n\u00b5\n \n\u2192\n \n0\nB\nB(\n0\n0.2\n0.4\n0.6\n0.8\n CL\n\u2212\n1 \n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\nSM\nCMS and LHCb (LHC run I)\nExtended Data Figure 5 | Con\ufb01dence level as a function of the B(B0 \u2192\u00b5+\u00b5\u2212)\nhypothesis. Value of 1 \u2212CL, where CL is the con\ufb01dence level obtained with the Feldman\u2013\nCousins procedure, as a function of B(B0 \u2192\u00b5+\u00b5\u2212) is shown in logarithmic scale. The points\nmark the computed 1\u2212CL values and the curve is their spline interpolation. The dark and light\n(cyan) areas de\ufb01ne the two-sided \u00b11\u03c3 and \u00b12\u03c3 con\ufb01dence intervals for the branching fraction,\nwhile the dashed horizontal line de\ufb01nes the con\ufb01dence level for the 3\u03c3 one-sided interval. The\ndashed (grey) curve shows the 1 \u2212CL values computed from the one-dimensional \u22122\u2206lnL\ntest statistic using Wilks\u2019 theorem. Deviations between these con\ufb01dence level values and those\nfrom the Feldman\u2013Cousins procedure30 illustrate the degree of approximation implied by the\nasymptotic assumptions inherent to Wilks\u2019 theorem29.\n44\n\na\nb\nc\nSM\ns\n0\nB\nS\n0\n0.5\n1\n1.5\n2\n2.5\nSM\n0\nB\nS\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n68.27%\n95.45%\n99.73%\n5\n\u2212\n10\n\u00d7\n6.3\n\u2212\n1\n7\n\u2212\n10\n\u00d7\n5.7\n\u2212\n1\n9\n\u2212\n10\n\u00d7\n2\n\u2212\n1\nSM\nCMS and LHCb (LHC run I)\na\nSM\ns\n0\nB\nS\n0\n0.5\n1\n1.5\n2\n2.5\nL\nln\n\u0394\n2\n\u2212\n0\n10\n20\n30\n40\nSM\nb\nSM\n0\nB\nS\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nL\nln\n\u0394\n2\n\u2212\n0\n2\n4\n6\n8\n10\nSM\nc\nExtended Data Figure 6 | Likelihood contours for the ratios of the branching frac-\ntions with respect to their SM prediction, in the SB0\nSM versus SB0\ns\nSM plane. a, The\n(black) cross marks the central value returned by the \ufb01t. The SM point is shown as the (red)\nsquare located, by construction, at SB0\nSM = SB0\ns\nSM = 1. Each contour encloses a region approxi-\nmately corresponding to the reported con\ufb01dence level. The SM branching fractions are assumed\nuncorrelated to each other, and their uncertainties are accounted for in the likelihood contours.\nb, c, Variations of the test statistic \u22122\u2206lnL for SB0\ns\nSM and SB0\nSM are shown in b and c, respectively.\nThe SM is represented by the (red) vertical lines. The dark and light (cyan) areas de\ufb01ne the\n\u00b11\u03c3 and \u00b12\u03c3 con\ufb01dence intervals, respectively.\n45\n\nYear\n1985\n1990\n1995\n2000\n2005\n2010\n2015\nLimit (90% CL) or BF measurement\n10\n\u2212\n10\n9\n\u2212\n10\n8\n\u2212\n10\n7\n\u2212\n10\n6\n\u2212\n10\n5\n\u2212\n10\n4\n\u2212\n10\n\u2212\n\u00b5\n+\n\u00b5\n \n\u2192\n \n0\ns\nSM: B\n\u2212\n\u00b5\n+\n\u00b5\n \n\u2192\n \n0\nSM: B\nD0\nL3\nCDF\nUA1\nARGUS\nCLEO\nCMS+LHCb\nATLAS\nCMS\nLHCb\nBaBar\nBelle\n2012\n2013\n2014\n10\n\u2212\n10\n9\n\u2212\n10\n8\n\u2212\n10\nExtended Data Figure 7 | Search for the B0\ns \u2192\u00b5+\u00b5\u2212and B0 \u2192\u00b5+\u00b5\u2212decays,\nreported by 11 experiments spanning more than three decades, and by the present\nresults. Markers without error bars denote upper limits on the branching fractions at 90%\ncon\ufb01dence level, while measurements are denoted with errors bars delimiting 68% con\ufb01dence\nintervals. The horizontal lines represent the SM predictions for the B0\ns \u2192\u00b5+\u00b5\u2212and B0 \u2192\u00b5+\u00b5\u2212\nbranching fractions1; the blue (red) lines and markers relate to the B0\ns \u2192\u00b5+\u00b5\u2212(B0 \u2192\u00b5+\u00b5\u2212)\ndecay. Data (see key) are from refs 17,18,31\u201360 ; for details see Methods. Inset, magni\ufb01ed view\nof the last period in time.\n46\n", "CERN-OPEN-2008-020\nDecember 2008\nExpected Performance of the ATLAS Experiment\nDetector, Trigger and Physics\nThe ATLAS Collaboration\nA detailed study is presented of the expected performance of the\nATLAS detector.\nThe reconstruction of tracks, leptons, photons,\nmissing energy and jets is investigated, together with the performance\nof b-tagging and the trigger.\nThe physics potential for a variety of\ninteresting physics processes, within the Standard Model and beyond, is\nexamined. The study comprises a series of notes based on simulations\nof the detector and physics processes, with particular emphasis given to\nthe data expected from the \ufb01rst years of operation of the LHC at CERN.\n\n\nDisplay of a high-pT H \u2192ZZ\u2217\u2192ee\u00b5\u00b5 decay (mH = 130 GeV), after full simulation and reconstruction in the\nATLAS detector. The four leptons and the recoiling jet with ET = 135 GeV are clearly visible. Hits in the Inner\nDetector are shown in green for the four reconstructed leptons, both for the precision tracker (pixel and silicon\nmicro-strip detectors) at the inner radii and for the transition radiation tracker at the outer radii. The other tracks\nreconstructed with pT > 0.5 GeV in the Inner Detector are shown in blue. The two electrons are depicted as\nreconstructed tracks in yellow and their energy deposits in each layer of the electromagnetic LAr calorimeter\nare shown in red. The two muons are shown as combined reconstructed tracks in orange, with the hit strips in\nthe resistive-plate chambers and the hit drift tubes in the monitored drift-tube chambers visible as white lines\nin the barrel muon stations. The energy deposits from the muons in the barrel tile calorimeter can also be seen\nin purple.\n\nContents\nThe ATLAS Collaboration\nvii\nAcknowledgments\nxxiv\nINTRODUCTION\n1\nPreface\n2\nCross-Sections, Monte Carlo Simulations and Systematic Uncertainties\n3\nPERFORMANCE\n15\nTracking\n15\nThe Expected Performance of the Inner Detector\n16\nElectrons and Photons\n43\nCalibration and Performance of the Electromagnetic Calorimeter\n44\nReconstruction and Identi\ufb01cation of Electrons\n72\nReconstruction and Identi\ufb01cation of Photons\n94\nReconstruction of Photon Conversions\n112\nReconstruction of Low-Mass Electron Pairs\n141\nMuons\n161\nMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte Carlo Samples\n162\nMuons in the Calorimeters: Energy Loss Corrections and Muon Tagging\n185\nIn-Situ Determination of the Performance of the Muon Spectrometer\n208\nTau Leptons\n229\nReconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays\n230\nJets and Missing Transverse Energy\n261\nJet Reconstruction Performance\n262\nDetector Level Jet Corrections\n298\nE/p Performance for Charged Hadrons\n327\nJet Energy Scale: In-situ Calibration Strategies\n335\nMeasurement of Missing Tranverse Energy\n368\nb-Tagging\n397\nb-Tagging Performance\n398\nVertex Reconstruction for b-Tagging\n432\nEffects of Misalignment on b-Tagging\n465\nSoft Muon b-Tagging\n481\nSoft Electron b-Tagging\n490\nb-Tagging Calibration with t\u00aft Events\n504\nb-Tagging Calibration with Jet Events\n534\nTrigger\n549\nTrigger for Early Running\n550\nHLT Track Reconstruction Performance\n565\nData Preparation for the High-Level Trigger Calorimeter Algorithms\n584\niv\n\nTau Trigger: Performance and Menus for Early Running\n592\nPhysics Performance Studies and Strategy of the Electron and Photon Trigger Selection\n619\nPerformance of the Muon Trigger Slice with Simulated Data\n647\nHLT b-Tagging Performance and Strategies\n683\nOverview and Performance Studies of Jet Identi\ufb01cation in the Trigger System\n697\nPHYSICS\n723\nStandard Model\n723\nA Study of Minimum Bias Events\n724\nElectroweak Boson Cross-Section Measurements\n747\nProduction of Jets in Association with Z Bosons\n777\nMeasurement of the W Boson Mass with Early Data\n788\nForward-Backward Asymmetry in pp \u2192Z0/\u03b3 \u2192e+e\u2212Events\n814\nDiboson Physics Studies\n833\nTop Quark\n869\nTop Quark Physics\n870\nTriggering Top Quark Events\n884\nJets from Light Quarks in t\u00aft Events\n898\nDetermination of the Top Quark Pair Production Cross-Section\n925\nProspect for Single Top Quark Cross-Section Measurements\n949\nTop Quark Mass Measurements\n978\nTop Quark Properties\n1003\nB-Physics\n1039\nIntroduction to B-Physics\n1040\nPerformance Study of the Level-1 Di-Muon Trigger\n1044\nTriggering on Low-pT Muons and Di-Muons for B-Physics\n1053\nHeavy Quarkonium Physics with Early Data\n1083\nProduction Cross-Section Measurements and Study of the Properties of the Exclusive B+ \u2192\nJ/\u03c8K+ Channel\n1111\nPhysics and Detector Performance Measurements for B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6 with Early\nData\n1121\nPlans for the Study of the Spin Properties of the \u039bb Baryon Using the Decay Channel \u039bb \u2192\nJ/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212)\n1132\nStudy of the Rare Decay B0\ns \u2192\u00b5+\u00b5\u2212\n1154\nTrigger and Analysis Strategies for B0\ns Oscillation Measurements in Hadronic Decay Channels\n1167\nHiggs Boson\n1197\nIntroduction on Higgs Boson Searches\n1198\nProspects for the Discovery of the Standard Model Higgs Boson Using the H\u2192\u03b3\u03b3 Decay\n1212\nSearch for the Standard Model H \u2192ZZ\u2217\u21924l\n1243\nSearch for the Standard Model Higgs Boson via Vector Boson Fusion Production Process in\nthe Di-Tau Channels\n1271\nHiggs Boson Searches in Gluon Fusion and Vector Boson Fusion using the H \u2192WW Decay\nMode\n1306\nSearch for t\u00aftH(H \u2192b\u00afb)\n1333\nStudy of Signal and Background Conditions in t\u00aftH,H \u2192WW \u2217and WH,H \u2192WW \u2217\n1364\nDiscovery Potential of h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1374\nSearch for the Neutral MSSM Higgs Bosons in the Decay Channel A/H/h \u2192\u00b5+\u00b5\u2212\n1391\nSensitivity to an Invisibly Decaying Higgs Boson\n1419\nCharged Higgs Boson Searches\n1451\nStatistical Combination of Several Important Standard Model Higgs Boson Search Channels\n1480\nv\n\nSupersymmetry\n1513\nSupersymmetry Searches\n1514\nData-Driven Determinations of W, Z and Top Backgrounds to Supersymmetry\n1525\nEstimation of QCD Backgrounds to Searches for Supersymmetry\n1562\nProspects for Supersymmetry Discovery Based on Inclusive Searches\n1589\nMeasurements from Supersymmetric Events\n1617\nMulti-Lepton Supersymmetry Searches\n1643\nSupersymmetry Signatures with High-pT Photons or Long-Lived Heavy Particles\n1660\nExotic Processes\n1695\nDilepton Resonances at High Mass\n1696\nLepton plus Missing Transverse Energy Signals at High Mass\n1726\nSearch for Leptoquark Pairs and Majorana Neutrinos from Right-Handed W Boson Decays in\nDilepton-Jets Final States\n1750\nVector Boson Scattering at High Mass\n1769\nDiscovery Reach for Black Hole Production\n1803\nvi\n\nThe ATLAS Collaboration\nG. Aad81, E. Abat18,\u2217, B. Abbott108, J. Abdallah11, A.A. Abdelalim48, A. Abdesselam115,\nO. Abdinov10, B. Abi109, M. Abolins86, H. Abramowicz148, B.S. Acharya158a,158b, D.L. Adams24,\nT.N. Addy55, C. Adorisio36a,36b, P. Adragna73, T. Adye126, J.A. Aguilar-Saavedra121a, M. Aharrouche79,\nS.P. Ahlen21, F. Ahles47, A. Ahmad144, H. Ahmed2, G. Aielli130a,130b, T. Akdogan18, T.P.A. \u02daAkesson77,\nG. Akimoto150, M.S. Alam1, M.A. Alam74, J. Albert163, S. Albrand54, M. Aleksa29, I.N. Aleksandrov63,\nF. Alessandria87a,87b, C. Alexa25a, G. Alexander148, G. Alexandre48, T. Alexopoulos9, M. Alhroob20,\nG. Alimonti87a, J. Alison 117, M. Aliyev10, P.P. Allport71, S.E. Allwood-Spiers52, A. Aloisio100a,100b,\nR. Alon164, A. Alonso77, J. Alonso14, M.G. Alviggi100a,100b, K. Amako64, P. Amaral29, C. Amelung22,\nV.V. Ammosov125, A. Amorim121b, G. Amor\u00b4os161, N. Amram148, C. Anastopoulos136, C.F. Anders57a,\nK.J. Anderson30, A. Andreazza87a,87b, V. Andrei57a, M-L. Andrieux54, X.S. Anduaga68, F. Anghinol\ufb0129,\nA. Antonaki8, M. Antonelli46, S. Antonelli19a,19b, B. Antunovic41, F.A. Anulli129a, G. Arabidze8,\nI. Aracena140, Y. Arai64, A.T.H. Arce14, J.P. Archambault28, S. Arfaoui29, J-F. Arguin14,\nT. Argyropoulos9, E. Arik18,\u2217, M. Arik18, A.J. Armbruster85, O. Arnaez4, C. Arnault112,\nA. Artamonov93, D. Arutinov20, M. Asai140, S. Asai150, S. Ask80, B. \u02daAsman142, D. Asner28,\nL. Asquith75, K. Assamagan24, A. Astbury163, A. Astvatsatourov51, T. Atkinson84, G. Atoian168,\nB. Auerbach168, E. Auge112, K. Augsten124, M.A. Aurousseau4, N. Austin71, G. Avolio157,\nR. Avramidou9, A. Axen162, C. Ay53, G. Azuelos91,a, Y. Azuma150, M.A. Baak29, G. Baccaglioni87a,87b,\nC. Bacci131a,131b, H. Bachacou133, K. Bachas149, M. Backes48, E. Badescu25a, P. Bagnaia129a,129b,\nY. Bai32,b, D.C. Bailey 152, J.T. Baines126, O.K. Baker168, F. Baltasar Dos Santos Pedrosa29, E. Banas38,\nS. Banerjee163, D. Ban\ufb0187a,87b, A. Bangert97, V. Bansal120, S.P. Baranov92, S. Baranov5,\nA. Barashkou63, T.B. Barber27, E.L. Barberio84, D. Barberis49a,49b, M.B. Barbero20, D.Y. Bardin63,\nT. Barillari97, M. Barisonzi41, T. Barklow140, N.B. Barlow27, B.M. Barnett126, R.M. Barnett14,\nS. Baron29, A. Baroncelli131a, A.J. Barr115, F. Barreiro78, J. Barreiro Guimar\u02dcaes da Costa56,\nP. Barrillon112, R. Bartoldus140, D. Bartsch20, J. Bastos121b, R.L. Bates52, J.R. Batley27, A. Battaglia16,\nM. Battistin29, F. Bauer133, M. Bazalova122, B. Beare152, P.H. Beauchemin115, R.B. Beccherle49a,\nN. Becerici18, P. Bechtle41, G.A. Beck73, H.P. Beck16, M. Beckingham47, K.H. Becks167,\nI. Bedajanek124, A.J. Beddall18,c, A. Beddall18,c, P. Bedn\u00b4ar141, V.A. Bednyakov63, C. Bee81,\nS. Behar Harpaz147, P.K. Behera140,d, M. Beimforde97, C. Belanger- Champagne159, P.J. Bell80,\nW.H. Bell48, G. Bella148, L. Bellagamba19a, F. Bellina29, M. Bellomo116a, A. Belloni56, K. Belotskiy94,\nO. Beltramello29, S. Ben Ami147, O. Benary148, D. Benchekroun132a, M. Bendel79, B.H. Benedict157,\nN. Benekos160, Y. Benhammou148, G.P. Benincasa121b, D.P. Benjamin44, M. Benoit112,\nJ.R. Bensinger22, K. Benslama127, S. Bentvelsen103, M. Beretta 46, D. Berge29,\nE. Bergeaas Kuutmann142, N. Berger4, F. Berghaus163, E. Berglund48, J. Beringer14, K. Bernardet81,\nP. Bernat112, R. Bernhard47, C. Bernius75, T. Berry74, A. Bertin19a,19b, N. Besson133, S. Bethke97,\nR.M. Bianchi47, M. Bianco70a,70b, O. Biebel96, J. Biesiada14, M. Biglietti100a,100b, H. Bilokon46,\nS. Binet14, A. Bingul18,c, C. Bini129a,129b, C. Biscarat173, M. Bischofberger84, U. Bitenc47,\nK.M. Black56, R.E. Blair5, G. Blanchot29, C. Blocker22, J. Blocki38, A. Blondel48, W. Blum79,\nU. Blumenschein53, C. Boaretto129a,129b, G.J. Bobbink103, A. Bocci44, B. Bodine 135, J. Boek167,\nN. Boelaert77, S. B\u00a8oser75, J.A. Bogaerts29, A. Bogouch88, C. Bohm142, J. Bohm122, V. Boisvert74,\nT. Bold157, V. Boldea25a, V.G. Bondarenko94, M. Bondioli157, M. Boonekamp133, C.N. Booth136,\nP.S.L. Booth71,\u2217, J.R.A. Booth17, A. Borisov125, G. Borissov69, I. Borjanovic70a, S. Borroni129a,129b,\nK. Bos103, D. Boscherini19a, M. Bosman11, M. Bosteels29, H. Boterenbrood103, J. Bouchami91,\nJ. Boudreau120, E.V. Bouhova-Thacker69, C. Boulahouache120, C. Bourdarios112, J. Boyd29,\nI.R. Boyko63, A. Braem29, P. Branchini131a, G.W. Brandenburg56, A. Brandt7, O. Brandt115,\nU. Bratzler151, J.E. Brau111, H.M. Braun167, B. Brelier91,e, J. Bremer29, R. Brenner159, S. Bressler147,\nD. Breton112, N.D. Brett115, D. Britton52, F.M. Brochu27, I. Brock20, R. Brock86, E. Brodet148,\nF. Broggi87a,87b, G. Brooijmans34, W.K. Brooks31b, E. Brubaker30, P.A. Bruckman de Renstrom38,\nvii\n\nD. Bruncko141, R. Bruneliere47, S. Brunet41, A. Bruni19a, G. Bruni19a, M. Bruschi19a, T. Buanes13,\nF.B. Bucci48, P. Buchholz138, A.G. Buckley75,f , I.A. Budagov63, V. B\u00a8uscher20, L. Bugge114, F. Bujor29,\nO. Bulekov94, M. Bunse42, T. Buran 114, H. Burckhart29, S. Burdin71, S. Burke126, E. Busato33,\nC.P. Buszello159, F. Butin29, B. Butler140, J.M. Butler21, C.M. Buttar52, J.M. Butterworth75, T. Byatt75,\nS. Cabrera Urb\u00b4an161, D. Caforio19a,19b, O. Cakir3, P. Cala\ufb01ura14, G. Calderini76, R. Calkins5,\nL.P. Caloba23a, R. Caloi129a,129b, D. Calvet33, P. Camarri130a,130b, M. Cambiaghi116a,116b,\nD. Cameron114, F. Campabadal Segura161, S. Campana29, M. Campanelli75, V. Canale100a,100b,\nJ. Cantero78, M.D.M. Capeans Garrido29, I. Caprini25a, M. Caprini25a, M. Capua36a,36b, R. Caputo144,\nC. Caramarcu25a, R. Cardarelli130a, T. Carli29, G. Carlino100a, L. Carminati87a,87b, B. Caron2,g,\nS. Caron47, S. Carron Montero152, A.A. Carter73, J.R. Carter27, J. Carvalho121b, D. Casadei105,\nM.P. Casado 11, M. Cascella119a,119b, C. Caso49a,49b,\u2217, A.M. Castaneda Hernadez165,\nE. Castaneda Miranda165, V. Castillo Gimenez161, N.F. Castro121a, G. Cataldi70a, A. Catinaccio29,\nJ.R. Catmore69, A. Cattai29, G. Cattani130a,130b, S. Caughron34, D. Cauz158a,158c, P. Cavalleri76,\nD. Cavalli87a, M. Cavalli-Sforza11, V. Cavasinni119a,119b, A. Cazzato70a,70b, F. Ceradini131a,131b,\nA.S. Cerqueira 23a, A. Cerri29, L. Cerrito73, F. Cerutti46, S.A. Cetin18,h, F. Cevenini100a,100b,\nA.C. Chafaq132a, D. Chakraborty5, J.D. Chapman27, J.W. Chapman85, E.C. Chareyre76,\nD.G. Charlton17, S.C. Chatterjii20, S. Cheatham69, S. Chekanov5, S.V. Chekulaev153a, G.A. Chelkov63,\nH. Chen24, T. Chen32, X. Chen165, S. Cheng32, T.L. Cheng74, A. Cheplakov52, V.F. Chepurnov63,\nR. Cherkaoui El Moursli132d, V. Tcherniatine24, D. Chesneanu25a, E. Cheu6, S.L. Cheung152,\nL. Chevalier133, F. Chevallier133, V. Chiarella46, G. Chiefari100a,100b, L. Chikovani50, J.T. Childers57a,\nA. Chilingarov69, G. Chiodini70a, S. Chouridou134, D. Chren124, I.A. Christidi149, A. Christov47,\nD. Chromek-Burckhart29, M.L. Chu146, J. Chudoba122, G. Ciapetti129a,129b, A.K. Ciftci3, R. Ciftci3,\nV. Cindro72, M.D. Ciobotaru157, C. Ciocca19a,19b, A. Ciocio14, M. Cirilli85, M. Citterio87a, A. Clark48,\nW. Cleland120, J.C. Clemens81, B. Clement54, C. Cl\u00b4ement142, D. Clements52, Y. Coadou29,\nM. Cobal158a,158c, A. Coccaro49a,49b, J. Cochran62, S. Coelli87a,87b, J. Coggeshall160, E. Cogneras16,\nC.D. Cojocaru28, J. Colas4, B. Cole34, A.P. Colijn103, C. Collard112, N.J. Collins17, C. Collins-Tooth52,\nJ. Collot54, G. Colon82, R. Coluccia70a,70b, P. Conde Mui\u02dcno121b, E. Coniavitis159, M. Consonni102,\nS. Constantinescu25a, C. Conta 116a,116b, F. Conventi 100a,i, J. Cook29, M. Cooke34, B.D. Cooper73,\nN.J. Cooper-Smith74, K. Copic34, T. Cornelissen29, M. Corradi19a, F.C. Corriveau83,j,\nA. Corso-Radu157, A. Cortes-Gonzalez160, G. Costa87a, M.J. Costa161, D. Costanzo136, T. Costin30,\nD. C\u02c6ot\u00b4e41, R. Coura Torres23a, L. Courneyea163, G. Cowan74, C.C. Cowden27, B.E. Cox80,\nK. Cranmer105, J. Cranshaw5, M. Cristinziani20, G. Crosetti36a,36b, R.C. Crupi70a,70b,\nS. Cr\u00b4ep\u00b4e-Renaudin54, C.-M. Cuciuc25a, C. Cuenca Almenar157, M. Curatolo46, C.J. Curtis17,\nP. Cwetanski60, Z. Czyczula35, S. D\u2019Auria52, M. D\u2019Onofrio11, A. D\u2019Orazio97,\nA. Da Rocha Gesualdi Mello23a, P.V.M. Da Silva23a, C.V. Da Via80, W. Dabrowski37, T. Dai85,\nC. Dallapiccola82, S.J. Dallison126, C.H. Daly135, M. Dam35, H.O. Danielsson29, D. Dannheim29,\nV. Dao48, G. Darbo49a, W.D. Davey84, T. Davidek123, N. Davidson84, R. Davidson69, A.R. Davison75,\nI. Dawson136, J.W. Dawson5, R.K. Daya39, K. De7, R. de Asmundis100a, S. De Castro19a,19b,\nP.E. De Castro Faria Salgado29, S. De Cecco76, N. De Groot102, P. de Jong103, E. De La Cruz-Burelo85,\nC. De La Taille112, L. De Mora69, M. De Oliveira Branco29, D. De Pedis129a, A. De Salvo129a,\nU. De Sanctis87a,87b, A. De Santo74, J.B. De Vivie De Regie112, G. De Zorzi129a,129b, S. Dean75,\nG. Dedes97, D.V. Dedovich63, P.O. Defay33, J. Degenhardt 117, M. Dehchar115, C. Del Papa158a,158c,\nJ. Del Peso78, T. Del Prete119a,119b, A. Dell\u2019Acqua29, L. Dell\u2019Asta87a,87b, M. Della Pietra100a,i,\nD. della Volpe100a,100b, M. Delmastro29, N. Delruelle29, P.A. Delsart54, S. Demers140, M. Demichev63,\nB. Demirk\u00a8oz29, W. Deng24, S.P. Denisov125, C. Dennis115, F. Derue76, P. Dervan71, K.K. Desch20,\nP.O. Deviveiros152, A. Dewhurst69, R. Dhullipudi24,k, A. Di Ciaccio130a,130b, L. Di Ciaccio4,\nA. Di Domenico129a,129b, A. Di Girolamo29, B. Di Girolamo 29, S. Di Luise131a,131b, A. Di Mattia86,\nR. Di Nardo130a,130b, A. Di Simone130a,130b, R. Di Sipio19a,19b, M.A. Diaz31a, E.B. Diehl85, J. Dietrich47,\nTHE ATLAS COLLABORATION\nviii\n\nS. Diglio131a,131b, K. Dindar Yagci39, D.J. Dingfelder47, C. Dionisi129a,129b, P. Dita 25a, S. Dita 25a,\nF. Dittus29, F. Djama81, R. Djilkibaev105, T. Djobava50, M.A.B. do Vale23a, M. Dobbs83,\nR. Dobinson 29,\u2217, D. Dobos29, E. Dobson115, M. Dobson29, O.B. Dogan18,\u2217, T. Doherty52, Y. Doi64,\nJ. Dolejsi123, I. Dolenc72, Z. Dolezal123, B.A. Dolgoshein94, M. Donega117, J. Donini54,\nT. Donszelmann136, J. Dopke167, D.E. Dorfan134, A. Doria100a, A. Dos Anjos165, M. Dosil11,\nA. Dotti119a,119b, M.T. Dova68, A. Doxiadis103, A.T. Doyle52, J.D. Dragic74, Z. Drasal123,\nN. Dressnandt117, C. Driouichi35, M. Dris 9, J. Dubbert97, E. Duchovni164, G. Duckeck96,\nA. Dudarev29, M. D\u00a8uhrssen 47, I.P. Duerdoth80, L. Du\ufb02ot112, M-A. Dufour83, M. Dunford30,\nA. Duperrin81, H. Duran Yildiz3,l, A. Dushkin22, R. Dux\ufb01eld136, M. Dwuznik37, M. D\u00a8uren51,\nW.L. Ebenstein44, S. Eckert47, S. Eckweiler79, K. Edmonds20, P. Eerola77,m, K. Egorov60,\nW. Ehrenfeld41,n, T. Ehrich97, T. Eifert48, G. Eigen13, K. Einsweiler14, E. Eisenhandler73, T. Ekelof159,\nM. El Kacimi4, M. Ellert159, S. Elles4, K. Ellis73, N. Ellis29, J. Elmsheuser 96, M. Elsing29, R. Ely14,\nD. Emeliyanov126, R. Engelmann144, A. Engl96, B. Epp61, A. Eppig 85, V.S. Epshteyn93, J. Erdmann97,\nA. Ereditato16, D. Eriksson142, I. Ermoline86, J. Ernst1, E. Ernst24, J. Ernwein133, D. Errede160,\nS. Errede160, M. Escalier112, C. Escobar161, X. Espinal Curull11, B. Esposito46, F. Etienne81,\nA.I. Etienvre133, E. Etzion148, H. Evans60, L. Fabbri19a,19b, C. Fabre29, P. Faccioli19a,19b, K. Facius35,\nR.M. Fakhrutdinov125, S. Falciano129a, A.C. Falou112, Y. Fang165, M. Fanti87a,87b, A. Farbin7,\nA. Farilla131a, J. Farley144, T. Farooque152, S.M. Farrington115, P. Farthouat29, F. Fassi161,\nP. Fassnacht29, D. Fassouliotis8, B. Fatholahzadeh152, L. Fayard112, F. Fayette76, R. Febbraro33,\nP. Federic141, O.L. Fedin118, I. Fedorko29, L. Feligioni81, C. Feng32, E.J. Feng30, A.B. Fenyuk125,\nJ. Ferencei141, J. Ferland91, W. Fernando106, S. Ferrag52, A. Ferrari159, P. Ferrari103, R. Ferrari116a,\nA. Ferrer161, M.L. Ferrer46, D. Ferrere48, C. Ferretti85, M. Fiascaris115, F. Fiedler79, A. Filip\u02c7ci\u02c7c72,\nA. Filippas9, F. Filthaut102, M. Fincke-Keeler163, L. Fiorini11, A. Firan39, G. Fischer41, M.J. Fisher106,\nH.F. Flacher29, M. Flechl159, I. Fleck138, J. Fleckner79, P. Fleischmann133, S. Fleischmann20,\nC.M. Fleta Corral161, T. Flick167, L.R. Flores Castillo165, M.J. Flowerdew71, F. F\u00a8ohlisch57a, M. Fokitis9,\nT. Fonseca Martin74, D.A. Forbush135, A. Formica133, A. Forti80, J.M. Foster80, D. Fournier112,\nA. Foussat29, A.J. Fowler44, K.F. Fowler 134, H. Fox69, P. Francavilla119a,119b, S. Franchino116a,116b,\nD. Francis29, S. Franz29, M. Fraternali116a,116b, S. Fratina117, J. Freestone80, R. Froeschl29,\nD. Froidevaux29, J.A. Frost27, C. Fukunaga151, E. Fullana Torregrosa5, J. Fuster161, C. Gabaldon78,\nO.G. Gabizon164, T. Gadfort34, S. Gadomski48,o, G. Gagliardi49a,49b, P. Gagnon60, E.J. Gallas115,\nM.V. Gallas29, B.J. Gallop126, E. Galyaev40, K.K. Gan106, Y.S. Gao140,p, A. Gaponenko14,\nM. Garcia-Sciveres14, C. Garc\u00b4\u0131a161, J.E. Garc\u00b4\u0131a Navarro48, R.W. Gardner30, N. Garelli49a,49b,\nH. Garitaonandia103, V.G. Garonne29, C. Gatti46, G. Gaudio116a, O. Gaumer48, P. Gauzzi129a,129b,\nI.L. Gavrilenko92, C. Gay162, G.G. Gaycken20, J-C. Gayde29, E.N. Gazis9, C.N.P. Gee126,\nCh. Geich-Gimbel20, K. Gellerstedt142, C. Gemme49a, M.H. Genest96, S. Gentile129a,129b, F. Georgatos9,\nS. George74, P. Gerlach167, C. Geweniger57a, H. Ghazlane132d, P. Ghez4, N. Ghodbane33,\nB. Giacobbe19a, S. Giagu129a,129b, V. Giangiobbe119a,119b, F. Gianotti29, B. Gibbard24, A. Gibson152,\nS.M. Gibson115, L.M. Gilbert115, M. Gilchriese14, V. Gilewsky89, A.R. Gillman126, D.M. Gingrich2,g,\nJ. Ginzburg148, N. Giokaris8, M.P. Giordani 158a,158c, P. Giovannini97, P.F. Giraud29, P. Girtler61,\nD. Giugni87a, P. Giusti19a, B.K. Gjelsten114, L.K. Gladilin95, C. Glasman78, A. Glazov41,\nK.W. Glitza167, G.L. Glonti63, K.G. Gnanvo73, J.G. Godfrey139, J. Godlewski29, T. G\u00a8opfert43,\nC. G\u00a8ossling42, T. G\u00a8ottfert97, V.G. Goggi116a,116b, S. Goldfarb85, D. Goldin39, T. Golling14,\nN.P. Gollub29, A. Gomes121b, R. Gonc\u00b8alo74, C. Gong32, S. Gonz\u00b4alez de la Hoz161,\nM.L. Gonzalez Silva26, S. Gonz\u00b4alez-Sevilla48, J.J. Goodson144, L. Goossens29, P.A. Gorbounov152,\nH. Gordon24, I. Gorelov101, G. Gor\ufb01ne167, B. Gorini29, E. Gorini70a,70b, A. Gori\u02c7sek72, E. Gornicki38,\nS.A. Gorokhov125, S.V. Goryachev125, V.N. Goryachev125, B. Gosdzik41, M. Gosselink103,\nM.I. Gostkin63, I. Gough Eschrich157, M. Gouighri132a, D. Goujdami132a, M. Goulette29,\nA.G. Goussiou135, S. Gowdy140, C. Goy4, I. Grabowska-Bold157, P. Grafstr\u00a8om29, K-J. Grahn143,\nTHE ATLAS COLLABORATION\nix\n\nL. Granado Cardoso121b, F. Grancagnolo70a, S. Grancagnolo70a,70b, V. Gratchev118, H.M. Gray34,q,\nJ.A. Gray144, E. Graziani131a, B. Green74, Z.D. Greenwood24,k, I.M. Gregor41, E. Griesmayer45,\nN. Grigalashvili63, A.A. Grillo134, K. Grimm144, Y.V. Grishkevich95, L.S. Groer152, J. Grognuz29,\nM. Groh97, M. Groll79, E. Gross164, J. Grosse-Knetter53, J. Groth-Jensen77, C. Gruse25a, K. Grybel138,\nV.J. Guarino5, C. Guicheney33, A.G. Guida70a,70b, T. Guillemin4, J. Gunther122, B. Guo152, A. Gupta30,\nY. Gusakov63, P. Gutierrez108, N.G. Guttman148, O. Gutzwiller29, C. Guyot133, C. Gwenlan115,\nC.B. Gwilliam71, A. Haas34, S. Haas29, C. Haber14, R. Hackenburg24, H.K. Hadavand39, D.R. Hadley17,\nR. H\u00a8artel97, Z. Hajduk38, H. Hakobyan48, H. Hakobyan169, R.H. Hakobyan2, J. Haller41,n,\nK. Hamacher167, A. Hamilton48, H. Han32, L. Han 32, K. Hanagaki113, M. Hance117, C. Handel79,\nP. Hanke57a, J.R. Hansen35, J.B. Hansen35, J.D. Hansen35, P.H. Hansen35, T. Hansl-Kozanecka134,\nP. Hansson143, K. Hara154, G.A. Hare134, T. Harenberg167, R.D. Harrington21, O.B. Harris75,\nO.M. Harris135, J.C. Hart126, J. Hartert47, F. Hartjes103, T. Haruyama64, A. Harvey55, S. Hasegawa99,\nY. Hasegawa137, K. Hashemi22, S. Hassani133, M. Hatch29, F. Haug29, S. Haug16, M. Hauschild29,\nR. Hauser86, M. Havranek122, R.J. Hawkings29, D. Hawkins157, T. Hayakawa65, H.S. Hayward71,\nS.J. Haywood126, M. He32, S.J. Head80, V. Hedberg77, L. Heelan28, B. Heinemann14,\nF.E.W. Heinemann115, M. Heldmann47, S. Hellman142, C. Helsens133, R.C.W. Henderson69,\nM. Henke57a, A.M. Henriques Correia29, S. Henrot-Versille112, T. Hen\u00df167, A.D. Hershenhorn147,\nG. Herten47, R. Hertenberger96, L. Hervas29, N.P. Hessey103, A. Hidvegi142, E. Hig\u00b4on-Rodriguez161,\nD. Hill5,\u2217, J.C. Hill27, K.H. Hiller41, S.J. Hillier17, I. Hinchliffe14, C. Hinkelbein57b, F. Hirsch42,\nJ. Hobbs144, N.H. Hod148, M.C. Hodgkinson136, P. Hodgson136, A. Hoecker29, M.R. Hoeferkamp101,\nJ. Hoffman39, D. Hoffmann81, M.H. Hohlfeld20, S.O. Holmgren142, T. Holy124, Y. Homma65,\nP. Homola124, T. Horazdovsky124, T. Hori65, C. Horn140, S. Horner47, S. Horvat97, J-Y. Hostachy54,\nS. Hou146, M.A. Houlden71, A. Hoummada132a, J. Hrivnac112, I. Hruska122, T. Hryn\u2019ova4, P.J. Hsu168,\nG.S. Huang108, J. Huang157, Z. Hubacek124, F. Hubaut81, F. Huegging20, E.W. Hughes34, G. Hughes69,\nR.E. Hughes-Jones80, P. Hurst56, M. Hurwitz30, T. Huse 114, N. Huseynov10, J. Huston86, J. Huth56,\nG. Iacobucci100a, M. Ibbotson80, I. Ibragimov138, R. Ichimiya65, L. Iconomidou-Fayard112, J. Idarraga91,\nP. Iengo29, O. Igonkina103, Y. Ikegami64, M. Ikeno64, Y. Ilchenko39, D.I. Iliadis149, Y. Ilyushenka63,\nM. Imori150, T. Ince163, P. Ioannou 8, M. Iodice131a, A. Ishikawa65, M. Ishino150, Y. Ishizawa153a,\nR. Ishmukhametov39, T. Isobe150, V. Issakov168, C. Issever115, S. Istin18, A.V. Ivashin125, W. Iwanski38,\nH. Iwasaki64, J.M. Izen40, V. Izzo100a, J.N. Jackson71, M. Jaekel29, M. Jahoda122, V. Jain60, K. Jakobs47,\nJ. Jakubek124, D. Jana108, E. Jansen102, A. Jantsch97, R.C. Jared165, G. Jarlskog77, P. Jarron29,\nK. Jelen37, I. Jen-La Plante30, P. Jenni29, P. Jez35, S. J\u00b4ez\u00b4equel4, W. Ji77, J. Jia144, Y. Jiang32, G. Jin32,\nS. Jin32, O. Jinnouchi64, D. Joffe39, L.G. Johansen13, M. Johansen142, K.E. Johansson142,\nP. Johansson136, K.A. Johns6, K. Jon-And142, A. Jones160, G. Jones80, R.W.L. Jones69, T.W. Jones75,\nT.J. Jones71, O. Jonsson29, D. Joos47, C. Joram29, P.M. Jorge121b, S. Jorgensen11, P. Jovanovic17,\nV. Juranek122, P. Jussel61, V.V. Kabachenko125, S. Kabana16, M. Kaci161, A. Kaczmarska38, M. Kado112,\nH. Kagan106, M. Kagan56, S. Kaiser97, E. Kajomovitz147, L.V. Kalinovskaya63, A. Kalinowski127,\nS. Kama41, N. Kanaya150, M. Kaneda150, V.A. Kantserov94, J. Kanzaki64, B. Kaplan168, A. Kapliy30,\nJ. Kaplon29, M. Karagounis20, M. Karagoz Unel115, K. Karr5, V. Kartvelishvili69, A.N. Karyukhin125,\nL. Kashif56, A. Kasmi39, R.D. Kass106, M. Kataoka29, Y. Kataoka150, E. Katsou\ufb01s 9, J. Katzy41,\nK. Kawagoe65, T. Kawamoto150, M.S. Kayl103, F. Kayumov92, V.A. Kazanin 104, M.Y. Kazarinov63,\nS.I. Kazi84, J.R. Keates80, R. Keeler163, P.T. Keener117, R. Kehoe39, M. Keil48, G.D. Kekelidze63,\nM. Kelly80, J. Kennedy96, M. Kenyon52, O. Kepka133, N. Kerschen136, B.P. Ker\u02c7sevan72, S. Kersten167,\nM. Khakzad28, F. Khalilzade10, H. Khandanyan160, A. Khanov109, D. Kharchenko63, A. Khodinov144,\nA.G. Kholodenko125, A. Khomich57a, G. Khoriauli20, N. Khovanskiy63, V. Khovanskiy93,\nE. Khramov63, J. Khubua50, G. Kilvington74, H. Kim7, M.S. Kim2, S.H. Kim154, O. Kind15, P. Kind167,\nB.T. King71, J. Kirk126, G.P. Kirsch115, L.E. Kirsch22, A.E. Kiryunin97, D. Kisielewska37,\nT. Kittelmann120, H. Kiyamura65, E. Kladiva141, J. Klaiber-Lodewigs42, M. Klein71, U. Klein71,\nTHE ATLAS COLLABORATION\nx\n\nK. Kleinknecht79, A. Klier164, A. Klimentov24, R. Klingenberg42, E.B. Klinkby44, T. Klioutchnikova29,\nP.F. Klok102, S. Klous103, E.-E. Kluge57a, T. Kluge71, P. Kluit103, M. Klute53, S. Kluth97,\nN.S. Knecht152, E. Kneringer61, B.R. Ko44, T. Kobayashi150, M. Kobel43, B. Koblitz29, A. Kocnar110,\nP. Kodys123, K. K\u00a8oneke41, A.C. K\u00a8onig102, S. K\u00a8onig47, L. K\u00a8opke79, F. Koetsveld102, P. Koevesarki20,\nT. Koffas29, E. Koffeman103, Z. Kohout 124, T. Kohriki64, T. Kokott20, H. Kolanoski15, V. Kolesnikov63,\nI. Koletsou4, I. Koletsou112, M. Kollefrath47, S. Kolos157,r, S.D. Kolya80, A.A. Komar92,\nJ.R. Komaragiri139, T. Kondo64, T. Kono29, A.I. Kononov47, R. Konoplich105, S.P. Konovalov92,\nN. Konstantinidis75, A. Kootz167, S. Koperny37, K. Korcyl38, K. Kordas16, V. Koreshev125, A. Korn14,\nI. Korolkov11, V.A. Korotkov125, O. Kortner97, V.V. Kostyukhin49a, M.J. Kotam\u00a8aki29, S. Kotov97,\nV.M. Kotov63, K.Y. Kotov 104, Z. Koupilova 123, C. Kourkoumelis8, A. Koutsman103, S. Kovar29,\nR. Kowalewski163, H. Kowalski41, T.Z. Kowalski37, W. Kozanecki133, A.S. Kozhin125, V. Kral124,\nV.A. Kramarenko95, G. Kramberger72, M.W. Krasny76, A. Krasznahorkay29, A.K. Kreisel148,\nF. Krejci124, A. Krepouri149, P. Krieger152, G. Krobath96, K. Kroeninger53, H. Kroha97, J. Kroll117,\nJ. Krstic12a, U. Kruchonak63, H. Kr\u00a8uger20, Z.V. Krumshteyn63, T. Kubota150, S.K. Kuehn47,\nA. Kugel57b, T. Kuhl167, D. Kuhn61, V. Kukhtin63, Y. Kulchitsky88, S. Kuleshov31b, C.K. Kummer96,\nM. Kuna81, A. Kupco122, H. Kurashige65, M.K. Kurata154, L.L. Kurchaninov153a, Y.A. Kurochkin88,\nV. Kus122, W. Kuykendall135, E.K. Kuznetsova129a,129b, O. Kvasnicka122, R. Kwee15, M. La Rosa84,\nL. La Rotonda36a,36b, L. Labarga78, J.A. Labbe54, C. Lacasta161, F. Lacava129a,129b, H. Lacker15,\nD. Lacour76, V.R. Lacuesta161, E. Ladygin63, R. Lafaye4, B. Laforge76, T. Lagouri78, S. Lai47,\nM. Lamanna29, M. Lambacher96, C.L. Lampen6, W. Lampl6, E. Lancon133, U. Landgraf47,\nM.P.J. Landon73, J.L. Lane80, A.J. Lankford157, F. Lanni24, K. Lantzsch29, A. Lanza116a, S. Laplace4,\nC.L. Lapoire81, J.F. Laporte133, T. Lari87a, A.V. Larionov 125, C. Lasseur29, M. Lassnig29, P. Laurelli 46,\nW. Lavrijsen14, A.B. Lazarev63, A-C. Le Bihan29, O. Le Dortz76, C. Le Maner152, M. Le Vine24,\nM. Leahu29, C. Lebel91, T. LeCompte5, F. Ledroit-Guillon54, H. Lee103, J.S.H. Lee145, S.C. Lee146,\nM. Lefebvre163, R.P. Lefevre48, M. Legendre133, A. Leger48, B.C. LeGeyt117, F. Legger97, C. Leggett14,\nM. Lehmacher20, G. Lehmann Miotto29, X. Lei6, R. Leitner123, D. Lelas163, D. Lellouch164,\nM. Leltchouk34, V. Lendermann57a, K.J.C. Leney71, T. Lenz167, G. Lenzen167, B. Lenzi133, C. Leroy91,\nJ-R. Lessard163, C.G. Lester27, A. Leung Fook Cheong165, J. Lev\u02c6eque81, D. Levin85, L.J. Levinson164,\nM.S. Levitski125, S. Levonian41, M. Lewandowska21, M. Leyton14, J. Li7, S. Li41, X. Li85, Z. Liang39,\nZ. Liang146, B. Liberti130a, P. Lichard29, M. Lichtnecker96, W. Liebig103, R. Lifshitz147, D. Liko29,\nJ.N. Lilley17, H. Lim5, M. Limper103, S.C. Lin146, S.W. Lindsay71, V. Linhart124, A. Liolios149,\nL. Lipinsky122, A. Lipniacka13, T.M. Liss160, A. Lissauer24, A.M. Litke134, C. Liu28, D.L. Liu146,\nJ.L. Liu85, M. Liu32,b, S. Liu2, T. Liu39, Y. Liu32, M. Livan116a,116b, A. Lleres54, S.L. Lloyd73,\nE. Lobodzinska41, P. Loch6, W.S. Lockman134, S. Lockwitz168, T. Loddenkoetter20, F.K. Loebinger80,\nA. Loginov168, C.W. Loh162, T. Lohse15, K. Lohwasser115, M. Lokajicek122, J. Loken 115,\nD. Lopez Mateos34,q, M. Losada156, M.J. Losty153a, X. Lou40, K.F. Loureiro106, L. Lovas141, J. Love21,\nA. Lowe60, F. Lu32,b, J. Lu2, H.J. Lubatti135, C. Luci129a,129b, A. Lucotte54, A. Ludwig43, I. Ludwig47,\nJ. Ludwig47, F. Luehring60, L. Luisa158a,158c, D. Lumb47, L. Luminari129a, E. Lund114,\nB. Lund-Jensen143, B. Lundberg77, J. Lundquist35, A. Lupi119a,119b, G. Lutz97, D. Lynn24, J. Lys14,\nE. Lytken29, H. Ma24, L.L. Ma152, M. Maa\u00dfen47, G. Maccarrone 46, A. Macchiolo97, B. Ma\u02c7cek72,\nR. Mackeprang29, R.J. Madaras14, W.F. Mader43, R. Maenner57b, T. Maeno24, P. M\u00a8attig167,\nC. Magass20, C.A. Magrath102, Y. Mahalalel148, K. Mahboubi47, A. Mahmood1, G. Mahout17,\nC. Maidantchik23a, A. Maio121b, G.M. Mair61, S. Majewski24, Y. Makida64, N.M. Makovec112,\nPa. Malecki38, P. Malecki38, V.P. Maleev118, F. Malek54, U. Mallik140, D. Malon5, S. Maltezos 9,\nV. Malychev104, M. Mambelli30, R. Mameghani96, J. Mamuzic41, A. Manabe64, L. Mandelli87a,87b,\nI. Mandi\u00b4c72, J. Maneira121b, P.S. Mangeard81, I.D. Manjavidze63, A. Manousakis-Katsikakis8,\nB. Mansoulie133, A. Mapelli29, L. Mapelli29, L. March Ruiz78, J.F. Marchand4, F.M. Marchese130a,130b,\nM. Marcisovsky122, C.N. Marques121b, F. Marroquim23a, R. Marshall80, Z. Marshall34,q,\nTHE ATLAS COLLABORATION\nxi\n\nF.K. Martens152, S. Marti i Garcia161, A. Martin73, A.J. Martin168, B. Martin29, B. Martin86,\nF.F. Martin117, J.P. Martin91, M. Martinez Perez11, V. Martinez Outschoorn56, A. Martini46,\nV. Martynenko153b, A.C. Martyniuk80, T. Maruyama154, F. Marzano129a, A. Marzin133, L. Masetti20,\nT. Mashimo150, R. Mashinistov94, J. Masik80, A.L. Maslennikov104, G. Massaro103, N. Massol4,\nA. Mastroberardino36a,36b, M. Mathes20, P. Matricon112, H. Matsumoto150, H. Matsunaga150,\nT. Matsushita65, J.M. Maugain29, S.J. Max\ufb01eld71, E.N. May5, A. Mayne136, R. Mazini152,\nM. Mazzanti87a,87b, P. Mazzanti19a, S.P. Mc Kee85, R.L. McCarthy144, C. McCormick157,\nN.A. McCubbin126, K.W. McFarlane55, S. McGarvie74, H. McGlone52, R.A. McLaren29,\nS.J. McMahon126, T.R. McMahon74, R.A. McPherson163,j, J.M. Mechnich103, M. Mechtel167,\nD. Meder-Marouelli167, M. Medinnis41, R. Meera-Lebbai108, R. Mehdiyev91, S. Mehlhase41,\nA. Mehta71, K. Meier57a, B. Meirose 47, A. Melamed-Katz164, B.R. Mellado Garcia165, Z.M. Meng146,\nS. Menke97, E. Meoni36a,36b, D. Merkl96, P. Mermod142, L. Merola100a,100b, C. Meroni87a, F.S. Merritt30,\nA.M. Messina29, I. Messmer47, J. Metcalfe101, A.S. Mete62, J-P. Meyer133, J. Meyer53, T.C. Meyer29,\nW.T. Meyer62, L. Micu25a, R. Middleton126, S. Migas71, L. Mijovi\u00b4c72, G. Mikenberg164, M. Miku\u02c7z72,\nD.W. Miller140, R.J. Miller86, B.M. Mills162, C.M. Mills56, M. Milosavljevic12a, D.A. Milstead142,\nS. Mima107, A.A. Minaenko125, M. Mi\u02dcnano161, I.A. Minashvili63, A.I. Mincer105, B. Mindur37,\nM. Mineev63, L.M. Mir11, G. Mirabelli129a, S. Misawa24, S. Miscetti46, A. Misiejuk74,\nJ.M. Mitrevski134, V.A. Mitsou161, P.S. Miyagawa80, J.U. Mj\u00a8ornmark77, D. Mladenov22, T. Moa142,\nM. Moch129a,129b, A. Mochizuki154, P. Mockett135, P. Modesto161, S. Moed56, V. Moeller27, K. M\u00a8onig41,\nN. M\u00a8oser20, B. Mohn13, W. Mohr47, S. Mohrdieck-M\u00a8ock97, R. Moles-Valls161, J. Molina-Perez29,\nG. Moloney84, J. Monk75, E. Monnier81, S. Montesano87a,87b, F. Monticelli68, R.W. Moore2,\nC.M. Mora Herrera48, A. Moraes52, A. Morais121b, J. Morel4, D. Moreno156, M. Moreno Ll\u00b4acer161,\nP. Morettini 49a, M. Morii56, J. Morin73, A.K. Morley84, G. Mornacchi29, S.V. Morozov94, J.D. Morris73,\nH.G. Moser97, M. Mosidze50, J.M. Moss106, A. Moszczynski38, E. Mountricha9, S.V. Mouraviev92,\nE.J.W. Moyse82, J. Mueller120, K. Mueller20, T.A. M\u00a8uller96, D.M. Muenstermann42, A.M. Muir162,\nR. Murillo Garcia157, W.J. Murray126, E. Musto100a,100b, A.G. Myagkov125, M. Myska122, J. Nadal11,\nK. Nagai24, K. Nagano64, Y. Nagasaka59, A.M. Nairz29, I. Nakano107, H. Nakatsuka65, G. Nanava20,\nA. Napier155, M. Nash75,s, N.R. Nation21, T. Naumann41, G. Navarro156, S.K. Nderitu20, H.A. Neal85,\nE. Nebot78, P. Nechaeva92, A. Negri116a,116b, G. Negri29, A. Nelson62, S. Nemecek122, P. Nemethy105,\nA.A. Nepomuceno23a, M. Nessi29, S.Y. Nesterov118, M.S. Neubauer160, A. Neusiedl79, R.N. Neves121b,\nP. Nevski24, F.M. Newcomer117, C. Ng154, C. Nicholson52, R.B. Nickerson115, R. Nicolaidou133,\nG. Nicoletti46, B. Nicquevert29, J. Nielsen134, A. Nikiforov41, N. Nikitin95, K. Nikolaev63,\nI. Nikolic-Audit76, K. Nikolopoulos8, H. Nilsen47, P. Nilsson7, A. Nisati129a, R. Nisius97,\nL.J. Nodulman5, M. Nomachi113, I. Nomidis149, H. Nomoto150, M. Nordberg29, D. Notz41,\nJ. Novakova123, M. Nozaki64, M. Nozicka41, A.-E. Nuncio-Quiroz20, G. Nunes Hanninger20,\nT. Nunnemann96, S.W. O\u2019Neale17,\u2217, D.C. O\u2019Neil139, V. O\u2019Shea52, F.G. Oakham28,a, H. Oberlack97,\nA. Ochi65, S. Odaka64, G.A. Odino49a,49b, H. Ogren60, S.H. Oh44, T. Ohshima99, H. Ohshita137,\nT. Ohsugi58, S. Okada65, H. Okawa150, Y. Okumura99, M. Olcese49a, A.G. Olchevski63, M. Oliveira121b,\nD. Oliveira Damazio24, J. Oliver56, E.O. Oliver Garcia161, D. Olivito 117, A. Olszewski38,\nJ. Olszowska38, C. Omachi65, A. Onea29, A. Onofre121b, C.J. Oram153a, G. Ordonez102, M.J. Oreglia30,\nY. Oren148, D. Orestano131a,131b, I.O. Orlov 104, R.S. Orr152, E.O. Ortega127, B. Osculati49a,49b,\nC. Osuna11, R. Otec124, F. Ould-Saada114, A. Ouraou133, Q. Ouyang32, O.K. \u00d8ye13, V.E. Ozcan75,\nK. Ozone64, N. Ozturk7, A. Pacheco Pages11, S. Padhi165, C. Padilla Aranda11, E. Paganis136,\nF. Paige24, K. Pajchel114, A. Pal7, S. Palestini29, J. Palla29, D. Pallin33, A. Palma121b, Y.B. Pan165,\nE. Panagiotopoulou9, B. Panes31a, N. Panikashvili85, S. Panitkin24, D. Pantea25a, M. Panuskova122,\nV. Paolone120, Th.D. Papadopoulou9, W. Park24,t, M.A. Parker27, S. Parker14, F. Parodi49a,49b,\nJ.A. Parsons34, U. Parzefall47, E. Pasqualucci129a, G. Passardi29, A. Passeri131a, F. Pastore131a,131b,\nFr. Pastore29, S. Pataraia97, J.R. Pater80, S. Patricelli100a,100b, P. Patwa24, T. Pauly29, L.S. Peak145,\nTHE ATLAS COLLABORATION\nxii\n\nM. Pecsy141, M.I. Pedraza Morales165, S.V. Peleganchuk104, H. Peng165, R. Pengo29, J. Penwell60,\nM. Perantoni23a, A. Pereira121b, K. Perez34,q, E. Perez Codina11, V. Perez Reale34, L. Perini87a,87b,\nH. Pernegger29, R. Perrino70a, P. Perrodo4, P. Perus112, V.D. Peshekhonov63, B.A. Petersen29,\nJ. Petersen29, T.C. Petersen29, C. Petridou149, E. Petrolo129a, F. Petrucci131a,131b, R. Petti24,t,\nR. Pezoa31b, M. Pezzetti29, B. Pfeifer47, A. Phan84, A.W. Phillips27, G. Piacquadio47,\nM. Piccinini19a,19b, R. Piegaia26, S. Pier157, J.E. Pilcher30, A.D. Pilkington80, J. Pina121b, J.L. Pinfold2,\nJ. Ping32, B. Pinto121b, O. Pirotte29, C. Pizio87a,87b, R. Placakyte41, M. Plamondon112, W.G. Plano80,\nM.-A. Pleier20, A. Poblaguev168, F. Podlyski33, P. Poffenberger163, L. Poggioli112, M. Pohl48,\nF. Polci112, G. Polesello116a, A. Policicchio135, A. Polini19a, J.P. Poll73, V. Polychronakos24,\nD.M. Pomarede133, K. Pomm`es29, L. Pontecorvo129a, B.G. Pope86, R. Popescu24, D.S. Popovic12a,\nA. Poppleton29, J. Popule122, X. Portell Bueso47, R. Porter157, G.E. Pospelov97, P. Pospichal29,\nS. Pospisil124, M. Potekhin24, I.N. Potrap97, C.J. Potter74, C.T. Potter83, K.P. Potter80, G. Poulard29,\nJ. Poveda165, R. Prabhu20, P. Pralavorio81, S. Prasad56, R. Pravahan7, T. Preda25a, K. Pretzl16,\nL. Pribyl29, D. Price69, L.E. Price5, M.J. Price29, P.M. Prichard71, D. Prieur126, M. Primavera70a,\nK. Proko\ufb01ev29, F. Prokoshin31b, S. Protopopescu24, J. Proudfoot5, H. Przysiezniak 4, C. Puigdengoles11,\nJ. Purdham85, M. Purohit24,t, P. Puzo112, Y. Pylypchenko114, M.T. P\u00b4erez Garc\u00b4\u0131a-Esta\u02dcn161, M. Qi32,\nJ. Qian85, W. Qian126, Z. Qian81, Z. Qin41, D. Qing146, A. Quadt53, D.R. Quarrie14, W.B. Quayle165,\nF. Quinonez31a, M. Raas102, V. Radeka24, V. Radescu41, B. Radics20, T. Rador18, F. Ragusa87a,87b,\nG. Rahal173, A.M. Rahimi106, D. Rahm24, S. Rajagopalan24, S. Rajek42, P.N. Ratoff69, F. Rauscher96,\nE. Rauter97, M. Raymond29, A.L. Read 114, D.M. Rebuzzi97, G.R. Redlinger24, R. Reece 117,\nK. Reeves167, E. Reinherz-Aronis148, I. Reisinger42, D. Reljic12a, C. Rembser29, Z. Ren146, P. Renkel39,\nS. Rescia24, M. Rescigno129a, S. Resconi87a, B. Resende103, E. Rezaie139, P. Reznicek123,\nA. Richards75, R.A. Richards86, R. Richter97, E. Richter-Was38,u, M. Ridel76, S. Rieke79,\nM. Rijpstra103, M. Rijssenbeek144, A. Rimoldi116a,116b, R.R. Rios 39, C. Risler15, I. Riu 11,\nG. Rivoltella87a,87b, F. Rizatdinova109, K. Roberts160, S.H. Robertson83,j, A. Robichaud-Veronneau48,\nD. Robinson27, A. Robson52, J.G. Rocha de Lima5, C. Roda119a,119b, D. Rodriguez156, Y. Rodriguez156,\nS. Roe29, O. R\u00f8hne114, V. Rojo1, S. Rolli155, A. Romaniouk94, V.M. Romanov63, G. Romeo26,\nD. Romero31a, L. Roos76, E. Ros161, S. Rosati129a,129b, G.A. Rosenbaum152, E.I. Rosenberg62,\nL. Rosselet48, L.P. Rossi49a, M. Rotaru25a, J. Rothberg135, I. Rottl\u00a8ander20, D. Rousseau112,\nC.R. Royon133, A. Rozanov81, Y. Rozen147, B. Ruckert96, N. Ruckstuhl103, V.I. Rud95, G. Rudolph61,\nF. R\u00a8uhr57a, F. Ruggieri131a, A. Ruiz-Martinez161, V. Rumiantsev89,\u2217, L. Rumyantsev63,\nN.A. Rusakovich63, D.R. Rust60, J.P. Rutherfoord6, C. Ruwiedel20, P. Ruzicka122, Y.F. Ryabov118,\nV. Ryadovikov125, P. Ryan86, A.M. Rybin125, G. Rybkin112, S. Rzaeva10, A.F. Saavedra145,\nH.F-W. Sadrozinski134, R. Sadykov63, H. Sakamoto150, G. Salamanna 103, A. Salamon130a,\nM. Saleem108, D. Salihagic97, A. Salnikov140, J. Salt161, B.M. Salvachua Ferrando5, D. Salvatore36a,36b,\nF. Salvatore74, A. Salzburger41, D. Sampsonidis149, B.H. Samset114, M.A. Sanchis Lozano161,\nH. Sandaker 13, H.G. Sander79, M. Sandhoff167, S. Sandvoss167, D.P.C. Sankey126, B. Sanny167,\nA. Sansoni46, C. Santamarina Rios83, L. Santi158a,158c, C. Santoni33, R. Santonico130a,130b,\nD. Santos121b, J.G. Saraiva121b, T. Sarangi 165, F. Sarri119a,119b, O. Sasaki64, T. Sasaki64, N. Sasao66,\nI. Satsounkevitch88, G. Sauvage4, P. Savard152,a, A.Y. Savine6, V. Savinov120, L. Sawyer24,k,\nD.H. Saxon52, L.P. Says33, C. Sbarra19a,19b, A. Sbrizzi19a,19b, D.A. Scannicchio, J. Schaarschmidt43,\nP. Schacht 97, U. Sch\u00a8afer79, S. Schaetzel29, A.C. Schaffer112, D. Schaile96, R. Schamberger144,\nA.G. Schamov 104, V.A. Schegelsky118, M. Schernau157, M.I. Scherzer14, C. Schiavi49a,49b, J. Schieck97,\nM. Schioppa36a,36b, S. Schlenker29, J.L. Schlereth5, P. Schmid29, M.P. Schmidt168,\u2217, C. Schmitt20,\nM. Schmitz20, M. Schott29, D. Schouten139, J. Schovancova122, M. Schram83, A. Schreiner140,d,\nM.S. Schroers167, S. Schuh29, G. Schuler29, J. Schultes167, H-C. Schultz-Coulon57a, J. Schumacher43,\nM. Schumacher47, B.S. Schumm134, Ph. Schune133, C.S. Schwanenberger80, A. Schwartzman140,\nPh. Schwemling76, R. Schwienhorst86, R. Schwierz43, J. Schwindling133, W.G. Scott126, E. Sedykh118,\nTHE ATLAS COLLABORATION\nxiii\n\nE. Segura11, S.C. Seidel101, A. Seiden134, F.S. Seifert43, J.M. Seixas23a, G. Sekhniaidze100a,\nD.M. Seliverstov118, B. Selld\u00b4en142, M. Seman141, N. Semprini-Cesari19a,19b, C. Serfon96, L. Serin112,\nR. Seuster163, H. Severini108, M.E. Sevior84, A. Sfyrla160, L. Shan32,b, J.T. Shank21, M. Shapiro14,\nP.B. Shatalov93, L. Shaver6, C. Shaw52, K.S. Shaw136, D. Sherman29, P. Sherwood75, A. Shibata105,\nM. Shimojima98, T. Shin55, A. Shmeleva92, M.J. Shochet30, M.A. Shupe6, P. Sicho122, A. Sidoti15,\nA. Siebel167, M. Siebel29, J. Siegrist14, D. Sijacki12a, O. Silbert164, J. Silva121b, S.B. Silverstein142,\nV. Simak124, Lj. Simic12a, S. Simion 112, B. Simmons75, M. Simonyan4, P. Sinervo152, V. Sipica138,\nG. Siragusa79, A.N. Sisakyan63, S.Yu. Sivoklokov95, J. Sj\u00a8olin142, P. Skubic108, N. Skvorodnev22,\nT. Slavicek124, K. Sliwa155, J. Sloper29, T. Sluka122, V. Smakhtin164, S.Yu. Smirnov94, Y. Smirnov24,\nL.N. Smirnova95, O. Smirnova77, B.C. Smith56, K.M. Smith52, M. Smizanska69, K. Smolek124,\nA.A. Snesarev92, S.W. Snow80, J. Snow 108, J. Snuverink103, S. Snyder24, M. Soares78, R. Sobie163,j,\nJ. Sodomka124, A. Soffer148, C.A. Solans161, M. Solar124, E. Solfaroli Camillocci129a,129b,\nA.A. Solodkov125, O.V. Solovyanov125, R. Soluk2, J. Sondericker24, V. Sopko124, B. Sopko 124,\nM. Sosebee7, V.V. Sosnovtsev94, L. Sospedra Suay161, A. Soukharev104, S. Spagnolo70a,70b, F. Span`o34,\nP. Speckmayer29, E. Spencer134, R. Spighi19a, G. Spigo29, F. Spila129a,129b, R. Spiwoks29,\nL. Spogli131a,131b, M. Spousta123, T. Spreitzer139, B. Spurlock7, R.D. St. Denis52, T. Stahl138,\nR. Stamen57a, S.N. Stancu157, E. Stanecka29, R.W. Stanek5, C. Stanescu131a, S. Stapnes114,\nE.A. Starchenko125, J. Stark54, P. Staroba122, J. Stastny122, A. Staude96, P. Stavina141,\nG. Stavropoulos14, P. Steinbach43, P. Steinberg24, I. Stekl124, H.J. Stelzer41, H. Stenzel51,\nK.S. Stevenson73, G. Stewart52, T.D. Stewart139, M.C. Stockton17, G. Stoicea25a, S. Stonjek97,\nP. Strachota123, A. Stradling7, A. Straessner43, J. Strandberg85, S. Strandberg14, A. Strandlie114,\nM. Strauss108, P. Strizenec141, R. Str\u00a8ohmer96, D.M. Strom111, J.A. Strong74,\u2217, R. Stroynowski39,\nB. Stugu13, I. Stumer24,\u2217, D. Su140, S. Subramania60, S.I. Suchkov94, Y. Sugaya113, T. Sugimoto99,\nC. Suhr5, M. Suk123, V.V. Sulin92, S. Sultansoy3,v, J.E. Sundermann47, K. Suruliz158a,158b, S. Sushkov11,\nG. Susinno36a,36b, M.R. Sutton75, T. Suzuki150, Yu.M. Sviridov125, I. Sykora141, T. Sykora123,\nR.R. Szczygiel38, T. Szymocha38, J. S\u00b4anchez161, D. Ta20, A.T. Taffard157, R. Ta\ufb01rout153a, A. Taga114,\nY. Takahashi99, H. Takai24, R. Takashima67, H. Takeda65, T. Takeshita137, M. Talby81, B. Tali149,\nA. Talyshev104, M.C. Tamsett74, J. Tanaka150, R. Tanaka112, S. Tanaka128, S. Tanaka64, G.P. Tappern29,\nS. Tapprogge79, S. Tarem147, F. Tarrade24, G.F. Tartarelli87a, P. Tas123, M. Tasevsky122, E.T. Tassi36a,36b,\nC. Taylor75, F.E. Taylor90, G.N. Taylor84, R.P. Taylor163, W. Taylor153b, F. Tegenfeldt62,\nP. Teixeira-Dias74, H. Ten Kate29, P.K. Teng146, S. Terada64, K. Terashi150, J. Terron78, M. Terwort41,n,\nR.J. Teuscher152,j, C.M. Tevlin80, J. Thadome167, R. Thananuwong48, M. Thioye168, J.P. Thomas17,\nT.L. Thomas101, E.N. Thompson82, P.D. Thompson17, R.J. Thompson80, A.S. Thompson52,\nE. Thomson117, R.P. Thun85, T. Tic 122, V.O. Tikhomirov92, Y.A. Tikhonov104,\nC.J.W.P. Timmermans102, P. Tipton168, F.J. Tique Aires Viegas29, S. Tisserant81, J. Tobias47,\nB. Toczek37, T.T. Todorov4, S. Todorova-Nova155, J. Tojo64, S. Tok\u00b4ar141, K. Tokushuku64,\nL. Tomasek122, M. Tomasek122, F. Tomasz141, M. Tomoto99, D. Tompkins6, L. Tompkins14, K. Toms101,\nA. Tonazzo131a,131b, G. Tong32, A. Tonoyan13, C. Topfel16, N.D. Topilin63, E. Torrence111, E. Torr\u00b4o\nPastor161, J. Toth81,w, F. Touchard81, D.R. Tovey136, S.N. Tovey84, T. Trefzger166, L. Tremblet29,\nA. Tricoli126, I.M. Trigger153a, S. Trincaz-Duvoid76, M.F. Tripiana68, N. Triplett62, W. Trischuk152,\nA. Trivedi24,t, B. Trocm\u00b4e54, C. Troncon87a, C. Tsarouchas9, J.C-L. Tseng115, I. Tsia\ufb01s149,\nM. Tsiakiris103, P.V. Tsiareshka88, G. Tsipolitis9, E.G. Tskhadadze50, I.I. Tsukerman93, V. Tsulaia120,\nS. Tsuno64, M. Turala38, D. Turecek124, I. Turk Cakir3,x, E. Turlay112, P.M. Tuts34, M.S. Twomey135,\nM. Tyndel126, D. Typaldos17, G. Tzanakos8, I. Ueda150, M. Uhrmacher53, F. Ukegawa154, G. Unal29,\nD.G. Underwood5, A. Undrus24, G. Unel157, Y. Unno64, E. Urkovsky148, P. Urquijo48, P. Urrejola31a,\nG. Usai 30, L. Vacavant81, V. Vacek124, B. Vachon83, S. Vahsen14, C. Valderanis97, J. Valenta122,\nP. Valente129a, S. Valkar123, J.A. Valls Ferrer161, H. Van der Bij29, H. van der Graaf103,\nE. van der Kraaij103, E. van der Poel103, N. van Eldik82, P. van Gemmeren5, Z. van Kesteren103,\nTHE ATLAS COLLABORATION\nxiv\n\nI. van Vulpen103, R. VanBerg117, W. Vandelli29, G. Vandoni29, A. Vaniachine5, P. Vankov71,\nF. Vannucci76, F. Varela Rodriguez29, R. Vari129a, E.W. Varnes6, D. Varouchas112, A. Vartapetian7,\nK.E. Varvell145, V.I. Vassilakopoulos55, L. Vassilieva92, E. Vataga101, F. Vazeille33, G. Vegni87a,87b,\nJ.J. Veillet112, C. Vellidis8, F. Veloso121b, R. Veness29, S. Veneziano129a, A. Ventura70a,70b,\nD. Ventura 135, S. Ventura 46, N. Venturi16, V. Vercesi116a, M. Verducci129a,129b, W. Verkerke103,\nJ.C. Vermeulen103, M.C. Vetterli139,a, I. Vichou160, T. Vickey165, G.H.A. Viehhauser115, M. Villa19a,19b,\nE.G. Villani126, M. Villaplana Perez161, E. Vilucchi46, M.G. Vincter28, V.B. Vinogradov63,\nM. Virchaux133,\u2217, S. Viret33, J. Virzi14, A. Vitale 19a,19b, O.V. Vitells164, I. Vivarelli119a,119b, R. Vives161,\nF. Vives Vaques11, S. Vlachos9, M. Vlasak124, N. Vlasov20, H. Vogt41, P. Vokac124, M. Volpi11,\nG. Volpini87a,87b, H. von der Schmitt97, J. von Loeben97, E. von Toerne20, V. Vorobel123,\nA.P. Vorobiev125, V. Vorwerk11, M. Vos161, R. Voss29, T.T. Voss167, J.H. Vossebeld71, N. Vranjes12a,\nV. Vrba122, M. Vreeswijk103, T. Vu Anh20, M. Vudragovic12a, R. Vuillermet29, I. Vukotic112,\nP. Wagner 117, H. Wahlen167, J. Walbersloh42, J. Walder69, R. Walker153a, W. Walkowiak138, R. Wall168,\nC. Wang44, J. Wang32, J.C. Wang135, S.M.W. Wang146, C.P. Ward27, M. Warsinsky47, P.M. Watkins17,\nA.T. Watson17, G. Watts135, S.W. Watts80, A.T. Waugh145, B.M. Waugh75, M. Webel47, J. Weber42,\nM. Weber126, M.S. Weber16, P. Weber57a, A.R. Weidberg115, J. Weingarten42, C. Weiser47,\nH. Wellenstein22, P.S. Wells29, M. Wen46, T. Wenaus24, S. Wendler120, T. Wengler80, S. Wenig29,\nN. Wermes20, M. Werner47, P. Werner29, U. Werthenbach138, M. Wessels57a, S.J. Wheeler-Ellis157,\nS.P. Whitaker21, A. White7, M.J. White27, S. White24, D. Whiteson157, D. Whittington60, F. Wicek112,\nD. Wicke167, F.J. Wickens126, W. Wiedenmann165, M. Wielers126, P. Wienemann20, C. Wiglesworth71,\nA. Wildauer29, M.A. Wildt79, I. Wilhelm123, H.G. Wilkens29, H.H. Williams117, W. Willis34,\nS. Willocq82, J.A. Wilson17, M.G. Wilson140, A. Wilson 85, I. Wingerter-Seez4, F.W. Winklmeier29,\nL. Winton84, M. Wittgen140, M.W. Wolter38, H. Wolters121b, B. Wosiek38, J. Wotschack29,\nM.J. Woudstra82, K. Wraight52, C. Wright52, B. Wrona71, S.L. Wu165, X. Wu48, S. Xella35, S. Xie47,\nY. Xie32, G. Xu32, N. Xu165, A. Yamamoto64, S. Yamamoto150, T. Yamamura150, K. Yamanaka62,\nT. Yamazaki150, Y. Yamazaki65, Z. Yan21, H. Yang85, U.K. Yang80, Y. Yang32, Z. Yang28, W-M. Yao14,\nY. Yao14, Y. Yasu64, J. Ye39, S. Ye24, M. Yilmaz3,y, R. Yoosoofmiya120, K. Yorita30, R. Yoshida5,\nC. Young140, S.P. Youssef21, D. Yu24, J. Yu7, M. Yu57b, X. Yu32, J. Yuan97, L. Yuan76, A. Yurkewicz144,\nR. Zaidan81, A.M. Zaitsev125, Z. Zajacova29, L. Zanello129a,129b, P. Zarzhitsky39, A. Zaytsev104,\nM. Zdrazil14, C. Zeitnitz167, M. Zeller168, P.F. Zema29, C. Zendler20, A.V. Zenin125, T. Zenis141,\nZ. Zenonos119a,119b, S. Zenz14, D. Zerwas112, Z. Zhan32, H. Zhang81,z, J. Zhang5, Q. Zhang5,\nW. Zheng120, X. Zhang32, L. Zhao105, T. Zhao135, Z. Zhao85, A. Zhelezko94, A. Zhemchugov63,\nS. Zheng32, J. Zhong146, B. Zhou85, N. Zhou34, S. Zhou146, Y. Zhou146, C.G. Zhu32,b, H. Zhu136,\nY. Zhu165, X.A. Zhuang97, V. Zhuravlov97, B. Zilka141, R. Zimmermann20, S. Zimmermann47,\nM. Zinna116a,116b, M. Ziolkowski138, R. Zitoun4, L. \u02c7Zivkovi\u00b4c34, V.V. Zmouchko125,\u2217, G. Zobernig165,\nA. Zoccoli19a,19b, M. zur Nedden15, V. Zychacek124.\n1 University at Albany, 1400 Washington Ave, Albany, NY 12222, United States of America\n2 University of Alberta, Department of Physics, Centre for Particle Physics, Edmonton, AB T6G 2G7,\nCanada\n3 Ankara University, Faculty of Sciences, Department of Physics, TR 061000 Tandogan, Ankara,\nTurkey\n4 LAPP, Universit\u00b4e de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France\n5 Argonne National Laboratory, High Energy Physics Division, 9700 S. Cass Avenue, Argonne IL\n60439, United States of America\n6 University of Arizona, Department of Physics, Tucson, AZ 85721, United States of America\n7 The University of Texas at Arlington, Department of Physics, Box 19059, Arlington, TX 76019,\nUnited States of America\n8 University of Athens, Nuclear & Particle Physics, Department of Physics, Panepistimiopouli,\nTHE ATLAS COLLABORATION\nxv\n\nZografou, GR 15771 Athens, Greece\n9 National Technical University of Athens, Physics Department, 9-Iroon Polytechniou, GR 15780\nZografou, Greece\n10 Institute of Physics, Azerbaijan Academy of Sciences, H. Javid Avenue 33, AZ 143 Baku, Azerbaijan\n11 Institut de F\u00b4\u0131sica d\u2019Altes Energies, IFAE, Edi\ufb01ci Cn, Universitat Aut`onoma de Barcelona, ES -\n08193 Bellaterra (Barcelona), Spain\n12 (a)University of Belgrade, Institute of Physics, P.O. Box 57, 11001 Belgrade; Vinca Institute of\nNuclear Sciences(b), Mihajla Petrovica Alasa 12-14, 11001 Belgrade, Serbia\n13 University of Bergen, Department for Physics and Technology, Allegaten 55, NO - 5007 Bergen,\nNorway\n14 Lawrence Berkeley National Laboratory and University of California, Physics Division,\nMS50B-6227, 1 Cyclotron Road, Berkeley, CA 94720, United States of America\n15 Humboldt University, Institute of Physics, Berlin, Newtonstr. 15, D-12489 Berlin, Germany\n16 University of Bern, Laboratory for High Energy Physics, Sidlerstrasse 5, CH - 3012 Bern,\nSwitzerland\n17 University of Birmingham, School of Physics and Astronomy, Edgbaston, Birmingham B15 2TT,\nUnited Kingdom\n18 Bogazici University, Faculty of Sciences, Department of Physics, TR - 80815 Bebek-Istanbul, Turkey\n19 INFN Sezione di Bologna(a); Universit`a di Bologna, Dipartimento di Fisica(b), viale C. Berti Pichat,\n6/2, IT - 40127 Bologna, Italy\n20 University of Bonn, Physikalisches Institut, Nussallee 12, D - 53115 Bonn, Germany\n21 Boston University, Department of Physics, 590 Commonwealth Avenue, Boston, MA 02215, United\nStates of America\n22 Brandeis University, Department of Physics, MS057, 415 South Street, Waltham, MA 02454, United\nStates of America\n23 Universidade Federal do Rio De Janeiro, Instituto de Fisica(a), Caixa Postal 68528, Ilha do Fundao,\nBR - 21945-970 Rio de Janeiro; (b)University of Sao Paolo, address in Sao Paolo, Brazil\n24 Brookhaven National Laboratory, Physics Department, Bldg. 510A, Upton, NY 11973, United States\nof America\n25 National Institute of Physics and Nuclear Engineering(a), Bucharest, P.O. Box MG-6, R-077125;\n(b)West University in Timisoara, Bd. Vasile Parvan 4, Timisoara, Romania\n26 Universidad de Buenos Aires, FCEyN, Dto. Fisica, Pab I - C. Universitaria, 1428 Buenos Aires,\nArgentina\n27 University of Cambridge, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, United\nKingdom\n28 Carleton University, Department of Physics, 1125 Colonel By Drive, Ottawa ON K1S 5B6, Canada\n29 CERN, CH - 1211 Geneva 23, Switzerland\n30 University of Chicago, Enrico Fermi Institute, 5640 S. Ellis Avenue, Chicago, IL 60637, United\nStates of America\n31 Ponti\ufb01cia Universidad Cat\u00b4olica de Chile, Facultad de Fisica, Departamento de Fisica(a), Avda.\nVicuna Mackenna 4860, San Joaquin, Santiago; Universidad T\u00b4ecnica Federico Santa Mar\u00b4\u0131a,\nDepartamento de F\u00b4\u0131sica(b), Avda. Esp\u02dcana 1680, Casilla 110-V, Valpara\u00b4\u0131so, Chile\n32 Institute of HEP, Chinese Academy of Sciences, P.O. Box 918, CN-100049 Beijing; USTC,\nDepartment of Modern Physics, Hefei, CN-230026 Anhui; Nanjing University, Department of Physics,\nCN-210093 Nanjing; Shandong University, HEP Group, CN-250100 Shadong, China\n33 Laboratoire de Physique Corpusculaire, CNRS-IN2P3, Universit\u00b4e Blaise Pascal, FR - 63177 Aubiere\nCedex, France\n34 Columbia University, Nevis Laboratory, 136 So. Broadway, Irvington, NY 10533, United States of\nTHE ATLAS COLLABORATION\nxvi\n\nAmerica\n35 University of Copenhagen, Niels Bohr Institute, Blegdamsvej 17, DK - 2100 Kobenhavn 0, Denmark\n36 INFN Gruppo Collegato di Cosenza(a); Universit`a della Calabria, Dipartimento di Fisica(b), IT-87036\nArcavacata di Rende, Italy\n37 Faculty of Physics and Applied Computer Science of the AGH-University of Science and\nTechnology, (FPACS, AGH-UST), al. Mickiewicza 30, PL-30059 Cracow, Poland\n38 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, ul.\nRadzikowskiego 152, PL - 31342 Krakow, Poland\n39 Southern Methodist University, Physics Department, 106 Fondren Science Building, Dallas, TX\n75275-0175, United States of America\n40 University of Texas at Dallas, 800 West Campbell Road, Richardson, TX 75080-3021, United States\nof America\n41 DESY, Hamburg and Zeuthen, Notkestr. 85, D-22603 Hamburg, Germany\n42 Universitaet Dortmund, Experimentelle Physik IV, DE - 44221 Dortmund, Germany\n43 Technical University Dresden, Institut fuer Kern- und Teilchenphysik, Zellescher Weg 19, D-01069\nDresden, Germany\n44 Duke University, Department of Physics, Durham, NC 27708, United States of America\n45 Fachhochschule Wiener Neustadt; Johannes Gutenbergstrasse 3 AT - 2700 Wiener Neustadt, Austria\n46 INFN Laboratori Nazionali di Frascati, via Enrico Fermi 40, IT-00044 Frascati, Italy\n47 Albert-Ludwigs-Universit\u00a8at, Fakult\u00a8at f\u00a8ur Mathematik und Physik, Hermann-Herder Str. 3, D - 79104\nFreiburg i.Br. , Germany\n48 Universit\u00b4e de Gen`eve, Section de Physique, 24 rue Ernest Ansermet, CH - 1211 Geneve 4,\nSwitzerland\n49 INFN Sezione di Genova(a); Universit`a di Genova, Dipartimento di Fisica(b), via Dodecaneso 33, IT -\n16146 Genova, Italy\n50 Institute of Physics of the Georgian Academy of Sciences, 6 Tamarashvili St., GE - 380077 Tbilisi;\nTbilisi State University, HEP Institute, University St. 9, GE - 380086 Tbilisi, Georgia\n51 Justus-Liebig-Universitaet Giessen, II Physikalisches Institut, Heinrich-Buff Ring 16, D-35392\nGiessen, Germany\n52 University of Glasgow, Department of Physics and Astronomy, Glasgow G12 8QQ, United Kingdom\n53 Georg-August-Universitat, II. Physikalisches Institut, Friedrich-Hund Platz 1, D-37077 Goettingen,\nGermany\n54 Laboratoire de Physique Subatomique et de Cosmologie, CNRS/IN2P3, Universit\u00b4e Joseph Fourier,\nINPG, 53 avenue des Martyrs, FR - 38026 Grenoble Cedex, France\n55 Hampton University, Department of Physics, Hampton, VA 23668, United States of America\n56 Harvard University, Laboratory for Particle Physics and Cosmology, 18 Hammond Street,\nCambridge, MA 02138, United States of America\n57 Ruprecht-Karls-Universitaet Heidelberg, Kirchhoff-Institut fuer Physik(a), Im Neuenheimer Feld\n227, DE - 69120 Heidelberg; ZITI Ruprecht-Karls-University Heidelberg(b), Lehrstuhl fuer Informatik\nV, B6, 23-29, DE - 68131 Mannheim, Germany\n58 Hiroshima University, Faculty of Science, 1-3-1 Kagamiyama, Higashihiroshima-shi, JP - Hiroshima\n739-8526, Japan\n59 Hiroshima Institute of Technology, Faculty of Applied Information Science, 2-1-1 Miyake Saeki-ku,\nHiroshima-shi, JP - Hiroshima 731-5193, Japan\n60 Indiana University, Department of Physics, Swain Hall West 117, Bloomington, IN 47405-7105,\nUnited States of America\n61 Institut fuer Astro- und Teilchenphysik, Technikerstrasse 25, A - 6020 Innsbruck, Austria\n62 Iowa State University, Department of Physics and Astronomy,Ames High Energy Physics Group,\nTHE ATLAS COLLABORATION\nxvii\n\nAmes, IA 50011-3160, United States of America\n63 Joint Institute for Nuclear Research, JINR Dubna, RU - 141 980 Moscow Region, Russia\n64 KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba-shi, Ibaraki-ken 305-0801,\nJapan\n65 Kobe University, Graduate School of Science, 1-1 Rokkodai-cho, Nada-ku, JP Kobe 657-8501, Japan\n66 Kyoto University, Faculty of Science, Oiwake-cho, Kitashirakawa, Sakyou-ku, Kyoto-shi, JP - Kyoto\n606-8502, Japan\n67 Kyoto University of Education, 1 Fukakusa, Fujimori, fushimi-ku, Kyoto-shi, JP - Kyoto 612-8522,\nJapan\n68 Universidad Nacional de La Plata, FCE, Departamento de F\u00b4\u0131sica, IFLP (CONICET-UNLP), C.C. 67,\n1900 La Plata, Argentina\n69 Lancaster University, Physics Department, Lancaster LA1 4YB, United Kingdom\n70 INFN Sezione di Lecce(a); Universit`a del Salento, Dipartimento di Fisica(b), Via Arnesano IT -\n73100 Lecce, Italy\n71 University of Liverpool, Oliver Lodge Laboratory, P.O. Box 147, Oxford Street, Liverpool L69 3BX,\nUnited Kingdom\n72 University of Ljubljana, Jo\u02c7zef Stefan Institute and Department of Physics, SI-1000 Ljubljana,\nSlovenia\n73 Queen Mary University of London, Department of Physics, Mile End Road, London E1 4NS, United\nKingdom\n74 Royal Holloway, University of London, Department of Physics, Egham Hill, Egham, Surrey TW20\n0EX, United Kingdom\n75 University College London, Department of Physics and Astronomy, Gower Street, London WC1E\n6BT, United Kingdom\n76 Laboratoire de Physique Nucl\u00b4eaire et de Hautes Energies, Universit\u00b4e Pierre et Marie Curie (Paris 6),\nUniversit\u00b4e Denis Diderot (Paris-7), CNRS/IN2P3, Tour 33, 4 place Jussieu, FR - 75252 Paris Cedex 05,\nFrance\n77 Lunds universitet, Naturvetenskapliga fakulteten, Fysiska institutionen, Box 118, SE - 221 00 Lund,\nSweden\n78 Universidad Autonoma de Madrid, Facultad de Ciencias, Departamento de Fisica Teorica, ES -\n28049 Madrid, Spain\n79 Universitaet Mainz, Institut fuer Physik, Staudinger Weg 7, DE - 55099 Mainz, Germany\n80 University of Manchester, School of Physics and Astronomy, Manchester M13 9PL, United Kingdom\n81 CPPM, Aix-Marseille Universit\u00b4e, CNRS/IN2P3, Marseille, France\n82 University of Massachusetts, Department of Physics, 710 North Pleasant Street, Amherst, MA\n01003, United States of America\n83 McGill University, High Energy Physics Group, 3600 University Street, Montreal, Quebec H3A 2T8,\nCanada\n84 University of Melbourne, School of Physics, AU - Parkvill, Victoria 3010, Australia\n85 The University of Michigan, Department of Physics, 2477 Randall Laboratory, 500 East University,\nAnn Arbor, MI 48109-1120, United States of America\n86 Michigan State University, Department of Physics and Astronomy, High Energy Physics Group, East\nLansing, MI 48824-2320, United States of America\n87 INFN Sezione di Milano(a); Universit`a di Milano, Dipartimento di Fisica(b), via Celoria 16, IT -\n20133 Milano, Italy\n88 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Independence Avenue\n68, Minsk 220072, Republic of Belarus\n89 National Scienti\ufb01c & Educational Centre of Particle & High Energy Physics, NC PHEP BSU, M.\nTHE ATLAS COLLABORATION\nxviii\n\nBogdanovich St. 153, Minsk 220040, Republic of Belarus\n90 Massachusetts Institute of Technology, Department of Physics, Room 24-516, Cambridge, MA\n02139, United States of America\n91 University of Montreal, Group of Particle Physics, C.P. 6128, Succursale Centre-Ville, Montreal,\nQuebec, H3C 3J7 , Canada\n92 P.N. Lebedev Institute of Physics, Academy of Sciences, Leninsky pr. 53, RU - 117 924 Moscow,\nRussia\n93 Institute for Theoretical and Experimental Physics (ITEP), B. Cheremushkinskaya ul. 25, RU 117\n259 Moscow, Russia\n94 Moscow Engineering & Physics Institute (MEPhI), Kashirskoe Shosse 31, RU - 115409 Moscow,\nRussia\n95 Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, RU - 119 991 GSP-1\nMoscow Lenskie gory 1-2, Russia\n96 Ludwig-Maximilians-Universit\u00a8at M\u00a8unchen, Fakult\u00a8at f\u00a8ur Physik, Am Coulombwall 1, DE - 85748\nGarching, Germany\n97 Max-Planck-Institut f\u00a8ur Physik, (Werner-Heisenberg-Institut), F\u00a8ohringer Ring 6, 80805 M\u00a8unchen,\nGermany\n98 Nagasaki Institute of Applied Science, 536 Aba-machi, JP Nagasaki 851-0193, Japan\n99 Nagoya University, Graduate School of Science, Furo-Cho, Chikusa-ku, Nagoya, 464-8602, Japan\n100 INFN Sezione di Napoli(a); Universit`a di Napoli, Dipartimento di Scienze Fisiche(b), Complesso\nUniversitario di Monte Sant\u2019Angelo, via Cinthia, IT - 80126 Napoli, Italy\n101 University of New Mexico, Department of Physics and Astronomy,Albuquerque, NM 87131, United\nStates of America\n102 Radboud University Nijmegen/NIKHEF, Department of Experimental High Energy Physics,\nToernooiveld 1, NL - 6525 ED Nijmegen , Netherlands\n103 Nikhef National Institute for Subatomic Physics, and University of Amsterdam, Kruislaan 409, P.O.\nBox 41882, NL - 1009 DB Amsterdam, Netherlands\n104 Budker Institute of Nuclear Physics (BINP), RU - Novosibirsk 630 090, Russia\n105 New York University, Department of Physics, 4 Washington Place, New York NY 10003, USA,\nUnited States of America\n106 Ohio State University, 191 West Woodruff Ave, Columbus, OH 43210-1117, United States of\nAmerica\n107 Okayama University, Faculty of Science, Tsushimanaka 3-1-1, Okayama 700-8530, Japan\n108 University of Oklahoma, Homer L. Dodge Department of Physics and Astronomy, 440 West\nBrooks, Room 100, Norman, OK 73019-0225, United States of America\n109 Oklahoma State University, Department of Physics, 145 Physical Sciences Building, Stillwater, OK\n74078-3072, United States of America\n110 Palack\u00b4y University in Olomouc, streetname, Czech Republic\n111 1274 University of Oregon, Eugene, OR 97403-1274, United States of America\n112 LAL, Univ. Paris-Sud, IN2P3/CNRS, Orsay, France\n113 Osaka University, Graduate School of Science, Machikaneyama-machi 1-1, Toyonaka, Osaka\n560-0043, Japan\n114 University of Oslo, Department of Physics, P.O. Box 1048, Blindern, NO - 0316 Oslo 3, Norway\n115 Oxford University, Department of Physics, Denys Wilkinson Building, Keble Road, Oxford OX1\n3RH, United Kingdom\n116 INFN Sezione di Pavia(a); Universit`a di Pavia, Dipartimento di Fisica Nucleare e Teorica(b), Via\nBassi 6, IT-27100 Pavia, Italy\n117 University of Pennsylvania, Department of Physics, High Energy Physics Group, 209 S. 33rd Street,\nTHE ATLAS COLLABORATION\nxix\n\nPhiladelphia, PA 19104, United States of America\n118 Petersburg Nuclear Physics Institute, RU - 188 300 Gatchina, Russia\n119 INFN Sezione di Pisa(a); Universit`a di Pisa, Dipartimento di Fisica E. Fermi(b), Largo B.Pontecorvo\n3, IT - 56127 Pisa, Italy\n120 University of Pittsburgh, Department of Physics and Astronomy, 3941 O\u2019Hara Street, Pittsburgh, PA\n15260, United States of America\n121 (a)Universidad de Granada, Departamento de Fisica Teorica y del Cosmos and CAFPE, E-18071\nGranada; Laboratorio de Instrumentacao e Fisica Experimental de Particulas - LIP(b), Avenida Elias\nGarcia 14-1, PT - 1000-149 Lisboa, Portugal\n122 Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ - 18221 Praha\n8, Czech Republic\n123 Charles University in Prague, Faculty of Mathematics and Physics, Institute of Particle and Nuclear\nPhysics, V Holesovickach 2, CZ - 18000 Praha 8, Czech Republic\n124 Czech Technical University in Prague, Zikova 4, CZ - 166 35 Praha 6, Czech Republic\n125 Institute for High Energy Physics (IHEP), Federal Agency of Atom. Energy, Moscow Region, RU -\n142 284 Protvino, Russia\n126 Rutherford Appleton Laboratory, Science and Technology Facilities Council, Harwell Science and\nInnovation Campus, Didcot OX11 0QX, United Kingdom\n127 University of Regina, Physics Department, Canada\n128 Ritsumeikan University, Noji Higashi 1 chome 1-1, JP - Kusatsu, Shiga 525-8577, Japan\n129 INFN Sezione di Roma I(a); Universit`a La Sapienza, Dipartimento di Fisica(b), Piazzale A. Moro 2,\nIT- 00185 Roma, Italy\n130 INFN Sezione di Roma Tor Vergata(a); Universit`a di Roma Tor Vergata, Dipartimento di Fisica(b) ,\nvia della Ricerca Scienti\ufb01ca, IT-00133 Roma, Italy\n131 INFN Sezione di Roma Tre(a); Universit`a Roma Tre, Dipartimento di Fisica(b), via della Vasca\nNavale 84, IT-00146 Roma, Italy\n132 Universit\u00b4e Hassan II, Facult\u00b4e des Sciences Ain Chock(a), B.P. 5366, MA - Casablanca; Centre\nNational de l\u2019Energie des Sciences Techniques Nucleaires (CNESTEN)(b), Rabat; Universit\u00b4e Mohamed\nPremier(c)LPTPM, Facult\u00b4e des Sciences, B.P.717. Bd. Mohamed VI, 60000, Oujda ; Universit\u00b4e\nMohammed V, Facult\u00b4e des Sciences(d), BP 1014, MO - Rabat, Morocco\n133 CEA, DSM/IRFU, Centre d\u2019Etudes de Saclay, FR - 91191 Gif-sur-Yvette, France\n134 University of California Santa Cruz, Santa Cruz Institute for Particle Physics (SCIPP), Santa Cruz,\nCA 95064, United States of America\n135 University of Washington, Seattle, Department of Physics, Box 351560, Seattle, WA 98195-1560,\nUnited States of America\n136 University of Shef\ufb01eld, Department of Physics & Astronomy, Houns\ufb01eld Road, Shef\ufb01eld S3 7RH,\nUnited Kingdom\n137 Shinshu University, Department of Physics, Faculty of Science, 3-1-1 Asahi, Matsumoto-shi, JP -\nNagano 390-8621, Japan\n138 Universitaet Siegen, Fachbereich Physik, DE - 57068 Siegen, Germany\n139 Simon Fraser University, Department of Physics, 8888 University Drive, CA - Burnaby, BC V5A\n1S6, Canada\n140 SLAC National Accelerator Laboratory, Stanford, California 94309, United States of America\n141 Comenius University, Faculty of Mathematics, Physics & Informatics, Mlynska dolina F2, SK -\n84248 Bratislava; Institute of Experimental Physics of the Slovak Academy of Sciences, Dept. of\nSubnuclear Physics, Watsonova 47, SK - 04353 Kosice, Slovak Republic\n142 Stockholm University, Department of Physics, AlbaNova, SE - 106 91 Stockholm, Sweden\n143 Royal Institute of Technology (KTH), Physics Department, SE - 106 91 Stockholm, Sweden\nTHE ATLAS COLLABORATION\nxx\n\n144 Stony Brook University, Department of Physics and Astronomy, Nicolls Road, Stony Brook, NY\n11794-3800, United States of America\n145 University of Sydney, School of Physics, AU - Sydney NSW 2006, Australia\n146 Insitute of Physics, Academia Sinica, TW - Taipei 11529, Taiwan\n147 Technion, Israel Inst. of Technology, Department of Physics, Technion City, IL - Haifa 32000, Israel\n148 Tel Aviv University, Raymond and Beverly Sackler School of Physics and Astronomy, Ramat Aviv,\nIL - Tel Aviv 69978, Israel\n149 Aristotle University of Thessaloniki, Faculty of Science, Department of Physics, Division of\nNuclear & Particle Physics, University Campus, GR - 54124, Thessaloniki, Greece\n150 The University of Tokyo, International Center for Elementary Particle Physics and Department of\nPhysics, 7-3-1 Hongo, Bunkyo-ku, JP - Tokyo 113-0033, Japan\n151 Tokyo Metropolitan University, Graduate School of Science and Technology, 1-1 Minami-Osawa,\nHachioji, Tokyo 192-0397, Japan\n152 University of Toronto, Department of Physics, 60 Saint George Street, Toronto M5S 1A7, Ontario,\nCanada\n153 TRIUMF(a), 4004 Wesbrook Mall, Vancouver, B.C. V6T 2A3; (b)York University, Department of\nPhysics and Astronomy, 4700 Keele St., Toronto, Ontario, M3J 1P3, Canada\n154 University of Tsukuba, Institute of Pure and Applied Sciences, 1-1-1 Tennoudai, Tsukuba-shi, JP -\nIbaraki 305-8571, Japan\n155 Tufts University, Science & Technology Center, 4 Colby Street, Medford, MA 02155, United States\nof America\n156 Universidad Antonio Narino, Centro de Investigaciones, Cra 3 Este No.47A-15, Bogota, Colombia\n157 University of California, Irvine, Department of Physics & Astronomy, CA 92697-4575, United\nStates of America\n158 INFN Gruppo Collegato di Udine(a); ICTP(b), Strada Costiera 11, IT-34014, Trieste; Universit`a di\nUdine, Dipartimento di Fisica(c), via delle Scienze 208, IT - 33100 Udine, Italy\n159 University of Uppsala , Department of Physics and Astronomy, P.O. Box 516, SE- 75120 Uppsala,\nSweden\n160 University of Illinois , Department of Physics, 1110 West Green Street, Urbana, Illinois 61801,\nUnited States of America\n161 Instituto de F\u00b4\u0131sica Corpuscular (IFIC) Centro Mixto UVEG-CSIC, Apdo. 22085 ES-46071\nValencia, Dept. F\u00b4\u0131sica At. Mol. y Nuclear; Univ. of Valencia, and Instituto de Microelectr\u00b4onica de\nBarcelona (IMB-CNM-CSIC) 08193 Bellaterra Barcelona, Spain\n162 University of British Columbia, Department of Physics, 6224 Agricultural Road, CA - Vancouver,\nB.C. V6T 1Z1, Canada\n163 University of Victoria, Department of Physics and Astronomy, P.O. Box 3055, Victoria B.C., V8W\n3P6, Canada\n164 The Weizmann Institute of Science, Department of Particle Physics, P.O. Box 26, IL - 76100\nRehovot, Israel\n165 University of Wisconsin, Department of Physics, 1150 University Avenue, WI 53706 Madison,\nWisconsin, , United States of America\n166 Julius-Maximilians-University of W\u00a8urzburg, Physikalisches Institute, Am Hubland, 97074\nWuerzburg , Germany\n167 Bergische Universitaet, Fachbereich C, Physik, Postfach 100127, Gauss-Strasse 20, D- 42097\nWuppertal, Germany\n168 Yale University, Department of Physics, PO Box 208121, New Haven CT, 06520-8121 , United\nStates of America\n169 Yerevan Physics Institute, Alikhanian Brothers Street 2, AM - 375036 Yerevan, Armenia\nTHE ATLAS COLLABORATION\nxxi\n\n170 ATLAS-Canada Tier-1 Data Centre 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada\n171 GridKA Tier-1 FZK, Forschungszentrum Karlsruhe GmbH, Steinbuch Centre for Computing (SCC),\nHermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany\n172 Port d\u2019Informaci Cient\ufb01ca (PIC), Universitat Autnoma de Barcelona (UAB), Edi\ufb01ci D, E-08193\nBellaterra, Spain\n173 Centre de Calcul CNRS/IN2P3, Domaine scienti\ufb01que de la Doua, 27 bd du 11 Novembre 1918,\n69622 Villeurbanne Cedex, France\n174 INFN-CNAF, Viale Berti Pichat 6/2, 40127 Bologna, Italy\n175 Nordic Data Grid Facility, NORDUnet A/S, Kastruplundgade 22, 1, DK-2770 Kastrup, Denmark\n176 SARA Reken- en Netwerkdiensten, Science Park 121, 1098 XG Amsterdam, Netherlands\n177 Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, No.128, Sec. 2, Academia\nRd., Nankang, Taipei, Taiwan 11529, Taiwan\n178 UK-T1-RAL Tier-1, Rutherford Appleton Laboratory, Science and Technology Facilities Council,\nHarwell Science and Innovation Campus, Didcot OX11 0QX, United Kingdom\n179 RHIC and ATLAS Computing Facility, Physics Department, Building 510, Brookhaven National\nLaboratory, Upton, New York 11973, United States of America\na Also at TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. V6T 2A3, Canada\nb Also at CPPM, Aix-Marseille Universit\u00b4e, CNRS/IN2P3, Marseille, France\nc Also at Gaziantep University, Turkey\nd University of Iowa, 203 Van Allen Hall, Iowa City IA 52242-1479, United States of America\ne Also at Laboratoire de Physique Subatomique et de Cosmologie, CNRS/IN2P3, Universit\u00b4e Joseph\nFourier, INPG, 53 avenue des Martyrs, FR - 38026 Grenoble Cedex, France\nf Also at Institute for Particle Phenomenology, Ogden Centre for Fundamental Physics, Department of\nPhysics, University of Durham, Science Laboratories, South Rd, Durham DH1 3LE, United Kingdom\ng Also at TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C. V6T 2A3, Canada\nh Currently at Dogus University, Kadik\ni Also at Universit`a di Napoli Parthenope, via A. Acton 38, IT - 80133 Napoli, Italy\nj Also at Institute of Particle Physics (IPP), Canada\nk Louisiana Tech University, 305 Wisteria Street, P.O. Box 3178, Ruston, LA 71272, United States of\nAmerica\nl Currently at Dumlupinar University, Kutahya, Turkey\nm Currently at Department of Physics, University of Helsinki, P.O. Box 64, FI-00014, Finland\nn Also at Institut f\u00a8ur Experimentalphysik, Universit\u00a8at Hamburg, Luruper Chaussee 149, 22761\nHamburg, Germany\no Also at H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland\np At Department of Physics, California State University, Fresno, 2345 E. San Ramon Avenue, Fresno,\nCA 93740-8031, United States of America\nq Also at California Institute of Technology, Physics Department, Pasadena, CA 91125, United States of\nAmerica\nr Also at Petersburg Nuclear Physics Institute, RU - 188 300 Gatchina, Russia\ns Also at Rutherford Appleton Laboratory, Science and Technology Facilities Council, Harwell Science\nand Innovation Campus, Didcot OX11 0QX, United Kingdom\nt University of South Carolina, Dept. of Physics and Astronomy, 700 S. Main St, Columbia, SC 29208,\nUnited States of America\nu Also at Institute of Physics, Jagiellonian University, Cracow, Poland\nv Currently at TOBB University, Ankara, Turkey\nw Also at KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary\nx Currently at TAEA, Ankara, Turkey\nTHE ATLAS COLLABORATION\nxxii\n\ny Currently at Gazi University, Ankara, Turkey\nz Also at Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918, CN-100049\nBeijing, China\n\u2217Deceased\nTHE ATLAS COLLABORATION\nxxiii\n\nAcknowledgements\nWe are greatly indebted to all CERN\u2019s departments and to the LHC project for their immense efforts\nnot only in building the LHC, but also for their direct contributions to the construction and installation of\nthe ATLAS detector and its infrastructure. We acknowledge equally warmly all our technical colleagues\nin the collaborating Institutions without whom the ATLAS detector could not have been built. Further-\nmore we are grateful to all the funding agencies which supported generously the construction and the\ncommissioning of the ATLAS detector and also provided the computing infrastructure.\nThe ATLAS detector design and construction has taken about \ufb01fteen years, and our thoughts are with\nall our colleagues who sadly could not see its \ufb01nal realisation.\nWe acknowledge the support of ANPCyT, Argentina; Yerevan Physics Institute, Armenia; ARC\nand DEST, Australia; Bundesministerium f\u00a8ur Wissenschaft und Forschung, Austria; National Academy\nof Sciences of Azerbaijan; State Committee on Science & Technologies of the Republic of Belarus;\nCNPq and FINEP, Brazil; NSERC, NRC, and CFI, Canada; CERN; NSFC, China; Ministry of Educa-\ntion, Youth and Sports of the Czech Republic, Ministry of Industry and Trade of the Czech Republic,\nand Committee for Collaboration of the Czech Republic with CERN; Danish Natural Science Research\nCouncil; European Commission, through the ARTEMIS Research Training Network; IN2P3-CNRS and\nDapnia-CEA, France; Georgian Academy of Sciences; BMBF, DESY, DFG and MPG, Germany; Min-\nistry of Education and Religion, through the EPEAEK program PYTHAGORAS II and GSRT, Greece;\nISF, MINERVA, GIF, DIP, and Benoziyo Center, Israel; INFN, Italy; MEXT, Japan; CNRST, Morocco;\nFOM and NWO, Netherlands; The Research Council of Norway; Ministry of Science and Higher Edu-\ncation, Poland; GRICES and FCT, Portugal; Ministry of Education and Research, Romania; Ministry of\nEducation and Science of the Russian Federation, Russian Federal Agency of Science and Innovations,\nand Russian Federal Agency of Atomic Energy; JINR; Ministry of Science, Serbia; Department of Inter-\nnational Science and Technology Cooperation, Ministry of Education of the Slovak Republic; Slovenian\nResearch Agency, Ministry of Higher Education, Science and Technology, Slovenia; Ministerio de Ed-\nucaci\u00b4on y Ciencia, Spain; The Swedish Research Council, The Knut and Alice Wallenberg Foundation,\nSweden; State Secretariat for Education and Science, Swiss National Science Foundation, and Cantons\nof Bern and Geneva, Switzerland; National Science Council, Taiwan; TAEK, Turkey; The Science and\nTechnology Facilities Council, United Kingdom; DOE and NSF, United States of America.\nxxiv\n\nIntroduction\n1\n\nPreface\nThe Large Hadron Collider (LHC) at CERN promises a major step forward in the understanding of\nthe fundamental nature of matter. The ATLAS experiment is a general-purpose detector for the LHC,\nwhose design was guided by the need to accommodate the wide spectrum of possible physics signatures.\nThe major remit of the ATLAS experiment is the exploration of the TeV mass scale where ground-\nbreaking discoveries are expected. In the focus are the investigation of the electroweak symmetry break-\ning and linked to this the search for the Higgs boson as well as the search for Physics beyond the Standard\nModel.\nIn this report a detailed examination of the expected performance of the ATLAS detector is provided,\nwith a major aim being to investigate the experimental sensitivity to a wide range of measurements and\npotential observations of new physical processes. An earlier summary of the expected capabilities of\nATLAS was compiled in 1999 [1]. A survey of physics capabilities of the CMS detector was published\nin [2].\nThe design of the ATLAS detector has now been \ufb01nalised, and its construction and installation have\nbeen completed [3]. An extensive test-beam programme was undertaken. Furthermore, the simulation\nand reconstruction software code and frameworks have been completely rewritten. Revisions incorpo-\nrated re\ufb02ect improved detector modelling as well as major technical changes to the software technology.\nGreatly improved understanding of calibration and alignment techniques, and their practical impact on\nperformance, is now in place.\nThe studies reported here are based on full simulations of the ATLAS detector response. A variety\nof event generators were employed. The simulation and reconstruction of these large event samples thus\nprovided an important operational test of the new ATLAS software system. In addition, the processing\nwas distributed world-wide over the ATLAS Grid facilities and hence provided an important test of\nthe ATLAS computing system \u2013 this is the origin of the expression \u201cCSC studies\u201d (\u201ccomputing system\ncommissioning\u201d), which is occasionally referred to in these volumes.\nThe work reported does generally assume that the detector is fully operational, and in this sense\nrepresents an idealised detector: establishing the best performance of the ATLAS detector with LHC\nproton-proton collisions is a challenging task for the future. The results summarised here therefore\nrepresent the best estimate of ATLAS capabilities before real operational experience of the full detector\nwith beam. Unless otherwise stated, simulations also do not include the effect of additional interactions\nin the same or other bunch-crossings, and the effect of neutron background is neglected. Thus simulations\ncorrespond to the low-luminosity performance of the ATLAS detector.\nThis report is broadly divided into two parts: \ufb01rstly the performance for identi\ufb01cation of physics\nobjects is examined in detail, followed by a detailed assessment of the performance of the trigger sys-\ntem. This part is subdivided into chapters surveying the capabilities for charged particle tracking, each of\nelectron/photon, muon and tau identi\ufb01cation, jet and missing transverse energy reconstruction, b-tagging\nalgorithms and performance, and \ufb01nally the trigger system performance. In each chapter of the report,\nthere is a further subdivision into shorter notes describing different aspects studied. The second major\nsubdivision of the report addresses physics measurement capabilities, and new physics search sensitiv-\nities. Individual chapters in this part discuss ATLAS physics capabilities in Standard Model QCD and\nelectroweak processes, in the top quark sector, in b-physics, in searches for Higgs bosons, supersymme-\ntry searches, and \ufb01nally searches for other new particles predicted in more exotic models.\nReferences\n[1] ATLAS Collaboration, CERN-LHCC/99-014, CERN-LHCC/99-015 (1999).\n[2] CMS Collaboration, G. L. Bayatian et al., J. Phys. G34 (2007) 995.\n[3] ATLAS Collaboration, G. Aad et al., JINST 3 (2008) S08003.\n2\n\nCross-Sections, Monte Carlo Simulations and Systematic\nUncertainties\nAbstract\nThe studies presented in this volume share several common features, including\nuse of the same event samples for Standard Model processes, and the same de-\ntector description and simulation framework for all samples. Common cross-\nsection assumptions were made. These assumptions, and the Monte Carlo\ngenerator programs employed, are listed. Information is also given on the dif-\nferent detector con\ufb01gurations and geometries simulated, and on the consistent\ntreatment of systematic uncertainties.\n1\nIntroduction\nThe studies presented in this volume have many shared features starting from a common simulation\nframework of the ATLAS detector, and the same detector description. They are based on a full simulation\nof the ATLAS detector using the GEANT4 [1] program and the event samples produced were shared by\nthe various analysis groups. For the simulation of the physics events standard event generators for high\nenergy proton-proton collisions were used and interfaced to the ATLAS simulation framework.\nIn many searches for new particles at the LHC Standard Model processes represent important back-\ngrounds and the signal signi\ufb01cance depends on the precise knowledge of these backgrounds. As dis-\ncussed in several studies presented in this book, methods were investigated on how to determine these\ncross-sections from the data themselves. However, this will not be always possible, and reliable theo-\nretical predictions must be used to estimate these backgrounds. In addition, the Standard Model cross-\nsections are relevant for the estimate of signal rates and consequent measurement precision for Standard\nModel parameters, or for tests of the Standard Model. All studies presented in this book made common\nassumptions on the cross-sections for Standard Model processes.\nIn this introductory note features common to the simulations used in these studies are discussed.\nAfter reviewing the cross-section assumptions and models used for different processes, the Monte Carlo\ngenerator programs employed are summarised. Information is given, next, on the different detector\ncon\ufb01gurations and geometries simulated. Finally, a common treatment is described of systematic uncer-\ntainties which affect many analyses.\n2\nCross-Sections of Physical Processes\nA consistent set of cross-sections for Standard Model processes was used in all studies reported in this\nvolume. Over recent years considerable progress has been made in the calculation of higher-order QCD\ncorrections (often expressed as \u201cK-factors\u201d) for many physics processes at the LHC. Wherever these\ncorrections are known for both the signal and the dominant background processes, they were included\nin the analyses. In case the K-factors are not known for the dominant background processes, the studies\nhave consistently refrained from using K-factors and resorted to Born-level predictions for both signal\nand backgrounds. In this note we detail the values of cross-sections that were used in the different studies\nreported in this volume: we do not discuss the uncertainties, such as those from missing higher order\ncorrections.\nFor the simulation of physics processes both leading order (LO) and next-to-leading order (NLO)\nMonte Carlo programs were used. For the simulation of several processes tree-level matrix element\ncalculations with parton shower matching were adopted. Unless otherwise stated, all tree-level Monte\n3\n\nCarlo calculations were normalized to the NLO cross-section calculation. In the case of parton shower\nmatching several \ufb01nal state parton multiplicities were simulated for prede\ufb01ned shower matching cuts\nand the sum of the exclusive cross-sections was normalized to the result of the higher-order calculation.\nBy applying this procedure, it is expected that the shapes of inclusive distributions are reasonably well\ndescribed. However, large uncertainties are expected in the absolute cross-section predictions in extreme\nphase-space regions such as, for example, \ufb01nal states with high jet multiplicities.\nTable 1: Leading order (LO) and higher order (N)NLO cross-sections for some important Standard\nModel production processes for pp collisions at a centre-of-mass energy of 14 TeV. In the calculation\nof all cross-sections the CTEQ6L and CTEQ6M structure function parametrizations have been used.\nFor inclusive W and Z production, the cross-section quoted includes the branching ratio into one lepton\ngeneration.\nProcess\nComments\nReference\nOrder in\n\u03c3 (nb)\npert. theory\nTotal inelastic pp\nPYTHIA [2]\n79\u00b7106\nNon Single Diffractive\nPYTHIA [2]\n65\u00b7106\nDijet\npjet\nT > 25 GeV\nPYTHIA [2]\nLO\n367\u00b7103\nNLOJET++ [3,4]\nNLO\n477\u00b7103\n\u03b3-jet\np\u03b3\nT > 25 GeV\nPYTHIA [2]\nLO\n180\nb\u00afb \u2192\u00b5 + X\np\u00b5\nT > 6 GeV\nPYTHIA [2]\nLO\n6.1\u00b7103\nb\u00afb \u2192\u00b5\u00b5 + X\np\u00b51/\u00b52\nT\n> 6 / 4 GeV\nPYTHIA [2]\nLO\n110\nt\u00aft\nNLO\n0.794\nRef. [5]\nNLO+NLL\n0.833\nSingle top\nt-channel\nAcerMC [6]\nLO\n0.251\nproduction\nRef. [7\u20139]\nNLO\n0.246\ns-channel\nAcerMC [6]\nLO\n0.007\nRef. [7]\nNLO\n0.011\nWt\nAcerMC [6]\nLO\n0.058\nRef. [10\u201312]\nNLO\n0.066\nW \u2192\u2113\u03bd\nFEWZ [13]\nLO\n16.8\nFEWZ [13]\nNLO\n20.7\nFEWZ [13]\nNNLO\n20.5\nZ \u2192\u2113\u2113\nm\u2113\u2113> 60 GeV\nFEWZ [13]\nLO\n1.66\nFEWZ [13]\nNLO\n2.03\nFEWZ [13]\nNNLO\n2.02\nWW\nmW (\u2217) > 20 GeV, pW\nT >10 GeV\nMCFM [14]\nLO\n0.072\nMCFM [14]\nNLO\n0.112\nWZ\nmW (\u2217)/Z(\u2217) > 20 GeV, pW/Z\nT\n> 10 GeV\nMCFM [14]\nLO\n0.032\nMCFM [14]\nNLO\n0.056\nZZ\nmZ(\u2217) > 12 GeV\nMCFM [14]\nLO\n0.0165\nMCFM [14]\nNLO\n0.0221\n\u03b3\u03b3\n(qq,qg \u2192\u03b3\u03b3)\n80 < m\u03b3\u03b3 <150 GeV\nRESBOS [15]\nNLO\n0.0209\n(gg \u2192\u03b3\u03b3)\n80 < m\u03b3\u03b3 <150 GeV\nRESBOS [15]\nNLO\n0.0080\nThe cross-sections for the most relevant Standard Model production processes are summarised in\nTable 1. The cross-sections for new physics signal processes are presented in the respective sub-chapters\nof this book. For the calculation of the leading order cross-sections the CTEQ6L [16, 17] set of struc-\nture function parametrizations was used. Processes available at (N)NLO were calculated by using the\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n4\n\nCTEQ6M [16,17] parametrizations. The following comments concern the various cross-sections:\n\u2022 The total pp cross-section at a centre-of-mass energy of 14 TeV is predicted by PYTHIA [2] to be\n102 mb. This is split into elastic (23 mb) and inelastic (79 mb) parts. The total inelastic pp cross-\nsection includes contributions from single and double-diffractive scattering which are estimated\nto be 14 and 10 mb, respectively. The non-single diffractive cross-section, which is usually also\ndenoted as the minimum bias cross-section, is given by \u03c3NSD = \u03c3inel. \u2212\u03c3SD = 65 mb.\n\u2022 Multijet production via QCD processes is the dominant high-pT process at the LHC and is an im-\nportant background in many physics studies. Even if next-to-leading order corrections are partially\nknown, the remaining uncertainties from missing higher-order corrections remain large. We there-\nfore used leading-order estimates in most physics studies and large errors were assigned to cover\nthe uncertainty.\n\u2022 The pair production of b-quarks provides a copious source of leptons at the LHC. The single and\ndimuon cross-sections from b\u00afb production were calculated with pT thresholds as expected at the\ntrigger level. A leading order PYTHIA calculation has been used in the present studies. Even if\nthe higher-order corrections are known [18], large uncertainties remain.\n\u2022 For the t\u00aft production cross-section several calculations beyond leading order exist. In the studies\npresented in this volume the NLO calculation including a next-to-leading log (NLL) resummation\n[5] was used. The cross-sections for the three relevant sub-processes for single-top production\nwere calculated at NLO.\n\u2022 The inclusive production cross-sections of W and Z bosons are known at next-to-next-to-leading\norder (NNLO) and these values were used in the studies. The residual uncertainties from variations\nof the renormalization and factorization scales are estimated to be at the level of a few percent [13].\nIn many cases the production of W and Z bosons with jets constitutes an important background to\nsearches. Exclusive W/Z + jet cross sections have in general been calculated with leading order\nMonte Carlos, such as PYTHIA, or the parton shower matched Monte Carlos ALPGEN or Sherpa.\nThese calculations were normalized to the inclusive NNLO cross-sections. Only in case of the\nWb\u00afb and Zb\u00afb production were exclusive NLO cross-sections calculated, to which the tree-level\nMonte Carlo generator results were normalized. The results of these calculations for a few rele-\nvant phase space regions are:\nProcess\nComments\nReference\nOrder in\n\u03c3 (pb)\npert. theory\nWb\u00afb\npb\nT > 10 GeV, |\u03b7b| < 2.5, \u2206Rb\u00afb >0.7\nALPGEN [19]\nLO\n68.7\nm(\u2217)\nW > 30 GeV, mb\u00afb > 9.24 GeV\nMCFM [14]\nNLO\n176.9\nZb\u00afb\npb\nT > 10 GeV, |\u03b7b| < 2.5, \u2206Rb\u00afb >0.7\nAcerMC [6]\nLO\n60.7\nm(\u2217)\nZ\n> 30 GeV, mb\u00afb > 9.24 GeV\nMCFM [14]\nNLO\n86.4\nZb\u00afb\npb\nT > 5 GeV, |\u03b7b| < 2.5, \u2206Rb\u00afb >0.7\nAcerMC [6]\nLO\n27.9\nm(\u2217)\nZ\n> 60 GeV, mb\u00afb > 9.24 GeV\nMCFM [14]\nNLO\n44.8\n\u2022 The cross-sections for diboson production are available at NLO. In addition to the q \u00afq-initiated\nprocesses, the gg box-diagram contributions are sizeable, and both have been taken into account\nin the analyses. For ZZ production the gg box contributions were estimated to be at the level of\n30% [20] and the NLO result was scaled accordingly. A re-evaluation of this contribution using\nthe program of Ref. [21] yielded a contribution of 23.8%. For the \u03b3\u03b3 production process the box\ncontribution was calculated using the RESBOS Monte Carlo program [15].\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n5\n\n3\nMonte Carlo Simulation\nThe samples of fully simulated events were made using a variety of Monte Carlo generators. Interfaces\nin the ATLAS software framework provided mechanisms to feed the particle-level events generated into\nthe ATLAS simulation software packages. The production of these events was a major effort: a plethora\nof physics processes were simulated, and over 1300 different data sets were produced. Unless otherwise\nstated, samples were produced simulating only one proton-proton interaction: the effect of additional\ninteractions was neglected.\nThe principal general-purpose Monte Carlo generators employed were PYTHIA, HERWIG, Sherpa,\nAcerMC, ALPGEN, MadGraph/MadEvent and MC@NLO. In addition to these, further generators were\nused for speci\ufb01c processes: Charybdis, CompHEP, TopReX and WINHAC. The versions of the gen-\nerators used are summarised in Table 2. Parton-level Monte Carlo generators used either PYTHIA or\nHERWIG/JIMMYfor hadronisation and underlying event modelling. HERWIG hadronisation was com-\nplemented by an underlying event simulation from the JIMMY program [22] (versions 4.2 and 4.31).\nThe underlying event model parameters were tuned, for PYTHIA and HERWIG/JIMMY, to published\ndata from Tevatron and other experiments, as described in Ref. [23] and references therein. For Sherpa,\nthe default parton shower and underlying event modelling was used. Examples of the speci\ufb01c processes\ngenerated with each program are given in the Appendix.\nTable 2: Monte Carlo event generators used for the production of event samples for the studies reported\nhere. The fourth column shows, for the parton-level event generators, which software was used for the\nhadronisation and underlying event (UE) simulation.\nGenerator\nVersions\nReference\nHadronisation+UE\nPYTHIA\n6.323-6.411\n[2]\nHERWIG\n6.508-6.510\n[24]\nJIMMY for UE\nSherpa\n1.008-1.011\n[25]\nAcerMC\n3.1-3.4\n[26]\nPYTHIA,HERWIG\nALPGEN\n2.05-2.13\n[19]\nHERWIG/JIMMY\nMadGraph/MadEvent\n3.X-4.15\n[27]\nPYTHIA\nMC@NLO\n3.1-3.3\n[28]\nHERWIG/JIMMY\nCharybdis\n1.001-1.003\n[29]\nHERWIG/JIMMY\nCompHEP\n\u2013\n[30]\nPYTHIA\nTopReX\n4.11\n[31]\nPYTHIA\nWINHAC\n1.21\n[32]\nPYTHIA\nThe decay of \u03c4 leptons was normally not treated by the main Monte Carlo generators themselves, but\nrather via the TAUOLA package [33], version 2.7. The radiation of photons from charged leptons was\nalso treated specially, using the PHOTOS QED radiation package, version 2.15 [34]. These two pack-\nages were used for a range of processes and generators: this required implementation of new interfaces\nfor HERWIG and Sherpa. When simulating speci\ufb01c b-hadron decays for B-physics analyses [35], the\nEvtGen [36] dedicated b-hadron decay package was used in combination with PYTHIA.\nThe Monte Carlo tools in ATLAS are taken, where available, from the LHC Computing Grid GENSER\n(generator services) sub-project [37]. These are modi\ufb01ed with custom ATLAS software patches when\nneeded. For most Monte Carlo programs more than one version was employed during the long series\nof simulations: changes in version were motivated by physical model, or technical improvements to the\npackage. Common particle mass de\ufb01nitions were also used where relevant (for example, the top mass\nwas taken to be 175 GeV, unless otherwise stated). The Monte Carlo tools are then either wrapped in-\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n6\n\nside the ATLAS Athena environment [38], or interfaced via the Les Houches accord event format [39],\ndepending on the implementation simplicity. The latter interfaces were used for the Sherpa, AcerMC,\nALPGEN, MadGraph/MadEvent, MC@NLO and CompHEP event generation. These interfaces rely on\nwidespread use of the HepMC C++-based event record format [40]: several improvements were made\nduring the series of event production processings.\nLHAPDF, the Les Houches accord PDF interface library [41], was used throughout, and was linked\nto all Monte Carlo event generators to provide the PDF set values. The PDF sets [16] used were CTEQ6L\nfor leading order (LO) Monte Carlo event generators, and CTEQ6M for the next-to-leading order (NLO)\nMonte Carlo event generator MC@NLO.\n4\nDetector Description\nOne important aspect of the Computing Commissioning Challenge was the test of the alignment and\ncalibration procedures with an imperfect, i.e. more realistic, description of the ATLAS detector. In\nparticular, misalignments were introduced for the inner detector and additional material was added in the\ninner detector and in front of the calorimeters. In addition, distorted magnetic \ufb01eld con\ufb01gurations were\nintroduced, where the symmetry axis of the \ufb01eld did not coincide with the beam axis.\nThe goal was to establish and validate the alignment and calibration procedures and to determine the\nknown distortions. This has a strong physics motivation: for example, a knowledge of the energy scale\nof the electromagnetic calorimeter with a precision of 0.02%, as required for a precise measurement of\nthe W mass, requires knowledge of the total radiation length of the material in the inner detector with a\nprecision at the level of 1%.\nTwo different geometries were used in the simulations. In a so-called as-built geometry realistic\nalignment shifts and distortions of the magnetic \ufb01eld were introduced. In the distorted geometry addi-\ntional material was added. The calibration samples were simulated and calibration constants determined\nwith the as-built geometry. All physics samples were, however, simulated with the distorted geometry\nand the calibrations constants as determined from the as-built geometry were applied.\nAs-built geometry\nThe as-built geometry includes misalignments of the main subdetectors (pixel de-\ntector, silicon microstrip tracker (SCT), and transition radiation tracker (TRT)) of the inner detector. The\nmisalignments were introduced as independent translations and rotations at three levels: (i) of the main\nsubdetector parts (pixel detector, SCT barrel, two SCT endcaps, TRT barrel and two TRT endcaps), (ii)\nof major detector sub-units, like pixel and SCT barrel layers, pixel and SCT endcap disks and TRT barrel\nmodules and (iii) of individual silicon detector modules. The sizes of displacements were chosen to lie\nwithin the expected build tolerances. The actual displacements were assigned randomly in most cases.\nThe shifts described in the following were applied for the levels (i) and (ii) in the global ATLAS co-\nordinate system, de\ufb01ned as a right-handed system with the x-axis pointing to the centre of the LHC ring,\nthe y-axis in the vertical direction and the z-axis along the beam direction. The level (iii) misalignments\nrefer to the local coordinate system of individual detector modules.\nAt level (i), the whole subdetector parts were displaced in the three spatial coordinates at the level of\n1-2 mm followed by rotations around the three axes at the level of 10-50 mrad.\nThe alignments of the endcap detector sub-units include additional in-plane (x-y) displacements and\nrotations around the z-axis. They were generated randomly from uniform distributions centred around\nzero with a width of \u00b1150 \u00b5m and \u00b11 mrad, respectively. For the TRT barrel modules the translations\nare generated randomly from uniform distributions around zero, with widths of \u00b1200 \u00b5m, \u00b1100 \u00b5m and\n\u00b1300 \u00b5m respectively for modules of the three TRT layers. In addition, a systematic radial shift of +1.0,\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n7\n\n-0.5 and +1.5 mm is applied for all modules of the respective layers. No rotations nor displacements\nwere applied to the TRT endcap modules.\nFor the individual pixel and SCT detector modules individual position displacements were applied\nrandomly from uniform distributions with widths of 30-50 \u00b5m for pixel and 100-150 \u00b5m for SCT mod-\nules, followed by rotations around the three axes, also randomly chosen from uniform distributions with\nwidths of \u00b11 mrad.\nDistorted geometry\nThe distorted geometry is based on the as-built geometry with additional material\nadded in different locations of the inner detector and in front of the electromagnetic calorimeter. Material\ncorresponding to an increase of 1-3% of a radiation length was added just behind the \ufb01rst pixel layer,\nand just behind the second SCT layer, and in the endcaps adjacent to one of the endcap pixel disks and\nadjacent to two of the endcap SCT disks. This amount of additional material is considered to be much\nlarger than the uncertainty on the knowledge of the exact amount of the material. Within the active\ntracking volume the material in regions of service routing was increased by 1-5% of a radiation lenght.\nFor services outside the active tracking volume the material was increased by up to 15% of a radiation\nlength. These increases are also expected to be larger than the uncertainties. It should be noted that for\nthe inner detector the extra material was only added in one half of the azimuthal angle (0 < \u03c6 < \u03c0) to\nallow for a straightforward study of the difference in calibration and performance with single particles.\nAdditional material was also added in a \u03c6-asymmetric way in front of the calorimeter. In the region\n\u03b7 >0 additional material corresponding to 8-11% X0 were added in front of the barrel cryostat, 5% X0\nbetween the barrel presampler and strip layers (in \u03c0/2 < \u03c6 < 3\u03c0/2), and 7-11% X0 behind the cryostat.\nIn the region \u03b7 <0, additional material corresponding to 5% X0 was added between the barrel presampler\nand the strip layer in the region \u2212\u03c0/2 < \u03c6 < \u03c0/2. The density of material in the gap between the barrel\nand the endcap cryostat was increased by 70%. Again, this is considered to be conservative and larger\nthan the uncertainties on the precise knowledge of the material distribution in this region of the detector.\nApplications in performance of physics studies\nSeveral performance studies were carried out using\nthe as-built and distorted geometries in simulation and the impact is documented elsewhere in this vol-\nume. Among the important studies is the impact of the misalignments on the b-tagging performance\nor on the reconstructed resolution of the Z resonance in muon \ufb01nal states. In addition the impact on\nthe mass resolution and reconstruction ef\ufb01ciencies was studied for H \u2192\u03b3\u03b3, H \u2192ZZ \u21924\u2113and Z \u2192ee\nsamples.\n5\nTreatment of systematic uncertainties\nThe results of the physics and performance studies are affected by systematic uncertainties, some of\nwhich are common to many studies. To allow a uniform treatment of these uncertainties across the\nvarious analyses, the following effects and prescriptions were applied.\nThere are detector-related uncertainties, such as those on particle identi\ufb01cation ef\ufb01ciencies, on back-\nground rejections, and on the precise knowledge of energy scales and resolution functions. These un-\ncertainties can be largely constrained and determined from the data themselves. However, this can only\nbe done with a \ufb01nite, and integrated luminosity-dependent, accuracy. In the present studies, rough esti-\nmates of these uncertainties were used, considering three canonical integrated luminosity values: 0.1, 1\nand 10 fb\u22121. Detector-related systematic uncertainties were applied to signal and background samples\nby varying the energy scale, resolution, or ef\ufb01ciency or rejections.\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n8\n\nIn addition, uncertainties come from the approximations made in Monte Carlo generators, modelling\nand from the theoretical calculation of cross-sections. Unless stated otherwise when discussing individ-\nual analyses, the following assumptions were applied, for the various systematic uncertainties.\n5.1\nUncertainties on the detector performance\nElectrons and photons\nFor electrons and photons, uncertainties on the identi\ufb01cation ef\ufb01ciency of\n1.0%, 0.5% and 0.2% were assumed for the three values of integrated luminosity, 0.1, 1 and 10 fb\u22121,\nrespectively. These values can be determined from data by applying the so called tag-and-probe meth-\nods [42,43] to known resonance decays, like Z \u2192ee. The uncertainty on the energy scale was assumed\nto be 1% (0.1%) for integrated luminosities below (above) 1 fb\u22121. The electron and photon resolutions\nwere estimated to be known with precisions of 20%, 10% and 5% at the three values of integrated lumi-\nnosity. The electron fake rates were assumed to have overall uncertainties of 50%, 20% and 10% at the\nthree integrated luminosity values. All uncertainties were assumed to be independent of pT and \u03b7.\nMuons\nUncertainties on the identi\ufb01cation ef\ufb01ciency of 1%, 0.3% and 0.1% were used for muons with\npT < 100 GeV for the three integrated luminosity values. As for electrons, it should be noted that these\nnumbers are expected to be conservative, since the statistical precision that can be obtained from studies\nof Z \u2192\u00b5\u00b5 decays amounts to 0.2% for an integrated luminosity of 0.1 fb\u22121. For higher muon momenta\nthe ef\ufb01ciencies must be estimated using extrapolations based on Monte Carlo and therefore larger values\nwere assumed: for muons with a pT of 1 TeV, for example, the uncertainties were assumed to be 5%, 3%\nand 1%, respectively.\nThe muon energy scale was assumed to be known with precisions of 1%, 0.3% and 0.1% for the\nthree integrated luminosity values. Furthermore, uncertainties of 12%, 4% and 1% were assumed on the\nmuon momentum resolution below 100 GeV, whereas a value of 100% was used for muons with pT of\n1 TeV. All these uncertainties were considered to be independent of \u03b7.\nJets and Missing ET\nUnless otherwise stated, the overall uncertainty on the jet energy scale was as-\nsumed to \u00b15% over the pseudorapidity region |\u03b7| <3.2 and \u00b110% for jets in the forward calorimeters,\n3.2 < |\u03b7| <4.9. This scale uncertainty is applied, independently of jet pT, for both light-quark jets\nand jets from b-quarks. In addition, unless stated otherwise, an uncertainty of 10% on the jet energy\nresolution was considered.\nThe missing transverse energy, Emiss\nT\n, is calculated by summing high-pT objects like leptons and\njets, in addition a component from unclustered energy is added. Part of the uncertainty in Emiss\nT\nis thus\ncorrelated with the jet and lepton energy scale uncertainties, but also a wrong calibration of unclustered\nenergy can affect Emiss\nT\n.\nAfter identi\ufb01ed objects were rescaled or smeared, the Emiss\nT\nwas re-calculated with the corrected\nenergies. In most of the studies also the low pT part of the unclustered energy was modi\ufb01ed. In this\nprocedure, the momenta of the leptons and jets with pT > 20 GeV were subtracted \ufb01rst from the Emiss\nT\n,\na 10% uncertainty on the remainder was applied, and then the effects of the leptons and jets were added\nback in.\nHeavy-\ufb02avour tagging\nFor the b-tagging ef\ufb01ciency a 5% relative uncertainty was assumed, indepen-\ndently of luminosity. This is considered to be a conservative estimate for integrated luminosities of\n1 fb\u22121 or higher. For the mistag rate of light and c-jets an integrated-luminosity independent uncertainty\nof 10% was assumed. It is expected that the mistag rates can be measured with this precsion or better\nfrom data sets exceeding an integrated luminosity of 0.1 fb\u22121. The ef\ufb01ciency and mistag variations were\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n9\n\nimplemented in analyses by randomly rejecting 5% of the jets tagged as b-jets or by randomly changing\nthe tag status of light and c-jets.\n5.2\nUncertainties on cross-sections and Monte Carlo modelling\nSeveral theoretical uncertainties affect the predicted cross-sections. The details and the size of the uncer-\ntainty depend on the signal and background processes considered and no general numbers can be quoted.\nThey are therefore usually addressed in the respective studies presented in this volume. The main effects\ncan be classi\ufb01ed as follows:\n\u2022 The theoretical calculations are affected by missing unknown higher-order corrections. These\nuncertainties are usually estimated by varying the renormalization and factorization scales within\nfactors of two around the nominal scale chosen.\n\u2022 Despite the normalization of tree-level Monte Carlo programs \u2013 with or without parton shower\nmatching \u2013 to the (N)NLO cross sections, large uncertainties remain, in particular for exclusive\n\ufb01nal states in speci\ufb01c phase space regions after the application of cuts. These uncertainties have\nbeen estimated either by varying parton-shower matching cuts or by comparisons with different\nMonte Carlo event generators.\n\u2022 Uncertainties in the parton distribution functions result in uncertainties on the calculated cross-\nsections which are typically of the order of 10%. These uncertainties have either been addressed\nby varying the eigenvalues of the CTEQ parametrization parameters [17] within the suggested\nvalues or by comparing the CTEQ and MRST2001 [44] parametrizations.\nAppendix\nIn the following, additional technical information is given on some of the Monte Carlo event generators\nemployed, together with example processes.\nPYTHIA\nThe PYTHIA Monte Carlo event generator [2] was employed for the event simulation of many samples.\nThe new implementation of parton showering, commonly known as pT -ordered showering, was used,\nas was the new underlying event model where the phase-space is interleaved/shared between initial-state\nradiation (ISR) and the underlying event. In addition to the standard processes implemented in PYTHIA,\ntwo extensions were implemented containing a chiral lagrangian model [45], and an R-hadron model.\nHERWIG and JIMMY\nHERWIG [24] was used, for example, for simulation of SUSY signal processes [46]. The pre-generated\ninput tables for these processes were provided by ISAJET and ISAWIG [47].\nSherpa\nThe Sherpa Monte Carlo event generator [25], was used for several processes, most notably for the\nproduction of electroweak bosons in association with jets: these pro\ufb01ted from the implemented CKKW\nparton-showering and matrix-element matching technique. Some representative processes for which\nSherpa was used are: a W or Z produced in association with up to four light jets; Higgs boson production\nvia vector boson fusion; and associated production of b\u00afbA.\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n10\n\nAcerMC\nSome processes for which AcerMC [26] was used were: Zb\u00afb production; Zt\u00aft production; t\u00aft production;\nsingle top processes; t\u00aftb\u00afb production; and t\u00aftt\u00aft production. The AcerMC program was used both with\nPYTHIA and HERWIG hadronisation, to allow tests of systematic uncertainties related to parton shower\nmodelling.\nA procedure was developed for combining samples with t\u00aft production modelled with MC@NLO\nwith samples from the AcerMC t\u00aftb\u00afb process. There is an overlap of the two samples since the extra\ngluon in the NLO t\u00aft calculation can split into a b\u00afb pair during parton showering. For studies where this\nchannel was relevant [48], events with additional b\u00afb pairs in the MC@NLO samples were rejected, since\nthe matrix-element t\u00aftb\u00afb generation is expected to describe such events better in the region of the phase\nspace selected by the analysis (especially for relatively large opening angle between the two quarks of\nthe b\u00afb pair). The corresponding number of events (10% of the total) was also removed from the high\njet-multiplicity t\u00aft sample for normalization purposes.\nALPGEN\nThe ALPGEN Monte Carlo event generator [19] was used for several processes, most notably for the\nproduction of electroweak bosons in association with jets, in order to pro\ufb01t from the implemented MLM\nparton-showering and matrix-element matching technique. Some processes for which ALPGEN was\nused were: W or Z production in association with up to \ufb01ve light jets; t\u00aft production with up to three\nadditional light jets; b\u00afb or c\u00afc production with up to three additional light jets; electroweak boson pair\nproduction in association with up to three jets Higgs production via vector boson fusion; and photon pair\nproduction in association with up to three jets.\nMadGraph/MadEvent\nThe MadGraph/MadEvent Monte Carlo event generator [27] was used for a selection of processes, for\nexample for exclusive \ufb01nal states involving multiple electroweak bosons and associated light jets, as\nwell as some Standard Model Higgs boson production channels. Although MadGraph/MadEvent pro-\ncesses in the 4.X versions can be combined with a native version of parton-showering and matrix-element\nmatching technique, this functionality was not used here. Some representative processes for which Mad-\nGraph/MadEvent was used are: W or Z production in association with four light partons; WW, WZ or\nZZ pair production in association with two light partons; electroweak boson production in association\nwith two photons; and photon pair production in association with two additional partons.\nMC@NLO\nThe MC@NLO event generator [28] is one of the few Monte Carlo tools incorporating full NLO QCD\ncorrections to a selected set of processes in a consistent way. It was used to simulate a number of\nprocesses, including: inclusive W or Z production; t\u00aft production; electroweak boson pair production;\nand Higgs boson production and decay, for the W +W \u2212and \u03b3\u03b3 Higgs boson decay modes.\nCharybdis\nThe Charybdis Monte Carlo event generator [29] is a special-purpose program implementing production\nand decay of microscopic black holes in models with TeV-scale gravity.\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n11\n\nCompHEP\nThe CompHEP Monte Carlo event generator [30] was used for a small set of processes: excited electron\nproduction, Z\u2032 \u2192e+e\u2212\u03b3, and the production of E6 heavy iso-singlet D quarks decaying to Z or W pairs,\nor to a ZH pair in association with additional quarks.\nTopReX\nThe TopReX Monte Carlo event generator [31] was used for top pair or single top production involving\n\ufb02avour-changing neutral current (FCNC) couplings in top quark decays, explicitly: t\u00aft production where\none top quark decays conventionally (to bW), and the other to either q\u03b3 or qZ; and single top production\nand decay to either q\u03b3 or qZ. TopReX was interfaced directly with PYTHIA for parton showering,\nhadronisation and the underlying event: a point to note is that TopReX single top generation is intimately\ninterfaced with the PYTHIA old (virtuality-ordered) parton showering model and thus cannot be used\nwith the new PYTHIA pT -ordered showering.\nWINHAC\nWINHAC [32] is a Monte Carlo event generator dedicated to the hadro-production of single W bosons\ndecaying into leptons. Comparisons done within ATLAS have shown that the WINHAC predictions\nmatch well the predictions of PHOTOS for radiative corrections to W boson leptonic decays. PHOTOS\nwas used throughout this work.\nReferences\n[1] S. Agostinelli et al., Nucl. Instrum. Meth. A 506 (2003) 250.\n[2] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[3] Z. Nagy, Phys. Rev. Lett. 88 (2002) 122003.\n[4] Z. Nagy, Phys. Rev. D68 (2003) 094002.\n[5] R. Bonciani, S. Catani, M. L. Mangano, and P. Nason, Nucl. Phys. B529 (1998) 424.\n[6] B. P. Kersevan and E. Richter-Was, The Monte Carlo event generator AcerMC version 2.0 with\ninterfaces to PYTHIA 6.2 and HERWIG 6.5, 2004, hep-ph/0405247.\n[7] Z. Sullivan, Phys. Rev. D70 (2004) 114012.\n[8] Q.-H. Cao, R. Schwienhorst, and C.-P. Yuan, Phys. Rev. D71 (2005) 054023.\n[9] Q.-H. Cao, R. Schwienhorst, J. A. Benitez, R. Brock and C.-P. Yuan,\nPhys. Rev. D72 (2005)\n094027.\n[10] A. Belyaev and E. Boos, Phys. Rev. D63 (2001) 034012.\n[11] T. M. P. Tait, Phys. Rev. D61 (2000) 034001.\n[12] J. Campbell and F. Tramontano, Nucl. Phys. B726 (2005) 109.\n[13] K. Melnikov and F. Petriello, Phys. Rev. Lett. 96 (2006) 231803.\n[14] J. Campbell and R. K. Ellis, User Guide available at http://mcfm.fnal.gov/ (2007).\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n12\n\n[15] C. Balazs, E. Berger, P. Nadolsky and C.-P. Yuan, Phys. Lett. B637 (2006) 235.\n[16] J. Pumplin et al., JHEP 07 (2002) 012.\n[17] J. Pumplin, A. Belyaev, J. Huston, D. Stump and W. K. Tung, JHEP 02 (2006) 032.\n[18] S. Catani and M.H. Seymour, Nucl. Phys. B485 (1997) 291.\n[19] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. D. Polosa, JHEP 07 (2003) 001.\n[20] ATLAS Collaboration, CERN-LHCC/99-014, CERN-LHCC/99-015 (1999).\n[21] T. Binoth, N. Kauer and P. Mertsch, Gluon-induced QCD corrections to pp \u2192ZZ \u2192\u2113\u2113\u2113\u2113, 2008,\narXiv:0807.0024.\n[22] J.M. Butterworth, J.R. Forshaw and M.H. Seymour, Z. Phys. C72 (1996) 637.\n[23] A. Moraes, C. Buttar and I. Dawson, Eur. Phys. J. C50 (2007) 435.\n[24] G. Corcella et al., JHEP 01 (2001) 010.\n[25] T. Gleisberg et al., JHEP 02 (2004) 056.\n[26] B.P. Kersevan and E. Richter-Was, Comput. Phys. Commun. 149 (2003) 142.\n[27] J. Alwall et al., JHEP 09 (2007) 028.\n[28] S. Frixione and B.R. Webber, JHEP 06 (2002) 029.\n[29] C.M. Harris, P. Richardson, and B.R. Webber, JHEP 08 (2003) 033.\n[30] E. Boos et al., Nucl. Instrum. Meth. A534 (2004) 250.\n[31] S.R. Slabospitsky and L. Sonnenschein, Comput. Phys. Commun. 148 (2002) 87.\n[32] W. Placzek and S. Jadach, Eur. Phys. J. C29 (2003) 325.\n[33] S. Jadach, Z. Was, R. Decker and J.H. Kuhn, Comput. Phys. Commun. 76 (1993) 361.\n[34] E. Barberio and Z. Was, Comput. Phys. Commun. 79 (1994) 291.\n[35] ATLAS Collaboration, Plans for the Study of the Spin Properties of the \u039bb Baryon Using the Decay\nChannel \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212), this volume.\n[36] D.J. Lange, Nucl. Instrum. Meth. A462 (2001) 152.\n[37] GENSER: http://lcgapp.cern.ch/project/simu/generator/.\n[38] ATLAS Collaboration, CERN-LHCC-2005-022 (2005).\n[39] E. Boos, et al., Generic user process interface for event generators, 2001, hep-ph/0109068.\n[40] M. Dobbs and J.B. Hansen, Comput. Phys. Commun. 134 (2001) 41.\n[41] M.R. Whalley, D. Bourilkov, and R.C. Group, The Les Houches Accord PDFs (LHAPDF) and\nLHAGLUE, 2005, hep-ph/0508110.\n[42] CDF Collaboration, D.E. Acosta et al., Phys. Rev. Lett. 94 (2005) 091803.\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n13\n\n[43] D0 Collaboration, V.M. Abazov et al., Phys. Rev. D76 (2007) 012003.\n[44] A.D. Martin, R.G. Roberts, W.J. Stirling and Thorne, R. S., Eur. Phys. J. C23 (2002) 73.\n[45] ATLAS Collaboration, Vector Boson Scattering at High Mass, this volume.\n[46] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[47] F.E. Paige, S.D. Protopopescu, H. Baer and X. Tata, ISAJET 7.69: A Monte Carlo event generator\nfor pp, pp, and e+e\u2212reactions, 2003, hep-ph/0312045.\n[48] ATLAS Collaboration, Search for t\u00aftH (H \u2192b\u00afb), this volume.\nINTRODUCTION \u2013 CROSS-SECTIONS, MONTE CARLO SIMULATIONS AND SYSTEMATIC . . .\n14\n\nTracking\n15\n\nThe Expected Performance of the Inner Detector\nAbstract\nThe ATLAS inner detector will see of the order of 1000 charged particle tracks\nfor every beam crossing at the design luminosity of the CERN Large Hadron\nCollider (LHC). This paper summarizes the design of the detector and outlines\nthe reconstruction software. The expected performance for reconstructing sin-\ngle particles is presented, along with an indication of the vertexing capabilities.\nThe effect of the detector material on electrons and photons is discussed along\nwith methods for improving their reconstruction. The studies presented focus\non the performance expected for the initial running at the start-up of the LHC.\n1\nIntroduction\nIn ATLAS, at the LHC design luminosity of 1034 cm\u22122s\u22121, approximately 1000 particles will emerge\nfrom the collision point every 25 ns within |\u03b7| < 2.5, creating a very large track density in the detec-\ntor. To achieve the momentum and vertex resolution requirements imposed by the benchmark physics\nprocesses, high-precision measurements will be made in the inner detector (ID), shown in Fig. 1. Pixel\nand silicon microstrip (SCT) trackers, used in conjunction with the straw tubes of the transition radiation\ntracker (TRT), will make high-granularity measurements. The original performance speci\ufb01cations were\nset out in 1994 and are detailed in [1] \u2013 the focus being on challenging physics channels such as the\nmeasurement of leptons from the decays of heavy gauge bosons and the tagging of b-quark jets.\nFigure 1: Cut-away view of the ATLAS inner detector.\nThe ID surrounds the LHC beam-pipe which is inside a radius of 36 mm. The layout of the detector\nis illustrated in Fig. 2 and detailed in [2]. Its basic parameters are summarised in Table 1. The ID is\n16\n\nimmersed in a 2 T magnetic \ufb01eld generated by the central solenoid, which extends over a length of 5.3 m\nwith a diameter of 2.5 m.\nFigure 2: Plan view of a quarter-section of the ATLAS inner detector showing each of the major elements\nwith its active dimensions.\nItem\nRadial extension (mm)\nLength (mm)\nPixel\nOverall envelope\n45.5 < R < 242\n0 < |z| < 3092\n3 cylindrical layers\nSensitive barrel\n50.5 < R < 122.5\n0 < |z| < 400.5\n2\u00d73 disks\nSensitive end-cap\n88.8 < R < 149.6\n495 < |z| < 650\nSCT\nOverall envelope\n255 < R < 549 (barrel)\n0 < |z| < 805\n251 < R < 610 (end-cap )\n810 < |z| < 2797\n4 cylindrical layers\nSensitive barrel\n299 < R < 514\n0 < |z| < 749\n2\u00d79 disks\nSensitive end-cap\n275 < R < 560\n839 < |z| < 2735\nTRT\nOverall envelope\n554 < R < 1082 (barrel)\n0 < |z| < 780\n617 < R < 1106 (end-cap )\n827 < |z| < 2744\n73 straw planes\nSensitive barrel\n563 < R < 1066\n0 < |z| < 712\n160 straw planes\nSensitive end-cap\n644 < R < 1004\n848 < |z| < 2710\nTable 1: Main parameters of the inner detector.\nThe precision tracking detectors (pixels and SCT) cover the region |\u03b7| < 2.5. In the barrel region,\nthey are arranged on concentric cylinders around the beam axis while in the end-cap regions, they are\nlocated on disks perpendicular to the beam axis. The highest granularity is achieved around the vertex\nregion using silicon pixel sensors. All pixel modules are identical and the minimum pixel size on a\nsensor is 50\u00d7400 \u00b5m2. The pixel layers are segmented in R\u2212\u03c6 and z with typically three pixel layers\ncrossed by each track. The \ufb01rst layer, called the \u201cvertexing layer\u201d, is at a radius of 51 mm. The intrinsic\naccuracies in the barrel are 10 \u00b5m (R\u2212\u03c6) and 115 \u00b5m (z) and in the disks are 10 \u00b5m (R\u2212\u03c6) and 115 \u00b5m\n(R). The pixel detector has approximately 80.4 million readout channels.\nFor the SCT, eight strip layers (four space points) are crossed by each track. In the barrel region, this\ndetector uses small-angle (40 mrad) stereo strips to measure both coordinates, with one set of strips in\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n17\n\neach layer parallel to the beam direction, measuring R \u2212\u03c6. Each side of a detector module consists of\ntwo 6.4 cm long, daisy-chained sensors with a strip pitch of 80 \u00b5m. In the end-cap region, the detectors\nhave a set of strips running radially and a set of stereo strips at an angle of 40 mrad. The mean pitch\nof the strips is also approximately 80 \u00b5m. The intrinsic accuracies per module in the barrel are 17 \u00b5m\n(R\u2212\u03c6) and 580 \u00b5m (z) and in the disks are 17 \u00b5m (R\u2212\u03c6) and 580 \u00b5m (R). The total number of readout\nchannels in the SCT is approximately 6.3 million.\nA large number of hits (typically 30 per track, with a maximum of 36, see Fig. 34) is provided by the\n4 mm diameter straw tubes of the TRT, which enables track-following up to |\u03b7| = 2.0. The TRT only\nprovides R \u2212\u03c6 information, for which it has an intrinsic accuracy of 130 \u00b5m per straw. In the barrel\nregion, the straws are parallel to the beam axis and are 144 cm long, with their wires divided into two\nhalves, approximately at \u03b7 = 0. In the end-cap region, the 37 cm long straws are arranged radially in\nwheels. The total number of TRT readout channels is approximately 351,000.\nItem\nIntrinsic accuracy\nAlignment tolerances\n(\u00b5m)\n(\u00b5m)\nRadial (R)\nAxial (z)\nAzimuth (R-\u03c6)\nPixel\nLayer-0\n10 (R-\u03c6) 115 (z)\n10\n20\n7\nLayer-1 and -2\n10 (R-\u03c6) 115 (z)\n20\n20\n7\nDisks\n10 (R-\u03c6) 115 (R)\n20\n100\n7\nSCT\nBarrel\n17 (R-\u03c6) 580 (z)1\n100\n50\n12\nDisks\n17 (R-\u03c6) 580 (R)1\n50\n200\n12\nTRT\n130\n302\n1. Arises from the 40 mrad stereo angle between back-to-back sensors on the SCT modules with axial (barrel)\nor radial (end-cap) alignment of one side of the structure. The result is pitch-dependent for end-cap SCT modules.\n2. The quoted alignment accuracy is related to the TRT drift-time accuracy.\nTable 2: Intrinsic measurement accuracies and mechanical alignment tolerances for the inner detector\nsub-systems, as de\ufb01ned by the performance requirements of the ATLAS experiment. The numbers in the\ntable correspond to the single-module accuracy for the pixels, to the effective single-module accuracy\nfor the SCT and to the drift-time accuracy of a single straw for the TRT.\nThe combination of precision trackers at small radii with the TRT at a larger radius gives very robust\npattern recognition and high precision in both R\u2212\u03c6 and z coordinates. The straw hits at the outer radius\ncontribute signi\ufb01cantly to the momentum measurement, since the lower precision per point compared to\nthe silicon is compensated by the large number of measurements and longer measured track length.\nThe inner detector system provides tracking measurements in a range matched by the precision mea-\nsurements of the electromagnetic calorimeter [2]. The electron identi\ufb01cation capabilities are enhanced by\nthe detection of transition-radiation photons in the xenon-based gas mixture of the straw tubes. The semi-\nconductor trackers also allow impact parameter measurements and vertex reconstruction (\u201cvertexing\u201d)\nfor heavy-\ufb02avour and \u03c4-lepton tagging. The secondary vertex measurement performance is enhanced by\nthe innermost layer of pixels, at a radius of about 5 cm.\nCharged particle tracks with transverse momentum pT > 0.5 GeV and |\u03b7| < 2.5 are reconstructed\nand measured in the inner detector and the solenoid \ufb01eld. However, the ef\ufb01ciency at low momentum is\nlimited because of the large material effect in the inner detector (see Fig. 3). The intrinsic measurement\nperformance expected for each of the inner detector sub-systems is summarised in Table 2. This per-\nformance has been studied extensively over the years [1], both before and after irradiation of production\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n18\n\nmodules, and also, more recently, during the combined test beam (CTB) runs in 2004 [2,3] and in a series\nof cosmic-ray tests in 2006 [2, 4]. The results have been used to update and validate the modelling of\nthe detector response in the Monte-Carlo simulation. This paper describes the expected performance of\nthe inner detector in terms of tracking, vertexing and particle identi\ufb01cation. The alignment of the inner\ndetector is described elsewhere ( [2] and the references therein).\n|\n\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n0\nRadiation length (X\n0\n0.5\n1\n1.5\n2\n2.5\n|\n\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n0\nRadiation length (X\n0\n0.5\n1\n1.5\n2\n2.5\nServices\nTRT\nSCT\nPixel\nBeam-pipe\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n\u03bb\nInteraction length (\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n\u03bb\nInteraction length (\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nServices\nTRT\nSCT\nPixel\nBeam-pipe\nFigure 3: Material distribution (X0, \u03bb) at the exit of the ID envelope, including the services and thermal\nenclosures. The distribution is shown as a function of |\u03b7| and averaged over \u03c6. The breakdown indicates\nthe contributions of external services and of individual sub-detectors, including services in their active\nvolume.\n2\nTrack reconstruction\nThe inner detector track reconstruction software [5] follows a modular and \ufb02exible software design,\nwhich includes features covering the requirements of both the inner detector and muon spectrometer [2]\nreconstruction. These features comprise a common event data model [6] and detector description [7],\nwhich allow for standardised interfaces to all reconstruction tools, such as track extrapolation, track \ufb01t-\nting including material corrections and vertex \ufb01tting. The extrapolation package combines propagation\ntools with an accurate and optimised description of the active and passive material of the full detector [8]\nto allow for material corrections in the reconstruction process. The suite of track-\ufb01tting tools includes\nglobal-\u03c72 and Kalman-\ufb01lter techniques, and also more specialised \ufb01tters such as dynamic noise adjust-\nment (DNA) [9], Gaussian-sum \ufb01lters (GSF) [10] and deterministic annealing \ufb01lters [11]. Optimisation\nof these tools continues and their performance will need to be evaluated on real data. The tools intended\nto cope with electron bremsstrahlung (DNA and GSF \u2013 see Section 5.1) will be run after the track re-\nconstruction, as part of the electron-photon identi\ufb01cation. Other common tracking tools are provided,\nincluding those to apply calibration corrections at later stages of the pattern recognition, to correct for\nmodule deformations or to resolve hit-association ambiguities.\nTrack reconstruction in the inner detector is logically sub-divided into three stages:\n1. A pre-processing stage, in which the raw data from the pixel and SCT detectors are converted\ninto clusters and the TRT raw timing information is translated into calibrated drift circles. The\nSCT clusters are transformed into space-points, using a combination of the cluster information\nfrom opposite sides of a SCT module.\n2. A track-\ufb01nding stage, in which different tracking strategies [5, 12], optimised to cover different\napplications, are implemented. (The results of studies of the various algorithms are reported else-\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n19\n\nwhere [13].) The default tracking exploits the high granularity of the pixel and SCT detectors to\n\ufb01nd prompt tracks originating from the vicinity of the interaction region. First, track seeds are\nformed from a combination of space-points in the three pixel layers and the \ufb01rst SCT layer. These\nseeds are then extended throughout the SCT to form track candidates. Next, these candidates are\n\ufb01tted, \u201coutlier\u201d clusters are removed, ambiguities in the cluster-to-track association are resolved,\nand fake tracks are rejected. This is achieved by applying quality cuts. For example, a cut is made\non the number of associated clusters, with explicit limits set on the number of clusters shared be-\ntween several tracks and the number of holes per track (a hole is de\ufb01ned as a silicon sensor crossed\nby a track without generating any associated cluster). The selected tracks are then extended into\nthe TRT to associate drift-circle information in a road around the extrapolation and to resolve the\nleft-right ambiguities. Finally, the extended tracks are re\ufb01tted with the full information of all three\ndetectors. The quality of the re\ufb01tted tracks is compared to the silicon-only track candidates and\nhits on track extensions resulting in bad \ufb01ts are labelled as outliers (they are kept as part of the\ntrack but are not included in the \ufb01t).\nA complementary track-\ufb01nding strategy, called back-tracking, searches for unused track segments\nin the TRT. Such segments are extended into the SCT and pixel detectors to improve the tracking\nef\ufb01ciency for secondary tracks from conversions or decays of long-lived particles.\n3. A post-processing stage, in which a dedicated vertex \ufb01nder is used to reconstruct primary ver-\ntices. This is followed by algorithms dedicated to the reconstruction of photon conversions and of\nsecondary vertices.\n3\nTracking performance\n3.1\nIntroduction to performance studies\nThe expected performance of the tracking system for reconstructing single particles and particles in\njets is determined using a precise modelling of the individual detector response (including electronic\nnoise and inef\ufb01ciencies), geometry and passive material in the simulation. In this paper, a consistent\nset of selection cuts for reconstructed tracks has been used. Generally, only prompt particles (those\noriginating from the primary vertex) with pT > 1 GeV and |\u03b7| < 2.5 are considered. Standard quality\ncuts require reconstructed tracks to have at least seven precision hits (pixels and SCT). In addition,\nthe transverse and longitudinal impact parameters at the perigee must ful\ufb01l respectively |d0| < 2 mm\nand |z0 \u2212zv| \u00d7 sin\u03b8 < 10 mm, where zv is the position of the primary vertex along the beam and\n\u03b8 is the polar angle of the track. Stricter selection cuts, called b-tagging cuts, are de\ufb01ned by: at least\ntwo hits in the pixels, one of which should be in the vertexing layer, as well as |d0| < 1 mm and\n|z0 \u2212zv|\u00d7sin\u03b8 < 1.5 mm. A reconstructed track is matched to a Monte-Carlo particle if at least 80%\nof its hits were created by that particle. The ef\ufb01ciency is de\ufb01ned as the fraction of particles which are\nmatched to reconstructed tracks passing the quality cuts, and the fake rate is de\ufb01ned as the fraction of\nreconstructed tracks passing the quality cuts which are not matched to a particle.\n3.2\nTrack parameter resolutions\nThe resolution of a track parameter X can be expressed as a function of pT as:\n\u03c3X(pT) = \u03c3X(\u221e)(1\u2295pX/pT)\n(1)\nwhere \u03c3X(\u221e) is the asymptotic resolution expected at in\ufb01nite momentum, pX is a constant representing\nthe value of pT for which the intrinsic and multiple-scattering terms in the equation are equal for the\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n20\n\nparameter X under consideration and \u2295denotes addition in quadrature. This expression is approximate,\nworking well at high pT (where the resolution is dominated by the intrinsic detector resolution) and at\nlow pT (where the resolution is dominated by multiple scattering). \u03c3X(\u221e) and pX are implicitly functions\nof the pseudorapidity. Figures 4, 5 and 6 show the momentum resolution for isolated muons and the trans-\nverse and longitudinal impact parameter resolutions for isolated pions1, all without a beam constraint and\nassuming the effects of misalignment, miscalibration and pile-up to be negligible. The resolutions are\ntaken as the RMS evaluated over a range which includes 99.7% of the data (corresponding to \u00b13\u03c3 for a\nGaussian distribution). The TRT measurements are included in the track \ufb01ts for tracks with |\u03b7| < 2.0,\nbeyond which there are no further TRT measurements. Table 3 shows the values of \u03c3X(\u221e) and pX for\ntracks in two \u03b7-regions, corresponding to the barrel and end-caps. The use of the beam-spot constraint\nin the track \ufb01t improves the momentum resolution for high-momentum tracks by about 5%. The impact\nparameter resolutions are quoted only for tracks with a hit in the vertexing layer (this requirement has a\nvery high ef\ufb01ciency, as illustrated in Fig. 14 by the small difference between the standard quality and the\nb-tagging quality tracks). Figure 7 shows the comparison of the impact parameter resolutions for pions\nand muons. The muon distributions are very close to Gaussian, while those for the pions are slightly\nbroader and have small tails, in addition. The tails are even larger for electrons, and this is discussed in\nSection 5.\nTrack parameter\n0.25 < |\u03b7| < 0.50\n1.50 < |\u03b7| < 1.75\n\u03c3X(\u221e)\npX (GeV)\n\u03c3X(\u221e)\npX (GeV)\nInverse transverse momentum (q/pT)\n0.34 TeV\u22121\n44\n0.41 TeV\u22121\n80\nAzimuthal angle (\u03c6)\n70 \u00b5rad\n39\n92 \u00b5rad\n49\nPolar angle (cot\u03b8)\n0.7 \u00d710\u22123\n5.0\n1.2\u00d710\u22123\n10\nTransverse impact parameter (d0)\n10 \u00b5m\n14\n12 \u00b5m\n20\nLongitudinal impact parameter (z0 \u00d7sin\u03b8)\n91 \u00b5m\n2.3\n71 \u00b5m\n3.7\nTable 3: Expected track-parameter resolutions (RMS) at in\ufb01nite transverse momentum, \u03c3X(\u221e), and\ntransverse momentum, pX, at which the multiple-scattering contribution equals that from the detector\nresolution (see Eq. (1)). The momentum and angular resolutions are shown for muons, whereas the\nimpact-parameter resolutions are shown for pions (see text). The values are shown for two \u03b7-regions,\none in the barrel inner detector where the amount of material is close to its minimum and one in the\nend-cap where the amount of material is close to its maximum. Isolated, single particles are used with\nperfect alignment and calibration in order to indicate the optimal performance.\nThe consequences of the pseudorapidity variation of the track parameter resolutions can be seen\nfrom the reconstructed J/\u03c8 \u2192\u00b5\u00b5 masses in the barrel and end-caps. This is shown in Fig. 8 where both\nmuons are either in the barrel or the end-caps.\nThe determination of the lepton charge at high pT is particularly important for measuring charge\nasymmetries arising from the decays of possible heavy gauge bosons (W \u2032 and Z\u2032). Typically, such mea-\nsurements require that the charge of the particle be determined to better than 3\u03c32. Whereas the charge\nof high-energy muons will be measured precisely in the muon system, the charge of high-energy elec-\ntrons can only be measured by the inner detector. Figure 9 shows the reconstructed values of q/pT for\nnegatively charged isolated muons and electrons with pT = 0.5 TeV and pT = 2 TeV. The peaks of the\ndistributions are at negative values, re\ufb02ecting the negative charges of the simulated particles. It can be\nseen that the shape of the muon distributions is unchanged in going from 0.5 to 2 TeV \u2013 at high momen-\n1Muons suffer less from interactions and hence provide the best reference; impact parameter determination is important for\nvertexing, and this is more commonly required for hadrons, for example when b-tagging.\n2The charge of a particle is considered well measured if it is at least 3\u03c3 from 0 in the variable q/p.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n21\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n)\nT\n(q/p\n\u03c3\n\u00d7\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n= 100 GeV\nT\np\n= 5 GeV\nT\np\n= 1 GeV\nT\np\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n (GeV)\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\nATLAS\nFigure 4: Relative transverse momentum resolution (left) as a function of |\u03b7| for muons with pT = 1, 5\nand 100 GeV. Transverse momentum, at which the multiple-scattering contribution equals the intrinsic\nresolution (corresponding to pX in Eq. (1)), as a function of |\u03b7| (right).\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n)(m m )\n0\n(d\n\u03c3\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n= 1 GeV\nT\np\n= 5 GeV\nT\np\n= 100 GeV\nT\np\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\nATLAS\nFigure 5: Transverse impact parameter, d0, resolution (left) as a function of |\u03b7| for pions with pT = 1, 5\nand 100 GeV. Transverse momentum, at which the multiple-scattering contribution equals the intrinsic\nresolution (corresponding to pX in Eq. (1)), as a function of |\u03b7| (right).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n22\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n)(m m )\n\u03b8\nsn\n\u00d7\n0\n(z\n\u03c3\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n= 1 GeV\nT\np\n= 5 GeV\nT\np\n= 100 GeV\nT\np\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n(GeV)\nT\np\n0\n1\n2\n3\n4\n5\n6\nATLAS\nFigure 6: Modi\ufb01ed longitudinal impact parameter, z0 \u00d7 sin\u03b8, resolution (left) as a function of |\u03b7| for\npions with pT = 1, 5 and 100 GeV. Transverse momentum, at which the multiple-scattering contribution\nequals the intrinsic resolution (corresponding to pX in Eq. (1)), as a function of |\u03b7| (right).\nEntries \nRMS 0.0429\n \n-0.3 -0.2\n-0.1\n0\n0.1\n0.2\n0.3\n1\n10\n2\n10\n3\n10\n 7769\n \n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n1\n10\n2\n10\n3\n10\nMuons\nPions\nEntries \nRMS 0.0383\n 8212\nEntries \nRMS 0.1507\n 7769\nMuons\nPions\nEntries \nRMS 0.1265\n 8212\n (mm)\n0\nd -\n0\nd\nrec\ntrue\n (mm)\n0\n0\nrec\ntrue\nrec\ntrue\nATLAS\nATLAS\nFigure 7: Resolution of the transverse impact parameter, d0 (left) and the modi\ufb01ed longitudinal impact\nparameter, z0 \u00d7sin\u03b8 (right) for 5 GeV muons and pions with |\u03b7| \u22640.5 \u2013 corresponding to the \ufb01rst two\nbins of the previous two \ufb01gures.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n23\n\n (GeV)\n\u00b5\n\u00b5\nm\n2.6 2.7 2.8 2.9\n3\n3.1 3.2 3.3 3.4 3.5 3.6\nProbability per bin\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nBarrel\n = 40 MeV\n\u03c3\nATLAS\n (GeV)\n\u00b5\n\u00b5\nm\n2.6 2.7 2.8 2.9\n3\n3.1 3.2 3.3 3.4 3.5 3.6\nProbability per bin\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nEnd-cap\n = 81 MeV\n\u03c3\nATLAS\nFigure 8: Probability for the reconstructed invariant mass of muon pairs from J/\u03c8 \u2192\u00b5\u00b5 decays in\nevents with prompt J/\u03c8 production. Distributions are shown for both muons with |\u03b7| < 0.8 (left) and\n|\u03b7| > 1.5 (right).\ntum, the resolution of q/pT is independent of the true momentum of the muon and determined by the\nintrinsic resolution of the detector.\nFor electrons, things are more complicated. As well as the intrinsic resolution, there are competing\neffects from bremsstrahlung (which lowers the track momentum and makes the charge easier to measure)\nand the conversion of bremsstrahlung photons (leading to pattern-recognition problems and degraded\ncharge determination). At 0.5 TeV, the effects of the conversions are signi\ufb01cant, causing the electrons to\nbe measured worse than the corresponding muons. However, at 2 TeV, the intrinsic resolution dominates\nthe electron charge misidenti\ufb01cation, and this is partially compensated for by the bremsstrahlung. The\nfractions of muons and electrons for which the sign of the charge is incorrectly determined are shown in\nFig. 10. For these plots, perfect alignment has been assumed; any misalignment will degrade the charge\nsign determination.\n3.3\nTrack reconstruction ef\ufb01ciency\nFigures 11, 12 and 13 show the ef\ufb01ciencies for reconstructing isolated muons, pions and electrons. In\naddition to multiple-scattering, pions are affected by hadronic interactions in the inner detector material,\nwhile electrons are subject to even larger reconstruction inef\ufb01ciencies which arise from the effects of\nbremsstrahlung. As a result, the ef\ufb01ciency curves as a function of |\u03b7| for pions and electrons re\ufb02ect the\nshape of the amount of material in the inner detector (see Fig. 3). As expected, the ef\ufb01ciency becomes\nlarger and more uniform as a function of |\u03b7| at higher energies.\nPrevious studies [1] have shown that the reconstruction ef\ufb01ciency is little affected by the \u201cpile-up\u201d of\nadditional minimum bias events at high luminosity (1034 cm\u22122s\u22121). A more challenging environment is\nfound in the core of an energetic jet. Figure 14 shows the track reconstruction ef\ufb01ciency for prompt pions\n(produced before the vertexing layer) and the fake rate for tracks in jets in t\u00aft events as a function of |\u03b7|.\nFor these events, the mean jet pT is 55 GeV, and the mean pT of the accepted tracks which they contain\nis 4 GeV. The loss of ef\ufb01ciency at |\u03b7| = 0 with the b-tagging criteria arises from inef\ufb01ciencies in the pixel\nvertexing layer, which are assumed here to be 1%; this improves at higher |\u03b7|, owing to the presence\nof larger clusters when the track incidence angle decreases. Beyond |\u03b7| \u223c1, the tracking performance\ndeteriorates, mostly because of increased material. As shown in Fig. 15, the fake rate increases near the\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n24\n\n(TeV 1)\nT\nq/p\n-10 -8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEntres/bn\n1\n10\n2\n10\n3\n10\nElectrons\n= 0.5 TeV\nT\np\n(TeV 1)\nT\nq/p\n-10 -8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEntres/bn\n1\n10\n2\n10\n3\n10\nM uons\n= 0.5 TeV\nT\np\nEntries\n39220\nwrong sign\n533\nEntries\n42417\nwrong sign\n387\n(TeV 1)\nT\nq/p\n-10 -8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEntres/bn\n1\n10\n2\n10\n3\n10\nElectrons\n= 2.0 TeV\nT\np\n(TeV 1)\nT\nq/p\n-10 -8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEntres/bn\n1\n10\n2\n10\n3\n10\nM uons\n= 2.0 TeV\nT\np\nEntries\n38594\nwrong sign 4936\nEntries\n42259\nwrong sign 5776\nATLAS\nATLAS\nATLAS\nATLAS\nFigure 9: Reconstructed inverse transverse momentum multiplied by the charge for high-energy muons\n(\u00b5\u2212) (left) and electrons (e\u2212) (right) for pT = 0.5 TeV (top) and pT = 2 TeV (bottom) and integrated\nover a \ufb02at distribution in \u03b7 with |\u03b7| \u22642.5. Those tracks which have been incorrectly reconstructed with\na positive charge are indicated by the shaded regions. At 2 TeV, the fraction of electrons (muons) whose\ncharge has been misidenti\ufb01ed is 12.8% (13.7%).\n (TeV)\nT\np\n0\n0.2 0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\nCharge misidentification probability\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nElectrons\nMuons\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nCharge misidentification probability\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nElectrons\nMuons\nATLAS\nFigure 10: Charge misidenti\ufb01cation probability for high-energy muons and electrons as a function of pT\nfor particles with |\u03b7| \u22642.5 (left) and as a function of |\u03b7| for pT = 2 TeV (right).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n25\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n= 1 GeV\nT\np\n= 5 GeV\nT\np\n= 100 GeV\nT\np\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n= 1 GeV\nT\np\n= 5 GeV\nT\np\n= 100 GeV\nT\np\nATLAS\nFigure 11: Track reconstruction ef\ufb01ciencies as a function of |\u03b7| for muons (left) and pions (right)\nwith pT = 1, 5 and 100 GeV.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n = 1 GeV\nT\np\n = 5 GeV\nT\np\n = 100 GeV\nT\np\nATLAS\nFigure 12: Track reconstruction ef\ufb01ciencies as\na function of |\u03b7| for electrons with pT = 1, 5\nand 100 GeV.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nElectrons\nPions\nMuons\nATLAS\nFigure 13: Track reconstruction ef\ufb01ciencies as a\nfunction of |\u03b7| for muons, pions and electrons\nwith pT = 5 GeV. The inef\ufb01ciencies for pions and\nelectrons re\ufb02ect the shape of the amount of mate-\nrial in the inner detector as a function of |\u03b7|.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n26\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nEfficiency\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\nFake rate\nEfficiency: reconstruction\nEfficiency: standard quality\nEfficiency: b-tagging quality\nFake rate: standard quality\nFake rate: b-tagging quality\nATLAS\nFigure 14: Track reconstruction ef\ufb01ciencies and\nfake rates as a function of |\u03b7|, for charged pions\nin jets in t\u00aft events and for different quality cuts (as\ndescribed in Section 3.1). \u201cReconstruction\u201d refers\nto the basic reconstruction before additional qual-\nity cuts.\n R\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4\n0.86\n0.88\n0.9\n0.92\n0.94\n0.96\n0.98\n1\nEfficiency\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\n0.016\n0.018\n0.02\nFake rate\n < 50 GeV\njet\nT\nEfficiency: E\n > 100 GeV\njet\nT\nEfficiency: E\n < 50 GeV\njet\nT\nFake rate: E\n > 100 GeV\njet\nT\nFake rate: E\nATLAS\nFigure 15: Track reconstruction ef\ufb01ciencies and\nfake rates as a function of the distance \u2206R (de-\n\ufb01ned as \u2206R =\np\n\u2206\u03b72 + \u2206\u03c6 2) of the track to the\njet axis, using the standard quality cuts and inte-\ngrated over |\u03b7| < 2.5, for charged pions in jets in\nt\u00aft events.\ncore of the jet, where the track density is the highest and induces pattern-recognition problems. This\neffect increases as the jet pT increases. Using alternative algorithms, a few percent ef\ufb01ciency can be\ngained at the cost of doubling the fake rate in the jet core.\nThe reconstruction described in Section 2 is aimed at tracks with pT > 0.5 GeV. Multiplicity studies\nin minimum bias events will be among the \ufb01rst analyses undertaken by ATLAS. In these events, the\npeak of the track pT spectrum is around 0.3 GeV. The reconstruction of these low-momentum tracks\nwill be dif\ufb01cult because of the high curvature of the tracks, increased multiple scattering, and at very\nlow momentum, reduced numbers of hits, since the tracks may fail to reach the outer layers of the\ninner detector. To complement the track-\ufb01nding strategy described in Section 2, an additional strategy\nis employed in which hitherto unused pixel and SCT hits are used. To further aid the reconstruction,\nthe algorithm for the space-point track seeding is modi\ufb01ed to use looser internal cuts and the cut on the\nnumber of precision hits is reduced to at least \ufb01ve hits. Tracks are accepted with pT > 0.1 GeV, and in\nsome cases, inef\ufb01ciencies for pT > 0.5 GeV are recovered. The resulting track reconstruction ef\ufb01ciency\nis shown in Fig. 16. The distribution of candidate fake tracks is shown in Fig. 17.\n4\nVertexing performance\n4.1\nPrimary vertices\nVertexing tools constitute important components of the higher-level tracking algorithms. The residuals of\nthe primary vertex reconstruction are shown in Fig. 18, as obtained without using any beam constraint,\nfor t\u00aft events and H \u2192\u03b3\u03b3 events with mH = 120 GeV. The results shown here for H \u2192\u03b3\u03b3 events are\nbased on tracks reconstructed from the underlying event and do not make use of the measurement of the\nphoton direction in the electromagnetic calorimeter. The primary vertex in t\u00aft events has always a rather\nlarge multiplicity and includes a number of high-pT tracks, resulting in a narrower and more Gaussian\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n27\n\n (GeV)\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nEfficiency \n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n| \n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency \n0\n0.2\n0.4\n0.6\n0.8\n1\n 0.5 (GeV)\n\u2264\n \nT\n0.1 < p\n 1.0 (GeV)\n\u2264\n \nT\n0.5 < p\nATLAS\nFigure 16: Track reconstruction ef\ufb01ciencies as a function of pT for |\u03b7| < 2.5 and pT > 0.1 GeV (left) and\nas a function of |\u03b7| for two different pT ranges (right) in minimum bias events (non-diffractive inelastic\nevents).\n (GeV)\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nFakes \n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\n| \n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nFakes \n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n 0.5 (GeV)\n\u2264\n \nT\n0.1 < p\n 1.0 (GeV)\n\u2264\n \nT\n0 5 < p\nATLAS\nFigure 17: Rate of candidate fake tracks as a function of pT for |\u03b7| < 2.5 and pT > 0.1 GeV (left) and\nas a function of |\u03b7| (right) in minimum bias events (non-diffractive inelastic events). The rate of such\ntracks is a function of the amount of material, indicating that a large fraction of them are secondaries for\nwhich the Monte-Carlo truth information is not kept\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n28\n\ndistribution than for H \u2192\u03b3\u03b3 events. Table 4 shows the resolutions of the primary vertex reconstruction\nin these t\u00aft and H \u2192\u03b3\u03b3 events, without and with a beam constraint in the transverse plane, as well as the\nef\ufb01ciencies to reconstruct and select correctly (within \u00b1300 \u00b5m) these primary vertices in the presence\nof pile-up at a luminosity of 1033 cm\u22122s\u22121.\nEvent type\nx-y resolution\nz resolution\nReconstruction\nSelection\n(\u00b5m)\n(\u00b5m)\nef\ufb01ciency (%)\nef\ufb01ciency (%)\nt\u00aft (no BC)\n18\n41\n100\n99\nt\u00aft (BC)\n11\n40\n100\n99\nH \u2192\u03b3\u03b3 (no BC)\n36\n72\n96\n79\nH \u2192\u03b3\u03b3 (BC)\n14\n66\n96\n79\nTable 4: Primary vertex resolutions (RMS), without and with a beam constraint (BC) in the transverse\nplane, for t\u00aft events and H \u2192\u03b3\u03b3 events with mH = 120 GeV in the absence of pile-up. Also shown, in the\npresence of pile-up at a luminosity of 1033 cm\u22122s\u22121, are the ef\ufb01ciencies to reconstruct and then select\nthe hard-scattering vertex within \u00b1300 \u00b5m of the true vertex position in z. The hard-scattering vertex is\nselected as the primary vertex with the largest \u03a3p2\nT, summed over all its constituent tracks.\nPrimary vertex residual in x (mm)\n-0.1\n-0.05\n0\n0.05\n0.1\nProbability\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\ntt\n\u03b3 \u03b3 \n\u2192\nH \nPrimary vertex residual in z (mm)\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\nProbability\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\ntt\n\u03b3 \u03b3 \n\u2192\nH \nFigure 18: Primary vertex residual along x, in the transverse plane (left), and along z, parallel to the\nbeam (right), for events containing top-quark pairs and H \u2192\u03b3\u03b3 decays with mH = 120 GeV. The results\nare shown without pile-up and without any beam constraint.\n4.2\nSecondary vertices\nThe resolution for the reconstruction of the radial position of secondary vertices for J/\u03c8 \u2192\u00b5\u00b5 decays\nin events containing B-hadron decays (mean pT of 15 GeV for the J/\u03c8) is shown in Fig. 19. While\nthere are some tails in the resolution distributions (left-hand plot), these are small. The corresponding\ndistributions for three-prong hadronic \u03c4-decays in Z \u2192\u03c4\u03c4 events (mean pT of 36 GeV for the \u03c4-lepton)\nare shown in Fig. 20. Because there are three charged tracks in close proximity, the reconstruction of\nthese decays is more challenging: the vertex resolutions are Gaussian in the central region, but have long\ntails as can be seen from the points showing 95% coverage in right-hand plot.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n29\n\nSecondary vertex radial residual (mm)\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n candidates\n\u03c8\nFraction of J/\n0\n10\n20\n30\n40\n50\n60\n70\n-3\n10\n\u00d7\nATLAS\n|\n\u03c8\nJ/\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nm)\n\u00b5\nSec. vertex radial resolution (\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nATLAS\nFigure 19: Resolution for the reconstruction of the radial position of the secondary vertex for J/\u03c8 \u2192\u00b5\u00b5\ndecays in events containing B-hadron decays for tracks with |\u03b7| around 0 (left) and as a function of the\npseudorapidity of the J/\u03c8 (right). The J/\u03c8 have an average transverse momentum of 15 GeV.\nSecondary vertex radial residual (mm)\n-3\n-2\n-1\n0\n1\n2\n3\n candidates\n\u03c4\nFraction of \n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\n|\n\u03c4\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nSec. vertex radial resolution (mm)\n0\n0.5\n1\n1.5\n2\n2.5\n3\nATLAS\n95% coverage\n68.3% coverage\n(fit)\n\u03c3\nFigure 20: Resolution for the reconstruction of the radial position of the secondary vertex for three-\nprong hadronic \u03c4-decays in Z \u2192\u03c4\u03c4 events for tracks with |\u03b7| around 0 (left) and as a function of\nthe pseudorapidity of the \u03c4 (right). In the right-hand plot, the circles with bars correspond to Gaussian\n\ufb01ts, as illustrated in the left-hand plot; the points showing 68.3% (95%) coverage show the width of the\nintegrated distribution containing 68.3% (95%) of the measurements (corresponding to 1\u03c3 (2\u03c3) for a\nGaussian distribution). The \u03c4-leptons have an average transverse momentum of 36 GeV.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n30\n\nFinally, Fig. 21 shows the resolution as a function of decay radius for the reconstruction of the radial\nposition of secondary vertices for K0\ns decays (mean pT of 6 GeV) in events containing B-hadron decays.\nThe resolution in each radial slice is determined from a Gaussian \ufb01t to the core of the distribution. It can\nbe seen that there are signi\ufb01cant tails: just before the barrel layers, the resolution for decays in the barrel\nregion is good, giving rise to the core; while that from the end-caps is variable, depending on the actual\nposition of the decay, giving rise to a broader distribution. The tails can be reduced and the resolutions\nimproved somewhat by tighter cuts on track quality and the reconstructed invariant mass, if desirable.\nThe effect of crossing the three successive pixel layers is clearly visible as well as the degraded resolution\nfor decays beyond the last pixel layer. Figure 22 shows the resolution as a function of decay radius for the\nreconstruction of the invariant mass of the charged-pion pair for the same K0\ns \u2192\u03c0+\u03c0\u2212decays. Figure 23\nshows the ef\ufb01ciency to reconstruct the K0\ns decays. The reconstruction requires 3D information provided\nby the silicon detectors, and hence the ef\ufb01ciency falls to zero once the decay is beyond the penultimate\nSCT layers.\n5\nParticle identi\ufb01cation, reconstruction of electrons and photon conver-\nsions\nThe reconstruction of electrons and of photon conversions is a particular challenge for the inner detector.\nThe fraction of energy lost by electrons traversing the inner detector is shown in Fig. 24. In the energy\nrange over which the inner detector will measure electrons, the fraction has little dependence on the\nactual electron energy. Electrons lose on average between 20 to 50% of their energy (depending on |\u03b7|)\nby the time they have left the SCT, as illustrated in Fig. 25. The probability for photons to convert is\nfairly independent of their energies for pT > 1 GeV. A histogram of the location of photon conversions\nin |\u03b7| < 0.8 is shown in Fig. 26 - the radial structure of the detector is clearly visible. Between 10 to 50%\nof photons have converted into an electron-positron pair before leaving the SCT, as illustrated in Fig. 27.\nThe TRT plays a central role in electron identi\ufb01cation, cross-checking and complementing the elec-\ntromagnetic calorimeter, especially at energies below 25 GeV [2]. In addition, the TRT contributes to the\nreconstruction and identi\ufb01cation of electron track segments from photon conversions down to 1 GeV and\nof electrons which have radiated a large fraction of their energy in the silicon layers.\n5.1\nElectron reconstruction\nIn the absence of bremsstrahlung, the distribution ptrue/precon should be Gaussian; but in the presence\nof bremsstrahlung, this is far from true, as can be seen for the end-cap in Fig. 28 (left-hand plot). By\n\ufb01tting electron tracks in such a way as to allow for bremsstrahlung, it is possible to improve the recon-\nstructed track parameters, as shown in Figs. 28 and 29 for two examples of bremsstrahlung recovery\nalgorithms. These algorithms rely exclusively on the inner detector information and therefore provide\nsigni\ufb01cant improvements only for electron energies below \u223c25 GeV. The dynamic noise adjustment\n(DNA) method extrapolates track segments to the next silicon detector layer. If there is a signi\ufb01cant \u03c72\ncontribution, compatible with a hard bremsstrahlung, the energy loss is estimated and an additional noise\nterm is included in the Kalman \ufb01lter [9]. The Gaussian-sum \ufb01lter (GSF) is a non-linear generalisation\nof the Kalman \ufb01lter, which takes into account non-Gaussian noise by modelling it as a weighted sum of\nGaussian components and therefore acts as a weighted sum of Kalman \ufb01lters operating in parallel [10].\nWith real data, to improve the \ufb01tted track parameters for electrons without deteriorating the \ufb01ts for non-\nelectrons, it is necessary to assess whether a track is likely to correspond to an electron or not. This\ncan be done to some extent by the algorithms themselves by looking at the \ufb01ts; additional information\ncan be obtained from the transition radiation in the TRT (see 5.2) and the electromagnetic calorimeter.\nUltimately, since information is lost during the bremsstrahlung, there is an unavoidable degradation of\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n31\n\n Rxy resolution (mm), 10 < Rxy < 20\nS\nK\n-2\n0\n2\n0\n20\n40\n60\n80\n100\n / ndf \n2\n\u03c7\n 33.84 / 25\nConstant \n 3.2\n\u00b1\n 101.5 \nMean \n 0.0126676\n\u00b1\n 0.0004913 \nSigma \n 0.0131\n\u00b1\n 0.4546 \nATLAS\n Rxy resolution (mm), 40 < Rxy < 50 5\nS\nK\n-1\n-0 5\n0\n0.5\n1\n0\n20\n40\n60\n80\n100\n120\n140\n / ndf \n2\n\u03c7\n 48.05 / 17\nConstant \n 4.0\n\u00b1\n 100.2 \nMean \n 3.674e 03\n\u00b1\n 4.958e 06 \nSigma \n 0.0046\n\u00b1\n 0.1101 \nATLAS\n Rxy resolution (mm), 130 < Rxy < 140\nS\nK\n-20\n-10\n0\n10\n20\n0\n5\n10\n15\n20\n25\n30\n35\n / ndf \n2\n\u03c7\n 19.56 / 24\nConstant \n 1.70\n\u00b1\n 28.81 \nMean \n 0.180\n\u00b1\n 0.492 \nSigma \n 0.210\n\u00b1\n 3.273 \nATLAS\n Rxy resolution (mm), 280 < Rxy < 299\nS\nK\n-5\n0\n5\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 14.3 / 11\nConstant \n 3.07\n\u00b1\n 35.95 \nMean \n 0.026457\n\u00b1\n 0.009057 \nSigma \n 0.0315\n\u00b1\n 0.4049 \nATLAS\nDecay radius (mm)\n0\n100\n200\n300\n400\nResolution of decay radius (mm)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\nFigure 21: Resolution for the reconstructed radial position of the secondary vertex for K0\ns \u2192\u03c0+\u03c0\u2212\ndecays in events containing B-hadron decays in various radial intervals (upper) and as a function of the\nK0\ns decay radius (lower). The resolutions are best for decays just in front of the detector layers. The\nbarrel pixel layers are at: 51, 89 and 123 mm; the \ufb01rst two SCT layers are at 299 and 371 mm.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n32\n\n Mass (MeV), 10 < Rxy < 20\nS\nK\n460\n480\n500\n520\n540\n0\n20\n40\n60\n80\n100\n120\n140\n / ndf \n2\n\u03c7\n 21.02 / 20\nConstant \n 3.9\n\u00b1\n 126 \nMean \n 0.2\n\u00b1\n 497.6 \nSigma \n 0.185\n\u00b1\n 5.905 \nATLAS\n Mass (MeV), 40 < Rxy < 50 5\nS\nK\n460\n480\n500\n520\n540\n0\n20\n40\n60\n80\n100\n120\n / ndf \n2\n\u03c7\n 19.77 / 20\nConstant \n 3.6\n\u00b1\n 104.3 \nMean \n 0.2\n\u00b1\n 497.7 \nSigma \n 0.222\n\u00b1\n 6.065 \nATLAS\n Mass (MeV), 130 < Rxy < 140\nS\nK\n450\n500\n550\n0\n5\n10\n15\n20\n25\n30\n35\n40\n / ndf \n2\n\u03c7\n 21.63 / 23\nConstant \n 1.96\n\u00b1\n 33.43 \nMean \n 0.4\n\u00b1\n 497.1 \nSigma \n 0.53\n\u00b1\n 8.33 \nATLAS\n Mass (MeV), 280 < Rxy < 299\nS\nK\n450\n500\n550\n0\n5\n10\n15\n20\n25\n30\n / ndf \n2\n\u03c7\n 15.15 / 22\nConstant \n 1.65\n\u00b1\n 24.46 \nMean \n 0.7\n\u00b1\n 497.7 \nSigma \n 0.80\n\u00b1\n 11.06 \nATLAS\nDecay radius (mm)\n0\n100\n200\n300\n400\nMass resolution (MeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nATLAS\nFigure 22: Resolution for the reconstruction of the invariant mass of the charged-pion pair for K0\ns \u2192\n\u03c0+\u03c0\u2212decays in events containing B-hadron decays in various radial intervals (upper) and as a function\nof the K0\ns decay radius (lower).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n33\n\nDecay radius (mm)\n100\n200\n300\n400\n500\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFigure 23: Ef\ufb01ciency to reconstruct charged-pion pairs for K0\ns \u2192\u03c0+\u03c0\u2212decays in events containing B-\nhadron decays as a function of the K0\ns decay radius (left) and as a function of the |\u03b7| of the K0\ns (right).\ne\nE\nbrem\nE\n \n\u2211\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 9\n1\nProbability\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n0 09\n = 10GeV\nT\nE\n = 25GeV\nT\nE\nATLAS\nFigure 24:\nProbability distribution as a func-\ntion of the fraction of energy lost by electrons\nwith pT = 10 GeV and 25 GeV (integrated over\na \ufb02at distribution in \u03b7 with |\u03b7| \u22642.5) traversing\nthe complete inner detector.\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\nFraction of energy lost\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0 6\n0.7\n0 8\n0 9\n1\nAfter TRT\nAfter SCT\nAfter Pixel\nATLAS\nFigure 25: Fraction of energy lost on average by\nelectrons with pT = 25 GeV as a function of |\u03b7|,\nwhen exiting the pixel, the SCT and the inner de-\ntector tracking volumes. For |\u03b7| > 2.2, there is\nno TRT material, hence the SCT and TRT lines\nmerge.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n34\n\nRadius (mm)\n0\n200\n400\n600\n800\n1000\n1200\n0\n100\n200\n300\n400\n500\n600\n700\n800\nATLAS\nFigure 26: Radial position of photon conversions\nin the barrel region (|\u03b7| < 0.8) deduced from\nMonte-Carlo truth information (arbitrary normali-\nsation).\nRadius (mm)\n0\n200\n400\n600\n800\n1000\n1200\nProbability of conversion\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n = 0\n\u03b7\n = 1\n\u03b7\n = 1.5\n\u03b7\n = 2\n\u03b7\nATLAS\nFigure 27: Probability for a photon to have con-\nverted as a function of radius for different values\nof |\u03b7|, shown for photons with pT > 1 GeV in\nminimum bias events.\nT\nRatio between true and reconstructed p\n0.5\n1\n1.5\n2\n2.5\n3\n3 5\n4\n4 5\n5\nProbability\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nT\nRatio between reconstructed and true p\n0\n0 2\n0.4\n0 6\n0.8\n1\n1 2\n1.4\nProbability\n0 01\n0 02\n0 03\n0 04\n0 05\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nFigure 28: Probability distributions for the ratio of the true to reconstructed momentum (left) and its\nreciprocal (right) for electrons with pT = 25 GeV and |\u03b7| > 1.5. The results are shown as probabilities\nper bin for the default Kalman \ufb01tter and for two bremsstrahlung recovery algorithms (see text).\nthe electron measurement. The algorithms serve to reduce the bias of the track \ufb01ts caused by the in-\ncreased track curvature. Only by adding additional information, such at the position of the cluster in the\nelectromagnetic calorimeter [2], is it possible to make a real improvement on the measured momentum.\nBy allowing for changes in the curvature of the track, the bremsstrahlung recovery algorithms \u201cfol-\nlow\u201d the tracks better and correctly associate more of the hits, leading to improvements in the recon-\nstruction ef\ufb01ciencies, as can be seen in Fig. 30. GSF has 2-3% greater ef\ufb01ciency than the default recon-\nstruction, since it does not \ufb02ag hits as outliers, hence a track is less likely to fail the quality cuts on the\nnumbers of hits.\nFigure 31 shows the improvements from bremsstrahlung recovery for the reconstructed J/\u03c8 \u2192\nee mass. Integrating over the complete pseudorapidity acceptance of the ID, and without using any\nbremsstrahlung recovery, only 42% of events are reconstructed within \u00b1500 MeV of the nominal J/\u03c8\nmass, whereas with the use of the bremsstrahlung recovery, this fraction increases to 53% and 56% for\nDNA and GSF respectively, and the bias of the peak position is reduced. In the inner detector alone, the\nJ/\u03c8 signal in the end-caps is more or less completely lost because of the effects of the increased material\ncompared to that in the barrel. The poor performance in the end-caps arises from the signi\ufb01cant fraction\nof energy lost by electrons (O(30)% by the time they have left the pixels) as well as the change in track\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n35\n\nT\nRatio between true and reconstructed p\n0.5\n1\n1.5\n2\n2.5\n3\n3 5\n4\n4 5\n5\nProbability\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\n0.22\n0.24\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nT\nRatio between true and reconstructed p\n0.5\n1\n1 5\n2\n2 5\n3\n3.5\n4\n4.5\n5\nProbability\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n0.14\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nFigure 29: Probability distributions for the ratio of the true to reconstructed momentum for electrons\nwith pT = 25 GeV and |\u03b7| < 0.8 (left) and pT = 10 GeV and |\u03b7| > 1.5 (right). The results are shown as\nprobabilities per bin for the default Kalman \ufb01tter and for two bremsstrahlung recovery algorithms (see\ntext).\n\u03b7\n0\n0 5\n1\n1.5\n2\n2.5\nEfficiency\n0.7\n0.75\n0 8\n0.85\n0 9\n0.95\n1\nGaussian\u2212sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\n\u03b7\n0\n0.5\n1\n1.5\n2\n2 5\nEfficiency\n0.7\n0.75\n0.8\n0 85\n0.9\n0 95\n1\nGaussian\u2212sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nFigure 30: Ef\ufb01ciencies to reconstruct electrons as a function of |\u03b7| for electrons with pT = 25 GeV (left)\nand pT = 10 GeV (right). The results are shown for the default Kalman \ufb01tter and for two bremsstrahlung\nrecovery algorithms (see text).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n36\n\n (GeV)\nee\nm\n1\n1 5\n2\n2 5\n3\n3.5\n4\nProbability per bin\n0\n0.005\n0.01\n0.015\n0.02\n0.025\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\n (GeV)\nee\nm\n1\n1.5\n2\n2.5\n3\n3 5\n4\nProbability per bin\n0.002\n0.004\n0.006\n0.008\n0 01\n0.012\n0.014\n0.016\nGaussian-sum filter\nDynamic noise adjustment\nDefault fitter\nATLAS\nFigure 31: Probability for the reconstructed invariant mass of electron pairs from J/\u03c8 \u2192ee decays\nin events with B0\nd \u2192J/\u03c8(ee)K0\ns . Distributions are shown for both electrons with |\u03b7| < 0.8 (left) and\n|\u03b7| > 1.5 (right). The results are shown for the default Kalman \ufb01tter and for two bremsstrahlung recovery\nalgorithms (see text). The true J/\u03c8 mass is shown by the vertical line.\ndirection. These distributions should be contrasted with those for the muonic decays of the J/\u03c8 in Fig. 8.\nTo conclude, the material of the inner detector causes a signi\ufb01cant amount of bremsstrahlung for\nelectrons, biasing their \ufb01tted parameters. This can be partially compensated within the inner detector\nusing the so-called bremsstrahlung recovery procedures, DNA and GSF. These algorithms should be\napplied to tracks in a way so as to improve electrons and not degrade pions or muons. DNA runs in a\ntime comparable with other simple \ufb01tters, while GSF, albeit producing better results, is a factor of twenty\nslower than DNA. Exactly how these algorithms are used will depend on individual physics analyses.\n5.2\nElectron identi\ufb01cation\nWhile the end-cap TRT (discrete radiator foils) is relatively easy to simulate, the barrel TRT (matrix of\n\ufb01bres) is harder and the best indication of the expected performance comes from the test beam (CTB),\nwhere a complete barrel TRT module was tested. Using pion, electron and muon samples in the en-\nergy range between 2 and 350 GeV, the barrel TRT response has been measured in the CTB in terms\nof the high-threshold hit probability, as shown in Fig. 32. The measured performance has been used\nto parametrise the response in the TRT barrel. The transition-radiation X-rays contribute signi\ufb01cantly\nto the high-threshold hits for electron energies above 2 GeV and saturation sets in for electron energies\nabove 10 GeV. Figure 33 shows the resulting pion identi\ufb01cation ef\ufb01ciency (probability of pions being\nmisidenti\ufb01ed as electrons) for an electron ef\ufb01ciency of 90%, achieved by performing a likelihood eval-\nuation based on the high-threshold probability for electrons and pions for each straw. Figure 33 also\nshows the effect of including time-over-threshold information, which improves the pion rejection by\nabout a factor of two when combined with the high-threshold hit information. At low energies, the pion\nrejection (the inverse of the pion ef\ufb01ciency plotted in Fig. 33) improves with energy as the electrons\nemit more transition radiation. The performance is optimal at energies of \u223c5 GeV, and pion-rejection\nfactors above 50 are achieved in the energy range of 2\u201320 GeV. At very high energies, the pions become\nrelativistic and therefore produce more \u03b4-rays and eventually emit transition radiation, which explains\nwhy the rejection slowly decreases for energies above 10 GeV.\nThe electron-identi\ufb01cation performance expected for the TRT in ATLAS, including the time-over-\nthreshold information, is shown as a function of |\u03b7| in Fig. 35 in the form of the pion identi\ufb01cation\nef\ufb01ciency expected for an electron ef\ufb01ciency of 90% or 95%. The shape observed is closely correlated to\nthe number of TRT straws crossed by the track (see Fig. 34), which decreases from approximately 35 to a\nminimum of 20 in the transition region between the barrel and end-cap TRT, 0.8 < |\u03b7| < 1.1, and which\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n37\n\nLorentz gamma factor\n10\n2\n10\n3\n10\n4\n10\n5\n10\nHigh-threshold probability\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\nPions \nMuons \nElectrons \nPions \nMuons \nElectrons \nATLAS\nFigure 32: Average probability of a high-threshold\nhit in the barrel TRT as a function of the Lorentz\n\u03b3-factor for electrons (open squares), muons (full\ntriangles) and pions (open circles) in the energy\nrange 2\u2013350 GeV, as measured in the combined\ntest-beam (CTB).\nEnergy (GeV)\n1\n10\n2\n10\nPion efficiency\n-3\n10\n-2\n10\n-1\n10\n1\nTime-over-threshold \nHigh-threshold \nCombined \nATLAS\nFigure 33: Pion ef\ufb01ciency shown as a function\nof the pion energy for 90% electron ef\ufb01ciency,\nusing high-threshold hits (open circles), time-\nover-threshold (open triangles) and their combina-\ntion (full squares), as measured in the combined\ntest-beam.\n|\n\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nNumber of TRT hits\n0\n5\n10\n15\n20\n25\n30\n35\n40\nATLAS\nFigure 34: Number of hits on a track as a function\nof |\u03b7| for a track crossing the TRT.\n|\u03b7|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nPion efficiency\n-3\n10\n-2\n10\n-1\n10\n1\n90% Electron efficiency\n95% Electron efficiency\nATLAS\nFigure 35: Pion ef\ufb01ciency expected from simula-\ntion as a function of |\u03b7| for an ef\ufb01ciency of 90%\nor 95% for electrons with pT = 25 GeV.\nalso decreases rapidly at the edge of the TRT \ufb01ducial acceptance for |\u03b7| > 1.8. Because of its more\nef\ufb01cient and regular foil radiator, the performance in the end-cap TRT is better than in the barrel TRT\nwhere it consists of radiating \ufb01bres [2].\n5.3\nConversion reconstruction\nFigure 36 shows the ef\ufb01ciency for reconstructing conversions of photons with pT = 20 GeV and |\u03b7| < 2.1\nas a function of the conversion radius and pseudorapidity, using the standard tracking algorithm com-\nbined with the back-tracking algorithm described in Section 2. At radii above 50 cm, the ef\ufb01ciency for\nreconstructing single tracks drops and that for reconstructing the pair drops even faster because the two\ntracks are merged. If both tracks from the photon conversion are reconstructed successfully, vertexing\ntools can be used to reconstruct the photon conversion with high ef\ufb01ciency up to radii of 50 cm. The over-\nall conversion-identi\ufb01cation ef\ufb01ciency can be greatly increased at large radii by \ufb02agging single tracks as\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n38\n\nphoton conversions under certain conditions. (The identi\ufb01cation is distinct from the reconstruction, since\nwith a single electron, the photon conversion cannot be reconstructed.) Only tracks which have no hits\nin the vertexing layer, which are not associated to any \ufb01tted primary or secondary vertex, and which pass\na loose electron identi\ufb01cation cut requiring more than 9% high-threshold hits on the TRT segment of the\ntrack are retained. The resulting overall ef\ufb01ciency for identifying photon conversions is almost uniform\nover all radii below 80 cm, as shown in Fig. 37.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack\nTrack pair\nVertex\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack \nTrack pair \nVertex \nFigure 36: Ef\ufb01ciency to reconstruct conversions of photons with pT = 20 GeV and |\u03b7| < 2.1, as a function\nof the conversion radius (left) and pseudorapidity (right). Shown are the ef\ufb01ciencies to reconstruct single\ntracks from conversions, the pair of tracks from the conversion and the conversion vertex.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTotal efficiency\nVertex reconstruction\nSingle-track conversions\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTotal efficiency\nVertex reconstruction\nSingle track conversions\nFigure 37: Ef\ufb01ciency to identify conversions of photons with pT = 20 GeV and |\u03b7| < 2.1, as a function\nof the conversion radius (left) and pseudorapidity (right). The overall ef\ufb01ciency is a combination of the\nef\ufb01ciency to reconstruct the conversion vertex, as shown also in Fig. 36, and of that to identify single-\ntrack conversions (see text).\n6\nConclusions\nThis paper documents the expected performance for the ATLAS inner detector, focusing on the low-\nluminosity running at the start-up of the LHC. Most of the performance speci\ufb01cations set out in [1] have\nbeen met \u2013 it is only at larger values of |\u03b7|, where there are signi\ufb01cant amounts of material, that the\ntrack-\ufb01nding ef\ufb01ciencies are less than the targets.\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n39\n\nThe reconstruction of muons, electrons and pions has been studied in detail as a function of transverse\nmomentum and pseudorapidity. For high-pT muons in the barrel region, the resolution for 1/pT is\nexpected to be 0.34 TeV\u22121 and the resolution for the transverse impact parameter 10 \u00b5m. The charge of\nmuons and electrons will be measured in the inner detector over the complete acceptance up to 1 TeV\nwith misidenti\ufb01cation probabilities on average of no more than a few percent. In the barrel region, muons\nwith pT \u22651 GeV can be identi\ufb01ed with ef\ufb01ciencies in excess of 98%. For high-pT muons, this rises\nto \u226599.5% across the whole acceptance. Electrons and pions suffer from material effects; for tracks\naround 5 GeV, they are reconstructed with ef\ufb01ciencies between 70 and 95%. The inner detector is able\nto reconstruct pions down to 0.2 GeV with ef\ufb01ciencies around 50%. Fake rates are low; even in the core\nof moderate-energy jets (O(50) GeV ET), rates are less than 1%.\nAlgorithms have been developed to reconstruct primary and secondary vertices, as well as K0\ns (and\nother V0s) decays and conversions. In the case of t\u00aft events, primary vertices can be identi\ufb01ed with 99%\nef\ufb01ciency in the presence of low-luminosity pile-up. K0\ns decays can be reconstructed up to a radius of\n400 mm, while conversions can be identi\ufb01ed by reconstructing pairs of tracks or tagging single electrons\nin the TRT with 80% ef\ufb01ciency all the way up to a radius of 800 mm.\nElectrons suffer from bremsstrahlung caused by the signi\ufb01cant material in the inner detector. Algo-\nrithms have been developed to improve the reconstruction of electrons, reducing the bias on the measured\nmomentum. While reasonable electron reconstruction is possible in the inner detector barrel, it is quite\ndif\ufb01cult in the end-caps because of the increased amount of bremsstrahlung \u2013 here, the use of the elec-\ntromagnetic calorimeter will be essential. Electrons can be identi\ufb01ed by their transition radiation in the\nTRT. For an electron ef\ufb01ciency of 90% at pT = 25 GeV, the pion misidenti\ufb01cation probability is of the\norder of a few percent over most of the acceptance, and the pion rejection will be optimal around 5 GeV.\nAfter many years of preparing the ATLAS inner detector software and having tested it on simulated\nand test-beam data, we are ready to reconstruct and analyse data from collisions. We now look forward\nto the \ufb01rst data from the LHC.\nReferences\n[1] The ATLAS Collaboration, Inner Detector: Technical Design Report, CERN/LHCC/97-016/017\n(1997).\n[2] The ATLAS Collaboration, G. Aad et al., The ATLAS Experiment at the CERN Large Hardon\nCollider, 2008 JINST 3 S08003.\n[3] S. Gonzalez-Sevilla et al., Alignment of the pixel and SCT modules for the 2004 ATLAS combined\ntest-beam, ATLAS Note ATL-INDET-PUB-2007-014 (2007).\n[4] E. Abat et al., Combined performance tests before installation of the ATLAS Semiconductor and\nTransition Radiation Tracking Detectors, JINST 3 (2008) P08003.\n[5] T. Cornelissen et al., Concepts, Design and Implementation of the ATLAS New Tracking, ATLAS\nNote ATL-SOFT-PUB-2007-007 (2007).\n[6] P.F. Akesson et al., ATLAS Tracking Event Data Model, ATLAS Note ATL-SOFT-PUB-2006-004\n(2006); T. G. Cornelissen et al., Updates of the ATLAS Tracking Event Data Model, ATLAS Note\nATL-SOFT-PUB-2007-003 (2007).\n[7] A. Salzburger, S. Todorova and M. Wolter, The ATLAS Tracking Geometry Description, ATLAS\nNote ATL-SOFT-PUB-2007-004 (2007).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n40\n\n[8] A. Salzburger, The ATLAS Track Extrapolation Package, ATLAS Note ATL-SOFT-PUB-2007-005\n(2007).\n[9] V. Kartvelishvili, Nucl. Phys. B (Proc. Suppl.) 172 (2007) 208\u2013211.\n[10] R. Fr\u00a8uhwirth, Comp. Phys. Comm. 100 (1997) 1.\n[11] R. Fr\u00a8uhwirth and A. Strandlie, Comp. Phys. Comm. 120 (1999) 197\u2013214.\n[12] The ATLAS Collaboration, xKalman and iPatRec, ATLAS Inner Detector Technical Design Report,\nCERN/LHCC/97-16 (1997) 37-40.\n[13] T. Cornelissen et al., Single Track Performance of the Inner Detector New Track Reconstruction\n(NEWT), ATLAS Note ATL-INDET-PUB-2008-002 (2008).\nTRACKING \u2013 THE EXPECTED PERFORMANCE OF THE INNER DETECTOR\n41\n\n\nElectrons and Photons\n43\n\nCalibration and Performance of the Electromagnetic\nCalorimeter\nAbstract\nThis note describes the calibration of electromagnetic clusters, as implemented\nin current releases of the ATLAS reconstruction program. A series of correc-\ntions are applied to calibrate both the energy and position measurements; these\ncorrections are derived from Monte-Carlo simulations and validated using test-\nbeam data. The possibility of obtaining inter-calibration energy corrections\nfrom Z \u2192ee data is also discussed.\n1\nIntroduction\nIn order to realise the full physics potential of the LHC, the ATLAS electromagnetic calorimeter must\nbe able to identify ef\ufb01ciently electrons and photons within a large energy range (5 GeV to 5 TeV), and to\nmeasure their energies with a linearity better than 0.5%. The W boson mass measurement, not considered\nhere, will require better precision.\nThe procedure to measure the energy of an incident electron or photon in the ATLAS electromag-\nnetic (EM) calorimeter has been described in Ref. [1]. Each step of the energy reconstruction has been\nvalidated by a series of beam tests over many years, both using only the calorimeter [2, 3] and also\ncombined with representative components from all detector sub-systems. This has allowed considerable\nre\ufb01nement of the calorimeter simulation. This simulation is then used to model the behaviour of the full\ndetector.\nOne of the key ingredients for the description of the detector performance is the amount and position\nof the upstream material. The understanding of the ATLAS detector geometry has also made progress\nover the years; an overview of the present knowledge of the detector and its expected performance can be\nfound in [4]. The amount of material in front of the calorimeter for the as-built detector is signi\ufb01cantly\nlarger than was initially estimated; this leads to larger energy losses for electrons and to a larger fraction\nof photons converting (see Figs. 1 and 2).\nThe standard ATLAS coordinate system is used: the beam direction de\ufb01nes the z-axis, and the x-y\nplane is transverse to the beam direction. The azimuthal angle \u03c6 is measured around the beam axis and\nthe polar angle \u03b8 is the angle from the beam axis. The pseudorapidity is de\ufb01ned as \u03b7 \u2261\u2212ln(tan(\u03b8/2)).\n1.1\nElectron and photon candidates\nThe \u201csliding window\u201d algorithm [5] is used to \ufb01nd and reconstruct electromagnetic clusters. This forms\nrectangular clusters with a \ufb01xed size, positioned so as to maximise the amount of energy within the clus-\nter. An alternate algorithm is available which forms clusters based on connecting neighbouring cells until\nthe cell energy falls below a threshold; this is not used by the default electron and photon reconstruction.\nThe optimal cluster size depends on the particle type being reconstructed and the calorimeter region:\nelectrons need larger clusters than photons due to their larger interaction probability in the upstream ma-\nterial and also due to the fact that they bend in the magnetic \ufb01eld, radiating soft photons along a range\nin \u03c6. Several collections of clusters are therefore built by the reconstruction software, corresponding to\ndifferent window sizes. These clusters are the starting point of the calibration and selection of electron\nand photon candidates.\nOne of the recent improvements in the calibration procedure is that electron and photon candidates\nare treated separately. For each of the reconstructed clusters, the reconstruction tries to \ufb01nd a matching\ntrack within a \u2206\u03b7 \u00d7\u2206\u03c6 window of 0.05\u00d70.10 with momentum p compatible with the cluster energy E\n44\n\n|\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nEnergy (GeV) \n0\n20\n40\n60\n80\n100\nE loss before PS\nE loss before strips\nUncorrected \nCorrected\nATLAS\nFigure 1: Average energy loss vs. |\u03b7| for E =\n100 GeV electrons before the presampler/strips\n(crosses/open circles), and reconstructed energies\nbefore/after (solid/open boxes) corrections.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nFraction of converted photons\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nR < 115 cm\nR < 80 cm\nATLAS\nFigure 2: Fraction of photons converting at a ra-\ndius of below 80 cm (115 cm) in open (full) cir-\ncles, as a function of |\u03b7| [4].\n(E/p < 10 [6, 7]). If one is found, the reconstruction checks for presence of an associated conversion.\nAn electron candidate is created if a matched track is found and no conversion is \ufb02agged. Otherwise, the\ncandidate is classi\ufb01ed as a photon.\nThis early classi\ufb01cation allows applying different corrections to electron and photon candidates.\nIt is the starting point of a more re\ufb01ned identi\ufb01cation based largely on shower shapes, described in\ncompanion notes [6, 7]. Four levels of electron quality are de\ufb01ned (loose, medium, tight, and tight\nwithout isolation). The available photon selection corresponds to the tight electron selection (excluding\ntracking requirements). The medium and tight selections are used in some parts of the calibration analysis\ndescribed in this note. But the corrections derived are then applied to all electron and photon candidates.\n1.2\nCalorimeter granularity\nThe electromagnetic calorimeter (Fig. 3) was designed to be projective in \u03b7, and covers the pseudorapid-\nity range |\u03b7| < 3.2. Precision measurements are however restricted to |\u03b7| < 2.5; regions forward of this\nare outside of the scope of this note. The calorimeter is installed in three cryostats: one containing the\nbarrel part (|\u03b7| < 1.475), and two which each contain the two parts of the end-cap (1.375 < |\u03b7| < 3.2).\nIts accordion structure provides complete \u03c6 symmetry without azimuthal cracks. The total thickness\nof the calorimeter is greater than 22 radiation lengths (X0) in the barrel and greater than 24X0 in the\nend-caps. It is segmented in depth into three longitudinal sections called layers, numbered from 1 to 3\noutwards from the beam axis. These layers are often called \u201cfront\u201d (or \u201cstrips\u201d), \u201cmiddle,\u201d and \u201cback.\u201d\nThe \u03b7 granularity of the calorimeter for the front and middle layers is shown in Table 1. The \u03c6 size of\ncells is 0.025 in layer 2 and 0.1 in layer 1. Layer 3 has a granularity of \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.050 \u00d7 0.025. For\n|\u03b7| < 1.8, a presampler detector is used to correct for the energy lost by electrons and photons upstream\nof the calorimeter. All these regions must be treated separately in deriving the individual corrections.\nThe effect of the choice of cluster size on electron and photon energy reconstruction has been studied\nin Refs. [1] and [8]. These results are still the baseline of the present software. For electrons, the energy\nin the barrel electromagnetic calorimeter is collected over an area corresponding to 3 \u00d7 7 cells in the\nmiddle layer, i.e. \u2206\u03b7 \u00d7\u2206\u03c6 = 0.075\u00d70.175. For unconverted photons, the area is limited to 3\u00d75 cells in\nthe middle layer, whereas converted photons are treated like electrons. The cluster width in \u03b7 increases\nwith increasing |\u03b7|; therefore, an area of 5 \u00d7 5 cells in the middle layer is used for both electrons and\nphotons in the end-cap calorimeter.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n45\n\n\u2206\u03d5 = 0 0245\n\u2206\u03b7 = 0 025\n37 5mm/8 = 4 69 mm\n\u2206\u03b7 = 0 0031\n\u2206\u03d5=0 0245x4\n36 8mmx4\n=147 3mm\nTrigger Tower\nTrigger\nTower\n\u2206\u03d5 = 0 0982\n\u2206\u03b7 = 0 1\n16X0\n4.3X0\n2X0\n1500 mm\n470 mm\n\u03b7\n\u03d5\n\u03b7 = 0\nStrip towers in Sampling 1\nSquare towers in\nSampling 2\n1.7X0\nTowers in Sampling 3\n\u2206\u03d5\u00d7\u2206\u03b7 = 0.0245\u00d70.05\nFigure 3: Sketch of the accordion structure of the\nEM calorimeter [8].\n|\u03b7| range\nCell \u03b7 size\nLayer 1\nLayer 2\nBarrel\n0\u20131.4\n0.025/8\n0.025\n1.4\u20131.475\n0.025\n0.075\nend-cap\n1.375\u20131.425\n0.05\n0.05\n1.425\u20131.5\n0.025\n0.025\n1.5\u20131.8\n0.025/8\n0.025\n1.8\u20132.0\n0.025/6\n0.025\n2.0\u20132.4\n0.025/4\n0.025\n2.4\u20132.5\n0.025\n0.025\nTable 1: Calorimeter \u03b7 granularity in layers 1\nand 2.\n1.3\nGeometries and data sets\nThe present knowledge of the detector geometry, resulting from the detector survey, is described in [4]\n(Sec. 9). But even before the \ufb01nal survey, it was known that the inner detector services located in the\ncrack region would be wider than originally expected, and that the end-cap electromagnetic calorimeter\nwould be shifted by about 4 cm, compared to the nominal (and pointing) geometry described in Ref. [1].\nThis is taken into account in the simulation, and is treated as a misalignment in the cell calibration\nprocedure described below.\nHigh statistics samples of single electrons and photons, processed with the full detector simulation\nbased on GEANT 4.7 [9], were used to derive and study the corrections. Two detector geometries are\navailable. The \ufb01rst is the \u201cideal geometry,\u201d which contains the best knowledge of the dead material,\nbut which has no misalignments except for the 4 cm shift of the end-caps. The data sets based on\nthis geometry are used to derive the corrections and for most of the performance studies. The second\navailable geometry is a distorted one, in which extra material is added between the tracking detectors and\nthe calorimeters, and in which misalignments are introduced. For example, the amount of material in the\ninner detector has increased in some regions by up to 7% of a radiation length for positive \u03c6, and the\ndensity of material in the gap between the barrel and end-cap cryostats has increased by a factor of 1.7.\nThe distorted data-sets using this geometry are used to estimate systematic uncertainties and to check the\nsensitivity of the methods to additional material. In addition to these single-particle data sets, Z \u2192ee\ndecays are also available.\nThe standard calorimeter reconstruction for simulated data includes the effects of possible cell-level\nmiscalibrations by smearing the measured energy of each cell (by about 0.7%), therefore increasing the\nconstant term of the energy resolution. (The fractional energy resolution is conventionally parametrised\nas \u03c3(E)/E = a/E \u2295b/\n\u221a\nE \u2295c, where a is the noise term, b is the sampling term and c is the constant\nterm.) Unless otherwise stated, the results in this note do not include this additional smearing, and\ntherefore correspond to assuming a perfect cell-level calibration.\n1.4\nEnergy and position reconstruction\nThe calibration of the LAr calorimeter is factorised into a channel-by-channel calibration of the electron-\nics readout and an overall energy scale determination.\nThe \ufb01rst step, often called \u201celectronics calibration\u201d, converts the raw signal extracted from each cell\n(in ADC counts) into a deposited energy. The method used for this step, which is beyond the scope of this\nnote, was described in Ref. [1]. It was re\ufb01ned and validated when \ufb01nal barrel and end-cap modules were\nstudied in test beams [2, 3]. In the past two years, the experience gained and the algorithm developed\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n46\n\nwere integrated into the standard ATLAS calibration software [10].\nThe second step deals with clusters. The energies deposited in the cells of each individual layer of\na cluster are summed, and an energy-weighted cluster position is calculated for each layer. There are\nseveral important effects which must then be understood:\n\u2022 Due to the accordion geometry, the amount of absorber material crossed by incident particles varies\nas a function of \u03c6. This produces a \u03c6 modulation of the reconstructed energy.\n\u2022 The shower is not fully contained in the \u03b7 window chosen for clusters, and the cells have a \ufb01nite\ngranularity. This introduces a modulation in the energy and a bias in the measured position (\u201cS-\nshape\u201d) which depend on the particle impact point within a cell.\n\u2022 A perfectly projective particle, coming from the origin of the coordinate system, intersects the cal-\norimeter at the same \u03b7 position in all layers. The luminous region, however, extends signi\ufb01cantly\nin z; a particle from a vertex away from the origin intersects the calorimeter at slightly different \u03b7\npositions in each layer. Properly combining these \u03b7 measurements requires an accurate parametri-\nsation of the shower depth within each layer.\nAn early study of these corrections, using both simulation and test beam data, can be found in [11].\nThe present prediction of these effects and their dependencies on the impact point and energy of the\nincident particle are described in detail in this note.\nThe measured energy and position of EM clusters are corrected as described below (see Fig. 4).\nThe required scale of the correction is illustrated by the upper points in Fig. 1, which shows the recon-\nstructed energies of E = 100 GeV electrons before and after calibration. It is about 10% over most of the\ncalorimeter, but is larger in the transition region between cryostats.\nFigure 4: Cluster correction steps.\n\u2022 To start with, the energies in the cluster cells are summed, and an energy weighted (\u03b7,\u03c6) position is\ncalculated for each calorimeter layer. Before applying the cluster corrections, the energy resolution\nhas a constant term of about 0.65% (quoted for photons at |\u03b7| = 0.3).\n\u2022 As the \ufb01rst step, corrections are applied to the cluster position, measured in each layer. These are\ndescribed in Sec. 2. The position measurements from the \ufb01rst two layers are then combined to de-\n\ufb01ne the shower impact point in the calorimeter, which can then be used for energy reconstruction.\n\u2022 The next step is to combine the energies deposited in each layer. Two separate procedures have\nbeen developed to do this which are described in Secs. 3.1 and 5. In the \ufb01rst one, per-layer energy\ncoef\ufb01cients, called longitudinal weights, are adjusted to optimise at the same time the energy\nresolution and the linearity of the response. In the second one, the simulation is used to correct for\ndifferent types of energy loss one by one, by correlating each of them with measured observables.\nThe corrections are calculated separately for electrons and photons, and determined as a function\nof |\u03b7|. This reduces the local constant term to about 0.61%.\n\u2022 The third step, described in Sec. 3.2, uses the shower impact point to correct the total energy for\nmodulations in \u03b7 and \u03c6. This reduces the local constant term to about 0.43%.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n47\n\nIn spite of the skill and care put into the detector construction, calibration, and operation, some local\nor \u201cmedium range\u201d inhomogeneities in the calorimeter response have to be expected: localised high-\nvoltage or temperature effects or unexpected additional dead material must be detected and corrected for\nusing data. It is planned to use Z \u2192ee decays to measure and correct for such effects and to help \ufb01x the\nabsolute energy scale. The method developed and the precision expected are described in Sec. 6.\n2\nCluster position measurement\nThe position of a cluster is measured in \u03b7 and \u03c6. The positions are \ufb01rst calculated independently for each\ncalorimeter layer as the energy-weighted barycenters of all cluster cells in the layer. (The barrel and end-\ncap are also treated separately at this stage.) Secondly, the individual layer measurements are corrected\nfor known systematic biases. Finally, the position measurements from layers 1 and 2 are combined to\nproduce the overall cluster position. The position corrections are derived using single-particle electron\nand photon data samples. Each sample is mono-energetic, and the available samples span the range\n5\u20131000 GeV.\nThe \u03b7 positions that are calculated at this stage are \u201cdetector\u201d-\u03b7, corresponding to the angle that\nwould be made by a particle originating from the origin of the detector coordinate system. In order\nto properly compare the calculated detector-\u03b7 positions with the \u03b7 of a generated incident particle,\nwhich will in general have its production vertex offset in z from the detector origin, one must assume\na depth for each calorimeter layer. Here, \u201cdepth\u201d refers to the radial distance from the beam axis for\nthe barrel calorimeter, and to the distance from the x \u2212y plane passing through the origin for the end-\ncap calorimeter. The depths used are those which optimise the \u03b7-position resolution; they are shown in\nFig. 5.\n\u03b7\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\nDepth (mm)\n1500\n1550\n1600\n1650\n1700\nLayer 1\nLayer 2\nATLAS\n(a) Barrel.\n\u03b7\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nDepth (mm)\n3750\n3800\n3850\n3900\n3950\n4000\nLayer 1\nLayer 2\nATLAS\n(b) End-cap.\nFigure 5: Calorimeter depths versus |\u03b7| for layers 1 and 2 and for 100 GeV photons. The points show\nthe derived optimal depths, and the curves are piecewise polynomial \ufb01ts to the points. For layer 2 of the\nbarrel, a single curve yielded an adequate \ufb01t across |\u03b7| = 0.8; this may be revisited in future versions.\nFrom 100 GeV photons.\n2.1\n\u03b7 position correction (S-shape)\nThe cluster \u03b7 position is \ufb01rst calculated in each layer as the energy-weighted barycenter of the cluster\ncells in that layer. (In layer 1, only the three strips around the cluster center are used, regardless of the\nspeci\ufb01ed cluster size.) Due to the \ufb01nite granularity of the readout cells, these measurements are biased\ntowards the centers of the cells. For examples, see Fig. 6. This \ufb01gure plots the difference in \u03b7 between\nthe incident particle and the reconstructed cluster (\u2206\u03b7 = \u03b7true \u2212\u03b7reco) as a function of v, the relative \u03b7\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n48\n\noffset of the cluster within the cell, which varies from \u22121/2...1/2 across the cell. (The sign of \u2206\u03b7 is\ninverted for negative \u03b7, and in plots it is usually shown as a fraction of the cell \u03b7 width.) The general\nfunctional form shown in this \ufb01gure is often referred to as \u201cS-shape\u201d.\n offset\n\u03b7\nRelative cell \n-0.5\n-0.4\n-0 3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\n0.5\n (cell widths)\n\u03b7\n\u2206\n-0.2\n-0.1\n0\n0.1\n0.2\nUncorrected\nCorrected\n < 0.4\n\u03b7\n0.00625 < \nATLAS\n(a) Layer 1, barrel.\n offset\n\u03b7\nRela ive cell \n-0.5\n-0.4\n-0.3\n-0 2\n-0.1\n-0\n0.1\n0.2\n0 3\n0.4\n0.5\n (cell widths)\n\u03b7\n\u2206\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\nUncorrected\nCorrected\nCorrected, v12\n < 1.8\n\u03b7\n1.50313 < \nATLAS\n(b) Layer 1, end-cap.\n offset\n\u03b7\nRelative cell \n-0.5\n-0.4\n-0 3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\n0.5\n (cell widths)\n\u03b7\n\u2206\n-0.2\n-0.1\n0\n0.1\n0.2\nUncorrected\nCorrected\n < 0.4\n\u03b7\n0 < \nATLAS\n(c) Layer 2, barrel.\n offset\n\u03b7\nRela ive cell \n-0.5\n-0.4\n-0.3\n-0 2\n-0.1\n-0\n0.1\n0.2\n0 3\n0.4\n0.5\n (cell widths)\n\u03b7\n\u2206\n-0.2\n-0.1\n0\n0.1\n0.2\nUncorrected\nCorrected\nCorrected, v12\n < 1.9\n\u03b7\n1.525 < \nATLAS\n(d) Layer 2, end-cap.\nFigure 6: \u2206\u03b7 versus v before and after correction for different regions and for 100 GeV electrons. Note\nthe small systematic offset in the end-cap due to a change in the end-cap geometry since the corrections\nwere derived. For comparison, the \u201cv12\u201d points show results reconstructed using the same geometry as\nthat used to derive the corrections.\nFigure 6 shows the correction averaged over an |\u03b7| range. The actual correction, however, varies\ncontinuously over \u03b7, due to changes in the detector geometry (the corrections change to a much greater\nextent near discontinuities in the calorimeter). For example, the calorimeter cells are not perfectly pro-\njective (as the inner and outer cell faces are parallel to the beam-line, rather than being perpendicular to a\nline from the detector origin); this induces a bias away from the center of the calorimeter. The correction\nwill also depend on the cluster energy, as that affects the average shower depth.\nTo derive the correction, the calorimeter is divided in \u03b7 into regions based on where the behaviour\nof the correction changes discontinuously. Within each region, an empirical function is constructed to\ndescribe the correction, and an unbinned \ufb01t is performed to simulated data for a particular cluster size,\ntype, and energy.\nThe function used for the empirical \ufb01t is of the form\nf(v) = Atan\u22121 Bv+Cv+D|v|+E,\n(1)\nwhere \u22121/2 \u2264v \u22641/2 across a cell (for the actual \ufb01t, the parameters are rede\ufb01ned to reduce correla-\ntions). To turn this into a function of \u03b7, the \ufb01t parameters are written as polynomials (usually of second\nor third degree) in |\u03b7|:\nA = \u2211\ni\nai|\u03b7|i,\n(2)\nand similarly for the other parameters. The \ufb01t parameters are then the coef\ufb01cients ai, bi, etc.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n49\n\nOne feature to note about this function is that, in general, f(\u22121/2) \u0338= f(1/2), so that it will be\ndiscontinuous crossing a cell boundary. For layer 1, this is usually acceptable, since reconstructed cluster\npositions cluster well away from the cell boundary (Fig. 7(a)). However, in layer 2, the distribution of\nreconstructed cluster positions remains populated across the cluster boundary (Fig. 7(b)). Therefore, for\nlayer 2, the function is modi\ufb01ed so that f(\u22121/2) = f(1/2).\n\u03b7\n0.2\n0.202\n0.204\n0.206\n0.208\n0.21\n0 212\n (cell widths)\n\u03b7\n\u2206\n-0.4\n-0.3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n100 GeV electrons, ba rel layer 1\nATLAS\n(a) Barrel layer 1\n\u03b7\n0.2\n0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29\n0.3\n (cell widths)\n\u03b7\n\u2206\n-0.2\n-0.1\n0\n0.1\n0.2\n100 GeV electrons, barrel layer 2\nATLAS\n(b) Barrel layer 2\nFigure 7: \u2206\u03b7 versus |\u03b7| in layers 1 and 2 of the barrel, along with the empirical \ufb01t function.\nIn some cases, there is still a signi\ufb01cant periodic residual after \ufb01tting to this form; in such cases, an\nadditional general trigonometric term is added to the \ufb01t:\nf \u2032(v) = f(v)+\u03b1 cos(\u03b2\u03c0v+\u03b3).\n(3)\nFinally, a few regions near the calorimeter edges do not exhibit the S-shape form; a general polynomial\nis used as the empirical function there.\nThe correction is evaluated separately for each cluster size and type (electrons, photons). The differ-\nence in the correction between electrons and photons is a few percent, and there is about a 10% difference\nbetween 5\u00d75 and 3\u00d7N clusters.\nThe correction also depends on energy; over the range 25\u20131000 GeV, the required correction varies\nby \u223c20%. To apply the correction for a given cluster, the correction is \ufb01rst tabulated for each of the\nenergies for which simulated data samples were available. The \ufb01nal correction is then found by doing\na cubic polynomial interpolation within this table. Note a subtlety here: the energies at which the cor-\nrections are tabulated are the true cluster energies. However, when the correction is applied, only the\nreconstructed cluster energy is known. Since the position corrections are done before the energy correc-\ntions, the reconstructed cluster energy will be systematically lower than the true energy. If this were used\nfor the interpolation, this would bias the position measurements. So, for the purpose of this interpolation,\na crude energy correction is performed by scaling the reconstructed cluster energy by the ratio of the true\nto reconstructed energy observed in a 100 GeV sample, parametrised as a function of |\u03b7|. This energy\ncorrection is used only for the energy interpolation of the position corrections.\nPlots of \u2206\u03b7 before and after corrections for several regions are shown in Fig. 6. Note that since the\npresent corrections were derived, the simulated detector geometry was changed slightly in the end-cap,\nin order to match more closely the as-built detector. This results in a small systematic offset of O(10\u22124)\nin these regions.\nThe \u03b7 position resolution for photons versus |\u03b7| is shown for the two main calorimeter layers (strips\nand middle) in Fig. 8. The resolution is fairly uniform as function of |\u03b7| and is 2.5\u20133.5 \u00d7 10\u22124 for the\nstrips (which have a size of 0.003 in \u03b7 in the barrel electromagnetic calorimeter) and 5\u20136\u00d710\u22124 for the\nmiddle-layer cells (which have a size of 0.025 in \u03b7). The regions with worse resolution correspond to the\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n50\n\nbarrel/end-cap transition region and, for the strips, to the region with |\u03b7| > 2, where the strip granularity\nof the end-cap calorimeter becomes progressively much coarser.\n \n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n 1000 \n\u00d7\n) \n\u03b7\n(\n\u03c3\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLayer 1\nLayer 2\nATLAS\nFigure 8: Expected \u03b7 position resolution versus\n|\u03b7| for E = 100 GeV photons for the two main lay-\ners of the barrel and end-cap EM calorimeters [4].\n\u03b7\n0\n0 5\n1\n1.5\n2\n2.5\n (cell widths)\n\u03c6\n\u2206\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\n0.08\nBefore correction \nAfter correction\nATLAS\nFigure 9: Pro\ufb01le plot of \u2206\u03c6 versus |\u03b7| before (tri-\nangles) and after (circles) correction. For 100 GeV\nelectrons.\n2.2\n\u03c6 position correction\nThe measurement of the cluster \u03c6 position must also be corrected. These corrections are applied only in\ncalorimeter layer 2 (the \u03c6 granularity is best in this layer). As opposed to the \u03b7 direction, the accordion\ngeometry results in more energy sharing between cells in the \u03c6 direction, which washes out the S-shape\nin this direction. There is, however, a small bias in the \u03c6 measurement which depends on the average\nshower depth with respect to the accordion structure (and thus on |\u03b7|). A pro\ufb01le plot of \u2206\u03c6 = \u03c6true \u2212\u03c6reco\nbefore the correction is shown in Fig. 9. (The sign of the offset is \ufb02ipped for \u03b7 < 0, as the two halves\nof the calorimeter are identical under a rotation.) The discontinuity at |\u03b7| = 0.8, where the absorber\nthickness and the middle layer depth change, is clearly visible.\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n1000\n\u00d7)\n\u03c6(\n\u03c3\n0\n0.5\n1\n1.5\n2\n2.5\ne\n\u03b3\nATLAS\nFigure 10: Expected \u03c6 position resolution as a\nfunction of |\u03b7| for electrons and photons with an\nenergy of 100 GeV.\n\u03b7\n0\n0 5\n1\n1.5\n2\n2.5\n1000\n\u00d7)\n\u03b7(\n\u03c3\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nAll clusters\n<5 mm\nz\nATLAS\nFigure 11: Resolution of \u03b7 position measurement\nfrom layers 1 and 2 combined for 100 GeV pho-\ntons.\nThe correction derived here is symmetric in \u03c6. In the real detector, the absorbers sag slightly due to\ngravity, causing a \u03c6-dependent modulation in the \u03c6 offset with a maximum value of about 0.5 mrad [8].\nThis has not been included in the present simulations, and it is therefore not taken into account in this\ncorrection. Studies have shown, however, that the extra smearing of the position measurement from this\neffect has a negligible contribution to the widths of the invariant mass distributions of e+e\u2212pairs. (These\nstudies were performed by generating decays of massive particles using a toy Monte Carlo, smearing the\ndecay products with energy and angular resolutions roughly appropriate to ATLAS, and comparing the\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n51\n\nwidths of the resulting invariant mass distributions before and after shifting the \u03c6 positions by Acos\u03c6.\nNo signi\ufb01cant broadening was observed for A < 50 mrad.) The contribution of this effect to the constant\nterm of the energy resolution has not been studied quantitatively, but should also be small.\nTo produce a correction, the data are binned in \u03b7. The result for one sample is shown in Fig. 9. This\nfunction is interpolated in \u03b7; it is then also interpolated in energy as for the \u03b7 position correction.\nThe \u03c6 position resolution versus |\u03b7| is shown for calorimeter layer 2 in Fig. 10. Electron clusters,\nwhich get smeared in the \u03c6 direction as they radiate while propagating through the magnetic \ufb01eld, have\na worse \u03c6 position resolution than do photon clusters. A discontinuous step is seen in the resolution\nat |\u03b7| = 0.8, where the absorber thickness changes, and the resolution is worst in the transition region\nbetween the cryostats.\n2.3\nPosition measurement combination\nThe individual layer \u03b7 and \u03c6 measurements are combined to produce the overall \u03b7 and \u03c6 for a cluster.\nFor \u03c6, only layer 2 is used, so the combination is trivial except in the overlap region, where the energy-\nweighted average of the barrel and end-cap \u03c6 measurements is used. For \u03b7, both layer 1 and layer 2 are\naveraged. However, layer 1 is weighted three times as much as layer 2 to roughly take into account the\nbetter resolution in layer 1. This prescription, which does not use the actual position resolutions and does\nnot account for correlations, is known to be suboptimal and will be improved in future software versions.\nNote that the \u03b7 combination implicitly assumes that the incoming particle is projective. If its produc-\ntion vertex is shifted from the origin, then the combined \u03b7 will be biased. This is illustrated in Fig. 11,\nwhich shows the resolution of the combined cluster \u03b7 measurement. Here, the measured cluster \u03b7 is\ncompared to the \u03b7 position of the calorimeter intersected by the true particle track at a depth correspond-\ning to the cluster barycenter. This is shown both for all clusters and for clusters with the z position of the\nproduction vertex within 5 mm of the detector center.\n2.4\nShower direction\nAt high luminosity, the inner detector cannot accurately determine the interaction vertex due to the large\nnumber of additional interactions. This is an issue for the reconstruction of a H \u2192\u03b3\u03b3 signal. For this\nanalysis, achieving the best possible resolution on the invariant mass of the photon pair is crucial for\nseparating the signal peak from the continuum background. If the z-position of the interaction vertex\nis unknown, then there will be a large uncertainty in the polar angle of the photons and thus in the\npair invariant mass. We can, however, recover information about the incidence angle of the photons by\ncomparing the impact points that are reconstructed in the \ufb01rst and second layers of the EM calorimeter.\nTo do this, we need to know the photon \u03b7 position and the shower barycenter in each of the two layers\n(Fig. 5). We can then draw a straight line between these two (\u03b7,depth) points; extending this line to the\nbeam axis gives an estimate of the position of the interaction vertex.\nHere, this method is applied to single photons with energies compatible with photons from H \u2192\u03b3\u03b3\ndecays. For mH = 120 GeV, these photons are predominantly in the range 50 \u2212100 GeV. Figure 12\nshows the resolutions of the photon angle and the interaction vertex measurements as functions of |\u03b7|.\nFigure 13 shows the same resolution as a function of the photon energy, for |\u03b7| < 0.5.\n3\nCluster energy measurement\nMost of the energy of an electromagnetically interacting particle is deposited in the sensitive volume of\nthe calorimeter, including the lead absorbers and the liquid-argon gaps. A small fraction is deposited in\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n52\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n)\nGeV\n\u00d7\n (mrad\nE\n\u00d7\n\u03b8\u03c3\n0\n20\n40\n60\n80\n100\n120\nATLAS\n(a) Angular resolution.\n|\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n)\nGeV\n (mm*\nE\n)*\ntrue\n(z-z\n\u03c3\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nATLAS\n(b) Vertex resolution.\nFigure 12: Angular and vertex resolution as functions of |\u03b7| (Gaussian \ufb01ts), multiplied by\n\u221a\nE.\nenergy (GeV)\n40\n50\n60\n70\n80\n90\n100\n110\n120\n)\nGeV\n (mrad*\nE\n)*\ntrue\n\u03b8-\u03b8(\u03c3\n0\n20\n40\n60\n80\n100\n120\nATLAS\n(a) Angular resolution.\nenergy (GeV)\n40\n50\n60\n70\n80\n90\n100\n110\n120\n)\nGeV\n (mm*\nE\n)*\ntrue\n(z-z\n\u03c3\n80\n90\n100\n110\n120\n130\n140\n150\n160\n170\n180\nATLAS\n(b) Vertex resolution.\nFigure 13: Angular and vertex resolution as functions of E (Gaussian \ufb01ts), for |\u03b7| < 0.5.\nnon-instrumented material in the inner detector, the cryostats, the solenoid, and the cables between the\npresampler and the \ufb01rst EM calorimeter layer. Energy also escapes from the back of the calorimeter.\nThe cluster energy is calculated as a linearly weighted sum of the energy in each of the three calorim-\neter layers plus the presampler. The factors applied to the four energies are called longitudinal weights\nand their purpose is to correct for the energy losses, providing optimum linearity and resolution.\nThe ATLAS longitudinal weighting method was \ufb01rst described in Ref. [8]. However, recent ATLAS\ntest beam analyses [2, 3, 12] provided simple extensions of the technique. They also allowed validating\nthis method with real data.\nThe \ufb01rst section below describes the weighting correction that is performed in current versions of\nthe reconstruction, called the 4-weight method. This is followed by a description of the corrections for\n\u03b7- and \u03c6-dependent modulations in the energy. A more advanced energy-dependent calibration scheme,\ncalled the calibration hit method, is described separately in Section 5.\n3.1\n4-weight method\nThe weighting method described in this section is is a modi\ufb01cation of that described in Ref. [8] and is\ncurrently the default in ATLAS reconstruction. The weights used are functions only of |\u03b7|; no energy\ndependencies are used. The method could be readily extended to include \u03c6- and energy-dependent\nweights in order to minimise residual non-linearities. The reconstructed energy is given by\nEreco = A(B+WpsEps +E1 +E2 +W3E3),\n(4)\nwhere Eps and E1...3 are the cluster energies in the presampler and the three layers of the calorimeter\n(including sampling fractions). The offset term B corrects for upstream energy losses for which the\ncorresponding electron has not reached the presampler (PS). In the limiting case of no energy in the\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n53\n\nPS, this offset corresponds to the energy an electron loses before it undergoes a hard bremsstrahlung\nfor which the resulting photon passes through the PS without converting (i.e., no energy recorded in the\nPS). The parameters A, B, Wps, and W3 are calculated by a \u03c72 minimisation of (Etrue \u2212Ereco)2/\u03c3(Etrue)2\nusing Monte Carlo single particle samples, where \u03c3(Etrue) is a parametrisation of the expected energy\nresolution. This minimisation is done for separate |\u03b7| bins, de\ufb01ned by the \u2206\u03b7 = 0.025 granularity of\nthe second layer of the calorimeter. Equal-sized samples with energies between 10 and 200 GeV are\ncombined for the \ufb01ts (the linearity of low energy points could be improved by using more events at those\nenergies.) The \ufb01ts are done separately for each cluster size and particle type (electron and photon).\nA special parametrisation is applied in the gap region between the barrel and end-cap calorimeters\n(1.447 < |\u03b7| < 1.55), within which the parametrisation of Eq. (4) is not adequate. Moreover, this region\nis instrumented with scintillator tiles that can be used to recover some of the energy lost in the gap. The\nparametrisation used in the crack is\nEreco = A(B+Eb +Ee +WscintEscint),\n(5)\nwhere Eb and Ee are the energies the cluster deposits in the barrel and end-cap calorimeters, respectively.\nEscint is the scintillator energy, andWscint the weight applied to it. This parametrisation is found to perform\nsigni\ufb01cantly better than that used in [1].\nThe longitudinal weights in Eq. (4) were extracted for electrons and photons and are shown as a\nfunction of |\u03b7| in Fig. 14. In Fig. 14(a) one can see that the overall scale A for electrons (solid) is larger\nthan that for photons. The reason is due to the fact that photons travel on average 9/7X0 before they\nstart losing energy. This effect is close to 1% in the middle of the barrel and increases with the increase\nof upstream material. The offset term B is shown in Fig. 14(b); photons have a very small offset, as\nexpected. (Future versions of the correction will use larger statistics to reduce the scatter observed in the\n\ufb01t results.) The PS weight Wps shown in Fig. 14(c) is the usual factor applied to preshower/presampler\nenergy responses to correct for upstream losses. Finally, in Fig. 14(d), W3 is a weight applied to the last\ncalorimeter layer to correct for energy leakage behind the calorimeter.\nDetailed studies have revealed that the physical meaning attributed to these weights is only approx-\nimate. For example, the weights compensate for losses after the PS via the minimisation procedure. In\naddition, the weights have a non-negligible energy dependence. However, this energy dependence does\nnot result in large non-linearities because the weights adjust their values to compensate. These effects\nare more evident at low energies E < 15 GeV, and with large amounts of upstream material. A more\nrigorous treatment of the longitudinal weighting is presented in Sec. 5.\nThe performance of this method is shown in Sec. 4\n3.2\nCluster energy modulation corrections\nAs the \u03c6 impact position of a particle shifts across the accordion structure of the absorbers, the amount of\npassive absorber material it encounters and thus the ratio R \u2261Ereco/Etrue varies slightly, with a periodicity\nequal to that of the absorber spacing. This effect is small, with a maximum value of about a half-percent.\nFurther, at lower energies, the \u03c6 position resolution becomes comparable to the absorber spacing; this\ncontributes to washing out the effect at these energies. The reconstructed energy is corrected for this.\nTo derive the correction, the calorimeter is binned in |\u03b7|. The binning used is not uniform, but is\nchosen so as to segregate regions of the calorimeter with non-uniform R. Within each |\u03b7| bin, R is\nplotted versus the \u03c6 offset of the cluster relative to the absorber. These plots are divided into \u03c6 bins, each\nbin is \ufb01t to a Gaussian, and the means of the \ufb01ts are plotted. The resulting plot is then normalised to\nunity and \ufb01t to a two-term Fourier series:\nf(\u03c6) = 1+A[\u03b1 cos(N\u03c6 +C)+(1\u2212\u03b1)cos(2N\u03c6 +D)],\n(6)\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n54\n\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nEMC Escale \n0.95\n1\n1.05\n1.1\n1.15\n1.2\nATLAS\n(a) Overall scale A.\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nEMC Offset (MeV)\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n9000\n10000\nATLAS\n(b) Offset B.\n\u03b7\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nEMC Wps \n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\n(c) Longitudinal weight Wps.\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nEMC W3 \n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nATLAS\n(d) Longitudinal weight W3.\nFigure 14: Fitted longitudinal weights for electrons (solid) and photons (open) as functions of |\u03b7|.\nfor \ufb01t parameters A, \u03b1, C, and D. Parameter \u03b1 is restricted to the range 0\u20131. N is the total number of\nabsorbers in 2\u03c0 (1024 in the barrel and 768 in the end-capend-cap). An example of such a \ufb01t is shown\nin Fig. 15.\nFits are performed separately for each energy, cluster size, and particle type. To apply the correction,\nit is calculated for each \u03b7 and energy bin. It is then interpolated both in \u03b7 and in energy. This correction\nreduces the constant term in the energy resolution (for photons at |\u03b7| = 0.3) from 0.61% to 0.50%.\nEnergy modulations are also observed along the \u03b7 direction. The energy of a cluster is de\ufb01ned as\nthe energy within a rectangular window of \ufb01xed size in \u03b7 \u00d7\u03c6. The window can only shift by an integral\nnumber of cells; however, the impact point of a particle may be anywhere within a cell. Thus, on average,\na larger fraction of the cluster energy will be contained in the window when the particle hits at the center\nof a cell than if it hits near an edge. The size of this effect is a few tenths of a percent, and is larger\nfor smaller cluster sizes. The modulation can be \ufb01t well with a quadratic; see Fig. 16. Note that this\nmodulation is very small, < 0.1%, in the \u03c6 direction, due to increased energy sharing between the cells;\nthis modulation is not presently corrected. (A larger modulation was seen in the test beam [13], which\nused 3\u00d73 clusters.)\nThe plots to \ufb01t are prepared in a similar manner as for the \u03c6 modulations, except that the x-axis\nis taken to be the \u03b7 offset within a cell. The plots from all bins where the detector is mostly uniform\nare then combined into a single plot; that is, the |\u03b7| ranges 0.05\u20130.75, 0.85\u20131.30, and 1.70\u20132.50. The\nresulting plot is then scaled so as to average to unity and \ufb01t to a quadratic. The correction is performed\nseparately for each energy, cluster size, and particle type. The \ufb01nal correction is then determined by\ninterpolating in energy. An example \ufb01t is shown in Fig. 16. Applying this correction further reduces the\nconstant term to 0.43%. A major contribution to the remaining constant term is from the \u03c6-dependency\nof the inner detector material distribution. (The present weighting correction is averaged over \u03c6.)\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n55\n\n offset from absorber\n\u03c6\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\nRelative response\n0.995\n0.996\n0.997\n0.998\n0.999\n1\n1.001\n1.002\n1.003\n1.004\n1.005\nATLAS\nFigure 15: Energy modulation in \u03c6 for 200 GeV\n3 \u00d7 7 electrons with 0.2 < |\u03b7| < 0.4, along with\nthe modulation \ufb01t.\n offset from cell edge\n\u03b7\n0\n0.005\n0.01\n0.015\n0 02\n0.025\nRelative response\n0 992\n0 994\n0 996\n0 998\n1\n1 002\n1 004\nATLAS\nFigure 16: Energy modulation in \u03b7 for 200 GeV\n3\u00d77 electrons, along with the modulation \ufb01t [4].\n4\nEnergy calibration performance\nThis section shows the performance of the calibration chain used in the current version of the ATLAS\nreconstruction software used for all of the electron and photon reconstruction and identi\ufb01cation studies\nreported here and elsewhere.\n4.1\nSingle electrons and photons\nIn Fig. 17, the energy response, plotted as the difference between measured and true energy divided by\nthe true energy, is shown for electrons with an energy of 100 GeV for two illustrative \u03b7-positions in\nthe barrel electromagnetic calorimeter. The central value of the energy is reconstructed with excellent\nprecision (\u223c3\u00d710\u22124) if one assumes perfect knowledge of the material in front of the calorimeter. Both\nthe Gaussian core and the non-Gaussian component of the tail of the energy distribution are signi\ufb01cantly\nworse at the point with larger |\u03b7| due to the larger amount of material in front of the calorimeter. The\nresolution and non-Gaussian tails are better for photons than for electrons, but are somewhat worse for\nall photons than for photons that do not convert before leaving the volume of the inner detector.\nThe linearity (relative difference between the \ufb01tted mean energy and the true energy) and resolution\nare shown in Fig. 18 for electrons and photons. The expected performance is very similar for electrons\nand photons, with a somewhat larger degradation at larger values of |\u03b7| in the case of electrons, as\nexpected from the impact of upstream material. For electrons, the linearity is shown for |\u03b7| = 0.3 (barrel)\nand |\u03b7| = 2.0 (end-cap). The deterioration of the performance seen in the end-cap is attributed to the\nabsence of a presampler (|\u03b7| > 1.8) and the relatively limited statistics of the simulated samples. The\nresolution shown in Fig. 18(b) is given for three |\u03b7| points: |\u03b7| = 0.3 (inner barrel), |\u03b7| = 1.1 (outer\nbarrel), and |\u03b7| = 2.0 (end-cap). The resolution drop at larger |\u03b7| is attributed to the signi\ufb01cant increase\nof upstream material in front of the calorimeter with respect to the small |\u03b7| region. The extra material\ncauses increased early showering upstream of the calorimeter, which affects the lateral shower shape in\nthe calorimeter. Since Eq. (4) absorbs the corrections for lateral losses into the overall scale constant A,\nan increase in lateral-loss \ufb02uctuations will result in a deterioration of the resolution. The \ufb01ts in Fig. 18(b)\ngive a sampling term of (10.17\u00b10.33)% at small |\u03b7|, and (14.5\u00b11.0)% in the end-cap.\nIn Fig. 19, the energy resolution for electrons and photons is shown as a function of |\u03b7|. The photon\nresolution is better than the electron resolution in regions with more material in front of the calorimeter.\nThe extracted constant term of the resolution is shown for photons in Fig. 20 after the weight and mod-\nulation corrections. This \ufb01gure also shows the constant term observed when the standard simulation of\ncell-level miscalibrations is enabled in the reconstruction program. In Fig. 21, the linearity and resolution\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n56\n\ntrue\n)/E\ntrue\n(E-E\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nArbitrary units\n0\n50\n100\n150\n200\n250\n 0.03)%\n\u00b1\n = (1.12 \n\u03c3\nATLAS\n(a) Electrons, |\u03b7| = 0.325.\ntrue\n)/E\ntrue\n(E-E\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nArbitrary units\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n 0.08)%\n\u00b1\n = (1.66 \n\u03c3\nATLAS\n(b) Electrons, |\u03b7| = 1.075.\ntrue\n)/E\ntrue\n(E-E\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nArbitrary units\n0\n20\n40\n60\n80\n100\n120\n140\n 0.05)%\n\u00b1\n = (1.37 \n\u03c3\nATLAS\n(c) All photons, |\u03b7| = 1.075.\ntrue\n)/E\ntrue\n(E-E\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nArbitrary units\n0\n20\n40\n60\n80\n100\n120\n140\n 0.05)%\n\u00b1\n = (1.26 \n\u03c3\nATLAS\n(d) Unconverted photons, |\u03b7| = 1.075.\nFigure 17: Difference between measured and true energy normalised to true energy at E = 100 GeV.\nas a function of |\u03b7| is shown for a range of energies for single photons.\n4.2\nMass resolution obtained in H \u21924e and H \u2192\u03b3\u03b3 \ufb01nal states\nFigure 22 shows the reconstructed distribution, after calibration, of the invariant mass of the electrons\nin H \u21924e decays, with mH = 130 GeV. (Loose electron selection applied, as de\ufb01ned in [6].) A global\nconstant term of 0.7% has been included in the electromagnetic calorimeter resolution for the two plots in\nthis subsection. The central value of the reconstructed invariant mass is correct to \u223c1 GeV, correspond-\ning to a precision of 0.7%, and the expected Gaussian resolution is \u223c1.5%. The non-Gaussian tails in the\ndistribution amount to 20% of events lying further than 2\u03c3 away from the peak. They are mostly due to\nbremsstrahlung, particularly in the innermost layers of the inner detector, but also to radiative decays and\nto electrons poorly measured in the barrel/end-cap transition region of the electromagnetic calorimeter.\nFigure 23 shows the reconstructed photon pair invariant mass for H \u2192\u03b3\u03b3 decays with mH = 120 GeV\n(tight photon selection applied and barrel/end-cap transition region excluded). The photon directions are\nderived from a combination of the direction measurement in the electromagnetic calorimeter described\nabove (see Section 2.4) with the primary vertex information from the inner detector. The central value of\nthe reconstructed invariant mass is correct to \u223c0.2 GeV, corresponding to a precision of 0.2%, and the\nexpected resolution is \u223c1.2%. Most of the non-Gaussian tails at low values of the reconstructed photon\npair mass are seen to be due to photons which convert in the inner detector. The shift in the means comes\nfrom the fact that the corrections to-date do not distinguish between converted and unconverted photons.\n4.3\nStudy of systematic effects using H \u21924e\nThe energy linearity for electrons in H \u21924e is shown in Fig. 24(a) for samples based on the ideal (full\ntriangles) and distorted (circles) geometries. The departure from linearity for the distorted geometry is\nattributed to the presence of extra material in front of the calorimeter. The corresponding resolution is\nshown in Fig. 24(b) for the distorted geometry.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n57\n\nEnergy (GeV)\n0\n100\n200\n300\n400\n500\nLinearity\n-0.01\n-0.008\n-0.006\n-0.004\n-0.002\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n| = 0.3\n\u03b7\n|\n| = 2.0\n\u03b7\n|\nATLAS\n(a) Electron energy linearity.\nEnergy (GeV)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nFractional energy resolution\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\n| = 0.3\n\u03b7\n|\n| = 1.1\n\u03b7\n|\n| = 2.0\n\u03b7\n|\nATLAS\n(b) Electron energy resolution.\nEnergy (GeV)\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nLinearity\n-0.01\n-0.008\n-0.006\n-0.004\n-0.002\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n| = 0.3\n\u03b7\n|\n| = 2.0\n\u03b7\n|\nATLAS\n(c) Photon energy linearity.\nEnergy (GeV)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nRelative resolution\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\n| = 0.3\n\u03b7\n|\n| = 1.1\n\u03b7\n|\n| = 2.0\n\u03b7\n|\nATLAS\n(d) Photon energy resolution.\nFigure 18: Energy linearity (left) and resolution (right) for electrons (top) and photons (bottom).\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nRelative resolution\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n3x7 Barrel 5x5 Ecap 100GeV e\n\u03b3\n3x5 Barrel 5x5 Ecap 100GeV \nATLAS\nFigure 19: Energy resolution for electrons and\nphotons as a function of |\u03b7|.\n\u03b7\n0\n0 5\n1\n1.5\n2\n2.5\nConstant term (%)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\nAfter weight corrn, miscalib\nAfter modulation corrn, miscalib\nAfter energy corrn\nAfter modulation corrn\nATLAS\nFigure 20: Extracted constant term of the energy\nresolution for photons, as a function of |\u03b7|, after\nweight and modulation corrections. Also shown\nwith cell-level miscalibrations enabled.\nThe uniformity in \u03c6 and \u03b7 observed in this sample is shown in Fig. 25. The non-uniformities seen\nat higher |\u03b7| and at positive \u03c6 are due to simulated extra material in these regions. In the \u03c6-uniformity\nplot (Fig. 25(a)) a residual modulation is observed. This is most likely due to an artefact in the simulation.\nThe longitudinal weights used in the reconstruction depend only on \u03b7, and are averaged over \u03c6. Adding\na dependency on \u03c6 as well would make the energy scale along \u03c6 more uniform and also improve the\nmass resolution of Z \u2192ee.\n5\nEnergy correction using calibration hits\nThis section describes an alternate method for calculating the total energy from the energies in the in-\ndividual calorimeter layers and the presampler. It is a development of ideas introduced in [14, 15] to\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n58\n\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n>\ntrue\n)/E\ntrue\n-E\nrec\n<(E\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n0.04\n 20 GeV\n 50 GeV\n 75 GeV\n100 GeV\n200 GeV\nATLAS\n(a) Energy linearity.\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\ntrue\n)/E\ntrue\n-E\nrec\n(E\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n 20 GeV\n 50 GeV\n 75 GeV\n100 GeV\n200 GeV\nATLAS\n(b) Energy resolution.\nFigure 21: Energy linearity and resolution for photons (5\u00d75 clusters).\n (GeV)\neeee\nm\n100\n105\n110\n115\n120\n125\n130\n135\n140\n145\n150\nArbitrary units\n0\n50\n100\n150\n200\n250\n300\n 0.05) GeV\n\u00b1\nMean = (129 05 \n 0 04) GeV\n\u00b1\n = (1.95 \n\u03c3\nATLAS\nFigure 22: M(eeee) from Higgs boson decays\nwith mH = 130 GeV (energy from calorimeter\nonly, with no Z boson mass constraint).\n (GeV)\n\u03b3\n\u03b3\nm\n90\n95\n100\n105\n110\n115\n120\n125\n130\n135\n140\nArbitrary units\n0\n100\n200\n300\n400\n500\n600\n700\n 0.02) GeV\n\u00b1\nMean = (119.8 \n 0.02) GeV\n\u00b1\n = (1.39 \n\u03c3\nATLAS\nFigure 23: M(\u03b3\u03b3) from Higgs boson decays with\nmH = 120 GeV. The shaded plot corresponds to at\nleast one photon converting at r < 80 cm.\nanalyse test beam data and is described in some detail in [16]. Special simulations are used in which the\nenergy deposited by a particle is recorded in all detector materials, not just the active ones. Through these\nsimulations, the energy depositions in the inactive material can be correlated with the measured quanti-\nties. For example, the energy lost in the material in front of the calorimeter (inner detector, cryostat, etc.)\ncan be estimated from the energy deposited in the presampler. The result is a method which provides a\nmodular way to reconstruct the energies of electrons and photons by decoupling all the different correc-\ntions. This approach eases comparisons between electrons and photons, and might be particularly useful\nin the initial stages of the experiment.\nThe cluster energy is decomposed into three pieces, which will be treated separately below:\nE = Ecal +Efront +Eback,\n(7)\nwhere Ecal is the energy deposited in the electromagnetic calorimeter, Efront is the energy deposited in\nthe presampler and in the inactive material in front of the calorimeter, and Eback is the energy that leaks\nout the rear of the EM calorimeter.\nThis analysis uses simulated single-particle, mono-energetic electron and photon samples, with en-\nergies ranging from 25 to 500 GeV.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n59\n\nEnergy (GeV)\n20\n40\n60\n80\n100\n>\ntrue\n)/E\ntrue\n<(E-E\n-0.015\n-0.01\n-0.005\n0\n0.005\n0.01\n0.015\nATLAS\n(a) Energy linearity.\nEnergy (GeV)\n10\n20\n30\n40\n50\n60\n70\n80\n (%)\ntrue\n)/E\ntrue\n-E\nrecon\n(E\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\nATLAS\n(b) Energy resolution.\nFigure 24: Electron linearity and resolution in H \u21924e for the ideal (full triangles) and distorted (circles)\ngeometries.\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\n>\ntrue\n)/E\ntrue\n<(E-E\n-0.015\n-0.01\n-0.005\n0\n0.005\n0.01\n0.015\nATLAS\n(a) Energy uniformity in \u03c6 integrated over pT and \u03b7.\n|\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n>\ntrue\n)/E\ntrue\n<(E-E\n-0.02\n-0.015\n-0.01\n-0.005\n0\n0.005\n0.01\n0.015\n0.02\nATLAS\n(b) Energy uniformity in \u03b7 integrated over pT and \u03c6.\nFigure 25: Electron energy uniformity in \u03b7 and \u03c6, integrated over other kinematic variables, for the\nideal (full triangles) and distorted (circles) geometries.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n60\n\n5.1\nReconstruction of the energy deposited in the calorimeter\nThe energy deposited by a particle in the EM calorimeter, Ecal, is estimated as\nEcal = Ccal(X,\u03b7)(1+ fout(X,\u03b7))Ecl,\n(8)\nwhere\n\u2022 Ecl = \u22113\ni=1 Ei, and E1...3 are the energies deposited in each of the three calorimeter layers in a given\ncluster. In the following, Eps will denote the energy deposited in the presampler. The energies Ei\navailable at this stage of the reconstruction are the energies deposited in the liquid-argon ionisation\nmedium divided by a region-dependent sampling fraction.\n\u2022 X is the the longitudinal barycentre or shower depth, de\ufb01ned by\nX = \u22113\ni=1 EiXi +EpsXps\n\u22113\ni=1 Ei +Eps\n,\n(9)\nwhere Ei is as above and Xi is the longitudinal depth, expressed in radiation lengths, of compart-\nment i, computed from the centre of the detector. The Xi, which are computed using a geantino1\nscan, are functions of \u03b7.\n\u2022 \u03b7 is the cluster barycentre, corrected for the S-shape effect (see Sec. 2.1).\n\u2022 fout is the fraction of the energy deposited outside the cluster.\n\u2022 Ccal(X,\u03b7) is the calibration factor for the energy in the EM calorimeter.\nThe calibration factor Ccal is de\ufb01ned as the average ratio between the true energy deposited in the EM\ncalorimeter (both absorbers and ionisation medium) and the reconstructed cluster energy Ecl. It is within\na few percent of unity, and takes into account effects such as the dependence of the sampling fraction\non \u03b7 and on the longitudinal pro\ufb01le of the shower. Once the correction factor Ccal is expressed as a\nfunction of X it is fairly energy independent. The correction factor averaged over all energies is shown\nin Fig. 26(a). Its dependence on X is parametrised with a second order polynomial. The \ufb01t is performed\nexcluding the bins with less than 0.5% of the total statistics. This criterion is also applied to all the \ufb01ts\nperformed in the following.\nDue to the presence of the magnetic \ufb01eld and bremsstrahlung radiation, the fraction of energy de-\nposited in the calorimeter outside of the cluster is energy dependent. Since only single electrons and\nphotons with no noise or underlying event are simulated, this fraction is easily calculated. The pro\ufb01le of\nthe out-of-cluster energy is asymmetric with the tail on the high side. However the most probable value,\nobtained with a Gaussian \ufb01t around the maximum of the distribution (\u22122\u03c3, +1.5\u03c3), is energy indepen-\ndent when plotted as a function of X. The most probable value of the fraction of energy deposited outside\nthe cluster averaged over all energies is shown in Fig. 26(b) for electrons and photons and the two |\u03b7|\nvalues. Electrons and photons behave similarly in the central region but differently in the forward region.\nThis is due to the large difference in the amount of material present in front of the calorimeter (\u223c2.5X0\nat |\u03b7| = 0.3 and \u223c7X0 at |\u03b7| = 1.65) combined with the presence of bremsstrahlung and the magnetic\n\ufb01eld.\n1A \u201cgeantino\u201d is an imaginary non-interacting particle used in the simulation. The properties of the material crossed by the\nparticle are recorded.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n61\n\n)\n0\nLongitudinal Barycenter (X\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\nCluster Accordion Correction \n0.96\n0.965\n0.97\n0.975\n0.98\n0.985\n0.99\n0.995\n1\n1.005\n1.01\nATLAS\n| = 0.3\n\u03b7\nElectron |\n| = 1.65\n\u03b7\nElectron |\n| = 0.3\n\u03b7\nPhoton |\n| = 1.65\n\u03b7\nPhoton |\n(a) Ccal vs. X.\n)\n0\nLongitudinal Barycenter (X\n6\n8\n10\n12\n14\n16\n18\nEnergy out of Cluster (%) \n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\nATLAS\n| = 0.3\n\u03b7\nElectron |\n| = 1.65\n\u03b7\nElectron |\n| = 0.3\n\u03b7\nPhoton |\n| = 1.65\n\u03b7\nPhoton |\n(b) Fraction of out-of-cluster energy.\nFigure 26: Correction factor Ccal and fraction of out-of-cluster energy as a function of the shower depth\nX, averaged over all energies, at two representative |\u03b7| points. The dashed lines show the results of the\nparametrisation.\n5.2\nEnergy deposited in front of the calorimeter\nThe energy lost in the material in front of the calorimeter (inner detector, cryostat, coil, and material\nbetween the presampler and strips) is parametrised as a function of the energy lost in the active material\nof the presampler (Eps):\nEfront = a(Ecal,\u03b7)+b(Ecal,\u03b7)Eps +c(Ecal,\u03b7)E2\nps.\n(10)\nAn example of this relation is shown in Fig. 27. All coef\ufb01cients are parametrised in terms of the energy\ndeposited by a particle in the calorimeter (Ecal) and \u03b7. The coef\ufb01cient c is used only in the end-cap,\n1.55 < |\u03b7| < 1.8, and is set to zero otherwise. Note explicitly that Efront includes the energy deposited in\nthe presampler and between the presampler and the strips. An alternate form for Efront, which depends\non the energy in the \ufb01rst calorimeter layer in addition to Eps, was also tried. This did not improve the\nresolution, so the simpler parametrisation above is retained.\n(MeV)\nPS\nE\n0\n1000\n2000\n3000\n4000\n5000\n6000\n (MeV) \nfront\nE\n0\n1000\n2000\n3000\n4000\n5000\n6000\nATLAS\nElectron\nPhoton\nFigure 27: Energy lost in front of the EM calorim-\neter as a function of the energy measured in the\npresampler at |\u03b7| = 0.3 for electrons of 100 GeV.\nThe dashed curve shows the parametrisation de-\nrived for electrons.\n)\n0\nLongitudinal Barycenter (X\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n (MeV) \nfront\nE\n0\n1000\n2000\n3000\n4000\n5000\n6000\nATLAS\nElectron\nPhoton\nFigure 28: Energy lost in front of the calorime-\nter as a function of shower depth X, for electrons\nof 100 GeV at |\u03b7| = 1.9, in a region where the cal-\norimeter is not instrumented with the presampler.\nIn the region 1.8 < |\u03b7| < 3.2, not instrumented with the presampler, the energy deposited in front of\nthe calorimeter is parametrised as a function of X with a second degree polynomial. Figure 28 shows\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n62\n\nthis correlation for electrons and photons of 100 GeV at |\u03b7| = 1.9. The coef\ufb01cients of this polynomial\nare parametrised in terms of Ecal.\n5.3\nLongitudinal leakage correction\nThe energy deposited by the showers behind the EM calorimeter is computed as a fraction of the energy\nreconstructed in the calorimeter. This fraction, when parametrised as a function of X, is fairly energy\nindependent both for electrons and photons. Averaged over the particle energies, it is parametrised by\nfleak \u2261Eback/Ecal = f leak\n0\n(\u03b7)X + f leak\n1\n(\u03b7)eX.\n(11)\nFigure 29 shows the leakage and the result of the \ufb01t for |\u03b7| = 0.3 and 1.65.\n)\n0\nLongitudinal Barycenter (X\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\nEnergy behind Accordion (%) \n0\n0.5\n1\n1.5\n2\n2.5\n3\nATLAS\nElectron\nPhoton\n(a) |\u03b7| = 0.3.\n)\n0\nLongitudinal Barycenter (X\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\nEnergy behind Accordion (%) \n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nElectron\nPhoton\n(b) |\u03b7| = 1.65.\nFigure 29: Fraction of energy deposited behind the calorimeter, averaged over particle energies, as a\nfunction of the shower depth X. The parametrisation used is superimposed.\n5.4\nResults\nThe total cluster energy is computed by adding these three contributions. Example distributions of re-\nconstructed energies are shown in Fig. 30. Mean values and standard deviations are found from a \ufb01t to a\nCrystal-Ball function (a Gaussian with a low-side tail of the form (1\u2212x)\u2212n).\nThe resolution is shown in Fig. 31 as a function of the particle energy for electrons and photons at\ntwo |\u03b7| values and in Fig. 32 for various photon energies and all \u03b7 values. The sampling term is shown\nin Fig. 33 as a function of |\u03b7| for electrons and photons.\nFor electrons, the sampling term increases from 8.7% at low |\u03b7| to 21% at |\u03b7| = 1.55. This worsening\nof the energy resolution is related to the increase of the material in front of the calorimeter. This effect is\nmuch less relevant for photons, which have a maximum sampling term of 12%. The constant term is in\ngeneral lower than 0.6% and is related to the energy modulation in a cell (see Sec. 3.2), not corrected at\nthis stage. The linearity, the ratio between the \ufb01tted mean value and the true particle energy, is shown in\nFig. 34. It is better than 0.5% over the full |\u03b7| range and in the energy interval 25\u2013500 GeV.\nThe results from the calibration hits correction are comparable in terms of resolution and linearity\nwith the longitudinal weights method. However there are a few differences worth mentioning. The coef-\n\ufb01cients of the longitudinal weights method are averaged over a range of energies, while the parametrisa-\ntions of the calibration hits method are energy dependent. This means that it should be easier to extend\nthe calibrated energy range for the calibration hits method without compromising energy linearity. An-\nother important difference is that while the coef\ufb01cients of the longitudinal weights method have no direct\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n63\n\nEnergy (GeV)\n20\n21\n22\n23\n24\n25\n26\n27\n28\n0\n20\n40\n60\n80\n100\nATLAS\nElectron\nPhoton\n(a) E = 25 GeV, |\u03b7| = 0.3.\nEnergy (GeV)\n20\n21\n22\n23\n24\n25\n26\n27\n28\n0\n5\n10\n15\n20\n25\n30\nATLAS\nElectron\nPhoton\n(b) E = 25 GeV, |\u03b7| = 1.65.\nEnergy (GeV) \n90\n95\n100\n105\n110\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nATLAS\nElectron\nPhoton\n(c) E = 100 GeV, |\u03b7| = 0.3.\nEnergy (GeV) \n90\n95\n100\n105\n110\n0\n10\n20\n30\n40\n50\n60\n70\n80\nATLAS\nElectron\nPhoton\n(d) E = 100 GeV, |\u03b7| = 1.65.\nFigure 30: Total reconstructed energy pro\ufb01les.\nEnergy (GeV)\n0\n100\n200\n300\n400\n500\n / E \n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\nElectron\nPhoton\n , c = 0 5610 (%)\nE\n9.3 %\nElectron: b = \n , c = 0.6097 (%) \nE\n8 6 %\nPhoton : b = \n(a) |\u03b7| = 0.3.\nEnergy (GeV)\n0\n100\n200\n300\n400\n500\n / E \n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nATLAS\nElectron\nPhoton\n , c = 0.43 (%)\nE\n19.4 %\nElectron: b = \n , c = 0.59 (%) \nE\n12.2 %\nPhoton : b = \n(b) |\u03b7| = 1.65.\nFigure 31: Resolution versus particle energy.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\nreco\nE\n\u03c3\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nATLAS\nE = 500 GeV\nFigure 32: Resolution for various photon energies\nas a function of |\u03b7|.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\nb (%)\n8\n10\n12\n14\n16\n18\n20\n22\nElectron\nATLAS\nPhoton\nFigure 33: Sampling term as a function of |\u03b7|.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n64\n\n| \n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n \ntrue\n/E\nreco\nE\n0.99\n0.995\n1\n1.005\n1.01\n1.015\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nATLAS\nE = 500 GeV\n(a) Electrons.\n| \n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n \ntrue\n/E\nreco\nE\n0.99\n0.995\n1\n1.005\n1.01\n1.015\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nE = 500 GeV\nE = 25 GeV\nE = 50 GeV\nE = 75 GeV\nE = 100 GeV\nE = 200 GeV\nATLAS\nE = 500 GeV\n(b) Photons.\nFigure 34: Linearity for various particle energies as a function of |\u03b7|.\nphysical meaning, the parametrisation of the calibration hits method allows isolating the different com-\nponents of the calibrated cluster energy: that deposited in the calorimeter, inside and outside of the\ncluster, and in front and behind of it. The knowledge of these separate contributions, which depend on\naccurate and detailed simulations of the tracker and the calorimeters, could be particularly useful in the\nearly stages of the experiment, for example to disentangle effects such as a miscalibration of the calo-\nrimeter or an imperfect knowledge of the inner detector material. It is also worth noting that the estimate\nof the energy lost in front of the calorimeter is crucial to obtaining a good resolution and linearity; at\nlow energies and large rapidities, a large fraction of the energy of an electron is deposited in front of the\ncalorimeter. The calculation of missing momentum could also bene\ufb01t from this separation of effects.\n6\nIn-situ calibration with Z \u2192ee events\n6.1\nMotivation\nIn the EM calorimeter, the construction tolerances and the calibration system ensure that the response is\nlocally uniform, with a constant term < 0.5% over regions of size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.2\u00d70.4. This has been\nshown with test beam data [13]. Electron pairs from Z boson decays can then be used to intercalibrate\nthe 384 regions of such size within the acceptance of |\u03b7| < 2.4. These regions must be intercalibrated\nto within 0.5% in order to achieve a desired global constant term of < 0.7%. The basic idea of this\ncalibration method is to constrain the di-electron invariant mass distribution to the well-known Z boson\nline shape. A second goal of the calibration is to provide the absolute calorimeter electromagnetic energy\nscale. This must be known to an accuracy of \u223c0.1% in order to achieve the ATLAS physics goals2.\n6.2\nDescription of the method\nLong-range non-uniformities can arise for many reasons, including variations in the liquid argon im-\npurities and temperature, amount of upstream material, mechanical deformations, and high voltage (as\nlocalised calorimeter defects may necessitate operating a small number of channels below nominal volt-\nage). For a given region i, we parametrise the long-range non-uniformity modifying the measured elec-\ntron energy as Ereco\ni\n= Etrue\ni\n(1+\u03b1i). Neglecting second-order terms and supposing that the angle between\nthe two electrons is perfectly known, the effect on the di-electron invariant mass is:\nMreco\ni j\n\u2243Mtrue\ni j (1+ \u03b1i +\u03b1 j\n2\n) = Mtrue\ni j (1+ \u03b2i j\n2 ),\n(12)\nwhere \u03b2i j \u2261\u03b1i +\u03b1 j.\n2Except for the W boson mass measurement, which needs a much better knowledge of the energy scale (\u223c0.02%).\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n65\n\nThe method to extract the \u03b1\u2019s is fully described in [17] and is done in two steps. First, the \u03b2\u2019s\nare determined, then the \u03b1\u2019s. For a given pair of regions (i, j), the coef\ufb01cient \u03b2i j and its associated\nuncertainty are determined by minimising the following log-likelihood:\n\u2212lnLtot =\nNi j\n\u2211\nk=1\n\u2212lnL\n\u0012\nMk/\n\u0012\n1+ \u03b2i j\n2\n\u0013\n,\u03c3M,k\n\u0013\n,\n(13)\nwhere k counts all selected events populating the pair of regions (i, j), Mk is the di-electron invariant\nmass of event k, and L(M,\u03c3M) quanti\ufb01es the compatibility of an event with the Z boson line shape\nand is described below. Fits with only one event are removed. Once the \u03b2\u2019s are determined from the\nminimisation, the \u03b1\u2019s can be found from the overdetermined linear system given by \u03b2i j \u2261\u03b1i +\u03b1 j. This\nis done using a generalised least squares method, and gives an analytic solution.\nThe Z boson line shape is modeled with a relativistic Breit-Wigner distribution [18,19]:\nBW(M) \u223c\nM2\n(M2 \u2212M2\nZ)2 +\u03932\nZM4/M2\nZ\n,\n(14)\nwhere MZ and \u0393Z are the mass and the width of the Z boson. They were measured precisely at LEP;\nthe values used are, respectively, 91.188 \u00b1 0.002 GeV and 2.495 \u00b1 0.002 GeV [20]. In proton-proton\ncollisions, the mass spectrum of the Z boson differs from the Breit-Wigner shape of the partonic process\ncross section. The probability that a quark and antiquark in the interacting pp system produce an object\nof mass M falls with increasing mass. In order to take this into account, the Breit-Wigner is multiplied\nby the ad-hoc parametrisation L (M) = 1/M\u03b2. The parton luminosity parameter \u03b2 is assumed to be a\nconstant and is determined by \ufb01tting the Z boson mass distribution obtained with events generated with\nPYTHIA version 6.403 [21]. Figure 35(a) shows the Z boson mass distribution \ufb01tted with a Breit-Wigner\nwith and without the parton luminosity factor. The \ufb01tted value of the parameter \u03b2 is 1.59 \u00b1 0.10; this\nwill be used in the following. Since the photon propagator and the interference term between the photon\nand the Z boson were not taken into account in the previous parametrisation, the parton luminosity term\nalso accounts for the effects of these two terms.\nATLAS\n (GeV)\n-e\ne\nM\n80\n82\n84\n86\n88\n90\n92\n94\n96\n98\n100\nNumber of events\n2\n10\n3\n10\n4\n10\n(a) Z line shape\ninj\n\u03b1\n - \nfit\n\u03b1\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\nNumber of regions\n0\n10\n20\n30\n40\n50\n60\n70\nATLAS\n(b) Residual distribution\nFigure 35: (a) Z boson mass distribution for PYTHIA events \ufb01tted with a Breit-Wigner distribution with\n(solid line) and without (dashed line) the parton luminosity factor. \u03c7 2/NDOF is 1.09 and 3.96, respec-\ntively. (b) Residual distribution \ufb01tted with a Gaussian.\nFinally, in order to take into account the \ufb01nite resolution of the electromagnetic calorimeter, the\nBreit-Wigner multiplied by the parton luminosity term is convoluted with a Gaussian:\nL(M,\u03c3M) =\nZ +\u221e\n\u2212\u221eBW(M \u2212u)L (M \u2212u) e\u2212u2/2\u03c32\nM\n\u221a\n2\u03c0\u03c3M\ndu,\n(15)\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n66\n\nwhere \u03c3M is the resolution of the measured mass. It is related to the electron energy resolution via\n\u03c3M\nM = 1\n2\ns\u0012\u03c3E1\nE1\n\u00132\n+\n\u0012\u03c3E2\nE2\n\u00132\n.\n(16)\nAt |\u03b7| = 0.3, the sampling term of the electron energy resolution is equal to 10.0% and increases with\nincreasing |\u03b7|. Technically, the integral is converted to a discrete summation over the convolution pa-\nrameter u which takes values between \u22125\u03c3M and +5\u03c3M.\n6.3\nGenerator-level tests\nThe method is \ufb01rst tested on generator-level Z \u2192ee Monte Carlo events. These were generated using\nPYTHIA 6.403 [21] with MZ = 91.19 GeV and \u0393Z = 2.495 GeV. Events are required to have at least one\nelectron with pT > 10 GeV and |\u03b7| < 2.7 and a di-electron invariant mass Mee > 60 GeV. To simulate\nthe detector resolution, generated electron energies are smeared to obtain \u03c3E/E = 10%/\np\nE/ GeV.\nFor each calorimeter region i, a bias \u03b1i is generated from a Gaussian distribution with a mean \u00b5bias\nand width \u03c3bias. These will be called the \u201cinjected\u201d \u03b1\u2019s, \u03b1inj.\nFor the \ufb01rst tests, \u00b5bias is \ufb01xed to 0 and \u03c3bias to 2%. The calibration method explained above is\napplied to 50,000 events after selection. The residual distribution (\u03b1\ufb01t \u2212\u03b1inj) is shown in Fig. 35(b).\nThe mean value of the residual distribution corresponds to the energy scale, and its width to the energy\nresolution. Thus it can be seen that the \ufb01tting method gives unbiased estimators of the injected \u03b1\u2019s.\nIn the case where \u00b5bias is different from zero, the mean value of the residual distribution will be\ndifferent from zero. For example, for \u00b5bias = \u22123%, \u27e8\u03b1\ufb01t \u2212\u03b1inj\u27e9= 0.1%. This is a consequence of\nneglecting the higher-order terms in the Taylor expansion of Eq. (12). Iterating the procedure twice\nsuf\ufb01ces to recover an unbiased estimate of the \u03b1\u2019s, as shown in Fig. 36(a).\nATLAS\nNumber of iterations\n0\n1\n2\n3\n4\n5\n>\ninj\n\u03b1\n-\nfit\n\u03b1\n<\n-0.005\n-0.004\n-0.003\n-0.002\n-0.001\n0\n0 001\n0.002\n0 003\n0.004\n0 005\n>=+0 05\ninj\n\u03b1\n<\n>=+0 03\ninj\n\u03b1\n<\n>= 0 00\ninj\n\u03b1\n<\n>=-0.03\ninj\n\u03b1\n<\n>=-0.05\ninj\n\u03b1\n<\n(a) Mean value.\nATLAS\n ee events\n\u2192\nNumber of Z \n0\n20\n40\n60\n80\n100 120 140 160 180 200\n3\n10\n\u00d7\ninj\n\u03b1\n-\nfit\n\u03b1\n\u03c3\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\n)\n-1\nIntegrated luminosity (pb\n0\n50\n100\n150 200 250\n300 350 400 450\n(b) Constant term.\nFigure 36: (a) Mean value of the Gaussian \ufb01tting the residual distribution as a function of the number of\niterations for different mean values of the injected \u03b1\u2019s; (b) Constant term as a function of the number of\nevents or as a function of the luminosity.\nFigure 35(b) also shows the resulting uniformity. After the \ufb01t, the RMS of the distribution has been\nreduced from 2% to 0.4%. The RMS of the residual distribution is a measure of the expected long-\nrange constant term. Figure 36(b) shows the long-range constant term as a function of the number of\nreconstructed Z \u2192ee decays or of the integrated luminosity assuming an event selection ef\ufb01ciency of\n25%. Therefore, by summing the local constant term of 0.5% with the long-range constant term of 0.4%\nobtained here, a total constant term of about 0.7% could be achieved with \u223c100 pb\u22121. These results\nassume perfect knowledge of the material in front of the electromagnetic calorimeter.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n67\n\n6.4\nResults with distorted geometry\nThe previous section showed results based on generator-level Monte Carlo. The results in this section\nuse PYTHIA events with full detector simulation and reconstruction, using a geometry with additional\nmaterial in front of the electromagnetic calorimeter.\nThe number of events available is 349,450 corresponding to an integrated luminosity of \u223c200 pb\u22121.\nEvents with at least two reconstructed electrons are kept. The two leading electrons are required to be of\nat least medium quality [6], to have pT > 20 GeV and |\u03b7| < 2.4, and to be of opposite sign. Finally, the\ndi-electron invariant mass is required to be within 80 < Mee < 100 GeV. The total selection ef\ufb01ciency is\n21.5%; the ef\ufb01ciency for \ufb01nding two electron candidates within |\u03b7| < 2.4 is 50%.\nThe calibration method is applied \ufb01rst without injecting any biases (\u03b1inj = 0 for all regions). How-\never, the presence of the misalignments and extra material means that there will be some biases intrinsic\nto the simulation. These \u201ctrue\u201d biases can be estimated using generator information:\n\u03b1true,i = 1\nNi\nNi\n\u2211\nk\npreco,k\nT\n\u2212pgen,k\nT\npgen,k\nT\n,\n(17)\nwhere k counts over the Ni electrons falling in region i, and preco,k\nT\nand pgen,k\nT\nare the reconstructed\nand true transverse momenta of electron k. The distribution of \u03b1true is shown in Fig. 37(a), as is the\nresults of the \ufb01t. The low-end tail corresponds to regions located in the gap between the barrel and end-\ncap cryostats (Fig. 38(a)), where the density of material has been increased by a factor of 1.7. There\nis fair agreement between the \u03b1\u2019s extracted using the data-driven method and those estimated from\ngenerator information. Figure 37(b) shows the difference between \u03b1\ufb01t and \u03b1true; a Gaussian \ufb01tted to\nthis distribution has a mean of 0.1% and a width of 0.5%. The distribution of \u03b1\ufb01t as a function of \u03b7\nand \u03c6 is shown in Fig. 38 for the ideal and distorted geometries. The asymmetry between positive and\nnegative \u03c6 is due to the effect of the extra material in the inner detector at positive \u03c6. The difference\nbetween positive and negative \u03c6 values is about 0.6%.\nThe same exercise is also done by introducing, on top of the non-uniformities due to extra material, a\nbias \u03b1inj generated from a Gaussian distribution with a mean \u00b5bias = 0 and width \u03c3bias = 2%. Results are\nshown in Fig. 39. The Gaussian \ufb01tted to this distribution also has a mean of 0.1% and a width of 0.5%.\nOne can conclude that, using \u223c87,000 reconstructed Z \u2192ee events (which corresponds to about\n200 pb\u22121), and with an initial spread of 2% from region to region, the long-range constant term should\nnot be greater than 0.5%.3 This should give an overall constant term \u223c0.7%. The bias on the absolute\nenergy should be small and of the order of 0.2%. If the exercise is repeated with only 100 pb\u22121 of data,\nthe Gaussian \ufb01tted to the residual distribution also has a mean of 0.2%, but the width is larger, leading to\na long-range constant term of 0.8%.\n7\nEstimation of the systematic uncertainty on the energy scale\nThe absolute energy scale has been obtained using electrons from Z \u2192ee decays. It has been determined\non events simulated with the misaligned geometry while the longitudinal weights were found with the\nideal geometry. On top of the non-uniformities due to extra material, a bias modeling the calorimeter\nnon-uniformities is introduced and is generated from a Gaussian distribution with a mean \u00b5bias = 0 and\nwidth \u03c3bias = 2%. The resulting bias on the energy scale can be assessed by comparing the \ufb01tted \u03b1\u2019s\nwith those from generator information; the bias is equal to 0.2%. This bias is understood and is due to\nthe fact that the model of the Z boson line shape doesn\u2019t take into account the effects of bremsstrahlung.\nWork is ongoing to improve this issue.\n3Part of the RMS of the residual distribution is also due to uncertainties on the measurement of \u03b1true.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n68\n\n\u03b1\n-0.12\n-0.08\n-0 04\n0\n0.04\nNumber of region\n0\n10\n20\n30\n40\n50\n60\n70\nATLAS\n(a) \u03b1\ufb01t (solid) and \u03b1true (dashed).\ntrue\n\u03b1\n - \nfit\n\u03b1\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\nNumber of regions\n0\n10\n20\n30\n40\n50\n60\nATLAS\n(b) Difference between \u03b1\ufb01t and \u03b1true.\nFigure 37: Fit results with distorted geometry and \u03b1inj = 0.\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1 5\n2\nfit\n\u03b1\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\nATLAS\n(a) \u03b1\ufb01t integrated over \u03c6 as a function of \u03b7.\n\u03d5\n-3\n-2\n-1\n0\n1\n2\n3\nfit\n\u03b1\n-0.035\n-0.03\n-0.025\n-0.02\n-0.015\n-0 01\n-0.005\n0\nATLAS\n(b) \u03b1\ufb01t integrated over \u03b7 as a function of \u03c6, \ufb01tted in two\nseparate regions.\nFigure 38: \u03b1\ufb01t distributions with \u03b1inj = 0 and with distorted/ideal (full/open circles) geometry.\n\u03b1\n-0.12\n-0.08\n-0 04\n0\n0.04\nNumber of region\n0\n5\n10\n15\n20\n25\n30\nATLAS\n(a) \u03b1\ufb01t (solid) and \u03b1true +\u03b1inj (dashed).\ntrue\n\u03b1\n - \ninj\n\u03b1\n - \nfit\n\u03b1\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\nNumber of regions\n0\n10\n20\n30\n40\n50\n60\nATLAS\n(b) Difference between \u03b1\ufb01t and \u03b1true +\u03b1inj.\nFigure 39: Fit results with distorted geometry and additional injected biases.\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n69\n\nThe background has been neglected but it has been checked that the contribution from QCD events\nwhere the two jets are misidenti\ufb01ed as electrons is small. Thus, it should have a negligible effect on the\ndetermination on the energy scale.\nElectrons from Z boson decays have a pT spectrum with a maximum value around 45 GeV. Care\nwill thus have to be taken to extrapolate the calibration obtained from Z \u2192ee decays to electron energy\nregions not well populated by these events. Corrections determined with Z boson decays were applied\nto single electron samples with different generated transverse momenta (20, 40, 120, and 500 GeV)\nreconstructed with the misaligned geometry. Figure 40 shows \u27e8\u03b1true\u27e9after correction as a function of pT\nfor four |\u03b7| bins. In principle, \u27e8\u03b1true\u27e9should be equal to zero. This is true for the 40 GeV electron sample\nat a level of 0.2% except in the bin (1.4 < |\u03b7| < 2.0) containing the crack region. For central electrons\n(|\u03b7| < 0.6), the dependence versus pT is smaller than 0.5%. The effect is worse for non-central electrons.\nFor instance, at pT = 120 GeV, \u03b1true after corrections varies from 1 to 1.6 percent. This non-linearity is\ndue to the presence of extra material in front of the calorimeter.\nATLAS\n (GeV)\nT\np\n0\n100\n200\n300\n400\n500\n >\n true\n\u03b1\n<\n-0 03\n-0 02\n-0.01\n-0\n0 01\n0.02\n0.03\n0.04\n0.05\n|<0.6\n\u03b7\n0.0<|\n|<1.4\n\u03b7\n0.6<|\n|<2.0\n\u03b7\n1.4<|\n|<2.4\n\u03b7\n2.0<|\n|<0.6\n\u03b7\n0.0<|\n|<1.4\n\u03b7\n0.6<|\n|<2.0\n\u03b7\n1.4<|\n|<2.4\n\u03b7\n2.0<|\n|<0.6\n\u03b7\n0.0<|\n|<1.4\n\u03b7\n0.6<|\n|<2.0\n\u03b7\n1.4<|\n|<2.4\n\u03b7\n2.0<|\nFigure 40: \u27e8\u03b1true\u27e9after correction as a function of pT for four \u03b7 bins.\nTo conclude, at the Z boson energy scale, the estimate of the systematic uncertainty is around 0.2%.\nAt other energy scales, the systematic uncertainty is dominated by effects of extra material. For central\nelectrons, corrections can be extrapolated over the full pT spectrum to a level of 0.5%. The linearity is\ndegraded for non-central electrons at a level of 1 or 2 percent except in the crack region where it is worse.\nThese numbers depend on the amount of extra material added to the misaligned geometry compared to\nthe ideal geometry and will likely be different with real data.\nThe performance presented here corresponds to our current understanding of the determination of\nthe absolute energy scale. Improvements are expected to achieve systematic uncertainties smaller than\n0.5%. For instance, including information from the E/p ratio measured for isolated high-pT electrons\nfrom W \u2192e\u03bd decays will compliment the direct calibration of the absolute scale with Z \u2192ee events.\nPhoton conversions can also help to determine the amount of material in front of the calorimeter.\nConclusion\nThe methods and algorithms described in this note were already mentioned in Ref. [1] many years ago.\nOver the years, they have reached a higher level of stability and maturity, and have been implemented in\nthe ATLAS reconstruction software. It is believed that, given the constraints of the ATLAS detector, in\nparticular the amount of dead material in front of the calorimeter, the performances described here will\nnot evolve much further.\nThe real challenge at the beginning of data-taking will be the detection and correction for additional\ninner detector material or calorimeter inhomogeneities which would not have affected the somewhat\nsmaller-scale detectors used in the test beam. Discrepancies between data and simulation will have to be\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n70\n\nunderstood prior to the use of the methods described above. The in-situ calibration with Z \u2192ee events\ndescribed in Section 6 will play an important role, and re\ufb01nements of the method presented here are\nexpected.\nReferences\n[1] ATLAS Collaboration, Detector and Physics Technical Design Report, Vol.1, CERN/LHCC/99-14\n(1999).\n[2] ATLAS Electromagnetic Liquid Argon Calorimeter Group (B. Aubert et al.), Nucl. Inst. Meth.\nA500 (2003) 202\u2013231.\n[3] ATLAS Electromagnetic Liquid Argon Calorimeter Group (B. Aubert et al.), Nucl. Inst. Meth.\nA500 (2003) 178\u2013201.\n[4] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\n2008 JINST 3 S08003 (2008).\n[5] W. Lampl et al., Calorimeter Clustering Algorithms: Description and Performance, ATLAS-\nLARG-PUB-2008-002 (2008).\n[6] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[7] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Photons, this volume.\n[8] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-41\n(1996).\n[9] GEANT Detector Description and Simulation Tool, 1994, CERN Program Library Long Write-up\nW5013.\n[10] M. Aleksa et al., Report ATL-LARG-PUB-2006-003, 2006.\n[11] R. Sacco et al., Nucl. Inst. Meth. A500 (2003) 178\u2013201.\n[12] S. Paganis, Nucl. Phys. Proc. Suppl. 172 (2007) 108\u2013110.\n[13] M. Aharrouche et al., Nucl. Inst. Meth. A582 (2007) 429\u2013455.\n[14] M. Aharrouche et al., Nucl. Inst. Meth. A568 (2006) 601\u2013623.\n[15] G. Graziani, Report ATL-LARG-2004-001, 2004.\n[16] L. C. D. Ban\ufb01and L. Mandelli, Report ATL-LARG-PUB-2007-012, 2007.\n[17] F. Djama, Report ATL-LARG-2004-008, 2004.\n[18] F. Berends et al., in Z physics at LEP 1, ed. G. Altarelli, R. Kleiss, and C. Verzegnassi, (CERN\nReport 89-08, 1989).\n[19] LEP Electroweak Working Group, Phys. Rep. 427 (2006) 257.\n[20] Particle Data Group (S. Eidelman et al.), Phys. Lett. B592 (2004) 1.\n[21] T. Sj\u00a8ostrand et al., Comp. Phys. Comm. 135 (2001).\nELECTRONS AND PHOTONS \u2013 CALIBRATION AND PERFORMANCE OF THE . . .\n71\n\nReconstruction and Identi\ufb01cation of Electrons\nAbstract\nThis note discusses the overall ATLAS detector performance for the recon-\nstruction and identi\ufb01cation of high-pT electrons over a wide range of trans-\nverse energies, spanning from 10 GeV to 1000 GeV.\nElectrons are reconstructed using information from both the calorimeter and\nthe inner detector. The reference of\ufb02ine performance in terms of ef\ufb01ciencies\nfor electrons from various sources and of rejections against jets is described. In\na second part, this note discusses the requirements and prospects for electrons\nas probes for physics within and beyond the Standard Model: Higgs-boson, su-\npersymmetry and exotic scenarios. In the last part, this note outlines prospects\nfor electron identi\ufb01cation with early data, corresponding to an integrated lumi-\nnosity of 100 pb\u22121 , focusing on the use of the signal from Z \u2192ee decays for\na data-driven evaluation of the of\ufb02ine performance.\n1\nIntroduction\nExcellent particle identi\ufb01cation capability is required at the LHC for most physics studies. Several\nchannels expected from new physics, for instance some decay modes of the Higgs boson into electrons,\nhave small cross-sections and suffer from large (usually QCD) backgrounds. Therefore powerful and\nef\ufb01cient electron identi\ufb01cation is needed to observe such signals. Even for standard processes, the signal-\nto-background ratio is usually less favourable than at past and present hadron colliders. The ratio between\nthe rates of isolated electrons and the rate of QCD jets with pT in the range 20-50 GeV is expected to be\n\u223c10\u22125 at the LHC, almost two orders of magnitude smaller than at the Tevatron p \u00afp collider. Therefore,\nto achieve comparable performances, the electron identi\ufb01cation capability of the LHC detectors must be\nalmost two orders of magnitude better than what has been achieved so far.\nPhysics channels of prime interest at the LHC are expected to produce electrons with pT between\na few GeV and 5 TeV. Good electron identi\ufb01cation is therefore needed over a broad energy range. In\nthe moderate pT region (20 - 50 GeV), a jet-rejection factor exceeding 105 will be needed to extract a\nrelatively pure inclusive signal from genuine electrons above the residual background from jets faking\nelectrons. The required rejection factor decreases rapidly with increasing pT to \u223c103 for jets in the TeV\nregion. For multi-lepton \ufb01nal states, such as possible H \u2192eeee in the mass region 130 < mH < 180\nGeV, a rejection of \u223c3000 per jet should be suf\ufb01cient to reduce the fake-electron backgrounds to a level\nwell below that from real electrons. In this case, however, the electrons have a rather soft pT spectrum\n(as low as 5 GeV), resulting in lower reconstruction and identi\ufb01cation ef\ufb01ciencies.\nSince the publication of the ATLAS physics TDR [1], the ATLAS detector description has been\ngreatly improved, with, in particular, the introduction of a more realistic material description for the\ninner detector and for the region between the inner detector and the \ufb01rst layer of the electromagnetic\ncalorimeter [2] [3]. This has led to some signi\ufb01cant changes in the expected performance. The re-\nconstruction software has also evolved signi\ufb01cantly. Each step of the energy reconstruction has been\nvalidated by a series of beam tests [4] [5] [6] using prototype modules of the liquid argon electromag-\nnetic calorimeter, and also more recently, combined with prototype modules of the inner detector. At\npresent, two electron reconstruction algorithms have been implemented in the ATLAS of\ufb02ine software,\nboth integrated into one single package and a common event data model.\n- The standard one, which is seeded from the electromagnetic (EM) calorimeters, starts from clusters\nreconstructed in the calorimeters and then builds the identi\ufb01cation variables based on information\nfrom the inner detector and the EM calorimeters.\n72\n\n- A second algorithm, which is seeded from the inner detector tracks, is optimized for electrons\nwith energies as low as a few GeV, and selects good-quality tracks matching a relatively isolated\ndeposition of energy in the EM calorimeters. The identi\ufb01cation variables are then calculated in the\nsame way as for the standard algorithm.\nThe standard algorithm is the one used to obtain the results presented in this note, while the track-\nbased algorithm is used for low pT and non-isolated electrons and is the subject of another note [7].\nThis note is organised as follows. Section 2 discusses the reconstruction and identi\ufb01cation of elec-\ntrons in the \ufb01ducial range of the ATLAS detector (|\u03b7| < 2.5), whereas section 3 describes the iden-\nti\ufb01cation of electrons in the forward region (2.5 < |\u03b7| < 4.9). Section 4 describes some important\nperformance aspects of electron identi\ufb01cation in discovery physics processes. Section 5 discusses the\nstrategies for measuring reconstruction and identi\ufb01cation ef\ufb01ciencies using a data-driven approach based\non Z \u2192ee events.\n2\nCalorimeter-seeded reconstruction and identi\ufb01cation\nIn the standard reconstruction of electrons, a seed electromagnetic tower with transverse energy above \u223c\n3 GeV is taken from the EM calorimeter [3] and a matching track is searched for among all reconstructed\ntracks which do not belong to a photon-conversion pair reconstructed in the inner detector. The track,\nafter extrapolation to the EM calorimeter, is required to match the cluster within a broad \u2206\u03b7 \u00d7\u2206\u03c6 window\nof 0.05\u00d70.10. The ratio, E/p, of the energy of the cluster to the momentum of the track is required to\nbe lower than 10. Approximately 93% of true isolated electrons, with ET > 20 GeV and |\u03b7| < 2.5, are\nselected as electron candidates. The inef\ufb01ciency is mainly due to the large amount of material in the inner\ndetector and is therefore \u03b7-dependent. As an example, 4% of electron candidates with pT = 40 GeV\nfail the cut E/p < 10 and most of the losses are in the end-cap region. Various identi\ufb01cation techniques\ncan be applied to the reconstructed electron candidates, combining calorimeter and track quantities and\nthe TRT information to discriminate jets and background electrons from the signal electrons. A simple\ncut-based identi\ufb01cation procedure is described below together with its expected performance. This is\nfollowed by a brief overview of the possibilities offered by more advanced methods, such as a likelihood\ndiscriminant.\n2.1\nElectron-jet studies\nFor the purposes of this note, the electron identi\ufb01cation ef\ufb01ciency is de\ufb01ned as\n\u03b5 = NId\ne\nNtruth\ne\n,\nwhere NId\ne\nis the number of reconstructed and identi\ufb01ed candidates and Ntruth\ne\nis the number of true\nelectrons selected using the appropriate kinematic cuts at the generator level. A geometrical matching\n(within a cone of size \u2206R = 0.2) between the reconstructed cluster and the true electron is required in\nthe calculation of NId\ne . A classi\ufb01cation is applied to de\ufb01ne whether a reconstructed electron candidate\nshould be considered as signal or background. This classi\ufb01cation is based on the type of the Monte Carlo\nparticle associated to the reconstructed track, as well as that of its non-electron parent particle. As shown\nin Table 1, candidates are divided into four categories and signal ef\ufb01ciencies are calculated separately\nfor isolated and non-isolated electrons.\nFor the jet rejection studies, the PYTHIA (version 6.4) [10] event generator has been used to produce\nthe large statistics of jet background samples required to assess both the trigger and of\ufb02ine performance\nof the electron reconstruction and identi\ufb01cation tools described in this note. Two different samples were\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n73\n\ngenerated to cover the ET -range of interest for single electrons (10-40 GeV). The \ufb01rst one, referred\nto as \ufb01ltered di-jets, contains all hard-scattering QCD processes with ET\n> 15 GeV, e.g. qg \u2192qg,\nincluding heavy-\ufb02avour production, together with other physics processes of interest, such as prompt-\nphoton production and single W/Z production. The second one, referred to as minimum bias, contains\nthe same processes without any explicit hard-scattering cut-off. A \ufb01lter was applied at the generator\nlevel to simulate the L1 trigger requirements [11], with the goal of increasing in an unbiased way the\nprobability that the selected jets pass the electron identi\ufb01cation cuts after GEANT [12] simulation. The\nsummed transverse energy of all stable particles (excluding muons and neutrinos) with |\u03b7| < 2.7 in\na region \u2206\u03c6 \u00d7 \u2206\u03b7 = 0.12 \u00d7 0.12 was required to be greater than a chosen ET -threshold for an event\nto be retained. For the \ufb01ltered di-jet sample, this ET -threshold is 17 GeV, while for the minimum-bias\nsample, it is 6 GeV. The \ufb01lter retains 8.3% of the di-jet events and 5.7% of the minimum-bias events.\nThe total number of events available for analysis after \ufb01ltering, simulation and reconstruction, amounts\nto 8.2 million events for the di-jet sample and to 4.1 million events for the minimum-bias sample.\nCategory\nType of particle\nType of parent particle\nIsolated\nElectron\nZ, W, t, \u03c4 or \u00b5\nNon-isolated\nElectron\nJ/\u03c8, b-hadron or c-hadron decays\nBackground electron\nElectron\nPhoton (conversions), \u03c00/\u03b7 Dalitz decays, u/d/s-hadron decays\nNon-electron\nCharged hadrons, \u00b5\nTable 1: Classi\ufb01cation of simulated electron candidates according to their associated parent particle.\nMuons are included as source because of the potential emission of a Bremsstrahlungs photon.\nET > 17 GeV\nET > 8 GeV\nIsolated\nNon-isolated\nBackground\nNon-isolated\nBackground\nW \u221275.0%\nb-hadrons \u221238.7%\n\u03b3-conv. \u221297.8%\nb-hadrons \u221239.3%\n\u03b3-conv. \u221298.4%\nZ \u221220.9%\nc-hadrons \u221260.6%\nDalitz decays \u22121.8%\nc-hadrons \u221259.7%\nDalitz decays \u22121.3%\nt \u2212< 0.1%\nJ/\u03c8 \u22120.7%\nu/d/s-hadrons \u22120.4%\nJ/\u03c8 \u22121.0%\nu/d/s-hadrons \u22120.3%\n\u03c4 \u22124.1%\nTable 2: Contribution and origin of isolated, non-isolated, and background electron candidates in the two\ndi-jet samples before the identi\ufb01cation criteria are applied.\nThe jet rejections quoted in this note are normalised with respect to the number of particle jets\nreconstructed using particle four-momenta within a cone size \u2206R = 0.4 and derived from a dedicated\nun-\ufb01ltered generated sample of di-jets or minimum-bias events. In the di-jet and minimum-bias samples,\nthe average numbers per generated event of such particle jets with ET above 17 and 8 GeV, respectively,\nand in the range |\u03b7| < 2.47, are 0.74 and 0.31, respectively.\nAfter reconstruction of electron candidates and before any of the identi\ufb01cation cuts are applied,\nthe signal is completely dominated by non-isolated electrons from b\u2212and c-hadron decays. The ex-\npected signal-to-background ratios for the \ufb01ltered di-jet (ET\nabove 17 GeV) and minimum-bias (ET\nabove 8 GeV) samples are 1:80 and 1:50, respectively. The residual jet background is dominated by\ncharged hadrons. Only a small fraction of the background at this stage consists of electrons from pho-\nton conversions or Dalitz decays, namely 6.4% and 9.4%, respectively. Table 2 summarises the relative\ncompositions of the \ufb01ltered di-jet and minimum-bias samples in terms of the three categories containing\nelectrons described in Table 1.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n74\n\nType\nDescription\nVariable name\nLoose cuts\nAcceptance of the detector\n|\u03b7| < 2.47\nHadronic leakage\nRatio of ET in the \ufb01rst sampling of the\nhadronic calorimeter to ET of the EM cluster\nSecond layer\nRatio in \u03b7 of cell energies in 3 \u00d7 7 versus 7 \u00d7 7 cells.\nR\u03b7\nof EM calorimeter.\nRatio in \u03c6 of cell energies in 3 \u00d7 3 versus 3 \u00d7 7 cells.\nR\u03c6\nLateral width of the shower.\nMedium cuts (includes loose cuts)\nFirst layer\nDifference between energy associated with\n\u2206Es\nof EM calorimeter.\nthe second largest energy deposit\nand energy associated with the minimal value\nbetween the \ufb01rst and second maxima.\nSecond largest energy deposit\nRmax2\nnormalised to the cluster energy.\nTotal shower width.\nwstot\nShower width for three strips around maximum strip.\nws3\nFraction of energy outside core of three central strips\nFside\nbut within seven strips.\nTrack quality\nNumber of hits in the pixel detector (at least one).\nNumber of hits in the pixels and SCT (at least nine).\nTransverse impact parameter (<1 mm).\nTight (isol) (includes medium cuts)\nIsolation\nRatio of transverse energy in a cone \u2206R < 0.2\nto the total cluster transverse energy.\nVertexing-layer\nNumber of hits in the vertexing-layer (at least one).\nTrack matching\n\u2206\u03b7 between the cluster and the track (< 0.005).\n\u2206\u03c6 between the cluster and the track (< 0.02).\nRatio of the cluster energy\nE/p\nto the track momentum.\nTRT\nTotal number of hits in the TRT.\nRatio of the number of high-threshold\nhits to the total number of hits in the TRT.\nTight (TRT) (includes tight (isol) except for isolation)\nTRT\nSame as TRT cuts above,\nbut with tighter values corresponding to about 90%\nef\ufb01ciency for isolated electrons.\nTable 3: De\ufb01nition of variables used for loose, medium and tight electron identi\ufb01cation cuts. The cut\nvalues are given explicitly only when they are independent of \u03b7 and pT . For a detailed description of\nthe cut variables used for the loose and medium cuts, refer to sections 2.1.1.1 and 2.1.1.2.\n2.1.1\nCut-based method description\nStandard identi\ufb01cation of high-pT electrons is based on many cuts which can all be applied indepen-\ndently. These cuts have been optimised in up to seven bins in \u03b7 and up to six bins in pT . Three reference\nsets of cuts have been de\ufb01ned: loose, medium and tight, as summarised in Table 3. This provides \ufb02ex-\nibility in analysis, for example to improve the signal ef\ufb01ciency for rare processes which are not subject\nto large backgrounds from fakes.\n2.1.1.1\nLoose cuts\nThis set of cuts performs a simple electron identi\ufb01cation based only on limited\ninformation from the calorimeters. Cuts are applied on the hadronic leakage and on shower-shape vari-\nables, derived from only the middle layer of the EM calorimeter (lateral shower shape and lateral shower\nwidth ). This set of cuts provides excellent identi\ufb01cation ef\ufb01ciency, but low background rejection.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n75\n\n2.1.1.2\nMedium cuts\nThis set of cuts improves the quality by adding cuts on the strips in the \ufb01rst\nlayer of the EM calorimeter and on the tracking variables:\n\u2022 Strip-based cuts are effective in the rejection of \u03c00 \u2192\u03b3\u03b3 decays. Since the energy-deposit pattern\nfrom \u03c00\u2019s is often found to have two maxima due to \u03c00 \u2192\u03b3\u03b3 decay, showers are studied in a\nwindow \u2206\u03b7 \u00d7\u2206\u03c6 = 0.125\u00d70.2 around the cell with the highest ET to look for a second maximum.\nIf more than two maxima are found the second highest maximum is considered. The variables\nused include \u2206Es = Emax2 \u2212Emin, the difference between the energy associated with the second\nmaximum Emax2 and the energy reconstructed in the strip with the minimal value, found between\nthe \ufb01rst and second maxima, Emin. Also included are: Rmax2 = Emax2/(1+9\u00d710\u22123ET), where ET\nis the transverse energy of the cluster in the EM calorimeter and the constant value 9 is in units\nof GeV\u22121; wstot, the shower width over the strips covering 2.5 cells of the second layer (20 strips\nin the barrel for instance); ws3, the shower width over three strips around the one with the maximal\nenergy deposit; and Fside, the fraction of energy deposited outside the shower core of three central\nstrips.\n\u2022 The tracking variables include the number of hits in the pixels, the number of silicon hits (pixels\nplus SCT) and the tranverse impact parameter.\nThe medium cuts increase the jet rejection by a factor of 3-4 with respect to the loose cuts, while\nreducing the identi\ufb01cation ef\ufb01ciency by \u223c10%.\n2.1.1.3\nTight cuts\nThis set of cuts makes use of all the particle-identi\ufb01cation tools currently available\nfor electrons. In addition to the cuts used in the medium set, cuts are applied on the number of vertexing-\nlayer hits (to reject electrons from conversions), on the number of hits in the TRT, on the ratio of high-\nthreshold hits to the number of hits in the TRT (to reject the dominant background from charged hadrons),\non the difference between the cluster and the extrapolated track positions in \u03b7 and \u03c6, and on the ratio\nof cluster energy to track momentum, as shown in Table 3. Two different \ufb01nal selections are available\nwithin this tight category: they are named tight (isol) and tight (TRT) and are optimised differently for\nisolated and non-isolated electrons. In the case of tight (isol) cuts, an additional energy isolation cut is\napplied to the cluster, using all cell energies within a cone of \u2206R < 0.2 around the electron candidate.\nThis set of cuts provides, in general, the highest isolated electron identi\ufb01cation and the highest rejection\nagainst jets. The tight (TRT) cuts do not include the additional explicit energy isolation cut, but instead\napply tighter cuts on the TRT information to further remove the background from charged hadrons.\nFigures 1 and 2 compare the distributions expected from Z \u2192ee decays and from the \ufb01ltered di-jet\nsample for a few examples of the basic discriminating variables described above for electron identi\ufb01ca-\ntion.\n2.1.2\nPerformance of cut-based electron identi\ufb01cation\nThe performance of the cut-based electron identi\ufb01cation is summarised in Tables 4 and 5. Table 4 shows,\nfor each of the background samples, the composition of each of the three categories of electron candi-\ndates containing real electrons, as it evolves from reconstruction (no identi\ufb01cation cuts) to loose, medium\nand tight cuts. In the case of non-isolated electrons, there is a strong reduction of the initially dominant\ncomponent from c-hadrons as the identi\ufb01cation cuts applied become tighter. In the case of background\nelectrons, there is a signi\ufb01cant reduction of the contribution from photon conversions when applying\ntight cuts, since the vertexing-layer requirement does not much affect electrons from Dalitz decays and\nu/d/s-hadrons. As shown in Table 5, the signal from prompt electrons is dominated by non-isolated elec-\ntrons from heavy \ufb02avours, which are usually close in space to hadrons from the jet fragmentation. The\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n76\n\n)\nhad1\nT\n+E\nT\n/(E\nT\nE\n0\n0.2\n0.4\n0.6\n0 8\n1\nProbability\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n1\n10\n1\nATLAS\n\u03b7\n\u2206\n-0.1 -0.08 -0.06 -0.04 -0.02\n0\n0 02\n0.04 0.06 0 08\n0.1\nProbability\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nFigure 1: Left: ratio between the transverse energy of the electron candidate and the sum of this trans-\nverse energy and that contained in the \ufb01rst layer of the hadronic calorimeter. The distributions are shown\nfor electrons from Z \u2192ee decays (solid line) and for \ufb01ltered di-jets (dotted line). Right: difference in \u03b7\nbetween cluster and extrapolated track positions for electrons from Z \u2192ee decays (solid line) and for\n\ufb01ltered di-jets (dotted line).\n\u03c6\nR\n0\n0.2\n0.4\n0.6\n0 8\n1\nProbability\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n1\n10\nATLAS\n\u03b7\nR\n0\n0 2\n0.4\n0.6\n0.8\n1\nProbability\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nFigure 2: Shower-shape distributions for electrons from Z \u2192ee decays (solid lines) compared to those\nfrom \ufb01ltered di-jets (dotted lines). Shown are the energy ratios R\u03c6 (left) and R\u03b7 (right) described in Ta-\nble 3.\nresulting overlap between the electron shower and nearby hadronic showers explains the much lower ef-\n\ufb01ciency observed for these electrons than for isolated electrons from Z \u2192ee decays. These non-isolated\nelectrons will nevertheless provide the most abundant initial source of signal electrons and will be used\nfor alignment of the electromagnetic calorimeters and the inner detector, for E/p calibrations, and more\ngenerally to improve the understanding of the material of the inner detector as a radiation/conversion\nsource. For tight cuts and an electron ET of \u223c20 GeV, the isolated electrons from W, Z and top-quark\ndecays represent less than 20% of the total prompt electron signal.\nFor the lower ET -threshold of 8 GeV, the expected signal from isolated electrons is negligible. Not\nsurprisingly, the tight (TRT) cuts are more ef\ufb01cient to select non-isolated electrons from heavy-\ufb02avour\ndecay, while the tight (isol) cuts are more ef\ufb01cient at selecting isolated electrons. After tight cuts, the\nsignal-to-background ratio is close to 3:1, and depends only weakly on the ET - threshold in the 10-\n40 GeV ET -range studied here. The residual background is dominated by charged hadrons, which could\nbe further rejected by stronger cuts (TRT and/or isolation). The initial goal of obtaining a rejection of the\norder of 105 against jets has been achieved with an overall ef\ufb01ciency of 64% for isolated electrons with\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n77\n\nIsolated\nET > 17 GeV\nNo cut\nLoose\nMedium\nTight (TRT)\nTight (isol)\nW\n75.0\n75.1\n74.9\n73.9\n73.6\nZ\n20.9\n20.9\n21.1\n22.4\n22.9\n\u03c4\n4.1\n4.0\n4.0\n3.7\n3.6\nNon-isolated\nET > 17 GeV\nET > 8 GeV\nNo cut\nLoose\nMedium\nTight (TRT)\nTight (isol)\nNo cut\nLoose\nMedium\nTight (TRT)\nTight (isol)\nb-hadrons\n38.7\n57.6\n71.1\n74.2\n79.1\n39.3\n51.2\n55.2\n57.0\n59.5\nc-hadrons\n60.6\n41.4\n27.6\n24.4\n19.6\n59.7\n47.6\n43.2\n41.3\n38.6\nJ/\u03c8\n0.7\n1.0\n1.3\n1.4\n1.3\n1.0\n1.2\n1.6\n1.7\n1.9\nBackground\nET > 17 GeV\nET > 8 GeV\nNo cut\nLoose\nMedium\nTight (TRT)\nTight (isol)\nNo cut\nLoose\nMedium\nTight (TRT)\nTight (isol)\n\u03b3-conv.\n97.8\n97.7\n94.9\n88.0\n88.1\n98.4\n98.1\n94.5\n78.5\n83.0\nDalitz decays\n1.8\n1.9\n4.0\n8.5\n8.0\n1.3\n1.4\n3.5\n12.5\n12.4\nu/d/s-hadrons\n0.4\n0.4\n1.1\n3.5\n3.9\n0.3\n0.5\n2.0\n9.0\n4.6\nTable 4: Percentage contribution and origin of isolated, non-isolated and background electrons in the\n\ufb01ltered di-jet and minimum-bias samples. The classi\ufb01cation is based on the type of the parent particle of\nthe electron.\nET \u223c10-40 GeV. The ef\ufb01ciency may be improved with further optimisation of the cuts, as discussed\nbelow.\nTable 6 shows the ef\ufb01ciencies for prompt electrons and the jet rejections in more detail in the case of\nmedium identi\ufb01cation cuts, using a \ufb01ne binning as a function of |\u03b7|. The ef\ufb01ciency for prompt electrons\nis signi\ufb01cantly worse in the end-cap region (|\u03b7| > 1.52) with a correspondingly higher background\nrejection. The overlap region region between the barrel and end-cap calorimeters (1.37 < |\u03b7| < 1.52)\nhas both worse ef\ufb01ciency and rejection, as expected because of the large amount of passive material in\nfront of the EM calorimeter. To improve the electron ef\ufb01ciency in the end-cap region, the EM calorimeter\ncuts in the \ufb01rst layer and the tracking cuts will need to be studied and tuned further.\n2.1.3\nExpected differential rates for inclusive electron signal and background\nFigure 3 (left: ET\n> 17 GeV and right: ET\n> 8 GeV) show the expected differential cross-sections\nfor electron candidates as a function of ET , for an integrated luminosity of 100 pb\u22121 . The different\nhistograms correspond to electron candidates before any identi\ufb01cation cuts and after the loose, medium,\ntight (TRT) and tight (isol) cuts. As illustrated in Table 5, these differential rates are dominated by the\njet background except when applying the tight cuts.\nThe expected differential cross-sections after tight (TRT) cuts are shown in Fig. 4, where they are\nbroken down into their three main components, isolated electrons from W, Z and top-quark decays, non-\nisolated electrons from b, c decay, and the residual jet background. The shapes of the spectra for the\nnon-isolated electrons and residual jet background are very similar, whereas the spectrum from isolated\nelectrons exhibits the expected behaviour for a sample dominated by electrons from W, Z decay. For an\nintegrated luminosity of 100 pb\u22121 , Fig. 4 (right) shows that one may expect approximately ten million\nreconstructed and identi\ufb01ed inclusive electrons from b, c decay with ET > 10 GeV, while Fig. 4 (left)\nshows that for the same integrated luminosity one may expect 500 000 such electrons with ET > 20 GeV,\nwith a dominant contribution from W, Z decays for ET > 35 GeV. These large data samples expected\nfor a modest integrated luminosity are an integral part of the trigger menu strategy for early data, as\nexplained in more detail in [11], and will clearly be extremely useful to certify many aspects of the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n78\n\nCuts\nET > 17 GeV\nET > 8 GeV\nEf\ufb01ciency (%)\nJet rejection\nEf\ufb01ciency (%)\nJet rejection\nZ \u2192ee\nb,c \u2192e\nSingle electrons\nb,c \u2192e\n(ET =10 GeV)\nLoose\n87.96 \u00b1 0.07\n50.8 \u00b1 0.5\n567 \u00b1 1\n75.8 \u00b1 0.1\n55.8 \u00b1 0.7\n513 \u00b1 2\nMedium\n77.29 \u00b1 0.06\n30.7 \u00b1 0.5\n2184 \u00b1 13\n64.8 \u00b1 0.1\n41.9 \u00b1 0.7\n1288 \u00b1 10\nTight (TRT.)\n61.66 \u00b1 0.07\n22.5 \u00b1 0.4\n(8.9 \u00b1 0.3)104\n46.2 \u00b1 0.1\n29.2 \u00b1 0.6\n(6.5 \u00b1 0.3)104\nTight (isol.)\n64.22 \u00b1 0.07\n17.3 \u00b1 0.4\n(9.8 \u00b1 0.4)104\n48.5 \u00b1 0.1\n28.0 \u00b1 0.6\n(5.8 \u00b1 0.3)104\nFraction of surviving candidates (%)\nFraction of surviving candidates (%)\nIsolated\nNon-isolated\nJets\nNon-isolated\nJets\nMedium\n1.1\n7.4\n91.5 (5.5 + 86.0)\n9.0\n91.0 (5.0 + 86.0)\nTight (TRT)\n10.5\n63.3\n26.2 (8.3 + 17.9)\n77.8\n22.2 (7.1 + 15.1)\nTight (isol)\n13.0\n58.3\n28.6 (8.7 + 19.9)\n75.1\n24.9 (6.4 + 18.5)\nTable 5: Expected ef\ufb01ciencies for isolated and non-isolated electrons and corresponding jet background\nrejections for the four standard levels of cuts used for electron identi\ufb01cation. The results are shown for\nthe simulated \ufb01ltered di-jet and minimum-bias samples, corresponding respectively to ET -thresholds of\n17 GeV (left) and 8 GeV (right). The three bottom rows show the fractions of all surviving candidates\nwhich fall into the different categories for the medium cuts and the two sets of tight cuts. The isolated\nelectrons are prompt electrons from W, Z and top-quark decay and the non-isolated electrons are from\nb, c decay. The residual jet background is split into its two dominant components, electrons from photon\nconversions and Dalitz decays (\ufb01rst term in brackets) and charged hadrons (second term in brackets).\nThe quoted errors are statistical.\nelectron identi\ufb01cation performance of ATLAS with real data. One example is the understanding of\nmaterial effects and of inter-calibration between inner detector and EM calorimeter using E/p for a\nclean subset of the inclusive electrons with ET > 10 GeV. This sample will be complementary to the\nsamples of low-mass electron pairs from J/\u03c8 and \u03d2 decays, discussed in [7]. A second example is the\ncerti\ufb01cation of the isolated electron identi\ufb01cation using a clean sample of W \u2192e\u03bd decays. Clearly,\nwith more statistics, the large samples of Z \u2192ee decays which will be collected will provide the\nopportunity to re\ufb01ne the understanding of the performance to an extremely high level of accuracy, as\ndiscussed in Section 5.\n2.1.4\nSystematic uncertainties on expected performance\nTo estimate possible systematic uncertainties related to the cut-based electron identi\ufb01cation, two shower\nshape variables have been studied as a function of the amount of material in front of the EM calorimeter.\nFigure 5 illustrates the impact of additional material, the effect of which has not been included in the\nEM cluster corrections which are applied as described in [3], for electrons from H \u2192eeee decays.\nThe results are shown in two |\u03b7|-ranges for the nominal material and for the case of additional material\naccounting in total to \u223c0.1 X0 and \u223c0.2 X0 (Fig. 5). It is evident that in regions with signi\ufb01cant\namounts of material the shower is broader (less energy in the core). These differences reduce the electron\nef\ufb01ciency; however, the true systematic error on the ef\ufb01ciency due to such effects will depend on how\nwell the inner-detector material can be measured using data.\nFigure 6 shows the fraction of energy in the strip layer outside the three core strips and inside the\nseven-strip window for the same |\u03b7|-ranges. The impact of the additional material is also clearly visible.\nThe estimated change in the electron ef\ufb01ciencies quoted in Table 5 is expected to be less than 2%. It is\nimportant to note that the material effects are more pronounced in the strip layer than in the middle layer\nof the calorimeter. Therefore, one should expect larger uncertainties from this source of systematics for\nthe medium electron cuts than for the loose electron cuts, which rely only on the middle layer of the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n79\n\n|\u03b7|\nET > 17 GeV\nET > 8 GeV\nEf\ufb01ciency (%)\nJet rejection\nEf\ufb01ciency (%)\nJet rejection\nZ \u2192ee\nb,c \u2192e\nSingle electrons\nb,c \u2192e\n(ET =10 GeV)\n0.00 \u22120.80\n88.2 \u00b1 0.1\n35 \u00b1 1\n3740 \u00b1 50\n79.3 \u00b1 0.2\n51 \u00b1 1\n1960 \u00b1 30\n0.80 \u22121.35\n83.5 \u00b1 0.1\n40 \u00b1 1\n1581 \u00b1 20\n70.6 \u00b1 0.2\n52 \u00b1 1\n914 \u00b1 11\n1.35 \u22121.50\n71.5 \u00b1 0.4\n41 \u00b1 2\n444 \u00b1 5\n49.6 \u00b1 0.5\n40 \u00b1 3\n342 \u00b1 5\n1.50 \u22121.80\n63.8 \u00b1 0.2\n18 \u00b1 1\n2440 \u00b1 40\n41.8 \u00b1 0.4\n24 \u00b1 2\n890 \u00b1 15\n1.80 \u22122.00\n62.5 \u00b1 0.2\n12 \u00b1 1\n9800 \u00b1 450\n55.1 \u00b1 0.4\n25 \u00b1 2\n4660 \u00b1 220\n2.00 \u22122.35\n65.8 \u00b1 0.2\n16 \u00b1 1\n8400 \u00b1 300\n55.0 \u00b1 0.3\n21 \u00b1 2\n6000 \u00b1 250\n2.35 \u22122.47\n67.8 \u00b1 0.3\n14 \u00b1 2\n4050 \u00b1 170\n62.5 \u00b1 0.6\n30 \u00b1 3\n3980 \u00b1 250\n0.00 \u22122.47\n77.3 \u00b1 0.06\n31 \u00b1 1\n2184 \u00b1 13\n64.8 \u00b1 0.1\n42 \u00b1 1\n1288 \u00b1 8\nTable 6: Expected ef\ufb01ciencies for isolated and non-isolated electrons and corresponding jet background\nrejections for the medium identi\ufb01cation cuts as a function of |\u03b7|. The results are shown for the simulated\n\ufb01ltered di-jet and minimum-bias samples, corresponding respectively to ET -thresholds of 17 GeV (left)\nand 8 GeV (right). The quoted errors are statistical.\n (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n per GeV\n-1\nEvents per 100 pb\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\nAll jets\nLoose\nMedium\nTight (isol)\nTight (TRT)\nATLAS\n (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n per GeV\n-1\nEvents per 100 pb\n5\n10\n6\n10\n7\n10\n8\n10\n9\n10\nAll jets\nLoose\nMedium\nTight (isol)\nTight (TRT)\nATLAS\nFigure 3: Differential cross-sections as a function of ET\nbefore identi\ufb01cation cuts and after loose,\nmedium, tight (TRT) and tight-isol cuts, for an integrated luminosity of 100 pb\u22121 and for the simulated\n\ufb01ltered di-jet sample with ET\nabove 17 GeV (left) and the simulated minimum-bias sample with ET\nabove 8 GeV (right).\ncalorimeter.\nAnother important source of systematics affects the jet rejections quoted in Table 5: this arises from\nthe exact pT -spectrum and mixture of quark and gluon jets, and to a certain extent from heavy \ufb02avour jets\npresent in the background under consideration. The numbers quoted in this note are related to the rather\nlow-pT di-jet background which is relevant for the search for early signals from single electrons. Other\nbackground samples relevant to certain physics studies have been shown to display worse rejections, by\nup to a factor of 3 to 5. This clearly indicates that the fake electron rates will only be better understood\nwith real data.\n2.1.5\nMultivariate techniques\nIn addition to the standard cut-based electron identi\ufb01cation described above, several multivariate tech-\nniques have been developed and implemented in the ATLAS software. These include a likelihood dis-\ncriminant, a discriminant called H-matrix, a boosted decision tree, and a neural network. Table 7 sum-\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n80\n\n (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n per GeV\n-1\nEvents per 100 pb\n3\n10\n4\n10\n5\n10\n6\n10\nJets \nW,Z->e\nb,c->e\nATLAS\n (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n per GeV\n-1\nEvents per 100 pb\n5\n10\n6\n10\n7\n10\nJets \nb,c->e\nATLAS\nFigure 4: Differential cross-sections as a function of ET\nafter tight (TRT) cuts, shown separately\nfor the expected components from isolated electrons, non-isolated electrons and residual jet back-\nground, for an integrated luminosity of 100 pb\u22121 and for the simulated \ufb01ltered di-jet sample with ET\nabove 17 GeV (left) and the simulated minimum-bias sample with ET above 8 GeV (right).\n\u03b7\nR\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\n< 1.25\n|\u03b7|\n1.12 < \n\u03b7\nR\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n0\n50\n100\n150\n200\n250\n300\n350\n400\nATLAS\n< 1.75\n|\u03b7|\n1.62 < \nFigure 5: Energy containment, R\u03b7 (Table 3), for 1.12 < |\u03b7| < 1.25 (left) and 1.62 < |\u03b7| < 1.75 (right).\nThe symbols correspond to the nominal description and the histogram to the one with additional material.\nmarises the gains in ef\ufb01ciency and rejection which may be expected with respect to the cut-based method\nby using the likelihood discriminant method. The gains appear to be arti\ufb01cially large in the case of the\nloose and medium cuts, because these cuts do not make use of all the information available in terms of\nelectron identi\ufb01cation, since they were designed for robustness and ease of use with initial data. Nev-\nertheless, they indicate how much the electron ef\ufb01ciency may be improved once all the discriminant\nvariables will be understood in the data.\nFigure 7 shows the rejection versus ef\ufb01ciency curve obtained using the likelihood discriminant\nmethod, compared to the results obtained for the two sets of tight cuts shown in Table 5. The likeli-\nhood discriminant method provides a gain in rejection of about 20-40% with respect to the cut-based\nmethod for the same ef\ufb01ciency of 61-64%. Alternatively, it provides a gain in ef\ufb01ciency of 5-10% (tight\nand medium cuts) for the same rejection. Multivariate methods of this type will of course only be used\nonce the detector performance has been understood using the simpler cut-based electron identi\ufb01cation\ncriteria.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n81\n\nside\nF\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n50\n100\n150\n200\n250\nATLAS\n< 1.25\n|\u03b7|\n1.12 < \nside\nF\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n20\n40\n60\n80\n100\n120\n140\n160\nATLAS\n< 1.75\n|\u03b7|\n1.62 < \nFigure 6: Energy fraction outside a three-strip core, Fside (Table 3), for 1.12 < |\u03b7| < 1.25 (left) and\n1.62 < |\u03b7| < 1.75 (right). The symbols correspond to the nominal description and the histogram to the\none with additional material.\nCuts\nCut-based method\nLikelihood method\nEf\ufb01ciency \u03b5e (%)\nRejection R j\nEf\ufb01ciency (%) at \ufb01xed R j\nRejection at \ufb01xed \u03b5e\nLoose\n87.97\u00b10.05\n567\u00b11\n89.11\u00b10.05\n2767\u00b117\nMedium\n77.29\u00b10.06\n2184\u00b17\n88.26\u00b10.05\n(3.77\u00b10.08)\u00d7104\nTight (isol)\n64.22\u00b10.07\n(9.9\u00b10.2)\u00d7104\n67.53\u00b10.06\n(1.26\u00b10.05)\u00d7105\nTight (TRT)\n61.66\u00b10.07\n(8.9\u00b10.2)\u00d7104\n68.71\u00b10.06\n(1.46\u00b10.06)\u00d7105\nTable 7: For the loose, medium and tight electron identi\ufb01cation cuts, expected electron ef\ufb01ciencies for\na \ufb01xed jet rejection and jet rejections for a \ufb01xed electron ef\ufb01ciency, as obtained from the likelihood\ndiscriminant method. The quoted errors are statistical.\n2.2\nIsolation studies\nMany physics analyses in ATLAS will be based on \ufb01nal states with isolated leptons from decays of W- or\nZ-bosons. These channels usually have the advantage of small background expectation from processes\nwith similar signature, compared to channels with hadronic \ufb01nal states. Nevertheless, they may also\nsuffer from jet background processes, namely if leptons from semi-leptonic heavy-quark decays mimic\nthe isolated leptons of the signal. Therefore, dedicated tools beyond the lepton identi\ufb01cation algorithms\nare needed in order to suppress such sources of background by factors of up to the order of 103. In\nthis section, the performance of a projective likelihood estimator for the separation of isolated electrons\nfrom non-isolated electron backgrounds is described. The four variables chosen as input to this isolation\nlikelihood are:\n- transverse energy deposited in a small cone of \u2206R < 0.2 around the electron cluster;\n- transverse energy deposited in a hollow cone of 0.2 < \u2206R < 0.4 around the electron cluster;\n- sum of the squares of the transverse momenta of all additional tracks measured in a cone of \u2206R <\n0.4 around the electron cluster;\n- impact parameter signi\ufb01cance of the electron track (with respect to the primary vertex in the trans-\nverse plane).\nElectrons from Z \u2192ee decays were used as a clean source of isolated electrons. The reconstructed\nelectrons from this sample were required to be matched to a Monte Carlo electron from Z-boson decay\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n82\n\nElectron efficiency (%)\n60\n65\n70\n75\n80\n85\n90\nRejection\n3\n10\n4\n10\n5\n10\n > 17 GeV\nT\nE\nLikelihood\nTight (TRT) cuts\nTight (isol.) cuts\nATLAS\nFigure 7: Jet rejection versus isolated electron ef\ufb01ciency obtained with a likelihood method (full circles)\ncompared to the results from the two sets of tight cuts (open triangle and open square).\nsignal efficiency\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0 8\n0.9\n1\nsignal efficiency\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0 8\n0.9\n1\nbackground rejection\n1\n10\n2\n10\n3\n10\n4\n10\n ee / electron medium\n\u2192\nZ \n| < 1.37\n\u03b7\n < 43GeV; 0 < |\nT\n27GeV < p\n| < 2.47\n\u03b7\n < 19GeV; 1.52 < |\nT\n15GeV < p\nATLAS\nsignal efficiency\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\nsignal efficiency\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\nbackground rejection\n1\n10\n2\n10\n3\n10\n4\n10\n / electron medium\ntt\n| < 1.37\n\u03b7\n < 43GeV; 0 < |\nT\n27GeV < p\n| < 2.47\n\u03b7\n < 19GeV; 1.52 < |\nT\n15GeV < p\nATLAS\nFigure 8: Background electron rejections versus signal ef\ufb01ciencies for electrons in Z \u2192ee decays (left)\nand in t\u00aft decays (right), for two illustrative bins in |\u03b7| and pT .\nand to pass the medium identi\ufb01cation cuts in order to be considered as signal electrons. Background\nelectrons were selected from a high-statistics t\u00aft sample, \ufb01ltered for a pair of like-sign Monte Carlo\nelectrons, and matched to a Monte Carlo electron from b/c-decay.\nThe results of the performance studies of the isolation likelihood are shown in Fig. 8 for two illus-\ntrative bins in |\u03b7| and pT . The best results are achieved for high-pT electrons measured in the barrel\nregion of the EM calorimeter. As can be seen in Fig. 8 left, for electrons with only little hadronic activity\nin the \ufb01nal state, such as those from Z \u2192ee and H \u2192eeee decays, the isolation likelihood provides a\nbackground rejection of the order of 103, for signal electron ef\ufb01ciencies of 80% (barrel) and 50% (end-\ncaps). The difference observed between barrel and end-caps is mostly due to the \u03b7-dependence of the\nmedium identi\ufb01cation cuts shown in Table 6. For comparison, the ef\ufb01ciency for the selection of signal\nelectrons in t\u00aft events is shown in Fig. 8 right: due to the additional hadronic activity in these \ufb01nal states,\nthe ef\ufb01ciency decreases by 5\u201310% for the same background rejection, when compared to that quoted for\nZ \u2192ee decays.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n83\n\nCELLMAXFRAC\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nCELLMAXFRAC\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\nLATERAL\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n1\n2\n3\n4\n5\n6\nLATERAL\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n1\n2\n3\n4\n5\n6\nATLAS\nFigure 9: Example of discriminating variables used in the forward region for signal electrons (full circles)\nand the QCD di-jet background (open circles). Shown in the case of the FCal are the fraction of the total\ncluster energy deposited in the cell with maximum energy (left) and the relative lateral moment (right).\n3\nElectron identi\ufb01cation outside the inner detector acceptance\nElectron identi\ufb01cation in the forward region (|\u03b7| > 2.5) will be important in many physics analyses, in-\ncluding electroweak measurements and searches for new phenomena. In contrast to the central electrons,\nforward electron reconstruction can only use information from the calorimeters, since the inner detector\ncovers only |\u03b7| < 2.5. Such electrons can therefore only be identi\ufb01ed cleanly above the background in\nspeci\ufb01c topologies, such as Z \u2192ee or H \u2192eeee decays.\nThis section describes the performance of a cut-based method used to identify electrons in the for-\nward region and separate them from the QCD background. The comparison of the performance obtained\nwith a likelihood method is also presented.\nSignal electrons are selected from Z \u2192ee decays and background electrons from a high-statistics\nsample of QCD di-jet events. Three |\u03b7|-regions are considered: the \ufb01rst one covers the inner wheel of the\nelectromagnetic end-cap, i.e. 2.5 < |\u03b7| < 3.2 (the HEC is not used), the second one covers the overlap\nregion between the electromagnetic end-cap and the forward calorimeter (FCal), i.e. 3.2 < |\u03b7| < 3.4, and\nthe last region covers the FCal acceptance, i.e. 3.4 < |\u03b7| < 4.9. A topological clustering algorithm [13]\nis used in this analysis and only clusters with ET > 20 GeV are considered. Two examples of the\ndiscriminating variables used in these studies are shown in Fig. 9, namely the fraction of the total cluster\nenergy deposited in the cell with maximum energy and the relative lateral moment. The relative lateral\nmoment is de\ufb01ned as lat2/(lat2 +latmax), where the lateral moments lat2 and latmax differ in the treatment\nof the two most energetic cells. Other examples include the \ufb01rst moment of the energy density, the\nrelative longitudinal moment, de\ufb01ned in the same way as the relative lateral moment only with two\nlongitudinal moments, the second moments of the distances of each cell to the shower barycentre and to\nthe shower axis, and the distance of the cluster barycentre from the front face of the calorimeter.\nThe likelihood discriminant uses the same variables as the cut-based method. Figure 10 shows the\nperformance of the cut-based and likelihood discriminant methods for electrons from Z \u2192ee decay\nwith ET > 20 GeV. For an electron identi\ufb01cation ef\ufb01ciency of 80%, both methods achieve the required\ngoal of \u223c1% fake rate from the QCD background. This performance is expected to yield, for example,\na clean Z \u2192ee sample with one electron already selected in the central region and one electron in the\nforward region [14]: the expected background contribution under the Z-boson peak is estimated to be\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n84\n\nSignal efficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nBackground rejection\n10\n2\n10\n3\n10\nLikelihood\nCut-based\n| < 3.2\n\u03b7\n2.5 < |\nSignal efficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nBackground rejection\n10\n2\n10\n3\n10\nLikelihood\nCut-based\n| < 4.9\n\u03b7\n3.4 < |\nFigure 10: Expected rejection against QCD jets versus ef\ufb01ciency for signal electrons from Z \u2192ee decay,\nfor the cut-based and likelihood discriminant methods in the inner wheel of the electromagnetic end-\ncap (left) and in the FCal (right). The rejection power of the likelihood method is expected to increase\nwhen additional variables beyond the minimal set shown here are added.\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\nElectron-ID efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nTight\nMedium\nLoose\nATLAS\nET (GeV)\n10\n20\n30\n40\n50\n60\nElectron-ID efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\nTight\nMedium\nLoose\nATLAS\nFigure 11: Electron identi\ufb01cation ef\ufb01ciency as a function of \u03b7 (left) and ET (right) for electrons with\nET > 5 GeV from H \u2192eeee decays.\nbelow \u223c1%.\n4\nElectrons as probes for physics within and beyond the Standard Model\n4.1\nElectrons in Higgs-boson decays\nElectrons from the H \u2192eeee decay with mH < 2mZ are an important benchmark for the evaluation of the\nperformance of the electron reconstruction and identi\ufb01cation [15]. Here, only electrons with |\u03b7| < 2.5\nand ET > 5 GeV are considered. The electron ef\ufb01ciency as a function of |\u03b7| and ET for loose, medium,\nand tight electron cuts is shown in Fig. 11. The drop in ef\ufb01ciency at low ET is mainly due to the loss of\ndiscrimination power of the shower-shape cuts at lower transverse energies. A loss of ef\ufb01ciency is also\nvisible in the transition region between the barrel and end-cap calorimeters. The results shown here are in\nquantitative agreement with those obtained for electrons from Z \u2192ee decay discussed in Section 2.1.2.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n85\n\n (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTight cuts (physics events)\nMedium\nLoose\nTight cuts (single electrons)\nMedium\nLoose\nATLAS\n\u03b7\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTight cuts\nMedium\nLoose\nATLAS\nFigure 12: Electron identi\ufb01cation ef\ufb01ciency as a function of ET\n(left) and |\u03b7| (right). The full sym-\nbols correspond to electrons in SUSY events and the open ones to single electrons of \ufb01xed ET . The\nef\ufb01ciencies as a function of |\u03b7| are shown only for electrons with ET > 17 GeV.\n4.2\nElectrons produced in decays of supersymmetric particles\nIn many supersymmetry (SUSY) scenarios, the most abundantly produced sparticles are squarks (directly\nor from a gluino decay), which generally decay into a chargino or neutralino and jets. In turn, charginos\nand neutralinos are very likely to decay into leptons. One interesting mode for SUSY searches is the\ntri-lepton signal, in which three isolated leptons are expected in the \ufb01nal state. Such SUSY events would\nfeature high-pT isolated leptons accompanied by a high multiplicity of high-ET jets. Hence, it is crucial\nto ef\ufb01ciently identify electrons in such an environment, while preserving the very high jet rejection\npresented in Section 2. The electron identi\ufb01cation ef\ufb01ciency in SUSY events is calculated using the\nSU3 ATLAS point [16]. In this scenario, a large number of charginos and neutralinos are produced and\nnumerous leptons are expected in the \ufb01nal state.\n R\n\u2206\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTight cuts\nMedium\nLoose\nATLAS\nFigure 13: Electron identi\ufb01cation ef\ufb01ciency as a function of the distance \u2206R to the closest jet in SUSY\nevents, for electrons with ET > 17 GeV.\nFigure 12 shows the identi\ufb01cation ef\ufb01ciency of the loose, medium and tight (isol) cuts as a function\nof ET and |\u03b7|. The ef\ufb01ciencies shown as a function of ET are compared with ef\ufb01ciencies for single\nelectrons of ET = 10, 25, 40, 60 and 120 GeV. As expected, single electrons display higher ef\ufb01ciencies\nthan those in SUSY events, because of the large hadronic activity in these events. The ef\ufb01ciencies\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n86\n\n (GeV)\nT\nE\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nLoose\nMedium\nATLAS\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nLoose\nMedium\nATLAS\nFigure 14: Electron identi\ufb01cation ef\ufb01ciency as a function of ET (left) and |\u03b7| (right), for electrons from\nZ\u2032 \u2192e+e\u2212decays with mZ\u2032 = 1 TeV.\nobtained for values of ET\nbelow 20 GeV, are signi\ufb01cantly below the plateau values at high ET , for\nwhich the cuts were initially optimised.\nThe ef\ufb01ciencies as a function of |\u03b7| show the same features as those discussed in Table 6, namely\nthe ef\ufb01ciency in the end-cap region is lower than in the barrel, whereas the jet rejection is signi\ufb01cantly\nhigher. Speci\ufb01c drops in ef\ufb01ciency can be seen for |\u03b7| \u223c1.35, which corresponds to the barrel/end-cap\ntransition region, and for |\u03b7| \u22480.8, which corresponds to the change in the lead thickness between the\ntwo types of electrodes in the barrel EM calorimeter.\nFigure 13 shows the electron identi\ufb01cation ef\ufb01ciency as a function of the distance \u2206R to the closest\njet in SUSY events. Jets are reconstructed from topological clusters using a \u2206R = 0.4 cone algorithm.\nFor values of \u2206R > 0.4, the ef\ufb01ciencies are compatible with those expected for single electrons, whereas\nfor values of \u2206R < 0.4, the ef\ufb01ciencies decrease because of the overlap between the hadronic showers\nfrom the jet and the electron shower itself.\nJet ET -range\n140\u2212280 GeV\n280\u2212560 GeV\n560\u22121120 GeV\nEf\ufb01ciency\nRejection\nEf\ufb01ciency\nRejection\nEf\ufb01ciency\nRejection\nLoose cuts\n86.6\u00b10.2%\n825\u00b135\n89.6\u00b10.1%\n620\u00b125\n91.5\u00b10.4%\n550\u00b120\nMedium cuts\n80.6\u00b10.2%\n4000\u00b1370\n84.6\u00b10.1%\n2300\u00b1170\n86.7\u00b10.5%\n1900\u00b1120\nTable 8: Electron identi\ufb01cation ef\ufb01ciencies and QCD di-jet background rejections obtained for loose and\nmedium identi\ufb01cation cuts, including a calorimeter isolation cut (see text), and for three different jet ET\n-ranges. The signal electrons are from Z\n\u2032 \u2192e+e\u2212decays with mZ\u2032 = 1 TeV and are required to have ET\n> 100 GeV.\n4.3\nElectrons in exotic events\nHigh-mass di-electron \ufb01nal states are a promising source of early discovery physics, because of the sim-\nplicity and robustness of very high-pT electron reconstruction, identi\ufb01cation and resolution. Very high-\npT electrons refer here to those with transverse momentum ranging from 100 GeV up to several TeV.\nThe backgrounds to very high-pT electron pairs are expected to be small, and, therefore, only loose or\nmedium identi\ufb01cation cuts are considered here. Isolated electrons are required to satisfy the calorimeter\nisolation cut described in Section 2.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n87\n\nFigure 14 shows ef\ufb01ciencies as a function of ET\nand |\u03b7| for the loose and medium identi\ufb01cation\ncuts, for electrons from Z\u2032 \u2192e+e\u2212decays with mZ\u2032 = 1 TeV [17]. From these curves, one can note\nthe slow increase in ef\ufb01ciency with ET before reaching a plateau in the very high-ET region. Overall\nef\ufb01ciencies of \u223c90% and of \u223c85% can be achieved for loose and medium electron cuts, respectively,\nwith a uniform behaviour limited to the barrel region, i.e. |\u03b7| < 1.5.\nThe QCD background rejection was studied as a function of the jet transverse energy, as shown\nin Table 8. Using the medium identi\ufb01cation cuts, which correspond to an overall ef\ufb01ciency of \u223c85%, a\njet rejection factor of several thousand can be achieved for ET > 100 GeV, which should be suf\ufb01cient\nto observe the signal in many exotic scenarios.\n5\nElectrons from Z \u2192ee decays in early data\nThe experimental uncertainty on the electron identi\ufb01cation ef\ufb01ciency is expected to be the source of one\nof the main systematic errors in many measurements, and in particular in cross-section determinations. In\naddition, a reliable monitoring of the electron identi\ufb01cation ef\ufb01ciency is important in the commissioning\nphase of the detector and software. The previous sections have shown detailed estimates of the expected\nelectron identi\ufb01cation ef\ufb01ciency based on simulated samples. This section focuses on the measurement\nof electron reconstruction and identi\ufb01cation ef\ufb01ciencies using a data-driven approach based on Z \u2192ee\nevents.\nThe tag-and-probe method [18] is used in this analysis. It consists of tagging a clean sample of events\nusing one electron, and then measuring the ef\ufb01ciency of interest using the second electron from the Z-\nboson decay. Although more dif\ufb01cult because of trigger-threshold issues and of more severe background\nconditions, the same approach could be applied to J/\u03c8 and \u03d2 resonances, thus covering the lower end of\nthe pT spectrum [7].\n5.1\nTag-and-probe method\nThe tag condition typically requires an electron identi\ufb01ed with tight cuts. Both electrons are also required\nto be above a pT threshold consistent with the trigger used. The invariant mass of the lepton pair is then\nused to identify the number of tagged events, N1 (containing Z \u2192ee decays), and a sub-sample N2,\nwhere the second pre-selected electron further passes a given set of identi\ufb01cation cuts. The ef\ufb01ciency for\na given signature is given by the ratio between N2 and N1.\nTo account for background, the lepton-pair invariant mass spectrum is \ufb01tted around the Z mass peak\nusing a Gaussian distribution convoluted with a Breit-Wigner plus an exponential function. The dominant\nbackground arises from QCD and is estimated using a procedure explained in [18]; its contribution is\nsmall in general and its impact on the measurement is therefore very limited.\nThe probe electron is checked against the selection as an electron candidate (to which only the pre-\nselection cuts are applied), and as a loose, medium or tight electron. To monitor in detail the ef\ufb01ciency\ndependence, the results are presented in bins of \u03b7 and pT , at the expense of an increased statistical error\nin each bin.\nA quantitative comparison between the ef\ufb01ciency computed with this tag-and-probe method (\u03b5TP)\nand the ef\ufb01ciency obtained from the Monte Carlo truth (\u03b5MC) is used to validate the tag-and-probe\nmethod.\n5.2\nElectron reconstruction ef\ufb01ciency\nThe reconstruction and identi\ufb01cation of electrons is based on seed-clusters in the electromagnetic calorime-\nter matched to tracks, as explained in Section 2. The tag electron is a reconstructed electron selected using\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n88\n\nFigure 15: Ef\ufb01ciency of the electron pre-selection as a function of |\u03b7| (left) and ET (right) for Z \u2192ee\ndecays, using the tag-and-probe method and the Monte Carlo truth information.\ntight (isol) cuts and also required to pass the trigger EM13i/e15i [11]. The tag electron is also required to\nbe outside the barrel/end-cap transition region (1.37 < |\u03b7| < 1.52). The probe electron is pre-selected\nby identifying a cluster in the opposite hemisphere, such that the azimuthal difference between tag and\nprobe electrons is \u2206\u03c6 > 3/4\u03c0. Both tag and probe electrons are required to have ET >15 GeV. The\ninvariant mass of the lepton pair is required to be between 80 and 100 GeV. Figure 15 compares \u03b5TP\nand \u03b5MC as a function of |\u03b7| and ET . Table 9 summarises the results obtained for this \ufb01rst step in the\nreconstruction and identi\ufb01cation of the probe electron.\nET\u2212range (GeV)\n15\u221225\n25\u221240\n40\u221270\n|\u03b7|\u2212range\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n0\u22120.80\n96.1\u00b10.4\n2.0\u00b10.4\n96.2\u00b10.2\n0.1\u00b10.2\n99.0\u00b10.1\n2.0\u00b10.1\n0.80\u22121.37\n94.9\u00b10.6\n1.5\u00b10.6\n96.0\u00b10.2\n1.6\u00b10.2\n95.1\u00b10.2\n-0.5\u00b10.2\n1.52\u22121.80\n89.0\u00b11.2\n3.6\u00b11.2\n88.8\u00b10.6\n1.3\u00b10.6\n91.9\u00b10.6\n1.7\u00b10.6\n1.80\u22122.40\n83.0\u00b11.0\n0.6\u00b11.0\n83.2\u00b10.6\n0.8\u00b10.6\n84.9\u00b10.6\n1.1\u00b10.6\nTable 9: Ef\ufb01ciency of the electron pre-selection, \u03b5TP, in percent as obtained from the tag-and-probe\nmethod, for different ranges of electron ET and |\u03b7|. The errors quoted for \u03b5TP are statistical and cor-\nrespond to an integrated luminosity of 100 pb\u22121 . Also shown is the difference, \u2206\u03b5TP/MC, between this\nestimate of the pre-selection ef\ufb01ciency and that obtained using the matching to the Monte Carlo electron.\n5.3\nElectron identi\ufb01cation ef\ufb01ciency.\nIn this section, the electron identi\ufb01cation ef\ufb01ciency is presented with respect to the reconstructed elec-\ntrons discussed in Section 5.2. The QCD background was not considered here, since it is less than a\nfew percent below the Z-boson mass peak. The reconstructed probe electron was checked against loose,\nmedium and tight selection cuts. Table 10 summarises the results obtained for this second step in the\nreconstruction and identi\ufb01cation of the probe electron. Figure 16 shows as a function of \u03b7 and pT the\ncomparison between \u03b5TP and \u03b5MC, for the medium cuts. The losses at high \u03b7 are due to the material in\nthe inner detector, as discussed in Section 2.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n89\n\n|\n\u03b7|\n0\n0.2 0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\n2.2 2.4\nEfficiency\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nMedium cuts\nTag-and-probe\nMonte Carlo truth\nATLAS\n (GeV)\nT\nE\n20\n30\n40\n50\n60\n70\n80\n90\n100\nEfficiency\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nMedium cuts\nTag-and-probe\nMonte Carlo truth\nATLAS\nFigure 16: Ef\ufb01ciency of the medium electron identi\ufb01cation cuts relative to the pre-selection cuts as a\nfunction of |\u03b7| (left) and ET (right) for Z \u2192ee decays, using the tag-and-probe method and the Monte\nCarlo truth information.\n5.4\nStatistical and systematic uncertainties\nA number of uncertainties may affect these tag-and-probe measurements once the accumulated data will\nprovide high enough statistics to perform similar measurements to those quoted above:\n\u2022 Differences between \u03b5TP and \u03b5MC\nThe relative difference \u2206\u03b5TP/MC in regions (in pT\nand |\u03b7|), where the ef\ufb01ciency is \ufb02at, is less\nthan 0.5%, assuming that the statistical error on \u03b5MC is negligible. \u2206\u03b5TP/MC marginally depends\non the de\ufb01nition of a true electron and the systematic uncertainty related to this is estimated to\nbe < 0.1%, when varying the cut on the separation in \u03b7/\u03c6 space (\u2206R) between the reconstructed\nelectron candidate and the true electron.\n\u2022 Statistical uncertainty.\nThe size of the available Z-boson sample is a source of systematic error. With an integrated lumi-\nnosity of 100 pb\u22121 , the error is expected to be in the range 1-2% for pT > 25 GeV, and \u223c4% in\nthe low-pT bin.\n\u2022 Selection criteria\nAnother source of systematic error comes from varying the selection criteria. For instance, un-\ncertainties introduced by varying the cut on the Z-boson mass or requiring an isolation criterion\nfor the probe electron were evaluated. The magnitude of the uncertainty introduced is smaller\nthan 0.5% for pT > 40 GeV. At low pT , this uncertainty is estimated to be in the 1-2% range.\n\u2022 QCD background contribution\nAdding the expected contribution from the QCD background to the signal does not degrade the\nresults, except for 1.52 < |\u03b7| < 1.8, a region which is close to the barrel/end-cap transition re-\ngion and also where the ef\ufb01ciency is not uniform. The contribution from the uncertainties on the\nresidual QCD background is expected to be negligible.\n6\nConclusion\nExcellent electron identi\ufb01cation will clearly play an important role at the LHC, since high-pT leptons\nwill be powerful probes for physics within and beyond the Standard Model. Based on this motivation,\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n90\n\nLoose\n15\u221225\n25\u221240\n40\u221270\n|\u03b7|\\pT\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n0\u22120.8\n95.2\u00b12.0\n\u22124.1\u00b12.0\n98.8\u00b10.3\n\u22120.5\u00b10.3\n99.8\u00b10.1\n0.2\u00b10.1\n0.8\u22121.37\n92.3\u00b12.1\n\u22126.9\u00b12.1\n98.9\u00b10.3\n\u22120.7\u00b10.3\n99.6\u00b10.2\n0.0\u00b10.2\n1.52\u22121.8\n100.0\u00b12.8\n1.7\u00b12.8\n99.4\u00b10.5\n0.0\u00b10.5\n99.6\u00b10.5\n0.0\u00b10.5\n1.8\u22122.4\n98.8\u00b11.6\n0.6\u00b11.7\n98.8\u00b10.5\n0.0\u00b10.5\n99.1\u00b10.4\n\u22120.2\u00b10.4\nMedium\n15\u221225\n25\u221240\n40\u221270\n|\u03b7|\\pT\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n0\u22120.8\n83.6\u00b12.3\n\u22124.3\u00b12.7\n89.7\u00b10.7\n\u22120.8\u00b10.8\n92.6\u00b10.5\n\u22120.2\u00b10.6\n0.8\u22121.37\n75.6\u00b12.8\n\u22127.5\u00b13.4\n87.6\u00b10.9\n0.7\u00b11.0\n90.9\u00b10.8\n\u22120.4\u00b10.8\n1.52\u22121.8\n71.9\u00b14.4\n5.9\u00b16.5\n76.9\u00b11.9\n\u22122.2\u00b12.4\n83.6\u00b11.9\n0.7\u00b12.3\n1.8\u22122.4\n78.0\u00b12.7\n6.5\u00b13.7\n79.2\u00b11.4\n1.7\u00b11.8\n82.5\u00b11.4\n\u22121.0\u00b11.6\nTight\n15\u221225\n25\u221240\n40\u221270\n|\u03b7|\\pT\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n\u03b5TP\n\u2206\u03b5TP/MC\n0\u22120.8\n68.7\u00b12.6\n\u22125.2\u00b13.5\n73.8\u00b11.0\n\u22121.2\u00b11.3\n77.0\u00b10.9\n\u22121.5\u00b11.1\n0.8\u22121.4\n61.8\u00b13.0\n\u22123.1\u00b14.7\n72.9\u00b11.2\n0.7\u00b11.7\n77.3\u00b11.1\n0.2\u00b11.5\n1.5\u22121.8\n55.7\u00b14.5\n6.8\u00b18.6\n65.9\u00b12.1\n\u22120.8\u00b13.1\n73.7\u00b12.2\n1.2\u00b13.1\n1.8\u22122.4\n66.2\u00b13.0\n8.5\u00b14.9\n66.0\u00b11.6\n2.6\u00b12.5\n73.4\u00b11.6\n0.7\u00b12.2\nTable 10: Loose, medium and tight electron identi\ufb01cation ef\ufb01ciencies relative to the pre-selection ef\ufb01-\nciencies for different bins in ET and |\u03b7|. The \ufb01rst error is statistical and corresponds to an integrated\nluminosity of 100 pb\u22121 . The second error is the difference obtained between \u03b5TP and \u03b5MC.\nvarious algorithms and tools have been developed to ef\ufb01ciently reconstruct and identify electrons and\nseparate them from the huge backgrounds from hadronic jets.\nPresently, two reconstruction algorithms have been implemented in the ATLAS of\ufb02ine software, both\nintegrated into one single package and a common event model. The \ufb01rst one relies on calorimeter seeds\nfor reconstructing electrons, whereas the second algorithm relies on track-based seeds, is optimised for\nelectrons with lower energies, and relies less on isolation.\nThe calorimeter based algorithm starts from the reconstructed cluster in the electromagnetic calorime-\nter, then builds identi\ufb01cation variables based on information from the calorimeter and the inner detector.\nThe rejection power with respect to QCD jets comes almost entirely from the identi\ufb01cation procedure.\nDepending on the electron transverse energy and the analysis requirements, rejection factors of 500 to\n100 000 can be achieved, for ef\ufb01ciencies of 88% to 64%, using a simple cut-based selection. More re-\n\ufb01ned identi\ufb01cation procedures combining calorimeter and track quantities using multivariate techniques\nprovide a gain in rejection of about 20 \u221240% with respect to the cut-based method, for the same ef\ufb01-\nciency of 61\u221264%. Alternatively, they provide a gain of 5\u221210% in ef\ufb01ciency, for the same jet rejection\n(tight and medium cuts).\nElectrons in the forward region can also be identi\ufb01ed and separated from the background. A simple\ncut-based method, exploring the energy depositions in the inner wheel of the electromagnetic end-cap\ncalorimeter and in the forward calorimeter as well as the shower-shape distributions, shows that \u223c99%\nof the QCD background can be rejected, for an electron identi\ufb01cation ef\ufb01ciency of \u223c80%. This per-\nformance should be suf\ufb01cient to select cleanly, for example, Z \u2192ee decays with one electron in the\nforward region.\nStudies of the strategies for measuring ef\ufb01ciencies and fake rates in early data show that the tag-and-\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n91\n\nprobe method is a good tool to estimate the electron identi\ufb01cation ef\ufb01ciency and to control the reliability\nof the Monte Carlo simulation. With 100 pb\u22121 , the method is limited by the statistics of the Z sample,\nwhereas its systematic uncertainty is of the order of 1 to 2 %.\nThe work presented here primarily addresses the description and performance of the of\ufb02ine recon-\nstruction and identi\ufb01cation of electrons. However, it also gives an overview of the possible path towards\nphysics discoveries with electrons in Higgs, SUSY, and exotic scenarios.\nReferences\n[1] ATLAS Collaboration, Detector and Physics Technical Design Report, Vol.1, CERN/LHCC/99-14\n(1999).\n[2] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\n2008 JINST 3 S08003 (2008).\n[3] ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this vol-\nume.\n[4] ATLAS Electromagnetic Liquid Argon Calorimeter Group, B. Aubert et al., Nucl. Inst. Meth. A500\n(2003) 202-231.\n[5] ATLAS Electromagnetic Liquid Argon Calorimeter Group, B. Aubert et al., Nucl. Inst. Meth. A500\n(2003) 178-201.\n[6] ATLAS Electromagnetic Barrel Calorimeter, M. Aharrouche et al., Nucl. Inst. Meth. A568 (2006)\n601-623.\n[7] ATLAS Collaboration, Reconstruction of Low-Mass Electron Pairs, this volume.\n[8] K. De, ATLAS Computing System Commissioning-Simulation Experience, and R. Jones, Summary\nof Distributed data analysis and information management, Proceedings of the 16th International\nConference on Computing and In High Energy and Nuclear Physics (2007).\n[9] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-\n41(1996).\n[10] T. Sjostrand, S. Mrenna and P. Skands, FERMILAB-PUB-06-052-CD, JHEP 0605:026 (2006).\n[11] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[12] GEANT4 Collaboration, Geant4 - A simulation toolkit, Nuclear Instruments and Methods in\nPhysics Research Section A 506 (2003) 250-303.\n[13] W. Lampl et al., Calorimeter Clustering Algorithms: Description and Performance, ATLAS-\nLARG-PUB-2008-002 (2008).\n[14] ATLAS Collaboration, Forward-Backward Asymmetry in pp \u2192Z/\u03b3 \u22c6\u2192e+e\u2212Events, this volume.\n[15] ATLAS Collaboration, Search for the Standard Model H \u2192ZZ\u2217\u21924l, this volume.\n[16] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n92\n\n[17] ATLAS Collaboration, Dilepton Resonances at High Mass, this volume.\n[18] CDF Collaboration, First measurements of inclusive W and Z cross sections from Run II of the\nFermilab Tevatron Collider, Phys. Rev. Lett. 94, 091803 (2005);\nD0 Collaboration, Measurement of the shape of the boson rapidity distribution for p \u00afp \u2192Z/\u03b3 \u22c6\u2192\ne+e\u2212+X events produced at \u221as of 1.96 TeV, hep-ex/0702025 (2007).\n[19] ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF ELECTRONS\n93\n\nReconstruction and Identi\ufb01cation of Photons\nAbstract\nThis note presents the description and performance of photon identi\ufb01cation\nmethods in ATLAS. The reconstruction of an electromagnetic object begins\nin the calorimeter, and the inner detector information determines whether the\nobject is a photon - either converted or unconverted - or an electron. Three pho-\nton identi\ufb01cation methods are presented: a simple cut-based method, a Log-\nlikelihood-ratio-based method and a covariance-matrix-based method. The\nshower shape variables based on calorimeter information and track informa-\ntion used in all three methods are described. The ef\ufb01ciencies for single pho-\ntons and for photons from the benchmark H \u2192\u03b3\u03b3 signal events, as well as the\nrejection of the background from jet samples, are presented. The performance\nof the cut-based method on high-pT photons from a graviton decay process\nG \u2192\u03b3\u03b3 is also discussed.\n1\nIntroduction\nIsolated photons with large transverse momentum, pT, in the \ufb01nal state are distinguishing signatures for\nmany physics analyses envisaged at the LHC. The Higgs particle has been sought over several decades\nin many high-energy experiments, including those currently running at the Tevatron. It is understood\nthat if the Standard Model Higgs particle exists, and unitarity is not violated, its mass is within the reach\nof LHC. As described in detail in other parts of this work [1], while the expected cross-section times\nbranching ratio of the Higgs particle decaying into the two photon \ufb01nal state is relatively small, given its\ndistinct signature, isolated high-pT photons may play a signi\ufb01cant role in discovering the Higgs particle\nin the low mass region. In addition, very high-pT photons are also signatures of more exotic particles,\nsuch as the graviton predicted in Ref. [2], which is expected to have mass larger than 500 GeV. These\nphotons appear as a single, isolated objects with most of their energy deposit in the electromagnetic\ncompartment of the calorimeter. Thus the primary source for background to these photons, namely fake\nphotons, result from jets that \ufb02uctuate highly electromagnetic which contain a high fraction of photons\nfrom neutral hadron decays, such as \u03c00 \u2192\u03b3\u03b3.\nSince the ATLAS electromagnetic calorimeter [3] is highly segmented with a three-fold granularity\nin depth and with an \u03b7 \u00d7\u03c6 granularity in the barrel of 0.003\u00d70.1, 0.025\u00d70.025, and 0.05\u00d70.025, re-\nspectively, in the front, middle and rear compartments assisted by a pre-sampler in front of the calorime-\nter, photon identi\ufb01cation methods in ATLAS should be much more powerful that those used in past\nexperiments. The experiment also employs elaborate trigger systems that select electrons and photons\nef\ufb01ciently, as described in detail in Ref. [4].\nThis paper presents three ATLAS photon identi\ufb01cation methods and their performance for single,\nisolated photons as well as for photons from physics processes.\n2\nData samples\nThe H \u2192\u03b3\u03b3 (mH = 120 GeV) process is used as the primary signal benchmark sample for medium pT\nphotons and with the pile-up that corresponds to the instantaneous luminosity 1033 cm\u22122s\u22121. Rejection\nstudies were conducted using a pre-\ufb01ltered jet sample (described in details in Ref. [5]), containing all\nrelevant hard-scattering QCD processes with pT > 15 GeV. A \ufb01lter is applied at the generator level,\nrequiring the summed transverse energy of all stable particles (excluding muons and neutrinos) in a\nregion of \u2206\u03c6 \u00d7 \u2206\u03b7 = 0.12\u00d70.12 to be above 17 GeV. A total number of 3 million events were used\n94\n\nin rejection studies. Two additional samples with 150 GeV < pT < 280 GeV (Jet5) and 280 < pT <\n400 GeV (Jet6) were also employed for high-pT photon rejection studies. Finally, an additional 300,000\nevent \u03b3+jet sample has been used for rejection and fake rate studies.\nIn addition to these signal and background samples, the three identi\ufb01cation methods described in\nthis paper were developed using single photon samples - events with no activity except the photon -\nwith full detector simulation in the energy range 10 \u22121000 GeV with \ufb02at pseudorapidity distributions\nover |\u03b7| < 2.5. For high-pT photons, graviton samples with masses of 0.5 and 1.0 TeV were employed.\nAll the samples used in this note were generated using PYTHIA and its fragmentation scheme and\nwere passed through the full detector simulation. Some of the simulations were done with the nominal\ngeometry and material distribution (\u201cideal\u201d) and others with additional material added (\u201cdistorted\u201d).\nIn order to maintain the consistency between different studies, the following requirements and de\ufb01-\nnitions are used for ef\ufb01ciencies and rejections.\n\u2022 Truth match: the reconstructed photons must lie within a cone of radius \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 < 0.2\nof the true photons in the simulation.\n\u2022 The reconstructed photons must be within the \ufb01ducial volume, pseudorapidity 0 < |\u03b7| < 1.37 or\n1.52 < |\u03b7| < 2.47 to avoid the overlap between the barrel and end-cap calorimeters.\nUsing the base samples that satisfy the above requirements, the ef\ufb01ciency is de\ufb01ned as follows:\n\u03b5 =\nNreco\n\u03b3\nNtruth\n\u03b3\n(1)\nwhere Ntruth\n\u03b3\nis the number of true photons in the simulation that satisfy all the requirements above with\nthe true ET greater than either 25 GeV or 40 GeV and Nreco\n\u03b3\nis the number of reconstructed photons that\nsatisfy all the requirements with the true ET greater than either 25 GeV or 40 GeV and that pass the\nthreshold for one of the three methods.\nSimilarly, the rejection from the pre-\ufb01ltered jet sample is computed as follows:\nR = Njet\nNfake\u03b3\nN1\nN2\n1\n\u03b5\u03b3\u2212filter\n(2)\nwhere Njet is the total number of jets reconstructed in the normalisation sample (same generation as the\nreconstructed sample but without the \ufb01lter requirements) using particle four-momenta from the generator\nhadron level within a cone size \u2206R = 0.4, and N2(= 400,000) is the number of events used in this\nnormalisation sample. The values for Njet/N2 in the \ufb01ducial volume of |\u03b7| < 1.37 or 1.52 < |\u03b7| < 2.37\nare 0.226 for jets with ET > 25 GeV and 0.042 for jets with ET > 40 GeV. Nfake\u03b3 is the number of\nfake photons in the reconstructed (\ufb01ltered) sample with the candidates that matched to true photons from\nthe hard scatter or from quark bremsstrahlung removed, and N1(= 3,095,900) is the number of events\nanalyzed from this sample. Finally, \u03b5\u03b3\u2212filter (= 0.082) is the ef\ufb01ciency of the generator level \ufb01lter applied\nto the jet sample.\n3\nPhoton identi\ufb01cation methods\nAs discussed in previous sections, three photon identi\ufb01cation methods have been developed and are\navailable at present in ATLAS: a simple cut-based identi\ufb01cation method, a Log-likelihood-ratio-based\nidenti\ufb01cation method (LLR) and the covariance-matrix-based identi\ufb01cation method (H-matrix). A par-\ntial description of the basic electromagnetic object reconstruction and a detailed presentation of their\ncalibration can be found in Ref. [6].\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n95\n\n3.1\nCharacteristic variables and cut-based photon identi\ufb01cation\nIn order to separate real photons from fake photons resulting from jets, several discriminating variables\nare de\ufb01ned using the information both from the calorimeters and the inner tracking system. Cuts on these\nvariables are developed to maintain high photon ef\ufb01ciency even in the presence of pile-up resulting from\nthe overlapping minimum bias events due to high instantaneous luminosity at the LHC. The discriminat-\ning variables used in this study are the same as in previous studies [7\u201311]. Calorimeter information is\nused to select events containing a high-ET electromagnetic shower. The \ufb01ne-grained \ufb01rst compartment\nallows to reject showers from photons from \u03c00 decays. Track isolation is used to improve the rejection.\nOnly electromagnetic clusters with ET > 20 GeV are used in this study.\n3.1.1\nVariables using calorimeter information\nIn the electromagnetic calorimeter, photons are narrow objects, well contained in the electromagnetic\ncalorimeter, while fake photons induced from jets tend to have a broader pro\ufb01le and can deposit a sub-\nstantial fraction of their energy in the hadronic calorimeter. Hence, longitudinal and transverse shower-\nshape variables can be used to reject jets.\n\u2022 Hadronic leakage : The hadronic leakage is de\ufb01ned as the ratio of the transverse energy in the\n\ufb01rst layer of the hadronic calorimeter in a window \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.24 \u00d7 0.24 to the transverse en-\nergy of the cluster in order to avoid boundary effects that could result from using readout cells.\nReal photons are purely an electromagnetic object, therefore they deposit their energy primarily\nin the electromagnetic compartment of the calorimeter. Fake photons induced from jets contain\nhadrons that would penetrate deeper into the calorimeter depositing sizable energy beyond the\nelectromagnetic calorimeter.\n\u2022 Variables using the second compartment of the ECAL : Electromagnetic showers deposit most\nof their energy in the second layer of the electromagnetic calorimeter. For this reason several\nvariables that measure the shape of the shower are available as follows:\n- The real photons deposit most of their energy in a \u2206\u03b7 \u00d7 \u2206\u03c6 = 3 \u00d7 7 window (in units of\nmiddle cells). The lateral shower-shape variables, R\u03b7 and R\u03c6, are given by the ratio of the\nenergy reconstructed in 3 \u00d7 7 middle cells to the energy in 7 \u00d7 7 cells and the ratio of the\nenergy reconstructed in 3\u00d73 cells to the energy in 3\u00d77 cells, respectively. Due to the effect\nof the magnetic \ufb01eld increasing the width of the converted photon contributions in the \u03c6\ndirection, R\u03c6 is less discriminating than R\u03b7.\n- The lateral width in \u03b7 is calculated in a window of 3\u00d75 cells using the energy weighted sum\nover all cells. w2 =\nr\n\u2211(Ec\u00d7\u03b72c )\n\u2211Ec\n\u2212\nh\n\u2211(Ec\u00d7\u03b7c)\n\u2211Ec\ni2\n, where Ec is the energy deposit in each cell,\nand \u03b7c is the actual \u03b7 position of the cell represented by the center of the cell in \u03b7 direction.\nTherefore, w2 is given in units of \u03b7. A correction is applied as a function of the impact point\nwithin the cell to reduce the bias from the \ufb01nite cell size.\n\u2022 Variables using the \ufb01rst compartment of the ECAL : Cuts applied on the variables in the\nhadronic calorimeter and the second layer of the electromagnetic calorimeter reject jets which\ncontain high-energy hadrons and resulting broad showers. Jets containing single or multiple neu-\ntral hadrons such as \u03b7 and \u03c00, provide the main contribution which can fake photons. The readout\nof the \ufb01rst layer of the calorimeter uses strips and provides very \ufb01ne granularity in pseudorapidity.\nThus, the information from this layer can be used to identify substructures in the showers and dis-\ntinguish isolated photons from the hard scatter and photons from \u03c0 0 decays ef\ufb01ciently. The lateral\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n96\n\nshower shape in the strips is exploited for |\u03b7| < 2.35 where the strip granularity is suf\ufb01ciently \ufb01ne,\nas long as a 0.5% or larger fraction of the total energy is reconstructed in this layer.\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n\n-\n10\n-3\n10\n-2\n10\n-1\n10\nSignal\nBackground\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n>\n\u03b7\n\n\u03c6\n\n2\n (GeV)\nmax2\n (MeV)\ns\n E\n\u2206\n<\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nSignal\nBackground\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n> \nside\n \ns3\n \nstot\n 1.5 stems from a combination of effects from\nthe variation of the quantity of the upstream material and changes in the strip-cell sizes in the end-cap\ncalorimeters. The dip in the hadronic leakage variable near |\u03b7| = 1.1 corresponds to a smaller coverage\nby the \ufb01rst hadronic layer in this region.\nHadronic Leakage\n0\n0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09\n0.1\n-5\n10\n-\n10\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\n\u03b7\nR\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\n\u03c6\nR\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\n2\nw\n0.006\n0.008\n0.01\n0.012\n0.014\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\n (GeV)\nmax2\nR\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\n (MeV)\ns\n E\n\u2206\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\nside\nF\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\ns3\nw\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\nstot\nw\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nBackground\nATLAS\nFigure 2: Normalised distributions of the discriminating variable for |\u03b7| < 0.7 for true and fake photons\n(before cuts) with 20 < ET < 30 GeV. The samples have been simulated with the geometry under the\nrealistic alignment scenario.\nThe cut values are tuned separately in six pseudorapidity intervals in |\u03b7| < 2.37 to re\ufb02ect the pseu-\ndorapidity dependence of these variables. The subdivision is motivated by the varying granularity and\nmaterial in front of the electromagnetic calorimeter. The quantities calculated using the \ufb01rst compart-\nment can be used only in the regions |\u03b7| < 1.37 and 1.52 < |\u03b7| < 2.37 since there are no strips in the\ncrack region or beyond |\u03b7| > 2.40. In addition, up to eight different bins in transverse energy are also\nused for the cut value adjustment. Figure 2 shows the distributions of the variables in the \ufb01rst \u03b7 bin and\nin one energy bin. The dashed vertical lines represent the cut values in this bin. The variables are shown\nfor all reconstructed electromagnetic objects before cuts.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n98\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n>\n\u03b7\n\nmax2\n40 cm\nRconv<40 cm\nATLAS\nFigure 4: Normalised distribution of the track-isolation variable for events passing the calorimeter selec-\ntion criteria. Left: comparison of true and fake photons. Right: comparison of early conversions (true\nconversion radius less than 40 cm) and late conversions (true conversion radius above 40 cm) for photons\nfrom H \u2192\u03b3\u03b3 decays.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n99\n\n3.1.2\nTrack isolation\nAfter the calorimeter cuts, the contamination of the inclusive signal from charged hadrons is greatly\nreduced. The remaining background is dominated by low track multiplicity jets containing high-pT \u03c00\nmesons. In order to further remove fake photons from these jets, the track-isolation variable is de\ufb01ned\nas the sum of the pT of all tracks with pT above 1 GeV within \u2206R < 0.3, where \u2206R is the \u03b7 \u2212\u03c6 distance\nbetween the track position at the vertex and the cluster centroid. Track pT > 1 GeV is imposed to\nminimise the effect of pile-up and underlying events.\nSince the tracks from photon conversions should not be included in computing this variable, some\nadditional selections are applied to tracks within \u2206R < 0.1 of the cluster centroid. The impact parameter\nwith respect to the beam line must be less than 0.1 mm. The track pT must not exceed 15 GeV to remove\ntracks from very asymmetric conversions, must not be part of a reconstructed conversion vertex and must\nhave a hit in the innermost pixel layer.\nThe plot on the left in Fig. 4 shows the distribution of the track-isolation variable for true and fake-\nphoton candidates, after the calorimeter shower-shape cuts. An additional rejection of factor 1.5 to 2 is\npossible for a relatively small ef\ufb01ciency loss. The plot on the right in this \ufb01gure shows the track-isolation\nvariable for early converted and late converted photons. The difference between the two distributions\nis rather small, showing that the tracks from conversions have been ef\ufb01ciently removed. At present, a\n4 GeV upper cut on the track-isolation variable is applied for this method.\n3.2\nLog-likelihood-ratio-based photon identi\ufb01cation\nIn the Log-likelihood-ratio (LLR)-based method, the distribution of each of the shower-shape variables\nis normalised to unity to obtain the probability density functions (PDF). The shower-shape variables\nare pseudorapidity-dependent, so they are separated in four regions of |\u03b7| and three bins in pT for this\nmethod. The PDF\u2019s are obtained using 1.6 million \u03b3+jet events which provided slightly over 100,000\nevents in each bin. Since the statistics for the PDF computation is somewhat low in some kinematic\nphase-space regions, further improvement can be obtained by using tools to smooth the PDF\u2019s to com-\npensate for the low statistics [13]. Once the PDF\u2019s are established, the Log-likelihood-ratio parameter is\nde\ufb01ned as:\nLLR =\nn\n\u2211\ni=1\nln(Lsi/Lbi),\n(3)\nwhere Lsi and Lbi are PDF\u2019s of the ith shower-shape variable for the photon and the jet, respectively.\nThe shower-shape variables used for the LLR method were the same as those used for the cut-based\nmethod described previously. Track isolation was also included as a discriminating variable in Equa-\ntion 3. Figure 5 shows the LLR parameter distribution for photons and for jets. The LLR cut can be\ntuned over \u03b7 and pT to obtain an optimal separation between photons and jets.\n3.3\nCovariance-matrix-based photon identi\ufb01cation\nThe shower-shape variables associated with a photon shower in the calorimeter are correlated. The co-\nvariance matrix (H-matrix) technique takes advantage of these correlations. The technique was employed\nsuccessfully in the D/0 experiment at the Tevatron and was used to identify electrons [14].\nThe ten photon shower-shape variables used in the ATLAS H-matrix method are as follows:\n\u2022 Five longitudinal shower-shape variables: fraction of energy deposited in pre-sampler layer; frac-\ntions of energy deposited in sampling layers 1, 2 and 3 separately; and the hadronic leakage, the\nenergy leakage into the \ufb01rst layer of the hadronic calorimeter.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n100\n\nLLR\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n1\n10\n2\n10\n3\n10\n4\n10\nPhoton\nJets\nATLAS\nFigure 5: Expected Log-likelihood ratio (LLR) cut-parameter distributions for photons (solid histogram)\nand for jets (dashed histogram).\n2\n\u03c7\n0\n20\n40\n60\n80\n100\n120\n140\n1\n10\n2\n10\n3\n10\n \u03b3\n\u03b3 \n\u2192\n H \n Jets\nATLAS\nFigure 6: The distributions of H-matrix \u03c72 for photons from the H \u2192\u03b3\u03b3 sample (solid histogram) and\nfor jets from the inclusive jet samples (dashed histogram).\n\u2022 Five transverse shower-shape variables: the ratio of the energy in 3\u00d73 cells to the energy in 7\u00d77\nin the second sampling layer of the electromagnetic calorimeter; wrms3, the corrected width in 3\nstrips in sampling layer 1; w2, the corrected width in a 3 \u00d7 5 window in sampling layer 2; the\nenergy outside of the shower core; R\u03c6, the ratio of energy in a 3\u00d73 to a 3\u00d77 window around the\ncluster centroid.\nUsing the above variables, a covariance matrix, M, is constructed as follows:\nMi j = 1\nN \u03a3N\nn=1(y(n)\ni\n\u2212yi)(y(n)\nj \u2212y j),\n(4)\nwhere indices i and j run over the ten variables, N is the total number of photons used in the training\nsample, yn\nj is the jth variable for the nth photon candidate, and y j is the mean value of y j variable for the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n101\n\ncontrol sample electrons/photons. These matrix elements are constructed for each \u03b7 bin and parametrised\nfor energy dependences. The photon likeness of an object is then measured by the value of the \u03c7 2, de\ufb01ned\nas follows:\n\u03c72 = \u03a3dim\ni, j=1(y(m)\ni\n\u2212yi)Hi j(y(m)\nj\n\u2212y j)\n(5)\nwhere H \u2261M\u22121, the inverse of the covariance matrix, and the indices i and j run from 1 to the total\nnumber of variables (ten) which is the same as the dimension of the matrix, dim.\nThe mean value of the \u03c72 is close to the number of dimensions for a photon shower. The shapes of\nthe distributions of the selected shower-shape variables depend on the \u03b7 and the energy of the incident\nphoton. These effects are taken into account in the construction of the H-matrix using single photon\nsamples of energies 10 \u2013 1000 GeV generated \ufb02at in |\u03b7| and parametrising each of the covariance terms\nin the matrix M of Eq. 4 as a function of the photon energy. The parametrisation as a function of photon\nenergy is obtained in each of the 12 \u03b7 bins. The discrimination power of the H-matrix between real\nphotons and jets is well illustrated in Fig. 6, where the \u03c72 distribution of the H-matrix for the jet sample\nis contrasted to that obtained from photons from H \u2192\u03b3\u03b3 decays.\nSince the H-matrix implementation at this time does not include the same variables as the other two\nmethods, its performance is currently not directly comparable. Consequently, the performance is not\nreported here, although the method is decribed for completeness.\n\u03b7\n-2 5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\nATLAS\n (GeV)\nT\nE\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEfficiency\n0.4\n0.5\n0 6\n0.7\n0 8\n0 9\n1\n1.1\n1 2\nATLAS\nFigure 7: Ef\ufb01ciency of the calorimeter cuts as a function of pseudorapidity (left) and transverse en-\nergy (right) of the photons for the distorted geometry.\nEf\ufb01ciency\n\u03b5 (calorimeter cuts)\n\u03b5 (track-isolation cut)\nNominal geometry no pile-up\n(87.6\u00b10.2)%\n(99.0\u00b10.1)%\nNominal geometry with pile-up\n(86.6\u00b10.5)%\n(98.0\u00b10.2)%\nDistorted geometry with pile-up\n(83.6\u00b10.2)%\n(98.1\u00b10.1)%\nTable 1: Overall ef\ufb01ciency for photons from H \u2192\u03b3\u03b3 decays for three different simulation choices.\n4\nPhoton identi\ufb01cation performance for medium-pT photons\nThis section describes the performance (ef\ufb01ciencies and rejections) of the cut-based method and the Log-\nlikelihood ratio method on medium-pT photons, in particular the photons from H \u2192\u03b3\u03b3 decays and the\njet background samples described in Section 2.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n102\n\n4.1\nPerformance of the cut-based method\nIn the performance studies presented in this section, all reconstructed electromagnetic objects, including\nboth electron and photon candidates are considered. The ef\ufb01ciency as de\ufb01ned in Section 2 includes both\nthe reconstruction ef\ufb01ciency and the ef\ufb01ciency of the identi\ufb01cation cuts.\nFigure 7 shows the ef\ufb01ciency of the calorimeter cuts for photons with ET > 25 GeV from H \u2192\u03b3\u03b3\ndecay as a function of pseudorapidity (left) and transverse energy (right) for events in the presence of the\npile-up expected at a luminosity of 1033 cm\u22122s\u22121. The optimisation of the cuts for the H \u2192\u03b3\u03b3 signal has\nled to an ef\ufb01ciency which is uniform for ET > 40 GeV, but which decreases substantially below 40 GeV\nbecause of the much larger fake backgrounds from jets expected at these lower transverse energies. The\naverage ef\ufb01ciencies of the calorimeter and track-isolation cuts are summarised in Table 1.\nAll\nQuark jets\nGluon jets\nN(jet)/N(generated events)\n0.23\n0.056\n0.177\nBefore isolation cut\nN(fake)/N(\ufb01ltered events)\n(5.43\u00b10.13).10\u22124\n(3.87\u00b10.11).10\u22124\n(1.44\u00b10.07).10\u22124\nRejection\n5070\u00b1120\n1770\u00b150\n15000\u00b1700\nAfter isolation cut\nN(fake)/N(\ufb01ltered events)\n(3.38\u00b10.10).10\u22124\n(2.47\u00b10.08).10\u22124\n(0.78\u00b10.49).10\u22124\nRejection\n8160\u00b1 250\n2760\u00b1100\n27500\u00b12000\nTable 2: Rejection (Equation 2) measured in the inclusive jet sample for ET > 25 GeV\nAll\nQuark jets\nGluon jets\nN(jet)/N(generated events)\n0.042\n0.011\n0.034\nBefore isolation cut\nN(fake)/N(\ufb01ltered events)\n(1.16\u00b10.06).10\u22124\n(8.3\u00b10.5).10\u22125\n(2.8\u00b10.3).10\u22125\nRejection\n4400\u00b1230\n1610\u00b1100\n15000\u00b11600\nAfter isolation cut\nN(fake)/N(\ufb01ltered events)\n(6.4\u00b10.4).10\u22125\n(4.6\u00b10.5).10\u22125\n(1.5\u00b10.2).10\u22125\nRejection\n7800\u00b1540\n2900\u00b1240\n28000\u00b14000\nTable 3: Rejection (Equation 2) measured in the inclusive jet sample for ET > 40 GeV\nThe rejection from the pre-\ufb01ltered jet sample is computed using Equation 2. The rejection is com-\nputed separately for all jets, for quark-initiated jets and for gluon-initiated jets. The quark or gluon\ninitiation is de\ufb01ned using the type of the highest ET parton from the PYTHIA record inside the cone\n\u2206R = 0.4 around the reconstructed jet object. The rejection values are summarised in Table 2 for the\nthree categories of jets. A small fraction (\u22481-2%) of jet objects are not classi\ufb01ed, so the sum of quarks\nand gluons is slightly smaller than the total. A cut ET > 25 GeV is applied to both reconstructed photons\nand jets. Table 3 shows the same computation, but for ET > 40 GeV.\nFigure 8 shows the fake rate, de\ufb01ned as the inverse of the rejection, as a function of pseudorapidity for\nall jets with ET greater than 25 GeV. There is a slight increase of fake rate as a function of pseudorapidity\ndue to the increase in material in front of the calorimeter, which imposes somewhat looser cuts to preserve\na constant ef\ufb01ciency. Some additional increase near |\u03b7| = 1.1 is also visible probably coming from the\nreduced energy in the \ufb01rst layer of the hadronic calorimeter as pointed out previously. This effect,\nhowever, gives a less than 10% increase in the overall fake rate.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n103\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nFake rate\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n-3\n10\n\u00d7\nBefore isolation cut\nAfter isolation cut\nATLAS\nFigure 8: Fake-photon rate as a function of pseudorapidity in the \ufb01ltered jet sample\n (GeV)\nT\nE\n20\n30\n40\n50\n60\n70\n80\n90\n100\n (pb/GeV)\nT\n/dE\n\u03c3\nd\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n9\n10\n R=0.4)\n\u2206\nTruth jet (\nUncorrected jets from parameterized fast simulation\nFake photons before isolation cut\nFake photons after isolation cut\nATLAS\nFigure 9: ET spectra from the inclusive jet sample, for the generated jets (solid squares for full simulation\nand solid triangles for uncorrected jets from parametrised fast simulation) and the fake-photon candidates\nbefore (inverted solid triangles) and after (open circles) the track-isolation cut. The normalisation is that\npredicted by PYTHIA.\nFigure 9 shows the ET distribution of the jets and of the fake photon candidates before and after the\ntrack-isolation cut. This \ufb01gure also shows that the rejection at 25 GeV is \u224830% lower if the normalisa-\ntion is based on the uncorrected parametrised jets from the fast simulation, as was done in Ref. [11].\nFigure 10 shows the \u03c00 content of the fake-photon candidates at three different cut levels; all recon-\nstructed electromagnetic objects, after the cut on the hadronic leakage and the second layer shower-shape\nvariables (Had+S2) and after all the cuts (Had+S1+S2). A fake photon is de\ufb01ned as coming from a \u03c0 0 if\nthe energy of the leading \u03c00 in the cone of 0.2 around the cluster centroid is more than 80% of the recon-\nstructed cluster energy. The \ufb01gure shows already after the second layer shower-shape cuts, the dominant\nbackground contribution comes from \u03c00 as expected. After all cuts, the fraction of \u03c00 is \u224870% of the\nremaining fake-photon candidates.\nFigure 11 shows the rejection of the cuts on the \ufb01rst layer variables for candidates from single \u03c0 0\u2019s\npassing the cuts on the hadronic leakage and the second layer shower-shape variables. As expected, the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n104\n\n (GeV)\nT\nE\n20\n30\n40\n50\n60\n70\n80\n90\n100\nNumber of candidates\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nEM objects, all fakes\n0\n\u03c0\nEM objects,\nHad+S2 cuts, all fakes\n0\n\u03c0\nHad+S2 objects, \nHad+S2+S1 cuts, all fakes\n0\n\u03c0\nHad+S2+S1 objects, \nATLAS\nFigure 10: ET distribution of fake-photon candidates in jets after different level of cuts. The contribution\nfrom \u201dsingle\u201d \u03c00 is also shown\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n in jets Rejection from S1 cuts\n0\n\u03c0\n0\n1\n2\n3\n4\n5\n6\n7\n|<0.8\n\u03b7\n0<|\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n in jets Rejection from S1 cuts\n0\n\u03c0\n0\n1\n2\n3\n4\n5\n6\n7\n|<1.37\n\u03b7\n0.8<|\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n in jets Rejection from S1 cuts\n0\n\u03c0\n0\n1\n2\n3\n4\n5\n6\n7\n|<2.37\n\u03b7\n1.52<|\nATLAS\nFigure 11: Rejection of the strip-layer cuts against fake photons coming from \u201dsingle\u201d \u03c0 0 in the jet\nsample as a function of the transverse energy, for three different pseudorapidity regions.\nrejection power against these isolated \u03c00\u2019s decreases with energy, as the opening angle between the two\nphotons from \u03c00 decays become smaller. The rejection is also better in the central part in the barrel as\nthere is less material than in the higher \u03b7 part of the barrel, and also opening angle is larger than in the\nend-cap for the same pT . As a cross-check, Fig. 12 shows the ef\ufb01ciency of the calorimeter cuts for single\nphotons and single \u03c00 of ET = 40 GeV, as a function of pseudorapidity. Again, the rejection is slightly\nhigher than 3 in the central part of the barrel calorimeter and is in reasonable agreement with \ufb01ndings\nfrom previous studies [15].\nThe rejections measured in these studies have to be taken with care as they rely strongly on the\nmodelling of the fragmentation tail in PYTHIA and the details of the simulation of the detector response.\nA discussion of the \ufb01rst effect can be found in Ref. [8] from which one would expect an uncertainty of\n50\u2212100%, and where the uncertainty is larger for gluon initiated jets. In addition, a recent investigation\non the differences in fragmentation algorithms in PYTHIA and HERWIG shows appreciable differences\nin \u03c00 production rates. Some differences in rejection are anticipated if the momentum distributions of\nthe \u03c00\u2019s from the two fragmentation algorithms differ.\n4.2\nPerformance of the Log-likelihood-ratio method\nThe ef\ufb01ciency for the Log-likelihood-ratio (LLR) method is computed for individual photons from the\nH \u2192\u03b3\u03b3 events generated with the nominal geometry. Figure 13 shows the photon ef\ufb01ciency as a function\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n105\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nefficiency of calorimeter cuts\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nphotons E =40 GeV\n Et=40 GeV\n0\n\u03c0\nATLAS\nFigure 12: Ef\ufb01ciency of calorimeter cuts versus pseudorapidity for 40 GeV ET single photons and \u03c00\n(distorted geometry without pile-up).\nof pT (left) and \u03b7 (right) for LLR cut values set at 8, 9 and 10. The overall ef\ufb01ciencies for LLR cuts\nat 8, 9 and 10 are summarised in Table 4. Jet rejection (left) and photon identi\ufb01cation ef\ufb01ciency (right)\nare shown in Fig. 14 as a function of LLR cut parameter values for three different jet pT ranges which\ncorrespond to the three mean jet pT values indicated.\nET > 25 GeV\nET > 40 GeV\nLLR cut\nLLR > 8\nLLR > 9\nLLR > 10\nLLR > 8\nLLR > 9\nLLR > 10\nEf\ufb01ciency(%)\n87.6\u00b10.3\n84.3\u00b10.2\n80.0\u00b10.2\n86.4\u00b10.3\n83.2\u00b10.2\n79.0\u00b10.2\nRej.(\u03b3+jet)\n1660\u00b1170\n2190\u00b1260\n2930\u00b1390\n1690\u00b1140\n2170\u00b1210\n2650\u00b1280\nRej. (di-jet)\n6820\u00b1440\n8930\u00b1650\n12430\u00b11070\n6780\u00b11000\n7800\u00b11230\n11550\u00b12220\nTable 4: Overall photon ef\ufb01ciencies and jet rejections for different Log-likelihood ratio (LLR) cut values.\nFigure 13 shows the pT-dependence of the photon ef\ufb01ciency. A looser cut on low-pT photons seems\nto be bene\ufb01cial in order to retain a \ufb02at photon ef\ufb01ciency as a function of pT. Furthermore, it might also\nbe useful to parametrise the LLR cut values as a function of photon pT for further optimisation. The\njet rejection is also pT-dependent as shown in the plot on the left in Fig. 14. A harder cut on LLR for\nvarying jet pT can help to keep the rejection constant as a function of pT.\nThe rejection for jets from \u03b3+jet and di-jet samples are shown in the fourth and \ufb01fth rows in Table 4.\nThe cuts on the photon and jet pT are 25 GeV and 40 GeV, respectively. The rejection against jets from\nthe di-jet samples is signi\ufb01cantly higher than that from the \u03b3+jet samples. This is largely due to the fact\nthat the jets in \u03b3+jet events are dominated by quark-initiated jets while those in di-jet events are enriched\nwith gluon-initiated jets.\n5\nPhoton identi\ufb01cation performance for high-pT photons\nSearches for particles of very high mass decaying to photons, such as the Randall-Sundrum graviton, G,\ndecaying via G \u2192\u03b3\u03b3 [2], require excellent detector and particle identi\ufb01cation performance in a kine-\nmatic region very different from the benchmark H \u2192\u03b3\u03b3 process. The pT-dependent effect caused by\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n106\n\n(GeV)\n\u03b3\nT\nP\n20\n40\n60\n80\n100\n120\n140\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nLikelihood LLR cut=8\nLikelihood LLR cut=9\nLikelihood LLR cut=10\nATLAS\n\u03b3\n\u03b7\n-2 5\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n2.5\nEfficiency\n0 2\n0 3\n0.4\n0 5\n0 6\n0.7\n0 8\n0 9\n1\nLikelihood LLR cut=8\nLikelihood LLR cut=9\nLikelihood LLR cut=10\nATLAS\nFigure 13: Photon ef\ufb01ciency as a function of pT and \u03b7 for different Log-likelihood ratio (LLR) cuts. The\nphotons are from H \u2192\u03b3\u03b3 decays simulated with the nominal geometry.\nLLR\n-30 -25 -20 -15 -10\n-5\n0\n5\n10\nRejection\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n> = 27 GeV\nT\n = 48 GeV\nT\n = 93 GeV\nT\n = 27 GeV\nT\n = 48 GeV\nT\n = 93 GeV\nT\n 100 GeV and\nmG > 500 GeV.\nAn isolation variable based on the calorimeter energy in a cone of size \u2206R = 0.45 around the cluster\ncentroid was studied. The cut on the calorimeter isolation was observed to produce roughly constant\nef\ufb01ciency as a function of pT. A linearly pT-dependent selection cut was determined for barrel and\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n107\n\n (GeV)\n\u03b3\nT\np\n0\n200\n400\n600\n800\n1000\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nNo photon ID cuts\nWith photon ID cuts\nWith photon ID cuts + isolation\nATLAS\n (GeV)\n\u03b3\nT\np\n0\n200\n400\n600\n800\n1000\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nNo photon ID cuts\nWith photon ID cuts\nWith photon ID cuts + isolation\nATLAS\nFigure 15: Photon ef\ufb01ciency in the 500 GeV graviton sample as a function of pT for barrel (left) and\nend-cap (right) calorimeters.\n [GeV]\n\u03b3\nT\np\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nRejection\n3\n10\n10\n5\n10\nWith Photon ID cuts\nWith Photon ID cuts + Isolation\nATLAS\n [GeV]\n\u03b3\nT\np\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nRejection\n3\n10\n10\n5\n10\nWith Photon ID cuts\nWith Photon ID cuts + Isolation\nATLAS\nFigure 16: Fake-photon rejection as a function of pT of the reconstructed photon object for high-pT\nbinned di-jet samples in the barrel (left) and end-cap (right) calorimeters.\nend-cap photons independently. The ef\ufb01ciencies of these pT-dependent cuts for barrel and end-cap\ncalorimeters are shown in Fig. 15 for photons from 500 GeV graviton decays. As can be seen in the\n\ufb01gures, these pT-dependent isolation cuts show about a 0.1% reduction in ef\ufb01ciency for photons over\nthe entire pT-range.\nThe Jet5 and Jet6 high-pT jet samples discussed in Section 2 were used for rejection studies. Fig-\nure 16 shows the pT dependence of jet rejection with and without the calorimeter energy isolation cuts. It\ncan be seen that while the ef\ufb01ciency loss is small, employing the isolation cut increases rejection across\nthe full pT range. In particular, the region below pT = 500 GeV shows a factor 5 \u221210 increase in re-\njection. Table 5 provides the measured rejections in the barrel and end-cap calorimeters using these two\ndi-jet samples.\n6\nComparison of the photon identi\ufb01cation methods\nFigure 17 shows the rejection and ef\ufb01ciency curves for two of the three currently available photon iden-\nti\ufb01cation methods - the cut-based method and the Log Likelihood Ratio method - for \u03b3+jet generated\nin speci\ufb01c photon momentum bins and the benchmark H \u2192\u03b3\u03b3 samples. Similarly, Fig. 18 shows the\nrejection and ef\ufb01ciency curves for these methods for di-jet and H \u2192\u03b3\u03b3 samples. Tables 6 and 7 provide\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n108\n\nnumerical comparisons of fake-photon rejections for the two methods, for similar photon identi\ufb01cation\nef\ufb01ciencies and for the \u03b3+jet and di-jet samples, respectively.\nThe \u03b3+jet events, with jets dominated by quark-initiated jets, are the source of the largest background\nto the H \u2192\u03b3\u03b3 process. It is apparent from Figs. 17 and 18 that the methods demonstrate signi\ufb01cantly\nreduced rejections for jets from the \u03b3+jet samples than for those from di-jet samples whose jets are pre-\ndominantly from gluons. As discussed in previous sections, this difference in rejection can be attributed\nto the fragmentation differences between the quark and gluon-initiated jets.\nFinally, Figs. 17 and 18 also illustrate that, for equal ef\ufb01ciencies, the Log-likelihood ratio method\nand the cut-based method perform comparably in rejecting jets.\nPhoton efficiency (%)\n65\n70\n75\n80\n85\n90\nRejection\n3\n10\n4\n10\nLikelihood\nCut-based\n > 25 GeV\nT\nE\nATLAS\nPhoton efficiency (%)\n65\n70\n75\n80\n85\n90\nRejection\n3\n10\n4\n10\nLikelihood\nCut-based\nATLAS\n > 40 GeV\nT\nE\nFigure 17: Jet rejection vs photon ef\ufb01ciency for binned \u03b3+jet and H \u2192\u03b3\u03b3 benchmark samples for\np\u03b3\nT, p jet\nT > 25 GeV(left) and p\u03b3\nT, p jet\nT > 40 GeV(right).\nPhoton efficiency (%)\n65\n70\n75\n80\n85\n90\nRejection\n4\n10\nLikelihood\nCut-based\n > 25 GeV\nT\nE\nATLAS\nPhoton efficiency (%)\n65\n70\n75\n80\n85\n90\nRejection\n4\n10\nLikelihood\nCut-based\n > 40 GeV\nT\nE\nATLAS\nFigure 18: Jet rejection vs photon ef\ufb01ciency of the two methods for \ufb01ltered di-jet and H \u2192\u03b3\u03b3 benchmark\nsamples for p\u03b3\nT, p jet\nT > 25 GeV (left) and p\u03b3\nT, p jet\nT > 40 GeV (right).\n7\nConclusions\nThis note presents the three photon identi\ufb01cation methods developed in ATLAS, the cut-based method,\nthe Log-likelihood ratio (LLR)-based method and the covariance-matrix-based method (H-matrix). The\nef\ufb01ciencies and fake-photon rejections of the \ufb01rst two methods have been measured using fully simulated\nH \u2192\u03b3\u03b3 (mH = 120 GeV), \u03b3+jet and \ufb01ltered electromagnetic di-jet samples. The cut-based and LLR\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n109\n\nmethods show similar rejection factors at equal ef\ufb01ciencies. The strength of the continuous methods\nsuch as the LLR and H-matrix is the ability to vary the cuts on LLR or \u03c7 2 values to optimise for speci\ufb01c\nphysics analyses. The performance of the cut-based method for very high-pT photons from Randall-\nSundrum graviton samples has also been studied and, while the cut selection was optimised at low-\npT compared to the signal in the graviton sample, the ef\ufb01ciency remains high. While the currently\navailable photon identi\ufb01cation methods perform very well in rejecting background, with high ef\ufb01ciency\nin retaining photons, it is of critical importance to study the performance of the methods with beam-\ncollision data.\nRegion\nRejection(\u00d7 103)\nRejection(\u00d7 103)\nBarrel\n1.55\u00b10.05\n6.59\u00b10.5\nEnd-cap\n0.84\u00b10.04\n7.66\u00b11.1\nTotal\n1.32\u00b10.04\n6.79\u00b10.4\nTable 5: Jet rejections obtained using two binned high-pT di-jet samples, using the cut-based photon\nidenti\ufb01cation without (left) and with (right) the track isolation cut.\nET > 25 GeV\nET > 40 GeV\nLLR\nCut-based\nLLR\nCut-based\nEf\ufb01ciency (%)\n84.3\u00b10.2\n84.5\u00b10.2\n87.1\u00b10.2\n86.3\u00b10.2\nRejection\n2190\u00b1250\n1940\u00b1230\n2170\u00b1210\n2030\u00b1190\nTable 6: Comparison of jet rejection (\u03b3+jet sample) versus photon ef\ufb01ciency for the cut-based and LLR\nmethods.\nET > 25 GeV\nET > 40 GeV\nLLR\nCut-based\nLLR\nCut-based\nEf\ufb01ciency(%)\n84.3\u00b10.2\n84.6\u00b10.2\n85.5\u00b10.2\n86.3\u00b10.2\nRejection\n8930\u00b1650\n8240\u00b1270\n9170\u00b11570\n9240\u00b1710\nTable 7: Comparison of jet rejection (di-jet sample) versus photon ef\ufb01ciency with the cut-based method\nand the Log-likelihood (LLR) method.\nReferences\n[1] ATLAS Collaboration, Prospects for the Discovery of the Standard Model Higgs Boson Using the\nH \u2192\u03b3\u03b3 Decay, this volume.\n[2] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).\n[3] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\n2008 JINST 3 S08003 (2008).\n[4] ATLAS Collaboration, Data Preparation for the High-Level Trigger Calorimeter Algorithms, this\nvolume.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n110\n\n[5] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[6] ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this vol-\nume.\n[7] G. Unal and L. Fayard, Photon identi\ufb01cation in \u03b3\u2212jet events with Rome layout simulation and\nbackground to H \u2192\u03b3\u03b3, ATL-PHYS-PUB-2006-025 (2006).\n[8] M. Escalier et al., Photon/jet separation with DC1 data, ATL-PHYS-PUB-2005-018 (2005).\n[9] M. Wielers, Photon identi\ufb01cation with the Atlas detector, ATLAS-PHYS-99-016 (1999).\n[10] M. Wielers, Isolation of photons, ATLAS-PHYS-2002-004 (2002).\n[11] ATLAS Collaboration, Detector and Physics Technical Design Report, Vol.1, CERN/LHCC/99-14\n(1999).\n[12] ATLAS Collaboration, Reconstruction of Photon Conversions, this volume.\n[13] K. Cranmer, Kernel estimation in high-energy physics, Computer Physics Communications, Vol-\nume 136, Number 3, 198-207(10) (2001).\n[14] V. Amazov et al., D/0 Collaboration, tt Production Cross-section in pp Collisions at \u221as = 1.8 TeV,\nPhys. Rev. D67 012004 (2003).\n[15] J. Colas et al., Position resolution and particle identi\ufb01cation with the ATLAS electromagnetic\ncalorimeter, Nucl. Instrum. Meth. A550, 96-115 (2005).\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF PHOTONS\n111\n\nReconstruction of Photon Conversions\nAbstract\nThe reconstruction of photon conversions in the ATLAS detector is important\nfor improving both the ef\ufb01ciency and the accuracy of the detection of particle\ndecays with photon \ufb01nal states, including H \u2192\u03b3\u03b3. In this note, the perfor-\nmance of the reconstruction of photon conversions for simulated events of dif-\nferent types is described, using both standard inside-out tracking and the more\nrecently implemented outside-in tracking.\n1\nIntroduction\nReconstruction of photon conversions in the ATLAS detector is important for a variety of physics mea-\nsurements involving electromagnetic decay products. In particular, the ef\ufb01ciency of detection of particles\nwith high-mass di-photon \ufb01nal states, such as the Higgs boson or a heavy graviton, is greatly enhanced\nby ef\ufb01cient conversion reconstruction. Conversion reconstruction will also be used for detector-related\nstudies: mapping the locations of the conversion vertices provides a precise localisation of the material\nin the ATLAS inner detector.\nAs photons may convert at any point in the tracker in the presence of material, the ability to recon-\nstruct conversions will depend strongly on the type of tracking algorithm used. Due to the structure of\nthe ATLAS tracker, photons which convert within 300 mm of the beam axis may be reconstructed with a\nhigh ef\ufb01ciency with standard (inside-out) Si-seeded tracking, while photons which convert further from\nthe beam pipe may only be reconstructed using (outside-in) tracks, which begin with TRT seeds with or\nwithout associated Si hits. Track reconstruction will be discussed in Section 2, while the reconstruction\nof conversion vertices will be discussed in Section 3, and the overall reconstruction of conversions will\nbe discussed in Section 4. Applications of photon conversion reconstruction in the case of neutral pion\ndecays and low-pT photons as well as the application of conversion reconstruction to the case of high-pT\nphysics measurements (such as H \u2192\u03b3\u03b3), will be found in Section 5. A summary and concluding remarks\nare found in Section 6.\n1.1\nTheory\nThe ATLAS detector is designed to measure, among other things, the energies and momenta of photons\nproduced in high-energy proton-proton collisions. The photons which are relevant to physics measure-\nments will have energies in excess of 1 GeV. These photons must pass through the ATLAS tracker\nbefore depositing their energy in the Liquid Argon Calorimeter. At photon energies above 1 GeV, the\ninteraction of the photons with the tracker will be completely dominated by e+e\u2212pair production in the\npresence of material, otherwise known as photon conversion. All other interactions between the photons\nand the tracker material, such as Compton or Rayleigh scattering, will have cross-sections which are\norders of magnitude below that for the photon conversion, and may thus be safely ignored. The leading-\norder Feynman diagrams for photon conversions in the presence of material are shown in Figure 1. The\npresence of the material is required in order for the conversion to satisfy both energy and momentum\nconservation.\nThe cross-section for the conversion of photons in the presence of material is both well understood\ntheoretically and thoroughly measured. Work on calculating this cross-section began almost immediately\nafter the discovery of the positron by Anderson in 1932 [1]. Bethe and Heitler \ufb01rst gave a relativistic\ntreatment of photon conversion in 1934 [2] in which the screening of the nuclear Coulomb \ufb01eld was\ntaken into account. A detailed review of the theory regarding photon conversion and the calculation of\n112\n\n\u03b3\ne\u2212\ne+\nZe\n\u03b3*\n\u03b3\ne+\ne\u2212\n\u03b3*\nZe\n\u03b3\nZ\nZ*\n\u03b3*\ne+\ne\u2212\nZ\ne\u2212\ne+\n\u03b3*\n\u03b3\nZ*\nZ\nZ\nFigure 1: Leading-order Feynman diagrams for photon conversions.\nthe conversion cross-section for a variety of materials was given by Tsai in 1974 [3]. A more modern\ntreatment of the topic of conversions, including corrections to the Bethe-Heitler formula for photon\nenergies above 5 TeV was given by Klein in 2006 [4].\nFor photon energies used in this study (1 GeV and above) the cross-section for the conversion process\nis almost completely independent of the energy of the incident photon, and may be given by the following\nequation [3]:\n\u03c3 =\n7A\n9X0NA\n.\n(1)\nIn this expression A is the atomic mass of the target given in g/mol, and NA = 6.022 \u00d71023 is Avo-\ngadro\u2019s number. X0 is known as the radiation length of the material through which the photon passes,\nwhich for elements heavier than helium may be approximated from the atomic mass A and the atomic\nnumber Z by the following relation [5]:\nX0 =\n716.4g cm\u22122 A\nZ(Z +1)ln(287\n\u221a\nZ).\n(2)\nThis radiation length is de\ufb01ned such that it is 7/9 of the mean free path for photon conversion. Plots\nshowing the total radiation length traversed by photons in the tracker before reaching the calorimeter\nmay be found in the next section.\nThe differential cross-section for photon conversions of energies of 1 GeV and above in terms of the\nquantity x = (Eelectron/Ephoton) is [4]:\nd\u03c3\ndx =\nA\nX0NA\n(1\u22124\n3x(1\u2212x)).\n(3)\nThis cross-section is symmetric in x and 1\u2212x, the electron and positron energies, and it implies that\nthe momentum of the photon is not simply shared equally between the electron and the positron. Some\nfraction of the photon conversions will be highly asymmetric, and either the electron or the positron\nmay be produced with a very low energy. If this energy falls below the threshold required to produce\na reconstructable track in the ATLAS tracker, then the converted photon will be seen to have only one\ntrack, and will be dif\ufb01cult to distinguish from a single electron or positron. This problem is more serious\nat lower photon energies, as the proportion of conversions which are asymmetric enough to cause the loss\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n113\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n0\nRadiation length (X\n0\n0.5\n1\n1.5\n2\n2.5\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n)\n0\nRadiation length (X\n0\n0.5\n1\n1.5\n2\n2.5\nServices\nTRT\nSCT\nPixel\nBeam-pipe\nFigure 2: Material in the inner detector as a function of |\u03b7|.\nof one of the two tracks increases as the photon energy decreases. The dif\ufb01culties involved in identifying\nthese highly asymmetric single-track conversions will be discussed in a later section.\n1.2\nExperimental setup\nIn this section a very brief description of the ATLAS tracker and electromagnetic calorimeter is included.\nThese are the two sub-systems necessary for the studies relevant to this note. A detailed description of\nthe ATLAS detector can be found in the ATLAS detector paper [6] and references therein.\nThe ATLAS tracker consists of several co-axial layers immersed in a 2T solenoidal magnetic \ufb01eld. In\nthe so-called barrel region, the innermost of these is a pixel detector consisting of three highly segmented\ncylindrical layers surrounded by four stereo-pair silicon microstrip (SCT) layers. In addition to the cylin-\ndrical layers forming the barrel, both the pixel and the SCT also have end-caps consisting of disk shaped\nsegments used for tracking particles with large pseudorapidities (|\u03b7| >1.5). The outermost portion of\nthe tracker consists of the Transition Radiation Tracker (TRT), which is comprised of many layers of\ngaseous straw tube elements interleaved with transition radiation material. The TRT is divided into a\nbarrel detector, covering the small pseudorapidity region |\u03b7| <1, and two end-cap detectors covering the\nlarge pseudorapidity region 1< |\u03b7| <2.1. The lack of TRT detector elements at higher pseudorapidities\nis the reason for all the results presented in this note having a cut-off at |\u03b7| = 2.1.\nThe amount of material in the tracker given in radiation lengths as a function of pseudorapidity can\nbe seen in Fig. 2 [6]. As mentioned earlier, the probability of a photon converting in any given layer\nis proportional to the amount of material in that layer. Overall, as many as 60 % of the photons will\nconvert into an electron-positron pair before reaching the face of the calorimeter [6]. This number varies\ngreatly with pseudorapidity as can be seen in Fig. 3 [6], for the case of photons with pT > 1 GeV in\nminimum-bias events. The probability is lowest in the most central region |\u03b7| <0.5, where the amount\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n114\n\nof tracker material is at its minimum. A plot showing the true position of photon conversions in the\nATLAS tracker, as obtained from a sample of 500,000 simulated minimum-bias events, can be seen in\nFig. 4 [6]; the three pixel layers and disks as well as the four barrel SCT layers and their corresponding\nend-cap layers can be clearly seen.\nRadius (mm)\n0\n200\n400\n600\n800\n1000\n1200\nProbability of conversion\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n = 0\n\u03b7\n = 1\n\u03b7\n = 1.5\n\u03b7\n = 2\n\u03b7\nFigure 3: Probability of a photon to have converted as a function of radius for different values of pseu-\ndorapidity.\nFinally, the energies of the electrons resulting from photon conversions are measured in the electro-\nmagnetic calorimeter segments. These are lead-liquid argon detectors with accordion-shaped absorbers\nand electrodes. Their \ufb01ne-grained lateral and longitudinal structure, ensures high reconstructed energy\nresolution for photons with ET > 2\u22123 GeV, as described in reference [7]. Although the daughter electron\ntracks and the vertices resulting from the converted photons are reconstructed without any calorimetric\ninformation, the latter plays a crucial role later in the reconstruction and particle identi\ufb01cation process.\n2\nTrack reconstruction\nThe current track reconstruction process consists of two main sequences, the primary inside-out track re-\nconstruction for charged particle tracks originating from the interaction region and a consecutive outside-\nin track reconstruction for tracks originating later inside the tracker. Both methods reconstruct tracks that\nhave both silicon (Si) and transition radiation tracker (TRT) hits and place these tracks in two distinct\ntrack collections. A third track category contains those tracks that have only TRT hits and no Si hits;\nthese TRT-only tracks are placed in their own distinct track collection. All three track collections are\nthen examined to remove ambiguities and double counting and are \ufb01nally merged into a global track col-\nlection to be used later during the vertex-reconstruction phase. For a track to be reconstructed by any of\nthese methods, a minimum transverse momentum pT > 0.5 GeV is required throughout. In the following\nsection, brief descriptions of the various tracking algorithms are provided. More detailed descriptions,\nin particular of the inside-out tracking, can be found in reference [8].\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n115\n\nFigure 4: Location of the inner detector material as obtained from the true positions of simulated photon\nconversions in minimum-bias events.\n2.1\nInside-out track reconstruction\nAfter the reconstruction of space points inside the pixel and SCT sub-detectors, candidate tracks (seeds)\nare then formed using three space-point combinations. These seeds are subject to some constraints, such\nas the curvature, to limit the number of possible combinations. Seeds which pass these constraints then\nbecome the starting points for reconstructing tracks. Once a seed has been formed a geometric tool is\nthen invoked in order to provide a list of Si-detector elements that should be searched for additional\nhits. A combinatorial Kalman-\ufb01tter/smoothing formalism is then used to add successive hits to the track.\nThe track information is updated after every step in the search and extraneous outlier hits are ef\ufb01ciently\neliminated through their large contribution to the \u03c72 of the track \ufb01t. Not all space-point seeds coming\nfrom Si hits result in a track; the rate at which seeds give rise to a fully reconstructed track is on the order\nof 10% in a typical t\u00aft physics event.\nA large fraction of the reconstructed track candidates either share hits, are incomplete, or may be\nfakes resulting from random combinations of hits. It is therefore necessary to evaluate the tracks based\non a number of quality criteria and score them accordingly, with the score providing an indication of\nthe likelihood of a speci\ufb01c track to describe a real particle trajectory. Tracks with the highest score are\nre\ufb01tted and used as the quality reference for all the remaining tracks. Shared hits are removed in this\nstage and the remaining part of the track is evaluated again and re\ufb01tted. Track candidates with too many\nshared hits are then discarded as well as any other track candidate that fails to comply with any of the\nquality criteria during evaluation.\nAt this stage, each one of the resolved track candidates is assigned a TRT extension. First, a geometric\nextension of the Si track is built inside the TRT and compatible measurements are selected. Possible TRT-\ntrack extensions are constructed by combining all such TRT measurements. The full track, including any\nTRT extension, is then re\ufb01tted and scored in a way analogous to that during the previous ambiguity-\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n116\n\nresolving stage. If the new track has a quality score which is higher than that of the original Si track,\nthe TRT extension is kept and added to the Si track, thus creating a \u201cglobal\u201d Inner Detector track. In\nother cases only the original Si track is kept, without the TRT extension. The \ufb01nal reconstructed tracks,\nwith or without TRT extensions, are then stored in a dedicated track collection. At this stage they can be\nclassi\ufb01ed into three categories:\n1. Tracks without TRT extensions (e.g. |\u03b7| > 2);\n2. Tracks with extensions which are used in the \ufb01nal \ufb01t;\n3. Tracks with extensions which are not used in the \ufb01nal \ufb01t (outliers).\nThis last category is characteristic of tracks that have suffered large material interactions as they propa-\ngated through the tracker material.\nThe inside-out track reconstruction (as described in the previous section) is a very powerful technique\nfor reconstructing tracks, especially in busy environments where the high granularity of the Si sub-\ndetectors (and in particular that of the pixel detector) can provide the necessary resolution for recovering\nthe track-hit pattern. However, it may also lead to fake tracks if not carefully implemented. In order to\nreduce the number of fake reconstructed tracks, a minimum number of Si hits is required for a track to\nbe reconstructed; in the present implementation of the algorithm this number is seven. This requirement\nimmediately leads to a decreased ef\ufb01ciency in reconstructing tracks that originate late inside the tracker,\ni.e. in the SCT. Furthermore, tracks which are present only inside the TRT will not be reconstructed at\nall. These tracks can appear in the cases of secondary decays inside the tracker (e.g. Ks decays) or during\nphoton conversions, the latter being of special interest to this note.\n2.2\nOutside-in track reconstruction\nThe outside-in track reconstruction (also referred to as back-tracking) can offer a remedy to the inef\ufb01-\nciency in reconstructing tracks which originate after the pixel detector.\nThe starting point for this type of track reconstruction is the TRT, where initial track segments are\nformed using a histogramming technique. The TRT tracker can be divided in two parts, a barrel and an\nend-cap one, the dividing line being at the |\u03b7| = 0.8 pseudorapidity range. In the R\u2212\u03c6 plane of a TRT\nbarrel sector or the R \u2212z plane of a TRT end-cap sector, tracks which originate roughly at the primary\ninteraction region appear to follow straight lines (this is exactly true in the second case). These straight-\nline patterns can be characterised by applying the Hough transform [9], which is based on the simple idea\nthat in the R\u2212\u03c6(R\u2212z) plane, a straight line can be parametrised using two variables: (\u03c60,cT) or (\u03c60,cz)\nrespectively, where cT and cz are the corresponding azimuthal and longitudinal curvatures and \u03c60 is the\ninitial azimuthal angle. As a result, in a two-dimensional histogram formed by these two parameters,\nTRT straw hits lying on the same straight line will fall within a single cell. Straight lines can therefore be\ndetected by scanning for local maxima in these histograms. To improve the accuracy in the longitudinal\ndirection, the TRT is divided into 13 pseudorapidity slices on either side of the \u03b7=0 plane. The slice\nsize varies, it being smaller around the TRT barrel/end-cap transition region and bigger inside the TRT\nbarrel or end-cap regions. The two-variable approximate track parameters can then be used to de\ufb01ne a\nnew set of geometric divisions inside the TRT, within which all straws that could possibly be crossed\nare included. Using the transformation described in [10], the curved trajectory suggested by the straw\nhits may be transformed into a straight line in a rotated coordinate system. This is the initial step for\na \u201clocal\u201d pattern recognition process, in which the best TRT segment may be chosen as the one that\ncrosses the largest number of straws in this straight-line representation. A cut on the minimum number\nof straw hits necessary to consider the segment as valid is applied during this step. A \ufb01nal Kalman-\ufb01lter\nsmoother procedure is then applied to determine as accurately as possible the \ufb01nal track parameters of the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n117\n\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nTrack reconstruction efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nCombined Tracking\nInside-Out Tracking\nFigure 5: Track reconstruction ef\ufb01ciency for conversions from 20 GeV pT photons as a function of the\nconversion radius. The gain in track reconstruction ef\ufb01ciency when tracks reconstructed moving inwards\nfrom the TRT are combined with tracks reconstructed by the inside-out algorithm, is evident particularly\nat higher radial distances.\nsegment. The above TRT-segment reconstruction procedure has been adopted from the original ATLAS\ntrack reconstruction algorithm xKalman as described in the references [11].\nThe reconstructed TRT segments are then fed into the second step of the back-tracking algorithm\nin which extensions are added to them from the Si sub-detectors. Space-point seeds are searched for in\nnarrow R\u2212\u03c6 wedges of the Si tracker, indicated by the transverse TRT-segment track parameters derived\nin the previous step. A minimum of two space points is required in this case, the search being con\ufb01ned\nto the last three SCT layers. To reduce the number of space-point combinations cuts on the curvature\nare then applied, with the third measurement point provided by the \ufb01rst hit in the initial TRT segment.\nAs soon as seeds with pairs of space points are formed, the initial-segment track parameters can then\nbe signi\ufb01cantly improved, especially the longitudinal components. A new geometric section through the\nSi-detector elements is then constructed and a combinatorial Kalman-\ufb01tter/smoother technique, as in the\ncase of the inside-out tracking, is applied to produce Si-track extension candidates. The Si-track exten-\nsions provide a much improved set of track parameters, which can be used to \ufb01nd new TRT extensions to\nbe assigned to every Si-track candidate, thus creating once more a \u201cglobal\u201d track. Ambiguity resolving\nand track re\ufb01tting follow afterwards in the appropriate manner. The \ufb01nal set of resolved tracks from this\nprocess is stored in a dedicated track collection. In order to reduce the time required for the reconstruc-\ntion and minimise double counting, the outside-in tracking procedure excludes all the TRT-straw hits and\nSi-detector space points that have already been assigned to inside-out tracks. The enhancement of the\ntrack reconstruction ef\ufb01ciency after the outside-in reconstructed tracks are included is shown in Fig. 5.\nHere the track reconstruction ef\ufb01ciency for photon conversions is plotted as a function of the radial dis-\ntance of the conversion for the case of 20 GeV pT single photons, before and after the outside-in tracking\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n118\n\nis performed. The bulk of the gain in tracking ef\ufb01ciency is, as expected, at larger radii. The inef\ufb01ciencies\nof this method as a function of radius are discussed further in Section 2.3 and again in Sections 4.3 and\n4.4. Due to the more limited pseudorapidity coverage of the TRT tracker, the outside-in tracking can be\nused to ef\ufb01ciently reconstruct tracks up to a pseudorapidity value of |\u03b7| = 2.1. All the results presented\nhere have therefore been restricted to within this pseudorapidity range.\n2.3\nStand-alone TRT tracks and \ufb01nal track collection.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nTrack reconstruction efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nCombined tracks\nSi tracks\nTRT tracks\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nTrack reconstruction efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nCombined tracks\nSi tracks\nTRT tracks\nFigure 6: Track reconstruction ef\ufb01ciency for conversions from 20 GeV pT converted photons (left) and\n5 GeV pT converted photons (right) as a function of conversion radius.\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrack reconstruction efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nCombined tracks\nSi tracks\nTRT tracks\n|\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nTrack reconstruction efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nCombined tracks\nSi tracks\nTRT tracks\nFigure 7: Track reconstruction ef\ufb01ciency for conversions from 20 GeV photons (left) and 5 GeV photons\n(right) as a function of pseudorapidity.\nAfter the inside-out track collection has been formed, all TRT segments that have not been assigned\nany Si extensions are then used as the basis of one more distinct track collection. These segments are\n\ufb01rst transformed into tracks, and the segment local parameters are used as the basis for producing the\ncorresponding track parameters assigned to the surface of the \ufb01rst straw hit. Perigee parameters are also\ncomputed, but no overall track re\ufb01tting is performed. These new TRT tracks are then scored and arranged\naccordingly and a \ufb01nal ambiguity resolving is performed in order to reject any tracks that share too many\nstraw hits. Finally, these stand-alone TRT tracks are then stored in a special track collection.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n119\n\nAt the end of the track reconstruction process, and before any primary or secondary vertex \ufb01tters are\ncalled or other post-processing tasks are executed, the three track collections described above are merged.\nOne last ambiguity resolving is performed in order to select unique tracks from all three collections,\nalthough this is mostly for consistency since the straw hits and Si space points associated with the inside-\nout tracks have already been excluded before the outside-in track reconstruction. This merged track\ncollection is then used by the photon conversion reconstruction algorithm.\nThe overall tracking ef\ufb01ciency after all three track collections discussed above are merged, is shown\nin Fig. 6 for both the case of a 20 GeV pT single photon sample, and also for a 5 GeV single photon\nsample, which is more indicative of the case of low track momenta. Two competing effects become\napparent as one observes these two plots. The overall track reconstruction ef\ufb01ciency for conversions that\nhappen early inside the tracker, i.e. in R < 150 mm, is higher in the case of the 20 GeV pT photons than\nthat for the 5 GeV pT ones. This is a clear indication of the larger effect that bremsstrahlung losses have\non low pT tracks, especially on those that originate early inside the tracker. Furthermore it is possible\nthat, depending on the amount of the incurred losses, only part of the track will be reconstructed, i.e.\nits TRT component, with the pattern recognition failing to recover the corresponding Si clusters. The\nsmall fraction of stand-alone TRT tracks that enhance the track reconstruction ef\ufb01ciency from early\nconversions, is primarily due to this effect. On the other hand the overall track reconstruction ef\ufb01ciency\nat higher radii is much better for the case of the 5 GeV pT photons. This is due to the fact that the\nradius of curvature, being much larger for those tracks, enables them to separate from each other faster\nas they traverse the tracker under the in\ufb02uence of the applied magnetic \ufb01eld. It is therefore easier in this\ncase to distinguish the two tracks and reconstruct them during the pattern recognition stage. Figure 7\nshows the track reconstruction ef\ufb01ciency as a function of pseudorapidity, for both 20 GeV and 5 GeV\npT photons. The overall track reconstruction ef\ufb01ciency is very uniform along the whole pseudorapidity\nrange, starting only to signi\ufb01cantly fall off as one approaches the limit of the TRT pseudorapidity extent\n(|\u03b7| = 2.1). The reduction in ef\ufb01ciency observed around |\u03b7| = 1, is due to the gap at the transition from\nthe barrel to the end cap TRT. The seemingly higher overall tracking ef\ufb01ciency in this plot compared to\nthat in Fig. 6, is due to the fact that the great majority of converted photons originate from the earlier\nlayers of the Si tracker. In this region, as Fig. 6 demonstrates, the converted photon track reconstruction\nef\ufb01ciency is very high.\n3\nVertex \ufb01tting\nTrack \ufb01nding is only the \ufb01rst step in reconstructing photon conversions; the next step is being able to\nreconstruct the conversion vertex using the pair of tracks produced by the converted photon. Recon-\nstruction of the conversion vertex is quite different from \ufb01nding the primary interaction vertex, since for\nconversions additional constraints can be applied that directly relate to the fact that the converted photon\nis a massless particle. A speci\ufb01c vertex algorithm, appropriately modi\ufb01ed in order to take into account\nthe massless nature of the conversion vertex, has been developed for use by the photon conversion algo-\nrithm.\nThe vertex \ufb01t itself is based on the fast-Kalman \ufb01ltering method; different robust versions of the\n\ufb01tting functional can also be set up in order to reduce the sensitivity to outlying measurements. The\nvertex \ufb01tting procedure uses the full 3D information from the input tracks including the complete error\nmatrices [12].\n3.1\nAlgorithm description\nThe goal of a full 3D vertex \ufb01t is to obtain the vertex position and track momenta at the vertex for all\ntracks participating in the \ufb01t as well as the corresponding error matrices. From the input tracks, the\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n120\n\nhelix perigee parameters de\ufb01ning the particle trajectory along with their weight matrix are extracted as\ndescribed in the references [13, 14]. If one assumes that the particle is created at the vertex \u20d7V, then the\ntrajectory parameters qi may be expressed as a function of the vertex position and the particle momentum\nat this vertex qi = T(\u20d7V,\u20d7pi). A vertex is then obtained by minimising:\n\u03c72 =\n2\n\u2211\ni=1\n(qi \u2212T(\u20d7V,\u20d7pi))\u22a4wi(qi \u2212T(\u20d7V,\u20d7pi)),\n(4)\nwhere wi is the 5\u00d75 weight matrix from the track \ufb01t. In order to \ufb01nd the \u20d7V and \u20d7pi which minimise the\nabove \u03c72, equation 4 can be linearised at some convenient point close to the vertex as:\n\u03c72 =\n2\n\u2211\ni=1\n(\u03b4qi \u2212Di\u03b4\u20d7V \u2212Ei\u03b4\u20d7pi)\u22a4Wi(\u03b4qi \u2212Di\u03b4\u20d7V \u2212Ei\u03b4\u20d7pi),\n(5)\nwhere Di = (\u2202T(\u20d7V,\u20d7pi))/(\u2202\u20d7V) and Ei = (\u2202T(\u20d7V,\u20d7pi))/(\u2202\u20d7pi) are matrices of derivatives. A fast method to\n\ufb01nd a solution that minimises equation 5 has been proposed in the references [13,14]. It can be shown that\nthis method is completely equivalent to a Kalman-\ufb01lter based approach [15], where the vertex position\nis recalculated after every new track addition.\nIf the initial estimation of the vertex position is far from the \ufb01tted vertex, then the track perigee\nparameters and the error matrix are extrapolated to the \ufb01tted point, all derivatives are recalculated and\nthe \ufb01tting procedure is repeated. The of\ufb01cial tracker extrapolation engine, along with a magnetic \ufb01eld\ndescription based on the actual measurement of the ATLAS tracker solenoidal \ufb01eld, is used in this case.\n3.2\nVertex \ufb01t constraints\nConstraints are included in the vertex \ufb01t algorithm via the Langrange multiplier method. A constraint\ncan be viewed as a function\nA j(\u20d7V,\u20d7p1,\u20d7p2,...,\u20d7pn) = const\n(6)\nwhich is added to the \ufb01tting function of equation 4 as\n\u03c72 = \u03c72\n0 +\nNconst\n\u2211\nj=1\n\u03bbj \u00b7A2\nj\n(7)\nHere \u03c72\n0 is the function without constraints, \u03bbj is a Lagrange multiplier and j is the constraint number.\nA2\nj(...) can be linearised around some point (\u20d7V0,\u20d7p0i) to obtain\n\u03c72 = \u03c72\n0 +\nNconst\n\u2211\nj=1\n\u03bbj \u00b7(A2\nj0 +H\u22a4\nj \u03b4V +\u03b4V \u22a4Hj +F\u22a4\nij \u03b4 pi +\u03b4 p\u22a4\ni Fij)\n(8)\nwhere Hj = (\u2202A j)/(\u2202\u20d7V),Fij = (\u2202A j)/(\u2202\u20d7pi), A j0 is an exact value of A j at the (\u20d7V0,\u20d7p0i) point, \u03b4\u20d7V =\u20d7V \u2212\u20d7V0\nand \u03b4\u20d7pi = \u20d7pi \u2212\u20d7p0i.\nThe solution of equation 8 then has the form \u20d7V =\u20d7V0 +\u20d7V1, \u20d7pi = \u20d7p0i +\u20d7p1i, where \u20d7V0,\u20d7p0i is the solution\nof the corresponding problem without the constraint \u03c72 = \u03c72\n0. The second component \u20d7V1,\u20d7p1i of the\nabove solution is obtained through the normal Lagrange multiplier system of equations. In the case of\nthe conversion vertex, a single angular constraint needs to be implemented. This requires that the two\ntracks produced at the vertex should have an initial difference of zero in their azimuthal and polar angles\n\u03b4\u03c60,\u03b4\u03b80 = 0. This is a direct consequence of having an initial massless particle, but it has the advantage\nof being much easier to implement.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n121\n\nThe right-hand plot in Fig. 8 shows the reconstructed photon inverse transverse momentum after\nvertex \ufb01tting for conversions where neither of the emitted electrons suffered signi\ufb01cant bremsstrahlung\n(less than 20% of the energy of each electron is lost in the inner detector material), while the left-hand plot\nshows the transverse momentum for the cases where signi\ufb01cant bremsstrahlung energy losses occurred.\nSimilarly, the corresponding radial position resolution for conversions with/without signi\ufb01cant energy\nlosses due to bremsstrahlung is shown in Fig. 9. Single converted photons with pT = 20 GeV were used\nfor the plots above, and the emitted electron tracks were required to have at least two silicon space points.\nThe angular constraints \u03b4\u03c6,\u03b4\u03b8 = 0, implemented as described earlier, have been used throughout. The\noverall vertex reconstruction ef\ufb01ciency will be discussed in the following section. It is evident that the\npresence of bremsstrahlung signi\ufb01cantly deteriorates the performance of the vertex \ufb01tter.\n / ndf \n2\n\u03c7\n 52.36 / 6\nConstant \n 11.7\n\u00b1\n 404.7 \nMean \n 0.00008\n\u00b1\n 0.05194 \nSigma \n 0.000068\n\u00b1\n 0.002258 \n)\n-1\n (GeV\nT\n1/p\n0.03 0.04 0.05 0.06 0.07 0.08 0.09\n0.1\n0\n50\n100\n150\n200\n250\n300\n350\n400\n / ndf \n2\n\u03c7\n 52.36 / 6\nConstant \n 11.7\n\u00b1\n 404.7 \nMean \n 0.00008\n\u00b1\n 0.05194 \nSigma \n 0.000068\n\u00b1\n 0.002258 \n / ndf \n2\n\u03c7\n 26.01 / 5\nConstant \n 11.7\n\u00b1\n 310.9 \nMean \n 0.00007\n\u00b1\n 0.05141 \nSigma \n 0.000062\n\u00b1\n 0.001772 \n)\n-1\n (GeV\nT\n1/p\n0.03 0.04 0.05 0.06 0.07 0.08 0.09\n0.1\n0\n50\n100\n150\n200\n250\n300\n / ndf \n2\n\u03c7\n 26.01 / 5\nConstant \n 11.7\n\u00b1\n 310.9 \nMean \n 0.00007\n\u00b1\n 0.05141 \nSigma \n 0.000062\n\u00b1\n 0.001772 \nFigure 8: Reconstructed inverse transverse momentum from 20 GeV pT converted photons with\n(left) and without (right) signi\ufb01cant energy losses due to bremsstrahlung.\nAs a further check of the performance of the vertex algorithm described in this section, one can apply\nit to the case of K0\ns \u2192\u03c0+\u03c0\u2212decays. The absence of losses due to bremsstrahlung for the pion tracks, as\nwell as the non-zero opening angle, provide a good test scenario for the constrained vertex \ufb01tting. Instead\nof the angular constraint used in the case of the photon conversions, a straightforward mass constraint is\nimplemented in this case. Figure 10 shows the resolution of both the reconstructed 1/pT and the radial\nposition for 10 GeV pT K0\ns decays. The absence of a bremsstrahlung-related tail in the left-hand plot\ncompared to those in Fig. 8 is striking.\nIn a direct comparison to the converted photon case, Fig. 11 shows the relative 1/pT resolution, with\nand without signi\ufb01cant bremsstrahlung losses (20%) respectively, for reconstructed 20 GeV pT converted\nphotons, together with that for 10 GeV pT K0\ns decays, as a function of the radial distance from the beam\naxis. In the case of the K0\ns decays, the reconstructed momentum resolution is better than 2% irrespective\nof the radial distance from the beam axis, deteriorating only slightly as one moves away from the beam\naxis. For the case of the photon conversions though, a deterioration in the transverse momentum recon-\nstruction resolution due to the presence of bremsstrahlung losses, is clearly observable when compared\nto the K0\ns case. Due to the bremsstrahlung losses, the reconstructed 1/pT distribution has a non-gaussian\nshape, characterised by a tail towards the higher 1/pT ranges, as shown in Fig. 8. As a result, a gaussian\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n122\n\n / ndf \n2\n\u03c7\n 57.4 / 11\nConstant \n 11.7\n\u00b1\n 527.1 \nMean \n 0.138\n\u00b1\n 3.749 \nSigma \n 0.120\n\u00b1\n 5.739 \n (mm)\ntruth\n - R\nrec\nR\n-100\n-50\n0\n50\n100\n0\n100\n200\n300\n400\n500\n / ndf \n2\n\u03c7\n 57.4 / 11\nConstant \n 11.7\n\u00b1\n 527.1 \nMean \n 0.138\n\u00b1\n 3.749 \nSigma \n 0.120\n\u00b1\n 5.739 \n / ndf \n2\n\u03c7\n 15.25 / 7\nConstant \n 9.8\n\u00b1\n 302 \nMean \n 0.137\n\u00b1\n 2.083 \nSigma \n 0.128\n\u00b1\n 4.623 \n (mm)\ntruth\n - R\nrec\nR\n-100\n-50\n0\n50\n100\n0\n50\n100\n150\n200\n250\n300\n / ndf \n2\n\u03c7\n 15.25 / 7\nConstant \n 9.8\n\u00b1\n 302 \nMean \n 0.137\n\u00b1\n 2.083 \nSigma \n 0.128\n\u00b1\n 4.623 \nFigure 9: Reconstructed vertex radial positions for 20 GeV pT converted photons, compared to\ntheir true values, with (left) and without (right) signi\ufb01cant energy losses due to bremsstrahlung.\n / ndf \n2\n\u03c7\n 43.41 / -3\nConstant \n 14.1\n\u00b1\n 813.9 \nMean \n 0.000224\n\u00b1\n -0.001253 \nSigma \n 0.0002\n\u00b1\n 0.0157 \n T\ntruth\nT )/ 1/p\nrec\nT -1/p\ntruth\n(1/p\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n / ndf \n2\n\u03c7\n 43.41 / -3\nConstant \n 14.1\n\u00b1\n 813.9 \nMean \n 0.000224\n\u00b1\n -0.001253 \nSigma \n 0.0002\n\u00b1\n 0.0157 \n / ndf \n2\n\u03c7\n 47.65 / 13\np0 \n 7.7\n\u00b1\n 317.9 \np1 \n 0.010331\n\u00b1\n 0.0\n3\n \np2 \n .\n\u00b1\n .\n \n (mm)\nrec\n - R\ntruth\nR\n-100\n-80\n-60\n-40\n-20\n0\n20\n40\n60\n80\n100\n0\n50\n100\n150\n200\n250\n300\n350\n / ndf \n2\n\u03c7\n 47.65 / 13\np0 \n 7.7\n\u00b1\n 317.9 \np1 \n 0.010331\n\u00b1\n 0.08367 \np2 \n 1.32\n\u00b1\n 4.825 \nFigure 10: Overall reconstructed relative 1/pT resolution (left) and radial position resolution\n(right) for K0\ns decays (to charged pions) with pT = 10 GeV. Only tracks with at least two sili-\ncon space points are used.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n123\n\n\ufb01t performed on the core of the 1/pT distribution, will result in a worse overall reconstructed momentum\nresolution, even in the case of small bremsstrahlung losses, as Fig. 11 demonstrates. The effect is even\nmore signi\ufb01cant if one recalls that the reconstructed converted photons have a transverse momentum\nwhich is twice that of the K0\ns decays shown in the same \ufb01gure. The fact that the photon is a massless par-\nticle, resulting in an extremely small angular opening of the emitted tracks, makes it also more dif\ufb01cult\nto reconstruct accurately the position of the conversion vertex, as shown in Fig. 12.\nConversion radius (mm)\n50\n100\n150\n200\n250\n300\n350\n400\n resolution\nT\nRelative 1/p \n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n = 20 GeV \n T\n E \n\u03b3\n = 10 GeV \n T\n E \n0\ns\nK\nConversion radius (mm)\n50\n100\n150\n200\n250\n300\n350\n400\n resolution\nT\nRelative 1/p \n0\n0 01\n0.02\n0 03\n0.04\n0 05\n0 06\n0 07\n0 08\n0 09\n0.1\n = 20 GeV \n T\n E \n\u03b3\n = 10 GeV \n T\n E \n0\ns\nK\nFigure 11: Reconstructed relative 1/pT resolution as a function of radial distance from the beam\naxis for 20 GeV pT converted photons and 10 GeV pT K0\ns decays to charged pions. In the plot on\nthe left, only converted photons, where both of the daughter electrons lost less than 20% of their\nenergy due to bremsstrahlung, are shown. In the plot on the right, all conversions are included.\n4\nConversion reconstruction\nWith the three track collections and the vertex \ufb01tting algorithm described in the previous two sections,\nwe now have all the necessary tools in place in order to fully reconstruct photons which convert as far as\n800 mm away from the primary interaction point. Beyond that radius, the track reconstruction ef\ufb01ciency\ndrops off dramatically due to the lack of a suf\ufb01cient number of hits in any sub-detector to reliably recon-\nstruct the particle trajectory and accurately predict its track parameters. The conversion reconstruction\nalgorithm is run within the framework of the overall Inner Detector reconstruction software; it is one of\nthe last algorithms run during the post-processing phase. The basic components of the conversion recon-\nstruction are: the track selection and subsequent track classi\ufb01cation, the formation of pairs of tracks with\nopposite charge, the vertex \ufb01tting and reconstruction of photon conversion vertex candidates, and \ufb01nally\nthe reconstruction of single-track conversions. The conversion candidates are then stored in a separate\nvertex collection, to be retrieved and further classi\ufb01ed through matching with electromagnetic clusters\nduring the next level of the event reconstruction. In the results presented in this section, the reconstruc-\ntion ef\ufb01ciency is estimated for those photon conversions that happen as far as 800 mm away from the\nprimary interaction point, emit daughter electrons with each having at least pT = 0.5 GeV and are within\nthe |\u03b7| = 2.1 pseudorapidity range. This amounts to \u223c77% of the total photons converted inside the\nATLAS tracker volume in the case of the H \u2192\u03b3\u03b3 sample.\n4.1\nTrack selection\nOnly a fraction of the possible track pairs reconstructed by the tracking algorithms and included in the\n\ufb01nal track collection come from converted photons. Although the wrong-track combinations may be\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n124\n\nConversion radius (mm)\n50\n100\n150\n200\n250\n300\n350\n400\n(R) (mm)\n\u03c3\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n = 20 GeV \n T\n E \n\u03b3\n = 10 GeV \n T\n E \n0\ns\nK\nFigure 12: Reconstructed radial resolution as a function of radial distance from the beam axis for\n20 GeV pT converted photons and 10 GeV pT K0\ns decays to charged pions. In the case of the\nconverted photons, all daughter electrons regardless of bremsstrahlung losses have been included.\nCut\nEf\ufb01ciency\nRejection\nNo Cuts\n0.7378\n1.00\nImpact d0\n0.7334\n1.16\nImpact z0\n0.7316\n1.18\nTR ratio\n0.7119\n2.12\nTable 1: Track selection cuts: cumulative ef\ufb01ciencies and rejection rates are presented.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n125\n\nrejected later during the conversion reconstruction process or by physics speci\ufb01c analysis, it is impor-\ntant to remove them as ef\ufb01ciently as possible at an early stage, not least because of the large amount of\nCPU time involved in processing every possible track pair. Cuts on the perigee impact and longitudinal\ntrack parameters, as well as the transverse momentum, are \ufb01rst applied. Tracks that are most probably\nassociated to electrons are then selected by cutting on the probability reconstructed by using the ratio of\nhigh-threshold TRT hits over the total number of TRT hits on each track. These cuts have been tuned\nusing H \u2192\u03b3\u03b3 events, with background present due to the underlying event. All the ef\ufb01ciencies and rejec-\ntion factors due to track selection cuts which are quoted in this note refer to this physics sample. Table 1\nshows the performance of these cuts in accepting tracks produced by converted photons and rejecting\nnon-conversion related tracks. The starting ef\ufb01ciency of \u223c74% re\ufb02ects entirely the inef\ufb01ciency of re-\nconstructing all the conversion related tracks during tracking. After applying these cuts, the surviving\ntracks are then arranged into two groups with opposite charges.\n4.2\nTrack-pair selection\nAt this point in the reconstruction process, all possible pairs of tracks with opposite signs are formed and\nfurther examined. There are three possible types of track pairs:\n1. Pairs in which both tracks have Si hits;\n2. Pairs in which one of the two tracks is a stand-alone TRT track;\n3. Pairs in which both tracks are stand-alone TRT tracks.\nCut\nEf\ufb01ciency\nRejection\nPolar angle\n0.7070\n10.8\nRadial distance between \ufb01rst hits\n0.7049\n12.5\nMinimum distance\n0.6970\n16.5\nVertex radius\n0.6959\n16.6\nMinimum arc length\n0.6935\n40.3\nMaximum arc length\n0.6890\n111.6\nDistance in z\n0.6870\n111.9\nTable 2: List of cuts employed during the track-pair selection for the three possible types of track\npairs.The cumulative ef\ufb01ciencies and rejection rates are presented (see text for the de\ufb01nition of the cut\nvariables).\nIn order to reduce the combinatorial background, a series of cuts are applied during the pair for-\nmation. These are common to all three track-pair types described above, although their actual values\nmay differ. Table 2 lists those cuts along with the corresponding ef\ufb01ciencies and rejection factors for\nselecting the correct track pairs and discarding fakes resulting from wrong track combinations. The \ufb01rst\ncriterion for accepting a track pair is that the difference in polar angles between the two daughter tracks\nin a conversion should be small, based on the fact that the photon is massless. Furthermore, the distance\nbetween the \ufb01rst hits of the two tracks in the pair should be reasonably close; this is particularly true\nin the case where both of them are stand-alone TRT tracks. Finally, the distance of minimum approach\nbetween the two tracks in the pair is checked. An iterative method has been implemented that uses the\nNewton approach to \ufb01nd the set of two points (one on each track) which are closest to each other. The\ndistance of minimum approach between the two tracks is then calculated and a cut is applied to reject\nthose cases where the tracks fail to come within a speci\ufb01ed distance from each other.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n126\n\nIn order to enhance the performance of the constrained vertex \ufb01tter, it is important to begin with\na reasonable initial estimate of the vertex position. Using the perigee parameters of the two tracks in\nthe pair, the corresponding radius of curvature and the centre of curvature of the track-helix projection\nin the R \u2212\u03c6 plane can be derived. As this track-helix projection is circular in the case of a uniform\nmagnetic \ufb01eld such as that of the ATLAS tracker, the estimated vertex position can be identi\ufb01ed as\neither the point of intersection of two circles, or in the case of non-intersecting circles, as the point of\nminimum approach between two circles. If the two circles do not intersect or approach each other closer\nthan a set minimum distance then the pair is discarded. In principle, two circles may intersect at two\npoints. Since two tracks originating from a conversion vertex (or any vertex for that matter) should also\nintersect in the R\u2212z plane, the correct intersection point in the R\u2212\u03c6 plane is then chosen to be the one\nwhich is closer to the point of minimum approach of the two tracks in the R \u2212z plane. The points of\nminimum approach both in the R \u2212\u03c6 and the R \u2212z planes should clearly be suf\ufb01ciently close to each\nother. If they are separated by more than a set minimum distance, then the track pair is discarded. A\ncut is also applied on the arc length of the R \u2212\u03c6 plane projection of the two track helices between the\nline connecting the centres of curvature of the two circles and the actual intersection points. This arc\nlength is required to fall within a speci\ufb01c range which again ideally should tend to be very small. Finally,\nthe distance from the track origin (the candidate conversion vertex location) and the actual points of\nintersection should also be small. Only track pairs with intersection or minimum-approach points that\nsatisfy the above criteria are further examined. Estimating the initial vertex position allows for a larger\nnumber of quality criteria of the track pair to be used in the overall selection process. All the cuts applied\nduring this step have been tested using the 120 GeV H \u2192\u03b3\u03b3 physics sample; the cuts are tuned so that\nat least two orders of magnitude of the combinatorial background can be rejected at this point without\nsigni\ufb01cant loss in overall conversion reconstruction ef\ufb01ciency. As a consequence, cut values have been\nintentionally kept fairly loose since even correct track pairs could be characterised by less than optimal\nselection quantities. This is especially true in cases where at least one of the two tracks involved has\nonly TRT hits resulting in reduced reconstructed track parameter accuracy along the z-axis, or in cases\nwhere the tracks have suffered substantial bremsstrahlung losses during their propagation through the\nATLAS tracker. In general, the position of the initially estimated vertex falls within a few millimetres\nof the actual conversion vertex for the correct pair combinations, all deviations being due to the reasons\nmentioned just before.\nCut\nEf\ufb01ciency\nRejection\nFit convergence\n0.6870\n171.5\nFit \u03c72\n0.6710\n288.9\nInvariant mass\n0.6626\n353.9\nPhoton pT\n0.6625\n377.1\nTable 3: Post-vertex \ufb01t selection cuts: cumulative ef\ufb01ciencies and rejection rates are presented.\n4.3\nVertex \ufb01tting\nThe original track perigee assigned during the track reconstruction process is set at the primary interac-\ntion point and for the case of photon conversions, especially those that happen far inside the tracker, this\nis a rather poor assignment. Using the initial estimate for the vertex position described previously, we\ncan rede\ufb01ne the perigee at this point. The new perigee parameters need to be recomputed by carefully\nextrapolating from the \ufb01rst hit of each track in the pair to this new perigee, taking into account all the\nmaterial encountered on the way. It is these tracks with their newly computed perigee parameters that\nare passed to the vertex \ufb01tter. This also has the desirable effect of avoiding long extrapolations during\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n127\n\nthe various iterations of the vertex \ufb01tting process, which might lead to distortions due to unaccounted-for\nmaterial effects. At the end of the process the new vertex position along with an error matrix and a\n\u03c72 value for the \ufb01t are computed. A vertex candidate is then reconstructed that also contains the track\nparameters as they are rede\ufb01ned at the \ufb01tted conversion vertex. The \ufb01t is always successful in the case of\nthe correct track pairs, and it often fails otherwise. After the \ufb01t is executed, post-selection cuts on the \u03c72\nof the \ufb01t, on the reconstructed photon invariant mass and on the reconstructed photon pT can be applied,\nto reduce even further the wrong pair combinations. These are listed in Table 3.\nThe track pair selection and the vertex \ufb01tting process result in a reduction in the combinatorial back-\nground rate by more than two orders of magnitude, with only a rather small loss in overall conversion\nreconstruction ef\ufb01ciency, amounting to \u223c8% in the case of H \u2192\u03b3\u03b3 decays with mH = 120 GeV. A more\nquantitative description of the conversion reconstruction ef\ufb01ciency in such decays is presented in Sec-\ntion 5.3. At this stage of the conversion vertex reconstruction, which is still within the tracking software\nframework, vertices which come from the combinatorial background outnumber the correct conversion\nvertices by almost a factor of six. The main part of this remaining background consists of reconstructed\nvertices where at least one of the participating tracks is not an electron at all. This is primarily due to the\nrather weak particle identi\ufb01cation capabilities of the tracker without any access to the electromagnetic\ncalorimeter information. Part of this background can be reduced by some more stringent requirements on\nthe reconstructed conversion vertices after the constrained \ufb01t is preformed. But effective improvement is\nonly expected during the subsequent stages of the photon conversion reconstruction, when information\nfrom the calorimeter becomes available. Use of the electromagnetic calorimeter should also help to re-\nduce a different type of combinatorial background originating when two electrons from different sources\nare combined in order to form a track pair. Recent studies indicate signi\ufb01cant reduction of both types\nof the combinatorial background, both by applying tighter vertex selection criteria after the vertex \ufb01t is\nperformed and by using the electromagnetic calorimeter information, although they are beyond the scope\nof this note. The possibility of using the reconstructed photon pT in order to reduce the number of recon-\nstructed fake vertices, is worth investigating. Figure 13 shows the pT distribution of the reconstructed\nconversion vertices along with the distribution for fake vertices resulting from wrong combinations. It\nis clear that the latter tend to concentrate at the lower pT region. Nevertheless a \ufb01nal cut on the recon-\nstructed photon pT will not be as ef\ufb01cient as expected, due to the limited ability at present to correct\nthe reconstructed track momentum for losses due to bremsstrahlung. This is evident in the \ufb01gure when\ncomparing the reconstructed converted photon pT distribution with (top row) and without (bottom row)\nsigni\ufb01cant bremsstrahlung losses. It becomes even more striking once it is compared to the truth pT\ndistribution of the converted photon. In the remaining part of this section, the overall performance of\nthe conversion reconstruction software, without utilising the electromagnetic calorimeter information, is\nexamined in the case of single 20 GeV pT photons, where the combinatorial background is minimal.\nFigure 14 shows the track, track-pair, and vertex reconstruction ef\ufb01ciencies for conversions coming\nfrom 20 GeV pT photons as a function of both conversion radius and pseudorapidity. Both the track\nand track pair ef\ufb01ciencies shown in the \ufb01gure are measured before any of the selection criteria described\nabove are applied. The large drop in the ef\ufb01ciency at R > 400 mm is primarily due to the inef\ufb01ciency\nof reconstructing both tracks in the track pair from the photon conversion. It is noteworthy that both\nthe track and the conversion vertex reconstruction ef\ufb01ciency are essentially constant as a function of\npseudorapidity. For completeness, Fig. 15 shows the slightly different version of the left-hand plot\nin Fig. 14 as published in Ref. [6].\nFinally, Fig. 16 shows the overall vertex reconstruction ef\ufb01ciency for converted photons with low\ntransverse momenta as a function of conversion radial position. The two competing effects, the brems-\nstrahlung losses that affect more severely the low pT tracks, and the higher radii of curvature that result\nin increased resolving ability of the smaller pT tracks, that were discussed in Section 2.3, are once more\nevident here.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n128\n\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\n3\n10\nCorrect Si pairs\nWrong Si pairs\nTruth Si pairs\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\nCorrect Trt pairs\nWrong Trt pairs\nTruth Trt pairs\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\n3\n10\nCorrect ST pairs\nWrong ST pairs\nTruth ST pairs\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\n3\n10\nCorrect Si pairs\nWrong Si pairs\nTruth Si pairs\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\nCorrect Trt pairs\nWrong Trt pairs\nTruth Trt pairs\n (GeV)\nT\nReconstructed p\n0\n20 40 60 80 100120140160 180200\n1\n10\n2\n10\n3\n10\nCorrect ST pairs\nWrong ST pairs\nTruth ST pairs\nFigure 13: Transverse momentum distribution of reconstructed photon conversions for both cor-\nrect and wrong track pairs for all three types of pairs: Silicon-Silicon (Si, left column), TRT-TRT\n(Trt, centre column), and Silicon-TRT (ST, right column). In the top row all electron tracks re-\ngardless of bremsstrahlung energy losses are considered for the case of the correct track pairs. In\nthe bottom row only track pairs where both electrons have lost less than 20% of their energy due\nto bremsstrahlung are shown. For comparison the truth pT of the converted photon is also shown.\n4.4\nSingle-track conversions\nDue to conversions which decay asymmetrically (as described in Section 1.1), as well as cases where the\nconversion happens so late that the two tracks are essentially merged, there are a signi\ufb01cant number of\nconversions where only one of the two tracks from the photon conversion is reconstructed. Depending\non the photon momentum scale, these \u201csingle-track\u201d conversions become the majority of the cases for\nconversions that happen late in the tracker and especially inside the TRT. The ability of the TRT to resolve\nthe hits from the two tracks is limited, especially if those tracks do not traverse a long enough distance\ninside the tracker for them to become fully separated. As a result, only one track is reconstructed, but it\nwill still be highly desirable to recover these photon conversions.\nAt the end of the vertex \ufb01tting process, all of the tracks that have been included in a pair that success-\nfully resulted in a new photon conversion vertex candidate, are marked as \u201cassigned\u201d to a vertex. The\nremaining tracks are then examined once more on an individual basis in order to determine whether or\nnot they can be considered as products of a photon conversion. For a track to be considered, it should\nhave its \ufb01rst hit beyond the pixel vertexing layer. Furthermore, the track should be electron-like, where\nagain the probability reconstructed by using the ratio of the high threshold TRT hits over the total number\nof TRT hits (as in the initial track selection described earlier in this section, but requiring a higher value)\nis used to select likely electron tracks. At the end of this selection tracks wrongly identi\ufb01ed as emerging\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n129\n\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack\nTrack pair\nVertex\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack\nTrack pair\nVertex\nFigure 14: Conversion reconstruction ef\ufb01ciency for conversions from 20 GeV pT photons as a function\nof conversion radius (left) and pseudorapidity (right). The solid histograms show the track reconstruction\nef\ufb01ciency, the dashed histograms show the track-pair reconstruction ef\ufb01ciency, and the points with error\nbars show the conversion vertex reconstruction ef\ufb01ciency.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTrack\nTrack pair\nVertex\nFigure 15: Conversion reconstruction ef\ufb01ciency for conversions coming from 20 GeV pT photons as a\nfunction of conversion radius. The solid histogram shows the track reconstruction ef\ufb01ciency, the dashed\nhistogram shows the track-pair reconstruction ef\ufb01ciency, and the points with error bars show the conver-\nsion vertex reconstruction ef\ufb01ciency as published in Ref. [6].\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n130\n\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n = 2 GeV\n T\nE \n = 5 GeV\n T\nE \nFigure 16: Conversion vertex reconstruction ef\ufb01ciency as a function of conversion radius for photons\nwith transverse energy of 2 and 5 GeV.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTotal efficiency\nVertex reconstruction\nSingle-track conversions\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTotal efficiency\nVertex reconstruction\nSingle track conversions\nFigure 17: Reconstruction ef\ufb01ciencies for conversions from 20 GeV pT photons as a function of con-\nversion radius (left) and pseudorapidity (right). The points with error bars show the total reconstruction\nef\ufb01ciency, the solid histograms show the conversion vertex reconstruction ef\ufb01ciency, and the dashed\nhistograms show the single-track conversion reconstruction ef\ufb01ciency.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n131\n\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTotal efficiency\nVertex reconstruction\nSingle-track conversions\nFigure 18: Conversion reconstruction ef\ufb01ciency for conversions coming from 20 GeV pT photons as a\nfunction of conversion radius. The points with error bars show the total reconstruction ef\ufb01ciency, the\nsolid histogram shows the conversion vertex reconstruction ef\ufb01ciency, and the dashed histogram shows\nthe single-track conversion reconstruction ef\ufb01ciency as published in Ref. [6].\nfrom photon conversions, outnumber the actual photon conversion electron tracks, by almost a factor of\ntwo. These are tracks which are not electrons at all, misidenti\ufb01ed as such due to the inherent weakness\nof the particle identi\ufb01cation process without the presence of any information from the electromagnetic\ncalorimeter.\nA conversion vertex candidate is then reconstructed at the position of the \ufb01rst track hit. It is clear that,\nespecially in the case where the \ufb01rst hit is inside the Si part of the tracker, the position of the conversion\nvertex reconstructed in this way can be off by as much as a detector layer. This discrepancy is normally\nmuch smaller in the case of a vertex inside the TRT due to the higher straw density. On the technical\nside, this type of reconstruction requires a careful transformation of the local track parameters and error\nmatrix into global ones that are directly assigned to the newly de\ufb01ned vertex. A new vertex candidate is\nthen stored, identical in structure to the one derived from a vertex \ufb01t with the important difference that\nit has only one track assigned to it. The effect of including the single-track conversions into the overall\nconversion reconstruction ef\ufb01ciency is signi\ufb01cant as is shown in Fig. 17. The plot shows the conver-\nsion reconstruction ef\ufb01ciency for 20 GeV pT photons as a function of both radius and pseudorapidity.\nAs expected, the single-track conversions become more and more dominant at higher radial positions,\nand single-track conversions are fairly uniformly distributed across the full pseudorapidity range. For\ncompleteness, Fig. 18 shows the slightly different version of the left-hand plot in Fig. 17 as published\nin Ref. [6]. While it is not possible to reconstruct the two merged tracks in these single-track conversions,\nit should be possible to separate such cases from very asymmetric conversions with the lower-energy part-\nner of the pair not reconstructed: the transition radiation information should correspond on average to\nthat expected from two electrons and the drift-time information should be inconsistent with that expected\nfrom a single track (resulting in a signi\ufb01cant fraction of unused drift circles in the track \ufb01t).\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n132\n\n5\nPhysics applications: low-pT conversions, \u03b3/\u03c00 separation, H \u2192\u03b3\u03b3\nIn this section some interesting applications of the usage of the photon conversions are presented. Only\nresults from photon conversions where both of the daughter electron tracks have been reconstructed are\nincluded. It needs to be stressed at this point, that everything that is presented here is meant only as an\napplication example and that nofull-scale analysis has been made.\n5.1\nLow-pT photon conversions\nOf particular interest during initial data taking is the use of the reconstruction of converted photons as\na tool to obtain a measurement of the amount of material inside the ATLAS tracker, including passive\nmaterial. The abundance of low-pT neutral pions in minimum bias events represents a very rich source of\nphotons and makes this approach particularly promising. The number of photon conversions measured on\na detector volume of known x/X0 can be used as a normalisation point to extract the amount of material\nat any other location inside the detector by counting the relative number of conversions occurring in that\nportion. To obtain an unbiased map of the tracker material it is necessary to correct the measured number\nof conversions by the conversion reconstruction ef\ufb01ciency. Several methods are being investigated to\nmeasure this ef\ufb01ciency from data, e.g. embedding Monte Carlo photon conversions in data or extracting\nit from the measure of decays with similar topology like K0\ns \u2192\u03c0+\u03c0\u2212.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n0\n200\n400\n600\n800\n1000\n1200\nTruth vertices\nReconstructed vertices\nFigure 19: Reconstructed radial positions for conversions of 5 GeV pT photons. The black his-\ntogram shows the truth radial position of the conversion vertices, and the gray histogram shows\nthe radial positions of the reconstructed vertices, regardless of the bremsstrahlung losses of their\ndaughter electrons.\nFigure 19 shows the reconstructed radial positions of photon conversions with 5 GeV pT. A few\nstructures may be identi\ufb01ed: the initial peak caused by the beampipe, the three layers of the pixel detec-\ntor and then with lower resolution and signi\ufb01cance the SCT layers and the TRT. The observed smearing\nof the reconstructed position of the conversion vertex is mainly due to bremsstrahlung effects. The po-\nsition resolutions (in the radial direction) of the reconstructed conversion vertex, for photon conversions\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n133\n\nproduced by the decay of neutral pions with various energies, are shown in Fig. 20 as a function of the dis-\ntance from the beam axis. All conversions regardless of the amount of energy lost due to bremsstrahlung\nby the daughter electrons, have been used. In the case of the lower pT neutral pions, more relevant in the\ncase of minimum bias events, the radial position resolution improves somewhat, as might be expected\nfrom the larger angular separation between the produced electrons. On the other hand the use of low\npT tracks can be limited by the lower tracking ef\ufb01ciency caused by multiple scattering and especially\nbremsstrahlung.\nIn order to be able to determine the amount of material at a given position, it is necessary to compare\nthe number of reconstructed converted photons at that position with the number of conversions recon-\nstructed at the position of some reference point. This necessitates being able to resolve the position of\nthe reference, which may not be trivial.\nConversion radius (mm)\n50\n100\n150\n200\n250\n300\n350\n400\n(R) (mm)\n\u03c3\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n = 5 GeV \n T\nE \n = 10 GeV \n T\nE \n = 20 GeV \n T\nE \nFigure 20: Reconstructed radial position resolution for converted photons produced by the decay\nof neutral pions with various energies.\n5.2\n\u03b3/\u03c00 Separation\nAnother application of conversion reconstruction is the possibility of using the converted photons to\nidentify, and subsequently remove, neutral pions in which at least one of the photons resulting from\nthe decay of the pion has converted. Low multiplicity pions constitute the dominant background to the\nphoton signal after all the calorimeter-speci\ufb01c cuts have been applied during photon identi\ufb01cation [16].\nIn the case of converted photons from \u03c00 decays, additional handles could be derived as soon as their\nreconstructed transverse momentum is made available. About 30% of the neutral pions will have at\nleast one of their daughter photons converted and subsequently reconstructed as such, thus providing an\nestimate of their pT.\nThe transverse momentum reconstruction resolution is important when attempting to use conversions\nto identify low pT neutral pions. The ratio of the reconstructed pT of a converted photon inside the\nATLAS tracker to the ET measured by the electromagnetic calorimeter is different for photons from \u03c00\ndecays and for prompt photons. Figure 21 shows such distributions for the case of converted 20 GeV\npT single photons and converted photons from the decay of a 20 GeV pT neutral pion. The photon pT\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n134\n\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nNo brem cleaning\n\u03b3\n0\n\u03c0\n 0.6\n<\n| \n\u03b7\n|\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nNo brem cleaning\n\u03b3\n0\n\u03c0\n 1.5\n<\n | \n\u03b7\n0.6 < |\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\nNo brem cleaning\n\u03b3\n0\n\u03c0\n 2.0\n<\n | \n\u03b7\n1.5 < |\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\nbrem < 20%\n\u03b3\n0\n\u03c0\n 0.6\n<\n|\u03b7\n|\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nbrem < 20%\n\u03b3\n0\n\u03c0\n 1.5\n<\n | \n\u03b7\n0.6 < |\nT\n/E\nT\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8 2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nbrem < 20%\n\u03b3\n0\n\u03c0\n 2.0\n<\n | \n\u03b7\n1.5 < |\nFigure 21: pT/ET distribution for 20 GeV pT converted photons and for photons from a 20 GeV \u03c00.\nThe top row shows the distribution for all photons irrespective of the daughter electron energy losses\ndue to bremsstrahlung. The bottom row shows the distribution only for those photon conversions in\nwhich the daughter electrons have lost less than 20% of their energy to bremsstrahlung. Three different\npseudorapidity ranges are shown, corresponding to the barrel (left), the barrel/end-cap transition (centre)\nand the end-cap (right) regions.\nshown is that reconstructed by the conversion algorithm, while the ET shown is taken from the truth value\nfrom the simulation. Three regions in pseudorapidity are shown separately, namely those corresponding\napproximately to the tracker barrel, barrel/end-cap transition and end-cap regions. The top row of plots\ninclude all converted photons, irrespective of losses due to bremsstrahlung of their daugter electrons,\nwhile the bottom row has only those converted photons where both of their daughter electrons have lost\n< 20% of their energy due to bremsstrahlung. Clearly the distinction between conversions from single\nphotons and conversions from photons produced in neutral pion decays is less pronounced in the case\nof strong bremsstrahlung losses, although an effective bremsstrahlung recovery mechanism should be\nable to signi\ufb01cantly improve the separation between the two distributions. A certain degredation is also\nevident as we move from the barrel to the end-cap tracker, due to the less accurate reconstruction of the\ntransverse momentum of the daughter electron tracks at higher pseudorapidities. Figure 22 shows the\nfraction of remaining \u03c00 particles as a function of converted photon ef\ufb01ciency, both with and without\nsigni\ufb01cant losses due to bremsstrahlung. The overall \u03c00 rejection corresponding to a photon acceptance\nof 90 % for the three different pseudorapidity regions, as described above, is shown in Fig. 23. Again\na distinction is made for the cases with and without signi\ufb01cant energy losses due to bremsstrahlung.\nAlthough reduced, the discriminatory power against \u03c00 is signi\ufb01cant even when severe losses due to\nbremsstrahlung are present.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n135\n\n efficiency\n\u03b3\n0\n0.2\n0.4\n0.6\n0.8\n1\n efficiency\n0\n\u03c0\n1 - \n0\n0.2\n0.4\n0.6\n0.8\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\n efficiency\n\u03b3\n0\n0.2\n0.4\n0.6\n0.8\n1\n efficiency\n0\n\u03c0\n1 - \n0\n0.2\n0.4\n0.6\n0.8\n1\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\n| < 0.6 \n\u03b7\n |\n| < 1.5\n\u03b7\n 0.6 < |\n| < 2.0\n\u03b7\n 1.5 < |\nFigure 22: Fraction of remaining \u03c00 as a function of converted photon ef\ufb01ciency with (left) and without\n(right) signi\ufb01cant bremsstrahlung losses of the corresponding daughter electrons, for three pseudorapid-\nity regions as described in the text.\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n rejection\n0\n\u03c0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nbrem < 20%\nno brem cleaning\nFigure 23: Rejection factors against \u03c00 corresponding to photon acceptance ef\ufb01ciencies of 90 %, with\nand without signi\ufb01cant energy losses due to bremsstrahlung for the three pseudorapidity regions de-\nscribed in the text. The results are shown for converted photons and \u03c00 with a pT of 20 GeV.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n136\n\n5.3\nH \u2192\u03b3\u03b3 decays\nAs mentioned in the introduction, the recovery of converted photons is of primary importance in the\nsearch for physics processes in which photons are the primary decay product. In particular, accurate\nreconstruction of the H \u2192\u03b3\u03b3 process is heavily dependent on the ability to properly reconstruct photon\nconversions for the following reasons:\n1. A signi\ufb01cant fraction of photons will convert inside the ATLAS tracker volume. Ef\ufb01cient recon-\nstruction of these photons will enhance the signal statistics for this process.\n2. Photon identi\ufb01cation, using a combination of inner detector and electromagnetic calorimeter se-\nlection criteria, will be improved with effective conversion reconstruction. Even single-track con-\nversions will be useful in this context.\n3. The electromagnetic calorimeter calibration will be signi\ufb01cantly enhanced when converted pho-\ntons are identi\ufb01ed as such. Again, even single-track conversions will be very useful.\n4. The ability to accurately point back to the mother Higgs particle is dramatically enhanced for the\ncase of reconstructed converted photons where both daughter electron tracks are properly recov-\nered.\nIt is important, therefore, to investigate the performance of the conversion reconstruction strategy in\nthis case, not least because of the higher transverse momenta which characterise the photons produced\nin H \u2192\u03b3\u03b3 decays. Decays to photon pairs from a Standard Model Higgs boson with 120 GeV mass have\nbeen studied throughout this section.\nConversion radius (mm)\n100\n200\n300\n400\n500\n600\n700\n800\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack\nTrack pair\nVertex\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTrack\nTrack pair\nVertex\nFigure 24: Track, track-pair, and vertex reconstruction ef\ufb01ciencies for converted photons from H \u2192\u03b3\u03b3\ndecays with mH = 120 GeV, as a function of radial distance from the beam axis (left) and pseudorapidity\n(right). The ef\ufb01ciency reduction at |\u03b7| \u223c0.8, is due to the track reconstruction inef\ufb01ciencies in the gap\nregion between the TRT barrel and end-cap detectors.\nFigure 24 shows the converted photon reconstruction ef\ufb01ciency as a function of both radius and pseu-\ndorapidity for photons coming from H \u2192\u03b3\u03b3 decays. The reduced ef\ufb01ciency at higher radii is primarily\ndue to the smaller distance which the produced electron tracks travel inside the magnetic \ufb01eld, reducing\nthe separation between them. The conversion reconstruction ef\ufb01ciency as a function of pseudorapidity is\nfairly \ufb02at, independent of the material distribution inside the ATLAS tracker, as expected. The effect of\nincluding the single-track conversions into the overall conversion reconstruction ef\ufb01ciency is also signif-\nicant for H \u2192\u03b3\u03b3 decays with large conversion radius and over the full pseudorapidity range, as shown\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n137\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nTotal efficiency\nVertex reconstruction\nSingle track conversions\nFigure 25: Reconstruction ef\ufb01ciencies for converted photons from H \u2192\u03b3\u03b3 decays with mH = 120 GeV,\nas a function of conversion radius (left) and pseudorapidity (right). The points with error bars show the\ntotal reconstruction ef\ufb01ciency, the solid histograms show the conversion vertex reconstruction ef\ufb01ciency,\nand the dashed histograms show the single-track conversion reconstruction ef\ufb01ciency.\n / ndf \n2\n\u03c7\n 83.61 / 10\nConstant \n 11.0\n\u00b1\n 592.7 \nMean \n 0.15\n\u00b1\n 5.63 \nSigma \n 0.124\n\u00b1\n 6.924 \n (mm)\ntruth\n - R\nrec\nR\n-100\n-50\n0\n50\n100\n0\n100\n200\n300\n400\n500\n600\n / ndf \n2\n\u03c7\n 83.61 / 10\nConstant \n 11.0\n\u00b1\n 592.7 \nMean \n 0.15\n\u00b1\n 5.63 \nSigma \n 0.124\n\u00b1\n 6.924 \nAll\nBremLoss < 20%\n 20%\n\u2265\nBremLoss \nFigure 26: Reconstructed vertex radial position resolution (in mm) for converted photons from H \u2192\u03b3\u03b3\ndecays with mH = 120 GeV. For comparison, the two cases where the participating tracks have lost\n> 20% (< 20%) of their energy due to bremsstrahlung are also shown separately.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n138\n\n / ndf \n2\n\u03c7\n 14.64 / 7\nConstant \n 13.0\n\u00b1\n 605.6 \nMean \n 6.504e-06\n\u00b1\n -2.023e-05 \nSigma \n 0.0000084\n\u00b1\n 0.0003217 \n (rad)\n\u03b8\n\u2206\n-0.006 -0.004 -0.002\n0\n0.002\n0.004\n0.006\n0\n100\n200\n300\n400\n500\n600\n / ndf \n2\n\u03c7\n 14.64 / 7\nConstant \n 13.0\n\u00b1\n 605.6 \nMean \n 6.504e-06\n\u00b1\n -2.023e-05 \nSigma \n 0.0000084\n\u00b1\n 0.0003217 \nFigure 27: Reconstructed polar angle resolution (in radians) for converted photons from H \u2192\u03b3\u03b3 decays\nwith mH = 120 GeV.\nin Fig. 25. The reconstructed conversion vertex radial position resolution is shown in Fig. 26 for recon-\nstructed converted Higgs photon vertices where the participating tracks have lost > 20% (< 20%) of their\nenergy due to bremsstrahlung, along with all vertices put together. The results are fairly comparable to\nthe ones shown for single photons in Section 4, despite the fact that the resulting photon momenta in this\ncase are on average at least a factor of two bigger and the fact that the presence of the underlying event\ncauses additional complications for the track reconstruction.\nOf particular interest for the reconstruction of the Higgs invariant mass is the resolution on the mea-\nsurement of the polar angle of the reconstructed converted photon. This is shown in Fig. 27 for the case\nof conversions where both electron tracks have Si hits. These account for \u223c58% of the reconstructed\nconverted photons inside the ATLAS tracker volume. The resulting resolution is of the order of 0.5 mrad\nregardless of the transverse momentum of the converted photon. This is an improvement of at least an or-\nder of magnitude with respect to the polar angle resolution derived using the electromagnetic calorimeter\nresponse [6].\n6\nSummary and conclusions\nThis note has described and presented a detailed performance evaluation of the conversion reconstruc-\ntion algorithm which will be used to reconstruct and study early data at the LHC. All three types track\ncollections delivered by the tracking software have been combined and used. A dedicated vertex \ufb01t al-\ngorithm has been developed for the purpose of reconstructing converted photon vertices. Special care\nhas been given to \ufb02agging possible conversions where only one of the produced electron tracks has been\nreconstructed (or where the two tracks are merged into one in the case of late conversions). Combining\nall of these tools, a reconstruction ef\ufb01ciency of almost 80% has been achieved for conversions that occur\nup to a distance of 800 mm from the beam axis. A transverse momentum reconstruction resolution of the\norder of 5% has been found for converted single photons of various energies. This has also been shown\nto be valid for the case of photons produced by the decay of a Standard Model Higgs boson with a mass\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n139\n\nof 120 GeV, as well as for those coming from the decay of low pT neutral pions. The position resolution\nis found to be better than 5 mm in the radial direction, making this a promising method for mapping the\nmaterial inside the ATLAS inner detector. The angular resolution is found to be below 0.6 mrad, giving\neffective pointing to converted photons from physics processes.\nReferences\n[1] C. D. Anderson, Phys. Rev. 41 (1932) 405.\n[2] H. A. Bethe and W. Heitler, Proc. R. Soc. A 146 (1934) 83.\n[3] Y. S. Tsai, Rev. Mod. Phys. 46 (1974) 815.\n[4] S. R. Klein, Radiat. Phys. Chem. 75 (2006) 696.\n[5] Particle Data Group, J. Phys. G: Nucl. Part. Phys. 33 (2006) 263.\n[6] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\n2008 JINST 3 S08003 (2008).\n[7] ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this vol-\nume.\n[8] T. Cornelissen et al., ATL-SOFT-PUB-2007-007 (2007).\n[9] R. Duda and P. Hart, Comm. ACM 15 (1972).\n[10] M. Hansroul et al., Nucl. Inst. and Meth. A270 (1988) 498.\n[11] I. Gavrilenko, ATL-INDET-97-165 (1997).\n[12] V. Kostyukhin, ATL-PHYS-2003-31 (2003).\n[13] P. Billoir, R. Fruhwirth and M. Regler, Nucl. Inst. and Meth. A241 (1985) 115.\n[14] P. Billoir and S. Qian, Nucl. Inst. and Meth. A311 (1992) 139.\n[15] R. Fruhwirth, Nucl. Inst. and Meth. A262 (1987) 444.\n[16] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Photons, this volume.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF PHOTON CONVERSIONS\n140\n\nReconstruction of Low-Mass Electron Pairs\nAbstract\nThis note discusses the reconstruction of J/\u03c8 and \u03d2 decays to electron pairs\nbased on ATLAS Monte Carlo simulated signal and background samples. The\npossible trigger strategies are described, one geared to select two low-energy\nelectromagnetic objects in direct production, the second one taking advantage\nof the possible presence of a muon in the \ufb01nal state in b\u00afb production followed\nby the decay of one b-quark to J/\u03c8 + X. The low-energy electrons are re-\nconstructed using a dedicated algorithm seeded by a track reconstructed in the\ninner detector and identi\ufb01ed combining information from the inner detector\nand the electromagnetic calorimeter. The performance of this algorithm is pre-\nsented and the potential of using such events for early LHC data studies is\ninvestigated.\n1\nIntroduction\nWhen switched on, the LHC will produce charm and beauty quarks in abundance which will be col-\nlected by the ATLAS experiment [1], even during the low luminosity periods. The number of produced\nquarkonium states such as J/\u03c8 and \u03d2, important for many physics studies, will be equally numerous.\nOn average, one in every hundred collisions will contain a b\u00afb pair. The large b\u00afb cross-section and the\nhigh luminosity of the machine give therefore a high rate for B-hadrons, making B-physics an interesting\nand competitive subject at the LHC. Low energy resonances, such as J/\u03c8 and \u03d2 will be one of the main\nsources of isolated electrons in the early data. Both the J/\u03c8 and \u03d2 signal samples are important for un-\nderstanding the production of prompt quarkonia. But there is another aspect which is the main focus of\nthis note: these samples are ideal to study the performances of trigger and of\ufb02ine reconstruction at low\nenergies as well as being potentially useful for the in-situ calibration of the electromagnetic calorimeter.\nThis note is organised as follows: Section 2 gives a description of the data-samples used in this\nnote, Section 3 details the trigger selections, and Section 4 describes the of\ufb02ine electron reconstruction\nand identi\ufb01cation procedure. Finally, in Section 5, the physics potential of these channels is explored\nwith initial data, assuming an instantaneous luminosity of 1031 cm\u22122 s\u22121 and an integrated luminosity\nof 100 pb\u22121.\n2\nData samples\nThe different data samples used in this study are summarised in Table 1. The total cross-sections for\ncharm production at LHC is 7.8 mb and the one for bottom production is 0.5 mb. Quarkonium production\nwas originally described by the colour singlet model which failed to reproduce the direct J/\u03c8 production\ncross section measured by the CDF experiment [2]. The colour octet model [3] was proposed as a\nsolution to this quarkonium de\ufb01cit. Direct quarkonia Monte Carlo samples comprise of directly produced\nJ/\u03c8 or \u03d2 in colour singlet and octet states, along with promptly-produced \u03c7\u2019s, which decay into J/\u03c8\u2019s or\n\u03d2\u2019s [4] [5]. The inclusive production cross sections of J/\u03c8 and \u03d2 are respectively \u223c90\u00b5b and \u223c0.7\u00b5b.\nA minimum transverse momentum of 3 GeV and a pseudo-rapidity \u03b7 <2.7 are required for the two\nelectrons. The resulting cross sections for the used data samples are respectively \u223c117nb and \u223c47nb.\nAnother sample used in this study is originated from Drell-Yan production. In addition to the electron\n\ufb01lter also applied to the J/\u03c8 and \u03d2 samples, the generated di-electron invariant mass mee(DY) has to be\n1 < mee(DY) < 60 GeV. Studies also include non-diffractive minimum-bias events with a total assumed\ncross section of 70 mb.\n141\n\nTable 1: Data samples: process, production cross-section and total number of events available.\nProcess\nCross section\nNumber of events (\u00d7103)\nDirect production\npp \u2192J/\u03c8(e3e3)X\n116.3 nb\n160\npp \u2192\u03d2(e3e3)X\n47.6 nb\n150\npp \u2192Drell-Yan(e3e3)\n2.9 nb\n250\nminimum-bias\n70 mb\n1,000\nb\u00afb production\nbBd \u2192\u00b5(6)J/\u03c8(e2e2)X\n0.2 nb\n50\nFor the production via the decay of b\u00afb, only J/\u03c8 events are considered. The signal sample is made\nof bBd \u2192\u00b5(6)J/\u03c8(ee) + X events, where the \u00b5(6) refers to a muon coming from the b quark with a\ntransverse momentum above 6 GeV. A minimum transverse momentum threshold of 2 GeV is applied to\nthe generated electrons.\nThe simulated data have been produced for the ATLAS Computing System Commissioning [6]. All\nsamples have been generated using the Pythia 6.403 [7] Monte Carlo event generator. More details on\nthe Monte Carlo generators used can be found in [8]. Data have been simulated using GEANT4 [9], with\nthe ATLAS software ATHENA [10], with a realistic geometry including material distortions in front of\nthe electromagnetic calorimeter. Studies presented here correspond to very early data taking, with an\ninitial luminosity of 1031 cm\u22122 s\u22121. No pile-up has been included. Detailed information about these\nsamples is given in Table 1.\nSignal electrons come from J/\u03c8 and \u03d2 decays1. The background electrons arise from other direct\n(b \u2192e, c \u2192e) and cascade (b \u2192c \u2192e) semileptonic decays of meson with an electron in the \ufb01nal\nstate and b \u2192\u03c4 \u2192e\u2212decays2. Other background electrons arise from \u03c00 Dalitz decays, \u03b3-conversions\noccurring in the inner detector and decays of light hadrons. Distributions of generator level transverse\nmomentum pT and pseudorapidity \u03b7 for electrons and pions are shown for the pp \u2192J/\u03c8 (ee) + X\nsample on Fig. 1. The \u03b7 distribution of electrons from conversion re\ufb02ects the amount of material in front\nof the electromagnetic calorimeter. Ref. [13] details the reconstruction of such electrons. Table 2 gives\nthe mean pT for each population in the different samples.\nFig. 2 shows the distance \u2206R, at generator-level, between the two signal electrons from J/\u03c8. On av-\nerage, electrons from direct reconstructed J/\u03c8(e3e3) are separated by \u2206R = 0.7, and are restricted from\nbeing produced at separations larger than 1.1. Electrons from J/\u03c8 originated from B hadrons on the con-\ntrary are on average more collimated, with a mean \u2206R = 0.6 and with a larger spread. In comparison, the\nhigher mass of of \u03d2 requires the electrons to have a much larger opening angle, with a broad distribution\nin \u2206R, the two electrons being almost back-to-back.\n3\nTrigger selection\n3.1\nGeneral requirements\nATLAS has a three level trigger system which reduces the 40 MHz bunch crossing rate to about 200 Hz\nto be recorded. The \ufb01rst level (L1) is a hardware-based trigger which makes a fast decision (in 2.5 \u00b5s)\nabout which events are of interest for further processing, with a rate reduced down to below 40 kHz in its\n1The corresponding branching ratio [11] is Br(J/\u03c8 \u2192ee) = (5.94\u00b10.06)% and Br(\u03d2 \u2192ee) = (2.38\u00b10.11)%.\n2The corresponding branching ratios [12] are Br(b \u2192l\u2212) = (10.71\u00b10.22)%, Br(b \u2192c \u2192l+) = (8.01\u00b10.18)%, Br(b \u2192\n\u00afc \u2192l\u2212) = (1.62+0.44\n\u22120.36)%, Br(b \u2192\u03c4 \u2192e\u2212) = (0.419\u00b10.055)% and Br(b \u2192(J/\u03c8,\u03d2) \u2192ee) = (0.072\u00b10.006)%.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n142\n\nFigure 1: Normalised distributions of generator-level transverse momentum pT (left) and pseudorapidity\n|\u03b7| (right) in the pp \u2192J/\u03c8X sample are shown for signal electrons (hatched histograms), electrons from\nconversions (dotted line histogram), and pions (plain histograms).\nR \n\u2206\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\nATLAS\nR \n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\nATLAS\nR \n\u2206\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\nATLAS\nFigure 2: Distance \u2206R at generator-level between the two signal electrons for direct J/\u03c8 events (top left),\ndirect \u03d2 (top right) and J/\u03c8 from b decays (bottom).\ninitial implementation. Coarse granularity information from the calorimeter and muon trigger systems\nare used at this stage of the trigger to identify regions of the detector which contain interesting signals\ncorresponding to, for instance, electrons, muons, taus, and jets. These are called \u201cRegions of Interest\u201d\n(RoIs) and are used to guide the later stages of the trigger reconstruction. The high level trigger (HLT)\nis software-based and is split into two levels. At level 2 (L2) the full granularity of the detector is used\nto con\ufb01rm the L1 signals and then to combine information from different sub-detectors within the RoIs\nidenti\ufb01ed at L1. Fast algorithms are used for the reconstruction at this stage and the rate is reduced to\n1\u22122kHz with an average execution time of about 40ms. Lastly, at the event \ufb01lter (EF), the whole event is\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n143\n\nTable 2: Mean generator-level pT (in GeV) for electrons and pions having pT > 2 GeV. Typical RMS on\ndistributions of Fig. 1 is 1.4 GeV.\nsample\nelectrons\npions\nsignal\nB and D hadrons\n\u03b3-conversions and \u03c00 Dalitz\npp \u2192J/\u03c8X\n4.7\n4.7\n4.3\n4.4\npp \u2192\u03d2X\n4.8\n4.5\n4.0\n4.2\npp \u2192Drell-Yan\n-\n5.9\n4.9\n4.7\nminimum bias\n-\n4.2\n4.2\n4.2\nbBd \u2192\u00b5(6)J/\u03c8X\n6.3\n5.5\n4.9\n5.1\navailable and \u201cof\ufb02ine-like\u201d algorithms are used along with better alignment and calibration information\nto form a \ufb01nal decision whether or not an event is accepted. With an execution time of about 4s, the rate\nis reduced to 200Hz.\nThe expected ATLAS trigger performance at an initial luminosity of 1031 cm\u22122 s\u22121 is studied using\nthe samples described in the previous section. Two trigger menus are considered here: the \ufb01rst is a\npurely electromagnetic menu which could be used only for early data taking; the second menu relies on\nthe B-trigger and could be extended for data taking at low luminosity 1033 cm\u22122 s\u22121. More details about\nthe overall trigger strategy, in particular for these channels, can be obtained in [14] and [15].\n/MeV\nT\n p\nhigh\ne\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n3\n10\n\u00d7\n/MeV\nT\n p\nlow\ne\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n3\n10\nATLAS\n/MeV\nT\n p\nhigh\ne\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n3\n10\n\u00d7\n/MeV\nT\n p\nlow\ne\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n3\n10\nATLAS\nFigure 3: Distribution of the generator-level transverse momentum of the less energetic electron versus\nthe transverse momentum of the most energetic electron in the direct J/\u03c8 (left) and \u03d2 (right) decays.\n3.2\nElectron selection\nJ/\u03c8 \u2192ee and \u03d2 \u2192ee events are very demanding for the trigger system. Due to their relatively low\nmasses, the electrons produced in the J/\u03c8 and \u03d2 decays are very soft. Figure 3 shows the distribution of\nthe transverse momentum of the less energetic electron versus the transverse momentum of the most en-\nergetic electron in J/\u03c8 (left) and \u03d2 (right) decays [5]. This poses a huge challenge for the L1 calorimeter\ntrigger. Its performance at the low-energy end is limited by the noise of typically 0.5 GeV per RoI and a\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n144\n\n3 GeV threshold is the limit of what is feasible for the L1 trigger. The 6.5 kHz L1 output rate for 2EM3\n(corresponding to two L1 electromagnetic clusters greater than 3 GeV ) makes it one of the biggest con-\nsumers of the total bandwidth [14]. The strategy to trigger on J/\u03c8 and \u03d2 \u2192ee events is based on low ET\nL1 electromagnetic RoIs and further electron identi\ufb01cation using calorimeter and inner detector informa-\ntion at the HLT. The inner detector tracks are reconstructed in regions of half-size \u2206\u03b7 \u00d7\u2206\u03d5 = 0.1 \u00d7 0.1\naround these electromagnetic RoIs.\nFigure 4 shows the distribution of the invariant mass of the pairs of electrons for signal and back-\nground events after the L1 selection. The J/\u03c8 and \u03d2 samples can be easily recognised by the resonance\npeaks. Table 3 gives the number of events which are expected to pass the L1 selection. The L1 trigger\nef\ufb01ciency is calculated with respect to the number of generated events, which in particular include a\nrequirement on the minimum transverse momentum of 3 GeV on each electron as detailed in Section2.\nThe selected events are in the tail of the J/\u03c8 distribution (see Figure 3). Additionally the requirement\nof ET > 3 GeV at L1 implies ET >= 4 GeV thus starting to cut into the peak of the \u03d2 distribution. The\nef\ufb01ciency of this level is measured to be 27% for J/\u03c8 and \u03d2 events. About 43% of Drell-Yan events\npass the L1 in the generated mass range. A total of 4.2\u00d7106 J/\u03c8 \u2192ee, 1.2\u00d7106 \u03d2 \u2192ee and 0.12\u00d7106\nDrell-Yan events are expected after this level. For the minimum bias sample, the enhancement above\n (GeV)\nee\nm\n0\n5\n10\n15\n20\n25\n30\n35\n40\n (nb/GeV)\nee\n/dm\n\u03c3\nd\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nATLAS\nFigure 4: Expected differential cross section for low-mass electron pairs using the 2EM3 trigger menu\nitem after L1 selection for J/\u03c8 decays (dotted histogram), \u03d2 decays (dashed histogram), Drell-Yan pro-\nduction (solid histogram) and expected background (full circles). The invariant mass is reconstructed\nwith calorimeter only information available at L1.\n6 GeV arises from the requirement of the presence of two L1 clusters with energy greater than 3GeV.\nStudies and implementation of an ef\ufb01cient HLT selection, based on the selection of two electrons with\nET > 5 GeV (2e5 menu) is ongoing. Typical rates are expected to be \u223c40 Hz at L2 and 6 Hz at EF.\nTable 3: Performance of the 2EM3 trigger at the luminosity of 1031 cm\u22122 s\u22121 for the direct production\nof J/\u03c8, \u03d2, Drell-Yan and background events. For signal events the ef\ufb01ciency \u03b5 is given as well as the\nnumber of expected events. For background the rate is provided. Quoted errors are statistical only.\nJ/\u03c8\n\u03d2\nDrell-Yan\nbackground\n\u03b5 (%)\n106 ev /\n\u03b5 (%)\n106 ev /\n\u03b5 (%)\n106 ev\nRate\n100 pb\u22121\n100 pb\u22121\n100 pb\u22121\n(Hz)\nL1\n27.4\u00b10.3\n4.17\u00b10.04\n27.3\u00b10.3\n1.22\u00b10.01\n43.0\u00b10.5\n0.12\u00b10.001\n6500\u00b127\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n145\n\n3.3\nB-physics\nThe B-trigger is expected to account for 5-10% of the total ATLAS trigger resources. The trigger for B-\nphysics is initiated by a single- or a di-muon selection at L1. At 1031 cm\u22122 s\u22121, a threshold pT > 4 GeV\nwill be used, rising to about 6 GeV at 1033 cm\u22122 s\u22121 to match the rate capabilities of the HLT. For\n\ufb01nal states such as the bBd \u2192\u00b5(6)J/\u03c8X events, inner detector tracks are combined to reconstruct the\nJ/\u03c8 particles. Two different strategies are used for \ufb01nding the tracks, depending on luminosity [16].\nAt 1031 cm\u22122 s\u22121 full reconstruction over the whole inner detector can be performed, since the L1\nmuon rate is comparatively modest, while at higher luminosities reconstruction will be limited to L1\nelectromagnetic RoIs with ET > 3 GeV. For the bBd \u2192\u00b5(6)J/\u03c8X events the L1 trigger ef\ufb01ciency\nis \u223c88%. This latter approach has lower ef\ufb01ciency for selecting the signal but requires fewer HLT\nresources for a \ufb01xed L1 rate. If one combines triggers for electromagnetic \ufb01nal states and pre-scaled\nsingle muon-triggers needed for trigger ef\ufb01ciency measurements, the overall rate for B-physics triggers\nis approximately 20 Hz at 1031 cm\u22122 s\u22121.\n4\nElectron reconstruction and identi\ufb01cation\nThe standard electron reconstruction procedure [17], optimised for high energetic electrons, is based on\ncalorimeter clusters to which tracks are associated in a second step. An alternative procedure will be\nused for the reconstruction of electrons originated from J/\u03a8 and \u03d2 decays. It takes full advantage of the\ntracking capabilities of the inner detector as well as the granularity of the electromagnetic calorimeter.\nThe method is seeded by a track which is extrapolated into the electromagnetic calorimeter and allows\nfor ef\ufb01cient reconstruction of electrons in jets for b-tagging purpose (cf. [18]) and very low pT electrons.\n4.1\nElectron reconstruction\nThe track-based algorithm could handle any charged track particles with a transverse momentum greater\nthan 0.5 GeV. Still, as it will be detailed further, in order to reduce the amount of fake candidates, in\nparticular in jets, only particles with pT > 2 GeV are considered. The inner detector coverage goes to\npseudorapidity values up to 2.5, except for the transition radiation tracker (TRT) which extends up to\n2. This subdetector being crucial nonetheless in the identi\ufb01cation procedure but also to preselect tracks,\nthe electron reconstruction is limited to |\u03b7| < 2. Strict selection criteria, similar to the b-tagging ones,\nare required to have at least nine precision hits (pixel and silicon detectors); at least two hits in the pixel\ndetector and at least one hit in the vertexing layer. The TRT plays a central role in electron identi\ufb01cation.\nSelection criteria are thus required to have at least 20 hits in the TRT and at least one high energy hit\n(HTR hit) in the TRT detector along the track. After these criteria, only 50% of initial tracks remain.\nAll the tracks that pass these criteria are extrapolated [19] to the second sampling of the electromagnetic\ncalorimeter. Around this position a cluster of size \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.075 \u00d7 0.125 (3 \u00d7 5 in units of cells in\nthe middle sampling) in the barrel and \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.125 \u00d7 0.125 (5 \u00d7 5) in the end-caps is built. The\ncell with the maximum energy is searched within a small \u03b7 and \u03c6 window, 0.075\u00d70.075 in the middle\nlayer, around the extrapolation point. Shower shapes are estimated with respect to this position.\nSince the algorithm is the same as for the reconstruction of electrons in jets [18], a set of preselection\ncriteria are applied to decrease the number of fake candidates:\n- the fraction of energy reconstructed in the core of the shower in the \ufb01rst sampling E1(core)/E >0.03;\n- the fraction of energy reconstructed in the core of the shower in the third sampling E3(core)/E <0.5;\n- the ratio of the energy E reconstructed in the electromagnetic calorimeter over the momentum p\nreconstructed in the inner detector E/p >0.7.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n146\n\nThe above selection rejects about 5% of signal electrons but also ensures that the shower shapes in the\n\ufb01rst sampling are correctly de\ufb01ned. Finally, candidates which are also reconstructed as originating from\na conversion [13] are vetoed, corresponding to a loss of 1-3% of signal electrons and pions.\nBy \ufb01tting electron tracks in such a way as to allow for bremsstrahlung, it is possible to improve\nthe reconstructed track parameters, as shown in Fig. 5 on the ratio between the reconstructed and the\ntrue momentum for electrons. These algorithms rely exclusively on the inner detector information. The\nmethod of dynamic-noise-adjustment extrapolates track segments to the next silicon layer. If it \ufb01nds\na signi\ufb01cant \u03c72 contribution, compatible with an energy loss by the track due to bremsstrahlung, the\nfraction of radiated energy is estimated and a corresponding additional noise term is included in the\nKalman \ufb01lter [1] [20].\n|\n\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nE(rec)/E(true)\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\nATLAS\nFigure 5: Left : ratio of the reconstructed to true momentum for electrons, for the default Kalman \ufb01lter\n(hatched histogram) and for bremsstrahlung recovery algorithm (plain histogram) in the J/\u03c8 samples.\nRight : ratio of the reconstructed to true energy versus \u03b7 for electrons.\nPosition and energy corrections are applied in the precise reconstruction of the electromagnetic clus-\nter and are described in [21]. These corrections have been tuned for high energy clusters and are not\noptimal for low energy electrons. Moreover, they have been determined with electron samples simulated\nwith a detector taken to be perfectly aligned. In Fig. 5 the ratio between the reconstructed and the true\nenergy is shown as a function of |\u03b7| for signal electrons from J/\u03c8 samples. It can be seen that these\ncorrections over-estimate the electron energy except in the crack region where the effect of extra-material\nin front of the calorimeter is important. Work is on going to improve the energy reconstruction at low\nenergy.\nBy default the four-momentum of an electron is de\ufb01ned as the energy reconstructed in the calorime-\nter, whereas direction is taken from the associated track. As in this note the main physics processes\nresult in electron transverse momenta of less than 15 GeV, the tracker momentum is used instead of the\nenergy unless stated otherwise. Future developments in ATLAS will ensure an optimal combination of\ncalorimeter and tracker measurements in the energy de\ufb01nition.\n4.2\nElectron identi\ufb01cation\nThe most common background processes for producing electron-like showers in the calorimeters were\ndescribed in section 2. Because the development of showers is different for electrons and hadrons, the\nelectron identi\ufb01cation algorithm incorporates variables that describe the shower shapes, quality of the\nmatch between the track and its corresponding cluster and the fraction of high threshold hits in the\ntransition radiation tracker.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n147\n\n4.2.1\nIdenti\ufb01cation of isolated electrons\nThe identi\ufb01cation for isolated electrons is based on cuts on the shower shapes, on information from the\nreconstructed tracks and on the combined reconstruction [17]. To be consistent with the trigger selection,\nonly particles having a transverse energy ET > 5 GeV are considered in the following. Three levels of\nselection are available:\n- \u201cloose\u201d, consisting of simple shower-shape cuts (longitudinal leakage, shower shape in the middle\nlayer of the electromagnetic calorimeter) and very loose matching cuts between reconstructed\ntracks and calorimeter clusters;\n- \u201cmedium\u201d, which adds shower shape cuts making use of the important information contained in\nthe \ufb01rst layer of the electromagnetic calorimeter and track-quality cuts; and\n- \u201ctight\u201d, with tighter track matching criteria and the cut on the energy-to-momentum ratio. This\nselection also explicitly requires the presence of a vertexing-layer hit on the track (to further reject\nphoton conversions) and a large ratio of high-threshold to low-threshold hits in the TRT detector\n(to further reject the background from charged hadrons). Additionally, further isolation of the\nelectron may be required by using calorimeter energy isolation beyond the cluster itself. Two sets\nof tight selection cuts are used to estimate the overall performance of the electron identi\ufb01cation.\nThey are labeled as \u201ctight(TRT)\u201d, in the case where a TRT cut with approximately 90% ef\ufb01ciency\nfor electrons is applied, and as \u201ctight(isol)\u201d, in the case where a TRT cut with approximately 95%\nef\ufb01ciency is applied in combination with a calorimeter isolation cut.\nThe discriminating variables show a signi\ufb01cant dependence on the pseudorapidity and a less pronounced\none on the transverse momentum. In \u03b7 the dependence corresponds to varying granularities, lead thick-\nness and material in front of the electromagnetic calorimeter. The separation between the distributions\nobtained for electrons and pions can vary also with \u03b7. The thresholds applied for cuts have been op-\ntimised in \ufb01ve \u03b7 bins, (0,0.8), (0.8,1.37), (1.37,1.52), (1.52,1.8), (1.8,2.0), and for transverse energies\nbelow 7.5 GeV, between 7.5 and 15 GeV and above 15 GeV.\nThe electron identi\ufb01cation ef\ufb01ciency is de\ufb01ned as \u03b5e = Nt\ne/Ne, where Ne is the number of signal elec-\ntron tracks, which pass the track cuts and Nt\ne is the number of signal electrons which pass identi\ufb01cation\ncuts. The charged pion rejection is de\ufb01ned as R\u03c0 = N\u03c0/Nt\n\u03c0, where N\u03c0 is the number of good quality\npion tracks and Nt\n\u03c0 is the number of good quality pion tracks misidenti\ufb01ed as signal electrons. Table 4\nshows the electron identi\ufb01cation ef\ufb01ciency and pion rejection factor after loose, medium, tight with no\nisolation requirement and tight selections for the different data samples. For tight selection the ef\ufb01ciency\nis \u03b5e \u223c65% for direct J/\u03c8 production. Performance is similar for the \u03d2 sample, despite the higher av-\nerage momentum of the signal electrons, due to the cut on ET > 5 GeV. Figure 6 shows in more detail\nthe overall reconstruction and identi\ufb01cation performance: the pT and \u03b7 dependences of the ef\ufb01ciencies\nfor electrons. There is still an important \u03b7 dependence due to a few discriminating variables and work is\nongoing to improve it.\n4.2.2\nIdenti\ufb01cation of electrons from b quark\nAnother identi\ufb01cation procedure is optimised for non-isolated electrons and is thus particularly useful\nfor b\u00afb events. The trigger anticipated for these events is based on a muonic decay mode of either the\nb or the \u00afb quark. All good quality tracks are considered above a transverse momentum pT >2 GeV.\nWhen possible we use the same variables as for the isolated electron identi\ufb01cation but some variables\n- like the hadronic leakage by the fraction of energy reconstructed in the third sampling - are replaced\nor only the core of the electromagnetic shower is used. In addition to the traditional cut-based analysis,\nmultivariate techniques have been developed, based on the similar variables, and in particular a likelihood\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n148\n\nTable 4: Expected ef\ufb01ciencites \u03b5e for electrons from J/\u03c8 and \u03d2 decay for the four standard levels of cuts\nused for isolated electron identi\ufb01cation. Only electrons with ET > 5 GeV, corresponding to the HLT\nthreshold, are considered. The crack region in the electromagnetic calorimeter, between 1.37 < |\u03b7| <\n1.52 is removed. The quoted errors are statistical only.\nSelection\npp \u2192J/\u03c8X\npp \u2192\u03d2X\n\u03b5e (%)\nR\u03c0\n\u03b5e (%)\nR\u03c0\nLoose\n84.3 \u00b1 0.1\n36 \u00b1 3\n83.7 \u00b1 0.4\n32 \u00b1 7\nMedium\n78.4 \u00b1 0.1\n72 \u00b1 9\n78.4 \u00b1 0.4\n49 \u00b1 13\nTight(TRT)\n71.4 \u00b1 0.1\n109 \u00b1 17\n71.3 \u00b1 0.4\n57 \u00b1 16\nTight (isol)\n65.5 \u00b1 0.1\n900 \u00b1 400\n66.1 \u00b1 0.5\n740 \u00b1 300\n|\n\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nElectron identification efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n (GeV/c)\nT\np\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\nElectron identification efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nFigure 6: Electron identi\ufb01cation ef\ufb01ciency with \u201cTight(TRT)\u201d cuts level as a function of the pseudora-\npidity (left) and the transverse momentum (right) in direct J/\u03c8 events.\ntechnique can also be used. Figure 7 shows the obtained pion rejection curve as a function of the electron\nidenti\ufb01cation ef\ufb01ciency. In the following the working point is an electron identi\ufb01cation ef\ufb01ciency of\nElectron identification efficiency\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nPion rejection factor\n10\n2\n10\n3\n10\n4\n10\nATLAS\nFigure 7: Pion rejection as a function of the electron identi\ufb01cation ef\ufb01ciency, in bBd \u2192\u00b5J/\u03c8X sample.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n149\n\n80%, corresponding to a pion rejection factor of \u223c1300. Figure 8 shows the overall reconstruction and\nidenti\ufb01cation performance in more details: the pT and \u03b7 dependencies of the ef\ufb01ciencies are shown for\nelectrons.\n|\n\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n\u2208\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\n (GeV)\np\n2\n4\n6\n8\n10\n12\n14\n\u2208\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\nATLAS\nFigure 8: Electron identi\ufb01cation ef\ufb01ciency in bBd \u2192\u00b5(6)J/\u03c8X sample as a function of the pseudorapid-\nity (left) and the transverse momentum (right). The mean electron identi\ufb01cation ef\ufb01ciency is \u03b5e = 80%.\n5\nExpected physics studies for early data\n5.1\nNumber of expected events\nAs described in section 3, for an initial luminosity of 1031 cm\u22122 s\u22121, the trigger seelction of two low\nenergy electrons (2EM3 menu at level 1) should provide good statistics for J/\u03c8 \u2192ee and \u03d2 \u2192ee decays.\nFig. 9 shows the expected differential cross-section for low-mass electron pairs using the 2EM3 trigger\nmenu item and the of\ufb02ine selection in linear (left) and log (right) scale. The invariant mass is recon-\nstructed with direction taken from the inner detector and energy from the electromagnetic calorimeter\nwhich allows a better reconstruction of the invariant mass than using calorimeter only information as\ndone at level 1. The signal-to-background ratio obtained is greater than one at the J/\u03c8 and \u03d2 peaks. With\nan integrated luminosity of 100 pb\u22121 and an ef\ufb01cient identi\ufb01cation and reconstruction of these low-mass\npairs, approximately two hundred thousand J/\u03c8 decays could be extracted (see table 5).\nTable 5: Number of expected events for direct production of J/\u03c8, \u03d2 and Drell-Yan events passing the\n2EM3 trigger and of\ufb02ine analysis. Numbers are given for an integrated luminosity of 100 pb\u22121 with\nearly data taking at 1031 cm\u22122 s\u22121. Quoted errors are statistical only.\nJ/\u03c8\n\u03d2\nDrell-Yan\n103 ev /\n103 ev /\n103 ev /\n100 pb\u22121\n100 pb\u22121\n100 pb\u22121\nof\ufb02ine + ET > 5 GeV\n256\u00b19\n45\u00b15\n13.9\u00b10.3\nof\ufb02ine + ET > 5 GeV + L1\n230\u00b19\n43\u00b15\n13.3\u00b10.3\nMoreover, the standard B-physics trigger, using a single muon above a threshold of pT > 4 GeV, can\ngive access to a sample of J/\u03c8 events originating from the b\u00afb production, without possible bias on the\nselection of electromagnetic objects. Due to its lower cross-section, the expected number of events is\nmuch less, around 2.3\u00d7103 after of\ufb02ine selection and \u223c1.9\u00d7103 after trigger and of\ufb02ine selection, but\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n150\n\n (GeV)\nee\nm\n0\n5\n10\n15\n20\n25\n30\n35\n40\n (nb/GeV)\nee\n/dm\n\u03c3\nd\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\n (GeV)\nee\nm\n0\n5\n10\n15\n20\n25\n30\n35\n40\n (nb/GeV)\nee\n/dm\n\u03c3\nd\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\nFigure 9: Expected differential cross section for low-mass electron pairs using the 2EM3 trigger menu\nitem and the of\ufb02ine selection in linear (left) and log (right) scale. Shown is the invariant di-electron\nmass distribution reconstructed using tracks for J/\u03c8 \u2192ee decays (dotted histogram), \u03d2 \u2192ee decays\n(dashed histogram) and Drell-Yan production (full histogram). Also shown is the expected background\n(full circles). The invariant mass is reconstructed with direction taken from the inner detector and energy\nfrom the electromagnetic calorimeter.\nwithout any selection on the electrons themselves. A better estimation of this number requires combining\na single muon trigger with a trigger for electromagnetic \ufb01nal states as described in section 3.3.\n5.2\nQuality of the mass reconstruction with initial data\nIn this section, we study the of\ufb02ine reconstruction of the J/\u03c8 and \u03d2 particles from their decay products.\nAfter a short description of the algorithm, we study the performance of the reconstruction for J/\u03c8s\noriginating from the b\u00afb decays. The invariant mass has been reconstructed with the inner detector only,\ncombining information from the inner detector and the electromagnetic calorimeter, and using only the\nlatter information. For the reconstruction with inner detector information we present results with and\nwithout the bremsstrahlung recovery procedure included. For direct production of J/\u03c8 and \u03d2, we only\nshow results using mass reconstruction with the inner detector.\n5.2.1\nReconstruction of J/\u03c8 and \u03d2 events\nThe identi\ufb01cation of electrons is performed using the electron reconstruction algorithm described above.\nElectrons are identi\ufb01ed with either the \u201ctight\u201d cuts for isolated electrons, or based on the likelihood\nmethod tuned to an electron identi\ufb01cation ef\ufb01ciency of 80%. Pairs of electrons are thus selected. These\npairs de\ufb01ne the overall detection ef\ufb01ciency of J/\u03c8 (or \u03d2) events which is the product of the losses due to\nthe removal of clusters located in the crack in the electromagnetic calorimeter, the track quality cuts, and\nthe electron identi\ufb01cation ef\ufb01ciency.\nPairs of reconstructed opposite-charge tracks are \ufb01tted to a common vertex. Only events with a\nquality of the \ufb01t with \u03c72 per degree of freedom < 6 are retained Fig. 10 shows the distribution of the\nreconstructed transverse decay length Lxy for direct J/\u03c8 events and events originated from B hadrons\ndecay. It is de\ufb01ned as: Lxy =\n\u20d7D\u00b7\u20d7pT (J/\u03c8)\n||\u20d7pT (J/\u03c8)|| , where D is the distance between the primary and secondary\nvertices and pT(J/\u03c8) is the J/\u03c8 reconstructed transverse momentum. It is used to distinguish between\nthe prompt J/\u03c8, which have a pseudo-proper time of zero (Lxy < 0.4 mm) , and B-hadron decays into\nJ/\u03c8+X having an exponentially decaying pseudo-proper time distribution due to the non-zero lifetime of\nthe parent B-hadrons (Lxy > 0.25 mm).\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n151\n\nFigure 10: Distributions of the reconstructed transverse decay length direct J/\u03c8 events (left) and J/\u03c8\nevents originated from B hadrons decay (right).\n5.2.2\nReconstruction of J/\u03c8 from b\u00afb decays\nAfter selection, only \u223c2000 events are reconstructed. This statistics is scaled to 1.9\u00d7103 events, corre-\nsponding to the expected statistics for an integrated luminosity of 100 pb\u22121.\nReconstruction in the inner detector:\nFig. 11 shows the electron pair invariant mass distribution using only the inner detector information for\nsignal events. The \ufb01tted function behaves as a Breit-Wigner distribution \u223c\u0393/(\u2206m2\n0 +(\u0393/2)2) to the left\nof the peak m0, and as a Gaussian of width \u03c3right to the right, as shown in Fig. 11. The parameter \u03c3right\n / ndf \n2\n\u03c7\n 101.8 / 46\nConst \n 5.5\n\u00b1\n 211.7 \n m \n\u2206\n 0.00659\n\u00b1\n -0.06636 \n \n\u0393\n 0.0187\n\u00b1\n 0.5409 \n \nR\n\u03c3\n 0.0042\n\u00b1\n 0.1005 \n (GeV)\nee\nm\n1.5\n2\n2.5\n3\n3.5\n4\nEvents per 0.05 GeV\n0\n50\n100\n150\n200\n250\n300\n / ndf \n2\n\u03c7\n 101.8 / 46\nConst \n 5.5\n\u00b1\n 211.7 \n m \n\u2206\n 0.00659\n\u00b1\n -0.06636 \n \n\u0393\n 0.0187\n\u00b1\n 0.5409 \n \nR\n\u03c3\n 0.0042\n\u00b1\n 0.1005 \nATLAS\nFigure 11: The electron pair invariant mass distribution for bBd \u2192\u00b5(6)J/\u03c8X events. The energy and\ndirection information are taken from the inner detector. An asymmetric \ufb01t is performed with a function\nwhich behaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to the right of\nthe peak. Results are shown without (crosses) and with (bullets) bremsstrahlung recovery included.\nSelection of events includes L1 trigger and of\ufb02ine and number of events is scaled to 100 pb\u22121.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n152\n\ncharacterises the effective resolution in the invariant mass distribution of the pair, while \u0393 is a measure\nof the intensity of energy loss by the electrons due to the bremsstrahlung. \u2206m0 = m0 \u2212MJ/\u03c8, where\nMJ/\u03a8 = 3096 MeV is the nominal J/\u03c8 mass. The \ufb01tted values of the parameters are shown in Table 6.\nThe J/\u03c8 reconstruction performance is assessed separately for the three cases: TRT barrel, when both\nelectrons have their track pseudorapidity |\u03b7| < 0.7, the TRT end-caps, when at least one electron has\n|\u03b7| > 0.7, and the full \u03b7 range. In general the quality of the \ufb01t is not very high, in particular we see\nTable 6: Results of an asymmetric \ufb01t to the invariant mass distributions for bBd \u2192\u00b5(6)J/\u03c8X events,\nwith a function that behaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to\nthe right of the peak. The direction and energy information are taken from the inner detector.\nbrem \ufb01t\n\u03b7 range\n\u2206m0 (MeV)\n\u0393 (MeV)\n\u03c3right (MeV)\nall\n\u221277\u00b17\n557\u00b120\n67\u00b14\nNo\nBarrel\n\u221271\u00b17\n393\u00b119\n65\u00b14\nEnd-caps\n\u2212178\u00b117\n688\u00b143\n123\u00b111\nAll\n\u221266\u00b16\n540\u00b118\n99\u00b14\nYes\nBarrel\n\u221245\u00b17\n417\u00b119\n77\u00b15\nEnd-caps\n\u2212128\u00b112\n657\u00b133\n155\u00b18\ndif\ufb01culties with correctly reproducing the peak. Table 6 shows the results of the \ufb01t of the invariant mass.\nA shift in the reconstructed mass is measured around 77 MeV, larger in the end-caps than in the barrel. As\nmentioned in [5], such mass shifts may be due to detector alignment, material effects, magnetic \ufb01eld scale\nand its stability. The CDF collaboration extensively and successfully used this method but it took many\nyears at the Tevatron to collect suf\ufb01cient statistics to allow for the disentanglement of various detector\neffects [22]. The parameter \u0393 is around 550 MeV. The Gaussian width, estimated from the right part of\nthe distribution is around 67 MeV. One can also notice the improvement in the mass reconstruction from\nbremsstrahlung recovery. Without any bremsstrahlung recovery, only 47% of events are reconstructed\nwithin \u00b1 200 MeV of the nominal J/\u03c8 mass, whereas with the use of the bremsstrahlung recovery, this\nfraction increases to approximately 55% for the dynamic-noise-adjustment algorithm.\nCombined reconstruction:\nThe J/\u03c8 mass can be also determined combining information from the inner detector and the electro-\nmagnetic calorimeter. The energy is taken from the electromagnetic calorimeter and the direction from\nthe more accurate measurements provided by the inner detector, taking into account the bremsstrahlung\nrecovery procedure. Figure 12 shows the di-electron invariant mass distribution obtained from the signal\nsample only. An asymmetric gaussian function is \ufb01tted, with different width, \u03c3left and \u03c3right, either side\nof the \ufb01tted peak mass m0. It is performed in a narrow mass interval, between 2.5 and 3.6 GeV. The\nparameter \u03c3right characterises the effective resolution in the invariant mass, while \u03c3left is a measure of the\ndeterioration of this resolution due to bremsstrahlung. The \ufb01tted values of the parameters are shown in\nTable 7. Performance is assessed separately for the three cases: TRT barrel, when both electrons have\ntheir track pseudorapidity |\u03b7| < 0.7, the TRT end-caps, when at least one electron has |\u03b7| > 0.7, and the\nfull \u03b7 range. The resolution obtained is highly asymmetric, \u223c387 MeV on the left and \u223c189 MeV on\nthe right. It can be also noticed that the quality of the \ufb01t is rather poor.\nReconstruction in the electromagnetic calorimeter:\nFinally it is interesting to investigate the performance if we rely only on the information from the elec-\ntromagnetic calorimeter. Fig. 13 shows the electron candidates invariant mass distribution obtained from\nthe signal sample only. The same function de\ufb01ned for the combined reconstruction is used to \ufb01t the\ndistributions. The \ufb01tted values of the parameters are shown in Table 8. Performance is assessed sepa-\nrately in three cases: the barrel region of the electromagnetic calorimeter, when both electrons have their\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n153\n\n / ndf \n2\n\u03c7\n 16.77 / 5\nProb \n 0.004966\nConst \n 13.6\n\u00b1\n 559.3 \n m \n\u2206\n 0.0144\n\u00b1\n 0.1009 \n \nL\n\u03c3\n 0.0122\n\u00b1\n 0.3273 \n \nR\n\u03c3\n 0.0108\n\u00b1\n 0.1888 \n (GeV)\nee\nm\n0\n1\n2\n3\n4\n5\n6\nEvents per 0.05 GeV\n0\n100\n200\n300\n400\n500\n600\n / ndf \n2\n\u03c7\n 16.77 / 5\nProb \n 0.004966\nConst \n 13.6\n\u00b1\n 559.3 \n m \n\u2206\n 0.0144\n\u00b1\n 0.1009 \n \nL\n\u03c3\n 0.0122\n\u00b1\n 0.3273 \n \nR\n\u03c3\n 0.0108\n\u00b1\n 0.1888 \nATLAS\nFigure 12: The electron pair invariant mass for bBd \u2192\u00b5(6)J/\u03c8X events. The energy is taken from the\nelectromagnetic calorimeter and the direction from the inner detector (including bremstrahlung recov-\nery). Selection of events includes L1 trigger and of\ufb02ine and number of events is scaled to 100 pb\u22121.\nTable 7: Asymmetric Gaussian \ufb01t results for bBd \u2192\u00b5(6)J/\u03c8X events. The energy is taken from the\nelectromagnetic calorimeter and the direction from the inner detector.\n\u03b7\n\u2206m0 (MeV)\n\u03c3left (MeV)\n\u03c3right (MeV)\nAll\n101\u00b114\n327\u00b112\n189\u00b111\nBarrel\n94\u00b116\n285\u00b112\n183\u00b112\nEnd-caps\n113\u00b128\n385\u00b127\n191\u00b121\npseudorapidity |\u03b7| < 1.4; the end-cap region, when at least one electron has |\u03b7| > 1.4; and for the full \u03b7\nrange. The resolution obtained from the width of the Gaussian is \u223c550 MeV.\nTable 8: Asymmetric Gaussian \ufb01t results for bBd \u2192\u00b5(6)J/\u03c8X events. The energy and direction infor-\nmation is taken from the electromagnetic calorimeter only.\n\u03b7\n\u2206m0 (MeV)\n\u03c3left (MeV)\n\u03c3right (MeV)\nall\n\u221217\u00b154\n567\u00b146\n541\u00b153\nbarrel\n\u22129\u00b162\n558\u00b150\n560\u00b160\nend-cap\n\u221268\u00b1102\n629\u00b1125\n414\u00b174\n5.2.3\nReconstruction of direct J/\u03c8 and \u03d2 events\nAfter selection, only \u223c4000 events are reconstructed. This statistics is scaled to 2.3\u00d7105 events, corre-\nsponding to the expected statistics for an integrated luminosity of 100 pb\u22121. Figure 14 shows the electron\npair invariant mass distribution using only the inner detector information. The same function as de\ufb01ned\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n154\n\n / ndf \n2\n\u03c7\n 16.24 / 12\nProb \n 0.1805\nConst \n 4.9\n\u00b1\n 142 \n m \n\u2206\n 0.05424\n\u00b1\n -0.01707 \n \nL\n\u03c3\n 0.0457\n\u00b1\n 0.5675 \n \nR\n\u03c3\n 0.0526\n\u00b1\n 0.5412 \n (GeV)\nee\nm\n0\n1\n2\n3\n4\n5\n6\nEvents per 0.05 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n / ndf \n2\n\u03c7\n 16.24 / 12\nProb \n 0.1805\nConst \n 4.9\n\u00b1\n 142 \n m \n\u2206\n 0.05424\n\u00b1\n -0.01707 \n \nL\n\u03c3\n 0.0457\n\u00b1\n 0.5675 \n \nR\n\u03c3\n 0.0526\n\u00b1\n 0.5412 \nATLAS\nFigure 13: The electron pair invariant mass for bBd \u2192\u00b5(6)J/\u03c8X events. The energy and direction\nare taken from the electromagnetic calorimeter. Selection of events includes L1 trigger and of\ufb02ine and\nnumber of events is scaled to 100 pb\u22121.\n / ndf \n2\n\u03c7\n 5.568e+05 / 36\nProb \n 0\nConst \n 37.3\n\u00b1\n 8846 \n m \n\u2206\n 0.00087\n\u00b1\n -0.09173 \n \n\u0393\n 0.0017\n\u00b1\n 0.3265 \n \nR\n\u03c3\n 0.00053\n\u00b1\n -0.06754 \n (GeV)\nee\nm\n1.5\n2\n2.5\n3\n3.5\n4\nEvents per 0.05 GeV\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n / ndf \n2\n\u03c7\n 5.568e+05 / 36\nProb \n 0\nConst \n 37.3\n\u00b1\n 8846 \n m \n\u2206\n 0.00087\n\u00b1\n -0.09173 \n \n\u0393\n 0.0017\n\u00b1\n 0.3265 \n \nR\n\u03c3\n 0.00053\n\u00b1\n -0.06754 \nATLAS\nFigure 14: The electron pair invariant mass distribution for pp \u2192J/\u03c8X events. The energy and direction\ninformation are taken from the inner detector. An asymmetric \ufb01t is performed with a function which\nbehaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to the right of the peak.\nSelection of events includes L1 trigger, of\ufb02ine and a cut on ET > 5 GeV for each electron to mimic the\nHLT. The number of events is scaled to 100 pb\u22121.\npreviously is \ufb01tted. The \ufb01tted values of the parameters \u2206m0, \u0393 and \u03c3right are shown in Table 9. The \ufb01tted\nmass value is shifted by about 100 MeV, the \u0393 factor is \u223c300 MeV and the resolution term is \u223c70 MeV.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n155\n\nTable 9: Results of an asymmetric \ufb01t to the invariant mass distributions for pp \u2192J/\u03c8X events, with a\nfunction that behaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to the right\nof the peak. The direction and energy information are taken from the inner detector.\n\u03b7\n\u2206m0 (MeV)\n\u0393 (MeV)\n\u03c3right (MeV)\nAll\n-98 \u00b1 1\n298 \u00b1 2\n71 \u00b1 1\nBarrel\n-77 \u00b1 1\n255 \u00b1 2\n62 \u00b1 1\nEnd-caps\n-142 \u00b1 2\n354 \u00b1 3\n87 \u00b1 2\n5.2.4\n\u03d2 reconstruction\nAfter selection, only \u223c1000 events are reconstructed. This statistics is scaled to 4.3\u00d7104 events, corre-\nsponding to the expected statistics for an integrated luminosity of 100 pb\u22121. Fig. 15 shows the electron\npair invariant mass distribution from the inner detector information. The \ufb01tted values of the parameters\n / ndf \n2\n\u03c7\n 4.68e+05 / 38\nProb \n 0\nConst \n 44.9\n\u00b1\n 5392 \n m \n\u2206\n 0.0047\n\u00b1\n -0.1812 \n \n\u0393\n 0.011\n\u00b1\n 1.098 \n \nR\n\u03c3\n 0.0029\n\u00b1\n 0.1371 \n (GeV)\nee\nm\n6\n7\n8\n9\n10\n11\n12\nEvents per 0.05 GeV\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / ndf \n2\n\u03c7\n 4.68e+05 / 38\nProb \n 0\nConst \n 44.9\n\u00b1\n 5392 \n m \n\u2206\n 0.0047\n\u00b1\n -0.1812 \n \n\u0393\n 0.011\n\u00b1\n 1.098 \n \nR\n\u03c3\n 0.0029\n\u00b1\n 0.1371 \nATLAS\nFigure 15: The electron pair invariant mass distribution for pp \u2192\u03d2X events. The energy and direction\ninformation are taken from the inner detector. An asymmetric \ufb01t is performed with a function that\nbehaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to the right of the peak.\nSelection of events includes L1 trigger, of\ufb02ine and a cut on ET > 5 GeV for each electron to mimic the\nHLT. Number of events is scaled to 100 pb\u22121.\nare shown in Table 10. The \ufb01tted mass value is shifted by about 180 MeV, the \u0393 factor is \u223c1 GeV and\nthe resolution term is \u223c140 MeV.\n5.3\nAssessment of performance in situ with initial data\nInitial studies have been performed for the J/\u03c8 \u2192ee tag-and-probe method brie\ufb02y outlined below, using\nevents satisfying a single electron trigger with ET > 5GeV. Due to too high rate at L1 (40 kHz) it has\nto be pre-scaled by a factor of 60, which reduces the \ufb01nal statistics. Those events are used to look for\nan opposite-charge electron pair identi\ufb01ed by the of\ufb02ine electron reconstruction with an invariant mass\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n156\n\nTable 10: Results of an asymmetric \ufb01t to the invariant mass distributions for pp \u2192\u03d2X events, with a\nfunction which behaves as a Breit-Wigner distribution to the left of the peak and as a Gaussian to the\nright of the peak. The direction and energy information are taken from the inner detector.\n\u03b7 range\n\u2206m0 (MeV)\n\u0393 (MeV)\n\u03c3right (MeV)\nAll\n-181 \u00b1 5\n1098 \u00b1 11\n137 \u00b1 3\nBarrel\n-177 \u00b1 5\n930 \u00b1 12\n137 \u00b1 3\nEnd-caps\n-252 \u00b1 11\n1335 \u00b1 25\n166 \u00b1 7\nnear the J/\u03c8 peak. Using the second electron as the probe which was not required to pass any trigger\nselection, the ef\ufb01ciency (relative to the of\ufb02ine selection) of a given trigger signature can be measured.\nWe expect to collect of the order of \u224820\u00d7103 J/\u03c8 signal events after the pre-scale with an integrated\nluminosity of 100 pb\u22121. Similar studies could be performed to study the of\ufb02ine electron selection.\nOne important ingredient in the calibration strategy for the electromagnetic calorimeter is the use of\nlarge statistics samples of Z \u2192ee decays to perform an accurate inter-calibration of regions with a \ufb01xed\nsize of \u2206\u03b7 \u00d7 \u2206\u03d5 = 0.2 \u00d7 0.4. To cross-check the calibration obtained from the Z0 decays and also to\ncheck the linearity of the calorimeter, it is important to have calibration coef\ufb01cients for a lower electron\nenergy range, which can be obtained using the J/\u03c8 \u2192ee and \u03d2 \u2192ee decays as shown in [23]. With\nthe expected statistics, a statistical precision of \u223c0.6% can be expected on the inter-calibration of the\nelectromagnetic calorimeter based on 100 pb\u22121. Still, more studies are needed in particular to improve\nthe energy reconstruction and to disentangle effects of inter-calibration with the distribution of material\nin front of the electromagnetic calorimeter.\nMore generally, these electron samples will allow us to study the performance of both the recon-\nstruction of tracks in the inner detector and clusters in the electromagnetic calorimeter, as well as the\nalignment between these two detectors. All these studies are crucial for the very \ufb01rst measurements\n(such as, for example cross-section measurements) to be performed by the ATLAS experiment on the\nearly data.\n6\nConclusion\nIn this note, the strategy to reconstruct J/\u03c8 and \u03d2 particles, decaying into electron-positron pairs, has\nbeen investigated. The possible trigger strategies have also been described. For initial luminosities\nof 1031 cm\u22122 s\u22121, a trigger on low-energy di-electron pairs (2EM3 at L1) should provide good statistics\nfor the direct production of these particles. Moreover the standard B-physics trigger, using a single\nmuon above a certain pT threshold can give access to these events through the b\u00afb production, without\nbiasing the selection of electromagnetic objects. For these studies, the electron reconstruction seeded by\na track in the inner detector has been used. Compared to previous studies, the main improvement comes\nfrom the identi\ufb01cation procedure, which can either use the standard cut-based analysis, with thresholds\ntuned at low energy, or a dedicated identi\ufb01cation developed for non-isolated electrons. The signal-to-\nbackground ratio obtained is larger than one at the J/\u03c8 and \u03d2 peaks, but the extraction of the Drell-Yan\nsignal requires further studies. With an integrated luminosity of 100 pb\u22121 and an ef\ufb01cient identi\ufb01cation\nand reconstruction of these low-mass pairs, approximately two hundred thousand J/\u03c8 decays could be\nisolated for detailed studies of the electron identi\ufb01cation and reconstruction performance, in particular in\nterms of matching energy and momentum measurements at a scale quite different from that of the more\ncommonly used Z \u2192ee decays.\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n157\n\nReferences\n[1] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\nJINST 3 S08003 (2008).\n[2] CDF Collaboration, F. Abe et al., Phys. Rev. Lett. 69 (1992) 3704.\n[3] G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51 (1995) 1125 [Erratum-ibid. D\n55(1997) 5853] [arXiv:hep-ph/9407339]; E. Braaten and S. Fleming, Phys. Rev. Lett. 74 (1995)\n3327 [arXiv:hep-ph/9411365].\n[4] ATLAS Collaboration, Introduction to B-Physics, this volume.\n[5] ATLAS Collaboration, Heavy Quarkonium Physics with Early Data, this volume.\n[6] Kaushik De, ATLAS Computing System Commissioning - Simulation Production Experience;\nRoger Jones, Summary of Distributed data analysis and information management; Proceedings\nof 16th International Conference on Computing In High Energy and Nuclear Physics, CHEP 2007,\n2-7 Sept Victoria BC, Canada..\n[7] T. Sjostrand, S. Mrenna and P. Skands, FERMILAB-PUB-06-052-CD-T, LU-TP-06-13 (2006) 576.\nPublished in JHEP 0605:026 (2006).\n[8] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[9] GEANT4 Collaboration,\nGeant4 - A simulation toolkit,\nNuclear Instruments and Methods in\nPhysics Research Section A 506 (2003) 250-303.\n[10] ATLAS Collaboration, ATLAS Computing Technical Design Report, CERN-LHCC-2005-022\n(2005).\n[11] Particle Data Group, W. M. Yao et al.,, J. Phys. G 33, 1 (2006).\n[12] The ALEPH Collaboration, the DELPHI Collaboration, the L3 Collaboration, the OPAL Collab-\noration, the LEP Electroweak Working Group, the SLD Electroweak and Heavy Flavour Groups,\nPrecision Electroweak Measurements on the Z Resonance, 2006, CERN-PH-EP/2005-041, SLAC-\nR-774, Physics Report Vol. 427, Nos. 5-6.\n[13] ATLAS Collaboration, Reconstruction of Photon Conversions, this volume.\n[14] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[15] N. Panikashvili, The ATLAS B-physics trigger, in Nucl.Phys.Proc.Suppl.156:129-134 (2006).\n[16] J. Kirk, J. T. M. Baines and A. T. Watson, ATLAS B-physics Trigger Studies using EM and Jet\nRoIs, ATL-DAQ-PUB-2006-004 (2006).\n[17] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[18] ATLAS Collaboration, Soft Electron b-Tagging, this volume.\n[19] A. Salzburger, The ATLAS Track Extrapolation Package, ATL-SOFT-PUB-2007-005 (2007).\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n158\n\n[20] V. Kartvelishvili, Electron bremsstrahlung recovery in ATLAS, Nucl. Phys. B (Proc. Suppl.) 172\n(2007) 208-211.\n[21] ATLAS Collaboration,\nCalibration and Performance of the Electromagnetic Calorimeter,\nthis\nvolume.\n[22] CDF Collaboration, D. E. Acosta et al., Phys. Rev. Lett. 96 (2006).\n[23] F. Derue, A. Kaczmarska and P. Schwemling, Reconstruction of DC1 J/\u03c8 \u2192e+e\u2212decays and use\nfor the low energy calibration of the ATLAS electromagnetic calorimeter, ATL-PHYS-PUB-2006-\n004 (2006).\nELECTRONS AND PHOTONS \u2013 RECONSTRUCTION OF LOW-MASS ELECTRON PAIRS\n159\n\n\nMuons\n161\n\nMuon Reconstruction and Identi\ufb01cation: Studies with\nSimulated Monte Carlo Samples\nAbstract\nThe strategy and performance for muon identi\ufb01cation and reconstruction in\nATLAS are described. Performance metrics include ef\ufb01ciency, fake rates and\nmomentum resolution. Results are based on data simulated and reconstructed\nin 2007.\n1\nIntroduction\nThe ATLAS experiment will detect particles created in 14 TeV proton-proton collisions produced by the\nCERN LHC (Large Hadron Collider). Only a tiny fraction of these collisions will correspond to inter-\nesting standard model processes and an even smaller fraction to new physics. Muons, especially those\nwith high-pT (transverse momentum) and those that are isolated (from other activity in the detector), will\nbe much more common in these interesting events than in the background, and thus provide important\nmeans to identify such events and to determine their properties. The ATLAS detector has been designed\nto be ef\ufb01cient in the detection of muons and to provide precise measurement of their kinematics up to\none TeV.\nIn parallel with the construction of the detector, software has been developed to reconstruct these\nmuons, i.e., for each recorded event, to identify muons and measure their position, direction and momen-\ntum. Here we describe the strategies being pursued for this reconstruction and the current performance\ncharacterized in terms of ef\ufb01ciency, fake rate and precision and accuracy of measurement. The results\nreported here are based on simulation data generated and reconstructed in 2007.\nWe begin with descriptions of the detector, the reconstruction algorithms and the means by which\nwe measure the performance. These are followed by sections documenting this performance for each of\nthe various reconstruction strategies and \ufb01nally a section summarizing results and commenting on future\ndevelopments.\n2\nDetector\nThe ATLAS detector [1] has been designed to provide clean and ef\ufb01cient muon identi\ufb01cation and precise\nmomentum measurement over a wide range of momentum and solid angle. The primary detector system\nbuilt to achieve this is the muon spectrometer, shown in Figure 1. The spectrometer covers the pseudo-\nrapidity range |\u03b7| < 2.7 and allows identi\ufb01cation of muons with momenta above 3 GeV/c and precise\ndetermination of pT up to about 1 TeV/c.\nThe muon spectrometer comprises three subsystems:\n\u2022 Superconducting coils provide a toroidal magnetic \ufb01eld whose integral varies signi\ufb01cantly as a\nfunction of both \u03b7 and \u03d5 (azimuthal angle). The integrated bending strength (Figure 2) is roughly\nconstant as a function of \u03b7 except for a signi\ufb01cant drop in the transition between the barrel and\nendcap toroid coils (1.4 \u223c<|\u03b7| \u223c<1.6).\n\u2022 Precision detectors are located in three widely-separated stations at increasing distance from the\ncollision region. Each station includes multiple closely-packed layers measuring the \u03b7-coordinate,\nthe direction in which most of the magnetic \ufb01eld de\ufb02ection occurs. Monitored drift tubes provide\nthese measurements everywhere except in the high-\u03b7 (|\u03b7| > 2.0) region of the innermost station\nwhere cathode strip chambers are used. The measurement precision in each layer is typically better\n162\n\n2\n4\n6\n8\n10\n12 m\n0\nRadiation shield\nMDT chambers\nEnd-cap\ntoroid\nBarrel toroid coil\nThin gap \nchambers\nCathode strip\n chambers\nResistive plate chambers\n14\n16\n18\n20\n2\n10\n12\n4\n6\n8\nm\nFigure 1: The ATLAS muon spectrometer.\nthan 100 \u00b5m. The cathode strip chambers additionally provide a rough (1 cm) measurement of the\n\u03d5-coordinate.\n\u2022 Resistive plate and thin gap chambers provide similarly rough measurements of both \u03b7 and \u03d5 near\nselected stations.\nHigh-pT muons typically traverse all three stations but there are \u03b7-\u03d5 regions where one, two or all\nthree stations do not provide a precision measurement, e.g. those regions with support structures or\npassages for services. There are also regions where overlaps allow two measurements from a single\nstation. Figure 3 shows the number of station measurements as function of \u03b7 and \u03d5. The resolution and\nef\ufb01ciency are degraded where one or more stations do not provide a measurement.\nFigure 4 shows how contributions to the muon spectrometer momentum resolution vary as a function\nof pT. At low momentum, the resolution is dominated by \ufb02uctuations in the energy loss of the muons\ntraversing the material in front of the spectrometer. Multiple scattering in the spectrometer plays an\nimportant role in the intermediate momentum range. For pT > 300 GeV/c, the single-hit resolution,\nlimited by detector characteristics, alignment and calibration, dominates.\nThe other ATLAS detector systems also play important roles in achieving the ultimate performance\nfor muon identi\ufb01cation and measurement. The calorimeter, with a thickness of more than 10 interaction\nlengths, provides an effective absorber for hadrons, electrons and photons produced by proton-proton\ncollisions at the center of the ATLAS detector. Energy measurements in the calorimeter can aid in muon\nidenti\ufb01cation because of their characteristic minimum ionizing signature and can provide a useful direct\nmeasurement of the energy loss [2].\nA tracking system inside the calorimeters detects muons and other charged particles with hermetic\ncoverage for |\u03b7| < 2.5, providing important con\ufb01rmation of muons found by the spectrometer over that\n\u03b7 range. This inner detector has three pixel layers, four stereo silicon microstrip layers, and, for |\u03b7| <\n2.0, a straw-tube transition radiation detector that records an average of 36 additional measurements on\neach track. A 2 Tesla solenoidal magnet enables the inner detector to provide an independent precise\nmomentum measurement for muons (and other charged particles). Over most of the acceptance, for pT\nroughly in the range between 30 and 200 GeV/c, the momentum measurements from the inner detector\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n163\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n m)\n\u22c5\nB dl (T \n\u222b\n-2\n0\n2\n4\n6\n8\nBarrel region\nregion\nEnd-cap\nTransition region\n=0\n\u03c6 \n/8\n\u03c0\n=\n\u03c6 \nFigure 2: ATLAS muon spectrometer integrated magnetic \ufb01eld strength as a function of |\u03b7|.\nFigure 3: Number of detector stations traversed by muons passing through the muon spectrometer\nas a function of |\u03b7| and \u03d5.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n164\n\nPt (GeV/c)\n10\n2\n10\n3\n10\nContribution to resolution (%)\n0\n2\n4\n6\n8\n10\n12\nTotal\nSpectrometer entrance\nMu tiple scattering\nChamber Alignment\nTube resolution and autocalibration (stochastic)\nEnergy loss fluctuations\nFigure 4: Contributions to the momentum resolution for muons reconstructed in the Muon Spec-\ntrometer as a function of transverse momentum for |\u03b7| < 1.5. The alignment curve is for an\nuncertainty of 30 \u00b5m in the chamber positions.\nand muon spectrometer may be combined to give precision better than either alone. The inner detector\ndominates below this range, and the spectrometer above it.\n3\nOverview of reconstruction and identi\ufb01cation algorithms\nATLAS employs a variety of strategies for identifying and reconstructing muons. The direct approach is\nto reconstruct standalone muons by \ufb01nding tracks in the muon spectrometer and then extrapolating these\nto the beam line. Combined muons are found by matching standalone muons to nearby inner detector\ntracks and then combining the measurements from the two systems. Tagged muons are found by ex-\ntrapolating inner detector tracks to the spectrometer detectors and searching for nearby hits. Calorimeter\ntagging algorithms are also being developed to tag inner detector tracks using the presence of a mini-\nmum ionizing signal in calorimeter cells. These were not used in the data reconstruction reported here\nand their performance is documented elsewhere [2].\nThe current ATLAS baseline reconstruction includes two algorithms for each strategy. Here we\nbrie\ufb02y describe these algorithms. Later sections describe their performance.\nThe algorithms are grouped into two families such that each family includes one algorithm for each\nstrategy. The output data intended for use in physics analysis includes two collections of muons\u2014one\nfor each family\u2014in each processed event. We refer to the collections (and families) by the names of the\ncorresponding combined algorithms: Staco [3] and Muid [4]. The Staco collection is the current default\nfor physics analysis.\n3.1\nStandalone muons\nThe standalone algorithms \ufb01rst build track segments in each of the three muon stations and then link the\nsegments to form tracks. The Staco-family algorithm that \ufb01nds the spectrometer tracks and extrapolates\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n165\n\nthem to the beam line is called Muonboy [3]. On the Muid side, Moore [5] is used to \ufb01nd the tracks and\nthe \ufb01rst stage of Muid performs the inward extrapolation.\nThe extrapolation must account for both multiple scattering and energy loss in the calorimeter. Muon-\nboy assigns energy loss based on the material crossed in the calorimeter. Muid additionally makes use\nof the calorimeter energy measurements if they are signi\ufb01cantly larger than the most likely value and the\nmuon appears to be isolated [6].\nStandalone algorithms have the advantage of slightly greater |\u03b7| coverage\u2014out to 2.7 compared to\n2.5 for the inner detector\u2014but there are holes in the coverage at |\u03b7| near 0.0 and 1.2 (see \ufb01gure 3).\nVery low momentum muons (around a few GeV/c) may be dif\ufb01cult to reconstruct because they do not\npenetrate to the outermost stations.\nMuons produced in the calorimeter, e.g. from \u03c0 and K decays, are likely to be found in the standalone\nreconstruction and serve as a background of \u201cfake\u201d muons for most physics analyses. There are a few\nexotic channels for which charged particles appearing in the calorimeter are a signal of interest.\n3.2\nInner detector\nThe primary track reconstruction algorithm for the inner detector is described in Ref. [7]. Space points\nare identi\ufb01ed in the pixel and microstrip detectors, these points are linked to form track seeds in the\ninner four layers, and tracks are found by extending these seeds to add measurements from the outer\nlayers. This strategy is expected to give very high detection ef\ufb01ciency over the full detector acceptance,\n|\u03b7| < 2.5.\n3.3\nCombined muons\nBoth of the muon combination algorithms, Staco and Muid, pair muon-spectrometer tracks with inner-\ndetector tracks to identify combined muons. The match chi-square, de\ufb01ned as the difference between\nouter and inner track vectors weighted by their combined covariance matrix:\n\u03c72\nmatch = (TMS \u2212TID)T (CID +CMS)\u22121 (TMS \u2212TID)\n(1)\nprovides an important measure of the quality of this match and is used to decide which pairs are retained.\nHere T denotes a vector of (\ufb01ve) track parameters\u2014expressed at the point of closest approach to the beam\nline\u2014and C is its covariance matrix. The subscript ID refers to the inner detector and MS to the muon\nspectrometer (after extrapolation accounting for energy loss and multiple scattering in the calorimeter).\nStaco does a statistical combination of the inner and outer track vectors to obtain the combined track\nvector:\nT = (C\u22121\nID +C\u22121\nMS)\u22121 (C\u22121\nID TID +C\u22121\nMS TMS)\n(2)\nMuid does a partial re\ufb01t: it does not directly use the measurements from the inner track, but starts from\nthe inner track vector and covariance matrix and adds the measurements from the outer track. The \ufb01t\naccounts for the material (multiple scattering and energy loss) and magnetic \ufb01eld in the calorimeter and\nmuon spectrometer.\n3.4\nTagged muons\nThe spectrometer tagging algorithms, MuTag [3] and MuGirl [8], propagate all inner detector tracks with\nsuf\ufb01cient momentum out to the \ufb01rst station of the muon spectrometer and search for nearby segments.\nMuTag de\ufb01nes a tag chi-square using the difference between any nearby segment and its prediction from\nthe extrapolated track. MuGirl uses an arti\ufb01cial neural network to de\ufb01ne a discriminant. In either case,\nif a segment is suf\ufb01ciently close to the predicted track position, then the inner detector track is tagged as\ncorresponding to a muon.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n166\n\nAt present, both algorithms simply use the inner-detector track to evaluate the muon kinematics, i.e.\nthe inner track and spectrometer hits are not combined to form a new track. This is not very important in\nthe low-pT regime that these algorithms were originally intended to address. Both algorithms are being\nfurther developed to allow extrapolation to other and multiple stations and add the capability to include\nthe spectrometer measurements in a track re\ufb01t.\nThere is an important difference in the way these algorithms are run in the standard reconstruction\nchain. MuGirl considers all inner-detector tracks and redoes segment \ufb01nding in the region around the\ntrack. MuTag only makes use of inner-detector tracks and muon-spectrometer segments not used by\nStaco. Thus MuTag serves only to supplement Staco while MuGirl attempts to \ufb01nd all muons. Obviously,\nMuTag is part of the Staco family and most sensibly used in that context. MuGirl muons are recorded as\npart of the Muid family.\n3.5\nMerging muons\nThe muon \ufb01nding ef\ufb01ciency (and fake rate) may be increased by including muons found by multiple\nalgorithms but care must be taken to remove overlaps, i.e. cases where the same muon is identi\ufb01ed by\ntwo or more algorithms. To a large extent, this is done when the collections are created. Standalone\nmuons that are successfully combined are not recorded separately. In those cases where a standalone\nmuon is combined with more than one inner-detector track, exactly one of the muons is \ufb02agged as \u201cbest\nmatch.\u201d In the Staco collection, the tagged and combined muons do not overlap by construction. In\nthe Muid collection, overlaps between MuGirl and Muid muons are removed by creating a single muon\nwhen both have the same inner detector track.\nAnalysts wishing to merge standalone and tagged muons or muons from different collections may\nmake use of a muon selection tool to remove overlaps. It requires muons have different inner-detector\ntracks and merges standalone muons that are too close to one another. Closeness is de\ufb01ned by \u03b7-\u03d5\nseparation with a default limit of 0.4.\n4\nTools for performance evaluation and classi\ufb01cation of tracks\nSimulation samples were created in the ATLAS framework by running an event generator (PYTHIA [9]\nor MC@NLO [10, 11]) and using GEANT4 [12] to propagate the \ufb01nal-state particles using ATLAS-\nspeci\ufb01c code to describe the geometry and response of the detector. The data were then reconstructed\nusing the software based on the algorithms described in the previous chapter.\n4.1\nTruth matching and track classi\ufb01cation\nMuon reconstruction performance is evaluated for each event by comparing selected reconstructed muons\nwith the true muons, i.e. those in the Monte Carlo truth record. The latter include muons created in the\ninitial event generation as well as secondaries produced during propagation through the tracking volume.\nMuons produced in the calorimeter or muon spectrometer are not included in the truth record. True\nmuons with transverse momentum below 2 GeV/c are also excluded to avoid spurious matches with\ncandidates we do not expect to be able to reconstruct.\nFor each event, a one-to-one matching is performed between the selected reconstructed muons and\nthe true muons. The matching makes use of two distance metrics: Dref is the reference distance measured\nfrom true muon to the reconstructed muon:\nDref =\ns\u0012\u03d5reco \u2212\u03d5true\n0.005\n\u00132\n+\n\u0012\u03b7reco \u2212\u03b7true\n0.005\n\u00132\n+\n\u0012\u2206pT/pT\n0.03\n\u00132\n(3)\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n167\n\nand Deva is the evaluation distance measured from the reconstructed muon to the true muon:\nDeva =\nq\n(Treco \u2212Ttrue)C\u22121\nreco (Treco \u2212Ttrue)\n(4)\nIn the \ufb01rst equation, \u2206pT/pT is the fractional momentum resolution:\n\u2206pT\npT\n= 1/pTreco \u22121/pTtrue\n1/pTtrue\n= pTtrue \u2212pTreco\npTreco\n(5)\nHere pT is signed (i.e. carries the charge sign), but elsewhere in the text it denotes the magnitude\nof the transverse momentum. In the second distance equation, T again denotes the vector of (\ufb01ve)\ntrack parameters (expressed at the distance of closest approach to the beam line) and C the associated\ncovariance matrix. Note that D2\neva is a chi-square with \ufb01ve degrees of freedom.\nThere is a maximum allowed value for each of these distances. For Deva the maximum value is 1000,\na very loose cut. The limit for Dref is 100 and we see from equation 3 this implies the matched muons\nmust be within a distance of 0.5 in \u03b7 and \u03d5 and have the same charge sign with pTreco > 0.25 pTtrue or\nopposite sign with pTreco > 0.50 pTtrue.\nThe matching is carried out by \ufb01rst examining each reconstructed muon and assigning it to the nearest\ntrue muon using the evaluation distance. The reconstructed muon is left unmatched if no distance is less\nthan the maximum allowed value. The reference distance is evaluated for each match and the match is\ndiscarded if it exceeds the threshold for that quantity. If more than one match remains for any true muon,\nthen only the match with the smallest reference distance is retained.\nTrue muons that are matched are said to be found and those left unmatched are lost. Found muons\nare classi\ufb01ed as good if they have Deva < 4.5 corresponding to a chi-square probability above 0.0011.\nReconstructed muons are said to be real if they are matched and fake if unmatched. Note that these\nfakes may correspond to true muons produced outside the tracking volume (e.g. in the calorimeter) and\nhence not included in the truth record.\n4.2\nPerformance measures\nOur performance measures include ef\ufb01ciency, fake rate, resolutions and resolution tails. The ef\ufb01ciency\nor \ufb01nding ef\ufb01ciency is de\ufb01ned to be the fraction of true muons that are found and is typically evaluated\nfor some kinematic selection (applied after matching). The good ef\ufb01ciency is the fraction of true muons\nthat are found and classi\ufb01ed as good (as de\ufb01ned in the previous section). The good fraction is the fraction\nof found muons that are classi\ufb01ed as good. In the sections that follow, we present the overall ef\ufb01ciency\nfor various physics samples and the ef\ufb01ciency as a function of \u03b7 for the primary benchmark sample.\nThe fake rate is de\ufb01ned to be the mean number of fake muons per event and it is presented for a\nvariety of pT thresholds corresponding to the values that might be chosen for different physics analyses.\nFive kinematic variables characterize a track, but here we examine only the measurement of the\ntransverse momentum. The precision and accuracy of the direction measurements are typically much\nbetter than that required for any physics analysis. The measurement of the initial position of the track\n(e.g. at the distance of closest approach to the beam line or vertex) is discussed in another note [13]. For\nthe momentum, we use the fractional residual, \u2206pT/pT, de\ufb01ned in equation 5. This distribution is \ufb01tted\nwith a Gaussian and the resolution is de\ufb01ned to be the sigma of this \ufb01t. The tails in the distributions\nare often more important than the core resolution and we characterize these by evaluating the fraction\nof found muons in \ufb01ve tail categories. The \ufb01rst three are those for which the magnitude of this residual\nexceeds 5%, 10% or 30%. The last category is the fraction for which the charge sign is incorrectly\nmeasured. Finally there is an intermediate category in which either the sign is incorrect or the magnitude\nof the measured momentum is more than two times larger than the true value.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n168\n\n4.3\nMonte Carlo samples\nOur primary benchmark sample is a collection of t\u00aft events requiring the presence of at least one lepton\n(electron, muon or tau). The initial inclusive sample was produced using MC@NLO in conjunction with\nHerwig [14]. This sample provides a variety of mechanisms for producing muons and we present results\nfor two: direct muons which do not have any quarks in their ancestry and indirect muons whose ancestry\nincludes a heavy quark (b or c) but not a tau. In this sample, the former are produced directly in the\nleptonic decay of a W-boson.\nPerformance metrics are plotted as a function of \u03b7 for t\u00aft direct muons. In addition, we tabulate\nef\ufb01ciencies and fake rates for these muons, for t\u00aft indirect muons, and for muons in separate low- and\nhigh-pT samples. The low-pT sample is taken from direct PYTHIA J/\u03c8 production with the J/\u03c8 forced\nto decay to two muons and a \ufb01lter selecting only those events where both muons have |\u03b7| < 2.5 and\npT > 4 GeV/c. Muons produced by other processes in these events are suppressed by restricting the\nanalyzed sample to muons that have a c-quark in their ancestry. The high-pT sample consists of direct\nmuons in PYTHIA production of Z\u2032 \u2192\u00b5\u00b5 with a Z\u2032 mass of 2 TeV. The generation also includes Z/\u03b3\nand interference but a dimuon mass cut (m\u00b5\u00b5 > 500 GeV/c) ensures that the average muon pT is above\n500 GeV/c.\nAt design luminosity, ATLAS will have many interactions in each beam crossing (pileup) and there\nwill be signi\ufb01cant background in the muon chambers from low-energy photons and neutrons (cavern\nbackground). To get an estimate of the effect this will have on our reconstruction algorithms, we pro-\ncessed a t\u00aft sample overlaid with the backgrounds expected for a reference luminosity of 1033 cm\u22122s\u22121.\nThe cavern background was included with a safety factor of 2.0, i.e. at twice the value expected for this\nluminosity. In the following, this sample is called the high-luminosity t\u00aft sample. Low luminosity refers\nto samples without any pileup or cavern background.\nThere is considerable uncertainty in the estimate of the cavern background and active development is\nunderway to improve reconstruction in this environment, and so the results presented here provide only\na rough indication of the performance we expect at high luminosity.\nFigure 5 shows the pT, \u03b7 and isolation energy distributions for the true muons in the samples studied\nin this note. The isolation energy was obtained by summing the calorimeter transverse energy in an \u03b7-\u03d5\ncone of radius 0.2 about the muon. The most probable value for the muon energy loss (as discussed in\nreference [2]) is subtracted from these values.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n169\n\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\ncounts\n0\n5000\n10000\nATLAS\n direct\ntt\nTruth\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n1000\n2000\n3000\nATLAS\n direct\ntt\nTruth\n/GeV)\nTisol\n(E\n10\nlog\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n1000\n2000\n3000\nATLAS\n direct\ntt\nTruth\n (GeV/c)\nT\np\n0\n10\n20\n30\n40\n50\ncounts\n0\n10000\n20000\n30000\nATLAS\n indirect\ntt\nTruth\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n1000\n2000\n3000\nATLAS\n indirect\ntt\nTruth\n/GeV)\nTisol\n(E\n10\nlog\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n2000\n4000\n6000\nATLAS\n indirect\ntt\nTruth\n (TeV/c)\nT\np\n0\n0.2 0.4 0.6 0.8\n1\n1.2\ncounts\n0\n500\n1000\n1500\nATLAS\nZ\u2019\nTruth\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n200\n400\n600\nATLAS\nZ\u2019\nTruth\n/GeV)\nTisol\n(E\n10\nlog\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n50\n100\n150\n200\nATLAS\nZ\u2019\nTruth\n (GeV/c)\nT\np\n0\n5\n10\n15\n20\ncounts\n0\n10000\n20000\n30000\nATLAS\n\u03a8\nJ/\nTruth\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n500\n1000\n1500\nATLAS\n\u03a8\nJ/\nTruth\n/GeV)\nTisol\n(E\n10\nlog\n-2\n-1\n0\n1\n2\n3\ncounts\n0\n500\n1000\n1500\n2000\nATLAS\n\u03a8\nJ/\nTruth\nFigure 5: True pT (left), \u03b7 (center) and isolation (right) distributions for the t\u00aft direct muons (top),\nt\u00aft indirect muons (second from top), Z\u2032 (mass 2 TeV) direct muons (third from top) and J/\u03c8 muons\n(bottom). Note that the pT range is different in each of the plots of that variable.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n170\n\n5\nStandalone muon performance\n5.1\nEf\ufb01ciencies and fake rates\nFigure 6 shows the standalone t\u00aft direct muon ef\ufb01ciencies and fake rates as functions of \u03b7 at low luminos-\nity (i.e. without any pileup or cavern background) and at our reference luminosity (1033 /cm2/sec with\ncavern background safety factor 2.0). Table 1 gives the integrated ef\ufb01ciencies and fake rates for these\nand other samples.\nEf\ufb01ciency\nFakes/(1000 events) above pT limit (GeV/c)\nSample\nfound\ngood\n3\n10\n20\n50\nMuonboy\nt\u00aft direct\n0.951 (1)\n0.812 (1)\n24.0 (3)\n4.4 (1)\n1.69 (7)\n0.52 (4)\nt\u00aft indirect\n0.949 (1)\n0.783 (2)\nhi-L t\u00aft direct\n0.950 (2)\n0.809 (3)\n53\n(1)\n8.2 (4)\n3.9 (2)\n1.9 (2)\nZ\u2032 direct\n0.914 (2)\n0.781 (3)\n141\n(4)\n79\n(3)\n61\n(3)\n37\n(2)\nJ/\u03c8\n0.959 (3)\n0.764 (6)\n51\n(1)\n5.0 (4)\n1.6 (2)\n0.6 (1)\nMoore/Muid\nt\u00aft direct\n0.943 (1)\n0.861 (1)\n19.8 (3)\n3.9 (1)\n1.44 (6)\n0.47 (4)\nt\u00aft indirect\n0.920 (2)\n0.838 (2)\nhi-L t\u00aft direct\n0.932 (2)\n0.836 (3)\n984\n(4)\n301\n(2)\n156\n(2)\n61\n(1)\nZ\u2032 direct\n0.887 (2)\n0.769 (3)\n168\n(4)\n102\n(3)\n75\n(3)\n43\n(2)\nJ/\u03c8\n0.830 (5)\n0.723 (6)\n6.7 (4)\n1.1 (2)\n0.5 (1)\n0.13 (6)\nTable 1: Muonboy and Moore/Muid ef\ufb01ciencies and fake rates for various samples (section 4.3).\nEf\ufb01ciencies are presented both for all found muons and for those with a good truth match (Deva <\n4.5). Both are calculated for true muons with |\u03b7| < 2.5 and pT > 10 GeV/c. Fake rates are\npresented for a variety of pT thresholds.\nComparing with Figure 3, we see most of the ef\ufb01ciency loss occurs in regions where the detector\ncoverage is poor, i.e. for |\u03b7| around 0.0 and 1.2. Otherwise, the t\u00aft muon ef\ufb01ciency is close to 100%\nfor Muonboy and around 99% for Moore/Muid. The Muid good fraction is signi\ufb01cantly higher than for\nMuonboy, presumably because of better handling of the material in the calorimeter. The algorithms have\nsimilar fake rates at low luminosity. At the higher luminosity, the Staco rate increases signi\ufb01cantly (by\na factor of 2-4) while the Moore/Muid rate increases dramatically (factor of 100). In the high-pT Z\u2032, the\nef\ufb01ciency falls by a few percent for both algorithms. For the low-pT (and non-isolated) J/\u03c8 muons, the\nMoore/Muid ef\ufb01ciency degrades signi\ufb01cantly while Muonboy remains high.\n5.2\nResolution\nFigure 7 shows the pT resolutions and tails as functions of \u03b7 and pT. The resolution is degraded at\nintermediate pseudorapidity (1.2 < |\u03b7| < 1.7) because of the reduced number of measurements (\ufb01gure 3),\nthe low \ufb01eld integral in the overlap between barrel and endcap toroids (\ufb01gure 2), and the material in the\nendcap toroid (\ufb01gure 1). The average resolution is very similar for the two algorithms. Despite having a\nlower good fraction, Muonboy has fewer muons for which the charge sign is incorrectly measured. This\nsuggests that, at least in the tails, Moore/Muid provides a better estimate of the momentum error while\nMuonboy provides a better estimate of its value. The Moore/Muid tails are likely due to the assignment\nof incorrect hits to spectrometer tracks.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n171\n\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nMuonboy\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nMoore/Muid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuonboy\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMoore/Muid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nMuonboy\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nMoore/Muid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nMuonboy\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nMoore/Muid\nFigure 6: Standalone ef\ufb01ciency and fake rate as functions of true \u03b7 for Muonboy (left) and\nMoore/Muid (right) for direct muons in t\u00aft at low (top) and high (bottom) luminosity. In the ef\ufb01-\nciency plots, the upper curve (blue) is the ef\ufb01ciency to \ufb01nd the muon while the lower curve (green)\nadditionally requires a good match (Deva < 4.5) between reconstructed and true track parameters.\nFake rates are shown for a variety of pT thresholds.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n172\n\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMuonboy\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMoore/Muid\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMuonboy\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMoore/Muid\n\u03b7\n-2\n-1\n0\n1\n2\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuonboy\n\u03b7\n-2\n-1\n0\n1\n2\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMoore/Muid\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuonboy\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMoore/Muid\nFigure 7: Standalone fractional momentum resolution (\u2206pT/pT) as function of \u03b7 (top) and pT\n(2nd row) and tails in that parameter also as functions of \u03b7 (3rd row) and pT (bottom). All are for\nboth Muonboy (left) and Moore/Muid (right). The tail is the fraction of reconstructed muons with\nmagnitude of \u2206pT/pT outside a range and is shown for a wide range of values. The last tail curve\n(red, \u201ccharge\u201d) includes only muons reconstructed with the wrong charge sign. The 4th tail curve\n(yellow, \u201c2X high\u201d) includes these and those with momentum magnitude more than two times the\ntrue value.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n173\n\n6\nInner detector performance\nFigure 8 shows the ef\ufb01ciency for t\u00aft direct muons and Table 2 gives the integrated ef\ufb01ciencies for all of the\nsamples. The ef\ufb01ciency is high for all \u03b7 (within the acceptance) and all samples. There is no evidence\nof degradation when pileup is added.\nThe inner detector momentum resolution is the same as that for tagged muons, reported later: see\nFigure 13 in section 8.\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nInner detector\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nInner detector\nFigure 8: Inner detector t\u00aft direct muon ef\ufb01ciency as a function of true \u03b7 at low (left) and high\n(right) luminosity. In each \ufb01gure, the upper curve (blue) is the ef\ufb01ciency to \ufb01nd the muon while\nthe lower curve (green) additionally requires a good match (Deva < 4.5) between reconstructed\nand true track parameters. The ef\ufb01ciency is for pT > 10 GeV/c.\nEf\ufb01ciency\nSample\nfound\ngood\nt\u00aft direct\n0.996 (1)\n0.950 (2)\nt\u00aft indirect\n0.997 (1)\n0.833 (5)\nhi-L t\u00aft direct\n0.995 (1)\n0.947 (2)\nZprime direct\n0.993 (1)\n0.966 (1)\nJ/\u03c8\n0.995 (1)\n0.941 (3)\nTable 2: Inner detector ef\ufb01ciencies. The samples and algorithms are described in the text. Ef\ufb01-\nciencies are presented both for all found muons and for those with a good truth match (Deva < 4.5).\nEf\ufb01ciencies are calculated for true muons with |\u03b7| < 2.5 and pT > 10 GeV/c.\n7\nCombined muon performance\n7.1\nEf\ufb01ciencies and fake rates\nFigure 9 shows the combined t\u00aft direct muon ef\ufb01ciency and fake rates for each algorithm as a function of\n\u03b7 for both low and high luminosity. Compared with the performance for standalone muons (\ufb01gure 6),\nStaco shows a small drop in ef\ufb01ciency with little reduction of the fake rate except for the lowest pT\nthreshold at high luminosity. In fact, the high-pT fake rates increase at either luminosity because low-pT\nstandalone muons are matched to high-pT inner-detector tracks. At low luminosity, Muid t\u00aft shows a\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n174\n\nsmall decrease in both ef\ufb01ciency and fake rate. When background is added, the dramatic increase in\nfakes for Moore standalone is not observed in Muid combined, i.e. the matching suppresses most of the\nfakes and the Muid high-pT fake rates are lower than those of Staco. However, the high-luminosity t\u00aft\nMuid ef\ufb01ciency is signi\ufb01cantly worse than that of Staco.\nWhen matching inner detector and muon spectrometer tracks, both Staco and Muid calculate \u03c72\nmatch\n(section 3.3) which serves as a discriminant for separating real and fake muons. The fakes include pion\nor kaon decays in or near the calorimeter. Figure 10 shows the \u03c72\nmatch distributions for both direct found\nmuons and fakes. We see that with a cut on this quantity, e.g. \u03c72\nmatch < 100, many of the Staco high-pT\nfakes can be suppressed with only a modest loss in ef\ufb01ciency. The higher Staco fake rates come from\nlooser cuts during reconstruction and, if the \u03c72\nmatch cuts are adjusted to give the same ef\ufb01ciencies, the\nStaco fake rate is lower.\nTable 3 shows the integrated Staco and Muid muon ef\ufb01ciencies and fake rates for all samples includ-\ning an entry showing the effect of the above cut on \u03c72\nmatch.\nEf\ufb01ciency\nFakes/(1000 events) above pT limit (GeV/c)\nSample\nfound\ngood\n3\n10\n20\n50\nStaco\nt\u00aft direct\n0.943 (1)\n0.875 (1)\n22.0 (3)\n9.6 (2)\n3.4 (1)\n0.62 (4)\nt\u00aft indirect\n0.933 (1)\n0.767 (2)\nt\u00aft direct cut\n0.924 (1)\n0.865 (1)\n14.8 (2)\n3.1 (1)\n0.39 (3)\n0.01 (1)\nhi-L t\u00aft direct\n0.941 (2)\n0.871 (3)\n25.9 (7)\n11.2 (4)\n4.3 (3)\n0.7 (1)\nZ\u2032\n0.910 (2)\n0.824 (3)\n14\n(1)\n8.4 (9)\n5.2 (7)\n3.4 (6)\nJ/\u03c8\n0.943 (3)\n0.873 (4)\n0.9 (2)\n0.24 (8)\n0.11 (5)\n0.0 (0)\nMuid\nt\u00aft direct\n0.926 (1)\n0.877 (1)\n15.4 (2)\n2.36 (9)\n0.48 (4)\n0.05 (1)\nt\u00aft indirect\n0.888 (2)\n0.748 (3)\nt\u00aft direct cut\n0.917 (1)\n0.871 (1)\n14.0 (2)\n1.96 (8)\n0.33 (3)\n0.03 (1)\nhi-L t\u00aft direct\n0.904 (2)\n0.854 (3)\n35.5 (8)\n5.0 (3)\n1.1 (1)\n0.24 (6)\nZ\u2032 direct\n0.872 (2)\n0.811 (3)\n11\n(1)\n4.5 (7)\n3.1 (6)\n2.7 (5)\nJ/\u03c8\n0.793 (5)\n0.741 (6)\n0.8 (1)\n0.03 (3)\n0.0 (0)\n0.0 (0)\nTable 3: Staco and Muid ef\ufb01ciencies and fake rates. The samples and algorithms are described in\nthe text. Algorithm names are followed by \u201ccut\u201d to indicate that reconstructed muons are required\nto have \u03c72\nmatch < 100 for both ef\ufb01ciency and fake calculations. Ef\ufb01ciencies are presented both for\nall found muons and for those with a good truth match. Both are calculated for true muons with\n|\u03b7| < 2.5 and pT > 10 GeV/c. The fake rates are presented for a variety of pT thresholds.\n7.2\nResolution\nFigure 11 shows the t\u00aft direct muon pT resolutions and tails as functions of \u03b7 and pT. Comparing\nwith the same for standalone reconstruction (\ufb01gure 7), we see, as expected, the combined resolution\nis signi\ufb01cantly better especially in the overlap region (|\u03b7| around 1.5) and for pT below 100 GeV/c.\nThere are also signi\ufb01cant reductions in the tails of momentum residuals. Misreconstruction and charge\nmisidenti\ufb01cation rates are around 0.01% for the combined muons instead of 0.1% for the standalone.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n175\n\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nStaco\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nMuid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nStaco\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nStaco\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nMuid\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nStaco\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nMuid\nFigure 9: Combined muon ef\ufb01ciency and fake rate for Staco (left) and Muid (right) as functions\nof true \u03b7 for direct muons in t\u00aft at low (top) and high (bottom) luminosity. In each ef\ufb01ciency plot,\nthe upper curve (blue) is the ef\ufb01ciency to \ufb01nd the muon while the lower curve (green) addition-\nally requires a good match (Deva < 4.5) between reconstructed and true track parameters. The\nef\ufb01ciencies are for pT > 10 GeV/c. Fake rates are shown for a variety of pT thresholds.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n176\n\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\n) (/event)\nmatch\n2\n\u03c7\n(\n10\ndN/dlog\n0\n0.1\n0.2\n0.3\nATLAS\n direct\ntt\nStaco\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\n) (/event)\nmatch\n2\n\u03c7\n(\n10\ndN/dlog\n0\n0.1\n0.2\n0.3\nATLAS\n direct\ntt\nMuid\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\nefficiency\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\n direct\ntt\nStaco\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\nefficiency\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\n direct\ntt\nMuid\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\n) (/event)\nmatch\n2\n\u03c7\n(\n10\ndN/dlog\n0\n0.005\n0.01\n0.015\n0.02\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nStaco\n)\nmatch\n2\n\u03c7\n(\n10\nlog\n-1\n0\n1\n2\n3\n4\n) (/event)\nmatch\n2\n\u03c7\n(\n10\ndN/dlog\n0\n0.005\n0.01\n0.015\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuid\nefficiency\n0.8\n0.85\n0.9\n0.95\n1\nfakes/event\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nStaco\nefficiency\n0.8\n0.85\n0.9\n0.95\n1\nfakes/event\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuid\nFigure 10: Distributions of \u03c72\nmatch for direct muons (top) and fakes (third from top). The fakes are\nshown for a variety of pT thresholds. The second row shows the ef\ufb01ciency as function of \u03c72\nmatch\nwhen muons above that value are rejected. The bottom row shows the fake rates as a function\nof ef\ufb01ciency as that threshold is varied. All are shown for both Staco (left) and Muid (right).\nThe sharp drops in the Staco \u03c72\nmatch distribution come from cuts on that quantity made during\nreconstruction, i.e. before \ufb01lling the output muon collection.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n177\n\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\np\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\n direct\ntt\nStaco\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\np\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\n direct\ntt\nMuid\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n resolution\nT\np\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\n direct\ntt\nStaco\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n resolution\nT\np\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\n direct\ntt\nMuid\n\u03b7\n-2\n-1\n0\n1\n2\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nStaco\n\u03b7\n-2\n-1\n0\n1\n2\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuid\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nStaco\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuid\nFigure 11: Combined muon fractional momentum resolution (\u2206pT/pT) as function of \u03b7 (top) and\npT (2nd row) and tails in that parameter also as functions of \u03b7 (3rd row) and pT (bottom). All\nare for both Staco (left) and Muid (right). The tail is the fraction of reconstructed muons with\nmagnitude of \u2206pT/pT outside a range and is shown for a wide range of values. The last tail curve\n(red, \u201ccharge\u201d) includes only muons reconstructed with the wrong charge sign. The 4th tail curve\n(yellow, \u201c2X high\u201d) includes these and those with momentum magnitude more than two times the\ntrue value.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n178\n\n8\nTagged muon performance\n8.1\nEf\ufb01ciencies and fake rates\nATLAS runs two tagging algorithms but only MuGirl attempts to \ufb01nd all muons. MuTag is run in a\nmanner to complement Staco and the performance of the combination of these two is reported in the\nfollowing section.\nFigure 12 shows the MuGirl direct muon ef\ufb01ciency and fake rates as a function of \u03b7 in t\u00aft at low and\nhigh luminosity. Table 4 gives the MuGirl integrated ef\ufb01ciencies and fake rates for all our samples.\nComparing with the combined muon results (\ufb01gure 9 and table 3), we see that MuGirl has lower\nef\ufb01ciency and a substantially higher fake rate. We also observe that its performance degrades faster\nwhen luminosity background is added. MuGirl has higher ef\ufb01ciency than Muid for reconstructing the\nlow-pT muons in the J/\u03c8 sample.\n8.2\nResolution\nFigure 13 shows the MuGirl pT resolution and tail as functions of \u03b7 and pT. MuGirl does not re\ufb01t the\ntracks and so this is just the resolution of the inner detector. Comparing with the standalone (\ufb01gure 7)\nand combined (\ufb01gure 11), we see how the standalone and inner measurements complement one another\nto give high precision over the full \u03b7 and pT range of the t\u00aft sample.\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nMuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nMuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nMuGirl\nFigure 12: MuGirl ef\ufb01ciency (left) and fake rates (right) as a function of true \u03b7 in t\u00aft at low (top)\nand high (bottom) luminosity. In each ef\ufb01ciency plot, the upper curve (blue) is the ef\ufb01ciency to \ufb01nd\nthe muon while the lower curve (green) additionally requires a good match (Deva < 4.5) between\nreconstructed and true track parameters. The ef\ufb01ciency is for muons with true pT > 10 GeV/c.\nFake rates are presented for a variety of pT thresholds.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n179\n\nEf\ufb01ciency\nFakes/(1000 events) above pT limit (GeV/c)\nSample\nfound\ngood\n3\n10\n20\n50\nt\u00aft direct\n0.911 (1)\n0.870 (1)\n105.0 (6)\n23.7 (3)\n7.3 (2)\n1.14 (6)\nt\u00aft indirect\n0.899 (2)\n0.748 (3)\nhi-L t\u00aft direct\n0.866 (3)\n0.825 (3)\n154\n(2)\n26.1 (7)\n7.6 (4)\n1.2 (1)\nZ\u2032 direct\n0.802 (3)\n0.781 (3)\n57\n(2)\n26\n(2)\n15\n(1)\n5.9 (8)\nJ/\u03c8 c-quark\n0.888 (4)\n0.839 (5)\n4.4 (3)\n0.11 (5)\n0\n(0)\n0\n(0)\nTable 4: MuGirl ef\ufb01ciencies and fake rates. The samples and algorithms are described in the text.\nEf\ufb01ciencies are presented both for all found muons and for those with a good truth match. Both\nare calculated for truth muons with |\u03b7| < 2.5 and pT > 10 GeV/c. The fake rates are presented for\na variety of pT thresholds.\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMuGirl\n\u03b7\n-2\n-1\n0\n1\n2\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuGirl\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n resolution\nT\np\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n direct\ntt\nMuGirl\n (GeV/c)\nT\np\n0\n50\n100\n150\n200\n tail fraction\nT\np\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n5%\n10%\n30%\n2X high\ncharge\nATLAS\n direct\ntt\nMuGirl\nFigure 13: MuGirl fractional momentum resolution (\u2206pT/pT) as a function of \u03b7 (top) and pT\n(bottom). Both the distribution (left) and tails (right) are shown for each. The tail is the fraction\nof reconstructed muons with magnitude of residual greater than a threshold and results are shown\nfor a variety of thresholds. The last tail curve (red, \u201ccharge\u201d) includes only muons reconstructed\nwith the wrong charge sign. The 4th tail curve (yellow, \u201c2X high\u201d) includes these and those with\nmomentum magnitude more than two times the true value.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n180\n\n9\nMerged muon performance\nFinally we consider merging the muons produced by different algorithms. There are many possible com-\nbinations but we restrict ourselves to two simple but important cases: merging the combined and tagged\nmuons separately within each collection (family), i.e. we examine Staco+MuTag and Muid+MuGirl.\nFigure 14 shows the corresponding direct muon ef\ufb01ciencies and fake rates in t\u00aft at low and high\nluminosity. The integrated ef\ufb01ciencies and fake rates for all samples are summarized in table 5. One\nof the primary goals of the tagging algorithms is to reconstruct low-pT muons which the standalone\nreconstruction misses because the energy loss in the calorimeter leaves these muons with very little\nmomentum in the muon spectrometer. Figure 15 shows the low-pT ef\ufb01ciency as function of pT for\ncombined alone and combined supplemented with tagged for each of the collections.\nSample\nEf\ufb01ciency\nFakes/(1000 events) above pT limit (GeV/c)\nfound\ngood\n3\n10\n20\n50\nStaco+MuTag\nt\u00aft direct\n0.948 (1)\n0.879 (1)\n49.0 (4)\n14.4 (2)\n4.8 (1)\n0.86 (5)\nt\u00aft indirect\n0.940 (1)\n0.772 (2)\nhi-L t\u00aft direct\n0.946 (2)\n0.876 (3)\n58\n(1)\n16.6 (5)\n6.1 (3)\n1.1 (1)\nZ\u2032 direct\n0.931 (2)\n0.844 (3)\n32\n(2)\n14\n(1)\n7.1 (9)\n4.2 (7)\nJ/\u03c8\n0.954 (3)\n0.883 (4)\n2.5 (3)\n0.3 (1)\n0.11 (5)\n0\n(0)\nMuid+MuGirl\nt\u00aft direct\n0.955 (1)\n0.903 (1)\n113.1 (6)\n24.9 (3)\n7.6 (2)\n1.17 (6)\nt\u00aft indirect\n0.946 (1)\n0.790 (2)\nhi-L t\u00aft direct\n0.952 (2)\n0.898 (2)\n181\n(2)\n29.8 (7)\n8.4 (4)\n1.2 (2)\nZ\u2032 direct\n0.929 (2)\n0.866 (3)\n61\n(3)\n28\n(2)\n16\n(1)\n7.5 (9)\nJ/\u03c8\n0.946 (3)\n0.885 (4)\n4.7 (4)\n0.11 (5)\n0\n(0)\n0\n(0)\nTable 5: Staco+MuTag and Muid+MuGirl ef\ufb01ciencies and fake rates. The samples and algorithms\nare described in the text. Ef\ufb01ciencies are presented both for all found muons and for those with\na good truth match. Both are calculated for truth muons with |\u03b7| < 2.5 and pT > 10 GeV/c. The\nfake rates are presented for a variety of pT thresholds.\nThe merge provides only a small improvement in the Staco ef\ufb01ciencies and a substantial increase in\nthe fake rates (factor of about four). For Muid, the ef\ufb01ciency gains are more substantial: the indirect\nt\u00aft ef\ufb01ciency increases by 6% and the J/\u03c8 by 15%. The fake rates are increased by a factor of \ufb01ve,\ni.e. slightly above the MuGirl rates. Overall, the Muid+MuGirl performance is very similar to that\nof Staco+MuTag. In both cases, we see the tagging algorithms do provide the signi\ufb01cant ef\ufb01ciency\nimprovement for pT below 10 GeV/c.\n10\nSummary\n10.1\nPresent status\nThe starting point for most ATLAS analyses are the combined muons, i.e. those muons constructed by\ncombining tracks found independently in the inner detector and muon spectrometer. Their momentum\nresolution and fake rate (with appropriate quality cuts) are both signi\ufb01cantly better than muons recon-\nstructed from either the spectrometer alone or muons identi\ufb01ed by tagging inner detector tracks. In t\u00aft\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n181\n\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nStaco+MuTag\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\ntt\nMuid+MuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nStaco+MuTag\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\ntt\nMuid+MuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nStaco+MuTag\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nefficiency\n0\n0.5\n1\nfound\ngood\nATLAS\n direct\nt\nL33sf02 t\nMuid+MuGirl\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nStaco+MuTag\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n (/event)\n\u03b7\ndN/d\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n>3\nT\np\n>10\nT\np\n>20\nT\np\n>50\nT\np\nATLAS\n direct\nt\nL33sf02 t\nMuid+MuGirl\nFigure 14: Muon ef\ufb01ciencies and fake rates for Staco+MuTag (left) and Muid+MuGirl (right) as\nfunctions of true \u03b7 in t\u00aft at low (top) and high (bottom) luminosity. In each ef\ufb01ciency plot, the\nupper curve (blue) is the ef\ufb01ciency to \ufb01nd the muon while the lower curve (green) additionally\nrequires a good match (Deva < 4.5) between reconstructed and true track parameters. The muon\nselection is described in the text. The ef\ufb01ciency is calculated for true pT > 10 GeV/c. The fake\nrates are presented for a variety of pT thresholds.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n182\n\n (GeV/c)\nT\np\n0\n5\n10\n15\n20\n25\nefficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nStaco\nStaco+MuTag\nATLAS\n indirect\ntt\n (GeV/c)\nT\np\n0\n5\n10\n15\n20\n25\nefficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMuid\nMuid+MuGirl\nATLAS\n indirect\ntt\nFigure 15: Low-pT muon \ufb01nding ef\ufb01ciencies for combined muons alone and combined plus\ntagged for the Staco (left) and Muid (right) collections. Results are show for the t\u00aft indirect se-\nlection. The other samples show similar behavior but have much poorer statistics at low-pT. The\nef\ufb01ciency is calculated for muons with |\u03b7| < 2.5.\nevents, for muons from W \u2192\u00b5\u03bd with |\u03b7| < 2.5, the Staco combined muon ef\ufb01ciency is 94% with most\nof the loss coming from regions of the spectrometer where the detector coverage is thin. The ef\ufb01ciency\nfalls by a few percent when the muon transverse momentum reaches the TeV scale where it is much\nmore likely that a muon will radiate a substantial fraction of its energy. The t\u00aft rate for fakes is a few per\nthousand events for pT > 20 GeV/c and this can be reduced by an order a of magnitude (with a 2% loss\nin ef\ufb01ciency) by cutting on the muon quality (\u03c72\nmatch). The performance of the Muid algorithm is only\nslightly worse for t\u00aft but it is signi\ufb01cantly less robust, losing additional ef\ufb01ciency at low-pT and high-pT\nand when luminosity background is added.\nThe combined muons can be supplemented with the standalone muons to extend the \u03b7 coverage to\n2.7 and to recover the percent or so ef\ufb01ciency loss in combination. We do not report on this merge\nbut it is clear from the standalone results that the fake rates will increase signi\ufb01cantly especially when\nluminosity background is present. In the case of Moore, the fake rate is likely intolerable.\nWe \ufb01nd that merging with MuTag provides only slight improvement to the Staco ef\ufb01ciency with a\nsigni\ufb01cant increase in fakes. This may re\ufb02ect the success of Staco more than de\ufb01ciencies in MuTag.\nMuGirl is able to improve the Muid ef\ufb01ciency, so that the merge Muid+MuGirl has performance similar\nto Staco or Staco+MuTag. By itself, the MuGirl ef\ufb01ciency is somewhat less than that of Staco especially\nfor high-pT muons, and the fake rates are substantially higher.\n10.2\nFuture\nThe results presented here re\ufb02ect the status of the ATLAS software used to reconstruct (Monte Carlo)\nproduction data in 2007. Work continues both to improve the algorithms described here and to add\nnew ones. The high-luminosity fake rate for Moore is being addressed by introducing timing cuts and\ninvestigating alternative approaches to the pattern recognition. The latter also has the goal of reducing the\nnumber of false hit assignments. Combined muons with large \u03c72\nmatch are being studied to see if a second\nstage of pattern recognition can reduce the ef\ufb01ciency loss or resolution tails. Efforts are underway to\nimprove or replace the existing spectrometer-tagging algorithms; in particular, code is already in place\nto extrapolate to additional stations enabling recovery of much of the standalone/combined ef\ufb01ciency\nloss near |\u03b7| = 1.2. Two calorimeter-tagging algorithms have been developed and offer the possibility\nof recovering much of the ef\ufb01ciency loss near \u03b7 = 0. Improvements in modularity will make it possible\nto mix components from the different algorithms, (e.g. to use Muid to combine Muonboy muons) and\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n183\n\nenable algorithms to share common tools such as those being developed to calculate energy loss, re\ufb01t\nmuon tracks, and repair muons with poor \ufb01t quality.\nReferences\n[1] ATLAS Collaboration, G. Aad et al., The ATLAS experiment at the CERN Large Hadron Collider,\n2008 JINST 3 S08003 (2008).\n[2] ATLAS Collaboration, Muons in the Calorimeters: Energy Loss Corrections and Muon Tagging,\nthis volume.\n[3] S. Hassini, et al., NIM A572 (2007) 77\u201379.\n[4] Th. Lagouri, et al., IEEE Trans. Nucl. Sci. 51 (2004) 3030\u20133033.\n[5] D. Adams, et al., ATL-SOFT-2003-007 (2003).\n[6] K. Nikolopoulos, D. Fassouliotis, C. Kourkoumelis, and A. Poppleton, IEEE Trans. Nucl. Sci. 54\n(2007) 1792\u20131796.\n[7] T. Cornelissen, et al., ATL-SOFT-PUB-2007-007 (2007).\n[8] S. Tarem, Z. Tarem, N. Panikashvili, O. Belkind, Nuclear Science Symposium Conference Record,\n2007 IEEE 1 (2007) 617\u2013621.\n[9] T. Sjostrand, S. Mrenna, and P. Skands, JHEP 05 (2006) 26.\n[10] S. Frixione and B.R. Webber, JHEP 0206 (2002) 029.\n[11] S. Frixione, P. Nason and B.R. Webber, JHEP 0308 (2003) 007.\n[12] J. Allison et al., IEEE Transactions on Nuclear Science 53 (2006) 270\u2013278.\n[13] ATLAS Collaboration, Production Cross-Section Measurements and Study of the Properties of the\nExclusive B+ \u2192J/\u03c8K+ Channel, this volume.\n[14] G. Corcella et al., hep-ph/0210213.\nMUONS \u2013 MUON RECONSTRUCTION AND IDENTIFICATION: STUDIES WITH SIMULATED . . .\n184\n\nMuons in the Calorimeters:\nEnergy Loss Corrections and Muon Tagging\nAbstract\nThe muon spectrometer is the outermost subdetector of the ATLAS detector,\nbeginning after a muon has traversed 100 radiation lengths of material. Muon\nmomentum measurements must be corrected for energy loss in the calorimeters\nand the inert material before the muons reach the muon spectrometer. Energy\nlost in the calorimeters can be estimated from parameterizations or from a\nmeasurement of the energy deposited in the calorimeters. In addition, the muon\nenergy loss measurement can be used to tag muons not reconstructed in the\nmuon spectrometer due to inef\ufb01ciencies, spectrometer acceptance or their low\nmomenta.\nIn this document we discuss different algorithms developed to perform the en-\nergy loss correction in the muon reconstruction. We compare the performance\nof the muon reconstruction algorithms before and after the energy loss correc-\ntion is applied. In addition, we describe the muon tagging algorithms, based\non measurements obtained in the calorimeters, and contrast their performance\nin different simulated data samples.\n1\nIntroduction\nMuons traverse the inner detector and the calorimeters in the ATLAS experiment before reaching the\nmuon spectrometer. The material thickness traversed by the muons before reaching the muon spectrom-\neter is over 100 radiation lengths (X0) (see Figure 1). By passing through this material, muons undergo\nelectromagnetic interactions which result in a partial loss of their energy. As over 80% of this material is\nin the instrumented areas of the calorimeters, the energy loss can be measured. Understanding how this\nenergy loss happens, its magnitude and how to measure it is essential to obtain the best performance in\nmuon reconstruction and identi\ufb01cation.\nIn this document we discuss the aspects of muon reconstruction and identi\ufb01cation that make use of all\navailable energy loss information in the ATLAS software. The Muonboy [1] and Muid [2] algorithms for\nmuon reconstruction take into account internally the calorimeter material effects for tracks already found\nin the muon spectrometer. Algorithms that calculate the energy loss and transport the track anywhere in\nthe detector are also available. The detailed computation of this correction is the main focus of Sections 2\nand 3, while Section 4 is devoted to the use of the energy loss information for muon identi\ufb01cation. This\nnote gives an overview of the current algorithms and techniques which will be used for the reconstruction\nof the \ufb01rst data.\n2\nAlgorithmic Treatment of Material Effects\nWhen a muon traverses the detector material, it undergoes successive de\ufb02ections and a loss of energy.\nThe total angular de\ufb02ection is an accumulation of many small angle de\ufb02ections, referred to as multiple\n(Coulomb) scattering; and it is well approximated by a gaussian distribution that is centered at a zero\nmean value. The expected root mean square of the projected scattering angle can be described by the\nformula of Highland [4]:\n\u03c3 proj\nms\n= 13.6 MeV\n\u03b2cp\n\u221a\nt[1+0.038lnt],\n(1)\n185\n\nFigure 1: Material distribution before the muon spectrometer in ATLAS as a function of \u03b7 [3]. The\nmaterial is expressed in radiation lengths (X0).\nwhere t is the thickness of the traversed material in units of the radiation length X0. The energy loss, on\nthe other hand, is non-gaussian. Throughout this document, we will study the energy loss of muons going\nthrough the ATLAS detector in detail. The discussion of multiple scattering, however, will be limited\nto this section, because it is simpler and it will be based on the Highland formula shown above. The\nthickness in the formula above is calculated from the geometry description for all algorithms. However,\nthere are small differences in how the multiple scattering information is used in the track \ufb01tting. These\ndifferences are explained below, as the different track \ufb01tting strategies are discussed.\nIn ATLAS track reconstruction applications, two main track \ufb01tting strategies are deployed: the classi-\ncal least squares method and the progressive method that corresponds to the Kalman \ufb01lter formalism [5].\nThe least squares \ufb01t:\nIn the global \ufb01tting technique, most material effects are directly integrated into\nthe \u03c72 function (the energy loss may or may not be \ufb01tted). This is done by introducing the de\ufb02ection\nangles and, possibly, energy losses as additional parameters to the \ufb01t.\nThe contribution of the \ufb01tted scattering angles to the \u03c72 function has to be regulated by the expected\nrange of the scattering process in the traversed material. Scattering effects are applied to the muon on two\nsurfaces along its trajectory, because the scattering effects from material bulk can be accurately described\nby two scattering centers. The Muonboy algorithm iterates its calculation of the muon trajectory in a\ncomplex geometry with many scattering centers. The number of scattering centers is reduced to two\nafter the iteration. The iteration allows for a calculation of the material traversed after the trajectory has\nbeen modi\ufb01ed to account for the energy loss. On the other hand, the Muid algorithm and the ATLAS\ntracking global-\u03c72 \ufb01tter [6] currently use a map of the material from the Monte Carlo on two surfaces.\nThe \u03b7 coordinate of the track on these two surfaces is then used to calculate the amount of material\ntraversed by the muon.\nThe least squares \ufb01t with the calorimeter energy loss as a \ufb01tted variable can only be performed in\na combined \ufb01t including measurements of both the muon spectrometer segments and the inner detector\nhits. If no inner detector hits exist, the treatment of the energy loss effects is fundamentally equivalent\nfor both a least-squares-inspired algorithm and a Kalman-\ufb01lter-inspired algorithm.\nTo minimize the number of degrees of freedom in the least-squares \ufb01t, the number of \ufb01tted variables\nmust be minimized. In particular, one energy loss variable in a track \ufb01t is preferable. This does not mean\nthat the trajectory cannot be affected smoothly by the energy loss, because an extended set of material\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n186\n\nlayers can be calculated using a detailed detector description as in Figure 2 and the \ufb01tted energy loss\nFigure 2: Left: 3-D view of the tracking geometry up to the muon spectrometer. Right: Example\nset of energy loss update layers (shown as additional surfaces with respect to the \ufb01gure on the left;\nupdate positions shown as squares) created during the extrapolation of a track (black line) through the\ncalorimeter.\ndistributed proportionally among these layers. This is done for the purpose of transporting the track\nthrough the calorimeters inside the Muonboy algorithm. An alternative approach is currently taken in the\nMuid and ATLAS tracking global-\u03c72 \ufb01tter. These algorithms apply the energy loss to the track on one\nsurface inside the calorimeters hence approximate the rate of change of curvature within the calorimeter\nvolume (i.e.: they assume the momentum of the muon changes only at one place along its trajectory).\nThe effect of this simpli\ufb01cation on the muon combined reconstruction is expected to be small, be-\ncause the energy loss only affects the trajectory of the track if the track is bending. However, the area\nwhere most of the energy loss happens (the calorimeter) has a small magnetic \ufb01eld. A quantitative es-\ntimate of the effect of the simpli\ufb01cation can be obtained by comparing the multiple scattering effects\non the track and the bending that the track undergoes from its entrance in the calorimeters to its exit.\nThe bending is shown in Figure 3. Equation 1 indicates that a 10 GeV (100 GeV) muon going through\nthe calorimeters scatters following a gaussian distribution with RMS \u224814-20 (1.4-2) milliradians (with\nX0 = 100-200 from Figure 1). Figure 3 shows that the deviation of the track due to the magnetic \ufb01eld is\ncomparable to the deviation expected from multiple scattering at least in the \u03c6 direction. Algorithms that\nuse one surface to apply the energy loss correction approximate the mean trajectory inside the calorime-\nter with a systematic offset that increases with depth to a maximum value at the calorimeter centre. The\nmagnitude of this offset is proportional to the magnetic bending scaled by the fraction of energy loss to\nmuon energy. It thus remains small with respect to the uncertainties caused by Coulomb scattering.\nProgressive \ufb01tting techniques:\nIn progressive \ufb01tting techniques, the particle-detector interaction is\npart of the transport process of the track to the next surface where a hit may exist (measurement sur-\nface). The transported track can then be compared (and updated) with the measurement obtained on the\nnext measurement surface. In this transport process magnetic \ufb01eld and material effects (multiple scat-\ntering and energy loss) are applied to the parameterization of the track. Multiple scattering is applied\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n187\n\n0\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n\u03b7\n \n\u2206\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\np=10 GeV\np=100 GeV\n0\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n\u03c6 \n\u2206\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\np=10 GeV\np=100 GeV\nFigure 3: Calculated difference between the calorimeter entrance and exit coordinates (\u2206\u03b7, left, and \u2206\u03c6,\nright) for 10 GeV (solid squares) and 100 GeV muons as a function of \u03b70 of the muon at the interaction\npoint. The lack of mirror symmetry is due to the combined effect of the return \ufb02ux of the solenoid\n(unidirectional) and the toroidal magnetic \ufb01eld (symmetric around the z axis).\nby increasing the uncertainties of the angular direction variables, while energy loss effects are taken into\naccount in two ways. A mean energy loss is applied to the track parameterization, and then an uncer-\ntainty is added to the corresponding covariance matrix term to account for the stochastic behavior of the\nenergy loss. The resulting increased covariance terms degrade the track prediction for the subsequent\nmeasurement surface.\nProgressive \ufb01tting tools rely, therefore, on a precise description of the detector material and magnetic\n\ufb01eld. An example is shown in Figure 2. The illustration on the right of Figure 2 shows material layers\nthat are calculated dynamically during the extrapolation process into the calorimeter active volumes.\nIn ATLAS, the stand-alone muon reconstruction algorithms (MOORE [7] and Muonboy) use ex-\nclusively the least-squares formalism to \ufb01t tracks in the muon spectrometer. On the other hand, the\ninner detector reconstruction uses by default the progressive \ufb01tting techniques. In combined muon re-\nconstruction, when the hits in the inner detector are used in combination with the muon spectrometer,\nthe Muonboy-based algorithm (STACO) combines tracks reconstructed in the inner detector and muon\nspectrometer independently, therefore being a mixture of the tracking \ufb01t and the least-squares \ufb01t carried\nout by Muonboy. On the other hand, the MOORE-based algorithm (Muid) performs a least-squares \ufb01t in\nboth subsystems.\n3\nCorrections for the Energy Loss from the Beam Pipe to the Muon Spec-\ntrometer\nIn this section we describe how the energy loss is calculated from GEANT4 [8] based parameterizations\nand/or measurements of the energy loss by the calorimeters. Muon isolation is also discussed in this\ncontext. Finally, the energy loss corrections are validated as part of the muon reconstruction algorithms.\n3.1\nParameterizations of the Energy Loss\nRelativistic muons going through matter lose energy mostly through electromagnetic processes: ion-\nization, e+e\u2212\npair-production, and bremsstrahlung. Ionization energy loss dominates for muons of\nmomenta \u2272100 GeV. Bremsstrahlung and e+e\u2212pair-production energy losses are often jointly referred\nto as radiative energy losses. Higher energy muons lose energy mostly through radiative energy losses.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n188\n\nHowever, when passing through materials made of high-Z elements the radiative effects can be already\nsigni\ufb01cant for muons of energies \u224810 GeV [9].\nIonization energy losses have been studied in detail, and an expression for the mean energy loss per\nunit length as a function of muon momentum and material type exists in the form of the Bethe-Bloch\nequation [10]. Other closed-form formulae exist to describe other properties of the ionization energy loss.\nBremsstrahlung energy losses can be well parameterized using the Bethe-Heitler equation. However,\nthere is no closed-form formula that accounts for all energy losses. Nevertheless, theoretical calculations\nfor the cross-sections of all these energy loss processes do exist. With these closed-form cross-sections,\nsimulation software such as GEANT4 can be used to calculate the energy loss distribution for muons\ngoing through a speci\ufb01c material or set of materials.\nThe \ufb02uctuations of the ionization energy loss of muons in thin layers of material are characterized\nby a Landau distribution. Here \u201cthin\u201d refers to any amount of material where the muon loses a small\npercentage of its energy. Once radiative effects become the main contribution to the energy loss, the\nshape of the distribution changes slowly into a distribution with a larger tail. Fits to a Landau distribution\nstill characterize the distribution fairly well, with a small bias that pushes the most probable value of the\n\ufb01tted distribution to values higher than the most probable energy loss [11]. These features are shown\nfor the energy loss distributions of muons going from the beam-pipe to the exit of the calorimeters in\nFigure 4.\n (MeV)\nloss\nE\n0\n2000\n4000\n6000\n8000\n10000 12000 14000\nEvents\n1\n10\n2\n10\n (MeV)\nloss\nE\n0\n2000\n4000\n6000\n8000\n10000 12000 14000\nEvents\n1\n10\n2\n10\nFigure 4: Distribution of the energy loss of muons passing through the calorimeters (|\u03b7| < 0.15) as\nobtained for 10 GeV muons (left) and 1 TeV muons (right) \ufb01tted to Landau distributions (solid line).\nAs can be seen in Figure 4 the Landau distribution is highly asymmetrical with a long tail towards\nhigher energy loss. For track \ufb01tting, where most of the common \ufb01tters require gaussian process noise,\nthis has a non-trivial consequence: in general, a gaussian approximation has to be performed for the\ninclusion of material effects in the track \ufb01tting [12].\nIn order to express muon spectrometer tracks at the perigee, the total energy loss in the path can be\nparameterized and applied to the track at some speci\ufb01c position inside the calorimeters. As the detector\nis approximately symmetric in \u03c6, parameterizations need only be done as a function of muon momentum\nand \u03b7. The \u03b7-dependence is included by performing the momentum parameterizations in different \u03b7\nbins of width 0.1 throughout the muon spectrometer acceptance (|\u03b7| < 2.7). The dependence of the most\nprobable value of the energy loss, Empv\nloss , as a function of the muon momentum, p\u00b5, is well described by\nEmpv\nloss (p\u00b5) = ampv\n0\n+ampv\n1\nln p\u00b5 +ampv\n2\np\u00b5,\n(2)\nwhere ampv\n0\ndescribes the minimum ionizing part, ampv\n1\ndescribes the relativistic rise, and ampv\n2\ndescribes\nthe radiative effects. The width parameter, \u03c3loss, of the energy loss distribution is well \ufb01tted by a linear\nfunction \u03c3loss(p\u00b5) = a\u03c3\n0 +a\u03c3\n1 p\u00b5. Some of these \ufb01ts are illustrated in Figure 5. This parameterization is\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n189\n\n (GeV)\n\u00b5\np\n10\n2\n10\n3\n10\n (GeV)\nloss\nmpv\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n|<0.5\n\u03b7\n0.4<|\n|<1.3\n\u03b7\n1.2<|\n|<2.1\n\u03b7\n2.0<|\n (GeV)\n\u00b5\np\n10\n2\n10\n3\n10\n (GeV)\nloss\n\u03c3\n0\n0.5\n1\n1.5\n2\n2.5\n|<0.5\n\u03b7\n0.4<|\n|<1.3\n\u03b7\n1.2<|\n|<2.1\n\u03b7\n2.0<|\nFigure 5: Parameterization of the Empv\nloss (left) and \u03c3loss (right) of the Landau distribution as a function of\nmuon momentum for different \u03b7 regions. One sees a good agreement between the GEANT4 values and\nthe parameterization.\nused as part of the Muid algorithm for combined muon reconstruction [3].\nAn alternative approach exists in the ATLAS tracking. In this approach, the energy loss is param-\neterized in each calorimeter or even calorimeter layer. The parameterization inside the calorimeters is\napplied to the muon track using the detailed geometry described in Section 2.\nThe most probable value and width parameter of the Landau distribution are not affected by radiative\nenergy losses in thin materials in the muon energy range of interest (\u223c5 GeV to a few TeV). This justi\ufb01es\ntreating energy loss in non-instrumented material, such as support structures, up to the entrance of the\nmuon spectrometer as if it was caused by ionization processes only. The most probable value of the\ndistribution of energy loss by ionization can be calculated if the distribution of material is known [13].\nSince material properties are known in each of the volumes in the geometry description used, it is easy\nto apply this correction to tracks being transported through this geometry.\nFor the instrumented regions of the calorimeters, a parameterization that accounts for the large radia-\ntive energy losses is required. To provide a parameterization that is correct for the full \u03b7 range and for\ntrack transport inside the calorimeters, a study of energy loss as a function of the traversed calorimeter\nthickness, x, was performed. Two parameters that characterize fully the pdf of the energy loss for muons\nwere \ufb01tted satisfactorily using several \ufb01xed momentum samples as\nEmpv,\u03c3\nloss\n(x, p\u00b5) = bmpv,\u03c3\n0\n(p\u00b5)x+bmpv,\u03c3\n1\n(p\u00b5)xlnx.\n(3)\nThe momentum dependence of the bi(p\u00b5) parameters was found to follow the same form as in Equa-\ntion 2. Fits for some of the absorber materials are shown in Figure 6. These parameterizations have\nbeen validated over the \u03b7 range from -3 to 3. A direct comparison of the most probable energy loss in\nGEANT4 simulation and in the geometry of the ATLAS tracking algorithms is shown in Figure 7 for\nmuons propagating from the beam-pipe to the exit of the electromagnetic calorimeters and to the exit of\nthe hadronic calorimeters.\n3.2\nMeasurements of the Energy Deposited in the Calorimeters\nIn this section the measurement of the muon energy loss in the calorimeters is discussed. Understanding\nthis measurement is important because it allows for an improvement in the energy loss determination.\nThis section provides a basic description of the ATLAS calorimeters and their measurements which is\nimportant for understanding the topics discussed in Sections 3.3, 3.4 and 4.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n190\n\nThickness (cm)\n0\n20\n40\n60\n80\n100\n120\n140\n (GeV)\n\u03c3\nmpv,\nloss\nE\n0\n0.5\n1\n1.5\n2\n2.5\nMost Probable Value (mpv)\nof Landau Distribution\n) of Landau Distribution\n\u03c3\nWidth (\n (GeV)\n\u00b5\np\n10\n2\n10\n3\n10\n (GeV/cm)\n0,1\nb\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n0.04\n in lead\n0\nb\n in lead\n1\nb\nFigure 6: Left: Fit to the most probable value and width of the Landau distribution as a function of\nthickness of iron for muons of momentum 200 GeV. The \ufb01tting function has the form b0x + b1xlnx.\nRight: Fit to the parameters b0 and b1 for the most probable value of the energy loss in lead as a function\nof muon momentum.\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n10 GeV\n(GeV)\nloss\nmpv\nE\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n1 TeV\n(GeV)\nloss\nmpv\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nFigure 7: Most probable value of the energy loss as parameterized in the geometry of the ATLAS tracking\n(points) and in GEANT4 for muons of momentum 10 GeV (left) and 1 TeV (right) as a function of\npseudorapidity. The solid line and points correspond to the energy loss of muons propagating from the\nbeam pipe to the exit of the hadronic calorimeters. The \ufb01lled histogram and hollow points correspond to\nthe energy loss of muons propagating from the beam pipe to the entrance of the hadronic calorimeters.\n3.2.1\nMuons in the Liquid Argon Calorimeters\nThe electromagnetic calorimeter is a lead-liquid argon sampling calorimeter with accordion shaped ab-\nsorbers and electrodes, covering the |\u03b7| range up to 3.2.\nThe hadronic end-cap calorimeter, also based on liquid argon technology, covers the |\u03b7| range from\n1.5 to 3.2. The absorbers are made of parallel plates of copper. The total thickness of the hadronic\nend-cap calorimeters is 10 interaction lengths (\u03bbint). The measurement of a muon signal in the hadronic\nend-cap is complicated because the noise levels are high compared to the muon signal itself [14].\nThe detailed geometrical description of the LAr calorimeters is presented in [15]. Only the aspects\nrelevant for muon studies will be recalled. Both barrel and end-cap calorimeters possess up to three\nlongitudinal samplings (called strip, middle and back). They are completed by a liquid argon presampler\ndetector to estimate the energy lost in upstream material. The signal and noise distributions in two\nlongitudinal calorimeter samples in the barrel of the electromagnetic calorimeter are shown in Figure 8\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n191\n\nFigure 8: Distribution of the muon energy deposited in one electromagnetic calorimeter cell by 150 GeV\nmuons, \ufb01tted to a Landau function convolved with a gaussian [16]. The gaussians on the left of each\nplot are the distributions of the noise. Left (right): energy deposit in a cell belonging to the \ufb01rst (middle)\nlongitudinal sampling traversed by the muon. The energy is the sum of the energies of the (up to two)\ncells belonging to the muon cluster (see Section 4). The data were collected in the 2004 Combined Test\nBeam.\nfor 150 GeV muons. Further discussion of how these distributions were calculated from the combined\ntest beam data can be found in Section 4. The signal can be separated from the noise, especially in the\nmiddle sampling. In addition, comparisons between GEANT4 simulation and test beam data show that,\ndespite the high noise in the \ufb01rst sampling, the electromagnetic calorimeter can measure reliably the\nenergy lost by muons traversing it.\n3.2.2\nMuons in the Tile Calorimeter\nThe Tile Calorimeter (TileCal) [17] is a plastic scintillator/steel sampling calorimeter, located in the\nregion |\u03b7| < 1.7; it is divided into three cylindrical sections, referred to as the barrel and extended\nbarrels. It extends from an inner radius of 2.28 m to an outer radius of 4.25 m. Modules are segmented\nin \u03b7 and in radial depth. In the direction perpendicular to the beam axis, the three radial segments span\n1.5, 4.1 and 1.8 \u03bbint in the barrel and 1.5, 2.6, 3.3 \u03bbint in the extended barrels. The resulting typical\ncell dimensions are \u2206\u03b7 \u00d7\u2206\u03c6 = 0.1\u00d70.1 (0.2\u00d70.1 in the outermost layer). This segmentation de\ufb01nes a\nquasi-projective tower structure.\nThe TileCal response to high-energy muons follows a Landau-type distribution with characteristi-\ncally long tails at high energies caused by radiative processes and energetic \u03b4\u2013rays. This response has\nbeen extensively studied in test beams with 180 GeV muons incident at projective angles. The peak\nvalues of the muon signals vary by more than a factor of two in projective geometry. An example of the\nmuon signal, expressed in units of collected charge (pC), is shown in Figure 9, both for the whole tower\nand the last radial compartment. The signal is well separated from the noise, with a signal-to-noise ratio\n(S/N) of \u223c44 and \u223c18 respectively. The muon response was shown to be uniform in \u03b7 to within 1.9 %\nover all modules tested. The energy deposition spectrum observed in the TileCal test beams is within a\nfew percent of the GEANT4 prediction.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n192\n\nFigure 9: Example of the isolated muon signal as measured at \u03b7 = 0.35 in the whole tower (left) and in\nthe last radial compartment (right). The narrow peaks represent the corresponding noise. The energy is\nmeasured in units of collected charge. For a muon 1 pC corresponds to roughly 1 GeV, yielding a noise\nwidth of roughly 40 MeV for the last radial compartment. The data were collected in test beams in 2002\nand 2003.\n3.2.3\nMeasurements in Muon Algorithms\nThe previous sections discussed the reconstruction of energy depositions at the cell level. To provide\nestimates of muon energy loss and muon isolation, several cells need to be used along the muon trajectory.\nIn addition, muon calibration factors such as the e/\u00b5 ratio for minimum ionizing muons, need to be\nadjusted in order to \ufb01nd the correct energy deposition.\nThe classical method for measuring the energy loss of muons in calorimeters is based on the concept\nof a calorimeter tower, where the muon is assumed to follow a straight trajectory inside the calorime-\nters. A tower is de\ufb01ned as all calorimeter cells within a cone of \ufb01xed radius \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 cen-\ntered around the muon trajectory. Motivated by this concept, but with a few muon-speci\ufb01c changes, the\nStraight Line method has been developed as part of the Muid algorithm for muon reconstruction. The\nStraight Line method calculates the coordinates of the relevant track at half the depth of the calorimeter\nby transporting the track to that position. These coordinates are used to calculate the calorimeter cells\nincluded in the measurement cone.\nIn the Track Update method, the muon trajectory through the calorimeters is extrapolated either from\ninner detector tracks or muon spectrometer tracks. Given this trajectory, the center of the measurement\ncone is recalculated at each calorimeter layer. Figure 10 shows a qualitative comparison between the\nStraight Line method and the Track Update method.\nFigure 3 illustrated the quantitative differences in the muon trajectories from the two methods. The\ndifference between the Straight Line and Track Update methods can be estimated by comparing the\ncoordinates of the muon at the entrance of the electromagnetic calorimeters and at the exit of the hadronic\ncalorimeters. The difference is clearly negligible for muons of pT > 100 GeV, even though it can be as\nbig as a third of a hadronic cell width for 10 GeV muons.\nIn Figure 11, a comparison between the measured energy and the true energy loss is shown for the\nTrack Update method. The average measured transverse energy loss in a cone of 0.2 around the muon\ntrajectory for single muons of momentum 10, 100 and 300 GeV is shown as a function of \u03b7. In the same\n\u03b7 bins the average true (as obtained from the GEANT4 full simulation) transverse energy lost between\nthe interaction point and the entrance of the muon spectrometer is shown. The energy lost by the muons\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n193\n\nFigure 10: Illustration of the Straight Line (left) and Track Update (right) concepts.\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n3\n (GeV)\nloss\nT\nE\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nloss\nT\nTrue E\nloss\nT\nMeasured E\n\u03b7\n0\n0.5\n1\n1.5\n2\n2 5\n3\n (GeV)\nloss\nT\nE\n0\n0 5\n1\n1 5\n2\n2 5\n3\n3 5\n4\n4 5\n5\nloss\nT\nTrue E\nloss\nT\nMeasured E\n\u03b7\n0\n0 5\n1\n1.5\n2\n2.5\n3\n (GeV)\nloss\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\nloss\nT\nTrue E\nloss\nT\nMeasured E\nFigure 11: Comparison between the average measured transverse energy deposition (points) and true\nenergy lost between the beam-pipe and the muon spectrometer (line) for muons of momentum 10 GeV\n(left), 100 GeV (center) and 300 GeV (right). The errors shown are statistical only.\nis well estimated by measurements in the calorimeters. The region around |\u03b7| = 1 corresponds to the\ncrack in the TileCal. Consequently, the measurement underestimates the energy loss in that region.\n3.3\nMuon Isolation\nThe previous studies demonstrate the capabilities of the calorimeters to measure the energy lost by\nmuons. However, these studies were all performed with single muon samples. In real physics sam-\nples, muons do not reach the calorimeters alone, but are often accompanied by additional particles that\ndeposit energy in the cells around the muon trajectory and contaminate the muon energy loss measure-\nment. Therefore, in order to determine the energy loss of such muons, isolation criteria must also be\nde\ufb01ned and optimized for maximum reliability in the energy measurement.\nIsolation criteria can be divided into two categories: calorimeter-based and track-based. In muon\nreconstruction an area is de\ufb01ned around the muon trajectory with a minimum and maximum radius for\nthe purpose of determining calorimeter isolation. This achieves the purpose of excluding the cells where\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n194\n\nthe muon deposits its energy. The size of this inner radius needs to be optimized to collect most of the\nenergy lost by the muon but as little energy as possible from other particles. The energy deposited in the\nannulus between the inner radius and the outer radius, where the muon deposits little energy, is what the\nfollowing paragraphs refer to as isolation energy. The optimal radii that de\ufb01ne this annulus depend on\nthe underlying event and luminosity. However, the muon shower is contained in a small cone of radius\n\u22480.1 [18]. Therefore, a choice of an inner radius much bigger than 0.1 does not achieve the purpose of\ncollecting the energy deposited by the muon, and it adds noise to the measurement.\nA study to determine possible isolation criteria [3] has been performed on a fully simulated t\u00aft sample,\nwhere the W bosons were forced to decay into a muon and a neutrino. Muons produced by the semi-\nleptonic decays of b quarks tend to be non-isolated, while those from W decays tend to be isolated. In\nFigure 12 the distribution of the isolation energy for muons originating from quarks and Ws is shown\nfor the electromagnetic and hadronic calorimeters. The isolation energy inner and outer radii are 0.075\n(0.15) and 0.15 (0.30) for the electromagnetic (hadronic) calorimeters, respectively. This re\ufb02ects their\ndifferent granularities. The electromagnetic isolation energy is a more powerful discriminant for the\nannuli radii chosen.\nEnergy (GeV)\n0\n20\n40\n60\n80\n100\n4\n10\n3\n10\n2\n10\n1\n10\n1\nmuons from W\nmuons from q\nEM Isolation\nEnergy (GeV)\n0\n20\n40\n60\n80\n100\n4\n10\n3\n10\n2\n10\n1\n10\n1\nmuons from W\nmuons from q\nHadronic Isolation\nFigure 12: Distribution of the isolation energy in the electromagnetic (0.075 < \u2206R < 0.15) (left) and\nhadronic calorimeters (0.15 < \u2206R < 0.30) (right) in muons from a t\u00aft sample without pile-up.\nBased on this \ufb01gure, for the purpose of the rest of the studies in this section, a cut of 2 GeV on electro-\nmagnetic isolation was used to discriminate isolated muons from non-isolated muons. An additional cut\nof 10 GeV in hadronic isolation was used, even though this cut does not help rejecting non-isolated muons\nin the vast majority of events. These cuts were relaxed slightly with increasing muon pT to account for\na possible slight increase of the transverse radius of the shower caused by muons in the calorimeters.\nTracking-based criteria can be used to determine isolation cuts independent of calorimeter-based\ncriteria. If used together, they can help eliminate non-isolated muons belonging to highly-collimated jets\nthat escape being identi\ufb01ed by calorimeter-based criteria. In Figure 13 the number of inner detector tracks\naround the muon are plotted for muons from quarks and Ws in the same samples used for Figure 12.\nThese distributions were obtained for muons that passed the calorimeter-based isolation cuts mentioned\nabove.\nThe production rate of low-pT non-isolated muons from b-quark decays is expected to be very sig-\nni\ufb01cant. At the same time, a typical muon from a W or Z decay, will have a pT of about 40 GeV. Thus,\nit is unlikely that low momentum muons will be isolated in a t\u00aft sample. For this reason, all muons with\na pT of less than 15 GeV were automatically tagged as non-isolated and are excluded. In most cases, the\nmuon originating from a W boson is not accompanied by other tracks in the inner detector. In fact, the\nonly track found in the track isolation cone is, essentially, the muon itself as reconstructed in the inner\ndetector. In contrast, several inner detector tracks can be found close to muons originating from quarks.\nFor an isolation cone of \u2206R=0.2, the most probable value is three tracks, including the muon itself, but it\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n195\n\nCharged tracks\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nmuons from W\nmuons from q\nTracking Isolation\nFigure 13: Distribution of the number of inner detector tracks (including the muon track) with \u2206R < 0.2\naround the muon spectrometer track, after the calorimeter isolation and pT threshold cuts are applied to\nmuons in a t\u00aft sample.\ncan be much larger. A cut on tracking isolation has been applied that complements the cut on calorimeter\nisolation. This cut constrains an isolated muon track to be accompanied by at most one extra track inside\nthe tracking isolation cone. Using the criteria described above (electromagnetic and hadronic calorimeter\nisolation, track isolation and p\u00b5\nT > 15 GeV) approximately 0.2% of the muons originating from b quarks\nhave an energy loss overestimated by more than 6 GeV. On the other hand, 80% of the muons originating\nfrom Ws are tagged as isolated.\nAll the cuts mentioned above are used by default as isolation criteria in the Muid muon reconstruction\nalgorithm, to establish the contamination of the calorimeter measurement. If the cuts were not chosen\ntightly enough, non-isolated muons would exhibit an arti\ufb01cial increase in energy loss. If this measure-\nment was then used in muon reconstruction, the reconstructed momentum at the interaction vertex would\nbe arti\ufb01cially increased. This could signi\ufb01cantly deteriorate the momentum measurement. A calorimeter\nmeasurement of the energy loss will then only make sense if the muon is tagged as isolated. These cuts\nwere considered conservative enough that they could be used by default without inducing biases in the\nmomentum reconstruction [3]. These cuts have not been studied with pile-up or in other samples with\nan important source of non-isolated muons, like high-pT, b\u00afb samples. Studies of this type are impor-\ntant in order to set conservative isolation cuts as default for muon reconstruction involving calorimeter\nmeasurements.\nIn addition, it is worth discussing the relationship between muon isolation in reconstruction and\nmuon isolation in physics analyses. While both concepts represent an attempt to determine whether a\nmuon is inside a jet, analysis cuts are also decided on the basis of criteria such as ef\ufb01ciency or fake\nrate that are not necessarily important for the momentum reconstruction. It is, however, important to\nemphasize that the optimization of the cuts on reconstruction isolation for speci\ufb01c analyses is possible.\nIt requires, nevertheless, a re\ufb01tting of the track with analysis-speci\ufb01c cuts; and it should, therefore, only\nbe attempted when the recovery of the Landau energy loss tails is crucial for the analysis and the standard\ntreatment is not adequate.\nFor muon tagging, however, isolation criteria can overlap with the criteria derived for speci\ufb01c anal-\nyses. Isolation studies are necessary to provide a reliable muon tag and do not affect the momentum\nreconstruction, because the tracking algorithms are independent of the tagger. Default isolation criteria\ncan, for example, be relaxed based on information from the physics sample and the speci\ufb01c analy-\nsis. As an example, Figure 14 shows the rejection on the Zb\u00afb background versus the Standard Model\nH(130 GeV) \u2192ZZ\u2217\u2192\u00b5+\u00b5\u2212\u00b5+\u00b5\u2212ef\ufb01ciency using the calorimeter isolation cuts [19]. At this stage,\nafter a preselection procedure, the four muon candidates have already been selected. Both absolute and\nnormalized (with respect to muon pT) isolation are presented. In these analyses, the isolation energy was\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n196\n\nSignal\n\u2208\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nZbb\nR\n1\n10\n2\n10\nAbsolute Calorimeter Isolation\n R = 0.10\n\u2206\n R = 0 20\n\u2206\n R = 0 30\n\u2206\nSignal\n\u2208\n0.8\n0 82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0 98\n1\nZbb\nR\n1\n10\n2\n10\nNormalized Calorimeter Isolation\n R = 0.10\n\u2206\n R = 0 20\n\u2206\n R = 0 30\n\u2206\nFigure 14: Rejection of the Zb\u00afb background as a function of the H(130 GeV) \u21924\u00b5 signal ef\ufb01ciency.\nDifferent radii (0.1 < \u2206R < 0.3) are compared for absolute, left, and normalized (with respect to muon\npT), right, calorimeter isolation. No pile up events were simulated.\nde\ufb01ned using a cone of \ufb01xed radius. The isolation energy of an event was then de\ufb01ned as the isolation\nenergy of the least isolated muon of the event. The optimum cone radius depends on signal ef\ufb01ciency,\nwith \u2206R of 0.2 being an ef\ufb01cient choice.\n3.4\nMeasurement/Parameterization Combination Methods\nTo integrate energy loss in tracking algorithms, the energy loss is assumed to be gaussian. If the param-\neterization is used exclusively to correct for the energy loss, any event in which muons undergo a large\nenergy loss will be incorrectly reconstructed. There is, thus, an advantage in using the parameterizations\ntogether with measurements in the calorimeters to optimize the energy loss reconstruction. Here we\ndescribe two algorithms developed to use the calorimeter information as well as the energy loss param-\neterizations for the muon reconstruction algorithms: the Hybrid Method [3] and the Bayesian Method.\nThe Hybrid Method is used by default after isolation cuts as part of Muid. The Bayesian Method is used\nif speci\ufb01ed by the user as part of Muonboy. By default, Muonboy uses a parameterization of the energy\nloss only.\nThe Hybrid Method consists in fully separating the two regions of the Landau distribution: the peak\nregion and the tail region. The calorimetric energy loss measurement is used when the energy deposition\nis signi\ufb01cantly larger than the most probable value (tail region); otherwise the parameterization is used\n(peak region). The transition point between the two regions is taken as Empv +2\u03c3Landau.\nThe Bayes Method is based on a statistical combination of the parameterization and the measurement\nin the calorimeters. This combination is performed using Bayes\u2019 theorem. This method uses informa-\ntion from the calorimeters, even when the measurement falls in the peak region. When the calorimeter\nmeasurement falls in the tail, the results provided by this method are similar to those obtained by the Hy-\nbrid Method. If the measurements falls in the peak region, the measurement still constrains the energy\nloss pdf, improving the energy loss reconstruction resolution. In addition, this method generalizes the\nselection procedure of the hybrid method, with an event-by-event optimization and for each calorimeter\nsubsystem. This generalization allows also, in principle, an automatic improvement in the energy loss\nreconstruction as the calorimeter calibration improves.\nThe full validation of these methods in muon reconstruction with all muon reconstruction effects is\nshown in the next section. The most signi\ufb01cant of these effects are the intrinsic resolutions of the inner\ndetector and muon spectrometer. However, to validate the methods standalone, it is necessary to do it in\na model free of these reconstruction effects.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n197\n\nThe Hybrid Method has been validated through the energy loss reconstruction distributions in the\nATLAS full simulation using the muon kinematics from the simulation. The ratio of the energy loss\nresolution for the Hybrid Method, \u03c3hybrid, with respect to the parameterization alone, \u03c3param, is presented\nin Figure 15. The resolution is de\ufb01ned as the square root of the variance of the energy loss resolution.\nFor low-pT values the ratio is close to unity, as expected due to the smaller fraction of events in the\nLandau tail. For increasing pT values the ratio decreases, approaching 30% at pT = 1 TeV. Thus, using\nthe Hybrid Method results in a signi\ufb01cant improvement in the energy loss estimation with respect to the\nparameterization alone.\n (GeV)\nT\np\n10\n2\n10\n3\n10\nparam\n\u03c3\nhybrid\n\u03c3\n0 0\n0 2\n0.4\n0 6\n0 8\n1 0\n30%\nFigure 15: Ratio of the energy loss resolution for the Hybrid Method with respect to the parameterization\nalone for single muons.\nIn addition, the performance of the Bayesian Method has been studied in a toy model under the\nassumption that the calorimeter calibration is understood. Muons of 1 TeV were shot through a block of\nmatter representative of one of the samplings of the hadronic calorimeter. A perfect muon spectrometer\nwas assumed as it is done for the Hybrid Method above. Figure 16 shows some results from this study that\ndemonstrate the potential of the Bayesian Method to reconstruct energy loss. The use of the measurement\n[GeV]\nmeas\nE\n0\n20\n40\n60\n80\n100\n[GeV]\nloss\nreco\n-E\nloss\ntrue\nE\n-4\n-2\n0\n2\n4\n6\n8\nParameterization\nMeasurement\nBayesian Combination\n [GeV]\nloss\nreco\n-E\nloss\ntrue\nE\n-10\n-5\n0\n5\n10\nEvents/GeV\n0\n5000\n10000\n15000\n20000\n25000\n30000\nParameterization\nMeasurement\nBayesian Combination\nFigure 16: Demonstration of the potential of the statistical method to reconstruct the energy loss. The\nleft plot shows the bias in the energy loss reconstruction, while the right plot shows the Etrue\nloss \u2212Ereco\nloss dis-\ntribution. Both plots compare the energy loss reconstruction using the parameterization only (triangles,\ndotted line), the measurement only (\ufb01lled circles, solid line) and both statistically combined through\nBayes\u2019 theorem (open circles, dashed line).\nby itself biases the energy loss reconstruction. The Bayesian Method, on the other hand, shows no\nbiases. Incidentally, there are no biases in the energy loss reconstruction if the muon spectrometer\nmeasurement is coupled to the energy loss reconstruction in these studies. In addition, the Etrue\nloss \u2212Ereco\nloss\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n198\n\ndistributions show that the resolution obtained with the Bayesian Method is better than that obtained\nusing the parameterization or the measurement only.\nThese studies prove the potential of these two methods. Now their performance is analyzed when\nthey are used as part of the reconstruction software.\n3.5\nImpact of the Energy Loss Corrections in Reconstruction\nEnergy loss estimates must be validated as part of the muon reconstruction algorithms. Effects such as\nthe resolution of muon reconstruction, biases intrinsic to the track transport or the effects of gaussian\nassumptions will be coupled to the energy loss reconstruction. However, the studies shown here are still\nimportant for understanding the energy loss correction. They also allow for an investigation of which\ndata samples are most sensitive to an incorrect estimation of the energy loss.\nIn Figure 17, two parameters that characterize the gaussian distributions 1/preco\nT\n\u22121/ptrue\nT\nare shown.\nIn these plots, the label \u201cMS\u201d corresponds to tracks from \ufb01ts in the muon spectrometer only. The label\n (GeV)\nT\np\n10\n2\n10\nT\n-1\n/p\nT\n-1\n p\n\u2206\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nMS\n correction\nloss\nMS+E\nID+MS\n (GeV)\nT\np\n10\n2\n10\nT\n-1\n/p\nT\n-1\np\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nMS\n correction\nloss\nMS+E\nID+MS\nFigure 17: Left: Muon reconstruction bias for different algorithms as a function of muon pT. Right:\nMuon reconstruction resolution for different algorithms as a function of muon pT. These plots were\nproduced with the Muonboy/STACO algorithms for muon reconstruction [1], but similar performance is\nobtained with the MOORE/Muid algorithms [2,7].\n\u201cMS+Eloss correction\u201d refers to tracks reconstructed at the muon spectrometer and transported to the\ninteraction point (IP), applying an energy loss correction (parameterized or hybrid). For Figure 17 the\nenergy loss correction was calculated using the Muonboy parameterization only. The label \u201cMS+ID\u201d\nrefers to tracks reconstructed with the muon spectrometer and the inner detector. To obtain these com-\nbined tracks, the energy loss correction needs to be considered in the \ufb01t. The distributions are calculated\nin 1/pT-space because the muon spectrometer reconstruction and inner detector reconstruction have\ngaussian \ufb02uctuations in 1/pT. These plots refer to muons reconstructed in the barrel (|\u03b7| < 1.0) of the\nmuon spectrometer. In the left plot, the bias in the reconstruction is shown, de\ufb01ned as the mean of the\ndistribution\n\u03b4 p\u22121\nT\np\u22121\nT\n= ptrue,IP\nT\n \n1\npreco\nT\n\u2212\n1\nptrue,IP\nT\n!\n,\n(4)\nwith ptrue,IP\nT\nbeing the true pT of the muon at the IP. Clearly, in the absence of an energy loss correction,\nthis reconstruction can be highly biased. Such a bias also causes a degradation in the resolution. The\napplication of an energy loss correction reduces this bias and improves the resolution. Further bias\nreduction and resolution improvement is obtained by using the inner detector together with the muon\nspectrometer to reconstruct the muon track. However, the combination of inner detector tracks and muon\nspectrometer tracks is only possible if a proper energy loss correction exists.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n199\n\nFigure 18 shows the invariant mass resolution (Mreco\ninv \u2212Mtrue\ninv ) for Z \u2192\u00b5\u00b5 and Z\u2032(1000 GeV) \u2192\u00b5\u00b5\nsamples. The events include a generation cut that requires the pT of both decay muons to be above 7 GeV\n (GeV)\ntrue\n-m\nreco\nm\n-30\n-20\n-10\n0\n10\n20\n30\nEvents/(0.5 GeV)\n0\n100\n200\n300\n400\n500\nMS\ncorrection\nLoss\nMS+E\nMS+ID\n (GeV)\ntrue\n-m\nreco\nm\n-400\n-300\n-200\n-100\n0\n100\n200\n300\n400\nEvents/(5 GeV)\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n1.8\n2.0\n3\n10\n\u00d7\nMS\ncorrection\nLoss\nMS+E\nMS+ID\nFigure 18: Left: Reconstruction resolution of the Z peak for different algorithms. Right: Reconstruction\nresolution of the Z\u2032 peak for a Z\u2032 \u2192\u00b5\u00b5 of mass 1 TeV for different algorithms. These plots were\nproduced with the MOORE/Muid algorithms for muon reconstruction [2,7], but similar performance is\nobtained with the Muonboy/STACO algorithms [1].\nfor Z decays and above 20 GeV for Z\u2032 decays. Inner detector and muon spectrometer tracks were required\nfor both reconstructed muons. The effect of the energy loss correction is most signi\ufb01cant in the Z-mass\nreconstruction. If the energy loss is not included a shift of about 7 GeV in the mass peak and a signi\ufb01cant\ndeterioration in the resolution are visible. These effects are much less pronounced in the reconstruction\nof the Z\u2032 peak. This happens because the more energetic muons from the Z\u2032 lose a smaller fraction of\ntheir total energy as they pass through the calorimeters.\nAn additional improvement in the Z and Z\u2032 resolution is possible if the energy loss correction uses\nthe calorimeter measurement [20]. This is demonstrated in Figure 19, where a comparison is shown\n (GeV)\ntrue\n-m\nreco\nm\n-30\n-20\n-10\n0\n10\n20\n30\nEvents/(0.5 GeV)\n0\n50\n100\n150\n200\n250\n300\n350\nParametrization Only\n+ Parametrization\nCalo Measurement\n-\n\u00b5\n+\n\u00b5\n\u2192\nZ\n (GeV)\ntrue\n-m\nreco\nm\n-400\n-300\n-200\n-100\n0\n100\n200\n300\n400\nEvents/(5 GeV)\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n3\n10\n\u00d7\nParametrization Only\n+ Parametrization\nCalo Measurement\n-\n\u00b5\n+\n\u00b5\n\u2192\nZ\u2019(1 TeV)\nFigure 19: Left: Reconstruction resolution of the Z peak for an algorithm using muon spectrometer\nstandalone tracks and the parameterized energy loss correction (\ufb01lled histogram) and an algorithm using\na combination of a parameterization and the calorimeter measurement for the energy loss correction\n(empty histogram). Right: Reconstruction resolution of the Z\u2032 peak for a Z\u2032 \u2192\u00b5\u00b5 of mass 1 TeV for the\nsame algorithms.\nfor the muon spectrometer reconstruction with energy loss correction with and without the calorimeter\nmeasurement. The same samples as for Figure 18 were used. A few events are recovered from the tails\nand populate the peak region. This results in \u22488% resolution improvement when the inner detector\nhits are not used. If the inner detector hits are used the resolution improves by \u22484%, showing that\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n200\n\nthe combined \ufb01t is less sensitive to the energy loss correction. These plots were produced with the\nMOORE/Muid algorithms for muon reconstruction using the Hybrid Method (see Section 3.4). A similar\nperformance is expected using the Bayesian Method, implemented in the ATLAS tracking.\n4\nTagging of Muons in the Calorimeters\nIn this section the different calorimeter-based muon identi\ufb01cation algorithms are described. Section 4.1\nprovides a detailed description of the algorithm that is currently part of the standard reconstruction; and\nSection 4.2 illustrates its performance in different physics samples.\nThese algorithms have been developed with the main goal of complementing the muon spectrometer\nin two ways: recovering muons with low transverse momentum (pT = 2-5 GeV), and in the regions of\nlimited spectrometer acceptance (especially in the \u03b7 \u223c0 region). For completeness, algorithms used for\ncommissioning or triggering are also discussed.\nThere are two types of calorimeter-based muon tagging algorithms. Their main difference lies in\nhow they initiate the muon search. The calorimeter-seed algorithms search for muons looking at the\nmeasured energy. Cells with energy depositions inside some energy range are used as seeds. The lower\nlimit of this range is known as the initiation threshold. The cluster of cells used to identify the muon is\nthen built up by adding cells around the seed cell whose energy is above a second lower threshold, so\ncalled continuation threshold. At the end of the clustering, the \u03b7 and \u03c6 directions of the reconstructed\ncluster can be used to match a track in the inner detector. There are two algorithms that correspond to\nthis description:\n\u2022 LArMuID is based on a topological clustering algorithm used by ALEPH [21]. A topological clus-\ntering algorithm groups neighboring cells whose energy is above a given threshold. Therefore,\nthe resulting clusters have a variable number of cells. This algorithm was used to \ufb01nd muons\nusing the electromagnetic calorimeter data during the test beam and the cosmic commissioning\ndata analysis. It builds the cluster from a seed cell in the middle sampling of the electromagnetic\ncalorimeter. Then, it creates the cluster adding another cell (if any) adjacent in \u03c6 above the con-\ntinuation threshold. Due to the accordion structure of the electromagnetic calorimeters there are\nno more than two adjacent cells in \u03c6 that can share the muon signal, thus the clusters consist of at\nmost two cells. The ef\ufb01ciency was measured with a muon beam during the combined test beam\nas the fraction of events with a reconstructed muon cluster. The ef\ufb01ciency and the probability to\ngenerate a fake muon from noise \ufb02uctuations were evaluated as a function of both thresholds. The\nclustering algorithm inherently biases the energy reconstruction, so the lower the thresholds the\nbetter the estimation of the reconstructed energy for the muon. The spectrum of energies collected\nhas been compared to and shown agreement with GEANT4.\n\u2022 TileMuId is simple and fast and is used for triggering purposes. Its clustering methods are sim-\nilar to those of LArMuID. This algorithm, however, runs by default as part of the reconstruction\nsoftware. It starts with a search for a \u201ccandidate\u201d muon in the cells belonging to the last TileCal\nsampling, where the muon gives the clearest signature, due to the screening effect of the two pre-\nvious samplings. If the measured energy is between a lower and and upper threshold, it uses the\n\u03b7 and \u03c6 coordinates of the cell to look for another cell with energy within the same thresholds in\nthe central sampling. If both searches are successful it looks for a third cell with energy within the\nthresholds in the \ufb01rst sampling. When cells with energies within the thresholds are found in all\nthree samplings, the candidate is con\ufb01rmed to be a muon. Performance studies of TileMuId can\nbe found in [22].\nThere are two track-seed algorithms that extrapolate inner detector tracks through the calorimeter\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n201\n\nidentifying those matching the energy deposition pattern of a muon. The track-seed algorithms use no\ntracking information from the muon spectrometer. The \ufb01rst track-seed algorithm, CaloMuonTag, will be\ndescribed in detail in the next section.\nThe second track-seed algorithm, CaloMuonLikelihoodTool, builds a likelihood ratio to discrim-\ninate muons from pions. The likelihood discriminant is built out of different energy ratios in order to\ncapture the global features of the energy depositions. The discrimination power of these ratios varies\nboth as a function of the momentum of the particles considered, and as a function of \u03b7. Therefore three\nbins in \u03b7 (barrel, crack, end-cap) and three bins in momentum (0-10 GeV, 10-50 GeV, 50-100 GeV) are\nused, and a different set of ratios is selected for each of the 9 regions. The likelihood ratio for the muon\ncandidate is then de\ufb01ned as\nL (x1,...,xN) =\nN\n\u220f\ni=1\nP\u00b5\ni (xi)\nP\u00b5\ni (xi)+P\u03c0\ni (xi).\n(5)\nWhere P\u00b5\ni and P\u03c0\ni , i = 1,...,N are the pdf for the energy ratios. The performance of this algorithm is still\nbeing studied, however, the \ufb01rst results show that it is comparable to the performance of CaloMuonTag\ndiscussed in Section 4.2.\n4.1\nCaloMuonTag\nCaloMuonTag extrapolates inner detector tracks through the calorimeters, collecting the energy in the\ncell closest to the extrapolated track for each traversed sampling. The muon can deposit energy in more\nthan one cell in the hadronic calorimeter, but the probability of this happening is rather low, as illustrated\nin Figure 20. For the purpose of this algorithm, it is enough to assume that all the energy deposited by\nthe muon is localized in the central cell. This also minimizes the electronic noise, which is particularly\nlarge in the HEC.\nEnergy (MeV)\n0\n500\n1000 1500 2000\n2500 3000 3500 4000 4500 5000\nArbitrary Units\n4\n10\n3\n10\n2\n10\n1\n10\n1\nCentral Cells\nSurrounding Cells\nTileCal\nATLAS\nEnergy (MeV)\n0\n500\n1000 1500 2000\n2500 3000 3500 4000 4500 5000\nArbitrary Units\n4\n10\n3\n10\n2\n10\n1\n10\nCentral Cells\nSurrounding Cells\nHEC\nATLAS\nHEC\nFigure 20: Energy found in the cell traversed by the extrapolated track (solid line) and the surrounding\ncells (dashed line) in the TileCal (left) and in the HEC (right). Distributions obtained for momentum\n100 GeV muons.\nA track preselection is made to reduce the number of fakes in the output of the algorithms. In\naddition, this preselection reduces the time needed by the algorithm to run on events with high track\nmultiplicity. The following cuts in pT, and transverse isolation energy (Eiso\nT ) inside a cone of 0.45 are\napplied:\n\u2022 pT > 2 GeV and Eiso\nT < 10 GeV for tracks pointing to the barrel (\u03b7 < 1.6).\n\u2022 pT > 3 GeV and Eiso\nT < 8 GeV for tracks pointing to the end-cap.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n202\n\nTracks are rejected if any of the collected energies are above veto values de\ufb01ned for each sampling. As\nmost fakes are seeded by low-pT tracks, more stringent cuts can be set for low-pT (< 10 GeV) track\ncandidates. These cuts can be relaxed for track candidates of higher pT.\nOnce calorimeter cells along the muon trajectory have been identi\ufb01ed, the algorithm determines the\nlower threshold energy cut that should be used for the tagging as a function of \u03b7:\n\u2022 Eth = Ebarrel\n0\nsin2 \u03b8 for |\u03b7| < 1.7,\n\u2022 Eth =\nEend\u2212cap\n0\n(1\u2212sin\u03b8)2 for |\u03b7| > 1.7,\nwhere \u03b8 is the polar angle. The values of Eth from these two equations roughly follow the shape of the\nmeasured energy distributions, which increases with the path length of the muon in the cell.\nEnergy depositions in the last sampling of the calorimeters give the most reliable muon signals.\nHowever, due to the gap between the TileCal barrel and extended barrel modules, and the transition\nregion between the TileCal and the end-cap (HEC) calorimeters, it is necessary to look in the two previous\nsamplings to obtain a good ef\ufb01ciency throughout \u03b7. For this reason, if the energy in the last sampling,\nor one of the two previous samplings depending on the \u03b7 of the track, is above the threshold cut, Eth, the\ntrack is tagged as a muon. A different tag is given depending on which sampling passes the threshold\ncut.\n4.2\nPerformance\nIn this section the performance of CaloMuonTag is analyzed. The performance of CaloMuonTag is\nstudied in some relevant physics samples:\n\u2022 pp \u2192J/\u03c8 \u2192\u00b5\u00b5. A direct production of a J/\u03c8 decaying to two muons with the following cuts at\ngeneration level: one muon with pT > 6 GeV and the other with pT > 4 GeV.\n\u2022 H \u2192ZZ\u2217\u21924\u2113. A Higgs generated with an invariant mass of 130 GeV is forced to decay into\ntwo Z\u2019s (one of them offshell) that decay leptonically. Only events with four muons are used for\nreconstructing the Higgs peak, but all events are used for the ef\ufb01ciency/fake rate calculation.\n\u2022 t\u00aft . A sample of pair produced top quarks with all decay channels allowed.\n\u2022 Zbb \u21924\u2113. A Z is produced in association with 2 b quarks, and is forced to decay into two charged\nleptons. The b quarks are also forced to decay into electrons or muons.\nAll samples were generated with pile-up with a safety factor of 5, i.e. \ufb01ve times nominal value\nexpected at a luminosity of 1033cm\u22122s\u22121. Except for the pp \u2192J/\u03c8 \u2192\u00b5\u00b5 sample, where a safety factor\nof 2 was used.\nFigure 21 shows the performance of the calorimeter muon tagger algorithm on selected samples. The\nvertical axis on the left shows the ef\ufb01ciency (top distributions). The vertical axis on the right (in red)\nshows the fake rate (the number of misidenti\ufb01ed tracks per event), represented by the shaded distribution\nat the bottom of the plots. The ef\ufb01ciency (fake rate) is de\ufb01ned as the fraction of muons that are found\nby the algorithm and (not) matched with a true MC muon. Muons from minimum-bias interactions were\nnot included in the ef\ufb01ciency calculation.\nFor the t\u00aft (Zbb \u21924\u2113) sample, the algorithm performs well in identifying isolated muons from W\u2019s\n(Z\u2019s). However, due to the isolation and veto cuts applied to reduce the number of fakes, the ef\ufb01ciency\nfor non-isolated muons from b quarks is very poor, affecting the overall ef\ufb01ciency.\nTo reduce the fake rate due to the low-pT tracks in the end-caps, some ef\ufb01ciency in that region needs\nto be sacri\ufb01ced. The \u201cpeaks\u201d in the fake rate in \u03b7 match the regions where the acceptance of the last\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n203\n\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFakes/Event\n0\n0 005\n0 01\n0 015\n0 02\n0 025\n0 03\n0 035\n0 04\n0 045\n0 05\n\u00b5\n\u00b5\n\u2192\n\u03c8\nJ/\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFakes/Event\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\n4l\n\u2192\nZZ*\n\u2192\nH\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFakes/Event\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\ntt\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFakes/Event\n0\n0 005\n0 01\n0 015\n0 02\n0 025\n0 03\n0 035\n0 04\n0 045\n0 05\n4l\n\u2192\nb\nZb\nFigure 21: Ef\ufb01ciency (and fakes per event, right axis in red and shaded histograms) vs \u03b7 for different\nsamples. Top left: pp \u2192J/\u03c8 \u2192\u00b5\u00b5. Top right: H(130) \u2192ZZ\u2217\u21924\u2113. Bottom left: t\u00aft. Bottom right:\nZbb \u21924\u2113.\ncalorimeter sampling is limited, and the two previous samplings are used for muon identi\ufb01cation. Due to\nthe higher electronic noise, CaloMuonTag presents a higher fake rate in the HEC than in the TileCal. The\nresults for these samples, and for dijet samples generated with different pT transfers at the hard scattering\ninteraction are summarized in Table 1.\nJ/\u03c8 \u2192\u00b5\u00b5\nH \u21924\u2113\nt\u00aft\nZbb \u21924\u2113\n1120-2240\n560-1120\n280-560\n70-140\n17-35\nEff.\n0.80\n0.86\n0.54\n0.69\n-\n-\n-\n-\n-\nf/e\n0.05\n0.09\n0.16\n0.14\n0.11\n0.12\n0.12\n0.13\n0.12\nTable 1: Summary of the ef\ufb01ciencies and fakes per event (f/e) for different physics processes and dijet\nsamples (top numbers show the ranges of pT transfers at the hard scattering interaction, in GeV).\nFinally, Figures 22 and 23 are used to evaluate the performance improvement when using calorimeter\nmuons to reconstruct the Higgs and the J/\u03c8 mass. The plots on the left show the invariant mass recon-\nstructed with muons from a combined muon reconstruction algorithm, which makes use of both inner\ndetector and muon spectrometer tracks. The plots on the right show the invariant mass including muons\ntagged by CaloMuonTag with momenta reconstructed by the inner detector.\nTo obtain the plots in Figure 22 the same set of cuts were used as in the H(130) \u2192ZZ\u2217\u21924\u2113stud-\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n204\n\n(GeV)\n\u00b5\n\u00b5\n\u00b5\n\u00b5\nM\n100\n105\n110\n115\n120\n125\n130\n135\n140\n145\n150\nEntries\n0\n50\n100\n150\n200\n250\n300\nEntries\n3009\nMean \n 0.05) GeV\n\u00b1\n(129.65 \n \n\u03c3\n 0.04) GeV\n\u00b1\n(2.12 \nMuon Combined\nATLAS\n(GeV)\n\u00b5\n\u00b5\n\u00b5\n\u00b5\nM\n100\n105\n110\n115\n120\n125\n130\n135\n140\n145\n150\nEntries\n0\n50\n100\n150\n200\n250\n300\n350\nEntries\n3448\nMean \n 0.05) GeV\n\u00b1\n(129.66 \n \n\u03c3\n 0.04) GeV\n\u00b1\n(2.13 \nMuon Combined\n+CaloTagging\nATLAS\nFigure 22: Reconstructed Higgs peak in the H \u21924\u2113invariant mass reconstruction for the standard com-\nbined muons (left) and for combined muons together with inner detector muons tagged by CaloMuonTag\nin the \u03b7 region |\u03b7| < 0.1 (right).\nies [19]. The increase on the number of reconstructed events was achieved by adding an extra muon\nfound by the CaloMuonTag algorithm during the muon preselection. The extra muon was requested to\nbe found in the last sampling of the TileCal and within the |\u03b7| < 0.1 region. No loss in mass resolution or\nshift in the mean of the mass peak are observed between the two selected muon samples. The acceptance\ngap around |\u03b7| < 0.1 represents 4% of the |\u03b7| < 2.5 region covered by the combined muon reconstruc-\ntion. Since, four muons are recontructed in this analysis, the total ef\ufb01ciency loss due to the gap is 16%.\nThis results shows that calorimeter identi\ufb01cation can recover almost all of the lost events (14.9%).\nFor the plots shown in Figure 23 the muons used to reconstruct the invariant mass peak were matched\n(MeV)\n\u00b5\n\u00b5\nM\n2600\n2800\n3000\n3200\n3400\n3600\nEntries\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nEntries\n1735\nMean \n 1) MeV\n\u00b1\n(3104 \n \n\u03c3\n 1) MeV\n\u00b1\n(51 \nMuon Combined\nATLAS\n(MeV)\n\u00b5\n\u00b5\nM\n2600\n2800\n3000\n3200\n3400\n3600\nEntries\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nEntries\n2000\nMean \n 1) MeV\n\u00b1\n(3104 \n \n\u03c3\n 1) MeV\n\u00b1\n(50 \nMuon Combined\n+CaloTagging\nATLAS\nFigure 23: Reconstructed J/\u03c8 peak in the J/\u03c8 \u2192\u00b5\u00b5 invariant mass reconstruction for standard com-\nbined muons (left) and for combined muons together with inner detector muons tagged by CaloMuonTag\nin the \u03b7 region |\u03b7| < 0.1 (right).\nto the Monte Carlo truth. In this case, all muons identi\ufb01ed by the calorimeter were added to the combined\nreconstruction muons. Again, no loss in mass resolution or shift in the mean of the mass peak are\nobserved between the two selected muon samples.\nCaloMuonTag shows very good ef\ufb01ciency and acceptable fake rate for a high-pT analysis like H \u2192\nZZ\u2217\u21924\u00b5. An additional 15% of events were reconstructed when muons identi\ufb01ed by CaloMuonTag\nwere added to the muons found by the standard reconstruction algorithm. In low-pT analyses, such as\nJ/\u03c8 \u21922\u00b5, tighter selection cuts need to be applied to keep an acceptable fake rate. This reduces the\nef\ufb01ciency of the tagging algorithms. However, an additional 15% of events were reconstructed when\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n205\n\nmuons from CaloMuonTag were also used.\n5\nConclusion\nThis document reviews the current status of the understanding of muon energy loss in the ATLAS\ncalorimeters. Although energy losses and their distribution along the muon track have a very small\nimpact on muon reconstruction inside the muon system, they play an important role in the transport of\na reconstructed muon track to the beam pipe. During this backtracking, the muon momentum can be\ncorrected using the energy measured in the calorimeter cells traversed. This procedure is justi\ufb01ed for\nmuons that have a catastrophic energy loss. In most cases, the muon momentum can be corrected using\na parameterization of energy loss, estimated from the reconstructed momentum and the amount and the\nnature of the material traversed by the reconstructed trajectory. Techniques that attempt to combine the\nmeasurement with the parameterization to improve the energy loss estimate have been developed and\nvalidated. A performance improvement is achieved in some important analyses through the use of these\ntechniques.\nMuon tagging algorithms that use calorimeter measurements and track information have been pre-\nsented. These algorithms have been developed with the main goal of complementing the muon spec-\ntrometer in two ways: recovering muons with very low transverse momentum, and in the regions of\nlimited spectrometer acceptance, especially in the \u03b7 \u223c0 region. The performance of the calorimeter\nmuon tagger algorithm in a few relevant data samples has been shown.\nReferences\n[1] S. Hassani et al., Nucl. Instr. and Meth. A 572 (2007) 77.\n[2] T. Lagouri et al., IEEE Trans. Nucl. Sci. 51 (2004) 3030.\n[3] K. Nikolopoulos et al., Muon Energy Loss Upstream of the Muon Spectrometer, ATLAS Note\nATL-MUON-PUB-2007-002.\n[4] V.L. Highland, Nucl. Instr. and Meth. 129 (1975) and Nucl. Instr. and Meth. 161 (1979).\n[5] R. Fr\u00a8uhwirth et al., Nucl. Instr. and Meth. A 262 (1987).\n[6] T. Cornelissen et al., Concepts, Design and Implementation of the ATLAS New Tracking (NEWT),\nATLAS Note ATL-SOFT-PUB-2007-007.\n[7] D. Adams et al., Track Reconstruction in the ATLAS Muon Spectrometer with Moore, ATLAS\nNote ATL-SOFT-2003-007 (2003).\n[8] The GEANT4 Collaboration, S.Agostinelli et al., Nucl. Instr. and Meth. A 506 (2003) 250.\n[9] W. Lohmann, R. Kopp and R. Voss, Energy Loss of Muons in the Energy Range 1-10000 GeV,\nCERN 85-03 (1985).\n[10] W.-M. Yao et al., Journal of Physics G 33 (2006) 1.\n[11] D. L\u00b4opez Mateos, E. W. Hughes and A. Salzburger, A Parameterization of the Energy Loss of\nMuons in the ATLAS Tracking Geometry, ATLAS Note ATL-MUON-PUB-2008-002.\n[12] A. Salzburger, S. Todorova and M. Wolter, The ATLAS Track Extrapolation Package, ATLAS Note\nATL-SOFT-PUB-2007-004.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n206\n\n[13] H. Bischel, Rev. Mod. Phys. 60 (1988) 663.\n[14] C. Cojocaru et al., Muon Results from the EMEC/HEC Combined Run corresponding to the AT-\nLAS Pseudorapidity Region 1.6< |\u03b7| <1.8, ATLAS Note ATL-LARG-PUB-2004-006.\n[15] ATLAS\nCollaboration,\nATLAS\nLiquid\nArgon\nCalorimeters\nTechnical\nDesign\nReport,\nCERN/LHCC/96-41 (1996).\n[16] T. Davidek and R. Leitner, Parametrization of the Muon Response in the Tile Calorimeter, ATLAS\nNote ATL-TILECAL-97-114.\n[17] ATLAS Collaboration, ATLAS Tile Calorimeter Technical Design Report, CERN/LHCC/96-42\n(1996).\n[18] G. Schlager, The Energy Response of the ATLAS Calorimeter System, CERN-THESIS-2006-056.\n[19] The ATLAS Collaboration, Search for the Standard Model H \u2192ZZ\u2217\u21924l, this volume.\n[20] K. Nikolopoulos et al., IEEE Trans. Nucl. Sci. 54 (2007) 1792.\n[21] J. P. Albanese, E. Kajfasz and P. Payre, Nucl. Instr. and Meth. A 253 (1986) 73.\n[22] The ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this vol-\nume.\nMUONS \u2013 MUONS IN THE CALORIMETERS: ENERGY LOSS CORRECTIONS AND MUON . . .\n207\n\nIn-Situ Determination of the Performance of the Muon\nSpectrometer\nAbstract\nThe ATLAS muon spectrometer consists of three layers of precision drift-tube\nchambers in a toroidal magnetic with a \ufb01eld integral between 2.5 and 6 Tm.\nMuon tracks are reconstructed with 97% ef\ufb01ciency and a momentum resolu-\ntion between 3% and 4% for 10 GeV< pT <500 GeV and better than 10% for\ntransverse momenta up to 1 TeV. In this note, the performance of a perfectly\ncalibrated and aligned muon spectrometer will be reviewed and the impact of\ndeteriorations of the magnetic \ufb01eld, the calibration and misalignment of the\nmuon chambers on the performance will be discussed. The main part of the\nnote describes how the performance of the muon spectrometer can be deter-\nmined using dimuon decays of Z bosons and J/\u03c8 mesons.\n1\nIntroduction\nMuons with a transverse momentum1 pT greater than 3 GeV are detected in the ATLAS muon spectrom-\neter, which is designed to measure muon momenta with a resolution between 3% and 4% for a range of\ntransverse momenta of 10 GeV< pT <500 GeV and better than 10% for pT\u2019s up to 1 TeV. The muon\nspectrometer consists of a system of superconducting air-core toroid coils producing a magnetic \ufb01eld\nwith a \ufb01eld integral between 2.5 and 6 Tm [1]. Three layers of chambers are used to precisely measure\nmuon momenta from the de\ufb02ection of the muon tracks in the magnetic \ufb01eld (see Figure 1). Three layers\nof trigger resistive-plate chambers (RPC) in the barrel and three layers of fast thin-gap chambers (TGC)\nin the end caps of the muon spectrometer are used for the muon trigger. The trigger chambers measure\nthe muon tracks in two orthogonal projections with a spatial resolution of about 1 cm. The precision\nmeasurement of the muon trajectory is performed by three layers of monitored drift-tube (MDT) cham-\nbers in almost the entire muon spectrometer and by cathode-strip chambers (CSC) in the innermost layer\nof the end caps at |\u03b7| > 2.2. The precision muon chambers provide track points with 35 \u00b5m resolution in\nthe bending plane of the magnetic \ufb01eld. The goal of a momentum resolution better than 10% up to 1 TeV\nscale requires the knowledge of the chamber positions with an accuracy better than 30 \u00b5m in addition to\nthe high spatial resolution of the chambers. This is achieved by a system of optical alignment monitoring\nsensors [1].\nIn the \ufb01rst part of this note, we review the performance of a perfectly calibrated and aligned muon\nspectrometer and discuss the dependence of the performance on the knowledge of the following quanti-\nties: the magnetic \ufb01eld, the calibration of the chambers, the alignment of the chambers, and the accuracy\nof the determination of the energy loss of the muons in the calorimeters. In the second and main part, we\ndescribe how the performance of the muon spectrometer can be determined by means of dimuon decays\nof Z bosons and J/\u03c8 mesons.\n2\nPerformance of a perfect and deteriorated spectrometer\n2.1\nMuon reconstruction\nThe muon spectrometer measures the momenta of charged particles at the entrance of the muon spec-\ntrometer. The energies lost by the muons on the passage through the calorimeters have to be added to the\n1The transverse momentum is de\ufb01ned as the components of momentum in the transverse plane.\n208\n\n2\n4\n6\n8\n10\n12 m\n0\nshielding\nend\u2212cap\ntoroid\ntoroid coil\n14\n16\n18\n20\n2\n10\n12\n4\n6\n8\nm\n\u00b5\n0.4 T\n\u03b7=2.7\n\u00b5\nFigure 1: Sketch of a quadrant of the ATLAS muon spectrometer.\nenergy measured at the entrance of the muon spectrometer in order to obtain the muon momentum at the\nprimary vertex. This reconstruction strategy is called stand-alone muon reconstruction. In order to cor-\nrect for the energy loss, the expected average energy loss is used as a \ufb01rst estimation; in a second step the\nenergy deposition measured in the calorimeters is used to account for the large energy losses of highly\nenergetic muons due to bremsstrahlung and direct e+e\u2212pair production. One speaks of combined muon\nreconstruction when the momentum measurement of the inner detector is combined with the stand-alone\nreconstruction. In this note, muon momenta will always be given at the pp interaction point.\nThe muon reconstruction is described in detail in [2,3]. The focus of this note is the measurement of\nthe performance of the stand-alone reconstruction from real data.\n2.2\nDe\ufb01nitions\nThe performance of the muon spectrometer is characterized in terms of ef\ufb01ciency and momentum res-\nolution.\nIn the analysis of simulated data, let \u03b7rec and \u03b7truth denote the pseudorapidities and \u03c6rec\nand \u03c6truth denote the azimuthal angles of the reconstructed and generated muons. The distance \u2206R =\np\n(\u03b7rec \u2212\u03b7truth)2 +(\u03c6rec \u2212\u03c6truth)2 of a reconstructed and generated muon is shown for a Monte Carlo\nsample with muons of pT = 50 GeV at the pp interaction point in Figure 2. More than 99.7% of all\nreconstructed muons have a distance \u2206R < 0.05. We therefore de\ufb01ne the muon reconstruction ef\ufb01ciency\nas the fraction of generated muons which can be matched to a reconstructed muon within a cone of\n\u2206R < 0.05.\nThe momentum resolution is measured by comparing the deviation of the reconstructed inverse trans-\nverse momentum from the generated inverse transverse momentum:\n\u03c1 =\n1\npT,truth \u2212\n1\npT,rec\n1\npT,truth\n(1)\n\u03c1 would be normally distributed for a muon spectrometer uniform in \u03b7 and \u03c6. The momentum resolution\nis not independent of \u03b7 and \u03c6 due to the nonuniformity of the magnetic \ufb01eld and the nonuniformity of the\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n209\n\nR\n\u2206\n0\n0.01 0.02\n0.03 0.04\n0.05\nArbitrary units\nStand\u2212alone reconstruction\nATLAS\nFigure 2: Distribution of distance \u2206R of reconstructed from generated muons in a 50 GeV single muon\nMonte Carlo sample.\nmaterial distribution in \u03b7 and \u03c6. This leads to non-Gaussian tails in the \u03c1 distribution when integrated\nover \u03b7 and \u03c6, as illustrated in Figure 3. In order to minimize the effect of tails, the momentum resolution\nis determined in the following way throughout this note: In the \ufb01rst step, a Gaussian g0 is \ufb01tted to the\ndistribution. In the next step i a Gaussian gi is \ufb01tted to the data between the xm,i\u22121 \u00b12\u03c3i\u22121, where \u03c3i\u22121\nis the \ufb01tted width of gi\u22121 and xm,i\u22121 its \ufb01tted mean. The iterative procedure is terminated when the\n\ufb01t relative change of the \ufb01t parameters from one to the next iteration is less than 0.1%. The standard\ndeviation of the \ufb01nal \ufb01t curve is taken as a measure for the momentum resolution. The mean of \ufb01nal \ufb01t is\nreferred to as the momentum scale, which is a measure for systematic shifts of measured muon momenta\nwith respect to the correct values.\n2.3\nPerformance of a perfect muon spectrometer\nWe brie\ufb02y review the performance of a perfectly calibrated and aligned muon spectrometer. We refer\nto [1] and [2] for a more detailed discussion of the performance.\nFigure 4(a) shows the reconstruction ef\ufb01ciency for muons with pT=50 GeV as a function of \u03b7 and \u03c6.\nThe ef\ufb01ciency is close to 100% in most of the \u03b7-\u03c6 plane. It drops signi\ufb01cantly in the acceptance gaps of\nthe muon spectrometer. The inef\ufb01ciency near |\u03b7| = 0 is caused by the gap for services of the calorimeters\nand the inner tracking detector. The inef\ufb01ciency near |\u03b7| = 1.2 will disappear after the installation of\nadditional muon chambers in the transition region between the barrel and the end caps which will not be\npresent in the initial phase of the LHC operation. The inef\ufb01ciencies at \u03c6 \u22481.2 and \u03c6 \u22482.2 for |\u03b7| < 1.2\nare related to acceptance gaps in the feet region of the muon spectrometer.\nThe stand-alone reconstruction ef\ufb01ciency is presented as function of pT in Figure 4(b). It rises from\n0 to its plateau value of 95% between pT = 3 GeV and 10 GeV.\nThe pT-resolution is independent of \u03c6 apart from the feet region where it is degraded due to the\nmaterial introduced by the support structure of the detector. The resolution also depends on pseudora-\npidity. It is almost constant in the barrel part of the spectrometer (|\u03b7| < 1.05). It is up to three times\nworse in the transition region between the barrel and the end caps for 1.05 < |\u03b7| < 1.7 mainly due to the\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n210\n\n)\nT, truth\n)/(1/p\nT, truth\n-1/p\nT, rec\n(1/p\n-0.4 -0.3 -0.2 -0.1\n-0\n0.1\n0.2\n0.3\n0.4\nArbitrary units\n0\nGaussian g\n4\nGaussian g\nATLAS\nFigure 3: Illustration of the iterative \ufb01t of normal distributions to the fractional deviation of the recon-\nstructed inverse momentum from the generated inverse momentum. g0 is the \ufb01tted Gaussian of iteration\nstep 0. g4 is the \ufb01tted Gaussian of \ufb01nal iteration step 4.\n\u03b7\n-2\n-1\n0\n1\n2\n\u03c6\n0\n1\n2\n3\n4\n5\n6\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nStand-alone reconstruction\nATLAS\n(a) Reconstruction ef\ufb01ciency vs.\n\u03b7 and \u03c6 for muons of\npT =50 GeV.\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n(b) Reconstruction ef\ufb01ciency vs. pT integrated over \u03b7 up to\n|\u03b7| < 2.7 and \u03c6.\nFigure 4: Ef\ufb01ciencies of the reconstruction of tracks in the muon spectrometer.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n211\n\nsmall integral of the magnetic \ufb01eld in this region. The momentum resolution becomes uniform again for\n|\u03b7| > 1.7.\n (GeV)\nT\np\n10\n2\n10\n3\n10\nResolution (%)\n0\n2\n4\n6\n8\n10\n12\n| < 1.05\n\u03b7|\nATLAS\n(a)\n (GeV)\nT\np\n10\n2\n10\n3\n10\nResolution (%)\n0\n2\n4\n6\n8\n10\n12\n| > 1.05\n\u03b7|\nATLAS\n(b)\nFigure 5: Stand-alone momentum resolution integrated over \u03b7 and \u03c6 as a function of pT for the barrel\n(5(a)) and the end-cap region (5(b)).\nThe stand-alone momentum resolution varies with pT (see Figure 5). The momentum resolution in\nthe barrel is dominated by \ufb02uctuations of the energy loss in the calorimeters for pT < 10 GeV where it\nis about 5% at pT = 6 GeV. It is best, 2.6% (4%) in the barrel (end cap), for pT \u224850 GeV where it is\ndominated by multiple scattering in the muon spectrometer. The momentum resolution at high momenta\nis limited by the spatial resolution and the alignment of the precision chambers and approaches 10% at\npT = 1 TeV.\n2.4\nDeterioration of the performance\nThe performance of the stand-alone muon reconstruction is affected by the limited knowledge of the\nmagnetic \ufb01eld in the muon spectrometer, the limited knowledge of the material distribution along the\nmuon trajectory required for the calculation of the energy loss, the calibration of the position measure-\nments by the monitored drift-tube chambers, and the alignment of the muon chambers.\nThe magnetic \ufb01eld will be known with a relative accuracy better than 5 \u00d7 10\u22123 based on the mea-\nsurements of 1840 magnetic \ufb01eld sensors which are mounted on the muon chambers. As a consequence\nthe relative impact on the momentum resolution is less than 3% [1].\nStudies for the technical design report of the muon spectrometer [4], which have been con\ufb01rmed by\nstudies in the context of this note, show that the space-drift-time relationship r(t) of the MDT chambers\nmust be determined with 20 \u00b5m accuracy in order to give a negligible contribution to the momentum\nresolution up to pT = 1 TeV. A strategy to calibrate r(t) with muon tracks with the required accuracy has\nbeen worked out and is described in detail in [5].\nThe muon chambers are installed with a positioning accuracy of 1 mm in the muon spectrometer with\nrespect to global \ufb01ducials in the ATLAS cavern. The studies for the technical design report, however,\nshowed that the muon chambers must be aligned with an accuracy better than 30 \u00b5m in the bending\nplane. A bias of 30 \u00b5m on the sagitta of a 1 TeV muon corresponds to a systematic shift of the measured\nmomentum of 60 GeV. The alignment of the muon spectrometer is based on a system of optical alignment\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n212\n\nsensors monitoring relative movements of the chambers on the level of a few micrometers. Muon tracks\nare used for the absolute calibration of the optical sensor with 30 \u00b5m accuracy. The optical system does\nnot cover the whole muon spectrometer. The positions of the end caps with respect to the barrel must\nbe measured with muon tracks traversing the overlap between the barrel and the end-cap part of the\nspectrometer. There are also chambers in the transition region between the barrel and end caps whose\npositions are not monitored by the optical system. These chambers will be aligned with the rest of the\nmuon spectrometer by muon tracks. The alignment of the muon spectrometer is discussed in [6].\nThe expectation of the muon energy loss in the calorimeters can be checked by comparing the muon\nmomentum as measured by the inner detector and the muon momentum at the entrance of the muon\nspectrometer, for instance. We shall not discuss the measurement of the muon energy loss in this article\nand refer the reader to [7].\nThe initial misalignment will be the dominant source of performance degradation. We shall show\nin the next section that Z \u2192\u00b5+\u00b5\u2212will lead to a clearly visible resonance peak in the dimuon mass\ndistribution even in the case of the initial misalignment. It will therefore be possible to measure the\nmuon performance of a misaligned muon spectrometer with Z \u2192\u00b5+\u00b5\u2212events.\nImpact of misalignment on the performance\nIn order to study the impact of the initial misalignment of the muon spectrometer on the performance,\nthe simulated data were reconstructed with a different geometry from the one used in the simulation.\nIn the reconstruction geometry, the chambers were randomly shifted from the nominal positions with\nGaussian distribution centred at 0 and a standard deviation of 1 mm and rotated randomly with Gaussian\ndistribution centred at 0 and a standard deviation of 1 mrad. Deformations of the chambers which are\nmonitored by an optical system mounted on the chambers were not considered in our studies.\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0.8\n0.85\n0.9\n0.95\n1\nStand-alone reconstruction\nAligned layout\nMisaligned layout\nATLAS\n(a) Ef\ufb01ciency vs. \u03b7 integrated over \u03c6 for pT =50 GeV.\n\u03c6\n0\n1\n2\n3\n4\n5\n6\nEfficiency\n0.8\n0.85\n0.9\n0.95\n1\nStand-alone reconstruction\nA igned layout\nMisaligned layout\nATLAS\n(b) Ef\ufb01ciency vs. \u03c6 integrated over \u03b7 for pT =50 GeV.\nFigure 6: Comparison of reconstruction ef\ufb01ciency for an aligned muon spectrometer and a misaligned\nmuon spectrometer with a average positioning uncertainty of 1 mm for a simulated single muon sample.\nFigure 6 illustrates the comparison of the stand-alone track reconstruction ef\ufb01ciency for 50 GeV\nmuons in the aligned and the misaligned case. Only a small decrease in the reconstruction ef\ufb01ciency can\nbe observed for muons with a momentum of 50 GeV, a momentum typical for muons originating from W\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n213\n\nor Z bosons. The relatively small decrease in the reconstruction ef\ufb01ciency is mainly due to the fact that\nthe used de\ufb01nition of ef\ufb01ciency is based on a simple \u03b7 and \u03c6 matching and does not take into account\nthe measured transverse momentum of the muons. The reconstruction ef\ufb01ciency could be increased in\nthe misaligned case by applying softer cuts in the pattern recognition stage of the track reconstruction.\nFigure 7(a) and 7(b) show the impact of a misaligned muon spectrometer on the fractional transverse\nmomentum resolution; the resolution is highly degraded. The overall observed fractional muon spec-\ntrometer resolution \u03c3tot can be expressed as the quadratic sum of the intrinsic fractional pT-resolution at\nthe ideal geometry (\u03c3ideal) and the fractional resolution due to the misaligned geometry (\u03c3Alignment).\n\u03c3tot =\nq\n\u03c32\nAlignment +\u03c32\nideal\nThis leads to \u03c3Alignment \u22480.14 for muons with pT \u224850 GeV as expected from the relationship be-\ntween sagitta and momentum. The effect on the momentum scale is relatively small for the overall muon\nspectrometer, since random misalignments cancel to a certain extent. In physics signatures, such as the\ndecay of a Z boson into two muons, the impact on the average momentum scale is even less, since a\nmisaligned geometry has the opposite effect for opposite charged muons to \ufb01rst order.\n)\nT, truth\n)/(1/p\nT, truth\n-(1/p\nT, rec\n1/p\n-0.4 -0.3 -0.2 -0.1\n-0\n0.1\n0.2\n0.3\n0.4\nArbitrary units\nStand-alone reconstruction\nAligned layout\nMisaligned layout\nATLAS\n(a) Overall pT -resolution\n\u03b7\n-2\n-1\n0\n1\n2\nResolution\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2 Stand-alone reconstruction\nAligned layout\nMisaligned layout\nATLAS\n(b) pT -resolution vs. \u03b7\nFigure 7: Comparison of the fractional pT-resolution for an aligned muon spectrometer and a misaligned\nmuon spectrometer.\nThe impact of initial misalignment of the muon spectrometer on the Z resonance is shown in Figure\n8. It is expected that the mean of the invariant mass distribution does not change signi\ufb01cantly, since the\nmomentum scale of the reconstructed muon pT is hardly affected by misalignment. On the other hand a\nlarge broadening of the distribution due to the degradation of the pT-resolution of the muons is expected,\nwhich is shown in Figure 8. The dependence of the reconstructed width of the Z boson mass distribution\non the size of the misalignment is shown in Figure 9. \u03c3scale\nm\nis a scaling factor applied to the initial\nmisalignment of 1 mm and 1 mrad. The observed dependence is the basis for the determination of the\nmuon spectrometer resolution with data, which is discussed in section 4. A more detailed discussion of\nmisalignment impacts on the muon spectrometer performance can be found in [8].\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n214\n\n (GeV)\n\u00b5\n\u00b5\nm\n60 65 70 75 80 85 90 95 100 105 110\nArbitrary units\nStand-alone reconstruction\nAligned layout\nMisaligned layout\nATLAS\nFigure 8: Reconstructed Z boson mass distribu-\ntions for an aligned and a misaligned (\u03c3scale\nm\n= 1)\nmuon spectrometer layout.\nm\nscale\n \n\u03c3\nmisalignment parameter \n0\n0.2\n0.4\n0.6\n0.8\n1\n [GeV]\nz\n\u03c3\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\nStand-alone reconstruction\nATLAS\nFigure 9: Width of the Z resonance peak includ-\ning the natural width of the Z vs. misalignment\nparameter \u03c3scale\nm\n.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n215\n\n3\nMeasurement of the reconstruction ef\ufb01ciency from pp collision data\nThe simulation of the ATLAS detector is still under development and is not expected to reproduce the\nactual performance of the detector in all details at the beginning of the LHC operation. Therefore it is\nnecessary to determine all ef\ufb01ciencies with data in order not to rely on the simulation.\n3.1\nReconstruction ef\ufb01ciency from dimuon decays of the Z boson\n3.1.1\nTag-and-probe method\nThe so-called \u201dtag-and-probe\u201d method can be used to determine the muon spectrometer reconstruction\nef\ufb01ciencies from pp collision data. Muons from Z decays will be detected by the inner tracking detector\nand the muon spectrometer in the common acceptance range of |\u03b7| < 2.5. The measurements of the inner\ndetector and the muon spectrometer are independent, though not necessarily uncorrelated. We require\ntwo reconstructed tracks in the inner detector, at least one associated track in the muon spectrometer,\nand the invariant mass of the two inner-detector tracks to be close to the mass of the Z boson. The\nlast requirement ensures that the reconstructed tracks are the tracks of the decay muons of the Z boson.\nMoreover, the two inner tracks are required to be isolated to reject possible OCD background. The inner\ntrack which could be associated to the track in the muon spectrometer is therefore a muon and is called\nthe tag muon. It is also required that the tag muon \ufb01red the 20 GeV single-muon trigger in order to\nensure that the event is recorded. This selection ensures that a Z \u2192\u00b5+\u00b5\u2212decay has been detected. The\nsecond inner track must then be a muon, too, which is called the probe muon (see Figure 10). In the\nanalysis of dimuon events from pp collisions, the probe muon plays the role of the generated muon in\nthe determination of the ef\ufb01ciency with simulated data.\nThe tag-and-probe technique is not restricted to the measurement of the stand-alone reconstruction\nef\ufb01ciency. It can, for instance, be used to measure the muon reconstruction ef\ufb01ciency of the inner detector\nor the trigger ef\ufb01ciency [9].\nProbe Muon\nZ\u2212Boson\nTag Muon\nFigure 10: Schematic illustration of the tag and probe method.\nOur studies show that the acceptance gaps of the muon trigger which are re\ufb02ected in uncovered\n\u03b7-\u03c6 regions of the tag muon do not create uncovered \u03b7-\u03c6 regions of the probe muon. The tag-and-\nprobe method therefore allows us to determine the ef\ufb01ciency over the full \u03b7 and \u03c6 coverage of the inner\ndetector.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n216\n\nSome systematic uncertainties of the tag-and-probe method must be considered. Muons from Z \u2192\n\u00b5+\u00b5\u2212decays usually \ufb02y in opposite directions in the plane transverse to the proton beam axis. Hence\ninef\ufb01ciencies which are symmetric in \u2206\u03c6 \u2248\u03c0 may not be detected with this method.\nThe topology of pp \u2192Z/\u03b3\u2217\u2192\u00b5+\u00b5\u2212events is characterized by two highly energetic and isolated\nmuons in the \ufb01nal state. A signi\ufb01cant QCD-background contribution is expected due to the huge cross\nsection of QCD processes. Moreover, the decay of a W \u00b1 boson into one highly energetic muon and a\nneutrino plus an additional muon from a QCD jet and the process Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5+ \u00af\u03bd\u03c4\u03bd\u00b5\u00b5\u2212\u03bd\u03c4 \u00af\u03bd\u00b5 were\nstudied as possible background processes in our analysis.\nBecause of the high collision energy of the LHC, the production of top quark pairs has a cross section\nof the order of the signal cross section. Top quarks mostly decay into a W boson and bottom quark. The\nW boson and the bottom quark can decay into muons or electrons, which also might fake the signal\nprocess.\nThe cross section of QCD processes is far too large to be simulated within a full Monte Carlo simu-\nlation of the ATLAS detector. Hence it is assumed that the dominant contribution from highly energetic\nmuons is due to the decay of b-mesons. A more detailed discussion of the selection of pp \u2192Z \u2192\u00b5+\u00b5\u2212\nevents and the background processes which must be considered can be found in [9].\n3.1.2\nSelection of candidate tracks\nFigure 11 shows the invariant dimuon mass and the transverse momenta of the selected muon track\ncandidates for the signal and the chosen background processes.\nThe following cuts have been applied to get a clean track selection. Tracks of opposite charge and\na difference in their \u03c6 coordinates greater than 2.0 rad are selected. The rapidity of the tracks is limited\nto a rapidity coverage of the inner detector of |\u03b7| < 2.5. Each of the selected muon candidate tracks is\nrequired to have pT > 20 GeV. The invariant mass M\u00b5\u00b5 of the two muon candidate tracks must agree with\nthe Z mass within \u00b110 GeV, i.e.|M\u00b5\u00b5 \u221291.2GeV| < 10 GeV.The following isolation cuts are applied to\nthe selected tracks:\n\u2022 number of reconstructed tracks in the inner detector within a hollow cone around the candidate\nmuon: NID Tracks\nr1 0.3. Our choice of r2 = 0.5 is the same as used in the measurement of the cross section of the\nprocess pp \u2192Z \u2192\u00b5+\u00b5\u2212(see [9]). The isolation criteria listed here are optimized for events without\npile-up of inelastic pp collisions in a selected event. Pile-up of inelastic pp collisions is expected for the\noperation of the LHC at a luminosity of 1033 cm\u22122 s\u22121 and will lead to more energy in a cone around\nthe muons. It was checked that the ef\ufb01ciency of our event selection is reduced by less than 5% in the\npresence of pile-up and that the purity of our selected samples is not affected by the presence of pile-up.\nThe distributions of the \ufb01rst two isolation variables for signal and background processes normalized\nto their cross sections are presented in Figure 11(c) and 11(d) in absence of pile-up. The selection of\nisolated high-pT muons allows for a substantial suppression of the background.\nCut Flow\n Candidates\n0\nZ\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10 Opposite\nCharge\nMass\nCut\nKinematic\nCuts\nIsolation\nRequirement\nElectron\nVeto\nTrue\nMuon\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n\u00b5\n\u2192\nW\n\u00b5\n\u00b5\n\u2192\nbb\n\u00b5\n\u00b5\n\u2192\ntt\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\nFigure 12: Cut-\ufb02ow diagram for probe muon tracks: (0) opposite charge requirement, (1) invariant mass\nrequirement, (2) kinematic cuts, (3) isolation requirements, (4) electron veto, (5) found at least one track\nin the muon spectrometer.\nThe cut-\ufb02ow diagram for probe muons is shown in Figure 12. The QCD background can be rejected\nwith isolation cuts. More problematic in this selection is the W \u2192\u00b5\u03bd background, and those t\u00aft-events\nin which at least one W boson decays into a muon and a neutrino. These processes produce one highly\nenergetic isolated muon track which passes all selection cuts for a tag muon. A further track in the\ninner detector which passes the other cuts and is not a muon will decrease the measured ef\ufb01ciency. Such\na track is most likely caused by an electron, since it is expected that electrons also appear as isolated\ntracks in the inner detector. Therefore it is required that no reconstructed electromagnetic jet in the\nelectromagnetic calorimeter can be matched to an inner track as an additional selection requirement. This\napplies especially for probe tracks stemming from a t\u00aft-event. Here, again, one has to distinguish between\ninner tracks, which result from the decay of the bottom quark or simple QCD-interactions and those,\nwhich result from the decay of the W boson. The \ufb01rst case is suppressed by the isolation requirement\nand can be neglected. The second case can lead to a highly energetic isolated electron, stemming from\nthe decay of the second W boson. These electrons are expected to be vetoed. The cut-\ufb02ow diagram also\nshows that the probe muon candidates from the background processes can also be associated to a muon\nspectrometer track and hence have no negative effect on the ef\ufb01ciency determination.\nAn overview of the remaining background expected from Monte Carlo is shown in Table 1; there\nwe have assumed at least three events surviving the cuts as a systematic uncertainty in order not to\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n219\n\nTable 1: Fractional background contribution in % based on Monte Carlo prediction including estimated\nsystematic and statistical uncertainties.\nb\u00afb \u2192\u00b5\u00b5\nW \u00b1 \u2192\u00b5\u00b1\u03bd\nZ/\u03b3\u2217\u2192\u03c4\u03c4\nt\u00aft \u2192W +bW \u2212b\nOverall\n\u22480+0.03\n\u22480+0.06\n\u22480\n\u22480.02\u00b10.01\n0.02\u00b10.1\nunderestimate the background contribution. After all selection cuts, the purity of our sample is high: less\nthan 0.1% of the selected dimuon events are from background processes.\nOur results are stable against variations of the track matching distance \u2206R from 0.05 to 0.3. The\nlarger track matching cut of \u2206R=0.3 takes account for possible misalignment effects in the \ufb01rst phase of\nLHC. The robustness of our results against the \u2206R matching cut indicates that our selected data sample\nwill allow an ef\ufb01ciency determination which is not signi\ufb01cantly affected by background processes even\nwith a possible misalignment of the muon spectrometer.\n3.1.3\nDetermination of the stand-alone reconstruction ef\ufb01ciency\nThe stand-alone reconstruction ef\ufb01ciency depends on pT, \u03b7 and \u03c6 of the muons. Hence, one should\ndetermine the ef\ufb01ciency in appropriate bins in these quantities. The lower value of the pT-binning is\ngiven by the selection cut of 20 GeV. The highest value is set to 70 GeV and 10 bins are used to ensure\nhigh enough statistics within each bin. For larger statistics also values above 100 GeV can be considered.\nA natural binning in \u03b7 and \u03c6 is given by the geometry of the muon spectrometer. The muon spec-\ntrometer consists of 16 sectors in the \u03c6 plane, small and large MDT chambers sequentially ordered as\nillustrated in Figure 13(a). Therefore 16 bins in \u03c6 are used. The same geometrical argument applies to\nthe \u03b7-plane of the detector. Three MDT-chambers which are projective to the interaction point de\ufb01ne\none tower. Twenty towers are de\ufb01ned in \u03b7 which are the basis for the chosen binning (Figure 13(b)). In\ntotal 320 regions are de\ufb01ned in the \u03b7 \u2212\u03c6 plane.\n\u03c6 = +1/12 \u03c0\n\u03c6 = \u22121/12 \u03c0\n(a) \u03c6-binning\n(b) \u03b7-binning\nFigure 13: Illustration of the choosen \u03c6 and \u03b7-binning of the muon spectrometer\nIt is important to note that the dominant effect of losing reconstruction ef\ufb01ciency is the acceptance\ngap due to the absence of MDT chambers. Hence it is a pure geometrical effect mainly in the \u03b7-direction.\nTherefore different physics samples with different \u03b7- and to a certain extent also different \u03c6- and pT-\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n220\n\nTable 2: Overall reconstruction ef\ufb01ciencies for different physics processes. Ef\ufb01ciencies with respect to\nthe Monte Carlo truth information are quoted for the sample of events that pass the single muon trigger.\nSample\n\u2206R = 0.05\n\u2206R = 0.075\n\u2206R = 0.15\nZ \u2192\u00b5+\u00b5\u2212\n0.952\n0.956\n0.958\nW \u00b1 \u2192\u00b5\u00b1\u03bd\n0.953\n0.958\n0.960\nt\u00aft \u2192W +W \u2212b\u00afb\n0.943\n0.948\n0.950\nb\u00afb \u2192\u00b5+\u00b5\u2212\n0.930\n0.944\n0.952\ndistributions will lead to different overall reconstruction ef\ufb01ciencies. An overview of the overall recon-\nstruction ef\ufb01ciencies for different physics samples and track matching distances is shown in Table 2.\nHence the in-situ determined ef\ufb01ciencies must be applied in an appropriate binning for different physics\nsamples.\nThe comparison of the ef\ufb01ciencies determined with Monte Carlo truth information and the trag-\nand-probe method is shown in Figure 14 for \u03b7 and pT, assuming an aligned muon spectrometer. A\ntrack matching distance of \u2206R < 0.075 was chosen. The ef\ufb01ciencies determined in both ways coincide\nwithin their statistical uncertainty for an integrated luminosity of 100 pb\u22121. This proves that possible\ncorrelations between tag and probe muons are small and can be neglected to a good extent.\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0.8\n0.85\n0.9\n0.95\n1\nStand-alone reconstruction\nMonte Carlo truth\nTag & Probe method\nATLAS\n(a) Ef\ufb01ciency integrated over \u03c6 and pT in Z \u2192\u00b5+\u00b5\u2212events\nvs. \u03b7\n [GeV]\nT\np\n20\n30\n40\n50\n60\n70\nEfficiency\n0.85\n0.9\n0.95\n1\n1.05\nStand-alone reconstruction\nMonte Carlo truth\nTag & Probe method\nATLAS\n(b) Ef\ufb01ciency integrated over \u03c6 and \u03b7 in Z \u2192\u00b5+\u00b5\u2212events\nvs. pT\nFigure 14: Comparison of the muon reconstruction ef\ufb01ciency of the muon spectrometer vs. \u03b7 and pT\ndetermined by the tag and probe method and via the Monte Carlo truth information.\nThe statistical error on the reconstruction ef\ufb01ciency \u03b5 can be calculated (for large N) by\n\u2206\u03b5 =\nr\n\u03b5(1\u2212\u03b5)\nN\n,\n(3)\nwhere N is the number of tag muons. Note that both muons can, and will, be chosen as tag muons\nin most cases, as the muon spectrometer is expected to have a reconstruction ef\ufb01ciency of 95% on\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n221\n\naverage. Figure 15 shows the distribution of the in-situ determined ef\ufb01ciencies for all 320 regions. The\noverall reconstruction ef\ufb01ciency can be determined to a high statistical precision even for relatively low\nintegrated luminosities. A statistical precision of 1% of the overall muon spectrometer reconstruction\nef\ufb01ciency can be reached with less than 1 pb\u22121. Figure 16 illustrates the statistical uncertainty averaged\nover all 320 regions versus the integrated luminosity.\nrec\n\u2208\nefficiency \n0.65 0.7 0.75 0.8 0.85 0.9 0.95\n1\nnumber of sections\n20\n40\n60\n80\n100\n120\nEntries \n 320\nMean \n 0.961\nRMS \n 0.08131\nEntries \n 320\nMean \n 0.961\nRMS \n 0.08131\nStand-alone\nreconstruction\nATLAS\nFigure 15: Distribution of muon reconstruction\nef\ufb01ciency of the 320 muon spectrometer regions.\n ]\n-1\nIntegrated Luminosity [pb\n20\n40\n60\n80 100 120 140 160\nstat. uncertainty\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nStand-alone reconstruction\nATLAS\nFigure 16: Average statistical error of reconstruc-\ntion ef\ufb01ciency of the 320 regions vs. integrated\nluminosity.\nA possible correlation between tag and probe muons could be caused by the trigger. The probability\nof reconstructing a muon is signi\ufb01cantly higher if it was triggered, as shown in Figure 17. Hence, it might\nbe suspected that this correlation implies also a correlation in real data, since data events must contain\nat least one muon which has been triggered. This is not a problem as long as the trigger requirement is\nonly applied on the tag muon.\nIn Section 3.1.1 it was already mentioned that the tag and probe approach has problems in detecting\ninef\ufb01ciencies which have a \u03c6 \u2248\u03c0 symmetry. Dividing the data sample in two parts differing in the\nangle \u2206\u03a6 could overcome this problem. One part contains reconstructed tag and probe muons with\n\u2206\u03a6 < 2.8 rad the second sample with \u2206\u03a6 > 2.8 rad. The chosen value of 2.8 rad leads to roughly\nequally sized samples. Applying the tag and probe method on both sub-samples will lead to different\nef\ufb01ciency distributions in case of \u03c6-symmetric inef\ufb01ciencies. Monte Carlo studies showed that for the\npresently simulated detector layout we expect only small differences (Fig. 18).\nTable 3 summarizes statistical and systematic uncertainties of the in-situ determined stand-alone\nreconstruction ef\ufb01ciency for two different integrated luminosities. The difference in |\u03b5in\u2212situ \u2212\u03b5true| is\ncalculated via\n|\u03b5in\u2212situ \u2212\u03b5true| =\nN\n\u2211\ni=1\n1\nN |\u03b5i\nin\u2212situ \u2212\u03b5i\ntrue|\n(4)\nwhere the index i runs over all bins in \u03b7-direction. This is treated as primary source of systematic\nuncertainty. One should note that the given systematic error has a strong statistical component from the\nMonte Carlo statistics which is re\ufb02ected in the large decrease of the systematic uncertainty in Table 3.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n222\n\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nStand-alone reconstruction\nTriggered Muon Track\nNot Triggered Muon Track\nATLAS\nFigure 17: Reconstruction ef\ufb01ciency of the muon\nspectrometer for muon tracks which have been\ntriggered and muon tracks which have not been\ntriggered.\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0.8\n0.85\n0.9\n0.95\n1\nStand-alone reconstruction\n<2.8\n\u00b5\n\u00b5\n\u03a6\n\u2206\n2.0<\n\u00b5\n\u00b5\n\u03a6\n\u2206\n2.8<\nATLAS\nFigure 18: Comparison of muon reconstruction\nef\ufb01ciencies determined via tag and probe ap-\nproach for two sets of muons differing by \u2206\u03c6.\nTable 3: Estimated uncertainties of in-situ determined muon spectrometer reconstruction ef\ufb01ciencies\nfor muons in a pT-range between 20 GeV and 70 GeV and within an \u03b7-range smaller than 2.5 from a\nZ \u2192\u00b5\u00b5 decay.\nR L\nStatistical\n|\u03b5in\u2212situ \u2212\u03b5true|\nBackground\nOverall\nUncertainty\nContribution\nSystematic\n100 pb\u22121\n0.08%\n0.9%\n0.02%\n\u22481%\n1 fb\u22121\n0.03%\n0.1%\n0.02%\n\u22480.1%\nWe take the difference between the ef\ufb01ciency obtained for the misaligned layout and the ef\ufb01ciency\nobtained for the aligned layout as a conservative estimate of the precision which can be achieved with the\ntag-and-probe method in case of small unresolved misalignments. The difference in both ef\ufb01ciencies for\nthe different \u2206\u03c6-sample is comparable within its statistical uncertainties. The background contribution\nis only estimated by the Monte Carlo prediction and treated as a systematic uncertainty.\nThe Gaussian sum of the two systematic uncertainties, namely |\u03b5in\u2212situ \u2212\u03b5true| and the background\ncontribution, is de\ufb01ned as the overall systematic uncertainty.\nThe given uncertainty estimation assumes that nearly all MDT chambers work and \u03b5true \u224896%. A\nlower value of \u03b5true will lead to an increase of the statistical uncertainty via Equation (3) and also to a\nhigher systematic uncertainty. For real data a conservative estimate of the systematic uncertainty would\nbe the difference of the Monte Carlo prediction for the ef\ufb01ciency and the ef\ufb01ciency determined with\ncollision data. Moreover, it should be noted that the given uncertainties apply for muons in a pT-range\nbetween 20 GeV and 60 GeV and within an \u03b7-range smaller than 2.5.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n223\n\n3.1.4\nAlternative approach\nThe tag-and-probe analysis presented above uses isolation cuts to reject background events and assumes\nthat a negligable background contribution remains. In this section, we explore the possibility of determin-\ning the reconstruction ef\ufb01ciency from collision data without isolation cuts and determine the background\ncontribution directly in data. We apply only cuts on the transverse momenta, e.g. pT > 10 GeV. This\nleads to a dominant background contribution in the lower invariant dimuon-mass region.\nIn this approach, a tag muon is de\ufb01ned as a muon spectrometer and inner detector combined muon\ntrack, with pT > 10 GeV. A probe muon is de\ufb01ned as any inner detector track, also with pT > 10 GeV.\nAn invariant mass is then calculated from every combinatoric tag and probe pair with opposite charges.\nThe size of this sample is denoted as N in the following (Figure 19(b)). Finally, we select a subsample\nrequiring that the probe muon also be a combined muon track. The size of this sample is denoted as n\n(Figure 19(a)).\n [GeV]\n\u00b5\n\u00b5\nm\n50\n60\n70\n80\n90\n100 110\nArbitrary units\n1 combined track\n1 inner track\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n\u00b5\n\u2192\nW\n\u00b5\n\u00b5\n\u2192\nbb\n\u00b5\n\u00b5\n\u2192\ntt\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\n(a) At least one of the muons is matched to a muon spectrom-\neter track.\n [GeV]\n\u00b5\n\u00b5\nm\n50\n60\n70\n80\n90\n100 110\nArbitrary units\n2 combined tracks\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n\u00b5\n\u2192\nW\n\u00b5\n\u00b5\n\u2192\nbb\n\u00b5\n\u00b5\n\u2192\ntt\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\n(b) Both muons are matched to muon spectrometer tracks.\nFigure 19: Expected invariant Masses M\u00b5\u00b5 resulting from two inner tracks where both muons must be\nmatched to a muon spectrometer track (a) or at least one of the muons must be matched to a muon\nspectrometer tracks (b).\nThe track-\ufb01nding effciency of the muon spectrometer, \u03b5, is then de\ufb01ned as n/N. Missing tracks in\nthe muon spectrometer will result in n < N and thus effciency loss. The main difference from the ap-\nproach presented in Section 3.1 is that no isolation cuts are used for the background rejection but instead\nthe background is directly estimated from data via side band subtraction. In this approach an exponential\nfunction is \ufb01tted to the invariant mass region between \u223c40 GeV to \u223c60 GeV, where it is assumed that\nthe background contribution is dominating. The exponential function is then extrapolated to the invariant\nmass region between \u223c81 GeV to \u223c101 GeV and used for subtraction of the background in this region.\nThe remaining number of events between \u223c81 GeV to \u223c101 GeV de\ufb01ne n and N, respectively. In this\nway, the background contribution is accounted for implicitly in data and no further assumptions on the\nMonte Carlo predictions are made. The disadvantage of this procedure are the systematic uncertainties\nof the \ufb01tting procedure and the choice of the \ufb01tting function. One possible improvement with higher\nstatistics of the background sample would be that the Monte Carlo prediction of the shape of the back-\nground distribution could be used to obtain a better \ufb01t function than the pure exponential for the side\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n224\n\nband subtraction.\nThe systematic uncertainty of this method is again estimated by the residual difference of the in-situ\ndetermined ef\ufb01ciency and the true ef\ufb01ciency. For a simulated data sample corresponding to an integrated\nluminosity of\nR Ldt = 100 pb\u22121 it is expected to determine the ef\ufb01ciency with this approach up to a\nprecision of\n\u2206\u03b5 = \u00b10.05(sys.)\n(5)\nThe relative large systematic uncertainty arises mainly from the limited available statistics of background\nMonte Carlo samples which has a direct impact on goodness of applied \ufb01t. Hence, further improvements\nare likely to be achieved in future studies.\n3.2\nDetermination of the reconstruction ef\ufb01ciency with J/\u03a8 events\nThe reconstruction ef\ufb01ciency for muons with transverse momenta less than 20 GeV is not determined\nfrom Z \u2192\u00b5+\u00b5\u2212events due to the cuts on the transverse momenta of the muons. Muons from J/\u03c8 \u2192\n\u00b5+\u00b5\u2212decays populate the momentum range below 20 GeV. We explored the possibility of using the\ntag-and-probe method on J/\u03c8 \u2192\u00b5+\u00b5\u2212events for the measurement of the reconstruction ef\ufb01ciency\nat low transverse momenta. The method works well on signal events. Yet the huge QCD background\ncontaminates the selected dimuon data sets so much that a reliable ef\ufb01ciency measurement becomes very\ndif\ufb01cult. Studies using muon isolation techniques have started. The muon reconstruction ef\ufb01ciency of\nlow-pT muons must therefore be extracted from Monte Carlo simulations and not be determined easily\nfrom data.\n4\nMeasurement of the momentum resolution and momentum scale\nThe muon momentum measurement will be affected by the limited knowledge of the magnetic \ufb01eld, the\nuncertainty in the energy loss of the muons, and the alignment of the muon spectrometer as discussed in\nSection 2.4.\nThe analysis of the measurements of the optical alignment sensors and the collision data with the\nswitched-off toroid coils will provide the position of the muon chambers with an accuracy better than\n100 \u00b5m at the start-up of the LHC [1]. A systematic error of 100 \u00b5m on the sagitta corresponds to an\nadditional systematic error in the muon momentum of about 0.1 TeV\u22121 \u00b7 p2 which amounts to 250 MeV\nfor p=50 GeV.\nMuons with energies below 100 GeV lose on average about 3 GeV of their energy on their passage\nthrough the calorimeters almost independently of their energy. The material distribution of the ATLAS\ndetector is modelled in the detector simulation with an accuracy better than a few percent [1]. A 5%\nuncertainty in the amount of the material traversed by the muons would re\ufb02ect in a 5% uncertainty of the\nenergy loss, that is an uncertainty of the average energy loss of \u00b1150 MeV.\nThe uncertainty in the bending power of the toroidal \ufb01eld will lead to a momentum uncertainty\nwhich is signi\ufb01cantly smaller than the energy loss uncertainty and the impact of the misalignment on the\nmomentum measurement. It can therefore be neglected with respect to energy loss uncertainties and the\nmisalignment of the spectrometer.\nA bias in the measured muon momentum translates into a bias in the measurement of the dimuon\nmass in Z \u2192\u00b5+\u00b5\u2212decays. An \u03b7, \u03c6, and momentum dependent bias will also broaden the dimuon mass\npeak. The shape of the dimuon invariant mass distribution for Z \u2192\u00b5+\u00b5\u2212decays can therefore be used\nto measure the accuracy of the momentum measurement with collision data.\nAs the momentum bias caused by misalignment is of the same magnitude, but of opposite sign for\n\u00b5+ and \u00b5\u2212leptons while the energy loss uncertainty has the same sign and magnitude for \u00b5+ and \u00b5\u2212\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n225\n\nleptons, it is possible to disentangle the effect of misalignment and the effect of energy loss errors on the\nreconstructed Z mass. The the sensitivities of the dimuon invariant mass spectrum to misalignment and\nerrors in the energy-loss correction were therefore studied separately to get a \ufb01rst insight.\n4.1\nDetermination of the energy-loss uncertainty with Z \u2192\u00b5+\u00b5\u2212events\nWe begin with the determination of the energy-loss uncertainty with Z \u2192\u00b5+\u00b5\u2212events. We assume\nthat the detector is aligned and that the magnetic \ufb01eld is known with the expected accuracy such that its\nimpact on the momentum scale can be neglected. We allow for an error in the energy-loss and, therefore,\ncorrect the reconstructed muon energy in each of the 320 spectrometer towers by a tower-dependent\nconstant \u03b4Erec,tower:\nErec,tower \u2192Erec,tower +\u03b4Erec,tower.\n(6)\nWe determine the 400 constants \u03b4Erec,tower by minimizing\n\u03c72 =\n\u2211\ndimuon pairs k\n[(pcorr,+,k + pcorr,\u2212,k)2 \u2212M2\nZ]2\n\u03c32\nk\n(7)\nwhere pcorr,\u00b1,k denotes the corrected measured \u00b5\u00b1 momentum and \u03c3k the expected dimuon mass reso-\nlution. To estimate the sensitivity to the energy-loss correction, we applied this \ufb01t to 40,000 simulated\nZ \u2192\u00b5+\u00b5\u2212events (corresponding to an integrated luminosity of 50 pb\u22121). The \ufb01t gives \u03b4Erec,tower with\na bias of 100 MeV and a stastitical error of the same size. Studies to improve the check of the energy-loss\ncorrection with collision data are ongoing.\n4.2\nDetermination of the momentum scale and resolution for a misaligned spectrometer\nIn a second step, we assume that the energy-loss correction is right and consider the misalignment of the\nmuon spectrometer as the only source of a deterioration of the momentum measurement.\nIf the Monte Carlo simulation describes the detector correctly, it also predicts the shape of the re-\nconstructed dimuon mass spectrum for Z \u2192\u00b5+\u00b5\u2212events correctly. The misalignment of the muon\nchambers causes a deviation of the measured from the predicted shape of the invariant dimuon mass\nspectrum. In order to match the Monte Carlo prediction with the experimental measurement, the recon-\nstructed simulated muon momenta must be smeared and shifted. The following procedure was adopted\nin our analysis: A random number \u03b4 p normally distributed around 0 with standard deviation \u03c3res was\nadded to the reconstructed simulated muon momenta prec,MC and multiplied by a scale factor \u03b1:\npcorr = \u03b1(prec,MC \u2212\u03b4 p).\n(8)\nThe inclusion of \u03b4 p corrects for an underestimation of the momentum resolution. The scale factor \u03b1\ntakes care of systematic shifts between the reconstructed momenta in the experiment and the simulation.\n\u03b1 and \u03c3res are determined by a \ufb01t of the corrected simulated invariant dimuon mass spectrum to the\nexperimentally measured spectrum.\nTo test this approach, the existing Z \u2192\u00b5+\u00b5\u2212Monte Carlo data set was divided into two subsamples\nof equal size corresponding to an integrated luminosity of 50 pb\u22121. The one sample serves as Monte\nCarlo reference for an aligned muon spectrometer, the other plays the role of the experimental data set.\nTwo scenarios were investigated:\n1. The Monte Carlo reference sample and the experimental sample were simulated and reconstructed\nwith the same (aligned) geometry. \u03c3res was \ufb01xed to 0 in the analysis of this scenario. Separate\nscale factors \u03b1B and \u03b1E were applied to muon in the barrel (|\u03b7| < 1) and the end-cap region\n(1 \u2264|\u03b7| < 2.7).\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n226\n\n2. The Monte Carlo reference sample was simulated and reconstructed with the same (aligned) ge-\nometry. But the experimental sample was reconstructed with a different geometry misaligned as\ndescribed in Section 2.4. In this scenario, two scale factors \u03b1B and \u03b1E for the barrel and end-cap\nparts of the muon spectrometer and a global standard deviation \u03c3res were used as \ufb01t parameters.\nTable 4: Fit results for the scale and resolution parameters for an integrated luminosity of 50 pb\u22121.\nLayout\n1\u2212\u03b1B\n1\u2212\u03b1E\n\u03c3res\nAligned\n(4\u00b114)10\u22124\n(1\u00b113)10\u22124\n\u2013\nMisaligned\n(6\u00b12)10\u22123\n(5\u00b12)10\u22123\n(11.6\u00b10.3) %\nThe results of the tests are summarized in Table 4. In the ideal case in which the reference and\nthe experimental sample are statistically independent, but equivalent otherwise, the \ufb01t gives factors \u03b1B\nand \u03b1E equal to 1 within the statistical errors as expected. In the second scenario, the uncorrected\nmisalignment in the experimental sample leads to a systematic shift of the reconstructed momenta, hence\n\u03b1B and \u03b1E differ from 1 slightly, but signi\ufb01cantly, and a large degradation of the momentum resolution\nfrom 3.5% to 12% is observed which is consistent with the degradation presented in Section 6. A large\nZ \u2192\u00b5+\u00b5\u2212sample would clearly allow for a \ufb01ner segmentation than the division in barrel and end-cap\nparts for the scale factors and lead to smaller values of \u03c3res.\n\u03b7\n-2\n-1\n0\n1\n2\n>\nrec,MC\n)/p\nrec,MC\n-p\ncorr\n1+<(p\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\nATLAS\nFigure 20: Dependence of < pcorr \u2212prec,MC > /prec,MC on \u03b7 integrated over pT and \u03c6 for Z \u2192\u00b5+\u00b5\u2212\nevents in the second scenario of a misaligned detector.\nThe mean value of 1+ pcorr\u2212prec,MC\nprec,MC\nis presented in Figure 20 as a function of \u03b7 for the second scenario.\nThe mean values are spread around 1 with a standard deviation of 0.3%. The maximum deviation from 1\nis less than 1%. This results indicates that the Z-mass distribution permits the detection of imperfections\nin the momentum reconstruction. Studies which use a more re\ufb01ned parametrization of the momentum\ncorrection and take into account energy-loss and alignment corrections at the same time are in progess.\nWe conclude from the studies in this section that it should be possible to control the muon momentum\nand energy scale on the level of 0.5 GeV for 50 GeV muons with 40,000 Z \u2192\u00b5+\u00b5\u2212events corresponding\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n227\n\nto an integrated luminosity of 50 pb\u22121.\n5\nConclusions\nThe performance of the ATLAS muon spectrometer can be predicted by Monte Carlo simulations. The\nperformance of the spectrometer will, however, differ from the prediction due to the initial misalignment\nof the muon chambers and imperfections in the corrections of the muon energy-loss. It is therefore\nimportant to measure the performance with collision data.\nWe showed in the present article that it is possible to measure the muon reconstruction ef\ufb01ciency\nwith Z \u2192\u00b5+\u00b5\u2212events with an accuracy better than 1% with an integrated luminosity of 100 pb\u22121.\nSelection cuts and the pT spectrum of the Z decay muons limit the momentum measurement to range of\n20 GeV< pT <70 GeV. The ef\ufb01ciency measurement can be extended to higher momenta with increased\nluminosity when the tails of the pT spectrum get populated.\nWe explored the possibility of measuring the ef\ufb01ciency at low transverse momenta with J/\u03c8 \u2192\n\u00b5+\u00b5\u2212events. Our studies show that a reliable ef\ufb01ciency measurement will be dif\ufb01cult due to large\nirreducible QCD background.\nWe \ufb01nally addressed the question of how the momentum and energy scale can be measured with\nZ \u2192\u00b5+\u00b5\u2212. According to our feasibility study it will be possible to control the energy-loss correction on\nthe level of 100 MeV and the momentum scale on the level of 1% for an integrated luminosity of about\n100 pb\u22121. More detailed studies are needed to obtain a better estimate of the achievable precision.\nReferences\n[1] The ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[2] The ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[3] The ATLAS Collaboration, Mouns in the Calorimeters: Energy Loss Corrections and Muon Tagging,\nthis volume.\n[4] The ATLAS Muon Collaboration,\nATLAS Muon Spectrometer Technical Design Report,\nCERN/LHCC 97-22.\n[5] P. Bagnaia et al., Calibration model for the MDT chambers of the ATLAS Muon Spectrometer, to\nbe submitted to JINST.\n[6] J.C. Barriere et al., The alignment system of the barrel part of the ATLAS muon spectrometer, to be\nsubmitted to JINST.\n[7] The ATLAS Collaboration, Muons in Calorimeters: Energy Loss Corrections and Muon Tagging,\nto be submitted to JINST.\n[8] N. Benekos et al., Impacts of misalignment on the muon spectrometer performance, ATL-MUON-\nPUB-2007-006.\n[9] The ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\nMUONS \u2013 IN-SITU DETERMINATION OF THE PERFORMANCE OF THE MUON SPECTROMETER\n228\n\nTau Leptons\n229\n\nReconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays\nAbstract\nIn this note the overall performance of the ATLAS detector is discussed for\nthe identi\ufb01cation of and measurements with hadronic decays of \u03c4 leptons in\na wide dynamic range of transverse energies, spanning from 10-15 GeV up\nto at least 500 GeV. In general, hadronically decaying \u03c4 leptons are recon-\nstructed by matching narrow calorimetric clusters with a small number of\ntracks. Two complementary approaches, a calorimeter-seeded and a track-\nseeded algorithm, have been developed to ef\ufb01ciently reconstruct these de-\ncays while providing the necessary large rejection against jets from QCD pro-\ncesses. The performance of these algorithms in terms of ef\ufb01ciency and rejec-\ntion against jets is discussed. In addition, the prospects for the determination\nof fake \u03c4 rates as well as the extraction of \u03c4 lepton signals from W and Z boson\ndecays and from t\u00aft events in early ATLAS data corresponding to an integrated\nluminosity of 100 pb\u22121 are discussed.\n1\nIntroduction\nTau leptons, and particularly their hadronic decays, will play an important role at the LHC. They will\nprovide an excellent probe in searches for new phenomena: the Standard Model Higgs boson at low\nmasses, the MSSM Higgs boson or Supersymmetry (SUSY). Therefore, understanding their selection\nef\ufb01ciencies and the cross-sections at which they will be produced is essential for discovering new physics.\nTau leptons are massive particles with a measurable lifetime undergoing electroweak interactions\nonly. The production and the decay of \u03c4 leptons are well separated in time and space (\u0393\u03c4/m\u03c4 \u223c10\u221211),\nproviding potential for unbiased measurements of the polarisation, spin correlations, and the parity of\nthe resonances decaying into \u03c4 leptons. The excellent knowledge of \u03c4 decay modes from low energy\nexperiments indeed makes this an ideal signature for the observations of new physics.\nThe interesting transverse momentum range of \u03c4 leptons spans from below 10 GeV up to at least\n500 GeV. Experiments at the LHC will thus have to identify them in a wide momentum range. The low\nenergy range should be optimized for analyses related to W and Z boson observability with \u03c4 decays and\nalso to Higgs boson searches and SUSY cascade decays. The higher energy range is mostly of interest\nin searches for heavy Higgs bosons in MSSM models and for extra heavy W and Z gauge bosons. For\nillustration, Fig. 1 shows the transverse energy spectrum of the visible decay products of \u03c4 leptons from\ndifferent processes of interest normalized to the predicted cross-section with which they will be produced\nat the LHC and to an integrated luminosity of 10 fb\u22121.\nThe reconstruction of \u03c4 leptons is usually understood as a reconstruction of the hadronic decay\nmodes, since it would be dif\ufb01cult to distinguish leptonic modes from primary electrons and muons.\nDespite a strong physics motivation for exploring data with \u03c4 leptons in the \ufb01nal state, their reconstruc-\ntion at hadron colliders remains a very dif\ufb01cult task in terms of distinguishing interesting events from\nbackground processes dominated by QCD multi-jet production. Another related challenge is providing\nef\ufb01cient triggering for these events while keeping trigger rates at manageable levels.\nThe availability of various decay modes makes \u03c4 leptons a rich but not totally unique signature.\nHadronically decaying \u03c4 leptons1 are distinguished from QCD jets on the basis of low track multiplicities\ncontained in a narrow cone, characteristics of the track system and the shapes of the calorimetric showers.\nIsolation from the rest of the event is required both in the inner detector and the calorimeter. From this\n1We will often use notation \u03c4had in this note when discussing objects reconstructed from the visible part of the hadronic\ndecay products of a \u03c4 lepton.\n230\n\n (GeV)\nT\nvis\nE\n0\n50\n100\n150\n200\n250\n/5GeV\n\u22121\nEvents/10fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nATLAS\n7\n10\n\u03c4\n\u03bd\n\u03c4\n\u2192\nW\n\u03c4\n\u03c4\n\u2192\nZ\ntt\nSUSY SU(1) point\n (120GeV)\n\u03c4\n\u03c4\n\u2192\nVBF h\n (800GeV)\n\u03c4\n\u03c4\n\u2192\nbbH, H\nATLAS\n (GeV)\nT\nvis\nE\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n/5GeV\n\u22121\nEvents/10fb\n1\n10\n2\n10\n3\n10\n4\n10\n (800GeV)\n (400GeV)\n\u03c4\n\u03c4\n\u03c4\n\u03c4\n\u2192\n\u2192\nbbH, H\nbbH, H\nSUSY SU(1) point\n (600GeV)\n\u03c4\n\u03c4\n\u2192\nZ\u2019\nFigure 1: The visible transverse energy of \u03c4 leptons from different physics processes: top quark decays,\nW/Z production, Standard Model vector boson fusion Higgs boson production for mH = 120 GeV with\nH \u2192\u03c4\u03c4, for \u03c4 leptons from low energy Supersymmetry with a light stau (SU1 sample), heavy Z\u2032 bosons,\nand heavy Higgs bosons from bbH production in the MSSM with tan\u03b2 = 20(45) for masses of 400 GeV\n(800 GeV).\ninformation, a set of identi\ufb01cation variables is built, to which either a traditional cut-based selection or\nmulti-variate discrimination techniques are applied.\nThe inner detector provides information on the charged hadronic track or the collimated multi-track\nsystem reconstructed in isolation from the rest of the event. These tracks should neither match track seg-\nments in the muon spectrometer nor reveal features characteristic of an electron track (e.g. high threshold\nhits in the Transition Radiation Tracker). In the case of a multi-track system, they should be well col-\nlimated in (\u03b7,\u03c6) space and the invariant mass of the system should be below the \u03c4 lepton mass. The\ncharge of the decaying \u03c4 lepton can be directly determined from the charge(s) of its decay product(s).\nCalorimetry provides information on the energy deposit from the visible decay products (i.e. all\ndecay products excluding neutrinos). Hadronically decaying \u03c4 leptons are well collimated (with an\nopening angle limited by the ratio m\u03c4/E\u03c4 ) leading to a relatively narrow shower in the electromagnetic\n(EM) calorimeter with, for single-prong decays with one or few \u03c00\u2019s, a signi\ufb01cant pure electromagnetic\ncomponent. On average in this case about 55% of the energy is carried by \u03c00s present among the decay\nproducts.\nThe calorimeter and tracking information should match, with narrow calorimeter cluster being found\nclose to the track(s) impact point in the calorimeter. Furthermore, the invariant mass of the cluster should\nbe small and the cluster should be isolated from the rest of the event.\nThe algorithms for the reconstruction of hadronically decaying \u03c4 leptons are considered higher level\nreconstruction as they use components provided by algorithms speci\ufb01c to different subdetectors like track\nreconstruction in the inner detector or topological clustering of the energy deposits in the calorimeter. At\npresent, two complementary algorithms have been implemented into the ATLAS of\ufb02ine reconstruction\nsoftware.\n\u2022 The calorimetry-based algorithm starts from clusters reconstructed in the hadronic and electromag-\nnetic calorimeters and builds the identi\ufb01cation variables based on information from the tracker and\nthe calorimeter.\n\u2022 The track-based algorithm starts from seeds built from few (low multiplicity) high quality tracks\ncollimated around the leading one. The energy is calculated with an energy-\ufb02ow algorithm based\nonly on tracks and the energy in the electromagnetic calorimeter. All identi\ufb01cation variables are\nbuilt using information from the tracker and the calorimeter.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n231\n\nA short overview of the features of \u03c4 lepton decays is included in Section 2. In Section 3 selected\ntopics on the performance of the detector directly relevant to the reconstruction and identi\ufb01cation of the\nhadronically decaying \u03c4 leptons are discussed. Of\ufb02ine reconstruction algorithms and performance results\nare described in Section 4. In the remaining part of the note strategies for analyses using \u03c4 leptons with\nthe \ufb01rst 100 pb\u22121 of data are presented.\n2\nTopology of \u03c4 leptons in LHC collisions\nThe transverse momentum range of interest spans from below 10 GeV up to 500 GeV. \u03c4 leptons decay\nhadronically in 64.8% of all cases, while in \u223c17.8% (17.4%) of the cases they decay to an electron\n(muon) [1]. From the detection point of view, hadronic modes are divided by the number of charged \u03c0s\namong the decay products into single-prong (one charged \u03c0) and three-prong (three charged \u03c0s) decays.\nThe small fraction (0.1%) of \ufb01ve-prong decays is usually too hard to detect in a jet environment. The\n\u03c4 \u2192\u03c0\u00b1\u03bd mode contributes 22.4% to single-prong hadronic decays and the \u03c4 \u2192n\u03c00\u03c0\u00b1\u03bd modes 73.5%.\nFor three-prong decays, the \u03c4 \u21923\u03c0\u00b1\u03bd decay contributes 61.6%, and the \u03c4 \u2192n\u03c003\u03c0\u00b1\u03bd mode only\n33.7%. In general, one- and three-prong modes are dominated by \ufb01nal states consisting of \u03c0\u00b1 and \u03c00.\nThere is a small percentage of decays containing K\u00b1 which nevertheless can be identi\ufb01ed using the same\ntechnique as for states with \u03c0\u00b1 from the ATLAS detector point of view. A small percentage of states\nwith K0\nS cannot be easily classi\ufb01ed as belonging to either the single-prong or three-prongs categories as\nthe number of registered prongs depends on the actual K0\nS interaction within the detector. Unless speci\ufb01c\nstudies are done, other multi-prong hadronic modes can be safely neglected.\nThe lifetime of the \u03c4 lepton (c\u03c4 = 87.11\u00b5m) in principle allows for the reconstruction of its decay\nvertex in the case of three-prong decays. The \ufb02ight path in the detector increases with the Lorentz\nboost of the \u03c4 lepton, but at the same time the angular separation of the decay products decreases. A\nresulting transverse impact parameter of the \u03c4 decay products can be used to distinguish them from\nobjects originating from the production vertex.\nThe incorporation of spin effects in \u03c4 lepton decays is often of importance. This was done within the\nframework of the ATLAS Monte Carlo simulation and events were generated using PYTHIA [2] interfaced\nwith TAUOLA [3]. The generation process has correctly included full spin correlations in production and\ndecays of the \u03c4 leptons. Tau leptons from the decay of gauge bosons, Higgs bosons or in SUSY cascade\ndecays will carry information on the polarisation of the decaying resonance and in the case of pair\nproduction also some information on the spin correlations. Tau leptons from W \u2192\u03c4\u03bd and H\u00b1 \u2192\u03c4\u03bd\nwill be 100% longitudinally polarised, with P\u03c4 = +1.0 and P\u03c4 = -1.0 respectively, resulting in different\ndistributions of the charged to total visible energy for single-prong decays in the center-of-mass system\nof the decaying resonance. At the LHC this effect can be used to suppress W \u2192\u03c4\u03bd background and to\nincrease the H\u00b1 \u2192\u03c4\u03bd observability [4]. The \u03c4 polarisation could also be used as a tool to discriminate\nbetween MSSM versus Extra Dimension scenarios [5]. The longitudinal polarisation of \u03c4 leptons from\nneutral Higgs boson decays will be democratic with 50% probability, thus \u03c4 leptons from Higgs boson\ndecays are effectively not polarized. The polarisation of \u03c4 leptons from Z boson decays will be a more\ncomplicated function of the center-of-mass energy of the system and the angle of the decay products [6].\nIn the cleaner environment of the ILC and also perhaps at the sLHC, building variables sensitive to the\nlongitudinal and transverse spin correlations may lead to a CP measurement of the Higgs boson [7,8].\n3\nPerformance of the ATLAS detector for \u03c4 identi\ufb01cation\nHadronic \u03c4 decays can be ef\ufb01ciently reconstructed and identi\ufb01ed using information from the inner de-\ntector and from the calorimeter. Reconstruction is done only for the visible part of the decay products,\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n232\n\nhowever, for speci\ufb01c analyses like H \u2192\u03c4\u03c4 the complete invariant mass of the \u03c4\u03c4 system may be re-\nconstructed using the collinear approximation [9] (neutrino momenta parallel to that of the visible decay\nproducts). A few selected topics related to the performance of the detector are discussed below before\nturning to the reconstruction algorithms.\n3.1\nTracking and vertexing\nThe reconstruction of tracks from charged pion decays is an important ingredient of the \u03c4had reconstruc-\ntion algorithms. The track-based algorithm is seeded by one or more good quality tracks which allow\nfor the calculation of the \u03c4had energy with the so called energy-\ufb02ow scheme. Both the calo-based and\nthe track-based algorithm determine the charge of the \u03c4had candidate by summing up the charge(s) of\nthe tracks reconstructed in the \u03c4had core region2. The tracking information is further used to identify\nhadronically decaying \u03c4 leptons and to discriminate them against the background from hadronic jets\nby considering the track multiplicity, the impact parameter and the transverse \ufb02ight path in the case of\nmulti-track candidates. The track selection should therefore ensure high ef\ufb01ciency and quality of the\nreconstructed tracks over a broad momentum range from 1 GeV to a few hundred GeV.\n3.1.1\nReconstruction ef\ufb01ciency and track quality\nThe ef\ufb01ciency for track reconstruction in \u03c4 decays is de\ufb01ned as the probability for a given charged \u03c0\nfrom a \u03c4 decay to be reconstructed as a track. With respect to the reference tracking performance of\nthe detector established for single muons in the low pT range a degradation due to hadronic interactions\n(a charged \u03c0 interacting with the material of the inner detector) is expected. In the higher pT range a\ndegradation is caused by the strong collimation of the multi-track system for three-prong decays.\nGood quality tracks reconstructed with pT as low as 1 GeV are required by the track-based algorithm,\nwhile the calorimeter-based algorithm accepts any track with pT > 2 GeV. A standard quality selection\nhas been de\ufb01ned in Ref. [10]. However, for the reconstruction of \u03c4 leptons a somewhat stricter selection\nhas been applied. Good quality tracks are required to satisfy \u03c72/n.d.f < 1.7, to have a number of pixel\nand SCT hits \u22658 and transverse impact parameters d0 < 1mm. For the leading track in addition the\nnumber of low threshold TRT hits has to be larger than 10 in a pseudorapidity \u03b7 range up to 1.9, while\nfor the second or third track the presence of a B-Layer hit and ratio of the of high-to-low threshold hits of\nsmaller than 0.2 are required. Both requirements were added to minimize the number of accepted tracks\nfrom conversions. A dedicated veto against electron tracks being used as leading tracks is not applied at\nthe reconstruction level. This will be taken care of separately as part of the identi\ufb01cation procedure.\nFigure 2 shows the reconstruction ef\ufb01ciency for pT = 1\u221250 GeV using the standard quality selection\nas de\ufb01ned in Ref. [10]. Adding the additional quality criteria as described above, the overall ef\ufb01ciency\nfor reconstructing good quality tracks from \u03c4 lepton hadronic decays is reduced to 82 \u221283%. The\nreconstruction ef\ufb01ciency is slightly higher for tracks from single prong decays compared to three-prong\ndecays, where tracks could be very collimated particularly for boosted \u03c4 leptons.\n3.1.2\nCharge misidenti\ufb01cation\nThe charge of the \u03c4 lepton is calculated as the sum of the charges of the reconstructed tracks. For the\nleading track, which is required (e.g. by the track-based algorithm) to have a transverse momentum 3\nlarger than 9 GeV, charge mis-identi\ufb01cation is limited to \u223c0.2% using the quality cuts described above.\n2The core region for the track-based (calo-based) algorithm is understood here as \u2206R < 0.2(0.3) cone in (\u03b7, \u03c6) around the\nreconstructed direction of the visible decay products.\n3The threshold pT > 9 GeV on the leading track was used for results presented here, while it was lowered to 6 GeV in the\nmore recent software releases.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n233\n\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nATLAS\nEfficiency\n0.86\n0.88\n0 9\n0.92\n0.94\n0.96\n decays\n\u03c4\n1\u2212prong \n decays\n\u03c4\n3\u2212prong \n|\n\u03b7\n|\n0\n0 5\n1\n1.5\n2\n2.5\nEfficiency\nATLAS\n0.7\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n decays\n\u03c4\n1\u2212prong \n = 15\u221225 GeV\nT\np\n = 5\u22126 GeV\nT\np\n = 1\u22122 GeV\nT\np\nFigure 2: Reconstruction ef\ufb01ciency for tracks from charged \u03c0s for one- and three-prong hadronic \u03c4\ndecays from W \u2192\u03c4\u03bd and Z \u2192\u03c4\u03c4 signal samples as a function of the transverse momentum of the track\n(left) and of the pseudorapidity for three different ranges of track pT (right).\nThe overall charge mis-identi\ufb01cation probability for the hadronically decaying \u03c4 lepton is however dom-\ninated by combinatorial effects: single-prong decays may migrate to the three-prong category due to\nphoton conversions or the presence of additional tracks from the underlying event. A three-prong decay\nmight be reconstructed as a single-prong decay due to inef\ufb01ciencies of the track reconstruction and selec-\ntion. This overall charge mis-identi\ufb01cation is estimated to be below \u223c3.6% without requiring additional\nquality cuts. In fact, the \u03c4 charge misidenti\ufb01cation is dominated by a combination of effects, but the\ncontributions from the charge misidenti\ufb01cation of the individual tracks should not be neglected.\nTable 1 shows the percentage of contamination for one- and three-prong candidates using the afore-\nmentioned quality criteria for tracks in the core region. For the roughly 3.9% contamination of the\nsingle-track candidates from three-prong decays, about 85% are due to hadronic interactions. A 3.8%\ncontamination of three-track candidates from one-prong decays is observed with 70% of them being due\nto conversions. The percentage of the overall charge misidenti\ufb01cation is also shown. Requiring at least\none B-Layer hit reduces the charge misidenti\ufb01cation both in the case of electron tracks from conver-\nsions and in the case of hadronic interactions at low radii. However, this happens at the expense of an\nadditional loss in ef\ufb01ciency in particular for three-prong decays.\n3.1.3\nTracks from conversions\nPhotons from \u03c00 decays might convert in the material of the inner detector and then contribute additional\ntracks to the core or isolation region of the \u03c4had candidate. This could result in one-prongs being recon-\nstructed as three-prong candidates, in an inef\ufb01ciency of the reconstruction and identi\ufb01cation criteria and\nin a degradation of the energy resolution as calculated from the energy-\ufb02ow algorithm.\nA large fraction of reconstructed \u03c4had candidates are accompanied by conversions. In 1.5% of the\ncases a conversion electron is reconstructed as the leading track of the one-prong candidate, while 5.7%\nof the three-prong candidates contain one reconstructed track coming from a conversion electron. In\nTable 1 the effects of charge misidenti\ufb01cation and contamination from photon conversions are quanti\ufb01ed.\n3.1.4\nImpact parameter\nThe mean proper lifetime of the \u03c4 lepton is about 0.29ps. Although the lifetime of the \u03c4 lepton is about\n\ufb01ve times shorter than that of the b-quark, the transverse impact parameters of its decay products are\nstill useful for \u03c4 identi\ufb01cation. The impact parameters, d0 and z0 sin(\u03b8), have been studied for one-prong\ncandidates reconstructed by the track-based algorithm. The transverse impact parameter d0 is de\ufb01ned\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n234\n\nTable 1: Percentage of one- and three prong \u03c4 lepton hadronic decays within reconstructed one-, two-\nand three-prong \u03c4had candidates by the track-based algorithm, matched to true \u03c4 decays. Tracks in\na cone of \u2206R = 0.2 around the leading good quality track are considered. A transverse momentum\nof pT > 9 GeV is required for the leading track. An estimate for electron contamination and charge\nmisidenti\ufb01cation is given in addition. Separately speci\ufb01ed are results for a subsample where no hadronic\nsecondary interaction of primary charged \u03c0 was recorded inside the inner detector volume. Events from\nZ \u2192\u03c4\u03c4 and W \u2192\u03c4\u03bd samples were used.\nSeeds for track-based\nReconstructed as\nReconstructed as\nReconstructed as\n\u03c4had-candidates\nsingle-prong\nthree-prong\ntwo-prong\nElectron contamination\n(from conversion)\n1.5%\n5.7%\n2.9%\n\u03c4 \u2192\u03c0\u00b1n\u03c00\u03bd\n96.1%\n3.8%\n23.8%\n\u03c4 \u21923\u03c0\u00b1n\u03c00\u03bd\n3.9 %\n96.2%\n76.2%\nCharge misid.\n1.7%\n3.6%\n(no had. interact.)\n0.4%\n2.1%\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\nm)\nATLAS\n\u00b5\n residual) (\n0\n(d\n\u03c3\n12\n14\n16\n18\n20\n22\n\u03bd\n\u03bd\n\u00b5\n\u2192\n\u03c4\n\u03bd\n)\n0\n\u03c0\n(\n\u03c0\n\u2192\n\u03c4\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nm)\nATLAS\n\u00b5\n) residual) (\n\u03b8\n sin(\n\u00d7\n0\n(z\n\u03c3\n40\n60\n80\n100\n120\n140\n\u03bd\n\u03bd\n\u00b5\n\u2192\n\u03c4\n\u03bd\n)\n0\n\u03c0\n(\n\u03c0\n\u2192\n\u03c4\nFigure 3: Transverse (left) and longitudinal (right) impact parameter resolution as a function of |\u03b7| from\na one-prong Z \u2192\u03c4\u03c4 sample. The open (full) circles are from \u03c4 \u2192\u03c0(\u03c00)\u03bd (\u03c4 \u2192\u00b5\u03bd \u00af\u03bd) events.\nas the smallest distance in the transverse plane between the track and the reconstructed primary vertex.\nThe impact parameter z0 is given by the distance in z-direction between the reconstructed primary vertex\nand the point of closest approach in the transverse plane of the track multiplied by sin(\u03b8) to obtain the\ncomponent transverse to the track direction. Tracks assigned to the \u03c4had candidate are not used in the\nprimary vertex \ufb01t.\nIn Fig. 3 the resolution of the transverse (left) and longitudinal (right) impact parameters are shown as\na function of |\u03b7|. The resolution for \ufb01nal state muons and pions from \u03c4 \u2192\u00b5\u03bd\u03bd and \u03c4 \u2192\u03c0(\u03c00)\u03bd decays\nare similar: about 13 \u00b5m for |\u03b7| < 1.0 and about 50 \u00b5m for |\u03b7| > 1.0 for the transverse and longitudinal\nimpact parameters, respectively. No degradation related to hadronic interactions for \u03c4 \u2192\u03c0\u03bd decays\nis observed. This has been veri\ufb01ed by studying events with elastic interaction in the Inner Detector\n(hadronic interaction), de\ufb01ned as events where the outgoing \u03c0\u00b1 carries more than 90 % of the transverse\nenergy of the incoming \u03c0\u00b1. This observation is consistent with that presented in Ref. [11].\nIn Fig. 4 distributions of the signi\ufb01cances of the impact parameters are presented. The signi\ufb01cance\nis de\ufb01ned as the impact parameters divided by its estimated error. The distribution shows a moderate\ndiscrimination power between one-prong candidates reconstructed from hadronic \u03c4 decays and fake one-\nprong candidates. Due to the limited resolution of the longitudinal impact parameter, the separation\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n235\n\nATLAS\n significance\n0\nd\n0\n5\n10\n15\n20\n25\n candidates\n\u03c4\nFraction of \n\u22123\n10\n\u22122\n10\n\u22121\n10\nfake 1\u2212prong (no b/c decays)\n1\u2212prong decays\n\u03c4\nATLAS\n) significance\n\u03b8\n sin(\n\u00d7\n0\nz\n0\n2\n4\n6\n8\n10\n12\n candidates\n\u03c4\nFraction of \n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n decays\n\u03c4\n1\u2212prong \nfake 1\u2212prong (no b/c decays)\nFigure 4: Signi\ufb01cances of the impact parameters d0 (left) and z0 sin(\u03b8) (right) for 1-prong \u03c4had candidates\nreconstructed by the track-based algorithm. Distributions are shown for \u03c4had candidates reconstructed\nfrom \u03c4 decays and for fake candidates which do not originate from the decays of b- or c-hadrons.\nbetween the two classes is less signi\ufb01cant in that case.\n3.1.5\nSecondary vertex reconstruction and transverse \ufb02ight path\nThe signi\ufb01cant lifetime of the \u03c4 lepton (c\u03c4 = 87.11\u00b5m) allows the reconstruction of its decay vertex\nfor three-prong decays. Currently, \ufb01ve vertex \ufb01tting algorithms [12\u201314] are implemented in the ATLAS\nreconstruction framework. Among these the adaptive vertex \ufb01tter [13], an iterative re-weighted \ufb01t which\ndown-weights tracks according to their weighted distance to the vertex, was found to give the optimal\nperformance.\nTo estimate its performance, secondary vertex \ufb01ts were performed using tracks associated with \u03c4had\ncandidates from Z \u2192\u03c4\u03c4 and W \u2192\u03c4\u03bd events. The quality criteria applied in the track-based reconstruc-\ntion were required to be met by the tracks. The \u03c4had candidates associated with a true hadronic \u03c4 decay\nwere divided into two classes. Candidates with three tracks successfully matched to true particles com-\ning from the same true three-prong hadronic \u03c4 decays were used as a reference. These candidates are\ndenoted hereafter as fully-matched. The second class is composed of the remaining candidates with at\nleast two tracks of which at least one is matched to a true particle coming from a hadronic \u03c4 decay. These\ncandidates are denoted hereafter as partially matched.\nThe resolution of the secondary vertex position varies strongly if measured in the perpendicular or\nparallel direction with respect the momentum of \u03c4had candidate. The resolution on the position of the\nsecondary vertex calculated in the plane perpendicular to the momentum of the \u03c4had candidate is expected\nto be better than in the parallel direction due to the collimation of tracks. To estimate the resolution in the\ntransverse plane, the residuals of the vertex position in the direction perpendicular to both momentum of\na \u03c4had candidate and the beam axis were calculated. The distributions were approximated by a double\nGaussian \ufb01t. For fully matched three-prong \u03c4had candidates there is no signi\ufb01cant difference between the\ndistributions obtained with different \ufb01tters. The distributions of residuals of the secondary vertex position\nobtained with the adaptive \ufb01tter, parallel and perpendicular to the direction of \ufb02ight of the \u03c4had candidate\nare presented in Fig. 5. Shown in Table 2 are the resolution4, the mean values of the \ufb01t and 68.3 % and\n95.0 % coverages5 for the fully matched, partially matched and combined samples. As expected, the\ntransverse resolution (\u03c3 \u223c10 \u00b5m) is far more accurate than the parallel one (\u03c3 \u223c600 \u00b5m). The non-\nGaussian tails are signi\ufb01cant in both cases, but far more important in the case of the parallel component.\nA precise reconstruction of the transverse \ufb02ight path is therefore possible, which is important for further\n4In the case of a double Gaussian \ufb01t, the width of the central Gaussian will be quoted as the resolution hereafter.\n5The coverage is the half-width of a symmetric interval covering a given percentage of the distribution.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n236\n\nATLAS\nSecondary vertex residual transverse (mm)\n\u22120.05\u22120.04\u22120.03\u22120.02\u22120.01\n0\n0 01 0.02 0.03 0 04 0.05\n candidates\n\u03c4\nFraction of \n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nfully matched 3\u2212prong\npartially matched\nATLAS\nSecondary vertex residual parallel (mm)\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\n candidates\n\u03c4\nFraction of \n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n0 09\nfully matched 3\u2212prong\npartially matched\nFigure 5: Residuals of the secondary vertex position parallel and perpendicular to the direction of \ufb02ight\nof the \u03c4had candidate using the adaptive vertex \ufb01tter. Fully (solid) and partially (open) matched three-\nprong \u03c4had candidates reconstructed with the track-based algorithm from Z \u2192\u03c4\u03c4 and W \u2192\u03c4\u03bd processes\nare used.\nTable 2: Resolution and mean of the distribution of residuals of the secondary vertex position in the\ndirections parallel and transverse to that of the reconstructed momentum vector of the \u03c4had candidate as\nobtained from the adaptive vertex \ufb01tter. Candidates with up to three associated tracks reconstructed by\nthe track-based algorithm were used. The resolution quoted is the \u03c3 of the core Gaussian of a double\nGaussian \ufb01t in the range [\u22124mm,4mm] in the parallel direction and [\u221250\u00b5m,50\u00b5m] in the transverse\ndirection. The 68.3% and 95% coverages are also quoted.\nResolution\nMean\n68.3%\n95%\nParallel\nFully matched 3-prong\n0.593\u00b10.008mm\n0.006\u00b10.006mm\n1.27mm\n5.33mm\nPartially matched\n0.703\u00b10.030mm\n\u22120.035\u00b10.020mm\n3.83mm\n> 15mm\nCombined\n0.613\u00b10.008mm\n0.004\u00b10.006mm\n1.89mm\n11.37mm\nTransverse\nFully matched 3-prong\n10.1\u00b10.2\u00b5m\n0.2\u00b10.1\u00b5m\n14.4\u00b5m\n36.9\u00b5m\nPartially matched\n11.3\u00b10.5\u00b5m\n\u22120.1\u00b10.2\u00b5m\n20.9\u00b5m\n72.2\u00b5m\nCombined\n10.5\u00b10.2\u00b5m\n0.1\u00b10.1\u00b5m\n16.4\u00b5m\n48.1\u00b5m\nrejection of the QCD background. It may also be possible to obtain a competitive measurement of the \u03c4\nlifetime, which requires a measurement of the \ufb02ight path and momentum of the \u03c4 lepton.\nShown in Fig. 6 is the resolution on the transverse \ufb02ight path as a function of the transverse mo-\nmentum and the pseudorapidity of the \u03c4had candidates. The resolution was obtained from a Gaussian \ufb01t\nto a central interval covering 80% of distributions of residuals of a transverse \ufb02ight path for the adap-\ntive vertex \ufb01tter for fully matched three-prong candidates. In addition the 68.3% and 95% coverages of\ndistributions of residuals are presented.\nDistributions of the signi\ufb01cance of the transverse \ufb02ight path, for different classes of three-prong can-\ndidates are shown in Fig. 7. This distribution might be used to discriminate between true \u03c4had candidates\nand fake candidates from light jets. The discrimination in the case of b- and c- jets seems however to be\ndif\ufb01cult.\nAn ef\ufb01cient rejection of tracks coming from photon conversions, decays of long-lived particles and\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n237\n\n (GeV)\nT\np\n10\n20\n30\n40\n50\n60\n70\n80\n90\nTransverse flight path res. (mm)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\n95%\n68.3%\n(fit)\n\u03c3\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nTransverse flight path res. (mm)\n0\n0.5\n1\n1.5\n2\n2.5\n(fit)\n\u03c3\n95%\n68.3%\nATLAS\nFigure 6: Resolution on the transverse \ufb02ight path reconstructed with the adaptive vertex \ufb01tter for fully\nmatched three-prong \u03c4had candidates as a function of the transverse momentum (left) and the pseudora-\npidity (right). Standard deviations of Gaussians \ufb01tted to central intervals covering 80% of the residual\ndistributions are shown (black points). In addition the 68.3% and 95% coverages of the distributions of\nresiduals of the secondary vertex position are shown (dashed and dot-dashed lines).\nATLAS\nTransverse flight path significance\n\u221210\n0\n10\n20\n30\n40\n50\n candidates\n\u03c4\nFraction of \n\u22125\n10\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\nfully matched\npartially matched\nfake (b/c jets)\nfake (light jets)\nFigure 7: Signi\ufb01cance of the transverse \ufb02ight path for fully matched and partially matched three-prong\nand for fake candidates with and without hadrons containing b or c quarks (the contribution from semilep-\ntonic decays of b/c jets into \u03c4 leptons was not subtracted).\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n238\n\nTable 3: Single prong candidates: fractions with zero, one and two or more reconstructed \u03c00 subclusters.\ndecay mode\nno \u03c00 subclusters\n1 \u03c00 subcluster\n\u22652 \u03c00 subclusters\nall \u03c4 \u2192had\u03bd\n32%\n35%\n33%\n\u03c4 \u2192\u03c0\u03bd\n65%\n20%\n15%\n\u03c4 \u2192\u03c1\u03bd\n15%\n50%\n35%\n\u03c4 \u2192a1(\u21922\u03c00\u03c0)\u03bd\n9%\n34%\n57%\nhadronic interactions in the material reduce the number of one-prong candidates wrongly reconstructed as\ntwo- or three-prong candidates and improve the separation between correctly reconstructed three-prong\ncandidates and candidates from light jets. It is a subject of further studies currently in progress.\n3.2\nReconstruction of \u03c00 subclusters\nThe high granularity of the electromagnetic calorimeter in ATLAS allows for the identi\ufb01cation of isolated\nsubclusters from \u03c00s inside the core region of the reconstructed \u03c4 lepton hadronic decays.\nStudies have been performed based on the topological clustering algorithm [15] with only the mid-\ndle layer of the calorimeter used for \ufb01nding primary maxima, and the strip layer used for \ufb01nding the\nsecondary maxima. The clustering was performed based on cells in a region \u2206R < 0.4 around the direc-\ntion of the leading track satisfying pT > 9 GeV and only subclusters with center within \u2206R < 0.2 were\ntaken. A subtraction procedure was applied \ufb01rst to reduce the impact from energy deposits of nearby\n\u03c0\u00b1\u2019s and of energy double-counting when adding the latter (track + \u03c00 clusters) to reconstruct the visible\n\u03c4had energy. Namely, before clustering procedure, cells being closest to the impact point of the track\n(\u2206R < 0.0375) were removed. The subtraction was stopped when the subtracted energy exceeded 70%\nof the track momentum. In the case of coincidence of large energy deposits in the hadronic calorime-\nter (above 40% of the track momentum) and in the presampler+strip layer close to the track, indicating\nsuperposition of \u03c00 and \u03c0\u00b1 showers, cells were subtracted only from the middle layer up to the point\nwhere the transverse energy of the remaining cells exceeded 2.5 \u00b7 ET collected in the presampler+strip\nlayer (always counted in \u2206R < 0.0375 from the track impact point).\nReconstructed subclusters were required to have ET > 1 GeV and be separated by \u2206R > 0.0375 from\nthe impact point of the track in the middle layer. In addition, subclusters were accepted if their recon-\nstructed energy in the strip+presampler layers exceeded 10% of their total energy. These requirements\nef\ufb01ciently removed about 50% of satellite clusters from charged \u03c0s in the case of \u03c4 \u2192\u03c0\u03bd decays. Ta-\nble 3 summarizes the results in terms of the fraction of one-prong candidates reconstructed with a given\nmultiplicity of \u03c00 subclusters.\nReconstructing the track and \u03c00 subclusters for single-prong decays allows for the de\ufb01nition of the\nenergy and visible mass of the hadronic \u03c4 decays from the vector sum of both components. The procedure\nwas evaluated for one-prong decays from W \u2192\u03c4\u03bd events, i.e. for \u03c4 leptons with visible transverse\nmomenta below 50 GeV. Figure 8 shows the response and resolution obtained by this algorithm for\nreconstructing the visible energy in decays of type \u03c4 \u2192\u03c1\u03bd from W \u2192\u03c4\u03bd events in case at least one \u03c00\nsubcluster is reconstructed. A Gaussian \ufb01t to the core region of the distribution yields a resolution of\n4.6% with an effective shift of \u22122.4%, dominated by the calibration of the electromagnetic calorimeter\nnot being optimal for the \u03c00 subcluster reconstruction.\nAs a \ufb01nal benchmark for the quality of the \u03c00 cluster reconstruction discussed above, the invariant\nmass of \u03c4 \u2192\u03c1\u03bd \u2192\u03c00\u03c0\u03bd decays is reconstructed from the track + \u03c00 subcluster system which is more\ndif\ufb01cult than the reconstruction of the transverse energy only since the resolution is dominated by the\nprecision of the reconstruction of the angle between the charged and the neutral pion. Figure 8 (right)\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n239\n\nATLAS\ntruth\n)/E\ntruth\n \u2212 E\nrec\n (E\n\u22121\n\u22120.8 \u22120.6 \u22120.4 \u22120 2\n\u22120\n0.2\n0.4\n0.6\n0.8\n1\n Arbitrary units \n0\n20\n40\n60\n80\n100\n\u03bd\n\u03c1\n\u2192\n\u03c4\n 0.2)% \n\u00b1\n mean = \u2212 (2.4 \n 0.2)% \n\u00b1\n = (4.6 \n\u03c3\nATLAS\n Invariant mass (GeV)\n0\n0.5\n1\n1.5\n2\n2.5\n Arbitrary units\n0\n20\n40\n60\n80\n100\n120\n140\n160\n\u03bd\n\u03c1\n\u2192\n\u03c4\n\u03bd\n) \n\u03c0\n0\n\u03c0\n 2 \n\u2192\n(\n1\n a\n\u2192\n\u03c4\n\u03bd\n\u03c0\n\u2192\n\u03c4\nFigure 8: The energy response obtained for the visible energy from \u03c4 \u2192\u03c1\u03bd events using candidates\nwith one \u03c00 subcluster (left). The invariant mass of the visible decay products for hadronic single-prong\n\u03c4 \u2192\u03c1\u03bd, \u03c4 \u2192a1(\u21922\u03c00\u03c0)\u03bd, and \u03c4 \u2192\u03c0\u03bd decays using candidates from W \u2192\u03c4\u03bd events with at least one\n\u03c00 subcluster reconstructed (right).\n|\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nEfficiency %\n0\n20\n40\n60\n80\n100\n\u03bd\n\u03c4 \n\u2192\nW\n\u03bd\n e\n\u2192\n W\nATLAS\n (GeV)\nLtrk\nT\nP\n0\n10\n20\n30\n40\n50\n60\n70\n80\nEfficiency %\n0\n20\n40\n60\n80\n100\n\u03bd\n\u03c4 \n\u2192\nW\n\u03bd\n e\n\u2192\nW\nATLAS\nFigure 9: The ef\ufb01ciency of the electron veto algorithm for W \u2192\u03c4\u03bd (rectangles) and W \u2192e\u03bd (triangles)\nevents as a function of |\u03b7| and pT of the leading track.\nshows the reconstructed visible mass for \u03c4 \u2192\u03c1\u03bd, \u03c4 \u2192a1(\u21922\u03c00\u03c0)\u03bd, and \u03c4 \u2192\u03c0\u03bd decays. The relative\ncontributions are proportional to the branching fractions convoluted with the experimental ef\ufb01ciencies\nof the algorithm applied to inclusive hadronic decays of the \u03c4 lepton. If more than one \u03c00 subcluster is\nreconstructed the energy weighted barycenter of the cluster system is taken.\n3.2.1\nCombined veto on electron tracks\nAn ef\ufb01cient rejection of tracks originating from isolated electrons is important for rejecting backgrounds\nfor example from W \u2192e\u03bd and Z \u2192ee events. One possibility would be to reject tracks that have been\nidenti\ufb01ed as good electron candidates by the standard electron reconstruction algorithm. With the so\ncalled tight selection this algorithm is found to reject \u223c85% of all electrons from W \u2192e\u03bd events with a\nloss of ef\ufb01ciency for true hadronic \u03c4 decays with ptrack\nT\n> 9 GeV of less than 1%.\nTo achieve a more stringent selection, a dedicated algorithm to veto electrons has been developed\naiming at a higher rejection rate while, at the same time, retaining a high fraction of hadronic \u03c4 decays.\nIt is based on the following variables:\n\u2022 The energy deposited in the hadronic part of the calorimeter (EHCAL).\n\u2022 The energy not associated with a charged track in the strip compartment of the electromagnetic\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n240\n\nTable 4: Ef\ufb01ciency for hadronically decaying \u03c4 leptons and true electrons from W \u2192\u03c4\u03bd for passing\nthe electron veto algorithm. The numbers given are normalized to true electrons with pT > 9 GeV and\n|\u03b7| < 2.5 (vs. true e) and to reconstructed one-prong or three-prong candidates with the leading track\nbeing matched to a \u03c0 from W \u2192\u03c4\u03bd events (vs. reconstructed \u03c4had). The probability that an electron from\nW \u2192e\u03bd events with pT > 9 GeV and |\u03b7| < 2.5 is reconstructed as one-prong (three-prong) candidate is\n\u223c70% (\u223c0.7%). In addition the performance of the standard algorithm for electron reconstruction [16]\nis shown. The statistical uncertainty on the numbers presented here is at the level of 0.1\u22120.5%.\nReconstructed as\nReconstructed as\nOverall\nCandidates\nsingle-prong\nthree-prong\nElectron-veto algorithm\n\u03c4 from W \u2192\u03c4\u03bd (vs reconstructed \u03c4had)\n94.1%\n96.2%\n94.9%\nElectron from W \u2192e\u03bd (vs true e)\n1.5%\n< 0.1%\n1.6%\nStandard algorithm (tight selection)\n\u03c4 from W \u2192\u03c4\u03bd (vs reconstructed \u03c4had)\n99.9%\n99.9%\n99.9%\nElectron from W \u2192e\u03bd (vs true e)\n15.6%\n0.4%\n16.4%\nStandard algorithm (medium selection)\n\u03c4 from W \u2192\u03c4\u03bd (vs reconstructed \u03c4had)\n90.6%\n95.1%\n92.1%\nElectron from W \u2192e\u03bd (vs true e)\n4.2%\n0.2%\n4.6%\npart of the calorimeter (Estrip\nmax ).\n\u2022 The ratio in the transverse plane of the associated energy in the electromagnetic calorimeter and\nthe track momentum (ET/pT).\n\u2022 The ratio of the number of high threshold to low threshold hits (including outliers) in the TRT\n(NHT/NLT).\nThe \ufb01rst two variables are used to divide tracks into categories in which discrimination is provided by\n\ufb01xed cuts on the remaining two variables.\nThe algorithm yields a rejection factor of 60 against electrons from W \u2192e\u03bd events at the expense of\nlosing 5% of the signal from W \u2192\u03c4\u03bd events. The ef\ufb01ciency of the algorithm 6 as a function of |\u03b7| and\npT is shown in Fig. 9 and its performance is summarized in Table 4. For completeness results from the\nstandard electron reconstruction algorithm are also shown. The dedicated electron-veto described here\ngives much better ef\ufb01ciency for rejecting isolated electrons from W decay than the standard electron\nreconstruction algorithm for comparable loss in accepting true hadronic \u03c4 decays.\n4\nOf\ufb02ine algorithms for \u03c4 reconstruction\nTwo complementary algorithms for the reconstruction of hadronic \u03c4 decays have been implemented\nin the ATLAS of\ufb02ine reconstruction software. Each algorithm is discussed separately below and their\nperformance is compared.\n6For hadronic decays of \u03c4 leptons the ef\ufb01ciency is de\ufb01ned w.r.t. the reconstructed \u03c4had candidates and for electrons w.r.t. to\nall electrons inside |\u03b7| \u22642.5 with pT > 9 GeV.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n241\n\n (GeV)\nT\nE\n0\n50\n100\n150\n200\n250\n300\nT\n / E\nT\nE\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n (GeV)\n\u03c4\u2212vis\n\u03c4\u2212vis\nT\nE\n0\n50\n100\n150\n200\n250\n300\nT\n / E\nE\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n\u03c4\n\u03c4\n\u2192\nZ \n\u03c4\n\u03c4\n\u2192\nH/A \nATLAS\n\u03c4\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nT\n / E\nT\nE\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n\u03c4\u2212vis\n\u03c4\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nT\n / E\nT\nE\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nATLAS\n\u03c4\n\u03c4\n\u2192\nZ \n\u03c4\n\u03c4\n\u2192\nH/A \nFigure 10: The ratio of the reconstructed (ET) and the true (E\u03c4\u2212vis\nT\n) transverse energy of the hadronic\n\u03c4 decay products is shown as a function of the visible true transverse energy E\u03c4,vis\nT\n(left), calculated in\n|\u03b7| < 2.5 and |\u03b7| (right) for taus from Z \u2192\u03c4\u03c4 (triangles) and A \u2192\u03c4\u03c4 with mA = 800 GeV (squares)\ndecays. The ordinate value is the mean and the error bars correspond to the sigma of the Gaussian \ufb01t\nperformed in the range 0.8 < ET/E\u03c4,vis\nT\n< 1.2. The results are obtained after applying the loose likelihood\nselection, see below.\n4.1\nThe calorimeter-based algorithm\nIn this approach [17], hadronically decaying \u03c4 candidates are reconstructed using calorimeter clusters as\nseeds. They are obtained from a sliding window clustering algorithm applied to so called calorimeter\ntowers which are formed from cells of all calorimeter layers on a grid of size \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.1 \u00d7 2\u03c0/64.\nThe energy and position are calculated from the clusters, while all cells with the full granularity of the\ncorresponding calorimeters are used to calculate the quantities involved in \u03c4 identi\ufb01cation as described\nin the following. Only clusters with a transverse energy ET > 15 GeV are used. The probability for a\ntrue \u03c4 to be reconstructed as a cluster increases from 20% to 68% over the visible \u03c4 transverse energy\nrange from 15 to 20 GeV and saturates at 98% for ET > 30 GeV.\nAll cells within \u2206R < 0.4 around the barycenter of the cluster are then calibrated with an H1-style\ncalibration [18]. The cell weights are a function of the cell energy density, \u03b7 and the calorimeter region.\nThese weights have been optimized for jets [18] and only approximately for hadronic \u03c4 decays. The\nmean and sigma of a Gaussian \ufb01t to the ratio of the reconstructed and the generated energy of the visible\n\u03c4 decay products, E\u03c4\u2212vis\nT\n, in the range from 0.8 to 1.2 is shown in Fig. 10 as a function of E\u03c4\u2212vis\nT\nand\n\u03b7. The resolution is of the order of 10% and an offset in the range from +5 to -7% is observed in the \u03c4\nenergy range from 20 to 50 GeV, while at larger energies the offset is of the order of -3 to -5%.\nSeveral quantities that exploit the \u03c4 lepton properties have been combined in a likelihood function\nto discriminate hadronic \u03c4 decays from fake candidates originating from QCD jets. These quantities are\ndescribed in the following:\n\u2022 The electromagnetic radius Rem:\nTo exploit the smaller transverse shower pro\ufb01le in \u03c4 decays, the electromagnetic radius Rem is\nused, de\ufb01ned as\nRem =\n\u2211n\ni=1 ET,i\nq\n(\u03b7i \u2212\u03b7cluster)2 +(\u03c6i \u2212\u03c6cluster)2\n\u2211n\ni=1 ET,i\n,\n(1)\nwhere i runs over all cell in the electromagnetic calorimeter in a cluster with \u2206R < 0.4. The\nquantities \u03b7i, \u03c6i, and ET,i denote their position and transverse energy in cell i. Cells may have\ndifferent sizes depending on the layer and their \u03b7 value. The size varies from \u2206\u03b7 \u00d7\u2206\u03c6 = 0.003\u00d7\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n242\n\n0.1 in the \u03b7-strip region of the barrel to 0.025\u00d70.025 for the second calorimeter layer. This leads\nto a dependence of the performance on \u03b7. This variable shows good discrimination power at low\nET but becomes less effective at higher ET.\n\u2022 Isolation in the calorimeter:\nClusters built from hadronic \u03c4 decays are well collimated and therefore rather tight isolation crite-\nria can be used. Here a ring of 0.1 < \u2206R < 0.2 was chosen as the isolation region and the quantity\n\u2206E12\nT = \u2211i ET,i\n\u2211j ET, j\n,\n(2)\nis calculated, where the indices i and j run over all electromagnetic calorimeter cells in a cone\naround the cluster axis with 0.1 < \u2206R < 0.2 and \u2206R < 0.4, respectively, and ET,i and ET, j denote\nthe transverse cell energies.\nLike Rem, the \u2206E12\nT distribution shows an ET dependence and becomes narrower with increasing\nET. This variable also depends on the event type and is expected to be less effective for events\nwith higher hadronic activity, like e.g. t\u00aft events.\n\u2022 Charge of the \u03c4 candidate:\nThe charge of a \u03c4 candidate is de\ufb01ned as the sum over the charge(s) of the associated track(s). The\nmisidenti\ufb01cation of the charge on the level of a few percent shows almost no ET dependence.\n\u2022 Number of associated tracks:\nThe number of tracks, Ntr, associated with a given cluster within \u2206R < 0.3. The tracks are required\nto have pT > 2 GeV and no speci\ufb01c requirements on the quality of the track reconstruction is made.\nA signi\ufb01cant fraction of events with zero, two, and even four tracks is observed for true hadronic\n\u03c4 decays.\n\u2022 Number of hits in the \u03b7 strip layer:\nThe number of hits in \u03b7 direction in the \ufb01nely segmented strip detector, Nstrip, in the \ufb01rst layer of\nthe electromagnetic barrel calorimeter is also used in the likelihood discrimination. Cells in the\n\u03b7 strip layer within \u2206R < 0.4 around the cluster axis are counted as hits if the energy deposited\nexceeds 200 MeV. In contrast to jets, a signi\ufb01cant fraction of \u03c4 leptons deposit nearly no energy in\nthe \u03b7 strip layer (\u03c4 \u2192\u03c0\u03bd decays) and the number of corresponding hits is small.\n\u2022 Transverse energy width in the \u03b7 strip layer\nThe transverse energy width \u2206\u03b7 is de\ufb01ned as\n\u2206\u03b7 =\nv\nu\nu\nt\u2211n\ni=1 Estrip\nTi\n(\u03b7i \u2212\u03b7cluster)2\n\u2211n\ni=1 Estrip\nTi\n.\n(3)\nwhere the sum runs over all strip cells in a cone with \u2206R < 0.4 around the cluster axis and Estrip\nTi\nis the corresponding strip transverse energy. Like Rem it is a powerful discriminator at low ET but\nloses discrimination power with increasing ET for higher collimated high ET jets.\n\u2022 Lifetime signed pseudo impact parameter signi\ufb01cance:\nAt present only a 2-dimensional impact parameter, also called the pseudo impact parameter, is\nused. It is de\ufb01ned as the distance from the beam axis to the point of closest approach of the track\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n243\n\nem\nR\n0\n0 05\n0.1\n0.15\n0.2\n0.25\n0.3\nATLAS\nNormalized to unit area\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n signal\n\u03c4\njet background\n\u03b7\n\u2206\n0\n0 01\n0 02\n0.03\n0.04\n0 05\n0 06\n0.07\nATLAS\nNormalized to unit area\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n signal\n\u03c4\njet background\nT\n12\nE\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\nATLAS\nNormalized to unit area\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n signal\n\u03c4\njet background\nT,1\n/p\nT\nE\nATLAS\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\nNormalized to unit area\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n signal\n\u03c4\njet background\nFigure 11: The distributions of a few discriminating variables (electromagnetic radius, energy isolation,\ntransverse energy width in the \u03b7 strip layer and ET over pT1 of the leading track) used in the calorimeter-\nbased tau identi\ufb01cation for true tau decays and jets with visible transverse cluster energies ET in the\nrange from 40 to 60 GeV and track multiplicities between 1 and 3.\nin the plane perpendicular to the beam axis. From this information and from the jet axis, a quantity\ndenoted as lifetime signed pseudo impact parameter signi\ufb01cance, de\ufb01ned as sigd0 = d0/\u03c32\nd0 where\n\u03c3 is the impact parameter resolution, is calculated.\n\u2022 ET over pT of the leading track: ET/pT1 :\nFor \u03c4 decays a large fraction of the energy is expected to be carried by the leading track and the\nratio of the cluster energy ET to the momentum of the leading track pT1 is expected to be large,\nclose to 1. This provides another discrimination against QCD jets, which are expected to have a\nmore uniform distribution of pT among the tracks. They are also expected to have more additional\nneutral particles. Values above one are also expected from \u03c4 decay modes involving additional \u03c00s\nand for three-prong decays. The ET dependence is rather modest for \u03c4 decays but more pronounced\nfor QCD jets, which tend to become more signal like with higher ET.\nIn Fig. 11 the distributions of a few discriminating variables are shown for signal and backgrounds\nfor transverse cluster energies ET in the range between 40 and 60 GeV and for candidates with 1 or 3\ntracks.\nFor the calorimeter-based algorithm the \u03c4 identi\ufb01cation is based on a one-dimensional likelihood\nratio constructed from three discrete variables (Ntr, Nstrip and the charge of the \u03c4 lepton) and \ufb01ve continu-\nous variables (Rem, \u2206E12\nT , \u2206\u03b7, sigd0, and ET/pT,1). For the discrete variables the ratios are directly taken\nfrom the reference histograms. For the continuous variables \ufb01ts of appropriate functions to each variable\nfor all ET bins have been performed. The distribution of the likelihood for taus and jets are shown in\nFig. 12. Despite any limitation from using only one-dimensional distributions it shows a good separation\npower.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n244\n\nLikelihood\n\u221210\n\u22125\n0\n5\n10\n15\n20\nArbitrary units\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n signal\n\u03c4\njet background\nATLAS\nEfficiency\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\nRejection\n2\n10\n3\n10\nEfficiency\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\nRejection\n2\n10\n3\n10\nATLAS\nall\n < 28.5\nT\nE\n < 43.5\nT\n28.5 < E\n < 61.5\nT\n43.5 < E\n < 88.5\nT\n61.5 < E\n < 133.5\nT\n88.5 < E\n < 217.5\nT\n133.5 < E\nFigure 12: Left: The log likelihood (LLH) distribution for \u03c4 leptons (solid) and jets from QCD production\n(dashed). The likelihood is applied after a preselection on the number of associated tracks, i.e. requiring\n1 \u2264Ntr \u22643. (Candidates with LLH < \u221210 had variables outside the boundaries of histograms used when\nobtaining the PDFs for the likelihood calculation). Right: Ef\ufb01ciency for \u03c4 leptons and rejection against\njets for different ET ranges, achieved with the likelihood selection.\nIt should be noted that the \u03c4 identi\ufb01cation ef\ufb01ciency chosen to keep enough signal events and to\nachieve the necessary rejection against background depends on the physics channel. Despite the use of\nET bins the likelihood discrimination shows a residual ET dependence. Therefore, a \ufb01xed cut on the\nlikelihood value neither will result in a generally \ufb02at ef\ufb01ciency, nor will it be optimal.\n4.2\nThe track-based algorithm\nIn this approach [19], the visible part of the hadronically decaying \u03c4 lepton is seen as a very well colli-\nmated object consisting of charged and neutral pions, with the charged component being the leading one,\ni.e. reproducing well the direction of the visible decay products and having signi\ufb01cant transverse mo-\nmentum. This assumption is followed by the requirement of a low multiplicity of tracks reconstructed in\nthe region considered the core of the \u03c4had candidate, and the requirement of only minimal energy deposit\nin the isolation region around the core. The energy-scale of the object and the calorimetric variables\nused in the identi\ufb01cation are built following this picture. For most of the analyses only one-track and\nthree-track candidates should be used. Including candidates with two tracks helps to recover a large\nfraction of lost three-prong candidates, however it also signi\ufb01cantly increases the background from QCD\nevents, in particular for \u03c4 leptons with visible transverse momentum below 30 GeV. Candidates with\ntrack multiplicities larger than three should be used for monitoring the level of fake candidates only.\nThe reconstruction step consists of identifying and qualifying a leading hadronic track7 which be-\ncomes a seed for building the \u03c4 candidate. Then up to six additional tracks are allowed in the core\nregion. The (\u03b7, \u03c6) position of the candidate is taken from the direction of the track at the vertex or the\ntrack-pT weighted bary-center in the case of multi-track candidates and the energy of the candidate is\ncalculated from the energy \ufb02ow method. In addition charge \u00b11 or 0 is required in the case of multi-\nprong candidates. The identi\ufb01cation step consists of calculating calorimetric and tracking quantities\nand then providing a decision either based on selection with cuts or a discriminating variable based on\nmulti-variate techniques.\n7The threshold pT > 9 GeV on the leading track was used for results presented here, while it was lowered to 6 GeV in the\nmore recent software releases.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n245\n\n4.2.1\nThe energy - \ufb02ow approach\nThe energy scale of the hadronic \u03c4had candidate is de\ufb01ned using an energy \ufb02ow algorithm. The energy\ndeposit in cells is divided into categories.\n\u2022 The pure electromagnetic energy, Eemcl\nT\n:\nThe energy is seeded by an isolated electromagnetic cluster which is isolated from the good quality\ntracks and which has no substantial hadronic leakage. The energy is collected in a narrow window\naround the seed. Only presampler, strip and middle layers are used.\n\u2022 The charged electromagnetic energy, EchrgEM\nT\n, EchrgHAD\nT\n:\nThe energy is seeded by the impact point of the track(s) in each layer and the energy is collected\nin a narrow window around it.\n\u2022 The neutral electromagnetic energy, EneuEM\nT\n:\nThe energy is seeded by the (\u03b7, \u03c6) of the track at the vertex and in each layer the closest cell is\nsearched for. The energy is collected from not yet used cells in a cone of \u2206R = 0.2 with respect to\nthe cell closest to the impact point. Only presampler, strip and middle layers are used.\nIn the energy-\ufb02ow approach the charged energy deposits EchrgEM\nT\n+ EchrgHAD\nT\nare replaced by the\ntrack(s) momenta (no hadronic neutrals) in order to de\ufb01ne the energy scale of the \u03c4had. The contribution\nfrom \u03c00\u2019s is included in Eemcl\nT\nand EneuEM\nT\n; the effects of \u03c00 and \u03c0\u00b1 depositing energy in the same\ncalorimeter cells or charged energy leakage outside a narrow cone around the track are corrected by\nadding two terms: \u2211resEchrgEM\nT\nand resEneuEM\nT\n. The complete de\ufb01nition for the energy scale Ee\ufb02ow\nT\nreads\nas follows:\nEe\ufb02ow\nT\n= Eemcl\nT\n+EneuEM\nT\n+\u2211ptrack\nT\n+\u2211resEchrgEMtrk\nT\n+resEneuEM\nT\n.\n(4)\nThe fractional energy response, calculated as (Erec \u2212Etruth)/Etruth, for one and three prong candidates is\nshown in Fig. 13.\nThe evident advantage from using the above approach for de\ufb01ning the energy scale comes from the\nfact that while performing well for true hadronic decays of \u03c4 leptons, it signi\ufb01cantly underestimates the\nnominal energy of fake \u03c4hads from jets. This effect is rather obvious since a cone of \u2206R = 0.2 is too\nnarrow to ef\ufb01ciently collect the energy of a QCD jet (particularly with low transverse momentum) and\nalso since a large fraction of the neutral hadronic component is largely omitted in the de\ufb01nition itself (as\nthe energy deposit in the hadronic calorimeter does not contribute to the energy calculations). This leads\nto a faster falling background spectrum as a function of ET compared to that using calibrated calorimetric\nclusters as implemented in the calorimeter-based algorithm (Section 4.1). This method leads however to\nmore non-Gaussian tails in the fractional energy response than the more conventional energy estimates\nfrom calorimetry only.\n4.2.2\nIdenti\ufb01cation with calorimetric and tracking variables\nSeveral calorimetric and tracking variables are used to discriminate a narrow, low track multiplicity\n\u03c4had cluster from a hadronic cluster originating from quarks or gluons. If not stated otherwise, the\ncalorimetric and tracking identi\ufb01cation quantities are calculated from cells/tracks within a core cone\nof \u2206R = 0.2 around the seed. The isolation criteria used here are checked in an isolation cone \u2206R =\n0.2 \u22120.4. Please note, that although some de\ufb01nitions are very similar for the calorimeter-based and\ntrack-based algorithms, in case of the latter the narrower core cone is often used for the calculation of\ncalorimetric quantities and a more explicit distinction between core and isolation cone is made.\nNot all discriminating quantities discussed in Section 3 have been already implemented in the iden-\nti\ufb01cation procedure. In particular transverse impact parameter, transverse \ufb02ight path and categorizing\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n246\n\n Fractional energy response\nATLAS\n\u22121\n\u22120.8 \u22120.6 \u22120.4 \u22120.2\n\u22120\n0.2\n0.4\n0 6\n0.8\n1\n Arbitrary units \n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n0 09\n0.1\n 0.2)% \n\u00b1\n Mean = \u2212 (1.0 \n 0.3)% \n\u00b1\n = (8.4 \n\u03c3\n Fractional energy response\n\u22121\n\u22120.8 \u22120 6 \u22120.4 \u22120.2\n\u22120\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n Arbitrary units \n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n 0.1)% \n\u00b1\n Mean = (0.97 \n 0.1)% \n\u00b1\n = (3.0 \n\u03c3\nFigure 13: The fractional energy response for single-prong (left) and three-prong (right) true \u03c4had candi-\ndates reconstructed with the track-based algorithm. Events from a W \u2192\u03c4\u03bd sample are shown.\nsingle-prong candidates using \u03c00 subclusters have been added only in the current releases of the recon-\nstruction software. Therefore they are not used for the results presented below.\n\u2022 Tracking quantities\n\u2013 The variance W \u03c4\ntracks (for multi-prong candidates only), de\ufb01ned as\nW \u03c4\ntracks = \u2211(\u2206\u03b7\u03c4,track)2 \u00b7 pT track\n\u2211pT track\n\u2212(\u2211\u2206\u03b7\u03c4,track \u00b7 pT track)2\n(\u2211pT track)2\n.\n(5)\n\u2013 The invariant mass of the tracks system (for multi-track candidates), mtrk3p,\n\u2013 The number of tracks in the isolation cone.\n\u2022 Calorimetric quantities\n\u2013 The electromagnetic radius of the \u03c4had candidate, R\u03c4\nem, as de\ufb01ned in Eq. (1) for the calorimeter-\nbased algorithm, but calculated from cells around the seed belonging to the \ufb01rst three sam-\nplings of the electromagnetic calorimeter only (presampler, strips and middle layer).\n\u2013 The number of \u03b7 strips, N\u03c4\nstrips, with energy deposits above a certain threshold.\n\u2013 The width of the energy deposit in the strips, as de\ufb01ned in Eq. (3) for the calorimeter based\nalgorithm but calculated in the core cone only.\n\u2013 The fraction of the transverse energy, fracET R12, deposited in a cone of radius 0.1 < \u2206R < 0.2\nwith respect to the total energy in a cone of \u2206R = 0.2. Cells belonging to all layers of the\ncalorimeter are used:\nfracER12\nT\n= \u2211Ecell\nT (R\u03c4,cell < 0.2)\u2212\u2211Ecell\nT (R\u03c4,cell < 0.1)\n\u2211Ecell\nT (R\u03c4,cell < 0.2)\n.\n(6)\n\u2013 The transverse energy, Ecore\nT\n, at the EM scale deposited inside the core cone.\n\u2013 The transverse energy, Eisol\nT\nand EisolHAD\nT\n, at the EM scale, deposited inside the isolation\ncone.\n\u2022 Tracking and calorimetric quantities\n\u2013 The ratio of transverse energy deposited in the hadronic calorimeter in the core region (at the\nEM scale), EchrgHAD\nT\n, with respect to the sum of the transverse momenta of the tracks.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n247\n\n (GeV) \neflow\nvis\n m\n0\n0.5\n1\n1.5\n2\n2 5\n3\n3.5\n4\n4.5\n5\n Probability \n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\n\u03c4\ntrue \n\u03c4\nfake \ncore\nT\n/E\nisol\nT\n E\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n Probability \n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\nATLAS\n\u03c4\ntrue \n\u03c4\nfake \ntrk3p\n\u03c4\n W\n0\n0.0010.0020.0030.0040.0050 0060.0070.0080 009 0.01\n Probability \n\u22123\n10\n\u22122\n10\n\u22121\n10\nATLAS\n\u03c4\ntrue \n\u03c4\nfake \n (GeV) \ntrk3p\n m\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n Probability \n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n\u03c4\ntrue \n\u03c4\nfake \nFigure 14: The distributions for signal and backgrounds for the visible mass meflow\nvis\nand ratio of the\ntransverse energy in the isolation and core region Eisol\nT\n/Ecore\nT\nfor single-prong candidates, and variance\nW \u03c4\ntracks and invariant mass of the track system mtrk3p for three-prong candidates. Distributions are shown\nfor the candidates in the transverse energy range ET = 20\u221240 GeV.\n\u2013 The visible mass meflow\nvis\ncalculated from cells used for the energy-\ufb02ow calculation and tracks.\nIn case of multi-prong candidates, where this mass is smaller than that calculated from the\nfour-momenta of the tracks, the invariant mass of the track system is taken instead.\nIn Fig. 14 as an example the distributions for signal and backgrounds for the meflow\nvis\n, the ratio\nEisol\nT\n/Ecore\nT\nfor single-prong candidates, the variance W \u03c4\ntracks and the invariant mass mtrk3p for three-prong\ncandidates are shown. Note that the me flow\nvis\ndistribution shows a double peak structure coming from\n\u03c4 \u2192\u03c0\u00b1\u03bd and \u03c4 \u2192\u03c1(a1)\u03bd decays. The separation for candidates with and without \u03c00 clusters was not\ndone for the distribution shown.\n4.2.3\nOverall ef\ufb01ciency and rejection\nThe identi\ufb01cation step is done by calculating discriminants using basic cut methods, cut methods opti-\nmized by the TMVA package [20], multi-variate analyses based on neural network technique, and from\nPDRS discrimination [21].\nThe rejection power expected from the identi\ufb01cation step only is quite modest, given that a quite\ngood rejection is already achieved in the reconstruction step. The overall performance is summarized\nin Table 5. For an ef\ufb01ciency of about 30% with respect to all hadronic decays in the energy range\n10 \u221230 GeV, rejection rates of 200/360 for one-prong/three-prong hadronic \u03c4 decays can be achieved\nwith the cut based selection and of 500/700 with multi-variate selection techniques.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n248\n\nTable 5: Ef\ufb01ciencies and rejection rates for different discrimination techniques for the track-based al-\ngorithm for \ufb01xed ef\ufb01ciencies. The ef\ufb01ciencies are normalized to all hadronic \u03c4 decays. The rejection\nrates are calculated with respect to jets reconstructed from true particles in the Monte Carlo. Events from\nZ \u2192\u03c4\u03c4 signal samples and QCD dijets were used. The errors given are statistical only.\nSelection\nEf\ufb01ciency\nRejection\nRejection\nRejection\nRejection\ncuts\nTMVA cuts\nNN\nPDRS\nET = 10-30 GeV\none-prong\n0.33\n225 \u00b1 10\n435 \u00b1 30\n510 \u00b1 40\n460 \u00b1 40\nthree-prong\n0.28\n360 \u00b1 25\n470 \u00b1 40\n740 \u00b1 70\n670 \u00b1 60\nET = 30-60 GeV\none-prong\n0.42\n140 \u00b1 10\n170 \u00b1 10\n440 \u00b1 40\n320 \u00b1 30\nthree-prong\n0.45\n60 \u00b1 2\n9 0 \u00b1 10\n160 \u00b1 10\n130 \u00b1 10\nTable 6: Rejection against jets from Monte Carlo true particles for a 30% ef\ufb01ciency and separately for\nthe one-prong (1p) and three-prong (3p) candidates. The ef\ufb01ciencies are normalized to true hadronic \u03c4\ndecays. For the signal Z \u2192\u03c4\u03c4 events and events from bbH, H \u2192\u03c4\u03c4 with mH = 800 GeV were used; for\nthe background QCD dijet-samples were used. The errors given are statistical only.\nAlgorithm\nET = 10-30 GeV\nET = 30-60 GeV\nET = 60-100 GeV\nET > 100 GeV\nTrack-based\n1p: 740 \u00b1 70\n1p: 1030 \u00b1 160\n(neural network)\n3p: 590 \u00b1 50\n3p: 590 \u00b1 70\nCalo-based\n1p: 1130 \u00b1 50\n1p: 2240 \u00b1 140\n1p: 4370 \u00b1 280\n(likelihood)\n3p: 187 \u00b1 3\n3p: 310 \u00b1 7\n3p: 423 \u00b1 8\n4.3\nComparison of the two algorithms\nFigure 15 shows the expected performance of the two algorithms, illustrated as curves describing the jet\nrejection versus the ef\ufb01ciency, separately for one and three-prong hadronic \u03c4-decays and for different\nranges of the visible transverse energy. The jet rejections are computed with respect to jets reconstructed\nfrom true particles in the Monte Carlo. The rejections obtained are between a factor of two and ten higher\nfor one-prong decays than for three-prong decays, depending on the algorithm and on the transverse\nenergy range considered. For an ef\ufb01ciency of 30% for one-prong decays, the rejection against jets\nis typically between 500 and 5000, as illustrated more quantitatively and as a function of the visible\ntransverse energy in Table 6.\nFigure 16 shows the normalized track-multiplicity spectra for hadronic \u03c4 candidates with visible\ntransverse energies above 20 GeV, from Z \u2192\u03c4\u03c4 decays and from jets, as reconstructed by the track-\nbased algorithm. The distributions are shown after the reconstruction step, after a cut-based identi\ufb01cation\nalgorithm and \ufb01nally after applying a neural network discrimination. The track multiplicity in the jet\nsample is quite different from that in the signal sample, independently from the cuts applied.\nAt the same time, Figure 16 indicates that the purity of one-prong and three-prong \u03c4had candidates\nimproves in the signal sample since the expected fractions of single versus three prongs are reproduced.\nFor one-prong (three-prong) candidates, the purity improves from 87% (74%) after reconstruction to 91%\n(86%) after cut-based identi\ufb01cation and to 92% (93%) after applying the neural-network discrimination\ntechnique.\nFigure 16 also shows that using candidates with track multiplicities above three to normalize the\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n249\n\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nRejection\n2\n10\n3\n10\n4\n10\n5\n10\n = 10 - 30 GeV\nT\n 1-prong, E\n = 30 - 60 GeV\nT\n 1-prong, E\n = 10 - 30 GeV\nT\n 3-prong, E\n = 30 - 60 GeV\nT\n 3-prong, E\nATLAS\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 9\n1\nRejection\n2\n10\n3\n10\n4\n10\n5\n10\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 9\n1\nRejection\n2\n10\n3\n10\n4\n10\n5\n10\n = 60 - 100 GeV\nT\n1-prong, E\n > 100 GeV\nT\n1-prong, E\n = 60 - 100 GeV\nT\n3-prong, E\n > 100 GeV\nT\n3-prong, E\nATLAS\nFigure 15: Expected performance for the track-based algorithm with a neural-network selection (left)\nand the calorimeter-based algorithm with the likelihood selection (right). The rejection rates against jets\nfrom Monte-Calo particles as a function of the ef\ufb01ciency for hadronic \u03c4 decays for various ranges of the\nvisible transverse energy are shown. For signal events Z \u2192\u03c4\u03c4 and bbH,H \u2192\u03c4\u03c4 with mH = 800 GeV\nwere used, for the background QCD dijet samples were used.\n Track multiplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n Probability \n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nReconstruction\nIdentification with cuts\nIdentification with NN\n\u03c4\n\u03c4\n\u2192\n Z \n Track mul iplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n Probability \n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nReconstruction\nIdentification with cuts\nIdentification with NN\n QCD jets \nFigure 16: Track multiplicity distributions obtained for hadronic \u03c4 decays with a visible transverse energy\nabove 20 GeV and below 60 GeV using the track-based \u03c4 identi\ufb01cation algorithm. The distributions are\nshown after reconstruction, after cut-based identi\ufb01cation and \ufb01nally after applying the neural network\n(NN) discrimination technique for an ef\ufb01ciency of 30% for the signal (left) and the background (right).\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n250\n\nTrack multiplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nProbability\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nReconstruction\nIdent fication with Likelihood\n\u03c4\n\u03c4\n\u2192\nZ \n\u03c4\n\u03c4\n\u2192\nZ \nTrack multiplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nProbability\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nReconstruction\nIdentification with Likelihood\nQCD jets\nQCD jets\nFigure 17: Track multiplicity distributions obtained for hadronic \u03c4had-decays with visible transverse en-\nergy above 20 GeV and below 60 GeV using the calorimeter-based \u03c4 identi\ufb01cation. The distributions are\nshown after reconstruction and after applying the likelihood discrimination technique (medium selection)\nfor the signal (left) and the background (right).\nQCD background will allow a reasonably precise calibration of the performance using real data, provided\nthe rejection against QCD jets is proven to be suf\ufb01cient to extract a clean signal in the one-prong and\nthree-prong categories. The sensitivity of such a method can be enhanced by also studying the track\nmultiplicity outside the narrow cone used for \u03c4-identi\ufb01cation and combining this information with that\npresented in Fig. 16.\nThe corresponding spectra for the calorimeter-based algorithm are shown in Figure 17 after recon-\nstruction and after applying the likelihood discriminant. The optimization of the likelihood results in a\nlower ef\ufb01ciency for accepting three-prong decays which biases the track multiplicity spectra. One should\nnote that candidates with 1-3 tracks are accepted as good \u03c4had candidates.\nThe application of these \u03c4 identi\ufb01cation algorithms to extract \u03c4 signatures from physics processes\nand to reject the large backgrounds from QCD processes is discussed in Section 6.\n5\nFake-rates from QCD di-jet samples\nThis study demonstrates a simple and generic method to determine the \u03c4had fake rate from jets in early\ndata. Since fake rates are expected to be in the range of 10\u22123 to few 10\u22122 for low pT \u03c4 leptons, and\nsince the expected rate of QCD jets far exceeds the rate of hadronically decaying \u03c4 leptons, a precise\nmeasurement of fake rates is expected to be crucial for many analyses, and also for a further optimization\nof the \u03c4had identi\ufb01cation algorithms. In the following, the method and the results are described and\nstatistical and systematic uncertainties are discussed.\nThe method proposed here uses a very clean sample of QCD jets, with no signi\ufb01cant contamination\nfrom true \u03c4 leptons. This is achieved by selecting dijet events with two jets having similar pT and being\nback-to-back in \u03c6 (see Fig. 18). One of the two jets is randomly chosen as the so-called \u2018tag jet\u2019, for\nwhich a cut on the number of tracks (nTrk \u22654 for pT \u226450 GeV + 1 track for each additional 50 GeV\ninterval in pT) ensures that it is not a true hadronic \u03c4had decay. If this cut is ful\ufb01lled, the other jet,\ncalled \u2018probe jet\u2019, can be used to measure the fake rate from QCD jets 8. This is performed both for the\ncalorimeter-based and the track-based \u03c4had reconstruction algorithm, with identi\ufb01cation according to the\nmedium likelihood selection and cut discriminant, respectively. Note also that, in order to avoid a direct\ndependence on the trigger, the probe jet should be required to not have caused the event to be triggered.\n8The fake rate is determined as the number of probe jets identi\ufb01ed as \u03c4had divided by the number of probe jets.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n251\n\nATLAS\n (rad)\n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n0\n1000\n2000\n3000\n4000\n5000\n3\n10\n\u00d7\n tag jet (GeV)\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n probe jet (GeV)\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n50\n100\n150\n200\n250\n300\n3\n10\n\u00d7\nATLAS\nFigure 18: Example of selections on a MC dijet sample, generated with 70 \u2264pT \u2264140 GeV. The two\njets have to ful\ufb01ll \u2206\u03c6 \u2265(\u03c0 \u22120.3) in order to be back to back in \u03c6 (left) and have similar pT values (right).\nTable 7: The \u03c4had fake rate from QCD jets and its statistical uncertainty for the available Monte Carlo\nstatistics and for expected 100pb\u22121 of data in bins of pT for both \u03c4had reconstruction algorithms.\nCalorimeter-based algorithm\nTrack-based algorithm\npT range\nMC stat.\nExpected stat. error\nMC stat.\nExpected stat. error\n(GeV)\n(%)\nfor 100 pb\u22121 (%)\n(%)\nfor 100 pb\u22121 (%)\n15-40\n2.3 \u00b1 0.3\n\u00b1 0.02\n2.5\u00b10.5\n\u00b1 0.02\n40-80\n5.2 \u00b1 2.2\n\u00b1 0.01\n6.7\u00b12.2\n\u00b1 0.01\n80-120\n0.5 \u00b1 0.2\n\u00b1 0.001\n1.8\u00b10.6\n\u00b1 0.002\n120-160\n0.2 \u00b1 0.2\n\u00b1 0.002\n1.4\u00b10.6\n\u00b1 0.004\nThis method, which achieves low statistical uncertainties even for small datasets, only relies on the\ndijet and tag jet selection to acquire a clean QCD jet sample and it does not depend, to \ufb01rst order, on\nthe number of true \u03c4 leptons present in the sample nor on the \u03c4had ef\ufb01ciencies. Also, the selection can\nbe easily adapted to select probe jets in an environment similar to the one of any given physics analysis\nusing \u03c4had candidates.\nTo perform these studies, Monte Carlo dijet samples (generated in various pT ranges) and samples\ncontaining true \u03c4 leptons (Z \u2192\u03c4\u03c4, W \u2192\u03c4\u03bd) were used. Proper weighting of the samples, including\ntrigger prescales for running at L = 1031 cm\u22122s\u22121, has been applied. To cross-check the method, it has\nbeen veri\ufb01ed that there is very good agreement between the values obtained with all selected jets and\nthose coming from jets matched to Monte Carlo particles jets only, which indicates a very high jet purity.\nThe numerical results of the fake rate determination using the available Monte Carlo statistics for the\ntwo algorithms can be found in Table 7. Systematic uncertainties (discussed below) are not included.\nNote that the uncertainty in the range 40 < pT < 80 GeV, for both algorithms using available Monte\nCarlo statistics, is dominated by one dijet event (with large weight) in one of the Monte Carlo samples.\nMore interesting are the expected statistical uncertainties in data, which are at the percent or sub-percent\nlevel for 100 pb\u22121, and even for 10 pb\u22121 of integrated luminosity. This demonstrates the relevance of\nthis method for very early data.\nGiven the statistical precision of the fake rate results, this measurement of the systematics of other\nmeasurements is going to be limited by its own systematic uncertainties. In the following, an outline of\nthe necessary systematic studies is given, including results where possible.\nThe presence of true hadronically decaying \u03c4 leptons in the selected Monte Carlo sample is not\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n252\n\nstatistically signi\ufb01cant enough to alter the results within their uncertainties. When more statistics are\navailable, tighter cuts on the tag side can be applied in order to remove more ef\ufb01ciently these types of\nevents.\nA slight tendency was observed for the jet samples with lower hard scattering transverse momenta, to\nshow higher fake rates. This can be explained by the fact that the jet characteristics depend on the degree\nof parton showering. Also, jets from gluons are wider and on average have higher tracks multiplicity\nthan jets from quarks. Then, the fake rate of gluon-jets should be smaller than that of quark-jets. Data\ntriggered with the jet-triggers, that has more gluon-jets than quark-jets, and with single photon triggers,\nwhere the quark-jets very likely will be dominant, can be used to understand this effect. However, this\ntype of systematic uncertainty will be small as long as the distributions of observable quantities (such as\nthe number of tracks and the jet isolation) of the probe jets studied for the fake rate is comparable with\nthe properties of the jets faking hadronically decaying \u03c4 leptons in the physics analysis.\nIn case there is a physical correlation between the properties of the tag and the probe jet, the selection\nof the tag jet would directly in\ufb02uence the properties of the probe jet, and hence distort the results. As\nan example of a possible observable correlation, the number of tracks per jet was studied and it has been\nfound that the correlations were in the sub-percent range. Hence it is concluded that given the current\nknowledge from Monte Carlo, this source of uncertainty can be neglected. For data, this can be revisited.\n6\nTau leptons in Standard Model processes\nThe goals for early \u03c4 physics in ATLAS include acquiring a sample of \u03c4 leptons from data with a pu-\nrity as high possible so that the \u03c4had identi\ufb01cation ef\ufb01ciency can be measured and the simulation can\nbe tuned. Collecting data with an integrated luminosity of 100 pb\u22121 at an instantaneous luminosity of\n1031cm\u22122s\u22121 will provide a unique opportunity to access and understand statistically signi\ufb01cant \u03c4 sam-\nples from Standard Model processes at relatively low transverse momenta. Processes, like the production\nof W and Z bosons and top quark pairs with their huge cross section will lead to samples of a few hun-\ndred to a few thousand identi\ufb01ed hadronic \u03c4 decays. Hadronically decaying \u03c4 leptons will then become\na well understood probe for discovery physics like searches for Higgs bosons, SUSY, or unexpected phe-\nnomena. Below we present feasibility studies for analyses which can be envisaged with an integrated\nluminosity of 100 pb\u22121.\n6.1\nThe W \u2192\u03c4\u03bd inclusive production\nThe W \u2192\u03c4\u03bd signal will be produced with \u03c3 \u00d7BR = 1.7\u00b7104 pb, and will be dominated by events with\nlow pT of the W-boson resulting in soft \u03c4 leptons with low missing transverse energy. The expected\ncross-section of the dominant background from hadronic jets is \u223c1010 pb (calculated for hard-scattering\nphard\nT\n> 8 GeV), about 6 orders of magnitude larger than the signal production.\nThe analysis is very sensitive to the performance of the hadronic \u03c4-trigger [22]. These events will\nhave to be triggered with a \u03c4+Emiss\nT\ntrigger, with a con\ufb01guration adequate to \ufb01t into the allowed budget\nfor trigger rates. Given the fact that the physics motivation is to get signal events with \u03c4had candidates\nat low transverse momenta, the present base-line con\ufb01guration for this analysis is to use \u03c420i+EFxE309,\nwith the Emiss\nT\ntrigger applied only at the Event Filter level. The present trigger optimization gives an\noverall \u223c70% trigger ef\ufb01ciency with respect to off-line analysis.\nThe signal will be extracted requiring one identi\ufb01ed hadronic \u03c4 decay with transverse energy ET =\n20\u221260 GeV and observing the characteristic track multiplicity spectrum of identi\ufb01ed hadronic \u03c4 decays.\nIn the present study the track-based algorithm was used with the medium identi\ufb01cation, corresponding\n9In this notation, \u03c420i+EFxE30 denotes a trigger which requires at least one \u03c4had candidate with a transverse energy above\n20 GeV and \u201cEFxE30\u201d is short for Emiss\nT\n> 30 GeV at the Event Filter level.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n253\n\nto rejection of 700-1000 for the single- and 600 for the three-prong \u03c4 selection against jets and 30% ef\ufb01-\nciency for true hadronic \u03c4had decays (see Table 6). The overwhelming background from QCD events will\nbe further suppressed by vetoing events with an additional isolated electrons or muons and by increasing\nthe threshold on Emiss\nT\n. An additional handle is to select only events with the topological con\ufb01guration\nof the \u03c4had, Emiss\nT\nor additional jets optimal for suppressing events with large fake Emiss\nT\n, i.e. excluding\nthose where the Emiss\nT\ndirection is close to the direction of the identi\ufb01ed \u03c4had or an additional jets (see\nRef. [23]).\nThe QCD background has been estimated with a mixture of full and fast simulation, taking into\naccount the necessary corrections for the different slopes in the Emiss\nT\ndistribution in the full and fast\nsimulations. It should be noted also that predictions for this overwhelming background are subject to\nlarge uncertainties.\nAn important background is also expected from W \u2192e\u03bd events, where an electron passes the\nhadronic \u03c4-trigger selection criteria. This channel, with an initial production cross-section of the same\norder as the signal, but contributing almost exclusively to the single-prong mode, will exceed the signal\nrates by some factor, before a dedicated electron veto is applied to the single-prong candidates. With the\nexpected performance of such an algorithm, as discussed in Section 3.2.1, this background can be ef\ufb01-\nciently suppressed, also providing a control channel for the topology of the hadronic part of the W \u2192\u03c4\u03bd\nevents passing the trigger and of\ufb02ine selections. Backgrounds from Z \u2192\u03c4\u03c4, t\u00aft, Z \u2192ee, W \u2192\u00b5\u03bd events\nwere also considered and it was estimated that they will be suppressed with the of\ufb02ine selection below a\nfew percent of the signal.\nTable 8 summarises the expected event yield at the various stages of the selection. With an Emiss\nT\nthreshold of 50 GeV, the expected signal-to-background ratio is 1:1 and about 3240 signal events would\nbe observed. Increasing the threshold to 60 GeV would reduce the number of accepted signal events to\n1550 but increase the signal-to-background ratio to 3:1. Figure 19 shows the expected track multiplicity\nspectrum after the \ufb01nal selection. The optimisation of this selection can be performed using control sam-\nples, i.e. W \u2192e\u03bd events extracted from the same \ufb01lter stream, hence modeling of the W-recoil part of the\nevent will be possible directly from the data. The \ufb01nal optimisation of the chosen ef\ufb01ciency/rejection and\nof\ufb02ine threshold on Emiss\nT\nwill have to be tuned with data, given the large uncertainties on Monte Carlo\npredictions for the background from hadronic jets. The control on the QCD background normalization\nwill be possible with fake \u03c4had with track multiplicity above 3, i.e in the signal-free region.\nTable 8: Expected number of events in 100 pb\u22121 of data for signal and background after subsequent steps\nof the selection. The track-based algorithm has been used for \u03c4had reconstruction. The QCD background\nhas been estimated combining fast and full simulation. Given are the expected number of events of track\nmultiplicity one to three, i.e. contributing to signal region only.\nSelection\nW \u2192\u03c4\u03bd\nW \u2192e\u03bd\nW \u2192\u00b5\u03bd\nQCD dijet\nt\u00aft, Z \u2192ee, Z \u2192\u03c4\u03c4\nTrigger \u03c420i+EFxE30\n8.8\u00b7104\n6.1\u00b7105\n3.2\u00b7104\n4.8\u00b7108\n3.0\u00b7105\nIdenti\ufb01ed \u03c4 + Emiss\nT\n> 30 GeV\n2.0\u00b7104\n2600\n200\n3.0 \u00b7106\n1600\nEmiss\nT\n> 50 GeV\n4200\n530\n90\n5.0\u00b7104\n550\nVeto fake Emiss\nT\ntopology\n3600\n500\n80\n1.8\u00b7104\n150\nRequire jet pT > 15 GeV\n3240\n450\n60\n3200\n80\nIncrease to Emiss\nT\n> 60 GeV\n1550\n150\n25\n500\n30\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n254\n\n Track multiplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n\u22121\n Events 100 pb\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\n\u03bd\n\u03c4\n\u2192\nW \nQCD (J0+J1+J2+J3)\n\u03bd\n e \n\u2192\nW \n\u03bd\n\u00b5\n\u2192\nW \n\u03c4\n\u03c4\n\u2192\nZ \n e e\n\u2192\nZ \nttbar\nATLAS\n Track multiplicity\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n\u22121\n Events 100 pb\n0\n200\n400\n600\n800\n1000\n1200\n\u03bd\n\u03c4\n\u2192\nW \nQCD (J0+J1+J2+J3)\n\u03bd\n e \n\u2192\nW \n\u03bd\n\u00b5\n\u2192\nW \n\u03c4\n\u03c4\n\u2192\nZ \n e e\n\u2192\nZ \nttbar\nATLAS\nFigure 19: The track multiplicity spectrum of accepted \u03c4had candidates after selection as described in the\ntext with thresholds respectively Emiss\nT\n> 50 GeV (left) and Emiss\nT\n> 60 GeV (right). The expected event\nnumbers are given for an integrated luminosity of 100 pb\u22121.\n6.2\nThe Z \u2192\u03c4\u03c4 inclusive production\nThe inclusive Z \u2192\u03c4\u03c4 process will provide a ten times lower rate compared to W \u2192\u03c4\u03bd, but will have\nmore robust prospects for analysis. It will be possible to cross-check channels with e \u03c4had and \u00b5 \u03c4had\n\ufb01nal states to control the background, comparing the number of events observed in the same-sign and\nopposite-sign samples. Moreover, events will be primarily triggered with lepton triggers providing an\nunbiased sample of hadronic \u03c4 decays which could also serve to understand ef\ufb01ciencies of the hadronic\n\u03c4-trigger. The measured cross-section for the Z \u2192\u03c4\u03c4 process will be an excellent check on the \u03c4 iden-\nti\ufb01cation ef\ufb01ciencies, while the lepton identi\ufb01cation and trigger ef\ufb01ciencies will be measured \ufb01rst from\nZ \u2192\u2113\u2113channels. A measurement of the visible mass of the \u2113\u03c4had system at low background levels will\nhave sensitivity to the energy scale of the reconstructed \u03c4hads.\nThe analysis presented here is designed to select in the \ufb01rst 100 pb\u22121 of data a suf\ufb01cient number of\nZ \u2192\u03c4\u03c4 \u2192\u2113\u03bd\u03bd \u03c4had\u03bd events with very low background, which then can be used to determine the \u03c4had\nenergy scale from the reconstructed \u2113\u03c4had visible mass and to determine the Emiss\nT\nscale [23] from the\nreconstructed complete invariant mass of the \u03c4\u03c4 pair (including neutrinos). Events, which have been\nselected by the single electron or single muon trigger stream are analysed and as a \ufb01rst step an isolated\nlepton (electron or muon) with p\u2113\nT > 15 GeV is required. Then, the set of basic selection cuts is applied.\nIt requires a missing transverse energy Emiss\nT\n> 20 GeV (to suppress Z \u2192\u2113\u2113and QCD backgrounds),\ntransverse mass of the lepton and Emiss\nT\nsystem m\u2113, Emiss\nT\nT\n< 30 GeV (against W \u2192\u2113\u03bd background), total\ntransverse energy deposited in the calorimeter \u03a3Ecalo\nT\n< 400 GeV (against t\u00aft and QCD backgrounds) and\n\ufb01nally no identi\ufb01ed b-jet (against t\u00aft and QCD backgrounds). In the next step, events with an identi\ufb01ed\n\u03c4had with pT > 15 GeV are selected. The track multiplicity of identi\ufb01ed \u03c4had is required to be one or three.\nIn addition the angular separation between the isolated lepton and \u03c4 is imposed, requiring \u2206\u03c6(\u2113,\u03c4had) to\nbe in the ranges between 1.0 - 3.1 or 3.2-5.3 .\nThe analysis was performed using \u03c4had reconstructed with the calorimeter-based algorithm and the\nidenti\ufb01cation with the likelihood discriminant. The thresholds on the likelihood discriminant were opti-\nmized for this analysis and correspond to an overall ef\ufb01ciency of \u223c35% with respect to all hadronic \u03c4\ndecays. The QCD background has been estimated with a mixture of full and fast simulation which as-\nsumes uncorrelated probabilities for a jet to produce an isolated lepton candidate (predominantly leptons\nfrom heavy \ufb02avor decays with a small contribution from fakes in the electron case) and for the second\njet to produce a fake \u03c4had candidate.\nTable 9 gives the expected number of signal and background events passing the selection criteria for\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n255\n\n (GeV)\n\u03c4\n\u03c4\nVisible m\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nExpected events in 100pb-1\n0\n50\n100\n150\n200\n250\nATLAS\nMean= 53.8 GeV\n= 10.6 GeV\n\u03c3\nSignal\nBackground\nTau Energy Scale\n0.9\n0.95\n1\n1.05\n1.1\n (GeV) \n\u03c4\n\u03c4\nVisible m\n50\n51\n52\n53\n54\n55\n56\n57\nATLAS\nFigure 20: Left: The reconstructed visible mass of the (\u2113\u03c4had) pair for Z \u2192\u03c4\u03c4 decays (solid line) and\nQCD, W \u2192\u2113\u03bd, Z \u2192\u2113\u2113backgrounds (dashed line). Right: The reconstructed visible mass of the (\u2113\u03c4had)\npair from Z \u2192\u03c4\u03c4 decays as a function of the \u03c4had energy scale (right). The dashed lines correspond\nto \u00b11\u03c3 and \u00b13\u03c3 with respect to the reconstructed peak position. The results were obtained with the\ncalorimeter-based algorithm.\nTable 9: Expected number of events in 100 pb\u22121 of data for signal and background after reconstruction\nof the \u03c4 candidate with the calorimeter-based algorithm and after application of the selection cuts for the\nZ \u2192\u03c4\u03c4 channel. The QCD background has been estimated combining fast and full simulation.\nSelection\nZ \u2192\u03c4\u03c4\nW \u2192\u2113\u03bd\nQCD dijet\nt\u00aft\nZ\u2192\u2113\u2113\nIsolated lepton\n1.5\u00b7104\n16.7\u00b7105\n1.1\u00b7107\n2.6\u00b7104\n2.2\u00b7105\nEmiss\nT\n> 20 GeV\n4750\n14.3\u00b7105\n3.2\u00b7105\n2.4\u00b7104\n1.0\u00b7104\nm\u2113,Emiss\nT\nT\n< 30GeV\n3200\n2.6\u00b7104\n1.8\u00b7105\n3650\n3200\n\u03a3ET < 400 GeV\n3000\n2.4\u00b7104\n1.7\u00b7105\n1280\n2800\nb-jet veto\n2780\n2.4\u00b7104\n2.7\u00b7104\n135\n2600\n\u03c4had-id + \u2206\u03c6(\u2113\u03c4had) cuts\n630\u00b130\n210 \u00b110\n74\u00b111\n10\u00b12\n30\u00b15\nOS events, m\u2113,\u03c4had = 37-75 GeV\n520\u00b130\n45 \u00b15\n29\u00b15\n< 5\n10 \u00b15\na data sample of 100 pb\u22121. About 520 signal events are expected in the visible mass m\u2113\u03c4had window\nbetween 37 \u221275 GeV. The expected background levels are 10% from W \u2192\u2113\u03bd events and about 5%\nbackground from QCD events. The reconstructed visible mass of the \u2113\u03c4had pair is shown in Figure 20 for\nopposite-sign events.\nThis selection for Z \u2192\u03c4\u03c4 events will provide access to signal-suppressed and signal-enriched sam-\nples. The same-sign events (e \u03c4had and \u00b5 \u03c4had) will be essentially signal-free. This will allow a study\nof \u03c4had identi\ufb01cation and mistagging ef\ufb01ciencies. The mistagging ef\ufb01ciency will be estimated from the\nratio of accepted to all candidates in different categories (one-prong with and without \u03c00 subclusters,\nmulti-prong). Then, this estimate can be used to predict the background component in opposite-sign\nevents and to tune the Monte Carlo predictions for the identi\ufb01cation variables. It will allow a con\ufb01rma-\ntion of the overall consistency and an estimate of the relative error on the background predictions in the\nsignal enriched sample. Finally, a measurement of the cross-section for Z \u2192\u03c4\u03c4 events relative to the\nZ \u2192ee,\u00b5\u00b5 channels will provide a cross-checks on the associated ef\ufb01ciencies.\nOnce the lepton energy scale is determined with the very \ufb01rst data, the selected Z \u2192\u03c4\u03c4 events can\nbe used to determine the \u03c4had energy scale in-situ. Subtracting the estimated background from opposite-\nsign events, as measured with the same-sign events, will allow for better estimates on the energy scale\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n256\n\nTable 10: Expected number of events in 100 pb\u22121 of data for t\u00aft \u2192W(\u2113\u03bd)W(\u03c4had,\u03bd\u03c4)b\u00afb signal and\nbackground after subsequent steps in the selection. The track-based algorithm has been used for \u03c4had\nreconstruction.\nSelection\nt\u00aft(\u2113,\u03c4had)\nW \u2192\u2113\u03bd +3 jets\nsingle t\nZ\u2192\u2113\u2113+ 2 jets\nIsolated lepton pT > 20 GeV\n1300\n3.9 \u00b7105\n4300\n630\nIdenti\ufb01ed \u03c4had pT > 15 GeV\n190\n22000\n210\n120\n1st jet ET > 50 GeV, 2nd jet ET > 30 GeV\n170\n4000\n170\n35\nEmiss\nT\n> 25 GeV\n150\n3400\n150\n15\n\u03a3ET > 250 GeV\n150\n1750\n130\n10\nOpposite-sign events\n130\n850\n54\n< 10\n1 b-jet tag\n67\n28\n20\nfrom the shape of the distribution of the visible mass. In Fig. 20 the sensitivity of the measured visible\nZ boson mass, as obtained from the reconstructed \u03c4 pairs, on the absolute \u03c4 energy scale is shown,\nassuming only signal events.The statistics correspond to 100 pb\u22121 of data. Taking into account only the\nstatistical uncertainties, the \u03c4had energy scale could be determined with a precision of \u223c3%.\n6.3\nThe \u03c4 leptons from t\u00aft production\nWith a cross-section of 833 pb [24], about 16500 events are expected in 100 pb\u22121 with a W boson de-\ncaying into a \u03c4 lepton. Due to the increased center of mass energy available at the LHC the cross section\nfor t\u00aft production increases by nearly two orders of magnitude over what is available at the Tevatron. The\nt\u00aft channel is discussed here as an additional source for \u03c4 leptons from the SM processes, supplementing\nsamples expected from W \u2192\u03c4\u03bd and Z \u2192\u03c4\u03c4 process.\nThe decay chain t\u00aft \u2192W(qq\u2032)W(\u03c4had\u03bd)b\u00afb requires events triggered using \u03c4 + Emiss\nT\ntriggers, \u03c4 triggers\nand multi\u2013jets triggers. In the latter case this will lead to an unbiased sample of \u03c4had candidates. The\nevent is required to have at least two light quark jets, two b-tagged jets, and an identi\ufb01ed hadronic \u03c4\ndecay. If the event has more than two light quark jets, the pair with the invariant mass closest to the\nnominal mass of the W bosons is chosen which is then combined with the closest b jet to constitute\nthe hadronically decaying top quark. With 100 pb\u22121 of data about 300 t\u00aft \u2192W(qq\u2032)W(\u03c4had\u03bd)b\u00afb signal\nevents with S:B of 20:1 are expected. These events can be used to study the \u03c4had reconstruction and\nidenti\ufb01cation performance and to commission the \u03c4 trigger. The pT range of identi\ufb01ed \u03c4 leptons will\nbe complementary to that available from the inclusive W and Z boson production. A more detailed\ndescription of the analysis is included in Ref. [25].\nThe decay chain t\u00aft \u2192W(e\u03bde,\u00b5\u03bd\u00b5)W(\u03c4had,\u03bd\u03c4)b\u00afb is also interesting for both its physics potential and\nthe possibility of using this channel to understand \u03c4had identi\ufb01cation. These events will be triggered\nwith single lepton triggers and the main background will come primarily from W(\u2192\u2113\u03bd)+jets, single top\nproduction and from Z(\u2192\u03c4\u03c4)+jets production. The analysis requires an isolated lepton and identi\ufb01ed\n\u03c4had. To suppress backgrounds from W+jets and Z+jets events it requires two additional high ET jets,\nsigni\ufb01cant energy deposition in the calorimeter \u03a3ET > 250 GeV and Emiss\nT\n> 25 GeV. Additional back-\nground suppression can be achieved by requiring that one or two jets are b-tagged. Table 10 summarizes\ncut \ufb02ow of the analysis.\nIn the \ufb01rst 100 pb\u22121 of data, 54 \u00b1 4 signal events in the e\u03c4had channel are expected, with a signal-\nto-background ratio (S:B) 1:10. The use of b-tagging rejects considerably the dominant W + 3 jets\nbackground (see Fig. 21). If at least one tight b-tag jet is required the expected number of signal events\ndecreases to 28\u00b13 with S:B improving to 1:1. When requiring a jet in the event that passes the tight b\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n257\n\n\u221210\n\u22125\n0\n5\n10\n15\n20\n25\n30\nNumber of Events\nb\u2212tagging weight\n1\n10\n)\u03c4\n e \n\u2192\n(tt\n) + 3 jets\ne\n\u03bd\n e+\n\u2192\nW(\nATLAS\n\u221210\n\u22125\n0\n5\n10\n15\n20\n25\nb\u2212tagging weight\nNumber of Events\n30\n1\n10\n)\u03c4\n\u00b5\n\u2192\n(tt\n) + 3 jets\n\u00b5\n\u03bd\n+\n\u00b5\n\u2192\nW(\nATLAS\nFigure 21: Combined b-tagging weights using impact parameter and secondary vertex information for\nthe \ufb01rst two leading ET jets, both in t\u00aft \u2192W(e\u03bde,\u00b5\u03bd\u00b5)W(\u03c4had\u03bd\u03c4)b\u00afb and W +3 jets background. The e \u03c4\n(\u00b5 \u03c4) channel is shown on the left (right). The cut value of 7 on the b-tagging weight is indicated with\nthe arrows. An integrated luminosity of 100 pb\u22121 of data is assumed.\ntagging criteria, the dominant source of background is still W(\u2192\u2113\u03bd)+jets, however the composition of\nthe background changes and single top production starts contributing signi\ufb01cantly, with quark or gluon\njets faking \u03c4had and true b-jets from b-quark fragmentation.\n7\nSummary\nTwo complementary algorithms for the identi\ufb01cation of hadronic \u03c4 decays in the ATLAS experiment\nhave been developed. The \ufb01rst one (calorimeter based) is seeded from a reconstructed cluster in the\ncalorimeter, the second one (track based) relies on seeds built from reconstructed tracks in the inner\ndetector. Several discrimination methods have been established, including a simple cut-based selection\nas well as multivariate selections based on likelihood, neutral network, and probability range search\ntechniques. Rejection factors against jets from QCD processes of a few hundred up to a few thousand\ncan be achieved for a \u03c4 ef\ufb01ciency of 30% in the pT range between 10 to 60 GeV. In addition, a dedicated\nalgorithm has been developed to reject electrons that pass the \u03c4 identi\ufb01cation criteria. In the low energy\nrange, rejection factors of the order of 50 and higher against electrons from W and Z bosons decays are\nachieved at the expense of a 5% ef\ufb01ciency loss for hadronic \u03c4 decays.\nIt has also been estimated that the expected performance in the ATLAS experiment will be adequate\nto extract \u03c4 signals in early LHC data from W \u2192\u03c4\u03bd and Z \u2192\u03c4\u03c4 decays. These signals are important to\nestablish and calibrate the \u03c4 identi\ufb01cation performance with early data. The study of dijet events from\nQCD processes will allow a determination of \u03c4 fake rates. It is expected that such rates can be measured\nwith a statistical precision at the percent level or better already with data corresponding to an integrated\nluminosity of 100 pb\u22121.\nReferences\n[1] W-M Yao et al 2006, J. Phys. G: Nucl. Part. Phys. 33 1.\n[2] T. Sjostrand, S. Mrenna and P. Skands, JHEP05 (2006) 026.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n258\n\n[3] S. Jadach et al., Comp. Phys. Commun. 76 (1993) 361.\n[4] K. Assamagan and Y. Coadou, The hadronic tau decay of a heavy charged Higgs in ATLAS, ATLAS\nNote, ATL-PHYS-2000-031.\n[5] K. Assamagan and A. Deansdrea, The hadronic \u03c4 decays of heavy charged Higgs in models with\nsinglet neutrino in large extra dimensions, ATLAS Note, ATL-PHYS-2001-019.\n[6] T. Pierzchala, E. Richter-Was, Z. Was and M. Worek, Acta Phys.Polon. B32 (2001) 1277.\n[7] G. R. Bower, T. Pierzchala, Z. Was and M. Worek, Phys. Lett. B 543 (2002) 227.\n[8] K. Desch, A. Imhof, Z. Was and M. Worek, Phys.Lett. B579 (2004) 157.\n[9] ATLAS Collaboration, ATLAS Performance and Physics Technical Design Report, ATLAS TDR\n15, CERN/LHCC/99-15, 25 May 1999.\n[10] The ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[11] ATLAS Collaboration,\nATLAS Inner Detector Technical Design Report, ATLAS TDR 4,\nCERN/LHCC/97-16, 30 April 1997.\n[12] P. Billoir, S. Qian, Nucl. Instr. and Meth. A311 (1992) 139-150.\n[13] R. Fruhwirth, K. Proko\ufb01ev, T. Speer, P. Vanlaer, W. Waltenberger, Nucl. Instr. and Meth. A502\n(2003) 699-701.\n[14] V. Kostyukhin, VKalVrt - package for vertex reconstruction in ATLAS, ATLAS Physics Note ATL-\nPHYS-2003-031.\n[15] The ATLAS Collaboration, Clustering in the ATLAS Calorimeters, in preparation.\n[16] The ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[17] M. Heldmann and D. Cavalli, An improved tau-Identi\ufb01cation for the ATLAS experiment, ATLAS\nNote, ATL-PHYS-PUB-2006-008.\n[18] The ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[19] E. Richter-Was and T. Szymocha,\nHadronic tau identi\ufb01cation with track based approach: the\nZ \u2192\u03c4\u03c4,W \u2192\u03c4\u03bd and dijet events from DC1 data samples, ATLAS Note, ATL-PHYS-PUB-2005-\n005.\n[20] A. Hoecker et al., TMVA Toolkit, http://tmva.sourceforge.net/.\n[21] T. Carli and B. Koblitz, Nucl. Instr. and Meth., A501 (2003) 576.\n[22] The ATLAS Collaboration, Tau Trigger: Performance and Menus for Early Running, this volume.\n[23] The ATLAS Collaboration, Meassurement on Missing Transverse Energy in ATLAS, this volume.\n[24] R. B. Bonciani, S. Catani, M. L. Mangano, Nucl. Phys. B529 (1998) 425.\n[25] The ATLAS Collaboration, Data-driven Determination of the W, Z and Top Backgrounds to Su-\npersymmetry, this volume.\nTAU LEPTONS \u2013 RECONSTRUCTION AND IDENTIFICATION OF HADRONIC \u03c4 DECAYS\n259\n\n\nJets and Missing Transverse Energy\n261\n\nJet Reconstruction Performance\nAbstract\nThis section summarizes the general aspects of jet reconstruction with the AT-\nLAS detector. General but brief descriptions of the available jet algorithms are\nprovided, together with a discussion of the performance expectations for the\nvarious algorithm con\ufb01gurations in different detector regions and for different\nphysics environments. The emphasis is on realistic estimates for the initial jet\nreconstruction performance, determined in the absence of experimental data.\nThe corresponding expectations for important jet reconstruction parameters\nlike signal linearity and uniformity, the relative energy resolution, and the jet\nreconstruction ef\ufb01ciency and purity, are presented.\n1\nIntroduction\nHigh quality and highly ef\ufb01cient jet reconstruction is an important tool for almost all physics analyses\nto be performed with the ATLAS experiment at the Large Hadron Collider (LHC) at CERN. The re-\nquirements especially for the absolute precision on the jet energy scale often exceed the corresponding\nachieved performance in previous experiments. Typically, an absolute systematic uncertainty of better\nthan 1% is desirable for precision physics like the measurement of the top quark mass, and the recon-\nstruction of some SUSY \ufb01nal states.\nThe principal detector for jet reconstruction is the ATLAS calorimeter system, with its basic compo-\nnents depicted in Fig. 1. It provides near hermetic coverage in a pseudorapidity range \u22124.9 < \u03b7 < 4.9.\nThe technology choices are well suited for high quality jet reconstruction in the challenging environ-\nment of the proton-proton (pp) collisions at \u221as = 14 TeV at the LHC. The electromagnetic liquid ar-\nFigure 1: The ATLAS calorimeter system.\n262\n\ngon/lead calorimeters feature an accordion geometry homogeneous in azimuthal coverage for |\u03b7| < 3.2.\nThe hadronic calorimeters surrounding them are iron with scintillating tile readout in the central region\n(|\u03b7| <\u223c1.7) and parallel plate liquid argon/copper in the endcap region (1.7 <\u223c|\u03b7| <\u223c3.2). The forward\nregion is covered by liquid argon/copper and liquid argon/tungsten calorimetry with a tubular electrode\nreadout accommodating the high ionization rates expected at LHC at design luminosity. The readout\nof the calorimeters is highly granular for the electromagnetic devices, with typically three longitudinal\nsegments with varying lateral cell sizes, e.g. \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.025 \u00d7 0.025 in the second segment con-\ntaining the electromagnetic shower maximum. The hadronic calorimeters are coarser, with typically\n\u2206\u03b7 \u00d7 \u2206\u03c6 = 0.1 \u00d7 0.1, but have also at least three longitudinal segments. The total number of readout\ncells in the ATLAS calorimeter system is close to 200,000. The total thickness of the ATLAS calorimeter\nsystem for hadrons is at least 10 absorption lengths over the whole acceptance region. More details on\nthe calorimeters, and any other detectors in ATLAS, can be found in Ref. [1].\nIn this note the approaches used by the ATLAS collaboration to achieve the challenging perfor-\nmance goals are discussed. First, the most commonly used jet \ufb01nders are brie\ufb02y introduced in Section 2,\ntogether with the theoretical and experimental guidelines for the ATLAS implementations. Then, the ex-\npectations for the performance of these algorithms using different detector signals are shown in Section 3.\nAs the focus is on the upcoming initial data taking period of ATLAS, some distortions in the detector\nalignment and material distributions have been included but not corrected in the results presented here.\nFinally, special challenges to jet reconstruction like forward going jets and jets in minimum bias events\nare discussed in Section 4, followed by conclusions in Section 5.\n2\nJet algorithms in ATLAS\nIn general an attempt is made to provide implementations of all relevant jet \ufb01nding algorithms in AT-\nLAS. These include \ufb01xed sized cone algorithms as well as sequential recombination algorithms and an\nalgorithm based on event shape analysis. This approach is a response to the fact that there is no universal\njet \ufb01nder for the hadronic \ufb01nal state in all topologies of interest. For example, for the measurement of the\ninclusive QCD jet cross-sections wider jets are typically preferred to capture the hard scattered parton\nkinematics, including possible small angle gluon radiation, completely. On the other hand, to reconstruct\na W boson decaying into two jets or to \ufb01nd jets in very busy \ufb01nal states like tt production or possible\nSUSY signatures, narrow jets are preferred.\nThe common feature of all jet \ufb01nder implementations in ATLAS is full four-momentum recombina-\ntion whenever the constituents of a jet change, either through adding a new constituent, or by removing\none, or by changing the kinematic contribution of a given constituent to the jet. Also, in the ATLAS re-\nconstruction software framework ATHENA, the same jet \ufb01nder code can be run on objects like calorimeter\nsignal towers, topological cell clusters in the calorimeters, reconstructed tracks, and generated particles\nand partons.\nIn this section the basics of the present default jet algorithms used in ATLAS are discussed after\na brief summary of the theoretical and experimental guidelines for jet algorithm implementation. In\naddition, some features of jet \ufb01nders not included in the more comprehensive presentation of jet recon-\nstruction performance in Section 3 are shown.\n2.1\nGuidelines for jet reconstruction\nThe basic guidelines for jet reconstruction in ATLAS have been extracted from Ref. [2]. They also\nre\ufb02ect the concept of jet de\ufb01nition discussed in Ref. [3], which is an attempt to provide a common\nunderstanding between experiments and theory on how a given jet \ufb01nding strategy should be speci\ufb01ed to\nassure the highest level of comparability between the results from various sources.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n263\n\n2.1.1\nTheoretical guidelines\nThe major theoretical guidelines for jet reconstruction are:\nInfrared safety: The presence of additional soft particles between two particles belonging to the same\njet should not affect the recombination of these two particles into a jet. In the same sense, the\nabsence of additional particles between these two should not disturb the correct reconstruction of\nthe jet. Generally, any soft particles not coming from the fragmentation of a hard scattered parton\nshould not effect the number of jets produced.\nCollinear safety: A jet should be reconstructed independent of the fact that a certain amount of trans-\nverse momentum is carried by one particle, or if a particle is split into two collinear particles.\nOrder independence: The same hard scattering should be reconstructed independently at parton-, par-\nticle- or detector level.\nNote that from the perspective of experimental data the particles mentioned in these guidelines can,\nto a point, be replaced by four-momentum type objects reconstructed from detector signals, see e.g.\nSection 2.5 and Section 2.6 below.\n2.1.2\nExperimental guidelines\nAdditional aspects of jet reconstruction in ATLAS include features also re\ufb02ected in the design of the\ndetector. They can be divided into three classes.\nDetector technology independence: The reconstructed jet and its kinematic variables should not de-\npendent on the signal source, i.e. all detector speci\ufb01c signal characteristics and inef\ufb01ciencies must\nbe calibrated out or corrected as much as possible.\nDetector resolution: contributions from the \ufb01nite spatial and energy resolution must be at a min-\nimum;\nDetector environment: effects from the detector environment like electronics noise, signal losses\nin un-instrumented (inactive) materials and cracks between detectors must be at a minimum;\nStable signals: the detector signal reconstruction and calibration must provide a stable input sig-\nnal to jet reconstruction.\nEnvironment independence: The jet reconstruction environment is characterized by the additional ac-\ntivity in the collision event due to multiple interactions and pile-up, the source of the jet, the\nunderlying event activity, and other features of the pp collisions at LHC.\nStability: a jet should be found and reconstructed safely even in the case of changing underly-\ning event activity and changing instantaneous luminosity, thus changing number of multiple\ninteractions;\nEf\ufb01ciency: all physically interesting jets from energetic partons must be identi\ufb01ed with high ef\ufb01-\nciency.\nImplementation: The jet algorithm implementation must be fully speci\ufb01ed in that the jet de\ufb01nition,\nwhich consists of the jet \ufb01nder and its con\ufb01guration together with the choice of kinematic recom-\nbination given in Ref. [3], must be complete. Also included must be all selections and, if important\nfor the measured jet, the signal choices. In addition, the implementation of the jet reconstruction\nmust make ef\ufb01cient use of computing resources, i.e. it must be suf\ufb01ciently fast and avoid excessive\nmemory consumption.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n264\n\nThe most commonly used jet \ufb01nder implementations in ATLAS are a seeded \ufb01xed cone \ufb01nder with split\nand merge (see below), and a kT algorithm [4, 5] implementation, with an initial implementation as\ndescribed in Ref. [6], but later replaced by a faster implementation similar to the one in the FASTJET\npackage [7]. It is anticipated that for the \ufb01rst experimental collision data all implementations of the\nFASTJET library (kT, anti-kT, Cambridge \ufb02avor kT [8]) will be available, as well as the seedless infrared-\nsafe cone algorithm SISCONE [9]. As there are no complete systematic evaluations of these algorithms\navailable for this note, they are excluded from further discussions here.\n2.2\nFixed cone jet \ufb01nder in ATLAS\nThe ATLAS implementation of the iterative seeded \ufb01xed-cone jet \ufb01nder follows the algorithm description\nof Ref. [2]. First, all input is ordered in decreasing order in transverse momentum pT. If the object with\nthe highest pT is above the seed threshold, all objects within a cone in pseudorapidity \u03b7 and azimuth\n\u03c6 with \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 < Rcone, where Rcone is the \ufb01xed cone radius, are combined with the seed.\nA new direction is calculated from the four-momenta inside the initial cone and a new cone is centered\naround it. Objects are then (re-)collected in this new cone, and again the direction is updated. This\nprocess continues until the direction of the cone does not change anymore after recombination, at which\npoint the cone is considered stable and is called a jet. At this point the next seed is taken from the input\nlist and a new cone jet is formed with the same iterative procedure. This continues until no more seeds\nare available. The jets found this way can share constituents, and signal objects contributing to the cone\nat some iteration maybe lost again due to the recalculation of the direction at a later iteration.\nThis algorithm is not infrared safe, which can be (at least) partly recovered by introducing a split\nand merge step after the jet formation is done. Jets which share constituents with more than a certain\nfraction fsm of the pT of the less energetic jet are merged, while they are split if the amount of shared pT\nis below fsm, with fsm = 0.5 in ATLAS. Other important parameters of the ATLAS cone jet \ufb01nder are a\nseed threshold of pT > 1 GeV, and a narrow (Rcone = 0.4) and a wide cone jet (Rcone = 0.7) option.\nFrom a theoretical standpoint this particular cone jet \ufb01nder is by design only meaningful to leading\norder for inclusive jet cross-section measurements and \ufb01nal states like W/Z +1 jet, but is not meaningful\nat any order for 3-jet \ufb01nal states, W/Z +2 jets, and for the measurement of the dijet invariant mass in 2\njets +X \ufb01nal states [10].\n2.3\nSequential recombination algorithms\nThe default implementation of a sequential recombination jet \ufb01nder in ATLAS is the kT algorithm. Here\nall pairs ij of input objects (partons, particles, reconstructed detector objects with four-momentum repre-\nsentation) are analyzed with respect to their relative transverse momentum squared, de\ufb01ned by\ndij = min(p2\nT,i, p2\nT, j)\n\u2206R2\nij\nR2 = min(p2\nT,i, p2\nT, j)\n\u2206\u03b72\nij +\u2206\u03c6 2\nij\nR2\n,\nand the squared pT of object i relative to the beam di = p2\nT,i. The minimum dmin of all dij and di is found.\nIf dmin is a dij, the corresponding objects i and j are combined into a new object k using four-momentum\nrecombination. Both objects i and j are removed from the list, and the new object k is added to it.\nIf dmin is a di, the object i is considered to be a jet by itself and removed from the list. This procedure\nis repeated for the resulting new sets of dij and di until all objects are removed from the list. This means\nthat all original input objects end up to be either part of a jet or to be jets by themselves. Contrary to the\ncone algorithm described earlier, no objects are shared between jets. The procedure is infrared safe. As\nit does not use seeds, it is also collinear safe. The distance parameter R, which is the only free parameter\nbesides the choice of recombination scheme in this inclusive implementation of the kT algorithm, allows\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n265\n\nTable 1: Default jet \ufb01nder con\ufb01gurations used in ATLAS.\nAlgorithm\nMain parameter\nClients\nSeeded \ufb01xed cone\nRcone = 0.4\nW \u2192j j in tt, SUSY\n(seed pT > 1 GeV)\nRcone = 0.7\ninclusive jet cross-section, Z\u2032 \u2192j j\nkT\nR = 0.4\nW \u2192j j in tt, SUSY\nR = 0.6\ninclusive jet cross-section, Z\u2032 \u2192j j\nsome control on the size of the jets. Default con\ufb01gurations in ATLAS are R = 0.4 for narrow and R = 0.6\nfor wide jets.\nTable 1 summarizes the algorithms and con\ufb01gurations which have been used by ATLAS for basically\nall pre-collision physics studies. Thus, these are the base for most predictions related to the performance\nof the hadronic \ufb01nal state reconstruction for all studied physics channels available to date.\n2.4\nAlternative jet \ufb01nders\nAs jet \ufb01nders others than the \u201cdefault\u201d algorithms and con\ufb01gurations discussed above can be more appro-\npriate for the precision analysis of speci\ufb01c \ufb01nal states, additional jet algorithms are available in ATLAS\nfor application at the analysis stage. Those are the mid-point variant of the \ufb01xed cone algorithm originally\nintroduced by CDF in Ref. [2, 11], and the \u201coptimal jet \ufb01nder\u201d discussed in Ref. [12]. Both algorithms\nhave been studied for ATLAS and in general provide a very similar performance when compared to the\ndefault seeded cone and kT implementations. This can be seen in Fig. 2 for the mid-point algorithm,\nwhich, as already said, is a \ufb02avour of the \ufb01xed cone algorithm with the modi\ufb01cation that the seeds are\nplaced between two particles with signi\ufb01cant pT, rather than just using an individual particle pT as seed\ndirectly. Besides a slightly smaller ef\ufb01ciency in the central region, there are no signi\ufb01cant differences\nbetween the studied jet \ufb01nders observed in this non-comprehensive investigation with simulated ttbb\nevents.\nThe optimal jet \ufb01nder is a departure from the traditional approach of reconstructing each jet rather\nindependent from previously reconstructed jets in the same event. Here the basic scheme is to calculate\na weight for each particle re\ufb02ecting the contribution to any jet by minimizing a test function event by\nevent. This function actually includes weights for contributions to transverse momentum not clustered\ninto any jet at all, thus using the overall event shape when reconstructing the jets. Parameters of the\nalgorithm are a jet cone size and a threshold for the test function. A more exclusive mode is available\nwhere the number of jets to be reconstructed can be \ufb01xed beforehand. In general this jet \ufb01nder works\nwell in busy \ufb01nal states like full hadronic top-quark decays in tt production. Predictions for the relative\ntop mass resolution, for example, are basically identical for the default kT implementation with R = 0.6\nand the optimal jet \ufb01nder for the same jet size.\n2.5\nCalorimeter jets\nThe most important detectors for jet reconstruction are the ATLAS calorimeters. In this section the input\nsignals and default calibration schemes for calorimeter jets are brie\ufb02y described.\nThe ATLAS calorimeter system [13] has about 200,000 individual cells of various sizes and with\ndifferent readout technologies and electrode geometries. For jet \ufb01nding it is necessary to \ufb01rst combine\nthese cell signals into larger signal objects with physically meaningful four-momenta. The two concepts\navailable are calorimeter signal towers and topological cell clusters.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n266\n\n0\n5\n10\n15\n20\n0\n1000\n2000\n3000\n4000\n5000\n-5 -4 -3 -2 -1 0 1\n2 3 4\n5\n0\n1000\n2000\n3000\n4000\n5000\n6000\n0\n100\n200\n300\n400\n500\n2\n10\n3\n10\n4\n10\n0\n100\n200\n300\n400\n500\n10\n2\n10\n3\n10\nseeded cone\nmid-point\nkT\nNumberofjets/event\nEntries\nseeded cone\nmid-point\nkT\nTransversemomentum (GeV)\nEntries\nTransversemomentum (GeV)\nalljets\nseeded cone\nmid-point\nkT\nleadingjet\nEntries\nEntries\nJetpseudorapidity\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nFigure 2: Performance comparison of the ATLAS seeded cone, kT, and the mid-point seeded cone for\nttbb events, as calculated from simulations. Shown are the distributions for jet multiplicity (top left), the\npT spectrum for all jets (top right), the rapidity distribution (bottom left) and the pT spectrum for the\nleading jets (bottom right).\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n267\n\n2.5.1\nCalorimeter tower signals\nIn case of the towers, the cells are projected onto a \ufb01xed grid in pseudorapidity (\u03b7) and azimuth (\u03c6). The\ntower bin size is \u2206\u03b7 \u00d7\u2206\u03c6 = 0.1\u00d70.1 in the whole acceptance region of the calorimeters, i.e. in |\u03b7| < 5\nand \u2212\u03c0 < \u03c6 < \u03c0 with 100 \u00d764 = 6,400 towers in total. Projective calorimeter cells which completely\n\ufb01t inside a tower contribute their total signal, as reconstructed on a basic electromagnetic energy scale1,\nto the tower signal. Non-projective cells and projective cells larger than the tower bin size contribute\na fraction of their signal to several towers, depending on the overlap fraction of the cell area with the\ntowers, see Fig. 3 for illustration.\nwcell\n1.0\n1.0\n0.25\n0.25\n0.25\n0.25\ncell \u01fb\u0218\u00d7\u01fb\u0133 =0.05\u00d70.05\ncell \u01fb\u0218\u00d7\u01fb\u0133 =0.1\u00d70.1\ncell \u01fb\u0218\u00d7\u01fb\u0133 =0.2\u00d70.2\nnon-projective cell\nFigure 3: Calorimeter cell signal contributions to towers on a regular \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.1 \u00d7 0.1 grid, for\nprojective and non-projective cells. The signal contribution is expressed as a geometrical weight and is\ncalculated as the ratio of the tower bin area over the projective cell area in \u03b7 and \u03c6.\nThus, the tower signal is the nondiscriminatory sum of possibly weighted cell signals (all cells are\nincluded). As the cell signals are on the basic electromagnetic energy scale, the resulting tower signal is\non the same scale. No further corrections or calibrations are applied at this stage.\n2.5.2\nTopological cell clusters\nThe alternative representation of the calorimeter signals for jet reconstruction are topological cell clus-\nters, which are basically an attempt to reconstruct three-dimensional \u201cenergy blobs\u201d representing the\nshowers developing for each particle entering the calorimeter. The clustering starts with seed cells\nwith a signal-to-noise ratio, or signal signi\ufb01cance \u0393 = Ecell\n\u000e\n\u03c3noise,cell , above a certain threshold S, i.e.\n|\u0393| > S = 4. All directly neighbouring cells of these seed cells, in all three dimensions, are collected into\nthe cluster. Neighbours of neighbours are considered for those added cells which have \u0393 above a certain\nsecondary threshold N (|\u0393| > N = 2). Finally, a ring of guard cells with signal signi\ufb01cances above a\nbasic threshold |\u0393| > P = 0 is added to the cluster. After the initial clusters are formed, they are analyzed\nfor local signal maximums by a splitting algorithm, and split between those maximums if any are found\n[15].\n1This is the raw signal from the ATLAS calorimeters. The nomenclature indicates that this scale has been derived from\nelectron signals, but it lacks all corrections applied in high precision electron or photon reconstruction as described in Ref. [14].\nIt typically includes all electronic corrections and the geometrically motivated corrections for high voltage problems, like\ninactive electrode sub-gaps and similar.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n268\n\nFigure 4 shows the average number of particles in Monte Carlo generated jets from QCD dijet pro-\nduction together with the number of topological cell clusters in the corresponding simulated calorimeter\njets. The \ufb01gure indicates that the clustering algorithm resolves the particle content of the jet in the pseu-\ndorapidity range 1.5 <\u223c|\u03b7| <\u223c2.5. The shower overlap between the particles in the jet cannot be resolved\nas well in the central region |\u03b7| <\u223c1.5, where the calorimeter cell sizes are a bit larger on the scale of\nthe hadronic shower. Here the ratio of number of particles per cluster is approximately 1.6. Similarly,\nin the forward region |\u03b7| >\u223c2.5 both the increase in shower overlap, due to the decreasing linear distance\nbetween jet particles, and the increase of the cell sizes reduce the resolution power of the clustering\nalgorithm for individual particle showers.\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n0\n5\n10\n15\n20\n25\n30\nNumberofconstituents\nclusters\nparticles\nATLASMC\nJetpseudorapidity\nFigure 4: Estimates for the average number of particles in seeded \ufb01xed size cone jets with Rcone = 0.7\nin fully simulated QCD dijet production, shown as function of the pseudorapidity \u03b7 of the jet. Also\nshown is the corresponding average number of topological clusters in matching jets found with the same\nalgorithm in the ATLAS calorimeters.\nLike towers, clusters are initially formed using the basic electromagnetic energy scale cell signals.\nThese clusters can already be used for jet reconstruction. In addition, clusters can be calibrated to a local\nhadronic energy scale. This calibration starts with a classi\ufb01cation step characterizing clusters as electro-\nmagnetic, hadronic, or noise, based on their location and shape. After that, cell signals inside hadronic\nclusters are weighted with functions depending on cluster location, energy, and the cell signal density.\nThen, a correction for energy losses in inactive materials close to or inside the cluster is applied. Finally,\na correction for signal losses due to the clustering itself (out-of-cluster correction) is applied. Note that\nall calibrations and corrections for topological clusters are derived from single particle simulations and\ndo not use the jet context.\n2.5.3\nCharacteristics of calorimeter input to jet \ufb01nding\nThere are attempts in ATLAS to go beyond the high quality reconstruction of the total jet signal with the\nbest possible resolution. Especially the reconstruction of jet structure, including the lateral and longitu-\ndinal signal distributions, can be useful to apply jet energy scale corrections jet by jet, or reconstruct the\norigin of a given jet. The ability to reconstruct this structure depends on the choice of the calorimeter\nsignal de\ufb01nition used in jet \ufb01nding, as is qualitatively indicated in the simulated high pT QCD event in\nFig. 5. A given calorimeter signal de\ufb01nition like clusters may reproduce the jet shape at particle level\nbetter in certain regions of the calorimeters than in others. For example, from the depicted event in this\n\ufb01gure the cluster signals represent the transverse energy \ufb02ow of particles inside a jet better than the tower\njets in the central and endcap regions, while in the forward region the clusters cannot resolve individual\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n269\n\n1\n2\n3\n0\n\u22121\n\u22122\n\u22123\n\u03d5 (ra d )\n\u22125 \u22124 \u22123 \u22122 \u22121\n0\n1\n2\n3\n4\n5\nra p id ity y\n10\n1\n1\n10\n102\n103\npt (G eV )\n1\n2\n3\n0\n\u22121\n\u22122\n\u22123\n\u03d5 (ra d )\n\u22125 \u22124 \u22123 \u22122 \u22121\n0\n1\n2\n3\n4\n5\nra p id ity y\n10\n1\n1\n10\n102\n103\npt (G eV )\n1\n2\n3\n0\n\u22121\n\u22122\n\u22123\n\u03d5 (ra d )\n\u22125 \u22124 \u22123 \u22122 \u22121\n0\n1\n2\n3\n4\n5\nra p id ity y\n10\n1\n1\n10\n102\n103\npt (G eV )\nto w er jets\nclu ster jets\nC o n e Rcone =\n0.7\n1\n3\n2\n4\ncalorimeter response\nsh o w erin g \u2295electro n ic n o ise\nd ea d m a teria l en erg y lo sses &\nlea ka g e\nn o ise ca n cella tio n w ith to w ers\ncalorimeter response\nsh o w erin g \u2295electro n ic n o ise\nd ea d m a teria l en erg y lo sses &\nlea ka g e\nclu ster b ia s &\nn o ise su p p ressio n\nh a d ro n jets\nFigure 5: A simulated QCD dijet event with four jets in the \ufb01nal state, as seen at particle level and in the\nATLAS calorimeters when using towers or clusters (extracted from Ref. [16]).\nshowers anymore and thus cannot reproduce the jet shape very well. Here the towers still re\ufb02ect some\nspatial structure of the incoming particles.\nAnother important difference between tower and cluster jets is the number of calorimeter cells used\nin the jet. While towers include all cells of the ATLAS calorimeters, topological clustering actually\napplies noise suppression due to the cell signal signi\ufb01cance cuts used. This means that many fewer cells\ncontribute to jets in case of clusters, and that the noise contribution per jet is also smaller for cluster jets\nthan for tower jets, see Section 3.3.1 for further discussion.\nJet \ufb01nding needs physical four-momenta on input. Thus, both towers and clusters are de\ufb01ned as\nmassless pseudo-particles with a four-momentum (E,\u20d7p), reconstructed from the reconstructed energy E\n(either electromagnetic or hadronic scale, see above), and the directions \u03b7 and \u03c6:\nE\n=\n|\u20d7p| =\nq\np2x + p2y + p2z\npx\n=\np\u00b7 cos\u03c6\ncosh\u03b7\npy\n=\np\u00b7 sin\u03c6\ncosh\u03b7\npz\n=\np\u00b7tanh\u03b7 .\nThe directions are \ufb01xed to the bin center in the (\u03b7,\u03c6) grid for each tower, while they are reconstructed\nfrom the energy-weighted barycenter for topological clusters.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n270\n\nTower Building\n(\u01fb\u0218\u00d7\u01fb\u0133=0.1\u00d70.1, non-discriminant)\nCaloCells\n(em scale)\nCaloTowers\n(em scale)\nJet Finding\n(cone, kT)\nRefined Physics Jet\n(calibrated to interaction level)\nIn-situ Calibra ion\n(underlying event, physics environment, etc.)\nTower Noise Suppression\n(cancel E<0towers by re-summation)\nProtoJets\n(E>0,em scale)\nJet Based Hadronic Calibra ion\n(cell signal weighting in jets etc.)\nJet Energy Scale Corrections\n(noise, pile-up, algorithm effects, etc.)\nCalorimeter Jets\n(em scale)\nCalorimeter Jets\n(fully calibrated had scale)\nPhysics Jets\n(calibrated to particle level)\nTopological Clustering\n(includes noise suppression)\nCaloCells\n(em scale)\nCaloClusters\n(em scale,E>0)\nJet Finding\n(cone, kT)\nJet Based Hadronic Calibra ion\n(cell signal weighting in jets etc.)\nRefined Physics Jet\n(calibrated to interaction level)\nIn-situ Calibration\n(underlying event, physics environment, etc.)\nCalorimeter Jets\n(em scale)\nJet Energy Scale Corrections\n(noise, pile-up, algorithm effects, etc.)\nCalorimeter Jets\n(fully calibrated had scale)\nPhysics Jets\n(calibrated to particle level)\nTopological Clustering\n(includes noise suppression)\nCaloCells\n(em scale)\nCaloClusters\n(em scale)\nCaloClusters\n(em scale, classified)\nCluster Classifica ion\n(identify em type clusters)\nCaloClusters\n(locally calibrated, E>0)\nHadronic Cluster Calibration\n(apply cell signal weighting dead material corrections, etc.)\nJet Energy Scale Corrections\n(noise, pile-up, algorithm effects, etc.)\nRefined Physics Jet\n(calibrated to interaction level)\nIn-situ Calibration\n(underlying event, physics environment, etc.)\nCalorimeter Jets\n(fully calibrated had scale)\nPhysics Jets\n(calibrated to particle level)\nJet Finding\n(cone, kT)\nI. TowerJets\nII. ClusterJets\nIII. ClusterJets\nJetReconstructionSequences\nCalorimeter Reconstruction\nDomain\nJet Reconstruction Domain\nAnalysis\nDomain\nFigure 6: Schematic view on the reconstruction sequences for jets from calorimeter towers (left), uncali-\nbrated (center) and calibrated (right) topological calorimeter cell clusters in ATLAS. The reconstruction\n(software) domains are also indicated.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n271\n\n2.5.4\nReconstruction \ufb02ow for calorimeter jets\nThe general reconstruction algorithm \ufb02ows for calorimeter jets are summarized in Fig. 6. They re\ufb02ect\nthe differences between tower and cluster signals. As already discussed, tower signals are on the elec-\ntromagnetic energy scale while topological clusters are either on this scale or are calibrated on a local\nhadronic energy scale. Also, tower signals do not include noise suppression, while topological clustering\nhas noise suppression built in.\nReconstruction sequence I: tower jets\nJet reconstruction from calorimeter towers (left diagram in\nFig. 6) starts with a re-summation step, which addresses a possible unphysical four-momentum due to\na negative (net) tower signal Etower < 0. This can be generated by signal \ufb02uctuations from noise (elec-\ntronics and physics from pile-up) in the cells entering into the corresponding towers. Simply ignoring\nthe negative signal towers enhances the contribution of positive noise \ufb02uctuations, but combining nega-\ntive signal towers with nearby positive signals such that the combined four-momentum is physical with\nEtower > 0, leads to cancellations of some of the noise \ufb02uctuations and avoids signal biases. Only negative\nsignal towers without nearby positive signals are completely dropped.\nThe resulting \u201cprotojets\u201d represent either one or a few towers, and have all physically valid four-\nmomenta. They are the input to the actual jet \ufb01nding algorithm like seeded \ufb01xed cone or kT. The outputs\nof the jet \ufb01nder are then jets with energies on the electromagnetic energy scale. Their constituents are\nthe original calorimeter towers. They are subjected to a cell signal based calibration discussed below in\nSection 2.5.5. After calibration, jets with pT < 7 GeV are discarded.\nMore re\ufb01ned corrections are needed to calibrate the tower jets to the particle level. Those include\ncorrections for residual non-linearities in the jet response due to algorithm effects, like missing energy\nfrom the jet, or adding energy not belonging to the jet, in the jet clustering procedure. Other corrections\ninclude suppression of signal contributions from the underlying event and/or pile-up. Most of these can\nonly be addressed in the context of a speci\ufb01c physics analysis.\nReconstruction sequence II: cluster jets\nWhen topological clusters on electromagnetic energy scale\nare used for jet reconstruction, the reconstruction \ufb02ow is rather similar to the tower jet reconstruction, see\ncenter diagram in Fig. 6. The main difference is the treatment of negative signals. Due to the symmetric\nnoise cut applied in the cell selection in the clustering step, some clusters may have net negative signal as\nwell. These can be ignored for jet reconstruction without signi\ufb01cantly biasing the jet signal by positive\nnoise contributions, because the noise suppression applied by the cell clustering already severely reduces\nany noise contribution. Some additional average cancellation is achieved by the symmetric noise cut,\nwhich allows inclusion of some negative cell signals even into positive (physical) clusters.\nThe cluster jets are initially on the electromagnetic energy scale as well. The same cell signal weight-\ning functions used for tower jets are applied to initially calibrate these jets, with some additional correc-\ntions for the fact that these calibration functions have not been optimized for the cluster signals, see\nSection 2.5.5 for more details. Like in reconstruction sequence I, all jets with pT < 7 GeV after calibra-\ntion are discarded.\nReconstruction sequence III: locally calibrated cluster jets\nIn this sequence the input objects to\njet \ufb01nding are already calibrated to the local hadronic energy scale [17]. This means that after the jets\nare formed, they are also calibrated on this scale. Additional corrections needed are related to the fact\nthat all calibrations and corrections for this particular scale have been derived from single pion response\nonly. Additional jet energy losses due to loss of particles in the magnetic \ufb01eld in ATLAS, or in inactive\nmaterial without leaving any signal above clustering threshold in the calorimeters, have to be corrected\nin the jet context itself, in addition to the corrections for the physics environment contributions already\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n272\n\ndiscussed for the tower jets. See the right hand side diagram in Fig. 6 for a schematic overview. Fully\ncalibrated jets from this sequence with pT < 7 GeV are again discarded.\n2.5.5\nCalorimeter jet calibration\nThe long standing calibration scheme for calorimeter jets in ATLAS is based on cell signal weighting.\nIt can be applied to both tower and cluster jets from the reconstruction sequences I and II, respectively.\nThe basic idea behind this approach, which was originally developed for the CDHS experiment [18] and\nfurther re\ufb01ned for the H1 experiment Ref. [19], is that low signal densities in calorimeter cells indicate\na hadronic signal in a non-compensating calorimeter and thus need a signal weight for compensation of\nthe order of the electron/pion signal ratio e/\u03c0, while high signal densities are more likely generated by\nelectromagnetic showers and therefore do not need additional signal weighting.\nTo apply the cell signal weighting, \ufb01rst all calorimeter cell signals contributing to a jet are retrieved.\nThis is possible even if the jets have not directly been reconstructed from these cells. The signal in each\ncell i in the jet is weighted by a function depending on the cell location \u20d7Xi and the cell signal density\n\u03c1i = Ei/Vi, with Ei being the electromagnetic energy signal of the cell, and Vi being its volume. The\nweighting factor is \u22481 for high density signals and rising up to 1.5, the typical e/\u03c0 for the ATLAS\ncalorimeters, with decreasing cell signal densities. The weighting functions are universal in that they\ndo not depend on any jet feature or variable. The calibrated jet four-momentum (Ejet,calo,\u20d7preco) is then\nrecalculated from the weighted cell signals, which are treated as massless four-momenta (Ei,\u20d7pi) with\n\ufb01xed directions:\n\u0000Ejet,calo,\u20d7pcalo\n\u0001\n=\n \nNcells\n\u2211\ni\nw(\u03c1i,\u20d7Xi)Ei,\nNcells\n\u2211\ni\nw(\u03c1i,\u20d7Xi)\u20d7pi\n!\n.\n(1)\nThe signal weighting functions have been determined using seeded \ufb01xed size cone jets (Rcone = 0.7)\nin fully simulated QCD dijet events by \ufb01ts of reconstructed calorimeter tower jet energies to matching\nMonte Carlo truth particle jet energies. Residual non-linearities (as function of pT) and non-uniformities\n(as function of \u03b7) are corrected by an additional calibration function parametrized in both variables.\nThese corrections have also been calculated for other standard jet \ufb01nding con\ufb01gurations and calorimeter\nsignals. The calibration has been determined using the ideal, non-distorted detector geometries. See\nRef. [17] for more details.\n2.6\nTrack jets\nFinding jets in reconstructed inner detector tracks is useful to recover possible inef\ufb01ciencies of the\ncalorimeter signals, especially for jets pointing to transition or crack regions. Even though the scheme of\nseeding calorimeter jets with track jets in these regions has not been completely evaluated, some recov-\nery may be possible. At least tagging of suspicious event topologies using track jets without matching\ncalorimeter jet, or matching a poorly reconstructed calorimeter jet, allows a suppression of events with\nsigni\ufb01cant fake missing transverse momentum in the hadronic \ufb01nal state reconstruction, thus improving\nthe quality of any given sample for physics analysis.\nMatching the track jets with calorimeter jets is another promising approach to re\ufb01ne the jet energy\nmeasurement jet by jet, and the hadronic \ufb01nal state reconstruction in general. First, the pT fraction\ncarried by tracks, de\ufb01ned as\nftrk = pT,track\npT,calo\n,\n(2)\nwith pT,track being the transverse momentum from tracks and pT,calo being the one reconstructed by the\ncalorimeter, can be measured for each jet within the inner detector acceptance |\u03b7| < 2.5. It can then be\nused to (relatively) improve the jet energy measurement, as indicated in Fig. 7. The \ufb01gure shows results\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n273\n\nobtained from simulations of QCD dijet processes of jets within |\u03b7| < 0.7 and 40 < pT < 60 GeV.\nEven though the calorimeter jet calibration performs well on average, there are residual dependencies of\nthe individual jet signal reconstruction quality on the jet fragmentation, i.e. the particle composition of\nthe jet, for which ftrk provides a handle for a relative correction which can be applied jet by jet. This\nfragmentation dependency can be understood in that jets with large ftrk have a larger amount of their\nenergy carried by charged hadrons, which tend to generate a smaller signal in the non-compensating\nATLAS calorimeters. The standard jet calibration based on the calorimeter cell signals alone cannot\ncompletely recover the corresponding signal loss. This is certainly one of the promising techniques for a\nrelative jet energy scale correction in the context of a re\ufb01ned jet calibration, with the immediate goal of\nimproving the relative jet energy resolution.\nJet \ufb01nders usually cluster four-momentum in two dimensions, like azimuth \u03c6 and pseudorapidity \u03b7.\nInner detector tracks in ATLAS have a reconstructed vertex associated, thus the zvtx coordinate can be\nadded as a third dimension to jet \ufb01nding from these tracks, see Fig. 8. Jet clustering in \u03c6, \u03b7, and zvtx then\nallows the assignment of a vertex to a matching calorimeter jet, which is especially of interest in events\nwith multiple interactions from pile-up. In this case jets not associated with the primary vertex can be\ntagged as such, and removed from the \ufb01nal state in jet counting experiments, e.g. a W +n jets analysis.\n2.7\nEnergy \ufb02ow jets\nIn Section 2.6 some aspects of the use of jets from charged tracks reconstructed with the inner detector\nare discussed. Another approach to improve the jet energy measurement is to match the calorimeter\nresponse in towers or clusters with a charged track pointing to it, and use the track kinematics if the track\nmomentum resolution is better than the calorimeter energy resolution for the matched cluster, which for\nhadrons in ATLAS is the case up to pT \u2248140 GeV at \u03b7 = 0. The principal method is referred to as\nenergy \ufb02ow reconstruction, and was pioneered at LEP [20] and is in use in hadron colliders; for example,\nthe CDF application is described in Ref. [21].\nThe most important feature of energy \ufb02ow reconstruction is the removal of the calorimeter signal\ngenerated by an accepted track. In ATLAS this has been studied using a track-cluster match approach.\nFigure 9 shows the relative variation of the pT resolution for cone jets from energy \ufb02ow objects and\ntopological clusters in QCD dijet production, both without \ufb01nal energy scale corrections. From this there\n0\n0\n2\n-\n3\n0\n1\n-\n0\n3\n0\n2\n-\n10\n0\n0\n0\n2\n-\n3\n0\n1\n-\n0\n3\n0\n2\n-\n10\n0\n100\n200\n300\n400\n500\n600\n0\n-5\n-10\n5\n10\np\n(GeV)\nT calo\n(%)\nT truth\nT\n(GeV)\nT\n(GeV)\nT\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\nEntries\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\nEntries\n2000\n0 20 5 GeV using the usual two-dimensional clustering algo-\nrithm in \u03b7 and \u03c6, with Rcone = 0.4 (same line patterns and shades indicate same jet). Clearly tracks from\ndifferent vertices can end up in the same jet. The right \ufb01gure shows cone jets from three-dimensional\nclustering for the same event, explicitly including the track vertices (Rcone = 0.4, \u2206z = 10mm).\nJet p (GeV)\n40\n50\n60\n70\n80\n90\n100\n110\n120\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\nATLAS\nt\nR = 0.7\ncone\nR = 0.4\ncone\n\u0131\n/\u0131\neflow\ncalo\nFigure 9: The ratio of the relative pT resolutions for energy \ufb02ow and cluster cone jets \u03c3e\ufb02ow/\u03c3calo, as de-\ntermined with fully simulated dijet events, as function of the jet pT. Results for both narrow (Rcone = 0.4)\nand wide (Rcone = 0.7) jets within |\u03b7| < 1.8 are shown.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n275\n\nare indications that for jets with pT <\u223c80 GeV in this environment, which is characterized by typically\nlow event activity in general, the jet energy resolution can be improved by the energy \ufb02ow technique.\nThe expected gain is most signi\ufb01cant at lower jet pT, e.g. about 15% (relative) at pT = 40 GeV.\n2.8\nParticle jets\nParticle jets are only available in simulated events. They are built from stable particles produced by the\nfragmentation model in the physics generator. Stable particles in ATLAS are those with a laboratory\nframe lifetime of about 10 picoseconds or more, thus typically including electrons, muons, photons,\ncharged pions, kaons, protons, neutrons, neutrinos, and their corresponding antiparticles. These particles\nrepresent the \u201ctruth\u201d reference of a hard scattering process for performance studies and simulation based\ncalibration approaches. The particle jets are therefore referred to as truth particle jets, or truth jets, in\nthe following sections of this note.\nNeutrinos and muons generated in the collision are excluded from these truth jets, as they have their\nown observables, i.e. missing transverse momentum for neutrinos and explicitly reconstructed tracks for\nmuons. Jet \ufb01nding with generated particles uses the same code as calorimeter reconstruction, obviously\nexcluding the signal preparation for towers in reconstruction sequence I and all calibration steps.\n3\nJet reconstruction performance in ATLAS\nThe performance of the ATLAS detector for jet reconstruction has been evaluated within the present\nday limitations of physics generators, mostly PYTHIA [22], and detector response simulations, all\nperformed with GEANT4 [23, 24]. All results presented here should therefore be considered to be\nexpectations and of preliminary nature.\n3.1\nPreliminaries\nThe comparisons of calibrated jet features discussed in this section uses calorimeter jets to which the\ncell signal based calibration has been applied, in addition to the overall scale correction for different\njet \ufb01nder con\ufb01gurations and calorimeter signal choices, i.e. jets from reconstruction sequence I and II\nintroduced in Section 2.5.4, with calibrations applied as described in Section 2.5.5. As already discussed\nin that section, the parameters of the corresponding calibration functions have been determined using\nsimulations of dijets from QCD processes with the ideal detector geometry, meaning no misalignment\nbetween detectors or detector elements, no detector shape distortions, and assuming a perfect knowledge\nof the material distribution from supports, services, cryostats, etc., in the complex ATLAS geometry.\nThe simulations performed for the evaluation of the jet reconstruction performance use the same\ngenerated physics, meaning the same events at particle level, but include small shifts in relative detector\npositioning and small changes to the amount (increased) and location (more realistic asymmetric distri-\nbution in pseudorapidity and azimuth) of dead material in the detector description. As a consequence,\nthe calorimeters do not respond optimally for this evaluation with respect to jet signals, but the esti-\nmated performance is likely closer to the initial one in ATLAS, with some a priori unknown distortions,\nmisalignments, and other imperfections.\nFinal corrections can be derived once experimental data from the detector become available with suf-\n\ufb01cient statistics by e.g. following the strategies lined out in Ref. [25]. For the performance expectations\npresented here these corrections, which could have been derived rather straight forwardly by using the\nmisaligned detector geometry in the simulations for calibration as well, are intentionally not applied to\nprobe some of the initial systematic uncertainties to be expected for the initial running of ATLAS. Note\nthat none of the results presented here include pile-up.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n276\n\n3.2\nComparing jet reconstruction algorithm performances\nJet reconstruction performance is typically expressed in terms of expected or measured signal linearity,\ni.e. \ufb02atness of the detector response to particle jets over the whole kinematic range of interest at the LHC\n(from pT \u224810 GeV to a few TeV), signal uniformity in pseudorapidity \u03b7 and azimuth \u03c6 over the whole\ndetector system coverage, and the achievable energy resolution. Additional features of jet reconstruction\nperformance are the ef\ufb01ciency to \ufb01nd jets, and the purity of the found jet sample, which is of course\nrelated to the number of fake jets reconstructed.\nOther jet features studied with the ATLAS detector are the possibility to reconstruct the original\nsource of a given jet. This is particularly interesting for heavily boosted heavy particle decays like for\ntop quarks, where the \ufb01nal state will likely be reconstructed as just one (narrow) jet. The measurement\nof the jet mass and a substructure analysis are experimental tools which could address this question.\nThe quality of the reconstructed variables depends on the choice of the calorimeter signal (towers or\nclusters), the choice of the jet \ufb01nder and its con\ufb01guration (wide/narrow jets), and the ability to unfold as\nmuch as possible the physics environment, like re\ufb02ected in underlying event and pile-up contributions.\nA high precision analysis of a given event topology may require different con\ufb01gurations than offered\nin default jet reconstruction to optimize the signal. In this section the expected effect of the choices\ndiscussed above on the performance variables is shown for selected con\ufb01gurations.\nIn most cases the performance is evaluated using a truth reference provided in the simulation by\njets reconstructed at particle level, see Section 2.8. The detector and truth jets are associated through\ndirectional matching. The following list of variables is used:\nJet directions are given by pseudorapidity \u03b7 and azimuth \u03c6. As \u03b7 is directly related to the polar angle\n\u03b8, and thus useful (even for massive jets) to understand the variations of the detector response, the\nrapidity y can be used for physics analysis motivated selections. The variables are de\ufb01ned as:\n\u03b7\n=\n\u22121\n2 ln\n\u0012 p+ pz\np\u2212pz\n\u0013\n= \u2212ln\n\u0014\ntan\n\u0012\u03b8\n2\n\u0013\u0015\n(3)\ny\n=\n\u22121\n2 ln\n\u0012E + pz\nE \u2212pz\n\u0013\n(4)\n\u03c6\n=\narctan\n\u0012 py\npx\n\u0013\n.\n(5)\nMatching radius Rm is de\ufb01ned by the directional distance between truth and detector jets, i.e.\nRm =\np\n\u2206\u03b72 +\u2206\u03c6 2 .\n(6)\nTwo jets are matched if the radial distance between them is Rm \u22640.2, if not stated otherwise. Only\none match is allowed for each reference (truth) jet. In case of two or more nearby jets, the one\nclosest to the reference is taken for ef\ufb01ciency and purity studies. For signal linearity and uniformity\nstudies the reference and the calorimeter jets are omitted in this case.\nSignal linearity can be determined by the ratio \u03bb of the energy reconstructed for the calorimeter jet\nEjet,calo and the matched truth jet energy Ejet,truth,\n\u03bb = Ejet,calo\nEjet,truth\n,\n(7)\nwhen \u03bb can be calculated as function of Ejet,truth or Ejet,calo.\nSignal uniformity is measured by the variation of the signal as function of the jet direction in the de-\ntector frame, as given by \u03b7 in Eq.(3). The variable \u03bb de\ufb01ned in Eq.(7) can be used to estimate the\nuniformity from simulations, if calculated as function of \u03b7.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n277\n\nRelative energy resolution is given by the width of the distribution of the relative difference between\nEjet,calo and Ejet,truth:\n\u03c3\nE =\nv\nu\nu\nt\n*\u0012Ejet,calo \u2212Ejet,truth\nEjet,truth\n\u00132+\n\u2212\n\u001cEjet,calo \u2212Ejet,truth\nEjet,truth\n\u001d2\n.\n(8)\nJet reconstruction ef\ufb01ciency \u03b5 is de\ufb01ned by the following ratio:\n\u03b5(Rm) = # matches of truth particle jets with reconstructed jets\n# truth particle jets\n= Njets\nm (Rm)\nNjets\ntruth\n.\n(9)\nIt depends on the matching radius Rm and is determined as function of the true jet energy, pT, or\n\u03b7.\nJet reconstruction purity \u03c0 is given by\n\u03c0(Rm) = # matches of truth particle jets with reconstructed jets\n# reconstructed jets\n= Njets\nm (Rm)\nNjets\nreco\n(10)\nand also depends on the choice for Rm. The fake rate f(Rm) is then given by f(Rm) = 1\u2212\u03c0(Rm).\nPurity is calculated as function of the reconstructed jet energy, pT, and/or direction.\nAdditional variables reconstructed from jets, like substructure and shape measures, are discussed in\nSection 3.6.\n3.3\nComparisons of basic jet signal features\nThe main data source for the evaluation of the performance of the ATLAS calorimeters for jet recon-\nstruction are fully simulated QCD dijet events with at least one of the hard scattered partons having a pT\nwithin a certain bin. Eight bins are de\ufb01ned, with incrementing delimiters approximately following a 2n\npower law: 17 \u219235 GeV, 35 \u219270 GeV, etc., up to the \ufb01nal bin pT > 2240 GeV with the upper limit set\nby the kinematic limit introduced by the parton direction and the 14 TeV center-of-mass energy in the pp\ncollisions at LHC.\n3.3.1\nSignal linearity and resolution\nSignal linearity has been studied in detail for the evaluation of the various calorimeter jet calibration\nschemes under discussion in ATLAS [17]. The general expectation from these studies with the distorted\ndetector is a response \ufb02at within \u00b11% for jets with pT >\u223c50 GeV, and a slightly larger deviation from\nlinearity for jets with lower transverse momentum down to \u223c10 GeV [17]. As the calibration functions\nare determined using one jet \ufb01nder con\ufb01guration and one simulated calibration sample in a perfect de-\ntector model (see discussion in Section 2.5.5), one can estimate the shift from a response \ufb02at within the\nmargins introduced by the distorted detector when other con\ufb01gurations and/or a different calorimeter\nsignal basis are considered. This shift can be expressed as the ratio of \u03bbalt, as given in Eq.(7), from a\ngiven alternative jet reconstruction to \u03bbref , the reference from the same jet reconstruction con\ufb01guration\nused to derive calibration functions in the ideal detector:\n\u03be = \u03bbalt\n\u03bbref\n=\nEalt\njet,calo\n.\nEalt\njet,truth\nEref\njet,calo\n.\nEref\njet,truth\n.\n(11)\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n278\n\n4\n100\n0.2 < |y| < 0.4\n2.0 < |y| < 2.2\n0\n2\n-2\n3\n1\n-1\n-3\n4\n0\n2\n-2\n3\n1\n-1\n-3\n0\n0\n0\n1\n0\n0\n1\n0\n0\n0\n1\n-4\nSeededConeJets\nRcone\n0.7 0.4\nTower\nCluster\nRcone\n0.7 0.4\nTower\nCluster\nR\n0.6 0.4\nTower\nCluster\nR\n0.6 0.4\nTower\nCluster\nk Jets\nT\nResidualcalibrationuncertainty\n1 (%)\nTruthjettransversemomentum (GeV)\nSeededConeJets\nk Jets\nT\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nFigure 10: Residual calibration uncertainties for reconstructed jets from various jet \ufb01nder con\ufb01gurations\nand the two calorimeter signals, as function of the truth jet pT and in two bins of jet rapidity y. The refer-\nence con\ufb01guration is seeded \ufb01xed cone tower jets with Rcone = 0.7. The residual calibration uncertainty\nis given by \u03be, as de\ufb01ned in Eq.(11).\n100\n0\n0\n5\n0\n5\n0\n1\n100\n10\n50\nR\n0.6 0.4\nTower\nCluster\nk Jets\nT\nRcone\n0.7 0.4\nTower\nCluster\n3.7<|y|<3.9\nSeededConeJets\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n1 (%)\nTruthjettransversemomentum (GeV)\nATLASMC\nATLASMC\nFigure 11: Residual calibration uncertainty \u03be, calculated relative to the \ufb01xed seeded cone (Rcone = 0.7)\ntower jet calibration as described by Eq.(11), as function of the truth jet pT in the forward direction of\nATLAS.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n279\n\nThe quantity \u03be can be viewed as a measure of the residual calibration uncertainty with respect to the best\ncalibrated jet reconstruction con\ufb01guration, and is thus an estimate of one of the systematic uncertainty\ncontributions in the general jet reconstruction. Note that\n\u03be \u2248\nEalt\njet,calo\nEref\njet,calo\nwhen the alternative reconstruction uses the same jet \ufb01nder with the same parameters as the reference,\nbecause Ealt\njet,truth \u2248Eref\njet,truth in this case. The prime example here is the comparison of seeded \ufb01xed cone\ntower jets with Rcone = 0.7 (the reference) with cluster jets found with the same con\ufb01guration.\nFigure 10 shows expectations for \u03be as function of the jet pT in two different regions of jet rapidity.\nFrom this simulation based study it can be concluded that the cell signal based jet calibration, with the ad-\nditional overall scale corrections discussed in Section 2.5.5 applied, is universal for the distorted detector\nat a level of about 2% for the studied QCD jets with pT > 20 GeV and the particular choice of distor-\ntions implemented in the detector description of the simulation program. As these distortions include\nadditional inactive material between the electromagnetic liquid argon and the hadronic tile calorimeter\n(about 10% increase in nuclear absorption length), the effect is in particular emphasized for low pT jets\nin the central region, which mostly occupy the 0.4 < |y| < 0.4 bin2. Here the sensitivity to the jet algo-\nrithm (seeded cone or kT), its con\ufb01guration (narrow or wide jets), and the choice of calorimeter signals\n(clusters or tower) is also largest, see Fig. 10.\nSensitivities to signal and jet \ufb01nder choices are stronger for jets within 3.7 < |y| < 3.9. The calorime-\nter jet shape in the corresponding forward region is dominated by (lateral) hadronic shower extension\nrather than the particle \ufb02ow in a cone in (\u03b7,\u03c6), meaning that a considerable part of the calorimeter signal\ncan be outside of a chosen jet cone and therefore be lost for the total jet signal. Jets from each of the\njet \ufb01nder con\ufb01gurations and calorimeter signal choices have been individually corrected for these signal\nlosses using simulations with the ideal detector geometry. The effect of the distorted detector, which\nincludes a change of the relative z position of the endcap and forward calorimeters in ATLAS and thus\na change of the aspect ratio of the particle level jet shape to the calorimeter jet shape and consequently\ndifferent energy losses, can be signi\ufb01cant especially for the kT jets, as indicated in Fig. 11. Again using\nthe seeded \ufb01xed-size cone tower jets with Rcone = 0.7 as a reference, the cluster jets reconstructed with\nthe same algorithm show a similar response, indicated by |\u03be \u22121| < 2% in the whole kinematic range\nstudied here. The narrow cone cluster jets lose about 1% of their energy, rather independent of their\npT, which can be expected due to the lateral hadronic shower size varying only slightly with energy.\nThe larger effects of the distorted detector on the kT jets, like the prediction of a nearly linear rise of\n\u03be with log pT for pT <\u223c100 GeV for all considered kT jets, but most pronounced for wide kT tower jets,\nrequire more investigation of the distortion effects and their re\ufb02ection in towers and clusters on the more\ncomplex dynamics driving the kT algorithm.\nThe jet energy resolution is the other important contribution to precision jet reconstruction. It has\nbeen evaluated in the distorted detector geometry with the same QCD sample. The results are again dis-\ncussed in more detail in Ref. [17]. A typical relative energy resolution, calculated as described by Eq.(8),\nand achieved without particular corrections for the distorted detector, has a stochastic term of about\n60%/\np\nE( GeV) and a high energy limit of about 3% in the central region of ATLAS, all determined\nwith these simulated events.\nIt is expected that the relative energy resolution depends on the calorimeter signal choice, the jet al-\ngorithm, the underlying event and pile-up activity, and the general particle density and \ufb02ow of the physics\nenvironment. Using QCD dijet simulations, with electronics noise included in the detector simulation but\nwithout any pile-up activity, the difference in resolution between tower and cluster jets can be estimated\n2Note that for the QCD jets under consideration here the jet mass m is generally small, in particular m \u226ap, i.e. y \u2248\u03b7.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n280\n\n10\n100\n1000\n10\n5\n0\n-5\n-10\n-15\nk R=0 6\nT\nseeded coneR\n=0 7\ncone\nk R=0 6\nT\nseeded coneR\n=0 7\ncone\nk R=0 4\nT\nseeded coneR\n=0 4\ncone\nk R=0 4\nT\nseeded coneR\n=0 4\ncone\n10\n100\n1000\n10\n5\n0\n-5\n-10\nTruthjetenergy(GeV)\n(%)\n(%)\n0.2<|y|<0.4\n2.0 <|y|<2.2\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nFigure 12: The difference in relative energy resolution \u03c8\u03c3 (see Eq.(12)) between seeded cone cluster and\ntower jets, and kT cluster and tower jets, respectively, as function of the matching particle jet energy, and\nin two different regions of jet rapidity y. A negative value for \u03c8\u03c3 indicates a better resolution for cluster\njets.\nwith the test variable \u03c8\u03c3, which uses the fractional difference \u2206\u03c3 in the energy resolution\n\u2206\u03c3 =\n\u0010\u03c3\nE\n\u00112\ncluster \u2212\n\u0010\u03c3\nE\n\u00112\ntower ,\nwith the relative resolutions \u03c3\n\u000e\nE as given in Eq.(8). \u03c8\u03c3 can then be de\ufb01ned as\n\u03c8\u03c3 =\n\u001a\n\u221a\u2206\u03c3\nfor\n\u2206\u03c3 > 0\n\u2212\u221a\u2212\u2206\u03c3\nfor\n\u2206\u03c3 < 0 .\n(12)\nFigure 12 shows the prediction for \u03c8\u03c3 for various jet con\ufb01gurations in two different kinematic regimes\nde\ufb01ned by the jet rapidity. As this variable mainly folds differences in the stochastic and noise contri-\nbution to the jet energy resolution, the effect of noise suppression implicit for cluster jets is particularly\nvisible at low energies and for wider jets, where more calorimeter cells with noise contribute to the tower\njets than in narrow jets. At higher jet energies, the energy resolution contribution introduced by sig-\nnal \ufb02uctuations from electronics noise is signi\ufb01cantly reduced and \u03c8\u03c3 is comparable with zero in both\nkinematic regimes.\nThe relative difference \u03c8\u03c3 can be transformed into an energy-equivalent difference in a straight\nforward manner:\n\u2206\u03c3abs(E) = \u03c8\u03c3(E)\u00b7E .\n(13)\nFigure 13 shows predictions for this difference for the QCD jets discussed here. The general \ufb02at (energy\nindependent) behaviour indicates that the differences between cluster and tower jets indeed are mostly\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n281\n\n50\n100\n150\n200\n250\n300\n350\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\nTruthjetenergy(GeV)\n(GeV)\nabs\n 50 GeV. There are indications that wide jets reconstructed from topological clusters have a lower\nnumber of fakes at low pT, especially in the central region. Also, the kT algorithm seems to generate\nfewer wide jets than the cone algorithm in this region, independent of the calorimeter signal choice.\nThese differences are expected to be much smaller for narrow jets.\n3.6\nJet composition and mass\nThe reconstruction of jet masses and substructure has gained interest at LHC, especially because of the\nexpected production of heavy particles with masses of O(100) GeV and transverse momenta of several\nhundred GeV. These may decay hadronically into very collimated \ufb01nal states. An important standard\nmodel example is the W boson [26]. Other examples include SUSY [27], exited heavy quarks [28], and\nin exotic \ufb01nal states involving extra dimensions [29].\nIn any case, the complete \ufb01nal state of a heavy and boosted particle may be reconstructed into one jet,\nwhich in the example of a fully hadronically decaying top quark actually contains three highly collimated\njets. The mass of the reconstructed jet is then one of the indicators of its origin, in addition to a possible\nsubstructure reconstruction re\ufb02ecting the three \u201cinternal\u201d jets.\nThe reconstruction of the jet mass is inherently dif\ufb01cult from calorimeter signals, as the shower\ndevelopment washes out the directions and energies of individual particles in the jet. In addition, the true\njet mass is of course best reconstructed if all of its original particles can be measured at high precision.\nThe mass reconstruction is thus disturbed by undetected particles, like the ones curling in the solenoidal\nmagnetic \ufb01eld in the inner detector cavity of ATLAS, and the ones losing too much energy in upstream\ninactive material to generate a signal above threshold in the calorimeters.\nFigure 19 shows the expected composition of kT jets with R = 0.6 built from particles, towers, and\nclusters in three different rapidity regions. The number of constituents shown in this \ufb01gure is of course\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n285\n\n0\n1\n-2\n50\n60\n80\n100\n10\n100\n1000\n10\n100\n1000\nTruthjettransversemomentum (GeV)\n(%)\n(%)\n70\n90\n-1\n2\n3\n4\n5\n6\n7\nkT\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nR\n=04\ncone\nR\n=07\ncone\nR\n=04\ncone\nR\n=07\ncone\nR=04\nR=06\nR=04\nR=06\nFigure 16: The calorimeter jet reconstruction ef\ufb01ciency \u03b5 in ATLAS, calculated from simulations using\nEq.(9), for seeded cone tower jets with Rcone = 0.7 and Rcone = 0.4, as function of the truth particle jet\npT, in 0.2 < |y| < 0.4 (top left). The plot on the top right shows predictions for wide (R = 0.6) and\nnarrow (R = 0.4) kT tower jet reconstruction ef\ufb01ciencies in the same kinematic regime. The difference\nin ef\ufb01ciency between cluster and tower jets, de\ufb01ned as \u2206\u03b5 = \u03b5cluster \u2212\u03b5tower, is shown in the lower left\nplot for cone and in the lower right plot for kT jets.\n0\n1\n-2\n50\n60\n80\n100\n10\n100\n1000\n10\n100\n1000\nTruthjettransversemomentum (GeV)\n(%)\n(%)\n70\n90\n-1\n2\n3\n4\n5\n6\n7\nkT\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nR\n=04\ncone\nR\n=07\ncone\nR\n=04\ncone\nR\n=07\ncone\nR=04\nR=06\nR=04\nR=06\nFigure 17: Predictions for the calorimeter jet reconstruction ef\ufb01ciency in ATLAS for wide and narrow\nseeded cone (top left) and kT (top right) tower jets with 2.0 < |y| < 2.2, shown together with correspond-\ning differences in ef\ufb01ciency between cluster and tower jets (bottom plots), again as function of the truth\nparticle jet pT (see caption of Fig. 16 for more details).\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n286\n\n0\n-5\n50\n60\n80\n100\n10\n100\nTruthjettransverseMomentum (GeV)\n(%)\n(%)\n70\n90\nkT\n50\n5\n10\n15\n20\n25\n10\n100\n50\n500\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nR\n=04\ncone\nR\n=07\ncone\nR\n=04\ncone\nR\n=07\ncone\nR=04\nR=06\nR=04\nR=06\nFigure 18: Jet reconstruction ef\ufb01ciencies \u03b5 as function of the truth particle jet pT, for wide and narrow\nseeded cone and kT tower jets in ATLAS (top), estimated with simulations of QCD dijet processes, in the\njet rapidity range 3.7 < |y| < 3.9. The corresponding difference in ef\ufb01ciency between cluster and tower\njets is shown in the bottom plots. See caption of Fig. 16 for more details.\ndepending on the calorimeter signal choice, i.e. towers or clusters. The variation in the number of clusters\nbetween the rapidity regions re\ufb02ects the changing spatial resolution power of the calorimeter with respect\nto resolving individual showers inside a jet. The observation that the number of particles inside jets seems\nto drop at highest pT indicates a change in the origin of the jets. Most jets at lower pT in the studied QCD\nsample are gluon jets, while for higher pT a signi\ufb01cant fraction of jets is produced by quarks. As gluons\nhave a larger probability to radiate off other gluons than quarks have, one can expect more particles\ninside gluon jets, and even more jets in the \ufb01nal state in case of gluons.\nThe relative sensitivity of the jet mass reconstruction to low signal contributions has been studied\nfor cluster, tower and particle jets with QCD dijet simulations. The relative change in the jet mass if pT\nthresholds are applied to the constituents, is de\ufb01ned as\n\u2206mrel(pmin\nT ) = m(pT > pmin\nT )\nm(pT > 0)\n.\n(14)\nHere m(pT > pmin\nT ) means the jet mass recalculated using only jet constituents with a transverse momen-\ntum above pmin\nT , while m(pT > 0) is the jet mass using all constituents. Figure 20 shows the expectations\nfor the variation of \u2206mrel as a function of the reconstructed m(pT > 0), for different pmin\nT . Especially\nfor high mass jets the cluster jets show a similar behaviour as the particle jets, indicating that clus-\nters are probably better re\ufb02ecting the particle composition in these jets than the tower jets. Note that\npT > 400 MeV is around the threshold for charged particles to reach the calorimeter in the magnetic \ufb01eld\nof the inner detector, and is also close to the general signal threshold for the calorimeters in the central\nregion of ATLAS.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n287\n\nparticles\ntowers\nclusters\nparticles\ntowers\nclusters\nparticles\ntowers\nclusters\n0 < |y| < 0.8\n1.7< |y| < 2.5\n3.7< |y| < 4.2\n10 GeV\n100 GeV\n1000 GeV\n1\n10\n100\n1\n10\n100\n1\n10\n100\n1\n2\n3\n4\nAveragenumberofconstituentsperjet\nlog (p /GeV)\n10\nT\nATLASMC\nATLASMC\nATLASMC\nFigure 19: The average number of constituents of kT jets with R = 0.6 as function of the jet pT, in\nthree different regions of ATLAS, as predicted by simulations of QCD dijet events (\ufb01gure adapted from\nRef. [16]).\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n288\n\nparticle jet\ntower jet\ncluster jet\nparticle jet\ntower jet\ncluster jet\nparticle jet\ntower jet\ncluster jet\np\n= 100MeV\nmin\nT\np\n= 400MeV\nmin\nT\np\n= 1GeV\nmin\nT\n0\n0.5\n1\n1.5\n2\n2.5\n3\nlog (m(p >0)/GeV)\n10\nT\n0\n20\n40\n60\n80\n100\n20\n40\n60\n80\n100\n20\n40\n60\n80\n100\n(%)\nrel\nATLASMC\nFigure 20: The variation of the jet mass re-reconstructed from its constituents with different levels of\nbiases in pT, as function of the least-biased mass using all constituents, for simulated tower, cluster, and\nparticle level jets in QCD dijet events in ATLAS (\ufb01gure adapted from Ref. [16]).\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n289\n\n3.7\nJet substructure\nThe sensitivity in the mass reconstruction observed in Fig. 20 suggests the need for jet variables less\nsensitive to the soft particle contribution and response, yet providing sensitivity to the possible origin of\nthe jet. One of the interesting variables is the characteristic scale yscale for sub-jet splitting in kT jets, i.e.\nthe pT scale at which the n last recombinations of the kT algorithm are undone. It can be de\ufb01ned using\nyn such that\ny2\nscale = p2\nT \u00d7yn .\nFor example, n = 2 means splitting into two sub-jets, identical to undoing the last recombination in the\nkT algorithm. yscale is logarithmically below the jet pT in gluon and quark jets, due to the strongly ordered\n(in kT) QCD evolution, see e.g. Ref. [30]. In case of a strongly boosted W boson decaying into quark\nand anti-quark, on the other hand, yscale is closer to the W mass mW. The left plot in Fig. 21 shows a\nqualitative comparison of the yscale spectrum for jets with masses mjet > 40 GeV in simulated QCD dijet\nprocesses with the one for jets from simulated boosted W boson decays with the same mass cut applied.\n0\n10 20 30 40 50 60 70 80 90 100\ny\n(GeV)\nscale\nArbitraryUnits\nQCD\nWW, :\u013aMM\nATLASMC\nFast Simulation\nFull Simulation\n-50\n-40\n-20\n-30\n-10\n0\n10\n20\n30\n40\n50\nArbitraryunits\n\u00a8y\n(GeV)\nscale\nATLAS MC\nFigure 21: Distributions of the scale variable yscale indicating the threshold for splitting a given jet with\nmass mjet > 40 GeV into two sub-jets, for simulated QCD dijet processes and boosted W bosons decaying\nhadronically (left \ufb01gure). The right \ufb01gure shows predictions of the resolution power for yscale for the\nboosted W bosons. The \ufb01lled area distribution shows the spectrum for \u2206yscale = yscale,reco \u2212yscale,truth\nobtained with fully detailed simulations, while the solid distribution shows the optimistic estimate from\na smeared particle-level calculation. Both distributions are normalized to unity.\nThe resolution power of ATLAS for a measurement of yscale has been studied for splitting into two\njets, i.e.:\nyscale = \u221ay2 \u00d7 pT ,\nwith a sample of simulated highly boosted W decaying hadronically. For these the corresponding yscale\ndistribution approximately peaks at mW/2, as expected, see Fig. 21. The resolution power for yscale can\nbe evaluated by comparing this variable reconstructed from the calorimeter jet with the one from the\nmatching particle level jet. The right plot in Fig. 21 shows the resolution for full simulation and for a\nsmeared particle-level fast simulation. Pending a full scale evaluation in the context of a physics analy-\nsis, the present observation based on the the similarity of both distributions is that the reconstruction of\nyscale does not seem to be too sensitive to details affecting the calorimeter signal, like showering, limited\nacceptance for low energetic particles, and similar. The prediction for the experimental yscale resolu-\ntion from this \ufb01gure is about 12%, while the optimistic simulation based on four-momentum smearing\npredicts about 9%.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n290\n\n4\nForward jet reconstruction and jets in minimum bias events\nThe ATLAS detector provides near hermetic coverage within pseudorapidities of approximately\n\u22124.9 < \u03b7 < 4.9. The forward region is particularly challenging for jet reconstruction, as the jets of\ninterest often have rather low transverse momentum (at high energy) and are thus closer to the \ufb02uctua-\ntions introduced by pile-up at design luminosity at LHC. For example, in a jet cone with Rcone = 0.7 one\nexpects \ufb02uctuations in transverse momentum of the order of 12 GeV [31], meaning that the minimum pT\nwhich can safely be reconstructed is around 40 GeV. The estimates for jet performance in the forward\nregion presented here have been calculated without pile-up, i.e. only electronics noise is folded into the\nreconstructed signals.\nEvents with depleted hadronic activity in the central region of the pp collisions are important signa-\ntures for discoveries, including but not limited to leptonically decaying Higgs bosons produced in vector\nboson fusion (VBF) events, like WW scattering. To reconstruct this signal with signi\ufb01cant ef\ufb01ciency a\ncentral jet veto can be applied. The effectiveness of this veto can be understood from the ef\ufb01ciency to\nreconstruct jets in minimum bias events without hard scattering, and the rate for fake jet reconstruction.\nThis has been studied with simulations for ATLAS and the results are presented in Section 4.2.\n4.1\nForward jets\nRecent studies indicate that the detection of forward going (light quark) jets with pseudorapidities\n2.7 \u2264|\u03b7| \u22644.9 helps to signi\ufb01cantly increase the discovery potential not only for heavy Higgs bosons\n[13], but also for intermediate mass Higgs bosons produced in VBF [32]. This region in the ATLAS de-\ntector features a complex calorimeter geometry in the transition region from the end-cap to the forward\ncalorimeters. This leads to a loss of precision from the changing readout geometries. Some aspects of\nthe performance of the ATLAS detector for these forward jets are discussed in this section.\nThe VBF events have a speci\ufb01c topology in that on average two hard tag jets are produced by the two\nquarks radiated off the vector boson. Figure 22 shows predictions for the jet multiplicity distributions\nin these events, both over the whole detector acceptance (|\u03b7| < 4.9), where most often the two tag jets\nare found, and in the forward direction (2.7 < |\u03b7| < 4.9) only. From this the expectation is in most\nevents only one of the jets is going into the forward direction, at least for the particular Higgs boson\nmass considered here (mH = 120 GeV). This observation is independent of the jet size for seeded cone\nand kT jets.\nThe relative transverse momentum resolution for both forward seeded \ufb01xed cone and kT jets in VBF\nproduced H \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 events is estimated at about 9% for 20 < pT < 120 GeV. Signal linearity is\nexpected to be within \u00b12% for these jets, at least for pT >\u223c30 \u221240 GeV, see Fig. 23. The precision\nachieved in the reconstruction of the jet kinematics for even lower pT, an attempt only realistic in low\nluminosity running at LHC, seems to be limited from this study to \u22485%.\nPredictions for the ef\ufb01ciency and purity of forward jets reconstructed with the seeded cone\n(Rcone = 0.4) \ufb01nder are shown in Fig. 24. Here the indication is that using topological cell clusters\nas calorimeter signals for jet reconstruction makes jet reconstruction more ef\ufb01cient at the likely less rel-\nevant lower end of the jet pT spectrum (pT <\u223c30\u221240 GeV), but generates more fake jets in the same pT\nrange, i.e. has a lower purity in this region for this event sample. As both calorimeter signals reconstruct\nkT jets with basically the same ef\ufb01ciency and purity in the whole kinematic range of interest for these\nVBF events, there is an indication that the splitting of cell signals to \ufb01ll towers, which is predominant in\nthe forward region, generates less seeds than the more integrating cell clustering, where cell signals are\nsummed up rather than split and thus create more likely signal objects above the seed threshold. See also\ntext and Fig. 3 in Section 2.5.1 for tower formation, and Section 2.5.2 for clustering.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n291\n\nMultiplicity\n0\n2\n4\n6\n8\n10\n1\n10\n2\n10\n3\n10\n4\n10\nMultiplicity\n0\n2\n4\n6\n8\n10\nNumberofentries\nforward jet multiplicities\nall jet multiplicities\ncluster jets\nparticle jets\ncluster jets\nparticle jets\nATLASMC\nATLASMC\nFigure 22: Simulated jet multiplicities for seeded cone jets (Rcone = 0.4) with pT > 20 GeV, built from\ntopological cell clusters and generated particles, respectively, in VBF produced Higgs boson events (left).\nThe Higgs boson decays as H \u2192\u03c4\u03c4 \u2192\u00b5\u00b5. The right plot shows the multiplicities of forward going jets\nwith rapidities 2.7 \u2264|y| < 4.9.\n10\nCalorimeterjetp (GeV)\n+2%\n\u20132%\nSeededCone\nR\n=0.7, 2.7<|y|<5.0\ncone\n+2%\n\u20132%\n+2%\n\u20132%\n+2%\n\u20132%\nSeededCone\nR\n=0.4, 2.7<|y|<5.0\ncone\nk\nR = 0.6, 2.7<|y|<5.0\nT\nk\nR = 0.4, 2.7<|y|<5.0\nT\nT\np /p (GeV)\nT\nT\nclusterjets\ntowerjets\nclusterJets\ntowerJets\nclusterjets\ntowerjets\nclusterjets\ntowerjets\n20\n30\n40\n50\n60\n70\n80\n90\n100\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n110\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\np /p (GeV)\nT\nT\nATLASMC\nATLASMC\nATLASMC\nATLASMC\nFigure 23: Relative deviation of reconstructed transverse momentum pT from calorimeter jets and the pT\nfrom the matched particle jet in VBF Higgs boson production, for various jet \ufb01nder con\ufb01gurations and\nthe two calorimeter signal de\ufb01nitions (towers and clusters).\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n292\n\n10\n20\n30\n40\n50\n60\n70\n80\n90 100 110\n10\n20\n30\n40\n50\n60\n70\n80\n90 100 110\n0\n20\n40\n60\n80\n100\n0.1\n1\n10\nTruthjettransversemomentum (GeV)\nCalorimeterjettransversemomentum (GeV)\nFakejetreconstrucrtionratef = 1\u2013\n(%)\nJetreconstructionefficiency\u0130 (%)\ntower\ncluster\ntower\ncluster\nATLASMC\nATLASMC\nFigure 24: Estimated ef\ufb01ciency to reconstruct narrow seeded cone tower and cluster jets (Rcone = 0.4)\ngenerated in VBF Higgs boson production in the forward direction (2.7 < |\u03b7| < 4.9), as function of the\ntruth jet transverse momentum (left). The plot on the right shows the corresponding fake reconstruction\nrate as function of the transverse momentum of the calorimeter jet.\n4.2\nJets in minimum bias events\nSoft underlying physics, as generated by the underlying event in hadron colliders and the multiple soft\ninteractions at high luminosity is an important source of jet production not directly related to the triggered\nhard scattering process of interest. For ef\ufb01cient application of a central jet veto, which is an important\ntool in background suppression in VBF produced Higgs boson events, it is crucial to understand the jet\nrate from soft interactions in this region, and the particular characteristics of these jets. The latter point\nis subject to ongoing studies, but \ufb01rst estimates on the jet multiplicity and rate from simulated single\nminimum bias events are available.\nFigure 25 shows the expected average number of jets in these events as function of the pT threshold\napplied in the \ufb01nal jet selection, for various calorimeter signal de\ufb01nitions and the most commonly used\njet \ufb01nder con\ufb01gurations. The kT jet multiplicity for narrow (R = 0.4) jets is rather independent of the\ncalorimeter signal choice, while for wider jets (R = 0.6) the cluster jets have a lower average multiplicity,\ni.e. are less problematic for a central jet veto. For seeded cone jets, the wider (Rcone = 0.7) tower and\ncluster jets have very similar multiplicities, while here the narrow tower jets (Rcone = 0.4) have a lower\nmultiplicity than the cluster jets.\nPredictions for the probability P\n\u0000Njet \u22651, pT > 20 GeV,\u03b7range\n\u0001\nof reconstructing at least one jet per\nsingle minimum bias event with pT > 20 GeV within a pseudorapidity range of |\u03b7| < \u03b7range is shown in\nFig. 26. Narrow jets from towers and clusters behave rather similarly for both the seeded cone and the kT\nalgorithm. Wider jets are more often found in calorimeter tower jets than in topological cluster jets. In\ngeneral the kT algorithm is less likely to reconstruct wider jets with R = 0.6 than the seeded cone is with\nRcone = 0.7. Here P\n\u0000Njet \u22651, pT > 20 GeV,\u03b7range\n\u0001\nhas been calculated including the occasional jet from\nthe minimum bias (soft or semi-hard) interaction as well as \u201ctrue\u201d fake jets from calorimeter signal \ufb02uc-\ntuations due to noise. Both lead to ef\ufb01ciency losses in an analysis selecting \ufb01nal states with no hadronic\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n293\n\n10\n15\n20\n25\n30\n-2\n10\n-1\n10\n1\n10\n15\n20\n25\n30\nAveragenumberofjets/event\np\nthreshold(GeV)\nT\nSeeded Cone Jets\nR\n=0.7Tower\ncone\nR\n=0.7Cluster\ncone\nR\n=0.4Tower\ncone\nR\n=0.4Cluster\ncone\nk Jets\nT\nR=0.6Tower\nR=0.6Cluster\nR=0.4Tower\nR=0.4Cluster\nATLAS MC\nATLAS MC\nFigure 25: Estimates for the average number of jets per minimum bias event, as function of the pT thresh-\nold applied to the \ufb01nal jet. Shown are results for wide and narrow cluster and tower jets in minimum bias\nsimulations.\n0\n1\n2\n3\n4\n5\nPseudorapidityrange\u0218\nSeeded Cone Jets\nk Jets\nT\nR\n=0.7Tower\ncone\nR\n=0.7Cluster\ncone\nR\n=0.4Tower\ncone\nR\n=0.4Cluster\ncone\nR=0.6Tower\nR=0.6Cluster\nR=0.4Tower\nR=0.4Cluster\n1.4 1.6 1.8\n2\n2.2 2.4\n2.6 2.8\n3\n3.2\n1.4 1.6 1.8\n2\n2.2 2.4\n2.6 2.8\n3\n3.2\nATLAS MC\nATLAS MC\nP(1\n\u0095 1, p >20GeV,\u0218\n\f(%)\njet\nT\nrange\nrange\nFigure 26: Prediction from full simulations for the probability P\n\u0000Njet \u22651, pT > 20 GeV,\u03b7range\n\u0001\nto re-\nconstruct at least one jet with pT > 20 GeV within a pseudorapidity range |\u03b7| < \u03b7range considered for jet\nreconstruction in single minimum bias events, as function of \u03b7range. The jet veto ef\ufb01ciency in the region\n|\u03b7| < \u03b7range can be estimated from these curves as 1\u2212P\n\u0000Njet \u22651, pT > 20 GeV,\u03b7range\n\u0001\n.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n294\n\nactivity in a given region |\u03b7| < \u03b7range. Note that the expectations for the jet veto ef\ufb01ciency discussed\nhere are estimated by 1\u2212P\n\u0000Njet \u22651, pT > 20 GeV,\u03b7range\n\u0001\nunder the assumption that the minimum bias\nevents generate a similar underlying activity as can be expected in signal events. An additional loss of\nsignal events is associated with the multiple soft interactions from pile-up. One expects \u223c25 minimum\nbias interactions per bunch crossing at the design luminosity of L = 1034cm\u22121s\u22121. Experimental effects\nintroduced by the calorimeter readout can increase this number by another factor of 2, giving jet veto ef\ufb01-\nciencies in the order of 95(50)% for narrow jets with pT > 20 GeV at L = 1033cm\u22122s\u22121(1034cm\u22122s\u22121).\nReconstructing jets in minimum bias events can provide important information for the modeling of\nsoft physics and on the underlying event for hard scattering processes if correlation effects are neglected.\nFor example, the pseudorapidity distributions of kT jets with pT > 10 GeV are shown in Fig. 27. Most\njets above threshold are centrally produced with |\u03b7| < 1 and reconstructed with some limited ef\ufb01ciency,\nboth for towers and clusters. The fake rate for jet reconstruction at this pT threshold can be considerable\n(O(30%) in the same central region), but decreases quickly with increasing jet pT, thus likely restricting\nthe accessible experimental phase space to test jet production in soft or semi-hard proton collisions with\nprecision on production rates or cross section.\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\nTruth particle jetpseudorapidity\nTruth particle jetpseudorapidity\n0\n20\n40\n60\n80\n100\n0\n20\n40\n60\n80\n100\n\u0130 (%)\n\u0130 (%)\n0\n1\n2\n3\n4\n5\n0\n1\n2\n0.5\n1.5\nrelative # of jets/(\u00a8\u0218 \u0013 \u0015)\nR = \u0013\u00116\nR = \u0013\u00116\nR = \u0013\u0011\u0017\nR = \u0013\u0011\u0017\nA7/$6 0&\nA7/$6 0&\nA7/$6 0&\nA7/$6 0&\nTRZHU\n3DUWLFOH\n&OXVWHU\nTRZHU\n3DUWLFOH\n&OXVWHU\nTRZHU\n&OXVWHU\nTRZHU\n&OXVWHU\nrelative # of jets/(\u00a8\u0218 \u0013 \u0015)\nFigure 27: The pseudorapidity distribution of jets with pT > 10 GeV in single minimum bias events in\nATLAS (top plots for kT with R = 0.6 and R = 0.4, respectively). The distributions for the calorimeter\njets exclude fake jets, i.e. each reconstructed calorimeter jet is matched with a truth particle jet. The\nef\ufb01ciency for jet reconstruction in these events is shown in the bottom plots.\n5\nConclusions and outlook\nATLAS supports a highly con\ufb01gurable and \ufb02exible jet reconstruction framework, which can easily be\nadapted to accommodate new jet algorithms or signal de\ufb01nitions from the detectors. At the same time,\na default set of con\ufb01gurations for jet \ufb01nding strategies is provided: a seeded \ufb01xed cone algorithm with\nsplit and merge, and the kT algorithm, both with two different parameters controlling the size of the\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n295\n\nreconstructed jet. For the seeded cone, cone radii of Rcone = 0.7 and Rcone = 0.4 are available. Similarly,\nthe default choices for narrow and wide kT jets are distance parameters R = 0.4 and R = 0.6, respectively.\nFor the detector jets, which are reconstructed from projective calorimeter towers or topological cell\nclusters, a calorimeter cell signal weighting based calibration is applied, with calibration weights derived\nfrom simulations with an ideal ATLAS detector geometry model, together with an additional jet energy\nscale correction parametrized in pseudorapidity and transverse momentum.\nPerformance predictions for a slightly misaligned and distorted ATLAS detector system have been\nextracted mostly from PYTHIA generated QCD dijet processes simulated through the detector with\nGEANT4. The emphasis in these studies was to estimate possible deviations from signal linearity and\nuniformity, the deterioration of the relative jet energy resolution, the effect on jet reconstruction ef\ufb01cien-\ncies and the fake jet reconstruction rate for the \ufb01rst collisions, when the inactive material distributions\nand the alignment of detector components may not be well known. The corresponding pre-collision\nphysics data estimates have been derived from Monte Carlo for the default jet con\ufb01gurations for the\ntwo considered calorimeter signal de\ufb01nitions (tower and cluster). A preliminary conclusion from these\nstudies is that the signal linearity can likely be controlled at the level of 2 \u22123%, depending on the de-\ntector region. The effect of the combination of a particular calorimeter signal choice with a given jet\nreconstruction con\ufb01guration has been found to be consistent with expectations, i.e. the noise suppression\nintrinsic to clusters can be observed. In general there are strong indications that the effect of uncertainties\nin the knowledge of the detector geometry only leads to a modest degradation of the jet reconstruction\nperformance.\nSpecial challenges to jet reconstruction in the forward direction or jet vetoes in the central region,\nhave been evaluated and found to be of acceptable performance for physics analyses like vector-boson\nfusion produced Higgs boson events. Pile-up at high LHC luminosities leads to considerable degradation\nespecially of the jet veto ef\ufb01ciency. Due the large uncertainties in the modeling of soft physics under-\nlying and overlapping the pp collisions, a precise quantitative evaluation of this degradation needs to\nbe postponed until experimental minimum bias data and other event topologies become available with\nsuf\ufb01cient data quality and statistics.\nIn preparation for the experimental data ATLAS is now focusing on \u201cdata only\u201d calibration ap-\nproaches using tools like pT balance in prompt photon production and in QCD dijets. Additional efforts\nare concentrating on the subtraction of the pile-up contribution to jets, which can be estimated measuring\nthe (transverse) energy scattered into a given area in pseudorapidity and azimuth in minimum bias events.\nReferences\n[1] ATLAS Collaboration, JINST 3 S08003 (2008).\n[2] Blazey, G.C. et al., Run II jet physics, Preprint hep-ex/0005012v2, 2000.\n[3] Buttar, C. et al., Standard Model Handles and Candles Working Group: Tools and Jets Summary\nReport, Preprint arXiv:0803.0678, 2008.\n[4] Catani, S. and Dokshitzer, Yuri L. and Webber, B. R., Phys. Lett. B285 (1992) 291\u2013299.\n[5] Ellis, Stephen D. and Soper, Davison E., Phys. Rev. D48 (1993) 3160\u20133166.\n[6] Butterworth, J.M., Couchman,J.P., Cox, B.E. and Waugh, B.M., Comput. Phys. Commun. 153\n(2003) 85\u201396.\n[7] Cacciari, M. and Salam, G.P., Phys. Lett. B641 (2006) 57\u201361.\n[8] Dokshitzer, Yuri L. and Leder, G. D. and Moretti, S. and Webber, B. R., JHEP 08 (1997) 001.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n296\n\n[9] Salam, G.P. and Soyez, G., JHEP 05 (2007) 086.\n[10] Salam, G.P., Theoretical aspects of jet \ufb01nding, (talk given at the 4th ATLAS Hadronic Calibration\nWorkshop, March 14-16, 2008, in Tucson, Arizona, USA)\nhttp://indico.cern.ch/conferenceDisplay?confId=26943.\n[11] CDF Collaboration (Acosta, D.E. et al.), Study of jet shapes in inclusive jet production in p \u00afp\ncollisions at \u221as = 1.96 TeV, Preprint hep-ex/0505013, 2005.\n[12] Grigoriev, D.Yu., Jankowski, E. and Tkachov, F.V., Comput. Phys. Commun. 155 (2003) 42\u201364.\n[13] ATLAS Collaboration,\nATLAS Detector and Physics Performance Technical Design Report,\nPreprint CERN/LHCC 99-14/15, 1999.\n[14] ATLAS Collaboration, Electromagnetic Calorimeter Calibration and Performance, in preparation.\n[15] ATLAS Collaboration, Clustering in the ATLAS Calorimeters, note in preparation.\n[16] Ellis, S.D., Huston, J., Hatakeyama, K., Loch, P. and Tonnesmann, M., Prog. Part. Nucl. Phys. 60\n(2008) 484\u2013551.\n[17] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[18] Dishaw, J. P., FERMILAB-THESIS-1979-08 (1979).\n[19] Abt, I. et al., Nucl. Instrum. Meth. A386 (1997) 348\u2013396.\n[20] Buskulic, D. et al., Nucl. Instrum. Meth. A360 (1995) 481\u2013506.\n[21] Lami, S., Bocci, A., Kuhlmann, S.E. and Latino, G., in Calorimetry in high energy physics. Pro-\nceedings, 9th International Conference, CALOR 2000, Annecy, France, October 9-14, 2000, vol-\nume XXI, (Frascati Physics Series, Frascati/Rome, Italy, 2000), Prepared for 9th Conference on\nCalorimetry in High Energy Physics (CALOR 2000), Annecy, France, 9-14 Oct 2000.\n[22] Sjostrand, T., Mrenna, S. and Skands, P., JHEP 05 (2006) 026.\n[23] Agostinelli, S. et al., Nucl. Instrum. Meth. A506 (2003) 250\u2013303.\n[24] Allison, J. et al., IEEE Trans. Nucl. Sci. 53 (2006) 270.\n[25] ATLAS Collaboration, Jet Energy Scale: In-situ Calibration Strategies, this volume.\n[26] Butterworth, J.M., Cox, B.E. and Forshaw, J.R., Phys. Rev. D65 (2002) 096014.\n[27] Butterworth, J.M., Ellis, J.R. and Raklev, A.R., JHEP 05 (2007) 033.\n[28] Holdom, B., JHEP 03 (2007) 063.\n[29] Lillie, B., Randall, L. and Wang, L.-T., JHEP 09 (2007) 074.\n[30] Altarelli, G. and Parisi, G., Nucl. Phys. B126 (1977) 298.\n[31] ATLAS Collaboration (Airapetian, A. et al.), ATLAS calorimeter performance technical design\nreport, CERN-LHCC-96-40, 1996.\n[32] Asai, S. et al., Eur. Phys. J. C32S2 (2004) 19\u201354.\nJETS AND MISSING ET \u2013 JET RECONSTRUCTION PERFORMANCE\n297\n\nDetector Level Jet Corrections\nAbstract\nThe jet energy scale is proven to be an important issue for many different\nphysics analyses. It is the largest systematic uncertainty for the top mass mea-\nsurement at Tevatron, it is one of the largest uncertainties in the inclusive jet\ncross section measurement, whose understanding is the \ufb01rst step towards new\nphysics searches. Finally, it is an important ingredient of many standard model\nanalyses. This note discusses different strategies to correct the jet energy for\ndetector level effects.\n1\nIntroduction\nThe jet calibration process can be seen as a two-step procedure. In the \ufb01rst step, the jet reconstructed\nfrom the calorimeters is corrected to remove all the effects due to the detector itself (nonlinearities due\nto the non-compensating ATLAS calorimeters, the presence of dead material, cracks in the calorimeters\nand tracks bending in/out the jet cone due to the solenoidal magnetic \ufb01eld). This calibrates the jet to the\nparticle level, i.e. to the corresponding jet obtained running the same reconstruction algorithm directly\non the \ufb01nal state Monte Carlo particles. The second step, is the correction of the jet energy back to the\nparton level, which will not be discussed in this section.\nThere are currently several calibration approaches studied in the ATLAS collaboration based on the\ncalorimeter response on the cell level or layer level and either in the context of jets or of clusters.\nThe \ufb01rst part of the section describes a possible approach for the calibration to the particle jet. The\nenergy of the jet is corrected using cell weights. The weights are computed by minimizing the resolution\nof the energy measurement with respect to the particle jet. The performance of the calibration in terms\nof jet linearity and resolution is assessed in a variety of events (QCD dijets, top-pairs and SUSY events).\nThe different structure of these events (different color structure, different underlying event) will manifest\nitself as a variation in the quality of the calibration. This method has been the most widely used so far in\nthe ATLAS collaboration.\nOther methods have also been studied. Here we discuss one alternative global calibration approach,\nwhich makes use of the longitudinal development of the shower to correct for calorimeter non-compen-\nsation. The jet energy is corrected weighting its energy deposits in the longitudinal calorimeter samples.\nAlthough the resolution improvement is smaller with respect to other methods, this method is simple and\nless demanding in terms of agreement between the detector simulation predictions and real data.\nThe second part of this section describes the concept of local hadronic calibration. First clusters are\nreconstructed in the calorimeters with an algorithm to optimize noise suppression and particle separa-\ntion. Shower shapes and other cluster characteristics are then used to classify the clusters as hadronic\nor electromagnetic in nature. The hadronic clusters are subject to a cell weighting procedure to com-\npensate for the different response to hadrons compared to electrons and for energy deposits outside the\ncalorimeter. In contrast to the cell weights mentioned above no minimization is performed and the actual\nvisible and invisible energy deposits in active and inactive calorimeter material as predicted by Monte\nCarlo simulations are used to derive the weights. One of the advantages of this method is that the jet\nreconstruction runs over objects which have the proper scale (in contrast to the global approach, where\nthe scale corrections are applied after the jet is reconstructed from uncorrected objects).\nThe third part of the note describes re\ufb01nements of the jet calibration that can be done using the\ntracker information: the residual dependence of the jet scale on the jet charged fraction can be accounted\nfor improving the jet resolution. An algorithm to correct the b-jet scale in case of semileptonic decays\nwill also be discussed.\n298\n\n2\nThe calibration to the truth jet\nAccording to the perturbative QCD, jets are the manifestations of scattered partons (quarks and gluons).\nAfter undergoing fragmentation, a collimated collection of hadrons emerges and its energy is measured\nin the calorimeter system. In addition to this hard scattering, the \ufb01nal state also contains energy coming\nfrom multiple proton\u2013proton (pile\u2013up) interactions and the underlying event.\nThe typical output of an event generator will provide theoretical predictions about the particle con-\ntent and spectra at this stage, the so called particle level. Jets resulting from the application of a jet\nreconstruction algorithm at the particle level are thus relevant as \u201ctruth\u201d, since they represent the \ufb01nal\nstate jets that ideally must be reconstructed starting from the detector level. In the following we refer to\nthem using the expression \u201ctruth jets\u201d.\nSince jet fragmentation functions are independent of jet energy, the fraction of the total jet energy\ncarried by the different particle types in a jet is basically independent of energy. Figure 1 shows the\nrelative contribution of the different particle types to the jet energy as a function of the jet ET. About\n (TeV)\nT\nJet E\nATLAS\n0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1 6\n1.8\n2.0\nFraction of the total jet energy\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n\u00b1\n\u03b3\n\u03c0\n\u00b1\nK\n0\nK\np\nn\nT\nJet E (TeV) \n0\n0.2\n0.4\n0 6\n0.8 1.0\n1.2\n1.4\n1.6\n1.8\n2.0\ntruth\nE/E\nATLAS\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\njet EM energy\nPreSampler\nEM sample 1\nEM sample 2\nEM sample 3\nHAD sample 1\nHAD sample 2+3\nFigure 1: Left: fractional energy carried by different particle types as a function of the jet energy. Right:\nfraction of true energy deposited in the different calorimeter samplings for a jet in the central (|\u03b7| < 0.7)\ncalorimeter region as a function of its true energy.\n40% of the total energy is carried by charged pions, 25% is carried by photons (mainly coming from the\n\u03c00 decay), another 20% is accounted for by kaons, nearly 10% by protons and neutrons. Therefore, 25%\nof the energy deposits in the calorimeters come directly from pure electromagnetic showers. The right\nplot of Fig. 1 shows the average fractional energy deposit in the different calorimeter samplings with\nrespect to the true jet energy in the central calorimeter regions (|\u03b7| < 0.7). Most of the energy (about\n2/3 of the reconstructed energy) is measured by the electromagnetic calorimeter. The total reconstructed\nenergy differs signi\ufb01cantly from the true jet energy. This is because of a number of detector effects:\n\u2022 if the calorimeters are non-compensating (as in ATLAS), their response to hadrons is lower than\nthat to electrons and photons, and is non-linear with the hadron energy.\n\u2022 part of the energy is lost because of dead material, cracks and gaps in the calorimeters, and is also\nnon-linear with hadron energy.\n\u2022 The solenoidal magnetic \ufb01eld will bend low energy charged particles outside the jet cone.\nThe reconstructed jet energy must be corrected for these effects to obtain the best estimator for true\njet energy.\nIn the following we will discuss two possible strategies. The \ufb01rst one (referred to as global calibra-\ntion) aims to provide calibration coef\ufb01cients at jet level; the second one, the local calibration, provides\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n299\n\ncalibration constants at the jet constituent level. The performance of both the approaches will be dis-\ncussed in detail. Both methods use simulated events to obtain the calibration coef\ufb01cients.\n3\nAn energy density based cell calibration\nThe shower produced by a jet impinging on the calorimeters is composed of an electromagnetic and\na hadronic component. The electromagnetic component is characterized by a compact, highly dense,\nenergy deposit, while the hadronic one is broader and less dense. This fact can be used to correct the\nenergy measurement to recover for the non-linear calorimeter response to the hadrons.\nAfter jet reconstruction using calorimeter cells calibrated at the electromagnetic scale, the total en-\nergy of a jet is reconstructed by summing the energies of its constituent cells multiplied by a weight\nwhich depends on the energy density of the cell itself. We thus de\ufb01ne the EM scale jet energy as:\nEem = \u2211\ni=cells\nEi\n(1)\nwhere Ei is the energy in the cell i for the considered jet. We then de\ufb01ne a jet weighted 4-vector\nE = \u2211\ni=cells\nwiEi\n\u20d7P = \u2211\ni=cells\nwi\u20d7Pi\n(2)\nwhere Ei, \u20d7Pi are the i-th cell energy and momentum (whose direction is de\ufb01ned by the position in the\ncalorimeter and whose magnitude is equal to Ei), and wi are correction factors that need to be determined.\nThey depend on the cell energy density Ei/Vi, where Vi is the volume of the i-th cell.\nIn order to reduce the number of weights to be computed, the following steps are done:\n\u2022 The energy density distributions of the cells are divided into different bins with width increasing\nlogarithmically with the cell energy density.\n\u2022 The calorimeters are subdivided into several regions k. The longitudinal segmentation is partially\nexploited. Broad pseudorapidity bins are also de\ufb01ned. Table 1 shows the de\ufb01ned regions.\n\u2022 The weight in the k-th calorimeter region, in the j-th energy density bin is de\ufb01ned to be:\nw(k,j)\ni\n=\nNp\u22121\n\u2211\nm=0\na(k)\nm logm(E/V)j\n(3)\nwhere Np (the number of parameters used in the \ufb01t) is a number which depends on the region k consid-\nered. The value of log(E/V)j is de\ufb01ned at the lower edge of the j-th bin.\nWith this procedure, the number of independent parameters to be determined is signi\ufb01cantly reduced\n(see Table 1). The pre-sampler and the strip-layer of the EM calorimeter have a single weight, constant\nwith respect to the density of the energy deposits. The last three rows of the table refer to three energy\nterms which are also corrected with a single multiplicative factor: they are the cryostat term, the scin-\ntillator term and the gap term. The cryostat term is computed as the geometrical average of the energy\ndeposited in the back of the electromagnetic barrel and the \ufb01rst layer of the TileCal barrel. It was in fact\nfound in the past [1] that this gives a good estimate of the energy loss in the cryostat. The scintillator and\ngap terms correspond to the energy deposited in the scintillation counters in the region between the Tile\nbarrel and extended barrel [2]. The weights applied to these terms are meant to recover for the presence\nof a large amount of dead material.\nThe parameters have been determined considering QCD dijet events, simulated with PHYTHIA6.4 [3]\nwith the ATLAS settings [4], and the detector simulated using GEANT4. The events have been generated\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n300\n\nTable 1: De\ufb01nition of regions de\ufb01ned for the minimization that determines the cell weights. The third\ncolumn shows the number of parameters used in the minimization.\nRegion name\nLongitudinal Sample\nNumber of parameters NP\nwemb0\nBarrel pre-sampler\n1\nwemb1\nBarrel EM strips\n1\nweme0\nEnd-Cap pre-sampler\n1\nweme1\nEnd-Cap EM strips\n1\nemb0\nBarrel middle and back sample, |\u03b7| < 0.8\n4\nemb1\nBarrel middle and back sample, |\u03b7| > 0.8\n4\neme0\nEndcap middle and back sample, |\u03b7| < 2.5\n4\neme1\nEndcap middle and back sample, |\u03b7| > 2.5\n4\ntil0\nBarrel\n4\ntil1\nExtended Barrel\n4\nhec0\nHadronic End-Cap, |\u03b7| < 2.5\n4\nhec1\nHadronic End-Cap, |\u03b7| > 2.5\n4\nfem\nFCal \ufb01rst layer\n3\nfhad\nFCal second and third layer\n3\ncryo\nCryostat term\n1\nscint\nScintillator term\n1\ngap\nGap term\n1\nTotal\n45\nTable 2: List of the QCD dijet events used to compute the calibration constants listed in the text.\nSample Tag\npT cut\nJ1\n17 GeV < pT < 35 GeV\nJ2\n35 GeV < pT < 70 GeV\nJ3\n70 GeV < pT < 140 GeV\nJ4\n140 GeV < pT < 280 GeV\nJ5\n280 GeV < pT < 560 GeV\nJ6\n560 GeV < pT < 1120 GeV\nJ7\n1120 GeV < pT < 2240 GeV\nJ8\npT > 2240 GeV\nin bins of the partonic pT, as illustrated in Table 2. Approximately 10k events have been used for each\nbin. The jets have been reconstructed using calorimeter towers as input. The jet reconstruction algorithm\nused is a seeded cone algorithm with a seed threshold of ET = 1 GeV, and a cone size Rcone = 0.7.\nJets with a reconstructed axis lying close to the gap region (1.3 < |\u03b7| < 1.5), or to the crack region\n(3.0 < |\u03b7| < 3.5), or in the very forward region (|\u03b7| > 4.4), are excluded from the minimization.\nReconstructed jets are associated to the nearest truth jet (in \u03c6 \u2212\u03b7 space), obtained, as discussed in\nSection 2, running the same reconstruction algorithm on the \ufb01nal state particles from the event generator.\nThe following quantity is minimized using MINUIT:\n\u03c72 = \u2211\ne\n \nE(e) \u2212E(e)\ntruth\nE(e)\ntruth\n!2\n,\n(4)\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n301\n\nwhere the sum runs over the considered events e, E(e) is de\ufb01ned in equation (2) and E(e)\ntruth is the energy\nof the matched truth jet.\nIt should be noted that this approach partially absorbs effects that are not purely calorimetric into the\nweights. In particular, the energy smearing introduced by the central solenoidal magnetic \ufb01eld, which\nbends low pT particles in and out of the jet cone, is not treated separately, but the effect is proven to be\nsmall for the cone Rcone = 0.7 jets used for the minimization.\nIn order to correct for residual non\u2013linearities in the jet response, a further, reconstruction algorithm\ndependent, correction function is introduced. The \ufb01nal 4-vector of a jet is thus de\ufb01ned as\nE\u03b4 = \u03c1\u03b4(ET, \u03b7)E\n\u20d7p\u03b4 = \u03c1\u03b4(ET, \u03b7)\u20d7P\n(5)\nwhere \u03b4 indicates the dependence on the jet reconstruction algorithm and ET and \u03b7 are the transverse\nenergy and the pseudorapidity of the 4-vector p\u00b5. The scale factor \u03c1\u03b4(ET,\u03b7) is obtained \ufb01tting the ratio\nET/ET,truth in 44 bins of \u03b7 as a function of ET with the following function:\nf(ET) =\n3\n\u2211\ni=0\nci logi ET\n(6)\nand, for a given \u03b4 and \u03b7 bin,\n\u03c1 = 1/f.\n(7)\nThe scale factor corrects for the residual non-linearity introduced by the cracks and gaps in the\ncalorimeter and for differences introduced by the use of different reconstruction algorithms, \ufb01nally re-\ncovering the truth jet scale. The size of this \ufb01nal correction is at the level of few percent (up to 5%) in\nthe crack and gap calorimeter region, while it is of the order of 1-2% (depending on the jet algorithm) in\nthe rest of the pT\u2013\u03b7 phase space.\nTherefore, the complete set of calibration parameters for a given reconstruction algorithm includes\nthe cell energy density dependent weights obtained with cone Rcone = 0.7 jets, plus speci\ufb01c scale factors.\n3.1\nResults on dijet events\nAll the jet corrections computed as described in the previous section (scale factor included) have been\napplied to dijet events. The parameters that are considered in order to assess the quality of the calibration\nare the jet linearity, de\ufb01ned as the ratio between the reconstructed jet energy and the corresponding truth\njet energy (as de\ufb01ned in Section 2) and the energy resolution.\nThe matching between the reconstructed jets and the truth jets is done considering their separation in\na \u03b7 \u2212\u03c6 plane, de\ufb01ned as\nRcone =\np\n\u2206\u03c6 2 +\u2206\u03b72\n(8)\nA truth jet is matched with a reconstructed jet if Rcone < 0.2.\nOnce the matching is done, the E \u2212\u03b7 phase space of the truth jets is subdivided into bins. For each\nbin in energy and pseudorapidity, a histogram is \ufb01lled with the ratio between the reconstructed energy and\nthe truth energy Erec/Etruth. The resulting histogram is \ufb01rst \ufb01tted with a gaussian in the whole histogram\nrange. This provides two estimates (\u00b5raw, \u03c3raw) for the mean value and the width of the distribution. The\n\ufb01t is then repeated in the range \u00b5raw \u00b1 2\u03c3raw. This provides the \ufb01nal values (\u00b5, \u03c3) that are used in the\nsummary plots. Two examples of such histograms are shown in Fig. 2 for two different pseudorapidity\nand energy bins.\nFigure 3 shows the dependence of \u27e8Erec/Etruth\u27e9(linearity, in the following) on the truth jet energy\nEtruth for jets reconstructed from calorimeter towers. The plot on the left refers to jets reconstructed with\na cone algorithm with radius of 0.7 while the one on the right is for kT algorithm with R = 0.6 [5].\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n302\n\ntruth\n/E\nrec\nE\nATLAS\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1 8\n0\n500\n1000\n1500\n2000\n2500\nATLAS\ntruth\n/E\nrec\nE\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1 6\n1.8\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nFigure 2:\nTwo example histograms of Erec/Etruth.\nOn the left, the histogram is done for\n88 GeV < Etruth < 107 GeV and |\u03b7| < 0.5, on the right for 158 GeV < Etruth < 191 GeV and\n1.0 < |\u03b7| < 1.5.\nATLAS\n [GeV]\nTruth\n E\n2\n10\n3\n10\nTruth\n/E\nReco\n E\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n<0.50\n\u03b7\nR=0.7 0.00<\n\u2206\n Cone \n<2.00\n\u03b7\nR=0.7 1.50<\n\u2206\n Cone \n [GeV]\nTruth\n E\n2\n10\n3\n10\nATLAS\nTruth\n/E\nReco\n E\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n<0.50\n\u03b7\n R=0.6 0.00<\nT\n K\n<2.00\n\u03b7\n R=0.6 1.50<\nT\n K\nFigure 3: Dependence of the ratio Erec/Etruth on Etruth for jets reconstructed with a cone algorithm with\nRcone = 0.7 and with a kT algorithm with R = 0.6. The black (white) dots refer to jet with |\u03b7| < 0.5\n(1.5 < |\u03b7| < 2). An ideal detector geometry has been used to simulate the events.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n303\n\nThe results show that the linearity is recovered over a wide energy range, both in the central (|\u03b7| < 0.5)\nand in the intermediate (1.5 < |\u03b7| < 2) regions. For the cone algorithm, at low energy (E = 20\u221230GeV),\nthe linearity differs by up to 5% from 1 in the central region. At low energy, there is a 5% residual non\nlinearity, not fully recovered by the parametrization chosen for the scale factor.\nConcerning the intermediate pseudorapidity region, we can see a similar behavior around 100 GeV\n(note that in this region E \u223c100GeV corresponds to ET = E/cosh\u03b7 \u223c35GeV).\nThe linearity plot for the kT algorithm shows a more pronounced deviation from 1 at low energy\n(\u27e8Erec/Etruth\u27e9= 5% at 50GeV, 8% at 30GeV). The linearity is fully recovered above \u223c100GeV in the\ncentral region, \u223c300GeV in the intermediate region.\nThe uniformity of the response over pseudorapidity is also satisfactory. Figure 4 shows the depen-\ndence of the ratio Erec\nT /Etruth\nT\non the pseudorapidity of the matched truth jet for three different transverse\nenergy bins. Again, the left plot refers to cone 0.7 jets, while the right one refers to kT jets with R = 0.6.\nWe can observe that for the lowest considered transverse energy bin, the ratio increases with the pseudo-\nrapidity. This is a consequence of the fact that energy increases with \u03b7 at \ufb01xed ET and that the linearity\nimproves with increasing energy.\nATLAS\nTruth\n\u03b7\n \n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\nTruth\nT\n/E\nReco\nT\n E\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n< 48 GeV\nT\nR=0.7 39 3.5) , the linearity is\noff by 5-6%.\n3.3\nA check of the systematics with real data\nWe applied the method discussed so far to single pions from the ATLAS combined test beam of the year\n2004 [11]. The weights have been computed on events fully simulated with GEANT4 using the test beam\ngeometry.\nPositively charged beams of different energy impinging with an incident angle of 20 degrees on\nthe calorimeters surface have been considered. The beams are composed of pions, protons, positrons\nand muons. Signals from scintillators present upstream and downstream of the calorimeters are used as\nvetoes to reject early showering particles and muons, respectively. To reject the electrons we required an\nenergy deposit in the \ufb01rst two layers of the electromagnetic calorimeter of less than a certain threshold\n(75% - 90% of the beam energy). A fraction of protons equal to that expected for the chosen beam line\nhas been added to the simulated sample.\nThe energy distributions obtained for each energy point at the electromagnetic scale and after the\ncalibration are \ufb01tted with a Gaussian function. The Gaussian mean values (\u27e8E\u27e9) are used to evaluate the\ncalibration procedure.\nIn Fig. 9 (left) the ratios \u27e8E\u27e9/Ebeam are shown as a function of the beam energy. The black dots refer\nto the Monte Carlo at the electromagnetic scale. The black squares refer to the Monte Carlo after the\nweighting. The procedure restores the linearity at the 2% level for the simulation.\nIn the same \ufb01gure the results on the real data are also shown (gray markers). In this case the linearity\nis also restored to within a few percent.\nTo evaluate these differences, we de\ufb01ne the ratio R = \u27e8Edata/EMC\u27e9. Fig. 9 (right) shows the double\nratio RHAD/REM of the points of Fig. 9 (left). This plot is showing the effect of the calibration procedure\non the agreement between data and simulation. The agreement is worse after the application of the\ncalibration procedure by maximum 4%.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n307\n\nBeam Energy (MeV)\n0\n50 100 150 200 250 300 350 400\n3\n10\n\u00d7\nBeam\n/E\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nBeam Energy (MeV)\n0\n50 100 150 200 250 300 350 400\n3\n10\n\u00d7\nEM\n/R\nHAD\nR\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\nATLAS\nATLAS\nFigure 9: On the left: \u27e8E\u27e9/Ebeam for simulated (black points) and real (gray points) data at the EM (dots)\nand calibrated (squares) scales. On the right: Double ratio RHAD/REM.\n3.4\nSummary\nThe tests discussed in this Section are meant to demonstrate the robustness of the jet corrections com-\nputed as discussed at the beginning of the present Section. Summarizing, we can say that the discussed\nstrategy is able to recover the linearity of the jet energy measurement over a wide energy range, invoking\na relatively low number of parameters (of the order of 50) constrained by a \ufb01t on QCD dijet events.\nThe fact that the jet corrections can be applied with success to events generated with different shower-\ning models, with a very different quark-gluon jet ratio and different topologies, gives con\ufb01dence in the\ncorrection strategy as a method to remove the detector effects.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n308\n\n4\nAlternative global calibration methods\nAlthough the discussed calibration scheme is the most widely used at present in the ATLAS collabora-\ntion, it is not the only one that has been investigated.\n4.1\nLongitudinal shower development\nOn average, the early part of a hadron shower is dominated by electromagnetic energy deposited by\nneutral pions and the ratio of visible to invisible energy is large. In the deeper part of the shower this ratio\nbecomes smaller and more of the hadron shower goes undetected. This can be seen in the a quantitative\nstudy that was carried out by the ATLAS TileCal collaboration in the 1996 test-beam [12]. It shows that\nin the \ufb01rst interaction length of the calorimeter approximately 70% of the energy of the hadron shower\nis deposited as visible electromagnetic energy. The fraction falls off with depth in the calorimeter and\nat 6\u03bb only 25% the energy of the hadron shower is deposited as electromagnetic energy. Therefore a\nlongitudinal weighting of energy deposition as a function of depth can provide improved resolution and\nlinearity [13]. Figure 1 (right) shows the fraction of energy deposited by a hadronic jet at different depths\nin the calorimeter. The layers used in this weighting scheme are de\ufb01ned below based on the properties\nand geometry of different calorimeters.\nThe above motivation for longitudinal weighting is based on the average shower behavior. Hadron\nshowers \ufb02uctuate event-by-event and in a jet, the incoming particle type and energy also varies depend-\ning on how the jet fragmentation proceeds. Figure 1 (left) shows the average energy carried by different\nparticle types in a jet. To better account for these differences in shower \ufb02uctuation and electromagnetic\ncontent of a hadronic jet, the longitudinal weighting is performed in bins of the fraction of energy de-\nposited in the LAr calorimeter. Furthermore, the Atlas calorimeter has a signi\ufb01cant variation in geometry\nas a function of pseudo-rapidity and we therefore \ufb01t the parameters in independent bins of jet \u03b7.\nAs shown below, a longitudinal weighting based on the above properties of hadron shower devel-\nopment and jets shows a signi\ufb01cant improvement in jet energy resolution and linearity with respect to\nuncorrected jet energy.\nLongitudinal weighting method\nIn general the choice of energy layers to be weighted are motivated from the following. In the barrel\nLAr calorimeter, the \ufb01rst three depths (presampler, EMB1, EMB2) provide a total of 24X0. This gives\n99% containment for photons with energies up to 140 GeV [14]. For hadronic jets, the energy in these\nlayers is expected to be predominately from neutral pions. The presampler and EMB1 are de\ufb01ned as a\nsingle layer for longitudinal weighting purposes. The weight for this layer is expected to be sensitive to\nenergy losses in the inner detector. EMB2, which has 18X0 is weighted alone. The EMB3 is thin and has\nsmall energy deposit. Therefore the energy in this layer is added to the energy in the \ufb01rst layer of the Tile\ncalorimeter. This allows for simulations to provide an average correction for energy loss in the cryostat.\nDepending on the jet pseudorapidity, a different number of calorimeter layers are used in the \ufb01tting. Up\nto a pseudorapidity of 1.5 the jet energy is \ufb01tted in four layers in the calorimeter de\ufb01ned as follows:\nE0\n=\nEpresampler +EEMB1\nE1\n=\nEEMB2\nE2\n=\nEEMB3 +ETile1\nE3\n=\nETile2 +ETile3 +EHCAL.\nFor a jet \u03b7 between 1.5 and 3.2 the jet is \ufb01tted for two layers in the calorimeter de\ufb01ned as follows.\nE0\n=\nEpresampler +ELArEM1 +ELArEM2\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n309\n\nE1\n=\nELArEM3 +ETile1 +ETile2 +ETile3 +EHCAL +EFCAL\nBeyond \u03b7 of 3.2 up to 4.4 the jet is not divided into calorimeter layer segments and the full jet energy is\n\ufb01tted.\nThe general strategy of deriving weights for different layers is to minimize the function:\nS = \u2211\nn\nh\u0000ERef\nn\n\u2212Erec\nn\n\u00012 +\u03bb\n\u0000ERef\nn\n\u2212Erec\nn\n\u0001i\n(10)\nwith\nErec\nn\n= \u2211\ni\nwiEi\n(11)\nwhere the wi are weights assigned to the elements Ei of a calorimeter layer in a jet. ERef\nn\n, the true energy\nto which we want to calibrate, is de\ufb01ned as the energy of all the MC generated particles contained\nin the cone of the reconstructed jet. The Lagrange multiplier \u03bb constrains the minimization such that\n\u27e8ERef \u2212Erec\u27e9= 0. The minimization is performed separately for jets classi\ufb01ed in bins of eta (44 eta bins\nof size 0.1), three fractional energies ( fem) deposited in the EM calorimeter and two energy bins. The\nfractional energy fem is de\ufb01ned as\nfem = (EPresampler +ELArEM1 +ELArEM2)/Erec.\n(12)\nThree bins in fem are chosen such that each bin has roughly the same statistics. At high energies\nthe three bins are (small: 0.0-0.65), (mid: 0.65-0.75) and (large: 0.75-1.0). At low energies they are\nJet Energy (GeV)\n0\n200\n400\n600\n800\n1000\nLongitudnal Weights\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nem\nSmall f\nLayer0\nLayer1\nLayer2\nLayer3\nJet Energy (GeV)\n0\n200\n400\n600\n800\n1000\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nem\nMid f\nJet Energy (GeV)\n0\n200\n400\n600\n800\n1000\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nem\nATLAS\nLarge f\nFigure 10: The longitudinal weights as a function of jet energy for four layers in three fem bins and for\ncentral jet \u03b7.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n310\n\n(0.0-0.75), (0.75-0.85) and (0.85-1.0). The bin size varies with energy since more energetic jets deposit\nmore energy in the deeper part of the calorimeter. Bins in fem are used only for jets with \u03b7 < 3.2.\nFor each layer, weights are chosen to have the following dependence on the true jet energy:\nw = a+blog(E/ECut),\n(13)\nwhere a and b are the parameters to be determined by minimization. When applying these weights to\njets, the uncorrected jet energy is used instead of the true jet energy. The result is iterated until a stable\nvalue of the corrected jet energy is obtained.\nIn the above equation, ECut is an arbitrary energy chosen according to the following criteria. Since the\nenergy range covered is quite large (25 GeV - 2 TeV) the \ufb01t is performed in two independent energy bins.\nFor |\u03b7| < 1.2, ECut = 300 GeV, for 1.2 < |\u03b7| < 3.2, ECut = 450 and for |\u03b7| > 3.2 it is set to 35\u00b7cosh(\u03b7)\nGeV. By choosing ECut to be the bin boundary one forces the weight to be equal to the value of a at the\nboundary. The energy range below ECut is \ufb01tted with a \ufb01xed value of a. This ensures a smooth behavior\nof weights across ECut and reduces the lower energy \ufb01t from a two parameter to a one parameter \ufb01t. The\nsame smoothness in the behavior of weights across \u03b7 and fem is not strictly imposed in the present \ufb01t,\nalthough the weights do not have strong variation across the bin boundaries.\nThe \ufb01tting procedure was applied to a fully simulated and reconstructed QCD dijet sample. To\nsuppress noise, topological clusters were used. The jet algorithm (cone Rcone = 0.7) is run on calorimeter\ntowers which contain only cells which are included in the reconstructed topological clusters. Half of the\nevents in the sample were used to determine the layer weights. These weights were then applied to the\nother half of the events to determine the effect of the weights on jet energy linearity and resolution.\nFigure 10 shows the behavior of the weights in bins of fem. A common feature in all the weight\ndistributions is a small variation with respect to the jet energy, especially for high energies. This ensures\ninsensitivity to the use of the true jet energy in equation 13. Layer 2, which measures the bulk of the\njet energy has a weight close to 1 when fem is large i.e when the jet is predominantly electromagnetic in\nnature. When fem is large i.e when the jet is predominantly hadronic, the layer 2 weights are around 1.4.\nLayer 1 acquires a generally higher weight due to losses in the inner detector, even though it is within the\nearly part of the jets. Layer 3 and 4 get weights larger than 1 corresponding to jets being predominantly\nhadronic in these layers. Layer 3 gets larger weights than layer 2 since it also corrects for energy lost in\nthe cryostat.\nFigure 11 shows the jet energy scale linearity as a function of jet energy (left). The corrected jet\nenergy scale is linear to about 2% with the largest non-linearity coming from low energies where the\nuncorrected non-linearity is approximately 30%. Figure 11 (right) shows the corresponding linearity as a\nfunction of detector pseudo-rapidity for jets of 1000 GeV in energy. The typical non-uniformity is about\n1%, increasing to about 2% in the region of \u03b7 \u223c3.0. Jet energy resolutions as a function of the jet energy\nscale is shown in Fig. 12 for two different jet eta regions. At high energy the jet resolution approaches\nabout 4%.\nIn terms of jet energy linearity, the longitudinal weighting and H1-style weighting scheme (Section\n3) have comparable performance, although the H1-style weighting scheme shows a slightly better reso-\nlution. This is expected since H1-style weighting uses local cell energy density to discriminate between\nEM and non-EM like energy deposits. In contrast, longitudinal weighting is less sensitive to local energy\n\ufb02uctuations, which may be an advantage in the early data taking period, when the simulation of energy\ndeposition in the calorimeter may not accurately reproduce the data.\n5\nLocal hadron calibration\nIn contrast to the global calibration method just described, where \ufb01rst jets are made from towers or\nclusters on the electromagnetic scale and the calibration is applied after jet-making on cell or sampling\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n311\n\nJet Energy (GeV)\n0\n500\n1000\n1500\n2000\nTruth\n/E\nReco\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n0.0 < Jet Eta < 0.7\nEM\nATLAS\nH1\nSamp\nJet Eta\n0\n1\n2\n3\n4\n5\nTruth\n/E\nReco\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\nJet 1000 GeV\nEM\nH1\nSamp\nATLAS\nFigure 11: Jet energy linearity as a function of jet energy (left), and as a function of jet pseudorapidity\n(right). The points are for jets reconstructed at the electromagnetic scale (EM), for the global weighting\nscheme described here (Samp) and for the H1-style calibration described in the previous Section. The\njets have a cone radius of Rcone = 0.7.\nJet Energy (GeV)\n0\n500\n1000\n1500\n2000\n/E\n\u03c3\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\n0.0 < Jet Eta < 0.7\nEM\nH1\nSamp\nATLAS\n \nJet Energy (GeV)\n0\n500\n1000\n1500\n2000\n/E\n\u03c3\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\n0.7 < Jet Eta < 1.5\nEM\nH1\nSamp\nATLAS\n \nFigure 12: Jet energy resolution for jets with a cone radius of 0.7 for two regions in pseudorapidity.\nThe three sets of point show the resolution at the detector (EM) scale, after H1-style and longitudinal\nweighting.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n312\n\nlevel, the local hadron calibrated jets are made from clusters which are already calibrated to the hadronic\nscale.\n5.1\nTopological clusters\nThe cluster algorithm used is described in detail in Ref. [15]. Clusters grow dynamically around seed\ncells based on noise thresholds and are re-grouped in a second splitter step around local maxima.\nThe aim of the clustering step before the actual jet making is two-fold:\n1. To suppress noise from electronics and pile-up by reducing the number of cells included in the jets\nvia noise-driven clustering thresholds.\n2. To improve the correspondence between clusters and particles. Due to the dynamic nature of the\ncluster growing, individual clusters correspond better to stable particles than towers or cells and\nthe jet constituents can serve to further study the substructure of jets.\nTo illustrate the effect of noise reduction by using topological clusters as input to jets the amount\nof noise at the electromagnetic scale and the number of cells per jet for cone jets with Rcone = 0.7 is\ncompared in Fig. 13 for jets from dijet simulations with towers as input and with topological clusters as\ninput. The noise reduction is a direct consequence of selecting fewer cells with topological clusters. The\neffect is largest for low energetic jets since the size and number of signal clusters becomes small. The\nnumber of cells per jet for tower jets does not depend on the energy since no threshold for the towers is\napplied. Subsequently the noise changes only if a cell included in a tower jet switches to a lower gain.\nFor the displayed energies this effect is visible in the forward region only. For jets from topological\nclusters the noise increases with energy and at transverse energies of 150GeV it is typically a factor of\n2 lower than for a corresponding tower jet except for the very forward region where the signals are so\ndense that the topological clusters again include almost all cells and the noise level reaches that of the\ntower jets.\nFigure 14 shows the correspondence of clusters and stable truth particles in a dijet simulation. The\nsample shown is a PYTHIA QCD dijet sample with the transverse energy of the leading jet between\n140GeV and 280GeV. Roughly 1.6 truth particles correspond to each of the 65\u00b130 clusters for a cut at\n1GeV in transverse energy, but the ratio does not depend on the cut. It is close to the expected ratio of\n\u223c4/3 since about 1/2 of the stable particles in jets are photons from \u03c00-decays, which usually merge to\none cluster.\n|\u03b7\nJet |\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3 5\n4\nJet noise (MeV)\n0\n2000\n4000\n6000\n8000\n10000\n12000\n < 13 GeV \nTower Jets 7 GeV < E\n < 13 GeV \nTopo Jets 7 GeV < E\n < 26 GeV \nTower Jets 14 GeV < E\n < 26 GeV \nTopo Jets 14 GeV < E\n < 65 GeV \nTower Jets 35 GeV < E\n < 65 GeV \nTopo Jets 35 GeV < E\n < 195 GeV \nTower Jets 105 GeV < E\n < 195 GeV \nTopo Jets 105 GeV < E\nATLAS\n|\u03b7\nJet |\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nNumber of Cells per Jet\n2\n10\n3\n10\n4\n10\nTower Jets\n < 13 GeV \nTopo Jets 7 GeV < E\n < 26 GeV \nTopo Jets 14 GeV < E\n < 65 GeV \nTopo Jets 35 GeV < E\n < 195 GeV \nTopo Jets 105 GeV < E\nATLAS\nFigure 13: Noise contents (left) and number of cells per jet (right) of Cone jets with Rcone = 0.7 for\ndifferent energies for towers as input (open symbols) and topological clusters as input (\ufb01lled symbols).\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n313\n\nATLAS\n > 1 GeV\ntruth particle E\nN\n0\n50\n100\n150\n200\n250\n > 1 GeV\ntopo cluster E\nN\n0\n20\n40\n60\n80\n100\n120\n140\n0\n50\n100\n150\n200\n250\n300\n1 cluster corresponds to 1.6 truth particles\nFigure 14:\nNumber of topo clusters with E\u22a5> 1GeV vs. number of stable truth particles with\nE\u22a5> 1GeV from a QCD dijet simulation.\n5.2\nCluster Calibration\nThe local hadron calibration of topological clusters is described in detail in Ref. [16]. The calibration\nstarts by classifying clusters as mainly electromagnetic, hadronic, or unknown depending on cluster\nshape variables, moments derived from the positive cell contents of the cluster and the cluster energy.\nThe classi\ufb01cation is based on predictions from GEANT4 [17, 18] simulations for charged and neutral\npions. The expected phase space population in logarithmic bins of the cluster energy, cluster depth in the\ncalorimeter, and average cell energy density and linear bins in |\u03b7| from neutral and charged pions with\na ratio of 1 : 2 is converted to a classi\ufb01cation weight, re\ufb02ecting the a-priori assumption that 2/3 of the\npions should be charged.\nRoughly 90% of the energy of charged pions is classi\ufb01ed as hadronic by this procedure for all en-\nergies, while for neutral pions 90% of their energy is classi\ufb01ed as electromagnetic on average beyond\n100GeV and the performance drops with the logarithm of the pion energy to about 50% at 10GeV.\nThe ideal fraction of 100% is not reached for the charged pions as sometimes the shower is split into\nmore than one cluster with one of them being predominantly electromagnetic in nature. At low energies\nneutral pion clusters occupy the same phase space as charged pion clusters and the a-priori precedence\nfor charged pions makes the classi\ufb01cation as electromagnetic less likely. This leads to the high fraction\nof neutral pion energy classi\ufb01ed as hadronic at low energies which is still acceptable, since the weights\napplied here are close to 1. Clusters classi\ufb01ed as hadronic receive cell weights derived from detailed\nGEANT4 simulations of charged pions with so-called calibration hits in active and inactive calorimeter\nmaterials, which contain the energy from ionization losses and also from invisible processes, such as\nnuclear excitation, and from escaping particles, such as neutrinos. Cells in individual calorimeter sam-\nplings are treated in 0.2-wide |\u03b7|-bins. The weights are binned logarithmically in cluster energy and cell\nenergy density. A \ufb02at distribution in the logarithm of the particle energy was used to generate the single\npion events.\nOut-of-cluster (OOC) corrections are applied to correct for energy deposits inside the calorimeter but\noutside calorimeter clusters due to the noise thresholds applied during cluster making. These corrections\ndepend on |\u03b7|, cluster energy and the cluster depth in the calorimeter.\nDead material (DM) corrections are applied to compensate for energy deposits in materials outside\nof the calorimeters. For deposits in upstream material like the inner wall of the cryostat the presampler\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n314\n\nsignals are found to be highly correlated with the lost energy and the corrections are derived from the\nsum of calibration hit energies in the upstream regions and the presampler signal.\nThe correction for energy deposited in the outer cryostat wall between the electromagnetic and\nhadronic barrel calorimeters is based on the geometrical mean of the energies in the samplings just\nbefore and just beyond the cryostat wall. Corrections for other energy deposits without clear correlations\nto cluster observables are obtained from lookup tables binned in cluster energy, |\u03b7|, and shower depth.\n5.3\nPerformance for jets\nThe aim in this section is to evaluate the degree of completeness of the local hadron calibration when\napplied to jets. The performance of the local hadronic calibration scheme was evaluated using the dijet\nsamples listed in Table 2 and two methods: by comparison to particle jets as described above in section\n3.1, and by comparison to the calibration hits in the GEANT4 record. Since no truth matching occurs\nin the derivation of the calibration constants genuine jet-level effects are expected to be visible once the\nreconstructed jet is compared to the matching jet made of stable truth particles. The main sources of\nremaining energy corrections are:\nMisclassi\ufb01cation Hadronic energy deposits which are treated as electromagnetic lead to a lower energy\nresponse, while electromagnetic energy deposits wrongly treated as hadronic lead to a higher en-\nergy response. The effect of energy underestimation dominates and is roughly 3% for p\u22a5\u2243150GeV.\nLost Particles Low energetic particles might be bent outside the acceptance cone of the reconstructed\njet or reach the calorimeter inside the acceptance cone but leaving a signal below threshold for the\nclustering. Both effects are estimated to add up to 5% for p\u22a5\u2243150GeV, with 3% stemming from\nlow energy deposits not included in the clusters and 2% from particles bent outside the acceptance\ncone.\nJets formed from topological clusters, calibrated using the local hadronic calibration scheme, were\ncompared to the truth jets as done with the previous calibration methods. Figure 15 shows the linearity\nfor Cone Rcone = 0.7 and kT R = 0.6 dijets for 3 different |\u03b7| regions as a function of the jet energy. The\nperformance in the forward region is especially low because of a scale error of 10% introduced in the\nsimulations1. The forward scale error highlights another strength of the calibration hits \u2013 they can in fact\nreveal that there is a problem in the predicted reconstructed energy. All calibration methods discussed\nin this note would yield an overestimation of the jet energy in the forward region in real data if this\nsimulation problem would not be \ufb01xed in the samples needed to derive the calibration constants.\nIn the other pseudo-rapidity regions the linearity is rising from 80% at 30GeV to over 95% at 1TeV.\nFigure 16 shows the linearity as a function of the true jet |\u03b7| for 4 different jet energies. Dips in the\nlinearity are clearly visible for the transition regions between the calorimeter systems at the gap region\n(1.3 < |\u03b7| < 1.5) and the crack region (3.0 < |\u03b7| < 3.5). For the forward region, the mentioned scale error\nis very clearly visible: the linearity cannot be recovered and the scale is off by 10%. The dependency of\nthe linearity on the jet energies can also be observed in these plots: while the linearity for jets with about\n100GeV can be recovered up to about 90% (85% in the gap region), high energy jets (of about 1TeV)\nshow a linearity of about 95 \u221297% which is compatible with the 3% loss due to misclassi\ufb01cation as\ndiscussed above. Although a simple scale function, such as given in Eq. (5) on the jet level, would restore\nthe linearity and give a comparable performance as the global calibration, our goal is to understand and\ncorrect for these effects in order to recover the linearity instead by correction functions based on the jet\nconstituents.\n1The assumed sampling fraction did not correspond to the actual sampling fraction in the FCal region and thus the assump-\ntion that electromagnetic showers can remain un-scaled leads to an underestimation of the energy.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n315\n\n (GeV)\ntruth\nE\n2\n10\n3\n10\ntruth\n/E\njet\n E\n0 8\n0.85\n0 9\n0.95\n1\n1.05\nATLAS\n < 0.4\n\uf8e6\n\u03b7\n\uf8e6\nC7 LC/MC Jets 0 2 < \n < 2 2\n\uf8e6\n\u03b7\n\uf8e6\nC7 LC/MC Jets 2 < \n < 3.9\n\uf8e6\n\u03b7\n\uf8e6\nC7 LC/MC Jets 3.7 < \n (GeV)\ntruth\nE\n2\n10\n3\n10\ntruth\n/E\njet\n E\n0.75\n0.8\n0 85\n0.9\n0 95\n1\n1 05\nATLAS\n < 0.4\n\uf8e6\n\u03b7\n\uf8e6\nKt6 LC/MC Jets 0.2 < \n < 2.2\n\uf8e6\n\u03b7\n\uf8e6\nKt6 LC/MC Jets 2 < \n < 3.9\n\uf8e6\n\u03b7\n\uf8e6\nKt6 LC/MC Jets 3.7 < \nFigure 15: Linearity for Cone jets with Rcone = 0.7 (left) and Kt jets with R = 0.6 (right), both calibrated\nwith the local hadron calibration method (LC), using truth particle jets (MC) as reference. The linearity\nis shown as a function of the matched truth jet energy.\n|\ntruth\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\ntruth\n/E\njet\n E\n0.75\n0 8\n0.85\n0 9\n0.95\n1\nATLAS\nC7 LC/MC Jets 39 < E < 48 [GeV]\nC7 LC/MC Jets 88 < E < 107 [GeV]\nC7 LC/MC Jets 488 < E < 587 [GeV]\nC7 LC/MC Jets 1020 < E < 1226 [GeV]\n|\ntruth\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\ntruth\n/E\njet\n E\n0.75\n0.8\n0 85\n0.9\n0 95\n1\n1 05\nATLAS\nKt6 LC/MC Jets 39 < E < 48 [GeV]\nKt6 LC/MC Jets 88 < E < 107 [GeV]\nKt6 LC/MC Jets 488 < E < 587 [GeV]\nKt6 LC/MC Jets 1020 < E < 1226 [GeV]\nFigure 16: Linearity for Cone jets with Rcone = 0.7 (left) and Kt jets with R = 0.6 (right), both calibrated\nwith the local hadron calibration method, using truth particle jets as reference. The linearity is shown as\na function of the matched truth jet |\u03b7|.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n316\n\nThe jet energy resolution is shown in Fig. 17 as a function of the true jet energy. Table 4 shows the\nparameterised resolution obtained using this method as a function of energy and rapidity. It\u2019s perfor-\nmance is typically 20% or more above that obtained using the global calibration method. We discuss\nsome possible improvements to the local hadronic calibration method below.\n (GeV)\ntruth\nE\n2\n10\n3\n10\n (%)\njet\n/E\nE\n\u03c3\n \n4\n5\n6\n7\n89\n10\n20\n30\n40\nATLAS\n < 0.5\n\uf8e6\n\u03b7\n\uf8e6\nC7 LC/MC Jets 0 < \n < 2.5\n\uf8e6\n\u03b7\n\uf8e6\nC7 LC/MC Jets 1 5 < \n (GeV)\ntruth\nE\n2\n10\n3\n10\n (%)\njet\n/E\nE\n\u03c3\n \n4\n5\n6\n7\n89\n10\n20\n30\n40\nATLAS\n < 0 5\n\uf8e6\n\u03b7\n\uf8e6\nKt6 LC/MC Jets 0 < \n < 2.5\n\uf8e6\n\u03b7\n\uf8e6\nKt6 LC/MC Jets 1 5 < \nFigure 17: Resolution for Cone jets normalized to the reconstructed jet energy with Rcone = 0.7 (left) and\nKt jets with R = 0.6 (right), both calibrated with the local hadron calibration method, using truth particle\njets as reference. The resolution is shown as a function of the matched truth jet energy.\nTable 4: Resolution as function of Etrue for jet with the local hadron calibration applied.\nReconstruction Algorithm\n0 < |\u03b7| < 0.5\n1.5 < |\u03b7| < 2.0\na (%)\nb (%)\nc (GeV)\na (%)\nb (%)\nc (GeV)\nCone Rcone = 0.7 LC\n78\u00b18\n3.5\u00b10.8\n2.3\u00b10.9\n98\u00b114\n7.7\u00b11.7\n3.3\u00b10.7\nkT R = 0.6 LC\n79\u00b18\n4.7\u00b10.7\n2.4\u00b10.6\n117\u00b115\n9.7\u00b11.9\n1.2\u00b12.3\nA detailed analysis of the performance of the local calibration when applied to jets is also presented\nin Ref. [19], where different local calibration approaches are compared to the performance of the H1\nglobal calibration.\n5.4\nFurther Improvement\nAs seen in the previous section several jet-level corrections need to be applied in order to bring jets made\nof local hadron calibrated topological clusters to the truth particle scale. However, the global method is\nseen to exhibit somewhat superior performance indicating that further improvements should be possible\nsince both methods use shower development as their fundamental basis.\nFigure 18 (left) shows the ratio of the corrected energy as obtained from the reconstructed calorimeter\ncells to the energy obtained from the GEANT4 calibration hits in the clusters and in dead material. A\nsigni\ufb01cant de\ufb01cit is seen at low energy. Figure 18 (right) shows the ratio of the the energy obtained\nfrom the GEANT4 calibration hits in the clusters and in dead material to the energy of the nearest truth\nparticle jet. In this case we see roughly unity at high energy and only a 10% de\ufb01cit at low energy. Since\nthis comparison is to the truth particle jet, we attribute this de\ufb01cit to out of cone energy. We therefore\nconclude that the dominant effects on the non-linearity at low energies seen in Fig. 18 stem from particles\nlost in the dead material upstream of the calorimeters. These low energy pions deposit most of their\nenergy in upstream materials and often do not leave a suf\ufb01ciently large signal in the calorimeters to\ncause a cluster to be formed. At present, no good observable on the local cluster level aids in recovering\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n317\n\n (GeV)\ntruth\nE\n2\n10\n3\n10\nin-cluster truth + DM truth\n/E\nweighted + DM corrected\n E\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\nATLAS\n < 0.4\n\uf8e6\n\u03b7\n\uf8e6\nC7 0 2 < \n < 2.2\n\uf8e6\n\u03b7\n\uf8e6\nC7 2 0 < \n < 3.9\n\uf8e6\n\u03b7\n\uf8e6\nC7 3.7 < \n (GeV)\ntruth\nE\n2\n10\n3\n10\ntruth\n/E\nin-cluster truth + DM truth\n E\n0 85\n0.9\n0 95\n1\n1 05\nATLAS\n < 0.4\n\uf8e6\n\u03b7\n\uf8e6\nC7 0.2 < \n < 2.2\n\uf8e6\n\u03b7\n\uf8e6\nC7 2.0 < \n < 3.9\n\uf8e6\n\u03b7\n\uf8e6\nC7 3.7 < \nFigure 18: Eweighted + DM corrected/Ein cluster truth + DM truth, the reconstructed weighted and\ndead-material corrected energy over the the predicted true energy inside clusters and associated dead\nmaterial regions (left) and Ein cluster truth + DM truth/Etruth, the ratio of the predicted true energy in-\nside clusters and associated dead material regions (the denominator in the left plot) over the energy of the\nmatched truth particle jet (right) as function of the matched truth jet energy for cone jets with Rcone = 0.7.\nthis lost energy and the local calibration method can not account for it. Corrections for these effects are\ncurrently being studied. A scaling function like Eq. (5) which is used in the global method would help\nto restore the linearity in Fig. 15 but would not improve the resolution. The generalization of cluster\nshape variables to the jet level (number of low energetic constituent clusters, energy distribution of the\nconstituent clusters, etc.) might help in order to obtain correction procedures that depend only indirectly\non the used jet algorithm, restore the linearity and improve the resolution. The missing energy content\ncan for example be estimated by extrapolating the actual distribution of constituent cluster energies to\nzero GeV to recover the lost contributions from low energetic particles. The in-situ methods as discussed\nin Ref. [20] can be used to validate the corrections obtained and to possibly compensate residual non-\nlinearities.\n6\nTrack-based improvement in the jet energy resolution\nWe present a track-based method for improving the jet energy resolution in ATLAS. Unlike energy-\ufb02ow\ntechniques reference, information is added to the reconstructed jet, after the global jet energy scale cor-\nrections have been implemented, and the track-based correction is applied based on the fraction of jet\nmomentum carried by charged tracks associated with the jet. Using this correction, a \u223c20% improve-\nment in jet energy resolution at low energy is achieved.\nIn this chapter we describe a technique that uses tracks in jets to extract information from the jet\ntopology and fragmentation in order to improve the jet energy resolution. The approach is conceptually\ndifferent from more traditional energy \ufb02ow methods, where precise track momentum measurements re-\nplace calorimeter clusters. In the proposed technique, tracks are used to correct the response of jets as a\nfunction of the jet particle composition, speci\ufb01cally using the ratio of track to calorimeter transverse mo-\nmentum ( ftrk =\nptracks\nT\npcalorimeter\nT\n). Using ftrk provides an improvement in jet energy resolution without changing\nthe jet energy scale applied during reconstruction.\nIn general, jets are composed primarily of neutral and charged pions. Charged particles leave tracks\nin the detectors, and so one might naively expect that approximately two-thirds of the jet energy will\nbe carried by tracks associated with that jet. Monte Carlo QCD dijet samples show Gaussian ftrk distri-\nbutions centered around 0.66, with small tails extending above 1. The tails are more prominent at low\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n318\n\nenergies and include, for example, jets with a true ftrk near one and one or more tracks with incorrectly\nmeasured momenta.\nThe fractional jet energy resolution,\n\u03c3(preco\nT\n\u2212ptrue\nT )\nptrue\nT\n, is proportional to the width of the jet energy re-\nsponse in bins of transverse energy, normalized to the average jet energy in a bin. If the response of\nthese jets varies signi\ufb01cantly with ftrk, the transverse jet energy resolution will be arti\ufb01cially broadened,\nas shown in Fig. 19. One sees that the total measured transverse jet energy resolution is considerably\nwider than either of the constituents corresponding to jets with different charged particle fractions. By\ncorrecting the jet response as a function of jet pT and ftrk we reduce the overall broadening of the energy\ndistribution and, hence, improve the jet energy resolution.\n (GeV)\nT\nparticle\n - E\nT\njet\nE\n-30\n-20\n-10\n0\n10\n20\n30\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n=5.4 GeV\n\u03c3\nUncorrected \n<0.45\ntrk\n0.35 f 1\ntrk and p2\nT is underestimated resulting in a positive bias on Emiss\nT\n. Similar argument explains a\nnegative Emiss\nT\nbias for \u2206ftrk > 0.\nFigure 23 (right) shows that the Emiss\nT\nscale is properly corrected after applying the track-based re-\nsponse correction to the leading two jets, and the Emiss\nT\nbias has been removed.\n6.4\nConclusions and future studies\nAlthough the corrections in this section were calculated only for cone jets with \u2206R = 0.4, they can be\ntrivially extended to any other jet collection, including kT jets.\nWe introduced a track-based method for correcting the response of jets in ATLAS that provides a\n\u223c20% improvement in jet energy resolution at 50 GeV. The corrections also improve missing energy\ndistributions. These corrections do not require new jet energy scale corrections and can be applied\nafter the standard reconstruction. By systematically adding information from the tracker to jets already\nreconstructed based on calorimeter information, considerable improvements can be made.\nThere are several additions being explored to further improve the jet energy resolution using this\ntechnique and other similar track-based variable methods. This technique will be expanded to correct\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n322\n\n [GeV]\nATLAS\nT,true\n\u03bd\n+\n\u00b5\njet+\np\n0\n100\n200\n300\n400\n500\nT,true\n\u03bd\n+\n\u00b5\njet+\n/p\nT\n\u03bd\np\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nFigure 24: Fraction of pT carried by the neutrino in b jets decaying semileptonically (b \u2192\u00b5X or\nb \u2192c \u2192\u00b5X). The abscissa corresponds to the total transverse component for the jet (all interacting\nparticles except muons), muon and neutrino momenta. We use b jets from QCD dijet samples as de-\nscribed in Section 7.1.\nb-jets in the same way that light quark jets have already been corrected. The radius used for track-\njet association may be adjusted to improve the performance. Track-based response corrections will be\nexpanded to include additional variables such as the fraction of transverse momentum carried by the\nleading track ( f 1\ntrk) and track multiplicity (ntrk).\n7\nJet energy scale corrections to semileptonic b jets\nIn this section, we discuss a possible strategy to correct the b-jet energy in case of semileptonic decays\nof the b quark.\nThe decay of b quarks usually produces a c quark, which subsequently decays to a d quark. The b\nquark decays into a muon and a neutrino \u224810% of the time. As a result, a b jet is accompanied by a\nneutrino and a muon \u224819% of the time and by two neutrinos and two muons \u22481% of the time. These\nneutrinos carry away a fraction of the jet energy, introducing a systematic underestimation of the energy\nof such jets. In this document, we concentrate on b jets that contain only one neutrino inside. The\nneutrino from the semileptonic b jet decay carries over 10% of the total jet pT.\nHowever, these jets can be tagged by the presence of a muon, if the muon is energetic enough to\nreach the Muon Spectrometer. Upon a successful tag, the jet energy scale can be corrected through a\nparameterization of the energy carried by the neutrino. In the following sections, a correction of the jet\nenergy scale as a function of jet and muon pT for semileptonic b jets is presented and validated.\n7.1\nMonte Carlo event selection\nFor the studies in this document, two data samples were used (250 k t\u00aft and the dijet samples described\nin Table 2)\nIn addition, for the present studies, semileptonic b jets were required to be tagged by the soft-b\ntagger [21] and be contained within |\u03b7| < 1.2. The \u03b7 cut is required because the jet response changes for\nhigher \u03b7. Studies in larger \u03b7 regions were not possible due to a lack of statistics. For the dijet sample,\nonly events that had two b jets with \u2206\u03c6 > 1.0 were used. This provides a sample composed mostly of b\u00afb\nevents as well as a few gg events where one of the gluons decays to b\u00afb.\nJETS AND MISSING ET \u2013 DETECTOR LEVEL JET CORRECTIONS\n323\n\n [GeV]\nATLAS\nT,true\n\u03bd\n+\n\u00b5\njet+\np\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nT true\n\u03bd\n+\n\u00b5\njet+\n/p\nT,reco\n\u00b5\njet+\np\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n<0.1\nT,reco\njet\n/p\nT,reco\n\u00b5\n0.05 10 mm) in the jet. Starting with\nthe highest energy, the particle energies are summed up until a fraction x of the jet energy is reached. The\nparticle that pushes this sum over the threshold is the LEJP. Figure 1 shows the mean LEJP energy for a\nvalue of x = 0.95 as a function of the jet energy for central (|\u03b7| < 1.5) and endcap (1.5 < |\u03b7| < 3.2) jets.\nTo reconstruct 95% of the jet energy in the central region we have to measure particle energies down to\n800 MeV. To reconstruct 99% of the jet energy we need to reach energies down to 200 MeV. The energy\nof the highest energy particle in the jet ranges from 10 GeV to 550 GeV.\nAny hadronic calibration scheme is required to be robust over the energy range 200 MeV to 550 GeV\nto ensure the correct jet energies scale. Furthermore a large fraction of particles in jets have energy below\n10 GeV and a large proportion of them are charged pions. Hence it is important to check the hadronic\ncalibration at low particle energies using the E/p method. The robustness of the hadronic calibration, the\nvalidity of the hadronic shower model in Monte Carlo, and the single charged hadron E/p performance\ncan be studied in several data samples which cover different energy ranges. The minimum bias sample\ncan reach down to a momentum of 400 MeV and the remainder of this note deals with studies of E/p in\nthe minimum bias sample.\n2\nStudy of E/p using Minimum Bias events\nAs discussed above, low energy hadrons carry a large portion of the energy in a jet. It is therefore\nimportant to study the E/p performance at low energies to obtain an ultimate calibration of the jet\nenergy scale to 1% precision. In early data, when a precise hadronic calibration will not be available, this\nstudy will be performed using the electromagnetic scale. Subsequently, each step of the local hadronic\n327\n\ncalibration can be cross-checked and improved. These steps include removal of noise via the use of\ntopological clusters, cluster classi\ufb01cation as electromagnetic or hadronic, and calibration of hadronic\nclusters to the local hadronic energy scale.\nMinimum bias samples were used to determine the feasibility of using charged hadrons in the pT\nrange between 1 to 10 GeV to cross-check the single hadron energy scale for topological clusters cali-\nbrated to the local hadronic energy scale [1]. The simulation used for this study replicates data collected\nover only a few days at a trigger bandwidth of 10Hz. A year of data-taking at low luminosity will reduce\nthe statistical uncertainty to less than 1%. The data collected in one year should allow the local hadronic\ncalibration to be checked as a function of both \u03b7 and \u03c6.\nThe calibration of topological clusters calibrated to the local hadronic energy includes corrections\nfor invisible and escaped energy in the hadronic shower as well as energy lost in dead material, such\nas the material of the inner detector. It does not include corrections for energy lost in cells outside the\ncluster (out-of-cluster). In the very low energy regime considered by this study, there are signi\ufb01cant\nenergy losses in dead material and from out-of-cluster effects. Even with cluster calibration, it is not\npossible to completely recover these losses, since many low energy particles do not leave suf\ufb01cient\nenergy in the calorimeter to meet the cluster reconstruction thresholds. As a consequence, we expect\nthe calibrated value of \u27e8E/p\u27e9to be below 1. However, as pT increases, these energy losses diminish\nand therefore \u27e8E/p\u27e9approaches 1. Measuring the E/p distributions for single hadrons can provide a\nway of determining the size of these energy losses in-situ. It can also be directly compared to the single\npion Monte Carlo used to derive the weights and cluster classi\ufb01cation used as part of the local hadronic\ncalibration.\n2.1\nIsolated pions in Minimum Bias events\nTo eliminate fake tracks and ensure an accurate momentum measurement, only tracks satisfying the\nfollowing criteria were considered in this study:\n\u2022 At least one hit in the B Layer of the pixel detector.\n\u2022 No more than one missing hit in the other pixel and SCT layers.\n\u2022 Good quality track \ufb01t satisfying \u03c72/ndof < 1.5.\nApproximately 76% of all reconstructed tracks pass these criteria. The pT range for pions surviving the\ntrack quality constraints is given by the dashed curve in Fig. 2. This shows that minimum bias events can\nJet Energy (GeV)\n0\n500\n1000\n1500\n2000\n2500\n3000\nMean LEJP Energy (x = 95%) (GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\nATLAS\nJet Energy (GeV)\n0\n500\n1000\n1500\n2000\n2500\n3000\nMean LEJP Energy (x = 95%) (GeV)\n0\n5\n10\n15\n20\n25\nATLAS\nFigure 1: Mean LEJP energy (x = 0.95) as a function of the jet energy for jets in central (left) and endcap\n(right) regions. The error bars represent the Full-Width-Half-Maximum of the LEJP energy spectrum.\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n328\n\n [GeV]\nT\nTrack p\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nTracks/0.2\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nATLAS\nFigure 2: Distribution of pT of all tracks (solid line) and selected tracks (dashed line) in minimum bias\nevents, scaled to 1\u00b5b\u22121.\nprovide a source of pions to check the hadronic energy scale from 500 MeV, the nominal lower energy\nrequired for a reconstructed track, up to energies of the order 10 GeV.\nThe pion energy deposited in the calorimeter is found by extrapolating the track direction to the\nsecond sampling layer of the EM calorimeter. From this position a cone is de\ufb01ned, \u2206Rcone = 1.0, and\nthe energy of each charged hadron is calculated as the sum of all topological clusters within this cone. A\ntopological cluster is considered to be inside the cone if its barycenter is within this \u2206Rcone = 1.0 around\nthe extrapolated track position.\nIn minimum bias events, energy from the underlying event inside the region de\ufb01ned by \u2206Rcone con-\nsiderably biases the measured pion energies. Photons originating from the decay of neutral pions are the\npredominant source of background. Charged particles also contribute to the background as the recon-\nstruction ef\ufb01ciency of tracks below 5 GeV can be lower than 80% [2]. Selection criteria were used to\nreduce the contamination from the underlying event. These criteria differ slightly for charged hadrons\nwith pT \u22643 GeV and pT > 3 GeV due to the low multiplicity of higher pT tracks in the event and the\ndifferent hadronic shower shapes in the calorimeter. The selection criteria used to minimise the amount\nof energy from the underlying event are:\n\u2022 Isolated from other tracks by at least \u2206R = 0.4. The track positions were taken at the second layer\nof the EM calorimeter.\n\u2022 The charged hadron must be one of the harder particles in the event.\n\u2013 pT\n\u000e \u2211\nall tracks\npT > 0.1 for pT \u22643 GeV.\n\u2013 pT\n\u000e \u2211\nall tracks\npT > 0.3 for pT > 3 GeV.\n\u2022 The energy in the hadronic calorimeter must be isolated by requiring the energy in the outer region\n0.4 < \u2206Rcone < 1.0 of the cone to be small.\n\u2013 EHAD1.0\u22120.4 < 0.01\u00d7 ptrack for pT \u22643 GeV.\n\u2013 EHAD1.0\u22120.4 < 0.05\u00d7 ptrack for pT > 3 GeV.\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n329\n\nE/p\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\nE/p\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\nE/p\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\nE/p\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nFigure 3: The E/p distributions for pions from minimum bias events before cuts (dotted line), after cuts\n(dark solid line) and for a reference sample of single particles (dashed line) for tracks in the pT range\n0.8 \u22121.2 GeV (top left), 1.6 \u22122.4 GeV (top right), 4 \u22126 GeV (bottom left) and 8 \u221212 GeV (bottom\nright). All distributions are normalised to unity. The negative E/p ratios are a consequence of clusters\nwith negative energy resulting from noise.\nFigure 3 shows the E/p distribution in minimum bias events before and after cuts, and compares it to\nsingle pions. All results shown here and in Section 2.2 are for tracks associated with real pions (studies\nof the impact of non-pion tracks are in progress). These selection criteria approximately halve the shift\nin \u27e8E/p\u27e9caused by other particles in the cone.\nThe shift of \u27e8E/p\u27e9caused by the selection is primarily due to the isolation cut in the hadronic\ncalorimeter. The shift was estimated using the pion from single particle Monte Carlo and was found\nto change \u27e8E/p\u27e9by 0.006 for 1 GeV pions, 0.002 for 2 GeV pions, negligible for 5 GeV pions and 0.001\nfor 10 GeV pions. The remaining background, due to energy from the underlying event, cannot be re-\nmoved with cuts. This is justi\ufb01ed by the absence of isolated charged hadrons in minimum bias events.\n2.2\nData-driven unfolding procedure\nThe remaining background, present inside the region de\ufb01ned by \u2206Rcone, was estimated using a data-\ndriven method described in Ref. [3]. This was then unfolded from the pion E/p distribution. Most of the\nenergy coming from the underlying event is deposited in the electromagnetic calorimeter. Charged pions\nwhich deposit most of their energy in the hadronic calorimeter were therefore selected in order to estimate\nthe energy contamination in the electromagnetic calorimeter. These are labelled as late showering pions.\nThe energy from the underlying event was studied by dividing \u2206Rcone into the following two regions:\n\u2022 A region where very little background energy is deposited, consisting of:\n\u2013 The hadronic calorimeter and\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n330\n\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.05\n0.1\n0.15\n0.2\nATLAS\nFigure 4: The total, (E/p)meas, (left) and underlying event, (E/p)contam, (right) distributions used to\nextract the E/p of isolated charged hadrons in the range 0.8 - 1.2 GeV. Error bars show the statistical\nerror on the distribution before \ufb01tting (solid line).\n\u2013 A core region close to the track:\n* \u2206Rcore = 0.1 for pT \u22643 GeV.\n* \u2206Rcore = 0.05 for pT > 3 GeV.\n\u2022 A ring surrounding the assumed trajectory of the pion through the electromagnetic calorimeter\ncontains energy of the underlying event, Eouter\u2212cone, de\ufb01ned to be \u2206Rcore < \u2206R < 1 in the electro-\nmagnetic calorimeter.\nWe use the energy in the Eouter\u2013cone of late-showering pions to estimate the underlying event energy.\nFor this study we assume that the energy in Eouter\u2013cone for late-showering charged particles is zero as they\nact as minimum ionising particles (mips) in the electromagnetic calorimeter.1\nLate-showering charged pions were identi\ufb01ed by two criteria based on the energy in a narrow cone\nof \u2206R < 0.05 around the track:\n\u2022 Energy in the electromagnetic calorimeter < 0.5\u00d7 ptrack.\n\u2022 Energy in the hadronic calorimeter > 0.5\u00d7 ptrack .\nThe background estimated using late-showering pions is applied to all pions (late and early showering\nones). Figure 4 shows the underlying event energy obtained by this method for tracks in the pT range\n0.8\u22121.2 GeV. The underlying event energy divided by the track momentum is de\ufb01ned as (E/p)contam.\nThe (E/p)meas distributions shown by the solid curves in Fig. 3 are a convolution of the E/p distri-\nbutions for isolated pions, (E/p)iso, and the underlying event energy. By deconvoluting the background\nfrom the measured E/p, we recovered (E/p)iso.\nThe convolution can be written in terms of the number of entries in each bin i in the measured E/p\nhistogram:\n(E/p)meas\ni\n= \u2211\nj\nPij \u00d7(E/p)iso\nj ,\n(1)\nwhere the elements of the matrix Pij represent the probability of background contamination shifting the\nenergy from bin j to bin i.\nEach element of Pij is taken from the energy deposited in Eouter\u2013cone (shown in Fig. 4 for pT = 1 GeV\npions). The matrix elements are de\ufb01ned as Pij = (E/p)contam\n(i\u2212j) , i.e. Pij is given by the ith \u2212jth bin con-\ntent of the normalised histogram in the region Eouter\u2013cone. The probability that each bin contributes to\n1We assumed that the mips penetrating depth was uncorrelated with the background.\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n331\n\nthe (E/p)meas value is given by Pij/det(Pij). The diagonal elements of the normalised matrix give the\nprobability that a measurement is free from contaminating energy.\nThe distribution (E/p)iso is derived by solving the set of linear equations described above via matrix\ninversion. The unfolding method is described in Ref. [4] and Ref. [5]. The background is \ufb01tted with two\nexponential functions: one above zero and one below. The measured E/p is \ufb01tted with an exponential\nfunction below zero, a 7th order polynomial function above zero up to half the maximum height, and an\nexponential function for the high E/p tail. The result of these \ufb01ts for 1 GeV pions is shown in Fig. 4.\nThe \ufb01nal distributions obtained for (E/p)iso are shown in Fig. 5. The subtraction:\n\u27e8E/p\u27e9iso = \u27e8E/p\u27e9meas \u2212\u27e8E/p\u27e9contam\n(2)\nis used to examine the shift caused by any remaining contamination or by the method itself. Results\nare shown in Table 1. The E/p values are consistent with the single particle mean, showing that this\nprocedure is promising. However, larger statistics are required to properly assess the ultimate precision\nof this method.\nWe compared charged hadrons in minimum bias Monte Carlo events of pT = 0.8 \u22121.2 GeV,\n1.6\u22122.4 GeV, 4 \u22126 GeV and 8 \u221212 GeV with single pion samples of 50000 events generated with\npT = 1 GeV, 2 GeV, 5 GeV and 10 GeV. As both minimum bias and single particle simulations are done\nwith the same detector geometry and showering model, the E/p distributions are identical, providing a\nway to test how well we can retrieve the single pion E/p distribution in minimum bias events.\nBoth positive and negative pions were used, and the results were combined to improve the statistical\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nATLAS\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\nE/p\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalised Number of Tracks\n0\n0.05\n0.1\n0.15\n0.2\nATLAS\nFigure 5: E/p distributions obtained from deconvolution for pions in minimum bias events (solid line)\nand single pions (dashed line) for the track momentum ranges 0.8 GeV < pT < 1.2 GeV (top left),\n1.6 GeV < pT < 2.4 GeV (top right), 4 GeV < pT < 6 GeV (bottom left) and 8 GeV < pT < 12 GeV\n(bottom right). The deconvolution also removes the effect of \u2018fake\u2019 clusters in Eouter\u2013cone, reconstructed\nfrom electronics noise.\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n332\n\nTable 1: \u27e8E/p\u27e9for pions at pT = 1, 2, 5 and 10 GeV compared to pions in single particle events.\nPion pT Range\nMinimum Bias\nSingle Particles\n0.8\u22121.2 GeV\n0.429\u00b10.052\n0.449\u00b10.003\n1.6\u22122.4 GeV\n0.622\u00b10.043\n0.609\u00b10.003\n4\u22126 GeV\n0.818\u00b10.015\n0.786\u00b10.002\n8\u221212 GeV\n0.870\u00b10.036\n0.869\u00b10.001\nprecision. Due to limited Monte Carlo statistics, here we bin only in pT . Ultimately, the E/p response\nwill be studied in bins of both energy and pseudorapidity, because the dead material distribution varies\ndramatically across |\u03b7|. In minimum bias events, the mean charged particle multiplicity is relatively \ufb02at\nin \u03b7 for a given pT . Single particle samples are weighted to have the same |\u03b7| distribution as minimum\nbias tracks.\n2.3\nSources of systematic uncertainties\nWe studied a number of effects which biased the E/p distribution. In our study we assumed that all\ncharged hadrons were pions. In minimum bias events, about 75% of all charged particles are pions, with\na small number of kaons and protons. Less than 2% of the tracks are due to heavier hadrons, electrons,\nmuons or are fake. However, the mix of particle types is different for late-showering hadrons. Biases\narising from this different particle mixture were studied by comparing the \u27e8E/p\u27e9calculated using all\ntrack types with the \u27e8E/p\u27e9derived frompion tracks alone. Within the available statistical precision, we\ncan put an upper limit of 10% on the shift. We use the energy in the Eouter\u2013cone of late-showering pions\nto estimate the contaminating energy. For this study we assume that the energy in Eouter\u2013cone for late-\nshowering charged particles is zero as they act as mips through the electromagnetic calorimeter. This\nassumption translates to a shift on \u27e8E/p\u27e9of less than 4%. The energy from the underlying event in the\nhadron calorimeter and in the \u2206Rcore region cannot be measured by this in-situ method. The shift of the\n\u27e8E/p\u27e9due to this background is estimated using single pions and was found to be less than 4%. The\nuncertainty in the energy scale is dominated by the unmeasured contaminating energy and the effect of\nnon-pion tracks. All the above systematic uncertainties are statistically dominated.\n3\nConclusions\nJet fragmentation studies show that low energy hadrons carry a large portion of the energy in a jet. This\nstudy shows that isolated charged hadrons produced in minimum bias events can be used to study the\nE/p performance in the pT range from 1 to 10 GeV to obtain an ultimate calibration of the jet energy\nscale. This sample will provide an in-situ test of the cluster level hadronic calibration down to 1 GeV.\nWithin a year at low luminosity, it will be possible to reduce the statistical uncertainty to less than 1%.\nWith the available Monte Carlo statistics we obtained a statistical uncertainty of 10% at 2 GeV which\ngoes down to 3% at 10 GeV, mostly dominated by the statistics of the late showering pion control sam-\nple. Systematic biases from several sources have been studied. Effects, such as unpredicted detector\ninhomogeneities, will be studied once data are available.\nReferences\n[1] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[2] ATLAS Collaboration, JINST 3 S08003 (2008).\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n333\n\n[3] Lobban, Olga Barbara, (2002), PhD Thesis, FERMILAB-THESIS-2002-45.\n[4] Blobel, V., UNFOLDING METHODS IN HIGH-ENERGY PHYSICS EXPERIMENTS, Lectures\ngiven at 1984 CERN School of Computing, Aiguablava, Spain, September.\n[5] Cowan, G., A survey of unfolding methods for particle physics, Prepared for Conference on Ad-\nvanced Statistical Techniques in Particle Physics, Durham, England, March.\nJETS AND MISSING ET \u2013 E/p PERFORMANCE FOR CHARGED HADRONS\n334\n\nJet Energy Scale: In-situ Calibration Strategies\nAbstract\nThis note outlines procedures for the in-situ determination of the jet energy\nscale and resolution of the ATLAS calorimeters. The jet energy scale is evalu-\nated using energy-balanced processes: \u03b3/Z + jet, dijet, and multijet events. The\njet energy resolution is obtained from dijet events. Generators using leading-\norder multiparton matrix element calculations merged with parton showers\nalong with leading-logarithmic Monte Carlo models are compared. Effects\non the energy-balance due to hadronization effects are also studied.\n1\nIntroduction\nPrecise reconstruction of the jet energy is a fundamental ingredient of many physics analyses at the\nLHC, such as the determination of the top quark mass, the reconstruction of dijet resonances, and the\nmeasurement of the inclusive jet cross-section. Moreover the performance obtained on jet reconstruction\nhas a direct impact on the quality of the measurement of the missing transverse energy which will play a\ndecisive role in many searches for new physics at the LHC.\nThe ultimate goal of the jet energy measurement is, in most cases, the reconstruction of the initial\nparton momentum. On the other hand, the measurement in the ATLAS detector starts from signals\nrecorded in the calorimeter cells which have been calibrated at the electromagnetic (EM) scale. This\nscale is set in test beams and is de\ufb01ned to reproduce correctly the electron energy in the beams.\nA subsequent software jet calibration procedure is performed in two major steps. First, corrections\nare made for detector effects, in particular calorimeter non-compensation, noise, losses in dead material\nand cracks, longitudinal leakage and particle de\ufb02ection in the magnetic \ufb01eld. The procedure is described\nin Ref. [1]. After this step the hadronic scale which provides the jet energy at the particle level is\nobtained, i.e. it should correspond to the jet energy obtained after running the same jet algorithm over all\ntrue momenta of the \ufb01nal state particles in the event. Throughout this note, we will refer to these jets as\n\u201cparticle-level jets\u201d or \u201ctruth jets\u201d. At the second step physics effects, such as clustering, fragmentation,\ninitial and \ufb01nal state radiation (ISR and FSR), underlying event (UE) and pile-up are considered. After\nthat the \ufb01nal scale is reached which corresponds to the energy at the parton level. These effects can\ndepend on the type of interaction, e.g. they can differ for quark and gluon jets, can depend on the parton\nmomentum scales and multiparton interactions, so that an individual study may be necessary for each\ndata analysis involving jets.\nThe validation of the whole jet calibration has to be performed in-situ using suitable physics pro-\ncesses. In the course of in-situ validation (also called in-situ calibration) the systematic uncertainty of\nthe hadronic energy scale is determined, and the \ufb01nal tuning of this scale is possibly performed. Fur-\nthermore, the level of physics effects affecting the \ufb01nal scale is estimated. In addition, the jet energy\nresolution can be determined in-situ.\nThe validation procedure will start with QCD dijet events, which allow us to check the uniformity of\nthe calibration as a function of azimuth \u03c6 and of pseudo-rapidity \u03b7. The uniformity in \u03c6 can be checked\nby studying jet rates; the uniformity in \u03b7 can be validated using pT balance between the jets. The dijet\nevents also open two ways of determining the jet energy resolution.\nAfter a uniform detector response is obtained, the absolute hadronic energy scale will be studied\nusing \u03b3 or Z + jet events, in which the Z boson is reconstructed via the Z \u2192e+e\u2212or \u00b5+\u00b5\u2212decay. The\npT balance between the jet and the boson in such events will be used to relate the hadronic scale of the\njets to the well understood energy of electromagnetic objects.\n335\n\nAt very high jet energies, the statistics of \u03b3/Z + jet events vanishes. After the validation of the absolute\njet energy scale (JES) with these events in a limited pT range, the scale at higher pT will be validated\nusing QCD multijet events by balancing the momentum of the leading jet to the momentum sum of the\nother jets. Alternatively, it can be inferred from the opening angle between the two leading charged\nparticle tracks associated with the jet.\nThese methods are discussed in the present note. Expectations of several Monte Carlo programs\nare compared for various jet algorithms. The statistical and systematic uncertainties of the methods are\nassessed with an emphasis on the \ufb01rst 100pb\u22121 and 1fb\u22121 of ATLAS data. It is important to note that\none missing contribution is the precision with which the Monte Carlo is tuned to and reproduces the data.\nThis, naturally, can only be determined once data are available.\nSeveral related studies are covered in other notes. The determination of JES from the invariant\nmass of the W boson in W \u2192qq decays is covered in Ref. [2]. The study of jet fragmentation and\nof the underlying event using tracks associated with the jets and in the complete event is discussed in\nRef. [3]. The measurement of E/p for isolated charged particle tracks in order to study the response of\nthe calorimeter is considered in [4].\nThis note is organized as follows. First, the Monte Carlo programs used for the present studies are\nbrie\ufb02y described. Then, the standard ATLAS jet reconstruction and calibration procedure is outlined. Af-\nterward, we discuss the basic features of \u03b3 and Z + jet events and of the pT balance calibration technique,\nthe physics effects in\ufb02uencing the calibration procedure, the limitations of the underlying models and\nthe expected systematic and statistical uncertainties of the jet energy scale. Subsequently, we consider\nthe calibration techniques in QCD dijet and multijet events, followed by the methods of determination of\nthe jet energy resolution. A summary is given at the end of the note.\n2\nMonte Carlo event generators\nThe general-purpose Monte Carlo programs HERWIG, PYTHIA and ALPGEN are used here to model the\n\ufb01nal states at the LHC energies. The event generation relies on phenomenological approaches to describe\nthe processes which occur at all levels apart from calculation of the matrix elements. This is done by\nfactorizing the event generation into several stages:\n\u2022 hard subprocess at a \ufb01xed order of perturbation theory,\n\u2022 initial and \ufb01nal state QCD radiation using parton shower models,\n\u2022 multiple parton interactions (MI) contributing to the underlying event (UE),\n\u2022 hadronization (fragmentation).\nPYTHIA and HERWIG include leading order (2 \u21922) matrix elements for generating \u03b3/Z + jet and QCD\ndijet events. Higher order QCD effects are modeled using parton showers, which can be insuf\ufb01cient to\ndescribe hard QCD radiation. These effects may signi\ufb01cantly affect the event kinematics and thus spoil\nthe determination of the jet energy scale and resolution. They are checked using ALPGEN which includes\nleading order matrix elements for generating multiparton \ufb01nal states. ALPGEN simulations are also used\nin addition to PYTHIA to study multijet events at very high transverse momenta, where such events\nprovide the main means to determine the jet energy scale.\n2.1\nPYTHIA\nPYTHIA 6.4 [5] is used with the on-shell leading order (LO) matrix element to model the \ufb01nal states.\nHigher-order QCD effects are simulated in the leading-logarithmic approximation with initial- and \ufb01nal-\nstate radiation following the DGLAP evolution [6]. Coherence effects from soft-gluon interference are\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n336\n\nincluded. The underlying event has been tuned to reproduce the CDF data. The parton density functions\n(PDF) CTEQ6ll [7] are used for the proton.\nThe initial-state shower is based on backward evolution to the shower initiators. Initial and \ufb01nal\nstate showers are matched to each other by maximum emission cones. The Lund string fragmentation\nmodel is used to produce the \ufb01nal state hadrons. The string model is based on linear con\ufb01nement, where\n(anti-)quarks or other color (anti-)triplets are located at the ends of the string, and gluons are energy\nmomentum carrying kinks on the string. When the invariant mass of a string piece gets small enough, it\nis identi\ufb01ed as a hadron, thus the whole system eventually evolves into hadrons.\n2.2\nHERWIG\nHERWIG 6.510 [8] is used in conjunction with the underlying event generator JIMMY 4.31 [9]. As with\nPYTHIA, the CTEQ6ll set is used for the proton PDFs. HERWIG uses the parton shower approach for\ninitial and \ufb01nal state QCD radiation, including color coherence effects and azimuthal correlations both\nwithin and between the jets. It includes the angular ordered parton shower algorithm which re-sums\nboth soft and collinear singularities. HERWIG uses the cluster fragmentation model [10, 11], where all\nthe outgoing gluons are \ufb01rst split into quark/anti-quark or diquark/anti-diquark pairs. Then, quarks are\ncombined with their nearest neighbor (in the color \ufb01eld) anti-quark or diquark to form color singlet\nclusters. These clusters have mass and spatial distributions peaked at relatively low values. For large\ncluster masses, the q\u2212distributions fall rapidly and are asymptotically independent of the hard subprocess\nscale. If a cluster is too light to decay into two hadrons, it is allowed to become the lightest hadron of the\nrelevant \ufb02avor. A similar cluster model is also used to model soft and underlying hadronic events.\n2.3\nALPGEN\nALPGEN 2.06 [12] is used with the HERWIG parton shower and the JIMMY underlying event model and\nwith the subsequent HERWIG cluster fragmentation. Similarly to PYTHIA and HERWIG simulations, the\nCTEQ6ll set is used for the proton PDFs. Each \ufb01nal state parton multiplicity is generated individually\nby ALPGEN. A matching using a given scheme between a generated parton with the parton shower is\nperformed in order to avoid double counting of the jet multiplicity. We use the MLM matching scheme.\n3\nJet reconstruction in ATLAS\nSeveral jet collections are built during event reconstruction in ATLAS, varying the input to the jet \ufb01nder\nand the jet \ufb01nding algorithm. The inputs considered for the jet \ufb01nder are \u201ccalorimeter towers\u201d (calo-\ntowers) and \u201ctopological clusters\u201d (topoclusters). In addition, \u201ctruth particles\u201d are used for simulated\nevents. Calorimeter towers are built from all calorimeter cells contained in a region of (d\u03b7 \u00d7d\u03c6) of size\n(0.1\u00d70.1). The initial cell energy is calibrated at the EM scale. Topological clusters are built according\nto criteria that identify signi\ufb01cant energy deposits in topologically connected cells. Three different levels\nof signal signi\ufb01cance are applied to the seed, the neighboring and peripheral cells. Currently, the settings\nof (4,2,0) in units of sigma of noise are used [1].\nThe jet \ufb01nder methods used are cone and kT algorithms. The seeded cone algorithm is used with radii\nof R = 0.4 or 0.7, pT of seeds = 1 GeV, and a split/merge fraction of 0.5. The inclusive kT algorithm\n(fast version) is run with a D parameter of 0.4, 0.6 or 1.0 [3].\nTwo calibration approaches are developed in ATLAS, the \u201cglobal\u201d and the \u201clocal\u201d schemes [1]. The\nglobal scheme uses H1-style weights [1] to correct calorimeter cells after jet \ufb01nding. The weights are\nbased on the energy density in a cell. This calibration is speci\ufb01c to each type of jet \ufb01nder. In the local\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n337\n\nscheme, jets are built from pre-calibrated topoclusters, which already include hadronic calibration, as\nwell as dead material and out-of-cluster corrections. In this note, we report on the \u201dglobal\u201d scheme1.\nFor most of the studies, a minimum transverse momentum pT of at least 10 GeV is required for a jet\nto be considered in the data analysis.\n4\nIn-situ studies using \u03b3/Z + jet events\n4.1\nElectromagnetic \ufb01nal state in \u03b3/Z + jet events\nThe Z boson is observed via its Z \u2192ee or Z \u2192\u00b5\u00b5 decay products. The good lepton identi\ufb01cation\ncapability of the ATLAS detector allows reconstruction of Z decays with very low background [13].\nBefore comparing the jet energy scales in data and in simulation using \u03b3/Z + jet events, basic pT and\n\u03b7 spectra of the vector bosons have to be checked. These spectra are affected mainly by the ef\ufb01ciency\nof photon or lepton identi\ufb01cation, and by the trigger ef\ufb01ciency. In the case of \u03b3 production, signi\ufb01cant\nbackground due to misidenti\ufb01ed jets in QCD dijet events remains despite the rejection power of the\ndetector and of the reconstruction algorithms. The theoretical systematic uncertainties associated with\nthe vector bosons are expected to be small at all levels. The effects on transverse momentum due to\nadditional photon radiation at the hadron level are predicted to be negligible.\n4.2\nUse of pT balance\nIn leading order of perturbation theory the \ufb01nal state of \u03b3/Z + jet events can be considered as a two-\nbody system in which the transverse momentum of the jet pT,jet is exactly balanced by the transverse\nmomentum of the vector boson pT,\u03b3 or pT,Z. The pT balance can thus be de\ufb01ned as\nB1 = pT,jet\npT,\u03b3/Z\n\u22121 .\n(1)\n1The local scheme approach was not yet fully developed when studies reported here were done; this approach will be studied\nand compared to the global scheme in the future.\nFigure 1: Mean jet multiplicity for jets with pT > 10 GeV as a function of pT of the Z boson in Z + jet\nevents.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n338\n\nFigure 2: \u2206\u03c6 between the photon and the jet for a) cone algorithm with R = 0.4, and b) kT algorithm\nwith D = 1.\nHowever in reality, these events contain more than one jet in the \ufb01nal state at parton, particle and detector\nlevel, so that considering only the leading (highest pT) jet is in general too crude an approximation of\nthe event kinematics. This is one of the major issues in this study and requires a detailed understanding\nof jet multiplicities, as well as their pT and angular spectra. The Monte Carlo models will have to be\ntuned to reproduce these jet properties and their energy dependence as observed with the data. A striking\nexample of the current uncertainty in modeling these quantities is shown in Fig. 1, in which the average\nmultiplicity of jets in Z + jet events, generated using PYTHIA and HERWIG, is depicted as a function of\nthe transverse momentum of the Z boson. Cone jets reconstructed with R = 0.7 at the particle level with\npT > 10 GeV in the pseudorapidity range |\u03b7| < 5 are used. HERWIG predicts a larger number of jets than\nPYTHIA mainly due to its mechanism of cluster formation and the assumptions used to model soft and\nunderlying hadronic events. Further extensive studies have been performed in order to understand the\ndifferences in the basic jet distributions at the parton and the particle level for various jet algorithms, and\nto quantify the in\ufb02uence of initial and \ufb01nal state radiation and of the underlying event model.\nA very useful quantity to consider is the azimuthal angular difference \u2206\u03c6 between the boson and\nthe leading jet. It provides information about the event topology and is sensitive to additional physics\neffects, like initial state radiation and \ufb01nal state radiation. Figure 2 shows the \u2206\u03c6 distribution at parton\nand at hadron level for three jet algorithms in \u03b3 + jet events with multiple interactions switched on and\noff, respectively. Although the hadronization effects are apparent for cone jets with R = 0.4, the resulting\nleading jet in most cases is in a back-to-back topology with the photon. In order to reduce the topological\nbias due to additional radiation, the boson and jets in both \u03b3 and Z + jet events are typically required in\nour studies to be back-to-back within \u2206\u03c6 of \u00b10.2.\nIn principle, one can consider two extreme ways of taking the physics effects into account:\n\u2022 Select only those events where the Z or \u03b3 is back-to-back to only one jet in the event. Require\nany other jet to have a small transverse momentum. The jet energy correction factors can then be\ndetermined from the requirement B1 = 0 as a function of energy and pseudorapidity. The strong\nback-to-back cut and the requirement against other jets in the event will severely cut the statistics\nin such an analysis.\n\u2022 The other extreme is to take all jets in the event that pass loose selection cuts and balance the sum\nof their momenta to the Z or \u03b3 momentum. The pT balance can then be de\ufb01ned as\nB\u03a3 = |\u2211jets\u20d7pT|\npT,\u03b3/Z\n\u22121 ,\n(2)\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n339\n\nFigure 3: Left in all rows: the mean value of the \ufb01tted pT balance B\u03a3 as a function of pT,Z in Z + jet\nevents. Particle level jets (squares) and jets reconstructed from detector signals (circles) are shown.\nMiddle in all rows: B\u03a3 distribution for pT,Z \u223c50 GeV for truth jets. Right in all rows: B\u03a3 distribution\nfor pT,Z \u223c50 GeV for reconstructed jets. Upper row: all jets with pT > 1 GeV are taken into account.\nMiddle row: only jets with pT > 10 GeV are used and the requirement |\u03c0 \u2212\u2206\u03c6| < 0.2 is imposed. Lower\nrow: in addition, no further jet with pT > 10 GeV is allowed.\nThis approach should be less sensitive to issues related to physics modeling. However, it is more\ndif\ufb01cult in this case to relate directly the measured balance to the energy scales of speci\ufb01c jets.\nAny kinematic selection cut will affect the global pT balance between the boson and the hadronic\nsystem. This is illustrated in Fig. 3. The central \ufb01gure in the upper row shows the momentum balance B\u03a3\nobtained by summing all particle level jets with pT > 1 GeV for events with pT,Z \u223c50 GeV. The actual\nbalance \ufb02uctuates around a mean value close to zero. The right plot shows the corresponding distribution\nfor reconstructed (H1) jets which is broader due to the detector resolution effects.\nThe left plot shows the pT balance obtained by \ufb01tting a Gaussian to the pT balance distribution in the\nvarious pT,Z bins2. The \ufb01tted mean shows a small negative bias (of the order of 1-3%) which decreases\nwith increasing pT,Z. Adding the pT of neutrinos and muons to that of the jets reduces the bias by about\n1%, so this cannot be the origin of this systematic effect, which is further discussed later on.\nThe effect of selection cuts is studied further, as shown in the middle row of Fig. 3, which presents the\n2Throughout this note we use the mean value of a Gaussian distribution \ufb01tted within a limited sigma range (typically \u00b11\u03c3)\nto characterize the pT balance. We refer to it also as the most probable value.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n340\n\npT balance for particle jets with pT > 10 GeV. In addition, the leading jet is required to be back-to-back\nwith the Z within |\u2206\u03c6| = (\u03c0 \u00b1 0.2). The bias increases and the spread deteriorates after increasing the\npT threshold for jets. The effects are still strong even though the \u2206\u03c6 cut is imposed. They become less\nsigni\ufb01cant as pT,Z increases. The main effect is due to \ufb02uctuations of the fragmentation combined with\nout-of-cone losses and with jet splitting. In addition, residual ISR/FSR contributes signi\ufb01cantly to the\nspread. The underlying event may also contribute particles to the clustered jet. Studies performed with\nPYTHIA \u03b3 + jet events [14, 15] indicate that the underlying event contributes \u223c20 MeV on average to the\ntransverse energy ET at truth particle level in each (\u2206\u03b7 \u00d7\u2206\u03c6) region of (0.1\u00d70.1) which corresponds to\none calorimeter tower. This results in \u223c1 GeV contribution per cone jet with R = 0.4 and \u223c3 GeV per\ncone jet with R = 0.7. The lower row of Fig. 3 shows the same distributions after an additional require-\nment to have no further jet with pT > 10 GeV in the event. The spread of the pT balance distributions is\nreduced. The negative bias is also reduced but remains signi\ufb01cant, especially at low pT,Z values.\nFurthermore, these effects strongly depend on the chosen jet algorithm. In Fig. 4 the pT balance for\nthe leading jet relative to the photon is depicted as a function of photon pT for cone jets with R = 0.4,\nR = 0.7 and for kT jets with D = 1. The jets are reconstructed at the truth particle level and at the parton\nlevel after parton showering in HERWIG \u03b3 + jet events and after applying the \u2206\u03c6 cut. The kT jets on\nparton level reveal an essentially perfect balance, as expected from theory. Cone jets are subject to out-\nof-cone losses due to parton showering. The relative losses increase with decreasing pT, and are bigger\nfor cone jets with smaller radii. They are much larger for particle level cone jets due to the lateral spread\nof the fragmentation. On the contrary, the kT algorithm tends to include particles originating from other\npartons, which leads to a signi\ufb01cant positive bias at low pT.\nA further important issue in the use of the pT balance is the quantity used as a reference to de\ufb01ne the\npT ranges. This is illustrated in Fig. 5 in which PYTHIA \u03b3 + jet events are used which were generated with\na minimum pT of 30 GeV for the hard scattering process. The scatter plot shows the photon pT versus\nthe pT of the parton as produced in the hard interaction. The events are distributed around the diagonal\nas a result of ISR. The cut at the generator stage is visible. If we choose pT,\u03b3 bins to study pT balance\ndistributions (e.g. the set of events with 30 GeV < pT,\u03b3 < 40 GeV contained between the two horizontal\nFigure 4: Mean value of the \ufb01tted pT balance (B1 + 1) as a function of pT,\u03b3 in \u03b3 + jet HERWIG events for\nvarious jet algorithms. The points correspond to particle level and parton level jets.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n341\n\nFigure 5: The pT of the parton versus the pT of the photon as produced in the hard interaction in \u03b3 + jet\nevents.\ndashed lines), we will observe a bias towards lower pT balance values, since in this case we populate\nthe distribution with signi\ufb01cantly more events from the left side of the diagonal than from the right side.\nThe events on the left side are generated on average in interactions with smaller center-of-mass energy,\nhence with higher cross-section. The cross-section decreases quickly with energy and the negative bias\nof the pT balance is signi\ufb01cant3. One should note also that the bias is proportional to the spread around\nthe diagonal. Hence it decreases with pT. It also decreases if one requires the parton and the \u03b3 to be\nback-to-back in azimuth within some \u2206\u03c6 limit, since the ISR spread is then reduced [14]. If we were\nable to select events according to (pT,\u03b3 + pT,parton)/2 (with lines perpendicular to the diagonal), then the\nsymmetry would be restored.\nThis can be seen in Fig. 6. The pT balance B1 for events with 101 < pT < 152 GeV is shown in the\n3Throughout this note, we will generically refer to such bias as \u201cbin migration effect\u201d.\n-\n\u03b3\nT\n/p\nJet\nT\np\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2 0.4 0.6 0.8\n0\n200\n400\n600\n800\n1000\n1200\n1400\nATLAS\nT\nAverage p\nT\nPhoton p\n cut\n\u03c6\n\u2206\n + \nT\nPhoton p\n (GeV)\nT\np\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\n\u03b3\nT\n/p\nJet\nT\np\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\nATLAS\nT\nAverage p\nT\nPhoton p\n cut\n\u03c6\n\u2206\n + \nT\nPhoton p\nFigure 6: Left: pT balance at particle level for events with 101 < pT < 152 GeV. The solid line shows\nthe balance when the pT reference for binning is taken as the average pT of the photon and the jet; the\ntriangles when it is taken as the photon pT. The circles show the balance when the photon pT is used and\nthe photon and the jet are required to be back-to-back within 0.2. Right: the pT dependence of the most\nprobable value of the particle level jet balance for these three cases.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n342\n\nleft panel of the \ufb01gure. The solid line shows the balance when the pT is taken as the average pT of the\nphoton and the jet4 and the triangles when it is taken as the photon pT. The difference in the shape is\nclearly visible with a more pronounced low tail for the pT,\u03b3 reference, because the cross-section favors\nthe case when ISR has reduced the leading jet pT, as discussed above. The circles show the balance with\nthe photon pT reference when the photon and the jet are required to be back-to-back within 0.2 to reduce\nISR. The resulting distribution is indeed more symmetric.\nThe right panel of the \ufb01gure shows the most probable value of the particle level jet balance for these\nthree cases. The effect of varying the quantity used to de\ufb01ne the pT bins can be as large as 3% for low\npT. The \u2206\u03c6 cut helps reducing the effect to the percent level. More details on this issue can be found\nin Ref. [14]. A disadvantage of using the average pT to de\ufb01ne the energy bins is to introduce a coupling\nwith the jet energy scale that one is trying to measure. Hence, we decided to use pT,\u03b3 and pT,Z in the\nbaseline study. The average pT will be used as a cross-check.\nThe above studies show that the level of imbalance is determined in \ufb01rst order by \u201cout-of-cone\u201d losses\nrelated to the jet algorithm under consideration. In addition ISR/FSR and UE in\ufb02uence the measured bal-\nance. ISR/FSR effects can be reduced by suitable cuts like a \u201cback-to-back\u201d requirement. UE can be\nestimated separately by looking at the energy outside jets and can be subtracted, if necessary. The im-\nbalance, depending on the algorithm and on the choice of the reference scale, is up to 5\u221210% at 20 GeV\nand becomes smaller than 1% around 100\u2212200 GeV. A careful tuning of Monte Carlo simulations will\nbe necessary to reproduce and disentangle the effects that cause the residual imbalance.\nIn the following, the speci\ufb01c issues of \u03b3 + jet and Z + jet data analyses are discussed. In particular,\nbackgrounds, event rates and the kinematic reach for each channel are considered.\n4.3\nAnalysis of \u03b3 + jet events\nThe data used in this section are \u03b3 + jet events generated using PYTHIA. They are generated in intervals\nof pT of the hard scattered partons to provide adequate statistical coverage over a wide range of pT. The\nsignal has been generated via the annihilation process q \u00afq \u2192g\u03b3 (ISUB = 15) [5], and the QCD Compton\nprocess qg \u2192q\u03b3 (ISUB = 30). The Compton process dominates over the whole pT range.\nThe main background comes from QCD dijet events, where one of the jets is misidenti\ufb01ed as a\nphoton in the calorimeter. For background estimation, QCD jets are simulated with the same version\nof PYTHIA and similar intervals of pT. Table 1 gives the cross-sections for the various pT intervals for\n\u03b3 + jet and QCD dijet events.\nIn this study, the leading jet pT balance method is used, which consists of \ufb01rst selecting the leading\nphoton in the event and then selecting the leading jet in the opposite hemisphere. The balance is inves-\ntigated at the reconstruction level using full detector simulation. The cone jet algorithm with R = 0.7 is\n4The jet pT is used as an approximation to the parton pT.\nTable 1: \u03b3 + jet and QCD dijet cross-sections for the various pT intervals. The total inelastic\ncross-section is 8\u00d71011 pb.\npT interval\n\u03b3 + jet \u03c3 (pb)\nDijet \u03c3 (pb)\n\u03c3 ratio (Dijet / \u03b3 + jet)\n17 < pT < 35 GeV\n2.61\u00d7105\n1.38\u00d7109\n5.29\u00d7103\n35 < pT < 70 GeV\n2.76\u00d7104\n9.33\u00d7107\n3.38\u00d7103\n70 < pT < 140 GeV\n2.59\u00d7103\n5.88\u00d7106\n2.27\u00d7103\n140 < pT < 280 GeV\n1.99\u00d7102\n3.08\u00d7105\n1.55\u00d7103\n280 < pT < 560 GeV\n1.17\u00d7101\n1.25\u00d7104\n1.07\u00d7103\n560 < pT < 1120 GeV\n4.90\u00d710\u22121\n3.60\u00d7102\n7.35\u00d7102\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n343\n\n (GeV)\n\u03b3\nT\np\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\n\u03b3\nT\n/p\nJet\nT\np\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\nATLAS\n selection\n\u03b3\nDefault \n selection\n\u03b3\nTight \nTruth\nFigure 7: The most probable value of the balance at reconstruction level for cone jets with R = 0.7. Black\nand dots are for default and tight selection, respectively, and the points show the truth level balance. The\nback-to-back \u2206\u03c6 cut is applied.\nused. Only jets with |\u03b7| < 2.5 are considered.\nTwo different photon selections have been considered. The tight photon selection adds isolation\ncriteria in the calorimeter and tracker to provide further jet rejection, as discussed later in this section. A\ncalorimeter isolation criterion is applied on the relative transverse isolation energy in a cone with half-\nopening angle 0.2, requiring that ET(cone)/pT,\u03b3 < 0.05. The track isolation criterion requires that the\nnumber of tracks pointing to any jet around the photon is less than three. Here, track parameters are\nmeasured at the origin. The tight selection maintains a good ef\ufb01ciency of > 60% above 100 GeV while\nit is signi\ufb01cantly reduced at low pT. These tight selection cuts have not been optimized. Their purpose\nin this note is to show that additional purity can be obtained, without too much loss of ef\ufb01ciency, at least\nfor the higher pT range. The photon energy calibration, pT(reconstructed)/pT(truth), has been checked\nand is between 0.995 and 1 over most of the pT range. No photons impinging in the calorimeter crack\nregions with 1.37 < |\u03b7| < 1.52 are used.\nThe average response of jets over the various calorimeter regions was checked and a residual miscal-\nibration of about 1% was found for all pT values. Jets close to the crack regions are not well calibrated,\ntherefore jets with 1.3 < |\u03b7| < 1.8 are excluded from further analysis. Eventually we will rely on dijet\nbalance to correct for such \u03b7-dependent effects in the calibration (see Section 5).\nFigure 7 shows the measured pT balance. The photon pT is used as the reference and the standard\nback-to-back \u2206\u03c6 cut is applied. Table 2 shows the \ufb01tted mean, the statistical uncertainty and the inte-\ngrated luminosity for each pT interval for the tight photon selection. The pT balance above 80 GeV is\n\ufb02attening at the level of -0.02. At low pT the balance with the tight photon selection is a few percent\nbelow the balance measured with the default cuts. The photon reconstruction ef\ufb01ciency is low, and the\nstringent isolation cuts likely bias the sample composition rejecting events with strong ISR or underlying\nevent. The match between the leading reconstructed jet and the leading truth jet is better than 98.5%\nfor jets above 70 GeV; it degrades to 85% for jets above 17 GeV. The reconstruction level pT balance\nis one percent below the truth level pT balance. This is the result of the residual miscalibration of the\njets in the particular release of the ATLAS event reconstruction software, as checked by comparing the\nreconstructed jet pT with the truth particle level jet pT.\nThe PYTHIA QCD jet samples described in Table 1 were used to estimate the in\ufb02uence of the dijet\nbackground. The jet rejection factors for the standard photon selection and the tight photon selection were\nstudied as a function of jet pT. With the default photon selection criteria, the probability of identifying\na jet as the leading photon is of the order of 10\u22123 and has some pT dependence. The resulting signal to\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n344\n\nTable 2: Fitted mean pT balance, error and integrated luminosity of the analysed samples for the\nvarious pT intervals for the tight photon selection. The last column shows the precision expected\nfor 10 pb\u22121 obtained by scaling the error according to recorded integrated luminosity.\npTlow edge\nBin width\nFitted balance\nIntegrated luminosity, pb\u22121\nError for 10 pb\u22121\n20 GeV\n10 GeV\n\u22120.052\u00b10.007\n0.67\n0.2%\n30 GeV\n15 GeV\n\u22120.042\u00b10.005\n0.67\n0.2%\n45 GeV\n22.5 GeV\n\u22120.047\u00b10.005\n9.1\n0.4%\n67.5 GeV\n33.5 GeV\n\u22120.027\u00b10.003\n9.1\n0.4%\n101 GeV\n51 GeV\n\u22120.026\u00b10.003\n47\n0.7%\n152 GeV\n76 GeV\n\u22120.018\u00b10.002\n47\n0.4%\n228 GeV\n114 GeV\n\u22120.016\u00b10.002\n535\n1.7%\n342 GeV\n171 GeV\n\u22120.021\u00b10.005\n535\n4%\n513 GeV\n256 GeV\n\u22120.006\u00b10.026\n535\n19%\nbackground ratio is estimated to be of the order of 1 above 100 GeV and degrades to about 0.1 for lower\npT. The tight photon selection improves the signal to background reduced by a factor of three or more.\nFigure 8 left shows the pT balance distribution for QCD background events passing the default photon\nselection in the interval 140 < pT,\u03b3 < 280 GeV. The back-to-back \u2206\u03c6 cut has been applied. The \ufb01tted\nmost probable value of the distribution with the default photon selection and the \u2206\u03c6 cut is 0.13. Applying\nthe tight selection reduces the number of background events, but a few events still remain in the tail. It\nwill thus be desirable to maintain a good signal to background ratio to avoid a bias that would be dif\ufb01cult\nto control. For the tight photon selection, the mean of the Gaussian \ufb01t to the signal shown in Fig. 8 (right)\nfor the interval 140 < pT,\u03b3 < 280 GeV changes by less than 1% when the background is added in.\nThus, the background studies have shown that above \u223c80 GeV, the signal to background ratio is\ngood enough to avoid bias. A more detailed and higher statistics study of the background rejection at\nlower pT should be carried out, to understand if the range of high precision could be extended to lower\npT.\nTable 2 shows that a good statistical precision is obtained for a relatively small integrated lu-\nminosity.\nFor example, 100 pb\u22121 is suf\ufb01cient to reach a precision of 1 \u22122% for jets in the range\n-1\n\u03b3\nT\n/p\nJet\nT\np\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n0\n5000\n10000\n15000\n20000\n25000\n30000\nATLAS\n selection\n\u03b3\nDefault \n selection\n\u03b3\nTight \n-1\n\u03b3\nT\n/p\nJet\nT\np\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n0\n2000\n4000\n6000\n8000\n10000\n12000\nATLAS\n + jet\n\u03b3\nDijet\nFigure 8: Left: pT balance for the background sample of 140 < pT < 280 GeV for the default and\ntight photon selection.\nRight:\npT balance for the signal and background sample in the interval\n96 < pT,\u03b3 < 224 GeV for tight photon selection.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n345\n\n300 < ET < 500 GeV. We expect that the threshold of the un-prescaled photon trigger will be 60 GeV\nfor early running. Hence above that value the full statistics should be recorded while prescale factors\nwill have to be applied for lower pT.\n4.4\nAnalysis of Z + jet events\nA sample of inclusive Z boson events corresponding to an integrated luminosity of 500 pb\u22121 has been\nproduced using ALPGEN. The MLM matching cut is imposed at pT > 20 GeV and |\u03b7| < 6, and the\nfactorization scale is set at m2\nZ + p2\nT,Z where mZ is the Z boson mass. The invariant mass is required\nto lie between 40 and 200 GeV. A generator-level \ufb01lter requires one truth cone jet with R = 0.4, with\npT > 20 GeV and |\u03b7| < 5.0 and two electrons/muons with pT > 10 GeV and |\u03b7| < 2.7 in the event.\nAnother sample of inclusive Z events corresponding to 120 pb\u22121 , as well as the relevant background\nsamples have been generated using PYTHIA. The signal has been generated via the Drell-Yan process\n(ISUB = 1) [5]. As for \u03b3 + jet events, the qg Compton process dominates over the whole pT range. The\nDrell-Yan process contributes due to higher order QCD radiation which may reproduce the leading jet.\nThe Z \u2192ee and W \u2192e\u03bd\nevents are produced with a generator-level \ufb01lter requiring one truth\nelectron with pT > 10 GeV and |\u03b7| < 2.7. The Z \u2192\u03c4\u03c4 events are generated with a \ufb01lter requiring two\nelectrons/muons with pT > 5 GeV and |\u03b7| < 2.8. For Z \u2192\u03c4\u03c4 and Z \u2192ee the dilepton mass is required\nto be larger than 60 GeV. For more details on the data samples see Ref. [16].\nThe fully simulated events are required to pass the isolated single-electron trigger with a pT threshold\nof 25 GeV or the isolated di-electron trigger with the pT threshold of 15 GeV at trigger level 1 and 2.\nElectrons are required to have pT > 25 GeV, |\u03b7| < 2.5 and to be outside the calorimeter cracks de\ufb01ned\nas 1.37 < |\u03b7| < 1.52. Jets are reconstructed with the cone tower algorithm with R = 0.7. They are\nrequired to have a distance of \u2206R > 0.4 from a reconstructed electron and pT > 30 GeV.\nThe Z bosons are selected by requiring two reconstructed electrons with invariant mass in the range\nmZ \u00b120 GeV. If more than two electrons are reconstructed, the pair with the invariant mass closest to mZ\nis chosen. The combined distribution of the invariant mass for the signal and background events is shown\nin the left panel of Fig. 9 for ALPGEN Z + jet events where jets with pT > 40 GeV are reconstructed using\nthe cone tower algorithm with R = 0.7. The main backgrounds are from QCD multijets and from top\nproduction, while Z \u2192\u03c4\u03c4 and W \u2192e\u03bd events are an order of magnitude smaller. The background\nlevel is reasonably low. Requiring the jet and the Z to be back-to-back in azimuth within 0.2 reduces the\nbackground to a negligible level.\nThe right panel of Fig. 9 shows the measured balance for cone jets with R = 0.7 as predicted by ALP-\nGEN for 500 pb\u22121 . The precision with which the pT balance can be measured experimentally depends\non the ef\ufb01ciency for reconstructing the Z in its electron or muon decay channels, on the trigger ef\ufb01ciency\nand on the experimental width of the pT balance distribution. Table 3 shows the \ufb01tted most probable\nvalue of the pT balance and the statistical precision for an integrated luminosity of 500 pb\u22121 obtained\nwith the Z \u2192ee sample. Below 200 GeV, the precision is of the order of 0.8%, while above 200 GeV,\nit gets worse. The Z \u2192\u00b5\u00b5 decay mode can also be used. A similar ef\ufb01ciency and background level\ncan be achieved as shown in [16] doubling the available statistics. A statistical precision of 1% can be\nachieved below 200 GeV with an integrated luminosity of 100 pb\u22121 , while above the precision is at the\nlevel of 2%. This assumes also that the complete \u03b7 range can be used for the measurement, relying on\ntechniques like dijet balancing to ensure uniformity across \u03b7 to the desired precision.\nThe measurement is also affected by systematic uncertainties. The balance is sensitive to the correct\nmodeling of higher order radiation. Comparing the predictions from different Monte Carlo simulation\nprograms gives an indication of the size of such effects. This is illustrated in Fig. 10, in which ALPGEN\nand PYTHIA samples of Z + jet events corresponding to 120 pb\u22121 and 500 pb\u22121 (ALPGEN only) are\ncompared after applying the \u2206\u03c6 cut, for cone jets with R = 0.7. PYTHIA predicts a more negative average\npT balance at low pT than ALPGEN. This effect is related to broader distributions and larger tails in the\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n346\n\nFigure 9: Left: Distribution of the dielectron mass for Z \u2192ee+ \u22651jet events and the relevant background\nin a simulated event sample corresponding to an integrated luminosity of 200 pb\u22121 with cone jets with\nR = 0.7. Right: The pT balance for an integrated luminosity of 500 pb\u22121 of cone jets with R = 0.7 in\nevents generated with ALPGEN in 5 bins of pT,Z. The red dots are for reconstructed jets, solid triangles\nfor truth jets and open triangles for truth in bins of average pT,Z and jet pT.\nTable 3: The \ufb01tted most probable value of the pT balance and the statistical precision for an\nintegrated luminosity of 500 pb\u22121 obtained with the Z \u2192ee + jets sample for reconstructed cone\njets with R = 0.7 and R = 0.4.\npT interval\ncone 0.7 jet balance\nerror\ncone 0.4 jet balance\nerror\n30 < pT < 40 GeV\n\u22120.032\n0.008\n\u22120.150\n0.007\n40 < pT < 60 GeV\n\u22120.059\n0.007\n\u22120.162\n0.008\n60 < pT < 100 GeV\n\u22120.032\n0.006\n\u22120.113\n0.007\n100 < pT < 200 GeV\n\u22120.027\n0.007\n\u22120.081\n0.008\n200 < pT < 400 GeV\n\u22120.026\n0.014\n\u22120.060\n0.016\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n347\n\nFigure 10: The pT balance for an integrated luminosity of 120pb\u22121 and 500pb\u22121 in events generated with\nALPGEN (dots and triangles, respectively) and for 120pb\u22121 in events generated with PYTHIA (squares)\nin bins of pT,Z for cone jets with R = 0.7.\nbalance distributions resulting from low pT activity in PYTHIA induced by higher order radiation. The\ndifferences between the two generators can be tested with \u223c100 pb\u22121 of data for pT < 100 GeV.\n4.5\nThe missing ET projection method\nThe missing \u20d7ET projection method is an alternative approach to test the jet energy scale and has been used\nsuccessfully by the D0 experiment to determine the response of their calorimeter to hadronic jets [17]. It\nis explained here for the example of \u03b3 + jet events, but it can also be used for Z+jet events. Details about\nthe study presented in this section can be found in Ref. [15].\nAt leading order, momentum conservation between the photon and the jet gives\n\u20d7ET,\u03b3 +\u20d7pT,parton = 0 .\n(3)\nNeglecting parton showering and hadronization effects, this can be rewritten at particle level as\n\u20d7ET,\u03b3 +\u20d7ET,jet \u22480 ,\n(4)\nwhere momentum has been replaced by energy, which is a good approximation for light quark jets.\nThe systematic effects of parton showering and hadronization, including initial state radiation (ISR)\nand \ufb01nal state radiation (FSR), can be reduced by requiring that the leading jet and the photon are back-\nto-back within 0.2 in azimuth in a similar way to what was shown in Fig. 2.\nAt the calorimeter level, the balance equation is modi\ufb01ed to\ne\u20d7ET,\u03b3 + j(Ejet)\u20d7ET,jet = \u2212\u20d7Emiss\nT\n.\n(5)\nwhere e, j are the electromagnetic and hadronic responses, Ecalo/Eparticle, of the calorimeters, respectively.\nIt is implicit in Eq. 5 that energy deposited in the calorimeters by the underlying event and pileup is\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n348\n\nsymmetric in \u03c6. These assumptions have been tested and their effect is small. Anticipating that the\nelectromagnetic scale will be well calibrated, for example by using the electrons from the decay of a Z\nboson, we can assume that e \u22481. The quantities can then be projected in the direction of the photon,\nyielding\nET,\u03b3 + j(Ejet)\u20d7ET,jet \u00b7 \u02c6n\u03b3 = \u2212\u02c6n\u03b3 \u00b7\u20d7Emiss\nT\n,\n(6)\nwhere \u02c6n\u03b3 is the unit vector in the direction of the photon. Using the relation\n\u20d7Emiss\nT\n= \u2212\u20d7ET,\u03b3 \u2212\u2211\n\u2032\u20d7ET ,\n(7)\nwhere \u2211\u2032 indicates a sum over all activity in the calorimeter other than the \u03b3 , the response can be further\nsimpli\ufb01ed as\nj = \u2211\u2032\u20d7ET \u00b7 \u02c6n\u03b3\n\u20d7ET,jet \u00b7 \u02c6n\u03b3\n= \u2211\u2032\u20d7ET \u00b7 \u02c6n\u03b3\nET,\u03b3\n,\n(8)\nwhere Eq. 4 was used in the last step. In this form it is clear that this method of measuring the response\nis independent of the underlying event, since the hadronic activity outside the \u03b3 + jet system is approxi-\nmately \u03c6-symmetric and its contribution to the sum cancels out. It is also (mostly) independent of the jet\nalgorithm.\nHowever, the jet response depends on the jet energy because the relative fraction of EM energy in the\ncalorimeter level jet increases with increasing energy, hence a correction for non-compensation must be\napplied. Thus, the response has to be measured as a function of the jet energy. If we bin the response as a\nfunction of the measured jet energy (Ejet), it would be biased towards lower ET,\u03b3 due to the bin migration\ndescribed in Section 4.2. Instead, the jet energy is taken as E\u2032 = ET,\u03b3 \u00b7cosh(\u03b7jet), which uses the much\nbetter measured energy of the photon and projects it in the jet direction; this procedure is based on the\nmomentum balance of Eq. 4. The EM scale jet energy distribution is \ufb01tted with a Gaussian in each bin of\nreference energy E\u2032, and the jet energy scale is then calculated. The correspondence between E\u2032 and the\nmeasured jet energy is also determined. The resulting jet energy scale can then be plotted as a function\nof Ejet.\nThe response function is then plotted for each algorithm as a function of the corresponding mean jet\nenergy and parameterized by\nj(E) = b0 +b1 ln\nE\nEscale\n+b2 ln2\nE\nEscale\n(9)\nwith Escale set to 200 GeV and the b parameters \ufb01tted, as shown in Fig. 11.\nThe \ufb01t function is used to correct the jet energy at the EM scale Emeas\nT\n.\nThe corrected energy\nEcalib\nT\n= Emeas\nT\n/j(E) is then compared to the truth information EMC\nT\nin the Monte Carlo simulation. Fig-\nure 12 is a plot of the ratio EMC\nT\n/Ecalib\nT\nas a function of jet energy, which shows a linear response within\n\u22482% over the range 50\u2212900 GeV.\nThis procedure accounts for the fact that the ATLAS calorimeters are non-compensating and that\nthe electromagnetic content of a hadronic shower is energy dependent. Further adjustments, such as\nout-of-cone corrections, must be made to obtain the \ufb01nal jet energy scale. It is only at this point that\njet algorithm dependent corrections are made and is therefore a useful method as a cross-check of our\nunderstanding of the energy scale with different sensitivity to systematic effects.\n4.6\nConclusions of the studies of \u03b3/Z + jet events\nThe use of the in-situ \u03b3/Z + jet processes allows us to propagate the knowledge of the electromagnetic\nscale characteristic of the \u03b3 or the Z \u2192\u2113\u2113decay to the hadronic recoil system. Typically the leading jet\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n349\n\n (GeV)\njet\nE\n100\n200\n300\n400\n500\nresponse\n0.66\n0.68\n0.7\n0.72\n0.74\n0.76\n0.78\n0.8\n0.82\nFigure 11: The energy dependence of the jet response for cone jets with R = 0.4. The solid line corre-\nsponds to the \ufb01t using Eq. 9.\n (GeV)\njet\nE\n100\n200\n300\n400\n500\n600\n700\n800\n900\nreconstructed/true\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\ncalibrated\nEM scale\nFigure 12: The ratios EMC\nT\n/Ecalib\nT\n(triangles) and EMC\nT\n/Emeas\nT\n(squares) for jets reconstructed using the\ncone algorithm with R = 0.4. See the text for an explanation of the symbols.\nis required to be back-to-back in azimuth with the \u03b3 or the Z boson, and the pT balance between them is\nused to connect the two scales.\nThe balance is affected by various physics effects which systematically limit the precision of the\nin-situ validation procedure. These effects can be as large as 5\u221210% at 20 GeV and tend to decrease to\nthe percent level at about 100 GeV.\nThe \u03b3 + jet process has the advantage of higher statistics compared to Z + jet. However, at low pT it\nmay be seriously affected by background from QCD jets. Hence it may turn out to be most useful above\n\u223c50 \u2212100 GeV where the signal to background ratio is more favorable and where an inclusive single\nphoton trigger is available. A statistical precision better than a percent is achieved already with 10pb\u22121\nat 100 GeV, and in the range 300\u2212500 GeV the percent level is reached with about 100pb\u22121. The Z + jet\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n350\n\nFigure 13: The jet response pT(reconstructed)/pT(truth) at the EM scale versus the jet pseudorapidity \u03b7\n.\nprocess allows us to measure the absolute energy scale in the low pT range with a statistical precision\nof 1% with \u223c300pb\u22121 of data. It provides also the highest pT reach with percent level precision in\nthe range 300\u2212500 GeV with \u223c200pb\u22121. Above \u223c500 GeV, other methods will be used as discussed\nfurther on.\n5\nIn-situ studies using QCD jet events\n5.1\nCalorimeter intercalibration in QCD dijet samples\nThe calorimeter response pT(reconstructed)/pT(truth) for jets at the EM scale reveals signi\ufb01cant vari-\nations with pseudorapidity \u03b7 , as shown in Fig. 13. The dips correspond to known cracks and dead\nmaterial regions. The response may also be non-uniform in azimuth \u03c6 for the same \u03b7 due to the varia-\ntions in the basic calorimeter response and due to the non-uniform distribution of the dead material. The\nresponse in \u03c6 and \u03b7 should become \ufb02at at the hadronic scale. This has to be checked in-situ with high\nprecision, and if necessary, an intercalibration of different regions of the calorimeter has to be performed.\nFor this study we use PYTHIA QCD jet events, generated in intervals of pT of the hard scattered partons,\nas described in Section 4.3.\n5.1.1\nIntercalibration in azimuth\nThe intercalibration in \u03c6 can be checked using the high rates of QCD jet events. As the scattering cross\nsection is constant in \u03c6, the jet rates above a \ufb01xed pT threshold have to be nearly equal in different \u03c6\nsectors, as shown in Fig. 14 (left) for 64 \u03c6 sectors in the \u03b7 range |\u03b7| < 0.1 which corresponds to the\nsegmentation of the ATLAS hadronic calorimeter in one calorimeter wheel. Strongly deviating rates in\nparticular sectors would point to dead calorimeter cells, losses in dead material, or noise.\nFor a perfectly calibrated calorimeter the spread of rates around the mean rate value N should be\n\u221a\nN following the Poissonian distribution. Thus, collecting on average e.g. \u223c1000 events per sector, one\nwould expect the spread of \u223c30 events, i.e. 3% of the average rate. A signi\ufb01cantly larger spread would\npoint to a relative miscalibration of different sectors. The spread can be obtained by \ufb01lling a histogram\nwith the rates and \ufb01tting it with a gaussian. Due to the strongly falling jet pT distribution the rates are\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n351\n\nATLAS\n threshold, GeV\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n threshold, GeV\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n1\nLuminosity, pb\n-2\n10\n-1\n10\n1\n10\nATLAS\nFigure 14: Left: The jet rate as a function of \u03c6 for jets with the transverse momentum above a certain\nthreshold. Right: Integrated luminosity required to collect 1000 events with jets above the given pT\nthresholds in each of the 64 \u03c6 sectors in the region |\u03b7| < 0.1.\nextremely sensitive to the jet energy scale: a 1.5\u22122% shift in the energy scale would result in \u223c6\u22129%\nchange of the rate, which is a 2\u22123\u03c3 effect for the above example with 1000 events per sector. Thus, the\nstatistics of 1000 events per sector should allow us to control the jet energy scale to within 1.5\u22122%. The\nluminosity necessary to collect such statistics in 64 \u03c6 sectors within the \u03b7 interval |\u03b7| < 0.1 is shown for\ndifferent pT thresholds in Fig. 14 (right). A study of the systematics for this method is on the way.\nThe trigger menu for the initial running period at the luminosity of 1031 cm\u22122s\u22121 is currently under\ndevelopment, and the effect of trigger prescaling has not yet been taken into account in this plot. The\nhighest pT threshold for the inclusive jet trigger is expected to be at 100 \u2212150 GeV, above which no\nprescaling will be applied. The prescale factors will steeply rise for lower thresholds, such that the\nrecorded event rate should be roughly \ufb02at in pT. Scaling the shown luminosity values for the lowest two\npT bins down with the currently foreseen prescale factors shows that the rate of recorded events will be\nstill suf\ufb01cient to reach the statistical precision of 1.5\u22122% with <\u223c10 pb\u22121 of data.\nHowever, the rates may be affected by the calibration of the level 1 calorimeter trigger. To avoid a\nbias, the pT thresholds chosen for this analysis should be signi\ufb01cantly higher than the respective trigger\nthresholds. This will lead to a loss of statistics, and thus a higher integrated luminosity will be necessary\nfor the same statistical precision.\n5.1.2\nIntercalibration in pseudorapidity\nThe intercalibration in \u03b7 can be done based on the pT balance in QCD dijet events. The roughly three\norders of magnitude higher cross section of dijet events, as compared to Z/\u03b3 + jet events, allows an\nintercalibration of the calorimeter with higher granularity, higher precision and for higher energy ranges\nthan can be achieved in Z/\u03b3 + jet events for the same integrated luminosity. Applying the calibration\nbased on the pT balance, one corrects for the relative difference in calorimeter response for jets, the noise\nand pile-up in different regions of pseudorapidity \u03b7 . The goal is to achieve a \ufb02at response in \u03b7 and to\nextend the previous calibrations for |\u03b7| < 2.5 to higher pseudorapidities.\nThe method is straightforward: one calorimeter region in pseudorapidity \u03b7 is chosen as the reference\nregion and jets in other \u03b7 regions are calibrated relative to jets in this region. Normally, one calorimeter\n\u03b7 wheel in the central range, far from the crack regions, will be chosen as the reference region. Other\nconsiderations are the existence of dead or noisy cells in a particular part of the calorimeter, the unifor-\nmity of the response in \u03c6 within one wheel etc. The width of the region will also depend on the available\nstatistics.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n352\n\nFigure 15: Left: The asymmetry A as measured with both jets in the central region |\u03b7| < 0.7 as de\ufb01ned in\nEq. 10. Right: The mean asymmetry obtained from gaussian \ufb01ts, plotted as a function of the half scalar\nsum of pT of both jets at the reconstruction level (closed circles) and at the truth particle level (stars).\nWe choose to characterize the pT-balance in dijet events by the asymmetry A given by\nA =\npprobe\nT\n\u2212pref\nT\n(pprobe\nT\n+ pref\nT )/2\n,\n(10)\nwhere pref\nT is the transverse momentum of the jet in the reference region, and pprobe\nT\nis that of the jet\nin the region to be calibrated. Using this form, the pT balance is symmetric, as shown in Fig. 15 (left)\nfor reconstructed cone jets with R = 0.7. It thus provides better properties than the simple de\ufb01nition\npprobe\nT\n/pref\nT which is intrinsically asymmetric.\nTo limit ISR/FSR and thereby reduce the width of the asymmetry distribution, a cut on the azimuthal\nangle between the two jets, \u2206\u03c6 > 3, is applied. The \ufb01tted mean value of the asymmetry as a function of\npT is displayed in the right panel of Fig. 15 and shows that for this de\ufb01nition there is very little bias both\nfor truth particle jets and for reconstructed jets at the hadronic scale.\nFurther cuts can be applied to obtain a cleaner dijet sample and thus reduce further the width of the\npT balance distributions. For example, the total number of reconstructed jets with pT > 10 GeV can be\nlimited to Njet < 4 or even more strongly to Njet = 2. However, these additional cuts reduce the statistics\nof the sample, as demonstrated in Fig. 16, which shows the integrated luminosity required to reach a\nstatistical precision of 0.5% of the pT balance \ufb01t mean value in the probe range 0.7 < \u03b7 < 0.8, where\n0 < |\u03b7| < 0.7 is taken as the reference region. The luminosity values are shown for different sets of\ncuts. For the case of applying only the back-to-back cut on the angle between the two leading jets, 0.5%\nprecision can be reached in this \u03b7 region with 10 pb\u22121 of data for pT\n<\u223c300 GeV, and with 100 pb\u22121 for\npT\n<\u223c500 GeV.\nSimilar plots were produced for the other \u03b7 regions, which show that an order of magnitude more\nluminosity is necessary for |\u03b7| > 2.5, compared to the central region. On the other hand, the size of the\nreference region can be increased sequentially, i.e. as soon as one \u03b7 has been checked or recalibrated, it\ncan be added to the reference region to study the next \u03b7 range.\nAs in the luminosity estimation for the \u03c6 intercalibration in Section 5.1.1, the trigger prescaling has\nnot yet been taken into account in Fig. 16. As in Sect. 5.1.1, scaling the shown luminosity values for\nthe lowest two pT bins down with the currently foreseen prescale factors shows that the rate of recorded\nevents will be suf\ufb01cient to reach 0.5% precision with <\u223c10 pb\u22121 of data.\nThe calibration method is further tested in the full \u03b7 region for different pT ranges. For each \u03b7\nregion i in each pT range j, the asymmetry A de\ufb01ned in Eq. 10 is \ufb01tted and the mean value Ai j is used to\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n353\n\ncalculate a correction factor ci j via\nci j = 2\u2212Ai j\n2+Ai j\n.\n(11)\nIn the case of an imperfect original calibration, factors deviating from 1 are obtained. Each jet pT can\nthen be multiplied by the appropriate factor to restore the balance of fully simulated jets. More details of\nthis study can be found in Ref. [18].\n5.2\nHigh pT jet calibration\nThe calibration of the jet energy scale for high pT jets (with pT\n>\u223c500 GeV) is a challenge at hadron\ncollider experiments. In this energy range, methods developed for lower pT jets, normally using well\nde\ufb01ned objects as reference, start to fail. This dif\ufb01culty will be further increased at the early stage of\ndata taking, where both our understanding of the detectors and the statistics of such high pT jets are\nusually limited. Our goal is to develop a calibration technique for jets with pT > 500 GeV based on\ndata collected with an integrated luminosity of 0.1\u20131 fb\u22121. The basic idea is to determine the energy\nscale of high pT jets from lower pT jets, for which the energy scale will be obtained by the techniques\ndescribed earlier in this note. Two calibration techniques are discussed in the following sections: 1)\nthe correlation between different pT jets in momentum balance in the transverse plane, and 2) the angle\nbetween particles in the jets.\n5.2.1\nMultijet pT balance method\nThis method is based on selecting events with multiple (> 2) jets and calibrating the energy scale of\nthe highest pT jet by requiring a pT balance between the leading jet and the system of remaining lower\npT jets. The absolute jet energy scale of the non-leading jets, which is expected to be obtained from\nphoton+jets, Z+jets and/or W \u2192jet jet studies, is thus propagated to the JES of the higher pT jets using\npT balance methods. The large QCD jet cross-section allows for a very high reach in pT. This method\nhas been studied with samples generated with both ALPGEN and PYTHIA using the fast and full detector\nsimulation. Two different analysis techniques were applied as described in the following.\nFigure 16: Integrated luminosity required to reach 0.5% precision for various pT ranges in the region\n0.7 < \u03b7 < 0.8 with different sets of selection cuts: all PYTHIA dijet events (circles), requiring \u2206\u03c6 > 3\nbetween the two leading jets (triangles), requiring in addition less than 4 reconstructed jets in an event\n(squares), requiring exactly two reconstructed jets (stars). The reference region is 0 < |\u03b7| < 0.7.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n354\n\nFigure 17: Energy scale (left) and energy scale uncertainty (right) of high pT jets relative to lower pT\nremnant jets as a function of jet pT, obtained by multijet pT balance method at an integrated luminosity\nof 1 fb\u22121. The error bars shown are statistical only.\nALPGEN study\nFor this study QCD multijet samples with 4, 5 and 6 partons were generated using ALPGEN interfaced\nwith JIMMY. Four data samples were formed by requiring the leading parton pT to be larger than 400,\n600, 800, or 1000 GeV, while the pT of the next-to-leading parton was required to be smaller than 200,\n300, 400, or 500 GeV, respectively. The total number of partons (pT > 40 GeV) can be 4, 5 and 6 in each\nof the above samples. All the partons are required to be in the range |\u03b7| < 3. These samples, referred to\nas PT400, PT600, PT800, and PT1000 hereafter, were processed through the full detector simulation.\nAt least four cone jets with R = 0.7 with pT > 40 GeV must be reconstructed in each event. The\nleading jet pT in the samples PT400, 600, 800, and 1000 must be in the interval 400 < pjet1\nT\n< 460 GeV,\n600 < pjet1\nT\n< 700 GeV, 800 < pjet1\nT\n< 920 GeV, and 1000 < pjet1\nT\n< 1140 GeV, respectively, while the\npT of the next-to-leading jet must correspondingly respect the bound pjet2\nT\n< 190 GeV, pjet2\nT\n< 280 GeV,\npjet2\nT\n< 370 GeV, and pjet2\nT\n< 470 GeV. In addition the leading jet and the vector sum of the remaining\nlower pT jets with pT > 40 GeV (called remnant jets) are required to be back-to-back in azimuth within\n\u00b120\u25e6. After all the cuts, about 3200, 310, 40, and 11 events remain in the PT400, 600, 800, and 1000\nsamples, respectively, for an integrated luminosity of 1 fb\u22121.\nThe distribution of the pT balance, de\ufb01ned as\nB\u2032\n\u03a3 =\npjet1\nT\nnon\u2212leading jets |\u2211pT| ,\n(12)\nis plotted for each sample and \ufb01tted by a Gaussian. The mean values of the Gaussian \ufb01ts with their\nuncertainties for 1 fb\u22121 are shown in Fig. 17 as a function of pjet1\nT . The \ufb01gure indicates that B\u2032\n\u03a3 could be\ndetermined with a statistical accuracy of 2% or better for high pT jets with 400 < pT < 1100 GeV and\nthat it shows a constant offset of 2-3% over the pjet1\nT\nrange, as also observed in the PYTHIA study.\nVarious potential sources of systematic effect have been studied. Low pT jets will not contribute to\nremnant jet system because of the 40 GeV pT threshold applied to the jets. If the threshold is varied by\n\u00b120 GeV, B\u2032\n\u03a3 varies by \u00b11% at most. The effect is smaller, for the same range of thresholds, than in the\nPYTHIA analysis because of the back-to-back requirement imposed on the system. A sizable fraction of\nthe soft radiation is still missed is the event. This is the main cause of the positive B\u2032\n\u03a3 offset. It could\nbe reduced by requiring the overall event pT to be balanced, e.g. by requiring that Emiss\nT\n< 40 GeV.\nIn that case, B\u2032\n\u03a3 decreases by 1\u20132% and becomes close to 1. However, an Emiss\nT\ncut should be used\nwith caution as fake Emiss\nT\ncould cause biases. The effect of the underlying event on B\u2032\n\u03a3 has also been\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n355\n\nevaluated by subtracting the ET measured in a cone (R = 0.7) placed randomly in a region of azimuth\nwithin 60\u25e6< \u2206\u03c6 < 120\u25e6from the leading jet and not overlapping with any of the remnant jets. After\nsubtraction, B\u2032\n\u03a3 increases by 1\u20132%.\nThe precision on the JES for high pT jets is affected by the JES uncertainty of the remnant jets.\nIf we assume the uncertainty to be \u00b17% for low pT jets with |\u03b7| < 3.2, which is the current linearity\nperformance of the H1 weight calibration method used in this analysis [1], vary the scale of the remnant\njets by \u00b17%, and apply again all the event selection, B\u2032\n\u03a3 changes by \u00b17% independently of pjet1\nT . This\nprovides an estimate of the JES uncertainty for high pT jets. The uncertainty on B\u2032\n\u03a3 is increased since\nmore events fail the next-to-leading jet pT cut that is included in the overall JES uncertainty.\nAdding the statistical and above systematic uncertainties in quadrature, the JES uncertainty obtained\nfrom multijet balance method is estimated to be about 8% in the pT range of 400 < pT < 1100 GeV\nand is totally dominated by the absolute JES uncertainty for lower pT remnant jets. If the absolute JES\nuncertainty is not included in the systematics, the relative JES uncertainty is 3%.\nPYTHIA study\nIn this study, PYTHIA samples with full and fast detector simulation were used. The fully simulated\nsample was generated with kinematic cuts of 280 < pT < 560 GeV for the hard scattering process. It\ncorresponds to an integrated luminosity of about 25 pb\u22121. Cone jets with R = 0.7 were reconstructed\nbased on calorimeter towers, topoclusters and on Monte Carlo truth particles.\nThe fast simulation package ATLFAST was used for a high statistics study. A cut on the hard scat-\ntered parton at pT > 280 GeV was applied. The sample represents an integrated luminosity of about\n0.8 fb\u22121. Cone jets with R = 0.4 were used for this study.\nEvents are selected with a minimum of three reconstructed jets, the leading jet being above a \ufb01xed\npT threshold, up to which the JES is assumed to be calibrated. All non-leading jets are required to be\nbelow that value. A further event selection cut is |\u03b7| < 2 for the leading jet. Generally non-leading jets\nhave been reconstructed up to |\u03b7| < 5 and down to pT > 10 GeV. For speci\ufb01c studies of their systematic\nin\ufb02uences all these cuts have been varied.\nFigure 18 presents results of the method for the sample using full detector simulation. The event\nselection cut on non-leading jets is pT < 300 GeV. On the left, the pT balance B\u2032\n\u03a3 is shown for leading\njets with 370 < pT < 380 GeV, together with a Gaussian \ufb01t. While non-Gaussian tails are visible, which\ncould be partly reduced by a stricter event selection, they do not in\ufb02uence the \ufb01t and it was thus decided\nto use the maximum statistics.\nTo reduce the bias of the pT balance due to migration effects, the division of the pT region into bins\nis done based on the average pT of the sum of the non-leading jets and the leading jet of each event. This\nreduces the bias to about 1% at truth level. This is similar to what is studied in the Z/\u03b3 + jet analyses\n(Section 4.2), where the average (pT,\u03b3/Z + pT,jet)/2 is an option for the binning.\nOn the right of Fig. 18 the JES was studied from 350 GeV to 550 GeV. The result is reasonably \ufb02at\nbut shows a systematic offset of about 2%, as also observed in the ALPGEN study. There are various\neffects contributing to this imbalance, mostly originating from soft radiation affecting the low pT jets\nin the hemisphere opposite the leading jet. At truth jet level, changing the minimum jet pT from 5\nto 10/20/40 GeV introduces a negative bias of 0.2/1/3%, respectively. The pT threshold value for real\ndata should be chosen taking the noise, pile-up conditions and jet \ufb01nding ef\ufb01ciency at low pT into\naccount. Out of cone losses also play a role: changing the cone size from 0.7 to 0.4 at truth level, affects\nthe measured balance by \u223c1%. Furthermore, imperfect calibration of low pT jets at the level of few\npercent [1] may be a cause of bias.\nIn a high statistics study, based on ATLFAST, the non-leading jets were restricted to a pT value below\n350 GeV during event selection. Figure 19 shows the result on the left. The pT balance distribution is\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n356\n\n-Balance\nT\np\n0.6\n0.8\n1\n1.2\n1.4\nEvents\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n 370 GeV < pT < 380 GeV\nATLAS\n(sum) )/2 [GeV]\nT\n(leading)+p\nT\nCenter of bin, ( p\n400\n450\n500\n550\n600\n-Balance\nT\np\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\n1.06\nCone 0.7 Tower Jets\nCone 0.7 Topo Jets\nCone 0.7 Truth Jets\n25 pb-1\nATLAS\nFigure 18: Left: the ratio of the absolute value of the vector sum of the non-leading jet pT to the leading\njet pT for the pT bin 370\u2013380 GeV \ufb01tted by a Gaussian. Right: this ratio as a function of jet pT. The\nmean and the error of the mean of the Gaussian \ufb01ts are shown. The average of the leading jet pT and of\nthe total pT of the non-leading jets is used for the binning.\n(sum) )/2 [GeV]\nT\n(leading)+p\nT\nCenter of bin, ( p\n400\n450\n500\n550\n600\n650\n700\n-Balance\nT\np\n1\n1.01\n1.02\n1.03\n1.04\n1.05\nATLAS\n800 pb-1\n(sum) )/2 [GeV]\nT\n(leading)+p\nT\nCenter of bin, ( p\n700\n800\n900\n1000\n1100\n1200\n1300\n1400\n1500\n-Balance\nT\np\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\n < 600 GeV\nnon leading jet p\n < 900 GeV\nnon leading jet p\n < 1200 GeV\nnon leading jet p\nATLAS\n800 pb-1\nFigure 19: Results using ATLFAST with cone jets with R = 0.4. Left: The \ufb01tted balance as a function of\nthe average leading and non-leading jets pT. Right: Iterations of the method using the pT range checked\nby one iteration as the reference region for the next.\nlower than for cone jets with R = 0.7, as discussed above. Truth and ATLFAST jets give closer results in\nthis case, since the latter are truth jets smeared for resolution effects.\nThe reach in pT of the method can be further increased by iterating the procedure. Apart from the\nQCD jet cross-section, the statistics are mainly limited by the cut on the pT of the non-leading jets during\nevent selection, essentially requiring that one parton in the hard scattering lost a signi\ufb01cant part of its\nenergy due to gluon radiation. For higher pT ranges this cut should be moved to higher values to obtain\nsuf\ufb01cient statistics. The procedure is thus, after applying the method once, up to a certain pT, to use\nthe range up to this pT as reference region for a next iteration. Results using this approach based on\nthe ATLFAST sample are shown in Fig. 19 on the right hand side. For the studied high pT region, the\nmultijet statistics predicted by PYTHIA may be an underestimation, as the PYTHIA parton shower model\nis not perfectly tuned for this pT range.\nA crucial feature for this method, as observed in PYTHIA simulations, is that the imbalance value\nremains essentially constant for one iteration if the tested JES is correct. The balance can differ between\nthe iterations. In general, it is slightly closer to 1 for higher pT ranges, as the system of non-leading jets\nbecomes harder and thus less sensitive to low energy effects. To ensure that the JES is correct, we require\nthat the beginning of the test region for a given iteration overlaps with the end of the region veri\ufb01ed in\nthe previous iteration, or at the very beginning veri\ufb01ed by another method.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n357\n\nA complete understanding of the feature that the balance should remain constant for all pT within\none iteration, is necessary in order to rely on it in data. In this case, in addition to the absolute JES\nuncertainty of the non-leading jets, the systematic uncertainty of this method is given by deviations of\nthe balance from a constant value as a function of pT.\nTo determine this additional systematic uncertainty, the deviations are split into a global slope of a\nlinear \ufb01t and into local deviations around this \ufb01t. As possible sources of systematic effects, the absolute\nJES of the remnant system, the choice of the pT binning, the lower and upper pT thresholds for the\nnon-leading jets, the effect of the underlying event and of the noise, and the effect of the varying jet\nmultiplicity in the remnant system are studied. To estimate the deviations quantitatively, the absolute\nJES is varied by 10%; the lower jet pT threshold is varied between 10 and 50 GeV; the upper threshold\nfor each iteration is varied by 100 GeV; the effect of the underlying event and of the noise is estimated by\nadding \u00b15 GeV to each jet in the event; and the analysis is performed separately for events with exactly\n4, 5 and 6 jets.\nThe slope of the \ufb01t is compatible with zero within statistical uncertainties for all variations of the\nsources. The corresponding systematic uncertainties for each source is estimated to be <\u223c0.1%. The\nestimation is limited by the available statistics. All local deviations from a linear \ufb01t are of the order\nof the statistical uncertainties. The width of their distribution is found to be less than 0.2% above the\nstatistical expectation for each of the above in\ufb02uences. Adding all uncertainties quadratically results in\na very small total systematic uncertainty of 0.5%. Thus, the main contribution to the JES uncertainty is\nexpected to be the accuracy of the calibration in the reference region. The JES can then be calibrated up\nto pT\n>\u223c1.5 TeV, with the speci\ufb01c uncertainties introduced by this method being below 1% and requiring\nless than 1fb\u22121 of integrated luminosity.\n5.2.2\nTrack angle method\nThe idea behind this method is that the invariant mass of two particles in a jet is approximately constant\n(given by the scale of \u039bQCD), which leads to a p\u22121\nT\nbehavior of the \u03b7-\u03c6 distance between two particles\nin a jet \u2206R, where pT is the transverse momentum of the jet. The dependence of \u2206R on p\u22121\nT\nof the jet\ncould provide a means of determining the energy scale of high pT jets once the JES of lower pT jets is\ncalibrated with some accuracy using other in-situ techniques. The procedure to determine the JES of\nhigh pT jets is as follows: 1) measure \u2206R for low pT jets with the calibrated JES in both data and Monte\nCarlo samples, 2) calibrate the simulation so that \u2206R in the simulation matches \u2206R in data in the low pT\nrange, then 3) measure the \u2206R for a sample of given high pT jets in data, and look for the Monte Carlo\njet pT scale corresponding to the measured \u2206R value on the curve of \u2206R(p\u22121\nT ).\nThe studies were performed on PYTHIA dijet samples generated in intervals of pT. The jets selected\nhave to have pT > 20 GeV and should not overlap with other physics objects within R < 0.4. Afterward\nall tracks are selected which fall in a cone of R = 0.4 around reconstructed jet axis of the jet with the\nhighest pT. If fewer than two tracks are found for the jet, the event is rejected. The \u2206R of two tracks is\nthen calculated for all combinations from two up to the \ufb01ve highest pT tracks in the jet. Figure 20 shows\nthe mean of the \u2206R values (one entry per event), normalized to an integrated luminosity of 1fb\u22121, for\nleading jets with 140 < ptruth\nT\n< 160 GeV (top-left) and 1120 < ptruth\nT\n< 1280 GeV (top-right). The two\nhistograms correspond to the \u2206R obtained from leading two and \ufb01ve tracks. When more low pT tracks\nare involved, the \u2206R distribution broadens as a result of jet fragmentation.\nThe bottom plots in Fig. 20 show the mean (left) and most probable value (MPV) obtained from a\nLandau \ufb01t to the peak (right) of the \u2206R distributions as a function of the leading jet truth pT. Both mean\nand MPV are well \ufb01t by a function of the form p0/x + p1 as shown by the curves. Figure 21 (top-left)\nshows the uncertainty of the jet pT scale obtained by evaluating the jet pT range on the curves covered\nby the statistical uncertainties of the data points in the bottom of Fig. 20 and dividing the pT range by\nthe jet truth pT. The pT scale uncertainty varies signi\ufb01cantly at high pT with different choices of \u2206R\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n358\n\nFigure 20: Top: Distributions of the mean of the \u2206R values for the leading two (solid histogram) and\n\ufb01ve (dashed histogram) tracks in jets with 140 < ptruth\nT\n< 160 GeV (left) and 1120 < ptruth\nT\n< 1280 GeV\n(right) for an integrated luminosity of 1fb\u22121. Bottom: Mean (left) and most probable value obtained\nfrom a Landau \ufb01t to the peak (right) of the \u2206R distributions as a function of the leading jet truth pT for\nthe leading two (solid points) and \ufb01ve (open points) tracks. The curves represent \ufb01ts with a function of\nthe form p0/x+ p1.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n359\n\nvalues. In general, the MPV is more stable than the mean value as it suffers less from \ufb02uctuations in jet\nhadronization. The MPV-based scale uncertainty seems less dependent on the leading track multiplicity\nin PYTHIA-only comparisons, but the situation changes when PYTHIA is compared with HERWIG as in\nFig. 21 (top-right). Apparently the choice of the leading two tracks is more robust against different\njet fragmentation models, and therefore the \u2206R obtained from the MPV of leading two tracks is used\nhereafter as a central value.\nFigure 21: Top-Left: Jet pT scale uncertainty (statistical uncertainty only) as a function of jet truth pT\nobtained for different choices of \u2206R values and track multiplicities. Top-Right: The most probable \u2206R\nof the leading two and \ufb01ve tracks as a function of the jet truth pT in PYTHIA (open points) and HERWIG\n(solid points). Bottom-Left: Default \ufb01t (solid curve) to the most probable \u2206R of the leading two tracks as\na function of the truth jet pT and the curves corresponding to \u00b15% JES variations at pjet\nT = 5 GeV (dashed\nand dotted). Bottom-Right: Total and individual systematic and statistical uncertainties as a function of\nthe truth jet pT expected to be obtained from the track angle method for an integrated luminosity of\n1fb\u22121.\nThe following sources of systematic uncertainties are considered: 1) the jet fragmentation model\nas discussed above, 2) the track selection cuts and reconstruction inef\ufb01ciencies, 3) absolute JES at low\nenergies, and 4) the uncertainty associated with the \ufb01t. The systematic uncertainty on the jet pT scale\nis evaluated by obtaining the \u2206R versus jet pT distributions shifted by \u00b11\u03c3 (or the equivalent amount\nspeci\ufb01ed) of the source, and looking at the variation in the jet pT at the measured \u2206R values. For 1), the\ndifference between PYTHIA and HERWIG is assigned. For 2), the deviated distributions are obtained by\napplying different selection cuts on tracks and assuming an extra 5% reconstruction inef\ufb01ciency for tracks\nin jets. The JES uncertainty for low pT jets is assumed to be \u00b15% at pjet\nT = 100 GeV, and the deviated\ndistributions are obtained by estimating the corresponding variations in \u2206R at pjet\nT = 100 GeV using the\ndefault \ufb01t function and transferring the variations to uncertainties on the parameters of the function. The\nJES deviated and default distributions are shown in Fig. 21 bottom-left. The total uncertainty obtained\nby adding all the systematic uncertainties and the statistical uncertainty in quadrature, and individual\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n360\n\nsystematic uncertainties as a function of the jet truth pT are shown in the bottom-right of the \ufb01gure. With\nthe assumption of \u00b15% JES uncertainty at pjet\nT = 100 GeV, the JES of 150, 300, 600, and 1200 GeV pT\njets can be potentially measured with an accuracy of 8, 10, 13, and 21%, respectively, with an integrated\nluminosity of 1fb\u22121.\n5.3\nObtaining jet energy resolution in QCD dijet sample\nA precise measurement of the jet energy resolution is necessary to model and control the systematic\neffects associated with it on jet observables and the quantities used in physics measurements. A key\nissue in estimating the jet energy and momentum resolution is the need to disentangle detector effects\nfrom those associated with physics such as the underlying event, and initial and \ufb01nal state radiation.\nTwo data-based techniques are presented which allow the jet energy resolution to be estimated, and\nthey were compared where appropriate to the resolution obtained using particle jets: the dijet balance\nmethod, used by the D\u00d8 collaboration, and the kT balance technique, developed by UA2 and used by\nCDF.\nThe QCD dijet events for this analysis were generated using PYTHIA in the pT range from 17 GeV\nup to 1120 GeV. Jets were reconstructed using the cone algorithm with R = 0.7.\nTo select dijet events the following basic cuts are applied:\n\u2022 One primary vertex;\n\u2022 Exactly two back-to-back leading jets with |\u2206\u03c6| < 0.3 and pT > 10 GeV;\n\u2022 Both jets in the same \u03b7 region |\u03b7| < 1.2.\nThe \u2206\u03c6 and minimum pT cuts are varied for some systematic studies.\n5.3.1\nDijet balance method\nThe determination of the jet pT resolution in the dijet balance technique is based on energy conservation\nin the transverse plane. It assumes that there are only two jets in the event which have similar pT. If one\nde\ufb01nes the asymmetry distribution A for the two jets as:\nA \u2261pT,1 \u2212pT,2\npT,1 + pT,2\n,\n(13)\nthen for jets in the same rapidity region, which therefore have the same resolution, the fractional trans-\nverse jet energy resolution can be expressed as a function of \u03c3A:\n\u03c3pT\npT\n=\n\u221a\n2\u03c3A ,\n(14)\nwhere pT = (pT,1 + pT,2)/2.\nThe asymmetry distribution A for two representative pT bins obtained by using cone jets with R = 0.7\nare shown in Fig. 22. The distributions have been symmetrized by computing either pT,1 \u2212pT,2 or\npT,2 \u2212pT,1 randomly for each event. The resolution function is well described by a Gaussian \ufb01t, al-\nthough it is worth mentioning that previous studies done by the D\u00d8 Collaboration suggest using a double\nGaussian \ufb01t for large pT bins, to absorb effects of non-Gaussian tails.\nThe simple dijet balance method does not return the true fractional transverse energy resolution\nassociated purely with detector effects, since the two leading jets of an event could be imbalanced due to\nundetected jets in the event with pT < 10 GeV such as from soft radiation. This radiation will broaden\nthe resolution function and a correction may be derived by studying the effect of the cut on the pT of any\nthird jet in the event as described in the next section.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n361\n\nFigure 22: Asymmetry distributions of two jets for two representative pT bins. Cone jets with R = 0.7\nin the pseudorapidity region |\u03b7| < 1.2 are used. The distributions were \ufb01tted with a single Gaussian\nfunction.\n5.3.2\nSoft radiation correction\nIn our basic event selection, both the \u2206\u03c6 cut and the cut requiring exactly two jets with pT > 10 GeV\nare implemented in order to reduce the broadening of the pT balance distribution due to soft radiation\neffects. However, the effects are not fully suppressed, as further jets with pT < 10 GeV may remain in\nthe selected events. To account for this effect, the jet resolution is computed by allowing a third jet with\ntransverse momentum pT,3 up to some threshold \u03b5, and varying the threshold values between \u03b5 = 12.5\nand 27.5 GeV. As before, the resolution distributions in the jet pT bins are \ufb01tted using single Gaussian\nfunctions. For each jet pT bin, the set of resolutions obtained from the different pT,3 thresholds are \ufb01tted\nwith a straight line and extrapolated to \u03b5 = 0. We de\ufb01ne this value as:\n\u0012\u03c3pT\npT\n\u0013pT,3\u21920\n,\n(15)\nwhich would be the resolution that we would have measured from an ideal dijet sample with \u03b5 = 0.\nExamples of the linear \ufb01ts and the extrapolations for two pT bins are presented in Fig. 23.\nAfter \ufb01tting the resolution for the different third jet thresholds, we calculate a correction factor,\nK(pT), as follows:\nK(pT) =\n\u0012\u03c3pT\npT\n\u0013pT,3\u21920\n/\n\u0012\u03c3pT\npT\n\u0013\u03b5=10 GeV\n.\n(16)\nFinally, correcting by this factor, the unbiased fractional transverse energy resolution is obtained via\n\u0012\u03c3pT\npT\n\u0013\ncorrected\n= K(pT)\u00d7\n\u0012\u03c3pT\npT\n\u0013\u03b5=10 GeV\nuncorrected\n.\n(17)\nSince the soft radiation bias should be larger at small transverse energies, and negligible at high pT we\nparametrize K(pT), with the function:\nK(pT) = 1\u2212exp(a\u2212bpT) .\n(18)\nThis parametrization can be used to correct the resolution for each pT bin and determine the unbiased\nresolution associated purely with detector effects. The jet energy resolutions with and without the soft\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n362\n\nFigure 23: Resolution versus the pT,3 threshold cut for different pT bins. The line corresponds to the\nlinear \ufb01t applied while the dashed-line shows the extrapolation to pT,3 = 0, which corresponds to an ideal\ndijet sample (\u03b5 = 0).\nradiation correction are shown in Fig. 24. As we will see below, by comparing this result to that ob-\ntained by other approaches we can establish an estimate of the systematic uncertainty of the jet energy\nresolution.\nFigure 24: Jet energy resolution for cone jets with\nR = 0.7 in the pseudorapidity range |\u03b7| < 1.2. The\nresults are obtained by using dijet balance tech-\nniques with and without applying the soft radia-\ntion correction.\nFigure 25: Sketch of the kT balance technique.\nThe \u03b7 axis corresponds to the azimuthal angular\nbisector of the dijet system while the \u03c8 axis is de-\n\ufb01ned as being orthogonal to the \u03b7 axis.\n5.3.3\nThe kT balance technique\nThe kT balance technique was developed by UA2 and studied at CDF. To extract the contributions of\ndetector effects on to the jet energy resolution, the imbalance vector \u20d7KT = \u20d7pT,1 +\u20d7pT,2 is projected onto\ntwo components (\u03c8,\u03b7) as shown in Fig. 25.\nThe \u03b7 axis corresponds to the azimuthal angular bisector of the dijet system while the \u03c8 axis is\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n363\n\nde\ufb01ned as being orthogonal to the \u03b7 axis. The two components, KT,\u03c8 and KT,\u03b7, are sensitive to different\neffects. The calorimeter energy resolution represents the main source for \u03c3\u03c8, the spread of KT,\u03c8. Gluon\nradiation effects are smaller but affect this component as well. On the other hand, \u03c3\u03b7, the spread of KT,\u03b7,\nis signi\ufb01cantly affected by gluon radiation. In addition, there are other smaller effects such as jet angular\nresolution, underlying event and out-of-cone \ufb02uctuations. In order to reduce the hard gluon radiation\neffects, events with pT,3 > 11 GeV are rejected. If we de\ufb01ne the contributions from the calorimeter\nresolution, \u03c3res, and from soft radiation, \u03c3SR\u2225and \u03c3SR\u22a5, then we can write\n\u03c3 2\n\u03c8\n=\n\u03c3 2\nres +\u03c3 2\nSR\u2225\n\u03c3 2\n\u03b7\n=\n\u03c3 2\nSR\u22a5.\nAssuming\n\u03c3 2\nSR\u2225= \u03c3 2\nSR\u22a5,\n(19)\nthe soft radiation effects are removed by subtracting in quadrature \u03c3\u03b7 from \u03c3\u03c8:\n\u03c3res =\nq\n\u03c3 2\u03c8 \u2212\u03c3 2\u03b7 .\n(20)\nThe data sample was divided into six pT regions, and the distributions KT,\u03b7 and KT\u03c8 were \ufb01tted with\nsingle Gaussians. Since in this method the measured resolution comes from the convolution of the single\njet resolution, to obtain the single jet energy resolution, \u03c3res must be scaled by a factor\n1\n\u221a\n2.\nFigure 26 shows the resulting\n1\n\u221a\n2\u03c3\u03c8 and\n1\n\u221a\n2\u03c3\u03b7 as a function of the square root of the average pT of\nboth jets. \u03c3\u03c8 has an approximately linear dependence with\nq\n\u27e8pT1,2\u27e9, while \u03c3\u03b7 has a \ufb02at dependence,\nespecially at high pT, as expected. The effective jet energy resolution after removing soft radiation effects\nby subtracting in quadrature \u03c3\u03b7 from \u03c3\u03c8 is shown in Fig. 27.\nFigure 26:\n1\n\u221a\n2\u03c3\u03c8 and\n1\n\u221a\n2\u03c3\u03b7 in dijet events as a function of the square root of the average pT of both jets.\n5.3.4\nComparison of dijet and kT balance techniques\nA comparison of the two methods, the dijet balance and the kT balance technique, allows an estimate of\nthe systematic uncertainty associated with the determination of the resolution associated with detector\nresponse. By comparing the reconstructed jets with the jets from Monte Carlo truth we obtain informa-\ntion on its dependence on the jet algorithm and the jet matching. Each of the \ufb01rst two leading calorimeter\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n364\n\nFigure 27: The effective jet energy resolution for\ncone 0.7 jets after removing soft radiation effects\nby subtracting in quadrature \u03c3\u03b7 from \u03c3\u03c8.\nFigure 28: True jet energy resolution for cone 0.7\ncompared with those obtained using dijet and kT\nbalance techniques.\njets is matched to particle jets, which lie within \u2206R < 0.1 w.r.t. the reconstructed jet. After matching, the\nresponse pcalo\nT\n/ptruth\nT\nis determined, and the true resolution is obtained by \ufb01tting the response with single\nGaussians. This is shown in Fig. 28 together with the results from the two data-driven estimates.\nThe two data-driven approaches agree within uncertainties, though a hint that the kT method is un-\nderestimating the true detector resolution might be visible. The determination of the resolution using\nreconstructed jets matched to particle jets gives results in between the two data-driven approaches and\ntogether with them provides a reasonable basis from which to estimate the systematic uncertainties in the\ndetermination of the noise, stochastic and constant terms in the jet energy resolution.\n6\nSummary and conclusions\nPrecise reconstruction of the jet energy is required by many physics analyses. In-situ processes provide\nthe platform against which our understanding, based on theory and detector simulation, must be tested\nin order to achieve maximum precision. From the analyses presented in this paper, we conclude that one\ncan characterize three ranges of jet pT, in which the different features of detector response and underlying\nphysics control the precision which can be achieved.\nFrom the reconstruction threshold of 10 GeV up to \u223c100 \u2212200 GeV, the combination of effects\nfrom jet clustering and physics effects like ISR/FSR and underlying event can be as large as 5\u221210% at\nlow pT, slowly decreasing to the percent level around 100 \u2212200 GeV. With QCD dijet events, we will\nbe able to control the uniformity of the response on the percent level with high granularity in \u03c6 and \u03b7\nalready with \u223c10pb\u22121. In turn, Z + jet balance is an adequate process to measure the absolute energy\nscale with a statistical precision of 1% with approximately 300pb\u22121 of data. Hence the precision will\nrather quickly be dominated by the systematic uncertainty. Validation of the Monte Carlo simulation to\nensure that both physics and detector effects are well modeled will be particularly important to control\nsystematic uncertainties. Differences between currently available Monte Carlo generators are on the level\nof 5\u221210% in some of the observables, which sets the scale for the challenge in this region of jet pT.\nThe medium pT region extends from 100 \u2212200 GeV to about 500 GeV. Physics effects are at the\nlevel of 1\u22122% in this region. The momenta of the particles resulting from jet fragmentation are within\nthe range of the test beam measurement. It will be an important range in which to validate the Monte\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n365\n\nCarlo description of the detector response. In addition the dijet balance is still statistically powerful, and\n1% precision for an \u03b7 bin size of 0.1 can be achieved with \u223c100pb\u22121. In \u03b3 + jet events the pT balance\ncan be measured with negligible bias from QCD background. The statistical precision is better than\none percent for 10pb\u22121 at 100 GeV, and in the range 300 \u2212500 GeV the percent level is reached with\n\u223c100pb\u22121.\nAbove 500 GeV, one enters a regime which is beyond any existing jet measurement and extrapolation\nof the Monte Carlo modeling and comparison to in-situ data is crucial. A much larger integrated lumi-\nnosity is required for in-situ measurements of similar precision. In addition, for the highest momentum\nparticles which may be produced in these jets, our simulation of the detector no longer has test beam\ndata available as a basis. Techniques such as multijet balancing or extrapolation based on jet particle\nproperties can be used and should allow us to control the scale at the level of a few percent with 1fb\u22121\nfor jets up to 1 TeV.\nReferences\n[1] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[2] ATLAS Collaboration, Jets from Light Quarks in t\u00aft Events, this volume.\n[3] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[4] ATLAS Collaboration, E/p Performance for Charged Hadrons, this volume.\n[5] T. Sj\u00a8ostrand, S. Mrenna and P. Skands, JHEP 0605 (2006) 026, arXiv:hep-ph/0603175.\n[6] Gribov, V. N. and Lipatov, L. N., Sov. J. Nucl. Phys. 15 (1972) 438; Gribov, V. N. and Lipatov, L.\nN., Sov. J. Nucl. Phys. 15 (1972) 675; Lipatov, L. N., Sov. J. Nucl. Phys. 20 (1975) 94; Dokshitzer,\nYu. L., Sov. Phys. JETP 46 (1977) 641; Altarelli, G. and Parisi, G., Nucl. Phys. B 126 (1977) 298.\n[7] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP 07 (2002) 012.\n[8] G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Syemour\nand B. R. Webbber, JHEP 0101 (2001) 010, arXiv:hep-ph/0011363.\n[9] J. M. Butterworth, J. R. Forshaw and M. H. Seymour,\nZ. Phys. C72 (1996) 637,\narXiv:hep-\nph/9601371.\n[10] B. R. Webber, Nucl. Phys. B238 (1984) 492.\n[11] G. Marchesini and B. R. Webber, Nucl. Phys. B310 (1988) 461.\n[12] M. L. Mangano, M. Moretti, F. Piccinini, R.\nPittau and A. Polosa,\nJHEP 0307 (2003) 001,\narXiv:hep-ph/0206293.\n[13] ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\n[14] S. Jorgensen,\n\u03b3 + Jet In-situ Process for Validation of the Jet Reconstruction with the ATLAS\nDetector, Master\u2019s thesis, Universitat Autonoma de Barcelona, 2006.\n[15] D. Schouten, Jet Energy Calibration in ATLAS, Master\u2019s thesis, Simon Fraser University, 2007.\n[16] ATLAS Collaboration, Production of Jets in Association with Z Bosons, this volume.\n[17] D0 Collaboration, B. Abbot et al., Nucl. Instrum. Meth. A424 (1998) 094.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n366\n\n[18] P. Weber, ATLAS Calorimetry: Trigger, Simulation and Jet Calibration, Ph.D. thesis, Universit\u00a8at\nHeidelberg, 2008.\nJETS AND MISSING ET \u2013 JET ENERGY SCALE: IN-SITU CALIBRATION STRATEGIES\n367\n\nMeasurement of Missing Tranverse Energy\nAbstract\nThis note discusses the overall ATLAS detector performance for the recon-\nstruction of the missing transverse energy, /ET. Two reconstruction algorithms\nare discussed and their performance is evaluated for a variety of simulated\nphysics processes which probe different topologies and different total trans-\nverse energy regimes. In addition, effects of fake /ET resulting from instru-\nmental effects and from false reconstructions are investigated. Finally, studies\nwith \ufb01rst data, corresponding to an integrated luminosity of 100pb\u22121, are sug-\ngested which can be used to assess and calibrate the /ET performance at the\nstartup of data taking.\n1\nIntroduction\nA very good measurement of the missing transverse energy, /ET, is essential for many physics studies\nin ATLAS. Events with large /ET are expected to be the key signature for new physics such as super-\nsymmetry and extra dimensions. A good /ET measurement in terms of linearity and resolution is also\nimportant for the reconstruction of the top-quark mass from t\u00aft events with one top quark decaying semi-\nleptonically. Furthermore, it is crucial for the ef\ufb01cient and accurate reconstruction of the Higgs boson\nmass when the Higgs boson decays to a pair of \u03c4-leptons.\nThis Note describes the overall performance of the /ET measurement in ATLAS. The performance is\nchecked using fully simulated Monte Carlo (MC) samples in different physics channels with differences\nin event topology and kinematics range. Events with no true /ET as well as events with a true /ET, /ETrue\nT\n,\ndue to particles unseen in the detector as neutrinos or lightest supersymmetric particles, ranging from\n\u223c20 to \u223c500 GeV are used.\nAn important requirement on the measurement of /ET is to minimize the impact of limited detector\ncoverage, \ufb01nite detector resolution, presence of dead regions and different sources of noise that produce\nfake /ET, /EFake\nT\n. The ATLAS calorimeter coverage extends to large pseudorapidity angles to minimize\nthe impact of high energy particles escaping in the very forward direction. Even so, there are inactive\ntransition regions between different calorimeters that produce /EFake\nT\n. Dead and noisy readout channels\nin the running detector, if present, will also produce /EFake\nT\n. Such /EFake\nT\nsources can signi\ufb01cantly enhance\nthe background from QCD multi-jet events in supersymmetry searches or the background from Z \u2192\u2113\u2113\nevents accompanied by high-pT jets in Higgs boson searches when the Higgs boson decays into two\nleptons and neutrinos.\nThe calorimeter plays a crucial role in the /ET measurement and an important \ufb01rst step of the /ET\nmeasurement is the suppression of noise in the calorimeter. Section 2 describes the techniques used for\nnoise suppression in calorimeters. The two /ET reconstruction algorithms used in ATLAS, Cell-based\nand Object-based, are described in detail in Sections 2.2 and 2.3. The overall performance of the /ET\nmeasurement in ATLAS is reported in Section 3. Any mis-measurement in the event, due to \ufb01nite\nresolution or acceptance of the detector or due to instrumental effects related to dead or noisy channels,\nwill degrade the /ET measurement. Such sources of /ET, that can lead to large values of fake /ET, are\nstudied in Section 4. Section 5 introduces the /ET algorithm for the ATLAS triggers and describes its\nperformance. Finally, Section 6 describes techniques in different physics channels that can be used with\nthe very \ufb01rst ATLAS data to validate the /ET measurement and determine the /ET scale in-situ.\n368\n\n2\nThe algorithms for /ET reconstruction in ATLAS\nThe transverse missing energy in ATLAS is primarily reconstructed from energy deposits in the calorime-\nter and reconstructed muon tracks. Apart from the hard scattering process of interest, many other sources,\nsuch as the underlying event, multiple interactions, pile-up and coherent electronics noise, lead to energy\ndeposits and/or muon tracks. Classifying the energy deposits into various types (e.g. electrons or jets)\nand calibrating them accordingly is the essential key for an optimal /ETmeasurement. In addition, the loss\nof energy in dead regions and readout channels make the /ET measurement a real challenge.\nThere are two algorithms for /ET reconstruction in ATLAS that emphasize different aspects of energy\nclassi\ufb01cation and calibration.\nThe Cell-based algorithm starts from the energy deposits in calorimeter cells that survive a noise\nsuppression procedure. The cells can be calibrated using global calibration weights depending on their\nenergy density. This procedure will be robust already at initial data taking because it does not rely on\nother reconstructed objects. In a subsequent step, the cells can be calibrated according to the recon-\nstructed object they are assigned to. Corrections are applied for the muon energy and for the energy lost\nin the cryostats.\nThe Object-based algorithm starts from the reconstructed, calibrated and classi\ufb01ed objects in the\nevent. The energy outside these objects is further classi\ufb01ed as low pT deposit from charged and neutral\npions and calibrated accordingly.\nThe noise suppression in the calorimeter is common for the Cell- and Object-based algorithm and is\ndescribed below, followed by a detailed description of the algorithms.\n2.1\nCalorimeter noise suppression\nThe electronics noise alone in the \u2248200k readout channels of the ATLAS calorimeter contributes about\n13 GeV to the width of the /ET distribution. Especially in events that do not have large /ET, such as in\nZ \u2192\u03c4\u03c4 used for an in-situ determination of the /ET scale (Section 6.2), the noise suppression is of crucial\nimportance.\nFor the /ET measurement, two noise suppression methods have been studied so far. Both require\nknowledge of the width of the noise distribution, \u03c3noise, which can be either purely electronics noise or a\ncombination of electronics and pile-up noise.\nStandard Noise Suppression Method. The \ufb01rst method is based on only using calorimeter cells\nwith energies larger than a threshold, generally corresponding to a certain number of \u03c3noise. The threshold\nis optimized for /ET resolution, the scale of /ET, the total transverse energy in the calorimeters, \u03a3/ET, and\nfor the highest pT jet to be close to the case without noise simulation. Two cases are studied: a symmetric\nthreshold (|Ecell| > n \u00d7 \u03c3noise) and an asymmetric one (Ecell > n \u00d7 \u03c3noise). A symmetric threshold with\nn = 2 for all calorimeters is generally used.\nNoise Suppression using TopoClusters. The second method only uses cells in 3-dimensional topo-\nlogical calorimeter clusters [1, 2], hereafter called TopoClusters. A TopoCluster is reconstructed starting\nfrom a seed cell with an absolute energy value |Ecell| > 4\u03c3noise to which neighbors with |Ecell| > 2\u03c3noise\nare added. Finally the cells at the boundary are required to have |Ecell| > 0\u03c3noise. The cells that constitute\nthe TopoCluster are hereafter called TopoCells. This set of thresholds, referred to as 4/2/0, is optimized\nto suppress electronics noise as well as pile-up from minimum bias events, while keeping the single pion\nef\ufb01ciency as high as possible.\nAs a result of the large energy density of electromagnetic showers, the \u03c00 reconstruction ef\ufb01ciency\nis high (close to 100% for energies > 4 GeV) for the 4/2/0 con\ufb01guration. On the other hand, the\nreconstruction ef\ufb01ciency for charged pions is very sensitive to the parameters of the TopoClusters. For\nexample, changing the cuts on neighbors from 4/2 to 6/3, the \u03c0\u00b1 ef\ufb01ciency signi\ufb01cantly decreases for\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n369\n\nTopoClusters with E < 4 GeV. This sensitivity highlights the importance of a good modeling of the noise\nlevel from \ufb01rst data.\nIn Z \u2192\u03bd \u00af\u03bd events simulated with electronics noise, the /ET resolution degrades by only 3 % for\nthe 4/2/0 con\ufb01guration as compared to the same events without noise added. Also, the TopoCluster\nalgorithm performs better in terms of linearity and resolution of the /ET measurement, compared to the\nstandard noise suppression method. Therefore Cell- and Object-based /ET algorithms apply the noise\nsuppression method based on TopoClusters with con\ufb01guration 4/2/0.\n2.2\nCell-based /ET reconstruction\nThe Cell-based /ET reconstruction includes contributions from transverse energy deposits in the calorime-\nters, corrections for energy loss in the cryostat and measured muons:\n/EFinal\nx,y\n= /ECalo\nx,y + /ECryo\nx,y + /EMuon\nx,y\n.\n(1)\nIn the following, the three terms in the above equation, referred to as calorimeter, cryostat and muon\nterms, are described in some detail.\n2.2.1\nThe /ET calorimeter term\nAs described in the previous section, the \ufb01rst step is to select calorimeter cells that belong to reconstructed\nTopoClusters to minimize the impact of noise.\nThe x and y components of the calorimeter /ET term are calculated from the transverse energies\nmeasured in TopoCells:\n/ECalo\nx,y = \u2212\u2211\nTopoCells\nEx,y.\n(2)\nThe total transverse energy in the calorimeters, \u03a3/ET, is calculated from the scalar sum of ET of all\nTopoCells:\n\u03a3/ET\nCalo =\n\u2211\nTopoCells\nET.\n(3)\nThe straightforward result, obtained by using the electromagnetic calibration for all cells, gives a\nlarge shift in the /ET scale of about 30% with respect to /ETrue\nT\n(see Section 3).\nThis result illustrates the necessity of developing a dedicated calibration scheme to reduce the sys-\ntematic shift of the /ET scale and optimize its resolution. This goal is achieved in several steps according\nto the cell classi\ufb01cation. The classi\ufb01cation depends on whether the energy deposits in the calorimeter\nare electromagnetic or hadronic in nature and whether they are associated with high pT particles.\nTo classify energy deposits, schemes to calibrate hadronic showers such as \u2018H1-like\u2019 calibration\nor \u2018Local-Hadronic\u2019 calibration [3] utilize the energy density in a cell. Electromagnetic showers tend\nto have higher energy densities as compared to hadronic showers. The \u2018Local-Hadronic\u2019 calibration\nscheme uses further information related to shape and depth of the calorimetric shower to classify a\nTopoCluster. The next step in the cell-based /ET reconstruction is to globally calibrate all calorimeter\ncells using the \u2018H1-like\u2019 or \u2018Local-Hadronic\u2019 calibration schemes. As can be seen in the performance\nsection, this already gives a very good /ET performance. The \ufb01nal re\ufb01nement step of the calibration using\nthe association of cells with reconstructed objects is described in Section 2.2.4. It improves the linearity\nand the resolution particularly for events containing electrons (Section 3).\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n370\n\n2.2.2\nThe /ET muon term\nThe /ET muon term is calculated from the momenta of muons measured in a large range of pseudorapidity,\nde\ufb01ned by |\u03b7| < 2.7:\n/EMuon\nx,y\n= \u2212\n\u2211\nRecMuons\nEx,y.\n(4)\nIn the region |\u03b7| < 2.5 only good-quality muons in the muon spectrometer with a matched track in\nthe inner detector are considered. The matching requirement reduces considerably contributions from\nfake muons, sometimes created from high hit multiplicities in the muon spectrometer in events with very\nenergetic jets. For higher values of the pseudorapidity (2.5 < |\u03b7| < 2.7), outside the \ufb01ducial volume of\nthe inner detector, there is no matched track required and the muon spectrometer is used alone.\nThe muon momentum measured by the muon spectrometer is taken in the two cases. Energy lost\nin the calorimeter is already included in the calorimeter term. No pT threshold cut is applied to re-\nconstructed muons. Apart from the loss of muons outside the acceptance of the muon spectrometer\n(|\u03b7| > 2.7), there is a loss of muons in other regions (see Section 4.1) due to limited coverage of the\nmuon spectrometer. The muons reconstructed from the inner detector and calorimeter energy deposits\ncould be used to recover these events, but they are not yet used here.\nAs can be seen in the performance section, the /ET resolution is only marginally affected by the muon\nterm, due to the good identi\ufb01cation ef\ufb01ciency and resolution of the ATLAS muon system. However,\nunmeasured, badly measured or fake muons can be a source of large fake /ET (see Section 4).\n2.2.3\n/ET cryostat term\nThe thickness of the cryostat between the LAr barrel electromagnetic calorimeter and the tile barrel\nhadronic calorimeter is about half an interaction length where hadronic showers can lose energy. The\n/ET reconstruction recovers this loss of energy in the cryostat using the correlation of energies between\nthe last layer of the LAr calorimeter and the \ufb01rst layer of the hadronic calorimeter. A similar correction\nfor the end-cap cryostats is applied. This correction is called the cryostat term when used for jet energy\ncorrection [3]. It is de\ufb01ned as follows:\n/ECryo\nx,y\n= \u2212\u2211\nrecJets\nE jetCryo\nx,y ,\n(5)\nwhere all reconstructed jets are summed in the event, and\nE jetCryo = wCryo\u221aEEM3 \u00d7EHAD,\n(6)\nwhere wCryo is a calibration weight (determined together with the cell calibration weights in the H1-like\ncalibration) and EEM3 and EHAD are the jet energies in the third layer of the electromagnetic calorimeter\nand in the \ufb01rst layer of the hadronic calorimeter, respectively. The cryostat correction turns out to be\nnon-negligible for high-pT jets. It contributes at the level of \u223c5% per jet with pT above 500 GeV.\n2.2.4\nRe\ufb01ned calibration of the /ET calorimeter term\nThe \ufb01nal step is the re\ufb01nement of the calibration of cells associated with each high-pT object. Calorime-\nter cells are associated with a parent reconstructed and identi\ufb01ed high-pT object, in a chosen order:\nelectrons, photons, muons, hadronically decaying \u03c4-leptons, b-jets and light jets. Re\ufb01ned calibration of\nthe object is then used in /ET to replace the initial global calibration cells. The calibration of these objects\nis known to higher accuracy than the global calibration, enabling to improve the /ET reconstruction.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n371\n\nEtMissTruth\u2212EtMissRec (GeV)\n\u221250\n\u221240\n\u221230\n\u221220\n\u221210\n0\n10\n20\n30\n40\n50\n Arbitrary units\n0\nATLAS\nMean=0.01GeV\n= 6.8GeV\n\u03c3\nEtMissTruth\u2212EtMissRec (GeV)\n\u221250\n\u221240\n\u221230\n\u221220\n\u221210\n0\n10\n20\n30\n40\n50\n Arbitrary units\n0\nATLAS\nMean=\u22120.98GeV\n = 8.5GeV\n\u03c3\nFigure 1: Distribution of the difference between true and reconstructed /ET for Z \u2192\u03c4\u03c4\nevents (left)\nincluding and (right) excluding cells in Topoclusters not associated with reconstructed high-pT objects.\nThe calorimeter cells are associated with the reconstructed objects through the use of an association\nmap. This map is \ufb01lled starting from the reconstructed/identi\ufb01ed objects in the chosen order, navigating\nback to their component clusters and back again to their cells. If a cell belongs to several kinds of\nreconstructed objects, only the \ufb01rst association is included in the map, i.e. the overlap removal is done\nat cell level. This avoids double counting of cells in the /ET calculation. If a cell belongs to more than\none object of the same kind, all associations are included in the map and the geometrical weight of the\ncells, accounting for the sharing of energy of cells owned by two different TopoClusters, is also included\nto avoid double counting.\nAttention has to be paid to the calibration of cells inside different objects. For example, for elec-\ntrons/photons, the \ufb01nal cluster-level calibration (which can be propagated back to the cell-level) corrects\nfor upstream material, longitudinal leakage and out-of-cone energy. The last correction should not be\napplied in the /ET calculation because the contribution of cells outside objects already accounts for it.\nIn a similar way, for \u03c4 lepton decays and for jets, the overall scale factors which correct the energy for\nphysics effects like \ufb01nal state radiation, fragmentation or the underlying event as well as for the effects\ndue to the clustering algorithm are not applied in the calculation of /ET, because they also contain the\nout-of-cluster correction.\nAll TopoCells, even if not associated with any high-pT reconstructed object, are used in the /ET\ncalculation. They are calibrated using the global calibration scheme. The importance of the energy\ndeposits of these low energy particles for the /ET calculation is shown in Fig. 1. The shift in the absolute\nvalue of the reconstructed /ET increases by about 1 GeV while the resolution is degraded by a factor\n\u223c1.25.\nOnce the cells are associated with categories of objects as described above, the contribution to /ET is\ncalculated as follows:\n/ECalo\nx,y = /ERefCalib\nx,y\n= \u2212(/ERefEle\nx,y\n+ /ERefTau\nx,y\n+ /ERefbjets\nx,y\n+ /ERefJets\nx,y\n+ /ERefMuo\nx,y\n+ /ERefOut\nx,y\n),\n(7)\nwhere each term is calculated from the negative of the sum of calibrated cells inside a speci\ufb01c object\nand /ERefOut\nx,y\nis calculated from the cells in TopoClusters which are not included in the reconstructed\nobjects. In the following the \ufb01nal /ET calculation obtained from Equation (1) with /ECalo\nx,y = /ERefCalib\nx,y\nwill\nbe referred to as /ERefFinal\nT\n.\n2.3\nObject-based /ET reconstruction\nThe motivation of the method is to reliably reconstruct /ET for analyses that are sensitive to low pT\ndeposits coming mostly from neutral and charged pions, from soft jets, from the underlying event and\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n372\n\nfrom pile-up. This is important, for example, in reconstructing the invariant mass of the Standard Model\nHiggs boson, mH, in the H \u2192\u03c4+\u03c4\u2212\ufb01nal state for masses in the range 115 < mH < 140 GeV [4].\nThe object-based method comprises two main steps:\n\u2022 Establish a classi\ufb01cation between two main types of objects: high pT (e/\u03b3,\u00b5,\u03c4, jets) and low\npT objects (\u03c00,\u03c0\u00b1, unclustered deposits) coming from underlying event, pile-up of multiple pp\ncollisions, initial and \ufb01nal state radiation, and other soft QCD processes.\n\u2022 Apply the object-based calibration optimized for /ET calculation.\nThe x and y components of /ET and \u2211ET are calculated by adding the contributions from each type of\ncomponents:\n/Ex,y\n=\n\u2212EHigh\nx,y\n\u2212ELow\nx,y\n(8)\n\u2211ET\n= \u2211EHigh\nT\n+\u2211ELow\nT\n,\n(9)\nwhere the indices \u2018High\u2019 and \u2018Low\u2019 correspond to the /ET and \u2211ET calculated from high pT and low pT\nobjects, de\ufb01ned below.\nThe object-based algorithm uses mostly the calorimeter to reconstruct /ET. Some objects such as\nelectrons and taus also use the inner detector tracking, while the muons use both, inner detector and\nmuon spectrometer information. Tracking is also used for the low pT deposits of soft objects.\nThe object-based method uses the TopoClusters 4/2/0 (Section 2.1) and \ufb01rst calculates all contribu-\ntions of high pT objects. Each TopoCluster is allowed to be included only once by the \ufb01rst object that is\nassociated with it. The classi\ufb01cation starts with the identi\ufb01cation of electrons, photons, muons and \u03c4\u2019s.\nOnce the clusters belonging to these objects are removed from the event record, hadronic jets above a\ncertain threshold are identi\ufb01ed. TopoCells not part of any of the above high pT objects are classi\ufb01ed as\nlow pT deposit. The next subsections discuss the calibration of these objects.\n2.3.1\nCalorimeter objects: electrons, hadronic \u03c4-jets, jets\nElectrons:\nThe electron objects are taken from the standard electron reconstruction and a matched\ntrack is always required. The default calibration of an electron is based on the \u2018sliding window\u2019 EM\nclusters [5]. To be consistent with the combined 4/2/0 TopoClustering used for the object-based recon-\nstruction, electrons are reconstructed from TopoClusters and they are calibrated by weighting the energy\ndeposits in the longitudinal calorimeter layers. The electron pT is required to be at least 8 GeV.\nTau Leptons:\nThe object-based method uses the calo-based reconstructed \u03c4-jets [6] and it calibrates\nthem as jets. A cut of 20 GeV on the \u03c4-jet pT is applied and a \u03c4 likelihood > 4 is required.\nJets:\nA cone (\u2206R = 0.7) jet algorithm running on the TopoClusters is used for calculating the /ET\ncontribution from jets. Jets not overlapping with the electron and tau jets are chosen. The jet energy\ncalibration is based on the \u2018H1-like\u2019 hadronic calibration [3], which corrects for the difference in response\nfor e/\u03b3 and hadrons, followed by a scale correction due to the non-uniformity of the reconstruction in \u03b7.\nIt is based on the /ET projection method (used by CDF and D0)[7] using a dijet sample where forward\njets are corrected with respect to well measured central jets (|\u03b7| < 0.8). The jet pT is required to be at\nleast 20 GeV .\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n373\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n>\ntrue\n)/E\ntrue\n-E\ncalib\n<(E\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n7-10 GeV\n5-6 GeV\n3-4 GeV\n1-2 GeV\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n>\ntrue\n)/E\ntrue\n-E\ncalib\n<(E\n-0.3\n-0.2\n-0.1\n0\n0.1\n0 2\n0 3\n7-10 GeV\n5-6 GeV\n3-4 GeV\n1-2 GeV\nATLAS\nFigure 2: Linearity for single charged \u03c0 (left) and single \u03c00 (right) as a function of \u03b7 for the energy bin\n1 < E < 10 GeV).\n2.3.2\nMuons\nIn general, the combined muons, reconstructed from the inner detector and the muon spectrometer, are\nused. In the region where the inner detector has no coverage (2.5 < |\u03b7| < 2.7) muons reconstructed from\nthe spectrometer only are used. To reduce the number of fake muons originating from punch through of\nhigh pT jets, strong quality requirements are imposed on the combined track from the inner detector and\nthe muon spectrometer. Additionally, if a muon passes inside a jet and the ratio of measured momenta in\nthe inner detector and in the muon spectrometer is below 0.2, the muon is rejected. If the muon is found\ninside a jet or the total pT at the EM scale of the TopoClusters within a cone of 0.2 around the muon is\n> 10 GeV, either the measured muon energy loss in the calorimeter is subtracted from the combined pT\nor the muon spectrometer pT is used. The combined muon pT is required to be at least 6 GeV.\nInner detector tracks may be used to improve the /ET reconstruction. They contain the muons not\ncovered by the combination of inner detector and muon spectrometer, especially in the crack regions of\nthe muon system. Only those tracks are retained which are isolated from others by a cone of size 0.3.\nThose tracks overlapping with electrons, muons or jets that are already used for /ET are discarded. The\ntracks should have pT > 6 GeV and should satisfy a muon likelihood criterion based on E/p and the\nenergy in the calorimeter sampling layers. In addition, isolated tracks (mostly pions) with little energy\ndeposits in the calorimeter can be used to improve /ET. These tracks are used only if pT less than 10 GeV,\nto avoid tracks with spurious high pT,which deteriorates the /ET performance.\n2.3.3\nLow pT depositions: classi\ufb01cation and calibration\nOnly those TopoClusters that have not been assigned to high pT objects are considered for classi\ufb01cation\nas low pT objects of either electromagnetic or hadronic nature. For this purpose, clusters are further sub-\ndivided into so-called mini-jets. Mini-jets are reconstructed from TopoClusters using a cone algorithm\nof a relatively small radius of \u2206R = 0.2 and a seed cluster of pT > 0.5 GeV. A mini-jet is required to\nhave pT > 0.5 GeV. The mini-jets are next classi\ufb01ed as charged and neutral pions.\nThe separation between charged and neutral pions is done only in |\u03b7| < 3.2. A mini-jet is de\ufb01ned\nto be a \u03c00 if the fractional energy in the hadronic compartments is less than 2% and pT > 10 GeV. The\nlow pT deposits are calibrated under single charged and neutral pion hypotheses in the full \u03b7 range. A\nsampling method similar to that used to extract longitudinal weights as implemented for the electron\nand photon calibration is used. The calorimeter sampling weights are determined separately for neutral\nand charged pions in different energy and \u03b7 regions. A good linearity is achieved for both neutral and\ncharged pion hypotheses. Figure 2 shows the linearity for charged and neutral pions in the central region,\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n374\n\nwhich roughly \ufb02uctuates within 5%.\nMini-jets will not saturate all the low pT calorimeter deposits. There will remain a non-trivial amount\nof energy left in the calorimeter and clustered in TopoClusters from very low momentum pions, which\nwill not form a mini-jet. These deposits are referred to as unassociated deposits. The energy calibration\nof these unassociated deposits has been estimated in three \u03b7\nregions, depending on the calorimeter\nregion (barrel, end-cap, forward), and has been added to the /ET calculation.\n3\nPerformance of the reconstructed /ET\nIn this section the performance of the /ET reconstruction is discussed, focusing on the linearity and resolu-\ntion of the reconstructed /ET as a function of the true missing transverse energy, /ETrue\nT\n. The measurement\nof the /ET direction and the dependence on topology are also discussed. Note that the performance of\nthe two /ET reconstruction methods is very similar, so it is not speci\ufb01ed which method has been used to\nproduce each performance plot.\n/ETrue\nT\nis de\ufb01ned from the sum of all stable and non-interacting particles in the \ufb01nal state (neutrinos\nand the lightest supersymmetric particles). Comparisons between /ET and /ETrue\nT\nare made for a number\nof physics processes with different topologies and \ufb01nal states.\nThe /ET performance in case of events with large /EFake\nT\n, which contribute predominantly to the tails\nof the /ET distribution, is described in the next section.\n3.1\nLinearity and resolution\nThe /ET linearity is de\ufb01ned by the following expression:\nLinearity = (/ETrue\nT\n\u2212/ET)//ETrue\nT\n,\n(10)\nwhere /ET and /ETrue\nT\nare reconstructed and true /ET, respectively. This de\ufb01nition of linearity assumes an\n/ETrue\nT\nvalue above a threshold and an /EFake\nT\nvalue that is small such that the /ET angle is well measured.\nFigure 3 shows the reconstructed linearity as a function of /ETrue\nT\nfor a number of physics processes.\nThe following statements summarize the behavior of the linearity distributions:\n\u2022 The uncalibrated /ET corresponds to the use of cell energies at the electromagnetic scale and shows\na large systematic bias of 30%. In W \u2192e\u03bd and W \u2192\u00b5\u03bd decays, the bias is smaller since the\nhadronic activity on average is smaller.\n\u2022 The reconstructed /ET based on globally calibrated cell energies and reconstructed muons gives a\nlinearity to within 5%.\n\u2022 The reconstructed /ET including the cryostat correction shows a linearity to within 1% for all pro-\ncesses except for W \u2192e\u03bd .\n\u2022 The re\ufb01ned /ET calibration, which optimizes the calibration with reconstructed object identity,\nrecovers the linearity for W \u2192e\u03bd events to within 1%. The re\ufb01ned calibration also gives the best\nresolution when compared with the above steps of calibration (see also Section 6).\nThe linearity for A \u2192\u03c4\u03c4 with mA = 800 GeV is shown in Fig. 3 (right) as a function of /ETrue\nT\n. The\nbias of linearity at low /ETrue\nT\nis due to the \ufb01nite resolution of the /ET measurement. The reconstructed\n/ET is positive by de\ufb01nition, so the linearity is negative when the true /ET is near to zero. Excluding the\nevents with /ETrue\nT\n< 40 GeV, which have a small statistics the observed linearity is found to be within\n2%.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n375\n\nThe resolution is estimated from the width of the /Ex,y \u2212/ETrue\nx,y\ndistribution in bins of the total trans-\nverse energy deposited in the calorimeters (\u03a3/ET). The core of each distribution is \ufb01tted with a Gaussian\nshape to estimate the width. Figure 4 shows the \u03c3 of the \ufb01t plotted as a function of \u03a3/ET when re\ufb01ned\ncalibration is applied. The /ET resolution approximately follows a stochastic behaviour as a function of\n\u03a3/ET. Deviations from this simple behaviour are expected, and observed for low values of \u03a3/ET where\nthe contribution of noise is important and for very high values of \u03a3/ET where the constant term in the\nresolution of the calorimetric energy measurement dominates.\nThe /ET resolution is \ufb01tted with a function \u03c3 = a\u00b7\np\n\u03a3/ET for values of \u03a3/ET between 20 and 2000 GeV.\nThe parameter a, which quanti\ufb01es the /ET resolution, varies between 0.53 and 0.57 (see Fig. 4 left and\nright, respectively). Re\ufb01ned /ET calibration yields the best results when compared to earlier stages of\nthe calibration as described above. For W \u2192e\u03bd decays the a parameter is reduced by 88% and for\nZ \u2192ee events it is reduced by 78% with respect to the global calibration with the cryostat correction\napplied. Figure 5 shows the resolution in the high \u03a3/ET region for QCD jet samples. The jet samples used\nare generated in parton pT bins: J1 corresponds to 17 < pT < 35 GeV, J2 to 35 < pT < 70 GeV, J3 to\n70 < pT < 140 GeV, J4 to 140 < pT < 280 GeV, J5 to280 < pT < 560 GeV, J6 to 560 < pT < 1120 GeV,\nJ7 to 1120 < pT < 2240 GeV. There is a clear degradation in the performance for the high pT jet samples\n(J6 and J7), where the linear term dominates.\nThe effect of angular calorimeter coverage on the /ET measurement is evaluated by comparing the res-\nolution with and without including the forward calorimeters (FCAL). In Z \u2192\u03c4\u03c4 events the /ET resolution\nis 7.8 and 10.1 GeV, respectively, showing that the ATLAS coverage minimises by design the effect of\nparticles escaping at very large \u03b7 and that the forward calorimeter is very important to guarantee that.\nProjections of /ET along suitable axes can be used to check calibration problems and understand\ntopology dependences. The quantity /EL (longitudinal /ET projection) is the /ET projection onto the axis\npointing in the direction of the genuine /ET of the event. In events without genuine /ET, such as Z \u2192\u2113\u2113\nevents this axis is reconstructed from the direction of \ufb02ight of the Z and in dijet events the projection is\ndone along the dijet thrust axis. The quantity /EP (perpendicular /ET projection) is de\ufb01ned as a projection\northogonal to the /EL direction.\nA bias of /EL usually indicates mis-calibration of the object\u2019s energy scale (in most cases the hadronic\n (GeV)\nmiss\nT\nTrue E\n0\n50\n100\n150\n200\n250\n300\nLinearity of response\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n global calibration+cryostat\nmiss\nT\nE\n refined calibration\nmiss\nT\nE\n calibration at EM scale\nmiss\nT\nE\n global calibration\nmiss\nT\nE\nATLAS\n (GeV)\nmiss\nT\nTrue E\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nLinearity of response\n-0.5\n-0.4\n-0.3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\n0.5\n refined calibration\nmiss\nT\nE\n\u03c4\n\u03c4 \n\u2192\nA\n calibration at EM scale\nmiss\nT\nE\n global calibration\nmiss\nT\nE\n global calibration+cryostat\nmiss\nT\nE\nATLAS\nFigure 3: (left) Linearity of response for reconstructed /ET as a function of the average true /ET for different\nphysics processes covering a wide range of true /ET and for the different steps of /ET reconstruction (see\ntext). The points at average true /ET of 20 GeV are from Z \u2192\u03c4\u03c4 events, those at 35 GeV are from W \u2192e\u03bd\nand W \u2192\u00b5\u03bd\nevents, those at 68 GeV are from semi-leptonic t\u00aft events, those at 124 GeV are from\nA \u2192\u03c4\u03c4 events with mA = 800 GeV, and those at 280 GeV are from events containing supersymmetric\nparticles at a mass scale of 1 TeV. (right) Linearity of response for reconstructed /ET as a function of the\ntrue /ET for A \u2192\u03c4\u03c4 events with mA = 800 GeV.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n376\n\n (GeV)\nT\n E\n\u03a3\n0\n100\n200\n300\n400\n500\n600\n700\nResolution (GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n\u03c4\n\u03c4 \n\u2192\nZ\n\u03bd\n e\n\u2192\nW\n\u03bd\n\u00b5\n \n\u2192\nW\n ee\n\u2192\nZ\nATLAS\n (GeV)\nT\n E\n\u03a3\n0\n200 400 600 800 100012001400160018002000\nResolution (GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\nSUSY\nQCD Jets\ntt\n\u03c4\n\u03c4\n\u2192\nA\nATLAS\nFigure 4: Resolution of the two /ET components with re\ufb01ned calibration as a function of the total trans-\nverse energy, \u03a3ET for low to medium values (left) and for higher values (right). The curves correspond to\nthe best \ufb01ts of \u03c3 = 0.53\u221a\u03a3ET through the points from Z \u2192\u03c4\u03c4 events (left) and \u03c3 = 0.57\u221a\u03a3ET through\nthe points from A \u2192\u03c4\u03c4 events (right). The points from A \u2192\u03c4\u03c4 events are for masses mA ranging from\n150 to 800 GeV and the points from QCD jets correspond to dijet events with 560 < pT < 1120 GeV.\n (GeV)\nT\n E\n\u03a3\n0\n500\n1000 1500 2000\n2500 3000 3500\n4000\nResolution (GeV)\n0\n10\n20\n30\n40\n50\n60\nQCD Jets J7\nJ6\nJ5\nJ4\nJ3\nJ2\nJ1\nATLAS\nFigure 5: Resolution of the two /ET components with re\ufb01ned calibration as a function of \u03a3/ET for QCD\ndijet samples (17 < pT < 2240 GeV). See text for the de\ufb01nition of samples J1-J7. The curve corresponds\nto \u03c3 = 0.55\np\n\u03a3/ET (combined \ufb01t in the low and medium \u03a3/ET regions).\n [GeV]\nmiss\nT,True\nE\n10\n2\n10\nmiss\nT,True\n)/E\nmiss\nL,Reco\n-E\nmiss\nT,True\n(E\n-0.05\n0\n0.05\n0.1\n0.15\n\u03c4\n\u03c4\n\u2192\nZ\n\u03bd\ne\n\u2192\nW\n\u03bd\n\u00b5\n\u2192\nW\n\u03c4\n\u03c4\n\u2192\nA\ntt\nSU3\nSU1\nATLAS\n [GeV]\nmiss\nT,True\nE\n10\n2\n10\nmiss\nT,True\n/E\nmiss\nP,Reco\nE\n\u22120.05\n\u22120.04\n\u22120.03\n\u22120.02\n\u22120.01\n0\n0 01\n0 02\n0 03\nATLAS\n\u03c4\n\u03c4\n\u2192\nZ\n\u03bd\ne\n\u2192\nW\n\u03bd\n\u00b5\n\u2192\nW\n\u03c4\n\u03c4\n\u2192\nA\ntt\nSU3\nSU1\nFigure 6: Linearity of response for /EL (left) and /EP (right) as a function of the average true /ET for\ndifferent physics processes. /EL and /EP are de\ufb01ned in the text.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n377\n\n [GeV]\nTrue\nT\nE\n\u03a3\n0\n500\n1000 1500 2000 2500 3000 3500 4000\n) [GeV]\nmiss\nL,Reco\n(E\n\u03c3\n0\n20\n40\n60\n80\n100\nJ1\nJ2\nJ3\nJ4\nJ5\nJ6\nJ7\nATLAS\n [GeV]\nTrue\nT\nE\n\u03a3\n0\n500\n1000 1500 2000 2500 3000 3500 4000\n) [GeV]\nmiss\nP,Reco\n(E\n\u03c3\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\nJ1\nJ2\nJ3\nJ4\nJ5\nJ6\nJ7\nATLAS\nFigure 7: Resolution of /EL(left) and /EP(right) as a function of \u03a3/ET for QCD jet samples. See text for the\nde\ufb01nition of samples J1-J7.\nscale). For events with signi\ufb01cant values of /ETrue\nT\n, /EP is a measure of the /ET angular resolution. For dijet\nevents and other back-to-back topologies with similarly de\ufb01ned /EP usually there is no bias in /EP, but the\nresolution of /EP is sensitive to soft radiation in the event. One possible source of bias in /EP comes from a\nbias in the angular measurement of the objects in the event, which will cause a shift in the same direction\non both sides of /EL.\nFigure 6 shows the /EL and /EP linearity as a function of the true /ET for different physics channels.\nThe /EL linearity is within 2% above 100 GeV and deviates by 5-10% at lower /ETrue\nT\n. The /EP bias is\nconsistent with zero throughout. Figure 7 shows the /EL and /EP resolution as a function of the true \u03a3/ET\nfor the QCD jet samples. As the /EL for jet events is de\ufb01ned as the /ET projection onto the thrust axis of\nthe two leading jets which are back-to-back, a much larger resolution in absolute terms is expected with\nrespect to /EP. The discontinuity in J4 (140 < pT < 280 GeV) and J5 (280 < pT < 560 GeV) /EP resolution\nis a result of dividing the dijet events into samples based on the parton pT. Events with the same \u03a3/ET\nin J4 and J5 can have different energies in the perpendicular direction due to differences in underlying\nevent, initial or \ufb01nal state radiation. This changes the /EP resolution in the two samples.\nA good performance in terms of linearity and resolution may enhance the ability to reconstruct the\nmass of \ufb01nal states which involve neutrinos. Despite the presence of several neutrinos in the \ufb01nal state,\nthe invariant mass of the \u03c4 pair can also be reconstructed in Z \u2192\u03c4\u03c4 and supersymmetric Higgs boson\n (GeV)\n\u03c4\n\u03c4\nm\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n Arbitrary units\n0\n20\n40\n60\n80\n100\n120\n140\n160\nMean = 89.4 GeV\n = 9 8 GeV\n\u03c3\nATLAS\n (GeV)\n\u03c4\n\u03c4\nm\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n Arbitrary units\n0\n20\n40\n60\n80\n100\n120\nMean = 446.0 GeV\n = 52.0 GeV\n\u03c3\nATLAS\nFigure 8: Distributions of the reconstructed invariant mass of \u03c4-lepton pairs with one \u03c4-lepton decaying\nto a lepton and the other one decaying to hadrons. The results are shown for Z \u2192\u03c4\u03c4 decays (left) and\nfor A \u2192\u03c4\u03c4 decays with mA = 450 GeV (right).\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n378\n\n (GeV)\nmiss\nT\nTrue E\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n (rad)\n\u03d5\n\u03c3\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0.6\n0.7\n0 8\nATLAS\ntt\n\u03c4\n\u03c4 \n\u2192\nZ \n\u03bd\n e\n\u2192\nW \nphi (rad)\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n (GeV)\nT\nFake Missing E\n-2\n-1.5\n-1\n-0.5\n0\n0 5\n1\n1 5\n2\nATLAS\nFigure 9: (left) Accuracy of the measurement of the azimuth of the /ET vector as a function of the true\n/ET for three different physics processes: semi-leptonic t\u00aft events, Z \u2192\u03c4\u03c4 and W \u2192e\u03bd events. (right)\n/EFake\nT\nas a function of the reconstructed \u03c6(/ET) in t\u00aft events, simulated with extra material in \u03c6.\ndecays like A \u2192\u03c4\u03c4 under simplifying assumptions [8, 9, 10]. Figure 8 shows reconstructed mass peaks\nof Z \u2192\u03c4\u03c4 and supersymmetric Higgs boson decays A \u2192\u03c4\u03c4 with mA = 450 GeV. The reconstructed\nmasses are correct to \u223c2% and the mass resolution is approximately 11%. Nevertheless, signi\ufb01cant tails\nremain in the distributions because of the highly non-Gaussian effects induced by mis-measurements of\n/ET and by the approximations used.\n3.2\nMeasurement of the /ET direction\nLarge energy \ufb02uctuations in the calorimeter or muon mis-measurements can produce large /EFake\nT\n. In\ngeneral, for events with genuine missing transverse energy, the /ET angular resolution will depend on the\nrelative fraction of /EFake\nT\nand on the event topology. Figure 9 shows the /ET azimuthal angular resolution\nas a function of the /ETrue\nT\nfor three different physics processes. The measurement of the /ET azimuth is\nclearly more accurate for W \u2192e\u03bd events, which in general contain one high-pT electron and moderate\nhadronic activity in addition, compared to t\u00aft events. For values of /ETrue\nT\nbelow 40 GeV, the accuracy\nof the measurement of the direction degrades rapidly. In contrast, for high values of /ETrue\nT\n, azimuthal\naccuracies below 100 mrad are achieved.\nDetector inef\ufb01ciencies may perturb the radial symmetry of the physics events. Thus, observations of\n\u03c6 asymmetries in reconstructed variables may be a hint of instrumental problems. Due to the increased\nmaterial (of \u223c5% to 10%) in the upper half of the detector that was added arti\ufb01cially into the simulation,\na \u03c6 asymmetry is observed in /ET as seen in Fig. 9 (right). This \u03c6 asymmetry can also be observed in the\n/ET computed at the event \ufb01lter trigger level.\nSimilarly, problematic \u03b7 regions may be spotted by looking at /ET correlations with jet pseudorapid-\nity, in particular in QCD events. In fact, in this kind of events, /ET is mainly due to jet mis-measurements\nwhich will affect more the /ET component parallel to the dijet axis than that perpendicular to it. Detector\nfailures or incorrect calibration sets may be revealed as unexpected peaks in such plots.\n4\nFake /ET\nThe reconstructed /ET has two constituents - one that is produced by particles that interact weakly with\nthe detector (/ETrue\nT\n) and the other one due to detector inef\ufb01ciencies and resolution (/EFake\nT\n). Figure 10\nshows the rate of /EFake\nT\nand /ETrue\nT\nfor the QCD sample generated with 560 < pT < 1120 GeV, where\n/EFake\nT\ndominates at lower values and also has a larger tail. The same \ufb01gure also shows these distributions\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n379\n\nafter excluding events with high pT jets within 17o of the reconstructed /ET in the transverse plane.\nThis considerably lowers the /EFake\nT\nrate compared to /ETrue\nT\n. For an accurate measurement of /ET it is\nimportant to have a good understanding of the sources of /EFake\nT\nin data. Since the goal here is to study the\nperformance and not the relative contributions of signal and background, comparisons between different\nphysics samples are made for a common number of events rather than for a common luminosity.\nThe \ufb01rst two subsections discuss the /EFake\nT\nfrom muons and from the calorimeter under the assump-\ntion that all detector readout channels are functional. The impact of dead-regions in the detector is\nexamined in the subsequent subsections.\n4.1\nFake /ET from muons\n/EFake\nT\nfrom muons can be caused either by inef\ufb01ciencies in reconstructing a high pT muon or by recon-\nstructing a fake high pT muon. The latter could be present due to a combination of a lower pT muon\nand/or random hits from high pT jet punch-throughs from the calorimeter to the muon chambers. It can\nbe argued that for reasonable muon identi\ufb01cation ef\ufb01ciencies, /EFake\nT\nfrom missed muons will only be a\nsmall fraction of the /ETrue\nT\nfrom neutrinos. For example in QCD samples the neutrino to muon ratio is\nroughly two. It gets higher in other physics samples depending on the fraction of \u03c4 candidates in the\nevent. On the other hand fake muons that are reconstructed from random hits in the muon chambers\ncan be arbitrarily hard and strongly contribute to /EFake\nT\n. However, the study here shows that /EFake\nT\nfrom\nmuons is dominated by missed muons rather than fake muons.\nThe total /EFake\nT\nin the MC sample can be de\ufb01ned as the vectorial difference of reconstructed /ET and\n/ETrue\nT\n, as follows:\n/EFake\nT\n=\nq\n/EFake\nx\n2 + /EFake\ny\n2\nwhere\n/EFake\nx,y\n= /Ex,y \u2212/ETrue\nx,y .\n(11)\n/Ex,y and /ETrue\nx,y are the x and y components of the \ufb01nal reconstructed /ET and of the /ETrue\nT\nde\ufb01ned in Section\n3.\nThe contribution to the total /EFake\nT\nfrom muon mis-measurements can be de\ufb01ned by\n/EFakeMuon\nx,y\n= /EMuon\nx,y\n\u2212/ETrueMuon\nx,y\n,\n(12)\nwhere /EMuon\nx,y\nand /ETrueMuon\nx,y\nare calculated by summing the reconstructed and true x and y components\nfrom muons in the event.\n (GeV)\nmiss\nT\nE\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nArbitrary units\n1\n10\n2\n10\n3\n10\n4\n10\nmiss\nT\nTrue E\nmiss\nT\nFake E\nATLAS\nBefore DeltaPhi Cut\n (GeV)\nmiss\nT\nE\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nArbitrary units\n1\n10\n2\n10\n3\n10\nmiss\nT\nTrue E\nmiss\nT\nFake E\nATLAS\nAfter DeltaPhi Cut\nFigure 10: The rates of /EFake\nT\nand /ETrue\nT\nin the QCD sample with 560 < pT < 1120 GeV: (left) overall\nrates, (right) requiring a \u2206\u03c6 separation between /ET and the leading high-pT jet in the event. The /EFake\nT\nrates can be strongly reduced. It should be noted though that such cuts are very analysis dependent.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n380\n\nTable 1: Number of events with /EFake\nT\nabove various thresholds from muon (top) and calorimeter (bottom)\nmis-measurements. The J6 (QCD jets in 560 < pT < 1120 GeV range), SU3, t\u00aft , and Z \u2192\u00b5\u00b5 samples\nare normalized to the same number of events (25k).\n/EFake\nT\n> 60 GeV\n> 90 GeV\n> 120 GeV\n> 150 GeV\n/EFake\nT\nfrom Muon\nJ6\n61\n33\n20\n13\nSU3\n195\n109\n57\n42\nt\u00aft\n147\n64\n33\n20\nZ \u2192\u00b5\u00b5\n436\n94\n37\n20\n/EFake\nT\nfrom Calorimeter\nJ6\n4273\n1249\n351\n110\nSU3\n1005\n176\n56\n53\nt\u00aft\n104\n15\n4\n2\nFigure 11 (left) shows the scatter plot of the two quantities de\ufb01ned in Equations (11) and (12) for\nthe QCD sample with 560 < pT < 1120 GeV. In order to separate the /EFake\nT\nfrom muons with respect\nto the calorimeter related /EFake\nT\nthe following cuts can be used: (a) /EFakeMuon\nT\n> /EFake\nT\n/2 which selects\nevents with fake /ET coming predominantly from muon mis-measurements, and (b) /EFakeMuon\nT\n< /EFake\nT\n/2\nwhich selects events with fake /ET coming predominantly from other sources like jet mis-measurements\nin the calorimeter. Figure 11 also shows how these cuts separate events with /EFake\nT\nfrom muons and from\ncalorimeter induced effects.\nTable 1 shows the number of events above various /EFake\nT\nthresholds for physics samples (QCD jets\nin the range 560 < pT < 1120 GeV, SU3, t\u00aft and Z \u2192\u00b5\u00b5 ) that are predominantly from muons (top\nrows) or from the calorimeter (bottom rows). It can be seen that the relative rate of /EFake\nT\nacross samples\ndepends on the muon and calorimeter activities.\nIn Table 2 different categories of muon mis-measurements and their relative contribution to /EFake\nT\nare shown1. The \ufb01rst two rows are from missed muons and the last two rows are from fake muons\nreconstructed from random hits in the muon chambers and with a possible match to soft muon tracks in\nthe inner detector. Table 2 shows a smaller contribution to /EFake\nT\nfrom fake muons compared to missed\nmuons. Therefore the dominant contribution to /EFake\nT\nfrom muons is due to inef\ufb01ciencies in the muon\n1Due to technical reasons a small fraction of muon events were not classi\ufb01ed in any category.\nMuon Fake E(x,y)Miss (GeV)\n-400 -300 -200 -100\n0\n100\n200\n300\n400\nTotal Fake E(x,y)Miss (GeV)\n-400\n-300\n-200\n-100\n0\n100\n200\n300\n400\nATLAS\nMuon Fake E(x,y)Miss (GeV)\n-400\n-300 -200 -100\n0\n100\n200\n300\n400\nTotal Fake E(x,y)Miss (GeV)\n-400\n-300\n-200\n-100\n0\n100\n200\n300\n400\nMuon Fake E(x,y)Miss (GeV)\n-400\n-300 -200 -100\n0\n100\n200\n300\n400\nTotal Fake E(x,y)Miss (GeV)\n-400\n-300\n-200\n-100\n0\n100\n200\n300\n400\nFigure 11: (left) Total /EFake\nT\nas a function of /EFake\nT\nfrom muon mis-measurements. (middle and right)\nCuts de\ufb01ned in (b) and (a) (see text) are used to separate calorimeter/jet and muon /EFake\nT\ncomponents.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n381\n\nEta of Missed Muons\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\nArbitrary units\n0\n50\n100\n150\n200\n250\n300\n350\nATLAS\n (GeV)\nT\nFake Missing E\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nNormalized Events\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nElectron Events\nMuon Events\nFigure 12: (left) The \u03b7 distribution of true muons that were missed during reconstruction in a Z \u2192\u00b5\u00b5\nhigh pT > 100 GeV sample. (right) /EFake\nT\nin t\u00aft events in the electron (hatched) and muon channel.\nidenti\ufb01cation.\nFigure 12 (left) shows the \u03b7 distribution of the true muons that were missed at the reconstruction\nlevel in the Z \u2192\u00b5\u00b5 sample with pT > 100 GeV. There are missed muons around \u03b7 = 0, |\u03b7|=1.2 and at\nhigh \u03b7 (|\u03b7|>2.7) where there is no muon coverage. Muon tracks cannot be reconstructed by the muon\nsystem around \u03b7 = 0 (\u22120.05 < \u03b7 < 0.05), because of service holes required for cables and cryogenics\npassage to the inner detectors and calorimeters. In the region around |\u03b7|=1 there is a loss of ef\ufb01ciency\nin muon reconstruction, due to the middle muon station missing for initial data taking. In these studies\nmuons missed due to limitations of muon detector coverage or poor muon reconstruction have not been\nrecovered. In the next software releases algorithms to recover some of these missed muons using energy\ndeposits in the calorimeter and tracks in the inner detector will be used.\nFigure 12 (right) shows the /EFake\nT\ndistributions for events in which the leptonically decaying W results\nin an electron and those resulting in a muon, respectively. The latter distribution clearly contains larger\nnon-Gaussian tails. As discussed above, the sources of these large tails are either missed or fake muons.\n4.2\nFake /ET from the calorimeter\nIn this section it is assumed that all calorimeter readout channels are functional. /EFake\nT\nin the calorimeter\nis then produced by mis-measurements of hadronic jets, taus, electrons or photons.\nThe calorimeter has cracks and gaps in the transition regions, which are also used for service out-\nlets. These regions have poorer resolution and are expected to have larger contributions to /EFake\nT\ncom-\npared to the rest of the calorimeter. There are two gap regions de\ufb01ned in the following \u03b7\nranges:\n(1.3 < |\u03b7| < 1.6) and (3.1 < |\u03b7|< 3.3). Figure 13 shows the \u03b7 distribution of the worst and the second\nworst measured jet (de\ufb01ned w.r.t. the closest true jet and their energy difference) in the calorimeter for the\nTable 2: The sources of mis-measured muons that contribute to /EFake\nT\n> 60 GeV. The columns are\nnormalized to the same number of events (25k).\nSources\nSU3\nJ6\nt\u00aft\nZ \u2192\u00b5\u00b5\nMC muon not reconstructed\n121\n17\n42\n332\nReconstructed muon failed quality cut\n30\n18\n40\n18\nMuon reconstructed with badly measured pT\n29\n3\n28\n28\nReco muon not close to MC muon (\u201cfake muon\u201d)\n11\n23\n0\n25\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n382\n\nQCD sample generated with 560 < pT < 1120 GeV. It shows that a large number of the worst measured\njets have \u03b7 pointing to |\u03b7| in 1.3-1.6. The \u03b7 distribution of the second worst measured jet is more \ufb02at\nand peaks around |\u03b7| in 0.6-0.9, the transition region of the barrel tile calorimeter to the extended barrel\ntile calorimeter.\nThe above correlation of worst measured jets and their \u03b7 suggests a large correlation between the\njet \u03b7\nand /EFake\nT\n. However, the /EFake\nT\ndistribution from full simulation samples suggests otherwise.\nFigure 14 shows the /EFake\nT\ndistribution in the QCD samples generated with 560 < pT < 1120 GeV and\n140 < pT < 280 GeV, when a jet points to the crack/gap region or not. The slope of the distributions\nsuggests no signi\ufb01cant correlation between jets pointing to cracks and /EFake\nT\n.\nThis apparent contradiction between Fig. 13 and Fig. 14 can be understood as follows: even though\nthe worst measured jet contributes strongly to the /EFake\nT\n, it is not the only source of /EFake\nT\nin the event.\nThe worst measured jet contributes on average about 60% and the second worst measured jet contributes\nabout 20% to /EFake\nT\n. But not all worst measured jets are along the crack region and each event has many\njets. In lower /EFake\nT\nregions there is a stronger correlation between /EFake\nT\nand jets pointing to cracks. For\nhigher /EFake\nT\n( > 50 GeV considered here ) there is more than one source contributing to /EFake\nT\nand the\ncorrelation of jets pointing to cracks is smeared out as can be seen in Fig. 14.\n4.3\nFake /ET from calorimeter leakage\nJet leakage from the calorimeters or \ufb02uctuations in large jet energy deposits in non-instrumented regions\nsuch as the cryostat between the liquid argon and tile calorimeters can also be a source of /EFake\nT\n. The\nmethod used to detect events with potential jet leakage is to look for large energy deposits in the follow-\ning regions: the outermost layers of the TileCal and the HEC, the outermost LAr barrel layer and the\ninnermost TileCal barrel layer, and in the TileCal gap and crack scintillators.\nThe following shows an example of selection cuts applied on different variables of the three leading\npT jets with pT> 100 GeV: ETile2/ETotal > 0.05, ETile10/ETotal > 0.7, ECryo/ETotal > 0.2, EGap/ETotal > 0.2\nand EHEC3/ETotal > 0.5, where ETotal is the total jet energy, ETile2 is the jet energy in the outermost tile\nlayer, ETile10 is the jet energy in the \ufb01rst two innermost tile layer, ECryo is the energy lost by the jet in the\ncryostat, EGap is the jet energy in the gap scintillators and EHEC3 is the jet energy in the outermost layer\nof the HEC calorimeters. If any of these cuts is satis\ufb01ed the event is rejected.\nFurthermore, as the tracks found in the inner detector are not affected by the reconstruction, com-\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nArbitrary units\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nATLAS\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nArbitrary units\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nATLAS\nATLAS\nFigure 13: The \u03b7 distribution of the worst (left) and second-worst measured jet (right) in the calorimeter\nin QCD events generated with 560 < pT < 1120 GeV.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n383\n\nFake EtMiss (GeV)\n100\n200\n300\n400\n500\n600\nArbitrary units\n1\n10\n2\n10\n3\n10\n4\n10\nNo jet in gap \nAt least one jet in gap\nCombined\nATLAS\nFake EtMiss (GeV)\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nArbitrary units\n1\n10\n2\n10\n3\n10\nNo jet in gap \nAt least one jet in gap \nCombined\nATLAS\nFigure 14: The /EFake\nT\nrate for QCD sample in 560 < pT < 1120 GeV range (left) and QCD sample in\n140 < pT < 280 GeV (right) due to calorimeter mis-measurements.\n (GeV)\nT\nE\n0\n100\n200\n300\n400\n500\n600\nFraction of remaining events\n0\n0 2\n0.4\n0 6\n0 8\n1\nATLAS\n (GeV)\nT\nE\n0\n100\n200\n300\n400\n500\n600\nFraction of remaining events\n0\n0 2\n0.4\n0 6\n0 8\n1\n (GeV)\nT\nE\nFake \n0\n100\n200\n300\n400\n500\n600\nFraction of remaining events\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n (GeV)\nT\nE\nFake \n0\n100\n200\n300\n400\n500\n600\nFraction of remaining events\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 15: Fraction of events remaining after the cuts discussed in the text as a function of /ET(left) and\n/EFake\nT\n(right) for the QCD sample generated with 560 < pT < 1120 GeV.\nplementary information on events with fake /ET can be obtained using /ETtrk from tracks which is the /ET\ncomputed only from tracks. A cut on (/ETtrk \u2212/ET > 50 GeV) was chosen for the optimization of the\nsignal signi\ufb01cance.\nFigure 15 shows the percentage of events remaining after the cuts described above are applied on\nQCD sample generated with 560 < pT < 1120 GeV. The right plot shows suppression of large fake /ET\ngenerated due to high pT jet leakage. Larger fake /ET are suppressed more strongly. It can also be noticed\nfrom the left plot that these cuts, although removing a large fraction of the events dominated by fake /ET,\nare not sensitive to the overall /ET in the event and the fraction of remaining events is fairly constant over\n/ET. The method is of course analysis dependent and the values of the cuts should be chosen taking into\naccount the signal ef\ufb01ciency.\n4.4\nFake /ET from instrumental effects\nIn real data there will be sources of /EFake\nT\nwhich are not fully modeled in Monte Carlo simulations in-\ncluding, for example, mis-modeling of material distributions and instrumental failures. As the details\nof these /EFake\nT\nsources will be understood with time, increasingly re\ufb01ned analyses will be developed\nto minimize their associated backgrounds while maintaining high selection ef\ufb01ciencies for signals with\ngenuine missing energy. While it is dif\ufb01cult to predict in advance the exact sources of mis-modeled\n/EFake\nT\n, it is nevertheless possible to insert problems into the Monte Carlo that match potential hardware\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n384\n\nMissing Et (GeV)\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nFraction of Events\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nMissing Et (GeV)\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nFraction of Events\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nDead Regions\nRegion 1 (2EM+1HAD)\nRegion 2 (1EM+1HAD)\nRegion 3 (Good)\nATLAS\n0\n0.1\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0 02\n0 04\n0.06\n0.08\n0.1\n0.12\n0.14\n0\n0.1\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0 02\n0 04\n0.06\n0.08\n0.1\n0.12\n0.14\nEM Fraction\n0\n0.1\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\nFraction of Events\n0\n0 02\n0 04\n0.06\n0.08\n0.1\n0.12\n0.14\nEM Fraction\n0\n0.1\n0.2\n0.3\n0.4\n0 5\n0.6\n0.7\n0.8\n0.9\n1\nFraction of Events\n0\n0 02\n0 04\n0.06\n0.08\n0.1\n0.12\n0.14\nDead Regions\nRegion 1 (2EM+1HAD)\nRegion 2 (1EM+1HAD)\nRegion 3 (Good)\nATLAS\nEM Fraction Window\nFigure 16: Cell-killed QCD sample in 560 < pT < 1120 GeV range: the /ET distribution (left) and the\nEM fraction (right). The histograms are normalized by area.\nfailures. These include trips in high-voltage channels or readout power supplies of the calorimeter or\nnoise in calorimeter channels or regions. The initial studies presented here are based on samples with\nsimulated dead regions of the calorimeter, so called \u2018cell-killed\u2019 samples: one dead front-end readout\ncrate in the LAr electromagnetic barrel calorimeter and one dead front-end readout crate affecting LAr\nelectromagnetic and endcap calorimeters. Based on the location of these hardware failures the calorime-\nter is divided into three regions of \u03c6(/ET): \u2018Region 1\u2019 with EM endcap and hadronic endcap problems,\n\u2018Region 2\u2019 with EM barrel problems, and \u2018Region 3\u2019 with no problems.\nThese samples were used as references for the development of cuts that reduce the /EFake\nT\nbackground\nwhile maintaining high ef\ufb01ciencies for potential signal events. Since we will not know the precise lo-\ncation and nature of hardware problems in advance, the cuts are not tuned assuming that knowledge. In\nreal data it will be possible to signi\ufb01cantly improve the analysis performance by cutting harder when\nenergy deposits are expected near regions with detector hardware problems, but that is not exploited in\nthe studies so far. Future work will also include using these samples to develop data-driven techniques\nfor predicting the /EFake\nT\ntails.\nThe high-pT (560 < pT < 1120 GeV) \u03b3+jet MC sample was processed with the cell-killed con\ufb01gu-\nration described above. Events with at least one back-to-back photon-jet pair were selected. Figure 16\nshows the /EFake\nT\ngenerated in the three regions. Large /ET tails are seen in Regions 1 and 2 where the holes\nin calorimeter coverage have been introduced. The effect of dead regions can also be seen in Table 3.\nThe columns show the number of events above various /EFake\nT\nthresholds. The \ufb01rst two rows show the\nnumber of events with no dead-regions and with the above dead-regions simulated. A very large increase\nin high /EFake\nT\nis seen.\nSeveral methods have been developed to suppress events with large fake /ET:\n\u2022 EM Fraction Method: The EM fraction method starts by \ufb01nding the closest calorimeter jet to the\n/ET direction vector using \u2206\u03c6 between the calorimeter jet and /ET. Figure 16 (right) shows the EM\nfraction distributions. Small EM fractions are due to a dead LAr EM calorimeter crates, whereas\nlarge EM fractions are due to a dead hadron calorimeter crates. The fake /ET generated this way\ncan be suppressed by requiring the EM fraction to be in a window from 0.40 to 0.96. The effect\nof this cut can be seen in the third row of Table 3 when compared to the increase in /EFake\nT\ndue to\ndead-regions in row 2. A rejection of 1.5 to 4 is seen from low to high /EFake\nT\nbins. The selection\nef\ufb01ciency can be de\ufb01ned as the ratio of the number of events after and before the cuts when events\nfall in Region 3 (Region 3 has small /EFake\nT\n). For the EM fraction method the selection ef\ufb01ciency is\n\u223c90%.\n\u2022 Track-Jet Methods: jets were reconstructed from inner detector tracks using the cone algorithm\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n385\n\nTable 3: The number of events from \u03b3+jet samples above various /EFake\nT\nthresholds with no dead-regions,\nwith simulated dead-regions and after applying various suppression techniques (see text). All numbers\nare normalized to 25k events sample size.\n/ETFake (GeV)\n> 100\n> 200\n> 300\n> 400\n> 500\nNo dead regions\n555\n18\n3\n1\n0\nw/ dead regions\n2482\n1308\n864\n501\n199\nw/ EM fraction method\n1651\n572\n287\n122\n50\nw/ track-jet cluster method\n1786\n664\n313\n129\n49\nw/ comb. track-jet cluster method\n1402\n392\n150\n46\n14\nwith \u2206R = 0.4. A \ufb01ducial volume cut of |\u03b7| < 2.5 is applied due to the tracking coverage. Since\ntrack-jets use the inner tracking detectors, they provide a complementary identi\ufb01cation of events\nwith fake /ET. A number of different methods of exploiting the track-jets were studied. An effective\nmethod which only uses information present in the Analysis Object Data (AOD) is to sum the ET\nof calorimeter topological clusters within the track-jet \u03b7-\u03c6 cone. The distributions of the ET ratio\nof the track-jet to the clusters has tails due to the dead calorimeter regions. A cut is applied\nrequiring ET ratios larger than 1.0; the value was chosen to maintain a signi\ufb01cant ef\ufb01ciency for\nsignal samples, and could be substantially tightened for different physics analyses. The fourth row\nof Table 3 shows the effectiveness of this cut. Rejections from \u03b7 = 1.4 to \u03b7 = 4 are achieved from\nthe low to high /EFake\nT\nregions, with ef\ufb01ciencies of \u223c93%.\nSince the EM fraction method and track-jet methods are largely uncorrelated, they can be combined\nfor better suppression of large /EFake\nT\n. The last row in Table 3 shows the performance of the combined\ntrack-jet method. The selection ef\ufb01ciency for this combined method is \u223c84%. It must be emphasized\nthat the results presented in this table represent the worst case since the cuts do not use the detailed infor-\nmation about detector problems that will be known from the detector control and data quality systems.\nIn a \ufb01nal analysis, much harder cuts can be applied in regions with known detector problems. Of course,\nthis will reduce the acceptance of the detector.\n5\nThe /ET Trigger algorithm performance\nThis section brie\ufb02y describes the /ET algorithms applied at the \ufb01rst level trigger (L1) and the higher-level\ntrigger (HLT). The HLT is a combination of second level trigger (L2), and a third level trigger (or event\n\ufb01lter, EF). The L1 algorithm is based on hardware, while the HLT algorithms are software based.\n5.1\nThe /ET at L1\nThe /ET L1 calorimeter triggers cover the region |\u03b7| < 4.9, which is the limit of the forward calorimeters\n[11]. The basic units of L1 /ET and \u03a3/ET trigger algorithms are \u2018jet elements\u2019, formed by summing over\ntrigger towers within windows of 0.2 \u00d7 0.2 in the (\u03b7,\u03c6) plane.2 They are processed by the Jet/Energy\nmodules, which compute Ex, Ey and \u03a3/ET of each jet element. Four thresholds are available on \u03a3/ET with\nvalues up to 2044 counts in steps of 4 (usually, 1 count = 1 GeV). Eight /ET thresholds are available,\nup to a maximum threshold value of 504 counts. If an over\ufb02ow occurs at any point in the /ET or \u03a3/ET\nalgorithm, all of the corresponding thresholds are set as passed.\n2For 2.4 < |\u03b7| < 3.2 the granularity is either \u2206\u03b7 = 0.2 or \u2206\u03b7 = 0.3, while FCAL jet elements extend from |\u03b7| = 3.2 to\n|\u03b7| = 4.9. The \u03c6 granularity of the FCAL jet elements is \u2206\u03c6 = 0.4.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n386\n\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nMET resolution (GeV)\nTrue SumET (GeV)\nL1\nEF\nOffline\nATLAS\n0\n200\n400\n600\n800\n1\nSumET resolution (GeV)\nTrue SumET (GeV)\n000 1200 1400 1600 1800 2000\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nL1\nEF\nOffline\nATLAS\nFigure 17: L1, EF and of\ufb02ine results for the /ET (left) and the \u03a3/ET (right) resolution as a function of the\ntrue \u03a3/ET in t\u00aft events.\nFor each event, the L1 Ex, Ey and \u03a3/ET are saved into one object of the RecEnergyRoI class, including\nover\ufb02ow \ufb02ags. If any threshold is passed, the JetEnergy RoI is also produced containing the bit pattern\nof the thresholds passed.\n5.2\n/ET at HLT\nThe of\ufb02ine algorithm described in Section 2.2 is too resource intensive (both in terms of memory access\nand calculations to be done) to be applied in the HLT. The following algorithms are ready for the \ufb01rst\ndata taking3:\n\u2022 The L2 algorithm uses the calorimeter information in RecEnergyRoI provided by the L1 trigger\nand applies a correction for L2 muon objects.\n\u2022 The default EF algorithm sums all calorimeter cells and applies a 0-th order hadronic calibration by\nmultiplying /ET and \u03a3/ET by a constant related to the hadronic/electromagnetic calorimeter energy\nfraction in a jet. Finally, the EF takes the muon contribution into account.\nBoth at L2 and EF, the muon correction may be switched off independently for each trigger chain.\nThe decision taken both at L2 and EF is carried out by the same software package. This hypothesis\ntesting code can be con\ufb01gured to accept events based on /ET, on \u03a3/ET or on both.\n5.3\nThe /ET and \u03a3/ET resolution at trigger level\nFigure 17 shows the /ET and \u03a3/ET resolution for the L1, EF and of\ufb02ine algorithms as a function of the true\n\u03a3/ET for t\u00aft events. Since the L2 algorithm takes the L1 result and applies relatively small corrections, the\npresent L2 resolution is practically the same as for L1 and therefore not shown. At true \u03a3/ET values of\n500 GeV, the L1 resolution on the /ET measurement is about 25 GeV which is a factor of two larger than\nwhat is achieved of\ufb02ine. The EF resolution, for both /ET and \u03a3/ET lies in between the values for L1 and\nof\ufb02ine resolution.\n3At present, work is in progress to detect fake sources due to detector effects like uninstrumented regions or hardware\nfailure, or physics environment, e.g. beam-halo or cosmic ray tracks.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n387\n\n6\n/ET in early data\nValidation of the /ET reconstruction described in the previous sections will be performed with the \ufb01rst\nLHC data accumulated by ATLAS. For the very \ufb01rst data, the two main issues are controlling instrumen-\ntal failures and calibration of energy deposits in the calorimeter. At this stage, the overwhelming number\nof minimum bias events will be used to monitor and diagnose /ET reconstruction problems.\nThe development of algorithms for data quality checks is being actively pursued to minimize the im-\npact of such failures and will be optimized when the \ufb01rst data is collected. The \u2018standard\u2019 /ET calculation,\nusing the calorimeter cells at the electromagnetic scale above a threshold will be always provided as a\nreference. The /ET calibration strategy follows the steps described in Section 3. First, a simple global\ncalibration for all the TopoCells will be used. As shown in Section 3 this already gives a good linearity\nbehavior. As the event reconstruction becomes more robust, the event objects (e.g. electrons, jets, taus)\nwill be used to obtain the best /ET resolution.\nFigure 3 already shows how the /ET linearity improves from a simple to a more re\ufb01ned /ET calculation.\nFigure 18 shows how the /ET resolution improves arriving in steps to the \ufb01nal re\ufb01ned calibration.\nSumET (GeV) \n100\n200\n300\n400\n500\n600\n700\n800\n900\n Final Resolution (GeV) \n5\n10\n15\n20\n25\n30\n global calib.+cryo\nmiss\nT\nE\n refined calibration\nmiss\nT\nE\n calib. at EM scale\nmiss\nT\nE\n global calibration\nmiss\nT\nE\nATLAS\nFigure 18: The /ET resolution as a function of true \u03a3/ET from the uncalibrated to the re\ufb01ned calibration\nas indicated for the following channels: W \u2192\u00b5\u03bd corresponding to true \u03a3/ET = 130 GeV, W \u2192e\u03bd to\n165 GeV, Z \u2192\u03c4\u03c4 to 210 GeV, t\u00aft to 470 GeV, A/H \u2192\u03c4\u03c4 to 843 GeV, J5 to 800 GeV and SUSY to\n906 GeV.\nOnce data of the order of 100 pb\u22121 are collected, the /ET validation focuses on physics channels with\nrelatively large /ET and/or \u03a3/ET. This section brie\ufb02y describes a few studies that will be performed with\nthe \ufb01rst data.\nThe Z \u2192\u03c4\u03c4 process, using the Z mass constraint, can be used to determine the /ET scale in-situ\nto about 8% accuracy. The Z \u2192\u2113\u2113process with decays to electrons and muons does not have any\nsigni\ufb01cant /ETrue\nT\nfrom neutrinos. The small background to these events will help to test possible /ET\nbiases, expected to be zero, and the resolution in a straightforward manner. The copiously produced\nW \u2192e\u03bd and W \u2192\u00b5\u03bd events can be used to test the reconstructed /ET in the (20\u2212150) GeV range. Two\nmethods to use these events are discussed. Semileptonic t\u00aft events also have genuine /ET and allow a\ntest of the /ET reconstruction in an environment relevant for many physics analyses and searches, notably\nSUSY.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n388\n\n) (GeV)\nmiss\nX,Y\n(E\n\u03c3\n-30\n-20\n-10\n0\n10\n20\n30\nNormalised Events / (1 GeV)\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n < 60 GeV\nE\n\u03a3\n50 < \n 0.01\n\u00b1\n Offset = 0.13 \n 0.004\n\u00b1\n Sigma = 3.923 \n \n < 120 GeV\nE\n\u03a3\n80 < \n 0.01\n\u00b1\n Offset = 0.24 \n 0.004\n\u00b1\n Sigma = 5.211 \n \n < 240 GeV\nE\n\u03a3\n200 < \n 0.03\n\u00b1\n Offset = 0.56 \n 0.02\n\u00b1\n Sigma = 7.68 \nATLAS\n (GeV)\nT\nE\n\u03a3\n0\n100\n200\n300\n400\n500\n600\n) (GeV)\nmiss\nX,Y\n(E\n\u03c3\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nT\nE\n\u03a3\n 0.003) \n\u00b1\n(0.520 \nMinimum Bias\nJ0\nJ1\nJ2\nJ3\nATLAS\nFigure 19: (left) The /Ex,y resolution for different \u03a3/ET regions in minimum bias events. (right) The\n/ET resolution in QCD dijet events (J0-J3: see Section 3.1 for de\ufb01nition) is shown together with the /ET\nresolution from minimum bias events (black \ufb01lled circles) as a function of \u03a3/ET. An integrated luminosity\nof the order of 10\u22125 pb\u22121 is used.\n6.1\nMinimum bias events\nMinimum bias interactions at the LHC are dominated by soft collisions of the two interacting protons.\nThese events are useful for /ET commissioning, especially in the early stages of the experiment, due to\ntheir large statistics and their comparatively simple event selection. The main background in minimum\nbias events will originate from empty, beam gas and beam halo events, especially at the beginning of the\nexperiment. Minimum bias events will be used to verify the /ET reconstruction procedure and estimate\nthe /ET resolution for low \u03a3/ET events.\nIn the early stages of the experiment, minimum bias events will be selected by three types of triggers:\nrandomly selected bunch crossings (MB1), randomly selected bunch crossings together with a SemiCon-\nductor Tracker space point trigger (MB2), and minimum bias trigger scintillator (MBTS2). The details\nof the triggers are described in Ref. [12].\nFor the study of /ET in minimum bias events, high signal ef\ufb01ciency and background rejection are\nrequired. The relative fraction of non-diffractive, single diffractive and double diffractive events in the\nsample is not a concern. The selection criteria require at least 20 semiconductor tracker space points to\nreject empty events and at least one good reconstructed track to reject beam gas and halo events.\nA Monte Carlo study predicts an overall trigger ef\ufb01ciency of 96.8%. The of\ufb02ine track selection\nef\ufb01ciency (with respect to events passing the trigger) is 80.6% for a total selection ef\ufb01ciency of 78.0%.\nThe /ET in minimum bias events is fairly low with a mean of 4.3 GeV. Fake /ET is caused mainly\nby calorimeter energy resolution (82%) and acceptance (18%). The true /ET is 0.06 GeV on average,\noriginating from K/\u03c0 decays-in-\ufb02ight and from the decay of charm and bottom particles. The true \u03a3/ET\nin non-diffractive minimum bias events is typically 64 GeV, while the reconstructed \u03a3/ET is on average\n49 GeV due to the loss of low energy particles which do not reach the calorimeters. Since minimum\nbias events are dominated by soft (low-pT) interactions, jets are reconstructed with a rate depending on\n\u03a3/ET. When minimum bias events with \u03a3/ET of 50 GeV are compared to events with \u03a3/ET of 250 GeV, the\naverage number of reconstructed jets with pT > 7 GeV increases from below one to about nine with an\naverage jet energy of 10 and 13 GeV, respectively.\nThe /ET resolution in minimum bias events is expected to scale as \u221a\u03a3ET because the stochastic term\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n389\n\nof the calorimeter resolution is dominant in \u03a3/ET regions as shown in the left plot of Fig. 19. These\ndistributions are well \ufb01tted by Gaussian functions with offsets of zero (in the case of no \u03c6 asymmetry)\nand resolutions which scale with \u03a3/ET.\nThe right plot of Fig. 19 shows the comparison of the /ET resolution evaluated in this study with the\nhigher \u03a3/ET region (\u03a3/ET > 300 GeV). The /ET resolution in QCD dijet events matches well the resolution\nobtained from minimum bias events.\n6.2\nDetermining the /ET scale using Z \u2192\u03c4\u03c4 events\nAt the beginning of ATLAS operation, about 70k events of type Z \u2192\u03c4\u03c4 with one leptonic and one\nhadronic \u03c4-decay will be produced in 100 pb\u22121 of data. Such events can be selected with a lepton\ntrigger. The Z \u2192\u03c4\u03c4 \u2192\u2113h are produced with genuine /ET of typically 20 GeV and \u03a3/ET of the order of\n200 GeV. In these events the peak position of the \u03c4\u03c4 invariant mass distribution is sensitive to /ET and\ncan be very useful in determining the /ET scale [10].\nThe main backgrounds come from W \u2192\u2113\u03bd+jets events, where one jet fakes a \u03c4 decay, and from\nQCD events (mainly b\u00afb). The t\u00aft background has a much lower cross-section; the Z \u2192ee and Z \u2192\u00b5\u00b5\nbackgrounds are also small and the WW background is negligible. Events with the \ufb01nal state lepton and\n\u03c4-jet of the same-sign are not expected to come from Z \u2192\u03c4\u03c4 events which have opposite-sign. The\nbackgrounds (apart from the t\u00aft background, which is anyway low) contribute in the same way to the\nopposite-sign and the same-sign samples. Hence, the effect of backgrounds will be minimized using\nsame-sign events, subtracted from the opposite-sign events.\nFor each reconstructed event, the leading and isolated lepton (electron or muon) with p\u2113\nT > 15 GeV\nand |\u03b7\u2113| < 2.5 is chosen and a set of basic cuts is applied: /ET > 20 GeV (rejects QCD events), the\ntransverse mass calculated from /ET and the lepton < 50 GeV (suppresses events from semileptonic W\ndecays), and \u03a3/ET < 400 GeV (suppresses QCD). In addition it is required to have no tagged b jets\n(suppresses t\u00aft and b\u00afb events). Then at least one identi\ufb01ed \u03c4-jet with p\u03c4\u2212jet\nT\n> 15 GeV, |\u03b7\u03c4\u2212jet| < 2.5,\nand a track multiplicity of one or three is required. The \u2206\u03c6 between the isolated lepton and the \u03c4-jet is\nrequired to be in the range between 1\u22122.8, which reduces badly reconstructed events and further rejects\nbackgrounds.\nWith 100 pb\u22121 of data, 210 signal events (opposite-sign) are expected in the invariant mass range\n66 GeV < m\u03c4\u03c4 < 116 GeV. A total background of 16 events is expected. Figure 20 (left) shows the\nreconstructed mass peak for Z \u2192\u03c4\u03c4 events as well as the small total backgrounds after analysis cuts for\nopposite-sign and same-sign events.\nFigure 20 (right) shows a very good sensitivity of the measured Z mass reconstructed from \u03c4-pairs\nto the absolute /ET scale. With an integrated luminosity of 100 pb\u22121, the Z mass can be reconstructed\nwith an uncertainty of \u00b10.8 GeV. Taking into account the statistical uncertainty only, the /ET scale could\nbe determined with a precision of \u223c3%. But systematic effects, such as the subtraction of same-sign\nevents and the stability of the \ufb01t will affect the measurement of the reconstructed mass peak. Therefore,\nassuming a resolution of \u00b13\u03c3 on the reconstructed Z mass, the /ET scale can be determined to about\n\u00b18%.\n6.3\nZ \u2192\u2113\u2113events\nThis analysis uses inclusive Z \u2192ee and Z \u2192\u00b5\u00b5 samples to investigate the scale and resolution of the\n/ET reconstruction in the \ufb01rst data. In these samples the transverse momentum of the two leptons from\nthe Z boson decay are balanced by the hadronic recoil and \u03a3/ET reaches values up to a few hundred GeV.\nEvents are selected by requiring two well reconstructed, identi\ufb01ed and isolated leptons with\npT > 25 GeV. They have to have equal or opposite charge and a reconstructed mass, m\u2113\u2113, in the interval\n70\u2212100 GeV. In a sample of 250pb\u22121 of data, about 400k events are expected.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n390\n\n (GeV)\n\u03c4\n\u03c4\nInvariant m\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nExpected events in 100pb-1\n0\n5\n10\n15\n20\n25\nATLAS\nMean= 89.9 GeV\n= 12 0 GeV\n\u03c3\nETmiss scale\n0.8\n0.9\n1\n1.1\n1.2\nZ Mass (GeV) \n80\n85\n90\n95\n100\nATLAS\nFigure 20: (left) Reconstructed invariant mass of the pair of \u03c4 leptons for Z \u2192\u03c4\u03c4 decays and all back-\ngrounds: opposite-sign background (dashed) and same-sign background (dotted). (right) Reconstructed\ninvariant mass of the pair of \u03c4 leptons for Z \u2192\u03c4\u03c4 decays as a function of the /ET scale. The horizontal\nlines correspond to \u00b11\u03c3 and to \u00b13\u03c3 w.r.t. the Z peak position. The analysis is based on an integrated\nluminosity of 100 pb\u22121 of data.\nBackgrounds from Z \u2192\u03c4\u03c4 and W \u2192\u2113\u03bd events are negligible. The background from QCD events\nin which two leptons are falsely identi\ufb01ed is expected to be small but has to be carefully evaluated when\ndata are available. In the present study, these backgrounds are not considered as they are expected to\nhave negligible impact.\nIn Section 3, projections of /ET, called /EL and /EP, were introduced. This analysis aims at optimizing\nthe principle of using projections by resolving the missing transverse momentum along the so called\n\u2019longitudinal axis\u2019 which is de\ufb01ned by the combined direction of \ufb02ight of the two leptons. The perpen-\ndicular axis is also de\ufb01ned in the transverse plane which is orthogonal to the longitudinal axis. The axes\nas reconstructed from the measured angles of the leptons and their measured energies are thus not used\nat this point, which would fully exploit the good angular resolution of the ATLAS detector. In general,\nthe longitudinal axis points in the direction of \ufb02ight of the Z boson and away from the hadronic recoil.\nFigure 21 (left) shows, for Z \u2192ee events, the average /ET resolved along both axes as a function of\nthe transverse momentum of the lepton system resolved along the longitudinal axis.\nThe results for the longitudinal axis exhibit a negative offset of up to \u223c4 GeV at high values of pT\nof the lepton system, while the results for the perpendicular axis are consistent with zero. For Z \u2192\u00b5\u00b5\nevents similar results are obtained. It has been veri\ufb01ed that this offset is not caused by real neutrinos in\nthe event. If the event topology is considered, it is clear that this is suggesting that the magnitude of the\nhadronic recoil pT is underestimated. The resolution of the /ET projection on both axes as a function of\nthe total scalar sum of the activity in the hadronic calorimeter, \u2211ET,cluster, is shown in Figure 21(right) for\nZ \u2192ee events. The \ufb01tted curve is of the form \u03c3(/ET) = P0\np\n\u2211ET,cluster +P1 and illustrates the stochastic\nbehavior of the calorimetric energy measurement.\nThese results on Z \u2192ee and Z \u2192\u00b5\u00b5 events demonstrate that potential problems of the /ET recon-\nstruction can be located with high accuracy using the \ufb01rst data.\n6.4\nW \u2192\u2113\u03bd events\nEvents with W \u2192e\u03bd and W \u2192\u00b5\u03bd will be copiously produced at the LHC. Tens of thousands of events\nwith an excellent signal-to-background ratio can be collected per pb\u22121 . With these events, a good\nunderstanding of the /ET reconstruction can be achieved up to /ET values of few hundred GeV. The\naverage \u03a3/ET is of the order of 150 GeV.\nIn order to isolate W \u2192\u2113\u03bd events, two basic selection cuts are required: existence of one high pT\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n391\n\npT(lepton system) along longitudinal (GeV)\n0\n20\n40\n60\n80\n100\nEtMiss along axis (GeV)\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nLongitudinal\nPerpendicular\nATLAS\n (GeV)\nTcluster\n E\n\u03a3\n0\n20\n40\n60\n80\n100\n120\n140\n160\nEtMiss resolution along axis (GeV)\n0\n1\n2\n3\n4\n5\n6\n7\n8\nLongitudinal\nPerpendicular\nATLAS\nFigure 21: For Z \u2192ee events: (left) /ET projected onto the longitudinal and perpendicular axes as\nexplained in the text as function of the pT of the lepton system resolved along the longitudinal axis.\n(right) The width \u03c3(/ET) as a function of \u2211ET,cluster. Both plots use a sample corresponding to 250 pb\u22121\nof data.\ncharged lepton with |\u03b7| < 2.5 and /ET > 20 GeV. Possible backgrounds are from t\u00aft production, W \u2192\u03c4\u03bd,\nZ \u2192\u2113\u2113, and QCD events.\nTwo methods have been investigated to check the /ET reconstruction using these events. The \ufb01rst\nis based on the fact that the average pT of the charged lepton and the neutrino are the same, so the\nratio R = pT,\u03bd/pT,\u2113has been studied. This variable should be \u223c1, but its distribution is distorted by\nthe kinematic and acceptance requirements on the charged leptons. The method and related systematics\nhave been checked with the fast ATLAS simulation. It is expected to be sensitive to values of /ET up to\n60 GeV even with 1pb\u22121 of data. Full simulation studies are in progress.\nThe second method, based on the shape of the reconstructed transverse mass of the W boson, is\nsensitive to both the /ET resolution and the scale. The transverse mass, mW\nT , is reconstructed under the\nhypothesis that /ET is completely due to p\u03bd\nT. An example of an mW\nT distribution is shown in the next\nsection for tt events, which have high values of \u03a3/ET of typically 500 GeV. The focus in this section\nhowever is on a dedicated analysis of the corresponding distribution for Drell-Yan events at lower \u03a3/ET\nas statistically required.\nThe mW\nT distribution (for Drell-Yan events) is \ufb01tted in a binned log-likelihood \ufb01t that uses template\nhistograms. To minimize the dependence on the kinematics of the W boson, e.g. on its transverse mo-\nmentum, the \ufb01t is restricted to values of mW\nT in the range of 65 to 90 GeV. The template histograms of the\nmW\nT distributions are generated by convolving the true transverse mass distribution with the /ET response:\n/Ex,y = \u03b1 p\u03bd\nT(x,y) \u2295Gauss(0,\u03c3) where parameters \u03b1 and \u03c3 are the /ET scale and resolution (in GeV),\nrespectively. Since the /ET resolution strongly depends on the activity in the calorimeter, the analysis is\nperformed in several \u03a3/ET intervals.\nFigure 22 (left) shows the resolution for W \u2192\u00b5\u03bd events. The results of the \ufb01t agree well with the\nexpectations using truth information labeled as \u2018pseudo-data\u2019. In Fig. 22 (right) the result for the /ET\nscale is shown. The scale is measured at the 1% level over a large range of \u03a3/ET, con\ufb01rming the excellent\nperformance of this technique. The template \ufb01tting performs well in the low \u03a3/ET region, while a small\ndiscrepancy is observed in the high \u03a3/ET region.\nThis method described so far is applicable to W\u2192\u00b5\u03bd events, whereas in W \u2192e\u03bd events it has to\nbe modi\ufb01ed because the electron is included in the \u03a3/ET calculation, while the muon is not. This leads\nto a signi\ufb01cant correlation between \u03a3/ET and the shape of the transverse W mass distribution when the\ntemplate is made including the \u03a3/ET dependence. Similar results for the /ET scale and resolution are\nobtained, but systematic uncertainties have not yet been estimated.\nAlso if the backgrounds, including the QCD background, cannot be ef\ufb01ciently suppressed by the\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n392\n\n0\n100\n200\n300\n400\n500\n0\n2\n4\n6\n8\n10\n12\n14\n (GeV)\nT\n E\n\u03a3\n0\n100\n200\n300\n400\n500\n Resolution (GeV)\nmiss\nX\nE\n0\n2\n4\n6\n8\n10\n12\n14\n\u2295\n \nT\n E\n\u03a3\n 0.02)\n\u00b1\n Reso = (0.53 \nmiss\nX\nE\n 0.4)(GeV)\n\u00b1\n(3.7 \nPseudo-data\nEstimation\nATLAS\n0\n100\n200\n300\n400\n500\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\n (GeV)\nT\n E\n\u03a3\n0\n100\n200\n300\n400\n500\n Scale\nmiss\nX\nE\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\nPseudo-data\nEstimation\nATLAS\nFigure 22: For W\u2192\u00b5\u03bd events: /ET resolution (left) and scale (right) as a function of \u03a3/ET, using the\nsecond method described in the text. The circular dots represent the value calculated from pseudo-data\nand the triangular markers represent the estimation.\nselection cuts, their in\ufb02uence could be non-negligible. Work is in progress on that.\n6.5\nSemileptonic t\u00aft events\nSemileptonic tt events have an interesting multi-jet topology. With genuine /ET in the range from 20 GeV\nto 100 GeV and a total transverse energy of typically 500 GeV, they are representative of other physics\nchannels such as SUSY. This section shows that the reconstructed transverse W mass as well as a kine-\nmatic \ufb01t that exploits all mass constraints in t\u00aft events without requiring b jet tagging, will be useful to\ninvestigate possible problems of the /ET measurement in early data. Both methods are sensitive to the\nscale of /ET to the level of a few percent (statistically) when a sample with an integrated luminosity of\n200 pb\u22121 is used. These methods are affected differently by jet energy scales and background and can\nprovide complementary information.\nAbout 7k events survive the selection requirements, which are: at least 3 jets with pT \u226540 GeV, at\nleast one more jet with pT \u226520 GeV, /ET \u226520 GeV, and one isolated lepton (e or \u00b5), with pT \u226520 GeV.\nThe requirements strongly suppress the background from QCD events, which is expected to have no\neffect and is ignored. The QCD background is expected to be < 10% in t\u00aft\nevents, so, after the require-\nments for the kinematic \ufb01t, this assumption should be safe. The background from W+jets events is at the\nlevel of 20% and is included in this study.\nIn tt analyses the usual assumption is that the /ET in an event can be assigned to the neutrino from the\nleptonically decaying W. With this assumption, the transverse mass mW\nT can be reconstructed from the /ET\nvector and the transverse momentum of the charged lepton. Figure 23 (left) shows that the shape of the\nmW\nT distribution is distinctly different for various ranges of fake /ET4, illustrating the power of these events\nto locate problems. To demonstrate that the transverse W mass distribution can be used to check the /ET\nscale in early data, two additional event samples with the true /ET scaled by 0.8 and 1.2, respectively have\nbeen produced and reconstructed. The samples are analysed by \ufb01tting a Gaussian shape to the core of the\npeak in the transverse mass distributions. The peak position shifts by -7 and +7 GeV for the sample with\nscale of 0.8 and 1.2 respectively, both with an statistical uncertainty of 0.5 GeV, indicating a sensitivity\n4Here fake /ET is de\ufb01ned as the scalar difference of reconstructed /ET and true /ET.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n393\n\nto the /ET scale at the level of 2%.\nNote that backgrounds other than W+jets events are not considered in this study. Background from\nSUSY events can have a severe impact on the distribution by shifting the peak and thus mimicking a\n/ET scale calibration offset. The existing knowledge of tt events can be combined in a kinematic \ufb01t to\nimprove the measured quantities and to investigate the scale of the /ET measurement. The following mass\nconstraints are available: mhad\nW = mlep\nW = 80.4 GeV, where mhad\nW is the reconstructed mass of two light jets\nof the hadronically decaying W and mlep\nW is the reconstructed mass of the lepton and the neutrino of the\nleptonically decaying W. The reconstructed mass of the leptonically decaying top quark and that of the\nhadronically decaying top quark are assumed to be mhad\ntop = mlep\ntop = 175 GeV. The neutrino\u2019s transverse\nmomentum is set equal to /ET and its longitudinal momentum is analytically calculated from the mlep\nW\nconstraint.\nThe \u03c72 function of the \ufb01t is built using the energy of the four leading jets, with \ufb01t parameters to\nscale the corrected jet energies, a constraint on the product of the \ufb01t parameters to the a-priori known or\nassumed overall jet energy scale and with the implementation of the four mass constraints. All twelve\npossible permutations of assigning jets to the two top quarks and W bosons respectively are considered.\nFinally, only the permutation with the lowest \u03c72 is selected in each event.\nIt is found that the /ET, re-calculated after the \ufb01t, is not signi\ufb01cantly improved. However, using a cut\non \u03c72 improves the resolution on /ET, so it is possible to use the \u03c72 of a kinematic \ufb01t to classify tt events\nwith a relatively good /ET measurement without using b tagging. In the \ufb01rst data this classi\ufb01cation helps\nto locate possible detector problems.\nThe kinematic \ufb01tting procedure can be utilized to check the /ET scale in early data. Background\nevents are expected to be incompatible with the constraints used in the \ufb01t and thus be reduced by a cut\non \u03c72. Therefore, in contrast to the study using the transverse W mass as described above, this method\nsuffers signi\ufb01cantly less from backgrounds.\nAfter applying the \ufb01t to the events and requiring \u03c72 < 10 and in additional /ET > 40 the background\nfrom W+jets event is reduced to the 1% level. A robust estimator of the /ET scale is the measured\ntransverse momentum difference of the (anti-) top quark mother of the leptonically and hadronically\ndecaying W respectively: \u2206pT = plep\nT \u2212phad\nT\nwhere plep\nT\nis the combined transverse momentum of the\nmeasured charged lepton, /ET and one b jet, while phad\nT\nis the momentum of the jets of the hadronically\ndecaying W and the other b jet. Of course, the assignment of the jets to the correct top quark is not\nguaranteed. Nevertheless, this quantity is remarkably sensitive to the /ET scale, as can be seen in Fig.\nTransverse W Mass (GeV)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nNumber of events in 200 (pb)\n0\n50\n100\n150\n200\n250\n300\nATLAS\nfake EtMiss < 10 GeV\n10 GeV < fake EtMiss < 20 GeV\nfake EtMiss > 20 GeV\n p (GeV)\nT\n\u2206\n\u2212150\n\u2212100\n\u221250\n0\n50\n100\n150\n\u22121\nNumber of events in 200 pb\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\nMET scale=1.0\nMET scale=0.8\nMET scale=1.2\nFigure 23: In semileptonic t\u00aft events, (left) the reconstructed transverse W mass in various ranges of fake\n/ET, (right) the distribution of the measured momentum difference of the two top quarks, \u2206pT for (true)\n/ET scales of 0.8, 1.0 and 1.2 as indicated. The analysis is based on an integrated luminosity of 200 pb\u22121\nof data.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n394\n\n23(right). The mean values of the distributions are \u221216.4\u00b10.9 GeV , \u22124.5\u00b10.8 GeV, and 4.5\u00b10.9 GeV\nfor scales of 0.8, 1.0, and 1.2, respectively. This implies a sensitivity on the /ET scale at the level of 2%.\nThe systematic variation due to a shift of the top quark mass of 2.5 GeV is about 2%.\n7\nSummary\nThe /ET in ATLAS is calculated from the energy in the calorimeter and from the reconstructed muons.\nThe energy in the calorimeter is classi\ufb01ed and calibrated according to the reconstructed objects to which\nit belongs. Two algorithms for reconstruction and calibration are presently implemented in the ATLAS\nsoftware, one Cell-based, where the /ET reconstruction and calibration is done starting from the energy\ndeposited in calorimeter cells, and the other one Object-based, where the /ET reconstruction is done from\nthe reconstructed, classi\ufb01ed and calibrated objects and from the energy outside of them. The performance\nof the two is similar.\nThe /ET performance has been checked on a large variety of events with physical /ET such as Z \u2192\u03c4\u03c4\n, A/H \u2192\u03c4\u03c4, SUSY, and t\u00aft, as well as events with no physical /ET like minimum bias events, events\nwith QCD jets, and Z+jets processes. The resulting linearity of the response is within 5%, even for\nlow true /ET values of the order of 40 GeV. The /ET resolution, \u03c3, follows an approximate stochastic\nbehaviour over a wide range of values of the total transverse energy deposited in the calorimeters. A\nsimple \ufb01t to a function \u03c3 = a\u00b7\u221a\u03a3ET yields values between 0.53 and 0.57 for the parameter a, for \u03a3ET\nvalues between 20 and 2000 GeV. Deviations from this simple behaviour are expected and observed for\nlow values of \u03a3ET where noise is an important contribution, and for very high values of \u03a3ET where\nthe constant term in the jet energy resolution dominates. For values of the true /ET below 40 GeV, the\naccuracy of the measurement of the direction of the /ET vector for small values of /ET degrades rapidly.\nIn contrast, for high values of the true /ET, azimuthal accuracies better than 100mrad can be achieved.\nThis accuracy of the measurement of the /ET direction allows an isolation cut on /ET, which can ef\ufb01ciently\nsuppress events with a badly measured jet and the resulting /ET pointing in the jet direction.\nA dedicated study of fake /ET shows that instrumental effects like hot/dead/noisy cells (regions) in\ncalorimeters, as well as beam-gas scattering or other machine backgrounds, or displaced vertices, are\nvery important, and that their understanding will be crucial in the \ufb01rst days of data taking. Different\nmethods can be used to clean events and to correct/recover the /ET measurement. Mis-measurements in\nthe detector itself, due to high-pT muons escaping from the \ufb01ducial acceptance or from large losses of\ndeposited energy in cracks or inactive materials, might also effectively limit the performance of the /ET\nreconstruction and have therefore been studied in detail.\nWith the \ufb01rst 100pb\u22121 the algorithms for /ET reconstruction and calibration can be checked studying\nthe /ET linearity and resolution in minimum bias events and in Standard Model processes like Z and W\ndecays and in t\u00aft processes. Complementary methods for the determination of the /ET scale in-situ have\nbeen studied and it has been shown that it will be possible to determine the /ET scale with a precision of\nat least 8%.\nReferences\n[1] Cojocaru, C. et al., Hadronic calibration of the ATLAS liquid argon end-cap calorimeter in the\npseudorapidity region 1.6-1.8 in beam tests, NIM, A531 (2004), 481-514.\n[2] ATLAS Collaboration, Performance of Calorimeter Clustering Algorithms, note in preparation.\n[3] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n395\n\n[4] Asai, S. et al, Prospects for the Search of a Standard Model Higgs Boson in ATLAS using Vector\nBoson Fusion, SN-ATLAS-2003-024 (2003).\n[5] ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this vol-\nume.\n[6] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[7] F. Abe, et al., Phys. Rev. Lett. 69, 2896 - 2900 (1992).\n[8] R. K. Ellis et al., Higgs decay to \u03c4+\u03c4\u2212: A possible signature of Intermediate Higgs Bosons at the\nSSC, Nucl. Phys. B297 (1988) 221.\n[9] L. DiLella,\nProceedings of the Large Collider Workshop, edited by G. Jarlskog and D. Rein\n(Aachen, 4-9 October 1990), CERN 90-10/ECFA 90-133, Vol. II, p. 530..\n[10] ATLAS Collaboration, ATLAS Performance and Physics Technical Design Report, ATLAS TDR\n15, CERN/LHCC/99-15 (25 May 1999).\n[11] The ATLAS L1Calo Group (E. Eisenhander), ATLAS Level-1 Calorimeter Trigger Algorithms, 9\nSep 2004, ATL-DAQ-2004-011.\n[12] ATLAS Collaboration, A Study of Minimum Bias Events, this volume.\nJETS AND MISSING ET \u2013 MEASUREMENT OF MISSING TRANSVERSE ENERGY\n396\n\nb-Tagging\n397\n\nb-Tagging Performance\nAbstract\nThe ability to identify jets stemming from the fragmentation and hadroniza-\ntion of b quarks is important for the high-pT physics program of ATLAS:\ntop physics, Higgs boson searches and studies, new phenomena. After an\noverview of the reconstruction of the key ingredients for b-tagging, the tag-\nging techniques are described. The performance of b-tagging algorithms is\nthen detailed, as well as the impact on performance of several factors and new\npromising directions. Finally, expected performance in the \ufb01rst data and the\nanticipated uncertainty with which it can be measured are brie\ufb02y discussed.\n1\nIntroduction\nThis note discusses the identi\ufb01cation of jets stemming from the hadronization of b quarks, or b-tagging.\nThe ability to identify jets containing b-hadrons is important for the high-pT physics program of a\ngeneral-purpose experiment at the LHC such as ATLAS. This is in particular useful to select very pure\ntop samples, to search and/or study Standard Model or supersymmetric (SUSY) Higgs bosons which\ncouple preferably to heavy objects or are produced in association with heavy quarks, to veto the large\ndominant t\u00aft background for several physics channels and \ufb01nally to search for new physics: SUSY decay\nchains, heavy gauge bosons, etc.\nThe large majority of these studies requires good b-tagging performance for jets with a transverse\nmomentum ranging from 20 to 150 GeV. However, for super-symmetric processes, jets of pT as high\nas 500 GeV may have to be tagged [1], and for exotic phenomena b-jets of up to a few TeV can be\nproduced. For top studies, the signal rates are very high at the LHC and therefore a moderate b-tagging\nef\ufb01ciency (> 50%) is acceptable, while a fraction of light jets mis-identi\ufb01ed as b-jets below a few per\nmille suppresses most of the W+jets background (see for instance Ref. [2]). One of the most demanding\nchannels for b-tagging is the production of a light Standard Model Higgs boson in association with a\ntop-antitop pair [3]: t\u00aftH(H \u2192b\u00afb). Four b-jets have to be tagged with very high ef\ufb01ciency (\u03b5b \u224870%)\nsince the signal cross-section is low, and the mis-tagging rate must be kept below 1% to \ufb01ght the large\nt\u00aft+jets background.\nThe identi\ufb01cation of b-jets takes advantage of several of their properties which allow us to distinguish\nthem from jets which contain only lighter quarks. First the fragmentation is hard and the b-hadron retains\nabout 70% of the original b quark momentum. In addition, the mass of b-hadrons is relatively high (> 5\nGeV). Thus, their decay products may have a large transverse momentum with respect to the jet axis\nand the opening angle of the decay products is large enough to allow separation. The third and most\nimportant property is the relatively long lifetime of hadrons containing a b quark, of the order of 1.5 ps\n(c\u03c4 \u2248450\u00b5m). A b-hadron in a jet with pT = 50 GeV will therefore have a signi\ufb01cant \ufb02ight path length\n\u27e8l\u27e9= \u03b2\u03b3c\u03c4, traveling on average about 3 mm in the transverse plane before decaying. Such displaced\nvertices can \ufb01rst be identi\ufb01ed inclusively by measuring the impact parameters of the tracks from the\nb-hadron decay products. The transverse impact parameter, d0, is the distance of closest approach of\nthe track to the primary vertex point, in the r \u2212\u03d5 projection. The longitudinal impact parameter, z0, is\nthe z coordinate of the track at the point of closest approach in r \u2212\u03d5. The tracks from b-hadron decay\nproducts tend to have rather large impact parameters which can be distinguished from tracks stemming\nfrom the primary vertex. The other more demanding option is to reconstruct explicitly the displaced\nvertices. These two approaches of using the impact parameters of tracks or reconstructing the secondary\nvertex will be referred to later on as spatial b-tagging. Finally, the semi-leptonic decays of b-hadrons\ncan be used by tagging the lepton in the jet. In addition, thanks to the hard fragmentation and high mass\n398\n\nof b-hadrons, the lepton will have a relatively large transverse momentum and also a large momentum\nrelative to the jet axis. This is the so-called soft lepton tagging (the lepton being soft compared to high-pT\nleptons from W or Z decays).\nThe tagging methods relying on the impact parameter of tracks are detailed in this note. Only a\nsummary and the main results of the other methods are given. The techniques employed to reconstruct\neither a single inclusive vertex or to attempt to resolve the complex topologies with a secondary b-\nhadron vertex and a tertiary c-hadron vertex are discussed in Ref. [4], as well as the reconstruction of the\nprimary vertex. The tagging with soft muons or electrons from b-hadron decays is detailed respectively\nin Ref. [5] and Ref. [6]. The expected performance of the b-tagging algorithms in ATLAS, and the impact\nof several factors, are explained in detail in this note. However, the assessment of the impact of residual\nmisalignments on the performance is just starting and \ufb01rst results are available in Ref. [7]. While a large\neffort is put into having a very accurate Monte Carlo simulation, the b-tagging performance must be\nmeasured in data. Several studies aiming at measuring the b-tagging ef\ufb01ciency in dijet events (Ref. [8])\nor in t\u00aft events (Ref. [9]) have been performed. The studies to measure the mis-tagging rates are just\nstarting and are not discussed. Finally, the high-level trigger of ATLAS has the capability to select b-jets.\nThis is particularly interesting for channels with several b-jets where jet thresholds can be lowered at\nthe \ufb01rst level thanks to the b-tagging applied at the second and event-\ufb01lter levels. The high-level trigger\nb-tagging performance and strategies are discussed in Ref. [10].\nThe layout of this note is as follows: in Section 2, the reconstruction of the key objects for b-\ntagging is brie\ufb02y explained and the performance summarized. Since the de\ufb01nition of the \ufb02avour of a\njet is not unambiguous in Monte Carlo, the estimators used to assess the performance are de\ufb01ned in\nSection 3. Section 4 is intended to be a pedagogical approach to the various tagging algorithms available\nand to the likelihood ratio formalism used by ATLAS. The b-tagging performance for various physics\nprocesses is described in Section 5, relying on the current state-of-the-art b-tagging production software.\nIn Section 6, a few additional studies aiming at better understanding some critical aspects of the b-\ntagging are detailed, while in Section 7 three studies showing new directions to improve the b-tagging\nperformance are presented. In both cases the studies are described in a separate section because either\nthey required speci\ufb01c datasets or they relied on software and/or cuts/optimizations which were different\nfrom the ones currently in use in the ATLAS software or they even required new software developments.\nIn addition, the anticipated uncertainty with which the b-tagging performance may be measured in data\nis discussed in Section 8. Finally in Section 9, the main \ufb01ndings and the expected performance in the\n\ufb01rst data are summarized.\n2\nReconstruction of the key objects\nThe reconstruction of the various objects needed for b-tagging and its performance are summarized in\nthis section.\n2.1\nCharged tracks\nThe tracks reconstructed in the ATLAS Inner Detector [11] are the main ingredient for b-tagging. On\naverage a track consists of 3 pixel hits, 4 space-points in the silicon micro-strip detector and about 36 hits\nin the Transition Radiation Tracker (TRT). The innermost pixel layer (the so-called b-layer) is located at\na radius of 5 cm, while the TRT extends up to a radius of 1 m. The tracker is immersed in a 2 T magnetic\n\ufb01eld generated by the central solenoid. The intrinsic measurement accuracy of the pixels is around 10\n\u00b5m in r\u03c6 and 115 \u00b5m in z. All these allow the tracker to measure ef\ufb01ciently and with good accuracy\nthe tracks within |\u03b7| < 2.5 and down to pT \u223c500 MeV. For a central track with pT = 5 GeV, which\nis typical for b-tagging, the relative transverse momentum resolution is around 1.5% and the transverse\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n399\n\nimpact parameter resolution is about 35 \u00b5m. Further details can be found in Refs. [11,12].\nMost of the results in this note are based on the default pattern-recognition and \ufb01tting algorithm,\nNewTracking. Its performance is described in Ref. [12]. When relevant, some comparisons are made\nwith an alternate algorithm, iPatRec.\n2.1.1\nBaseline track selection\nThe track selection for b-tagging is designed to select well-measured tracks and reject fake tracks and\ntracks from long-lived particles (Ks,\u039b or other hyperon decays) and material interactions (photon con-\nversions or hadronic interactions).\nTwo different quality levels are used. For the standard quality level, at least seven precision hits\n(pixel or micro-strip hits) are required. The transverse and longitudinal impact parameters at the perigee\nmust ful\ufb01l |d0| < 2 mm and |z0 \u2212zpv|sin\u03b8 < 10 mm respectively, where zpv is the longitudinal location\nof the primary vertex. Only tracks with pT > 1 GeV are considered. For the b-tagging quality, the extra\nrequirements are: at least two hits in the pixel detector of which one must be in the b-layer, as well as\n|d0| < 1 mm and |z0 \u2212zpv|sin\u03b8 < 1.5 mm. This selection is used by all the tagging algorithms relying\non the impact parameters of tracks, while slightly different selections are used by the secondary vertex\nalgorithms as discussed in Ref. [4].\n2.1.2\nTracking ef\ufb01ciency\nThe b-tagging performance strongly depends upon the tracking ef\ufb01ciency. The tracking performance\ninside jets, where the track density may be high, is discussed in the following. The tracking performance\nfor single tracks is discussed in Ref. [12].\nFigure 1 shows the tracking ef\ufb01ciency and fake rate for tracks in t\u00aft events as a function of the track\npseudo-rapidity. For the ef\ufb01ciency denominator, only charged primary pions1 produced well before the\nb-layer (|x\u2212xpv| < 10 mm, |y\u2212ypv| < 10 mm) and with pT > 1 GeV and |\u03b7| < 2.5 are considered. The\n\ufb01rst level of the ef\ufb01ciency corresponds to the basic reconstruction ef\ufb01ciency, where a track matched to\na Monte Carlo particle is found. The fake rate is de\ufb01ned as the fraction of reconstructed tracks which\ndo not pass the matching criteria used for the ef\ufb01ciency, i.e. less than 80% of their hits are coming from\nthe same Monte Carlo particle. At high pseudo-rapidities, the tracking performance deteriorates mostly\nbecause of increased material and more ambiguous measurements.\nFigure 2 shows the tracking ef\ufb01ciency and fake rate for tracks in t\u00aft events as a function of their\ndistance \u2206R =\np\n\u2206\u03c6 2 +\u2206\u03b72 to the axis of the closest jet, for tracks ful\ufb01lling the b-tagging quality cuts.\nThe tracking performance degrades near the core of the jet where the track density is the highest and\ninduces pattern-recognition problems. This is especially visible for high-pT (> 100 GeV) jets.\nFinally, in Figure 3 the tracking ef\ufb01ciency and fake rates obtained with the default algorithm and\nwith iPatRec are compared. The \ufb01rst plot shows the comparison for several bins in the track pT for all\njets, while the second plot is as a function of the distance to the jet axis for jets with ET > 100 GeV.\nIt is interesting to note that the two algorithms have a different working point: the default algorithm\nmaintains a low level of fakes at the price of losing in ef\ufb01ciency, while the complementary choice was\ntaken for iPatRec. This difference in treatment will lead to different b-tagging performance for jets with\nhigh momentum, as discussed in particular in Section 5.6. The features seen in these plots are speci\ufb01c to\nthe pattern-recognition inside jets: for instance the decrease of the NewTracking ef\ufb01ciency at high track\npT is not visible for isolated tracks; it is here correlated with the local track density since high-pT tracks\nare more likely to originate from denser high-pT jets.\n1For the tracking studies only pions were considered, but similar results are expected for charged kaons, protons, etc. which\nare all used for b-tagging.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n400\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nTrack efficiency\nreconstruction\nstandard quality\nb-tagging quality\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\nFake rate\nstandard quality\nb-tagging quality\nATLAS\nFigure 1: Tracking ef\ufb01ciency (top plot) and fake\nrate (bottom plot) versus track pseudo-rapidity, for\nthree levels of track selection: matching (blue tri-\nangles), standard quality cuts (red squares) and b-\ntagging quality cuts (black circles), in t\u00aft events.\n R\n\u2206\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nTrack efficiency\n < 50 GeV\njet\nT\nE\n > 100 GeV\njet\nT\nE\nATLAS\n R\n\u2206\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\n0.007\n0.008\n0.009\n0.01\nFake rate\n < 50 GeV\njet\nT\nE\n > 100 GeV\njet\nT\nE\nATLAS\nFigure 2: Tracking ef\ufb01ciency (top plot) and fake\nrate (bottom) versus distance to jet axis, for tracks\nful\ufb01lling the b-tagging quality cuts and associated\nto low-pT jets (black symbols) or high-pT jets\n(green symbols), in t\u00aft events.\n (GeV)\nT\nTrack p\n1\n1 5\n2\n3\n4\n5\n10\n20\n50\n100\n\u221e\n+\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nTrack efficiency\nNewTracking\niPatRec\nATLAS\n1\n1 5\n2\n3\n4\n5\n10\n20\n50\n100\n\u221e\n+\n-3\n10\n-2\n10\nFake rate\nNewTracking\niPatRec\nATLAS\n(a) for several bins of track pT\n R\n\u2206\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nTrack efficiency\n > 100 GeV\njet\nT\nNewTracking, E\n > 100 GeV\njet\nT\niPatRec, E\nATLAS\n R\n\u2206\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\nFake rate\n > 100 GeV\njet\nT\nNewTracking, E\n > 100 GeV\njet\nT\niPatRec, E\nATLAS\n(b) versus the distance to the jet axis\nFigure 3: Tracking ef\ufb01ciency (top plots) and fake rate (bottom plots) in t\u00aft events after the b-tagging qual-\nity cuts, for two tracking algorithms: default NewTracking (black symbols) and iPatRec (red symbols).\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n401\n\n R\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nFraction of tracks with shared hits\nb-layer\npixels\nstrips\nstandard\ntt\nATLAS\nFigure 4: Fraction of tracks with shared hits ver-\nsus distance to the jet axis. Tracks ful\ufb01lling the b-\ntagging quality cuts, and with at least one shared\nhit in the silicon systems are shown. The standard\nde\ufb01nition of shared hits (see text) is shown as well.\nTransverse impact parameter significance\n0\n5\n10\n15\n20\n25\n30\n35\n40\nArbitrary units\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nTracks without shared hits\nTracks with shared hits\nATLAS\nFigure 5: Transverse impact parameter signi\ufb01-\ncance d0/\u03c3d0 for tracks in light jets. Two cate-\ngories of tracks are used: regular ones (red plain\ncurve) and tracks with shared hits (blue dashed).\nBoth distributions are normalized to unity.\n2.1.3\nTracks with shared hits\nTracks originating from the same point and passing the track selection cuts will not necessarily have the\nsame impact parameter distributions. First of all, even using the track parameters normalized to their\nerror will not compensate for all resolution effects, such as non-Gaussian tails. In addition, the pattern-\nrecognition process itself can produce tracks of variable quality depending on their hit contents. Those\ntracks require a special treatment to be \ufb02agged appropriately. The most signi\ufb01cant subset of such tracks\nis formed by the tracks which are sharing some of their hits with other tracks.\nFigure 4 shows the fraction of tracks which are sharing at least one hit with another reconstructed\ntrack versus the distance of the track to the jet axis, for jets originating from t\u00aft events. Currently for\nb-tagging purposes, a track is de\ufb01ned as a track with shared hits if it has at least one shared hit in the\npixels or two shared hits in the strips. As expected, the fraction of tracks with shared hits increases with\nthe local track density, and is therefore higher for high-pT jets and in the core of the jets. In t\u00aft events\nthe average pT for taggable (i.e. pT > 15 GeV and |\u03b7| < 2.5) b-jets and light jets are respectively 74\nand 55 GeV. The fraction of tracks with shared hits is about 2%. For jets with a transverse momentum\nof about 140 GeV (WH events with mH=400 GeV, see below), this fraction is twice as high. In both\ncases the fraction is roughly similar for NewTracking and iPatRec. In an extreme case, for Z\u2032 \u2192b\u00afb\nevents with mZ\u2032 = 2 TeV, a majority of tracks have shared hits and the fraction depends signi\ufb01cantly on\nthe reconstruction algorithm (cf. Section 5.6). Even when the overall level of shared hits is relatively\nlow, it has been demonstrated that those tracks should be treated appropriately since their impact on the\nb-tagging performance is signi\ufb01cant. Indeed, the impact parameter signi\ufb01cances, de\ufb01ned as the ratios\nd0/\u03c3d0 and z0/\u03c3z0 of the impact parameters to their measured error, for tracks in light jets exhibit a very\ndifferent behavior depending on whether the track is a regular one or a track with shared hits, as shown\nin Figure 5. It is clear that tracks with shared hits can mimic lifetime more easily.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n402\n\n (GeV)\nT\np\n1\n10\n2\n10\nm)\n\u00b5\n) (\n0\n(d\n\u03c3\n0\n50\n100\n150\n200\n250\n| < 0.5\n\u03b7\n|\n| < 1.0\n\u03b7\n0.5 < |\n| < 1.5\n\u03b7\n1.0 < |\n| < 2.0\n\u03b7\n1.5 < |\n| < 2.5\n\u03b7\n2.0 < |\nATLAS\n(a) Transverse impact parameter\n (GeV)\nT\np\n1\n10\n2\n10\nm)\n\u00b5\n) (\n0\n(z\n\u03c3\n0\n200\n400\n600\n800\n1000\n| < 0.5\n\u03b7\n|\n| < 1.0\n\u03b7\n0.5 < |\n| < 1.5\n\u03b7\n1.0 < |\n| < 2.0\n\u03b7\n1.5 < |\n| < 2.5\n\u03b7\n2.0 < |\nATLAS\n(b) Longitudinal impact parameter\nFigure 6: Track impact parameter resolution versus track pT, for several bins in the track pseudo-rapidity.\n2.1.4\nImpact parameter resolution\nThe resolution of the track impact parameter is a crucial ingredient to be able to discriminate tracks\ncoming from long-lived hadrons and prompt tracks. To estimate it, all the reconstructed tracks in t \u00aft events\nful\ufb01lling the b-tagging quality cuts and matched to a good Monte-Carlo track as de\ufb01ned in Section 2.1.2\nwere used. The difference between the reconstructed and the true impact parameter within a bin was\n\ufb01tted with a single gaussian, whose \u03c3 is reported on Figures 6(a) and 6(b), for respectively the transverse\nand longitudinal impact parameters. For a central track with pT = 5 GeV, which is typical for b-tagging,\nthe transverse impact parameter resolution is about 35 \u00b5m.\n2.2\nPrimary vertex \ufb01nding\nAnother key ingredient for b-tagging is the primary vertex of the event. The impact parameters of tracks\nare recomputed with respect to its position and tracks compatible with the primary vertex are excluded\nfrom the secondary vertex searches. At LHC the beam-spot size will be \u03c3xy = 15 \u00b5m and \u03c3z = 5.6 cm:\ntherefore the primary vertex is especially important for the z direction, while in the transverse plane only\nthe beam-line could be used. The strategies to \ufb01nd the primary vertex and their performance are explained\nin Ref. [4]. The ef\ufb01ciency to \ufb01nd the primary vertex is very high in the high-pT events of interest, and the\nresolution on its position is around 12 \u00b5m in each transverse direction and 50 \u00b5m along z. With pile-up,\nthe presence of additional minimum bias vertices makes the choice of the primary vertex less trivial: at\na luminosity of 2 \u00d7 1033 cm\u22122s\u22121 (on average 4.6 minimum bias events per bunch-crossing) a wrong\nvertex can be picked up as the primary vertex in about 10% of the cases [4], thus causing a deterioration\nin the b-jet tagging ef\ufb01ciency.\n2.3\nJet algorithms\nThe baseline jet algorithm for the studies in this note is a seeded cone algorithm using the calorimeter\ntowers with a cone size of \u2206R = 0.4, and where the cells were calibrated using the H1 method (see\nRef. [13] for details). The impact on b-tagging performance of using other jet algorithms is discussed in\nSection 6.4.\nFor b-tagging purposes, only the jet direction is relevant. In the \ufb01rst place, this direction is used\nto de\ufb01ne which tracks should be associated with the jets. The actual tagging is done on this subset of\ntracks. Currently tracks within a distance \u2206R < 0.4 of the jet axis are associated to the jet. A given track\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n403\n\nis associated to only one jet (the closest in \u2206R). This is the case for actually any jet collections, regardless\nof the cone size of the jet. The jet direction is also used to sign the impact parameters of the tracks in the\njet as explained in Section 4.1.2.\nExcept when stated otherwise, there was no attempt to remove from the reconstructed jet collection\nthe jets which are composed of only electrons. In the t\u00aft sample (semi-leptonic and di-leptonic channels),\nabout 5% of the taggable reconstructed jets are electrons. There is no dedicated treatment for muons.\nIsolated muons are very unlikely to fake jets, at least for the common processes under consideration\nin this note where pT(\u00b5) < 100 GeV. Muons in jets, stemming from b/c-hadron semi-leptonic decays\nand measured in the muon spectrometer, deposit on average about 3 GeV in the calorimeter but their\nmomentum as measured in the inner detector and the muon system is not used to re\ufb01ne the kinematics\nof the jet, which remain purely calorimeter-based.\nOnly jets ful\ufb01lling pT > 15 GeV and |\u03b7| < 2.5 are deemed taggable and considered in the perfor-\nmance studies.\n2.4\nSoft lepton reconstruction\nLeptons arising from semi-leptonic decays of b-hadrons or subsequent c-hadrons can be used to tag\nb-jets.\nSoft muons are reconstructed [5] using two complementary reconstruction algorithms. A combined\nmuon corresponds to a track fully reconstructed in the muon spectrometer that matches a track in the\ninner detector. Low-momentum muons (below p \u223c5 GeV) which cannot reach the muon middle and\nouter stations are identi\ufb01ed by matching an inner detector track with a segment in the muon spectrometer\ninner stations. Muons satisfying some basic requirements (pT > 3 GeV, |d0| < 4 mm) are associated to\nthe closest jet provided that \u2206R < 0.5. Finally, the kinematic properties of the jet-muon system are used\nin order to reject the background caused by punch-throughs and decays-in-\ufb02ight in light jets.\nReconstructing soft electrons [6] in the calorimeter inside a jet is more dif\ufb01cult. This is achieved\nby matching an inner detector track to an electromagnetic cluster. For a given track, only the energy\ncontained in a small window around the track extrapolation is used. The contribution of neighbouring\nhadronic showers is therefore reduced. The identi\ufb01cation procedure takes full advantage of the tracking\ncapabilities of the inner detector as well as of the granularity of the electromagnetic calorimeter: a\nlikelihood ratio combines inner detector information such as transition radiation hits with shower shape\nvariables from the calorimeter. The performance is, however, highly dependent on the track density in\njets as well as the quantity of matter in front of the electromagnetic calorimeter.\n3\nPerformance estimators\n3.1\nLabelling\nTo de\ufb01ne b-tagging performance, the Monte Carlo event history is used to know the type of parton\nfrom which a jet originates. This labelling procedure is not unambiguous and is not strictly identical\nfor different Monte Carlo generators. For the results presented here, a quark labelling has been used: a\njet is labelled as a b-jet if a b quark with pT > 5 GeV is found in a cone of size \u2206R = 0.3 around the\njet direction. The various labelling hypotheses are tried in this order: b quark, c quark and \u03c4 lepton.\nWhen no heavy \ufb02avour quark nor \u03c4 lepton satis\ufb01es these requirements, the jet is labelled as a light-jet.\nNo attempt is made to distinguish between u, d, s quarks and gluon since such a label is even more\nambiguous.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n404\n\n3.2\nEf\ufb01ciency and rejection\nFor performance studies, only jets ful\ufb01lling pT > 15 GeV and |\u03b7| < 2.5 are considered and refered to as\ntaggable jets. In the following, jets for which no track passed the b-tagging quality cuts are still counted\nin the performance estimators. However, events where the primary vertex could not be reconstructed\nare ignored. In addition, b-jets were not categorized according to the nature of the b-hadron decay: b-\njets with semi-leptonic decays behave quite differently from jets with hadronic decays, even when using\npurely spatial methods, but in the following no distinction was made.\nThe tagging ef\ufb01ciency is naturally de\ufb01ned as the fraction of taggable jets labelled as b-jets (see\nprevious section) which are actually tagged as b-jets by the tagging algorithm under study. The mis-\ntagging rate is the fraction of taggable jets not labelled as b which are actually tagged as b-jets. For\nhistorical reasons the jet rejection is used instead: this is simply the inverse of the mis-tagging rate.\n3.3\nPuri\ufb01cation\nA dif\ufb01culty arises as soon as the jet multiplicity is high and various jet \ufb02avours are present in a single\nevent: a jet with \u2206R(jet\u2212b) = 0.31 is labelled as a light jet, although tracks from b-hadron decay with\nhigh lifetime content are likely to be associated to it.\nThis leads to a decrease of the estimated performance, not related to the b-tagging algorithm itself\nbut to the labelling procedure which strongly depends on the activity of the event. In order to obtain\na more reliable estimation of b-tagging performance, a puri\ufb01cation procedure has been devised: light\njets for which a b quark, a c quark or a \u03c4 lepton is found within a cone of size \u2206R = 0.8 around the jet\ndirection are not used to compute the rejection.\nThe performance estimated after puri\ufb01cation represents the intrinsic power of the b-tagging algo-\nrithms and should be similar for different kinds of hard event, whereas results obtained for the complete\nlight jet sample are more dependent on the event type. On the other hand, the latter is more representative\nof the actual b-tagging power for a given physics analysis. This is illustrated in Figure 7: the light jet\nrejection in simple WH events is similar without or with puri\ufb01cation (left plot), while for busier t \u00aft events\n(right plot) the two curves differ in the region where lifetime content as opposed to resolution effects\ndominates (i.e. for \u03b5b < 80%). In the following, jets ful\ufb01lling the puri\ufb01cation procedure will be referred\nto as puri\ufb01ed or pure jets, the ones failing this procedure will be called non-pure jets, while all the jets\nwill be called raw jets.\n4\nb-tagging algorithms\nIn this section the various algorithms used in ATLAS to tag b-jets are explained. The spatial algorithms,\nbuilt on tracks and subsequently vertices, are the most powerful ones. Most of them are based on a\nlikelihood ratio approach, but simpler and more robust tagging algorithms are also available. Soft lepton\ntagging algorithms are also very important, in particular since the correlation with the previous ones is\nminimal. Their performance is summarized in section 4.3.\n4.1\nSpatial algorithms based on likelihood ratio\nAll tracks in the jet ful\ufb01lling the b-tagging quality cuts described in 2.1.1 are considered for the spatial\nb-tagging algorithms. In typical t\u00aft events, the average number of those tracks per light (b-) jet is 3.7 (5.5)\nand their average pT is 6.6 (6.3) GeV, respectively.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n405\n\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nJet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nWH, light jets\nWH, c-jets\nWH, purified light jets\nWH, purified c-jets\nATLAS\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nJet rejection\n1\n10\n2\n10\n3\n10\n4\n10\n, light jets\ntt\n, c-jets\ntt\n, purified light jets\ntt\n, purified c-jets\ntt\nATLAS\nFigure 7: Rejection of light jets and c-jets with and without puri\ufb01cation versus b-jet ef\ufb01ciency for WH\n(mH =120 GeV) and t\u00aft events, using the tagging algorithm based on 3D impact parameter and secondary\nvertex.\n4.1.1\nV 0 and secondary interactions rejection\nThe preselection cuts on impact parameters reject a large fraction of long-lived particles and secondary\ninteractions. Among the remaining tracks, the ones identi\ufb01ed by the secondary vertex search (sec-\ntion 4.1.3) as likely to come from V 0 decays are rejected (they amount to between 1% and 3% of the\ntracks in light and b-jets respectively). To do so, the search starts by building all two-track pairs that\nform a good vertex. The mass of the vertex is used to reject the tracks which are likely to come from\nKs,\u039b decays and photon conversions. The radius of the vertex is compared to a crude description of\nthe innermost pixel layers to reject secondary interactions in material. The cuts and performance of this\nselection are described in Ref. [4].\n4.1.2\nImpact parameter tagging algorithms\nFor the tagging itself, the impact parameters of tracks are computed with respect to the primary vertex (cf.\nsection 2.2). On the basis that the decay point of the b-hadron must lie along its \ufb02ight path, the impact\nparameter is signed to further discriminate the tracks from b-hadron decay from tracks originating from\nthe primary vertex. The sign is de\ufb01ned using the jet direction \u20d7Pj as measured by the calorimeters (cf.\nsection 2.3), the direction \u20d7Pt and the position \u20d7Xt of the track at the point of closest approach to the primary\nvertex and the position \u20d7Xpv of the primary vertex:\nsign(d0) = (\u20d7Pj \u00d7\u20d7Pt)\u00b7\n\u0010\n\u20d7Pt \u00d7(\u20d7Xpv \u2212\u20d7Xt)\n\u0011\nThe experimental resolution generates a random sign for the tracks originating from the primary vertex,\nwhile tracks from the b/c hadron decay tend to have a positive sign. The sign of the longitudinal impact\nparameter z0 is given by the sign of (\u03b7 j \u2212\u03b7t)\u00d7z0t where again the t subscript refers to quantities de\ufb01ned\nat the point of closest approach to the primary vertex.\nThe distribution of the signed transverse impact parameter d0 is shown on Figure 8, left plot, for\ntracks coming from b-jets, c-jets and light jets. The right plot shows the signi\ufb01cance distribution d0/\u03c3d0\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n406\n\nSigned transverse impact parameter (mm)\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nTracks in b-jets\nTracks in c-jets\nTracks in light jets\nATLAS\nSigned transverse impact parameter significance\n-20\n-10\n0\n10\n20\n30\n40\nArbitrary units\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nTracks in b-jets\nTracks in c-jets\nTracks in light jets\nATLAS\nFigure 8: Signed transverse impact parameter d0 distribution (left) and signed transverse impact param-\neter signi\ufb01cance d0/\u03c3d0 distribution (right) for b-jets, c-jets and light jets.\nwhich gives more weight to precisely measured tracks. Combining the impact parameter signi\ufb01cances of\nall the tracks in the jet is the basis of the \ufb01rst method to tag b-jets. Three tagging algorithms are de\ufb01ned\nin this way: IP1D relies on the longitudinal impact parameter, IP2D on the transverse impact parameter\nand \ufb01nally IP3D which uses two-dimensional histograms of the longitudinal versus transverse impact\nparameters, taking advantage of their correlations.\n4.1.3\nSecondary vertex tagging algorithms\nTo further increase the discrimination between b-jets and light jets, the inclusive vertex formed by the\ndecay products of the bottom hadron, including the products of the eventual subsequent charm hadron\ndecay, can be sought. The reader is referred to Ref. [4] for all details. The search starts by build-\ning all two-track pairs that form a good vertex, using only tracks far enough from the primary vertex\n(L3D/\u03c3L3D > 2 where L3D \u2261\u2225\u20d7Xpv \u2212\u20d7Xt\u2225is the three dimensional distance between the primary vertex and\nthe point of closest approach of the track to this vertex). Vertices compatible with a V 0 or material inter-\naction are rejected. All tracks from the remaining two-track vertices are combined into a single inclusive\nvertex, using an iterative procedure to remove the worst track until the \u03c7 2 of the vertex \ufb01t is good. Three\nof the vertex properties are exploited: the invariant mass of all tracks associated to the vertex, the ratio\nof the sum of the energies of the tracks participating to the vertex to the sum of the energies of all tracks\nin the jet and the number of two-track vertices. These properties are illustrated in Figure 9 for b-jets\nand light jets. The so-called SV tagging algorithms make different use of these properties: SV1 relies\non a 2D-distribution of the two \ufb01rst variables and a 1D-distribution of the number of two-track vertices,\nwhile SV2 is based on a 3D-histogram of the three properties which requires quite some statistics. The\nsecondary vertex \ufb01nding ef\ufb01ciency depends in particular on the event topology, but the typical ef\ufb01ciency\n\u03b5SV\nb\nis higher than 60% in b-jets. The SV taggers require an a priori knowledge of \u03b5 SV\nb\nand \u03b5SV\nu .\nA completely new algorithm, JetFitter, is also available, which exploits the topological structure of\nweak b- and c-hadron decays inside the jet. A Kalman \ufb01lter is used to \ufb01nd a common line on which the\nprimary vertex and the beauty and charm vertices lie, as well as their position on this line approximating\nthe b-hadron \ufb02ight path. With this approach, the b- and c-hadron vertices are not merged, even when\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n407\n\nSecondary vertex mass (GeV)\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nb-jets\nLight jets\nATLAS\nSecondary vertex charged energy fraction\n0\n0.1 0.2\n0.3\n0.4 0.5\n0.6\n0.7\n0.8\n0.9\n1\nArbitrary units\n0\n0.01\n0.02\n0.03\n0.04\nb-jets\nLight jets\nATLAS\nNumber of two-track vertices\n0\n5\n10\n15\n20\n25\n30\nArbitrary units\n-5\n10\n-\n10\n-3\n10\n-2\n10\n-1\n10\n1\nb-jets\nLight jets\nATLAS\nFigure 9: Secondary vertex variables: invariant mass of all tracks in vertex (left), energy fraction ver-\ntex/jet (center) and number of two-track vertices (right) for b-jets and light jets.\nonly a single track is attached to each of them. The discrimination between b-, c- and light jets is based\non a likelihood using similar variables to the SV tagging algorithm above, and additional variables such\nas the \ufb02ight length signi\ufb01cances of the vertices. This algorithm and its performance are also described in\ndetail in Ref. [4].\n4.1.4\nFormalism of likelihood ratio\nFor both the impact parameter tagging and the secondary vertex tagging, a likelihood ratio method is\nused: the measured value Si of a discriminating variable is compared to pre-de\ufb01ned smoothed and nor-\nmalized distributions for both the b- and light jet hypotheses, b(Si) and u(Si). Two- and three-dimensional\nprobability density functions are used as well for some tagging algorithms. The ratio of the probabilities\nb(Si)/u(Si) de\ufb01nes the track or vertex weight, which can be combined into a jet weight WJet as the sum\nof the logarithms of the NT individual track weights Wi:\nWJet =\nNT\n\u2211\ni=1\nlnWi =\nNT\n\u2211\ni=1\nln b(Si)\nu(Si)\n(1)\nThe distribution of such a weight is shown in Figure 10 for b-, c- and light jets for two different tagging\nalgorithms: IP2D and the sum of the weights from IP3D and SV1. When no vertex is found, the SV\ntaggers return a weight of ln 1\u2212\u03b5SV\nb\n1\u2212\u03b5SV\nu . To select b-jets, a cut value on WJet must be chosen, corresponding\nto a given ef\ufb01ciency. The relation between the cut value and the ef\ufb01ciency depends on the jet transverse\nmomentum and rapidity, and therefore is different for different samples.\n4.1.5\nLikelihood ratio and track categories\nAs seen already, tracks may exhibit different behavior even after the track selection, such as the tracks\nwith shared hits (Figure 4). One idea to take advantage of the different properties of tracks is to arrange\nall tracks into various categories and use dedicated probability density functions for each category. The\nlikelihood ratio formalism permits to incorporate such categories in a straightforward way. After the\ndivision of the tracks into disjoint categories j, where every category has its own set of reference his-\ntograms b j and u j, the jet weight can simply be written as the sum over all tracks in each category N j\nT\nand all categories NC:\nWJet =\nNC\n\u2211\nj=1\n\uf8eb\n\uf8ed\nN j\nT\n\u2211\ni=1\nln b j(Si)\nu j(Si)\n\uf8f6\n\uf8f8\n(2)\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n408\n\n2D impact parameter weight\n-20\n-10\n0\n10\n20\n30\n40\nArbitrary units\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nb-jets\nc-jets\nLight jets\nATLAS\n3D impact parameter + secondary-vertex weight\n-20\n-10\n0\n10\n20\n30\n40\nArbitrary units\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nb-jets\nc-jets\nLight jets\nATLAS\nFigure 10: Jet b-tagging weight distribution for b-jets, c-jets and puri\ufb01ed light jets. The left plot is for\nthe IP2D tagging algorithm. The right plot corresponds to the IP3D+SV1 tagging algorithm.\nCurrently in the b-tagging software, two track categories are used: the Shared tracks (tracks with\nshared hits), and the complementary subset of tracks called Good tracks. These track categories are only\nused for the time being for the IP1D, IP2D and IP3D tagging algorithms.\n4.2\nOther spatial algorithms\nThe spatial algorithms based on likelihood ratios require an a-priori knowledge of the properties of both\nb-jets and light jets. Methods to measure them in data are being devised for the b-jets [8, 9] but will\nrequire at least about 100 pb\u22121. In addition, there is no clear way to extract a pure enough sample of\nlight jets, and Monte Carlo simulation will probably have to be used once a thorough validation against\ndata has been performed. A few other spatial tagging algorithms, less powerful, are therefore developed,\nwhich have less reliance on Monte Carlo and are expected to be easier and faster to commission with the\n\ufb01rst real data.\nThe simplest approach that could be used, at least at the beginning, is the counting of tracks with\nlarge impact parameter or large impact parameter signi\ufb01cance. Requiring a few of these tracks provides\na sample enriched in b-jets. The performance of such a tagging algorithm is not discussed in this note\nbecause it is not yet fully implemented in ATLAS. Such a simple tagger may also be very useful at the\ntrigger level.\nAnother approach is to combine the impact parameter of all the tracks in the jet. JetProb is an imple-\nmentation of the ALEPH tagging algorithm [14], used extensively at LEP and later at the Tevatron. The\nsigned impact parameter signi\ufb01cance d0/\u03c3d0 of each selected track in the jet is compared to a resolution\nfunction R for prompt tracks, in order to measure the probability that the track i originates from the\nprimary vertex (Figure 11(a)):\nPi =\nZ \u2212|di\n0/\u03c3i\nd0|\n\u2212\u221e\nR(x)dx\n(3)\nThe resolution function can be measured in data using the negative side of the signed impact param-\neter distribution (cf. section 6.5.1), assuming there is no contribution from heavy-\ufb02avour particles which\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n409\n\nis not strictly true.\nThe individual probability of each of the N tracks associated to the jet are then combined to obtain a\njet probability P jet which discriminates b-jets against light jets (Figure 11(b)):\nP jet = P0\nN\u22121\n\u2211\nj=0\n(\u2212lnP0) j\nj!\n(4)\nwhere\nP0 =\nN\n\u220f\ni=1\nP\u2032\ni\nand\n(\nP\u2032\ni = Pi\n2\nif di\n0 > 0\nP\u2032\ni =\n\u0010\n1\u2212Pi\n2\n\u0011\nif di\n0 < 0\n(5)\nTrack probability\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nArbitrary units\n-2\n10\n-1\n10\nTracks in b-jets\nTracks in purified c-jets\nTracks in purified light jets\nATLAS\n(a) Individual track probability Pi \u00d7Sign(di\n0)\n)\njet\n-log(P\n0\n5\n10\n15\n20\n25\nArbitrary units\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nb-jets\nPurified c-jets\nPurified light jets\nATLAS\n(b) Jet probability P jet\nFigure 11: Distributions of the probability of compatibility with the primary vertex for individual tracks\n(left plot) and for all tracks in the jet (right plot) as de\ufb01ned for JetProb. The cases of b-jets (red plain),\nc-jets (green dashed) and light jets (blue dotted line) are shown.\n4.3\nSoft lepton algorithms\nSoft lepton tagging relies on the semi-leptonic decays of bottom and charm hadrons. Therefore it is in-\ntrinsically limited by the branching ratios to leptons: at most 21% [15] of b-jets will contain a soft lepton\nof a given \ufb02avour, including cascade decays of bottom to charm hadrons. However, tagging algorithms\nbased on soft leptons exhibit very high purity and low correlations with the track-based tagging algo-\nrithms, which is very important for checking and cross-calibrating performance in data (see for instance\nRef. [8]).\n4.3.1\nSoft muons\nOnce a reconstructed muon is associated to a jet as explained brie\ufb02y in Section 2.4, a likelihood permits\nto discriminate light jets from b-jets. The algorithm and its performance are detailed in Ref. [5] and will\nnot be discussed further in this note. To summarize, a light jet rejection of about 300 can be achieved for\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n410\n\na b-tagging ef\ufb01ciency of 10%. Those numbers include the semi-leptonic branching ratio, the detector ac-\nceptance, the reconstruction ef\ufb01ciency as well as the jet-muon association ef\ufb01ciency. This was estimated\nin t\u00aft events, including a simulation of the cavern background (low-energy neutrons and photons stem-\nming from the interaction of forward particles with the shielding) which reduces the rejection level by\nabout 30%. The performance is relatively steady in the jet pT range 15-100 GeV and in pseudo-rapidity.\n4.3.2\nSoft electrons\nA likelihood ratio is also used for soft electrons. The algorithm and its performance are detailed in\nRef. [6] and will not be discussed further in this note. A light jet rejection of about 100 can be achieved\nfor a b-tagging ef\ufb01ciency of 7%. The ef\ufb01ciency of the soft electron identi\ufb01cation is high, since two-thirds\nof the true b-jets containing a real soft electron are tagged by the soft electron algorithm. However, about\n25% of light jets are mis-tagged by real electrons from photon conversions and Dalitz decays. This\nwas estimated in WH (mH = 120 GeV) events without pile-up. Based on previous study [16], a further\ndegradation by 10% (30%) is expected when on average 4.6 (23) minimum-bias events are added. While\nthe performance is constant in jet pT in the range 15-100 GeV, it degrades quickly with the jet pseudo-\nrapidity because of the higher amount of dead material, the poor performance in the transition region\nbetween the barrel and end-cap cryostats of the electromagnetic calorimeter (1.37 < |\u03b7| < 1.52) and the\nabsence of the TRT beyond |\u03b7| > 2.\n4.4\nCombining tagging algorithms\nCurrently only the likelihood-based tagging algorithms have been combined, since the formalism is\neasy in this case: the weights of the individual tagging algorithms are simply summed up. The most\ncommonly used tagging algorithm, IP3D+SV1, is actually such a combination. It should be noted that\nthe SV tagging algorithms have been optimized to work in conjunction with the IP ones. Another one\ncombines IP3D and JetFitter. Multivariate approaches to combine all tagging algorithms, including the\nsoft lepton ones, have not received much attention so far. There are, however, some new studies and the\nuse for instance of boosted decision trees is discussed in Section 7.3.\n4.5\nCalibration of tagging algorithms\nThe likelihood-based tagging algorithms require knowledge of the probability density functions of the\ndiscriminating variables for both the b- and light jet hypotheses: this is called the calibration of the\ntagging algorithms, or their reference histograms. In the following, those functions have been derived\nfrom a large sample of jets coming from t\u00aft and t\u00aft j j events. Several issues about the calibration and its\nimpact on b-tagging performance are discussed in Section 6.5.\n5\nPerformance for various physics processes\nIn this section, the b-tagging performance is reviewed for several physics channels of interest. Several\nspatial tagging algorithms are considered: JetProb and IP2D which are best suited for the initial period,\nIP3D and then IP3D+SV1 for regular operations once the secondary vertexing is understood and \ufb01nally\nIP3D+JetFitter for the ultimate performance.\n5.1\nDependence on jet transverse momentum and pseudo-rapidity\nThe spatial b-tagging performance depends strongly on the jet momentum and rapidity: the pT and \u03b7\ndependencies of the b-tagging ef\ufb01ciency and light jet rejection for a given cut on the b-tagging weight\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n411\n\n (GeV)\nT\np\n50\n100\n150\n200\n250\n300\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\nb-jet efficiency\nATLAS\n (GeV)\nT\np\n50\n100\n150\n200\n250\n300\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nLight jet rejection\nATLAS\n(a) versus jet pT\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\nb-jet efficiency\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nLight jet rejection\nATLAS\n(b) versus jet |\u03b7|\nFigure 12: b-tagging ef\ufb01ciency and puri\ufb01ed light jet rejection obtained with the IP3D+SV1 tagging\nalgorithm operating at a \ufb01xed cut of 4 on the b-tagging weight, for t\u00aft events.\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nLight jet rejec ion\n50\n100\n150\n200\n250\n300\n350\n400\n450\ntt\nWH120\nATLAS\n(a) All jet pT\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nLight jet rejec ion\n50\n100\n150\n200\n250\n300\ntt\nWH120\nATLAS\n(b) Jets with 30 < pT < 45 GeV\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nLight jet rejec ion\n100\n200\n300\n400\n500\n600\n700\n800\ntt\nWH120\nATLAS\n(c) Jets with 60 < pT < 100 GeV\nFigure 13: Rejection of light jets with puri\ufb01cation versus jet \u03b7 for the IP3D+SV1 tagging algorithm and\nfor two different physics channels: jets from t\u00aft events and from WH (mH = 120 GeV) events, for a \ufb01xed\n60% tagging ef\ufb01ciency in each bin.\nare shown in Figure 12. At high pT or at high |\u03b7|, the b-jet tagging performance is poor, regardless of\nwhich tagging algorithm is used. At low pT, maintaining a reasonable b-jet ef\ufb01ciency is possible only by\nloosening the cut on the weight, at the price of a very low rejection of light jets. The strong dependence,\nespecially in pT, makes the extraction of the b-jet ef\ufb01ciency from data complicated and means that more\nintegrated luminosity will be required, since several bins are needed.\nBecause of these strong pT and \u03b7 dependencies, and since various samples have very different spec-\ntra, it is not straightforward to compare between channels the integrated rejection numbers shown in\nthe following. It is worth noting that this dependence is really a two-dimensional one, thus Figure 12\nis useful for illustrative purposes but the (pT,|\u03b7|) spectrum of the jets in the sample considered is not\nproperly factorized out. This is important for instance to parametrize the b-tagging performance. This is\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n412\n\n (GeV)\nT\np\n0\n50 100 150 200 250 300 350 400 450 500\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\ntt\nH\ntt\nb\nb\ntt\nSU3\nWH120\nWH400\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\ntt\nH\ntt\nb\nb\ntt\nSU3\nWH120\nWH400\nATLAS\n (GeV)\nT\np\n0\n50 100 150 200 250 300 350 400 450 500\n-4\n10\n-3\n10\n-2\n10\n-1\n10\ntt\nH\ntt\nb\nb\ntt\nSU3\nWH120\nWH400\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\n0.055\ntt\nH\ntt\nb\nb\ntt\nSU3\nWH120\nWH400\nATLAS\nFigure 14: pT and |\u03b7| spectra of b (upper plots) and light (lower plots) jets for the various channels\nconsidered in this section.\nfurther illustrated in Figure 13: the rejections achieved in two different samples become more similar as\na function of \u03b7 when looking in bins of pT. The remaining differences are mostly because the binning in\npT is still too large, but also because of other minor differences between the samples: for example they\nhave been generated with different Monte Carlo generators (cf. section 6.6).\nFor reference, the pT and |\u03b7| spectra of b and light jets in the various samples used in the following\nare shown on Figure 14. They affect the integrated rejections for the various channels.\n5.2\nSimple topologies: WH channels\nThis \ufb01rst class of events illustrates the performance obtained on simple event topologies where the jet\nmultiplicity is very low. As discussed in Section 3.3, puri\ufb01cation is not an issue in this case.\nEvents from Higgs boson production in association with a W boson are interesting in this respect\nand are a benchmark for b-tagging performance, even though the channel itself is no longer thought\nto be very promising at the LHC (see however Ref. [17] for a recent re-investigation). The W decays\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n413\n\nleptonically, and there are only two jets coming from the hard process, originating from the H decay. To\nstudy the b-tagging ef\ufb01ciency the decay H \u2192b\u00afb is simulated while here for the rejection of charmed and\nlight jets the Higgs boson is forced to decay to c\u00afc or to the unlikely u \u00afu channel respectively.\nThe b-tagging performance obtained on this kind of events and for mH = 120 GeV is shown in\nTable 1 for the tagging algorithms considered. Two typical b-tagging ef\ufb01ciencies were considered: 50%\nand 60%. For each tagging algorithm, the cuts on the weight required to achieve these ef\ufb01ciencies were\ndetermined over the whole sample, and then applied to estimate the rejections.\nTo study more energetic jets, similar physics processes have been considered for a different Higgs\nboson mass, mH=400 GeV (again such a choice is unphysical since a 400 GeV Higgs boson would not\ndecay to b\u00afb but is useful for these studies). The results are shown in Table 1 for the light jet rejection\nand in Table 2 for the c-jet rejection. The differences in performance between the two mass cases are the\nresult of the different pT and \u03b7 spectra: the jets for mH = 400 GeV are more energetic and explain most\nof the discrepancy, this effect being only slightly balanced by the fact that jets for mH = 120 GeV are\nmore forward. For this channel, the gain obtained with JetFitter is more visible.\n5.3\nMulti-jets channels: the top case\nThe jet multiplicity in pair-produced top quark events is much higher. In the following, the channels\nwhere at least one of the W bosons decays to leptons are considered. For the dominant lepton+jets chan-\nnel, there are usually at least four jets from the hard process and extra jets from radiation. Several \ufb02avours\nof jets are present at the same time in the event: two b-jets from the top quarks, light jet(s) and often a\nc-jet from the W decaying hadronically. This increases the likelihood of having light jets contaminated\nwith heavy \ufb02avour and also makes the labelling of jets even more ambiguous as discussed previously.\nThe benchmark curves of jet rejection versus b-tagging ef\ufb01ciency are shown on Figures 15(a) and 15(b),\nfor light jets and for several tagging algorithms. The jets of the various \ufb02avours were taken from the\nsame sample in this case, unlike for events of the WH channels. Table 1 shows the light jet rejection\nachieved in t\u00aft events and in t\u00aft j j events, both samples being generated with MC@NLO+HERWIG. The\nlatter events are t\u00aft events which were \ufb01ltered in order to have at least six jets, of which four are taggable.\nSince the performance in those two samples is similar, they have been merged. For light jets, both the\nraw (without puri\ufb01cation) and puri\ufb01ed rejections are shown. For c-jets and \u03c4-jets the puri\ufb01cation does\nnot make any signi\ufb01cant difference. The rejection power of c-jets (Table 2 and Figure 15(c)) is naturally\nvery limited because of the lifetime of c-hadrons and is almost independent of the physics process. With-\nout any optimization, the b-tagging algorithms also prove to be useful for the identi\ufb01cation of \u03c4-jets, as\nshown on Figure 15(d). The small discontinuities in the curves on Figure 15, visible notably for the IP3D\ntagger, are due to the conjunction of a coarser binning of the underlying probability density functions\nfor this tagger and the presence of single-track jets (notably electrons faking jets). This effect is more\npronounced for the \u03c4-jets (Figure 15(d)) where single-prong decays are abundant.\nThe impact on the light jet rejection of electrons faking jets can be seen in the fourth block of\nTable 1. Electron jets are seldom mis-tagged as b-jets, since they have usually a single prompt high-\npT track which is well-measured. In this sample, the high-pT electrons are coming from W \u2192e\u03bd or\nindirectly from W \u2192\u03c4\u03bd. In the fourth part of Table 1, a jet j is considered as an electron faking a\njet, and therefore discarded, if it matches with a reconstructed electron candidate e: \u2206R(e, j) < 0.1 and\nET(e)/ET(j) > 0.75.\nIt is interesting to notice that, despite the more complex topology of these t\u00aft events, the integrated\nlight-jet rejection achieved is higher than for the WH (mH=120 GeV) case. This is mostly because jets\nin t\u00aft events are more central than the ones in WH (mH=120 GeV) production (cf. Figure 14), and the\nb-tagging performance degrades quickly at large pseudo-rapidities as seen already.\nTable 1 shows the light jet rejection achieved in even more complex topologies with at least six jets.\nThose channels are relevant for the Higgs discovery channel t\u00aftH(b\u00afb) which requires a high b-tagging\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n414\n\nTable 1: Integrated rejection of light jets (with and without puri\ufb01cation when it applies), for various\nevent types and for several tagging algorithms. For each case, the cut on the b-tagging weight is chosen\nto lead to the quoted average b-tagging ef\ufb01ciency \u03b5b over the sample considered. The quoted errors are\nstatistical only.\nJetProb\nIP2D\nIP3D\nIP3D+SV1\nIP3D+JetFitter\nWH (mH = 120 GeV) events\n\u03b5b = 50%\n83\u00b11\n116\u00b12\n190\u00b13\n458\u00b113\n555\u00b117\n\u03b5b = 60%\n30\u00b10\n42\u00b10\n59\u00b11\n117\u00b12\n134\u00b12\nWH (mH = 400 GeV) events\n\u03b5b = 50%\n73\u00b11\n163\u00b13\n179\u00b13\n298\u00b17\n396\u00b111\n\u03b5b = 60%\n27\u00b10\n56\u00b11\n58\u00b11\n96\u00b11\n123\u00b12\nt\u00aft and t\u00aft j j events\nRaw, \u03b5b = 50%\n91\u00b10\n146\u00b11\n232\u00b12\n456\u00b14\n635\u00b17\nPuri\ufb01ed, \u03b5b = 50%\n97\u00b10\n186\u00b11\n310\u00b13\n789\u00b110\n924\u00b113\nRaw, \u03b5b = 60%\n28\u00b10\n46\u00b10\n67\u00b10\n154\u00b11\n189\u00b11\nPuri\ufb01ed, \u03b5b = 60%\n28\u00b10\n51\u00b10\n76\u00b10\n206\u00b11\n224\u00b12\nt\u00aft and t\u00aft j j events, once electrons faking jets are removed\nRaw, \u03b5b = 50%\n92\u00b10\n142\u00b11\n219\u00b11\n423\u00b14\n593\u00b16\nPuri\ufb01ed, \u03b5b = 50%\n99\u00b10\n181\u00b11\n293\u00b12\n732\u00b110\n863\u00b112\nRaw, \u03b5b = 60%\n31\u00b10\n49\u00b10\n67\u00b10\n144\u00b11\n180\u00b11\nPuri\ufb01ed, \u03b5b = 60%\n33\u00b10\n56\u00b10\n76\u00b10\n194\u00b11\n213\u00b12\nt\u00aftH events\nRaw, \u03b5b = 60%\n23\u00b10\n35\u00b10\n49\u00b11\n90\u00b12\n113\u00b12\nPuri\ufb01ed, \u03b5b = 60%\n25\u00b10\n48\u00b11\n72\u00b11\n188\u00b15\n188\u00b15\nRaw,\u03b5b = 70%\n10\u00b10\n14\u00b10\n18\u00b10\n32\u00b10\n31\u00b10\nPuri\ufb01ed, \u03b5b = 70%\n11\u00b10\n17\u00b10\n22\u00b10\n46\u00b11\n37\u00b11\nt\u00aftbb events\nRaw, \u03b5b = 60%\n23\u00b10\n34\u00b10\n50\u00b11\n100\u00b12\n123\u00b12\nPuri\ufb01ed, \u03b5b = 60%\n24\u00b10\n41\u00b10\n64\u00b11\n156\u00b14\n166\u00b14\nRaw, \u03b5b = 70%\n10\u00b10\n13\u00b10\n18\u00b10\n32\u00b10\n28\u00b10\nPuri\ufb01ed, \u03b5b = 70%\n10\u00b10\n15\u00b10\n20\u00b10\n40\u00b10\n31\u00b10\nSUSY SU3 events\nRaw, \u03b5b = 50%\n66\u00b11\n140\u00b14\n162\u00b15\n246\u00b19\n328\u00b114\nPuri\ufb01ed, \u03b5b = 50%\n68\u00b11\n161\u00b15\n183\u00b16\n290\u00b113\n375\u00b119\nRaw, \u03b5b = 60%\n24\u00b10\n50\u00b11\n55\u00b11\n89\u00b12\n110\u00b13\nPuri\ufb01ed, \u03b5b = 60%\n25\u00b10\n53\u00b11\n58\u00b11\n99\u00b13\n117\u00b13\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n415\n\nTable 2: Integrated rejection of c- and \u03c4-jets, for various event types and for several tagging algorithms.\nFor each case, the cut on the b-tagging weight is chosen to lead to the quoted average b-tagging ef\ufb01ciency\n\u03b5b over the sample considered.\nJetProb\nIP2D\nIP3D\nIP3D+SV1\nIP3D+JetFitter\nc-jet rejection for WH (mH = 400 GeV) events\n\u03b5b = 50%\n7.9\u00b10.1\n9.7\u00b10.1\n10.7\u00b10.2\n12.4\u00b10.2\n12.7\u00b10.2\n\u03b5b = 60%\n4.7\u00b10.0\n5.7\u00b10.1\n6.1\u00b10.1\n6.8\u00b10.1\n7.3\u00b10.1\nc-jet rejection for t\u00aft and t\u00aft j j events\n\u03b5b = 50%\n8.4\u00b10.0\n9.5\u00b10.0\n10.6\u00b10.0\n12.4\u00b10.1\n12.3\u00b10.1\n\u03b5b = 60%\n5.1\u00b10.0\n5.8\u00b10.0\n6.5\u00b10.0\n7.4\u00b10.0\n7.4\u00b10.0\n\u03c4-jet rejection for t\u00aft and t\u00aft j j events\n\u03b5b = 50%\n10.2\u00b10.1\n13.9\u00b10.1\n20.3\u00b10.2\n45.2\u00b10.8\n36.9\u00b10.6\n\u03b5b = 60%\n5.1\u00b10.0\n6.4\u00b10.0\n8.0\u00b10.1\n24.6\u00b10.3\n19.3\u00b10.2\nef\ufb01ciency since four jets are b-tagged and the cross section is low: therefore the more typical working\npoints of \u03b5b around 60-70% are shown. As shown in Figure 14, the pT spectrum for the b-jets in these\nsamples is harder than for b-jets in t\u00aft events, explaining partly the differences in performance. In addition\nthe high b-jet multiplicity in t\u00aftH events leads to some lifetime contamination in the few light jets available\nin this sample. All these samples are based on PYTHIA Monte Carlo, unlike the t\u00aft j j sample which is\na background for this channel as well but is based on MC@NLO+HERWIG Monte Carlo and was kept\nseparate for this reason.\n5.4\nHigh-pT jets: SUSY\nEvents from the SUSY bulk region (SU3 point, see Ref. [1]) were considered. In these events, the average\ntaggable jet multiplicity is about 5.3 and a large number of \u03c4-leptons are produced in the decay chain of\ncharginos and neutralinos. There are on average 0.6 b-jets per event, with a relatively hard pT spectrum\nas shown on Fig. 14: the average pT is 144 GeV. On average about 0.6 taggable jets per event are labelled\nas \u03c4, compared to 0.2 in the semi-leptonic t\u00aft channel. They are not considered as light jets. The results\nare shown in Tables 1 and 2: because the pT of the jets is quite high, the light jet rejection is similar to\nthat achieved for WH (mH = 400 GeV) events but signi\ufb01cantly worse than for the other channels.\n5.5\nDegradation of performance at low and high pT\nAt low pT, performance is degraded mostly because multiple scattering is increased. This also holds\nfor the high |\u03b7| region, where the amount of material in the tracking region increases very signi\ufb01cantly,\ninducing more secondary interactions. There is currently no rejection of secondary interactions found in\nthe pixel disks, unlike in the barrel (cf. Section 4.1.3). More importantly, the increase of the extrapolation\ndistance from the b-layer to the primary vertex at large pseudo-rapidities signi\ufb01cantly degrades the z0\nresolution as seen in Figure 6(b).\nSeveral effects conspire to reduce the b-tagging performance as the jet pT increases above 120 GeV.\nFirst of all, the fraction of fragmentation tracks increases with the parton transverse momentum, as shown\nin Figure 16, while the jet is collimated into a narrower cone: since a \ufb01xed-size cone is currently used\nto associate tracks to the jet this leads to a dilution of the discriminating power in b-jets. The density\nof tracks in the core of energetic jets challenges the pattern-recognition ability of the software and of\nthe inner detector itself, leading to either a reduced tracking ef\ufb01ciency or a high level of fakes as shown\nin Figure 3 for jets with ET > 100 GeV. Finally, for very energetic b-hadrons the Lorentz boost leads\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n416\n\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nIP2D\nIP3D\nIP3D+SV1\nJetProb\nIP3D+JetFitter\nATLAS\n(a) Non-puri\ufb01ed light jets\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nIP2D\nIP3D\nIP3D+SV1\nJetProb\nIP3D+JetFitter\nATLAS\n(b) Puri\ufb01ed light jets\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nc-jet rejection\n1\n10\nIP2D\nIP3D\nIP3D+SV1\nJetProb\nIP3D+JetFitter\nATLAS\n(c) c-jets\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nTau-jet rejection\n1\n10\n2\n10\nIP2D\nIP3D\nIP3D+SV1\nJetProb\nIP3D+JetFitter\nATLAS\n(d) \u03c4-jets\nFigure 15: Rejection of light jets, c- and \u03c4-jets versus b-jet ef\ufb01ciency for t\u00aft and t\u00aft j j events and for all\ntagging algorithms: JetProb, IP2D, IP3D, IP3D+SV1, IP3D+JetFitter.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n417\n\nto a much enhanced decay length. The typical c\u03c4 (\u223c450\u00b5m) of b-hadrons is thus scaled by a factor\n\u03b3 \u223c|pB|/mB which can be large. For high pT jets, the b-hadron can decay at a rather large radius RB, as\nillustrated in Table 3: close to the inner radius of the pixel detector, leading to more tracking ambiguities\nin the \ufb01rst detection layers, or even after the \ufb01rst pixel layer. In the latter case, the current requirement\n(for the IPnD and JetProb tagging algorithms) of a hit on the b-layer actually kills the signal. At very\nhigh pT (above 500 GeV), these effects become so critical that a dedicated strategy has to be devised, as\ndiscussed in the next section. In the current simulation, the b-hadrons decaying at a radius larger than the\nbeam-pipe or the b-layer radii do not interact with these objects, while in real events this will even more\nreduce the performance.\n (GeV)\nT\np\n50\n100\n150\n200\n250\n300\nFragmentation good track fraction\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nATLAS\nFigure 16: Fraction of selected tracks which are\nnot from B/D decays versus jet pT, in b-jets from\nWH (mH = 400 GeV) events.\nTable 3: Fraction of b-jets in WH (mH = 400\nGeV) events for which the b-hadron decays be-\nyond the beam-pipe vacuum (\ufb01rst column) or be-\nyond the b-layer (second column).\nRB > 2.9 cm\nRB > 5.1 cm\nall ET\n9.0%\n2.8%\nET > 100 GeV\n12.2%\n3.9%\nET > 200 GeV\n21.1%\n7.9%\n5.6\nThe case of very high-pT jets: exotic physics\nThe very high pT range is de\ufb01ned as jets exceeding a transverse energy of 500 GeV. Identi\ufb01cation of\nsuch very high pT b-jets is required for the search for heavy resonances with (predominantly) hadronic\ndecays. A large number of exotic physics models presents signatures with very high pT b-jets, up to a\nfew TeV. An example is the decay ZH \u2192Zh in the little Higgs model [18], where Z \u2192e+e\u2212and h \u2192b\u00afb.\nIn the following, three samples corresponding to the process Z\u2032 \u2192q \u00afq, where q denotes u, b and c\nquarks respectively were used. The Z\u2032 mass is chosen to be 2 TeV, so that the primary partons have\ntransverse momenta in the range from 300 GeV to 1 TeV.\nThe b-tagging algorithms rely particularly on the determination of the jet axis as an approximation of\nthe b- and c-hadron \ufb02ight direction. The difference between the jet pseudo-rapidity and the true b-hadron\ndirection exhibits a narrow Gaussian core. The widths of the core range are \u03c3\u03b7 \u22480.025 and \u03c3\u03c6 \u22480.010\nmrad, with a moderate dependence on jet ET and pseudo-rapidity. Non-gaussian tails give rise to large\nRMS: RMS \u03b7,\u03c6 \u22480.050. The particles from the decay of the highly boosted b-hadron are emitted at very\nsmall angles. Up to half of the tracks from the b-hadron decay lie within the azimuthal angle between the\nb-hadron and the jet. In these cases the sign of the impact parameter cannot be determined accurately.\nThe reconstruction of tracks in high pT jets presents a series of speci\ufb01c challenges, as already ex-\nplained in Section 5.5. Particles are associated to reconstructed jets using a \u2206R < 0.4 criterion. To\nhighlight reconstruction effects only true pions reaching the outer radius of the tracker are taken into ac-\ncount. Particles are moreover required to originate from a well-de\ufb01ned vertex: either the primary vertex\nof the event or the b/c-hadron decay vertex. Only the \ufb01rst level of the ef\ufb01ciency, i.e. the matching to\nhits (Section 2.1.2), is considered. With this de\ufb01nition the ef\ufb01ciency on a reference sample of low pT\njets is close to 100% and essentially independent of the jet energy and of the distance to the jet axis. In\nFigure 17 the track ef\ufb01ciency in the Z\u2032 sample is plotted versus the jet transverse energy, for the default\ntrack reconstruction - NewTracking - and for iPatRec.\nThe algorithmic reconstruction ef\ufb01ciency for prompt tracks is only slightly degraded. Even in the\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n418\n\njet transverse energy (TeV)\n0\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9\n1\nefficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nprompt tracks\niPatRec\nNew Tracking\nB/D-decay\niPatRec\nNew Tracking\nFigure 17:\nAlgorithmic tracking ef\ufb01ciency for\nlong-lived pions as a function of the jet trans-\nverse energy, for prompt tracks or tracks from b/c-\nhadron decays, and for two reconstruction algo-\nrithms: NewTracking and iPatRec.\n (TeV)\nT\njet E\n0\n0.2\n0.4\n0.6\n0.8\n1\nlight-jet rejection\n1\n10\n2\n10\nATLAS\n = 40 %\nb\n\u2208\n = 50 %\nb\n\u2208\n = 60 %\nb\n\u2208\nFigure 18: Raw light jet rejection for jets from\nZ\u2032 \u2192q \u00afq with mZ\u2032 = 2 TeV, versus jet transverse\nenergy, for the IP3D+SV1 tagging algorithm (with\ntracks from iPatRec). and for three b-tagging ef\ufb01-\nciencies.\nvery harsh environment of a 1 TeV jet, the ef\ufb01ciency is approximately 90%. The degradation is most\npronounced in the core of the jet ( \u2206R < 0.1 ). For pions originating in b/c-hadron decays a much more\nsigni\ufb01cant degradation of the ef\ufb01ciency towards high jet ET is observed. For 1 TeV jets the ef\ufb01ciency is\napproximately 50%. The ef\ufb01ciency shows a strong dependence on the decay vertex radius. It is worth\nmentioning that NewTracking and iPatRec assign very different errors to the positions de\ufb01ned by large\npixel or SCT clusters arising in the inner layers with such dense jets: the former assigns a very small\nerror assuming only one particle was involved in the cluster, while the latter is assuming the opposite and\nassigns the maximal error (cluster width/\n\u221a\n12).\nIn very high pT jets the probability that two or more tracks share a hit is very high (> 10%), unlike\nwhat was seen for low and moderate pT jets (cf. Figure 4). The number of shared hits per track - eval-\nuated for individual sub-detectors, or for the complete silicon tracker - is a factor 2-3 larger in iPatRec.\nFor particles from very displaced b/c-hadron decay vertices reconstructed with iPatRec, tracks with a\nshared hit in the b-layer actually outnumber the tracks with an unambiguous assignment. Again the two\ntracking algorithms have made opposite choices for their working point: NewTracking considers shared\nhits are stemming from pattern-recognition errors and tries to assign them to the best track, which is\nnot necessarily meaningful when the cluster is really originating from several near-by particles, while\niPatRec does not try to resolve the ambiguity.\nThe high multiplicity of fragmentation tracks, the degraded tracking ef\ufb01ciency, the ambiguities in hit\nassignment particularly in the innermost layer and the uncertainty in the impact parameter sign, all render\nhigh pT jets a harsh environment. This may be improved though by the use of dedicated reconstruction\nalgorithms. A priori, the current simulation should also be updated to transport properly the b-hadrons\nthrough the material. While studies have started, they are beyond the scope of this note. For the time\nbeing, a re-optimization of the default tagging algorithm parameters has been performed with the aim\nof improving the b-tagging performance over a large jet ET range (from 200 GeV to 1 TeV). The cone\nsize for the jet-to-track association was reduced to 0.2 (see Section 7.2 for a possible improvement of the\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n419\n\ncurrent treatment), the pT cut on tracks raised to 5 GeV and the use of tracks without a hit in the b-layer\nwas allowed (see also Section 7.1).\nThe tagging performance on iPatRec tracks is found to be on average 60% better than for the default\nalgorithm. The choice of iPatRec to maintain high tracking ef\ufb01ciency inside dense jets (cf. Figure 3),\neven at a price of higher fake rates, seems to be instrumental in achieving better performance here. The\nresulting b-tagging performance is presented in Figure 18. Given the modest level of rejection achieved,\na tagging ef\ufb01ciency of 40% is considered here. Without any tuning, the rejection level of the IP3D+SV1\ntagging algorithm would be about three times worse for the same b-tagging ef\ufb01ciency.\nIn this study, the standard (low pT) reference histograms were used for the tagging algorithms. So\nfar, none of the methods developed to extract the calibration histograms from data has been shown to\nwork for these very high pT jets. Reference histograms for very high pT jets may be extracted from\nMonte Carlo simulation, provided it reliably describes the data. Doing so, a modest improvement of\nthe performance (up to 50% higher light jet rejection for the same b-tagging ef\ufb01ciency compared to the\nresults shown here) can be achieved.\nTo conclude, b-tagging for very high pT jets faces a series of speci\ufb01c dif\ufb01culties. This study demon-\nstrated that a rejection between 10 and 70 for jets with pT > 500 GeV can be achieved by tuning the cur-\nrent algorithms. Further improvements require dedicated treatments at the clustering level (with probably\na second-pass approach to break down large clusters coming from near-by particles) and at the pattern-\nrecognition stage of the track reconstruction. On small preselected datasets, retracking with a specially\noptimized pattern-recognition algorithm should be possible.\n6\nSpeci\ufb01c studies to characterize b-tagging performance\nIn this section, a few additional studies aimed at better understanding some critical aspects of the b-\ntagging performance are detailed. Those studies are described in a separate section because either they\nrequired speci\ufb01c datasets or they rely on software and/or cuts/optimizations which are different from the\nones currently in use in the ATLAS software.\n6.1\nImpact of residual misalignments\nAll the studies in this note do not take into account the effect of residual misalignments. While all\nthe samples studied were simulated with misalignments, they were reconstructed assuming a perfect\nknowledge of those misalignments. However, detailed studies, discussed in Ref. [7], are in progress on\nthis subject. Two different approaches were used: residual misalignment sets and actual realignment.\nIn the former, the events simulated with misalignments are reconstructed using the knowledge of the\nmisalignments, but the true detector elements positions are shifted and/or rotated slightly from their\nactual position to mimic residual misalignments. The individual pixel modules were shifted by about\n10 \u00b5m in x and 30 \u00b5m in y and z, and rotated by about 0.3 mrad. The pixel layers, disks and the\nwhole detector were displaced by slightly smaller amounts. In this case, the light jet rejection drops by a\nfactor 2 for the same b-tagging ef\ufb01ciency. For residual misalignments about half as big, the drop in light\njet rejection is degraded by 40% compared to the ideal case. The reduction of residual misalignments\nrelies on the actual alignment procedure, which is performed to obtain the new positions of the detector\nelements. This is the most realistic case considered so far, and includes many (but not all) systematic\ndeformations caused by the alignment procedure itself. In this case, the light jet rejection is at most 25%\nlower for the same b-tagging ef\ufb01ciency.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n420\n\n6.2\nImpact of the tracker material on performance\nA major effort has been invested in describing accurately the material in the tracking volume of ATLAS.\nHowever, some underestimation is possible. To assess the impact of extra material on the b-tagging per-\nformance, results with different geometries were compared. Extra material was added, mostly beyond\nthe b-layer, increasing the thickness in radiation lengths by about 8% (15%) at |\u03b7| \u22480(1). The \ufb01rst\nnoticeable effect is the degradation of the impact parameter resolution. The other effect is an increased\nfraction of particles undergoing interactions in the matter of the detector and producing secondary par-\nticles which can, directly or through pattern-recognition problems, fake non-prompt tracks. At a 60%\nb-tagging ef\ufb01ciency, the extra material decreases by 10% the light jet rejection power. About 60% of\nthe loss of rejection is explained by the worsening of the impact parameter resolution, and about 40% by\nextra secondaries.\n6.3\nImpact of the pixel detector conditions\nThe pixel detector and notably the innermost b-layer are critical for achieving good b-tagging perfor-\nmance. The detector ef\ufb01ciency clearly affects the tracking performance but is also explicitly a key in-\ngredient for b-tagging since the b-tagging quality cuts require that each track have at least two pixel hits\nof which one is in the b-layer. These pixel hit requirements are made in order to maintain the highest\nresolution on the impact parameter of tracks.\nA single pixel inef\ufb01ciency of 5% has been used to simulate the events. Measurements on the pixel\nstaves before the detector integration gave a single pixel inef\ufb01ciency below \u223c0.3% (and below \u223c0.1%\nfor the b-layer for which the highest quality components were used). The effect of this inef\ufb01ciency is\nespecially relevant at small |\u03b7| where half of the pixel clusters contain only one pixel. The impact of\nvarying the fraction of randomly distributed dead pixels was studied for three tagging algorithms on\na large statistics (600k events) t\u00aft sample and the results are shown in Table 4. When decreasing the\nfraction of dead pixels from 5% to 1%, the tracking ef\ufb01ciency for tracks ful\ufb01lling the b-tagging quality\ncuts improves by up to 2.5% absolute (around \u03b7 \u223c0), leading to a relative gain in rejection of about\n10%.\nTable 4: Reference light jet rejection for several tagging algorithms and the relative change with vari-\nous con\ufb01gurations of the pixel system (see text) for a 60% b-tagging ef\ufb01ciency in t\u00aft events. The used\nreference histograms were produced with the respective samples.\nIP2D\nIP3D\nIP3D+SV1\nReference rejection (5% of dead pixels)\n54\u00b11\n77\u00b12\n229\u00b110\nRelative change with 1% of dead pixels\n+9%\n+10%\n+17%\nRelative change with a dead half-stave on b-layer\n-8%\n-8%\n-10%\nRelative change with a dead bi-stave on b-layer\n-34%\n-34%\n-28%\nRelative change with a dead half-stave on external pixel layer\n< 1%\n< 1%\n-1%\nRelative change with a dead bi-stave on external pixel layer\n-1%\n-1%\n-4%\nMore global problems, such as chip and module inef\ufb01ciencies were not considered in the studies.\nTheir effect has been studied in detail in Ref. [19] and can be very important. However, the latest\nmeasurements made right before the detector integration indicate that only one module (in the middle\nlayer) out of 1744 is dead and that fewer than 5 chips are dead out of 27904. Besides single module\nfailures, more dramatic failures might happen. During the pixel operation, it is thought that the two\nmost likely sources of potential failures could be an opto-board failure, leading to half a stave (at most\n7 modules) not functioning and a cooling problem implying that a whole bi-stave (26 modules) could\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n421\n\nnot be used. To study those scenarios, the pixel digitization was modi\ufb01ed to disable the corresponding\nmodules, in either the b-layer or the external pixel layer. The impact on b-tagging performance of these\ntwo scenarios is shown in Table 4. In the case of well-identi\ufb01ed module failures, it is clear that some\nrecovery strategies can be used, either directly in the tracking code or at least in the b-tagging algorithm,\nfor instance by not requiring a hit on a dead module.\n6.4\nJet algorithms\nFor b-tagging purposes, an accurate knowledge of the jet direction is relevant. In the \ufb01rst place, this\ndirection is used to de\ufb01ne which tracks should be associated to the jets. Then it is used to sign the impact\nparameter of tracks.\nAs mentioned earlier, all b-tagging results are given for jets reconstructed with a cone algorithm of\nsize \u2206R = 0.4. Since a given physics analysis may opt for a different jet algorithm, the impact of this\nchoice on the b-tagging performance is tested in this section. In all cases, as it is the default in the b-\ntagging software, only the tracks within a distance \u2206R < 0.4 of the jet axis were used for the tagging,\neven for jet algorithms which could bene\ufb01t from a less geometric track-jet association such as the kT\nalgorithm.\nSeveral cone sizes \u2206R and size parameters R were studied for the cone algorithm and the kT algo-\nrithm: from 0.2 to 0.8 in steps of 0.1. Finally, the b-tagging performance of the mid-point algorithm [20],\nan alternate jet algorithm addressing the infrared sensitivity of cone algorithms, was also checked, for\ntwo different cone size of \u2206R = 0.4 and 0.7. In this study, electrons faking jets were removed.\nFigure 19 shows the rejection of light jets versus the b-tagging ef\ufb01ciency obtained with the IP3D+SV1\ntagging algorithm, for several jet algorithms run on t\u00aft events. Results with and without puri\ufb01cation are\nvery different. With puri\ufb01cation (Figure 19(b)) there is no signi\ufb01cant difference in performance in the\nrelevant range of b-tagging ef\ufb01ciency (40% < \u03b5b < 75%).\nb\n\u2208\nB-tagging efficiency, \n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection factor\n1\n10\n2\n10\n3\n10\n10\nATLAS\nCone4\nCone7\nKt4\nKt6\na) All light jets\nb\n\u2208\nB-tagging efficiency, \n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection factor\n1\n10\n2\n10\n3\n10\n10\nATLAS\nCone4\nCone7\nKt4\nKt6\nb) Purified light jets\nb\n\u2208\nB-tagging efficiency, \n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection factor\n1\n10\n2\n10\n3\n10\n10\nc) All light jets after relabelling\n cut\nJet - b\nR\n\u2206\n0.3\n0.4\nCone4\nCone7\nATLAS\nFigure 19: Rejection of light jets versus b-tagging ef\ufb01ciency for the IP3D+SV1 tagging algorithm applied\non jets reconstructed with different algorithms: cone algorithm with size \u2206R = 0.4,0.7 or kT algorithm\nwith parameter R = 0.4,0.6. See text for the last plot.\nThis stability is the anticipated behavior, since only the jet direction is meaningful for b-tagging\npurposes and it does vary with the jet algorithm but not drastically for moderate jet pT: the mean of the\ndistance \u2206R(b, jet) for a 50 GeV jet is 0.081 for a jet of size \u2206R = 0.4 and 0.095 for a jet of size \u2206R = 0.7\n(see Ref. [9] for more details). For completeness, it should be mentioned that no differences were found\nbetween tower-based and topological cluster-based jets.\nWithout the puri\ufb01cation procedure (Figure 19(a)), the results are different for different jet de\ufb01ni-\ntions. However, the interpretation is not straightforward. In principle broader jets could be more easily\ncontaminated by neighbouring tracks originating from distinct partons whose showers could not be re-\nsolved: light jets for instance could be contaminated by heavy-\ufb02avour decay products. However, this\neffect should be marginal since the maximum track-jet distance for association is kept to \u2206R = 0.4 in all\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n422\n\ncases.\nA better explanation is linked to the ambiguity and arbitrariness of the labelling procedure: with\nfewer, broader jets the assignment of partons to the jets is more ambiguous and more likely to have\n\u2206R(b, jet) > 0.3, and thus more jets wrongly labelled as light jets. Therefore, for example, the rejection\nat \u03b5b = 50% with a cone radius \u2206R = 0.7 appears to be three times less than with a cone of radius 0.4, by\nrelabelling the jets with a \u2206R cut of 0.4 instead of 0.3 this difference can be virtually eliminated as seen\nin Figure 19(c). Thus although it appears to be more dif\ufb01cult to de\ufb01ne the true \ufb02avour of a broader jet\nthis does not necessarily exclude the choice of a cone size of 0.7 for a given analysis.\n6.5\nSensitivity to the calibration of tagging algorithms\nMost of the ATLAS tagging algorithms make use of an a priori knowledge to discriminate b-jets from\nlight jets, which comes in various forms. The simplest of these ingredients is the transverse impact\nparameter resolution function used by the JetProb tagging algorithm to measure the compatibility of\ntracks with the primary vertex. The likelihood ratio tagging algorithms rely on several such distributions,\nwith the further complication that they must be known for both the light and the b- hypothesis. In\nthis section, the way this knowledge may affect the performance is studied. It is not currently possible\nto know if these settings are a good representation, both in nature and amplitude, of the differences\ndata/Monte Carlo that will be observed, but at least they give information about the robustness of the\ntagging algorithms. All the results are given for the t\u00aft sample.\n6.5.1\nJetProb tagging algorithm\nJetProb is expected to be one of the \ufb01rst tagging algorithms to be commissioned in ATLAS. To perform\nwell, the resolution function (cf. Section 4.2) must be measured in data to avoid possible short-comings\nof the Monte Carlo simulation (resolutions and non-gaussian tails mostly). One of the major advantages\nof this tagging algorithm is that a priori any track from any physics process, e.g. the tracks from the \ufb01rst\nminimum-bias events, could be used to calibrate the resolution function, provided the contamination of\nnon-prompt tracks can be kept at a very low level.\nThe sensitivity to this last point was studied by checking two different scenarios to select tracks\nin order to build the resolution functions. In all cases, only reconstructed tracks with negative impact\nparameter signi\ufb01cance and ful\ufb01lling the b-tag quality cuts are used. This was done on t\u00aft events but\nsimilar or better (because of less heavy \ufb02avour contamination) results are expected for minimum-bias\nevents. In the ideal case, the tracks are required to match to a true particle whose true origin is at the\nprimary vertex of the event. In the realistic case, this requirement was not enforced. The distributions of\nthe negative impact parameter signi\ufb01cance d0/\u03c3d0 of tracks obtained in the two cases exhibit signi\ufb01cant\ndifferences in the tails: in the ideal case, 0.6% of the tracks have |d0| > 5\u03c3d0 (the RMS of the distribution\nis 1.3) while this fraction is 3.2% for the realistic case (RMS is 2.1). These distributions are then used\nas resolution functions to measure the b-tagging performance on the same events: at a 50% b-tagging\nef\ufb01ciency, the light jet rejection with the realistic scenario is 15% lower than for the ideal case.\n6.5.2\nLikelihood-based tagging algorithms\nFor the likelihood-based tagging algorithms, the probability density functions for all the variables (cf.\nSection 4.1) are built for the b-jet and light jet hypotheses using Monte Carlo. The t\u00aft channel can be\nused in data to isolate a sample of pure b-jets from which the various distributions can be derived, using\nthe methods described in [9]. However, more than a few hundreds of pb\u22121 of data are needed. For the\nlight jets, it seems very dif\ufb01cult to isolate a pure enough sample in data. In this section, the sensitivity\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n423\n\nto the calibration is estimated using reference histograms obtained from Monte Carlo with very different\nsettings.\nFirst the impact of using a different tracking algorithm for the calibration (iPatRec) and for the\nperformance measurement (NewTracking) was assessed and led to a very small variation of the rejection\npower, below 10%. Another study consisted of using different detector descriptions for calibrating and\ntesting: the two geometries compared were relatively similar, with a relative difference in the amount\nof material in the tracking volume of 8% (15%) at \u03b7 \u223c0 (1). At most a 5% change in rejection power\nis seen in this case. Another issue is the sample composition of the reference histograms: using only t \u00aft\nevents or a mix of t\u00aft, WH (mH = 120,400 GeV) and SUSY events does not change signi\ufb01cantly (< 5%\nrelative change on rejection power) the b-tagging performance on a t\u00aft sample. However, larger effects\nare expected when b-tagging is run on a very different sample from the one used for the calibration.\nA possible bias when building the calibration distributions and looking at performance on the same\nevent sample was studied by dividing the sample into two. The bias on the resulting rejection factors was\nfound to be usually negligible, and in all cases below 10%.\nFinally, it was checked what statistics are needed to de\ufb01ne the underlying histograms for the various\ntagging algorithms in order for results to be stable. This was checked on semi-leptonic t\u00aft events by\nhalving a 600k event sample, building calibrations on 10k, 50k, 100k and 300k events from the \ufb01rst half-\nsample and checking the performance on the other half. To obtain a rejection level stable within 3%, 50k\nevents are needed for all the IP and SV tagging algorithms when used in a regime where \u03b5b \u226550%.\n6.6\nSensitivity to the Monte Carlo modelling\nIn the Monte Carlo modelling, several parameters can affect the ability to tag b-jets. Any effect that\ncan change the lifetimes of the produced particles, the multiplicity of the charged tracks or the momenta\nof these tracks can potentially change the tagging ef\ufb01ciency. This modelling is not necessarily a good\ndescription of data, and in addition it is also performed differently across generators.\n6.6.1\nFragmentation\nFirst of all, various fragmentation models, describing the non-perturbative process in which quarks\nhadronize into colorless hadronic states, are implemented in the Monte Carlo generators. For heavy-\n\ufb02avour quarks, two options are available in the PYTHIA generator: the Lund-Bowler model and the\nPeterson fragmentation model. While the former has been found to give reasonable agreement with\nexperimental data at LEP, SLC and HERA, the latter is currently the default in ATLAS PYTHIA produc-\ntions. The impact of these various fragmentation models was investigated with six different t \u00aft samples.\nFor the Peterson fragmentation, three samples were produced with different values for the \u03b5b parameter:\n0.003, 0.006 (default), 0.012. For the Lund-Bowler model, the rQ parameter was varied: 0.50, 0.75,\n1.0 (default). The maximum relative discrepancy in the b-tagging ef\ufb01ciency was found to be around\n6%, comparing the Peterson model with \u03b5b = 0.012 to the Lund-Bowler model for rQ = 0.5. However,\nthis choice of parameters is a bit extreme: the difference between the default Peterson model and the\nLund-Bowler model with rQ = 0.75 (which was found to \ufb01t best the OPAL and SLD data) leads to an\nuncertainty on the b-tagging ef\ufb01ciency of 1.1% for a \ufb01xed b-tagging cut leading to a b-tagging ef\ufb01ciency\nof 72%.\n6.6.2\nHeavy \ufb02avour production\nThe production fraction of various b/c-hadron species can also lead to different b-tagging ef\ufb01ciencies\nsince they have different lifetimes and decay modes. The measured b-hadron fractions [15] and their\nvalues in the generators are shown in Table 5. For HERWIG, the defaults have been changed following\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n424\n\nthe CDF tuning [21] by setting the CLPOW parameter to 1.2, in order to obtain a b-baryon fraction in\nagreement with the PDG and with PYTHIA. Another ingredient is the production of excited bottom and\ncharm states which can give rise to soft charged pions or kaons, affecting the topology of the events: this\nhas not been studied yet.\nTable 5: Fraction (in %) of b-hadron species from the PDG (assuming f(Bd) = f(B\u00b1)) and in PYTHIA,\nthe default HERWIG and HERWIG tuned for ATLAS (CLPOW=1.2).\nBd\nB\u00b1\nBs\nBaryons\nPDG\n39.8\u00b11.0\n39.8\u00b11.0\n10.4\u00b11.4\n9.9\u00b11.7\nPYTHIA (ATLAS)\n39.7\n39.2\n12.1\n9.1\nHERWIG\n44.3\n44.8\n10.8\n0.0\nHERWIG (tuned)\n39.4\n39.9\n10.4\n10.3\nThe various production fractions of each type of the b-mesons were varied according to the mea-\nsured errors from PDG 2006 [15], and the impact on a simulated PYTHIA t\u00aft sample was studied by\na re-weighting technique. This source of systematics can be safely neglected since the net effect is an\nuncertainty below the per mil level on the tagging ef\ufb01ciency.\n6.6.3\nb-hadron lifetimes and decays\nThe uncertainty on the lifetime of the various b hadrons was also studied and found to give rise to an\nuncertainty of 0.3% for a b-tagging ef\ufb01ciency of 72%.\nThe uncertainty in the charged track multiplicity of b hadron decays was estimated by comparing\nPYTHIA with measurements from LEP [22]. The resulting uncertainty on the b-tagging ef\ufb01ciency was\nfound to be 0.9%.\n6.6.4\nHeavy \ufb02avour decays with EvtGen\nThe two event generators used in ATLAS to fragment and decay particles, PYTHIA and HERWIG,\nimplement different algorithms to simulate the decays of generated particles, using their own decay\ntables to specify decay modes and branching fractions. The sophistication of the decay simulation and\nthe scope of decay tables vary considerably between generators. For B meson decays, arguably the most\ndetailed simulation is currently provided by EvtGen [23].\nSince the b-tagging performance on Monte-Carlo samples may depend on details of simulated parti-\ncle decays, such as the charged particle multiplicity or the spatial distribution of secondary decay vertices\nin B decays, the impact of using EvtGen as a decayer instead of PYTHIA was studied on t\u00aft events. For\nthis study, a decay \ufb01le for inclusive decays was assembled based on the latest (as of summer 2005)\nversion of the decay \ufb01les used by the BaBar and CDF experiments. For decay channels where experi-\nmental data is available, branching fractions were taken from PDG [15], while the remaining decays are\nsimulated generically with JETSET.\nFor this study, two speci\ufb01c samples were generated: the \ufb01rst t\u00aft sample was generated by PYTHIA\nand the decays were handled by PYTHIA. The second one was generated in the same way except that\nparticle decays were simulated by EvtGen. As expected, changing the particle decay simulation leads to\nsmall differences in some distributions of generator\u2013level quantities. For example, the mean multiplicity\nof charged pions in decays of B\u00b1 and B0 mesons, not including decays of long-lived weakly decaying\nstrange particles such as K0\ns and \u039b, is 3.89 (RMS 2.19) with PYTHIA and 3.62 (RMS 2.13) with EvtGen.\nThe average multiplicity obtained by EvtGen agrees well with the experimental value of 3.58\u00b10.07 [15].\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n425\n\nThe b-tagging weight distributions obtained with the two generators are thus slightly different. For\na \ufb01xed b-tagging weight cut, the b-jet ef\ufb01ciency varies by about 1%. Tuning the cut to keep the same\nb-tagging ef\ufb01ciency in both samples leads to non-negligible changes in the light jet rejection: it de-\ncreases by about 5% to 15% when EvtGen is used, depending on the tagging algorithm and chosen b-jet\nef\ufb01ciency.\n7\nSpeci\ufb01c studies for improving b-tagging performance\nIn this section, three studies aiming at improving the b-tagging performance are presented. Most of them\nrely on speci\ufb01c software developments.\nIn the \ufb01rst part, new track categories are de\ufb01ned to make a better use of the slight differences in e.g.\nimpact parameter resolution that such tracks may exhibit. A second study evaluates the potential gain\nby varying the way tracks are associated to jets. The last study shows the improvement obtained when\ncombining several tagging algorithms in a multivariate approach. Those studies were done independently\nand no attempt was made yet to combine them. It is worth noting that some approaches advocated in the\n\ufb01rst two studies are expected to be highly correlated.\n7.1\nImproving performance with track categories\nGrouping the tracks used for b-tagging in several categories has been discussed in Section 4.1.5. Ded-\nicated treatment for Shared tracks (cf. 2.1.3) is already implemented and used in the current b-tagging\nsoftware. Using dedicated probability density functions for the Shared tracks improves the light jet re-\njection by 23% (7%) for a b-jet tagging ef\ufb01ciency of 50% (60% respectively) in t\u00aft events. This is the\ndefault treatment in the software. This effect is sample-dependent and is more important for samples\nwith high jet multiplicities and energetic jets, which tend to be more collimated.\nUsing additional track categories to improve the b-tagging performance is being further investigated.\nA possible interest of the track categories is to try to loosen the track quality cuts and therefore gain in\nef\ufb01ciency without diluting the discrimination power of the good tracks. As discussed in Section 2.1.2,\nrequiring each track to have a hit on the b-layer leads to an absolute loss in ef\ufb01ciency of about 2.5%,\nwhich is not negligible for b-tagging purposes where few tracks are available. Thus one attempt consisted\nof trying to keep tracks with no b-layer hit in a special category. About 4% of the tracks in jets from t \u00aft\nevents which pass the rest of the b-tagging selection fall in this category.\nThe categories could also be used to deal with the non-Gaussian resolution tails and the imperfect\ntreatment of the matter in the tracking error estimation process. A priori some fraction of these effects\nwould be better treated from \ufb01rst principles directly in the tracking, but the experience with previous\nexperiments shows that this is dif\ufb01cult in practice and therefore ad-hoc treatments may be justi\ufb01ed. The\nnatural variables to partition tracks are pT (actually p for multiple-scattering) and pseudo-rapidity (since\nthe material is very non-uniform in \u03b7).\nFinally, another potential use of track categories was studied: in b-jets, the fragmentation tracks\naccompanying the b-hadron decay products are prompt and should therefore have different distributions\nof the discriminating variables. Tracks with pT(track)/pT(jet) < 0.04 were de\ufb01ned as fragmentation\ntracks since those are in principle softer and were put in a special category. In typical b-jets from the t \u00aft\nsample, this cut selects 13% of the tracks. Some correlation with the treatment in pT bins (previous case\nabove) is expected.\nThe use of these categories brings some improvement to the light jet rejection, as high as 60% for\nthe binning in track pT which is the most powerful way of partioning tracks. The improvement for some\ncategories depends on the sample: the dedicated category for fragmentation tracks for example is more\nhelpful for the WH (mH =400 GeV) sample where the actual decay products of the b-hadron are very\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n426\n\ncollimated and the \ufb01xed-size cone for associating tracks to the jets brings in a larger fraction of prompt\ntracks.\nVarious ways to combine all the new categories were investigated. The gain in rejection brought by\nthe best combinations, using 11 partitions formed with the aforementioned categories, ranges from 20%\nto 70% depending on the sample and the tagging algorithm, for a 60% b-tagging ef\ufb01ciency.\n7.2\nOptimizing the track-to-jet association\nAs the jet transverse momentum increases, its particles are collimated into a narrower cone. But currently\nall tracks within \u2206R < 0.4 of the jet axis are associated with the jet, regardless of its momentum. For a\n300 GeV b-jet, only 30% of the tracks associated to the jet comes from the b-hadron decay products, as\nshown in Figure 16. Therefore at high pT the b-tagging discriminating power is diluted since a larger\nfraction of the tracks in the jet may be picked up from environmental contamination: underlying event,\npile-up or neighbouring jets in busy events. An alternative track-to-jet association has been studied, with\na \u2206R cut varying with the jet pT: \u2206R < f(pT). Based on the distribution of \u2206R(jet,track) for tracks\noriginating from b-hadron decays in b-jets, a functional form f(pT) has been chosen which ensures that\n95% of the tracks from b-hadron decays in these events are associated to the jet for any jet pT in the\nrange [15,500] GeV.\nThe impact on b-tagging performance of using this association instead of the standard one is checked\non t\u00aft events. The relative improvement on the overall raw light jet rejection is 46% (7%) for respectively\na b-tagging ef\ufb01ciency of 50% (60%). This improved treatment actually affects only the non-pure jets\n(22% of the light jets in this sample), for which the rejection triples for \u03b5b = 50% and doubles for\n\u03b5b = 60%. Obviously the fraction of non-isolated jets and therefore the possible gain with this method\nare sample-dependent.\n7.3\nCombining tagging algorithms with boosted decision trees\nSeveral multi-variant techniques exist that can combine different b-tagging algorithms into a single clas-\nsi\ufb01er for discriminating b-jets from light jets. We investigated boosted decision trees (BDT).\nBDT can be applied to any classi\ufb01cation problem and their use for combining several b-tagging\nalgorithms into a single classi\ufb01er for discriminating b-jets from light jets was investigated [24]. In this\nstudy, a BDT classi\ufb01er was optimized on a training sample containing b-jet and light jet patterns extracted\nfrom WH (mH = 120 GeV, H \u2192b\u00afb or H \u2192u \u00afu) and t\u00aft samples. The following input variables were used:\nthe weight from the IP3D tagging algorithm, the three variables on which the SV tagging algorithms\nare based (cf. Figure 9), the number of tracks associated with the secondary vertex, the weights of the\nsoft muon and soft electron tagging algorithms, the largest transverse and longitudinal impact parameter\nsigni\ufb01cances and transverse momentum of the tracks in the jet, the jet transverse momentum and the\nnumber of tracks in the jet. For a fair comparison with IP3D+SV1, a BDT classi\ufb01er with only the \ufb01rst\nfour variables was also studied. The predictive power of the classi\ufb01er was estimated using a distinct\nsample of b-jet and u-jet patterns (test sample).\nTable 6: Rejection of light jets given by IP3D+SV1 and the boosted decision tree for WH (with mH=120\nGeV) and t\u00aft events, for \ufb01xed b-tagging ef\ufb01ciencies of 50% and 60% in each sample.\nIP3D+SV1\nBDT 4 variables\nBDT 12 variables\n\u03b5b = 50%\n\u03b5b = 60%\n\u03b5b = 50%\n\u03b5b = 60%\n\u03b5b = 50%\n\u03b5b = 60%\nWH (mH=120 GeV)\n529\u00b140\n155\u00b16\n682\u00b179\n189\u00b112\n762\u00b193\n201\u00b113\nt\u00aft\n393\u00b116\n143\u00b13\n484\u00b134\n161\u00b16\n563\u00b142\n187\u00b18\nt\u00aft after puri\ufb01cation\n720\u00b142\n205\u00b16\n808\u00b173\n226\u00b111\n1021\u00b1103\n278\u00b115\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n427\n\nTable 6 compares the rejection of light jets given by the two BDT con\ufb01gurations and the likelihood\nratio weight IP3D+SV1 for WH events and t\u00aft events. It shows that with the same variables the BDT\noutperforms IP3D+SV1 by 10 to 30%. When using additional information, including the soft lepton tag-\nging, the light jet rejection on both event topologies increases by about 50% with respect to IP3D+SV1.\nFor these results, the training and test samples were based on similar events (WH or t\u00aft). When train-\ning the BDT on WH events and using t\u00aft events for the test sample, the gain in rejection compared to\nIP3D+SV1 is lower but still interesting (> 20%).\n8\nMeasuring b-tagging performance in data\nFor analyses using b-tagging, the estimation of the backgrounds from well-known Standard Model pro-\ncesses requires knowledge of the tagging and mis-tagging ef\ufb01ciency for the various \ufb02avours of jets with\nhigh accuracy. The quality of Monte Carlo simulation of these properties is unknown and therefore\nstrategies must be developed to measure the tagging and mis-tagging ef\ufb01ciencies directly in data.\n8.1\nb-tagging ef\ufb01ciency\nSeveral strategies for measuring the b-tagging ef\ufb01ciency directly in data are investigated in detail. The\nrelative precision they permit has been estimated for a typical b-tagging ef\ufb01ciency of 60%.\nThe \ufb01rst approach, described in Ref. [8], relies on a sample of the abundantly produced dijet events,\nin which one of the jets contains a muon. A muon+jet trigger has been conceived and proposed for this\npurpose. Two methods, also employed at the Tevatron, are used to estimate the b-content of the dijet\nsample. The pTrel method is based on templates of the muon pT relative to the jet axis. The templates\nare derived from Monte Carlo events for the three types of jets: bottom, charm and light (the latter will\neventually be derived from data). The so-called System 8 method uses two samples of differing bottom\nquark content and two uncorrelated tagging algorithms, typically the soft muon one and the tagging\nalgorithm to be calibrated, to form a system of equations from which the b-tagging ef\ufb01ciency can be\nextracted. Using 50 pb\u22121 of data, a detailed pT- or \u03b7-dependent calibration curve could be derived with\nthe pTrel method and with System 8. Since it is expected that the systematic uncertainties will dominate\nrapidly the total error for these methods, a careful study of systematics errors has to be done which was\nnot fully completed for this note: the systematic errors studied so far indicate that it should be possible to\ncontrol the absolute error on \u03b5b to 6%. Currently the two methods are proven to work well for jets below\na pT of 80 GeV.\nThe second approach, discussed in Ref. [9], makes use of t\u00aft events and is complementary: a little\nmore data is needed but the tagging ef\ufb01ciency of higher pT jets can be measured. Two distinct ways are\ndescribed: by counting the number of selected t\u00aft events with one, two or more b-tagged jets, or by study-\ning directly the output distributions of b-tagging algorithms on samples of b-jets pre-selected by several\nmethods (topological, kinematic or likelihood selection). The counting method allows measurement of\nthe integrated b-tagging ef\ufb01ciency with a relative precision of \u00b12.2(stat.)\u00b13.5(syst.)% in the lepton+jets\nchannel and \u00b13.7(stat.)\u00b12.7(syst.)% in the di-lepton channel for 100 pb\u22121 of data. For the topological\nselection, 200 pb\u22121 of data are needed and allow a relative precision of \u00b17.7(stat.)\u00b13.2(syst.)%.\n8.2\nMis-tagging rates\nMeasuring the mis-tagging rate in data is more dif\ufb01cult and under study. The main approach is to use\nthe negative tags (either in impact parameter or decay length) which describe the effects of a limited\nresolution on a priori prompt tracks and then to correct for long-lived particles (Ks, \u039b, etc), material\ninteractions and heavy \ufb02avour jets which are negatively tagged. So far no study in ATLAS has estimated\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n428\n\nthe accuracy with which fake rates can be measured. However, based on the Tevatron experience, it\nseems that a 10% relative error could be achievable with 100 pb\u22121.\n8.3\nExtracting reference distributions from data\nFor the likelihood tagging algorithms, reference distributions for light and b-jets are needed. In the\ncase of b-jets, they could in principle [25] be measured in data from a pure sample of b-jets using the\ntechniques developed for the b-tagging ef\ufb01ciency estimation in t\u00aft events. As shown in Ref. [9], the\nvarious distributions can be checked in data with a few hundred pb\u22121. However, much more data is\nneeded to extract multi-dimensional likelihoods. For light jets, it seems dif\ufb01cult to extract from data a\nsample with suf\ufb01cient purity. In any case, a Monte Carlo accurately describing the data is also needed\nto extrapolate those reference distributions to ranges where they certainly can not be measured, the very\nhigh-pT regime for instance.\n9\nConclusions and outlook: realistic performance in \ufb01rst data\nThe \ufb01rst tagging algorithm to be commissioned with real data is expected to be (besides the track count-\ning method) JetProb, using the tracks from any kind of events to de\ufb01ne its resolution function. For a\nb-tagging ef\ufb01ciency of 60%, a light jet rejection of around 30 could be achieved with this tagging algo-\nrithm but further improvements are expected. The soft lepton tagging algorithms will be commissioned\nat the same time, leading to higher rejection levels when considering semi-leptonic b-jets. Once the qual-\nity of the Monte Carlo simulation is checked and better understood with data, a tagging algorithm relying\non Monte Carlo templates for b and light jet hypotheses such as IP3D can be used, perhaps doubling the\nrejection power. The commissioning of the tagging algorithms relying on secondary vertexing may take\nmore time, but tagging algorithms like SV1 should quadruple the initial rejection level, bringing it above\n100. Finally the combination of the ultimate JetFitter tagging algorithm and the various improvements\ndescribed in this note should permit a rejection of 200, or more interestingly to maintain a rejection of\n100 at a higher b-tagging ef\ufb01ciency, around 70%.\nThose estimates do not take into account the impact of residual misalignments in the tracker. How-\never, a \ufb01rst study has been performed in which the actual alignment procedure was run. This is the most\nrealistic study so far, and includes many systematic deformations caused by the alignment procedure\nitself. It concludes that the mis-tagging rate is at most 30% lower for the same b-tagging ef\ufb01ciency with\na realistic early detector alignment.\nThe impact of several other effects on the b-tagging performance has been studied in this note. In\nthe simulation used, the fraction of dead pixels is overestimated. Using 1% instead of 5% dead pixels\nimproves the light jet rejection by about 10%. Relative improvement in the light jet rejection, from\n10% in typical t\u00aft events to 50% for high-pT samples, could be achieved with a tuning of the tracking in\njets. The sensitivity to the accuracy of the passive material description in the simulation could be quite\ndramatic. However, a large effort has been made in describing accurately the material in the tracking\nvolume. If an 8% to 15% discrepancy between Monte Carlo and data would remain, the impact on the\nb-tagging performance is a 10% relative change in light jet rejection power.\nNew ideas to improve the performance have been studied: the generalization of the track categories\ncould bring a 10% to 60% improvement, optimizing the track-to-jet association could help signi\ufb01cantly\nin busy events and \ufb01nally the use of multivariate techniques such as BDT could lead to gains in the range\n10-50%. However, all these potential gains only apply to some tagging algorithms, some pT region, etc.\nFurthermore some correlations are expected among them. Therefore it will be interesting to assess the\nnet impact of these improvements when they are all available, used simultaneously and optimized.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n429\n\nFinally, detailed studies have shown that the b-tagging ef\ufb01ciency can be measured directly in data\nusing dijet or t\u00aft events. With 100 pb\u22121, a relative precision of about 5% can be achieved for b-jet ef\ufb01-\nciency. The accuracy with which the mis-tagging rates can be measured deserves more study, however,\na 10% precision seems feasible based on the Tevatron experience.\nReferences\n[1] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[2] ATLAS Collaboration, Top Quark Mass Measurements, this volume.\n[3] ATLAS Collaboration, Search for t\u00aftH(H \u2192b\u00afb), this volume.\n[4] ATLAS Collaboration, Vertex Reconstruction for b-Tagging, this volume.\n[5] ATLAS Collaboration, Soft Muon b-Tagging, this volume.\n[6] ATLAS Collaboration, Soft Electron b-tagging, this volume.\n[7] ATLAS Collaboration, Effects of Misalignment on b-Tagging, this volume.\n[8] ATLAS Collaboration, b-Tagging Calibration with Jet Events, this volume.\n[9] ATLAS Collaboration, b-Tagging Calibration with t\u00aft Events, this volume.\n[10] ATLAS Collaboration, HLT b-Tagging Performance and Strategies, this volume.\n[11] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[12] ATLAS Collaboration, The Expected Performance of the ATLAS Inner Detector, this volume.\n[13] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[14] ALEPH Collaboration, A precise measurement of \u0393Z\u2192b\u00afb/\u0393Z\u2192hadrons, Phys. Lett. B313, (1993)\n535; D. Brown, M. Frank, Tagging b-hadrons using track impact parameters, ALEPH-92-135.\n[15] S. Eidelman et al., Phys. Lett. B 592, 1 (2004), and 2005 partial web update for the 2006 edition.\n[16] T. Bold et al., Pile-up studies for soft electron identi\ufb01cation and b-tagging with DC1 data, ATL-\nPHYS-PUB-2006-001.\n[17] J. M. Butterworth, A. R. Davison, M. Rubin, G. P. Salam, Jet substructure as a new Higgs search\nchannel at the LHC, Phys. Rev. Lett. 100, 242001 (2008).\n[18] G. Azuelos et al., Exploring Little Higgs Models with ATLAS at the LHC, hep-ph/0402037; SN-\nATLAS-2004-038, S. Gonzalez de la Hoz, L. March and E. Ros, Search for hadronic decays of ZH\nand WH in the Little Higgs model, ATL-PHYS-PUB-2006-003.\n[19] S. Corr\u00b4eard et al., b-tagging with DC1 data, ATL-PHYS-2004-006.\n[20] A. Cheplakov, A. S. Thompson, MidPoint algorithm for jet reconstruction in ATLAS, ATL-PHYS-\nPUB-2007-007.\n[21] J. Lys, private communication.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n430\n\n[22] The LEP/SLD Heavy Flavour Working Group, Final input parameters for the LEP/SLD heavy\n\ufb02avour analyses, LEPHF-2001-01.\n[23] D. Lange and A. Ryd, http://www.slac.stanford.edu/~lange/EvtGen/; D. Lange, Nucl.\nInstr. Meth. A 462 (2001) 152.\n[24] J. Bastos, Performance of boosted decision trees for combining ATLAS b-tagging methods, ATL-\nPHYS-PUB-2007-019.\n[25] S. Corr\u00b4eard, b-tagging calibration and search for the Higgs boson in the t\u00aftH channel with ATLAS,\nPhD thesis (in french), 2005, Universit\u00b4e de la M\u00b4editerran\u00b4ee.\nb-TAGGING \u2013 b-TAGGING PERFORMANCE\n431\n\nVertex Reconstruction for b-Tagging\nAbstract\nTagging of b-quark jets, \u201cb-tagging\u201d, is an important ingredient for Standard\nModel analyses as well as for searches for new physics. A property of b-quark\njets exploited by b-tagging algorithms is the presence of secondary b- and c-\nhadron decay vertices. In this note, methods for the explicit reconstruction\nof secondary and/or tertiary decay vertices of b- and c-hadron decays are pre-\nsented. The performance of the secondary vertex based b-tagging algorithms\nand the dependences on the event topology and jet kinematics are studied. The\nef\ufb01cient reconstruction of the primary interaction vertex is also crucial for b-\ntagging, especially in the presence of pile-up interaction vertices at LHC lumi-\nnosity. The ATLAS primary vertex reconstruction strategies and performances\nare presented in this note as well.\n1\nIntroduction\nIdenti\ufb01cation of b-quark jets relies on the properties of the production and weak decay of b-hadrons.\nThe most important one is their relatively large lifetime of about 1.5 ps (c\u03c4 \u2248450\u00b5m). The resulting\nb-hadron \ufb02ight path < l >= \u03b2\u03b3c\u03c4 leads to a signature of one or more displaced secondary vertices (e.g.\ninside a jet originating from a b-quark with transverse momentum of 50 GeV b-hadrons travel on average\nabout 3 mm in the transverse plane before their decay).\nNumerous methods can be used for the identi\ufb01cation of b-quark jets (usually called b-jet tagging or\njust b-tagging), based e.g. on the presence of leptons inside jets due to semileptonic b-hadron decays,\nkinematical properties of jets or explicit b- or c-hadron reconstruction. The most ef\ufb01cient tagging meth-\nods are based on the presence of displaced vertices inside jets. Such vertices can be detected either by\nthe presence of tracks incompatible with the primary event vertex or by explicit reconstruction of those\nsecondary vertices. Many track based and vertex based b-tagging methods are known together with\ncombined methods using both track impact parameters and vertex reconstruction simultaneously.\nThe reconstruction of secondary b-hadron decay vertices inside jets is challenging for several reasons.\nThe multiplicity of charged particle tracks belonging to the vertex is, contrary to the reconstruction of ex-\nclusive decay modes, a-priori not known. In cases of less than two reconstructed charged particles, a well\nde\ufb01ned secondary vertex cannot be reconstructed. This can happen either because of the charged particle\nmultiplicity produced in the decay or limitations in the track reconstruction ef\ufb01ciency, as imposed by the\ngeometrical acceptance of the inner tracking detectors or interactions in the detector material. Secondary\nvertex reconstruction ef\ufb01ciencies thus show an upper limit. In addition, weak b-hadron decays almost\nalways lead to one or more charm hadrons which subsequently decay through weak interaction. Since\nc-hadrons also have signi\ufb01cant lifetimes, the resulting topology is a set of charged particle tracks either\nstemming from the primary event vertex, the secondary b-hadron or tertiary c-hadron decay vertices. The\nresolution of the ATLAS tracking system does not resolve this decay topology in all cases. Vertex recon-\nstruction inside jets for b-jet tagging thus has to be done in an inclusive way. It should be targeted towards\nhighest ef\ufb01ciency to detect secondary vertices and identify its topology as well as possible. Kinematical\nfeatures of reconstructed vertices like e.g. the invariant mass may be used in combination with spatial\nfeatures (track-vertex and vertex-vertex distances, etc.) to increase the b-jet identi\ufb01cation power of the\nalgorithms.\nAnother important ingredient for tagging b-quark jets is the reconstruction of the primary event\nvertex. The size of the beamspot in the transverse plane (about 15 \u00b5m) is suf\ufb01ciently small to allow\nthe application of b-tagging algorithms if only information as de\ufb01ned in the transverse plane is used,\n432\n\nonce the position of the beam is known with high precision. Explicit reconstruction on event by event\nbasis does not improve signi\ufb01cantly the resolution of the primary event vertex in the transverse plane.\nIn the longitudinal direction along the beam, however, the a-priori knowledge of the interaction point is\nonly poor (several cm). Explicit reconstruction is thus mandatory if b-tagging algorithms are not only\nbased on track and vertex information in the transverse plane. Furthermore, at nominal running of the\nLHC, additional minimum bias events produce additional so-called pile-up vertices which have to be\ndistinguished from the hard primary interaction. The main task of the primary vertex reconstruction for\nb-tagging is thus to reconstruct and identify the signal event vertex out of all interaction vertices along\nthe beam.\nAt the LHC, b-tagging has to be applied to jets covering a wide kinematic range both in transverse\nmomentum and pseudorapidity. b-tagging has to be applied over the full acceptance of the tracking de-\ntectors of about |\u03b7| < 2.5. The track reconstruction performance, and thus also the vertex reconstruction\nand b-tagging performance, varies strongly with transverse momenta and pseudorapidities of charged\nparticle tracks.\nThis note focuses on aspects of primary and secondary vertex reconstruction relevant for b-tagging.\nOther aspects, also more technical ones, and performance issues are addressed in notes dedicated to\nprimary [1] and secondary vertex reconstruction [2, 3]. The note is structured as follows. In Section 2\nsome information on de\ufb01nitions, physics input objects and data sets used in this note is given. Section\n3 describes the reconstruction of the primary event vertex, its performance and impact on b-tagging.\nAlgorithms designed for the inclusive reconstruction of secondary decay vertices inside jets based on\ntwo different methods are described in Section 4. The performance of these algorithms in terms of\nsecondary vertex related quantities is discussed in Section 5. Their combination with the pure track\nimpact parameter based b-tagging algorithms is described in Section 6. The b-tagging performance of\nthe algorithms is presented in Section 7. Section 8 gives a summary of the note together with an outlook\ntowards possible future improvements.\n2\nDe\ufb01nitions, Reconstruction Details and Datasets\nThis section gives de\ufb01nitions and technical details of data reconstruction and analysis procedures used\nin this note. More detailed information can be found in [4].\nThe ef\ufb01ciency to tag a jet of \ufb02avour q as b-jet, \u03b5q, is de\ufb01ned as:\n\u03b5q = Number of jets of real \ufb02avour q tagged as b\nNumber of jets of real \ufb02avour q\n.\n(1)\nUsually \u03b5b is called tagging ef\ufb01ciency and \u03b5udsc mistagging rate. The inverse of the mistagging rate\nrudsc = 1/\u03b5udsc is called b-tagging rejection power or simply rejection. The assignment of a certain\n\ufb02avour to a jet in the Monte Carlo simulation is not unambiguously de\ufb01ned. The following de\ufb01nition\nhas been introduced: the jet \ufb02avour is the \ufb02avour of the heaviest quark after gluon radiation and splitting\nwithin a cone of some size around the jet direction. The default cone size used in ATLAS and in the\ncurrent note is \u2206R < 0.3. To test the pure algorithmic performance of the algorithms, a procedure called\n\u201cpuri\ufb01cation\u201d may be applied. Here, a light quark jet is only considered if there is no heavy parton (b- or\nc-quark) or \u03c4 lepton within a cone of 0.8 around the jet direction.\nSeveral jet reconstruction algorithms are available in ATLAS [5]. The b-tagging performance may\ndepend on the jet algorithm, but the studies of this dependence are outside the scope of this note (see [4]\nfor such studies). For the studies in this note, an iterative cone algorithm with a cone size of \u2206R = 0.4\nusing combined calorimeter towers as input, has been used. Charged particle tracks have been recon-\nstructed with a Kalman \ufb01lter based algorithm [6].\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n433\n\nOf\ufb02ine ATLAS jet reconstruction and track reconstruction are independent. An assignment of tracks\nto jets is thus necessary. The current ATLAS method used also in this note is also based on a geometrical\ncone around the jet direction. All charged tracks within a certain cone (the default value is \u2206R < 0.4)\naround the jet axis are assigned to a jet.\nThe following fully simulated Monte Carlo samples have been used for the performance studies\ndescribed in this note:\n\u2022 Higgs boson production in association with a W boson. The W boson was forced to decay into a\nmuon and its anti-neutrino, W \u2192\u00b5\u03bd\u00b5, the Higgs boson was forced to decay into pairs of b-, c- or\nu-quarks: H \u2192bb, H \u2192cc, H \u2192uu. This ensures that the jets of different quark \ufb02avour have very\nsimilar kinematics. To cover a wide range of jet transverse momenta, samples with Higgs boson\nmasses of mH = 120 GeV and mH = 400 GeV have been produced.\n\u2022 Events with pairs of top quarks, tt, where one or both W bosons decayed leptonically.\n\u2022 Events with pairs of top quarks and at least two additional jets: tt j j. These events show a large\nhadronic activity with a high probability of overlapping jets.\nDuring the \ufb01rst few years the LHC will operate at a luminosity of 2 \u00b71033 cm\u22122s\u22121 (low luminosity\nmode), reaching 1034 cm\u22122s\u22121 (high luminosity mode) at later stages. Each signal event triggered and\nreconstructed in the ATLAS detector will be overlayed by several low-pT proton-proton interactions,\ncommonly denoted as minimum bias interactions. The average number of minimum bias interactions\nper bunch crossing is 4.6 and 23 for the low and high luminosity modes, respectively. To study the\nin\ufb02uence of these additional so-called Pile-Up interactions, fully simulated Monte-Carlo samples for the\nlow luminosity mode have also been generated for the WH (mH = 120 GeV) data set.\nTo parametrize the trajectory of a charged particle in a magnetic \ufb01eld, so-called \u201cperigee\u201d parameters\nare used [6]. The ATLAS track based b-tagging algorithms use d0 and z0, the transverse and longitudinal\nimpact parameters at the point of closest approach of the trajectory to the primary vertex in the transverse\nplane. To reduce the dependence on the track parameter resolutions, the corresponding variables are\ndivided by their errors. Each impact parameter signi\ufb01cance also gets a sign based on the track and jet\ndirections. The sign is positive if the track crosses the jet axis in front of the primary vertex and negative\nif behind. Most of the tracks produced in b-hadron decays have a positive sign whereas tracks originating\nfrom the primary vertex have both signs with equal probabilities [4]. The distance between the primary\nand secondary vertices may also have a sign based on the jet direction.\n3\nPrimary Vertex Reconstruction\nIn this section different strategies for the reconstruction of primary vertices currently implemented in\nthe ATLAS reconstruction software are described. The evaluation of the algorithms is performed in the\nsingle collision and low luminosity pile-up modes.\nThe reconstruction of primary vertices can generally be subdivided into two problems: vertex \ufb01nding\nand vertex \ufb01tting. The primary vertex \ufb01nding deals with the association of reconstructed tracks to a par-\nticular vertex candidate. The task of the vertex \ufb01tting is to reconstruct the position of the primary vertex\nand its covariance matrix, recalculate the parameters of the incident tracks using the vertex constraint\nand provide a measure of goodness of the \ufb01t, such as for example the \u03c7 2 of the \ufb01t [7]. In addition, the\n\u03c72 of the re\ufb01t of track parameters with the knowledge of the reconstructed vertex is a criterion of track\nto vertex compatibility.\nA brief description of the mathematical properties of the algorithms for primary vertex reconstruction\nand evaluation of their performance with respect to b-tagging are presented below. For a more detailed\ndescription of the algorithms the reader is referred to [1].\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n434\n\n3.1\nAlgorithms for Vertex Fitting\nSeveral strategies for vertex \ufb01tting are currently implemented in the ATLAS reconstruction software.\nAll implemented vertex \ufb01tters are based on the minimization of a \u03c72 function with respect to a position\nof the vertex and parameters of incident tracks at this position. In addition, all \ufb01tters are currently\nusing the exact analytical solution for the dependence of the track parameters on the vertex position and\ntrack parameters at the vertex. Indeed, the full solution with respect to the ATLAS version of perigee\nparametrization has a simple form, which is also computationally economical [1]. The approach to the\nminimization of the \u03c72, treatment of components of track momenta in the vicinity of the vertex candidate\nand reweighting of tracks during the iterative process, however, differs from algorithm to algorithm.\n3.1.1\nThe Billoir Full and Fast Vertex Fitting Algorithms\nTwo algorithms, the Billoir Full and the Billoir Fast Vertex Fitter were implemented, following the\nschema presented in [8]. Here, the inversion of the full (3n + 3) \u00d7 (3n + 3) matrix1 of parameters of\nthe \ufb01t, where n is the number of tracks, is replaced with n inversions of (3 \u00d7 3) matrices. Compared to\nthe global \u03c72 minimization, this approach leads to a signi\ufb01cant gain in CPU time due to the inversion\nof smaller matrices. In addition to the reconstruction of the vertex position and its covariance matrix,\nthe Billoir Full Vertex Fitter also re\ufb01ts the parameters of the incident tracks with the knowledge of the\nvertex.\nThe Billoir Fast Vertex Fitter is a simpli\ufb01ed version of the vertex \ufb01t, where the trajectories of charged\nparticles are approximated with straight lines in the vicinity of the vertex and their momentum compo-\nnents p = (\u03b8,\u03c6v,q/p) are considered to be constant. While the precision of this approach is only a little\nsmaller than the one of the Full Billoir Vertex Fitter, the \ufb01t itself is signi\ufb01cantly faster due to the reduc-\ntion of the size of covariance matrices to be inverted. It should also be noted, that the Fast Vertex Fit does\nnot re\ufb01t the momenta of the incident tracks. Due to its reasonable resolution and high CPU performance,\nthis is the default vertex \ufb01tter to be used with InDetPriVxFinder, as explained in Section 3.2.1.\n3.1.2\nThe Sequential and Adaptive Vertex Fitting Algorithms\nThe Sequential Vertex Fitter implements the conventional Kalman Filter for vertex \ufb01tting as described\nin [7]. The vertex estimate is updated iteratively using the information from a single track at a time. The\nSequentialVertexSmoother allows the re\ufb01t of parameters of incident trajectories with the knowledge of\nthe reconstructed vertex position. In addition, the smoother allows for a calculation of the smoothed \u03c7 2\nof a track, which is a good criterion of compatibility of a track to a vertex.\nA robust version of the above algorithm is the AdaptiveVertexFitter. It is an iterative reweighted\nKalman Vertex Fitter, where each track is down-weighted according to its compatibility to the actual ver-\ntex position [9]. The dependence of the weighting factor on the iteration number of the \ufb01t is determined\nby a thermodynamic annealing procedure. The assignment of tracks to a vertex candidate thus becomes\nstronger with iterations and the outliers are ef\ufb01ciently discarded.\n3.1.3\nThe TrkVKalVrtFitter Algorithm\nThe TrkVKalVrtFitter is a universal vertex \ufb01tter with constraints. It uses the Billoir method [8] to estimate\nthe local vertex position and calculate re\ufb01t track parameters with the requirement of passing through the\nvertex position. The possibility of applying a beam spot constraint when reconstructing the primary\nvertex is also provided. Neutral and charged particles can be used simultaneously in the \ufb01t.\n1In the vicinity of the vertex, the polar angle \u03b8 and the momentum p of the trajectories are considered to be constant.\nThe number of parameters of the \ufb01t therefore reduces to 3n + 3: 3 remaining parameters for each of n tracks and 3 vertex\ncoordinates.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n435\n\nIn the presence of badly measured tracks the precision and stability of the \ufb01t may be improved by the\noptional use of robust functionals. In each iteration step the error matrix for each track is recalculated\nbased on an eigenvector decomposition and downweighting of badly measured directions in the track\nparameter space. Several functionals for downweighting known as M-type estimators are implemented\n[2].\n3.2\nVertex Finding Strategies\nThree different strategies for primary vertex \ufb01nding are currently implemented. These are the InDet-\nPriVxFinder, the InDetAdaptiveMultiPriVxFinder and the VKalVrtPrim. In the InDetPriVxFinder the\nprocess of primary vertex \ufb01nding is decoupled from the vertex \ufb01tting and the maximal number of re-\nconstructed vertices is therefore de\ufb01ned at the seeding step. The latter two algorithms exhibit a \ufb01nding\nthrough \ufb01tting approach, where the number of vertex candidates changes according to the results of the\nprevious iteration of the \ufb01t.\n3.2.1\nThe InDetPriVxFinder Algorithm\nThe reconstruction strategy of the Inner Detector Primary Vertex Finder consists of three steps. It starts\nwith the selection of good quality tracks originating from the beam crossing area (the detailed selection\ncuts can be found in [1]).\nAfter this initial track preselection, clusters in z are searched for in the resulting set of tracks. A\nsimple sliding window algorithm is used for this purpose. First, the tracks are ordered in ascending order\nof their z0 impact parameter. The full range of z0 impact parameters is then scanned and clusters of \ufb01xed\nlength are formed. In the low luminosity scenario, the default maximal cluster length was chosen to\nbe 3 mm. The resulting clusters of tracks are considered as independent primary vertex candidates and\ncorresponding vertices are reconstructed with the provided vertex \ufb01tting algorithm.\nAfter the reconstruction of the initial vertex candidates, the tracks least compatible with a given\nvertex candidate are rejected and the vertex candidate is re\ufb01tted (the Billoir Fast Vertex Fitter described\nin 3.1.1 is used by default) using one of the following procedures:\n\u2022 All tracks, with a \u03c72 contribution greater than a prede\ufb01ned value (by default, the threshold of\n\u03c72 = 5 per track is chosen) are discarded and the vertex candidate is reconstructed again using\nremaining tracks.\n\u2022 The least compatible tracks are removed from the vertex candidate iteratively one by one until no\ntrack with a \u03c72 contribution greater than a prede\ufb01ned value is left or the number of remaining\ntracks is too little to continue. The vertex candidate is re\ufb01tted at each iteration.\nAt present, the \ufb01rst algorithm is used as the default one. At the last stage of the primary vertex reconstruc-\ntion, the obtained vertex candidates are sorted in descending order according to the sum of transverse\nmomenta of their tracks. The vertex with the highest \u2211pT of the tracks is tagged as the signal one.\nIt should be noted that the maximum number of reconstructed primary vertices is fully de\ufb01ned by the\noutput of the cluster \ufb01nding in the beginning of the algorithm. The iterative re\ufb01t of the vertex candidates\nfollowed by the rejection of incompatible tracks serves for the re\ufb01nement of the knowledge of the vertex\npositions only. The minimum number of tracks to form a vertex candidate is one in the case when the\nbeam position is used as constraint, and two otherwise.\n3.2.2\nThe InDetAdaptiveMultiPriVxFinder Algorithm\nThe InDetAdaptiveMultiPriVxFinder is an example of a \ufb01nding-through-\ufb01tting approach to the primary\nvertex reconstruction. The reconstruction starts with the preselection of tracks originating from the\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n436\n\nbeam crossing region (the detailed selection cuts can be found in [1]). A single vertex seed is created\nout of the preselected set of tracks. A vertex candidate is then reconstructed using the Adaptive Multi\nVertex Fitter [10], as described in 3.1.2. The tracks which were considered to be outliers during the\n\ufb01rst \ufb01t are used to create a new vertex seed. At the next iteration a simultaneous \ufb01t of two vertices\nis performed. Each track is down-weighed with respect to the two vertices. The number of vertex\ncandidates is growing with iterations and the vertices are competing with each other in order to attain\nmore tracks. An annealing procedure is applied to this process: the assignment of tracks to vertices is\nbecoming harder with iterations. The result of the \ufb01t is a set of reconstructed vertices with an almost\nsolid track assignment. It has to be noted that for the adaptive \ufb01tters the starting point of the \ufb01t is of great\nimportance.\n3.2.3\nThe VKalVrtPrim Algorithm\nIn this algorithm, primary vertex reconstruction starts with the selection of a subset of tracks close to the\nbeamspot position. A sliding window type algorithm (with window size \u22484.5 mm) selects a position\nalong the beam which maximizes the vertex candidate quality value. This position becomes a seed for\nthe vertex \ufb01tter. It accepts all tracks close to the found vertex candidate position and tries to \ufb01t a single\nvertex. If the quality of the vertex is not satisfactory, one or several tracks with the biggest \u03c7 2 contribution\nare rejected and the \ufb01t is repeated. The algorithm works until a vertex with good quality is obtained. Best\nresults may be achieved with the combination of a robust \ufb01tting functional and the rejection of tracks\nduring the \ufb01t. After a successful \ufb01t, the participating tracks are removed from the set of selected tracks\nand the sliding window algorithm starts a search of the next vertex candidate for the remaining tracks.\nVKalVrtPrim runs until no more vertex candidates can be obtained in the remaining track sample.\nThe vertex candidate quality value used in the search is a sum of the track transverse momenta,\nthe transverse mass and pT nonuniformity in the transverse plane. The vertex \ufb01tter uses the beam spot\nposition as constraint in the \ufb01t.\n3.3\nPerformance of Primary Vertex Reconstruction\nIn this section, the performance of different primary vertex reconstruction algorithms is evaluated. The\nstudies are performed in single collision and low luminosity pile-up modes.\nAs mentioned above, the main tasks of primary vertex \ufb01nding algorithms are:\n\u2022 To \ufb01nd all primary vertices in a bunch crossing and reconstruct their positions with highest possible\naccuracy.\n\u2022 To identify the hard scatter signal primary vertex among the set of reconstructed vertices with\nhighest possible ef\ufb01ciency.\nThese two aspects will be investigated in the following. In this section the performance of \ufb01ve strate-\ngies for primary vertex reconstruction are compared: VKalVrtPrim, InDetAdaptiveMultiPriVxFinder and\nInDetPriVxFinder used with SequentialVertexFitter, Billoir Fast and Billoir Full Vertex Fitters. Monte\nCarlo samples of WH(120) \u2192\u00b5\u03bdbb and WH(120) \u2192\u00b5\u03bduu events with and without low luminosity\npile-up are used for this study.\n3.3.1\nEf\ufb01ciency of Hard Scatter Signal Primary Vertex Identi\ufb01cation\nAs mentioned above, an average of 4.6 minimum bias events are expected to overlay the signal event\nduring low luminosity running of the LHC. The number of simulated primary vertices per bunch crossing,\ncorresponding to the low luminosity mode of the LHC is shown in Figure 1 (left), together with the\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n437\n\nnumber of vertices\n0\n2\n4\n6\n8\n10\n12\n14\nnormalized to unity\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\nATLAS\nSim. Vrt.\nInDetAdaptiveMult PriVxFinder\nVKalVrtPrim\nBilloir fitter\nPurity P\n0\n0.2\n0.4\n0.6\n0.8\n1\nnormalized to unity\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\nPurity of vertex fit\nFigure 1: Left: Number of simulated (black line) and reconstructed vertices per event for different\nreconstruction algorithms (dotted lines); right: distribution for the InDetAdaptiveMultiPriVxFinder of\nthe primary vertex purity as de\ufb01ned in Eq. (2). The WH(mH = 120GeV) \u2192\u00b5\u03bdbb event sample has been\nused for these studies.\nnumber of primary vertices reconstructed with different algorithms. All primary vertex \ufb01nders return\ncontainers of reconstructed vertices ordered according to the probability of a given vertex to be produced\nin a signal collision. The identi\ufb01cation of a signal vertex (\ufb01rst in the list) is performed in different ways\ndepending on the algorithm. The InDetPriVxFinder orders the vertices according to the sum of transverse\nmomenta of incident tracks, while the output of the InDetAdaptiveMultiPriVxFinder is sorted according\nto the sum of squares of transverse momenta. In all cases, the \ufb01rst vertex in the list is considered to be the\nprimary signal vertex and is used by the b-tagging algorithms. In order to estimate the ef\ufb01ciency to \ufb01nd\nthe correct signal vertex from the list of primary vertices two methods are used. In the \ufb01rst method the\nsignal vertex is considered as reconstructed correctly if it is closer than 500 \u00b5m in the z direction from\nthe truth: |zrec \u2212ztruth| < 500 \u00b5m. The second method is based on the purity of reconstructed vertices.\nThe de\ufb01nition of the primary vertex purity is based on the association of tracks \ufb01tted to a primary vertex\nto truth particles:\nP =\n\u2211wsignal\n\u2211wsignal +\u2211wpileup +\u2211wnoCorres\n(2)\nwhere \u2211wsignal is the sum of weights of all tracks associated with the signal primary vertex, \u2211wpile\u2212up is\nthe sum of weights of all tracks associated with pile-up events and \u2211wnoCorres is the sum of weights of all\ntracks which were not matched to truth particles. It can be noted that for vertex algorithms which do not\nassign lower weights to tracks with respect to the vertex candidate during the \ufb01t, the sum of the weights of\nall tracks \ufb01tted to the vertex is equal to the track multiplicity. If the value of the purity for a reconstructed\nprimary vertex candidate is above 0.5, it is assumed that the main contribution to the reconstructed vertex\nstems from signal tracks and therefore the signal primary vertex is correctly identi\ufb01ed.\nIn Figure 1 (right) the distribution of the purity of the \ufb01rst vertex in the output list of the InDetAdap-\ntiveMultiPriVxFinder for WH(120) \u2192\u00b5\u03bdbb events is shown. It can be noted that in the majority of\ncases the purity of a tagged signal primary vertex is close to unity.\nIn Table 1 the fraction of events with correctly identi\ufb01ed vertices for both distance based and pu-\nrity based de\ufb01nitions are shown for different reconstruction algorithms. The WH(120) \u2192\u00b5\u03bdbb and\nWH(120) \u2192\u00b5\u03bduu Monte Carlo samples with low luminosity pile-up were used for this study. It can be\nnoted that the best performance is shown by the InDetAdaptiveMultiPriVxFinder and by VKalVrtPrim.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n438\n\nTable 1: Fractions of correctly identi\ufb01ed primary vertices for different primary vertex reconstruction al-\ngorithms. The fractions are calculated according to the purity based (1) and distance based (2) de\ufb01nitions\nof the ef\ufb01ciency. The fraction of events where the signal vertex is in the list of reconstructed vertices\n(column denoted in list) is calculated according to the distance based de\ufb01nition.\nWH \u2192\u00b5\u03bdbb\nWH \u2192\u00b5\u03bduu\nAlgorithm\n(1) [%]\n(2) [%]\nin list [%]\n(1) [%]\n(2) [%]\nin list [%]\nInDetAdaptiveMultiPriVxFinder\n93.7\u00b10.1\n93.8\u00b10.1\n99.1\u00b10.1\n96.1\u00b10.1\n96.2\u00b10.1\n99.3\u00b10.1\nVKalVrtPrim\n94.4\u00b10.1\n94.5\u00b10.1\n99.1\u00b10.1\n95.1\u00b10.1\n95.2\u00b10.1\n99.4\u00b10.1\nInDetPriVxFinder (Billoir Full)\n89.8\u00b10.2\n89.3\u00b10.2\n97.6\u00b10.1\n94.0\u00b10.2\n93.8\u00b10.2\n98.2\u00b10.1\nInDetPriVxFinder (Billoir Fast)\n89.8\u00b10.2\n89.3\u00b10.2\n97.6\u00b10.1\n94.0\u00b10.2\n93.8\u00b10.1\n98.2\u00b10.1\nAlso no signi\ufb01cant difference is observed between purity based and distance based de\ufb01nitions of the\nef\ufb01ciency. In addition, the observation is made that in the single-collision mode, the rate of wrongly\nidenti\ufb01ed vertices is essentially zero for all algorithms.\nThe misidenti\ufb01cation of the signal vertex leads to a wrong estimate of the longitudinal impact pa-\nrameters of tracks. This wrong estimate may lead to an incorrect identi\ufb01cation of b- and light quark jets\nand a decrease of the b-tagging performance. A dependence of the b-tagging performance on the type of\nthe primary vertex reconstruction algorithm is therefore expected.\n3.3.2\nPointing Lepton\nIn the events containing isolated leptons (electrons or muons), or even a lepton inside a jet coming\npossibly from semileptonic decays of heavy hadrons, the properties of these leptons can be used to\nfurther increase the ef\ufb01ciency to identify correctly the primary vertex. The trajectory of a reconstructed\nlepton can be extrapolated to the interaction region. Each reconstructed vertex, for which the lepton\nhas a longitudinal impact parameter z0 < 3mm, gets an additional weight and can then be tagged as the\nsignal vertex after reordering the list of reconstructed vertices. In Table 2 the fractions of events with\ncorrectly identi\ufb01ed primary vertices after reordering according to the pointing lepton information are\nshown for different primary vertex \ufb01nding algorithms. To estimate these fractions, the distance based\nde\ufb01nition of ef\ufb01ciency is used. Comparing to Table 1, it can be noted that the use of information from\na reconstructed lepton increases the ef\ufb01ciency of correctly identifying the signal primary vertex in case\nof the Billoir \ufb01tters, which use the sum of squares of transverse momenta of tracks as sorting criteria. In\nmost cases of misidenti\ufb01ed vertices, the direction of the isolated lepton from the W boson decay is not in\nthe kinematical acceptance of the inner detector, e.g. for the InDetAdaptiveMultiPriVxFinder (73\u00b11)%\nof the outliers have the isolated muon with |\u03b7\u00b5| > 2.5. Events with a well reconstructed isolated lepton,\nas it is the case in many analyses, thus show a much lower fraction of misidenti\ufb01ed primary vertices.\nTable 2: Fraction of correctly identi\ufb01ed primary vertices for different algorithms using the distance based\nde\ufb01nition with reordering due to a lepton matched to the primary vertex.\nWH \u2192\u00b5\u03bdbb\nWH \u2192\u00b5\u03bduu\nInDetAdaptiveMultiPriVxFinder\n94.7\u00b10.1\n96.0\u00b10.1\nVKalVrtPrim\n94.6\u00b10.1\n95.2\u00b10.1\nInDetPriVxFinder (Billoir Full)\n93.7\u00b10.1\n95.0\u00b10.1\nInDetPriVxFinder (Billoir Fast)\n93.7\u00b10.1\n95.0\u00b10.1\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n439\n\n3.4\nPrimary Vertex Resolution\nIn presence of the pile-up vertices spatial resolutions of the reconstructed primary vertex may degrade\ndue to the partial acceptance of tracks from the superposed events. Tables 3 and 4 show the resolutions\nfor the x and z coordinates of reconstructed primary vertices for different reconstruction algorithms.\nTable 3: Resolutions on the x coordinate of primary vertices reconstructed with different strategies in\nWH \u2192\u00b5\u03bdbb and WH \u2192\u00b5\u03bduu signal only and pile-up scenarios. The numbers shown are the widths of\na \ufb01t with a single Gaussian to the corresponding distributions of residuals.\n\u03c3x [\u00b5m] in WH \u2192\u00b5\u03bdbb\n\u03c3x [\u00b5m] in WH \u2192\u00b5\u03bduu\nAlgorithm\nsignal only\npile-up\nsignal only\npile-up\nInDetAdaptiveMultiPriVxFinder\n11.46\u00b10.05\n11.66\u00b10.05\n10.13\u00b10.05\n10.34\u00b10.05\nVKalVrtPrim\n11.44\u00b10.05\n11.59\u00b10.05\n10.04\u00b10.05\n10.25\u00b10.06\nInDetPriVxFinder (Billoir Full)\n12.22\u00b10.05\n12.51\u00b10.05\n11.01\u00b10.06\n11.17\u00b10.05\nInDetPriVxFinder (Billoir Fast)\n12.23\u00b10.05\n12.50\u00b10.05\n11.01\u00b10.06\n11.17\u00b10.06\nTable 4: Resolutions on the z coordinate of primary vertices reconstructed with different strategies in\nWH \u2192\u00b5\u03bdbb and WH \u2192\u00b5\u03bduu signal only and pile-up scenarios. The numbers shown are the widths\nof a \ufb01t with two Gaussians to the corresponding distribution of residuals (\u03c3z,N for the narrow and \u03c3z,T\nfor the broad component, respectively). Core Fraction is the fraction of events contained in the narrow\nGaussian.\nWH \u2192\u00b5\u03bdbb\nWH \u2192\u00b5\u03bduu\nCore\nCore\nAlgorithm\n\u03c3z,N, [\u00b5m]\n\u03c3z,T , [\u00b5m]\nFraction [%]\n\u03c3z,N, [\u00b5m]\n\u03c3z,T , [\u00b5m]\nFraction [%]\nInDetAdaptiveMulti-\nsignal only\n41.3\u00b10.5\n98\u00b12\n76.3\n35.3\u00b10.5\n79\u00b12\n75.8\nPriVxFinder\npile-up\n40.9\u00b10.5\n95\u00b12\n75.1\n34.9\u00b10.5\n77\u00b12\n75.5\nsignal only\n40.2\u00b10.5\n92\u00b12\n71.1\n36.0\u00b10.5\n82\u00b12\n78.1\nVKalVrtPrim\npile-up\n41.2\u00b10.5\n98\u00b12\n74.1\n34.3\u00b10.5\n76\u00b12\n73.2\nInDetPriVxFinder\nsignal only\n49.3\u00b10.5\n132\u00b13\n76.3\n40.4\u00b10.6\n99\u00b13\n76.4\n(Billoir Full)\npile-up\n48.6\u00b10.5\n127\u00b13\n76.7\n41.0\u00b10.5\n103\u00b13\n79.1\nInDetPriVxFinder\nsignal only\n49.3\u00b10.5\n132\u00b13\n76.2\n40.3\u00b10.6\n98\u00b13\n76.0\n(Billoir Fast)\npile-up\n48.6\u00b10.5\n127\u00b13\n76.5\n40.9\u00b10.5\n103\u00b13\n79.0\nThe numbers shown are the widths of a \ufb01t with a single Gaussian for the x coordinate and two Gaussians\nfor the z coordinate, respectively, to the corresponding distribution of the residuals. In addition the ratio\nof the narrow Gaussian and the sum of the two Gaussians is given for the z coordinate. It can be noted\nthat the best results are obtained with the VKalVrtPrim and InDetAdaptiveMultiPriVxFinder and that\nthe values of coordinate resolutions for all algorithms are very close to those obtained for the non-pile-\nup case. It can therefore be concluded, that in the low-luminosity conditions the degradation of spatial\nresolution appears to be very small.\n3.5\nImpact on b-Tagging Performance\nThe beam interaction region in ATLAS has an approximately gaussian transverse pro\ufb01le with \u03c3 = 15\u00b5m.\nThis size is smaller than the typical transverse impact parameter (d0) [6] resolution of charged particle\ntracks. b-tagging algorithms based on transverse impact parameter signi\ufb01cances only (IP2D method [4])\nare thus only slightly sensitive to the details of the primary vertex reconstruction and the presence of\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n440\n\nTable 5: Light jet rejection for WH(mH = 120 GeV) events (signal only and pile-up scenarios) using\ndifferent primary vertex reconstruction algorithms. Only jets with at least one track associated are con-\nsidered in these performance studies. IP2D,IP3D and IP3D+SV1 b-tagging methods are described in\ndetails in [4]\nIP2D\nIP3D\nIP3D + SV1\nalgorithm\n50%\n60%\n50%\n60%\n50%\n60%\nsignal only\n133\u00b16\n46\u00b11\n226\u00b114\n67\u00b12\n438\u00b136\n119\u00b15\nInDetAdaptiveMulti-\npile-up\n135\u00b16\n45\u00b11\n160\u00b18\n52\u00b11\n230\u00b114\n82\u00b13\nPriVxFinder\nratio [%]\n102\u00b16\n98\u00b13\n71\u00b18\n78\u00b14\n53\u00b110\n69\u00b16\nsignal only\n131\u00b16\n46\u00b11\n234\u00b114\n69\u00b12\n486\u00b142\n129\u00b16\nVKalVrtPrim\npile-up\n141\u00b16\n47\u00b11\n136\u00b16\n50\u00b11\n220\u00b112\n80\u00b13\nratio [%]\n108\u00b16\n102\u00b12\n58\u00b17\n72\u00b14\n45\u00b110\n68\u00b16\nsignal only\n123\u00b15\n46\u00b11\n225\u00b113\n68\u00b12\n449\u00b138\n113\u00b15\nInDetPriVxFinder\npile-up\n124\u00b15\n41\u00b11\n140\u00b16\n48\u00b11\n220\u00b112\n71\u00b12\n(Billoir Fast)\nratio [%]\n101\u00b16\n89\u00b13\n62\u00b17\n71\u00b13\n49\u00b110\n62\u00b13\nsignal only\n123\u00b15\n46\u00b11\n225\u00b113\n68\u00b12\n450\u00b138\n114\u00b15\nInDetPriVxFinder\npile-up\n124\u00b15\n41\u00b11\n140\u00b16\n48\u00b11\n221\u00b112\n71\u00b12\n(Billoir Full)\nratio [%]\n101\u00b16\n89\u00b13\n62\u00b17\n71\u00b13\n49\u00b110\n62\u00b13\npile-up vertices. This is demonstrated in the \ufb01rst column of Table 5. Since the vertex reconstruction\naccuracy in the longitudinal direction is also better than the typical longitudinal impact parameter res-\nolution (z0 [6]), the b-tagging performance is not in\ufb02uenced signi\ufb01cantly by the choice of the primary\nvertex algorithm in the case where only the signal vertex is present. This can be seen by comparing the\nrows labelled signal only in Table 5 for the different primary vertex reconstruction algorithms.\nThe presence of pile-up vertices, however, changes the situation for the longitudinal coordinate con-\nsiderably. The z position resolution is not affected signi\ufb01cantly by the presence of additional vertices as\nis shown in Table 4, but the longitudinal size of the beam interaction region is much bigger (\u03c3z \u22485.6 cm)\nthan the transverse one. Any misidenti\ufb01cation of the primary interaction vertex thus produces arti\ufb01cially\nlarge z0 track impact parameters. Consequently, most of the tracks are rejected by the b-tagging track\nselection procedure in these cases and the jets to be tagged do not have any tracks associated. Such jets\ncan not be tagged as b-quark jets anymore. Since the vertex misidenti\ufb01cation probability is not negligible\nin some event topologies, as can be seen from Table 1, the performance of b-tagging algorithms using\ninformation from the longitudinal coordinate is appreciably affected. The degradation of the b-tagging\nperformance in the presence of pile-up vertices for these algorithms is shown in the second and third\ncolumns of Table 5 for the IP3D and IP3D+SV1 algorithms which use this information.\nAn additional complication for b-tagging with pile-up originates from the rather large amount of soft\njets produced in pile-up interactions. These jets do not have reconstructed tracks inside at all in many\ncases and are thus considered as light quark jets by the b-tagging algorithms. This, however, causes\nan unphysical change of the b-tagging performance not related to the performance of the algorithms\nthemselves, because a different set of jets is used to estimate the performance. To minimize this effect,\nthe results in Table 5 are obtained for jets with at least one associated track. This approach is different\nfrom the one normally used for b-tagging performance studies. The numbers in Table 5 thus have to be\ntaken with care when comparing with other b-tagging results. The observed degradation of the b-tagging\nperformance con\ufb01rms the results obtained in a previous study [11], where a more dramatic decrease of\nthe b-tagging performance was demonstrated for the case of the nominal LHC luminosity (1034cm\u22122s\u22121)\nwhen each beam crossing produces 24 pile-up events on average.\nThere are several possibilities to improve the b-tagging performance in pile-up scenarios. The pres-\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n441\n\nence of jets without any tracks associated to them (especially if the requirement of a small longitudinal\nimpact parameter is not ful\ufb01lled for most of the tracks) is an indication that the correct primary vertex\nhas not been reconstructed in this particular event. In such cases, one could either try to use the second\nvertex from the list of primary vertex candidates (according to the ordering of vertices as applied by\nthe primary vertex reconstruction algorithm) or drop the information in the longitudinal direction, thus\nfalling back to a b-tagging algorithm working in the transverse plane only. The reconstruction of the\nprimary event vertex, as currently implemented, is a universal procedure not depending on the topology\nof the event. Adding information speci\ufb01c to a particular analysis could help in some cases to increase the\nfraction of correctly identi\ufb01ed primary vertices, e.g. reconstructing the primary vertex only from prompt\nisolated high pT leptons for channels where these are present. These options have to be studied in the\nfuture.\n4\nInclusive Secondary Vertex Reconstruction in Jets\nA b-jet originates from a b-quark, which produces a b-hadron in the fragmentation. The b-hadron then\ndecays due to electroweak interactions, which cause the transition of the b-quark preferably into a c-\nquark (|Vcb|2 \u226b|Vub|2), which then subsequently also undergoes a weak decay. As a result, the typical\ntopology of the particles in a b-jet seen in the detector is a decay chain with two vertices, one stemming\nfrom the b-hadron decay and at least one from c-hadron decays. The eventual intermediate presence\nof excited b- or c-hadron states does not change this picture because their strong or electromagnetic\ndecays do not cause measurable lifetimes. A unique feature of jets originating from the fragmentation of\nb-quarks is thus the presence of b- and c-hadron decay vertices.\nAn exclusive reconstruction of these decays cannot be done with high ef\ufb01ciency. The large b-hadron\nmasses lead to a huge number of possible decay modes with very small branching ratios, many of them\ninvolving neutral particles (which cannot be used for vertex reconstruction). The reconstruction of sec-\nondary b- and c-hadron decay vertices in jets thus has to be done in an inclusive way, where the number\nof charged particle tracks originating from b- and c-hadron decays is not known a-priori.\nTrying to resolve the b- and c-hadron vertices of the decay cascade separately is very dif\ufb01cult for the\nfollowing reasons:\n\u2022 The probability to have at least two reconstructed charged particle tracks both from the b- and c-\nhadron decays is much less than 100%. This is both because of the charged particle multiplicities\ninvolved in these decays as well as the limited track reconstruction ef\ufb01ciency, mainly because of\nmaterial interactions in the detector (as discussed in Section 5).\n\u2022 The resolutions of the relevant track parameters, especially at low transverse momenta, are not\nsuf\ufb01cient to separate the two vertices ef\ufb01ciently.\nTwo different approaches for the inclusive reconstruction of secondary vertices are presented in Sec-\ntions 4.1 and 4.2. The \ufb01rst one is based on a classical approach of \ufb01tting a single geometrical vertex.\nAs explained, this is strictly speaking not the correct hypothesis, however, for the reasons given above,\nthis is an approximation that works well for a large fraction of cases. The second algorithm is based on\na kinematical approach, assuming that the primary event vertex and the b- and c-hadron decay vertices\nlie approximately on the same line, the \ufb02ight path of the b-hadron. These underlying assumptions are\ndiscussed in more detail in the corresponding sections.\nThe most important issues in inclusive vertex reconstruction are to reconstruct the decay vertices\nwith high ef\ufb01ciency and to associate ef\ufb01ciently to the vertices the charged particle tracks coming from\nthe corresponding decays of b- and c-hadrons.\nAnother important issue is the detection and removal of sources of tracks with large impact parame-\nters which do not have any relation to the b-quark content of a jet. K0 and \u039b0 decays, \u03b3-conversions and\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n442\n\nhadronic interactions in the detector material must be removed as ef\ufb01ciently as possible before applying\nb-tagging.\nCombining the information from secondary vertices and track impact parameters allows the opti-\nmization of the b-tagging performance and is decribed in Section 6.\n4.1\nThe BTagVrtSec Algorithm\nThe main purpose of the BTagVrtSec algorithm is ef\ufb01cient b-jet tagging based on the detection of a\nsecondary vertex inside a jet. It reconstructs secondary vertices due to b- and/or c-hadron decays inside\na jet with high ef\ufb01ciency and calculates a jet weight, a discriminating variable which may be combined\nwith similar variables from other tagging algorithms (see Section 6). This algorithm is based on the\nVKalVrt [2] vertex reconstruction package.\n4.1.1\nBTagVrtSec Vertex Reconstruction\nAs stated above, to separate b-quark jets from jets produced by light quarks and gluons, it is suf\ufb01cient\nto detect unambiguously b- and c-hadron decay vertices inside the jet. The idea of the BTagVrtSec algo-\nrithm is to maximize the b/c-hadron vertex detection ef\ufb01ciency, keeping at the same time the probability\nto \ufb01nd a fake vertex inside light jets low. The default version of the algorithm constructs a single sec-\nondary vertex from the b- and c-hadron decay products. As justi\ufb01cation of such an approach it should be\nnoted, that the ability to reconstruct b- and c-hadron decay vertices separately is quite limited as already\nexplained previously. Moreover, the precise reconstruction of the decay chain is less important for b-\ntagging than the detection of the secondary decay itself. The single vertex approximation allows a high\nsecondary vertex detection ef\ufb01ciency, necessary for powerful b-tagging at the price of an imprecise kine-\nmatical reconstruction in cases when the distance between the b-and c-hadron vertices is big. Another\nadvantage of the single vertex approximation is a more simple algorithm that might be easier to tune and\ncalibrate on data.\nThe BTagVrtSec algorithm starts with a selection of tracks inside a jet. Tracks are selected with the\nsame quality cuts as for the primary vertex reconstruction algorithm VKalVrtPrim, except for a relaxed\ncut on the transverse track impact parameter (d0 \u22643.5 mm) and no requirement of the presence of a hit\nin the \ufb01rst layer (b-layer) of the pixel detector. This is done in order to maximize the ef\ufb01ciency to re-\nconstruct V0 decays and material interactions with subsequent removal of the corresponding tracks from\nthe b-tagging procedure. Tracks are selected in a cone around the jet axis. The size of the cone is a tun-\nable parameter (the default value is \u2206R = 0.4) which currently does not depend on the jet reconstruction\nalgorithm.\nThe vertex search itself starts with a determination of all track pairs which form good (\u03c7 2 < 4.5) two-\ntrack vertices inside the jet. In addition, each track of the pair must have a three dimensional distance\nfrom the primary vertex2 divided by its error higher than 2.0 and the sum of these two signi\ufb01cances must\nbe higher than 6.0. In order to decrease the fake rate an additional requirement (\u20d7V2tr \u2212\u20d7Vprimary,\u20d7Pjet) > 0\nis used.\nSome of the reconstructed two-track vertices stem from K0\ns and \u039b0 decays, \u03b3 \u2192e+e\u2212conversions\nand hadronic interactions in the detector material. The corresponding distributions are shown in Figure 2.\nFigures 2 a) and b) show the invariant \u03c0+\u03c0\u2212and p\u03c0\u2212mass spectra for accepted two particle vertices\nwith peaks due to K0\ns and \u039b0 decays. Figure 2 c) shows the distance between the primary and secondary\nvertices in the transverse plane with peaks due to interactions in the material of the beam pipe and\npixel detector layers. Charged particle tracks coming from such vertices are marked as bad and do not\nparticipate further in the following b-tagging procedure for the given jet.\n2The distance between the primary vertex and the point of closest approach of the track to this vertex.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n443\n\n inv. mass [MeV]\n\u03c0\n-\n\u03c0 \n200\n300\n400\n500\n600\n700\n800\n0\n20\n40\n60\n80\n100\n120\n140\n a)\n-p inv. mass [MeV]\n\u03c0 \n1000\n1050\n1100\n1150\n1200\n1250\n0\n10\n20\n30\n40\n50\n60\n70\n80\n b)\nTransv. distance from beam axis [mm]\n20\n40\n60\n80\n100\n120\n140\n0\n50\n100\n150\n200\n250\n c)\nATLAS\nATLAS\nATLAS\nFigure 2: Some distributions for reconstructed two track vertices:\na) the \u03c0+\u03c0\u2212invariant mass spectrum with a peak of K0 decays; b) the p\u03c0 invariant mass spectrum with\na peak of \u039b0 decays; c) the distance in the transverse plane between the primary and secondary vertices\nwith the peaks due to interactions in the beam pipe (two walls at R\u224830 mm) walls and pixel layers\n(R=50.5 mm and R=88.5 mm).\nIn the next step of the algorithm all tracks inside the jet from accepted two-track vertices except for\nmarked V0 decays and material interactions are combined into one secondary track list and the vertex\n\ufb01tting procedure from the VKalVrt package tries to \ufb01t a single secondary vertex out of all these tracks.\nIf the resulting vertex has an unacceptable \u03c72, the track with the highest contribution to the vertex \u03c72 is\ndeleted from the secondary track list and the vertex \ufb01t is redone. This procedure iterates until a good \u03c7 2\nof the vertex \ufb01t is obtained or all tracks from the secondary track list have been removed.\nSecondary vertices in light quark jets mainly stem from tracks coming from the primary vertex,\ntypically with a bad measurement of their track parameters and errors.\nSome b-tagging ef\ufb01ciency and rejection calibration algorithms require negative tail vertices. For the\nuse in those algorithms the requirement for two-track vertices (\u20d7V2tr \u2212\u20d7Vprim,\u20d7Pjet) > 0 may be dropped. In\nthis condition in some cases BTagVrtSec reconstructs a \ufb01nal single secondary vertex behind the primary\nvertex: (\u20d7Vsec \u2212\u20d7Vprim,\u20d7Pjet) < 0. Such secondary vertices are mostly fake vertices but give the necessary\nreference for calibration.\n4.1.2\nb-Tagging with BTagVrtSec\nEach b-tagging algorithm is based on variables which show signi\ufb01cantly different behaviour for b-jets\nand light jets. For secondary vertex based algorithms the \ufb01rst variable is the presence of a reconstructed\nvertex in the jet itself, whose probability is big for b-quark jets and small for light quark jets. The vertex\nreconstruction procedure can, however, provide much more information which also may be used in a\nb-tagging algorithm to increase the ef\ufb01ciency. In order not to have a too complex procedure which is still\neasy to calibrate and to control, only the most sensitive variables should be taken into account.\nAlthough BTagVrtSec can be used as a standalone b-tagging algorithm, it was developed primarily for\nworking in combination with track impact parameter based algorithms [4]. The distance between primary\nand secondary vertices is thus not used because this kind of lifetime information is already contained in\nthe track impact parameters. Three additional variables have been chosen for the BTagVrtSec tagging\nalgorithm:\n1. The mass of the reconstructed secondary vertex: M.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n444\n\n2. The ratio of the energy of charged particle tracks included in the secondary vertex and the total\nenergy of all charged particle tracks in the jet: R;\n3. The number of good (excluding identi\ufb01ed V 0 decays or material interactions) two-track vertices in\nthe jet: N.\nThe distributions of the \ufb01rst two variables are shown in Figure 9 in Section 5 for light, charm and b-jets.\nThe distributions of the number of two-track vertices can be found in [4]. In standalone mode (with-\nout combination with track impact parameter based tagging algorithms) the three dimensional distance\nbetween the primary and secondary vertices may also be used.\nTo be reliable any b-tagging algorithm must be calibrated on data. To facilitate the calibration and to\nreduce the necessary amount of data the chosen variables have been transformed (for details see [12]):\n\u2022 Invariant mass: M\u2032 =\nM\nM +1;\n\u2022 Energy ratio: R\u2032 = R0.7;\n\u2022 Number of good two-track secondary vertices: N\u2032 = logN.\nDue to the ef\ufb01ciency to reconstruct a secondary vertex inside a jet not reaching 100%, the probability\ndensity functions (PDF) of the vertex based variable have to contain a \u03b4\u2013function [12].\nPDF = (1\u2212\u03b5)\u00b7\u03b4(M\u2032,F\u2032,N\u2032)+\u03b5 \u00b7ASH(M\u2032,F\u2032,N\u2032)\nwith \u03b5 being the ef\ufb01ciency to reconstruct a secondary vertex inside a jet. The continuous probability\ndensity function of the vertex variables is constructed from multidimensional calibration histograms\nusing the ASH smoothing method [13].\nTwo slightly different taggers based on the BTagVrtSec algorithms are available in ATLAS, denoted\nSV1 and SV2. They use exactly the same variables but handle them in a different way. SV1 treats M\u2032\nand R\u2032 jointly and adds N\u2032 as independent variable (2+1 decomposition), whereas SV2 uses joint three-\ndimensional probability density functions.\nThe only criterion for the selection of variables and tuning of the BTagVrtSec algorithm was b-\ntagging performance. Other quantities like the purity of the reconstructed secondary vertices were not\nconsidered. Although the achieved quality of the b-hadron decay vertex is quite good (see Section 5), for\napplications other than b-tagging BTagVrtSec may require a different tuning.\n4.2\nThe JetFitter Algorithm\nA new inclusive secondary vertexing algorithm which exploits the topological structure of weak b- and\nc-hadron decays inside a jet was recently developed.\n4.2.1\nReconstruction of the Decay Chain Topology\nAs already stated, the fragmentation of a b-quark results in a decay chain with two vertices, one stemming\nfrom the b-hadron decay and at least one from c-hadron decays.\nAs described in Section 4.1, the BTagVrtSec algorithm relies on a vertexing algorithm in which\ndisplaced tracks are selected and an inclusive single vertex is obtained using a Kalman based \u03c7 2 \ufb01t (as\nsketched in Figure 3).\nThe algorithm described here, called JetFitter, is based on a different hypothesis. It assumes that the\nb- and c-hadron decay vertices lie on the same line de\ufb01ned through the b-hadron \ufb02ight path. All charged\nparticle tracks stemming from either the b- or c-hadron decay thus intersect this b-hadron \ufb02ight axis.\nThere are several advantages to this method:\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n445\n\nFigure 3: BTagVrtSec \ufb01ts all displaced\ntracks to an inclusive vertex.\nFigure 4: JetFitter performs a multi-vertex \ufb01t using the\nb-hadron \ufb02ight direction as constraint.\n\u2022 Incomplete topologies can also be reconstructed (in principle even the topology with a single track\nfrom the b-hadron decay and a single track from the c-hadron decay is accessible).\n\u2022 The \ufb01t evaluates the compatibility of the given set of tracks with a b-c-hadron like cascade topol-\nogy, increasing the discrimination power against light quark jets.\n\u2022 Constraining the tracks to lie on the b-hadron \ufb02ight axis reduces the degrees of freedom of the \ufb01t,\nincreasing the chance to separate the b/c-hadron vertices.\nFrom the physics point of view this hypothesis is justi\ufb01ed through the kinematics of the particles\ninvolved as de\ufb01ned through the hard b-quark fragmentation function and the masses of b- and c-hadrons.\nThe lateral displacement of the c-hadron decay vertex with respect to the b-hadron \ufb02ight path is small\nenough not to violate signi\ufb01cantly the basic assumption within the typical resolutions of the tracking\ndetector (see Figure 4).\nThis hypothesis, extensively used in the JetFitter algorithm, was explored for the \ufb01rst time in the\nghost track algorithm developed by the SLD Collaboration [14], where the already de\ufb01ned b-hadron\n\ufb02ight axis is substituted by a ghost track and where a numerical global \u03c7 2 minimisation procedure was\nused to perform the multi-vertex \ufb01t.\n4.2.2\nThe JetFitter Vertex Reconstruction Algorithm\nIn JetFitter the vertexing task is mathematically implemented as an extension of the Kalman Filter for-\nmalism for vertex reconstruction [7] and the decay chain is described through the determination of the\nfollowing variables:\n\u20d7d = (xPV,yPV,zPV,\u03c6,\u03b8,d1,d2,...,dN),\n(3)\nwith:\n\u2022 (xPV,yPV,zPV): the primary vertex position.\n\u2022 (\u03c6,\u03b8): the azimuthal and polar directions of the b-hadron \ufb02ight axis.\n\u2022 (d1,d2,...,dN): the distances of the \ufb01tted vertices, de\ufb01ned as the intersections of one or more tracks\nand the b-hadron \ufb02ight axis, to the primary vertex position along the \ufb02ight axis (N representing the\nnumber of vertices).\nBefore starting the \ufb01t, the variables are initialised with their prior knowledge:\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n446\n\n\u2022 The primary vertex position (with covariance matrix), as provided by the primary vertex \ufb01nding\nalgorithm.\n\u2022 The b-hadron \ufb02ight direction, approximated by the direction of the jet axis, the error being provided\nby the convolution of the jet direction resolution with the average displacement of the jet axis\nrelative to the b-hadron \ufb02ight axis, as determined from Monte Carlo simulations.\nThe \ufb01t is then performed, resulting in the minimization of the \u03c72 containing the weighted residuals of\nall tracks with respect to their vertices on the b-hadron \ufb02ight axis. The charged particle tracks to be used\nin the determination of the decay chain are selected according to the \u2206R matching criterion explained in\nSection 2 and a further track selection is applied, in order to reduce the amount of fake tracks.\nAfter the primary vertex and the b-hadron \ufb02ight axis have been initialised, a \ufb01rst \ufb01t is performed\nunder the hypothesis that each track represents a single vertex along the b-hadron \ufb02ight axis, until \u03c7 2\nconvergence is reached, obtaining a \ufb01rst set of \ufb01tted variables (\u03c6,\u03b8,d1,d2,...,dN).\nA clustering procedure is then performed, where all combinations of two vertices (picked up among\nthe vertices lying on the b-hadron \ufb02ight axis plus the primary vertex) are taken into consideration, \ufb01lling\na table of probabilities. After the table of probabilities is \ufb01lled, the vertices with the highest compatibility\nare merged, a new complete \ufb01t is performed and a new table of probabilities is \ufb01lled. This procedure is\niterated until no pairs of vertices with a probability above a certain threshold remain.\nThe result of this clustering procedure is a decay topology with a well de\ufb01ned association of tracks\nto vertices along the b-hadron \ufb02ight axis, with at least one track for each vertex.\nMore details about the JetFitter vertex reconstruction algorithm can be found in [3].\n4.2.3\nThe JetFitter based b-Tagging Algorithm\nThe b-tagging algorithm implemented as a \ufb01rst application of JetFitter is based on separating b-jets from\nc- and light-quark (u,d,s) jets by means of the de\ufb01nition of a likelihood function.\nThe decay topology is described by the following discrete variables:\n1. Number of vertices with at least two tracks.\n2. Total number of tracks at these vertices.\n3. Number of additional single track vertices on the b-hadron \ufb02ight axis.\nwhile the vertex information is condensed in the following variables:\n1. Mass: the invariant mass of all charged particle tracks attached to the decay chain.\n2. Energy Fraction: the energy of these charged particles divided by the sum of the energies of all\ncharged particles associated to the jet.\n3. Flight length signi\ufb01cance\nd\n\u03c3(d): the weighted average vertex position divided by its error.\nThe use of these variables allows the de\ufb01nition of a likelihood function of the form:\nLb,l,c(x) = \u2211\ncat\ncoeff(cat)\u00b7PDFcat(mass)\u00b7PDFcat(energyFraction)\u00b7PDFcat\n\u0012\nd\n\u03c3(d)\n\u0013\n,\n(4)\nwhich has to be parametrised separately for each of the three different \ufb02avours.\nThe information about the decay topology of the jet as reconstructed by JetFitter is represented by\nthe category (the coef\ufb01cient coeff(cat) representing how probable it is to \ufb01nd a certain topology for a\ngiven \ufb02avour), while the vertex information is contained in the probability distribution functions (PDFs).\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n447\n\nFigure 5: 13 different topologies are de\ufb01ned, combining the three discrete variables in such way as to\nreduce their correlations. For the case of one single vertex with at least two tracks (1), the discrete PDFs\nfor both the other two variables, total tracks at vertices (2) and single additional tracks (3), are used, but\nthey are then considered as uncorrelated, so that their corresponding coef\ufb01cients are just multiplied.\nThe discrete variables describing the decay topology are combined according to the scheme of Fig-\nure 5 into 13 category coef\ufb01cients.\nIn order to reduce the correlations between the decay topology and vertex related variables and to\nincrease the discrimination power, the PDFs are made category dependent. This splitting of PDFs is\ndone only when strictly needed.\nThe templates for the vertex variables are shown in Table 6 for all three \ufb02avours. Each PDF was\nsplit independently into the categories it was found to be most correlated with, in order to maintain the\nnumber of split PDFs to be determined on Monte Carlo simulated events as low as possible. They were\ndetermined on the WH(mH = 120 GeV) Monte Carlo events with H \u2192bb, H \u2192cc and H \u2192uu and on\ntt Monte Carlo events.\nThe JetFitter based b-tagging algorithm can be either used as a stand-alone algorithm or in combina-\ntion with pure impact parameter based algorithms (see Section 6).\n5\nSecondary Vertex Reconstruction Performance\nIn this section, the performance of the inclusive secondary vertex reconstruction algorithms as described\nin Sections 4.1 and 4.2 is discussed.\nTable 6 shows the rate of reconstructed secondary vertices in b-quark and light quark jets in bins\nof jet transverse momentum and pseudorapidity for both secondary vertex reconstruction algorithms, as\nobtained on the tt and tt j j samples.\nAbove a certain transverse momentum, the ef\ufb01ciency to identify the secondary vertex in a b-jet\nfor both algorithms approaches approximately a constant value around 75 \u221280%, while the number of\nvertices reconstructed in light-jets consistently increases with higher jet transverse momentum.\nBoth effects have to do mainly with the ability to separate real or fake secondary tracks from the\nprimary vertex: tracks from secondaries are selected according to the impact parameter signi\ufb01cance of\na track with respect to the primary vertex or to the three dimensional \ufb02ight length signi\ufb01cance of the\nsecondary vertex. Therefore, these quantities are strictly related and, above a certain threshold, they\nare nearly invariant regardless of the boost and thus the \ufb02ight length of the displaced b- or c-hadron\nproduced. For low transverse momenta, the charged particle tracks from b-hadron decays suffer from\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n448\n\nMass\nEnergy Fraction\nFlight length signi\ufb01cance\nb-jets\nMass [GeV]\n0\n1\n2\n3\n4\n5\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n2 Tracks\n3 or more Tracks\nATLAS\nEnergy fraction\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\n0.007\n1 single Track\n2 single Tracks\n2 Tracks\n3 Tracks\n4 or more Tracks\nATLAS\nWeighted flight length significance\n0\n5\n10\n15\n20\n25\n30\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\nno Vertex\n1 or more Vertices\nATLAS\nc-jets\nMass [GeV]\n0\n1\n2\n3\n4\n5\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n2 Tracks\n3 or more Tracks\nATLAS\nEnergy fraction\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\n0.007\n0.008\n0.009\n1 single Track\n2 single Tracks\n2 Tracks\n3 Tracks\n4 or more Tracks\nATLAS\nWeighted flight length significance\n0\n5\n10\n15\n20\n25\n30\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nno Vertex\n1 or more Vertices\nATLAS\nlight-jets\nMass [GeV]\n0\n1\n2\n3\n4\n5\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n2 Tracks\n3 or more Tracks\nATLAS\nEnergy fraction\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n1 single Track\n2 single Tracks\n2 Tracks\n3 Tracks\n4 or more Tracks\nATLAS\nWeighted flight length significance\n0\n5\n10\n15\n20\n25\n30\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nno Vertex\n1 or more Vertices\nATLAS\nFigure 6: The PDFs for the mass, the energy fraction and the \ufb02ight length signi\ufb01cance are shown,\nseparately for the three different jet-\ufb02avours and split according to the decay chain topology found by\nJetFitter.\nlarger multiple scattering, thus showing less signi\ufb01cant displacements from the primary event vertex and\nreducing the secondary vertex reconstruction ef\ufb01ciency.\nThe rising amount of fake vertices in light quark jets with increasing jet transverse momenta is partly\ndue to the nature of the fragmentation process in light quark jets, which produces a larger number of\ntracks coming from the primary interaction vertex the larger the transverse jet momentum is. Assuming\nthe probability for a reconstructed track to represent an outlying measurement is approximately constant\nto \ufb01rst approximation, the probability of having tracks which fake secondaries increases roughly linearly\nwith the number of primary tracks. The real secondary vertices produced in light quark jets, like photon\nconversions and V0 decays represent an additional source of vertices not related to heavy hadron decays.\nFurthermore, the pattern recognition during the track reconstruction phase is more dif\ufb01cult in dense jets\nas it is the case for higher jet transverse momenta (see [4]).\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n449\n\nTable 6: The fraction of jets with at least one reconstructed secondary vertex passing the selection criteria\nto be used by the b-tagging algorithms in b-, c- and light quark jets for BTagVrtSec (top) and JetFitter\n(bottom). These numbers, given in percent, have been obtained on the tt and tt j j samples, applying the\npuri\ufb01cation procedure.\n0< |\u03b7| <0.5\n0.5< |\u03b7| <1.0\n1.0< |\u03b7| <1.5\n1.5< |\u03b7| <2.0\n2.0< |\u03b7| <2.5\npT[GeV]\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\n15\u201330\n56.9\n21.2\n3.0\n56.3\n20.5\n2.6\n55.3\n18.5\n2.5\n51.7\n16.7\n2.9\n41.7\n14.1\n3.2\n54.4\n19.6\n2.3\n53.4\n18.8\n2.1\n52.2\n17.6\n2.0\n49.5\n15.3\n2.4\n41.4\n13.8\n3.0\n30\u201350\n72.4\n29.6\n5.3\n72.1\n28.9\n4.5\n70.7\n28.1\n4.6\n66.5\n24.0\n5.1\n58.5\n21.0\n5.6\n69.6\n27.1\n4.1\n68.5\n25.7\n3.6\n66.8\n24.5\n3.7\n62.9\n21.9\n4.4\n56.8\n21.1\n5.6\n50\u201380\n78.2\n35.1\n7.5\n78.3\n33.9\n6.4\n76.5\n32.0\n6.7\n72.7\n29.5\n7.3\n65.8\n27.5\n7.9\n74.7\n31.1\n5.4\n73.9\n29.4\n4.9\n71.9\n28.2\n5.2\n67.7\n25.7\n6.2\n63.1\n25.2\n7.9\n80\u2013120\n80.3\n39.3\n10.4\n80.2\n38.5\n9.2\n78.7\n36.8\n9.2\n74.6\n34.3\n9.6\n67.4\n31.7\n10.9\n76.3\n33.9\n6.9\n75.4\n32.6\n6.2\n73.4\n30.9\n6.3\n69.1\n28.5\n7.9\n64.2\n28.6\n10.1\n120\u2013200\n78.4\n42.6\n14.7\n78.0\n39.8\n13.3\n76.9\n39.9\n13.5\n71.8\n36.5\n14.1\n64.2\n32.1\n14.8\n76.3\n36.8\n8.9\n74.5\n32.2\n8.1\n72.4\n32.5\n8.6\n67.0\n30.6\n10.0\n59.9\n27.3\n13.5\nThe dependence of the vertex reconstruction ef\ufb01ciency on the jet pseudorapidity is mainly a conse-\nquence of the different resolutions which can be achieved in different regions of the Inner Detector: for\nincreasing rapidities, the track resolutions close to the Interaction Point get worse, the track reconstruc-\ntion ef\ufb01ciency starts to decrease and the number of fake tracks rises (a detailed quantitative explanation\nof these effects can be found in [6] and [4]).\nIt can also be concluded that the BTagVrtSec algorithm is slightly more ef\ufb01cient in reconstructing\nsecondary vertices inside b quark jets, at the cost of a slightly higher rate of fake vertices produced in\nlight quark jets compared to the JetFitter algorithm, at least in the barrel region of the Inner Detector.\nTable 7 shows the population of some reconstructed topologies for b-quark, c-quark and light quark\njets for JetFitter, as a function of the jet transverse momentum and pseudorapidity. As stated in Sec-\nTable 7: Population of the different topologies of the vertices reconstructed by JetFitter in b-,c- and light\nquark jets , shown as a function of the jet transverse momentum pT (top) and the jet pseudorapidity\n\u03b7. These numbers, given in percent, have been obtained on the tt sample, applying the puri\ufb01cation\nprocedure.\n15< pT <30\n30< pT <50\n50< pT <80\n80< pT <120\n120< pT <200\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\nNothing\n30.7\n66.0\n87.9\n18.5\n56.7\n83.0\n13.7\n51.3\n79.7\n11.7\n46.8\n76.8\n10.8\n43.5\n71.9\n1 Single Track\n15.3\n15.2\n9.4\n11.4\n16.5\n12.3\n9.9\n17.4\n13.6\n9.3\n18.0\n14.7\n9.7\n19.1\n16.5\n2 Single Tracks\n2.8\n1.3\n0.4\n3.7\n2.1\n0.7\n4.5\n2.6\n1.0\n5.5\n3.5\n1.4\n6.8\n4.3\n2.2\n1 Single Vertex\n42.8\n16.2\n2.2\n50.3\n22.3\n3.9\n49.6\n25.1\n5.2\n46.3\n26.8\n6.4\n42.2\n26.9\n8.1\n1 Vertex + 1 Track\n6.7\n1.2\n0.09\n11.9\n2.2\n0.2\n15.9\n3.1\n0.4\n19.2\n4.2\n0.7\n21.7\n5.3\n1.1\n2 Vertices\n1.7\n0.1\n0.01\n4.2\n0.3\n0.02\n6.3\n0.5\n0.04\n8.0\n0.6\n0.08\n8.8\n0.9\n0.2\n0.0< |\u03b7| <0.5\n0.5< |\u03b7| <1.0\n1.0< |\u03b7| <1.5\n1.5< |\u03b7| <2.0\n2.0< |\u03b7| <2.5\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\nb\nc\nl\nNothing\n15.2\n54.8\n88.8\n16.2\n56.4\n88.5\n17.6\n57.6\n87.5\n20.5\n59.5\n85.7\n25.5\n62.5\n84.6\n1 Single Track\n10.1\n16.1\n8.0\n10.2\n16.1\n8.4\n11.1\n16.4\n9.2\n12.9\n17.2\n10.4\n14.8\n16.7\n10.9\n2 Single Tracks\n4.2\n2.2\n0.5\n4.4\n2.2\n0.5\n4.7\n2.4\n0.5\n5.1\n2.5\n0.7\n5.0\n2.3\n0.7\n1 Single Vertex\n46.8\n23.3\n2.5\n47.3\n22.1\n2.4\n46.9\n21.1\n2.5\n44.7\n18.3\n3.0\n41.1\n16.2\n3.5\n1 Vertex + 1 Track\n16.8\n3.1\n0.2\n15.6\n2.7\n0.2\n14.3\n2.3\n0.2\n12.8\n2.2\n0.2\n10.5\n2.0\n0.3\n2 Vertices\n6.9\n0.5\n0.03\n6.3\n0.4\n0.02\n5.5\n0.3\n0.03\n4.1\n0.3\n0.02\n3.1\n0.3\n0.02\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n450\n\nInclusive B hadron vertex residual [mm]\n-5\n0\n5\n10\n15\n0\n200\n400\n600\n800\n1000\nJetFitter\nBTagVrtSec\nATLAS\nInclusive B vertex transverse residual [mm]\n-4\n-2\n0\n2\n4\n6\n8\n10\n0\n200\n400\n600\n800\n1000\nJetFitter\nBTagVrtSec\nATLAS\nFigure 7: Residuals of the reconstructed three dimensional (left) and transverse (right) \ufb02ight length of\nthe inclusive secondary vertex with respect to the true b\u2212hadron position for both vertexing algorithms.\ntion 4.2, the key feature of JetFitter is the ability to distinguish several decay chain topologies, in addition\nto recognizing the presence of a single inclusive decay vertex. The ef\ufb01ciencies and mistagging rates given\nabove for the different categories show that most of the achievable gain is due to the 1 Vertex+1 Track\nand 2 Vertices categories, where a gain in rejection against light quark jets of a factor \u223c4 and \u223c16 can\nbe obtained on approximately \u223c10% and \u223c5% of the reconstructed b-jets, respectively. The dependence\non pT and \u03b7 follows the same pattern as already described for the inclusive vertex reconstruction.\nFigure 7 shows the resolution achieved on the inclusively reconstructed b-hadron decay vertex with\nrespect to the true b-hadron position. A core can be seen, corresponding to the cases where most of\nthe reconstructed tracks really stem from the b-hadron vertex, approaching the intrinsic resolution of\nthe vertex reconstruction, while a very large tail to higher \ufb02ight lengths can be observed, due to tracks\ncoming from the decay of the charmed hadron of the b \u2192c-hadron cascade.\nAnother criterion to estimate the algorithmic performance of the secondary vertex \ufb01nders is the\nfraction of charged particles arising from the decays of b- or c-hadrons and reconstructed as tracks in\nthe Inner Detector that are correctly associated to a displaced vertex (ef\ufb01ciency) and \u2013at the same time\u2013\nwhich fraction of the tracks assigned by the secondary vertex \ufb01nders to displaced vertices really stem\nfrom real b- or c-hadron decays (purity).\nThe average charged particle multiplicities at the secondary and tertiary decay vertices as obtained\nfrom the Monte Carlo generator PYTHIA was analyzed, where a minimum transverse momentum of 500\nMeV was required for the charged particles. The decay products of a strong or electromagnetic b-hadron\ndecay (e.g. pions from B\u2217\u2217decays) are not counted as coming from the secondary vertex, because of\nthe lifetime of these states the decay particles emerge from the primary vertex. The decay products\nof a strongly or electromagnetically decaying c-hadron (e.g. D\u2217or D\u2217\u2217) are considered as stemming\nfrom the b-hadron vertex, while only the decay products of weakly decaying c-hadrons are considered\nas originating from the c-hadron vertex.\nThe average charged particle multiplicity of the inclusive b/c-hadron vertex is \u223c4.7, as shown in\nFigure 8, distributed in \u223c2.3 charged particles stemming from the b-hadron vertex and \u223c2.4 charged\nparticles originating from the c-hadron vertex. In the same \ufb01gure the decay multiplicity at generator level\n(left) is compared with the number of tracks coming from the b- and c-hadron vertices which have been\nreconstructed as tracks in the Inner Detector (right). Around 80% of their charged decay products are\ncorrectly reconstructed as tracks and pass the standard track quality selection cuts. In order to strongly\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n451\n\nTrack Multiplicity at the B/D decay vertices\n0\n2\n4\n6\n8\n10\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\nTrue tracks from B/D\nTrue tracks from B\nTrue tracks from D\nATLAS\nTrack Multiplicity at the B/D decay vertices\n0\n2\n4\n6\n8\n10\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\nSelected tracks from B/D\nSelected tracks from B\nSelected tracks from D\nATLAS\nFigure 8: Average charged particle decay multiplicity of the b- and/or c-hadrons at generator level\n(left), compared with the number of charged particles coming from the b- and/or c-hadron vertices\nreconstructed as tracks in the Inner Detector and passing some standard quality criteria (right). The\nWH(H \u2192b\u00afb) sample has been used.\nTable 8: Ef\ufb01ciency (fraction of reconstructed tracks from the decays of b- or c-hadrons that are associated\nto the secondary vertices) and purity (fraction of tracks \ufb01tted to the secondary vertices that stem from\nreal b- or c-hadron decays) for the two secondary vertex \ufb01nders, separately for different topologies in the\ncase of JetFitter. The WH(H \u2192b\u00afb) sample has been used.\nAlgorithm\nTopology\nTrack ef\ufb01ciency\nTrack purity\nBTagVrtSec\n1 inclusive B/D vertex\n69 %\n92 %\n1 vertex\n74 %\n91 %\nJetFitter\n1 vertex + 1 track\n80 %\n85 %\n2 vertices\n85 %\n89 %\nreduce the contamination of reconstructed secondary vertices by other charged particles originating from\nthe primary interaction point, tracks originating from the b- or c-hadron vertices, but not distinguishable\nfrom primary tracks, are also suppressed to some extent by the track selection cuts. This and other\nselection criteria further reduce the b- and c-hadron decay products reconstruction ef\ufb01ciency, resulting\nin a compromise between the highest possible ef\ufb01ciency and a reasonable purity. In Table 8 the track\nassociation ef\ufb01ciencies and purities of the displaced tracks stemming from the b- or c- hadrons for the\nBTagVrtSec and JetFitter algorithms are shown, the ef\ufb01ciencies being normalized to the number of tracks\nfrom b/c-hadron decays which are reconstructed by the tracking detector. The \ufb01t of an inclusive b/c-\nhadron decay vertex, as performed by BTagVrtSec, allows to obtain a very high purity, but at the cost of\nstarting to loose some tracks when the distance between the b- and c-hadron vertices starts to be relevant.\nJetFitter is able to recover a good part of this inef\ufb01ciency, thanks to the ability of reconstructing more\ncomplex decay chain topologies, at the cost of a slightly lower purity.\nSeveral topological and kinematical variables related to the reconstructed secondary vertices are used\nby the b-tagging algorithms, as described in sections 4.1 and 4.2. The invariant mass of charged particles\nassociated to the vertex and the fraction of charged energy at the vertex relative to that of the jet, are used\nby both algorithms. The distributions of these variables are shown in Figure 9 for different regions of\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n452\n\ninv. mass at sec. vertex [GeV]\n1\n2\n3\n4\n5\n6\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\ninv. mass at sec. vertex [GeV]\n1\n2\n3\n4\n5\n6\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\ninv. mass at sec. vertex [GeV]\n1\n2\n3\n4\n5\n6\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\nfractional energy at sec. vertex\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nArbitrary Units\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\nATLAS\nfractional energy at sec. vertex\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nArbitrary Units\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nfractional energy at sec. vertex\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nflight distance significance\n10\n20\n30\n40\n50\n60\n70\n80\nArbitrary Units\n-3\n10\n-2\n10\n-1\n10\nATLAS\nflight distance significance\n10\n20\n30\n40\n50\n60\n70\n80\nArbitrary Units\n-\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nflight distance significance\n10\n20\n30\n40\n50\n60\n70\n80\nArbitrary Units\n-3\n10\n-2\n10\n-1\n10\nATLAS\nFigure 9: Variables related to the properties of reconstructed secondary vertices as computed by the\nBTagVrtSec algorithm for different jet transverse momenta and pseudorapidities for b-quark jets (solid),\nc-quark jets (dotted) and light quark jets (dashed). Left: 0 < |\u03b7| < 0.5, 15 < pT < 30 GeV; middle:\n0 < |\u03b7| < 0.5, 80 < pT < 120 GeV; right: 2 < |\u03b7| < 2.5, 80 < pT < 120 GeV. The top row shows the\ninvariant mass of charged particle tracks associated to the reconstructed secondary vertices, the middle\nrow the energy of charged particle tracks associated to the reconstructed secondary vertices divided by\nthe energy of all charged particles in the jet, and the bottom row the \ufb02ight distance signi\ufb01cance as de\ufb01ned\nin the text.\njet transverse momenta and pseudorapidities for the BTagVertSec algorithm. The \ufb02ight distance signif-\nicance, de\ufb01ned as the distance between the primary and secondary vertices divided by its error, is also\nshown there. The observed dependence of the secondary vertex reconstruction performance on the jet\nkinematics will directly impact the performance of the b-tagging algorithms. This will be discussed in\nSection 7.\nEssentially all b-tagging algorithms use the direction of the jet, as reconstructed from calorimeter\ntowers, to assign e.g. the lifetime sign to the impact parameters of charged particle tracks. The jet di-\nrection is a reasonably good approximation of the b-quark direction, however, for b-tagging it is mainly\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n453\n\nthe direction of the b-hadron that matters. The direction of the b-hadron \ufb02ight path can be estimated\nusing information from reconstructed primary and secondary vertices, e.g. for BTagVrtSec the line join-\ning the primary and secondary vertices can be used as the b-hadron direction if a secondary vertex is\npresent in the jet. The more sophisticated JetFitter algorithm delivers by construction an estimate for the\nb-hadron \ufb02ight direction using information from both the calorimeters and vertices of charged particle\ntracks. Figure 10 shows a comparison of the resolutions achieved for the azimuth angle \u03c6 for the different\napproaches. Using an improved b-hadron direction may decrease the contribution of charged particles\nfrom the decays of b-hadrons to the negative tail of the impact parameter distribution. This contribution\nmainly comes from a wrong assignment of the lifetime sign if the b-hadron direction has not been recon-\nstructed suf\ufb01ciently precisely. This will facilitate the calibration and improve the b-tagging performance.\nAzimuthal b-hadron direction resolution [rad]\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\nJetFitter\nBTagVrtSec\nCalorimeter\nATLAS\nFigure 10: Angular resolution of the b-hadron \ufb02ight direction in the azimuth angle \u03c6 as reconstructed\nwith the JetFitter and BTagVrtSec algorithms (for the latter, the line joining the primary and secondary\nvertices has been used in the case where a secondary vertex is present), compared with the corresponding\nresolution as obtained from calorimeter jets. The WH (H \u2192b\u00afb; mH=120 GeV) sample was used for this\nstudy.\n6\nCombination with Impact Parameter based b-tagging Algorithms\nThe b-tagging algorithms presented in the previous sections provide all information needed to be used\nas stand-alone algorithms. Secondary vertex based b-tagging algorithms are, however, limited by the\nef\ufb01ciency to reconstruct a secondary vertex inside a jet. To obtain maximum performance, the secondary\nvertex based algorithms can be combined with other algorithms. b-tagging algorithms purely based on\nthe impact parameter signi\ufb01cances of charged particle tracks do not have this limitation. They do not\noffer, however, the amount of topological and kinematical information as the secondary vertex based\nalgorithms.\nIn ATLAS, the impact parameter information can be used either in two (r\u03c6 plane only) or three\ndimensions. The corresponding algorithms and their performance are described in detail in [4]. They\ncalculate a likelihood ratio of the probability density functions for observed track impact parameter\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n454\n\nsigni\ufb01cances S for tracks coming from b-quark jets and light quark jets: wtrack = b(S)/u(S). The jet\nlikelihood ratio (called jet weight) is the sum of track ratios: wIP\njet = \u2211Ntrack\ni=1 lnwtrack,i. Assuming that the\ntracks are independent, the jet likelihood ratio is an optimal variable for making a decision about the jet\norigin.\nSecondary vertex algorithms were designed in a way facilitating combination with track only based\nalgorithms. They provide likelihood ratios of various parameters for b-jets and light jets, which may\nbe simply summed with track likelihood ratios. To preserve an optimal performance, secondary vertex\nvariables have been chosen to be maximally independent on track impact parameters (i.e. the distance\nbetween primary and secondary vertex is strongly correlated with track impact parameters and then\nshould be used with care). The combined jet weight is then computed as sum of the likelihood ratios of\nthe different algorithms: W combined\njet\n= W SV\njet +W IP\njet.\nThe likelihood ratio approach used in ATLAS makes b-tagging an easily scalable procedure. Any\nnew algorithm or new variable can be added in the same way to already existing tagging information.\nChoice of independent variables (or at least weakly correlated ones) guarantees an optimality of com-\nbined procedure.\n7\nb-Tagging Performance\nIn this section, the performance of the algorithms described in this note is discussed. The data samples\ndescribed in Section 2 have been used for these studies. Jets had to be within the acceptance of the\ntracking detectors (|\u03b7| < 2.5) and their reconstructed transverse momenta had to exceed 15 GeV: p jet\nT >\n15 GeV. The performance is shown in terms of b-tagging ef\ufb01ciency, \u03b5b, and light quark rejection, ru,c as\nde\ufb01ned in Section 2. A certain working point is chosen by placing a cut on the weight as computed by\nthe algorithm.\nThe performance was studied both using only the information as delivered by the secondary vertex\nbased algorithms (denoted BTagVrtSec and JetFitter as in the previous sections) and after combination\nwith a tagging algorithm based on a combination of transverse and longitudinal impact parameter signif-\nicances as described in Section 6. The b-tagging algorithm purely based on the information from impact\nTable 9:\nThe rejection against light quark jets for \ufb01xed b-tagging ef\ufb01ciencies of 50% and 60% for\ndifferent data samples without and with applying the puri\ufb01cation procedure, denoted as raw and puri\ufb01ed,\nrespectively.\nSample\n\u03b5b\nBTagVrtSec\nJetFitter\nBTagVrtSec+IP3D\nJetFitter+IP3D\nWH(120)\n50% raw\n97 \u00b1 1\n156 \u00b1 3\n454 \u00b1 13\n545 \u00b1 17\n60% raw\n37 \u00b1 0\n52 \u00b1 0\n116 \u00b1 2\n133 \u00b1 2\nWH(120)\n50% puri\ufb01ed\n98 \u00b1 1\n156 \u00b1 3\n462 \u00b1 13\n554 \u00b1 17\n60% puri\ufb01ed\n38 \u00b1 0\n52 \u00b1 1\n118 \u00b1 2\n134 \u00b1 2\nWH(400)\n50% raw\n55 \u00b1 1\n101 \u00b1 1\n285 \u00b1 6\n379 \u00b1 10\n60% raw\n25 \u00b1 0\n45 \u00b1 0\n93 \u00b1 1\n121 \u00b1 2\nWH(400)\n50% puri\ufb01ed\n55 \u00b1 1\n101 \u00b1 1\n296 \u00b1 7\n390 \u00b1 11\n60% puri\ufb01ed\n25 \u00b1 0\n46 \u00b1 0\n95 \u00b1 1\n123 \u00b1 2\ntt +tt j j\n50% raw\n110 \u00b1 1\n176 \u00b1 1\n456 \u00b1 4\n633 \u00b1 7\n60% raw\n48 \u00b1 0\n66 \u00b1 0\n154 \u00b1 1\n190 \u00b1 1\ntt +tt j j\n50% puri\ufb01ed\n130 \u00b1 1\n189 \u00b1 1\n791 \u00b1 11\n924 \u00b1 14\n60% puri\ufb01ed\n53 \u00b1 0\n68 \u00b1 0\n206 \u00b1 1\n226 \u00b1 2\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n455\n\nTable 10: The rejection against charm quark jets for \ufb01xed b-tagging ef\ufb01ciencies of 50% and 60% for\ndifferent data samples. The puri\ufb01cation procedure has not been applied here.\nSample\n\u03b5b\nBTagVrtSec\nJetFitter\nBTagVrtSec+IP3D\nJetFitter+IP3D\nWH(400)\n50% raw\n8.1 \u00b1 0.1\n9.8 \u00b1 0.2\n12.4 \u00b1 0.2\n12.6 \u00b1 0.2\n60% raw\n4.8 \u00b1 0.0\n6.1 \u00b1 0.1\n6.8 \u00b1 0.1\n7.3 \u00b1 0.1\ntt +tt j j\n50% raw\n9.9 \u00b1 0.0\n10.3 \u00b1 0.0\n12.4 \u00b1 0.1\n12.3 \u00b1 0.1\n60% raw\n5.9 \u00b1 0.0\n6.2 \u00b1 0.0\n7.4 \u00b1 0.0\n7.4 \u00b1 0.0\nparameter signi\ufb01cances of charged particle tracks showing the best performance is called IP3D and is\nused in the following studies. Details about this algorithm can be found in [4]. The results from the\ncombined algorithms are denoted BTagVrtSec+IP3D and JetFitter+IP3D, respectively. Tables 9 and 10\nshow the rejection rates against light quark and charm quark jets for different tagging algorithms and\ndata samples.\nFigure 11 shows the rejection of light quark (u,d,s) and gluon jets, ru, versus the b-tagging ef\ufb01ciency\n\u03b5b for the pure secondary vertex based algorithms and a comparison with the most performant tagging\nalgorithm purely based on three dimensional impact parameter information, IP3D. It can be seen that\nthe maximum achievable b-tagging ef\ufb01ciency of the vertex based algorithms is limited by the ef\ufb01ciency\nto reconstruct a displaced vertex or b-hadron decay topology. It is higher in the case of JetFitter which\nimposes only very soft requirements on the topology. The performance of the impact parameter based\ntagging algorithm IP3D is better over almost the full range of b-tagging ef\ufb01ciencies. There is also a\nsigni\ufb01cant difference between BTagVrtSec and JetFitter, the latter one showing better performance. It\nhas to be noted, however, that JetFitter explicitely uses lifetime information (the \ufb02ight distance signi\ufb01-\ncance), which is not used by BTagVrtSec to decorrelate the algorithm better from IP3D. The right plot\nof Figure 11 exhibits some steep structures at b-tagging ef\ufb01ciencies of about 50% and 70%. These can\nbe related to sudden drops in the rejection rate of the IP3D algorithm for these b-tagging ef\ufb01ciencies,\nas can be seen in the left part of Figure 11. This behaviour can be explained mainly by the presence of\njets with only a single track associated to them and the \ufb01nite binning of the reference distributions for\nthe probability density functions of the impact parameter signi\ufb01cances as used by the IP3D b-tagging\nalgorithm (see [4] for details).\nFigure 12 shows the rejection against charm quark jets. The rejection against charm quark jets is\nsigni\ufb01cantly lower compared to light quark jets because of the real lifetime of charm hadrons and thus\nsimilar topology. Here, the vertex based algorithms show a performance that is much closer to the impact\nparameter based algorithm.\nFigures 13 and 14 show the rejections against light quark jets and charm quark jets for the secondary\nvertex based tagging algorithms after combination with the IP3D algorithm, again compared with IP3D.\nThis combination results in a signi\ufb01cant increase in rejection power, especially for light quark jets.\nThe dependence of the performance on the jet kinematics is of particular importance. Figures 15\nand 16 show the rejection against light quark jets for a \ufb01xed b-tagging ef\ufb01ciency of 50% versus the jet\ntransverse momentum and jet pseudo rapidity, respectively. Table 11 shows the rejection against light\nquark jets for a \ufb01xed b-tagging ef\ufb01ciency of 50% for several regions of jet transverse momenta and\npseudorapidities.\nThe reasons for the observed behaviour are manifold. For larger pseudorapidities, the particles pass\nthrough more material and thus the detector resolution is worse. Another reason for degradation of\nthe longitudinal impact parameter at high pseudorapidity is the dramatic increase of the extrapolation\ndistance from b-layer hit to the vertex. The degradation for high jet transverse momenta is caused by\nan increased fragmentation multiplicity, resulting in an increased combinatorics in the secondary vertex\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n456\n\nb-jet efficiency\n0.1 0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8 0.9\n1\nlight quark rejection\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nATLAS\nb-jet efficiency\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nlight jet rejection ratio\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\nATLAS\nFigure 11: Left: Light jet rejection versus b-tagging ef\ufb01ciency for BTagVrtSec (triangles, green) and\nJetFitter (full circles, red). The pure impact parameter based algorithm IP3D is also shown for compar-\nison (open circles, blue); right: The ratio with respect to IP3D for BTagVrtSec (dashed line, green) and\nJetFitter (full line, red). These results have been obtained on the tt and tt j j samples. No puri\ufb01cation of\nlight quark jets (see Section 2) has been applied.\nb-jet efficiency\n0.1 0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8 0.9\n1\nc quark rejection\n1\n10\n2\n10\n3\n10\nATLAS\nb-jet efficiency\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nc jet rejection ratio\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\nATLAS\nFigure 12: Left: Charm jet rejection versus b-tagging ef\ufb01ciency for BTagVrtSec (triangles, green) and\nJetFitter (full circles, red). The pure impact parameter based algorithm IP3D is also shown for compar-\nison (open circles, blue); right: The ratio with respect to IP3D for BTagVrtSec (dashed line, green) and\nJetFitter (full line, red). These results have been obtained on the tt and tt j j samples.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n457\n\nb-jet efficiency\n0.1 0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8 0.9\n1\nlight quark rejection\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nATLAS\nb-jet efficiency\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nlight jet rejection ratio\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\nFigure 13: Left: Light jet rejection versus b-tagging ef\ufb01ciency for BTagVrtSec (triangles, green) and Jet-\nFitter (full circles, red) after combination with IP3D. The pure impact parameter based algorithm IP3D\nis also shown for comparison (open circles, blue); right: The ratio with respect to IP3D for BTagVrtSec\n(dashed line, green) and JetFitter (full line, red) combined. These results have been obtained on the tt\nand tt j j samples. No puri\ufb01cation has been applied.\nb-jet efficiency\n0.1 0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8 0.9\n1\nc quark rejection\n1\n10\n2\n10\n3\n10\nATLAS\nb-jet efficiency\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nc jet rejection ratio\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\nFigure 14: Left: Charm jet rejection versus b-tagging ef\ufb01ciency for BTagVrtSec (triangles, green) and\nJetFitter (full circles, red) after combination with IP3D. The pure impact parameter based algorithm\nIP3D is also shown for comparison (open circles, blue); right: The ratio with respect to IP3D for\nBTagVrtSec (dashed line, green) and JetFitter (full line, red) combined. These results have been ob-\ntained on the tt and tt j j samples.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n458\n\nTable 11: The rejection against light quark jets (with puri\ufb01cation) for a \ufb01xed b-tagging ef\ufb01ciency of 50%\nfor the tt and tt j j samples in regions of jet transverse momenta and pseudorapidities for the secondary\nvertex based b-tagging algorithms (top: BTagVrtSec; bottom: JetFitter ) after combination with the pure\nimpact parameter based tagging algorithm, IP3D.\n0< |\u03b7| <0.5\n0.5< |\u03b7| <1.0\n1.0< |\u03b7| <1.5\n1.5< |\u03b7| <2.0\n2.0< |\u03b7| <2.5\n15 GeV< pT <30GeV\n177 \u00b1 4\n180 \u00b1 4\n158 \u00b1 4\n74 \u00b1 1\n28 \u00b1 0\n200 \u00b1 5\n183 \u00b1 4\n149 \u00b1 3\n74 \u00b1 1\n25 \u00b1 0\n30 GeV< pT <50GeV\n1170 \u00b1 79\n1140 \u00b1 79\n782 \u00b1 48\n375 \u00b1 18\n92 \u00b1 2\n1269 \u00b1 90\n1286 \u00b1 93\n957 \u00b1 65\n409 \u00b1 21\n111 \u00b1 3\n50 GeV< pT <80GeV\n1534 \u00b1 132\n2613 \u00b1 306\n1380 \u00b1 127\n536 \u00b1 36\n149 \u00b1 6\n2354 \u00b1 251\n2415 \u00b1 272\n1678 \u00b1 170\n677 \u00b1 51\n195 \u00b1 9\n80 GeV< pT <120GeV\n1698 \u00b1 203\n2050 \u00b1 281\n1293 \u00b1 152\n559 \u00b1 50\n143 \u00b1 8\n2286 \u00b1 317\n3293 \u00b1 573\n1311 \u00b1 156\n715 \u00b1 73\n196 \u00b1 12\n120GeV< pT <200GeV\n1016 \u00b1 128\n1116 \u00b1 152\n736 \u00b1 86\n235 \u00b1 17\n63 \u00b1 3\n1231 \u00b1 171\n1370 \u00b1 206\n1194 \u00b1 178\n299 \u00b1 25\n67 \u00b1 3\n\ufb01nding stage when trying to \ufb01nd the tracks stemming from the b-hadron decay. Furthermore, the pattern\nrecognition in the track reconstruction becomes more dif\ufb01cult in the very dense environment of jets\nwith very large transverse momenta. The steep fall for low jet transverse momenta is mainly due to the\nstrongly enhanced multiple scattering of low momentum charged particle tracks, leading to signi\ufb01cantly\ndegraded impact parameter resolutions. The observed dependence of the b-tagging performance on the\njet kinematics can be related to the peformance of the secondary vertex reconstruction as discussed in\nSection 5. It can be seen there, that the secondary vertex reconstruction ef\ufb01ciency in b-quark jets drops\nin the same kinematical regions as the resulting b-tagging performance, with an increased rate of (fake)\nvertices in light quark jets.\nTwo of the most discriminating variables, for both algorithms, are the invariant mass of charged\nparticle tracks associated to the secondary vertex and the fraction of the charged energy at the secondary\nvertex divided by the total charged energy in the jet. Figure 9 in Section 5 shows these variables for b-\nquark, c-quark and light quark jets for various jet transverse momenta and pseusorapidities. The loss of\ndiscrimination power in the regions where the degradation of the b-tagging performance is observed, is\nclearly visible. Apart from the kinematic dependence, the b-tagging performance also depends critically\non the contamination of the light quark jets by displaced tracks stemming from nearby b- or c-quark\njets, as can already be concluded comparing the b-tagging performance before and after application of\nthe puri\ufb01cation procedure. It is however worth looking at this dependence in more detail, analyzing the\nb-tagging performance as a function of the distance \u2206R of the light quark jets to the nearest b- or c-quark\nor \u03c4 lepton.\nTable 12 shows, both for the pure secondary vertex based algorithms and after combination with the\nIP3D algorithm, that the more the light quark jets are contaminated by b- or c-hadron decay products\n(smaller values of \u2206R), the stronger the degradation of the b-tagging performance is. At very small\nangles of \u2206R the light quark-jets can be barely distinguished from the nearby heavy \ufb02avour jet. A small\nkinematical bias (slightly different pT and \u03b7 distribution of the jets for different \u2206R intervals) should\nalso be taken into account when interpreting these results.\nThere is a noticeable difference in the behaviour of JetFitter compared to BTagVrtSec, the second\nbeing less robust against building up vertices which catch up contributions from nearby heavy \ufb02avour\njets. As stated in Section 4.2.2, JetFitter uses the jet direction as reconstructed by the calorimeter as a\nconstraint in the \ufb01t of the hypothetical b-hadron \ufb02ight axis, thus being more ef\ufb01cient in discarding tracks\ncoming from nearby jets.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n459\n\npt [GeV]\n50\n100 150 200 250 300 350 400 450 500\nlight jet rejection\n200\n400\n600\n800\n1000\nATLAS\npt [GeV]\n50\n100 150 200 250 300 350 400 450 500\nlight jet rejection ratio\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\npt [GeV]\n50\n100 150 200 250 300 350 400 450 500\nlight jet rejection\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\nATLAS\npt [GeV]\n50\n100 150 200 250 300 350 400 450 500\nlight jet rejection ratio\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\nFigure 15: Left: Light jet rejection for a \ufb01xed b-tagging ef\ufb01ciency of 50% versus the jet transverse mo-\nmentum for BTagVrtSec (triangles, green) and JetFitter (full circles, red) after combination with IP3D.\nThe pure impact parameter based algorithm IP3D is also shown for comparison (open circles, blue);\nright: The ratio with respect to IP3D for BTagVrtSec (triangles, green) and JetFitter (full circles, red)\ncombined. The plots in the top (bottom) row show the performance without (with) applying the puri\ufb01ca-\ntion procedure. These results have been obtained on the tt and tt j j sample.\n8\nSummary and Outlook\nIn this note, an overview of vertex reconstruction algorithms used in ATLAS, both for the reconstruction\nof the primary event vertex and the inclusive reconstruction of secondary decay vertices inside jets, has\nbeen given. The focus has been put on applications to the tagging of b-quark jets.\nSeveral primary vertex reconstruction algorithms are available in ATLAS. The performance of these\nalgorithms has been studied both for the case where only the hard signal interaction is present and for\na luminosity of 2 \u00d7 1033cm\u22122s\u22121, when 4.6 additional pile-up vertices are present on average. It was\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n460\n\neta\n0\n0.5\n1\n1.5\n2\n2.5\nlight jet rejection\n200\n400\n600\n800\n1000\nATLAS\neta\n0\n0.5\n1\n1.5\n2\n2.5\nlight jet rejection ratio\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nATLAS\neta\n0\n0.5\n1\n1.5\n2\n2.5\nlight jet rejection\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\nATLAS\neta\n0\n0.5\n1\n1.5\n2\n2.5\nlight jet rejection ratio\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nATLAS\nFigure 16: Left: Light jet rejection for a \ufb01xed b-tagging ef\ufb01ciency of 50% versus the jet pseudorapidity\nfor BTagVrtSec (triangles, green) and JetFitter (full circles, red) after combination with IP3D. The pure\nimpact parameter based algorithm IP3D is also shown for comparison (open circles, blue); right: The ra-\ntio with respect to IP3D for BTagVrtSec (triangles, green) and JetFitter (full circles, red) combined. The\nplots in the top (bottom) row show the performance without (with) applying the puri\ufb01cation procedure.\nThese results have been obtained on the tt and tt j j sample.\ndemonstrated that the presence of additional vertices does not degrade the primary vertex reconstruc-\ntion precision signi\ufb01cantly. A more severe problem is the misidenti\ufb01cation of a pile-up vertex as the\nsignal vertex. For the luminosity of 2\u00d71033cm\u22122s\u22121 and the event topologies studied in this note, this\nmisidenti\ufb01cation rate can be as high as 5%. This misidenti\ufb01cation leads to a signi\ufb01cant degradation\nof the performance of the b-tagging algorithms that use information of charged particle tracks in the\nlongitudinal direction. Possible procedures to recover a large part of this performance loss have been\ndiscussed and will be studied an implemented in the future.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n461\n\nTable 12: The rejection against light quark jets for different b-tagging ef\ufb01ciencies (\u03b5b) as function of the\ndifference in \u2206R of the light quark jets to the nearest b-, c- or \u03c4-jet (top row: BTagVrtSec; bottom row:\nJetFitter), for the secondary vertex based b-tagging algorithms used stand-alone (upper table) and after\ncombination with the impact parameter based tagging algorithm IP3D (lower table).\n\u03b5b\n0.3 < \u2206R < 0.35\n0.35 < \u2206R < 0.4\n0.4 < \u2206R < 0.45\n0.45 < \u2206R < 0.5\n0.5 < \u2206R < 0.6\n0.6 < \u2206R < 0.7\n50%\n12.4 \u00b1 0.3\n28 \u00b1 1\n80 \u00b1 5\n177 \u00b1 14\n231 \u00b1 11\n244 \u00b1 10\n29 \u00b1 1\n89 \u00b1 6\n244 \u00b1 27\n363 \u00b1 43\n345 \u00b1 20\n327 \u00b1 16\n60%\n7.3 \u00b1 0.1\n14 \u00b1 0.3\n8.7 \u00b1 1\n68 \u00b1 3\n91 \u00b1 3\n91 \u00b1 3\n17.3 \u00b1 0.4\n43 \u00b1 2\n30 \u00b1 6\n113 \u00b1 7\n128 \u00b1 5\n119 \u00b1 4\n\u03b5b\n0.3 < \u2206R < 0.35\n0.35 < \u2206R < 0.4\n0.4 < \u2206R < 0.45\n0.45 < \u2206R < 0.5\n0.5 < \u2206R < 0.6\n0.6 < \u2206R < 0.7\n50%\n18.4 \u00b1 0.5\n51 \u00b1 2\n179 \u00b1 17\n467 \u00b1 62\n939 \u00b1 92\n951 \u00b1 79\n31 \u00b1 1\n141 \u00b1 12\n501 \u00b1 80\n793 \u00b1 138\n1133 \u00b1 121\n1077 \u00b1 95\n60%\n10.1 \u00b1 0.2\n23 \u00b1 1\n66 \u00b1 4\n143 \u00b1 11\n265 \u00b1 14\n266 \u00b1 12\n17.0 \u00b1 0.4\n50 \u00b1 2\n158 \u00b1 14\n222 \u00b1 20\n309 \u00b1 17\n302 \u00b1 14\nMany interesting physics events at the LHC have a lepton with large transverse momentum in the\n\ufb01nal state, so one may try to decrease the misidenti\ufb01cation rate by selecting the reconstructed interac-\ntion vertex closest to this lepton. This strategy, however, does not provide a signi\ufb01cant improvement\nin comparison with the standard primary vertex selection algorithm since the presence of a well recon-\nstructed high pT lepton increases the weight of the corresponding vertex and then is taken into account\nautomatically.\nTwo algorithms are available in ATLAS for the inclusive reconstruction of secondary decay ver-\ntices in jets, following different approaches. The \ufb01rst algorithm, BTagVrtSec, reconstructs explicitly\ngeometrical secondary vertices inside the jet. The second algorithm, JetFitter, is based on the speci\ufb01c\nkinematics of the b- and c-hadrons decay chain. The performance of the algorithms has been investigated\nthoroughly. The b-tagging performance of both algorithms has been studied using only the information\nfrom the secondary vertex algorithms as well as after combination with b-tagging algorithms based on\ncharged track impact parameters. A strong dependence of the vertex reconstruction and thus b-tagging\nperformance on the jet pseudorapidity and transverse momentum was demonstrated. As explained in the\ntext, this is caused by physics or instrumental effects.\nSeveral new developments and further improvements are planned for the future. A dedicated recon-\nstruction of V0 decays and material interactions will also be available in JetFitter soon. Together with\nother improvements, like a modi\ufb01ed seeding procedure and the application of multivariate techniques, a\nsigni\ufb01cant improvement can be expected for the JetFitter based b-tagging algorithm in the near future.\nAn extension of the BTagVrtSec algorithm is able to reconstruct several vertices in a jet. The de\ufb01nition\nof variables related to the additional information to be used for b-tagging will be done in the near future\nand increase the b-tagging performance. The implementation of another inclusive vertex reconstruction\nalgorithm, the so-called Topological Vertex Finder is in progress. It is based on an algorithm originally\ndeveloped by the SLD collaboration [15].\nIn the inclusive secondary vertex reconstruction algorithms presented in this note, different cuts are\napplied at different stages during vertex \ufb01nding and \ufb01tting. Currently, these cuts do not depend on the jet\nparameters. Due to the strong dependence of the b-tagging performance on them, however, it seems more\nappropriate to optimize these parameters depending on the kinematics of the jet under consideration.\nOne quantity worth investigating is the size of the cone around the jet axis within which charged particle\ntracks are associated to the jet and thus used by the vertex reconstruction and b-tagging algorithms.\nFor large jet transverse momenta, the cone that contains most of the particles from the decays of heavy\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n462\n\n (GeV/c)\nT\np\n0\n100\n200\n300\n400\n500\nRejection Tuned / Rejection Default\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n (GeV/c)\nT\np\n0\n100\n200\n300\n400\n500\nRejection Tuned / Rejection Default\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\nATLAS\nATLAS\nFigure 17: Ratios of the tuned rejections to the default rejection as a function of the jet transverse momentum for a b-tagging\nef\ufb01ciency of 60%. The left hand side plot shows this ratio for light quark jet rejection, while the right hand side plot shows the\nratio for charm jet rejection.\nb- and c-hadrons as well as from fragmentation, will be signi\ufb01cantly smaller than for lower transverse\nmomenta. It is thus desirable to choose the size of this track association cone depending on the transverse\nmomentum of the jet. Since this is not restricted to secondary vertex based b-tagging algorithms, this\npoint is addressed in detail in [4]. To give an idea of what can be expected from such a parameter tuning,\none parameter of the BTagVrtSec algorithm has been optimized in bins of the jet transverse momentum.\nThis parameter is a cut on the signi\ufb01cance of the displacement of vertex candidates built from pairs of\ntracks from the primary event vertex. Table 13 shows the values chosen after the optimization procedure.\nIt can be seen, that the optimal value varies strongly with the jet transverse momentum. Figure 17\nTable 13: Optimal values for the signi\ufb01cance cut on the displacement of two track vertex candidates from\nthe primary event vertex for the different jet pT bins.\nJet pT [GeV]\n15-30\n30-50\n50-80\n80-120\n120-200\n200-400\n400-1000\nOptimal Cut\n3.5\n4.5\n5.0\n6.0\n6.5\n7.0\n7.0\nshows the gain in b-tagging performance that is achieved by the parameter tuning. It can be seen that the\nrejection against light quark jets improves by a factor of about two in the region of large jet transverse\nmomenta, whereas the gain in charm jet rejection is more moderate. This parameter tuning will be\ncontinued in the future and will be included in the b-tagging algorithms.\nReferences\n[1] G. Piacquadio, K. Proko\ufb01ev, A. Wildauer, ATLAS Primary Vertex Reconstruction, ATLAS Note in\npreparation.\n[2] V. Kostyukhin, VkalVrt \u2013 a package for vertex reconstruction in ATLAS, ATL-PHYS-2003-031.\n[3] G. Piacquadio, C. Weiser, A new inclusive secondary vertex algorithm for b-jet tagging in ATLAS,\nProceedings of the International Conference on Computing in High Energy and Nuclear Physics,\nCHEP 2007, Victoria, Canada.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n463\n\n[4] ATLAS Collaboration, b-Tagging Performance, this volume.\n[5] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[6] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[7] R. Fr\u00a8uhwirth, Application of Kalman Filtering to Track and Vertex Fitting, Nucl. Instrum. and\nMethods 225 (1984) 352.\n[8] P. Billoir, S. Qian, Fast vertex \ufb01tting with a local parametrization of tracks, Nucl. Instrum. Meth.\nA311 (1992) 139-150.\n[9] R.Fr\u00a8uhwirth et al., Nucl. Instrum. Meth. A502 (2003) 699.\n[10] R.Fr\u00a8uhwirth, W. Waltenberger, Proceedings of the International Conference on Computing in High\nEnergy and Nuclear Physics , CHEP 2004, Interlaken, Switzerland.\n[11] S. Correard at al., b-tagging with DC1 data, ATL-PHYS-2004-006.\n[12] V. Kostyukhin, Secondary vertex based b-tagging, ATL-PHYS-2003-033.\n[13] D.W. Scott, Multivariate density estimation theory, practice, and visualization, New York, NY Wi-\nley 1992.\n[14] K. Abe et al., SLD Collaboration, Time dependent B/s0 anti-B/s0 mixing using inclusive and\nsemileptonic B decays at SLD, Proc. of the 19th Intl. Symp. on Photon and Lepton Interactions\nat High Energy LP99, ed. J.A. Jaros and M.E. Peskin.\n[15] D.J. Jackson, A Topological vertex reconstruction algorithm for hadronic jets, Nucl. Instrum. Meth.\nA388 (1997) 247-253.\nb-TAGGING \u2013 VERTEX RECONSTRUCTION FOR b-TAGGING\n464\n\nEffects of Misalignment on b-Tagging\nAbstract\nThis note investigates the effects of misalignment on b-tagging performance\nusing Monte Carlo simulations. Four different alignment sets were consid-\nered, two with known random misalignments, one produced with the ATLAS\nalignment procedures and one with a perfectly aligned detector. Error tun-\ning was investigated to compensate for the larger effective hit errors caused\nby misalignment. In addition the effects of misalignment on the tracking and\nvertexing performance were evaluated.\n1\nIntroduction\nThe ATLAS detector has been built to provide high precision tracking and vertexing which are essen-\ntial for good b-tagging performance. Misalignment of the detector will degrade the tracking resolution\nand consequently the performance of the b-tagging is expected to be sensitive to the alignment of the\ndetector. As well as random misalignments of modules which give an effective smearing of each hit,\nsystematic distortions introduced by the structure of the detector and by the alignment algorithms can\nhave unexpected consequences.\nThe effects of misalignment on b-tagging have been studied with Monte Carlo simulations using a\nnumber of different alignment sets. These include a set that perfectly aligns the detector, two hand-made\nsets with known levels of random misalignment and an alignment set produced with the actual alignment\nalgorithms to be used to align the ATLAS detector.\nThe assignment of correct errors for the hits is important for proper track and vertex reconstruction.\nBecause module misalignments add to the intrinsic error of the module, the errors assigned to the hits\nneed to be adjusted depending on the level of misalignment. Samples were investigated with and without\nthis hit error adjustment.\nThe note is organized as follows: Section 2 describes the four alignment sets. The error tuning\nprocedure and resulting scale factors used to adjust the hit errors are presented in Section 3. Studies were\nmade with both t\u00aft and WH(mH = 120 GeV) samples and a brief description of these samples is given\nin Section 4. Section 5 describes the effects of misalignment on the tracking and vertexing performance.\nThe effects of misalignment on the b-tagging performance, as measured by comparing the b-jet ef\ufb01ciency\nversus light jet rejection for the different alignment sets, are presented and discussed in Section 6.\n2\nResidual misalignment sets\nIn order to study the effects of misalignment, a number of different alignment scenarios were consid-\nered. The Monte Carlo simulation used in this investigation includes misalignments introduced at the\nsimulation stage. The level of misplacement is representative of the amount of misalignment expected\nbefore any attempt to align the detector. The misalignments are of the order of 10\u2013100 \u00b5m at the level\nof individual modules and assembly structures such as layers and disks and misalignments of the order\nof a few mm at the whole subsystem level. The level of these misalignment was based on known fab-\nrication precisions and survey measurements. [1]. The misalignments introduced are too large to allow\nfor reasonable reconstruction. What is desired is to reconstruct the resulting data sets with alignment\ncorrections that are typical of what is expected in the real detector, after which only small misalignments\nshould remain. Four alignment sets were used in this study:\n\u2022 Perfect: This is the ideal case where the same set of alignments used in the simulation are used in\nthe reconstruction and so one does not see any misalignment.\n465\n\n\u2022 Aligned: This uses an alignment set produced using the actual track based alignment algorithms\ndeveloped for the ATLAS detector. It is expected to include any systematic deformations that\nthe alignment procedure itself causes. While some systematic effects were included in the mis-\nalignments introduced in the simulation, such as clocking effects where each subsequent layer was\nrotated by increasing amounts, it does not contain all the systematic deformations which are ex-\npected. In particular large scale structures such as layers and discs were treated as rigid objects\nwithout any internal deformations such as a twist. Also pixel stave bows which are known to occur\nwere not introduced. So it is possible that this set is still optimistic. This set is a \ufb01rst attempt at the\nfull scale alignment of the inner detector and so should not be considered the \ufb01nal word on what\nwill be seen in the real detector. However, it is considered to be the most realistic case studied\nhere.\n\u2022 Random10: This is a hand-made alignment set that takes the misalignment set used in simulation\nand randomly shifts the module positions by small amounts. These residual misalignments were\nintroduced at different levels in the hierarchy. Random shifts and rotations were made to individual\nmodules, and whole layers and disks. A small shift and rotation was also made to the whole pixel\nstructure. Since the degradation of the b-tagging performance is expected to be dominated by the\nalignment of the pixel system, only pixel residual misalignments were introduced, The SCT and\nTRT were corrected perfectly as in the perfect alignment case. Due to movements of higher level\nstructures in this set, some systematic effects may exist. The levels of misalignment are given in\nTable 1. The axis de\ufb01nitions for the module level uses a local frame where x and y are the r\u03c6 and \u03b7\nmeasurement directions respectively and z is out of the plane. For higher levels they correspond to\nthe global frame with z-axis along the beam direction. RotX, RotY, RotZ are rotations around the\ncorresponding axes. The module level shifts in the r\u03c6 measurement direction are around 10 \u00b5m.\nThe set attempts to emulate the level of misalignments expected during the early running period. It\nis not well known what levels of misalignments are expected after certain running periods so this\nis just an indication rather than being a \ufb01rm prediction of what is expected at start up. Comparison\nwith the real alignments (\u201cAligned\u201d set) shows this to be a rather pessimistic scenario.\n\u2022 Random5: As with \u201cRandom10\u201d, but with levels of misalignment better by about a factor of 1.5 to\n2. This is an estimate of what might be expected after several years of running. Like \u201cRandom10\u201d,\nthis set introduces misalignments at the three levels of hierarchy with levels of misalignment given\nin Table 2.\nTable 1: Residual misalignment for \u201cRandom10\u201d. Random misalignments were generated with a Gaus-\nsian distribution with \u03c3 as tabulated. Shifts are in \u00b5m and rotations are in mrad.\nLevel\nx\ny\nz\nRotX\nRotY\nRotZ\nModule\n10\n30\n30\n0.3\n0.5\n0.2\nLayer\n10\n10\n15\n0.05\n0.05\n0.1\nDisk\n10\n10\n30\n0.2\n0.2\n0.1\nWhole pixel\n10\n10\n15\n0.1\n0.1\n0.1\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n466\n\nTable 2: Residual misalignment for \u201cRandom5\u201d. Random misalignments were generated with a Gaussian\ndistribution with \u03c3 as tabulated. Shifts are in \u00b5m and rotations are in mrad.\nLevel\nx\ny\nz\nRotX\nRotY\nRotZ\nModule\n5\n15\n15\n0.15\n0.3\n0.1\nLayer\n7\n7\n10\n0.02\n0.02\n0.05\nDisk\n7\n7\n20\n0.1\n0.1\n0.05\nWhole pixel\n7\n7\n10\n0.05\n0.05\n0.05\n3\nError scaling\n3.1\nError scaling procedure\nThe intrinsic error of a hit will depend on a number of factors such as the cluster width and track direc-\ntion. These factors are taken into account when calculating the intrinsic error of the hit. In the case of a\nperfectly aligned detector, if these intrinsic errors are properly determined one expects the pull distribu-\ntion (the distribution of the hit residuals divided by the calculated intrinsic error) to have a width close to\none.\nThe differences between the real positions of individual hits and those recorded by a misaligned\ndetector lead to an additional error term that must be added in quadrature to the intrinsic error of the hits.\nThe errors on the hits directly affect whether a hit is associated to a track, the track propagation and\ntrack parameter errors and the objects that use tracks as input, such as vertices. Of particular importance\nto b-tagging is the precision of the impact parameter and the vertexing performance. It is therefore\nnecessary to have accurately assigned hit errors.\nIn this section hits will refer to clusters in the silicon detectors (pixel and SCT) and drift circles in the\nTRT. To correct the hit errors the diagonal elements of the error matrix are modi\ufb01ed using two parameters\na and c:\n\u03c3\n\u20322 = a2 \u00b7\u03c3 2 +c2\n(1)\nwhere:\n\u2022 \u03c3 is the original error assigned to the hit which is a function of the cluster size and track angle.\nThis should normally be close to the intrinsic resolution if properly determined,\n\u2022 a is a multiplicative factor on the error, which is meant to compensate for inaccuracies in the\nintrinsic error determination,\n\u2022 c is a constant added in quadrature to the error. This is meant to correct effects attributed purely to\nresidual misalignments.\nSince each detector component can have signi\ufb01cantly different behaviour, the granularity of each\ndetector component has to be taken into account, and therefore different sets of (a, c) have to be computed\nseparately for the barrel and endcap regions for each detector technology, as well as for the different r\u03c6\nand \u03b7 measurement directions in the case of the pixel detector.\nFor the derivation of the (a, c) pairs, the distributions of hit residuals and their pull distributions are\nanalyzed, and in particular the deviations of the pull widths from the ideal value of 1 are investigated.\nSince the scale factor a is intended to correct the intrinsic resolutions, this is most easily obtained\nwith a perfectly aligned geometry. Naturally, this is not possible with real data, where more in depth\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n467\n\nstudies will be needed to determine if the assigned intrinsic errors are appropriate. Currently the factor\na is needed as the errors used in the reconstruction do not match those observed in the simulation.\nIt is assumed, however, that the best knowledge from test-beam and simulation will be put into the\ndetermination of the intrinsic error such that a will be close to 1 and any remaining differences would be\nabsorbed into the parameter c.\nThe widths of the resulting pull distributions can be used directly as the scaling factors a. This is\niterated a few times, applying the correction, rerunning reconstruction and then determining new values\nof a. The iterations are necessary due to correlations between detector components. The factor c is set to\nzero when determining the a factor.\nThe resulting factors a are then kept constant when used for the misaligned detector. Several itera-\ntions (apply (a, c) factors, reconstruct sample, analyze pulls) are performed using a misaligned detector,\nin order to determine the c factor. It is computed using the formula:\nc2\ni = (p2\nobs \u22121)a2\u03c3 2\n0 + p2\nobsc2\ni\u22121\n(2)\nwhere ci and ci\u22121 are the values of the c factor obtained in the iteration i and i \u22121, respectively, pobs is\nthe hit residual pull width observed at step i, and \u03c30 is the average intrinsic detector resolution.\nThe determination of c does not rely on any information about the actual detector positions and\nthe procedure can be applied to real data. For this study a sample of high energy single muons was\nused, while in practice one would need to study the feasibility of extracting the error tuning with a more\nrealistic event sample and track selection.\n3.2\nError scaling parameters\nThe resulting parameters after the tuning are shown in Table 3. The values of a are seen to be well below\none for the SCT and TRT. This is due to an overestimate of the intrinsic errors. This is being improved.\nThe value for c gives some indication of the level of residual misalignment. For the \u201cRandom5\u201d and\n\u201cRandom10\u201d sets, the values of c are higher than what was input for the module shifts. This is possibly\ndue to a larger error being needed to compensate for the effects of the layer and disc movements. It can\nbe seen that the real alignment results in small values of c compared to the hand-made sets. In the pixel\nr\u03c6 measurement direction one gets 3 \u00b5m and in the \u03b7 measurement direction one gets around 15 \u00b5m for\nthe \u201cAligned\u201d set.\nTable 3: Error scaling parameters for the different alignment scenarios. The parameter a was tuned using\nthe \u201cPerfect\u201d case and used for all alignment scenarios.\nAll\nPerfect\nRandom10\nRandom5\nAligned\na\nc(\u00b5m)\nc(\u00b5m)\nc(\u00b5m)\nc(\u00b5m)\nPixel barrel r\u03c6\n1.03\n0\n31\n13\n3\nPixel barrel \u03b7\n0.97\n0\n71\n34\n13\nPixel endcap r\u03c6\n1.05\n0\n30\n14\n3\nPixel endcap \u03b7\n1.08\n0\n43\n11\n15\nSCT barrel\n0.78\n0\n0\n2\n7\nSCT endcap\n0.86\n0\n6\n5\n8\nTRT barrel\n0.82\n0\n11\n3\n37\nTRT endcap\n0.77\n0\n11\n10\n19\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n468\n\nTable 4: Ef\ufb01ciency of track reconstruction.\nSetup\nef\ufb01ciency (%)\nPerfect\n97.09\u00b10.02\nRandom10\n95.50\u00b10.03\nRandom10 + error scaling\n97.22\u00b10.02\nAligned\n97.07\u00b10.02\nAligned + error scaling\n97.04\u00b10.02\n4\nMonte Carlo Samples\nThe performance of b-tagging was investigated with t\u00aft and WH(mH = 120 GeV) samples which are\nstandard samples used in b-tagging performance studies in ATLAS [2]. The main difference between\nthese two samples is that the WH events have lower jet multiplicities.\nThe t\u00aft sample includes semi-leptonic and di-lepton channels and this sample is used for measuring\nboth b-jet and light jet ef\ufb01ciencies. The WH(120) sample contains two sub samples. WH(120) \u2192\n\u00b5\u03bdbb is used to measure b-jet ef\ufb01ciencies and WH(120) \u2192\u00b5\u03bduu for light jet ef\ufb01ciencies. The samples\ncontained no pile-up.\n5\nEffects of misalignment on tracking and vertexing\nThe tracking and vertexing performance was studied with the WH(120) \u2192\u00b5\u03bdbb sample, although the\nother samples could equally have been chosen. A sample size of 27,000 events was used. This sample\nwas reconstructed using three of the alignment sets described in Section 2: \u201cPerfect\u201d, \u201cRandom10\u201d and\n\u201cAligned\u201d. All other settings were kept the same. For the \u201cRandom10\u201d and \u201cAligned\u201d sets, samples were\ninvestigated with and without error scaling.\n5.1\nTracking performance\nThe track reconstruction ef\ufb01ciency was computed for each scenario by comparing true tracks to cor-\nresponding reconstructed tracks. Tracks with pT > 1 GeV and |\u03b7| < 2.5 were selected. A true track\nwas considered to match a reconstructed track if the true track was the source of at least 50% of the\nhits associated to the reconstructed track. Next, the ef\ufb01ciency was computed as the ratio of the number\nof matched tracks to the number of all true tracks. The results for the ef\ufb01ciency for each of the three\nscenarios are shown in Table 4. The presence of residual misalignment in the \u201cRandom10\u201d set causes a\nloss of about 2% in the ef\ufb01ciency, while the introduction of error scaling completely recovers the loss of\nperformance. The \u201cAligned\u201d set shows no signi\ufb01cant change with respect to the \u201cPerfect\u201d case, with or\nwithout error scaling.\nThe number of fake tracks was also investigated in a similar manner to the track reconstruction\nef\ufb01ciency calculation. A track was labeled as \u201cfake\u201d if it had fewer than 50% of its hits from a single true\ntrack. The percentage of fake tracks from the total accepted tracks is shown in Table 5 for the different\nalignment scenarios. The misalignments result in more fakes, and as with the ef\ufb01ciency, this is recovered\nwith the introduction of error scaling.\n5.2\nVertexing performance\nThe performance of the primary vertex \ufb01nding algorithm was also investigated for the same \ufb01ve scenarios\nof alignment and error scaling. The ef\ufb01ciency for the primary vertex \ufb01nding was computed as the ratio\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n469\n\nTable 5: Ratio of fake tracks to the total number of accepted tracks.\nSetup\nfake tracks (%)\nPerfect\n2.33\u00b10.02\nRandom10\n2.46\u00b10.02\nRandom10 + error scaling\n2.29\u00b10.02\nAligned\n2.34\u00b10.02\nAligned + error scaling\n2.27\u00b10.02\nbetween the total number of reconstructed vertices to the total number of true vertices. It was found that\nthis remains constant, at a value of 99.68\u00b10.04%, irrespective of the misalignment scenario considered.\nThe primary vertex resolution was evaluated by looking at the difference between the reconstructed\nand the true vertex position. The resulting distributions for x and z directions are displayed in Fig. 1.\nThe results for the y direction were similar to that in the x direction. The introduction of residual mis-\nalignment causes the distributions to become wider as would be expected with a degradation of the hit\nresolutions. The shift for the hand-made sets is consistent with the shift of the entire pixel detector that\nwas introduced. For the \u201cAligned\u201d set a shift in z of about 90 \u00b5m is apparent. The alignment procedures\ndo not fully constrain the six degrees of freedom of the whole detector and no attempt was made to cor-\nrect to the average primary vertex position in the z direction. Because of this, the alignment procedure\ncan easily result in such a shift when comparing with truth information.\nThe values for the resolution are computed as the width of a Gaussian \ufb01t to the distributions in\nFig. 1 and are shown in Table 6. The resolution is degraded by residual misalignment, for both x and z\ndirections. Error scaling helps to partially recover the loss of performance for the \u201cRandom10\u201d scenario.\nx (mm)\n\u2206\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\nEntries\n0\n200\n400\n600\n800\n1000\nATLAS\nPerfect\nRandom10\nRandom10 + ES\nAligned\nAligned + ES\n(a) x-direction\nz (mm)\n\u2206\n-0.4\n-0.3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\nEntries\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nATLAS\nPerfect\nRandom10\nRandom10 + ES\nAligned\nAligned + ES\n(b) z-direction\nFigure 1: Primary vertex resolution, shown for the x direction (a) and z direction (b) for the various\nmisalignment scenarios. ES denotes error scaling.\nThe number of primary vertex outliers was also investigated. Since the shift observed when looking\nat the resolution should not affect reconstruction, the true vertex position must be corrected by this shift.\nIn the following, a primary vertex was \ufb02agged as \u201coutlier\u201d if the distance between the reconstructed\nvertex and the corrected true vertex position was greater than three sigma (30 \u00b5m in the x direction and\n150 \u00b5m in the z direction).\nThe percentage of outliers is shown in Table 7, which shows that residual misalignment introduces\nadditional outliers, and therefore indicates a degradation in the primary vertex \ufb01nding. The number of\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n470\n\nTable 6: Primary vertex resolution.\nSetup\nres. in x (\u00b5m)\nshift in x (\u00b5m)\nres. in z (\u00b5m)\nshift in z (\u00b5m)\nPerfect\n11.4\u00b10.1\n\u22120.13\u00b10.07\n51.1\u00b10.4\n\u22128.2\u00b10.3\nRandom10\n15.1\u00b10.1\n4.2\u00b10.1\n63.0\u00b10.4\n1.4\u00b10.4\nRandom10 + error scaling\n13.2\u00b10.1\n2.6\u00b10.1\n56.6\u00b10.4\n2.3\u00b10.4\nAligned\n13.9\u00b10.1\n\u22120.18\u00b10.09\n53.7\u00b10.4\n\u221291.5\u00b10.4\nAligned + error scaling\n13.8\u00b10.1\n\u22120.15\u00b10.09\n55.4\u00b10.4\n\u221291.6\u00b10.4\nTable 7: Fraction of primary vertex outliers.\nSetup\noutliers in x (%)\noutliers in z (%)\nPerfect\n1.7\u00b10.1\n4.1\u00b10.1\nRandom10\n5.5\u00b10.2\n8.3\u00b10.2\nRandom10 + error scaling\n2.8\u00b10.1\n6.1\u00b10.2\nAligned\n3.2\u00b10.1\n8.2\u00b10.2\nAligned + error scaling\n3.2\u00b10.1\n8.0\u00b10.2\noutliers is however partially diminished by the application of error scaling for \u201cRandom10\u201d. For the\n\u201cAligned\u201d scenario the corresponding scaling factors are much smaller than for \u201cRandom10\u201d and the\neffect of error scaling on the primary vertex performance is negligible.\n6\nEffects of misalignment on b-tagging performance\nFor the study of the impact of the residual misalignment on the b-tagging performance, several data sets\nwere produced with WH(mH = 120 GeV) and t\u00aft events. Eight cases were considered corresponding\nto each speci\ufb01c scenario of residual misalignment (\u201cPerfect\u201d, \u201cAligned\u201d, \u201cRandom10\u201d and \u201cRandom5\u201d)\nwith and without error scaling as described in Sections 2 and 3. The performance of the b-tagging has\nbeen assessed by looking at the rejection rate of light quarks at b-jet ef\ufb01ciencies of 50% and 60% using\nvarious tagging algorithms: IP2D, IP3D, SV1 and the combined tagger IP3D+SV1. A description of the\ndifferent taggers can be found in Ref. [2].\nFor each of the scenarios using WH(120) samples, 45,000 WH(120) \u2192\u00b5\u03bdbb events and 175,000\nWH(120) \u2192\u00b5\u03bduu events were used. The t\u00aft samples contained 50,000 events each with the exception of\nthe \u201cPerfect\u201d scenario without error scaling which had 570,000 events and the \u201cAligned\u201d scenario with\nerror scaling which had 500,000 events.\n6.1\nResults\nFigure 2 shows the b-jet ef\ufb01ciency versus light jet rejection for t\u00aft and WH(120) samples for the four\nmisalignment sets with and without error scaling. Rejections for the IP3D and IP3D+SV1 tagger at b-tag\nef\ufb01ciencies of 50% and 60% are tabulated in Table 8 for WH(120) and in Table 9 for t\u00aft.\nThe results for the IP3D+SV1 are also summarized in Fig. 3. As expected, the larger the misalign-\nment, the greater the degradation of the b-tagging performance. In the case of \u201cRandom10\u201d, which\nrepresents the highest amount of misalignment (shifts of 10 \u00b5m in the pixel r\u03c6 measurement direction),\nthere is almost a factor 2 drop in performance. For \u201cRandom5\u201d, where the level of misalignment is lower\n(shifts of the order of 5 \u00b5m), the decrease of the light jet rejection rates is lower than in the previous\ncase at around 30% degradation. For the \u201cAligned\u201d set the loss in performance is around 10 to 20%\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n471\n\nTable 8: Light jet rejection rates computed for b-jet ef\ufb01ciencies of 50% and 60% for the IP3D and\nIP3D+SV1 taggers for the various misalignment scenarios with and without error scaling (ES) for\nWH(120) events.\nRejection rate\nSetup\nIP3D (50%)\nIP3D (60%)\nIP3D+SV1 (50%)\nIP3D+SV1 (60%)\nPerfect\n211\u00b14\n67\u00b11\n399\u00b111\n104\u00b12\nPerfect + ES\n215\u00b15\n67\u00b11\n372\u00b111\n98\u00b12\nRandom10\n51\u00b11\n23\u00b11\n49\u00b11\n21\u00b11\nRandom10 + ES\n80\u00b11\n29\u00b11\n166\u00b13\n49\u00b11\nRandom5\n144\u00b13\n49\u00b11\n165\u00b13\n53\u00b11\nRandom5 + ES\n182\u00b17\n53\u00b11\n311\u00b116\n80\u00b12\nAligned\n193\u00b14\n62\u00b11\n300\u00b18\n84\u00b11\nAligned + ES\n190\u00b14\n62\u00b11\n306\u00b18\n87\u00b11\nTable 9: Standard light jet rejection rates computed for b-jet ef\ufb01ciencies of 50% and 60% for the IP3D\nand IP3D+SV1 taggers for the various misalignment scenarios with and without error scaling (ES) for t \u00aft\nevents.\nRejection rate\nSetup\nIP3D (50%)\nIP3D (60%)\nIP3D+SV1 (50%)\nIP3D+SV1 (60%)\nPerfect\n238\u00b111\n68\u00b12\n480\u00b130\n166\u00b16\nPerfect + ES\n244\u00b111\n70\u00b12\n474\u00b130\n161\u00b16\nRandom10\n86\u00b12\n32\u00b11\n95\u00b13\n38\u00b11\nRandom10 + ES\n71\u00b12\n25\u00b10\n242\u00b111\n77\u00b12\nRandom5\n192\u00b17\n56\u00b11\n290\u00b114\n95\u00b13\nRandom5 + ES\n133\u00b14\n46\u00b11\n360\u00b120\n116\u00b14\nAligned\n234\u00b110\n67\u00b12\n442\u00b127\n143\u00b15\nAligned + ES\n206\u00b18\n62\u00b11\n428\u00b124\n138\u00b15\nTable 10: Puri\ufb01ed light jet rejection rates computed for b-jet ef\ufb01ciencies of 50% and 60% for the IP3D\nand IP3D+SV1 taggers for the various misalignment scenarios with and without error scaling (ES) for t \u00aft\nevents.\nRejection rate\nSetup\nIP3D (50%)\nIP3D (60%)\nIP3D+SV1 (50%)\nIP3D+SV1 (60%)\nPerfect\n331\u00b119\n80\u00b12\n914\u00b186\n243\u00b112\nPerfect + ES\n332\u00b119\n80\u00b12\n872\u00b179\n234\u00b111\nRandom10\n97\u00b13\n34\u00b10\n106\u00b13\n41\u00b11\nRandom10 + ES\n76\u00b12\n26\u00b10\n316\u00b117\n89\u00b13\nRandom5\n250\u00b112\n62\u00b12\n387\u00b123\n113\u00b14\nRandom5 + ES\n154\u00b16\n50\u00b11\n558\u00b141\n148\u00b16\nAligned\n321\u00b118\n77\u00b12\n714\u00b159\n190\u00b18\nAligned + ES\n273\u00b114\n70\u00b12\n706\u00b156\n180\u00b17\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n472\n\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nPerfect\nPerfect + ES\nRandom10\nRandom10 + ES\nRandom5\nRandom5 + ES\nAligned\nAligned + ES\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight jet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nPerfect\nPerfect + ES\nRandom10\nRandom10 + ES\nRandom5\nRandom5 + ES\nAligned\nAligned + ES\nATLAS\nFigure 2: Light jet rejection versus b-tagging ef\ufb01ciency for the four different alignment sets for\nIP3D+SV1 for t\u00aft (left) and WH(120) (right). ES denotes error scaling.\nand lies somewhere between the \u201cPerfect\u201d alignment and the \u201cRandom5\u201d set. This is consistent with the\nlevel of misalignment suggested by the parameter c in the error tuning which is 3 \u00b5m in the pixel r\u03c6\nmeasurement direction.\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n100\n200\n300\n400\n500\nttbar With ES\nttbar No ES\nWH(120) With ES\nWH(120) No ES\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n20\n40\n60\n80\n100\n120\n140\n160\nttbar With ES\nttbar No ES\nWH(120) With ES\nWH(120) No ES\nATLAS\nFigure 3: Light jet rejections using IP3D+SV1 tagger for the four misalignment scenarios at b-tagging\nef\ufb01ciency working points of 50% (left) and 60% (right). Results are shown before and after error scaling\n(ES).\nThe rejections for WH(120) are systematically lower than that for t\u00aft as observed in other studies [2],\nhowever, in general they both show similar trends with misalignment. Some differences are observed\nwith the effects of error scaling which are discussed below. Results are shown mainly for t\u00aft, although\nsimilar conclusions are reached for both samples.\nFigure 4 shows the b-tag weight for IP3D+SV1 tagger for the different alignment scenarios. The\ndifferences between the \u201cAligned\u201d and \u201cPerfect\u201d sets are dif\ufb01cult to see in such plots but for the larger\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n473\n\nmisalignments (\u201cRandom10\u201d and \u201cRandom5\u201d) it is seen that the light jets have slightly larger weights\nwhile the b-jets have lower weights resulting in the loss of discrimination.\nJet weight\n-20\n-10\n0\n10\n20\n30\n40\nEntries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nRandom10 (b)\nRandom10 (light)\nRandom5 (b)\nRandom5 (light)\nAligned (b)\nAligned (light)\nPerfect (b)\nPerfect (light)\n(a) t\u00aft\nJet weight\n-20\n-10\n0\n10\n20\n30\n40\nEntries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nRandom10 (b)\nRandom10 (light)\nRandom5 (b)\nRandom5 (light)\nAligned (b)\nAligned (light)\nPerfect (b)\nPerfect (light)\nATLAS\n(b) WH(120)\nFigure 4: Jet weight distributions for the IP3D+SV1 tagger for the different alignment scenarios with\nerror scaling for t\u00aft (a) and WH(120) (b).\n6.2\nEffects of error scaling\nIt is observed in Fig. 3 that for the larger misalignment scenarios (\u201cRandom10\u201d and \u201cRandom5\u201d) the\nerror scaling gives a signi\ufb01cant improvement, while for the \u201cAligned\u201d and \u201cPerfect\u201d case the impact of\nerror scaling is small.\nFigure 5 compares the b-tag weights with and without error scaling. Only the \u201cRandom10\u201d results\nare shown. For the other scenarios the differences were less pronounced. The t\u00aft events show some\ndifferences in behaviour for the error scaling as compared with the WH events. For t\u00aft, the error scaling\nresults in only a small difference for the light jets while for the b-jets the differences are more evident.\nThis is in contrast with the WH events where the light jets show more differences and the b-jets are less\naffected.\nJet weight\n-20\n-10\n0\n10\n20\n30\n40\nEntries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nb-Jets (No ES)\nu-Jets (No ES)\nb-Jets (With ES)\nu-Jets (With ES)\n(a) \u201cRandom10\u201d, t\u00aft\nJet weight\n-20\n-10\n0\n10\n20\n30\n40\nEntries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nb-Jets (No ES)\nu-Jets (No ES)\nb-Jets (With ES)\nu-Jets (With ES)\nATLAS\n(b) \u201cRandom10\u201d, WH(120)\nFigure 5: Jet weight distributions for the IP3D+SV1 tagger comparing with and without error scaling\n(ES) for \u201cRandom10\u201d scenario for t\u00aft (a) and WH(120) (b).\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n474\n\nThe differences are thought to be associated with the pT spectra of light jets and b-jets which are\ndifferent from each other and different for the two event types. The effectiveness of the error scaling\nis expected to have some pT dependence since for lower pT, the multiple scattering will dominate and\ndifferences in hit errors will be less important. There was insuf\ufb01cient statistics in the samples however\nto verify if this was indeed the case.\nIn some cases the use of error scaling results in worse performance. This is discussed further in\nSection 6.4.\n6.3\nPuri\ufb01ed jets\nFor comparison with other studies [2] puri\ufb01ed jets were also studied. Puri\ufb01cation excludes labelling jets\nas light jets when there is a b-quark within a cone of 0.8. This gives a more physics independent measure\nof the performance (although differences will still be seen between samples because of the different pT\nand \u03b7 distributions of the jets contained in the samples). Table 10 shows the results for puri\ufb01ed jets for\nt\u00aft. For WH events only standard jets were considered as other studies [2] show similar results with and\nwithout puri\ufb01cation. Figure 6 compares standard and puri\ufb01ed jets for t\u00aft events and it can be seen that\nthe rejections are higher for puri\ufb01ed jets but the trends are similar for the different alignment scenarios.\nThe degradation of the \u201cAligned\u201d case with respect to the \u201cPerfect\u201d alignment is more pronounced after\npuri\ufb01cation (19 \u2013 23% degradation) than for the standard jets (10 \u2013 14% degradation). The effects of\nerror scaling showed similar behaviour for both standard and puri\ufb01ed jets.\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n200\n300\n400\n500\n600\n700\n800\n900\nttbar standard\nttbar purified\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n80\n100\n120\n140\n160\n180\n200\n220\n240\nttbar standard\nttbar purified\nATLAS\nFigure 6: Comparison of light jet rejections using IP3D+SV1 tagger for standard and puri\ufb01ed jets in t \u00aft\nevents. Left plot: 50% b-tag ef\ufb01ciency. Right plot: 60% b-tag ef\ufb01ciency.\n6.4\nComparison of the different taggers\nFigure 7 shows the rejections for different taggers for standard jets. The impact parameter based taggers\nare the most affected by misalignment with the \u201cAligned\u201d set showing 10 \u2013 20% lower rejections than\nthe \u201cPerfect\u201d case and up to a factor 3 degradation for the largest misalignment. After error scaling, the\nSV1 tagger shows rather uniform performance for all scenarios considered, with the \u201cAligned\u201d set giving\n10% degraded performance with respect to the \u201cPerfect\u201d case.\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n475\n\nWithout error scaling (see Fig. 8) the SV1 tagger shows signi\ufb01cant differences for the different align-\nment scenarios. The ratio between rejections with error scaling to those without error scaling is shown\nin Fig. 9. It can be seen that the error scaling has the most bene\ufb01cial effect with the larger misalignments\n(\u201cRandom10\u201d and \u201cRandom5\u201d) for the SV1 performance. For the \u201cAligned\u201d scenario the error scaling\nhas little effect while for the \u201cPerfect\u201d case it actually degrades the performance slightly. For the impact\nparameter based taggers the error scaling has a smaller effect on the b-tagging performance and even\ndegrades the performance in t\u00aft events.\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n100\n200\n300\n400\n500\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n20\n40\n60\n80\n100\n120\n140\n160\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nFigure 7: Comparison of the light jet rejections for the different taggers, IP2D, IP3D, SV1 and the\ncombined tagger IP3D+SV1. Left plot: 50% b-tag ef\ufb01ciency. Right plot: 60% b-tag ef\ufb01ciency. Results\nare with error scaling using t\u00aft events.\nDue to the bene\ufb01cial effect of the error scaling on the secondary vertexing, the overall performance\nof the combined tagger (IP3D+SV1) is also improved with error scaling in the case of the \u201cRandom10\u201d\nand \u201cRandom5\u201d sets. The error scaling parameter c is zero for the \u201cPerfect\u201d alignment and small for the\n\u201cAligned\u201d set and consequently for both cases the effect of error scaling on the performance of b-tagging\nfor the combined tagger is also small. For the \u201cAligned\u201d case, while the relative difference is smaller\nthan the hand-made sets, the error scaling degrades the performance slightly.\nThe reason for loss of performance with error scaling for some cases can be explained by the fol-\nlowing: since the error scaling will generally increase the errors, it will reduce the impact parameter\nsigni\ufb01cance. This is desirable for light jets as it will make them more compatible with zero impact pa-\nrameter. For b-jets, however, it also reduces the signi\ufb01cance and so will reduce the b-tagging ef\ufb01ciency\nfor a given weight cut, or in other words, one needs a lower weight cut to obtain the same ef\ufb01ciency and\nhence results in lower rejection for light jets for a given b-jet ef\ufb01ciency. The overall effect depends on\nthese two competing effects and so can potentially lead to a loss in performance. While a decrease in\nperformance with error scaling was observed in t\u00aft events for the IP2D and IP3D taggers, the opposite\nwas observed for WH events. As was already discussed above for the b-tag weight in Fig. 5, the error\nscaling affects the light jets and b-jets in the two physics samples differently and this is thought to lead\nto the differences in the error scaling behaviour seen here.\nThe effect of error scaling on the secondary vertex tagger will be to recover some secondary vertices\nwhich would have otherwise failed quality cuts due to an underestimated error. One will lose some true\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n476\n\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n100\n200\n300\n400\n500\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n20\n40\n60\n80\n100\n120\n140\n160\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nFigure 8: As in Fig. 7 but without error scaling.\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nRatio rejection with ES/without ES\n0.5\n1\n1.5\n2\n2.5\n3\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nRatio rejection with ES/without ES\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nIP3D+SV1\nIP3D\nIP2D\nSV1\nATLAS\nFigure 9: Ratio of rejections with error scaling to rejections without error scaling. Left plot: 50% b-tag\nef\ufb01ciency. Right plot: 60% b-tag ef\ufb01ciency.\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n477\n\nsecondary vertices that are close to the primary vertex as the larger error will make them compatible with\nthe primary vertex, however for similar reasons it will result in fewer fake secondary vertices close to the\nprimary vertex.\n6.5\nEffects of recalibration\nThe taggers require probability distribution functions for light jets and b-jets as described in Ref. [2]\nand the process of obtaining the set of these reference distributions is known as calibration. The results\npresented here use the same set of calibrations as used in Ref. [2]. Since misalignments will alter these\ndistributions, it is possible that one can obtain some more discriminating power by recalibrating using\nthe misaligned sample. Methods for obtaining these calibrations from real data are explored in Ref. [3].\nTo investigate whether recalibrating results in any gain in performance, a new set of reference dis-\ntributions was obtained for each sample with and without error scaling. In practice one should use\nindependent samples to calibrate and to test the performance, however, here the reference distributions\nwere obtained with the same or a subset of the sample used to measure the performance.\nAs seen in Fig. 10 recalibration gives better performance, although after error scaling the difference\nbetween the \ufb01xed calibration and recalibration is only marginal.\nOne might expect that recalibration may compensate any miscalculation of the errors in a similar\nway to the error scaling. This is only partially the case as can be seen in Fig. 11, where the relative\nimprovement with error scaling is reduced when recalibrating.\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n250\n300\n350\n400\n450\n500\nFixed calib.\nRe-calib.\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nLight jet rejection\n80\n100\n120\n140\n160\nFixed calib.\nRe-calib.\nATLAS\nFigure 10: Comparison of the light jet rejection obtained for the IP3D+SV1 tagger using a \ufb01xed calibra-\ntion or recalibrating for each separate sample. Left plot: 50% b-tag ef\ufb01ciency. Right plot: 60% b-tag\nef\ufb01ciency.\n7\nConclusion\nThe effect of misalignment on the tracking performance, as measured by tracking ef\ufb01ciency and fake\nrates, was small, and error scaling recovered the performance almost to the level that was seen with\nthe perfect alignment. The degradation of the primary vertex was more signi\ufb01cant, with resolutions\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n478\n\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nRatio rejection with ES/without ES\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\nFixed cal b.\nRe-calib.\nATLAS\nAlignment set\nRandom10\nRandom5\nPerfect\nAligned\nRandom10\nRandom5\nPerfect\nAligned\nRatio rejection with ES/without ES\n1\n1.2\n1.4\n1.6\n1.8\n2\nFixed cal b.\nRe-cal b.\nATLAS\nFigure 11: Ratio of rejections with error scaling to rejections without error scaling. Results are shown\nfor the IP3D+SV1 tagger. Left plot: 50% b-tag ef\ufb01ciency. Right plot: 60% b-tag ef\ufb01ciency. Compares\nusing a \ufb01xed calibrations and recalibrating for each separate sample.\nabout 2.5 \u00b5m degraded and an increase in the number of outliers. The \u201cAligned\u201d set showed similar\nperformance to the \u201cRandom10\u201d despite better b-tagging performance.\nThe performance of b-tagging was clearly degraded with misalignment and the amount of degrada-\ntion was found to be roughly proportional to the amount of random displacement of modules. Systematic\neffects are expected to also play an important role, however, the random displacement was the only as-\npect that was quanti\ufb01ed in this study by the parameter c obtained in the error scaling procedure. In\norder to disentangle the contributions from random and systematic effects it would be necessary to create\ndedicated residual misalignment sets with known systematic distortions.\nThe impact parameter based taggers were observed to be the most affected by misalignment and\nthe introduction of error scaling brought little or even negative bene\ufb01t to the b-tagging performance in\nthe case of t\u00aft events. Error scaling was important for the performance of the secondary vertex \ufb01nd-\ning, and without it, for larger misalignments the degradation for the secondary vertex based tagger was\nsigni\ufb01cant. With error scaling most of the degradation was recovered and the secondary vertex tagger\nshowed uniform performance for all alignment scenarios considered. The behaviour of the combined\ntagger, IP3D+SV1, follows what one might conclude from the behaviour of the separate taggers, that is,\nit bene\ufb01ts from error scaling but shows a degradation with misalignment even after error scaling.\nThe \u201cAligned\u201d set was the most realistic misalignment scenario studied here and the results were\nencouraging with rather moderate degradation in the b-tagging performance. In puri\ufb01ed jets from t \u00aft,\nthe degradation was more evident with 19% loss of rejection at 50% b-tagging ef\ufb01ciency. However, in a\nmore realistic environment, as seen by looking at standard jets, the amount of degradation was only 10%.\nAt 60% b-tagging ef\ufb01ciency, the loss of rejection was slightly larger with 23% degradation for puri\ufb01ed\njets and 14% degradation for standard jets. For WH events the loss of rejection was similar with around\n18% degradation at 50% b-tagging ef\ufb01ciency and 11% degradation at 60% b-tagging ef\ufb01ciency.\nThe amount of residual misalignment remaining after applying the actual alignment procedures re-\nsulted in only a small loss of performance and so misalignments are not expected to cause a major\nproblem for doing b-tagging in ATLAS.\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n479\n\nReferences\n[1] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003\n[2] ATLAS Collaboration, b-Tagging Performance, this volume.\n[3] ATLAS Collaboration, b-Tagging Calibration with t\u00aft Events, this volume.\nb-TAGGING \u2013 EFFECTS OF MISALIGNMENT ON b-TAGGING\n480\n\nSoft Muon b-Tagging\nAbstract\nb-jets can be identi\ufb01ed by taking advantage of the presence of a muon coming\nfrom the semi-leptonic decay of the b hadrons. This note describes a soft muon\ntagging algorithm and its performance when applied to different Monte Carlo\nphysics samples in ATLAS. A b-jet tagging ef\ufb01ciency of about 10% (includ-\ning the inclusive b \u2192\u00b5\u03bdX branching ratio of \u224820%) is achieved for a light\njet rejection of better than 300. The effect of pile-up events and cavern back-\nground on the performance is also considered and is found to be signi\ufb01cant but\nmanageable.\n1\nIntroduction\nSoft-lepton tagging relies on the semi-leptonic decays of b and c hadrons. Indeed the presence of a\nmuon is enhanced in b-jets thanks to the signi\ufb01cant semi-leptonic decay branching ratio of b hadrons\n(BR(b \u2192\u00b5\u03bdX) \u224811%), and of c hadrons produced by the b hadron decay (sequential semi-leptonic\ndecay, BR(b \u2192c \u2192\u00b5\u03bdX) \u224810%). A soft muon tagger, while intrinsically limited by the small semi-\nleptonic branching ratio, offers a good alternative or complement to the more performant lifetime taggers.\nThanks to its good purity and low correlation with lifetime taggers, it can be used to do cross-calibrations\nof the two types of tagger [1], or to enhance the lifetime tagger performance by combining the two.\nFinally, it permits derivation of speci\ufb01c jet energy corrections [2].\nThe properties of the soft muons and of the various backgrounds are shown in Section 2. The al-\ngorithm is then described in detail in Section 3 while its performance applied to different Monte Carlo\nsamples is discussed in Section 4.\n2\nProperties of muons from semi-leptonic decays and their backgrounds\nThere are three sources of background from particles within light jets: muons coming from the decay\nof light hadrons (mostly pions), hadrons managing to go through the calorimeter and reaching the muon\nspectrometer (\u201cpunch-through\u201d), and hits caused by the neutron gas that will be surrounding the detector\nduring data taking, producing fake tracks in the muon spectrometer (\u201ccavern background\u201d). c-jets are\nalso a source of background as far as b-tagging is concerned. Figures 1, 2, 3, and 4 show, respectively,\nthe distance to the closest jet \u2206R =\np\n\u03b72 +\u03c6 2, the muon transverse momentum, the impact parameter,\nand the transverse momentum relative to the closest jet axis prel\nT , for muons from (direct) b decays,\nsequential b \u2192c \u2192\u00b5\u03bdX decays, c decay, light hadron decays, and fake muons, in jets of ET > 15GeV\nand |\u03b7| < 2.5 in t\u00aft events. prel\nT is de\ufb01ned as the muon momentum in the plane orthogonal to the jet axis,\nwhere the jet axis is corrected for the presence of a muon by adding the muon momentum to the jet\nmomentum. Contributions from true muons are estimated at the generator level while fake muons are\nestimated with the full simulation and de\ufb01ned as a reconstructed muon associated with a jet while no\nmuon of momentum larger than 2 GeV was found at the generator level within \u2206R = 0.6 of that same jet.\nNote that the distinction between fake muons and muons from light hadron decays is somewhat arbitrary\nsince the latter can also be produced in the calorimeter as part of the hadronic shower; such muons are\npresent in the full simulation but are not distinguished from fake muons because long-lived particles and\nshowers are taken care of by GEANT and the full GEANT information was not available in the present\nstudy. Muons produced by direct b hadron decays have a signi\ufb01cantly larger transverse momentum than\nthe various backgrounds, especially muons from light hadron decays; additionally, since light hadrons\nsuch as charged pions and charged kaons have a long lifetime, those muons tend to have a large impact\n481\n\nparameter. Those two properties will be used to reject this important background ef\ufb01ciently. Thanks to\nthe b hadrons high mass, muons from direct b decays tend to be more boosted in a plane transverse to the\njet axis, i.e. have a larger prel\nT than the backgrounds. This property is used in the tagger to further separate\nb-jets from light jets through a likelihood technique. It is important to note that muons from sequential b\ndecay are much more dif\ufb01cult to separate from background since they have a much softer spectrum both\nin pT and prel\nT than those from direct b decay. Finally, Fig. 5 shows that the prel\nT distribution in t\u00aft and WH\nevents is very similar. Indeed the prel\nT variable is not very correlated with the jet ET or pseudo-rapidity.\nThus it is not very dependent on the process producing the b-jets.\n-jet\n\u00b5\nR\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \nATLAS\nFigure 1: Distribution of \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 between closest jet and muons from b hadron decays, c\nhadron decays, light hadron decays, and fakes, in jets of ET > 15GeV and |\u03b7| < 2.5 in t\u00aft events. The red\nline shows the cut applied for the basic selection described in Section 3. All histograms in Fig. 1 to 5 are\nnormalized to unity.\n3\nDescription of the algorithm\nThe algorithm works in three steps, described in the following sections:\n\u2022 The standard muon reconstruction algorithms are used to identify muons.\n\u2022 Muons satisfying some basic requirements are then associated to jets.\n\u2022 Finally, a 1-dimensional likelihood ratio using the prel\nT variable discriminates further signal from\nbackground.\n3.1\nMuon reconstruction\nTwo complementary muon reconstruction algorithms are used by the soft-muon tagger: so-called \u201ccom-\nbined\u201d muons, which correspond to a track fully reconstructed in the muon spectrometer and matched\nwith a track in the inner detector; and \u201ctagged\u201d muons, which cannot reach the muon middle and outer\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n482\n\n (GeV)\nT\nMuon p\n0\n5\n10\n15\n20\n25\n30\n35\n40\nArbitrary Units\n-3\n10\n-2\n10\n-1\n10\n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \nATLAS\nFigure 2: Transverse momentum distribution of muons from b hadron decays, c hadron decays, light\nhadron decays, and fakes, in jets of ET > 15GeV and |\u03b7| < 2.5 in t\u00aft events. The last bin includes\nover\ufb02ows. The red line shows the cut applied for the basic selection described in Section 3.\nMuon Impact Parameter (mm)\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nArbitrary Units\n-3\n10\n-2\n10\n-1\n10\n1\n10\n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \nATLAS\nFigure 3: Impact parameter distribution of muons from b hadron decays, c hadron decays, light hadron\ndecays, and fakes, in jets of ET > 15GeV and |\u03b7| < 2.5 in t\u00aft events. The last bin includes over\ufb02ows. The\nred line shows the cut applied for the basic selection described in Section 3.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n483\n\n (GeV)\nT\nrel\nMuon p\n0\n0.5\n1\n1.5\n2\n2.5\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \n X\n\u03bd \n\u00b5\n \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\n c \n\u2192\nb \n X\n\u03bd \n\u00b5\n \n\u2192\nc \n X\n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n\u00b5\nFake \nATLAS\nFigure 4: Distribution of the transverse momentum relative to the jet axis of muons from b hadron decays,\nc hadron decays, light hadron decays, and fakes, in jets of ET > 15GeV and |\u03b7| < 2.5 in t\u00aft events. The\nlast bin includes over\ufb02ows.\n (GeV)\nT\nrel\nMuon p\n0\n0.2\n0.4 0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n X\n\u03bd \n\u00b5\n ) \n\u2192\n (c \n\u2192\n, b \ntt\n X\n\u03bd \n\u00b5\n ) \n\u2192\n (c \n\u2192\nWH, b \n\u00b5\n X and fake \n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n, \ntt\n\u00b5\n X and fake \n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\nWH, \n X\n\u03bd \n\u00b5\n ) \n\u2192\n (c \n\u2192\n, b \ntt\n X\n\u03bd \n\u00b5\n ) \n\u2192\n (c \n\u2192\nWH, b \n\u00b5\n X and fake \n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\n, \ntt\n\u00b5\n X and fake \n\u03bd \n\u00b5\n \n\u2192\n/K \n\u03c0\nWH, \nATLAS\nFigure 5: Distribution of the transverse momentum relative to the jet axis of muons from b hadron decays\nand from background sources, in jets of ET > 15GeV and |\u03b7| < 2.5 for t\u00aft events and WH events. The\nlast bin includes over\ufb02ows.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n484\n\nstations and are identi\ufb01ed by matching an inner detector track with a segment in the muon inner sta-\ntions only. The ATLAS muon spectrometer is able to fully reconstruct muons of momentum larger than\nabout 5 GeV, providing a precise measurement of its momentum, allowing \u2013 in combination with the\ninner detector track \u2013 a very good rejection of the combinatoric background in the dense environment of\njets. Muon spectrometer tracks that fail to be combined with an inner detector track are not used by the\nsoft-muon tagger because of the contamination from fakes and muons from light hadron decays. Tagged\nmuons are less pure than combined muons but allow one to recover some ef\ufb01ciency in the crucial low\nmomentum range. Thus both combined muons and tagged muons are used by the soft-muon tagger. For\nmore details of muon reconstruction and identi\ufb01cation, see Ref. [3].\n3.2\nJet-muon association and basic selection\nMuons are associated with the closest jet (in \u03b7 \u00d7 \u03c6) in the event (only jets with ET > 15 GeV and\n|\u03b7| < 2.5 are considered) and the jet-muon pair is required to satisfy \u2206R(jet-muon)< 0.5. Additionally,\nmuons are required to satisfy the following requirements:\n\u2022 Impact parameter with regard to the primary vertex |d0| < 4 mm\n\u2022 pT > 4 GeV\n\u2022 Matching between the muon spectrometer and inner detector tracks of \u03c7 2/dof < 10\n3.3\nLikelihood ratio\nMuons from semi-leptonic b-decays are further separable because of their particular kinematics. As\nshown in Section 1, the muon transverse momentum relative to the jet (prel\nT ) is a good discriminant vari-\nable, and it is used in a likelihood ratio to discriminate between the b and light jet hypotheses. No attempt\nwas made to speci\ufb01cally discriminate between b- and c-jets. The prel\nT probability density functions were\nestimated on fully simulated t\u00aft and WH \u2192\u00b5\u03bdb\u00afb/WH \u2192\u00b5\u03bdu \u00afu samples of several hundred thousand\nevents and are shown in Fig. 6 and 7 for tagged and for combined muons separately. Here pile-up and\ncavern background are omitted. The normalized variable prel\nT /(prel\nT +0.5GeV) is used instead of prel\nT in\norder to facilitate the smoothing of the probability density functions. The likelihood is found to be less\ndiscriminating for tagged muons than for combined muons because muons at low momentum tend to\nbe produced by b \u2192c \u2192\u00b5X sequential decays, which also tend to yield a smaller prel\nT as shown in the\nprevious section. This is visible in the probability density function as a second peak at a value of \u22480.5\n(compared to \u22480.7 for direct b \u2192\u00b5X decays).\nEach likelihood is normalized with the probability\n(estimated on the same fully simulated samples) that a reconstructed muon be associated with a jet of a\ngiven \ufb02avor. For each type of reconstructed muon (tagged or combined), the likelihood ratio Q can be\nwritten as follows:\nQ = \u03b50\nb \u00d7L(prel\nT |b)\n\u03b50\nl \u00d7L(prel\nT |l)\nwhere \u03b50\nb (\u03b50\nl ) is the fraction of b-jets (light jets) that contain a muon satisfying the basic selection and\nL(prel\nT |b) (L(prel\nT |l)) is the probability density function for a b-jet (light jet). It was found that \u03b5 0\nb/\u03b50\nl \u22486.6\nfor tagged muons and \u03b50\nb/\u03b50\nl \u224844.4 for combined muons, re\ufb02ecting the fact that combined muons are\npurer and contribute to a large fraction of the ef\ufb01ciency.\nSeveral muons can be associated with a jet. In such a case, the muon with highest transverse momen-\ntum is considered. At this point, no attempt has been made to use the information given by the presence\nof an additional muon in the jet.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n485\n\n+0.5 GeV)\nT\nrel\n/(p\nT\nrel\np\n0\n0.1 0.2 0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nProbability\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nb-Jets\nLight Jets\nFigure 6: Probability density function used in the algorithm likelihood for the prel\nT variable, for the tagged\nmuons.\n+0.5 GeV)\nT\nrel\n/(p\nT\nrel\np\n0\n0.1 0.2 0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nProbability\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\nb-Jets\nLight Jets\nFigure 7: Probability density function used in the algorithm likelihood for the prel\nT\nvariable, for the\ncombined muons.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n486\n\n4\nPerformance\nThe algorithm performance was estimated on t\u00aft and WH \u2192\u00b5\u03bdb\u00afb/WH \u2192\u00b5\u03bdu \u00afu Monte Carlo samples\nof several hundred thousand events. The jet \ufb02avor is determined at the generator level by matching\nreconstructed jets with quarks considered after \ufb01nal state radiation (for details, see Ref. [4]). Figures 8\nand 9 show the b-tagging ef\ufb01ciency and the light jet tagging rate, respectively, with and without a cut\non the likelihood ratio, as a function of jet ET and pseudorapidity in t\u00aft events. An average b-tagging\nef\ufb01ciency of 10% is reached for a cut on the likelihood ratio of lnQ > 3.05, which corresponds to\nrejecting all tagged muons and selecting combined muons with prel\nT > 360 MeV. No requirement on\nthe b decay is made, so that the b-tagging ef\ufb01ciency includes the semi-leptonic branching ratios as well\nas the jet-muon association ef\ufb01ciency, the detector acceptance, and the muon reconstruction ef\ufb01ciency\nand selection. Likewise, the light jet tagging rate includes both light hadron decay muons and fake\nmuons. The b-tagging ef\ufb01ciency tends to decrease as the jet ET increases, mostly because of a drop\nin the tracking ef\ufb01ciency of the inner detector in highly collimated jets. Not surprisingly, the light jet\ntagging rate increases signi\ufb01cantly with the jet ET. After the basic selection stage, light hadron decays\naccount for 8% (1.6%) of combined muons (tagged muons) present in tagged light jets in t\u00aft events.\n\u03b7\nJet \n-3\n-2\n-1\n0\n1\n2\n3\nb-Tagging Efficiency\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\nAll tags\nln Q > 3.05\n (GeV)\nT\nJet E\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nb-Tagging Efficiency\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\nAll tags\nln Q > 3.05\nFigure 8: Probability for a b-jet to be tagged by the soft-muon tagger as a function of jet pseudorapidity\n(left) and transverse energy (right: the last bin includes over\ufb02ows) without and with a requirement on the\nlikelihood ratio corresponding to an average b-tagging ef\ufb01ciency of 10%.\n\u03b7\nJet \n-3\n-2\n-1\n0\n1\n2\n3\nLight Jet Tagging Rate\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\n0.007\nATLAS\nAll tags\nln Q > 3.05\n (GeV)\nT\nJet E\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\nLight Jet Tagging Rate\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\nATLAS\nAll tags\nln Q > 3.05\nFigure 9: Probability for a light jet to be tagged by the soft-muon tagger as a function of jet pseudora-\npidity (left) and transverse energy (right, the last bin includes over\ufb02ows) without and with a requirement\non the likelihood ratio corresponding to an average b-tagging ef\ufb01ciency of 10%.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n487\n\nFigures 10 and 11 show the b-tagging ef\ufb01ciency vs light jet rejection (the inverse of the light jet\ntagging rate) for different cuts on the likelihood ratio. Figure 10 compares the performance in t \u00aft and WH\nevents. The rejection for a given ef\ufb01ciency is slightly better in t\u00aft events than in WH events, due to the\nfact that jets in t\u00aft events are more central, while the tagger performance is degraded in the forward region\nof the detector. The soft-muon tagger reaches a rejection of about 300 in WH events and 380 in t\u00aft events\nfor an ef\ufb01ciency of 10%.\nFigure 11 shows the effect of pile-up (the superposition of several events occuring within the same\nbunch crossing) and cavern background on the tagger performance. Here, only jets matched to the hard-\nscatter process quarks are considered in order to make a fair comparison of the algorithm performance\nwith and without cavern background and pile-up. Indeed, soft jets from pile-up events tend to have a\nlower light jet tagging rate and would bias the comparison. For a luminosity of 2\u00d71033cm\u22122\u00b7s\u22121, pile-\nup and cavern background decrease the rejection by about 15% (for a given ef\ufb01ciency of 10%), which is\nsigni\ufb01cant but not dramatic.\nb-jet efficiency\n0.04 0.05 0.06 0.07 0.08 0.09\n0.1\n0.11 0.12\nLight-jet rejection\n2\n10\n3\n10\n4\n10\nWH (120 GeV)\ntt\nATLAS\nFigure 10: b-tagging ef\ufb01ciency vs light jet rejection estimated in t\u00aft and WH (without pile-up/cavern\nbackground).\nPerformance will have to be evaluated in data, using techniques similar to those developed at the\nTevatron [5]. The muon reconstruction ef\ufb01ciency can be measured using a tag-and-probe method ap-\nplied to J/\u03c8 and Z samples. The light jet tagging rate may be measured using jet events, although\ndisentangling background from heavy-\ufb02avor muons is a complex issue. Jet samples may also be used to\ntest the likelihood probability distribution functions against data. Those issues have not been studied in\nthe context of soft muon tagging in ATLAS yet.\n5\nConclusion\nThe soft-muon tagger developped for the ATLAS detector shows excellent performance across a large jet\nET spectrum, with a light jet rejection of more than 300 for a b-tagging ef\ufb01ciency of 10%. The event pile-\nup and the cavern background appear to have a signi\ufb01cant but not dramatic effect on the performance,\nwith a decrease of about 15% on the light jet rejection at a luminosity of 2\u00d71033cm\u22122\u00b7s\u22121.\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n488\n\nb-jet efficiency\n0.08\n0.09\n0.1\n0.11\n0.12\nLight-jet rejection\n2\n10\n3\n10\ntt\n with pile-up and cavern bgd\ntt\nATLAS\nFigure 11: b-tagging ef\ufb01ciency vs light jet rejection estimated on a t\u00aft sample with and without pile-\nup/cavern background.\nReferences\n[1] ATLAS Collaboration, \u2018b-Tagging Calibration with Jet Events\u2019, this volume.\n[2] ATLAS Collaboration, \u2018Detector Level Jet Corrections\u2019, this volume.\n[3] ATLAS Collaboration, \u2018Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples\u2019, this volume.\n[4] ATLAS Collaboration, \u2018b-Tagging Performance\u2019, this volume.\n[5] D. Acosta et al., The CDF Collaboration, Phys. Rev. D72, 032002 (2005).\nb-TAGGING \u2013 SOFT MUON b-TAGGING\n489\n\nSoft Electron b-Tagging\nAbstract\nThe presence of an electron coming from the semi-leptonic decay of a B hadron\ncan be used to tag b-jets. This note describes a soft electron tagging algorithm\nand its performance when applied to ATLAS Monte Carlo simulation data. Jets\nare built from the energy reconstructed in the electromagnetic and hadronic\ncalorimeters with a cone algorithm. Electrons, reconstructed by a track-seeded\nalgorithm, are sought among charged tracks associated to the jets. The tagging\nof jets originating from b quarks is based on kinematics and on the identi-\n\ufb01cation capabilities of the inner tracker and the electromagnetic calorimeter.\nThe performance of the electron identi\ufb01cation and b-tagging procedure are\npresented. A b-jet tagging ef\ufb01ciency of about 7% (including the inclusive\nb \u2192e\u03bdX branching ratio of \u223c20%) is achieved for a light jet rejection of\nbetter than 100.\n1\nIntroduction\nA variety of interesting physics processes at LHC, such as the H \u2192b\u00afb decay for an intermediate Higgs\nboson mass range, top physics or searches for new physics require ef\ufb01cient identi\ufb01cation of b-quarks.\nThe performance of b-tagging algorithms in ATLAS are studied in Ref. [1]. The semi-leptonic decays\nof heavy quarks provide a clean signature used to identify the \ufb02avour composition of jets. The semi-\nleptonic decay modes are b \u2192\u2113, c \u2192\u2113and the cascade decay b \u2192c \u2192\u2113. Electrons produced in b\ndecays (through direct and cascade decays) can be detected using the electromagnetic calorimeter and\nthe inner detector. Since these electrons are non-isolated and with low transverse momentum, excellent\nelectron/hadron separation capability is required. As a b-\ufb02avour tag, the lepton tag is not competitive\nwith the lifetime tag because the branching ratio is low for such decays (about 20% for B-meson decays\nto leptons, including cascade decays, per lepton family) and is limited by the ef\ufb01ciency to reconstruct\nand identify electrons within jets. Still this method can be used with the vertex algorithms to provide a\ncomplement to the overall b-tagging performance and for cross-checks and calibration.\nThe note is organised as follows. Monte Carlo data samples used in this analysis are described in\nSection 2. The jet and track selections are described in Section 3. The electron identi\ufb01cation algorithm\nis described in Section 4. The b-tagging algorithm and its performance are described in Section 5.\n2\nMonte Carlo samples\nThe samples used in this study contain events with electrons in jets from Higgs boson associated pro-\nduction WH, with W \u2192\u00b5\u03bd. We take the mass of the Higgs boson to be mH = 120 GeV. The signal\nsample consists of H \u2192b\u00afb events and the background sample of H \u2192u \u00afu events. Another sample of\nH \u2192b\u00afb events is enriched in true electrons with a \ufb01lter at the generation level. This \ufb01lter is de\ufb01ned as\nfollows: both b quarks (before \ufb01nal state radiation, FSR) are required to have a transverse momentum\npb\nT > 15 GeV and a pseudorapidity |\u03b7b| < 2.5; at least one true electron with pe\nT > 1 GeV is required to\nbe found in a cone \u2206R < 0.4 around each b-quark direction (before FSR). This sample will be used only\nin Section 4 to model signal electrons with enough statistics.\nAll samples have been generated using the PYTHIA 6.403 [2] Monte Carlo event generator. More\ndetails on the Monte Carlo generators used can be found in [3]. Data have been passed through a full\ndetector simulation based on GEANT4. No pile-up has been included but its effect on performance,\nbased on previous studies, is mentioned below where relevant.\n490\n\nThe signal electrons come from direct (b \u2192e) and cascade (b \u2192c \u2192e) semi-leptonic decays of\nB-hadrons. Apart from the previous sources, there are also some other sources1, mainly b \u2192\u03c4 \u2192e and\nb \u2192(J/\u03c8,\u03c8\u2032) \u2192e+e\u2212. The background electrons arise from \u03c00 Dalitz decays, \u03b3-conversions occurring\nin the inner detector and decays of light hadrons. The fraction of electrons from photon conversions\nbecomes substantial at large pseudo-rapidities and large transverse momenta.\nDistributions of true transverse momentum, pT, and pseudo-rapidity, \u03b7, for electrons and pions are\nshown in Fig. 1 for the samples considered. Table 1 shows the mean values of the true transverse mo-\n (GeV)\nT\np\n5\n10\n15\n20\n25\n30\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nATLAS\n\u03b7\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\nFigure 1: Normalized distributions of true transverse momentum pT (left) and pseudo-rapidity \u03b7 (right)\nare shown for signal electrons (hatched histograms), electrons from conversions (dotted line histograms)\nand pions (plain histograms).\nmentum distributions for signal and background electrons and pions in the two samples.\nTable 1: The mean true pT (in GeV) for electrons and pions in various data samples.\nsample\nelectrons\npions\nB hadrons\nD hadrons\n\u03b3-conversions and \u03c00 Dalitz\nother sources\nH \u2192bb\n10.8\n11.9\n4.9\n7.3\n5.9\nH \u2192u \u00afu\n-\n-\n5.2\n4.2\n7.1\n3\nJet and track selection\nThe reconstruction of the various objects needed for b-tagging and the estimation of its performance are\nsummarized in this section. The reconstruction of soft electrons will be detailed in the next section.\nWe follow the default jet reconstruction and labelling procedure described in Ref. [1]. Jets are re-\nconstructed in the calorimeters using a standard cone algorithm with a size of \u2206R = 0.4. Jets with\npT > 15 GeV and |\u03b7| < 2.5 are considered for b-tagging. To assess quantitatively the b-tagging perfor-\nmance, Monte-Carlo information is used to determine the type of parton (a quark-based labelling) from\nwhich a jet originates. Jets are labelled as b-jets if a b quark with pT > 5 GeV (after FSR) is found in a\ncone \u2206R = 0.3 around the jet direction. The labelling for c-jets (and \u03c4-jets) is done in the same way. By\nlight jets we denote all other reconstructed jets.\n1The corresponding branching ratios [4] are Br(b \u2192\u2113\u2212) = (10.71\u00b10.22)%, Br(b \u2192c \u2192\u2113+) = (8.01\u00b10.18)%, Br(b \u2192\n\u00afc \u2192\u2113\u2212) = (1.62+0.44\n\u22120.36)%, Br(b \u2192\u03c4 \u2192e) = (0.419\u00b10.055)% and Br(b \u2192(J/\u03c8,\u03c8\u2032) \u2192e+e\u2212) = (0.072\u00b10.006)%.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n491\n\n number of tracks in jets\n0\n2\n4\n6\n8\n10\n12\n14\n \n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\n of jet (GeV)\nT\n p\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n \n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\nATLAS\nFigure 2: Track multiplicity in jets (left) and jet transverse momentum (right) for b jets (hatched his-\ntograms) and light jets (solid line). Only jets having at least one good quality track with pT > 2 GeV are\nconsidered.\nFor the soft electron b-tagging algorithm, a track-based electron reconstruction algorithm is used and\nwill be described in the next section. In order to be able to identify track candidates as electrons, strict\ntrack selection criteria are applied and called hereafter good track quality cuts. To reduce the number of\nfake candidates in jets, only tracks with pT > 2 GeV are considered. The inner detector coverage extends\nto pseudo-rapidity values of \u00b12.5, except for the transition radiation tracker (TRT) which extends up to\n\u00b12. This sub-detector is crucial in the identi\ufb01cation procedure, so the track selection requires |\u03b7| < 2.\nTracks are required to have at least nine precision hits (pixels and SCT), at least two hits in the pixel\ndetector, at least one hit in the vertexing layer (the so-called b-layer) and an unsigned transverse impact\nparameter at the perigee smaller than 1 mm. The TRT may record either of two types of hits, \u2018low-\nenergy\u2019 hits which are used for track reconstruction and \u2018high-energy\u2019 hits which are used for electron\nidenti\ufb01cation. Selection criteria thus require at least 20 low-energy hits and at least one high-energy hit\nin the TRT detector along the track. After this selection, only about 50% of initial tracks remain. About\n50% of actual b-jets and 60% of light jets, in the WH sample, have no good quality track associated.\nFigure 2 shows the multiplicity of good quality track inside jets and the jet transverse momenta. For jets\nhaving at least one good quality track the mean multiplicity is 3.8 (3.3) for b-jets (light jets). Light jets,\nwhich include ISR, FSR and underlying events, have a softer transverse momentum than b jets, which\nare originated from the H decay, with a mean pT of 51 GeV against 57 GeV, but with a large spread, an\nRMS of \u223c35 GeV.\nThe fraction of jets containing electrons with a good quality track is given in Table 2 for signal and\nbackground samples.\nTable 2: Fraction of jets (in %) with an electron at the generator level that also have a good quality track,\nfor the signal and background samples.\nSample\n\u03b3-conversions and \u03c00 Dalitz\nB hadrons\nD hadrons\nOther sources\nH \u2192b\u00afb\n1.6\n3.4\n2.2\n0.3\nH \u2192u \u00afu\n1.3\n< 10\u22124\n< 10\u22124\n0.1\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n492\n\n4\nElectron reconstruction and identi\ufb01cation\nThe standard electron reconstruction procedure [5] is based on calorimeter clusters, with a subsequent as-\nsociation to tracks. While this method is ef\ufb01cient for high-energy isolated electrons, such as those arising\nfrom W or Z decays, it is not effective for electrons inside hadronic jets, such as those from semi-leptonic\ndecays. Indeed hadron and electron showers tend to overlap in collimated jets so that electron cluster\ncharacteristics are obscured. An alternative procedure takes full advantage of the tracking capabilities\nof the inner detector as well as the granularity of the electromagnetic calorimeter. The method relies\non the extrapolation of reconstructed charged particle trajectories into the electromagnetic calorimeter.\nThe most common background processes for producing electron-like showers in the calorimeters were\ndescribed in Section 2. Because the development of showers is different for electrons and hadrons, the\nelectron identi\ufb01cation algorithm incorporates variables that describe the shower shapes, quality of the\nmatch between the track and its corresponding cluster, and the fraction of high-energy hits in the tran-\nsition radiation tracker. This algorithm is used also for the reconstruction of low pT electrons in J/\u03c8\nevents [6].\n4.1\nElectron reconstruction\nAll the tracks that pass the good track quality cuts, described in the previous section, are extrapolated to\nthe second (also known as middle) sampling layer of the electromagnetic calorimeter. Around this posi-\ntion a cluster of size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.125\u00d70.125 (5\u00d75 cells in this sampling layer) is built. The cell with\nthe maximum energy is sought within a small \u03b7 and \u03c6 window (0.075\u00d70.075) around the extrapolation\npoint. Shower shapes are estimated with respect to this cell. The contribution of neighbouring hadronic\nshowers is therefore reduced.\nA set of preselection criteria are applied to decrease the number of fake candidates per jet:\n- The ratio of energy reconstructed in the core of the shower in the \ufb01rst sampling layer to the to-\ntal shower energy reconstructed in the core of the cluster, must ful\ufb01l E1(core)/E(core) >0.03.\nE1(core) is the energy reconstructed in a window of size \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.009375 \u00d7 0.1 in the \ufb01rst\nsampling layer (3 \u00d7 1 cells). E(core), the core energy in the cluster, is computed in the follow-\ning windows: 0.075 \u00d7 0.3 (3 \u00d7 3 cells) in the presampler, 0.046875 \u00d7 0.2 (15 \u00d7 2 cells) in the\nstrips, 0.125\u00d70.125 (5\u00d75 cells) in the middle, 0.15 \u00d70.125 (3\u00d75 cells) in the back. This ratio\ntends to be larger for electrons than for hadrons due to the different development of hadronic and\nelectromagnetic showers. This quantity is discussed in detail in the following section.\n- Similarly, the fraction of energy reconstructed in the core of the shower in the third sampling layer\nto the energy reconstructed in the core of the cluster, E3(core)/E(core), must be smaller than 0.5.\nE3(core) is the energy reconstructed in a window of size \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.15 \u00d7 0.075 in the third\nsampling layer (3 \u00d7 3 cells). This ratio is larger for hadrons than it is for low-energy electrons\nwhich almost never reach this layer and is discussed in the following section.\n- The ratio of the energy E reconstructed in the electromagnetic calorimeter over the momentum p\nof the track reconstructed in the inner detector is required to ful\ufb01l E/p >0.7.\nThese preselection criteria cut out less than 5% of signal electrons. Finally, candidates which are also\nreconstructed as originating from a conversion are vetoed, corresponding to a loss of 9% of all signal and\nbackground tracks.\nPosition and energy corrections are applied in the precise reconstruction of the electromagnetic clus-\nter and are described in [7]. These corrections have been tuned for high-energy clusters and are not\noptimal for low-energy electrons. In Fig. 3 the ratio between the reconstructed and the true electron\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n493\n\n|\n\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nE(rec)/E(true)\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n1.6\nATLAS\np(rec)/p(true)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\nFigure 3: Ratio between reconstructed and true energy as a function of the electron pseudo-rapidity |\u03b7|\n(left) and ratio of the reconstructed to true momentum for electrons (right).\nenergies is shown as a function of |\u03b7| for signal electrons from the H \u2192b\u00afb sample. It can be seen that\nthe corrections over-estimate the electron energy. Moreover, as electrons are embedded in jets, there is\na contamination from other hadrons in the energy determination which is not visible with the isolated\nelectrons from a J/\u03c8 sample [6]. Work is on going to improve the energy reconstruction at low energy.\nBy default the four-momentum of an electron is de\ufb01ned as the energy reconstructed in the calorime-\nter, whereas the direction is taken from the associated track. Since in this note the main physics processes\nlead to electron transverse momenta of less than 15 GeV, the momentum measured in the tracker is used\ninstead of the energy unless stated otherwise. The reconstructed momentum of the electron is shown in\nFig. 3. The track reconstructs the momentum of the electron close to its true value for most candidates.\nThe small downward shift of the peak from unity and the tail towards lower values are due to photon\nbremsstrahlung. Future developments in ATLAS will ensure an optimal combination of calorimeter and\ntracker measurements in the energy de\ufb01nition.\n4.2\nElectron identi\ufb01cation variables\nThe hadronic calorimeter has a granularity of \u2206\u03b7 \u00d7\u2206\u03c6 = 0.1\u00d70.1 which is too large to disentangle the\nenergy deposit of an electron inside a jet. In the electromagnetic calorimeter, electrons are narrow objects\nwhile jets tend to have a broader pro\ufb01le, allowing a discrimination. For this purpose, we use the \ufb01ner\ngranularity (\u2206\u03b7 \u00d7\u2206\u03c6 = 0.05\u00d70.025) of the third sampling layer of the electromagnetic calorimeter. The\nratio E3(core)/E(core), de\ufb01ned above, is larger for pions than for electrons and is clearly discriminating\nas can be seen in Fig. 4.\nElectromagnetic showers deposit most of their energy in the second sampling layer of the electro-\nmagnetic calorimeter. The following variables are used:\n- The lateral shower shape R\u03b7 (cf. Fig. 5 on left) is given by the ratio of the energy reconstructed in a\nwindow of size 0.075\u00d70.175 (3\u00d77 cells of the middle sampling layer) to the energy reconstructed\nin 0.175\u00d70.175 (7\u00d77 cells).\n- The lateral width \u03c9\u03b72 =\nr\n\u2211Ec\u00d7\u03b72\n\u2211Ec\n\u2212\n\u0010\n\u2211Ec\u00d7\u03b7\n\u2211Ec\n\u00112\n(cf. Fig. 5 on right) is calculated in a window of\nsize 0.075\u00d70.125 (3\u00d75 cells of the middle sampling layer) using the energy weighted sum over\nall cells, which depends on the particle impact point inside the cell.\nThe \ufb01rst layer, with its very \ufb01ne granularity in pseudo-rapidity, can be used to detect sub-structures\nwithin a shower and thus isolated \u03c00\u2019s and \u03b3\u2019s can be discriminated against ef\ufb01ciently. For all variables\ncomputed in the \ufb01rst sampling layer, two cells in \u03c6 are summed.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n494\n\n(core)/E\n3\nE\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n4\n10\n3\n10\n2\n10\n1\n10\n1\nATLAS\nFigure 4: Ratio E3(core)/E(core) (see text) for electrons in the H \u2192b\u00afb sample (hatched histogram) and\nfor charged pions in the H \u2192u \u00afu sample (solid line). The distributions are normalized to unit area.\n\u03b7\nR\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\n2\n\u03b7\n\u03c9\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\nFigure 5: Lateral shower shape R\u03b7 (left) and lateral width \u03c9\u03b72 (right) in the second layer of the elec-\ntromagnetic calorimeter (see text for details). The distributions are shown for electrons in the H \u2192b\u00afb\nsample (hatched histograms) and for charged pions in the H \u2192u \u00afu sample (solid lines). The distributions\nare normalized to unit area.\nThe ratio E1(core)/E(core), de\ufb01ned above, is larger for electrons than for hadrons as can be seen in\nFig 6.\nThe lateral shower shape in the strips is now exploited.\n- The total shower width in strips \u03c9stot is determined in a window \u2206\u03b7 = 0.0625 (corresponding to 20\nstrips in the barrel for instance). It is calculated from: \u03c9stot =\nq\n\u2211Ei \u00d7(i\u2212imax)2 /\u2211Ei, where i\nis the strip number and imax the strip number of the \ufb01rst local maximum. This width is shown for\nelectrons and pions in Fig. 7.\n- The shower width using three strips around the one with the maximal energy deposit is shown in\nFig. 7 on the right. It is given by the following formula:\n\u03c9s3 =\nq\n\u2211Ei \u00d7(i\u2212imax)2 /\u2211Ei, where i is the number of the strip and imax the strip number of the\nmost energetic one.\nThe pion and jet rejection can be signi\ufb01cantly improved by ensuring consistency between the elec-\ntromagnetic calorimeter and the inner detector information.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n495\n\n(core)/E\n1\nE\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\nFigure 6: Ratio E1(core)/E(core) (see text) for electrons in the H \u2192b\u00afb sample (hatched histogram) and\nfor pions in the H \u2192u \u00afu sample (solid line). The distributions are normalized to unit area.\nstot\n\u03c9\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\ns3\n\u03c9\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\nFigure 7: Total shower width \u03c9stot (left) and shower width in three strips \u03c9s3 (right) in the \ufb01rst layer\nof the electromagnetic calorimeter. The distributions are shown for electrons in the H \u2192b\u00afb sample\n(hatched histograms) and pions in the H \u2192u \u00afu sample (solid lines). The distributions are normalized to\nunit area.\nFirst, the angular matching between the track and the electromagnetic cluster is checked (cf. Fig. 8):\n|\u2206\u03b7| =\ni=im+7\n\u2211\ni=im\u22127\nEi \u00d7 (i \u2212im)/\ni=im+7\n\u2211\ni=im\u22127\nEi, which gives the difference between the track and the shower\npositions measured in units of distance between the strips, where im is the impact cell for the track\nreconstructed in the inner detector and Ei is the energy reconstructed in the i-th cell in the \u03b7 direction, at\nconstant \u03c6 given by the track parameters.\nSubsequently, the energy E measured in the electromagnetic calorimeter is compared to the momen-\ntum p measured in the inner detector (cf. Fig. 9 on the left). In the case of an electron, the momentum\nshould match the energy. The large tails at high values of the ratio in the signal distribution are due to\nsoft bremsstrahlung.\nA further reduction of the charged hadron contamination is obtained by rejecting tracks having a low\nfraction of high-energy hits in the TRT. Figure 9 (right) shows the ratio NHTR/Nstraw between the number\nof high threshold hits NHTR and the total number of TRT hits Nstraw.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n496\n\n sampling)\nst\n (1\n\u03b7\n\u2206\n#Sum \n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nFigure 8: Angular matching between charged tracks extrapolated to the electromagnetic calorimeter\nand electromagnetic clusters in pseudo-rapidity (|\u2206\u03b7|). The distributions are shown for electrons in the\nH \u2192b\u00afb sample (hatched histogram) and for pions in the H \u2192u \u00afu sample (solid line). The distributions\nare normalized to unit area.\nE/p\n1\n1.5\n2\n2.5\n3\n3.5\n4\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\nstraw\n/N\nHTR\nN\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nFigure 9: Ratio E/p between the energy of the electromagnetic clusters and the momentum of recon-\nstructed charged tracks (left) and fraction NHTR/Nstraw of high-energy hits in the TRT (right). The distri-\nbutions are shown for electrons in the H \u2192b\u00afb sample (hatched histograms) and for pions in the H \u2192u \u00afu\nsample (solid lines). The distributions are normalized to unit area.\n4.3\nRejection of electrons from \u03b3-conversions and Dalitz decays\nA signi\ufb01cant source of low-pT electron tracks in jets are photon conversions and Dalitz decays. Such\ntracks might be identi\ufb01ed by the algorithm as signal electron tracks. The good quality track cuts help in\npart to suppress that type of background. In case of \u03b3-conversions and Dalitz decays, e+e\u2212pairs with\nsmall invariant mass are observed in the detector. To \ufb01nd them the conversion \ufb01nding algorithms can\nbe used. Ref. [8] details the last developments on the reconstruction of such electrons. Unfortunately,\nthese were not available for the electron reconstruction algorithms at the time of this study. As detailed in\nSection 4.1, about 9% of signal electrons are mis-identi\ufb01ed as conversions. Based on previous studies [9],\nfor an electron ef\ufb01ciency \u03b5e = 80%, the rejection factor of electrons from conversions and Dalitz decays\nis \u223c3 with the conversion package and \u223c2 without.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n497\n\n5\nb-tagging algorithm\nThe variables described in the previous section have been shown to be ef\ufb01cient in distinguishing electron\ntracks from non-electron tracks or electron tracks from \u03b3-conversions and Dalitz decays.\nIn order to construct a b-tagging algorithm we combine these variables with additional variables to\nexploit the speci\ufb01c features of b-jets. First we take advantage of the fact that the electron is coming\nfrom a b quark and thus can have a signi\ufb01cant transverse impact parameter d0. Figure 10 shows the\ncorresponding distributions. In addition, because of the B hadron\u2019s high mass, electrons from direct\n (mm)\n0\nd\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n4\n10\n3\n10\n2\n10\n1\n10\nATLAS\nFigure 10: Transverse impact parameter for electrons in the H \u2192b\u00afb sample (hatched histogram) and for\npions in the H \u2192u \u00afu sample (solid line). The distributions are normalized to unit area.\nbottom decays tend to be more boosted in a plane transverse to the jet axis, i.e. have a larger prel\nT than\nthe backgrounds, as shown in Fig. 11. prel\nT is de\ufb01ned as the electron momentum in the plane orthogonal\nto the jet axis.\n (GeV) \nrel\n p\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n \n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\nFigure 11: Distribution of the track transverse momentum prel\nT relative to the jet axis for signal electron\ntracks in b jets (hatched histogram) and for pion tracks in light jets (solid line).\nThe combination of all variables is performed in two steps; \ufb01rst for variables independent of the jet\nand second including a jet dependent variable as explained in Section 5.1. Finally the performance of the\nalgorithm will be detailed in Section 5.2.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n498\n\n5.1\nb-tagging procedure\nA likelihood-ratio method is used to combine the variables described in the previous section along with\nthe electron track impact parameter d0. This likelihood ratio uses information only on the characteristics\nof the electron and is independent of the parameters of the jet. The discriminating variables are compared\nto pre-de\ufb01ned normalized distributions (probability density functions) for both the electron and the pion\nhypotheses. We use the signal sample of H \u2192b\u00afb \ufb01ltered for electrons and part of the H \u2192u \u00afu background\nsamples. The variables show a signi\ufb01cant dependence on pseudo-rapidity and a less pronounced one\non transverse momentum. In \u03b7 the changes correspond to varying granularities, lead thickness and\nmaterial in front of the electromagnetic calorimeter. The separation between the distributions obtained\nfor electrons and pions can vary also with \u03b7. Therefore probability density functions are de\ufb01ned in \ufb01ve\n|\u03b7| bins: (0-0.8), (0.8-1.37), (1.37-1.52), (1.52-1.8), (1.8-2).\ntrack\nD\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\nFigure 12: Discriminating function Dtrack for electrons in the H \u2192b\u00afb sample (hatched histogram) and\nfor pions in the H \u2192u \u00afu sample (solid line). The distributions are normalized to unit area.\nFor each good quality track the discriminating function Dtrack is calculated as:\nDtrack =\n\u220fi Pe(xi)\n\u220fi Pe(xi)+\u220fi Ph(xi),\n(1)\nwhere xi denotes the value of the i-th variable for a given track, Pe(xi) is the probability obtained from\nthe single variable xi that the track originates from a signal electron, Ph(xi) is the probability that the\ntrack originates from a hadron, and i runs through all the variables used by the algorithm. Distributions\nof Dtrack obtained for signal electrons and background pions are shown in Fig. 12. Dtrack tends to 1 for\nelectrons and tends to 0 for pions. The identi\ufb01cation of a candidate track as originating from a signal\nelectron track is based on the value of Dtrack. Those tracks for which Dtrack is below a given threshold are\nrejected. Typically, for an electron identi\ufb01cation ef\ufb01ciency of 80%, a pion rejection factor of about 200\ncan be achieved in H \u2192u \u00afu events.\nFor each good quality track in the jet the value of the discriminating function for electron identi\ufb01-\ncation, Dtrack, de\ufb01ned previously in Eq. 1, has been calculated. For each jet, the track with the highest\nvalue max(Dtrack) is chosen and this single track will now be used to estimate the discriminating function\nDjet for the jet. In addition to the variables used for electron identi\ufb01cation based on the inner detector\nand electromagnetic calorimeter information, the track transverse momentum prel\nT relative to the jet axis,\nshown in Fig. 11 is included. For each jet the discriminating function Djet is calculated using the selected\ntrack as:\nDjet = max(Dtrack)\u00d7\nPe(prel\nT )\nPe(prel\nT )+Ph(prel\nT ),\n(2)\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n499\n\nwhere Pe(prel\nT ) is the probability obtained from the single variable prel\nT that the track originates from a\nb-jet and Ph(prel\nT ) is the probability that the track originates from a light jet. Distributions of Djet obtained\nfor b\u2212and light jets are shown in Fig. 13. For a given threshold Dthr\njet, a jet with Djet > Dthr\njet is tagged as a\nb-jet.\njet\nD\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n \n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\nFigure 13: Discriminating function Djet for b-jets in the H \u2192b\u00afb sample (hatched histogram) and light\njets in the H \u2192u \u00afu sample (solid line). The distributions are normalized to unit area.\n5.2\nPerformance of the b-tagging algorithm\nThe b-tagging ef\ufb01ciency is de\ufb01ned as \u03b5b = Nt\nb/Nb where Nt\nb is number of the tagged b-labelled jets and\nNb is the total number of jets labelled as b-jets. The de\ufb01nition includes the semi-leptonic branching\nratios as well as the detector acceptance and the electron reconstruction and identi\ufb01cation ef\ufb01ciencies.\nThe jet rejection factor is calculated as Rlightjet = Nj/Nt\nj, where Nj is the number of light jets and Nt\nj is\nthe number of light jets tagged by mistake as b-jets.\nFigure 14 shows the rejection of light jets as a function of the b-tagging ef\ufb01ciency \u03b5b. The rejection\nfactors achieved against light jets are presented in Table 3.\nFor a b-tagging ef\ufb01ciency \u03b5b = 7% on\nb-jet efficiency\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nLight-jet rejection\n2\n10\n3\n10\nATLAS\nFigure 14: Rejection factor of light jets Rlight jet versus b-tagging ef\ufb01ciency \u03b5b.\ninclusive b-jets, the light jet rejection factor is about 110. This operating point corresponds to a 61%\nb-tagging ef\ufb01ciency on semi-electronic b-jets.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n500\n\nTable 3: Light jet rejection factors Rlight jet for various b-tagging ef\ufb01ciencies \u03b5b on inclusive jets. Errors\nare statistical only.\n\u03b5b (%)\nRlightjet\n8\n80\u00b11\n7\n110\u00b12\n6\n160\u00b13\nThis study has been performed on Monte Carlo simulated data which do not include pile-up effects.\nBased on previous study [10], a further degradation of the light jets rejection factor by 10% (30%) is\nexpected when on average 4.6 (23) minimum-bias events per beam-crossing are added.\nFigure 15 shows the light jet rejection as a function of the jet pT and |\u03b7| for a total b-tagging ef\ufb01-\nciency \u03b5b = 7%. Performance are estimated in \ufb01ve bins in |\u03b7| and in seven bins in pT. The rejection of\nlight jets does not depend signi\ufb01cantly on jet pT over the range 30-80 GeV. For lower pT, jets are wider\nand an electron can escape outside the cone of \u2206R = 0.4 and this leads to lower rejections for the same\nb-tagging ef\ufb01ciency. For higher jet energies, the jet is narrower and showers coming from the particles in\nthe jet overlap more and thus it is more dif\ufb01cult to separate the electrons, leading to a drop in rejection. A\nloss in the jet rejection factor can also be observed in the region 1.37 < |\u03b7| < 1.52 corresponding to the\ncrack between the barrel and the end-caps of the electromagnetic calorimeter. Even though soft electrons\nare reconstructed only within |\u03b7| < 2, some sensitivity is retained for jet axes just beyond the cut-off as\nshown in Fig.15.\n of jet (GeV)\nT\np\n0\n20\n40\n60\n80\n100\n120\nLight jet rejection\n2\n10\n3\n10\nATLAS\n| eta | of jet\n0\n0.5\n1\n1.5\n2\n2.5\nLight jet rejection\n10\n2\n10\n3\n10\nATLAS\nFigure 15: Light jet rejection factor as a function of jet pT (left) and jet |\u03b7| (right) for a b-tagging\nef\ufb01ciency \u03b5b = 7%.\nTable 4 shows the fraction of jets tagged of a given type of track for \u03b5b = 7%. Most b-jets are tagged\nby true electron tracks; in particular by signal electrons in \u223c65% of cases. Light jets are tagged in \u223c25%\nof cases by electrons from \u03b3-conversions and Dalitz decays. Light jets are also tagged in \u223c60% of cases\nby pions.\n6\nConclusion\nSoft electron tagging relies on the semi-leptonic decays of bottom and charm hadrons. It is therefore\nintrinsically limited by the branching ratios to electrons: about 20% of b-jets will contain a soft electron,\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n501\n\nTable 4: Fraction of jets (%) in the WH sample tagged by a speci\ufb01ed type of track for \u03b5b = 7%. The \u201de\nfrom * \u201d column corresponds to electrons from conversions and Dalitz decays. Statistical errors on these\nnumbers are negligible.\nFraction of jets tagged by a speci\ufb01ed type of track [%]\nJet type\nall e\ne from b\ne from c\ne from *\nother e\n\u03c0\nothers\nb\n67.6\n42.0\n19.4\n3.6\n2.6\n23.9\n8.5\nlight\n27.2\n0.2\n0.4\n25.5\n1.1\n58.7\n14.1\nincluding cascade decays of bottom to charm hadrons. However, when a signal electron is present the\nalgorithm is quite ef\ufb01cient. In addition, tagging algorithms based on soft leptons have low correlations\nwith the track-based b-tagging algorithms, which is very important for checking and cross-calibrating\nperformance with data.\nThe study presented here was based on a sample of WH events which have two high pT and well\nseparated jets. A b-jet tagging ef\ufb01ciency of about 7% (including the inclusive b \u2192e\u03bdX branching\nratio of \u223c20%) is achieved for a light jet rejection better than 100. The ef\ufb01ciency of the soft electron\nidenti\ufb01cation is high, since two-thirds of the b-jets are tagged by the true electron. Work is ongoing to\nprepare similar analyses with other Monte Carlo simulated samples with different topologies as well as\nto prepare the measurement with real ATLAS data.\nReferences\n[1] ATLAS Collaboration, b-Tagging Performance, this volume.\n[2] Torbjorn Sjostrand (Lund U., Dept. Theor. Phys.) , Stephen Mrenna, Peter Skands (Fermi-\nlab) . FERMILAB-PUB-06-052-CD-T, LU-TP-06-13, Mar 2006. 576pp. Published in JHEP\n0605:026,2006..\n[3] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[4] W.-M.Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) and 2007 partial update for the 2008\nedition.\n[5] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[6] ATLAS Collaboration, Reconstruction of Low-Mass Electron Pairs, this volume.\n[7] ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this\nvolume.\n[8] ATLAS Collaboration, Reconstruction of Photon Conversions , this volume.\n[9] Derue F., Kaczmarska A., Soft electron identi\ufb01cation and b-tagging with DC1 data, 2004, ATL-\nPHYS-2004-026.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n502\n\n[10] Bold, T., Derue F., Kaczmarska A., Stanecka, E., Wolter, M., Pile-up studies for soft electron\nidenti\ufb01cation and b-tagging with DC1 data, 2006, ATL-PHYS-PUB-2006-001.\nb-TAGGING \u2013 SOFT ELECTRON b-TAGGING\n503\n\nb-Tagging Calibration with t\u00aft Events\nAbstract\nThis note describes various studies of b-jet reconstruction and b-tagging in\nsimulated ATLAS t\u00aft events. The performance of several jet algorithms on\nt\u00aft event b-jets is studied. Techniques for measuring the b-tagging ef\ufb01ciency\ndirectly from data t\u00aft events, using both tag counting and explicit b-jet selec-\ntion, are described and compared. Finally, the optimisation of b-tagging for t\u00aft\nevents, using both Monte Carlo and data samples, is discussed. Both semilep-\ntonic and dilepton t\u00aft decay channels are considered, for an initial integrated\nluminosity of 100 pb\u22121.\n1\nIntroduction\nThe identi\ufb01cation of b-jets is of crucial importance to many physics analyses at the LHC, including\ntop physics and the search for new particles including Higgs bosons. The performance of b-tagging\nalgorithms will have to be understood using real data, as Monte Carlo will only give an approximate\ndescription of the tracking and vertexing performance of the detector, at least initially. Light jet rejection\nfactors can be measured in inclusive jet samples (where the heavy \ufb02avour content is small), but pure\nsamples of b-jets are required to measure the b-jet tagging ef\ufb01ciency. One solution, already widely used\nat the Tevatron, exploits dijet events in which one of the jets is b-tagged using a soft lepton tag [1].\nAt the LHC, the large t\u00aft production cross-section offers an alternative source of b-jets, in a distinctive\ntopology which is relatively easy to trigger on and isolate, providing at least one of the W-bosons from\nthe top decays leptonically. Providing the top quark is assumed to have Standard Model properties (in\nparticular that Br(t \u2192Wb) = 1), each t\u00aft event has two b-jets, together with at least one high-ET lepton,\nmissing energy and additional high-ET jets from hadronically decaying W-bosons. The environment\n(high jet multiplicity, high-ET b-jets) is also much closer to that which b-tagging ef\ufb01ciency measurements\nare typically needed than in dijet events.\nThe b-tagging ef\ufb01ciency can be extracted from t\u00aft events in two ways\u2014either by counting events\nwith different numbers of tagged jets, or by reconstructing the t\u00aft decay topology in order to identify a\npure sample of b-jets. Both techniques are explored in this note, which is organised as follows. Sec-\ntion 2 brie\ufb02y describes the Monte Carlo simulation samples and common event selection which is used\nthroughout, and Section 3 discusses reconstruction of b-jets in t\u00aft events, as an essential preliminary to\nstudies of b-jet tagging. The counting and b-jet selection methods are discussed in Sections 4 and 5.\nFinally, Section 6 discusses the possibilities for optimising b-tagging performance speci\ufb01cally for t \u00aft\nevents, using both Monte Carlo and data.\n2\nDatasets and event selection\nAll studies were performed using ATLAS Monte Carlo production samples as discussed in more detail\nin [2] and [3]. Semileptonic and dileptonic t\u00aft decays were generated with MC@NLO with Herwig\nhadronisation. AcerMC with Pythia hadronisation was used as an alternative. The background in the\nsemileptonic channel is dominated by W+multijet production, which was simulated with ALPGEN (in-\ncludingWb\u00afb and Wc\u00afc), and single top production, simulated with AcerMC. In the dilepton channel (used\nonly for the counting method b-tagging ef\ufb01ciency determination), additional backgrounds from Z+jets\n(simulated with ALPGEN) and diboson production (simulated with Herwig) are also important. Back-\nground coming from QCD multijet events has not been studied, as this background is dif\ufb01cult to simulate\n504\n\nElectron channel\nMuon channel\nDilepton channel\nt\u00aft (except all hadronic)\n45232\n45232\n45232\nTrigger\n10430\n12116\n21417\nLepton ID\n8350 (80.1 %)\n11268(93.0 %)\nIsolation\n8063 (96.6 %)\n9909 (87.9 %)\nLepton pair selection\n1549 (7.23 %)\nMissing ET > 20 GeV\n6362 (78.9 %)\n7834 (79.1 %)\nMissing ET cut\n1355 (87.5 %)\n\u22654 jets ET > 20 GeV\n3651 (57.4 %)\n4555 (58.1 %)\n\u22652 jets ET > 20 GeV\n1160 (85.6 %)\n\u22654 jets ET > 30 GeV\n2329 (63.8 %)\n2927 (64.3 %)\n\u22652 jets ET > 30 GeV\n1000 (86.2 %)\nW mass window cut\n1958 (84.1 %)\n2487 (85.0 %)\n-\n-\ntop mass window cut\n1378 (70.4 %)\n1773 (71.3 %)\n-\n-\nTable 1: Numbers of events from t\u00aft production expected with 100 pb\u22121 in the lepton+jets and dilepton\nchannels. The cut ef\ufb01ciency w.r.t. the previous line is shown in parenthesis. The fully hadronic decay t \u00aft\ncontribution is not included but is expected to be small. Contributions from non-t\u00aft background are not\nincluded.\nand samples were not available. The normalisation of such background (if signi\ufb01cant) will eventually\nhave to be extracted from data.\nSystematic errors have been evaluated following the prescriptions discussed in detail in [2] and [4]\nwherever possible. The sensitivity to incorrect b-tagging of non-b jets was assessed by doubling and\nsetting to zero the corresponding jet tagging ef\ufb01ciencies, separately for light quark and charm jets. The\njet energy scale was varied by \u00b15%. The Monte Carlo event generation sensitivity was assessed by using\nAcerMC instead of MC@NLO, including samples with modi\ufb01ed ISR, FSR and parton shower cutoff Q2.\nThe backgrounds from W+multijet events and single top production were independently doubled and set\nto zero. In all cases, the effect of these variations was computed without adjusting parameters of the\nanalysis (e.g. acceptance factors and background estimates) to compensate for changes made to the input\nMonte Carlo samples.\nThe analyses make use of isolated high ET electrons and muons (with ET > 20 GeV) and jets (with\nET > 20 GeV or higher depending on the particular analysis), selected according to standard ATLAS\nobject de\ufb01nitions and \ufb01ducial cuts [2]. In the semileptonic channel, events are required to have exactly\none high ET lepton, at least four jets and missing transverse energy of at least 20 GeV. In the dilepton\nchannel, two leptons of opposite charge and a missing transverse energy of at least 20 GeV are required;\nin the e+e\u2212and \u00b5+\u00b5\u2212channels, the Z+jets background was further reduced by vetoing events with\ndilepton mass between 81 and 101 GeV and by requiring a missing transverse energy of at least 35 GeV.\nIn both cases, at least one lepton in the event was required to pass the ATLAS level-1, level-2 and event\n\ufb01lter triggers, using trigger signatures appropriate for the 20 GeV of\ufb02ine lepton ET cuts. For electrons,\nthe signatures e25i and e60 were used (the e60 trigger improves the ef\ufb01ciency at high lepton ET), and for\nmuons, the signature mu20i was used. Further studies of the ATLAS trigger performance on t\u00aft events\ncan be found in [5].\nThe resulting estimated event yields at various stages of the event selection are shown in Table 1 for\n100 pb\u22121. Non-t\u00aft backgrounds are not included. The individual analyses apply further speci\ufb01c selec-\ntion cuts as discussed below. The effects of the tighter selections used only by the tag counting analysis\ndescribed in Section 4 are also shown in Table 1. The hadronic W mass window cut was applied by se-\nlecting the pair of jets with invariant mass closest to the W mass and requiring this to be within \u00b120 GeV\nof the nominal value; a top mass cut was applied similarly by adding the jet giving a reconstructed top\nmass closest to the nominal, and requiring it to be within \u00b130 GeV of the top mass.\nAll studies were performed with the default ATLAS b-tagging algorithm (IP3D+SV1), which uses\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n505\n\na likelihood weight w constructed from the results of the IP3D impact parameter and SV1 secondary\nvertex-based taggers [6]. This likelihood weight is large for b-jets and small for light and c-quark jets.\nFor jets from top decay with ET > 20 GeV, a cut w > 4 gives a b-jet tagging ef\ufb01ciency of around 70 %\nper jet and a light jet rejection of 50 while a w > 7 cut gives an ef\ufb01ciency of 60 % and a rejection of 200,\nthough these values are somewhat dependent on jet ET and \u03b7. Detailed studies of the expected b-tagging\nperformance can be found in [6] (e.g. in Table 1 therein). For the purposes of comparison, b-tagging\nef\ufb01ciency measurements have been done at reference ef\ufb01ciencies of 50, 60 and 70 %. Various other cut\nvalues are used internally by the selections in the individual analysis methods. When considering Monte\nCarlo truth information, jets have been labelled b, c and light using the standard ATLAS jet matching\nand labelling procedures [6].\n3\nb jet reconstruction in t\u00aft events\nThe choice of jet reconstruction algorithm is an important issue for top physics analysis in ATLAS, where\ngood resolution for the reconstruction of the original quark energy and direction is mandatory. These\nquestions are explored below, using various jet algorithms and parameter choices. The analysis uses a\nsample of 250k semileptonic t\u00aft events generated with MC@NLO and passed through the standard top\nselection as discussed in Section 2. The choice of jet algorithm also affects the b-tagging performance,\nas studied in detail elsewhere [6].\nThe standard reconstruction outputs jet collections made with the Cone (with \u2206R = 0.4 and \u2206R = 0.7)\nand kT (with D = 0.4 and D = 0.6) jet algorithms, each based on either Precluster Projective Towers\n(\u2018Tower\u2019) or Topological Cell Clusters (\u2018Topo\u2019) (see [7] for more information on jet reconstruction in\nATLAS). For this study, these standard jet reconstruction algorithms and parameter choices have been\ncomplemented by additional Cone and kT jets with a larger variety of \u2206R and D parameters. To compare\nall these jet algorithm and parameter choices in a controlled environment, re-reconstruction of jets was\nperformed at the AOD level, using \u2018Topological Cell Clusters\u2019 calibrated by \u2018Local Hadron Calibration\u2019\n(see [8] and [9] for details about the different strategies used to exploit and calibrate calorimeter infor-\nmation). All parameters except for the D parameter (kT) or \u2206R (Cone) were left unchanged with respect\nto the standard jet algorithms.\nIt should be noted that these re-reconstructed jets do not contain the calorimeter energy corrections\napplied in the standard calibration procedure described in [7] and [8]. Therefore a comparison of the\noverall performance between the different jet algorithms with different parameters is valid, but no direct\ncomparison between corrected and non-corrected jets should be made.\n3.1\nJet energy and angle resolution\nReconstructed jets are matched to quarks from the t\u00aft decay following the standard procedure [6]. The\nresults are shown in Fig. 1.\nThe top plots of Fig. 1 show the width of the distributions (Equark \u2212E jet)/Equark (i.e. the energy\nresolution) as a function of Equark, for both kT and Cone. To calculate the width, a Gaussian is \ufb01tted\nto the individual distributions. The distributions show the expected behaviour. The smallest width is\nobtained for the jet sizes 0.4, 0.5 and 0.6, for both Cone and kT. However, the differences between the\ndifferent jet algorithms are small, so no strong conclusions can be drawn from them.\nThe two lower plots of Fig. 1 show an investigation of the angular resolution. The mean distance\nbetween the initial quark and the resulting jet in \u2206R is plotted as function of Equark for Cone and kT. The\nexpected behaviour is that for bigger jet sizes the deviations between the jet axis and the \ufb02ight direction\nof the initial quark should increase; this behaviour is observed in Fig. 1. It can also be seen that for larger\njets and higher quark energies, the kT jet algorithm performs better than Cone.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n506\n\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)\nQuark\n)/E\nJet\n-E\nQuark\n (E\n\u03c3\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\nATLAS\nR=0.30\n\u2206\nCone \nR=0.40\n\u2206\nCone \nR=0.50\n\u2206\nCone \nR=0.60\n\u2206\nCone \nR=0.70\n\u2206\nCone \nR=0.80\n\u2206\nCone \n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)\nQuark\n)/E\nJet\n-E\nQuark\n ((E\n\u03c3\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\nATLAS\nKt D=0.30\nKt D=0.40\nKt D=0.50\nKt D=0.60\nKt D=0.70\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\nR(Quark,Jet)>\n\u2206\n<\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n0.11\n0.12\nATLAS\nR=0.30\n\u2206\nCone \nR=0.40\n\u2206\nCone \nR=0.50\n\u2206\nCone \nR=0.60\n\u2206\nCone \nR=0.70\n\u2206\nCone \nR=0.80\n\u2206\nCone \n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\nR(Quark,Jet)>\n\u2206\n<\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n0.11\n0.12\nATLAS\nKt D=0.30\nKt D=0.40\nKt D=0.50\nKt D=0.60\nKt D=0.70\nFigure 1: Studies of b-jet resolution: width of (Equark \u2212E jet)/Equark and average of \u2206R(Quark,Jet) for\nCone and kT with different jet sizes.\nThe choice of the Cone algorithm with \u2206R = 0.4 that was driven by the need to reconstruct properly\nW hadronic decays [10] has been found to be an appropriate choice for the t\u00aft signal. Background studies\nthat will be performed in the near future will complete the picture.\n4\nb-tagging ef\ufb01ciency measurement via tag counting\nConceptually, in the absence of background, the simplest way to determine the b-tagging ef\ufb01ciency in\nt\u00aft events is to count the number of events with different numbers of b-tagged jets; this allows both the\nb-tagging ef\ufb01ciency and the t\u00aft production cross-section to be measured simultaneously. This method is\ndiscussed in detail below, with an emphasis on the b- (and c-) tagging ef\ufb01ciency measurements. More\ninformation on t\u00aft cross-section measurement can be found elsewhere [4].\nIn the following analysis, the event selection has been slightly tightened from that used elsewhere, in\norder to reduce the background. Jets are required to have ET > 30 GeV. In the lepton+jets channel, the\nsingle top background is signi\ufb01cantly reduced by applying a cut on the W and top reconstructed masses,\nas described in Section 2.\n4.1\nMethod\nTop pair-production events give rise to two b-jets in the \ufb01nal state. Assuming for pedagogical purposes\nthat every selected event contains two b-jets in the detector acceptance and that only b-jets can be tagged,\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n507\n\nthen it is clear that the expected number of events with one b-tagged jet is proportional to N2\u03b5b(1\u2212\u03b5b)\nwhile the expected number of events with two b-tagged jets is proportional to N\u03b5 2\nb, where:\n\u2022 \u03b5b is the b-tagging ef\ufb01ciency, i.e. the probability to tag a b-jet\n\u2022 N is the number of selected t\u00aft events prior to any b-tagging requirement, which is proportional to\nthe t\u00aft production cross-section.\nIt can be seen that it is possible to estimate both the b-tagging ef\ufb01ciency and the t\u00aft production cross-\nsection from the observed number of events with one and two b-tagged jets.\nIn reality, c-jets and light jets (either from the hadronic W decay or from ISR/FSR) are present\nand contribute to the number of tagged jets in the event. Moreover not all b-jets coming from the top\ndecays end up being selected, whilst a small number of b-jets are produced through gluon radiation. To\ntake these effects into account, the event \ufb02avour content is estimated from Monte Carlo with a large\nsimulation t\u00aft sample. The factors Fi jk are de\ufb01ned as the fractions of selected events (prior to any b-\ntagging requirement) with i b-jets, j c-jets, and k light jets (i, j,k = 0,1,2,3,...). The expected number\nof events with n tagged jets < Nn > can be written as the sum over all possible combinations of i b-jets,\nj c-jets, and k light jets, as a function of b-, c-, and light jet tagging ef\ufb01ciency:\n< Nn >= (L\u00b7\u03c3t\u00aft \u00b7Apre\u2212tag)\u00b7 \u2211\ni, j,k\nFi jk\n\u2211\ni\u2032+ j\u2032+k\u2032=n\nAi\u2032\ni \u00b7\u03b5i\u2032\nb \u00b7(1\u2212\u03b5b)i\u2212i\u2032 \u00b7A j\u2032\nj \u00b7\u03b5 j\u2032\nc \u00b7(1\u2212\u03b5c) j\u2212j\u2032 \u00b7Ak\u2032\nk \u00b7\u03b5k\u2032\nl \u00b7(1\u2212\u03b5l)k\u2212k\u2032\n(1)\nwhere Ai\u2032\ni is the number of arrangements i!/(i\u2032!\u00b7(i\u2212i\u2032)!), the prime subscript corresponding to the number\nof tagged jets of a given \ufb02avour; \u03c3t\u00aft is the total production cross-section; Apre\u2212tag is the acceptance for\nt\u00aft events prior to any b-tagging requirement (including trigger ef\ufb01ciency, lepton reconstruction and ID\nef\ufb01ciency, etc.) and L is the integrated luminosity. The assumption that there is no correlation between\ntags in a given event is discussed later and is treated as a systematic uncertainty.\nFinally, the following likelihood can be written:\nL = \u03a0(Poisson(Nn,< Nn >)))\n(2)\nwhere Nn is the observed number of events with n tags. In practice only events with one, two, or three\ntags in the lepton+jets channel and one or two tags in the dilepton channel are taken into account in\nthe likelihood. Events with no tag suffer from signi\ufb01cant background, whilst there are few events with\nmore than three (two in the dilepton channel) tags. In the lepton+jets channel, both b- and c-tagging\nef\ufb01ciencies are allowed to \ufb02uctuate in the \ufb01t together with the t\u00aft cross-section (hence three variables and\nthree constraints); the light jet tagging ef\ufb01ciency is \ufb01xed in the \ufb01t and must be measured elsewhere. In\nthe dilepton channel, the c-jet tagging ef\ufb01ciency is also \ufb01xed (hence two variables and two constraints).\nTables 2 and 3 show the Fi jk values for the lepton+jets and dilepton channels, estimated from a sample\nof 265k t\u00aft events. It is interesting to note that the \u2018nominal\u2019 combination (two b-jets and two light jets\nfor the lepton+jets channel; two b-jets for the dilepton channel) represents only about one third of the\nevents, due to the presence of ISR/FSR light jets and c-jets from W decays. The signi\ufb01cant presence of\nc-jets in the lepton+jets channels allows the c-jet tagging ef\ufb01ciency to also be measured.\nFigures 2 and 3 show the expected yield of events in the lepton+jets and dilepton channels for an\nintegrated luminosity of 100 pb\u22121, as a function of the number of tagged jets. A b-jet is considered\ntagged if its b-tagging weight w is greater than 7.\nThe method was applied to a sample of t\u00aft\nevents corresponding to about 400 pb\u22121 of data and\nindependent of those used to estimate the acceptance factors. Table 4 compares the measured ef\ufb01ciencies\nand cross-section to their true value for three different b-tagging purity levels. No bias is visible within\nthe available statistics. The small deviation for the cross-section measurement in the dilepton channel is\nexplained by the lack of statistics in the sample used to estimate the Fi jk factors; this issue is discussed\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n508\n\nNumber of light jets\n1\n2\n3\n4\nany\n2 b-jets, 1 c-jet\n15.9 %\n10.6 %\n3.00 %\n0.85 %\n30.5 %\n2 b-jets, 0 c-jet\n-\n24.4 %\n13.8 %\n3.74 %\n42.8 %\n1 b-jet, 1 c-jet\n-\n6.46 %\n2.38 %\n0.74 %\n9.75 %\n1 b-jet, 0 c-jet\n-\n-\n7.60 %\n3.21 %\n11.6 %\n0 b-jet, 1 c-jet\n-\n-\n0.38 %\n0.11 %\n0.49 %\n0 b-jet, 0 c-jet\n-\n-\n-\n0.46 %\n0.65 %\nTable 2: Fractions of selected events with a certain number of b, c and light jets in the lepton+jets channel\nfor the counting method. Only the dominant contributions are shown.\nNumber of light jets\n0\n1\n2\n3\nany\n2 b-jets, 1 c-jet\n1.02 %\n0.73 %\n0.27 %\n<0.1 %\n2.08 %\n2 b-jets, 0 c-jet\n35.2 %\n20.9 %\n6.64 %\n1.39 %\n64.3 %\n1 b-jet, 1 c-jet\n1.68 %\n1.08 %\n0.46 %\n0.22 %\n3.54 %\n1 b-jet, 0 c-jet\n-\n18.9 %\n6.26 %\n1.66 %\n27.2 %\n0 b-jet, 1 c-jet\n-\n0.29 %\n0.11 %\n<0.1 %\n0.40 %\n0 b-jet, 0 c-jet\n-\n-\n1.11 %\n0.31 %\n1.50 %\nTable 3: Fractions of selected events with a certain number of b, c and light jets in the dilepton channel\nfor the counting method. Only the dominant contributions are shown.\nlater together with other systematic uncertainties. With 100 pb\u22121, a statistical precision of 2.7% (4.2%)\ncan be achieved on the b-tagging ef\ufb01ciency, and 2.4% (4.8%) on the t\u00aft cross-section, respectively in\nthe lepton+jets channel and dilepton channel. In the lepton+jets channel, the statistical uncertainty on\nthe c-tagging ef\ufb01ciency is rather large, because this measurement is mostly determined by the number of\nevents with three tagged jets.\n4.2\nBackgrounds\nIn the lepton+jets channel, the main backgrounds areW+jets and single top. Other sources of background\nare Z+jets (where one lepton fails to be identi\ufb01ed), WW/WZ/ZZ+jets, and QCD processes (which has\n\u03b5b (%)\n\u03b5c (%)\n\u03c3t\u00aft (pb)\ntrue\nmeas.\ntrue\nmeas.\nw > 4\n72.1\n71.7\u00b10.7\n22.3\n21.9\u00b11.5\n841\u00b19\nLepton+jets\nw > 7\n60.4\n59.8\u00b10.8\n12.8\n13.8\u00b11.3\n844\u00b110\nw > 10\n48.1\n47.4\u00b10.9\n6.7\n8.2\u00b11.4\n832\u00b113\nw > 4\n72.9\n72.9\u00b11.0\n-\n-\n882\u00b117\nDilepton\nw > 7\n61.1\n60.5\u00b11.2\n-\n-\n883\u00b119\nw > 10\n48.4\n47.9\u00b11.3\n-\n-\n883\u00b125\nTable 4: Counting method: tagging effciencies and cross-section measured on a control sample and\ncompared to their true value for three levels of b-tagging purity, for the lepton+jets and dilepton channels.\nThe t\u00aft production cross-section was assumed to be 833 pb. The uncertainties are statistical only and\ncorrespond to about 400 pb\u22121 of data.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n509\n\n# tagged jets\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n-1\n# events / 100 pb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\ntt\nW/Z+jets\nWt\ns-channel\nt-channel\nDiboson+jets\nATLAS\nFigure 2: Yield expected for an integrated luminosity of 100 pb\u22121 in the lepton+jets channel as a func-\ntion of the number of tagged jets. The expected background from W/Z+jets, single top, and diboson\nproduction is also shown.\n# tagged jets\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n1\n# events / 100 pb\n2\n10\n1\n10\n1\n10\n2\n10\ntt\nZ+jets\nSingle top\nDibosons+jets\nATLAS\n# tagged jets\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n1\n# events / 100 pb\n2\n10\n1\n10\n1\n10\n2\n10\n3\n10\ntt\nZ+jets\nSingle top\nDibosons+jets\nATLAS\nFigure 3: Yield expected for an integrated luminosity of 100 pb\u22121 in the dilepton+jets channels (left:\nee/\u00b5\u00b5; right: e\u00b5) as a function of the number of tagged jets. The expected background from Z+jets and\nsingle top is also shown.\nnot been studied, as discussed in Section 2). Figure 2 shows the total background due to W/Z+jets, single\ntop, and diboson+jets production and Fig. 4 (left) shows the expected signal over background ratio as a\nfunction of the number of tagged jets. Events with one, or more than one, tagged jets have good purity,\nwith signal over background ratios of 14.4 and 26.8 respectively, but the background does need to be\ntaken into account. The estimated background is subtracted from each sub-sample.\nIn the dilepton+jets channel, the main source of background is Z+jets production (but in the e\u00b5\nchannel, only Z \u2192\u03c4\u03c4 \u2192e\u00b5\u03bd\u03bd is signi\ufb01cant). WW/WZ/ZZ+jets and single top also contribute. Figure 3\nshows the total background due to Z+jets and diboson+jets production. The purity of the dilepton+jets\nsample (especially of the e\u00b5 channel) is good enough for the background estimate not to be an issue.\nFigure 4 shows that the expected signal over background ratio for events with exactly one tagged jet\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n510\n\nChannel\nLepton+Jets\nDilepton\nSource\n\u03b5b\n\u03b5c\n\u03c3t\u00aft\n\u03b5b\n\u03c3t\u00aft\nLight & \u03c4 jets\n< 0.1\n18\n< 0.1\n0.7\n0.3\nc-jets\n-\n-\n-\n0.8\n0.8\nb-jet labelling\n1.4\n12\n0.1\n1.4\n0.1\ntag correlation\n< 0.2\n< 0.2\n< 0.2\n< 0.2\n< 0.2\nJet energy scale\n0.9\n2.9\n+6.8\n\u22129.9\n0.5\n+1.3\n\u22123\nb-jet energy scale\n< 0.1\n1.5\n0.8\n0.2\n< 0.1\n(MC statistics\n0.5\n7\n0.5\n3\n3)\nBackground\n1.2\n3.5\n4.8\n0.3\n0.4\nAcerMC vs MC@NLO\n< 0.1\n9\n(4.9)\n2\n6\nISR/FSR\n2.7\n12.5\n8.9\n2\n(4)\ntop quark mass\n0.3\n-\n2.2\n0.5\n2\nLuminosity\n-\n-\n5\n-\n5\nLepton ID/trigger/pdf\u2019s\n-\n-\n2.8\n-\n2.8\nTotal\n3.4\n27\n+12.4\n\u221214.4 \u00b12.8\u00b15\n3.5\n+6.6\n\u22127.2 \u00b12.8\u00b15\nStatistical (100 pb\u22121)\n2.7\n18\n2.4\n4.2\n4.8\nTable 5: Relative systematic and statistical uncertainties (in percent) for the lepton+jets channel for a\nb-tagging ef\ufb01ciency of \u03b5true = 0.6 and jet ET > 30 GeV.\nis 80 in the ee and \u00b5\u00b5 channels and 175 in the e\u00b5 channel; the background is completely negligible for\nevents with two or more tagged jets. It is remarkable that the e\u00b5 0-tagged jet sub-sample is also quite\npure and could be used in the \ufb01t to improve its statistical power, provided a reliable background estimate\nis available.\n# tagged jets\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nS/B\n1\n10\n2\n10\nATLAS\n# tagged jets\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nS/B\n1\n10\n2\n10\n3\n10\n channel\n\u00b5\ne\n channels\n\u00b5\n\u00b5\nee/\nATLAS\nFigure 4: Signal over background ratio vs the number of tagged jets in the lepton+jets channel (left) and\nin the dilepton ee/\u00b5\u00b5 and e\u00b5 dilepton+jets channels (right).\n4.3\nSystematic uncertainties\nTable 5 summarizes the resulting systematic uncertainties for the counting method in the lepton+jets and\nthe dilepton channels. Some effects speci\ufb01c to this method are discussed in detail below.\nThe acceptance factors Fi jk depend upon the de\ufb01nition of jet \ufb02avour, which is arbitrary to some ex-\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n511\n\ntent. By default, reconstructed jets are matched to the closest heavy quark (after FSR) in \u2206R =\np\n\u03b72 +\u03c6 2;\nthe jet is attributed the quark \ufb02avour if \u2206R < 0.3 (in case of ambiguity, b quarks have priority over c\nquarks). Jets that are not associated to any b or c quark are considered light jets. Another possibility is\nto match jets with hadrons, following the same procedure. It was checked that the choice of matching\nhadrons or quarks has a negligible effect on the de\ufb01nition of jet \ufb02avour. To assess the systematic uncer-\ntainty, the cut was shifted from 0.2 to 0.5 (nominal cut: 0.3) and the Fi jk factors were re-estimated for\neach value. The shift observed on the same pseudo-experiments was taken as systematic effect.\nThe counting method assumes that there is no correlation between b-tags within an event, while\nsome detector effects or the reconstructed primary vertex might induce such a correlation. To check\nthis assumption, events with two reconstructed b-jets in the detector acceptance were selected. The\ncovariance between the tagging of the two b-jets is:\ncov(tag1,tag2) = N2b\u2212tags\nN\n\u2212\u03b52\nb\n(where N2b\u2212tags is the number of events with two tagged b-jets, N is the total number of events, and \u03b5b is\nthe true b-tagging ef\ufb01ciency). It was found that cov(tag1,tag2) = (8.8\u00b127)\u00b710\u22124, which is consistent\nwith 0; the statistical uncertainty corresponds to a bias on the measured ef\ufb01ciency of 0.2 %, which is\nconservatively taken as systematic uncertainty.\nBackgrounds are subtracted in each sub-sample and a 100% uncertainty is assumed. In the lep-\nton+jets sample, for 100 pb\u22121, 106 events from W/Z+jets are expected to populate the lepton+jets 1-tag\nsub-sample and 34.6 the 2-tag sub-sample. In the dilepton channel, 4.4 events with one tagged jet are\nexpected for all three channels (mostly in the ee and \u00b5\u00b5 channels), resulting in a small uncertainty.\nA 5% uncertainty on the jet energy scale, a 1% additional uncertainty on the b-jet energy scale, and\na 2 GeV uncertainty on the top mass, are also taken into account.\nThe statistical uncertainty on the Fi jk factors was estimated by comparing the results given by two\ndifferent training samples. It is not negligible in the dilepton+jets channel (3 %). However it could easily\nbe reduced by employing a larger t\u00aft sample (1M events would suf\ufb01ce); thus it was not included in the\ntotal uncertainty.\nThe cross-section measurement is very sensitive to the jet multiplicity, which is driven mostly by\nISR and FSR. This uncertainty appears also in the comparison of the two MC generators since the\nhadronisation models (Herwig in one case, Pythia in the other) need to be tuned in data and display\nimportant differences. In order to avoid to count twice the uncertainty on jet multiplicity, only the largest\nof the two estimates (ISR/FSR and MC generators) was considered in the total systematic uncertainty.\nSystematic uncertainties on \u03c3t\u00aft that are not speci\ufb01c to this analysis are discussed elsewhere [4].\nUncertainties relative to integrated luminosity and event selection prior to b-tagging (namely, lepton\nidenti\ufb01cation ef\ufb01ciency, trigger ef\ufb01ciency and pdf\u2019s) amount to 5 % and 2.8 %, respectively.\n4.4\nTag counting results\nWith 100 pb\u22121 of data, the counting method allows the b-tagging ef\ufb01ciency at a working point of \u03b5true =\n0.6 to be measured with a relative precision of \u00b12.7(stat.)\u00b13.4(syst.) % in the lepton+jets channel, and\n\u00b14.2(stat.)\u00b13.5(syst.) % in the dilepton channel. A better understanding of ISR/FSR could signi\ufb01cantly\nreduce the systematic uncertainty.\nThe uncertainty on the t\u00aft production cross-section is somewhat larger in both channels, with\n\u00b12.4(stat.)+12.7\n\u221214.7(syst.)\u00b15(lum.) % in the lepton+jets channel, and \u00b14.8(stat.)+7.2\n\u22127.7(syst.)\u00b15(lum.) % in the\ndilepton channel, mostly because of the uncertainties on the jet multiplicity (ISR/FSR), jet energy scale,\nand background estimate, uncertainties that can be improved in the long term and have been assessed\nconservatively here.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n512\n\nThe lepton+jets channel also allows the c-tagging ef\ufb01ciency to be measured. Unfortunately it is very\nsensitive to light jet contamination, and the uncertainty on light jet rejection and jet multiplicity makes\nany precision measurement impossible. Isolating a purer c-jet sample through some kinematic selection\nmight help but has not been attempted here.\n5\nSelecting b jet samples in data\nGoing beyond the b-tagging ef\ufb01ciency measurement from the counting method discussed above, the\nkinematics and topology of semileptonic t\u00aft events also allow pure samples of b-jets to be identi\ufb01ed\ndirectly. Providing this selection is done without biasing any properties of the selected b-jets, they can\nthen be used to measure the b-tagging ef\ufb01ciency, simply by studying the distribution of the tagging\ndiscriminant variable(s) in the selected jets. With enough statistics, this technique should also allow the\nmeasurement of the tagging ef\ufb01ciency as a function of other variables (e.g. jet ET and \u03b7).\nObtaining a pure sample of identi\ufb01ed b-jets requires full reconstruction of the t\u00aft decay chain, as-\nsigning four jets in the event to the two b-jets coming directly from the t \u2192Wb decays and the jets\nfrom hadronic W \u2192qq decay. For any given event, many different assignments are possible, especially\nwhen spectator jets (not from the t\u00aft decay) are also present. The correct combination can be determined\nby making use of kinematic information, including the reconstruction of the hadronic and leptonic top\nmasses for each considered combination, and the classi\ufb01cation can be further improved by requiring a\nb-tag for one of the jets assigned to the t \u2192Wb decay, providing the other presumed b-jet is left unbiased.\nThree similar techniques have been explored for making this jet identi\ufb01cation, all of which consider\neach combinatorial jet assignment and try to determine which one is correct:\n\u2022 A \u2018topological\u2019 selection based on the reconstructed masses for each combination.\n\u2022 A \u2018likelihood\u2019 selection, exploiting reconstructed top mass, jet momentum and angular informa-\ntion.\n\u2022 A \u2018kinematic\u2019 selection based on applying a kinematic \ufb01t to each combination and choosing the\none with the best \u03c72 value.\nAll of these methods start from the selection of semileptonic t\u00aft events discussed in Section 2, i.e. events\nwith a high-ET lepton, signi\ufb01cant missing energy and at least four jets. None of the methods result\nin a sample which is 100 % pure in b-\ufb02avoured jets, so background subtraction techniques are needed\nto derive pure samples on a statistical basis. The three methods, their associated background subtrac-\ntion techniques, and their application to the measurement of the b-tagging ef\ufb01ciency for the standard\nIP3D+SV1 tagger, are discussed in Sections 5.1, 5.2 and 5.3 below. Comparisons of their performance\nin terms of b-jet sample selection and b-tagging ef\ufb01ciency measurement are then given in Sections 5.4\nand 5.5.\n5.1\nTopological selection\nThe topological selection of b-jets from the basic sample has two stages: reconstruction of t\u00aft pairs,\nfollowed by \ufb01tting the top mass distributions to extract the b-jet sample and estimate the remaining back-\nground. To improve the purity, an explicit b-tag is required on the jet from the hadronic top decay, whilst\nthe b-jet from the leptonic top is left unbiased, and is used to form the sample of b-jets for measuring the\ntagging ef\ufb01ciency.\nAn attempt is made to reconstruct both hadronic and leptonic top decays in each event. First, the\ninvariant mass of every pair of jets is calculated to look for combinations consistent with coming from\nthe decay W \u2192j j. Combinations satisfying 60 < m j j < 100 GeV are retained, and combined with a third\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n513\n\njet to form a candidate t \u2192bW \u2192bj j decay. One jet from the W decay and the candidate b-jet must\nhave jet ET > 40 GeV, and the second W decay jet must have ET > 20GeV. To reduce background, this\ncandidate b-jet is required to have a b-tagging weight of w > 3, corresponding to an ef\ufb01ciency of about\n74 % for genuine b-jets from top decay. Additionally, the two W jets are both required to have b-tagging\nweights of w < 3, to reduce the probability that the b-jet from the top decay is included in the W. No\nmass requirements are placed on the hadronic top candidate at this stage.\nA leptonic top is then reconstructed from one of the other jets and a reconstructed leptonic W decay.\nThe leptonic W is formed from the identi\ufb01ed lepton and a neutrino, whose transverse momentum (px, py)\nis taken to be equal to the missing transverse momentum vector of the event. The longitudinal momentum\nof the neutrino is inferred using the constraint of the known W mass, which leads to a quadratic equation\nfor pz which has either two or no solutions. In the case of two solutions, the one with the smaller pz is\nchosen. If there is no solution, the measured missing ET is scaled down, preserving its direction, until\na solution is possible. The reconstructed W is then combined with another jet which was not used in\nmaking the hadronic W, which is assumed to be the b-jet from the leptonic top decay. This jet is required\nto have ET > 20 GeV. No requirements are placed on the b-tagging weight for this jet, which is instead\nenhanced in b-\ufb02avour due to the topological reconstruction of the t\u00aft event.\nThis procedure is performed for all possible combinations of jets in each event. In an event with four\njets, several assignments of jets to the hadronic top b-jet, leptonic top b-jet and W decay jets are possible,\nconstrained by the requirements made on the b-tagging weights for the jets assigned to the hadronic\ntop decay. In events with more than four jets, some jets will be left unassigned, and are assumed to\nbe spectator jets from initial or \ufb01nal state radiation or the underlying event. As the number of jets in\nthe event increases, the number of combinations satisfying all the requirements increases very rapidly,\nfrom typically one or two combinations in events with four jets to an average of nine combinations for\nevents with six or more jets. The combination with the largest scalar sum of the pT of the two tops is\nretained for further analysis. In 100 pb\u22121 of fully-simulated t\u00aft events plus W+jets background, 3028\nevents are selected, of which 80 % are semileptonic t\u00aft events with t \u2192be\u03bd or b\u00b5\u03bd, with the background\nbeing dominated by t\u00aft with b \u2192b\u03c4\u03bd (11 %) and W+jets (6 %), together with smaller contributions from\ndilepton and single top events.\n5.1.1\nMass \ufb01tting\nAfter all these selections, only one assignment of jets and leptons to the hadronic and leptonic top de-\ncays remains. The resulting distributions of reconstructed hadronic and leptonic top masses are shown\nin Fig. 5. Clear top mass peaks are seen in both distributions, though with signi\ufb01cant combinatorial\nbackground and a small contribution from W+jet and single top background events. Contributions from\nnon-t\u00aft events (denoted class 1), events where both tops are incorrectly reconstructed (class 2), events\nwhere one top (hadronic or leptonic) is correctly reconstructed and the other is not (classes 3 and 4), and\nevents where both tops are correctly reconstructed (class 5) are shown separately. For these purposes, a\ntop decay is considered correctly reconstructed if the associated b-jet is actually labelled as a b-jet by the\nMonte Carlo truth analysis, and the direction of the reconstructed top decay is within \u2206R of 0.5 (2.0) for\nthe hadronically (leptonically) decaying top. The hadronic top mass distribution in Fig. 5 shows peaks\nfor classes 3 and 5, and the leptonic top mass shows peaks for classes 4 and 5, though with a consider-\nably worse mass resolution. Both distributions also show some \u2018peaking\u2019 structure in the combinatorial\nbackgrounds.\nThe analysis aims to extract a pure sample of b-jets from the reconstructed leptonic top decay. The\nleptonic top is chosen since it does not suffer from combinatorial background within the top decay\nitself\u2014by contrast, in the hadronic top decay with three jets combined to give the top mass, a mis-\nassignment of jets to W decay and b will give the same top mass, with only the reconstructed hadronic\nW mass changing. Since the resolution on the latter quantity is relatively poor, many reconstructed bj\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n514\n\nHadronic top mass (GeV)\n100\n150\n200\n250\n300\n350\n400\nEvents / 4 GeV\n0\n20\n40\n60\n80\n100\n120\n140\nHadronic top mass (GeV)\n100\n150\n200\n250\n300\n350\n400\nEvents / 4 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n5. both tops correct\n4. hadronic top b/g\n3. leptonic top b/g\n2. both tops b/g\n1. non tt background\nATLAS\nLeptonic top mass (GeV)\n100\n150\n200\n250\n300\n350\n400\nEvents / 4 GeV\n0\n20\n40\n60\n80\n100\nLeptonic top mass (GeV)\n100\n150\n200\n250\n300\n350\n400\nEvents / 4 GeV\n0\n20\n40\n60\n80\n100\nATLAS\nFigure 5: Reconstructed hadronic (left) and leptonic (right) top masses for the selected jet combi-\nnation, showing the contributions from correctly reconstructed t\u00aft events, combinatorial and non-t\u00aft\nbackground, normalised to 100 pb\u22121. The numbers refer to the classes discussed in the text.\ncombinations are compatible with the W mass, and the W mass requirement gives little discrimination.\nIn the leptonic top decay, the W has no decay jets, and this problem does not arise.\nThe resolution on the reconstructed leptonic top mass is poor, and there is a large combinato-\nrial background. This is reduced by \ufb01rst requiring that the hadronic top mass is in the signal region\n(140 < mjjj < 190 GeV), and then dividing the sample into \ufb01ve sub-samples according to the recon-\nstructed ET of the leptonic top b-jet, as the level of background depends strongly on this jet energy. The\nresulting leptonic top mass distributions can be seen in Fig. 6, where it can be seen that the top signal\nis signi\ufb01cantly enhanced, especially for high leptonic top jet ET. Events from classes 4 and 5 have cor-\nrectly reconstructed leptonic tops, where the leptonic top jet is pure b \ufb02avour, whilst the other events are\ncombinatorial background, with a mixture of jet \ufb02avours (they can include b-jets from the hadronic top,\nand jets which are not unambiguously from a single parton, containing some particles from the decay of\nB hadrons).\nIn order to correct for this background of event classes 1\u20133 under the leptonic top mass peak, both its\nsize and \ufb02avour composition must be determined. This is done on a statistical basis using the sideband\nregion with high mb\u2113\u03bd to normalise the background contribution, and a control sample to determine the\nshape of its mass distribution. The control sample is generated from events where the reconstructed\nhadronic top mass satis\ufb01es 200 < mjjj < 400GeV, and where the leptonic top b-jet satis\ufb01es a cut on the\nb-tagging weight of w < 4. These samples are dominated by events in classes 2 and 3, and provide a\nreasonable model of the background shapes in the signal sample.\nThe amount of background under the signal is then extracted using a simultaneous \ufb01t to both signal\nand control sample leptonic top mass distributions. The control sample is described using a \ufb01t function\nFb(mb\u2113\u03bd) given by:\nFb(mb\u2113\u03bd) = E((mb\u2113\u03bd \u2212c0)/400),\n(3)\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n515\n\n (GeV)\nb\n\u03bdl\nm\n100\n150\n200\n250\n300\n350\n400\nevents / 8 GeV\n0\n5\n10\n15\n20\n25\n (GeV)\nb\n\u03bdl\nm\n100\n150\n200\n250\n300\n350\n400\nevents / 8 GeV\n0\n5\n10\n15\n20\n25\n<40 GeV\nT\n20 0\n0\nif x < 0 .\n(4)\nThe signal is described by a \ufb01t function Fs(mb\u2113\u03bd) consisting of a scaled background function plus a\nGaussian representing the signal, given by:\nFs(mb\u2113\u03bd) = c4Fb(mb\u2113\u03bd)+c5G((mb\u2113\u03bd \u2212c6)/c7).\n(5)\nThe parameter c4 represents the ratio of class 1\u20133 background contributions in signal to control samples,\nand c5 the amount of top signal with \ufb01tted mean c6 and RMS width c7. All eight parameters are extracted\nin a simultaneous \u03c72 \ufb01t to the signal and control sample mass distributions, thus determining the shape of\nthe background under the signal peak from the control sample, and the normalisation of the background\nfrom the sideband of the signal distribution at high mb\u2113\u03bd. Separate \ufb01ts are performed in each leptonic\ntop jet ET bin, and the results are shown in Fig. 6. The \ufb01ts are performed over the mass range b1 and\nb2, where b1 is set to 90, 90, 110, 120, and 130 GeV for the 20\u201340, 40\u201380, 80\u2013120, 120\u2013160 and 160-\n200 GeV jet ET bins, re\ufb02ecting the differing kinematic cut-off in each jet mass bin.\n5.1.2\nBackground subtraction\nThe sample of leptonic top b-jets is divided using the reconstructed leptonic top mass into a signal region\nde\ufb01ned by s1 < mb\u2113\u03bd < s2 where s1 = c6 \u22122c7 and s2 = c6 +2c7 (i.e. mb\u2113\u03bd within \u00b12\u03c3 of the \ufb01tted top\nmass peak position) and a sideband region with mb\u2113\u03bd outside this range. The distribution of the b-tagging\nweight in the signal region contains contributions both from pure b-jets (events of classes 4 and 5), and\nfrom the mixture of \ufb02avours forming the combinatorial background under the signal peak. This latter\nmixture is well described by the jets in the sideband region, so its effect is corrected for by subtracting\nthe b-tagging weight distribution in the sideband region, scaled according to the expected normalisation\nderived from the mass \ufb01t discussed in Section 5.1.1. The scale factor S is given by:\nS =\nR s2\ns1 Fb(mb\u2113\u03bd)dmb\u2113\u03bd\nR s1\nb1 Fb(mb\u2113\u03bd)dmb\u2113\u03bd +\nR b2\ns2 Fb(mb\u2113\u03bd)dmb\u2113\u03bd\n(6)\nand varies between around 4 for the 40-80 GeV bin to 0.3 for the 160-200 GeV bin. Once this scaled\nbackground has been subtracted, the resulting b-tagging weight distribution in the signal region is sta-\ntistically compatible with that expected from pure b-jets. The uncertainty on the amount of background\nto subtract in each bin of the b-tagging weight distribution has two components: the uncertainty on the\nnumber of background events in each bin in the sideband distribution, scaled by S, and the uncertainty\non S itself, which is correlated across all bins. The latter is calculated using equation 6 together with the\nfull correlation matrix for the parameters c0 to c6 which are used in the background function Fb(mb\u2113\u03bd).\nIn order to check that this selection does not introduce a bias, the b-tagging weight distribution of\ntrue b-jets in the selected signal region was checked, and found to be compatible with that of all b-jets\nwithin the \u03b7 and ET acceptance. Hence this selected sample of b-jets can be safely used to measure the\nb-tagging ef\ufb01ciency.\n5.1.3\nTopological selection results\nThe results of applying this analysis procedure to full simulation events (including background) are\nshown as the \u2018Topological\u2019 entries in Table 6 in Section 5.4. For each leptonic top jet ET bin, the number\nof jets selected in the window s1 < mb\u2113\u03bd < s2, the number remaining after subtracting the scaled sideband\nbackground, and the purity of the selected sample are given, together with the background-subtracted\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n517\n\nsample b-\ufb02avour purity, i.e. the fraction of the background-subtracted sample which is made up of b-\n\ufb02avour jets according to the Monte Carlo truth information. It can be seen that in all cases the \ufb02avour\npurity is compatible with unity within errors, showing that the background subtraction procedure is\nworking well and producing a statistically pure sample of b-jets. Table 6 also shows the results integrated\nfrom 40-200 GeV. The sample size and purity in the 20\u201340 GeV jet ET bin is not suf\ufb01cient to make a\nsensible measurement of the b-tagging ef\ufb01ciency, and this bin is not considered in what follows.\nUsing this b-jet selection, the b-tagging ef\ufb01ciency corresponding to any cut on the b-tagging weight\ncan be obtained by integration of the b-tagging weight distribution, i.e. calculating the fraction of the\nbackground-subtracted weight distribution above the cut value. This ef\ufb01ciency is shown as a function of\nb-tagging weight cut for each b-jet ET bin in Fig. 7 as the points with error bars. The solid histogram\nshows the same distribution for an unbiased sample of pure b-jets in t\u00aft events without any event selection,\nderived using Monte Carlo truth information. If the method is correct, the two distributions should agree\nwithin errors. The statistical errors on the measured b-tagging ef\ufb01ciency (which are highly correlated\nbetween bins) have two components: the binomial errors due to the \ufb02uctuations in numbers of events\npassing the cut for signal and background, and the uncertainty due to the background subtraction scale\nfactor S. Figure 7 also shows the difference \u03b4 = \u03b5meas \u2212\u03b5true between the estimated and true ef\ufb01ciency,\nwhich should be compatible with zero if the method is working well. This is seen to be the case except\nfor very high b-tagging ef\ufb01ciencies in the two highest jet ET bins, where the statistics are limited. The\ncombined ef\ufb01ciency curve for b-jet ET > 40 GeV is shown in Fig. 8(a). These results are derived by\nweighting the individual b-tagging ef\ufb01ciencies measured in each energy bin by the b-jets ET distribution\nin t\u00aft events.\nThe method has been validated using ensemble tests based on sets of Monte Carlo subsamples of\nvarious integrated luminosities, derived from a sample of 1793 pb\u22121. Studies of the distributions of \ufb01t\nresults, estimated uncertainties and pulls show that the uncertainty on the b-tagging ef\ufb01ciency returned\nfrom the \ufb01t underestimates the true uncertainty by about 20 %. They also show that the \ufb01t shows sig-\nni\ufb01cant biases and does not always converge correctly for samples of 100 pb\u22121. With 200 pb\u22121 of data,\nthe \ufb01t results are unbiased and the \ufb01t converges in 98 % of the test samples; hence this is considered the\nminimum amount of data for which this technique can be used.\nFigure 8(b) shows the absolute uncertainty returned by the tagging measurement as a function of the\nef\ufb01ciency itself, scaled to an integrated luminosity of 200 pb\u22121. At \u03b5true = 0.6, the statistical error is\nabout 0.038, corresponding to a relative error of \u03c3\u03b5true/\u03b5true =6.4 %.\nSystematic uncertainties have been evaluated as discussed in Section 4.3, with the exception that no\nuncertainties were evaluated for b-jet labelling, Monte Carlo statistics and the top quark mass, which are\nnot relevant for this analysis. The systematic errors are summarised in Table 7.\n5.2\nLikelihood-based selection\nThe likelihood selection uses templates based on event and jet kinematic variables to determine the best\nassignment of jets to t\u00aft decay products within an event. These same likelihoods are also used to select\nevents for which the jet assignments are most likely to be correct.\nTemplates are constructed using several kinematic variables to provide discrimination between \u2018cor-\nrect\u2019 and \u2018incorrect\u2019 permutations. To maximize discrimination, templates are constructed separately for\neach jet multiplicity. All possible permutations of assignments of jets to \ufb01nal-state quarks are considered,\nand, for each permutation within each event, the leptonic and hadronic top quark and hadronic W boson\nare reconstructed, using the reconstructed momenta. The permutation is labelled \u2018correct\u2019 if the jets used\nto reconstruct the particle (t, W, b-quark, or light quark from W decay) are correctly matched to the\nquarks arising from the hard-scatter vertex. To limit the number of jet-parton assignment combinations,\nevents with more than six jets are rejected.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n518\n\nb-tag weight cut\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\n0 9\n1\nb-tag efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n<40 GeV\nT\n20 6. Then a discriminant value D is calculated for each jet\ncombination in the event using the templates, which are taken to be likelihood distribution functions for\neach variable. The \u2018correct combination\u2019 templates are used to get the \u2018s\u2019 values for the ith variable, and\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n521\n\ndiscriminant value\n0\n0.2\n0.4\n0.6\n0.8\n1\n# events\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\ndiscriminant value\n0\n0.2\n0.4\n0.6\n0.8\n1\n# events\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nATLAS\n, correct perm\ntt\n, incorrect perms\ntt\nW+jets\nWbb\ndiscriminant value\n0.985\n0.99\n0.995\n1\n# events\n0\n10\n20\n30\n40\n50\ndiscriminant value\n0.985\n0.99\n0.995\n1\n# events\n0\n10\n20\n30\n40\n50\nATLAS\n, correct perm\ntt\n, incorrect perms\ntt\nW+jets\nWbb\nFigure 10: Discrimination between correct and incorrect permutations, best permutation chosen for each\nevent, for entire range of D, and for D \u22650.985. Events are chosen which have at least 1 b-tagged jet.\nthe \u2018incorrect combination\u2019 templates are used to get the \u2018b\u2019 values. They are combined according to:\nD =\n\u220fi(si/bi)\n1+\u220f(si/bi).\n(7)\nIn each event, the combination with the largest value of D is retained. The resulting distributions are\nshown in Fig. 10, normalised to 100 pb\u22121. The contributions from the correct combination, incorrect\ncombinations and non-t\u00aft events are shown separately. As can be seen from the right-hand plot, very\nhigh discriminant values are required to select a sample with high purity.\nThe b-jet purity is shown vs. the number of selected events in Fig. 11, for several ranges of jet\nET. Higher purity samples can be obtained by tightening the cut on D, but at the expense of selection\nef\ufb01ciency. A cut of D > 0.985 was chosen for these studies assuming 100 pb\u22121 samples, which could be\nraised to improve the purity once the data sample size allows.\n5.2.2\nBackground subtraction\nAssuming the cuts used to discriminate between correct and incorrect jet-parton assignments reduce the\nbackground from non-t\u00aft events to a negligible level, the primary background to be considered arises\nfrom jets incorrectly assigned to b-quarks. These jets can be from light, c, or s-quarks from W decay, and\nfrom ISR/FSR jets. To estimate the effect of the background on the b-tagging ef\ufb01ciencies, it is necessary\nto determine the tagging rate of jets in background events, as well as the fraction of signal (and hence\nbackground) events in the data sample. Using Monte Carlo truth information to determine the true \ufb02avour\nof the jet assigned to the leptonic top decay (and assumed to be a b-jet), signal (S) and background (B)\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n522\n\n# events\n0\n50\n100\nb-frac ion\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n < 40 GeV\nT\n20 < p\nATLAS\n# events\n0\n500\nb-frac ion\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n < 80 GeV\nT\n40 < p\nATLAS\n# events\n0\n200\n400\nb-frac ion\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n < 120 GeV\nT\n80 < p\nATLAS\n# events\n0\n100\n200\nb-fraction\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n < 160 GeV\nT\n120 < p\nATLAS\n# events\n0\n50\n100\nb-fraction\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n < 200 GeV\nT\n160 < p\nATLAS\nFigure 11: Likelihood selection: b-jet purity vs. number of selected events (discriminant cut value\nranging from 0.975 to 1) for each b-jet ET bin.\ntemplates are formed, binned by discriminant value. Using these templates, a likelihood is constructed\nto \ufb01nd the fraction fsgn of signal events. The likelihood formed from data (D) and templates is:\nlnL (fsgn) =\n#bins\n\u2211\ni\n\u2212Di ln(fsgnSi +(1\u2212fsgn)Bi),\n(8)\nwhere Di is the number of data events in the ith bin, and Si and Bi are the values of the ith bins of signal and\nbackground templates. The associated background b-tagging ef\ufb01ciencies are determined using events\npassing a looser discriminant cut (D > 0.9), since the tag rate for jets in the background do not depend\nstrongly on the value of this cut. These are shown for several ranges of jet ET in Fig. 12. The average of\nthe b-tagging ef\ufb01ciencies of non-b-jets over all jet ET bins is used, giving \u03b5bkgd\nbtag = 0.021\u00b10.004. Once\nthe b-tagging ef\ufb01ciencies for background events and fsgn are obtained, the following equation is used to\nsolve for \u03b5b-jets\nbtag :\n\u03b5b-jets\nbtag =\n1\nfsgn\n\u0010\n\u03b5all jets\nbtag\n\u2212(1\u2212fsgn)\u03b5bkgd\nbtag\n\u0011\n(9)\n5.2.3\nResults for b-tagging ef\ufb01ciency measurement\nThe b-tagging ef\ufb01ciencies are determined for events binned in b-jet ET, with bin sizes chosen to match\nthe kinematic and topological methods. To simulate the 100 pb\u22121 sample, histograms have been scaled\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n523\n\nDiscriminant value\n0.985\n0.99\n0.995\n1\nb-tagging efficiency\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.01\n\u00b1\n=0.012 \nbkg\n\u2208\n < 40\nT\n20 < E\nsignal b-jets\nbackground jets\nATLAS\nDiscriminant value\n0.985\n0.99\n0.995\n1\nb-tagging efficiency\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.005\n\u00b1\n=0.022 \nbkg\n\u2208\n < 80\nT\n40 < E\nsignal b-jets\nbackground jets\nATLAS\nDiscriminant value\n0.985\n0.99\n0.995\n1\nb-tagging efficiency\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.007\n\u00b1\n=0.021 \nbkg\n\u2208\n < 120\nT\n80 < E\nsignal b-jets\nbackground jets\nATLAS\nDiscriminant value\n0.985\n0.99\n0.995\n1\nb-tagging efficiency\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.012\n\u00b1\n=0.024 \nbkg\n\u2208\n < 160\nT\n120 < E\nsignal b-jets\nbackground jets\nATLAS\nDiscriminant value\n0.985\n0.99\n0.995\n1\nb-tagging efficiency\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.024\n\u00b1\n=0.048 \nbkg\n\u2208\n < 200\nT\n160 < E\nsignal b-jets\nbackground jets\nATLAS\nFigure 12: b-tagging ef\ufb01ciencies for signal (b-jets), and tag rate for light and c-jets (background) for\nevents passing a discriminant cut of 0.9. Each plot was done for a different range of jet ET.\nto the number of events expected in the sample. The sample purities are shown for the ET-binned sample\nin Table 6 for comparison with the other methods, and the b-tagging ef\ufb01ciencies are shown in Fig. 13.\nThe average of b-tagging ef\ufb01ciencies for jet ET > 40 GeV is 0.674 \u00b1 0.086, consistent with the actual\nvalue of 0.658.\nEnsemble testing was done using 100 pseudo-experiments, verifying the same central value and error.\nThe pull distribution of the 100 pseudo-experiments has a width of 0.60 standard deviations, so the error\n(0.086) is scaled by 0.60 to get an expected statistical error 0.05 for the 100 pb\u22121 sample. The low pull\nwidth arises because, for some pseudo-experiments in the ensemble, likelihood \ufb01ts of signal fractions\nare close to 0 or 1. Failing to determine asymmetric errors properly for these pseudo-experiments results\nin an overestimation of the error.\nSystematic uncertainties are determined for the effects discussed in Section 4.3, using the full avail-\nable MC statistics for all except the effect of background events in the sample. Ensemble testing was\nused to evaluate this error, using double the expected number of events and no background events. In\ngeneral, the systematic errors are large for the cuts chosen for the 100 pb\u22121 sample. These are expected to\nimprove once data samples are available and the discriminants are optimised, especially once the sample\nsize allows tighter jet ET and discriminant cuts to be used in order to reduce the background from non-t\u00aft\nand wrong combinations.\n5.3\nKinematic selection\nThis section describes the selection of a high purity b-jet sample through the use of a kinematic \ufb01t and\ncuts based on the resulting \ufb01t \u03c72. Other selection criteria, including the use of a b-tag on the hadronic top\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n524\n\n (GeV)\nT\nE\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nb-tagging efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n \"data\"\n-1\n100 pb\nMC truth\nATLAS\nFigure 13: Likelihood method: simulation of b-tagging ef\ufb01ciencies vs. ET for a 100 pb\u22121 sample\nusing the best permutation for events selected with a discriminant cut. The solid line shows the\ntrue b-tagging ef\ufb01ciencies from the full MC sample using truth information. (b-tag weight=6.0,\ndiscriminant cut 0.985)\nb-jet are also used to enhance the purity. As with the other methods described above, it is dif\ufb01cult to get\nhigh purity whilst maintaining suf\ufb01cient statistics, and a data-based background subtraction procedure is\nemployed to derive an effective pure b-jet sample.\n5.3.1\nKinematic \ufb01t and performance\nThe analysis uses the kinematic \ufb01t HITFIT [11], originally developed at D\u00d8. A W mass constraint is\nincluded and the two reconstructed tops are constrained to have the same mass. The top mass can also be\nconstrained. For this study the mean top mass obtained with the unconstrained \ufb01t (172 GeV) was used\nas a constraint in subsequent \ufb01ts. The mean top mass obtained from the \ufb01t was 172 GeV. Both neutrino\nsolutions are considered and the one with the lower \u03c72 is used. The \ufb01t requires calibrations of the jet\nenergy to the parton energy and resolutions of the jets and leptons, which were determined by comparing\nreconstructed quantities with the Monte Carlo truth information.\nOnly the four largest ET jets in the event were used in the kinematic \ufb01t, giving rise to 12 permutations\nwhich were each \ufb01tted. The correct combination is not always in the four leading jets. In 49 % of\nthe events passing the basic semileptonic event selection discussed in Section 2, the four jets from the\nt\u00aft system are reconstructed and pass the jet selection cuts. Out of the events where all four jets are\nreconstructed 44 % contain the ttbar jets in the four leading jets, rising to 92 % of events if the \ufb01rst six\njets are used. However, this leads to a large increase in combinatorial background and was not considered\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n525\n\nfurther.\n2\n\u03c7\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n-1\nEvents / 100 pb\n0\n50\n100\n150\n200\n250\n300\n350\n2\n\u03c7\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n-1\nEvents / 100 pb\n0\n50\n100\n150\n200\n250\n300\n350\nCorrect combination\nWrong combination\nSingle top\nW+jets\nATLAS\n2\n\u03c7\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n-1\nEvents / 100 pb\n0\n10\n20\n30\n40\n50\n60\n70\n80\n2\n\u03c7\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n-1\nEvents / 100 pb\n0\n10\n20\n30\n40\n50\n60\n70\n80\nCorrect combination\nWrong combination\nSingle top\nW+jets\nATLAS\nFigure 14: Kinematic selection: Distribution of the \u03c72 for the permutation with the minimum \u03c72 showing\ncontributions of the signal and backgrounds with standard selection cuts (left plot), and with additional\nrequirements according to selection S3 described in the text (right plot).\nFrom the four leading jets, the permutation with the lowest \u03c72 was chosen, and events where this\n\u03c72 was below a particular cut value were retained. If the four leading jets are four jets from the t\u00aft\nsystem, then the correct permutation is the one with the lowest \u03c72 in 58 % of the cases. Figure 14 (left)\nshows the \u03c72 distribution for the selected combination, including the contributions from correct and\nwrong combinations in t\u00aft events, and from W+jets and single top backgrounds. It can be seen that the\nfraction of correct combinations is not high, even for low \u03c72 values. Several additional selections beyond\nthe \u2018standard cuts\u2019 S0 de\ufb01ned above were tried in order to enhance the purity as follows. Selection S1\nrequires a b-tag with weight w > 5 on the jet assigned as the hadronic b-jet; the effect of this is mainly\nto reduce the W+multijet background. Selection S2 adds a b-tag veto (w < 5) on both jets assigned to\nthe hadronically decaying W. Selection S3 also requires there are six or less jets with ET > 20 GeV, and\nselection S4 requires that the hadronic top pT satis\ufb01es pT > 150 GeV. The relative reduction of wrong\ncombinations and background can be seen in the \u03c72 distribution after selection S3 as shown in Fig. 14\n(right).\nFigure 15 shows the results of these additional selections, in terms of the fraction of jets assigned as\nthe leptonic top b-jet which are really b-jets, and the number of selected events for 100 pb\u22121. Purities of\nup to 90 % are reachable, but at the cost of low selection ef\ufb01ciency. To retain a reasonable number of\nevents, a signal sample is de\ufb01ned using selection S3 with a cut \u03c72 < 10, which leaves around 600 events\nfor 100 pb\u22121.\n5.3.2\nBackground subtraction\nAs for the topological method, a background control sample is used to estimate the composition of the\nremaining background in the sample of selected jets from data. The use of the kinematic \ufb01t excludes\nmost events with masses outside the top mass window, so it is not possible to use top mass sidebands\nto estimate the background composition. However, events with high \u03c7 2 are predominantly wrong com-\nbinations (see Fig. 14). The wrong-combination fraction can be enhanced by selecting events that pass\nthe standard selection S0 and requiring that one of the jets assigned to the W is tagged as a b-jet (w > 5).\nThe \u03c72 distribution of this control sample follows closely that of the wrong combination background in\nthe selected jet sample. The shape of the \u03c72 distribution is used to predict the amount of combinatorial\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n526\n\n cut\n2\n\u03c7\n0\n10\n20\n30\n40\n50\n60\n70\n80\nb-jet purity\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nStandard cuts\n1\nSelection S\n2\nSelection S\n3\nSelection S\n4\nSelection S\nATLAS\n cut\n2\n\u03c7\n0\n5\n10\n15\n20\n25\n30\n35\n40\n-1\nEvents / 100 pb\n2\n10\n3\n10\n4\n10\nStandard cuts\n1\nSelection S\n2\nSelection S\n3\nSelection S\n4\nSelection S\nATLAS\nFigure 15: Left: The purity (fraction of true b jets) of the jet assigned as the b-jet on the leptonic side as\na function of the \u03c72 cut. Right: The corresponding number of events. The different selection criteria are\ndescribed in the text.\nbackground in the signal sample, normalising the two samples in the region 30 < \u03c7 2 < 100. Any test\ndistribution (e.g. the b-tagging weight) extracted from the signal sample can then be corrected for this\ncontribution of background events, taking the shape of the test distribution in background from the region\nof the control sample with \u03c72 > 30. This background subtraction method is very similar to that discussed\nin Section 5.1, with the high \u03c72 region playing the role of the top mass sideband, and the control sample\nwith a b-tagged jet from the W decay corresponding to the sample with high hadronic top mass in the\ntopological selection.\n5.3.3\nResults for b-tagging ef\ufb01ciency measurement\nThe results of applying this selection to simulated data including background and scaling the event count\nto 100 pb\u22121 are shown in Table 6. The purity in the 20-40 GeV jet ET bin is rather low, and the back-\nground from the signi\ufb01cant contribution of single top is not well-estimated. As for the topological\nanalysis, this bin is not used for calculating the b-tagging ef\ufb01ciency. The combined b-tagging weight\ndistribution for the other bins (ET > 40 GeV) is shown in Fig. 16. The b-tagging ef\ufb01ciency correspond-\ning to any given cut can be calculated by integration, and the corresponding statistical errors for various\ntag working points can be seen in Table 7.\n5.4\nComparison of selection methods\nThe performance of the different b-jet selection methods are compared in Table 6, which shows the\nnumber of jets selected as a function of jet ET, the effective number of jets after background subtraction\nprocedures have been performed, the corresponding purity of the original sample, and the b-jet fraction\nof the \ufb01nal background-subtracted sample, which should be compatible with one.\nThe different selections have roughly similar overall performance, with the topological selection\ngiving relatively more jets at high ET, and the kinematic selection more at low ET. All selections allow\na sample of several hundred b-jets to be selected in 100 pb\u22121 of data, although the selections of low ET\nb-jets (20\u201340 GeV) suffer from large backgrounds.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n527\n\nb-tag weight\n-10 -5\n0\n5\n10 15 20 25 30 35 40\n-1\nEvents / 100 pb\n0\n5\n10\n15\n20\n25\n30\n35\nb-tag weight\n-10 -5\n0\n5\n10 15 20 25 30 35 40\n-1\nEvents / 100 pb\n0\n5\n10\n15\n20\n25\n30\n35\nCombined\n > 40 GeV)\nT\n(E\nATLAS\nb-tag weight\n-10 -5\n0\n5\n10 15 20 25 30 35 40\n-1\nEvents / 100 pb\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nCombined\n > 40 GeV)\nT\n(E\nATLAS\nFigure 16: Kinematic selection: (Left): The b-tag weight distribution for the uncorrected sample (un-\n\ufb01lled histogram), for the estimated background sample (\ufb01lled histogram) and the corrected distribution\ncalculated from the difference (data points). Right: The b-tag weight distribution for the corrected sam-\nple (data points) compared with the distribution for true b-jets (histogram). Both plots are normalised to\n100 pb\u22121, but use 967 pb\u22121 of simulated data.\n5.5\nComparison of ef\ufb01ciency measurements\nThe performance of the different b-tagging ef\ufb01ciency measurements is compared in Table 7, which shows\nthe statistical and signi\ufb01cant systematic errors for a true tagging ef\ufb01ciency of 0.6 for all methods. The\nsystematic errors have been evaluated as discussed in [2] and Section 2. The differences in systematic\nuncertainties re\ufb02ect the different uses made of Monte Carlo information by the various methods. The\nexpected statistical errors for other tagging ef\ufb01ciencies, and the simpler IP2D tagging algorithm, are\nshown (where available) in Table 8.\nWith 100 pb\u22121 of data, the counting method can measure the overall b-tagging ef\ufb01ciency to a preci-\nsion of better than 5 %, and, particularly as the luminosity increases through 200 pb\u22121 several alternative\napproaches are possible that also enable the ef\ufb01ciency dependence on other variables (e.g. jet ET) to be\nstudied.\n6\nOptimisation of b-tagging for t\u00aft events\nThe ATLAS multivariate b-tagging algorithms rely heavily on likelihood reference distributions for light-\nand b-quark jets derived from Monte Carlo simulation. The default reference distributions are produced\nusing a mixture of physics processes. In principle, using reference histograms from Monte Carlo t \u00aft\nevents alone could lead to an improvement in tagging performance on t\u00aft events. The selection of a pure\nsample of b-jets from t\u00aft data offers an opportunity to tune the b-tagging algorithms directly on data,\nreducing the dependence on Monte Carlo simulation. Both these topics are discussed below.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n528\n\nJet ET\nSelected\nEffective\nPurity\nEstimated b\nrange (GeV)\njets\njets\n(%)\n\ufb02avour purity (%)\nTopological\n20\u201340\n144\n51\n54\n99\u00b18\n40\u201380\n340\n189\n67\n92\u00b13\n80\u2013120\n223\n138\n78\n98\u00b13\n120\u2013160\n122\n92\n84\n98\u00b13\n160\u2013200\n75\n54\n86\n108\u00b14\n40\u2013200\n819\n515\n60\n-\nLikelihood\n20\u201340\n52\n24\n47\n86\u00b16\n40\u201380\n225\n130\n58\n94\u00b13\n80\u2013120\n204\n143\n70\n97\u00b13\n120\u2013160\n110\n91\n83\n89\u00b13\n160\u2013200\n54\n40\n73\n104\u00b15\n40\u2013200\n593\n403\n68\n-\nKinematic\n20\u201340\n164\n102\n53\n74\u00b16\n40\u201380\n284\n182\n73\n93\u00b14\n80\u2013120\n113\n78\n88\n107\u00b15\n120\u2013160\n38\n30\n90\n103\u00b15\n160\u2013200\n17\n13\n94\n107\u00b16\n40\u2013200\n451\n302\n79\n98\u00b13\nTable 6: Summary of b-jet selection method performance, showing the number of selected b-jets, the\nnumber of jets after background subtraction, the selected sample purity, and estimated b-jet purity of the\n\ufb01nal sample after background subtraction, for each selection method. The results correspond to 100 pb\u22121\nof MC@NLO t\u00aft Monte Carlo plus backgrounds from W+jets, Wb\u00afb, Wc\u00afc and single top production.\nSystematic\nCounting\nTopological\nLikelihood\nKinematic\nlepton+jet\ndilepton\nLight jets and \u03c4\n0.1\n0.7\n0.5\n5.2\n0.6\nCharm jets\n0.0\n0.8\n0.7\n4.6\n2.2\nJet energy scale\n0.9\n0.5\n0.5\n2.5\n1.1\nb-jet labelling\n1.4\n1.4\n-\n-\n-\nMC generators\n0.1\n2\n0.2\n5.9\n5.5\nISR/FSR\n2.7\n2\n1\n2.2\n0.5\nW+jet background\n1.2\n0.3\n2.8\n9.6\n0.3\nSingle top background\n0.1\n0.1\n1.2\n-\n1.2\nTop quark mass\n0.3\n0.5\n-\n4.1\n-\nTotal systematic\n3.4\n3.5\n3.4\n14.2\n6.2\nStatistical (100 pb\u22121)\n2.7\n4.2\n-\n5.0\n7.7\nStatistical (200 pb\u22121)\n1.9\n3.0\n6.4\n4.4\n5.5\nTable 7: Summary of systematic and statistical uncertainties on the measurement of the b-tagging ef\ufb01-\nciency at a true ef\ufb01ciency of \u03b5true = 0.6, for the counting method in lepton+jets and dilepton channels,\nand the topological, likelihood and kinematic jet selection methods. The uncertainties are expressed as\nrelative errors (in %).\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n529\n\nTag\n\u03b5true\nCounting\nTopological\nLikelihood\nKinematic\nlepton+jet\ndilepton\nIP3D+SV1\n0.5\n2.8\n4.0\n6.2\n8.8\n6.1\nIP3D+SV1\n0.6\n1.9\n3.0\n6.4\n5.2\n5.5\nIP3D+SV1\n0.7\n1.4\n2.0\n6.7\n5.1\n4.9\nIP2D\n0.5\n7.4\n4.7\n6.2\nIP2D\n0.6\n6.5\n5.1\n5.5\nIP2D\n0.7\n5.6\n5.1\n5.0\nTable 8: Expected statistical errors (relative errors in %) on the b-tagging ef\ufb01ciency for 200 pb\u22121 mea-\nsured using each technique, for IP3D+SV1 and IP2D taggers at various working points.\nIP3D+SV1 weight\n-10\n-5\n0\n5\n10\n15\n20\n25\n30\n35\n40\nEvents\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nb jets default ref histograms\nb jets top sample ref histograms\nlight jets default ref histograms\nlight jets top sample ref histograms\nATLAS\nb tag efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nlight jet rejection\n10\n2\n10\n3\n10\n4\n10\nR=0.40 Tower\n\u2206\nCone \nR=0.40 Tower NewRef\n\u2206\nCone \nATLAS\nR=0.40 Tower\n\u2206\nCone \nR=0.40 Tower NewRef\n\u2206\nCone \nFigure 17: Comparison of b tagging weights and b tag performance using default and special top sample\nreference histograms.\n6.1\nUsing t\u00aft speci\ufb01c reference histograms\nFor this study, reference histograms based only on t\u00aft events (without the light jet puri\ufb01cation procedure\nwhich discards light jets biased by nearby b-jets [6]) were created using a total of 250k events. By\ncontrast, the default reference histograms were produced using a variety of physics processes, light jet\npuri\ufb01cation, as well as different versions of the detector geometry, simulation, and reconstruction. The\nfollowing comparison does not attempt to disentangle the various effects of those differences; for more\ndetails, see [6]. The resulting t\u00aft event b-tagging weights are compared to those calculated using the\ndefault reference histograms, for the IP3D+SV1 b-tagging algorithm with the default tower-based Cone\njet algorithm with \u2206R = 0.4. The results are shown in Fig. 17. The left plots shows the b-tagging weights\nfor b-jets and light jets calculated with both sets of reference histograms.\nThe weights for both b-jets and light quark jets calculated with the top sample reference histograms\nare on average smaller than those from the default reference histograms. However, because the b-tagging\nweights are smaller for both b-jets and light jets, the performance should not change signi\ufb01cantly. This\nis con\ufb01rmed by the right plot in Fig. 17, showing the b-tag ef\ufb01ciency vs the light jet rejection. Within\nthe statistical uncertainty there is no difference in the performance. So there appears to be no signi\ufb01cant\nadvantage in using special dedicated t\u00aft reference histograms when applying b-tagging to t\u00aft events.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n530\n\n6.2\nCalibrating b-tagging using data\nIn principle, the b-jet selection methods discussed in Section 5 should allow the reference distributions\nfor b-jets in t\u00aft events to be determined directly from data, removing the need for Monte Carlo b-jets\ncompletely. However, none of the methods produce a pure b-jet sample without the need for back-\nground subtraction, and hence do not identify a pure sample of b-jets from which multiple variables\n(and their correlations) can be extracted simultaneously on a jet-by-jet basis. Instead, background-\nsubtracted distributions are produced. These can be used directly as reference distributions only for\none-dimensional likelihoods with a single input variable. For n-dimensional likelihoods (for example\nthe standard tagging weight which is a two-dimensional combination of IP3D and SV1 taggers), an n-\ndimensional background-subtracted distribution would be needed in order to properly model both the two\ninput distributions and their correlation. For higher-dimensional distributions, the required data statistics\nwould quickly become prohibitive.\nAt least for initial data, a more feasible approach would be to use the background-subtracted b-jet\nsamples to check each of the likelihood input variables individually, to determine how well the Monte\nCarlo simulation models the data. Monte Carlo would then be used to form the likelihood reference\ndistributions as before (including correlations between input variables), with the comparison with data\nbeing used to assess systematic uncertainties, e.g. by reweighting Monte Carlo events to more precisely\nfollow the data distributions if discrepancies are seen.\nThis technique is illustrated in Fig. 18, which shows background-subtracted distributions of \ufb01ve\nvariables related to the b-tagging weight computation, derived from the b-jet sample selected using the\ntopological technique of Section 5.1, compared to the true distributions from Monte Carlo. The inte-\ngrated luminosity is 948 pb\u22121. The \ufb01rst two variables are IP3D, the weight derived from the 3D-impact\nparameters of all tracks in the jet; and SV1, the weight derived from the SV1 secondary vertex recon-\nstruction algorithm. The others are all input variables used to form the SV1 secondary vertex weight:\nN2Track, the number of two-track vertices found; SVMass, the mass of the reconstructed secondary\nvertex, and SVEFrac, the energy fraction of the jets associated to the vertex. The spikes around zero for\nthese last three variables correspond to jets where no secondary vertex was found. The variables have\nbeen transformed linearly onto the range [0,1] to simplify the subtraction procedure.\nIt can be seen that the background-subtracted distributions are consistent with the Monte-Carlo truth,\ndemonstrating the validity of the method. It would be straightforward to construct reweighting factors\nfrom these distributions, to explore possible systematic variations. However, it should also be noted that\nthe techniques discussed in Section 5.5 already allow the b-tagging ef\ufb01ciency to be measured with min-\nimal dependency on the Monte Carlo\u2014the main use of this technique would then be to understand how\nto improve the Monte Carlo simulation of b-jets, which could help to increase the b-tagging performance\nin t\u00aft events by giving each variable its optimal weight in the likelihood.\n7\nConclusions\nThe studies of jet reconstruction presented above show that the b-jet energy resolution in t\u00aft events is not\nvery sensitive to the jet algorithm and parameters chosen. The jet angular resolution is more sensitive,\ndegrading in particular with large jet cone sizes.\nWith 100 pb\u22121 of data, several methods are available to make useful measurements of the b-tagging\nef\ufb01ciency in t\u00aft events. The tag counting method can reach an overall relative precision of around 5 %, in\nboth lepton+jets and dilepton channels. However, this method only gives an \u2018integrated\u2019 measurement,\nvalid for the ET and \u03b7 distribution of b-jets selected by the t\u00aft event selection. Monte Carlo techniques\nwould have to be used to extrapolate this measurement for other jet ET and \u03b7 distributions, perhaps also\nincorporating information derived from studies of dijet samples [1].\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n531\n\nIP3D weight\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\n0 9\n1\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nSV1 weight\n0\n0.1\n0.2\n0 3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nN2Track\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\n0 9\n1\n-3\n10\n-2\n10\n-1\n10\nSVMass\n0\n0.1\n0.2\n0 3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSVEFrac\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\n0 9\n1\n-3\n10\n-2\n10\n-1\n10\nFigure 18: Background-subtracted b-tagging variable distributions derived from the b-jet sample\nselected by the topological method, with 948 pb\u22121 of simulated t\u00aft plus background data. The\nderived distributions are shown by the points with error bars, and the Monte Carlo truth for an\nunbiased sample of b-jets is shown by the solid histograms.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n532\n\nOther techniques, based on the topology and kinematics of t\u00aft events, can be used to select a sample\nof jets enriched in b-\ufb02avour, which can then be used to measure the b-tagging ef\ufb01ciency as a function\nof other variables. This requires that the remaining non-b background in the selected jet samples be\nestimated and removed, and a variety of techniques are available for doing that, based either on data or\nMonte Carlo. These techniques are less statistically powerful than the tag counting method, achieving\noverall b-tagging uncertainties of around 10 % with 100 pb\u22121, but will become increasingly powerful as\nmore data becomes available.\nCalibrating the b-tagging likelihood reference distributions from Monte Carlo t\u00aft events rather than\nthe generic event mixture used by default does not signi\ufb01cantly affect the performance of the standard\nalgorithms, which demonstrates the robustness of the b-tagger. On the other hand, the b-jet selection\nmethods discussed above also allow reference distributions from t\u00aft data to be obtained; with moderate\nintegrated luminosity these are likely to be more useful to cross-check the Monte Carlo description of\nlikelihood input variables rather than as a direct input to b-tag calibration.\nReferences\n[1] ATLAS Collaboration, \u2019b-Tagging Calibration with Jet Events\u2019, this volume.\n[2] ATLAS Collaboration, \u2019Top Quark Physics\u2019, this volume.\n[3] ATLAS Collaboration, \u2019Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties\u2019,\nthis volume.\n[4] ATLAS Collaboration, \u2019Determination of the Top Quark Pair Production Cross-Section\u2019, this vol-\nume.\n[5] ATLAS Collaboration, \u2019Triggering Top Quark Events\u2019, this volume.\n[6] ATLAS Collaboration, \u2019b-Tagging Performance\u2019, this volume.\n[7] S.D. Ellis, J. Huston, K. Hatakeyama, P. Loch and M. Toennesmann, Jets in Hadron-Hadron colli-\nsions, 18th October 2007.\n[8] R. Seuster, Hadronic Calibration of the ATLAS Calorimeter, proceedings of the CALOR 2006\nconference.\n[9] S. Sorgensen, Jet Reconstruction and Calibration in the ATLAS Calorimeters, proceedings of the\nCALOR 2006 conference.\n[10] ATLAS Collaboration, \u2019Jets from Light Quarks in t\u00aft Events\u2019, this volume.\n[11] S. Snyder, Measurement of the top quark mass at D\u00d8, FERMILAB-THESIS-1995-27.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH t\u00aft EVENTS\n533\n\nb-Tagging Calibration with Jet Events\nAbstract\nThis note describes two strategies for data-based measurement of the semi-\nleptonic b-tagging ef\ufb01ciency of ATLAS lifetime b-tagging algorithms using jet\ndata. The pT,rel method uses templates of the muon pT relative to the jet+muon\naxis for bottom, charm, and light jets to estimate the b-quark content of a\njet sample. The b-tagging ef\ufb01ciency is obtained by measuring the b-quark\ncontent before and after tagging a sample. The second method, System 8, uses\ntwo samples of jets of differing b-quark content and two uncorrelated tagging\nalgorithms to form a system of 8 equations and 8 unknowns, one of which\nis the b-tagging ef\ufb01ciency. Both methods use a Monte Carlo scale factor to\nconvert the measured semi-leptonic ef\ufb01ciency to an inclusive ef\ufb01ciency. Both\nmethods give results binned in pT and \u03b7. Good agreement was found between\nthe b-tagging ef\ufb01ciencies determined by both techniques and true Monte Carlo\nfor 15 < pT < 80 GeV, however above 80 GeV both methods have dif\ufb01culty.\nInitial systematics studies have been performed which indicate that it should\nbe possible to control the absolute error on b-tagging ef\ufb01ciency to 6% for both\nmethods. This error does not include the error associated with converting the\nsemi-leptonic ef\ufb01ciency to the inclusive ef\ufb01ciency.\n1\nIntroduction\nMany analyses at the LHC will rely on the presence of b-quarks. Top production, Standard Model\nHiggs boson searches, and searches for physics beyond the Standard Model, for example, all have \ufb01nal\nstates involving b-quarks. To estimate the backgrounds from well known Standard Model processes\nafter applying b-tagging algorithms it is necessary to know the tagging ef\ufb01ciency for b-jets, for light-jets\n(fake rate or mistagging rate), and for c-jets (charm-tagging ef\ufb01ciency). All three ef\ufb01ciencies should\nbe measured as accurately as possible: systematic errors in the b-tagging calibration can translate to\nlarge errors in an analysis. Although the fake rate and c-tagging rate are important, only the b-tagging\nef\ufb01ciency is considered in this note.\nIn order to measure the b-tagging ef\ufb01ciency we must know the bottom quark content (\u2018b-content\u2019)\nof a calibration sample well. Unfortunately, it is dif\ufb01cult to select a pure b-jet sample in the data. Two\nindependent methods to calibrate the b-tagging algorithms are currently under study in ATLAS. The \ufb01rst\nmethod uses a high purity sample of top quark events. Full kinematic reconstruction enables the proper\nidenti\ufb01cation of the jet resulting from the fragmentation of the b-quark from the top quark decay. A\ntagging algorithm can be run on that sample of jets and the ef\ufb01ciency measured [1]. Similarly, one can\ncount tags in a high purity sample of top events and estimate both the tag rate and the cross section [1].\nThis note describes the determination of the b-tagging ef\ufb01ciency in QCD jet data. Un\ufb01ltered QCD\njet data have a very small fraction of b-jets at small jet energy and small effective \u221as, however. In order\nto increase the fraction of b-jets we require that jets in the sample contain a muon. Though muons come\nfrom other sources, a major source is the semi-leptonic decay of b-quarks or c-quarks resulting from the\nb-quark decays. A consequence is that only the lifetime tagging ef\ufb01ciency in semi-leptonic decays of\nb-jets is measured by the techniques described here. The semi-leptonic ef\ufb01ciency must be corrected to\nobtain an inclusive b-tagging ef\ufb01ciency. The scaling is determined from Monte Carlo; this note only\nbrie\ufb02y touches on the determination of this scale factor.\nTwo standard lifetime-based b-tagging algorithms, IP2D and IP3D+SV1 [2], are used to demon-\nstrate the calibration methods and estimate systematic errors. Brie\ufb02y, IP2D uses reconstructed tracks\n534\n\nand their transverse impact parameters to look for jets with displaced tracks inconsistent with light-jets.\nIP3D+SV1 is a combined tagger: IP3D is similar to IP2D, but also takes the longitudinal impact pa-\nrameter into account; SV1 reconstructs a secondary vertex from tracks near a jet. SV1 uses a likelihood\nmade up of the invariant mass of the tracks associated with the secondary vertex, the ratio of the energy\nof tracks in the secondary vertex to the energy of tracks associated to the jet, and the total number of\ntwo-track vertices reconstructed in a jet. Methods that measure the b-tagging ef\ufb01ciency that work for\nthese particular taggers are expected to work for other lifetime taggers as well.\nTwo separate calibration techniques are described in this note:\n\u2022 The pT,rel method, described in Section 3, uses Monte Carlo-derived templates, for b-, c-, and\nlight-jets, of the relative pT of a muon with respect to the jet+muon axis. The b-content of a jet\ndata sample can then be determined by \ufb01tting the pT,rel distribution of the data with these templates\nbefore and after the lifetime tagging algorithms are applied. The b-tagging ef\ufb01ciency is derived\nfrom the changing b-fraction.\n\u2022 The System 8 method, described in Section 4, employs two samples with different b-content and\ntwo uncorrelated tagging algorithms to construct a system of 8 nonlinear equations and 8 un-\nknowns. One of the unknowns is the b-lifetime tagging ef\ufb01ciency.\nBoth of these techniques require a large sample of jets with muons. Section 2 describes a dedicated\ntrigger that will be used to collect this sample along with the Monte Carlo samples and selection cuts\nused in this study.\nThe performance of the tagging algorithms varies with both jet pT and \u03b7 [2]. This is caused by\nboth geometrical acceptance effects and variations in the track reconstruction ef\ufb01ciency. Both methods\ndescribed in this note measure the ef\ufb01ciency as a function of pT and \u03b7. The dependence on other\nvariables could also be measured if required.\nThe ef\ufb01ciency measured from jet data is largely uncorrelated with that measured from the t\u00aft data,\nsince the data sets and the techniques are uncorrelated. Thus the results obtained with the two methods\ncan be combined to further improve the understanding of b-tagging and reduce associated systematic\nerrors. At low jet energies the t\u00aft method is rather sensitive to background contamination, a region where\nthe jet method will perform best. At higher jet energies the t\u00aft method will have a better accuracy.\n2\nSamples and selection\nSeveral sets of Monte Carlo QCD jet events were generated specially for this study. The jet samples were\ngenerated with the standard dijet process using the PYTHIA Monte Carlo generator and full ATLAS\ndetector simulation and detector reconstruction software. ATLAS splits generation of its QCD samples\nby requiring the hard scatter parton pT to be within a certain range: between 17 and 35 GeV, between 35\nand 70 GeV, between 70 and 140 GeV, and between 140 and 280 GeV. Approximately 100,000 events\nwere generated in each range. After generation the samples are combined for the analysis.\nThe b-jet statistics in the QCD sample are not suf\ufb01cient to test the methods discussed here. To\nincrease statistics we also generated muon+jet samples, which further required in each event a muon\nfrom any source with a true pT > 3 GeV and |\u03b7| < 2. The pT cut was chosen as a representative lower\nlimit for muons that can accurately be reconstructed and identi\ufb01ed (we make a reconstructed muon\npT > 4 GeV cut). The requirement of a muon has a dramatic effect on the \ufb02avor composition of the\nsample, increasing the b-jet content by about a factor of 10, and increasing the c-jet content by about a\nfactor of 5.\nIdenti\ufb01cation of electrons in jets is more challenging than that of muons, and so in the studies reported\nhere we restrict ourselves to the muon channel.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n535\n\n [GeV]\nT\nMuon p\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nFraction of Secondary Muons\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nATLAS\nmuon+jets sample\nQCD jet sample\n [GeV]\nT\nJet p\n0\n50\n100\n150\n200\n250\n300\n350\n400\n-jets that originate from b-quark\n\u00b5\nFraction of \n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nmuon+jets sample\nQCD jet sample\nFigure 1: The left plot shows the fraction of all muons with reconstructed pT > 4 GeV that are secondary\nmuons vs muon pT in the QCD samples (\ufb01lled circles) and in the muon+jet samples (open circles). The\ndifference is caused by the generator-level \ufb01ltering of the \u00b5 samples before ATLAS simulation has a\nchance to create the secondary muons. The right plot shows the fraction of muon-tagged jets that are\ndue to a b-quark as identi\ufb01ed by the default Monte Carlo labeling algorithm. In both plots, the black\nopen circles represent muon-tagged jets found in the muon+jet sample and the red \ufb01lled circles represent\nmuon-tagged jets found in the QCD jet sample.\n2.1\nSelection cuts\nThis analysis depends, primarily, on two reconstructed objects: jets and muons. Jets are found as \u2206R <\n0.4 cone jets with a pT > 15 GeV [3]. Jets are calibrated with a standard jet energy scale calibration (and\nthe jet pT includes the muon pT) [4]. Muons are reconstructed from tracks in the outer muon detectors\nand must match an inner detector track with a \ufb01t \u03c72 < 10. The muons must have a reconstructed pT > 4\nGeV [5]. A muon-tagged jet is a jet with a muon contained within a cone of \u2206R < 0.4 of the jet axis.\nThe \ufb02avor of each jet must be determined (b-, c-, or light-jet) in Monte Carlo. The ATLAS \ufb02avor\nlabeling algorithm [2] is used. A jet is labeled as a b-jet if a b-quark with pT > 5 GeV is found in a cone\nof size \u2206R = 0.3 around the jet direction. If no b-quark is present, but instead a c-quark is found then the\njet is labeled as a charm jet. Remaining jets are labeled as light-jets. Light-jets include jets that originate\nfrom a gluon as well as a u-, d-, or s-quark. A b- or c-quark that originates from gluon splitting will be\nclassi\ufb01ed as a b- or c-jet as long as the b- or c-quark is within \u2206R < 0.3 of the jet axis.\n2.2\nMonte Carlo biases\nRequiring that a true muon from b or c decay is present as imposed on the muon+jet Monte Carlo sample\nmeans that almost all muons from decays of \u03c0/K, or from material interactions, are missing. These latter\nsources are here denoted secondary muons. They are present in the inclusive jet sample, of course.\nThe QCD jet sample predicts the secondary muon rate shown by the \ufb01lled circles in Fig. 1 (left). The\nmuon+jet samples have a very different secondary muon average fraction, especially at low muon pT,\nas seen by the open circles in Fig. 1 (left). Fig. 1 (right) shows the fraction of jets with selected muons\nwhich are b-jets in the two samples.\nThe adequacy of the modeling of the secondary muons was checked, \ufb01rstly by checking that the\nsecondary muon rates were consistent separately for b-jets, c-jets, and light-jets between the inclusive jet\nand muon+jet samples. Secondly, we compared the lifetime tagging rates of b-jets and light-jets in the\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n536\n\n [GeV]\nT\nJet p\n0\n50\n100\n150\n200\n250\n300\n350\n-Jets\n\u00b5\nb-quark Tag Rate in \n0\n0.2\n0.4\n0.6\n0.8\n1\nmuon+jets sample\nQCD jet sample\nATLAS\n [GeV]\nT\nJet p\n0\n50\n100\n150\n200\n250\n300\n350\n400\n-Jets\n\u00b5\nlight-quark Tag Rate in \n-0.1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nATLAS\nmuon+jets sample\nQCD jet sample\nFigure 2: Tag rates (IP3D+SV1 weight > 4) for jets containing a reconstructed muon. The left plot\nare jets labeled as b-jets and the right plot are jets labeled as light-jets. In both plots, the open circles\nrepresent muon-tagged jets found in the muon+jet sample and the \ufb01lled circles represent muon-tagged\njets found in the QCD jet sample.\ntwo samples as a function of pT after requiring a reconstructed muon. The results are shown in Fig. 2.\nThe b-jet tag rates (a tag is de\ufb01ned as a jet having an IP3D+SV1 weight greater than 4) in the QCD jet\nand muon+jet samples are consistent within statistics. The light-jet lifetime-tag rate is a factor of about\nthree higher in the muon+jet sample than in the muon-tagged inclusive jet sample. This arises from semi-\nleptonic heavy \ufb02avor decays in nearby jets which contaminate the light-jets with a muon and a displaced\nvertex. Muon-tagged jets in the QCD jet sample are less likely to suffer from this contamination because\nthe muon is more likely to be a secondary, and thus not be associated with an event containing a b-quark.\nReal data is expected to look more like the QCD jet sample with the lower lifetime-tagger tag rate. We\nhave checked that neither tagging calibration technique is affected by changes in the relative mix of\nlight-jet muon sources as far as current Monte Carlo statistics allow.\n2.3\nTrigger\nDedicated trigger signatures are necessary to obtain the required number of muon+jet events. We con-\nsider the statistics obtainable as a function of jet pT. We also discuss a more sophisticated trigger to\nincrease statistics at high jet pT compared to a single jet trigger. A full discussion of the operation of the\nATLAS jet and muon trigger systems can be found elsewhere [6,7].\nThe most obvious choice for a muon+jet trigger is a simple coincidence of lepton and jet triggers\nrequiring no geometrical correlation. The rate for such a trigger is high, so that it must be prescaled,\nespecially at low pT. The \ufb02exible multi-level trigger system of ATLAS allows geometrical correlations\nto be used, explicitly requiring that the muon is close to the triggering jet direction.\nIn the current trigger menu foreseen for running at luminosities around 1031 cm\u22122s\u22121 [8], various\nmuon and jet trigger thresholds are available at Level-1 (L1). Example combinations of these thresholds\nwhich are promising for the studies reported here are the two triggers L1 MU4 J10 and L1 MU6 J10,\nwhich are L1 signatures with a muon with pT > 4 or 6 GeV and a jet with pT > 10 GeV.\nAt Level-2 (L2) the muon selection is re\ufb01ned [7]: the selection sequence is started by the muFast\nalgorithm which con\ufb01rms L1 muon candidates and makes a more precise muon momentum measurement\nusing muon spectrometer hit information. A fast track combination algorithm, muComb, matches tracks\nfound by muFast with tracks found in the inner detector. For the studies reported here, no further selection\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n537\n\nis made at the third trigger level, the event \ufb01lter (EF).\nSince the trigger rate is likely to be limited by bandwidth considerations at low pT rather than the\nphysics rate, the key parameter in considering the trigger performance is the purity of the sample in\nterms of the \ufb01nal selected events which are desired: the of\ufb02ine muon-tagged jets. We de\ufb01ne the purity\nof the triggered sample as the fraction of events passing the trigger that contain such an of\ufb02ine muon-\ntagged jet. For the purpose of this study, the of\ufb02ine muon-tagged jet candidate is as de\ufb01ned in Section 2\n(pT > 4 GeV matching a reconstructed jet with pT > 15 GeV). The purities of jet samples selected by\nthe different trigger requirements discussed above are shown in Table 1.\nThe second and subsequent rows of Table 1 show that a further re\ufb01nement is possible by ask-\ning for angular matching between the trigger muon and jet directions (taken here to be within \u2206R =\np\n\u2206\u03c6 2 +\u2206\u03b72 < 0.4). The choice between L1 MU4 J10 and L1 MU6 J10 will be driven essentially by\nthe required muon pT acceptance. Overall, purities relative to the of\ufb02ine selected sample of around 80%\nare attainable. This re\ufb01ned algorithm will be implemented for data-taking.\nTable 1: Purities of muon-tagged jet events in the triggered sample for different trigger selections. The\npurity is shown for four triggers with two L1 muon trigger thresholds (X). Errors are purely Monte Carlo\nstatistics.\nSignature\nX = 4 GeV\nX = 6 GeV\nL1 MUX J10\n20\u00b11%\n40\u00b13%\nL1 MUX J10 (\u00b5-jet matching)\n51\u00b13%\n79\u00b17%\nL2 muX(muFast) J10 (\u00b5-jet matching)\n70\u00b15%\n82\u00b18%\nL2 muX(muComb: \u00b5+ID) J10 (\u00b5-jet matching)\n78\u00b16%\n84\u00b18%\nA further concern is to provide a good coverage in jet pT extending from low pT as discussed above to\nmuch higher jet pT, where the highest jet threshold will run unprescaled. The strategy adopted, similar to\nthe one used for the inclusive jet trigger, consists of building up a set of muon-jet triggers with different jet\ntrigger thresholds with prescale factors that diminish as pT rises. Figure 3 (left) shows the pT distribution\nof the jet belonging to the muon-jet candidate selected using the signature L2 mu4 J10. Using the set\nof signatures L2 mu4 J10, L2 mu4 J18, L2 mu4 J23, L2 mu4 J35, L2 mu4 J42 with prescale factors\n50/15/12/12/1 a more uniform jet pT distribution is obtained as shown in Fig. 3 (right).\nUnder the assumption that the rate budget for the muon+jet trigger is 1 Hz, 100 000 muon+jet events\nare expected for around 30 hours of running time, corresponding to 1 pb\u22121 of data at a luminosity of\n1031 cm\u22122s\u22121. The combined muon-jet sample used in this study is therefore equivalent to roughly 5\npb\u22121 of data, assuming that the pT acceptance of the trigger is comparable to that generated in the Monte\nCarlo samples.\n3\nThe pT,rel method\nThe pT,rel method is based on the different relative transverse momentum distributions of muons in b-\njets, c-jets, and light-jets. This arises because the muon typically originates from the semi-leptonic decay\nof a heavy hadron in heavy-\ufb02avor jets. The variable pT,rel is de\ufb01ned as the pT of the muon with respect\nto the jet+muon axis. As can be seen Fig. 4, pT,rel has good discrimination between b-jets and c-jets and\nlight-jets.\nThe fraction of b-jets in the muon-tagged jet sample is estimated by performing a \ufb01t to the pT,rel\ndistribution of muons using templates describing the pT,rel shape from b-jets, c-jets and light-jets. The\n\ufb01rst two templates are determined from Monte Carlo using muons originating either from b- or c-hadron\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n538\n\n [GeV]\nT\nJet p\nHz\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nATLAS\n20\n40\n60\n80\n100\n120\n140\n [GeV]\nT\nJet p\nHz\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\n20\n40\n60\n80\n100\n120\n140\nFigure 3: Jet pT distribution for trigger L2 mu4 J10 (left plot) and the jet pT distribution for the sum\nof triggers L2 mu4 J10, L2 mu4 J18, L2 mu4 J23, L2 mu4 J35, L2 mu4 J42 (right plot). In the case\nof the sum of triggers, the triggers were relatively prescaled by factors 50/15/12/12/1. In both plots the\nmuon is con\ufb01rmed at L2 by the muComb algorithm.\ndecays. The template for light-jets is obtained by picking random tracks from jets with no heavy \ufb02avor\nin close proximity, assuming a uniform probability that such tracks fake a muon. We plan on using the\nsame procedure to determine the light-jet templates from data once data is available, although we will\nstill use Monte Carlo for the b- and c-templates. A systematic uncertainty will arise from the presence\nof non b- and c-jets in the real data sample, as discussed in Section 3.3.\nThe pT,rel templates are determined in bins of jet pT and \u03b7 to allow the b-tagging ef\ufb01ciency to be\nmeasured as a function of these variables. The pT,rel distribution is \ufb01tted by allowing the normalization of\nthe three templates to vary and minimizing a likelihood that also accounts for the template statistics [9].\nThe \ufb01t results are expressed in terms of \ufb01t fractions of the b-, c-, and light-jet pT,rel templates, Fb, Fc and\nFlight. The b-tagging ef\ufb01ciency is obtained from the \ufb01t results by:\n\u03b5data,i\nb\n=\nNtag,i\n\u00b5\u2212jetFtag,i\nb\nNi\n\u00b5\u2212jetFi\nb\n(1)\nwhere Ni\n\u00b5\u2212jet and Ntag,i\n\u00b5\u2212jet are, respectively, the number of \u00b5-jets in the i\u2019th jet pT and \u03b7 bin before and\nafter tagging.\nAs described in Section 5, a Monte Carlo-based correction is needed to correct the ef\ufb01ciency for\nb-jets with a muon to inclusive b-jets. In this section we discuss only the lifetime-tagging ef\ufb01ciency\nmeasurement for b-jets with muons.\n3.1\nMeasuring the b-tagging ef\ufb01ciency using pT,rel\nThe full muon+jet sample was split into two equal parts. The \ufb01rst half was used to obtain the pT,rel\ntemplates for light-, c- and b-jets, while the second half was used to measure the tagging performance.\nAs mentioned above, the light-jet pT,rel templates were built from the pT,rel of all tracks within a cone\nof \u2206R < 0.4 and pT > 4 GeV of any reconstructed jet labeled as \u2018light\u2019. The candidate jet was further\nrequired to be at least \u2206R away from any other non-light-labeled jet.\nRepresentative templates are shown in Fig. 4. The pT,rel distributions depend on jet pT, especially for\nb-jets, and the templates are therefore derived in several bins of jet pT. For high-pT jets, the separation\npower of the pT,rel variable signi\ufb01cantly decreases: both the shape and peak value of the pT,rel distribution\nfor b-jets approaches that of c- and light-jets. This can be seen in the right plot of Fig. 4.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n539\n\nThe ROOT TFractionFitter [9] algorithm is used to \ufb01t the templates to the data (the second half of the\nMonte Carlo sample for this study). TFractionFitter uses a standard likelihood \ufb01t that takes into account\nboth the template and data statistics. It includes the constraint that the templates must sum to the data\ndistribution. The histograms in Fig. 5 show the results of the \ufb01t applied to muon-tagged jet samples\nbefore applying the IP3D+SV1 tagger (left) and after (right). Since the shape of the templates for c- and\nlight-jets do not differ greatly, the relative rate of c- and light-jets is not so well determined. The shape of\nthe template for b-jets does differ signi\ufb01cantly, and so the fraction of b-jets can be reliably determined.\nThe b-tagging ef\ufb01ciency is then determined directly using Equation (1).\nAs a \ufb01rst step, an inclusive b-tagging ef\ufb01ciency was measured, averaged over the pT and \u03b7 spectra\nof the jets. The results for the inclusive b-tagging ef\ufb01ciency, for various cuts on the tagger weight w, are\npresented in Table 2. Good agreement is observed between the true Monte Carlo b-tagging ef\ufb01ciency\nand that measured with the pT,rel method, within 1-2% statistical precision.\nTable 2: True Monte Carlo ef\ufb01ciencies and ef\ufb01ciencies obtained with the pT,rel method for 2 taggers\nusing the combined muon+jet samples. The errors are statistical only.\nTagger\nWeight cut\n\u03b5true\n\u03b5meas\nw > 4\n0.748\n0.758 \u00b1 0.018\nIP3D+SV1\nw > 7\n0.627\n0.630 \u00b1 0.013\nw > 10\n0.489\n0.475 \u00b1 0.010\nw > 2\n0.731\n0.715 \u00b1 0.017\nIP2D\nw > 3\n0.640\n0.631 \u00b1 0.013\nw > 4\n0.550\n0.541 \u00b1 0.009\n [GeV]\nT,rel\np\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nb-jet\nc-jet\nlight jet\nATLAS\n [GeV]\nT,rel\np\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nb-jet\nc-jet\nlight jet\nATLAS\nFigure 4: pT,rel templates obtained at low pjet\nT (15 < pjet\nT < 28 GeV) (left) and high pjet\nT (163 < pjet\nT < 300\nGeV) region. Intermediate pjet\nT ranges have distributions lying between these extremes.\nThe stability and sensitivity of the algorithm was tested by varying the fraction of b-jets in the Monte\nCarlo data-like test sample. This can be done in two ways: by decreasing the number of b-jets or by\nadding more light-jets to the initial sample. We have chosen the second approach.\nWe varied the input fraction of light-jets in the Monte Carlo test sample (and thus the fraction of\nb-jets) and re-measured the ef\ufb01ciency. The true input fractions and those obtained from \ufb01ts to templates\nare shown in Table 3. We \ufb01nd agreement within statistical errors.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n540\n\n [GeV]\nT,rel\np\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0\n1000\n2000\n3000\n4000\n5000\n6000\nb-jet\nc-jet\nlight jet\nATLAS\n [GeV]\nT,rel\np\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nb-jet\nc-jet\nlight jet\nATLAS\nFigure 5: A \ufb01t of the pT,rel templates to the test sample. The test sample (black error bars) was \ufb01t with\nthe pT,rel templates obtained from QCD jet Monte Carlo samples (green triangle: light-jet, blue square:\nc-jet, and red dot: b-jet). The red histogram is the result of the \ufb01t. The left plot shows the \ufb01t results for\nall muon-tagged jets, and the right shows that obtained after tagging.\nTable 3: The stability of the pT,rel method as a function of changing b-, c-, and light-jet fractions. The\nfraction of b-jets was varied by altering the number of light-jets as described in the text. The \ufb01rst two\ncolumns show the true and \ufb01tted fractions of b-jets in the muon-tagged jet sample ( fB - true and fB -\nresult of \ufb01t). The remaining columns show the ef\ufb01ciency for two taggers (IP3D+SV1 with w > 7 and\nIP2D with w > 3) as measured directly in Monte Carlo (\u03b5true, and as determined by the pt,rel method\n(\u03b5meas).\nfB - true\nfB - result of \ufb01t\n\u03b5wIP3D+SV1>7\ntrue\n\u03b5wIP3D+SV1>7\nmeas\n\u03b5wIP2D>3\ntrue\n\u03b5wIP2D>3\nmeas\n0.259\n0.260 \u00b1 0.005\n0.627\n0.630 \u00b1 0.024\n0.640\n0.632 \u00b1 0.014\n0.298\n0.298 \u00b1 0.005\n0.627\n0.632 \u00b1 0.013\n0.640\n0.633 \u00b1 0.013\n0.347\n0.349 \u00b1 0.006\n0.627\n0.630 \u00b1 0.015\n0.640\n0.631 \u00b1 0.014\n0.398\n0.397 \u00b1 0.006\n0.627\n0.634 \u00b1 0.015\n0.640\n0.635 \u00b1 0.012\n0.457\n0.463 \u00b1 0.010\n0.627\n0.625 \u00b1 0.016\n0.640\n0.625 \u00b1 0.016\n3.2\nb-tagging ef\ufb01ciency as a function of jet pT and \u03b7\nThe b-tagging ef\ufb01ciency is strongly dependent on jet pT and \u03b7 [2]. The above Monte Carlo test is an av-\nerage and is only applicable for physics analysis that have the same kinematic properties as the muon+jet\nsample. In order to properly account for such effects the b-tagging ef\ufb01ciency should be parameterized\nand measured as a function of at least these two variables. Since the Monte Carlo statistics are limited,\nthe method is tested by binning separately in pT and \u03b7. With more statistics a two-dimensional (pT,\u03b7)-\nbinning will be used. For the \ufb01rst case, the pT,rel templates are derived in several jet pT bins. Event\nsamples in each pT bin are split in half as before: the \ufb01rst half was used to determine the b, c, and light\njet pT,rel templates, while the second half was used as a data-like test sample to measure the b-tagging\nef\ufb01ciency. The ef\ufb01ciency obtained in this way is integrated over the whole jet \u03b7 spectrum. The procedure\nwas repeated to measure the ef\ufb01ciency dependence on jet |\u03b7|. In this case, the ef\ufb01ciency was integrated\nover the pT spectrum of jets.\nThe measured pT dependence of the b-tagging ef\ufb01ciency is shown in Fig. 6 (left) for the tagger\nIP3D+SV1. We observe a good agreement between measured and true ef\ufb01ciencies in this low jet pT\nregion. For jets with pT > 80 GeV, not shown, the statistical error from the \ufb01t becomes large and\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n541\n\nthe results become unreliable. At present, therefore, we conclude that the ef\ufb01ciency can be reliably\ndetermined only in the low jet pT region (pT < 80 GeV). This is related to the poor separation of b-jet\ntemplates from c- and light-jet templates in the high jet pT region (compare the plots in Fig. 4 for an\nexample). In view of this, the |\u03b7|-dependence of the b-tagging ef\ufb01ciency was studied only for jets with\npT < 80 GeV (Fig. 6 right). Good agreement over the whole |\u03b7| range is observed.\n [GeV]\njet\nT\np\n20\n30\n40\n50\n60\n70\n80\n90\nefficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMonte Carlo truth\n method\nT,rel\np\nATLAS\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nefficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nMonte Carlo truth\n method\nT,rel\np\nATLAS\nFigure 6: Ef\ufb01ciency as a function of jet pT (left) and jet |\u03b7| (right) for the tagger IP3D+SV1 as measured\nusing the pT,rel method. The dots are the true value as measured in the Monte Carlo, and the squares\n(with error bars) are determined from the pT,rel method. The lines are parameterizations to the measured\npT,rel points. At high jet pT the pT,rel measurement technique fails and so we do not attempt to measure\nb-tagging performance above 80 GeV. The |\u03b7| plot (right) includes only jets with pT < 80 GeV.\n3.3\nExpected Errors\nThe high yield of muon-tagged jets from the muon-jet trigger means that the statistical error for determin-\ning ef\ufb01ciencies with the pT,rel method should rapidly become small: for 100 pb\u22121 of data, for example,\nthe overall statistical error would already be well below 1%.\nThe study of the systematic errors in the pT,rel method is in progress, and will require real data for\ndetailed evaluation. Sources of systematic error being considered include:\n\u2022 The major uncertainty of this method is the use of Monte Carlo to model the pT,rel templates for\nb- and c-jets. A change in the fragmentation function, for example, will likely change the muon\npT,rel spectrum. We estimated the contribution of these effects by scaling the pT,rel shape of the b\nand c templates, resulting in an change in \u03b5meas of 5%.\n\u2022 The light-jet templates will be drawn from data and thus will have some heavy \ufb02avor contamina-\ntion. QCD Monte Carlo predicts a jet sample will contain 2.5% b-jets and 5% c-jets. We expect\nlittle error to be introduced by c-jets as their pT,rel distribution is so similar to light-jets. We tested\nthe effect of 2.8% b-jets in the pool of jets that was used to determine the light-jet template and\nre-ran the pT,rel \ufb01t. We observed a systematic shift to smaller b-jet ef\ufb01ciencies by 3%. We add\n\u00b13% as a systematic error due to heavy \ufb02avor contamination of the light jet templates. There is\nevidence we can mitigate the size of this error by rejecting jets from the light-jet template that\nsatisfy a loose lifetime tagging requirement.\n\u2022 Detector modeling has also been examined as a source of further systematic error. Jet pT resolu-\ntion, the muon pT resolution, and the jet and muon direction resolution are all potential contribu-\ntors. Studies indicate the error due to this are of order a few percent. Detector modeling of muon\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n542\n\nsystematics have not been studied as it is assumed that the Monte Carlo modeling errors will be\nlarger.\n\u2022 We have an implicit assumption that all tracks in jets correctly model the pT,rel distribution for\nlight jets. A further systematic will exist because pT,rel distribution for fake muons in light jets is\nnot the same as the tracks associated with light jets.\nThese preliminary studies to date indicate that the systematic error sources should be controllable at the\nlevel of 6% or better on the lifetime tagging ef\ufb01ciency.\n4\nThe System 8 method\nThe System 8 technique is designed to measure the b-tagging ef\ufb01ciency with reduced dependence on\nMonte Carlo [10], [11]. This method uses two data samples with different b-fractions and two uncorre-\nlated tagging algorithms. A system of 8 nonlinear equations involving known quantities - like the total\nnumber of jets tagged in each sample - and 8 unknown quantities - like the b-tagging ef\ufb01ciency - can be\nwritten down and solved.\nBefore writing down the system of 8 equations we de\ufb01ne the taggers and two samples more fully.\nThe two taggers used must be as uncorrelated as possible. For this study we use the muon-in-jet tagger\nalgorithm (SMT) [5] as one tagger. The SMT algorithm forms a 1-dimensional likelihood using the pT,rel\nof the muon. In the present analysis an event is said to be tagged by the SMT tagger if the likelihood\nvalue is greater than 1.4. The second tagger, the one whose ef\ufb01ciency we want to measure is either\nthe IP3D+SV1 or the IP2D algorithm. We abbreviate this second algorithm as \u201cLT\u201d, short for \u201clifetime\ntagger\u201d.\nThe two samples are denoted the \u201cn-sample\u201d and the \u201cp-sample.\u201d The n-sample is the full sample of\njets containing a muon described in Section 2. The p-sample is a subset of the n-sample selected to have\nan enhanced b-content. A muon-tagged jet in the p-sample is required to have at least one back-to-back\n(\u2206\u03c6 > 2.5) lifetime-tagged (IP3D+SV1 weight > 3) jet. This selection criterion increases the b-fraction\nof the p-sample relative to the n-sample by about a factor of two. The cuts for the p-sample were chosen\nto keep the statistics of the p-sample as large as possible and also to ensure the stability of the method.\n4.1\nThe 8 equations\nFour numbers are measured in each sample: the number of jets before tagging (n in the n-sample, p in\nthe p-sample), the number of jets tagged by the LT algorithm (nLT, pLT), the number of jets tagged by\nthe SMT algorithm (nSMT, pSMT), and the number of jets tagged by both algorithms (nboth, pboth).\nWhile the total number of muon-tagged jets in each sample is an experimental observable, their \ufb02avor\ncomposition is not. We denote the number of b-jets in each sample as (nb, pb) and c- and light-jets as\n(ncl, pcl). The tagging ef\ufb01ciencies of the algorithms on the selected b-jets are (\u03b5 LT\nb , \u03b5SMT\nb\n) and non-b-jets\ntagging ef\ufb01ciencies are (\u03b5LT\ncl , \u03b5SMT\ncl\n) \u2014 which are also unknown. Unless otherwise stated, each ef\ufb01ciency\nis that which would apply to tagging of the n-sample.\nThese 8 quantities can be related by 8 equations. These equations also contain parameters encoding\nthe extent to which the following assumptions are valid: that the ef\ufb01ciency of each tagger is the same on\nthe n- and p-sample, and that the two tagging algorithms are uncorrelated. The parameters introduced\nare \u03b1i as follows:\n\u03b5both\nb\n=\n\u03b11 \u03b5LT\nb \u03b5SMT\nb\n(2)\n\u03b5both\ncl\n=\n\u03b12 \u03b5LT\ncl \u03b5SMT\ncl\n(3)\n\u03b5SMT\ncl\n(on p-sample)\n=\n\u03b13 \u03b5SMT\ncl\n(on n-sample)\n(4)\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n543\n\n\u03b5LT\ncl (on p-sample)\n=\n\u03b14 \u03b5LT\ncl (on n-sample)\n(5)\n\u03b5SMT\nb\n(on p-sample)\n=\n\u03b15 \u03b5SMT\nb\n(on n-sample)\n(6)\n\u03b5LT\nb\n(on p-sample)\n=\n\u03b16 \u03b5LT\nb\n(on n-sample)\n(7)\nThe \u03b11 and \u03b12 coef\ufb01cients measure how correlated the two taggers are on b-jets and non-b-jets. The\n\u03b13, \u03b14, \u03b15, and \u03b16 are sensitive to any tag rate differences caused by the selection of the p-sample. The\nmethod is constructed in such a way that the \u03b1i should each be approximately unity. The values of the\n\u03b1i must be determined from Monte Carlo and possible differences of each \u03b1i from that in data must be\nincluded in the systematic error. The current method used to evaluate this systematic is described in\nSection 4.3.\nThe eight jet counts enumerated above can be related by the following eight equations, including the\n\u03b1i:\nn\n=\nnb +ncl\n(8)\np\n=\npb + pcl\n(9)\nnLT\n=\n\u03b5LT\nb nb +\u03b5LT\ncl ncl\n(10)\npLT\n=\n\u03b16 \u03b5LT\nb\npb +\u03b14 \u03b5LT\ncl pcl\n(11)\nnSMT\n=\n\u03b5SMT\nb\nnb +\u03b5SMT\ncl\nncl\n(12)\npSMT\n=\n\u03b15 \u03b5SMT\nb\npb +\u03b13 \u03b5SMT\ncl\npcl\n(13)\nnboth\n=\n\u03b11 \u03b5LT\nb \u03b5SMT\nb\nnb +\u03b12 \u03b5LT\ncl \u03b5SMT\ncl\nncl\n(14)\npboth\n=\n\u03b11 \u03b15 \u03b16 \u03b5LT\nb \u03b5SMT\nb\npb +\u03b12 \u03b13 \u03b14 \u03b5LT\ncl \u03b5SMT\ncl\npcl\n(15)\nThis system of eight equations (giving the method its name) is well speci\ufb01ed if the value of each\n\u03b1i is known. The \u03b5LT\nb\nis the unknown that is of most interest \u2014 most of the others are not directly\nusable for other analysis. The System 8 method is based on a technique used by the D0 experiment\nat the Tevatron [10]. The CDF experiment has also used jet events to calibrate their lifetime b-tagging\nef\ufb01ciency [12] using a different technique.\n4.2\nSolving System 8, statistical error, and stability\nSolving the system of 8 equations is in general straightforward with tools like Mathematica (analytical\nsolution) or MINUIT (numerical solution). However, the nonlinearity of the 8 equations makes eval-\nuating the statistical errors nontrivial. As a result Monte Carlo methods are employed. The System 8\nobservables, the jet counts {n, p,nLT, pLT,nSMT, pSMT,nboth, pboth} are correlated; from them 8 uncor-\nrelated jet counts {x1,..,x8} are de\ufb01ned by dividing the n-sample into non-overlapping subsets. These\nparameters are varied according to Gaussian distributions with standard deviation \u221axi. The variation of\nall xi was performed simultaneously assuming no correlations between them. The counts were varied in\nthis way 100,000 times and the 8 equations were solved each time. The resulting distribution of \u03b5 LT\nb\nwas\nused to determine the one-sigma statistical error. Statistical errors are shown for current Monte Carlo\nstatistics in Table 5.\nThe System 8 solution is not well constrained when the equations are close to being linearly-dependent.\nAs the equations near linear dependence, the System 8 solution becomes increasingly sensitive to statis-\ntical \ufb02uctuations, resulting in unreliable values of \u03b5LT\nb . The term \u2018stability\u2019 will be used to describe the\nsensitivity of System 8 to statistical variations in the data.\nThe 8 equations are linearly independent as long as the b-content of the n- and p-samples differ, and\nas long as \u03b5b \u0338= \u03b5cl for both the SMT and LT tagging algorithms. In practice the \ufb01rst condition is easily\nmet by construction of the p-sample (which requires a back-to-back b-tagged jet), but in the case of the\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n544\n\nSMT the second stability requirement (\u03b5SMT\nb\n\u0338= \u03b5SMT\ncl\n) becomes increasingly dif\ufb01cult to satisfy at high jet\npT.\nThe SMT algorithm is highly correlated with the pT,rel distribution of muons to distinguish between\nb-, c- and light-jets. These distributions become very similar at high jet pT (see Fig. 4), leading to the\npoor ability of the SMT to separate b and non-b-jets at high momentum. It is for this reason we restrict\nthe analysis to pT < 80 GeV.\n4.3\nCorrelation systematic error\nIt is important to determine how well the Monte Carlo describes the \u03b1i in the data. Possible deviations\nshould be re\ufb02ected in the systematic error. We evaluate this contribution as the change in \u03b5 LT\nb\nobtained\nby shifting each \u03b1i from its value in Monte Carlo to unity. The total contribution to the systematic error,\nformed by adding the individual shifts in quadrature, is abbreviated as the correlation error.\nEach \u03b1i is measured from Monte Carlo and the results are shown for the IP3D+SV1 tagger (w > 4)\nin Table 4. The errors on each \u03b1i come only from Monte Carlo statistics. We have checked other tagging\nalgorithms and weight cuts and the results are similar. It can be seen that only \u03b13 differs by much more\nthan one sigma from unity, and the others lie within 3% of unity.\nTable 4: The \u03b1 coef\ufb01cients measured on Monte Carlo for jet 15 < pT < 80 GeV, for the IP3D+SV1 tagger\nweight w > 4 and SMT cut of 1.4 (\u03b1meas\ni\n). The last two columns show how the b-tagging ef\ufb01ciency (\u03b5b)\nis affected by different variations in \u03b1i: a 1% variation (\u03b1i = 1\u00b10.01) and the measured offset of each\n\u03b1i from unity (\u03b1i = 1 \u00b1 (\u03b1meas\ni\n\u22121)). The change in \u03b5b is labeled \u2206\u03b5b. The latter column is added in\nquadrature to determine the total systematic error for the correlation error (see text).\nAssumption\nValue (\u03b1meas\ni\n)\n\u2206\u03b5b for \u03b1i = 1\u00b10.01\n\u2206\u03b5b for \u03b1i = 1\u00b1(\u03b1meas\ni\n\u22121)\n\u03b11\n1.016\u00b10.012\n0.027\n0.043\n\u03b12\n1.018\u00b10.024\n0.002\n0.004\n\u03b13\n1.052\u00b10.019\n0.006\n0.031\n\u03b14\n1.028\u00b10.020\n< 0.001\n< 0.001\n\u03b15\n1.011\u00b10.011\n< 0.001\n< 0.001\n\u03b16\n1.005\u00b10.010\n0.016\n0.008\nWe vary each \u03b1i by \u00b10.01 to give an idea of how each \u03b1i contributes to the error in \u03b5LT\nb . Table 4 shows\nthat variations in \u03b12, \u03b14 and \u03b15 should have rather less impact on the b-tagging ef\ufb01ciency measurement\nthan \u03b11, \u03b13 and \u03b16. The measured values of the coef\ufb01cients \u03b11 and \u03b16 are statistically consistent with\nunity and show little statistically-signi\ufb01cant dependence on jet pT or SMT cut. The coef\ufb01cient \u03b13, on the\nother hand, is not consistent with unity and shows a pT dependence, and has a pronounced effect on the\nmeasured ef\ufb01ciency at high jet pT. The non-unity \u03b13 is understood to be primarily due to the different\nrelative fractions of charm and light in the n- and p-samples.\nIn order to work out the correlation error we evaluate the shift in \u2206\u03b5LT\nb for a variation in \u03b1i of \u00b1(\u03b1i \u2212\n1), as shown in Table 4. Adding the errors in quadrature gives an estimate of the correlation error of 6%.\nLarger Monte Carlo samples will help improve our understanding of this error and help better understand\nwhich \u03b1i really aren\u2019t unity.\n4.4\nTests on Monte Carlo\nWe evaluated the System 8 method on the muon+jet Monte Carlo sample, for the following standard\nATLAS taggers: IP2D, and the default combination of IP3D+SV1 for jets with pT < 80 GeV.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n545\n\nTo derive pT and \u03b7 dependent ef\ufb01ciency curves, the System 8 method was applied in bins of pT and\n\u03b7. Due to lack of Monte Carlo statistics it is not currently possible to bin in both pT and \u03b7 simultane-\nously; instead, System 8 was tested in pT bins for |\u03b7| < 2.5, and separately in \u03b7 bins for 15 < pT < 80\nGeV. With larger Monte Carlo statistics and much larger data statistics (such as with 50 pb\u22121) we should\nhave enough for four bins in pT and four in |\u03b7| simultaneously for jet pT < 80 GeV. The exact binning\ncon\ufb01guration will be optimized to give the best possible resolution at low jet pT where the b-tagging ef-\n\ufb01ciency is changing most rapidly. For this study, three bins in pT (15-30 GeV, 30-50 GeV, 50-80 GeV),\nand four bins in |\u03b7| (0.0-0.5, 0.5-1.0, 1.0-1.5, 1.5-2.5) were considered.\nTable 5 shows the results of calibrating the IP3D+SV1 tagger (w >4) and IP2D tagger (w >3) in bins\nof pT and \u03b7. The statistical error is shown. Recall the correlation error is an additional 6% which should\nbe added in quadrature.\nTable 5: Measured ef\ufb01ciencies, the statistical error, and their deviation from the true ef\ufb01ciencies in bins\nof pT and \u03b7, as described in the text. The statistical error is for the muon+jet Monte Carlo statistics. The\ncorrelation error, estimated to be \u00b10.06, must be added as well.\nTagger\nBin\nMeasured \u03b5b\n|\u2206meas.,true|\npT:\n15-30\n0.672\u00b10.036\n0.040\npT:\n30-50\n0.723\u00b10.026\n0.004\nIP3D+SV1\npT:\n50-80\n0.755\u00b10.029\n0.017\n|\u03b7|: 0.0-0.5\n0.748\u00b10.041\n0.008\n|\u03b7|: 0.5-1.0\n0.734\u00b10.045\n0.029\n|\u03b7|: 1.0-1.5\n0.736\u00b10.038\n0.017\n|\u03b7|: 1.5-2.5\n0.707\u00b10.043\n0.001\npT:\n15-30\n0.520\u00b10.030\n0.002\npT:\n30-50\n0.619\u00b10.027\n0.003\nIP2D\npT:\n50-80\n0.671\u00b10.033\n0.011\n|\u03b7|: 0.0-0.5\n0.663\u00b10.043\n0.003\n|\u03b7|: 0.5-1.0\n0.656\u00b10.052\n0.016\n|\u03b7|: 1.0-1.5\n0.606\u00b10.036\n0.034\n|\u03b7|: 1.5-2.5\n0.587\u00b10.046\n0.018\nTo conclude, System 8 works well for different types of lifetime tagging algorithms for jet pT < 80\nGeV. It demonstrates stable results for different cuts on b-tagging weights.\n5\nThe inclusive b-tagging ef\ufb01ciency\nThis note describes two methods which measure the lifetime-tagging ef\ufb01ciency for b-jets containing\nmuons. In this section we brie\ufb02y discuss how to convert from the measured tag ef\ufb01ciency to a lifetime\ntagging ef\ufb01ciency relevant to inclusive jet samples.\nFig. 7 shows the ratio of the muon-jet lifetime tag rate to the inclusive-jet tag rate for the default\nIP3D+SV1 tagger (w > 4) as a function of pT. The difference between the tag rates in the two samples\nis primarily due to about a 50% difference in the pT of the highest pT track and in the average number\nof tracks per jet.\nWe de\ufb01ne a scale factor, Sb, to describe the difference in tag rates. The scale factor is de\ufb01ned in\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n546\n\n [GeV]\nT\nJet p\n20\n40\n60\n80\n100\n120\n140\n (IP3D+SV1, w > 4)\nhad. b-jet eff\nsemilept. b-jet eff\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n1.6\n1.7\n1.8\nATLAS\nFigure 7: The right hand plot shows the ratio of ef\ufb01ciencies for semi-leptonic jet tagging and hadronic\njet tagging in the QCD jet sample.\nMonte Carlo:\n\u03b5MC\nb\u2192had(pT,\u03b7) = Sb(pT,\u03b7)\u03b5MC\nb\u2192\u2113\u03bdX(pT,\u03b7)\n(16)\nand thus, given a hadronic Monte Carlo b-jet, one calculates its calibrated lifetime tagging ef\ufb01ciency as\nfollows:\n\u03b5b\u2192had(pT,\u03b7) = \u03b5b(pT,\u03b7)Sb\u2192had(pT,\u03b7)\n(17)\nwhere \u03b5b is the tagging ef\ufb01ciency measured with System 8 or pT,rel in muon-tagged jets.\nTo understand the systematic error on the scale factor we need a better understanding of the causes\nof the differences in tag rate. This work is in progress.\n6\nConclusions\nWe have presented two methods to calibrate lifetime b-tagging algorithms using dijet data. Trigger stud-\nies were performed in order to assure that there will be enough data for the b-tagging calibration. Detailed\nb-tagging performance can be obtained with data corresponding to 50 pb\u22121 of integrated luminosity.\nThe suggested methods, pT,rel and System 8, were studied using Monte Carlo jet events, at least one\nof which has an associated muon. Good agreement is observed between true semi-leptonic b-tagging\nef\ufb01ciency and that measured by pT,rel and System 8. Both methods were veri\ufb01ed in different jet \u03b7 and\npT regions. We found that the current version of the pT,rel method can be used for jets below 80 GeV in\nentire \u03b7 region. System 8 was also proved to work well up to 80 GeV in the entire \u03b7 region.\nThe total error of both methods is expected to be rapidly dominated by systematic uncertainties. The\nsystematic errors studied so far indicate that both methods should be able to control the absolute error on\n\u03b5b to 6%. The additional systematic uncertainties associated with converting the semi-leptonic ef\ufb01ciency\nto the inclusive ef\ufb01ciency have not yet been determined The two methods are complementary to those\ndiscussed in [1], in that they are most useful in measuring the turn-on of the b-tagging ef\ufb01ciency at low\njet pT.\nReferences\n[1] ATLAS Collaboration, b-Tagging Calibration with t\u00aft Events, this volume.\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n547\n\n[2] ATLAS Collaboration, b-Tagging Performance, this volume.\n[3] ATLAS Collaboration, Jet Reconstruction Algorithms and their Performance, this volume.\n[4] ATLAS Collaboration, Jet Calibration, this volume.\n[5] ATLAS Collaboration, Soft Muon b-Tagging, this volume.\n[6] ATLAS Collaboration, Overview and Performance Studies of Jet Identi\ufb01cation in the Trigger Sys-\ntem, this volume.\n[7] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this volume.\n[8] ATLAS Collaboration, Trigger for Early Running, this volume.\n[9] R. Barlow and C. Beeston, Comp. Phys. Comm. 77 (1993) 219\u2013228.\n[10] Benoit Clement, Production electrofaible du quark top au Run II de l\u2019experience D0, Ph.D. thesis,\nStrasbourg I, April 2006.\n[11] V. Abazov, et. al., Phys. Ref. D74 (2006) 112004.\n[12] Christopher Neu, in International Workshop on Top Quark Physics, (Proceedings of Science, 2006).\nb-TAGGING \u2013 b-TAGGING CALIBRATION WITH JET EVENTS\n548\n\nTrigger\n549\n\nThe Trigger for Early Running\nAbstract\nThe ATLAS trigger and data acquisition system is based on three levels of\nevent selection designed to capture the physics of interest with high ef\ufb01ciency\nfrom an initial bunch crossing rate of 40 MHz. The selections in the three\ntrigger levels must provide suf\ufb01cient rejection to reduce the rate to 200 Hz,\ncompatible with of\ufb02ine computing power and storage capacity. The LHC is\nexpected to begin its operation with a peak luminosity of 1031 cm\u22122 s\u22121 with a\nrelatively small number of bunches, but quickly ramp up to higher luminosities\nby increasing the number of bunches, and thus the overall interaction rate.\nDecisions must be taken every 25 ns during normal LHC operations at the\ndesign luminosity of 1034 cm\u22122 s\u22121, where the average bunch crossing will\ncontain more than 20 interactions. Hence, trigger selections must be deployed\nthat can adapt to the changing beam conditions while preserving the interesting\nphysics and satisfying varying detector requirements. In this paper, we provide\na menu of trigger selections that can be deployed during the startup phase at\neach trigger level and show its evolution to higher luminosities. The studies\npresented in this paper are based on simulated data.\n1\nIntroduction\nThe ATLAS trigger [1, 2] is composed of three levels of event selection: Level 1 (L1) [3] which is\nhardware-based using ASICs and FPGAs, the Level 2 (L2) and Event Filter (EF) (collectively referred\nto as the High Level Trigger or HLT [4]) based on software algorithms analyzing the data on large\ncomputing farms. The three levels of the ATLAS trigger system must reduce the output event storage\nrate to \u223c200 Hz (about 300 MB/s) from an initial LHC bunch crossing rate of 40 MHz. It is evident\nfrom Fig. 1 that large rejection against QCD processes is needed while maintaining high ef\ufb01ciency for\nlow cross section physics processes that include searches for new physics.\nDuring the ATLAS startup phase, where low luminosity conditions (1031 cm\u22122 s\u22121) are expected to\nprevail, the focus of the trigger selection strategy will be to commission the trigger and the detector and to\nensure that established Standard Model processes are observed. It is therefore important to deploy loose\nselection criteria at each stage. In early operations many triggers will operate in pass-through mode,\nwhich entails executing the trigger algorithms but accepting the event independent of the algorithmic\ndecision. This allows the trigger selections and algorithms to be validated to ensure that they are robust\nagainst the varying beam and detector conditions that are hard to predict before data-taking. As the\nluminosity increases, the use of higher thresholds, isolation criteria and tighter selections at HLT become\nnecessary to reduce the background rates while achieving selection of interesting physics with high\nef\ufb01ciency.\nThis note describes the possible triggers that can be deployed during the initial low luminosity\nrunning and discusses the strategy for triggering as the LHC ramps up to its design luminosity of\n1034 cm\u22122 s\u22121. The performance of the various trigger algorithms at each of the three trigger levels\nis described in a set of additional accompanying notes. It should be emphasized that the rate estimates\ndiscussed in this note are based on simulations and are subject to several sources of uncertainty which in-\nclude lack of knowledge of the exact cross-sections, detector performance, and beam related background\nconditions. Observations with early data will allow validation of these estimated rates and extrapolations\nto higher luminosities.\n550\n\nFigure 1: Expected event rates for several physics processes at the LHC design luminosity.\n2\nLevel 1 trigger\nThe Level 1 trigger system receives data at the full LHC bunch crossing rate of 40 MHz and must make\nits decision within 2.5 \u00b5s to reduce the output rate to 75 kHz (\u223c40 kHz during ATLAS start-up). The\nL1 trigger has dedicated access to data from the calorimeter and muon detectors. The L1 calorimeter\ntrigger [5] decision is based on the multiplicities and energy thresholds of the following objects observed\nin the ATLAS Liquid Argon [6] and Tile [7] calorimeter sub-system: Electromagnetic (EM) clusters,\ntaus, jets, missing transverse energy (/ET), scalar sum ET (\u2211ET) in calorimeter, and total transverse\nenergy of observed L1 jets (\u2211ET(jets)). These objects are computed by the L1 algorithms using the\nmeasured ET values in trigger towers of 0.1\u00d70.1 granularity in \u2206\u03b7 \u00d7\u2206\u03c6. The L1 muon trigger [8] uses\nmeasurement of trajectories in the different stations of the muon trigger detectors: the Resistive Plate\nChambers [9] (RPC) in the barrel region and the Thin Gap Chambers [8] (TGC) in the endcap region.\nThe input to the trigger decision is the multiplicity for various muon pT thresholds.\nThere are a limited number of con\ufb01guration choices that are available at L1. The most common\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n551\n\ndifference between con\ufb01guration choices is the amount of transverse energy or momentum required, so\nwe refer to these con\ufb01gurations as \u201cthresholds,\u201d but note that in addition to the ET threshold condition,\nthree different isolation criteria can be applied for L1 EM and tau objects, and three different window\nsizes can be speci\ufb01ed for L1 jet objects. Table 1 gives the number of these so-called thresholds that can\nbe set for each object type. The total number of thresholds allowed for EM and tau objects is 16, where\n8 are dedicated to be EM objects and 8 can be con\ufb01gured to be either EM or tau objects. The forward\njets have four thresholds that can be set independently in each of the detector arms.\nObject\nEM\nTaus\nJets\nFor. Jets\n/ET\n\u2211ET\n\u2211ET(jets)\n\u00b5\u226410 GeV\n\u00b5>10 GeV\n# of thresholds\n8 - 16\n0 - 8\n8\n4+4\n8\n4\n4\n3\n3\nTable 1: Number of L1 thresholds that can be set for each L1 object type at any given time (see text for\ndetails).\nThe total number of allowed L1 con\ufb01gurations (also called L1 items) that can be deployed at any\ntime is 256. Each of these L1 items, programmed in the Central Trigger Processor (CTP) [10], is a\nlogical combination of the speci\ufb01ed multiplicities of one or more of the con\ufb01gured L1 thresholds. As\nan example L1 EM25i and L1 EM25 (A single L1 EM object with ET > 25 GeV with and without\nisolation respectively) uses two L1 EM thresholds while L1 2EM25i (Two L1 isolated EM object with\nET > 25 GeV) uses the same L1 threshold as the L1 EM25i item. Furthermore, for each of the 256\nL1 items, a prescale factor N can be speci\ufb01ed (where only 1 in N events is selected and passed to the\nHLT for further consideration). As the peak luminosity drops during a \ufb01ll, the L1 prescale value can\nbe adjusted to keep the output bandwidth saturated without stopping and restarting a data-taking run, if\ndesired. A given data-taking run is sub-divided into time intervals of the order of one minute. These\nsub-divisions, called luminosity blocks [11], provide the smallest granularity at which various data will\nbe monitored and available for physics analysis. The trigger con\ufb01guration, including the L1 prescale\nsettings, remains unchanged within this luminosity block and adjustments to L1 prescale factors will be\nmade on luminosity block boundaries.\n3\nLevel 2\nThe L2 trigger is software-based, with the selection algorithms running on a farm of commodity PCs.\nThe selection is largely based on regions-of-interest (RoI) identi\ufb01ed at L1 and uses \ufb01ne-grained data\nfrom the detector for a local analysis of the L1 candidate. A seed is constructed for each trigger accepted\nby L1 that consists of a pT threshold and an \u03b7-\u03c6 position. The L2 algorithms use this seed to construct\nan RoI window around the seed position. The size of the RoI window is determined by the L2 algorithms\ndepending on the type of triggered object (for example, a smaller RoI is used for electron triggers than for\njet triggers). The L2 algorithms then use the RoI to selectively access, unpack and analyze the associated\ndetector data for that \u03b7-\u03c6 position. The ability to move, unpack, and analyse the local data only around\nthe seed position greatly reduces both the processing times and the required data bandwidth.\nThe L2 algorithms provide a re\ufb01ned analysis of the L1 features based on \ufb01ne-grained detector data\nand more optimal calibrations to provide results with improved resolution. They provide the ability to use\ndetector information that is not available at L1, most notably reconstructed tracks from the Inner Detector.\nThe information from individual sub-systems can then be matched to provide additional rejection and\nhigher purity at L2. For each L1 RoI, a sequence of L2 algorithms is executed which compute event\nfeature quantities associated with the RoI. Subsequently, a coherent set of selection criteria is applied on\nthe derived features to determine if the candidate object should be retained.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n552\n\nThe L2 farm will consist of around 500 quad-core CPUs. On average, the L2 can initiate the process-\ning of a new event every 10 \u00b5s. The average processing time available for L2 algorithms is 40 ms, which\nincludes the time for data transfers. The L2 system must provide an additional rejection compared to L1\nof about 40 to reduce the output rate down from \u223c75 (40) kHz to \u223c2 (1) kHz during nominal (startup)\noperations.\n4\nEvent Filter\nThe \ufb01nal online selection is performed by software algorithms running on the Event Filter (EF), a farm\nof processors that will consist of 1800 dual quad-core CPUs. The EF receives events accepted by L2 at\na rate of 2 kHz (1 kHz) during nominal (startup) operations and must provide the additional rejection to\nreduce the output rate to \u223c200 Hz, corresponding to about 300 MB/s. An average processing time of 4\ns per event is available to achieve this rejection. The output rate from the Event Filter is limited by the\nof\ufb02ine computing budget and storage capacity.\nAs in L2, the EF works in a seeded mode, although it has direct access to the complete data for a\ngiven event as the EF selection is performed after the event building step. Each L2 trigger that has been\naccepted can be used to seed a sequence of EF algorithms that provide a more re\ufb01ned and complete anal-\nysis. Unlike L2, which uses specialized algorithms optimized for timing performance, the EF typically\nuses the same algorithms as the of\ufb02ine reconstruction. The use of the more complex pattern recognition\nalgorithms and calibration developed for of\ufb02ine helps in providing the additional rejection needed at the\nEF.\n5\nTrigger rate estimation\nTrigger rates have been estimated using a sample of simulated events. The design of a speci\ufb01c trigger\nmenu often requires several iterations of selection optimization to ensure that the output rate is within\nallowed bandwidths and that interesting physics is triggered with high ef\ufb01ciency.\nThe \ufb01rst step in approximating trigger rates is to choose an appropriate input simulation sample. Most\ntrigger selections are dominated by backgrounds from common processes, so samples with large physics\ncross-sections are generally used. However, these typically contain very few events that satisfy the trigger\ncriteria and hence a very large number of events are required to obtain adequate statistical uncertainties\non the estimated rates. In order to design the trigger menu for a luminosity of 1031 cm\u22122 s\u22121, a minimum-\nbias dataset containing seven million non-diffractive events with a cross-section of approximately 70 mb\nwas used. To estimate the trigger rates with comparable statistical uncertainties for higher luminosities\nwould require prohibitively large generated samples, hence other approaches are being pursued. These\ninclude using a combination of QCD and minimum bias event samples or alternatively using the so-called\nenhanced bias sample. The enhanced bias sample is a loosely \ufb01ltered minimum bias sample requiring the\nlowest L1 pT thresholds for muon, EM, or jet to have been ful\ufb01lled. Only events that pass the \ufb01ltering\nprocess are reconstructed, resulting in a much more effective use of the computing resources. In addition\nto QCD processes, other high cross-section physics processes, such as W and Z boson production, need\nto be considered for estimating trigger rates at very high luminosities. Although such simulated samples\nprovide a reasonable starting point to establish a data taking menu, these trigger menus will evolve as\nour understanding of the detector and trigger evolve, and as the physics requirements mature. Once data\ntaking operations begin, dedicated data samples for further menu optimization and rate estimations will\nbe collected.\nIn order to compute the initial trigger rates, the full trigger simulation (L1, L2, and EF) is executed on\na minimum bias data sample generated with PYTHIA [12] and simulated with realistic detector effects\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n553\n\nin Geant4 [13]. The rate estimates presented in this paper are based on an analysis of seven million\nminimum-bias events. At a luminosity of 1031 cm\u22122 s\u22121 each unprescaled event corresponds to a rate of\nabout 0.1 Hz. These raw rates are subsequently weighted for any applied prescale factors, which allows\nmore accurate rate measurements as it makes use of all the events in the data sample. For each level, the\nindividual trigger rates are computed using the equation\nR = L \u00d7 naccepted\nntotal\n\u00d7\n1\n\u220fcurrent level\nl=lowest level Pl\n\u00d7\u03c3\n(1)\nwhere R is the rate at the current level, L is the instantaneous luminosity, Pl is the prescale factor applied\nat a speci\ufb01c level, naccepted is the number of events accepted after the speci\ufb01c trigger level studied (and\nhence all the previous lower levels as well), and ntotal is the total number of events in the dataset and \u03c3\nis the cross section.\nTrigger rates are estimated by assigning a probability for an event to have been accepted. The com-\nputation of rates based on probabilities makes maximal use of the available set of simulated events from\na statistical point of view. The probability Pri of an event being accepted by a trigger item i is given by:\nPri(event) = Di(event)/Pi,\n(2)\nwhere Di is the decision probability accepting an event when no prescale factor is applied, and Pi is the\noverall prescale associated with the trigger item.\nIn order to compute the overall acceptance rate of a speci\ufb01c menu, the overlap in acceptance from\ndifferent trigger items needs to be correctly taken into account. The probability that two triggers accept\nan event simultaneously is then given by:\nPr12(evt) = Pr1(evt)\u00d7Pr2(evt).\n(3)\nThe overall probability of accepting an event in a menu of two triggers, including their correlations,\nis thus given by\nPrmenu(evt) = Pr1(evt)+Pr2(evt)\u2212Pr1(evt)\u00d7Pr2(evt)\n(4)\nThis computation, although simple in the case of two triggers, becomes increasingly complex as the\nnumber of items in the menu increases. Fortunately, this problem can be solved recursively. Dedicated\ntools employing these methods have been developed to compute trigger acceptance rates and overlaps\nfor various trigger menus.\n6\nTrigger menu for a luminosity of 1031 cm\u22122 s\u22121\nThe initial LHC startup luminosity is expected to be approximately 1031 cm\u22122 s\u22121 with a low number\nof bunches in the machine. These conditions will be ideal for commissioning the trigger and detector\nsystems, as well as for the initial data taking, which will be dedicated to high cross section Standard\nModel signatures. Hence, the trigger selections deployed during this early running phase will primarily\nbe a combination of low pT thresholds and loose selection criteria. Triggers at higher selection stages\nwill be operated in pass-through mode wherever possible.\nTrigger menus are tables of triggers that incorporate the signatures for various physics objects at\neach of the three trigger levels. These signatures fully specify the thresholds and selection criteria at\neach level, providing a recipe for triggering on various physics processes. Each signature is considered\ncarefully addressing its physics goals, the ef\ufb01ciency and background rejection it provides for meeting\nthese goals and the trigger bandwidth it consumes. Trigger menus also must include additional triggers\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n554\n\nfor trigger validation, monitoring, calibration and measuring the performance of the physics triggers.\nWith these considerations, a trigger menu for the startup phase has been developed. The rates have been\nestimated using the previously described simulated minimum-bias events.\nThe following notation is used to label the different trigger items: e (electron), g (photon), EM\n(electromagnetic), J (jets), FJ (forward jets), XE (Missing ET), TE (Total scalar sum ET), JE (Scalar sum\nof jet ET), MU (muons), and tau (tau leptons). A typical example of a trigger item is 2e15i (two isolated\nelectrons with a pT greater than 15 GeV) or tau20i XE30 (an isolated tau decaying hadronically with\nvisible pT above 20 GeV and /ET above 30 GeV). A pre\ufb01x to the item name is used to specify the trigger\nlevel at which the item is deployed. If the presence of several trigger object types are required, the AND\nof these multiple object types is shown using an \u201c \u201d, for example, tau25i XE30 requires an isolated tau\nlepton with a pT above 25 GeV AND a Missing ET above 30 GeV (when objects are combined with no\nquali\ufb01er a simpler notation can be used, for example, e+ \u00b5 for a trigger with an electron and a muon).\n6.1\nL1 items foreseen for a luminosity of 1031 cm\u22122 s\u22121\nAll rates given in this section are measured using simulated events with a luminosity of 1031 cm\u22122 s\u22121.\nTable 2 shows a potential set of EM L1 signatures, their prescale factors and estimated rates that could\nbe deployed during start-up for an assumed luminosity of 1031 cm\u22122 s\u22121. It shows the eight L1 EM\nthresholds and the multi-EM object thresholds that are direct combinations of the single EM thresholds.\nAt low luminosities, a single non-isolated trigger of 7 GeV can be used without the application of prescale\nfactors at the \ufb01rst trigger level with a rate of about 5 kHz. All multi-object EM triggers at L1 have\nsuf\ufb01ciently low trigger rates and can be deployed without the application of any prescale factors. The\ntotal L1 output rate out for the EM objects de\ufb01ned in Table 2 is about 10 kHz after correctly accounting\nfor events that have passed multiple L1 EM object signatures. The L1 EM object triggers are then used\nto seed both electron and photon signatures at the HLT.\nTrigger Item\nEM3\nEM7\nEM13\nEM13I\nEM18\nEM18I\nEM23I\nEM100\nPrescale\n60\n1\n1\n1\n1\n1\n1\n1\nRate (Hz)\n674\n4900\n950\n480\n369\n143\n53\n1.5\nTrigger Item\n2EM3\n2EM7\n2EM13\n2EM13I\n2EM18\n2EM18I\n2EM23I\n3EM7\nPrescale\n1\n1\n1\n1\n1\n1\n1\n1\nRate (Hz)\n6500\n534\n108\n8\n47\n2\n0.6\n53\nTable 2: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for electromagnetic objects.\nSeveral higher threshold signatures are deployed with and without isolation, even though lower\nthresholds can be deployed without the application of prescale factors at low luminosities. This allows\nthe validation of the higher thresholds and trigger items that will be needed at high luminosities when\nthe lower threshold triggers can only be deployed with prescale factors due to rate considerations.\nThe inclusive L1 jet trigger items and corresponding prescale factors, as shown in Table 3, are chosen\nto given an approximately \ufb02at trigger rate across the steeply falling jet ET spectrum. At a luminosity of\n1031 cm\u22122 s\u22121, a single jet trigger with a threshold ET of 120 GeV can be deployed without prescale\nfactors and has a L1 output rate of about 8 Hz. Figure 2 shows that triggered jet ET spectrum is fairly\n\ufb02at up to the threshold value of 120 GeV and then falls with the jet cross section. This strategy provides\nsuf\ufb01cient statistics across the ET spectrum for the measurement of the differential cross sections and for\nmeasuring the ef\ufb01ciencies and performance of different algorithms.\nAt a luminosity of 1031 cm\u22122 s\u22121, the HLT algorithms for the inclusive jet triggers are run in pass-\nthrough mode with the rate controlled only by using L1 prescale factors. This allows validation of the\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n555\n\nTrigger Item\nJ10\nJ18\nJ23\nJ35\nJ42\nJ70\nJ120\n3J10\n3J18\n4J10\n4J18\n4J23\nPrescale\n42000\n6000\n2000\n500\n100\n15\n1\n150\n1\n30\n1\n1\nRate (Hz)\n4\n1\n1\n1\n4\n4\n9\n40\n140\n40\n20\n7\nTable 3: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for jet objects.\n of leading jet (GeV)\nT\nE\n10\n2\n10\n3\n10\n)\n-1\n (GeV\nT\ndN / dE\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n9\n10\n10\n10\n11\n10\nFigure 2: Jet ET spectrum at 1031 cm\u22122 s\u22121 before (dashed) and after (solid) pre-scaling at L1.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n556\n\nHLT algorithms for jet triggers that can then be deployed at higher luminosities.\nUnlike single jet triggers, where the output rates are controlled by applying prescale factors at L1,\njet triggers with higher multiplicities (multi-jets) have a larger allocated L1 output bandwidth to allow\nthe use of additional selection algorithms only applicable at the HLT (e.g. b-tagging). Their total output\nrate to disk storage is subsequently controlled at the HLT with either a combination of jet algorithms\nand additional prescale factors (leading to normal jet signatures) or additional highly rejective selections,\n(e.g. b-tagging algorithms leading to b-jet signatures).\nThe prescale factors and rates for forward jet triggers are shown in Table 4. The HLT algorithms at\nlow luminosity are executed in pass-through mode with rates controlled using L1 thresholds and prescale\nfactors.\nTrigger Item\nFJ18\nFJ35\nFJ70\nFJ120\n2FJ18\n2FJ35\nPrescale\n7000\n700\n20\n1\n100\n1\nRate (Hz)\n1\n1\n1\n1\n1\n2\nTable 4: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for forward jet objects.\nTable 5 shows the rates for the suite of single muon and dimuon signatures; these triggers can all\nbe deployed at 1031 cm\u22122 s\u22121 without L1 prescale factors with further selection at HLT to control the\noutput rates. Three of the six available muon thresholds must be established below pT of 10 GeV and\nare based on a coincidence of only two of the inner three stations. The lowest possible muon threshold\nof 4 GeV is set by opening the coincidence window in the two stations to the maximum allowed size.\nThe remaining three high pT threshold L1 muon triggers (pT > 10 GeV) require a coincidence in all\nthree muon trigger stations. The largest contribution to the rates shown in Figure 3 come from b, c quark\ndecays and in-\ufb02ight decays of pions and kaons. The L1 muon trigger is highly ef\ufb01cient (99%) for pT\nabove the threshold values within the \ufb01ducial acceptance of the detector.\nTrigger Item\nMU4\nMU6\nMU10\nMU15\nMU20\nMU40\nRate (Hz)\n1730\n640\n360\n30\n20\n10\nTrigger Item\n2MU4\nMU4 MU6\n2MU6\n2MU10\n2MU20\n3MU6\nRate (Hz)\n70\n45\n14\n7\n0.2\n0.7\nTable 5: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for muon objects.\nSome of the signatures and estimated rates for single and double tau triggers at 1031 cm\u22122 s\u22121 are\nshown in Table 6. The triggers at low luminosity are chosen to collect large statistics of W and Z boson\ndecays to tau leptons. For W boson decays, additional cuts on /ET help reduce the rates. However,\nreliance on /ET is limited during startup as it is very sensitive to several detector and acceptance effects,\nand will take time to validate. Alternative approaches that use /ET only in the Event Filter seeded with a\nsingle tau signature at L1 are being studied. In addition to the 2\u03c4 triggers at L1, \u03c4 +e and \u03c4 + \u00b5 triggers\nhave been implemented at L1 to trigger on Z \u2192\u03c4\u03c4 decays with one of the taus decaying leptonically.\nThe eight /ET thresholds likely to be deployed at the L1 stage are shown in Table 7. The strategy here\nis similar in nature to that of the jet triggers, with L1 prescale factors tuned to provide a \ufb02at rate across\nthe /ET spectrum. The reliance on inclusive /ET trigger will be small especially during the early running\nperiod as it is sensitive to various detector effects that will require time to understand. Most of the /ET\nthresholds are expected to be used in combination with other signatures.\nIn addition to the /ET trigger thresholds, there are four thresholds available for the scalar sum ET (TE)\nand the scalar sum ET of observed L1 jets (JE). As for the /ET triggers, reliance on such triggers will be\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n557\n\n threshold (GeV)\nT\nMuon p\n3\n4\n5\n6\n7 8 9 10\n20\n30\n40\nRate (Hz)\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\nCharm\nBeauty\n/K decays\n\u03c0\nW\nTotal\nFigure 3: Estimated muon trigger rate for a luminosity of 1031 cm\u22122 s\u22121. Shown are the total rates and\nvarious contributions.\nSignature\ntau6\ntau9I\ntau11I\ntau16I\ntau25\ntau25I\ntau40\nPrescale\n750\n300\n1500\n10000\n20\n10\n1\nRate (Hz)\n19\n16\n2\n< 0.1\n16.1\n25\n83\nSignature\n2tau6\n2tau9I\n2tau16I\ntau6 tau16I\ntau9I EM13I\ntau9I MU6\ntau9I XE30\nPrescale\n100\n1\n1\n10\n1\n1\n1\nRate (Hz)\n19\n413\n65\n46\n100\n25\n160\nTable 6: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for tau objects.\nTrigger Item\nXE15\nXE20\nXE25\nXE30\nXE40\nXE50\nXE70\nXE80\nPrescale\n30000\n7000\n1500\n200\n20\n2\n1\n1\nRate (Hz)\n2.5\n3\n4\n7.5\n7.5\n14\n2\n1\nTable 7: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for Missing ET objects.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n558\n\nlimited in the early running period, but could prove to be valuable to ensure that very high ET events\nare recorded. Table 8 shows the selections, the pre-scale factors necessary to achieve the desired rate\nreduction, and estimated L1 output rates for the TE and JE triggers that could be deployed at startup.\nTrigger Item\nTE150\nTE250\nTE360\nTE650\nJE120\nJE220\nJE280\nJE340\nPrescale\n100k\n1100\n40\n1\n150\n10\n2\n1\nRate (Hz)\n2\n3\n1\n0.5\n0.5\n0.5\n0.5\n0.1\nTable 8: L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for the scalar \u2211ET (TE) and \u2211E jet\nT\n(JE)\ntriggers.\nIn addition to L1 triggers that rely on thresholds and multiplicities of a single object type (EM, Jet,\nmuon etc.), several triggers are formed by combining multiple L1 object types (e.g: EM + muon, Jet\n+ missing ET etc.). Table 9 shows some of the typical combined signatures and their estimated rates.\nThe rates for these triggers are generally small because they combine objects of different types at L1\nand can thus be executed without prescale factors. Combining object types at L1 provides a mechanism\nto control the rates while maintaining low enough thresholds to meet the physics goals of the trigger.\nEven though single object triggers may suf\ufb01ce for low luminosity running, it is necessary to deploy the\nmulti-object triggers at low luminosity to validate them and ensure their reliability as the LHC moves to\nhigh luminosity operations.\nTrigger Item\nEM13 XE20\nEM7 MU6\nMU11 XE15\nMU10 J18\nRate (Hz)\n225\n10\n13\n33\nTrigger Item\n2J42 XE30\n4J23 EM13I\n4J23 MU11\nEM13I J42 XE30\nRate (Hz)\n13\n6.5\n1\n6.5\nTable 9: A representative list of L1 trigger items and estimated rates at 1031 cm\u22122 s\u22121 for triggers\ncombining several object types. The \u201c \u201d notation is used to show the AND between two object types.\n6.2\nHLT signatures foreseen for a luminosity of 1031 cm\u22122 s\u22121\nDuring low luminosity running, most of the triggers at Level 2 and Event Filter are either executed in\npass-through mode or with loose selections. Table 10 shows some of the lowest threshold trigger items\nthat can be executed without applying prescale factors and their estimated rates for 1031 cm\u22122 s\u22121. Higher\nthreshold triggers, which will become important during high luminosity running are also deployed so that\nthey can be validated with early data.\nTrigger Item\ne12\n2e5\ng20\ntau60\ntau25i XE30\nMU10\n2MU4\ne10 MU6\nJ120\n4J23\n2b23\nRate (Hz)\n19\n7\n7\n10\n3.5\n18\n2.3\n0.5\n9\n7\n3\nTable 10: Examples of low threshold trigger terms executed without prescale factors and estimated rates\nthat can be deployed at 1031 cm\u22122 s\u22121.\nFigure 4 shows a graphical summary of the EF output rates for each trigger group and the cumulative\nrates, which provide a running total of the rates. The sum of the rates for all the trigger groups is more\nthan the cumulative rates due to overlaps between the groups. The grouping is done as follows: single\nand multi-object triggers of the same object type are grouped together, hence \u201cElectrons\u201d refers to the\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n559\n\ntotal rates estimated for all single and multi-electron triggers including triggers executed with prescale\nfactors and in pass-through mode. \u201cB-Physics and Topological\u201d refers primarily to B-physics triggers\nand other triggers where invariant mass cuts have been applied during the selection process, such as in\nselection of J/\u03c8 , \u03d2 , and Z decays. The \u201cOther Topological\u201d triggers require two or more object types,\nsuch as e+ jets, \u03c4 + /ET etc.\nThe trigger grouping and associated rates are shown in \ufb01ner detail in Table 11 for each of the trigger\nlevels. The rates for each trigger grouping accounts for overlaps between signatures in that group, but not\nacross groups. The \u201cTotal\u201d row gives the cumulative rates for this trigger menu, accounting for overlaps\nbetween the trigger groups as well. The total output rates for each trigger level, for the proposed trigger\nmenu at a luminosity of 1031 cm\u22122 s\u22121, is estimated to be within the available bandwidth, although\nthere are large uncertainties inherent in the simulation. The estimated rate out of L1/L2 is 12 kHz/620\nHz well below their respective targets of 40 kHz and 1 kHz available during the LHC startup phase.\nThe selections have been tuned to yield the targeted EF output rate of 200 Hz, but it is evident that this\npreliminary trigger list will need to be optimized based on early experience with real data.\n7\nData streams\nATLAS has adopted an inclusive streaming model whereby raw data events can be streamed to one or\nmore \ufb01les based on the trigger decision. A proposed initial streaming con\ufb01guration consists of four raw\ndata streams called egamma, jetTauEtmiss, muons, and minbias. Each stream consists of events that pass\none or more trigger signatures. The stream names indicate the type of trigger signatures they will contain,\nRate (Hz)\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nOther Topological\nMinimum Bias\nB-physics & Topological\nTotal Jet E\nTotal E\nMissing Et\nMuons\nTaus\nPhotons\nElectrons\nbjets\nJets\nRates\nCumulative Rates\nFigure 4: HLT unique (black) and cumulative (gray) estimated rates at 1031 cm\u22122 s\u22121 for different trigger\ngroups as described in the text.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n560\n\nObject\nL1 (Hz)\nL2 (Hz)\nEF (Hz)\nSingle-electrons\n5580\n176\n27.3\nMulti-electrons\n6490\n41.1\n6.9\nMulti-photons\ncommon\n2.9\n< 0.1\nSingle-photons\ncommon\n33.4\n9.1\nMulti-Jets\n221\n7.9\n7.9\nSingle-Jets\n24.4\n24.4\n24.4\nMulti-Fjets\n2.7\n2.7\n2.7\nSingle-Fjets\n3.7\n3.7\n3.7\nMulti-bjets\ncommon\n12.9\n2.6\nSingle-bjets\ncommon\n11.6\n11.6\nMulti-taus\n465\n14.5\n12.4\nSingle-taus\n148\n32.9\n22.3\nMulti-muons\n68.6\n5.8\n2.3\nSingle-muons\n1730\n204\n21.8\nMissing ET\n37.9\n31.\n3.8\nTotal ET\n6.3\n6.3\n1\nTotal Jet ET\n1.6\n1.6\n1.6\nBPhysics\ncommon\n25\n13\nMuti-Object\n5890\n134\n48\nMinimum Bias\n1000\n10\n10\nTotal\n12000\n620\n197\nTable 11: L1, L2, and EF estimated rates for several groups of trigger items at a luminosity of\n1031 cm\u22122 s\u22121. The total rate accounts for overlaps between the groups. The L1 objects labeled \u201ccom-\nmon\u201d have the same L1 triggers as other object types and hence do not require any additional L1 band-\nwidth.\nfor example, events passing electron or photon triggers will be written to the egamma stream. Events\npassing certain topological triggers could be written to more than one stream. Two examples, e+ /ET and\ne + \u00b5, can be used to demonstrate the two possible modes for streaming events that pass a topological\ntrigger. For the e+ /ET signature, events are only written to the egamma stream unless they also pass an\ninclusive /ET signature after pre-scaling, in which case they are also written to the jetTauEtmiss stream.\nFor the e+ \u00b5 signature, events are written to both egamma and muon stream regardless of whether they\npass the inclusive single electron or single muon trigger.\nStreams are chosen to have approximately the same proportion of events and to keep the total overlap\n(event duplication across streams) to less than 10%. The \ufb01nal optimization of these streams can only be\nachieved with an understanding of the overlaps observed with real data. Furthermore, the number and\ntype of raw data streams may be optimized for use at different luminosity settings.\nTable 12 shows the total and the unique rates of the proposed early stream con\ufb01guration. The unique\nrate re\ufb02ects the number of events written solely to the speci\ufb01ed stream, hence the difference between the\ntotal rate and the unique rate is the rate of replicated events in each stream.\nAs shown in the Table, in addition to the raw data streams, an express stream and a calibration stream\nhave also been de\ufb01ned. An express stream containing a subset of triggers can be used to provide rapid\nfeedback on the quality of the data. It is therefore reconstructed \ufb01rst and any relevant knowledge of\nthe quality of data is incorporated into the reconstruction of the remaining streams. Events in express\nstream are primarily intended for monitoring and not for physics analysis. Hence, by de\ufb01nition, events\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n561\n\nappearing in express stream would also appear in one of the primary raw data streams.\nAdditional triggers required for detector calibration can be run in a parasitic mode during data taking\noperations. These include triggers that provide data needed for detector alignment and energy scale\ndetermination. Such data can be written to their own raw data stream with the advantage of being\nprocessed early and the extracted calibration constants used as part of the bulk reconstruction of the\nprimary raw data streams.\n8\nEvolution to higher luminosities\nExperience with early running will allow further optimization of the trigger algorithms and menus and\nimprove the ability to estimate rates in the high luminosity regime. As the LHC ramps up to its de-\nsign luminosity, complex trigger signatures with multiple observables, higher pT thresholds and tighter\nselections will be deployed to maintain the output Event Filter rates at about 200 Hz.\nAs noted in Section 2, there are a limited number of L1 thresholds available for each object type. The\nintent is to keep the L1 thresholds as stable as possible. With increasing luminosity, higher L1 thresholds\nneed to be introduced at the expense of some of the lower thresholds. However, many of the thresholds\nwill be retained providing common points of comparison across luminosity regimes. At high luminosity,\nthe luxury of running in pass-through mode or with loose selections will not be possible, and tighter\nHLT selections will be implemented to achieve the required rejection. For example, jet triggers that used\nonly the L1 prescale to control the rates at low luminosity, will enable the HLT at high luminosity to\nobtain the additional rejection needed to control the EF output rates. In addition, topological triggers that\ninclude jets at lower thresholds than the inclusive jet triggers but in combination with other objects or\nrequirements to achieve reduction in output rate, are deployed to increase the physics acceptance.\nAt high luminosities, the trigger software and selection must be robust against high detector oc-\ncupancies, pile-up effects and cavern backgrounds. Pile-up effects becomes signi\ufb01cant with increas-\ning luminosities with an average of more than 20 interactions per crossing expected at a luminosity of\n1034 cm\u22122 s\u22121. The trigger should ensure coverage of the full physics programme, including searches\nfor new physics and precision measurements of Standard Model parameters. The signatures include lep-\nton, photon, and jet triggers, but with higher thresholds and tighter selection criteria employed to control\nthe rates. Additional requirements that operate in pass-through mode at low luminosities, such as isola-\ntion, large /ET and other complex criteria such as \ufb02avour tagging, must also be deployed to achieve the\nnecessary rate reduction.\nTable 13 shows a representative sample of L1 and HLT trigger items that can be expected to be\ndeployed without prescale factors at a luminosity of 2\u00d71033 cm\u22122 s\u22121. A comparison of this menu to\nthe one at a luminosity of 1031 cm\u22122 s\u22121 illustrates the evolution of the rates and thresholds as a function\nof luminosity. The evolution is not linear as some of the triggers also have employed tighter selection\nconditions at higher luminosity. While Table 13 gives a \ufb02avour of some of the primary triggers and\nStream\nTotal Rate (Hz)\nUnique Rate (Hz)\negamma\n55\n48\nmuon\n35\n29\njetTauEtmiss\n104\n89\nminBias\n10\n10\nexpress\n18\n0\ncalibration\n15\n13\nTable 12: Total and unique rates at 1031 cm\u22122 s\u22121 for a selected raw data stream con\ufb01guration.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n562\n\nL1 item\nRate (kHz)\nEM18I\n12.0\n2EM11I\n4.0\nMU20\n0.8\n2MU6\n0.2\nJ140\n0.2\n3J60\n0.2\n4J40\n0.2\nJ36 XE60\n0.4\ntau16I XE30\n2.0\nMU10 EM11I\n0.1\nOthers\n5.0\nHLT item\nRate (Hz)\ne22i\n40\n2e12i\n< 1\ng55i\n25\n2g17i\n2\nMU20i\n40\n2MU10\n10\nJ370\n10\n4J90\n10\nJ65 XE70\n20\ntau35i XE45\n5\n2MU6 for B-physics\n10\nTable 13: Subset of trigger items from two illustrative trigger menus at L1 (left) and at the HLT (right)\nfor a luminosity of 2\u00d71033 cm\u22122 s\u22121.\nexpected rates, the full physics trigger menu will consist of many additional signatures for precision\nmeasurements and the discovery program, as well as triggers required for calibration and background\nstudies.\nPreliminary rate studies suggest that about 30% of the 200 Hz bandwidth will be available for electron\nand photon triggers, 25% for muon triggers, 15% for jet triggers, and 15% for triggers involving taus and\n/ET. About 5% of the bandwidth is allocated to B-physics related triggers which will involve low pT\ndi-muon signatures with additional mass cuts to select J/\u03c8 and other rate B-meson decays, with the\nbalance of the bandwidth used for calibration and background triggers. This proposed distribution, will\nof course evolve with experience, and will be tuned to ensure full coverage for discovery and precision\nphysics at all luminosities.\n9\nSummary\nThe LHC is expected to begin its operation at a low luminosity of about 1031 cm\u22122 s\u22121 and ramp up\nto the design luminosity of 1034 cm\u22122 s\u22121 over the \ufb01rst few years of operation. The three levels of the\nATLAS trigger have been designed to handle the high rates and occupancies at high luminosity. The\ntrigger items and their performance have been studied in detail in both the low and high luminosity\nregimes and a comprehensive trigger menu has been developed for the LHC startup phase. Details of\nthe triggers comprising this menu have been discussed in this note and primarily consist of low pT\nthresholds and loose selections that would allow for rapid commissioning and preparation for the high\nluminosity regime. The rates estimated for a trigger menu that will likely be deployed during the initial\nphase of the LHC run are within the limits of the TDAQ bandwidths, but are subject to fairly large\nuncertainties due to the use of simulations that extrapolate from the 2 TeV center-of-mass energy of\nthe Tevatron to the 14 TeV expected for the LHC. The trigger menu in the high luminosity regime will\nuse high pT thresholds and complex triggers involving multiple objects to provide ef\ufb01cient selection of\nphysics processes and high background rejection. A \ufb02avour of such signatures has been discussed in this\nnote. The initial running will allow further optimization of the trigger menus, which will evolve as the\nluminosity increases over three orders of magnitude to the design luminosity.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n563\n\nReferences\n[1] ATLAS Collaboration,\nDetector and Physics Performance Technical Design Report,\nCERN/LHCC/99-14/15 (1999).\n[2] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[3] ATLAS Collaboration, Level 1 Trigger Technical Design Report, CERN/LHCC/98-14 (1998).\n[4] ATLAS Collaboration, High-Level Trigger, Data Acquisition and Controls Technical Design Re-\nport, CERN/LHCC/03-022 (2003).\n[5] Calorimeter Trigger Groups, JINST 3 (2008) P03001.\n[6] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-041,\n(1996).\n[7] ATLAS Collaboration, Tile Calorimeter Technical Design Report, CERN/LHCC/96-042, (1996).\n[8] ATLAS Collaboration,\nMuon Spectrometer Technical Design Report, CERN/LHCC/97-022,\n(1997).\n[9] S. Veneziano et al., IEEE Trans. Nucl. Sci. 51 (2004) 1581\u20139.\n[10] Central Trigger Groups, IEEE Trans. Nucl. Sci. 52 (2005) 3211\u20133215.\n[11] Luminosity Blocks, Web page: https://twiki.cern.ch/twiki/bin/view/Atlas/LuminosityBlock.\n[12] T. Sj\u00a8ostrand, S. Mrenna, P. Skands, JHEP 0605 (2006) 026.\n[13] S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res. A506 (2003) 250\u2013303.\nTRIGGER \u2013 TRIGGER FOR EARLY RUNNING\n564\n\nHLT Track Reconstruction Performance\nAbstract\nThis note reviews the tracking algorithms used at the L2 and Event Filter stages\nof the High Level Trigger of ATLAS. The tracking performance (ef\ufb01ciency,\nresolution) is studied for different topologies (single tracks, high and low pT\njets) using simulated data. Detailed information on the execution time of the\nalgorithms is also given.\n1\nIntroduction\nThe aim of this note is to describe the tracking algorithms used at the L2 and Event Filter stages of the\nHigh Level Trigger of ATLAS and to study their performance.\nThe de\ufb01nitions of the relevant quantities (ef\ufb01ciency, fake rate, and resolution) given in this note can\ndiffer with the ones used in the different selection algorithms of speci\ufb01c trigger objects (e/\u03b3, muon, taus,\nb-jet and B-physics): here the purpose is to de\ufb01ne a common language to study and compare the different\ntracking algorithms.\nA detailed description of the complete ATLAS detector and its performance can be found in [1].\nIn addition to a description of the trigger system, it also contains relevant information on the ATLAS\ntracking detectors, the Inner Detector (ID) and its subsystems (Pixel, SCT and TRT).\n2\nTrack reconstruction at L2\n2.1\nData preparation\nDetector data should be converted before it can be used by tracking algorithms. The conversion process\nincludes the bytestream decoding, the cluster formation in the Pixel and SCT detectors [1], and their\nconversion in spatial coordinates (space points).\n2.2\nIDScan\nIDScan is a set of algorithms for fast pattern recognition and track reconstruction at the second level trig-\nger, using space points provided by the tools described in Section 2.1. These algorithms \ufb01rst determine\nthe z-position of the interaction point along the beam axis and then perform combinatorial tracking only\ninside groups of space points that point back to that determined position.\nThe \ufb01rst algorithm, aiming to determine the z-position of the primary vertex, divides the region-\nof-interest (RoI) into many equally-sized \u03c6 slices, whose width is tuned according to the individual\nRoI type, based on the lowest track momenta desired and the level of background hits in the detector.\nWhile tracks of high momenta produce most of their hits in a small number of neighbouring slices, hits\nfrom lower-momentum, curved tracks populate several different slices. Every space point is paired (or\noptionally every space point from the innermost three silicon layers) in each slice to the other space\npoints in that slice and in a few neighboring slices, and each pair is used to calculate a z-position by\nlinear extrapolation to the beam line. (This exploits the fact that helical trajectories of charged particles\nin a solenoidal magnetic \ufb01eld are straight lines in the \u03c1-z projection.) A one-dimensional histogram\naccumulates all the calculated z values, and the peak(s) in this histogram provide the rest of the IDScan\nalgorithms with the z-coordinate of the pp interaction point. The correct position is identi\ufb01ed in more\nthan 98% of the RoIs, with a resolution between 150 and 200 \u00b5m (depending on the type of RoI) for the\ncentral RoIs.\n565\n\nUsing the z-position previously reconstructed, the second algorithm computes the pseudorapidity for\nall the space points in the RoI and \ufb01lls a two-dimensional histogram in (\u03b7,\u03c6). Since all hits from a given\n(suf\ufb01ciently) high-PT track tend to be contained in a small solid angle (with its apex at the origin for the\ntrack), the space points from each track that originates from the computed z-position on the beam axis\nform a cluster of neighbouring bins in this histogram. When the bin size is small enough, the occupancy\nfor each bin is low and each cluster, called a group, often contains the space points of a single track.\nFake candidates are reduced by keeping track of which detector layers contribute space points to each\nbin and requiring that at least four out of an expected seven layers to have contributed to a given bin or\nits immediate neighbours, before that bin is included in a group.\nAfter the groups have been identi\ufb01ed random space points and/or space points from multiple tracks\nin each group are separated. This is achieved by considering all possible triplets of space points within\na group and making use of the fact that any three hits from a track can be used to extract the same\ntrack parameters \u03c60 and 1/PT in the transverse plane. The algorithm \ufb01lls a two-dimensional histogram\nwith extracted (\u03c60,1/PT) values and considering combinations containing space points from at least four\ndifferent silicon layers.\nFinally the cleaned groups are subjected to the clone removal algorithm, which identi\ufb01es groups\nsharing at least a certain number of space points (currently 2 or 3 depending on the RoI type) and\nremoves all but the one with the highest number of space points. Furthermore, a group is removed if it\nshares more than 45% of its space points with others. This step signi\ufb01cantly reduces the number of fake\ngroups that contain a few random space points in addition to a small number of space points from an\nactual track.\nAfter all these steps, the remaining groups are passed on to a track \ufb01tter. The default \ufb01tter used by\nIDScan is described in Section 2.5.\n2.3\nSiTrack\nThe SiTrack L2 algorithm adopts a combinatorial pattern recognition approach to reconstruct tracks\nstarting from space points formed in the ID silicon detectors.\nIn order to perform space point combinations, these are \ufb01rst of all grouped into sets from which the\nentries of each combination will then be extracted; the grouping is implemented in SiTrack, using the\nidea of \u201clogical layers\u201d. These correspond to a list of physical detector layers, i.e. barrel layers and\nend-cap disks, and are labeled with increasing numbers moving away from the beam line. The same\nphysical layer can be included in more logical layers, to increase the robustness of the track \ufb01nding\nprocess. To provide a tangible example, the \ufb01rst logical layer adopted for the reconstruction of high-pT\nisolated leptons includes the innermost two pixel barrel layers and the innermost pixel end-cap disk.\nOnce the space points have been associated to the logical layers they belong to, the track reconstruc-\ntion algorithm proceeds through the following \ufb01ve steps:\n\u2022 formation of track seeds;\n\u2022 optional primary vertex reconstruction along the beam line;\n\u2022 extension of track seeds;\n\u2022 merging of extended seeds;\n\u2022 clone removal.\nThe formation of track seeds corresponds to a combinatorial pairing of space points coming from the\ninnermost two logical layers. For each seed, the extrapolation to the beam line is evaluated, using a\nstraight line approximation; this process is depicted in Fig.\n1. At this point a cut on the transverse\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n566\n\nFigure 1: Pictorial scheme of the SiTrack combinatorial strategy for track seeds formation (left) and track\nseeds extension (right).\nimpact parameter is applied. This cut, meant to reduce the number of seeds to be further processed, is\nparticularly important, as it \ufb01xes the lowest reconstructible track pT value.\nThe subsequent step is the reconstruction of the position of the primary interaction vertex along the\nbeam line, used to reject tracks not coming from the primary interaction. The vertex reconstruction\nis performed \ufb01lling a histogram with the longitudinal impact parameter of the seeds and searching for\nhistogram maxima; more vertex candidates can be retained and seeds not pointing to any of the recon-\nstructed vertexes are discarded. This optional step is useful for high track multiplicity topologies like\njets, but is typically skipped in the case of low multiplicity event topologies, e.g. for the reconstruction\nof single isolated leptons. Each retained seed is extended, as depicted in Fig. 1, extrapolating it to the\nouter logical layers and forming one or more space point triplets for each seed; extensions are selected\napplying a cut on the distance between the outer space point and the extrapolated seed. Each extended\nseed is then \ufb01tted by a straight line in the longitudinal plane and parametrized as a circle in the transverse\nplane.\nAll the extensions found for each seed must then be merged into a single full track, grouping the\ntriplets having similar track parameters after the \ufb01t. The full track is thus formed by the union of the\nspace points from all the merged extensions. All the triplets not involved in the merging process are\ndiscarded, while track parameters are re-evaluated for the full track, \ufb01tting it with a straight line in the\nlongitudinal plane and a circle in the transverse one.\nTwo full tracks obtained from different track seeds may still share most of their space point; these\ntracks are de\ufb01ned as clones. To eliminate these ambiguous cases, only the clone track containing the\nlargest number of space points is retained; in case more clone tracks contain the same number of space\npoints, the one with the lowest \u03c72 value prevails. The retained full tracks are \ufb01nally re\ufb01t using one of the\navailable common \ufb01t tools.\n2.4\nTRT tracking\nInformation from the TRT part of Inner Detector can be used as the basis of a L2 tracking algorithm.\nThe core of the algorithm is a set of utilities from the of\ufb02ine reconstruction package xKalman [2] for\nthe reconstruction of tracks in the TRT detector. It is based on the Hough-transform (histogramming)\nmethod. At the initialization step of the algorithm, a set of trajectories in the \u03c6 \u2212R(Z) space is calculated\nfor the barrel and endcap parts of the TRT. The value of the local magnetic \ufb01eld is taken into account\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n567\n\nat each straw position and coordinate along it when calculating the trajectories. After initialization, a\nhistogram (with a size of 500 bins in \u03c6 and 70 bins in curvature) is \ufb01lled for each event with the TRT hit\npositions. The track candidates can be identi\ufb01ed from peaks in the histogram. Bins with at least eight\nhits are considered as track candidates. These track candidates should satisfy some quality parameters\nlike the number of unique hits and the ratio of hits to number of straws crossed by the trajectory. For each\ntrack candidate, the parameters are tuned so that the track lies on the maximum number of drift circle\npositions. It is at this stage that drift information is taken into account to further improve the resolution\nof the track parameters.\n2.5\nTrack \ufb01tting tools\nThe track \ufb01tting procedure used by the L2 ID algorithms in Pixel and SCT detectors is based on a Kalman\n\ufb01ltering technique.\nAt \ufb01rst, space points are dissolved into clusters and a \ufb01ltering node is created for each cluster. The\n\ufb01ltering nodes encapsulate implementations of the Kalman \ufb01lter algorithm for various measurement\nmodels. The \ufb01tter object uses the \ufb01ltering nodes to update a track state described as a 5-dim vector of\ntrack parameters (local x, local y, angles \u03c6 and \u03b8 given in the global coordinate system, and track inverse\nmomentum Q) and corresponding covariance matrix.\nThe track state update consists of three steps. First, the track state is extrapolated using a sim-\nple parabolic approximation of a trajectory in uniform magnetic \ufb01eld. The material-related corrections\n(multiple scattering, energy losses) are added to the covariance matrix during this step. The extrapolated\ntrack state is used to validate the next hit: if the \u03c72 distance between the hit and state is less then a\nprede\ufb01ned cut for this \ufb01ltering node the track state is updated. These \u201cextrapolate-validate-update\u201d steps\nare repeated for every node. After that, a standard backward smoother is applied.\nThere exists another tool which performs track \ufb01t and simultaneous pattern recognition in the TRT.\nThe implementation of this tool is based on a distributed approach. More details on the L2 TRT track\nextension tool can be found in Ref. [3].\n2.6\nVertex Fitting tools\nAn essential part of the L2 event selection (e.g. B-physics event selection) is vertex \ufb01nding and \ufb01tting us-\ning tracks reconstructed by the L2 tracking algorithms as input. Due to the L2 timing constraints a vertex\n\ufb01tting algorithm for the L2 application has to be fast. An additional requirement stems from the L2 track\nreconstruction which provides input track parameter errors in form of a covariance matrix. In contrast,\nvertex \ufb01tting algorithms proposed in literature assume uncertainties of the input track parameters to be\ndescribed by weight (inverse covariance) matrices. However, if only track covariance matrices are avail-\nable, these algorithms requires them to be inverted beforehand thus resulting in substantial computing\ntime overhead.\nTo alleviate this drawback a fast vertex \ufb01tting algorithm capable of using track covariance matri-\nces directly (i.e. without time-consuming inversion) has been developed. The speci\ufb01c feature of the\nalgorithm is that track momenta at perigee points rather than \u201cat-vertex\u201d momenta are selected as the\n\ufb01t parameters. Such a choice of \ufb01t parameters makes it possible to apply a decorrelating measurement\ntransformation so that the transformed measurement can be partitioned into two uncorrelated vectors\n\u2013 measured momenta and its linear combination with measured track coordinates at the perigee. This\nlinear combination comprises a new 2-dim measurement model while the measured momenta and the\ncorresponding blocks of the input track covariance matrices are used to initialise a vertex \ufb01t parameter\nvector and covariance matrix of the Kalman \ufb01lter. This approach provides a mathematically correct and\nnumerically stable initialisation of the vertex \ufb01t. A reduced size (2-dim instead of the usual 5-dim) of\nthe measurement model makes the proposed Kalman \ufb01lter very fast and therefore suitable for an online\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n568\n\napplication in the ATLAS Level 2 Trigger. A detailed description of the L2 vertex \ufb01tting algorithm can\nbe found in Ref. [4].\n3\nTrack reconstruction at EF\nID reconstruction at the EF is performed using ATLAS \u201cNew Tracking\u201d software [5]. A common ap-\nproach between of\ufb02ine and online is possible thanks to the modular New Tracking design which allows\nthe replacement of time-critical components and full-featured of\ufb02ine modules by trigger-speci\ufb01c im-\nplementations. New Tracking currently covers two sequences, the main inside-out track reconstruction\n(track \ufb01nding starts from the Silicon and then is extended to the TRT) and outside-in tracking (from\nthe TRT to the Silicon). The primary pattern search concepts for both sequences have been to a large\nextent adopted from the already existing ATLAS ID reconstruction program xKalman [2], but integrated\nand incorporating additional components in the common New Tracking approach. In the following note,\nonly the inside-out reconstruction of tracks is described since is it the only one used in the EF ID online\nreconstruction. In the future, an outside-in approach is intended to be used in the trigger in cases where\nphoton conversions are present.\nThe EF ID reconstruction runs for many different signatures, such as electrons, muons, taus, and b-\njets. Each of these triggers contains a very similar algorithm sequence as the ID inside-out tracking and\nis followed, depending on a given object, by dedicated event reconstruction algorithms including vertex\n\ufb01nding, b-tagging or electron processing. In the EF realization of New Tracking dedicated algorithms\nsteer the underlying tools with RoI-seeded input collections 1. The tools used are directly taken from\nthe of\ufb02ine reconstruction chain but operated in a RoI-seeded mode, where the trigger signature de\ufb01nes a\nwidth of the RoI.\nThe EF ID algorithm sequence is divided into three stages de\ufb01ned as pre-processing, inside-out track\n\ufb01nding and post-processing. The pre-processing stage is responsible for building clusters and drift circles\nin the Silicon and TRT detectors, respectively, and the creation of space points as three-dimensional\nrepresentations of the Silicon detector measurements.\nThe inside-out track \ufb01nding starts from the Pixel and SCT to \ufb01nd track seeds and creates track\ncandidates based on the seeds primarily found. The seeded track \ufb01nding results in a very high number of\ntrack candidates, that have to be resolved before an extension into the TRT detector can be done. Many of\nthese tracks share hits, are incomplete, or describe fake tracks, hence ambiguity resolution is necessary.\nThe track extension from the Silicon to the TRT is divided into two modules. First, tracks found in the\nSilicon detector are used as an input to \ufb01nd a compatible set of TRT measurements. Then each extended\ntrack is evaluated with respect to the original Silicon track. A track scoring mechanism is then used to\ncompare the original track with the one after re\ufb01tting, and the best track is chosen.\nThe last stage, post-processing, starts from a primary-vertex search, which is based on the Billoir\n\ufb01tting method [6]. A track object is created which is a representation of the track reconstruction results\naimed for analysis applications.\nCurrently several different \ufb01tting techniques are implemented in New Tracking and can be chosen at\na con\ufb01guration level:\n\u2022 Kalman Fitter as a straightforward implementation of the Kalman \ufb01lter technique [7] that has been\nadopted for the track \ufb01tting in high energy physics experiments. For the ATLAS Silicon detector,\nthe Kalman Fitter has a dedicated extension for \ufb01tting of tracks from electrons, that lose stochas-\ntically a signi\ufb01cant part of their energy due to bremsstrahlung effects. In that case, an assumption\nabout purely Gaussian noise is far from being optimal. A special Dynamic Noise Adjustment tech-\n1The FullScan operation is an exception which assumes track reconstruction in the entire detector.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n569\n\nnique has been developed [8]. It still uses a Gaussian error assumption but modi\ufb01es the applied\nvariance based on the amount of traversed material.\n\u2022 Deterministic Annealing Filter is a deterministic annealing technique [9] which combines the stan-\ndard Kalman \ufb01lter formalism with a probabilistic description of the measurement assignment to a\ntrack.\n\u2022 Gaussian Sum Filter is a special multi-Gaussian extension of the standard Kalman \ufb01tter [10],\ndedicated to reconstruction of electron tracks. In the GSF approach, the highly non-gaussian\nprobability density function of electron energy loss is modeled by a mixture of several Gaussians.\n\u2022 Alignment Kalman Filter is an extended version of the Kalman \ufb01lter [11] that integrates an update\nof the detector surface orientation and position into an intrinsic measurement update of a Kalman\nFitter step.\n\u2022 Global Chi2 Fitter [12] is a track \ufb01t through a minimization of \u03c72 value. Given purely Gaussian\nprocess noise, the minimization of the \u03c72 value that is built from hit residuals at every measurement\nsurface gives the best set of estimators of the track trajectory. Material effects enter the \u03c72 function\nas additional \ufb01tting parameters.\nThe Kalman Fitter approach without the Deterministic Annealing Filter extension is a default \ufb01tter\nat the EF ID. Other \ufb01tters described above can be chosen during the con\ufb01guration step.\n4\nPerformance\n4.1\nTiming measurement\nThis section presents a summary of CPU timing measurements for various steps of data preparation and\ntrack reconstruction in L2 ID and EF ID algorithms.\n4.1.1\nL2 ID\nThe L2 ID timing has been measured on a quad-core 3GHz Woodcrest CPU machine. Timers provided\nby the standard trigger monitoring framework have been used for these measurements.\nThe data preparation timing measurements obtained on t\u00aft data for the Pixel and SCT are shown in\nTable 1 for e/\u03b3, muon, and tau triggers. The average cluster collection and space point multiplicities per\nRoI are presented in Table 2.\nThe track reconstruction timing measurements are summarized in Table 3 (note that SiTrack \ufb01t timing\nis included in the pattern recognition time). The average track multiplicity is presented in Table 4.\nTables 5,6, 7, and 8 present a comparison between RoI-based and FullScan running for B\u2212physics\ntriggers on b\u00afb \u2192\u00b5X data. These show, respectively, the time of data formation, average space point\nmultiplicity, time of L2 ID track reconstruction, and average track multiplicity for the two cases.\n4.1.2\nEF ID\nThe EF ID timing measurements are shown in Table 9. They were done on a 3 GHz Intel Xeon 5160\nCPU with 8GB of memory. The EF ID software was run in the emulator of the event \ufb01lter processing and\nexecution times for the algorithms were obtained as mean values from the timing histograms provided\nby the HLT framework. The results are representative in terms of algorithm execution times but do not\naccount for data collection times, which are platform dependent. Two event samples were used in the\ntests, one corresponding to a single electrons with 100GeV, the other was a simulation of t\u00aft production.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n570\n\nData preparation step\nMean time [ms]\n\u00b5\ne/\u03b3\n\u03c4\nRegionSelector\n0.23\n0.26\n0.32\nRobDataProvSvc\n0.02\n0.02\n0.02\nCluster IDCs retrieval\n0.03\n0.03\n0.02\nBS-to-clusters, Pixel\n0.63\n0.73\n1.02\nBS-to-clusters, SCT\n0.60\n0.69\n0.95\nPixel space point formation\n0.24\n0.27\n0.35\nSCT space point formation\n0.31\n0.37\n0.40\nTotal time\n2.11\n2.45\n3.23\nTable 1: The timing measurements of the data formation per RoI.\nData preparation step\nMultiplicity\n\u00b5\ne/\u03b3\n\u03c4\nPixel cluster coll.\n46.2\n45.6\n104.4\nSCT cluster coll.\n82.8\n83.5\n245.8\nPixel space points\n66.4\n65.9\n131.6\nSCT space points\n36.5\n38.8\n87.1\nTable 2: Average cluster/space point multiplicities per RoI.\nThe most CPU demanding operation is the track \ufb01nding in the silicon detectors with typical exe-\ncution times of 30 ms per RoI ( 300 ms in FullScan mode). Next is the processing of TRT extensions\nand resolution of ambiguities each with a CPU cost of about 20 ms per RoI (approximately 170 ms in\nFullScan). Another important contribution to the processing time is the data preparation step which takes\nabout 20 ms per RoI for all detectors (and about 300 ms in FullScan mode). The total time to process t\u00aft\nevents in full-scan mode is about 1s.\n4.2\nEf\ufb01ciency and resolution de\ufb01nition\nIn order to evaluate the performance of any tracking algorithm, three kinds of information have to be\nprovided: track reconstruction ef\ufb01ciency, the percentage of fake reconstructed track candidates, and the\nTrack reconstruction step\nMean time [ms]\n\u00b5\ne/\u03b3\n\u03c4\nIDScan : Pattern recognition\n0.60\n0.70\n1.45\nIDScan : Track Fit\n0.28\n0.29\n0.49\nIDScan : TRT data preparation\n1.14\n1.32\n\u2013\nIDScan : TRT tracking\n2.96\n2.87\n\u2013\nSiTrack : Pattern recognition\n0.62\n0.66\n\u2013\nSiTrack : TRT data preparation\n1.15\n1.39\n\u2013\nSiTrack : TRT tracking\n2.85\n3.66\n\u2013\nTable 3: The timing measurements of the L2 ID track reconstruction with IDScan and SiTrack.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n571\n\nL2 ID algorithm\nTracks/RoI\n\u00b5\ne/\u03b3\n\u03c4\nIDScan\n1.92\n1.63\n4.50\nSiTrack\n2.05\n2.66\n\u2013\nTable 4: The average track multiplicity per RoI for L2 ID track reconstruction with IDScan and SiTrack.\nData preparation step\nMean time [ms]\nRoI 0.75\u00d70.75\nFullScan\nRegionSelector\n0.67\n4.76\nRobDataProvSvc\n0.02\n0.41\nCluster IDCs retrieval\n0.03\n0.06\nBS-to-clusters, Pixel\n2.13\n11.7\nBS-to-clusters, SCT\n1.89\n13.1\nPixel space point formation\n0.78\n5.27\nSCT space point formation\n0.68\n5.65\nTotal time\n6.67\n44.5\nTable 5: The timing measurements of the data formation for RoI-based and FullScan running of\nB\u2212physics triggers.\nresolution of the track parameters.\nAll the results shown in this section refer to reconstructed Monte Carlo (MC) simulated data samples,\nwhere the track parameters for both the reconstructed and the simulated tracks are available. In addition,\neach space point used to build a given track can be traced back to the MC particle that generated the cor-\nresponding charge deposit. This information is used by the ID trigger analysis packages to evaluate two\nadditional quantities for each reconstructed track, which prove fundamental for the ef\ufb01ciency de\ufb01nition:\n\u2022 the number of space points which trace back to the same MC track;\n\u2022 the link between a reconstructed track and the MC track that generated most of its space points.\nIn this context we de\ufb01ne:\n\u2022 reconstructible MC particle: a particle passing a set of geometrical selection cuts (being contained\nin one of the processed RoIs, pointing to the primary vertex) and a pT cut;\nData preparation step\nMultiplicity\nRoI 0.75\u00d70.75\nFullScan\nPixel cluster coll.\n266.2\n1744\nSCT cluster coll.\n824.7\n8176\nPixel space points\n246.2\n1591.5\nSCT space points\n119.6\n910.3\nTable 6: The average cluster/space point multiplicities for RoI-based and FullScan running of B\u2212physics\ntriggers.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n572\n\nTrack reconstruction step\nMean time [ms]\nRoI 0.75\u00d70.75\nFullScan\nIDScan : Pattern recognition\n3.00\n34.6\nIDScan : Track Fit\n0.55\n2.19\nIDScan : TRT data preparation\n2.05\n9.50\nIDScan : TRT tracking\n5.43\n19.5\nTable 7: The timing measurements of the L2 ID track reconstruction for RoI-based and FullScan running\nof B\u2212physics triggers.\nL2 ID algorithm\nTracks/RoI\nRoI 0.75\u00d70.75\nFullScan\nIDScan\n4.26\n16.9\nTable 8: The average track multiplicity for RoI-based and FullScan running of the B\u2212physics triggers.\n\u2022 good track: a reconstructed track linked to a reconstructible particle by the majority of its space\npoints; the geometrical and pT cuts used for the MC particles are applied to the reconstructed\ntracks too;\n\u2022 best track: for each reconstructible particle, more than one good track can be available; the best\ntrack is de\ufb01ned as the one sharing the largest percentage of space points with the linked particle;\n\u2022 fake track: a reconstructed track (passing geometrical and pT cuts) which is not a good track;\nThe most natural choice for the de\ufb01nitions of ef\ufb01ciency, fake fraction and resolution is then:\n\u2022 ef\ufb01ciency: ratio between the best tracks and reconstructible particles;\n\u2022 fake fraction: ratio between fake tracks and all the reconstructed tracks passing the applied cuts;\n\u2022 resolution: difference between the track parameter of a good track and that of the linked recon-\nstructible MC particle;\nThese de\ufb01nitions are used to produce the set of plots used in the following subsections to summarize the\nperformance of a given tracking algorithm.\nThe track reconstruction ef\ufb01ciency is shown as a function of the absolute value of \u03b7 and pT of the\nreconstructible MC particle while the fake fraction is shown as a function of the absolute value of \u03b7 and\npT of the reconstructed track. The track parameter resolutions are shown as a function of the absolute\nvalue of \u03b7 and pT of the reconstructible MC particle: the resolutions on \u03c6, 1/pT, transverse impact\nparameter (d0) and longitudinal impact parameter (z0) are shown as a function of the absolute value of\n\u03b7 while resolutions on d0 and 1/pT are shown as a function of pT. The track parameter resolutions are\nevaluated with a gaussian \ufb01t to the resolution distribution for each parameter.\n4.3\nResults with isolated electrons\nThe tracking performance for electrons was evaluated with a data sample of single electrons uniformly\ndistributed over a transverse momentum range of 7 to 80 GeV. Figure 2 shows the reconstruction ef\ufb01-\nciency and the fake fraction as a function of \u03b7 and pT for SiTrack, IDScan and EF tracking algorithms.\nFigure 3 summarizes, for the same algorithms, the track parameters resolutions. As shown in the \ufb01gures,\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n573\n\nMean time [ms]\nsingle e 100GeV\nt\u00aft\nAlgorithm\nElectron\nElectron\nMuon\nTau\nFullScan\nPix\n2\n2\n2\n3\n61\nSCT\n8\n8\n10\n10\n85\nData preparation\nTRT\n8\n6\n8\n9\n140\nSpace point \ufb01nder\n1\n1\n1\n2\n30\nTrack \ufb01nding in Si\n6\n29\n6\n31\n310\nAmbiguity solving\n4\n15\n5\n11\n135\nTRT track extensions\n1\n3\n1\n1\n31\nTRT extension processing\n5\n19\n8\n13\n170\nVertex \ufb01nding\n0.1\n1\n1\n-\n23\nParticle creation\n0.4\n2\n1\n1\n24\nTotal\n35\n86\n43\n81\n1009\nTable 9: Timing of EF reconstruction steps per RoI in two samples of events, single e\u2212of 100 GeV and\nt\u00aft events. Electron, muon, and tau times were measured in the corresponding triggers, FullScan mode\ncomes from the execution of B-physics triggers. The RoI sizes were 0.1\u00d70.1 (\u2206\u03c6 \u00d7\u2206\u03b7) for the electron\nand muon triggers, 0.2\u00d70.2 for tau triggers.\nthe ef\ufb01ciency is typically 95% or greater, except for low pT or high \u03b7 where it drops to about 90%. The\nfake fractions tend to be below 2% except at low pT or high \u03b7 where they can exceed 6%. Resolutions\nare observed to be quite good and are also somewhat degraded at low pT or high \u03b7.\n4.4\nResults with isolated muons\nThe tracking performance for muons was evaluated with a data sample of single muons with transverse\nmomenta of 6, 9, 21 and 30 GeV. Figure 4 shows the reconstruction ef\ufb01ciency and the fake fraction as a\nof function \u03b7 and pT for SiTrack, IDScan and EF tracking algorithms. Figure 5 summarizes, for the same\nalgorithms, the track parameter resolutions. As shown in the \ufb01gures, the muon performance is even better\nthan for electrons, with close to 100% ef\ufb01ciency throughout the kinematic range and an extremely low\nfake rate. Resolutions are slightly better than for electrons, and show similar pT and angular dependence.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n574\n\n (GeV)\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nEfficiency (%)\n30\n40\n50\n60\n70\n80\n90\n100\n110\nSiTrack\nIDScan\nEF\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency (%)\n30\n40\n50\n60\n70\n80\n90\n100\n110\nATLAS\n (GeV)\nT\np\n10\n20\n30\n40\n50\n60\n70\nFake fraction (%)\n0\n2\n4\n6\n8\n10\n12\n14\n16\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nFake fraction (%)\n0\n2\n4\n6\n8\n10\n12\n14\n16\nATLAS\nFigure 2: Electron track reconstruction ef\ufb01ciency (top) for single electrons as functions of pT and \u03b7 for\nSiTrack (full triangles), IDScan (empty triangles) and EF tracking (empty circles). Bottom plots show\nfake fraction as a function of the reconstructed pT and \u03b7.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n575\n\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n)[rad]\n\u03c6\n(\n\u03c3\n0\n0 0002\n0 0004\n0 0006\n0 0008\n0 001\n0 0012\n0 0014\n0 0016\nSiTrack\nIDScan\nEF\nATLAS\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n]\n-1\n)[MeV\nT\n(1/p\n\u03c3\n0\n0.000002\n0.000004\n0.000006\n0.000008\n0 00001\n0.000012\nATLAS\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n (d0)[mm]\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nATLAS\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n (z0)[mm]\n\u03c3\n0\n0.1\n0 2\n0 3\n0.4\n0 5\nATLAS\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n (d0)[mm]\n\u03c3\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n]\n-1\n)[MeV\nT\n (1/p\n\u03c3\n0\n0.000005\n0 00001\n0.000015\n0 00002\n0.000025\nATLAS\nFigure 3: Track parameter resolutions for single electrons as a function of \u03b7 and pT for SiTrack (full\ntriangles), IDScan (empty triangles) and EF tracking (empty circles).\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n576\n\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\nEfficiency (%)\n70\n75\n80\n85\n90\n95\n100\n105\n110\nSiTrack\nIDScan\nEF\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency (%)\n70\n75\n80\n85\n90\n95\n100\n105\n110\nATLAS\n (GeV)\nT\np\n2\n4\n6\n8\n10\n12\n14\n16\n18\nFake fraction (%)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nFake fraction (%)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nATLAS\nFigure 4:\nMuon track reconstruction ef\ufb01ciency (top) for single muons as functions of pT and \u03b7 for\nSiTrack (full triangles), IDScan (empty triangles) and EF tracking (empty circles). Bottom plots show\nfake fraction as a function of the reconstructed pT and \u03b7.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n577\n\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n)[rad]\n\u03c6\n(\n\u03c3\n0\n0 0001\n0 0002\n0 0003\n0 0004\n0 0005\n0 0006\n0 0007\n0 0008\n0 0009\nSiTrack\nIDScan\nEF\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n]\n-1\n)[MeV\nT\n(1/p\n\u03c3\n0\n0.000001\n0.000002\n0.000003\n0.000004\n0.000005\n0.000006\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n (d0)[mm]\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n|\u03b7|\n0\n0 5\n1\n1.5\n2\n2.5\n (z0)[mm]\n\u03c3\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\n0.35\n0.4\n0.45\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n (d0)[mm]\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n]\n-1\n)[MeV\nT\n (1/p\n\u03c3\n0\n0.000001\n0.000002\n0.000003\n0.000004\n0.000005\n0.000006\n0.000007\nFigure 5: Track parameter resolutions for single muons as a function of \u03b7 and pT for SiTrack (full\ntriangles), IDScan (empty triangles) and EF tracking (empty circles).\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n578\n\n4.5\nResults with jets\nThe tracking performance has also been evaluated using a sample of b-jets produced in the decay of a\nHiggs boson (mass 120 GeV) produced in association with a leptonically-decaying W boson. This is\nthe benchmark sample for b-tagging selection. Only tracks formed with at least four space points are\nconsidered.\nFigure 6 shows the reconstruction ef\ufb01ciency and the fake fraction as a function of \u03b7 and pT for\nSiTrack, IDScan and EF tracking algorithms. Figure 7 summarizes, for the same algorithms, the track\nparameter resolutions. Not surprisingly, the ef\ufb01ciency for this sample is a bit lower (80 to 90 %) than the\nsingle electron and single muon samples, and has a bit higher fake rates. Resolutions are comparable or\nslightly worse.\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\nEfficiency (%)\n0\n20\n40\n60\n80\n100\n120\nSiTrack\nIDScan\nEF\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency (%)\n0\n20\n40\n60\n80\n100\n120\nATLAS\n (GeV)\nT\np\n2\n4\n6\n8\n10\n12\n14\n16\n18\nFake fraction (%)\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nFake fraction (%)\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nATLAS\nFigure 6: Reconstruction ef\ufb01ciency (top) for tracks in b-jets yielded by Higgs decay as functions of\npT and \u03b7 for SiTrack (full triangles), IDScan (empty triangles) and EF tracking (empty circles). The\nef\ufb01ciency as a function of \u03b7 is computed for tracks with pT > 3 GeV. Bottom plots show fake fraction\nas a function of the reconstructed pT and \u03b7.\n4.6\nResults with \u03c0 and K in B-physics events\nUsing Bs decay to \u03c6\u03c0 \u2192KK\u03c0 the reconstruction ef\ufb01ciency for both kaons and pions have been evaluated.\nFigure 8 shows the reconstruction ef\ufb01ciency as a function of \u03b7 and pT for SiTrack, IDScan and EF\ntracking algorithms. The ef\ufb01ciency is typically close to 95% dropping somewhat at low pT or high \u03b7.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n579\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\n)[rad]\n\u03c6\n(\n\u03c3\n0\n0.0002\n0.0004\n0.0006\n0.0008\n0.001\n0.0012\n0.0014\n0.0016\nSiTrack\nIDScan\nEF\n|\n\u03b7\n|\n0\n0 5\n1\n1.5\n2\n2.5\n]\n-1\n)[MeV\nT\n(1/p\n\u03c3\n0\n0 000002\n0 000004\n0 000006\n0 000008\n0 00001\n0 000012\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\n (d0)[mm]\n\u03c3\n0\n0.01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n|\n\u03b7\n|\n0\n0 5\n1\n1.5\n2\n2.5\n (z0)[mm]\n\u03c3\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n (d0)[mm]\n\u03c3\n0\n0.01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n[MeV]\nT\np\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n]\n-1\n)[MeV\nT\n (1/p\n\u03c3\n0\n0 000002\n0 000004\n0 000006\n0 000008\n0 00001\n0 000012\n0 000014\n0 000016\n0 000018\nFigure 7: Track parameter resolutions for tracks in b-jets yielded by Higgs decay as a function of \u03b7 and\npT for SiTrack (full triangles), IDScan (empty triangles) and EF tracking (empty circles).\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n580\n\n (GeV)\nT\np\nEfficiency (%)\n0\n20\n40\n60\n80\n100\n2\n4\n6\n8\n10\n12\n14\nSiTrack\nIDScan\nEF\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency (%)\n0\n20\n40\n60\n80\n100\nATLAS\nATLAS\n (GeV)\nT\np\nEfficiency (%)\n0\n20\n40\n60\n80\n100\n2\n4\n6\n8\n10\n12\n14\nSiTrack\nIDScan\nEF\nATLAS\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency (%)\n0\n20\n40\n60\n80\n100\nATLAS\nATLAS\nFigure 8: Reconstruction ef\ufb01ciency for kaons (top plot) and pions (bottom plot) yielded from a decay\nof the Bs meson to \u03c6\u03c0 \u2192KK\u03c0 (sample 16701 with misaligned geometry), as functions of pT and \u03b7 for\nSiTrack (full triangles), IDScan (empty triangles) and EF tracking (empty circles).\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n581\n\n4.7\nComparison between the EF and the of\ufb02ine tracking performance\nSince the track reconstruction in the EF is based on the same software as used for of\ufb02ine reconstruction,\nthe EF tracking performance was studied under conditions equivalent to those used of\ufb02ine. This study\nwas done using release 13.0.30.4 with perfectly aligned detector geometry.\nTo factorize out the bare EF performance, fake L1 RoIs were produced and passed through the L2 to\nseed the EF tracking, based on the MC truth information from particles with a pT > 1 GeV and a |\u03b7| < 3.\nThe same selection as normally used for of\ufb02ine studies was applied, where only particles within\n|\u03b7| < 2.5, |d0| < 2 mm and |z0 \u2212zv|\u00d7sin\u03b8 < 10 mm were taken into account. The accepted tracks had\nto pass the requirement that at least 80% of the their hits were caused by the matched MC particle as well\nas the quality requirement of having at least 7 hits in the Pixel or SCT detectors together.\nFigure 9 (left) shows the reconstruction ef\ufb01ciency as a function of \u03b7, for single electrons and muons\nwith a pT = 5 or 100 GeV. The ef\ufb01ciency is de\ufb01ned as the fraction of particles that produce an accepted\ntrack and the average ef\ufb01ciencies based on all electrons (muons) were found to be 83.9\u00b10.2% (99.50\u00b1\n0.03) for a pT = 5 GeV and 92.9 \u00b10.1% (99.52 \u00b10.03) for a pT = 100 GeV. Figure 9 (right) together\nwith Fig. 10 shows the muon resolution of 1/pT, \u03c6 and d0 for accepted tracks as functions of \u03b7, where\nthe inverse pT resolution is scaled by the pT value for easier comparison. In accordance with the of\ufb02ine\nstudies, the resolution is determined from the root-mean-squared of the tracks within a region containing\n99.7% of the distributions, i.e. within 3 standard deviations from the mean of a Gaussian distribution.\nAll results are shown together with the of\ufb02ine results presented in [1], which is represented in the plots\nby the superimposed lines. The results agrees well, however, small deviations are seen due to slightly\ndifferent software setup with respect to Ref. [1].\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nReconstruction Efficiency\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n = 100 GeV\nT\n Muon, p\n = 5 GeV\nT\n Muon, p\n = 100 GeV\nT\n Electron, p\n = 5 GeV\nT\n Electron, p\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\n ) \nt\n( 1/p\n\u03c3\n x \nt\n p\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n = 100 GeV\nT\n Muon, p\n = 5 GeV\nT\n Muon, p\nATLAS\nFigure 9: Reconstruction ef\ufb01ciency (left) and scaled 1/pT resolution (right) as functions of |\u03b7|. The superimposed\nlines represent results from the of\ufb02ine track reconstruction.\n5\nSummary and conclusions\nWe have reviewed the track reconstruction algorithms used at the L2 and Event Filter stages of the High\nLevel Trigger of ATLAS.\nThe algorithms performance and timing have been studied running on simulated data different chains\nof trigger selection.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n582\n\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\n ) [mrad]\n\u03c6\n( \n\u03c3\n \n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n = 100 GeV\nT\n Muon, p\n = 5 GeV\nT\n Muon, p\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nm]\n\u00b5\n( d0 ) [\n\u03c3\n \n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n = 100 GeV\nT\n Muon, p\n = 5 GeV\nT\n Muon, p\nATLAS\nFigure 10: \u03c6 (left) and d0 (right) resolution as functions of |\u03b7|. The superimposed lines represent results from the\nof\ufb02ine track reconstruction.\nReferences\n[1] ATLAS Collaboration, The Atlas Experiment at the CERN Large Hadron Collider.\n[2] I. Gavrilenko, Description of Global Pattern Recognition Program (XKALMAN), ATL-INDET-\n97-165 (1997).\n[3] D. Emeliyanov, Nucl. Instrum. Meth. A566 (2006) 50\u201353.\n[4] D. Emeliyanov, A fast vertex \ufb01tting algorithm for ATLAS Level 2 Trigger, XI International Work-\nshop on Advanced Computing and Analysis Techniques in Physics Research ACAT07 (2007).\n[5] T. Cornelissen et al., Concepts, Design and Implementation of the ATLAS New Tracking, CERN-\nATL-COM-SOFT-2007-002 (2007).\n[6] P.Billoir, S.Qian, Nucl. Instrum. Meth. A311 (1992) 139.\n[7] R. Fruhwirth, Nucl. Instrum. Meth. A262 (1987) 444\u2013450.\n[8] V. Kartvelishvili, Electron bremsstrahlung recovery in ATLAS, Proceedings of the 10th Topical\nSeminar on Innovative Particle and Radiation Detectors, IPRD06 (2006).\n[9] R. Fruhwirth et al., Nucl. Instrum. Meth. A502 (2003) 702\u2013704.\n[10] R. Fruhwirth, A. Strandlie, Track \ufb01nding and \ufb01tting with the Gaussian-sum Filter, CHEP (1998).\n[11] R. Fruhwirth et al., J. Phys. G29 (2003) 561\u2013574.\n[12] L. Bugge, J. Myrheim, Nucl. Instrum. Meth. 179 (1981) 365\u2013381.\nTRIGGER \u2013 HLT TRACK RECONSTRUCTION PERFORMANCE\n583\n\nData Preparation for the High-Level Trigger Calorimeter\nAlgorithms\nAbstract\nThis note describes the data preparation necessary to enable the ATLAS High\nLevel Trigger Calorimeter Algorithms.\nAn overview of the infrastructure,\nwhich provides the transition from the calorimeter electronics to data recon-\nstruction and trigger algorithm implementation, is given. This infrastructure\nis detailed as a separate note since it is relevant to all trigger algorithms re-\nquiring calorimeter information (electrons, photons, taus, jets, missing ET and\nmuons).\n1\nIntroduction\nThe calorimeters and part of the muon system were designed to participate in the ATLAS \ufb01rst level\nhardware-based trigger (L1) [1\u20134], while all sub-detectors participate in the software-based high level\ntrigger (HLT) [5], comprised of Level 2 (L2) and the Event Filter (EF). One important phase for any\ntrigger software algorithm is the data preparation step which provides the conversion of the bytes of data\nproduced by the detector electronics into a convenient form for the trigger algorithms. In the case of the\ncalorimeters, the digital information provided by the detector must be converted into calorimeter cells as\ninput to the reconstruction algorithms. A good data preparation step will provide the input to the trigger\nsoftware in an organized manner, so that access to the prepared data is optimized. This note describes\nthis step for the calorimeter trigger software in the HLT. The same software data preparation layer is used\nin algorithms that are used to identify electrons, photons, taus, jets and muons [6].\n1.1\nCalorimeter readout\nThe fundamental LAr calorimeter readout unit is the calorimeter cell. The cell electrodes receive the\ncurrent due to the drift electrons in the liquid argon and form a triangular shaped signal [1]. The shaping\nand readout of this signal is performed by the Front-End Electronics. To preserve the dynamic range and\nthe energy resolution, the signal is shaped with three possible gains. The Front-End Boards (FEBs) save\nanalog samples of the signals coming from the detector at the bunch crossing rate (25 ns). Each FEB can\nprocess up to 128 LAr calorimeter cells.\nThe signals are converted by the FEBs to a digital format if the event is accepted by the L1 Trigger.\nThe digital information is sent to the ReadOut-Drivers (RODs). These are Digital Signal Processor (DSP)\nbased machines, fast enough to deal with a number of input channels (2 FEBs feed one ROD DSP). From\nthe pulse shape digitized at the FEB, the energy deposited in any cell can be calculated.\nData from each ROD are sent to a ReadOut Buffer (ROB). The ROBs keep this data fragment until\nit is requested by L2 or the Event Builder (EB). While L2 only requests a limited amount of data frag-\nments, the EB will request fragments from the whole detector for events approved by L2 for subsequent\nprocessing in the EF computer nodes.\nIn the Tile Calorimeter [2], the photons produced in the scintillators are measured by photomultipli-\ners, which produce a negative shaped pulse. The digitized electronic signal is saved into an on-detector\nmemory waiting for the accept signal from the L1 trigger. For each of the 256 Tile Calorimeter modules,\na so-called drawer (inserted in the back of the calorimeter structure) contains up to 48 photomultipliers\nand all the readout electronics.\nThe analog signals from the detector cells are also summed up by dedicated hardware by detector\nregions in depth. Trigger Towers (TT) are coarse granularity combinations of the detector cells and can be\n584\n\nFigure 1: Different parts of the data preparation processing and their relation to the calorimeter algorithm\nat the L2. For details, see text.\nprovided in analog mode to the hardware L1 processing. Except for the very forward regions, the TT size\nis 0.1\u00d70.1 in \u03b7 \u00d7\u03c6. The L1 hardware algorithm uses some minimal TT energy and isolation quantities\nto de\ufb01ne a possible L1 calorimeter candidate. A pointing to the found candidate \u03b7 \u00d7 \u03c6 position is sent\nas a seed for software trigger processing. This seed is used to open a region (usually de\ufb01ned in terms of\nTT coordinates) called Region of Interest (RoI), where the full detector granularity ca be accessed by the\nreconstruction algorithms.\n2\nData preparation\nFrom a general point of view the preparation of the LAr and Tile Calorimeters data is similar. Figure 1\ndepicts the global scope of the data preparation for the L2 calorimeter algorithm as described below. The\nEF structure is similar and is discussed brie\ufb02y later in the note (see Ref. [7] for additional details of the\nfull HLT data preparation).\nThe L2 software component called Steering receives the L1 information on the acceptance of an\nevent along with the \u03b7 and \u03c6 coordinates corresponding to the L1 triggered object. The reconstruction\nalgorithm gathers a list of ROB identi\ufb01ers which contain data for a given RoI. Each ROB may partially\ncontain data from TTs not pertaining to the RoI (ROB data access is not usually de\ufb01ned by the RoI, but\nrather by the hardware cabling). An optimal way to map cells to the towers and to the addresses of the\nROB must be provided.\nThe mapping of the ROBs and TT are part of the geometry description and are also used in the of\ufb02ine\nreconstruction software framework. The access to the of\ufb02ine detector description databases which maps\nany physical position into a set of identi\ufb01ers is typically very slow, as the full detector description is\ncomprised of a great amount of data. In order to provide faster access, compatible with the L2 speed\nrequirements, a look-up table called the Region Selector is prepared in the initialization phase of the\ntrigger software.\nThe ROB identi\ufb01ers are translated to network addresses of the ROB machines and the data are sub-\nsequently requested. The processing of the trigger selection algorithms is inhibited while the network\nacquires the data. Operating in a multiprocessing environment, as forseen for the ATLAS trigger, reduces\nthis dead time [5,8]. The ROB data provider receives the list of ROB identi\ufb01ers and returns the detector\ndata to the algorithms.\nWhen data are received, pointers to the beginning of the different fragments are passed to the\ndetector-speci\ufb01c bytestream conversion code. Bytestream conversion is the decoding of the data format\nproduced by the detector RODs, and packaging of the data into an accessible format for the algorithms,\nin this case calorimeter cells. The last part of the data preparation is to provide the cells in a manner\norganized for the reconstruction algorithms. For instance, cells are provided by detector layer.\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n585\n\n2.1\nData processing in the Read-Out Drivers\nThe LAr Digital Signal Processors (DSPs) are able to prepare data in different formats, the most im-\nportant one is termed \u201cphysics mode.\u201d In this mode the DSPs process the nominal 5 samples per cell\nprovided by the front-end electronics. These samples are used to compute the energy deposited in the\ncell by the particles using an optimal \ufb01ltering (OF) [9]. This processing is a simple weighted sum of the\nsamples. The weights include the noise autocorrelation, electronics calibration constants, and a normal-\nization factor that converts ADC counts to MeV. For cells with energy above a programmable threshold\nthe timing of the signal and the quality of the pulse shape compared to the expectation are calculated.\nFinally, for each cell, the choice of electronic gain applied to the analog signal in the FEB is recorded.\nBeyond the cell-based data, the DSP can also extract global information at the FEB or TT level,\nwhich can be used to improve the L2 and EF processing speed. The DSP can sum up the energy in a\ngiven region in space providing Ex, Ey, and Ez sums for these regions. The cell energies are added within\nthese regions using cell-position-based projection coef\ufb01cients loaded in the DSP from a database. Zero\nsuppression is applied for cells below a given threshold. FEB\u2019s or TT\u2019s can be used to reconstruct jets\nor missing ET at L2 and EF if unpacking the full detector is too time consuming. Currently FEB\u2019s are\nbeing used to provide the energy sums, however, using the TT information instead is under evaluation to\nimprove jet and missing ET resolutions.\nThe pulses from the Tile Calorimeter photomultipliers are also sampled and digitized by 10-bit\nADCs. During a physics data taking, 7 samples (175ns) of the signal pulses are acquired and trans-\nmitted to the RODs. The information is processed using DSPs which also apply optimal \ufb01ltering for cell\nenergy reconstruction [10].\n2.2\nRegion selector\nAs mentioned earlier, part of the information is stored in lookup tables for fast access to the detector\ndescription. In the LAr calorimeter case, the information unit to be correlated to the L1 position is the\nTrigger Tower. The \u03b7 \u00d7 \u03c6 minimum and maximum and the ROD identi\ufb01er for each TT is arranged\nin a large matrix. Multiple tables corresponding to the different calorimeter layers are available. For\nthe transition region from barrel to endcap calorimeter the data of the \ufb01ducial volume covered by a TT\nmay be provided by more than one ROD. In the Tile Calorimeter case, the geometry information is\nassociated with the calorimeter module identi\ufb01er and, again, the ROB identi\ufb01ers. The Look-Up tables\nwith geometry information for LAr and Tile are prepared by accessing the relevant conditions database.\n2.3\nData containers\nThe data structure of a calorimeter cell includes a part common to LAr and Tile, and parts speci\ufb01c to\nboth subdetectors. In the software these cells are organized in vectors, called collections. For the Liquid\nArgon Calorimeter each cell collection holds data for a LAr ROD, corresponding to two FEBs or, at most\n256 cells. In the case of the Tile cell collection, there are either 23 cells (in the Barrel) or 13 cells (in\nthe Extended Barrel) per collection. Data for four cell collections are associated with a single ROD. A\nTile Calorimeter ROD has data for at most 92 Tile cells. Finally, the collections are organized in a vector\nwhich is called a container.\nThe containers for LAr and Tile are stored permanently in memory and the cells and collections\nare never deleted. This way, on-the-\ufb02y memory allocation, which is typically a slow operation in a\ncomputing system, is avoided. One problem with reusing collections is that the container must keep\ntrack of which collections have already been decoded in a given event. This information is provided by\nthe tools that access the container. If requested subsequently in the same event, the collection will not be\ndecoded again.\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n586\n\n2.4\nBytestream conversion\nThe ROD fragments, containing the energy encoded information are provided to the appropriate HLT\nbytestream conversion code. Based on the ROD fragment identi\ufb01er, the corresponding cell collection is\nlocated by the proper container (LAr or Tile containers). Subsequently, subdetector speci\ufb01c code is used\nto perform the data unpacking.\nThe LAr bytestream conversion code automatically identi\ufb01es the fragment type using the ROD ver-\nsion encoded in the bytestream itself. Depending on the detected format, the corresponding internal\ninfrastructure is selected.\nThe bytestream conversion software unpacks the energy information using the DSP physics output\nformat as described in Section 2.1. The conversion provides the cell energy, hardware gain, pulse peak\ntime, and pulse-\ufb01t quality information (if available) for each of the ROD fragment channels. The channel\nnumber is used as an index to the cell position in the cell collection, so that each LAr channel is associated\nto a single prede\ufb01ned cell object in the collection. Each cell is updated with the current values of energy,\ntime, quality and hardware gain. In the unpacking step, typically more cells are requested than those\ncontained in the RoI as data from one FEB may extend over several TTs. Furthermore, the trigger\nreconstruction algorithms require data access on a layer-by-layer basis. This results in a very complex\noperation with many checks of cell layer and position. Maps between TT identi\ufb01ers and the associated\ngroups of cells are prepared prior to algorithm execution, to speed up the process. Using the TT identi\ufb01er\nlist obtained from the Region Selector, a chain of cells for those TTs can be obtained, simplifying the\nalgorithm code.\nThe bytestream conversion software for the Tile calorimeter data also checks the ROD format, ensur-\ning that the correct method of unpacking the data is chosen. The data is decoded and the energy values\nare stored in a pre-allocated raw data structure. This is again used to avoid online memory allocation. The\nenergy, time, and quality are stored together with the ADC identi\ufb01er for each cell in a Tile Calorimeter\ndrawer. This raw data is copied into the cell structure. The mapping of raw data to cells is the same for\nevery drawer in a given calorimeter sector. To speed up the processing a mapping is built to the indices\nof the cells that correspond to each raw data.\nEach Tile drawer is unpacked into a cell collection. The data providing in this case is much simpler\nthan in the LAr case. Algorithms are able to iterate through the whole collection after the unpacking is\ndone.\n2.5\nData preparation in the EF\nThe Data Preparation tools in the EF make use of the same data unpacking approach that is used by L2,\ndumping this information into an of\ufb02ine cell container. As the EF has a larger time budget, however,\nmore sophisticated algorithms and tools developed for of\ufb02ine reconstruction are used to process the cells\nstored in this container.\nFor each of the subdetectors (EM, HEC, FCal and Tile), the EF cell container is \ufb01lled. This provides\nthe possibility of unpacking only selected calorimeter sections, as needed. Once the container has been\n\ufb01lled with the corresponding calorimeter cells, a set of software tools are executed to organize and check\nthe container, and to perform cell-based calibrations.\n3\nAlgorithm performance\nIn this section, the performance of representative HLT algorithms (e/\u03b3 for L2 and missing ET for EF)\nand data preparation is studied. The results are based on bytestream \ufb01les prepared with a format similar\nto the ATLAS raw output data.\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n587\n\n| of the L2 Cluster in a 0.2 RoI\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nNumber of LAr Cells used\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n| of the L2 Cluster in a 0.2 RoI\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nNumber of Tile Cells used\n0\n50\n100\n150\n200\n250\n300\nFigure 2: Number of cells used in the L2 e/\u03b3 selection algorithm as a function of \u03b7 for the LAr (EM, EM\nendcaps and HEC) Calorimeters (left) and for the Tile Calorimeter (right). The RoI size was 0.4\u00d70.4 in\n\u03b7 \u00d7\u03c6.\n| of the clusters\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEM section Time (ms)\n0\n0.2\n0.4\n0.6\n0.8\n1\nProcess ng ime\nTotal\nReg on Se ector\nReg on Se ector bytestream conversion\n| of the clusters in a 0.2 RoI\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nHadronic section Time (ms)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nProcessing Time\nTotal\nRegSelSvc\nByteStream Cnv\nAlgorithm\nFigure 3: Cumulative time spent in the different phases (Region Selector, bytestream conversion, and\nalgorithm) of the L2 e/\u03b3 selection as a function of \u03b7 for the electromagnetic part (left) and for the\nhadronic part (right) for an RoI size of 0.4\u00d70.4 in \u03b7 \u00d7\u03c6 (a 2.3 GHz machine was used to perform these\nmeasurements).\nThe primary performance issue is processing time. The processing time depends on the number of\ncells required, which is a function of \u03b7. Figure 2 shows the number of cells separately for LAr (left)\nand Tile (right) calorimeters; the overlapping bins in the \ufb01gure are due to variable \u03c6 segmentation in\ntransition regions between different calorimeter modules. The distribution on the left shows that the\nnumber of active cells in the barrel is quite uniform; since the endcap granularity is smaller, the number\nof unpacked cells decreases with increasing \u03b7. The distribution of the number of cells unpacked for the\nTile Calorimeter depends on the number of drawers to be unpacked. In the very central region (|\u03b7| < 0.4),\ndata from negative and positive rapidities must be accessed to complete the RoI, doubling the amount of\ndata to be unpacked. A similar effect is observed in the region between the TileCal Barrel and Extended\nBarrel.\nFor the standard L2 e/\u03b3 selection based on a RoI size of 0.4\u00d70.4 in \u03b7 \u00d7\u03c6, the execution time for each\nof the processing steps was measured. The results, based on a sample of about 15,000 single electron\nevents are shown in Fig. 3 separately for the EM (left: LAr) and for the hadronic (right: Tile and HEC)\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n588\n\nReco. step\nRegion Selector\nbytestream conversion\nAlgorithm\nTotal\nEM 2nd layer\n29\u00b5s\n169\u00b5s\n146\u00b5s\n347\u00b5s\nEM 1st layer\n13\u00b5s\n171\u00b5s\n113\u00b5s\n301\u00b5s\nEM other layers\n21\u00b5s\n158\u00b5s\n56\u00b5s\n243\u00b5s\nHadronic\n46\u00b5s\n334\u00b5s\n43\u00b5s\n438\u00b5s\nTotal\n109\u00b5s (8%)\n833\u00b5s (63%)\n358\u00b5s (27%)\n1.33 ms\nTable 1: Processing time for different algorithm steps and for different actions. Improvements for the\nTile calorimeter data preparation are envisaged. Time measurement excludes ROB data retrieval time (a\n2.3 GHz machine was used).\nsections. It is important to stress that the processing time per RoI does not depend on event type, since\nthe cluster sizes are constant for a given RoI. It can be seen that the Region Selector comprises a small\nportion of the total time, and that the bytestream conversion is the dominant source of time, with the\nalgorithm itself taking only about 35% (10%) of the total time for the EM (Hadronic) calorimeters. Even\nthough fewer cells are used in the EM calorimeter crack region (around \u03b7 = 1.5 as shown in Fig. 2),\nthese cells are distributed in two ROBs (one from the Barrel and another from the EM endcap), resulting\nin an overall increase in the processing time. Finally, we note that the conversion times are especially\nlarge in the regions covered by the Tile calorimeter and in proportion to the number of Tile calorimeter\nmodules accessed. Work is ongoing to reduce these large processing times. The timing results averaged\nover \u03b7 are also summarized in Table 1. ROB data retrieval times are not included, since they can only be\nevaluated during real data taking.\nThese time measurements indicate that the preparation of the Tile calorimeter data needs to be im-\nproved. Even though about six times fewer cells are accessed for the barrel region, the data preparation\ntime to run the hadronic part is comparable to the EM part.\nOther trigger algorithms such as tau or jet identi\ufb01cation need larger RoI sizes and consequently\nrequire more time. As an example, a jet algorithm which uses a 1.0\u00d71.0 RoI size takes 10 to 12 ms.\n3.1\nEF missing ET performance\nThe EF missing ET reconstruction algorithm accesses data from all the calorimeters and computes the\nmissing ET with its Ex, Ey components as well as the total scalar energy sum. In addition, corrections\ndue to energy deposits from muons can be taken into account by including the results from the EF muon\nreconstruction.\nTo access the calorimeter data the algorithm uses the same data preparation layer used by L2. Since\nthe ATLAS calorimeters contains about 200,000 cells, the access to every single cell can become too\ntime consuming at the trigger level. A faster option is to use energy sums at the FEB level (discussed\nearlier in Section 2.1). FEB unpacking has only been implemented for LAr data, where the impact on\nthe unpacking time is most signi\ufb01cant.\nIn Fig. 4 the processing time of the EF missing ET algorithm is shown for full unpacking and FEB-\nbased unpacking. On average, the time to process the whole calorimeter is dramatically reduced from\n57 ms for the cell method to 2.4 ms for the FEB method.\nThe total scalar sum and the Missing ET calculations were performed using the two unpacking meth-\nods. The missing ET calculation does not depend on the method, while the scalar sum is systematically\nreduced in the FEB calculation due to the effect of the zero suppression. However, due to the drastic\nimprovement in speed, the FEB algorithm is a valid option for the missing ET reconstruction.\nIn addition to the timing studies detailed here, a thorough study of the memory usage and initial-\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n589\n\ntime[ms]\n0\n20\n40\n60\n80\n100\nentries\n1\n10\n2\n10\n3\n10\ncell-based method\nFEB-based method\nFigure 4: Processing time of the EF missing ET algorithm. The timing distributions for the cell and FEB\nmethod are shown. A 2GHz machine was used for this test.\nization time was performed. A substantial fraction of the initialization time is taken by the detector\ngeometry preparation, including the \ufb01lling of the cell coordinates and the Region Selector tables. This\ninitialization step requires access to databases containing information on detector conditions, and pos-\nsibly \ufb01les with complementary information. It was determined that the initialization time is acceptable\nand does not inhibit the running of any of the desired algorithms. Furthermore, the memory usage of the\nalgorithms was measured to be stable and within acceptable operating limits.\n4\nData preparation summary\nThis note describes the implementation of the whole data preparation step for the HLT calorimeter trigger\nfrom the detector electronics up to the reconstruction level. It is fundamental that a data preparation layer\nis ef\ufb01cient and fast, leaving time for the real physics algorithms. The High-Level Trigger Calorimeter\ntools described here have been used extensively with simulated data to commission the ATLAS trigger. A\nunique interface provides access to detector physics quantities (calorimeter cells) obtained with complex\ncomputations from the readout data. Knowledge of the detector details is, of course, a fundamental input\ninto optimizing the strategy to be followed in this unpacking procedure. The critical performance issue\nfor calorimeter data preparation is that it be accomplished within the online time budget, and this goal has\nbeen achieved with the current system. Even for special algorithms, like the missing ET which process\ncells from the whole detector, the data preparation performance is still within the required processing\ninterval restrictions. Whenever FEB summary information can be used, signi\ufb01cant timing reductions can\nbe achieved. Further optimization studies are still in progress.\nIn addition to studies with simulated data, the tools and algorithms discussed here have been applied\nto commissioning runs of the ATLAS detector using cosmic rays. Until the LHC begins taking data, this\nis the only exercise that can approximate the real trigger usage in LHC conditions. Many trigger objects,\nsuch as taus, jets, and missing ET are being successfully debugged in this manner, providing important\nfeedback to the algorithm developers.\nReferences\n[1] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-041\n(1996).\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n590\n\n[2] ATLAS Collaboration, Tile Calorimeter Technical Design Report, CERN/LHCC/96-042 (1996).\n[3] ATLAS Collaboration,\nMuon Spectrometer Technical Design Report, CERN/LHCC/97-022\n(1997).\n[4] ATLAS Collaboration, Atlas First Level Trigger Technical Design Report, CERN/LHCC/98-14\n(1998).\n[5] ATLAS Collaboration, High-Level Trigger, Data Acquisition and Controls Technical Design Re-\nport, CERN/LHCC/03-022 (2003).\n[6] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[7] D.O. Damazio on behalf of the ATLAS High-Level Egamma Trigger Calorimeter, ICATPP Con-\nference (2007).\n[8] Andre dos Anjos et al, IEEE Trans. Nucl. Sci. 51 (2004).\n[9] W.E. Cleland, E.G. Stern, Nucl. Instrum. Methods A338 (1994) 467\u2013497.\n[10] E. Fullana et al, IEEE Trans. Nucl. Sci. 53:4 (2006) 2139\u20132143.\nTRIGGER \u2013 DATA PREPARATION FOR THE HIGH-LEVEL TRIGGER CALORIMETER . . .\n591\n\nTau Trigger: Performance and Menus for Early Running\nAbstract\nThe selection of events with handronically decaying tau leptons is challenging\ndue to high background rates at the LHC. On the other hand, ef\ufb01cient selection\nof events with tau leptons increases the discovery potential of ATLAS in many\nphysics channels, notably Standard Model or Supersymmetric (SUSY) Higgs\nboson production. In this note we describe the ATLAS tau trigger system,\nfocusing on the early data taking period, and present results from studies based\non simulated events, including trigger rates and the acceptance of tau leptons\nfrom W and Z boson decays, Higgs Boson decays, and SUSY processes. In\norder to cope with the rate and optimize the ef\ufb01ciency of important physics\nchannels, the results of the current simulation studies indicate that ATLAS tau\ntriggers should include either relatively high transverse momentum single tau\nsignatures, or low transverse momentum tau signatures in combination with\nother signatures, such as missing transverse energy, leptons, or jets.\n1\nIntroduction\nTau triggers are designed to select hadronic decays of tau leptons, which mainly consist of one or three\ncharged pions accompanied with a neutrino and possibly neutral pions. Leptonic tau decays are typically\nselected by electron [1] or muon [2] triggers. Tau triggers are an important part of the ATLAS trigger\nsystem, a fundamental component of the ATLAS detector [3].\nATLAS will collect data at different luminosities, starting from 1031 cm\u22122 s\u22121. At the lowest lumi-\nnosity the focus of tau triggers is to collect samples that are useful for understanding the detector and\nthe tau reconstruction software. Tau signatures combined with missing transverse energy signatures are\nessential to provide data samples enriched in W\u2192\u03c4\u03bd events, which provide an important sample of real\ntaus needed to re\ufb01ne tau identi\ufb01cation algorithms. Additionally, single tau triggers with large prescale\nfactors will provide samples for tau fake rates studies.\nAt higher luminosities, tau triggers will cope with the event rate increase by using higher ET thresh-\nold requirements, more restrictive identi\ufb01cation requirements, or demanding a combination of different\nsignatures, such as missing transverse energy, jets, or leptons. At high luminosity, tau triggers will be\nessential to enable the collection of data samples for searches based on single tau lepton \ufb01nal states, like\nMinimal Supersymmetric Standard Model (MSSM) H\u00b1 \u2192\u03c4\u03bd [4] decays. They will also be used for\n\ufb01nal states with more than one tau lepton, like SM Higgs boson [5], MSSM neutral Higgs boson [6], or\nZ\u2032 boson [7] decays.\nThe results presented in this paper are based on events fully simulated with GEANT4. The text is\norganized as follows. An overview of the three-level trigger selection for single tau triggers is presented\nin Section 2, while the performance in terms of resolution, rates, and ef\ufb01ciencies is described in Section 3.\nTiming studies of tau trigger algorithms are presented in Section 4. The current tau trigger menu, which\nincludes various single and combined tau triggers, is described in Section 5, with a focus on the early\ndata taking period corresponding to a luminosity of 1031 cm\u22122 s\u22121. Finally, a summary is presented in\nSection 6.\n592\n\n2\nOverview of single tau trigger selection\n2.1\nLevel 1 selection\nThe L1 tau trigger selection is closely related to the L1 electron/photon trigger (e/\u03b3), and is fully doc-\numented in [8]. It is a hardware trigger based on electromagnetic (e.m.) and hadronic calorimeter\ninformation, and uses trigger towers of approximate size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.1\u00d70.1, with a coverage up to |\u03b7|\n< 2.5 (given by the inner-detector coverage and the high-granularity e.m. calorimetry).\nThe algorithm considers a rectangular Region of Interest (RoI) of 4\u00d74 towers (0.4\u00d70.4 in \u03b7 \u00d7\u03c6) in\nboth the e.m. and hadronic calorimeters, and makes use of different elements, each formed by summing\nET over a group of towers. The algorithm uses the following quantities:\n\u2022 the central 2\u00d72 core cluster is the energy measured in the central 2\u00d72 e.m. and hadronic towers\n\u2022 the TauCluster is the energy de\ufb01ned by the two most energetic neighboring central towers in the\ne.m. calorimeter plus the central 2\u00d72 towers of the hadronic calorimeter\n\u2022 EmIsol is the energy in the e.m. isolation ring (the region between 2\u00d72 and 4\u00d74 towers in the e.m.\ncalorimeter).\n\u2022 HadIsol is the energy in the hadronic isolation ring (region between 2\u00d72 and 4\u00d74 towers in the\nhadronic calorimeter).\nThe L1 tau trigger candidate is accepted if the core cluster is a local ET maximum and also satis\ufb01es\nadditional conditions on TauCluster, EmIsol and HadIsol [8]. Its position is taken as the center of the\n4\u00d74 tower RoI, and its energy is calibrated using a procedure derived for jets (see Section 2.1.1). A\nmaximum of eight trigger thresholds are available at L1 for taus. Each threshold is a combination of\nrequirements of ET thresholds for TauCluster, EmIsol and HadIsol. A L1 tau trigger candidate passing\nthe requirements is then passed to L2 for further examination.\n2.1.1\nLevel 1 Calorimeter Calibration\nTrigger towers are formed by the analogue summation of calorimeter cells. Calibration of the trigger\nconsists of adjusting the overall gains of the towers. The e.m. towers are calibrated to optimize the e.m.\ntrigger response. The gains of the hadronic towers are adjusted to provide a uniform jet response in \u03b7\nusing a jet sample with an ET range 50-100GeV and making \u03b7-dependent adjustments to the trigger\nthresholds.\n2.2\nLevel 2 selection\nThe L2 tau trigger selection uses the full calorimeter granularity and the inclusion of tracking information\nfrom the Inner Detector to re\ufb01ne the L1 selection. The selection is designed to further reject QCD jet\nbackgrounds by exploiting more of the characteristics of a hadronic tau decay, such as collimation and\nlow track multiplicity.\n2.2.1\nLevel 2 calorimeter selection\nAt this stage, the selection of the single tau triggers is based on the calorimeter shower shape variables\nand the energy of a reconstructed cluster within the RoI to enrich the sample of tau candidates. Shape\nvariables are calculated using only the second e.m. sampling layer (out of four). The second sampling\nis where most of the e.m. energy is deposited, therefore it provides the most information about the\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n593\n\ne.m. shower shape. The cluster energy is calculated with all available e.m. and hadronic layers. Three\ndifferent rectangular windows are de\ufb01ned, centered on a seed cluster, with areas of \u03b7 \u00d7 \u03c6 = 0.1 \u00d7 0.1\n(narrow, Nar), 0.2\u00d70.2 (wide, Wid), and 0.3\u00d70.3 (normal, Nor) 1. The Nor window is equivalent to the\nRoI used at L2.\nThe algorithm consists of several steps. First, a seed cluster is found, using the second e.m. sampling.\nThe algorithm unpacks cells in the Nor window centered around the L1 RoI position, and \ufb01nds the cell\nwith the highest energy deposition. In a Wid window around the most energetic cell, the cluster position\nis de\ufb01ned as the energy weighted mean position of the cells. Then, shape variables are reconstructed\nusing the different windows around the seed, as described in the following. At the same time, the total\nenergy in all calorimeter samplings is computed. Finally, the total energy is corrected with a simple\nsampling calibration.\nThe variables used by the L2 Calorimeter selection are the following:\n\u2022 EMRadius is the energy weighted squared radius of the seed, which is obtained from the sum of the\nindividual energy weighted squared cell distances from the seed. It is calculated in a Nor window\naround the seed, in the second sampling of the e.m. calorimeter, i.e.\nEMRadius =\n\u2211\nNor\nEcell \u00b7R2\ncell\n\u2211\nNor\nEcell\n.\n(1)\n\u2022 IsoFrac is the difference in energy between the Nar and Wid window, normalized to the Wid\nwindow. It is calculated in the second sampling of the e.m. calorimeter. The de\ufb01nition is\nisoFrac =\n\u2211\nWid\nEcell \u2212\u2211\nNar\nEcell\n\u2211\nWid\nEcell\n.\n(2)\n\u2022 StripWidth is the width of the energy deposition, de\ufb01ned as the energy weighted standard devia-\ntion in \u03b7. It is calculated in a Nor window around the seed, in the second sampling of the e.m.\ncalorimeter. The formula is\nstripWidth =\nv\nu\nu\nu\nu\nt\n\u2211\nNor\n\u03b72\ncell \u00b7Ecell\n\u2211\nNor\nEcell\n\u2212\n\uf8ee\n\uf8ef\uf8f0\n\u2211\nNor\n\u03b7cell \u00b7Ecell\n\u2211\nNor\nEcell\n\uf8f9\n\uf8fa\uf8fb\n2\n.\n(3)\n\u2022 EtCalib is the calibrated total transverse energy, calculated in the e.m. and hadronic calorimeters,\nin a Nor region around the seed.\nThe distributions of EMRadius, IsoFrac and stripWidth are shown in Fig. 1 for tau trigger candidates\nfrom generated tau leptons decaying hadronically and for QCD jets for two different ET regions. In\nthe top row distributions for low ET tau leptons from W \u2192\u03c4\u03bd decays are compared to background\nQCD jets distributions, while in the bottom row high ET tau leptons from Supersymmetric neutral Higgs\ndecays (with a mass of 800 GeV) are compared to QCD background. The top row shows the dif\ufb01culty\nin triggering on low ET taus as the separation between signal and background is not so dramatic; the\nseparation is much better for high ET taus.\n1The window sizes are currently subject of optimization studies.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n594\n\nEMRadius\n-0.01 -0.005\n0\n0.005\n0.01\n0.015\n0.02\n0.025\nEvents\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n) \n\u03bd \u03c4 \n\u2192\nTau signal (W \nQCD jets 8 1.5GeV are reconstructed in a rectangular RoI of size \u03b7 \u00d7\u03c6 = 0.6\u00d70.6 centered\non the L2 Calorimeter seed. The output of the L2 Tracking algorithm is a list of tracks found in the RoI.\nWithin this region, two selection cones are de\ufb01ned, corresponding to a distance \u2206R =\np\n(\u2206\u03b7)2 +(\u2206\u03c6)2\nof 0.15 (Core) and 0.3 (Nor) with respect to the direction of the highest pT track found in the RoI. An\nisolation ring (Iso) with \u2206R between 0.15 and 0.3 is also de\ufb01ned.\nThe following selection variables are then calculated from the track list:\n\u2022 Pt leading is the pT of the track with the highest pT. By requiring a minimum pT this criterion\nalso effectively requires that at least one track is found in the RoI.\n\u2022 Pt Iso/Core is the ratio of the scalar sum of pTs of all tracks in the Core and Iso region \u2211piso\nT /\u2211pcore\nT\n.\n\u2022 N Slow tracks is the number of slow tracks found in the Core region. A slow track is de\ufb01ned as a\ntrack with pT below a certain threshold, typically 7.5GeV/c. The rejection power of this variable\nmight depend on the pile-up conditions.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n595\n\n\u2022 Charge is de\ufb01ned as the absolute value of the sum of charges of all tracks found in the Nor region.\n\u2022 N Tracks is the total number of tracks found in the Nor region.\nThe L2 tracking selection places requirements on these \ufb01ve variables. The set of requirements can be\ndifferent for different single tau signatures. The three most important criteria are requiring that at least\none track be found with a minimum Pt leading, an isolation cut on the maximum amount of energy de-\nposited in the Iso region, and a cut on the maximum number of slow tracks. The requirements on charge\nand total tracks are very loose, due to the higher number of fake tracks found by the L2 tracking algo-\nrithm compared to the more sophisticated of\ufb02ine reconstruction. In addition, the of\ufb02ine reconstruction\nof single tau lepton \ufb01nal states (e.g. from W \u2192\u03c4\u03bd) relies on an unbiased track distribution to estimate\nbackgrounds and extract the number of signal events. The distributions of Pt leading, N Slow tracks and\nPt Iso/Core are shown in Fig. 2 for tau trigger candidates from generated tau leptons decaying hadron-\nically and for QCD jets for two different ET regions. QCD jet background is compared to low ET tau\nleptons from W \u2192\u03c4\u03bd decays (top row), and high ET tau leptons from Supersymmetric neutral Higgs de-\ncays (bottom row). Tau trigger candidates are required to pass different L1 and L2 Calorimeter selection\ncriteria based on their ET. A L2 tau trigger candidate passing the calorimeter and tracking requirements\nis passed to the EF for further consideration.\nL2 Pt leading\n0\n50\n100\n150\n200\nEvents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n)\n\u03bd\n\u03c4\n\u2192\nTau Signal (W\nQCD Jets 17 2GeV found in a \u2206R < 0.2 region around\nthe trigger candidate from L2.\n\u2022 Pt leading track is the highest pT track among the tracks found in a \u2206R < 0.2 region around the\ntrigger candidate from L2.\n\u2022 EtCalib is the energy calculated in all e.m. and hadronic cells found in the \u2206R < 0.3 region around\nthe trigger candidate from L2, and calibrated with the procedure described in [9] and an additional\ntau speci\ufb01c jet calibration.\nSome of the variables used in the EF selection, namely EtCalib, IsoFrac and EMRadius, are shown\nin Fig. 3 for tau trigger candidates from generated tau leptons decaying hadronically and for QCD jets for\ntwo different ET regions. As for previous \ufb01gures, QCD background is compared to standard tau signal\nsamples. Events with a tau candidate that pass the EF thus pass the trigger and are recorded for of\ufb02ine\nanalysis.\n3\nPerformance of single tau triggers\n3.1\nPerformance overview\nThis section describes in detail the expected trigger ef\ufb01ciencies and background event rates obtained from\nthe various single tau triggers available in the ATLAS trigger menu, while combined triggers including\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n597\n\nEF Et calib\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nEvents\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n)\n\u03bd\n \n\u03c4\n \n\u2192\nTau signal (W \nQCD jets 8 12GeV)\n24000\n5.54nb\nZ\u03c4\u03c4\n23000\n0.246nb\nH\u03c4\u03c4\u2192\u2113hX(120)\n22924\n0.145\nH\u03c4\u03c4\u2192hhX(120)\n40950\n0.073\nA\u03c4\u03c4(800)\n26250\n10\nSU3\n22250\n18.59\nt\u00aft\n41700\n800\nTable 1: GEANT4 simulated data samples used in the note.\n3.1.1\nNaming convention\nIn the ATLAS trigger menu, different single tau triggers are implemented, corresponding to different ET\nthreshold requirements 2: tau10i, tau15i, tau20i, tau25i, tau35i, tau45i, tau60. For tau10i and\ntau15i the isolation criteria are only applied at the L2 and EF level. For some ET thresholds, additional\ntriggers are de\ufb01ned using looser isolation criteria (e.g. tau10). Hadronic isolation at L1 is not applied\nin any selection. Due to the ET resolution at the three trigger levels, the actual cut applied on ET at each\nstage is generally lower than the nominal ET to maintain high ef\ufb01ciency.\n3.1.2\nTrigger ef\ufb01ciency de\ufb01nition\nThe tau trigger ef\ufb01ciency is optimized with respect to generated tau leptons decaying hadronically, where\nthe visible tau momentum (p\u03b1\nvis = p\u03b1\n\u03c4 \u2212p\u03b1\n\u03bd ) is in the sensitive region of the detector (|\u03b7| \u22642.5) and is\ngreater than the nominal ET threshold requirement for a given signature. Furthermore, the ef\ufb01ciency is\noptimized to select those tau leptons which are likely to be selected by the tau identi\ufb01cation algorithms of\nthe of\ufb02ine reconstruction software. This constitutes what we subsequently call the tau trigger reference.\nMore speci\ufb01cally, a geometrical match of a trigger candidate to a generated tau lepton within a cone\nregion \u2206R < 0.2 is requested. Generated tau leptons are considered for calculating signal ef\ufb01ciencies\nonly if the tau lepton is also selected by either of the two tau of\ufb02ine reconstruction algorithms [11]:\nthe calorimeter based or the track based algorithm. It should be noted here, that detailed optimization\nwith respect to 1-prong (1 charged pion) and 3-prong (3 charged pions) tau lepton decays has not been\n2The \ufb01rst symbol of the signature represents the particle type, the following number is the ET threshold and the \u201ci\u201d indicates\nthat an isolation requirement is applied.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n599\n\nperformed for this study. This results in different ef\ufb01ciencies for these classes of events, as pointed out\nin the following sections. Total trigger ef\ufb01ciencies shown in this section are estimated on various physics\nprocesses which cover different kinematic ranges. The samples used are therefore speci\ufb01ed in the text.\n3.2\nEnergy and angular resolution\nThe relative resolutions (in %) on ET, \u03b7, and \u03c6 as a function of visible ET and \u03b7 for tau trigger candidates\nat the different trigger levels are shown in Fig. 4 for tau20i. The visible four-momentum of the tau\nlepton is reconstructed from all decay products except neutrinos. The resolutions are rather \ufb02at as a\nfunction of the generated visible ET, however, some dependence on the distributions as a function of the\ngenerated visible \u03b7 is observed. In particular a degraded resolution in ET and \u03b7 in the transition region\nbetween the barrel and endcap calorimeters is clearly visible. Due to the inclusion of track information,\nthe angular resolution at L2 is better than that of L1. The \u03b7 and \u03c6 of the tau trigger candidate at the\nend of the EF algorithm execution is set according to the calorimeter based tau reconstruction algorithm,\nhence the EF angular resolution is slightly worse than at L2 where tracking information is used.\nTrue Visible Et (GeV)\n20\n40\n60\n80\n100\n120\nEt Resolution (percent)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nTrue Visible Et (GeV)\n20\n40\n60\n80\n100\n120\n Resolution\n\u03b7\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nTrue Visible Et (GeV)\n20\n40\n60\n80\n100\n120\n Resolution\n\u03c6\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nL1\nL2\nEF\nATLAS\n\u03b7\nTrue Visible \n-2\n-1\n0\n1\n2\nEt Resolution (percent)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n\u03b7\nTrue Visible \n-2\n-1\n0\n1\n2\n Resolution\n\u03b7\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n\u03b7\nTrue Visible \n-2\n-1\n0\n1\n2\n Resolution\n\u03c6\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nFigure 4: Relative angular and energy resolution for \u03c4 candidates as a function of generated visible ET and \u03b7. Resolution (in\n%) is calculated using a variety of simulated tau lepton samples passing the tau20i trigger.\n3.3\nL1 performance studies\nThe standard reconstruction of the visible energy of L1 tau candidates (TauCluster) reveals a serious\nlimitation when trying to obtain a high ef\ufb01ciency above a given ET threshold at L1. A systematic shift\nof about 30% and a relative resolution of 33% are observed for the reconstructed energy with respect to\nthe generated values. Therefore other possible reconstruction methods have been explored. The energy\nreconstructed with the standard algorithm (TauCluster) has been compared with other reconstruction\nmethods: (1) E4\u00d74, de\ufb01ned as the sum over all towers (e.m. and hadronic part) in the 4\u00d74 RoI region,\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n600\n\n(2) Jet4 \u00d7 4, obtained as the total energy in the 4 \u00d7 4 RoI region calculated with the L1 Jet algorithm\n(which is described in Ref. [8]), and (3) Jet6\u00d76. An improvement of 10% in resolution can be achieved\nwith E4\u00d74 and Jet4\u00d74 algorithms with respect to TauCluster. However, a comparison of the ef\ufb01ciencies\nof the different methods, shown in Fig. 5, indicates that the TauCluster algorithm ef\ufb01ciency is system-\natically the highest. While these other algorithms that more fully contain the ET of the tau lepton give\nbetter resolution than TauCluster, this gain in resolution is accompanied by a loss in ef\ufb01ciency and dis-\ncrimination, motivating the continued use of TauCluster as the default tau algorithm.\nOffline Et (GeV)\n10\n15\n20\n25\n30\n35\n40\nL1 Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nTauClus > 13 GeV \nE4x4 > 20 GeV\nJ4x4 > 18 GeV\nJ6x6 > 21 GeV\nATLAS\nFigure 5: Ef\ufb01ciency curves as a function of the of\ufb02ine ET for different L1 reconstruction methods; threshold requirements\nare chosen to give the same rate among the different cases.\nUsing TauCluster, the rates for a luminosity of 1031 cm\u22122s\u22121 are evaluated by using simulations\nof the relevant QCD backgrounds (see Table 2). The expected rate including all physical processes\n(minimum bias rate) is shown as a function of the cut value applied to TauCluster in Fig. 6. The effect\nof the isolation cut can also be seen in Fig. 6.\nThe L1 selection used in tau trigger implementation is presented in Table 2; the cuts have been tuned\nto maintain a high ef\ufb01ciency, and the signatures are all observed to have an ef\ufb01ciency > 95% 3. The\nef\ufb01ciency has been obtained using simulated samples of W \u2192\u03c4\u03bd and 800 GeV Supersymmetric Higgs\nA \u2192\u03c4\u03c4 events, while background is evaluated using QCD events with two jets with hard parton 8 <\npT < 140 GeV. In Fig. 7, the ef\ufb01ciency is plotted as a function of the generated visible ET for different\ntau signatures. The rather slow increase of the ef\ufb01ciency curves limits the overall performance of tau\ntriggers.\n3.4\nL2 performance studies of the calorimeter selection\nAt L2, the full granularity calorimeter and tracking information is available, allowing a more sophisti-\ncated selection of tau leptons. As shown in Section 3.2, the angular and energy resolutions are improved\nwith respect to L1.\nThe L2 calorimeter based selection of tau trigger candidates is optimized with respect to generated\ntau leptons that pass the L1 selection and are successfully reconstructed by the of\ufb02ine reconstruction\nsoftware (of\ufb02ine details are given in Section 3.1.2). The optimization is obtained using simulated samples\n3The ef\ufb01ciency de\ufb01nition is described in Section 3.1.2\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n601\n\n L1 reconstructed tau energy (GeV)\n10\n20\n30\n40\n50\n60\n70\n (Hz)\n-1\n s\n-2\n cm\n31\n Rate for L=10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nNon-isolated\nIsolated\nATLAS\nFigure 6: Expected rate including all physical processes at a luminosity of L = 1031 cm\u22122s\u22121, as a function of the cut\napplied to TauCluster and with and without the isolation cut EmIsol.\nSignature\nET threshold (GeV)\nEmIsol (GeV)\nEff.(%)\nRate (Hz)\ntau10i\n6\n-\n97\n13945\ntau15i\n6\n-\n98\n13945\ntau20i\n9\n6\n96\n4823\ntau25i\n11\n6\n96\n2822\ntau35i\n16\n6\n96\n990\ntau45i\n25\n6\n96\n263\ntau60\n40\n-\n97\n97\nTable 2: Single tau signatures, associated L1 thresholds, and ef\ufb01ciency and rates determined from signal and background\nsamples as described in the text (L =1031 cm\u22122 s\u22121).\nof W \u2192\u03c4\u03bd and 800 GeV Supersymmetric Higgs A \u2192\u03c4\u03c4 events, and simulated background samples of\nQCD events with two jets with hard parton 8 < pT < 140 GeV.\nThe L2 variables based on calorimetry introduced in Section 2.2 are optimized in the following way:\n\u2022 Since some correlation among the calorimeter shower shape variables (EMRadius, isoFrac and\nstripWidth) is expected, the three variables are simultaneously optimized. The thresholds are de-\ntermined by scanning the possible cut values for each variable and choosing the set of cuts giving\nthe lowest background rate for a requested minimum signal ef\ufb01ciency.\n\u2022 The threshold for the variable EtCalib is determined by requiring that the ef\ufb01ciency becomes \ufb02at\nstarting at the nominal ET of the trigger (see Fig. 8).\nThe optimized L2 calorimeter requirements for tau signatures and the corresponding ef\ufb01ciencies\nand rates are presented in Table 3. The cut value on EtCalib increases for higher ET signatures, as we\naim to select higher ET taus. The shower shape variables, a measure of the narrowness of the shower,\nare tighter for higher ET signatures, since higher ET taus are more boosted and their decay products\nare more collimated. The three shower shape variables requirements have been optimized to give an\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n602\n\n (GeV)\nT\nTrue visible E\n20\n40\n60\n80\n100\n120\nL1 efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\ntau10i\ntau15i\ntau20i\ntau25i\ntau35i\ntau45i\ntau60\nATLAS\nFigure 7: L1 ef\ufb01ciency curves for different tau signatures.\nef\ufb01ciency of \u224895%, although the observed ef\ufb01ciency values are a little lower due to the additional\nEtCalib requirement.\nThe ef\ufb01ciency is detailed further in Table 4 for two typical tau signatures, one with low and one with\nhigh ET. For each signature, ef\ufb01ciency is recalculated using as a reference different tau lepton samples\nreconstructed of\ufb02ine. Either the sample from each tau algorithm is considered separately, or the sample\nreconstructed by either of them (\u201cOR\u201d), or by both simultaneously (\u201cAND\u201d), is considered. The errors\nquoted are statistical only. In order to achieve the needed rejection of QCD backgrounds, the calorimeter-\nbased algorithm of the of\ufb02ine reconstruction biases the distribution of decays towards 1-prong decays\nusing calorimeter information. A similar rejection and ef\ufb01ciency is achieved in a different manner using\nthe track-based algorithm, which requires a large transverse momentum for the leading track in the tau\nlepton decay. Therefore, the L2 calorimeter selection has a high and uniform ef\ufb01ciency for the sample\nreconstructed of\ufb02ine by the calorimeter-based algorithm, while it is lower on the sample reconstructed\nusing the track-based algorithm in the 3-prong category.\nSignature\nEtCalib (GeV)\nEMRadius\nIsoFrac\nStripWidth\nEff.(%)\nRate(Hz)\nL1/L2 rate\ntau10i\n8.0\n0.023\n0.74\n0.058\n95\n9251\n1.51\ntau15i\n9.7\n0.022\n0.71\n0.057\n94\n5933\n2.35\ntau20i\n12.2\n0.019\n0.66\n0.055\n94\n3070\n1.57\ntau25i\n17.0\n0.016\n0.65\n0.051\n92\n1224\n2.31\ntau35i\n26.5\n0.015\n0.6\n0.048\n91\n351\n2.82\ntau45i\n33.5\n0.00807\n0.43\n0.0465\n93\n119\n2.21\ntau60\n44.9\n0.00345\n0.35\n0.04\n93\n47\n2.06\nTable 3: Single tau signatures, associated L2 calorimeter thresholds and ef\ufb01ciency on W \u2192\u03c4\u03bd sample and rates on QCD\nbackground samples for L =1031 cm\u22122 s\u22121.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n603\n\ntau20i\ntau60\nOf\ufb02ine Identi\ufb01cation method\nall taus\n1-prong\n3-prong\nall taus\n1-prong\n3-prong\nCalo-based\n97.6\u00b10.1\n97.5\u00b10.1\n98.3\u00b10.4\n97.8\u00b10.1\n97.8\u00b10.1\n96.8\u00b10.5\nTrack-based\n92.5\u00b10.2\n95.2\u00b10.2\n88.4\u00b10.4\n94.9\u00b10.2\n95.7\u00b10.2\n91.7\u00b10.5\nCalo- OR Track-based\n94.2\u00b10.2\n96.3\u00b10.2\n88.9\u00b10.4\n96.6\u00b10.1\n97.3\u00b10.1\n92.8\u00b10.4\nCalo- AND Track-based\n97.2\u00b10.2\n97.0\u00b10.2\n98.2\u00b10.4\n96.6\u00b10.2\n96.6\u00b10.2\n96.1\u00b10.9\nTable 4: Tau signatures and corresponding ef\ufb01ciencies (in %) for different reference samples of tau leptons identi\ufb01ed by\nthe of\ufb02ine reconstruction. Ef\ufb01ciencies have been estimated on low and high ET generated samples of tau leptons. Errors are\nstatistical only. Ef\ufb01ciencies are for L2 calorimeter selection only.\n (GeV)\nT\nTrue visible E\n20\n40\n60\n80\n100\n120\nL2/L1 efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\ntau10i\ntau15i\ntau20i\ntau25i\ntau35i\ntau45i\ntau60\nATLAS\nFigure 8: Ef\ufb01ciency curves of L2 selection relative to L1 for different tau signatures.\n3.5\nL2 performance studies of the tracking selection\nThe addition of tracking information at L2 allows an improvement in the discrimination between hadronic\ndecays of tau leptons and QCD jet backgrounds, although at the cost of a non-negligible loss of trigger\nreconstruction ef\ufb01ciency. This loss is most noticeable for low ET tau signatures, mainly due to the re-\nquirement of one leading track above a \ufb01xed pT threshold. Overall, the L2 tracking algorithm is about\n95% ef\ufb01cient for isolated tracks with ET above 5GeV (for example from W \u2192\u03c4\u03bd). In W \u2192\u03c4\u03bd events,\nhowever, only 90% of generated tau leptons that are identi\ufb01ed by the of\ufb02ine reconstruction and pass the\nL2 calorimeter selection have at least one track with pT > 5GeV reconstructed at L2.\nThe L2 tracking selection of tau trigger candidates is optimized with respect to generated tau leptons\nthat pass the L1 and L2 calorimeter selection and are found by the of\ufb02ine reconstruction software. Details\nof the of\ufb02ine reference and ef\ufb01ciency de\ufb01nition are described in Section 3.1.2. The optimization is\nobtained with the standard samples described previously.\nThe ef\ufb01ciency and rejection power of some of the L2 tracking variables can be seen in Fig. 9, where\nthe integrated ef\ufb01ciency for tau samples and background are shown as a function of the applied cut value.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n604\n\nFor low ET signatures, the minimum requirement on Pt leading along with the upper limit on Pt Iso/Core\nare the two most important criteria. For higher ET signatures, the upper limit on N Slow tracks becomes\nmore important, as background QCD jets tend to have a higher multiplicity of soft tracks compared to\nmulti-track hadronic decays of tau leptons. The multiplicity requirement, N Track, is potentially a useful\ndiscriminant for higher ET signatures, although a tight cut tends to bias the multiplicity distribution of\nthe tau leptons found by of\ufb02ine reconstruction. To avoid such bias a very soft cut is applied.\nThe optimized L2 tracking requirements for tau signatures and the corresponding ef\ufb01ciencies and\nrates are presented in Table 5. Aside from the Pt leading requirement, which is tightened with increasing\nET threshold, the requirements on Pt Iso/Core<0.1, N Slow tracks\u22642, Charge\u22642 and 1\u2264N Track\u22647 are\nkept constant at values which work reasonably well for all signatures, and therefore are not shown in the\nTable.\nThe ef\ufb01ciency is detailed in Table 6 for two typical tau signatures, one with low and one with high\nET. For each signature, ef\ufb01ciency is recalculated using different reference samples based on of\ufb02ine\nreconstruction as in the previous section. Again, the errors quoted are statistical only. For the high ET\nsignatures, there is not a strong ef\ufb01ciency dependence on the particular reference sample chosen. For\nthe low ET signatures, however, the different selections used in the of\ufb02ine algorithms, particularly in\nselecting 1-prong tau lepton decays, are apparent. Since the track-based algorithm also requires a track\nwith some minimum pT when applied to these events the L2 tracking selection is quite ef\ufb01cient. The\nL2 tracking selection is considerably less ef\ufb01cient when applied to events selected with the calorimeter\nbased algorithm, where no such requirement on the tracks is made.\nThe overall L2 trigger ef\ufb01ciency for various single tau signatures, using the optimized selection\ndescribed in Sect. 3.4- 3.5, is shown in Fig. 8.\nSignature\nPt lead (GeV)\nEff. (%)\nRate (Hz)\nL2Calo/L2Track\ntau10i\n1.5\n86\n3980\n2.32\ntau15i\n2.5\n85\n2900\n2.04\ntau20i\n5.0\n81\n947\n3.24\ntau25i\n5.0\n74\n351\n3.48\ntau35i\n5.0\n75\n107\n3.28\ntau45i\n5.0\n80\n39\n2.01\ntau60\n5.0\n79\n15\n3.13\nTable 5: Single tau signatures, associated L2 tracking thresholds and ef\ufb01ciencies for W \u2192\u03c4\u03bd sample and rates for QCD\nbackground samples for L =1031 cm\u22122 s\u22121.\ntau20i\ntau60\nOf\ufb02ine Identi\ufb01cation method\nall taus\n1-prong\n3-prong\nall taus\n1-prong\n3-prong\nCalo-based\n87.1\u00b10.3\n86.6\u00b10.3\n91.8\u00b10.8\n97.5\u00b10.1\n97.9\u00b10.1\n90.3\u00b10.9\nTrack-based\n95.5\u00b10.2\n96.5\u00b10.2\n93.9\u00b10.3\n95.8\u00b10.2\n97.3\u00b10.2\n89.3\u00b10.6\nCalo- OR Track-based\n88.9\u00b10.2\n87.5\u00b10.3\n92.8\u00b10.4\n96.5\u00b10.1\n97.5\u00b10.1\n89.3\u00b10.5\nCalo- AND Track-based\n97.3\u00b10.2\n97.4\u00b10.2\n96.6\u00b10.6\n97.9\u00b10.1\n98.2\u00b10.1\n92.4\u00b11.3\nTable 6: Tau signature ef\ufb01ciencies (in %) for different reference samples of tau leptons identi\ufb01ed by the of\ufb02ine reconstruction.\nEf\ufb01ciencies have been estimated on low and high ET generated samples of tau leptons. Errors are statistical only. Ef\ufb01ciencies\nare for L2 tracking only.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n605\n\nLeading Pt (GeV)\n0\n50\n100\n150\n200\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (kHz)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nL2 N Slow\n0\n1 2\n3\n4\n5 6\n7\n8\n9 10\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (kHz)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nL2 Pt Iso/Core\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (kHz)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n Eff.\n\u03bd\n\u03c4\n\u2192\nW\nQCD Jet Rate (Hz)\nATLAS\nL2 Pt leading\n0\n50\n100\n150\n200\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (Hz)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\nL2 N Slow\n0\n1 2\n3\n4\n5 6\n7\n8\n9 10\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (Hz)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\nL2 Pt Iso/Core\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nRate (kHz)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n Eff.\n\u03c4\n\u03c4\n\u2192\nA\nQCD Jet Rate (Hz)\nATLAS\nFigure 9: Performance of L2 tracking variables to distinguish QCD background jets from low ET (top) and high ET (bottom)\ntau leptons. For each plot, the closed circle data points show the cumulative ef\ufb01ciency (left-hand scale) for tau leptons as\na function of cut value, while the open triangle data points show the QCD jet rates (right-hand scale) for a luminosity of\nL = 1031 cm\u22122s\u22121.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n606\n\n3.6\nEF performance studies\nAs described in Section 2.3, the tau identi\ufb01cation algorithm developed for of\ufb02ine reconstruction is\nadapted for EF use. The resolution in ET and direction achieved at the EF are shown in Section 3.2,\nand provide a clear improvement in ET determination with respect to L2.\nThe EF selection of tau trigger candidates is optimized with respect to generated tau leptons that\npass the L1 and L2 selection and are found by the of\ufb02ine reconstruction software. Details of the of\ufb02ine\nreference and ef\ufb01ciency de\ufb01nition are described in Section 3.1.2. The optimization is performed using\nthe standard samples described previously.\nThe cuts on calorimeter shape variables and ET are optimized separately, in analogy to the L2 pro-\ncedure previously described. First, the correlation between the ET of the tau lepton and the pT of the\nleading track associated with the tau lepton is studied in simulated samples, and then a combined re-\nquirement on these two variables is applied to each tau signature. Finally, the calorimeter shower shape\nvariables are studied, and a further requirement is applied on these variables.\nIn Table 7 the optimized threshold requirements and corresponding ef\ufb01ciencies and background\nrates are presented. As for L2, the shower shape variables are tightened and the cut value on EtCalib\nand pT lead are raised as a function of the ET of the tau signature. The two shower shape variables\nrequirements have been optimized to give an overall ef\ufb01ciency of \u224890%. The requirement on nTracks\nis not stringent, so as not to bias the distribution for this variable, which is a key of\ufb02ine variable for the\nevaluation of tau lepton purity. Fig. 10 shows the ef\ufb01ciency for various single tau signatures, using the\noptimized selection summarized in Table 7.\nThe ef\ufb01ciency is detailed in Table 8 as in previous sections. At EF clearly the ef\ufb01ciency is highest\nfor the tau leptons identi\ufb01ed by the calorimeter based algorithm of the of\ufb02ine reconstruction.\n (GeV)\nT\nTrue visible E\n20\n40\n60\n80\n100\n120\nEF/L2 efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\ntau10i\ntau15i\ntau20i\ntau25i\ntau35i\ntau45i\ntau60\nATLAS\nFigure 10: Ef\ufb01ciency curves of EF selection relative to L2 for different tau signatures.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n607\n\nSignature\nEtCalib (GeV)\npT lead. (GeV)\nEMRadius\nIsoFrac\nnTracks\nEff.(%)\nRate (Hz)\ntau10i\n10.\n5.\n0.13\n0.38\n1-8\n90\n1611\ntau15i\n14.\n6.\n0.13\n0.32\n1-8\n85\n897\ntau20i\n19.\n6.\n0.11\n0.33\n1-8\n86\n349\ntau25i\n22.\n7.\n0.1\n0.3\n1-8\n86\n175\ntau35i\n31.\n8.\n0.09\n0.24\n1-8\n87\n64\ntau45i\n36.\n8.\n0.08\n0.19\n1-8\n92\n24\ntau60\n51.\n8.\n0.09\n0.24\n1-8\n93\n8\nTable 7: Single tau signatures, associated EF thresholds and ef\ufb01ciencies for the W \u2192\u03c4\u03bd sample and rates for the QCD\nbackground sample for L =1031 cm\u22122 s\u22121.\ntau20i\ntau60\nOf\ufb02ine Identi\ufb01cation method\nall taus\n1-prong\n3-prong\nall taus\n1-prong\n3-prong\nCalo-based\n90.9\u00b10.3\n90.3\u00b10.3\n95.5\u00b10.6\n98.5\u00b10.1\n98.5\u00b10.1\n98.7\u00b10.4\nTrack-based\n84.7\u00b10.3\n88.9\u00b10.4\n77.4\u00b10.6\n97.3\u00b10.1\n97.7\u00b10.1\n95.8\u00b10.4\nCalo- OR Track-based\n85.0\u00b10.3\n87.9\u00b10.3\n77.9\u00b10.6\n98.0\u00b10.1\n98.2\u00b10.1\n96.4\u00b10.3\nCalo- AND Track-based\n93.7\u00b10.3\n93.2\u00b10.3\n97.1\u00b10.5\n98.2\u00b10.1\n98.2\u00b10.1\n98.6\u00b10.6\nTable 8: Tau signature ef\ufb01ciencies (in %) for different reference samples of tau leptons identi\ufb01ed by the of\ufb02ine reconstruction.\nEf\ufb01ciencies have been estimated on low and high ET generated samples of tau leptons. Errors are statistical only. Ef\ufb01ciencies\nare for EF only.\n3.7\nCombined performance of single tau triggers\nAfter evaluating each trigger level separately, we now present the overall combined performance (L1 +\nL2 + EF) of the single tau triggers. Figures 11 and 12 show the dependence of the ef\ufb01ciency on ET.\nThe shape of the ef\ufb01ciency curves is determined by the ET resolution, which is different for the different\ntrigger levels. The ET threshold requirement of the signature is selected such that the ef\ufb01ciency curve\nreaches a plateau at the visible ET of the generated tau lepton greater than this threshold. Since the\nef\ufb01ciency turn-on is slowest at L1, the cut on ET at L1 is set signi\ufb01cantly lower than for L2 and EF.\nThe ef\ufb01ciency is detailed in Table 9 for two typical tau triggers as in the previous sections. In addition\nto the observations of the individual trigger level sections, one can see that the overall performance for\nthe low ET tau trigger is about 70% with respect to the reference, while at high ET it is about 90%. This\nis due to relatively tighter cuts needed to control the large backgrounds present for the low ET signature.\nOne can also see that the ef\ufb01ciency at low ET is low in particular for 3-prong decays when the reference\nis the sample of tau leptons identi\ufb01ed by the track-based algorithm. This re\ufb02ects the previous observation\nof Section 3.4, and points to the need for the execution of the track-based algorithm at the EF as well as\nat L2.\n4\nTrigger timing studies\n4.1\nOnline setup\nPrior to \ufb01rst LHC collisions, it is desirable to test the trigger software and data acquisition system in\nconditions resembling real data taking. There are two type of tests which can be performed: cosmic runs,\nwhere the detector signals left by cosmic rays activate the L1 trigger, and technical runs where simulated\nL1 trigger signals are used. These runs allow the monitoring system to be assessed, the algorithm timing\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n608\n\ntau20i\ntau60\nOf\ufb02ine Identi\ufb01cation package\nall taus\n1-prong\n3-prong\nall taus\n1-prong\n3-prong\nCalo-based\n76.5\u00b10.4\n75.5\u00b10.4\n85.2\u00b11.0\n93.8\u00b10.2\n94.3\u00b10.2\n86.1\u00b11.0\nTrack-based\n70.9\u00b10.4\n79.5\u00b10.4\n58.3\u00b10.7\n88.4\u00b10.3\n90.9\u00b10.3\n78.1\u00b10.8\nCalo- OR Track-based\n68.3\u00b10.3\n72.5\u00b10.4\n58.6\u00b10.6\n91.3\u00b10.2\n93.1\u00b10.2\n79.6\u00b10.7\nCalo- AND Track-based\n87.9\u00b10.4\n87.4\u00b10.4\n91.1\u00b10.9\n92.8\u00b10.3\n93.1\u00b10.3\n87.1\u00b11.6\nTable 9: Tau trigger ef\ufb01ciencies (in %) for different reference samples of tau leptons identi\ufb01ed by the of\ufb02ine reconstruction.\nEf\ufb01ciencies have been estimated on low and high ET generated samples of tau leptons. Errors are statistical only. Ef\ufb01ciencies\nis for L1 + L2 + EF selection.\n (GeV)\nT\nTrue visible E\n0\n20\n40\n60\n80\n100\n120\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\ntau20i\ntau25i\ntau35i\ntau45i\ntau60\nATLAS\nFigure 11: Overall trigger ef\ufb01ciency (L1 + L2 + EF) for different tau triggers.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n609\n\n (GeV)\nT\nTrue Visible E\n0\n20\n40\n60\n80\n100\n120\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL2\nEF\nATLAS\nFigure 12: Ef\ufb01ciency for tau20i trigger.\nto be measured (although the composition of the input events is not representative of the expected L1\ntrigger output when real data are taken) and the interplay between triggers to be studied. All studies are\nperformed on CPUs dedicated to timing studies in order to minimize the possible in\ufb02uence of other users\non timing results. Each of these machines is a dual-core Intel(R) XEON(TM) CPU 2.20GHz machine.\n4.2\nTiming results\nThe CPU time performance of the trigger is a crucial ingredient in the optimization of the trigger. Current\ndesign constrains the total execution time per event to 40 ms at L2 and 1 s at EF for the whole trigger.\nRecent timing studies performed on tau triggers include:\n\u2022 tests of individual triggers to gauge the impact of increasing threshold levels on the total execution\ntime of the trigger.\nDuring this test, each of the tau triggers is run individually (and no other triggers are run at the\nsame time). Although the average execution time of each algorithm remains roughly equal between\ntriggers (see Table 10), the average total time per event decreases as a result of the lower number\nof RoIs per event for high energy triggers. The results shown in Table 10 indicate that the time\nperformance of the tau trigger should be well within the constraint for total execution time at L2\nand EF.\n\u2022 a veri\ufb01cation of caching of data from the liquid argon calorimeter in L2. This test requires running\nthe tau algorithms and other calorimeter-based algorithms (electron algorithm, for example) for\nthe same event. In case data in a given RoI is needed by more than one signature, then the caching\nprocedure ensures that data are requested only once. Recent tests verify that caching is correctly\nimplemented and provides roughly a factor of four time savings in the L2 calorimeter part.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n610\n\nThreshold Signature\nAlgorithm\ntau10i\ntau15i\ntau20i\ntau25i\ntau35i\nL2 Calo\n8.1\n8.0\n8.0\n8.1\n8.1\nL2 Tracking\n15.4\n15.5\n15.0\n14.9\n14.7\nL2 Combined\n1.9\n1.9\n2.0\n2.0\n2.2\nL2 TotalTime\n41.6\n35.9\n19.7\n14.1\n7.9\nEF Calo\n12.3\n12.5\n13.4\n13.0\n14.0\nEF Tracking\n289.7\n297.7\n269.5\n268.4\n247.8\nEF Combined\n77.0\n76.9\n80.7\n77.8\n78.9\nEF TotalTime\n149.1\n133.6\n67.5\n51.2\n24.6\nTable 10: Mean algorithm execution time for each of the tau triggers. All times are given in ms and per RoI, except the L2\nand EF total times are given per event, in ms. The measurements are performed on a simulated sample of limited statistics, 950\nQCD background events with hard parton 35 2TeV, for the same tau trigger, the tracking approach is\nslightly faster than the calorimeter approach, 299 versus 330ms respectively. The longer execution\ntime on high energy jet samples with respect to low energy ones is mainly due to the longer\nexecution time of the L2 tracking algorithm. This result shows that the L2 tracking selection\nprovides greater background rejection power than the L2 calorimeter one against high energy jets,\nand therefore suggests that the tracking-approach is advisable for high ET tau triggers.\n5\nTau trigger menu\nThe single tau signatures are the basic element in the ATLAS trigger menu for collecting hadronic decays\nof tau leptons. Therefore, Section 2 and 3 have been devoted to the selection and performance of the\nsingle tau signatures. In this section we describe the full tau trigger menu, with an emphasis on triggers\nthat combine tau signatures with other signatures and the physics goals they address. Such combined\ntriggers are very important for collecting samples of tau leptons of moderate ET from several SM or\neven beyond the SM processes. As shown in Sect. 3, the minimal requirement on ET for a single tau\ntrigger must be high, even at low luminosity, to be allowed to run without prescale factors. A combined\nrequirement of a moderate ET tau signature with other signatures provides a way to achieve the necessary\nrejection against backgrounds and avoid prescale factors.\n5.1\nCombined tau triggers\nThe following triggers aiming at collecting hadronic decays of tau leptons are currently implemented in\nthe ATLAS trigger menu, in addition to the single tau triggers already introduced:\n\u2022 tau+missing ET (tau+Emiss\nT\n). This type of trigger covers a wide spectrum of physics channels. At\nlow luminosity, when the trigger rejection can be relaxed, the selection of events with W \u2192\u03c4\u03bd is\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n611\n\nthe priority. t\u00aft events with tau leptons in the \ufb01nal state are also selected by this trigger. Such events\nare characterized by relatively soft ET range of tau leptons as well as low Emiss\nT\n. The tau+Emiss\nT\ntriggers at design luminosity are intended for SM or SUSY Higgs (neutral or charged) searches as\nwell as for searches of new exotic particles like Z\u2032. The Emiss\nT\ntrigger [14] uses the same threshold\nrequirement at all trigger levels. The turn-on of the Emiss\nT\nef\ufb01ciency curve is mainly limited by\nthe L1 missing ET resolution. Since the average Emiss\nT\nin W \u2192\u03c4\u03bd events is low, and the EF Emiss\nT\nresolution is better, additional triggers where the Emiss\nT\nrequirement is applied only at EF are under\nstudy.\n\u2022 tau+\u2113(+jets), \u2113= e,mu. This type of trigger aims at selecting events with two relatively soft tau\nleptons in the \ufb01nal state. Two tau leptons are found in events with Z boson, neutral SM or SUSY\nHiggs. In addition, the tau+\u2113combination selects events with multiple leptons like t\u00aft or lepton\n\ufb02avor violating processes. The combination of two trigger signatures allows the use of lower\nthreshold requirements than for the case of the single tau trigger. In case of excessive rates for this\ntype of trigger at design luminosity, the additional requirement of jets or Emiss\nT\ncan be introduced.\n\u2022 tau+tau(+jets). This type of trigger records events where both tau leptons decay hadronically.\nWhile the rejection rate is less favorable than the tau+\u2113case, the sample collected is complemen-\ntary to the above and both increases statistics and allows the reduction of systematics uncertainties\ndue to lepton identi\ufb01cation. This trigger is highly relevant for searches of Higgs boson or new\nexotic particles like Z\u2032 and will also be bene\ufb01cial for SUSY double tau end point analyzes.\n\u2022 tau+jets, tau+b-jets. This type of trigger is an interesting alternative for t\u00aft studies. At low lu-\nminosity, it allows the study of events with low jet ET thresholds, while at high luminosities it is\nnecessary to reduce QCD and multiple interaction background events.\n5.2\nCommissioning triggers\nIn addition to single tau triggers there are single track triggers, highly optimized to select RoIs with\none track only. The main purpose of this type of trigger is alignment of the tracker or hadronic calibra-\ntion. These triggers work in parasitic mode, taking all L1 RoIs passing 6GeV or 9GeV with isolation\nrequirements in a given event. In this manner, a suf\ufb01cient amount of tracks for commissioning can be\nobtained.\nFurthermore, additional triggers like tau15i PT and 2tau25i PT are included in the ATLAS trigger\nmenu (PT stand for pass-through). For pass-through triggers, all events that are accepted by the L1\nalgorithm are recorded for of\ufb02ine study of the HLT algorithms. At L2 and EF the algorithms are executed\nand their result is stored in the event record, however, their decision is not considered in the global trigger\ndecision. As the output rate of these triggers is equal to the L1 rate, only a small fraction can be recorded,\ntypically \u223c0.1Hz after prescale factors.\n5.3\nTau trigger menu performance\nIn this section we summarize tau trigger ef\ufb01ciencies for various physics signals, see Table 11, and the\ncorresponding rates estimated on minimum bias samples for 100 pb\u22121, see Table 12. For the results\nshown, the physics signal ef\ufb01ciencies are calculated per event, using the following references:\n\u2022 trigger with one (two) tau leptons: at least one (two) tau leptons at generator level with visible ET\ngreater than the tau trigger threshold(s) are required. Furthermore, the generated tau leptons are\nidenti\ufb01ed by the of\ufb02ine reconstruction algorithms.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n612\n\n\u2022 trigger with tau+e and tau+mu: besides the tau lepton requirement (see item above), the addi-\ntional lepton is required at generator level to have an ET greater than the chosen lepton trigger\nthreshold. The generated lepton additionally is identi\ufb01ed by the \u201cloose\u201d of\ufb02ine reconstruction\nalgorithm [1], [2].\n\u2022 trigger tau+Emiss\nT\n: besides the tau lepton requirement (see item above), the missing ET at generator\nlevel as well as the missing ET reconstructed by the of\ufb02ine reconstruction algorithms [14] are\nrequired to be above the chosen trigger threshold.\nIntroducing the triggers described above is important for most physics signals with tau leptons in the\n\ufb01nal state because:\n\u2022 allows increased statistics\n\u2022 it is a robust approach against failure or inef\ufb01ciency of a particular trigger (e.g. due to detector\nproblems)\n\u2022 allows reduction of systematic uncertainty by comparing results of the same analysis repeated on\nsamples selected with different triggers.\nIn Table 11 and Table 12 the symbol tau+xe stands for the tau+Emiss\nT\ntriggers, and j stands for the\njet triggers.\n5.4\nTau trigger menus for different luminosity periods\nAccording to the foreseen LHC start-up plans, ATLAS will commence data taking at a low luminosity\nof about 1031 cm\u22122 s\u22121. Over the course of the \ufb01rst year or so, it is expected that the luminosity will\nincrease to a rather high luminosity of about 1033 cm\u22122 s\u22121. While the input rate rapidly increases during\nthis period, the maximal output rate of the complete trigger is expected to be constant at about 200Hz\n(due to limitations on storage capacities and recording speed), putting a signi\ufb01cant burden on the trigger\nsystem.\nAs mentioned in Section 1, the low luminosity period will be used to commission the detector and\ntrigger system. During this period, the focus of the trigger selection is Standard Model physics and\nevents necessary for calibration and ef\ufb01ciency studies. The total sample collected is expected to be of\nthe order of 100pb\u22121. Concerning hadronic decays of tau leptons, the absolute scale of tau leptons and\nthe characteristics and rate of QCD jets misidenti\ufb01ed as tau leptons are estimated from simulated data\nstudies only, and need to be veri\ufb01ed and understood with collider data. To address this, several triggers\nare proposed, and outlined in the next section. For each trigger, a method of measuring the ef\ufb01ciency on\nreal data should also be proposed.\nThe transition to higher luminosity is foreseen to be done smoothly, dropping triggers of the low\nluminosity period menu which were used for commissioning or with unacceptably large rate, and keeping\nor introducing triggers without any prescale factors which focus on discovery physics.\nThe high luminosity menu will be obtained either by tightening the threshold requirements and cuts\nof triggers present in the low luminosity menu, or adding new triggers, especially combinations of several\nsignatures. Only some ideas for a tau trigger menu for a luminosity of L =1033 cm\u22122 s\u22121 currently exist.\nGiven the current background rates, shown in Section 3, the high luminosity menu will include single\nhigh ET signatures with threshold requirements higher than what shown in Section 3 (most probably\ntau100). Furthermore, the high luminosity menu will be composed mostly of combined triggers like\ntau35i xe45, tau25i e25i, tau25i mu20, 2tau35i, tau20i j150 and tau20i 4j50.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n613\n\nTrigger Item\nW\u03c4\u2192hX\nZ\u03c4\u03c4\nt\u00aft\nA\u03c4\u03c4(800)\nSU3\nH\u03c4\u03c4\u2192\u2113hX\nH\u03c4\u03c4\u2192hhX\ntau10\n82.6\u00b10.3\n91.9\u00b10.2\n93.6\u00b10.4\n97.1\u00b10.1\n94.3\u00b10.3\n93.8\u00b10.2\n96.9\u00b10.1\ntau10i\n78.7\u00b10.4\n89.8\u00b10.2\n91.1\u00b10.4\n96.4\u00b10.2\n92.0\u00b10.4\n92.1\u00b10.3\n95.8\u00b10.1\ntau15\n78.2\u00b10.4\n88.7\u00b10.3\n91.9\u00b10.4\n96.5\u00b10.1\n92.4\u00b10.4\n91.6\u00b10.3\n95.4\u00b10.1\ntau15i\n74.1\u00b10.4\n86.0\u00b10.3\n89.1\u00b10.5\n96.1\u00b10.2\n90.4\u00b10.4\n90.0\u00b10.3\n94.1\u00b10.1\ntau20i\n68.5\u00b10.5\n79.9\u00b10.3\n83.2\u00b10.6\n89.8\u00b10.2\n82.5\u00b10.5\n85.0\u00b10.4\n89.8\u00b10.2\ntau25i\n66.5\u00b10.6\n76.0\u00b10.4\n80.1\u00b10.7\n89.0\u00b10.3\n79.7\u00b10.6\n82.0\u00b10.4\n87.1\u00b10.2\ntau35i\n65.8\u00b10.9\n70.0\u00b10.6\n77.4\u00b10.9\n87.5\u00b10.3\n76.9\u00b10.7\n78.2\u00b10.5\n82.0\u00b10.2\ntau45\n82.7\u00b11.3\n78.7\u00b10.8\n88.0\u00b10.9\n94.9\u00b10.2\n89.6\u00b10.6\n86.2\u00b10.5\n88.5\u00b10.2\ntau45i\n72.1\u00b11.5\n68.5\u00b10.9\n76.0\u00b11.2\n86.1\u00b10.3\n75.1\u00b10.9\n75.8\u00b10.7\n78.5\u00b10.3\ntau60\n77.5\u00b12.6\n74.4\u00b11.5\n74.7\u00b11.7\n91.4\u00b10.2\n78.2\u00b11.1\n76.1\u00b10.9\n77.5\u00b10.4\ntau100\n83.9\u00b16.6\n78.2\u00b14.1\n80.2\u00b13.5\n90.0\u00b10.3\n81.7\u00b11.9\n79.1\u00b11.6\n80.7\u00b10.7\n2tau25i\n0.0\u00b10.0\n47.2\u00b11.5\n60.0\u00b111.0\n62.6\u00b11.2\n62.6\u00b12.7\n61.5\u00b16.7\n59.3\u00b10.6\n2tau35i\n0.0\u00b10.0\n43.1\u00b13.1\n57.1\u00b118.7\n60.6\u00b11.3\n62.0\u00b13.8\n50.0\u00b19.1\n55.6\u00b10.9\ntau15i xe20\n56.3\u00b10.6\n48.4\u00b10.8\n80.1\u00b10.7\n92.7\u00b10.2\n89.5\u00b10.4\n80.8\u00b10.5\n80.2\u00b10.3\ntau20i xe30\n45.4\u00b10.9\n38.6\u00b11.2\n70.1\u00b10.9\n84.5\u00b10.3\n81.4\u00b10.6\n73.9\u00b10.6\n73.2\u00b10.4\ntau25i xe30\n44.2\u00b11.0\n38.0\u00b11.3\n67.5\u00b11.0\n83.8\u00b10.3\n78.7\u00b10.6\n71.4\u00b10.7\n71.1\u00b10.4\ntau35i xe20\n55.1\u00b11.2\n42.0\u00b11.2\n68.7\u00b11.1\n84.5\u00b10.3\n76.3\u00b10.7\n70.8\u00b10.7\n69.5\u00b10.4\ntau35i xe30\n47.7\u00b11.5\n38.5\u00b11.7\n63.3\u00b11.2\n82.3\u00b10.3\n76.2\u00b10.7\n69.2\u00b10.8\n66.9\u00b10.4\ntau35i xe40\n42.1\u00b12.5\n39.2\u00b12.4\n58.0\u00b11.4\n80.8\u00b10.4\n75.6\u00b10.8\n68.3\u00b11.0\n65.3\u00b10.5\ntau45 xe40\n54.7\u00b13.6\n48.3\u00b13.0\n67.4\u00b11.6\n87.6\u00b10.3\n88.2\u00b10.7\n76.5\u00b11.0\n71.0\u00b10.6\ntau45i xe20\n60.1\u00b12.1\n43.8\u00b11.7\n67.3\u00b11.4\n83.2\u00b10.3\n74.7\u00b10.9\n69.0\u00b10.9\n66.7\u00b10.4\ntau20i e10\n0.0\u00b10.0\n68.1\u00b11.2\n73.7\u00b12.9\n79.6\u00b10.8\n77.1\u00b11.7\n73.2\u00b10.8\n0.0\u00b10.0\ntau20i mu6\n0.0\u00b10.0\n72.0\u00b10.9\n81.4\u00b12.4\n80.3\u00b10.7\n83.3\u00b11.3\n79.4\u00b10.7\n0.0\u00b10.0\ntau20i j70\n70.8\u00b11.4\n78.8\u00b10.7\n81.6\u00b10.7\n89.4\u00b10.2\n82.7\u00b10.6\n65.6\u00b10.7\n72.6\u00b10.3\ntau20i 3j23\n61.1\u00b12.1\n80.2\u00b10.8\n82.0\u00b10.7\n89.9\u00b10.2\n83.2\u00b10.6\n83.7\u00b10.7\n80.7\u00b10.3\ntau20i 4j23\n58.2\u00b14.1\n82.7\u00b11.6\n80.5\u00b10.9\n90.3\u00b10.3\n84.5\u00b10.6\n86.9\u00b11.7\n83.9\u00b10.7\nTable 11: Physics signal ef\ufb01ciency without prescale factors. The requirements at generator level are\nsummarized in Section 5.3. The Higgs boson mass for the last two columns is 120 GeV. Errors are\nstatistical only.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n614\n\nTrigger\nLevel 1\nLevel 2\nEvent Filter\nSelection\nEvents\nRate (Hz)\nEvents\nRate (Hz)\nEvents\nRate (Hz)\ntauNoCut\n79802\n23342\n79252\n23181\n77231\n22590\u00b181\ntau10\n48854\n14290\n16235\n4749\n7748\n2266\u00b126\ntau10i\n48854\n14290\n14066\n4114\n5413\n1583\u00b121\ntau15\n48854\n14290\n10472\n3063\n4054\n1186\u00b119\ntau15i\n48854\n14290\n9764\n2856\n2953\n864\u00b116\ntau15i PT\n48854\n14290\n10237\n2994\n10237\n2994\u00b130\ntau20i\n16298\n4767\n3322\n972\n1229\n359\u00b110\ntau25i\n9404\n2751\n1565\n458\n631\n185\u00b17\ntau35i\n3149\n921\n473\n138\n215\n63\u00b14\ntau45\n1062\n311\n321\n94\n255\n75\u00b15\ntau45i\n750\n219\n154\n45\n79\n23\u00b13\ntau60\n262\n77\n35\n10.2\n25\n7.3\u00b11.5\ntau100\n262\n77\n7\n2.0\n4\n1.2\u00b10.6\ntau15i xe20\n5625\n1645\n1329\n389\n198\n58\u00b14\ntau20i xe30\n525\n154\n139\n40.7\n23\n6.7\u00b11.4\ntau20i xe30 PT\n525\n154\n142\n41\n142\n41\u00b14\ntau25i xe30\n385\n113\n83\n24.3\n17\n5.0\u00b11.2\ntau35i xe20\n784\n229\n129\n37.7\n42\n12.3\u00b11.9\ntau35i xe30\n203\n59\n41\n12.0\n10\n2.9\u00b10.9\ntau35i xe40\n58\n17\n15\n4.4\n3\n0.9\u00b10.5\ntau45 xe40\n47\n14\n18\n5.3\n6\n1.7\u00b10.7\ntau45i xe20\n278\n81\n54\n15.8\n19\n5.6\u00b11.3\nTable 12: Minimum bias event rates without prescale factors. The cross section value used is \u03c3 = 70mb\nand the peak luminosity used is L = 1031 cm\u22122s\u22121. Errors are statistical only.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n615\n\n5.4.1\nRunning at L =1031 cm\u22122 s\u22121\nThe trigger menu for a luminosity of L =1031 cm\u22122 s\u22121 covers largely SM physics channels (W \u2192\u03c4\u03bd,\nZ \u2192\u03c4\u03c4, t\u00aft). A fair amount of the bandwidth is given to commissioning triggers (< 1Hz each), which\nare needed to monitor trigger rates and variables used for tau lepton identi\ufb01cation in different ET ranges.\nTable 13 gives the trigger menu proposed for initial data taking, including expected prescale factors\nand corresponding trigger rates, with overlap between triggers taken into account. The prescale factors\nare necessary to restrict the total rate from low ET tau triggers, since there are many physics topics that\nneed to share limited bandwidth. The initial prescale values have been determined from simulation, and\nwill be optimised based on experience with early data. Event yields for several tau-based physics topics\nare shown in Table 14. In this table the results of only one typical trigger are reported for a set of triggers,\ncorresponding to the one currently considered as the most suitable for the physics signals targeted at low\nluminosity. However, as physics simulation studies are progressing and as background rates are veri\ufb01ed\non data, it is likely that the trigger menu will be modi\ufb01ed.\n6\nSummary\nThis note describes in detail the ATLAS tau trigger system, which is dedicated to the selection of hadronic\ndecays of tau leptons. These results are obtained from simulations prior to LHC operations. In the\nselection at L1, energy deposition in the e.m. and hadronic calorimeters are used, while at L2 and EF\ncalorimeter shower shape and energy information is combined with tracking information from the Inner\nDetector. At design luminosity, tau triggers are envisaged to be used without prescale factors to select\nsingle tau trigger candidates with ET above 100GeV. The events with tau trigger candidates with lower\nET will be selected using combined triggers which employ tau signatures in conjunction with missing ET\nelectron, muon, jet or another tau signatures. The largest contribution to the rate will be misidenti\ufb01ed\nlow ET QCD jets, that are narrow and contain few particles mimicking hadronic decays of tau leptons.\nIn the \ufb01rst months of LHC operation a low luminosity of 1031 cm\u22122 s\u22121 is anticipated, and the data\nwill primarily be used for commissioning the detector and trigger system. At that time the main focus\nof tau triggers will be on Standard Model physics such as W \u2192\u03c4\u03bd, Z \u2192\u03c4\u03c4 and t\u00aft events with hadronic\ndecays of tau leptons in the \ufb01nal state. The typical tau trigger ef\ufb01ciency at low luminosity for generated\ntau leptons reconstructed by the algorithms of the of\ufb02ine reconstruction is expected to be around 80%\nfor a wide range of physics channels, resulting in a total tau trigger rate of 28Hz.\nTrigger\nPrescale\nRate (Hz)\nCumulative Rate (Hz)\ntau100\n1\n2.4\u00b10.5\n2.4\u00b10.5\ntau60\n1\n10.7\u00b11.0\n10.7\u00b11.0\ntau45i\n10\n2.5\u00b10.2\n12.6\u00b11.1\ntau45\n20\n4.1\u00b10.1\n16.0\u00b11.4\ntau20i xe30\n1\n4.9\u00b10.7\n20.1\u00b11.4\ntau20i e10\n1\n1.2\u00b10.4\n21.2\u00b11.5\ntau20i mu6\n1\n2.8\u00b10.5\n23.7\u00b11.6\n2tau25i\n1\n2.6\u00b10.5\n25.3\u00b11.6\ntau20i 4j23\n1\n0.1\u00b10.1\n25.4\u00b11.6\ntau20i 3j23\n1\n0.9\u00b10.3\n25.8\u00b11.6\ntau20i j70\n1\n7.1\u00b10.9\n28.6\u00b11.7\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n616\n\nTable 13: Tau trigger menu for L =1031 cm\u22122 s\u22121.\nTrigger Item\nW\u03c4\u2192hX\nZ\u03c4\u03c4\nt\u00aft\nA\u03c4\u03c4(800)\nSU3\nH\u03c4\u03c4\u2192\u2113hX(120)\nH\u03c4\u03c4\u2192hhX(120)\ntau15i\n128.4\n9.53\n2.56\n0.37\n0.002\n0.003\n0.004\ntau45\n816\n121.4\n63.9\n26.2\n0.17\n0.11\n0.17\ntau45i\n1406\n211.4\n110.3\n47.5\n0.30\n0.20\n0.31\ntau60\n4399\n670\n568\n484\n3.07\n1.18\n1.87\ntau100\n699\n84\n116\n406\n2.58\n0.31\n0.48\n2tau25i\n0\n544\n13\n37\n0.24\n0.02\n0.68\n2tau35i\n0\n114\n4\n35\n0.22\n0.01\n0.33\ntau20i xe30\n29005\n668\n2097\n429\n2.72\n2.30\n2.01\ntau35i xe40\n3379\n178\n831\n374\n2.37\n1.03\n1.00\ntau20i e10\n0\n1191\n182\n83\n0.53\n1.36\n0.00\ntau20i mu6\n0\n2003\n227\n96\n0.61\n1.94\n0.00\ntau20i j70\n8672\n1278\n2457\n2.96\n320\n2.04\n0.00\ntau20i 3j23\n3852\n1019\n2697\n2.31\n288\n1.30\n0.00\ntau20i 4j23\n957\n232\n1803\n1.31\n226\n0.23\n0.00\nTable 14: Number of events expected in 100pb\u22121at 1031 cm\u22122 s\u22121 for different physics signals. Cross-sections are given in\nTable 1. The requirements imposed at generator level are summarized in Section 5.3.\nReferences\n[1] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[2] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this volume.\n[3] ATLAS Collaboration,\nThe ATLAS Experiment at the CERN Large Hadron Collider, JINST\n3:S08003, 2008.\n[4] ATLAS Collaboration, Charged Higgs Boson Searches, this volume.\n[5] ATLAS Collaboration,\nSearch for the Standard Model Higgs Boson via Vector Boson Fusion\nProduction Process in the Di-Tau Channels, this volume.\n[6] ATLAS Collaboration, Discovery Potential of h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd, this volume.\n[7] ATLAS Collaboration, Dilepton Resonances at High Mass, this volume.\n[8] J.Garvey et al., Use of a FPGA to identify electromagnetic clusters and isolated hadrons in the\nATLAS Level-1 Calorimeter trigger, Nuclear Instruments and Methods A,vol. 512 no. 3 (2003)\npp.506-516.\n[9] H1 Collaboration, Nucl. Inst. and Meth. A 386, 348 (1997)\n[10] ATLAS Collaboration, HLT Track Reconstruction Performance, this volume.\n[11] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[12] ATLAS Collaboration, HLT b-Tagging Performance and Strategies, this volume.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n617\n\n[13] ATLAS Collaboration, Overview and Performance Studies of Jet Identi\ufb01cation in the Trigger Sys-\ntem, this volume.\n[14] ATLAS Collaboration, Measurement of Missing Transverse Energy, this volume.\nTRIGGER \u2013 TAU TRIGGER: PERFORMANCE AND MENUS FOR EARLY RUNNING\n618\n\nPhysics Performance Studies and Strategy of the Electron and\nPhoton Trigger Selection\nAbstract\nThis note gives an overview of the implementation and performance of the\nelectron and photon selection by the ATLAS trigger system. Trigger menus\nfor commissioning as well as for the \ufb01rst physics run are presented together\nwith the strategy for the early data taking phase. The physics performance\nin terms of selection ef\ufb01ciency and background rejection has been estimated\nusing Monte Carlo simulations for various luminosity scenarios. An example\nof a method to determine trigger ef\ufb01ciency from real data using Z \u2192ee events\nis discussed.\n1\nIntroduction\nThis note gives an overview of the implementation and performance of the electron and photon selection\nby the ATLAS trigger system. Electron and photon trigger baseline signatures and menus for LHC\ncommissioning and \ufb01rst physics run are presented. The principles that have determined their design are:\n\u2022 Coverage of the physics needed for commissioning the trigger and detector systems as well as the\nof\ufb02ine reconstruction.\n\u2022 Coverage of the physics channels that allow standard model studies and searches for new physics.\n\u2022 Keeping the rates within the allowed bandwidth.\nEvents with electrons and photons in the \ufb01nal state are important signatures for many physics ana-\nlyses envisaged at the LHC. A good selection by the electron/photon (e/\u03b3) triggers will be important for\nmany analyses from searches for new physics, such as the Higgs boson, SUSY, Z\u2032 boson to standard\nmodel (SM) precision physics such as top quark and W boson mass measurement, rare B decays, etc.\nIn the early running processes such as Z \u2192ee, J/\u03c8 \u2192ee, W \u2192e\u03bd and \u03b3-jet events will be crucial for\nthe understanding of the detector. These decays are important benchmark channels for the calibration,\nalignment and monitoring of the detector performance. The e/\u03b3 trigger needs to cover the transverse\nenergy range between a few GeV and several TeV. An overview of some relevant physics channels\nwith electrons and photons in the \ufb01nal state, classi\ufb01ed according to the corresponding transverse energy\nthresholds is given in Table 1.\nTo achieve this physics reach the trigger algorithms have to be optimized in terms of physics perfor-\nmance (signal ef\ufb01ciency, background rejection) and system performance (execution time, data require-\nments, etc). The trigger menu has to ensure a good selection of the above physics channels within the\nallocated rate for the various luminosities during LHC running.\nIn the following sections the implementation, performance and selection strategy are described in\ndetail. Section 2 explains how e/\u03b3 candidates are reconstructed and selected at the different trigger levels.\nSection 3 presents the selection strategy for LHC start-up, describing the schema currently envisaged for:\ncommissioning, \ufb01rst menu for an initial luminosity of L\u223c1031 cm\u22122 s\u22121 and the subsequent development\ntowards higher luminosity scenarios. In Section 4 the performance of the various electron and photon\ntriggers for a startup luminosity of L\u223c1031 cm\u22122 s\u22121 and a luminosity scenario of L\u223c1033 cm\u22122 s\u22121\nis discussed. Examples of trigger ef\ufb01ciencies for physics processes with electrons and photons in the\n\ufb01nal state over the transverse energy (ET) spectrum from a few GeV up to several TeV are included. A\ndiscussion of the robustness of the trigger selection follows in Section 5. Section 6 explains how the\ntrigger ef\ufb01ciency will be determined from real data using Z \u2192ee events.\n619\n\nMomentum range\nExamples of some important processes\nlow pT \u223c5-15 GeV\nBd \u2192J/\u03c8K0\ns \u2192ee\u03c0\u03c0\nBs \u2192K\u2217\u03b3\nJ/\u03c8 \u2192ee, Drell-Yan\nhigh pT \u223c20\u2212100 GeV\nH \u2192\u03b3\u03b3 (for m(H)<130GeV)\nH \u2192ZZ(\u2217) \u2192eeee,ee\u00b5\u00b5 (for 130 < m(H) < 700 GeV)\ntop physics, Z \u2192ee,W \u2192e\u03bd,\ndirect photon production\nvery high pT \u223c100\u22121000 GeV\nZ\u2032 \u2192ee, W\n\u2032 \u2192e\u03bd\nG \u2192\u03b3\u03b3,G \u2192ee,\npp \u2192ee\u2217\u2192ee\u03b3\nTable 1: Examples of some important processes requiring a good electron and photon trigger selection\n2\nElectron and photon trigger selection\nIn this section the electron and photon trigger reconstruction and selection are described. The recon-\nstruction and selection variables for each of the trigger levels are summarized in separate subsections.\n2.1\nL1 selection\nAt L1 trigger information from the electromagnetic (EM) and hadronic calorimeter system in the form\nof so-called trigger towers is used. A trigger tower has a dimension \u2206\u03b7 \u00d7\u2206\u03c6 \u223c0.1\u00d70.1. In this region\nall the cells are summed over the full depth of either the electromagnetic or hadronic calorimeter. The\nL1 selection algorithm for electromagnetic clusters is based on a sliding 4\u00d74 window of trigger towers\nwhich looks for local maxima [1].\nFigure 1: L1 calorimeter trigger schema, showing how trigger towers (each spanning a 0.1\u00d70.1 \u03b7 \u00d7\u03c6\nregion) are used to determine the energy for the electromagnetic cluster as well as for the electromagnetic\nisolation, hadronic core and hadronic isolation.\nThe trigger object is considered to contain an electron or photon candidate if the following require-\nments are satis\ufb01ed:\n\u2022 The central 2\u00d72 \u2018core\u2019 cluster consisting of both EM and hadronic towers is a local ET maximum\nThis requirement prevents double counting of clusters by overlapping windows.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n620\n\n\u2022 The most energetic of the four combinations of two neighbuoring EM towers passes the electro-\nmagnetic cluster threshold.\nFigure 1 shows the L1 trigger tower schema used to determine the L1 selection variables. Isolation\nrequirements can be imposed if required to control the rate:\n\u2022 EEM\nisol : The total ET in the 12 EM towers surrounding the 2\u00d72 core cluster is less than the electro-\nmagnetic isolation threshold.\n\u2022 EHAD\ncore : The total ET in the 4 towers of the hadronic calorimeter behind the 2\u00d72 core cluster of the\nelectromagnetic calorimeter is less than the hadronic core threshold.\n\u2022 EHAD\nisol : The total ET in the 12 towers surrounding the 2\u00d72 core cluster in the hadronic calorimeter\nis less than the hadronic isolation threshold.\nThe distributions of these isolation variables for signal and background are shown in Fig. 2 from Monte\nCarlo simulations. For signal, single electrons with an ET between 7 and 80 GeV with a \ufb02at distribu-\ntion are used (solid line, hatched histogram). In comparison, background candidates from a simulated\nsample of QCD background (referred to as dijets) with ET> 17 GeV are shown (dashed line, hollow his-\ntogram). Most of the samples discussed in this note, unless otherwise speci\ufb01ed, use the Pythia 6.403 [2]\nMonte Carlo event generator. The ATLAS detector Monte Carlo simulation is based on GEANT4 [3].\nThe Monte Carlo simulations store details of the generated particles including the type and kinematic\nvariables, this so-called MC-Truth information can then be used as a control in subsequent analyses of\nthe simulated data. In this case the truth information has been used to guarantee that no real electrons\nare included in the background distributions in Fig. 2. The distributions shown have been normalized to\nunit area. It can be seen that isolation, in particular L1 EM isolation, provides a good handle to reduce\njet background rate, typically needed at low transverse energy thresholds. As isolation depends on the\ntopology and energy distribution of the event, as well as on other parameters such as luminosity and\nbeam conditions, isolation cuts need to be well understood and applied carefully during data taking.\n (GeV)\nL1\n \nEM\nIsol\nE\n0\n5\n10\n15\n20\n25\n30\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n (GeV)\nL1\n \nEM\nIsol\nE\n0\n5\n10\n15\n20\n25\n30\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n (GeV)\nL1\n \nEM\nIsol\nE\n0\n5\n10\n15\n20\n25\n30\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n (GeV)\nL1\n \nHAD\nCore\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nElectron signal\nDi-jet background\nATLAS\n (GeV)\nL1\n \nHAD\nCore\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n (GeV)\nL1\n \nHAD\nCore\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n (GeV)\nL1\n \nHAD\nIsol\nE\n0\n5\n10\n15\n20\n25\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n (GeV)\nL1\n \nHAD\nIsol\nE\n0\n5\n10\n15\n20\n25\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n (GeV)\nL1\n \nHAD\nIsol\nE\n0\n5\n10\n15\n20\n25\nNormalized Entries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nFigure 2: L1 isolation variables for single electrons with an ET between 7 and 80 GeV with a \ufb02at\ndistribution (solid line, hatched histogram). In comparison, background candidates from the ET> 17 GeV\ndijet sample are shown (dashed line, hollow histogram). For the background, only clusters that do not\nmatch to a true electron within a \u2206R cone of 0.1 are considered. The distributions for electromagnetic\nisolation (left), hadronic core energy (middle), and hadronic isolation (right) are shown.\n2.2\nL2 selection\nL2 is seeded by the L1 EM Region of Interest (RoI). Thus L2 receives the reconstructed L1 object with\nthe \u03b7 and \u03c6 positions and the transverse energy thresholds passed. L2 accesses a subsample of the\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n621\n\ndetector data around the given \u03b7 and \u03c6 position and applies trigger speci\ufb01c reconstruction algorithms\ncharacterized for their speed and robustness. Both photon and electron selection use the full granularity,\nfull precision calorimeter information now available in the \ufb01rst selection step. The transverse cluster\nenergy and various shower shape variables calculated in the different layers of the EM calorimeter are\nused to identify e/\u03b3 candidates. The electron selection uses in addition inner detector information. Tracks\nare reconstructed in the inner detector and matched to the calorimeter energy clusters. Thus track \ufb01nding\nand track-cluster matching variables can be used to select electrons.\n2.2.1\nCalorimeter based electron and photon selection\nL2 calorimeter reconstruction is seeded by the \u03b7 and \u03c6 positions provided by L1. Calorimeter cells in a\nwindow of size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.4\u00d70.4 are retrieved (for more details on the data preparation see [4]). At\nthe L2 trigger the cluster building algorithm scans the cells in the second layer of the EM calorimeter and\nsearches for the cell with highest ET. Subsequently, a cluster of 0.075 \u00d7 0.175 in \u03b7 \u00d7 \u03c6 is built around\nthis seed cell. The larger cluster size in \u03c6 reduces the low-energy tails due to photon conversion and\nelectron bremsstrahlung. Electrons and photons deposit nearly all of their energy in the EM calorimeter\nand deposit typically less than 1% of their energy into the hadronic calorimeter. In addition, showers\nfrom electrons and photons are typically smaller in the plane transverse to its direction than showers\nfrom jets. These quantities are used to select a low-background sample of electrons and photons.\nIn detail, the L2 electron and photon calorimeter algorithms select events base on the following\nquantities:\n\u2022 Transverse energy of the EM cluster (EEM\nT\n): Due to the energy dependence of the jet cross-section,\na cut on EEM\nT\nprovides the best rejection against jet background for a given high pT signal process.\n\u2022 Transverse energy in the \ufb01rst layer of the hadronic calorimeter (EHad\nT\n): This is required to be below\na given threshold. This cut is relaxed for high ET triggers (90 GeV and above) as the leakage into\nthe hadronic calorimeter increases with energy.\n\u2022 Shower shape in \u03b7 direction in the second EM sampling: The ratio of the energy deposit in\n3 \u00d7 7 cells (corresponding to 0.075 \u00d7 0.175 in \u2206\u03b7 \u00d7 \u2206\u03c6) over that in 7 \u00d7 7 cells is calculated:\nRcore = E3x7/E7x7. Photons and electrons deposit most of their energy in 3 \u00d7 7 cells and thus the\ncorresponding ratio is typically larger than 80 %.\n\u2022 Search for a second maximum in the \ufb01rst EM sampling: After applying the cuts in the hadronic\ncalorimeter and the second sampling of the EM calorimeter, only jets with very little hadronic\nactivity and narrow showers in the calorimeter remain. The \ufb01ne granularity in rapidity in the \ufb01rst\nsampling of the EM calorimeter allows checks to be made for substructures within a shower for\na further rejection of background such as single or multiple \u03c00s or \u03b7s decaying to photons. The\nenergy deposit in a window \u2206\u03b7 \u00d7\u2206\u03c6 = 0.125\u00d70.2 is examined. The shower is scanned for local\nmaxima in the \u03b7-direction. The ratio of the difference between the energy deposited in the bin with\nhighest energy E1st and the energy deposited in the bin with second highest energy E2nd divided by\nthe sum of these two energies is calculated: Rstrips = (E1st \u2212E2nd)/(E1st +E2nd). This ratio tends\nto one for isolated electrons and photons, and tends to zero for photons coming for example from\n\u03c00 decay.\nFigure 3 shows typical distributions of the above shower shape variables for a signal sample of Higgs\ndecaying into \u03b3\u03b3 and a the dijet background sample. A clear rejection power against background of the\nET is seen for a cut above 20 GeV. The shower shape variables in the \ufb01rst and second EM sampling of the\ncalorimeter provide a good discrimination power above 0.8. These shower shape variables will have a\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n622\n\nnarrower distribution for photons compared to electrons. The high granularity of the \ufb01rst EM sampling of\nthe ATLAS detector permits ef\ufb01cient photon identi\ufb01cation using only calorimeter information, tracking\ninformation is not used at all in the selection.\n (GeV)\nEM\nT\nE\n10\n20\n30\n40\n50\n60\n70\n80\nNormalized Entries\nATLAS\nSignal\nDi-jets BG\n (GeV)\nHAD\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized Entries\nATLAS\nSignal\nDi-jets BG\nRcore\n0\n0 2\n0.4\n0.6\n0.8\n1\nNormalized Entries\nATLAS\nSignal\nDi-jets BG\nRstrips\n0\n0.2\n0.4\n0.6\n0.8\n1\nNormalized Entries\nATLAS\nSignal\nDi-jets BG\nFigure 3: Selection variables for a L2 calorimeter energy cluster. The distributions are shown for signal\ncandidates from a simulated H \u2192\u03b3\u03b3 sample (dashed line) and for dijet background candidates that do not\nhave a photon or electron matched within a \u2206R cone of 0.1 and that have at least 1 jet with ET> 17 GeV\n(black solid line). Both distributions have been normalized to unity. The plots show the transverse energy\nof the EM cluster (top left), transverse energy deposited in the \ufb01rst layer of the hadronic calorimeter (top\nright), shower shape in the \u03b7 direction in the second EM sampling (Rcore) (bottom left), and the search\nfor a second maximum in the \ufb01rst electromagnetic sampling (Rstrips) (bottom right).\n2.2.2\nInner detector electron selection\nIf all the criteria of the calorimeter based electron selection are ful\ufb01lled, a search for tracks is performed\nin front of the cluster, electron trigger candidates are identi\ufb01ed by the presence of a matching recon-\nstructed tracks [5].\n2.2.3\nCombined calorimeter and inner detector based electron selection\nA further rate reduction, while maintaining a high electron ef\ufb01ciency, can be achieved by combining\nthe calorimeter and inner detector information. The background rate can be reduced by cutting on \u03b7\nand \u03c6 between the EM cluster and the extrapolated track into the calorimeter. As shown in Fig. 4 these\ndistributions are narrower for electrons than for jets. Another quantity useful for electron selection is the\nratio of the cluster ET and the track pT. This quantity is affected by bremsstrahlung effects which cause\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n623\n\na tail in the ET/pT distribution towards high values (see Fig. 4), so it is not intended to use an upper cut\non ET/pT in the early data-taking.\nL2\n (Track - Cluster)\n\u03b7\n \n\u2206\n-0.04\n-0.02\n0\n0.02\n0.04\nNormalized Entries\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nATLAS\nL2\n (Track - Cluster)\n\u03b7\n \n\u2206\n-0.04\n-0.02\n0\n0.02\n0.04\nNormalized Entries\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nL2\n (Track - Cluster)\n\u03c6 \n\u2206\n-0.04\n-0.02\n0\n0.02\n0.04\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nATLAS\nL2\n (Track - Cluster)\n\u03c6 \n\u2206\n-0.04\n-0.02\n0\n0.02\n0.04\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nL2\n \nTrack\nT\n/p\nCluster\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nElectron signal\nDi-jet background\nATLAS\nL2\n \nTrack\nT\n/p\nCluster\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nEF\n (Track - Cluster)\n\u03b7\n \n\u2206\n-0.02\n-0.01\n0\n0.01\n0.02\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nATLAS\nEF\n (Track - Cluster)\n\u03b7\n \n\u2206\n-0.02\n-0.01\n0\n0.01\n0.02\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nEF\n (Track - Cluster)\n\u03c6 \n\u2206\n \u2022\nq \n-0.03\n-0.02\n-0.01\n-0\n0.01\n0.02\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nEF\n (Track - Cluster)\n\u03c6 \n\u2206\n \u2022\nq \n-0.03\n-0.02\n-0.01\n-0\n0.01\n0.02\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nEF\n \nTrack\nT\n/p\nCluster\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nElectron signal\nDi-jet background\nATLAS\nEF\n \nTrack\nT\n/p\nCluster\nT\nE\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized Entries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nFigure 4: L2 (top) and EF (bottom) electron selection variables based on the combined calorimeter and\ninner detector information. From left to right the following distributions are shown: the difference in\n\u03b7 (left) and \u03c6 (middle) between the cluster and track (extrapolated to calorimeter) position. and are\nshown: ratio of the ET of the EM cluster and the pT of the reconstructed tracks (right). Distributions are\nshown for signal (solid line, hatched histogram) and background (dashed line, hollow histogram). The\nreconstructed electrons come from a 7 < ET < 80 GeV sample. The background candidates come from\na \ufb01ltered dijet simulated sample, only candidates with no match to a truth electron within a \u2206R cone of\n0.1 rad are selected.\n2.3\nEF selection\nAt the EF trigger level of\ufb02ine reconstruction algorithms and tools are used as much as possible. An\nimportant difference, however, between the of\ufb02ine and the EF reconstruction is that the of\ufb02ine recon-\nstruction is run once per event accessing the whole detector, while the EF uses a seeded approach; runs\nseveral times per event, once for each RoI given by L2, accessing only the corresponding subsample of\nthe detector.\nCurrently, in the photon trigger selection only calorimeter information is used. EM clusters are\nsearched for and reconstructed in RoIs of size \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.4 \u00d7 0.4. The EF calorimeter clustering\nalgorithm searches for a local energy maximum with calorimeter trigger tower granularity. For electron\nand photon reconstruction only the data from the EM calorimeter is used, in contrast with L2 where the\nhadronic energy is also computed. The clusters should have an ET above a given threshold. The default\ncluster size used is 0.125\u00d70.125 in \u03b7 \u00d7\u03c6 (whilst the of\ufb02ine reconstruction algorithms perform clustering\nwith different window sizes, a single clustering option is used in the EF ). Once found by the clustering\nalgorithm the cluster parameters (position, energy, etc.) are computed and further re\ufb01ned by a set of\ncluster correction (position and energy calibration) tools [5]. Also, corrections for the transition region\nbetween barrel and end-cap calorimeters are possible using the information from a set of scintillators.\nFor electron triggers, tracks are subsequently reconstructed in the inner detector. The EF tracking\ncurrently implements an inside-out track reconstruction (track \ufb01nding starts from the inner silicon de-\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n624\n\ntectors and then is extended to the transition radiation tracker). In the future, an outside-in approach is\nintended to be used in the trigger in cases where photon conversions are present. There is the possibility\nto attempt bremsstrahlung recovery using of\ufb02ine tools. This option is not foreseen to run in the electron\ntriggers for start-up but might be applied when running at higher luminosities with tighter selections. At\nL\u223c1031 cm\u22122 s\u22121 bremsstrahlung effects do not affect the trigger ef\ufb01ciency since the selection cuts are\nsuf\ufb01ciently loose to be insensitive to the performance improvements.\nElectron and photon identi\ufb01cation in the EF is very similar to the of\ufb02ine [6]. Calorimeter shower\nshapes, leakage into the hadronic calorimeter and the ET of the EM cluster are used for the calorimeter\nbased selection for electrons and photons. Compared to L2 more shower shape variables are used.\nTogether with improved calibrations this results in a further rate reduction. For electrons track-cluster\nmatching variables, track quality cuts, transverse impact parameter and for high luminosity running\npotentially transition radiation information could be used to further reduce the rate.\nAs an example a loose electron EF selection will use the following selections: longitudinal leakage,\nshower shapes in the middle layer of the EM calorimeter, and very loose track-cluster matching cuts.\nTighter selections might also use the shower shapes in the \ufb01rst EM calorimeter layer, information on\nthe transverse impact parameter and on the track quality (number of hits in the pixels and strip silicon\ndetectors and number of hits in the \ufb01rst pixel layer). Distributions for the track-cluster matching variables\nat EF are shown in Fig. 4. The distributions are very similar to those of the L2 track-cluster matching,\nbut more re\ufb01ned algorithms are available at this stage, with more up-to-date calibration and alignment\ninformation.\n3\nElectron and photon trigger selection strategy\nIn this section the foreseen trigger selection strategy from the start-up phase up to physics running at\nnominal low luminosity is discussed. First the various commissioning steps at start-up are explained.\nThis is followed by a discussion of a possible electron and photon trigger menu for the \ufb01rst physics run\nassuming a luminosity of L\u223c1031 cm\u22122 s\u22121.\nWhen LHC turns on the trigger menus will need to provide data for commissioning and for analy-\nsis. In these paragraphs analysis is used to mean standard model measurements and searches for new\nphysics. Typically these two objectives require very different trigger selection criteria. Commissioning\nusually demands loose selections to allow for more basic understanding of the detector and trigger, but\nloose selections accept more background events. Analysis is favoured with tight trigger selections that\nmaximize the signal to background ratio in the allocated bandwidth. At start-up commissioning tasks\nwould be prioritized, though signatures that provide data for a physics analysis will be included in the\nmenu whenever possible. Following the progress on commissioning, loose trigger selections will be sub-\nstituted by tighter ones that increase the analysis capabilities. The main challenge for the ATLAS trigger\nis the big difference (approximately six orders of magnitude) between the collision rate and the rate at\nwhich data can be stored. This imposes tight constraints on the trigger menus.\nThese principles used to determine the trigger menus, are developed in more detail in the following\nsubsections, which also include early trigger menu tables.\nThe naming conventions for the various e/\u03b3 triggers used in the following sections are as follows.\nThe name for L1 electromagnetic candidates is EM. This is followed by the ET threshold applied for this\ntriggers and if isolation criteria are applied an \u201ci\u201d is added at the end of the name. The number preceding\nEM indicates the object multiplicity. For example 2EM13I requires that at least two isolated electron or\nphoton candidates are identi\ufb01ed at L1 passing a ET = 13 GeV threshold. The naming conventions for L2\nand EF are very similar. For example 2\u03b317i denotes a trigger which selects events in which two isolated\nphotons are found passing a ET threshold cut of 17 GeV at EF level. Similarly a possible e20 xe15\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n625\n\ntrigger selects events in which at least one electron candidate with ET (EF) > 20 GeV is identi\ufb01ed, in\naddition, the missing transverse energy at EF exceeds 15 GeV.\n3.1\nCommissioning\nAt LHC start-up an initial luminosity of L\u223c1031 cm\u22122 s\u22121 is expected. This will allow lower ET thresh-\nolds compared to those at the nominal LHC luminosity. The start-up menu has to provide the data\nsamples needed to commission the trigger and detectors and at the same time provide useful data to be\nused for physics analysis. Therefore, the trigger has to guarantee the selection of the following standard\nmodel channels: W \u2192e\u03bd, J/\u03c8 \u2192ee,\u03d2 \u2192ee, Drell-Yan, and direct photon production. For example:\nZ \u2192ee, J/\u03c8 \u2192ee and \u03d2 \u2192ee will provide input for the electromagnetic calibration, alignment, ef-\n\ufb01ciency measurements, etc. Electrons from bottom and charm quark decays will be useful for studies\nof E/p. Direct photon production will provide input for the jet calibrations using \u03b3-jet events where\nthe photon and jet are back-to-back. For comparison, in the \ufb01rst 100 pb\u22121 of data we expect 235k of\nJ/\u03c8 \u2192ee, 40k of \u03d2 \u2192ee, 10k of Drell-Yan events, 10M b,c \u2192e, 100k direct photons and 250k of\nW \u2192e\u03bd.\nThe strategy is to apply L1 selections and run the High-Level Trigger (HLT) in pass-through mode\n(the selection criteria are tested and the trigger decision is recorded but no event is rejected). Table 2\nshows the e\u03b3 triggers foreseen. This will provide the \ufb01rst data samples for the low and high-pT spec-\ntrum and the rates for the various e/\u03b3 triggers. Fig. 5 shows the expected L1 e/\u03b3 rate for a luminosity\nof L\u223c1031 cm\u22122 s\u22121 with and without isolation criteria applied as a function of the transverse energy\nthreshold.\nL1\nRate w/o\nPre-\nHLT Rate\nTrigger\nitem\nprescale [Hz]\nscale\n[Hz]\nem5 passHLT\nEM3\n40000\n20000\n2\nem10 passHLT\nEM7\n5000\n1300\n4\nem15 passHLT\nEM13\n800\n200\n4\nem15i passHLT\nEM13I\n390\n100\n4\nem20 passHLT\nEM18\n280\n70\n4\nem20i passHLT\nEM18I\n100\n25\n4\nem25i passHLT\nEM23I\n41\n10\n4\nem105 passHLT\nEM100\n1\n1\n1\n2em5 passHLT\n2EM3\n6500\n1600\n4\n2em15 passHLT\n2EM13\n80\n20\n4\n2em20 passHLT\n2EM18\n35\n10\n4\nTable 2: \u2018L1-only selection\u2019 trigger menu items for the LHC start-up including prescale factors. Depend-\ning on the rate, prescale factors might be readjusted. The L1 selection is applied and HLT selection is\nrun in pass-through mode.\nThis will provide the input, based on real data, to devise a trigger menu best suited for the \ufb01rst com-\nmissioning and physics run with HLT selection enabled. Note that current rate estimates are affected by\nan uncertainty factor of two or three coming from the theoretical uncertainties in the jet cross-section.\nThough the L1 pass-through triggers will mainly select background events they are useful samples and\ncan be used to look for clusters and tracks in the whole \u03b7 \u2212\u03c6 space and check that known dead and noisy\nchannels and/or disconnected regions are correctly \ufb02agged. In addition the distributions of the e/\u03b3 selec-\ntion variables from data can be compared to those from Monte Carlo simulations. For example, signal\nover background distributions will be studied for variables with good discrimination power (e.g. Rcore).\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n626\n\nL2 and EF performance can be checked and studies undertaken to evaluate the tracking performance of\nthe different L2 tracking algorithms.\nIn the next phase of the commissioning the HLT selection will be progressively enabled. Several mon-\n (GeV)\nT\nE\n5\n10\n15\n20\n25\n30\n35\n40\nL1 Rate (Hz)\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n (GeV)\nT\nE\n2\n4\n6\n8\n10\n12\n14\n16\n18\nL1 Rate (Hz)\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 5: L1 rate for single (left) and double (right) e/\u03b3 triggers for a luminosity of L\u223c1031 cm\u22122 s\u22121.\nThe open correspond to non-isolated triggers. Errors are statistical only.\nitoring triggers will be kept, though with increased prescale factors applied. For example, L2 and EF in\npass-through mode or loose \u03b3 triggers (to monitor tighter calorimeter cuts as well as tracking ef\ufb01ciency\nfor the electron triggers).\n3.2\nFirst physics run\nAfter the commissioning phase of the detector the \ufb01rst physics run is foreseen. At the physics run, each\nof the trigger menu signatures including the HLT will be enabled as soon as the understanding of the\ndetector and trigger allow. Table 3 gives an overview of the main electron and photon physics triggers.\nThe aim is to select events with at least one electron above \u223c10 GeV or one photon above \u223c20 GeV,\nin addition to the relevant double object triggers, e.g. for selecting J/\u03c8, \u03d2, and Z events. J/\u03c8 \u2192ee\nand \u03d2 \u2192ee events are particularly demanding events for the trigger system. The trigger rates errors for\neach trigger menu are statistical. Due to their relatively low masses, the electrons produced in the J/\u03c8\nand \u03d2 decays are very soft (with an average transverse momenta of less that 5 GeV). This poses a huge\nchallenge to the L1 calorimeter trigger. Its performance at the low-energy end is limited by the noise of\ntypically 0.5 GeV per RoI. A 3 GeV threshold is the limit for the L1 trigger. The 6.5 kHz L1 output rate\nfor 2e5 makes it one of the biggest consumers of the total bandwidth.\nTo keep the rate at an acceptable level selections for the electron triggers at low-pT (e.g. 2e5) have\nto apply tighter HLT selections compared to the higher-pT triggers. A prescaled e5 trigger will allow\nmeasurement of the ef\ufb01ciencies and optimization of the selection cuts. A range of signatures is foreseen\nin the trigger menu to adapt to running conditions. If the trigger rate should prove to be too high back-up\nitems with higher thresholds are included and/or prescale factors can be adjusted. Note, the uncertainties\nrelated to the detector response and the theoretical uncertainties on the jet cross-section. To ensure the\nselection of important physics channels, redundant triggers are present. As an example Table 4 shows\nthe various triggers which will be useful for triggering on W \u2192e\u03bd, these include triggers which combine\nelectrons and missing transverse energy.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n627\n\nL1\nEF\nL1\nPre-\nHLT\nSignature\nitem\nselection\nRate\nscale\nRate\nMotivation\ne10\nEM7\nmedium\n5.0 kHz\n1\n21 Hz\ne\u00b1 from b,c decays, E/p studies\n\u03b320\nEM18\nloose\n0.3 kHz\n1\n5.4\u00b10.2 Hz\ndirect photon production, jet calibration\nusing \u03b3-jet events, high-pT physics\ne20\nEM18\nloose\n0.3 kHz\n1\n4.3\u00b10.2 Hz\nhigh-pT physics, Z \u2192ee,W \u2192e\u03bd\nem105 passHLT\nEM100\n1 Hz\n1\n1.0\u00b10.1 Hz\nNew physics, check for possible problems\n2e5\n2EM3\nmedium\n6.5 kHz\n1\n6 Hz\nJ/\u03c8 \u2192ee, Y \u2192ee, Drell-Yan production\n2\u03b310\n2EM7\nloose\n0.5 kHz\n1\n< 0.1 Hz\ndi-photon cross-section\n2e10\n2EM7\nloose\n0.5 kHz\n1\n0.4\u00b10.2 Hz\nZ \u2192ee\nTable 3: Summary of the main electron and photon triggers envisaged for the \ufb01rst physics run at\nL\u223c1031 cm\u22122 s\u22121. In this table the main physics triggers are listed including their expected rates and\ntheir physics motivation.\nL1\nEF\nPre-\nRate\nSignature\nitem\nselection\nscale\n[Hz]\nMotivation\ne20\nEM18\nloose\n1\n4.3\u00b10.2\nmain physics trigger\n\u03b320\nEM18\nloose\n1\n5.4\u00b10.2\nredundancy, check of tracking eff. and\nperformance\ne15 xe20\nEM13 XE20\nloose\n1\n1.0\u00b10.4\naccess to lower pT -range\ne10 xe30\nEM7 XE30\nmedium\n1\n0.3\u00b10.3\naccess to lower pT -range\ne20i\nEM18I\nloose\n1\n2.8\u00b10.1\nbackup if rate too high\ne25i\nEM23I\nloose\n1\n1.4\u00b10.1\nbackup if rate too high\ne20 xe15\nEM18 XE15\nloose\n1\n1.6\u00b10.1\nbackup if rate is too high\n\u03b320 xe15\nEM18 XE15\nloose\n1\n1.9\u00b10.2\nbackup if rate is too high, check tracking eff and\nperformance\nTable 4: Summary of the main and redundant triggers for selecting W \u2192e\u03bd events foreseen for the\nL\u223c1031 cm\u22122 s\u22121 trigger menu.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n628\n\n3.3\nElectron and photon trigger menus\nThis section collects detailed examples of the foreseen trigger menus. Table 5 shows a summary of the\ntrigger menu for the \ufb01rst physics run assuming a luminosity L\u223c1031 cm\u22122 s\u22121. Each row corresponds to\na different trigger signature. The convention to interpret the name of a trigger signature is explained in\nSection 3. For each signature the table has three blocks of information. The \ufb01rst block of three columns\ngives L1 information:\n\u2022 Name of the L1 trigger item. Which includes the transverse energy threshold required and an \u201dI\u201d\nif isolation cuts (as described in Section 2.1) are applied.\n\u2022 Prescale factor applied after L1 selection.\n\u2022 Corresponding rate after prescale factors applied.\nThe second block of three columns summarizes the EF:\n\u2022 Tightness of the EF selection cuts.\n\u2022 Prescale factor.\n\u2022 Corresponding HLT rate.\nThe last column illustrates some relevant channels that the corresponding trigger would collect.\nTables 6 and 7 have the same structure described above. Table 6 gives examples of trigger signatures\nwith tighter selection cuts, to be used if the rates given by the ones presented in Table 5 are too high.\nA summary of the main trigger signatures foreseen for a higher luminosity scenario of L\u223c1033 cm\u22122 s\u22121,\nis shown in Table 7.\n4\nElectron and photon trigger physics performance\nIn this section the performance of the different signatures is presented with trigger ef\ufb01ciency plots as a\nfunction of transverse energy ET and pseudo-rapidity \u03b7.\nThe trigger ef\ufb01ciency optimization of a given electron/photon trigger menu is a compromise between\nseveral factors: trigger ef\ufb01ciency for signal, QCD background rate which depends on the luminosity\n(constrained by allowed HLT bandwidth) and constrains of the average execution time at each trigger\nlevel. The performance of the main electron and photons triggers has been evaluated for a start-up lumi-\nnosity of L\u223c1031 cm\u22122 s\u22121and for a higher luminosity of L\u223c1033 cm\u22122 s\u22121. In sections 4.2 and 4.3 the\nperformance of these triggers is discussed for electrons and photons respectively. For these studies two\ntypes of events have been used, the so called ideal and the misaligned detector geometry. The misaligned\ndetector geometry simulation contains expected distortions of the detector and in addition contains ex-\ntra material coming from a more accurate description of cooling, powering and cabling services. This\nincreases signi\ufb01cantly the amount of material in the region 1.4 < |\u03b7| < 1.8 compared to the ideal geom-\netry, thus affecting the calorimeter energy calibration which was extracted using the ideal geometry. In\nsection 4.2 a comparison is given for the performance based on these two layouts for one of the electron\ntriggers.\n4.1\nData Samples\nThe signal samples used for electron and photon trigger performance studies in this note are summarized\nin Table 8. For the electron and photon trigger optimization and turn-on curves samples with an energy\nrange of 7 < ET < 80 GeV (\ufb02at energy spectrum) are used.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n629\n\nLevel-1\nHLT\nSignature\nItem\nPre-\nRate\nSel-\nPre-\nRate\nMotivation\nscale\n[kHz]\nection\nscale\n[Hz]\ne5\nEM3\n60\n0.7\nmedium\n1\n4.8\u00b10.2\nJ/\u03a8 \u2192ee, Y \u2192ee, Drell-Yan\n2e5\n2EM3\n1\n6.5\nmedium\n1\n6\nJ/\u03c8 \u2192ee, Y \u2192ee, Drell-Yan\nJpsiee\n2EM3\n1\n6.5\nmedium\n1\n1\nJ/\u03c8 \u2192ee, Y \u2192ee\ne10\nEM7\n1\n5.0\nmedium\n1\n21\ne\u00b1 from b,c decays, E/p studies\n\u03b310\nEM7\n1\n5.0\nmedium\n100\n0.6\u00b10.1\ne\u00b1 direct photon cross-section,\ne-no-track trigger\ne10 xe30\nEM7\n1\n0.2\nmedium\n1\n0.3\u00b10.3\naccess low pT -range for\nXE30\nW \u2192e\u03bd\n2\u03b310\n2EM7\n1\n0.5\nloose\n1\n< 0.1\ndi-photon cross-section\n2e10\n2EM7\n1\n0.5\nloose\n1\n0.4\u00b10.2\nZ \u2192e+e\u2212\nZee\n2EM7\n1\n0.5\nloose\n1\n< 0.1\nZ \u2192e+e\u2212\n2e12i L33\n2EM7\n1\n0.5\ntight\n1\n< 0.1\ntrigger for L\u223c1033 cm\u22122 s\u22121\n\u03b315\nEM13\n1\n0.7\nmedium\n10\n1.3\u00b10.1\ne\u00b1 direct photon cross-section\ne15 xe20\nEM13\n1\n0.2\nloose\n1\n1.0\u00b10.4\naccess low pT -range for\nXE20\nW \u2192e\u03bd\n2g17i L33\n2EM13I\n1\n0.1\ntight\n1\n< 0.1\ntrigger for L\u223c1033 cm\u22122 s\u22121\n\u03b320\nEM18\n1\n0.3\nloose\n1\n5.4\u00b10.2\ndirect photons, jet calibration\nusing \u03b3-jet events, high-pT\nphysics,check tracking eff.\ne20\nEM18\n1\n0.3\nloose\n200\n< 0.1\ncheck L2EF performance\npassL2\ne20\nEM18\n1\n0.3\n125\n0.1\ncheck L2EF performance\npassEF\nem20\nEM18\n1\n0.3\n750\n0.5\u00b10.1\ncheck HLT performance\npassEF\nem20i\nEM18I\n1\n0.1\n300\n0.5\u00b10.1\ncheck L1 isolation\npassEF\ne22i L33\nEM18I\n1\n0.1\ntight\n1\n1.2\u00b10.1\ntrigger for L\u223c1033 cm\u22122 s\u22121\n\u03b355 L33\nEM18\n1\n0.3\ntight\n1\n1.2\u00b10.1\ntrigger for L\u223c1033 cm\u22122 s\u22121\nem105\nEM100\n1\n1\n1\n1.0\u00b10.1\nNew physics, check for possible\npassHLT\nproblems\n\u03b3150\nEM100\n1\n1\n1\n< 0.1\ncheck for possible problems in\npassHLT\nexpress stream\nTable 5: Summary of triggers for the \ufb01rst physics run assuming a luminosity of L\u223c1031 cm\u22122 s\u22121. For\neach signature rates and the motivation for this trigger are given.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n630\n\nLevel-1\nEvent Filter\nSignature\nItem\nPre-\nRate\nSel-\nPre-\nRate\nback-up for trigger\nscale\n[kHz]\nection\nscale\n[Hz]\ne5 e7\n2EM3\n1\n6.5\nmedium\n1\n4.3\u00b10.2\n2e5\ne5 e10\nEM3 EM7\n1\n6.5\nmedium\n1\n4.3\u00b10.2\n2e5\n3g10\n3EM7\n1\n< 0.1\ntight\n1\n< 0.1 Hz\n2g10, 2e10\ne20 xe15\nEM18 XE15\n1\n0.1\nloose\n1\n1.6\u00b10.1\ne20 for W \u2192e\u03bd selection\n\u03b320 xe15\nEM18 XE15\n1\n0.1\nloose\n1\n1.9\u00b10.2\ng20 for W \u2192e\u03bd selection\ne20i\nEM18I\n1\n0.1\nloose\n1\n2.8\u00b10.1\ne20\ne25\nEM18I\n1\n0.1\nloose\n1\n2.4\u00b10.1\ne20\ne25\nEM18I\n1\n0.1\nloose\n1\n2.4\u00b10.1\ne20\ne25i\nEM23I\n1\n< 1\nloose\n1\n1.4\u00b10.1\ne20\n\u03b3105\nEM100\n1\n<< 1\n1\n< 0.1\nem105 passHLT\ne105\nEM100\n1\n1\n1\n< 0.1\nem105 passHLT\nTable 6: Summary of backup triggers de\ufb01ned in case the rate is too high for a start-up luminosity of\nL\u223c1031 cm\u22122 s\u22121. For each signature rates and the motivation for this trigger are given.\nLevel-1\nHLT\nSignature\nItem\nPre-\nRate\nSel-\nPre-\nRate\nMotivation\nscale\n[kHz]\nection\nscale\n[Hz]\n2e12i\n2EM7\n1\n0.5\ntight\n1\n1\nZ \u2192ee\n2\u03b317i\n2EM13I\n1\n0.1\ntight\n1\n\u223c1\nnew physics e.g. H \u2192\u03b3\u03b3\ne22i\nEM18I\n1\n10\ntight\n1\n120\nhigh-pT electron physics\n\u03b355\nEM18\n1\n30\ntight\n1\n20\u00b13\nhigh-pT photon physics\n\u03b3105\nEM100\n1\n0.1\nloose\n1\n1\nnew very high-pT physics\ne105\nEM100\n1\n0.1\nloose\n1\n< 1\nnew very high-pT physics\nTable 7: Summary of triggers assuming a luminosity of L\u223c1033 cm\u22122 s\u22121. For each signature rates and\nthe motivation for this trigger are given.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n631\n\nPhysics\nET(GeV)\nGeometry\nsingle photons\n60\nmisaligned\nsingle photon scan\n7-80\nmisaligned\u2013ideal\nsingle photons\n20\nmisaligned\nsingle electrons\n25\nmisaligned\nsingle electron scan\n7-80\nmisaligned\u2013ideal\nZ\u2192ee\n\u2013\nmisaligned\u2013ideal\ndirect J/Psi\n\u2013\nmisaligned\nH\u2192\u03b3\u03b3\n120\nmisaligned\nW\u2192e\u03bd\nmisaligned\nG\u2192ee\n500\nmisaligned\nZ\n\u2032 \u2192ee\n1000\nmisaligned\nG\u2192\u03b3\u03b3\n500\nmisaligned\nPhoton+Jet1\n17-35\nmisaligned\nPhoton+Jet2\n35-70\nmisaligned\nPhoton+Jet3\n70-140\nmisaligned\nPhoton+Jet4\n140-280\nmisaligned\nPhoton+Jet5\n280-560\nmisaligned\nPhoton+Jet6\n560-1120\nmisaligned\nTable 8: Main electron/photon signal and physics samples.\npT(hard)\njet \ufb01lter\n\u03c3 after \ufb01ltering\n6GeV\ndefault\n4.214mb\n7GeV\nloose\n6.531mb\n7GeV\ndefault\n3.788mb\n17GeV\nloose\n0.373mb\n17GeV\ndefault\n0.191mb\n35GeV\nloose\n0.039mb\n35GeV\ndefault\n0.021mb\nTable 9: Main background samples and their cross sections.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n632\n\nBackground samples and their expected cross-sections are summarized in Table 9. The minimum bias\nMonte Carlo sample corresponds to our best knowledge of the inclusive expected backgrounds (including\nboth hard and soft processes). Unfortunately most of the events in it are at low energies < 7 GeV and it\nis not very practical for high-statistics studies above this energy. To increase our ef\ufb01ciency for the events\nwith electrons and photons we use a \ufb01lter which is based on the combination of the EM cluster ET cut\nand the area of the EM cluster. Two types of the \ufb01lter, \u201cdefault\u201d and \u201cloose\u201d are used to check for the\npotential biases in the L1 trigger rate which could occur if the area required by the \ufb01lter is too small or\nthe ET cut too high for the trigger threshold studied.\nFor the trigger rate studies in the intermediate energy range 6\u221217 GeV we use minimum bias events\nwith a transverse energy above 6 GeV and default \ufb01lter (a rejection factor of 16.61). Above 17 GeV the\ndijet processes become the most prominent background for electrons and photons. Dijet samples with a\nthreshold cut of 15 GeV and different level of \ufb01lters (default and loose respectively) are used to provide\nbackground estimates in that area (the physics processes such as W, Z, direct photons have been added).\nFor the very high energy studies dijet samples with a threshold cut of 35 GeV are used.\nFor this note two detector geometries are used:\n\u2022 \u201cideal\u201d which uses the detector geometry to our best knowledge.\n\u2022 \u201cmisaligned\u201d where the detector has misalignments and material distortions.\nThe misaligned detector geometry has been generated to test the robustness of our reconstruction and\ntrigger algorithms with respect to incorrect alignment and calibration of the detector due to unexpected\nexcess of material. Extra material was added in the misaligned detector geometry with respect to the\nideal:\n\u2022 For the inner detector, extra thin layers of material were added in the azimuthal angle range of\n0 < \u03c6 < \u03c0 only. The amount of material added varies in the z direction, from a few percent of X0\non the active detector elements up to 1 X0 in the areas occupied by services.\n\u2022 For the electromagnetic calorimeter, more material was added in the barrel cryostat (\u223c8\u221211% of\nX0), between the barrel presampler and \ufb01rst calorimeter sampling (\u223c5% X0, always for positive\n\u03c6), and in the gap between the barrel and endcap cryostats (factor 1.7 increase of material density).\n4.2\nElectron trigger performance\nThe performance of the electron trigger has been evaluated for the trigger menus foreseen for the lumi-\nnosity expected at early running L\u223c1031 cm\u22122 s\u22121 and for a higher luminosity of L\u223c1033 cm\u22122 s\u22121.\nThe trigger ef\ufb01ciencies are quoted with respect to electrons identi\ufb01ed with of\ufb02ine particle identi\ufb01cation\ncuts [6]. The trigger ef\ufb01ciencies have been evaluated using simulated single electron samples with a\ntransverse energy spectrum of 7 < ET < 80 GeV and other physics samples such as J/\u03c8 \u2192ee, Z \u2192ee,\netc. Rates have been estimated using simulated dijet events or minimum bias background depending on\nthe trigger thresholds.\nIn the following the performance for the start-up trigger items e5, e10, e20, e105 and for a possible\ne22i trigger for higher luminosity running are discussed.\nFigure 6 shows the ef\ufb01ciencies as a function of ET and |\u03b7| of the low-pT e5 trigger for the three trigger\nlevels L1, L2 and EF. The e5 trigger menu is a trigger with prescale factor at L\u223c1031 cm\u22122 s\u22121and the\nmain trigger is the 2e5 trigger, which applies the same selection cuts. The ef\ufb01ciencies are obtained for\nelectrons from a misaligned detector geometry J/\u03c8 \u2192ee sample. In the of\ufb02ine analysis these electrons\ntypically will be identi\ufb01ed via the \u201cmedium set\u201d of of\ufb02ine \u201csoft-electron\u201d selection cuts (see [7] for\nmore details). Therefore, the ef\ufb01ciencies shown in Fig. 6 are normalized with respect to such an of\ufb02ine\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n633\n\n (GeV)\nT\nE\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n50\n100 150 200 250 300 350 400 450 500 550\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0 8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n50\n100 150 200 250 300 350 400 450 500 550\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0 8\n1\n|\u03b7\n|\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nTrigger efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nFigure 6: Trigger ef\ufb01ciencies at L1 (solid circles), L2 (open squares) and EF (solid triangles) as a function of true electron ET\n(left) and |\u03b7| (right) for the e5 (top), e10 (second from top), e20 (third from top) e105 (bottom) menu items. The ef\ufb01ciencies are\nobtained from the following Monte Carlo simulated samples: J/\u03c8 \u2192ee decays simulated with misaligned detector geometry\nfor e5 trigger item, Z\u2032 \u2192ee (1TeV) for e105 and single electrons simulated with ideal detector geometry for e10 and e20. Trigger\nef\ufb01ciencies are normalized with respect to the medium set of of\ufb02ine soft-electron cuts for e5, with respect to the medium set\nof of\ufb02ine electron cuts for e10 and with respect to the loose set of of\ufb02ine electron cuts for e20 and e105. For trigger ef\ufb01ciency\nversus |\u03b7| plots, an ET cut according to the corresponding menu item has been applied: for e5 ET > 10 GeV, for e10 ET > 15\nGeV, for e20 ET > 30 GeV and for e105 ET > 130 GeV. For e5 trigger item no data is shown for electrons for |\u03b7| > 2 as this is\nbeyond the coverage of the transition radiation tracker whose information is used for the of\ufb02ine electron selection. Errors are\nstatistical only.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n634\n\nselection. As seen in the right \ufb01gure, the ef\ufb01ciencies drop signi\ufb01cantly in the transition region between\nthe barrel and end-cap calorimeter. A better optimization of the trigger selection cuts in this region might\nhelp to recover part of the inef\ufb01ciencies. Figure 6 shows L1, L2 and EF ef\ufb01ciencies as a function of\nET and of |\u03b7| of the e10 trigger, which is the lowest pT unprescaled single electron trigger foreseen for\nrunning at L\u223c1031 cm\u22122 s\u22121. The e10 trigger selects events with at least one good electron candidate\nwith ET > 10 GeV. The ef\ufb01ciencies are obtained for single electrons using ideal detector geometry and\nare normalized with respect to the medium set of of\ufb02ine electron cuts as discussed in Section 2.3. The\nef\ufb01ciency reaches a plateau value for ET approximately above 15 GeV and is quite uniform as a function\nof |\u03b7|, except for a 10\u221220% dip in the transition region between the barrel and end-cap calorimeters. In\nFig. 7 e10 trigger ef\ufb01ciencies are compared for samples that use ideal and misaligned detector simulation.\nThe biggest effects are observed at lower ET for the turn-on curve (left) and in the region 1.4 < |\u03b7| < 1.8\n(right) where a signi\ufb01cant increase of material in the so-called misaligned geometry with respect to the\nideal one was introduced. Trigger ef\ufb01ciency plots as a function of ET and |\u03b7| for the electron triggers\ne20 and e105 are shown in Fig. 6. Compared to the e10 trigger signature, the e20 trigger applies looser\nelectron identi\ufb01cation cuts. The e105 trigger is aimed at selecting very high pT electrons with very loose\nselection cuts for L\u223c1032 cm\u22122 s\u22121. At L\u223c1031 cm\u22122 s\u22121this trigger will only apply the L1 selection.\nFor several physics channels a global trigger ef\ufb01ciency with respect to the of\ufb02ine loose selection is\nshown in Table 10 for each trigger level. An average trigger ef\ufb01ciency of \u223c98% is obtained after the EF\nlevel trigger. An ef\ufb01ciency close to 100% is expected for very high pT electrons, therefore the selection\nhas been optimized towards this goal.\nFigure 8 (left) shows L1, L2 and EF ef\ufb01ciencies as a function of ET of the signature e22i, the menu\nitem selecting an electron with ET > 22 GeV. The ef\ufb01ciencies are obtained for single electrons using\nideal detector geometry are normalized with respect to a loose set of of\ufb02ine electron cuts as discussed\nin [6]. The ef\ufb01ciency reaches a plateau value for ET approximately above 25 GeV.\nFigure 8 (right) shows an example of trigger ef\ufb01ciency dependency on the of\ufb02ine electron identi-\n\ufb01cation cuts. Trigger ef\ufb01ciency has been determined with respect to loose, medium and tight of\ufb02ine\nelectron identi\ufb01cation selections as described in [6] for e15i. This menu item applies medium electron\nidenti\ufb01cation cuts at EF, therefore its ef\ufb01ciency with respect to loose of\ufb02ine reconstructed electrons is\nsigni\ufb01cantly lower than with respect to medium or tight of\ufb02ine electrons.\n (GeV)\nT\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\nTrigger efficiencies ratio\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\n |\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiencies ratio\n0.94\n0.95\n0.96\n0.97\n0.98\n0.99\n1\nATLAS\nFigure 7: Ratio of trigger ef\ufb01ciencies for single electrons reconstruction in misaligned and ideal detector\ngeometry as a function of true electron ET (left) and |\u03b7| (right) for the e10 menu item. Events in the |\u03b7|\nplot are required to verify ET > 15 GeV. Errors are statistical only.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n635\n\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\nTrigger Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\ne15i Single e without pileup\nloose\nmedium\ntight\nFigure 8: Trigger ef\ufb01ciencies at L1, L2 and EF as a function of true electron ET for the e22i menu\nitem (left). The ef\ufb01ciencies are obtained for single electrons using ideal detector geometry and are\nnormalized with respect to loose set of of\ufb02ine electron cuts. Trigger ef\ufb01ciency dependency on the of\ufb02ine\nelectron identi\ufb01cation (right). Trigger ef\ufb01ciency for the e15i signature is determined with respect to\nloose, medium and tight of\ufb02ine electron identi\ufb01cation selection (described in [6]). Errors are statistical\nonly.\n4.3\nPhoton trigger performance\nThe physics performance of the photon trigger menus presented in Section 3 has been evaluated for early\nrunning at L\u223c1031 cm\u22122 s\u22121and for a luminosity of L\u223c1033 cm\u22122 s\u22121. The performance has been eval-\nuated in terms of trigger ef\ufb01ciency after each trigger level using simulated single photons with transverse\nenergies between 7 and 80 GeV. Rate estimates were calculated using dijet background simulations.\nA \u03b320 trigger with loose selection has been de\ufb01ned for the \ufb01rst physics run at L\u223c1031 cm\u22122 s\u22121. At this\nstage the selections still need to be understood and the photon trigger is also used to check the tracking\npart of the electron selection. Therefore, the same calorimeter selection cuts are used as for electrons.\nFigure 9 (top right) shows the relative rate for each trigger level as a function of |\u03b7|. Photons in the\ntransition region between barrel and end-cap calorimeters (1.37 < |\u03b7| < 1.52) are not well measured and\nare excluded in the physics analysis.\nThe single photon trigger at L\u223c1033 cm\u22122 s\u22121 selects photons above ET =55 GeV. To keep the rate under\ncontrol, this trigger has to apply very tight L2 and EF calorimeter selections.\nFigure 9 shows the trigger ef\ufb01ciencies as a function of ET and |\u03b7| for the \u03b355 trigger using single\nphotons. Only photons with |\u03b7| < 1.37 or 1.52 < |\u03b7| < 2.45 are considered. With respect to loosely\nselected of\ufb02ine photons the \u03b355 trigger is 95.5% ef\ufb01cient.\nThe double object trigger 2\u03b317i is another of the main photon triggers for running at L\u223c1033 cm\u22122 s\u22121.\nSince the single photon dataset only contains one photon per event, the 2\u03b317i trigger ef\ufb01ciency was\nestimated as the square of the single photon trigger ef\ufb01ciency (Eff2\u03b317i= Eff2\n\u03b317i). The overall trigger\nef\ufb01ciency estimated from this sample is 93.9\u00b10.2%.\nFigure 9 shows the \u03b3 17i turn-on curve and ef\ufb01ciency as a function of |\u03b7| using single photon events.\nThe trigger ef\ufb01ciencies shown for the turn-on are normalized with respect to tight of\ufb02ine photon selection\ncriteria. In addition, the photons are required to be within the region |\u03b7| < 1.37 or 1.52 < |\u03b7| < 2.45.\nThis plot shows that the \u03b317i trigger is well set up and is fully ef\ufb01cient at 25 GeV.\nThe photon trigger performance has been studied not only for single photon samples but also for\nseveral physics channels. Table 11 shows a summary of photon trigger ef\ufb01ciencies for simulated samples\nof standard model direct photon decays, Higgs decaying into two photons (low mass range 120 GeV)\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n636\n\nDataset (geometry)\nTrigger Level\nTrigger ef\ufb01ciency (%)\nW \u2192e\u03bd (misaligned)\nL1\n98.2\u00b10.1\n(e20)\nL1 + L2\n96.0\u00b10.2\nL1 + L2 + EF\n94.3\u00b10.2\nZ\u2032 \u2192ee (misaligned)\nL1\n99.7+0.3\n\u22120.7\n(e105)\nL1 + L2\n98.9\u00b10.7\nL1 + L2 + EF\n98.8\u00b10.7\nelectrons 500 GeV (misaligned)\nL1\n99.1\u00b10.6\n(e105)\nL1 + L2\n97.6\u00b10.5\nL1 + L2 + EF\n97.5\u00b10.5\nTable 10: Global trigger ef\ufb01ciencies for the trigger items e20 and e105. The signal ef\ufb01ciencies are\ndetermined from several different signal samples: W \u2192e\u03bd Z\u2032 \u2192ee and a sample of single electrons\nof \ufb01xed transverse energy of 500 GeV. The simulation used misaligned detector geometry. Trigger\nef\ufb01ciencies are determined with respect to loose of\ufb02ine electron selection. In the W \u2192e\u03bd case the of\ufb02ine\nreconstructed electron is required to be within the |\u03b7| < 2.5 region and to have a transverse energy above\n25 GeV. Ef\ufb01ciencies for the e105 item are determined in the kinematic region |\u03b7| < 2.5, the transition\nregion between barrel and end-cap calorimeters removed (1.37 < |\u03b7| < 1.52), and with a minimum true\ntransverse energy of 130 GeV.\nDataset (luminosity)\nTrigger Level\nTrigger ef\ufb01ciency (%)\n\u03b3+Jet (L\u223c1031 cm\u22122 s\u22121)\nL1\n100.0\u00b10.0\n(\u03b320)\nL1 + L2\n99.8\u00b10.1\nL1 + L2 + EF\n95.0\u00b10.3\nG \u2192\u03b3\u03b3 (L\u223c1032 cm\u22122 s\u22121)\nL1\n99.5\u00b10.1\n(\u03b3105)\nL1 + L2\n98.8\u00b10.1\nL1 + L2 + EF\n98.7\u00b10.2\nH \u2192\u03b3\u03b3 (L\u223c1033 cm\u22122 s\u22121)\nL1\n95.6\u00b10.2\n(2\u03b317i)\nL1 + L2\n93.6\u00b10.2\nL1 + L2 + EF\n91.2\u00b10.2\nTable 11: Trigger ef\ufb01ciencies after each trigger level, normalized with respect to the loose \u03b3 selection,\nfor different physics channels covering a wide range in ET. In the case of H \u2192\u03b3\u03b3 standard kinematical\ncuts are applied in addition. For each physics process the ef\ufb01ciencies for the main physics trigger to\nselect these events for a given luminosity scenario are shown.\nand an exotic signature: graviton decaying into a pair of photons G\u2192\u03b3\u03b3 (500 GeV).\nTrigger ef\ufb01ciencies after each level are given. Ef\ufb01ciencies are determined with respect to a loose\nof\ufb02ine selection using the main physics trigger for a given luminosity to select these events. In the case\nof H \u2192\u03b3\u03b3 standard kinematical cuts are also applied. A more detailed study of trigger ef\ufb01ciencies for\ndifferent physics channels can be found in [8] and [9].\n5\nTrigger robustness studies\nThe electron/photon HLT selection must be robust against detector effects such as mis-calibration, mis-\nalignment, dead and noisy read-out cells or sectors, luminosity and beam conditions changes etc. This\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n637\n\n (GeV)\nT\nE\n0\n5\n10\n15\n20\n25\n30\n35\n40\nTrigger efficiency\n0\n0 2\n0.4\n0 6\n0 8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n(GeV)\nT\nE\n30\n35\n40\n45\n50\n55\n60\n65\n70\n75\n80\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nLVL1\nLVL2\nEF\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLVL1\nLVL2\nEF\nATLAS\n(GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n70\n80\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nLVL1\nLVL2\nEF\nATLAS\n|\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLVL1\nLVL2\nEF\nATLAS\nFigure 9: Trigger ef\ufb01ciencies at L1, L2 and EF as a function of the generated photon ET (top left)and\n|\u03b7| (top right) for the \u03b320 trigger. The ef\ufb01ciencies are obtained for single photons simulated with ideal\ndetector geometry and are normalized with respect to the loose set of of\ufb02ine photon cuts. Note, the |\u03b7|\nplot includes an additional cut of ET > 23 GeV. Trigger ef\ufb01ciencies at L1, L2 and EF as a function\nof the generated photon ET (middle left) and |\u03b7| (middle right) for the \u03b355 trigger. The ef\ufb01ciencies\nare normalized with respect to photons with ET > 55 GeV passing the loose set of of\ufb02ine photon cuts.\nTrigger ef\ufb01ciencies at L1, L2 and EF as a function of the generated photon ET (bottom left) and |\u03b7|\n(bottom right) for the \u03b317i trigger. The ef\ufb01ciencies are normalized with respect to the tight set of of\ufb02ine\nphoton cuts. Errors are statistical only.\nwill be especially important during early running. Depending on the bunch structure of the LHC, the\neffect of pile\u2013up might already be important even at a luminosity of L\u223c1032 cm\u22122 s\u22121. More than\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n638\n\nTrigger Level\ne12i no pile-up\ne12i with pile-up\ne22i no pile-up\ne22i with pile-up\nL1\n94.8\u00b10.1%\n94.8\u00b10.3%\n96.0\u00b10.1%\n95.5\u00b10.3%\nL1 + L2\n86.8\u00b10.2%\n86.7\u00b10.4%\n90.2\u00b10.2%\n89.4\u00b10.4%\nL1 + L2 + EF\n81.5\u00b10.2%\n81.3\u00b10.5%\n88.7\u00b10.2%\n88.0\u00b10.4%\nTable 12: The e12i and e22i trigger ef\ufb01ciency from a sample of electrons of 7< ET < 80 GeV, with and\nwithout pile-up at a luminosity of L\u223c2\u00d7 1033 cm\u22122 s\u22121\none proton-proton interaction might occur per bunch crossing, the proton-proton interactions that are\nnot interesting for analysis but happen in the same bunch crossing that the interesting one are typically\ndenoted as \u2019pile-up\u2019. At L\u223c2\u00d71033 cm\u22122 s\u22121 around 4.6 minimum bias events are expected per bunch\ncrossing. In this section only the effects of pile-up and mis-calibrations due to additional detector material\nin front of the calorimeter are discussed.\n5.1\nEffect of pile-up\nThe robustness of several electron triggers was studied with simulated data which included overlapping\nevents (\u201cpile-up\u201d) for a luminosity L\u223c2\u00d7 1033 cm\u22122 s\u22121. The presence of pile-up might have effects in\nreconstruction ef\ufb01ciency, (mostly for tracks but also for calorimeter energy clusters), as well as in the\nidenti\ufb01cation of isolated electrons and photons, both at the trigger and of\ufb02ine reconstruction level.\nTable 12 shows the effect of pile-up on the e12i and e22i trigger for single electron events. As can\nbe seen the effect of pile-up on the trigger ef\ufb01ciency at L\u223c2\u00d7 1033 cm\u22122 s\u22121 is \u223c3%. There is a \u223c2%\neffect due to the isolation criteria at L1 when tight isolation cuts are applied (e12i) and a \u223c1% loss\nat the HLT level. This results show that the trigger ef\ufb01ciency is only slightly more affected by pile-up\neffects than of\ufb02ine electron reconstruction. The effect of pile-up on trigger performance determined with\nrespect to MC-Truth electrons as well as on the background rate is being studied.\n5.2\nEffect of additional detector material\nA simulated data sample consisting of single electrons as described above was used to study the effect\nof additional inactive material in the detector. Despite the efforts to accurately describe the detector in\nMonte Carlo simulation it is not expected to be perfect. The biggest and more problematic differences\nbetween simulation and reality are expected to come from the description of inactive material (for exam-\nple pipes for cooling, power and signal cables, etc). Trigger robustness against those possible distortions\nhas to be tested. Methods to identify and correct those effects have to be developed. The detector simula-\ntion used to produce this data sample included distorted material distributions in both the inner detector\nvolume and the electromagnetic calorimeter.\nA detailed description of the material added in the Monte Carlo sample is given in Section 4.1 The\namount of extra material with respect to the non-distorted simulation, grows from a few percent of a\nradiation length at \u03b7 = 0 up to \u223c1X0 at 1.5 < |\u03b7| < 1.8, and then decreases towards higher values of\n|\u03b7|. The amount of material added in front of the active elements was larger than the uncertainty on the\nmaterial distribution.\nThe effect of the extra inactive material on the electron trigger was studied by comparing the trigger\nef\ufb01ciency for \u03c6 > 0, where extra material was added in the detector simulation, and for \u03c6 < 0, where\nno extra material was added. The resulting ef\ufb01ciencies are shown in Fig. 10. The ef\ufb01ciency is plotted\nas a function of the kinematic variables of the electron candidate reconstructed of\ufb02ine. A loose of\ufb02ine\nelectron selection was used for normalization.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n639\n\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n > 0\n\u03c6\n < 0\n\u03c6\nATLAS\n [GeV]\nT\nE\n10\n20\n30\n40\n50\n60\n70\n80\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n > 0\n\u03c6\ne10, \n < 0\n\u03c6\ne10, \n > 0\n\u03c6\ne15i, \n < 0\n\u03c6\ne15i, \nATLAS\nFigure 10: Effect of additional inactive material in the detector on the electron trigger ef\ufb01ciency. The\ntrigger ef\ufb01ciency is compared for the nominal material distribution (at \u03c6 < 0) and for increased inactive\nmaterial (at \u03c6 > 0) for the electron triggers e10 and e15i. The ef\ufb01ciency is plotted as a function of |\u03b7|\n(left) and ET (right) of the electron candidate reconstructed of\ufb02ine. The left histograms correspond to\nthe e15i trigger only. Errors are statistical only.\nIt can be seen that the effect of the added material is more pronounced for the e15i signature than\nfor e10. The e15i signature applies tighter selection cuts than the e10. In particular e15i requires the\nso-called medium electron identi\ufb01cation cuts in EF, this explains the lower trigger ef\ufb01ciency for e15i. If\ntrigger ef\ufb01ciency was computed with respect to medium or tight of\ufb02ine electron identi\ufb01cation selection,\nthe trigger ef\ufb01ciency would be higher, as shown in Fig. 8.\n6\nTrigger ef\ufb01ciency determination from real data\nThe trigger ef\ufb01ciency will need to be determined from data, reducing the dependence on Monte Carlo\nsimulation as much as possible. Before data-taking starts some of the methods to study the trigger\nperformance without relying on the MC-Truth information are being developed, an example is given in\nthis section.\nThe so-called \u201ctag and probe\u201d method has been studied using a Monte Carlo simulation sample of\nZ \u2192ee. In the \ufb01rst subsection the basis of this method is explained, followed by the detailed explanation\nof the selection criteria chosen for this study, the trigger ef\ufb01ciency computation and its comparison with\nMC-Truth information. In the following subsection the performance of the method is presented for some\nloose trigger selections that will be used in early running.\n6.1\nEf\ufb01ciency extraction method\nThe so-called \u201ctag and probe\u201d method uses of\ufb02ine identi\ufb01cation of Z \u2192ee decays to select a clean\nsample of electrons, which are then used to determine the electron trigger ef\ufb01ciency. During data-taking\na data sample to perform an analysis will be characterized by a given trigger signature being satis\ufb01ed.\nIn the study summarized in this section the data sample is de\ufb01ned by a given single electron trigger\nsignature. The electron candidate that has satis\ufb01ed the trigger is reconstructed and identi\ufb01ed of\ufb02ine, it\nis the so-called \u201ctag\u201d electron. Z \u2192ee decays are selected requiring a second electron to be identi\ufb01ed\nof\ufb02ine together with some identi\ufb01cation conditions on the Z particle. This second electron is the so-\ncalled \u201cprobe\u201d and it is used to study the trigger performance, since it is know to be a \u201cgood electron\u201d it\ncan be used to verify if electron trigger selection cuts are ef\ufb01cient to identify electrons.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n640\n\nThe discrimination criteria applied to identify of\ufb02ine the tag and probe electrons and the Z can vary.\nIn the following paragraphs we specify the identi\ufb01cation criteria chosen to perform the study presented\nin this section.\nSelection of the tag electron involves tight electron identi\ufb01cation cuts [6] in the of\ufb02ine reconstruction\nto reduce background, and this electron must also trigger the event on its own, through a single electron\ntrigger chain. As trigger ef\ufb01ciencies are measured with respect to one of the established of\ufb02ine electron\nde\ufb01nitions (the so-called \u201cloose\u201d, \u201cmedium\u201d or \u201ctight\u201d electron identi\ufb01cation set of cuts, described in\n[6]), this selection is the one initially applied to the probe electron.\nAdditionally, both of\ufb02ine reconstructed electrons must pass kinematic cuts, i.e. ET > Ecut\nT\nand |\u03b7| <\n2.4, and not lie in the region between the barrel and endcap calorimeters (1.37 < |\u03b7| < 1.52 region is\nexcluded). The value of Ecut\nT\nis chosen to be where the ef\ufb01ciency reaches its high-energy plateau in curves\nthat show trigger ef\ufb01ciency versus transverse energy (such as the one shown in Fig. 11 ). When a trigger\nef\ufb01ciency is plotted as a function of ET or \u03b7, the relevant kinematic selection is relaxed. Finally, there\nare topological constraints, namely that the two electrons have opposite charge, and that their combined\ninvariant mass lies in the range 70 < mee < 110 GeV.\nAt this point, the pair of electrons (tag and probe) may be considered for analysis. The trigger\nef\ufb01ciency is de\ufb01ned by the frequency with which the probe electron in this sample passes the relevant\ntrigger selection.\nIt is perfectly possible for the probe electron to satisfy the tag selection as well. In this case, the\nroles of tag and probe may be swapped, the tag becoming the probe and vice versa. Because the tag\nselection is at least as tight as the probe selection at every stage, the new probe passes the trigger selection\nautomatically. Thus, tag and probe events fall into one of three categories:\n\u2022 N1 f events where only one electron passes the tag cuts and the probe fails the trigger selection\n\u2022 N1p events where only one electron passes the tag cut and the probe passes the trigger selection\n\u2022 N2p events where both electrons pass the tag selection\nCounting these events, the measured ef\ufb01ciency may be expressed as\n\u03b5\u201ctag and probe\u2032\u2032 =\nN1p +2N2p\nN1 f +N1p +2N2p\n= Np\nNT\n(1)\nwhere Np and NT are de\ufb01ned by this equation. Assuming that the uncertainty in each variable is\nsimply\n\u221a\nN, the statistical error on \u03b5 is\n\u03c3\u03b5 = 1\nNT\nq\u0002\n(1\u22122\u03b5)Np +\u03b52NT +(1\u2212\u03b5)2 \u00b72N2p\n\u0003\n.\n(2)\nEquation 2 may be generalized to allow for a more comprehensive uncertainty in Np and NT. Equa-\ntions 1 and 2 can be extended to be used for differential trigger ef\ufb01ciency measurements.\nWhen using Monte Carlo simulated events, the truth record (MC-Truth) can be used to provide an-\nother estimate of the trigger ef\ufb01ciency. To understand the systematic uncertainty of the tag and probe\nmethod, the fractional ef\ufb01ciency difference between the trigger ef\ufb01ciency determined using tag and probe\nmethod (\u03b5\u201ctag and probe\u2032\u2032) and the trigger ef\ufb01ciency determined with respect to the MC-Truth information\n(\u03b5MC\u2212Truth) can be used:\nFractional Ef\ufb01ciency Difference = \u03b5\u201ctag and probe\u2032\u2032 \u2212\u03b5MC\u2212Truth\n\u03b5MC\u2212Truth\n.\n(3)\nTo reduce kinematic bias, the MC-Truth events have been required to satisfy the same kinematic cuts as\nthe tag and probe events, although some bias can remain from the detector resolution. To reduce this, and\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n641\n\nestimate just the bias from the tag and probe method itself, reconstructed quantities (ET and \u03b7) are used\nto determine the acceptance. Non-reconstruction of a true electron is not a problem here, as the trigger\nef\ufb01ciency is always measured relative to some level of of\ufb02ine reconstruction.\nTrigger Level\nw.r.t. loose (%)\nw.r.t. medium (%)\nw.r.t. tight(%)\n(truth)\n(truth)\n(truth)\nL1\n99.995 \u00b1 0.005\n99.995 \u00b1 0.005\n99.997 \u00b1 0.005\n(99.994 \u00b1 0.002)\n(99.995 \u00b1 0.002)\n(99.998 \u00b1 0.001)\nL2\n98.74 \u00b1 0.07\n99.59 \u00b1 0.04\n99.68 \u00b1 0.04\n(98.67 \u00b1 0.03)\n(99.54 \u00b1 0.02)\n(99.62 \u00b1 0.02)\nEF\n98.66 \u00b1 0.07\n99.15 \u00b1 0.06\n99.96 \u00b1 0.01\n(98.59 \u00b1 0.03)\n(99.12 \u00b1 0.02)\n(99.96 \u00b1 0.06)\nL1 + L2 + EF\n97.41 \u00b1 0.09\n98.74 \u00b1 0.07\n99.63 \u00b1 0.04\n(97.28 \u00b1 0.04)\n(98.65 \u00b1 0.03)\n(99.57 \u00b1 0.02)\nTable 13: Single object tag and probe ef\ufb01ciencies for the e10 selection used in the 2e10 signature, with\ncomparison to ef\ufb01ciencies derived using truth information from simulation. Ef\ufb01ciencies are given with\nrespect to the previous trigger level(s), as well as for the whole trigger (rows) and the given of\ufb02ine\nelectron identi\ufb01cation selection (columns). The errors given are statistical only. Errors on tag and probe\nvalues are scaled up, to correspond to 50 pb\u22121of data. For this table, the invariant mass cut is 70 < mee <\n100 GeV. A signal sample of Z0 \u2192ee Monte Carlo simulation without background was used to obtain\nthese results.\n6.2\nEf\ufb01ciency extraction for early running\nEarly running at ATLAS will be vital for understanding the performance of the detector as well as the\ntrigger and the of\ufb02ine reconstruction. There will be several single object triggers with low thresholds\nand loose selections that will be impossible to use later on in the experiment. Table 13 shows example\nresults for the e10 trigger selection used to build the 2e10 signature. The single object ef\ufb01ciency is\nshown, as the tag electron has been required to pass the tighter single electron trigger e10. Both trigger\nsignatures are listed in Table 3. Table 13 displays the relative trigger ef\ufb01ciency for each trigger level\nas well as the overall one, comparing results obtained from tag and probe method and from simulation\ntruth information, that show a good agreement within the statistical error. Figure 11 shows these results\ndifferentially, along with the fractional ef\ufb01ciency difference de\ufb01ned in Equation 3. This shows good\nagreement between the two methods, and that the loose e10 trigger has high ef\ufb01ciency for Z0 \u2192ee\nelectrons. The results presented in this Section have been obtained from a sample of Z0 \u2192ee Monte\nCarlo simulation without adding possible background. Studies performed adding Monte Carlo simulated\nbackground have shown that the presence of background could degrade the resolution of the method\nto a few percent level. The use of a low ET threshold and the loose electron identi\ufb01cation cuts on the\nprobe of\ufb02ine selection means that backgrounds will be signi\ufb01cantly higher than in standard data-taking\nat higher luminosities, in which tighter selection cuts would be applied. The ET low threshold will,\nhowever, mean that background will be present in the invariant mass distribution of the two electrons for\nvalues smaller than the Z mass, allowing both sidebands to be used for background subtraction below\nthe Z peak. Even with higher ET thresholds, where only one sideband can be used, it is possible to\nextract the correct signal with a small additional systematic error [10].\nThe e20 signature foreseen for early running phase has looser electron identi\ufb01cation cuts than the\nother single electron signature present in this menu, e10. Even though no isolation to other electro-\nmagnetic or hadronic activity in the calorimeters is required, the threshold of the transverse energy is\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n642\n\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.8\n0.85\n0.9\n0.95\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nTrigger efficiency\n0.8\n0.85\n0.9\n0.95\n1\n Fractional efficiency difference\n-0.02\n0\n0.02\nL1 \n-0.02\n0\n0.02\n-0.02\n0\n0.02\nL1+L2 \n-0.02\n0\n0.02\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n-0.02\n0\n0.02\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n0\n10\n20\n30\n40\n50\n60\n-0.02\n0\n0.02\n Fractional efficiency difference\n-0.02\n0\n0.02\nL1 \n-0.02\n0\n0.02\n-0.02\n0\n0.02\nL1+L2 \n-0.02\n0\n0.02\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n-0.02\n0\n0.02\nL1+L2+EF\nATLAS\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n-0.02\n0\n0.02\nFigure 11: Single object tag and probe ef\ufb01ciencies for the e10 selection of the 2e10 trigger signature. The\nef\ufb01ciencies shown are relative to a tight of\ufb02ine electron identi\ufb01cation selection as described in [6], as a\nfunction of the reconstructed ET(left) and \u03b7 (right). The tag and probe method (points) is compared to\nMC truth (lines). The lower two plots show the fractional ef\ufb01ciency difference (see Equation 3) between\nthe two. The number of events used corresponds to 50 pb\u22121. For this \ufb01gure, the invariant mass cut is\n70 < mee < 100 GeV. Errors are statistical only. A signal sample of Z0 \u2192ee Monte Carlo simulation\nwithout background was used to obtain these results.\nsuf\ufb01cient to sustain a manageable rate. The trigger ef\ufb01ciencies for the different trigger levels with re-\nspect to the of\ufb02ine electron identi\ufb01cation selections for the probe electron are shown in Table 14, both\nfor the \u201ctag and probe\u201d method and with respect to MC-Truth, showing good agreement within the sta-\ntistical error, and high trigger ef\ufb01ciencies. In Fig. 12 the trigger ef\ufb01ciency for e20 signature as a function\nof ET and \u03b7 is presented. It can be seen that the L2 ef\ufb01ciency is close to 100% with respect to the L1\nef\ufb01ciency already at very low transverse energy, the EF is almost 100% ef\ufb01cient with respect to L2. The\noptimization for this trigger item made to minimize the loss of ef\ufb01ciency in these areas, especially not\nlosing ef\ufb01ciency in the HLT with respect to L1 at large transverse energy. In the bottom part of the same\n\ufb01gure the fractional ef\ufb01ciency difference between the \u201ctag and probe\u201d and MC-Truth method as de\ufb01ned\nin Eq. 3 is shown, good agreement between both methods is observed.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n643\n\nTrigger Level\nw.r.t. loose (%)\nw.r.t. medium (%)\nw.r.t. tight(%)\n(truth)\n(truth)\n(truth)\nL1\n99.74 \u00b1 0.03\n99.83 \u00b1 0.03\n99.88 \u00b1 0.02\n(99.84 \u00b1 0.01)\n(99.93 \u00b1 0.01)\n(99.95 \u00b1 0.01)\nL2\n98.55 \u00b1 0.07\n99.48 \u00b1 0.04\n99.58 \u00b1 0.04\n(98.48 \u00b1 0.03)\n(99.44 \u00b1 0.02)\n(99.53 \u00b1 0.02)\nEF\n98.67 \u00b1 0.07\n99.16 \u00b1 0.06\n99.96 \u00b1 0.01\n(98.60 \u00b1 0.03)\n(99.13 \u00b1 0.02)\n(99.959 \u00b1 0.06)\nL1 + L2 + EF\n97.0 \u00b1 0.01\n98.48 \u00b1 0.08\n99.41 \u00b1 0.05\n(96.95 \u00b1 0.04)\n(98.51 \u00b1 0.03)\n(99.44 \u00b1 0.02)\nTable 14: Tag and probe trigger ef\ufb01ciencies for the e20 signature, with comparison to ef\ufb01ciencies de-\nrived using truth information from simulation. Ef\ufb01ciencies are given with respect to the previous trigger\nlevel(s), as well as for the whole trigger (rows) and the given of\ufb02ine electron identi\ufb01cation selection\n(columns). The errors given are statistical only. Errors on tag and probe values are scaled up, to corre-\nspond to 50 pb\u22121of data. For this table, the invariant mass cut is 70 < mee < 100 GeV. A signal sample\nof Z0 \u2192ee Monte Carlo simulation without background was used to obtain these results.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n644\n\n (GeV)\nT\nE\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nTrigger efficiency\n0.8\n0.85\n0.9\n0.95\n1\nL1\nL1+L2\nL1+L2+EF\nATLAS\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nTrigger efficiency\n0.8\n0.85\n0.9\n0.95\n1\n Fractional efficiency difference\n-0.02\n0\n0.02\nL1 \n-0.02\n0\n0.02\n-0.02\n0\n0.02\nL1+L2 \n-0.02\n0\n0.02\n (GeV)\nT\nE\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n-0.02\n0\n0.02\nL1+L2+EF\nATLAS\n (GeV)\nT\nE\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n-0.02\n0\n0.02\n Fractional efficiency difference\n-0.02\n0\n0.02\nL1 \n-0.02\n0\n0.02\n-0.02\n0\n0.02\nL1+L2 \n-0.02\n0\n0.02\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-0.02\n0\n0.02\nL1+L2+EF\nATLAS\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-0.02\n0\n0.02\nFigure 12: Trigger ef\ufb01ciency from the \u201ctag and probe\u201d method with Z \u2192ee for the e20 trigger signature.\nThe ef\ufb01ciencies are shown w.r.t. a tight of\ufb02ine electron selection as described in [6], as a function of the\nreconstructed ET (left) and the reconstructed \u03b7 (right). The \u201ctag and probe\u201d method (points) is compared\nwith the MC-Truth method (solid line) for all three trigger levels, L1 (solid circles), L2 (open triangles),\nand the EF (solid squares), The fractional ef\ufb01ciency difference (see Eq. 3) between the \u201ctag and probe\u201d\nand MC-Truth methods is shown in the bottom two plots. The number of Z \u2192ee events used corresponds\nto 100 pb\u22121. Errors are statistical only. A signal sample of Z0 \u2192ee Monte Carlo simulation without\nbackground was used to obtain these results.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n645\n\n7\nSummary\nAn electron and photon trigger baseline for LHC commissioning and the \ufb01rst physics run have been\npresented. Many studies and tests have been summarized, without \ufb01nding any problems that could com-\npromise the successful start-up of ATLAS data-taking. Electron and photon trigger performance have\nbeen studied in detail in a wide energy range using single electron and single photon simulated samples.\nTrigger ef\ufb01ciency dependencies on transverse energy (ET) and pseudo-rapidity (\u03b7) have been observed\nand studies are ongoing to explore the possibility to minimize them. Trigger ef\ufb01ciencies for the e/\u03b3 selec-\ntion have been evaluated for simulations of different physics samples such as H \u2192\u03b3\u03b3, Z \u2192ee, W \u2192e\u03bd\nand some exotic channels. The electron and photon trigger menus for these selections have proven to\nbe ef\ufb01cient above the threshold of the corresponding transverse energy cut with respect to of\ufb02ine recon-\nstruction. The corresponding background rates have been estimated to be within the allocated bandwidth.\nIt should be noted that due to current uncertainty in the cross-sections used for background estimations,\nrates could vary signi\ufb01cantly. This could require the use of tighter selections with corresponding loss\nof signal ef\ufb01ciency. Some examples of backup signatures for such situations have been shown. Trig-\nger robustness studies have been started, and are currently being extended. Trigger reconstruction and\nselection ef\ufb01ciencies do not show signi\ufb01cant drops with respect to of\ufb02ine reconstructed electrons and\nphotons. A method of trigger ef\ufb01ciency determination from data using Z \u2192ee decays has been studied\nin depth. This results compare well to trigger ef\ufb01ciency computed with respect to Monte Carlo truth.\nThe extension of this method to other channels and samples are being developed.\nReferences\n[1] J.Garvey et al., Use of a FPGA to identify electromagnetic clusters and isolated hadrons in the\nATLAS Level-1 Calorimeter trigger, Nuclear Instruments and Methods A,vol. 512 no. 3 (2003).\n[2] T. Sjostrand, S. Mrenna and P. Skands, JHEP 0605 (2006) 026.\n[3] S. Agostinelli et al., Nucl. Instrum. Methods Phys. Res. A 506 (2003) 250.\n[4] ATLAS Collaboration, Data Preparation for the High-Level Trigger Calorimeter Algorithms, this\nvolume.\n[5] ATLAS Collaboration, HLT Track Reconstruction Performance, this volume.\n[6] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[7] ATLAS Collaboration, Reconstruction of Low-Mass Electron Pairs, this volume.\n[8] ATLAS Collaboration, Prospects for the Discovery of the Standard Model Higgs Boson Using the\nH\u2192\u03b3\u03b3 Decay, this volume.\n[9] ATLAS Collaboration, Dilepton Resonances at High Mass, this volume.\n[10] ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\nTRIGGER \u2013 PHYSICS PERFORMANCE STUDIES AND STRATEGY OF THE ELECTRON AND . . .\n646\n\nPerformance of the Muon Trigger Slice with Simulated Data\nAbstract\nThe overall functionality and performance of the muon trigger system with re-\nspect to data produced as part of the ATLAS Computing System Commission-\ning effort is described. The physics performance in terms of trigger ef\ufb01ciency\nand accepted rates is studied for the muon inclusive signatures for different\nluminosity scenarios. Dedicated studies on physics samples with single and\ndouble muon \ufb01nal states are also performed in order to evaluate the trigger ef-\n\ufb01ciencies on realistic data and background rejection capabilities. Methods to\nevaluate muon trigger ef\ufb01ciencies from real data are discussed. Furthermore,\nstrategies to use the ATLAS calorimeters to tag and select isolated muons are\npresented.\n1\nIntroduction\nTriggering and identifying muons will be crucial for many LHC physics analyses. In accordance with\nthe ATLAS general trigger scheme, the muon trigger system has three distinct levels: L1, L2, and the\nEvent Filter (EF). The paper discusses the software tools used for muon trigger reconstruction and the\nalgorithm selection strategy and trigger con\ufb01guration. Next, the resolution and selection ef\ufb01ciencies of\nthe various muon triggers are presented, followed by a discussion of the trigger rates for various lumi-\nnosities. Subsequently, the rejection of background from in-\ufb02ight meson decays and selection of isolated\nmuons using calorimeter information is discussed. Finally, the trigger performance on the di\u2212muon \ufb01-\nnal states Z \u2192\u00b5\u00b5and Z\u2032 \u2192\u00b5\u00b5 is presented along with a description of plans to determine the trigger\nef\ufb01ciency from collider data.\n2\nDetector simulation and data samples\nThe samples used in this paper were produced using a full GEANT4 based simulation of the ATLAS de-\ntector. The trigger simulation options included both standard and B-physics trigger simulation con\ufb01gura-\ntions, which correspond to the standard and the low trigger thresholds (see Section 3). The deterioration\nof ef\ufb01ciency due to the geometrical acceptance and the limited size of coincidence window are taken into\naccount in the L1 simulation and trigger logic emulator.\nLarge samples of single prompt muons, simulated uniformly in \u03b7 \u2212\u03c6, with \ufb01xed pT ranging from\n2 GeV to 1 TeV, have been used to study the muon trigger performance. One of the main backgrounds\nfor the muon trigger selection comes from in-\ufb02ight decays of charged kaons and pions. This has been\nevaluated using samples of minimum bias events and single pions, where the mesons are forced to decay\ninside the Inner Detector cavity in order to facilitate the production of a sizable sample of in-\ufb02ight \u03c0/K\ndecays. Muon trigger rates were determined using both single muons and minimum bias events. The\nselection of muons using the Tile Calorimeter has been studied using low pT (4 and 6 GeV) single muons\nand semi-inclusive b quark decays, b\u00afb \u2192\u00b5X. Muon trigger studies on high-pT dimuon \ufb01nal states and\nthe determination of trigger ef\ufb01ciency from data have been performed using Z \u2192\u00b5\u00b5and Z\u2032 \u2192\u00b5\u00b5 as\nsignal processes and B \u2192\u00b5\u00b5, W boson decays, Z \u2192\u03c4\u03c4 and top-pair events as background processes.\n3\nMuon trigger algorithms and con\ufb01guration\nThe L1 muon trigger selects active RoIs, in the event using Resistive Plate Chambers (RPC) [1] in\nthe barrel (|\u03b7| < 1.05) and Thin Gap Chambers (TGC) [1] in the endcaps (1.05 < |\u03b7| < 2.4). The\n647\n\ntrigger algorithms look for hit coincidences within different RPC or TGC detector layers inside the\nprogrammed geometrical windows which de\ufb01ne the transverse momentum region. A coincidence is\nrequired in both \u03b7 and \u03c6 projections. The information about muon candidates in both the barrel and the\nend-cap is transmitted to the Muon to Central Trigger Processor Interface (MuCTPI) [1], which calculates\nthe number of L1 muon candidates for six different pT thresholds and takes overlaps between the trigger\nsectors into account by using look-up-tables (LUT). There are several L1 signatures each corresponding\nto a different pT threshold:\n\u2022 mu0, mu5, mu6, mu8, mu10 for the low pT selection;\n\u2022 mu11, mu20, mu40 for the high pT selection.\nThe integer numbers after the \u201cmu\u201d symbolize the required pT threshold. L1 also provides the coordi-\nnates in \u03b7 and \u03c6 of the selected RoIs. The mu0 threshold represents a L1 con\ufb01guration with completely\nopen coincidence windows; it is also called the \u201cCosmic\u201d threshold as it can be used to trigger on cosmic\nrays during the detector commissioning phase and between the LHC \ufb01lls. Similar thresholds, labeled\nwith \u201cmuXX\u201d, have been de\ufb01ned for L2 and EF.\nThe muon HLT runs L2 and EF algorithms. It starts from the RoI delivered by the L1 trigger and\napplies trigger decisions in a series of steps, each re\ufb01ning the existing measurement by acquiring ad-\nditional information from the ATLAS detectors. A list of physics signatures, implemented in the event\nreconstruction and selection algorithms, are used to build signature and sequence tables for all HLT steps.\nThis stepwise and seeded processing of events is controlled by the trigger steering. The reconstruction\nprogresses by calling feature extraction algorithms. These typically request detector data from within the\nRoI and attempt to identify muon features. Subsequently, a hypothesis algorithm determines whether the\nidenti\ufb01ed feature meets the criteria necessary to continue. The decision to reject the event or continue is\nbased on the validity of signatures, taking into account prescale and pass-through factors. Thus, events\ncan be rejected after an intermediate step if no signatures remain viable.\nThe main algorithm of the muon L2 system, muFast, runs on full granularity data within the RoI\nde\ufb01ned by L1. An optimized strategy is used to avoid heavy calculations and access to external services\nto reduce the execution time of the algorithm. After pattern recognition driven by the trigger hits which\nselects Monitored Drift Tubes (MDT) regions crossed by the muon track, a track \ufb01t is performed using\nMDT drift time precision measurements. The pTevaluation is performed using LUT. Reconstructed\ntracks in the Inner Detector can be combined with the tracks found by muFast by a fast track combination\nalgorithm called muComb.\nThe L2 algorithm (muIso) is used to discriminate between isolated and non-isolated muon candidates\nby examining energy depositions in the electromagnetic and hadronic calorimeters. The algorithm is\nseeded by muons selected by muFast or muComb and decodes LAr and Tile Calorimeter quantities in\ncones centered around the muon direction. For the muon selection two different concentric cones are\nde\ufb01ned: an internal cone chosen to contain the energy deposit deposited by the muon itself, and an\nexternal cone, containing energy only from detector noise, pile-up and jet particles.\nA strategy for tagging muons at L2 in the TileCal is implemented in the TileMuId algorithm. It can\nprovide additional redundancy and robustness to the muon trigger, as well as enhance the ef\ufb01ciency in\nthe low pT region. The search starts from the outermost calorimeter layer, which contains the cleanest\nsignals, and once a deposited energy is compatible with a muon, the algorithm checks the energy de-\nposition in the neighboring cells for the internal layers. Candidates are considered tagged muons when\nmuon compatible cells are found following a \u03b7-projective pattern in all the three TileCal layers. There\nare two different variants of this algorithm : one (TrigTileLookForMuAlg) is fully executed on the L2\nProcessing Unit (L2PU) while the other (TrigTileRODMuAlg) has a core part executed on the Readout\nDriver (ROD).\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n648\n\nThe EF accesses the full event with its full granularity. Given the larger admissible latency, it is pos-\nsible to adapt algorithms developed for the off-line reconstruction to the on-line framework, an approach\nthat minimises algorithm development. The EF processing starts by reconstructing tracks in the Muon\nSpectrometer around the muons found by L2 and is done by three instances of the EF algorithm; the \ufb01rst\ninstance reconstructs tracks inside the Muon Spectrometer, starting with a search for regions of activity\nwithin the detector, and subsequently performing pattern recognition and full track \ufb01tting. The second\nstep extrapolates muon tracks to their production point. Finally the information from the \ufb01rst two steps\nis combined with the reconstructed tracks from the Inner Detector.\nThe hypothesis algorithms de\ufb01ne a set of HLT trigger thresholds by applying cuts on the pT of the\nmuon candidate. The muon trigger ef\ufb01ciency is de\ufb01ned as\nThe number of events with a triggered muon\nThe number of events with a muon\n(1)\nThe effective trigger thresholds are obtained in such a way that at the nominal threshold value the ef-\n\ufb01ciency is 90% of the corresponding ef\ufb01ciency without cuts. For this reason effective thresholds are\nslightly lower than nominal thresholds.\n4\nL1 performance\n4.1\nBarrel muon trigger performance\nAs mentioned earlier, studies of muon trigger performance were conducted using simulated samples\nof single muon events generated over a large pT and angular range. L1 selection algorithms show an\nef\ufb01ciency greater than 99% for muons with pT above threshold. The overall acceptance (82% low-pT,\n78% high-pT) is due exclusively to geometrical regions of the Muon Spectrometer not covered by the\nRPC. Figure 1 shows the inef\ufb01cient regions corresponding to the magnet support structures (\u22122.3 \u2264\n\u03c6 \u2264\u22121.7 and \u22121.4 \u2264\u03c6 \u22640.9) and the spectrometer central crack at \u03b7 \u223c0, not covered by RPCs. The\noverall loss in geometrical acceptance due to the \u03b7 = 0 crack is approximately 7% while the loss due to\nthe support structure is about 5%. Moreover smaller inef\ufb01ciency patterns are clearly visible which are\ndue to magnetic ribs in small trigger sectors. The geometrical acceptance effects are visible also in Fig. 2\nwhere the L1 ef\ufb01ciency above threshold is shown with respect to \u03b7 and \u03c6.\n\u03b7\n-1\n-0.5\n0\n0 5\n1\n \n\u03d5\n-3\n-2\n-1\n0\n1\n2\n3\nFigure 1: L1 geometrical acceptance in the \u03b7-\u03c6 plane.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n649\n\n\u03b7\n-1\n-0.5\n0\n0.5\n1\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n \n\u03d5\n0\n1\n2\n3\n4\n5\n6\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nFigure 2: \u03b7 and \u03c6 dependence of barrel trigger ef\ufb01ciency for single muons with a pT=75 GeV.\nThreshold\nPlateau Ef\ufb01ciency\nEffective Threshold (GeV)\nSharpness(GeV)\nmu6\n0.82\n5.3\n2.2\nmu8\n0.82\n6.1\n1.9\nmu10\n0.82\n6.7\n2.2\nmu11\n0.78\n10.9\n3.7\nmu20\n0.78\n15.3\n7.1\nmu40\n0.78\n27.8\n19.7\nTable 1: Plateau ef\ufb01ciencies, effective thresholds, and sharpness for L1 signatures. Sharpness is de\ufb01ned\nas the difference of pT corresponding to 90% and 10% of the plateau ef\ufb01ciency.\nFigure 3 shows turn-on curves for low-pT and high-pT thresholds; the ef\ufb01ciencies at plateau and\neffective thresholds are summarized in Table 1.\nMuon tracks are de\ufb02ected in the r \u2212\u03b7 plane under the action of the toroidal magnetic \ufb01eld. Their\ntrajectories are symmetrical under charge exchange and re\ufb02ection with respect to the plane z = 0, but\nthe layout of the Muon Spectrometer is not. This asymmetry, could, in principle, produce a bias in the\ntrigger ef\ufb01ciency calculation. From the single muon data sample, it was found that for muons with pT\ngreater than the L1 threshold the asymmetry in the ef\ufb01ciency is quite small (< 1%).\nParticular attention was devoted to the study of muons with 2 < pT < 3.5 GeV in the barrel region\n(|\u03b7| <1.05). Given the large inclusive cross-section with muons in the \ufb01nal state, this very low-pT region\nrepresents the most signi\ufb01cant contribution to the total expected muon rate. Table 2 shows the fraction\nof these events that produce hits in the RPCs and the L1 barrel ef\ufb01ciency for passing the mu6 trigger.\nMost of the low pTmuons that pass L1 have |\u03b7| \u22431.\nMuon pT (GeV)\nPercentage of events with hits in RPC\nL1 Ef\ufb01ciency\n2\n0.15%\n(1.4\u00b10.1)\u00b710\u22123\n2.5\n0.35%\n(3.4\u00b10.1)\u00b710\u22123\n3\n0.48%\n(4.8\u00b10.1)\u00b710\u22123\n3.5\n3.36%\n(33.4\u00b10.3)\u00b710\u22123\nTable 2: L1 RPC ef\ufb01ciency for very low-pT single muon events with |\u03b7| <1.05.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n650\n\n(GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nThreshold 1 = 6 GeV\nThreshold 2 = 8 GeV\nThreshold 3 = 10 GeV\nATLAS\n(GeV)\nT\np\n0\n10\n20\n30\n40\n50\n60\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nThreshold 4 = 11 GeV\nThreshold 5 = 20 GeV\nThreshold 6 = 40 GeV\nATLAS\nFigure 3: L1 barrel ef\ufb01ciency as a function of pT for low-pt (left) and high-pt (right) thresholds.\nVery low-pT muons produced in the acceptance of the TGC (|\u03b7| >1.05) sometimes give hits in the\nRPC (|\u03b7| <1.05) because they are strongly de\ufb02ected by the magnetic \ufb01eld. The fraction of muons with\n|\u03b7| >1.05 that give RPC hits ranges from 46% at pT = 2 GeV to about 10% at 3.5 GeV, and is negligible\nabove 4 GeV. The overall ef\ufb01ciency for such muons to pass the mu6 trigger is about 10\u22123.\nFigure 4 shows L1 end-cap ef\ufb01ciency curves for low pT (left) and high pT thresholds (right). Ef-\n\ufb01ciencies at the threshold and plateau are summarized in Table 3. The ef\ufb01ciency of mu6 at threshold\nis 77%, relatively lower than other cases. This is due to the limited window-size of the three-station\ncoincidence for muons having pT of 6 GeV. The \u03b7 dependence of the mu6 and mu20 ef\ufb01ciency are\n (GeV)\nT\np\nATLAS\n0\n5\n10\n15\n20\nEfficiency\n0\n0.5\n1\n trigger efficiency\nT\nLow-p\nMU6 \nMU8 \nMU10\n (GeV)\nT\np\n0\n20\n40\n60\nEfficiency\n0\n0.5\n1\n trigger efficiency\nT\nHi-p\nMU11\nMU20\nMU40\nATLAS\nFigure 4: The end-cap trigger ef\ufb01ciency curves for each pT threshold. The left plot shows the low-pT\nthresholds of 6, 8, and 10 GeV and the right plot shows the high-pT thresholds of 11, 20 and 40 GeV.\npT threshold (GeV)\n6\n8\n10\n11\n20\n40\nThreshold\n77%\n84%\n88%\n88%\n92%\n90%\nPlateau\n95%\n95%\n95%\n95%\n94%\n93%\nTable 3: Trigger ef\ufb01ciencies at threshold and plateau for various muon pT thresholds.\nshown in Fig. 5 (at threshold) and Fig. 6 (at plateau) with respect to the sign of charge of muon q \u00d7 \u03b7.\nBecause the two muon end-cap stations are made as mirror images, \u00b5 \u2212(+) with \u03b7 > (<) 0 behaves the\nsame as \u00b5+(\u2212) with \u03b7 < (>) 0. The difference of ef\ufb01ciency between the two signs of q \u00d7 \u03b7 is large\nat the geometrical boundary for muons near the pT = 6 threshold as shown in Fig. 5. One more point\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n651\n\nworth noting is the dip at \u03b7=2 for the mu6 signature. Muons in the dip region pass through chambers\nwhich belong to different trigger sectors, consequently the requirement of a three-station coincidence is\nnot satis\ufb01ed and trigger ef\ufb01ciency is reduced. Figure 7 shows the \u03c6 dependence of mu6 (left) and mu20\n(right) trigger ef\ufb01ciencies at the plateau and at threshold. The effect of octant symmetry of the magnetic\n\ufb01eld is seen in the plot of the mu6 ef\ufb01ciency for threshold muons. For the mu6 signature at plateau and\nfor the mu20 signature, this effect is not observed, resulting in an approximately uniform ef\ufb01ciency.\n\u03b7\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.5\n1\nMU6 (threshold)\nZ*Q>0\nZ*Q<0\nATLAS\n\u03b7\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.5\n1\nMU20 (threshold)\nZ*Q>0\nZ*Q<0\nATLAS\nFigure 5: \u03b7 dependence of end-cap trigger ef\ufb01ciency for mu6 (left) and mu20 (right). The solid circles\nrepresent q\u00d7\u03b7 > 0, the open circles represent q\u00d7\u03b7 < 0.\n\u03b7\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.5\n1\nMU6 (plateau)\nZ*Q>0\nZ*Q<0\nATLAS\n \n\u03b7\n1\n1.5\n2\n2 5\nEfficiency\n0\n0.5\n1\nMU20 (plateau)\nZ*Q>0\nZ*Q<0\nATLAS\nFigure 6: \u03b7 dependency of end-cap trigger ef\ufb01ciency at plateau for mu6 (left) and mu20 (right). The\nsolid circles represent q\u00d7\u03b7 > 0, the open circles represent q\u00d7\u03b7 < 0.\n5\nPerformance of L2 muon algorithms\nAs described in Section 2, algorithm performance is evaluated on samples of single muons generated with\ndifferent transverse momenta. The resolution of the inverse of the measured momentum with respect to\nthe generated transverse momentum is studied. Due to the non-uniform magnetic \ufb01eld in the Muon\nSpectrometer it is divided into four regions according to the pseudorapidity of the muon candidate: the\nBarrel region with |\u03b7| < 1.05, and three end-cap regions with 1.05 < |\u03b7| < 1.5, 1.5 < |\u03b7| < 2.0, and\n2.0 < |\u03b7| < 2.4.\nFor the Muon Spectrometer standalone reconstruction (muFast), the resolution of inverse pT as a\nfunction of the muon transverse momentum is shown in Fig. 8(left). The degradation in the resolution\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n652\n\n\u03c6\n-2\n0\n2\nEfficiency\n0.4\n0.6\n0.8\n1\nATLAS\n\u03c6\n-2\n0\n2\nEfficiency\n0.4\n0.6\n0.8\n1\nATLAS\nFigure 7: \u03c6 dependence of end-cap trigger ef\ufb01ciency for mu6 (left) and mu20 (right) for muons with\npT = 45 GeV. The open circles show the ef\ufb01ciency at threshold and the solid circles show the ef\ufb01ciency\nat plateau.\nwith respect to previous results [2] is caused by the realistic geometry misalignment introduced in the\nmuon simulation. Resolution as function of \u03b7 and \u03c6Loc1 is shown in Fig. 8(right). The degradation of\nthe resolution in the endcap regions is evident. The muFast ef\ufb01ciency with respect to L1 selection as a\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n)\nT\n(1/P\n\u03c3\n0\n0.05\n0.1\n0.15\n0 2\n0.25\nATLAS\n|<1.0\n\u03b7|\n|<1.5\n\u03b7\n1 0<|\n|<2.0\n\u03b7\n1 5<|\n|<2.4\n\u03b7\n2 0<|\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nLocal\n\u03c6\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.1\n0 2\n0 3\n0.4\n0 5\nATLAS\nFigure 8: 1/pT resolution (Muon Spectrometer StandAlone) as a function of pT (left) and \u03b7 \u2212\u03c6Loc (right).\nfunction of muon momentum are shown for mu4, mu6, and mu20 selections in Fig. 9. The low rejection\nat small momentum (2.5 < pT < 4.5 GeV), in particular in the barrel region, is caused by candidate\ntracks not pointing to the nominal interaction vertex due to large scattering angles.\nEf\ufb01ciencies of the MS standalone reconstruction (muFast) (mu6 trigger selection) with respect to L1\nselection as a function of \u03b7 and \u03c6Loc for muons with PT = 6 GeV are shown in Fig. 10.\nThe combination of a Muon Spectrometer standalone muon candidate with an Inner Detector track\nfound by the L2 tracking algorithms is performed by muComb. For muons with pT < 50 GeV the Inner\nDetector measurement has a better resolution than the Muon Spectrometer standalone measurement.\nTherefore, the combination of the two measurements gives better resolutions in the low-pT range. Figure\n11 shows the 1/pT resolution as a function of pT and also the resolution as function of \u03b7 and \u03c6Loc. The\nmuComb ef\ufb01ciency with respect to muFast as a function of pT for mu4, mu6, and mu20 is shown in\nFig. 12. The problem of low rejection for low-pT muons is partially solved when the Muon Spectrometer\ncandidates are combined with Inner Detector tracks.\n1\u03c6Loc is the azimuthal angle folded up in [0,\u03c0/16] such to cover half of an odd MS sector ([0,\u03c0/32]) and half of an even\nMS sector [\u03c0/32,\u03c0/16].\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n653\n\n (GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nmu 4\nmu 6\nmu 20\nATLAS\n|<1.05\n\u03b7\n|\n (GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<1.5\n\u03b7\n1.05<|\n (GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<2.0\n\u03b7\n1.5<|\n (GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<2.4\n\u03b7\n2.0<|\nFigure 9: muFast ef\ufb01ciency with respect to L1 selection for the mu4, mu6, and mu20 triggers for different\n\u03b7 regions.\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0.2\n0.4\n0.6\n0.8\n1\n = 6 GeV\nT\nP\nATLAS\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0.2\n0.4\n0.6\n0.8\n1\n = 6 GeV\nT\nP\nATLAS\nFigure 10: Ef\ufb01ciency of muFast as a function of \u03b7 (right) and \u03c6Loc (left) for muons with pT = 6 GeV.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n654\n\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n)\nT\n(1/P\n\u03c3\n0 02\n0 04\n0 06\n0 08\n0.1\nATLAS\n|<1.0\n\u03b7|\n|<1.5\n\u03b7\n1.0<|\n|<2.0\n\u03b7\n1.5<|\n|<2.4\n\u03b7\n2.0<|\n\u03b7\n-2 5\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n2 5\nLocal\n\u03c6\n0\n0 05\n0.1\n0.15\n0 2\n0 25\n0 3\n0 35\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\nATLAS\nFigure 11: The muon combined 1/pT resolution as a function of pT (left) and as a function of \u03b7 \u2212\u03c6Loc\n(right).\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nmu 4\nmu 6\nmu 20\nATLAS\n|<1.05\n\u03b7\n|\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<1.5\n\u03b7\n1.05<|\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<2.0\n\u03b7\n1.5<|\n(GeV)\nT\nP\n0\n10\n20\n30\n40\n50\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEfficiency\nATLAS\n|<2.4\n\u03b7\n2.0<|\nFigure 12: The muComb algorithm ef\ufb01ciency with respect to mu4, mu6, and mu20 triggers for the\ndifferent \u03b7 regions.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n655\n\nEf\ufb01ciencies of muComb (mu6 trigger selection) with respect to muFast selection as a function of \u03b7\nand \u03c6Loc for muons with pT = 6 GeV are shown in Fig. 13.\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0 2\n0.4\n0.6\n0 8\n1\n = 6 GeV\nT\nP\nATLAS\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0.2\n0.4\n0.6\n0.8\n1\n = 6 GeV\nT\nP\nATLAS\nFigure 13: Ef\ufb01ciency of muComb as a function of \u03b7 (right) and \u03c6Loc (left) for single muons with pT = 6\nGeV.\n6\nEvent \ufb01lter performance\nThe full reconstruction in the Muon EF has been executed on the simulated samples described in Sec-\ntion 2. The reconstruction in the Muon Spectrometer is carried out by the MOORE algorithm, the\nextrapolation to the vertex of the muon track found in the Muon Spectrometer is performed by the MuId\nstandalone algorithm and the combination of the tracks found in the Muon Spectrometer and in the Inner\nDetector by the MuId Combined algorithm.\nEf\ufb01ciency for single muon events is de\ufb01ned as the ratio of events with a reconstructed track at the\nEF after the execution of each reconstruction step to all events which have passed L1 and L2. The\nef\ufb01ciency with respect to L2 as a function of muon pT is shown in Fig. 14 for all three EF algorithms.\nThe ef\ufb01ciency is de\ufb01ned on an event basis, and counts only once events having L2 muon-feature or EF\n (GeV) \nT\nMuon p\n3 4 5 6\n10\n20 30\n2\n10\n2\n10\n\u00d7\n2\n3\n10\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMOORE\nMuId Standalone\nMuId Combined\nATLAS\nFigure 14: Ef\ufb01ciency as a function of muon pT for MOORE, MuId Standalone and MuId Combined.\ntrack multiplicity greater than 1. According to this de\ufb01nition, the ef\ufb01ciency to trigger an event with more\nthan one muon is expected to be higher with respect to what is estimated here.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n656\n\nThe ef\ufb01ciencies are lower for 3 < pT < 6 due to multiple scattering and energy loss \ufb02uctuation\neffects. Moreover, in the case of MuId Combined, at very high pT the increasing probability of muon\nshowering is responsible for a small loss in ef\ufb01ciency. The ef\ufb01ciencies as a function of \u03b7 and \u03c6 show\na structure, especially at low momentum, explainable with some residual dependence in \u03b7 and \u03c6 on the\nMuon Spectrometer geometrical acceptance and on the magnetic \ufb01eld inhomogeneities which affect less\nprevious levels. It can be seen in Fig. 15 where the ef\ufb01ciency is shown for 6 GeV muons. In Fig. 16\n\u03b7\n-2\n-1\n0\n1\n2\n Efficiency\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\n Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nFigure 15: Ef\ufb01ciency of MuId Combined as a function of \u03b7 (left) and of \u03c6 (right) for 6 GeV muons.\nthe MuId combined ef\ufb01ciency with respect to L2 for different thresholds is shown on the left, while the\noverall trigger ef\ufb01ciency (L1 + L2 + EF) with respect to the generated muons is shown on the right. All\nef\ufb01ciency values are averaged over the whole |\u03b7| <2.4 range.\n (GeV/c)\n T\n Muon p\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nmu4\nmu5\nmu6\nmu8\nmu10\nmu11\nmu15\nmu20\nmu40\nATLAS\n (GeV)\nT\nMuon p\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEfficiency\n0\n0 2\n0.4\n0 6\n0 8\n1\nmu4\nmu6\nmu10\nmu20\nmu40\nATLAS\nFigure 16: MuId combined ef\ufb01ciencies for various pT thresholds with respect to L2 (Left) and with\nrespect to generated truth muons (Right).\nIn Fig. 17, the 1/pT resolution is shown as a function of muon pT for all EF algorithms. For a muon\nwith pT below 50 GeV the Inner Detector dominates the reconstruction precision so the combination of\nmeasurements greatly improves the resolutions. For a muon with pT above 100 GeV, the Muon System\ndominates the measurement of the muon combined transverse momentum. 1/pt resolution as a function\nof \u03b7 is shown in Fig. 18 for 20 GeV muons. The worsening of the resolution in the region 1.0 < |\u03b7| <\n1.5 can be attributed to the highly inhomogeneous magnetic \ufb01eld in the transition regions of the Muon\nSpectrometer. This effect is recovered by means of the combined reconstruction which exploits the Inner\nDetector performance.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n657\n\n (GeV)\nT\np\n2\n3\n4 5 6 7 8 10\n20\n30 40\n2\n10\n2\n10\n\u00d7\n2\n resolution\nT\n1/p\n0.01\n0.1\nMOORE\nMuId standalone\nMuId combined\nATLAS\nFigure 17: 1/pT resolution as a function of pT for MOORE, MuId Standalone and MuId Combined.\n\u03b7\n-2\n-1\n0\n1\n2\n resolution\nT\n1/p\n0.02\n0.04\n0.06\n0.08\n0.1\nMOORE\nMuId Standalone\nMuId Combined\nATLAS\nATLAS\nFigure 18: 1/pT resolution for MuId Combined as a function of \u03b7 for muons with pT = 20 GeV.\n7\nMuon trigger rates\nThe trigger rates for single muon event originating from all the physical processes expected in ATLAS\nwere obtained using the EF MuiD combined algorithm (the events must of course also pass the L1 and\nL2 muon algorithms). Various luminosity scenarios expected during LHC operation (from L = 1031\ncm\u22122 s\u22121 to 1034 cm\u22122 s\u22121) were considered. Trigger rates were typically computed by convolving,\nover a given pT range, the estimated ef\ufb01ciencies with the cross-sections of processes representing the\nmain muon sources at LHC. For the i-th process with cross-section \u03c3i, the rate is\nRi = L\nZ d\u03c3i\ndpT\n\u03b5(pT)dpT\n(2)\nwhere L is the instantaneous luminosity and \u03b5(pT) is the muon trigger ef\ufb01ciency for a given pT value.\nIn order to take into account the \u03b7 dependence, separate estimates for different \u03b7 regions have been\nconsidered. An 0.5 GeV step has been applied in the numerical integration. The inclusive muon cross-\nsections at the LHC for b \u2192\u00b5 and c \u2192\u00b5 decays have been parameterized by using PYTHIA 6.403 [3]\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n658\n\nL1 muon trigger rates\nL = 1031 cm\u22122 s\u22121\nL = 1033 cm\u22122 s\u22121\nL = 1034 cm\u22122 s\u22121\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\n\u201cCosmic\u201d\n6 GeV\n20 GeV\n\u03c0/K\n454\n199\n8600\n5300\n1100\n5200\nbeauty\n85\n74\n4400\n5100\n2500\n3300\ncharm\n124\n104\n6100\n6900\n2800\n4400\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.3\n0.5\nW\n<0.1\n<0.1\n3.0\n4.4\n26\n41\nTOTAL\n663\n377\n19100\n17300\n6400\n12900\n5 GeV\n8 GeV\n40 GeV\n\u03c0/K\n162\n81\n2200\n3800\n470\n1900\nbeauty\n54\n53\n2900\n4000\n1100\n1300\ncharm\n76\n73\n3800\n4700\n1200\n1400\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.3\n0.3\nW\n<0.1\n<0.1\n4\n4.5\n23\n33\nTOTAL\n292\n207\n8900\n12500\n2800\n4600\nTable 4: Single muon trigger rates at L1, for various low and high pT thresholds, at L = 1031 cm\u22122 s\u22121,\nL = 1033 cm\u22122 s\u22121 and L = 1034 cm\u22122 s\u22121.\nL2 muon standalone trigger rates\nL = 1031 cm\u22122 s\u22121\nL = 1033 cm\u22122 s\u22121\nL = 1034 cm\u22122 s\u22121\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\n4 GeV\n6 GeV\n20 GeV\n\u03c0/K\n190\n140\n4300\n3700\n410\n1800\nbeauty\n50\n67\n3000\n3900\n540\n1500\ncharm\n70\n94\n4000\n5200\n520\n1700\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.2\n0.4\nW\n<0.1\n<0.1\n3\n4\n24\n38\nTOTAL\n310\n301\n11300\n12800\n1494\n5038\n5 GeV\n8 GeV\n40 GeV\n\u03c0/K\n82\n120\n840\n1500\n200\n690\nbeauty\n37\n59\n1000\n2200\n87\n280\ncharm\n49\n81\n1300\n2900\n83\n290\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.1\n0.2\nW\n<0.1\n<0.1\n3\n4\n17\n23\nTOTAL\n168\n260\n3143\n6604\n387\n1283\nTable 5: Single muon trigger rates at L2 muon standalone, for various low and high pT thresholds, at\nL = 1031 cm\u22122 s\u22121, 1033 cm\u22122 s\u22121 and 1034 cm\u22122 s\u22121. The large expected rate in particularly in\nthe endcap, caused by the relatively low rejection of low pT muons, can be reduced by improving the\nselection algorithm.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n659\n\nL2 muon combined trigger rates\nL = 1031 cm\u22122 s\u22121\nL = 1033 cm\u22122 s\u22121\nL = 1034 cm\u22122 s\u22121\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\n4 GeV\n6 GeV\n20 GeV\n\u03c0/K\n130\n124\n3500\n2600\n68\n890\nbeauty\n48\n66\n2700\n3400\n320\n830\ncharm\n66\n91\n3800\n4400\n280\n840\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.2\n0.4\nW\n<0.1\n<0.1\n3\n4\n22\n35\nTOTAL\n244\n281\n10000\n11000\n690\n2590\n5 GeV\n8 GeV\n40 GeV\n\u03c0/K\n44\n55\n400\n530\n6\n310\nbeauty\n31\n45\n660\n1100\n31\n92\ncharm\n41\n61\n780\n1300\n26\n99\ntop\n<0.1\n<0.1\n<0.1\n<0.1\n0.1\n0.1\nW\n<0.1\n<0.1\n3\n4\n7\n12\nTOTAL\n116\n161\n1840\n2900\n70\n513\nTable 6: Single muon trigger rates at L2 muon combined, for various low and high pT thresholds, at\nL = 1031 cm\u22122 s\u22121, 1033 cm\u22122 s\u22121, and 1034 cm\u22122 s\u22121.\nEvent Filter muon trigger rates\nL = 1031 cm\u22122 s\u22121\nL = 1033 cm\u22122 s\u22121\nL = 1034 cm\u22122 s\u22121\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\nBarrel (Hz)\nEndcaps (Hz)\n4 GeV\n6 GeV\n20 GeV\n\u03c0/K\n125\n119\n1890\n1230\n46\n40\nbeauty\n44\n56\n1870\n2190\n260\n380\ncharm\n60\n76\n2390\n2780\n220\n330\ntop\n< 0.1\n< 0.1\n< 0.1\n< 0.1\n0.2\n0.3\nW\n< 0.1\n< 0.1\n2.9\n3.9\n21\n31\nTOTAL\n229\n251\n6150\n6200\n550\n780\n5 GeV\n8 GeV\n40 GeV\n\u03c0/K\n36\n25\n290\n260\n0.14\n0.2\nbeauty\n27\n33\n550\n800\n10.5\n16.3\ncharm\n36\n43\n640\n930\n7.1\n11.1\ntop\n< 0.1\n< 0.1\n< 0.1\n< 0.1\n< 0.1\n< 0.1\nW\n< 0.1\n< 0.1\n2.8\n3.8\n3.9\n6.1\nTOTAL\n99\n101\n1480\n1990\n21.7\n33.7\nTable 7: Single muon trigger rates at EF muon combined, for various low and high pT thresholds, at\nL = 1031 cm\u22122 s\u22121, 1033 cm\u22122 s\u22121, and 1034 cm\u22122 s\u22121.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n660\n\n threshold (GeV)\nT\nMuon p\n3\n4\n5\n6\n7 8 9 10\n20\n30\n40\nRate (Hz)\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\nCharm\nBeauty\n/K decays\n\u03c0\nW\nTotal\nATLAS\nFigure 19: Expected EF rates at L = 1031 cm\u22122 s\u22121 for single muon processes as a function of muon\npT threshold integrated over |\u03b7| < 2.4.\nwhich produces conservative estimates since it predicts cross-sections about 2 to 3 times higher than\nprevious descriptions [4]. Top quark and W/Z decays were simulated using PYTHIA 5.7 [5]. Rates of\nmuon in-\ufb02ight decays from \u03c0/K mesons have been computed using the DPMJET Monte Carlo program\n[6].\nTo verify the results obtained with this method and to understand the systematics, an alternative\napproach, relying on event counting, has been applied to the minimum bias events (counting method).\nThe convolution and counting methods give EF \ufb01nal rates which are in good agreement, within statistical\nerrors due to the limited size of the minimum bias sample, starting from pT threshold of 6 GeV. The\nvalues obtained with the counting method for lower pT thresholds (4 and 5 GeV) are a factor of two to\nfour less for muons from \u03c0/K decays with respect to the convolution (provided by DPMJET) of Eq. 2.\nThe rates obtained for some low and high pT thresholds in the barrel and in the endcaps after L1, L2\nmuFast, L2 muComb and EF selection are shown in Tables 4, 5, 6 and 7.\nIn Fig. 19 the total (barrel+endcaps) EF rates at L = 1031 cm\u22122 s\u22121 are shown as a function of the pT\nthreshold. In this \ufb01gure, to keep uniformity among the rate results, mostly provided by PYTHIA 6.403,\nit has been chosen to report for the 4 and 5 GeV thresholds the EF rates obtained with the counting\nprocedure.\n7.1\nFake dimuon trigger rate\nA single muon can be detected in multiple muon trigger sectors, causing such events to erroneously\nsatisfy dimuon triggers. Such fake triggers can be suppressed by the overlap handling implemented in\nthe MuCTPI . For the single muon samples used in the analysis, the fake dimuon trigger probability is\nde\ufb01ned as\nPfake = Number of events with more than one muon triggered\nNumber of events with a triggered muon\n(3)\nFour sources of fake double-counts have been considered :\n\u2022 Barrel-Barrel double counts (BB): When a single muon is detected by two overlapping RPC sec-\ntors.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n661\n\n\u2022 Barrel-Endcap double counts (BE): When a single muon is detected by an overlapping RPC-TGC\nsector pair.\n\u2022 Endcap-Endcap double counts (EE): When a single muon is detected by two overlapping \u201cEndcap\u201d\nTGC sectors.\n\u2022 Forward-Forward double counts (FF): When a single muon is detected by two overlapping \u201cFor-\nward\u201d TGC sectors.\nThe probabilities that a single muon would cause any of these fake double counts have been calcu-\nlated separately. The effect of the MuCTPI overlap handling can be seen in Fig. 20, where the left plot\nshows the BE fake dimuon trigger probabilities for the 6 pT thresholds in the 2 to 50 GeV range with-\nout using the overlap handling, while the right plot shows the probabilities after applying the MuCTPI\noverlap handling.\n (GeV) \nT\np\n0\n10\n20\n30\n40\n50\nFake BE double-count prob. (%)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\na)\nL1_2MU6\nL1_2MU8\nL1_2MU10\nL1_2MU11\nL1_2MU20\nL1_2MU40\n (GeV) \nT\np\n0\n10\n20\n30\n40\n50\nFake BE double-count prob. (%)\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nL1_2MU6\nL1_2MU8\nL1_2MU10\nL1_2MU11\nL1_2MU20\nL1_2MU40\nb)\nATLAS\nATLAS\nFigure 20: Barrel-Endcap fake dimuon trigger probabilities without (a) and with (b) using the\noverlap handling of the MuCTPI.\nThe probabilities for 6 and 20 GeV single muons to produce a fake dimuon trigger if they caused a\nsingle-muon trigger, for all available L1 muon thresholds, can be seen in Table 8.\nThe fake probabilities can be used to calculate the single-muon trigger rates according to\nRfake = L\npin f\nT\nZ\npcuto f f\nT\n\u03c3p(pT)\u03b5(pT)Pfake(pT)dpT\n(4)\nwhere L is the instantaneous luminosity of the accelerator, \u03c3p is the inclusive muon production cross-\nsection at LHC and \u03b5 is the L1 trigger ef\ufb01ciency. The fake dimuon trigger rates are presented in Table 9.\n8\nRejection of muons from \u03c0/K decays\nDespite the large theoretical uncertainties on the rates of the muon production processes at low transverse\nmomentum, it is clear that in \ufb02ight decays of pions and kaons are a signi\ufb01cant source of single muons\nand, therefore, a strategy must be developed to reject these events in the trigger. Rejection of muons from\n\u03c0 and K decays at the EF is described below. A study describing rejection at L2 can be found in [7].\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n662\n\nTrigger item\npT\u02dc[GeV]\nBB prob. [%]\nBE prob. [%]\nEE prob. [%]\nFF prob. [%]\n2mu4\n6.0\n1.56 \u00b1 0.07\n1.39 \u00b1 0.08\n1.00 \u00b1 0.07\n0.81 \u00b1 0.06\n20.0\n1.43 \u00b1 0.06\n0.13 \u00b1 0.02\n0.49 \u00b1 0.05\n0.55 \u00b1 0.05\n2mu5\n6.0\n1.14 \u00b1 0.06\n1.17 \u00b1 0.07\n0.40 \u00b1 0.05\n0.56 \u00b1 0.06\n20.0\n1.43 \u00b1 0.06\n0.13 \u00b1 0.02\n0.49 \u00b1 0.05\n0.55 \u00b1 0.05\n2mu6\n6.0\n1.11 \u00b1 0.05\n0.97 \u00b1 0.06\n0.39 \u00b1 0.04\n0.55 \u00b1 0.05\n20.0\n1.43 \u00b1 0.06\n0.13 \u00b1 0.02\n0.49 \u00b1 0.05\n0.55 \u00b1 0.05\n2mu8\n6.0\n0.87 \u00b1 0.05\n0.38 \u00b1 0.06\n0.31 \u00b1 0.05\n0.58 \u00b1 0.07\n20.0\n1.33 \u00b1 0.06\n0.10 \u00b1 0.02\n0.42 \u00b1 0.05\n0.45 \u00b1 0.05\n2mu10\n6.0\n0.68 \u00b1 0.05\n0.12 \u00b1 0.08\n0.21 \u00b1 0.09\n0.54 \u00b1 0.13\n20.0\n1.26 \u00b1 0.06\n0.10 \u00b1 0.02\n0.36 \u00b1 0.04\n0.36 \u00b1 0.04\n2mu11\n6.0\n0.43 \u00b1 0.21\n0.00 \u00b1 0.00\n0.32 \u00b1 0.15\n0.42 \u00b1 0.16\n20.0\n0.86 \u00b1 0.05\n0.00 \u00b1 0.00\n0.33 \u00b1 0.04\n0.32 \u00b1 0.04\n2mu20\n6.0\n0.28 \u00b1 0.28\n0.00 \u00b1 0.00\n0.48 \u00b1 0.34\n0.00 \u00b1 0.00\n20.0\n0.75 \u00b1 0.05\n0.00 \u00b1 0.00\n0.24 \u00b1 0.03\n0.18 \u00b1 0.03\n2mu40\n6.0\n0.42 \u00b1 0.42\n0.00 \u00b1 0.00\n0.00 \u00b1 0.00\n0.00 \u00b1 0.00\n20.0\n0.49 \u00b1 0.04\n0.00 \u00b1 0.00\n0.08 \u00b1 0.03\n0.08 \u00b1 0.03\nTable 8: Probabilities that single muons with transverse momenta 6 and 20 GeV which caused a single\nmuon trigger, to also passes a fake dimuon signature at the same threshold.\nTrigger item\nBB rate [Hz]\nBE rate [Hz]\nEE rate [Hz]\nFF rate [Hz]\nTotal fake rate [Hz]\n2mu4\n1846.6 \u00b1 119.2\n271.6 \u00b1 14.1\n136.2 \u00b1 24.5\n69.2 \u00b1 12.3\n2323.7 \u00b1 123.1\n2mu5\n243.9 \u00b1 13.0\n203.1 \u00b1 10.6\n35.3 \u00b1 10.5\n33.3 \u00b1 6.5\n515.5 \u00b1 20.8\n2mu6\n193.9 \u00b1 12.4\n82.6 \u00b1 7.1\n24.6 \u00b1 6.0\n24.7 \u00b1 4.7\n325.7 \u00b1 16.2\n2mu8\n114.1 \u00b1 9.8\n16.1 \u00b1 2.1\n9.7 \u00b1 3.0\n12.4 \u00b1 3.3\n152.3 \u00b1 11.0\n2mu10\n79.2 \u00b1 8.0\n4.9 \u00b1 1.2\n4.8 \u00b1 2.2\n5.5 \u00b1 2.0\n94.4 \u00b1 8.6\n2mu11\n11.7 \u00b1 1.8\n0.1 \u00b1 0.1\n3.9 \u00b1 2.0\n4.5 \u00b1 1.8\n20.1 \u00b1 3.2\n2mu20\n2.4 \u00b1 0.4\n0.1 \u00b1 0.0\n2.4 \u00b1 1.9\n0.7 \u00b1 0.5\n5.5 \u00b1 2.0\n2mu40\n0.8 \u00b1 0.1\n0.0 \u00b1 0.0\n1.7 \u00b1 1.7\n0.1 \u00b1 0.1\n2.6 \u00b1 1.7\nTable 9: Rates of various fake dimuon triggers at L = 1033 cm\u22122 s\u22121.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n663\n\n8.1\nData samples and their validation\nMinimum bias samples would be the most suitable for studies involving pion and kaon decays. However,\nthe probability that pions or kaons produced in low or moderate pT QCD scattering would decay before\ninteracting hadronically in the calorimeters is low, between 0.1% and 1% depending on the meson pT.\nIn order to enhance the number of charged pion and kaon decays in the sample, the simulation of events\nwithout any charged meson with pT above a given threshold is aborted and one \u03c0\u00b1 or K\u00b1 is forced to\ndecay in the Inner Detector cavity.\nThe samples produced are:\n\u2022 106 single pions with pT > 2.5 GeV and kinematics (pT \u00d7 \u03b7) generated according to a double\ndifferential cross-section of primary pions in minimum bias events\n\u2022 105 minimum bias events, where one charged \u03c0 or K with pT > 2 GeV per event is forced to decay;\nIn order to estimate cross-sections or trigger rates, the abundance of forced decays must be re-weighted\non an event by event basis according to meson decay probability. In addition to the above samples,\nstandard minimum bias events have been used as a reference to cross check the results obtained from\nthese dedicated productions.\nThe muon pT spectra observed in minimum bias events and single pions, forced to decay, were\nfound to be consistent, after appropriate re-weighting, with each other and in agreement with previous\npredictions and unforced minimum bias events.\n8.2\nRejection strategy at the event \ufb01lter\nThe fraction of in \ufb02ight decay muons retained at the EF, normalised to the L2 ef\ufb01ciency, for the mu6\ntrigger item, has been measured as a function of the muon pT. There is a very poor rejection capability\n(\u227290%) for muons coming from pion decays, which demonstrates that the standard muon identi\ufb01cation\nprocedures are not very sensitive, as expected, to the small kink between the pion and muon tracks. The\nkinematics of charged kaon two-body decays, which are the dominating kaon contribution to the muon\nrate, is much more favorable toward rejection due to the larger average value of the angle between the\nkaon and the muon tracks. In order to improve the rejection capability, additional measured parameters\nproviding some discriminating power between background and primary muons have been identi\ufb01ed:\n\u2022 the impact parameter, d0, of the track reconstructed in the inner tracker;\n\u2022 the number of hits associated to the Inner Detector track in the Pixel Detector (Nhits(Pixel)), in the\npixel B-layer (Nhits(Blayer)) and in the Silicon Tracker (Nhits(SCT));\n\u2022 the ratio pTID/pTMS between the transverse pT in the Inner Detector and in the Muon Spectrometer,\nafter back-extrapolation to the interaction point and correction for the measured energy loss in the\ncalorimeters;\n\u2022 the \u03c72\nmatching of the matching between the track parameters as reconstructed in the Muon Spectrom-\neter and in the Inner Detector.\nThe discrimination power of each variable has been studied by measuring the fraction of accepted events\nas a function of the cut applied for both isolated muons and fake muons above a given pT threshold.\nThe results, shown in Fig. 21, are based on the simulations of single muons and single pions with forced\ndecays. For each variable, the fraction of events retained after the cut is normalised to the number\nof events passing the EF reconstruction before the application of any hypothesis algorithms. From the\nanalysis of the exclusive rejection power of the individual variables, the set of cuts listed below have been\nde\ufb01ned. These cuts try to minimize the ef\ufb01ciency loss for prompt muons while reducing the background:\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n664\n\n0.06 0.08\n0.1\n0.12 0.14 0.16 0.18\n0.2\n0.22 0.24\nEfficiency\nd0 (mm)\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nN Pixel\n0.5\n1\n1.5\n2\n2.5\n3\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nEfficiency\nN SCT \n3.5\n4\n4.5\n5\n5.5\n6\n6.5\n7\n7.5\n8\nEfficiency\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nPt(ID)/Pt(MS)\n1.1\n1.15\n1.2\n1.25\n1.3\nEfficiency\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n\u03c72\n10\n15\n20\n25\n30\n35\n40\n45\nEfficiency\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\nno cuts\npT > 2 GeV/c \npT > 4 GeV/c\npT > 6 GeV/c\npT > 8 GeV/c\nprompt muons\nmuons from pions\nFigure 21: Ef\ufb01ciency for prompt muons and muons from pion decays as a function of the cut on some\ndiscriminating variables.\n\u2022 |d0| < 0.15 mm, Nhits(Blayer) \u22651, Nhits(Pixel) \u22653, Nhits(SCT) \u22656,\n\u2022 pTID/pTMS < 1.25, \u03c72\nmatching \u226426.\nIn particular, these values have been chosen by considering ef\ufb01ciency and background rejection at pT =\n4 GeV. It is assumed that cuts will be optimized for each muon item in the trigger menu.\nFrom the application of these cuts on the reference sample of events accepted at the EF, the ef\ufb01ciency\nfor prompt muons and in \ufb02ight decay muons shown in Fig. 22 have been obtained. A loss of ef\ufb01ciency\nbetween 25% at the 4 GeV threshold and 10% at 20 GeV correspond to a reduction in background of\n65% and 75%, respectively. The rejection achieved for kaon decays is slightly better than that achieved\nfor \u03c0 decays, as expected from the different decay kinematics. These results are derived from nominal\ndetector performance and algorithm resolutions. However, they demonstrate that cuts can be adjusted to\nobtain reasonable trigger rate at the very low pT threshold of 4 GeV which is reached mostly by reducing\nuninteresting events at the cost of some ef\ufb01ciency loss for prompt muons. An optimization of the cuts,\nwith speci\ufb01c tuning for each trigger element, will eventually further improve the signal to background\nratio.\n9\nMuon isolation\n9.1\nOptimization procedure\nThe L2 isolation algorithm is seeded by either muFast or muComb. The algorithm decodes LAr and Tile\nCalorimeter quantities (i.e. transverse energy deposit or sums of calorimetric cells above a prede\ufb01ned\nenergy threshold) in cones centered around the muon direction. The geometrical de\ufb01nition of these\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n665\n\nd0\nPixel\nBLayer\nSCT\n(SA)\nT\n( D)/p\nT\np\n match\n2\n\u03c7\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nd0\nPixel\nBLayer\nSCT\n(SA)\nT\n( D)/p\nT\np\n match\n2\n\u03c7\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nd0\nPixel\nBLayer\nSCT\n(SA)\nT\n( D)/p\nT\np\n match\n2\n\u03c7\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nmuon from pion\nmuon from kaon\nATLAS\nFigure 22: EF ef\ufb01ciency as a function of pT for different rejection cuts for prompt muons (a), muons\nfrom single pion decays (b), minimum bias events (c and d). In (c) \u03c0/K contribution has been separated.\nEach ef\ufb01ciency curve shows the data reduction obtained by the addition of the corresponding cut to the\noverall selection procedure. The speci\ufb01c values of the cuts are discussed in the text.\ncones is given by the condition \u2206R < \u2206RMAX, where \u2206R =\np\n(\u2206\u03b72 +\u2206\u03c6 2), and \u2206\u03b7, \u2206\u03c6 are the distances\nin pseudorapidity and azimuthal angle between the calorimetric cell and the cone axis. Because the\nmuon itself contributes to the energy deposit inside the cone, to improve the discriminating power of\nthe isolation algorithm, two different concentric cones are de\ufb01ned: an internal cone chosen to contain\nthe energy deposit released by the muon itself, and an external one, supposed to include contributions\nonly from detector noise, pile-up and jet particles if present. The optimization of the muon isolation\nalgorithm consists of determining the optimal size of the inner and outer cone radius, the values of the\ncell energy thresholds, used to compute the transverse energy and number of cells sums, and the isolation\nrequirements.\nTable 10 summarizes the samples that have been used to optimize the algorithms and to measure their\nperformance. Half of the events in the samples number 1 and 2 in the Table have been used as signal\nand background, respectively, in the optimization of the algorithm parameters, the remaining events for\nsample 1 and 2 and the other samples listed in the Table have instead been used to estimate the algorithm\nperformances.\nOnly the parameters relative at the muon trigger in the barrel region (|\u03b7| < 1.05) have been studied.\nSimulation of the electronic readout noise for both LAr and Tile Calorimeters has been also included.\nA muon track passing through the calorimetry will deposit energy in the cells which immediately\nsurround it. The deposited energy can be contained within some cone of radius RInner, where R =\np\n\u2206\u03b72 +\u2206\u03c6 2. If the muon is isolated, there will be little energy deposited in cells which lie in an outer\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n666\n\nProcess\nGenerator\nNumber of events\n1\nZ \u2192\u00b5+\u00b5\u2212\nPythia\n1 104\n2\nbb \u2192\u00b5(15)X\nPythia\n1.5 104\n3\nbb \u2192\u00b5(6)X\nPythia\n1 104\n4\nq \u00afq \u2192\u00b5X\nPythia\n2.1 104\n5\nSingle-\u00b5(pT=100 GeV)\nSingle-Mu gun\n2 105\n6\nSingle-\u00b5(pT=38 GeV)\nSingle-Mu gun\n2 105\n7\nSingle-\u00b5(pT=19 GeV)\nSingle-Mu gun\n2 105\nTable 10: Data samples used in the muon isolation algorithm optimization.\nannulus around this (R \u2208[RInner,ROuter]). The radius of the inner cone (i.e. the cone fully containing the\nmuon) has been determined from the distribution of the summed transverse energy contained within a\ncone of increasing radius around the muon direction from Z \u2192\u00b5\u00b5, as shown in Figure 23. The value\nof R corresponding to the inner cone radius is visible as a change in the slope of the curve. Once the\nradius for which all the muon energy is contained in the cone is reached, for each further increase of the\ncone radius only noise will be summed, resulting in a reduction of the slope of the energy sum curve.\nThe reduction in the slope depends on the level of electronic readout noise per cell, as shown in Fig. 23,\nwhere curves for several values of the threshold cut on the calorimetric cell energy is shown, ranging\nfrom 40 to 90 MeV. The effect of the electronic noise is only relevant for the LAr calorimeter. From\nthe two \ufb01gures it can be seen that a cone of radius 0.1 (one readout cell), is suf\ufb01cient to contain the\nmuon energy deposition in the hadronic calorimeter, while a radius of about 0.07 (one to three readout\ncells, depending on position), is suf\ufb01cient for the electromagnetic calorimeter, due to the \ufb01ner readout\ngranularity. The value of the outer cone radius is instead constrained by timing requirements. Increasing\nthe outer cone radius requires a larger fraction of the calorimeter to be read out and decoded. Because\nthe readout step of the algorithm dominates the execution time (> 90% of the overall algorithm time) the\nrequirement to keep the overall timing below O(10) ms constrains the maximum outer cone radius to be\nbelow about 0.4. We have veri\ufb01ed that optimal background rejection is obtained by keeping the outer\ncone radius at is maximum value.\nAn analysis has been performed over all the quantities used in the isolation hypothesis testing, with\na goal of minimizing the number of variable used in the optimization step. Each variable used in the\noptimization is listed in Table 11, together with the respective separation power expressed in term of\nminimum variance bound [8]. The optimal value of the cell energy cut thresholds, used to compute the\ntransverse energy and number of cell sums, has been obtained by maximizing the background rejection\nafter applying a \ufb01xed cut on the isolation variables (var1 and var2 in Table 11), giving a 95% ef\ufb01ciency\nfor the Z \u2192\u00b5\u00b5 signal. A common threshold value of 60 MeV has been obtained with this procedure for\nboth the LAr and Tile calorimeter. Algorithm performances are stable for threshold variations of \u00b110\nMeV around the optimal values. The distributions of some of the most powerful variables for signal\nselection and background rejection are shown in Fig. 24.\nOptimal cut values for the isolation variables described above have been obtained in a multivariate\noptimization procedure by simultaneously varying all the cuts in sensible ranges and by minimizing the\nb\u00afb \u2192\u00b5X background ef\ufb01ciency at \ufb01xed Z \u2192\u00b5\u00b5 signal ef\ufb01ciency. In the optimization procedure, both\nbackground and signal ef\ufb01ciencies are calculated with respect to muons satisfying the L2 muFast mu20\nrequirement. In Fig. 25 the background rejection,de\ufb01ned as 1/\u03b5BG where \u03b5BG is the ef\ufb01ciency for the\nb\u00afb background sample, and (1 \u2212\u03b5BG) as a function of the Z \u2192\u00b5\u00b5 signal ef\ufb01ciency, obtained after the\noptimization procedure, are shown. The chosen working point for the isolation algorithm yields a factor\nof 10 reduction for the b\u00afb background at a 95% signal ef\ufb01ciency for muons with pT >20 GeV.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n667\n\n R\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4\n Et> [MeV]\n\u2211\n<\n0\n1000\n2000\n3000\n4000\n5000\n6000\n, threshold: 40\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 50\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 60\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 70\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 90\n\u00b5\n \n\u00b5\n \n\u2192\nZ\nLAr\nMeV\n R\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4\n Et> [MeV]\n\u2211\n<\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n, threshold: 40\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 50\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 60\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 70\n\u00b5\n \n\u00b5\n \n\u2192\nZ\n, threshold: 90\n\u00b5\n \n\u00b5\n \n\u2192\nZ\nTile\nMeV\nATLAS\nATLAS\nFigure 23: The total transverse energy contained within a cone of increasing radius around the muon\ncandidate track from Z \u2192\u00b5\u00b5 signal events in the LAr calorimeter (left) and Tile calorimeter (right). The\ndifferent curves on each \ufb01gure correspond to different thresholds applied on the cell energy.\nLabel\nvariable\nSeparation\nvar1\nIsoLAr = \u2211E\u2206R<0.07\nT\n/\u2211E\u2206R<0.4\nT\n0.21\nvar2\nIsoTile = \u2211E\u2206R<0.1\nT\n/\u2211E\u2206R<0.4\nT\n0.29\nvar3\nEO\nLAr = \u2211E\u2206R\u2208[0.07,0.4]\nT\n0.75\nvar4\nEO\nTile = \u2211E\u2206R\u2208[0.1,0.4]\nT\n0.40\nvar5\nEI\nLAr = \u2211E\u2206R<0.07\nT\n0.23\nvar6\nEI\nTile = \u2211E\u2206R<0.1\nT\n0.06\nvar7\nNumber of LAr cells above threshold with \u2206R \u2208[0.07,0.4]\n0.72\nvar8\nNumber of Tile cells above threshold with \u2206R \u2208[0.1,0.4]\n0.34\nvar9\nNumber of LAr cells above threshold with \u2206R < 0.07\n0.31\nvar10\nNumber of Tile cells above threshold with \u2206R < 0.1\n0.07\nTable 11: Variable used in the muon isolation optimization procedure. The separation is zero for identical\nsignal and background shapes, and it is one for shapes with no overlap.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n668\n\nNumber of cells\n0\n50\n100\n150\n200\n250\n300\n350\nNormalized entries\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\n\u00b5\n\u00b5\n\u2192\nS: Z\n15X\n\u00b5\n\u2192\nb\nB: b\nLAr\n[0.07,0.4]\n\u2208\nR\n\u2206\nATLAS\n(a) Number of LAr cells above threshold in\nthe outer ring\n [MeV]\nT\n E\n\u2211\n0\n20\n40\n60\n80\n100\n3\n10\n\u00d7\nNormalized entries\n-3\n10\n-2\n10\n-1\n10\n1\n\u00b5\n\u00b5\n\u2192\nS: Z\n15X\n\u00b5\n\u2192\nb\nB: b\nLAr\n[0 07,0.4]\n\u2208\n R\n\u2206\nATLAS\n(b) Transverse energy sum in the outer ring\nof LAr\n [MeV]\nT\n E\n\u2211\n0\n2000\n4000\n6000\n8000 10000 12000\nNormalized entries\n-3\n10\n-2\n10\n-1\n10\n1\n\u00b5\n\u00b5\n\u2192\nS: Z\n15X\n\u00b5\n\u2192\nb\nB: b\nTile\n[0.1,0.4]\n\u2208\n R\n\u2206\nATLAS\n(c) Transverse energy sum in the Tile in\nthe outer ring\nHAD. Isolation\n0\n0.1 0.2 0 3 0.4 0.5 0.6 0.7 0.8 0.9\n1\nNormalized entries\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\n\u00b5\n\u00b5\n\u2192\nS: Z\n15X\n\u00b5\n\u2192\nb\nB: b\nATLAS\n(d) Isolation variable in Tile calorimeter\nFigure 24: Most powerful variables for calorimetry-based muon isolation.\n9.2\nPerformance\nThe performance of the isolation algorithms in terms of b\u00afb and dijet background reduction, ef\ufb01ciency\nof benchmark signal channels and timing is presented below. The performance of isolation algorithms\ncan be affected by the instantaneous luminosity since the pile-up requires higher thresholds for the same\nnominal ef\ufb01ciency. This is particularly true for calorimetry-based isolation, while for track-based iso-\nlation the effect can be reduced by requiring that the contributing tracks come from the same primary\nvertex as the muon. For this reason, the results of this study should be taken as preliminary and valid\nonly in the framework of the approximations used in the simulated events production for these studies.\nPossible changes and further development may occur as soon as real data is available.\nThe effect of isolation algorithms on various sources of non-isolated muons at L2 is shown in Ta-\nble 12. The quantity 1\u2212\u03b5BG is shown for the isolation requirements corresponding to a working point for\nthe isolation algorithm with a nominal Z \u2192\u00b5\u00b5 signal ef\ufb01ciency of 95%. Results from dijet decays give\nan estimate of the rejection power of the isolation algorithm for high-pT muons from K and \u03c0 in \ufb02ight\ndecays. The rejection power for low-pT muons from b\u00afb decays selected by the level 2 mu6 requirement\nhas also been estimated. The reduction in rejection power, from a factor 10 to a factor of about 2, at the\nlow-pT limit is expected, given the low energy associated with the jets. As already mentioned, calorime-\ntry based isolation algorithms are not effective against these kind of muons, and the track-based isolation\nis expected to be much more powerful in reducing this kind of background.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n669\n\nSignal Efficiency\n0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98\n1\nBackground Rejection\n0\n5\n10\n15\n20\n25\n30\n35\n40\nATLAS\nSignal Efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1-Background Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n0.820.840.860.88 0.9 0.920.940.960.98\n1\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\nFigure 25: Background rejection (1/\u03b5BG) (left), and 1\u2212\u03b5BG (right), as a function of the signal ef\ufb01ciency\nas obtained in the muon isolation algorithm optimization procedure.\nProcess\nTrigger item\nAverage muon pT (GeV)\n1\u2212\u03b5BG (%)\nbb \u2192\u00b5(15)X\nmu20\n25.0\n89.4\u00b10.7\nbb \u2192\u00b5(6)X\nmu6\n9.0\n54.6\u00b10.9\nq \u00afq \u2192\u00b5X\nmu20\n40.0\n99.6\u00b10.1\nq \u00afq \u2192\u00b5X\nmu6\n20.0\n97.3\u00b10.2\nTable 12: Muon isolation algorithm 1 \u2212\u03b5BG for muons from several background samples. Ef\ufb01ciencies\nare calculated with respect to muons passing the level 2 mu20 or mu6 requirements, as speci\ufb01ed.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n670\n\nThe isolation algorithm has been tuned such that the ef\ufb01ciency is 95% at the chosen working point.\nThe ef\ufb01ciency of the isolation requirement has been studied as a function of pT using samples of single\nmuons with a pT of 11, 39, and 100 GeV. No sizable change in the muon ef\ufb01ciency are visible, indicating\nthat radiation effects are small for pT in this range. Evaluation of the effect of the muon radiation for\nvery high pT muons (500 to 1000 GeV) is ongoing. The ef\ufb01ciencies for muons from Z \u2192\u00b5\u00b5 decays\nand for single muons are reported in Table 13.\nProcess\nTrigger path\n\u03b5 (%)\nZ \u2192\u00b5+\u00b5\u2212\nmu20\n95.5\u00b10.4\nSingle \u00b5 pT=100 GeV\nmu20\n98.68\u00b10.07\nSingle \u00b5 pT=39 GeV\nmu20\n98.97\u00b10.07\nSingle \u00b5 pT=6 GeV\nmu6\n98.54\u00b10.09\nTable 13: Muon isolation algorithm ef\ufb01ciencies for muons from several processes and thresholds.\nThe time available for running L2 algorithms in the on-line trigger is limited to approximately 20 ms.\nThe CPU processing time is therefore a relevant parameter for the feasibility of algorithms to be included\nin the trigger chain. The results obtained indicate a typical overall time of less than 10 ms. Further and\nmore detailed timing studies performed on the actual L2 processors are ongoing.\n10\nMuon identi\ufb01cation using the tile calorimeter\nThe muon signatures in the three radial layers of the Tile Calorimeter are well measured quantities with\na typical pattern that can be used to identify the muons ef\ufb01ciently down to very low pT. This information\ncan be used to con\ufb01rm the Muon Spectrometer Triggers (i.e. provide redundancy in noisy/dead regions)\nor to enhance the selection ef\ufb01ciency for very soft muons typically out of reach for the spectrometer.\nThe algorithm exploits the radial and transverse calorimeter segmentation. The search starts from\nthe outermost layer, which is the one with the cleanest signal, and once a cell is found with energy\ncompatible with a muon, the algorithm checks the energy deposition in the neighbor cells for the most\ninternal layers. These \u201ccandidate patterns\u201d are considered as muons when cells compatible with the\ntypical muon energy deposition are found following a \u03b7-projective pattern in all the three TileCal layers.\nMore details can be found in Ref. [9].\n10.1\nPerformance\nThe performance of the TileMuId algorithms has been studied with MonteCarlo single muons and semi-\ninclusive muon production (b\u00afb \u2192\u00b5(4)X) samples. The effect of minimum-bias pileup at low luminosity\n(L = 1033cm\u22122s\u22121) has been investigated as well.\nTwo algorithms, implementing complementary strategies are described, one (TrigTileLookForMuAlg)\nis fully executed on the LVL2 Processing Unit (PU) the second (TrigTileRODMuAlg) has a core part ex-\necuted on the Read Out Driver Digital Signal Processor (ROD-DSP) in order to save time. This allows a\nvery fast processing of the entire detector (full scan) as opposed to the RoI based processing typical of the\ntrigger algorithm running on the LVL2 PUs. Since each ROD-DSP processes a small part of the detector\nreadout the TrigTileRODMuAlg acceptance is lower compared with that of TrigTileLookForMuAlg.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n671\n\n10.1.1\nSpatial resolution\nThe spatial resolution of the algorithms can be studied using the distributions of the residuals \u2206\u03b7 =\n\u03b7(\u00b5Tile)\u2212\u03b7(\u00b5Truth) and \u2206\u03c6 = \u03c6(\u00b5Tile)\u2212\u03c6(\u00b5Truth) in single muon events with 2 \u2264pT \u226415 GeV. The dis-\ntributions are well described by a Gaussian and resolution can be de\ufb01ned as \u03c3\u03b7 = 0.05 for TrigTileROD-\nMuAlg ( \u03c3\u03b7 = 0.04 for TrigTileLookForMu) and \u03c3\u03c6 = 0.03 rad. To characterize the performance of the\nalgorithms with MC physics events a matching region with the MC truth will be used. For this analysis\na matching region of \u2206\u03b7 \u00d7\u2206\u03c6 = 0.2\u00d70.12 is used.\n10.1.2\nEf\ufb01ciency\nThe muon-tagging ef\ufb01ciency is de\ufb01ned as the ratio of the number of tagged muons which match a truth\nmuon (Ntag) to the number of generated truth muons (Ngen). Figure 26 shows the ef\ufb01ciency as a function\n\u03b7\n-1\n-0.5\n0\n0.5\n1\n-tagging efficiency\n\u00b5\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n \n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\n-tagging efficiency\n\u00b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n-tagging efficiency\n\u00b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\nFigure 26: Ef\ufb01ciency as a function of \u03b7 (left), \u03c6 (center) and pT (right)for TrigTileLookForMu (\ufb01lled\ncircles) and TrigTileRODMu (open squares) using single muon events.\n\u03b7\n-1\n-0.5\n0\n0.5\n1\n-tagging efficiency\n\u00b5\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n (GeV)\nT\np\n2\n4\n6\n8\n10\n12\n14\n16\n-tagging efficiency\n\u00b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n (GeV)\nT\np\n2\n4\n6\n8\n10\n12\n14\n16\n-tagging efficiency\n\u00b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nwithout pileup\nwith pileup\nwithout pileup\nwith pileup\nATLAS\nFigure 27: Ef\ufb01ciency as a function of \u03b7 (left) and pT (center) for TrigTileLookForMu (\ufb01lled circles)\nand TrigTileRODMu (open squares) in b\u00afb \u2192\u00b5(6)X events. Right plot show for TrigTileLookforMu\nthe effect of pileup of Minimum Bias events at low luminosity (\ufb01lled circles) compared with the case\nwithout pileup (open squares).\nof \u03b7, \u03c6, and pT of the muon for the two algorithms as obtained using the single muon sample. The\nef\ufb01ciency of TileRODMu is lower than that of TileLookForMu. In the region 0.8 \u2264|\u03b7| \u22641.1 the towers\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n672\n\nare split between the barrel and the extended barrels, and the cells belonging to different partitions are\nprocessed by different ROD DSPs. Similar effects are observed for the boundary at \u03b7 \u223c0. Except\nfor these two regions of low geometrical acceptance both algorithms show ef\ufb01ciency \u223c85% with good\nagreement. Since TileCal is homogeneous in \u03c6, the ef\ufb01ciency is uniform as a function of \u03c6, see Fig. 26\n(center). The ef\ufb01ciency decreases with the muon pT for pT < 3 GeV and is about 42% at pT = 2 GeV.\nMost of the muons with pT < 2 GeV stop in the Tile calorimeter. For pT > 4 GeV the ef\ufb01ciency is \ufb02at\nat about 60%. Figure 27 (left) and (center) show the ef\ufb01ciency curves for both algorithms as obtained\nin b\u00afb \u2192\u00b5(6)X events. These results are in good agreement with the performance obtained using single\nmuons, indicating that the algorithms are not too sensitive to the additional hadronic activity in b\u00afb events.\nTo evaluate the performance in a realistic LHC operation scenario a sample of b\u00afb \u2192\u00b5(6)X events\nsimulated with pileup of minimum-bias events at a luminosity L = 1033 cm\u22122s\u22121 was used. As shown\nin Fig. 27 (right), the ef\ufb01ciencies as a function of pT for two cases are similar for pT > 5 GeV. The\nadditional muons from minimum-bias events make the ef\ufb01ciency worse in the low pT region. The average\nef\ufb01ciency in the sample with pileup (67.97\u00b10.81)% is slightly lower than the one obtained without pileup\n(74.25\u00b10.79)%. It can be concluded that the ef\ufb01ciency is not substantially affected by minimum-bias\npileup.\n10.1.3\nFraction of fakes\n\u03b7\n-1\n-0.5\n0\n0.5\n1\nfraction of fakes\n0\n1\n2\n3\n4\n5\n6\n-3\n10\n\u00d7\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n \n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nfraction of fakes\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n-3\n10\n\u00d7\nTrigTileLookForMuAlg \nTrigTileRODMuAlg \nATLAS\n\u03b7\n-1\n-0.5\n0\n0.5\n1\nfraction of fakes\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n-3\n10\n\u00d7\nwi hout pileup\nwi h pileup\nwi hout pileup\nwi h pileup\nATLAS\nFigure 28: Fraction of fakes as a function of \u03b7 (left) and \u03c6 (center) for TrigTileLookForMu (\ufb01lled circles)\nand for TrigTileRODMu (open squares) in b\u00afb \u2192\u00b5(6)X events. The right plot compare performance of\nTrigTileLookForMu in samples with (\ufb01lled circles) and without pileup (open squares).\nThe muon tags which are not matched with truth muons are considered fake. The same \u2206\u03b7 \u00d7 \u2206\u03c6\nmatching cuts are used for the ef\ufb01ciency and fake computation. The fraction of fakes in a given data\nsample is de\ufb01ned as the ratio of the number of misidenti\ufb01ed muons to the total number of events.\nThe left and center plots of Fig. 28 show the fraction of fakes as a function of \u03b7 and \u03c6 obtained\nby the two algorithms. Both algorithms show a very small fake rate in the central region (0.12% for\n|\u03b7| < 0.7). The main contribution of fakes comes from the extended barrel and gap regions, where the\ncell segmentation is coarse and the projectivity is the worst. The fraction of fakes in the whole range\n|\u03b7| < 1.4 is 2.7 \u00b1 0.1% for TrigTileRODMu and 4.1 \u00b1 0.1% for TrigTileLookForMu. The fraction of\nmisidenti\ufb01ed muons as a function of \u03c6 is \ufb02at as expected.\nFigure 28 (right) shows the performance of TrigTileLookForMu in b\u00afb \u2192\u00b5(6)X events with and\nwithout the pileup of minimum-bias events at low luminosity. The fraction of fakes increase from 3.7 \u00b1\n0.1% to 6.0 \u00b1 0.1% when the minimum bias pileup at L = 1033 cm\u22122s\u22121 is taken into account. The\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n673\n\nfake rate increases at larger values of \u03b7 (gap and extended barrel), where the cell granularity is worse\nand more minimum bias event are expected, compared to the central \u03b7 region.\n10.2\nCombined performance with the inner detector\nIn order to measure the pT of the identi\ufb01ed muon, the secondary RoI produced by the TileMuId algorithm\nis used to seed the Inner Detector (ID) track reconstruction algorithm. The size of the ID RoI that requires\nprocessing is de\ufb01ned by the Tile algorithm resolution and by the bending in the central solenoid. For\npT(\u00b5Truth) > 2 GeV, \u2206\u03c6 = \u03c6(\u00b5Tile)\u2212\u03c6(\u00b5Track) \u22480.2 is required. If at least one track is found within the\nregion \u2206\u03b7 \u00d7 \u2206\u03c6 = 0.1 \u00d7 0.2 and with pT > 2 GeV, the calorimetric tag is con\ufb01rmed to be a muon and\nthe trigger sequence is successful.\nN(tracks)\n0\n1\n2\n3\n4\n5\n6\nEntries\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n=0.1\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.2\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.1\n\u03c6\n\u2206\n=0.2, \n\u03b7\n\u2206\n=0.1\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.2\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.1\n\u03c6\n\u2206\n=0.2, \n\u03b7\n\u2206\n=0.1\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.2\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n=0.1\n\u03c6\n\u2206\n=0.2, \n\u03b7\n\u2206\nATLAS\nN(tracks)\n0\n1\n2\n3\n4\n5\n6\nEntries\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nwithout pileup\nwith pileup\nwithout pileup\nwith pileup\nATLAS\n (GeV)\nT\np\n5\n10\n15\n20\n25\n-tagging efficiency\n\u00b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nT le\n\u00b5\n=0.1)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\n=0.2)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\nT le\n\u00b5\n=0.1)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\n=0.2)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\nT le\n\u00b5\n=0.1)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\n=0.2)\n\u03c6\n\u2206\n=0.1, \n\u03b7\n\u2206\n (\nT le+Track\n\u00b5\nATLAS\nFigure 29: The number of tracks within the given RoI for b\u00afb \u2192\u00b5(4)X (left) and with the \ufb01xed RoI\nsize of \u2206\u03b7 = 0.1 and \u2206\u03c6 = 0.2 for b\u00afb \u2192\u00b5(6)X with/without pileup (center). The right plot shows the\nef\ufb01ciency as a function of pT for the muons tagged by only TileCal (TileLookForMu) and the muons\ncombined with the associated track.\nFigure 29 shows the multiplicity of track in the ID RoI; left plot shows that a region with \u2206\u03c6 = 0.1\nmisses the low pT tracks and results in more events with zero track within the RoI. The RoI with \u2206\u03b7 = 0.2\ndoes not give any advantage. The RoI with a size \u2206\u03b7 = 0.1 and \u2206\u03c6 = 0.2 is a good compromise; the\nef\ufb01ciency to reconstruct the muon track is good and the multiplicity of tracks (ambiguity) is acceptable.\nIn the case of reconstruction of multiple tracks, the closest is chosen as the best-matched for the \u00b5 tagged\nby TileCal, and all tracks are saved since the ambiguity cannot be further resolved at this level. As shown\nin Figure 29 (center), the multiplicity of tracks within the RoI is not signi\ufb01cantly affected by the pileup.\nFigure 29 (right) shows the overall combined (TileCal+ID) ef\ufb01ciency for \u2206\u03c6 = 0.1 and \u2206\u03c6 = 0.2\nas a function of muon pT. The combined ef\ufb01ciency obtained with \u2206\u03c6 = 0.2 is approximately equal to\nthat of the TileCal stand-alone except for pT < 3.5 GeV. The ef\ufb01ciency from the matched track shows\nno dependence on \u03b7 or \u03c6. The ef\ufb01ciency, purity and acceptance using the different sizes of RoI are\nsummarized in Table 14. The ef\ufb01ciency and acceptance are signi\ufb01cantly improved from \u2206\u03c6 = 0.1 to\n\u2206\u03c6 = 0.2. For \u2206\u03c6 = 0.2, 97% of tagged muons by TileCal match the associated track. The purity and\nacceptance of \u2206\u03c6 = 0.3 are similar to those of \u2206\u03c6 = 0.2. However, the size of \u2206\u03b7 does not affect the\nef\ufb01ciency of the matched track with \u00b5 signi\ufb01cantly. The differences due to the minimum-bias pileup are\nobserved to be about 2 to 3% due to the small number of events from pileup samples.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n674\n\nTileLookForMu\nRoI size with (\u2206\u03b7, \u2206\u03c6) for matching tracks\n(0.1, 0.1)\n(0.1, 0.2)\n(0.1, 0.3)\nEf\ufb01ciency (%)\n73.08 \u00b1 0.17\n42.02 \u00b1 0.19\n70.91 \u00b1 0.18\n72.06 \u00b1 0.18\nUnmatched \u00b5Tile (%)\n42.50 \u00b1 0.36\n2.98 \u00b1 0.08\n1.40 \u00b1 0.05\nEf\ufb01ciency (pT > 4 GeV)\n44.09 \u00b1 0.20\n72.94 \u00b1 0.18\n73.06 \u00b1 0.18\nPurity (pT > 4 GeV )\n98.51 \u00b1 0.88\n98.79 \u00b1 0.67\n98.69 \u00b1 0.67\nAcceptance (pT > 4 GeV)\n40.78 \u00b1 0.31\n71.93 \u00b1 0.45\n72.01 \u00b1 0.45\nTable 14: Performance with the matched track for b\u00afb \u2192\u00b5(4)X.\n11\nMuon trigger performance for Z \u2192\u00b5+\u00b5\u2212\n11.1\nThe \u201ctag and probe\u201d method\nThe trigger ef\ufb01ciency is a fundamental parameter in physics analyses and therefore it is important to have\nseveral independent methods for estimating it. The \u201cTag and Probe\u201d method is a concrete application of\na data-driven technique for performance analysis. This method is based on the de\ufb01nition of a \u201cprobe-\nlike\u201d object, used to make the performance measurement, within a properly \u201ctagged\u201d sample of events.\nPhysics processes suitable for this method are generally those characterized by a double-object \ufb01nal state\nsignature. The decay of the Z provides two high-pT muons that can lead to two trigger tracks in the Inner\nDetector and Muon Spectrometer and to a combined object. These two measurements are in principle\nindependent, thought not necessarily uncorrelated.\n\u201cTagged\u201d events require one triggered track with pT > 20 GeV and \u201cProbe\u201d objects can be de\ufb01ned\nas Inner Detector of\ufb02ine reconstructed tracks (ID-Probe), where measurements are referred to the of\ufb02ine\nInner Detector reconstruction ef\ufb01ciency (\u223c100%), or as Muon Spectrometer of\ufb02ine reconstructed tracks\n(MS-Probe), where values are normalized to the of\ufb02ine Muon Spectrometer reconstruction ef\ufb01ciency\n(standalone or combined with the Inner Detector).\nThe trigger performance is measured by checking for L1, L2, and EF trigger tracks associated with\neach probe object. A schematic illustration of the method is shown in Fig. 30. It must be veri\ufb01ed that se-\nlected tracks come from a Z decay. A background process with two isolated tracks in the Inner Detector,\nof which only one is a real muon, would introduce a systematic error in the ef\ufb01ciency evaluation. For\nthis reason, cuts have to be applied in order to select a clean signal sample.\nA signi\ufb01cant background contribution is expected from QCD processes, which have large cross-sections.\nof the two tracks\nThe invariant mass \nin the MS.\ncorresponding track\nTest if there is\nZ\u2212Boson mass.\nshould be near the\nMuon Spectrometer\nInner Tracker\nProbe Muon\nZ\u2212Boson\nTag Muon\nProcess\nGeneration cuts\n\u03c3 [pb]\nZ \u2192\u00b5+\u00b5\u2212\nM\u00b5\u00b5 > 60 GeV/c2\n1497\n1\u00b5: |\u03b7| < 2.8, pT > 5 GeV\nW \u2192\u00b5\u03bd\n1\u00b5: |\u03b7| < 2.8, pT > 5 GeV\n11946\nBB \u2192\u00b5\u00b5X\n1\u00b5: |\u03b7| < 2.5, pT > 15 GeV\n4000\n1\u00b5: |\u03b7| < 2.5, pT > 5 GeV\nt\u00aft \u2192W +bW \u2212b\nonly leptonic decay\n461\nZ \u2192\u03c4+\u03c4\u2212\n\u03c4\u03c4 \u2192ll,M\u00b5\u00b5 > 60 GeV/c2\n77\n1\u00b5: |\u03b7| < 2.8, pT > 5 GeV\nFigure 30: Illustration of the Tag and Probe method (left) and cross-sections with generation cuts for\nsignal and background processes (right).\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n675\n\nThis background has been studied by considering the dominant contribution of muons from decays of B-\nmeson pairs. Also the muonic W boson decay, which can give a higher energetic muon plus an additional\nmuon from a QCD jet and the Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5+\u03bd\u00b5 \u00af\u03bd\u03c4 \u00b5\u2212\u00af\u03bd\u00b5\u03bd\u03c4 process have been considered.\nMoreover the top-pair production cross-section at LHC is of the same order of magnitude as Z boson\ncross-section. Top quarks decay with a 99.9% probability into a Wboson and a b quark. Therefore muons\noriginating from W boson and b-quark decays can also give a signal-like signature. Cross-sections and\ngeneration cuts of the processes considered are reported in Fig. 30. PYTHIA [5] is used to generate the\nprocesses.\nAnother possible source of background is muons from cosmic-rays. An estimation of cosmic rates\nin the trigger system has been done in Ref. [10] and shows a negligible effect on trigger performance.\nThe isolation variables chosen for this analysis are the number of reconstructed tracks in the Inner\nDetector (NID\ncone), the sum of pT of the Inner Detector tracks (\u2211pID\nT,cone), the energy of a jet candidate\n(E jet\ncone) and the sum of reconstructed energy in the cells of the Calorimeter (\u2211EEM\ncone). Muons from QCD\nprocesses tend to be produced within a large cascade of other particles and therefore should not appear\nisolated in the detector. In the case of the decay of top pairs, one highly energetic and isolated muon\ncan come from one W boson decay while the second W boson can decay leptonically into a high-pT\nelectron which appears as an isolated track in the Inner Detector. In order to not count this as a false\nprobe, electrons are vetoed. The values of the selection cuts applied in this analysis have been de\ufb01ned\nin [11]. The isolation cuts allow for background rejection of approximately 99% while retaining a signal\nef\ufb01ciency of about 76%. After applying the probe selection cuts the signal to background ratio is more\nthan 103. In addition, probe muons selected from background processes can be associated to trigger\ntracks and hence have no negative impact on trigger ef\ufb01ciency measurements.\n11.2\nDetermination of trigger ef\ufb01ciencies\nTwo measurement scenarios have been studied:\n\u2022 Low luminosity (\nR L dt \u224350 pb\u22121): in order to not rely on the combined reconstruction based on\nInner Detector and Muon Spectrometer matching, only the tracks from the Muon Spectrometer are\nused. The isolation cuts are also based only on Inner Detector quantities;\n\u2022 High luminosity (\nR L dt \u22431000 pb\u22121): full combined information from Inner Detector and Muon\nSpectrometer is used and also Calorimeter based cuts are applied to select isolated tracks.\nIn each scenario both the ID- and MS-Probe methods have been studied. The ef\ufb01ciency dependence on\n\u03c6 and \u03b7 is determined by the Muon Spectrometer layout. A pT cut of 20 GeV has been applied on the\nprobe tracks to test the system in its plateau region. The ef\ufb01ciency as a function of pT has been also\nestimated from data in the high luminosity scenario.\n11.2.1\nLow luminosity measurements\nThe relative ef\ufb01ciency as a function of \u03b7, measured at each trigger level, is shown in Fig. 31 using the\nID-probe. L1 acceptance losses are related to an incomplete coverage of the trigger detectors due to\nthe presence of support and access structures. The L2 ef\ufb01ciency, with respect to the L1 selection, is\nabout 96% in the barrel region with a small decrease in the endcap, an improvement is expected due to\noptimization of the TGC cabling in next software releases. The EF shows an \u03b7 ef\ufb01ciency distribution,\nwith respect to L2, close to 99% in the barrel region and a very small decrease from |\u03b7| > 2.0. In the\nregion 1.05 < |\u03b7| < 1.3 the absence of the some MDT chambers in the ATLAS initial layout resulted in\nan ef\ufb01ciency loss of about 10%.2\n2The missing chambers are scheduled to be installed by the end of 2009.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n676\n\n0.7\n0 8\n0 9\n1\nL1\n0.7\n0 8\n0 9\n1\nL2 (wrt L1)\n\u03b7\n-2\n-1 5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n0.7\n0 8\n0 9\n1\nEF (wrt L2)\nTag & D-Probe\nMC truth\nTrigger efficiency\nATLAS\n-0.04\n-0.02\n0\n0 02\n0 04\nL1\n-0.04\n-0.02\n0\n0 02\n0 04\nL2 (wrt L1)\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-0.04\n-0.02\n0\n0 02\n0 04\nEF (wrt L2)\nFractional efficiency difference\nATLAS\nFigure 31: The muon trigger ef\ufb01ciency for each trigger level (left) and fractional ef\ufb01ciency difference\n(right) as a function of \u03b7 in the low luminosity scenario using the ID-Probe. The ef\ufb01ciencies determined\nwith the Tag and Probe method are compared to those calculated in a Monte Carlo truth-based analysis.\n0.7\n0 8\n0 9\n1\nL1\n0.7\n0 8\n0 9\n1\nL2 (wrt L1)\n\u03b7\n-2\n-1 5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n0.7\n0 8\n0 9\n1\nEF (wrt L2)\nTag & MS-Probe\nMC truth\nTrigger efficiency\nATLAS\n-0.04\n-0.02\n0\n0 02\n0 04\nL1\n-0.04\n-0.02\n0\n0 02\n0 04\nL2 (wrt L1)\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-0.04\n-0.02\n0\n0 02\n0 04\nEF (wrt L2)\nFractional efficiency difference\nATLAS\nFigure 32: The muon trigger ef\ufb01ciency for each trigger level (left) and fractional ef\ufb01ciency difference\n(right) as a function of \u03b7 in the low luminosity scenario using the MS-Probe. The ef\ufb01ciencies determined\nwith the Tag and Probe method are compared to those calculated in a Monte Carlo truth-based analysis.\nThe observed agreement with the Monte Carlo truth-based analysis is very good. In order to quantita-\ntively estimate the bin-by-bin differences the \u201cfractional ef\ufb01ciency difference\u201d\n\u03b5Tag&Probe \u2212\u03b5MC\n\u03b5MC\n(5)\nhas been computed. This quantity is shown for each trigger level in Fig. 31 as a function of \u03b7.\nThe agreement between Tag and Probe method and Monte Carlo analysis is very high, more than 99%\nover all the trigger coverage. The only observed deviations, at the level of 2%, are found in the central\ncrack at \u03b7 = 0 and in the transitions from barrel to endcap at |\u03b7| = 1.05. The results obtained by the\napplication of the Tag and Probe method using the standalone MS-Probe are reported in Fig. 32 as a\nfunctions of \u03b7. With respect to the values shown in Fig. 31 inef\ufb01ciencies due to L1 acceptance cracks\nare partially factorized in the of\ufb02ine muon reconstruction ef\ufb01ciency of the MS-Probe (e.g. the \u03b7 = 0\nregion.). The same effect is clearly evident at the EF level for the ef\ufb01ciency loss at 1.05 < |\u03b7| < 1.3\nvisible in Fig. 31.\nTable 15 shows the uncertainties on the overall trigger ef\ufb01ciency in each case, calculated also only\nin barrel and endcap regions. The statistical uncertainty is reported together with expected systematic\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n677\n\nDetector region\nBarrel\nEndcap\nOverall\n(|\u03b7 < 1.05|)\n(1.05 < |\u03b7| < 2.4)\n(0 < |\u03b7| < 2.4)\nLow luminosity - ID probe (\nR L dt = 50 pb\u22121)\nTrigger Ef\ufb01ciency\n71.65\n83.59\n77.38\nStatistical Uncertainty\n0.42\n0.36\n0.28\n|\u03b5TRUTH \u2212\u03b5TP|\n0.23\n0.40\n0.10\nExpected Background Contribution\n0.57\n0.17\n0.40\nOverall Systematic Uncertainty\n0.61\n0.43\n0.41\nLow luminosity - MS probe (\nR L dt = 50 pb\u22121)\nTrigger Ef\ufb01ciency\n76.94\n87.83\n82.13\nStatistical Uncertainty\n0.41\n0.34\n0.27\n|\u03b5TRUTH \u2212\u03b5TP|\n0.17\n0.64\n0.33\nExpected Background Contribution\n0.01\n0.00\n0.01\nOverall Systematic Uncertainty\n0.17\n0.64\n0.33\nTable 15: Estimated uncertainties of in-situ determined muon overall trigger ef\ufb01ciency for the low lu-\nminosity scenario, using an ID- and an MS-Probe track. Systematic uncertainties are reported for back-\nground contribution and absolute difference with Monte Carlo truth-based analysis.\nDetector region\nBarrel\nEndcap\nOverall\n(|\u03b7 < 1.05|)\n(1.05 < |\u03b7| < 2.4)\n(0 < |\u03b7| < 2.4)\nHigh luminosity - ID probe (\nR L dt = 1000 pb\u22121)\nTrigger Ef\ufb01ciency\n73.24\n86.31\n79.73\nStatistical Uncertainty\n0.10\n0.08\n0.06\n|\u03b5TRUTH \u2212\u03b5TP|\n0.02\n0.72\n0.58\nExpected Background Contribution\n0.05\n0.01\n0.03\nOverall Systematic Uncertainty\n0.05\n0.72\n0.58\nTable 16: Estimated uncertainties of in-situ determined muon overall trigger ef\ufb01ciency for the high lu-\nminosity scenario using the ID-Probe. Systematic uncertainties are reported for background contribution\nand absolute difference with Monte Carlo truth-based analysis.\nerrors. Two sources of systematic uncertainties are considered: the absolute difference with respect to\nthe value measured in a Monte Carlo truth-based analysis and the background contribution, evaluated\nby comparing the ef\ufb01ciency calculated with Tag and Probe method using only the signal sample and\nusing a cross-section weighted sum of all processes. Both systematics are less than 0.5%. A greater\nbackground contribution is observed when using ID-Probe, since the isolation is based only on Inner\nDetector quantities.\n11.2.2\nHigh luminosity measurements\nAfter early data is collected and analyzed, a better understanding of the detector, in terms of calibration\nand alignment, will allow to use all the available information such as Calorimeter quantities for track iso-\nlation and combination of Inner Detector and Muon Spectrometer tracks. The trigger ef\ufb01ciency measure-\nments from data in this scenario are reported using the high luminosity dataset of\nR L dt = 1000 pb\u22121.\nAs in the low luminosity case the measured differences between the Tag and Probe and Monte Carlo\nanalysis are compatible with zero. Small deviations at the level of 1 to 2% are observed in the endcap\nfor the L2 trigger ef\ufb01ciency in the |\u03b7| > 1.5 region. These effects are expected to be reduced by the\nL2 algorithm optimization. Results are shown in Table 16. With the addition of the calorimeter-based\nisolation, the background systematic contribution is reduced by a factor of 10 with respect to the low\nluminosity scenario.\nThe dependence of the trigger ef\ufb01ciency on the pT shows the typical shape of a\nturn-on curve. The sharpness of the curve is related to the \ufb01nite pT resolution, \u223c30% at L1, \u223c5% at\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n678\n\n(GeV)\nT\np\n0\n10\n20\n30\n40\n50\n60\nTrigger efficiency\n0\n0 2\n0.4\n0.6\n0.8\n1\nTag & Probe\nL1\nL1+L2\nL1+L2+EF\nMC gen.\nL1\nL1+L2\nL1+L2+EF\nT\np\n0\n10\n20\n30\n40\n50\n60\nTrigger efficiency\n0\n0 2\n0.4\n0.6\n0.8\n1\nATLAS\n-0.05\n0\n0.05\nL1\n-0.05\n0\n0.05\nL1+L2\n (GeV/c)\nT\np\n0\n10\n20\n30\n40\n50\n-0.05\n0\n0.05\nL1+L2+EF\nATLAS\nFigure 33: Muon trigger ef\ufb01ciency turn-on curve after each trigger level determined by the Tag and Probe\nmethod and by the Monte Carlo truth-based analysis in the high luminosity scenario using the ID-Probe\n(left). In the right plot the fractional ef\ufb01ciency difference is shown.\nL2, and \u223c3% at the EF. Turn-on curves are shown in Fig. 33 using the ID-probe and similar results are\nobtained with the MS-probe. The turn-on point and the plateau values are correctly reproduced from data.\nThe fractional ef\ufb01ciency difference is shown for each trigger level. The disagreement near the threshold\nis within 5%, due mainly to resolution effects, while in the plateau region the observed difference is less\nthan 1%.\n12\nHigh pT Dimuon \ufb01nal states\nIn principle, the high mass dilepton/diphoton resonance search should have a fairly straightforward trig-\nger strategy as there are very high energy leptons in the event. However, there are several questions that\nremain: what trigger requirements are optimal for the analysis? What pT thresholds and object quality\nselection should be applied? How can one estimate the trigger ef\ufb01ciency from data for such rare (or\nnon-existent) events? Are the same object quality requirements that are appropriate for lower pT objects\nappropriate for very high energy objects?\nThis Section addresses these questions, evaluates the trigger ef\ufb01ciency for the signal samples of in-\nterest, and discusses the trigger strategy for the earliest data taking periods. It is expected that during both\nlow and high luminosity periods there will be an unprescaled single muon trigger without an isolation\nrequirement. The 20 or 40 GeV threshold are expected to be highly ef\ufb01cient for a high mass resonance\ndecaying into two muons.\n12.1\nEf\ufb01ciency estimate\nThe muon trigger ef\ufb01ciency is estimated using several methods. The \ufb01rst method is to rely on simulation;\nwhile this is the simplest and most direct method it is believed to be somewhat more optimistic (better\nresolution, higher ef\ufb01ciency). Therefore, the trigger ef\ufb01ciency is also estimated using methods which\ncan be applied to real data.\nThe trigger ef\ufb01ciencies are calculated with respect to the of\ufb02ine event selection. Two combined\nmuons are required to satisfy the cuts: |\u03b7| < 2.7, pT > 30 GeV, track \ufb01t\n\u03c72\nD.O.F < 10 and Inner Detector\nand Muon Spectrometer track match\n\u03c72\nD.O.F < 10. The trigger ef\ufb01ciencies for the dimuon heavy resonance\nMonte Carlo samples are shown in Table 17. The ef\ufb01ciency as a function of pT has been \ufb01t to\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n679\n\nSample\nL1 %\nL2 %\nEF %\nTotal Trigger Ef\ufb01ciency %\n400 GeV \u03c1T/\u03c9T\n97.6 \u00b1 0.10\n98.8 \u00b1 0.07\n99.5 \u00b1 0.05\n96.0 \u00b1 0.13\n600 GeV \u03c1T/\u03c9T\n98.1 \u00b1 0.08\n98.5 \u00b1 0.08\n99.2 \u00b1 0.06\n95.9 \u00b1 0.13\n800 GeV \u03c1T/\u03c9T\n97.6 \u00b1 0.10\n98.7 \u00b1 0.07\n99.2 \u00b1 0.05\n95.6 \u00b1 0.13\n1 TeV \u03c1T/\u03c9T\n97.6 \u00b1 0.09\n98.7 \u00b1 0.07\n99.2 \u00b1 0.05\n95.6 \u00b1 0.12\n1 TeV Z\u2019 (E6)\n97.8 \u00b1 0.09\n98.9 \u00b1 0.06\n99.5 \u00b1 0.04\n96.3 \u00b1 0.1\n2 TeV Z\u2019 (SSM)\n97.6 \u00b1 0.14\n98.7 \u00b1 0.11\n98.9 \u00b1 0.10\n95.3 \u00b1 0.2\nTable 17: Trigger ef\ufb01ciencies of dimuon resonance samples. For the meaning of E6 and SSM see [12].\nTrigger Level\nA0\nA1\nA2\nL1\n12.5 \u00b1 0.3\n3.7 \u00b1 0.4\n0.845 \u00b1 0.02\nL2\n19.6 \u00b1 0.2\n1.59 \u00b1 0.19\n0.976 \u00b1 0.02\nEF\n19.5 \u00b1 0.4\n1.56 \u00b1 0.3\n0.931 \u00b1 0.01\nTable 18: Fitted parameter for the L1, L2, and EF of the trigger pT turn on curves\n.\nf(pT) = 0.5\u00b7A2 \u00b7(1.0+er f( pT \u2212A0\n\u221a\n2\u00b7A1\n))\n(6)\nwhere er f is the error function, A0, A1, and A2 are the \ufb01t parameters which represent the pT value at\nwhich the ef\ufb01ciency reaches half its maximum value, the slope of the turn-on curve, and the maximum\nef\ufb01ciency in the plateau region, respectively.\nThere are several methods to evaluate the trigger ef\ufb01ciency from the data itself. A possible one is\nto look at the trigger ef\ufb01ciency for a known experimentally clean signature that is similar to the \ufb01nal\nstate of interest; Z \u2192\u00b5+\u00b5\u2212is one of such signatures. Since the Z is light compared to the total center\nof mass energy, it can be produced with a signi\ufb01cant pT distribution. The trigger ef\ufb01ciency on the\nZ can be measured and extrapolated to high pT. The advantage of this method is that it uses data to\nmeasure the trigger ef\ufb01ciency which is the most accurate method of measuring the Z trigger ef\ufb01ciency.\nA disadvantage is that the muon trigger ef\ufb01ciency is being extrapolated to a pT by a factor of 10 higher\nthan the mean pT of the muons from the Z decay.\nThe strategy of evaluating the trigger ef\ufb01ciency from data is as follows. It is \ufb01rst necessary to use\none of several methods to estimate the muon trigger ef\ufb01ciency as a function of the muon pT and its\nuncertainty. The single object trigger ef\ufb01ciency allow the construction of the probability for an event\nwith N objects to pass the trigger. This probability can be written as:\nP = 1\u2212\nN\n\u220f\ni=1\n(1\u2212Pi)\n(7)\nwhere Pi is the probability for the i-th object to pass the trigger.\nTwo common methods that have been used extensively at the Tevatron are the selection by orthogonal\ntriggers and the \u2019Tag and Probe\u2019 method using Z \u2192\u00b5\u00b5 decay. The \u2019Tag and Probe\u2019 requires two of\ufb02ine\nmuons to have an invariant mass within 12 GeV2 of 91.1 GeV2. The turn on curves as a function of the\nof\ufb02ine muon pT, obtained using this method, is \ufb01t to equation 6. This procedure was repeated for all\nthree trigger levels and the results are summarized in Table 18.\nA second possible method of evaluating the trigger ef\ufb01ciency with data is by the method of orthog-\nonal triggers. To obtain a sample of unbiased events we select events that pass one of the calorimeter\nbased triggers, the single 20 GeV jet trigger. We then perform the of\ufb02ine analysis and require that we\nhave a dimuon pair using identical event selection to the \u2019Tag and Probe\u2019 analysis. From this sample we\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n680\n\nSample\nL1Mu20 Ef\ufb01ciency %\nL2Mu20 Ef\ufb01ciency %\nEFMu20 Ef\ufb01ciency\nTotal Ef\ufb01ciency\nZ\u2019 1 TeV (SSM)\n97.7 \u00b1 0.11\n99.0 \u00b1 0.07\n99.6 \u00b1 0.04\n96.3 \u00b1 0.01\nZ \u2192\u00b5+\u00b5\u2212\n97.83 \u00b1 0.04\n98.86 \u00b1 0.03\n99.52 \u00b1 0.02\n96.26 \u00b1 0.05\nTable 19: L1Mu20 trigger ef\ufb01ciencies at L1, L2, and Event Filter w.r.t of\ufb02ine reconstruction using\northogonal trigger selection to record events\n.\nsimply check the fraction of events that pass the L1, L2, and EF trigger conditions for the 20 GeV muon\ntrigger. The results are shown in Table 19 and are in good agreement with the \u2019Tag and Probe\u2019 method\nand direct emulation of the trigger on the Monte Carlo sample. Unfortunately, in the real experiment a\nsingle jet trigger with a threshold of 20 GeV would be very highly prescaled and hence will suffer from\npoor statistics. Events that passed any calorimeter trigger could be used for this study if biases in the\nevent topology were taken into account, however, such a study is beyond the scope of this note.\nWe have developed two methods that could be used to evaluate the trigger ef\ufb01ciency from data.\nExtraction of the muon trigger ef\ufb01ciency as a function of the reconstructed muon kinematics via a tag\nand probe method and an orthogonal trigger method agree well with the simulated trigger ef\ufb01ciency.\nThese methods will allow us to more accurately estimate the trigger ef\ufb01ciency for LHC data.\n13\nSummary\nIn this paper Muon trigger baseline performance and rates for initial and standard LHC operation have\nbeen presented. Trigger ef\ufb01ciency has been studied in detail in a wide energy range using single muon\nsimulated samples. From ef\ufb01ciencies the muon rates have been evaluated. It should be noted that due\nto the uncertainties of the inclusive muons cross-sections, rates could vary signi\ufb01cantly and different\nthreshold cuts could be adopted. A further rate reduction should come from dedicated strategies to reject\nmuon from in-\ufb02ight decays of K and \u03c0; in this paper a preliminary analysis is presented at Event Filter.\nIt is demonstrated that a good rejection can be achieved with contained losses of prompt muons.\nThe possibility to select at the ATLAS second level trigger with high ef\ufb01ciency isolated muons\nfrom W and Z decays reducing the ones from heavy quark decays has been studied in depth. Although\nelectronic readout and pileup noise have been simulated, no cavern background has been yet included. A\nfactor of ten reduction on high-pT muons from heavy-quark decays has been obtained while maintaining\na 95% ef\ufb01ciency on Z \u2192\u00b5+\u00b5\u2212\ufb01nal state. Next step will be to investigate how much the use of the\nlongitudinal granularity of the calorimeters and inner tracker detector will increase the muon isolation\nrejection power.\nThe overall performance of the TileCal muon tagging algorithm has been presented, using MC sam-\nples of single muons and inclusive B-Physics processes, including minimum-bias pileup at low luminos-\nity.\nWe \ufb01nally addressed the question of how the muon trigger ef\ufb01ciency can be measured with Z \u2192\n\u00b5+\u00b5\u2212and Z\u2032 \u2192\u00b5\u00b5 using the tag and probe method. This technique shows a very good agreement with\nresults based on Monte Carlo studies.\nReferences\n[1] ATLAS Collaboration, Muon Spectrometer Technical Design Report, CERN/LHCC/97-022 (1997).\n[2] A. Sidoti, The ATLAS trigger muon \u2019vertical slice, Nucl. Instrum. Meth. A 572 (2007) 139.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n681\n\n[3] T. Sjostrand, S. Mrenna and P. Skands, PYTHIA 6.4 physics and manual, JHEP 0605 (2006) 026.\n[4] ATLAS Collaboration, ATLAS High-Level Trigger, Data Acquisition and Controls Technical Design\nReport, CERN/LHCC/2003-022 (2003).\n[5] T. Sjostrand, Pythia 5.7 And Jetset 7.4: Physics And Manual, CERN-TH-7112-93-REV (1995).\n[6] J.Ranft, DPMJET version H3 and H4, INFN-AE-97-45 (1997).\n[7] ATLAS Collaboration, Triggering on Low-pTMuons and Di-Muons for B-Physics, this volume.\n[8] BABAR Collaboration (P.F. Harrison and H. Quinn (editors) et al.), The BABAR Physics Book,\nSLAC-R-0504 (1998).\n[9] G. Usai Nucl. Instrum. Meth. 518 (2004) 36.\n[10] ATLAS Collaboration, First Level Trigger Technical Design Report, CERN/LHCC/98-14 (1998).\n[11] ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\n[12] ATLAS Collaboration, Dilepton Resonances at High Mass, this volume.\nTRIGGER \u2013 PERFORMANCE OF THE MUON TRIGGER SLICE WITH SIMULATED DATA\n682\n\nHLT b-Tagging Performance and Strategies\nAbstract\nThe ability to trigger on b-jets improves the \ufb02exibility and physics performance\nof the High Level Trigger (HLT), especially for topologies containing more\nthan one b-jet. It will be shown that the acceptance for b-jets can be increased\nand background reduced by lowering jet transverse energy thresholds and ap-\nplying b-tagging selections based on the impact parameter of tracks in jets.\nThis note reviews the b-jet selection in the HLT and discusses its integration\ninto the ATLAS trigger menu.\n1\nIntroduction\nFinal states containing b-jets have been proposed as signatures with substantial discovery potential in\na variety of physics channels. The ability to separate b-jets from light-quark and gluon jets is thus an\nimportant ingredient of the online selection strategy in ATLAS.\nOne of the most interesting physics cases addressed by such a b-jet trigger selection involves events\nwith \ufb01nal states containing four b-jets. This event class is relevant for Higgs bosons search in the low\nmass range, mH < 130 GeV. The most promising channels are the H \u2192b\u00afb decay, where the Standard\nModel Higgs boson is produced by way of the associated production channel t\u00aftH and, in supersymmetric\ntheories, the channels b\u00afbH, b\u00afbA with H/A \u2192b\u00afb or H \u2192hh \u2192b\u00afbb\u00afb.\nThe selection of b-jets at the trigger level is mainly meant to improve the \ufb02exibility of the HLT,\nextending its physics performance for the topologies described above. This is achieved by increasing the\nacceptance for signal events, while concurrently reducing the background.\nThe b-jet selection relies on tracking information which is only available starting with the Second\nLevel Trigger (L2). Therefore, the acceptance for signal can only be increased by simultaneously low-\nering L1 jet thresholds and applying a more discriminating b-jet selection in the High Level Trigger (L2\nand EF). High rejection power from the b-jet trigger is required to compensate for less rejection due to\nlower L1 thresholds and thereby to comply with L2 and EF output rate limitations.\n2\nMonte Carlo samples\nThe b-tagging performance on single jets, presented in this note, is evaluated on b-jets from H \u2192b\u00afb\ndecays, where the Higgs boson has a mass of 120 GeV and is produced in association with a W decaying\nleptonically. The standard background for single-jet studies are the corresponding u-jets, obtained by\narti\ufb01cially replacing the b-quarks from the Higgs decay with u-quarks. While these events imprecisely\nmodel the real background from light-\ufb02avour jets they can be seen as a worst case scenario since the\nkinematical properties of signal and background are very similar.\nEven in this very simple situation, the association between Regions of Interest (RoI), identi\ufb01ed by\nthe L1 trigger, and jets is not uniquely de\ufb01ned: a generic x-quark in the \ufb01nal state of an interaction or a\ndecay can radiate gluons and, therefore, change its direction. An RoI from H \u2192b\u00afb or H \u2192u \u00afu is labeled\nas x-jet (x = b, u) if an x-quark from the original hard process points, after \ufb01nal state radiation, along the\nRoI direction within an angular distance of \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 < 0.1.\nIn order to evaluate the rate of the b-jet trigger menu, the rejection power must be evaluated on a\nmore representative background sample. As for many of the trigger studies in ATLAS, dijet samples\nare chosen for this purpose since they correctly include all contributions to the b-tagging background,\nincluding c-quarks and taus.\n683\n\nAll data samples studied in this note have been generated without pile-up, leaving the in\ufb02uence\nof pile-up for further studies. The activity due to underlying event is taken into account since it is\nautomatically included in the PYTHIA [1] event generation.\n3\nHLT b-jet selection\n3.1\nL1 con\ufb01guration\nThe HLT reconstruction starts from the RoIs selected by the L1 trigger [2]. In particular, the b-jet trigger\nstarts from a L1 jet-RoI \u2206\u03b7 \u00d7\u2206\u03c6 = 0.8\u00d70.8 and performs track and vertex reconstruction in a smaller\nRoI \u2206\u03b7 \u00d7\u2206\u03c6 = 0.4\u00d70.4 in order to reduce data access and consequently processing time.\n3.2\nb-jet trigger feature extraction algorithms\nThe \ufb01rst step in the b-jet trigger chain, both at L2 and EF, is the reconstruction of the relevant quantities\nneeded to perform the selection. The b-jet RoIs can be separated from light jet RoIs using the impact\nparameters of the charged tracks, the properties of reconstructed secondary vertices, or soft leptons; all\nthese quantities are related to the b-quark lifetime and to its decay properties.\nThe present b-jet trigger implementation relies only on the impact parameters of charged tracks.\nPrimary vertex reconstruction is performed only in the z direction while its coordinates in the transverse\nplane are assumed to be compatible with the origin.\nTrack reconstruction algorithms are described, together with their performance, in [3]. The two Inner\nDetector tracking algorithms available at L2 show equivalent performance when operating on jet sam-\nples [3]. Thus to avoid unnecessary comparisons, the results obtained with the SiTrack algorithm are\npresented. For EF track reconstruction, the algorithm corresponding to that used for of\ufb02ine reconstruc-\ntion has been adopted (NewTracking).\n3.2.1\nPrimary vertex reconstruction\nAlong the z direction no a priori knowledge of primary vertex zvtx is available; consequently, this has to\nbe reconstructed, starting from the tracks available in the RoI. This information is needed for the correct\nevaluation of the longitudinal parameter of each track with respect to the primary interaction position.\nThe adopted algorithm, a simple histogramming method based on a sliding window, yields an ef\ufb01-\nciency of 98(99)% and a resolution on zvtx of about 120(100)\u00b5m at L2(EF) as illustrated in Fig. 1.\n3.3\nTagging variables\nThe HLT b-jet tagging methods are based on the transverse and longitudinal impact parameters of the\nreconstructed tracks. Since the methods are the same for L2 and EF they will be described using L2\nvariables only.\n3.3.1\nTransverse impact parameter\nThe most natural choice is to build the b-tagging discriminant variable from the transverse impact pa-\nrameter d0 of the reconstructed tracks. Since the hadrons containing b-quarks have a \ufb01nite lifetime\n(\u03c4 \u223c1.6 ps), tracks from their decays are characterized by large d0 values, while tracks from u-jets come\ndominantly from the primary vertex (dvtx = 0).\nIn particular, the signi\ufb01cance of the transverse impact parameter S = d0/\u03c3(d0) is used, where \u03c3(d0)\nis the error on the impact parameter. The error on the transverse impact parameter at L2 is parametrized\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n684\n\nrec\n-z\ntrue\nz\n-3\n-2\n-1\n0\n1\n2\n3\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n-3\n10\n\u00d7\nFigure 1: The distribution of the difference between the true and the reconstructed z primary vertex\ncoordinates at L2 (full line) and EF (dashed line). The widths as determined by a \ufb01t to the distributions\nare 120 \u00b5m and 100 \u00b5m, respectively.\nas a function of reconstructed pTas:\n\u03c3(d0) =\ns\np2\n0 +\n\u0012 p1\npT\n\u0013p2\nwhere p0 is the asymptotic term, p1 is the term due to multiple scattering, and p2 is the exponent of the\nmultiple scattering contribution (close to two). Although L2 tracking algorithms have recently reached a\ngood level of precision, the above error parametrization is still applicable at L2 during early data, while\nfor the EF the reconstructed error is used.\nFigure 2 shows the distributions of the impact parameter signi\ufb01cance d0/\u03c3(d0) for b-jets and light\njets at L2. The signi\ufb01cance has been rescaled according to the function f(x) = log(1 + |x|) in order\nto have a reasonably uniform bin population along the x axis. From these plots it can be guessed that\nthe impact parameter signi\ufb01cance is a promising choice for the discriminant variable, since the two\ndistribution are very well separated.\n3.3.2\nLongitudinal impact parameter\nThe longitudinal impact parameter (z0), i.e. the track\u2019s z-intercept, can be adopted, as well as the trans-\nverse impact parameter, to discriminate between b-jets and light jets. After the primary vertex position\nhas been reconstructed, the \u03b4z0 = z0 \u2212zvtx variable can be used to form a discriminant which can then\nbe used for b-jet selection. Figure 3 shows the distributions of the longitudinal impact parameter signif-\nicance (\u03b4z0/\u03c3(z0)) of b-jets and light jets at L2. The signi\ufb01cance has been rescaled as described above\nfor the transverse impact parameter.\nAs for Fig. 2, the signal and background distributions are different although much less so than for\nthe transverse impact parameter signi\ufb01cance. From this comparison, it is clear that most of the discrim-\nination will be provided by the measured transverse impact parameter signi\ufb01cance. The resolution of\nthe longitudinal impact parameter signi\ufb01cance is not as good due to the coarser resolution of the silicon\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n685\n\n ))\n0\n( d\n\u03c3\n /\n0\nf( d\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nFraction of tracks\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nFigure 2: Distribution of the rescaled function (de-\nscribed in the text) of the transverse impact pa-\nrameter signi\ufb01cance for tracks coming from b-jets\n(solid line) and light jets (dashed line) at L2.\n ))\n0\n( z\n\u03c3\n)/\nvtx\n - z\n0\nf(( z\n0\n0.5\n1\n1 5\n2\n2.5\n3\nFraction of tracks\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nATLAS\nFigure 3: Distribution of the rescaled function (de-\nscribed in the text) of the longitudinal impact pa-\nrameter signi\ufb01cance for tracks coming from b-jets\n(solid line) and light jets (dashed line) at L2.\ntracking detectors along the z-direction, bigger extrapolation distance from innermost silicon layer hit to\nprimary vertex at high \u03b7, and to the resolution of the reconstructed primary vertex.\n3.4\nHLT b-jet tagging methods\nIn this Section, HLT b-tagging methods are described. The likelihood ratio method is quite general and\ncan be applied to different variables while the \u03c72 method is essentially designed to test the compatibility\nof the tracks with respect to the primary vertex using the transverse impact parameter.\nThe likelihood ratio, using information on the signal and background shape that have to be estimated\non real data, is both more powerful and more dif\ufb01cult to tune than the \u03c72 method.\n3.4.1\nThe likelihood-ratio method\nThe likelihood-ratio method is a statistical tool used to separate two or more event classes, and is based\non a set of characteristic variables. The likelihood-ratio variable W is evaluated, for a given event, as\nthe ratio between the probability distributions for two alternative hypotheses. In its application to b-jet\nselection, the likelihood-ratio variable is de\ufb01ned as\nW = S(s)/S(b),\nwhere S(s) and S(b) are the probability densities for the signal, the b-jets, and the background, rep-\nresented in this case by the u-jets. This variable is widely used to obtain the best possible separation\nbetween signal and background, in terms of a single variable, in \ufb01ts aimed at extracting the fraction of\nsignal events in a given sample. The same variable can be also directly used, as in the b-jet selection\ncase, to select signal events, for example by applying a cut on the likelihood-ratio variable itself.\nThe probability density distributions used in the b-tagging application can be functions of some\nparameter of each track (e.g. the transverse impact parameter d0) or of some collective property of the\njet (e.g. its track multiplicity). In the \ufb01rst case, these distributions take the form\ns(par1, par2, par3,..., parn),\nb(par1, par2, par3,..., parn),\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n686\n\nwhere the 1,...,n indices identify each track belonging to the jet. The corresponding likelihood-ratio\nvariable is thus de\ufb01ned as\nW = s(par1, par2, par3,..., parn)\nb(par1, par2, par3,..., parn)\nExact evaluation of the s and b functions is very dif\ufb01cult, since it would require an almost in\ufb01nite amount\nof simulated data; for example, in order to reasonably populate an n-dimensional cube, about 100 entries\nare needed for each dimension, corresponding to n100 tracks; even worse, the number of tracks in a jet is\nnot \ufb01xed. However, if we assume that the variables corresponding to different tracks are independent, the\nratio between the overall probability densities reduces to the product of the ratios of the single probability\ndensities:\nW =\nn\n\u220f\ni=1\ns(pari)\nb(pari),\nwhich is much easier to evaluate. In the b-tagging case, track parameters have complex correlations\nwhich depend on the proper time for the B hadron and on its decay kinematics. Nevertheless, it can be\nproven that, neglecting these correlations does not invalidate this variable, but results only in a slight\nreduction of its discriminating power.\nThe W variable, can take any value between 0 (for the background) and +\u221e(for the signal). For\npractical reasons, it is useful to handle a variable de\ufb01ned on a \ufb01nite interval; to achieve this, W is usually\nreplaced by another variable\nX =\nW\n1+W ,\nwhich can only range between 0 and 1.\nAs an illustration of the method, Fig. 4 and Fig. 5 show the distributions of the discriminant variable\nX which is based on the combination of the transverse and longitudinal impact parameter for b-jets and\nlight jets respectively at L2 and EF. It can be seen that signal events (b-jets) accumulate near X = 1, while\nthe background (light jets) tends to have X close to 0.\nX\n0\n0.2\n0.4\n0.6\n0 8\n1\nEvents\n0\n200\n400\n600\n800\n1000\n1200\nATLAS\nFigure 4: Distribution of the discriminant variable\nX based on the combination of the transverse and\nlongitudinal impact parameter signi\ufb01cances for b-\njets and u-jets (dark area) at L2.\nX\n0\n0.2\n0.4\n0.6\n0.8\n1\nEvents\n0\n200\n400\n600\n800\n1000\n1200\nATLAS\nFigure 5: Distribution of the discriminant variable\nX based on the combination of the transverse and\nlongitudinal impact parameter signi\ufb01cances for b-\njets and u-jets (dark area) at EF.\nContrary to the of\ufb02ine b-tagging methods based on likelihood ratio, the sign of the impact parameters\nis currently not used at HLT since the RoI direction does not give a precise estimation of the b-jet\ndirection. Future studies will use the impact parameter sign determination respect to a track based cone\njet described in the next Section.\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n687\n\n3.4.2\n\u03c72 method\nThe \u03c72 method offers an alternative tagging approach that is more robust since it is less dependent on\nthe details of the impact parameter distributions. This method has been studied and characterized only at\nL2.\nThe \u03c72 method computes the probability for a jet to originate from the primary vertex, based on\nthe signed transverse impact parameter signi\ufb01cance of tracks pointing to the jet. This technique was\noriginally developed by the ALEPH collaboration and extensively used at LEP and Tevatron experiments\n[6] [7] [8]. One of the main advantages of this method is that it only relies on the transverse impact\nparameter signi\ufb01cance distribution of prompt tracks in multi-jet events, which can be easily derived\ncompletely from real data. On the other hand the performance of this method is limited due to the fact\nthat tracks from beauty and charm particles produce signi\ufb01cant tails with negative impact parameters.\nThese negative tails originate from the differences of the direction of the estimated jet and B-hadrons and\nalso in the differences of the direction of B-hadrons and charmed hadrons in the cascade decays.\nThe de\ufb01nition of the sign of the transverse impact parameter is based on the angle between the jet\naxis and the line between the primary vertex and the point of closest approach of the track, such that it\nis negative when the track appears to originate behind the primary vertex (i.e. when the angle is greater\nthan \u03c0/2) as illustrated in Fig. 6.\nd0 = |\u03b4|\nd0 = \u2212|\u03b4|\nFigure 6: De\ufb01nition of the sign of the transverse impact parameter. When the angle between the jet axis\nand the line between the primary vertex and the point of closest approach of the track is lower (greater)\nthan \u03c0/2 the sign is positive (negative).\nTracks from light-quark jets have equal probability to have positive or negative transverse impact\nparameters, and the width of the signed transverse impact parameter distribution depends on the tracking\ndetector resolution and multiple-scattering effects. The signed transverse impact parameter distribution\nof tracks from displaced b-jets, on the other hand, has a large positive asymmetry due to the fact all that\nmost of the long-lived particles from b-hadron decays are produced with positive impact parameters.\nGood jet angular resolution is a key to achieving a good b/light-quark jet discrimination since the\ndirection of the jet axis enters into the calculation of the sign of the impact parameter. Poor jet angular\nresolution results in frequent mis-assignment, particularly for tracks with small angle with respect to the\njet direction.\nIn order to improve the resolution of the azimuthal angle (\u03c6) of the jet, a track-based simple cone jet\nreconstruction algorithm is used instead of the jet-RoI \u03c6 direction. Figure 7 shows that the \u03c6 resolution\nimproves by more than a factor of two when tracks are used to compute the jet direction. The effect of\njet \u03c6 resolution on b/light quark jet discrimination can be seen in Fig. 8, which shows the distribution\nof signed transverse impact parameter signi\ufb01cance for b-jet tracks when \u03c6 is computed using truth, RoI,\nand track-jet \u03c6 directions.\nThe negative transverse impact parameter signi\ufb01cance is computed using a parameterization for the\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n688\n\nTrack Jet multiplicity\n2\n3\n4\n5\n6\n7\n resolution (rad)\n\u03c6\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nATLAS\nRoI resolution\nFigure 7: \u2206\u03c6 between the true b-quark direction\nand its estimate using RoIs (solid line) and track-\nbased jets (dashed line), as a function of the track-\njet multiplicity.\nSigned IP significance\n-20\n-15\n-10\n-5\n0\n5\n10\n15\n20\nEvents\n1\n10\n2\n10\n3\n10\nTruth\nTrackJet\nRoI\nATLAS\nFigure 8: Distribution of the signed impact param-\neter signi\ufb01cance for b-jets when the jet \u03c6 direction\nis computed using truth, track-jet, and RoI infor-\nmation.\nNegative IP significance\n-14\n-12\n-10\n-8\n-6\n-4\n-2\n0\nEvents\n10\n2\n10\n3\n10\nATLAS\n< 7 pixel hits\nFigure 9: Negative transverse impact parameter\nsigni\ufb01cance and the resolution function R(S) for\ntracks with less than 7 hits in the Silicon detectors.\nNegative IP significance\n-14\n-12\n-10\n-8\n-6\n-4\n-2\n0\nEvents\n1\n10\n2\n10\n3\n10\nATLAS\n 7 pixel hits\n\u2265\nFigure 10: Negative transverse impact parameter\nsigni\ufb01cance and the resolution function R(S) for\ntracks with at least 7 hits in the Silicon detectors.\ntransverse impact parameter error as a function of pscat = psin\u03b8 3/2 and the number of hits in the pixel\ndetector. A double-Gaussian \ufb01t to the distribution of negative transverse impact parameter signi\ufb01cance\n(R(S)) is used to de\ufb01ne ptrk(S), the probability for a track to originate from a primary vertex:\nptrk(S) =\nR \u2212|S|\n\u221215 R(S)dS\nR 0\n\u221215 R(S)dS\n(1)\nwhere only tracks with positive impact parameter are used in the calculation. The distribution of negative\ntransverse impact parameter signi\ufb01cance and the resolution function R(S) is shown in Fig. 9 and Fig. 10\nfor tracks with less and more than 7 Silicon detectors hits.\nThe de\ufb01nition of ptrk ensures a uniform distribution between 0 and 1 for tracks originating from the\nprimary vertex. Tracks from displaced B decays result in ptrk \u223c0.\nA \u03c72 jet probability is de\ufb01ned by considering the probabilities of all tracks with positive transverse\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n689\n\nimpact parameter in a jet [6]:\npjet = \u03a0\nN\u22121\n\u2211\nj=0\n(\u2212log\u03a0)j\nj!\n(2)\nwhere \u03a0 = \u220fN\n1 ptrk(S).\nFigure 11 shows the ptrk distribution for light and b-quark jets. The spike at small probability for\nlight quarks tracks is due to tracks from V 0 decays, which have positive transverse impact parameter.\nFigure 12 shows the pjet distribution for light and b-quark jets. Jets are tagged as b, if the pjet is\nbelow some value, typically between 0.5% and 5%.\n probability\n2\n\u03c7\nTrack \n0\n0.2\n0.4\n0.6\n0.8\n1\nEvents\n10\n2\n10\n3\n10\nb-jets\nuds-jets\nATLAS\nFigure 11: Track \u03c72 probability (ptrk) for b-jets\n(full histogram) and light jets (shaded histogram).\n probability\n2\n\u03c7\nJet \n0\n0.2\n0.4\n0.6\n0.8\n1\nEvents\n1\n10\n2\n10\nb-jets\nuds-jets\nATLAS\nFigure 12: Jet \u03c72 probability (pjet) for b-jets (full\nhistogram) and light jets (shaded histogram).\n4\nHLT b-jet selection performance on single jet-RoIs\nEvery tagging method will be characterized by the curve showing the light-jet rejection versus the ef\ufb01-\nciency to select b-jets (\u03b5b). The light-jet rejection is de\ufb01ned as the inverse of the ef\ufb01ciency of selecting\nu-jets (Ru = 1/\u03b5u) where we have assumed that u-jets are representative of light jets in general.\n4.1\nLikelihood ratio method using impact parameters\nFigures 13 and 14 show, respectively, the b-tagging performance for L2 and EF when the transverse\nimpact parameter signi\ufb01cance is used in de\ufb01ning the discriminant variable X, while \ufb01gures 15 and 16\nshow the b-tagging performance curves for L2 and EF, when the signi\ufb01cance of the longitudinal impact\nparameter with respect to the primary vertex is used instead.\nFigures 17 and 18 show the b-tagging performance curves for L2 and EF when the likelihood ratio\nmethod is built on the combination of the transverse and longitudinal impact parameter signi\ufb01cances.\n4.2\n\u03c72 method\nThe performance of the \u03c72 b-tagging algorithm, evaluated as a function of the \u03c72 cut is shown in Fig. 19.\nThe limited ef\ufb01ciency of the method is due to the request of at least two reconstructed tracks to de\ufb01ne\nthe track-jet. Clearly, an effort should be made to include RoIs having only a single track. Nonetheless,\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n690\n\nb-jet efficiency\n0.2\n0.4\n0.6\n0.8\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 13:\nPerformance of the b-jet selection\nbased on the d0 signi\ufb01cance discriminant variable\nat L2.\nb-jet efficiency\n0.2\n0.3\n0.4\n0.5\n0 6\n0.7\n0.8\n0 9\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 14:\nPerformance of the b-jet selection\nbased on the d0 signi\ufb01cance discriminant variable\nat EF.\nb-jet efficiency\n0\n0 2\n0.4\n0.6\n0.8\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 15:\nPerformance of the b-jet selection\nbased on the \u03b4z0 signi\ufb01cance discriminant vari-\nable at L2.\nb-jet efficiency\n0\n0 2\n0.4\n0 6\n0.8\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 16:\nPerformance of the b-jet selection\nbased on the \u03b4z0 signi\ufb01cance discriminant vari-\nable at EF.\nb-jet efficiency\n0 2\n0.4\n0 6\n0.8\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 17:\nPerformance of the b-jet selection\nbased on the combination of the transverse and\nlongitudinal impact parameter signi\ufb01cances at L2.\nb-jet efficiency\n0.2\n0.4\n0 6\n0 8\n1\nlight jet rejection\n1\n10\n2\n10\n3\n10\nATLAS\nFigure 18:\nPerformance of the b-jet selection\nbased on the combination of the transverse and\nlongitudinal impact parameter signi\ufb01cances.\nwe note that the strength of the method lies in its impact intrinsic robustness and this advantage must\nalso be considered when comparing its performance with that of the likelihood method.\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n691\n\nb-jet efficiency\n0\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9\n1\nlight jet rejection\n1\n10\n2\n10\nATLAS\nFigure 19: Performance of the b-tagging selection based on the jet \u03c72 probability variable.\n4.3\nComparison with the of\ufb02ine selection\nTo tune the online working points so as to ensure the attainment of the overall (i.e. including of\ufb02ine cuts)\nef\ufb01ciency goal of 60% for b-jet tagging and avoid biases, it is crucial to evaluate the correlation between\nthe online and of\ufb02ine algorithms.\nThe performance of the L2 and EF trigger algorithms based on impact parameters in the transverse\nplane has been compared to that obtained with the corresponding of\ufb02ine algorithm. This choice is mo-\ntivated by the wish to perform a coherent comparison; more exhaustive comparison studies will be per-\nformed on speci\ufb01c physics selections.\nFigure 20 demonstrates that the L2, EF and Of\ufb02ine selections are well correlated. In particular it is\nalways possible to recover the full of\ufb02ine performance at a given b-jet ef\ufb01ciency if the L2 and EF working\npoints are set at an appropriate higher ef\ufb01ciency. In particular for the trigger menu studies shown in the\nfollowing, a working point of about 80% ef\ufb01ciency at L2 and about 70% at EF have been chosen in order\nto ensure full acceptance for the standard of\ufb02ine working point (60%).\nFuture studies will address remaining differences between EF and of\ufb02ine algorithms.\n4.4\nExecution time at L2 and EF\nThe execution time needed to reconstruct relevant quantities described in this note and to perform b-jet\nselection was evaluated both at L2 and EF. Results highlight that the timing performance \ufb01ts design\nrequirements and that the overall time spent is dominated by data preparation and track reconstruction\nalgorithms. Further details are given in [3].\n5\nb-tagging trigger strategy\nAfter having de\ufb01ned and characterized the b-jet selection algorithm on single b-jet RoIs the b-jet trigger\nmenu has to be built. Figure 21 illustrates the online b-jet selection algorithm\u2019s performance as evaluated\nusing high statistics samples. The performance of the L2 algorithm is indicated along with the perfor-\nmance of the EF algorithm on events which are selected by L2 (at the nominal working point of 80%\nef\ufb01ciency).\nSince the b-tagging cut is \ufb01xed, the b-tagging ef\ufb01ciencies vary with ETthreshold. Typical\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n692\n\nb-jet efficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight-jet rejection\n1\n10\n2\n10\n3\n10\nEF working point\nLVL2 working point\nOffline after HLT b-jet selection\nOffline\nATLAS\nFigure 20: The correlation between L2, EF and of\ufb02ine taggers\nL2(EF) b-tagging ef\ufb01ciencies are \u03b5b = 76(67)% at ET= 18 GeV and \u03b5b = 80(73)% at ET= 70 GeV.\nThis variation of the working point as a function of ETcompensates for the effect of the worsening of the\nb-tagging performance at low ET, so the rate reduction does not change signi\ufb01cantly with ET.\nIt is clear that b-jet selection can play an important role especially for events with multiple b-jets\nbecause the selective \ufb01ltering of b-jets can produce very high rejection and thereby allow a signi\ufb01cant\ndecrease of the L1 thresholds while keeping the jet-RoI output rate of L2 and EF almost constant.\n5.1\nb-jet trigger menu\nThe possible b-jet signatures initiated by multi-jet L1 signatures with given ETthresholds can be repre-\nsented in general as nbET mL1JET, where n indicates the number of b-tagged jets required out of m\nL1 jets with transverse energy greater than ET. The HLT b-tagging working point is the one describe in\nsection 4.3. The rate reduction as a function of the available L1 thresholds is shown in Fig. 22. The EF\noutput rates of different multi b-jet signatures at the luminosity of 1031 cm\u22122s\u22121 are given in Table 1.\nThe rates and uncertainties of these rates have been computed for dijet samples using the relations\npi = Ni\nEF/Ni\nTotal\nR = L \u2211pi\u03c3i\n\u03c3(R) = L\nr\n\u2211pi(1\u2212pi)\nNi\nTotal \u03c32\ni\n(3)\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n693\n\nb-jet efficiency\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLight-jet rejection\n1\n10\n2\n10\nL2\nEF\nATLAS\nFigure 21: b-jet performance based on the combination of the transverse and longitudinal impact param-\neter (EF selection starts from the chosen L2 working point).\n (GeV)\nT\nE\n20\n30\n40\n50\n60\n70\nRate reduction\n1\n10\n2\n10\n3\n10\n4\n10\n3b(HLT)_4J(L1)\n2b(HLT)_3J(L1)\n4b(HLT)_4J(L1)\n3b(HLT)_3J(L1)\nATLAS\nFigure 22: Rate reduction achieved with HLT b-jet as a function of the L1 ETthreshold.\nwhere Ni\nEF and Ni\nTotal are respectively the number of events selected at the end of the trigger chain and the\ntotal number of events in the sample Ji, \u03c3i is the cross-section of the sample Ji and L is the luminosity.\nThe uncertainties in the tables indicate that at high transverse energy, the rate computation is not very\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n694\n\nprecise. Nevertheless, with the requirement of keeping the EF output rate at a few Hz for each multi b-jet\nsignature, trigger menus for different luminosities can be chosen as:\n\u2022 luminosity 1031 cm\u22122s\u22121: 3b23 3L1J23, 3b18 4L1J18\n\u2022 luminosity 1032 cm\u22122s\u22121: 2b42 3L1J42, 3b35 3L1J35, 3b23 4L1J23, 4b18 4L1J18\n\u2022 luminosity 1033 cm\u22122s\u22121: 2b70 3L1J70, 3b42 3L1J42, 3b35 4L1J35, 4b23 4L1J23\nIt can be noticed that as the luminosity increases, requiring more b-tagged jets is a viable alternative to\nincreasing ETthresholds.\nTransverse energy\nSignature rate [Hz]\nET[GeV]\n2bET 3L1JET\n3bET 3L1JET\n3bET 4L1JET\n4bET 4L1JET\n18\n47\u00b111\n1.5\u00b10.4\n1.0\u00b10.3\n0.2\u00b10.1\n23\n18\u00b17\n0.5\u00b10.2\n0.4\u00b10.2\n0.004\u00b10.002\n35\n1.0\u00b10.2\n0.04\u00b10.01\n0.02\u00b10.01\n0.0007\u00b10.00006\n42\n0.4\u00b10.1\n0.02\u00b10.01\n0.01\u00b10.01\n0.0007\u00b10.00006\n70\n0.01\u00b10.02\n0.0008\u00b10.0006\n0.0007\u00b10.0006\n0.0007\u00b10.00006\nTable 1: EF output rates for the different multiple b-jet signatures at 1031 cm\u22122s\u22121.\nThe strategy behind the evolution of the b-jet signatures is to select more aggressively as luminosity\nincreases and HLT tracking becomes better understood. Before the b-jet trigger achieves full perfor-\nmance, a good online resolution of track impact parameters must be achieved. In turn, this requires\nadequate knowledge of the inner detector alignment and suf\ufb01cient understanding of the overall detector\nperformance.\n5.2\nProspects for measuring ef\ufb01ciency and correlation with of\ufb02ine on real data\nThe HLT b-tagging group is working closely with the of\ufb02ine b-tagging group to develop a method to\nmeasure the b-jet ef\ufb01ciency with real data. For an explanation of the method and a discussion of its\nperformance we refer to the b-tagging note on dijets [5].\nIn addition to the \u201cphysics\u201d triggers listed in the previous Section , the b-jet group has introduced\nseveral \u201ctechnical\u201d triggers in order to study rate and correlation of the online and of\ufb02ine algorithms:\n\u2022 single b-jet signatures: b18, b23, b35, b42, b70: prescaled to limit their contribution to the EF\noutput to few Hz;\n\u2022 each multi jet item is duplicated with an identical signature which selects, independently of the\nHLT b-jet result, one over n events (where n is presently set at 1000 but will be tuned according to\nthe rate allocated to b-jet triggers).\n6\nSummary and conclusions\nThe b-jet selection at the L2 and EF stages of the ATLAS High Level Trigger has been described and\ncharacterized. An HLT b-tagging trigger menu has been implemented which demonstrates the feasibility\nof increasing the acceptance of events with more than one b-jet by decreasing L1 jet ETthresholds while\ncontrolling the output rate by introducing a b-jet selection at the HLT.\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n695\n\nReferences\n[1] T. Sjostrand, L. Lonnblad, S. Mrenna and P. Skands, PYTHIA 6.3: Physics and Manual, arXiv:hep-\nph/0308153.\n[2] ATLAS Collaboration,\nThe Atlas Experiment at the CERN Large Hadron Collider, JINST\n3:S08003,2008.\n[3] ATLAS Collaboration, HLT Track Reconstruction Performance, this volume.\n[4] ATLAS Collaboration, b-Tagging Performance, this volume.\n[5] ATLAS Collaboration, b-Tagging Calibration with Jet Events, this volume.\n[6] ALEPH Collaboration, A precise measurement of \u0393Z\u2192b\u00afb/\u0393Z\u2192hadrons, Phys. Lett. B313 (1993) 535.\n[7] D0 Collaboration, A Search for Wb\u00afb and WH Production in p \u00afp Collisions at \u221as = 1.96 TeV, Phys.\nRev. Lett. 94, 091802 (2005).\n[8] CDF Collaboration, Measurement of the t\u00aft production cross-section in p \u00afp collisions at \u221as =1.96\nTeV using lepton+jets events with jet probability b-tagging, Phys. Rev. D74, 072006 (2006).\nTRIGGER \u2013 HLT b-TAGGING PERFORMANCE AND STRATEGIES\n696\n\nOverview and Performance Studies of Jet Identi\ufb01cation in the\nTrigger System\nAbstract\nThis note describes in detail the algorithms used to identify jets in the ATLAS\ntrigger system. Results from performance studies of these jet algorithms are\npresented. An initial trigger menu using jets and proposed strategy to adapt to\nincreases in luminosity are also discussed.\n1\nIntroduction\nA critical component of the ATLAS trigger system is the ability to ef\ufb01ciently identify hadronic jets in an\nevent. The performance of the jet reconstruction depends on the trigger jet energy resolution and scale.\nIn this note we discuss the algorithms at the different trigger levels and evaluate their performance.\n2\nL1 jet trigger algorithm\nA detailed description of the L1 jet trigger algorithm can be found in [1]; however, for completeness, a\nsummary of the relevant features of this algorithm is presented below.\nThe ATLAS electromagnetic and hadronic calorimeters are segmented into approximately 7200 trig-\nger towers, with granularity of approximately 0.1\u00d70.1 in \u03b7 \u00d7\u03c6 space. The granularity varies slightly in\ndifferent sub-detector systems, for further details see [1]. Analog signals from these trigger towers are\ntransmitted directly to the L1 system. The L1 hardware digitises the trigger tower signals, associates them\nwith a bunch crossing and performs pedestal subtraction. The L1 system also applies a noise suppression\nthreshold and transverse energy calibration. The electromagnetic tower ET response is calibrated at the\nEM scale and the hadronic tower ET response is calibrated for jets.\nThe L1 trigger constructs \u201cjet elements\u201d made of the sum of 2 \u00d7 2 trigger towers in the electro-\nmagnetic (EM) calorimeter added to 2 \u00d7 2 trigger towers in the hadronic calorimeter which gives a\ngranularity of 0.2\u00d70.2 in \u03b7 \u00d7\u03c6 space. The jet reconstruction algorithm consists of a sliding window of\nprogrammable size that could be either 2 \u00d7 2, 3 \u00d7 3 or 4 \u00d7 4 jet elements. A jet is reconstructed if the\ntotal transverse (EM+Hadronic) energy within the window is above a given threshold. The step size for\nthe sliding window is 0.2 in both \u03b7 and \u03c6 which implies signi\ufb01cant overlap of the window in neighbour-\ning positions. To prevent the L1 algorithm from identifying overlapping jets, the transverse energy of a\ncluster, de\ufb01ned as a region spanned by 2\u00d72 jet elements, is required to be a local maximum within \u00b10.4\nunits in \u03b7 and in \u03c6. The L1 jet algorithm identi\ufb01es jets within the region of |\u03b7| < 3.2. Figure 1 shows a\nschematic diagram of the jet reconstruction algorithm at L1.\nIn contrast to the other calorimeters, the L1 forward calorimeter (FCAL) trigger towers have a granu-\nlarity of approximately 0.4\u00d70.4 in \u03b7 and \u03c6. The forward jet trigger electronics was originally designed\nto only be used for the calculation of missing ET at L1, and not to identify in addition jets in the forward\nregions of the detector. As a consequence, limited granularity of the FCAL data is available at L1. A jet\nelement in the FCAL is formed by summing calorimeter towers in \u03b7. Therefore, the FCAL jet elements\nhave a \u03c6 granularity of 0.4 with only a single \u03b7 bin at each end. This has an impact on how the HLT\nforward jet reconstruction algorithm is implemented, as discussed in Section 5.\nIn the tentative menu proposed for early data taking, a sliding window size of 4\u00d74 jet elements has\nbeen chosen for almost all thresholds; the exception is the algorithm used to reconstruct b-jets which\nhas a proposed transverse energy threshold of 5 GeV and uses a window size of 2 \u00d7 2 to minimise the\nidenti\ufb01cation of fake jets associated with possible calorimeter noise.\n697\n\nFigure 1: Schematic diagram of the L1 jet algorithm showing a window of 4 \u00d74 jet elements spanning\nthe electromagnetic and hadronic calorimeter in depth, and a local maximum transverse energy cluster\nof 2\u00d72 jet elements.\nTable 1: Simulated dijet event samples used to study the performance of the jet trigger algorithms. The\nlast row gives a summary of the cuts applied on the hard scatter parton in the event.\nEvent Sample\nJ0\nJ1\nJ2\nJ3\nJ4\nJ5\nJ6\nJ7\nJ8\nCross-section (mb)\n17.6\n1.4\n9.3E-2\n5.9E-3\n3.14E-4\n1.3E-5\n3.6E-7\n5.3E-9\n2.22E-11\nET Range (GeV)\n8-17\n17-35\n35-70\n70-140\n140-280\n280-560\n560-1120\n1120-2240\n> 2240\n3\nL1 performance\nDijet events were used to study the performance of the L1 jet trigger algorithm. Table 1 provides a\nsummary of the simulated data samples used along with their respective cuts on the hard scatter parton\nand cross-section. These simulated dijet event samples, together, span the whole ET jet spectrum relevant\nfor jet identi\ufb01cation in the trigger.\nThe transverse energy scale of L1 jets is de\ufb01ned as the ratio between the transverse energy measured\nin L1 divided by the truth jet ET. Each jet identi\ufb01ed by the L1 trigger was matched to a truth jet found\nusing the cone algorithm with R = 0.4. The matching criterion consists in searching for the closest truth\njet in the \u03b7 \u2212\u03c6 plane, where the distance is de\ufb01ned as \u2206R =\np\n(\u03b7L1 \u2212\u03b7Reco)2 +(\u03c6L1 \u2212\u03c6Reco)2. The L1 jet\ntransverse energy scale as function of truth jet ET is shown in Fig. 2(a). The transverse energy scale at\nL1 varies from about 70% to 90%, increasing with the transverse energy of the jet. There are several\neffects that contribute to this behaviour. The \ufb01rst one is the noise suppression mentioned in Section 2.\nThe lower the transverse energy of the jet, the larger is the number of trigger towers that do not satisfy this\nnoise suppression threshold leading to an underestimation of the jet transverse energy. In addition, each\nL1 trigger tower signal must be associated with a particular Bunch Crossing Identi\ufb01cation number. The\nef\ufb01ciency of this requirement is approximately 50% for 1 GeV trigger tower signals, reaching nearly\n100% for 3 GeV trigger tower signals. Again, this inef\ufb01ciency particularly affects lower transverse\nenergy jets that will tend to contain a larger fraction of trigger towers with low energy signals. The\nmost important reason for the lower jet transverse energy scale with respect to truth jets comes from the\ndifferent e/\u03c0 response of EM and hadronic towers. For presentation purposes, a common conversion\nfactor is used to translate the number of counts measured in an EM or hadronic tower into units of\ntransverse energy. This results in an apparent lower jet transverse energy scale compared to truth jets. It\nis important to note that thresholds in the L1 are applied in terms of the internal L1 quantity \u201ccounts\u201d\nand not in units of transverse energy. In Fig. 2(b), the L1 jet transverse energy scale is also shown as\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n698\n\n [GeV]\nT\nTruth jet E\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nTruth\nT\n / E\nL1\nT\nE\n0.6\n0 65\n0.7\n0.75\n0.8\n0 85\n0.9\n0 95\n1\n1 05\n1.1\nATLAS\n(a)\n|\n\u03b7\nTruth jet |\n0\n0.5\n1\n1.5\n2\n2.5\n3\nTruth\nT\n / E\nL1\nT\nE\n0 6\n0.65\n0.7\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\nATLAS\n(b)\nFigure 2: The L1 jet transverse energy scale as function of truth jet transverse energy (a) and pseudo-\nrapidity (b).\n [GeV]\nT\nTruth jet E\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n resolution\nL1\nT\nE\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n| < 0 6\n\u03b7\n0.1 < |\nATLAS\n(a)\n [GeV]\nT\nOffline jet E\n0\n50\n100\n150\n200\n250\nL1 Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n > 10 GeV\nL1\nT\nE\n > 18 GeV\nL1\nT\nE\n > 23 GeV\nL1\nT\nE\n > 35 GeV\nL1\nT\nE\n > 42 GeV\nL1\nT\nE\n > 70 GeV\nL1\nT\nE\n > 120 GeV\nL1\nT\nE\n(b)\nATLAS\nFigure 3: L1 jet transverse energy resolution as a function of truth jet transverse energy (a) and the L1 jet\ntrigger ef\ufb01ciency as function of the of\ufb02ine reconstructed jet ET for different L1 energy thresholds (b).\na function of the pseudo-rapidity (\u03b7) of the truth jet. The response of the different calorimeter sub-\ndetectors can be identi\ufb01ed. Figure 3(a) shows the L1 transverse energy resolution as function of truth jet\nET. The transverse energy resolution is de\ufb01ned as the width of the EL1\nT \u2212Etruth\nT\ndistribution in each Etruth\nT\nbin, divided by the Etruth\nT\nof that bin.\nFigure 3(b) shows the L1 jet trigger ef\ufb01ciency as function of of\ufb02ine reconstructed jet ET for different\nL1 jet trigger thresholds. The limited jet transverse energy resolution of the L1 system particularly affects\nthe higher L1 energy thresholds.\nThe effect of pile-up on the performance of the L1 jet trigger reconstruction was also studied. At a\nluminosity of 1033s\u22121cm\u22122, an average of approximately 2 inelastic collisions are expected per bunch\ncrossing. Simulated dijet events including this level of pile-up were generated. The effect of increased\noccupancy in the calorimeters will have some impact on the reconstructed transverse energy of the jet.\nFigure 4 shows the impact of this pile-up on the L1 jet transverse energy scale and jet trigger ef\ufb01ciency.\nThe transverse energy scale increases due to the additional energy deposited in the calorimeter from pile-\nup events. The L1 transverse energy resolution also worsens as seen on Fig. 4(b). The effect is clearly\nmore important for low energy jets where the contribution of pile-up energy can be of the same order of\nmagnitude as the jet energy itself.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n699\n\n [GeV]\nT\nTruth jet E\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nTruth\nT\n / E\nL1\nT\nE\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\nATLAS\n(a)\n [GeV]\nT\nOffline jet E\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nL1 efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nj35\nL1\nL1 Pile-Up\n(b)\nATLAS\nFigure 4: The L1 jet transverse energy scale as function of truth jet transverse energy (a) for simulated\ndijet events with pile-up. The L1 jet trigger ef\ufb01ciency as function of of\ufb02ine reconstructed jets (b) for a\n35 GeV L1 trigger threshold, with and without taking into account pile-up.\n4\nHLT jet algorithms\nThe HLT object reconstruction is guided by the result of the L1 system. HLT algorithms typically only\naccess data from a limited region of the detector in the vicinity of an RoI provided by L1. The position\nof this RoI is successively updated and re\ufb01ned by the HLT algorithms.\nHLT algorithms are classi\ufb01ed in two types:\n\u2022 \u201cFeature Extraction algorithms\u201d: Algorithms that retrieve and unpack detector data and create\nsimple classes composed of useful physics observables. These algorithms consume most of the\navailable time.\n\u2022 \u201cHypothesis algorithms\u201d: Algorithms that retrieve the physics information produced in the preced-\ning Feature Extraction algorithms, and validate a speci\ufb01c hypothesis (e.g. ET threshold). These\nalgorithms have a very fast execution time.\nThis separation between Feature Extraction and Hypothesis algorithms optimises the overall execu-\ntion time since the data retrieved by a single Feature Extraction algorithm can be used to provide input\nto several fast Hypothesis algorithms to test various physics signatures, and hence avoids multiple data\naccess and unpacking.\nFigure 5 shows a schematic diagram of the sequence of algorithms used to reconstruct jets in the HLT.\nThe Hypothesis algorithms for jets reconstructed at L2 and EF compare the energy of the jet candidates\nto some prede\ufb01ned ET thresholds. The next few sections describe in detail each Feature Extraction\nalgorithm appearing in Fig. 5.\n5\nL2 jet algorithm\nStandard L2 jets are de\ufb01ned within the |\u03b7| < 3.2 region and are reconstructed using the electromagnetic\nand hadronic calorimeter data. Forward jets are de\ufb01ned within the range 3.2 < |\u03b7| < 5 and are recon-\nstructed using data from the forward calorimeters. As described below, the forward jet reconstruction is\ndifferent than the standard jet algorithm due to the limited \u03b7 position resolution of L1 jets.\nThe output of the L2 Feature Extraction algorithm is a reconstructed jet with a given energy and\nposition in \u03b7 and \u03c6. The algorithm contains three distinct parts described below: data preparation, jet\n\ufb01nding and calibration.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n700\n\nLevel\u22121 Jet RoI\nJet Hypothesis\nJet Reconstruction\nJet Hypothesis\nData Unpacking\nTrigger Tower Making\nJet Reconstruction\nLevel\u22122\nEvent Filter\nFigure 5: Schematic diagram of the sequence of algorithms used to reconstruct jets in the HLT. The ovals\nand diamonds represent Feature Extraction algorithms and Hypothesis algorithms, respectively.\n5.1\nL2 jet data preparation\nThe data preparation for the L2 jet trigger is a critical part of the algorithm chain. It provides the col-\nlection of data from the detector readout drivers (ROD) to the L2 processing units and the conversion\nfrom the raw data into bytestream \ufb01les readable by the HLT algorithms. The RODs receive data from\nthe calorimeters front-end boards (FEB) via optical \ufb01bres. The FEBs are installed on the detector and\ncontain the electronics for amplifying, shaping, sampling, pipelining, and digitising the signals [2,3].\nThe ATLAS calorimeters consist of more than 105 individual readout channels; therefore, in order\nto meet the L2 timing performance goals of 40 ms total processing time per event, the amount of data\nunpacked must be kept to a minimum while simultaneously maximising the physics performance of the\nalgorithm.\nThe L2 jet trigger algorithm accesses calorimeter data that lies in a rectangular region centred around\nthe L1 jet RoI position with a width \u2206\u03b7 and \u2206\u03c6 that can be de\ufb01ned to have any size. The widths \u2206\u03b7 and\n\u2206\u03c6 are parameters that are speci\ufb01ed at trigger con\ufb01guration time. Figure 6 shows a schematic diagram\nof the L2 jet reconstruction algorithm.\nThe position and transverse energy of each detector element that falls into the chosen (\u2206\u03b7, \u2206\u03c6)\nwindow is read out by the algorithm. As a result the calorimeter read out region can be regarded as\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n701\n\n\u03b7\n\u03c6\nHalf width\nHalf width\nLevel\u22121 RoI\nN iterations\n\u03c6\n\u03b7\nLevel\u22122 Jet\nFigure 6: Schematic diagram summarising the L2 jet algorithm. The data unpacking step reads in the\nnecessary calorimeter data within a prede\ufb01ned window size and de\ufb01nes a grid of calorimeter elements\neach with an associated energy and position. The size of grid elements depends on the calorimeter data\nunpacking method used. The dark (red) boxes in the diagram represent grid elements with substantial\nenergy deposition. The algorithm is seeded by the L1 position as shown on the left. The \ufb01nal jet is found\nafter a given number of iterations. The position of the jet is calculated as the energy weighted average of\nthe grid elements position within a given cone size. The energy of the jet is calculated as the sum of the\nenergy of each grid elements falling within the given cone size.\npartitioned into a grid of elements with associated energies and (\u03b7,\u03c6)-coordinates as shown in Fig. 6.\nTherefore, the amount of data accessed is equivalent to the number of grid elements.\nTwo different data unpacking approaches are implemented and described below. One of the methods,\nthe cell-based approach, has \ufb01ner granularity and hence produces more accurate energy and transverse\nenergy reconstruction, but is more time consuming. The other method, the front-end board approach, is\nfaster but the coarser granularity produces a less precise reconstruction. Both methods are, as we will\nsee in section 6, reasonably within the L2 time budget limits. The \ufb01nal decision of what approach should\nbe used will be made depending on the \ufb01nal High Level Trigger setup.\n5.1.1\nThe cell-based approach\nThis method uses the full granularity of the calorimeters [1]. Each grid element in Fig. 6 corresponds\nto a calorimeter cell with a given transverse energy and (\u03b7,\u03c6)-coordinate provided by the ROD. In the\nfollowing discussions, jets reconstructed using this data unpacking approach are referred to as \u201ccell-based\njets\u201d.\n5.1.2\nThe front-end board approach\nThis method uses a coarser granularity than the cell-based data unpacking. Instead of reading out ev-\nery cell over a speci\ufb01ed region of the liquid argon (LAr) calorimeters, only information from the LAr\ncalorimeters front-end boards is used. There are 128 readout channels per FEB and two FEBs are con-\nnected to one ROD. For the tile calorimeter, the full cell granularity is still used.\nIn the RODs, the sums of the Cartesian components of the cell energies are calculated for each FEB:\nEx\n=\n128\n\u2211\ni=1\nEi\ncos\u03c6i\ncosh\u03b7i\n(1)\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n702\n\nEy\n=\n128\n\u2211\ni=1\nEi\nsin\u03c6i\ncosh\u03b7i\n(2)\nEz\n=\n128\n\u2211\ni=1\nEi tanh\u03b7i\n(3)\nwhere Ei is the energy and \u03c6i, \u03b7i the position of each cell. This sum is computed per FEB and runs over\nall channels with an energy Ei > 2\u00b7\u03c3noise. The noise cut value, which is a con\ufb01guration parameter, has\nbeen determined from performance studies with QCD dijet events, such as to give the similar jet energy\nscale as obtained with the cell-based approach, which will be presented in the next section. The total\nenergy of the cells connected to a FEB is then obtained from the quadratic sum of the three components,\nEtot =\nq\nE2x +E2y +E2z . The corresponding \u03b7 and \u03c6 coordinates are calculated as\n\u03b7 = atanh(Ez/Etot),\n\u03c6 = atan2(Ey/Ex),\nwhere the function atan2 returns the angle \u03c6 \u2208[\u2212\u03c0,\u03c0]. The resulting values for the energy and the (\u03b7,\n\u03c6)-coordinate are then used to de\ufb01ne the grid of elements in a region around the L1 RoI position, as\nis illustrated in Fig. 6. In the following text, jets reconstructed using this data unpacking method are\nreferred to as \u201cFEB-based jets\u201d.\n5.2\nL2 jet \ufb01nding algorithm\nJets are de\ufb01ned as a cone-shaped object in the (\u03b7,\u03c6)-space with a given radius \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2. The\nvalue \u2206R is a parameter of the algorithm that is de\ufb01ned at trigger con\ufb01guration time. The jet energy and\nposition are found through an iterative procedure with the following steps:\n\u2022 The L1 jet RoI is used as a seed for the algorithm. A reference jet is created, labeled j0, de\ufb01ned\nby the L1 jet RoI position with the pre-de\ufb01ned cone radius \u2206R (see left-hand side of Fig. 6). Note\nthat the possible positions of the reference jet j0 are discreet due to the L1 granularity.\n\u2022 Grid elements that fall within the (\u03b7, \u03c6)-region encompassed by the reference jet j0 are used to\nrecalculate the jet energy and position according to:\n\u03b7j1\n=\n\u2211k\ni=1 Ei\u03b7i\n\u2211k\ni=1 Ei\n,\n(4)\n\u03c6j1\n=\n\u2211k\ni=1 Ei\u03c6i\n\u2211k\ni=1 Ei\n.\n(5)\nThe sum runs over the k grid elements that are contained in the cone de\ufb01ned by the reference jet\nj0. A grid element is included in the sum if its centre falls within the region spanned by the cone\nradius \u2206R. The total energy and coordinates (\u03b7j1, \u03c6j1), computed in Equations (4) and (5), are used\nto de\ufb01ne the new reference jet j1.\n\u2022 The previous step is repeated with j0 replaced by j1 in Equations (4) and (5), which results in\nupdated coordinates \u03b7j2 and \u03c6j2 to de\ufb01ne the updated jet j2. This algorithm can be repeated N\ntimes to create jet jN.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n703\n\n\u2022 A predetermined \ufb01xed number of iterations are executed. The energy of the \ufb01nal jet is calculated\nas the sum of the energy of all the grid elements falling within the cone radius. The position of\nthe jet is obtained as the energy weighted average of the position of each grid elements within the\ncone, as shown in Fig. 6.\nThe outcome of this algorithm is a jet de\ufb01ned by its (\u03b7,\u03c6) position and total energy. The calorimeter\nenergy scale, at this point, is set at the electromagnetic scale which does not provide an accurate measure\nof the jet energy. The next Section describes the calibration weights applied to correct the total jet energy\nfor non-electromagnetic shower components.\n5.3\nL2 jet calibration\nThe ATLAS calorimeter response to the electromagnetic component of a hadron shower is not equal to\nthe response to the non-electromagnetic component. In general, the hadronic response (h) is smaller than\nthe electromagnetic response (e),\ne/h > 1.\nThis effect is mainly due to the energy lost in the breakup of nuclei or in nuclear excitation. In order\nto correct for it, a weight is applied to each element that makes up a jet. Depending on the calibration\nmethod used, a jet can be regarded as composed, for example, of individual calorimeter cells or of energy\ndeposits in calorimeter samplings. The calibrated jet energy can then be written as:\nErec\njet =\nn\n\u2211\ni=1\nwiEi\n(6)\nwhere the sum runs over the n constituents of the jet.\nThe weights wi in Equation (6) are extracted using simulated event samples by minimising the func-\ntion:\nS =\nNjets\n\u2211\nm=1\n\u0014(Etruth\nm\n\u2212Erec\nm )\n\u03c3m\n\u00152\n(7)\nThe sum runs over all the jets in the events. The true energy of the m-th jet in the event is labeled\nEtruth\nm\nand is obtained from the Monte Carlo (MC) truth information, running a cone jet algorithm with\nradius \u2206R = 0.4 over the MC truth particles and \ufb01nding the truth jet that is closest to the m-th jet. A\ntruth jet is made up of all particles generated, excluding neutrinos and muons which have their own\nobservables, missing transverse energy for neutrinos and reconstructed tracks for muons. By minimising\nS with respect to the true jet energy, an improvement of the jet energy scale and resolution is obtained.\nDifferent calibration methods can be applied, which differ in the partitioning of the jet energy into\ncalorimeter components (e.g. cells, layers). The calibration method used here is the so-called sampling\ntechnique [4]. In this method, individual weights can be applied to the energy deposited in each of the\nelectromagnetic (EM) and hadronic (HAD) calorimeter sampling layers. The energy dependence of the\nweights is chosen to be:\nwi = a+blog(E).\n(8)\nIn the implementation used for L2 jets, only two weights are calculated and applied to calibrate\nthe reconstructed jet energy; one weight for the total energy deposited in the EM calorimeter, and one\nweight for the total energy deposited in the hadronic calorimeter. Furthermore, the \u03b7 range is split in 32\nbins with a size of 0.1 in the region 0 < |\u03b7| < 3.2. This procedure assumes an azimuthally symmetric\nresponse. This assumption will need to be validated with real data. A \ufb01t to Equation (8) is performed\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n704\n\nTable 2: Parameters used in the L2 jets reconstruction. The value of the cone size radius is de\ufb01ned for\neach iteration.\nParameter\nStandard Jets\nForward Jets\nNumber of iterations\n3\n3\nCone radius\n0.4/0.4/0.4\n1/0.7/0.4\n\u2206\u03b7 window size\n1.4\n3 < |\u03b7| < 5\n\u2206\u03c6 window size\n1.4\n1.4\nusing the MINUIT2 package [5]. It yields the values of the two parameters of Equation (8) for each\n\u03b7-bin and for the electromagnetic and hadronic calorimeter sampling. The computed weights are then\nstored in a con\ufb01guration \ufb01le, which serves as input to the L2 jet algorithm that applies the weights to\neach identi\ufb01ed jet.\n5.4\nL2 jet parameters\nIn the con\ufb01guration of the L2 jet trigger algorithm, the values of the following parameters need to be set:\n\u2022 the data unpacking method: cell-based or FEB-based,\n\u2022 the calorimeter window size \u2206\u03b7 and \u2206\u03c6, where data need to be unpacked,\n\u2022 the radius of the cone \u2206R used in the jet \ufb01nding algorithm,\n\u2022 the number of iterations used in the jet \ufb01nding algorithm,\n\u2022 the calibration constants used.\nA set of parameter values which yields the optimal balance between short execution times and ade-\nquate physics performance must be chosen.\n6\nL2 performance\nThe performance of the L2 jet algorithm was studied using the simulated dijet event samples described\nin Table 1.\nThe parameters used in the reconstruction of the L2 jets are summarised in Table 2. These parameters\nwere found to be a good compromise between the physics performance (e.g., energy resolution and scale)\nand the algorithm execution time.\nThe \ufb01rst parameter studied was the number of iterations of the jet \ufb01nding algorithm. The variation in\nthe jet (\u03b7,\u03c6) coordinate and transverse energy after each iteration of the jet reconstruction algorithm is\nshown in Fig. 7. The largest variation in ET,\u03b7 and \u03c6 happens after the \ufb01rst iteration and thus it has the\nlargest impact on the measurement precision. This suggests that the number of iterations could possibly\neven be reduced to 2 without losing too much precision on this measurement.\nIn order to study the effect of the window size used to unpack calorimeter data, the total time spent\nby the jet algorithm running with different sizes was studied. Windows with dimensions of 1.0\u00d71.0 (in\n\u03b7 \u00d7\u03c6) and 1.4\u00d71.4 were studied. A window size of 1.0\u00d71.0 is only slightly larger than the diameter of\na jet with \u2206R = 0.4. The maximum initial displacement of a jet with respect to a truth jet is approximately\n0.2 in \u2206\u03b7 or \u2206\u03c6, as can be seen in Fig. 7. Therefore, a window size of 1.0\u00d71.0 should be adequate for\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n705\n\nNo. of iterations\n1\n2\n3\n4\n5\n [GeV]\nT\n E\n\u2206\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n(a)\nATLAS\n vs No. iterations\nT\n E\n\u2206\nNo. of iterations\n1\n2\n3\n4\n5\n\u03c6\n\u2206\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n(b)\nATLAS\n vs No. iterations\n\u03c6\n\u2206\nNo. of iterations\n1\n2\n3\n4\n5\n\u03b7\n\u2206\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n(c)\nATLAS\n vs No. iterations\n\u03b7\n\u2206\nFigure 7: Variation in the (a) transverse energy, (b) \u03c6 position and (c) \u03b7 position of jets as function\nof number of iterations performed by the L2 jet reconstruction algorithm. The area of the boxes is\nproportional to the number of entries in each bin.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n706\n\ntime[ms]\n0\n5\n10\n15\n20\n25\n30\n35\n40\nJet RoI\n0\n500\n1000\n1500\n2000\n2500\nRoI 1.4x1.4\nRoI 1.0x1.0\nRoI 1.4x1.4\nRoI 1.0x1.0\nRoI 1.4x1.4\nRoI 1.0x1.0\nRoI 1.4x1.4\nRoI 1.0x1.0\nATLAS\nFigure 8: Time spent by the L2 jet reconstruction algorithm for two different window sizes: 1.4 \u00d7 1.4\n(dashed line) and 1.0\u00d71.0 (solid line).\nthe jet reconstruction. The total time spent by the L2 jet algorithm for two different window size and\nusing three iterations is shown in Fig. 8. A reduction of the window size from 1.4 \u00d7 1.4 to 1.0 \u00d7 1.0\nresults in a considerable reduction (of order 30%) in the processing time. As shown in the next section,\nthe energy scale and resolution is not signi\ufb01cantly affected by this reduction of the size of the window.\n6.1\nPerformance for cell-based reconstruction\nThe calibration constants used to reconstruct cell-based jets in L2 were extracted using dijet events\nsimulated with PYTHIA [6] and following the approach described in Section 5.3. The L2 jet transverse\nenergy scale and resolution for cell-based jets after calibration are presented in Fig. 9. The transverse\nenergy scale is de\ufb01ned as the L2 jet transverse energy divided by the truth jet ET. Truth jets are identi\ufb01ed\nby applying the cone algorithm with Rcone = 0.4 on the collection of truth \ufb01nal state particles. The\ntransverse energy scale is close to unity for all the \u03b7 coverage of the L2 jet trigger and all the transverse\nenergies studied, demonstrating that the transverse energy is correctly measured within 2%. The jet\ntransverse energy resolution decreases from 12% for the lowest transverse energies to 4% for transverse\nenergies above 1000 GeV. The resolution curves were \ufb01tted with the following expression that includes\na stochastic term convoluted with a constant term:\n\u03c3(E)\nE\n= A\n\u221a\nE \u2295B\n(9)\nTable 3 shows the result of the \ufb01ts for all the \u03b7 bins, before and after calibration. A few percent improve-\nment in the resolution is obtained with the current calibration method. A further improvement can be\nachieved in the future by exploiting the correlation between the fraction of electromagnetic energy and\nthe calibration weights [7].\nIn another study, two different window sizes were used in order to study the effect on the jet energy\nscale and resolution. L2 jets were reconstructed using a window size of 0.7\u00d70.7 (in \u03b7 \u00d7\u03c6) which was\nchosen to be slightly smaller than the jet cone diameter (2\u00d7\u2206R = 2\u00d70.4 = 0.8) such that some of the\nenergy of the jet may lie outside the window considered. Results were compared with the performance\nobtained using the window size dimension of 1.4\u00d71.4. The jet energy calibration constants were calcu-\nlated independently in both cases and the resulting jet energy scale and resolutions were compared. In\nboth cases, the jet energy scale was found to be within 2% of unity. The resolution of the jets was also\nfound to be similar for both window sizes. This means that the calibration algorithm can adequately cor-\nrect for a small fraction of the jet energy lost outside the window considered. Therefore, using a window\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n707\n\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\ntruth\nT\n/E\nL2\nT\nE\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\n(a)\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\n resolution\nL2\nT\nE\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\n(b)\nFigure 9: Jet energy scale for the L2 jets as a function of the truth jet ET (a), for four different bins in \u03b7.\nJet energy resolution as a function of the truth energy of the jet (b), for four different bins in \u03b7. These\nresults are obtained after calibration.\nTable 3: Results of the jet energy resolution \ufb01t as a function of the truth jet energy, before and after\napplying the calibration. The \ufb01t was done using Equation (9).\n\u03b7 region\nBefore calibration\nAfter calibration\nA\nB\nA\nB\n(0.0,0.7)\n1.03 \u00b1 0.03\n0.059 \u00b1 0.001\n0.96 \u00b1 0.02\n0.039 \u00b1 0.001\n(0.7,1.5)\n1.28 \u00b1 0.03\n0.064 \u00b1 0.001\n1.18 \u00b1 0.03\n0.041 \u00b1 0.001\n(1.5,2.5)\n1.53 \u00b1 0.04\n0.046 \u00b1 0.001\n1.37 \u00b1 0.03\n0.025 \u00b1 0.002\n(2.5,3.2)\n1.86 \u00b1 0.13\n0.063 \u00b1 0.003\n1.46 \u00b1 0.08\n0.040 \u00b1 0.003\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n708\n\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\ntruth\nT\n/E\nL2\nT\nE\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\n1.06\nPythia\nHerwig\n| < 0.7\nATLAS\n\u03b7\n(a)\n0.0 < |\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\n resolution\nL2\nT\nE\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nPythia\nHerwig\n| < 0.7\nATLAS\n(b)\n\u03b7\n0.0 < |\nFigure 10: Comparison of the L2 jet energy scale and resolution obtained for two different MC genera-\ntors, PYTHIA ( blue circles) and HERWIG (red triangles), for jets in the region 0 < \u03b7 < 0.7.\nsize of 1.0\u00d71.0 will reduce processing time while keeping essentially the same physics performance as\nthe larger window (1.4\u00d71.4).\nThe jet energy measured in the calorimeter may be sensitive to the shower development and the\nhadronisation mechanism that was introduced in the MC simulation. In order to test the sensitivity of the\ncalibration procedure to the simulation, a set of dijet event samples generated with HERWIG [8] was used.\nCalibration constants were extracted with the PYTHIA dijet samples and used in the reconstruction of the\nHERWIG dijet events. The jet energy scale and resolution obtained in this way with the HERWIG data\nsample was compared, in different \u03b7 regions and ET values, with the one obtained for PYTHIA. Figure 10\nshows, as an example, such a comparison in one particular \u03b7 region. Differences between the two\ngenerators were found to be smaller than 2%, for all regions of \u03b7 and jet ET, suggesting that the L2 jet\nenergy scale is relatively insensitive to the hadronisation model used in MC generators.\nFigure 11 shows the L2 trigger ef\ufb01ciency as function of of\ufb02ine jet ET after calibration has been\napplied for four different L2 thresholds. The L1 threshold of 15 GeV was chosen to be signi\ufb01cantly\nsmaller than that for L2 in order to avoid a mixture of resolution and jet energy scale effects from the two\ndifferent trigger levels. The limited sharpness of the curves shown on Figure 11 is, therefore, dominated\nby the resolution of the L2 jet energy.\nInitially, the detector simulation is not expected to provide an exact model of the real detector. The\nenergy measurement will be mainly affected by an incomplete knowledge of the dead material distribu-\ntion in front of the calorimeters. To study the effect that the limited knowledge of the detector geometry\nmay have on the performance of the trigger and reconstruction algorithms, dedicated MC dijet event\nsamples were produced. They were reconstructed with a geometry where detectors were slightly dis-\nplaced from their nominal positions and extra dead material was added. This accounted for 7-10% of a\nradiation length in the inner detector and a few percent of one radiation length in front of the calorimeter.\nThe knowledge of the dead material distribution is assumed to be worst at the interface between different\ncalorimeter subsystems.\nThe calibration constants obtained assuming a perfect geometry were used to identify L2 jets in\nthe misaligned samples. Hence, the resulting jet transverse energy scale and resolution can serve as\nan estimation of how much the performance of the L2 jet reconstruction may be degraded due to the\nlimited knowledge of the detector geometry and dead material distribution at the beginning of the data\ntaking period. Figure 12 shows the jet transverse energy scale and resolution obtained for dijet events\nreconstructed with this mismatch of calibration constants. For most of the pseudo-rapidity region, the\nlinearity with energy is within 3-4%, slightly worse than before. In the region (1.5 < |\u03b7| < 2.5) the jet\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n709\n\n(GeV)\nT\nOffline jet E\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nL2 Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n > 35 GeV\nL2\nT\nE\n > 42 GeV\nL2\nT\nE\n > 70 GeV\nL2\nT\nE\n > 100 GeV\nL2\nT\nE\nATLAS\nFigure 11: Trigger ef\ufb01ciency as function of of\ufb02ine jet transverse energy for L2 jets after calibration, for\nfour different thresholds (35 GeV, 42 GeV, 70 GeV and 100 GeV). The statistical uncertainty on each\npoint is smaller than the symbols.\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\ntruth\nT\n/E\nL2\nT\nE\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\n(a)\n [GeV]\nT\nTru h jet E\n2\n10\n3\n10\n resolution\nL2\nT\nE\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\n(b)\nFigure 12: Jet transverse energy scale for L2 jets as a function of the truth jet transverse energy (a),\nfor four different \u03b7 regions. Jet transverse energy resolution as a function of the truth jet transverse\nenergy (b), for four different \u03b7 regions. Both plots were obtained using dijet event samples reconstructed\nassuming a limited knowledge of the detector\u2019s dead material distribution.\nenergy scale drops to about 94% due to the extra dead material. The transverse energy resolution is also\ndegraded, as shown in Table 4. The performance of the calibration at the beginning of data taking can\nbe improved using in-situ calibration procedures used to extract the calibration constants directly from\nthe data or to correct the detector response in the MC. Several different procedures are currently under\nstudy.\nThe reconstructed jet position is another parameter used to measure the algorithm performance. Cur-\nrently no selection on jet position is made at the trigger level, but this may prove useful in the future\nfor some physics channels. The position resolution is shown in Fig. 13. This \ufb01gure is also included for\ncompleteness to compare with the FEB unpacking approach that uses a coarser granularity of data.\n6.2\nPerformance for FEB-based reconstruction\nStudies were done to evaluate the performance of the L2 jet reconstruction using the FEB-based method\nof data unpacking. For comparison with results presented in Fig. 12, dijet event samples that assume\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n710\n\nTable 4: Results of the jet energy resolution \ufb01t as a function of the truth jet energy for the event samples\nwhere a limited knowledge of the detector\u2019s dead material is assumed. The \ufb01t was done assuming\nEquation (9).\n\u03b7 region\nAfter calibration\nA\nB\n(0.0,0.7)\n1.04 \u00b1 0.02\n0.038 \u00b1 0.002\n(0.7,1.5)\n1.24 \u00b1 0.03\n0.055 \u00b1 0.001\n(1.5,2.5)\n1.95 \u00b1 0.04\n0.018 \u00b1 0.004\n(2.5,3.2)\n1.66 \u00b1 0.09\n0.039 \u00b1 0.002\n\u03b7\n \n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n\u03c6\n \n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0 2\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\nFigure 13: The \u03b7-resolution (a) and \u03c6-resolution (b) of L2 cell-based jets with respect to the truth jet\nenergy. The mean and standard deviation of a Gaussian \ufb01t of (a) is 0.0006 and 0.03, while the mean and\nstandard deviation of a Gaussian \ufb01t of (b) is 0.00005 and 0.01.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n711\n\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\nT\ntruth\n/E\nT\nL2\nE\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\n1.15\n1 2\n1.25\n1 3\n(a)\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\n resolution\nT\nL2\nE\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n(b)\nATLAS\n| < 0.7\n\u03b7\n0 < |\n| < 1.5\n\u03b7\n0.7 < |\n| < 2.5\n\u03b7\n1.5 < |\n| < 3.2\n\u03b7\n2.5 < |\nFigure 14: (a) Jet energy scale for the L2 FEB-based jets as a function of the truth jet ET for four different\nbins in \u03b7. (b) Jet energy resolution as a function of the truth energy of the jet for four different bins in \u03b7.\nBoth plots were obtained using dijet event samples reconstructed assuming a limited knowledge of the\ndetector\u2019s dead material distribution.\na limited knowledge of the detector dead material were used to study the transverse energy scale and\nresolution of FEB-based jets. The transverse energy of jets reconstructed using the FEB-based data\nunpacking approach was weighted using the default L2 calibration constants obtained using the cell-\nbased method.\nFigure 14 shows the jet transverse energy scale and resolution. The energy scale stays within 5% of\nunity for most of the pseudorapidity range. The transverse energy resolution distribution was \ufb01tted using\nEquation (9) and the results are presented in Table 5. The transverse energy resolution of FEB-based jets\nis comparable to that of cell-based jets presented in Table 3. The transverse energy scale and resolution\nof the FEB-based jets depend strongly on the energy cut-off introduced in Equation (3). It was found\nthat using a cut-off at 2\u00b7\u03c3noise gave the best result in terms of transverse energy scale and resolution.\nFigure 15 shows the \u03b7 and \u03c6 resolution. These distributions were obtained from the difference\nbetween a L2 FEB-based jet and its nearest MC truth jet. These results are comparable with those\nobtained using the cell-based method as shown in Fig. 13.\nThe L2 trigger ef\ufb01ciency for different thresholds as function of reconstructed jet transverse energy\nfor FEB-based jets is presented in Fig. 16. The initial slope of these ef\ufb01ciency curves is similar to\nthe results obtained with the cell-based method shown in Fig. 11. This indicates that FEB-based jets\nhave a selection ef\ufb01ciency that is comparable to the cell-based one. The FEB-based jet reconstruction\nsigni\ufb01cantly reduces the amount of data to be unpacked at L2 compared to the cell-based approach. The\nimpact of the unpacking choice on the processing time of the jet reconstruction algorithm is presented in\nSection 6.4.\n6.3\nForward jets\nThe implementation of L2 forward jet reconstruction must consider constraints on the precision of the\nL1 forward jet RoI position. Since each L1 FCAL trigger tower spans the entire \u03b7 range of the FCAL\ndetector, a dedicated optimisation of the jet reconstruction algorithm is required. In order to properly\naccount for the overlap region between the FCAL and endcap calorimeters, a window size of 3.0 <\n|\u03b7| < 5 was chosen. The cone size (\u2206R) must also be modi\ufb01ed in order to remove any bias from the\ninitial L1 RoI seed position. Similar to the standard jet reconstruction, three iterations of the jet \ufb01nding\nalgorithm are performed. An initial cone size of \u2206R = 1 is used to collect suf\ufb01cient data to remove the\nL1 bias. In the second and third iteration of the jet \ufb01nding algorithm, the cone size is reduced to 0.7\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n712\n\n\u03b7\n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\n\u03c6\n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\n0\n2000\n4000\n6000\n8000\n10000\n12000\nFigure 15: The \u03b7-resolution (a) and \u03c6-resolution (b) of L2 FEB-based jets with respect to the truth jet\nenergy. The mean and standard deviation of a Gaussian \ufb01t of (a) is 0.002 and 0.03, while the mean and\nstandard deviation of a Gaussian \ufb01t of (b) is -0.00007 and 0.009.\nTable 5: Results of the jet energy resolution \ufb01t as a function of the truth jet energy for FEB-based jets\nafter applying the default calibration constants obtained using the cell-based data unpacking method.\nThe \ufb01t was performed assuming Equation (9).\n\u03b7 region\nAfter calibration\nA\nB\n(0.0,0.7)\n0.93 \u00b1 0.05\n0.02\u00b1 0.01\n(0.7,1.5)\n1.18 \u00b1 0.05\n0.03\u00b1 0.01\n(1.5,2.5)\n1.56 \u00b1 0.04\n0.05\u00b1 0.01\n(2.5,3.2)\n1.93 \u00b1 0.01\n0.01\u00b1 0.01\n [GeV]\nT\nOffline jet E\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nL2 Effciency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\n > 35 GeV\nL2\nT\nE\n > 42 GeV\nL2\nT\nE\n > 70 GeV\nL2\nT\nE\n > 100 GeV\nL2\nT\nE\nFigure 16: L2 trigger ef\ufb01ciency as function of reconstructed jet transverse energy for FEB-based jets\nafter calibration, for four different thresholds (35 GeV, 42 GeV, 70 GeV and 100 GeV).\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n713\n\nTable 6: L2 trigger ef\ufb01ciency for L2 forward jets with respect to truth jets with ET > 25 GeV.\nTagged Objects\nData unpacking method\ncell-based jets (%)\nFEB-based jets (%)\nHighest ptruth\nT\nforward jets\n98\u00b11\n98\u00b11\nAll forward jets\n97\u00b11\n91\u00b11\nand subsequently to 0.4. Calibration constants for forward jets are derived using the method described\nin Section 5.3.\nThe L2 forward jet trigger ef\ufb01ciency was determined with respect to truth jet. Reconstructed jets\nwere matched to truth particle jets using the requirement that \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 < 0.2. In addition,\ntruth jets were required to satisfy pT>25GeV. Results from this study are presented in Table 6.\n6.4\nL2 jet timing\nThe time budget of approximately 40 ms per event and the strong rejection power needed at the L2 trigger\nimpose strong constraints on the L2 algorithms speed and physics performance.\nDuring the commissioning of the ATLAS Trigger/DAQ system, dedicated Technical Runs are per-\nformed in order to test HLT algorithm performance. In these runs all the detector Read Out Systems\n(ROS) and the full Trigger/DAQ infrastructure are dedicated to exercising the data acquisition system\nand the trigger. Bytestream \ufb01les1 containing a mixture of events close to that expected in LHC collisions\n(mainly QCD jets, mixed with a few Z and W decays to leptons, t\u00aft events, etc.) are preloaded into the\nROS. These events, which contain the RoIs obtained from the L1 simulation, are then processed by the\nHLT system. The measurements presented here were made during the Technical Run that took place in\nNovember 2007.\nIn order to compare the difference between the cell-based method and the FEB-based method, two\ndata-collection runs were recorded, one with L2 jets reconstructed using the cell-based approach, and\none with L2 jets reconstructed using the FEB-based method. The timing distributions obtained from the\ncell and the FEB-based methods are shown in Fig. 17(a). Both distributions have a similar shape with\npeaks corresponding to the number of RoIs per event. The FEB-based approach is however almost 50%\nfaster than the cell-based method.\nThe distribution of the total processing time shown in Fig. 17(a) includes the data unpacking, jet\n\ufb01nding algorithm and calibration, as well as the data collection time from the detector Read Out System\n(ROS) to the L2 processors, which is shown in Fig. 17(b). The data collection time contributes sig-\nni\ufb01cantly to the total L2 processing time, about 30% for the cell-based method and about 50% for the\nFEB-based approach. A detailed description of the data preparation methods and performance can be\nfound in [9].\nThe processing time distribution per RoI for the different steps involved in the L2 jet reconstruction\nare shown in Fig. 18(a) and (b) for the cell-based and FEB-based method, respectively. These mea-\nsurements show that the algorithm execution time is dominated by the data unpacking step. The small\nfeatures observed in the unpacking time distributions outside the main peak come from RoIs that point\nin regions where less data needs to be unpacked.\nTiming measurements of the L2 forward jet algorithm were also performed. A comparison of the\nreconstruction time between cell-based and FEB-based jets is presented in Table 7. Due to the limited\ntime available during dedicated Technical Runs, these measurements were obtained by running the L2 jet\n1Files with the same format as the raw data that will come out of the ATLAS detector.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n714\n\ntime[ms]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n5000\n10000\n15000\n20000\n25000\nATLAS\nFEB-based method\ncell-based method\ntotal processing time per L2 event\n(a)\ntime[ms]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\ndata collection time per event\nATLAS\n(b)\nFigure 17: The total processing time per event (a) for the L2 jet algorithm. The solid line is the processing\ntime measured using the FEB-based method (mean 13 ms). The dashed line is the processing time\nmeasured using the cell-based method (mean 22 ms). The total data collection time per RoI (b) for both\nthe cell-based and FEB-based data unpacking methods.\ntime[ms]\n0\n2\n4\n6\n8\n10\n12\n0\n5000\n10000\n15000\n20000\n25000\ntotal\ndata unpacking\ncone tool\ncalib. tool\nL2 algo processing time per RoI\nATLAS\n(a)\ntime[ms]\n0\n2\n4\n6\n8\n10\n12\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\ntotal\ndata unpacking\ncone tool\ncalib. tool\nL2 algo processing time per RoI\n(b)\nATLAS\nFigure 18: L2 jet algorithm processing time per jet RoI for the cell-based method (a) and FEB-based\nmethod (b). The total processing time is shown together with the execution time of the individual steps\ninvolved in the L2 jet reconstruction.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n715\n\nTable 7: Comparison of the average L2 jet reconstruction time between the standard and forward jet\nalgorithms in units of ms. Different data unpacking methods are also compared.\nTagged Objects\nData unpacking method\ncell-based jets\nFEB-based jets\nForward Jets\n0.9\n0.5\nStandard Jets\n6.1\n2.1\nalgorithms on of\ufb02ine computing resources rather than making use of the full Trigger/DAQ infrastructure.\nAlthough the absolute values of reconstruction time should only be taken as an approximate indication\nof the performance to be expected on the online trigger system, the relative comparison of each measure-\nment is nevertheless informative. For example, although the L2 forward jet algorithm uses a larger \u03b7 \u00d7\u03c6\nwindow than the standard L2 jet algorithm, it requires less than 25% of the total time used to reconstruct\nstandard L2 jets. This is due to the larger granularity of the forward calorimeter, as compared to the\nliquid Argon barrel and endcap calorimeters, which results in a smaller amount of data being unpacked\non average.\n7\nThe event \ufb01lter jet algorithms\nThe jet reconstruction in the Event Filter (EF) can be divided into two tasks: the input data preparation\nand the jet \ufb01nding. These two tasks are carried out by algorithms used in the of\ufb02ine reconstruction\nbut adapted to run in the online trigger environment. Once an EF jet has been identi\ufb01ed, it is passed\non to a Hypothesis algorithm which validates whether or not the reconstructed jet satis\ufb01es a prede\ufb01ned\ntransverse energy threshold.\n7.1\nInput data preparation\nThere are three calorimeter data preparation algorithms which, respectively, unpack the calorimeter cell\ninformation, build trigger towers and construct calorimeter clusters. The implementation of these data\npreparation algorithms in the EF has been adapted to allow the running of a subset of the algorithms\nthereby reducing computing time.\nThe \ufb01rst data preparation algorithm unpacks calorimeter cell information in a prede\ufb01ned window\naround the position of the jet found at L2. The size of the window where data needs to be unpacked is a\nparameter that can be adjusted and is con\ufb01gured at trigger initialisation. The energy of each calorimeter\ncell, at this point, is set at the EM scale [2, 3]. Although not currently used, this unpacking algorithm\nprovides the ability to apply calibration weights to the energy of individual calorimeter cells.\nThe second data preparation algorithm performs the calorimeter tower reconstruction. A calorimeter\ntower is an array of calorimeter cells within an (\u2206\u03b7,\u2206\u03c6) = (0.1,0.1) region. The EF calorimeter trigger\ntowers granularity is four times \ufb01ner than that of the L1. Calorimeter trigger towers are the inputs to the\njet \ufb01nding algorithm described in the next Section.\nA third data preparation algorithm, currently being studied, is also available in the EF. This algorithm\nconstructs three-dimensional calorimeter clusters instead of towers. These clusters can alternatively be\nused as input to the jet \ufb01nding algorithm instead of calorimeter towers.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n716\n\nParameter\nValue\nWindow size (\u03b7 \u00d7\u03c6)\n1.6\u00d71.6\nInput objects\ntowers\nProto-jet ET cut\nET > 2 GeV\nJet \ufb01nding algorithm\ncone\nJet \ufb01nding parameter\nRcone = 0.7\nCalibration scheme\n\u201cEnergy density\u201d-based cell calibration\nFinal jet ET cut\nET > 10 GeV\nTable 8: Parameter values for the EF jet reconstruction.\n7.2\nJet \ufb01nding algorithm\nThe EF jet reconstruction uses the of\ufb02ine reconstruction algorithms [10] adapted for the EF. It takes as\ninput any ET ordered list of calorimeter objects (cells, towers or clusters). The jet reconstruction consists\nof the following steps:\n\u2022 Removal of negative energy towers (or clusters) by combining them with adjacent ones. A list of\nproto-jets is also constructed using a simple pre-clustering algorithm.\n\u2022 Removal of proto-jets with transverse energy smaller than a given threshold.\n\u2022 Running of a jet \ufb01nding algorithm (cone or fast KT algorithm [11]).\n\u2022 Jet calibration\n\u2022 Removal of reconstructed jets below a given transverse energy\nMany different parameters can be modi\ufb01ed as part of the jet reconstruction. The parameters used\nfor the con\ufb01guration of the EF jet reconstruction are summarized in Table 8. Unless speci\ufb01ed explicitly,\nperformance studies described subsequently use this con\ufb01guration.\nAll calibration methods available for the of\ufb02ine jet reconstruction can be used by the EF jet algorithm.\nThe default method used in the EF is an \u201cenergy density\u201d-based cell calibration described in details\nin [12].\n8\nEvent \ufb01lter performance\nThe performance and parameter optimisation of the EF jet reconstruction algorithms were made using\nthe simulated dijet event samples summarised in Table 1.\nThe window size de\ufb01ning how much data is unpacked was chosen by studying the position differ-\nence between of\ufb02ine reconstructed jets and jets found by the L2 system. A distribution of the distance\n\u2206R =\np\n(\u03b7L2 \u2212\u03b7of\ufb02ine)2 +(\u03c6L2 \u2212\u03c6of\ufb02ine)2 is shown in Fig. 19. Most L2 jet RoI are well within \u2206R < 0.2\nof of\ufb02ine reconstructed jets using a cone algorithm with \u2206R = 0.7. A window size of 1.6\u00d71.6 in \u03b7 \u00d7\u03c6\nwas therefore chosen to ensure that data is unpacked at the EF in a calorimeter region of suf\ufb01cient size to\nreconstruct correctly a jet similar to an of\ufb02ine jet while ensuring complete overlap with the L1 RoI. Ad-\nditional studies could include the optimization of a variable window size as function of the jet transverse\nenergy as measured by L2.\nThe EF jet energy scale and resolution were assessed using the same technique as described in Sec-\ntion 6.1. The results are shown in Fig. 20 as a function of the truth jet ET. In general, the energy scale\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n717\n\n\u2206R\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0\n1000\n2000\n3000\n4000\n5000\nATLAS\nFigure 19: Distance \u2206R =\np\n(\u03b7L2 \u2212\u03b7of\ufb02ine)2 +(\u03c6L2 \u2212\u03c6of\ufb02ine)2 between L2 and of\ufb02ine reconstructed jets\nusing a cone algorithm of Rcone = 0.7.\nimproves with increasing truth jet ET. For truth jet energies larger than 200 GeV, the EF jet energy scale\nis within 2% of unity. The limited window size within which the jet reconstruction takes place in the EF\nresults in some energy leakage that is not corrected for by the of\ufb02ine calibration used in the EF. These\nresults nevertheless suggest that of\ufb02ine calibration are adequate for use in the EF jet reconstruction.\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\ntruth\nT\n/E\nEF\nT\nE\n0.8\n0.85\n0.9\n0.95\n1\n1.05\nATLAS\n(a)\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\n resolution\nEF\nT\nE\n0\n0.05\n0.1\n0.15\n0 2\n0.25\nATLAS\n(b)\nFigure 20: The EF jet transverse energy scale (a) and resolution (b) as function of truth jet ET.\nThe effect of pile-up corresponding to a luminosity of 1033s\u22121cm\u22122 on the jet energy scale and\nresolution was also studied. Figure 21 shows a comparison of (a) the EF jet transverse energy scale and\n(b) the EF resolution for simulated dijet event samples with and without pile-up. The effect of pile-up\non the overall energy scale is observed to be insigni\ufb01cant, however, a noticeably worse resolution is\nobserved for events with pile-up. The effect is clearly more important for low jet energies where the\ncontribution of pile-up energy can be comparable to the total jet energy.\nThe EF jet trigger ef\ufb01ciency as function of of\ufb02ine jet energy is shown in Fig. 22 for two different\nsignatures. For an EF trigger threshold close to the L1 threshold, the trigger selection performance is\nlimited by the L1 energy resolution. For EF trigger thresholds signi\ufb01cantly higher than the L1 threshold,\nthe excellent EF energy scale improves slightly the performance of the trigger selection as compared to\nthe current L2 capability. These plots emphasize the importance of correctly optimizing the jet trigger\nthresholds used for each jet signature.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n718\n\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\ntruth\nT\n/E\nEF\nT\nE\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\nATLAS\n(a)\nno pile-up\npile-up\n [GeV]\nT\nTruth jet E\n2\n10\n3\n10\n resolution\nEF\nT\nE\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n0 35\n0.4\n0.45\n0.5\nATLAS\n(b)\nno pile-up\npile-up\nFigure 21: The EF jet transverse (a) energy scale (b) and resolution as a function of truth jet ET for\nsimulated dijet event samples with and without pile-up.\n [GeV]\nT\nOffline jet E\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n | < 2.5\n\u03b7\n| \nL1\nL2\nEF\nATLAS\n(a)\n [GeV]\nT\nOffline jet E\n50\n100\n150\n200\n250\n300\n350\nTrigger efficiency\n0\n0 2\n0.4\n0 6\n0 8\n1\n | < 2.5\n\u03b7\n| \nL1\nL2\nEF\nATLAS\n(b)\nFigure 22: EF trigger ef\ufb01ciency as function of of\ufb02ine jet transverse energy for two different signatures\nconsisting of a set of L1, L2 and EF trigger thresholds: (a) EL1\nT > 10 GeV, EL2\nT > 30 GeV, EEF\nT\n> 50 GeV;\nand (b) EL1\nT > 70 GeV, EL2\nT > 150 GeV, EEF\nT\n> 255 GeV.\n8.1\nEvent \ufb01lter jet algorithm timing\nThe timing performance of the EF jet reconstruction algorithm has been measured in the November 2007\nTechnical run described in Section 6.4. Figure 23(a) shows the execution time per RoI for the two EF\ndata preparation steps: the unpacking of calorimeter cell data and the construction of calorimeter towers\nused by the jet algorithm. Figure 23(b) shows the execution time of the different steps involved in the jet\nreconstruction described in Section 7.2. The EF jet reconstruction total time per RoI is of order 100 ms.\nAssuming approximately 4 to 5 jet RoI per event implies a total processing time of order half a second\nper event which falls within the design budget of approximately one second per event.\n9\nJet trigger menu\nJet triggers will be used to record many different types of events. Single and multi-jet signatures will\nidentify useful events for various Standard Model QCD measurements. This event sample will also be\nvaluable to study the properties of background events for other analyses and to measure the misidenti\ufb01ca-\ntion ef\ufb01ciency of different of\ufb02ine reconstruction algorithms. Jet trigger requirements are also important\nwhen combined with other trigger criteria to identify rare signal events with well-de\ufb01ned topologies.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n719\n\nTime [ms]\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n10000\n20000\n30000\n40000\n50000\n60000\n70000\n80000\nCell Data Unpacking\nTower Reconstruction\nATLAS\n(a)\nTime [ms]\n0\n20\n40\n60\n80\n100\n120\n0\n20\n40\n60\n80\n100\n120\n140\n3\n10\n\u00d7\nTotal\nCone Algorithm\nNoise Rejection\nCalibration\nATLAS\n(b)\nFigure 23: Execution time per RoI for different steps in the EF data preparation (a) and the jet recon-\nstruction (b).\nTrigger threshold\nJ5\nJ10\nJ18\nJ23\nJ35\nJ42\nJ70\nJ120\n3J10\n3J18\n4J10\n4J18\n4J23\nPrescale factor\n300000\n42000\n6000\n2000\n500\n100\n15\n1\n150\n1\n30\n1\n1\nLevel 1 rate (Hz)\n1\n4\n1\n1\n1\n4\n4\n8\n40\n140\n40\n20\n8\nTable 9: Summary of the L1 single-jet and multi-jet triggers optimised for the initial data taking period.\nThe L1 prescale factors and expected rate at a luminosity of 1031cm\u22122s\u22121 for each threshold are also\npresented.\nThe trigger strategy adopted is to de\ufb01ne a set of single and multi-jet signatures that, together, will\nselect events with approximately uniform rates over the entire jet energy spectrum. Table 9 shows the\nset of L1 single and multi-jet signatures and associated L1 prescale factors optimised for this purpose,\nassuming an initial luminosity of 1031 cm\u22122s\u22121. The trigger rates were calculated using close to 7 mil-\nlion simulated non-diffractive inelastic events, with an estimated cross-section of 70 mb. These large\nsimulated event samples result in a statistical uncertainty of approximately 0.1 Hz for the rates of un-\nprescaled triggers. Note that a maximum of 8 different jet thresholds can be de\ufb01ned in the L1 system.\nThe L1 thresholds and prescale factors for the single-jet signatures were chosen to signi\ufb01cantly limit the\nL1 output event rate thereby initially avoiding the need to use the HLT at the beginning of data-taking.\nThe L1 jet trigger menu was also designed to be compatible with a luminosity of up to 1032 cm\u22122s\u22121\nwithout any changes. Figure 24 shows the differential distribution for the number of events selected by\nthe L1 trigger menu as function of of\ufb02ine reconstructed jet transverse energy for 1 fb\u22121 of recorded data.\nFor commissioning purposes, it is foreseen that the L2 and EF jet algorithms will be initially run for\nthe single-jet signatures in so-called pass-through mode where the result of the HLT selection is recorded\nwith the event data but no events are rejected based on the result of the algorithm selection. The rate of\nthe multi-jet signatures listed in Table 9 will be reduced by using L2 and EF jet requirements. Table 10\nsummaries the expected rate out of the HLT for all jet signatures foreseen to be run at the beginning of\ndata-taking. In addition to the single and multi-jet signatures discussed above, forward jets signatures\nare also foreseen. These are also shown in Table 10.\nIt should be noted that, due to the very large prescales used for the lower threshold jet triggers, the\noverlap between individual triggers is greatly reduced. This implies that the cumulative rates will rapidly\ngrow, as can be observed in Table 10. The total rate of the entire jet menu has been approximated to be\n37 Hz, which represents a little over 18% of the overall trigger output rate budget of 200 Hz.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n720\n\n of leading jet (GeV)\nT\nE\n10\n2\n10\n3\n10\n)\n-1\n (GeV\nT\ndN / dE\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n9\n10\n10\n10\n11\n10\nFigure 24: Differential number of events selected as function of the of\ufb02ine reconstructed transverse\nenergy of the leading jet in the event for 1 fb\u22121 of data. The dashed and solid lines show the expected\ndistributions before and after applying the L1 jet trigger menu criteria described in Table 9.\nOverall\nCumulative\nTrigger\nPrescale\nRate (Hz)\nRate (Hz)\n4j23\n1\n6.9\n(\u00b1 0.8)\n6.9\n(\u00b1 0.8)\n4j18\n100\n0.14\n(\u00b1 0.01)\n7.0\n(\u00b1 0.6)\n4j10\n300\n0.045\n(\u00b1 0.004)\n7.0\n(\u00b1 0.6)\n3j18\n100\n0.92\n(\u00b1 0.03)\n7.9\n(\u00b1 0.3)\n3j10\n1500\n0.061\n(\u00b1 0.002)\n7.9\n(\u00b1 0.2)\nTotal Multi-Jets\n7.9\n(\u00b1 0.2)\nj120\n1\n8.7\n(\u00b1 0.9)\n15.3\n(\u00b1 0.5)\nj70\n15\n4.2\n(\u00b1 0.2)\n18.7\n(\u00b1 0.5)\nj42\n100\n3.73\n(\u00b1 0.06)\n22.3\n(\u00b1 0.3)\nj35\n500\n1.37\n(\u00b1 0.02)\n23.6\n(\u00b1 0.3)\nj23\n2000\n1.37\n(\u00b1 0.008)\n24.9\n(\u00b1 0.2)\nj18\n6000\n1.02\n(\u00b1 0.004)\n26.0\n(\u00b1 0.1)\nj10\n42000\n3.9\n(\u00b1 0.003)\n29.9\n(\u00b1 0.02)\nj5\n300000\n0.9470\n(\u00b1 0.0004)\n30.8\n(\u00b1 0.01)\nTotal Single-Jets\n24.40\n(\u00b1 0.01)\n2fj70\n1\n0\n30.8\n(\u00b1 0.01)\n2fj35\n1\n1.7\n(\u00b1 0.4)\n32.5\n(\u00b1 0.01)\n2fj18\n100\n0.94\n(\u00b1 0.03)\n33.4\n(\u00b1 0.01)\nTotal Multi-Fjets\n2.65\n(\u00b1 0.09)\nfj120\n1\n0.9\n(\u00b1 0.3)\n34.1\n(\u00b1 0.01)\nfj70\n20\n1.16\n(\u00b1 0.08)\n35.2\n(\u00b1 0.01)\nfj35\n700\n0.68\n(\u00b1 0.01)\n35.8\n(\u00b1 0.01)\nfj18\n7000\n1.04\n(\u00b1 0.004)\n36.9\n(\u00b1 0.02)\nTotal Single-Fjets\n3.74\n(\u00b1 0.01)\nTable 10: Estimated trigger rates for jet signatures foreseen at the beginning of data-taking with a lumi-\nnosity of 1031 cm\u22122s\u22121.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n721\n\n10\nSummary\nA detailed description of the algorithms used to reconstruct jets in the L1, L2 and Event Filter was\npresented. The performance of each of these algorithms was shown. The physics performance and\nalgorithm timing has been shown to be within the design targets. Nevertheless, optimisation studies\nto further improve the performance of these algorithms are ongoing. An example trigger menu for jet\nsignatures proposed for the beginning of data-taking was presented. The overall trigger strategy for\nselecting events based on jet signatures was also described.\nReferences\n[1] R. Achenbach et al., The ATLAS Level-1 Calorimeter Trigger, ATL-DAQ-PUB-2008-001 (2008).\n[2] ATLAS Collaboration, Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-041\n(1996).\n[3] ATLAS Collaboration, Tile Calorimeter Technical Desgin Report, CERN/LHCC/96-042 (1996).\n[4] A. Gupta, M. Wood, Jet Energy Calibration in the ATLAS detector using DC1 samples , CERN-\nATL-COM-CAL-2005-002 (2005).\n[5] F. James and M. Roos,\nMinuit - A System For Function Minimization And Analysis Of The\nParameter Errors And Correlations, Comput. Phys. Commun. 10 (1975) 343.\n[6] T. Sjostrand, L. Lonnblad, S. Mrenna and P. Skands, PYTHIA 6.3: Physics and manual, arXiv:hep-\nph/0308153.\n[7] A. Gupta , F. Merritt and J. Proudfoot,\nJet Energy Correction Using Longitudinal Weighting.\nCERN-ATL-COM-PHY-2006-062 (2006).\n[8] G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M.H. Seymour\nand B.R. Webber, HERWIG 6.5, JHEP 0101 (2001) 010.\n[9] ATLAS Collaboration, Data Preparation for the High-Level Trigger Calorimeter Algorithms, this\nvolume.\n[10] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[11] S.D. Ellis and D. Soper, Phys. Rev. D48, 3160 (1993).\n[12] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\nTRIGGER \u2013 OVERVIEW AND PERFORMANCE STUDIES OF JET IDENTIFICATION IN THE . . .\n722\n\nStandard Model\n723\n\nA Study of Minimum Bias Events\nAbstract\nThis note describes the methods developed for the measurement of the prop-\nerties of minimum bias events during low luminosity running using the\nATLAS detector. These methods aim to reconstruct the inclusive pseudo-\nrapidity and transverse momentum distributions of charged particles with\npT > 150 MeV produced from 14 TeV pp collisions. The triggers used\nto record minimum bias events are described and their acceptances evalu-\nated. An analysis to measure the inclusive distributions is presented and the\nsystematic uncertainties discussed. Finally, there is an overview of future\nphysics studies with minimum bias samples.\n1\nIntroduction\nThis note focuses on how the ATLAS detector [1] can be used to measure the central pseudorapidity\nand transverse momentum distributions of charged particles produced in inelastic proton-proton (pp)\ncollisions during early running at the LHC. Measuring the characteristics of these collisions allows\nan understanding of the physics behind these processes to be developed, particularly their energy de-\npendence. The minimum bias events allow the soft-part of the underlying event in high-pT collisions\nto be characterised. Studies of inclusive particle distributions in minimum bias events in pp collisions\nare important to provide the baseline for measurements in heavy-ion collisions, such as allowing dif-\nferences in the number of particles to be attributed to QCD effects rather than the simple scaling of\nthe number of nucleons. Finally these interactions will be a major background during low luminosity\nrunning (1033 cm\u22122s\u22121) and high luminosity running (1034 cm\u22122s\u22121), where the average number of\nsuch interactions per beam crossing is \u223c2 and \u223c18, respectively.\nThe total proton-proton cross-section can be divided into elastic and inelastic components, and\nthe inelastic component can be further divided into: non-diffractive, single diffractive and double\ndiffractive components [2]. The total cross-section (\u03c3tot) can then be written as:\n\u03c3tot = \u03c3elas +\u03c3sd +\u03c3dd +\u03c3nd\nwhere these cross-sections are elastic (\u03c3elas), single diffractive (\u03c3sd), double diffractive (\u03c3dd) and\nnon-diffractive (\u03c3nd), respectively. The cross-sections for the inelastic subprocesses determined using\nPYTHIA [3], which was used to generate the event samples for this study, are given in Table 1. For\ncomparison, the cross-sections predicted by PHOJET [4] are also shown in Table 1. The PHOJET\npredictions include central diffraction, however this hard proton-pomeron interaction only contributes\nto the cross-section at the few per cent level. As this is not simulated in PYTHIA, it was not considered\nfurther in this note.\nThe acceptance of inelastic events is de\ufb01ned by the trigger, which is usually known as a minimum\nbias trigger. It is designed to avoid bias in the sample, such as selecting high-pT events by triggering\non high-pT objects. However, some bias is usually introduced due to effects such as the geometrical\nacceptance of or minimum energy thresholds in the trigger detector. It is therefore not unusual to\n\ufb01nd different de\ufb01nitions for minimum bias events in the literature. Historically, the minimum bias\ntriggering used in hadron collider experiments [5\u201311] often used triggers based on forward-backward\ncoincidences that favoured the detection of non-single diffractive inelastic events (NSD), i.e. \u03c3nsd =\n\u03c3tot \u2212\u03c3elas \u2212\u03c3sd. Thus, NSD events have often been classi\ufb01ed as \u2018minimum bias events\u2019. In this\n724\n\nnote, results from simulated events selected using the minimum bias triggers are presented. These\nresults have been corrected for detector reconstruction and acceptance effects. The results for the non-\nsingle diffractive sample are also presented to allow comparison with previous results from hadron-\ncollider experiments. However, this requires correcting for the trigger acceptance for each of inelastic\nprocesses, which depends on the physics model used to generate the different processes.\nMinimum bias interactions have previously been studied at a range of different energies at the\nCERN ISR [5], CERN SppS [6\u20138] and Fermilab\u2019s Tevatron [9\u201311] and RHIC colliders. Based on\nthese results, Monte Carlo models have been tuned to generate predictions for LHC multiplicities [12].\nFigure 1 shows a comparison of model predictions for the central charged particle density in NSD p\u00afp\nevents for a wide range of centre-of-mass energies (\u221as). The data points shown are corrected for\ndetector and trigger effects and ef\ufb01ciencies back to the particle level. Figure 1 compares predictions\ngenerated with two different tunings of PYTHIA [3] (ATLAS and CDF tune-A [12]) with the central\ncharged particle density generated with PHOJET [4,13]. It is clear from this \ufb01gure that there is a large\nuncertainty in the predicted central particle density of non-single diffractive interactions at the LHC\nenergy even though the models have been tuned to agree with data at lower energies. This uncertainty\narises because the energy dependence in a variety of different models for low-pT hadronic processes\nis not well understood. Measuring the central particle density at the LHC will thus be crucial to\ndetermining the energy dependence of the central particle density and constraining models of inelastic\nevents.\n0\n2\n4\n6\n8\n10\n10\n2\n10\n3\n10\n4\n10\n5\nPYTHIA6.214 - ATLAS\nPYTHIA6.214 - CDF tune A\nPHOJET1.12\n pp interactions\n-\n UA5 and CDF data\n ATLAS\n\u221as (GeV)\ndNch/d\u03b7 at \u03b7=0\nFigure 1: Central charged particle density for non-single diffractive inelastic events as a func-\ntion of energy. The lines show predictions from PYTHIA using the ATLAS tune and CDF\ntune-A, and from PHOJET. The data points are from UA5 and CDF p\u00afp data.\nThis paper is organized as follows: In section 2 we brie\ufb02y describe the experimental setup and\nthe trigger strategies that have been developed to accept inelastic collisions with minimum bias. The\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n725\n\nanalysis procedure, corrections, as well as the systematic effects involved in this study are discussed\nin section 3. Section 4 presents an overview of future work planned to be done with ATLAS minimum\nbias measurements. Finally, in section 5 we present our conclusions.\nCross-section (mb)\nProcess\nPHOJET\nPYTHIA\nnon-diff.\n69\n55\nsingle diff.\n11\n14\ndouble diff.\n4\n10\ncentral diff.\n1\n-\ntotal inelastic\n85\n79\nelastic\n35\n23\ntotal\n120\n102\nTable 1: Cross-section predictions for pp interactions at \u221as = 14 TeV from PYTHIA and PHOJET.\n1.1\nCharacteristics of inelastic events\nThe pseudorapidity (\u03b7) and transverse momentum (pT) distributions of charged particles generated\nusing PYTHIA [3], with the parameter set de\ufb01ned in Ref. [14] and PHOJET [4, 13] with default\nparameters are shown in Figs. 2(a) and 2(b). These distributions correspond to non-diffractive, single-\nand double-diffractive inelastic pp interactions at \u221as = 14 TeV, respectively. They clearly show large\nuncertainties in model predictions for the LHC and that the events are dominated by low-pT particles\nwith the highest densities found in the central region |\u03b7| < 3.0. Much of this central region is covered\nby the ATLAS inner detector. The charged particle distributions will be reconstructed from tracks\nwhich are measured by the inner detector for |\u03b7| < 2.5, with pT greater than 150 MeV.\n1.2\nBackgrounds\nThe main backgrounds in minimum bias events, particularly during early running, will be beam-gas\ncollisions within the beampipe over the length of ATLAS, and beam-halo from interactions in the\ntertiary collimators in the accelerator. These backgrounds can provide spurious triggers that must be\nremoved from the inelastic event sample to prevent distortion of its characteristics. During early low\nluminosity running a large fraction of bunch crossings will have no pp interaction. Using a trigger\nbased only on bunch-crossings would result in a large number of empty events, which only contain\ndetector noise, being recorded. Therefore, the trigger must be able to reject such events in order\nto optimise the use of the trigger bandwidth. In this paper we will present results which include\ndiscussions on beam-gas events and empty events but not on beam-halo.\n2\nSimulation and experimental setup\nThe samples of single-, double-, and non-diffractive inelastic events used in this study were gener-\nated with PYTHIA version 6.403 [3]. The PYTHIA event generator was con\ufb01gured according to an\nunderlying event tuning \ufb01t [14] from previous experiments and is expected to provide a reasonable\ndescription of the non-diffractive part of minimum bias events.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n726\n\n \u03b7\n \n-6\n-4\n-2\n0\n2\n4\n6\n \n\u03b7\n dN/d\nevents\n1/N\n0\n2\n4\n6\n8\n10\n12\n14\nnon-diffractive (PYTHIA) \nnon-diffractive (PHOJET) \nsingle diffractive (PYTHIA)\nsingle diffractive (PHOJET)\ndouble diffractive (PYTHIA)\ndouble diffractive (PHOJET)\nATLAS\n (GeV) \nT\n p\n0\n0.5\n1\n1.5\n2\n2.5\n3\n \nT\n dN/dp\nevents\n1/N\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nnon-diffractive (PYTHIA) \nnon-diffractive (PHOJET) \nsingle diffractive (PYTHIA) \nsingle diffractive (PHOJET) \ndouble diffractive (PYTHIA) \ndouble diffractive (PHOJET) \nATLAS\n(a)\n(b)\nFigure 2: Pseudorapidity (a) and transverse momentum distribution (b) of stable charged particles\nfrom simulated 14 TeV pp inelastic collisions generated using PYTHIA and PHOJET event generators.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n727\n\n2.1\nThe ATLAS inner detector\nThe pseudorapidity and transverse momentum distributions of charged particles are measured using\nthe ATLAS inner detector. The inner detector is described in detail elsewhere [1]. It consists of, in\norder of increasing radius, a silicon pixel system, a silicon microstrip system (SCT) and a gas-based\ntransition radiation detector (TRT). The inner detector is mounted inside a solenoid magnet which\nprovides a 2 T magnetic \ufb01eld.\nThe inner detector sub-detectors are designed as independent but also complementary systems.\nThe pixels cover radii of 50.5 mm-149.6 mm, the SCT covers 299 mm-560 mm and the TRT covers\n563 mm-1066 mm. The precision tracking detectors (pixel and microstrip) cover |\u03b7| < 2.5 and are\ndivided into barrel (|\u03b7| < 1.4) and endcaps (1.4 < |\u03b7| < 2.5).\nThe ATLAS inner detector will provide hermetic and robust pattern recognition, excellent mo-\nmentum resolution and both primary and secondary vertex measurements for charged tracks above a\npT\nthreshold, which is nominally 500 MeV but can be as low as 100 MeV within |\u03b7| < 2.5. The\nnominal pT-cut of 500 MeV corresponds to tracks traversing the full inner detector, however as dis-\ncussed in section 1.1 a measurement of the properties of minimum bias events requires a pT-cut of \u2264\n200 MeV. A pT-cut of 150 MeV, used in this paper, corresponds to tracks that traverse the precision\nSi tracker (pixels and SCT) allowing low-pT tracks to be well reconstructed.\n2.2\nThe minimum bias trigger scintillators\nThe Minimum Bias Trigger Scintillators (MBTS) [15] are mounted on the inner surface of the liq-\nuid argon endcap cryostats and cover a pseudorapidity range of 2.12 < |\u03b7| < 3.85. The MBTS is\nconstructed from 2 cm polystyrene-based scintillator counters. Each side of the MBTS is made up\nof 16 counters each of which is split into two regions of equal pseudorapidity (2.12 < |\u03b7| < 2.83,\n2.83 < |\u03b7| < 3.85) and covering \u03c0\n4 in azimuth. The MBTS is read out through the tile calorimeter\nelectronics providing a fast L1 signal, which is discriminated above a voltage threshold, relative to the\nbunch-crossing signal.\n3\nMinimum bias trigger scenarios\nA minimum bias trigger should select inelastic collisions with as little bias as possible, precluding the\nuse of the standard high-pT triggers. Ideally, the L1 random trigger [16] with beam pickup would\nbe used to accept events with zero bias, and inelastic collisions would be selected of\ufb02ine. However,\nduring early running when the luminosity is expected to be < 1030 cm\u22122s\u22121, the random trigger will\nbe very inef\ufb01cient since the probability of an interaction during a bunch crossing is < 1%. Therefore,\nvalidation of the L1 random trigger is required in the high-level-trigger (HLT). The use of tracking in\nthe HLT to validate the random trigger and a dedicated L1 trigger based on the minimum bias trigger\nscintillators (MBTS) has been studied. A minimum bias trigger stream consisting of the random\ntrigger, track trigger and the MBTS is shown in Figure. 3. The random-based track trigger and the\nMBTS triggers are discussed in sections 3.1 and 3.2, respectively. In addition, the L1 MBTS could be\nused in conjunction with the pixel and SCT spacepoints reconstructed at L2 and the Event Filter (EF)\ntrack trigger. However, this was not studied in this note.\nAs the luminosity increases from \u223c1031 cm\u22122s\u22121 to 1032 cm\u22122s\u22121 and higher values, the mean\nnumber of interactions per bunch crossing will be around 1. The random trigger will then record\ninteractions for each crossing without requiring further triggers at L2 or EF to reject empty bunch\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n728\n\nevents. This will allow a zero bias sample to be ef\ufb01ciently accepted by ATLAS using the random\ntrigger.\nFor the purposes of this note, a luminosity of 1031 cm\u22122s\u22121 with a bunch spacing of 75 ns has\nbeen assumed. The rate of inelastic events under those conditions is 792 kHz, and the mean number\nof events per bunch crossing is 0.06. Trigger ef\ufb01ciencies were calculated using around 105 events of\nSpace Point\nMBTS Lvl 1\nRecon. Tracks\nRandom\nLevel 1\nLevel 2\nEvent Filter\nFigure 3: Minimum bias trigger slice.\nsimulated hydrogen beam-gas, single diffractive, double diffractive, non-diffractive and empty events.\nEach of these simulated samples were reconstructed and passed through the trigger logic and the\ntrigger ef\ufb01ciency was then calculated from the number of events satisfying the trigger logic.\n3.1\nRandom-based track trigger\nThe selection of minimum bias events by a track trigger is performed by the high-level trigger. The\naim is to reject empty bunch and beam-gas events. After the random event selection at L1, the L2\ntrigger rejects empty events by requiring a minimum number of spacepoints in the pixel and SCT\ndetector. The trigger ef\ufb01ciency curves for different types of events (ddiff: double diffractive, ndiff:\nnon-diffractive and sdiff: single diffractive) are shown in Figure 4. The ef\ufb01ciency of empty bunch\nevents as a function of spacepoints clearly shows that a modest constraint on either the number of\npixel or SCT spacepoints rejects events containing only random noise. The thresholds for the number\nof pixel and SCT spacepoints were determined from the requirement to have a signal to background\nfor non-diffractive to empty bunch events of 100:1. Given that the beam conditions assumed in this\npaper correspond to a probability of a pp non-diffractive inelastic interaction of 0.05, this corresponds\nto constraining the ef\ufb01ciency of empty bunch events to be less than 5\u00d710\u22124. This requires setting the\nthreshold on the number of spacepoints to be 12 and 3 in the pixel and SCT respectively.\nWhile the spacepoint (SP) trigger reduces the number of beam-gas events accepted, the rate can\nbe further reduced by requiring the presence of reconstructed tracks within a small z-region around\nthe nominal interaction point. A full track reconstruction scan with a minimum pT of 200 MeV is\ncarried out in the EF on the events that pass the SP trigger. These tracks are then used to select events\nusing the cuts de\ufb01ned in Table 2. The trigger ef\ufb01ciency is plotted with respect to the number of\nreconstructed tracks in Figure. 5. The empty events are rejected by the cut on the number of pixel and\nSCT spacepoints resulting in an ef\ufb01ciency of zero.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n729\n\nPixel Space Point Threshold \n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nTrigger Efficiency \n0\n0 2\n0.4\n0 6\n0 8\n1\nempty\nsdiff\nddiff\nndiff\nbeamgas\nATLAS\nSCT Space Point Threshold \n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nTrigger Efficiency \n0\n0.2\n0.4\n0.6\n0.8\n1\nempty\nsdiff\nddiff\nndiff\nbeamgas\nATLAS\n(a)\n(b)\nFigure 4: Trigger ef\ufb01ciency as a function of the number of pixel spacepoints (a) and the number of\nSCT spacepoints (b).\nTrack parameter\n2 Trigger cut\nNumber of tracks\n\u22652\nTrack z0\n< 200 mm\nTable 2: Track cuts for EF track trigger.\nNumber of Tracks Cut \n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nTrigger Efficiency \n0\n0 2\n0.4\n0 6\n0 8\n1\nempty\nsdiff\nddiff\nndiff\nbeamgas\nATLAS\nFigure 5: Trigger ef\ufb01ciency as a function of the number of reconstructed tracks for events satisfying\nthe L2 spacepoint requirement.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n730\n\n3.2\nMinimum bias triggers using the MBTS\nTwo simple MBTS L1 trigger strategies were considered for minimum bias event selection: MBTS 1 1\nand MBTS 2. MBTS 1 1 is de\ufb01ned as at least one MBTS counter above threshold on each side, where\nthe threshold of 40 mV was chosen from measurements of cosmic commissioning data. MBTS 2 is\nde\ufb01ned as two or more MBTS counters above threshold anywhere in the MBTS system. The trigger\nef\ufb01ciencies as a function of MBTS counter threshold for inelastic non-diffractive, double-diffractive,\nsingle-diffractive, beam-gas and empty bunch events are given in Fig. 6.\nMBTS Lvl 1 Threshold (mV) \n0\n50\n100\n150\n200\n250\n300\n350\n400\nTrigger Efficiency \n0\n0 2\n0.4\n0 6\n0 8\n1\nempty\nsdiff\nddiff\nndiff\nbeamgas\nATLAS\nMBTS Lvl 1 Threshold (mV) \n0\n50\n100\n150\n200\n250\n300\n350\n400\nTrigger Efficiency \n0\n0.2\n0.4\n0.6\n0.8\n1\nempty\nsdiff\nddiff\nndiff\nbeamgas\nATLAS\n(a)\n(b)\nFigure 6: MBTS L1 trigger threshold scans for the two trigger con\ufb01gurations: (a) MBTS 1 1 (b) and\nMBTS 2.\n3.3\nTrigger ef\ufb01ciency\nA summary of the trigger ef\ufb01ciencies for the track-based and MBTS triggers are given in Table 3. The\nef\ufb01ciency of diffractive events is around half of that of non-diffractive events. This is primarily due to\nthe low particle multiplicity in diffractive events and because the triggers cover the central region and\nare therefore only sensitive to a fraction of the diffractive cross-section corresponding to high mass\ndiffractive states.\nThe acceptances for the different processes i.e. the ef\ufb01ciencies weighted by the fraction of the\ninelastic cross-section are given in table 4. This shows that due to lower ef\ufb01ciencies and smaller\ncross-sections the acceptance of diffractive events is signi\ufb01cantly suppressed. The acceptance of\nthe proposed minimum bias triggers is around 85-92% and this will consist of around 80% of non-\ndiffractive events and roughly equal numbers of single and double diffractive events.\n4\nAnalysis\nThe goal of the analysis is to reconstruct the number of primary charged particles per unit of pseudora-\npidity and per unit of transverse momentum for inelastic pp interactions taken with the minimum bias\ntrigger. Primary particles are de\ufb01ned as particles produced in the pp collision, but excluding secondary\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n731\n\nMBTS 1 1\nMBTS 2\nSP\nSP & EF Tracks\nNon-diffractive\n99%\n100%\n100%\n100%\nDouble-diffractive\n54%\n83%\n66%\n65%\nSingle-diffractive\n45%\n69%\n57%\n57%\nBeam-gas\n40%\n54%\n47%\n40%\nTable 3: MBTS and random-track trigger ef\ufb01ciencies.\nMBTS 1 1\nMBTS 2\nSP\nSP & EF Tracks\nNon-diffractive\n69%\n70%\n70%\n70%\nDouble-diffractive\n7%\n10%\n8%\n8%\nSingle-diffractive\n8%\n12%\n10%\n10%\nTable 4: MBTS and random-track trigger acceptances.\nparticles from weak decays of strange hadrons or from electromagnetic or hadronic interactions in the\ndetector material.\nA sample of \u223c150,000 inelastic events, with ND, SD and DD events mixed in the proportion given\nby the PYTHIA cross-sections, was reconstructed and used in this study (MB sample). A typical non-\ndiffractive event contains around 45 reconstructed tracks of which 37 are from primary particles and 8\nare from secondary particles. The ef\ufb01ciencies and corrections were derived from half the sample and\nused in the analysis of the other half of the sample.\n4.1\nEvent selection\nTwo selection criteria are applied to the set of reconstructed events: the event must be triggered by the\nminimum bias trigger and it must contain at least one reconstructed vertex. The sample of inelastic\nevents selected by the MBTS 2 trigger, described in Section 3.2, was used for this analysis. No beam-\ngas or pileup events were included in the sample studied here. An additional criterion should be\nadded to exclude events with multiple pp interactions in a bunch-crossing but this was not included\nin this analysis as the samples of simulated data used for this study contained events with a single pp\ninteraction in a bunch-crossing.\n4.2\nTrack selection\nTracks were reconstructed using tracking with the minimum pT set to 100 MeV rather than the default\n500 MeV. To avoid threshold effects, tracks with pT > 150 MeV were used in the analysis. The relative\npT-resolution, \u03c3( 1\npT )pT, was found to be around 1.5% for |\u03b7| < 0.8 and 4.3% for |\u03b7| > 1.6.\nCuts on the measured track parameters were used to select a set of well reconstructed tracks for\nthe analysis. These cuts are listed in Table 5. The requirement of a hit in the inner pixel layer,the\nb-layer, removes a sizable portion of fake tracks and tracks associated to secondary particles since\nthey frequently do not leave a hit in the \ufb01rst layer of the pixel detector. The cut on the number of pixel\nand SCT hits is a standard track scoring cut applied during reconstruction and is listed here only for\ncompleteness. The values of the cuts were chosen by \ufb01tting each of the distributions with a gaussian\nand cutting at \u223c3\u03c3.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n732\n\nQuality cuts\nNo. of b-layer hits \u22651\nNo. of Silicon hits \u22655\nResolution cuts\n|\u03c3d0| < 1.6 mm\n|\u03c3z0| < 6.0 mm\n|\u03c3\u03c6| < 0.03\n|\u03c3\u03b8| < 0.015\n|\u03c3q/pT | < 0.0003 ( GeV)\u22121\nTrack-to-vertex cut\nN\u03c3 < 3\nTable 5: Track selection cuts used in this analysis. The resolutions \u03c32\nd0, \u03c32\nz0, \u03c32\n\u03c6, \u03c32\n\u03b8 and \u03c32\nq/pT\nare the \ufb01ve diagonal elements in the track parameter covariance matrix. For more information\non the tracking Event Data Model (EDM) see [17].\nThe track-to-vertex cut is the selection that most effectively cuts away tracks from secondary\nparticles while accepting tracks from primaries. It is made by cutting on the distance of closest\napproach to the nearest reconstructed vertex, normalized by the error. The normalized distance to the\nvertex is de\ufb01ned as\n\u2206R\n\u2261\ns\u0012\u2206d0\n\u03c3d0\n\u00132\n+\n\u0012\u2206z0\n\u03c3z0\n\u00132\n,\n(1)\nwhere \u2206d0/\u03c3d0 and \u2206z0/\u03c3z0 are the normalized distances in the transverse and longitudinal directions,\nrespectively. The number of \u03c3 to the vertex as a function of \u2206R (for a two-dimensional gaussian) is\ngiven by\nN\u03c3\n=\n\u221a\n2erf\u22121(1\u2212e\u2212\u2206R2/2).\n(2)\nNote that the above formula assumes no correlations between the resolutions in the transverse and\nlongitudinal direction.\nTo determine the effects of the cuts and evaluate ef\ufb01ciencies and acceptances, the reconstructed\ntracks are matched to the generated primary and secondary particles. The track that has the highest\npercentage of hits that overlap with the trajectory of a generated particle is matched to that generated\nparticle. A track is well matched to a particle if greater than 50% of its hits overlap with the generated\nparticle\u2019s trajectory. A primary track is one matched to a primary particle and similarly a secondary\ntrack is one matched to a secondary particle. If a track is not matched to any generated particle, it is\nclassi\ufb01ed as a fake.\nTable 6 shows the in\ufb02uence of the track cuts on the reconstructed sample. Each row shows the\npercentage of tracks that did not pass each of the speci\ufb01ed cuts. Note that a single track can fail several\ncuts and therefore give counts in several rows. Three of the rows show the percentage of tracks that fail\nany of the quality cuts (\u2018Quality\u2019), any of the resolution cuts (\u2018Resolution\u2019) and any of the quality or\nresolution cuts (\u2019Q || R\u2019). The strongest and most effective cut is the track-to-vertex cut, which rejects\nabout 88% of the secondaries. The second last row shows the percentage of reconstructed tracks that\nare outside the pseudorapidity and pT range used in the analysis (|\u03b7| > 2.5, pT < 150 MeV).\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n733\n\nCut\n% Cut All\n% Cut Primary tracks\n% Cut Secondary tracks\nb-layer hit\n15.9\n8.5\n46.8\ncovd0\n11.5\n6.0\n34.2\ncovz0\n9.4\n5.0\n27.4\ncov\u03c6\n8.9\n5.1\n24.3\ncov\u03b8\n4.9\n4.2\n8.2\ncovq/pT\n6.4\n4.3\n14.9\nQuality\n15.9\n8.5\n46.8\nResolution\n16.7\n10.9\n40.4\nQ || R\n24.6\n15.6\n62.1\nTrack-to-Vtx\n30.7\n16.9\n87.8\n\u03b7 || pT\n1.2\n1.3\n0.9\nTotal\n38.6\n24.6\n96.5\nTable 6: Fraction of tracks cut away by the selection cuts.\n4.3\nProcedure & corrections\nThe dNch/d\u03b7 and dNch/dpT distributions are obtained by starting with the measured number of se-\nlected tracks in selected events and applying the following three corrections:\n\u2022 Track-to-particle correction\n\u2022 Vertex reconstruction correction\n\u2022 Trigger bias correction\nThe \ufb01rst correction accounts for the difference between the number of measured tracks and the\nnumber of primary charged particles. This is essentially a correction for the inner detector accep-\ntance and ef\ufb01ciency of the tracking software [18]. The second correction takes into account the vertex\nreconstruction ef\ufb01ciency and corrects for events that have no reconstructed vertex. These two correc-\ntions account for detector dependent effects and produce the minimum bias sample, in which the data\nhave been corrected for detector reconstruction and acceptance but have not been corrected for the\ntrigger acceptance.\nThe trigger bias correction depends both on the detector simulation and on the physics model\nused in the event generator to simulate inelastic pp interactions. Different corrections for the trigger\ncan be applied to correct the measured distributions back to different physics processes, i.e. inelastic,\nnon-single-diffractive or non-diffractive interactions.\nThe track-to-particle correction is applied only at the track level. The vertex correction and the\ntrigger bias correction are applied at the track and event level. The track-level vertex and trigger bias\ncorrections are needed to compensate for any bias on the measured track distribution due to vertex\nand trigger requirements. All track-level corrections are determined as a function of pseudorapidity\n(\u03b7), pT and the z-position of the collision vertex, vz. The event level corrections are determined as a\nfunction of vz and the number of reconstructed tracks in the event.\nThe corrections are 3-D and 2-D histograms but the principal corrections shown in the \ufb01gures\nbelow are plotted as projections of pT \u03b7 z-position or the number of reconstructed tracks as appropriate\nfor clarity.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n734\n\n4.3.1\nTrack-to-particle correction\nThe number of selected reconstructed tracks differs slightly from the number of primary charged\nparticles due to a number of different effects: the acceptance of the detector, the detector and track\nreconstruction ef\ufb01ciency, the contribution from secondaries and fakes, and the acceptance of the track\nselection cuts. The track-to-particle correction takes all these effects into account and is calculated as\nCtrk(\u03b7,vz, pT)\n\u2261\nNo. of primary charged particles\nNo. of selected reconstructed tracks.\n(3)\nThe numerator and denominator are calculated for the same events taken through the full detector\nsimulation and reconstruction.\nFigure 7 shows the projection of the 3-dimensional track-to-particle correction onto the \u03b7 and\npT axes. The correction is signi\ufb01cant and changes rapidly with pT below 200 MeV where the recon-\nstruction ef\ufb01ciency is lower due to a lower number of hits on a track and the effects of material and\nmultiple scattering. Above 200 MeV the correction is small and has a small dependence on pT.\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0 5\n0\n0.5\n1\n1.5\n2\n2.5\nTrack-to-ParticleCorrection\n1.4\n1.5\n1.6\n1.7\n1.8\nATLAS\n [GeV]\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nTrack-to-Particle Correction\n5\n10\n15\n20\n25\nATLAS\n(a)\n(b)\nFigure 7: The track-to-particle correction Ctrk as a function of (a) \u03b7 and (b) pT.\n4.3.2\nVertex reconstruction correction\nThe vertex correction takes into account the bias introduced by events that are not counted because\ntheir vertex was not found by the vertex reconstruction algorithm. The event-level correction is calcu-\nlated as a function of vz and number of reconstructed tracks in the event:\n\u02dcCvtx(vz,N)\n\u2261\nNo. of triggered events\nNo. of triggered events with \u22651 reconstructed vertex.\n(4)\nThe track-level vertex correction is calculated as a function of \u03b7, vz and pT:\nCvtx(\u03b7,vz, pT)\n\u2261\nNo. of tracks in all triggered events\nNo. of tracks in triggered events with \u22651 reconstructed vertex.\n(5)\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n735\n\nAlthough the vertex correction is essentially a detector correction, some model dependence is\npresent since only triggered collisions are taken into account to compute the correction factors. How-\never, the use of only triggered events has the advantage that the correction can be computed directly\nfrom the data, without relying on any simulation. Once data are available it will also be possible\nto compare the properties of the triggered events with no reconstructed vertex to the corresponding\nevents in the simulation. This may help minimize and better estimate any systematic uncertainties.\nFigure 8 shows the event-level vertex reconstruction correction as a function of the number of re-\nconstructed tracks, N, and vertex z-position. A vertex can be de\ufb01ned using a single well reconstructed\ntrack. As the number of tracks increases, the correction approaches unity. For events with N > 10, a\nvertex is always found and the correction is no longer required.\nFigure 9 shows projections of the 3-dimensional track-level vertex correction onto the vz and\npT axes. These corrections are found to be at the level of a few percent.\n [mm]\nz\nv\n-200\n-150\n-100\n-50\n0\n50\n100\n150\n200\nEvent-level Vertex Correction\n1 06\n1 08\n1.1\n1.12\n1.14\n1.16\n1.18\n1.2\nATLAS\n(a)\nN\n0\n5\n10\n15\n20\n25\nEvent-level Vertex Correction\n0\n1\n2\n3\n4\n5\nATLAS\n(b)\nFigure 8: The event-level vertex correction as a function of (a) vz and (b) the number of recon-\nstructed tracks (N).\n4.3.3\nTrigger bias correction\nThe trigger bias correction accounts for the difference between the MB sample selected by the mini-\nmum bias trigger and the physics process of interest. This correction depends on the trigger detector\nsimulation and on the models of the pp interactions used in the event generator. Therefore, this cor-\nrection is dependent on the relative cross-sections of the inelastic processes used and on the modelling\nof particle production for the different inelastic processes.\nAfter an initial model-independent measurement is made, the MB sample, the trigger bias correc-\ntion can be used to obtain distributions for other samples of interest: non-diffractive (ND), non-single\ndiffractive (NSD) or inelastic (INEL) collisions. Each of these samples corresponds to a different\ntrigger correction and each correction can be applied to yield the \ufb01nal distributions for the different\ncollision samples. In general the correction from MB to NSD collisions is the smallest since these\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n736\n\n [mm]\nz\nv\n-200\n-150\n-100\n-50\n0\n50\n100\n150\n200\nTrack-level Vertex Correction\n1\n1.005\n1.01\n1.015\n1 02\nATLAS\n(a)\n [GeV]\nT\np\n0\n0 2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1 6\n1.8\n2\nTrack-level Vertex Correction\n0 97\n0 98\n0 99\n1\n1 01\n1 02\n1 03\nATLAS\n(b)\nFigure 9: The track-level vertex correction as a function of (a) vz and (b) pT.\ntwo event samples are almost identical, while the correction from MB to INEL is on the order of 1.2\n(integrated over N and vz).\nThe trigger bias correction is determined on event level as a function of vz and multiplicity, de\ufb01ned\nas in the vertex correction:\n\u02dcCtrig(vz,N)\n\u2261\nNo. of interactions in sample of interest\nNo. of triggered events\n,\n(6)\nand on track-level as a function of \u03b7, vz and pT:\nCtrig(\u03b7,vz, pT)\n\u2261\nNo. of tracks in sample of interest\nNo. of tracks in triggered events .\n(7)\nIn this analysis it is assumed that there is only one interaction per event since the events have been\nsimulated in this way. This will need to be veri\ufb01ed in the real data for any events with more than one\nreconstructed vertex by looking at the multiplicity of each of the vertices and the distance between\nthe vertices. As in the vertex correction, all tracks are counted since the track-to-vertex distance is\nunde\ufb01ned for events with no reconstructed vertex.\nFigure 10 shows the event-level trigger bias correction for the NSD sample as a function of multi-\nplicity and vertex z-position. Using the MBTS 2 trigger, the correction is only important for N < 25;\nfor higher multiplicities the correction factor is not needed. It is largest for N < 5 which are prin-\ncipally diffractive events that have a lower trigger ef\ufb01ciency relative to the non-diffractive events as\ndiscussed in section 3.\nFigure 11 shows projections of the 3-dimensional track-level trigger bias correction for the NSD\nsample to two of the three 2-dimensional planes and to the vz and pT axes.\n4.4\nCorrected distributions\nAn \u03b7-vz-pT (3-D) histogram is \ufb01lled for each track in each event and weighted with the values of\nthe track-level corrections described above. A vz-N (2-D) histogram is also \ufb01lled for each event and\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n737\n\n [mm]\nz\nv\n-200\n-150\n-100\n-50\n0\n50\n100\n150\n200\nEvent-level Trigger Correction\n0 82\n0 84\n0 86\n0 88\n0.9\n0 92\n0 94\n(a)\nN\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEvent-level Trigger Correction\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n(b)\nFigure 10: The event-level trigger bias correction for the NSD sample as a function of (a) vz\nand (b) number of reconstructed tracks (N).\n [mm]\nz\nv\n-200\n-150\n-100\n-50\n0\n50\n100\n150\n200\nTrack-level Trigger Correction\n0.965\n0 97\n0.975\n0 98\n0.985\n0 99\n(a)\n [GeV/c]\nT\np\n0\n0 2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1 6\n1.8\n2\nTrack-level Trigger Correction\n0 96\n0 97\n0 98\n0 99\n1\n1 01\n1 02\n(b)\nFigure 11: The track-level trigger bias correction for the NSD sample as a function of (a) vz\nand (b) pT.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n738\n\nweighted with the values of the event-level corrections. This histogram is needed to provide the proper\nnormalization factor for the analysis.\nAfter \ufb01lling the histograms, a vertex range is chosen and the vz variable is integrated out. In\nthe case of dNch/d\u03b7, the pT variable is integrated for pT > 150 MeV; in the case of dNch/dpT, the\n\u03b7 variable is integrated over \u22122.5 < \u03b7 < 2.5. Each \u03b7-bin or pT-bin is then divided by the total number\nof events, calculated by integrating the weighted event distribution histogram over N and vz. Finally,\nthe distribution is normalized by the inverse width of the bins. No correction was made for the effect\nof the pT cutoff in the reconstruction. However, the stability of the results will be tested by varying\nthe pT cutoff in data.\nThe distributions are presented for the sample events accepted by the minimum bias trigger. For\nthis analysis MBTS 2 is used, and are labelled as MB. The MB distributions have only been corrected\nfor the acceptance and ef\ufb01ciencies associated with reconstructing tracks and vertices. To obtain the\nNSD distributions to allow comparisons with other results, the MB distributions are corrected for the\ntrigger bias.\nThe correction procedure can be expressed mathematically for one bin, corresponding to a certain\nregion of phase space, in the following way. The number of particles P and number of interactions I\nare calculated as:\nP(\u03b7,vz, pT)\n=\n\u2211\nevents \u2211\ntracks\n(Ctrk(\u03b7,vz, pT)\u00b7Cvtx(\u03b7,vz, pT)\u00b7Ctrig(\u03b7,vz, pT)),\n(8)\nI(vz,N)\n=\n\u2211\nevents\n( \u02dcCvtx(vz,N)\u00b7 \u02dcCtrig(vz,N)).\n(9)\nTracks are weighted by the track-to-particle correction Ctrk(\u03b7,vz, pT), by the track-level vertex cor-\nrection Cvtx(\u03b7,vz, pT) and the track-level trigger bias correction Ctrig(\u03b7,vz, pT). Events are weighted\nby the event-level vertex correction \u02dcCvtx(vz,N) and the event-level trigger bias correction \u02dcCtrig(vz,N).\nFor a given vertex range [V1,V2] the dNch/d\u03b7 and dNch/dpT are then calculated as:\ndNch\nd\u03b7\n\f\f\f\f\n\u03b7=\u03b7\u2032\n=\nR V2\nV1\nR P(\u03b7\u2032,vz, pT)dpTdvz\nR V2\nV1\nR I(vz,N)dNdvz\n,\n(10)\ndNch\ndpT\n\f\f\f\f\npT =p\u2032\nT\n=\nR V2\nV1\nR P(\u03b7,vz, p\u2032\nT)d\u03b7dvz\nR V2\nV1\nR I(vz,N)dNdvz\n.\n(11)\nTo exercise the analysis chain, the complete reconstructed sample was divided in half: one part\nwas used to calculate the corrections and the other used as \u2018data\u2019 input to the analysis.\nFigures 12 and 13 show the corrected pseudorapidity distribution (pT > 150 MeV) and the cor-\nrected transverse momentum spectrum (|\u03b7| < 2.5) for the MB and NSD event samples. Statistical\nerrors on the corrected distributions are shown. The aim was to achieve statistical errors on the cor-\nrections of less than 2% per bin. The errors are mostly negligible since suf\ufb01cient statistics were used\nto determine the correction factor. Data in regions where small statistical errors could not be achieved\n(i.e. near the edges of the acceptance) are not included in the analysis.\n4.5\nSystematic uncertainties\nThe systematic uncertainties have been estimated by changing the parameters in the generation, re-\nconstruction or analysis and then re-evaluating the corrections and applying them to the analysis input\nsample. Although many of the systematic uncertainties are correlated, the different effects are studied\nhere independently. The systematic uncertainties investigated include:\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n739\n\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n\u03b7\n/d\nch\ndN\nev\n1/N\n4.6\n4.8\n5\n5.2\n5.4\n5.6\n5.8\n0.95\n1\n1.05\n1.1\n1.15\n1.2\nMC charged primaries\nCorrected newTracking\nRatio: Corrected/MC\nATLAS\n(a)\n [GeV]\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nT\n/dp\nch\ndN\nev\n1/N\n0\n10\n20\n30\n40\n50\nMC charged primaries\nCorrected newTracking\nATLAS\n(b)\nFigure 12: Corrected normalised pseudorapidity and pT distributions, together with the input\nMonte Carlo truth (full line) for the MB sample (blue triangles). (a) \u03b7 distributions for pT >\n150 MeV, where the lower part, the ratio of the analysis result over the Monte Carlo prediction\nis shown. The corresponding scale is drawn on the right axis. (b) pT spectra for |\u03b7| < 2.5.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n740\n\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n\u03b7\n/d\nch\ndN\nev\n1/N\n5\n5.2\n5.4\n5.6\n5.8\n6\n6.2\n6.4\n0.95\n1\n1.05\n1.1\n1.15\n1.2\nMC charged primaries\nCorrected newTracking\nRatio: Corrected/MC\nATLAS\n(a)\n [GeV]\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nT\n/dp\nch\ndN\nev\n1/N\n0\n10\n20\n30\n40\n50\n60\nMC charged primaries\nCorrected newTracking\nATLAS\n(b)\nFigure 13: Corrected normalised pseudorapidity and pT distributions, together with the input\nMonte Carlo Truth (full line) for the NSD sample (blue triangles). (a) \u03b7 distributions for pT >\n150 MeV, where the lower part, the ratio of the analysis result over the Monte Carlo prediction\nis shown. The corresponding scale is drawn on the right axis. (b) pT spectra for |\u03b7| < 2.5.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n741\n\n\u2022 Track selection: Based on the estimated track resolutions (\u03c3) for their distance from the vertex\nof the interaction, d0, tracks with d0 > 3\u03c3 are removed from the track sample. The error asso-\nciated with this cut was estimated by varying the cut value by \u00b10.5\u03c3 and observing the change\nin the number of accepted tracks. A mis-estimate of \u00b10.5\u03c3 leads to a change in the number of\naccepted tracks of less than 2%.\n\u2022 Secondaries: Before track selection cuts are applied, the number of tracks originating from\nsecondaries is about 25% of the number of tracks originating from primaries. After the track\nselection the total number of accepted secondary tracks is about 2.2% of the number of the\naccepted tracks. The error on the number of secondaries was estimated by changing the number\nof secondaries in the reconstructed sample by \u00b150%. The total number of accepted secondary\ntracks was found to change by 1.1%. The effect is strongest in the low-pT region and vanishes\nonly for pT>5 GeV. The systematic uncertainty was therefore estimated to be 1.5%.\n\u2022 Vertex reconstruction bias: Since the z-position of the reconstructed vertex is integrated out,\nit is possible that a bias from the reconstruction of the vertex could introduce a systematic\neffect on the measurement. Bias due to the vertex reconstructed was evaluated by repeating\nthe dNch/d\u03b7 analysis using the generated vz instead of the reconstructed vz. The observed\ndifference was found to be 0.1%.\n\u2022 Misalignment: The systematic effect from misalignment was estimated by re-running the re-\nconstruction with a different geometry that corresponded to a misaligned and distorted detector,\nand comparing the dNch/d\u03b7 produced with that produced for a detector that is ideally aligned.\nThe misaligned geometry was misaligned both globally and locally. However, the local mis-\nalignments had been corrected for using the alignment procedure. The two distributions agreed\nat the level of 5-6% across the barrel and forward regions. This is the exepected level that\ncan achieved with cosmics and early data. A systematic uncertainty of 6% was attributed to\nmisalignment.\n\u2022 Beam-gas interactions: The presence of background events coming from beam-gas would result\nin additional systematics on the measurement.\nThe rate of beam-gas interactions is highly dependent on the particular beam conditions during\nstartup such as the number of protons per bunch and the beam current. Studies by the LHC\ngroup have estimated the rate of beam-gas collisions within ATLAS to be 100 Hz [19]. As-\nsuming a pp collision rate during early running of 8\u00d7105 Hz this corresponds to approximately\n1 beam-gas event per 8000 pp events. Preliminary studies with simulated beam-gas events\nhave also shown that only a very small fraction (<1%) of beam-gas events passed the vertex\nreconstruction requirement. Therefore the effect of beam-gas events is expected to be small.\nThe systematic uncertainty due to beam-gas events was estimated to be \u223c1%.\n\u2022 Particle composition: The track-to-particle correction is calculated from events generated with\nPYTHIA [14]. Although \u03c0\u00b1, K\u00b1, and p\u00b1 compose over 98% of the charged particle multi-\nplicity in these events, the ef\ufb01ciency for detecting each of these is considerably different for\npT < 500 MeV. This model dependent effect introduces an additional systematic error on the\nmeasurement since relative abundances in PYTHIA could differ from reality.\nRelative abundances of charged pions, kaons and protons and anti-protons were enhanced and\nreduced by \u00b150% to estimate the systematic uncertainty due to variations in the particle com-\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n742\n\nposition. The systematic uncertainty obtained by this method is estimated to be around 2%.\nThis is highly dependent on the low-pT cut used in track reconstruction.\n\u2022 Relative process frequency: The trigger bias and vertex reconstruction corrections are calculated\nfrom a sample of inelastic events where the relative cross-sections are as predicted by PYTHIA\n[3]. Since the trigger and vertex reconstruction ef\ufb01ciencies are different for each of the inelastic\ncomponents (non-diffractive, single diffractive, and double-diffractive), these corrections are\ndependent on the relative cross sections of the different components.\nThe relative cross sections between non-diffractive, single-diffractive and double-diffractive\ncomponents were enhanced and reduced to estimate the systematic due to the uncertainty from\nthe PYTHIA event generator. The corrections have been calculated by changing the diffractive\ncross sections by \u00b150% of the PYTHIA prediction, i.e. 7.1 mb < \u03c3SD < 21.4 mb and 5.1 mb <\n\u03c3DD < 15.3 mb, which, as can be seen in Table 1, covers the difference in the predicted relative\ncross sections between PYTHIA and PHOJET.\nChanging the diffractive cross sections by \u00b150% changes the result of the analysis by about 4%\non the \ufb01nal NSD sample. For the minimum bias sample in which no trigger bias correction is\napplied, this systematic error is approximately zero.\nName\nLevel\nEstimated Uncertainty\nTrack selection cuts\nAnalysis\n2%\nMis-estimate of secondaries\nAnalysis\n1.5%\nVertex reconstruction bias\nReconstruction\n0.1%\nMisalignment\nReconstruction\n6%\nBeam-gas and pileup\nOf\ufb02ine Trigger\n1%\nParticle composition\nGeneration/Simulation\n2%\nDiffractive cross sections (NSD sample)\nGeneration\n4%\nTotal\n8%\nTable 7: Summary of the various systematic uncertainties and the level at which they are in-\ntroduced. The total systematic uncertainty assumes each of the individual uncertainties are\nindependent.\nA summary of the systematic uncertainties is given in Table 7 along with the step in the full\nchain at which they are introduced. The uncertainties in the track selection, vertex reconstruction bias\nand mis-estimate of secondaries are dominated by the low-pT tracks (<500 MeV). Any uncertainties\nat the generator level are due to uncertainties in predictions of physics models at LHC-energy and\nare unavoidable in the \ufb01nal analysis. However, the principal error in the reconstruction arises from\nalignment of the inner detector. The estimate of 6% is for initial running and is likely to improve.\n5\nFuture work\n5.1\nWork required for \ufb01rst data\nA number of issues have arisen during the work for this note that need to be studied further. Many of\nthese studies are already in progress and should be completed before the \ufb01rst pp collisions from the\nLHC are recorded. The main topics currently under investigation are:\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n743\n\n\u2022 Studies with other Monte Carlo generators: The studies of pp interactions in this note have been\ncarried out using PYTHIA [3]. The biases introduced by the trigger will certainly depend on\nthe particular physics models employed by PYTHIA.\nThe generator PHOJET [4,13] is being used to simulate samples of LHC inelastic pp collisions\n(non-diffractive, single- and double-diffractive). The physics studies discussed previously in\nthe analysis section are going to be repeated with PHOJET samples and the results compared\nwith those shown in this note. Comparing the results from analyses in different samples will\nprovide us indications on the systematic uncertainties due to different physics models.\n\u2022 Vertexing: During initial running at low luminosities, there will still be periods where there will\nbe more than one event per bunch crossing. It is therefore important to be con\ufb01dent that an\nevent contains only one interaction by identifying events with a single vertex. Further work is\nrequired to look at vertex reconstruction with low levels of additional events to evaluate how\nwell events with several vertices can be reconstructed.\n\u2022 MBTS readout: The MBTS L1 trigger readout is currently being upgraded as part of the tile\ncalorimeter refurbishment. As a part of this refurbishment the 3-in-1 cards connected to the\nMBTS readout are being switched from low gain to high gain. This modi\ufb01cation means that\nthe signal to noise should be 5-6 times better than the values used in Section 3.2. In addition\nto the L1 improvements, the MBTS will be readout at L2 to allow veri\ufb01cation of the L1trigger\ndecision using the precision readout of the Tile Calorimeter electronics. Work is ongoing to\nimplement software to match these requirements. Once the software has been validated, the\nMBTS L1and L2 trigger performance will be reevaluated.\n\u2022 Beam-gas and beam halo estimate from commissioning runs: Recent efforts to produce more\naccurate predictions for beam gas rates will allow a re-run of studies on how best to optimize the\nMBTS and the track-trigger to reduce this background in the measured minimum bias sample.\nFor both cases, strategies on how to estimate the rates of beam-gas and halo events from data\nduring commissioning runs with a single proton beam are beginning to be discussed.\n\u2022 ATLAS Beam Conditions Monitor The Beam Conditions Monitor [20] is designed to distin-\nguish collisions from background through time-of-\ufb02ight measurement and can improve our\nunderstanding of beam-gas and halo rates.\n5.2\nPhysics studies beyond \ufb01rst data\nFollowing the \ufb01rst physics studies with minimum bias data a series of applications can be foreseen.\nAmong them we would highlight:\n\u2022 Retuning Monte Carlo generators: LHC predictions for minimum bias events generated with\ntuned MC generators PYTHIA and PHOJET indicate that although these tuned models give\ncomparable descriptions of lower energy data, they disagree typically by \u223c30% for minimum\nbias multiplicity distributions [12].\nMeasuring the global properties of minimum bias interactions as presented in this paper will\nprovide enough information to revisit the generator predictions and retune event generators\nto describe interactions at the LHC energy. This will not only allow us to distinguish which\nphysics model and assumptions better agree with the data, but will also allow the reassessment\nof systematic uncertainties in various channels.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n744\n\n\u2022 Multiparton interactions: Charged particle multiplicity distributions [21] have been widely used\nas important tools for studying multiple particle production in inelastic hadronic events [5, 6,\n10, 11]. They are particularly useful when displayed in terms of multiplicity scaled variables\nknown as KNO variables [21]. Plotted as a function of KNO variables, the charged multiplicity\ndistributions provide a clearer display of \ufb02uctuations seen for both very low (less than half of the\naverage multiplicity) or very high multiplicity (more than the double the average) events. The\nrise of the high multiplicity tail in these distributions has been interpreted as an effect caused by\nmultiparton interactions [10,11] and the LHC measurement of this effect will contribute greatly\nto a better understanding of the underlying physics in inelastic collisions.\n\u2022 Contribution to the measurement of the total cross section: A measurement of the total inelastic\nrate by combining the NSD analysis with a measurement of single diffractive cross section by\nthe ALFA detector should be possible. Simultaneously measuring the elastic t-spectrum, which\ncan then be extrapolated to t \u21920, will enable us to determine the total cross section (\u03c3tot) in\na luminosity-independent way or to calibrate the absolute luminosity in \u03c3tot-independent way,\nusing the optical theorem.\n\u2022 Baseline for heavy-ion studies: A measurement of the particle yield from a single minimum\nbias event can and will be used to cross-check components and assumptions made by models\nfor heavy-ion collisions which will then be tuned according to the LHC data. This procedure is\nexpected to help in generating more reliable predictions for the heavy-ion runs.\n6\nConclusions\nWe have investigated methods for measuring the characteristics of inelastic collisions with the ATLAS\ndetector during early LHC running. The main goal of our study was to reconstruct the normalised\ncentral pseudorapidity ( 1\nNev\ndN\nd\u03b7 ) and transverse momentum ( 1\nNev\ndN\ndpT ) distributions of charged primaries\nin pp interactions selected by a minimum bias trigger. Triggering strategies for minimum bias event\nselection have been developed and an analysis to determine the charged particle distributions were\npresented.\nAiming at selecting inelastic collisions with as little bias as possible, two scenarios were proposed\nfor triggering: a random-based track trigger and using the minimum bias trigger scintillators. The\nrandom-based track trigger combines random event selection at L1 with the use of information from\nthe ID in the HLT; spacepoints from the pixel detector and the SCT at L2 and tracks reconstructed in\nthe EF. Minimum bias selection with the MBTS is performed by recording events that pass L1 MBTS\nhit requirements. It has been shown that both triggers are highly ef\ufb01cient at selecting non-diffractive\ninelastic samples. However, the acceptance of the diffractive component is highly suppressed relative\nto the non-diffractive component, and the acceptance of the single-diffractive sample is similar to that\nof the double-diffractive sample. This means that the ATLAS minimum bias triggers do not select a\nNSD sample as previous experiments have and therefore model dependent corrections will be required\nto compare ATLAS measurements to results from previous experiments.\nResults were presented for two samples: the MB sample, which has only been corrected for\ndetector effects, and the NSD sample where the MB sample has been further corrected for the trigger\nacceptance, which is model dependent. The analysis was performed on a sample of \u223c75,000 events,\ncorresponding to a luminosity of 10\u22126 pb\u22121. The uncertainty on\n1\nNev\ndN\nd\u03b7 for both samples is dominated\nby the systematic uncertainty from alignment and there is an additional uncertainty on the NSD sample\ndue to the model dependence of the relative cross-sections. The systematic uncertainty on\n1\nNev\ndN\nd\u03b7 for\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n745\n\nthe MB sample was estimated to be 6% and 8% for the NSD sample. This will be suf\ufb01cient to\ndistinguish between different models of minimum bias events.\nReferences\n[1] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[2] Schuler, G. A. and Sjostrand, T., Phys. Rev. D 49 (1994) 2257.\n[3] Sjostrand, T. and Mrenna, S. and Skands, P., JHEP 05 (2006) 026.\n[4] PHOJET\nmanual\n(program\nversion\n1.05c,\nJune\n96),\nhttp://physik.uni-leipzig.de/\n\u02dceng/phojet.html.\n[5] Breakstone, A., Phys. Rev. D 30 (1984) 528.\n[6] Alner, G. J., Phys. Rep. 154 (1987) 247.\n[7] Ansorge, R. E. et al., Z. Phys. C37 (1988) 191\u2013213.\n[8] Ansorge, R. E. et al., Z. Phys. C 43 (1989) 357.\n[9] Abe, F. et al., Phys. Rev. D41 (1990) 2330.\n[10] Alexopoulos, T. et al., Phys. Lett. B 435 (1998) 453.\n[11] Matinyan, S. G., and Walker, W. D., Phys. Rev. D 59 (1999) 034022.\n[12] Moraes, A., Buttar, C. and Dawson, I., Eur. Phys. J. C 50 (2007) 435.\n[13] Engel, R., Z. Phys. C 66 (1995) 203.\n[14] The ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncer-\ntainties, this volume.\n[15] Artikov, A., Chokheli D., Huston J., Miller B., and Nessi M., Technical Report AT-GE-ES-0001\n(2004).\n[16] Spiwoks, Ralf et al, ATL-DAQ-CONF-2005-030; CERN-ATL-DAQ-CONF-2005-030 (2005).\n[17] \u02daAkesson, P. F. et al., ATL-SOFT-PUB-2006-004 (2006).\n[18] The ATLAS Collaboration,\nThe Expected Performance of the ATLAS Inner Detector,\nthis\nvolume.\n[19] Rossi, A., LHC Project Report 783 (2004).\n[20] Ask, S., ATL-LUM-PUB-2006-001 (2005).\n[21] Koba, Z. and Nielsen, H. B. and Olesen, P., Nucl. Phys. B40 (1972) 317.\nSTANDARD MODEL \u2013 A STUDY OF MINIMUM BIAS EVENTS\n746\n\nElectroweak Boson Cross-Section Measurements\nAbstract\nThis report summarises the ATLAS prospects for the measurement of W\nand Z production cross-section at the LHC. The electron and muon decay\nchannels are considered. Focusing on the early data taking phase, strategies\nare presented that allow a fast and robust extraction of the signals. An over-\nall uncertainty of about 5% can be achieved with 50 pb\u22121in the W channels,\nwhere the background uncertainty dominates (the luminosity measurement\nuncertainty is not discussed here). In the Z channels, the expected precision\nis 3%, the main contribution coming from the lepton selection ef\ufb01ciency un-\ncertainty. Extrapolating to 1 fb\u22121, the uncertainties shrink to incompressible\nvalues of 1-2%, depending on the \ufb01nal state. This irreducible uncertainty is\nessentially driven by strong interaction effects, notably parton distribution\nuncertainties and non-perturbative effects, affecting the W and Z rapidity\nand transverse momentum distributions. These effects can be constrained\nby measuring these distributions. Algorithms allowing the extraction of the\nZ differential cross-section are presented accordingly.\n1\nW and Z cross-section measurements at the LHC\nThe study of the production of W and Z events at the LHC is fundamental in several respects. First,\nthe calculation of higher order corrections to these simple, colour singlet \ufb01nal states is very advanced,\nwith a residual theoretical uncertainty smaller than 1% [1]. Such precision makes W and Z production\na stringent test of QCD.\nSecondly, more speci\ufb01cally for Z production, the clean and fully reconstructed leptonic \ufb01nal states\nwill allow a precise measurement of the transverse momentum and rapidity distributions, respectively\nd\u03c3/dpT and d\u03c3/dy. The transverse momentum distribution will provide more constraints on QCD,\nmost signi\ufb01cantly on non-perturbative aspects related to the resummation of initial parton emissions,\nwhile the rapidity distribution is a direct probe of the parton density functions (PDFs) of the pro-\nton. The high expected counting rates will bring signi\ufb01cant improvement on these aspects, and this\nimprovement translates to virtually all physics at the LHC, where strong interaction and PDF uncer-\ntainties are a common factor.\nFrom the experimental point of view, the precisely measured properties of the Z boson provide strong\nconstraints on the detector performance. Its mass, width and leptonic decays can be exploited to mea-\nsure the detector energy and momentum scale, its resolution, and lepton identi\ufb01cation ef\ufb01ciency very\nprecisely.\nFinally, a number of fundamental electroweak parameters can be accessed through W and Z \ufb01nal\nstates (MW, through the W boson decay distributions; sin2\u03b8W, via the Z forward-backward asymme-\ntry; lepton universality, by comparing electron and muon cross-sections). These measurements are\nlong term applications where the understanding of the hadronic environment at the LHC is crucial,\nand to which the above-mentioned measurements are necessary inputs.\n747\n\nThe present note summarises the ATLAS preparations for W and Z cross-section measurements, in\nthe context of the early running of ATLAS and the LHC. The electron and muon decay channels are\nconsidered. A baseline integrated luminosity of L = 50 pb\u22121 is assumed for the total cross-section\nanalyses; based on these results, we estimate our prospects for L = 1 fb\u22121. Anticipating that the mea-\nsurement precision will soon be limited by the above-mentioned theoretical uncertainties, differential\ncross-section analyses are presented in the second part of this work. We consider the Drell-Yan mass\nspectrum below the Z peak, and the y and pT distributions on the Z resonance.\nThe note is organised as follows. Section 2 gives technical details about cross-section measurements,\nlists the simulation samples used in the analyses, and reviews the main reconstruction aspects. Sec-\ntions 3 and 4 describe the selections that allow extraction of the W and Z signals, give the expected\nstatistics, and discuss the uncertainties on the background rates, as these are speci\ufb01c to each channel.\nCommon systematic uncertainties affecting the cross-section determination are discussed in Section 5.\nSection 6 then presents the expected performance for total cross-section measurement. Differential\ncross-sections are discussed in Section 7, and Section 8 summarizes our results.\n2\nGeneral discussion\nThis section describes the general procedure used to extract physical cross-sections, and the simulation\nsamples used to evaluate the expected performance.\n2.1\nTotal cross-section measurements\nThe number of events N passing a given set of selections is expressed as follows:\nN = L \u03c3 A \u03b5 +B\n(1)\nwhere L is the integrated luminosity; \u03c3 the signal cross-section; A the acceptance of the signal,\nde\ufb01ned as the fraction of the signal that passes the kinematic and angular cuts; \u03b5 is the reconstruction\nef\ufb01ciency of the signal within the \ufb01ducial acceptance; B is the number of background events. In the\nabove, \u03b5 is to be understood as averaged over the phase space accepted by the selections. Conversely,\nthe measured total cross-section is expressed as:\n\u03c3 = N \u2212B\nL A \u03b5\n(2)\nand the overall measurement uncertainty gets contributions from the different terms as below:\n\u03b4\u03c3\n\u03c3 = \u03b4N \u2295\u03b4B\nN \u2212B\n\u2295\u03b4L\nL \u2295\u03b4A\nA \u2295\u03b4\u03b5\n\u03b5\n(3)\nAbove, \u03b4N \u223c\n\u221a\nN is of purely statistical origin, and the relative uncertainty decreases with increasing\nluminosity following \u03b4N/N \u223c1/\n\u221a\nL . The terms \u03b4B, \u03b4A and \u03b4\u03b5 are of both theoretical and experi-\nmental origin. They are considered as systematic uncertainties in the cross-section measurements, but\ncan be constrained via auxiliary measurements. We thus expect these terms to improve over time, pro-\nvided the auxiliary measurements have statistically dominated uncertainties. The machine luminosity\nL will be measured with different methods. The uncertainty on this parameter, \u03b4L , is expected to\ndecrease through improved understanding of the LHC beam parameters and of the ATLAS luminosity\ndetector response [2].\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n748\n\n2.2\nSignal and background samples. Benchmark cross-sections\nOur main signals, W and Z events decaying into electrons and muons, are generated using PYTHIA [3].\nThe analysis described in Section 7, a measurement of the low-mass Drell-Yan cross-section, exploits\nsamples produced using HERWIG [4].\nThe W and Z samples are \ufb01ltered at generation-level, requiring at least one lepton within the \ufb01ducial\nacceptance. The electron channels require |\u03b7e| < 2.7 and pe\nT > 10 GeV; the muon channels require\n|\u03b7\u00b5| < 2.8 and p\u00b5\nT > 5 GeV. These \ufb01lters have an ef\ufb01ciency of about 85% for Z events, and about\n65% for W events. In the case of the Z sample, the available energy for the hard process is limited\nby\n\u221a\n\u02c6s > 60 GeV. The low-mass Drell-Yan samples have the same \ufb01ducial cuts on both leptons, but\nrequire 8 <\n\u221a\n\u02c6s < 60 GeV. The W and Z cross-sections are normalised to the NNLO cross-sections as\nprovided by the FEWZ program [1].\nThe backgrounds considered in the analyses originate from W and Z events decaying to \u03c4-leptons,\nwith subsequent leptonic \u03c4 decays; t\u00aft events involving at least one semileptonic decay, and from in-\nclusive jet events \ufb01ltered to favour the presence of real leptons or hadrons misidenti\ufb01ed as leptons.\nLow-mass Drell-Yan events, analysed only in the electron channel (\u03b3\u2217\u2192ee), also account for back-\ngrounds from boson pair production.\nThe W \u2192\u03c4\u03bd\u03c4 and Z \u2192\u03c4\u03c4 events are produced as the signal samples (generators and \ufb01lters). The\nt\u00aft samples are generated inclusively, using MC@NLO [5] to provide both the \ufb01nal states and the cross-\nsection. They are \ufb01ltered for the presence of at least one electron or muon, without kinematic con-\nstraints. Diboson events, one of the main background in the low-mass Drell-Yan analysis, are gener-\nated using MC@NLO. For the WW process only W \u2192e\u03bd decays are considered, while the ZZ and the\nWZ are generated inclusively. No \ufb01lters are applied.\nThe jet events are produced using PYTHIA. The transverse momentum de\ufb01ned in the rest frame of\nthe hard interaction is required to be above 15 GeV for jet samples used in W and Z analyses, whilst\nno such pT cut is required for the sample used in low-mass Drell-Yan analysis. Jet backgrounds for\nthe muon channels are generated as inclusive jets, then requiring a \ufb01nal state with one (W analysis;\npT(\u00b5) > 15 GeV) or two (Z analysis; pT(\u00b5) > 5 and 15 GeV) muons from b-hadron decays with\n|\u03b7\u00b5| < 2.5. Background events from hadron punch-through and from decays in \ufb02ight of long lived\nparticle are found negligible. Background events from cosmic muons can be eliminated in a very\nef\ufb01cient way with timing cuts. Relying on the Tevatron results [6], this background is neglected. This\nappears as a safe approximation for the ATLAS experiment, since the Tevatron experiments are built\nclose to the surface, while the ATLAS detector is \u223c100 m underground. In the electron channels, fake\nelectrons are an important issue. Therefore, rather than requiring a true electron in the \ufb01nal state, the\nevents are required to contain at least one narrow cluster of energetic \ufb01nal state particles. In practice,\nthere should exist a tower of size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.12\u00d70.12 containing a total transverse energy greater\nthan 17 GeV for use in W and Z analyses and 6 GeV for low-mass Drell-Yan analysis. Events passing\nthis \ufb01lter are considered likely to produce fake electrons and passed through the simulation step.\nAll samples are interfaced to the CTEQ6L1 or CTEQ6M parton density sets [7] depending if the\ngenerator uses a leading or next to leading order calculation, respectively. The events are processed\nthrough full simulation using Geant 6.4 and a special misaligned geometry, as described in Ref. [8].\nWhile summarised here, the cross-sections used are described and justi\ufb01ed, together with their uncer-\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n749\n\ntainties, in Ref. [9]. Tables 1 and 2 summarise the signal and background samples and their properties.\nThe \ufb01rst column in these Tables indicates explicitely the cases in which a speci\ufb01c leptonic decay have\nbeen required at the generation level. For this reason, the second column represents in some case (like\nfor the t\u00aft dataset) the total production cross section and in other cases the total cross-section multi-\nplied by the leptonic branching ratio(s). The third column indicates the ef\ufb01ciency of the \ufb01lter which\nis applied on the generated \ufb01nal states described in the \ufb01rst column.\nChannel\n\u03c3(\u00d7 Br)\n\u03b5filter\nNevt (\u00d7103)\nL (pb\u22121)\nW \u2192e\u03bd\n20510 pb\n0.63\n140\n11\n\u03b3/Z \u2192ee,\n\u221a\n\u02c6s > 60 GeV\n2015 pb\n0.86\n399\n230\n\u03b3/Z \u2192ee,\n\u221a\n\u02c6s < 60 GeV\n9220 pb\n0.022\n197\n969\nW \u2192\u03c4\u03bd\u03c4\n20510 pb\n0.20\n32\n8\nZ \u2192\u03c4\u03c4\n2015 pb\n0.05\n13\n129\nt\u00aft\n833 pb\n0.54\n382\n850\nInclusive jets (pT >6 GeV)\n70 mb\n0.058\n2480\n0.0006\nInclusive jets (pT >17 GeV)\n2333 \u00b5b\n0.09\n3725\n0.02\nWW\u2192(e\u03bd)(e\u03bd)\n1.275 pb\n1.\n20\n15608\nZZ\n14.8 pb\n1.\n43\n2922\nWZ\n29.4 pb\n1.\n50\n1699\nTable 1: Signals and background samples in the electron channels. W and Z cross-sections are nor-\nmalised to the NNLO prediction; the t\u00aft cross-section is computed at NLO; the jet cross-section is the\nLO result. The \ufb01lters are described in the text. The number of simulated events and the corresponding\nintegrated luminosity are also indicated.\nChannel\n\u03c3(\u00d7 Br)\n\u03b5 filter\nNevt (\u00d7103)\nL (pb\u22121)\nW \u2192\u00b5\u03bd\n20510 pb\n0.69\n190\n13\n\u03b3/Z \u2192\u00b5\u00b5,\n\u221a\n\u02c6s > 60 GeV\n2015 pb\n0.89\n446\n249\nW \u2192\u03c4\u03bd\u03c4\n20510 pb\n0.20\n32\n8\nZ \u2192\u03c4\u03c4\n2015 pb\n0.05\n13\n129\nt\u00aft\n833 pb\n0.54\n382\n850\nb\u00afb \u2192\u00b5 +X\n766 \u00b5b\n2.1\u00d710\u22124\n110\n0.67\nb\u00afb \u2192\u00b5\u00b5 +X\n25 \u00b5b\n1.6\u00d710\u22124\n140\n35\nTable 2: Signals and background samples in the muon channels. W and Z cross-sections are nor-\nmalised to the NNLO prediction; the t\u00aft cross-section is computed at NLO; the b\u00afb cross-section is the\nLO result. The \ufb01lters are described in the text. The number of simulated events and the corresponding\nintegrated luminosity are also indicated.\n2.3\nCommon selection aspects\nAs already mentioned, W and Z boson \ufb01nal states are selected through their decays into electrons\nand muons. The reconstruction of electrons is based on a cluster measured in the electromagnetic\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n750\n\ncalorimeter, geometrically matching a track reconstructed in the Inner Detector. The identi\ufb01cation of\nisolated high-pT electrons is then based on the shapes of the electromagnetic showers, and on track\nreconstruction information. Three sets of identi\ufb01cation criteria have been de\ufb01ned. The Loose crite-\nrion consists of simple shower-shape cuts; the Medium criterion adds further cuts on shower-shape\nand on track quality; the Tight criterion tightens the track-matching requirement, adds a cut on the\nenergy-momentum ratio and further selections based on the vertexing-layer hits and on the Transition\nRadiation Tracker. Electron reconstruction and its performance are described in Ref. [10].\nThe muon reconstruction is done with the Muon Spectrometer, possibly completed by the Inner De-\ntector. Stand-alone muons are de\ufb01ned as consisting of a reconstructed track in the spectrometer only,\nand combined muons are the subset of the above that include a matching track in the Inner Detector.\nMuon reconstruction is documented in Ref. [11].\nThe measurement of missing energy in the transverse plane (/ET) is an important requirement for W\nboson cross-section measurements, as signi\ufb01cant /ET re\ufb02ects the presence of at least one neutrino in\nthe \ufb01nal state. The algorithm exploits the energy deposits in the calorimeter cells, the reconstructed\nmuon tracks, and an estimate of the energy lost in the cryostat. The calorimeter cells are calibrated\naccording to the physical object they represent (electrons or photons, taus, jets and muons). Cells\ncorresponding to electrons, photons and muons are calibrated at the electromagnetic scale, whereas\nall other cells are calibrated at the hadronic scale. The /ET value is then computed as the vector sum\nof the cell transverse energies. If muons are reconstructed in the event, their transverse momentum\nis added to the calorimetric sum. A complete description of the /ET reconstruction can be found in\nRef. [12].\nJets are reconstructed from calorimeter cells. The Cone algorithm is used, where the jet size parame-\nter, \u2206R =\np\n(\u2206\u03b7)2 +(\u2206\u03c6)2, is set to \u2206R = 0.7.\nAt low luminosity, L = 1031 cm\u22122s\u22121, the relevant trigger items require at least one electron or muon\nwith pT > 10 GeV, at least two electrons with pT > 5 GeV, or two muons with pT > 4 GeV. No iso-\nlation criteria are imposed on the leptons. As the LHC luminosity ramps up towards its design value,\ntighter selections will be needed to control the rates. The thresholds are raised, and isolation criteria\nare imposed on the electrons. The trigger items relevant for W boson selection require at least one\nisolated electron with pT > 22 GeV, or one muon with pT > 20 GeV. For Z production, two isolated\nelectrons with pT > 12 GeV or two muons with pT > 10 GeV can be required in addition to the\nabove. The trigger items described above are summarised in Table 3. Many more trigger items exist;\na complete description can be found in Ref. [13,14].\nThe reconstruction ef\ufb01ciency for electrons and muons, and the resolution of the /ET reconstruction al-\ngorithm are illustrated in Fig. 1. For electrons the Medium identi\ufb01cation ef\ufb01ciency is illustrated, and\nfor muons the combined reconstruction ef\ufb01ciency is shown. With looser criteria, higher ef\ufb01ciency and\nweaker \u03b7 dependence are obtained, at the cost of larger backgrounds. A complete description of the\nATLAS detector and its performance can be found in Ref. [15].\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n751\n\nTrigger item\nDescription\ne10, e20\nOne electron, pT > 10,20 GeV\nmu10, mu20\nOne muon, pT > 10,20 GeV\n2e5\nTwo electrons, pT > 5 GeV\n2mu4\nTwo muons, pT > 4 GeV\ne22i\nOne isolated electron, pT > 22 GeV\nmu20\nOne isolated muon, pT > 20 GeV\n2e12i\nTwo isolated electrons, pT > 12 GeV\n2mu10\nTwo isolated muons, pT > 10 GeV\nTable 3: Main trigger items relevant for the selection of W and Z boson \ufb01nal states. The \ufb01rst group of\ntrigger items is relevant to the L = 1031 cm\u22122s\u22121 trigger menu; the second group is relevant for the\nL = 1033 cm\u22122s\u22121 trigger menu.\n\u03b7\n-2 -1.5 -1 -0 5 0\n0 5\n1\n1.5\n2\nEfficiency\n0.4\n0.45\n0 5\n0.55\n0 6\n0.65\n0.7\n0.75\n0 8\n0.85\n0 9\nATLAS\n\u03b7\n-2.5 -2 -1 5 -1 -0.5 0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\nATLAS\n [GeV]\ntrue\nT\nE\n - \nrec\nT\nE\n-30\n-20\n-10\n0\n10\n20\n30\n% of events / GeV\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\n events\ne\n\u03bd\ne\n\u2192\nW\nGauss fit\nMean = 0.3 GeV\nSigma = 6.1 GeV\nFigure 1: From left to right : Medium identi\ufb01cation ef\ufb01ciency for electrons vs. \u03b7; muon combined\nreconstruction ef\ufb01ciency vs. \u03b7; /ET resolution. The ef\ufb01ciencies are obtained from Z boson events, and\nintegrated over pT > 20 GeV. The /ET resolution is obtained from W \u2192e\u03bd events.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n752\n\nSelection\nW \u2192e\u03bd\njets\nW \u2192\u03c4\u03bd\nZ \u2192ee\nTrigger\n37.01\u00b1 0.09\n835\u00b118\n1.73\u00b10.02\n6.07\u00b10.01\nET > 25 GeV, |\u03b7| < 2.4\n30.84\u00b10.09\n383\u00b112\n1.03\u00b10.01\n3.23\u00b10.01\nElectron ID\n26.77\u00b10.09\n110\u00b16\n0.91\u00b10.01\n2.95\u00b10.01\n/ET > 25 GeV\n22.06\u00b10.09\n4.6\u00b10.7\n0.55\u00b10.01\n0.06\u00b10.01\nMT > 40 GeV\n21.71\u00b10.08\n1.5\u00b10.4\n0.43\u00b10.01\n0.04\u00b10.01\nTable 4: Number of expected signal and background events (\u00d7104) in the W \u2192e\u03bd channel after\nall selections, for an integrated luminosity of 50 pb\u22121. The quoted uncertainties refer to the \ufb01nite\nMonte-Carlo statistics only; systematic uncertainties are discussed in the text.\n3\nElectron \ufb01nal states\nThis section describes the event selections in the electron \ufb01nal states, the expected event rates, and\nestimations of the uncertainties on the remaining backgrounds.\n3.1\nW \u2192e\u03bd\nEvent selection.\nThe selection of W \u2192e\u03bd events proceeds as follows. First, the e20 trigger item of\nthe 1031 trigger menu should be passed. Then, exactly one electromagnetic (EM) cluster, matched with\na track and such that ET > 25 GeV, | \u03b7 |< 1.37 or 1.52 <| \u03b7 |< 2.4, should be present in the event.\nThis object should satisfy the Medium electron identi\ufb01cation criterion. Finally, the reconstructed\nmissing transverse energy, re\ufb02ecting the missing \ufb01nal state neutrino, should satisfy /ET > 25 GeV, and\nthe transverse mass of the (l,\u03bd) system should satisfy MT > 40 GeV.\nDue to the high di-jet cross-section and the high rejection power of the selections, the available Monte\nCarlo statistics is not suf\ufb01cient to evaluate this background directly. To overcome this dif\ufb01culty, the\njet background has been estimated by applying the trigger and electron identi\ufb01cation selections only,\nand correcting the result with a factor obtained by computing the rejection power due to the /ET and\nMT cuts only.\nThe number of signal and background events after the successive cuts are given in Table 4 for an\nintegrated luminosity of 50 pb\u22121. The statistical uncertainty on the expected number of events corre-\nsponding to 50 pb\u22121is \u2206NS = 0.04\u00b7104. The resulting transverse mass distribution is shown in Fig. 2.\nBackground estimation.\nAs can be seen from Table 4, jet events constitute the largest background\ncomponent. In addition, the jet production cross-section and fragmentation properties at the LHC\nare largely unknown and induce a signi\ufb01cant uncertainty on the magnitude of this background; an\nuncertainty of about a factor 3 is estimated. It is therefore important to develop methods allowing to\nmonitor the jet background using the data. An attempt is presented below.\nThe principle of the method is to measure the normalisation and shape of the jet background ahead\nof the /ET cut, in a suf\ufb01ciently pure jet sample. It is thus needed to \ufb01nd a jet sub-sample that is free\nof signal events, but exhibits a transverse mass distribution and jet multiplicity close to that of the\njet background to W \u2192e\u03bd at this level of the selection. This sub-sample is then used to evaluate the\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n753\n\n [GeV]\nTW\nM\n0\n20\n40\n60\n80\n100\n120\n events / GeV\n3\n10\n-2\n10\n-1\n10\n1\n10\ne\n\u03bd\nWe\nQCD\n\u03c4\n\u03bd\n\u03c4\nW\nZee\nATLAS\n-1\n50 pb\nFigure 2: Transverse mass distribution in the W \u2192e\u03bd channel, for signal and background after all\nselections, for L = 50 pb\u22121 after all selections except MT cut.\nrejection of /ET cut, allowing a realistic estimation of the jet background in the W \u2192e\u03bd selection.\nIn this approach, the signal sample is obtained by applying the same trigger, kinematics and electron\nidenti\ufb01cation selection as described before and removing in addition events with a second high-pT\nelectromagnetic cluster giving an invariant mass, together with \ufb01rst selected electron, close to the Z\nboson mass (65 < Mll < 130 GeV).\nThe jet background control sample is selected using a single photon trigger with ET > 20 GeV, and\nsubsequent photon identi\ufb01cation using the same calorimetric variables as the electron identi\ufb01cation.\nThe photon cluster should also satisfy the same kinematics cuts of the electron candidate in the signal\nsample. There should be no Inner Detector track matching the photon cluster, to reject events with\ntrue electrons (e.g. W events) contaminating this photon sample. Simulation studies show that these\nselections provide a sample essentially composed of jet events, even at high values of /ET, and that the\nshape of the /ET distribution is identical, within the statistical precision, to that of the jet background in\nthe W \u2192e\u03bd sample (see Fig. 3). Above /ET > 10 GeV, the slope can be described with the convolution\nof an exponential and a second degree polynomial function.\nAfter the subtraction of the estimated background to the signal sample, the analysis then proceeds\napplying the /ET selection mentioned above. This data-driven estimation yields a jet background\nfraction of (0+4\u22120)%. The uncertainty corresponds to a number of events, \u03b4B = 0.92\u00d7104 events.\nBesides, a relative uncertainty of 3% is assumed on the W \u2192\u03c4\u03bd background, as estimated from\nthe experimental uncertainties on the W and \u03c4 branching fractions. This process thus contributes\n\u03b4B = 0.01\u00d7104 events.\n3.2\nZ \u2192ee\nEvent selection.\nThis analysis relies on the e10 trigger. Events are further preselected by requiring\ntwo EM clusters with ET > 15 GeV and |\u03b7| < 2.4. The presence of two electrons in the \ufb01nal state al-\nlows application of the Loose electron identi\ufb01cation criteria, which we brie\ufb02y describe below. Three\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n754\n\n [GeV]\nT\nE\n0\n10\n20\n30\n40\n50\n60\nPhoton\n / N\nElectron\nN\n-1\n0\n1\n2\n3\n4\n5\n6\nATLAS\n [GeV]\nT\nE\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEvents / 2 5 GeV\n3\n10\n4\n10\n5\n10\nATLAS\nFigure 3: Left: ratio of the /ET distributions in jet background events and in the control sample. Right:\ncomparison of the jet background (points with error bars) and the \ufb01tted background (rectangles), for\nan integrated luminosity of 50 pb\u22121.\nEthad1/Et37\n-0.01\n-0\n0.01\n0.02\n0.03\n0.04\n0.05\na.u.\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSignal\nBackground\nATLAS\nWidth(S1)\n0\n1\n2\n3\n4\n5\n6\na.u.\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\nSignal\nBackground\nATLAS\nFigure 4: The electron identi\ufb01cation criteria described in the text: the cluster hadronic to EM energy\nratio (left); the cluster width in the \ufb01rst calorimeter sampling (right). The distributions are normalised\nto the number of background entries.\ndiscriminant variables are used to separate EM clusters, deposited by electrons, from the hadronic\nbackground.\nThe \ufb01rst one is based on the longitudinal shower shape, and represents the ratio of the transverse en-\nergy deposited in the \ufb01rst compartment of the hadronic calorimeter divided by the transverse energy\nof the EM cluster. This ratio is expected to be small for EM objects, and large for hadronic clusters.\nThe second and third one are based on the shower width measured in the EM calorimeter. In the\nsecond compartment of the EM calorimeter, the width is computed from the ratio of the shower en-\nergy deposited in a region of size \u2206\u03b7 \u00d7\u2206\u03c6 = 0.075\u00d70.175, divided by the energy deposited within\n\u2206\u03b7 \u00d7\u2206\u03c6 = 0.175\u00d70.175 around the cluster barycenter. In the \ufb01rst compartment, the cluster spread\nis used, computed as the root-mean-square (RMS) of the cluster energy distribution. These two vari-\nables discriminate the narrow EM clusters from the wider hadronic clusters. Distributions of the three\ndiscriminators for electrons and hadrons are shown in Fig. 4 and in Fig. 5.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n755\n\nE237/E277\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\na.u.\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nSignal\nBackground\nATLAS\nCalo\n/Et\nCone\nEt\n0\n0.2\n0.4\n0.6\n0.8\n1\na.u.\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nSignal\nBackground\nATLAS\nFigure 5: The electron identi\ufb01cation criteria described in the text: cluster width in the second\ncalorimeter sampling (left) and electron isolation variable (right). The distributions are normalised\nto the number of background entries.\nSelection\nZ \u2192ee\njets\nTrigger\n6.70 \u00b1 0.01\n3110 \u00b1 40\nET > 15 GeV, |\u03b7| < 2.4, 80 GeV < Mee < 100GeV\n2.76 \u00b1 0.01\n11.1 \u00b1 0.8\nElectron ID\n2.64 \u00b1 0.01\n0.8 \u00b1 0.2\nIsolation\n2.48 \u00b1 0.01\n0.2 \u00b1 0.1\nTable 5: Number of expected signal and background events (\u00d7104) in the Z \u2192ee channel after all\nselections, for an integrated luminosity of 50 pb\u22121. The quoted uncertainties refer to the \ufb01nite Monte-\nCarlo statistics only; systematic uncertainties are discussed in the text.\nElectrons identi\ufb01ed as above are then required to be isolated. The isolation variable is computed from\nthe total measured energy in a cone of size \u2206R = 0.45 around and excluding the electron, divided by\nthe electron energy. Electrons are isolated if this ratio is smaller than 0.2. Distributions of this variable\nfor the signal and the background are shown in Fig. 5.\nThe number of signal and background events after the successive cuts are given in Table 5 for an inte-\ngrated luminosity of 50 pb\u22121. The expected signal counting rate is N = (2.48\u00b10.02)\u00d7104 events.The\nuncertainty quoted here is obtained by scaling the statistics of the Monte-Carlo sample to 50 pb\u22121. The\nresulting di-electron invariant mass distribution is shown in Fig. 6.\nBackground estimation.\nAs in the W \u2192e\u03bd analysis, the simulation-based jet background estimate\nof Table 5 is replaced by a data-driven estimate. In this analysis, the signal and background fractions\nare estimated simultaneously, via a \ufb01t to both contributions. The signal is described by the convolution\nof a Breit-Wigner and a Gaussian resolution function, and the background, completely dominated by\njet events, by an exponential function.\nAt the preselection level (just ahead of the electron identi\ufb01cation and without the Mee cut), the back-\nground largely dominates the signal and allows to determine the exponential slope. After the identi\ufb01-\ncation and isolation cuts, the \ufb01t yields a background fraction of (8.5\u00b11.5)%, or B = (0.23\u00b10.04)\u00d7\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n756\n\nInvariant Mass Mee (GeV)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/GeV\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\nInvariant Mass Mee (GeV)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/GeV\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n \n-1\n50 pb\nExtrapolated Background\nSignal\n 50)\n\u00d7\nQCD MC stat (\nATLAS\nFigure 6: Di-electron invariant mass distribution in the Z \u2192ee channel, for signal and background,\nfor 50 pb\u22121, after all selection cuts, except Mee cut.\n104 events. The uncertainty on the background fraction derives from the modelling of the signal and\nbackground shapes.\nThe relatively important background rate is explained by the rather loose identi\ufb01cation cuts. The\npresent selections are chosen to illustrate the robustness of the signal extraction, and to exemplify the\nbackground extraction method.\n4\nMuon \ufb01nal states\n4.1\nW \u2192\u00b5\u03bd\nEvent selection.\nThe W \u2192\u00b5\u03bd signal is selected as follows. The events should contain exactly one\nmuon track candidate, passing the mu20 trigger item and satisfying |\u03b7| < 2.5 and pT > 25 GeV. The\nenergy deposited in the calorimeter around the muon track, within a cone of radius \u2206R = 0.4, is re-\nquired to be lower than 5 GeV. The event missing transverse energy should satisfy /ET > 25 GeV, and\nMT > 40 GeV is required.\nFor the initial luminosity the pT cut of the trigger on the muon track is expected to be 20 GeV. Having\na higher pT threshold, however, can further reduce the backgrounds in particular from heavy \ufb02avour\nhadron decays and from decays in \ufb02ight of long lived particles. The isolation, /ET and MT cuts are\nalso effective to reduce those backgrounds.\nAfter all selections, the overall ef\ufb01ciency for the signal is expected to be close to 80%, with very large\nrejection factors for b\u00afb and t\u00aft events. The number of events that are expected to pass the selection\ncriteria for an initial integrated luminosity of 50 pb\u22121 are shown in table 6. The expected background\nlevel corresponds to a fraction of \u223c7%. Figure 7 shows the corresponding W transverse mass distri-\nbution before the transverse mass cut (last cut of table 6).\nBackground estimation.\nIn contrast to the electron channels, the jet background is less important\nhere and does not dominate the overall background. Muons from heavy \ufb02avour decays are rejected\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n757\n\nSelection\nW \u2192\u00b5\u03bd\nW \u2192\u03c4\u03bd\nZ \u2192\u00b5\u00b5\nbb \u2192\u00b5X\nt\u00aft\nTrigger\n44.44 \u00b1 0.07\n1.53 \u00b1 0.01\n2.03 \u00b1 0.01\n83.34 \u00b1 0.09\n0.53\u00b10.07\npT > 25GeV, |\u03b7| < 2.5\n35.55 \u00b1 0.06\n1.22 \u00b1 0.01\n1.62 \u00b1 0.01\n68.27 \u00b1 0.08\n0.42\u00b10.06\nIsolation\n34.80 \u00b1 0.06\n1.20 \u00b1 0.01\n1.59 \u00b1 0.01\n9.67 \u00b1 0.03\n0.35\u00b10.06\n/ET > 25 GeV\n28.59 \u00b1 0.05\n0.72 \u00b1 0.01\n1.10 \u00b1 0.01\n1.00 \u00b1 0.01\n0.30\u00b10.05\nMT > 40 GeV\n28.03 \u00b1 0.05\n0.57 \u00b1 0.01\n1.10 \u00b1 0.01\n0.10 \u00b1 0.01\n0.24 \u00b10.05\nTable 6: Number of expected signal and background events (\u00d7104) in the W \u2192\u00b5\u03bd channel, for an\nintegrated luminosity of 50 pb\u22121. The quoted uncertainties refer to the \ufb01nite Monte-Carlo statistics.\n [GeV]\nTW\nM\n0\n20\n40\n60\n80\n100\n120\n140\nEvents / GeV\n2\n10\n3\n10\n4\n10\n\u00b5\n\u03bd\n\u00b5\nW\n \n\u03c4\n\u03bd\n\u03c4\nW\n\u00b5\n\u00b5\nZ\n t\nt \nQCD\nATLAS\nFigure 7: Transverse mass distribution in the W \u2192\u00b5\u03bd channel, for signal and background, for\n50 pb\u22121 after all selections except MT cut.\nusing the pT and the isolation cuts, and muons from decays in \ufb02ight of long lived particles could be\nfurther rejected using loose impact parameter cuts. The t\u00aft background and its uncertainty are small.\nAs can be seen in Table 6, the dominant backgrounds are expected from W \u2192\u03c4\u03bd and Z \u2192\u00b5\u00b5 events.\nThese processes are well understood theoretically, in particular with respect to the W \u2192\u00b5\u03bd signal,\nand can be safely estimated based on simulation. A relative uncertainty of 3% is assumed on the\nW \u2192\u03c4\u03bd background, as estimated from the experimental uncertainties on the W and \u03c4 branching\nfractions. Exploiting the CTEQ6.5 eigenvector sets (cf. Section 5), an uncertainty of 2% is assumed\non the Z event rate passing the selections.\nThe jet background (mostly muons from b-hadron decays) is theoretically not well known. An uncer-\ntainty of 100% is assumed on this background component.\nA theoretical uncertainty of about 15% on the t\u00aft cross-section is assumed. In addition, an uncertainty\nof 10% is considered on the rejection obtained from the isolation cut. This leads to a total uncertainty\nof about 20% on the t\u00aft background rate.\n4.2\nZ \u2192\u00b5\u00b5\nEvent selection.\nThe Z \u2192\u00b5\u00b5 analysis uses the 10 GeV single muon trigger. The triggered data\nsample is further reduced by requiring at least two reconstructed muon tracks. The present analysis\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n758\n\nID Tracks\n0 05 20 GeV. The reconstructed charges must be opposite, and the invariant mass of the muon pair is\nrequired to ful\ufb01l |91.2 GeV-M\u00b5\u00b5| <20 GeV.\nMuons in jet events tend to be produced within a decay cascade of further particles, and should there-\nfore not appear isolated in the detector, in contrast to the leptonic decays of Z and W bosons. To\nquantify the isolation of the muons, the number of Inner Detector tracks within a cone around the\ncandidate muon, as well as the total transverse momentum of these tracks are used. The cone size is\n\u2206R = 0.5, and the muon track itself is excluded from the calculation.\nThe distributions of the isolation variables for signal and background processes normalised to their\ncross sections is shown in Fig. 8, after the above-mentioned cuts.\nThe isolation and pT cuts are chosen to minimise the statistical uncertainty on the cross-section mea-\nsurement. The expected number of events after each cut are shown in Table 7. The chosen cuts select\nabout 70% of the Z \u2192\u00b5\u00b5 events with muons in the detector acceptance. The residual background\nfraction of this selection is 0.004 \u00b1 0.001(stat). The corresponding invariant mass distribution is\nshown in Fig. 9.\nBackground uncertainty.\nIn this channel, the dominant background originates from t\u00aft events. Be-\nsides a theoretical uncertainty of about 15% on the cross-section, an uncertainty of 10% is assumed\non the rejection obtained from the isolation cuts. This leads to a total uncertainty of about 20% on the\nt\u00aft background rate.\nThe jet background (mostly muons from b-hadron decays) is expected to be smaller, but is theoreti-\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n759\n\nSelection\nZ \u2192\u00b5\u00b5\nbb \u2192\u00b5\u00b5X\nW \u2192\u00b5\u03bd\nZ \u2192\u03c4\u03c4\nt\u00aft\nTrigger\n3.76\u00b10.01\n10.08\u00b10.04\n36.7\u00b10.1\n0.09\u00b10.01\n0.69\u00b10.01\n2 muons +\nopp. charge\n3.33\u00b10.01\n3.00\u00b10.04\n1.14\u00b10.02\n0.04\u00b10.01\n0.35\u00b10.01\nM\u00b5\u00b5 cut\n3.04\u00b10.01\n0.26\u00b10.01\n0.04\u00b10.01\n(14\u00b14)\u00d710\u22124\n0.02\u00b10.01\npT cut\n2.76\u00b10.01\n0.125\u00b10.001\n0.004\u00b10.001\n(11\u00b14)\u00d710\u22124\n(134\u00b18)\u00d710\u22124\nIsolation\n2.56\u00b10.01\n(18\u00b15)\u00d710\u22124\n(9\u00b15)\u00d710\u22124\n(11\u00b14)\u00d710\u22124\n(66\u00b14)\u00d710\u22124\nTable 7: Number of expected signal and background events (\u00d7104) in the Z \u2192\u00b5\u00b5 channel, for an\nintegrated luminosity of 50 pb\u22121. The quoted uncertainties refer to the \ufb01nite Monte-Carlo statistics.\n [GeV]\n\u00b5\n\u00b5\nm\n40\n50\n60\n70\n80\n90\n100 110 120\nNumber of Events/GeV\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000 ATLAS\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n\u00b5\n\u2192\nW\n\u00b5\n\u00b5\n\u2192\nbb\n\u00b5\n\u00b5\n\u2192\ntt\n\u03c4\n\u03c4\n\u2192\nZ\nFigure 9: Di-muon invariant mass distribution in the Z \u2192\u00b5\u00b5 channel, for signal and background, for\n50 pb\u22121, after all cuts, except the isolation and M\u00b5\u00b5 cuts.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n760\n\ncally not well known. An uncertainty of 100% is assumed on this background component.\nThe other backgrounds are smaller, theoretically well known in comparison to the above, and con-\ntribute negligibly to the overall background uncertainty.\n5\nCommon systematic uncertainties\n5.1\nTrigger and reconstruction ef\ufb01ciency\nAs has been seen in Sections 3 and 4, the selection of leptonic Z boson decays provides clean signals\nwith low backgrounds. This allows determination of the lepton trigger [13, 14] and reconstruction\nef\ufb01ciencies [10,11] using the well-known tag-and-probe method, which is brie\ufb02y outlined below.\nSelecting Z \u2192ee and Z \u2192\u00b5\u00b5 events as in Sections 3 and 4, i.e. requiring a single lepton trigger\nand two reconstructed leptons, the ef\ufb01ciency of a given trigger item is de\ufb01ned as the fraction of the\nselected events where the second reconstructed lepton passes this trigger item.\nThe off-line reconstruction ef\ufb01ciency can be determined in a similar way. Requiring one reconstructed\nlepton satisfying tight identi\ufb01cation criteria, and requiring a second isolated, high-pT object such that\nthe invariant mass of the pair is close to the Z boson mass, provides a suf\ufb01ciently pure Z \u2192ll sample;\nthe ef\ufb01ciency of a given identi\ufb01cation criterion is then de\ufb01ned as the fraction of events where the\nsecond object is indeed identi\ufb01ed. Conversely, the ef\ufb01ciency of the isolation cuts can be determined\nby requiring the second object to be identi\ufb01ed, and counting the fraction of events where the isolation\ncut is passed.\nThe above methods are exact in the limit where backgrounds vanish. For tight trigger and off-line\ncuts, this is the case in practice : the background magnitude and uncertainty have a negligible im-\npact on the ef\ufb01ciency determination. Backgrounds are larger when assessing looser identi\ufb01cation\nand isolation cuts, and lower trigger thresholds. In this case, interpreting the observed dilepton mass\nspectrum as a sum of signal and background contributions (described by the convolution of a Breit-\nWigner resonance and a Gaussian resolution function, and by an exponential or polynomial function,\nrespectively) allows to extract the background fraction and correct the computation accordingly. This\nprocedure was performed and shown to provide ef\ufb01ciency estimates that are unbiased within the sta-\ntistical precision expected for L = 50 pb\u22121.\nFigures 10 and 11 illustrate this discussion, on the examples of the e20 trigger item and Medium\nelectron identi\ufb01cation cut, and of the mu20 trigger item and combined muon reconstruction. For the\nselections used in the analyses of Section 3 and 4, the overall ef\ufb01ciency can be reconstructed with a\nprecision of \u03b4\u03b5/\u03b5 = 0.02 for electrons and muons.\nThe overall reconstruction ef\ufb01ciencies in Fig. 10, 11 re\ufb02ect the performance of the reconstruction\nsoftware at the time of writing this note. Improved performance and results are presented in [10, 11,\n13,14].\n5.2\nTheoretical systematic uncertainties\nThis section presents comparisons on the acceptance for W \u2192l\u03bd and Z \u2192ll events, as obtained from\nthe Pythia, Herwig and MC@NLO. The purpose of this study is to determine the contribution of the\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n761\n\n\u03b7\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nEfficiency\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\nATLAS\nTag & Probe\nMC truth\nFigure 10: Electron detection ef\ufb01ciency vs. \u03b7, as measured from the tag-and-probe method and\ncompared to the truth, for 50 pb\u22121. The product of the e20 trigger ef\ufb01ciency, and Medium electron\nidenti\ufb01cation ef\ufb01ciency is represented.\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nMuon Id: Monte Carlo truth\nMuon Id: Tag & Probe \nTrig: Monte Carlo truth\nTrig: Tag & Probe \nFigure 11: Muon detection ef\ufb01ciency vs. \u03b7, as measured from the tag-and-probe method and com-\npared to the truth, for 50 pb\u22121. The mu20 trigger ef\ufb01ciency, and the combined muon reconstruction\nef\ufb01ciency are represented.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n762\n\nuncertainties on the acceptance to the overall systematic uncertainty on the cross-section.\nThe kinematic cuts described in Sections 3 and 4 are applied to the generator-level particles for each\nof the above generators. For W events, the acceptance varies by 2.5% from one program to the other.\nFor Z events the observed variation is of order 3.2%. The sources which could explain the observed\ndifferences are the Initial State Radiation (ISR), the intrinsic kT for the incoming partons, the Under-\nlying Event (UE), \ufb01nal state photon radiation, Parton Density Functions (PDFs) and matrix element\ncorrections applied to the parton shower (ME).\nTo quantify the impact of the individual sources, samples are generated with ISR, kT, UE and ME all\nswitched off. The impact of each effect is then studied by switching on this effect individually. For\nthe sake of clarity, the discussion is given explicitly for W \u2192e\u03bd production only; at the end of the\nsection results are given for both W and Z production.\nThe effects of electroweak corrections on the acceptance have been studied using PHOTOS. By running\nalternatively with and without PHOTOS, one obtains an effect of 1.8% for W events.\nSwitching on ISR, or changing the intrinsic kT of the incoming partons has an important impact on the\nlepton \u03b7 and pT distributions. Speci\ufb01cally, ISR introduces a difference of 10.2% on the acceptance\nfor W events. Similarly, turning on and off the kT, ME and UE, the following differences on the W\nacceptance are obtained: 1.9% for the intrinsic kT, 1.0% for the UE and no effect for the ME.\nFor these sources, the systematic uncertainty is estimated as 20% of the above numbers, which\namounts to assuming that the models describing the above are correct within 20%. One thus ob-\ntains the following uncertainties for W \u2192e\u03bd: 2.0% (ISR), 0.4% (kT) and 0.2% (UE). In the case of\nPHOTOS, one has an uncertainty of 0.3%.\nThe PDFs are an important source of differences in the acceptances. The uncertainty is determined\nusing the CTEQ6.5 PDF uncertainty sets. An uncertainty of 0.9% is found.\nTo simplify the procedure, we assume no correlations between the different sources and calculate\nthe total uncertainty from the quadratic sum of all numbers, \ufb01nding \u03b4A/A = 2.3% for W events.\nRepeating the same exercise with Z events gives a very comparable systematic uncertainty. While\nthese uncertainties will be signi\ufb01cantly reduced with the analysis of the LHC data, we assume these\n\ufb01gures hold for our initial cross-section measurements.\n6\nTotal cross-section results\nCross-section results for L = 50 pb\u22121 are presented \ufb01rst. At the end of the section, the performance\nis extrapolated to higher luminosity.\n6.1\nResults for L = 50 pb\u22121\nWe gather below the results of the analyses performed in Sections 3 and 4, and of the discussion of\nsystematic uncertainties of Section 5. Table 8 contains our estimations of statistical and systematic un-\ncertainties, the cross-section values and their uncertainties computed according to Equations 2 and 3.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n763\n\nProcess\nN(\u00d7104)\nB(\u00d7104)\nA\u00d7\u03b5\n\u03b4A/A\n\u03b4\u03b5/\u03b5\n\u03c3 (pb)\nW \u2192e\u03bd\n22.67\u00b10.04\n0.61\u00b10.92\n0.215\n0.023\n0.02\n20520\u00b140\u00b11060\nW \u2192\u00b5\u03bd\n30.04\u00b10.05\n2.01\u00b10.12\n0.273\n0.023\n0.02\n20530\u00b140\u00b1 630\nZ \u2192ee\n2.71\u00b10.02\n0.23\u00b10.04\n0.246\n0.023\n0.03\n2016\u00b116\u00b1\n83\nZ \u2192\u00b5\u00b5\n2.57\u00b10.02\n0.010\u00b10.002\n0.254\n0.023\n0.03\n2016\u00b116\u00b1\n76\nTable 8: Measured cross-sections, their uncertainties and overall selection ef\ufb01ciency A \u00d7 \u03b5, for an\nintegrated luminosity of 50 pb\u22121. The uncertainty on N is statistical, the other sources are systematic.\nThe quoted cross-section uncertainties include the mentioned statistical and systematic contributions\nbut not an overall luminosity uncertainty.\nAs can be seen from Table 8, the results are dominated by the systematic error, even for L = 50 pb\u22121.\nThe luminosity uncertainty is common to all cross-sections, and vanishes in cross-section ratios, e.g\n\u03c3W/\u03c3Z. In the W channels, the systematic uncertainty is dominated by the background uncertainty.\nThis can be expected given the important fraction of jet events. This background could be further\nreduced, notably by requiring the absence of jets, but this would jeopardize the inclusive nature of\nthe cross-section measurement. The ef\ufb01ciency and acceptance uncertainties give a slightly smaller\ncontribution.\nThe Z channels bene\ufb01t from smaller backgrounds, due to the presence of two decay leptons. For\nthe same reason, the ef\ufb01ciency uncertainty is also larger than in the W channels. Given the smaller\nacceptance uncertainty, the ef\ufb01ciency uncertainty is the largest source of uncertainty.\n6.2\nProspects for L = 1 fb\u22121\nFor higher integrated luminosity, the statistical uncertainty on the counting (N) becomes negligible,\nand the ef\ufb01ciency uncertainty, which is determined from measurement and also of statistical nature,\nstrongly decreases.\nWith increased luminosity, a number of modi\ufb01cations will have to be applied to the analyses. Most\nprominently, in the electron channels, the single electron trigger threshold will be increased to 22 GeV,\nand the Tight electron identi\ufb01cation is expected to be used. In Z \u2192\u00b5\u00b5 channel, spectrometer muons\nare replaced by combined muons, and the muon isolation cuts are re\ufb01ned by exploiting calorimetric\ninformation in addition to the track-based isolation used in the low-luminosity analysis. The W \u2192\u00b5\u03bd\nanalysis is unchanged.\nTable 9 summarizes the expected signal yields and the cross-section determination in this case. On\nthis timescale, L might be measured with improved precision, exploiting elastic proton scattering at\nvery small angles [2]. Compared to the low-luminosity analysis, the systematic uncertainties from\nbackgrounds and ef\ufb01ciency are expected to scale with statistics. Without further input, the acceptance\nuncertainty does not decrease and dominates the result.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n764\n\nProcess\nN(\u00d7105)\nB(\u00d7105)\nA\u00d7\u03b5\n\u03b4A/A\n\u03b4\u03b5/\u03b5\n\u03c3 (pb)\nW \u2192e\u03bd\n45.34\u00b10.02\n1.22\u00b10.41\n0.215\n0.023\n0.004\n20520\u00b1 9\u00b1516\nW \u2192\u00b5\u03bd\n60.08\u00b10.02\n4.02\u00b10.05\n0.273\n0.023\n0.004\n20535\u00b1 7\u00b1480\nZ \u2192ee\n5.42\u00b10.01\n0.46\u00b10.02\n0.246\n0.023\n0.007\n2016\u00b1 4\u00b1 49\nZ \u2192\u00b5\u00b5\n5.14\u00b10.01\n0.02\u00b10.001\n0.254\n0.023\n0.007\n2016\u00b1 4\u00b1 49\nTable 9: Measured cross-sections, their uncertainties and overall selection ef\ufb01ciency A \u00d7 \u03b5, for an\nintegrated luminosity of 1 fb\u22121. The uncertainty on N is statistical, the other sources are systematic.\nThe quoted cross-section uncertainties include the mentioned statistical and systematic contributions\nbut not an overall luminosity uncertainty.\n7\nDifferential cross-sections\nAs it is clear from the previous sections, total cross-section measurements are dominated by the sys-\ntematic uncertainty even for modest integrated luminosity. The main cross-section uncertainty is\nrelated to the acceptance uncertainty, which in turn comes from our limited knowledge of the under-\nlying physics (notably non-perturbative mechanisms and PDFs). It is therefore important to measure\nthe distributions, which will help to constrain these uncertainties. Three examples are given below,\nnamely the measurement of the Drell-Yan invariant mass spectrum at low mass, and the rapidity and\ntransverse momentum distributions for Z events.\nCompared to the inclusive analyses, the differential measurements require larger statistics. For this\nreason the differential distributions shown in this section refer to an integrated luminosity of 200 pb\u22121,\nwhich corresponds to the available statistics of the Monte Carlo signal samples.\n7.1\nLow-mass Drell-Yan production\nEvent selection. This study relies on a low threshold single electron trigger, e10, possible at low\nluminosity. At the reconstruction level, exactly two oppositely charged electrons are required, each\nsatisfying the tight identi\ufb01cation criteria, and with pT > 10 GeV. Of\ufb02ine electron reconstruction is\nlimited to |\u03b7| < 2.5. After these preselections, the reconstructed missing transverse energy in the\nevent, Emiss\nT\n, should be smaller than 30 GeV. Finally, the di-electron invariant mass, mee, is required to\nbe in the range 20 < mee < 60 GeV. Table 10 shows the impact of these cuts on signal and background.\nOnly the main backgrounds except the one arising from QCD dijets are considered at this level; the\ndijet background is discussed separately.\nThe kinematical acceptance, given by the \ufb01nal state requirement of two electrons satisfying pT >\n10 GeV and |\u03b7| < 2.5, is 17% in the range 20 < mee < 60 GeV. For 40 < mee < 60 GeV, the accep-\ntance reaches 34%. The e10 trigger channel provides an ef\ufb01ciency of about 89% for signal events\nwithin the kinematical acceptance. The trigger ef\ufb01ciency is about 74% for di-electron pair masses of\nmee = 20 GeV, and reaches 97% at mee = 60 GeV. The of\ufb02ine electron selection ef\ufb01ciency is 36% [10],\nand the further kinematic selections have an ef\ufb01ciency of 83%.\nDijet background estimation. The background contributions listed in Table 10 are estimated from\nsimulation, by counting the events that pass the selection criteria described above. This method can\nnot be applied to the dijet background which, due to very high rejection factors, can not be simulated\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n765\n\ncut\n\u03b3\u2217\u2192ee\n\u03c4\u03c4\nt\u00aft\ndi-boson\nPreselections\n2632\u00b112\n48\u00b13\n218\u00b13\n342\u00b13\nEmiss\nT\n< 30 GeV\n2604\u00b112\n38\u00b13\n28\u00b11\n164\u00b12\n20 < mee < 60 GeV\n2189\u00b111\n30\u00b13\n7\u00b11\n7\u00b11\nTable 10: Signal and background event rates, following the selections described in the text. For all\nsamples, the normalization corresponds to 50 pb\u22121. The \u03b3\u2217/Z \u2192ee signal with mee > 60 GeV is\nexcluded from these numbers, at all levels of the selection. The dominant dijet background is not\ndisplayed here, and discussed separately below.\nin suf\ufb01cient amounts.\nAn alternative estimation, based on single electron rejection factors, is used. This method relies on the\nprobability for an event to display a single fake electron. On the inclusive jet sample, this probability\nis found to be (1.5\u00b10.1)\u00d710\u22124. Assuming no correlations, the probability to \ufb01nd a fake di-electron\npair with opposite charge is then estimated as one-half of the square of the single fake probability.\nThe invariant mass distribution of fake electron pairs is estimated using Monte Carlo information.\nThe invariant mass distribution of the signal and backgrounds are displayed in Figure 12 (left). The\nestimated background represents about one third of the selected sample. It is dominantly composed\nof inclusive jets (96%), the other backgrounds being negligible.\nTwo thirds of the dijet events that contain one tight electron candidate are true electrons from heavy\nquark decays, while the remainder are due to light hadrons mis-identi\ufb01ed as electrons and to photon\nconversions. It may be possible to reduce the jet background further by optimizing the selection crite-\nria for these low ET electrons. Additional event variables, like hadronic activity estimators, could also\nbe used to reduce or constrain the size of the dijet background. However, the large fraction of elec-\ntrons from heavy quark decays indicates that the uncertainty on the background composition related\nto different rejection factors for heavy \ufb02avour and light jets under the the Drell-Yan signal is large and\nrequires further study.\nMeasurement of the cross-section. The raw measured differential cross-section may be corrected\nbin by bin in di-electron mass, as follows:\n\u0012 d\u03c3\ndM\n\u0013\ni\n=\nNi \u2212Bi\n\u03b5iAi\u2206miL\n(4)\nwhere Ni is the number of signal events in mass bin i, Bi is the expected number of background events,\nAi is the kinematical and angular acceptance ef\ufb01ciency, \u03b5i is the overall ef\ufb01ciency accounting for trig-\nger, identi\ufb01cation and further selections. \u2206mi is the width of bin i and L represents the integrated\nluminosity.\nIn practice, the corrections can be considered to be of two types: those correcting for experimental\neffects (backgrounds and ef\ufb01ciencies), and those correcting for the kinematic acceptance of the elec-\ntron pT and \u03b7 requirements. Figure 12, right, illustrates the two corrections. The agreement between\nthe corrected distribution and the expected distribution from theory provides a technical consistency\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n766\n\n [GeV]\nee\nm\n20\n25\n30\n35\n40\n45\n50\n55\n60\n [nb/GeV]\nee\n/dm\n\u03c3\nd\n-6\n10\n-5\n10\n-4\n10\n-3\n10\nmeasured\nsignal\njets\n-\u03c4\n+\n\u03c4\ntt\ndiboson\nATLAS\n [GeV]\nee\nm\n20\n25\n30\n35\n40\n45\n50\n55\n60\n [nb/GeV]\nee\n/dm\n\u03c3\nd\n-3\n10\n-2\n10\n-1\n10\ntheory, full\ntheory, acc\nmeasured\ncorrected\nATLAS\nFigure 12: Left: Mass distributions of the measured raw events (solid line), Drell-Yan signal events\n(dashed line) and background contributions arising from inclusive jets, \u03c4\u03c4, t\u00aft, di-boson in decreasing\nnumerical importance. Right: invariant mass distributions of the selected sample before any correc-\ntions (rectangles with error bars), the theoretical signal within the \ufb01ducial acceptance (dashed line),\nthe corrected Drell-Yan signal sample (unshaded rectangles with error bars) and the complete theoret-\nical distribution (solid line).\ncheck of the method.\nThe integrated cross-section can be calculated by integrating the corrected histogram; the statistical\nerror on the cross-section is estimated by adding the error from each bin in quadrature. The total\nDrell-Yan cross section in the electron channel, for 20 < mee < 60 GeV is \u03c3DY = 1.07 nb. The corre-\nsponding statistical uncertainty is 4% for L = 50 pb\u22121and 1% for L = 1 fb\u22121. This can be compared\nwith the PDF contribution to the cross-section uncertainty, estimated to be 6.9% using CTEQ6.1M [7].\nThe statistical sensitivity provides a natural target for the different contributions to the systematic un-\ncertainty: the knowledge of the background level, and of the ef\ufb01ciency and acceptance corrections\nshould match the statistical sensitivity. The ef\ufb01ciency can be determined with suf\ufb01cient precision\nusing the methods discussed in Section 5. The acceptance corrections are mostly affected by the\ntransverse momentum distribution of the Drell-Yan pairs in this mass range; this has large theoretical\nuncertainties, and will have to be measured from data. The invariant mass resolution, about 1 GeV, is\nfound to have no signi\ufb01cant effect on the Drell-Yan spectrum. As discussed above, the most serious\nchallenge is posed by the understanding of the jet background, where the current uncertainties are\nmuch larger than the expected statistical precision. Further study is needed to assess the precision\nof techniques to constrain this background directly from data; this is beyond the scope of the current\nwork.\n7.2\nZ differential cross-section : bin by bin correction method\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n767\n\nCategory i\nDe\ufb01nition\nni\n1\nAll events\n398 750\n2\nFiducial and kinematics (generation)\n172 544\n3\nTrigger and off-line (\ufb01ducial, kinematics and ID)\n49 754\n4\nIntersection of categories 2 and 3\n48 436\nTable 11: Event categories used for the extraction of detector smearing corrections, geometric accep-\ntance and event selection ef\ufb01ciency in the electron channel.\nElectron channel.\nIn the electron channel, only events that pass the 2e12i trigger condition are\nconsidered. Furthermore, it is required that they contain exactly two, oppositely charged electrons,\neach of them satisfying |\u03b7| < 2.5 and PT > 20 GeV. Both electrons are required to pass the Tight\nelectron identi\ufb01cation criteria.\nThe background is dominated by hadrons misidenti\ufb01ed as electrons in inclusive jet events. Taking\ninto account that with the Tight identi\ufb01cation criteria the expected rate of hadrons misidenti\ufb01ed as\nelectrons is very low (see [10]), the background to the di-electron signal is neglected in the following.\nAfter all selections, the following event categories are de\ufb01ned. In the following, n1 denotes the total\nsample size; n2 is the number of events having two generator-level electrons satisfying |\u03b7| < 2.5,\npT > 20 GeV, and 75 GeV < Mee < 105 GeV. The number of events satisfying these conditions at the\nreconstruction level is noted n3; \ufb01nally, n4 counts the events passing these criteria on both generation\nand reconstruction levels. Table 11 summarises these de\ufb01nitions and contains values for the ni, di-\nrectly counted from the simulated signal sample.\nMuon channel.\nIn the muon channel, only events that pass the mu20 trigger condition are consid-\nered. The events should further contain exactly two oppositely charged muons, each of them satisfying\n|\u03b7| < 2.5. Both muons should be reconstructed in the Inner Detector and in the Muon Spectrometer.\nThe most energetic muon should satisfy pT > 20 GeV; the second one should have pT > 15 GeV. The\nmuon pair invariant mass should lie between 76 and 106 GeV.\nContamination from W \u2192\u00b5\u03bd and t\u00aft events effectively disappears after the selection process, but\nb\u00afb \u2192\u00b5\u00b5 contamination is still about 3.5% of the signal. To minimise the b\u00afb background, two isola-\ntion quantities are studied. The \ufb01rst one is the number of tracks in a cone of size \u2206R =0.45 around the\nmuon track ; the second one is the total calorimeter transverse energy in the same cone. The distribu-\ntions of these two quantities for the four samples, corresponding to 40 pb\u22121of integrated luminosity,\nare shown in Fig. 13. A muon track is accepted if the \ufb01rst isolation variable is less than six and the\nsecond isolation variable is less than 20 GeV. These cuts are applied to both muons in the event.\nThe isolation cut ef\ufb01ciency for the signal sample is larger than 98%, and the residual contamination is\nless than 0.5%. The sample is pure enough at this point that we can neglect the background contami-\nnation in the differential cross-section plots.\nAs in the electron channel, four event categories are de\ufb01ned to allow the computation of the differen-\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n768\n\nTracks in cone\n0\n2\n4\n6\n8\n10\n12\n14\nEvents\n1\n10\n2\n10\n3\n10\n4\n10\n\u00b5\n\u00b5\nZ->\n\u00b5\n\u00b5\n->\nb\nb\n\u03bd\n\u00b5\nW->\ntt\nATLAS\nTracks in cone\n0\n2\n4\n6\n8\n10\n12\n14\nEvents\n1\n10\n2\n10\n3\n10\n4\n10\n\u00b5\n\u00b5\nZ->\n\u00b5\n\u00b5\n->\nb\nb\n\u03bd\n\u00b5\nW->\ntt\nATLAS\n [GeV]\nT\nE\ncone\u2211\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\nEvents/2 GeV\n1\n10\n2\n10\n3\n10\n4\n10\n\u00b5\n\u00b5\nZ->\n\u00b5\n\u00b5\n->\nb\nb\n\u03bd\n\u00b5\nW->\ntt\nATLAS\n [GeV]\nT\nE\ncone\u2211\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\nEvents/2 GeV\n1\n10\n2\n10\n3\n10\n4\n10\n\u00b5\n\u00b5\nZ->\n\u00b5\n\u00b5\n->\nb\nb\n\u03bd\n\u00b5\nW->\ntt\nATLAS\nFigure 13: Number of tracks (top) and calorimeter ET in a cone R = 0.45 (bottom). Distributions for\nthe muon with the higher value of the quantity is shown on the left, and distributions for the muon with\nthe lower value of the quantity on the right. Black line: Z \u2192\u00b5\u00b5, red (or dark grey line): W \u2192\u00b5\u03bd,\ndashed line: b\u00afb \u2192\u00b5\u00b5, green (or light grey line): t\u00aft.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n769\n\nCategory i\nDe\ufb01nition\nni\n1\nAll events\n445650\n2\nFiducial and kinematics (generation)\n234610\n3\nTrigger and off-line (\ufb01ducial, kinematics and ID)\n181652\n4\nIntersection of categories 2 and 3\n180260\nTable 12: Event categories used for the extraction of detector smearing corrections, geometric accep-\ntance and event selection ef\ufb01ciency in the muon channel.\ntial cross-section. The categories and their sizes ni are given in Table 12.\nExtraction of d\u03c3Z/dpTdy\nThe Z boson phase space is sliced in rapidity and transverse momentum\nregions, or bins. In each region, labeled \u03b1, the differential cross-section is obtained from the raw\nevent count using the usual expression:\n\u03c3\u03b1 = S\u03b1\nL\nd\u03b1 \u2212b\u03b1\n\u03b5\u03b1A\u03b1\n,\n(5)\nwhere S\u03b1, \u03b5\u03b1 and A\u03b1 respectively represent the detector smearing correction (correcting for event\nmigration to and from bin \u03b1, due to resolution effects), overall event selection ef\ufb01ciency and geometric\nacceptance in region \u03b1; d\u03b1 is the observed event count and b\u03b1 the estimated background in this region,\nand L is the integrated luminosity. In terms of the de\ufb01nitions in Tables 11 and 12, we have:\nS\u03b1 = n3,\u03b1\nn4,\u03b1\n, \u03b5\u03b1 = n3,\u03b1\nn2,\u03b1\n, A\u03b1 = \u03b5filter\nn2,\u03b1\nn1,\u03b1\n, d\u03b1 = n3,\u03b1,\n(6)\nwhere the ni,\u03b1 are computed in each bin \u03b1 of the Z phase space. The acceptance values account for\nthe generator-level \ufb01ltering ef\ufb01ciency, as described in Section 2.2.\nDifferential cross-section results\nIn the electron channel, the Z boson phase space was divided in\n50 pT bins and 9 rapidity bins. The pT bins have a width of 2 GeV, in the range 0 < pT < 100 GeV.\nThe rapidity bins have a width of 0.3, in the range 0 < |y| < 2.7. A good agreement is found between\nthe reconstructed cross-sections and the true distributions, obtained from a statistically independent\nsample. Figure 14 shows the Z boson differential cross-section in the electron channel in rapidity and\ntransverse momentum bins.\nIn the muon channel, the Z boson phase space is divided as in the electron channel. A good agreement\nis again found between the reconstructed cross-sections and the true distributions. Figure 15 shows\nthe Z boson differential cross-section in the dimuon channel in rapidity and transverse momentum\nbins.\nThe plots have been normalised to the total NNLO cross-section of 2015 pb times a global accep-\ntance factor of 0.73. Since the correction factors and measurement were both extracted from the same\ndataset, the good agreement is a check of consistency of the method.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n770\n\nZ |rapidity|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n]\n|y| unit\npb\n [\nd|y|\n\u03c3\nd\n0\n100\n200\n300\n400\n500\n600\nATLAS\nMC\nMeasured, before corrections\nMeasured, after corrections\n [GeV]\nT\nZ P\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n]\nGeV\npb\n [\nT\ndP\n\u03c3\nd\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nATLAS\nMC\nMeasured, before corrections\nMeasured, after corrections\nFigure 14: Left: d\u03c3Z/dy, integrated over pT. Right: d\u03c3Z/dpT, integrated over \u22122.7 < y < 2.7.\nDistributions obtained in the electron channel, with a precision corresponding to an integrated lumi-\nnosity of 200 pb\u22121. The black line histograms correspond to the generated cross-section, the dashed\nhistograms to the measured cross-section before corrections are applied, while the crosses show the\nmeasured cross-section after all corrections have been applied.\n|Z rapidity|\n0\n0.5\n1\n1.5\n2\n2.5\n3\n]\n|Y| unit\npb\n [\nd|Y|\n\u03c3\nd\n0\n100\n200\n300\n400\n500\n600\nMC\nMeasured, before corrections\nMeasured, after corrections\nATLAS\n [GeV]\nT\nZ P\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\n]\nGeV\npb\n [\nT\ndP\n\u03c3\nd\n0\n10\n20\n30\n40\n50\n60\n70\n80\nMC\nMeasured, before corrections\nMeasured, after corrections\nATLAS\nFigure 15: Left: d\u03c3Z/dy, integrated over pT. Right: d\u03c3Z/dpT, integrated over \u22122.7 < y < 2.7.\nDistributions obtained in the muon channel, with a precision corresponding to an integrated lumi-\nnosity of 200 pb\u22121. The black line histograms correspond to the generated cross-section, the dashed\nhistograms to the measured cross-section before corrections are applied, while the crosses show the\nmeasured cross-section after all corrections have been applied. .\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n771\n\n7.3\nZ differential cross-section : alternative method\nThe method presented here attempts to fully exploit the phase space of the Z boson and its decay\nproducts. Writing the cross-section in terms of the complete phase space allows to extract, in addition\nto the Z boson distributions, possible pT, \u03b7 or \u03c6 dependencies of the lepton selection ef\ufb01ciency.\nMethod\nThe events are classi\ufb01ed in bins both for the Z and for the decay leptons. We de\ufb01ne NyZ\nbins along yZ, and NptZ bins along pZ\nT. As before, the Z boson phase space intervals are labelled \u03b1. In\naddition, we de\ufb01ne NEt intervals in the lepton transverse energy distribution, and N\u03b7 intervals for the\nleptons pseudorapidity. The lepton phase space is labelled i, j (one index for each lepton).\nFor each \u03b1, we measure N\u03b1\nij, which is the number of lepton pairs reconstructed with one lepton in\nbin i and one lepton in bin j. The following relation holds, in the practical absence of background, as\njusti\ufb01ed in the previous sections:\nN\u03b1\nij = \u03b5i\u03b5jP\u03b1\nij L \u2206\u03c3\u03b1,\n(7)\nwhere P\u03b1\ni j is the probability, computed on Monte Carlo, that a Z boson produced in bin \u03b1 decays into\ntwo leptons in bins i and j; \u03b5i is the lepton reconstruction ef\ufb01ciency in bin i; L is the integrated\nluminosity, and \u2206\u03c3\u03b1 is the Z production cross-section in bin \u03b1.\nResolution effects, primarily on the lepton ET, are accounted for as follows. When the P\u03b1\nij histograms\nare \ufb01lled, the lepton ET is \ufb01rst smeared according to its expected, ET and \u03b7 dependent resolution. The\nsmeared quantities are then used to compute the Z variables (pt, y). In this way the above equation is\nunchanged and all detector effects can be incorporated in the P\u03b1\nij factors. Writing the above for all \u03b1,\ni, j provides an over-constrained system whose unknowns are the ef\ufb01ciencies and cross-sections. We\ncan then compute the \u03b5i in each bin \u03b1, up to a factor related to L \u2206\u03c3\u03b1.\nThe system can be solved analytically, using for example the singular value decomposition method,\nor SVD. A drawback of this method is that it is based on least squares; it is thus not valid in the case\nof low statistics. In particular, at low luminosity, the statistics are such that several bins contain only\na few events. To avoid bias in the ef\ufb01ciency determination, a likelihood using Poisson probabilities is\nconstructed and used to \ufb01t the ef\ufb01ciencies numerically. In order to help the \ufb01t to converge, we \ufb01rst\nsolve the system using the SVD method, and we use the results as initial parameters of the \ufb01t. Since\nthe \u03b5i are expected not to depend on \u03b1, we can compute their weighted average over the bins \u03b1.\nIn case of low statistics, the bin sizes should be large enough to integrate a suf\ufb01cient statistics in each\nbin. If the lepton reconstruction ef\ufb01ciency is not constant within each bin, the hypothesis that the\nef\ufb01ciency does not depend on the Z boson phase space might be violated. To avoid such effects, the\nlepton binning is chosen such that the ef\ufb01ciency is a priori constant within each bin. This results in\nbins with variable width, which does not affect the method.\nIn any given Z phase space interval \u03b1, we can write for each lepton bin (i, j) the following relation:\nL \u2206\u03c3\u03b1 =\nN\u03b1\nij\n< \u03b5i >< \u03b5j > P\u03b1\nij\n,\n(8)\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n772\n\nZ\ny\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n\u03c3\n\u2206\nL\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\nMC truth\npseudo data\nATLAS\n[GeV]\nZ\nPt\n0\n10\n20\n30\n40\n50\n60\n\u03c3\n\u2206\nL\n0\n5000\n10000\n15000\n20000\n25000\nMC truth\npseudo data\nATLAS\nFigure 16: Left: L \u2206\u03c3 versus yZ, integrated over pZ\nT. Right: L \u2206\u03c3 versus pZ\nT, integrated over yZ.\nwhere < \u03b5i > and < \u03b5j > are the average ef\ufb01ciencies computed at the previous step. Finally, L \u2206\u03c3\u03b1\nis computed by averaging over all (i, j).\n\u201cClassical limit\u201d of the method.\nAs discussed above, the method proposed here might need sig-\nni\ufb01cant integrated luminosity to be applied safely. The classical method is reached by simply setting\nNEt = N\u03b7 = 1, and accordingly computing the acceptance and ef\ufb01ciencies from Monte-Carlo in each\nZ boson phase space interval \u03b1.\nResolution effects are taken into account as before, by smearing the Monte Carlo input before deter-\nmining the acceptance. Once the acceptance and ef\ufb01ciency are determined in each bin \u03b1, just counting\nthe number of events N\u03b1 in the bin and allows to deduce the differential cross-section using the usual\ncross-section expression in the absence of background:\nL \u2206\u03c3\u03b1 =\nN\u03b1\n\u03b5\u03b1\u03b5\u03b1A\u03b1 .\n(9)\nResults.\nThe complete method has been tested on the Z \u2192\u00b5\u00b5 samples described in Section 2.2.\nDue to the limited statistics, the Z phase space was mapped using NptZ =10 for 0 < pZ\nT < 60 GeV, NyZ\n=5 for \u22122.5 < yZ < 2.5. The muon reconstruction ef\ufb01ciency has no pT-dependence above 10 GeV;\nthis allows to set NEt =1. The de\ufb01nition of the muon \u03b7 intervals is dictated by the detector geometry\nwhich affects the ef\ufb01ciency as a function of \u03b7; we set N\u03b7 =7, with the intervals [-2.7,-1.6], [-1.6,-1.4],\n[-1.4,-0.1], [-0.1,0.1], [0.1,1.4], [1.4,1.6], [1.6,2.7].\nThe results are illustrated in Fig. 16. The Z boson rapidity and pTdistributions are correctly recon-\nstructed. Measured and true distributions agree within the statistical precision, which varies from 3%\nin regions where the differential cross-section is high, to about 20% in the tails of the Z boson phase\nspace (yZ > 1.5). In addition, the \u03b7 dependence of the reconstruction ef\ufb01ciency can be measured\naccurately. Given the interval de\ufb01nition above and the size of our sample, a precision of about 2% is\nobtained for each point. This is competitive with the tag-and-probe determination described in Sec-\ntion 5, and illustrated in Fig. 17.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n773\n\n\u00b5\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\n\u00b5\n\u2208\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 17: Muon reconstruction ef\ufb01ciency versus \u03b7, measured simultaneously with the differential\ncross-section.\nFor cross-checks, the classical limit of the method has been tested using the Z \u2192ee samples. The inter-\nvals are de\ufb01ned as before, except NyZ =10 and NptZ =20. The following selection criteria are applied:\ntwo reconstructed electrons of opposite charge are required in the detector acceptance (|\u03b7| \u22652.5),\nwith 20 GeV \u2264pt \u226480 GeV. Both electrons should pass the Tight identi\ufb01cation criterion. Z events\nare selected around the mass peak (87 GeV \u2264MZ \u226495 GeV), with pZ\nT \u226460 GeV. The acceptance\ncuts on the electrons imply yZ \u22642.5.\nThe results of the differential cross-section d\u03c3/dyZ, integrated over pZ\nT, and d\u03c3/dpZ\nT, integrated\nover yZare shown in Fig. 18. The squares represent the raw distribution, the dots represent the mea-\nsurements, corrected by the acceptance and the ef\ufb01ciency factors. The shows the input value. The\nmeasurements are consistent with the input, which proves the consistency of the method.\n8\nSummary and perspectives\nThis work presents the ATLAS prospects for the measurement of W and Z boson cross-sections at the\nLHC. In the four considered channels (W \u2192e\u03bd, Z \u2192ee, W \u2192\u00b5\u03bd, Z \u2192\u00b5\u00b5), the analyses con\ufb01rm\nthe high purity of the samples after fairly usual selections (high-pTlepton identi\ufb01cation, isolation, and\n/ET in the W \ufb01nal states). The jet background is poorly predicted, and dedicated studies are needed to\nmonitor its magnitude using real data. Data-driven methods are presented that seem to have suf\ufb01cient\nsensitivity to keep the jet background at a level where it does not prevent a precise cross-section mea-\nsurement.\nWith 50 pb\u22121, the background and signal acceptance uncertainties contribute similarly to the mea-\nsured cross-section uncertainty, at the level of 2-4% depending on the channel. The uncertainty on\nthe integrated luminosity is not included in the present discussion. Extrapolating to 1 fb\u22121, all un-\ncertainties are expected to scale with statistics, except the acceptance uncertainty. This leads to the\nconclusion (see also, for example, [16,17]) that the W and Z cross-sections can not be measured to a\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n774\n\nZ\nY\n-2\n0\n2\n\u03c3\n\u2206\nL\n0\n5000\n10000\n15000\nMC truth\npseudo data\nraw distr\nATLAS\n[GeV]\nZ\nPt\n0\n20\n40\n60\n\u03c3\n\u2206\nL\n0\n5000\n10000\nMC thruth\npseudo data\nraw distr\nATLAS\nFigure 18: Left: L \u2206\u03c3 versus yZ, integrated over pZ\nT. Right: L \u2206\u03c3 versus pZ\nT, integrated over yZ.\nprecision better than about 2 %.\nThis argument however ignores the additional input from differential cross-section measurements.\nIn contrast to total cross-sections, the differential ones bene\ufb01t from small acceptance uncertainties,\nand have the potential to constrain the uncertainties that affect total cross-sections. The examples\nof the dilepton mass spectrum below the Z peak, and of the Z boson rapidity and pT distributions\nare studied here. The methods presented are shown to provide correct estimations of the differential\ncross-sections. The natural next step of these analyses, i.e. quantify their physical implications, is\nbeyond the scope of this note and reserved for the real data.\nReferences\n[1] K. Melnikov and F. Petriello, Phys. Rev. D74, 114017 (2006).\n[2] ATLAS Collaboration, ATLAS Forward Detectors for Measurement of Elastic Scattering and\nLuminosity, CERN/LHCC/2008-004.\n[3] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05, 026 (2006).\n[4] G. Corcella et al., JHEP 01, 010 (2001).\n[5] S. Frixione and B. R. Webber, JHEP 06, 029 (2002).\n[6] CDF Collaboration, Phys. Rev. Lett. 94, 091803 (2005).\n[7] J. Pumplin et al., JHEP 07, 012 (2002).\n[8] A. Rimoldi et al., ATLAS detector simulation: Status and outlook, Prepared for 9th ICATPP\nConference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics Applica-\ntions, Villa Erba, Como, Italy, 17-21 Oct 2005.\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n775\n\n[9] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume .\n[10] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume .\n[11] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume .\n[12] ATLAS Collaboration, Measurement of Missing Transverse Energy, this volume .\n[13] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon\nTrigger Selection, this volume .\n[14] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this volume\n.\n[15] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003 .\n[16] S. Frixione and M. Mangano, JHEP 05, 056 (2004).\n[17] CMS Collaboration, CMS technical design report, volume II: Physics performance, J.Phys.G\n34, 995 (2007).\nSTANDARD MODEL \u2013 ELECTROWEAK BOSON CROSS-SECTION MEASUREMENTS\n776\n\nProduction of Jets in Association with Z Bosons\nAbstract\nWe simulate a measurement of the inclusive Z(\u2192e+e\u2212/\u00b5+\u00b5\u2212) + jets cross-\nsection with the ATLAS experiment in pp collisions at 14 TeV for an in-\ntegrated luminosity of 1 fb\u22121 using fully-simulated signal and background\nMonte Carlo data sets. The reconstruction of leptons and of missing trans-\nverse energy becomes more complex in the presence of a multi-jet \ufb01nal\nstate. We quantify the reconstruction differences with respect to those ob-\nserved for inclusive Z production. We derive statistical and systematic lim-\nitations in terms of probing the perturbative QCD predictions and discrimi-\nnating between predictions of different event generators.\n1\nIntroduction\nThe production of W/Z + jets in pp collisions at 14 TeV is an important part of the physics program at\nATLAS. The processes are interesting in their own right as tests of perturbative QCD at the LHC, as\nwell as forming important backgrounds for both Standard Model and Beyond Standard Model physics\nprocesses. The results of the measurements can be compared directly with \ufb01xed-order predictions at\nleading order (LO) and next-to-leading order (NLO) in QCD and the gauge boson mass provides a\nlarge scale for the pertubative calculations. In addition, the measurements can be used to test the\nperformance of Monte Carlo event generators that will also be used to simulate the backgrounds for\nother physics processes.\nIn this analysis we present a feasibility study of the cross-section measurements for data corre-\nsponding to an integrated luminosity of 1 fb\u22121 performed with fully-simulated signal and background\nMonte Carlo samples. The goal of the analysis is to test the performance of the lepton and jet trig-\ngering and reconstruction algorithms in high jet multiplicity events, to develop the necessary analysis\ntechniques (unfolding, background subtraction) and to evaluate the statistical and systematic limita-\ntions of the data, in terms of probing the \ufb01xed-order QCD predictions and of discriminating between\npredictions of different Monte Carlo event generators. The primary end-result of the analysis with\nreal ATLAS data will be hadron-level cross-sections. In this note we will concentrate on Z + jets in\n\ufb01nal states with electrons and muons, but with techniques applicable to the case of W + jets as well.\nMuch of the effort on the triggering and reconstruction of leptons is in common with the inclusive\nW/Z note [1]; thus, we do not reproduce all of the details from that note, but rather comment on the\nimpact of a multi-jet environment on these issues.\n2\nReference Cross-Sections and Monte Carlo Datasets\nReference cross-sections are collected in [2], but we brie\ufb02y discuss here the cross-sections relevant for\nthis note. NLO is the \ufb01rst order at which the Z + jets cross-sections have a realistic normalization (and\nrealistic shape for some kinematic distributions) [3]. The current state of the art for NLO calculations\nis for Z + 2 jets, although there is ongoing work for the calculation of 3 jet \ufb01nal states. Cross-sections\nfor Z + 0,1 and 2 (3) jet \ufb01nal states can be conveniently calculated at LO and NLO (LO only) using\nthe parton-level MCFM [4] program (version 5.1. interfaced with LHAPDF 5.2.3 [5]), and it is from\nthis program that we determine our reference cross-sections. We use the CTEQ6.1 parton distribution\nfunctions (PDFs) [6] and a dynamic renormalization/factorizationscale of m2\nZ + p2\nT,Z. We apply similar\n777\n\nkinematic cuts on the leptons and jets and the same jet algorithm on the partons as will be described\nin Section 3. The error on the cross-section stemming from the PDF uncertainty is calculated using\nthe complete set of error PDFs in the CTEQ6.1 set.\n2.1\nMonte Carlo Datasets\nThe most important Monte Carlo data sets for the signal processes (Z \u2192e+e\u2212and Z \u2192\u00b5+\u00b5\u2212) used\nin these studies are generated with ALPGEN [7] (v 2.05), interfaced with HERWIG [8] and using\nthe leading order PDF set CTEQ6LL [9]. (Hereafter, when we refer to ALPGEN it is understood\nthat it is interfaced with HERWIG.) The generation is done with a renormalization/factorization scale\nof m2\nZ + p2\nT,Z and a MLM [10] matching cut at pT = 20 GeV (jets below this cut are generated by\nthe parton shower and not by the matrix element) and |\u03b7| < 6. A discussion of the uncertainty in\npredictions for Z + jets \ufb01nal states using different matrix element + Monte Carlo calculations and\ndifferent matching cuts is beyond the scope of this study, but is given in Ref. [10].\nThe \ufb01nal Monte Carlo data sets are obtained following the standard prescription [10], by merging\nthe samples of Z + n partons (where n=0-5), each sample weighted with the product of the respective\nsample cross-section, the MLM matching ef\ufb01ciency and the ef\ufb01ciency of the generator-level \ufb01lter.\nAll but the highest jet multiplicity sample are exclusive, i.e. events are only kept if all jets with\npT > 20 GeV and |\u03b7| < 6 are matched to a matrix element parton. The highest multiplicity sample,\nZ +5 partons, is inclusive; events with additional jets softer than the partons from the matrix element\nare not discarded. Thus, there can be more than 5 jets in this sample. The di-lepton mass is required to\nbe larger then 40 GeV and lower than 200 GeV. A generator-level \ufb01lter requires one seeded-cone jet,\nwith a radius of R =\np\n\u2206\u03b72 +\u2206\u03c6 2 = 0.4, with pT > 20 GeV and |\u03b7| < 5.0, and two electrons/muons\nwith pT > 10 GeV and |\u03b7| < 2.7 in the event.\nFor the comparison with the \ufb01xed-order theoretical predictions, the merged data sets are normal-\nized to the NLO inclusive Z \u2192e+e\u2212and Z \u2192\u00b5+\u00b5\u2212cross-sections. Because of the jet \ufb01lter used\nin their generation, the fully-simulated data sets can not be used to derive the global normalization\nfactor. For this purpose, we use additional Z \u2192e+e\u2212and Z \u2192\u00b5+\u00b5\u2212ALPGEN data sets which are\nproduced with the same conditions, but without the generator-level \ufb01lter applied.\nPYTHIA [11] signal and background samples are generated with version 6.323 (Z \u2192e+e\u2212,\nZ \u2192\u00b5+\u00b5\u2212, Z \u2192\u03c4\u03c4, and W \u2192e\u03bd) or 6.403 (t\u00aft, \ufb01ltered QCD multi-jet) using the corresponding\nATLAS underlying-event tune [2]. PYTHIA Z \u2192e+e\u2212and W \u2192e\u03bd events are preselected with\na generator-level \ufb01lter requiring one electron with pT > 10 GeV and |\u03b7| < 2.7. The \ufb01lter for the\ncorresponding processes with muon \ufb01nal states requires one muon with pT > 5 GeV and |\u03b7| < 2.8.\nPYTHIA Z \u2192\u03c4\u03c4 events are generated with a \ufb01lter requiring two electrons/muons with pT > 5 GeV\nand |\u03b7| < 2.8. For each of the Z \u2192\u2113\u2113samples, the di-electron (di-muon, di-tau) mass is required to\nbe larger than 60 GeV. The jet background for the electron channel is simulated with a PYTHIA QCD\nmulti-jet sample with a minimum hard-scattering transverse momentum of 15 GeV. A generator-level\n\ufb01lter requires a jet of pT = 17 GeV clustered in a narrow region of \u2206\u03b7/\u2206\u03c6 = 0.06, a size similar to an\nelectron cluster. The QCD multi-jet background for the muon channel is estimated with a PYTHIA\nb\u00afb sample. Two muons with pT > 4 GeV and 6 GeV, respectively, are required in the \ufb01nal state.\n2.2\nCorrections from Parton to Hadron Level\nComparisons of data cross-section measurements and LO/NLO predictions are to be made at the\nhadron level (particle level). Hence, the MCFM predictions for the observables have to be corrected\nwith respect to the non-perturbative effects resulting from jet fragmentation and from the underlying\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n778\n\nevent. The impact of the underlying event correction is to add energy to the MCFM jets, while the jet\nfragmentation correction subtracts energy. Both corrections are expected to decrease with increasing\njet pT. The non-perturbative corrections are determined from the current ATLAS PYTHIA tune by\ncomparing the multiplicity and the pT distribution of jets with a cone radius of 0.4 clustered on the\n\ufb01nal-state particles in Z \u2192\u00b5+\u00b5\u2212Monte Carlo samples generated with PYTHIA 6.403 (a) using\nthe standard ATLAS PYTHIA tune [2] and (b) with fragmentation and multiple-particle interactions\nswitched off. To the extent to which the two partons that can comprise a jet in MCFM mimic the effects\nof the parton shower in PYTHIA, the corrections derived from the above procedure can be applied to\nthe MCFM output [3]. For jets with cone radius 0.4 with pT > 40 GeV, the effects of fragmentation\nand underlying event cancel up to a residual correction at the percent level, which is then applied\nto the MCFM predictions. These corrections are expected to be re-done with the underlying event\nmeasurements determined from ATLAS data.\n3\nParticle Identi\ufb01cation and Trigger\nWe adopt as much as possible de\ufb01nitions and cuts in common with the other analyses, and in particular\nwith the inclusive W/Z study [1].\n3.1\nParticle Identi\ufb01cation\nThe electron candidates are required to have pT > 25 GeV, and to lie in the range |\u03b7| < 2.4, excluding\nthe barrel-to-endcap calorimeter crack region (1.37< |\u03b7| <1.52). The electrons are required to ful\ufb01ll\nthe medium electron-identi\ufb01cation signature [12], which consists of requirements on the calorimeter\nshower-shape and the matched track. The Z selection requires two electron candidates with an invari-\nant mass of 81 < mee < 101 GeV and \u2206R > 0.2 between the electrons. No calorimeter isolation cuts\nare applied for this analysis, although they will be applied for actual data analysis. There is an implicit\nisolation cut, however, present in the trigger [13].\nA muon candidate requires the combined reconstruction of an inner detector track and a track\nin the muon spectrometer [14].\nMuons are required to have pT > 15 GeV and |\u03b7| < 2.4, with\nthe range 1.2 < |\u03b7| < 1.3 being excluded. Isolation is applied by requiring the energy deposition\nin the calorimeter to be less than 15 GeV in a cone of \u2206R = 0.2 around the extrapolation of the\nmuon track. The Z selection requires that there be two muon candidates with an invariant mass of\n81 < m\u00b5\u00b5 < 101 GeV.\nFor the analyses in this study, we use jets clustered with the standard ATLAS seeded-cone algo-\nrithm with a radius of R = 0.4, built from either calorimeter towers (Z \u2192e+e\u2212analysis) or topological\nclusters [15] (Z \u2192\u00b5+\u00b5\u2212analysis), and calibrated to the hadron level. The lepton and jet candidates\nmust be separated by \u2206Rl j > 0.4. It is required that the jet transverse momentum be larger than\n40 GeV and that the jet be in the range |\u03b7| < 3.0.\n3.2\nTrigger Selection\nThe trigger selection used here is the same as that used in the inclusive analyses [1]. In the electron\nchannel, Z \u2192e+e\u2212+ jets events are required to pass the isolated di-electron trigger or the isolated\nsingle-electron trigger. In the muon channel, Z \u2192\u00b5+\u00b5\u2212+ jets events are required to pass the isolated\ndi-muon trigger. The trigger ef\ufb01ciencies at the \ufb01rst, second and event \ufb01lter levels are evaluated as\na function of the jet multiplicity. The trigger ef\ufb01ciency is also studied as a function of the overall\nhadronic activity, the pT of the leading jet and the Z transverse momentum. For this purpose, the\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n779\n\ngenerated Monte Carlo information and the data driven tag-and-probe method are compared. Good\nagreement between the two methods is found. The ef\ufb01ciency for an electron to pass the isolated\nsingle-electron trigger is found to decrease with increasing jet multiplicity, pT of the leading jet and\nwith decreasing distance to the closest jet.\n4\nMeasurement of Z + jets Cross-Sections\nWe study the comparison of theory and measurement for quantities suited to compare with a \ufb01xed-\norder NLO calulation: the inclusive cross-section for Z \u2192\u2113\u2113\u02d9 with at least 1 jet, 2 jets and 3 jets and\nthe differential cross-sections with respect to the pT of the leading and the next-to-leading jets.\n4.1\nLepton Reconstruction in a Multi-jet Environment\nThe presence of additional jets in the event has an impact on the kinematics of both the leptons and\njets: the leptons are more boosted (larger pT and lower \u2206\u03c6 between leptons) in events with jets and\nthe distance between leptons and jets becomes smaller in high-multiplicity events. The average jet\npT increases with the number of jets. Due to the combination of the single electron and di-electron\ntrigger channels used in this analysis and due to the boost of the electrons with large jet activity, the\nef\ufb01ciency loss of the isolated electron triggers for large jet multiplicities has only a negligible impact.\nThe total Z reconstruction ef\ufb01ciency (of\ufb02ine+trigger) is stable with respect to both the jet multiplicity\nand the transverse momentum of the leading jet.\nMuon reconstruction ef\ufb01ciencies and rejections for QCD multi-jet background are investigated\nfor different isolation requirements. The isolation requirement for this analysis (see Section 3.1) is\nchosen such that it presents no signi\ufb01cant bias for events with large jet multiplicities and large jet pT\nwhile at the same time providing a suf\ufb01ciently large rejection for the QCD multi-jet background.\n4.2\nBackground Estimation\nFor the evaluation of backgrounds to the Z \u2192e+e\u2212+jets signal we consider processes with real elec-\ntrons (t\u00aft, W \u2192e\u03bd, Z \u2192\u03c4+\u03c4\u2212) and QCD multi-jet production. Statistics of the multi-jet background\nsample are increased by applying a very loose electron selection and then reweighting the events with\nthe rejection from the \ufb01nal electron identi\ufb01cation cuts. For the Z \u2192\u00b5 +\u00b5\u2212analysis the background\nis dominated by processes with real muons (t\u00aft, W \u2192\u00b5\u03bd, and QCD multi-jets). QCD multi-jet back-\ngrounds for isolated highly-energetic muons result mainly from decays of b\u00afb mesons. We thus use a\nb\u00afb(\u2192\u00b5+\u00b5\u2212) sample to evaluate this background. For both analyses, all backgrounds are estimated\nfrom fully-simulated Monte Carlo samples, generated with PYTHIA. They are compared with the\nsignal distributions, derived from the respective ALPGEN Z + jets data sets.\nTable 1 provides an overview of the accepted cross-section and the corresponding signal and\nbackground fractions within the selected event sample, for several jet multiplicities and for the electron\nand the muon channel respectively. The uncertainties displayed in the table are of statistical nature\nonly. The total background is at the level of 5-15 % depending on the jet multplicity. With increasing\njet multiplicity, t\u00aft replaces QCD multi-jet production as the dominant background source in both\nanalysis channels. Due to the larger acceptance and the larger lepton reconstruction ef\ufb01ciency, we\nobtain more than twice as many signal events in the muon channel. Since the dominant (t\u00aft) background\nalso contains two real leptons, the signal-to-background ratio is comparable in both analyses.\nFigures 1(a+b) show the combined distribution of the di-muon mass and the jet multiplicity for\nevents with at least one jet for signal and background events in the Z \u2192\u00b5 +\u00b5\u2212+ jets channel. Fig-\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n780\n\nZ \u2192\u2113\u2113+ \u22651jet\nZ \u2192\u2113\u2113+ \u22652jets\nZ \u2192\u2113\u2113+ \u22653jets\nProcess\n\u03c3 (fb)\nfraction (%)\n\u03c3 (fb)\nfraction (%)\n\u03c3 (fb)\nfraction (%)\nZ \u2192e+e\u2212+jets analysis\nZ \u2192e+e\u2212\n23520\u00b1145\n91.9\u00b10.8\n4894\u00b145\n87.9\u00b11.3\n900\u00b115\n80.0\u00b12.4\nQCD jets\n1545\u00b189\n6.0\u00b10.4\n336\u00b142\n6.0\u00b10.8\n78\u00b120\n6.9\u00b11.8\nt\u00aft\n496\u00b128\n1.9\u00b10.1\n333\u00b123\n6.0\u00b10.4\n146\u00b115\n13.0\u00b11.4\nW \u2192e\u03bd\n(28\u00b113)\n(0.1\u00b10.05)\n(5.9\u00b12.6)\n(0.1\u00b10.05)\n(1.1\u00b10.5)\n(0.1\u00b10.05)\nZ \u2192\u03c4+\u03c4\u2212\n3.2\u00b11.2\n0.01\u00b10.01\n(0.67\u00b10.25)\n(0.01\u00b10.01)\n(0.1\u00b10.05)\n(0.01\u00b10.01)\nZ \u2192\u00b5+\u00b5\u2212+jets analysis\nZ \u2192\u00b5+\u00b5\u2212\n59400\u00b1650\n96.2\u00b11.0\n12600\u00b1300\n90.1\u00b11.9\n2450\u00b1100\n89.7\u00b13.7\nQCD(b\u00afb)\n1230\u00b1550\n2.0\u00b10.9\n600\u00b1300\n4.3\u00b12.2\n0\u00b1110\n0.0\u00b14.0\nt\u00aft\n1140\u00b1110\n1.8\u00b11.8\n790\u00b190\n5.7\u00b10.2\n275\u00b150\n10.2\u00b11.9\nW \u2192\u00b5\u03bd\n0\u00b1180\n0.0\u00b10.3\n0\u00b130\n0.0\u00b10.2\n0\u00b15\n0.0\u00b10.2\nTable 1: The accepted cross-sections (\u03c3, in fb) and the corresponding fraction of the total sample\n(in %) for signal and for the background channels in the Z \u2192e+e\u2212+jets and the Z \u2192\u00b5+\u00b5\u2212+jets\nanalyses, after applying the cuts outlined in Section 3. The numbers in brackets are extrapolated from\nresults obtained for a lower jet multiplicity. Errors shown are statistical only.\nures 1(c+d) show the distribution of signal and backgrounds for the pT of the leading and the next-\nto-leading jet in the Z \u2192e+e\u2212+ jets channel. The jets from the QCD multi-jet background have a\nsimilar pT distribution as the jets from the signal events, while the jets from the t\u00aft background tend\nto be harder.\n4.2.1\nBackground Subtraction\nThe Z \u2192\u03c4+\u03c4\u2212, t\u00aft and W \u2192e\u03bd backgrounds are subtracted using the Monte Carlo estimates. The\nsystematic uncertainty from the limited background statistics is propagated into the systematic uncer-\ntainty of the cross-section measurement. Special care will be needed in validating against data the\ndifferential cross-section for the t\u00aft process, since it is the dominant background for large jet multiplic-\nities. The QCD multi-jet background is expected to be determined with data-driven methods. From\nthe simulations we expect a multi-jet background fraction independent of the jet pT such that it can\nbe subtracted by applying a global factor. We assume in the following an uncertainty of 20% on the\nmeasurement of the QCD multi-jet fraction. The error is propagated into the systematic error on the\nmeasured cross-section.\n4.3\nUnfolding of Detector Effects\nThe reconstructed data have to be unfolded from the detector level to the hadron level, correcting for\nef\ufb01ciency, resolution and non-linearities in electron and jet reconstruction. In this study, the individual\nunfolding corrections are assumed to factorize in leading approximation, and the individual contribu-\ntions are investigated and corrected for separately. The corrections are detailed in the following for\nthe case of the Z \u2192e+e\u2212channel. Unfolding of the Z \u2192\u00b5+\u00b5\u2212\ufb01nal state is done in a similar way.\nAll corrections are derived with fully-simulated ALPGEN Monte Carlo samples.\nThe dominant correction on the inclusive cross-section for the Z \u2192e+e\u2212channel stems from the\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n781\n\n) (GeV)\n\u00b5,\u00b5\nM(\n60\n70\n80\n90\n100\n110\n120\n130\n140\n150\n / 3GeV\n-1\nevents / 1fb\n10\n2\n10\n3\n10\n4\n10\n + bkg\n\u00b5 \u00b5 \n\u2192\nZ \nJets\nTop\n\u03c4 \u03c4 \n\u2192\nZ \n\u03bd \u00b5 \n\u2192\nW \nATLAS\nZ->mumu +1jet incl.\n(jet)>40GeV)\nT\n Njets (P\n\u2265\n1\n2\n3\n4\n-1\nevents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n + bkg\n\u00b5 \u00b5 \n\u2192\nZ \nJets\nTop\n\u03c4 \u03c4 \n\u2192\nZ \n\u03bd \u00b5 \n\u2192\nW \nATLAS\n leading jet (GeV) \nT\nP\n50\n100\n150\n200\n250\n300\n / 10GeV\n-1\nevents / fb\n10\n2\n10\n3\n10\n4\n10\n ee + bkg\n\u2192\nZ \nJets\nTop\n\u03c4 \u03c4 \n\u2192\nZ \n\u03bd\n e\n\u2192\nW \n \n \nATLAS\n 2nd leading jet (GeV) \nT\nP\n20\n40\n60\n80\n100 120 140 160 180 200\n / 10GeV\n-1\nevents / fb\n1\n10\n2\n10\n3\n10\n4\n10\n ee + bkg\n\u2192\nZ \nJets\nTop\n\u03c4 \u03c4 \n\u2192\nZ \n\u03bd\n e\n\u2192\nW \n \n \nATLAS\n(a)\n(b)\n(c)\n(d)\nFigure 1: The distribution of the di-muon mass (a) and the inclusive jet multiplicity (b) for signal\nand backgrounds in the muon channel. In order to provide higher statistics for the background deter-\nmination, background events in an invariant mass window of 51 \u2212131 GeV, are scaled down for an\ninvariant mass window of 81\u2212101 GeV. Also shown is the distribution of pT of the leading (c) and\nthe next-to-leading (d) jet in the electron channel for\nR Ldt = 1 fb\u22121. The vertical lines in (a), (c) and\n(d) indicate the kinematic cuts applied in the analysis.\nelectron reconstruction. For each of the two electrons, the cross-section is corrected for the electron\nreconstruction ef\ufb01ciency, given as a function of the electron pseudo-rapidity and transverse momen-\ntum. The cross-section is also corrected for the trigger ef\ufb01ciency with respect to the of\ufb02ine selection.\nCorrections from jet reconstruction have a comparably small impact on the overall cross-section but\nbias the jet pT spectrum since, in general, the detector effects are greater for low pT jets. The recon-\nstructed jet pT is corrected for the non-linearity of the jet energy scale, and for each jet in the required\nselection, the cross-section is corrected for the reconstruction ef\ufb01ciency and for the effect of the jet\nenergy resolution. The uncertainties on deriving these corrections, stemming from the limited Monte\nCarlo statistics, are taken into account as systematic uncertainties on the cross-section measurement.\nFigure 2 compares the distributions of the pT of the leading jet and the next-to-leading jet, in differ-\nent unfolding stages, with the pT distribution of the original (hadron-level) Monte Carlo jets. Within\nthe statistical and systematic errors, the pT distributions of the Monte Carlo jets and the corrected\nreconstructed jets are in agreement, thus providing a consistency check for the unfolding corrections.\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n782\n\n leading jet (GeV)\nT\nP\n50\n100\n150\n200\n250\nCross section (fb) /10GeV\n2000\n4000\n6000\n8000\n10000\n12000\nMonte Carlo jets\nReco jets, all corrections \nReco jets, electron corrections \nReco jets, uncorrected \n \n \n \nATLAS\n 2nd leading jet (GeV)\nT\nP\n40\n60\n80 100 120 140 160 180 200\nCross section (fb) /10GeV\n0\n500\n1000\n1500\n2000\n2500\n3000\nMonte Carlo jets\nReco jets, all corrections \nReco jets, electron corrections \nReco jets, uncorrected \n \n \n \n \nATLAS\n(a)\n(b)\nFigure 2: Comparison of the distribution of the pT of the leading jet (a) and the next-to-leading jet\n(b) for the generated (hadron-level) Monte Carlo and for the reconstructed quantities without any cor-\nrection, after the corrections for electron triggering and reconstruction and after applying in addition\nthe jet-releated corrections.\n4.4\nComparison of Event Generator and MCFM Predictions at the Hadron Level\nOne of the goals of our study is to evaluate the statistical and systematic precision of the Z + jets\ncross-section measurement and to compare this precision with the size of the uncertainties that are\nexpected in the \ufb01rst inverse femotbarn of data. Since this study deals with the measurements from\nthe \ufb01rst data, we compare the precision of the measurement with the differences in the predictions of\nour LO and NLO QCD calculations and with the predictions from matrix element and parton-shower\ngenerators.\n4.4.1\nGenerator Comparisons\nIn this section we compare the prediction for the inclusive jet cross-section from the generators\nPYTHIA and ALPGEN with those from the MCFM partonic level event generator. In order to sep-\narate the reconstruction from the generation effects we use only Monte Carlo hadron-level generator\ninformation.\nFigures 3(a)-(c) show the comparison of the distribution of the jet multiplicities and the pT of\nthe leading and next-to leading jets for ALPGEN and PYTHIA Z \u2192\u00b5+\u00b5\u2212+ jets samples with the\nNLO (LO) calculations from MCFM. The errors on the generator distributions are purely Monte Carlo\nstatistics whereas the errors on the MCFM cross-section correspond to the PDF uncertainties and to\nthe error from the unfolding to the hadron level. MCFM predictions are corrected to the hadron level\nas speci\ufb01ed in section 2.2. The two Monte Carlo samples are normalized to the inclusive NLO Z\ncross-section, as determined in MCFM.\nThe NLO MCFM predictions for the Z + 1 jet and Z + 2 jets cross-sections are, in general, greater\nthan the LO predictions by 20 to 30%. PYTHIA predicts a larger Z + 1 jet cross-section than ALP-\nGEN, but also predicts a lower average jet multiplicity. Both Monte Carlo generators predict a lower\ncross-section than the NLO MCFM calculation for \ufb01nal states with more then one jet. The differ-\nence between the predictions of PYTHIA and ALPGEN, and between both generators and MCFM,\namounts to 10-60% depending on the jet multiplicity. A comparison of the differential cross-section\nas a function of the jet pT indicates that the inclusive cross-sections shown in Figure 3(a) depend very\nmuch on the minimum jet pT required by the selection. PYTHIA predicts larger cross-sections than\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n783\n\n(jet)>40GeV)\nT\n Njets (P\n\u2265\n0\n1\n2\n3\n4\nCross section (fb)\n3\n10\n4\n10\n5\n10\n6\n10\nmcfm NLO\nmcfm LO\nPythia\nAlpgen\nATLAS\nPt, leading jet (GeV)\n50\n100\n150\n200\n250\n300\nCross section (fb) /10GeV\n2\n10\n3\n10\n4\n10\nmcfm NLO\nPythia\nAlpgen\nATLAS\nPt, 2nd leading jet (GeV)\n40\n60\n80\n100\n120\n140\n160\nCross section (fb)/10GeV\n10\n2\n10\n3\n10\n4\n10\nmcfm NLO\nPythia\nAlpgen\nATLAS\n(a)\n(b)\n(c)\nFigure 3: Comparison of the inclusive jet cross-section (a) and the pT of the leading jet (b) and of the\nnext-to-leading jet (c) for the Z \u2192\u00b5+\u00b5\u2212+ jets channel from PYTHIA and ALPGEN Monte Carlo\nwith NLO (LO) MCFM predictions. The MCFM predictions have been corrected to the hadron level.\neven NLO MCFM for low jet pT. But, while the shape of the jet pT distribution predicted by ALP-\nGEN agrees well with the NLO MCFM prediction, PYTHIA generates a clearly softer pT spectrum,\nas expected.\n4.4.2\nStatistical and Systematic Errors\nIn order to determine the expected precision of the analysis, the cross-section measurement is per-\nformed on the fully-simulated ALPGEN Z + jets data sets, which are corrected to the hadron level,\nfollowing the prescription of Section 4.3. Systematic errors from the corrections are included. In the\nnext step we evaluate the impact of the uncertainties expected for real ATLAS data taking. ATLAS ex-\npects a limited precision of the jet energy scale in the \ufb01rst years, starting from uncertainties at the level\nof 10% and converging eventually towards 1%. We obtain two benchmark scenarios by propagating\njet energy scale uncertainties of 5% and 10% into the measured cross-sections. Several backgrounds\nwill be estimated with data-driven methods, introducing additional systematic errors. We account for\nthat in a \ufb01rst approach by adding an error of 20% on the fraction of the multi-jet background for each\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n784\n\njet multiplicity. The statistical uncertainties in the samples are scaled to the number of events expected\nto be selected for an integrated luminosity of 1 fb\u22121.\nFigure 4 compares, for the Z \u2192e+e\u2212+jets channel, the inclusive jet multiplicity (a) and the pT\nof the leading jet (b) for MCFM and the fully-simulated corrected ALPGEN sample. The errors on\nthe MCFM predictions result from the PDF uncertainty and from the errors from the correction for\nthe non-perturbative effects. The errors on the ALPGEN Monte Carlo data include all the statistical\nand systematic uncertainties described in this section with the jet energy scale uncertainty set to 5%.\nAn additional systematic uncertainty is introduced on the unfolding correction for the jet resolu-\ntion due to the uncertainty on the jet resolution measurement and to the uncertainty on the shape of\nthe pT distribution which we use to derive the corrections. Using corrections from different event\ngenerators and varying the jet resolution within its uncertainty results in a systematic error on the\ncross section at the percent level.\n(jet)>40 GeV)\nT\n N jets (P\n\u2265\n0\n1\n2\n3\n4\n5\ncross section (fb)\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nmcfm NLO\nmcfm LO\nAlpgen\nATLAS\n, leading jet (GeV)\nT\nP\n50\n100\n150\n200\n250\n300\ncross section (fb) /10GeV\n2\n10\n3\n10\n4\n10\nmcfm NLO\nAlpgen\n \n \nATLAS\n(a)\n(b)\nFigure 4: The inclusive jet cross-section (a) and the distribution of the pT of the leading jet (b),\nas predicted by NLO (LO) MCFM (corrected to the hadron-level) and by ALPGEN for the Z \u2192\ne+e\u2212+jets process.\nThe uncertainty on the theoretical predictions and on the measured cross section, as shown in\nFigure 4, are propagated on the data/theory ratio. Figure 5 shows the resulting uncertainty on a ratio\nof 1 for the inclusive cross-section and for the pT of the leading jet. The systematic uncertainty on the\ninclusive cross-section from a jet energy scale uncertainty of 5% is twice as large as as the sum of all\nthe other statistical and systematic uncertainties. In this case, the overall precision on the data/theory\nratio expected with the \ufb01rst fb\u22121 of data is at the level of 8-15% for topologies with 1-3 jets. A\njet energy scale uncertainty of 10% results in the dominant error on the cross-section. In this case,\nthe total uncertainty on the cross section is at the level of 15-30%, which is at the same order as the\ntypical differences expected between LO and NLO predictions, or between predictions from PYTHIA,\nALPGEN and MCFM. Statistical limitations become sizable for large jet pT (\u226b200 GeV).\n5\nConclusions\nFinal states containing Z + jets will serve as one of the Standard Model benchmarks for physics\nanalyses at the LHC. We have simulated cross-section measurements for theoretically well-de\ufb01ned\nquantities such as the inclusive Z + jets cross-section, and the jet transverse momentum for the leading\nand next-to-leading jets. An unfolding technique from the detector to the hadron level has been\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n785\n\nInclusive jet multiplicity\n1\n2\n3\n4\nCross section ratio uncertainty\n0 2\n0.4\n0 6\n0 8\n1\n1 2\n1.4\nPDF uncertainty\n+ Unfolding, Backgrounds, Statistics \n+ 5% Jet energy scale uncertainty\n+ 10% Jet energy scale uncertainty\nATLAS\nZ->ee+jets\n leading jet (GeV)\nT\n P\n50\n100\n150\n200\n250\n300\nCross section ratio uncertainty\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\nPDF uncertainty\n+ Unfolding, Backgrounds, Statistics\n+ 5% Jet energy scale uncertainty\n+ 10% Jet energy scale uncertainty\nATLAS\nZ->ee+jets\n(a)\n(b)\nFigure 5: Uncertainty on the ratio of measurement and theory for the inclusive jet cross-section (a)\nand the pT of the leading jet (b) for the Z \u2192e+e\u2212+jets process.\ndeveloped, and results are presented at the hadron level. Theoretical corrections from parton to hadron\nlevel, necessary for comparisons of data to parton level predictions, are determined.\nThe main background sources are found to be QCD multi-jet processes for low jet multiplicities\nand t\u00aft for large jet multiplicities and amount to the level of 5-20%, depending on the jet multiplic-\nity. Predictions from the Monte Carlo generators PYTHIA and ALPGEN have been compared with\nMCFM NLO (LO) calculations. The inclusive cross-section predictions differ by 10-60%, with larger\ndiscrepancies for the PYTHIA parton shower prediction (with respect to MCFM and ALPGEN) with\nincreasing jet pT. Statistical and systematic uncertainties on the ratio data/theory have been deter-\nmined. A jet energy scale uncertainty of 5% would be the dominant systematic uncertainty on the\nmeasured cross section, resulting in a total uncertainty of 8-15% for \ufb01nal states with 1-3 jets. A\njet energy scale uncertainty of 10% results in an overall precision at the level of 15-30% which is\nat the same order as the typical differences expected between LO and NLO predictions or between\npredictions from PYTHIA, ALPGEN and MCFM.\nReferences\n[1] ATLAS Collaboration, \u201cElectroweak Boson Cross-Section Measurements\u201d, this volume.\n[2] ATLAS Collaboration, \u201cCross-Sections, Monte Carlo Simulations and Systematic Uncertain-\nties\u201d, this volume.\n[3] J. M. Campbell, J. W. Huston and W. J. Stirling, Rept. Prog. Phys. 70, 89 (2007).\n[4] J. Campbell, R.K. Ellis, http : //mcfm.fnal.gov/; J. Campbell, R.K. Ellis, Phys. Rev. D65\n113007 (2002).\n[5] M. R. Whalley, D. Bourilkov and R. C. Group, arXiv:hep-ph/0508110.\n[6] D. Stump, J. Huston, J. Pumplin, W. K. Tung, H. L. Lai, S. Kuhlmann and J. F. Owens, JHEP\n0310, 046 (2003).\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n786\n\n[7] M.L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A. Polosa, JHEP 0307,001 (2003).\n[8] G. Corcella et al., JHEP 0101, 010 (2001).\n[9] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP 0207, 012\n(2002).\n[10] J. Alwall et al., Eur. Phys. J. C 53, 473 (2008).\n[11] T. Sjostrand et al., Comp. Phys. Commun.135, 238 (2001).\n[12] ATLAS Collaboration, \u201cReconstruction and Identi\ufb01cation of Electrons\u201d, this volume.\n[13] ATLAS Collaboration, \u201cPhysics Performance Studies and Strategy of the Electron and Photon\nTrigger Selection\u201d, this volume.\n[14] ATLAS Collaboration, \u201cMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples\u201d, this volume.\n[15] ATLAS Collaboration, \u201cJet Reconstruction Performance\u201d, this volume.\nSTANDARD MODEL \u2013 PRODUCTION OF JETS IN ASSOCIATION WITH Z BOSONS\n787\n\nMeasurement of the W Boson Mass with Early Data\nAbstract\nWe present new methods for measuring the W mass at ATLAS, and show\ntheir performance on simulated data. The experimental systematic uncer-\ntaintiess and their impact on the mW measurement are evaluated, with sam-\nples downscaled to 15 pb\u22121. The electron transverse momentum analysis\nyields a precision of \u03b4mW = 120(stat) \u2295117(syst) MeV. The systematic\nuncertainty is dominated by the energy scale. In the muon channel, the\ntransverse mass analysis gives \u03b4mW = 57(stat) \u2295231(syst) MeV, where\nthe dominant contribution comes from the recoil calibration. PDF uncer-\ntainties contributes \u03b4mW = 25 MeV. Other theoretical uncertainties were\nnot explicitely considered, but expected to be small in comparison to exper-\nimental uncertainties in early mW measurements.\n1\nIntroduction to the W mass measurement at the LHC\nThe mass of the W boson is currently measured to be mW = 80.399 \u00b1 0.025 GeV [1]. Since the W\nboson mass and the top quark mass are the largest sources of uncertainty in the indirect determination\nof the Higgs boson mass, improved precision is desirable. The expected total inclusive W cross sec-\ntion at the LHC is about 20.5 nb for each lepton channel [2]. In 10 fb\u22121 of data, around 30\u00d7106 W\nevents will be selected in each leptonic decay channel (W \u2192e\u03bd,\u00b5\u03bd), providing a combined statistical\nsensitivity of about 2 MeV. Systematic errors will need to be controlled to comparable precision.\nThe present note is however concerned with the early ATLAS data (L \u223c10 \u221220 pb\u22121), with an\nexpected statistical precision of about 100 MeV. In this context, the main sources of systematic uncer-\ntainty are of experimental origin (energy and momentum scales, resolution, ef\ufb01ciency). Other sources,\nrelated to the theoretical description of W production, play a less signi\ufb01cant role.\nThe aim of the following is to establish an unbiased W mass \ufb01t with templates, demonstrate that using\nZ events for calibration is valid, and show that the experimental sources of systematic uncertainties\ncan be controlled to the level of the statistical sensitivity. In doing so, we test the readiness for the W\nmass measurement in the \ufb01rst years of data taking.\nThis note is structured as follows. First a general discussion in Section 2 gives the outline of the\nanalysis, the ingredients involved in a W mass measurement, and the challenges in controlling them.\nTemplate based W mass \ufb01ts are presented in Sections 3 to 5, exploiting the electron and muon chan-\nnels. In a \ufb01rst step, all ingredients entering the templates are supposed perfectly known. We then\nevaluate the dependence of the \ufb01t results on each of them. Section 6 describes the calibration of the\nabsolute lepton energy scale and resolution using Z decays. This section also discusses the effect of\nthe lepton reconstruction ef\ufb01ciencies. Background uncertainties are treated in Section 7. Section 8\nquanti\ufb01es residual systematic uncertainties after in situ calibration. Finally, Section 9 summarizes the\nanalysis and concludes.\n788\n\n2\nOutline and strategy of the analysis\n2.1\nSimulation and data sets\nThe simulatedW and Z samples on which this note is based are generated using the PYTHIA event gen-\nerator [3]. Photon radiation is carried out by PHOTOS [4], and \u03c4 decays are handled by TAUOLA [5].\nDetector simulation is done using GEANT4 version 4.0 [6], and reconstruction with Athena ver-\nsion 12.0.6. These fully simulated events are reconstructed using the ATLAS software, and used\nas real data (\u201cpseudo-data\u201d). For the production of templates, we use the generator-level information\nonly, together with estimated detector smearing corrections. Simulated statistics of our main signal\nsamples are shown in Table 1. Our W signal samples correspond to roughly 15 pb\u22121. In the following,\nall results will be normalized to this luminosity, i.e. downscaling results from the larger Z samples.\nChannel\nNb. of events\nCross section [pb]\n\u03b5 of \ufb01lter\nCorresponding L [pb\u22121]\nW \u2192e\u03bd\n170143\n20510\n0.624\n13.3\nW \u2192\u00b5\u03bd\n189903\n20510\n0.686\n13.5\nZ \u2192ee\n377745\n2015\n0.857\n218.7\nZ \u2192\u00b5\u00b5\n150650\n2015\n0.896\n83.4\nTable 1: Number of events, cross sections (at NNLO [2]), and corresponding luminosity of the simu-\nlated W and Z signal samples used in the analysis.\n2.2\nEvent selection\nSince the dijet cross section at hadron colliders is several orders of magnitude larger than the W bo-\nson cross section, the hadronic decay modes of W and Z bosons are not usable. Therefore, only the\nleptonic decay modes W \u2192\u2113\u03bd and Z \u2192\u2113\u2113(\u2113= e,\u00b5) are considered. While the W and Z bosons are\nproduced with a small transverse momentum on average (see Figure 2(a)), their longitudinal boost can\nbe large. However, this boost leaves the lepton transverse momenta unchanged, which subsequently\nis a good distribution to study W boson decays.\nW events are required to have one isolated lepton with pT above 20 GeV and missing transverse energy\n(/ET) in excess of 20 GeV. Z events are required to have two isolated leptons with pT above 20 GeV\nof opposite charge (see Figure 1). The triggers providing these events are an isolated 15 GeV electron\ntrigger and a 20 GeV muon trigger. The electrons are required to pass tight identi\ufb01cation criterion [7],\nand only combined muons (with reconstructed tracks in both the inner detector and the muon spec-\ntrometer [8]) are used. Both electrons and muons are required to lie within the tracking range |\u03b7| < 2.5\n(see Figure 2(b)). In addition, the calorimeter barrel-endcap transition range 1.3 < |\u03b7| < 1.6 is ex-\ncluded for electrons.\nIn addition to this basic selection, some other requirements apply. To reject backgrounds from jet and\nt\u00aft events, the signal events are required not to have large hadronic transverse activity. A summary of\nthe requirements can be found in Table 2.\nThe expected numbers of events in 15 pb\u22121 from the above mentioned event selection are summarized\nin Table 3. Though the expected number of reconstructed Z events is an order of magnitude smaller\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n789\n\nW \u2192\u2113\u03bd\n(a)\n\u03bd\n\u2113\npx\npy\nu\n\u2206\u03c6\u2113\u03bd\nZ \u2192\u2113\u2113\n(b)\n\u2113\n\u2113\npx\npy\nu\npT(Z)\nFigure 1: Transverse view of a W \u2192\u2113\u03bd (a) and a Z \u2192\u2113\u2113(b) event. The combined transverse momen-\ntum of the recoil u, which should match that of the boson, is used to estimate the momentum of the\nundetected neutrino in the W \u2192\u2113\u03bd decay. The dotted ellipses represent the uncertainties.\nRequirement\nW \u2192e\u03bd\nW \u2192\u00b5\u03bd\nReconstructed lepton\npT > 20 GeV, |\u03b7| < 2.5\npT > 20 GeV, |\u03b7| < 2.5\nIsolation\nEcone\nT\n/ET < 0.2\nMissing energy\n/ET > 20 GeV\n/ET > 20 GeV\nCrack region\nRemove 1.30 < |\u03b7| < 1.60\nRecoil momentum\npT < 50 GeV\nRequirement\nZ \u2192ee\nZ \u2192\u00b5\u00b5\nReconstructed leptons\npT > 20 GeV, |\u03b7| < 2.5\npT > 20 GeV, |\u03b7| < 2.5\nIsolation\nEcone\nT\n/ET < 0.2\nCrack region\nRemove 1.30 < |\u03b7| < 1.60\nRecoil momentum\npT < 50 GeV\nTable 2: Selection criteria for the W and Z decays. See text for details.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n790\n\n [GeV]\nT\nBoson p\n0\n10\n20\n30\n40\n50\n60\nFraction of events\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\n0.016\n0.018\n0.02\n0.022\n W events \n Z events \nATLAS\n(a)\n\u03b7\nMuon \n-2\n-1\n0\n1\n2\nFraction of events\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n W events \n Z events \nATLAS\n(b)\nFigure 2: (a) Reconstructed transverse momentum of W and Z bosons. The larger resolution in the\nW events causes the wider peak at low pT, while at higher pT the Z spectrum slightly dominates. (b)\nDistribution in \u03b7 of reconstructed muons from W and Z events.\nthan that of W events, the fact that Z events are fully reconstructed and thus have much better mass\nresolution compensates for this de\ufb01cit.\nChannel\nW \u2192e\u03bd\nW \u2192\u00b5\u03bd\nZ \u2192ee\nZ \u2192\u00b5\u00b5\nDetector acceptance [%]\n44.3\n45.4\n42.4\n39.9\nReconstruction ef\ufb01ciency [%]\n21.7\n39.1\n10.4\n33.4\nNb. of events for 15 pb\u22121 [103 events]\n66.7\n120.2\n3.2\n10.1\nTable 3: Acceptances, total reconstruction ef\ufb01ciencies, and resulting statistics for 15 pb\u22121 of data.\nThe W cross sections are inclusive, while the Z cross sections are for invariant masses above 60 GeV.\nBoth are at NNLO and contain the relevant branching fractions. The acceptance is the fraction of\nevents which lies within the detector acceptance, while the total reconstruction ef\ufb01ciency is the overall\nef\ufb01ciency for an event to pass all selection criteria including the acceptance.\n2.3\nInput to W mass \ufb01t\nWhile the Z decay can be fully reconstructed, and its mass calculated from the invariant mass of\nthe decay leptons, this is not the case for W decays, where the neutrino goes undetected. From the\nmomentum imbalance one can infer the missing energy, but with limited precision and only in the\ntransverse direction. This means that the invariant mass can not be determined, and one is forced to\nconsider other variables sensitive to the W mass. In principle there are three sensitive variables:\n\u2022 The lepton transverse momentum, p\u2113\nT.\n\u2022 The missing transverse momentum, p\u03bd\nT \u2261/ET.\n\u2022 The W transverse mass, de\ufb01ned as: mW\nT \u2261\nq\n2p\u2113\nT p\u03bd\nT(1\u2212cos(\u03c6 \u2113\u2212\u03c6 \u03bd)).\nThe lepton transverse momentum is measured with an accuracy of about 2% for electrons and muons\n[7,8] in the momentum range of interest (see Section 6.2). This is an order of magnitude better com-\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n791\n\npared to the accuracy of the missing transverse energy determination, which has a resolution of about\n20-30% [9]. Finally, the W transverse mass combines the two momenta along with the azimuthal\nangle between them.\nAll of the above distributions have a Jacobian peak either at mW/2 (p\u2113\nT and p\u03bd\nT) or mW (mW\nT ), which is\nsensitive to the W mass. The sharpness of the peak is affected both by the resolution and the boson\npT. While the lepton pT has a very good resolution, the pT of the boson smears this Jacobian edge.\nOn the contrary, mW\nT is to \ufb01rst order insensitive to the pT of the boson, but here the edge is smeared\nby the poor resolution of the missing transverse energy (see Figure 3). Finally, p\u03bd\nT suffers from both\neffects, and is therefore the poorest candidate for a \ufb01tting variable. Since mW\nT is formed from p\u2113\nT and\np\u03bd\nT, it is of course statistically correlated with p\u2113\nT. However, the statistical correlation between mW\nT and\np\u2113\nT is only about 30%, and since they have different systematic errors, combining the measurements\nbased on these observables could improve the sensitivity.\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\nNumber of Events / (0.5 GeV)\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n(W) = 0, no smearing \nT\n p\n 0, no smearing \n\u2260\n(W) \nT\n p\n 0, with smearing \n\u2260\n(W) \nT\n p\nATLAS\n(a)\n [GeV]\nT\nm\n40\n50\n60\n70\n80\n90\n100\n110\n120\nNumber of Events / (1 GeV)\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n(W) = 0, no smearing \nT\n p\n 0, no smearing \n\u2260\n(W) \nT\n p\n 0, with smearing \n\u2260\n(W) \nT\n p\nATLAS\n(b)\nFigure 3: Fitted distributions of p\u2113\nT (a) and mW\nT (b), showing the Jacobian peak, and the effects of\n\ufb01nite detector resolution (i.e. smearing) and recoil (i.e. pT of the W). While p\u2113\nT is more sensitive to\nthe recoil than to the resolution, the converse is true for the mW\nT distribution.\n2.4\nFitting the W mass with templates\nThe lepton transverse momentum and W transverse mass distributions, p\u2113\nT and mW\nT , shown in Fig-\nure 3, are the result of several non trivial effects. For this reason no analytical expression describes\nthe distributions in detail, and one is forced to use numerical methods. One method for \ufb01tting these\ndistributions is template \ufb01tting [10,11]. Templates of the p\u2113\nT and mW\nT distributions are produced with\nvarying mW values, and compared to the corresponding distribution observed in data (see Figure 6).\nThe comparison is based on a binned \u03c72 method.\nTo estimate the impact of a given effect on the W mass determination, templates unaware of the effect\nunder consideration are produced and subsequently \ufb01tted to data, which includes this effect. Assuming\nan unbiased \ufb01t, when the effect is not included in the data (see Sections 3 and 4), the resulting shift\nin \ufb01t value measures the systematic error on the W mass from not including the effect. By gradually\nchanging the size of an effect, the systematic error on the W mass as a function of this effect can be\ndetermined. As most effects are small, the dependencies are approximately linear. They are in general\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n792\n\ndifferent for the p\u2113\nT and mW\nT \ufb01ts. If an effect can be characterized by one parameter a, the systematic\nerrors (\u03b4mW) can be calculated from the derivative \u2202mW/\u2202a times the size of the uncertainty \u03b4a. If\nmore parameters are required, the systematic uncertainty is calculated from all parameters ai and their\ncovariances Covi, j.\n\u03b4mW = \u2202mW\n\u2202a \u03b4a\n(Single parameter)\n\u03b4mW\n2 = \u2211\ni, j\n\u2202mW\n\u2202ai\n\u2202mW\n\u2202a j\nCovi, j\n(Multi parameter)\nIn the following, the \u03b4a are to be understood as relative uncertainties, and the derivatives are with\nrespect to these relative uncertainties. Our results for \u2202mW/\u2202a are normalized in MeV/%.\n2.5\nCalibration procedure\nThe calibration of the absolute energy/momentum1 lepton scale plays a central role, as it is the largest\nsystematic uncertainty and the starting point of all other calibrations.\n2.5.1\nAverage calibration\nTo \ufb01rst order, a single average lepton scale factor, de\ufb01ned as \u03b1E = Erec/Etrue, independently of \u03b7\nand pT, can be obtained by demanding that the reconstructed Z peak matches its known mass. While\nthis assures the correct lepton scale and resolution for Z events, the energy scale obtained in this way\nmight not apply to W events. Because of non linearities and non uniformities, the different pT and \u03b7\ndistributions in W and Z events can possibly introduce signi\ufb01cant bias.\n2.5.2\nDifferential calibration\nIf needed, an upgrade to a differential calibration can be performed, which contrary to the average\ncalibration includes variations of scale and resolution with energy/momentum, \u03b7, and/or \u03c6. The three\nkey ingredients to such a calibration are the precise knowledge of the Z mass, width, and decay kine-\nmatics, the non zero transverse momentum of the Z bosons, and the very large sample of Z bosons\nproduced at the LHC.\nThe calibration uses a large sample of reconstructed Z \u2192\u2113\u2113events along with corresponding tem-\nplates, representing our knowledge of the Z lineshape, which we assume known. Through a compar-\nison of the two in bins of the variables of interest (lepton pT, \u03b7, and \u03c6) one can extract the scale and\nresolution in each of these bins [12].\nOnce the absolute scale is set for the leptons, the hadronic recoil scale can be determined by com-\nparing it to the transverse momentum of the leptons from the Z. Again, this calibration can be done\ndifferentially, measuring the missing momentum response as a function of pT(Z), the recoil size, and\nthe hadronic transverse activity (\u2211Ehadrons\nT\n). While this calibration is naturally not as accurate as that\nof the lepton scale, due to the poorer resolution of the hadronic recoil, it fortunately turns out that the\nmass \ufb01t is less sensitive to the recoil scale (see Section 4.3).\n1These two terms cover the same aspect, but will generally be used about electrons and muons, respectively. Angular\nuncertainties are omitted throughout this note, as they play an insigni\ufb01cant role.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n793\n\n2.5.3\nEf\ufb01ciency determination\nThe ef\ufb01ciency is determined using the \u201ctag and probe\u201d methods [13], again applied to Z \u2192\u2113\u2113events.\nThe different spectra in W and Z events is accounted for by determining the ef\ufb01ciency as a function\nof pT and \u03b7, which has been found to yield ef\ufb01ciencies compatible between W and Z [7,8].\nThe following sections attempts to quantify the above outline.\n3\nFitting the W mass with templates - electron channel\n3.1\nModelling templates for W mass \ufb01t\nAs no analytical expression matches the lepton transverse momentum and W transverse mass distri-\nbutions p\u2113\nT and mW\nT , we \ufb01t the W mass using the template method (see Section 2.4). For the templates\nof varying W mass to match the measured distribution well, all effects in\ufb02uencing these distributions\nmust be included when producing the templates. The principle in\ufb02uences are scale, resolution, non\ngaussian tails, ef\ufb01ciency and background effects, which are (with the exception of background) pri-\nmarily obtained from the similar but more constrained Z \u2192\u2113\u2113events, as discussed in Section 6.\nTwo assumptions have to be validated \ufb01rst, namely the lack of bias of the \ufb01t in itself, and the porta-\nbility of the calibration from the Z to the W. The lack of bias is tested by assuming perfectly known\nphysics and detector response. In practice, the detector response is determined at this stage from direct\ncomparisons of the lepton reconstruction to the generator level kinematics, using the W sample that\nis used in the mass \ufb01ts. Then the \ufb01t is repeated using templates with the detector response estimated\nfrom the Z sample, still comparing reconstructed to simulated kinematics. An unbiased result vali-\ndates the portability, i.e. that detector parameters can indeed be ported from Z to W events, justifying\nan in situ determination of these parameters using Z events.\nIn addition it has to be tested that the template components can be included without biasing the \ufb01t,\nand thus that a subsequent calibration, which matches the truth, will yield unbiased templates. This is\ntested in the following. The statistical sensitivity of our W \u2192e\u03bd sample, corresponding to 15 pb\u22121 of\ndata, is about 120 MeV, and we provide an estimate of the required precision on the detector response\nparameters to keep the systematic uncertainty within this limit.\n3.2\nFits to mW using templates: Validation of the method\nIn this section, the detector parameters are determined from \ufb01ts to Erec/Etrue, the ratio of reconstructed\nto true energy of the decay electrons. The \ufb01ts are done using the so-called \u201cCrystal Ball\u201d PDF [14],\nwhich aims at describing the result of calorimetric resolution together with upstream energy loss in\na single function. It has four parameters and displays a gaussian core, and a power-law tail at low\nenergy. Its expression is, up to normalization factors:\nCB(x)\n=\n(\ne\u2212( x\u2212\u03b1E\n\u03c3E )2,\nx > \u03b1E \u2212n\u03c3E\n(\u03b2/n\u2212|n|\u2212x)\u2212\u03b2,\nx < \u03b1E \u2212n\u03c3E\n(1)\nwhere x = Erec/Etrue, \u03b1E is the position of the peak, \u03c3E the gaussian width; n gives, in units of \u03c3E, the\npoint of transition between the gaussian and power-law descriptions, and \u03b2 is the exponent control-\nling the tails. The relative normalization of the two components preserves continuity at \u03b1E \u2212n\u03c3E, up\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n794\n\ntrue\n / E\nrec\nE\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\n 0.00068\n\u00b1\n = 0.99623 \nE \n\u03b1\n 3.9\n\u00b1\n = 5.0 \n\u03b2\n 0.00054\n\u00b1\n = 0.02020 \nE \n\u03c3\n 0.26\n\u00b1\n = 1.15 \nn\ntrue\n / E\nrec\nE\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\nATLAS\n(a)\ntrue\n / E\nrec\nE\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1 2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\n 0.0017\n\u00b1\n = 0.9871 \nE \n\u03b1\n 0.36\n\u00b1\n = 5.00 \n\u03b2\n 0.0013\n\u00b1\n = 0.0277 \nE \n\u03c3\n 0.095\n\u00b1\n = 1.058 \nn\ntrue\n / E\nrec\nE\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1 2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n(b)\ntrue\n / E\nrec\nE\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\n 0.0015\n\u00b1\n = 0.9855 \nE \n\u03b1\n 0.50\n\u00b1\n = 5.00 \n\u03b2\n 0.0011\n\u00b1\n = 0.0332 \nE \n\u03c3\n 0.055\n\u00b1\n = 0.930 \nn\ntrue\n / E\nrec\nE\n0.75\n0 8\n0.85\n0 9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n(c)\ntrue\n / E\nrec\nE\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1 2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n 0.0011\n\u00b1\n = 0.9954 \nE \n\u03b1\n 0.22\n\u00b1\n = 5.00 \n\u03b2\n 0.00079\n\u00b1\n = 0.01892 \nE \n\u03c3\n 0.040\n\u00b1\n = 0.679 \nn\ntrue\n / E\nrec\nE\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1 2\n1.25\nEvents / ( 0.01 )\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nATLAS\n(d)\nFigure 4: Examples of detector response functions \ufb01tted to Erec/Etrue, for 30 < pe\nT < 40 GeV. From\nupper left to lower right: 0.4 < |\u03b7| < 0.5 (a), 0.8 < |\u03b7| < 0.9 (b), 1.3 < |\u03b7| < 1.4 (c), and 1.9 < |\u03b7| <\n2.0 (d).\nto the \ufb01rst derivative. While not fully satisfactory from a theoretical point of view (the combination\nof resolution effects and radiation should in principle be given by a proper convolution), it is very\neffective in describing the observed response.\nThe \ufb01ts are performed vs. \u03b7 and pT. The angular range 0 < |\u03b7| < 2.5 is divided in intervals of size\n\u2206\u03b7 = 0.1. In each interval, \ufb01ts are done for 10 < pT < 70 GeV, in intervals \u2206pT = 10 GeV. Figure 4\nshows a number of examples, at different values of \u03b7 and pT. The \u03b7 dependence of the parameters,\nfor 30 < pT < 40 GeV, are displayed in Figure 5, where the shaded regions correspond to the excluded\n|\u03b7| region described in Section 2.2.\nIn our \ufb01ts the \u03b2 parameter was constrained to the range 0 < \u03b2 < 5. As the examples in Figure 4\nillustrate, the \u03b2 parameter appears to systematically choose values close to its upper bound, while sat-\nisfactory \ufb01ts are still obtained. Therefore, we \ufb01x \u03b2 = 5 in the remaining of the analysis, and treat the\nresponse functions in terms of \u03b1E, \u03c3E and n only. The pT spectrum templates are produced from gen-\nerator level W \u2192e\u03bd events, where the electrons are smeared using the above function and parameters\naccording to their kinematic variables. Three example template distributions are shown in Figure 6(a),\ncorresponding to three values of mW. The number of events used to produce the templates is increased\nby repeatedly smearing generator level particles. Although this limits the impact of statistical \ufb02uctu-\nations in the templates on the result, template \ufb02uctuations are still visible. Distributions on Figures 6\nare plotted on a wide range to assure that the entire pT spectrum is under control. The \ufb01tting range\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n795\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nE\n\u03b1\n0.92\n0.93\n0.94\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\nATLAS\n(a)\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\nE\n\u03c3\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\n(b)\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nn\n0\n0.5\n1\n1.5\n2\n2.5\n3\nATLAS\n(c)\nFigure 5: \u03b7 dependence of \u03b1E (a), \u03c3E (b) and n (c), for 30 < pe\nT < 40 GeV. The shaded regions\ncorrespond to the excluded |\u03b7| region described in the event selection (Section 2.2).\n [GeV]\nT\np\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nEvents/(1.0)\n500\n1000\n1500\n2000\n2500\n = 0.98\nm\n\u03b1\n = 1.00\nm\n\u03b1\n = 1.02\nm\n\u03b1\nATLAS\n(a)\n [GeV]\nT\np\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nEvents/(1.0)\n500\n1000\n1500\n2000\n2500\nbest fit\ndata\nATLAS\n(b)\nFigure 6: (a) Templates obtained at three example mass points, namely \u03b1m = mW/mtrue\nW\n= 0.98,1,1.02.\n(b) Best \ufb01t template (histogram), compared to the pseudo-data (points).\nis chosen to be between 30 and 60 GeV to avoid edge effects and to reject backgrounds (see Section 7).\nThe mass \ufb01t is performed using binned \u03c72 comparisons between the pseudo-data and the template\nhistograms. Given that all pT bins contain at least several hundred events, the \u03c72 of a given compari-\nson can be de\ufb01ned as:\n\u03c72 =\nN\n\u2211\ni=1\n(ni,data \u2212ni,template)2\n\u03c3 2\ni,data +\u03c3 2\ni,template\n,\n(2)\nwhere the sum is over the histogram bins, and n and \u03c3 are the bin contents and their errors, re-\nspectively. Computed as a function of \u03b1m = mW/mtrue\nW , the \u03c72 follows the parabola illustrated in\nFigure 7, which can be used to determine the m fit\nW and its error. The obtained parabola is satisfactory\ndespite the \ufb02uctuations of the \u03c72 points with respect to the \ufb01tted curve, which are due to the \ufb01nite\nstatistics of the templates. We obtain m fit\nW = 80.468 \u00b1 0.117 GeV, to be compared to the input value\nmtrue\nW\n= 80.405 GeV. The best \ufb01t template is shown in Figure 6(b). The stability of this result is ver-\ni\ufb01ed by repeating this exercise a number of times, with the detector smearing applied independently\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n796\n\nm\n\u03b1\n0.99\n0.995\n1\n1.005\n1.01\n2\n\u03c7\n146\n148\n150\n152\n154\n156\n158\n160\nATLAS\nFigure 7: \u03c72 vs. \u03b1m = mW/mtrue\nW , for the comparisons of pseudo-data and templates described in the\ntext.\nin each exercise (i.e, producing independent sets of templates). The distribution of m fit\nW has a spread\nwell compatible with the estimated \ufb01t uncertainty.\nWe thus conclude that within the statistical sensitivity of the W \u2192e\u03bd sample, the current procedure\nprovides an unbiased estimate of mW. We now proceed to relax our main assumptions and quantify\nthe dependence of the \ufb01t on the detector response parameters.\n3.3\nSensitivity of m fit\nW to the template components\nThis section quanti\ufb01es the stability of m fit\nW under variations of the assumptions used to produce the\ntemplates. As stated earlier, we leave phenomenological considerations aside and concentrate on\nexperimental effects. We study explicitly the effect of non gaussian tails in the detector response\nfunction, reconstruction and identi\ufb01cation ef\ufb01ciency, and backgrounds. The dependence of m fit\nW on\nthe detector scale and resolution was studied in [15], and reviewed here. The bias \u03b4mW = m fit\nW \u2212mW\nas a function of the fractional error on the lepton scale (\u03b1E) and resolution (\u03c3E) is found to be:\n\u2202mW/\u2202\u03b1E = 800 MeV/%, \u2202mW/\u2202\u03c3E = 0.8 MeV/%.\n(3)\nThe impact of non gaussian tails is studied as follows. Starting from the detector response parametriza-\ntion decribed in Section 3.2, we suppress the tails of the distribution and assume a pure gaussian\nresponse. The parameters describing scale and resolution are kept to their previous value. We then\nproduce templates and perform the \ufb01t as above. The procedure is illustrated in Figure 8. The response\ndistribution can be compared to Figure 4 to assess the impact of neglecting the non gaussian part of\nthe distribution. As can be seen, the corresponding templates are biased towards higher pT; we thus\nanticipate, as otherwise expected, that an underestimation of the tails should imply a negative \u03b4mW.\nWe obtain a bias \u03b4mW = \u2212555 MeV, corresponding to an underestimation of the non gaussian tails\nby 100%. Denoting \u03c4 the non gaussian fraction of the response function, we thus estimate the bias as\na function of the relative error on the tails as:\n\u2202mW/\u2202\u03c4 = \u22125.5 MeV/%.\n(4)\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n797\n\ntrue\n/E\nsmeared\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nEvents/(0.01)\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n9000\nATLAS\n(a)\n [GeV]\nT\np\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nEvents/(1.0)\n500\n1000\n1500\n2000\n2500\ndata\n 1.00\nm\n\u03b1\n 1.00 no tails\nm\n\u03b1\nATLAS\n(b)\nFigure 8: (a) Response function at 0.2 < \u03b7 < 0.3, 20 < pT < 30 GeV, removing the non gaussian part\nof the distribution. (b) Pseudo-data (points), compared to templates produced assuming mW = mtrue\nW ,\nwith non gaussian tails included (full line) or not (dashed line).\n [GeV]\nT\np\n10\n20\n30\n40\n50\n60\n/(1.0)\n\u03b5\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n|<1.3\n\u03b7\nbarrel 0.<|\n|<2.5\n\u03b7\ntotal 0.<|\n|<2.5\n\u03b7\nend-cap 1.6<|\nATLAS\nFigure 9: Electron reconstruction ef\ufb01ciency as a function of pT, for different regions in \u03b7.\nDistortions in the pT distribution can also be caused by the lepton reconstruction ef\ufb01ciency, as soon\nat it has a non trivial pT dependence, i.e. \u03b5\u2113= \u03b5\u2113(pT). This is the case in the electron channel, as\nillustrated in Figure 9.\nAs above, we quantify the impact of this pT dependence by taking the pseudo-data as they are, but\nassuming a \ufb02at ef\ufb01ciency in the templates. Since \u03b5\u2113(pT) is an increasing function of pT, we expect\nthat the templates will be biased towards lower pT values, inducing a positive shift in m fit\nW . Perform-\ning the mass \ufb01t indeed yields \u03b4mW = 360 MeV (this bias corresponds to a perfectly \ufb02at ef\ufb01ciency\nassumption). We estimate the bias per percent relative error on the pT dependence of \u03b5\u2113to be:\n\u2202mW/\u2202\u03b5\u2113= 3.6 MeV/%.\n(5)\nNote that the present analysis only relies on the pT dependence of \u03b5\u2113and not on its absolute value.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n798\n\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\n(Z)\nE\n\u03b1\n(W) / \nE\n\u03b1\n0.98\n0.985\n0.99\n0.995\n1\n1.005\n1.01\n1.015\n1.02\nATLAS\n(a)\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2 5\n(Z)\nE\n\u03c3\n(W) / \nE\n\u03c3\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\nATLAS\n(b)\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nn(W) / n(Z)\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\n(c)\nFigure 10: Ratio of the \ufb01tted values of \u03b1E, \u03c3E and n, between W and Z events. Each histogram\nrepresents the \u03b7 dependence of the parameter \u03b1E (a), \u03c3E (b) and n (c), for 30 < pe\nT < 40 GeV.\n3.4\nComparison of W and Z events\nBefore explicitly calibrating detector parameters from Z events and applying them in the mW \ufb01t, we\nverify that this procedure is indeed justi\ufb01ed. To this end, we perform the detector response \ufb01ts as\ndescribed in Section 3.2 on our Z \u2192ee sample, obtaining a map of the response parameters \u03b1E, \u03c3E\nand n as a function of \u03b7 and pT of the electrons.\nA \ufb01rst check is to compare the obtained values to those extracted from theW sample. This is illustrated\nin Figure 10. For all parameters, agreement is found within the statistical sensitivity throughout the\nanalysed electron phase space, except for the resolution parameter in the shaded \u03b7 region, excluded in\nthe study as explained in Section 2.2. We thus expect that templates produced using detector response\nto Z events will provide an adequate description of W events.\nA mW \ufb01t is performed next. Templates are produced from generator level W \u2192e\u03bd events, smeared\naccording to detector performance found on Z events. The resulting distributions are shown in Fig-\nure 11(a) together with their ratio in Figure 11(b); good agreement is observed. Fitted with a straight\nline, Figure 11(b) shows a slope of (3\u00b12) 10\u22124, compatible with 0, but which yields a small bias to-\nwards higher masses. Accordingly, the result of the \ufb01t is m fit\nW = 80.567\u00b10.118 GeV, to be compared\nto m fit\nW = 80.468 \u00b1 0.117 GeV obtained with detector performance found on W events. The result is\ncompatible with the input value mtrue\nW\n= 80.405 GeV.\n4\nFitting the W mass with templates - muon channel\nThis section repeats the discussion of Section 3 for the muons channel. In addition, a template \ufb01t of\nthe mW\nT distribution is described.\n4.1\nTemplate \ufb01ts to the muon transverse momentum\nRepeating the analysis from Section 3 for the muon channel yields m fit\nW = 80.538 \u00b1 0.106 GeV, ob-\ntained with detector performance found on W events, and m fit\nW = 80.508 \u00b1 0.106 GeV, with detector\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n799\n\n [GeV]\nT\np\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nEvents/(1.0)\n5000\n10000\n15000\n20000\n25000\ndetector response:\nfrom W\nfrom Z\nATLAS\n(a)\n [GeV]\nT\np\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\ndet. resp. from W event / from Z event\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\nATLAS\n(b)\n-4\n 2) 10\n\u00b1\nSlope = (3 \nFigure 11: (a) Templates obtained for \u03b1m = mW/mtrue\nW\n= 1, with detector performance obtained from\nW events (full line) and from Z events (dashes). (b) Ratio of the previous histograms, \ufb01tted with a\nstraight line.\nperformance found on Z events. The differences with the electron channel are described in the fol-\nlowing.\nThe dependence of the template \ufb01t on the scale and resolution is the same in the muon channel as in\nthe electron channel. The muon momentum resolution is generally slightly worse, and whereas the\nelectron resolution improves with pT, the converse is true for the muon resolution. Figure 12 shows\nfour examples of the momentum ratio distributions prec\nT /ptrue\nT\nfor muons \u2013 two from W events and\ntwo from Z events. As can be seen, the shapes can be modeled well with a core gaussian distribution\ndescribing the general muon bias and resolution complemented by an outlier gaussian distribution\naccounting for the muons, which are encountering parts of the detector with poor muon spectrometer\ncoverage and increased material, resulting in a slightly degraded resolution.\nTo check the portability, the \ufb01tted constants are again compared between the W and the Z events, as\ncan be seen in Figure 13. The correspondance between the \ufb01tted parameters is satisfactory. According\nto Figures 13(b) and 13(d), the resolution parameters are systematically smaller in W events. The dif-\nference between the resolutions in W and Z events averaged over \u03b7 is 3.6%, which combined to Eq. 3\nleads to a bias of 3 MeV. As will be seen in Section 6, this bias can be neglected given the precision\nof the in situ scale and resolution determination.\nUnlike the electron case, the muon reconstruction ef\ufb01ciency does not vary signi\ufb01canly over the mo-\nmentum range of interest. As can be seen from Figure 14, the ef\ufb01ciency is quite constant above\n10 GeV, varying only slightly between barrel (\u03b5 = 95.8%) and endcap (\u03b5 = 94.3%) region, due to\nincrease in material. As the reconstructed muons are required to have a momentum above 20 GeV,\nthe ef\ufb01ciency is essentially constant.\nThe \ufb02atness of the ef\ufb01ciency is not expected to change until at several hundred GeV, where radiative\nlosses grow larger than those due to ionization [1]. Using the \u201ctag-and-probe\u201d method, the hypothesis\nof a \ufb02at muon ef\ufb01ciency will be tested. The uncertainty in the linear \ufb01t translates for 15 pb\u22121 into a\nsystematic error of 16 MeV, which is much less than in the electron channel, as expected.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n800\n\ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n100\n200\n300\n400\n500\n 0.00039\n\u00b1\n = 0.99914 \n\u00b5\n 0.00042\n\u00b1\n = 0.01816 \n1\n\u03c3\n 0.0036\n\u00b1\n = 0.0444 \n2\n\u03c3\n 0.022\n\u00b1\nFraction = 0.904 \ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n100\n200\n300\n400\n500\n(a)\nATLAS\ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n100\n200\n300\n400\n500\n600\n700\n 0.00038\n\u00b1\n = 0.99887 \n\u00b5\n 0.00049\n\u00b1\n = 0.01898 \n1\n\u03c3\n 0.0029\n\u00b1\n = 0.0477 \n2\n\u03c3\n 0.024\n\u00b1\nFraction = 0.857 \ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n100\n200\n300\n400\n500\n600\n700\n(b)\nATLAS\ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\n300\n350\n400\n 0.00063\n\u00b1\n = 1.00126 \n\u00b5\n 0.00081\n\u00b1\n = 0.02940 \n1\n\u03c3\n 0.0061\n\u00b1\n = 0.0848 \n2\n\u03c3\n 0.023\n\u00b1\nFraction = 0.863 \ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\n300\n350\n400\n(c)\nATLAS\ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\n300\n 0.00073\n\u00b1\n = 0.99975 \n\u00b5\n 0.00098\n\u00b1\n = 0.02832 \n1\n\u03c3\n 0.0056\n\u00b1\n = 0.0798 \n2\n\u03c3\n 0.029\n\u00b1\nFraction = 0.829 \ntrue\n / LepPt\nrec\nLepPt\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\n1.25\nEvents / ( 0.01 )\n0\n50\n100\n150\n200\n250\n300\n(d)\nATLAS\nFigure 12: Distributions of transverse momentum ratios prec\nT /ptrue\nT\nfor muons from W ((a) and (c)) and\nZ ((b) and (d)) decays at |\u03b7| < 0.36 ((a) and (b)) and 1.79 < |\u03b7| < 2.14 ((c) and (d)) in the momentum\nrange 35-40 GeV.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n801\n\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n [GeV]\n\u00b5\n0.996\n0.998\n1\n1.002\n1.004\n1.006\n Z events \n W events \nATLAS\n Z events \n W events \nATLAS\n(a)\n\u03c72 = 8.5, Prob(\u03c72) = 0.29\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n [GeV]\n1\n\u03c3\n0.016\n0.018\n0.02\n0.022\n0.024\n0.026\n0.028\n0.03\n0.032\n0.034\n Z events \n W events \nATLAS\n Z events \n W events \nATLAS\n(b)\n\u03c72 = 9.4, Prob(\u03c72) = 0.22\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\n [GeV]\n2\n\u03c3\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n Z events \n W events \nATLAS\n Z events \n W events \nATLAS\n(c)\n\u03c72 = 9.4, Prob(\u03c72) = 0.22\n\u03b7\n0\n0.5\n1\n1.5\n2\n2.5\nGaussFraction\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n Z events \n W events \nATLAS\n Z events \n W events \nATLAS\n(d)\n\u03c72 = 4.6, Prob(\u03c72) = 0.71\nFigure 13: Comparison of \ufb01tted mean (a), core resolution (b), outlier resolution (c), and out-\nlier fraction (d) between W (circles) and Z (squares) events for muons in the momentum range\n30 < pT < 35 GeV in seven bins of |\u03b7|. The markers have been arti\ufb01cially shifted, left (W) and\nright (Z), in |\u03b7| to increase readability.\n [GeV]\nT\nmuon p\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nReconstruction efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n(a)\n [GeV]\nT\nmuon p\n10\n20\n30\n40\n50\n60\n70\nReconstruction efficiency\n0.9\n0.91\n0.92\n0.93\n0.94\n0.95\n0.96\n0.97\n0.98\n0.99\n1\nATLAS\nP(\u03b5W\n\u00b5 (pT) = \u03b5W\n\u00b5 ) = 22%\n [GeV]\nT\nmuon p\n10\n20\n30\n40\n50\n60\n70\nReconstruction efficiency ratio W/Z\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\n(b)\nSlope \u03b5W\n\u00b5 /\u03b5Z\n\u00b5 = (6.3\u00b16.5)\u00d710\u22125\n\u03c72/Nd.o.f. = 42.8/58\nFigure 14: (a) Muon ef\ufb01ciency as a function of pT for W (circles) and Z (squares) events. Insert shows\na zoomed view on the range of interest along with a constant \ufb01t to each of the graphs. The hypothesis\nof a \ufb02at probability in the range 10-70 GeV has been tested to be valid. (b) Muon ef\ufb01ciency ratio\nbetween W and Z events. No pT dependence is seen, and a linear \ufb01t yields a slope of (6.3 \u00b1 6.5) \u00d7\n10\u22125, consistent with zero.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n802\n\n4.2\nFitting the transverse W mass\nHaving tested the template \ufb01tting of the p\u2113\nT distribution, we now move to the mW\nT distribution. In ad-\ndition to the lepton residuals, this \ufb01t requires residuals for the missing momentum. Since the missing\nmomentum is a transverse quantity, it does not depend on the \u03b7 of the lepton(s) in the event. However,\nthe detector response depends on the total transverse hadronic activity \u03a3ET and the recoil momentum\nperpendicular to the direction of the leptons (cf. Figure 1).\nTo describe the response, \u03a3ET is divided in 10 bins in the range [0,200] GeV and recoil momen-\ntum into 10 bins in the range [0,40] GeV, each with an additional over\ufb02ow bin. In each bin, the\ndistributions are well described by two gaussian distributions with a common mean, as the missing\nmomentum residuals are not expected to have any asymmetric tails.\nTo study the response, it is useful to project the /ET momentum components onto two axes, de\ufb01ned\nevent by event in the transverse plane. The parallel axis is de\ufb01ned such that the azimuthal angles\nbetween the leptons (\u2113and \u03bd) and this axis are minimized and equal, and the perpendicular axis is de-\n\ufb01ned as perpendicular to the parallel axis. This reference system adapts better to the individual event\ntopology than \ufb01xed axes. Examples of the residual distributions projected on these axes are shown in\nFigure 15.\nMissing momentum residual [GeV]\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n30\n40\n50\nNumber of events / (1 GeV)\n0\n20\n40\n60\n80\n100\n120\nATLAS\n(a)\nMissing momentum residual [GeV]\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n30\n40\n50\nNumber of events / (1 GeV)\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n(b)\nFigure 15: Distribution of /ET residuals /ET\nrec \u2212/ET\ntrue for W decays. The /ET momentum compo-\nnents along the parallel (a) and perpendicular (b) axes are shown, for a recoil mometum in the range\n[8,12] GeV, and \u03a3ET in the range [20,30] GeV. The \ufb01tting function describes the distributions well.\nUsing the above modelling of the missing momentum response, we produce mW\nT templates and test\nif the \ufb01t is unbiased or not. Unlike the lepton case, no additional ef\ufb01ciency curve has to be in-\ncluded, as the missing momentum is calculated for every event. As can be seen from Figure 16, the\nmW\nT templates match the reconstructed distribution, and the \ufb01t is unbiased, giving a \ufb01tted value of\n80.421\u00b10.059 GeV compared to an input value of 80.405 GeV.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n803\n\nTransverse Mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\nEntries/GeV\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n(a)\nATLAS\nScale\n0.98\n0.99\n1\n1.01\n1.02\n2\n\u03c7\n200\n400\n600\n800\n1000\n/ ndf\n2\n\u03c7\n1818 / 38\np0\n16.18\n\u00b1\n7.5e+06\np1\n8.161\n\u00b1\n-7.501e+06\np2\n4.045\n\u00b1\n1.875e+06\n/ ndf\n2\n\u03c7\n1818 / 38\np0\n16.18\n\u00b1\n7.5e+06\np1\n8.161\n\u00b1\n-7.501e+06\np2\n4.045\n\u00b1\n1.875e+06\n(b)\nATLAS\nFigure 16: (a) Reconstructed mW\nT distribution (middle curve) along with templates produced with\nthe W mass hypothesis 78.792 GeV (left curve) and 82.008 GeV (right curve), before any kinematic\nselections. (b) \u03c72 value of \ufb01tting templates to the reconstructed distribution as a function of the\ntemplate\u2019s (fraction of) W mass hypothesis (compared to the nominal mass). The \ufb01t yields 80.421 \u00b1\n0.059 GeV in agreement with the input value of 80.405 GeV.\n4.3\nFitting the transverse W mass using the Z events for calibration\nThe dependence of the m fit\nW on the relative recoil scale and resolution uncertainty was determined to\nbe [15]:\n\u2202mW/\u2202\u03b1recoil = \u2212200 MeV/%, \u2202mW/\u2202\u03c3recoil = \u221225 MeV/%.\n(6)\nThese parameters can again be measured on Z events. To test the portability from the W to the Z of\nthe mW\nT \ufb01t, we model the missing momentum using the Z events and compare this to the one obtained\nfrom the W events. However, unlike the lepton case, the detector response is not exactly the same for\nW and Z events. The difference is caused by the /ET reconstruction algorithm, which in its current\nstate does not correctly subtract lepton calorimetric signals from the hadronic recoil. This results in a\ndifference between W events where only one lepton is present, and Z events containing two leptons.\nTo illustrate this point, consider again the parallel and perpendicular axes de\ufb01ned in the previous sec-\ntion. The residuals of the recoil momentum components are projected on both axes, and the response\nin W and Z events is compared, cf. Figure 17. Along the parallel axis, the average difference be-\ntween the residuals is \u2206W\u2212Z = 17 \u00b1 35 MeV. Along the perpendicular axis, the difference is larger,\n\u2206W\u2212Z = 1964\u00b135 MeV. Using a Z-based calibration in the W mass \ufb01t is thus expected to be biased;\nperforming this exercise indeed yields m fit\nW = 79.752 \u00b1 0.062 GeV compared to the input value of\n80.405 GeV. The Z based recoil calibration is thus not exploitable at present.\nInstead, we assume that the needed improvements to the /ET reconstruction algorithm will be done\nin time for the measurement, providing equal response between W and Z events. The statistical\nsensitivity based on the Z-based calibration is about 50 MeV for 15 pb\u22121, serving as a lower bound.\nGiven the present uncertainties and the performance of similar analysis [16], we assume that the in situ\ncalibration can be performed with a precision of 1 % with an associated uncertainty \u03b4mW = 200 MeV,\naccording to Equation 6. The effect of pile-up on the missing momentum has not been studied.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n804\n\nMissing energy residual [GeV]\n-20\n-10\n0\n10\n20\nFraction of events\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n W events \n Z events \nATLAS\n(a)\nMissing energy residual [GeV]\n-20\n-10\n0\n10\n20\nFraction of events\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n W events \n Z events \nATLAS\n(b)\nFigure 17: Distribution of /ET residuals /ET\nrec \u2212/ET\ntrue parallel (a) and perpendicular (b) to the lepton\naxis for W and Z decays.\n5\nStatistical uncertainty as a function of \ufb01tting range\nAs previously stated, the sensitivity to the W mass comes from the Jacobian edge in the \ufb01tting distri-\nbution. Generally the Jacobian edge is slightly sharper for the mW\nT distribution (see Figure 3), yielding\na smaller statistical uncertainty. To test the in\ufb02uence of the \ufb01tting range, three different \ufb01tting ranges\nhas been tested for the p\u2113\nT and mW\nT distributions for the W \u2192\u00b5\u03bd sample. Since the typical mW\nT values\nare twice as large as the p\u2113\nT values, the range size has been chosen accordingly. The result can be seen\nin Table 4.\nTransverse lepton momentum, p\u2113\nT\nTransverse W mass, mW\nT\nFitting range [GeV]\n\u03c3stat. [MeV]\nFitting range [GeV]\n\u03c3stat. [MeV]\n10-80\n87\n20-160\n54\n20-70\n93\n40-140\n55\n30-60\n106\n60-120\n57\nTable 4: Statistical uncertainty as a function of \ufb01tting range for p\u2113\nT and mW\nT \ufb01ts. The uncertainties in\nthe p\u2113\nT \ufb01t are larger, because the Jacobian edge is less sharp than in the mW\nT \ufb01t (see Figure 3).\nAs can be seen from Table 4, the p\u2113\nT statistical uncertainty changes of about 30% with \ufb01tting range,\nwhile the mW\nT statistical uncertainty is essentially insensitive to the range, and generally somewhat\nlower as expected. Considering that most systematic effects (such as backgrounds, electron calibration\nand ef\ufb01ciency, etc.) are largest at low momenta, a loss in p\u2113\nT statistical uncertainty will be countered\nby a gain in systematic uncertainty. For the mW\nT \ufb01t a narrow range is surely preferable. However, it is\nnot possible to quantify this gain until all systematic uncertainties have been calculated.\n6\nLepton performance determination in situ\nIn this section we review algorithms to calibrate the lepton response using Z events, and feed back the\nresults to the mW \ufb01t.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n805\n\n [GeV]\nee\nm\n80\n82\n84\n86\n88\n90\n92\n94\n96\n98\n100\nEvents/(0.25)\n0\n200\n400\n600\n800\n1000\n1200\n1400\ndata\nbest fit\n=0.02\nE\n\u03c3\n=1. \nE\n\u03b1\nATLAS\nFigure 18: Fully simulated Z pseudo-data (dots with error bars), compared to an example Z resonance\ntemplate with \u03b1E = 1, \u03c3E = 0.02, and to the best \ufb01t.\n6.1\nAverage scale and resolution\nWe \ufb01rst perform a global scale analysis, to verify whether neglecting possible non linearities in the\nresponse can be expected to induce a signi\ufb01cant bias. We restrain ourselves to the electron channel.\nFixing the non gaussian tail parameters to n = 0.8 and \u03b2 = 5, as expected from the studies performed\nin Section 3.3, we produce templates of the Z resonance by varying the electron scale and resolution.\nThese response parameters are applied to generator level electrons as before.\nThe templates are then \ufb01tted to the fully simulated Z peak. A very good \ufb01t is obtained, as shown in\nFigure 18. An average scaling factor of \u03b1E = 0.9958\u00b10.0003, and an average relative resolution of\n\u03c3E = 0.0207 \u00b1 0.0003 provide a statisfactory description of the resonance. The precision of the \ufb01t\ncorresponds to the complete Z event sample, i.e. L = 200 pb\u22121. Scaling to our default luminosity\nL = 15 pb\u22121, the precision becomes \u03b4\u03b1E = 0.0013 and \u03b4\u03c3E = 0.0013.\n6.2\nDifferential scale and resolution\nThe calibration uses a (large) sample of reconstructed Z \u2192\u2113\u2113events and a corresponding simulated\nsample (representing our knowledge of the Z lineshape). For each event the two leptons are assigned\nto bins i and j (choosing i \u2265j) according to energy/momentum, \u03b7, and/or \u03c6. Based on the lepton\nbins, events are divided into categories (i, j), as shown in Figure 19.\nFor each category (i, j), the reconstructed sample is compared to the known Z lineshape (obtained\nfrom the corresponding simulated sample), and a Z mass resolution function Ri j is obtained from\nrequiring that its convolution with the theoretical lineshape matches the reconstructed distribution\n(see Equation 7). Each of these Z mass resolutions Ri j is the direct result of combining two lepton\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n806\n\nMapping of leptons to bins:\npT bin (GeV)\n\u03b7 bin\n60 \u2013 \u221e\n55 \u2013 60\n50 \u2013 55\n45 \u2013 50\n40 \u2013 45\n35 \u2013 40\n30 \u2013 35\n25 \u2013 30\nBarrel\nEndcap\n15\n14\n13\n12\n11\n10\n9\n8\n7\n6\n5\n4\n3\n2\n1\n0\nMapping of events to catagories:\nN lepton bins =\u21d2\nN \u00d7(N +1)/2 classes\nData:\nEvent\npT\n\u03b7\n\u03c6\nBin\n1: \u21131\n44.1\n2.21 -2.98\n11\n\u21132\n28.4\n1.78\n0.43\n8\n2: \u21131\n34.2\n1.67 -0.93\n9\n\u21132\n38.7 -0.92\n2.66\n2\n. . .\nSimulation:\nEvent\npT\n\u03b7\n\u03c6\nBin\n1: \u21131\n41.9 -1.01 -1.58\n3\n\u21132\n37.6 -1.26\n1.52\n2\n2: \u21131\n58.5\n0.79 -2.31\n6\n\u21132\n27.8\n0.45\n1.44\n0\n. . .\n\t\nHHHHHHHHHHHHH\nj\nexample of mapping\nBin of lepton 1\nBin of lepton 2\nBB\nBE\nEE\nFigure 19: Illustration of scheme to categorize Z \u2192\u2113\u2113events. Each lepton is assigned a bin according\nto its pT and |\u03b7|, here eight pT bins and two |\u03b7| bins (barrel (B) and endcap (E)) thus 8\u00d72 = 16 bins\ntotal, as demonstrated (left). Z \u2192\u2113\u2113events from data/simulation (middle box) are then divided into\ncategories (squares right) according to the reconstructed/truth pT and |\u03b7| bin of both leptons.\n \n \n0\n1000\n2000\n3000\n4000\n5000\n6000\n Z lineshape \n Z reconstructed \nATLAS\nZ mass (GeV)\n75\n80\n85\n90\n95\n100\n0\n1000\n2000\n3000\n4000\n5000\n6000\n Z lineshape \n Z reconstructed \nATLAS\n...\nTotal: N \u00d7(N +1)/2\n=\u21d2\n=\u21d2\n \n \n \n0\n200\n400\n600\n800\n1000\n1200\nATLAS\nZ mass residual (GeV)\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n200\n400\n600\n800\n1000\n1200\nATLAS\n...\nTotal: N \u00d7(N +1)/2\n\uf8fc\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8fd\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8fe\n=\u21d2\nGlobal \ufb01t\n \n \n \n0\n500\n1000\n1500\n2000\n2500\nATLAS\n residual (GeV)\nLepton p\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n0\n500\n1000\n1500\n2000\n2500\nATLAS\nT\n...\nTotal: N\nFigure 20: For each category a Z mass resolution function (middle) is determined from folding it\nwith the simulated distribution to match the reconstructed one (left). The lepton bias and resolution\nparameters are determined for each of the 16 lepton bins, by globally \ufb01tting the 16 \u00d7 17/2 = 136 Z\nmass resolutions, which each is a result of two individual lepton resolutions (right).\nmomentum resolutions Ri and R j:\nf(mZ)Reco\ni j\n=\nf(mZ)Truth\ni j\n\u2297Ri j,\nRi j = Ri \u2297R j\n(7)\nThe complicated lepton scale and resolution calibration can thus be split into two parts, which both\nsaves computing time and allows for intermediate checks and changes.\nGiven N lepton bins and thus lepton resolution functions to determine, there are N \u00d7(N +1)/2 Z mass\nresolution functions, and thus the overconstrained system can be solved by a global \u03c7 2 \ufb01t. This cali-\nbration procedure is illustrated in Figure 20, and allows for a determination of the detector response\nfor all combinations of pT and \u03b7.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n807\n\n\u03b7\nT\np\nBin in ( , )\n0\n2\n4\n6\n8\n10\n12\n14\nCorrection factor\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\nTruth \nReco \nATLAS\n(a)\nBarrel\nEndcap\n\u03b7\nT\np\nBin in ( , )\n0\n2\n4\n6\n8\n10\n12\n14\nCorrection factor\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\nTruth \nReco \nATLAS\n(b)\nBarrel\nEndcap\nFigure 21: Lepton scale constants for electrons (a) and muons (b) as obtained from simpli\ufb01ed cali-\nbration to the Z peak (squares) and from truth (circles) using full Z samples (see Table 1). The \ufb01rst\neight bins are scale constants for leptons of increasing pT reconstructed in the barrel, while the last\neight are for those in the endcap (see text). The result is in good agreement with average scale of\n0.9958\u00b10.0003 (indicated by the line in plot (a)) found in Section 6.1.\nA simpli\ufb01ed version of the above analysis has been performed, with the aim of obtaining only the\nscales. In this simpli\ufb01ed procedure, the resolution functions R in Equation 7 reduces to calibration\nconstants. The result of the calibration using the full Z samples (see Table 1) is shown for both elec-\ntrons and muons in Figure 21, along with the scales obtained from the truth information.\nAs can be seen from the \ufb01gure, the simpli\ufb01ed calibration yields the correct behaviour of the scales in\ngeneral. Some \ufb02uctuations around the expected values are observed induced by the above simpli\ufb01ca-\ntions. Scaled to 15 pb\u22121, the uncertainties are to be increased by a factor 3.8 and 2.4 for electrons and\nmuons, respectively.\n6.3\nLepton reconstruction ef\ufb01ciency\nThe p\u2113\nT and mW\nT distributions of W events are also in\ufb02uenced by any pT and \u03b7 dependence of the\nlepton reconstruction ef\ufb01ciency. Any difference between the data and the simulation used to produce\nthe templates will induce a difference in the distribution and cause a bias in the W mass \ufb01t.\nThough the method to obtain the (differential) ef\ufb01ciency is conceptually the same for electrons and\nmuons, the two cases are different in that electron reconstruction is generally more dependent on pT\nand \u03b7 than the muon reconstruction. For this reason, we have chosen to consider the electron recon-\nstruction ef\ufb01ciency in the following. The electron reconstruction ef\ufb01ciency can be determined from\nthe data with Z events, using the so-called \u201ctag and probe\u201d method [10], which we brie\ufb02y summarize\nhere. Events are selected with one well-identi\ufb01ed electron, and an additional high pT object. The\ninvariant mass of these two objects is required to be within 10 GeV of the nominal Z boson mass.\nAssuming that this selects Z events with enough purity, the identi\ufb01cation ef\ufb01ciency is then simply ob-\ntained by computing the fraction of events where the second object is indeed identi\ufb01ed as an electron.\nThe ef\ufb01ciency of the isolation criterion is obtained in a similar way.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n808\n\nThe studies reported in [17] indicate that for an integrated luminosity of 100 pb\u22121, the electron ef\ufb01-\nciency can be reconstructed with a precision of 1.5% in the range 20 < pe\nT < 70 GeV. The uncertainty\nis statistically dominated. Scaling this number down to L = 15 pb\u22121, we anticipate a precision of\n3.9%.\n7\nBackground uncertainties\nThe leptonic W channel does not suffer from large backgrounds, due to the high cross section and\nthe cleanness of the signal. The backgrounds are mostly from similar vector boson decays, such\nas W \u2192\u03c4(\u2192\u2113\u03bd\u03bd)\u03bd, Z \u2192\u2113\u2113(missing one lepton), and Z \u2192\u03c4(\u2192\u2113\u03bd\u03bd)\u03c4. With the good particle\nidenti\ufb01cation capabilities of the ATLAS detector [13], jet events will despite their large cross section\nnot be dominant. The backgrounds from t\u00aft and W +W \u2212events are negligible. The backgrounds and\nthe uncertainties in their sizes are estimated below.\nW \u2192\u03c4(\u2192\u2113\u03bd\u03bd)\u03bd events:\nA large background (largest in the electron channel) is from W \u2192\u03c4\u03bd\nevents, where the \u03c4 decays into a lepton. This background is irreducible, as the \ufb01nal state is identical\nto the signal; however, its p\u2113\nT and mW\nT distributions are generally below the \ufb01tting range, as both the\nlepton and missing momentum are much reduced, leaving only a tail into the \ufb01tting range. Though a\nquite signi\ufb01cant background, its uncertainty is small, as only the \u03c4 \u2192\u2113X branching ratio (1.0%) and\nthe acceptance relative to the signal (2.5%) enter.\nZ \u2192\u2113\u2113events:\nAnother large background (largest in the muon channel) comes from Z \u2192ll events,\nwhere one lepton is either undetected or not identi\ufb01ed. A loose lepton identi\ufb01cation for the second\nlepton can reduce this background, and possibly further reduction can be obtained with a Z veto,\nshould the associated uncertainty still be signi\ufb01cant. We do not apply this veto in the present analysis.\nThe Z \u2192\u2113\u2113background extends signi\ufb01cantly into the p\u2113\nT and mW\nT distributions, except in the mW\nT\nelectron channel, where the missed electron cluster still reduces the missing momentum, effectively\nlowering the apparent mW\nT . The size of this background has uncertainties from the W to Z cross section\nratio RWZ (1.8%), Z veto ef\ufb01ciency (2.0%), and the acceptance (2.5%).\nZ \u2192\u03c4(\u2192\u2113\u03bd\u03bd)\u03c4 events:\nA small background origins from Z \u2192\u03c4\u03c4 events, where one \u03c4 decays\nleptonically, while the other is not identi\ufb01ed. While the cross section for such a process is small, it\ncan fake missing momentum. The largest uncertainty in the size of this background comes from the \u03c4\ndetector response (5.0%), along with cross section ratio RWZ (1.8%), and acceptance (2.5%).\nJet events:\nThis background is not studied here, because it can not be evaluated reliably using\nsimulation only. Relying on Tevatron experience [16], we will assume it is small and it will not be\ndiscussed in this note.\nImpact of backgrounds:\nIf the size and shape of the backgrounds were perfectly known, then they\nwould not affect the W mass measurement, as they could be included in the templates. It is thus the\nuncertainty on the size and shape of the backgrounds, in the \ufb01tting range of the p\u2113\nT and mW\nT spectra,\nwhich gives rise to systematic errors. The uncertainties on the size of backgrounds arise from uncer-\ntainties relative to those of the signal events in cross sections, branching ratios and acceptances. These\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n809\n\nElectron channel\nMuon channel\nProcess\nEvts / 15pb\u22121\nFraction [%]\nProcess\nEvts / 15pb\u22121\nFraction [%]\nW \u2192e\u03bd\n45468\n97.8\nW \u2192\u00b5\u03bd\n83263\n93.9\nW \u2192\u03c4\u03bd\n666\n1.4\nW \u2192\u03c4\u03bd\n1238\n1.4\nZ \u2192ee\n305\n0.7\nZ \u2192\u00b5\u00b5\n3483\n3.9\nZ \u2192\u03c4\u03c4\n30\n0.1\nZ \u2192\u03c4\u03c4\n153\n0.2\nTable 5: Signal and expected backgrounds in 15 pb\u22121 after the event selection described in Section 2.2\nand in the p\u2113\nT range [30,60] GeV.\nare obtained from PDG [1] and ef\ufb01ciency studies (see Section 6.3).\nThe background shapes are determined from simulation. They are essentially unaffected by variations\nin the production, decay and resolution model. For jet events background, which was ignored in the\npresent study, both normalisation and shape will have to be measured directly from the data.\nWe \ufb01rst assess the overall impact of the backgrounds. The backgrounds remaining after the selection\ndescribed in Section 2.2 are given in Table 5, and the pT spectrum of each process is shown in Fig-\nure 22.\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\n65\n70\nNumber of events / (0.5 GeV)\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\n65\n70\nNumber of events / (0.5 GeV)\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n\u03bd\n e\n\u2192\nW\n\u03bd\n\u03c4 \n\u2192\nW\n ee\n\u2192\nZ\n\u03c4\n\u03c4 \n\u2192\nZ\nATLAS\n(a)\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\n65\n70\nNumber of events / (0.5 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\n65\n70\nNumber of events / (0.5 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n\u03bd\n\u00b5\n \n\u2192\nW\n\u03bd\n\u03c4 \n\u2192\nW\n\u00b5\n\u00b5\n \n\u2192\nZ\n\u03c4\n\u03c4 \n\u2192\nZ\nATLAS\n(b)\nFigure 22: pT distribution for signal and backgrounds for electrons (a) and muons (b) after the selec-\ntions described in Section 2.2. The pT range used in the mass \ufb01t is 30 < pT < 60 GeV.\nIgnoring the background altogether in the templates leads to a bias \u03b4mW = \u221210 MeV. This is however\nthe result of a conspiracy : the W \u2192\u03c4\u03bd background alone gives a bias of \u221280 MeV, while the Z \u2192\u2113\u2113\nbackground gives a bias of +70 MeV; both sources of background can vary independently within the\nuncertainties given above. The other backgrounds have negligible impact. We thus estimate the bias\nper percent relative error on the background normalization (checked to scale linearly with the size of\nthe background) to be:\n\u2202mW/\u2202N\u03c4\u03bd\u2212bkg\n=\n\u22120.8 MeV/%,\n(8)\n\u2202mW/\u2202N\u2113\u2113\u2212bkg\n=\n0.7 MeV/%.\n(9)\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n810\n\nWe remind that the above does not include the jet events study.\n8\nSummary of uncertainties for L = 15 pb\u22121\nThe response parameters determined in situ using Z events (cf. Section 6.1) are used to produce tem-\nplates of the p\u2113\nT spectrum in W events, as shown in Figure 23, for the electron channel. The resulting\n\ufb01t yields mW = 80.466 \u00b1 0.110 GeV, with no bias with respect to the true value. This results shows\nthat for L = 15 pb\u22121, propagating a global scale determined on Z events does not induce a signi\ufb01cant\nbias in the analysis. Given that the global scale calibration had a precision of 0.13% and Equation 3,\nthe scale-induced systematic uncertainty is \u03b4mW(\u03b1E) = 110 MeV. Likewise, the resolution uncer-\ntainty contributes \u03b4mW(\u03c3E) = 5 MeV.\n [GeV]\nT\np\n20\n25\n30\n35\n40\n45\n50\n55\n60\n65\n70\nEvents/(1 0)\n0\n500\n1000\n1500\n2000\n2500\ndata\nW template from Z best fit\nATLAS\n(a)\nm\n\u03b1\n0.98 0.985 0.99 0.995\n1\n1.005 1.01 1.015 1.02\n2\n\u03c7\n200\n220\n240\n260\n280\n300\n320\nATLAS\n(b)\nFigure 23: (a) p\u2113\nTspectrum from fully simulated W decays (dots with error bars), and p\u2113\nTtemplate\nobtained assuming the Z based scale and resolution and the true value of mW. (b) Template \ufb01t to mW.\nWe did not attempt to control the non gaussian tails in situ. We assume that this contribution can be\ndetermined to 5% with 15 pb\u22121, yielding a contribution of 28 MeV to the systematic uncertainty. As\ncan be seen by comparing Figure 4 and Figure 12, the effect is smaller in the muon channel.\nThe expected precision of the in situ ef\ufb01ciency measurement (Section 6.3) and Equation 5 imply a\nsystematic uncertainty on the \ufb01t result of about \u03b4mW = 14 MeV. This result holds for the electron\nchannel. Given the \ufb02atness of the muon reconstruction ef\ufb01ciency, the systematic uncertainty in the\nmuon channel is expected to be much smaller.\nIt was not attempted to determine the recoil calibration in situ. We assume that this calibration can be\nperformed to 1%, yielding a systematic contribution of 200 MeV from Equation 6. This contribution\naffects the transverse mass analysis only.\nThe background uncertainty is discussed in the electron channel, and assumed identical in the muon\nchannel. The Z \u2192\u03c4\u03c4 background is negligible. Given the current knowledge of the W and \u03c4 branch-\ning ratios [1], a realistic estimate of the \u03c4 background uncertainty is 2.5%. Injecting the nominal\nbackground in the templates, then varying them within this range, we \ufb01nd a systematic uncertainty\n\u03b4mW(bkg) = 2 MeV. Similarly, the contribution from the Z \u2192ee background is found to be 2 MeV.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n811\n\nThe total background contribution to the systematic uncertainty is thus expected to be 3 MeV.\nA detailed discussion of theoretical uncertainties is provided in [15]. At the start-up of LHC, the\ndominant theoretical contribution comes from the proton parton density functions, which contribute\n25 MeV.\nIn summary, for an integrated luminosity of 15 pb\u22121, we found that the analysis of the p\u2113\nT spectrum\ngives a statistical sensitivity of about \u03b4mW = 110 MeV per channel, while the transverse mass pro-\nvides \u03b4mW = 60 MeV. These numbers have experimental systematic uncertainties of 114 MeV in the\np\u2113\nT analysis, and 230 MeV in the transverse mass analysis. The uncertainty on the lepton and recoil\nscales dominate these numbers. Finally, the uncertainty from PDFs is about 25 MeV and compara-\ntively small. Our numbers are summarized in Table 6.\nMethod\npT(e) [MeV]\npT(\u00b5) [MeV]\nMT(e) [MeV]\nMT(\u00b5) [MeV]\n\u03b4mW (stat)\n120\n106\n61\n57\n\u03b4mW (\u03b1E)\n110\n110\n110\n110\n\u03b4mW (\u03c3E)\n5\n5\n5\n5\n\u03b4mW (tails)\n28\n< 28\n28\n< 28\n\u03b4mW (\u03b5)\n14\n\u2013\n14\n\u2013\n\u03b4mW (recoil)\n\u2013\n\u2013\n200\n200\n\u03b4mW (bkg)\n3\n3\n3\n3\n\u03b4mW (exp)\n114\n114\n230\n230\n\u03b4mW (PDF)\n25\n25\n25\n25\nTotal\n167\n158\n239\n238\nTable 6: Summary of contributions to \u03b4mW, for the different \ufb01tting methods described in the text.\nFrom top to bottom: statistical uncertainty; systematic uncertainties related to the absolute scale,\nresolution, non gaussian tails, reconstruction ef\ufb01ciency, recoil calibration, and backgrounds; total\nexperimental systematic uncertainty; uncertainty from PDF; total systematic uncertainty.\n9\nConclusions\nThis note presents a \ufb01rst attempt towards mW \ufb01ts, confronting distributions obtained from fully simu-\nlated W \u2192e\u03bd,\u00b5\u03bd events to templates produced using a simpli\ufb01ed detector model.\nThe simpli\ufb01ed detector model used here relies on empirical functions to describe the energy and mo-\nmentum scale, resolution, and non-gaussian tails, as well as the lepton selection ef\ufb01ciency. These\nfunctions are \ufb01rst determined, as a function of pT and \u03b7, using simulated W events, i.e. the signal\nitself; the resulting \ufb01t, unbiased, provides a technical validation of the method.\nIn a second step, the model parameters are used as extracted in situ, from the analysis of Z events.\nThe Z peak provides the detector scale and resolution; the tag-and-probe method [10], applied to its\ndecay leptons, is used to estimate the ef\ufb01ciency. A \ufb01t of the Z-based templates to the W data again\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n812\n\nshows no signi\ufb01cant bias.\nOur current approach can thus be considered valid, within a statistical sensitivity of about 60 MeV,\nfor the transverse mass-based \ufb01t in the muon channel, and of 120 MeV for the transverse momentum-\nbased \ufb01t in the electron channel.\nThis note has focused on experimental issues. Phenomenological uncertainties, related to QED, QCD\nand parton density functions are discussed in detail in [15].\nReferences\n[1] Particle Data Group, J. Phys.G33 (2006) 1\u20131232, including 2007 updates.\n[2] K. Melnikov and F. Petriello, Phys. Rev. Lett.74 (2006) 114017.\n[3] T. Sjostrand and S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[4] E. Barberio and Z. Was, Comp. Phys. Comm.79 (1994) 291\u2013308.\n[5] S. Jadach, Z. Was, R. Decker and J. H. Kuhn, Comp. Phys. Comm.76 (1993) 361\u2013380.\n[6] J. Allison et al, IEEE Trans. Nucl. Sci. 53 (2006) 270.\n[7] ATLAS Collaboration, \u201cReconstruction and Identi\ufb01cation of Electrons\u201d, this volume.\n[8] ATLAS Collaboration, \u201cMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples\u201d, this volume.\n[9] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, 2007.\n[10] B. Abbott et al. [D0 Collaboration], Phys. Rev.D 61 (2000) 032004.\n[11] A. A. Affolder et al. [CDF Collaboration], Phys. Rev.D 64 (2001) 052001.\n[12] N. Besson and M. Boonekamp, Determination of the Absolute Lepton Scale Using Z Boson\nDecays. Application to the Measurement of mW, ATL-PHYS-PUB-2006-007.\n[13] ATLAS Collaboration, \u201cATLAS detector and physics performance : Technical Design Report,\n1\u201d, (Geneva: CERN, 1999).\n[14] J. E. Gaiser et al. [Crystal Ball Collaboration], Charmonium Spectroscopy from Radiative De-\ncays of the J/Psi and Psi-Prime, Ph.D. thesis, 1982, SLAC-R-255.\n[15] N. Besson, M. Boonekamp, E. Klinkby, S. Mehlhase, T. Petersen, (2008), arXiv:0805.2093, to\nbe published in EPJC.\n[16] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. Lett.99 (2007) 151801.\n[17] ATLAS Collaboration, \u201cElectroweak Boson Cross-Section Measurements\u201d, this volume.\nSTANDARD MODEL \u2013 MEASUREMENT OF THE W BOSON MASS WITH EARLY DATA\n813\n\nForward-Backward Asymmetry in pp \u2192Z/\u03b3\u2217X \u2192e+e\u2212X\nEvents\nAbstract\nThis paper describes a study on the measurement of the forward-backward\nasymmetry in pp \u2192Z/\u03b3\u2217X \u2192e+e\u2212X events with the ATLAS detector for\nan integrated luminosity of 100 fb\u22121. Such a measurement can be used to\ndetermine the effective weak mixing angle, sin2 \u03b8 lept\ne f f . We will demonstrate\nthat a very high accuracy on the weak mixing angle, \u03b4 sin2 \u03b8\nlept\ne f f = (1.5(stat)\u00b1\n0.3(exp)\u00b12.4(PDF))\u00d710\u22124, can be reached. This is possible due to the large\ncross-section for the production of Z bosons at the LHC and by using electron\nreconstruction in the forward calorimeters of ATLAS (2.5 < |\u03b7| < 4.9).\n1\nIntroduction\nThe forward-backward asymmetry, AFB, measurement is one of the important precision measurements\nthat can be done at the Large Hadron Collider (LHC). It will improve the knowledge of Standard Model\nparameters and test the existence of physics beyond the Standard Model.\nThe Z boson events in pp collisions originate from the annihilation of valence quarks with sea anti-\nquarks or from the annihilation of sea quarks with sea antiquarks. Since the valence quarks carry on\naverage a larger momentum fraction than the sea quarks, the boost direction of the dilepton system\ncan indicate the quark direction. However, dilepton events which originate from the annihilation of sea\nquarks with sea antiquarks do not contribute to the observed asymmetry.\nAFB measurements with quarks and leptons at the Z peak provide a precise determination of the weak\nmixing angle sin2 \u03b8\nlept\nef f . The weak mixing angle is an important parameter in the electroweak theory that\ndescribes the mixing between weak and electromagnetic interactions. In the global \ufb01t of the Standard\nModel, the weak mixing angle has an impact on indirect constraints on Higgs mass.\nWith the experimental capabilities of the ATLAS experiment at the LHC and an expected integrated\nluminosity of up to 100 fb\u22121 it becomes interesting to perform a study on the measurement of the asym-\nmetry, AFB. In order to improve the measurement precision, it will be necessary to detect leptons in the\nvery forward pseudo-rapidity region, which favors electrons over muons at ATLAS. In 100 fb\u22121 data\naround 1.5\u00d7108 Z events will be produced, of which \u223c5\u00d7106 decay to an electron-positron pair, pro-\nviding the measurement of AFB (and sin2 \u03b8\nlept\ne f f ) with a competitive precision to the current world average\nvalue [1], \u03b4 sin2 \u03b8\nlept\nef f =0.00016.\nThis paper is organized as follows. In section 2 we present a short introduction of the theoretical\naspects of the measurement. An overview of the ATLAS detector is given in section 3. In section\n4 the electron measurement in ATLAS is presented, both in the central and forward regions the latter\nbeing necessary for a precise measurement of the forward-backward asymmetry. We then present the\nsimulated data samples used in section 5 and the de\ufb01nition of the electron polar angle in section 6. The\nevent selection cuts are discussed in section 7. The charge misidenti\ufb01cation is given in section 8. The\npile-up effect is discussed in section 9. The systematic uncertainties are summarized in section 10. The\nexpected precision on the asymmetry around the Z mass is shown in section 11.\n814\n\n2\nForward-backward asymmetry\nIn proton-proton collisions, e+e\u2212pairs are predominantly produced via the annihilation of a quark q and\nan antiquark \u00afq. In the Standard Model, quark-antiquark annihilations proceed via an intermediate [2, 3]\n\u03b3\u2217at low invariant mass M(e+e\u2212) or via a \u03b3\u2217/Z interference at M(e+e\u2212) around the Z mass. The elec-\ntroweak neutral current in the Standard Model lagrangian violates parity (due to the presence of vector\nand axial-vector couplings of the quarks and leptons to the Z-boson) and leads to an asymmetry in the\npolar emission angle of the electron in the rest frame of the electron-positron pair. The asymmetry can\nonly be extracted with respect to the boost direction of the di-electron system since the quark direction\nis not known (see Sec. 6).\nThe differential cross-section for the production of an electron-positron pair in q \u00afq annihilation via\nthe s-channel can be written, in the electron-positron rest frame [4, 5], as:\nd\u03c3\nd cos\u03b8 = Nc[(1+cos2 \u03b8)F0(s)+2cos\u03b8F1(s)]\n(1)\nwhere \u03b8 is the emission angle of the e\u2212relative to the momentum vector of the quark in the e+e\u2212rest\nframe and s is the center-of-mass energy squared. F0(s), F1(s) are form factors and Nc (1/3) is the colour\nfactor:\nF0(s)\n=\n\u03c0\u03b12\n2s (q2\nqq2\nl +2Re\u03c7(s)qqqlCq\nVCl\nV +|\u03c7(s)|2((Cq\nV)2 +(Cq\nA)2)((Cl\nV)2 +(Cl\nA)2))\n(2)\nF1(s)\n=\n\u03c0\u03b12\n2s (2Re\u03c7(s)qqqlCq\nACl\nA +|\u03c7(s)|22Cq\nVCl\nV2Cq\nACl\nA),\n(3)\nwith\n\u03c7(s) =\ns\ns\u2212M2\nZ +is\u0393Z/MZ\n(4)\nwhere qq,l is the electric charge of the quark or lepton and CV, CA are the vector and axial-vector coupling\nto the Z.\nThe angular dependence of the various terms is either cos\u03b8 or (1+cos2 \u03b8). Only the (1 + cos2 \u03b8)\nterm contributes to the total cross-section, as the cos\u03b8 term integrates to zero. However, it induces a\nforward-backward asymmetry. Thus, the differential cross-section can be written in a simple expression:\n1\n\u03c3\nd\u03c3\nd cos\u03b8 = [3\n8(1+cos2 \u03b8)+AFB(s)cos\u03b8]\n(5)\nwhere \u03c3 = 8\n3F0(s)\u00d7Nc and\nAFB(s)\n=\n1\n\u03c3 [\u03c3(cos\u03b8 > 0)\u2212\u03c3(cos\u03b8 < 0)]\n(6)\n=\n3\n4\nF1(s)\nF0(s)\n(7)\nAFB(s = M2\nZ)\n\u223c\n3\n4\n2Cq\nVCq\nA\n(Cq\nV)2 +(Cq\nA)2\n2Cl\nVCl\nA\n(Cl\nV)2 +(Cl\nA)2\n(8)\nThe forward-backward asymmetry is commonly de\ufb01ned using the number of forward produced\n(cos\u03b8 > 0) events (NF) and backward-produced (cos\u03b8 < 0) events (NB)\nAFB = NF \u2212NB\nNF +NB\n(9)\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n815\n\n)\n2\n (GeV/c \ne+e-\nM\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nFB\nA\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\nATLAS\nFigure 1: SM prediction of the forward-backward charge asymmetry AFB in the electron pair channel\nversus the di-electron invariant mass Me+e\u2212for |ye+e\u2212| >1 and for at least one electron in the central\nregion (|\u03b7| < 2.5).\nwhere\nF =\nZ 1\n0\nd\u03c3\nd cos\u03b8 d cos\u03b8,\nB =\nZ 0\n\u22121\nd\u03c3\nd cos\u03b8 d cos\u03b8\n(10)\n2.1\nDependence of AFB on Me+e\u2212\nIn Figure 1 we show the Standard Model prediction, using MRST PDF [6], of the forward-backward\ncharge asymmetry as function of the di-electron invariant mass. At the Z-pole we see a small asymmetry\n(as expected) which is dominated by a small vector coupling in Z \u2192e+e\u2212with the dominant axial\ncoupling. Around the Z mass the asymmetry is linear with the weak mixing angle sin2 \u03b8 lept\nef f . It was\nestimated that (in a good approximation) the weak mixing angle can be determined from the measurement\nof the forward-backward asymmetry (this is the raw forward backward asymmetry measured at detector\nlevel) when averaged over the rapidity of the electron pair as follow [7, 8, 9]:\nAFB = b(a\u2212sin2 \u03b8 lept\nef f )\n(11)\nthe parameters a and b depend on the parton distribution functions (PDFs).\nAt large invariant mass, AFB is dominated by the properties of the interference between the propaga-\ntors of the \u03b3\u2217and the Z and is almost constant at a large positive value, close to 0.6, independent of the\ninvariant mass.\n3\nDetector overview\nThe ATLAS detector has been described in detail in [10]. It consists of an inner tracking system, with\npseudo-rapidity coverage of |\u03b7| < 2.5, inside a 2 T solenoidal magnetic \ufb01eld, followed by the calorime-\nters, and an outer muon spectrometer, with pseudo-rapidity coverage of |\u03b7| < 2.7, installed in a large\ntoroidal magnet system. We brie\ufb02y describe the parts of the detector relevant to this analysis.\nFigure 2 shows a schematic transversal view of the ATLAS calorimeter system. It has been designed\nto be hermetic to |\u03b7| < 4.9 with a \ufb01ne lateral and longitudinal segmentation. A liquid argon (LAr) sam-\npling calorimeter in a barrel-endcap geometry provides the electromagnetic and hadronic calorimetry. At\n|\u03b7| <1.2 the hadronic calorimetry is completed by a tile (Iron/scintillator) hadronic calorimeter.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n816\n\nFigure 2: Schematic transversal view (r-z view) of the calorimeters in the ATLAS detector. The cylin-\ndrical coordinate system is used with the z axis along the proton-beam direction and r is the transverse\ncoordinate.\nThe electromagnetic barrel calorimeter, covering a pseudo-rapidity range of |\u03b7| < 1.475, shares its\ncryostat with the superconducting solenoid, the calorimeter being behind the solenoid. Each electromag-\nnetic calorimeter end-cap (EMEC) covers the pseudo-rapidity range 1.4-3.2. To correct for the energy\nlost in the material in front of the calorimeters, both end-caps and barrel are preceded with pre-sampler\ndetectors in the region |\u03b7| < 1.8. The performance expected gives for the energy resolution a sampling\nterm of 10%/\np\nE(GeV) and a constant term better than 0.7%. The hadronic end-cap calorimeter (HEC)\nand the forward calorimeter (FCal) share the same cryostat with the EMEC and cover the pseudo-rapidity\nrange 1.5-3.2 and 3.1-4.9 respectively. The design of the FCal was constrained by the high radiation level\nin the very forward region. It consists of three consecutive modules along the beam line: one electro-\nmagnetic module (FCal1) and two hadronic modules (FCal2 and FCal3). To optimize the resolution,\ncopper was chosen as the absorber for FCal1, while tungsten was used in FCal2 and FCal3, to provide\ncontainment and minimize the lateral spread of hadronic showers.\nThe electron energy can be measured either in the central electromagnetic calorimeter (|\u03b7| <2.5)\nand/or in the forward calorimeters (2.5 < |\u03b7| < 4.9). The |\u03b7| < 2.5 region corresponds to the EM barrel\nand the EMEC outer wheel.\n4\nElectron identi\ufb01cation\n4.1\nCentral electrons\nAn electron candidate is reconstructed in the central calorimeters if there is a cluster with energy E and\na charged track matched to the cluster with the condition of E/p < 7 and |\u2206\u03b7| < 0.05 and |\u2206\u03c6| < 0.1.\n\u2206\u03b7 (\u2206\u03c6) is the difference between the \u03b7 (\u03c6) position of the track and the position of the cluster. The\ntrack is then extrapolated to the cluster. The energy of the electron is determined by the total energy\nit deposits in the EM calorimeter. The transverse momentum (pT) of the electron is determined by the\nenergy measured in the calorimeter and by the track angle at the nominal interaction point. The charge\nof the electron (qe) is determined from the sign of the curvature of the track.\nThe development of electromagnetic and hadronic showers is quite different so that shower shape\ninformation can be used to differentiate between electrons and hadrons. Electrons deposit almost all\ntheir energy in the electromagnetic section of the calorimeter, while hadrons are typically much more\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n817\n\n (GeV/c)\nT\nelectron p\n0\n20\n40\n60\n80\n100\n120\nelectron ID efficicency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nATLAS\nFigure 3: Central Electron ID ef\ufb01ciency vs\nelectron pT for events with |\u03b7| < 1.3 and |\u03b7| >\n1.6.\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nelectron ID efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\nFigure 4: Central Electron ID ef\ufb01ciency vs\nelectron \u03b7. The ef\ufb01ciency is integrated over\npT > 20 GeV.\npenetrating. To obtain the best discrimination against hadrons, we use both longitudinal and transverse\nshower shapes. For example, for electrons passing tight identi\ufb01cation criteria, the hadronic leakage and\nthe lateral shower shape in the \ufb01rst and second sampling of the calorimeter are used. After the selections\nbased on calorimeter information, we also take into account the inner detector information. We ask for\na good track pointing to the calorimeter and ful\ufb01lling the consistency of the spatial and energy matching\nbetween the calorimeter and the inner detector.\nFigure 3 and Figure 4 show the electron identi\ufb01cation ef\ufb01ciency, 62.0\u00b11.0 % on average, as a func-\ntion of the electron transverse momentum and pseudo-rapidity \u03b7 using electrons (and positrons) from\nZ \u2192e+e\u2212events (the samples used are described in section 5). Tight cuts have been applied to iden-\ntify the central electrons. We observe an expected increase in the ef\ufb01ciency as function of pT. This\ndependence (in particular at low pT) is due to the lower performance for low pT electrons. The drop in\nthe ef\ufb01ciency versus \u03b7 happens at the transition region between barrel and end-cap calorimeters, 1.37\n< |\u03b7| <1.52. A more detailed description of the electron identi\ufb01cation in the central calorimeters is\ngiven elsewhere [11].\n4.2\nForward electrons\nIn contrast to the central region, forward electron reconstruction can use only calorimeter information\nas the tracking system is limited to the central region (|\u03b7| < 2.5). In this case we can not distinguish\nbetween an electron, positron or photon. The electron candidate in the forward calorimeter1 is recon-\nstructed if there is a cluster with ET > 20 GeV. The direction of the electron is de\ufb01ned by the barycenter\nof the cells belonging to the cluster in the calorimeter.\nTo discriminate between electron and hadron a multivariate analysis [12] is used. Variables are\nde\ufb01ned using cluster moments or a combination of them.\nThe cluster moment of degree n for a variable x is de\ufb01ned as:\n\u27e8xn\u27e9=\n1\nEnorm\n\u00d7\u2211\ni\nEi xn\ni ,\n(12)\nwhere Enorm =\u2211i Ei, Ei is the cell energy and i is the cell index of the cluster.\n1the EM forward calorimeters are the EMEC inner wheel (2.5 < |\u03b7| < 3.2) and the front compartment of the FCal. These\nEM calorimeters are completed by the HEC and the last 2 compartments of the FCal (3.2 < |\u03b7| < 4.9).\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n818\n\nWe use the following \ufb01ve discriminants in the electron ID:\n\u2022 ri = | (\u20d7xi \u2212\u20d7c)\u00d7\u20d7u|:\nElectromagnetic and hadronic showers have different shapes in both the transverse and the lon-\ngitudinal directions. To evaluate the shower shapes in the transverse direction we use the second\nmoment of the distance ri of each cell i (\u20d7xi) to the shower axis (\u20d7c). \u20d7u is the shower axis.\n\u2022 lat2/(lat2 +latmax):\nA modi\ufb01ed lateral moment is derived as above. It takes into account the two most energetic cells\n(shower core). So, lat2 is the second moment of the variable ri for which we impose that the\ndistance r = 0 for the two most energetic cells. For latmax we impose that r = 4 cm for the two\nmost energetic cells and r = 0 for the remaining cells.\n\u2022 long2/(long2 +longmax):\nTo evaluate the shower shapes in the longitudinal direction we use an equivalent variable to the\nprevious one where the distance of the each cell to the shower centre is used.\n\u2022\n1\nEnorm \u00d7\u2211\ni\nEi (Ei/Vi):\nwhere Vi is the volume of the cell i. The electromagnetic shower is narrow and deposits energy\nmore locally than a hadronic shower.\n\u2022 fmax\nFraction of the energy in the most energetic cell of the cluster. By measuring the energy fractions\ndeposited in the cells of a segmented calorimeter it is usually possible to distinguish incident\nhadrons from electrons and photons.\nIn order to combine the electron identi\ufb01cation information from the various discriminants into a\nsingle quantity that provides optimal discrimination power, we calculate the likelihood for each discrim-\ninant based on probability density functions. For each discriminant, the signal likelihood (ps) and the\nbackground likelihood (pB) are separately calculated and combined using the likelihood ratio:\nRL =\n\u220fNvar\nj=1 ps(j)\n\u220fNvar\nj=1 ps(j)+\u220fNvar\nj=1 pB(j)\n(13)\nwhere j runs over each discriminant. Figure 5 shows the distribution of RL using all the discriminants\ndescribed above. Both electrons (signal) and background are shown. As can be seen, good separation is\nachieved with this variable. The electron identi\ufb01cation ef\ufb01ciency determined using Z \u2192e+e\u2212events as\nfunction of the electron pT and \u03b7 as shown in Figures 6 and 7. The drop in the ef\ufb01ciency plot versus \u03b7\nhappens at the transition region between inner wheel of the electromagnetic end-cap and the FCal.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n819\n\nLikelihood ratio\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\nArbitrary unit\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\nLikelihood ratio\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\nArbitrary unit\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\nATLAS\nFigure 5: The likelihood ratio RL for the signal (yellow) and background (solid line). Due to the fact that\nthe likelihood ratio is strongly peaked at 0 and 1, in the plot, a transformation is applied that zooms into\nthe peaks.\n (GeV/c)\nelectron p\n30\n40\n50\n60\n70\n80\n90\n100\n110\n120\nforward electron ID efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nFigure 6: Forward Electron ID ef\ufb01ciency vs\nelectron pT for events with 2.5 < |\u03b7| < 4.9.\n|\n\u03b7\n|\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\n4\n4.2\n4.4\n4.6\n4.8\nelectron ID efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\nFigure 7: Forward Electron ID ef\ufb01ciency vs\nelectron \u03b7 for events with pT > 20 GeV.\n5\nMonte-Carlo samples\nThe Monte Carlo events are generated at a centre of mass of \u221as = 14 TeV using PYTHIA [13] (version\n6.3) for the signal pp \u2192Z/\u03b3\u2217\u2192e+e\u2212and the background pp \u2192j j with the CTEQ6LL [14] parton\ndistribution functions. Table 1 shows the summary of the cross-sections, number of events and the\nequivalent luminosity for the signal and background simulated events.\n5.1\nSignal\nThe pp \u2192Z/\u03b3\u2217X \u2192e+e\u2212X events generated are \ufb01ltered requiring at least one electron with |\u03b7| < 2.7\nand with transverse momentum pT > 10 GeV and a dilepton mass, \u02c6m, greater than 60 GeV. Figures 8 and\n9 show the pT distribution of electrons and the invariant mass of the electron pairs in the signal events.\n5.2\nBackground\nThe dominant sources of background to the signal process pp \u2192Z/\u03b3\u2217X \u2192e+e\u2212X are:\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n820\n\n (GeV)\nT\nelectron P\n20\n40\n60\n80\n100\n120\n140\n160\n180\nArbitrary unit\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nATLAS\nFigure 8: The electron ET distribution normal-\nized to unit for events with |\u03b7| < 1.3 and |\u03b7| >\n1.6.\n )\n 2\n (GeV/c\n ee\nM\n50\n60\n70\n80\n90\n100\n110\n120\n130\n140\n150\nEntries\n3\n10\n4\n10\n5\n10\n6\n10\nATLAS\nFigure 9: Di-electron invariant mass distribu-\ntion for events with |\u03b7| < 1.3 and |\u03b7| > 1.6.\n\u2022 dijet production: this is the largest background when two jets fake an electron. The cross-section\nof this process is greater by several orders of magnitude than the signal one, and dominates at low\ntransverse momentum.\n\u2022 pp \u2192t\u00aftX \u2192e+e\u2212X: The top quark decays into the W boson and a b quark, followed by the W\ndecay into electron and neutrino (t \u2192Wb, W \u2192e\u03bd). It has the same signature as the signal one as\nthe two electrons of the \ufb01nal state can simulate the two electrons from Z.\n\u2022 pp \u2192W +X \u2192e\u03bde +X: where X is a photon or a jet misidenti\ufb01ed as an electron\nThese events are passed through a detector simulation program to model detector response. Two\ndetector simulation tools are used: a full detector simulation tool, based on GEANT4 [15], and a fast\nsimulation program, ATLFAST [16] which simulates the detector response using ef\ufb01ciencies and smear-\ning parameters measured from detailed simulation data. ATLFAST was used due to the high di-jet\ncross-section, the high rejection power of the selections and the available Monte Carlo statistics of fully\nsimulated events which is not suf\ufb01cient to evaluate the background. The Monte Carlo samples processed\nwith the fast detector simulation were used only for estimation of the background contributions.\nPhysics process\nCross section (nb)\n\u03b5filter\nNumber of events\nEquivalent luminosity (pb\u22121)\nZ \u2192e+e\u2212\n2.015\n0.126\n5.105\n248.14\nInclusive jets\n21.104\n0.09\n3.107\n0.15\nt\u00aft\n0.833\n6.105\n720.3\nW +X\n38.2\n1.106\n26.2\nTable 1: List of signal and background samples.\nRef. [17] discusses expectation for electron triggers at different luminosities. The Z/\u03b3\u2217events used\nin this measurement are selected by high transverse momentum triggers on one or two electrons. This\nselection requires at least one isolated electron with pT > 20 GeV or at least two isolated electrons with\npT > 12 GeV. At Level 1, electrons are selected by the presence of an energy deposition in an EM\ncalorimeter tower. The Level 2 decision, which is based on the result of the Level 1 trigger, can take into\naccount the information from all ATLAS subdetector systems in the regions of interest (ROIs) and the\nevent \ufb01lter (EF) performs its task only after the complete event has been assembled in the event builder\n(EB).\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n821\n\n6\nAngular distribution\nThe Z production can be either from the annihilation of valence quarks with sea antiquarks or from the\nannihilation of sea quarks with sea antiquarks. Since the original quark direction is unknown in proton-\nproton collisions (it can originate with equal probability from either proton), the sign of cos\u03b8 is not\ndirectly measurable.\nAs the valence quarks have, on average, a much larger momentum than the sea quarks, in valence-sea\nquark collisions, the longitudinal motion of the dilepton system approximates the quark direction and the\nangle between the lepton and the quark in the e+e\u2212rest frame can be extracted with respect to the beam\naxis. A lepton asymmetry can thus be expected with respect to the boost direction. For sea-sea quark\ncollisions no such asymmetry is expected, diluting the overall effect.\nTo minimize the effect of the unknown transverse momenta of the incoming quarks in the measure-\nment of the forward and backward cross-sections, we use the Collins-Soper reference frame [18]. This\nreference frame reduces the uncertainty in electron polar angle due to the \ufb01nite transverse momentum\nof the incoming quarks. The particle four-vectors are transformed to the e+e\u2212rest frame and the polar\nangle \u03b8 \u2217is measured with respect to the axis, which bisects the two quark momentum vectors.\ncos\u03b8 \u2217=\n2\nm(e+e\u2212)\nq\nm2(e+e\u2212)+ p2\nT(e+e\u2212)\n[p+(e\u2212)p\u2212(e+)\u2212p+(e+)p\u2212(e\u2212)]\n(14)\nwhere p\u00b1 =\n1\n\u221a\n2(E \u00b1 pz), E is the energy and pz is the longitudinal component of the momentum. To\ntake into account our supposition that the Z boost and the quark direction are the same we add the sign\nof the Z boost to the de\ufb01nition:\ncos\u03b8 \u2217= |pz(e+e\u2212)|\npz(e+e\u2212) \u00d7cos\u03b8 \u2217\n(15)\nFigure 10 shows the resulting distributions of events for which th e+e\u2212invariant mass is close to the\nZ mass. We should note that the detector itself doesn\u2019t introduce false asymmetries with the geometry\nused in the MC samples.\n *)\n\u03b8\ncos(\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nEntries\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\nATLAS\nFigure 10: Distribution in cos\u03b8 \u2217for reconstructed events in the Z pole region.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n822\n\n7\nAnalysis method\n7.1\nEvent selection\nIn this analysis we search for events with two electrons. An electron must ful\ufb01ll certain quality and\nkinematic requirements. It must \ufb01rst satisfy the tight electron criteria outlined in Section 4.1. In addition\nthe following cuts were applied:\n\u2022 C1\nWe require an electron transverse momentum higher than 20 GeV (pT > 20 GeV) to emulate the\nenergy threshold of the electron trigger\n\u2022 C2\nWe require the e+e\u2212invariant mass, M(e+e\u2212), to be within a window of 12 GeV around the Z mass,\n85.2 GeV < M(e+e\u2212) < 97.2 GeV (Z pole)\n\u2022 C3 |ye+e\u2212| > 1\nIn contrast to Tevatron p \u00afp collisions, sea quark effects dominate at the LHC. At central rapidity,\nye+e\u2212, the probability that the valence quark direction and the dielectron boost coincide is lower\ndue the smallness of the valence quark distribution. This reduces the forward backward asymme-\ntry. Since the valence quark dominates at high values of x, the events where one parton carries\na large fraction of the proton momentum are more sensitive and they give a large rapidity to the\ndilepton system. In this region the most signi\ufb01cant measurements can be performed, as shown in\nFigure 11. A purer, though smaller, signal sample can thus be obtained by introducing a rapidity\ncut. For the following studies we will impose a |ye+e\u2212| > 1 cut.\n\u2022 C4 Emiss\nt\n< 20 GeV\nWe require the missing transverse momentum to be less than 20 GeV. This cut rejects ef\ufb01ciently\nthe background coming from pp \u2192ttX channel where both top quarks decay semileptonically.\n7.2\nAnalysis cases\nA study using fast simulated events [19] showed that the use of forward electrons improves the precision\nof the forward-backward asymmetry measurement (and the weak mixing angle). As can be seen in Figure\n12, a very high electron identi\ufb01cation performance in the forward calorimeters is not needed, as already\nwith a rejection of 100 against jets the in\ufb02uence of the remaining QCD background is negligible. Figure\n12 shows only the statistical uncertainty on AFB versus the jet rejection in the forward calorimeters (with\na \ufb01xed electron ef\ufb01ciency of 50%). Thus, it is required that one of the two electrons lies in the central\nregion (|\u03b7| < 2.5), while the other electron may be either in the central region or in the forward region\nup to |\u03b7| = 4.9:\n\u2022 |\u03b7| < 2.5 for both electrons (C-C), or\n\u2022 |\u03b7| < 2.5 for one of the two electrons and |\u03b7| < 4.9 for the other (C-F).\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n823\n\n)\n-e\n+\n(e\ny\n0\n1\n2\n3\n4\n5\nEntries\n0\n2000\n4000\n6000\n8000\n10000\n12000\nATLAS\nFigure 11: Di-electron rapidity distribution for\nall events (upper line) and for the events with\ncorrect quark direction (lower line).\nForward e/jet rejection\n1\n10\n2\n10\n3\n10\n4\n10\nFB\n A\n\u03b4\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n3\n10\n\u00d7\nATLAS\nFigure 12: Forward-Backward asymmetry sta-\ntistical accuracy versus the forward jet rejec-\ntion in the events where at least one electron is\nin the central region and keeping the ef\ufb01ciency\nof the electron in the forward region at 50%.\nIn the region 2.5 < |\u03b7| < 3.2 the calorimeters used are the EMEC and the HEC and for |\u03b7| > 3.2 the\nforward calorimeter (FCal) is used. Note that we can not reconstruct the electron track in the forward\nregion (2.5 < |\u03b7| < 4.9) as the tracking system of ATLAS is limited to the region |\u03b7| < 2.5. In addition,\nthe forward calorimeters have a coarser granularity than the central ones (a factor 2 in both eta and phi\ndirections). Figure 13 shows the the ET distribution of electron for events with at least one electron in\nthe central region.\n (GeV)\nT\nelectron E\n20\n40\n60\n80\n100\n120\n140\n160\n180\nArbitrary unit\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\nATLAS\nFigure 13: The electron ET distribution for the\ncentral-forward events, normalized to unity.\n (GeV)\n(e+e-)\nT\nP\n0\n10\n20\n30\n40\n50\n60\nEntries\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\nC-C\nC-F\nATLAS\nFigure 14: Di-electron pT distribution for the\ncentral-central events (C-C) and the central-\nforward events (C-F).\nUsing the forward electrons we gain about 30% in the statistics as shown in \ufb01gure 14, where we\ncompare the di-electron pT distribution in the two analysis cases, C-C and C-F. Furthermore the value of\nthe asymmetry is higher in the C-F events. The expected numbers of the signal and background events\nof each process are shown in table 2 in the two analysis regions, C-C and C-F.\nEvent statistics corresponding to a 100 fb\u22121 would be required for this analysis to reach a very\nhigh precision on the determination of the weak mixing angle from the forward-backward asymmetry\nmeasurement. Nevertheless the measurement can be also made at low luminosity in order to test the\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n824\n\nconsistency with the Standard Model. This can be done as function of Me+e\u2212to enhance sensitivity to\npossible deviations at high mass scales.\n7.3\nAFB calculation\nThe forward-backward asymmetry is calculated according to Eqs 9 and 10.\nIf we assume that the distribution of NF and NB follows a binomial distribution, then the uncertainty\non the two quantities can be written as follows (which is valid only for small asymmetries): \u03c3NF = \u03c3NB =\n\u221aNFNB/\u221aNF +NB, and the AFB uncertainty is \u03c3AFB =\nq\n1\u2212A2\nFB\nN\n.\nSelection cut\nSignal\ndijet\nW+X\nt\u00aft\nC-C\nC1\n2.39802\u00d7107\n4741\n73312\n315178\nC2\n1.87808\u00d7107\n404\n6048\n28204\nC3\n7.31282\u00d7106\n144\n2212\n9937\nC4\n7.30496\u00d7106\n142\n205\n741\nC-F\nC1\n3.09742\u00d7107\n447408\n2764790\n336714\nC2\n2.41535\u00d7107\n35920\n172321\n29824\nC3\n1.26855\u00d7107\n35340\n168486\n11556\nC4\n1.25967\u00d7107\n35128\n15868\n864\nTable 2: Summary of expected number of C-C and C-F signal and background events for 100 fb\u22121 of\nintegrated luminosity. Results are given after the application of cuts C1-C4.\n8\nElectron charge identi\ufb01cation\nAny misidenti\ufb01cation of the electron charge dilutes the asymmetry. Where possible, the charge of both\nelectrons is measured and it is required that the signs differ. When both electrons are in the central re-\ngion both charges can be measured and the condition that they have opposite charges removes the events\nwhere the charge of one of the two electrons is misidenti\ufb01ed. In this case the forward-backward asym-\nmetry is not signi\ufb01cantly affected by charge misidenti\ufb01cation.\nThe situation is different when one electron is forward and the other central. Only the charge of the\ncentral electron can be measured. A misidenti\ufb01cation of the charge of the electron changes the sign of\ncos\u03b8 \u2217and a forward event may be taken as a backward one. This effect can be corrected for if the charge\nmisidenti\ufb01cation fraction is known.\nTo measure the charge misidenti\ufb01cation we use two methods:\n\u2022 MC method\nWe use the two electrons coming from Z and we count the number of events where the generated\ncharge (qgen) and reconstructed charge (qreco) of the individual electrons differ. We de\ufb01ne the\ncharge misidenti\ufb01cation fraction as follow:\nr = N(qreco \u0338= qgen)\nNtot\n.\n(16)\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n825\n\n\u2022 Tag and probe method\nThis method is used with the tag electron e1 having the tight electron requirements, pT >20 GeV\nand |\u03b7| < 1.5. The tag and probe electron pair must have a dielectron mass within \u00b16 GeV of MZ.\nThe rate at which the second electron e2 has the same charge gives an estimation of the charge\nmisidenti\ufb01cation fraction.\nThe true asymmetry can be deduced from the raw asymmetry using the relation:\nAFBtrue = AFB \u2212r+ +r\u2212\n1\u2212r+ \u2212r\u2212\n.\n(17)\nwhere r\u2212is the fraction of true e\u2212misidenti\ufb01ed as e+ and r+ is the fraction of true e+ misidenti\ufb01ed as\ne\u2212.\nFigure 15 shows the misidenti\ufb01cation fraction as function of the electron pseudo-rapidity obtained\nwith these two methods. The misidenti\ufb01cation fraction is small. The difference between the misidenti\ufb01-\ncation fraction for e+ and e\u2212is shown in \ufb01gure 16.\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nCharge misidentification rate\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\nMC\nTag and Probe\nATLAS\nFigure 15: Electron charge misidenti\ufb01cation\nfraction versus the electron pseudo-rapidity:\nData method of tag-and-probe measuring the\ncharge misidenti\ufb01cation fraction (open points),\nand Monte Carlo driven charge misidenti\ufb01ca-\ntion fraction (full points).\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n-\n - r\n+\nr\n-0.015\n-0.01\n-0.005\n0\n0.005\n0.01\n0.015\nATLAS\nFigure 16: The difference in charge misidenti-\n\ufb01cation fraction of positrons and electrons ver-\nsus the electron pseudo-rapidity.\n9\nEffect of pile-up\nPile-up originates from the fact that several pp collisions can occur during the same bunch crossing. This\ncauses extra activity in the detector and therefore in\ufb02uences the event selection. The effect of pile-up is\nassessed by superimposing additional events on top of the signal when events are simulated; hits from\nseveral bunch crossings are overlaid. In this study, pile-up events corresponding to 1033 cm\u22122 s\u22121 were\ninvestigated.\nThe pile-up affects the electron selection ef\ufb01ciency due to the presence of additional activity in the\nevents. Figure 17 displays the electron identi\ufb01cation ef\ufb01ciency with and without pile-up. We can see\nalso in Table 3 the summary of the results for the C-C and C-F events, after all selection cuts. The results\nshow a loss of about 3% of signal events.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n826\n\nC-C\nC-F\nNo pile-up\n7,304,960\n1.25967\u00d7107\nWith pile-up\n7,026,653\n1.217696\u00d7107\nTable 3: Number of expected events, at 100 fb\u22121, after all cuts, for the signal, and for C-C and C-F events.\nThe numbers are shown for the two cases: with and without pile-up. The reference pile-up luminosity\nused is 1033 cm\u22122 s\u22121.\n (GeV/c)\nT\nelectron p\n20\n40\n60\n80\n100\n120\nelectron ID efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nwithout pileup\nwith pileup\nATLAS\nFigure 17: Effect of pile-up on the electron identi\ufb01cation ef\ufb01ciency. The reference pile-up luminosity\nused is 1033 cm\u22122 s\u22121.\n10\nSystematic Uncertainties\nWe have considered several sources of systematic uncertainties. There are PDF uncertainties and experi-\nmental ones including the energy scale, energy resolution, reconstruction ef\ufb01ciency and the background\nestimation.\n10.1\nParton Distribution Functions\nSince the vector and axial vector couplings of the u and d quarks to the Z boson are different, the forward-\nbackward asymmetry is expected to depend on the ratio of the u and d quark parton distribution function.\nThus, the choice of the parton distribution functions (PDFs) will affect the measured lepton forward-\nbackward asymmetry.\nThe MRST PDF parametrization [6] is used to assess the uncertainty arising from the PDFs. Thirty\neigenvectors are used in this parametrization to indicate the effect of \u00b11\u03c3 variations. Figure 18 shows\nthe e+e\u2212asymmetry for each eigenvector. The deviation of AFB from the central value is of the same\norder of magnitude as the statistical accuracy.\nTo study the effect of the PDFs on the asymmetry, a PDF reweighting technique is used to reduce the\nneed for Monte Carlo generations and simulation. Thus, we generate the events with the best \ufb01t central\nvalue (PDF0) and then we reweight to PDFi of the set i by weighting each event via:\nfPDFi(x1,Q2, flav1).fPDFi(x2,Q2, flav2)\nfPDF1(x1,Q2, flav1).fPDF1(x2,Q2, flav2)\n(18)\nwhere x fPDF(x,Q2, flav) is the parton momentum distribution for \ufb02avour, flav, at scale, Q2, and mo-\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n827\n\nmentum fraction, x.\nMRST06 PDF set\n5\n10\n15\n20\n25\n30\nFB\nA\n0.023\n0.0235\n0.024\n0.0245\n0.025\n0.0255\n0.026\nATLAS\nFigure 18: The forward-backward asymmetry for each MRST eigenvector; the red star is the central\nvalue.\n10.2\nBackground subtraction\nThe determination of AFB (with real data) requires knowledge of the number of background events and\nthe forward-backward charge asymmetry of the background events. Thus the central value of AFB we\nshowed above can be obtained from the data events by subtracting the background events in the forward\nand backward regions separately from the raw forward-backward asymmetry. The number of back-\nground events estimated thus gives rise to a source of systematic uncertainties on AFB.\nThe systematic uncertainty is evaluated by varying the estimated numbers of background events by\n30%. The uncertainty value is taken as the shift in AFB. The largest shift is less than 0.01%.\n10.3\nDetector performance\nVarious effects due to uncertainties on the knowledge of the detector performance have to be taken into\naccount:\nEnergy scale\nThe electron energy scale uncertainty, which arises from calorimeter calibration uncer-\ntainties, affects the forward-backward asymmetry by causing a shift in the e+e\u2212invariant mass over\nwhich we integrate AFB. The effect is signi\ufb01cant in the Z-pole region as can be seen in Figure 1. To take\nthese effects into account, the central calorimeter scale is varied by 0.1% and the forward calorimeter\nscale is varied by 0.5% to estimate the systematic uncertainties. The positive and negative variations are\nconsidered separately and the largest shift is taken as the uncertainty.\nReconstruction ef\ufb01ciency\nThe impact of the uncertainties on the electron reconstruction in the AFB\nmeasurement can be estimated by removing 0.2% and 0.5% fraction of the reconstructed electrons in the\ncentral region and forward region respectively. These values used here are based on our study on the\nforward calorimeters reconstruction.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n828\n\nEnergy resolution\nThe forward backward asymmetry is sensitive to the variations in the energy res-\nolution. These variations are mainly due to the dead material distribution, known with an insuf\ufb01cient\naccuracy. To evaluate the impact of this contribution the central electron energy is degraded by an extra-\nterm 0.01 ET and the forward calorimeter energy by 0.05 ET.\nCharge identi\ufb01cation\nA systematic variation in charge misidenti\ufb01cation fraction would directly trans-\nlate into uncertainties of the forward-backward asymmetry. The systematic uncertainty is estimated by\ncomparing the measurement as performed as in the data (tag and probe method), to that using the true\nMonte Carlo. As it is shown in \ufb01gure 15 a difference of about 0.1% is observed.\nTable 4 reports all the systematic uncertainties at 100 fb\u22121. As expected, the dominant contribution\nto the overall uncertainty is from the PDF uncertainties.\nSource\n\u03b4AFB (abs)\n\u03b4 sin2 \u03b8\nlept\nef f (abs)\nEnergy scale\n2.7\u00d710\u22125\n1.5\u00d710\u22125\nReco. Eff.\n3.4\u00d710\u22125\n1.9\u00d710\u22125\nEnergy resol.\n1.9\u00d710\u22126\n1.1\u00d710\u22126\nCharge ID\n2.6\u00d710\u22125\n1.4\u00d710\u22125\nBackground subtraction.\n< 10\u22125\n< 10\u22125\nPDFs\n-\n\u22122.4\u00d710\u22124\n+1.3\u00d710\u22124\na and b parameters\n-\n3\u00d710\u22125\nStatistical error\n2.7\u00d710\u22124\n1.5\u00d710\u22124\nTable 4: Summary of the systematic and statistical uncertainties on AFB and sin2 \u03b8\nlept\nef f for events with at\nleast one electron in the central region (C-F). The uncertainty on sin2 \u03b8\nlept\nef f is determined using Eqs. 11\nand a and b parameters from \ufb01gure 21.\n11\nResults\nFigure 19 shows the dielectron invariant mass spectrum expected in terms of the number of events per\nGeV for an integrated luminosity of 100 fb\u22121 after the application of cuts C1, C3 and C4. The yellow\nhistogram corresponds to the signal contribution. The light blue displays the contributions from dijet\nevents. The green and violet histograms display the contribution of W + X and t\u00aft backgrounds respec-\ntively. The background contributions were obtained with MC samples with a fast detector simulation.\nThe signal contribution was obtained with a full detector simulation.\nTable 2 shows the expected number of background and signal events for 100 fb\u22121 of integrated\nluminosity after the application of cuts C1-C4. It indicates that the contribution from background events\nis at the level of 0.2%.\nIn Figure 20 we display the variation of the charge asymmetry versus the rapidity of the two elec-\ntrons. It is observed that the asymmetry increases when allowing the second electron to be up to |\u03b7| =\n4.9. Using |ye+e\u2212| >1 and going from C-C to C-F events, the integrated asymmetry increases from 1.3%\nto 2.7%. The precision on the forward-backward asymmetry improves from 3.7\u00d710\u22124 to 2.7\u00d710\u22124.\nUsing the parameters a = 0.23\u00b10.03 and b = 1.832\u00b10.255, of Eqs. 11, derived from the linear \ufb01t\nof the \ufb01gure 21, we can estimate the error expected for sin2 \u03b8\nlept\nef f from a measurement of the forward-\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n829\n\n)\n2\n (GeV/c\nee\nM\n50\n60\n70\n80\n90\n100\n110\n120\n130\n140\n150\n2\nEntries per 1 GeV/c\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n50\n60\n70\n80\n90\n100\n110\n120\n130\n140\n150\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n ee\n\u2192\n\u03b3\nZ/\nDijet Background\nW+X Background\n Background\ntt\nATLAS\nFigure 19: Dielectron invariant mass distribution for the signal and background events normalized to 100\nfb\u22121, with the \ufb01nal selection except that the cut C2 is removed.\n)\ne\n+\n(e\ny\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n (%)\nFB\nA\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\nC-C\nC-F\nATLAS\nFigure 20: Forward-backward asymmetry versus dielectron rapidity in the C-C events (open points) and\nin the C-F events (full points).\nbackward asymmetry at the Z pole, for an integrated luminosity of 100 fb\u22121:\n\u03b4 sin2 \u03b8\nlept\nef f = (1.5(stat)\u00b10.3(exp)\u00b12.4(PDF))\u00d710\u22124\n(19)\n12\nConclusion\nWe report on a detailed study of the forward-backward charge asymmetry AFB, at LHC with the AT-\nLAS detector, of electron pairs resulting from the process pp \u2192Z/\u03b3\u2217X \u2192e+e\u2212X. This measure-\nment provides a test of the Standard Model. In the vicinity of the Z-pole this measurement can be\nused to determine the effective weak mixing angle sin2 \u03b8\nlept\nef f . The precision on sin2 \u03b8\nlept\nef f obtained is\n\u03b4 sin2 \u03b8\nlept\ne f f = (1.5(stat) \u00b1 0.3(exp) \u00b1 2.4(PDF)) \u00d7 10\u22124 for a 12 GeV mass window around the Z mass,\nand 100 fb\u22121 of integrated luminosity. Electron identi\ufb01cation in the forward region (2.5 < |\u03b7| < 4.9) of\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n830\n\n-0.2315\neff\nept\n\u03b8\n2\nsin\n-0.5\n-0.4\n-0.3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\n0.5\n3\n10\n\u00d7\nFB\nA\n0.0245\n0.025\n0.0255\n0.026\n0.0265\n0.027\nFigure 21: Forward backward asymmetry AFB versus the weak mixing angle sin2 \u03b8 lept\nef f at the Z pole. The\nstraight line is a \u03c72 \ufb01t to the points shown. Fast simulated events are used.\nthe ATLAS detector is very important for the measurement. In this region an electron ID ef\ufb01ciency of\n80% is achieved with less than 3% QCD background.\nThe main systematic effects relevant for forward-backward asymmetry measurements with 100 fb\u22121\nof data are addressed, including systematic uncertainties on detector effects and MRST PDF uncertainty.\nAn advanced technique was developed and used to estimate the error due to the PDF uncertainties. This\nstudy showed that the uncertainty in the weak mixing angle determination due to PDF\u2019s is of the same\norder as the measurement statistical error, which means that the precision on the weak mixing angle\nat LHC can be competitive to the current world average. In addition we expect that in the future the\nknowledge of the PDF\u2019s will improve from the constraints imposed by Tevatron, HERA and \ufb01rst LHC\nmeasurements (e.g. using W asymmetry), and the systematic uncertainty due the uncertainty in the\nPDF\u2019s should decrease by the time ATLAS high luminosity data is available. If this is not the case, the\nasymmetry measurements can be used, conversely, to constrain the parton distribution functions.\nReferences\n[1] Particle Data Group, J. Phys. G33, 1 (2006).\n[2] S. D. Drell and T.-M. Yan, Phys. Rev. Lett. 25, 316 (1970).\n[3] S. D. Drell and T.-M. Yan, Ann. Phys. 66, 578 (1971).\n[4] S. Jadach and Z. Was, CERN report 89-09 (1989).\n[5] P. Langacker et al., Phys. Rev. D30 (1984) 1470.\n[6] MRST Collaboration, Phys. Lett. B652, 292 (2007).\n[7] J. L. Rosner, Phys. Lett. B. 221, 85 (1989).\n[8] J. L. Rosner, Phys. Rev. D 35, 2244 (1987).\n[9] J. L. Rosner, Phys. Rev. D 54, 1078 (1996).\n[10] ATLAS Collaboration, The ATLAS experiment at the CERN Large Hadron Collider, JINST 3 (2008)\nS08003.\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n831\n\n[11] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[12] H. B. Prosper, Prepared for Conference on Advanced Statistical Techniques in Particle Physics,\nDurham, England, 18-22 Mar 2002.\n[13] T. Sj\u00a8ostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[14] CTEQ Collaboration, J. Huston et al., Phys. Rev. D51, 6139 (1995).\n[15] S. Agostinelli et al, GEANT4 : A Simulation Toolkit, Nuclear Instruments and Methods in Physics\nResearch, Nucl. Instr. Meth. A 506 (2003), 250-303.\n[16] E. Richter-Was et al., internal note, ATL-PHYS-98-131 (1998).\n[17] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[18] J. C. Collins and D. E. Soper, Phys. Rev. D 16, 2219 (1977).\n[19] M. Aharrouche, PhD thesis, CERN-THESIS-2007-027 (2006).\nSTANDARD MODEL \u2013 FORWARD-BACKWARD ASYMMETRY IN pp \u2192Z0/\u03b3 \u2192e+e\u2212EVENTS\n832\n\nDiboson Physics Studies\nAbstract\nThis note presents studies of the sensitivity of the ATLAS experiment to Stan-\ndard Model diboson (W +W \u2212, W \u00b1Z, ZZ, W \u00b1\u03b3, and Z\u03b3) production in pp\ncollisions at \u221as = 14 TeV, using \ufb01nal states containing electrons, muons and\nphotons. The studies use ATLAS simulated data, which include trigger in-\nformation and detector calibration and alignment corrections. The in\ufb02uence of\nbackgrounds on diboson detection is assessed using large samples of fully sim-\nulated background events. The cross-section measurement uncertainties (both\nstatistical and systematic) are estimated as a function of integrated luminos-\nity (from 0.1 to 30 fb\u22121). The studies show that the Standard Model W +W \u2212,\nW \u00b1Z, W \u00b1\u03b3, and Z\u03b3 signals can be established with signi\ufb01cance better than\n5\u03c3 for the \ufb01rst 0.1 fb\u22121 of integrated luminosity, and the ZZ signal can be\nestablished with 1 fb\u22121 of integrated luminosity. The ATLAS experiment\u2019s\nsensitivity to anomalous triple gauge boson couplings is also estimated. The\nanomalous triple gauge boson coupling sensitivities can be signi\ufb01cantly im-\nproved, even with 0.1 fb\u22121 of data, over the results from the Tevatron that use\n1 fb\u22121 of data.\n1\nIntroduction\nThis paper presents studies of the ATLAS experiment\u2019s sensitivity to diboson (W +W \u2212, W \u00b1Z, ZZ, W \u00b1\u03b3,\nZ\u03b3) production using lepton and photon \ufb01nal states, and the corresponding ability to set limits on anoma-\nlous triple gauge boson couplings (TGC). The analysis of diboson production at the LHC provides an\nimportant test of the high energy behavior of electroweak interactions. Vector boson self-couplings\nare fundamental predictions of the Standard Model [1], resulting from the non-Abelian nature of the\nSU(2)L\u00d7U(1)Y gauge symmetry theory, which was demonstrated by precision measurements of W +W \u2212\nand ZZ pair production at LEP II [2].\nAny theory predicting physics beyond the Standard Model while maintaining the Standard Model\nas a low-energy limit may introduce deviations in the gauge couplings at some high energy scale. Pre-\ncise measurements of the couplings will not only provide stringent tests of the Standard Model, but will\nalso probe for new physics in the bosonic sector. These tests will provide complementary information\nto other direct searches for new physics at the LHC. Many models predict deviations of vector boson\nself-couplings from the Standard Model at the 10\u22123 \u221210\u22124 level [3]. Experiments that can reach this\nsensitivity could provide powerful constraints on these models. The signature for such anomalous cou-\nplings is enhanced diboson production cross-sections, particularly at high transverse momentum (pT) of\nthe bosons. Experimental limits on non-Standard Model TGC\u2019s can be obtained by comparing the shape\nof the measured pT or mass distributions (or transverse mass, MT, for \ufb01nal states involving W) with\npredictions, provided that the signal is not overwhelmed by background.\nThe analysis uses over 30 million fully simulated and reconstructed events, with a detector layout\nand trigger system that re\ufb02ects the ATLAS experiment as it will operate at LHC turn-on at 14 TeV\ncenter of mass energy, thus providing a realistic understanding of the detection of these diboson \ufb01nal\nstates. A Boosted Decision Tree [4] technique is applied to selected channels, signi\ufb01cantly enhancing\nmeasurement sensitivities. These are among the ways this study improves on our understanding and the\nresults of the previous ATLAS diboson studies [5]- [10].\n833\n\n1.1\nDiboson production cross-sections\nTree-level Feynman diagrams for electroweak diboson production at hadron colliders are shown in Fig-\nure 1. The s-channel diagram contains the vector-boson self-interaction vertices of interest here. The\ncross-sections are calculated to next-to-leading-order (NLO) in [11]- [13]. The Standard Model diboson\nproduction cross-sections are listed in Table 1.\n\u00afq\nq\nV1\nV2\n\u00afq\nq\nV2\nV1\nV\n\u00afq\nq\nV1\nV2\nTGC vertex\nt-channel\nu-channel\ns-channel\nFigure 1: The generic Standard Model tree-level Feynman diagrams for diboson production at hadron\ncolliders; V,V1,V2 = {W,Z,\u03b3}. The s-channel diagram contains the trilinear gauge boson vertex. In the\nStandard Model, only WW\u03b3 and WWZ vertices are allowed.\nTable 1: The Standard Model diboson production total cross-sections, calculated to the NLO, at the Teva-\ntron (\u221as = 1.96 TeV) and the LHC (\u221as = 14 TeV). The references in the \ufb01rst column indicate the MC\ngenerators used for the calculations, with parton density function (PDF) CTEQ6M and the electroweak\nparameters [14]. The theoretical uncertainty from the PDF and the QCD scale factor is typically 5%.\nDiboson mode\nConditions\n\u221as = 1.96 TeV\n\u221as = 14 TeV\n\u03c3[pb]\n\u03c3[pb]\nW +W \u2212[15]\nW-boson width included\n12.4\n111.6\nW \u00b1Z [15]\nZ and W on mass shell\n3.7\n47.8\nZZ [15]\nZ\u2019s on mass shell\n1.43\n14.8\nW \u00b1\u03b3 [16]\nE\u03b3\nT > 7 GeV, \u2206R(\u2113,\u03b3) > 0.7\n19.3\n451\nZ\u03b3 [17]\nE\u03b3\nT > 7 GeV, \u2206R(\u2113,\u03b3) > 0.7\n4.74\n219\nThe LHC diboson production rates will exceed those of the Tevatron by at least a factor 100 (10\ntimes higher in cross-sections and at least 10 times higher in luminosity). Furthermore, because the\nenergy reach at the LHC will be 7 times higher than at the Tevatron, the LHC sensitivity to anomalous\nTGC\u2019s is expected to be improved by orders of magnitude over that which can be reached at the Tevatron\nor LEP.\n1.2\nEffective Lagrangian for charged TGC\u2019s\nThe most general effective Lagrangian, that conserves C and P separately, for charged triple gauge boson\ninteractions is [19]:\nL/gWWV = igV\n1 (W \u2217\n\u00b5\u03bdW \u00b5V \u03bd \u2212W\u00b5\u03bdW \u2217\u00b5V \u03bd)+i\u03baVW \u2217\n\u00b5W\u03bdV \u00b5\u03bd + \u03bbV\nM2\nW\nW \u2217\n\u03c1\u00b5W \u00b5\n\u03bd V \u03bd\u03c1\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n834\n\nwhereV refers to the neutral vector-bosons, Z or \u03b3, X\u00b5\u03bd \u2261\u2202\u00b5X\u03bd \u2212\u2202\u03bdX\u00b5 and the overall coupling constants\ngWWV are given by gWW\u03b3 = \u2212e, gWWZ = \u2212e cot\u03b8W, with e the positive electron charge and \u03b8W the weak\nmixing angle. The Standard Model triple gauge boson vertices are recovered by letting gV\n1 = \u03baV = 1\nand \u03bbV = 0. Experimentally, deviations from the Standard Model couplings is searched for; thus the\nanomalous coupling parameters are de\ufb01ned as\n\u2206gZ\n1 \u2261gZ\n1 \u22121,\n\u2206\u03ba\u03b3 \u2261\u03ba\u03b3 \u22121,\n\u2206\u03baZ \u2261\u03baZ \u22121,\n\u03bb\u03b3,\nand \u03bbZ.\nNote that electromagnetic gauge invariance requires g\u03b3\n1 = 1 or \u2206g\u03b3\n1 = 0.\nStudies of three different diboson \ufb01nal states, W +W \u2212, W \u00b1Z and W \u00b1\u03b3 will provide complementary\nsensitivities to the charged anomalous TGC\u2019s [17]. For example, the \u2206\u03baV terms in W +W \u2212production are\nproportional to \u02c6s, de\ufb01ned as the square of invariant mass of the vector-boson pair, whereas these terms\nare only proportional to\n\u221a\n\u02c6s in W \u00b1Z and W \u00b1\u03b3 production. W +W \u2212production is thus expected to be more\nsensitive to \u2206\u03baV than W \u00b1Z and W \u00b1\u03b3 production. Conversely, W \u00b1Z production is expected to be more\nsensitive to \u2206gZ\n1 than W +W \u2212production because terms in \u2206gZ\n1 are proportional to \u02c6s in W \u00b1Z production.\nThe \u03bb-type anomalous couplings have an \u02c6s dependence in all three cases, thus the sensitivities will be\nenhanced at the high center-of-mass energy of the LHC.\nWith non-Standard Model coupling parameters, the amplitudes for gauge boson pair production grow\nwith energy, eventually violating tree-level unitarity. The unitarity violation is avoided by introducing an\neffective cutoff scale, \u039b [18]. The anomalous couplings take a form, for example,\n\u2206\u03ba(\u02c6s) =\n\u2206\u03ba\n(1+ \u02c6s/\u039b2)n ,\nwhere \u2206\u03ba is the coupling value in the low energy limit. The scale \u039b is physically interpreted as the mass\nscale where the new phenomenon, which is responsible for the anomalous couplings, would be directly\nobservable. The value of n = 2 is used for charged anomalous TGC, and n = 3 for neutral anomalous\nTGC.\n1.3\nEffective Lagrangian for neutral TGC\u2019s\nIn the Standard Model, neutral boson pairs, ZZ and Z\u03b3, are produced via the t-channel diagrams shown\nin Figure 1. While the Standard Model ZZZ and ZZ\u03b3 triple gauge boson couplings are zero at tree level,\nanomalous couplings may contribute. This study considers the effect of anomalous couplings on the pro-\nduction of pairs of on-shell Z bosons only. In this case, the most general form of the Z\u03b1(q1)Z\u03b2(q2)V \u00b5(P)\n(V = Z, \u03b3) vertex function which respects Lorentz invariance and electromagnetic gauge invariance may\nbe written as [20]\ngZZV\u0393\u03b1\u03b2\u00b5\nZZV = eP2 \u2212M2\nV\nM2\nZ\n[ ifV\n4 (P\u03b1g\u00b5\u03b2 +P\u03b2g\u00b5\u03b1)+i fV\n5 \u03b5\u00b5\u03b1\u03b2\u03c1(q1 \u2212q2)\u03c1 ]\nwhere MZ is the Z-boson mass and e is the positive electron charge; q1,q2 and P are the 4-momenta of the\ntwo on-shell Z bosons and the s-channel propagator, respectively. The effective Lagrangian generating\nthe gZZV vertex function is\nL = \u2212e\nM2\nZ\n[fV\n4 (\u2202\u00b5V \u00b5\u03b2)Z\u03b1(\u2202\u03b1Z\u03b2)+ fV\n5 (\u2202\u03c3V\u03c3\u00b5) \u02dcZ\u00b5\u03b2Z\u03b2],\nwhere V\u00b5\u03bd = \u2202\u00b5V\u03bd \u2212\u2202\u03bdV\u00b5 and \u02dcZ\u00b5\u03b2 = 1\n2\u03b5\u00b5\u03bd\u03c1\u03c3Z\u03c1\u03c3. The couplings fV\ni (i = 4, 5) are dimensionless com-\nplex functions of q2\n1, q2\n2 and P2 and are zero at tree level. All couplings are C odd; CP invariance forbids\nfV\n4 , while parity conservation requires that fV\n5 vanishes. Because f Z\n4 and f \u03b3\n4 are CP-odd, contributions\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n835\n\nto the helicity amplitudes proportional to these couplings will not interfere with the Standard Model\nterms, and hence ZZ production is not sensitive to the sign of these couplings. The CP conserving cou-\nplings fV\n5 contribute to the Standard Model cross-section at the one-loop level, but this contribution is\nO(10\u22124) [20].\n1.4\nCurrent Tevatron results on diboson physics\nDiboson production measurements and studies of anomalous TGC\u2019s have been performed at the Tevatron\nwith the CDF and D0 experiments, using up to 2 fb\u22121 of integrated p \u00afp luminosity. Diboson cross-section\nmeasurements using e/\u00b5 decay modes, and their event statistics, measurement precision, and background\nevents are summarized in Table 2. The measurments from Tevatron experiments are consistent with the\nStandard Model predictions based upon NLO matrix element calculations.\nTable 2: Summary of Tevatron p \u00afp \u2192diboson cross-sections. For the W +W \u2212, W \u00b1Z, and ZZ channels\ntotal production cross-sections are quoted.\nProcess\nSource\nL\nobserved\nbackground\n\u03c3(data) [pb]\n\u03c3(theory)\nfb\u22121\nevents\nevents\n\u00b1 (stat)\u00b1(sys)\u00b1(lum)\n[pb]\nW +W \u2212\nCDF [21]\n0.83\n95\n38\u00b15\n13.6\u00b12.3\u00b11.6 \u00b1 1.2\n12.4\u00b10.8\n(ee, \u00b5\u00b5, e\u00b5)\nD0 [22]\n0.25\n25\n8.1\u00b1.5\n13.8\u00b14.1\u00b11.1 \u00b1 0.9\n\u201d\nW \u00b1Z\nCDF [23]\n1.1\n16\n2.7\u00b10.4\n5.0+1.8\n\u22121.4 \u00b10.4\n3.7\u00b10.3\n(\u2113\u00b1\u03bd\u2113+\u2113\u2212)\nD0 [24]\n1.0\n13\n4.5\u00b10.6\n2.7 +1.7\u22121.3 (total)\n\u201d\nZ\u03b3\nCDF [25]\n0.2\n72\n4.9\u00b11.1\n4.6 \u00b10.6 (sta+sys) \u00b1 0.3\n4.5\u00b10.3\n(\u2113+\u2113\u2212\u03b3)\nD0 [26]\n1.0\n968\n117\u00b112\n4.96 \u00b10.3 (sta+sys) \u00b1 0.3\n4.7\u00b10.2\nW \u00b1\u03b3\nCDF [25]\n0.2\n323\n114\u00b121\n18.1 \u00b13.1 (sta+sys) \u00b1 1.2\n19.3\u00b11.4\n(\u2113\u00b1\u03bd\u03b3)\nD0 [27]\n0.16\n273\n132\u00b17\n14.8 \u00b11.9 (sta+sys) \u00b1 1.0\n16.0\u00b10.4\nZZ\nCDF [28]\n1.9\n2\n0.014\n1.4+0.7\n\u22120.6\u00b10.6\n1.5\u00b10.2\n(\u2113+\u2113\u2212\u2113+\u2113\u2212)\nD0 [29]\n1.0\n1\n0.13\n< 4.4\n\u201d\nThe Tevatron\u2019s p \u00afp collisions produce the charged states of W \u00b1Z and W \u00b1\u03b3. These states can be used\nto study the W +W \u2212Z and the W +W \u2212\u03b3 couplings independently, which is in contrast with the anomalous\nTGC measurements made at LEP [32] from the W +W \u2212\ufb01nal state, where certain assumptions relating the\nW +W \u2212Z and the W +W \u2212\u03b3 couplings were made. The Tevatron limits for the WW\u03b3 and WWZ anomalous\nTGC\u2019s are summarized in Table 3. These limits will improve signi\ufb01cantly by combining the constraints\nfrom the W \u00b1\u03b3, W \u00b1Z and W +W \u2212channels, and by increasing the datasets using the expected integrated\nluminosity of 6 fb\u22121 at the end of the Tevatron running.\n2\nSignal and background modeling and simulated data samples\n2.1\nMC generators used to produce fully simulated events\nThe diboson physics analyses focus on leptonic decay channels of the boson pairs (W +W \u2212, W \u00b1Z, ZZ,\nW \u00b1\u03b3, and Z\u03b3) produced in the proton-proton collisions at the LHC.\nDiboson productions of the W +W \u2212, W \u00b1Z, and ZZ \ufb01nal states, as well as the subsequent pure lep-\ntonic decays, are modeled by the MC@NLO [15] Monte Carlo generator. The generator incorporates the\nnext-to-leading-order (NLO) QCD matrix elements into the parton shower by interfacing to the HER-\nWIG/Jimmy [33] programs. A branching ratio of 0.0336 for Z \u2192\u2113+\u2113\u2212and 0.108 for W + \u2192\u2113+\u03bd is used\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n836\n\nTable 3: Anomalous gauge coupling limits (95% C.L.) for WW\u03b3 and WWZ from the Tevatron experi-\nments, with \u039b = 2 TeV.\nCoupling\nSource\nL (fb\u22121)\n\u03bbZ\n\u2206\u03baZ\n\u2206\u03ba\u03b3\n\u03bb\u03b3\nWW\u03b3 from W \u00b1\u03b3\nD0 [27]\n0.16\n[-0.88, 0.96]\n[-0.2, 0.2]\nWWZ from W \u00b1Z\nD0 [24]\n1.0\n[-0.17, 0.21]\n[-0.12, 0.29]\nWWZ from W \u00b1Z\nCDF\n1.9\n[-0.13, 0.14]\n[-0.82, 1.27]\nWWZ = WW\u03b3\nfrom W +W \u2212\nD0 [30]\n0.25\n[-0.31, 0.33]\n[-0.36, 0.33]\nfrom W +W \u2212, W \u00b1Z\nCDF [31]\n0.35\n[-0.18, 0.17]\n[-0.46, 0.39]\nfor each lepton \ufb02avor (e, \u00b5, \u03c4). The gauge-boson decays into tau leptons are included in the MC event\ngenerator and these tau leptons decay to all the possible \ufb01nal states. Hard emission is treated as in NLO\ncomputations and soft/collinear emission is treated as in a regular parton shower MC. The matching be-\ntween these two regions is smooth (no double-counting). W-boson width and spin-spin correlations are\nincluded in the generator. However, \u2018zero-width\u2019 approximations are used in W \u00b1Z and ZZ calculations,\nand no Z/\u03b3\u2217interference terms are included. MC@NLO does not include anomalous triple gauge boson\ncouplings. The process of W +W \u2212production via gluon-gluon fusion and the leptonic decays of the W,\ngg \u2192W +W \u2212\u2192\u2113\u03bd\u2113\u2032\u03bd, is modeled by the MC generator GG2WW [34]. The W \u00b1\u03b3 and the Z\u03b3 produc-\ntion processes and subsequent leptonic decays of the W \u00b1 and the Z are modeled by the PYTHIA MC\ngenerator [35], which only incorporates the leading-order (LO) QCD matrix elements into the parton\nshower. To include the off-shell Z and \u03b3\u2217into the ZZ analysis, we have also used PYTHIA to generate\nthe Z/\u03b3\u2217+Z/\u03b3\u2217\u2192\u2113+\u2113\u2212\u2113\u2032+\u2113\u2032\u2212events. The Z/\u03b3\u2217mass threshold is set to 12 GeV in PYTHIA. Table 4\nlist all the diboson signal samples used in this paper.\nMajor physics backgrounds for diboson signal detection come from top pairs and hadronic jets as-\nsociated with W or Z gauge bosons. We have used MC@NLO to model t\u00aft \u2192\u2113+ X production (700k\nevents). The inclusive W + X and Z + X (X = jets, or \u03b3) processes are modeled by the PYTHIA (30M\nevents) and ALPGEN [36] (1.1M events).\nWhenever LO event generators are used, the cross-sections are corrected to NLO by using k-factors\nfrom NLO matrix element calculations to normalize the expected signal and background events.\n2.2\nMC generators for TGC studies\nMonte Carlo generators BosoMC [16] and BHO [17] are used for anomalous TGC studies. These MC\nprograms are numerical parton level generators. They are used to calculate both LO and NLO cross-\nsections for all \ufb01ve diboson \ufb01nal states (W +W \u2212, W \u00b1Z, ZZ, W \u00b1\u03b3, Z\u03b3) with anomalous coupling pa-\nrameters. However, they do not include parton showers automatically. We use the BHO MC to model\nthe ZZ, W +W \u2212, and Z\u03b3 production cross-sections and kinematics with Standard Model and anomalous\ncouplings. BosoMC is used for W \u00b1Z and W \u00b1\u03b3 diboson \ufb01nal-state TGC studies. The calculated dibo-\nson production rates from these generators are accurate to NLO. The W +W \u2212, W \u00b1Z and ZZ production\ncalculations with the Standard Model couplings are compared with the MC@NLO calculations using\nPDF CTEQ6M. We found that both cross-sections and kinematic distributions are in good agreement, as\nshown in Figure 2. The left plot shows the W \u00b1Z production differential cross-section as a function of\nthe transverse mass of the W \u00b1Z system. The right plot shows the W +W \u2212production differential cross-\nsection as a function of the W transverse momentum. The discrepancies between MC@NLO and the\nBHO MC are within 2%.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n837\n\nTable 4: Diboson signal production processes, cross-sections including branching ratios of W/Z leptonic\ndecays and fully simulated number of MC events. The MC simulation \u2018\ufb01lter\u2019 is the event selection at\nthe generator level. The corresponding \ufb01lter ef\ufb01ciencies are given in the table. We also indicate the MC\ngenerators used to produce the MC events and to calculate the cross-sections given in this table.\nProcess\ncross-section (fb)\n\u03b5\ufb01lter\nNMC\nGenerator\nq \u00afq\u2032 \u2192W +W \u2212\u2192\u2113+\u03bd\u2113\u2212\u03bd\n11718\n1.0\n180,000\nMC@NLO\ngg \u2192W +W \u2212\u2192\u2113+\u03bd\u2113\u2212\u03bd\n540.0\n0.96\n180,000\nGG2WW\n(\u2113= e, \u00b5, \u03c4)\nq \u00afq\u2032 \u2192W +Z \u2192\u2113+\u03bd\u2113+\u2113\u2212\n441.7\n1.0\n50,000\nMC@NLO\nq \u00afq\u2032 \u2192W \u2212Z \u2192\u2113\u2212\u03bd\u2113+\u2113\u2212\n276.4\n1.0\n50,000\nMC@NLO\n(\u2113= e, \u00b5; Z on mass shell)\nq \u00afq\u2032 \u2192ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212\n66.8\n1.0\n49,250\nMC@NLO\nq \u00afq\u2032 \u2192ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd\n397\n1.0\n118,000\nMC@NLO\n(\u2113= e, \u00b5; Z on mass shell)\nq \u00afq\u2032 \u2192ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212\n159\n0.219\n43,000\nPYTHIA\n(\u2113= e, \u00b5, \u03c4; MZ/\u03b3\u2217> 12 GeV )\n(4 leptons (e, \u00b5), p\u2113\nT > 5 GeV, |\u03b7\u2113| < 2.7)\nq \u00afq\u2032 \u2192W +\u03b3 \u2192\u2113+\u03bd\u03b3\n10220\n1.0\n38,400\nPYTHIA\nq \u00afq\u2032 \u2192W \u2212\u03b3 \u2192\u2113\u2212\u03bd\u03b3\n6820\n1.0\n25,600\nPYTHIA\n(\u2113= e, \u00b5; E\u03b3\nT > 10 GeV )\nq \u00afq\u2032 \u2192Z\u03b3 \u2192\u2113+\u2113\u2212\u03b3\n5280\n1.0\n66,000\nPYTHIA\n(\u2113= e, \u00b5; E\u03b3\nT > 10 GeV )\nA somewhat different procedure is used in the estimation of neutral triple gauge couplings from\nZZ events. In this case, the signal expectation with anomalous couplings was determined from the\nleading order Monte Carlo calculation of BHO, corrected using a pT dependent k-factor derived from\nMC@NLO.\n3\nDiboson event selection\nThis section discusses features of \ufb01ve diboson signals, (W \u00b1Z, W \u00b1\u03b3, W +W \u2212, Z\u03b3, ZZ), the major back-\ngrounds and the analysis cuts required to discriminate between them. The varied event topolology of\neach diboson signal precludes a common set of universal cuts. Two analysis approaches are employed.\nThe \ufb01rst is based on a sequence of straight cuts on kinematic quantities. The second is a re\ufb01ned, multi-\nvariate analysis based on Boosted Decision Tree (BDT) which is brie\ufb02y described in Section 3.2 . Some\nof the diboson analyses employ both techniques. The major results of these analyses are included here.\n3.1\nPhysics objects\nThe ATLAS detector and its performance is described in detail elsewhere [37]. A brief description of the\nphysics objects used in diboson analysis is given below.\nThe major physics objects used in diboson physics analysis are electrons, photons, muons, missing\nET (/ET), and hadronic jets. Electrons are identi\ufb01ed by their distinctive pattern of energy deposition in\nthe calorimeter and by the presence of a track in the inner tracker that can be extrapolated from the\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n838\n\nMCAtNLO\nBosoMC(BHO)\nMT(W+Z)(GeV)\nd\u03c3/dMT(fb/10GeV)\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\n10\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nMCAtNLO\nBHO\nW+ PT(GeV)\nd\u03c3/dPT(fb/10GeV)\n10\n-3\n10\n-2\n10\n-1\n1\n10\n10 2\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nFigure 2: Comparison of MC@NLO MC to BHO MC for W \u00b1Z and W +W \u2212production. The histograms\nare normalized to production cross-sections. Left plots: the W \u00b1Z MT distribution from W \u00b1Z production.\nRight plots: the W + pT distribution from W +W \u2212production.\ninteraction vertex to a cluster of energy in the calorimeter. To ensure high trigger ef\ufb01ciency, for events\nwith a single electron, the transverse energy of an single electron must satisfy ET > 25 GeV. For events\nwith dielectrons, both electrons are required to have ET > 10 GeV. The electrons must be isolated from\nother energy clusters. An electron is required to pass a set of cuts on shower shape, track quality and track\nto calorimeter cluster matching. Photon identi\ufb01cation is similar to an electron in the EM calorimeter,\nbut no charged tracks in the inner tracker should match the EM energy cluster. The average electron\nidenti\ufb01cation ef\ufb01ciency in the barrel is about 75% and in the endcaps about 60%.\nMuons are reconstructed using information from the outer muon spectrometer (MDT chambers and\ntrigger chambers), the inner tracking detectors and the calorimeters. Muons are identi\ufb01ed with a tracking\nalgorithm that associates a track found in the muon spectrometer with the corresponding inner detector\ntrack, after the former is corrected for energy loss in the calorimeter. The combined muon detection\nrapidity coverage is |\u03b7| < 2.5. The minimum pT of reconstructed muon track is 5 GeV. The candidate\nmuons are required to be isolated in the calorimeter and inner tracker to minimize the contributions of\nmuons originating from hadronic jets. The average muon identi\ufb01cation ef\ufb01ciency is about 95%.\nThe hadronic jets are reconstructed using the \ufb01xed-cone jet algorithm. The cone size used in this\nanalysis is 0.7. The jet seed threshold on the transverse energy in a tower is set to Es = 1 GeV, and the\n\ufb01nal energy cut on a jet is ET > 7 GeV. With this cut the minimum measurable jet ET should be 20 GeV.\nMissing transverse energy, /ET, is calculated from the energy deposited in all calorimeter cells and\nfrom muons. A correction is applied for the energy lost in the cryostat. For diboson events with neutrinos\nin \ufb01nal states, the /ET resolution we found to be 6.5 GeV based on our studies using Z \u2192\u2113+\u2113\u2212MC events.\nThe ATLAS trigger consists of three levels of event selection: Level-1 (L1), Level-2 (L2) and the\nevent \ufb01lter (EF). The L2 and EF together form the High-Level Trigger (HLT). According to the present\nphysics trigger menu for initial running, diboson candidate events with multi-lepton \ufb01nal states will be\nrecorded with single muon, single electron, dielectron and dimuon triggers. The trigger ef\ufb01ciencies\nfor diboson events, de\ufb01ned as the fraction of events accepted by the analysis cuts that have satis\ufb01ed\nthe trigger requirements, are expected to be in a range of 95% - 100%, with the exception of a lower\nef\ufb01ciency (\u223c80%) for W\u03b3 events. The events that are accepted by the trigger are used for the analysis\nresults.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n839\n\n3.2\nBoosted Decision Trees\nA rather new multivariate analysis technique, Boosted Decision Tree, has been used in our analysis to\nimprove the detection sensitivity for diboson signals. BDTs have been used in HEP data analysis in\nrecent years [38], and details can be found in the Ref. [4]. A further development, allowing for weighted\nevents, is used in these diboson physics studies [39].\nThe BDT technique involves a fast \u2019training\u2019 procedure for event pattern recognition. It works with\na set of data including both signal and background. Data are represented by a set of physics variable\ndistributions. A decision-tree splits data recursively based on cuts on the input variables until a stopping\ncriterion is reached. Every event ends up in a signal (score=1) or a background (score=-1) leaf of the\ndecision-tree. Misclassi\ufb01ed events will be given larger weights in the next tree (boosting). This procedure\nis repeated several hundreds to thousands of times until the performance is optimal. The discriminator\nfrom the BDT training is the sum of the weighted scores from all the decision-trees. If the total score for\na given event is relatively high this event is most likely a signal event, and if the score is low it is likely a\nbackground event.\n3.3\nW \u00b1Z \u2192\u2113\u00b1\u03bd\u2113+\u2113\u2212selection\nThe W \u00b1Z production at hadron colliders uniquely probes the WWZ trilinear gauge boson coupling as\nshown in Figure 1, the Standard Model tree-level Feynman diagrams.\nW \u00b1Z candidate events have three charged lepton \ufb01nal states, referred to as trileptons, produced when\nZ \u2192\u2113+\u2113\u2212and W \u00b1 \u2192\u2113\u00b1\u03bd, where \u2113\u00b1 are e\u00b1 or \u00b5\u00b1. Standard Model backgrounds can be highly sup-\npressed by requiring three isolated high pT leptons and large missing transverse energies (/ET). However,\nthe pure leptonic decay mode of the W \u00b1Z events only has a 1.5% branching ratio [2]. The total cross-\nsections times the branching ratio are 442 fb and 276 fb for W +Z and W \u2212Z, respectively. Event selection\nwith high ef\ufb01ciency is important for early observations of this channel.\nMajor backgrounds to the W \u00b1Z trilepton \ufb01nal states come from ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212with one lepton\nundetected; Z + X \u2192\u2113+\u2113\u2212+ X (X=jets, or photon) with a jet or a photon faking a lepton; and t\u00aft \u2192\nW +W \u2212b\u00afb \u2192\u2113+\u2113+\u2113+X.\nAfter a trigger, W \u00b1Z events are selected in two stages: (1) pre-selection with relatively loose cuts,\nand (2) \ufb01nal selection with tightened cuts or with BDT multivariate discriminator. The overall trigger\nef\ufb01ciency for W \u00b1Z events with trileptons in the \ufb01nal state is (98.9\u00b1 1.0)% using a combination of single\nlepton and dilepton triggers.\nThe pre-selection of the W \u00b1Z events is done by identifying three leptons (at least one lepton with\npT > 25 GeV) and requiring /ET > 15 GeV in an event with characteristics consistent with Z dilepton\ndecays (M\u2113\u2113= (91.18\u00b120) GeV) and W leptonic decays (10 GeV < MT(\u2113, /ET) < 400 GeV). The overall\npre-selection ef\ufb01ciency for W +Z events is 26%, and for W \u2212Z events is 29%. The acceptance difference\nis due to the differing \u03b7 distributions of the leptons decaying from W + and W \u2212. After the preselection,\nthe known background is about 70 times larger than the signal.\nTo bring the background level below the signal, a rejection power better than 100 in the second stage\nof event selections is required. To achieve this, events with /ET < 25 GeV and with signi\ufb01cant hadronic\njet activities are rejected. Events must contain no more than one hadronic jet with E jet\nT\n> 30 GeV and\n|\u03b7 jet| < 3.0. The transverse recoil of the W \u00b1Z system, calculated using the vector sum of the pT\nof\nthe charged leptons and /ET, is required to be less than 120 GeV and the sum of the hadronic transverse\nenergy must be less than 200 GeV. These requirements effectively reject the t\u00aft and hadronic jet events.\nTo reject the Z + X background, the third lepton (not from the Z boson decay) pT\nis required to be\ngreater than 20 GeV and 25 GeV for muons and electrons, respectively. Any pair of leptons must satisfy\n\u2206R =\np\n(\u2206\u03b72 +\u2206\u03c6 2) > 0.2. Leptons must be isolated from other energy clusters based on calorimeter\nand inner tracker measurements. All three leptons must be associated with isolated tracks that originate\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n840\n\nTable 5: Number of expected W \u00b1Z signal (NWZ) and background (NB) for 1 fb\u22121 data with cut-based\nanalysis.\nWZ\nZZ\nt\u00aft\nZ +jet\nZ +\u03b3\nDrell-Yan\nTotal bkg\nNWZ/NB\nN events\n53\n2.7\n.023\n1.9\n0.18\n2.5\n7.3\n7.3\n% of background\n-\n37\n.32\n26\n2.5\n35\n-\n-\nfrom the same collision point. The dilepton invariant mass best matching the mass of Z must be within\nthe Z-mass window of |MZ \u2212M\u00b5\u00b5| < 12 GeV or |MZ \u2212Mee| < 9 GeV. These mass windows are set by\nthe mass resolutions. The MT determined by the third lepton and the /ET must be within the transverse\nW-mass window: 40 GeV < MT < 120 GeV.\nThe total and selected number of the signal and the background events for each trilepton \ufb01nal state,\nand for 1 fb\u22121 of integrated luminosity, are listed in Table 5. The overall signal ef\ufb01ciency is 8.7% and\n7.1% for W \u2212Z and W +Z, respectively. For 1 fb\u22121 of data, 53 W \u00b1Z signal events and 7 background events\nare expected. The dominant background contributions are from ZZ, Z+jet and Drell-Yan processes, while\nZ\u03b3 and t\u00aft contribute a small fraction of the total background events.\nTable 6: Number of expected W \u00b1Z signal (NWZ), and background (NB) for 1 fb\u22121 of data with BDT\nanalysis using the cut BDT > 200.\nWZ\nZZ\nt\u00aft\nZ +jet\nZ +\u03b3\nOther\nTotal bkg\nNWZ/NB\nN events\n128\n7.7\n2.8\n2.5\n2.0\n1.1\n16\n7.9\n% of background\n48\n17\n16\n12\n7.0\n-\n-\nFor 0.1 fb\u22121 of integrated luminosity, only 5 signal events (NS) with 0.7 background event (NB)\ncontamination are expected. The W \u00b1Z detection signi\ufb01cance, de\ufb01ned as the probability from Poisson\ndistribution with mean NB to observe equal or greater than NS + NB events, converted in equivalent\nnumber of sigmas (standard deviations) of a Gaussian distribution, will be 3.6\u03c3 only. To improve the\ndetection sensitivity, the BDT analysis technique is employed. This BDT analysis is conducted with a\ntotal of 1000 trees with 20 tree-split nodes. Based on the variables used in the cut-based analysis, and the\nBDT training Gini-index (a measure of a variable effectiveness in separating signal from background),\na total of 22 kinematic and topology variables are selected for the BDT training. About 12000 pre-\nselected signal events and 18000 pre-selected background events are used in this BDT-based analysis,\nwhere 50% of the signal and background events are used for the training, and another 50% of statistically\nindependent events allocated to the BDT test sample sets. The BDT output discriminator from the testing\nsample, used to separate the signals from the background, is shown in Figure 8 (right), see Section 4.1.\nThis spectrum will be used to determine (\ufb01t) the W \u00b1Z production cross-section.\nResults of the W \u00b1Z event selection with the cut BDT > 200 are shown in Table 6. Expected numbers\nof signal and background events are given for 1 fb\u22121 of integrated luminosity. The estimated background\nuncertainties are 15-20% due to the limited number of simulated events available. The overall W \u00b1Z\nevent selection ef\ufb01ciency is about 13.7% for signal, resulting in 12.8 signal and 1.6 background events\nfor 0.1 fb\u22121. The W \u00b1Z detection signi\ufb01cance is expected to be 5.9\u03c3 (including both statistical and 20%\nsystematic uncertainties) for 0.1 fb\u22121 of integrated luminosity.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n841\n\n3.4\nW \u00b1\u03b3 \u2192\u2113\u00b1\u03bd\u03b3 selection\nThe W \u00b1\u03b3 signal events are modeled with PYTHIA, which includes tree-level diagrams as shown in Figure\n1 for W production with initial state radiation (ISR) (the t\u2212and u\u2212channels) and the s\u2212channel pro-\nduction depending on the triple-gauge-coupling WW\u03b3 vertex. The WW\u03b3 vertex introduces a destructive\ninterference of zero amplitude at cos\u03b8 \u00afq,\u03b3 = \u00b11/3 for W \u00b1 production, where \u03b8 \u00afq,\u03b3 is the photon scattering\nangle to the incoming anti-quarks.\nThe W \u00b1\u03b3 diboson events are selected from pp collisions using pure W leptonic decays. The experi-\nmental signature is a \ufb01nal states with one high pT lepton (electron or muon), one high pT photon and\nlarge /ET. Major backgrounds are from the processes:\n\u2022 Inclusive W +X production with W +X \u2192\u2113\u03b3\u03bd +X , where the \u03b3 is from \ufb01nal state radiation (FSR)\nfrom the lepton.\n\u2022 Inclusive W +X \u2192\u2113\u03bd +X productions, with X = jets and the jets faking a photon.\n\u2022 Inclusive Z +X \u2192\u2113\u2113+X productions, with one lepton escaping detection, and with X = \u03b3 or jets\nfaking a photon.\nA photon isolation cut is effective in suppressing these backgrounds.\nTo study the W \u00b1\u03b3 detection sensitivity about 1.3 million inclusive W events and about 100,000 in-\nclusive Z events were generated with the PYTHIA MC generator. In these datasets, the photon transverse\nenergy threshold is 10 GeV and the lepton and photon separation, \u2206R(\u2113,\u03b3) was required to be greater\nthan 0.7.\nThe W \u00b1\u03b3 candidates are inclusive e\u00b1\u03b3 or \u00b5\u00b1\u03b3 events having one electron or muon observed and the\nabsence of the oppositely charged lepton of the same \ufb02avor. The photon selected is the most energetic\none in the events. Ef\ufb01ciencies for three trigger types are investigated: isolated muon with pT > 20 GeV,\nisolated electron with pT > 22 GeV and photon with ET(\u03b3) > 55 GeV. The overallW \u00b1\u03b3 trigger ef\ufb01ciency\nis about 80% based on our study.\nBackground to the W \u00b1\u03b3 signal is dominated by inclusive W \u00b1 events with radiated jets faking a\nphoton. Contamination from inclusive Z events with an undetected lepton is also signi\ufb01cant. Figure 3\nshows the W \u00b1\u03b3 signal (\ufb01rst column) scatter plots compared to those for major backgrounds: the inclusive\nW events with \ufb01nal state radiation (FSR) (the 2nd column), and with fake photon (the third column), and\nthe Z events with one lepton escaping detection and a photon of any type reconstructed (the 4th column).\nThe BDT method is used to select the W \u00b1\u03b3 signal events. Three trainings are done to separate: 1)\nThe \u2113\u03b3\u03bd events with FSR photons from other sources, 2) The W \u00b1\u03b3 signal photons from fake photons,\nand 3) The signal photons from the contamination of Z inclusive events. Nineteen variables are used in\nthe BDT analysis. Cuts are applied to the BDT output spectra for the three trainings. The cuts chosen\nfor signal selection correspond to a W \u00b1\u03b3 selection ef\ufb01ciency of 65% with a signal to background ratio of\n0.95 (0.98) for electron (muon) \ufb01nal states, respectively. The numbers of events selected with the BDT\ncuts are listed in Table 7. The selected events are further required to pass the trigger requirements as the\n\ufb01nal accepted events, which are listed in the Table as well.\nThe BDT discriminates signal photons effectively from FSR and fake photons in the high ET(\u03b3) re-\ngion. This preserves a high detection ef\ufb01ciency in the region that is sensitive to discovery of phenomenon\nbeyond Standard Model predictions.\n3.5\nW +W \u2212\u2192\u2113+\u03bd\u2113\u2212\u03bd selection\nThe production of W pairs has been investigated extensively at LEP and at the Tevatron. The experi-\nmental W +W \u2212signature is two high transverse momentum leptons with opposite charge associated with\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n842\n\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(a) ISR\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(b) FSR\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(c) fake-\u03b3\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(d) Z cont\nATLAS\n|\u03c6(\u00b5)-\u03c6(MET)|\n\u2206R(\u00b5,\u03b3)\n|\u03c6(\u00b5)-\u03c6(MET)|\n\u2206R(\u00b5,\u03b3)\n|\u03c6(\u00b5)-\u03c6(MET)|\n\u2206R(\u00b5,\u03b3)\n|\u03c6(\u00b5)-\u03c6(MET)|\n\u2206R(\u00b5,\u03b3)\nmT(\u00b5\u03bd) [GeV]\nmT(\u00b5\u03bd\u03b3) [GeV]\nmT(\u00b5\u03bd) [GeV]\nmT(\u00b5\u03bd\u03b3) [GeV]\nmT(\u00b5\u03bd) [GeV]\nmT(\u00b5\u03bd\u03b3) [GeV]\nmT(\u00b5\u03bd) [GeV]\nmT(\u00b5\u03bd\u03b3) [GeV]\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n0\n50\n100\n150\n200\n0\n50 100 150 200\n0\n50\n100\n150\n200\n0\n50 100 150 200\n0\n50\n100\n150\n200\n0\n50 100 150 200\n0\n50\n100\n150\n200\n0\n50 100 150 200\nFigure 3: Distributions of the W \u00b1(\u00b5\u00b1\u03bd)\u03b3 event variables, with a photon from the W \u00b1\u03b3 signal (ISR), and\nfrom backgrounds, FSR, fake \u03b3, and inclusive Z contamination.\nlarge transverse missing energy. W +W \u2212production involves both WWZ and WW\u03b3 triple gauge boson\ncouplings and is most sensitive to the \u2206\u03baV anomalous coupling parameters. Furthermore, the W pair pro-\nduction provides an important background to Higgs boson searches in the pp \u2192H \u2192WW (\u2217) \u2192\u2113\u03bd\u2113\u03bd\nchannel at the LHC. In dileptonic W-decays no Higgs mass peak can be reconstructed, so this back-\nground cannot be estimated from the measured data via sideband interpolation. An understanding of the\nirreducible W-pair continuum background is therefore crucial.\nAt the LHC the major background processes (t\u00aft, inclusive W and Z, and Drell-Yan) have much higher\ncross-sections than W +W \u2212. It will be necessary to achieve very high background rejection power to\nsuppress the events with mis-identi\ufb01ed leptons (from jet, photon and instrumentation effects) and leptonic\ndecays from heavy-\ufb02avor quark jets. In the Drell-Yan process the mis-measured /ET also contributes non-\nnegligible background.\nEvent selection consists of the trigger, pre-selection (two high pT leptons plus /ET), and \ufb01nal selection\nwith a set of conventional cuts or with BDT selection cuts. The W +W \u2212events are required to pass\none of two high-level trigger paths: a single, isolated electron with pt > 25 GeV or a single muon,\nwith pt > 20 GeV. The trigger ef\ufb01ciencies for WW \u2192ee, WW \u2192\u00b5\u00b5 and WW \u2192e\u00b5 events with two\nopposite sign isolated leptons (pT > 20 GeV, | \u03b7 |< 2.5) are estimated as follows: 98.2 %, 95.9%; and\n97.4% respectively.\nThe cut-based analysis rejects background events with tight lepton identi\ufb01cation criteria and iso-\nlation requirements as well as with event topology variables which clearly distinguish the signal and\nsigni\ufb01cantly suppress the main background processes t\u00aft and Z + X. The W +W \u2212leptonic decay events\nare selected by requiring two well identi\ufb01ed isolated leptons with opposite charge, and with p\u2113\nT > 20\nGeV and | \u03b7 |< 2.5. A jet veto requirement rejects events with any jet (pjet\nT\n> 20 GeV) in the rapid-\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n843\n\nTable 7: The number of W \u00b1\u03b3 signal and background events after pre-selection, BDT selection and trigger\nrequirement, for an integrated luminosity of 1 fb\u22121. The signal and total background are then scaled to\nNLO cross-sections with the k-factors indicated. For the signal, the k-factor is obtained using BosoMC.\nFor background, the k-factors are obtained by comparing the cross-sections calculated with MC@NLO\nand PYTHIA generators.\nSignal\nBackground\nW \u00b1\u03b3\nW+FSR \u03b3\nW+fake \u03b3\nZ(\u2113\u2113/)\u03b3\nTotal\n\u2113= e\nPre-selected\n1710\n11440\n7890\n32480\nBDT selection\n1145\n242\n791\n101\nTriggered\n966\n188\n628\n93\nNLO scaled\n1604 (k=1.66)\n1183 (k=1.3)\n\u2113= \u00b5\nPre-selected\n2680\n28410\n10250\n3950\nBDT selection\n1793\n413\n961\n409\nTriggered\n1305\n177\n595\n260\nNLO scaled\n2166 (k=1.66)\n1342 (k=1.3)\nity region | \u03b7 |< 3. This cut is ef\ufb01cient in t\u00aft suppression since t\u00aft contains one or two energetic b jets\nin addition to the W +W \u2212signature. An event with /ET < 50 GeV is rejected to reduce the background\narising from the event pileup and from Z/\u03b3\u2217events in the Drell-Yan process. To reject the dilepton\nevents from inclusive Z production, a Z mass veto is applied. Finally, angular variable cuts are imposed.\nFor cross-section measurements, events must pass a cut: \u03c6\u2113\u2113< 2 rad, where \u03c6\u2113\u2113is the angle between\nthe transverse momentum of the two leptons. For anomalous TGC studies, this cut is replaced with:\n\u03a6(p\u2113+,\u2113\u2212\nT\n,pmiss\nT\n) > 175deg, where \u03a6 is the angle between the transverse momenta of the lepton pair, and\nthe missing transverse momentum. The \ufb01rst angular cut (selection-A) results in high signal detection\nef\ufb01ciency, but it is not optimized for high pT(\u2113) and pT(\u2113\u2113) event detection and thus could decrease the\nsensitivity to anomalous TGC\u2019s. The second angular cut (selection-B) results in lower signal detection\nef\ufb01ciencies, but has higher ef\ufb01ciency for high pT(\u2113) and pT(\u2113\u2113) events. The yields of the W +W \u2212se-\nlection with the cut-based analysis are summarized in Table 8. Both signal and background events are\nnormalized to 1 fb\u22121 of data. Figure 4 shows the transverse momentum distributions of leptons (left)\nand lepton pairs (right) after applying the kinematic cuts of Selection-B. The distributions are shown for\nsum of signal and various backgrounds, and for individual backgrounds, for an integrated luminosity of\n1 fb\u22121 of data.\nTheW +W \u2212overall signal detection ef\ufb01ciency is 1.4-3%, depending on the selection cuts and the \ufb01nal\nlepton states. The signal detection signi\ufb01cance for 0.1 fb\u22121 of data is expected to be 4.7\u03c3 (for Selection\nA), after taking into account a 20% background systematic uncertainty. The detection ef\ufb01ciencies can\nbe improved by using the multivariate BDT technique. In this W +W \u2212analysis one thousand decision\ntrees, wherein one tree has 20 splitting-nodes, are used to separate signal from background based on the\ninput variables. The input data for the BDT analysis must \ufb01rst pass the pre-selection cuts (two leptons\nwith p\u2113\nT > 10 GeV and /ET > 15 GeV). The pre-selected simulated samples are divided into two equal\nparts: one sample is used for BDT training and the other to test event selection performance. The BDT\noutput spectra for both signal and background are shown in Figure 8 (left). By varying the location of\nthe cut along the BDT scores (x-axis), the signal to background ratio can be optimized. Table 9 presents\nthe detection sensitivities with total integrated luminosity of 1 fb\u22121: the selected number of signal events\n(NWW), the corresponding signal ef\ufb01ciency (\u03b5WW), the number of background (Nbkg.) events, and signal\nto background ratio (NWW/Nbkg) are shown. The breakdown of background contributions are also given\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n844\n\nTable 8: Yield and total event detection ef\ufb01ciency of the WW selection for 1 fb\u22121 of data. The errors\nshown are statistical only.\nef\ufb01ciency\nNWW\nNbackground\nNsig./Nbkg.\nSelection-A\ngg \u2192WW\nq \u00afq \u2192WW\ngg \u2192WW\nq \u00afq \u2192WW\nee\n2.1%\n1.3%\n1.3\u00b10.05\n17.4 \u00b1 1.1\n1.4 \u00b10.3\n13.3\u00b13.0\n\u00b5\u00b5\n4.1%\n2.8%\n2.4\u00b10.08\n36.4 \u00b1 2.2\n10.7 \u00b1 2.1\n3.6\u00b1 0.8\ne\u00b5\n2.8%\n1.9%\n3.3\u00b10.13\n50.6\u00b1 1.8\n7.2 \u00b1 1.2\n7.5 \u00b1 1.3\nll\n3.0%\n2.0%\n7.0\u00b10.16\n104.4\u00b12.4\n19.3\u00b12.4\n5.8 \u00b1 0.8\nSelection-B\nee\n0.94%\n0.92%\n0.6\u00b10.04\n12.0 \u00b1 0.9\n2.8\u00b1 1.2\n4.5 \u00b1 1.9\n\u00b5\u00b5\n2.1%\n2.0%\n1.1\u00b10.03\n25.5 \u00b1 1.8\n4.8\u00b11.0\n5.5 \u00b1 1.2\ne\u00b5\n1.3%\n1.4%\n1.5\u00b10.09\n35.3 \u00b1 1.5\n7.4\u00b1 1.3\n5.0 \u00b1 0.9\nll\n1.4%\n1.4%\n3.2\u00b10.10\n72.8 \u00b1 2.5\n15.0 \u00b1 2.0\n5.1 \u00b1 0.8\n (l) [GeV]\nT\np\n20\n40\n60\n80\n100\n120\n140\n160\n-1\nevents / 10GeV / 1fb\n-1\n10\n1\n10\nATLAS\nWW + Backgrounds\nAll Backgrounds\nttWZ\nZZ\n\u03c4\n\u03c4\n\u2192\nZ\n l\n\u03c4\n\u2192\nWW\n (ll) [GeV]\nT\np\n20\n40\n60\n80\n100\n120\n140\n160\n-1\nevents / 5GeV / 1fb\n-1\n10\n1\n10\nATLAS\nWW + Backgrounds\nAll Backgrounds\ntt\nWZ\nZZ\n\u03c4\n\u03c4\n\u2192\nZ\n l\n\u03c4\n\u2192\nWW\nFigure 4: Transverse momentum distributions of leptons (left) and lepton pairs (right) after applying\nkinematic cuts from Selection-B. The distributions are shown for sum of signal and various backgrounds,\nand for separated backgrounds for L=1 fb\u22121.\nin this table. For initial measurements using early LHC data based on 0.1 fb\u22121 of integrated luminosity,\nthe application of BDT is compelling. As inferred from Table 8, the initial data is expected to yield a total\nfor all decay channels of \u223c10 signal events using conventional cuts, whereas the BDT-based analysis,\nwhich gives a similar signal to background ratio as the conventional cuts is expect to yield total 47 signal\nevents. With an estimated background contribution of 9.2 events the W +W \u2212detection signi\ufb01cance is\nabout 10\u03c3 (including 20% background systematic uncertainties).\n3.6\nZ\u03b3 \u2192\u2113+\u2113\u2212\u03b3 selection\nZ\u03b3 signals are produced through initial state radiation (ISR) of the photon from the quarks as illustrated\nby the t- and u-channel diagrams shown in Figure 1. The s-channel Z\u03b3 production contains the Z\u03b3V (V =\nZ,\u03b3) vertex, which is forbidden at tree-level in the Standard Model. The cross-section measurement of the\nZ\u03b3 production would provide a sensitive probe to anomalous Z\u03b3V couplings, which can be investigated\nthrough this channel by measuring the ET(\u03b3) distribution, expecially at large values.\nThe cleanest Z\u03b3 experimental signature is two high pT leptons from the decay of the Z boson and an\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n845\n\nTable 9: WW \u2192leptons detection sensitivities of accepted signal and background events for 1 fb\u22121 of\nintegrated luminosity. Results from the BDT analysis are shown with cuts that give similar signal to\nbackground ratio as the cut-based analysis. The quoted ef\ufb01ciencies in the table are the BDT selection\nef\ufb01ciencies including the trigger requirements based on pre-selected events.\nBackground fraction\nModes\n\u03b5WW(%)\nNWW\nNbkg\nt\u00aft\nW \u00b1Z\nZ +X\nNWW/Nbkg\ne\u03bd\u00b5\u03bd\n32.7\n347\u00b1 3\n64\u00b1 5\n47.7%\n27.8%\n21.8%\n5.4\n\u00b5\u03bd\u00b5\u03bd\n12.1\n70\u00b1 2\n17\u00b1 2\n54.1%\n34.6%\n11.3%\n4.1\ne\u03bde\u03bd\n13.7\n52\u00b1 1\n11\u00b1 1\n81.4%\n7.2%\n11.4%\n4.7\nisolated high pT photon (from ISR). The backgrounds to this Z\u03b3 signal are: 1) the Z boson production\nwith a FSR photon from the leptons decay from the Z, 2) the Z boson production with a fake photon from\njets, and 3) a small contamination from W +X production reconstructed as a \u2113+\u2113\u2212\u03b3 \ufb01nal state. Some of\nthe event variables for different photon sources are shown in Figure 5.\nEvents are pre-selected with ET(\u03b3) > 10 GeV, a value chosen to be above the PYTHIA generator\nthreshold and as low as is reasonably achievable by detector reconstruction. The FSR event rate is almost\nan order of magnitude higher than the ISR rate in the inclusive Z production process. Backgrounds with\na Z boson and a fake photon are comparable to the Z\u03b3 signal photon rate.\nThe event selection is conducted with BDTs trained to separate Z\u03b3 events of different photon types.\nThe training is in two stages: \ufb01rst to identify the FSR photon background events and then to distinguish\nthe signal (ISR) photon from Z events with fake photons. Separate BDT training is done for the electron\nand muon Z decay channels.\nThe BDTs are trained with 19 variables in total. As one example, FSR photons can be identi\ufb01ed\nfrom the opening angle from the nearest lepton. Fake photons originating from high pT neutral mesons\ndecaying to two photons can not be directly identi\ufb01ed within the limits of the spatial resolution provided\nby the ECAL segmentation. However, they are often accompanied by jet secondaries or underlying\nremnant particles. By counting the charged tracks in a neighborhood (a cone of 0.45 rad in this case), or\nsumming their energies, parameters useful for differentiating background from isolated ISR photons can\nbe formed.\nWith the chosen BDT cuts the signal selection ef\ufb01ciency is 67%, and the signal to background ratio\nis 2.0 and 1.8 for the electron and muon Z decay channels, respectively. The estimated numbers of\nreconstructed Z\u03b3 candidates for an integrated luminosity of 1 fb\u22121 are listed in Table 10.\nThe FSR and fake photons contribute approximately equally to the total background but have impor-\ntant distinctions. The fake photons populate the low ET(\u03b3) region, and are differentiated from the signal\nphoton (ISR) in the ET(\u03b3) > 20 GeV region. The shape of the ET distribution in the low energy region\nis important for calibration and measurement of the production cross-section with ISR photons. On the\nother hand, the FSR photons have an ET(\u03b3) distribution similar to the ISR photons which carry signa-\ntures of the coupling to the colliding quarks. Event rates in the high ET(\u03b3) region, where the background\nis primarily FSR, is an important probe of new physics phenomena.\n3.7\nZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212selection\nThe cleanest experimental signature for ZZ detection is through the four lepton decay channels:\npp \u2192ZZ \u2192e+e\u2212e+e\u2212, \u00b5+\u00b5\u2212\u00b5+\u00b5\u2212,\ne+e\u2212\u00b5+\u00b5\u2212.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n846\n\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(a) ISR\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(b) FSR\n\u03b7(\u03b3)\nET(\u03b3) [GeV]\n(c) fake-\u03b3\nATLAS\n\u2206R(e+,\u03b3)\n\u2206R(e-,\u03b3)\n\u2206R(e+,\u03b3)\n\u2206R(e-,\u03b3)\n\u2206R(e+,\u03b3)\n\u2206R(e-,\u03b3)\nm(ee) [GeV]\nm(ee\u03b3) [GeV]\nm(ee) [GeV]\nm(ee\u03b3) [GeV]\nm(ee) [GeV]\nm(ee\u03b3) [GeV]\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n20\n40\n60\n80\n100\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n5\n0\n1\n2\n3\n4\n5\n0\n50\n100\n150\n200\n0\n50 100 150 200\n0\n50\n100\n150\n200\n0\n50 100 150 200\n0\n50\n100\n150\n200\n0\n50\n100 150 200\nFigure 5: Distributions of Z(ee)\u03b3 event variables for ISR (left column), FSR (middle column.) and fake\nphotons (right column).\nThe ZZ \u21924\u2113\u2032 (\u2113\u2032 = e, \u00b5, \u03c4) signal is modeled at LO by the PYTHIA event generator using the CTEQ6L\nPDF. The Z/\u03b3\u2217interference terms are included in the generator. With the 12 GeV mass cut on the\ndileptons decay from Z/\u03b3\u2217, the cross-section times the dilepton decay branching ratio, \u03c3 \u00d7BR is 159 fb.\nA \ufb01lter is applied to the simulated data to pre-select four lepton (e and \u00b5 only) events by requiring that\nthe lepton transverse momenta must be greater than 5 GeV, and the lepton rapidity, \u03b7\u2113, must be in a range\n| eta |< 2.7. The overall \ufb01lter ef\ufb01ciency is 0.219. The \u03c4 lepton contribution to the four lepton channels\n(4e, 4\u00b5, 2e2\u00b5) is less than 4% in the event sample after the \ufb01lter. The fraction of the on-shell ZZ events\n(both lepton pair masses are between 70 GeV to 110 GeV) in the sample is about 73%. Next-to-leading-\norder calculations give higher production cross-sections. The k-factor is about 1.35 when both Z\u2019s are on\nmass shell. However, when the Z/\u03b3\u2217are off the Z mass shell, the k-factor varies from 1.15 to 1.52 for the\n(Z/\u03b3\u2217)(Z/\u03b3\u2217) mass range from 115 GeV to 405 GeV, which is determined by using the MCFM Monte\nCarlo calculations [11]. The k-factor is set constant at 1.35 to normalize the ZZ \u21924\u2113signal events. The\nfour-lepton events have high trigger ef\ufb01ciencies close to 100%.\nMajor background processes for four lepton \ufb01nal states are t\u00aft \u2192WWb\u00afb \u21924\u2113+X and Zb\u00afb \u21924\u2113+X.\nThe t\u00aft background events, generated using MC@NLO, has a total production cross-section of 833 pb.\nThe Zb\u00afb background events are generated using AcerMC, with cross-section scaled to NLO by a k-\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n847\n\nTable 10: The number of Z\u03b3 signal and background events after pre-selection and BDT selection is\nlisted, for an integrated luminosity of 1 fb\u22121. The signal and total background are then scaled to NLO\ncross-sections with the k-factors indicated. For the signal, the k-factor is obtained using BHO.\nSignal\nBackground\nZ\u03b3\nZ+FSR \u03b3\nZ+fake \u03b3\nW(l\u03bd)\u03b3\nTotal\n\u2113= e\nPre-selected\n430\n2760\n490\n44\nBDT selection\n288\n70\n74\n0\nTriggered\n282\n65\n79\n0\nNLO scaled\n367 (k=1.3)\n187 (k=1.3)\n\u2113= \u00b5\nPre-selected\n950\n7500\n790\n930\nBDT selection\n636\n173\n186\n0\nTriggered\n578\n164\n165\n0\nNLO scaled\n751 (k=1.3)\n429 (k=1.3)\n)\n2\n4l invariant mass (MeV/c\n100\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\n3\n10\n\u00d7\nEvents/10 GeV\n0\n2\n4\n6\n8\n10\n12\n-1\nScaled to 10 fb\nsignal\nZbb background\nttbar background\nATLAS\n)\n2\n4l invariant mass (MeV/c\n100\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\n3\n10\n\u00d7\nEvents/10 GeV\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n-1\nScaled to 10 fb\nsignal\nZbb background\nttbar background\nATLAS\nFigure 6: The four-lepton invariant mass distributions of ZZ signal, Zb\u00afb and t\u00aft background events with\ntight (left) and loose (right) Z mass cut on the lepton pairs. The number of events correspond to an\nintegrated luminosity of 10 fb\u22121.\nfactor. Leptons from b quark decays in these processes are produced in association with hadrons. Their\ncontributions can be highly suppressed by lepton isolation requirements. For muons, the ratio between\nthe transverse energy deposited in a cone around the muon track of radius \u2206R = 0.4 and the transverse\nenergy of the muon E\u00b5\nT must be below 0.2. A similar isolation cut is applied to the electron selections.\nTo reject background with leptons not originating from the Z decays, the two opposite sign lepton pairs\nmust have at least one lepton with pT greater than 20 GeV, and at least one lepton pair must have the\ninvariant mass between 70 GeV- 110 GeV. This is referred to as the loose Z mass cut. A tight Z mass cut\nrequires the second lepton pair also to have invariant mass between 70 GeV- 110 GeV. The separation\nbetween the two leptons must be \u2206R(\u2113+\u2113\u2212) > 0.2. Table 11 lists the signal selection cut ef\ufb01ciencies for\nall the four lepton \ufb01nal states. Each cut ef\ufb01ciency value is relative to the previous selection. The quoted\nuncertainties of the selected numbers of events are statistical only.\nThe total selection ef\ufb01ciencies for the Zb\u00afb background using these same tight cuts are 0.13% \u00b1\n0.06%, 0.61% \u00b1 0.14%, and 0.51% \u00b1 0.13% for the 4\u00b5, 4e, and 2\u00b52e channels, respectively. For t\u00aft\nthese ef\ufb01ciencies are 0.07% \u00b1 0.07% for all three channels. The expected number of signal and back-\nground events for L = 1 fb\u22121 requiring tight Z mass cut are given in Table 12. The expected signal and\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n848\n\nTable 11: ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212signal selection cut ef\ufb01ciencies\n4\u00b5 [%]\n4e [%]\n2\u00b52e [%]\nLepton Preselection\n70.7\n62.3\n65.4\nPair formation, dR\n99.3\n88.0\n93.4\nIsolation, pmax\nT\n81.1\n58.6\n59.1\nZ Mass\ntight\nloose\ntight\nloose\ntight\nloose\n72.7\n92.0\n76.1\n93.5\n77.8\n95.2\nTotal\n41.4\u00b10.6\n52.4\u00b10.7\n24.4\u00b10.5\n30.0\u00b10.6\n28.1\u00b10.4\n34.3\u00b10.4\nTable 12: Expected number of ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212signal and background events at L = 1 fb\u22121 using the\ntight Z mass cut.\n4\u00b5 events\n4e events\n2\u00b52e events\nTotal\nSignal\n4.5\u00b10.05\n2.6\u00b10.04\n6.2\u00b10.06\n13.3 \u00b10.09\nZb\u00afb\n0.01\u00b10.003\n0.04\u00b10.01\n0.04\u00b10.01\n0.08\u00b10.01\nt\u00aft\n0.04\u00b10.04\n0.04\u00b10.04\n0.04\u00b10.04\n0.12\u00b10.07\nTotal background\n0.05\u00b10.04\n0.08\u00b10.04\n0.08\u00b10.04\n0.20\u00b10.07\nbackground events with only one on-shell Z (Loose Z mass cut) are in Table 13. Uncertainties quoted\nin these tables are statistical only. Figure 6 shows the four-lepton invariant mass distributions for the ZZ\nsignal, Zb\u00afb and t\u00aft background with tight and loose Z mass cut on the lepton pairs. Based on these results\nthe ATLAS experiment will establish the ZZ \u21924\u2113signal with a signi\ufb01cance of 6.8\u03c3 (after taking into\naccount 20% background systematic errors) with the \ufb01rst 1 fb\u22121 of integrated luminosity.\n3.8\nZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd selection\nThe ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd signature is two high-pT charged leptons with a large missing transverse energy (/ET)\ndue to the neutrino pair leaving the detector. The main backgrounds will either come from channels with\nlarge cross sections, such as t\u00aft and Z \u2192\u2113+\u2113\u2212, or those with a similar signature to the signal, such as the\nW \u00b1Z diboson channel. Both signal (ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd) and background (t\u00aft, W \u00b1Z, W +W \u2212, and Drell-Yan\ndileptons) are modeled by the generator MC@NLO, except for high pT Z (pT(Z) > 100 GeV) events\nwhich are modeled by PYTHIA.\nTo reduce the backgrounds, a set of simple cuts on discriminating parameters is invoked. In general,\neach cut is used to suppress a particular background channel, as described below.\nFirst, two oppositely charged good quality leptons with pT > 20 GeV are selected. This reduces much\nTable 13: Expected ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212signal and background events at L = 1 fb\u22121 using the loose Z mass\ncut.\n4\u00b5 events\n4e events\n2\u00b52e events\nTotal\nSignal\n5.7\u00b10.06\n3.2\u00b10.04\n7.6\u00b10.07\n16.5\u00b10.1\nZb\u00afb\n0.1\u00b10.01\n0.5\u00b10.02\n0.3\u00b10.02\n0.9\u00b10.1\nt\u00aft\n0.1\u00b10.06\n0.5\u00b10.14\n0.4\u00b10.13\n1.0\u00b10.2\nTotal background\n0.2\u00b10.06\n1.0\u00b10.14\n0.7\u00b10.13\n1.9\u00b10.2\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n849\n\nof the t\u00aft background which contains softer leptons than the signal. This cut also reduces the background\nfrom Z \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u2212\u03bd\u2113\u00af\u03bd\u2113\u03bd\u03c4 \u00af\u03bd\u03c4 as the electrons and muons are produced with reduced pT. The leptons\nmust also lie within the inner detector pseudorapidity range, |\u03b7| < 2.5.\nThe charged lepton pairs are required to have an invariant mass close to the Z mass, speci\ufb01cally\n|M\u2113\u2113\u221291.2 GeV| < 10 GeV. This is equivalent to \u223c5\u03c3 of the signal width, and helps to reduce back-\nground combinatorics where the lepton pair does not come directly from a Z decay. A lepton veto is\nimposed by combining the good quality and loose lepton selection to remove any events with more than\ntwo leptons in total. This reduces background from the W \u00b1Z channel, whose Z has an almost identical\nsignature to the signal, and the neutrino from W decay also appears as /ET. The third-lepton veto sup-\npresses the W \u00b1Z background by \u223c30%. If the lepton from the W is not reconstructed, however, this\nbackground channel becomes almost indistinguishable from the signal.\nA main characteristic of the signal decay is a large missing transverse energy (/ET) from the Z \u2192\u03bd \u00af\u03bd\ndecay. An important background, due to its large cross section, comes from the Z \u2192\u2113+\u2113\u2212Drell-Yan\nprocess, where jets are produced in addition to the leptons. If these jets are aligned with cracks in\nthe detector, then they will fake /ET as they will not be fully accounted for in the calorimeters. This\nbackground can be signi\ufb01cantly reduced by applying a 50 GeV /ET cut. The background from ZZ \u21924\u2113\nis also reduced, but this is less signi\ufb01cant as it has a much smaller cross-section. The W \u00b1Z channel is\nsuppressed by this cut as only one neutrino is produced, and hence the /ET distribution is slightly softer.\n(Z)\nT\n(Z)) / p\nT\n - p\nT\n(Missing E\n-1\n-0.5\n0\n0.5\n1\n1 5\n2\n2.5\n3\nFraction of Events\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n\u03bd\n\u03bd \n-l\n+\n l\n\u2192\nZZ \n + X\n\u00b5\n\u00b5\n ee, \n\u2192\nZ + X \n + X\n\u00b5\n\u00b5\n ee, \n\u2192\nZW \nATLAS\n(Z)\n\u03c6\n) - \nT\n(Missing E\n\u03c6\n0\n50\n100\n150\n200\n250\n300\n350\nFraction of Events\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n\u03bd \n\u03bd -l\n+\n l\n\u2192\nZZ \n + X\n\u00b5\n \n\u00b5\n ee, \n\u2192\nZ + X \n + X\n\u00b5\n \n\u00b5\n ee, \n\u2192\nZW \nATLAS\nFigure 7: The /ET \u2212pT(Z) magnitude (left) and angle matching (right) distributions before cuts for\nZZ \u21924\u2113(solid), Z \u2192\u2113+\u2113\u2212(dash) and W \u00b1Z (dot). The plots are normalised to unit area for comparison\nof distribution shapes.\nThe signal is expected to have missing pT equal and opposite to that of the reconstructed Z, when\nthe ZZ pair is produced with no initial pT and they decay back-to-back. Figure 7 (left and right) shows\na clear peak in the signal for both magnitude and angle matches. The W \u00b1Z background shows a worse\nmagnitude match as some of the W momentum is lost to either an electron or muon on decay. This\nmeans that the missing pT will not quite match up with that of the recoiling Z. The angular distribution\nshows a peak in both the W \u00b1Z and Z \u2192ll channels. In the case of W \u00b1Z, this is because the W and Z\nare produced in approximately opposite directions. When the W decays, the neutrino will be de\ufb02ected\nand so the peak has a wider distribution. In a similar way, in Z \u2192ll, the Z is likely to be produced with\nsome quarks recoiling against it. These will manifest themselves as jets which can fake /ET. Cuts at\n(|/ET \u2212pT(Z)|)/pT(Z) < 0.35\nand\n145\u25e6< \u03c6/ET \u2212\u03c6Z < 215\u25e6, reduce the W \u00b1Z background.\nA jet veto reduces backgrounds with large hadronic activity. For example, the predominant decay\nchannel for the top quark in t\u00aft is the t \u2192Wb \ufb01nal state, resulting in several high pT jets. Its contribution\ncan be reduced by applying a veto on events containing any jet with pjet\nT > 30 GeV\nand\n|\u03b7 jet| < 3.0.\nThe \ufb01nal cut to be applied is on the pT of the reconstructed Z boson. This reduces the background\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n850\n\nTable 14: Cut \ufb02ow table for ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd signal and background after cuts for an integrated luminosity\nof 1 fb\u22121. The values in brackets indicate the percentage of events passing each cut relative to the\nprevious cut. Note that this Z \u2192ll MC sample already requires pT(Z) > 100 GeV.\nCut\nZZ \u2192\u2113\u2113\u03bd\u03bd\nZZ \u21924l\nZ \u2192ll\nt\u00aft\nW \u00b1Z\nW +W \u2212\nZ \u2192\u03c4\u03c4\nLeptons\n130.1\n54.3\n13100\n4530\n271.2\n491.1\n2170\nThird-lepton veto\n101.9\n3.1\n1900\n428.9\n52.9\n375.6\n1690\n(78.3%)\n(5.7%)\n(14.5%)\n(9.5%)\n(19.5%)\n(76.5%)\n(77.9%)\nDilepton mass\n100.2\n2.7\n1740\n110.2\n45.3\n83.8\n40.1\n(98.3%)\n(87.1%)\n(91.6%)\n(25.7%)\n(85.6%)\n(22.3%)\n(3.4%)\nMissing ET\n38.0\n0.34\n3.8\n17.9\n9.4\n18.3\n0\n(39.9%)\n(12.6%)\n(0.2%)\n(16.2%)\n(20.8%)\n(21.8%)\n(0.0%)\nJet veto\n34.4\n0.30\n0.44\n6.0\n7.6\n16.7\n0\n(90.5%)\n(88.2%)\n(11.6%)\n(33.5%)\n(80.9%)\n(91.3%)\n(0.0%)\npZ\nT\n10.2\n0.08\n0.4\n3.0\n1.7\n0.02\n0\n(29.7%)\n(26.7%)\n(90.9%)\n(50.0%)\n(22.4%)\n(0.1%)\n(0.0%)\nStat. Error [90%CL]\n0.2\n0.01\n0.2\n2.1\n0.1\n0.22\n[1.6]\nTable 15: The expected ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd signal yields and total signal selection ef\ufb01ciency for 1 fb\u22121 of\nintegrated luminosity. The errors shown are statistical only.\nNsignal\nSignal ef\ufb01ciency\nNbackground\nNS/NB\n10.2\u00b10.2\n2.6%\n5.2\u00b12.6\n2.0\u00b10.8\nfrom the single Z channel, whose pT(Z) distribution drops much faster than the signal. A cut of pT(Z) >\n100 GeV signi\ufb01cantly reduces this background, and has a negligible effect on the sensitivity to anomalous\ncouplings, which predominantly manifest at high pT.\nUsing the single isolated electron trigger (effective ET > 22 GeV) and the single isolated muon trigger\n(effective pT > 20 GeV), the trigger ef\ufb01ciency for selected ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd events is expected to be 97%.\nTable 14 gives a summary of the cuts applied and presents the expected number of events passing the\ncuts. The \ufb01nal row in each column gives the statistical error. If no events pass cuts, the \ufb01gure given is\nthe number of expected events at the 90% con\ufb01dence level. The dominant background is t\u00aft . Table 15\nsummarizes the expected yield and sensitivity of the ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd channel.\n4\nTotal cross section measurements\nA binned likelihood method is used to determine the most likely cross-sections. This likelihood method\nis also used to extract the sensitivities to the anomalous TGCs which will be described in Section 5. The\nlikelihood is based on Poisson statistics convoluted with Gaussian probabilities to model the signal and\nbackground uncertainties. What follows is a more detailed description of the binned likelihood method\nfollowed by a description of the statistical and systematic uncertainties for the diboson cross-section\nmeasurements using the \ufb01rst 1.0 fb\u22121 of data.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n851\n\n4.1\nBinned likelihood\nIn the binned likehood method, expected events are determined from high statistics Monte Carlo sim-\nulation, and observed events are also determined from Monte Carlo simulation for this work, but with\nappropriate statistical \ufb02uctuation according to the luminosity. The events are binned by one or more\nobservables. As an example, in the case of the cross-section measurement the BDT output spectrum, an\nexample of which is shown in Figure 8, could be used. In the TGC analysis described in Section 5 the\nMT(VV) and pT(V) spectra are choosen.\nFor each bin expected signal and background are compared to the observed number of events (n\nevents in the bin) with a likelihood, which is based on Poisson statistics. We assume the systematic un-\ncertainties of the signal and background are Gaussian and uncorrelated for each bin. Thus, two Gaussian\ndistributions are convolved with the Poisson distribution to form the likelihood\nL =\nZ 1+3\u03c3b\n1\u22123\u03c3b\nZ 1+3\u03c3s\n1\u22123\u03c3s\ngs gb\n(fs\u03bds + fb\u03bdb)n e\u2212(fs\u03bds+fb\u03bdb)\nn!\nd fs d fb with gi =\ne(1\u2212fi)2/2\u03c32\ni\nR \u221e\n0 e(1\u2212fi)2/2\u03c32\ni (i = s,b),\nhere the total systematic uncertainty of signal and background appear as \u03c3s and \u03c3b, respectively.\nFrom these likelihoods a total log-likelihood is formed from all the bin likelihoods. Some pro-\ncesses may also be separated into multiple channels (such as the three decay combinations of WW \u2192\nee,e\u00b5,\u00b5\u00b5). Also, a factor of -2 is included to make this test statistic comparable to a chi-squared distri-\nbution. Thus, the negative log-likelihood is\n\u22122lnL = \u22122\n\u2211\nk=channels \u2211\ni=bins\nlog(Lk\ni ).\nIn cross-section measurements, the likelihood is determined as a function of cross-section in each bin of\na measured spectrum for each channel (e.g. the BDT output spectrum for the W +W \u2212\u2192e\u03bd\u00b5\u03bd channel as\nshown on the left in Figure 8). The log-likelihoods are then combined and the minimum of the negative\nlog-likelihood determines the most likely cross-section (or anomalous TGC). The 68% C.L. limits (\u00b11\u03c3)\nare taken from the minimum of the negative log-likelihood plus 1.0. To set the 95% con\ufb01dence-level\ninterval of the anomalous TGC limits, likelihood minimum+1.92 is taken when \ufb01tting one parameter,\nand the minimum+2.99 for a \ufb01t of two parameters (e.g. two independent anomalous couplings).\n4.2\nStatistical uncertainties\nBased on the diboson event selections described in Section 3, the expected number of signal and back-\nground events for 1 fb\u22121, and the expected detection signi\ufb01cance of observing the Standard Model sig-\nnals, are summarized in Table 16, after taking into account the known background contributions and 20%\nsystematic uncertainties of the background estimate. The expected signal statistical uncertainties are also\ngiven in the 5th column of the table. For 1 fb\u22121 they range from 2.1% to 31% depending on the channel.\nFor early LHC data with 0.1 fb\u22121 integrated luminosity, the statistical uncertainties are large. How-\never, based on BDT analysis, with an assuption of a 20% systematic uncertainty, the signal detection\nsigni\ufb01cances could reach 9.9\u03c3 and 5.9\u03c3 for W +W \u2212and W \u00b1Z, respectively. The overall detection sig-\nni\ufb01cance is expected to be greater than 10\u03c3 for both W \u00b1\u03b3 and Z\u03b3 signals with 0.1 fb\u22121 of data.\n4.3\nSystematic uncertainties\nThe major theoretical uncertainties on the production cross-sections come from the PDF uncertainties\nand the QCD factorization scaling uncertainties (for NLO calculations). By varying the PDF\u2019s and scale\nvalues for W +W \u2212, W \u00b1Z, and ZZ cross-section calculations, the differences of the calculated cross-\nsections are found to range from 3.4% to 6.2%.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n852\n\n1\n10\n10 2\n10 3\n10 4\n10 5\n-1000 -750\n-500\n-250\n0\n250\n500\n750\n1000\nBDT Output\nATLAS (1 fb-1)\nMC Data\nSignal+Background\nSignal(ww\u2192 e\u03bd\u00b5\u03bd)\nBackground\n1\n10\n10 2\n10 3\n10 4\n-1000 -750\n-500\n-250\n0\n250\n500\n750\n1000\nBDT Output\nATLAS (1 fb-1)\nMC Data\nSignal+Background\nSignal(zw\u2192 lll\u03bd)\nBackground\nFigure 8: BDT-output spectra from a Monte Carlo experiment for W +W \u2212(left) and W \u00b1Z (right) detec-\ntion with 1 fb\u22121. The dots in the plots are Monte Carlo \u2018mock data\u2019. The dashed histograms represent\nthe signal and the dotted, background.\nThe major experimental systematic effects in the cross-section measurements arise from the un-\ncertainties of the luminosity determination, the lepton identi\ufb01cation ef\ufb01ciencies and energy/momentum\nresolutions, the jet energy scale and resolutions, and background model and estimate.\nA promising possibility for the precise determination of the luminosity is to use the W and Z pro-\nduction and leptonic decays. The estimates show that in this way the luminosity uncertainties could be\ncontrolled to \u223c5% [40]. It should be noted that a 6.5% luminosity uncertainty was quoted in Tevatron\nRun II physics papers.\nThe lepton acceptance uncertainty is about 2-3% mainly due to the isolation requirement which\ninvolves the hadronic jet energy uncertainties. The lepton trigger ef\ufb01ciency uncertainties also contribute.\nWith large Z samples, this uncertainty could be minimized. Z decays can typically be triggered and\nidenti\ufb01ed using only one of the two decay leptons. This leaves the second lepton unbiased from the point\nof view of trigger and of\ufb02ine identi\ufb01cation. The rate at which the unbiased lepton passes the trigger and\nID requirements provides a measurement of the respective ef\ufb01ciencies.\nIn the studies using the ATLAS simulated events the background estimate dominates the systematics\nwith uncertainties of 15-25% for all the diboson channels except for the ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212channel, where\nthe background uncertainty should be less than 2%. Even though more than 30 million fully simulated\nevents are used to estimate the background, the analyses are still largely limited by W + jets event\nsample statistics in the diboson background estimate. Tevatron experiments have used data to estimate\nthe background, and typical uncertainties for diboson physics analyses are around 10% for 1 fb\u22121 of data.\nWith early LHC data (0.1 fb\u22121), the background estimate uncertainty would be comparable to current\nTevatron diboson background uncertainties, and with more data the uncertainties of the background\nestimate should decrease.\nThe lepton and jet energy resolution uncertainties will contribute to additional background estimate\nuncertainties which will further propagate to the cross-section measurement uncertainties. A study has\nbeen performed in W \u00b1Z analysis to estimate the size of such uncertainties. In this study, the W \u00b1Z BDTs\nare \ufb01rst trained with Monte Carlo signal and background events simulated with the \u2018standard\u2019 detector\nenergy resolutions and calibrated energy scale. For independent test samples, 10% and 3% are added\nto the jet and lepton energy resolutions, respectively, and the reconstructed energy related quantities are\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n853\n\nTable 16: Summary of signal and background of all diboson \ufb01nal states (\u2113denotes e and \u00b5) for 1 fb\u22121\nof integrated luminosity. The 4th column indicates the overall signal selection ef\ufb01ciency and the type\nof analysis, The 5th column gives the signal statistical uncertainty. The last two columns indicate the\np-value and the signi\ufb01cance (in Gaussian standard deviations) where p-value is the probability of the\nbackground \ufb02uctating to the expected total observation assuming 20% systematic uncertainties.\nDiboson mode\nSignal\nBackground\nSignal eff.\n\u03c3signal\nstat\np-value\nSig.\nW +W \u2212\u2192e\u00b1\u03bd\u00b5\u2213\u03bd\n347\u00b13\n64\u00b15\n12.6% (BDT)\n5.4%\n3.6\u00d710\u2212166\n27.4\nW +W \u2212\u2192\u00b5+\u03bd\u00b5\u2212\u03bd\n70\u00b11\n17\u00b12\n5.2% (BDT)\n12.0%\n8.8\u00d710\u221230\n11.3\nW +W \u2212\u2192e+\u03bde\u2212\u03bd\n52\u00b11\n11\u00b12\n4.9% (BDT)\n13.9%\n1.9\u00d710\u221224\n10.1\nW +W \u2212\u2192\u2113+\u03bd\u2113\u2212\u03bd\n103\u00b13\n17\u00b12\n2.0% (cuts)\n9.9%\n1.4\u00d710\u221254\n15.5\nW \u00b1Z \u2192\u2113\u00b1\u03bd\u2113+\u2113\u2212\n128\u00b12\n16\u00b13\n15.2% (BDT)\n8.8%\n3.0\u00d710\u221276\n18.4\n53\u00b12\n8\u00b11\n6.3% (cuts)\n13.7%\n3.1\u00d710\u221230\n11.4\nZZ \u21924\u2113\n17\u00b10.5\n2\u00b10.2\n7.7% (cuts)\n24.6%\n6.0\u00d710\u221212\n6.8\nZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd\n10\u00b10.2\n5\u00b12\n2.6% (cuts)\n31.3%\n7.7\u00d710\u22124\n3.2\nW\u03b3 \u2192e\u03bd\u03b3\n1604\u00b165\n1180\u00b1120\n5.7% (BDT)\n2.5%\nsigni\ufb01cance > 30\nW\u03b3 \u2192\u00b5\u03bd\u03b3\n2166\u00b188\n1340\u00b1130\n7.6% (BDT)\n2.1%\nsigni\ufb01cance > 30\nZ\u03b3 \u2192e+e\u2212\u03b3\n367\u00b112\n187\u00b119\n5.4% (BDT)\n5.2%\n1.2\u00d710\u221291\n20.3\nZ\u03b3 \u2192\u00b5+\u00b5\u2212\u03b3\n751\u00b123\n429\u00b143\n11% (BDT)\n3.6%\n5.9\u00d710\u2212171\n27.8\nTable 17: Change of background acceptance in a test of BDT (W \u00b1Z vs. ZZ) performed by smearing jet\nenergy, E jet, and missing ET, /ET, by an additional 10%; and the lepton energy E\u2113\nT by an additional 3%.\nSignal Ef\ufb01ciency\nBackground Eff.\nBackground Eff.\nBackground Eff.\nNo additional smearing\n10% for E jet & /ET\n10% for E jet& /ET, 3% for E\u2113\nT\n40%\n4.0%\n4.2% (+5.7%)\n4.2%(+6.7%)\n50%\n8.6%\n8.9% (+3.7%)\n9.0%(+4.8%)\n60%\n14.6%\n14.9% (+2.2%)\n15.1%(+3.7%)\n70%\n22.3%\n22.7% (+2.0%)\n23.0%(+3.4%)\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n854\n\n\u2018smeared\u2019 to re\ufb02ect the uncertainties of the diboson detection sensitivity (signal to background ratio). In\nthis study the signal ef\ufb01ciencies are \ufb01xed and changes to the background acceptance are gauged. The\nresults are summarized in Table 17. As an example, for a BDT signal selection ef\ufb01ciency of 60%, the\nchange of the signal to background ratio is 3.4%. For the W \u00b1Z cross-section measurement with 1 fb\u22121\nof integrated luminosity, the 3.4-6.7% background contribution uncertainty would result in additional\ncross-section measurement uncertainties of about 2-3%.\n4.4\nMeasurement uncertainties vs. selection cuts and luminosities\nThe cross-section measurement uncertainties are estimated for various event selection cuts and integrated\nluminosities in the W +W \u2212and W \u00b1Z BDT based analysis. The BDT output spectra are used to build the\nlog-likelihood by using \u2018mock data\u2019, which is a sample of simulated events with appropriate statistics\naccording to the luminosity and the Standard Model. For example, the BDT-output spectra for a Monte\nCarlo experiment with 1 fb\u22121 of data are shown in Figure 8 for W +W \u2212\u2192e\u00b1\u03bd\u00b5\u2213\u03bd detection (left)\nand for W \u00b1Z \u2192\u2113\u00b1\u03bd\u2113+\u2113\u2212detection (right). The Standard Model \u2018mock data\u2019 (points) are compared to\nexpected signal (dashed histogram) and background (dotted histogram).\n10\n12\n14\n16\n18\n20\n-200 -100\n0\n100\n200\n300\n400\nBDT Cut\nUncertainty of \u03c3(WW \u2192 e\u03bd\u00b5\u03bd) (%)\nATLAS\npp \u2192 WW \u2192 e\u03bd\u00b5\u03bd\n1 fb-1\n10 fb-1\nno BDT cut\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n-200 -100\n0\n100\n200\n300\n400\nBDT Cut\nUncertainty of \u03c3(ZW \u2192 lll\u03bd) (%)\nATLAS\npp \u2192 ZW \u2192 lll\u03bd\n1 fb-1\n5 fb-1\n10 fb-1\nFigure 9: The total relative uncertainties for W +W \u2212(left) and for W \u00b1Z (right) cross section measure-\nments as the BDT cut is varied for different luminosities. The optimal BDT cut is between 200 and 300.\nAn overall 9.2% systematic uncertainty was included in the \ufb01tting process.\nTo understand the optimal cut on the BDT spectra for cross-section measurements, the cuts on the\nBDT spectra are varied and the cross-section measurements are repeated. A total 9.2% systematic un-\ncertainty is included in the \ufb01tting process. Figure 9 shows the cross-section measurement uncertainty as\na function of the BDT cut for different integrated luminosities from the W +W \u2212and the W \u00b1Z analysis.\nFigure 10 shows the relative cross-section uncertainties as a function of integrated luminosity (with\nBDT spectrum cut at 200) for W +W \u2212(left) and W \u00b1Z (right) cross-section measurements. From these\nplots it should be noted that the systematic uncertainty starts to dominate after 5 fb\u22121 of integrated\nluminosity for W +W \u2212cross-section measurements, and after 10 fb\u22121 for W \u00b1Z.\n5\nSensitivity to anomalous couplings\nThe signature of anomalous couplings in diboson production is an increase in the cross-section at high\nvalues of gauge boson transverse momentum (pT) and diboson transverse mass (MT). The ATLAS\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n855\n\n10\n12\n14\n16\n18\n20\n10\n-1\n1\n10\nIntegrated Luminosity (fb-1)\nUncertainty of \u03c3(WW \u2192e\u03bd\u00b5\u03bd) (%)\nATLAS\npp \u2192WW \u2192e\u03bd\u00b5\u03bd\n10\n15\n20\n25\n30\n35\n10\n-1\n1\n10\nIntegrated Luminosity (fb-1)\nUncertainty of \u03c3(ZW \u2192lll\u03bd) (%)\nATLAS\npp \u2192ZW \u2192lll\u03bd\nFigure 10: The W +W \u2212(left) and the W \u00b1Z (right) cross-section measurement uncertainties as a function\nof integrated luminosity (with BDT spectrum cut at 200). An overall 9.2% systematical uncertainty was\nincluded in the \ufb01tting process.\nsensitivity to anomalous TGC\u2019s is investigated by comparing the \u2019measured\u2019 diboson production cross-\nsections and the vector boson pT\nor diboson MT distributions to models with anomalous TGC\u2019s. A\nbinned likelihood \ufb01tting procedure using the MT or pT spectrum for each channel is followed to extract\nthe 95% C.L. intervals of anomalous coupling parameters. The most dramatic effect is an increase\nin the high MT or high pT\ncross-sections, so it is important for the binned likelihood calculation to\ninclude events up to the highest values of the observables. Details of the binned likelihood method are\ndescribed in Section 4.1. One- and two-dimensional limits are set on the charged CP-conserving coupling\nparameters from the W +W \u2212, W \u00b1Z, and W \u00b1\u03b3 \ufb01nal states. The ZZ \ufb01nal state is used to probe the neutral\nanomalous TGC sensitivity.\nThe values of the form factor scale \u039b are chosen such that the extracted experimental anomalous\ncoupling limit from data for a certain diboson production process is less than the unitarity limit [41].\nFor this study, with 0.1-1.0 fb\u22121 of integrated luminosity at early LHC running, \u039b values of 2-3 TeV are\nused. The same \u039b values of 2-3 TeV are also used to estimate the anomalous coupling sensitivities for\nhigher luminosities for simplicity. It should be noted that as the luminosity increases, the \u039b value should\nhave increased accordingly.\n5.1\nRe-weighting the fully simulated events\nTo avoid producing an impractically large number of fully simulated events in non-Standard Model\nanomalous coupling parameter space, a re-weighting method was invoked to study the ATLAS de-\ntector sensitivities to anomalous coupling parameters.\nThe BHO and the BosoMC calculations are\nused with different anomalous coupling parameters to re-weight the fully simulated events generated\nby MC@NLO. As an example, Figure 11 shows the W +W \u2212production differential cross-section distri-\nbutions for Standard Model and some anomalous coupling parameters (left plot) and the corresponding\ndifferential cross-section ratio, d\u03c3(non-SM)/dMT\nd\u03c3(SM)/dMT\n(right plot). These ratios have been used as weights to\nre-weight the fully simulated events to probe the anomalous TGC sensitivities. The weights are generated\nin one-dimensional and two-dimensional anomalous coupling space according to parton level kinematics\nusing the BHO and the BosoMC programs. To produce the weights the step size in coupling parameter\nspace ranges from 0.1 \u00d7 10\u22123 to 1.0 \u00d7 10\u22123. For each point in the coupling parameter space 5 million\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n856\n\nTGC from WW with PDF CTEQ6M\nStandard Model\n\u2206\u03baZ = -0.1\n\u03bbZ = -0.3\n\u2206g1Z = 0.4\n\u2206\u03ba\u03b3 = 0.5\n\u03bb\u03b3 = 0.5\nMT(W+W-)(GeV)\nd\u03c3/dMT(fb/10GeV)\n10\n-2\n10\n-1\n1\n10\n10 2\n0\n200\n400\n600\n800\n1000\nTGC from WW with PDF CTEQ6M\nStandard Model\n\u2206\u03baZ = -0.1\n\u03bbZ = -0.3\n\u2206g1Z = 0.4\n\u2206\u03ba\u03b3 = 0.5\n\u03bb\u03b3 = 0.5\nMT(W+W-)(GeV)\nDifferential cross-section ratio\n1\n10\n10 2\n0\n200\n400\n600\n800\n1000\nFigure 11: Left: WW transverse mass, MT, distributions. Events are generated with the Standard Model\ncoupling (black line) and anomalous couplings (colored symbols); Right: the corresponding differential\ncross-section ratio.\n(WZ) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n0\n5\n10\n15\n20\n25\n30\n35\n(WZ) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n0\n5\n10\n15\n20\n25\n30\n35\nOverflow\n int. lum.\n-1\nMock data for 1.0 fb\nBackground MC\nSM WZ MC stacked on bkgd\n=0.15\nZ\n\u03ba\n\u2206\nAC WZ MC \n=0 02\nZ\n\u03bb\nAC WZ MC \nATLAS\n(WZ) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n0\n200\n400\n600\n800\n1000\n(WZ) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n0\n200\n400\n600\n800\n1000\nOverflow\n int. lum.\n-1\nMock data for 30.0 fb\nBackground MC\nSM WZ MC stacked on bkgd.\n=0.15\nZ\n\u03ba\n\u2206\nAC WZ MC \n=0.02\nZ\n\u03bb\nAC WZ MC \nATLAS\nFigure 12: The expected signal+background of the Standard Model, superimposed with \u2018mock data\u2019\n(points with error bars showing statistical uncertainty), and the non-Standard Model (anomalous cou-\nplings) predicted signal+background histograms (dashed and dotted histograms). The left plot is for\n1 fb\u22121 of data and the right plot is for 30 fb\u22121 of data.\nevents were generated to obtain the theoretical \u2019reference\u2019 distributions. The fully simulated events with\nthe Standard Model couplings are required to pass the event selection cuts, and then reweighted accord-\ning to the parton level kinematics. The weighted events are equivalent to fully simulated events with the\ncorresponding anomalous couplings. The distributions of variables, sensitive to the anomalous coupling,\nsuch as lepton pT, of the data events, can be compared to those of simulated events with anomalous cou-\nplings included, to extract the limits on the anomalous couplings. In this study the Standard Model \u2018mock\ndata\u2019 are used to probe the ATLAS detector sensitivities to anomalous triple gauge boson couplings.\n5.2\nWWZ anomalous TGC sensitivity in W \u00b1Z analysis\nThe W \u00b1Z diboson production involves exclusively the WWZ coupling, in contrast to the W +W \u2212diboson\n\ufb01nal state which contains bothWWZ andWW\u03b3 couplings. To extract the 95% C.L. sensitivity intervals of\nthe anomalous parameters, \u2206\u03baZ,\u2206gZ\n1, and \u03bbZ, from the W \u00b1Z diboson \ufb01nal state, both the transverse mass\nof W \u00b1Z (MT(W \u00b1Z)) and the transverse momentum of Z (pT(Z)) spectra are used to \ufb01t the anomalous\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n857\n\nTable 18: Summary of WWZ one-dimensional anomalous coupling parameter 95% CL sensitivities using\nthe MT(W \u00b1Z) \ufb01tting for \u039b = 2 TeV and \u039b = 3 TeV for integrated luminosities of 0.1, 1, 10 and 30 fb\u22121.\nInt. Lumi\nCutoff \u039b\n\u2206\u03baZ\n\u03bbZ\n\u2206gZ\n1\n(fb\u22121)\n(TeV)\n0.1\n2.0\n[-0.440, 0.609]\n[-0.062, 0.056]\n[-0.063, 0.119]\n1.0\n2.0\n[-0.203, 0.339]\n[-0.028, 0.024]\n[-0.021, 0.054]\n10.0\n2.0\n[-0.095, 0.222]\n[-0.015, 0.013]\n[-0.011, 0.034]\n30.0\n2.0\n[-0.080, 0.169]\n[-0.012, 0.008]\n[-0.005, 0.023]\n0.1\n3.0\n[-0.399, 0.547]\n[-0.050, 0.046]\n[-0.054, 0.094]\n1.0\n3.0\n[-0.178, 0.281]\n[-0.020, 0.018]\n[-0.017, 0.038]\n10.0\n3.0\n[-0.135, 0.201]\n[-0.015, 0.013]\n[-0.013, 0.018]\n30.0\n3.0\n[-0.069, 0.131]\n[-0.008, 0.005]\n[-0.003, 0.016]\ncouplings.\nMonte Carlo experiments are performed with 0.1, 1, 10, and 30 fb\u22121 of integrated luminosities to\nstudy the anomalous coupling sensitivities. Figure 12 shows the expected signal+background of the\nStandard Model, superimposed with the \u2018mock data\u2019 (points with error bars), and the non-Standard\nModel (anomalous couplings) predicted signal+background distributions. Table 18 shows the summary\nof 1-dimensional 95% C.L. anomalous coupling parameter intervals based on the MT(W \u00b1Z) spectra\n\ufb01tting. Results corresponding to 0.1, 1, 10 and 30 fb\u22121 of integrated luminosities for cutoff, \u039b = 2 TeV\nand \u039b = 3 TeV are listed. It should be noted that even for 0.1 fb\u22121 of integrated luminosity, the ATLAS\nsensitivity to WWZ anomalous couplings could be much better than the Tevatron limits based on 1 fb\u22121\nof p \u00afp collision data.\nTo understand the systematic uncertainty effects on the TGC sensitivity, three different systematic\nuncertainty assumptions are considered: (1) ideal case with no systematic uncertainties: \u03c3S = 0, and\n\u03c3B = 0; (2) expected uncertainty of 7.2% for signal, and 12% for background, based on estimate from\nvarious contributions; and (3) worse than expected systematic uncertainty of 9.2% for signal, and 18.3%\nfor background. Unless otherwise stated, (3) was used to evaluate coupling limits.\nThe 95% C.L. 1-dimensional limits for the WWZ anomalous couplings, obtained from the \ufb01ts to the\npT(Z) assuming \u039b = 2 TeV are shown in Table 19, for different scenarios of systematic uncertainties.\nFrom this table it is seen that only when reaching 30 fb\u22121 of integrated luminosity do the systematic\nuncertainties become signi\ufb01cant enough to affect the TGC sensitivities.\nThe studies on the WWZ anomalous couplings in two-dimensional space are also based on the pT(Z)\n\ufb01ts for different integrated luminosities (0.1, 1, 10 and 30 fb\u22121) and for two cutoff values, \u039b = 2 TeV\nand 3 TeV. The anomalous coupling limit contours are not very sensitive to these cutoff values. The\neffects of different systematic uncertainties on the 2-dimensional TGC sensitivity contour are shown in\nFigure 13. The left plot shows the 95% C.L. anomalous TGC limit contour of \u03bbZ vs. \u2206\u03baZ = \u2206gZ\n1 without\nsystematic uncertainties, and the right plot shows the 95% C.L. TGC limit contour with the systematic\nuncertainties (\u03c3S = 9.2%, \u03c3B = 18.3%) included. Again, the systematic uncertainties become signi\ufb01cant\nwhen the integrated luminosity reaches 30 fb\u22121.\n5.3\nWW\u03b3 anomalous TGC sensitivity in W \u00b1\u03b3 analysis\nThe W \u00b1\u03b3 diboson production involves exclusively the WW\u03b3 triple gauge coupling. To extract the 95%\nC.L. sensitivity intervals of the anomalous parameters, \u2206\u03ba\u03b3 , and \u03bb\u03b3, from the W \u00b1\u03b3 diboson \ufb01nal state,\nthe photon transverse energy ET(\u03b3) distribution is used to \ufb01t the anomalous couplings, with \u039b = 2 TeV.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n858\n\nFigure 13: The left plot: 95% C.L. WWZ TGC limit contour of \u03bbZ vs. \u2206\u03baZ = \u2206gZ\n1; without the system-\natic uncertainties. The right plot: the 95% C.L. WWZ TGC limit contour of \u03bbZ vs. \u2206\u03baZ = \u2206gZ\n1, with\nsystematic uncertainties (\u03c3S = 9.2%, \u03c3B = 18.3%) included. The anomalous coupling limit contours\nfrom outer to inner corresponding integrated luminosities of 0.1, 1, 10 and 30 fb\u22121, respectively. The\nsystematic uncertainties become signi\ufb01cant when the integrated luminosity reaches 30 fb\u22121.\nTable 19: Comparison of WWZ one-dimensional anomalous coupling parameter 95% C.L. sensitivities\nfor different systematic uncertainties. Results obtained in this table are using the pT(Z) \ufb01t for \u039b = 2 TeV\nfor integrated luminosities of 0.1, 1, 10 and 30 fb\u22121.\nSystematic\nInt. Lumi\n\u2206\u03baZ\n\u03bbZ\n\u2206gZ\n1\nuncertainties\n(fb\u22121)\n\u03c3S = 0\n0.1\n[-0.942, 1.130]\n[-0.203, 0.193]\n[-0.227, 0.324]\n\u03c3B = 0\n1.0\n[-0.561, 0.664]\n[-0.093, 0.082]\n[-0.106, 0.154]\n10.0\n[-0.233, 0.231]\n[-0.033, 0.024]\n[-0.025, 0.061]\n30.0\n[-0.128, 0.136]\n[-0.024, 0.013]\n[-0.009, 0.047]\n\u03c3S = 7.2%\n0.1\n[-0.950, 1.140]\n[-0.204, 0.194]\n[-0.228, 0.325]\n\u03c3B = 12.0%\n1.0\n[-0.574, 0.692]\n[-0.093, 0.083]\n[-0.106, 0.158]\n10.0\n[-0.228, 0.302]\n[-0.033, 0.027]\n[-0.022, 0.070]\n30.0\n[-0.164, 0.212]\n[-0.026, 0.018]\n[-0.009, 0.055]\n\u03c3S = 9.2%\n0.1\n[-0.956, 1.150]\n[-0.204, 0.194]\n[-0.229, 0.326]\n\u03c3B = 18.3%\n1.0\n[-0.583, 0.706]\n[-0.094, 0.084]\n[-0.106, 0.159]\n10.0\n[-0.241, 0.316]\n[-0.033, 0.028]\n[-0.024, 0.071]\n30.0\n[-0.184, 0.228]\n[-0.028, 0.020]\n[-0.011, 0.056]\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n859\n\nTable 20: 95% C.L. intervals for the anomalous WW\u03b3 coupling parameters obtained from \ufb01tting the\nET(\u03b3) distribution to the NLO expectations using the combined sample of W(e\u03bd)\u03b3 and W(\u00b5\u03bd)\u03b3 events,\nwith \u039b = 2 TeV.\nW(\u2113\u03bd)\u03b3\n1 fb\u22121\n10 fb\u22121\n30 fb\u22121\n\u03bb\u03b3\n[-0.09, 0.04]\n[-0.05, 0.02]\n[-0.02,0.01]\n\u2206\u03ba\u03b3\n[-0.43, 0.20]\n[-0.26, 0.07]\n[-0.11,0.05]\nThe intervals are calculated for W \u00b1\u03b3 events by combining the electron and the muon decay channels.\nFigure 14 shows an ET(\u03b3) distribution from W \u00b1(\u2113\u00b1\u03bd)\u03b3 normalized to 1 fb\u22121 of data. The signal\nexpectations at LO and NLO are shown by the dashed and dotted lines on the left in Figure 14. On the\nright in Figure 14 is shown the 95% con\ufb01dence contour in the \u03bb\u03b3-\u2206\u03ba\u03b3 parameter space for 1 fb\u22121 of data.\nThe 1-dimensional 95% C.L. intervals of \u03bb\u03b3 and \u2206\u03ba\u03b3 are listed in Table 20.\nMock data\nBackground\nLO Expected\nNLO Expected\nET(\u03b3) [GeV]\nEvents [1fb-1]\nATLAS\n\u03bb\u03b3\n\u2206\u03ba\u03b3\nATLAS\n1\n10\n10 2\n10 3\n50\n100\n150\n200\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n-0.3 -0.2 -0.1\n0\n0.1\n0.2\n0.3\nFigure 14: Left: the ET(\u03b3) distributions of W(\u2113\u03bd)\u03b3 (\u2113= e, \u00b5) events for 1 fb\u22121 of data. Right: the\n95 % con\ufb01dence contour in the \u03bb\u03b3-\u2206\u03ba\u03b3 parameter space (\u039b = 2 TeV) for 1 fb\u22121 of W \u00b1\u03b3 data (with\nW \u2192e\u03bd, \u00b5\u03bd).\n5.4\nWWZ and WW\u03b3 anomalous TGC sensitivity in W +W \u2212analysis\nThe MT spectrum of W +W \u2212pair is \ufb01tted to obtain the WWZ and WW\u03b3 anomalous TGC sensitivity\nintervals at 95% con\ufb01dence level. A comparison of the MT(WW) distribution of the \u2018mock data\u2019 to that\nof models with anomalous coupling is shown in Figure 15. Five anomalous coupling parameters, (\u2206\u03baZ,\n\u03bbZ, \u2206gZ\n1, \u2206\u03ba\u03b3, \u03bb\u03b3), have been studied with only one parameter varied at the time; the remaining pa-\nrameters are \ufb01xed to Standard Model values. One dimensional anomalous coupling sensitivity intervals\nat 95% C.L. for different integrated luminosities are given in Table 21. The cutoff \u039b = 2 TeV is used\nin these calculations. The two-dimensional anomalous coupling limits from W +W \u2212production with\ndifferent scenarios relating the anomalous coupling parameters have also been investigated in this study.\nThe two-dimensional contours of the TGC limits at 95% con\ufb01dence level for 0.1, 1, 10 and 30 fb\u22121\nintegrated luminosities are shown in Figure 16. The left contours are the limits calculated with the HISZ\nassumption [43]. The right contours are calculated by assuming \u03bbZ = \u03bb\u03b3 and \u2206\u03baZ = \u2206\u03ba\u03b3.\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n860\n\n(WW) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n-1\n10\n1\n10\n2\n10\n(WW) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n-1\n10\n1\n10\n2\n10\nOverflow\n int. lum.\n-1\nMock data for 1.0 fb\nBackground MC\nSM WW MC stacked on bkgd.\n=0.16\nZ\n\u03ba\n\u2206\nAC WW MC \n=0.16\nZ\n\u03bb\nAC WW MC \nATLAS\n(WW) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n1\n10\n2\n10\n3\n10\n4\n10\n(WW) / GeV\nT\nM\n0\n100\n200\n300\n400\n500\nEvents / 50GeV\n1\n10\n2\n10\n3\n10\n4\n10\nOverflow\n int. lum.\n-1\nMock data for 30.0 fb\nBackground MC\nSM WW MC stacked on bkgd\n=0.16\nZ\n\u03ba\n\u2206\nAC WW MC \n=0.16\nZ\n\u03bb\nAC WW MC \nATLAS\nFigure 15: W +W \u2212transverse mass distributions for 1 (left) and 30 (right) fb\u22121 of integrated luminosities.\nThe last bins in the plots are \u2019over\ufb02ow\u2019-bins.\nTable 21: One-dimensional 95% C.L. interval of the WWZ and WW\u03b3 anomalous coupling sensitivities\nfrom the WW \ufb01nal state analysis for 0.1, 1, 10 and 30 fb\u22121 integrated luminosities, with \u039b = 2 TeV.\nInt. Lumi (fb\u22121)\n\u2206\u03baZ\n\u03bbZ\n\u2206gZ\n1\n\u2206\u03ba\u03b3\n\u03bb\u03b3\n0.1\n[-0.242, 0.356]\n[-0.206, 0.225]\n[-0.741, 1.177]\n[-0.476, 0.512]\n[-0.564, 0.775]\n1.0\n[-0.117, 0.187]\n[-0.108, 0.111]\n[-0.355, 0.616]\n[-0.240, 0.251]\n[-0.259, 0.421]\n10.0\n[-0.035, 0.072]\n[-0.040, 0.038]\n[-0.149, 0.309]\n[-0.088, 0.089]\n[-0.074, 0.165]\n30.0\n[-0.026, 0.048]\n[-0.028, 0.027]\n[-0.149, 0.251]\n[-0.056, 0.054]\n[-0.052, 0.100]\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n861\n\nFigure 16: The two-dimensional anomalous TGC limits at 95% C.L. for 0.1, 1, 10 and 30 fb\u22121 integrated\nluminosities.\n(Z) [GeV]\nT\np\n0\n100\n200\n300\n400\n500\n600\n700\n800\nEvents\n1\n10\n2\n10\nMock data\nStandard Model\nBest fit\nZ\n4\n95% C.L. on |f\n llll\n\u2192\nZZ \n-1\n10 fb\nATLAS\n(Z) [GeV]\nT\np\n100\n200\n300\n400\n500\n600\n700\n800\nEvents\n1\n10\n2\n10\nMock data\nStandard Model\nBest fit\nZ\n4\n95% C.L. on |f\n\u03bd\n\u03bd\n ll\n\u2192\nZZ \n-1\n10 fb\nATLAS\nFigure 17: Example of a \ufb01t to one \u2018mock data\u2019 sample in each channel. The points show the total number\nof data events in each bin (not number per unit pT ). The histograms show the Standard Model prediction\n(solid), the best \ufb01t (dashed) and the 95% C.L. limit on |f Z\n4 | (dotted).\n5.5\nZZZ and ZZ\u03b3 anomalous TGC sensitivity in ZZ analysis\nMeasurements of the pp \u2192ZZ differential cross-section can be used to measure, or set limits on, ZZZ\nand ZZ\u03b3 couplings. These couplings are zero at tree level in the Standard Model. Measurements of\nthe couplings provide a sensitive test of the Standard Model, and non-zero values would indicate the\npresence of new physics beyond the Standard Model.\nIn order to estimate limits on anomalous couplings which may be obtained from measurements of\nZZ production in early ATLAS data, the pT distribution of the Z boson is considered. In the ZZ \u2192\u2113\u2113\u03bd\u03bd\nchannel the visible Z boson reconstructed from the charged leptons is used. In the ZZ \u2192\u2113\u2113\u2113\u2113channel one\nof the two reconstructed Z bosons is chosen in each event at random. Simulated \u2018mock data\u2019 distributions\nare \ufb01tted with the sum of expected signal and background distributions, where the signal distribution\ndepends on the anomalous couplings. A binned maximum likelihood \ufb01t is employed, with systematic\nuncertainties included by convolution with the predictions. Fits are performed to each channel separately,\nand a combined \ufb01t is performed by multiplying together the likelihoods from the two channels assuming\nno correlated uncertainties.\nAn example \ufb01t for each channel is shown in Figure 17. The results presented here use four pT bins\nfor the \u2113\u2113\u03bd\u03bd channel and six pT\nbins for the 4-lepton channel, as shown in Figure 17. Reasonable\nmodi\ufb01cations to the number or position of pT bins change the expected limits by up to 15% (12%) in\nthe \u2113\u2113\u03bd\u03bd (\u2113\u2113\u2113\u2113) channel. Removing the \ufb01rst two pT bins for the \u2113\u2113\u2113\u2113channel, and \ufb01tting only the region\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n862\n\nTable 22: Expected 95% C.L. intervals on anomalous couplings from \ufb01ts to the ZZ \u2192\u2113\u2113\u2113\u2113channel,\nthe ZZ \u2192\u2113\u2113\u03bd\u03bd channel and both channels together for various values of integrated luminosity, with\n\u039b = 2 TeV. In each case, other anomalous couplings are assumed to be zero.\nInt. Lumi / fb\u22121\nf Z\n4\nf Z\n5\nf \u03b3\n4\nf \u03b3\n5\nZZ \u2192\u2113\u2113\u2113\u2113\n1\n[\u20130.023, 0.023]\n[\u20130.024, 0.024]\n[\u20130.028, 0.028]\n[\u20130.029, 0.028]\n10\n[\u20130.010, 0.010]\n[\u20130.010, 0.010]\n[\u20130.012, 0.012]\n[\u20130.013, 0.012]\n30\n[\u20130.008, 0.008]\n[\u20130.008, 0.008]\n[\u20130.009, 0.009]\n[\u20130.009, 0.009]\nZZ \u2192\u2113\u2113\u03bd\u03bd\n1\n[\u20130.024, 0.024]\n[\u20130.024, 0.025]\n[\u20130.029, 0.029]\n[\u20130.030, 0.029]\n10\n[\u20130.012, 0.012]\n[\u20130.012, 0.012]\n[\u20130.014, 0.014]\n[\u20130.015, 0.014]\n30\n[\u20130.009, 0.009]\n[\u20130.009, 0.009]\n[\u20130.011, 0.011]\n[\u20130.011, 0.011]\nCombined\n1\n[\u20130.018, 0.018]\n[\u20130.018, 0.019]\n[\u20130.022, 0.022]\n[\u20130.022, 0.022]\n10\n[\u20130.009, 0.009]\n[\u20130.009, 0.009]\n[\u20130.010, 0.010]\n[\u20130.011, 0.010]\n30\n[\u20130.006, 0.006]\n[\u20130.006, 0.007]\n[\u20130.008, 0.008]\n[\u20130.008, 0.008]\npT > 100 GeV has a negligible effect on the limits.\nTable 22 shows the mean expected limits from each channel separately, and from combining the\nchannels, for various values of integrated luminosity. With an integrated luminosity of 1 fb\u22121 the sensi-\ntivities of the two channels are very similar. At higher luminosities, the \u2113\u2113\u2113\u2113channel becomes somewhat\nmore sensitive, because it has lower background and hence a lower associated systematic uncertainty.\nWith as little as 1 fb\u22121 of data it should be possible to improve the LEP limits [32] on f Z\n4 , f Z\n5 and f \u03b3\n5\nby an order of magnitude using a single channel, while a similar improvement on f \u03b3\n4 will require both\nchannels.\nAt an integrated luminosity of 10 fb\u22121, the expected limits have only a low sensitivity to the back-\nground level and to the systematic uncertainties. With the same signal ef\ufb01ciency but no background,\nthe limits from the \u2113\u2113\u03bd\u03bd channel improve by 10%, while those from the \u2113\u2113\u2113\u2113channel change by only\n\u223c0.2%; in the latter case, doubling the background has an effect of only \u223c0.4%. Reducing all systematic\nuncertainties to zero improves the limits by 7% (6%) in the \u2113\u2113\u03bd\u03bd (\u2113\u2113\u2113\u2113) channel. Thus, the background\nlevel and systematic uncertainties are unlikely to be important factors in obtaining limits from early data.\nAs discussed above, the expected limits are affected by the choice of pT bins. The number of bins is\ncurrently limited by the statistics of the fully simulated Monte Carlo events. Future studies would bene\ufb01t\nfrom increased signal Monte Carlo statistics, particularly in the high pT region. In addition, samples\nof fully simulated events with anomalous couplings should be used to investigate the dependence of the\nef\ufb01ciency at a particular pT value on the production diagram.\n6\nSummary\nThis note presents studies of the production of W +W \u2212, W \u00b1Z, ZZ,W \u00b1\u03b3 and Z\u03b3 dibosons from pp col-\nlisions at the LHC, using leptonic decays of W \u00b1 and Z bosons. The simulated measurements are done\nusing the ATLAS detector with full detector simulation and event reconstruction, and the statistics ex-\npected in the initial data taking periods. It focuses on the sensitivities that ATLAS can achieve in the\nearly running of LHC, rather than the ultimate sensitivites that ATLAS might reach after running at the\ndesign luminosity. The advanced analysis technique BDT is used in analysis of most of the \ufb01nal states,\nwhich improves the sensitivities signi\ufb01cantly. Table 16 lists the expected numbers of signal and back-\nground events using 1 fb\u22121 of data, and the signi\ufb01cance of the Standard Model signals after taking into\naccount the known background contributions with 20% systematic uncertainties. It concludes that with\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n863\n\nTable 23: 95% C.L. interval of the anomalous coupling sensitivities from W +W \u2212, W \u00b1Z, W \u00b1\u03b3 \ufb01nal\nstates with 10.0 fb\u22121 of integrated luminosity and the cutoff \u039b = 2TeV. The table also indicates the\nvariables used in the \ufb01t to set the AC sensitivity interval. For reference, some recently published limits\nfrom Tevatron and LEP are also listed. These limits caculation assumptions are given in the table as well.\nDiboson,\n\u03bbZ\n\u2206\u03baZ\n\u2206gZ\n1\n\u2206\u03ba\u03b3\n\u03bb\u03b3\n(\ufb01t spectra)\nWZ, (MT)\n[-0.015, 0.013]\n[-0.095, 0.222]\n[-0.011, 0.034]\nW\u03b3, (p\u03b3\nT)\n[-0.26, 0.07]\n[-0.05, 0.02]\nWW, (MT)\n[-0.040, 0.038]\n[-0.035, 0.073]\n[-0.149, 0.309]\n[-0.088, 0.089]\n[-0.074, 0.165]\nWZ, (D0)\n(1.0 fb\u22121)\n[-0.17, 0.21]\n[-0.12, 0.29] (\u2206gZ\n1 = \u2206\u03baZ)\nW \u00b1\u03b3 (D0),\n(0.16 fb\u22121)\n[-0.88,0.96]\n[-0.2,0.2]\nWW, (LEP)\n[-0.051,0.034]\n[-0.105,0.069]\n[-0.059,0.026]\n(\u03bb\u03b3 = \u03bbZ,\u2206\u03baZ = \u2206gZ\n1 \u2212\u2206\u03ba\u03b3 tan2 \u03b8W)\nTable 24: Expected 95% C.L. intervals on anomalous couplings from \ufb01ts to the ZZ \u2192\u2113\u2113\u2113\u2113channel, the\nZZ \u2192\u2113\u2113\u03bd\u03bd channel and both channels together for 10 fb\u22121 of integrated luminosity, with \u039b = 2 TeV. In\neach case, other anomalous couplings are assumed to be zero. The 95% C.L. limits on neutral TGC from\nLEP ZZ detection are also listed.\nf Z\n4\nf Z\n5\nf \u03b3\n4\nf \u03b3\n5\nZZ \u2192\u2113\u2113\u2113\u2113\n[\u20130.010, 0.010]\n[\u20130.010, 0.010]\n[\u20130.012, 0.012]\n[\u20130.013, 0.012]\nZZ \u2192\u2113\u2113\u03bd\u03bd\n[\u20130.012, 0.012]\n[\u20130.012, 0.012]\n[\u20130.014, 0.014]\n[\u20130.015, 0.014]\nCombined\n[\u20130.009, 0.009]\n[\u20130.009, 0.009]\n[\u20130.010, 0.010]\n[\u20130.011, 0.010]\nLEP Limit\n[\u20130.30, 0.30]\n[\u20130.34, 0.38]\n[\u20130.17, 0.19]\n[\u20130.32, 0.36]\n0.1 fb\u22121 of integrated luminosity the Standard Model signals of W +W \u2212, W \u00b1Z, W \u00b1\u03b3 and Z\u03b3 can be\nestablished with signi\ufb01cance better than 5\u03c3 assuming 20% systematic uncertainties. ZZ production can\nbe established with 1 fb\u22121 of data using the four-lepton decay channels.\nAny signi\ufb01cant deviation from the Standard Model prediction for these \ufb01nal states can lead to in-\ndications of new physics phenomena. In Section 5, the sensitivities to anomalous TGC are presented.\nThe sensitivities are expressed in terms of constraints on the anomalous triple gauge boson couplings in\nthe effective Lagrangian. Table 23 compares the 95% con\ufb01dence level sensitivity interval for charged\nanomalous TGC\u2019s using observables from different diboson \ufb01nal states with 10 fb\u22121 of integrated lumi-\nnosity.\nThe neutral anomalous TGC\u2019s can be explored with the Z\u03b3 and ZZ \ufb01nal states. In this note, only\nZZ pairs are used for constraining the anomalous coupling, with the study using Z\u03b3 still in progress.\nBoth the ZZ \u2192\u2113+\u2113\u2212\u2113+\u2113\u2212and ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd \ufb01nal states are used to constrain the neutral anomalous\nTGC parameters ( f Z\n4 , f Z\n5 , f \u03b3\n4 , f \u03b3\n5 ). The 95% C.L. intervals on the anomalous couplings for 10 fb\u22121 of\nintegrated luminosity are listed in Table 24.\nThe current status of the Monte Carlo generators for diboson is less than satisfactory. MC@NLO\nis integrated with a parton shower (Herwig), but it does not have matrix elements for the effective\nLagrangian beyond the Standard Model with anomalous couplings. The BHO program can generate\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n864\n\nparton-level LO and NLO diboson events with anomalous couplings, but can not be correctly integrated\nwith the parton shower programs. In the current analysis, MC@NLO is used to simulate the Standard\nModel events. The BHO MC with anomalous TGCs is then used to re-weight the events so that the fully\nsimulated events can effectively have the anomalous TGC\u2019s, and be used directly to compare with the\nsimulated \u2019mock data\u2019.\nBecause of the higher center of mass energy at the LHC, the cross-sections for diboson production\nare an order of magnitude higher than at the Tevatron. This will allow ATLAS to improve the Tevatron\nmeasurements in the early running of the LHC. The large signal statistical signi\ufb01cances and signal to\nbackground ratios determined from these studies suggest that early observations of these channels will\ntake place at the LHC start up with 0.1 to 1 fb\u22121 of data. Systematic uncertainties will dominate the cross-\nsection measurement errors starting from 5-30 fb\u22121 of data. With increasing luminosity, the constraints\non the anomalous couplings will provide important probes of physics beyond the Standard Model.\nReferences\n[1] S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967);\nA. Salam, p. 367 of Elementary Particle Theory, ed. N. Svartholm (Almquist and Wiksells, Stock-\nholm, 1969);\nS.L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285 (1970).\n[2] Particle Data Group: W.-M. Yao et al., Journal of Physics, G 33, 1 (2006).\n[3] J. Ellison and J. Wudka, Annu. Rev. Nucl. Part. Sci. 48, 33(1998).\n[4] H.-J. Yang et al., Nucl. Instrum. & Meth. A 555 (2005) 370-385, [physics/0508045]; Nucl. Instrum.\n& Meth. A 543 (2005) 577-584, [physics/0408124]; Nucl. Instrum. & Meth. A 574 (2007) 342-349,\n[physics/0610276].\n[5] ATLAS Collaboration, \u2018ATLAS Detector and Physics Performance, Technical Design Report\u2019, AT-\nLAS TDR 15, CERN/LHCC 99-15.\n[6] Proceedings of the Workshop on Standard Model Physics (and more) at the LHC, CERN Yellow\nReport, CERN 2000/004, May 2000, - 117p, editors: G.Altarelli and M.L.Mangano.\n[7] M. Dobbs, M. Lefebvre, \u2018Prospects for probing the three gauge boson couplings in W + photon\nproduction at the LHC\u2019, ATL-PHYS-2002-022\n\u2018Prospects for probing the three gauge boson couplings in W + Z production at the LHC\u2019, ATL-\nPHYS-2002-023.\n[8] S. Hassani, \u2018Prospect for measuring neutral gauge boson couplings in Z\u03b3 production with the AT-\nLAS detector\u2019, ATLAS-PHYS-2003-023.\n[9] S. Hassani, \u2018Prospects for measuring neutral gauge boson couplings in ZZ production with the\nATLAS detector\u2019, ATL-PHYS-2003-022.\n[10] Lj. Simi\u00b4c et al., \u2018Prospects for Measuring Triple Gauge Boson Couplings in WW Production at the\nLHC\u2019, ATL-PHYS-2006-011, CERN 2006.\n[11] J.M. Campbell and R.K. Ellis, Phys. Rev. D60, 113006(1999).\n[12] L. Dixon, Z. Kunszt, A. Signer, Phys. Rev. D60, 114037(1999).\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n865\n\n[13] J. Ohnemus, Phys. Rev. D47, 940(1993);\nV. Barger, T. Han, D. Zeppenfeld, J. Ohnemus, Phys. Rev. D41, 2782(1990).\n[14] http://projects.hepforge.org/lhapdf/pubs\nJ. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P. Nadolsky, W.K. Tung,\n\u2018New Generation of Parton Distributions with Uncertainties from Global QCD Analysis\u2019, hep-\nph/0201195.\nATLAS CSC note on \u201cMonte Carlo Generators for the ATLAS Computing System Commission-\ning\u201d.\n[15] S. Frixione and B.R.Webber, JHEP 0206 (2002) 029;\nS. Frixione, P. Nason and B.R.Webber, JHEP 0308 (2003) 007.\n[16] M. Dobbs, \u2018Probing the Three Gauge-boson Couplings in 14 TeV Proton-Proton Collisions\u2019, Ph.\nD. Thesis (2002), University of Victoria;\nM. Dobbs, M. Lefebvre, \u2018Unweighted event generation in hadronic WZ production at the \ufb01rst order\nin QCD\u2019, ATL-PHYS-2000-028.\n[17] U. Baur, T. Han and J. Ohnemus, Phys. Rev., D50, 1917 (1994);\nU. Baur, T. Han and J. Ohnemus, Phys. Rev., D51, 3381 (1995);\nU. Baur, T. Han and J. Ohnemus, Phys. Rev., D53, 1098 (1996);\nU. Baur, T. Han and J. Ohnemus, Phys. Rev., D57, 2823 (1998).\n[18] U. Baur, \u2018Selfcouplings of electroweak bosons: Theoretical aspects and tests at hadron colliders.\u2019\nEurophysics Conf. on High Energy Physics, Brussels, Belgium, Jul 27-31, 1995. Published in Brus-\nsels EPS HEP 1995:197-200 (hep-ph/9510265)\n[19] F. Larios, M.A. Perez, G. Tavares-Velasco, J.J. Toscano, Phys. Rev. D63, 113014(2001);\nU. Baur and D. Zeppenfeld, Phys. Lett. B201, 383(1988);\nK. Hagiwara, R.D. Peccei, D. Zeppenfeld, Nucl. Physics B282, 253(1987).\n[20] U. Baur, T. Han and J. Ohnemus, Phys. Rev. D57, 2823(1998);\nG. J. Gounaris, J. Layssac, F.M. Rennard, Phys. Rev. D62, 073013(2000);\nU. Baur, D. Rainwater, Phys. Rev. D62, 113011(2000);\nM.A. Perez and F. Ramirez-Zavaleta, \u2018CP violation effects in the decay Z \u2192\u00b5+\u00b5\u2212\u03b3 induced by\nZZ\u03b3 and Z\u03b3\u03b3 couplings\u2019, hep-ph/0410212v4, 11 Jan. 2005.\n[21] E. Lipeles, \u2018 WW and WZ Production at the Tevatron\u2019, 33rd International Conference on High\nEnergy Physics (ICHEP 06), Moscow, Russia, 26 Jul - 2 Aug 2006. arXiv:hep-ex/0701038 (2007).\n[22] V. M. Abazov et al., D\u00d8 Collaboration, Phys. Rev. Lett. 94, 151801 (2005).\n[23] A. Abulencia et al., CDF Collaboration, Phys. Rev. Lett. 98, 161801 (2007).\n[24] V. M. Abazov et al., D\u00d8 Collaboration, Phys. Rev. D 76, 111104 (2007).\n[25] D. Acosta et al., CDF Collaboration, Phys. Rev. Lett. 94, 041803 (2005).\n[26] V. M. Abazov et al., D\u00d8 Collaboration, Phys. Lett. B653, 378(2007).\n[27] V. M. Abazov et al., D\u00d8 Collaboration, Phys. Rev. D 71, 091108 (2005).\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n866\n\n[28] T. Aaltonen et al., CDF Collaboration, \u2018First Measurement of ZZ production in p \u00afp Collision at\n\u221as = 1.96 TeV\u2019, hep-ex/0801.4806 (2008).\n[29] V. M. Abazov et al., D\u00d8 Collaboration, \u2018 Search for ZZ and Z\u03b3\u2217production in p \u00afp collisions at\n\u221as = 1.96 TeV and limits on anomalous ZZZ and ZZ\u03b3\u2217couplings\u2019, submitted to Phys. Rev. Lett.,\nhep-ex/0712.0599 (2007).\n[30] V. M. Abazov et al., D\u00d8 Collaboration, Phys. Rev. D 74 057101 (2006).\n[31] T. Aaltonen et al., CDF Collaboration, Phys. Rev. D 76 111103 (2007).\n[32] D. Abbaneo et al., ALEPH, DELPHI, L3, OPAL Collaborations and LEP Electroweak Working\nGroup and SLD Heavy Flavor and Electroweak Group, CERN-EP-2001-098 [hep-ex/0112021];\nReview of Particle Physics (PDG), p1098 (2004);\nThe LEP collaborations ALEPH, DELPHI, L3, OPAL and the LEP electroweak working group, A\nCombination of Preliminary Electroweak Measurements and Constraints on the Standard Model:\nCERN-PH-EP-2006-042, hep-ex/0612034, November 2006.\n[33] http://hepwww.rl.ac.uk/theory/seymour/herwig/hw65 manual.htm\n[34] T. Binoth, M. Ciccolini, N. Kauer and M. Kraemer, JHEP12, 046(2006).\n[35] T. Sjostrand et al., Comput. Phys. Commun., 135, 238259 (2001).\n[36] M.L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A. Polosa, JHEP 0307:001 (2003).\n[37] ATLAS Collaboration, G. Aad et al., \u2018The ATLAS Experiment at the CERN Large Hadron Col-\nlider\u2019, JINST 3 (2008) S08003.\n[38] The MiniBooNE Collaboration, A. A. Aguilar-Arevalo et al., Phys. Rev. Lett. 98, 231801 (2007);\nThe BABAR Collaboration, B. Aubert et al., [hep-ex/0607112];\nD0 Collaboration, V. M. Abazov et al., Phys. Rev. Lett. 98 , 181802 (2007);\nJ. Bastos, [physics/0702041].\n[39] H.-J. Yang et al., [arXiv:0708.3635]; JINST 3 p04004 (2008).\n[40] M. Dittmar, F. Pauss, D. Zuercher, Phys. Rev. D 56 (1997) 7284-7290.\n[41] U. Baur and D. Zeppenfeld, Phys. Lett. B 201 (1988) 383. H. Aihara et al., FERMILAB-Pub-\n95/031, March 1995\n[42] The LEP Collaborations ALEPH, DELPHI, L3, OPAL and the LEP Electroweak Working Group,\nCERN-EP/2006-042,p.52, 2006; hep-ex/0612034.\n[43] K. Hagiwara, S. Ishihara, R. Szalapski, and D. Zeppenfeld, Phys. Rev. 48, 2182(1993).\nSTANDARD MODEL \u2013 DIBOSON PHYSICS STUDIES\n867\n\n\nTop Quark\n869\n\nTop Quark Physics\nAbstract\nIn the early days of data taking at the LHC, top quark physics will have a role of\nprimary importance for several reasons. At start-up, already with the \ufb01rst few\nfb\u22121 of integrated luminosity, a top quark signal can be clearly separated from\nthe background even with an imperfectly calibrated detector and the top quark\npair production cross-section can be extracted at better than 20% accuracy and\nwith negligible statistical error. The \ufb01rst measurement of the top quark mass\nwill provide feedback on the detector performance and top quark events can be\nused to understand and calibrate the light jet energy scale and the b-tagging.\nAdditionally in scenarios beyond the Standard Model, new particles may decay\ninto top quarks, therefore a detailed study of the top quark properties may\nprovide a hint of new physics. A good understanding of top quark physics\nis also essential as top quark events are a background for many new physics\nsearches.\n1\nIntroduction\nThe top quark, discovered at Fermilab in 1995 [1], completed the three generation structure of the Stan-\ndard Model and opened up the new \ufb01eld of top quark physics. Produced predominantly, in hadron-hadron\ncollisions, through strong interactions, the top quark decays rapidly without forming hadrons, and almost\nexclusively through the single mode t \u2192Wb. The W-boson can then decay leptonically or hadronically.\nThe relevant CKM coupling is already determined by the (three-generation) unitarity of the CKM ma-\ntrix. Yet the top quark is distinguished by its large mass, about 35 times larger than the mass of the\nnext heavy quark, and close to the electroweak symmetry breaking scale. This unique property raises a\nnumber of interesting questions. For example if the top quark mass is generated by the Higgs mechanism\nas the Standard Model predicts and if its mass is related to the top-Higgs-Yukawa coupling, or if it does\nplay an even more fundamental role in the electroweak symmetry breaking mechanism. Non Standard\nModel physics could \ufb01rst manifest itself in non-standard couplings of the top quark which show up as\nanomalies in top quark production and decays. By studying the top quark, some of these questions may\nbe answered. Further insight in top quark properties will come from measurements done with the high\nstatistics sample of t\u00aft pairs such as top quark and W polarization studies sensitive to anomalous Wtb cou-\nplings, searches for rare top quark decays indicating the presence of new physics, or for new resonances\ndecaying to t\u00aft pairs.\nThe LHC will be a top quark factory, producing millions of t\u00aft pairs in a sample of 10 fb\u22121, which is\nexpected to be collected during the \ufb01rst years of LHC operation.\nThe understanding of the experimental signatures for top quark events involves most parts of the ATLAS\ndetector and is essential for claiming potential discoveries of new physics.\nSince numerous single (anti-)top quark events are produced via electroweak interactions, the top quark\nproperties, such as the Wtb coupling, can be examined with high precision at the LHC during its \ufb01rst\nyears of running.\n2\nTop quark pair production\nIn proton-proton collisions top quark pairs are produced through both gluon-gluon and quark-antiquark\nscattering (Figure 1). The relative importance of both amplitudes depends on the center of mass energy\nof the collision and nature of the beams: at the LHC the gluon scattering process dominates (\u223c90% of\n870\n\nthe cases) while at the Tevatron, production of top quark pairs is kinematically restricted to the quark\ndominated region. This difference appears also in the values of the cross-section: that is about 100 times\nlarger at the LHC than at the Tevatron. The large top quark mass (mt) ensures that top quark production\nis a short-distance process, and that the perturbative expansion, given by a series in powers of the small\nparameter \u03b1s(mt), converges rapidly. The cross-section used throughout this note for production at the\nLHC has been calculated up to NLO order including NLL soft gluon resummation, and results in about\n833\u00b1100 pb, where the uncertainty re\ufb02ects the theoretical error obtained from varying the renormalisa-\ntion scale by a factor of two [2]. The effect of PDF errors accounts for a few percent uncertainty, while\nvarying the top mass by a factor of two, an uncertainty of about 6% on the cross-section is obtained. A\ncalculation that includes NNLL soft-gluon corrections results in a central value for the tt cross-section of\n872.8 pb [3]. This translates to about 83,000 top quark pairs in a sample of 100 pb\u22121 and of the order of\n107 top quark pairs produced per year before any selection or detection criteria are applied.\nFigure 1: Top production processes at lowest order: gluon-gluon scattering diagrams (a)\nand b)) and quark-quark scattering diagram c).\n2.1\nObservables and phenomenology\nIn the Standard Model, the decay of top quarks takes place almost exclusively through the t\u2192Wb decay\nmode. A W-boson decays in about 1/3 of the cases into a charged lepton and a neutrino. All three lepton\n\ufb02avors are produced at approximately equal rate. In the remaining 2/3 of the cases, the W-boson decays\ninto a quark-antiquark pair, and the abundance of a given pair is instead determined by the magnitude\nof the relevant CKM matrix elements. Speci\ufb01cally, the CKM mechanism suppresses the production of\nb-quarks as |Vcb|2 \u22431.7 \u00d7 10\u22123. Thus, the quarks from W-boson decay can be considered as a clean\nsource of light quarks.\nFrom an experimental point of view, one can characterise the top quark decay by the number of W-\nbosons that decay leptonically. A value of 10.8% and 67.6% has been used for the leptonic and hadronic\nbranching ratio (BR) of the W-boson, respectively [4]. The following signatures can be identi\ufb01ed:\n\u2022 Fully leptonic: represents about 1/9 of the tt events. Both W-bosons decay into a lepton-neutrino\npair, resulting in an event with two charged leptons, two neutrinos and two b-jets. This mode is\nidenti\ufb01ed by requiring two high pT leptons and the presence of missing transverse energy (/ET),\nand allows a clean sample of top quark events to be obtained. However, this sample has limited\nuse in probing the top quark reconstruction capability of the ATLAS experiment, due to the two\nneutrinos escaping detection.\n\u2022 Fully hadronic: represents about 4/9 of the tt decays. Both W-bosons decay hadronically, which\ngives at least six jets in the event: two b-jets from the top quark decay and four light jets from the\nW-boson decay. In this case, there is no high pT lepton to trigger on, and the signal is not easily\nTOP \u2013 TOP QUARK PHYSICS\n871\n\ndistinguishable from the abundant Standard Model QCD multi-jets production, which is expected\nto be orders of magnitude bigger than the signal. Another challenging point of this signature is the\npresence of a high combinatorial background when reconstructing the top quark mass.\n\u2022 Semi-leptonic: represents about 4/9 of the tt decays. The presence of a single high pT lepton\nallows to suppress the Standard Model W+jets and QCD background. The pT of the neutrino can\nbe reconstructed as it is the only source of /ET for signal events.\nIn this document, top pair production is studied in the semi-leptonic and fully leptonic decay modes.\n3\nSingle Top Quark Production\nIn the Standard Model single-top quark production is due to three different mechanisms: (a) W-boson and\ngluon fusion mode, which includes the t-channel contribution and is referred to as t-channel or Wg as a\nwhole (b) associated production of a top quark and a W-boson, denoted Wt, and (c) s-channel production.\nThe corresponding diagrams are shown in Fig. 2. We note however that these de\ufb01nitions are valid only\nat leading order (LO): next to leading order (NLO) calculations may introduce diagrams which cannot\nbe categorised so unambiguously. The total NLO cross-section amounts to about 320 pb at the LHC.\nAmong those channels, the dominant contribution comes from the t-channel processes, which account\nfor about 250 pb; the Wt contribution amounts to about 60 pb while the s-channel mode is expected with\na cross-section of about 10 pb [5] [6].\nFigure 2: Main graphs corresponding to the three production mechanisms of single-top\nquark events: (a) t-channel (b) Wt associated production (c) s-channel.\nIn the following notes, when discussing the analysis strategy in the s- and t-channels, we will use only\nthe leptonic decay of the W-bosons (l\u03bdb\u00afb and l\u03bdb(\u00afb)q \ufb01nal states, respectively)1. For the associated Wt\nproduction, we will consider events where one of the W-bosons ( either the one produced together with\nthe top quark or the one appearing in the top quark decay) decays leptonically and the other hadronically.\nThe \u03c4 decay modes were included in all relevant simulated event samples, though signal selection is\naimed at electron and muon signatures.\nWe note that in pp collisions, the cross-section for single-top quark is not charge symmetric. The\ns-channel t\u00afb \ufb01nal state cross-section is predicted to be a factor 1.6 higher than the one corresponding\nto the \u00aftb \ufb01nal state. This ratio is 1.7 if only the t-channel processes are included. This feature is of\nspecial interest since it generates a charge asymmetry in the leptonic \ufb01nal state that can be exploited in\nthe analysis to reduce the contamination from the top quark pair production, which constitutes the main\n1The hadronic decay modes have obvious disadvantages for triggering and the lack of a lepton signature increases the\nbackground signi\ufb01cantly\nTOP \u2013 TOP QUARK PHYSICS\n872\n\nbackground to our signal. On the other hand, the rates for the charge-conjugate processes W\u2212+t and\nW+ +\u00aft are identical.\nSigni\ufb01cant sources of uncertainties affect the theoretical predictions of the production cross-sections.\nThe s-channel is known with a precision of 9.1% at NLO [5,7], while the t-channel has an uncertainty of\n4.8% [5,7]. An uncertainty of 3% is quoted for the Wt channel [6]. Those uncertainties come from three\nmain sources. The uncertainty in the parton luminosity, depending upon the choice of the parton density\nfunctions, is particularly important (2 to 4% for the s- and t-channels), since the b parton or the gluons are\ninvolved in the hard processes. The choice for the renormalization and factorization scales accounts for\nabout 2 and 3% uncertainty in s- and t-channel calculations respectively. Finally, a few GeV uncertainty\non the top quark mass mt results in percent level variation of the cross-sections. The uncertainty in \u03b1s\nenters marginally in the total error at a value below the 1% level.\n4\nMonte Carlo samples\nThe Monte Carlo samples which have been used for the top quark analyses reported are described in this\nsection. The calculation of many processes bene\ufb01t from methods such as resummation of next-to-leading\nlog terms and some are calculated at the full NLO accuracy. All the samples used have been normalized\nusing \u201dK-factors\u201d, to the NLO theoretical cross-section calculations whenever available [8]. The value\nof mt = 175 GeV has been used for the generation of all samples and all cross-sections correspond\nto this value. Most samples were processed with the full GEANT4 ATLAS detector simulation and\nreconstruction code. In some cases, the fast simulation package ATLFAST has been used.\nThe effect of pile-up in the cavern corresponding to a luminosity of 1033 cm\u22122s\u22121 has been simulated\nboth for tt and single top events.\n4.1\nSimulation of t\u00aft signal events\nTop quark pair production has been simulated using the Monte Carlo generator MC@NLO [9] version\n3.1. The hard process of tt production is calculated at NLO, so that diagrams that produce one additional\nparton in the \ufb01nal state are included at matrix element level. The parton density function CTEQ6M [10]\nis used. Fragmentation and hadronisation is simulated using HERWIG [11] and the underlying event\nby Jimmy [12]. The tt main samples for analysis are a sample of single and double leptonic events and\none of fully hadronic events. There are no cuts applied at generation level other than the lepton \ufb02avor\nseparation according to W-boson decay type that allowed subdividing the generated events into these\ntwo samples. A number of other samples mainly aimed at systematic studies have been produced and\nare listed in Table 1. Among these AcerMC [13] samples interfaced with PYTHIA for the hadronisation\nand fragmentation and simulation of the underlying event, aimed at initial and \ufb01nal state radiation (ISR\nand FSR) studies, that will be discussed later in the text. For the tt rare decays samples were produced\nwith TopRex [14] interfaced with PYTHIA for the hadronisation and fragmentation and simulation of\nthe underlying event.\n4.2\nSimulation of single top quark events\nFor the single top quark signal production, the AcerMC matrix element generator was used in conjunction\nwith PYTHIA, that was used for hadronisation, fragmentation and simulation of the underlying event.\nThe parton density functions CTEQ6M have been used. Compared to TopRex which was previously\nused in ATLAS, its t-channel generation method is based on a more physically motivated method [15]\nfor combining LO and tree level NLO diagrams. The contribution from NLO diagrams is rather important\nfor the t-channel as the gluon splitting to b\u00afb tends to be underestimated with the parton shower method.\nTOP \u2013 TOP QUARK PHYSICS\n873\n\nTable 1: tt and single top quark simulated samples used throughout the notes. (mt=175 GeV)\nis used as default in the generation. Given are a short description of the simulated physics\nprocess, the generator used, the production cross-section (\u03c3), and the K-factor that should\nbe applied to the quoted cross-section.\nMC@NLO + HERWIG tt \u2013 fully simulated events \u2013 K-factor = 1.0\n\u03c3(pb)\u00d7BR\nFully leptonic and semi-leptonic tt\n450\nFully hadronic tt (mt=175 GeV)\n380\nFully leptonic and semi-leptonic tt (mt=160 GeV)\n450\nFully leptonic and semi-leptonic tt (mt=170 GeV)\n450\nFully leptonic and semi-leptonic tt (mt=180 GeV)\n450\nFully leptonic and semi-leptonic tt (mt=190 GeV)\n450\nFully leptonic and semi-leptonic tt no UE\n450\nInclusive tt (pT(t) \u2265200 GeV)\n100\nAcerMC+PYTHIA \u2013 tt \u2013 fully simulated events \u2013 K-factor = 1.0\n\u03c3(pb)\nFully leptonic and semi-leptonic tt\n450\nFully leptonic and semi-leptonic tt, different ISR/FSR (low top mass)\n450\nFully leptonic and semi-leptonic tt, different ISR/FSR (high top mass)\n450\nAcerMC+PYTHIA single top quark Wt-channel \u2013 full sim. events K-factor = 1.14\n\u03c3(pb)\nSingle top quark associated Wt production, semi-leptonic decay\n25.5\nAcerMC+PYTHIA single top quark s-channel \u2013 full sim. events K-factor = 1.5\nSingle top quark s-channel leptonic decay\n2.3\nAcerMC+PYTHIA single top quark t-channel \u2013 full sim. events K-factor = 0.98\nSingle top quark t-channel leptonic decay\n81.3\nTopRex+PYTHIA \u2013 tt rare decays \u2013 fully simulated events\ntt\u2192bW(\u2113\u03bd)+q\u03b3\ntt\u2192bW(\u2113\u03bd)+qZ(\u2113\u2113); \u2113= e,\u00b5\ntt\u2192bW(\u2113\u03bd)+qg\nThe s-channel and Wt-channel are generated at LO accuracy only. All three channels were generated\nwith W-bosons forced to decay leptonically (e or \u00b5 or \u03c4). In the case of Wt, either the associated W-\nbosons or the W-bosons from top quark decay is forced to decay leptonically and no dileptonic events\nare included. The Monte Carlo samples that have been used in the analyses and the corresponding\nnormalisation cross-sections can be found in Table 1.\n4.3\nSimulation of background W + jet events\nFor the W + jets production, the ALPGEN [16] generator with HERWIG [11] clustering has been used.\nHERWIG has been used for the simulation of the fragmentation and the hadronisation and Jimmy for the\nunderlying event. The MLM [17] algorithm has been used to match the parton shower and the matrix\nelement calculations. The matching parameters are the minimum pT of the partons and the minimum \u2206R\namong two partons, de\ufb01ned as the separation of two objects in the \u03b7-\u03c6 space, (\u2206R)2 = (\u2206\u03b7)2 +(\u2206\u03c6)2.\nHere, \u03b7 is the pseudorapidity of an object, de\ufb01ned as \u03b7 = \u2212ln(tan(\u03b8/2)) and \u03c6 and \u03b8 are the azimuthal\nand polar angles, respectively. All cones are de\ufb01ned in \u03b7-\u03c6 space. The values of the matching parameters\nthat are used in this note are pT = 20 GeV and \u2206R = 0.3.\nA fraction of this background contains heavy quarks. This background is treated separately in ALPGEN\nTOP \u2013 TOP QUARK PHYSICS\n874\n\nby producing W+b\u00afb and W+c\u00afc (plus light jets) samples. The W-boson background samples used\nthroughout the notes are described in Table 2 2.\n4.4\nSimulation of background Z \u2192\u2113\u2113+ jets events\nThe Z \u2192\u2113\u2113+ n jets background events, where the lepton \ufb02avor can be any charged lepton, has been\ngenerated with ALPGEN, while HERWIG has been used for the simulation of the fragmentation and\nthe hadronisation and Jimmy for the underlying event. The MLM algorithm has been used to match the\nparton shower and the matrix element calculations. The matching parameters values are pT = 20 GeV\nand \u2206R = 0.3.\nThe contribution of those backgrounds to our analyses is non-negligible only when there is at least one\njet in addition to the Z. The samples have been generated with up to 5 additional jets. Samples generated\nwith PYTHIA have also been used: the complete list of the samples can be found in Table 33.\n4.5\nSimulation of di-boson background\nDi-boson events produced with light jets can be a background for the tt and single top quark signal. WW,\nWZ and ZZ processes with all decay modes have been generated with HERWIG: a \ufb01lter was applied to\nselect those events with an electron or a muon with pT > 10 GeV. WW events with the W-boson decaying\nleptonically into \ufb01nal states with two electrons, an electron (muon) and a \u03c4-lepton and two \u03c4-leptons have\nbeen generated with MC@NLO interfaced with HERWIG for the hadronisation and fragmentation ( see\nTable 4).\n4.6\nQCD background\nQCD multi-jet events are a background for tt and single top quark analyses if at least one of the jets\nin the event is misidenti\ufb01ed as an isolated lepton. The level of QCD multi-jet background has large\nuncertainties with the currently available generation tools, which are based on a leading order description:\nALPGEN has been used to generate these events with the same matching parameters as discussed in\nsection 4.3. Given the large cross-section for this process only fast simulated events (ATLFAST) have\nbeen produced and used for the present studies. Events with 2 to 5 light jets and b\u00afb+0,1,2,3 light jets\nhave been generated requiring at least 3 jets in the \ufb01nal state with pT > 30 GeV. Di-jet fully simulated\nPYTHIA events are available and have been used for comparison with the ATLFAST results (see Table 5).\nIn practice, the level of background will be derived directly from the data and will strongly depend on the\nlepton fake rate, and can depend on the topology of the event. Different cuts can be applied to strongly\nreduce this background. In fully hadronic tt decays, QCD multi-jet events are the main background and\na different strategy has to be developed. These decays are not studied in details in this document.\n5\nReconstruction of physics objects\nWe use de\ufb01nitions of high level reconstructed objects (electrons, muons, jets, etc.) that are standard in\nATLAS. They are described in the following sections. In the de\ufb01nitions, we often use the distance \u2206R\nbetween objects.\n2The difference in the cross section for the different leptons in the \ufb01rst set of events in Table 2 (fully simulated W boson\nevents with ALPGEN) is due to the truth jet \ufb01lter. Electrons and \u03c4 leptons can also be reconstructed as a jet: it is more probable\nfor electrons than for \u03c4 leptons that are reconstructed via their visible decay products.\n3In the truth jet \ufb01lter applied to the fully simulated Z boson events with ALPGEN in Table 3 jets made from leptons are\nremoved at the \ufb01lter level.\nTOP \u2013 TOP QUARK PHYSICS\n875\n\nTable 2: W-boson background samples used throughout the notes. Given are a short descrip-\ntion of the simulated physics process, the generator used, the production cross-section (\u03c3)\nincluding \ufb01lter, matching ef\ufb01ciency for ALPGEN and selection ef\ufb01ciency, and the K-factor\nthat should be applied to the quoted cross-section.\nALPGEN + Jimmy \u2013 W-boson \u2013 fully simulated events \u2013 K-factor = 1.15\n\u03c3(pb)\nW\u2192e\u03bd + 2 partons; truth \ufb01lter 3jets with pj\nT \u226530 GeV\n214\nW\u2192e\u03bd + 3 partons\n124\nW\u2192e\u03bd + 4 partons\n54\nW\u2192e\u03bd + 5 partons\n22\nW\u2192\u00b5\u03bd + 2 partons; truth \ufb01lter 3jets with pj\nT \u226530 GeV\n16\nW\u2192\u00b5\u03bd + 3 partons\n65\nW\u2192\u00b5\u03bd + 4 partons\n36\nW\u2192\u00b5\u03bd + 5 partons\n20\nW\u2192\u03c4\u03bd + 2 partons; truth \ufb01lter 3jets with pj\nT \u226530 GeV\n88\nW\u2192\u03c4\u03bd + 3 partons\n87\nW\u2192\u03c4\u03bd + 4 partons\n46\nW\u2192\u03c4\u03bd+ \u22655 partons\n21\nALPGEN + Jimmy \u2013 W boson \u2013 Atlfast sample \u2013 K-factor = 1.15\n\u03c3(pb)\nW\u2192e\u03bd + 0 parton\n13400\nW\u2192e\u03bd + 1 parton\n2610\nW\u2192e\u03bd + 2 partons\n826\nW\u2192e\u03bd + 3 partons\n239\nW\u2192e\u03bd + 4 partons\n67.4\nW\u2192e\u03bd+ \u22655 partons\n24.0\nW\u2192\u00b5\u03bd + 0 parton\n13400\nW\u2192\u00b5\u03bd + 1 parton\n2590\nW\u2192\u00b5\u03bd + 2 partons\n826\nW\u2192\u00b5\u03bd + 3 partons\n236\nW\u2192\u00b5\u03bd + 4 partons\n68.3\nW\u2192\u00b5\u03bd+ \u22655 partons\n24.3\nW\u2192\u03c4\u03bd + 0 parton\n13400\nW\u2192\u03c4\u03bd + 1 parton\n2620\nW\u2192\u03c4\u03bd + 2 partons\n828\nW\u2192\u03c4\u03bd + 3 partons\n239\nW\u2192\u03c4\u03bd + 4 partons\n67.7\nW\u2192\u03c4\u03bd+ \u22655 partons\n24.4\nALPGEN + Jimmy \u2013 W+bb \u2013 fully simulated events \u2013 K-factor = 2.57\n\u03c3(pb)\nW +bb + 0 parton; no \ufb01lter\n6.26\nW +bb + 1 parton\n6.97\nW +bb + 2 partons\n3.92\nW +bb + 3 partons\n2.77\nALPGEN + Jimmy \u2013 W+cc \u2013 fully simulated events \u2013\n\u03c3(pb)\nW +cc + 0 parton; no \ufb01lter\n6.72\nW +cc + 1 parton\n7.49\nW +cc + 2 partons\n4.36\nW +cc + 3 partons\n2.45\nTOP \u2013 TOP QUARK PHYSICS\n876\n\nTable 3: Z boson background samples used throughout the note. Given are a short descrip-\ntion of the simulated physics process, the generator used, the production cross-section (\u03c3)\nincluding \ufb01lter, selection ef\ufb01ciency and matching ef\ufb01ciency for ALPGEN, and the K-factor\nthat should be applied to the quoted cross-section.\nALPGEN + Jimmy \u2013 Z boson \u2013 fully simulated events \u2013 K-factor = 1.24\n\u03c3(pb)\nZ \u2192e+e\u2212+ 1 parton; pe\nT \u226510 GeV, one jet with pj\nT \u226520 GeV\n138\nZ \u2192e+e\u2212+ 2 partons\n50.5\nZ \u2192e+e\u2212+ 3 partons\n16.2\nZ \u2192e+e\u2212+ 4 partons\n4.6\nZ \u2192e+e\u2212+ \u22655 partons\n1.7\nZ \u2192\u00b5+\u00b5\u2212+ 1parton; p\u00b5\nT \u226510 GeV, one jet with pj\nT \u226520 GeV\n136\nZ \u2192\u00b5+\u00b5\u2212+ 2 partons\n51.7\nZ \u2192\u00b5+\u00b5\u2212+ 3 partons\n16.3\nZ \u2192\u00b5+\u00b5\u2212+ 4 partons\n4.6\nZ \u2192\u00b5+\u00b5\u2212+ \u22655 partons\n1.7\nZ \u2192\u03c4+\u03c4\u2212+ 1 parton; p\u2113\nT \u226510 GeV, one jet with pj\nT \u226520 GeV\n57\nZ \u2192\u03c4+\u03c4\u2212+ 2 partons\n21.3\nZ \u2192\u03c4+\u03c4\u2212+ 3 partons\n7.0\nZ \u2192\u03c4+\u03c4\u2212+ 4 partons\n2.2\nZ \u2192\u03c4+\u03c4\u2212+ \u22655 partons\n0.8\nPYTHIA \u2013 Z boson \u2013 fully simulated events \u2013 K-factor = 1.22\n\u03c3(pb)\nZ \u2192e+e\u2212; pe\nT \u226510 GeV, m\u2113\u2113\u226520 GeV\n1432\nZ \u2192\u00b5+\u00b5\u2212; p\u00b5\nT \u226510 GeV, m\u2113\u2113\u226520 GeV\n1497\nZ \u2192\u03c4+\u03c4\u2212; p\u2113\nT \u22655 GeV, m\u2113\u2113\u226520 GeV\n77\n5.1\nElectron de\ufb01nition\nElectron candidates are reconstructed and identi\ufb01ed by the calorimeters and inner tracker of ATLAS and\nare reconstructed in the pseudorapidity range |\u03b7| < 2.5. An electron candidate is de\ufb01ned as a medium\nelectron identi\ufb01ed by the isEM algorithm [18].\nIf an electron is found in the calorimeter crack region 1.37 < |\u03b7| < 1.52, it is vetoed. The electron\nhas to be isolated based on calorimeter energy: the additional transverse energy ET in a cone with radius\n\u2206R = 0.2 around the electron axis is required to be less than 6 GeV. The pT and |\u03b7| cuts depend on the\nevent signature and are detailed in the various relevant sections.\nFor electrons above 20 GeV and |\u03b7| < 2.5 and outside the crack region, the average identi\ufb01cation\nef\ufb01ciency in tt events is about 67%, with a purity of about 97%.\n5.2\nMuon de\ufb01nition\nMuons are reconstructed by the muon spectrometer and the inner detector. The muon reconstruction is\nperformed using the Staco algorithm [19], and muons are de\ufb01ned from the best match combination of\nthe muon chambers and the tracker information. Muons are reconstructed in the pseudorapidity range\n|\u03b7| < 2.5 and have to be isolated based on calorimeter energy: the additional transverse energy ET in\na cone with radius \u2206R = 0.2 around the muon is required to be less than 6 GeV. The pT and |\u03b7| cuts\napplied to the muons are given in the selection cuts described in the various sections. For muons above\nTOP \u2013 TOP QUARK PHYSICS\n877\n\nTable 4: Diboson background samples used throughout the notes. Given are a short descrip-\ntion of the simulated physics process, the generator used, the production cross-section (\u03c3)\nincluding \ufb01lter, matching ef\ufb01ciency and selection ef\ufb01ciency for ALPGEN, and the K-factor\nthat should be applied to the quoted cross-section.\nHERWIG + Jimmy \u2013 WW \u2013 fully simulated events \u2013 K-factor = 1.57\n\u03c3 (pb)\n1 e or \u00b5 p\u2113\nT \u226510 GeV\n24.5\nHERWIG + Jimmy \u2013 ZZ \u2013 fully simulated events \u2013 K-factor = 1.29\n1 e or \u00b5 p\u2113\nT \u226510 GeV\n2.1\nHERWIG + Jimmy \u2013 WZ \u2013 fully simulated events \u2013 K-factor = 1.89\n1 e or \u00b5 p\u2113\nT \u226510 GeV\n7.8\nMC@NLO + HERWIG \u2013 WW \u2013 fully simulated events \u2013 K-factor = 1.0\n\u03c3(pb)\nW+W\u2212\u2192e+\u03bd e\u2212\u03bd; no \ufb01lter\n1.1\nW+W\u2212\u2192e+\u03bd \u03c4\u2212\u03bd\n1.1\nW+W\u2212\u2192\u03c4+\u03bd e\u2212\u03bd\n1.1\nW+W\u2212\u2192\u00b5+\u03bd \u03c4\u2212\u03bd\n1.1\nW+W\u2212\u2192\u03c4+\u03bd \u00b5\u2212\u03bd\n1.1\nW+W\u2212\u2192\u03c4+\u03bd \u03c4\u2212\u03bd\n1.1\n20 GeV, the average reconstruction ef\ufb01ciency in tt events is 88%. The fake rate, de\ufb01ned as the rate at\nwhich an object that is not associated with a true muon is mis-identi\ufb01ed as a muon, is 0.1\u00b10.01 %.\n5.3\nJet de\ufb01nition\nJets are reconstructed with the standard ATLAS cone algorithm in \u03b7 \u2212\u03c6 space, for |\u03b7| < 2.5 and a cone\nradius of 0.4, operating on energy depositions in calorimeter towers [20]. In tt events, jets coinciding\nwithin \u2206R < 0.2 with electrons (as de\ufb01ned in section 5.1) are removed.\nA jet is identi\ufb01ed as originating from a b-quark by determining the probability that it contains a secondary\nvertex. The three-dimensional impact parameter (IP3D) and the secondary vertex (SV1) [21] algorithms\nare used and we require that the resulting output weight of the event is larger than 7.05. The requirement\non the weight is chosen such that an ef\ufb01ciency of about 60% for jets with pT > 30 GeV in tt semi-leptonic\nevents is reached, with a mistag rate of 100.\n5.4\nMissing transverse energy de\ufb01nition\nFor the missing transverse energy (/ET), we determine the sum of \ufb01ve components.\n1. the contribution of cells in identi\ufb01ed electron or photon clusters;\n2. the contribution of cells inside jets;\n3. the contribution of cells in topological clusters outside identi\ufb01ed objects;\n4. the contribution from muons;\n5. the cryostat correction.\nFor the calculation of /ET we use the standard ATLAS variable [22]. The sum of the tranverse energy in\nsemi-leptonic top events is about 500 GeV, which gives a typical /ET resolution of the order of 10 GeV.\nTOP \u2013 TOP QUARK PHYSICS\n878\n\nTable 5: QCD background samples used throughout the notes. Given are a short descrip-\ntion of the simulated physics process, the generator used, the production cross-section (\u03c3)\nincluding \ufb01lter, matching ef\ufb01ciency and selection ef\ufb01ciency for ALPGEN.\nPYTHIA \u2013 QCD Dijets \u2013 fully simulated events \u2013\n\u03c3(pb)\nDijets; e/\u03b3 \ufb01lter pT \u226515 GeV\n1.91\u00b7108\nAlpgen + HERWIG \u2013 jets \u2013 Atlfast \u2013\n2 partons; one jet with pj\nT \u226530 GeV\n1.13\u00b7106\n3 partons\n2.03\u00b7106\n4 partons\n1.10\u00b7106\n\u22655 partons\n0.32\u00b7106\nAlpgen + HERWIG \u2013 bb+jets \u2013 Atlfast \u2013\n\u03c3(pb)\nbb + 0 parton; one jet with pj\nT \u226530 GeV\n5.3\u00b7103\nbb + 1 parton\n33.6\u00b7103\nbb + 2 partons\n29.5\u00b7103\nbb+ \u22653 partons\n18.9\u00b7103\n5.5\nOverlap removal\nIn some cases when there is ambiguity in the de\ufb01nition of an object, the overlaps are removed: if an\nobject is identi\ufb01ed as an electron it is not counted in the category of photons or taus or jets.\n6\nSystematics\nIn this section, we list the sources of systematics common to all analysis and describe how they have\nbeen consistently treated.\n6.1\nEstimate of the luminosity and its uncertainty\nAt the LHC start-up only a rough measurement of the machine parameters will be available. The expected\nuncertainty on the luminosity during this phase will be of the order of 20-30%. A better determination\nof the beam pro\ufb01les using special runs of the machine will lead ultimately to a systematic uncertainty of\nthe order of 5%. The proposed ALFA detector will measure elastic scattering in the Coulomb-nuclear\ninterference region using special runs and beam optics, determining the absolute luminosity with an\nexpected uncertainty of the order of 3%. The optical theorem, in conjunction with a precise external\nmeasurement of the total cross-section, can achieve a similar 3% precision [23].\n6.2\nLepton identi\ufb01cation ef\ufb01ciency\nFor the \ufb01rst 100 pb\u22121 of integrated luminosity, the lepton identi\ufb01cation ef\ufb01ciency error is expected to be\nof the order of 1% for electrons and muons, while the error on the fake rate is expected to be 50% and\n20%, respectively [18,19].\n6.3\nLepton trigger ef\ufb01ciency\nThe lepton trigger ef\ufb01ciency is measured from data using Z events. We expect the uncertainty to be of\nthe order of 1% for an integrated luminosity of 100 pb\u22121 [24].\nTOP \u2013 TOP QUARK PHYSICS\n879\n\n6.4\nJet energy scale\nIn the dif\ufb01cult hadron-hadron collision environment, the determination of the jet energy scale is rather\nchallenging [25]. While several methods are proposed such as using \u03b3+jet events to propagate the\nelectromagnetic scale to the hadronic scale, the jet energy scale depends on a variety of detector and\nphysics effects. This includes non-linearities in the calorimeter response due, for example, to energy\nlosses in \u201cdead\u201d material, and additional energy due to the underlying event. Energy lost outside the jet\ncone can also affect the measured jet energy. Effects due to the initial and \ufb01nal state radiation (ISR/FSR)\nmodelling could also affect the jet energy scale but they are evaluated separately. The ultimate goal in\nATLAS is to arrive at a 1% uncertainty on jet energy scale though such performance is only reachable\nafter several years of study. The jet energy resolution used throughout the note is 60%/\n\u221a\nE \u22955%.\nTo estimate the sensitivity of the analyses to the uncertainty on the jet energy scale in early data we\nhave repeated them while arti\ufb01cially rescaling the energies of the jets by \u00b15%. The resulting variation in\nthe measurement from the analyses (e.g. cross-section, mass etc.) gives a good measure of the systematic\nuncertainty due to the jet energy scale.\nSince several analyses are using the missing transverse energy in the event to reduce the backgrounds,\nthe effect of the variation of the jet energy scale on the missing energy has been taken into account by\ncalculating the contribution to the transverse missing energy coming from unscaled jets and subtracting\nit from the overall missing transverse energy in the event. Finally the contribution from the rescaled jets\nis calculated and added to the missing transverse energy of the event.\n6.5\nb-tagging uncertainties\nThe use of b-tagging in tt and single top quark events is essential in order to reduce the backgrounds,\nin particular that from W+jets, and the combinatorial background when reconstructing the top quark.\nAt the beginning of data taking the b-tagging performance will need to be understood and tt events will\nbe used as a calibration tool for the determination of the b-tagging ef\ufb01ciency. To avoid having a large\ndependence on the b-tagging ef\ufb01ciency in the early days of data taking we have studied methods to\nextract the tt cross-section and the top quark mass without applying b-tagging. The uncertainty on the\nb-jet ef\ufb01ciency is currently estimated to be of the order of \u00b15% and the uncertainty on the mistag rate is\n50% [21].\n6.6\nISR and FSR systematics\nMore initial and \ufb01nal state QCD radiation (ISR and FSR) increases the number of jets and affects the\ntransverse momentum of particles in the event. Selection cuts for top quark events include these quan-\ntities, therefore ISR and FSR will have some effect on the selection ef\ufb01ciency. In order to evaluate the\neffect of the ISR and FSR systematics, several studies have been performed using the AcerMC [13]\ngenerator interfaced with the PYTHIA parton showering.\nSamples of tt and single top quark events with separate variations of the PYTHIA ISR and FSR\nparameters have been generated. The study was limited to parameters which have been shown to have\nthe biggest impact on the reconstructed top mass at the generator level. The choices of the parameters\ndepend on the analysis and include ISR \u039bQCD, the ISR cutoff, FSR \u039bQCD, and the FSR cutoff. The effect\nof the selection ef\ufb01ciency can be as large as 10%, depending on the analysis cuts.\n6.7\nParton density uncertainties\nThe systematic error due to the parton density functions (PDF) uncertainties is evaluated on tt signal\nsamples. Both the PDF error sets CTEQ6M and MRST2002 [26] at NLO are used. Both sets have pos-\nitive and negative error PDFs. In order to evaluate the systematic effect on an observable, the following\nTOP \u2013 TOP QUARK PHYSICS\n880\n\nformula [27] could be adopted:\n\u2206X = 1\n2\nq\n\u03a3(X+\ni \u2212X\u2212\ni )2\nwhere i varies over the set of PDF errors and X+ and X\u2212is the observable evaluated with the positive\nand negative error PDFs respectively.\nThe error PDFs do not guarantee that X+\ni > X0 and X\u2212\ni < X0 \u2200i (here X0 is the value of the observable\nas computed with the default PDF set). An alternative approach has thus been proposed in reference [28],\nwhich entails the use of the following asymmetric formulas, that are used here:\n\u2206X+\nmax =\nq\n\u03a3[max(X+\ni \u2212X0,X\u2212\ni \u2212X0,0)]2\n\u2206X\u2212\nmax =\nq\n\u03a3[max(X0 \u2212X+\ni ,X0 \u2212X\u2212\ni ,0)]2.\nIn order to avoid generating a sample for each set of PDF errors, a re-weighting method has been\nused. Once an event has been generated with a certain PDF, PDF1, it can be re-weighted as if it would\nhave been generated with a different PDF, PDF2, by using the following re-weight factor:\nevent(reweights) = fPDF2(x1, flav1,Q)\nfPDF1(x1, flav1,Q)\nfPDF2(x2, flav2,Q)\nfPDF1(x2, flav2,Q)\n(1)\nThe variable flavi is the \ufb02avor of parton i = 1,2, which initiates the hard scattering, xi its momentum\nfraction, and Q is the mass scale used by the Monte Carlo in the computation of the PDFs.\nEq.1 is an approximation and should be checked by comparing samples obtained with the re-weighting\ntechnique and generated ones. Using the re-weighting technique is not the same as generating the sam-\nples with the different sets of PDFs, the reason being that in the generator the Sudakov factors of the\ninitial state radiation depend on the PDFs and the dependence does not factorize, i.e. it is not a multi-\nplicative factor. The effect is believed to be generally small, but has been checked for each process by\ncomparing ATLFAST subsamples of our signal events generated with the PDFs and re-weighted sam-\nples: the selection ef\ufb01ciencies for those samples have been compared for the tt and single top quark\nanalyses and the results agree within the statistical errors.\n6.8\nW+jets normalization\nFor \ufb01nal states with at least one top decaying leptonically, the ones studied in this document, one of the\nmost important backgrounds is W-boson production in association with jets where the W-boson decays\nleptonically. The uncertainty on the normalization of this process is particularly relevant in analyses\nwhere the background contribution is estimated on the basis of the Monte Carlo expectations rather than\n\ufb01tted from the data.\nTo evaluate this background we used Monte Carlo samples of W+0,1,2,3,4 jets produced with the\nALPGEN Monte Carlo, and we evaluated the selection ef\ufb01ciencies for this background. For the nor-\nmalisation of the exclusive samples we used the leading order cross-section prediction of the ALPGEN\nMonte Carlo, with standard settings for the renormalisation and factorisation scales. The inclusive cross-\nsection is then normalised to the NNLO value [8]. However, the normalisation of the exclusive samples\nhas a large theoretical uncertainty due to the matching: we therefore envisage to determine it from data\nitself.\nThe exclusive cross-section for W-boson produced in association with jets (\u03c3(W+nj)) can be ex-\ntracted from the data by using the following relation:\n\u03c3(Wincl)\n\u03c3(W+nj) = \u03c3(Zincl)\n\u03c3(Z+nj)\n(2)\nTOP \u2013 TOP QUARK PHYSICS\n881\n\nwhere the inclusive W-boson and Z-boson cross-sections (\u03c3(Wincl) and \u03c3(Zincl)) and the exclusive cross-\nsection for Z produced in association with n jets (\u03c3(Z+nj),n = 0\u22124) are extracted from the data.\nEquation (2) is demonstrated to be valid to a few percent level in [29], depending on the selection cuts\napplied (e.g. pT cut on jets).\nWhen the data will be available the normalisation of the W+j background will be extracted from\nrelation (2) using Z+nj samples selected in Z \u2192ee events.\nObtaining the normalisation for this background from the data has shown to be essential, since the\nuncertainty on the exclusive cross-section of the W+nj background obtained from ALPGEN can be as\nlarge as 50% [30]. The largest uncertainties affect the topologies with higher number of jets that are\ntypical of tt events. We have veri\ufb01ed that such large variations of the exclusive cross-sections are found\nwhen selecting events with at least 4 jets with pT > 40 GeV in ALPGEN W+nj fast simulated samples\ngenerated with different sets of matching parameters. While the normalisation has large uncertainties, the\nshapes of the distributions are found to be basically independent of the choice of the matching parameters.\nWith data driven methods and about 1 fb\u22121 of luminosity, a 20% uncertainty on the W+nj normalisation\nshould be reachable.\nReferences\n[1] CDF Coll., Phys. Rev. D 50 (1994) 2966; Phys. Rev. Lett. 74 (1995) 2626; Phys. Rev. Lett. 73\n(1994) 225.\nD0 Coll., Phys. Rev. Lett. 74 (1995) 2632.\n[2] R. Bonciani et al., Nucl., Phys. B529, (1998) 424.\n[3] N. Kidonakis et al., Phys. Rev. D68, (2003) 114014 .\n[4] C. Amsler et al., Physics Letters B667, 1 (2008).\n[5] Z. Sullivan, Phys. Rev. D70, (2004) 114012;\n[6] J. Campbell and F. Tramontano, Nucl. Phys. B726, (2005) 109.\n[7] J. Campbell, R.K. Ellis and F. Tramontano, Phys. Rev. D70, (2004) 094012.\n[8] ATLAS Collaboration, \u201dCross-Sections, Monte Carlo Simulations and Systematic Uncertainties\u201d,\nthis volume.\n[9] S. Frixione and B.R. Webber, JHEP 0206 (2002) 029, [arXiv:hep-ph/0204244];\nS. Frixione et al., JHEP 0308 (2003) 007, [arXiv:hep-ph/0305252].\n[10] J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. Nadolsky and W. K. Tung, JHEP 0207 (2002)\n012, [arXiv:hep-ph/0201195].\n[11] G. Corcella et al., JHEP 0101, (2001) 010 , [hep-ph/0011363], [arXiv:hep-ph/0210213].\n[12] J.M. Butterworth et al., Zeit. f\u00a8ur Phys. C72, (1996) 637.\n[13] B.P. Kersevan and E. Richter-Was, [arXiv:hep-ph/0405247v1].\n[14] S. Slabospitsky, and L. Sonnenschein, Comput. Phys. Commun. Vol 148, (2002) .\n[15] B. P. Kersevan, and I. Hinchliffe, [arXiv:hep-ph/0603068].\nTOP \u2013 TOP QUARK PHYSICS\n882\n\n[16] M.L. Mangano et al., JHEP. 0307,(2003) 001.\n[17] J. Alwall et al., Eur. Phys. J. C53 (2008) 473, [arXiv:0706.2569 [hep-ph]].\n[18] ATLAS Collaboration, \u201dReconstruction and Identi\ufb01cation of Electrons\u201d, this volume.\n[19] ATLAS Collaboration, \u201dMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples\u201d, this volume.\n[20] ATLAS Collaboration, \u201dJet Reconstruction Performance\u201d, this volume.\n[21] ATLAS Collaboration, \u201db-Tagging Calibration with t\u00aft Events\u201d, this volume.\n[22] ATLAS Collaboration, \u201dMeasurement of Missing Tranverse Energy\u201d, this volume.\n[23] CERN/LHCC/2008-004, ATLAS TDR 18, (2008).\n[24] ATLAS Collaboration, \u201dTriggering Top Quark Events\u201d, this volume.\n[25] ATLAS Collaboration, \u201dJet Energy Scale: In-situ Calibration Strategies\u201d, this volume.\n[26] A. D. Martin, R. G. Roberts, W. J. Stirling and R. S. Thorne, Eur. Phys. J. C 28 (2003) 455,\n[arXiv:hep-ph/0211080].\n[27] J. Pumplin et al., Phys. Rev. D 65, (2002) 014013, [arXiv:hep-ph/0101032].\n[28] Z. Sullivan, Phys. Rev. D 66 (2002) 075011, [arXiv:hep-ph/0207290].\n[29] F.A. Berends et al., Phys. Lett. B 224,(1989) 237.\n[30] M.L. Mangano \u201dUnderstanding the Standard Model, as a bridge to the discovery of new phenomena\nat the LHC.\u201d CERN-PH-TH-98-019, [arXiv:0802.0026].\nTOP \u2013 TOP QUARK PHYSICS\n883\n\nTriggering Top Quark Events\nAbstract\nCollisions at the LHC occur at a rate of up to 40 MHz, much larger than the\n200 Hz storage capacity of the ATLAS experiment. The ATLAS trigger sys-\ntem has the challenging task of rejecting 99.9995 % of the events produced in\ncollisions, while keeping those needed to achieve the physics goals of the ex-\nperiment. This note evaluates the expected performance of the trigger system\nin top quark events by investigating the response of the trigger system to single\nobjects such as a muon, an electron or a jet originating from top quark decays.\nIn addition, the methodology needed to ef\ufb01ciently select top quark events in\nthe online trigger system is discussed including methods to determine trigger\nef\ufb01ciencies from data.\n1\nIntroduction\nTriggering at the Large Hadron Collider (LHC) is a challenging task. The selection system is required\nto reduce the initial bunch-crossing rate of 40 MHz down to a manageable 100-200 Hz while retaining\nand recording the \ufb01ve in one million most interesting physics events. ATLAS has designed a three-level\ntrigger which aims to select these events, with the highest possible ef\ufb01ciency and lowest possible bias.\nThe ATLAS trigger is largely based on signatures of high transverse-momentum particles and large\nmissing transverse energy. The \ufb01rst trigger level (L1) is implemented using custom electronics and\nis based on coarse-resolution data from the calorimeters and dedicated fast muon detectors [1]. The\nlevel-2 trigger (L2) and the Event Filter (EF), referred to together as the High Level Trigger (HLT), are\nimplemented in software and run on a commodity computing cluster [2]. The L2 design is based on the\nconcept of Regions of Interest (RoIs). Algorithms request full-resolution data only from the region of the\ndetector corresponding to the L1 candidate object and perform a more re\ufb01ned analysis of its features. The\nEF works also in a seeded mode although it has access to the full-resolution data of the entire detector.\nIt runs more sophisticated of\ufb02ine reconstruction and selection algorithms.\nAt the LHC top quarks are mainly produced either in pairs or singly. A large set of different and\ncomplex event signatures is expected. For t\u00aft events, approximately 44% of the decays will be fully\nhadronic, resulting in a \ufb01nal state with six jets1: four light jets from the W-boson decays and two b-jets.\nAnother 44% of the decays will be semi-leptonic, with a \ufb01nal state containing one lepton, one neutrino,\ntwo b-jets and two light jets. Roughly 11% of the t\u00aft decays will be purely leptonic, with two leptons,\ntwo neutrinos, and two b-jets in the \ufb01nal state. In single-top events, the W-boson decays hadronically\ntwo-thirds of the time and leptonically one-third. More details about the properties and decay modes of\ntop events are discussed in the introduction [3].\nThe trigger ef\ufb01ciencies for top events of the most relevant single object triggers are studied in Sec-\ntion 2 of this note. The rich topologies of top events results in large overlap between trigger signatures.\nThis feature can be exploited to monitor trigger ef\ufb01ciencies as discussed in Section 3. Finally, in Sec-\ntion 4, the electron trigger ef\ufb01ciency is extracted from Z\u2192ee events and is compared to the true ef\ufb01ciency\nin t\u00aft events.\n2\nSingle object trigger performance in top quark events\nResults are presented for the basic trigger signatures using electron, muon and jet trigger objects, as well\nas missing transverse energy (Emiss\nT\n). The main trigger criteria from the ATLAS trigger tables for the\n1Neglecting for now initial or \ufb01nal state radiation.\n884\n\ninitial data taking phase are evaluated using simulated top quark signal samples. Two types of t\u00aft signal\nsamples are used in this note. The \ufb01rst is the fully hadronic sample with only jets in the \ufb01nal state and\nthe second is a leptonic sample, consisting of a combination of semi-leptonic and di-leptonic events, and\nwill be referred to as leptonic sample in the following. For top quarks produced singly, the s, t, and Wt\nchannels are simulated and only those events which result in an electron or a muon from the W-boson\ndecay are considered here. More details about the data samples are given in [3].\nTrigger items are described by a combination of letters and numbers. The trigger object is represented\nby an abbreviation consisting of one or two letters. It is preceded by a number representing the object\nmultiplicity and followed by a number signifying the transverse momentum (pT) of the trigger threshold.\nIf an isolation requirement is applied, it is indicated by the letter \u2018i\u2019 after the pT threshold. For example,\nthe item name \u20182EM18I\u2019 represents a trigger on two electromagnetic objects, with a threshold of 18 GeV\neach, including isolation requirements. The L2 and EF item naming conventions are the same as L1\nexcept that lower-case letters are used. A trigger chain consists of the L1, L2, and EF trigger items an\nobject must satisfy and is referred to using the HLT notation. A trigger menu is a list of triggers enabled\nduring a data taking run. For a more complete description, see [4].\nThe dependence of a trigger on the actual pT cut will be investigated here by means of turn-on\ncurves, which shows the fraction of objects passing a certain trigger as a function of the reconstructed or\ntrue simulated pT of that object. Trigger candidate objects are matched to reconstructed or Monte Carlo\nsimulated objects by cutting on \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 between the two objects.\nIn the following sections, single object triggers are evaluated in detail \ufb01rst in t\u00aft events, and then in\nsingle-top events.\n2.1\nElectron triggers in t\u00aft events\n2.1.1\nIntroduction\nLeptonic t\u00aft decays will form a statistically large sample of events early on at the LHC. Figure 1 (a) shows\nthe simulated pT spectrum of the electron from a W-boson decay in leptonic t\u00aft events. The plot gives an\nidea of the expected fraction of events the trigger system is confronted with above certain pT values. The\nsingle-electron trigger threshold is expected to be around 20 GeV, indicating that complex multi-object\ntriggers (with correspondingly lowered thresholds) may be unnecessary.\n2.1.2\nSingle electron triggers\nThe L1 electron triggers operate on reduced granularity (0.1\u00d70.1 in \u2206\u03b7 \u00d7\u2206\u03c6) calorimeter trigger towers\nwhich cover the range |\u03b7| < 2.5. A central cluster of four towers is formed in the electromagnetic and\nhadronic calorimeters, along with a ring of 12 towers around this central cluster. The ring is used to\nselect candidates using isolation criteria by cutting on the amount of energy deposited around the central\ncluster. At L2, electromagnetic clusters are formed, tracking is then performed for the \ufb01rst time, and,\n\ufb01nally, the reconstructed cluster is matched to a track. In the \ufb01nal stage, the EF, tracking and cluster\ndetermination is performed with more accurate algorithms, further re\ufb01ning the trigger decision. More\ndetails can be found in [4].\n2.1.3\nSingle electron trigger ef\ufb01ciencies\nThe lowest unprescaled trigger threshold depends on the luminosity. For a luminosity of 1033 cm\u22122 s\u22121,\nthe e22i trigger is the unprescaled trigger with the lowest pT threshold. For the start-up luminosity of\n1031 cm\u22122 s\u22121, an e12i trigger is available. The e12i chain has a lower threshold and hence a higher\nef\ufb01ciency in leptonic t\u00aft events.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n885\n\n[GeV]\nT\nMonte Carlo Truth p\n0\n20\n40\n60\n80\n100\n120\n140\n-1\nEvents / 1 pb\n0\n1\n2\n3\n4\n5\n6\n7\n8\nATLAS\n(a)\n[GeV]\nT\nReconstructed electron p\n0\n20\n40\n60\n80\n100\n120\n140\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n[GeV]\nT\nReconstructed electron p\n0\n20\n40\n60\n80\n100\n120\n140\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nLVL1\nLVL2\nEF\n(b)\nFigure 1: (a): pT spectrum of electrons from the decay W\u2192e\u03bd in leptonic t\u00aft events. The number\nof electrons is scaled to an integrated luminosity of 1 pb\u22121, and is shown as a function of the\ntrue simulated electron pT. (b): Turn-on curves for the e22i trigger determined with leptonic t\u00aft\nevents. The ef\ufb01ciencies are shown with respect to an of\ufb02ine selection (excluding the cut on pT) as\na function of the of\ufb02ine reconstructed pT of the electron that \ufb01red the trigger.\nTable 1: Ef\ufb01ciency of the e22i and e12i trigger for leptonic t\u00aft events with a W\u2192e\u03bd decay. The binomial\nerrors \u2206on the ef\ufb01ciencies for the different trigger levels are quoted for an integrated luminosity of\n100 pb\u22121, and are calculated as \u22062 = \u03b5(1 \u2212\u03b5)/N, where \u03b5 is the ef\ufb01ciency. Note that no matching\nconstraint is imposed between the trigger and the reconstructed or true simulated electrons. Moreover,\nthe ef\ufb01ciencies are determined for |\u03b7| < 2.5 by cutting on the \u03b7 of the trigger as well as the reconstructed\nor simulated electrons.\nCompared to Monte Carlo\nCompared to of\ufb02ine selection\nTrigger\nEff. [%]\nEff. [%]\ne22i:\nL1 EM18I\n74.7 \u00b1 0.5\n96.0 \u00b1 0.6\nL2 e22i\n59.6 \u00b1 0.6\n92.7 \u00b1 0.9\nEF e22i\n52.9 \u00b1 0.6\n89.8 \u00b1 1.0\ne12i:\nL1 EM7I\n83.6 \u00b1 0.4\n98.6 \u00b1 0.3\nL2 e12i\n66.7 \u00b1 0.5\n92.6 \u00b1 0.8\nEF e12i\n63.5 \u00b1 0.5\n91.8 \u00b1 0.8\nTable 1 shows the fraction of events passing each trigger level in the e22i chain per 100 pb\u22121. The\ne22i trigger chain consists of the L1 trigger L1 EM18I, and the e22i trigger at L2 and EF. The ef\ufb01ciency\nhas been calculated for each trigger level with respect to the total number of leptonic t\u00aft events with a\nW\u2192e\u03bd decay and with respect to the number of events reconstructed and selected in the commissioning\nanalysis [5], requiring |\u03b7| < 2.5 for the trigger and reconstructed or simulated electrons. The cuts are:\n\u2022 At least one reconstructed isolated electron with pT > 20 GeV;\n\u2022 Emiss\nT\n> 20 GeV;\n\u2022 At least 3 reconstructed jets with pT > 40 GeV and at least 4 reconstructed jets with pT > 20 GeV.\nAlso shown in Table 1 are the percentage of events passing each trigger level in the e12i chain.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n886\n\nCompared to e22i, a larger fraction of events passes this looser chain at each level, as expected. Note\nthat the large value of the trigger ef\ufb01ciency with respect to the selection, exceeding 90%, is partly due to\njets ful\ufb01lling the electron trigger. Eventually this effect has to be accounted for when determining trigger\nef\ufb01ciency corrections to be used in an analysis.\nFigure 1 (b) shows the turn-on curves for each trigger level in the e22i chain, determined from\nsimulated leptonic t\u00aft events. The turn-on behaviour of the trigger is sharp at all levels. From the L1 to the\nHLT the pT dependence is very similar, the curves reveal a \ufb02at plateau once beyond the turn-on region.\nNote that the slight decrease in ef\ufb01ciencies at large pT values are due to the isolation requirements of the\ne22i trigger. This small loss can be recovered using a high-threshold non-isolated trigger, although it has\nnot been considered in this study.\nIn summary, the single electron trigger ef\ufb01ciency in t\u00aft events is high for t\u00aft events with a W\u2192e\u03bd\ndecay in the current physics trigger menus. The electron trigger chain will be, together with the muon\nchain discussed in the next section, the main trigger for selecting t\u00aft events in the golden leptonic decay\nchannel. Simple and ef\ufb01cient high-pT isolated single electron triggers exist to select t\u00aft events, avoiding\nconsiderable complications in the determination of trigger ef\ufb01ciencies for complex combined trigger\nsignatures.\n2.2\nMuon triggers in t\u00aft events\n2.2.1\nIntroduction\n[GeV]\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n-1\nEvents / 1 pb\n0\n1\n2\n3\n4\n5\n6\n7\n8\nATLAS\n(a)\n[GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEff c ency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nLVL1\nLVL2\nEF\nLVL1\nLVL2\nEF\nATLA S\n(b)\nFigure 2: (a): pT spectrum of muons from W\u2192\u00b5\u03bd decays in leptonic t\u00aft events. The muon pT is\nthe true simulated value. The distribution is scaled to correspond to an integrated luminosity of\n1 pb\u22121. (b): Trigger ef\ufb01ciencies for the mu20 with respect to an of\ufb02ine selection (excluding the\ncut on pT), given as a function of reconstructed muon pT.\nThe pT spectrum of truth muons from the W\u2192\u00b5\u03bd decay in t\u00aft events is shown in Fig. 2 (a). As for\nelectrons, rather high-pT single muon triggers can be used to select t\u00aft events with at least one W-boson\ndecaying to a \u00b5 and \u03bd\u00b5 without much loss of ef\ufb01ciency.\n2.2.2\nSingle muon triggers in ATLAS\nThe L1 muon trigger consists of fast electronics establishing coincidences between hits of different detec-\ntor layers of the muon system inside programmed geometrical windows. The size of the window de\ufb01nes\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n887\n\nthe transverse momentum interval corresponding to the de\ufb02ection of the muon in the toroidal magnetic\n\ufb01eld. One of six programmable pT thresholds is assigned to the candidate. The L2 processing consists\nof three reconstruction steps applied to full granularity data of the region de\ufb01ned by L1. First, the muon\ncandidate is reconstructed in the muon spectrometer. Then inner detector tracks are reconstructed around\nthe muon candidate. Both are combined to form the L2 muons upon which the trigger decision is based.\nCurrently only the pT of the muon candidate is checked. Isolation requirements or constraints on the\n\u03c72 of the combined inner detector and muon spectrometer track are not imposed here (but might be in\nfuture). The muon reconstruction in the Event Filter is done using of\ufb02ine algorithms. The EF muon\ntrigger decision at the moment is also based solely on the pT of the reconstructed muon candidate. A\nmore complete description of the muon trigger can be found in [4].\n2.2.3\nSingle muon trigger ef\ufb01ciencies\nUsing the standard L1 muon thresholds, six different trigger items have been de\ufb01ned in the simulated\nsamples under study; L1 MU06, L1 MU08, L1 MU10, L1 MU11, L1 MU20 and L1 MU40. The ef\ufb01-\nciencies for each trigger item are shown in Fig. 3 (a). Each ef\ufb01ciency is calculated with respect to the\nnumber of simulated leptonic t\u00aft events with a W\u2192\u00b5\u03bd decay. It can be seen that the high-pT L1 single\nmuon triggers provide a high ef\ufb01ciency for selecting the events. When running at an increased luminosity\nof 1034 cm\u22122 s\u22121, the threshold could be raised to 40 GeV without an unacceptable loss in ef\ufb01ciency.\nTrigger item\nL1_MU06 L1_MU08 L1_MU10 L1_MU11 L1_MU20 L1_MU40\nL1_MU06 L1_MU08 L1_MU10 L1_MU11 L1_MU20 L1_MU40\nEfficiency\n0.66\n0.68\n0.7\n0.72\n0.74\n0.76\n0.78\n0.8\n0.82\n0.84\n(a)\nATLAS\nLVL1\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n(b)\nATLAS\nLVL2\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEfficiency\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n(c)\nATLAS\nEF\nFigure 3: Ef\ufb01ciencies of the single muon triggers for L1 (a), L2 (b), and EF (c), determined using\nleptonic t\u00aft events with a W\u2192\u00b5\u03bd decay. For the L1 items, the ef\ufb01ciencies are calculated for the\nsix available thresholds. The HLT ef\ufb01ciencies are plotted as a function of the pT cut applied. In\nFig. (b) the L2 chain is started by L1 RoIs passing the MU06 threshold and in Fig. (c) the EF\nchain is started by muon candidates passing the mu06 signature at L2. Note that the ef\ufb01ciencies\nare calculated with respect to the number of simulated muons within |\u03b7| < 2.4.\nFigure 3 (b) shows the absolute ef\ufb01ciency of the L2 single muon trigger in the case of the HLT\nchain being started by a MU06 RoI. The pT cut applied by the L2 algorithm is shown on the horizontal\naxis. Similar ef\ufb01ciencies are shown in Fig. 3 (c) for the EF when the EF chain is started by a L2 muon\ncandidate ful\ufb01lling the mu06 signature. The absolute trigger ef\ufb01ciency for the HLT cannot in principle\nbe inferred directly from these plots, as for instance the L2 mu20 processing will only be initiated by L1\nRoIs which ful\ufb01ll the L1 MU20 requirements. On the other hand, the ef\ufb01ciencies for each trigger level,\nnormalized to the number of events with a true simulated muon from a W-boson decay within |\u03b7| < 2.4,\nhave been calculated for a few trigger signatures and are shown in Table 2. Comparing Table 2 with\nFig. 3, one can see that the differences are small. Hence these \ufb01gures can be used to indicate the effects\nof a change in trigger threshold cuts.\nThe ef\ufb01ciencies of the single muon trigger signatures have also been evaluated for the events selected\nby the commissioning analysis [5]. The same cuts as described in the electron section 2.1.3 are applied.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n888\n\nTable 2: Ef\ufb01ciencies of the mu06, and mu20 trigger chains for leptonic t\u00aft events with at least one\nW\u2192\u00b5\u03bd decay. The numbers are absolute trigger ef\ufb01ciencies, the reference of\ufb02ine selection is\ngiven in [5]. The binomial errors \u2206are calculated as \u22062 = \u03b5(1 \u2212\u03b5)/N, where \u03b5 is the ef\ufb01ciency,\nfor an integrated luminosity of 946pb\u22121, which corresponds to the available Monte Carlo statistics.\nNote that the ef\ufb01ciencies are determined for \u03b7 < |2.4| by cutting on the \u03b7 of the trigger as well as\nthe reconstructed or true simulated muons.\nCompared to Monte Carlo\nCompared to of\ufb02ine selection\nTrigger\nEff. [%]\nEff. [%]\nmu06:\nL1\n83.8 \u00b1 0.3\n91.9 \u00b1 0.4\nL2\n80.2 \u00b1 0.3\n88.7 \u00b1 0.4\nEF\n73.1 \u00b1 0.2\n83.1 \u00b1 0.4\nmu20:\nL1\n74.6 \u00b1 0.2\n86.4 \u00b1 0.4\nL2\n66.3 \u00b1 0.2\n82.3 \u00b1 0.4\nEF\n58.8 \u00b1 0.2\n76.6 \u00b1 0.4\nThe results are given in Table 2 for the mu20 trigger chain, which consists of the L1 trigger L1 MU20,\nand the mu20 trigger at L2 and EF. The table shows that the mu20 signature is effective in selecting\nevents for the commissioning analysis.\nOne can also determine the turn-on curve of the trigger ef\ufb01ciency for single muons in t\u00aft events.\nFor that purpose a L1 muon is matched to a reconstructed muon by requiring \u2206R < 0.15 while L2 and\nEF trigger muons are matched by requiring \u2206R < 0.12. Figure 2 (b) shows the mu20 trigger chain\nef\ufb01ciencies for reconstructed muons as a function of their reconstructed pT. The muons are required to\nhave |\u03b7\u00b5| < 2.4, as this is the reach of the muon trigger chambers. The L1 turn-on is less steep than\nthose for the higher trigger levels, due to the coarser pT threshold assignment at L1 than at the HLT.\nThe thresholds at the different levels are set such as to reach the plateau at the same value of the of\ufb02ine\nreconstructed pT. At all trigger levels, once the plateau is reached, the ef\ufb01ciencies remain \ufb02at versus pT.\nIn summary, as for the electrons, the single muon trigger ef\ufb01ciency in t\u00aft events is reasonably large.\nThe mu20 is the most relevant muon trigger for selecting t\u00aft events with at least one W-boson decaying to\na muon.\n2.3\nJet triggers in t\u00aft events\nJet triggers are dominated by QCD multi-jet events, which have production cross-sections orders of\nmagnitudes larger than the top signal processes. Therefore it is not obvious that multi-jet triggers giving\nacceptable rates will correspond to pT thresholds ef\ufb01cient for selecting top events. In order to character-\nize jet distributions in t\u00aft events, Fig. 4 (a) shows the pT distribution of the six highest-pT jets (ordered\nin pT and de\ufb01ned using a cone jet algorithm with radius 0.4) for hadronic t\u00aft events as obtained after a\nfull event reconstruction. The characteristics of top events are a large number of high-pT jets. This is\nexpected to provide some discriminatory power against the background, which has a steeply falling pT\nspectrum.\nIn Fig. 4 (b), turn-on curves are given for different pT thresholds at L1, for leptonic t\u00aft events. The\nplot is obtained by matching a jet triggered at L1 with a corresponding fully reconstructed jet within\n2The \u2206R cuts were chosen after studying the \u2206R distributions for the different trigger levels.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n889\n\nof jet [GeV]\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\nJet1\nJet2\nJet3\nJet4\nJet5\nJet6\nATLAS\nEvents (x 10 )\n6\n(a)\n[GeV]\nT\np\n0\n50\n100\n150\n200\n250\nTrigger\n\u03b5\n0\n0 2\n0 4\n0 6\n0 8\n1 ATLAS\n(b)\nJ3\nJ13\nJ21\nJ42\nJ68\nJ118\nthreshold [GeV]\nT\np\n0\n50\n100\n150\n200\n250\n0\n0 2\n0 4\n0 6\n0 8\n1\nNjets=1\nNjets=2\nNjets=3\nNjets=4\nNjets=5\nNjets=6\nATLAS\n(c)\nTrigger\n\u03b5\nFigure 4: (a): Reconstructed pT distribution of the six leading jets for hadronic t\u00aft events. (b):\nTurn-on curves relative to the reconstructed jet pT for jets triggered at L1 at various threshold\nvalues for leptonic t\u00aft events. (c): L1 trigger ef\ufb01ciency versus trigger threshold for multi-jet triggers\nfor hadronic t\u00aft events. The ef\ufb01ciency is calculated with respect to all events in the sample.\n\u2206R < 0.2. The curves reveal, compared to the lepton triggers, a rather slow turn-on of the L1 jet triggers,\nresulting from coarse resolution at L1 (cf. [6]).\nTable 3: Jet trigger ef\ufb01ciencies for t\u00aft signal and trigger rates, the latter also for the most important\nbackground events (the background samples are described in [3]). The ef\ufb01ciencies are for the\nwhole trigger decision (after the EF), and are calculated with respect to the total number of events.\nThe order of magnitude of the trigger rates are given for a luminosity of 1031 cm\u22122 s\u22121.\nProcess\nj20\nj160\n4j50\nEff. [%]\nRate\nEff. [%]\nRate\nEff. [%]\nRate\nLeptonic t\u00aft\n99.8\nO(10\u22123 Hz)\n11.2\nO(10\u22124 Hz)\n9.9\nO(10\u22124 Hz)\nHadronic t\u00aft\n100.0\nO(10\u22123 Hz)\n12.9\nO(10\u22124 Hz)\n21.0\nO(10\u22124 Hz)\nQCD\n-\nO(103 Hz)\n-\nO(Hz)\n-\nO(10\u22121 Hz)\nW-boson+Jet\n-\nO(10\u22123 Hz)\n-\nO(10\u22124 Hz)\n-\nO(10\u22124 Hz)\nFigure 4 (c) shows the L1 trigger ef\ufb01ciency for different jet multiplicities as a function of the trigger\npT threshold for hadronic t\u00aft events. Single jet triggers will be more than 90% ef\ufb01cient for thresholds\nup to about 60 GeV, and roughly 45% ef\ufb01cient at 100 GeV. Table 3 summarises trigger ef\ufb01ciencies for\nsignal and background rates for a selection of single and multi-jet triggers. Depending on how high the\njet trigger thresholds are set, the signal ef\ufb01ciency varies between 10 and 100%. Due to large QCD rates,\nonly high single-jet thresholds or carefully optimised multi-jet triggers are affordable. For example, for\nthe j160, a rate of O(Hz) is to be expected from QCD multi-jets already for an instantaneous luminosity\nof 1031cm\u22122s\u22121.\n2.3.1\nMulti-jet triggers for the fully-hadronic t\u00aft channel\nThe multi-jet trigger item 4J50 listed in the previous section is intended to be general purpose, appli-\ncable to a wide range of physics channels. In order to optimize the signal ef\ufb01ciency of the jet triggers,\nespecially for the fully-hadronic t\u00aft decays not accessible with lepton triggers, other trigger combina-\ntions for multi-jet triggers are studied. The aim is to identify optimum trigger combinations that reduce\nQCD background rates, while keeping a sizable signal acceptance in the fully-hadronic t\u00aft decay channel.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n890\n\nTable 4: Set of optimum multi-jet trigger combinations for fully-hadronic t\u00aft events. The QCD\nmulti-jet background rates are given relative to the background rate of the 4j50 trigger (cf. Table 3).\nEf\ufb01ciencies and rates at the EF are calculated with respect to the total number of events. Note that\nthe names of the triggers are inclusive, \u201c4j60 2j100 j170\u201d means 4 jets have to pass the 60 GeV\ntrigger, 2 jets the 100 GeV, and another 1 jet has to pass the 170 GeV trigger.\nTrigger\nSignal Ef\ufb01ciency [%]\nRelative Background Rate\nS/B\n4j60 2j100 j170\n6\n0.13\n2.8\u00b710\u22123\n5j45 2j60 j100\n16\n0.34\n3.0\u00b710\u22123\n6j35 5j45 4j50 3j60\n10\n0.18\n3.7\u00b710\u22123\nTherefore, trigger combinations requiring at least 4, 5 or 6 jets for a given set of jet thresholds, were\ntested.\nTable 4 summarizes signal ef\ufb01ciencies and increased background suppression for a set of trigger\ncombinations. As \ufb01gure of merit, the ratio of the trigger ef\ufb01ciency for the signal and QCD events is\nused. A strong suppression of QCD is observed when tightening the cuts on the jet energies, as expected.\nThe signal-to-background ratio of the 4J50 trigger (cf. Table 3) is improved by a factor of two in the\n5J45 2J60 J100 trigger (cf. Table 4) for roughly the same signal ef\ufb01ciency. Overall, the three trigger\ncombinations given in Table 4 are optimal in terms of the \ufb01gure of merit, and the 5 jet trigger combination\nleads to the best signal ef\ufb01ciency with the lowest background rate for fully-hadronic t\u00aft events. It is worth\npointing out, that the reliable determination of trigger ef\ufb01ciencies from data is another challenging aspect\nof multi-jet triggers.\nLarge uncertainties are inherent in predictions for LHC energies, hence the QCD background trigger\nrates given here and the jet trigger de\ufb01nitions are preliminary and subject to tuning as soon as data\ntaking starts. This is especially true for the effect of pile-up, which also impacts the signal trigger\nef\ufb01ciencies. It is shown nevertheless that it should be possible to trigger on fully-hadronic t\u00aft decays\nwith reasonable ef\ufb01ciency by optimising the choice of thresholds and multiplicity. Further HLT studies\nare underway to fully exploit also advanced methods for background suppression, such as multi-variate\nanalysis techniques.\n2.4\nMissing ET triggers in t\u00aft events\nThe L1 Emiss\nT\ntrigger performance in t\u00aft events is presented in this section. The HLT performance is not\ndiscussed due to ongoing development effort at the time of this writing.\nThe L1 energy triggers calculate missing transverse energy (Emiss\nT\n, trigger item name: XE) based on\nreduced granularity calorimeter data (the trigger towers) without taking muons into account, across an \u03b7\nrange of |\u03b7| < 5.0 [4].\nFigure 5 shows the Emiss\nT\nspectra at L1 for t\u00aft signal and background events normalized to an integrated\nluminosity of 1 pb\u22121. Shown is the QCD background for which Emiss\nT\nis mainly faked by jet response\n\ufb02uctuations and losses in non-instrumented regions of the calorimeters. In the W-boson+jets background,\na neutrino from the W-boson decay is present and produces real Emiss\nT\n. Single top quark events are also\nshown, with a combined rate of about one third of t\u00aft. As can be seen from the \ufb01gure, high QCD rates\nwill not permit inclusive Emiss\nT\ntriggers with low thresholds, hence L1 trigger ef\ufb01ciencies for t\u00aft events\nwill be small at larger luminosities. While for example L1 XE30 has an ef\ufb01ciency of 81% for leptonic\nevents (applying no selection cuts in the ef\ufb01ciency calculation), the ef\ufb01ciency decreases to 19% for\nL1 XE100. For comparison, the lowest un-prescaled Emiss\nT\nthreshold for the early running at a luminosity\nof 1031 cm\u22122 s\u22121 is expected to be L1 XE70 [4].\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n891\n\n[GeV]\nmiss\nT\nE\n0\n50\n100\n150\n200\n250\n300\n350\n400\n]\n-1\n[10 GeV\nT\n/dE\n-1\nEvents\n1 pb\n2\n10\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n9\n10\n10\n10\nQCD di-jets\nW+jets\n(leptonic)\ntt\n(all-hadronic)\ntt\nsingle top (t-channel)\nsingle top (s-channel)\nsingle top (Wt)\nATLAS\nFigure 5: Emiss\nT\nspectra as measured by the L1 trigger for leptonic and fully-hadronic t\u00aft signals and\nthe most signi\ufb01cant backgrounds to t\u00aft. The samples are normalized to an integrated luminosity of\n1 pb\u22121. Note that the W + jets samples used here include W-boson decays to electrons, muons,\nand taus, as described in Table 2 of [3].\n2.5\nSingle-top trigger\nThe \ufb01nal state of leptonic single-top events in the s, t, and Wt channels are characterized by one high-pT\nmuon or electron, Emiss\nT\n, and by one to three jets. Since these leptons are among the high-pT products\nof a W-boson decay, a relatively large lepton pT threshold can be used to select the single-top events at\nthe trigger level. Therefore, the most important triggers for selecting single-top events are the high-pT\nmuon and electron triggers. Multi-jet and Emiss\nT\ntriggers can be used in combination with lower threshold\nelectron and muon triggers in order to enhance acceptance.\nThe turn-on curves for the mu20 and e22i trigger are shown in Fig. 6. The trigger ef\ufb01ciencies are\nshown with respect to the single-top selection (the cut-based one listed in detail in [7]), and are very\nsimilar to the ones found in t\u00aft events shown in the previous sections. Both triggers exhibit a sharp turn-\non behaviour and a \ufb02at plateau up to 100 GeV.\nThe single-top event selection will include the trigger combination e22i OR e55 OR mu20. The\nef\ufb01ciency for this combination, as well as the total trigger ef\ufb01ciencies for the individual items in the\nmuon and electron channels, are shown in Table 5. The ef\ufb01ciencies are found to be high, above 80% in\nthe muon channel, and up to 90% in the electron channel.\n3\nTrigger redundancy in top quark events\nDue to the rich event topologies, top quark events satisfy many trigger items simultaneously. This redun-\ndancy may be exploited to enhance signal over background rates by forming combined trigger items and\nto monitor the trigger by providing information on trigger ef\ufb01ciencies from data.\nCombining suitable trigger items may reduce signi\ufb01cantly the background rate. For example, in\na combined jet and Emiss\nT\ntrigger, the Emiss\nT\nrequirement will suppress the QCD background. For the\nsame allocated bandwidth, the jet pT threshold of the combined trigger can be lowered compared to the\ninclusive single jet trigger. Overall this will increase the number of recorded leptonic t\u00aft events which\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n892\n\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\nEff c ency\n0\n0.2\n0.4\n0.6\n0.8\n1\nmu20 Wt channel\nmu20 s channel\nmu20 t channel\nATLAS\nT\nReconstructed Muon p ( GeV )\nT\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90 100\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\ne22i Wt channel\ne22i s channel\ne22i t channel\nReconstructed Electron p ( GeV )\nEff c ency\n(a)\n(b)\nFigure 6: Turn-on curves are shown for the mu20 (a) and the e22i (b) trigger. In both plots,\nthe circles represent Wt-channel single-top, the squares represent s-channel single-top, and the\ntriangles represent t-channel single-top events.\nhave good acceptance for a moderate threshold on Emiss\nT\n.\nOn the other hand, if there is suf\ufb01cient overlap between two triggers, the ef\ufb01ciency for one of the\ntriggers can be measured by selecting of\ufb02ine a clean sample of t\u00aft events which satis\ufb01ed the other trigger.\nFor example, the lepton triggers used to select leptonic t\u00aft events could be monitored in events that have\nbeen triggered by the combined jet and Emiss\nT\ntrigger. Possible biases due to correlation should be checked\nand eventually corrected for.\n3.1\nTrigger item overlap in t\u00aft events\nThe correlation among different trigger items is given in Fig. 7, with plot (a) showing overlaps for fully-\nhadronic t\u00aft events and plot (b) showing overlaps for leptonic t\u00aft events. The plots show the percentage of\nevents triggered by the item on the x-axis that were also triggered by the item on the y-axis. The trigger\nitems on the axes were representative of the ATLAS trigger menu at the time of this writing.\nAs expected, there is considerable overlap for the leptonic t\u00aft events, and the event topology of these\nevents is clearly illustrated. The leptonic triggers have very low acceptance in the fully-hadronic t\u00aft\nevents. Only the very low-pT muon triggers, which will be prescaled [4], have considerable ef\ufb01ciency\ndue to muons from b-jets. Any combination of trigger items used to enhance the signal-to-background\nratio in the fully-hadronic sample will have to rely on the jet triggers (cf. Section 2.3.1) only. For the\nleptonic channel, trigger combinations involving Emiss\nT\nare potentially useful. Studies done at L1 have\nshown that Emiss\nT\ntrigger items indeed overlap considerably with the leptonic and jet triggers in leptonic\nt\u00aft events.\n4\nDetermination of trigger ef\ufb01ciencies from data and application to top\nquark events\nTrigger ef\ufb01ciencies should be determined from data in order to reduce systematic uncertainties, as the\nshape as a function of pT and the absolute value of trigger ef\ufb01ciencies are hard to describe precisely in\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n893\n\nTable 5: Total trigger ef\ufb01ciencies for the three single-top channels. Ef\ufb01ciencies for the muon\n(W\u2192\u00b5\u03bd) and electron (W\u2192e\u03bd) channels are shown separately. The errors are calculated using\nthe full available Monte Carlo statistics. Note that the reference event selection [7] selects one and\nonly one isolated lepton for the electron and muon channel. Hence the trigger effciency in the Wt\nchannel does not increase when taking the OR of electron and muon triggers as compared to the\nsingle electron or muon triggers.\nSample\nMuon Channel\nElectron Channel\nTrigger\nEf\ufb01ciency (%)\nTrigger\nEf\ufb01ciency (%)\nmu06\n88.4 \u00b1 0.6\ne22i\n87.1 \u00b1 0.7\nWt\nmu20\n82.5 \u00b1 0.7\ne22i OR e55\n90.6 \u00b1 0.6\ne22i OR e55 OR mu20\n82.5 \u00b1 0.7\ne22i OR e55 OR mu20\n90.8 \u00b1 0.6\nmu06\n88.0 \u00b1 0.6\ne22i\n89.2 \u00b1 0.7\ns\nmu20\n82.6 \u00b1 0.7\ne22i OR e55\n90.7 \u00b1 0.6\ne22i OR e55 OR mu20\n82.6 \u00b1 0.7\ne22i OR e55 OR mu20\n91.0 \u00b1 0.6\nmu06\n86.0 \u00b1 0.7\ne22i\n89.5 \u00b1 0.7\nt\nmu20\n79.6 \u00b1 0.8\ne22i OR e55\n90.6 \u00b1 0.7\ne22i OR e55 OR mu20\n79.6 \u00b1 0.8\ne22i OR e55 OR mu20\n90.9 \u00b1 0.7\nATLAS\n5\n0\n0\n0\n6\n20\n4\n100\n98\n92\n21\n24\n1\n3\n100\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n50 100\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n6\n100\n0\n0\n0\n0\n0\n0\n0\n1\n1\n1\n7\n15\n13 100\n83 100\n16\n6\n7\n8\n8\n19\n9\n7\n19\n16 100 100 100\n20\n20\n20\n21\n21\n22\n22\n0\n4\n4\n23\n9 100\n4\n4\n4\n5\n5\n6\n6\n100 100 100 100 100 100 100 100 100 100 100 100 100\n100 100\n99\n99\n99\n99\n99 100 100 100 100 100 100\n100\n96\n95\n93\n93\n94\n92\n94 100 100\n99\n97\n97\n7\n19\n47\n23\n23\n28\n21\n21\n23 100\n67\n61\n59\n0\n20\n60\n26\n26\n31\n24\n24\n25\n75 100\n77\n73\n0\n10\n45\n3\n3\n6\n1\n1\n2\n33\n36 100\n66\n0\n1\n45\n5\n5\n20\n13\n3\n4\n36\n40\n76 100\n1\n22\n9\n41\n44\n27\n98\n90\n69\n10\n14\n8\n11\n100\n5\n6\n0\n0\n0\n1\n1\n1\n1\n1\n1\n95 100\n89\n12\n13\n9\n22\n24\n26\n33\n29\n25\n23\n48\n36 100\n5\n4\n9\n10\n11\n22\n22\n20\n16\n15\n23\n23 100\n95 100\n41\n40\n37\n35\n37\n40\n43\n17\n26\n26 100 100 100\n43\n42\n39\n37\n40\n42\n45\n4\n11\n11\n65\n61 100\n27\n25\n23\n21\n23\n26\n29\n100 100 100\n97\n97\n97 100 100 100 100 100 100 100\n98\n95\n96\n86\n86\n84\n91 100 100 100 100\n98\n97\n82\n80\n81\n61\n62\n58\n70\n77 100 100\n93\n88\n85\n12\n15\n24\n8\n8\n8\n10\n11\n14 100\n52\n44\n37\n17\n19\n35\n13\n13\n12\n15\n16\n19\n75 100\n68\n55\n7\n9\n17\n8\n8\n8\n8\n9\n10\n35\n37 100\n53\n10\n12\n21\n12\n12\n12\n11\n12\n14\n41\n43\n77 100\nall\n2e12i\ne22i\ne55\nmu6\nmu6i\nmu20\n2j20\n3j20\n4j20\n4j50\n3j65\n2j120\nj160\nJ160\n2J120\n3J65\n4J50\n4J20\n3J20\n2J20\nmu20\nmu6i\nmu6\ne55\ne22i\n2e12i\n100\n90\n80\n70\n60\n50\n40\n30\n20\n10\n0\nall\n2e12i\ne22i\ne55\nmu6\nmu6i\nmu20\n2j20\n3j20\n4j20\n4j50\n3j65\n2j120\nj160\nJ160\n2J120\n3J65\n4J50\n4J20\n3J20\n2J20\nmu20\nmu6i\nmu6\ne55\ne22i\n2e12i\n100\n90\n80\n70\n60\n50\n40\n30\n20\n10\n0\n(a) Fully-hadronic ttbar\n(b) Leptonic ttbar\nFigure 7: Trigger item overlap at the HLT for fully-hadronic (a) and leptonic (b) t\u00aft events. The\nnumbers in the plots indicate the percentage of events triggered by the item on the x-axis also\ntriggered by the item on the y-axis. Note that, by de\ufb01nition, the values on the diagonal have full\nacceptance. The bottom row in each plot gives the total ef\ufb01ciency of the corresponding item on\nthe x-axis.\nsimulations.\nA methodology is tested to determine the electron trigger ef\ufb01ciency for top events in data. Events\nwith Z-boson decays are used to parameterize the electron trigger ef\ufb01ciency as a function of pT and \u03b7 by\nmeans of the tag and probe method [8]. These parametrized ef\ufb01ciencies yield correction factors which\ncan then be applied to top events.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n894\n\nTop Mass [GeV]\n0\n50\n100 150 200 250 300 350 400\n-1\nEvents / 100 pb\n0\n20\n40\n60\n80\n100\n120\n140\n160\nTop Mass [GeV]\n0\n50\n100 150 200 250 300 350 400\n-1\nEvents / 100 pb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n \nATLAS\n [GeV]\nT\nElectron p\n0\n20\n40\n60\n80 100 120 140 160 180 200\n-1\nEvents / 100 pb\n0\n100\n200\n300\n400\n500\n [GeV]\nT\nElectron p\n0\n20\n40\n60\n80 100 120 140 160 180 200\n-1\nEvents / 100 pb\n0\n100\n200\n300\n400\n500\n \nATLAS\n\u03b7\nElectron \n-3\n-2\n-1\n0\n1\n2\n3\n-1\nEvents / 100 pb\n0\n100\n200\n300\n400\n500\n600\n700\n\u03b7\nElectron \n-3\n-2\n-1\n0\n1\n2\n3\n-1\nEvents / 100 pb\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\n\u03c6\nElectron \n-3\n-2\n-1\n0\n1\n2\n3\n-1\nEvents / 100 pb\n0\n50\n100\n150\n200\n250\n300\n350\n\u03c6\nElectron \n-3\n-2\n-1\n0\n1\n2\n3\n-1\nEvents / 100 pb\n0\n50\n100\n150\n200\n250\n300\n350\nATLAS\nFigure 8: Plots of the reconstructed top mass, reconstructed electron pT, \u03b7 and \u03c6. The darker\nhistogram is the reconstructed value, the black points include the correction from Z\u2192ee. The\nlighter histogram is from simulation where no trigger selection is applied.\nThe Standard Model Z-boson decaying to two leptons is relatively free of backgrounds at the LHC,\nand therefore provides a clean source of events for the tag and probe method. This method relies on the\nability to obtain a clean sample of Z-boson events using selection cuts after obtaining the initial sample\nusing a single electron trigger. From the di-electron \ufb01nal state one can tag the electron that \ufb01red the\ntrigger, and probe the other in order to measure the trigger ef\ufb01ciency. Once this ef\ufb01ciency is extracted\nit can be applied to other processes which have been obtained using the same trigger, in this case top\nevents.\nHaving selected top events using the commissioning selection [5], a correction for the trigger ef\ufb01-\nciency is applied to recover the number of events that would be measured by an ideal detector. For each\nevent, a weight is applied according to the pT and the position in \u03b7 of the electron in the event. The\nweight is taken as the inverse ef\ufb01ciency extracted from look-up tables, which have been obtained with\nthe tag-and-probe method.\nFigure 8 shows the pT \u03b7, and \u03c6 distributions of the electron in the t\u00aft event. The dark histogram rep-\nresents events that have passed the trigger selection, the black points show the events after the correction\nis applied. The lighter histogram is from a sample of events run with the trigger disabled. Also shown in\nthe \ufb01gure is the top quark mass as measured using the above selection, after a correction for the trigger\nef\ufb01ciency. It can be seen from the \ufb01gure that the ef\ufb01ciency correction works well, the effect of the trigger\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n895\n\ncan be recovered to reproduce the simulated distributions. The effect of additional jet activity in t\u00aft events\nas compared to Z\u2192ee events is thus indicated not to have a big effect at the current level of precision.\nThe \ufb01nal value of the trigger ef\ufb01ciency, used as a correction to the cross section measurement of the\nleptonic t\u00aft decay channel with one electron in the \ufb01nal state, is a value \u03b5trigger of 92.6 \u00b1 0.4 % for an\ne12i trigger chain and 91.5 \u00b1 0.4 % for an e22i trigger chain for 100pb\u22121 . These values are obtained\nby taking the ratio of the number of events before and after the trigger correction, and the uncertainty is\nstatistical only. Note that to obtain these numbers, a matching between the trigger and the reconstruction\nelectron candidates has to be done (\u2206R < 0.2), in contrast to the numbers in Table 1.\nIn conclusion, it is shown that the tag-and-probe ef\ufb01ciency can be successfully applied to leptonic\ntop decays. The method appears robust, however, the issue of background events passing the Z\u2192ee\nselection and the possible bias introduced thereby needs to be investigated.\n5\nConclusions and outlook\nThe \ufb01rst studies of the expected ATLAS trigger performance for top events have been shown. All levels\nof the electron and muon triggers are found to be highly ef\ufb01cient for the golden leptonic t\u00aft decays. The\njet triggers, especially important for hadronically decaying tops, are much more challenging to use due\nto the high rate of QCD jets. High jet multiplicities of 5 or 6 jets with optimised pT thresholds may\nprovide the best acceptance.\nTop quark events at the LHC will have especially rich event topologies and will result in many trigger\nitems being ful\ufb01lled simultaneously. The overlap of trigger items was investigated to identify combina-\ntions of trigger items with improved signal ef\ufb01ciency and trigger rate, as well as potential monitoring\ntriggers. The use of the Emiss\nT\ntrigger should be further investigated.\nThe trigger ef\ufb01ciency should be determined from data with the least possible bias. This must be val-\nidated with Monte-Carlo simulations, comparing the ef\ufb01ciencies derived with the data driven methods\nto the true ef\ufb01ciencies. Such a study, albeit not yet complete, was shown for the electron trigger ef\ufb01-\nciency using simulated Z \u2192ee samples. By using the trigger ef\ufb01ciency correction to the reconstructed\nkinematical distributions, it was shown that the simulated top quark distributions are very well recovered.\nReferences\n[1] The ATLAS Collaboration: ATLAS First Level Trigger - Technical Design Report, ATLAS TDR 12,\nCERN/LHCC 98-14, (1998).\n[2] The ATLAS Collaboration: ATLAS High-Level Trigger, Data Acquisition and Controls - Technical\nDesign Report, ATLAS TDR 16, CERN/LHCC 2003-022 (2003).\n[3] ATLAS Collaboration, \u2019Top Quark Physics\u2019, this volume.\n[4] ATLAS Collaboration, \u2019Trigger for Early Running\u2019, this volume.\n[5] ATLAS Collaboration, \u2019Determination of the Top Quark Pair Production Cross-Section\u2019, this vol-\nume.\n[6] ATLAS Collaboration, \u2019Overview and Performance Studies of Jet Identi\ufb01cation in the Trigger Sys-\ntem\u2019, this volume.\n[7] ATLAS Collaboration, \u2019Prospect for Single Top Quark Cross-Section Measurements\u2019, this volume.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n896\n\n[8] ATLAS Collaboration, \u2019Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection\u2019, this volume.\nTOP \u2013 TRIGGERING TOP QUARK EVENTS\n897\n\nJets from Light Quarks in t\u00aft Events\nAbstract\nThis note describes the properties of jets from light quarks (u, d, s and c) in\nt\u00aft events, with the goal of obtaining a good reconstruction of the hadronically\ndecaying W-boson, which will be used for an in-situ jet energy scale mea-\nsurement and will enter, together with jets from b quarks, into the top quark\nreconstruction.\n1\nIntroduction\nThe measurement of the top quark mass with a precision of 1 GeV is one of the goals of the LHC\nexperiments. In order to achieve such a precision, several complementary methods can be used [1]. The\nmost straightforward method, namely the measurement of the tri-jet invariant mass from the hadronically\ndecaying top quark in the t\u00aft \u2192l\u03bdb qqb channel, can in principle reach such a precision, provided that\nthe three jets are well reconstructed and calibrated.\nThis note describes some studies of the reconstruction and calibration of jets from light quarks (u, d, s\nand c) in t\u00aft events, with the goal of obtaining the best possible reconstruction of the hadronically decaying\nW-boson. After a comparison of various jet algorithms, two methods of in-situ jet calibration using the\nW-boson mass distribution will be presented. Finally, the stability of the W-boson reconstruction with\ndifferent gluon radiation settings in the Monte Carlo event generator will be shown.\nUnless otherwise speci\ufb01ed, the studies presented here have been performed using t\u00aft events generated\nwith MC@NLO + Herwig, with the top quark mass equal to 175 GeV, at least one of the W-bosons\ndecaying leptonically, and a full GEANT simulation of the ATLAS detector. The simulation statistics\ncorresponds to a luminosity of about 0.9 fb\u22121. By default, no pile-up is included in the simulation, except\nin a few dedicated studies. Triggering was not considered, as t\u00aft \u2192l\u03bdb qqb events will be triggered mainly\nby the leptonic decay of the second top quark, without biasing the jets on the hadronic side.\n2\nA comparison of jet reconstruction algorithms\nThe current default jet algorithm used for t\u00aft event reconstruction in ATLAS is the cone algorithm with a\nsize \u2206R = 0.4. A small cone size was indeed found in previous studies to give the best mass resolution and\nsignal over background ratio. This section presents new studies of the optimal jet algorithm, performed\nby looking at the jet energy, angular resolutions and at the W-boson mass reconstruction. For these\nstudies, the cone and kT algorithms, with various parameters, were tried. Details on jet algorithms can\nbe found in Ref. [2].\nCone algorithms de\ufb01ne jets as the combination of input objects from generated stable particles or\ncalorimeter energy deposits within a cone of radius R around the jet directions \u03b7 and \u03c6. In an iterative\nprocedure, the jets are repeatedly reconstructed until a stable con\ufb01guration is found. Two different\nimplementations exist: the \ufb01rst one, referred to as seeded cone jet \ufb01nder, used in this paper, uses high\nET objects in the event as a starting point, whereas the second, seed-less implementation, is much slower\nbut theoretically more accurate. In both scenarios, the jets obtained undergo a split-merge procedure, to\nde\ufb01ne non-overlapping exclusive jets. The resulting jets then need to be calibrated as explained below.\nThe second class of jet algorithms consists of the kT algorithm, which reconstructs jets via a cluster-\ning procedure. Such jets do not necessarily have a cone-shape with a \ufb01xed radius. Instead, the algorithm\nclusters \u201cnearest\u201d protojets together, depending on their relative transverse momentum. Thus, it also\nensures a unique association of input clusters to jets, without the need for split/merge procedures as in\ncone algorithms.\n898\n\nThe kT algorithm introduces a distance measurement \u2206R and a recombination scheme [3]. The\ndistance measurement decides which pair of protojets should be merged and when to stop merging a\nprotojet any further. Deciding whether to merge the two closest jets or \ufb02agging one of the protojets as\na \ufb01nal jet is executed recursively in the algorithm, until there are no more mergeable protojets left. The\nrecombination scheme determines how to combine two protojets into a new protojets. Here we use the E\nrecombination scheme.\nThere are two modes of operation for the kT algorithm, the inclusive and exclusive mode. The\ninclusive kT algorithm is intended for de\ufb01ning inclusive jet cross sections, as they are typically used\nin hadron-hadron interactions. It has a parameter R, which controls the decision to merge protojets or\ndeclare them as \ufb01nal jets, and plays a role comparable to the cone size in cone jet algorithms.\nThe kT algorithm in its exclusive mode must account for the proton remnants and the underlying\nevent in the p-p interaction for the calculation of exclusive cross sections. Its parameter Dcut controls the\nscale which separates \u201cbeam jets\u201d from the \u201chard jets\u201d during the clustering. Moreover, the value of Dcut\ncan also be determined dynamically if one \ufb01xes the desired number N of \ufb01nal jets.\nThe basic input objects for both cone and kT jet algorithms are either calorimeter towers, de\ufb01ned as a\ngroup of cells in a \ufb01xed (\u2206\u03b7, \u2206\u03c6) grid, or topological clusters, de\ufb01ned as a group of cells formed around\na seed cell [4]. These calorimeter towers or topological clusters are given at the electromagnetic scale.\nThe jets obtained are then calibrated to the hadronic scale using different weighting schemes such as the\nH1-style [5], whose major drawback is that the set of corrections is speci\ufb01c for each type of jet \ufb01nder\nand each value of its parameters.\nThe comparisons of jet algorithms were performed on t\u00aft \u2192l\u03bdb j jb events. In order to consider only\njets relevant for the top quark mass measurement, an event selection was performed, requiring:\n\u2022 a missing transverse energy > 20 GeV to account for the unmeasured neutrino.\n\u2022 one isolated electron or muon, de\ufb01ned as described in [6], with pT > 20 GeV and |\u03b7| <2.5.\n\u2022 at least 3 jets with pT > 40 GeV, a 4th jet with pT > 20 GeV, with |\u03b7| < 2.5.\n2.1\nJet energy resolution and linearity\nThis section presents the energy and position measurement performance for various jet algorithms, cal-\nibrated with the H1 weighting scheme. Although we investigated, in this section, all the combinations\nof cone / inclusive kT algorithm, 2 jets sizes, made from towers / topological clusters, with / without\npile-up, for the sake of clarity not all results are shown in the \ufb01gures.\nIn the events passing the event selection cuts, the jets considered for the resolution studies are the\ntwo jets closest to the two quarks from the W-boson decaying hadronically, when their distance \u2206R to\nthe quark is less than 0.3. As the \ufb01nal goal is to improve the two jet invariant mass reconstruction, the\njet energies (and directions) are hereafter compared directly to the ones of the associated quarks.\nFigure 1 shows, for four jet algorithms, the distributions of the energy difference between the matched\nquark and jet, divided by the quark energy, for two different jet energy ranges. Larger jets lead, especially\nat low energies, to a worse resolution and to larger tails because the jet energies are overestimated when\nthey overlap with other particles in the underlying event.\nThese energy distributions were \ufb01tted with a Gaussian distribution 1. The width of the distribution,\nas a function of the energy, is shown on \ufb01gure 2 and in Table 1. The resolutions obtained here are\nsigni\ufb01cantly worse than the detector resolution itself, as shown in Ref. [5], mainly because they include\nthe \ufb02uctuations of the energy lost outside the jets, as relevant to determine the best algorithm for the\n1To make the \ufb01t stable, a \ufb01rst Gaussian was \ufb01tted between the mean of the histogram \u00b1 2 times the RMS. A second \ufb01t was\nthen performed in the same way using the mean and width of the \ufb01rst \ufb01t.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n899\n\nQuark\n)/E\nJet\n-E\nQuark\n(E\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\nQuark\n)/E\nJet\n-E\nQuark\n(E\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\nTower Jets\nR=0.40\n\u2206\nCone \nR=0.70\n\u2206\nCone \nKt R=0.40\nKt R=0.60\nFigure 1: Distributions of (Equark - E jet)/Equark for the jets from the W-boson decay, for two\ndifferent quark energy ranges (left \ufb01gure: quark energy between 15 and 50 GeV, right \ufb01gure:\nquark energy above 350 GeV).\nW-boson (and the top quark) mass reconstruction. To quantify this effect, Figure 3 compares these\nresolutions to the ones obtained by using the jets made from the Monte Carlo hadrons (\u201cTruthjets\u201d). The\nlatter ones are typically 20% better, and comparable to the resolutions shown in [5].\nJet energy resolutions were also studied with events including the pile-up expected at a luminosity of\n1033 cm\u22122s\u22121 (\ufb01gure 4 and Table 1), showing that:\n\u2022 When jets are made from towers, small sizes are preferable, especially for the cone algorithm. For\nexample, Figure 4 shows that the energy resolutions of cone 0.4 jets made from towers is degraded\nby 30% to 50% in presence of pile-up.\n\u2022 The algorithms using topological clusters seem to behave very well, even in the presence of pile-\nup, as can also be seen on this \ufb01gure.\nFor cone 0.4 algorithms, the reconstructed jet energy is on average 4% lower than the quark energy,\nfor quarks with transverse momenta above 40 GeV. This 4% miscalibration can a priori come from the\ndetector calibration itself, from the energy lost outside the jet, or from the underlying event. Figure 5\nshows that, in the current simulation, the detector is very well calibrated, to a precision better than 3%\nfor all algorithms, and to better than 1% for the cone 0.4 algorithm.\nOn the other hand, Figure 6 shows that the out-of-cone energy is important, and accounts for the 4%\nenergy shift observed with cone 0.4.\nThe difference between the quark and the reconstructed jet energies, for quark energies between 15\nand 50 GeV, is shown in Figure 7 with and without pileup, for the cone 0.4 from topological clusters\nalgorithm. For such a small jet size and a topological cluster noise suppression, the average energy is\nshifted by 2.5 %.\n2.2\nJet angular resolution\nFigure 8 shows, for four jet algorithms, the distributions of the distance \u2206R between the quark and\nthe matched jet, for the lowest and the highest energy bins. It can be seen that smaller jets have a\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n900\n\nTable 1: Energy resolution (in %) as a function of the quark energy, for various jet algorithms, with and\nwithout pile-up.\nEnergy range [GeV]\nalgorithm\n15 - 50\n50 - 100\n100 - 150\n150 - 250\n250 - 350\n> 350\nCone \u2206R = 0.4, Tower\n18.3\n14.7\n13.0\n11.2\n9.4\n8.2\nCone \u2206R = 0.4, Topo\n18.5\n14.8\n12.6\n11.0\n9.5\n8.3\nCone \u2206R = 0.7, Tower\n25.2\n16.3\n13.5\n11.6\n10.3\n8.7\nCone \u2206R = 0.7, Topo\n20.4\n14.3\n12.5\n11.2\n9.3\n8.6\nkT R = 0.4, Tower\n21.4\n16.7\n14.4\n11.7\n9.6\n8.0\nkT R = 0.4, Topo\n20.4\n16.2\n13.1\n10.9\n9.5\n8.2\nkT R = 0.6, Tower\n22.1\n16.1\n13.4\n11.2\n10.3\n8.9\nkT R = 0.6, Topo\n19.3\n14.8\n12.6\n10.6\n9.8\n8.2\nCone \u2206R = 0.4, Tower, pile-up\n27.8\n20.0\n16.1\n13.6\n11.1\n8.8\nCone \u2206R = 0.4, Topo, pile-up\n20.9\n15.8\n13.1\n12.2\n10.6\n8.5\nCone \u2206R = 0.7, Tower, pile-up\n41.7\n26.8\n20.4\n19.1\n15.8\n13.4\nCone \u2206R = 0.7, Topo, pile-up\n34.2\n19.4\n14.6\n13.2\n11.8\n9.6\nkT R = 0.4, Tower, pile-up\n30.4\n23.7\n18.3\n15.5\n12.8\n10.3\nkT R = 0.4, Topo, pile-up\n24.4\n17.3\n14.6\n12.9\n10.9\n9.3\nkT R = 0.6, Tower, pile-up\n33.3\n24.0\n19.6\n17.0\n14.8\n11.6\nkT R = 0.6, Topo, pile-up\n26.1\n18.3\n14.4\n12.8\n11.6\n9.3\nmore precise direction determination. This can also be seen from Figure 9 where the full width at half\nmaximum (FWHM) of these distributions are plotted. It was checked that, as for the energy resolution,\nthe same conclusion remains when pile-up is added, and that jets made from topological clusters are less\nsensitive to pile-up.\nIt is observed that, for large cone sizes and large transverse momenta, the distributions of the distance\nbetween the quark and the matched jet have larger tails (larger fraction of jets with a distance to the\nassociated quark between 0.1 and 0.3), because of a higher overlap probability.\n2.3\nW-boson mass reconstruction\nThis section compares the W-boson mass reconstruction performances for the cone algorithms with sizes\n0.4 and 0.7 and for the kT jet algorithms with different choices of parameters, both using topological\nclusters.\nThe choice of the jet algorithm parameters is crucial for the performance of the W-boson reconstruc-\ntion. Indeed, the probability, averaged over the W-bosons selected in this section, for the two quarks\nfrom the W-boson decay to be at a distance \u2206R smaller than 1.4 is 25%, leading to non-negligible over-\nlap effects for jet sizes of the order of 0.7, as already seen in section 2.1, and eventually to the merging\nof the two jets coming from the light quarks into a single one. On the contrary, the probability for the 2\nquarks from the W-boson decay to be at a distance smaller than 0.8 is only 4%.\nThe same event selection as the one described in section 2.1 is performed, apart for the requirement\nthat the fourth jet satis\ufb01es pT > 40 GeV, which is needed to improve the W-boson purity. On the selected\nevents, the three jets whose four-momentum sum has the highest pT are chosen to belong to the hadronic\ntop quark. Among these three jets, the di-jet combination whose mass is closest to the known value of the\nW-boson mass (80.4 GeV) is taken to represent the W-boson. The remaining third jet is assumed to be\nthe b quark; no further b-tagging information is used in this study. The distribution for the reconstructed\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n901\n\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)\nQuark\n/E\nJet\n)/mean(E\nQuark\n/E\nJet\n(E\n\u03c3\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\n0.26\nATLAS\nR=0.40 Tower\n\u2206\nCone \nR=0.70 Tower\n\u2206\nCone \nKt R=0.40 Tower\nKt R=0.60 Tower\nFigure 2: Energy resolution for jets from light quarks (integrated over all \u03b7 values), as a function\nof the quark energy, for various jet algorithms (events simulated without pileup).\nW-boson mass is shown in Figure 10.\nTo obtain mass values from the invariant mass spectra of Figure 10, the sum of a Gaussian and a\n4th degree Chebychev polynomial is \ufb01tted to the distribution. The polynomial describes the background\nfrom wrong jet combinations and from background events, whereas the mean value of the Gaussian and\nits error are interpreted as the mass (mW) and its statistical error, \u03c3stat. The width of the Gaussian is\nreferred to as \u03c3Gauss. Table 2 shows the obtained W-boson mass with the E recombination scheme for\nvarious choices of the kT parameters.\nThe error resulting from 1% variation on the jet energy scale (JES) is obtained by varying the recon-\nstructed jet energies by \u00b11% followed by a linear \ufb01t across the three W-boson masses (-1%, nominal\nvalue, +1%).\nWith increasing R and Dcut parameter values, the reconstructed W-boson (and also top quark) mass\nrise monotonically. Higher parameter values lead to fewer but more energetic jets and thus their com-\nbination has a higher invariant mass. Part of this effect could in principle be absorbed by the in-situ\ncalibration, but on the other hand, the event is more likely to be misreconstructed due to unwanted jet\nmerging, which makes the choice of the three jets maximizing the pT-sum unpredictable.\nThe ef\ufb01ciencies quoted in Table 2, de\ufb01ned as the number of events in the gaussian part of the mass\ndistribution divided by the initial number of events, which can be as high as 5.8%, drop to less than 4%\nwhen the jets become too big.\nTable 2 also shows the purity of the W-boson reconstruction, de\ufb01ned as the fraction of events in the\ngaussian part of the distribution, in the range [\u22121\u03c3gaus, 1\u03c3gaus] from the mean value of the gaussian \ufb01t.\nA purity around 64% can be obtained with some choices of the algorithms / parameters, for example\ncone 0.4 or kT with R = 0.4, whereas other choices may lead to purities about 15% smaller.\nThis study indicates that, for the W-boson mass reconstruction in t\u00aft events, the cone 0.4 algorithm\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n902\n\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)\nQuark (MC Jet)\n/E\nJet\n)/mean(E\nQuark (MC Jet)\n/E\nJet\n(E\n\u03c3\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\nR=0.40 Tower Quark-Jet\n\u2206\nCone \nR=0.70 Tower Quark-Jet\n\u2206\nCone \nR=0.40 Tower Monte Carlo Jet-Jet\n\u2206\nCone \nR=0.70 Tower Monte Carlo Jet-Jet\n\u2206\nCone \nFigure 3: Comparison of the jet energy resolutions with respect to the Monte Carlo hadrons\n(\u201cMonte Carlo jets\u201d) and with respect to the initial quarks from the W-boson decay, for events\nsimulated without pileup.\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)\nQuark\n/E\nJet\n)/mean(E\nQuark\n/E\nJet\n(E\n\u03c3\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\n0.26\n0.28\nATLAS\nR=0.40 Topo\n\u2206\nCone \nR=0.40 Tower\n\u2206\nCone \nR=0.40 Topo with PileUp\n\u2206\nCone \nR=0.40 Tower with PileUp\n\u2206\nCone \nFigure 4: Comparison of the jet energy resolutions for events simulated with and without pile-up.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n903\n\n [GeV]\nMonte Carlo Jet\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)>\nMonte Carlo Jet\n)/E\nJet\n-E\nMonte Carlo Jet\n<((E\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\nATLAS\nR=0.40 Tower\n\u2206\nCone \nR=0.70 Tower\n\u2206\nCone \nKt R=0.40 Tower\nKt R=0.60 Tower\nFigure 5: Relative difference between the Monte Carlo jet energy and the reconstructed jet energy,\nas a function of the Monte Carlo jet energy, for events simulated without pileup.\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\n)>\nQuark\n)/E\nMonte Carlo Jet\n-E\nQuark\n<((E\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\nATLAS\nR=0.40 Tower\n\u2206\nCone \nR=0.70 Tower\n\u2206\nCone \nKt R=0.40 Tower\nKt R=0.60 Tower\nFigure 6: Relative difference between the quark energy and the Monte Carlo jet energy, as a\nfunction of the quark energy, for events simulated without pileup.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n904\n\nQuark\n)/E\nJet\n-E\nQuark\n(E\n-1\n-0.5\n0\n0.5\n1\nEvents\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nATLAS\nR=0.4 Topological\n\u2206\nCone \nw/o PileUp\nwith PileUp\nFigure 7: Relative difference between the quark and the jet energy, for quark energies between 15\nand 50 GeV, with and without pileup, for the cone 0.4 algorithm from topological clusters.\nR(Quark,Jet)\n\u2206\n0\n0.02 0.04 0.06 0.08 0.1 0.12 0.14\nEvents\n0 02\n0 04\n0 06\n0 08\n0.1 ATLAS\nR(Quark,Jet)\n\u2206\n0\n0.02 0.04 0.06 0.08\n0.1 0.12 0.14\nEvents\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nR=0.40 Tower\n\u2206\nCone \nR=0.70 Tower\n\u2206\nCone \nKt R=0.40 Tower\nKt R=0.60 Tower\nATLAS\nFigure 8: Distance between the jet and the quark, for various jet algorithms / parameters and for\ntwo different quark energy ranges (left \ufb01gure: quark energy between 15 and 50 GeV, right \ufb01gure:\nquark energy above 350 GeV)\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n905\n\n [GeV]\nQuark\nE\n50\n100\n150\n200\n250\n300\n350\n400\nR(Quark,Jet)\n\u2206\nFWHM of \n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\nR=0.40 Tower\n\u2206\nCone \nR=0.70 Tower\n\u2206\nCone \nKt R=0.40 Tower\nKt R=0.60 Tower\nFigure 9: Resolution (de\ufb01ned as the full width at half maximum) on the distance between the jet\nand the quark, as a function of the quark energy, for various jet algorithms / parameters.\nTable 2: Reconstructed hadronic W-boson mass for different kT-parameters with statistical uncer-\ntainty, ef\ufb01ciency, purity and the systematic uncertainty from jet energy scale. (*) The cone jet\nalgorithms use uncalibrated topological clusters with H1-style cell weights.\nW mass\nkT parameter\nmW\n\u03c3Gauss\n\u03c3stat\nef\ufb01ciency\npurity\n1% \u2206JES\n[GeV]\n[GeV]\n[GeV]\n[%]\n[%]\n[GeV]\nR = 0.4\n78.30\n7.37\n0.18\n4.4\n63\n\u00b10.26\nR = 0.6\n79.75\n7.09\n0.18\n4.4\n63\n\u00b10.28\nR = 0.8\n80.47\n6.95\n0.23\n3.1\n58\n\u00b10.20\nDcut = (10 GeV)2\n81.25\n7.03\n0.17\n5.4\n54\n\u00b10.21\nDcut = (20 GeV)2\n81.69\n7.40\n0.18\n5.8\n55\n\u00b10.27\nDcut = (30 GeV)2\n81.84\n7.44\n0.20\n5.3\n57\n\u00b10.33\nDcut = (40 GeV)2\n82.00\n7.12\n0.22\n4.2\n57\n\u00b10.39\nN = 5\n82.02\n7.35\n0.21\n4.5\n54\n\u00b10.34\n* Cone R = 0.4\n81.00\n6.38\n0.14\n5.6\n64\n\u00b10.36\n* Cone R = 0.7\n85.15\n8.03\n0.26\n3.9\n53\n\u00b10.55\nleads to the best performance both in terms of resolution and in terms of ef\ufb01ciency / purity.\nFinally, in addition to this study which uses jets calibrated with H1-style weights, a study of the W-\nboson reconstruction using local hadron calibration, described in detail in [5] and in [7], has been started.\nAlthough the local hadron calibration algorithm is still being improved, the W-boson mass reconstruction\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n906\n\nReconstructed W mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEntries / 2 GeV\n0\n500\n1000\n1500\n2000\n2500\nSignal + background\nFit Gauss + Chebychev\nFit Chebychev\nPhysics background\nATLAS\nFigure 10: Invariant di-jet mass as an estimate of the hadronically decaying W-boson mass in the\nselected events. The luminosity used corresponds to 1 fb\u22121 of signal and background events. The\ninclusive kT algorithm in the E scheme with R=0.4 is used for jet reconstruction. The data points\nfor signal and background events are shown in black. The hatched histogram shows the distribution\nfor background events (fully hadronic t\u00aft events, single top events and W + jets events).\ncapabilities are similar to the ones obtained with H1-weighted jets, both in terms of mass resolution and\npurity.\n2.4\nConclusion\nThe studies shown here indicate that a small jet size should be preferred for a proper reconstruction of\nthe jets in t\u00aft events, to avoid overlap effects spoiling the energy and angular resolutions and, eventually,\nleading to the merging of jets. Thus, the cone 0.4 jet algorithm from towers used in the following sections\nand in most top physics studies is a good choice for looking for top events in the \ufb01rst LHC data, although\nit could be complemented by an algorithm using topological clusters, which seem to be robust against\npileup. The effect of the pile-up on the W-boson mass reconstruction needs however to be assessed.\n3\nMeasuring the light jet energy scale\n3.1\nIntroduction\nThe miscalibration of jet energies is one of the main sources of systematic error in the measurement\nof the top quark mass in the three-jet invariant mass method [1]. Indeed, a 1% error on the jet energy\ntranslates into a 0.9 GeV error on the top quark mass, 0.2 GeV coming from the light jet energy scale\nand 0.7 GeV from the b-jet energy scale. The goal of measuring the top quark mass with a precision of\n1 GeV thus puts the limit on the miscalibration at 1% or better.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n907\n\nSeveral physics processes will be used in ATLAS to achieve such a precision [8]: di-jet events will\nhelp check the uniformity of the response as a function of rapidity; Z+jet and \u03b3+jet events will be used\nto measure the energy scale as a function of energy. However, these processes cannot be applied directly\nto the jets in t\u00aft events, for several reasons:\n1. These processes contain a mixture of jets from light quarks, jets from b quarks and jets from\ngluons, with calibration factors probably different by a few % due to their different fragmentation\nand neutrino content\n2. The underlying event may be different in t\u00aft events\n3. Jet selection performed to purify the t\u00aft sample could lead to a different average jet energy scale in\nthis sample\nThe use of W \u2192j j from the t\u00aft events themselves (in-situ calibration) will thus be very important.\nAfter having shown how to select a clean W \u2192j j signal from t\u00aft events, two possible methods for\nextracting the light jet energy scale will be presented. All the studies presented in this section (apart\nfrom the check of the stability with different top quark masses shown in section 3.6.3) use the default\nMC@NLO + HERWIG simulated events (with a top quark mass of 175 GeV), without pileup. The\ncone 0.4 jet algorithm from towers with the H1-style calibration is used for all studies in this section.\n3.2\nEvent and j j pair selection\nIn order to measure the jet energy scale with a precision of about 1%, a clean W \u2192j j sample must be\nselected. In this section the following selection cuts, which are stricter than the ones used previously, are\nthus used:\n\u2022 One and only one isolated lepton (electron or muon) with PT > 20 GeV\n\u2022 Missing ET > 20 GeV\n\u2022 At least 4 jets with pT > pcut\nT\n\u2022 Among them, 2 and only 2 jets must be tagged as b-jets. The other jets are called \u201clight jets\u201d in\nthe following.\nIn order to increase the purity, the W-boson candidate j j pairs are selected among all light jet pairs\nwhich lead to a reconstructed top quark mass between 150 and 200 GeV. In addition, one may want to\nconsider only events with only two light jets.\nThe estimated number of j j pairs selected for 1 fb\u22121 and the purity of the selection, de\ufb01ned as the\nfraction of j j pairs with both jets within \u2206R = 0.25 of the two W-boson quarks, are shown in table 3 as a\nfunction of pcut\nT , and whether or not one uses only events with two light jets.\nRequiring two light jets only reduces the number of j j pairs by about a factor of almost two, but is\nnecessary if one aims to measure the jet energy scale down to 20 GeV, in order to minimize the bias due\nto the combinatorial background.\nFigure 11 shows the j j mass distribution for pcut\nT\n= 40 GeV and exactly two light jets. The com-\nbinatorial background (shown in grey) is almost \ufb02at. The systematic error due to the knowledge of the\ncombinatorial background will be discussed later. Because of the requirement for 2 b-tagged jets, the\nbackground from other processes is of the order of a few percent and is neglected here.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n908\n\nTable 3: Number of selected W \u2192j j pairs (for 1 fb\u22121) and purity of the selected pairs (the statistical\nuncertainty on the purity is about 1%)\n2 jets only\n2 jets or more\npcut\nT [GeV]\nj j pairs\npurity [%]\nj j pairs\npurity [%]\n20\n3100\n76.9\n7100\n64.3\n30\n2300\n77.7\n4100\n71.5\n40\n1200\n81.0\n1900\n79.1\n [GeV]\njj\nm\n40\n60\n80\n100\n120\n140\n160\nEvents / 2 GeV\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\nFigure 11: Invariant mass m j j of the selected jet-jet pairs when the two jets are at \u2206R < 0.25 from\nthe two quarks from the W-boson decay (white histogram) and when at least one of the jets is not\nfrom the W-boson decay (grey histogram).\n3.3\nThe PT cut effect in the Jet Energy Scale measurement\nWhen measuring the jet energy scale, one must be aware of a shift introduced by any cut on the transverse\nmomentum of the jets needed for the event selection. Indeed, when one selects jets with a reconstructed\npT greater than pcut\nT , jets with a true pT lower than the cut but a reconstructed one above are selected,\nwhereas jets with a true pT above the cut but a reconstructed one below are lost. These two effects lead\nto a ratio (reconstructed energy) / (true energy) higher than one near the cut, even if the calibration is\nperfect.\nThis can easily be seen, and the size of the effect measured, with a simple Monte Carlo simulation\nwhere the momenta of the quarks from the W boson decays in t\u00aft are smeared according to the expected\njet resolution 2, and a pT cut on the smeared quark momenta is applied.\nFigure 12 shows the apparent calibration as a function of the jet pT cut, using this simple simulation.\n2The value \u03c3(E) = 3.8 GeV+0.063\u00d7Eq was used.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n909\n\nThis apparent calibration is greater for jets whose energy is closer to the value of the pT cut. The size\nof the effect is fully determined once the p, pT spectra and the detector resolution are known. With the\nexpected resolution of the ATLAS calorimeter, the global apparent calibration is 2% for a pT cut = 40\nGeV.\n [GeV]\ncut\nT\np\n0\n10\n20\n30\n40\n50\n>\nquark\n / E\njet\n 40 GeV is 0.961\u00b10.003, as can be seen in \ufb01gure 15.\nAs shown in section 2.1, this 4% miscalibration is mainly due to the out-of-cone energy.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n910\n\n [GeV]\ncut\nT\np\n0\n10\n20\n30\n40\n50\n> [GeV]\njj\n, due to the pcut\nT\non the jet energies.\nThe error bars indicate how the bias varies when changing the jet resolution by \u00b1 20%. This \ufb01gure\nwas obtained using the simple simulation described in the text.\n [GeV]\ncut\nT\np\n0\n10\n20\n30\n40\n50\n> [GeV]\njjb\n, due to the pcut\nT\non the jet energies. The\nerror bars indicate how the bias varies when changing the jet resolution by \u00b1 20%. This \ufb01gure\nwas obtained using the simple simulation described in the text.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n911\n\nquark\n/E\njet\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\nATLAS\nFigure 15: E jet/Equark for jets originating from a W-boson and with pT(quark) > 40 GeV.\n3.5\nThe iterative rescaling method\n3.5.1\nMethod\nThis method uses the precisely known W-boson mass as a reference to extract the light jet energy scale.\nThe invariant mass of the two jets with energies E1 and E2 and an opening angle \u03b8j j, originating from\nthe W-boson can be written as :\nMj j =\nq\n2E1E2(1\u2212cos(\u03b8j j))\nFigure 16 shows that the angle between the two jets is measured without any signi\ufb01cant bias for most\njet-jet pairs. Any deviation of Mj j therefore comes mainly from the energy miscalibration.\nThe peak value of this invariant mass matches the PDG W-boson mass value if the appropriate jet\nenergy scale factors K(E1) and K(E2) are used:\nMPDG\nW\n=\nq\n2(K(E1)E1)(K(E2)E2)\u00d7(1\u2212cos(\u03b8 j j)) =\np\nK(E1)K(E2)Mj j\nIf the jet calibration is independent of the energy (K = K(E1) = K(E2)), the jet energy scale factor K\nis simply K = MPDG\nW\n/Mj j. The simple rescaling gives the effective jet energy scale, taking into account\nthe pT cut effect from the jet selection.\nWith 1 fb\u22121 of luminosity, around 4000 jets originating from the W in the t\u00aft sample are available\nfor calibration. Normalizing the sample to 1 fb\u22121, the truth calibration, for jets with PT > 40 GeV,\nis Ktruth = (E jet/Eparton)\u22121 = 1.014 \u00b1 0.002. The value obtained by the simple rescaling of jet pairs\noriginating from a W boson (no background contribution) is K = MPDG\nW\n/Mj j = 1.014\u00b10.003 . The 1%\ngoal on the precision on the global jet energy scale is therefore obtainable with 1 fb\u22121, provided the\nluminosity dependence is small or can be corrected for.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n912\n\n)\njj\n\u03b8\n cos(\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\n)\nqq\n\u03b8\n)/(1-cos(\njj\n\u03b8\n(1-cos(\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\nFigure 16: (1 \u2212cos(\u03b8j jMC))/(1 \u2212cos(\u03b8j j)) as function of the reconstructed cos(\u03b8j j), where \u03b8j j\nis the reconstructed angle between the two jets and \u03b8j jMC the angle between the two associated\nquarks.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n913\n\nSince the calibration is not constant over the energy and pseudorapidity, and since the two jets from\nthe W-boson decay have in general different energies, the rescaling method has to be adapted to get the\ncalibration K(var) (var=jet energy, jet pseudorapidity or any other jet variable). Instead of building one\njj mass distribution, the \ufb01rst step is to split the studied jet variable in N bins, and to build all associated jj\ninvariant mass distributions. In such a way, the distributions become correlated to the studied variable.\nIt can be shown that, if the rescaling method is iterated M times, extracting at each iteration j the\ncorrection factor for the bin i (K j\ni ) and recomputing the invariant mass by adding the new K j\ni for the next\niteration, the exact correction Ki per bin i can be obtained (thus the function K(var)):\nKi = \u220f\nj=1,M\nK j\ni\n(1)\nThis method converges in 3-4 iterations, and is stopped when the maximum difference between K j\nand K j\u22121 is less than 1%. The number of bins N depends on the available jet statistics.\n3.5.2\nResults\nThe simple rescaling method allows to determine a global jet energy scale factor. A W-boson mass\nvalue MW = 79.12\u00b10.25 GeV is obtained from a \ufb01t with a polynomial+gaussian function to the jet-jet\ninvariant mass spectrum. The resulting jet energy scale factor is thus K = MPDG\nW\n/Mj j = 1.016\u00b10.003 3.\nThis value is very close to the one obtained previously by a \ufb01t on the same sample without combinatorial\nbackground included.\nFigures 17 and 18 show the effective calibration to be applied on the selected jets after the t\u00aft selection\nfor 10 fb\u22121 of integrated luminosity 4. The observed discrepancy between the \ufb01t result and the truth K\nfactors is due to the (\u03b7, E) correlations existing on the jet energy scale factors. This is particularly true\nfor high jet \u03b7 and high jet energy. The discrepancy at low energy is a threshold effect which could be\nremoved by lowering the pTcut on the jets to 30 GeV when measuring the jet energy scale above 40\nGeV. Nevertheless the jet energy scale as a function of \u03b7 and E can be extracted with a precision of the\norder of 1%, without any a priori knowledge of the function shape before the \ufb01t. The treatment of the\ncorrelation could be resolved by a \ufb01t on W mass distributions de\ufb01ned as a function of both jet \u03b7 and E.\nFor 1 fb\u22121 of integrated luminosity, the number of available jets (\u22484000) limits the number of bins\nand therefore the accuracy of the extracted jet energy scale functions (K(\u03b7) and K(E) ). The resulting\nplots for 1 fb\u22121 are shown in Figures 19 and 20. A precision better than 2% is obtained in each energy\nor \u03b7 bin.\n3.5.3\nSystematic uncertainties\nThe systematic uncertainties associated to each point are of three types:\n\u2022 the \ufb01rst is related to the method itself. Performing the \ufb01t on a large sample shows up to 1%\ndeviation, due to the (\u03b7,E) correlations on the jet energy scale which are not taken into account\nyet.\n\u2022 the second is related to the impact of the background on the mass peak measurements. It is rather\nlow since the W-boson sample has a purity above 80%. Further puri\ufb01cation cuts can be applied\nto increase the purity. The associated error depends on the available statistics and is higher for\n3The W boson mass is set to MW = 80.4 GeV in the simulation.\n4The calibration factors are large in the barrel-endcap transition region. In principle this dependence is corrected at the level\nof jet reconstruction algorithm using a pT balance method in di-jet events. This correction has not been applied on the used\nsample.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n914\n\n [GeV]\njet\nE\n0\n50\n100\n150\n200\n250\n300\n350\n400\nK\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\nFigure 17: Result of the iterative rescaling \ufb01t as a function of Ejet, with 10 fb\u22121: the expected\neffective calibration factors are shown as square points, in addition to the \ufb01tted calibration factors\nwith circles. The calibration factor obtained from Monte Carlo truth information Ktruth(E) =\n(Eparton/E jet) are shown as square points while the calibration factor K(Ei) obtained in the iterative\nrescaling procedure as described in section 3.5.1 are described with circles.\nlow jet energy where the background contribution is higher. It should be noticed that the jet\npairs contributing to the background are mainly composed of one jet originating from the W-\nboson, the others being jets coming from the remaining part of the event or gluon radiation. An\nevent mixing technique, described in [1] paragraph 4.2, will be useful to assess the shape of the\nbackground contribution on real data. To evaluate the systematics induced by the background\ncontribution, the background contribution was changed by +20%, separately for the FSR and non-\nFSR contributions 5. The \ufb01tted MW values are all within 0.2 GeV, compatible with the statistical\nuncertainty leading to an uncertainty of 0.003\u00b10.003 for the global jet energy scale factor.\n\u2022 the last comes from the correction factor to be applied on the \ufb01tted value to take into account the\npT bias discussed in section 3.3. This correction of the effect is fully determined once the jet p, pT\nspectra and energy resolution are known. The size of this correction is \u22121% above 100 GeV and\nup to 2% at 40 GeV. In order to assess the error on these values, the resolution has been rescaled\nby \u00b110%, leading to variation less than one percent of the correction factors.\n5The shapes of the background when a jet coming from the W-boson decay is associated with a FSR or a non FSR jet are\ndifferent. They are taken from a fast simulation Monte Carlo.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n915\n\n| \njet\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nK\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\nFigure 18: Result of the iterative rescaling \ufb01t as a function of \u03b7jet, with 10 fb\u22121: the expected\neffective calibration factors are shown as square points, in addition to the \ufb01tted calibration factors\nwith circles.\n3.6\nThe template method\n3.6.1\nMethod\nThe template method for the light jet energy scale determination is similar to the method described in [9]\nfor the electromagnetic energy scale determination using Z0 \u2192e+e\u2212events. It uses template histograms\nwith various energy scales \u03b1 and relative (to the default jet energy resolution) energy resolutions \u03b2. The\n\u03c72 between each template histogram and the \u201cdata\u201d is then computed. The minimum of the \u03c72 is found\nin the (\u03b1, \u03b2) plane. With 1 fb\u22121, this method \ufb01ts both the average jet energy scale and a relative jet\nresolution. With enough data, it can be extended to measure these quantities as a function of the jet\nenergy or rapidity.\nThe template histograms were generated from W \u2192qq decays in 1.2 million PYTHIA t\u00aft events by\nsmearing the quark energies by a gaussian number with width equal to 3.8 GeV+0.063\u00d7Eq, determined\non reconstructed jets in an older simulation of t\u00aft events. As will be shown later, the exact choice of the\ndefault energy resolution in the templates is not very important, as it will lead at the end only to a change\nin the \ufb01tted \u03b2 and not in the \ufb01tted \u03b1. However, in order to obtain a \u03b2 value close to 1, the jet angles\nare also smeared, according to the expected resolution, in the templates and the observed correlation\nbetween the two jet energies is added by using correlated gaussian numbers for the energy smearing.\nAfter smearing the quark energies, the same pcut\nT\nas used in the data is applied. This ensures that the\n\ufb01tted energy scale is not affected by the bias described in section 3.3. Figure 21 shows the reconstructed\njet-jet mass (for events with two jets or more, with the combinatorial background included), the template\nhistogram for \u03b1 = 1, \u03b2 = 1 and the best \ufb01t histogram.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n916\n\n [GeV]\njet\nE\n0\n50\n100\n150\n200\n250\n300\n350\n400\nK\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\nFigure 19: Result of the iterative rescaling \ufb01t as a function of E jet, with 1 fb\u22121: the expected\neffective calibration factors are shown as square points, in addition to the \ufb01tted calibration factors\nwith circles.\n3.6.2\nResults\nTable 4 summarizes the results obtained for jets with PT > 40 GeV. The combinatorial background,\nwhich is \ufb02at as shown in Figure 11, doesn\u2019t affect the \ufb01tted jet energy scale (less than 0.6%), but degrades\nthe \ufb01tted relative resolution by 30 to 40%. The choice to use or not events with more than two jets is also\nnot changing the \ufb01tted jet energy scale.\nFinally, these \ufb01tted energy scales are in good agreement with the expected value from the Monte-\nCarlo (0.961\u00b10.003), as obtained in section 3.4.\nTable 4: Fitted jet energy scale and relative jet energy resolution using the template method, for jets\nwith transverse momentum greater than 40 GeV. Good combinations refers to the cases where the two\njets come from the W-boson decay, while the results with all combinations include the effect of the\ncombinatorial background.\n\u03b1\n\u03b2\n2 jets, good combinations\n0.9693\u00b10.0045\n1.145\u00b10.054\n2 jets, all combinations\n0.9638\u00b10.0049\n1.434\u00b10.064\n\u22652 jets, good combinations\n0.9696\u00b10.0033\n1.089\u00b10.035\n\u22652 jets, all combinations\n0.9660\u00b10.0036\n1.308\u00b10.041\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n917\n\n| \njet\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2.5\nK\n0.9\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\n1.1\nATLAS\nFigure 20: Result of the iterative rescaling \ufb01t as a function of \u03b7 jet, with 1 fb\u22121: the expected\neffective calibration factors are shown as square points, in addition to the \ufb01tted calibration factors\nwith circles.\n3.6.3\nSystematic uncertainties\nSeveral checks of the stability of the method have been performed:\n\u2022 The in\ufb02uence of the combinatorial background, and the choice of using or not events with more\nthan two jets was already described in the previous section. All \ufb01tted energy scales are compatible\nwithin \u00b1 0.3 %.\n\u2022 The stability with respect to the ingredients used in the templates was checked by generating\ntemplate histograms without the smearing of the angles, or without the correlation between the jet\nenergies, or with a default jet resolution degraded by 20%. The \ufb01tted jet energy scales were found\nto be compatible within \u00b1 0.3%, and only the \ufb01tted relative resolutions were changing. This shows\nthat the method is not very sensitive to the simulation used for the templates.\n\u2022 The jet energy scales were \ufb01tted on t\u00aft events simulated with various top masses but the same\nversion of the simulation and reconstruction codes. The results are shown in Figure 22. All results\nare compatible within \u00b1 0.5%, even when including top masses in a very wide range.\n3.6.4\nStability of the template method with smaller integrated luminosities\nIn order to check the stability of the template method at lower luminosities, the 770 pb\u22121 full dataset was\nsplit into sixteen parts, each part thus corresponding to 48 pb\u22121. The \ufb01tted jet energy scales in the sixteen\npseudo-experiments are shown in Figure 23. The average of the sixteen measurements is 0.9534, in good\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n918\n\njet-jet mass (GeV)\n60\n65\n70\n75\n80\n85\n90\n95\n100\nEvents [arbitrary scale]\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n = 1.\n\u03b2\n = 1., \n\u03b1\nTemplate \n = 1.33\n\u03b2\n = 0.96, \n\u03b1\nBest fit \nATLAS\nFigure 21: Jet-jet invariant mass in fully simulated events (dots) superimposed on the template\nhistogram with \u03b1 = 1, \u03b2 = 1 and the best \ufb01t histogram.\ntop mass [GeV]\n160\n165\n170\n175\n180\n185\n190\nFitted energy scale\n0.954\n0.956\n0.958\n0.96\n0.962\n0.964\n0.966\n0.968\n0.97\nATLAS\nFigure 22: Fitted jet energy scale as a function of the top mass.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n919\n\nagreement with the \ufb01t on the full sample (0.9562 \u00b1 0.0039). The RMS of the sixteen measurements is\n1.9%, only slightly worse than the value expected by a scaling with the square root of the luminosity\n(1.6%). In addition, the average of the errors given by the \ufb01t is 1.5%, showing that this error is correctly\nestimated by the \ufb01t even at low luminosities.\nMeasurement number\n0\n2\n4\n6\n8\n10\n12\n14\n16\nFitted energy scale\n0.9\n0.92\n0.94\n0.96\n0.98\nATLAS\nFigure 23: Fitted jet energy scale for sixteen 48 pb\u22121 pseudo-experiments. The horizontal lines\nshow the result of the \ufb01t on the full sample with its error bar.\n3.7\nConclusion on light jet energy scale\nTwo complementary methods for measuring the light jet energy scale from the W \u2192j j mass distribution\nin t\u00aft events have been studied. The template method is well suited to measure the bare jet energy scale\n(integrated over some transverse momenta), with a precision which could be around 2% with 50 pb\u22121.\nWithin the statistical precision of the available datasets, no systematic error larger than 0.5% has been\nidenti\ufb01ed. The required precision of 1% on the light jet energy scale should thus be achievable. The\niterative method, on the other hand, is well suited to measure the jet energy scale of the selected jet\nsample, possibly as a function of the energy or as a function of rapidity.\nIn this study. the invariant mass of selected jet pairs present a clear W-boson signal on top of a\n\ufb02at background dominated by combinatorial from top events (Figure 11). This is possible because b\njets are tagged with a high ef\ufb01ciency and purity. In the early data-taking phase, b-tagging may be less\nperformant and the level of background will be much higher with contribution from QCD or W+jet\nevents. The performance of the methods for calibration of the light jet energy scale in these conditions\nneed to be evaluated.\nThe dependence of the jet energy scale with the level of pile-up has to still to be investigated, in order\nto decide whether a speci\ufb01c correction is needed.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n920\n\n4\nW-boson mass reconstruction and gluon radiation\nThe stability of the W-boson reconstruction with different QCD-related jet activity, commonly referred\nto as initial- and \ufb01nal-state radiation (ISR and FSR) has been evaluated by using the standard HERWIG +\nMC@NLO simulation and the \u201clow mass\u201d and \u201chigh mass\u201d ACERMC + PYTHIA event samples described\nin [6].\n4.1\nReconstructed W-boson masses\nThe same event selection (described in the previous section) and mass reconstructions is applied on the\n3 samples, with jets being reconstructed with the \u2206R = 0.4 cone algorithm from towers.\nFigure 24 shows that the W-boson mass distributions for the 3 samples, normalized to the same\nnumber of events after selection, are clearly not compatible before calibration. The results of the mass\npeak \ufb01ts are shown in Table 5. The difference between the high mass dataset and the low mass dataset is\n1.7\u00b10.2 GeV.\n [GeV]\njj\nm\n40\n50\n60\n70\n80\n90\n100\n110\n120\nEvents per 2 GeV\n0\n50\n100\n150\n200\n250\n300\nATLAS\nhigh mass\nlow mass\nstandard simulation\nFigure 24: Reconstructed W-boson mass distribution (before calibration) in datasets with different\ngluon radiation settings. The distributions are normalized to the number of events after selection\nin the standard simulation and \ufb01tted with a gaussian function.\nTable 5: Fitted top and W masses for the three datasets with different gluon radiation settings.\nmaximum mass\nminimum mass\nMC@NLO + Herwig\nW mass (GeV)\n81.29\u00b10.12\n79.59\u00b10.15\n80.44\u00b10.14\n\ufb01tted energy scale\n0.9779\u00b10.0024\n0.9489\u00b10.0026\n0.9636\u00b10.0025\nW mass after calibration (GeV)\n82.46\u00b10.12\n82.38\u00b10.14\n82.63\u00b10.14\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n921\n\nThe jet energy scales obtained with the template method described in section 3.6 are also shown in the\ntable, together with the W-boson masses obtained after recalibrating the jet four-momenta. One observes\nthat the calibrated W-boson masses are above the true W-boson mass because of the bias explained in\nsection 3.3, but are all compatible within errors, showing that the calibration method is indeed working\nwell.\n4.2\nLight jet properties\nAlthough the in-situ calibration leads to W-boson mass distributions which are independent of the gluon\nradiation level, we looked for additional measurable quantities which could help to understand these\neffects and tune the Monte Carlo simulations.\nFigure 25 show the pT distributions for the light jets coming from the W-boson decay 6. Only a very\nsmall difference, at low energies, is visible, which would probably be very dif\ufb01cult to measure in the\ndata.\n of the light jets from W decay [GeV]\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents per 20 GeV\n0\n200\n400\n600\n800\n1000\nhigh mass\nlow mass\nstandard simulation\nATLAS\nFigure 25: pT distribution of the jets from the hadronic W-boson decay for datasets with different\ngluon radiation settings. The distributions are normalized to the number of events after selection\nin the standard simulation. In order to look for a possible difference at low values, the cut on the\npT value of the jets has been reduced to 20 GeV for this \ufb01gure.\nOn the contrary, a very large difference is visible in the number of jets, as can be seen for example\nin the total number of jets with pT > 10 GeV reconstructed in the events, shown in Figure 26. If\nthe jet reconstruction ef\ufb01ciency is well understood, this distribution in the data could help to tune the\nsimulations, although the number of jets may also depend on the underlying event and may need to be\ncorrected for luminosity.\nFinally, no large difference has been seen in the pT distributions for the jets not assigned to top quark\ndecays, as shown in Figure 27.\n6A cut pT > 20 GeV is applied in these \ufb01gures\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n922\n\n > 10 GeV\nT\nnumber of jets with p\n4\n6\n8\n10\n12\n14\nEvents\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nATLAS\nhigh mass\nlow mass\nstandard simulation\nFigure 26: Total number of reconstructed jets with pT > 10 GeV for datasets with different gluon\nradiation settings. The distributions are normalized to the number of events after selection in the\nstandard simulation.\n [GeV]\nT\np\n0\n20\n40\n60\n80\n100\nEvents per 2 GeV\n0\n100\n200\n300\n400\n500\nATLAS\nstandard simulation\nhigh mass\nlow mass\nFigure 27: pT of the additional jets for datasets with different gluon radiation settings. The distri-\nbutions are normalized to the number of events after selection in the standard simulation.\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n923\n\n5\nConclusions\nThis note has presented several aspects of the W-boson reconstruction in t\u00aft events.\nFirst, it was shown in section 2 that small jet sizes should be prefered to avoid overlap effects. The\ncurrent default (cone algorithm with \u2206R = 0.4) is well suited for the study of the \ufb01rst data, but could\nbe complemented by a reconstruction using topological clusters, which seems robust in the presence of\npileup.\nTwo methods for the in-situ calibration of the light jet energy scale have been studied (section 3).\nThe two methods should be able to provide a light jet energy scale to the 1% level with 1 fb\u22121, and\ncould perhaps be used to follow the jet energy scale with time and/or luminosity. The two methods use\ncomplementary approaches and should be both applied in real data, up to the level of a top quark mass\nmeasurement, to allow for cross-checks.\nA study of simulations performed with different gluon radiation settings (section 4) has demonstrated\nthat, although the reconstructed W-boson mass can change by a large amount with different settings, the\nin-situ calibration method is able to correct for it.\nMore generally, the clean and large W-boson sample which should be available in t\u00aft events will be a\ngood laboratory to study the performance of jet reconstruction and calibration in real data, and compare\nthem with the performance in Monte Carlo simulated events.\nMost studies presented in this note were performed without including pile-up effects. The depen-\ndence of the results with luminosity should thus be checked. In addition, a scenario of not yet optimal\ndetector performance, which would lead to higher backgrounds, should also be studied in order to un-\nderstand the potential of the method for the early phase of data-taking.\nFinally, in order to reconstruct properly the top quarks, the knowledge of the b jets will be of partic-\nular importance. For instance, the b jet energy scale is, in our simulation, about 5% lower than the light\njet energy scale. This difference should be checked in the data to reach the ultimate precision for the top\nquark mass measurement.\nReferences\n[1] ATLAS Collaboration, Top Quark Mass Measurements, this volume.\n[2] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[3] Butterworth, J.M., Couchman, J.P., Cox, P.E. and Waugh, B.M., Comput.Phys.Commun. 153(2003),\n86-96.\n[4] ATLAS Collaboration, Performances of Calorimeter Clustering Algorithms, note in preparation.\n[5] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[6] ATLAS Collaboration, Top Quark Physics, this volume.\n[7] ATLAS Collaboration, Topological Cluster Classi\ufb01cation and Weighting, note in preparation.\n[8] ATLAS Collaboration, Jet Energy Scale: In-situ Calibration Strategies, this volume.\n[9] N. Besson and M. Boonekamp, ATL-PHYS-PUB-2006-007 (2005).\nTOP \u2013 JETS FROM LIGHT QUARKS IN t\u00aft EVENTS\n924\n\nDetermination of Top Quark Pair Production Cross-Section\nAbstract\nAn accurate determination of the top quark pair production cross-section at the\nLHC provides a valuable check of the Standard Model. Given the high statis-\ntics which will be available, corresponding to about one top-quark pair per\nsecond, at a luminosity of 1033 cm\u22122s\u22121, the cross-section measurement can\nbe performed relatively fast after the turnon of the LHC. Prospects for measur-\ning the total top quark pair production cross-section with the ATLAS detector\nduring the initial period of LHC are presented in this note. The cross-section\nis determined in the semi-leptonic channel, and in the dilepton channel. For\nthe semi-leptonic channel we perform the measurement both with and without\nrelying on the tagging of b-quark initiated jets.\n1\nIntroduction\nThe determination of the top quark pair production cross section is one of the measurements that will\nbe carried out once the \ufb01rst data samples are available at the ATLAS experiment. It casts light on the\nintrinsic properties of the top quark and its electroweak interactions. Cross section measurements are also\nan important test of possible new production mechanism, as non Standard Model top quark production\ncan lead to a signi\ufb01cant increase of the cross section. New physics may also modify the cross section\ntimes branching ratio differently in various decay channels, as for example predicted by Supersymmetric\nmodels [1] with charged Higgs particles, t \u2192H\u2212\u00afb, or with super-partners of the top quark, t \u2192\u02dct\u03c70. The\nselection of top quark events is based on the identi\ufb01cation of a jet from a b-quark, assuming a branching\nratio BR(t \u2192Wb) = 1. The consistency of this assumption, performed with kinematic methods, is\nanother important check of the Standard Model prediction but falls outside the scope of this paper.\nLast but not least, the top pair production process will be valuable for the in-situ calibration of\nthe ATLAS detector during the commissioning phase. The large cross section and the large signal to\nbackground ratio for the semileptonic channel, allows to identify high purity samples with large statistics\nin a short period of time. Understanding the experimental signatures of top events involves most parts of\nthe ATLAS detector and is essential for claiming discoveries of new physics.\nThe cross-section values and the Monte Carlo samples which have been used throughout this note,\nare described in [9].\n1.0.1\nCross section measurements at Tevatron\nDuring Tevatron Run I (1992-1996) an integrated luminosity of about 100 pb\u22121at a centre of mass energy\nof \u221as = 1.8 TeV allowed to measure top pair production cross sections of 6.5+1.7\n\u22121.4 pb and 5.7 \u00b1 1.6 pb\nby the CDF and D\u00d8 collaborations respectively [2]. The Tevatron Run II started in 2001 and until\nspring 2006 about 1 fb\u22121 of p \u00afp collisions at \u221as = 1.96 TeV have been collected and analysed. At this\nhigher centre of mass energy an increase of about 30% in the cross section is expected. The most recent\ncalculations predict a cross section of 6.7+0.7\n\u22120.9 pb [3] at NLO+NLL or 6.8\u00b10.6 pb [4] at NLO+ threshold\nresummation for a top mass, mt = 175 GeV. CDF and D\u00d8 measured a combined channels cross-section\nequal to 7.3\u00b10.5(stat) \u00b10.6(sys)\u00b10.4(lum) [5] and 7.4\u00b10.5(stat)\u00b10.6(sys)\u00b10.4(lum) [6] respectively.\nAll the measurements are in good agreement with the predictions. From a combination of all results, an\nexperimental error of the order of the theoretical error is expected.\n925\n\n2\nSingle lepton channel\nIn this section the strategy for the determination of the t\u00aft cross-section in the semi-leptonic decay mode\nis described. This channel, which has a branching fraction of approximately 45%, has a clear signature,\nis experimentally easily accessible and is expected not to suffer from large backgrounds.\nA robust analysis is presented of the \ufb01rst 100 pb\u22121 ATLAS data, which are expected to be collected\nduring the \ufb01rst few months of the LHC data taking period. In particular it is studied whether a pure t\u00aft\nsample can be identi\ufb01ed without utilizing the full ATLAS b-tagging capabilities. This is brought about\nby the fact that ef\ufb01cient tagging of jets originated from the hadronization of b-quarks, called b-tagging\nfrom now on, is non trivial and implies a precise alignment of the inner detector, which will probably\nrequire several months of data taking. This analysis solely relies on the measurement of jets, leptons and\nEmiss\nT\n(transverse missing energy), and requires a functioning lepton triggering system. Thanks to the\nover-constrained kinematics of the t\u00aft system, with the selected events it will be possible to measure the\nb-tagging performance and the Emiss\nT\n, as well as to calibrate the light jet energy scale.\n2.1\nEvent selection\nThe identi\ufb01cation of semi-leptonic t\u00aft events starts by requiring a highest level (event \ufb01lter) lepton trigger\nto have \ufb01red. In this study we assume that either the single isolated electron trigger e22 or the muon\ntrigger mu20 (for the de\ufb01nition see [7]) has \ufb01red. A correct description of the trigger ef\ufb01ciencies is vital\nfor the cross-section determination. The strategy for determining the trigger ef\ufb01ciencies from the Monte\nCarlo, as well as from the data without relying on Monte Carlo, is not pursued in this note, but included\nin [7].\nFurther, we de\ufb01ne a candidate t\u00aft event as having one reconstructed high-pT isolated lepton (electron\nor muon), a minimal amount of missing energy and at least four reconstructed jets. The de\ufb01nition of\nelectrons, muons and jets in our analysis has been discussed before.\nFor our default off-line selection the events are required to ful\ufb01l the following:\n\u2022 One lepton (electron or muon) with pT> 20 GeV.\n\u2022 Emiss\nT\n> 20 GeV.\n\u2022 At least four jets with pT> 20 GeV.\n\u2022 Of which at least three jets with pT> 40 GeV.\nThe fraction of events passing the individual selection requirements and the overall selection ef\ufb01-\nciency are shown in Table 1 for semi-leptonic events. In this table we split the ef\ufb01ciencies for semi-\nleptonic t\u00aft events according to the W decay in the Monte Carlo generator: t\u00aft (electron) where it decayed\nto an electron and a neutrino and t\u00aft (muon) where it decayed to a muon and a neutrino.\nWe observe a combined ef\ufb01ciency for these requirements which is somewhat larger for the t\u00aft (muon)\nevents compared to the t\u00aft (electron) events.\n2.1.1\nReconstructing t\u00aft events\nBefore discussing additional requirements to improve the purity of the t\u00aft event selection, we present\nthe second step in the event reconstruction. In this step we test the events for compatibility with a t\u00aft\nhypothesis. In the t\u00aft candidates, three of the reconstructed jets are expected to form the hadronic top-\nquark. In the absence of b-tagging there is an additional ambiguity in choosing the correct three-jet\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n926\n\nTable 1: Fraction of events passing the various selection criteria and the combined \u2018default\u2019 selection\nef\ufb01ciency for semi-leptonic (electron and muon) analyses respectively. The statistical uncertainties on\nthese numbers are negligible.\nTrigger\nLepton\nEmiss\nT\nJet req. (I)\nJet req. (II)\nCombined\neff (%)\neff (%)\neff (%)\neff (%)\neff (%)\neff (%)\nt\u00aft (electron)\n52.9\n52.0\n91.0\n70.7\n61.9\n18.2\nt\u00aft (muon)\n59.9\n68.7\n91.6\n65.5\n57.3\n23.6\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nATLAS\n(a)\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\nATLAS\n(b)\nFigure 1: (a): Three-jet invariant mass distribution for the electron analysis default selection, normalised\nto 100 pb\u22121. The statistical errors in each bin are indicated. (b): The same distribution after the additional\nW-boson mass constraint..\ncombination among the reconstructed jets. We de\ufb01ne our top-quark decay candidate as the three-jet\ncombination of all jets that has the highest transverse momentum sum.\nFig. 1 (a) shows the reconstructed top mass for this selection (from now on referred as default selec-\ntion) for the t\u00aft sample. The top mass peak is clearly visible, and the tails of the distributions correspond\nto the combinatorial background.\n2.1.2\nSelection variations: I\nApart from the default event selection as described above, a number of additional criteria are de\ufb01ned to\nfurther increase the purity of the top sample. Here we improve on the simple t\u00aft analysis by exploiting\nadditional information: every three-jet combination that originates from a top decay also contains a two-\njet combination that originates from a W-boson decay. To illustrate the presence of the W-boson we take\nthe three jets that constitute the top quark, and select from the three combinations of di-jets the one that\nresults in the highest value of the sum of the pT of the two jets. The W-boson mass is then the invariant\nmass of the two jet system. In Fig. 2 (a) this mass distribution is shown for the electron analysis, and the\nW-boson mass peak around 80 GeV is clearly visible.\nHowever we prefer an unbiased W-boson mass distribution in the analysis, for which we choose not\nto pick/de\ufb01ne one particular W-boson di-jet pair out of the three combinations, but rather require that at\nleast one of the three di-jet invariant masses is within 10 GeV of the reconstructed mass of the W-boson\n(taken as the peak value of the mass distribution of the W-boson candidates). This selection will be\nreferred to as the W-boson mass constraint selection. The distribution of all three di-jet combinations in\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n927\n\n in top candidate [GeV]\njj\nM\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents / 5 GeV\n0\n50\n100\n150\n200\nATLAS\n(a)\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n50\n100\n150\n200\n250\n300\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n50\n100\n150\n200\n250\n300\n in top candidate [GeV]\njj\nM\nNumber of events / 2.1 GeV\nATLAS\n(b)\nselected \nFigure 2: (a): The di-jet combination with highest pT (left) for the electron analysis. (b): The three di-jet\ncombinations invariant masses among the top-quark candidates in a 100 pb\u22121 event sample for the muon\nanalysis.\nthe top candidate is shown in Fig. 2 (b). Note that each event enters three times in this distribution. In\nthis \ufb01gure the background, as discussed in the next section, is already included.\nThe distribution of the three-jet invariant mass after the additional requirement that at least two jets\nare compatible with the mass of the W-boson is shown in Fig. 1 (b). This requirement shows a substantial\nreduction in the t\u00aft combinatorial background compared to Fig. 1 (a). Notice that, compared to the default\nselection, the top mass peak becomes narrower and the tail of the distribution is reduced. However, the\nW-boson mass constraint also introduces a visible shoulder in the distribution which makes \ufb01tting to the\ndata more subtle.\nIn Table 2 we show the fraction of t\u00aft events that pass these various selection requirements.\nTable 2: Ef\ufb01ciencies at different stages of the electron and muon analyses for several event types: after\ntrigger and event selection (left column), after a cut on the di-jet masses (see text for details) in the top\ncandidate (middle column) and events with, in addition to the di-jet mass cut, a hadronic top mass 141 <\nmt < 189 GeV (right column). The \ufb01rst three rows correspond to the single-lepton \ufb01nal states, the fourth\nrow to the di-lepton \ufb01nal state and the last row to the hadronic \ufb01nal state.\nElectron analysis\nMuon analysis\nEvent type\nTrigger+Selection (%)\nTrigger+Selection (%)\nW const.\nmt win\n+ W const.\nmt win\nt\u00aft (elec)\n18.2\n9.2\n4.5\n0.1\n0.0\n0.0\nt\u00aft (muon)\n0.0\n0.0\n0.0\n23.6\n12.0\n5.8\nt\u00aft (tau)\n1.4\n0.7\n0.3\n2.0\n1.0\n0.5\nt\u00aft (di-lepton)\n2.2\n1.0\n0.2\n3.0\n1.3\n0.4\nt\u00aft (hadron)\n0.0\n0.0\n0.0\n0.1\n0.1\n0.0\n2.1.3\nBackground evaluation\nWe consider a number of background processes. The dominant expected background is W-boson+jets,\nbut also single top production, Z-boson+jets and Wb\u00afb are sizeable. Tables 3 and 4 summarise the ex-\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n928\n\nTable 3: Number of events which pass the various electron selection criteria for the t\u00aft signal and for the\nmost relevant backgrounds normalised to 100 pb\u22121.\nElectron analysis\nSample\ndefault\nW const.\nmt win\nW const.\nW const.\nW const.\n+ |\u03b7| < 1\n+ 1 b-tag\n+ 2 b-tag\nt\u00aft\n2555\n1262\n561\n303\n329\n208\nhadronic t\u00aft\n11\n4\n0.0\n0.8\n0.6\n0.0\nW+jets\n761\n241\n60\n38\n7\n1\nsingle top\n183\n67\n23\n12\n18\n7\nZ\u2192ll +jets\n115\n35\n8\n5\n2\n0.4\nW b\u00afb\n44\n15\n3\n5\n5\n0.7\nW c\u00afc\n19\n6\n1\n1\n0.4\n0.0\nWW\n7\n4\n0.4\n0.0\n0.0\n0.0\nWZ\n4\n1\n0.4\n0.2\n0.0\n0.0\nZZ\n0.5\n0.2\n0.1\n0.0\n0.0\n0.0\nSignal\n2555\n1262\n561\n303\n329\n208\nBackground\n1144\n374\n96\n63\n33\n10\nS/B\n2.2\n3.4\n5.8\n4.8\n10.0\n20.8\npected numbers of signal and background events for the electron and muon analysis respectively. The\n\ufb01rst column of the two tables shows the event numbers obtained by applying the default selection, whilst\nthe second column gives the corresponding numbers with the W-boson mass constraint. All numbers\nare normalised to 100 pb\u22121. The evaluation of the QCD fake rate deserves a separate discussion. The\nQCD production of pp \u2192b\u00afb is characterised by a cross-section of about 100 \u00b5b, and can therefore be\nan important background for our signal. Requiring the presence of a high pT lepton and missing energy\ncan reduce its contribution, but since the cross-section enhancement relative to the signal is so large,\nthere might be QCD events with a fake lepton and/or poor missing energy reconstruction that pass these\nrequirements as well.\nThe rate for extra (medium [8]) electrons is studied and found to be roughly 1.0 \u00d710\u22123 per jet. This\nnumber is divided between semi-leptonic B(D) decays and true fakes, i.e. hadronic objects identi\ufb01ed as\nelectrons. The origin of extra isolated muons is dominated by semi-leptonic B decays, i.e. by the presence\nof hard b-quarks. The isolated muon rate per b-parton reaches a few times 10\u22123 for b-parton momenta\naround 40 GeV, while the fake rate is only a few times 10\u22125. By studying their origin and dependence on\njet/parton kinematics like the pT, \u03b7, jet multiplicity and quark content of the jet, we can get an estimate\nof the fraction of multi-jet events that will pass the lepton requirement in the event selection. The validity\nof this approach has been checked using a large sample of di-jet events at various transverse momenta.\nAs a result, the QCD background has been evaluated to be smaller than the W-boson+jets background\nand will not be discussed further.\nThe distribution of the invariant mass of the three-jet combination that forms the hadronic top-quark\ncandidate with the default selection and with the backgrounds added together, is shown in Fig. 3 (a). The\nevents where the correct jets were selected to reconstruct the hadronically decaying top quark candidate\nare clearly visible as the mass peak (open histogram) on top of a smooth background distribution. This\nbackground is partially composed of events from non-top processes (light shaded histogram), but is\ndominated by the (combinatorial) background from semi-leptonic t\u00aft events (dark shaded histogram). The\ncombinatorial background was determined using the matching of the top candidate with the generated\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n929\n\nTable 4: Number of events which survive the various muon analysis requirements for the t\u00aft signal and\nfor the most relevant backgrounds normalised to 100 pb\u22121.\nMuon analysis\nSample\ndefault\nW const.\nmt win\nW const.\nW const.\nW const.\n+ |\u03b7| < 1\n+ 1 b-tag\n+ 2 b-tag\nt\u00aft\n3274\n1606\n755\n386\n403\n280\nhadronic t\u00aft\n35\n17\n7\n6\n5\n2\nW+jets\n1052\n319\n98\n47\n11\n0.0\nsingle top\n227\n99\n25\n19\n19\n10\nZ\u2192ll +jets\n84\n23\n3\n2\n0.5\n0.0\nW b\u00afb\n64\n19\n4\n4\n5\n2\nW c\u00afc\n26\n9\n3\n0.7\n0.1\n0.0\nW W\n7\n3\n0.7\n0.7\n0.0\n0.0\nW Z\n7\n3\n0.8\n0.5\n0.0\n0.0\nZ Z\n0.7\n0.3\n0.1\n0.0\n0.0\n0.0\nSignal\n3274\n1606\n755\n386\n403\n280\nBackground\n1497\n495\n143\n84\n42\n14\nS/B\n2.2\n3.2\n5.3\n4.6\n9.6\n20.1\ntop-quark in a cone of size \u2206R < 0.2.\nIn Fig. 3 (b) the reconstructed three-jet mass after the W-boson mass constraint is presented. The\nbackground is also shown.\nTable 3 and 4 show the number of signal and background events in a 100 pb\u22121 data sample. To give\nan indication of the signal purity in the top mass peak region, in the third column of Tables 3 and 4 we\ngive the number of events in a hadronic top mass region: 141 < mt < 189 GeV. Although not all signal\nevents are correctly reconstructed, in both the electron and muon analyses the purity of the signal in the\ntop mass window is close to 80%.\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n300\n350\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n300\n350\n [GeV]\njjj\nM\nNumber of events / 10.0 GeV\nATLAS\n(a)\nTTbar (muon)\nTTbar (muon comb.)\nBackground\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n [GeV]\njjj\nM\nNumber of events / 10.0 GeV\nATLAS\n(b)\nTTbar (muon)\nTTbar (muon comb.)\nBackground\nFigure 3: (a): Expected distribution of the three-jet invariant mass after the standard selection. The white\narea represents the t\u00aft signal in the muon channel. The dark shaded area is the combinatorial background\nand the light shaded area represents the background contribution. (b): The same after the W-boson mass\nconstraint in a 100 pb\u22121event sample. Both plots are for the muon analysis.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n930\n\n2.1.4\nSelection variations: II\nAdditional ways to kinematically select top events other than the W-boson mass constraint, or to improve\nthe signal purity after having applied the W-boson mass cut itself, were explored. In the commissioning\nphase, it can happen that the barrel calorimetry will be better calibrated than the forward one. Therefore,\nit can be useful to apply the additional request that the three highest pT jets are all at |\u03b7| < 1. The\nreconstructed top mass in this case is shown in Fig. 4.\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nttbar\nother\nsingle t\nW+jets\nATLAS\n(a)\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/10GeV\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/10GeV\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nttbar\nother\nsingle t\nW+jets\nATLAS\n(b)\nFigure 4: (a): Reconstructed top mass after W-boson mass constraint for the electron analysis. The\nwhite area represents the t\u00aft signal in the electron channel, while the three shaded areas corresponds,\ngoing from the lighter to the darker, to the background from W-boson+jets, single top and all the other\nbackground sources considered in the analysis. The distribution is normalised to 100 pb\u22121. (b): The\nsame distribution, but in addition requiring that the three highest pT jets are at |\u03b7|<1.\nThe centrality requirement applied after the default selection allows to reach the same signal-over-\nbackground that one obtains after applying the W-boson constraint. Tables 3 and 4 show the signal-over-\nbackground and signal ef\ufb01ciencies for the electron and muon analyses if the centrality requirement is\napplied in addition to the W-boson constraint (\ufb01fth column).\nOther variables were exploited as well, like the cos\u03b8 \u22171 and the total invariant mass of the event. In\nthe following no cuts on these variables are used in the analysis.\n2.2\nDetermination of the cross-section\nIn this section two complementary methods to determine the t\u00aft\ncross-section of the commissioning\nanalysis are presented. The \ufb01rst method estimates the t\u00aft signal by performing a maximum likelihood\n\ufb01t on the three-jet invariant mass distribution. The second is based solely on counting the number of\ntop candidate events that pass the selection, and subtracting all backgrounds in order to get the yield of\nt\u00aft events in the sample. The two methods are affected by different systematics. Whereas this counting\nmethod needs all backgrounds to be properly addressed and normalised, it does not rely on a correct\nreconstruction of the top quark. The peak-\ufb01t method is rather insensitive to background normalisation\nand ef\ufb01ciencies, but requires a fairly well understood top mass peak.\n1It is the angle that one jet forms with the direction of the incoming proton in the centre of mass of the event (it is expected\nthat the top decay products are emitted more centrally than the W-boson+jets and jets from QCD)\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n931\n\n2.2.1\nLikelihood \ufb01t method\nTo extract the number of completely reconstructed t\u00aft events (after having applied the default + W-boson\nmass constraint selection) a maximum likelihood \ufb01t is performed to the three-jet mass distribution with a\nGaussian signal on top of the background described by a Chebychev polynomial, see Fig. 5. It has been\nveri\ufb01ed that the background model correctly describes the combined t\u00aft combinatorial and background\ndistribution in the signal region by comparing the \ufb01tted background to the subset of events that are not\nfully reconstructed signal as determined from truth matching information.\nUsing 10000 pseudo-experiments, based on the input from the full simulation Monte Carlo events, one\ncan extract the average fraction of signal events that pass all selection requirements and enter in the\npeak (i.e., the fraction correctly reconstructed). The average number of events in the peak in the muon\nanalysis, i.e. correctly reconstructed semi-leptonic t\u00aft (muon) events, in 100 pb\u22121 is 508 events as shown\nin Fig. 5 (a). This corresponds to an ef\ufb01ciency of (4.23 \u00b1 0.57)%. For the electron analysis this ef\ufb01ciency\nis (2.73 \u00b1 0.47)%.\nThe signal signi\ufb01cance is de\ufb01ned using the likelihood ratio from two hypotheses: the presence of a\nsignal (a peak) and its absence (only the Chebychev polynomial). The amount of data needed to make\na statistically signi\ufb01cant observation of the t\u00aft signal depends on the amount of background. For low\nluminosities, for example for 25 pb\u22121, the sampling \ufb02uctuations are too large and there is no typical\nplot like the one of Fig. 3. To quantify the relation between signal signi\ufb01cance, luminosity and the\namount of background, 10000 pseudo-experiments based on the full simulation distribution of the three-\njet mass as a function of the integrated luminosity, have been modelled and \ufb01tted. The expected statistical\nsigni\ufb01cance is shown in Fig. 5 (b), where the yellow band is obtained by assuming the nominal level of\nQCD W-boson+jets background, while the red one refers to the case when this background is multiplied\nby two. .\n100\n150\n200\n250\n300\n350\n0\n50\n100\n150\n200\n250\n100\n150\n200\n250\n300\n350\n0\n50\n100\n150\n200\n250\n [GeV]\njjj\nM\nNumber of events / 10.0 GeV\nATLAS\n(a)\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n]\n-1\nIntegrated luminosity [pb\nExpected significance\nATLAS\n(b)\nBackground (nominal)\nBackground (x2)\nFigure 5: (a): Fit to the top signal. The Chebychev polynomial \ufb01t to the background is indicated by the\ndotted line and the Gaussian \ufb01t of the signal events is indicated by the full line. (b): Distribution of the\nexpected statistical signi\ufb01cance of the top signal in the peak as a function of the integrated luminosity\nfor two background scenarios. The yellow band is obtained by assuming the nominal level of QCD\nW-boson+jets background, while the red one by assuming that this background is doubled.\nTo go from a \ufb01tted number of properly reconstructed hadronic top quarks to a cross-section, one\nneeds to correct for the event selection ef\ufb01ciency and the hadronic top reconstruction ef\ufb01ciency. The\nstatistical error is estimated from having simulated 100000 pseudo-experiments, applying the \ufb02uctuations\nwhich are expected in 100 pb\u22121to both signal and background and \ufb01tting the peak in both the electron\nand muon channels.\nOne of the biggest uncertainties is the correct modelling of the jet multiplicity distribution as it affects\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n932\n\nthe fraction of t\u00aft signal events that are correctly reconstructed using the algorithm described earlier. An\noverview of the systematic uncertainties is given in [9].\n2.2.2\nCounting method\nThe t\u00aft cross-section can be obtained by performing a counting experiment:\n\u03c3 =\nNsig\nL \u00d7\u03b5 = Nobs \u2212Nbkg\nL \u00d7\u03b5\nNbkg, the number of background events estimated from Monte Carlo simulations and/or data samples,\nis subtracted from Nobs, the number of observed events meeting the selection criteria of a top-event\nsignature. This difference is divided by the integrated luminosity L and the total ef\ufb01ciency \u03b5. The\nlatter includes the geometrical acceptance, the trigger ef\ufb01ciency and the event selection ef\ufb01ciency, and is\nslightly dependent on mt . The advantage of using event counts in the commissioning phase is that, early\non, the Monte Carlo simulations may not predict the shapes of distributions very well.\nIn order to perform the counting experiment the Monte Carlo samples were divided into two, statisti-\ncally independent: one which represents real data, used to obtain Nobs and the other one used as a Monte\nCarlo to obtain both \u03b5 and Nbkg.\n2.2.3\nSystematic uncertainties\nThe main sources of systematic uncertainties are described in [9]. Some relevant points for the analyses\npresented here are discussed for the case of the default selection plus the W-boson mass constraint. The\nsystematic uncertainty on the cross-section due to the luminosity determination, is factorised and men-\ntioned as a separate uncertainty on the overall results. The event selection ef\ufb01ciencies have a nearly linear\ndependency for jet energy scale variations, which affects the counting method directly. The hadronic top\nreconstruction ef\ufb01ciency has an inverse dependence on the jet energy scale, caused by the algorithm that\npicks the three-jet combination that are considered to be the hadronic top. If the jet energy scale is low-\nered, the jet multiplicity (and therefore the number of three-jet combinations) increases. The probability\nthat the algorithm picks the right combination generally decreases with the number of combinations to\nchoose from.\nThe effect of ISR and FSR parameter variations (chosen in such a way to maximise the effect on\nthe cross-section measurement) has been evaluated. For the uncertainties related to the PDFs, both the\nuncertainty coming from CTEQ and MRST, have been considered and the largest one (coming from\nCTEQ) has been used for the \ufb01nal systematics evaluation.\nThe main systematics uncertainties for the two analysis are listed in Table 5. For the likelihood\nmethod a 5% change in jet energy scale causes a 2.3% (0.9%) change in the combined reconstruction\nef\ufb01ciency for the electron (muon) channel. The different jet multiplicity distributions affect not only the\nevent selection ef\ufb01ciencies (jet requirements), but also the overall ef\ufb01ciency of the hadronic top recon-\nstruction algorithm. A comparison between the two generators MC@NLO and ALPGEN has been made to\nstudy these systematic effects. ALPGEN predicts 7% and 4% larger selection ef\ufb01ciencies in the electron\nand muon channels respectively. For the overall ef\ufb01ciencies the values are 10.5% and 4.7% larger in the\nelectron and muon channel. However, these numbers were not added in the \ufb01nal result since there is\noverlap with the ISR/FSR systematics. Systematics effects on the shape of the \ufb01t as well as the normali-\nsation of the peak \ufb01t w.r.t. background is estimated with toy Monte Carlo\u2019s. Deviations of 14.0 (10.4)%\nfor the electron (muon) channel are found, while the effect of changing the \ufb01t-ranges is negligible.\nFor the counting analysis the uncertainty arising from the Monte Carlo used to generate the signal pro-\ncess has been taken into account as well. This has been done by comparing the cross-section obtained\napplying the same analysis to t\u00aft events generated with MC@NLO and with the ACERMC Monte Carlo.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n933\n\nTable 5: Systematic uncertainties on the commissioning likelihood and counting method cross-section\nmeasurement, in percent.\nLikelihood \ufb01t\nCounting method (elec)\nSource\nElectron\nMuon\nDefault\nW const.\n(%)\n(%)\n(%)\n(%)\nStatistical\n10.5\n8.0\n2.7\n3.5\nLepton ID ef\ufb01ciency\n1.0\n1.0\n1.0\n1.0\nLepton trigger ef\ufb01ciency\n1.0\n1.0\n1.0\n1.0\n50% more W+jets\n1.0\n0.6\n14.7\n9.5\n20% more W+jets\n0.3\n0.3\n5.9\n3.8\nJet Energy Scale (5%)\n2.3\n0.9\n13.3\n9.7\nPDFs\n2.5\n2.2\n2.3\n2.5\nISR/FSR\n8.9\n8.9\n10.6\n8.9\nShape of \ufb01t function\n14.0\n10.4\n-\n-\nThe W-boson+jets normalization uncertainty has been evaluated using the Z-boson+jets sample as dis-\ncussed in the general introduction of systematic uncertainties, but also varying the level of the expected\nW-boson+jets level by 20%, 50% and even by a factor of two. For the \ufb01nal selection (including the\nW-boson mass constraint) this corresponds to an uncertainty of 4%, 10% and 19% respectively. As\nreference value to calculate the overall systematic error, the 50% case will be used.\n2.2.4\nContributions of new physics\nMany models of physics beyond the Standard Model contain new particles which couple to top-quarks.\nFor example, in a supersymmetric estension of the Standard Model (SUSY) these new particles are top\nsquarks [10] and in warped extra dimensions they are Kaluza-Klein resonances [11]. Since the new\nparticles are expected around the TeV scale, the typical cross-sections are of order a few pico barns and\nhence one can expect a few hundreds new physics events in the \ufb01rst 100 pb\u22121 of data. In principle, these\nnew physics events could represent a signi\ufb01cant background to the cross-section measurement. For new\nphysics models with much lower masses, e.g. low mass supersymmetry models, there will be many more\nevents: this case will be considered later on. Here the existence of a new particle V which decays only\ninto t\u00aft \u02dcpairs, V \u2192t\u00aft it is assumed. It is further assumed that this particle has a production cross-section\nof 5 pb, so that 25/9 pb is the cross-section for the non-fully hadronic decays of V. As a model for V a 1\nTeV Z\u2019 is used. The ef\ufb01ciency for these events with respect to the default selection + the W-boson mass\nconstraint is roughly twice the one obtained for Standard Model t\u00aft events, and the number of events\npassing the selection will be of the order of 1% or less of the t\u00aft events. Hence the new particle V will\nnot affect the cross-section determination signi\ufb01cantly.\nThe predictions at several mSUGRA benchmark points [12] have been studied as well. The results\nare shown in Table 6 and demonstrate that the expected signals are small. At speci\ufb01c parameter points\nhowever, like SU4 [12], the cross-section is sizeable and the event topology is similar to that from top\nquark pairs which results in additional backgrounds as large as the total Standard Model background. In\nFig. 6 one can see that the shape of the SU4 supersymmetry signal in the top quark candidate three-jet\ninvariant mass distribution is very similar to that from the Standard Model background.\nThe separation of t\u00aft events and these new physics signals is addressed in more detail in [12], dedi-\ncated to searches for supersymmetry.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n934\n\nTable 6: Expected number of events in a 100 pb\u22121 data sample at different stages of the analysis for\nseveral event types: after trigger and event selection (left column), after a cut on the di-jet masses in the\ntop-quark candidate (middle column) and events with in addition to the di-jet mass cut a hadronic top\nmass cut 141 < mt < 189 GeV(right column).\nElectron analysis\nMuon analysis\nEvent type\nTrigger+Selection\nTrigger+Selection\nW const.\nmt win\nW const.\nmt win\nSU1\n53\n9\n1\n64\n12\n2\nSU2\n10\n2\n0.5\n13\n3\n0.7\nSU3\n108\n22\n4\n124\n26\n4\nSU4\n1677\n541\n155\n2141\n700\n199\nSU6\n29\n5\n0.6\n35\n6\n0.6\nSU8\n27\n5\n0.6\n33\n6\n0.8\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n [GeV]\njjj\nM\nNumber of events / 10.0 GeV\nATLAS\n(a)\nTTbar (electron)\nTTbar (electron comb.)\nBackground\nSU(4)\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n300\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n0\n50\n100\n150\n200\n250\n300\n [GeV]\njjj\nM\nNumber of events / 10.0 GeV\nATLAS\n(b)\nTTbar (muon)\nTTbar (muon comb.)\nBackground\nSU(4)\nFigure 6: (a): Expected distribution of the three-jet invariant masses among the top-quark candidates after\nthe requirement on the mass of the di-jet system in the electron channel in a 100 pb\u22121 event sample. (b):\nSame distribution for the muon channel. The light histogram represents the Standard Model background.\ni.e. the background from mSUGRA point SU4 is shown separately.\n2.3\nImplementation of b-tagging\nThe possibility to identify b-\ufb02avoured jets (b-tagging) will improve the signal to background ratio of the\nselection. The b-tagging requirements are described in [9]. The number of \u201ctagged\u201d b-jets in the t\u00aft ,\nsingle top and W-boson+jet events which pass the default selection is shown in Fig. 7.\nTables 3 and 4 list the number of t\u00aft and background events in the electron and muon channel which\nsurvive the default selection plus the W-boson mass constraint, and the request of having one and only\none, or two and only two b-jets (column six and seven). For all these cases, the corresponding signal to\nbackground ratios are given. Requiring one or two b-tagged jets improves the purity of the sample by\nmore than a factor of four, while the signal ef\ufb01ciency is only reduced by a factor of two.\nIn Fig. 8 the reconstructed three-jet mass is shown when one or two b-tagged jets are required for the\ndefault selection (a) and for the default selection + the W-boson mass constraint (b). To reconstruct the\ntop mass, we \ufb01nd the three-jet combination with the highest possible pT, obtained by requiring that one\nand only one of the three jets is a b-jet. The W-boson mass constraint can then be applied to the two jets\nwhich are not b-tagged (among the three). If the three-jet combination chosen above is such that the two\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n935\n\nNumber of b-tagged jets\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\nEvents\n0\n200\n400\n600\n800\n1000\n1200\n1400\nNumber of b-tagged jets\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\nEvents\n0\n200\n400\n600\n800\n1000\n1200\n1400\nttbar\nother\nsingle t\nW+jets\nATLAS\nFigure 7: Number of jets tagged as coming from a b-quark in t\u00aft, single top and W-boson+jet events after\nthe default electron selection.\nnon-b-jets don\u2019t combine to give a W-boson candidate, that event is rejected.\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\nttbar\nother\nsingle t\nW+jets\n(a)\nATLAS\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n [GeV]\ntop\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nttbar\nother\nsingle t\nW+jets\nATLAS\n(b)\nFigure 8: (a): Reconstructed three-jet mass for t\u00aft , single top and W-boson + jet events for the default\nelectron selection, requiring one or two jets tagged as coming from a b-quark. (b): Same distribution for\nthe default selection + the W-boson mass constraint and requiring one or two jets tagged as coming from\na b-quark.\nThe statistical error on the cross-section which is obtained by requiring one or two b-tagged jets is\n4.5%. The systematic error due to the jet energy scale is in this case of 4.9%, while a wrong normalization\nof the W-boson+jets background by a factor of 20%, 50% or even a factor two, brings a systematic error\non the cross-section of 3.4%, 4.7% and 6.9% respectively. A 5% relative error on the b-tagging ef\ufb01ciency\nis expected from present studies for an ef\ufb01ciency of 50-60% and for a luminosity of 100 pb\u22121. The\nresulting uncertainty on the cross-section turns out to be negligible. The undertainty on the mistag rate\nis assumed to be of the order of 50%.\n2.4\nResults\nWith the \ufb01rst 100 pb\u22121of data, we can observe a t\u00aft signal and determine its production cross-section.\nThis will be determined with a number of methods and we expect to reach the following accuracies (for\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n936\n\nthe default selection with the W-boson mass constraint, using electron and muons):\nLikelihood method:\n\u2206\u03c3/\u03c3 =\n(7(stat)\u00b115(syst)\u00b13(pdf)\u00b15(lumi))%\n(1)\nCounting method:\n\u2206\u03c3/\u03c3 =\n(3(stat)\u00b116(syst)\u00b13(pdf)\u00b15(lumi))%\n(2)\n2.5\nDifferential cross-sections\nWe studied several differential distributions for t\u00aft production. First, we present the momentum and\nrapidity distribution of the hadronically decaying top quarks, after having applied the default selection\nand the W-boson mass constraint. The results are shown in Fig. 9 (a) and (b).\npt (top) [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\npt (top) [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / 10GeV\n0\n20\n40\n60\n80\n100\n120\nttbar\nother\nsingle t\nW+jets\nATLAS\n(a)\n (top)\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEvents / 0.4\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n (top)\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEvents / 0.4\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nttbar\no her\nsingle t\nW+jets\n(b)\nATLAS\nFigure 9: (a): Momentum distribution of the reconstructed three-jet mass for t\u00aft , single top and W-\nboson+jet events for the electron analysis. Right plot: Rapidity distribution of the hadronically decaying\ntop quark.\nA more detailed study has been performed for the differential cross-section as a function of the t\u00aft\nsystem mass, and for several double differential distributions as shown in the following sections.\nThe differential cross-section for t\u00aft production can be measured as a function of the invariant mass\nof the t\u00aft system in the semi-leptonic channel (with no tau leptons in the \ufb01nal state). Such a measure-\nment provides an important check of the Standard Model and, at the same time, deviations from the t\u00aft\ncontinuum could indicate the presence of new physics, for example new heavy resonances decaying into\na t\u00aft pair [14].\nThe standard commissioning selection is applied and the momenta of the four jets with highest pT,\nthe lepton and the best estimate of the Emiss\nT\nvector are used as inputs to a least squares \ufb01t with the con-\nstraints that, in each event, the masses of both the W-boson and top-quark are consistent with 80.4 GeV\nand 175 GeV respectively. The \ufb01t procedure is documented in [15]. The goal is to improve the measure-\nment of the reconstructed \ufb01nal state particles\u2019 four vectors by incorporating the precise knowledge of the\nmasses of the W-boson boson and the top-quark. No b-tagging is used in this analysis and hence there\nare 12 possible combinations to assign jets to the (anti-) top. All combinations were investigated and and\none was chosen: the assignment which returned the smallest weighted sum of squared residuals obtained\nfrom the kinematic \ufb01t. A simpler reconstruction scheme obtains the t\u00aft mass by deriving the leptonic\nW-boson momentum from the lepton and missing energy momenta with the W-boson mass constraint\nand then combining it with the momenta of the four highest pT jets.\nThe reconstructed mass distributions for the two methods are compared to the true di-top mass distri-\nbutions in Fig. 10 (a) for the non-hadronic signal. The true di-top mass distribution is in better agreement\nwith the result obtained by making use of the full event \ufb01tting technique.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n937\n\nIn this case, the expected mass resolution ranges from 5% to 9% between 200 and 850 GeV. A\nvariable bin size of about twice the expected resolution is used to take such variation into account and\nreduce bin-to-bin migrations. The di-top mass spectrum (dN/dmtt), reconstructed with the full event \ufb01t,\nis shown in Fig. 10 (b) for the signal and the backgrounds studied. Backgrounds include: full hadronic\ntop, single top, W-boson+jets, Wb\u00afb , Wc\u00afc , inclusive Z-boson to leptons. The contribution from the\ndi-boson (WW,WZ and ZZ) backgrounds is negligible.\n[GeV]\nt\nM_t\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n (1/30.0GeV)\nt\n1/N dN/dM t\n0\n0.0005\n0.001\n0.0015\n0 002\n0.0025\n0.003\n0.0035\n0 004\nTrue di-top mass\nReconstructed di-top mass\nFull event fit\n(a)\nATLAS\nMass[GeV]\n500\n1000\n1500\n2000\n2500\n3000\nEvents/bin\n10\n2\n10\n3\n10\nMass[GeV]\n500\n1000\n1500\n2000\n2500\n3000\nEvents/bin\n10\n2\n10\n3\n10\nt\nNon Hadronic t\nW + light jets \nSingle top\nOther backgrounds\n(b)\nATLAS\nFigure 10: (a): Normalised di-top mass distribution for the more complex (dashed line) and the simple\nreconstruction (dotted line). The normalised true di-top mass is also shown for reference (solid line).\n(b): Expected reconstructed di-top mass distribution after all cuts for signal and studied backgrounds,\nnormalised to 100 pb\u22121.\n2.5.1\nDouble differential cross-section as function of pT and y\nThe double differential cross-section for t\u00aft production is sensitive to possible new physics beyond the\nStandard Model, e.g. extra dimensions based on studies of the top quark spin correlation [13], which\ndepends on the knowledge of the top quark\u2019s momentum. A measurement investigates the decay products\nof the top quark in its rest frame and therefore good knowledge of its pT and y as de\ufb01ned in (3), for a top\nquark of energy E and longitudinal momentum pz, is needed.\ny = 1\n2 ln\n\u0012E + pz\nE \u2212pz\n\u0013\n(3)\nTheoretical predictions can be found in [4]. Here we present a feasibility study which, since the\nneutrino momentum cannot be directly measured, concentrates on the reconstruction of the hadronically\ndecaying top quark in semileptonic t\u00aft events. Since in this case a high purity is needed, the default\nevent selection is tightened by requiring exactly two b-tagged jets. The reconstruction of the hadronic\ntop quark proceeds as follows: all possible combinations of two non-b-tagged jets with 60 GeV< mj j <\n100 GeV are selected as W-boson candidates. The nearest b-tagged jet for every W-boson candidate is\nfound. The combination with the highest transverse vector sum momentum is then taken as the recon-\nstructed hadronic top quark. This results in a purity of well reconstructed top quarks of 45%. The main\nbackground is due to combinatorics.\nFigure 11 shows the reconstructed double-differential distribution of the hadronic top scaled to an\nintegrated luminosity of 1 fb\u22121. In (a) the truth distribution of the t\u00aft signal is presented, while in (b)\nthe distribution of reconstructed hadronic top-quarks is shown. In this distribution the contribution of\nbackground (from single top, W-boson + jet, Wb\u00afb and Wc\u00afc), which is very small after the requirement\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n938\n\n|y|\n0\n1\n2\n3\n4\n [GeV]\nT\np\n0\n50 100 150 200 250 300 350 400\n,y) [fb]\nT\n(p\n40GeV,0.5\n\u03c3\n0\n5000\n10000\n15000\n20000\n25000\nATLAS\n(a)\n|y|\n0\n1\n2\n3\n4\n [GeV]\nT\np\n0\n50\n100 150 200 250 300 350 400\n,y)\nT\n(p\n40GeV,0.5\nN\n0\n200\n400\n600\n800\n1000\n1200\n1400\nATLAS\n(b)\nFigure 11: (a): Distribution of pT and y of hadronically decaying top quarks calculated by MC@NLO.\n(b): Reconstructed distribution of pT and y of hadronically decaying top quarks from fully simulated\nsamples scaled to an integrated luminosity of 1 fb\u22121.\nof two b-tagged jets, has been added. After such a selection, the number of expected events limits the\nregion of interest to |y| < 2 and 50 GeV< pT< 280 GeV. 1 fb\u22121 is a reasonable statistic which allows\nto \ufb01ll a signi\ufb01cant number of bins with an appropriate statistical error. A lower integrated luminosity\nof 100 pb\u22121 would increase the statistical error of the bin contents at the edge of the interesting area\nfrom 10% to approximately 30%, which would limit the measurement to a smaller phase-space. The\nsystematic uncertainties of this feasibility study are expected to be small and under control.\nThe potential to determine the double differential cross-section of t\u00aft events decaying semileptonically\nhas been estimated. The phase space can be determined with an average ef\ufb01ciency of 3.98\u00b10.04% and\na peak ef\ufb01ciency of 8% near the central rapidity region and for pT \u2264140 GeV.\nThe main systematic uncertainties for this study will come from the jet energy scale and from the\ninitial and \ufb01nal state radiation: each source contributing with an uncertainty of the order of \u00b1 15% in the\ncentral region.\n3\nDi-Lepton channel\nIn this section the determination of the t\u00aft cross-section where both W-bosons decay leptonically is pre-\nsented. This measurement depends crucially on the correct identi\ufb01cation of leptons. We proceed by\ninvestigating the channel with two electrons, one electron and a muon, and two muons in the \ufb01nal state.\nFinal states with tau leptons are not studied here. The determination of the cross-sections is performed\nwith a simple \u2018cut and count\u2019 method, a template method and a likelihood \ufb01t.\n3.1\nEvent selection\nThe di-lepton sample is expected to be triggered with high ef\ufb01ciency using a combination of single-lepton\nand di-lepton triggers [7]. The overall trigger ef\ufb01ciency for the electron-muon channel is (97\u00b11)%, for\nthe two electron channel it is (98\u00b11)% and for the two muon channel it is (96\u00b11)%. Due to the trigger\nOR condition between the channels and the high statistics available for ef\ufb01ciency measurements, the\nuncertainty is small.\nThe of\ufb02ine selection of di-lepton events is based on the identi\ufb01cation of leptons as described in the\nintroductory section. Two high-pTopposite signed leptons, i.e. two electrons, two muons, or one electron\nand one muon, are required. These requirements de\ufb01ne the preselection sample and additional selection\ncriteria are imposed depending upon the t\u00aft cross-section extraction method. The expected number of\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n939\n\nevents produced after the preselection cuts of two isolated opposite charged leptons is shown in Table 7.\nNone of the selections makes use of b-tagging.\nTable 7: Simulated Monte Carlo samples and expected events produced for 100 pb\u22121of integrated lumi-\nnosity. Cross-sections \u03c3 are at least Next-to-Leading Order total cross-sections, and \u03c3eff are the effective\nMonte Carlo cross-sections including generator level \ufb01lter ef\ufb01ciencies (reported in the \u201dFilter(%)\u201d col-\numn). The last three columns show the number of preselected events after requiring two opposite signed\nleptons.\nSample\n\u03c3(pb)\nFilter(%)\n\u03c3eff(pb)\ne\u00b5\nee\n\u00b5\u00b5\nt\u00aft (di-lepton)\n833\n7(2l)\n55\n699\n312\n381\nt\u00aft (semi-leptonic)\n48(1l)\n397\n31\n20\n8\nZ \u2192e+e\u2212\n2015\n86\n1733\n5\n37418\n0\nZ \u2192\u00b5+\u00b5\u2212\n2015\n89\n1793\n153\n0\n51139\nZ \u2192\u03c4+\u03c4\u2212\n2015\n5\n101\n249\n101\n159\nW \u2192e\u03bd\n20510\n63\n12920\n42\n69\n0\nW \u2192\u00b5\u03bd\n20510\n69\n14150\n152\n0\n40\nWW\n117\n35\n41\n76\n32\n44\nWZ\n48\n29\n14\n6\n41\n52\nZZ\n15\n19\n3\n1\n25\n31\nsingle top\n324\n31\n99\n5\n3\n2\n3.1.1\nLepton identi\ufb01cation and isolation\nThe inclusive di-lepton selection requires at least one of the electrons to be identi\ufb01ed with the \u2018tight-\nelectron\u2019 algorithm2 to improve the fake lepton rejection.\nOne of the major backgrounds in this channel is given by semi-leptonic t\u00aft events where the second\nlepton candidate is faked by a jet. A requirement on the isolation of the electrons lowers this background\nsubstantially. Fig. 12 (a) shows the distribution of the variable \u03a3\u2206R<0.2ET, de\ufb01ned to be the energy\ndeposited in a hollow cone with radius \u2206R of 0.2 around the electron candidate. The \ufb01gure shows this\nvariable for reconstructed electrons in the semi-leptonic t\u00aft\nbackground sample which are close to a\nmonte carlo truth electron (\u2206R < 0.1 to a truth electron from the W-boson decay) and for reconstructed\nelectrons with \u2206R > 0.1. With the requirement \u03a3\u2206R<0.2ET< 6 GeV, the signal is reduced by only \u223c4%\nwhereas the semi-leptonic t\u00aft background is reduced by a factor of two.\nTwo cuts are used to select muons from W-boson decays while simultaneously rejecting muons from\nb-jets. The \ufb01rst cut selects the muon candidate with tracks in the muon spectrometer that match best with\ntracks in the inner detector. Additionally it is required that the muon is not closer than \u2206R < 0.2 to a jet,\notherwise the muon is removed.\nFig. 12 (b) shows the distance of muons to the closest jet in the event. Muons that are close (\u2206R < 0.2)\nto a monte carlo truth b-quark are separated from muons that are close to a monte carlo truth muon\n(\u2206R < 0.1). A \u2206R cut of 0.2 removes the muons that do not originate from the W-boson decay. This\nrequirement reduces the semi-leptonic t\u00aft background by \u223c25%, whereas the signal is reduced by only\n0.8%.\n2The tight-electron algorithm makes full use of the TRT information as described in Ref. [16].\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n940\n\n (a) \n [GeV] \nT\n E\n R < 0.2\n\u2206\n\u03a3\nElectron Isolation \n0\n2\n4\n6\n8\n10\n12\n14\nEvents (norm.)\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\n (b)\n R (Muon|Jet)\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEvents (norm.)\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\nFigure 12: (a) The \u03a3\u2206R<0.2ET variable for reconstructed electrons of the semi-leptonic t\u00aft background, in\nblack are electrons matched to truth electrons, in white otherwise. (b) \u2206R from a muon to the closest jet\nin the semi-leptonic t\u00aft sample. In white are muons matched to truth muons, in black are muons that are\nclose to a b-quark.\n3.2\nBackgrounds\nThe backgrounds to the t\u00aft di-lepton signal can be classi\ufb01ed into two main categories: prompt leptons\noriginating from an electroweak decay, or non-isolated non-prompt leptons and jets that are falsely iden-\nti\ufb01ed as leptons mainly originating from QCD jets.\nFor the estimation of the electroweak backgrounds we use Monte Carlo samples, as shown in Ta-\nble 7. For the same-\ufb02avour Drell-Yan processes we made an exception, as the size of this contamination\ndepends on the determination of the Emiss\nT\nwhich is dif\ufb01cult to model. As a default we use the shape\nof the Emiss\nT\ndistribution for events with a di-lepton mass inside a window around the Z-boson mass, to\ncorrect the shape of the Emiss\nT\ndistribution in the Monte Carlo. The same correction factor is used for\nDrell-Yan processes with di-lepton invariant masses outside the Z-boson mass window.\nThe backgrounds from fake leptons are estimated from the QCD dijet samples. These estimations of\nfake leptons are subsequently applied to all objects that can lead to fake leptons (e.g. jets) in the inclusive\nsingle electron or muon samples.\n3.3\nCross-section measurement\nAs mentioned, three methods to determine the cross-section for the di-lepton channel are presented. The\ndi-lepton channel pro\ufb01ts from having smaller backgrounds and systematics and the methods are comple-\nmentary to each other. The robust \u2019cut and count\u2019 method can be replaced with the more sophisticated\ntemplate and likelihood method with increased accumulated data.\n3.3.1\n\u2018Cut and count\u2019 method\nA \u2018cut and count\u2019 analysis is the most straightforward method to determine the cross-section. It can\nbe used as the basis and reference for the more elaborate likelihood methods and act as a cross check\nbetween the different approaches.\nThe selection criteria are de\ufb01ned to maximise the ef\ufb01ciency \u03b5 and the purity p at the same time. The\n\ufb01gure of merit is the product\n\u03b5 \u00d7 p \u221d\nS\n\u221a\nS+B = s\nwhich is referred to as signi\ufb01cance.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n941\n\n(a)\nM(ll) [GeV]\n40\n50\n60\n70\n80\n90\n100\n110\n120\n130\n140\nEvents\n0\n5\n10\n15\n20\n25\n30\n35\nM(ll) [GeV]\n40\n50\n60\n70\n80\n90\n100\n110\n120\n130\n140\nEvents\n0\n5\n10\n15\n20\n25\n30\n35\n signal\nt\nt \n lepton+jets\nt\nt \n e e\n\u2192\nZ \n\u00b5\n \n\u00b5\n \n\u2192\nZ \n\u03c4 \u03c4 \n\u2192\nZ \nWW (Herwig)\nZZ (Herwig)\nWZ (Herwig)\nATLAS\nMissingET [GeV]\n50\n100\n150\n200\n250\nEvents\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n(b)\nMissingET [GeV]\n50\n100\n150\n200\n250\nEvents\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n signal\nt\nt \n lepton+jets\nt\nt \n e e\n\u2192\nZ \n\u00b5\n \n\u00b5\n \n\u2192\nZ \n\u03c4 \u03c4 \n\u2192\nZ \nWW (Herwig)\nZZ (Herwig)\nWZ (Herwig)\nATLAS\nFigure 13: (a) Di-lepton mass in signal, semi-leptonic t\u00aft and Z \u2192\u2113+\u2113\u2212events. (b) Distribution of the\nEmiss\nT\nfor signal and various backgrounds, normalised to 100 pb\u22121\n.\nThe variables that best characterise the signal events are the transverse momenta of the two leptons\nand the two jets, as well as the missing transverse energy. The jet momenta are high since they originate\nfrom the b-quarks, not present in the prominent background processes Z \u2192\u2113+\u2113\u2212or dibosons \u2192\u2113+\u2113\u2212\n(WW, WZ and ZZ). A large amount of missing transverse energy is expected in signal events due to the\ntwo escaping neutrinos. In addition a veto on events with a di-lepton invariant mass around the Z-boson\nmass is applied. Fig. 13 (a) shows the di-lepton mass distribution in Z \u2192\u2113+\u2113\u2212events. Most of the events\nare found to have an invariant mass between 85 and 95 GeV. In the case of the Z \u2192\u03c4+\u03c4\u2212events the\npeak is shifted and broadened, since the visible leptons do not come directly from the Z-boson. Also\nthe neutrinos from the \u03c4 decay add to the missing transverse energy. It is therefore expected that this\nbackground will be dominant, although the branching ratio for both \u03c4\u2019s decaying leptonically is only\n\u223c9%. The optimal selection was found from a multidimensional scan of the signi\ufb01cance s. Exactly two\nleptons are required and at least two jets. The requirements on the lepton and jet transverse momenta and\non the Emiss\nT\nis then varied from 20 to 60 GeV. Finally, the cuts with the maximum signi\ufb01cance are used\nto evaluate the cut and count performance.\nAs a result, the multidimensional scan indicates that the values of the preselection requirement of 20\nGeV for the two leptons and for the two jets with the highest transverse momentum already maximise the\nsigni\ufb01cance. One additional cut is imposed: the Emiss\nT\nis required to be at least 30 GeV for a selection of\ntwo leptons (all sub-channels together), at least 20 GeV for the e\u00b5 decay channel and at least 35 GeV for\nthe same \ufb02avour lepton channels. The distribution of the missing transverse momentum for the signal\nand the background samples is presented in Fig. 13 (b). The ef\ufb01ciencies, signal over background ratios\nand the signi\ufb01cance for an integrated luminosity of 100 pb\u22121 are shown in Table 8.\nThe cross-section is derived from:\n\u03c3 =\nNsig\nL \u00d7\u03b5 = Nobs \u2212Nbkg\nL \u00d7\u03b5\nTo evaluate the statistical uncertainty on \u03c3, the error on Nobs is taken to be Gaussian assuming it will be\nmeasured in the data. The error on Nbkg is calculated here from Monte Carlo and scaled to the desired\nluminosity. The relative error on the ef\ufb01ciency \u03b5 (the product of geometrical acceptance and selection\nef\ufb01ciency) here is also calculated from the Monte Carlo. The expected statistical error on the cross-\nsection measurements for different integrated luminosities is given in Table 9. In data the ef\ufb01ciencies\nregarding leptons will be estimated from Z data events using tag and probe. Also the rates of backgrounds\ncontaining misidenti\ufb01ed leptons can only be measured in data reliably.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n942\n\nTable 8: Number of events which survive the optimised selection criteria for signal and background\nsamples, scaled to a luminosity of 100 pb\u22121.\ndataset\ne\u00b5\nee\n\u00b5 \u00b5\nall channels\nt\u00aft (di-lepton)\n555\n202\n253\n987\n\u03b5 [%]\n6.22\n2.26\n2.83\n11.05\nt\u00aft (semi-leptonic)\n24\n11\n4\n39\nZ \u2192e+e\u2212\n0.0\n9\n0.0\n20\nZ \u2192\u00b5+\u00b5\u2212\n5\n0\n51\n79\nZ \u2192\u03c4+\u03c4\u2212\n17\n4\n6\n25\nW W\n6\n2\n2\n10\nZ Z\n0\n0.2\n0.4\n0.9\nW Z\n1\n0.6\n1\n3\nW \u2192e\u03bde\n7\n7\n0.0\n14\nW \u2192\u00b5\u03bd\u00b5\n25\n0.0\n7\n33\nsingle top Wt\n0.7\n0.5\n0.0\n1\nsingle top s-chann.\n0.0\n0.0\n0.0\n0.1\nsingle top t-chann.\n2\n0.8\n1\n4\nTotal bkg.\n86\n36\n73\n228\nS/B\n6.3\n5.6\n3.4\n4.3\nTable 9: Expected statistical error on the cross-section determination for the cut and count analysis for\ndifferent luminosities.\nLuminosity [pb\u22121]\n10\n100\n1000\n\u2206\u03c3/\u03c3\ne\u00b5\n14.1 %\n4.5 %\n1.5 %\nee\n23.7 %\n7.6 %\n2.6 %\n\u00b5\u00b5\n22.5 %\n7.6 %\n3.6 %\nAll channels\n11.0 %\n3.6 %\n1.5 %\n3.3.2\nInclusive template method\nThe inclusive template method is based on the observation that the three dominant sources of isolated\nleptons which can be selected in the e\u00b5 channel are t\u00aft, WW and Z \u2192\u03c4\u03c4. However, these three processes\ncan be separated looking at the two-dimensional plane spanned by Emiss\nT\nand number of jets, as shown in\nFig. 14. Table 7 shows that there might be instrumental effects that introduce non-prompt non-isolated\nor falsely identi\ufb01ed leptons, primarily in single W-boson and Drell-Yan decays to muons. These non-\nprompt non-isolated or falsely identi\ufb01ed leptons can weaken the separation of the templates if their\ncontribution is too large. To reduce this effect we add a \u2018tight-electron\u2019 requirement on one of the\nelectrons. Signal sensitivity and robustness against systematic uncertainties are improved by adding also\nthe ee and \u00b5\u00b5 channels. In the \u00b5\u00b5 channel we reject events where the Emiss\nT\nis aligned along any of the\nreconstructed muons. To further reduce the Drell-Yan background in the ee and \u00b5\u00b5 channels a Emiss\nT\n> 35\nGeV cut and a Z-veto are added in those channels. The estimated number of events remaining after these\nadditional background rejection cuts are shown in Table 10.\nBy constructing normalised 2D templates for each channel we determine the relative size of the t\u00aft,\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n943\n\ntt njets\n0\n1\n2\n3\n4\n5\n6\n7\ntt MET (GeV)\n0\n50\n100\n150\n200\n250\n300\nATLAS\n(a)\nWW njets\n0\n1\n2\n3\n4\n5\n6\n7\nWW MET (GeV)\n0\n50\n100\n150\n200\n250\n300\nATLAS\n(b)\n njets\n\u03c4\u03c4\nZ\n0\n1\n2\n3\n4\n5\n6\n7\n MET (GeV)\n\u03c4\n\u03c4\nZ\n0\n50\n100\n150\n200\n250\n300\nATLAS\n(c)\nFigure 14: Monte Carlo e\u00b5 templates spanning the plane Emiss\nT\nand number of jets for t\u00aft (a), WW (b)\nand Z \u2192\u03c4\u03c4 (c).\nTable 10: Estimated number of events remaining after the background rejection cuts used in the inclusive\ntemplate analysis.\nSample\ne\u00b5\nee\n\u00b5\u00b5\nt\u00aft (di-lepton)\n516\n213\n178\nt\u00aft (semi-leptonic)\n12\n11\n2\nZ \u2192e+e\u2212\n3\n9\n0\nZ \u2192\u00b5+\u00b5\u2212\n9\n0\n18\nZ \u2192\u03c4+\u03c4\u2212\n151\n10\n2\nW \u2192e\u03bd\n35\n28\n0\nW \u2192\u00b5\u03bd\n11\n0\n11\nWW\n57\n17\n19\nWZ\n5\n3\n2\nZZ\n1\n1\n1\nsingle top\n3\n1\n1\nWW and Z \u2192\u03c4\u03c4 contribution by performing a binned log likelihood \ufb01t to pseudo-experiments. To en-\nsure a \ufb01t with a pull distribution compatible with a Gaussian with zero mean and unit sigma we relax the\ntemplate likelihood using nuisance parameters constrained to their expected errors. The nuisance param-\neters are: common acceptance and common background normalization for each \ufb01nal state. Bias from\npotential new physics is avoided by adding one free parameter with an associated orthogonal background\ntemplate. Orthogonal in this context means that an additional background template does not introduce a\nbias when only SM events are present in the pseudo-experiments. The \ufb01t has in total ten free parameters\nincluding the t\u00aft, WW and Z \u2192\u03c4\u03c4 cross-sections.\nMany different con\ufb01gurations of background templates are scanned and the template with the highest\nprobability is selected. For robustness, the \ufb01t is \ufb01rst performed in the e\u00b5 channel, and then the \ufb01tted\nparameters are fed as start values into the full \ufb01t which includes all channels: e\u00b5, ee and \u00b5\u00b5. The result\nfrom the full \ufb01t applied to pseudo-experiments including all systematics is shown in Fig. 15.\nSystematic uncertainties enter in two ways: in the acceptance of the two leptons, and in the shapes\nof the 2D templates exempli\ufb01ed in Fig. 14. The impact of the systematic uncertainties is estimated using\npseudo-experiments where all uncertainties and correlations, as discussed in section 3.4, are included,\nexcept the luminosity. Note that the acceptance is by de\ufb01nition not affected by the jet energy scale,\nbut has a 2% uncertainty from QCD showering. The shape has a 2% uncertainty from QCD initial\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n944\n\nstate showering, and 2% from the jet energy scale. QCD \ufb01nal state showering only comes from t\u00aft and\nis found not to have any measurable effects on the \ufb01t when all channels are included. The projected\nsigni\ufb01cance versus integrated luminosity including all systematic uncertainties, except luminosity, is\nshown in Fig. 15.\nNumber of Jets\n0\n2\n4\n6\n8\n10\n-1\nNumber of Events/100 pb\n0\n50\n100\n150\n200\n250\n300\n350\nNumber of Jets\n0\n2\n4\n6\n8\n10\n-1\nNumber of Events/100 pb\n0\n50\n100\n150\n200\n250\n300\n350\nATLAS\n(a)\n ll\ntt\n\u03c4\n\u03c4\nZ\nWW\nWZ\nZZ\nZee\n\u00b5\n\u00b5\nZ\n l+j\ntt\nWe\n\u00b5\nW\n)\n-1\nIntegrated luminosity (pb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\ntt\n\u03c3\nSignificance \n5\n10\n15\n20\n25\nATLAS\n(b)\nFigure 15: (a) Total composition of the inclusive di-lepton selection versus number of jets. (b) Pro-\njected signi\ufb01cance from pseudo-experiments for the inclusive template \ufb01t versus integrated luminosity\nincluding all channels and all systematic uncertainties.\n3.3.3\nLikelihood method\nThe likelihood method uses the following log-likelihood function to extract the parameters Nsig and Nbkg\ngiven the \ufb01xed total number of events Ntot and the measurements (xi):\nL = \u2212\nNtot\n\u2211\ni=1\nln(G[xi|Nsig,Nbkg])+Ntot\nwith\nG(x) = Nsig \u00d7S(x)+Nbkg \u00d7B(x)\nThe multidimensional function G(x) is the sum of the functions S(x) which describes the signal\ndistribution and of B(x) that describes the background distribution. The functions are determined by\n\ufb01tting Chebychev polynomials to the signal and background Monte Carlo distributions after the cut and\ncount cuts were applied in the variables |\u2206\u03d5(lepton0,Emiss\nT\n)| (\u2206\u03d5 between the highest pT lepton and the\nmissing transverse energy vector) and |\u2206\u03d5|(jet0,Emiss\nT\n)| (\u2206\u03d5 between the highest pT jet and the Emiss\nT\nvector). Fig. 16 shows one of the distributions and the solid line shows the \ufb01ts to the distribution that are\nused as S(x) and B(x).\nThe sum of the semi-leptonic t\u00aft , Z \u2192\u2113+\u2113\u2212and WW events are considered as background and added\nup according to their cross-section to produce one single background distribution.\nTo estimate the error on the cross-section, ensemble tests were performed for different integrated\nluminosities ranging from 10 pb\u22121to 1 fb\u22121. The relative statistical errors are presented in Table 11.\n3.4\nSystematic uncertainties\nThe systematic uncertainties have been evaluated according to the standard prescription [9]. In particular,\nthe lepton ID ef\ufb01ciency will be measured from data using Z-boson events and the uncertainty is expected\nto be of the order 1%. The lepton trigger ef\ufb01ciency will be measured from data using Z events with an\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n945\n\nATLAS\n (a)\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n20\n40\n60\n80\n100\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n20\n40\n60\n80\n100\nATLAS\n(b)\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n(c)\n | MissingET)\n0\n (Lepton\n\u03c6 \n\u2206\n0\n0 5\n1\n1.5\n2\n2.5\n3\nEvents\n0\n20\n40\n60\n80\n100\n120\n140\nFigure 16: Distribution of \u2206\u03d5 between the highest pT lepton and the Emiss\nT\nmomentum vector for (a)\nsignal, (b) background and (c) signal/background composition according to the ratio obtained from the\ncut analysis.\nTable 11: Expected statistical error evaluated from ensemble tests on the cross-section measurement for\nthe likelihood method for different luminosities. For 10 pb\u22121 the \ufb01ts in the subchannels do not converge\nwell enough to give results.\nLuminosity [pb\u22121]\n10\n100\n1000\n\u2206\u03c3/\u03c3\ne\u00b5\n-\n9.1 %\n2.7 %\nee\n-\n16.0 %\n4.6 %\n\u00b5\u00b5\n-\n7.8 %\n2.5 %\nAll channels\n18.2 %\n5.2 %\n1.7 %\nTable 12: Uncertainties on the cross-section measurement for the cut and count and the likelihood meth-\nods.\ncut and count method\nlikelihood method\n\u2206\u03c3/\u03c3 [%]\ne\u00b5\nee\n\u00b5\u00b5\nall\ne\u00b5\nee\n\u00b5\u00b5\nall\nCTEQ6.1 set\n2.4\n2.9\n2.0\n2.4\n0.3\n0.4\n0.2\n0.2\nMRST2001E set\n0.9\n1.1\n0.7\n0.9\n0.2\n0.2\n0.1\n0.2\nJES-5%\n-2.0\n0.0\n-3.1\n-2.1\n-5.4\n1.1\n4.9\n8.3\nJES+5%\n2.4\n4.1\n4.7\n4.6\n7.8\n3.9\n-4.6\n-4.4\nFSR\n2.0\n2.0\n4.0\n2.0\n0.2\n0.4\n0.0\n0.3\nISR\n1.1\n1.1\n1.2\n1.1\n2.5\n1.8\n0.0\n1.7\nparameters-1\u03c3\n-3.0\n-0.2\n-2.1\n-1.8\nparameters+1\u03c3\n3.2\n0.8\n2.0\n2.0\nuncertainty which should also be of the order 1%. The lepton fake rate uncertainty is estimated from\ndijet events, and during the initial phase of data taking we expect this uncertainty to be of the order of\n50%. The systematic effect due to the uncertainty of the jet energy scale is investigated by scaling the\nreconstructed jet energies by \u00b15%. The value of the Emiss\nT\nis rescaled accordingly. The initial and \ufb01nal\nstate radiation was investigated and the results are summarised in Table 12 as well.\nFor the likelihood, the \ufb01t parameters of the Chebychev polynomials were varied by 1 \u03c3 at the same\ntime in the same direction. The results can be seen in Table 12.\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n946\n\nThe reweighting technique, to assess the systematic uncertainties from parton densities is also de-\nscribed in Section [9]. To cross-check the technique ATLFAST samples with different PDFs were used.\nFor the cut and count method the ef\ufb01ciency using MRST PDFs is larger than the ef\ufb01ciency using CTEQ\nPDFs. Table 12 summarises the changes in the selection ef\ufb01ciency. For the cut and count analysis this\ndirectly translates into an uncertainty on the cross-section determination. For the likelihood method the\nreweighted events were used to \ufb01t the Nsig and Nbkg to the templates which were generated with the\nunmodi\ufb01ed fully simulated events.\n3.5\nContribution of new physics\nMany models of physics beyond the Standard Model can have a signi\ufb01cant branching ratio to the di-\nlepton \ufb01nal state. In particular the \u2019cut and count\u2019 method is sensitive to these potential contributions. In\nsome SUSY scenarios the contribution can be as large as one-third of the total t\u00aft signal. This indicates\nhow crucial it is to include all \ufb01nal states in order to verify the global consistency of the t\u00aft cross-section.\nThe template/likelihood methods are able to consider more distinctive t\u00aft event properties and can be\nmade much more robust against non-Standard Model sources.\nData-driven methods which consider the full kinematics of the di-lepton t\u00aft system can further help\nto disentangle new physics, as described in other notes [12] of this volume.\n3.6\nResults\nThe \ufb01nal results in percent for the combined di-lepton channels for an integrated luminosity of 100 pb\u22121\nare summarised here\nCut and Count method:\n\u2206\u03c3/\u03c3 =\n(4(stat)+5\n\u22122(syst)\u00b12(pdf)\u00b15(lumi))%\n(4)\nTemplate method:\n\u2206\u03c3/\u03c3 =\n(4(stat)\u00b14(syst)\u00b12.(pdf)\u00b15(lumi))%\n(5)\nLikelihood method method:\n\u2206\u03c3/\u03c3 =\n(5(stat)+8\n\u22125(syst)\u00b10.2(pdf)\u00b15(lumi))%\n(6)\n4\nDiscussion and outlook\nIn this note we have demonstrated that ATLAS will be able to reliably determine the t\u00aft\nproduction\ncross-section already from the startup period of LHC. We have determined this cross-section for the t\u00aft\nsystem decaying both into a single electron or muon with associated jets, or two electrons or muons with\njets. For the single-lepton mode, we have investigated robust selection criteria that do not depend on the\nb-quark tagging. For the di-lepton channel various complementary channels have been investigated.\nWith only 100 pb\u22121 of accumulated data, we have shown that we can observe the top-quark signal\nand measure its production cross-section. Various methods have been presented and the corresponding\nuncertainties studied. Apart from the luminosity uncertainty, the overall uncertainties are of the order of\n(5-10)% and are dominated by systematics. Consistency between the methods constrain contributions of\nnew physics as they affect the various methods differently.\nReferences\n[1] J.F. Gunion, H. Haber, G. Kane, S. Dawson and H.E. Haber, \u201cThe Higgs Hunter\u2019s Guide\u201d, ISBN-10:\n073820305X, Westview Press, 2000.\n[2] CDF Collaboration, Phys. Rev. D 64, 032002 (2001); CDF Collaboration Phys. Rev. Lett. 80 (1998)\n2779-2784;\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n947\n\nD\u00d8 Collaboration Phys. Rev. Lett. 83 (1999) 1908; D\u00d8 Collaboration Phys. Rev. D 60 (1999)\n12001; D\u00d8 Collaboration Phys. Rev. Lett. 83 1908 1999; D0 Coll. Phys. Rev. D 67, 012004 (2003).\n[3] M. Cacciari et al. JHEP 0404 (2004) 068 [arXiv:hep-ph/0303085].\n[4] N. Kidonakis, R. Vogt, Physical Review D 68, 114014 (2003).\n[5] CDF Collaboration, \u201cCombination of CDF top quark pair production cross section measurements\nwith up to 760 pb\u22121\u201d, CDF-CONF-NOTE-8148.\n[6] V. Sharyy, for the D\u00d8 Collaboration, proceedings of the International Workshop on Top Quark\nPhysics, La Biodola, Elba, Italy, 18-24 May 2008.\n[7] ATLAS Collaboration, \u201cTrigger for Early Running\u201d, this volume.\n[8] ATLAS Collaboration, \u201cReconstruction and Identi\ufb01cation of Electrons\u201d, this volume.\n[9] ATLAS Collaboration, \u201cTop Quark Physics\u201d, this volume.\n[10] S. P. Martin, \u201cA Supersymmetry Primer\u2019, arXiv:hep-ph/9709356.\n[11] K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, Phys. Rev. D 77 (2008) 015003\n[arXiv:hep-ph/0612015].\n[12] ATLAS Collaboration, \u201cSupersymmetry Searches\u201d, this volume.\n[13] M. Arai, N. Okada, K. Smolek, V. Simak, Phys.Rev. D 70 (2004) 115015.\n[14] R. Frederix and F. Maltoni, \u201cTop pair invariant mass distribution: a window on new physics\u201d,\narXiv:0712.2355.\n[15] S. Snyder, FERMILAB-THESIS-1995-27.\n[16] The ATLAS collaboration, \u201cThe ATLAS Experiment at the CERN Large Hadron Collider\u201d,JINST\n3 (2008) S08003\nTOP \u2013 DETERMINATION OF THE TOP QUARK PAIR PRODUCTION CROSS-SECTION\n948\n\nProspect for Single Top Quark Cross-Section Measurements\nAbstract\nAt the LHC, the single top quarks will be produced at a third of the rate of\ntop quark pairs. With more than two million single top quark events produced\nevery year during the low luminosity run, a precise determination of all con-\ntributions to the total single top quark cross section seems achievable. Com-\nparison between the measured cross section and the theoretical prediction will\nprovide a crucial test of the Standard Model. These measurements will lead to\ndirect measurement of Vtb at the few percent level of precision, and constitute a\npowerful probe for new physics, via the search for evidence of anomalous cou-\nplings to the top quark or the measurements of additional boson contributions\nto single top quark production.\nThe single top quark production mechanism proceeds through three different\nsub-processes resulting in distinct \ufb01nal states, topologies and backgrounds.\nGiven the level of backgrounds affecting the individual selections and the im-\nportance of the systematic uncertainties, the use of sophisticated methods ap-\npears mandatory to unambigiously observe each process and determine pre-\ncisely the corresponding cross sections. This report presents the methods de-\nveloped to optimize the selection of single top quark events in the three chan-\nnels and establishes the ATLAS potential for the cross section measurements\nfor the early data period and for a 30 fb\u22121 low luminosity run.\n1\nIntroduction\nThe top quark is one of the key particles in the quest for the origin of particle mass. In particular the\nelectroweak interaction of the top quark is sensitive to many types of new physics. The electroweak\nproduction of top quark leads to a \ufb01nal state of a single top quark plus other particles. The production\ncross section is sensitive to contributions from new particles such as new heavy bosons W\u2032 or charged\nHiggs bosons H\u00b1. Other processes such as \ufb02avor-changing neutral currents also result in a single top\nquark \ufb01nal state [1]. Furthermore, single top quark production is an important background to many\nsearches for new physics.\nThe D0 [2] and CDF [3] collaborations at the Fermilab Tevatron reported evidence for single top\nquark production and a \ufb01rst direct measurement of the CKM matrix element Vtb. This involved advanced\nanalysis methods to extract the small single top quark signal out of the large backgrounds. The Tevatron\nexperiments will collect several fb\u22121 of data, and expect to not only observe single top quark production\nat the 5 sigma level but also separate two different production modes: the s-channel and the t-channel.\nHowever, the single top quark production cross section is small at Tevatron energies and single top quark\nmeasurements will be limited by statistics.\nAt the LHC, the number of signal events is not a problem anymore. The LHC will not only be a\nstrong interaction top quark factory but will also produce several million single top quark events. The\ncross section for all three modes of single top quark production as well as the CKM matrix element\nVtb can be measured with high precision [4]. Once the single top quark signal has been established,\ndetailed measurements of the process will follow, for example of the top quark polarization, ratios of\ncross sections, and charge asymmetries. Searches in each of the single top quark channels are sensitive\nto new physics even before the Standard Model single top quark signal is found. The D0 collaboration\nhas published limits on W\u2032 boson production and \ufb02avor changing neutral currents [5,6].\n949\n\nThis paper describes the cross section measurements for the three single top quark production modes\nand is organized as follows: the single top quark phenomenology is introduced in Section 2. All studies\nare based on a common event preselection, presented in Section 3. The prospects for the cross section\nmeasurements for the t-channel, s-channel and Wt-channel are then presented in Sections 4, 5, and 6.\nFinally, we summarize our conclusions in Section 7.\n2\nPhenomenology and strategy for single top quark analyses in ATLAS\nIn the Standard Model single-top quark production is due to three different mechanisms: (a) W-boson\nand gluon fusion mode, which includes the t-channel contribution and is referred to as t-channel as a\nwhole (b) associated production of a top quark and a W-boson, indicated as Wt-channel, and (c) s-\nchannel production coming from the quark anti-quark annihilation. Among those channels, the dominant\ncontribution comes from the t-channel processes which account for 246+12\n\u221212 pb [7, 8]. The Wt-channel\ncontribution amounts to 66 \u00b1 2 pb [9] while the s-channel mode is expected to have a cross section of\n11 \u00b1 1 pb [7, 8]. The cross sections are calculated at the next-to-leading Order (NLO) with an input\ntop quark mass of 175 GeV. A 4.3 GeV uncertainty on the top quark mass is included in t-channel\nand s-channel cross section uncertainties, while the Wt-channel uncertainty includes strong energy scale\nvariations only.\nIn the Standard Model, the top quark is assumed to decay almost exclusively into a W-boson and a b\nquark. The W-boson can then decay leptonically or hadronically. In the following, when discussing the\nanalysis strategy in the s- and t-channels, only the leptonic decays of the W-boson are considered (l\u03bdb\u00afb\nand l\u03bdb\u00afbq \ufb01nal states, respectively)1. For the associated production (Wt-channel), only the modes where\na lepton originating either directly from the W-boson produced together with the top quark or from the\ntop quark decay are used. The \u03c4 decay modes are included in all relevant samples and treated as a signal\nfor leptonic \u03c4 decays, since the signal selection is aimed at electron and muon signatures.\nTop quark pair production constitutes a dominant background to single-top quark events. The LHC\ntotal production cross section computed at NLO with next-to-leading logarithmic resummations is \u03c3(t\u00aft) =\n833 \u00b1 100 pb [10] [11], about 3 times larger than the single top quark cross section, and more than 80\ntimes that of the s-channel. Given the fact that single top quark \ufb01nal state topology is characterized\nby one high pT lepton, missing energy and jets, t\u00aft production represents a signi\ufb01cant background in\nits lepton+jets decay mode, i.e. when one of the W\u2019s decays leptonically and the other hadronically\n(t\u00aft \u2192l\u03bdbjjb), with a \ufb01nal state containing two jets from the hadronization of b quarks and two jets from\nlight quarks, a high pT lepton and missing energy. The \u201cdilepton\u201d channel (t\u00aft \u2192l\u03bdbl\u03bdb) where a lepton\nis lost in acceptance also constitutes a major background. Finally, top quark pairs with one or both W-\nboson(s) decaying into a \u03c4 lepton where the \u03c4 decays into an electron or a muon, may also survive the\nselection.\nW+jets events constitute another major source of background because of a cross section several\norders of magnitude above the one of the single top quark production. The Leading Order (LO) Alpgen\n[12] generator with the HERWIG [13] parton shower algorithm was used for the generation of W+jets\nand Wb\u00afb+jets events in this analysis. The corresponding LO cross-sections have also been used. A\n20% uncertainty on the W+jets and Wb\u00afb+jets cross-sections is considered in the following. WW and\nWZ diboson processes were also studied using samples generated with the HERWIG generator. The\ncorresponding cross-sections are reported in [10].\nWhile QCD dijet and multijet processes do not have features of the signal, they contribute to the\nbackground due to their overwhelming cross section and small but \ufb01nite rate of object misidenti\ufb01cation.\n1The hadronic decay modes have obvious disadvantages for triggering and the lack of lepton signature increases the back-\nground signi\ufb01cantly.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n950\n\nThe estimation of this background needs to be done using data-driven methods and has been studied\nusing full simulated dijet events generated with PYTHIA [14].\n3\nSingle top quark event preselection\nThe three production modes of single top quark events are characterized by similar features that motivate\na common set of preselection criteria. This preselection, which classi\ufb01es the events according to exclu-\nsive electron and muon selections, is also aimed at reducing the level of three types of processes which\nconstitute the main backgrounds to single top quark analyses: the top quark pair production, the W+jets\nand the QCD events.\n3.1\nTriggering and event preselection\nThe triggers for single top quark events rest upon the use of the inclusive isolated electron and muon\ntriggers. Their design and performance for the three levels of trigger are presented extensively else-\nwhere [15]. Triggering ef\ufb01ciency is 84\u00b11% overall for top pair quark events. Only mariginal differences\nare seen in single top events. Note that for fast simulation samples like W+jets datasets, where no trigger\ninformation is available, a trigger weight derived from turn on curves established on t\u00aft events is applied\nto every event.\nSelected events must have at least one of\ufb02ine high pT isolated lepton in the central region with\n|\u03b7| \u22642.5. The isolation criterion requires that the energy in a cone of \u2206R= 0.2 around the lepton direction\nbe less than 6 GeV and is important for the rejection of QCD background in which a jet can fake an\nelectron or a muon [10]. Muons and electrons are required to have a transverse momentum greater\nthan 30 GeV ensuring that the trigger ef\ufb01ciency is on the plateau and hence less sensitive to trigger\nuncertainties. Finally, the sign of the highest pT lepton gives the \ufb02avor of the decaying top quark.\nThe event must then pass a second isolated lepton veto cut, applied to any lepton with a pT above\n10 GeV and in the pseudo-rapidity region |\u03b7| \u22642.5 in order to reduce contamination from dilepton\nbackgrounds. The rejection of t\u00aft events in the dilepton channel is increased by a factor 2.5 as this\nrequirement is applied. The impact on the signal ef\ufb01ciency is limited, with a loss of 3.6% in both the s-\nand t-channel and 2.7% in the Wt-channel.\nEvents are preselected if at least two jets are reconstructed with a pT above 30 GeV in the pseudo-\nrapidity region |\u03b7| \u22645.0. The t\u00aft production being the dominant background to single top quark analyses,\nthe use of a jet veto appears mandatory. The event jet multiplicity is thus further required to be lower or\nequal to four, where the extra jets must be reconstructed with pT above 15 GeV. It is important to keep\nthis threshold as low as possible, since lowering the veto pT threshold from 30 to 15 GeV results in a\nrejection of t\u00aft events increased from 5 to almost 10. Among those events, the l+jets decay modes are\nthe most sensitive to such a requirement with a rejection rate that is doubled compared to the 30 GeV\nthreshold. Dilepton events are less affected with a rejection rate going from 5 to 6.6. This requirement\nresults in a relative loss of 20 to 25% of the single top quark in the t- and Wt-channel channels and of\n7% in the s-channel.\nAmong the highest pT jets, one at least must be b-tagged, have a pT above 30 GeV and be in the\ncentral pseudo-rapidity region |\u03b7| \u22642.5. The b-tagging algorithms are described elsewhere [10]. A cut\non the b-tag weight corresponding to a 60% ef\ufb01ciency and a mistag rate of light jets of 100 [16] is used.\nThe mistag rates being small, we use an additional method to estimate backgrounds which do not contain\nb partons in the \ufb01nal states but are present in the selected sample because of a cross section several orders\nof magnitude above that of the signal. This is the case for the W+jets production. In those events, each\njet is assigned a tag weight based on the parametrization of the mistag rate as function of the jet pseudo-\nrapidity and transverse momentum. The combination of all jets results in a weight assigned to the event\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n951\n\nto be considered as a \u201c1 b-tag inclusive\u201d, \u201c2 b-tags\u201d etc... event. Known as the \u201ctagging rate function\u201d,\nthis method, which applies on Monte Carlo events, improves the statistics in the distributions of such\nevents, while keeping a global normalization corresponding to the actual mistag rates [17].\nFinally the transverse missing energy is required to be larger than 20 GeV. This criterion is consistent\nwith the leptonic decays of a W-boson while reducing the contamination from QCD events.\n3.2\nPreselection ef\ufb01ciency\nPreselection ef\ufb01ciencies as well as event yield for an integrated luminosity of 1 fb\u22121 are reported in\nTable 1. The single top quark ef\ufb01ciency ranges between 5 and 6% in the electron channel and between\n5.5 and 7.5% in the muon channel respectively. These numbers translate into a total of approximately\n5,000 and 4,200 single top quark events in the muon and electron channel respectively including \u03c4 decays.\nThe production of t\u00aft events constitutes the dominant source of background to single top quark analy-\nses. The t\u00aft events in the l+jets (l = e,\u00b5) modes are selected with an ef\ufb01ciency lower than 5%, resulting\nin a total of 22,580 events. The \u03c4 +l (and \u03c4\u03c4) modes also contribute signi\ufb01cantly with about 6,000 ex-\npected events. Despite the use of a second lepton veto dilepton events, where a lepton escapes detection,\nalso contribute to the preselected sample signi\ufb01cantly with about 4,000 events surviving the selection.\nThe production of W+jets events is also an important source of background, with about 13,000 events\nin the preselected sample. However these events populate mostly the lower jet multiplicity bin and their\nselection depends crucially on the mistag rates. The selection of Wb\u00afb+jets events results in about 1,000\nevents.\nQCD events may also contribute to the selected sample of events. However, the requirements of the\npresence of at least one isolated identi\ufb01ed lepton and one jet tagged as a b-jet reduce very signi\ufb01cantly\ntheir level as discussed in [11]. Typically QCD background is expected to be smaller than the W+jets\nbackground. Further rejection may be achieved by applying more restrictive requirements on the lepton\nidenti\ufb01cation, or on the missing transverse energy and its correlation in \u03c6 with reconstructed objects like\nleptons and jets [18]. The uncertainty on the remaining level of QCD background may be large. The\nQCD background contamination in selected samples should preferably be monitored, for example by the\nreconstruction of the transverse W-boson or top quark reconstructed masses [19].\n3.3\nCross-section determination and systematic uncertainties\nSpeci\ufb01c selections have been de\ufb01ned for the t-, s- and Wt- channels analyses. A general procedure to\ndetermine the cross-section on the selected samples and assess the errors associated to the measurement\nhas been de\ufb01ned and is common to all three single top quark analyses. The following expression is used\nto calculate the cross section, \u03c3:\n\u03c3 =\nNsig\na\u00d7L = Ntot \u2212B\na\u00d7L ,\n(1)\nwhere Nsig and Ntot are the number of signal and all selected events respectively, B is the number of back-\nground events, a is the signal acceptance and L is the luminosity of the data sample. In the following\nstudies, these numbers are estimated using Monte Carlo samples only. Data driven methods are expected\nbe used to estimate speci\ufb01c backgrounds in the forthcoming data analyses.\nThe propagation of the errors into the cross-section has been done in a consistent way among the\nthree channels. They are combined and propagated to the measured cross section using a Monte Carlo\nmethod, which randomly generates Ntot according to a Poisson distribution, and varies randomly B and\na for every systematic source by an amount chosen around its central value, according to a gaussian\ndistribution. This procedure is performed a few thousand times and the RMS of the resulting distribution\nis interpreted as the total uncertainty.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n952\n\nTable 1: Preselection ef\ufb01ciency, including trigger, for signal and background events. The\nuncertainties come from Monte Carlo statistics only. The convention l = e,\u00b5 is used.\nProcess\nMuon channel\nElectron channel\n\u03b5(%)\nN(1fb\u22121)\n\u03b5(%)\nN(1fb\u22121)\ns-channel\u2192l\n7.1\u00b10.1%\n166\u00b13\n5.8 \u00b10.%\n136\u00b13\ns-channel\u2192\u03c4\n0.7\u00b10.1%\n8\u00b11\n0.5\u00b10.1%\n6\u00b11\nt-channel\u2192l\n5.9\u00b10.2%\n3143\u00b180\n5.2\u00b10.1%\n2787\u00b176\nt-channel\u2192\u03c4\n0.6\u00b10.1%\n169\u00b119\n0.3\u00b10.05%\n92\u00b114\nWt-channel\u2192l\n6.8\u00b10.1%\n1314\u00b127\n5.6\u00b10.1%\n1091\u00b124\nWt-channel\u2192\u03c4\n1.0\u00b10.1%\n93\u00b17\n0.8\u00b10.1%\n77\u00b17\nt\u00aft \u2192l+jets\n4.9\u00b10.05%\n11846\u00b1130\n4.4\u00b10.05%\n10734\u00b1124\nt\u00aft \u2192\u03c4 +jets\n0.6\u00b10.05%\n757\u00b134\n0.5\u00b10.02%\n625\u00b131\nt\u00aft \u2192ll\n5.8\u00b10.1%\n2257\u00b158\n4.6\u00b10.1%\n1762\u00b151\nt\u00aft \u2192l+\u03c4\n7.9\u00b10.2%\n3055\u00b166\n6.7\u00b10.2%\n2595\u00b161\nt\u00aft \u2192\u03c4\u03c4\n1.6\u00b10.2%\n158\u00b116\n1.6\u00b10.2%\n151\u00b115\nWbb+jets\u2192l or \u03c4\n2.6\u00b10.05%\n514\u00b121\n2.1\u00b10.05%\n424\u00b119\nW+jets\u2192l or \u03c4\n0.014\u00b10.001%\n7437\u00b1105\n0.011\u00b10.002%\n5449\u00b190\nWW\n0.3\u00b10.04%\n78\u00b111\n0.3\u00b10.04%\n65\u00b110\nWZ\n0.6\u00b10.04%\n50\u00b13\n0.5\u00b10.04%\n39\u00b13\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n953\n\nThe total uncertainty is calculated using a common procedure as described in Section 4.2.3 in the\nthree individual analyses. The main sources of experimental systematic errors taken into account are\nthe b-tagging ef\ufb01ciency, jet energy scale, luminosity, for which central values are provided in the corre-\nsponding sections. Theoretical uncertainties that have been considered are the errors on the background\ncross-sections, as well as the impact of the uncertainties in the parton distribution functions and the\nb-quark fragmentation in the selection ef\ufb01ciency. Note that we consider the errors as fully correlated\nbetween signal and background for jet energy scale, b-tagging, and luminosity.\n4\nMeasurement of the t-channel cross section\nThe t-channel is the most promising channel for single top quark observation at the LHC. It has the\nlargest theoretical cross section of the three channels and its event features give us reasonable visibility\nof the signal according to the studies done so far [20]. In addition to the cross section measurement,\nthe t-channel single top quark is one of very few candidate channels for the Vtb and the top quark po-\nlarization measurements. It is hoped that these measurements will shed light on our understanding of\nthe electroweak symmetry breaking since these quantities have not been studied with high precision in\npast experiments. Compared to t\u00aft , the t-channel single top quark analysis suffers from a higher level\nof background due to its lower jet multiplicity, which makes the selection sensitive to QCD and W+jets\nbackgrounds whose cross sections are several orders of magnitude higher than that of the signal. Thus,\nwhile the signal production rate is not statistically limited at the LHC, a good strategy for signal extrac-\ntion is required and a careful estimation of the background rate is necessary.\n (GeV)\nT\nP\n0\n20\n40\n60\n80 100 120 140 160 180 200\nEntries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n (GeV)\nT\nP\n0\n20\n40\n60\n80 100 120 140 160 180 200\nEntries\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n \n \n \nt-channel\ntt\nWjets\nATLAS\nNumber\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nEntries\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nNumber\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nEntries\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n \nt-channel\nWt-channel\ns-channel\n)\n\u00b5\n l+jets (l=e\n\u2192\n tt\n)\n\u00b5\n ll (l=e\n\u2192\n tt\n+jets\n\u03c4\n/\u03c4\n+\n\u03c4\n/\u03c4\n l+\n\u2192\n tt\nWbb\nWjets\nATLAS\nFigure 1: Signal and background distributions of the b-tagged jet pT and multiplicity of jets with pT >\n30 GeV after the t-channel selection.\n4.1\nCut based event selection\nAfter the common preselection, the contribution from the background is still high mainly due to W+jets\nat the lower end of the kinematic distributions (such as in the jet pT spectrum) and t\u00aft at the higher end.\nThe b-tagged jets coming from t\u00aft and the t-channel single top quark tend to have high pT and to be located\nmore centrally since they mainly originate from top quark decays. On the other hand, b-tagged jets from\nW-boson events are much softer as they primarily come from mistagged jets originating from extra gluon\nradiation. Furthermore, the recoiling forward quark in the t-channel single top quark produces a high pT\nlight jet in the forward direction. This was found to be one of few features useful to reject t\u00aft background\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n954\n\nevents because light jets from the t\u00aft events are typically initiated from hadronic W-boson decays and are\ntherefore more central. A cut on b-tagged jet pT > 50 GeV reduces the W+jets signi\ufb01cantly, while a cut\non the hardest light jet |\u03b7| > 2.5 can reject t\u00aft . Figure 1 shows the pT distribution of the hardest b-tagged\njet and the composition of the sample in terms of the jet multiplicity after the additional event selection.\nTable 2 lists the number of preselected events, the number of events selected after the cut on b-tagged\njet pT and the number after the light jet \u03b7 cut for the signal and the background processes. The signal\nef\ufb01ciency is 1.81% and the signal to background ratio after all selection is 37%. Note that the single top\nquark \u03c4 decays are included in the signal count. By far the largest background contribution comes from\nthe t\u00aft process; the l+jets top quark pair events contribute the most, although dilepton events have a higher\nsurvival probability of 1.36% compared to 0.64% of the l+jets. W+jets is the second largest background\nwhile the Wb\u00afb contribution is relatively small. The s-channel single top quark contribution is almost\nnegligible and the diboson background is even smaller and therefore is not included in the table.\nTable 2: Number of events selected after each cut in the t-channel analysis. The last column shows\nthe number of remaining events in the cut-based analysis at the integrated luminosity of 1 fb\u22121.\nNote that the convention l = e,\u00b5 is used.\nProcess\nPreselected\nb Jet pT\nlight jet \u03b7\n\u03b5(%)\nN(1fb\u22121)\n\u03b5(%)\nN(1fb\u22121)\n\u03b5(%)\nN(1fb\u22121)\nt-channel\n7.7%\n6191\u00b1112\n5.5%\n4412\u00b195\n1.8%\n1460\u00b156\n\u00b5 channel\n4.1%\n3312\u00b183\n2.9%\n2352\u00b171\n0.9%\n728\u00b140\ne channel\n3.6%\n2879\u00b178\n2.6%\n2060\u00b166\n0.9%\n732\u00b140\ns-channel\n9.0%\n316\u00b15\n7.0%\n245\u00b14\n0.8%\n26\u00b11\nWt-channel\n8.9%\n2575\u00b137\n6.4%\n1854\u00b132\n0.4%\n122\u00b19\nt\u00aft l+jets\n9.3%\n22580\u00b1176\n7.3%\n17775\u00b1158\n0.6%\n1556\u00b148\nt\u00aft \u2192l+\u03c4/\u03c4 +\u03c4/\u03c4+jets\n4.3%\n7342\u00b1104\n3.4%\n5776\u00b193\n0.4%\n740\u00b134\nt\u00aft \u2192ll\n10.4%\n4018\u00b175\n8.1%\n3143\u00b167\n1.3%\n520\u00b128\nW+jets\n0.025%\n12886\u00b1138\n0.012%\n6082\u00b195\n0.0017%\n873\u00b136\nWb\u00afb\n4.7%\n939\u00b127\n3.0%\n597\u00b122\n0.4%\n69\u00b18\nS/B\n0.12\n0.12\n0.37\nS/\n\u221a\nB (\u03c3)\n27.5\n23.4\n23.4\n\u221a\nS+B/S\n3.9%\n4.5%\n5.0%\nAs seen in Table 2, a precision (\n\u221a\nS+B/S) of 5% can be obtained after the \ufb01nal selection. Note,\nhowever, that the selection cut does not optimize the precision nor the signi\ufb01cance of the signal obser-\nvation. From purely statistical arguments, the t-channel cross section can be measured to a few percent\naccuracy with a few fb\u22121 of data.\nIn comparison to the previous study in the ATLAS physics TDR [20], which reported S/B a ratio of 3,\nthere is a signi\ufb01cant apparent reduction in the event selection performance. The cut-based selection used\nhere is similar to that used in the TDR and we would have expected a similar result. Further investigation\nrevealed several issues with the TDR analysis. Firstly, Monte Carlo (MC) generators changed drastically\nin recent years. PYTHIA introduced a new parton shower algorithm, which is much more radiative.\nThe matrix-element generator for the signal has also changed to AcerMC, which combines the NLO\ndiagram contribution to the LO ones as opposed to PYTHIA, which only uses LO. For the W+jets\nbackground production, Alpgen is used because it is shown that it reproduces better the high pT tails of\njet distributions at the TeVatron [21], while Herwig was used in the TDR. In addition, the TDR analysis\ndid not include some of the crucial background processes, like dilepton t\u00aft channels and \u03c4 decay modes\nwhich are shown to contribute signi\ufb01cantly in the present analysis. Therefore, the result of the TDR can\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n955\n\nnow be seen as too optimistic.\nNote that the presence of pile-up affects the reconstruction of the objects selected in the event. In\nparticular, the selection ef\ufb01ciency is directly affected by the presence of extra jets in the events. Speci\ufb01c\nMonte Carlo samples of single top quark and t\u00aft events have been produced with or without pile-up events\nsuperimposed. The use of events with pile-up results in a decrease of about 25% for signal events, and\n34% for t\u00aft events. No systematic uncertainties will be associated with this value. The use of data will\nbe mandatory for the tuning of the pile-up modeling and the corresponding uncertainty is expected to be\nbrought down to a negligible value with respect to the other sources of error.\n4.2\nSystematic uncertainties\nThe systematic uncertainties have been evaluated following a procedure common to all three analyses.\nThis procedure is de\ufb01ned here and the results speci\ufb01c to all analyses are reported in the corresponding\nsections.\n4.2.1\nExperimental systematic uncertainties\nVarious criteria need to be considered to assess the systematic effects as it depends on a number of\ndetector sub-components and theoretical assumptions. A general procedure has been de\ufb01ned to assess\nall systematic errors in a consistent way for the three single top quark analyses. The estimate is shown\nhere for the t-channel analysis only.\nThe effect of the uncertainties on the measured cross section is summarized in Table 4. While the\nstatistical uncertainty is not a constraint for the t-channel cross section analysis even with the early data,\nsystematic uncertainties can only be reduced with detailed understanding of the detector performance\nand theoretical uncertainties. The measurement in the t-channel is largely limited by such effects.\nTable 3: Effect of b-tag and jet energy scale systematics. Numbers are\nquoted from relative variation of selected event.\nProcess\nb-tag -5%\nb-tag +5%\nJES -5%\nJES +5%\nt-channel\n-4.0%\n+4.8%\n-4.8%\n+5.0%\ns-channel\n-5.2%\n+3.6%\n-6.6%\n+12.7%\nWt-channel\n-8.9%\n+8.9%\n-2.0%\n+6.9%\nt\u00aft\n-6.4%\n+6.8%\n-3.1%\n+5.9%\nWb\u00afb\n-4.0%\n+8.9%\n-12.6%\n+12.7%\nW+jets\n-1.6%\n+2.5%\n-9.9%\n+14.6%\nTotal bkgd.\n-4.6%\n+6.1%\n-4.8%\n+8.1%\nThe uncertainty in the b-tagging performance and jet energy scale can have crucial effects on the\nmeasured cross section since we rely on jet kinematics to reduce the background. In particular, the\nlarge background contribution from t\u00aft can cause a large \ufb02uctuation on the total event rate with these\nuncertainties, which leads to a large error on the cross section measured. The jet energy scale uncertainty\naffects the pT distribution of jets strongly at the low end of the distribution. Cutting on pT in this region\ncan lead to a larger uncertainty on the signal acceptance. The effect of 5% variation of the b-tagging\nperformance has been considered together with the corresponding change in the mistag rate of non b-\ntagged jets. The effect of a 5% change of the jet energy scale determination (JES) has also been evaluated\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n956\n\non the ef\ufb01ciency. The impact of both effects on the selection is summarized in Table 3. It should be noted\nthat the Wb\u00afb and W+jets backgrounds are more affected by the jet energy scale due to the fact that most\nof the jets in these sample are in the low-pT region, which means that they are more likely to enter or\nleave the acceptance as the scale is changed.\nThe uncertainty due to the trigger requirements has been estimated by computing the variation in\nthe signal and background rates resulting from a bias of 1% in the inclusive lepton trigger ef\ufb01ciency.\nThis corresponds to the expected level of precision derived from turn on curves determination with the\nearly data. Similarly, a 1% uncertainty in the lepton identi\ufb01cation was considered and the corresponding\nimpact on the cross section measurement assessed. These two effects are expected to contribute to less\nthan 2% of the total uncertainty with 1fb\u22121.\nNote that for all those results, the limited statistics of the Monte Carlo samples may result in \ufb02uctu-\nations in the variable distributions used to discriminate signal from background events. The uncertainty\nassociated to the low statistics is found to be 6-8% with W+jets being the largest cotrigger requirements.\n4.2.2\nTheoretical and Monte Carlo systematic uncertainties\nSince the event selection relies heavily on the jet multiplicity, the number of additional jets from the\nparton shower can affect the selection ef\ufb01ciency. To evaluate the effect of ISR/FSR uncertainty, two sets\nof PYTHIA parameter variations were considered for comparison, which control the free parameters in\nthe underlying event, initial- and \ufb01nal-state radiation, showering, and multiple interactions. The varia-\ntions were combined to maximize the variation in the number of selected events to give a conservative\nestimate. The effect on the jet multiplicity is shown in Figure 2. It can be seen that the loose jet (pT\n> 15 GeV) distribution is affected more severely, which affects the selection ef\ufb01ciency due to the jet\nveto cut. The parameter variation set that gave the largest uncertainty leads to an overall uncertainty in\nthe t-channel selection ef\ufb01ciency of \u221211% +7%, and is quoted as a systematic uncertainty.\nNumber\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nEntries\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\nISR/FSR default\nISR/FSR 3/4jet\nISR/FSR 2/3jet\n \nATLAS\nNumber\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nEntries\n0\n1000\n2000\n3000\n4000\n5000\n6000\n \nATLAS\nFigure 2: Variation in t-channel multiplicity for the loose (pT > 15 GeV, left) and the tight (pT > 30\nGeV, right) jets due to ISR/FSR parameter variation. The distributions are shown without applying the\nt-channel selection cuts. The jet veto cut (\u22644 loose jets) and the requirement of b-tagged jet were also\nremoved for these plots to show the uncertainty over all multiplicities2. Black points are the nominal\nentries while the mesh band shows variation from \u201c3/4 jet parameter set\u201d and the \ufb01lled band shows\nthat of \u201c2/3\u201d, which are the two sets of parameter variations compared to study different jet multiplicity\nevents.\nThe uncertainty due to PDF was calculated using a re-weighting method together with error PDF\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n957\n\nsets provided by the PDF packages. While the event generation was done only for the central value PDF,\nweights were calculated in each event according to:\nw\u00b1\ni = f1(x1,Q;S\u00b1\ni )\u00b7 f2(x2,Q;S\u00b1\ni )\nf1(x1,Q;S0)\u00b7 f2(x2,Q;S0) ,\n(2)\nwhere, f1 and f2 are the PDF values for a given hard scattering process (characterized by \ufb02avors f\nand momentum fractions x of the initial partons, and by Q, the event energy scale) evaluated for the ith\nerror PDF pair S\u00b1\ni . The variation in ef\ufb01ciency was calculated by applying an event selection similar to\nthe preselection cuts at the generator level. The variations in ef\ufb01ciency were added using the Hessian\nformalism and the results from CTEQ and MRST PDF error sets [22] [23] were consistent. The effect of\nthe PDF uncertainty on the signal was evaluated to be +1.4% -1.1% and it is a minor contribution to the\n\ufb01nal systematics. A larger effect of +6.2% -5.5% was seen on the t\u00aft background. The PDF uncertainty\nwas estimated for the leading contribution from the t\u00aft process only.\nIn addition to the above, the t-channel process has a fairly large uncertainty from MC generator pre-\ndictions. Comparing various combinations of ME and PS generators, it was observed that the Pythia and\nHerwig parton shower algorithms give signi\ufb01cantly different jet multiplicities. While we assume that this\ndifference can be eliminated by tuning the parameters to the observed data3, the instability of theoretical\nprediction from matrix element generators is an outstanding issue and a 4.2% variation in signal accep-\ntance was seen by comparing AcerMC+Herwig and MC@NLO+Herwig. We quote this as an estimate\nfor systematic uncertainty from the theoretical prediction. In our present analysis, the background is es-\nTable 4: Summary of all uncertainties that affect the measured cross section, shown for the cut-\nbased analysis and the BDT analysis. \u201cData statistics\u201d represents the Poisson error one would\nexpect from real data\nSource\nAnalysis of 1 fb\u22121\nAnalysis of 10 fb\u22121\nVariation\nCut-based\nBDT\nVariation\nCut-based\nBDT\nData Statistics\n5.0%\n5.7 %\n1.6%\n1.8 %\nMC Statistics\n6.5 %\n7.9%\n2.0 %\n2.5%\nLuminosity\n5%\n18.3 %\n8.8%\n3%\n10.9 %\n5.2%\nb-tagging\n5%\n18.1 %\n6.6%\n3%\n10.9%\n3.9%\nJES\n5%\n21.6%\n9.9%\n1%\n4.4 %\n2.0%\nLepton ID\n0.4%\n1.5 %\n0.7%\n0.2%\n0.6 %\n0.3%\nTrigger\n1.0%\n1.7 %\n1.7%\n1.0%\n3.6 %\n1.7%\nBkg x-section\n22.9%\n8.2%\n6.9 %\n2.5%\nISR/FSR\n+7.2 -10.6%\n9.8 %\n9.4%\n+2.2 -3.2%\n2.7 %\n2.5%\nPDF\n+1.38 -1.07%\n12.3 %\n3.2%\n+1.38 -1.07%\n12.3 %\n3.2%\nMC Model\n4.2%\n4.2 %\n4.2%\n4.2%\n4.2 %\n4.2%\nTotal\n45%\n22%\n22%\n10%\ntimated from Monte Carlo and its normalization is currently estimated based on theoretical uncertainties.\nWhen data will be available, the t\u00aft and the W+jets backgrounds will be measured from data as well. It\n3The current tunings of Pythia and Herwig parton shower weres obtained independently based on extrapolation from the\nTevatron data. [24]\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n958\n\nis beyond the scope of this paper to discuss methods for the data-driven background estimation and the\nuncertainty from the background is currently estimated based on theoretical uncertainties.\n4.2.3\nSummary of uncertainties\nA large part of the \ufb01nal uncertainty is due to the overwhelming amount of t\u00aft background. For this\nreason, the event selection optimized for statistical signi\ufb01cance or statistical precision does not give the\nsmallest total uncertainty when systematics are included. Table 4 reports the uncertainties associated\nthe cross section determination. The total uncertainty is dominated by systematic effects related to the\nbackground normalization. Reducing the background contamination to increase signal to background\nratio would help to minimize the systematic uncertainty. It is therefore desirable to further optimize the\nselection beyond what can be achieved with simple cuts on the existing variables.\nNote that for an analysis based on 10 fb\u22121, the table reports the expected performance assuming a\nbetter understanding of the experimental aspects of the detection. Assuming a b-tagging ef\ufb01ciency known\nwith a precision of 3%, the jet energy scale determined at 1%, a luminosity known at 3% and a better\nunderstanding of the background to the 3% level and the radiation modeling at 3%, a total systematic\nuncertainty of 10% seems achievable for the BDT analysis.\n4.3\nMultivariate event selection\nIn the cut-based analysis no variable was found that was effective to reject the t\u00aft background. One\ncommonly employed separation technique is a Multivariate Analysis (MVA), which effectively factorizes\nthe process of cut optimization using a set of rules for separating the signal from the background events.\nIn the present analysis, an attempt to eliminate the remaining background contribution from t\u00aft makes use\nof the Boosted Decision Tree (BDT) method [25] within the TMVA [26] framework. The sample used is\nselected with the b-tagged jet pT cut selection, without applying the forward jet \u03b7 cut. This cut is indeed\neffective to reduce the t\u00aft contribution but not very ef\ufb01cient. About 40 object/event level variables were\nstudied using a genetic algorithm, which scanned a large number of variable sets. Extensive studies of this\nvariable sets revealed that a small subset of the variables can achieve signal to background discrimination\nclose to what was achieved using all variables. This set was further re\ufb01ned so that the chosen variables\nare not too sensitive to JES systematics:\n\u2022 pT of the leading b-tagged jet and non-b-tagged jet;\n\u2022 \u03b7 of the leading non-b-tagged jet and cos\u03b8 of the leading jet;\n\u2022 Centrality ( p jet0\nT\n+p jet1\nT\n|p|jet0+|p|jet1 );\n\u2022 Scalar sum of the pT of the two highest energy jets, the transverse missing energy /ET, and the\nlepton pT;\n\u2022 \u2206R between the two jets with the highest transverse mometum\n\u2022 \u2206R between the leading jet and the lepton;\n\u2022 \u2206R between the leading non-b-tagged jet and the lepton;\n\u2022 the lepton, and the W-boson transverse mass;\n\u2022 \u03b7 of the jet with largest |\u03b7|;\n\u2022 the number of jets with pT > 30 GeV.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n959\n\nFigure 3 (left) shows the BDT output discriminator constructed from the variables discussed above.\nBy cutting on a high value of the discriminator, the t\u00aft background can be removed more effectively than\nby cutting on individual input variables. Since the BDT was optimized for the t\u00aft separation, as expected\nthe output is not effective against W+jets. It can be seen in the right \ufb01gure that a high level of signal\npuri\ufb01cation is achieved using the BDT discriminator. We optimized the cut on the BDT output by min-\nBDT output\n-1\n-0.8\n-0.6\n-0.4\n-0 2\n0\n0.2\n0.4\n0.6\n0.8\n1\nEntries\n0\n500\n1000\n1500\n2000\n2500\n3000\nBDT output\n-1\n-0.8\n-0.6\n-0.4\n-0 2\n0\n0.2\n0.4\n0.6\n0.8\n1\nEntries\n0\n500\n1000\n1500\n2000\n2500\n3000\n \nt-channel\nWt-channel\ns-channel\ntt\nWbb\nWjets\nATLAS\nM (GeV)\n0\n50\n100\n150\n200\n250\n300\n350\n400\nEntries\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nM (GeV)\n0\n50\n100\n150\n200\n250\n300\n350\n400\nEntries\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n \nt-channel\nWt-channel\ns-channel\ntt\nWbb\nWjets\nATLAS\nFigure 3: Boosted decision tree output for signal and background after the b-tagged jet pT cut (left) and\nleptonic top quark mass distribution using cut on BDT output at 0.6 (right).\nimizing the \ufb01nal uncertainty on the measured cross section, including the systematic effects. For each\ncut, the systematic uncertainties were calculated assuming that the relative systematic uncertainty stays\nconstant for each channel for each source of uncertainty. This is a fairly reasonable assumption consid-\nering that the relative uncertainty changes slowly with the cuts and the variables were chosen to avoid\nlarger systematics. For most cut values, the systematic effects are dominant and the total uncertainty is\nreduced with increasing signal to background ratio. On the other hand, with very tight cuts the statistical\nerror becomes larger than systematics. The overall minimum was found to be at 0.6 where the signal to\nbackground ratio is 1.3 and 542 signal events are left as shown in Table 5. The reconstructed top mass\ndistrubution after applying BDT selection is shown in \ufb01gure 3 (right). The top mass was reconstructed\nfrom the lepton, /ET and the highest pT b-tagged jet. The W-boson mass was constrained to be 80.4\nGeV to obtain two solutions for neutrino kinematics and the one with the smaller pz was selected. The\nstatistical uncertainty is 5.7% while the total uncertainty is 22% as shown in Table 4.\nTable 5: Final event yield after the cut on BDT discriminator at 1fb\u22121.\nProcess\nt-channel\ns-channel\nWt-channel\nt\u00aft\nW+jets\nWb\u00afb\nS/B\nN(1fb\u22121)\n542\n3\n15\n184\n201\n10\n1.31\n4.4\nSensitivity at 1 fb\u22121 and the measurement of |Vtb|\nAlthough the estimated systematic uncertainty of the cut-based analysis is rather large (44.7%), it has\nbeen shown that this can be reduced by rejecting the t\u00aft background using boosted decision trees. The\ntotal uncertainty decreases as the S/B ratio increases and the estimated uncertainty at 1 fb\u22121 is\n\u2206\u03c3\n\u03c3 = \u00b15.7%stat \u00b122%sys = \u00b123%.\n(3)\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n960\n\nThe t-channel cross section is proportional to |fLVtb|2, where the parameter fL is the weak left-handed\ncoupling and fL = 1 in the Standard Model. In the theory predictions, the product |fLVtb|2 is always set\nto unity. Thus, if one measures the cross section, and then divides by the theoretical cross section, one\nobtains a measurement of |Vtb|2, making the Standard Model assumption that fL = 1 [27].\nThe relative uncertainty on Vtb is the relative uncertainty on |Vtb|2 divided by two since \u03b4|Vtb|/|Vtb| =\n\u03b4|Vtb|2/2|Vtb|2. However, there are additional systematic uncertainties in the Vtb measurement due to the\npresence of the theoretical cross section in the denominator. Here, we quote the uncertainty calculated\nin [7], in which a theoretical uncertainty of +3.8 \u22124.1% is reported including the contributions due\nto the strong scale, PDF and top quark mass uncertainties. We use the average of the positive and the\nnegative uncertainties. Therefore, the estimated uncertainty on the measured value of Vtb is\n\u2206|Vtb|\n|Vtb| = \u00b111%stat+sys \u00b14%theo = \u00b112%.\n(4)\n4.5\nSummary\nThe cross section measurement of the single top quark t-channel was studied in this chapter. The charac-\nteristics of the signal and background were investigated in detail and an analysis strategy was developed\n\ufb01rst using simple cuts and then using boosted decision trees.\nWhile a cut-based event selection can achieve a statistical precision of a few percent at an integrated\nluminosity of 1 fb\u22121, the t\u00aft background is dif\ufb01cult to reduce. This results in large systematic uncer-\ntainties coming from both experimental and theoretical origins. Uncertainties in the jet energy scale,\nb-tagging and luminosity all affect the measurement considerably. The uncertainty on the background\ncross section is also rather large though we expect that it will be constrained at higher accuracy with\nthe data. This is also true for the QCD background, which is not included in our current analysis. The\nresults shown are obtained on samples without any pile-up and no systematic uncertainty was associated\nto it. Data-driven background estimation methods should be developed once data is available. Among\nthe theoretical issues, the ISR/FSR uncertainty degrades the measurement more signi\ufb01cantly than other\ntheoretical effects such as the PDF and the Monte Carlo generator model.\nA multivariate background discrimination method is very effective in reducing the background and\nthus reducing the total uncertainty to nearly a half of the cut-based analysis. We conclude that multivari-\nate analysis tools are highly effective for a t-channel cross section measurement and further studies of\nthese techniques will be very bene\ufb01cial for the improvement of the analysis in the future. However, to\nreach a precision at a few percent level, studies of systematic uncertainties and an excellent understanding\nof the detector response will be necessary.\n5\nMeasurement of the s-channel cross section\nThe measurement of the single top quark s-channel appears the most delicate of the three main single-\ntop quark processes. Suffering from a low cross section compared to the main backgrounds, the event\ntopology makes this channel very sensitive to the presence of both t\u00aft and W+jets events. Because of\nthe low jet multiplicity of such events, the analysis is also expected to be sensitive to dijet production,\ndespite the tight requirements on the presence of at least two b jets. The s-channel is however one of the\nmost interesting because the production of tb \ufb01nal state events is directly sensitive to contributions from\nextra W-bosons or charged Higgs bosons as predicted in two Higgs doublet model (2HDM) [28].\nThe event selection is presented in three steps. A \ufb01rst one makes use of a standard cut-based analy-\nsis, and will serve as a reference with the early data. In a second step, likelihood functions designed to\nimprove the discrimination against speci\ufb01c backgrounds are presented together with the sets of discrim-\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n961\n\ninant variables that enter their de\ufb01nition. Finally, the selection criteria applied on those likelihoods are\nde\ufb01ned so that the total uncertainty affecting the cross section determination is minimized.\n5.1\nSequential cut analysis\nAfter applying the common preselection described in Section 3, only two b-tagged jet events with pT\nabove 30 GeV are selected, and a jet veto is applied on any other jet with a transverse momentum above\n15 GeV. This strong requirement is used to reject t\u00aft events which represent the dominant background\nto our signal at this stage. This set of requirements also reduces the W+jets and QCD multijet contam-\nination, since those events feature much softer b jets or no b jets at all. The selection also requires the\nopening angle \u2206R between the two jets to be between 0.5 and 4.0, the scalar sum of total jet transverse\nmomenta HT(jet) to be above 80 and below 220 GeV and \ufb01nally the sum of the transverse missing energy\n(/ET) and lepton transverse momentum (pT) to be in the range between 60 and 130 GeV.\nSelected event yields are reported in Table 6 for the three single top quark processes, and all t\u00aft\nand W+jets backgrounds. When adding all contributions, the overall signal ef\ufb01ciency is about 1.1% in\nthe electron channel and 1.6% in the muon channel. This corresponds to a total of about 25 selected\ncandidates for an integrated luminosity of 1 fb\u22121. The signal to background ratio is about 10%. The\ndominant background is composed of the t\u00aft events which account for about 60% of the total background\nyield. Among those, the t\u00aft in the lepton+jets mode, including \u03c4 decays, contribute about 40%. The\nremaining backgrounds originate from the Wb\u00afb+jets production, which constitutes about 14% of the\nbackground yield, and almost equally from the single top quark t-channel (11%) and W+jets (9%) events.\nAs expected, W+jets events are removed due to the requirement of b-tagged jets, with a \ufb01nal yield\ndepending upon the mistag rate. Diboson contributions (WW and WZ) are found to be negligible.\nTable 6: Event yield for signal and background for the cut-based analysis in the 2-jet multi-\nplicity bin for 1 fb\u22121. Uncertainties come from Monte Carlo statistics only. The convention\nl = e,\u00b5 is used.\nEvents in 1fb\u22121\ne channel\n\u00b5 channel\ne+ \u00b5 combined\ns-channel\n10.3 \u00b1 0.8\n14.5 \u00b1 1\n24.8 \u00b1 1.3\nt-channel\n17.0 \u00b1 5.7\n13.6 \u00b1 5.1\n30.6 \u00b1 7.9\nWt-channel\n6.5 \u00b1 1.9\n2.4 \u00b1 1.2\n8.9 \u00b1 2.3\nt\u00aft \u2192l+jets\n18.8 \u00b1 4.3\n20.5 \u00b1 5.3\n39.3 \u00b1 5.3\nt\u00aft \u2192ll\n29.0 \u00b1 5.5\n15.4 \u00b1 5.0\n44.4 \u00b1 7.4\nt\u00aft \u2192l\u03c4\n20.5 \u00b1 5.6\n40.9 \u00b1 6.9\n61.4 \u00b1 8.9\nWb\u00afb+jets\n18.9 \u00b1 2.0\n19.7 \u00b1 2.0\n40.6 \u00b1 2.5\nW+jets\n14.8 \u00b1 1.4\n11.0 \u00b1 2.2\n25.8 \u00b1 2.3\nTotal Bkg\n125.5\u00b1 10.3\n123.5 \u00b1 10.6\n251.0 \u00b1 14.2\nS/B\n8.2%\n11.7%\n9.8%\nS/\n\u221a\nB\n0.9\n1.3\n1.6\n\u221a\nS+B/S\n1.1\n0.8\n0.7\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n962\n\n5.2\nLikelihood selection\nThe cut based analysis shows that a simple approach to select single top quark s-channel events is ham-\npered by a high level of background. The use of a likelihood discriminator is aimed at improving the per-\nformance of the discrimination against backgrounds in order to purify the selected signal samples. This\napproach assumes that the distributions entering the de\ufb01nition of likelihood functions are well known\nand validated on data itself. This result can be achieved by cross-checking at every step the agreement\nbetween data and Monte Carlo distributions on selected sub-samples where a high level of t\u00aft and W+jets\nbackground is expected. In the following, only pre-selected events with exactly two jets, both of which\nare b tagged are considered. A jet veto on any other jet is applied.\n5.2.1\nDe\ufb01nition of the likelihood functions\nThe main background processes to our signal show very distinct features in the \ufb01nal state and topology\nthat lead us to de\ufb01ne several likelihood functions each devoted to the discrimination of a speci\ufb01c process:\nthree likelihood functions are devoted to t\u00aft events in the dilepton, the l+\u03c4 and the l+jets decay modes and\ntwo likelihood functions have been developed to discriminate against W+jets and t-channel events. Due\nto the limited Monte Carlo statistics, these likelihood discriminators have been de\ufb01ned by combining\nboth muon and electron channels.\nThe list of variables entering a likelihood function is derived from a procedure of optimization that\nselects only the variables that bring a signi\ufb01cant discrimination between signal and the considered back-\nground. The discriminating power of a given variable is computed using the selection ef\ufb01ciencies for\nboth signal and background in the plane (\u03b5S,\u03b5B). When the discriminating power of a variable is low, the\nvariation of the background ef\ufb01ciency \u03b5B follows that of the signal \u03b5S. On the contrary, a high discrim-\ninating variable results in a larger decrease of \u03b5B compared to the variation seen in \u03b5S. This variation,\ncomputed for each \u03b5S and integrated over the full range of \u03b5S can thus be seen as an estimator of the\ndiscriminating power of the variable. In this analysis, the variable is selected if the discriminating power\nis about a few percent. The use of higher thresholds results in a degradation of the performance due to\nthe loss of discriminating power of the formed likelihoods. The set of discriminant variables is built from\n16 relevant kinematical variables:\n\u2022 the opening angles between the lepton and the jets \u2206R(l,b1), \u2206R(l,b2)\n\u2022 the angles cos\u2206\u03a6(l,b1) and cos\u2206\u03a6(l,b2);\n\u2022 the opening angle between the two b tagged jets \u2206R(b1,b2);\n\u2022 the pseudo-rapidity of the b tagged jets \u03b7b1 and \u03b7b2;\n\u2022 the invariant mass formed by the systems of the two b tagged jets Minv(b1,b2)\n\u2022 the invariant mass formed by the reconstructed W leptonic boson and the b tagged jets M(Wlep,b1)\nand M(Wlep,b2);\n\u2022 the transverse momentum of the reconstructed top quark candidates pT (top1) and pT (top2)\n\u2022 the sum of the missing transverse energy and lepton transverse momentum /ET+ pT (l);\n\u2022 the transverse mass of the leptonic W-boson candidate MT(Wlep);\n\u2022 the scalar sum of the jet transverse momenta HT(jets);\n\u2022 global event shape variables: sphericity, aplanarity and centrality.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n963\n\nlikelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n combined]\n\u00b5\n[e+\n l+jets\n\u2192\n t\na) Likelihood W* vs t\n \n-1\nNumber of events in L=1fb\ns-channel \n\u2022\nWt-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n)\n\u00b5\n l+jets (l=e,\n\u2192\nWbb \n)\n\u00b5\n l+jets (l=e,\n\u2192\nWjj \nlikelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 9\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\nATLAS\n combined]\n\u00b5\n[e+\n dilepton\n\u2192\n t\nb) Likelihood W* vs t\n \n-1\nNumber of events in L=1fb\ns-channel \n\u2022\nWt-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n)\n\u00b5\n l+jets (l=e,\n\u2192\nWbb \n)\n\u00b5\n l+jets (l=e,\n\u2192\nWjj \nlikelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nNumber of events\n0\n50\n100\n150\n200\n250\nATLAS\n combined]\n\u00b5\n[e+\n \u03c4 \u03c4\n / \n\u03c4\n l+\n\u2192\n t\nc) Likelihood W* vs t\n \n-1\nNumber of events in L=1fb\ns-channel \n\u2022\nWt-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n)\n\u00b5\n l+jets (l=e,\n\u2192\nWbb \n)\n\u00b5\n l+jets (l=e,\n\u2192\nWjj \nlikelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 9\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\nATLAS\n combined]\n\u00b5\n[e+\n l+jets\n\u2192\nd) Likelihood W* vs W \n \n-1\nNumber of events in L=1fb\ns-channel \n\u2022\nWt-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n)\n\u00b5\n l+jets (l=e,\n\u2192\nWbb \n)\n\u00b5\n l+jets (l=e,\n\u2192\nWjj \nlikelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nATLAS\n combined]\n\u00b5\n[e+\ne) Likelihood W* vs t-channel \n \n-1\nNumber of events in L=1fb\ns-channel \n\u2022\nWt-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n)\n\u00b5\n l+jets (l=e,\n\u2192\nWbb \n)\n\u00b5\n l+jets (l=e,\n\u2192\nWjj \nFigure 4: Distributions of the \ufb01ve likelihood functions for an integrated luminosity of 1fb\u22121. a) Like-\nlihood against t\u00aft in the l+jets channel; b) Likelihood against t\u00aft in the dilepton channel; c) Likelihood\nagainst t\u00aft in the l + \u03c4 channel; d) Likelihood against W+jets events; e) Likelihood against t-channel\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n964\n\n5.2.2\nOptimization of the likelihood selection\nThe likelihood function distributions corresponding to an integrated luminosity of 1 fb\u22121 are shown in\nFigure 4. Thresholds have been applied on each of the 5 likelihood values. In the present analysis, the\nthresholds on the likelihood values have been set so that the total uncertainty affecting the cross section\nmeasurement is minimized. The total uncertainty was calculated as described in Section 4.2.3. The main\nsources of systematic errors taken into account are the b-tagging ef\ufb01ciency, jet energy scale, luminosity\nand uncertainties on the background level, for which central values are provided in Section 5.3. Note that\nwe consider the errors as fully correlated between signal and background for jet energy scale, b-tagging,\nand luminosity.\nThe thresholds set on the \ufb01ve likelihood outputs resulting from the minimization of the total uncer-\ntainty are listed below:\nLt\u00aft/lepton+jets > 0.34,\nLt\u00aft/dilepton > 0.56,\nLt\u00aft/\u03c4+lepton > 0.80,\nLW+jets > 0.32,\nLt\u2212channel > 0.46\nTable 7 reports the number of events expected for all signal and backgrounds for an integrated lu-\nminosity of 1 fb\u22121. The overall signal to background ratio is improved signi\ufb01cantly compared to the\nsequential cuts analysis with a purity increased from 9.8% to 18.7%. This is an expected outcome of the\noptimization procedure since the main source of errors comes from the uncertainties in the background.\nTable 7: Numbers of expected events for an integrated luminosity of 1 fb\u22121 expected from\nthe likelihood analysis in the two jet \ufb01nal state events. The results are shown separately\nfor the electron and muon channels. Statistical uncertainties correspond to the Monte Carlo\nstatistics only. The convention l = e,\u00b5 is used.\nEvents in 1fb\u22121\ne channel\n\u00b5 channel\ne+ \u00b5 combined\ns-channel\n6.3 \u00b1 0.7\n9.1 \u00b1 0.8\n15.4 \u00b1 1.0\nt-channel\nnegl.\n1.7 \u00b1 1.7\n1.7 \u00b1 1.7\nWt-channel\n1.8 \u00b1 1.0\nnegl.\n1.8 \u00b1 1.0\nt\u00aft \u2192l+jets\n7.6 \u00b1 2.6\n7.7 \u00b1 3.5\n15.3 \u00b1 4.4\nt\u00aft \u2192ll\n6.0 \u00b1 2.6\n6.0 \u00b1 2.6\n12.0 \u00b1 3.8\nt\u00aft \u2192l+\u03c4\n6.8 \u00b1 3.4\n14.5 \u00b1 4.1\n21.3 \u00b1 5.3\nWb\u00afb+jets\n10.0 \u00b1 3.2\n7.0 \u00b1 2.6\n17.0 \u00b1 4.1\nW+jets\n6.2 \u00b1 1.2\n7.3 \u00b1 2.1\n13.5 \u00b1 2.4\nWZ+WW\nnegl.\nnegl.\nnegl.\nTotal Bkg\n36.8 \u00b1 5.8\n45.9 \u00b1 6.6\n82.7 \u00b1 8.6\nS/B\n17.3%\n19.8%\n18.7%\nS/\n\u221a\nB\n1.0\n1.3\n1.7\n\u221a\nS+B/S\n1.0\n0.8\n0.6\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n965\n\nThe dominant background comes from t\u00aft production, which contributes about 60% of the total event\nyield. Among those events, the main contribution originates from the l+\u03c4 decay modes (l=e,\u00b5), which\ncorresponds to 45% of the t\u00aft yield, followed by the dilepton and the l+jets channels. The production of\nWb\u00afb+jets represents about 20%, while the W+jets events still contribute 16% of the total background\nyield. Finally, the contamination originating from the other single top quark channels is smaller than the\nsignal expected event yield with a contribution of 4% from the sum of t- and Wt- channels. The results\nshow a similar statistical sensitivity compared to the standard cut-based analysis, with an improved signal\nto background ratio.\nAs described in Section 4.1 the presence of pile-up affects the reconstruction of the objects selected\nin the event. The use of events with pile-up results in a decrease of about 9% for signal events, and 15%\nfor t\u00aft events. No systematic uncertainty is associated to this difference, as t\u00aft events completely dominate\nthe selected sample. Dedicated studies with data will be used to tune all Monte Carlo generators.\n5.3\nSystematic uncertainties\nThe systematic uncertainties have been evaluated on the likelihood analysis. We follow the procedures\nde\ufb01ned in Section 4.2.\n5.3.1\nExperimental systematic uncertainties\nThe uncertainties on the b-tagging ef\ufb01ciency and the mistag rates have been estimated by varying the b\nweight cut value corresponding to a change of \u00b15% in the b-tag ef\ufb01ciency with respect to the reference\nvalue of 60%. Table 8 shows the impact of such effects on signal and background events. As the b-\ntag ef\ufb01ciency is varied by +5% and -5%, the signal selection ef\ufb01ciency is shifted by 7.1% and -7.7%\nrespectively. For background events, the impact of such variations result in both cases in an increase\nof the background level which reaches +15% and +5% respectively because of the change affecting the\nmistag rates. Table 9 reports the impact on the total cross-section determination. The understanding of\nthe b-tagging performance completely drives the analysis strategy.\nTable 8: Effect of the main systematic effects, b-tag ef\ufb01ciency and mistag rate variation and of the jet\nenergy scale variation on the number of expected events for an integrated luminosity of 1 fb\u22121 expected\nfrom the likelihood analysis in the two jet \ufb01nal state events. Numbers in parentheses are the relative\nvariations.\nEvents in 1fb\u22121\nb-tag -5%\nb-tag +5%\nJES -5%\nJES +5%\ns-channel\n14.2 (-7.7%)\n16.5( +7.1%)\n16.9 (+9.7%)\n15.4 (negl.)\nt and Wt-channel\n6.9 (+97%)\n3.5 (negl.)\n5.1 (+45%)\n5.1 (+45%)\nt\u00aft combined\n47.8 (-1.6%)\n58.1 (+19.5%)\n49.5 (+1.8%)\n46.9 (-3.5%)\nWb\u00afb+jets\n15.5 (-8.8%)\n16.4 (-3.5%)\n17.0 (negl.)\n17.0 (negl.)\nW+jets\n17.0 (+26%)\n17.0 (+26%)\n15.4 (+14%)\n15.1 (+11.8%)\nTotal bkg\n87.2 (+5.4%)\n94.9 (+14.8%)\n87.7 (+6%)\n84.9 (+2.6%)\nA variation of -5% and +5% of the jet energy scale has been propagated to the jet reconstruction\nand the selection ef\ufb01ciencies were re-assessed. Backgrounds change by about 6% and 3% respectively,\nwhile the signal acceptance is found to vary by about \u00b110%. Again, in both cases the background is\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n966\n\nincreased with any change of the jet energy scale. Indeed, as the jet scale factor is decreased, top quark\npair events in the dilepton and l+jets modes tend to have a lower multiplicity, resulting in an increased\ncontamination. As the scale factor goes up, the low multiplicity events are favored while top quark pair\nproduction is almost not affected. Table 8 shows the effects of the jet energy scale variation on the signal\nand background event yield.\nThe impact of the trigger ef\ufb01ciency and lepton identi\ufb01cation uncertainties has been estimated as\nexplained in the t-channel Section. This re\ufb02ects as an uncertainty of 6% on the total cross-section mea-\nsurement. Table 9 reports the impact on the total cross-section determination.\nTable 9: Summary of all uncertainties that affect the measured cross section. Data statistics\nis the Poisson error one would expect from real data while MC Statistics is the uncertainty\non the estimated quantities due to MC statistics.\nSource of\nAnalysis for 1 fb\u22121\nAnalysis for 10 fb\u22121\nuncertainty\nVariation\n\u2206\u03c3/\u03c3\nVariation\n\u2206\u03c3/\u03c3\nData Statistics\n64%\n20%\nMC Statistics\n29%\nLuminosity\n5%\n31%\n3%\n18%\nb-tagging\n5%\n44%\n3%\n25%\nJES\n5%\n25%\n1%\n5%\nLepton ID\n1%\n6%\n1%\n6%\nBkg x-section\n10.3%\n47%\n3%\n16%\nISR/FSR\n9%\n52%\n3%\n17%\nPDF\n2%\n16%\n2%\n16%\nb-fragmentation\n3.6%\n19%\n3.6%\n19%\nTotal Systematics\n95%\n48%\n5.3.2\nTheoretical and Monte Carlo systematic uncertainties\nIn the present analysis, uncertainties on the background estimates come from the theoretical uncertainties\nassociated with their cross section. The main background contributions are t\u00aft (60%), Wb\u00afb+jets (20%)\nand W+jets (16%), so 10% uncertainties on the t\u00aft cross-section prediction and 20% on the W+jets and\nWb\u00afb+jets events lead to a total of 10.3% uncertainty on the total background. The understanding of the\nbackground level is thus a crucial point for a precise cross-section determination. Note that despite very\ndistinct topologies, the selections of the s-, t- and Wt- channels analyses are not orthogonal. However it\nis believed that correlations can be properly addressed with dedicated study and enough statistics.\nThe selection of a 2-jet \ufb01nal state is very sensitive to the presence of extra jets originating from gluon\nradiation. Any uncertainty in the ISR/FSR modeling is thus expected to have a signi\ufb01cant impact on the\nselection ef\ufb01ciencies, in particular for the s-channel and the t\u00aft events. Speci\ufb01c Monte Carlo samples\nhave been generated with ISR/FSR settings leading to the largest cross section variations. Variations of\n5% of the signal selection ef\ufb01ciencies are expected, and are due to the change in the jet multiplicity.\nThe uncertainties however reach large values for the t\u00aft production, with variations of 17.8% between\nthe two extreme cases. Note that these variations have been assessed with non-calibrated jets, although\nthere is a high expected correlation between jet energy scale and ISR/FSR gluon modeling. An overall\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n967\n\n9% uncertainty corresponding to half the variation is quoted. Note that the s-channel being produced via\nquark-antiquark annihilation, some constraints coming from the use of W-boson events should allow the\ntuning of the showering interfaces.\nAnother uncertainty is related to the choice of the PDFs. The procedures used to assess the impact of\nsuch choice is presented in Section 4.2.2. The expected bias on the signal is below 3% while this number\nis below 2% for t\u00aft events.\nFinally the effect of the b-fragmentation parametrization has also been investigated using fast simu-\nlation. The b quark fragmentation is performed according to the Peterson parametrization, with one free\nparameter \u03b5b. Varying the default value from \u03b5b = \u22120.006 by \u00b10.0025 [29] and taking the difference as\na systematic uncertainty leads to a change of 3.6% in the t\u00aft and signal selection ef\ufb01ciencies.\nTable 9 lists all sources of uncertainties and reports their impact on the cross-section determination.\nTwo cases are considered: one de\ufb01ned by the level of uncertainty in the b-tagging, JES, luminosity\nthat will presumably characterize the early data taking period and a second one assuming a reasonable\nimprovement on those effects with an integrated luminosity of 10 fb\u22121. The assumptions made in the\nlatter case are the same as the ones listed in Section 4.2.3.\n5.4\nSummary\nThe determination of the s-channel cross section constitutes a challenging measurement, due to the pres-\nence of large backgrounds from the t\u00aft production and from the W+jets channels. With an expected\nsignal to background ratio of 18% the measurement will be hampered not only by a signi\ufb01cant statistical\nuncertainty but also by the systematic effects affecting both signal and background. The measurement\nwith an integrated luminosity of 1 fb\u22121 is thus both statistically and systematically limited, with about\n60% of statistical and 90% of systematic uncertainties.\nGiven the present limitation on the background knowledge, early measurements will have to be\ndevoted to the understanding of the background, in terms of shape and absolute normalization. For\nthis purpose, speci\ufb01c studies performed on enriched background samples can be used. In this area, the\nknowledge of the effects of the ISR/FSR gluon radiation will need dedicated studies, in particular in\nt\u00aft events. The constraint from data itself will thus be very important, and a tuning `a la CDF [30] will\nbe crucial for the understanding of these radiations. From the detector side, a reliable cross-section\nmeasurement requires a good knowledge of the b-tagging tools performance, since double-tag events are\nconsidered. A good determination of the jet energy scale is also mandatory for the selection, at the level\nof better than 5%. PDF and b-fragmentation effects are expected to have a signi\ufb01cant impact only at\nhigher luminosity.\nIn this context, the use of sophisticated statistical methods appears mandatory to discriminate the\nsignal from the background and to establish convincing evidence for a signal. Their use however requires\nan a priori good understanding of the background normalization and shapes. With an improved situation\nfor the b-tagging and jet energy scale, with a background normalization determined from the data and a\nbetter ISR/FSR knowledge, evidence at 3 \u03c3 should be achievable with 30 fb\u22121.\n6\nMeasurement of the Wt-channel cross section\nThe Wt-channel is characterized by the associated production of a top quark and a W-boson. At the\nLHC, this single top quark process is the second highest cross-section after t-channel production, with\nan expected cross section of 66 pb. The \ufb01nal state features two W-bosons and a b jet, making this channel\nexperimentally very close to top quark pair production, from which it differs by the absence of a second\nb jet in the \ufb01nal state. With a cross section 15 times larger than the Wt-channel processes, top quark pair\nevents will thus constitute the dominant source of backgrounds and drive the de\ufb01nition of the selection\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n968\n\ncriteria in higher jet multiplicity events. On the other hand, low jet multiplicity events will suffer from\nW+jets contamination. In this report, we consider only the case where one of the two bosons decays into\nleptons while the other decays into jets. Two approaches have been used to estimate the sensitivity to the\nWt-channel cross section measurement: a sequential cut-based analysis, which will provide reference\nnumbers, and an analysis based on the use of Boosted Decision Trees.\n6.1\nSequential cuts analysis\nThe common preselection de\ufb01ned for all three single top quark processes has been extended further to\naccount for the speci\ufb01c topology of Wt-channel events. Selected events must have exactly one high pT\nb-tagged jet above 50 GeV. A veto on any other b tagged jet above 35 GeV is applied in order to reject\nt\u00aft events. This b-tag veto utilizes a looser b-tag weight cut which has been optimized according to the\nsignal over t\u00aft background ratio: a ratio of 18% is reached in 2- and 3- jet \ufb01nal states events while 14%\nis found in 4-jet events. The corresponding ef\ufb01ciency is about 30% on signal events and 10% on t\u00aft\nevents. For events containing more than three high pT jets, the selection requires that the invariant mass\nof the two highest pT non b-tagged jets to be between 50 and 125 GeV. The number of selected events is\nreported in Table 10 for signal and backgrounds.\nTable 10: Number of expected events for an integrated luminosity of 1 fb\u22121 as function\nof the jet multiplicity and for the electron and muon channel combined in the sequential\ncut-based analysis. Errors shown are statistical only. The convention l = e,\u00b5 is used.\nEvents in 1fb\u22121\n2 jets (1b1j)\n3 jets (1b2j)\n4 jets (1b3j)\nWt-channel\n435 \u00b1 16\n164\u00b1 10\n40\u00b1 5\nt-channel\n1218 \u00b1 47\n94 \u00b1 13\n58 \u00b1 11\ns-channel\n42 \u00b1 2\n5 \u00b1 0.6\n0.6 \u00b1 0.2\nt\u00aft \u2192l+jets\n1260 \u00b1 38\n664 \u00b1 27\n240 \u00b1 16\nt\u00aft \u2192dilepton\n291 \u00b1 18\n50 \u00b1 7\n17 \u00b1 4\nt\u00aft \u2192l+\u03c4\n428 \u00b1 22\n55 \u00b1 8\n17 \u00b1 5\nW+jets\n2983 \u00b1 71\n207 \u00b1 19\n38 \u00b1 6\nWb\u00afb+jets\n137 \u00b1 33\n13 \u00b1 3\n6 \u00b1 2\nTOTAL bkg\n6359 \u00b1 232\n1088 \u00b1 74\n377 \u00b1 42\nS/B\n6.8%\n15.0%\n10.6%\nS/\n\u221a\nB\n5.4\n5.0\n2.1\n\u221a\nS+B/S\n0.19\n0.21\n0.51\nIn two jet events (labeled as \u20181b1j\u2019), the signal yield is about 430 signal events for an integrated lumi-\nnosity of 1 fb\u22121, with a signal to background ratio of 6.8%, combining both electron and muon channels.\nThe W+jets production is the dominant background with more than 45% of the total background yield.\nThe t\u00aft contamination in the l+jets channel constitutes about 20% of the background, while the other t\u00aft\nmodes combined contribute 11%. In this low jet multiplicity bin, the single top quark t-channel contam-\nination is signi\ufb01cant and represents 19% of the total.\nIn the three jet \ufb01nal state events (labeled as \u20181b2j\u2019), 160 signal events are expected in 1 fb\u22121, with\na signal to background ratio close to 15%. In this \ufb01nal state, the use of the hadronic W boson mass\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n969\n\nconstraint helps improve the rejection of W+jets and the other single top quark events. The background\nis made up of t\u00aft events which represent 70% of the total background yield, and of about 20% of W+jets\nevents. Among the t\u00aft events, the l+jets mode is dominant and constitutes about 85% of the total.\nThe four jet \ufb01nal state events (labeled as \u20181b3j\u2019) only bring a marginal improvement to the analysis.\nThe number of expected Wt-channel single top quark events is small and expected to be 40 for 1 fb\u22121\nwith a signal to background ratio of 10.6%. In this high jet multiplicity bin, the main background comes\nfrom the t\u00aft events in the l+jets mode, which constitute 64% of the background. The rest originate mostly\nfrom the single top quark t-channel and from W+jets events, each being of the same order as the signal.\n6.2\nBoosted decision tree analysis\nAs in the s-channel analysis, several multivariate discriminators have been de\ufb01ned to optimize the dis-\ncrimination against backgrounds. Two Boosted Decision Tree (BDT) functions are de\ufb01ned to separate\nsignal and t\u00aft events, one devoted to the discrimination from the dominant l+jets channel Dt\u00aft/l+jets, and\nthe other against the dilepton channels Dt\u00aft/dilepton including \u03c4\u2019s. A function DW+jets has been formed to\nseparate signal from the W+jets sample, de\ufb01ned as the total contribution from light and heavy \ufb02avor jets.\nAnother BDT discriminator is devoted to the separation of the signal and the single top quark t-channel\nevents Dt\u2212channel. The analysis being based upon events with jet multiplicity between two and four, spe-\nci\ufb01c BDTs have been de\ufb01ned in each jet multiplicity bin for each background. The electron and muon\nchannels are being treated in a combined way, thus leading to the de\ufb01nition of 3 (jet multiplicity) x 4\n(background) ie: 12 BDT discriminators in total.\n6.2.1\nDe\ufb01nition of the discriminant variables\nThe set of discriminant variables is derived from the same procedure of optimization as the one explained\nfor the s-channel analysis. The \ufb01nal set of discriminant variables is built from 25 relevant kinematical\nvariables:\n\u2022 the opening angles between the lepton and the jets \u2206R(l,b), \u2206R(l, j1), \u2206R(l, j2) where j1, j2 and\nj3 are the non b-tagged pT ordered jets\n\u2022 the opening angle between the jets \u2206R(b, j1), \u2206R(b, j2), \u2206R(j1, j2);\n\u2022 the angles cos\u2206\u03a6(j1, j2) and the pseudo-rapidity of the non b-tagged jets \u03b7j2 and \u03b7j3;\n\u2022 the invariant mass formed by the sum of all jets Minv(jets) and by the reconstructed W-boson and\ntop quark candidates M(W +t);\n\u2022 the mass of the hadronic W-boson candidate M(Whad);\n\u2022 the sum of the missing transverse energy and lepton transverse momentum /ET+ pT(l);\n\u2022 the transverse mass of the leptonic W-boson candidate MT(Wlep)\n\u2022 the transverse mass of the systems formed by the b jet and the reconstructed W-bosons M(b,Whad)\nand M(b,Wlep);\n\u2022 the scalar sum of the jet transverse momenta HT(jets) and of all objects in the events HT(tot);\n\u2022 the transverse jet momenta pT (b), pT(j1), pT(j2);\n\u2022 the longitudinal momentum of the neutrino solution computed with the top quark mass;\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n970\n\n\u2022 the global event shape variables, sphericity, aplanarity and centrality.\nThe BDT output distributions associated to each of the four backgrounds are represented in Figure 5 for\nthe 3 jet \ufb01nal state analysis for the electron+muon channels for 1 fb\u22121.\nBDT output\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\nATLAS\n combined]\n\u00b5\n[e+\n l+jets\n\u2192\n t\na) BDT for W+t vs t\n \n-1\nNumber of events in L=1fb\nWt-channel \n\u2022\ns-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n l+jets \n\u2192\nWbb \n l+jets \n\u2192\nWjj \nBDT output\n-1\n-0 8 -0.6 -0.4 -0 2\n0\n0.2\n0.4\n0.6\n0 8\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nATLAS\n combined]\n\u00b5\n[e+\nb) BDT for W+t vs W+jets \n \n-1\nNumber of events in L=1fb\nWt-channel \n\u2022\ns-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n l+jets \n\u2192\nWbb \n l+jets \n\u2192\nWjj \nBDT output\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nATLAS\n combined]\n\u00b5\n[e+\n dilepton\n\u2192\n t\nc) BDT for W+t vs t\n \n-1\nNumber of events in L=1fb\nWt-channel \n\u2022\ns-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4\n / \n\u03c4\n l+\n\u2192\n tt\n l+jets \n\u2192\nWbb \n l+jets \n\u2192\nWjj \nBDT output\n-1\n-0 8 -0.6 -0.4 -0 2\n0\n0.2\n0.4\n0.6\n0 8\n1\nNumber of events\n0\n20\n40\n60\n80\n100\n120\n140\nATLAS\n combined]\n\u00b5\n[e+\nd) BDT for W+t vs t-channel \n \n-1\nNumber of events in L=1fb\nWt-channel \n\u2022\ns-channel \nt-channel \n) \n\u00b5\n l+jets (l=e,\n\u2192\n tt\n) \n\u00b5\n l l (l=e,\n\u2192\n tt\n+jets \n\u03c4\n / \n\u03c4\n+\n\u03c4/ \n\u03c4\n l+\n\u2192\n tt\n l+jets \n\u2192\nWbb \n l+jets \n\u2192\nWjj \nFigure 5: Distributions for the four BDT de\ufb01ned in the 3 jet (\u20191b2j\u2019) \ufb01nal state analysis. a) BDT against\nt\u00aft in the \u2018l+jets\u2019 channel; b) BDT against W+jets events; c) BDT against t\u00aft in the dilepton lepton (+tau)\nchannel; d) BDT against single top quark t-channel events.\n6.2.2\nResults with the Boosted Decision Trees\nSeveral selections can be designed, allowing for different levels of signal purity. In this analysis as in\nthe s-channel, the cuts on the discriminant BDTs have been set so that the total uncertainty affecting the\ncross section measurement is minimized.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n971\n\nThe thresholds set on the three BDT outputs are:\nDttlj > 0.6\nDttl\u03c4 > \u22120.36\nDWjet > 0.30\nDt\u2212chan > 0.18\nThe number of events for signal and the different backgrounds is reported in Table 11 for an integrated\nluminosity of 1 fb\u22121. In two jet events (\u20181b1j\u2019), the signal yield is about 60 with a signal to background\nratio of 35%, combining electron and muon analyses. This result represents an improvement by a factor 6\ncompared to the cut-based analysis. This feature is important since one of the main sources of systematic\nuncertainty originate from the imperfect knowledge of the background levels. Regarding the composition\nof the background, the W+jets production constitutes the dominant background and contributes 58%\nof the background yield. t\u00aft production in the l+jets mode represents about 40% of the total. The\nonly remaining single top quark events originate from the t-channel which accounts for 6% of the total\nbackground yield. The statistical signi\ufb01cance for this \ufb01nal state analysis alone is 4.5\u03c3.\nTable 11: Number of expected events for an integrated luminosity of 1 fb\u22121 as function of\nthe jet multiplicity after the BDT analysis. The convention l = e,\u00b5 is used.\nEvents in 1fb\u22121\n2 jet (1b1j)\n3 jet (1b2j)\n4 jet (1b3j)\nWt-channel\n58.0 \u00b1 5.8\n20.9 \u00b1 3.5\n6.6 \u00b1 2.0\nt-channel\n10.2 \u00b1 4.2\nnegl.\n1.7 \u00b1 1.7\ns-channel\n1.4 \u00b1 0.3\nnegl.\nnegl.\nt\u00aft \u2192all jet\nnegl.\nnegl.\nnegl.\nt\u00aft \u2192l + jet\n56.3 \u00b1 8.2\n41.8 \u00b1 6.3\n13.7 \u00b1 3.4\nt\u00aft \u2192dilepton\n1.7 \u00b1 1.2\nnegl.\nnegl.\nt\u00aft \u2192l +\u03c4\nnegl.\nnegl.\nnegl.\nW+jets\n92.1 \u00b1 8\n3.2 \u00b1 1.4\n0.2 \u00b1 0.1\nWb\u00afb+jets\n3.9 \u00b1 3.9\nnegl.\nnegl.\nTotal bkg\n165.6 \u00b1 9.2\n45.1 \u00b1 6.3\n15.6 \u00b13.4\nS/B\n35.0%\n46%\n36.2%\nS/\n\u221a\nB\n4.5\n3.1\n1.7\n\u221a\nS+B/S\n0.25\n0.39\n0.71\nIn three jet \ufb01nal state events (\u20181b2j\u2019), about 20 signal events are expected with 1 fb\u22121, with a signal\nto background ratio of 46%. Again, one notices a gain of more than a factor 3 compared to the cut-based\nanalysis. The background events are made up almost exclusively (95%) of t\u00aft events in the lepton+jets\nevents. The use of the jet-jet invariant mass reduces the W+jets background to a few percent. The\nselection in this \ufb01nal state alone provides a signal statistical signi\ufb01cance of 3.1 \u03c3.\nIn the four jet \ufb01nal state channel (\u20181b3j\u2019), the number of expected Wt-channel single top quark events\nis 7 with 1 fb\u22121. In this bin, the signal to background ratio is about 36%, which corresponds to a gain of a\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n972\n\nfactor 4 compared to the sequential cut analysis. In this jet multiplicity bin, the only competing processes\nis the t\u00aft events in the l+jets. The signal signi\ufb01cance remains small, around 1.7\u03c3 with a corresponding\nstatistical precision of 72%.\nThe effect of pile-up has been investigated with signal and t\u00aft samples produced with a pile-up\ncorresponding to a 1032 cm2s\u22121 luminosity run. The results show decreases of 18%, 47% and 26% of the\nsignal event yield in the 2, 3 and 4 jet \ufb01nal states. For backgrounds, similar variations of 16%, 39% and\n20% in the 2, 3 and 4 jet \ufb01nal states are seen. As expected the increase of the number of light jets seen\nin the events directly impacts the tight selection of 2- and 3- jet \ufb01nal states. No systematic uncertainty is\nassociated to this effect, as for the two previous analyses, as only dedicated studies using data itself will\nbe used to tune all Monte Carlo signal and background generators.\n6.3\nSystematic uncertainties\nThe systematic uncertainties have been evaluated on the BDT analysis. We follow the procedures de\ufb01ned\nin Section 4.2.\n6.3.1\nExperimental systematic uncertainties\nThe b-tagging uncertainties affect the Wt-channel selection because of the requirement of one b-tagged\njet on one side, and the use of a veto for any second b tagged jet on the other side. The variation by\n5% of the b tagging ef\ufb01ciency and the corresponding mistag rate results in a 7% change of the signal\nselection ef\ufb01ciency in the 2 jet \ufb01nal state. The sensitivity is higher in the higher multiplicity bins, with\neffects of 10% seen in the 3 jet bin. Regarding backgrounds, the impact of this uncertainty increases with\nthe jet multiplicity, with t\u00aft events being the dominant background. Variations of 3% and 5% are seen\nrespectively in 3 jet and 4 jet \ufb01nal states. Table 12 reports the relative changes in signal and background\nevents. Table 13 reports the impact on the total cross section determination, all \ufb01nal states combined.\nTable 12: Effect of the b-tag ef\ufb01ciency and mistag rate variation and of the jet energy scale\nvariation on the number of expected events for an integrated luminosity of 1 fb\u22121 expected\nfrom the BDT analysis.\nProcess\nEvents in 1fb\u22121\nb-tag \u00b1 5%\nJES \u00b1 5%\n2-jet events\n- signal\n58.0\n\u00b1 7.0%\n\u00b10.5%\n- total bkg\n165.6\n\u00b1 3.0%\n\u00b13.1%\n3 jet events\n- signal\n20.9\n\u00b110.1%\n\u00b17.0%\n- total bkg\n45.1\n\u00b13.2%\n\u00b13.0%\n4 jet events\n- signal\n6.6\n\u00b13.1%\n\u00b17.9%\n- total bkg\n15.6\n\u00b15.1%\n\u00b14.0%\nThe precise knowledge of the jet energy scale is important for the Wt-channel analysis because of\nthe requirements made on the mass reconstruction and pT thresholds used to select jets. A 5% variation\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n973\n\nof the jet energy scale has been propagated to the jet reconstruction and the selection ef\ufb01ciencies are\nre-assessed. Table 12 shows the impact of the jet energy scale variation on signal and background event\nyields. In two jet events, the effects of the scale variation is about 1% on the signal events and 3% on the\nsum of all backgrounds. In three jet events a variation of 7% of the signal event yield is observed, with\na change of 3% in the backgrounds. In four jet events, variations of 8% and 4% are seen in signal and\nbackground respectively. Table 13 reports the impact on the total cross section determination.\nAn uncertainty of 1% in the lepton identi\ufb01cation or in the trigger ef\ufb01ciency would impact the number\nof selected events. Such an uncertainty would re\ufb02ect in an uncertainty of 2.6% on the total cross section\nmeasurement, which is negligible with respect to the others.\n6.3.2\nTheoretical and Monte Carlo uncertainties\nUncertainties on the background estimates come from the theoretical uncertainties associated to the cross\nsections. An uncertainty of 10% is quoted for the t\u00aft events while 20% is associated to the W+jets and\nWb\u00afb+jets events. This translates into a total of 12.5% in the 2 jet \ufb01nal state and 10% in the higher jet\nmultiplicity bins where t\u00aft events completely dominate the background. Note that despite very distinct\ntopologies, the selections of the Wt- and the t- channels analyses are not orthogonal. However it is\nbelieved that correlations can be properly addressed.\nTable 13: Summary of all uncertainties that affect the measured cross section. Data statistics\nis the Poisson error one would expect from real data while MC Statistics is the uncertainty\non the estimated quantities due to MC statistics. (*) background to 2j (12.5%) and 3j and 4j\n\ufb01nal states (10%)\nSource of\nAnalysis for 1 fb\u22121\nAnalysis for 10 fb\u22121\nuncertainty\nVariation\n\u2206\u03c3/\u03c3\nVariation\n\u2206\u03c3/\u03c3\nData Statistics\n20.6%\n6.6%\nMC Statistics\n15.6%\nLuminosity\n5%\n20%\n3%\n7.9%\nb-tagging\n5%\n16%\n3%\n6.6%\nJES\n5%\n11%\n1%\n1.5%\nLepton ID\n1%\n2.6%\n1%\n2.6%\nBkg x-section\n12.5/10%(*)\n23.4%\n3%\n9.6%\nISR/FSR\n9%\n24.0%\n3%\n7.8%\nPDF\n2%\n5.2%\n2%\n5.2%\nb-fragmentation\n3.6%\n9.4%\n3.6%\n9.4%\nTotal Systematics\n48%\n19.4%\nThe selection of a low jet multiplicity \ufb01nal state is very sensitive to the presence of extra jets origi-\nnating from gluon radiations. Any uncertainty in the ISR/FSR modelling is thus expected to have a sig-\nni\ufb01cant impact on the selection ef\ufb01ciencies, in particular for the Wt-channel and top quark pair events.\nWe quote an overall 9% uncertainty due to the modelling of gluon radiation in the t\u00aft events.\nThe uncertainties in the PDF may affect the topologies as well as the momentum distributions of\nthe \ufb01nal state objects, hence impacting the determination of the selection ef\ufb01ciency for both signal and\nbackgrounds. The procedure to estimate the impact of the choice of the PDF to the selection ef\ufb01ciency is\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n974\n\ndetailed in Section 4.2.2. Complete studies have been performed in each \ufb01nal state and a 2% uncertainty\nis quoted for signal and t\u00aft events.\nFinally the effect of the b-fragmentation parametrization has also been investigated following a sim-\nilar procedure of that de\ufb01ned in Section 5.3.2 from fast simulation. The relative uncertainties of the\ndifferent channel and \ufb01nal state selection ef\ufb01ciencies due to the b-fragmentation uncertainty is found to\nbe 3.6%.\nTable 13 lists all sources of uncertainties and reports their impact on the cross section determination.\nTwo cases are considered: one de\ufb01ned by the level of uncertainty in the b-tagging, jet energy scale and\nluminosity that will presumably characterize the early data taking period; another assuming reasonable\nimprovements on those effects with an integrated luminosity of 10 fb\u22121. The assumptions made in the\nlatter case are listed in Section 4.2.3.\n6.4\nSummary\nThe determination of the Wt-channel cross section constitutes a challenging measurement with the early\ndata, due to the presence of important t\u00aft and W+jets backgrounds. This measurement makes use of\nthe events with a jet multiplicity between two and four jets. With a signal to background ratio of about\n30-40%, the analysis requires a good knowledge of the W+jets production in the lower multiplicity bins,\nand of the t\u00aft process in higher bins. The estimates of the shapes and normalization of those processes\nwill have to rely upon the use of data. Strategies exist for QCD and W+jets events, but the discrimination\nagainst t\u00aft events remains a challenge.\nAs for the t-channel single top quark analysis, the cross section determination will very early be\ndominated by systematic uncertainties. The dominant effect is constituted by the background uncertain-\nties, followed by the modeling of the gluon radiation. From the detector side, the dominant source of\nuncertainty is the b-tagging because of the imperfect knowledge of the b-tag and b-tag veto ef\ufb01ciencies\nas well as of the mistag rates. Another source is the determination of the jet energy scale, which affects\nthe reconstruction of the W-boson mass and all the jet energies used in the analysis. Note that the de-\ntermination of the luminosity to better than 5% is required in order to ensure a good measurement, or\nthe use of ratio of different Wt-channel \ufb01nal states [31] can be used as well with higher luminosity. A\n3 \u03c3 evidence can be reached with a few fb\u22121 of data taking and a precision of 20% on the cross section\nmeasurement is achievable with about 10 fb\u22121 provided that improvements are made in both the experi-\nmental aspects of the detection (backgrounds from data, b-tagging, jet energy scale and luminosity) and\nfrom the theoretical side.\n7\nConclusion\nAt the LHC the production of single top quark events accounts for about a third of the t\u00aft production,\nwhich leads to about 2.5 million events per year during a run at 1032cm2s\u22121. Similarly to the situation\nat the Tevatron, the selection of single top quark events will suffer from the presence of both W+jets\nand t\u00aft backgrounds, which are produced at much higher rates. Thus, careful approaches devoted to\nthe understanding of these backgrounds in terms of shape and normalization performed directly from\ndata will have to be de\ufb01ned. Besides, except for the s-channel, single top quark analyses will be very\nearly dominated by the systematic uncertainties, and will require a good control of b-tagging tools and a\nreliable determination of the jet energy scale.\nIn a context of low signal over background ratio, the use of sophisticated tools like genetic algorithms,\nlikelihoods and Boosted Decision Trees appears very useful if one wants to establish the signal or to\ndetermine its cross section precisely. These techniques, which are now in common use at the Tevatron,\nwill require the use of reliable event samples for modeling signal and backgrounds, that will presumably\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n975\n\nbe produced from the data. The analyses should also be optimized with respect to the total level of\nsystematic uncertainty, which will be the main limiting factor for 30 fb\u22121 measurements.\nFinally, a precise determination of single top quark cross sections can be achieved for a few fb\u22121\nin the t-channel and the Wt-channel , while for the s-channel, higher statistics will be required. Their\npossible interpretation in terms of new physics should thus come at a later stage, once the systematic\neffects are under control.\nReferences\n[1] Tait, T. M. P. and Yuan, C. -P., Phys. Rev. D (2001) 014018.\n[2] D/0 Collaboration, Phys. Rev. Lett. 98 (2007) 181802.\n[3] CDF collaboration, CDF/PUB/TOP/PUBLIC/8968 (2008).\n[4] T.Lari et al., Report of Working Group 1 of the CERN Workshop \u2019Flavour in the era of the LHC\u2019,\narXiv:0801.1800v1 (2008).\n[5] Abazov, V. M. (D0 Collaboration), Phys.Lett. B 641 (2006) 423\u2013431.\n[6] Abazov, V. M. (D0 Collaboration), Phys. Rev. Lett. 99 (2007) hep\u2013ex/0702005.\n[7] Sullivan, Z., Phys. Rev. D70 (2004) 114012.\n[8] Campbell, J. and Ellis R. K. and Tramontano, F, Phys. Rev. D70 (2004) 094012.\n[9] Campbell, J. and Tramontano, F., Nucl. Phys. B726 (2005) 109\u2013130.\n[10] Atlas Collaboration, Top Quark Physics, this volume.\n[11] Atlas Collaboration, Determination of the Top Quark Pair Production Cross-Section, this volume.\n[12] Mangano, L.M., JHEP 0307 (2003).\n[13] Corcella, G. and others, JHEP 0101 (2001) 010\u2013103.\n[14] Sjostrand, T. and Mrenna, S. and Skands, P., JHEP 0605 (2006) 026.\n[15] ATLAS Collaboration, Triggering Top Quark Events, this volume.\n[16] ATLAS Collaboration, b-Tagging Performance, this volume.\n[17] Shibata, A. and Clement, B., ATL-PHYS-PUB-2007-011 (2007).\n[18] D0 Collaboration, Phys.Rev. D75 (2000) 092007.\n[19] B. Clement, FERMILAB-THESIS-200606 (2006).\n[20] ATLAS Collaboration, CERN/LHC 99-14 (1999).\n[21] S. Muanza, Talk on \u201dMC validation for W/Z+jets production at the Tevatron\u201d, Top Physics Work-\nshop, Grenoble 18-20 Oct. (2007).\n[22] J. Pumplin et al., Phys. Rev., D 65 (2001) 014013.\n[23] A.D. Martin et al., Eur. Phys. J. C28 (2002) 455\u2013473.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n976\n\n[24] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[25] D0 Collaboration, Arxiv 080307.0739v1 (2008).\n[26] A. Hoecker and P. Speckmayer and J. Stelzer and F. Tegenfeldt and H. Voss and K. Voss, arXiv\n(2007) 92.\n[27] Kane, G.L. and Ladinsky, G.A. and Yuan, C. -P., Phys. Rev D (1992) 124\u2013141.\n[28] Lucotte, A. and F. Chevallier, ATL-PHYS-PUB-2006-014 (2008).\n[29] D. Abbaneo et al., ALEPH Coll., Phys. Rep. 294 (1998) 1..\n[30] CDF Collaboration, PRD 70, 072002 (2004) (2004).\n[31] C.E. Gerber et al., FERMILAB-CONF 07-052 (2007) 125\u2013138.\nTOP \u2013 PROSPECT FOR SINGLE TOP QUARK CROSS-SECTION MEASUREMENTS\n977\n\nTop Quark Mass Measurements\nAbstract\nThis note summarizes studies performed in order to estimate the potential\nof ATLAS to measure the top quark mass from the \ufb01rst few hundred pb\u22121\nof data. The analyses shown here, based on fully simulated events, have\nbeen performed for the channel where the top quarks decay into one lepton\nplus a number of jets, using various methods to extract the top quark mass.\nThe performance of the detector has been evaluated, including triggering,\nparticle identi\ufb01cation, and jet reconstruction. For each method, the expected\nbackground, statistical and systematic uncertainties, and linearity have been\nstudied. This work shows that the precision on the top quark mass depends\nmainly on the jet energy scale uncertainty: a precision of the order of 1\nto 3.5 GeV should be achievable with 1 fb\u22121, assuming a jet energy scale\nuncertainty of 1 to 5%.\n1\nIntroduction\nAt the LHC, top quarks will be produced mainly in pairs through the hard processes gg \u2192t\u00aft (90%)\nand q \u00afq \u2192t\u00aft (10%). The corresponding cross section, at next-to-leading order, is 833 pb [1]; therefore,\nwe expect roughly 800 000 t\u00aft pairs to be produced with an integrated luminosity of 1 fb\u22121, correspond-\ning to about two weeks at a luminosity equal to 1033 cm\u22122s\u22121. In contrast to earlier measurements\nof the top quark mass [2], which concentrated on preserving as much of the signal as possible in or-\nder to minimize the statistical uncertainty, the LHC will produce so many top quark pairs that rather\nstringent requirements can be imposed, to restrict the measurement to regions in which the systematic\nuncertainties can be well-controlled. With 1 fb\u22121 of data, the measurement will already be completely\ndominated by systematic uncertainties of the order of 1 GeV. The dominant contribution to the sys-\ntematic uncertainty is expected to be the jet energy scale. In-situ calibration methods will allow the\nlight jet energy scale to be known to the percent level precision after 1 fb\u22121 of collected data [3]. This\nhigh precision can be, at least in part, translated to the b-jet energy scale, although differences are\nexpected. Detailed studies with the data will be necessary to reach the desired precision.\nThe top quark mass measurements described here are based on \ufb01nding the peak in the invariant\nmass distribution of the top quark\u2019s decay products: a W boson and a b-quark jet. This closely\ncorresponds to the pole mass of the top quark. Because of fragmentation effects, it is believed that\nthe top quark mass determination in a hadronic environment is inherently ambiguous by an amount\nproportional to \u039bQCD [4]: the intrisic amibiguity is of the order of 100 MeV.\nThis note describes several ways to measure the top quark mass in the semi-leptonic channel,\nwhich corresponds to a t\u00aft \ufb01nal state where one W boson decays leptonically while the other one\ndecays into two jets. The primary results rely on a full reconstruction of the \ufb01nal state, with the mass\nestimator taken as the invariant mass of the three jets from the hadronically-decaying top quark. This\nhas been studied for two cases. In the \ufb01rst case, both b-jets are identi\ufb01ed via displaced vertices, and\ntwo different mass measurement methods are presented. In the second case, fewer b-jets are identi\ufb01ed.\nThis latter case is expected to be important during early running, before the detector is fully calibrated.\nAn analysis which relies on a kinematic \ufb01t is also presented. Other t\u00aft decay channels can also be used,\nbut have not been considered in this note.\nAnother possibility relies on the determination of the mean distance of travel of b-\ufb02avoured\nhadrons from top quark decays [5]. The top quark mass can be inferred from the averaged lifetime\n978\n\nin the laboratory frame of the b-\ufb02avoured hadron, since the bottom quark\u2019s boost directly impacts the\nlifetime of the b-\ufb02avoured hadron. Rather than measuring the lifetime, the transverse decay length of\nthe b-\ufb02avoured hadron is used in this method. The mean of the transverse decay length distribution is\ndetermined for different assumed top quark masses, providing an estimator for the experimental data\nin the mean decay length as a function of the top quark mass. Since this analysis relies mainly on\ntracking, the systematic uncertainties are mostly uncorrelated with those of other methods; in partic-\nular, the in\ufb02uence of the jet energy scale as a source of uncertainty is negligible. Work is ongoing on\nthis method, which is not shown here.\nA last possibility is to estimate the top quark mass from the measured t\u00aft production cross section.\nThe errors on these quantities are related, in the Standard Model, via \u2206\u03c3tt/\u03c3tt \u223c5\u2206mtop/mtop [6]. This\nwould allow a determination of mtop independent of the kinematic reconstruction. In addition, it would\nbe clear that the top quark mass is the one used in the perturbative calculations (i.e. the pole mass).\nHowever, even without considering experimental uncertainties, the achievable precision would already\nbe limited to 2 GeV due to the uncertainty of the theoretical calculations. The scale dependence,\nwhich is the dominant source of uncertainty, might be reduced to the order of 6 % by performing the\ncomputation at higher orders, including the resummation of next-to-leading logarithmic corrections\n(NLL). This scale dependence can also be reduced by using a different mass de\ufb01nition such as the\nrunning mass1. This method is not considered further in this note.\n2\nMotivations for a precise top quark mass measurement\nElectroweak precision observables in the Standard Model and the Minimal Supersymmetric Standard\nModel (MSSM) depend on the value of the top quark mass. Therefore, a precise measurement of\nthe top quark mass is important for consistency tests of the Standard Model, to constrain the Higgs\nboson mass within the Standard Model, and to increase the sensitivity to physics beyond the Standard\nModel.\nThe most important dependency of the electroweak observables on the top quark mass arises via\nthe one-loop radiative correction term \u2206r [9], which is related to theW boson mass through the relation\nm2\nW =\n\u03c0\u03b1\n\u221a\n2GF sin2\n\u0398W\n(1 + \u2206r) (\u0398W being the weak mixing angle, \u03b1 the \ufb01ne structure constant and GF\nthe Fermi coupling constant). The top quark mass is present in \u2206r as terms proportional to m2\ntop/m2\nZ,\nwhile the Higgs boson mass is present only in terms proportional to log(mH/mZ). Therefore, the\ndependence on the Higgs boson mass is much weaker than the dependence on the top quark mass.\nThe precision of the indirect prediction of the Higgs boson mass depends mainly on the uncertainty\non the following quantities: the hadronic contribution to the electromagnetic coupling at the scale mZ\n\u2206\u03b1had, sin2\n\u0398W , W boson mass and top quark mass. For the current value of the top quark mass (mtop\n= 172.6 \u00b1 1.4 GeV) [10], mH = 87+36\n\u221227 GeV, implying mH < 160 GeV at 95% C.L [11]. In order to\nensure a similar contribution to the indirect prediction of the Higgs mass, the precision on mW and\nmtop must satisfy \u2206mW \u22430.07\u2206mtop. At the LHC, we expect to reach an accuracy of 15 MeV on\nmW [12] and 1 GeV on mtop. With these precision measurements, the relative precision on a Higgs\nboson mass of 115 GeV would be of the order of 18% [13].\n1The dependency of the perturbative calculations convergence on the quark mass de\ufb01nition has been observed in other\nobservables in which the running mass has led to better results [7, 8]. This would allow as well a determination of the top\nrunning mass.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n979\n\n3\nTop quark mass measurement in the semi-leptonic channel with the\nstandard ATLAS b-tagging\nIn this section we investigate the determination of the top quark mass using the standard ATLAS\nb-tagging.\n3.1\nPhysics background\nThe major sources of background, listed in Table 1, are single top events (Wt and t channels) and\nW boson production (W boson with W \u2192l\u03bd decay, W+b\u00afb and W+c\u00afc). It has been shown that back-\ngrounds from Z +jet events with Z \u2192ll, WW, WZ, and ZZ gauge boson pair production have much\nsmaller contributions [14]: therefore, their contribution has not been re-evaluated here. Backgrounds\nfrom QCD multi-jets and b\u00afb production have not been investigated with full simulation. Nevertheless,\nstudies performed on fast simulation have shown that these backgrounds are negligible after leptonic\ncuts (lepton pT, /ET) [14].\nAnother source of background comes from t\u00aft events themselves (fully leptonic or fully hadronic\nchannels). Moreover, t\u00aft events in which the W boson decays into \u03c4\u03bd\u03c4 are classi\ufb01ed in the following\nway: \u03c4 decaying leptonically belong to signal events, whereas \u03c4 decaying hadronically belong to\nbackground (fully hadronic t\u00aft).\nBefore any selection requirements, the signal to background ratio is of the order of 800pb\n80mb , i.e.\n10\u22128.\nTable 1: Main backgrounds to the semi-leptonic (\u2113= e,\u00b5) signal listing the number of events in 1 fb\u22121\nbefore and after the selection cuts (samples used here have comparable weights).\nProcess\nNumber\n1 isolated lepton\n>= 4 jets\n2 b-jets\nof events\npT > 20 GeV\npT > 40 GeV\npT > 40 GeV\nand /ET> 20GeV\nSignal\n313200\n132380\n43370\n15780\nW boson backgrounds\n9.5 \u00d7105\n154100\n9450\n200\nall-jets (top pairs)\n466480\n1020\n560\n160\ndi-lepton (top pairs)\n52500\n16470\n2050\n720\nsingle top, t channel\n81500\n24400\n1230\n330\nsingle top, W t channel\n9590\n8430\n770\n170\nsingle top, s channel\n720\n640\n11\n5\n3.2\nCombinatorial background\nWhen a t\u00aft semi-leptonic decay is reconstructed, one must choose which jets in the event to associate\nwith the hadronic W boson decay and also which jets correspond to each of the two b-jets. When at\nleast one of these choices is wrong, the event is classi\ufb01ed as combinatorial background.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n980\n\n3.3\nJets\nAll particles (electrons, muons, jets) forming the t\u00aft \ufb01nal state are required to lie within |\u03b7| < 2.5,\nsince b-jets cannot be tagged and muons are not reconstructed for higher values of |\u03b7|. See Ref. [15]\nfor a description of the features of jet selection that are common to all top quark analyses; only the\npoints speci\ufb01c to the analyses in this note are discussed below.\n3.3.1\nJet calibration\nThis analysis uses jets de\ufb01ned as in [15]. The jet calibration effects are removed by performing a jet\ncalibration to the parton level using the Monte Carlo information. This allows jet calibration to be\ndisentangled from other effects on the top quark mass measurement from the other effects (selection,\nreconstruction, measurement methods). This is done by matching jets to partons before radiation\n(requiring \u2206R(quark,jet) lower than 0.2) and deriving the difference between reconstructed jet energy\nand the parton energy as a function of the parton energy. This is performed separately for b-quark jets\nwith and without muons and for light jets. This procedure leads to a perfect and unbiased jet energy\nscale.\nUncertainties on the top quark mass measurement arising from the jet energy scale uncertainties\nwill be assesed here by applying miscalibration factors to the calibrated jets.\nJet scales on data will be obtained in a different way. The light jet energy scale determination is\nexplained in detail in a separate note [3]; the b-jet energy scale will be measured using Z+jets samples.\nThe Z +jets yield will be low at the start of LHC running; therefore, the b-jet scale will probably be\nderived from the measured light jet scale, together with a Monte Carlo correction term modelling the\ndifference between the two jet energy scales.\n3.3.2\nJet labelling\nA jet is called purely electromagnetic if the distance \u2206R to the nearest electromagnetic cluster is lower\nthan 0.2 and the ratio between the cluster and jet energies is greater than 0.8. Only 0.15% of jets\nproduced by hadronisation pass these cuts. Such objects are ignored for the remainder of the analysis.\nA jet is tagged as a b-jet if its b-weight is larger than 6 (the weight is de\ufb01ned by the three-\ndimensional space b-tagging, described in the introduction of this chapter [15]). The b-tagging ef\ufb01-\nciency for this weight in t\u00aft events is equal to 62% and the light (i.e. u, d and s \ufb02avoured) jet rejection\nto 130 for isolated (\u2206R(jet,jet) > 0.8) jets with pT greater than 15 GeV (Fig. 1).\nAll remaining jets (i.e. non b-tagged jets nor purely electromagnetic jets) are called light jets.\nTherefore, a b-jet which is not tagged by the b-tag algorithm is considered as a light jet.\n3.3.3\nJet multiplicity\n\u2022 The light jet multiplicity, for signal events, is illustrated in Fig. 2.(a), for all light jets, and for\nlight jets above the pT cut applied (40 GeV). The multiplicity is often higher than two (47% of\nevents, for jets above the pT cut), due to the presence of initial and \ufb01nal state radiation. This\nhas of course an impact on the combinatorial background size and shape.\n\u2022 The b-jet multiplicity, illustrated in Fig. 2.(b), re\ufb02ects the b-tagging ef\ufb01ciency.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n981\n\nlight jet rejection \n0\n100\n200\n300\n400\n500\n600\n700\n efficiency (%)\n45\n50\n55\n60\n65\n70\n75\n80\nATLAS\nFigure 1: b-tagging ef\ufb01ciency as a function of light (i.e. u, d and s \ufb02avoured) jet rejection in t \u00aft events,\nfor isolated (\u2206R(jet,jet) > 0.8) jets with pT greater than 15 GeV.\n3.4\nEvent selection\n3.4.1\nTrigger\nThe following Event Filter trigger [16] selections have been applied:\n\u2022 At least one isolated electron with pT greater than 25 GeV (\u201ce22i\u201d). This trigger is satis\ufb01ed by\n53% of t\u00aft e+jets events, and 71% of e+jets with pT(e) greater than 25 GeV pass.\n\u2022 At least one isolated muon with pT greater than 20 GeV (\u201cmu20\u201d). This trigger is satis\ufb01ed by\n59 % of t\u00aft \u00b5 +jets events, and 74% of \u00b5 +jets with pT(\u00b5) greater than 20 GeV pass.\n3.4.2\nStandard cuts\nA sequence of consecutive cuts is applied in order to reduce the contribution from physics background.\n\u2022 Exactly one isolated lepton, with pT > 20 (25) GeV for muons (electrons) and |\u03b7| < 2.5. This\ncut corresponds to the trigger selection. Moreover, the isolation criteria reject a large fraction\nof the leptonic b-decays in the all-jets channel: 99.6% of the t\u00aft events with both W bosons\ndecaying hadronically are rejected by this \ufb01rst selection step.\n\u2022 Missing transverse energy cut: /ET > 20 GeV. Together with the lepton requirement, this cut\nreduces QCD background.\n\u2022 At least four jets with pT > 40 GeV. Below 40 GeV, jets are known to be less precisely cal-\nibrated; the jet energy scale will be discussed later on, as a source of systematic uncertainty.\nTherefore, they are removed in order to improve the precision of the top quark mass measure-\nment [3]. Only 34% of hadronically-decayingW bosons have both jets passing this requirement.\nIf it is relaxed so that one jet can have pT down to 20 GeV, 88% of these W bosons pass, but\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n982\n\nnumber of light jets\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n cut\nT\nbefore p\n cut\nT\nafter p\nATLAS \nnumber of b jets\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n cut\nT\nbefore p\n cut\nT\nafter p\nATLAS \nFigure 2: a) Light jet and b) b-jet multiplicity in semi-leptonic t\u00aft events before (solid line) and after\n(dashed line) requiring that the jet pT be greater than 40 GeV(plots are normalised to unity).\nthe combinatorial and physical backgrounds increase. Moreover, due to initial and \ufb01nal state\nradiation (ISR, FSR), 30% of the signal events have more than two light jets with pT > 40 GeV.\nTherefore, no requirement is made on the number of light jets.\n\u2022 Among these jets, exactly two must be b-tagged.\n3.4.3\nPurity de\ufb01nition\nWhen a t\u00aft semi-leptonic decay is reconstructed, one must choose which jets in the event to associate\nwith the hadronicW boson decay and also which jets correspond to each of the two b-jets. The success\nof an algorithm for making such as choice is quanti\ufb01ed as its purity, the fraction of events in which\nthis choice is correct, based on looking at the Monte Carlo parentage information. For this purpose,\njets are matched to the closest Monte Carlo parton with \u2206R < 0.25. Purities are de\ufb01ned for identifying\nthe hadronically-decaying W boson (both light jets chosen are within 0.25 from the quark stemming\nfrom the W boson), the hadronic b-quark, and the hadronically-decaying top quark. Note that the top\nquark purity is not the product of the other two due to correlations.\n3.5\nHadronic W boson mass reconstruction\nSeveral algorithms have been tried to choose the two light jets from the hadronically-decaying W bo-\nson. Three have been identi\ufb01ed that give the best compromise between ef\ufb01ciency and purity:\n\u2022 the \u03c72 minimization method,\n\u2022 the geometric method: this method consists in choosing the two closest jets,\n\u2022 choosing the two light jets that give the mass closest to the known mass of the W boson [14].\nThe \ufb01rst and last methods are quite similar, but the \ufb01rst one contains in addition an event-by-event\nrescaling. Therefore, the last method will not be described here.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n983\n\n [GeV]\njj\nM\n0\n50\n100\n150\n200\n250\nEvents/2 GeV\n0\n50\n100\n150\n200\n250\nSignal \nPhysics background\nCombinatorial background\nATLAS\n-1\n1 fb\nFigure 3: Invariant mass of light jet pairs for\nevents with only two light jets (the contribution\nof physics background is shown in black, the one\nfrom combinatorial background, in grey).\n minimization [GeV]\n2\n\u03c7\n after \nW\nM\n50\n60\n70\n80\n90\n100\n110\nEvents/0.5 GeV\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nSignal \nPhysics background\nCombinatorial background\nATLAS\n-1\n1 fb\nFigure 4:\nHadronic W boson mass after \u03c72\nminimization (the contribution of physics back-\nground is shown in black, the one from combina-\ntorial background, in grey).\n3.5.1\nHadronic W boson mass reconstruction with \u03c72 minimization method\nEvents kept after the selection described above have at least two light jets above the pT threshold (50%\nof the events have more than two). Figure 3 shows the distribution of the invariant mass of the light\njet pairs, in events with only two light jets. As a \ufb01rst step, we select the hadronic W boson candidates\nin a mass window of (\u00b1 30 GeV) around the peak value of this distribution (82 GeV).\nThe energy scale of the jets may be shifted, due to effects that include the energy lost out of the\njet cone and initial and \ufb01nal state radiation effects, not taken into account in the default jet energy\ncalibration [17]. Moreover, the effects of the jet pT cut applied during event selection (explained\nin [3], section 3.3) contribute to the jet energy scale shift. To reduce the effect of such shifts on the\n\ufb01nal measured top quark mass, the jets are rescaled by constraining the pair to the known W boson\nmass using a \u03c72 minimization. The quantity to be minimized is shown in Eq. (1). The \ufb01rst term\nconstrains the jet pair mass Mj j to the W boson mass and width from the Particle Data Group [18]\n(MPDG\nW\n, \u0393PDG\nW\n). The other two terms are the usual \u03c72 terms for scaling the jets with multiplicative\nconstants \u03b1Ej1,j2; \u03c31,2 are the light jet energy resolutions2.\n\u03c72 = (Mjj(\u03b1Ej1,\u03b1Ej2) \u2212MPDG\nW\n)2\n(\u0393PDG\nW\n)2\n+ (Ej1(1 \u2212\u03b1Ej1))2\n\u03c3 2\n1\n+ (Ej2(1 \u2212\u03b1Ej2))2\n\u03c3 2\n2\n.\n(1)\nThis \u03c72 is minimized, event by event, for each light jet pair. The pair with the smallest \u03c7 2 is kept\nas the hadronic W boson candidate. This minimization procedure also gives the corresponding energy\ncorrection factors \u03b1Ej1 and \u03b1Ej2, shown in Fig. 5. Given the jet energy resolution, the \ufb01rst term in Eq.\n(1) dominates the \u03c72. Therefore, the hadronic W boson mass reconstructed with the light jets chosen\n2The light jet energy resolution has been estimated from the gaussian \ufb01t of the difference between a light jet energy and\nthe corresponding quark energy. The expression thus obtained is the following: \u03c3E = E \u2217\np\n(a2/E)+b2, where a = 0.989\nGeV1/2 and b = 0.075.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n984\n\nby this \u03c72 minimization is very narrow, as shown in Fig. 4. Further on, only the hadronic W boson\ncandidates within a mass window of \u00b1 2 \u0393MW (\u0393PDG\nMW = 2.1 GeV) are kept; this cut is called C0.\njet energy [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n(E)\n\u03b1\n0.92\n0.94\n0.96\n0.98\n1\n1.02\n1.04\n1.06\n1.08\nATLAS\nFigure 5: Energy correction factors estimated by the \u03c72 minimization.\n3.5.2\nHadronic W boson mass reconstruction with geometric method\nIn this method, the light jet pair with the smallest \u2206R distance between the two jets is taken as the\nhadronic W boson candidate. This method is simple and does not depend on the accuracy of the jet\nenergy scale. The resulting W boson mass distribution is shown in Fig. 6. Only hadronic W boson\ncandidates within a mass window of \u00b1 2 \u03c3MW (\u03c3MW = 10.4 GeV) around the peak value of the invariant\nmass distribution of all light jet pairs are kept; this cut is called C1.\n3.6\nLeptonic W boson mass reconstruction\nThe main dif\ufb01culty in reconstructing the leptonic W boson comes from the kinematics of the neutrino.\nThe missing transverse momentum /ET is used as an estimate of the neutrino transverse momentum.\nThis is, however, only an approximation, illustrated in Fig.7, as there may be other, softer, neutrinos\nin the event, such as from leptonic b-decay. With this hypothesis, p\u03bd\nT is underestimated by more than\n2% (miscalibration of /ET and fake missing /ET also contributes to this shift).\nUsing the known W boson mass, four-momentum conservation for the W \u2192\u2113+\u03bd decay gives a\nquadratic equation for the longitudinal component of the neutrino momentum p\u03bd\nz (\u2113stands for lepton\nand \u03bd stands for neutrino):\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n985\n\n]\n [GeV\njj\nM\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/2 GeV\n0\n50\n100\n150\n200\n250\n300\n350\n]\n [GeV\njj\nM\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/2 GeV\n0\n50\n100\n150\n200\n250\n300\n350\nSignal\nComb. background\nPhysics background\nATLAS \n-1\n1 fb\nFigure 6: Hadronic W boson mass with the geometric method (the contribution of physics background\nis shown in black, the one from combinatorial background, in grey).\n\u03bd\nMC \nT\n/p\nmiss\nT\nE\n0\n0.5\n1\n1.5\n2\n2.5\n3\nEvents/0.02 GeV\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nATLAS\nFigure 7: Ratio of /ET to the generated neutrino transverse momentum, after C0 cut. The neutrino\nconsidered here is the one from the leptonic W boson decay.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n986\n\nM2\nW = m2\nl \u22122(pl\nxp\u03bd\nx + pl\nyp\u03bd\ny)+2El\nq\n/ET\n2 +(p\u03bdz )2 \u22122(pl\nzp\u03bd\nz ).\nThis equation has no solution if the measured /ET \ufb02uctuates such that the neutrino-lepton invariant\nmass is above the W boson mass; this happens in 30% of the remaining events after the C0 cut. In\nthis case, p\u03bd\nT is reduced until a solution is found, with the restriction that the transverse W boson\nmass remain below 90 GeV (see Fig. 8). Only 11% of the events still have no solution after this\nprocedure. Otherwise, the equation has two solutions. The choice among the two p\u03bd\nz is performed\ntogether with the association of the b-jet to the corresponding W boson: the combination giving the\nsmaller difference between the hadronic and leptonic top quark masses is kept.\nW transverse mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\nMC\ndelta>0\ndelta<0\nATLAS\n-1\n1 fb\nW transverse mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nbefore modification\nafter modification\nATLAS\n-1\n1 fb\nFigure 8: Transverse W boson mass (distributions are normalized to unity). On the left, the Jacobian\npeak is clearly seen at the generator level (solid line); events for which no p\u03bd\nz solution is found (dashed\nline) can be distinguished from events for which a solution is found (dotted line). On the right, the\neffect of the p\u03bd\nT modi\ufb01cation for events for which no p\u03bd\nz solution is found, before (dashed line) and\nafter (solid line) modi\ufb01cation: a fraction of these events are recovered.\n3.7\nTop quark reconstruction\nThe two methods used for the hadronic W boson reconstruction lead to two methods for the top\nquark mass reconstruction. Moreover, additional cuts are applied in order to increase the purity of the\nselected sample; their relevance is illustrated below.\nOnce the hadronic W boson is reconstructed, the next step is to choose from the two b-jets the\none to associate with the hadronic W boson in order to reconstruct the hadronic top quark. Several\nmethods have been investigated:\n\u2022 choose the b-jet that maximizes the hadronic top quark pT.\n\u2022 Choose the b-jet closest to the hadronic W boson.\n\u2022 Choose the b-jet furthest from the leptonic W boson.\nAll three methods give similar results, but the second method has a slightly higher purity, so that\none has been chosen. The remaining b-jet and the leptonic W boson then de\ufb01ne the leptonic top quark.\nThe performance of the analyses before any additional cuts is summarized in Tables 2 and 3, in a\nfull top quark mass window and within \u00b1 3 \u03c3mtop, where \u03c3mtop = 10 GeV.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n987\n\nTable 2: Ef\ufb01ciency of cuts applied and \ufb01nal purities (full top quark mass window and within \u00b1 3\n\u03c3mtop, where \u03c3mtop = 10 GeV), with respect to t\u00aft semi-leptonic sample (e,\u00b5), for both methods.\nCuts applied\nEf\ufb01ciency (%)\nW boson purity (%)\nb purity (%)\ntop purity (%)\n\u03c72 minimization method\nCut C0\n2.22 \u00b1 0.03\n59.4 \u00b1 0.8\n61.6 \u00b1 0.8\n40.2 \u00b1 0.8\nCut C0\n1.40 \u00b1 0.04\n70.4 \u00b1 0.8\n77.3 \u00b1 0.8\n60.7 \u00b1 0.8\nwithin \u00b1 3 \u03c3mtop\nCuts C0, C2 and C3\n1.25 \u00b1 0.04\n59.3 \u00b1 0.8\n82.2 \u00b1 0.8\n56.5 \u00b1 0.8\nCuts C0, C2 and C3\n0.90 \u00b10.03\n74.9 \u00b10.9\n91.1 \u00b1 0.9\n73.6\u00b1 0.9\nwithin \u00b1 3 \u03c3mtop\nCuts C0, C2, C3, C4 and C5\n0.91 \u00b1 0.05\n80.1 \u00b1 0.8\n92.8 \u00b1 0.8\n77.1 \u00b10.8\nGeometric method\nCut C1\n1.26 \u00b1 0.03\n68.8 \u00b1 0.8\n69.7 \u00b1 0.8\n53.8 \u00b1 0.9\nCut C1\n1.01 \u00b1 0.04\n77.6 \u00b1 0.8\n77.7 \u00b1 0.8\n65.9 \u00b1 0.8\nwithin \u00b1 3 \u03c3mtop\nCuts C1, C2 and C3\n0.85 \u00b1 0.03\n68.7 \u00b10.9\n84.7 \u00b10.8\n66.1 \u00b10.9\nCuts C1, C2 and C3\n0.70 \u00b1 0.03\n79.4 \u00b10.9\n90.7 \u00b10.7\n78.1 \u00b10.9\nwithin \u00b1 3 \u03c3mtop\nCuts C2, C3, C4 and C5\n0.57 \u00b1 0.05\n86.9 \u00b1 0.9\n94.0 \u00b1 0.6\n86.4 \u00b1 0.9\nTable 3: Number of events in 1 fb\u22121 (signal and background) after selection cuts (full top quark mass\nwindow and within \u00b1 3 \u03c3mtop, where \u03c3mtop = 10 GeV), for both methods. \u03c4 + jets events correspond\nto: hadronic W boson \u2192\u03c4\u03bd and \u03c4 decays hadronically. Leptonic \u03c4 decays are counted together with\nthe signal.\nNumber of events for 1 fb\u22121\nsignal\nW +\n\u03c4\ndi-lepton\nall-jets\nsingle\njets\n\u2192jets\ntop\n\u03c72 minimization method\nCut C0\n6946\n19\n14\n191\n51\n148\nCut C0\n4382\n12\n3\n62\n20\n71\nwithin \u00b1 3 \u03c3mtop\nCuts C0, C2 and C3\n3918\n7\n10\n104\n28\n67\nCuts C0, C2 and C3\n2863\n4\n3\n24\n28\n24\nwithin \u00b1 3 \u03c3mtop\nCuts C0, C2, C3, C4 and C5\n2850\n1\n2\n10\n17\n19\nGeometric method\nCut C1\n3949\n9\n10\n19\n39\n89\nCut C1\n3155\n4\n6\n9\n7\n56\nwithin \u00b1 3 \u03c3mtop\nCuts C1, C2 and C3\n2643\n4\n5\n11\n33\n48\nCuts C1, C2 and C3\n2198\n4\n3\n5\n0\n27\nwithin \u00b1 3 \u03c3mtop\nCuts C2, C3, C4 and C5\n1785\n0\n1\n2\n7\n13\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n988\n\n3.7.1\nAdditional cuts\nAdditional cuts can be applied in order to increase the \ufb01nal top purity (combinatorial background\nrejection).\n\u2022 Cut C2: the invariant mass of the hadronic W boson and the b-jet associated to the leptonic\nW boson must be greater than 200 GeV.\n\u2022 Cut C3: the invariant mass of the lepton and the b-jet associated to the leptonic W boson must\nbe lower than 160 GeV.\nThese cuts are illustrated in Figs. 9 and 10. Their effects on ef\ufb01ciency and purity are shown in\nTables 2 and 3.\n]\n [GeV\njjbl\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/5 GeV\n0\n20\n40\n60\n80\n100\nAll Events\nComb. Background\nATLAS \nFigure 9: Invariant mass of the hadronic W bo-\nson and the leptonic b-jet for events satisfying\nC1.\nThe vertical line corresponds to Mj jbl =\nM(Whad,blep) > 200 GeV.\n]\n [GeV\nlbl\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/5 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\nAll Events\nComb. Background\nATLAS \nFigure 10:\nInvariant mass of the lepton and\nthe leptonic b-jet for events satisfying C1 and\nC2.\nThe vertical line corresponds to Mlbl =\nM(l,blep) < 160 GeV.\nThe combinatorial background can be further suppressed with two more cuts [19]. These are\nde\ufb01ned based on the following variables, where E\u2217denotes the energy of a particle in the top quark\nrest frame:\nX1 = E\u2217\nW \u2212E\u2217\nb = E\u2217\nj1 +E\u2217\nj2 \u2212E\u2217\nb = M2\nW \u2212M2\nb\nMtop\n,\n(2)\nX2 = 2E\u2217\nb = M2\ntop \u2212M2\nW +M2\nb\nMtop\n.\n(3)\nWe call the peak and width of the X1,2 distributions \u00b51,2 and \u03c31,2, as is found from simulated t\u00aft\nevents with mtop = 175 GeV that satisfy all previous requirements. Then the two following cuts are\nde\ufb01ned:\n\u2022 Cut C4: |X1 \u2212\u00b51| < 1.5\u03c31,\n\u2022 Cut C5: |X2 \u2212\u00b52| < 2\u03c32.\nThese cuts are illustrated in Figs. 11 and 12. With respect to C2 and C3, these cuts reduce the\nef\ufb01ciency by 30% but increase the purity to 85%, as shown in Tables 2 and 3. The numbers are\nidentical in the full top quark mass window and within \u00b1 3 \u03c3mtop, since C4 and C5 restrict the top\nquark mass to a more stringent window than \u00b1 3 \u03c3mtop around the peak value.\nTable 4 summarizes the cuts applied in these analyses.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n989\n\n [GeV]\nb\n*\n-E\nW\n*\nE\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/ 2 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nAll Events\nComb. Background\nATLAS \nFigure 11: Distribution of X1 \u2261E\u2217\nW \u2212E\u2217\nb for\nevents passing C2 and C3. Vertical lines corre-\nspond to the bounds of the C4 cut.\n [GeV]\n*\nb\n2 E\n0\n50\n100\n150\n200\n250\n300\nEvents/ 3 GeV\n0\n20\n40\n60\n80\n100\n120\nAll Events\nComb. Background\nATLAS \nFigure 12: Distribution of X2 \u22612E\u2217\nb for events\npassing C2, C3, and C4. Vertical lines corre-\nspond to the bounds of the C5 cut.\nTable 4: Additional cuts applied, after the event selection, for both methods (Xi, \u00b5i and \u03c3i are de\ufb01ned\nin the text of this section).\nCut label\nDescription\nCut C0 (\u03c72 minimization)\n|Mrec\nW \u2212MPDG\nW\n| < 2\u0393PDG\nMW\n(Mrec\nW is the reconstructed hadronic W and \u0393PDG\nMW = 2.1 GeV)\nCut C1 (geometric method)\n|Mrec\nW \u2212Mpeak\nW\n| < 2\u03c3MW (\u03c3MW = 10.4 GeV)\nCut C2 (both methods)\nM(Whad,blep) > 200 GeV\nCut C3 (both methods)\nM(lepton,blep) < 160 GeV\nCut C4 (both methods)\n|X1 \u2212\u00b51| < 1.5\u03c31\nCut C5 (both methods)\n|X2 \u2212\u00b52| < 2\u03c32\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n990\n\n3.8\nTop quark mass measurement\nIn Fig. 13, the hadronic top quark mass reconstructed with the \u03c72 minimization method is \ufb01t to the\nsum of a Gaussian and a polynomial (third degree). For 1 fb\u22121, the \ufb01t Gaussian has its mean at\n175.0 \u00b1 0.2 GeV and a width of 11.6 \u00b1 0.2 GeV (\u03c72/dof = 137/67). It is seen that C2 and C3 do not\nsigni\ufb01cantly shift the top quark mass: mtop = 174.8 \u00b1 0.3 GeV with a width equal to 11.7 \u00b1 0.4 GeV\n(\u03c72/dof = 82/67: C2 and C3 improve signi\ufb01cantly this value).\n [GeV]\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nSignal \nCombinatorial background \nPhysics background \nATLAS \n-1\n1 fb\n [GeV]\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nSignal \nCombinatorial background \nPhysics background \nATLAS \n-1\n1 fb\nFigure 13: The hadronic top quark mass reconstructed with the \u03c72 minimization method, \ufb01t with a\nsum of a Gaussian and a third order polynomial, scaled to 1 fb\u22121. Left, after C0: mtop = 175.0 \u00b1 0.2\nGeV, with a width equal to 11.6 \u00b1 0.2 GeV. Right, after C2 and C3: mtop = 174.8 \u00b1 0.3 GeV with a\nwidth equal to 11.7 \u00b1 0.4 GeV\nFigure 14 shows the result of the hadronic top mass reconstruction using the geometric method,\n\ufb01t to the sum of a Gaussian and a threshold function3(left, \u03c72/dof = 97/75) and to a pure Gaussian\n(right, \u03c72/dof = 38/24). After all cuts, the Gaussian mean \ufb01ts to 175.0 \u00b1 0.4 GeV with a width of\n14.3\u00b10.3 GeV. The width is larger than with the \u03c72 minimization method since no attempt is made\nto perform an event-by-event rescaling of the light jets. Nevertheless, the contribution of the light jets\nto the top quark mass resolution can be removed to \ufb01rst order by computing the top quark mass as\nmtop = Mjjb \u2212Mjj +Mpeak\nW\n. The results of this geometric method with rescaling are shown in Fig. 15.\nThe width decreases to 10.6 GeV, consistent with the results from the \u03c7 2 minimization method.\nTable 5 summarizes the \ufb01t results from all the methods discussed here.\n3The formula of the threshold function used is the following:\nA\u00b7e\u22121\n2\n\u0010 x\u2212Mtop\n\u03c3top\n\u00112\n+CstBd f \u00b7(x\u2212threshold)b \u00b7e\u2212c(x\u2212threshold)\n(4)\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n991\n\n]\n [GeV\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n50\n100\n150\n200\n250\n]\n [GeV\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n50\n100\n150\n200\n250\nF t\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\n]\n [GeV\njjb\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n]\n [GeV\njjb\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nFit\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\nFigure 14: The hadronic top quark mass reconstructed with the geometric method, \ufb01t with a sum of a\nGaussian and a threshold function (left) and with a pure Gaussian (right), scaled to 1 fb\u22121. Left, after\nC1, C2, and C3: mtop = 174.6 \u00b1 0.5 GeV, with a width equal to 11.1 \u00b1 0.5 GeV; right, after C2, C3,\nC4, and C5: mtop = 175.0 \u00b1 0.4 GeV, with a width equal to 14.3 \u00b1 0.3 GeV.\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n50\n100\n150\n200\n250\n300\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjb\nM\n50\n100\n150\n200\n250\n300\n350\n400\nEvents/4 GeV\n0\n50\n100\n150\n200\n250\n300\nF t\nSignal\nComb. background\nPhys cs background\nATLAS \n-1\n1 fb\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjb\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nFit\nSignal\nComb. background\nPhysics background\nATLAS \n-1\n1 fb\nFigure 15: The hadronic top quark mass reconstructed with the geometric method with rescaling,\n\ufb01t with a sum of a Gaussian and a threshold function, scaled to 1fb\u22121. Left, after C1, C2, and C3:\nmtop = 175.4 \u00b1 0.4 GeV, with a width equal to 10.6 \u00b1 0.4 GeV (\u03c72/dof = 109/73); right, after C2,\nC3, C4, and C5: mtop = 175.3 \u00b1 0.3 GeV, with a width equal to 10.6 \u00b1 0.2 GeV (\u03c72/dof = 43/16).\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n992\n\n2\n\u03c7\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n Nb of Events\n50\n100\n150\n200\n250\n300\n350\nAll Event\nComb. Background\nATLAS \n-1\n1 fb\nFigure 16: \u03c72 distribution (with combinatorial\nbackground), with cuts C2 and C3 applied.\n2\n\u03c7\n0\n0.5\n1\n1 5\n2\n2.5\n3\n3.5\n4\n]\n2\n [GeV/c\nfit\ntop\nM\n160\n165\n170\n175\n180\n185\n190\n \n2\n\u03c7\n \n=174.8-2.025\nfit\ntop\nM\nATLAS \n-1\n1 fb\nFigure 17: Top quark mass as a function of \u03c72.\nThe points are \ufb01tted by a linear function to ex-\ntract mtop = m\ufb01t\ntop(\u03c72 = 0)\n.\n3.9\nKinematic \ufb01t\nThe top quark mass can be extracted from a kinematic \ufb01t using a \u03c72 based on the entire \ufb01nal state, as\nde\ufb01ned in equation (5). The terms in the \ufb01rst line consist of the usual \u03c7 2 terms4, while the last four\nconstrain the object masses. The resolutions are extracted from Monte Carlo. The \u03c7 2 is calculated\nevent by event and the resulting \u03c72 distribution, shown in Fig. 16, exhibits a higher purity for lower\n\u03c72 values. The purity of the \ufb01nal sample could be improved by cutting on the \u03c7 2.\n\u03c72 = \u2211\njets\n((\u03b7m\ni \u2212\u03b7f\ni\n\u03c3 i\u03b7\n)2 +(\u03c6 m\ni \u2212\u03c6 f\ni\n\u03c3 i\n\u03c6\n)2)+ \u2211\njets,lepton\n(Em\ni \u2212Ef\ni\n\u03c3 i\nE\n)2 + \u2211\nx,y,z\n(pm\ni\u03bd \u2212pf\ni\u03bd\n\u03c3i\u03bd\n)2\n+(mjj \u2212MPDG\nW\n\u03c3W\n)2 +(ml\u03bd \u2212MPDG\nW\n\u03c3W\n)2 +(mjjbh \u2212m\ufb01t\ntop\n\u03c3t\n)2 +(ml\u03bdbl \u2212m\ufb01t\ntop\n\u03c3t\n)2.\n(5)\nThe \u03c72 minimization provides a high constraint on the jets from W boson. In an earlier study [14],\nit has been shown that the accuracy of the determination of the top quark mass depends on the \u03c7 2.\nFor events in which the b-quark jets are well measured and extra \ufb01nal state effects are small, the \u03c7 2\nof the \ufb01t is close to 0 and produces a top quark mass value re\ufb02ecting the Monte Carlo generated top\nquark mass. For larger \u03c72 value, this top quark mass value decreases while the fraction of b-quarks\nwith a large gluon radiation increases. This observation can be used by performing a linear \ufb01t to the\nextracted top quark mass as a function of the \u03c72. The \ufb01t is shown on Fig. 17 where the top mass\ndistribution is \ufb01tted by a gaussian for each \u03c72 slice. The most accurate estimate of the top quark mass\nis obtained by extrapolating this linear \ufb01t to \u03c72 = 0. This procedure should lead to a lower sensitivity\nto \ufb01nal state radiation effects of the extracted top quark mass, which is found to be mtop = 174.8\u00b10.4\nGeV, where the uncertainty is statistical.\nThis method is more computationally intensive than the others to assess the systematics, and is\nnot considered further in this note.\n4The m index stands for measured quantities and the f index, for \ufb01tted quantities. E, \u03b7 and \u03c6 are respectively the energy,\npseudo-rapidity and polar angle of the considered objects.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n993\n\nTable 5: Fitted peaks for the hadronic top quark mass and corresponding widths for several methods.\nFrom simulated events with mtop = 175 GeV, for 1 fb\u22121.\nMethod\nCuts\nTop quark mass\n\u03c3\nPull\nPull\n[GeV]\n[GeV]\nbias\nwidth\n\u03c72 minimization\nC0\n175.0 \u00b1 0.2\n11.6 \u00b1 0.2\n\u22120.3\n1.23\n\u03c72 minimization\nC0, C2, and C3\n174.8 \u00b1 0.3\n11.7 \u00b1 0.4\n\u22120.2\n1.11\n\u03c72 minimization\nC0, C2, C3, C4, and C5\n174.8 \u00b1 0.3\n11.8 \u00b1 0.4\n\u22120.5\n1.00\nGeometric\nC1, C2, and C3\n174.6 \u00b1 0.5\n14.1 \u00b1 0.5\n\u22120.39\n1.03\nGeometric\nC2, C3, C4 and C5\n175.0 \u00b1 0.4\n14.3 \u00b1 0.3\n\u22120.37\n1.11\nGeometric and rescaling\nC1, C2, and C3\n175.4 \u00b1 0.4\n10.6 \u00b1 0.4\n0.51\n1.10\nGeometric and rescaling\nC2, C3,C4, and C5\n175.3 \u00b1 0.3\n10.6 \u00b1 0.2\n0.17\n1.15\nKinematic \ufb01t\n174.8 \u00b1 0.4\n3.10\nStatistical uncertainties\nPull\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEvents/0 5\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nATLAS \n-1\n1 fb\nPull\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEvents/0.5\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nATLAS \n-1\n1 fb\nFigure 18: Pull distributions for the top quark mass measurement. Left, \u03c7 2 minimization method and\nright, geometric method. Both plots after C2, C3, C4, and C5.\nThe statistical uncertainties quoted have been evaluated using a single simulated experiment with\nstatistics corresponding to 1fb\u22121. To evaluate the reliability of these estimates, a bootstrap resampling\ntechnique has been used [20].\nThe pull distributions for the top quark mass measurement (Mi \u2212Mgen)/\u03c3Mi have been produced\nfor each method using 1200 pseudo-experiments. The biases and widths are reported in Table 5 for\nall the analyses shown in this note. Fig. 18 shows the pull distributions for the \u03c7 2 minimization\nmethod and for the geometric method, after cuts C2 through C5. All pull mean values are of size 0.5\nor less: this indicates that the biases induced by the methods of measuring the top quark mass are of\nthe order of 0.1 to 0.2 GeV depending on the cuts applied. The pull widths are slightly larger than 1;\nthis indicates that the statistical uncertainty of the \ufb01t is slightly underestimated.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n994\n\n3.11\nSystematic uncertainties\nThe statistical uncertainty on the top quark mass being negligible with a few fb\u22121 of collected data,\nthe total uncertainty will quickly be dominated by the systematic uncertainties. All the contributions\nare listed below and summarized in Table 6.\nTable 6: Systematic uncertainties on the top quark mass measured in the semi-leptonic channel.\nSystematic uncertainty\n\u03c72 minimization method\ngeometric method\nLight jet energy scale\n0.2 GeV/%\n0.2 GeV/%\nb jet energy scale\n0.7 GeV/%\n0.7 GeV/%\nISR/FSR\n\u22430.3 GeV\n\u22430.4 GeV\nb quark fragmentation\n\u22640.1 GeV\n\u22640.1 GeV\nBackground\nnegligible\nnegligible\nMethod\n0.1 to 0.2 GeV\n0.1 to 0.2 GeV\n3.11.1\nJet energy scale (JES)\nThe effect of the uncertainty of the jet energy scale on the top quark mass measurement has been\nestimated by multiplying separately the light jet and b-jet momenta by several rescaling factors (20\nfactors, between \u221210% and +10%). Neither the event selection nor the /ET have been changed after\nthis jet energy rescaling.\nThe resulting top quark mass depends linearly on the rescaling factor. The related systematic\nuncertainty on the top quark mass can therefore be expressed as a percentage of the light jet and b-jet\nenergy scale miscalibration.\n\u2022 The uncertainty in the b-jet energy scale produces an uncertainty in the top quark mass of 0.7\nGeV/%. The b-jet scale will ultimately be determined with data from Z + jets. However, at\nthe start of LHC running, the Z + jets statistics will be low, so the b-jet scale will be derived\nfrom the measured light jet scale togheter with a Monte Carlo correction term modelling the\ndifference between the two jet energy scales. The systematic uncertainty associated with these\nmethods has not been yet evaluated.\n\u2022 The uncertainty in the light jet energy scale produces an uncertainty in the top quark mass of\n0.2 GeV/%. The reduced dependence compared to that of the b-jet energy scale is due to the\nW boson mass constraint used in the rescaling (\u03c72 minimization method or kinematical \ufb01t) or\nthe de\ufb01nition of the top quark mass estimator (geometric with rescaling method). It has been\nshown that the light jet energy scale should be known with a precision of 1% in 1 fb\u22121 of\ndata [3]: the corresponding uncertainty on the top quark mass would therefore be 0.2 GeV.\n3.11.2\nInitial and \ufb01nal state radiation (ISR and FSR)\nThe study of the effect of initial and \ufb01nal state radiation on the top quark mass measurement is still\npreliminary. Several samples have been simulated for this study, corresponding to different sets of\nparameters:\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n995\n\nTable 7: Top quark mass measured with several ISR/FSR parameters (\u03c7 2 minimization method, after\ncut C0 and jet calibration).\nSample\nTop quark mass [GeV]\n\u03c3 [(GeV]\n1\n176.6 \u00b1 0.4\n13.4 \u00b1 0.6\n2\n176.3 \u00b1 0.7\n13.7 \u00b1 0.8\n3\n176.3 \u00b1 0.5\n12.7 \u00b1 0.6\n\u2022 Sample 1: AcerMC t\u00aft events, with maximum reconstructed top quark mass (half the default\nvalue of \u039b(QCD) for FSR; twice the default value of \u039b(QCD) for ISR).\n\u2022 Sample 2: AcerMC t\u00aft events, with default ISR and FSR parameters.\n\u2022 Sample 3: AcerMC t\u00aft events, with minimum reconstructed top quark mass (twice the default\nvalue of \u039b(QCD) for FSR, half the default value of \u039b(QCD) for ISR\nFor each sample, a speci\ufb01c jet calibration has been applied (separately for b-jets and light jets).\nThe measured top quark masses are summarised in Table 7. A shift on the top quark mass is\nobserved. A \ufb01rst estimate of the systematic uncertainty due to initial and \ufb01nal state radiation can be\nestimated from the relative difference between these three top quark mass values: it is approximately\nequal to 0.3 GeV (more statistics would be necessary for a more precise estimate).\nThis preliminary study shows the impact on the top quark mass measurement of a given change\nof ISR/FSR parameters, but the estimate of the systematic uncertainty due to ISR or FSR will bene\ufb01t\nfrom a measurement of these effects with ATLAS data. Figure 19 shows, for example, that the jet\nmultiplicity could help to determine the size of the initial and \ufb01nal state radiation contribution. Initial\nstate radiation could be measured with Drell-Yan events, as has been done at the Tevatron.\nNumber of light jets with Pt > 40 GeV by event\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nATLAS\n-1\n1 fb\nSample 1\nSample 2\nSample 3\nNumber of b-jets with Pt > 40 GeV by event\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nATLAS\n-1\n1 fb\nSample 1\nSample 2\nSample 3\nFigure 19: Light and b-jet multiplicity for several values of the ISR/FSR parameters (pT(jet) > 40\nGeV).\n3.11.3\nb-quark fragmentation\nThe effect of b-quark fragmentation has been estimated by varying the Peterson parameter within its\nuncertainty (study performed on fast simulation [14]).\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n996\n\nGenerated top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\nReconstructed top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\n195\n / ndf \n2\n\u03c7\n 2.928 / 2\np0 \n 1.893\n\u00b1\n -1.027 \np1 \n 0.01074\n\u00b1\n 1.007 \n / ndf \n2\n\u03c7\n 2.928 / 2\np0 \n 1.893\n\u00b1\n -1.027 \np1 \n 0.01074\n\u00b1\n 1.007 \nafter cut C0\nATLAS \nGenerated top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\nReconstructed top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\n / ndf \n2\n\u03c7\n 0.5239 / 2\np0 \n 7.481\n\u00b1\n 4.731 \np1 \n 0.04281\n\u00b1\n 0.9712 \n / ndf \n2\n\u03c7\n 0.5239 / 2\np0 \n 7.481\n\u00b1\n 4.731 \np1 \n 0.04281\n\u00b1\n 0.9712 \nATLAS \nFigure 20: Reconstructed top quark mass with 2 b-tagged jets as a function of the generated top quark\nmass (left: \u03c72 minimization method, after C0 cut; right: geometric method after C1 cut). The method\nhas good linearity.\nThe resulting uncertainty is lower than 0.1 GeV.\n3.11.4\nBackground estimate\nVariations in the size of the background have no noticeable effect on the extracted top quark mass.\nNevertheless, it is important to extract the shape of the background from data.\n3.12\nLinearity of the method\nThe analysis leading to the top quark mass measurement has been applied to samples corresponding\nto several values of generated top quark mass. Figures 20 and 21 show that both methods have good\nlinearity. The reconstructed top quark mass lies above the generated one by an average offset equal to\n0.2% of mtop. This comes from the pT jet spectrum which is different for each sample with a different\ngenerated top quark mass [3]. The jet energy scale is then a little bit different in each sample due to\nthe pT cut applied on jets.\n4\nTop quark mass measurement in the semi-leptonic channel with re-\nlaxed requirements on the b-tagging\nAt the start of LHC running, the detector will not be optimized and will require a commissioning phase\nwith \ufb01rst data to calibrate its sub-components. This is particularly true for the pixel detector and its\ncapability to tag b-jets. Thus, it could be useful to have a top quark mass measurement analysis in\nwhich the use of b-tagging is reduced. This is addressed in this section by performing a \ufb01rst analysis in\nwhich exactly one b-jet is b-tagged (the assumed b-tagging ef\ufb01ciency is the same as before: \u03b5b \u224360%).\nThis sample has no events in common with the sample used in section 3. In a second analysis, b-\ntagging is not used in the reconstruction of the t\u00aft events. Even if not used, this sample contains events\nwith 0, 1, or 2 b-tagged jets and overlap with the other two samples.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n997\n\nGenerated top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\n (%)\ngene\n)/M\ngene\n - M\nreco\n(M\n-1\n-0.5\n0\n0.5\n1\nafter cut C0\nATLAS \nGenerated top mass [GeV]\n160\n165\n170\n175\n180\n185\n190\n (%)\ngene\n/M\ngene\n-M\nreco\nM\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS \nFigure 21: Difference between the reconstructed and generated top quark mass, as a function of the\nlatter (left: \u03c72 minimization method, after C0 cut; right: geometric method after C1 cut).\n4.1\nDisplaced vertex b-tagging, 1 b-tagged jet\nThe sample is here limited to events with no more than \ufb01ve jets. In this case, the best method to select\nthe two light jets from the W boson is the one which minimizes Mjj \u2212Mpeak\nW\n. The b-jet associated with\nthe hadronic top quark decay is then chosen among the remaining light jets and the tagged b-jet. The\nbest choice is the one which minimizes\np\n(X1 \u2212\u00b51)2 +(X2 \u2212\u00b52)2 (see equations (2) and (3)).\nA large fraction of the non-hadronic b-jets is removed by requiring the b-jet to be closer to the\nreconstructed W boson than the lepton originating from the leptonic top quark decay:\n\u2022 cut C6 : \u2206R(lepton,bhad)\u2212\u2206R(W,bhad) > 1\nAs in previous sections, the puri\ufb01cation cuts C1 and C3 are applied. Harder puri\ufb01cation cuts (C4\nand C5) could also be applied. The top quark mass spectra derived after applying the two sets of\npuri\ufb01cation cuts are shown in Fig. 22.\nTable 8 summarizes the reconstruction ef\ufb01ciency and purity related to this reconstruction method\nfor both sets of cuts.\nTable 8: Single b-tagged sample: ef\ufb01ciency of cuts applied and \ufb01nal purities (within \u00b1 3 \u03c3mtop), with\nrespect to semi-leptonic events.\nCuts\nEf\ufb01ciency (%)\nW boson purity (%)\nb purity (%)\ntop purity (%)\nNumber of events\nC1+C3+C6\n0.54\u00b10.02\n70 \u00b11\n69\u00b11\n62\u00b11\n1063\nC3+C4+C5+C6\n0.52\u00b10.02\n71\u00b11\n70\u00b11\n63\u00b11\n1016\nThe systematic uncertainties on the top quark mass measurement, determined in the same way as\nin the previous section, are summarized in Table 9.\nThe top quark mass values obtained are shown in Table 10 together with the pull distribution\nresults. The single-tag sample can be added to the double-tagged sample to perform a top quark mass\nmeasurement with 50% more signal events.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n998\n\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n100\n150\n200\n250\n300\n350\nEvents/4 GeV\n0\n20\n40\n60\n80\n100\n120\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n100\n150\n200\n250\n300\n350\nEvents/4 GeV\n0\n20\n40\n60\n80\n100\n120\nFit\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n100\n120\n140\n160\n180\n200\n220\n240\nEvents/3 GeV\n0\n20\n40\n60\n80\n100\n120\nFit\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\nFigure 22: Events with only 1 b-tagged jet: mtop = Mjjb \u2212Mjj +Mpeak\nW\nwith the geometric method and\nrescaling, after puri\ufb01cation cuts (left, C1, C3, and C6 cuts: mtop = 176.0 \u00b1 0.7 GeV, with a width\nequal to 9.4 \u00b1 0.8 GeV(\u03c72/dof = 58/52) ; right, C3, C4, C5, and C6 cuts: mtop = 174.0 \u00b1 0.4 GeV,\nwith a width equal to 12.7 \u00b1 0.4 GeV) (\u03c72/dof = 27/13).\nTable 9: Systematic uncertainties on the top quark mass with rescaling measured in the semi-leptonic\nchannel, with 1 b-tagged jet and no b-tagging, using the geometric method.\nSystematic uncertainty\n1 b-tagged jet\nNo b-tagging\nLight jet energy scale\n0.3 GeV/%\n0.4 GeV/%\nb jet energy scale\n0.7 GeV/%\n0.7 GeV/%\nISR/FSR\n\u22430.4 GeV\n\u22430.4 GeV\nb quark fragmentation\n\u22640.1 GeV\n\u22640.1 GeV\nBackground\n< 1 GeV\n1 GeV\nTable 10: Fitted top quark mass value and corresponding widths for 1 b-tag and no b-tag samples, in\n1 fb\u22121. Pull bias and width are also given.\nGeometric method\nCuts\nTop quark mass\n\u03c3\npull\npull\nwith rescaling\n[GeV]\n[GeV]\nbias\nwidth\n1 b-tagged jet\nC1, C3 and C6 cuts\n176.0 \u00b1 0.7\n9.4 \u00b1 0.8\n\u22120.48\n1.17\n1 b-tagged jet\nC3, C4, C5 and C6 cuts\n174.0 \u00b1 0.4\n12.7 \u00b1 0.4\n\u22120.05\n1.07\nNo b-tagged jet\nC1 and C3 cuts\n175.0 \u00b1 0.4\n11.7 \u00b1 0.5\n0.40\n1.12\nNo b-tagged jet\nC3, C4 and C5 cuts\n175.2 \u00b1 0.5\n12.4 \u00b1 0.8\n\u22120.15\n0.94\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n999\n\n4.2\nTop quark mass measurement in the semi-leptonic channel assuming no b-tagging\nThe same analysis is performed with no use of b-tagging information. The main difference with\nthe two b-tagged analysis comes from the larger contribution of the combinatorial and physics back-\nground.\nThe corresponding top mass spectra are given in Fig. 23 for both sets of cuts. Table 11 summarizes\nthe ef\ufb01ciency and purity related to this method.\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/4 GeV\n0\n100\n200\n300\n400\n500\n600\n]\n [GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/4 GeV\n0\n100\n200\n300\n400\n500\n600\nFit\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\n]\n[GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n130\n140\n150\n160\n170\n180\n190\n200\n210\n220\n230\nEvents/3 GeV\n0\n50\n100\n150\n200\n250\n]\n[GeV\npeak\njj\n+M\njj\n-M\njjbh\nM\n130\n140\n150\n160\n170\n180\n190\n200\n210\n220\n230\nEvents/3 GeV\n0\n50\n100\n150\n200\n250\nFit\nSignal\nComb. background\nPhysical background\nATLAS \n-1\n1 fb\nFigure 23: Events without b-tagging: mtop = Mjjb \u2212Mjj + Mpeak\nW\nwith the geometric method, after\npuri\ufb01cation cuts (left, C1 and C3 cuts: mtop = 175.0 \u00b1 0.4 GeV, with a width equal to 11.7 \u00b1 0.5\nGeV(\u03c72/dof = 130/69) ; right, C3, C4 and C5 cuts: mtop = 175.2 \u00b1 0.5 GeV, with a width equal to\n12.4 \u00b1 0.8 GeV(\u03c72/dof = 41/24)).\nTable 11: Ef\ufb01ciency of cuts applied and \ufb01nal purities (within \u00b1 3 \u03c3mtop), with respect to semi-leptonic\n(e,\u00b5) events, assuming no b-tagging.\nCuts\nEf\ufb01ciency (%)\nW boson purity (%)\nb purity (%)\ntop purity (%)\nNumber of events\nC1+C3\n1.59 \u00b1 0.03\n49.5 \u00b1 0.9\n46.8 \u00b1 0.9\n58.4 \u00b1 0.9\n3115\nC3+C4+C5\n1.48 \u00b10.03\n51.1 \u00b1 0.9\n49.0 \u00b1 0.9\n58.9 \u00b1 0.9\n2916\nThe systematic uncertainties on the top quark mass measurement are summarized in Table 9. The\nobtained top quark mass values together with the pull distribution results are shown in Table 10.\nFor the second set of cuts (right plot of Fig. 23), the background contribution (\u224345 % of the\nsample) is peaked exactly below the signal contribution, preventing a \ufb01t using a parametrization like\ngaussian function (signal) + polynomial function (background). An event mixing technique has been\nused to \ufb01x the background shape in the parametrization. The event mixing technique consists in\nreplacing one of the two jets momentum associated to the W with a simulated jet whose energy, \u03c6 and\n\u03b7 distribution is randomly selected according to the global energy, \u03c6 and \u03b7 distributions observed for\nthe jets associated to the W. This technique looks very promising as shown in Fig. 24 comparing data\nand event mixing samples for the two jet and three jet invariant masses after preselection.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n1000\n\n]\n [GeV\njj\nM\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/1 GeV\n0\n20\n40\n60\n80\n100\n120\n140\nevent mixing\nbackground\nATLAS \n-1\n1 fb\n]\n [GeV\njjb\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents/5 GeV\n0\n50\n100\n150\n200\n250\n300\n350\nevent mixing\nbackground\nATLAS \n-1\n1 fb\nFigure 24: Events without b-tagging: comparison between background and event mixing samples for\ntwo jets (left) and three jets (right) invariant mass.\n5\nConclusion\nSeveral methods have been investigated in order to perform an accurate top quark mass measurement\nwith 1 fb\u22121 of collected data, in the t\u00aft semi-leptonic channel. The best top quark mass determination\nis achieved with two b-tagged events and a top mass estimator taken as the invariant mass of the\nthree jets from hadronically-decaying top quark; the uncertainty on the top quark mass measurement\nwith this analysis will be dominated by systematics, the statistical uncertainty being already small\n(\u22640.4 GeV). The precision on the top quark mass relies mainly on the jet energy scale uncertainty: a\nprecision of the order of 1 to 3.5 GeV should be achievable with 1 fb\u22121, assuming a jet energy scale\nuncertainty of 1 to 5%. W boson sample can be extracted from the t\u00aft sample in order to constrain the\nlight jet energy scale. The main uncertainty on the top quark mass measurement will come from the\nb-jet energy scale.\nEvents with one or no b-tagged jets lead also to an interesting measurement if the background\n(physical and combinatorial) shape is constrained from data. The estimated precision on the top quark\nmass value is below 2 GeV (assuming a jet energy scale uncertainty of the order of the percent), with\na very good signal over background ratio. These samples are thus very useful for jet energy scale or\nb-tagging studies during the commissioning phase with early data.\nReferences\n[1] R. Bonciani et al., Nucl. Phys. B 529 (1998) 424.\n[2] The Tevatron Electroweak Working Group, hep-ex/0703034.\n[3] ATLAS Collaboration, Jets from Light Quarks in t\u00aft Events, this volume.\n[4] M. Smith and S. Willenbrock, Phys. Rev. L. 79 (1997) 3825.\n[5] C.S. Hill and J.R. Incandela and J.M. Lamb, Phys. Rev. D 71 (2005) 054029.\n[6] M. Beneke et al., Report of the 1999 CERN Workshop on Standard model physics (and more)\nat the LHC (1999) 419\u2013529.\n[7] M. Bilenky et al., Phys. Rev. D 60 (1999) 114006.\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n1001\n\n[8] J. Abdallah et al., Eur. Phys. J. C46 (2006) 569.\n[9] A. Sirlin, Phys. Rev. D 22 (1980) 971.\n[10] T. Aaltonen et al., arXiv:hep-ex/0708.3642.\n[11] The LEP Electroweak Working Group, //lepewwg.web.cern.ch/LEPEWWG/.\n[12] ATLAS Collaboration, Detector and Physics Performance Technical Design Report, 1999.\n[13] Snowmass Working Group on Precision Electroweak measurements, Present and future Elec-\ntroweak precision measurements and the indirect determination of the mass of the Higgs boson.\n[14] I. Borjanovic et al, Eur. Phys. J C39S2 (2005) 63\u201390.\n[15] ATLAS Collaboration, Top Quark Physics, this volume.\n[16] ATLAS Collaboration, Triggering Top Quark Events, this volume.\n[17] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[18] Particle Data Group, J. Phys. G33 (2006) 1\u20131232.\n[19] E. Cogneras, Ph.D. thesis, 2007, Universit\u00b4e Blaise Pascal.\n[20] R. Barlow, MAN-HEP-99-4 (1999).\nTOP \u2013 TOP QUARK MASS MEASUREMENTS\n1002\n\nTop Quark Properties\nAbstract\nThe ATLAS potential for the study of top quark properties and physics beyond\nthe Standard Model in the top sector, is reviewed in this paper. Measurements\nof the top quark charge, the spin and spin correlations, the Standard Model\ndecay (t \u2192bW), rare top quark decays associated to \ufb02avour changing neutral\ncurrents (t \u2192qX,X = \u03b3,Z,g) and t\u00aft resonances are discussed. The expected\nsensitivity of the ATLAS experiment is estimated for an integrated luminosity\nof 1 fb\u22121 at the LHC. For the Standard Model measurements the expected pre-\ncision is presented. For the tests of physics beyond the Standard Model , the\n5\u03c3 discovery potential (in the presence of a signal) and the 95% con\ufb01dence\nlevel limit (in the absence of a signal) are given.\n1\nIntroduction\nSeveral properties of the top quark have already been explored by the Tevatron experiments, such as the\nmass, charge and lifetime, the rare decays through \ufb02avour changing neutral currents (FCNC) and the\nproduction cross-sections. The structure of the Wtb vertex and the main top quark decay mode (t \u2192bW)\nwithin the Standard Model were also investigated together with the measurements of the W-boson he-\nlicity fractions. Many of these studies were performed by reconstructing t\u00aft pairs in the semileptonic,\ndileptonic and fully hadronic decay modes. Given the current Tevatron luminosity, most of these studies\nare limited by the statistics acquired.\nThe electric charge of the top quark is one of its fundamental properties and will be probed with high\nstatistics at the LHC. The measurement of the top quark charge can be performed either by identifying\nthe charge of its decay products in the main decay channel t \u2192bW or by studying radiative top quark\nprocesses. At the Tevatron the D0 [1] and CDF [2] collaborations have already initiated the study of\nthe top quark charge and, with the available statistics, they showed that the data gives preference to the\nStandard Model top quark hypothesis (with a charge of +2/3) over the scenario with an exotic quark\n(XM) of charge \u22124/3 and mass \u2248170 GeV, fully consistent with the present precision electroweak data\n[3,4]. The D0 and CDF exclude the exotic quark hypothesis with 92 and 87 % con\ufb01dence, respectively.\nAs the top quark decays before it can form hadronic bound states, a consequence of its high mass,\nthe spin information of the top quark is propagated to its decay products. This unique behaviour among\nquarks allows direct top quark spin studies, as spin properties are not washed out by hadronization.\nThrough the measurement of the angular distributions of the decay products the information of the top\nquark spin can be reconstructed. Top quark spin polarization and correlations in t\u00aft events produced at the\nLHC are precisely predicted by the Standard Model and are sensitive to the fundamental interactions in-\nvolved in the top quark production and decay. By testing only the top quark decay, the W-boson polariza-\ntion measurement complements top quark spin studies, helping to disentangle the origin of new physics,\nif observed. The W-boson polarization states can be measured through the longitudinal (F0), left-handed\n(FL) and right-handed (FR) helicity fractions. At the present, the most stringent limits on the W-boson he-\nlicity fractions were obtained at the Run-II of the Tevatron [5\u201313]. Analysing 1.9 fb\u22121 of data, the CDF\nexperiment measured [5] F0 = 0.62 \u00b1 0.11 with FR \ufb01xed to zero and FR = \u22120.04 \u00b1 0.05 with F0 \ufb01xed\nto the Standard Model expectation for mt = 175 GeV. For 2.7 fb\u22121, the D0 experiment measured [10]\nF0 = 0.490\u00b10.106(stat)\u00b10.085(syst) with FR \ufb01xed to zero, and FR = 0.110\u00b10.059(stat)\u00b10.052(syst)\nwith F0 \ufb01xed to the Standard Model value.\nWithin the Standard Model, the Wtb coupling is purely left-handed (at the tree level), and its size is\ngiven by the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vtb. In Standard Model extensions,\n1003\n\nTable 1: The values of the branching ratios of the FCNC top quark decays, predicted by the SM, the\nquark-singlet model (QS), the two-higgs doublet model (2HDM), the minimal supersymmetric model\n(MSSM) and SUSY with R-parity violation are shown [30\u201336].\nProcess\nSM\nQS\n2HDM\nMSSM\nR\u0338\nSUSY\nt \u2192uZ\n8\u00d710\u221217\n1.1\u00d710\u22124\n\u2212\n2\u00d710\u22126\n3\u00d710\u22125\nt \u2192u\u03b3\n3.7\u00d710\u221216\n7.5\u00d710\u22129\n\u2212\n2\u00d710\u22126\n1\u00d710\u22126\nt \u2192ug\n3.7\u00d710\u221214\n1.5\u00d710\u22127\n\u2212\n8\u00d710\u22125\n2\u00d710\u22124\nt \u2192cZ\n1\u00d710\u221214\n1.1\u00d710\u22124\n\u223c10\u22127\n2\u00d710\u22126\n3\u00d710\u22125\nt \u2192c\u03b3\n4.6\u00d710\u221214\n7.5\u00d710\u22129\n\u223c10\u22126\n2\u00d710\u22126\n1\u00d710\u22126\nt \u2192cg\n4.6\u00d710\u221212\n1.5\u00d710\u22127\n\u223c10\u22124\n8\u00d710\u22125\n2\u00d710\u22124\ndepartures from the Standard Model expectation Vtb \u22430.999 1 are possible [14, 15], as well as new\nradiative contributions to the Wtb vertex [16, 17]. These deviations might be observed in top quark\nproduction and decay processes at LHC. The most general Wtb vertex for on mass shell W-boson, top\nquark and b quark, containing terms up to dimension \ufb01ve can be written as\nL\n=\n\u2212g\n\u221a\n2\n\u00afb\u03b3\u00b5 (VLPL +VRPR)t W \u2212\n\u00b5 \u2212g\n\u221a\n2\n\u00afb i\u03c3 \u00b5\u03bdq\u03bd\nMW\n(gLPL +gRPR)t W \u2212\n\u00b5 +h.c.,\n(1)\nwith q = pt \u2212pb the W-boson momentum and PR(L) the chirality projectors. Additional \u03c3 \u00b5\u03bdk\u03bd and k\u00b5\nterms, where k = pt + pb, can be absorbed into this Lagrangian using Gordon identities. If the W-boson\nis on its mass shell or it couples to massless fermions q\u00b5\u03b5\u00b5 = 0, and terms proportional to q\u00b5 can be\ndropped from the effective vertex.\nThe new constants VR, gL and gR [18, 19], are vector like (VR) and\ntensor like (gL and gR) anomalous couplings, can be related to f R\n1 , f L\n2 and f R\n2 in Ref. [20] (and references\ntherein) as f R\n1 = VR, f L\n2 = \u2212gL and f R\n2 = \u2212gR. If we assume CP is conserved, these couplings can be\ntaken to be real. Within the Standard Model VL \u2261Vtb \u22430.999 and the other couplings (VR, gL, gR) vanish\nat the tree level, while nonzero values are generated at higher orders [21,22]. Indirect limits on the Wtb\nvertex anomalous couplings can be inferred from radiative B-meson decays and B \u00afB mixing [23]. Taking\ninto account the current world average [23], BR( \u00afB \u2192Xs\u03b3) = (3.55\u00b10.24+0.09\n\u22120.10 \u00b10.03)\u00d710\u22124, varying\none parameter at a time, the 95% C.L. bounds on VR, gL and gR are in the range [\u22120.0007,0.0025],\n[\u22120.0015,0.0004] and [\u22120.15,0.57], respectively [22,24].\nFlavour Changing Neutral Currents are strongly suppressed in the Standard Model due to the Glashow-\nIliopoulos-Maiani (GIM) mechanism [25]. Although absent at tree level, small FCNC contributions are\nexpected at one-loop level, determined by the CKM mixing matrix [26\u201329]. For the top quark within\nthe framework of the Standard Model, these contributions limit the FCNC decay branching ratios to\nthe gauge bosons, BR(t \u2192qX,X = Z,\u03b3,g), to below 10\u221212. There are however extensions of the SM,\nlike supersymmetry (SUSY) [30], multi-Higgs doublet models [31] and models with exotic (vector-like)\nquarks [32\u201334], which predict the presence of FCNC contributions already at tree level and signi\ufb01cantly\nenhance the FCNC decay branching ratios compared to the Standard Model predictions [35, 36]. The\nbranching ratio for the different models are shown in Table 1. FCNC processes associated with the pro-\nduction and decay of top quarks have been studied at colliders and the observed upper limits on the\nbranching ratios at 95% C.L., from the direct searches, are shown in Table 2.\nSince the top quark mass is much larger than the other quarks, the top quark may play a privileged\nrole in the electroweak symmetry breaking (EWSB) mechanism. Any new physics connected to the\nEWSB could be preferentially coupled to the top quark sector. This would lead to deviations from the\n1Three generations of quarks and unitarity of the CKM matrix are assumed.\nTOP \u2013 TOP QUARK PROPERTIES\n1004\n\nTable 2: Experimental observed upper limits on the branching ratios at 95%C.L. for the FCNC top quark\ndecays.\nLEP\nHERA\nTevatron\nBR(t \u2192qZ)\n7.8% [37\u201341]\n49% [42]\n3.7% [43]\nBR(t \u2192q\u03b3)\n2.4% [37\u201341]\n0.75% [42]\n3.2% [44]\nBR(t \u2192qg)\n17% [45]\n13% [42,46,47]\n0.1\u22121 % (estimated from [46,48])\nexpected Standard Model t\u00aft production rate and could distort the top quark kinematics. New resonances\nand gauge bosons strongly coupled to the top quark are expected in a large variety of models, in particular\nthose with strong EWSB [49\u201351]. The t\u00aft \ufb01nal states are also interesting for leptophobic Z\u2032 bosons which\ncan appear in Grand Uni\ufb01cation Models [52]. These new particles could reveal themselves in the t\u00aft\ninvariant mass distribution.\nAt the Tevatron experimental upper limits were set at 95 %C.L. for the\n\u03c3(p\u00afp \u2192Z\u2032)\u00d7BR(Z\u2032 \u2192t\u00aft) with Z\u2032 masses between 450 GeV and 900 GeV. A topcolor leptophobic Z\u2032 is\nruled out below 720 GeV and the cross section of any narrow Z\u2032 decaying to a t\u00aft is less than 0.64 pb at\n95%C.L., for Z\u2032 masses above 700 GeV [53].\nIn this note the ATLAS potential for the study of the top quark properties and tests of physics beyond\nthe Standard Model in the top quark sector are reviewed for an expected luminosity of 1 fb\u22121 at the\nLHC. The note is organized as follows: the basic event selection and the trigger used are reminded in\nSection 2. In Sections 3, 4, 5 and 6 the studies of the top quark charge, the W-boson and top quark\npolarisation studies and the Wtb anomalous couplings, the top quark FCNC decays and the production\nof t\u00aft resonances are discussed respectively. The summary and conclusions are presented in Section 7.\nThe top quark mass, one of the most important top quark properties, is not investigated here as a separate\nnote is devoted to this issue [54].\n2\nBasic event selection\nAs most of the studies performed in this paper are related to either the semileptonic (tt \u2192WWbb \u2192l\u03bdj1j2bb\nwith l = e,\u00b5) or the dileptonic (tt \u2192WWbb \u2192l\u03bdl\n\u2032\u03bd\n\u2032bb with l,l\n\u2032 = e,\u00b5) decays of t\u00aft events, basic criteria\nfor the event selection were de\ufb01ned for each one of these \ufb01nal state topologies. Changes to the criteria\nare to be expected depending on the type of top quark property under study. For the background studies\nseveral sources were considered, t\u00aft, W+jets, Wb\u00afb+jets, Wc\u00afc+jets, Z+jets, WW, ZZ, WZ and single top\nevents (see the introduction of the Top Chapter for a full list of backgrounds). The backgrounds are also\ndescribed in more detail separatly for each section of the note. All signal and background events were\nrequired to pass the single lepton trigger requirements for electrons and muons. The triggers considered\nwere L1 EM18I (L1 MU20,L1 MU40) for electrons (muons) at L1, e22i (mu20) for electrons (muons)\nat L2 and e22i (mu20) for electrons (muons) at the Event Filter (EF) [55].\nDifferent selection criteria are applied for the top quark FCNC analyses, as the \ufb01nal state topology is\ndifferent from those considered above. These criteria are explained in Section 5.\nSemileptonic topology\nIn the semileptonic topology, signal events have a \ufb01nal state with one isolated lepton (electron or\nmuon), at least four jets (two of them from the hadronization of b quarks and labelled b-jets) and large\ntransverse missing energy from the undetected neutrino. More information on the signal can be found\nin the introduction of the Top Chapter. The basic selection criteria were de\ufb01ned by requiring that the\nevents should have:\nTOP \u2013 TOP QUARK PROPERTIES\n1005\n\nTable 3: Cumulative ef\ufb01ciencies of the standard top quark selection criteria for the semileptonic and\ndileptonic type of events with electrons and muons for the pseudorapidity range |\u03b7| \u22642.\ncriterion\n\u03b5(%)\ncriterion\n\u03b5(%)\nSemileptonic events\n100\nDileptonic events\n100\n1 isol.lept. (pT >25/20 GeV)\n58.9\n2 isol.lept. (pT >25/20 GeV)\n35.5\n\u22654 jets (pT >30 GeV)\n34.2\n\u22652 jets (pT >30 GeV)\n31.8\n\u22652 b-tagged\n10.5\n= 2 b-tagged\n8.3\nmissing ET > 20 GeV\n8.5\nmissing ET > 30 GeV\n6.5\n\u2022 exactly one isolated electron (muon) with |\u03b7| < 2.5 and pT > 25 GeV (pT > 20 GeV);\n\u2022 at least 4 jets with |\u03b7| < 2.5 and pT > 30 GeV;\n\u2022 at least 2 jets tagged as b-jets;\n\u2022 missing transverse energy above 20 GeV.\nDileptonic topology\nIn the dileptonic topology, signal events have a \ufb01nal state with two isolated leptons (electrons and/or\nmuons), at least two jets (tagged as b-jets) and large transverse missing energy from the two undetected\nneutrinos. The basic selection criteria were de\ufb01ned by requiring that the events should have:\n\u2022 exactly two isolated electrons (muons) with |\u03b7| < 2.5 and pT > 25 GeV (pT > 20 GeV);\n\u2022 at least 2 jets with |\u03b7| < 2.5 and pT > 30 GeV;\n\u2022 2 jets tagged as b-jets;\n\u2022 missing transverse energy above 30 GeV.\nSelection ef\ufb01ciency\nThe ef\ufb01ciency of the\nbasic selection criteria was examined using \u2248450 000 events from the\nt\u00aft \u2192bWbW \u2192bqqb\u2113\u03bd,b\u2113\u03bdb\u2113\u03bd signal sample. The results are presented in Table 3.\nThe effect of the trigger ef\ufb01ciency is investigated separately for the individual analysis.\n3\nTop quark charge reconstruction\nThere are several techniques to determine the electric charge of the top quark at hadron collider ex-\nperiments [56\u201358]. The top quark charge measurement presented here is based on the reconstruction\nof the charges of the top quark decay products. As the dominant decay channel of the top quark is\nt \u2192W+b(\u00aft \u2192W\u2212\u00afb), the top quark charge determination requires the measurement of both the W boson\nand the b quark charges. While the charge of the W boson can be determined through its leptonic decay,\nthe b quark charge is not directly measurable due to quark con\ufb01nement in hadrons. In this note two\npossible ways to determine the b quark charge were investigated:\nTOP \u2013 TOP QUARK PROPERTIES\n1006\n\n\u2022 The charge weighting technique: this approach is based on \ufb01nding a correlation between the b\nquark charge and the charges of the tracks belonging to the b-jet [59,60].\n\u2022 The semileptonic b-decay approach: in this case the b quark charge is determined using the\nsemileptonic b-decays (b \u2192c,u+W\u2212,W\u2212\u2192\u2113\u2212+ \u00af\u03bd\u2113), where the sign of the soft lepton indicates\nthe sign of the b quark charge.\nTwo major issues have to be addressed. The \ufb01rst one is to \ufb01nd the selection criteria to perform the correct\npairing of the lepton and the b-jet originated in the same top quark decay. In the Standard Model a b-\njet, coming from a b quark, should be associated with a positive lepton (\u2113+), while in the exotic case it\nshould be associated with a negative one (\u2113\u2212). The second issue is the assignment of a charge to the b-jet\nselected by the pairing criterion. While the former issue is common for both the approaches, the latter\none is tackled in different ways.\n3.1\nEvent generation and selection\nThe standard t\u00aft \u2212\u2192W+bW\u2212\u00afb samples were used as signal events in both the semileptonic and the dilep-\ntonic channels (only electrons and muons are taken as signal). For the background studies, the W+jets\nsample was used. The t\u00aft all jets channels as well as the semileptonic and dileptonic channels of \u03c4 leptons\nwere analysed as they can contribute to background (all jets channel) and to signal (events with the lep-\ntonic decays of \u03c4 leptons). In the present analysis the common selection criteria were used, as de\ufb01ned in\nSection 2. In addition, for each approach, speci\ufb01c criteria were applied to the events.\n3.2\nThe lepton and b-jet pairing algorithm\nThe lepton and b-jet pairing was done using the invariant mass distribution of the lepton and the b-tagged\njet, m(l,bjet). If the assignment is correct, m(l,bjet) is limited by the top quark mass, otherwise there is\nno such restriction, as can been seen in Figure 1, where the signal sample with the standard cuts applied\nwas analysed. To \ufb01nd the connection between the b-quarks and reconstructed b-jets and the parton level\nleptons and reconstructed leptons, the MC truth was used: the matching was treated as successful if the\ncone difference, \u2206R between b-quark and b-jet was less than 0.4 (in the lepton case \u2206R < 0.2). For\ndouble b-tagged events, only the b-jets that satisfy\nm(l,b(1,2)\njet\n) < mcr\nand\nm(l,b(2,1)\njet\n) > mcr\n(2)\nwere accepted. In the di-lepton case both leptons should ful\ufb01ll the condition (2). The optimal value\nfor the pairing mass cut, mcr = 155 GeV, is a trade-off between the ef\ufb01ciency (\u03b5) and purity (P) of the\npairing method. The factor \u03b5(2P \u22121)2 was maximised to \ufb01nd the optimum working point. As this\ncriterion requires events with two b-tagged jets and one combination for the lepton and b-jet invariant\nmass must be below mcr and the other one above mcr, the ef\ufb01ciency of the method is small. On the other\nhand, this criterion gives a high purity sample as is shown in Section 3.5.1. In the analysis two variants\nof b-tagged events treatment were considered. In the \ufb01rst one exactly two b-jets were required while in\nthe second one two and more b-jets were allowed (the two with the highest pT treated as true b-jets).\nSlightly better results were obtained for the former variant and the results presented here correspond to\nthis case. To suppress the background some additional cuts were tried: W boson mass (MW) window,\ntop quark mass (mtop) window, etc. By using the combined W boson and top quark mass window the\nbackground can be reduced by factor more than 10 at the expense of a factor 2 loss in signal. The MW\nwindow requires that at least one pair of non b-tagged jets should have an invariant mass within 10 GeV\nof the W boson mass. The mtop window requires that the reconstructed W boson can be combined with\na b-jet (not previously paired with a high-pT lepton) to give an invariant mass within 40 GeV of the top\nTOP \u2013 TOP QUARK PROPERTIES\n1007\n\nm(lepton,bjet) [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n3\n10\n\u00d7\nEvents / 2 GeV\n0\n1000\n2000\n3000\n4000\n5000\nATLAS\nFigure 1: Lepton - b-jet invariant mass spectra for the lepton and b-jet pairs from the same top quark (full\nline) and from different top quarks (dashed line).\nquark mass. This extra mass cut was applied by default in the whole top quark charge analysis using the\nweighting approach.\n3.3\nThe jet track charge weighting approach\nThe determination of the average b-jet charge was done using a weighting technique in which the b-jet\ncharge is evaluated as the weighted sum of the b-jet track charges:\nQbjet = \u2211i qi|\u20d7ji \u00b7\u20d7pi|\u03ba\n\u2211i |\u20d7ji \u00b7\u20d7pi|\u03ba\n(3)\nwhere qi(pi) is the charge (momentum) of the ith track inside the jet and \u20d7j is the b-jet axis unit vector.\nThe \u03ba parameter was optimised for the best separation between b- and \u00afb-jets and the optimum value\nwas found to be \u03ba = 0.5. In addition, for the charge weighting technique, it was further required, using\nonly tracks with pT > 1.5 GeV, that at least two tracks must be found within a cone with \u2206R < 0.4 with\nrespect to the jet axis. For b-jets with more than seven such tracks, only the seven with the highest pT\nare used. The parameters of the weighting procedure are the result of a maximisation of the difference\nbetween the mean values of the b- and \u00afb-jet charge distributions - these mean values were found for a\nset of the parameters values (\u03ba and track pT) and compared. For the procedure optimisation the signal\nt\u00aft-sample was used.\n3.4\nSemileptonic b-decay approach\nIn this approach the pairing procedure described in Section 3.2 is also used. But in this case the b quark\ncharge is determined through its semileptonic decay. The sign of the b-jet charge is determined by the\nlepton charge within the b-jet,\nb \u2192c,u+\u2113\u2212+ \u00af\u03bd ,\n\u00afb \u2192\u00afc, \u00afu+\u2113+ +\u03bd.\nThe lepton from the b-decay will be identi\ufb01ed as a non-isolated lepton inside the corresponding b-\njet, and its charge (QnonIs) de\ufb01nes the b quark charge. The non-isolated lepton is searched for among\nthe tracks pointing to the treated b-jet and originating in the corresponding secondary vertex. Several\nprocesses can lead to an incorrect b quark charge assignment with this approach. Semileptonic decays\nof D mesons produced in the B decay chain, and the B0- \u00afB0 mixing are examples of such processes. To\nTOP \u2013 TOP QUARK PROPERTIES\n1008\n\nsuppress the contribution from D mesons, the non-isolated lepton transverse momentum with respect to\nthe b-jet axis, prel\nT , can be used. The fact that the lepton prel\nT from b-decays is, on average, higher than\nfrom D meson decays can be used to diminish this contamination. The prel\nT cut was optimised using a\nsample of \u2248555000 signal t\u00aft events and the value of 1 GeV has been found as the optimum cut. An\nadditional source of wrong b quark charge assignments is mistagging, i.e. light jets incorrectly tagged as\nb-jets.\nThe main drawback of this approach is that, from all the selected lepton plus b-jet pairs, only those\nwith a b-jet containing a non-isolated lepton can be used in the analysis. In addition to that, due to\ndif\ufb01culties in selecting a pure sample of electrons from within jets, only muons were taken as the non-\nisolated leptons.\n3.5\nResults\nIn both approaches, the Standard Model scenario of top quark production and decay is assumed. The\ncorresponding results are discussed in the following sections.\n3.5.1\nWeighting technique approach results\nAs a \ufb01rst step, the ef\ufb01ciency and purity of the lepton b-jet pairing was investigated. Using the events\nwhich passed the selection criteria, the obtained pairing ef\ufb01ciency is \u03b5 = 30.5% and the pairing purity\nis P = 85.6%.\nThe purity of pairing is de\ufb01ned as P = Ngood/Nall, where Ngood (Nall) is the number of\ncorrectly paired lepton \u2013 b-jet pairs (all treated pairs) and the Monte Carlo truth is used to \ufb01nd Ngood.\nThe b-jet charge spectra reconstructed using the Monte Carlo truth and invariant mass pairing pro-\ncedure for the signal t\u00aft events are presented in Figure 2, left and right respectively. From Figure 2, the\nshift of the b-jet charges associated with \u2113+, Q(+)\nbjet, and \u2113\u2212, Q(\u2212)\nbjet, (or with b and \u00afb quark in the Monte\nCarlo case) is clearly seen. The obtained b-jet charge purity, de\ufb01ned as the percentage of b-jets with the\ncorrect charge (Q(+)\nbjet < 0 and Q(\u2212)\nbjet > 0), is P \u224862%. In addition to that, the Qcomb b-jet charge spectrum,\nde\ufb01ned as Q(\u2113) \u00d7 Q(\u2113)\nbjet, has been reconstructed. The in\ufb02uence of trigger was also investigated, namely\nthe lepton level 1 and level 2 triggers as well as the event \ufb01lter (EF). The results with and without trigger\nare summarised in Table 4. No signi\ufb01cant impact of the trigger is observed. A small asymmetry in favour\nof the positive b-jet charge, as was revealed by the analysis, is due to the dominance of positive charge\nin the initial state (two colliding protons).\nNote that the peaks at \u00b11 in Fig. 2 correspond to the cases when all the tracks pointing to a b-jet\nhave the same charge sign - in this case the weighting procedure (2) gives Qbjet = \u00b11.\nTable 4: The mean b-jet charge associated with positive (Q+) and negative (Q\u2212) lepton and combined\nb-jet charge (Qcomb) without (no) and with (yes) EF trigger; two b-tags required.\ntrigger\nQ+\nQ\u2212\n| Qcomb |\nNevent\nef\ufb01ciency\nno\n-0.092 \u00b1 0.006\n0.103 \u00b1 0.006\n0.097 \u00b1 0.004\n7129\n100.0\nyes\n-0.095 \u00b1 0.006\n0.106 \u00b1 0.006\n0.101 \u00b1 0.004\n6130\n86.0\nThe main background processes for the top quark charge measurement in the semileptonic mode are:\nW+ jets production (the most important background in this mode), QCD multi-jets, di-boson and single\ntop quark production. The single top production is not a genuine background as it gives the same sign\nof the b-jet charge asymmetry as the signal. For the selection criteria that were used, the ratio of the\naccepted semileptonic t\u00aft events to the accepted single lepton ones is more than 15:1. In the dileptonic\nTOP \u2013 TOP QUARK PROPERTIES\n1009\n\nb jet charge\n-1\n-0.5\n0\n0.5\n1\nEvents / 0 02\n0\n2000\n4000\n6000\n8000\n10000\nATLAS \n-1\nL = 1 fb\nb jet charge\n-1\n-0.5\n0\n0.5\n1\nEvents / 0 02\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nATLAS\n-1\nL = 1 fb\nFigure 2: The b-jet charge associated with positive (full line) and negative (dashed line) lepton using the\nMonte Carlo truth (left) and invariant mass criteria (right) for the \u2113b-pairing.\nmode, the background is composed of Drell-Yan pairs (the most signi\ufb01cant background), multi-jet QCD\nprocesses and di-boson production [2].\nThe background studies for this analysis require large Monte Carlo samples (in addition to the stan-\ndard cuts the invariant mass criterion is highly restrictive) not available at present. The ideal way to\ndetermine the basic background parameters, the S:B ratio and background charge asymmetry, is to use\nthe W+jets (dominant background) samples. However, after applying the selection criteria to the avail-\nable W+jets samples, only a few events remained (20 lepton b-jet pairs). It is clear that due to poor\nstatistics the samples are not suitable for a valuable background analysis. Nonetheless, combining the\nb-jet charge spectra, obtained for the individual W+jets channels (W+n\u00d7jets and Wb\u00afb, Wc\u00afc + n \u00d7jets)\nscaled according to their cross sections to 1 fb, a S:B ratio of \u224838 \u00b1 8 was obtained. To \ufb01x the S:B\nratio we need to include other backgrounds and take a regard for the poor statistics. Taking into account\nonly the standard cuts with a loose MW window (\u00b130 GeV) a value of 7:1 was obtained for the S:B ratio\nwhich is compatible with that of the CDF background studies [2]. As a result, a nominal S:B ratio of\n30:1 has been assumed, with 7:1 as a very conservative lower limit for studying systematic uncertainties\nrelated to the background.\nThe poor statistics of the available W+jets samples does not enable the background b-jet charge\nasymmetry to be determined precisely, the obtained value being \u2248\u22120.02\u00b10.05. On the other hand, as it\nwas shown by CDF [2], no marked background asymmetry is expected. For this reason, as a background,\nwe use the signal events but without the pairing of leptons and b-jets. As a consequence the obtained\nb-jet charge spectrum is not correlated with the high pT lepton charge and should not have any charge\nasymmetry. Assuming the nominal S:B ratio, the spectrum is normalized to 1/30 of the signal statistics.\nThe analysis showed that this background exhibits practically no asymmetry. For the systematics studies,\na background corresponding to S:B=7:1 was also considered.\nTo \ufb01nd a realistic b-jet charge distribution, the signal and background distributions are combined. In\nFigure 3 (left) the expected b-jet charge (Qcomb) distribution combining the signal with the background\n(full line) and the background itself (dashed line) are shown. From the reconstructed b-jet charge spectra\nusing the two treated backgrounds, the expected mean b-jet charge (assuming the Standard Model) is:\nQcomb = \u22120.094\u00b10.0042 (stat).\nThe Qcomb value is obtained as the mean value of the signal plus background (S+B) distribution\ncombining signal with the background.\nIn conclusion, \u22486000 \u2113b combinations could be selected for the top quark b-jet charge analysis,\nusing the 1 fb\u22121 sample. The expected combined b-jet charge purity, N(Qbjet < 0)/Nall, is \u22480.62\u00b10.01\nfor the Standard Model case.\nTOP \u2013 TOP QUARK PROPERTIES\n1010\n\nb-jet charge\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\nEvents / 0 02\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nS + B\nB\nATLAS\n-1\nL = 1 fb\ntop charge\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n6\nEvents / 0.1\n0\n50\n100\n150\n200\n250\nS + B\nB\nATLAS\n-1\nL = 1 fb\nFigure 3: Left: the full S+B b-jet charge (Qcomb) distribution (full line) and the background itself (dashed\nline); right: the reconstructed top quark charge (Qcomb\nt\n) (full line) and its background (dashed line).\nTaking into account the statistical uncertainty of the obtained mean b-jet charge (Qcomb) it can be\nstated that the obtained value will differ from 0 by more than 20\u03c3. Using a simple statistical treatment\nit is easy to show that for a reliable determination of Qcomb (\u22655\u03c3) a sample of \u22480.1 fb\u22121 should\nbe suf\ufb01cient. In addition to that the analysis has revealed that the reconstructed b-jet charge is more\nin\ufb02uenced by the size of the S:B ratio than by the background asymmetry: going from the pure signal b-\njet charge spectrum to that of the 7:1 mixture of signal and background, the mean b-jet charge decreased\nby 14%, while a replacement of the symmetric background by the asymmetric one with an asymmetry\n1/4 of the signal one, leads to only 3% change of the charge at the 7:1 S:B ratio.\nThe direct reconstruction of the top quark charge can be done relying on the obtained value of Qcomb\n(see above). Using the Standard Model value of the b quark charge (Qb = \u22121/3) and the mean re-\nconstructed value of the b-jet charge (Qcomb), the b-jet charge calibration coef\ufb01cient Cb = Qb/Qcomb is\n3.54\u00b10.16 and the top quark charge then reads:\nQt = Q(\u2113+)+Q(+)\nbjet \u00d7Cb ,\nQ\u00aft = Q(\u2113\u2212)+Q(\u2212)\nbjet \u00d7Cb\n(4)\nwhere Q(\u2113\u00b1) = \u00b11 is the lepton charge and Q(\u00b1)\nbjet is as above.\nThe reconstructed top quark charge is shown in Figure 3 (right) for the sample of 1 fb\u22121. The\nabsolute value of top quark charge obtained by combining Qt and Q\u00aft for the above mentioned sample\nis Qcomb\nt\n= 0.67\u00b10.06 (stat)\u00b10.08 (syst). The statistical error assumes that the relative error of Cb is\nthe same as that of Qcomb. The systematic error of Qcomb\nt\ncan be studied comprehensively only by using\nexperimental data 2. In this case the main source of the systematic error is the weighting procedure that\nin\ufb02uences the coef\ufb01cient Cb, that should be determined independently on the investigated b-jet charge,\nas well as the mean b-jet charge. In our case only the systematics stemming from determination of the\nmean b-jet charge were taken into account.\n3.5.2\nSemileptonic b-decay approach results\nThe charge of the non-isolated lepton found within the b-jet provides discrimination between the Stan-\ndard Model and the exotic hypotheses on a statistical basis. Figure 4 shows the number of b-jets, which\nhave been paired with positive (left) and negative (right) high pT lepton and which contain inside a non-\nisolated lepton, as a function of the charge (QnonIs) of the contained non-isolated lepton. The mean values\n2The reconstructed b-jet charge or coef\ufb01cient Cb for an experimental sample, e.g. dijet b\u00afb data, should be compared with\nthe corresponding Monte Carlo one to look for a possible difference in the b-jet track topology between Monte Carlo and real\ndata.\nTOP \u2013 TOP QUARK PROPERTIES\n1011\n\nof the non-isolated lepton charge obtained from these \ufb01gures are:\n\u00afQ(+)\nnonIs = N(\u2113+)\u2212N(\u2113\u2212)\nN(\u2113+)+N(\u2113\u2212) = \u22120.32\u00b10.05,\n\u00afQ(\u2212)\nnonIs = N(\u2113+)\u2212N(\u2113\u2212)\nN(\u2113+)+N(\u2113\u2212) = 0.30\u00b10.05,\nwhere \u00afQ(+)\nnonIs ( \u00afQ(\u2212)\nnonIs) is the mean charge of the non-isolated leptons in the b-jets paired with the positive\n(negative) high pT lepton. N(\u2113\u2212) (N(\u2113+)) is the number of b-jets with a negative (positive) charged\nlepton. The quantity Q(\u2113)\u00d7Q(\u2113)\nnonIs, where Q(\u2113) is the charge of the lepton paired with the b-jet containing\na non-isolated lepton, can be used to combine both histograms. The obtained mean combined charge in\nthe Standard Model is \u00afQ(comb)\nnonIs\n= \u22120.31\u00b10.04, showing a potential to distinguish between the Standard\nmodel and exotic hypothesis even with 1 fb\u22121 of data, as in the case of the exotic scenario the opposite\nvalue of \u00afQ(comb)\nnonIs\nis expected.\nCharge\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n-1\nEvents / 1 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\nCharge\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n-1\nEvents / 1 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\nB-meson\nD-meson\nOther\nFake\nATLAS\nCharge\n-2\n-1 5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-1\nEvents / 1 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nCharge\n-2\n-1 5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-1\nEvents / 1 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nB-meson\nD-meson\nOther\nFake\nATLAS\nFigure 4: Number of b-jets, containing a non-isolated lepton inside, associated with positive (left) and\nnegative (right) high pT lepton vs the charge of the non-isolated lepton. The contribution of different\nsources of leptons are marked by different shading styles.\n3.6\nSystematic uncertainties\nThe systematic studies have been done following the prescription described in Section 6 of Chapter\n1. The resulting systematic errors are summarised in Table 5. The systematic uncertainty caused by\nthe top quark mass was estimated from the absolute difference between the Qcomb reconstructed at the\nnominal value (175 GeV) and mt=160 and 190 GeV and rescaling to an effective 2 GeV uncertainty. The\nsystematic uncertainty connected with the signal to background ratio was found assuming that this ratio\nis known with 30% uncertainty. The background asymmetry systematics was estimated assuming that\nthe background charge spectrum asymmetry is at a level of 10% of the signal one.\nThe systematic uncertainties due to Monte Carlo modeling of t\u00aft signal were studied by comparing\nsamples with different fragmentation parameters: an AcerMC/Pythia sample and the standard signal\nMC@NLO/Herwig one, giving values of 18 \u00b1 13% and 16 \u00b1 13% for the weighting and semileptonic\napproaches, respectively. The large uncertainties are due to a limited Monte Carlo statistics, so these\nvalues cannot be considered as a reliable estimate of the corresponding systematic uncertainties and are\ntherefore not included in Table 5.\nPileup background affects the weighting technique procedure, as tracks from additional minimum-\nbias interactions get included in the jet charges. The associated systematic uncertainty was evaluated by\ncomparing the standard sample to a dedicated t\u00aft sample including pileup, leading to a shift of 20\u00b118%.\nSince the Monte Carlo statistical error is large, and it is expected that any pileup effect can be minimised\nTOP \u2013 TOP QUARK PROPERTIES\n1012\n\n(at least at moderate LHC luminosities) by applying track impact parameter cuts to eliminate tracks from\npileup vertices, this value is also not included Table 5.\nTable 5: The systematic uncertainties (%) of the mean reconstructed charge, Qcomb, the weighting tech-\nnique and b-decay approaches.\nSource\nWeighting (%)\nb-decay (%)\njet scale\n0.7\n0.3\nb-jet scale\n1.9\n6\n\u2206mt\n1.3\n7\nPDF\n0.6\n\u2013\nISR\n2.8\n15\nFSR\n7.8\n8\nPile-up\n\u2013\n1.8\nBackground asymmetry\n1\n\u2013\nS/B ratio\n9\n\u2013\ntotal\n12.5\n19.3\n4\nPolarization studies in t\u00aft semileptonic events\nThe measurements of the W-boson and top quark polarizations in t\u00aft events provide a powerful test of\nthe top quark production and decay mechanisms and are a sensitive probe of new physics. W-boson\nor top quark spin information can be inferred from the angular distributions of the daughter particles\nin the W-boson or top quark rest frame, respectively. The W-boson can be produced with right, left or\nlongitudinal polarizations, with corresponding partial widths \u0393R, \u0393L, \u03930 that depend on new anomalous\ncouplings [61] (VR, VL, gL and gR) which can appear at the Wtb vertex (see Eq. 1).\n4.1\nW-boson polarization and t\u00aft spin correlation measurements\nThe probability for the three helicity states of W-boson produced in top quark decay, F0 (longitudinal),\nFL (left-handed) and FR (right-handed), can be extracted from the \u03a8 angular distribution [61] :\n1\nN\ndN\nd cos\u03a8 = 3\n2\n\"\nF0\n\u0012sin\u03a8\n\u221a\n2\n\u00132\n+FL\n\u00121\u2212cos\u03a8\n2\n\u00132\n+FR\n\u00121+cos\u03a8\n2\n\u00132#\n,\n(5)\nwhere \u03a8 is the angle between the W-boson direction in the top quark rest frame and the charged lepton\ndirection in the W-boson rest frame obtained by a boost along the W-boson \ufb02ying direction in the top\nquark rest frame. The correlation between the parameter couples (F0,FL), (F0,FR) and (FL,FR) are -0.9,\n-0.8 and 0.4, respectively.\nAlthough, in the Standard Model, top quarks are produced unpolarised in t\u00aft events, their spins are\ncorrelated [62]. The production asymmetry A in these events, measures the spin correlation and is de\ufb01ned\nas\nA = \u03c3(t\u2191\u00aft\u2191)+\u03c3(t\u2193\u00aft\u2193)\u2212\u03c3(t\u2191\u00aft\u2193)\u2212\u03c3(t\u2193\u00aft\u2191)\n\u03c3(t\u2191\u00aft\u2191)+\u03c3(t\u2193\u00aft\u2193)+\u03c3(t\u2191\u00aft\u2193)+\u03c3(t\u2193\u00aft\u2191),\n(6)\nTOP \u2013 TOP QUARK PROPERTIES\n1013\n\nwhere \u03c3(t\u2191/\u2193\u00aft\u2191/\u2193) denotes the production cross-section of a top quark pair with spins up or down with\nrespect to a selected quantisation axis. It can be extracted from the \u03b81 and \u03b82 angular distributions [62]:\n1\nN\nd2N\nd cos\u03b81d cos\u03b82\n= 1\n4(1\u2212A|\u03b11\u03b12|cos\u03b81 cos\u03b82),\n(7)\nwhere \u03b81 (\u03b82) is the angle between the t (\u00aft) direction, measured in the t\u00aft rest frame, and the direction\nof the t (\u00aft) decay product in the t (\u00aft) rest frame obtained by a boost along t (\u00aft) direction in the t\u00aft rest\nframe, \u03b1i is the spin analysing power of the top quark decay product i, which ranges between \u22121 and 1\nand measures the degree to which its direction is correlated with the spin of the parent top quark. The\nparameter AD de\ufb01ned in [20], used to measure the production asymmetry in another basis, is extracted\nfrom the \u03a6 angular distribution [62] :\n1\nN\ndN\nd cos\u03a6 = 1\n2(1\u2212AD|\u03b11\u03b12|cos\u03a6),\n(8)\nwhere \u03a6 is the angle between the direction of \ufb02ight of the two spin analysers, de\ufb01ned in the t and \u00aft rest\nframes respectively.\nTable 6: Standard Model values of W-boson polarization parameters(F0, FL, FR) at the next-to-leading\norder and t\u00aft spin correlation parameters (A, AD) at leading order for a top quark mass of 175 GeV. For A\nand AD the asterisk superscript means that mt\u00aft < 550 GeV is applied.\nF0\nFL\nFR\nA*\nAD*\n0.695\n0.304\n0.001\n0.422\n-0.290\nThe Standard Model predictions for the W-boson polarization (F0, FL, FR), at next-to-leading or-\nder, and t\u00aft spin correlation (A, AD), at leading order, are given in Table 6. The ATLAS sensitivity to\nthese observables has been evaluated with an ATLFAST simulation [20] and a full simulation of a per-\nfect detector [63]. A precision of 1% to 5% should be achievable with 10 fb\u22121 of data, dominated by\nsystematic uncertainties (in particular from the b-jet energy scale). This measurement requires a com-\nplete reconstruction of the t\u00aft system and a reliable Monte Carlo description to correct the distortion\ninduced by trigger, cuts and reconstruction. In this section the robustness of the analysis with a realis-\ntic detector simulation including triggering is assessed. Only the semileptonic topology of the t\u00aft events\n(tt \u2192WWbb \u2192\u2113\u03bdj1j2bb with \u2113= e,\u00b5) is used as signal (an analysis using t\u00aft dilepton events as signal\ncan improve the results of this study, especially for the t\u00aft spin correlation measurements). In this case the\nmost powerful spin analysers of the top quark are the charged lepton (\u03b11 = 1) and the least energetic non\nb-jet in the top quark rest frame (\u03b1jet = 0.51) [64], which are chosen afterwards for the spin correlation\nmeasurement.\n4.1.1\nEvent simulation and selection\nThe largest statistics Monte Carlo sample was generated with MC@NLO which does not implement t\u00aft\nspin corelations, so it can only be used to study W-boson polarisation. Spin correlations were studied\nusing the smaller AcerMC sample. In both cases, non-semileptonic t\u00aft, semileptonic t\u00aft which decay to \u03c4,\nW-boson+jets and single top quark events were considered as background. Semileptonic signal events\nare characterised by one (and only one) isolated lepton, at least 4 jets, of which at least 2 jets are tagged\nas b-jets, and missing transverse energy. Following the common criteria for the semileptonic selection,\nall kinematic cuts are summarised in Table 7 together with the corresponding signal ef\ufb01ciencies.\nAfter kinematic cuts are applied, the event is fully reconstructed, as described below. The angles \u03a8,\n\u03b81, \u03b82 and \u03a6 are computed and the polarization parameters are extracted.\nTOP \u2013 TOP QUARK PROPERTIES\n1014\n\nTable 7: Selection cuts used and corresponding ef\ufb01ciencies for semileptonic t\u00aft MC@NLO events and t\u00aft\nAcerMC events.\nVariables\nCuts\nEf\ufb01ciency (%)\nMC@NLO\nAcerMC\nLepton\nexactly 1 identi\ufb01ed\n57.8\n58.7\nJets\nat least 4 selected jets\n59.3\n62.1\nb-tagging\nat least 2 are tagged as b\n32.0\n31.0\nMissing energy\npmiss\nT\n> 20 GeV\n92.0\n92.2\nCumulative ef\ufb01ciency\n9.4\n9.8\n4.1.2\nW-boson and top quark reconstruction\nThe energies of all jets are calibrated according to the comparison with the energies of corresponding\nparton level quarks before selection and reconstruction. Then, in the event reconstruction, the light jet\npair with invariant mass mjj closest to the known W-boson mass, mW, is selected to reconstruct the W-\nboson which decays hadronically. This W-boson is then combined with one of the b-jets to reconstruct\nthe top quark. As there are several possible combinations, the one which gives the mass closest to the\ntop quark mass mt is assumed to be the correct one. The b-jet which is closest to the lepton in \u2206R among\nthe remaining b-jets, is reserved for reconstructing the other top quark whose daughter W-boson decays\nleptonically. To reconstruct the W-boson which decays leptonically, the neutrino pT is taken as the\nmissing transverse energy. Its longitudinal component pz is determined by constraining ml\u03bd to mW [63].\nWhen two solutions for pz are found, the one giving m\u2113\u03bdb closer to mt is kept.\nQuality cuts |mjjb \u2212mt| < 35 GeV, |m\u2113\u03bdb \u2212mt| < 35 GeV and |mjj \u2212mW| < 20 GeV are applied to\nreject badly reconstructed events. At this stage, 2.8% of the signal events are kept for MC@NLO events\nand 2.7% for AcerMC events, corresponding to 7000 signal events for 1 fb\u22121 of data (Table 8). After this\nevent selection, the main background comes from the t\u00aft \u2192\u03c4 +X events, where the tau decays to electron\nor muon. The number of events from W-boson+jets and single top quark channels is less than 3% of the\nselected number of signal events, so we neglect them in the following sections. Due to this cancellation of\nthe background, the S/B ratio can be affected as much as 20%, which is taken as a systematic uncertainty\n(see Table 10).\nAfter event reconstruction, the angle \u03a8 (W-boson polarization) as well as the angles \u03b81, \u03b82 and \u03a6\n(t\u00aft spin correlations) are computed using the prescription descibed at the beginning of Section 4. The\nmeasured distributions of cos\u03a8, cos\u03b81\u00d7cos\u03b82 and cos\u03a6 are distorted, compared with their distributions\nat parton level. The detector resolution results in much smaller smearing effect on the \ufb01nal particles than\nthat coming from particle radiation, quark fragmentation-hadronization and \ufb01nal event reconstruction.\nThat is to say, the latter effects dominate the resolution of the reconstructed objects from top quark de-\ncay [65]. A correction function, taken from the ATLFAST simulation, is used to recover the distributions\nat parton level. With ATLFAST data, the correction function is obtained from the ratio between the two\nnormalized distributions of the cos\u03a8 (i.e. after reconstruction of the signal and main background events\nand at parton level of the pure signal). To correct for the distortion, a weight derived from this function\nis applied on all the reconstructed cos\u03a8 of full simulation, on an event by event basis, allowing to re-\ncover, as much as possible, the shape of the distribution of the cos\u03a8 of the pure signal at parton level. A\ndetailed description of the method can be found in [20].\nTOP \u2013 TOP QUARK PROPERTIES\n1015\n\nTable 8: The number of signal (MC@NLO) and the most important background events before (left) and\nafter (right) selection for 1 fb\u22121. \u2217: in the single top quark decay W\u2192e/\u00b5/\u03c4 +\u03bd mode\nEvents for\nSelected events\n1 fb\u22121(\u00d7103)\nfull simulation\nSignal (t\u00aft semileptonic)\n250\n7000\nt\u00aft \u2192\u03c4 +X\n130\n710\nW(\u2192l\u03bd)+ jets\n800\n[10,55]\nSingle t (Wt channel)\n25\u2217\n90\nSingle t (t channel)\n80\u2217\n55\n4.1.3\nImpact of the trigger on the analysis\nSemileptonic t\u00aft events are characterised by a single isolated lepton, which can be used to trigger the\nevents with high ef\ufb01ciency. Applying the trigger selection to events passing the standard selection cuts,\n15% of well reconstructed events are lost. The measurement results with and without trigger applied on\nthe data, while keeping all other aspects of the measurement unchanged, were compared. The effect of\nthe trigger on the measurements of the W-boson polarization is almost zero But the effect on the t\u00aft spin\ncorrelations is not negligible, and is taken as a systematic error, shown in Table 10.\n4.1.4\nMeasurement of the W-boson polarization\nFigure 5 shows the correction function (left) and the reconstructed cos\u03a8 distribution (right) after applying\nthe correction function. This distribution is \ufb01tted to Eq. (5) varying F0, FL and FR, but constrained by\nF0 + FL + FR = 1. The \ufb01t is restricted to the region \u22120.9 < cos\u03a8 < 0.8, which is the most extended\nregion where the correction is varying slowly. The results are shown in Table 9.\n\u03a8\ncos\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\n1/weight\n0.5\n1\n1.5\n2\n2.5\nATLAS\n\u03a8\ncos\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\nEvents (normalized)\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n-1\nL = 730 pb\nFigure 5: Left: Correction function taken from ATLFAST simulation \ufb01tted with a third order polynomial\nfunction. Right: Normalised reconstructed and corrected distribution of cos\u03a8, the full line corresponds\nto the \ufb01t to Eq. (5). The sample has an integrated luminosity of 730 pb\u22121.\nTwo complementary methods to extract the W-boson helicity fractions, using the observed angular\ndistribution between the charged lepton direction in the W-boson rest frame and the W-boson direction in\nthe top quark rest frame, are currently under development at ATLAS inspired on Tevatron methods [5,66].\nTOP \u2013 TOP QUARK PROPERTIES\n1016\n\n4.1.5\nMeasurement of t\u00aft spin correlation\nAt parton level, before any phase space cut, the two estimators C = \u22129 \u00d7 cos\u03b81 cos\u03b82 and D = \u22123 \u00d7\ncos\u03a6 are unbiased [20]. Figure 6 shows the reconstructed distributions of \u22129 \u00d7 cos\u03b81 cos\u03b82/0.51 and\n\u22123 \u00d7 cos\u03a6/0.51 after correction. It should be stressed that, in the evaluation of the t\u00aft spin correlation\nparameters, the theoretical value for the spin analyzing power for signal events (0.51) was assumed for\nboth cases. The means of the distributions are unbiased estimators of A and AD, provided corrections for\n/0 51\n2\n\u03b8\n*cos\n1\n\u03b8\n-9*cos\n-15\n-10\n-5\n0\n5\n10\n15\nEvents\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\nATLAS\n-1\nL = 220 pb\n/0.51\n\u03a6\n-3*cos\n-4\n-2\n0\n2\n4\nEvents\n20\n40\n60\n80\n100\n120\n140\n160\nATLAS\n-1\nL = 220 pb\nFigure 6: Left: Reconstructed and corrected distribution of \u22129 \u00d7 cos\u03b81 cos\u03b82/0.51. Right: Recon-\nstructed and corrected distribution of \u22123 \u00d7 cos\u03a6/0.51. The integrated luminosity of the sample is 220\npb\u22121 in each case.\nphysics effects and detector effects are fully carried out.\nDue to the fact that the ATLFAST was used to extract the correction function, an additional system-\natic uncertainty of 0.25 was derived for the A spin correlation parameter. This uncertainty re\ufb02ects the\ndifferent parametrizations of the Monte Carlo simulations. Preliminary studies suggest that this shift can\nbe removed by using high statistics full simulation samples to derive the correction functions and for this\nreason this uncertainty was not included in Table 10.\nTable 9: W-boson polarization and top quark spin correlation parameters extracted after triggering. The\nindicated errors are statistical and systematic, respectively.\nW-boson polarization\nFL\nF0\nFR\n0.29 \u00b10.02 \u00b10.03\n0.70 \u00b10.04 \u00b10.02\n0.01 \u00b10.02 \u00b10.02\nt\u00aft spin correlation\nA\nAD\n0.67 \u00b10.17\u00b10.18 \u00b10.25\n-0.40 \u00b10.11 \u00b10.09\n4.1.6\nSystematic uncertainties\nThe systematic uncertainties were estimated with ATLFAST simulation for the factorisation scale, struc-\nture function, ISR, FSR, b-fragmentation, top quark mass, hadronization scheme and pile-up effects, and\nwith full simulation for the b-tagging ef\ufb01ciency, b-jet energy scale, light jet energy scale and signal to\nbackground ratio (S/B scale) as listed in Table 10, for the measurement of the W-boson helicity fractions\nand top quark pair spin correlations respectively.\nWith data, t\u00aft events can be reconstructed without requiring b-jet tagging on the side of top quark\nwhose daughter W-boson decays leptonically. This can provide a pure sample of b-jets which can be\nTOP \u2013 TOP QUARK PROPERTIES\n1017\n\nTable 10: Systematics for W-boson polarization and top quark spin correlation measurement.\nSource of uncertainty\nFL\nF0\nFR\nA\nAD\nFactorisation\n0.000\n0.001\n0.001\n0.029\n0.006\nStructure function\n0.003\n0.003\n0.004\n0.033\n0.012\nISR\n0.001\n0.002\n0.001\n0.002\n0.001\nFSR\n0.009\n0.007\n0.002\n0.023\n0.016\nb-fragmentation\n0.001\n0.002\n0.001\n0.031\n0.018\nHadronization scheme\n0.010\n0.016\n0.006\n0.006\n0.008\nPile-up (2.3 events)\n0.005\n0.002\n0.006\n0.001\n0.005\nInput top quark mass (2 GeV)\n0.015\n0.011\n0.004\n0.028\n0.013\nb-tagging ef\ufb01ciency (5%)\n0.007\n0.002\n0.005\n0.027\n0.07\nb-jet energy scale (5%)\n0.02\n0.002\n0.02\n0.07\n0.015\nlight-jet energy scale (5%)\n-\n-\n-\n0.11\n0.017\nS/B scale (20%)\n0.004\n0.002\n0.001\n0.000\n0.004\nTrigger\n-\n-\n-\n0.10\n0.03\nTOTAL\n0.03\n0.02\n0.02\n0.18\n0.09\nused to check the uncertainty on the b-tagging ef\ufb01ciency [67]. The b-jet energy miscalibration can also\nbe obtained from other control samples, such as Z+b-jet events [68].\n4.2\nAnomalous couplings at the Wtb vertex\nThe W-boson polarisation is sensitive to new anomalous couplings (VL, VR, gL and gR) associated with\nthe Wtb vertex. Although the W-boson helicity fractions (F0, FL and FR) depend on these couplings, the\nhelicity ratios \u03c1R,L \u2261\u0393R,L/\u03930 = FR,L/F0, were found to be more sensitive to VL, VR, gL and gR. The\n\u03c1R and \u03c1L observables are independent quantities and take the LO values \u03c1R = 5.1\u00d710\u22124, \u03c1L = 0.423\nin the Standard Model. General expressions for \u03c1R,L in terms of the new anomalous couplings can\nbe found in Ref. [19]. As for the helicity fractions, the measurement of helicity ratios sets bounds on\nVR, gL and gR. A third and simpler method to extract information about the Wtb vertex is through\nangular asymmetries involving the angle of the charged lepton in the W-boson rest frame and the W-\nboson direction in the top quark rest frame (introduced in the previous section). For any \ufb01xed z in the\ninterval [\u22121,+1], one can de\ufb01ne asymmetries as the difference between the number of events above and\nbelow z, normalised to the total number of events. The most obvious choice is z = 0, giving the forward-\nbackward asymmetry AFB [18,69]. The forward-backward asymmetry is related to the W-boson helicity\nfractions by AFB = 3\n4 [FR \u2212FL]. Other convenient choices are z = \u2213(22/3 \u22121). De\ufb01ning \u03b2 = 21/3 \u22121,\nwe have A+ = 3\u03b2[F0 + (1 + \u03b2)FR] and A\u2212= \u22123\u03b2[F0 + (1 + \u03b2)FL]. Thus, A+ (A\u2212) only depend on F0\nand FR (FL). The LO Standard Model values of these asymmetries are AFB = \u22120.223, A+ = 0.548,\nA\u2212= \u22120.840. They are sensitive to anomalous Wtb interactions, and their measurement allows to probe\nthis vertex without the need of a \ufb01t to the distribution of the angle between the charged lepton direction\nin the W-boson rest frame and the W-boson direction in the top quark rest frame. In the present analysis\nthe ATLAS sensitivity to the \u03c1L, \u03c1R, AFB, A+ and A\u2212observables is studied.\n4.2.1\nEvent selection\nIn this section an alternative two-level likelihood analysis is explored for the semileptonic channel, i.e.\nt\u00aft \u2192W+bW\u2212\u00afb where one of the W-bosons decays hadronicaly and the other one decays in the leptonic\nTOP \u2013 TOP QUARK PROPERTIES\n1018\n\nchannel W \u2192\u2113\u03bd\u2113(with \u2113= e,\u00b5). Any other process constitutes a background to this signal. In particular,\nit should be noticed that the fully hadronic, dileptonic and semileptonic (with one of the W-bosons\ndecaying into \u03c4\u03bd) t\u00aft channels are considered backgrounds to the present analysis.\nAdditionally, the\nfollowing Standard Model processes were considered as background: single top production, W+jets,\nWb\u00afb+jets, Wc\u00afc+jets, Z \u2192e+e\u2212, Z \u2192\u00b5+\u00b5\u2212, Z \u2192\u03c4+\u03c4\u2212, WW, ZZ and WZ. The likelihood analysis\nis based on the construction of a discriminant variable which uses distributions of some kinematical\nproperties of the events. In the \ufb01rst analysis level (called the pre-selection), the common selection criteria\nfor the semileptonic topology, with the exception of the b-tagging requirement on jets, was applied to the\nevent. The full event reconstruction was performed using a \u03c72, de\ufb01ned by\n\u03c72 = (m\u2113\u03bdja \u2212mt)2\n\u03c3 2t\n+ (mjbjcjd \u2212mt)2\n\u03c3 2t\n+ (m\u2113\u03bd \u2212mW)2\n\u03c3 2\nW\n+ (mjcjd \u2212mW)2\n\u03c3 2\nW\n,\n(9)\nwhere mt = 175 GeV, mW = 80.4 GeV, \u03c3t = 14 GeV and \u03c3W = 10 GeV are the expected top quark\nand W-boson mass resolutions3, \u2113represents the selected electron or muon, m\u2113\u03bd is the invariant mass\nof the electron (muon) and the neutrino, and ja,b,c,d corresponds to all the possible combinations among\nthe four jets with highest pT (with m\u2113\u03bdja, mjbjcjd and mjcjd being the corresponding invariant masses).\nThe neutrino was reconstructed using the missing transverse energy and allowing the p\u03bd\nz to vary in the\nrange [\u2212500,+500] GeV. The solution corresponding to the minimum \u03c7 2 was chosen. The jets used\nto reconstruct the hadronic W-boson will be labelled \u201cnon-b\u201d jets and the remaining two are labelled\n\u201cb-jets\u201d. It should be stressed that no b-tagging information was used so far. The pre-selection was\ncompleted by requiring \u03c72 < 16. In the second level (the \ufb01nal selection), signal and background-like\nprobabilities were constructed for each event (Psignal\ni\nand Pback.\ni\n, respectively) using probability density\nfunctions (p.d.f.) built from relevant physical variables: the cosine of the angle between the leptonic top\nquark and the leptonic \u201cb-jet\u201d, the transverse momentum of the hadronic W, the hadronic and leptonic\ntop quark masses, the transverse momentum of the two \u201cb-jets\u201d, the transverse momentum of the lepton\nand the\np\n\u03c72 distribution. It should be stressed that the objective is to test the sensitivity for new physics\nexclusion, under the hypothesis that the Standard Model holds, and the simulation was done assuming\nno anomalous couplings. Signal (LS = \u03a0n\ni=1Psignal\ni\n) and background (LB = \u03a0n\ni=1Pback.\ni\n) likelihoods\n(with n = 8, the number of p.d.f.) are used to de\ufb01ne a discriminant variable LR = log10(LS/LB). The\ndistribution of this variable is shown in Figure 7(a). The \ufb01nal event selection is done by applying the\ncut LR > 0.1 on the discriminant variable. The number of signal and background events (normalised to\nL = 1 fb\u22121) after the pre-selection and \ufb01nal selection are shown in Table 11. After the \ufb01nal selection\n(including the trigger), the dominant backgrounds are W+jets and semileptonic t\u00aft with taus in the \ufb01nal\nstate (corresponding to 49%, and 29% of the total background, respectively, as shown in Table 12).\nThe effect of the single lepton trigger on the event selection was studied. The results are summarised\nin Table 11. In what follows, only events passing the trigger are considered.\nOnce b-tagging is well understood, additional information can be used. In this case only jets with\na positive b-tagging weight were considered as \u201cb-jet\u201d candidates for the \u03c7 2 minimisation method. In\naddition, the b-tagging weights of these jets were considered as p.d.f.s for the discriminant variable\nevaluation. In this case, the number of selected signal and background events for L = 1 fb\u22121 is expected\nto be (6.6\u00b10.1)\u00d7103 and (0.9\u00b10.1)\u00d7103, respectively. The t\u00aft background is expected to be dominant\n(72% of the total background, mainly due to the semileptonic channel with taus in the \ufb01nal state) and the\nW+jets and single top processes correspond to 15% and 13% of the total background, respectively. The\ndiscriminant variables corresponding to the analysis with and without b-tagging are shown in Figure 7.\n3These resolutions are taken from the top quark mass measurement analyses [70]. It should be noticed that \u03c3t and \u03c3W can\nbe interpreted as weights for each term of the \u03c72 de\ufb01nition. By changing their values by a factor \u223c2, the obtained observables\n(\u03c1L, \u03c1R,A+ and A\u2212) are the same within the statistical error.\nTOP \u2013 TOP QUARK PROPERTIES\n1019\n\nTable 11: Number of signal t\u00aft \u2192\u2113\u03bdb\u00afbq\u00afq\u2032 and background events (and corresponding statistical error),\nnormalised to L = 1 fb\u22121, after the pre-selection and \ufb01nal selection for the analysis without b-tagging.\nThe effect of the trigger on the event selection is also shown.\ne+ \u00b5 sample\ne sample\n\u00b5 sample\nTotal background\npresel.\n(15.8\u00b10.4)\u00d7103\n(7.2\u00b10.3)\u00d7103\n(8.6\u00b10.3)\u00d7103\n\ufb01nal sel.\n(5.2\u00b10.2)\u00d7103\n(2.5\u00b10.2)\u00d7103\n(2.8\u00b10.2)\u00d7103\ntrigger\n(4.0\u00b10.2)\u00d7103\n(1.8\u00b10.2)\u00d7103\n(2.1\u00b10.2)\u00d7103\nSignal\npresel.\n(27.4\u00b10.2)\u00d7103\n(12.0\u00b10.1)\u00d7103\n(15.5\u00b10.1)\u00d7103\n\ufb01nal sel.\n(15.2\u00b10.1)\u00d7103\n(6.5\u00b10.1)\u00d7103\n(8.8\u00b10.1)\u00d7103\ntrigger\n(12.6\u00b10.1)\u00d7103\n(5.8\u00b10.1)\u00d7103\n(6.9\u00b10.1)\u00d7103\nTable 12: Background composition and corresponding statistical error, normalised to L = 1 fb\u22121, after\nthe \ufb01nal selection, including the effect of the trigger, for the analysis without b-tagging.\ne+ \u00b5 sample\ne sample\n\u00b5 sample\nW+jets, Wbb+jets, Wc\u00afc+jets\n(19.6\u00b11.9)\u00d7102\n(8.8\u00b11.4)\u00d7102\n(10.3\u00b11.4)\u00d7102\nZ+jets\n(1.6\u00b10.4)\u00d7102\n(1.2\u00b10.4)\u00d7102\n(0.5\u00b10.3)\u00d7102\nWZ, ZZ, WW\n(0.4\u00b10.2)\u00d7102\n(0.3\u00b10.1)\u00d7102\n(0.2\u00b10.1)\u00d7102\nt\u00aft (except signal)\n(13.1\u00b10.6)\u00d7102\n(5.4\u00b10.3)\u00d7102\n(7.9\u00b10.4)\u00d7102\nsingle top\n(5.3\u00b10.3)\u00d7102\n(2.5\u00b10.2)\u00d7102\n(2.7\u00b10.2)\u00d7102\n4.2.2\nMeasurement of the angular distribution and asymmetries\nThe experimentally observed angular distribution, which includes the t\u00aft signal as well as the Standard\nModel background, is affected by detector resolution, t\u00aft reconstruction and selection criteria [71]. In\norder to recover the Standard Model distribution, it is necessary to subtract the background and correct\nfor the effects of the detector, event selection and reconstruction. For this purpose, two different sets\nof signal and background event samples were used: one \u201cexperimental\u201d set, which simulates a possible\nexperimental result, and one \u201creference\u201d set, which is used to parametrise the effects mentioned, and cor-\nrect the previous sample. The procedure is as follows. After subtracting reference background samples,\nthe full \u201cexperimental\u201d distribution is multiplied by a correction function fc in order to recover the Stan-\ndard Model one. This correction function is determined by assuming that the charged lepton distribution\ncorresponds to the Standard Model. In case that a deviation from Standard Model predictions (corre-\nsponding to anomalous couplings) is found, the correction function must be modi\ufb01ed accordingly, and\nthe expected distribution recalculated in an iterative process. These issues have been analysed in detail in\nRef. [20], where it was shown that this process quickly converges. The correction function is calculated,\nfor each bin of the angular distribution, by dividing the number of generated events by the number of\nselected events, using the reference sample. In order to avoid non-physical \ufb02uctuations due to the limited\namount of Monte Carlo statistics, a smoothing procedure was applied to the obtained correction function.\nThe value of fc is in the range [0.2,1.4]. Other methods of correcting the angular distribution are under\ninvestigation.\nThe procedure of correcting for detector and reconstruction effects in the asymmetries is similar to\nthat used with the full angular distribution, but using only two or three bins. This has the advantage\nthat the asymmetry measurements are less sensitive to the extreme values of the angular distributions,\nTOP \u2013 TOP QUARK PROPERTIES\n1020\n\n\u2014 signal\nbackground\n)\nB\n/L\nS\n (L\n10\n = log\nR\nL\n-3\n-2\n-1\n0\n1\n2\n3\nevents/bin\n0\n500\n1000\n1500\n2000\n2500\nATLAS\n-1\nL = 1 fb\n (no b-tag)\n\u00b5\ne+\n-3\n-2\n-1\n0\n1\n2\n3\n0\n500\n1000\n1500\n2000\n2500\n)\nB\n/L\nS\n (L\n10\n = log\nR\nL\n-3\n-2\n-1\n0\n1\n2\n3\nevents/bin\n0\n200\n400\n600\n800\n1000\nATLAS\n-1\nL = 1 fb\n (b-tag)\n\u00b5\n e+\n-3\n-2\n-1\n0\n1\n2\n3\n0\n200\n400\n600\n800\n1000\n(a)\n(b)\nFigure 7: Discriminant variables for the Standard Model background (shaded region) and the t\u00aft signal\n(full line), normalised to L = 1 fb\u22121 corresponding to the (a) analysis without b-tagging and (b) analysis\nusing the b-tagging weights of the \u201cb-jets\u201d selected by the \u03c72 minimisation method.\nwhere correction functions deviate from unity. Moreover, it should be noticed that the extreme bins of\nthe angular distribution have a very signi\ufb01cant impact on the measurement of the \u03c1L and \u03c1R helicity\nratios. The values obtained from a \ufb01t to the corrected distribution, as well as the angular asymmetries\nAFB, A\u00b1, are collected in Table 13, with their statistical uncertainties. Although the statistical errors of the\nobservables obtained for the analyses without and with b-tagging are similar, the use of this tool allows to\nimprove the signal to background ratio, leading to smaller systematic uncertainties, as discussed below.\nTable 13: Expected values and corresponding statistical errors for the helicity ratios and angular asym-\nmetries. The results for an integrated luminosity of 1 fb\u22121 (analyses with and without b-tagging) are\nshown.\n\u03c1L\n\u03c1R\nAFB\nA+\nA\u2212\nAnalysis without b-tagging\ne+ \u00b5\n0.402 \u00b1 0.050\n-0.008 \u00b1 0.008\n-0.220 \u00b1 0.025\n0.560 \u00b1 0.024\n-0.845 \u00b1 0.012\nAnalysis with b-tagging\ne+ \u00b5\n0.453 \u00b1 0.048\n-0.004 \u00b1 0.007\n-0.229 \u00b1 0.026\n0.542 \u00b1 0.028\n-0.830 \u00b1 0.014\n4.2.3\nSystematic uncertainties\nThe study of the systematic uncertainties considered possible errors from different sources: jet energy\nscale, luminosity, top quark mass, background level, ISR and FSR, Monte Carlo generator and pile-up.\nThe jet calibration used in the present analyses is described in Ref. [70]. As for the reference analyses,\nfull simulation Monte Carlo samples were used for the study of all the systematic sources of uncertainty.\nOnly the simulated sample used as the \u201cexperimental\u201d set (which fakes the data) was changed for each\nsystematic source of uncertainty. The correction function and the Monte Carlo sample used to perform\nthe background subtraction were kept unchanged. The impact on the measurements is summarised in\nTables 14 and 15. As the background subtraction is based on Monte Carlo simulation, the background\nestimation required a luminosity value and therefore the corresponding systematic uncertainty was con-\nsidered. Once the cross-sections for known backgrounds are measured with data, a data-driven normali-\nTOP \u2013 TOP QUARK PROPERTIES\n1021\n\nsation will be possible and the luminosity systematic error should be reduced. Moreover, with data it will\nbe possible to compare the discriminant variable distributions for selected events obtained from data and\nMonte Carlo. This comparison will allow the correction of systematic uncertainties caused by inaccurate\ndescription of data by the Monte Carlo simulation.\nTable 14: Sources of systematic uncertainties in the determination of the helicity ratios and angular\nasymmetries (analysis without b-tagging).\nSource\n\u03c1L\n\u03c1R\nAFB\nA+\nA\u2212\nJet energy scale\n0.02\n0.003\n0.004\n0.006\n0.002\nLuminosity\n0.02\n0.002\n0.006\n0.005\n0.001\nTop quark mass\n0.02\n0.002\n0.009\n0.006\n0.004\nBackground\n0.01\n0.002\n0.005\n0.003\n0.002\nISR+FSR\n0.13\n0.009\n0.044\n0.046\n0.011\nMC generator\n0.18\n0.013\n0.039\n0.042\n0.001\nPile-up\n0.14\n0.004\n0.053\n0.039\n0.017\nTotal\n0.27\n0.017\n0.080\n0.074\n0.021\nTable 15: Sources of systematic uncertainties in the determination of the helicity ratios and angular\nasymmetries (analysis with b-tagging).\nSource\n\u03c1L\n\u03c1R\nAFB\nA+\nA\u2212\nJet energy scale\n0.04\n0.001\n0.010\n0.004\n0.002\nLuminosity\n0.01\n0.000\n0.006\n0.005\n0.001\nTop quark mass\n0.03\n0.003\n0.013\n0.008\n0.006\nBackground\n0.01\n0.000\n0.003\n0.002\n0.004\nISR+FSR\n0.05\n0.006\n0.024\n0.028\n0.015\nMC generator\n0.01\n0.008\n0.009\n0.011\n0.000\nPile-up\n0.15\n0.006\n0.012\n0.041\n0.022\nTotal\n0.16\n0.012\n0.033\n0.052\n0.027\n4.2.4\nConstraints on the anomalous couplings\nUsing the parametric dependence of the observables on VR, gL and gR (and considering the correlations\nbetween them, which are shown in Table 16), constraints can be set on the anomalous couplings. The\nhelicity ratios \u03c1R,L and the asymmetries A\u00b1 were used as input for the program TopFit [19]. The\nexpected 68% CL allowed regions on the Wtb anomalous couplings for L = 1 fb\u22121 (analyses with and\nwithout b-tagging) are shown in Figure 8. In addition to the allowed regions of Figure 8, additional\nsolutions can be found at gR \u223c0.8. Such solutions are due to a large cancellation between O(gR) and\nO(gR2) terms and can be excluded by the measurement at the LHC of the single top cross-section [72].\nTOP \u2013 TOP QUARK PROPERTIES\n1022\n\nTable 16: Correlation matrix for the A\u00b1, \u03c1R,L observables.\nA+\nA\u2212\n\u03c1L\n\u03c1R\nA+\n1\n0.16\n-0.73\n-0.14\nA\u2212\n0.16\n1\n-0.10\n0.55\n\u03c1L\n-0.73\n-0.10\n1\n0.42\n\u03c1R\n-0.14\n0.55\n0.42\n1\nFigure 8: Expected 68% CL allowed regions on the Wtb anomalous couplings for luminosities of 1 fb\u22121\n(with and without b-tagging), obtained from the \u03c1R,L and A\u00b1 observables using TopFit.\n5\nRare Top Quark Decays and FCNC\nThis section discusses the study of rare top quark decays via FCNC (t \u2192qX,X = \u03b3,Z,g) using t\u00aft events\nproduced at the LHC. These decays are strongly suppressed in the Standard Model at tree level due to\nthe GIM mechanism. In the effective Lagrangian approach [73,74] the new top quark decay rates to the\ngauge bosons can be expressed in terms of the \u03bag\ntq, \u03ba\u03b3\ntq, (|vZ\ntq|2 + |aZ\ntq|2) and \u03baZ\ntq anomalous couplings to\nthe g, \u03b3 and Z bosons respectively, and \u039b, the energy scale associated with the new physics.\n5.1\nEvent samples\nThe signal event samples used in this analysis correspond to t\u00aft \u2192b\u2113\u03bdqX, where X = \u03b3,Z \u2192\u2113\u2113,g and \u2113=\ne,\u00b5. The following common Standard Model samples were considered as background: fully hadronic,\nfully leptonic and semi-leptonic t\u00aft, all from MC@NLO; Wt, s- and t- channels of single top production,\nall from AcerMC; W+jets, Wb\u00afb+jets and Wc\u00afc+jets, all from ALPGEN; Z \u2192e+e\u2212, Z \u2192\u00b5+\u00b5\u2212and\nZ \u2192\u03c4+\u03c4\u2212, all from PYTHIA; WW, ZZ and WZ, all from HERWIG.\n5.2\nEvent selection\nThe t\u00aft \ufb01nal states corresponding to the different FCNC top quark decay modes lead to different topologies\naccording to the number of jets, leptons and photons. There is however a common characteristic of all\nchannels under study, i.e. in all of them one of the top quarks is assumed to decay through the dominant\nStandard Model decay mode t \u2192bW and the other is forced to decay via one of the FCNC modes t \u2192qZ,\nt \u2192q\u03b3 or t \u2192qg. The QCD backgrounds at hadron colliders make the search for the signal via the fully\nhadronic channels (when the W and the Z bosons decay to quarks) dif\ufb01cult. For this reason only the\nTOP \u2013 TOP QUARK PROPERTIES\n1023\n\nTable 17: Selection cuts applied to the FCNC analyses. For the t \u2192qg channel, Evis, pTg and mqg\nrepresent the total visible energy, the transverse momentum of the jet associated with the gluon and the\nreconstructed mass of the top quark with FCNC decay, respectively (see text for details).\nChannel\nt\u00aft \u2192bWq\u03b3\nt\u00aft \u2192bWqg\nt\u00aft \u2192bWqZ\nPre-selection\n= 1\u2113(pT > 25 GeV)\n= 1\u2113(pT > 25 GeV)\n= 3\u2113(pT > 25,15,15 GeV)\n\u22652j (pT > 20 GeV)\n= 3j (pT > 40,20,20 GeV)\n\u22652j (pT > 30,20 GeV)\n= 1\u03b3 (pT > 25 GeV)\n= 0\u03b3 (pT > 15 GeV)\n= 0\u03b3 (pT > 15 GeV)\n\u0338 pT > 20 GeV\n\u0338 pT > 20 GeV\n\u0338 pT > 20 GeV\nFinal\npT\u03b3 > 75 GeV\nEvis > 300 GeV\n2 \u2113same \ufb02avour,\nselection\npTg > 75 GeV\noppos. charge\nmqg > 125 GeV\nmqg < 200 GeV\nTrigger\ne22i, mu20 or g55\ne22i or mu20\ne22i or mu20\nTable 18: The trigger ef\ufb01ciency, in percentage, for the background and signal events after all the other\ncuts of the FCNC analyses.\nt \u2192q\u03b3\nt \u2192qZ\nt \u2192qg\nSig.\nBack.\nSig.\nBack.\nSig.\nBack.\nTrigger\n99.6\n99.5\n99.2\n95.0\n83.2\n82.2\nleptonic decays of both W and Z to e and \u00b5 were taken into account. Only isolated muons, electrons\nand photons separated by \u2206R > 0.4 from other reconstructed objects, were considered. Speci\ufb01c pre-\nselection and selection cuts were applied for each FCNC channel, as outlined in Table 17.\nFor the\nt \u2192q\u03b3 channel, exactly one reconstructed lepton and one reconstructed photon where required in the\nevents. Additionally, at least two jets were required. For the t \u2192qg channel, the events had to have\nexactly one reconstructed lepton, three jets and no reconstructed photon. Finally, for the t \u2192qZ channel,\nonly the events with at least two jets, exactly three reconstructed leptons and no reconstructed photons\nwere accepted. Therefore, the selection criteria for these channels are orthogonal. The expected number\nof background events and signal ef\ufb01ciencies after the \ufb01nal selection are shown in Table 19. The effect of\nthe trigger on the background and signal events, after all the other cuts, is shown in Table 18. It should be\nnoticed that the events of the t \u2192q\u03b3 (t \u2192qZ) channel can be triggered by the lepton or the photon (one of\nthe three leptons), which results on higher trigger ef\ufb01ciencies, when compared with the t \u2192qg channel\nwith just one lepton. For the t \u2192q\u03b3 channel, the dominant backgrounds are t\u00aft, Z+jets and W+jets\nevents, which correspond to 38%, 30% and 29% of the total background. The total background for the\nt \u2192qZ channel is mainly composed of t\u00aft and Z+jets events (59% and 28% of the total background,\nrespectively), while for the t \u2192qg it is mainly composed of W+jets and t\u00aft events (which correspond,\nrespectively, to 64% and 25% of the total background).\nFor all the channels, the top quark with Standard Model semileptonic decay (t \u2192b\u2113\u03bd) cannot be\ndirectly reconstructed due to the presence of an undetected neutrino in the \ufb01nal state. The neutrino four-\nmomentum was estimated with a method similar to the one used in Section 4.2, by \ufb01nding the p\u03bd\nZ value\nand the jet combination (and the lepton combination in the case of the qZ topology) which minimizes the\nfollowing expression:\n\u03c72 =\n\u0000mFCNC\nt\n\u2212mt\n\u00012\n\u03c3 2\nt\n+\n\u0000m\u2113a\u03bd j \u2212mt\n\u00012\n\u03c3 2\nt\n+ (m\u2113a\u03bd \u2212mW)2\n\u03c3 2\nW\n+ (m\u2113b\u2113c \u2212mZ)2\n\u03c3 2\nZ\n,\n(10)\nTOP \u2013 TOP QUARK PROPERTIES\n1024\n\nTable 19: The expected number of background events and signal ef\ufb01ciencies after the \ufb01nal selection level\n(the trigger is included) of the analyses for each FCNC channel. The corresponding statistical errors are\nalso shown. The expected background numbers are normalised to L = 1 fb\u22121.\ne\n\u00b5\n\u2113\nt\u00aft \u2192bWq\u03b3:\nTotal\n(4.4\u00b10.6)\u00d7102\n(2.2\u00b10.6)\u00d7102\n(6.5\u00b10.7)\u00d7102\nSignal %\n3.6\u00b10.2\n4.1\u00b10.2\n7.6\u00b10.2\nt\u00aft \u2192bWqZ:\nTotal\n(0.3\u00b10.6)\u00d7102\n(0.1\u00b10.6)\u00d7102\n(1.3\u00b10.6)\u00d7102\nSignal %\n1.4\u00b10.1\n2.5\u00b10.1\n7.6\u00b10.2\nt\u00aft \u2192bWqg:\nTotal\n(11.0\u00b10.3)\u00d7103\n(8.3\u00b10.2)\u00d7103\n(19.3\u00b10.4)\u00d7103\nSignal %\n1.3\u00b10.1\n1.5\u00b10.1\n2.9\u00b10.1\nwhere mFCNC\nt\n, m\u2113a\u03bd j, m\u2113a\u03bd and m\u2113b\u2113c are, for each jet and lepton combination, the reconstructed mass of\nthe top quark decaying via FCNC, the top quark decaying through the Standard Model, the W-boson from\nthe top quark with Standard Model decay and the Z boson from the top quark FCNC decay, respectively.\nThe last term of Eq. 10 was only used in the t \u2192qZ channel. The following values are used for the\nconstraints: mt = 175 GeV, mW = 80.42 GeV, mZ = 91.19 GeV, \u03c3t = 14 GeV, \u03c3W = 10 GeV and \u03c3Z =\n3 GeV4. No b-tag information was used to reconstruct the event kinematics. The jet chosen to reconstruct\nthe top quark with Standard Model decay is labeled as b quark. For the t \u2192q\u03b3 and the t \u2192qZ channels,\nthe other jet, which was used to reconstruct the top quark with FCNC decay, is denoted by q quark. For\nthe t \u2192qg channel, it is assumed that the jet created by the gluon is the most energetic from the two\nwhich reconstruct the top quark with FCNC decay and the other is created by the light quark.\nFollowing the selection cuts, a likelihood-based type of analysis was applied, as described in sec-\ntion 4.2.\nDue to the small statistics of the available full simulation samples, ATLFAST samples were\nused to obtain the probability density functions (p.d.f.s). The p.d.f.s of the t \u2192q\u03b3 channel were built\nbased on the following variables: the mass of the top quark with FCNC decay (mFCNC\nt\n); the recon-\nstructed mass of the photon and the b quark (mb\u03b3) and the transverse momentum of the leading photon\n(p\u03b3\nT). For the t \u2192qZ channel, the p.d.f.s were based on the following physical distributions: the mass of\nthe top quark with FCNC decay (mFCNC\nt\n); the minimum invariant mass of the three possible combinations\nof two leptons (mmin\n\u2113\u2113); the reconstructed mass of the Z and the b quark (mbZ); the reconstructed mass of\nthe two quarks (mqb); the transverse momentum of the third lepton (p\u21133\nT ) and the transverse momentum\nof the light quark (pq\nT). The following variables were used to build the p.d.f.s of the t \u2192qg channel: the\nmass of the top quark with FCNC decay (mFCNC\nt\n); the mass of the top quark with Standard Model decay\n(m\u2113a\u03bd j); the reconstructed mass of the light and the b quark (mqb); the transverse momentum of the b\nquark (pb\nT); the transverse momentum of the light quark (pq\nT) and the angle between the lepton and the\ngluon (\u03b1\u2113g). The distributions of the discriminant variables are presented in Figure 9. It can be seen that\nATLFAST describes the fully simulated distributions fairly well, when there are suf\ufb01cient statistics to\ntell.\n4These resolutions are taken from the top quark mass measurement analyses [70]. The effect of changing their values was\nconsidered as one of the systematic source of uncertainties. Its impact on the observables is below the statistical error.\nTOP \u2013 TOP QUARK PROPERTIES\n1025\n\n\u2212Signal ATLFAST\n+ Signal FullSim\nBackground ATLFAST\nBackground FullSim\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\n0.35\n0.4\n0.45\nATLAS\ne\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\n0.35\n0.4\n0.45\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nATLAS\n\u00b5\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n0 35\n0.4\nATLAS\n\u00b5\ne+\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n0 35\n0.4\na)\nb)\nc)\nR\nL\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\n0.35\nATLAS\n3e\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\n0.35\nR\nL\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nATLAS\n\u00b5\n3\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nR\nL\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n0 35\n0.4\n0.45\nATLAS\n3l\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n0 35\n0.4\n0.45\nd)\ne)\nf)\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0 2\n0.25\nATLAS\ne\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0 2\n0.25\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nATLAS\n\u00b5\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nR\nL\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0 05\n0.1\n0.15\n0.2\n0 25\nATLAS\n\u00b5\ne+\n-6\n-4\n-2\n0\n2\n4\n6\n0\n0 05\n0.1\n0.15\n0.2\n0 25\ng)\nh)\ni)\nFigure 9: Distributions of the normalised discriminant variables for the expected background and signal\nafter the \ufb01nal selection level of the t \u2192q\u03b3 channel when the isolated lepton is identi\ufb01ed as (a) an electron,\n(b) a muon and (c) electron or muon; of the t \u2192qZ channel when the 3 isolated leptons are identi\ufb01ed as\n(d) electrons, (e) muons and (f) electrons or muons and of the t \u2192qg channel, when the isolated lepton\nis identi\ufb01ed as (g) an electron, (h) a muon and (i) electron or muon.\nTOP \u2013 TOP QUARK PROPERTIES\n1026\n\nTable 20: The expected 95% con\ufb01dence level limits on the FCNC top quark decay branching ratio, in the\nabsence of signal, are shown for a luminosity of L = 1 fb\u22121. The central values are represented together\nwith the 1\u03c3 bands, which include the contribution from the statistical and systematic uncertainties.\n\u22121\u03c3\nExpected\n+1\u03c3\nt\u00aft \u2192bWq\u03b3:\ne\n4.3\u00d710\u22124\n1.1\u00d710\u22123\n1.9\u00d710\u22123\n\u00b5\n4.5\u00d710\u22124\n8.3\u00d710\u22124\n1.3\u00d710\u22123\n\u2113\n3.8\u00d710\u22124\n6.8\u00d710\u22124\n1.0\u00d710\u22123\nt\u00aft \u2192bWqZ:\n3e\n5.5\u00d710\u22123\n9.4\u00d710\u22123\n1.4\u00d710\u22122\n3\u00b5\n2.4\u00d710\u22123\n4.2\u00d710\u22123\n6.4\u00d710\u22123\n3\u2113\n1.9\u00d710\u22123\n2.8\u00d710\u22123\n4.2\u00d710\u22123\nt\u00aft \u2192bWqg:\ne\n1.3\u00d710\u22122\n2.1\u00d710\u22122\n3.0\u00d710\u22122\n\u00b5\n1.0\u00d710\u22122\n1.7\u00d710\u22122\n2.4\u00d710\u22122\n\u2113\n7.2\u00d710\u22123\n1.2\u00d710\u22122\n1.8\u00d710\u22122\n5.3\nResults and systematic uncertainties\nIn the absence of a FCNC top quark decay signal, expected limits at 95% CL were derived using the\nmodi\ufb01ed frequentist likelihood method [75] and the discriminant variables obtained with the full simu-\nlation samples. No cuts on the discriminant variables were used. Using the Standard Model t\u00aft production\ncross-section these limits were converted into limits on the branching ratios. The central values of these\nlimits are shown in Table 20. The branching ratio sensitivity for each FCNC channel, assuming a sig-\nnal discovery with a 5\u03c3 signi\ufb01cance, is on average 3.0 times larger than the central values presented in\nTable 20.\nSeveral sources of systematic uncertainties were studied following the common criteria used for this\nnote and the results are shown in Table 21. The jet energy scale (the jet calibration used in the present\nanalyses is described in Ref. [70]), the luminosity, the in\ufb02uence of the cross-section values, ISR/FSR,\nMonte Carlo generator and pile-up effects were studied. For the top quark mass, the full simulation\nsamples were analysed using the values of 170 and 180 GeV (i.e. p.d.f.s, Eq. 10 and limit computation).\nThe systematic error was taken from a linear \ufb01t of the values found, for a top quark mass error of\n\u00b12 GeV. To study the effect of the mass resolutions in Eq. 10, and since no cut is applied to the \u03c7 2\ndistribution, the ratio \u03c3t/\u03c3W was changed by a factor 2. The total systematic uncertainties, computed as\nthe quadratic sum of these individual contributions, are also shown in Table 21. The analysis stability was\nalso cross-checked by varying the kinematic cuts by about 10%, and the maximum relative change on the\nexpected 95% CL limits was 3%, 9% and 5% for the t \u2192q\u03b3, t \u2192qZ and t \u2192qg channels, respectively.\nTable 20 shows the obtained central values for the BR limits. The \u00b11\u03c3 contributions from statistical and\nsystematic uncertainties (added in quadrature) are also shown. The contribution from the luminosity and\nthe absolute value of background level may be reduced with data, by normalising to measured processes.\nFigure 10 shows the ATLAS 95% CL expected sensitivity for the \ufb01rst fb\u22121 in the absence of signal,\nfor the t \u2192q\u03b3 and t \u2192qZ channels taking into account the contributions from both the statistical and\nsystematic uncertainties.\nTOP \u2013 TOP QUARK PROPERTIES\n1027\n\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\nBR(t\u2192q\u03b3)\nBR(t\u2192qZ)\nLEP\nZEUS\n(q=u only)\nZEUS\n(q=u only)\n(630 pb-1)\nCDF\nCDF\n(2 fb-1)\nATLAS (1 fb-1)\n95% C.L.\nEXCLUDED\nREGIONS\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\nFigure 10: The present 95% CL observed limits on the BR(t \u2192q\u03b3) vs. BR(t \u2192qZ) plane are shown\nas full lines for the LEP, ZEUS and CDF collaborations. The expected sensitivity at ZEUS, CDF and\nATLAS (together with the statistic plus systematic 1\u03c3 band) is also represented by the dotted and dashed\nlines.\nTable 21: Maximum changes (with respect to the central values of Table 20) of the expected 95% CL\nlimits for each FCNC top quark decay branching ratio for different systematic error sources.\nt \u2192q\u03b3\nt \u2192qZ\nt \u2192qg\nSource\ne\n\u00b5\n\u2113\n3e\n3\u00b5\n3\u2113\ne\n\u00b5\n\u2113\nJet energy calibration\n1%\n2%\n2%\n3%\n2%\n5%\n4%\n4%\n4%\nLuminosity\n9%\n8%\n10%\n3%\n2%\n6%\n10%\n8%\n10%\nTop quark mass\n7%\n7%\n6%\n6%\n4%\n12%\n7%\n5%\n5%\nBackgrounds \u03c3\n6%\n10%\n7%\n4%\n7%\n12%\n17%\n16%\n15%\nISR/FSR\n21%\n18%\n17%\n6%\n29%\n7%\n3%\n7%\n9%\nPile-up\n37%\n21%\n22%\n30%\n14%\n0%\n8%\n10%\n13%\nGenerator\n34%\n18%\n4%\n4%\n14%\n14%\n5%\n0%\n4%\n\u03c72\n5%\n0%\n4%\n2%\n5%\n7%\n3%\n7%\n9%\nTotal\n56%\n36%\n32%\n32%\n36%\n25%\n24%\n24%\n27%\nTOP \u2013 TOP QUARK PROPERTIES\n1028\n\n6\nt\u00aft resonances\nNew resonances or gauge bosons strongly coupled to the top quark could manifest themselves in the t\u00aft\ninvariant mass distribution. Due to the large variety of models and their parameters, studies have been\ndone in a model-independent way searching for a \u201cgeneric\u201d narrow resonance decaying into t\u00aft (semilep-\ntonic channel) [51,76]. The ATLAS discovery potential is assessed using the latest available simulations\nand detector description, performing the t\u00aft event reconstruction along the same lines as done for the\nhigh precision measurement of the top quark mass in the semileptonic decay channel [54]. Alternative\nmethods are currently under investigation to study the production of high mass resonances (m > 2 TeV),\nwhere the decay products of the top quark are close together, so requiring a modi\ufb01ed selection.\n6.1\nEvent generation and selection\nIn this study, t\u00aft resonances were produced with PYTHIA. The Z\u2032 \u2192t\u00aft channel without interference in\nthe Z\u2032 production has been chosen [77]. Only the semileptonic decay (electrons and muons) of t\u00aft pairs\nis considered. Five samples of Z\u2032 resonances with mass 700 GeV (the lower limit from CDF and D/0\nmeasurements [78,79]), 1000 GeV, 1500 GeV, 2000 GeV and \ufb01nally 3000 GeV have been produced.\nThe common t\u00aft semileptonic selection criteria were used to accept signal events. Once these criteria\nare applied, the main source of physical background to be considered in the search for t\u00aft resonances\ncomes from Standard Model t\u00aft events. The other sources of background, dominated by W+jets events,\nare negligible [54].\n6.2\nData characteristics\n6.2.1\nt\u00aft reconstruction\nSeveral ways to reconstruct the W-bosons and the top quarks have been investigated [54]. The simplest of\nthem is used here. This method selects, among all jets from light quarks (u,d,c and s), the two jets which\nare closest in \u2206R to build the hadronic W-boson. The hadronic top quark is reconstructed combining the\nnearest b-jet to the hadronic W-boson. For the leptonic side, the constraint on the W-boson mass is used\nto compute the longitudinal momentum of the neutrino, identifying the missing transverse energy as the\nneutrino transverse momentum. Among the 2 pz\u03bd solutions, the one providing the leptonic top quark\nmass closest to the mean value of the hadronic top quark mass is chosen. To reduce both the physical\nbackground and the combinatorial background (which dominates), cuts are applied on the hadronic W-\nboson mass spectrum, and on both top quark mass spectra. The resulting t\u00aft mass distribution, given in\nFigure 11, is used as a starting point for the discovery potential determination.\nThis method does not need a well understood jet energy scale and it is also one of the most ef\ufb01cient.\nMore sophisticated methods to select the top quarks, such as a kinematic \ufb01ts of the t\u00aft-pairs (used by the\nD/0 experiment [79]), or a matrix-element motivated method (used by CDF [78]), are not described here.\nThe method used could be considered as a baseline for the t\u00aft resonance search.\n6.2.2\nEvent yield\nThe reconstruction ef\ufb01ciency of Standard Model t\u00aft pairs corresponding to the reconstruction scheme and\ncuts described above is shown in Figure 13. The fact that the produced particles are closer together when\nthe generated t\u00aft mass is higher explains the drop of ef\ufb01ciency observed as a function of the t\u00aft mass. Part\nof the ef\ufb01ciency can be recovered if another jet \ufb01nding algorithm, better at resolving nearby jets (such as\na cone jet algorithm with smaller cone radius), is used.\nFigure 14 gives the reconstruction ef\ufb01ciency of Z\u2032 resonances as a function of their mass. This\nreconstruction ef\ufb01ciency is of the same order as for the Standard Model t\u00aft pairs. Nevertheless, some\nTOP \u2013 TOP QUARK PROPERTIES\n1029\n\n [GeV]\nt\nt \nM\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\nEvts/20GeV\n0\n50\n100\n150\n200\n250\n300\n350\nReconstructed Evts\nCombinatorial Background\nStandard Model\nATLAS\nFigure 11:\nStandard Model t\u00aft mass spectrum.\nThe black area represents the combinatorial back-\nground where at least one of the selected jets or\nleptons does not match the corresponding\nparton.\n [GeV]\nt\nt \nM\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\nEvts/20GeV\n0\n10\n20\n30\n40\n50\n60\n70\n80\nReconstructed Evts\nCombinatorial Background\nZ\u2019 700 GeV\nATLAS\nFigure 12: A 700 GeV Z\u2032 reconstructed mass\nspectrum. The black area represents the combi-\nnatorial background where at least one of the se-\nlected jets or leptons does not match the corre-\nspondent parton.\nMass [GeV]\n700\n800\n900\n1000 1100 1200 1300 1400 1500\nEfficiency [%]\n0.5\n1\n1.5\n2\n2.5\n3\nATLAS\nFigure 13: Reconstruction ef\ufb01ciency of Standard\nModel t\u00aft pairs as a function of the t\u00aft mass.\nMass [GeV]\n700\n800\n900\n1000 1100 1200 1300 1400 1500\nEfficiency [%]\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nATLAS\nFigure 14: Reconstruction ef\ufb01ciency of Z\u2032 \u2192t\u00aft\nresonances as a function of the Z\u2032 mass.\nTOP \u2013 TOP QUARK PROPERTIES\n1030\n\nMass [GeV]\n600\n800\n1000\n1200\n1400\n1600\n1800\nResolution [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n1.81711x-607.785 \n \n\u00d7\nf(x) = 1.62261\nFit function : \nATLAS\nFigure 15: Z\u2032 mass resolution as a function of the\nZ\u2032 mass.\nMass [GeV]\n700\n800\n900\n1000 1100 1200 1300 1400 1500\n Br) [pb]\n\u00d7\n \n\u03c3\n(\n-2\n10\n-1\n10\n1\n10\n2\n10\n-1\nLuminosity = 1 fb\n-1\nLuminosity = 10 fb\n-1\nLuminosity = 30 fb\n-1\nLuminosity = 100 fb\n-1\nLuminosity = 300 fb\nATLAS\nFigure 16: 5\u03c3 discovery potential of a generic nar-\nrow t\u00aft resonance as a function of the integrated lu-\nminosity.\nsmall differences arise due to the different production mechanism and spin. Thus, the \ufb01nal result is\nnot completely model-independent. The purity (fraction of well reconstructed events among all selected\nevents) in each Z\u2032 sample is of the order of 80-85%.\n6.3\nDiscovery potential\n6.3.1\nMethod and results\nThe method used to extract the 5\u03c3 discovery sensitivity consists of counting the number of Standard\nModel t\u00aft events in a sliding mass window over the invariant mass spectrum. The 5\u03c3 sensitivity means\nthat an effect is seen over the expected background with a deviation at least 5 times the background\n\ufb02uctuation in the mass window. The width of the window is twice the detector resolution for a given\nresonance mass. Then, the lowest cross section times branching ratio \u03c3 \u00d7 Br(Z\u2032 \u2192t\u00aft) is computed for\nthe discovery of a resonance at a given mass.\nThe produced resonances are expected to have a width smaller than the resolution, leading to a\ngaussian shape for the reconstructed invariant mass. The discovery potential is thus estimated here only\nfor narrow t\u00aft resonances.\nThis method, explained in detail in [76], requires as input the Z\u2032 mass resolution (Figure 15), the\nreconstruction ef\ufb01ciency of both Standard Model t\u00aft events and resonance events, and the purity of the\n\ufb01nal samples.\nThe resulting sensitivity is shown on Figure 16. For example, a 700 GeV Z\u2032 resonance produced with\na \u03c3 \u00d7Br(Z\u2032 \u2192t\u00aft) of 11 pb should be discovered with a 5\u03c3 signi\ufb01cance after 1 fb\u22121 of data taking. The\nt\u00aft mass spectrum associated with such a case is shown in Figure 17.\n6.3.2\nMeasurement uncertainties\nUncertainties on the sensitivity arise from:\n\u2022 the reconstruction ef\ufb01ciency for the Z\u2032 signal and t\u00aft background. The main contribution arises\nfrom the expected error on the b-tag ef\ufb01ciency, which is set to \u00b15%.\n\u2022 the background contribution (Standard Model t\u00aft). The main contribution comes from the t\u00aft cross\nsection uncertainty +6.2\n\u22124.7 %.\nTOP \u2013 TOP QUARK PROPERTIES\n1031\n\nMass [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800\nNb of Events\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nMass [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800\nNb of Events\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nZ\u2019 (700 GeV)\nt\nSM t\n-1\nL=1 fb\nATLAS\nFigure 17: Expected t\u00aft invariant mass spectrum for the discovery threshold of a 700 GeV Z\u2032 resonance\n\u03c3 \u00d7Br(Z\u2032 \u2192t\u00aft) = 11.07 pb with 1 fb\u22121 of data.\nTable 22: Sources of uncertainties considered on the 5\u03c3 discovery potential computation.\nSource of uncertainty\nError (%)\nEffect on the discovery potential (%)\nReconstruction ef\ufb01ciency\n16.6\n8.3\nBackground contribution\n+6.2\n\u22124.7\n3.1\nt\u00aft mass resolution\n\u00b11\u03c3resolution\n2 to 11\nLuminosity\n5\n2.5\nJet energy scale\n5\n-\n\u2022 the t\u00aft mass resolution (Figure 15). The effect on the discovery potential increases with the reso-\nnance mass.\n\u2022 the uncertainty on the integrated luminosity.\nThe 5\u03c3 discovery potential is given as a function of the t\u00aft resonance mass. The position of the\nresonance mass peak depends on the accuracy of the jet energy scale. This will be constrained by the\nW-boson and top quark events themselves.\nAll these quantities have been varied within expected errors. The impact on the sensitivity is reported\nin Table 22.\n7\nSummary and conclusions\nThe ATLAS sensitivity to the measurement of several top quark properties was reviewed in this paper\nfor an expected luminosity of 1 fb\u22121 at the LHC. The precision of several measurements was estimated,\nusing the full simulation of the ATLAS detector. For the tests of physics beyond the Standard Model\nassociated with the production of top quarks, the 95% CL limit (in the absence of a signal) was presented.\nIn Table 23 a summary of the expected sensitivity on these observables is shown, for a luminosity of\n1 fb\u22121. Several sources of systematic errors were considered using an approach common to all studies\nappearing in this note.\nTOP \u2013 TOP QUARK PROPERTIES\n1032\n\nTable 23: Expected ATLAS sensitivity for the top quark properties, for a luminosity of 1 fb\u22121. For the\nStandard Model measurements the sensitivity is given as the total error divided by the expected Standard\nModel value, for the searches the absolute value is presented.\nObservables\nExpected Precision\nTop quark charge (2/3 versus -4/3)\n\u22655\u03c3\nSpin Correlations:\nA\n50%\nAD\n34%\nW-boson Polarisation:\nF0\n5%\nFL\n12%\nFR\n0.03\nAngular Asymmetries:\nAFB\n19%\nA+\n11%\nA\u2212\n4%\nAnomalous Couplings:\nVR\n0.15\ngL\n0.07\ngR\n0.15\nTop quark FCNC decays (95% C.L.):\nBr(t \u2192q\u03b3)\n10\u22123\nBr(t \u2192qZ)\n10\u22123\nBr(t \u2192qg)\n10\u22122\nt\u00aft Resonances (discovery):\n\u03c3 \u00d7Br (mt\u00aft=700GeV)\n\u226511 pb\nThe sensitivity of the ATLAS experiment to the top quark charge measurement was evaluated. The\nanalysis shows that using the weighting technique, already with 0.1 fb\u22121 it is possible to distinguish\nwith a 5\u03c3 signi\ufb01cance, between the b-jet charges associated with leptons of opposite charges, which\nallows to distinguish the Standard Model from an exotic scenario. For the semileptonic b-decay method\nthe required luminosity is \u22431 fb\u22121. The top quark charge itself was reconstructed relying on a Monte\nCarlo calibration of the b-jet charge. Although the reconstruction of the numeric value of the top quark\ncharge using the weighting technique seems possible with \u22431 fb\u22121, it will be necessary to check the\nperformance of the method with real data e.g. di-jet b\u00afb events, once available. A more realistic treatment\nof the background processes will be required for a full understanding of the top quark charge issues.\nA study of the W-boson polarisation fractions (F0, FL and FR) and t\u00aft spin correlation parameters (A\nand AD) has been performed in the semileptonic t\u00aft channel. Reconstructed angular distributions were\nused to set the ATLAS sensitivity to the measurement of the W-boson polarisations and top quark spin\ncorrelation parameters.\nThe W-boson polarisation ratios (\u03c1R and \u03c1L) and the angular asymmetries (A+ and A\u2212) dependence\non the anomalous couplings (VR, gL and gR) was used to \ufb01nd the sensitivity to the Wtb anomalous\ncouplings (for the analyses with and without b-tag).\nTop quark rare decays through FCNC processes (t \u2192qZ,q\u03b3,qg) were studied in this note using t\u00aft\nevents produced at the LHC. Expected limits on the branching ratios were set at 95% CL in the absence\nTOP \u2013 TOP QUARK PROPERTIES\n1033\n\nof signal.\nThe discovery potential of the ATLAS experiment for narrow t\u00aft resonances decaying in the semilep-\ntonic channel, was studied as a function of the resonance mass.\nReferences\n[1] V. M. Abazov et al., Phys. Rev. Lett. 98 (2007) 041801.\n[2] A. Abulencia et al., First CDF Measurement ot the TopQuark Charge using the Top Decay Products,\n2007, CDF Note 8783.\n[3] D. Chang, W.F. Chang, E. Ma, Phys. Rev. D 59 (1999) 091503.\n[4] D. Chang, W.F. Chang, E. Ma, Phys. Rev. D 61 (2000) 037301.\n[5] CDF Collaboration,\nMeasurement of W-Boson Helicity Fractions in Top-Quark Decays Using\ncos\u03b8 \u2217, 2008, Conf. Note 9431.\n[6] Abulencia, A. et al., Phys. Rev. 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Pallin, Generic t\u00aft resonance search with the ATLAS detector, 2006, ATL-\nPHYS-PUB-2006-033.\n[77] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[78] CDF Collaboration, Limit on Resonant t\u00aft Production in p \u00afp Collisions at \u221as=1.96 TeV, 2007, CDF\nNote 8675.\n[79] D0 Collaboration, Search for t\u00aft Resonance in the Lepton+Jets Final State in p \u00afp Collisions at\n\u221as = 1.96 TeV, 2007, Note 5443-CONF.\nTOP \u2013 TOP QUARK PROPERTIES\n1037\n\n\nB-Physics\n1039\n\nIntroduction to B-Physics\n1\nATLAS B-physics programme\nThe ATLAS B-physics programme covers many aspects of beauty \ufb02avour physics. First, by mea-\nsuring production cross-sections of beauty and charm hadrons and of the heavy-\ufb02avour quarkonia,\nJ/\u03c8 and \u03d2, ATLAS will provide sensitive tests of QCD predictions of production in proton-proton\ncollisions at the LHC. Secondly, ATLAS will study the properties of the entire family of B mesons\n(B0\nd, B+, B0\ns, Bc and their charge-conjugate states) and B baryons, thereby broadening our knowledge\nof both the spectroscopic and dynamical aspects of B-physics. However, the main emphasis will be\non precise measurements of weak B hadron decays. In the Standard Model, all \ufb02avour phenomena of\nweak hadronic decays are described in terms of quark masses and the four independent parameters\nin the Cabibbo-Kobayashi-Maskawa (CKM) matrix [1]. Enormous quantities of data collected in the\npast decade by the experiments BaBar, Belle, CDF and D0 allowed very precise measurements of\n\ufb02avour and CP-violating phenomena. Whilst the analysis of the remaining data of these experiments\nmay still push the boundaries, no evidence of physics beyond the Standard Model, nor any evidence\nfor CP violation other than that originating from the CKM mechanism, has yet been found. At the\nLHC, thanks to the large beauty production cross-section and the high luminosity of the machine, the\nsensitivity of B decay measurements is expected to substantially improve. Whilst direct detection of\nnew particles in ATLAS will be the main avenue to establish the presence of new physics, indirect\nconstraints from B decays will provide complementary information. In particular, precise measure-\nments and computations in B-physics are expected to play a key role in constraining the unknown\nparameters of any new physics model emerging from direct searches at the LHC.\nIn ATLAS, the main B-physics measurements will be made with an instantaneous luminosity\nof around 1033 cm\u22122 s\u22121; however, the B-physics potential begins during early data taking at low\nluminosity (1031 cm\u22122 s\u22121). With an integrated luminosity of 10 pb\u22121 ATLAS will already be able to\nregister about 1.3\u00b7105 events containing J/\u03c8 \u2192\u00b5+\u00b5\u2212selected by the low luminosity trigger menu\n[2]. Recorded events will contain J/\u03c8 \u2192\u00b5+\u00b5\u2212produced both directly in proton-proton interactions\nas well as indirectly from decays of B hadrons. With these statistics, beauty and quarkonia studies\nwill play an important role in the early data-taking period.\nIn this document we present studies for several periods of beauty measurements in ATLAS. First,\nthere will be a period of integrated luminosity of order of 10 - 100 pb\u22121 when B-physics and heavy-\n\ufb02avour quarkonia signatures will serve in helping to understand detector properties and the muon\ntrigger, as well as measuring production cross-sections. The physics analyses in this period will deal\nwith prompt J/\u03c8 and \u03d2 events, along with inclusive B hadron decays to muon pairs via J/\u03c8 . Further\non, the exclusive decays of B+ \u2192J/\u03c8K+, B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6 will be studied.\nDuring the next period, from about 200 pb\u22121 to 1 fb\u22121, we expect to collect the same or higher\nstatistics as are currently available at the Tevatron. During this period we will start to improve upon\ncurrent measurements of B hadron properties and set new decay rate limits or possibly give evidence\nfor rates above Standard Model predictions for rare decays (e.g. in the channel B0\ns \u2192\u00b5+\u00b5\u2212).\nIn the most important period for ATLAS B-physics we expect to achieve about 10 - 30 fb\u22121 at\nan instantaneous luminosity of mostly around 1033 cm\u22122 s\u22121. It is expected that ATLAS can achieve\nthis integrated luminosity in about three years. We are preparing to study a large variety of B-physics\ntopics covering both the production and decay properties of B hadrons. In this document we give\nexamples of performance studies for this period with polarization measurements of heavy-\ufb02avour\nquarkonia and of the baryon \u039bb, by the oscillation phenomena of the B0\ns \u2212B0s system, and the rare\n1040\n\ndecay measurement B0\ns \u2192\u00b5+\u00b5\u2212. We expect to achieve sensitivities allowing the con\ufb01rmation of\npossible contributions of physics beyond the Standard Model.\n2\nTrigger\nAll B-physics studies reported in the current document include trigger reconstruction. The ATLAS\ntrigger comprises three levels and the selection of B-physics events is initiated by a di-muon or a\nsingle-muon trigger at the \ufb01rst level trigger (L1). At 1031 cm\u22122 s\u22121 the lowest possible threshold of\nabout pT> 4 GeV will be used, rising to 6 - 8 GeV at 1033 cm\u22122 s\u22121 for at least one of the L1 muons.\nThe muon is con\ufb01rmed at the second trigger level (L2), \ufb01rst using muon-chamber information alone,\nand then combining muon and inner-detector (ID) information. The use of the more precise muon\ninformation available at L2 allows rejection of below-threshold muons that passed the L1 trigger.\nCombining information from the muon chambers and ID track segments gives rejection of muons\nfrom \u03c0 and K decays.\nFollowing the con\ufb01rmation of the L1 muon(s), cuts on invariant mass and secondary vertex re-\nconstruction of B decay products are used to select speci\ufb01c channels of interest. Channels such as\nB+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+ and B0\ns \u2192\u00b5+\u00b5\u2212are triggered by requiring two muons ful\ufb01lling J/\u03c8 or B0\ns\nmass cuts. At 1031 cm\u22122 s\u22121 a single muon is required at L1, with the second muon either originating\nfrom an additional L1 trigger or found at L2 in an enlarged Region of Interest (RoI) around the trigger\nmuon. At luminosities above about 1033 cm\u22122 s\u22121, a L1 dimuon trigger is used, giving an acceptable\nrate while keeping a low pT threshold for both of the two muons.\nFor hadronic \ufb01nal states such as B0\ns \u2192Ds\u03c0, ID tracks are combined to reconstruct \ufb01rst the\n\u03c6\u2192K+K\u2212, then the Ds\u2192\u03c6\u03c0 , and \ufb01nally the B0\ns. Two different strategies are used for \ufb01nding the\ntracks, depending on luminosity. Full reconstruction of the whole ID can be performed at 1031 cm\u22122 s\u22121.\nAt higher luminosities, reconstruction will be limited to regions of interest de\ufb01ned by the L1 calorime-\nter jets.\nIn all studies reported in the current document the trigger decision was used to accept or reject a\ngiven event. The trigger menu used to produce the datasets contained low-pT L1 muon thresholds of\n4, 5 and 6 GeV. These were used to initiate selections at L2 of decays containing J/\u03c8 \u2192\u00b5+\u00b5\u2212, like\nB+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+, and B0\ns \u2192\u00b5+\u00b5\u2212. The lowest thresholds for J/\u03c8 or B0\ns required two 4 GeV\nmuons. In addition there were selections for B0\ns \u2192Ds\u03c0 based either on full ID reconstruction or on\na RoI-based reconstruction in L1 Jet RoIs with a 4 GeV threshold. More detailed information on the\nB-physics trigger is presented in three studies in this document. Speci\ufb01c questions on the L1 di-muon\ntrigger performance for B-physics are addressed in Section 1 of this chapter. L2 triggering on muons\nand di-muons is presented in Section 2. Finally, triggers for B decays to purely hadronic \ufb01nal states\nhave been studied in the last part of this chapter, Section 8.\nIf not stated otherwise, the trigger ef\ufb01ciencies in di-muon events were calculated with respect to\nMonte Carlo samples generated with cuts of pT > 6 GeV and pT > 4 GeV for the \ufb01rst and second\nmuon respectively and with pseudorapidity cuts of |\u03b7| < 2.4 on both muons.\n3\nSimulation of the events\nSome 1 million B hadron events, along with around 400 000 prompt J/\u03c8 and \u03d2(1S) as well as c\u00afc\nevents, were produced using PYTHIA 6.4 [3]. The simulations were performed with the CTEQ6L set\nof parton distribution functions. For quarkonium production, the NRQCD matrix element parameters\nB-PHYSICS \u2013 INTRODUCTION TO B-PHYSICS\n1041\n\nin PYTHIA were tuned to \ufb01t Tevatron data [4]. In the production of non-resonant b\u00afb and c\u00afc \ufb02avour-\ncreation, PYTHIA models describing \ufb02avour-excitation and gluon-splitting were included. The frag-\nmentation of b quarks and c quarks to hadrons was simulated according to the Peterson fragmentation\nfunction with parameter 0.006 and 0.05 respectively. The choice of parameters was motivated by\nTevatron measurements [5]. Kinematic selections on \ufb01nal state particles from B decays were applied\nso that most of the generated B events passed the trigger threshold at the reconstruction stage.\nThe total b\u00afb or c\u00afc cross-section is not well de\ufb01ned in PYTHIA when one includes processes other\nthan those of the lowest order for b\u00afb (c\u00afc ) production, since PYTHIA takes the partons to be massless\nand therefore the cross-section diverges when the transverse momentum approaches zero. However,\nonly part of the cross section is relevant for our studies - in the phase space of events passing B\ntriggers.\nTable 3 summarises the predicted single and di-muon cross-sections from charm, beauty and onia\nproduction expected at ATLAS from PYTHIA with cuts on the transverse momenta of the muons of\n6 or 4 GeV (as appropriate) and pseudorapidity cuts on both muons of |\u03b7| < 2.4. The cuts re\ufb02ect\nthe trigger thresholds and were selected to allow most of the simulated events to be accepted by the\ntrigger.\nProcess (\u00b56 threshold)\nCross-section\nProcess (\u00b54 threshold)\nCross-section\nbb \u2192\u00b56X\n6.1\n\u00b5b\nbb \u2192\u00b54X\n19.3\n\u00b5b\ncc \u2192\u00b56X\n7.9\n\u00b5b\ncc \u2192\u00b54X\n26.3\n\u00b5b\nbb \u2192\u00b56\u00b54X\n110.5\nnb\nbb \u2192\u00b54\u00b54X\n212.0\nnb\ncc \u2192\u00b56\u00b54X\n248.0\nnb\ncc \u2192\u00b54\u00b54X\n386.0\nnb\npp \u2192J/\u03c8(\u00b56\u00b54)X\n23.0\nnb\npp \u2192J/\u03c8(\u00b54\u00b54)X\n28.0\nnb\npp \u2192\u03d2(\u00b56\u00b54)X\n4.6\nnb\npp \u2192\u03d2(\u00b54\u00b54)X\n43.0\nnb\nbb \u2192J/\u03c8(\u00b56\u00b54)X\n11.1\nnb\nbb \u2192J/\u03c8(\u00b54\u00b54)X\n12.5\nnb\nTable 1: Predicted PYTHIA cross-sections for various muon and di-muon sources. The numbers fol-\nlowing each symbol \u00b5 denote the pT thresholds that were used in generating the events with PYTHIA.\nAfter PYTHIA simulation, the events were passed through detector simulation (based on GEANT4\n[6]) which \ufb01rst modelled the behavior of the particles as they passed through the detector, and simu-\nlated the response of the active detector components to the energy deposition by these particles. The\nlayout of the detector used by the simulation code was published in Ref. [7]. The output of the simu-\nlation was then reconstructed as if it were real data. Following this, reconstructed muons and hadrons\nwere analysed using the dedicated B-physics analysis software.\n4\nOrganization of the B-physics chapter\nThe following reports on B-physics present our best current understanding of the ATLAS B-physics\nprogramme. As the B trigger plays a role in all the studies presented here, the chapter starts with\ntwo reports, in Sections 1 and 2, dealing with L1 and L2 muon triggers respectively. There follow\nthree physics studies typical for the early data period: physics of heavy-\ufb02avour quarkonia (Section 3),\nmeasurements of beauty cross-sections (Section 4) and early physics and performance measurements\nwith decays of B0\nd and B0\ns mesons in Section 5. Finally there are Sections 6, 7 and 8, which give typical\nexamples of ATLAS B measurements that can only be achieved during the more advanced data taking\nperiod; they are measurements of the polarization of the baryon \u039bb, the rare decay B0\ns \u2192\u00b5+\u00b5\u2212and\nB-PHYSICS \u2013 INTRODUCTION TO B-PHYSICS\n1042\n\n\ufb01nally the oscillation measurement of the B0\ns \u2212B0s system.\nReferences\n[1] N. Cabibbo, Phys. Rev. Lett. 10, p. 531 (1963); M.Kobayashi and T.Maskawa, Prog. Theor.\nPhys. 49, p. 652 (1973).\n[2] ATLAS collaboration, \u2019Trigger for Early Running\u2019, this volume.\n[3] T. Sjostrand, S. Mrenna, P. Skands, JHEP 05, 026 (2006).\n[4] G. Altarelli, (Ed.), M. L. Mangano, (Ed.) CERN-2000-004, p. 231-304 (2000).\n[5] M. Cacciari, S. Frixione , M.L. Mangano, P. Nason, G. Ridol\ufb01, JHEP 07, 033 (2004); M.\nCacciari, P. Nason, Phys. Rev. Lett. 89, 122003 (2002).\n[6] ATLAS collaboration, Computing Technical Design Report, ATLAS-TDR-017, CERN-\nLHCC-2005-022 (2005).\n[7] ATLAS collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST\n3 (2008) S08003.\nB-PHYSICS \u2013 INTRODUCTION TO B-PHYSICS\n1043\n\nPerformance Study of the Level-1 Di-Muon Trigger\nAbstract\nAn event with two muons in the \ufb01nal state is a distinctive signal and can be\ntriggered ef\ufb01ciently with the use of the level-1 di-muon trigger. Nevertheless\ntriggering is still an issue if these muon tracks are fairly soft and fake di-muon\ntriggers originating from muons that traverse more than one region of the trig-\nger chambers increase the trigger rate. It is important to provide an acceptable\ntrigger rate, while keeping high trigger ef\ufb01ciency to study low-pT B-physics\nsuch as rare B hadron decays or CP violation in the B-events, especially in a\nmulti-purpose experiment like ATLAS. In this note, the level-1 di-muon trigger\nand its expected performance are described.\n1\nIntroduction\nATLAS is a multi-purpose experiment and its main focus is the direct search for and study of physics\nbeyond Standard Model. However the indirect search for new physics will also play an important role in\nrevealing the (\ufb02avor) structure of a non-trivial Higgs sector, which cannot be obtained by direct searches.\nThe B 0\ns,d \u2192\u00b5+\u00b5\u2212rare decay is one of the interesting signatures which are sensitive to new physics\nat the TeV energy scale. The precise measurement of the forward-backward asymmetry [1] or branch-\ning ratio in the semi-muonic B decay B \u2192\u00b5+\u00b5\u2212X requires good understanding of the possible biases\nintroduced by event selection. Also important are precise measurements of Standard Model parameters,\nincluding CP-violation in B-events, such as B 0\ns \u2192J/\u03c8\u03c6 and B 0\nd \u2192J/\u03c8K0\ns . The key to the detection\nof these B signals in ATLAS is to achieve a high trigger ef\ufb01ciency for low-pT di-muon events, keep-\ning an acceptable trigger rate. It is also essential to understand the acceptance and ef\ufb01ciency using\npp \u2192J/\u03c8(\u00b5+\u00b5\u2212)X or pp \u2192\u03d2(\u00b5+\u00b5\u2212)X [2].\nFirst, the level-1 muon trigger is brie\ufb02y explained in Section 2, then trigger simulation and MC\nsamples used in this note are described in Section 3. The performance of the level-1 single- and di-muon\ntrigger as well as the effect of an algorithm to resolve muons traversing more than one trigger chambers\nare described in Section 4. Finally, the performance and the impact of various level-1 muon trigger\ncon\ufb01gurations on some example B signal events are discussed in Section 5.\n2\nLevel-1 muon trigger\nThe ATLAS trigger system architecture is organised in three levels; level-1, level-2 and event \ufb01lter. The\nlevel-2 and event \ufb01lter triggers provide a software-based event selection after the level-1 trigger and\nevents accepted by this trigger chain are \ufb01nally reconstructed and analyzed of\ufb02ine.\nThe ATLAS level-1 muon trigger is based on dedicated, fast and \ufb01nely segmented muon cham-\nbers (RPC and TGC) [3] and a trigger logic implemented in hardware. The muon trigger system provides\nacceptance in pseudo-rapidity up to |\u03b7| \u223c2.4 and in the full azimuthal angle (\u03c6) range. A muon track\nis triggered by the coincidence of two or three detector stations (consists of chamber doublet or triplet)\nwithin a certain road (coincidence window). The transverse momentum of a muon candidate is deter-\nmined by its deviation from the trajectory of an in\ufb01nite-momentum track (i.e. a straight line). A three\nstation coincidence is required for any pT threshold in the endcap and forward regions (|\u03b7| > 1.05) to\navoid high trigger rates caused by accidental coincidences due to background.1 As a result, the accep-\ntance at large |\u03b7| becomes small for low-pT muons, as shown in Section 4.\n1The number of stations used for coincidence is programmable giving the possibility of lowering a pT threshold at low\nluminosity if background conditions allow it.\n1044\n\nThe granularity of the level-1 muon trigger, the size of a Region of Interest (RoI), is \u2206\u03b7 \u00d7 \u2206\u03c6 =\n0.1 \u00d7 0.1 in the barrel region (|\u03b7| < 1.05) and \u223c0.03 \u00d7 0.03 in the endcap regions (1.05 < |\u03b7| < 2.4).\nIn short, if two muons leave tracks in the same RoI, they are counted as a single muon candidate by the\ntrigger system. The level-1 muon trigger decisions from different regions are sent to the Muon Central\nTrigger Processor Interface (MuCTPI) which combines the information and calculates the multiplicity\nof muon candidates for each pT threshold over the whole detector. In forming the multiplicities, care\nis taken to avoid double counting of single-muon tracks, reconstructed separately in adjacent trigger\nsectors, while retaining a high ef\ufb01ciency for genuine di-muons. The overlap handling is carried out\nusing Lookup Tables (LUT) to give \ufb02exibility and programmability. The LUTs are generated based on\nMonte Carlo simulations of single-muon events, selecting the regions of the level-1 muon system that\ncan be traversed by a single muon.\nThe overlap handling is mandatory to avoid unacceptably high trigger rates caused by doubly-counted\nsingle muons, so called fake di-muon triggers. Most of the overlaps are resolved by the MuCTPI, which\ntakes the muon candidate with the higher pT into account when calculating the muon multiplicity and\n\ufb01nding overlapping muon candidates. The MuCTPI consists of independent 16 octant modules and\noverlap resolving is performed in each module. Therefore, overlapped regions connected to two different\noctant modules cannot be solved in MuCTPI and should be treated in each subdetector (RPC and TGC)\nby masking channels or \ufb02agging a overlap bit. The parameters used in the overlap handling, such as the\ncombination of RoIs and masked channels are programmable. More details are described in Refs. [3, 4].\n3\nMonte Carlo samples and trigger con\ufb01guration\nSingle-muon Monte Carlo samples with various, \ufb01xed pT values are used for performance tests of the\nlevel-1 single muon trigger logic. Single-muon events are generated uniformly over the full azimuthal\nangle range and |\u03b7| < 2.7 with a \ufb01xed pT value. The detector response is simulated using Geant4 [4] with\nthe ATLAS geometry in the Athena framework [5]. Trigger simulation is performed using the trigger\ncon\ufb01guration for luminosity of 1031-1033cm\u22122s\u22121 running, with a set of pT thresholds of 4, 5, 6, 11,\n20 and 40 GeV. The production vertex is smeared with a Gaussian distribution with \u03c3x = \u03c3y = 15 \u00b5m\nand \u03c3z = 56 mm. The level-1 single- and di-muon trigger menu items are named as MUx (single-\nmuon trigger) and 2MUx (di-muon trigger with the same threshold for both muons) respectively, where\nx represents the pT threshold. The exceptions are MU0 and 2MU0, which correspond to completely\nopened coincidence windows. However, even in this case, the acceptance of the coincidence windows is\nlimited by connectivity as well as by the dimension of the coincidence matrix ASICs [6].\nThe trigger ef\ufb01ciencies of various level-1 trigger con\ufb01gurations are also studied using B-physics\nMonte Carlo events. Event generation is done using PYTHIA [7]. Only interesting events associated\nwith at least two muons with pT > 6 GeV (the leading muon) and 4 GeV (the second muon) within\n|\u03b7| < 2.5 are studied. The B-physics samples used in this note are B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6 (47,650 events),\nB 0\ns \u2192\u00b5+\u00b5\u2212(47,450 events) and B+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+ (49,250 events). The last sample is chosen\npartly as a control sample. The opening angle of the two muons is smaller in this sample than in the\nother two samples.\nIn this note, only the level-1 muon trigger is simulated and events triggered by level-1 are studied.\n4\nLevel-1 muon trigger ef\ufb01ciency in single-muon events\nDetailed performance studies of the single muon trigger were performed in the barrel and endcap regions\nseparately and the results are described in Ref. [8]. The single muon trigger ef\ufb01ciencies as a function\nof the transverse momentum of the simulated muon, over the whole muon trigger system are shown in\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1045\n\nFigure 1. The single muon trigger ef\ufb01ciency is de\ufb01ned by:\n\u03b5(MUx) =\n# of events triggered\n# of single muon events with |\u03b7| < 2.5 .\n(1)\nThe range of pseudo-rapidity applied in the ef\ufb01ciency calculation is |\u03b7| < 2.5 and not 2.4 as used in\nRef. [8], since |\u03b7| < 2.5 is applied for muons in the B-physics samples (Muons with |\u03b7| > 2.4 can be\ntriggered if their momentum is relatively low and the track is bent towards smaller |\u03b7|). The ef\ufb01ciency,\n\u03b5(MUx), includes all contributions from geometrical acceptance and coincidence window coverage. The\ntrigger ef\ufb01ciency of MU5 and MU6 is lower than MU0 even for high pT muon tracks. This is because all\nregions don\u2019t have full (100 %) acceptance except MU0 which accepts all muons within station coinci-\ndence windows. Figures 2 (a) and (b) show the trigger ef\ufb01ciency as a function of the |\u03b7| of the simulated\n (GeV)\n\u00b5\n of \nT\np\n0\n5\n10\n15\n20\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nMU0\nMU5\nMU6\nFigure 1: Trigger ef\ufb01ciency as a function of pT with each low-pT threshold; MU0 (\ufb01lled circles),\nMU5 (\ufb01lled triangles) and MU6 (open squares) for muons with |\u03b7| < 2.5 at the interaction point.\nmuon with pT at threshold and with pT=19 GeV for MU0 and MU6 trigger selections, respectively. The\nef\ufb01ciency at the plateau is predominantly determined by geometrical acceptance. Ef\ufb01ciency losses at\n|\u03b7| \u223c0, 0.4 and 0.7 are caused by cracks and inactive material, like ribs, detector support structures and\nthe elevator hole. Around the transition region between the barrel and the endcap, |\u03b7| \u223c1.05, some ef\ufb01-\nciency is lost because the station coincidence cannot be satis\ufb01ed. A small ef\ufb01ciency gap at the boundary\nbetween the endcap and forward regions (|\u03b7| \u223c2) is also due to the station coincidence, since the endcap\nand forward systems are treated separately. However, this effect is smaller than in the transition region\nbetween the barrel and the endcap. Poor MU0 ef\ufb01ciency at pT = 4 GeV is seen in the endcap region\ndue to the requirement of three station coincidence, not two as required in the barrel. The trigger was\noriginally designed for pT > 6 GeV as the lowest threshold, but can be applied below this threshold at\nvery low luminosity.\nFigures 3 (a) and (b) show the trigger ef\ufb01ciency as a function of \u03c6 (\u03c6=0 and \u00b1\u03c0 denote directions\nperpendicular to the beam axis in the horizontal plane) of the simulated muon with pT at threshold and\nwith pT=19 GeV for MU0 and MU6 trigger selections, respectively. The ef\ufb01ciency loss can be clearly\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1046\n\n\u00b5\n | of \n\u03b7\n| \n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n(a) MU0\nATLAS\n19GeV\n4GeV\n\u00b5\n | of \n\u03b7\n| \n0\n0.5\n1\n1.5\n2\n2.5\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n(b) MU6\nATLAS\n19GeV\n6GeV\nFigure 2: The |\u03b7| dependency of the trigger ef\ufb01ciency for MU0 (a) and MU6 (b) trigger selections.\nSolid lines correspond to the simulated muons with pT=19 GeV, dotted lines are for muons with\npT at threshold (in the case of MU0 this threshold is set to 4 GeV).\nseen around \u03c6 \u223c\u22121.2 and \u22122 at the magnet\u2019s feet, especially for high pT muons. The geometrical\nstructure is in general more visible in ef\ufb01ciency using higher pT muons, as they produce straighter\ntracks.\n\u00b5\n of \n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n(a) MU0\nATLAS\n19GeV\n4GeV\n\u00b5\n of \n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n(b) MU6\nATLAS\n19GeV\n6GeV\nFigure 3: The \u03c6 dependency of the trigger ef\ufb01ciency for MU0 (a) and MU6 (b) trigger selections.\nSolid lines correspond to the simulated muons with pT=19 GeV, dotted lines are for muons with\npT at threshold (in the case of MU0 this threshold is set to 4 GeV).\n5\nLevel-1 muon trigger performance in B-physics events\nA detailed level-1 trigger simulation is mandatory to \ufb01nd effective trigger menus and thresholds for\ncertain physics processes and to determine the trigger ef\ufb01ciency and rate as well as to study the trigger\nbias. In this section, di-muon and single-muon trigger ef\ufb01ciencies with different pT thresholds and the\ndependency of di-muon trigger ef\ufb01ciencies as a function of the opening angle between simulated muons\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1047\n\nare discussed using B-physics Monte Carlo samples.\n5.1\nEf\ufb01ciency with various trigger con\ufb01gurations\nThe ef\ufb01ciency of the level-1 muon trigger for three different B-physics processes, B 0\ns \u2192\u00b5+\u00b5\u2212, B 0\ns \u2192\n\u00b5+\u00b5\u2212\u03c6 and B+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+ is studied with various trigger con\ufb01gurations. The ef\ufb01ciencies of\nthe single muon triggers (MU0 and MU6) and the di-muon triggers (2MU0 and 2MU6) are summarized\nin Table 1. The ef\ufb01ciency of the single muon trigger is high, about 95 %, since multiple muons have\na higher probability to be triggered by a single muon trigger. The 2MU0 trigger gives better ef\ufb01ciency\nthan 2MU6 by \u223c16 % for di-muon events with pT above 6 GeV (4 GeV) for the fastest (second fastest)\nmuon. The ef\ufb01ciency loss due to the MuCTPI overlap handling is seen in all physics processes, although\nthe relative ef\ufb01ciency loss is small, \u223c0.5 %.\nEf\ufb01ciency [%]\nTrigger Menu / Process\nB 0\ns \u2192\u00b5+\u00b5\u2212\nB+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+\nB 0\ns \u2192\u00b5+\u00b5\u2212\u03c6\nMU0\n97.0\u00b10.1\n96.8\u00b10.1\n97.0\u00b10.1\nMU6\n93.0\u00b10.1\n92.9\u00b10.1\n93.1\u00b10.1\n2MU0\n67.9\u00b10.2\n68.8\u00b10.2\n69.0\u00b10.2\n2MU6\n51.6\u00b10.2\n52.9\u00b10.2\n53.2\u00b10.2\n2MU0 (w/o MuCTPI overlap handling)\n68.2\u00b10.2\n69.1\u00b10.2\n69.4\u00b10.2\n2MU6 (w/o MuCTPI overlap handling)\n52.0\u00b10.2\n53.4\u00b10.2\n53.7\u00b10.2\nTable 1: The level-1 trigger ef\ufb01ciency of various con\ufb01gurations. The ef\ufb01ciency is calculated with\nrespect to the number of generated events (not to the number of muons) of three different physics\nprocesses. The errors are statistical only.\n5.2\nOpening-angle dependency\nIn case of measuring some quantity as a function of a certain parameter, one must ensure that the trigger\nef\ufb01ciency is independent of that parameter, or correct the measurement to avoid a bias from the trigger.\nFigure 4 shows the 2MU0 and 2MU6 trigger ef\ufb01ciencies as a function of \u2206R (=\np\n\u2206\u03b72 +\u2206\u03c6 2) between\nthe two leading muons in B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6 events. The \u03b7 and \u03c6 are true parameters of muon \ufb02ight direction\nat the production vertex. No of\ufb02ine selection is applied in order to see see the bias from the level-1\ntrigger. The trigger ef\ufb01ciency clearly depends on the opening angle of the two leading muons. The\nef\ufb01ciency is lower at large opening angles because in this case the Bs system is not boosted i.e. momenta\nof the muons are lower. Since overlap removal between the muon candidates doesn\u2019t play a role at large\nopening angles, this effect is purely due to kinematics. Figure 5 (a) shows the pT distribution of the\nleading muons for three different \u2206R ranges: \u2206R < 0.1, 0.2 < \u2206R < 0.4 and \u2206R > 0.5. The muons at\nlarge opening angles clearly have a softer pT spectrum. The effect is even more clearly visible for higher\nthreshold di-muon trigger items, as the probability of having muons at large \u2206R with transverse momenta\nhigh enough to trigger a high threshold di-muon trigger item is very small, but non-negligible at small\nopening angles.\nThe small ef\ufb01ciency loss at very small opening angles (\u2206R < 0.1) is however due to the trigger\nsystem. In the case that the muons both leave hits in the same RoI, only one muon can be triggered by\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1048\n\n\u00b5\n\u00b5\n R\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n2MU0 efficiency with MuCTPI\n2MU6 efficiency with MuCTPI\n2MU0 efficiency with MuCTPI\n2MU6 efficiency with MuCTPI\n(a)\nATLAS\n\u00b5\n\u00b5\n R\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\neff(with MuCTPI) / eff(w/o MuCTPI)\n0.95\n0.96\n0.97\n0.98\n0.99\n1\n1.01\n1.02\n1.03\n1.04\n1.05\n2MU0, eff(with MuCTPI) / eff(w/o MuCTPI)\n2MU6, eff(with MuCTPI) / eff(w/o MuCTPI)\n2MU0, eff(with MuCTPI) / eff(w/o MuCTPI)\n2MU6, eff(with MuCTPI) / eff(w/o MuCTPI)\nATLAS\n(b)\nFigure 4: (a) Trigger ef\ufb01ciency as a function of \u2206R in the semi-leptonic rare B decay B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6\nusing the 2MU0 (\ufb01lled circles) and 2MU6 (open squares) with MuCTPI. (b) Effect of MuCTPI as\na function of the opening angle, \u03b5(without MuCTPI)/\u03b5(with MuCTPI) for 2MU0 (\ufb01lled circles)\nand 2MU6 (open squares).\n [GeV]\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\nNormalized\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nR < 0.1\n\u2206\nmuons with \nR < 0.4\n\u2206\nmuons with 0.2 < \nR > 0.5\n\u2206\nmuons with \nR < 0.1\n\u2206\nmuons with \nR < 0.4\n\u2206\nmuons with 0.2 < \nR > 0.5\n\u2206\nmuons with \nATLAS\n(a)\n\u00b5\n\u00b5\n R\n\u2206\n0\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9\n1\n2MU0 efficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n2MU0 : Two muons are closer on MS\n2MU0 : Two muons are separated on MS\n2MU0 : Two muons are closer on MS\n2MU0 : Two muons are separated on MS\n(b)\nATLAS\nFigure 5: (a) The truth pT distribution of the two leading muons is different opening angles range\nin B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6 events: \u2206R < 0.1 (\ufb01lled circles), 0.2 < \u2206R < 0.4 (\ufb01lled triangles) and \u2206R > 0.5\n(\ufb01lled squares). (b) The ef\ufb01ciency of 2MU0 as a function of opening angles for two cases: the \u2206R\nseparation of the two muons is either larger (\ufb01lled circles) or smaller (open circles) at the muon\ntrigger system compared to that at the primary vertex.\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1049\n\nthe system. Figure 5(b) shows the 2MU0 ef\ufb01ciency as a function of the opening angle, but events are\ndivided into two classes: In one case we select the muon pairs whose separation is expected to shrink\nwhen reaching the muon spectrometer (\ufb01lled circles), while in the other case (open squares) we select\nthe muon pairs whose separation is expected to grow.\n [GeV]\n\u00b5\n\u00b5\nm\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n-1\nEvents / 30 pb\n0\n100\n200\n300\n400\n500\nNo LVL1 selection\n2MU0\n2MU6\nNo LVL1 selection\n2MU0\n2MU6\nATLAS\n(a)\ns\nB\n2\n/m\n\u00b5\n\u00b52\nm\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n2MU0 efficiency\n2MU0 relative efficiency w.r.t average\n2MU6 efficiency\n2MU6 relative efficiency w.r.t average\n2MU0 efficiency\n2MU0 relative efficiency w.r.t average\n2MU6 efficiency\n2MU6 relative efficiency w.r.t average\nATLAS\n(b)\nFigure 6: (a) Scaled di-muon invariant mass-squared distribution in B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6 events: no\nlevel-1 selection (open histogram), triggered by 2MU0 (hatched histogram) and by 2MU6(cross\nhatched histogram). (b) Ef\ufb01ciencies of 2MU0 (\ufb01lled circles) and 2MU6 (open squares) as a func-\ntion of di-muon invariant mass-squared. The two lines show the relative ef\ufb01ciency with respect to\nthe corresponding average value for 2MU0 (solid line) and 2MU6 (dotted line).\nOne example B-physics study is to look at the differential decay rate dBr(B \u2192\u00b5+\u00b5\u2212\u03c6) / d\u02c6s or\nforward-backward asymmetry AFB as a function of di-muon invariant mass to discriminate between\nStandard Model and new physics contributions. The \u02c6s is m2\n\u00b5\u00b5/m2\nB and the AFB(\u02c6s) is de\ufb01ned as\n\u0000Z 1\n0\nd\u0393\nd \u02c6s\u02c6zd\u02c6z\u2212\nZ 0\n\u22121\nd\u0393\nd \u02c6s\u02c6zd\u02c6z\n\u0001\n/\nZ 1\n\u22121\nd\u0393\nd \u02c6s\u02c6zd\u02c6z,\n(2)\nwhere \u02c6z = cos\u03b8 (\u03b8 is the angle between the \u00b5+ and \u03c6 in the \u00b5+\u00b5\u2212rest frame) and d\u0393/d\u02c6z is the differ-\nential event rate of B0\ns \u2192\u00b5+\u00b5\u2212\u03c6.\nFigure 6 (a) shows the \u00b5+\u00b5\u2212invariant mass distribution with and without level-1 triggers in B 0\ns \u2192\n\u00b5+\u00b5\u2212\u03c6 events. Trigger ef\ufb01ciency with 2MU0 and 2MU6 are shown as a function of \u00b5+\u00b5\u2212invariant\nmass in Figure 6 (b). The relative trigger ef\ufb01ciency, normalized to the ef\ufb01ciency averaged over a whole\nm2\n\u00b5\u00b5/m2\nB range, is also shown to illustrate the trigger bias. The invariant mass dependency of the level-1\ndi-muon trigger ef\ufb01ciency is weak compared to the opening angle dependency and almost independent\nof the trigger threshold. A ef\ufb01ciency drop can be seen at small m\u00b5\u00b5, which is also because the two muons\nare triggered as a single muon by the muon trigger system.\nSimilarly, the forward-backward asymmetry AFB is shown as a function of \u02c6s in Figure7(a). The dif-\nference (AFB[2MUx] - AFB[no selection]) is also shown in Figure 7(b). It should be noted that signi\ufb01cant\ndifferences between forward and backward samples in terms of momentum, pseudo-rapidity and \u00b5+\u00b5\u2212\nopening angle distributions are observed. Nevertheless, as illustrated in Figure 7, the forward-backward\nasymmetry is more robust to the effects of level-1 di-muon triggering than di-muon mass distributions\n(see Figure 6).\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1050\n\ns\nB\n2\n/m\n\u00b5\n\u00b52\nm\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nFB\nA\n-0.5\n-0.4\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\nNo LVL1 selection\n2MU0\n2MU6\nNo LVL1 selection\n2MU0\n2MU6\nATLAS\n(a)\ns\nB\n2\n/m\n\u00b5\n\u00b52\nm\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nFB\nDifference of A\n-0.1\n-0.05\n0\n0.05\n0.1\n difference w r.t. no cuts\nFB\n2MU0 A\n difference w r.t. no cuts\nFB\n2MU6 A\n difference w r.t. no cuts\nFB\n2MU0 A\n difference w r.t. no cuts\nFB\n2MU6 A\nATLAS\n(b)\nFigure 7: (a) Forward-Backward asymmetry in B 0\ns \u2192\u00b5+\u00b5\u2212\u03c6 events: no level-1 selection (\ufb01lled\ntriangles), triggered by 2MU0 (\ufb01lled circles) and by 2MU6(open squares). (b) deviation between\nAFB\u2019s with and without triggers (AFB[2MUx] - AFB[no selection]: 2MU0 (\ufb01lled circles) and\n2MU6 (open squares).\n6\nSummary\nThe level-1 di-muon trigger is essential for selecting rare B decays that have low-pT muons in the \ufb01nal\nstate. The rate for a single-muon trigger at the relevant thresholds would be unacceptably high. A detailed\nlevel-1 muon trigger simulation is implemented and used for the study of the trigger ef\ufb01ciency and its\nbias for B-physics events. The level-1 di-muon trigger ef\ufb01ciencies of 2MU0 and 2MU6 are high enough\n(about 70 % and 50 %, respectively) in the interesting B-physics events. The fake level-1 di-muon trigger\nrate is 2.3 kHz [8] while the genuine di-muon event rate is \u223c600 Hz (muons with pT > 4 GeV from c\u00afc\nand b\u00afb) at L = 1033cm\u22122s\u22121. The ef\ufb01ciency loss from the MuCTPI overlap handling is found to be\nnegligible.\nThe trigger bias in regard to the opening angle and invariant mass of two muons was also studied.\nAn opening angle dependence is clearly seen, of the order of \u00b110 % and \u00b115 % for 2MU0 and 2MU6,\nrespectively. It is explained by the single-muon ef\ufb01ciency curves and muon kinematics in signal events.\nThis dependency is stronger for higher pT thresholds. No clear bias is seen due to the presence of the\nMuCTPI overlap handling. The trigger ef\ufb01ciency is rather \ufb02at over the invariant mass and less dependent\non the trigger threshold since the invariant mass is not as strongly correlated to muon momenta as the\nopening angle is.\nReferences\n[1] A. Policicchio and G. Grosetti, ATL-COM-PHYS-2007-019 (2007).\n[2] The ATLAS Collaboration, Triggering on Low-pTMuons and Di-Muons for B-Physics, this volume.\n[3] The ATLAS Collaboration, The ATLAS experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003, 2008.\n[4] S. Agostinelli et al., Nucl. Instr. and Meth. 506, 250 (2003).\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1051\n\n[5] The ATLAS Collaboration, CERN-LHCC-2005-022 (2005).\n[6] The ATLAS Collaboration, CERN-LHCC-98-14 (1998).\n[7] T. Sj\u00a8ostrand, S. Mrenna and P. Skands, JHEP 05, 026 (2006).\n[8] The ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this vol-\nume.\nB-PHYSICS \u2013 PERFORMANCE STUDY OF THE LEVEL-1 DI-MUON TRIGGER\n1052\n\nTriggering on Low-pT Muons and Di-Muons for B-Physics\nAbstract\nMuon pairs from J/\u03c8 decay are a clear signature of b hadrons. As a large\nfraction of b hadrons are produced at low-pT, a low rate, ef\ufb01cient di-muon\ntrigger for low-pT muons and a good understanding of the trigger ef\ufb01ciency\nare essential. Di-muon \ufb01nal states will also play a key role in calibration,\nalignment and determination of the trigger ef\ufb01ciencies. The performance of\nthe level-2 dimuon trigger algorithms is discussed, together with a method\nfor reducing backgrounds from decays-in-\ufb02ight. A strategy for calculating\nthe single muon and di-muon trigger ef\ufb01ciencies at level-1 and level-2 using\nJ/\u03c8 from the data themselves is presented.\n1\nIntroduction\nB-physics is one of the areas of the physics programme of the ATLAS experiment. It includes the\nstudy of production cross sections, searches for rare b decays and measurements of CP violation\neffects. These studies make use of the large b\u00afb production cross section at the LHC where b\u00afb pairs are\nabundant in the low transverse momentum (pT) region. On the other hand, one must extract signals\nfrom amongst the large QCD background, mostly composed of light quarks. For this purpose, one of\nthe main channels for B physics study involves decay channels with one or more muons in the \ufb01nal\nstate, especially the channel J/\u03c8 \u2192\u00b5+\u00b5\u2212.\nThe output rate of the \ufb01rst level trigger at a luminosity of 1033cm\u22122s\u22121 is expected to contain\n20 kHz of events where one muon passed the pT threshold of 6 GeV. Early running is envisioned to\ninclude even lower pT thresholds, down to the lowest threshold achievable in the hardware.\nAt the second level trigger this rate of events must be reduced to 1-2 kHz, of which 5-10% are\navailable for channels of interest only to B-physics. Currently this goal is achieved for level-1 muon\ntriggers by \ufb01rst con\ufb01rming that a muon over the nominal threshold is reconstructed in the muon\nspectrometer (MS), and then con\ufb01rming that there is a matching track in the inner detector (ID).\nThis selection criterion removes many muons from K and \u03c0 decays, but does not by itself produce\nthe required rate reduction. To achieve the required rate pT thresholds need to be raised and many\ninteresting b events are likely to be \ufb01ltered out. We therefore focus also on di-muon \ufb01nal states.\nWe developed an algorithm, TrigDiMuon, which achieves high ef\ufb01ciency at level-2 for the golden\nCP channels (J/\u03c8), using the identi\ufb01cation of relatively low-pT muons from J/\u03c8 decay. TrigDiMuon\nsearches for di-muon pairs from J/\u03c8 or other resonant sources, when only one of the muons passed\nthe level-1 or level-2 single muon selection. The use of TrigDiMuon can enhance J/\u03c8 ef\ufb01ciency at\nlow-pT compared to the trigger based on two muons found at level-1, with an acceptable increase in\nthe fake rate.\nIn this note, we present the performance of the TrigDiMuon algorithm, that looks for a second\nlow-pT muon partner to a single muon triggered at level-1. We compare it to the performance of an\nalgorithm that requires a di-muon level-1 trigger. The comparison is based on a sample of J/\u03c8 which\ndecayed into muons with low-pT, such that the second muon of each decay may be below the level-1\nthreshold.\nIn addition to the foreseen specialised trigger strategies for di-muon signatures, it is important\nto optimize the rejection of muons from K and \u03c0 decays for the standard single muon selection in\norder to have the lowest possible threshold on the inclusive single muon trigger. This is achieved\n1053\n\nby extrapolating the muon track from the MS back to the interaction vertex and requiring a good\nmatch between this track and the associated track from the ID. Muons from light hadron decays do\nnot match accurately the ID track, which in this case is the track produced by the parent hadron (or\nfrom a mixture of hits from the parent and the daughter muon) and not by the muon track. This\nnote presents a method implemented at the level-2 trigger for rejecting muons from K and \u03c0 decays.\nWe summarize the rejection power of this method, show that the ef\ufb01ciency loss is minimal for direct\nmuons and estimate the ef\ufb01ciency loss for low-pT muons from J/\u03c8 decay.\nCross section measurements or searches for rare decays require a good understanding of the ef-\n\ufb01ciency of the event selection. As we are interested in events with rather low-pT, the understanding\nof the trigger ef\ufb01ciency is crucial and we must have a strategy for measuring it from data with high\nprecision. The tag-and-probe method for measuring the single muon trigger ef\ufb01ciency using J/\u03c8\nevents is presented, and we demonstrate that the obtained trigger ef\ufb01ciency can be applied to calcu-\nlate the di-muon trigger ef\ufb01ciency. A calibration trigger is proposed to collect an unbiased sample of\nsingle muons with an enhanced J/\u03c8 fraction, and the expected performance of the trigger ef\ufb01ciency\nmeasurement in the early days of the data-taking is discussed.\nParticles from additional collisions in the same bunch-crossing (pile-up) are not simulated in the\nsamples used for this paper, and therefore this additional background is not taken into account in the\nanalysis.\n2\nSimulated datasets used and production tools\nSince the subject of this note is low-pT muons, we use simulated samples that were produced with\nespecially low-pT cuts at the event generation level. Samples were generated using the PYTHIA\nevent generator [1]. Except for the minimum bias events, a generator level \ufb01lter was applied to\npre-select ef\ufb01ciently the events in the sample. The di-muons sample passed a \ufb01lter which required\nthe existence of at least two muons with the appropriate pT and \u03b7\ncuts. For the inclusive muon\nsamples the \ufb01lter required the existence of a single muon passing the corresponding selection. Events\nwere processed with the full simulation of the ATLAS detector based on the GEANT package [2].\nThe level-1 simulation, High Level Trigger (HLT) selection and of\ufb02ine event reconstruction were\nperformed.\nThe following di-muon samples were used:\n\u2022 An 8000 event sample of the channel \u039bb \u2192J/\u03c8\u039b with J/\u03c8 \u2192\u00b5+\u00b5\u2212, where one of the muons\nis required at the event generation level to have pT > 4 GeV and the second muon is required to\nhave pT > 2.5 GeV.\n\u2022 Simulated samples of direct J/\u03c8 production and b\u00afb \u2192J/\u03c8 production, with the generator\nlevel \ufb01lter requiring the existence of at least two muons with pT > 6 GeV for the highest pT\nmuon and pT > 4 GeV for the second highest pT muon. For both processes, 150000 events\nwere generated.\n\u2022 Two samples of inclusive muon from b decays were used. A 200000 event sample of b\u00afb \u2192\u00b5X\nwith a generator level \ufb01lter requiring one muon with pT > 4 GeV, and a sample of 250000 b\u00afb\nevents with at least one muon with pT > 6 GeV in the \ufb01nal state.\n\u2022 Since this note deals speci\ufb01cally with methods of rejecting muons from K and \u03c0 decays, a large\nsample of such decays was required. A minimum bias sample where pions and kaons were\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1054\n\nforced to decay inside the inner tracker volume was produced for this purpose. The method\ndeveloped for producing this \u201cforced-decay\u201d sample is described in detail below.\n\u2022 Events containing a single muon each were used to study the effect on prompt muons of the\nmethod for rejecting muons from K and \u03c0 decays. Some of the single muon samples were\nsimulated with a perfectly aligned detector geometry, while some other samples were simulated\nwith a misaligned detector description.\nThe trigger and reconstruction software used for some of the samples are of a later version than\nthat used in other notes, because the level-2 and reconstruction software used here have improved\nsigni\ufb01cantly in recent version. The software modi\ufb01cation will be explained where each package is\ndescribed. Table 1 summarizes the simulated Monte Carlo samples used in this note.\nSamples\nGenerator level \ufb01lter\nStatistics\nSignal\nsamples\nDirect J/\u03c8 \u2192\u00b5+\u00b5\u2212\np\u00b51,2\nT\n> 6,4 GeV\n150 k\nb\u00afb \u2192J/\u03c8 \u2192\u00b5+\u00b5\u2212\np\u00b51,2\nT\n> 6,4 GeV\n150 k\n\u039bb \u2192J/\u03c8\u039b (J/\u03c8 \u2192\u00b5+\u00b5\u2212)\np\u00b51,2\nT\n> 4,2.5 GeV\n7.6 k\nBackground\nsamples\nbb \u2192\u00b5 +X\np\u00b5\nT > 6 GeV\n250 k\nb\u00afb \u2192\u00b5 +X\np\u00b5\nT > 4 GeV\n185 k\nMinimum bias (forced K /\u03c0)\n114 k\nMinimum bias (standard)\n500 k\nTable 1: Summary of MC samples.\n2.1\nProduction tools and samples employed for K and \u03c0 decays\nMinimum bias events are the most copious source of pions and kaons. These particles are produced\nmainly with very low-pT, and typically the muons coming from their in \ufb02ight decays do not escape the\nATLAS hadronic calorimeter. On the other hand pions and kaons with high-pT have a low probability\nto decay before the calorimeter because of their high energy. As a consequence it is not ef\ufb01cient to\nuse minimum bias events as a source of decays in \ufb02ight to muons. Estimates made for this analysis\nindicated that the simulation of 5000 minimum bias events would be needed to provide one muon\nfrom K or \u03c0 decay capable of passing the 6 GeV threshold of the ATLAS level-1 muon trigger.\nTo increase the statistics of events with charged pions and kaons decaying in \ufb02ight, a special\nsimulation tool is applied. Since we are interested in decays which happen inside the detector, the\ndecays cannot be made on generator level but must happen in the GEANT simulation. The program\nto force the K /\u03c0 to decay in the detector is an extension to GEANT which runs before the simulation\nitself.\nIn each event a list of all charged pions and kaons with pT > 2 GeV is compiled, and one of the\nparticles in the list is randomly selected. Events with no charged pions or kaons with pT > 2 GeV are\ndropped at this stage, such that the events are not further simulated and nothing is written to output.\nThe point of decay is selected by \ufb01rst computing the trajectory length from the production vertex\nto where the particle would exit the ID (neglecting curvature in the magnetic \ufb01eld). The decay position\nis then determined by taking a random fraction of this maximum track length. Since particles assigned\na late decay have a larger probability to be stopped through hadronic interactions, this procedure may\nintroduce a weak bias towards shorter decay lengths.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1055\n\nFor this study a minimum bias sample of 114 k events was simulated with forced decays. The\ntransverse momentum cut of 2 GeV applied to the light hadrons reduces the cross section of the\nsample to (43.41 \u00b1 0.07)% of the minimum bias cross section. In addition to this a minimum bias\nsample of 500 k events, simulated with the standard GEANT simulator, was also employed to provide\na cross-check from a single source for both the muons from K /\u03c0 decay and the prompt muons.\n3\nThe muon trigger\nThe ATLAS trigger system [3] reduces the event rate from the 40 MHz beam crossing rate to \u223c200 Hz\nfor mass storage, keeping the events that are potentially the most interesting for physics. The \ufb01rst\nlevel trigger [4] selection is performed by custom hardware and identi\ufb01es a detector region for which a\ntrigger element was found. The second level trigger [5] is performed by dedicated software, making its\ndecision based on data acquired from the Region of Interest (RoI) identi\ufb01ed at level-1. Eventually, the\nevent \ufb01lter [5] uses the complete event data, and algorithms adapted from the of\ufb02ine reconstruction,\nto re\ufb01ne the selection of level-2 and further reduce the trigger rate by about a factor 10. An event must\npass all trigger levels to be kept for analysis.\nA detailed description of the ATLAS muon trigger and the estimated trigger rates are presented\nin [6]. Here we give a very brief summary of the principles of the level-1 and level-2 muon triggers.\n3.1\nThe level-1 muon trigger\nThe level-1 muon trigger is based on dedicated fast detectors: the Resistive Plate Chambers (RPC) in\nthe barrel and the Thin Gap Chambers (TGC) in the end-caps [7]. The basic principle of the algorithm\nis to require a coincidence of hits in the different trigger stations within a prede\ufb01ned angular region,\ncalled a \u201droad\u201d, from the interaction point through the detector. The width of the road is related to the\nbending of the muon in the magnetic \ufb01eld and thus to the pT threshold to be applied.\nThe trigger in both the barrel and the end-cap regions is based on three trigger stations at different\ndistances from the interaction point [4]. The low-pT triggers (4 to 10 GeV) are derived from a coin-\ncidence in two stations, while the high-pT triggers (over 10 GeV) require an additional coincidence\nwith the third station. In the end-cap, there is an option to use all three stations also for the low-pT\ntrigger. This option is the one used in the trigger performance studies in Reference [6].\nThe level-1 trigger provides for each muon candidate the region where it was found, called the\nregion of interest (RoI). For the muon trigger, the size of the level-1 RoI is \u2206\u03b7 \u00d7\u2206\u03c6 = 0.1\u00d70.1 in the\nbarrel and \u2206\u03b7 \u00d7\u2206\u03c6 = 0.03\u00d70.03 in the end-cap region, respectively.\n3.2\nThe level-2 single-muon trigger\nThe level-2 trigger is a software-based trigger and uses the information of the Region of Interest\nprovided by the level-1 trigger. Level-2 algorithms only process data around the RoI, using the full\ngranularity of the detector readout within the RoI.\nThe HLT trigger selection proceeds in \u201ctrigger chains\u201d. A chain consists of a series of reconstruc-\ntion and decision (hypothesis) algorithms that process the data in a RoI identi\ufb01ed by level-1. The role\nof the level-2 muon trigger is to con\ufb01rm muon candidates \ufb02agged by the level-1 and to give more\nprecise track parameters for the muon candidate.\nThe level-2 muon selection is performed in two stages. The \ufb01rst stage is performed by the muFast\nalgorithm [8], which starts from a level-1 muon RoI and reconstructs the muon in the spectrometer,\nusing the more precise Monitored Drift Tubes (MDT) to perform a new pT estimate for the muon\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1056\n\ncandidate and creating a new trigger element. The hypothesis algorithm cuts on the estimated pT and\npasses the validated trigger elements to the next algorithm.\nTrack \ufb01nding in the inner detector is based on the region of the candidate found by muFast. The\nmuFast candidate and ID tracks are passed to the next algorithm, muComb, which matches an ID\ntrack with the trigger element from the muon spectrometer and re\ufb01nes the pT estimate [5].\n3.2.1\nmuFast\nFor level-1 RoI\u2019s \ufb02agged by the RPC (barrel region) and the TGC (end-cap region), muFast performs\nglobal pattern recognition, a local segment \ufb01t in each muon station and a fast pT estimation. The\nglobal pattern recognition is designed to select clusters in MDT tubes belonging to a muon track\nwithout using the drift time measurements. It is divided into two steps, \ufb01rstly the pattern recognition\nin the trigger chambers seeded by the level-1 RoI, and the subsequent MDT pattern recognition seeded\nby the result of the previous step. In the MDT pattern recognition muon roads are opened in selected\nMDT chambers, and the loactions of hit tubes are collected. A contiguity algorithm is applied on the\nselected hits to remove the background.\nThe track reconstruction approximates a muon track as a series of segments built separately in each\nMDT chamber. Segments are reconstructed using the drift time measurements and an approximate\ncalibration to obtain hit radii from them. The \ufb01tted segments provide a precision measurement of the\npoint where the \ufb01tted line crosses the middle of the MDT chamber, called the super-point.\nThe track bending is measured in a different way in the barrel and the end-cap. In the barrel, the\nsagitta is computed from the three super-points found in the three stations. In the end-cap, the track\nbending is measured by the angle \u03b1 between the track direction measured by the muon chambers in\nthe middle and outer stations of the muon spectrometer, and the direction obtained by connecting the\nnominal interaction vertex with the mean hit position in the middle station.\nThe muon transverse momentum is estimated using an inverse linear relationship between the\nmeasured sagitta (in the barrel) or \u03b1 (in the end-cap) and pT. The detector region is divided into bins\nin \u03b7 and \u03c6 and the parameters of this inverse linear function are estimated in each bin.\n3.2.2\nmuComb\nThe muComb algorithm matches the muon track found by muFast to ID tracks reconstructed at level-\n2 citeID-CSC. In reconstructing the level-2 ID tracks, only hits from the pixel and SCT detectors were\nused, for speed.\nThe matching between muFast and ID track segments proceeds as follows. First, a preselection of\nID tracks is made based on the difference in \u03b7 and \u03c6 between muFast and ID track segments. In the\nbarrel, this preselection also makes use of the difference in the Z of the extrapolated track segments at\nthe radius of the barrel calorimeter. A weighted combined pT, and a matching \u03c72, are calculated for\neach ID track passing the preselection in combination with the muon track information, and the ID\ntrack giving the lowest \u03c72 is selected as the best match to the muFast track.\nThe version of the algorithm used in this study is improved with respect to that used in [6]. The\nresolution of muFast tracks assumed in combining with the ID tracks have been retuned, using the\ncorrect pT resolutions for the different end-cap regions, and for the misaligned detector geometry. A\nspeci\ufb01c tuning of the matching windows is used to improve the resolution for very low pT muons.\nThis algorithm will be referred to as \u201cthe baseline muComb selection\u201d in Section 5, where a modi\ufb01ed\nalgorithm with better rejection for muons from K and \u03c0 decays is also described, and the performance\nof the two algorithms is compared.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1057\n\n3.2.3\nLevel-2 muon hypotheses\nThe pT cuts corresponding to each nominal threshold are set so that 90% of the muons at the nominal\nthreshold would pass the selection. The actual cuts used depend on the resolution of the pT estimation.\nTherefore the cuts are different for different regions of the detector as well as different between muFast\nand muComb. Thus for a nominal threshold of 6 GeV the muFast hypothesis cuts at estimated pT\nvalues between 4.5 and 5.4 GeV in the different \u03b7 regions, while the muComb hypothesis cuts at\nestimated pT of 5.8 GeV in the barrel and end-cap and 5.6 GeV in the forward region. Since the pT\nresolution of muComb is better than that of muFast, the cuts are closer to the nominal thresholds, and\nreject more muons with pT below the threshold. A special case is the 4 GeV nominal threshold which\nis meant to accept lower pT muons and the cuts are set at 3 GeV in the barrel and 2.5 GeV in the\nend-cap for both muFast and muComb.\n3.3\nThe level-2 di-muon triggers\nThere are two approaches at level-2 for selecting di-muon events from a resonance such as J/\u03c8 and\n\u03d2. The \ufb01rst approach is to start from a di-muon trigger at level-1 which produces two muon regions of\ninterest. In this approach, reconstruction of a muon is con\ufb01rmed separately in each RoI as described\nabove and the two muons are subsequently combined to form a resonance and to apply a mass cut.\nWe will refer to this trigger as the \u201ctopological di-muon trigger\u201d.\nAn alternative approach is to start with a level-1 single muon trigger and search for two muons\nin a wider \u03b7 and \u03c6 region. This approach starts from reconstructing tracks in the inner detector and\nextrapolating the track to the muon spectrometer to tag muon tracks. Since this method does not\nexplicitly require the second muon at level-1, it has an advantage for reconstructing J/\u03c8 at low-pT.\nThis is implemented in the TrigDiMuon algorithm. The two approaches using either two or one muon\nRoI are illustrated in Figure 1.\nFigure 1: A schematic picture of RoI based di-muon trigger, using two RoI\u2019s (left) and seeded by a\nsingle muon RoI (right).\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1058\n\n3.3.1\nThe TrigDiMuon algorithm\nTrigDiMuon is a level-2 trigger algorithm based on associations established between ID tracks and MS\nhits. Each time a pair of oppositely charged ID tracks, above a minimal invariant mass, is successfully\nassociated with the MS hits, a muon pair object is created with the parameters of these ID tracks.\nLater, in the hypothesis step, an additional invariant mass selection can be applied, thus selecting\ninteresting physics objects such as J/\u03c8 or B.\nThe motivation for developing this algorithm comes from the fact that while di-muon \ufb01nal states\nexist in many interesting B-physics channels, the cross sections for di-muon \ufb01nal states are orders\nof magnitude smaller than those for single muons of the same pT. An additional advantage is that\nresonant \ufb01nal states can also be used to calibrate trigger ef\ufb01ciencies as will be shown in Section 5.\nFirst, the initial muon RoI is extended in order to search for a second muon, which was not\ntriggered by level-1. The input muon may be from a region of interest identi\ufb01ed at level-1, but the\ninput rate to the algorithm can be reduced if, prior to the RoI extension, the level-1 RoI would be\ncon\ufb01rmed in the level-2 trigger by the muFast and (possibly also) the muComb algorithms. The\nperformance of these options is studied in Section 4. The size of the extended RoI is based on the\ndistribution of angular distance in \u03b7 and \u03c6 between two muons from J/\u03c8 decay. Figure 2 shows\nthe probability of including the second muon from J/\u03c8 decays RoI as a function of the extended RoI\nsize for different samples. The current default region size in TrigDiMuon is \u2206\u03b7 \u00d7\u2206\u03c6 = 0.75\u00d70.75.\n square region\n\u03b7\n\u2206\n \n\u00d7 \n\u03c6 \n\u2206\nSide length of \n0.4\n0.5\n0.6\n0.7\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n > 6GeV\nT\np\n > 4GeV\nT\np\nFigure 2: Probability of including the second muon from J/\u03c8 decays RoI as a function of the extended\nRoI size for different samples. Open squares are from J/\u03c8 decays where one muon has pT > 6 GeV\nand the other pT > 3 GeV. Full squares are from J/\u03c8 decays where one muon has pT > 4 GeV and\nthe other pT > 2.5 GeV.\nThe ID tracks in the search region are found using the trigger-tracking program IdScan or SiTrack [9],\nand are selected if they form a pair of oppositely charged tracks with invariant mass M > 2.8 GeV.\nEach selected track is extrapolated to the different stations of the MS using a formula parameterizing\nthe expected track bending in the magnetic \ufb01eld. The bending parameterization is calculated sep-\narately for different regions of the muon spectrometer to account correctly for the inhomogeneous\ntoroidal \ufb01eld in the end-cap region. Figure 3 shows the difference, \u2206\u03b7, between \u03b7 measured in the\ninner detector and that measured in the middle station of the muon spectrometer. The lines indicate\nthe choice of \u03b7 regions for the parameterization. The parameterization was also subdivided in \u03c6.\nThe algorithm then searches for muon hits within a road around the extrapolated track. The road\nsize also differs for different \u03b7 regions. If a suf\ufb01cient number of muon hits are found in the MS, the\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1059\n\nFigure 3: The \u03b7 direction of muons at the intercation point vs. the difference in \u03b7 position between\nthe inner detector and the middle station of the muon spectrometer, for muons with pT = 6 GeV. The\nlines indicate the choice of \u03b7 regions for the parameterization.\ntrack is identi\ufb01ed as a muon. If both tracks from the pair are identi\ufb01ed as muons, a muon pair object\nis created. The two tracks are \ufb01t to a common vertex, and the vertex \u03c72 is calculated to allow a later\nselection of only the pairs with a good quality vertex.\n4\nPerformance of the level-2 di-muon triggers for J/\u03c8\nIn this Section the ef\ufb01ciency and fake rates resulting from the two approaches to selecting di-muons\nat level-2 will be presented and compared. For the TrigDiMuon algorithm we calculate the ef\ufb01ciency\nand fake rates in three different trigger chains.\nIn the \ufb01rst con\ufb01guration, TrigDiMuon runs directly after the level-1 trigger based on the RoI\nproduced by level-1. The performance of this trigger is compared to the ef\ufb01ciency and fake rate of the\nlevel-1 di-muon trigger.\nThe other two trigger chains con\ufb01rm a single level-2 muon before calling TrigDiMuon. The\npurpose of these chains is not to reduce the fake di-muon trigger rate, but rather to reduce processing\ntime by reducing the input rate to TrigDiMuon. Since TrigDiMuon starts from ID track reconstruction\nin an extended region around the muon region of interest, the tracking in the inner detector requires\nthree times longer than if only reconstructing ID tracks in the narrow road used by muComb. Thus, this\ntime consuming process can be avoided for candidates for which the level-1 trigger is not con\ufb01rmed\nat level-2.\nIn the second chain TrigDiMuon runs after muFast. The input to TrigDiMuon in this case is a\nmuon con\ufb01rmed in the MS, with a cut on the pT estimated at this stage. The ef\ufb01ciency of this trigger\nis compared with that of a topological di-muon trigger based on a level-1 di-muon with two oppositely\ncharged muons con\ufb01rmed in the MS at level-2.\nIn the third chain TrigDiMuon runs after muComb. The input to TrigDiMuon in this case is a\nmuon con\ufb01rmed in the MS and the ID, with a cut on the pT estimated at this stage. The ef\ufb01ciency\nof this trigger is compared with that of the topological di-muon trigger with two oppositely charged\nlevel-2 combined muons, within the same invariant mass window. The invariant mass window can be\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1060\n\napplied in this chain, and not the second chain, because only after muComb the momentum resolution\nis suf\ufb01cient for a reasonable selection on invariant mass.\nThe ef\ufb01ciency and fake rates of these trigger sequences were studied for two different trigger\nthresholds, a 4 GeV threshold that is envisioned to run at initial luminosity, and a 6 GeV threshold that\nwill be the lowest threshold for running at a luminosity of 1033cm\u22122s\u22121.\nA selection requiring the two muons to be oppositely charged, and the pair to have invariant mass\nbetween 2.8 GeV and 3.4 GeV was applied to both TrigDiMuon and the topological di-muon trigger.\nFor the topological algorithm the invariant mass selection was only applied after muComb. The fake\nrates were calculated as follows: the probability of each of the level-2 strategies to \ufb01nd a di-muon\npair in events which contain only a single muon was estimated separately for the b events and the\nminimum-bias events. This probability was multiplied by rates which were estimated independently\nfrom [6], but are consistent with it. The fake probability in b events was taken to be representative\nof that in all events with prompt muons. For the topological di-muon trigger, the probability was\ncalculated relative to the number of di-muon level-1 triggers, and multiplied by the level-1 fake di-\nmuon trigger rate from [6].\n4.1\nEf\ufb01ciency relative to events accepted at level-1\nTable 2 gives the ef\ufb01ciency, relative to level-1, for the two di-muon trigger algorithms for a trigger\nthreshold of 4 GeV. Table 3 gives the ef\ufb01ciencies, relative to level-1, for a trigger threshold of 6 GeV.\nThe ef\ufb01ciencies in these tables are calculated with respect to the J/\u03c8 events accepted by the corre-\nsponding level-1 single muon trigger. In parenthesis we give the ef\ufb01ciency relative to J/\u03c8 events at\nthe starting point of the di-muon algorithm.\nOne can see that the TrigDiMuon ef\ufb01ciency is signi\ufb01cantly higher than the topological di-muon\ntrigger in all cases. As a matter of fact, the topological di-muon trigger, which applies pT cuts on both\nmuons, can have only a limited acceptance for J/\u03c8 events passing a single muon trigger because the\nsecond muon is very frequently below the trigger threshold. To pass the topological di-muon trigger\nthe second, lower pT muon also has to pass the level-2 selections.\nBecause TrigDiMuon can reconstruct muons below the level-1 thresholds, the TrigDiMuon ef-\n\ufb01ciency, shown in brackets, remains nearly the same with the different chains. However, the total\nef\ufb01ciency is reduced when starting from the single muons accepted by muFast or muComb, because\nof the pT cut imposed by those algorithms. In particular, in Table 3 muFast and muComb reject suc-\ncessively more of the muons below the nominal threshold and this explains the big drop from row to\nrow for TrigDimuon and even bigger drop for the topological trigger.\nThe loss of ef\ufb01ciency in the single muon triggers is smaller for the 4 GeV threshold, because the\nlevel-2 cuts for the 4 GeV threshold are quite loose, as mentioned above. When calculating the 4\nGeV trigger ef\ufb01ciency using only muons from J/\u03c8 with generated pT above the 4 GeV threshold,\nTrigDiMuon has an ef\ufb01ciency of 90% and the topological trigger has an ef\ufb01ciency of 64%.\nAs discussed earlier, in spite of some loss of ef\ufb01ciency, the trigger chains with TrigDiMuon run-\nning after a level-2 con\ufb01rmed muon might be more suitable to an overall planning of the ATLAS\ntrigger menu due to the reduced input rate they have to sustain.\n4.2\nFake rates\nTable 4 gives the expected fake rates for TrigDiMuon with the different chains described above, for\na trigger threshold of 4 GeV at a luminosity of 1031cm\u22122s\u22121. Table 5 gives the rates for a trigger\nthreshold of 6 GeV at a luminosity of 1033cm\u22122s\u22121.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1061\n\nChain\nstarting from\nTrigDiMuon\n(%)\nTopological\ntrigger\n(%)\nlevel-1\n73 (73)\n51\nmuFast\n71 (73)\n43\nmuComb\n70 (74)\n33\nTable 2: Ef\ufb01ciency, relative to level-1, of the two di-muon trigger algorithms for a trigger threshold\nof 4 GeV. In parenthesis is the ef\ufb01ciency calculated relative to J/\u03c8 events that passed the single\nmuon trigger that selects the input to TrigDiMuon. To estimate the ef\ufb01ciency we used a sample of\n\u039bb \u2192J/\u03c8\u039b, where J/\u03c8 \u2192\u00b5(pT > 2.5 GeV)\u00b5(pT > 4 GeV).\nChain\nstarting from\nTrigDiMuon\n(%)\nTopological\ntrigger\n(%)\nlevel\u22121\n75 (75)\n56\nmuFast\n67 (77)\n25\nmuComb\n60 (78)\n15\nTable 3: Ef\ufb01ciency, relative to level-1, of the two di-muon trigger algorithms for a trigger threshold\nof 6 GeV. In parenthesis is the ef\ufb01ciency calculated relative to J/\u03c8 events that passed the single\nmuon trigger that selects the input to TrigDiMuon. To estimate the ef\ufb01ciency we used a sample of\n\u039bb \u2192J/\u03c8\u039b, where J/\u03c8 \u2192\u00b5(pT > 2.5 GeV)\u00b5(pT > 4 GeV).\nSource\nChain\nstarting from\nInput rate\n(Hz)\nFake\nacceptance\n(%)\nFake rate\n(Hz)\nb + c\nlevel\u22121\n460\n0.42\n1.9\nmuFast\n380\n0.42\n1.6\nmuComb\n340\n0.43\n1.5\nK /\u03c0\nlevel\u22121\n620\n0.07\n0.43\nmuFast\n270\n0.11\n0.29\nmuComb\n170\n0.09\n0.15\nTotal\nlevel\u22121\n1080\n0.22\n2.3\nmuFast\n650\n0.29\n1.9\nmuComb\n510\n0.32\n1.6\nTable 4: Fake rate of the TrigDiMuon algorithm for muons from different sources and total fake rate\nusing a trigger threshold of 4 GeV, at a luminosity of 1031cm\u22122s\u22121. The b and c components were\nestimated from a sample of b\u00afb \u2192\u00b5 +X with p\u00b5\nT > 4 GeV and the K /\u03c0 component from the minimum\nbias sample with forced decays\nFake rates can be further reduced by reconstructing the J/\u03c8 decay vertex from the two muon\ntracks. Selecting J/\u03c8\nwith a good quality vertex \ufb01t will reduce fake rates from unrelated track\ncombinations. Figure 4 shows the distribution of the vertex \u03c72 for true J/\u03c8 decays and for fake\ndi-muon triggers. A cut of \u03c72 < 30 reduces the fake rate by 20-30% and only reduces the trigger\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1062\n\nSource\nChain\nstarting from\nInput rate\n(Hz)\nFake\nacceptance\n(%)\nFake rate\n(Hz)\nb + c\nlevel-1\n21500\n0.48\n103\nmuFast\n12500\n0.60\n76\nmuComb\n10300\n0.75\n76\nK/\u03c0\nlevel-1\n15800\n0.22\n34\nmuFast\n5000\n0.30\n15\nmuComb\n3500\n0.41\n14\nTotal\nlevel-1\n37400\n0.37\n137\nmuFast\n17500\n0.51\n91\nmuComb\n13700\n0.66\n90\nTable 5: Fake rate of the TrigDiMuon algorithm for muons from different sources and total fake rate\nusing a trigger threshold of 6 GeV, at a luminosity of 1033cm\u22122s\u22121. The b and c components were\nestimated from a sample of b\u00afb \u2192\u00b5 +X with p\u00b5\nT > 4 GeV and the K /\u03c0 component from the minimum\nbias sample with forced decays\nef\ufb01ciency by 1-2%. The vertex position can also be used to reject J/\u03c8\nproduced at the primary\ninteraction and accept only J/\u03c8 from b hadron decays, but a study of this is outside the scope of this\nnote.\n2\n\u03c7\n0\n20\n40\n60\n80\n100\nEntries/2\n-2\n10\n-1\n10\n1\n\u03c8\nJ/\nBackground\nATLAS\nFigure 4: Distribution of the vertex \u03c72 for true J/\u03c8 decays (shaded) and for fake di-muon triggers\n(open histogram).\nFinally Table 6 compares the total rates and ef\ufb01ciencies of the two level-2 di-muon algorithms.\nWhen TrigDiMuon runs after muComb, the signal to background ratio is worse than when it runs after\nmuFast. Using the input rates from Table 4 and 5, one can calculate that the time needed to reconstruct\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1063\n\nthe ID tracks is also the smallest when TrigDiMuon runs after muFast, reduced by 1/3 for the 4 GeV\nthreshold and by 1/2 for the 6 GeV threshold with respect to running after L1.\nIt can be seen from this table that the fake rate for the topological di-muon trigger is small. The\nfake rate from the TrigDiMuon algorithm is much higher but these output rates from level-2 should\nbe acceptable for the gain in ef\ufb01ciency, at the initial low luminosity.\nThreshold\n(Luminosity)\nChain\nstarting\nfrom\nTrigDiMuon\nTopological\nEf\ufb01ciency\n(%)\nJ/\u03c8\nrate\n(Hz)\nTotal\nrate\n(Hz)\nEf\ufb01ciency\n(%)\nJ/\u03c8\nrate\n(Hz)\nTotal\nrate\n(Hz)\n4 GeV\n(1031cm\u22122s\u22121)\nlevel\u22121\n71\n1.17\n3.1\n51\n0.8\n24\nmuFast\n70\n1.15\n2.7\n43\n0.7\n-\nmuComb\n69\n1.14\n2.4\n33\n0.5\n0.6\n6 GeV\n(1033cm\u22122s\u22121)\nlevel\u22121\n74\n43\n151\n56\n32.5\n357.5\nmuFast\n66\n38\n114\n25\n14.5\n-\nmuComb\n59\n34\n109\n15\n8.7\n9.3\nTable 6: Total rate and ef\ufb01ciency relative to level-1 of the TrigDiMuon algorithm including the vertex\ncut \u03c72 < 30, and of the topological di-muon trigger. The ef\ufb01ciency is estimated from a sample of\n\u039bb \u2192J/\u03c8\u039b, where J/\u03c8 \u2192\u00b5(pT > 2.5 GeV)\u00b5(pT > 4 GeV).\nThe b-physics trigger rate from TrigDiMuon requires further reduction for L = 1033. This can be\nachieved by introducing an additional trigger with a cut on the J/\u03c8 decay length. Then the trigger\nwithout decay length cut will be prescaled to an acceptable rate for calibration and alignment purposes,\nas for example in Section 6. An event \ufb01lter algorithm will further reduce the rates for a luminosity of\n1033cm\u22122s\u22121.\n4.3\nEf\ufb01ciency relative to reconstructed events\nOur goal is to maximize trigger ef\ufb01ciency at the level-2 trigger for the muons that can later be identi-\n\ufb01ed of\ufb02ine. The ef\ufb01ciencies for the two algorithms and thresholds were re-estimated with respect to\nthe J/\u03c8 events reconstructed with the muon identi\ufb01cation program MuGirl [10], which is ef\ufb01cient\nfor low-pT muons. The resulting ef\ufb01ciencies are given in Table 7 for a trigger thresholds of 4 GeV\nand 6 GeV respectively. Figure 5 shows the ef\ufb01ciency of TrigDiMuon relative to muons identi\ufb01ed by\nMuGirl for the higher pT muon (left) and the second muon (right).\nThreshold\n(Luminosity)\nChain\nstarting\nfrom\nTrigDiMuon\nEf\ufb01ciency (%)\nTopological Trigger\nEf\ufb01ciency (%)\n4 GeV\n(1031cm\u22122s\u22121)\nlevel\u22121\n84\n58\nmuComb\n81\n42\n6 GeV\n(1033cm\u22122s\u22121)\nlevel\u22121\n81\n45\nmuComb\n66\n17\nTable 7: Ef\ufb01ciency of the TrigDiMuon and Topological di-muon algorithms for J/\u03c8 reconstructed\nby MuGirl. To estimate the ef\ufb01ciency we used a sample of \u039bb \u2192J/\u03c8\u039b, where J/\u03c8 \u2192\u00b5(pT >\n2.5 GeV)\u00b5(pT > 4 GeV).\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1064\n\n(GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\nEfficiency\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0.6\n0.7\n0 8\n0 9\n1\n at level-1 (4GeV)\n\u00b5\none \n at level-1 (6GeV)\n\u00b5\none \n(GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n at level-1 (4GeV)\n\u00b5\none \n at level-1 (6GeV)\n\u00b5\none \nFigure 5: Ef\ufb01ciency of TrigDiMuon relative to muons identi\ufb01ed by MuGirl for the higher pT muon\n(left) and the second muon (right).\n5\nRejection of muons from K and \u03c0 decays\nThe lowest single muon pT threshold in the original ATLAS HLT design [5] was chosen to be 6 GeV.\nThis is because below this pT value the rate of muons from K and \u03c0 decays becomes higher than that\nfrom b and c decays. Nevertheless, during the low luminosity phase, it is desirable to collect muons\nwith lower pT, both for detector and trigger calibration and for initial physics studies. If thresholds are\nlowered, K and \u03c0 decays become the dominant source of single muon triggers. These decay muons\nmust be rejected as early as possible so as not to dominate the single muon trigger rate, thus ensuring\nwe can achieve the physics and calibration studies with prompt muons.\n5.1\nDescription of the method\nThe method we describe rejects K and \u03c0 decays based not on their pT but on the topology of the\ndecay. The track position of a prompt muon, extrapolated from the MS to the interaction vertex, is\na gaussian distributed around the ID track position. The corresponding distribution of a decay muon\naround the light hadron from which it decayed is broader because of the contribution of the decay\nkink in addition to the multiple scattering effect. Thus if the track seen in the inner detector is that of\nthe K or \u03c0, this discrepancy with prompt muons can be used to reject some of the muons from light\nhadron decays.\nWith this method, we can reject the muons from K and \u03c0 decays by using a matching window\ntuned for prompt muons, with the window width varying according to the track pT. Due to time\nconstraints, a precise propagation of tracks in the magnetic \ufb01eld can not be done at level-2, so instead\nthe muon track from the MS is extrapolated back to the interaction vertex using a parameterization\nthat is a function of measured \u03b7, \u03c6 and pT (exploiting the linear relationship between the bending and\n1/pT). Multiple scattering effects can be parameterized in the same way to estimate the corresponding\nerrors of the back extrapolation, which determine the window size.\nThree main regions are identi\ufb01ed for the \ufb01eld parameterization used to propagate the muon tracks,\none in the barrel and two in the end-cap. To account for the relative inhomogeneity of the magnetic\n\ufb01eld inside each region, the parameters of the back extrapolation are computed as a function of \u03b7, \u03c6,\nmuon charge and spectrometer side (z or \u2212z). A different tuning is used for high and low-pT tracks,\nto take into account the \ufb02uctuations of the energy loss in the calorimeter which are important for the\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1065\n\npropagation of the latter. In the end-cap, the innermost station of the MS does not provide a complete\ngeometric coverage, thus for the muons with no hits in the innermost station, a seed from the middle\nstation is used to extrapolate the track back. This is the most dif\ufb01cult case since an extrapolation\nthrough the toroids must be performed and the resulting precision is spoiled by a factor of two with\nrespect to the other cases. Therefore the back extrapolation in the end-cap is treated separately for\nregions with inner station coverage and region without inner station coverage.\nThe strategy for the level-2 combined muon reconstruction described in [5] is to use only the pixel\nand the SCT data. With this setup, the decays in \ufb02ight happening near or after the last SCT layer are\nreconstructed using mainly the hits of the decaying K or \u03c0. Some rejection of these events can be\nachieved by checking the \u03b7 and \u03c6 position of the extrapolated MS track relative to the ID track with\na matching window whose size is based on the position spread coming out from the muon multiple\nscattering. Some of the decays between the pixel and the SCT can be rejected by applying a cut on\nthe \u03c72 of the Inner Detector \ufb01t.\nThe cuts studied, ordered in terms of increasing rejection are:\n\u2022 A loose-window cut, using the muon track position from muFast, and the track position from\nthe ID reconsrtruction. The window size was tuned to recover almost 100% of the multiple\nscattering for a muon pT equal to the threshold value (4 GeV and 6 GeV);\n\u2022 A tight-window cut, re\ufb01ning the muon back-extrapolation by exploiting the measurement of\nthe interaction vertex from the ID reconstruction. The window size was tuned to 2.7 \u03c3 of the\nmultiple scattering spread for that muon pT; the combined pT estimation is used to tune the\nwindow width;\n\u2022 The normalized \u03c72 of the ID track \ufb01t is required to be less than 3.2.\n5.2\nPerformance of the method\n5.2.1\nRejection results for K and \u03c0 decays\nThe 6 GeV threshold is used as a benchmark to estimate the K and \u03c0 rejection achieved by the various\ncuts. The forced-decay minimum bias sample has been used to study and tune the cuts to reject muons\nfrom K and \u03c0 decays. The results shown in Table 8 are expressed in terms of trigger rate, computed\nusing the cross section of these events.\nCut\n\u03c0/K rate (Hz)\nBaseline muComb\n3470\u00b1380\nLoose window cut\n2920\u00b1430 (-16%)\nTight window cut\n2800\u00b1440 (-20%)\nTight window + \u03c72 cut\n2550\u00b1440 (-26%)\nTable 8: Expected rate with a 6 GeV single muon threshold from the muComb algorithm for the \u03c0\nand K decays. The rejection with respect to the baseline muComb algorithm is shown in parenthesis.\nThese rates were estimated from the forced-decay minimum bias sample\nFigure 6 shows the trigger ef\ufb01ciency for muons from K and \u03c0 decays as a function of pT for the\nbaseline muComb selection, compared to the tight window selection described above.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1066\n\n (GeV)\nT\nMuon P\n0\n2\n4\n6\n8\n10\n12\n14\n16\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nComb selection\n\u00b5\nStandard \nComb selection\n\u00b5\nOptimized \n (GeV)\nT\nMuon P\n0\n2\n4\n6\n8\n10\n12\n14\n16\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nComb selection\n\u00b5\nStandard \nComb selection\n\u00b5\nOptimized \nFigure 6: Ef\ufb01ciency for muons from K and \u03c0 decays as a function of pT for the baseline muComb se-\nlection, compared to the optimized muComb selection described in Section 5.1 for the 4 GeV threshold\n(left) and the 6 GeV threshold (right).\n (GeV)\nT\nMuon P\n0\n5\n10\n15\n20\n25\nEfficiency\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\nMU06, aligned setup\n\u03c3\nTight window at 3\n\u03c3\nTight window at 2.7\n\u03c3\nTight window at 2\nFigure 7: Ef\ufb01ciency of the tight window match on single muons simulated with the aligned detector\nsetup. The ef\ufb01ciency drop for the 6 GeV threshold is shown according to different \u03c3 cuts.\n5.2.2\nEf\ufb01ciency loss for prompt muons\nThe ef\ufb01ciency loss for prompt muons due to the matching window cuts has been estimated with a\nsingle muon sample. Figure 7 shows the relative ef\ufb01ciency obtained for the aligned detector setup.\nThe relative ef\ufb01ciency is seen to be almost constant in the pT range of 4-40 GeV and its value for\nthe cut at 2.7 \u03c3 is about 98%. The detector misalignment reduces the ef\ufb01ciency plateau to 95% as\nshown in Figure 8, but the relative ef\ufb01ciency can be recovered by 1% with a speci\ufb01c tuning of the\nback extrapolator.\nThe rate reduction for b decays is calculated reliably from the b \u2192\u00b5(4)+X sample. The results\nare shown in Table 9. A good agreement between b events and single muons is found for the ef\ufb01ciency\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1067\n\n (GeV)\nT\nMuon P\n0\n5\n10\n15\n20\n25\nEfficiency\n0.75\n0.8\n0.85\n0.9\n0.95\n1\nATLAS\nMU06, misaligned setup\n tuned for misaligned\n\u03c3\nTight window at 2.7\n untuned\n\u03c3\nTight window at 2.7\nFigure 8: Ef\ufb01ciency of the tight window match at 2.7 \u03c3 on single muons simulated with the misaligned\ndetector setup. The relative ef\ufb01ciency is shown for the 6 GeV threshold.\nloss due to the tight window match.\nCut\nb\u2192\u00b5(4)+X\nrate (Hz)\nBaseline muComb\n4850\u00b120\nLoose window cut\n4780\u00b120 (-1.5%)\nTight window cut\n4710\u00b120 (-3%)\nTight window + \u03c72 cut\n4560\u00b120 (-6%)\nTable 9: Expected rate with a 6 GeV single muon threshold from the muComb algorithm for the b\ncomponent. In parenthesis is the percentage rejection with respect to the baseline muComb.\n5.2.3\nResulting muon trigger rates\nA coherent description of the full trigger rate after the muComb algorithm is obtained using the stan-\ndard minimum bias sample and is shown in Table 10 and in Table 11. All the cuts mentioned were\napplied. A very good agreement is found with both the forced sample for the K /\u03c0 component, and\nthe b \u2192\u00b5 +X sample for the b component.\nThe optimized version of muComb improves the rejection of muons from decays in \ufb02ight by about\n30% at the 4 GeV threshold and of about 20% at the 6 GeV threshold with respect to the baseline\nmuComb algorithm. The rejection of muons from b events is 20% at the 4 GeV threshold and 7% at\nthe 6 GeV threshold. Thus while the total trigger rate is reduced the purity of the sample increases.\nGiven the uncertainties on the estimation of the production cross section for K and \u03c0 this optimization\nis crucial for the low-pT single muon trigger.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1068\n\nSample\nmuFast rate (Hz)\nmuComb rate (Hz)\nmuComb + \u03c0/K cuts rate (Hz)\n\u03c0/K\n224\u00b115\n210\u00b19\n145\u00b19\nb\n145\u00b17\n140\u00b16\n114\u00b16\nc\n234\u00b18\n200\u00b18\n168\u00b18\nTable 10: Expected output rate of muFast and muComb for a 4 GeV threshold at the 1031cm\u22122s\u22121\nLuminosity.\nSample\nmuFast rate (Hz)\nmuComb rate (Hz)\nmuComb + \u03c0/K cuts rate (Hz)\n\u03c0/K\n5050\u00b1760\n3530\u00b1380\n2860\u00b1410\nb\n5550\u00b1600\n4900\u00b1400\n4550\u00b1430\nc\n6900\u00b1700\n5390\u00b1420\n5050\u00b1450\nTable 11: Expected output rate of muFast and muComb for a 6 GeV threshold at the 1033cm\u22122s\u22121\nLuminosity.\nChecking the effect of this method to reject muons from K and \u03c0 decays on the two level-2 di-\nmuon strategies showed that both ef\ufb01ciency and trigger rates are reduced. There is no signi\ufb01cant gain\nin purity from this method for the di-muon selections, because the rejection is achieved by using the\nJ/\u03c8 reconstruction and mass cuts, and most of the fake rate comes from b and c decays.\n6\nMeasuring trigger ef\ufb01ciency for low-pT muons from ATLAS data\n6.1\nMethod description\nCross section measurements require a good understanding of the ef\ufb01ciency of the event selections. A\nprecise understanding of the trigger ef\ufb01ciency is crucial and we must have a strategy for measuring\nit from data with high precision. We study the performance of measuring the trigger ef\ufb01ciency from\ndata with the tag-and-probe method which uses di-muon \ufb01nal states for measuring the single muon\ntrigger ef\ufb01ciency. In this method, a single triggered muon from a reconstructed di-muon decay of a\nspeci\ufb01c particle identi\ufb01ed by mass cuts provides the tag that allows us to probe the trigger ef\ufb01ciency\nof the second muon.\nFor B physics we are interested in events with rather low-pT muons, so the tag-and-probe method\nfor measuring the single muon trigger ef\ufb01ciency using J/\u03c8 events is presented. We demonstrate\nthat the obtained trigger ef\ufb01ciency can be applied to calculate the di-muon trigger ef\ufb01ciency. This\nprinciple can also be applied to Z decays to calibrate the high-pT trigger ef\ufb01ciency [11].\n6.1.1\nMeasuring single muon ef\ufb01ciency\nWe use the tag-and-probe method to measure the muon trigger ef\ufb01ciency, using as the calibration\nsample events collected by a single muon trigger where the J/\u03c8 is found in the of\ufb02ine reconstruction.\nIn this sample, one of the muons forming the J/\u03c8 is triggered, while the other one may or may not\nbe triggered, thus providing an unbiased sample of muons to study the single muon trigger ef\ufb01ciency.\nFirst, the triggered muon is matched to one of the reconstructed muons from an identi\ufb01ed J/\u03c8 .\nThis muon is called the tagged-muon. Once the tagged-muon is identi\ufb01ed, the other muon, the probe-\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1069\n\nmuon is used to check whether it is also triggered or not. A matching between the reconstructed muon\nand the one found at the trigger level is needed here too.\nAt the high level trigger, the position of the muon found at the trigger level is stored, and can be\ncompared precisely to the reconstructed muon. However, at level-1 the position granularity is that of\nthe RoI. Due to the limited precision of the location of the RoI, care must be taken when matching a\nmuon RoI to the reconstructed muon. The bending of the muon tracks in the magnetic \ufb01eld and the\nfact that high-pT decay muons have small opening angles between them also introduces an ambiguity\nin the matching.\nThe single muon trigger ef\ufb01ciency, \u03b51\u00b5, is calculated as the ratio between the number of probe\nmuons which were triggered (Nprobe&triggered) to the total number of probe muons (Nprobe),\n\u03b51\u00b5 = Nprobe&triggered\nNprobe\n.\n(1)\nThe single muon ef\ufb01ciency can be obtained in detail as a function of kinematic variables (pT, \u03b7,\n\u03c6) of the muons using as \ufb01ne a binning as the statistics allows. A \ufb01ne binning is, in fact, necessary\nsince the ef\ufb01ciency depends on these variables, especially at level-1 where there are sharp changes in\nthe ef\ufb01ciency due to structural features such as the experiment\u2019s support structures. Because of this\nthe overall ef\ufb01ciency depends on the distribution of the muons produced. We call the detailed map of\nef\ufb01ciencies in each region of the phase space a trigger ef\ufb01ciency map.\nOur primary goal is to demonstrate that it is possible to obtain the trigger ef\ufb01ciency map from\ndata alone. The di-muon trigger ef\ufb01ciency can then be calculated from it, given the distribution of the\nparent particles and the decay angular distribution.\n6.1.2\nCalculating di-muon trigger ef\ufb01ciency\nThe di-muon trigger ef\ufb01ciency can be calculated using the obtained single muon ef\ufb01ciencies, taking\ninto account the dependence on kinematic variables of the muons. For example, the ef\ufb01ciency of J/\u03c8\nparticles are different depending on the kinematic distribution of the two decay muons. The J/\u03c8\nef\ufb01ciency, \u03b5J/\u03c8 can be calculated using the single muon trigger ef\ufb01ciency map as\n\u03b5J/\u03c8(pJ/\u03c8\nT\n,\u03b7J/\u03c8,\u03c6 J/\u03c8) = 1\n2\u03c0\nZZ\n\u03b51\u00b5(p\u00b51\nT ,\u03b7\u00b51,\u03c6 \u00b51)\u03b51\u00b5(p\u00b52\nT ,\u03b7\u00b52,\u03c6 \u00b52)f(cos\u03b8 \u2217)d cos\u03b8 \u2217d\u03c6 \u2217.\n(2)\nHere, f(cos\u03b8 \u2217) is the angular distribution of the decay muon from the J/\u03c8 where \u03b8 \u2217represents the\ndecay angle of the muon in the J/\u03c8 rest frame with the z-axis taken as the direction of the J/\u03c8\nin the laboratory frame. The variable \u03c6 \u2217is the azimuthal angle of the decay muon in the J/\u03c8 rest\nframe, normalized as\nR f(cos\u03b8 \u2217)d cos\u03b8 \u2217= 1. Kinematic variables of the decay muons (p\u00b51\nT , p\u00b52\nT ,\u03b7\u00b51,\n\u03b7\u00b52, \u03c6 \u00b51, \u03c6 \u00b52) are functions of the J/\u03c8 variables, cos\u03b8 \u2217and \u03c6 \u2217. To get the overall ef\ufb01ciency of J/\u03c8\nevents, the integration of J/\u03c8 variables must be performed in the kinematic region of the cross-section\nde\ufb01nition.\nNote that this formula is universal and can be applied to other resonances such as Bs,d \u2192\u00b5\u00b5X\nusing the same single muon ef\ufb01ciency map. The cos\u03b8 \u2217distribution depends on the polarization state\nof the J/\u03c8 which re\ufb02ects the J/\u03c8 production mechanism. For the unpolarized case, this distribution\nis \ufb02at. In certain analysis, the production mechanism of the parent particle could be of interest, so\nwe cannot assume the distribution to be \ufb02at. In such cases, it is necessary to be able to calculate the\nef\ufb01ciency as a function of cos\u03b8 \u2217as well. In these cases, Equation 2 would become,\n\u03b5J/\u03c8(pJ/\u03c8\nT\n,\u03b7J/\u03c8,\u03c6 J/\u03c8,cos\u03b8 \u2217) = 1\n2\u03c0\nZ\n\u03b51\u00b5(p\u00b51\nT ,\u03b7\u00b51,\u03c6 \u00b51)\u03b51\u00b5(p\u00b52\nT ,\u03b7\u00b52,\u03c6 \u00b52)d\u03c6 \u2217\n(3)\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1070\n\nwithout the cos\u03b8 \u2217integration. Equation 3 is simply expressing the ef\ufb01ciency of events where J/\u03c8 is\nproduced with a \ufb01xed momentum and the decay angle is also \ufb01xed, so the decay muon momenta are\nalso \ufb01xed. Some variables could be integrated out, but the important thing is that the ef\ufb01ciency with\nrespect to cos\u03b8 \u2217can also be obtained from the single muon ef\ufb01ciency map, \u03b51\u00b5(p\u00b5\nT,\u03b7\u00b5,\u03c6 \u00b5).\n6.2\nPerformance studies\nIn order to emulate the ef\ufb01ciency measurement from data, we use J/\u03c8 events with two muons in\nthe of\ufb02ine reconstruction passing the single muon threshold of 6 GeV and a di-muon invariant mass\nbetween 2.88 GeV and 3.3 GeV.\n6.2.1\nMatching of muons at trigger and reconstruction\nThe \ufb01rst step of the tag-and-probe method is to \ufb01nd out which of the two of\ufb02ine muons was triggered.\nThis is done by \ufb01nding the best match using \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2, where \u2206\u03b7 and \u2206\u03c6 are the difference\nof \u03b7 and \u03c6 between the of\ufb02ine muon and the triggered muon. For the matching with level-2 muons,\ntrack parameters at the perigee are used. On the other hand, for level-1, the position of the triggered\nmuon is taken as the center of the RoI. In this case, the matching must be done carefully as the opening\nangle of the two muons from the J/\u03c8 is small and the bending, of the rather low-pT muons, in the\nmagnetic \ufb01eld is non-negligible. The of\ufb02ine muon tracks are extrapolated to the plane of the RPC or\nTGC chamber which de\ufb01nes the RoI.\nFigure 9 shows the \u2206R distrbution between the level-1 RoI and of\ufb02ine track with and without\nusing the extrapolation. The improvement obtained by the extrapolation is signi\ufb01cant and as a result\na good matching is established by requiring \u2206R < 0.15. To further reduce the possibility of having\na wrong match, in this study we only use events where the opening angle between the two muons is\n\u2206R > 0.4.\nFigure 10 shows the \u2206R distribution between the level-2 muon and the of\ufb02ine track. The resolution\nof \u2206R becomes an order of magnitude better than at level-1 since the level-2 muon tracks use the\nmeasurements from the ID. The condition \u2206R < 0.005 is used for the matching between the of\ufb02ine\ntrack and the level-2 track.\nR\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5\nEntries\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n < 6GeV\n\u00b5\nT\np\n < 15GeV\n\u00b5\nT\n6GeV < p\n\u00b5\nT\n15GeV < p\nATLAS\nR\n\u2206\n0\n0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5\nEntries\n0\n5000\n10000\n15000\n20000\n25000\n30000\nATLAS\nFigure 9: The distribution of \u2206R between the level-1 RoI and the of\ufb02ine muon track, (a) using the\nof\ufb02ine track parameters at the perigee and (b) by extrapolating the of\ufb02ine track to the RoI position.\nThe dashed line shows the value where the cut was applied for the matching.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1071\n\nR\n\u2206\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\nEntries\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n20000\n22000\nATLAS\nFigure 10: The distribution of \u2206R between the level-2 muon and the of\ufb02ine muon track. The dashed\nline shows the value where the cut was applied for the matching.\n6.2.2\nLevel-1 ef\ufb01ciency\nUsing the method described in Section 6.1 and the matching criteria, we obtain the single muon\nef\ufb01ciency as a function of the pT of the muon. Figure 11 shows the single muon ef\ufb01ciency as a\nfunction of pT by evaluating how often the probe-muon was triggered. The points are \ufb01tted with the\nfunction\n\u03b5(pT) =\nA\n1+exp(\u2212a\u00d7(pT \u2212b))).\n(4)\nAlso shown in Figure 11 is the ef\ufb01ciency measured directly in the single muon Monte Carlo sample\nwhich provides an unbiased value of the ef\ufb01ciency. The agreement of the ef\ufb01ciencies obtained by the\ntwo methods is around 5% in the turn-on region (4 GeV < pT < 8 GeV) and becomes smaller as the\npT increases, becoming within a few percent at pT > 10 GeV.\nTo calculate the di-muon trigger ef\ufb01ciency using Equation 2, the ef\ufb01ciency curve must be mea-\nsured in each \u03b7 and \u03c6 region. For this, we divided the detector into 10 \u00d7 10 regions for the barrel\n(\u22121.05 < \u03b7 < 1.05). For the end-cap region (1.05 < |\u03b7| < 2.4), we assumed that there is a complete\nsymmetry between octants and divided one octant into 8\u00d76 regions. Ef\ufb01ciency curves as a function\nof pT are obtained in each of the regions. Figure 12 shows the three \ufb01t parameters, A, a and b in\nEquation 4 as a function of \u03b7 and \u03c6. The \ufb01gure shows that the ef\ufb01ciency curve behaves differently\nfor different regions but in a smooth way, except for a small region around \u03b7 = 0.725 and \u03c6 = \u22121.6.\nIn this region the ef\ufb01ciency is very low due to the MS layout and as a result the \ufb01t is unreliable. These\nresults are used to calculate the di-muon ef\ufb01ciency.\nDistributions of of\ufb02ine J/\u03c8 variables, pJ/\u03c8\nT\n, \u03b7J/\u03c8 and cos\u03b8 \u2217are shown in Figure 13 after ap-\nplying the selection criteria of muons (p\u00b5\nT > 6 GeV and |\u03b7\u00b5| < 2.4). The open histograms are for all\nJ/\u03c8 in the MC sample and the \ufb01lled histograms are for events where the level-1 di-muon trigger,\nrequiring at least two muons with pT > 6 GeV, has \ufb01red. The generator level \ufb01lter with the pT cut for\nthe highest (second highest) pT muon of pT > 6(4) GeV was applied for the MC sample.\nThe cos\u03b8 \u2217distribution re\ufb02ects the polarization state of the J/\u03c8 and is \ufb02at for the non-polarized\ncase. Since the cos\u03b8 \u2217distribution is an interesting quantity to measure in its own right, we do not\nmake any assumptions about this distribution but instead try to measure the ef\ufb01ciency as a function\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1072\n\n (GeV)\nT\np\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nTrigger efficiency / GeV\n0\n0.2\n0.4\n0.6\n0.8\n1\ntag-and-probe method\ndirect Monte Carlo values\nATLAS\nFigure 11: The overall ef\ufb01ciency of the level-1 single muon trigger with respect to the of\ufb02ine selection\nobtained by the tag-and-probe method (\ufb01lled circles) and the ef\ufb01ciency estimated from a single muon\nMonte Carlo sample (open circles). The curve is a \ufb01t to the ef\ufb01ciency obtained by the tag-and-probe\nmethod from Equation 4.\nof cos\u03b8 \u2217. Although the generated cos\u03b8 \u2217distributions were \ufb02at, reconstructed distributions will be\nbiased by the p\u00b5\nT cuts applied at the generator level. At |cos\u03b8 \u2217| = 1, one of the decay muons \ufb02ies\nin the opposite direction to the J/\u03c8 and has low transverse momentum, therefore these events are\nmore likely to be rejected by the pT cut for the highest (second highest) pT muon of pT > 6(4) GeV\nrequirement.\nFigure 14 shows the di-muon trigger ef\ufb01ciencies calculated in two methods. The open circles\nare obtained by checking the decision of the level-1 di-muon trigger for each event. The ef\ufb01ciencies\ncalculated using the parameterization in Figure 12 are shown by the \ufb01lled circles. They are calculated\nby assigning an ef\ufb01ciency for each event according to the kinematics of the two muons in the \ufb01nal\nstate using Equation 3. The same technique may be used once data are collected by the experiment.\nThe effect of the systematic uncertainty of the method has been estimated by changing the procedure\nto obtain the trigger ef\ufb01ciency map, namely by using 16\u00d716 bins in \u03b7\u2013\u03c6 in the barrel and 15\u00d710 in\nthe endcap. In addition, the \ufb01tting function has been changed by adding a linear function c(pT \u2212d) to\nthe original function for pT > d. This was done to better describe a drop of ef\ufb01ciency for higher pT.\nc and d are additional \ufb01t parameters. Both statistical and systematic errors are a few % in most of the\nregion, but the systematic uncertainty increases where the change of ef\ufb01ciency is rapid. In Figure 14,\nthe statistical and systematic errors are added in quadrature.\nResults of the two methods agree within a few % in most regions. Ef\ufb01ciency losses at \u03b7J/\u03c8\naround -1, 0 and +1 are due to the layout of the muon trigger chambers. These plots con\ufb01rm that the\nrequirement of p\u00b5\nT > 6 GeV on two muons introduces an effective cut of pT > 12 GeV for the J/\u03c8\nand the ef\ufb01ciency with respect to cos\u03b8 \u2217is \ufb02at across the region between \u22120.8 < cos\u03b8 \u2217< 0.8. The\noverall ef\ufb01ciencies calculated in the kinematic region of pJ/\u03c8\nT\n> 12 GeV and |\u03b7J/\u03c8| < 2 are 76.1% and\n77.0% using the trigger decision and the trigger ef\ufb01ciency map, respectively, which is in agreement\nwithin the statistical and systematic errors. The size of the systematic errors may be improved by\ncreating the ef\ufb01ciency map with \ufb01ner granularity, which requires more statistics.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1073\n\nFigure 12: Fit parameters (A, a and b in Equation 4) of the ef\ufb01ciency curve in different \u03b7 and \u03c6\nregions.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1074\n\nFigure 13: Distributions of J/\u03c8\nvariables, pT , \u03b7\nand cos\u03b8 \u2217. The open histograms are for all\nreconstructed J/\u03c8 s with the generator level cut of p\u00b51\nT > 6 GeV and p\u00b52\nT > 4 GeV. Filled histograms\nare distributions of events passing the level-1 di-muon trigger.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1075\n\n (GeV)\n\u03a8\nJ/\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency from the map\nEfficiency from trigger decision \n\u03a8\nJ/\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency from the map\nEfficiency from trigger decision \n*\n\u03b8\ncos\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nTrigger efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency from the map\nEfficiency from trigger decision \nFigure 14: Di-muon trigger ef\ufb01ciency with p\u00b5\nT > 6 GeV. Open circles are the result obtained from\ndecision of the level-1 di-muon trigger and \ufb01lled circles are the ef\ufb01ciency obtained using the parame-\nterization shown in Figure 12.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1076\n\n6.2.3\nLevel-2 ef\ufb01ciency\nThe single muon level-2 ef\ufb01ciency can be de\ufb01ned in two ways: level-2 ef\ufb01ciency with respect to\nof\ufb02ine reconstruction (L2/rec) and level-2 ef\ufb01ciency with respect to level-1 (L2/L1). The L2/rec ef-\n\ufb01ciency is obtained in the same way as the ef\ufb01ciency with respect to level-1. The only difference is\nthat the probe muon must have both level-1 and level-2 trigger objects associated to be considered as\ntriggered.\nFor the calculation of the L2/L1 ef\ufb01ciency the set of probe muons is restricted to only those that\nhave an associated level-1 RoI. This way the ef\ufb01ciency with respect to level-1 is obtained. Overall\nef\ufb01ciencies as a function of pT are shown in Figure 15. The points were \ufb01tted with the functional\nform of Equation 4. Ef\ufb01ciency curves calculated using all of\ufb02ine muons matched to generated muons\nare plotted in the same \ufb01gure to check that the selection of probe muons is unbiased. It is clear that\nthere is a good agreement between the measured ef\ufb01ciency and the direct Monte Carlo ef\ufb01ciency.\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nMeasured efficiency\nMeasured efficiency (fit)\nUnbiased efficiency\nATLAS\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nTrigger Efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nMeasured efficiency\nMeasured efficiency (fit)\nUnbiased efficiency\nATLAS\nFigure 15: The overall ef\ufb01ciency of the level-2 single muon trigger, (a) with respect to of\ufb02ine recon-\nstruction, (b) with respect to level-1.\nTo calculate level-2 di-muon ef\ufb01ciency the trigger ef\ufb01ciency map was created in the same way as\nfor level-1. The \u03b7\u2013\u03c6 plane was divided into regions as described in Section 6.2.2 and in each region\nan ef\ufb01ciency curve was constructed and \ufb01tted with Equation 4. This was done for L2/rec as well as\nfor L2/L1 ef\ufb01ciencies.\nUsing the trigger ef\ufb01ciency map for the L2/rec ef\ufb01ciency, we can calculate the level-2 trigger\nef\ufb01ciency. To check that the map was created correctly, the single-muon ef\ufb01ciency curves were con-\nstructed using level-2 muons associated to the of\ufb02ine muons with the \u2206R matching criteria explained\nin Section 6.2.2. To get an agreement between the two methods one must use the same data sample. In\nFigure 16, open triangles represent a straightforward calculation of the ef\ufb01ciency using matched trig-\nger objects while the solid circles are the ef\ufb01ciencies calculated using the map. To each of\ufb02ine muon\nfrom the sample the probability that it would be triggered was assigned using the map. In each pT\nbin the ef\ufb01ciency was calculated as an average of these probabilities. Systematic uncertainties were\nestimated in the same way as the level-1 ef\ufb01ciency by changing the procedure to calculate the trigger\nef\ufb01ciency map. The same method was used for other two variables \u03b7 and \u03c6. The two methods give\nan agreement within 6% in most regions while the difference gets as large as 15% at some regions\n(\u03c6 \u2243\u22121,\u22122) where the ef\ufb01ciency is low and therefore the precision of the \ufb01t to create the trigger\nef\ufb01ciency map was poor. Also, since the average ef\ufb01ciency is calculated in each bin of the map this\ncauses discrepancies in the regions where ef\ufb01ciency changes rapidly.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1077\n\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEfficiency from trigger decision\nEfficiency from the map\nATLAS\n\u03b7\n-2\n-1\n0\n1\n2\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEfficiency from trigger decision\nEfficiency from the map\nATLAS\n (rad)\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEfficiency from trigger decision\nEfficiency from he map\nATLAS\nFigure 16: The overall L2/rec single-muon trigger ef\ufb01ciency as a function of pT , \u03b7 and \u03c6. Ef\ufb01ciency\nis calculated using the trigger ef\ufb01ciency map (black circles) and it is compared to the one calculated\nusing matched level-1 and level-2 trigger objects (open triangles).\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1078\n\nThe ef\ufb01ciency of the level-2 di-muon trigger for J/\u03c8 was calculated in the same way as for level-\n1. Again two methods were used: \ufb01rstly direct calculation using the trigger decision for the di-muon\ntrigger and secondly using the ef\ufb01ciency map. Since a simple di-muon trigger without any cut on\ninvariant mass was used, all the muons in the sample must be used in calculation of the ef\ufb01ciency (not\njust those from J/\u03c8 ). To each of\ufb02ine muon in the event the probability \u03b5i that it would be triggered\nwas assigned. The probability that the whole event will be triggered by the di-muon trigger is then\n\u03b52\u00b5 = 1\u2212\u220f\ni\n(1\u2212\u03b5i)\u2212\u2211\ni\n\u03b5i\u220f\nj\u0338=i\n(1\u2212\u03b5j)\n(5)\nwhere the products and sums run over all decay muons used in the measurement.\nThe di-muon ef\ufb01ciency is calculated in the same way as the single-muon ef\ufb01ciency, as an average\nof probabilities \u03b52\u00b5 in each bin of a given variable. In our case it is either the pT , \u03b7, \u03c6 or the cos\u03b8 \u2217\nof the J/\u03c8 reconstructed in the event. Figure 17 shows a comparison of the J/\u03c8 ef\ufb01ciency curves.\nLike the single muon ef\ufb01ciency results, the agreement between the two methods is within 6% in most\nregions except for some regions where the available statistics was low. The overall J/\u03c8 ef\ufb01ciency\n(L2/rec) in the kinematic region, pJ/\u03c8\nT\n> 15 GeV, |\u03b7J/\u03c8| < 2 with the cuts on the muons (p\u00b5\nT > 6 GeV,\n|\u03b7\u00b5| < 2.4) is 69.2% and 69.4% using the trigger decision and the trigger ef\ufb01ciency map, respectively.\nWe have a good agreement on the overall ef\ufb01ciency integrated in the above phase space.\n (GeV)\n\u03c8\nT,J/\np\n10\n20\n30\n40\n50\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n efficiency from trigger decision\n\u03c8\nJ/\n efficiency from the map\n\u03c8\nJ/\nATLAS\n\u03c8\nJ/\n\u03b7\n-2\n-1\n0\n1\n2\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n efficiency from trigger decision\n\u03c8\nJ/\n efficiency from the map\n\u03c8\nJ/\nATLAS\n\u03c8\nJ/\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n efficiency from trigger decision\n\u03c8\nJ/\n efficiency from the map\n\u03c8\nJ/\nATLAS\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0 5\n1\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n efficiency from trigger decision\n\u03c8\nJ/\n efficiency from the map\n\u03c8\nJ/\nATLAS\nFigure 17: The overall di-muon J/\u03c8 trigger ef\ufb01ciency as a function of pT , \u03b7, \u03c6 and cos\u03b8 \u2217. Ef\ufb01cien-\ncies from the trigger decision bit (open triangles) and the ones calculated from the trigger ef\ufb01ciency\nmap (black circles) are shown.\nIn Figure 18 the ef\ufb01ciency as a function of the distance, \u2206R, in the \u03b7\u2013\u03c6 plane between the two\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1079\n\nJ/\u03c8 muons is shown.\nR\n\u2206\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nTrigger efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n efficiency from trigger decision\n\u03c8\nJ/\n efficiency from the map\n\u03c8\nJ/\nATLAS\nFigure 18: The overall di-muon J/\u03c8 trigger ef\ufb01ciency as a function of \u2206R. Ef\ufb01ciencies from the trigger\ndecision bit (open triangles) and the ones calculated from the trigger ef\ufb01ciency map (black circles) are\nshown.\n6.3\nRequirements on the trigger menu\nIn order to use the method developed here for real data, we need a large sample of J/\u03c8 events with at\nleast one muon unbiased by the trigger selection. The following selection criteria at each trigger level\nwill satisfy this requirement:\nLevel-1 Single muon trigger above a certain threshold;\nLevel-2 J/\u03c8 reconstruction within one RoI using the TrigDiMuon algorithm to enhance J/\u03c8 events;\nEvent Filter (EF) No further selection is imposed so as to avoid biasing the sample;\nIn this Section, we give some estimates of the statistics of the J/\u03c8\nsample using this trigger\nselection and show the precision on the trigger ef\ufb01ciency with a certain luminosity. Taking into\naccount the limit on the EF output rate of 200 Hz it is plausible to use a few Hz of the bandwidth for\nthis calibration trigger. The parameters to optimize are the prescale factor, to reduce the rate when it\nis too high, and the threshold value.\nThe level-1 single muon trigger rate has been studied in detail taking into account contributions\nfrom different sources. At low-pT , the main contribution is from K /\u03c0 in-\ufb02ight decay and muons\nfrom b and c quarks. The rejection of these non-J/\u03c8 events by the topological di-muon trigger at\nlevel-2 has been studied using a genererated sample of b\u00afb \u2192\u00b5 +X, where the ef\ufb01ciency of non-J/\u03c8\nevents to be selected was found to be 0.8%. This factor is used to estimate the rate reduction by the\nlevel-2 selection.\nTable 12 shows the expected rate of the level-1 single muon trigger and the contribution of the\nJ/\u03c8 \u2192\u00b5+\u00b5\u2212to the rate assuming a luminosity of 1031 cm\u22122s\u22121. The rate of J/\u03c8 events is the sum\nof J/\u03c8 direct production and from b\u00afb production. If we could allocate a bandwidth of 1 Hz to this\ntrigger chain with 6 GeV level-1 threshold, we must apply a prescale factor of 3 to reduce the rate\ndown to around 1 Hz. Given the fraction of J/\u03c8 \u2192\u00b5+\u00b5\u2212events among this rate is 6%, we get a rate\nof 0.06 Hz for collecting the calibration sample.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1080\n\nrate (Hz)\nJ/\u03c8 fraction\nlevel-1\n380 (0.21)\n0.05%\nlevel-2\n3 (0.19)\n6%\nTable 12: The rates after level-1 and level-2 using the proposed calibration trigger for a luminosity of\n1031 cm\u22122s\u22121 with the threshold of pT > 6 GeV. The contribution of J/\u03c8 \u2192\u00b5+\u00b5\u2212process to the\nrate is also shown in parentheses.\nWith one year of data, we expect to collect about 300 k J/\u03c8 events according to this triggering\nstrategy, which is comparable to the statistics used in this study (150 k direct J/\u03c8 and 150 k b\u00afb \u2192\nJ/\u03c8). Therefore, we expect a similar performance (for \u22431 Hz calibration trigger rate) to that shown\nin Section 6.2 after the \ufb01rst year of data-taking. The number of events may increase if we allocate\nmore than 1 Hz for the calibration trigger.\n7\nConclusions\nIn this note we presented methods to ef\ufb01ciently select J/\u03c8 events at the second level trigger, reject\nmuons from K and \u03c0 decays and measure the trigger ef\ufb01ciencies from the ATLAS data.\nTrigDiMuon is a second-level trigger algorithm that selects ef\ufb01ciently at level-2 events which\ninclude J/\u03c8 or other di-muon states, starting from a single level-1 muon trigger. The ef\ufb01ciency of\nTrigDiMuon for events accepted by level-1 and the level-2 single muon trigger is between 73% for the\n4 GeV trigger threshold and 60% for the 6 GeV threshold. This may be compared with the topological\ndi-muon trigger ef\ufb01ciencies of 33% for the 4 GeV threshold and 15% for the 6 GeV threshold. The fake\ntrigger rates of TrigDiMuon are estimated to be 2 Hz for a trigger threshold of 4 GeV at a luminosity\nof 1031cm\u22122s\u22121, and 90 Hz for a trigger threshold of 6 GeV at a luminosity of 1033cm\u22122s\u22121. For the\nB-physics trigger at L = 1033cm\u22122s\u22121 the rate will have to be further reduced by means of a decay\nlength cut on the J/\u03c8 decay vertex.\nExtrapolating the muon track from MS back to the interaction vertex improves the single muon\ntrigger selection at the level-2 stage and allows increased rejection of muons from K and \u03c0 decays\nwithout a signi\ufb01cant loss of ef\ufb01ciency for b events. The back extrapolator provides a further reduction\nfactor of about 20% at the trigger threshold of 4 GeV and of about 10% at the trigger threshold\nof 6 GeV with respect to the output trigger rate of the baseline muComb selection. Despite this\ngood performance, its use for triggering on low pT di-muon objects is not recommended, since the\nbackground to TrigDiMuon is dominated by muons from b and c rather than by muon from K and \u03c0\ndecays. However, because the rate of muons from K and \u03c0 decays may be even higher than in our\nsimulation, it is important to have it available for the single muon triggers.\nThe J/\u03c8 trigger ef\ufb01ciency can be measured from ATLAS data using the tag-and-probe method.\nAs the ef\ufb01ciency of the single muon trigger depends on the \u03b7 and \u03c6 regions, it is necessary to measure\nthe ef\ufb01ciency as a function of these variables. With 300k J/\u03c8 events, it is possible to measure the\nef\ufb01ciency at level-1 and level-2 with better than 5 % precision for each region. The uncertainty comes\nmainly from the lack of statistics to measure the ef\ufb01ciencies for each region of \u03b7 and \u03c6 and will\nimprove as more J/\u03c8 events become available. To collect an unbiased J/\u03c8 sample which can be\nused for the trigger ef\ufb01ciency measurement, we plan to use a level-1 single muon trigger with a J/\u03c8\nreconstruction using the inner detector at level-2. With this trigger we can collect around 300k events\nfor an integrated luminosity of 100 pb\u22121 while keeping the rate of this calibration trigger around 1 Hz.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1081\n\nWith the methods provided it is possible to collect a large number of J/\u03c8 events at luminosities\nof around 1031cm\u22122s\u22121, without an overly high rate from K and \u03c0 decays. Furthermore, these low-pT\nJ/\u03c8 events can also be used to calibrate trigger ef\ufb01ciencies from the actual ATLAS data, and provide\nthe trigger ef\ufb01ciencies for analyses that use low-pT muons.\nReferences\n[1] T. Sjostrand, S. Mrenna and P. Skands, PYTHIA 6.4: Physics and manual, JHEP, 05, 026\n(2006).\n[2] S. Agostinelli et al., Nucl. Inst. and Meth. 506 250 (2003).\n[3] ATLAS Collaboration, ATLAS Technical Proposal, CERN/LHCC 94-43, LHCC/P2, (1994)\n[4] ATLAS Level-1 Trigger Group, Level-1 Technical Design Report, ATLAS TDR 12, (1998).\n[5] ATLAS HLT/DAQ/DCS Group, High-Level Trigger, Data Acquisition, and Control Technical\nDesign Report, ATLAS TDR 16, (2002).\n[6] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this vol-\nume.\n[7] ATLAS Muon Collaboration,\nATLAS Muon Spectrometer Technical Design Report,\nCERN/LHCC 97-22, (1997)\n[8] A. Di Mattia et al., A Level-2 trigger algorithm for the identi\ufb01cation of muons in the ATLAS\nMuon Spectrometer, ATL-DAQ-CONF-2005-005, (2005)\n[9] ATLAS Collaboration, The Expected Performance of the Inner Detector, this volume.\n[10] S. Tarem et al, MuGirl - Muon identi\ufb01cation in ATLAS from the inside out, Nuclear Science\nSymposium Conference Record, IEEE Volume 1, 617 (2007).\n[11] ATLAS Collaboration, In-Situ Determination of the Performance of the Muon Spectrometer,\nthis volume.\nB-PHYSICS \u2013 TRIGGERING ON LOW-pT MUONS AND DI-MUONS FOR B-PHYSICS\n1082\n\nHeavy Quarkonium Physics with Early Data\nAbstract\nResults are reported on an analysis on simulated data samples for production\nof heavy quarkonium states J/\u03c8 \u2192\u00b5\u00b5 and \u03d2\u2192\u00b5\u00b5, corresponding to an inte-\ngrated luminosity of 10 pb\u22121. It is shown that the pT dependence of the cross-\nsection for both J/\u03c8 and \u03d2 should be measured reasonably well in a wide\nrange of transverse momenta, pT \u224310\u221250 GeV. The precision of J/\u03c8 polari-\nsation measurement is expected to reach 0.02\u22120.06, while the projected error\non \u03d2 polarisation is around 0.2. Observation of radiative decays of \u03c7c states,\nand the feasibility of observing \u03c7b \u2192J/\u03c8J/\u03c8 decays are also discussed.\n1\nIntroduction and theoretical motivation\nThe number of J/\u03c8 \u2192\u00b5+\u00b5\u2212and \u03d2 \u2192\u00b5+\u00b5\u2212decays produced at the LHC is expected to be quite large.\nTheir importance for ATLAS is threefold: \ufb01rst, being narrow resonances, they can be used as tools for\nalignment and calibration of the trigger, tracking and muon systems. Secondly, understanding the details\nof the prompt onia production is a challenging task and a good testbed for various QCD calculations,\nspanning both perturbative and non-perturbative regimes. Last, but not the least, heavy quarkonium\nstates are among the decay products of heavier states, serving as good signatures for many processes of\ninterest, some of which are quite rare. These processes have prompt quarkonia as a background and, as\nsuch, a good description of the underlying quarkonium production process is crucial to the success of\nthese studies.\nThis note mainly concentrates on the capabilities of the ATLAS detector to study various aspects of\nprompt quarkonium production at the LHC. The methods of separating promptly produced J/\u03c8 and \u03d2\nmesons from various backgrounds are discussed, and strategies for various measurements are outlined.\n1.1\nTheory overview\nQuarkonium production was originally described in a model where the quark pair was assumed to be\nproduced endowed with the quantum numbers of the quarkonium state that it eventually evolved into [1].\nThis approach, subsequently labelled as the Colour Singlet Model (CSM), enjoyed some success before\nCDF measured an excess of direct J/\u03c8 production [2], more than an order of magnitude greater than\npredicted (see Figure 1(a)).\nThe Colour Octet Model (COM) [5] was proposed as a solution to this quarkonium de\ufb01cit. COM\nsuggests that the heavy quark pairs produced in the hard process do not necessarily need to be produced\nwith the quantum numbers of physical quarkonium, but could evolve into a particular quarkonium state\nthrough radiation of soft gluons later on, during hadronisation. This approach isolates the perturbative\nhard process from the non-perturbative long-distance matrix elements, which are considered as free pa-\nrameters of the theory. However, their universality means that their values can be extracted independently\nfrom a number of different processes, such as deep inelastic scattering, hadro- and photoproduction.\nHence the good description of the Tevatron data by the Colour Octet Model shown in Figure 1(a)\nis, at least in part, due to the fact that the values of some parameters were determined from the same\ndata. Tests of other COM predictions have not been so successful: Figure 1(b) shows the polarisation\ncoef\ufb01cient in \u03d2 \u2192\u00b5\u00b5 decay as a function of its transverse momentum, where the COM prediction\ndisagrees with the data.\nA model based on kT factorisation in QCD showers [6] claims to be able to describe both the lack\nof transverse polarisation in J/\u03c8 decays [4,7] and the high cross-section of J/\u03c8 production. Another\n1083\n\n10\n-3\n10\n-2\n10\n-1\n1\n10\n5\n10\n15\n20\nBR(J/\u03c8\u2192\u00b5+\u00b5-) d\u03c3(pp\n_\u2192J/\u03c8+X)/dpT (nb/GeV)\n\u221as =1.8 TeV; |\u03b7| < 0.6\npT (GeV)\ntotal\ncolour-octet 1S0 + 3PJ\ncolour-octet 3S1\nLO colour-singlet\ncolour-singlet frag.\n(a)\nD\n, Run 2 Preliminary, 1.3 fb\n\u20141\n(b)\nFigure 1: (a) Differential cross-section of J/\u03c8 production at CDF, with predictions from CSM\nand COM mechanisms (from [3]). (b) \u03d2 polarisation measured as a function of pT at D\u00d8 (black\ndots) and CDF (green triangles), compared to the limits of the kT factorisation model (dashed and\ndotted curves [6]) and COM predictions [5], depicted by a shadowed band (from [4]).\nmodel [8] argues that the de\ufb01cit in the cross-section as predicted by CSM can be largely explained by\nthe production of a quarkonium state in association with an additional heavy quark, and also predicts\nlower levels of polarisation.\nIn the following, we show that ATLAS is capable of detailed checks of the predictions of various\nmodels by measuring not only pT and \u03b7 distributions of onium states in a wide range of these variables,\nbut also the degree of polarisation and the production of C-even states. In the absence of a comprehensive\nMonte Carlo generator capable of simulating all aspects of all theoretical models, we used the PYTHIA\n6.403 generator [9] incorporating the Colour Octet Mechanism, with model parameters \ufb01xed through\na combination of theoretical and experimental constraints [10]. Inevitably, this simulation is unable to\nreproduce adequately some features of the data, notably the polarisation angle distributions and hadronic\naccompaniment of the quarkonium states. However, the simulated samples allowed us to study the\nacceptance and ef\ufb01ciency of ATLAS to detect all required particles and measure their parameters, across\nthe whole range of the accessible phase space.\n1.2\nClassi\ufb01cation of production mechanisms in the simulation\nIn the following, we will use a simple classi\ufb01cation of the quarkonium production mechanisms based on\nthe model implemented in the PYTHIA generator.\nA sample diagram describing the leading colour-singlet subprocess g + g \u2192J/\u03c8 + g is shown in\nFigure 2(a). In the accessible range of transverse momenta of J/\u03c8 its contribution is expected to be\nsmall. The dominant contribution at the lower pT comes from the subprocess shown in Figure 2(b),\nwhere both singlet and octet c\u00afc states with various quantum numbers contribute to J/\u03c8 production,\nthrough \u03c7cJ \u2192J/\u03c8+\u03b3 decays and/or soft gluon emission.\nAt high pT, the gluon fragmentation subprocess shown in Figure 2(c) becomes increasingly domi-\nnant. According to COM, this is unlikely to produce anything other than 3S1 quarkonium states. Hence,\nthe fraction of J/\u03c8 mesons produced from \u03c7cJ decays should decrease with increasing pT. The pro-\nduction mechanisms for the radially excited \u03c8 \u2032(3686) meson follows the same pattern, except for the\nabsence of respective \u03c7\u2032\ncJ contributions, thus one should expect different pT distributions for J/\u03c8 and\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1084\n\n\u0000\u0000\u0001\n\u0002\n\u0001\n\u0003\u0005\u0004\u0007\u0006\n(a)\n\b\n\b\n\t\n\n\t\n\u000b\r\f\u000f\u000e\n(b)\n\u0010\n\u0010\n\u0011\n\u0012\n\u0014\n(c)\nFigure 2: Some example diagrams for the singlet and octet J/\u03c8 production mechanisms imple-\nmented in PYTHIA.\n\u03c8 \u2032.\nThe overall picture is expected to be similar for bottomonium production, except the number of\nradial excitations below the open beauty threshold is now three, and many more radiative transitions are\npossible between the various n3PJ and n3S1 state. However, compared to J/\u03c8 , the accessible range of\npT for \u03d2 is signi\ufb01cantly extended towards smaller transverse momenta. This opens up the range of pT\ndominated by the colour singlet contribution, which may make it directly observable for \u03d2.\n1.3\n\u03c7b \u2192J/\u03c8J/\u03c8 decay\nDespite much higher production cross-sections, C-even states of quarkonia are far more dif\ufb01cult to ob-\nserve than their vector counterparts. The usual way of studying \u03c7c,b (and \u03b7c,b) states has been so far\nthrough radiative decays of or into respective vector states. However, in the high energy hadronic colli-\nsion environment, observation of the photon in \u03c7b \u2192\u03d2+\u03b3 may be problematic (see Section 5.1).\nWe have performed a feasibility study to assess the capability of ATLAS to observe \u03c7b \u2192J/\u03c8J/\u03c8 \u2192\n\u00b5+\u00b5\u2212\u00b5+\u00b5\u2212decay with the standard di-muon trigger. The results are presented in Section 5.2. The\nobservation and measurement of these \ufb01nal states will give a valuable insight into the heavy quark bound\nstate dynamics from several separate viewpoints.\n2\nTrigger considerations\nDetails of the triggers to be used in ATLAS B physics programme can be found in [11]. This section\ndiscusses the trigger signatures relevant for quarkonium production at ATLAS, the implications they\nhave on the measured cross-section, and the expected effects they have on our ability to make various\nphysics measurements.\nTwo speci\ufb01c types of di-muon triggers dedicated to quarkonium are: the topological di-muon trig-\ngers, which require two level-1 regions of interest (RoIs) corresponding to two muon candidates with pT\nthresholds of 6 and 4 GeV, and di-muon triggers that only require a single level-1 RoI above a threshold\nof 4 GeV and searches for the second muon of opposite charge in a wide RoI at level-2. They are dis-\ncussed in Section 2.1. An additional trigger scenario is based on a single muon trigger with a higher pT\nthreshold of 10 GeV, discussed in Section 2.2.\n2.1\nDi-muon triggers\nBeing able to determine the trigger ef\ufb01ciency of measured J/\u03c8 and \u03d2 is crucial to correctly infer the\nproduction cross-section of quarkonium at the LHC. Indeed, using J/\u03c8 and \u03d2 (as well as the Z boson)\nto construct a trigger ef\ufb01ciency map is a necessary step in order to perform cross-section measurements\nin ATLAS.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1085\n\nStudies are being conducted in ATLAS into developing a calibration method to obtain the low-pT\nsingle muon trigger ef\ufb01ciency, and henceforth the di-muon trigger ef\ufb01ciency of events using real data by\nvirtue of the so-called tag-and-probe method (see Ref. [11] for details). In the absence of data, we have\nperformed our own studies of trigger ef\ufb01ciencies, based on Monte Carlo simulation.\nIf not stated otherwise, the quoted trigger ef\ufb01ciencies have been calculated with respect to the Monte\nCarlo samples, generated with the cuts pT(\u00b51) > 6 GeV, pT(\u00b52) > 4 GeV, where \u00b51 (\u00b52) is the muon\nwith the largest (second largest) transverse momentum in the event.\nThe level-1 trigger is a hardware trigger that uses coarse calorimeter and muon spectrometer infor-\nmation to identify interesting signatures to pass to the level-2 and Event Filter stage. Figure 3 shows the\nvarious individual level-1 trigger ef\ufb01ciencies as a function of the pT of the di-muon system. The total\ntrigger ef\ufb01ciency at level-1, running over direct J/\u03c8 events, is 87%.\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nEfficiency\n-1\n10\n1\nLVL1_Muon\nL1_MU06\nL1_MU11\nL1_2MU06\nL1_MU05\nL1_MU00\nL1_MU20\nL1_MU40\nATLAS\nFigure 3: Ef\ufb01ciency of various level-1 triggers for prompt J/\u03c8 events versus pT of the di-muon\nsystem. Only the triggers with ef\ufb01ciencies greater than 2% in some region of pT are displayed.\nThe relevant triggers are the single muon pT threshold triggers labelled L1 MUXX (where XX indi-\ncates the pT threshold in GeV) and the di-muon trigger L1 2MU06. Each pT range of these triggers\nis exclusive. The ef\ufb01ciency curve labelled LVL1 Muon is the sum of all level-1 single muon ef\ufb01-\nciencies (excluding the di-muon trigger L1 2MU06).\nThe level-2 trigger is software-based and is designed to reduce the output rate of the data, passed to\nit from level-1, by two orders of magnitude. Within regions of interest de\ufb01ned by the level-1 trigger, full\ngranularity of the detector is accessible. The ef\ufb01ciency of the level-2 triggers for prompt J/\u03c8 events is\nplotted in Figure 4 as a function of di-muon pT. The total level-2 trigger ef\ufb01ciency in the reconstructed\nprompt J/\u03c8 events (relative to level-1) is 97%. The di-muon trigger scenario \u00b56\u00b54, considered in the\nmajority of this note, uses all the above trigger signatures.\n2.1.1\nEffect of di-muon trigger cuts on quarkonium rates\nFigures 5(a) and 5(b) illustrate the distribution of cross-sections across the values of the pT of the harder\nand softer muon from the quarkonium decay without any muon cuts applied at generator level. The lines\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1086\n\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\nEfficiency\n-1\n10\n1\nLVL2 Pass\nL2_BJpsimu0mu0\nL2_BJpsimu5mu5\nL2_BJpsimu6mu6\nL2_mu20i\nATLAS\nFigure 4: Ef\ufb01ciency of various level-2 triggers for prompt J/\u03c8 events versus pT of the di-muon\nsystem. Only the triggers with ef\ufb01ciencies greater than 2% in some region of pT are displayed.\nThe level-2 trigger signatures of interest include single muon pT threshold triggers L2 MUXX and\n\u2018TrigDiMuon\u2019 triggers L2 BJpsimuXmuY which are specialised for searching for J/\u03c8\n[11]. The\nef\ufb01ciency curve labelled LVL2 Pass in (b) is the sum of all level-2 ef\ufb01ciencies.\noverlaid on the plots represent various nominal muon pT thresholds: (6 GeV, 4 GeV) and (4 GeV, 4 GeV),\nas well as the nominal thresholds (10 GeV, 0.5 GeV) corresponding to the single muon trigger \u00b510 (see\nbelow).\nFor J/\u03c8 the bulk of the cross-section lies near the (4 GeV, 1 GeV) region, far from the low-pT muon\ntrigger thresholds proposed for ATLAS, and we see only a small increase in accessible cross-section\nby lowering the cut on the harder muon from 6 GeV to 4 GeV (although this reduction in the effective\nJ/\u03c8 pT threshold is useful from a physics standpoint). The situation for \u03d2 is signi\ufb01cantly different\nhowever, as the relatively large mass of the \u03d2 shifts the bulk of the production to the region near muon\npT thresholds of (5 GeV, 4 GeV). This means that by lowering the di-muon trigger cuts from (6 GeV,\n4 GeV), which sits just above the highest density area of \u03d2 production, to (4 GeV, 4 GeV), a much\nhigher fraction of the produced \u03d2 can be recorded, leading to a predicted order-of-magnitude increase\nin the accessible cross-section. The predicted cross-sections for the processes pp \u2192J/\u03c8(\u00b5 +\u00b5\u2212)X and\npp \u2192\u03d2(\u00b5+\u00b5\u2212)X (before incorporating trigger and reconstruction ef\ufb01ciencies) for a number of trigger\nscenarios are presented in Table 1. Although no higher \u03c8 and \u03d2 states have been simulated for this\nanalysis, their expected cross-sections are also shown in Table 1, as estimated using Tevatron results on\ntheir relative yields [12]. Numbers include feed-down from \u03c7 states and higher radial excitations to\nlower ones. Due to the expected ATLAS mass resolution for the \u03d2 states, however, it is unlikely that\nthe higher state resonances will be separable. These predictions have been obtained by extrapolating the\nColour Octet Model, tuned to describe the Tevatron results, to the LHC energy. Although every care have\nbeen taken to ensure stability of this extrapolation, inevitably there is an uncertainty in the overall scale\nof the predicted cross-sections (linked to the uncertainties in the parton distribution functions at small x),\nwhich we estimate at the level of \u00b150%.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1087\n\n (GeV)\nT\n muon: p\nT\nhigh p\n0\n2\n4\n6\n8\n10\n12\n (GeV)\nT\n muon: p\nT\nlow p\n0\n2\n4\n6\n8\n10\n12\n cuts 6+4 GeV\nT\nMuon p\n cuts 4+4 GeV\nT\nMuon p\n cuts 10+0.5 GeV\nT\nMuon p\nATLAS\n(a) J/\u03c8\n (GeV)\nT\n muon: p\nT\nhigh p\n0\n2\n4\n6\n8\n10\n12\n (GeV)\nT\n muon: p\nT\nlow p\n0\n2\n4\n6\n8\n10\n12\n cuts 6+4 GeV\nT\nMuon p\n cuts 4+4 GeV\nT\nMuon p\n cuts 10+0.5 GeV\nT\nMuon p\nATLAS\n(b) \u03d2\nFigure 5: Densities of J/\u03c8 \u2192\u00b5\u00b5 (a) and \u03d2\u2192\u00b5\u00b5 (b) production cross-section as a function of\nthe two muon transverse momenta. No cut was placed on the generated sample. The overlaid lines\nrepresent the nominal thresholds of observed events with various trigger cuts applied: \u00b56\u00b54 (solid\nline), \u00b54\u00b54 (dashed line) and \u00b510+track (dash-dotted line).\nIt is likely that the cross-section accessible by ATLAS will be higher than the values quoted in\nTable 1, as during early running the low pT muon trigger will run with an open coincidence window\nin \u03b7 at level-1 and no requirement of an additional level-2 di-muon trigger. This trigger item has a\nturn-on threshold at around 4 GeV, giving the (4 GeV, 4 GeV) trigger scenario described above, but in\npractice there is a non-zero trigger ef\ufb01ciency below 4 GeV, which, combined with the large rate of low\npT onia, may add a signi\ufb01cant extra contribution to the overall observed cross-section. Even including\nthis contribution, the overall rate of signal events from all quarkonium states is likely to remain below the\nrate of 1 Hz at a luminosity of 1031 cm\u22122s\u22121, which is a small fraction of the available trigger bandwidth.\nQuarkonium\nCross-section, nb\n\u00b54\u00b54\n\u00b56\u00b54\n\u00b510\n\u00b56\u00b54\u2229\u00b510\nJ/\u03c8\n28\n23\n23\n5\n\u03c8\u2032\n1.0\n0.8\n0.8\n0.2\n\u03d2(1S)\n48\n5.2\n2.8\n0.8\n\u03d2(2S)\n16\n1.7\n0.9\n0.3\n\u03d2(3S)\n9.0\n1.0\n0.6\n0.2\nTable 1: Predicted cross-sections for various prompt vector quarkonium state production and de-\ncay into muons, with di-muon trigger thresholds \u00b54\u00b54 and \u00b56\u00b54 and the single muon trigger\nthreshold \u00b510 (before trigger and reconstruction ef\ufb01ciencies). The last column shows the overlap\nbetween the di-muon and single muon samples.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1088\n\n2.1.2\nEffect of trigger cuts on analysis of octet states\nAs discussed above, the quarkonium cross-section is composed of three main classes of processes: direct\ncolour singlet production, colour octet production and singlet/octet production of \u03c7 states. Figure 6\nillustrates the contributions of these three classes to the overall production rate for \u03d2, once the pT trigger\ncuts of 6 and 4 GeV are applied to the muons. Lower pT trigger cuts will strongly enhance the \u03d2 rate and\n (GeV)\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n(nb/GeV)\nT\n+X)/dp\n\u03a5\n\u2192\n(pp\n\u03c3\n)d\n\u00b5\n+\n\u00b5\n\u2192\n\u03a5\nBR(\n3\n10\n2\n10\n1\n10\n1\n|<2.5\n\u03b7\nATLAS |\ntotal\ncolour singlet\n1\nS\n3\ncolour octet \nJ\nP\n3\n+\n0\nS\n1\ncolour octet \nFigure 6: Expected pT-distribution for \u03d2 production, with contributions from direct colour singlet,\nsinglet \u03c7 production and octet production overlaid.\nallow for analysis of colour singlet production, which is expected to dominate for \u03d2 with pT < 10 GeV.\nLower trigger cuts available during early running, such as the \u00b54\u00b54 trigger described above, will allow\nthe opportunity to extend the low-pT region down to pT \u22430 in the case of \u03d2 and help separate octet and\nsinglet contributions.\n2.1.3\nAcceptance of cos\u03b8 \u2217with di-muon triggers\nAn important consideration for calculating the di-muon trigger ef\ufb01ciencies of J/\u03c8 and \u03d2 is the angular\ndistribution of the decay angle \u03b8 \u2217, the angle between the direction of the positive muon (by convention)\nfrom quarkonium decay in the quarkonium rest frame and the \ufb02ight direction of the quarkonium itself in\nthe laboratory frame (Figure 7).\n\u03b8\u2217\nP\nP \u2217\n+\nP \u2217\n\u2212\nFigure 7: Graphical representation of the \u03b8 \u2217angle used in the spin alignment analysis. The angle is\nde\ufb01ned by the direction of the positive muon in the quarkonium decay frame and the quarkonium\nmomentum direction in the laboratory frame.\nThe distribution in cos\u03b8 \u2217may depend on the relative contributions of the various production mech-\nanisms, and is as of yet not fully understood. Crucially, Monte Carlo studies have shown that different\nproduction mechanisms (and thus different angular distributions) can have signi\ufb01cantly different trigger\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1089\n\nacceptances, and without the measurement of the spin-alignment of quarkonium it will be dif\ufb01cult to be\nsure that the full trigger ef\ufb01ciency has been calculated correctly.\nIt is clear that cos\u03b8 \u2217\u22430 corresponds to events with both muons having roughly equal transverse\nmomenta, while in order to have cos\u03b8 \u2217close to \u00b11 one muon\u2019s pT needs to be very high while the\nother\u2019s pT is very low. In the case of a di-muon trigger, both muons from the J/\u03c8 and \u03d2 decays must\nhave relatively large transverse momenta. Whilst this condition allows both muons to be identi\ufb01ed, it\nalso severely restricts acceptance in the polarisation angle cos\u03b8 \u2217, meaning that for a given pT of J/\u03c8 or\n\u03d2 a signi\ufb01cant fraction of the total cross-section is lost.\nExamples of the polarisation angle distributions for the \u00b56\u00b54 trigger are shown by solid lines in\nFigure 8. Here, the samples for both J/\u03c8 and \u03d2 were generated with zero polarisation, so with full\nacceptance the corresponding distribution in cos\u03b8 \u2217should be \ufb02at, spanning from \u22121 to +1. Clearly,\n* \u03b8\ncos\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nPercent/bin\n0\n0.5\n1\n1.5\n2\n2.5\nATLAS\n(a) J/\u03c8\n* \u03b8\ncos\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nPercent/bin\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\n(b) \u03d2\nFigure 8: Reconstructed polarisation angle distribution for \u00b56\u00b54 di-muon triggers (solid line) and\na \u00b510 single muon trigger (dashed line), for J/\u03c8 (a) and \u03d2 (b). The distributions are normalised\nto unit area. The generated angular distribution is \ufb02at in both cases.\nnarrow acceptance in |cos\u03b8 \u2217| would make polarisation measurements dif\ufb01cult.\n2.2\nSingle muon trigger\nAnother possibility for quarkonium reconstruction is to trigger on a single identi\ufb01ed muon. The non-\nprescaled level-1 single muon trigger L1 MU10 with a 10 GeV pT threshold is expected to produce man-\nageable event rates at low luminosities [11]. Once this muon triggers the event, of\ufb02ine analysis can\nreconstruct the quarkonium by combining the identi\ufb01ed muon with an oppositely-charged track in the\nevent. In Figure 5 this trigger corresponds to the dash-dotted lines, with the predicted cross-sections\nalso shown in Table 1. With this trigger (referred to as \u00b510 in the following) one removes the need for\nthe other muon to have a large pT, i.e. one has a fast muon, which triggered the event, and one track,\nwhose transverse momentum is only limited by the track reconstruction capabilities of ATLAS, with the\nthreshold around 0.5 GeV.\nThus, the onium events with a single muon trigger typically have much higher values of |cos\u03b8 \u2217|, as\nillustrated by the dotted lines in Figure 8, complementing the di-muon trigger sample. So, the single-\nand di-muon samples may be used together to provide excellent coverage across almost the entire range\nof cos\u03b8 \u2217in the same pT range of onia.\nIt\u2019s worth noting that the di-muon and single muon samples have comparable cross-sections and\nsimilar pT dependence. They are not entirely independent: at high transverse momenta the two samples\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1090\n\nhave signi\ufb01cant event overlap (see Table 1 for more details), which could be useful for independent\ncalibration of muon trigger and reconstruction ef\ufb01ciencies.\n3\nReconstruction and background suppression\n3.1\nQuarkonium reconstruction with two muon candidates\nIn each event which passes the di-muon trigger, all reconstructed muon candidates are combined into\noppositely charged pairs, and each of these pairs is analysed in turn. The invariant mass is calculated\nand, if the mass is above 1 GeV, the two tracks are re\ufb01tted to a common vertex. If a good vertex \ufb01t is\nachieved, the pair is accepted for further analysis. If the invariant mass of the re\ufb01tted tracks is within\n300 MeV of the nominal mass in the case of J/\u03c8 , or 1 GeV in the case of \u03d2 , the pair is considered as a\nquarkonium candidate. The values quoted by the Particle Data Group [13], 3097 MeV and 9460 MeV for\nJ/\u03c8 and \u03d2 respectively, are used throughout this paper, and the widths of the mass windows are chosen\nto be about six times the expected average mass resolution (see Table 2).\nFor those pairs for which the vertex \ufb01t is successful (more than 99% for both J/\u03c8 and \u03d2 ), the\ninvariant mass is recalculated. The invariant mass resolution depends on the pseudorapidities of the two\nmuon tracks. To illustrate this effect, all accepted onia candidates are divided into three classes depending\non \u03b7 of the muons, and Gaussian \ufb01ts are performed to determine the resolutions and mass shifts. The\nresults are presented in Table 2. It is found that the mass resolution is the highest when both tracks are\nQuarkonium\nMrec \u2212MPDG, MeV\nResolution \u03c3, MeV\nAverage\nBarrel\nMixed\nEndcap\nJ/\u03c8\n+4\u00b11\n53\n42\n54\n75\n\u03d2\n+15\u00b11\n161\n129\n170\n225\nTable 2: Mass shifts and resolutions for di-muon invariant mass distributions after the vertex \ufb01t,\nfor J/\u03c8 and \u03d2 candidates.\nreconstructed in the barrel area, |\u03b7| < 1.05, degrades somewhat if both tracks are reconstructed in the\nendcap regions, |\u03b7| > 1.05, and is close to its average value for the mixed \u03b7 events, with one muon in the\nbarrel and the other in the endcap. It should be noted that no signi\ufb01cant non-gaussian tails are observed\nin either of these mass distributions, and the \ufb01t quality is good. Also shown in the table are the shifts of\nthe mean reconstructed invariant mass from the respective nominal values. The observed mass shifts are\ndue to a problem with simulation of material effects in the endcap, which has since been understood and\ncorrected.\nThe reconstructed muon pairs that remain after vertexing cuts are considered to be good quarkonium\ncandidates, and further analysis is done using these pairs only. The transverse momentum distributions\nof these candidates are shown in Figure 9.\nAs can be seen from the Figure 9(a), prompt J/\u03c8 are mainly selected with pT above around 10 GeV,\ndue to the di-muon trigger cuts applied to the events. The decay kinematics of \u03d2 is somewhat different\ndue to its larger mass, thus allowing \u03d2 to be selected with pT as low as 4 GeV. Even at these, relatively\nlow, statistics one expects to see signi\ufb01cant numbers of both types of quarkonia at large pT, which will\nallow statistically signi\ufb01cant high-pT analyses beyond the reach of the Tevatron.\nFigure 10(a) presents the J/\u03c8 acceptance as a function of the J/\u03c8 transverse momentum, relative\nto the Monte Carlo generated dataset, which requires the two muons to be within |\u03b7| < 2.5 and have\ntransverse momenta greater than 6 and 4 GeV, respectively. Geometric acceptance of the detector and\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1091\n\n (GeV)\nT\np\n0\n10\n20\n30\n40\n50\nEvents\n10\n2\n10\n3\n10\n4\n10\n\u03c8\nAll J/\n|<1 05 \n\u03b7\n in |\n\u03c8\nJ/\n|>1 05 \n\u03b7\n in |\n\u03c8\nJ/\nATLAS\n(a) J/\u03c8\n (GeV)\nT\np\n0\n10\n20\n30\n40\n50\nEvents\n10\n2\n10\n3\n10\n\u03a5\nAll \n|<1 05 \n\u03b7\n in |\n\u03a5\n|>1 05 \n\u03b7\n in |\n\u03a5\nATLAS\n(b) \u03d2\nFigure 9: Transverse momentum distribution of triggered reconstructed quarkonium candidates,\nalso shown separately for quarkonia found in the barrel and endcap regions of the detector. Statis-\ntics shown in the \ufb01gures correspond to integrated luminosities of about 6 pb\u22121 and 10 pb\u22121 for\nJ/\u03c8 and \u03d2, respectively.\n) (GeV)\n\u03c8\n(J/\nT\np\n0\n10\n20\n30\n40\n50\nAcceptance\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n(a) J/\u03c8 acceptance with pT\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nAcceptance\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n(b) J/\u03c8 acceptance with \u03b7\nFigure 10: Acceptance of reconstructed prompt J/\u03c8 as a function of J/\u03c8 transverse momentum\nand pseudorapidity (relative to the MC generated dataset with \u00b56\u00b54 cuts).\nreconstruction ef\ufb01ciency losses due to vertexing, as well as trigger ef\ufb01ciencies have been taken into\naccount. When J/\u03c8 are produced with a transverse momentum above 10 GeV, we see a sharp rise in the\nacceptance as J/\u03c8 above this threshold are able to satisfy the muon trigger requirements within a certain\nkinematic con\ufb01guration.\nThe structure in the plot of the \u03b7-dependence of J/\u03c8\nreconstruction ef\ufb01ciency, shown in Fig-\nure 10(b), highlights the con\ufb01guration necessary in order for muons from the J/\u03c8 to be able to pass\nthe di-muon trigger, described below. The distribution of reconstructed quarkonium candidates with the\nangular separation of the two muons, described by the variable \u2206R =\np\n\u2206\u03c6 2 +\u2206\u03b72, is shown in Fig-\nure 11. On average, muons from reconstructed J/\u03c8 (\u00b56\u00b54) candidates are separated by \u2206R \u22430.47, and\nare restricted from being detected with separations larger than around 0.7.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1092\n\nR\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\nFraction\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n\u03c8\nJ/\n\u03a5\nATLAS\n(a) \u2206R with \u00b56\u00b54 cuts\nR\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nFraction\n0\n10\n20\n30\n40\n50\n60\n-3\n10\n\u00d7\n\u03c8\nJ/\n\u03a5\nATLAS\n(b) \u2206R with \u00b510 cuts\nFigure 11: Distribution of \u2206R separation of the two muons from J/\u03c8 and \u03d2 candidates with\ndi-muon \u00b56\u00b54 generator-level cuts (left) and single muon \u00b510 cuts (right) applied.\nIn comparison, the higher mass of \u03d2 requires the muons in the \u00b56\u00b54 case to have a much larger\nopening angle, with a broad distribution in \u2206R peaking at around 1.8 and spanning up to 2.6. One can\nsee that for the single \u00b510 case in Figure 11(b) the distributions are much broader, and generally with\nsmaller separation in \u2206R, re\ufb02ecting the lower pT constraint on the second muon.\nThe small separation of muons in \u2206R for the J/\u03c8 (\u00b56\u00b54) case has consequences for the J/\u03c8 recon-\nstruction ef\ufb01ciency as a function of pseudorapidity, shown in Figure 10(b). Signi\ufb01cant dips in ef\ufb01ciency\nare seen near \u03b7 \u00b1 1.2 and \u03b7 = 0, due to the muon spectrometer layout [14]. As the muons from J/\u03c8\nare on average separated by only \u2206R = 0.47, they are subject to similar material and detector effects,\nand so these effects are carried over into the J/\u03c8 reconstruction with very little smearing. Hence, this\ndistribution has a similar shape to the individual muon reconstruction ef\ufb01ciency distribution in ATLAS.\n) (GeV)\n\u03a5\n(\nT\np\n0\n10\n20\n30\n40\n50\nAcceptance\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n(a) \u03d2 acceptance with pT\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nAcceptance\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n(b) \u03d2 acceptance with \u03b7\nFigure 12: Acceptance of reconstructed prompt \u03d2 as a function of transverse momentum and\npseudorapidity of the quarkonium state (relative to the Monte Carlo generated dataset with \u00b56\u00b54\ncuts).\nThis contrasts with the \u03d2 reconstruction ef\ufb01ciency dependence on pseudorapidity, shown in Fig-\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1093\n\nure 12(b), which is much smoother than in J/\u03c8 case: the two muons have large angular separation and\nthe detector layout effects are smeared over a broader range of \u03b7 values. Figure 12(a) shows the variation\nof acceptance with the \u03d2 transverse momentum, and re\ufb02ects the fact that with the \u00b56\u00b54 trigger \u03d2 can be\nreconstructed with a lower pT threshold. In the absence of a dedicated topological trigger for \u03d2, trigger\nef\ufb01ciency at low pT suffers due to the differing decay kinematics between J/\u03c8 and \u03d2 as only specialised\nJ/\u03c8 triggers exist in reconstruction software used in this analysis. At larger pT both acceptances reach\na plateau at around 80\u201385%.\n3.2\nOf\ufb02ine monitoring using quarkonium\nThe di-muon decays of J/\u03c8 and \u03d2 will be used in both online and of\ufb02ine monitoring at ATLAS. Mass\nshifts for the reconstructed quarkonium states, plotted versus a number of different variables, have been\nproposed to monitor detector alignment, material effects, magnetic \ufb01eld scale and its stability, as well as\nto provide checks of muon reconstruction algorithm performance. The CDF collaboration extensively\nand successfully used this method, although it took many years at the Tevatron to collect suf\ufb01cient\nstatistics to allow for the disentanglement of various detector effects [15].\nThe expected rate of quarkonium production at ATLAS is such that we can expect to be able to\nperform meaningful monitoring and corrections online. There are many examples of where monitoring of\nquarkonium mass shifts can be useful in data-taking. Mass shifts in quarkonia as a function of transverse\nmomentum can reveal problems with energy loss corrections and the muon momentum scale. As a\nfunction of pseudorapidity this can be a good probe of over- or under-correction of material effects in\nthe simulated detector geometry and of magnetic \ufb01eld uniformity. J/\u03c8 mass shifts in Monte Carlo\nsimulations have already helped to improve muon reconstruction algorithms in ATLAS.\nAn example of a reconstructed J/\u03c8 mass shift measurement at ATLAS with the statistics correspond-\ning to 6 pb\u22121 is presented in Figure 13. This is the dependence of \u2206M on the difference in curvatures\n)\n-1\n) (TeV\n-\u00b5\n(\nT\n)-1/p\n+\n\u00b5\n(\nT\n1/p\n-150\n-100\n-50\n0\n50\n100\n150\n mass (GeV)\n\u03c8\nJ/\n3.08\n3.085\n3.09\n3.095\n3.1\n3.105\n3.11\nATLAS\nFigure 13: J/\u03c8 mass shift plotted versus the difference of curvature between the positive and\nnegative muons. Statistics corresponds to the integrated luminosity of about 6 pb\u22121.\nof positive and negative muons, which allows for checks of a potentially important effect seen at CDF:\nhorizontal misalignments in some detector elements may result in a constant curvature offset that can\nlead to signi\ufb01cant charge-dependent tracking effects. A misalignment may be such that a negative track\nhas a higher assigned curvature (and hence lower momentum) than is truly the case, whilst a positive\ntrack would be affected in the opposite way. The sample shown in the \ufb01gure is simulated with ideal\ngeometry and does not show any signi\ufb01cant effects of this kind.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1094\n\nFor detector alignment and data monitoring purposes, quarkonium provides a low pT point for cali-\nbration, complementary to the Z boson sample, and allows for the possibility to identify any systematic\nvariations that may develop at higher pT.\nIn order to be able to analyse mass shifts due to two-variable correlations and disentangle various\ndetector effects, signi\ufb01cant statistics of J/\u03c8 and \u03d2 di-muon decays have to be accumulated. A dedicated\nstudy is being performed in ATLAS to optimise the strategy of real time and of\ufb02ine monitoring using\nthis method, but these results lie beyond the scope of this note.\n3.3\nBackground suppression in di-muon case\nThe expected sources of background for prompt quarkonium with a di-muon \u00b56\u00b54 trigger are:\n\u2022 indirect J/\u03c8 production from b\u00afb events;\n\u2022 continuum of muon pairs from b\u00afb events;\n\u2022 continuum of muon pairs from charm decays;\n\u2022 di-muon production via the Drell-Yan process;\n\u2022 decays in \ufb02ight of \u03c0\u00b1 and K\u00b1 mesons.\nThe most important background contributions are expected to come from the decays b \u2192J/\u03c8+X,\nand the continuum of di-muons from b\u00afb events. Both of these have been simulated and analysed. The\nestimated total contribution from charm decays is higher than that from b\u00afb events. However, this back-\nground has not been simulated, as it is not expected to cause problems for prompt quarkonium recon-\nstruction because the transverse momentum spectrum of the muons falls very steeply and the probability\nof producing a di-muon with an invariant mass within the range of interest is well below the level ex-\npected from b\u00afb events. Only a small fraction of the Drell-Yan pairs survive the di-muon trigger cuts of\n\u00b56\u00b54 in the J/\u03c8\u2212\u03d2mass range, which makes this background essentially negligible, as estimated from\ngenerator-level simulation. Muons from decays in \ufb02ight also have a steeply falling muon momentum\nspectrum, and in addition require random coincidences with muons from other sources in the quarko-\nnium invariant mass range. This is estimated to be at the level of a few percent of the signal rate, spread\nover a continuum of invariant masses.\nAll background di-muon sources mentioned above, apart from Drell-Yan pairs, contain muons which\noriginate from secondary vertices, which makes it possible to suppress these backgrounds by remov-\ning such di-muons whenever a secondary vertex has been resolved, based on the pseudo-proper time\nmeasurement. The pseudo-proper time is de\ufb01ned as\nPseudo-proper time = Lxy \u00b7MJ/\u03c8\npT(J/\u03c8)\u00b7c,\n(1)\nwhere MJ/\u03c8 and pT(J/\u03c8) represent the mass and the transverse momentum of the J/\u03c8 candidate, c is\nthe speed of light in vacuum, and Lxy is the measured radial displacement of the two-track vertex from\nthe beamline. Once the two muons forming a J/\u03c8 candidate are reconstructed, the pseudo-proper time is\nused to distinguish between the prompt J/\u03c8 , which have a pseudo-proper time of zero, and J/\u03c8 coming\nfrom B-hadron decays and hence having an exponentially decaying pseudo-proper time distribution, due\nto the non-zero lifetime of the parent B-hadrons.\nThe dependence of the resolution in radial decay length Lxy on di-muon pseudorapidity \u03b7 is shown\nin Figure 14, while the variation of the expected resolution in the pseudo-proper time with di-muon\npT is shown in Table 3. An improvement in the resolution is seen with increasing pT of the J/\u03c8 and\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1095\n\n|\n\u03c8\nJ/\n\u03b7|\n0\n0.5\n1\n1.5\n2\n2 5\nm)\n\u00b5\nSec. vertex radial resolution (\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nATLAS\nFigure 14: Radial position resolution of secondary vertex for J/\u03c8 decays as a function of the J/\u03c8\npseudorapidity.\nJ/\u03c8\ntransverse mo-\nmentum (GeV)\n9\u221212\n12\u221213\n13\u221215\n15\u221217\n17\u221221\n> 21\nPseudo-proper\ntime\nresolution (ps)\n0.107\n0.103\n0.100\n0.093\n0.087\n0.068\nTable 3: Pseudo-proper time resolution of direct J/\u03c8 events as a function of J/\u03c8 pT.\ndecreasing |\u03b7|. Here a perfect detector alignment is assumed, with the resulting average resolution\nestimated at around 0.1 ps.\nFigure 15(a) illustrates the pseudo-proper time distribution for both the prompt and indirect J/\u03c8\nsamples. By making a cut on the pseudo-proper time, one can ef\ufb01ciently separate most of the indirect\nJ/\u03c8 from a prompt J/\u03c8 sample (or vice-versa). The ef\ufb01ciency and purity of the pseudo-proper time\ncuts for prompt J/\u03c8 are presented in Figure 15(b). A pseudo-proper time cut of less than 0.2 ps allows to\nretain prompt J/\u03c8 with the ef\ufb01ciency of 93% and the purity of 92%. Note that the distribution shown in\nFigure 15(a) is, in a sense, self-calibrating: the part to the left of the maximum can be used to determine\nthe resolution \u03c3, and an appropriate cut of 2\u03c3 can be applied to remove the \u2018tail\u2019 of secondary J/\u03c8\ncandidates on the right hand side.\nThe background levels of beauty and Drell-Yan production under the \u03d2 peak are similar to those\nfor the J/\u03c8 , except that here one does not have to contend with sources of non-prompt quarkonia\nfrom B-decays. However, the bb \u2192\u00b56\u00b54 background continuum under the \u03d2 is more problematic:\nhigher invariant masses around the \u03d2 mean that the two triggered muons will necessarily come from two\nseparate decays, meaning that the pseudo-proper time cut is far less effective.\nFortunately, \ufb02ags associated to individual reconstructed muon tracks provide further vertexing infor-\nmation, which could be used for suppressing of the bb \u2192\u00b56\u00b54 continuum background. Reconstructed\ntracks are assigned to either come from the primary vertex, a secondary vertex, or are left undetermined.\nBy requiring that both of the muons combined to make a J/\u03c8 or a \u03d2 candidate are determined to have\ncome from the primary vertex, background from the bb \u2192\u00b56\u00b54 continuum can be reduced by a factor\nof three or more, whilst reducing the number of signal events by around 5% in both cases.\nFigure 16 illustrates the quarkonium signal and main background invariant mass distributions in the\nmass range 2\u221212 GeV, for those events which satisfy the \u00b56\u00b54 trigger requirements, with reconstruction\nef\ufb01ciencies and background suppression cuts taken into account. Peaks from the J/\u03c8 and \u03d2(1S) clearly\ndominate the background. As no higher \u03c8 and \u03d2 states were simulated for this analysis, their peaks are\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1096\n\nPseudo-Proper time (ps)\n-0.4 -0.2\n0\n0.2\n0.4\n0.6 0.8\n1\n1.2 1.4\nEvents\n2\n10\n3\n10\n4\n10\nPrompt\nPrompt+Indirect\nATLAS\n(a)\nPseudo-Proper time (ps)\n-0.4 -0.2\n0\n0.2\n0.4\n0.6 0.8\n1\n1.2 1.4\nEfficiency/Purity\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03c8\nEfficiency,Prompt J/\n\u03c8\nPurity,Prompt J/\nATLAS\n(b)\nFigure 15: (a) Pseudo-proper time distribution for reconstructed prompt J/\u03c8 (dark shading) and\nthe sum of prompt and indirect J/\u03c8 candidates (lighter shading). (b) Ef\ufb01ciency (solid line) and\npurity (dotted line) for prompt J/\u03c8 candidates as a function of the pseudo-proper time cut. Statis-\ntics correspond to the integrated luminosity of 6 pb\u22121.\nnot shown. The dotted line indicates the level of the background continuum before the vertexing cuts.\nIn conclusion, we \ufb01nd that the level of the backgrounds considered for both J/\u03c8 and \u03d2 do not\nrepresent any serious problem for reconstruction and analysis of direct quarkonia with the di-muon \u00b56\u00b54\ntrigger.\n3.4\nReconstruction and background suppression with a single muon candidate\nBy using the \u00b510 trigger, one selects events with at least one identi\ufb01ed muon candidate with pT above\n10 GeV. In this part of the analysis, each reconstructed single muon candidate is combined with oppositely-\ncharged tracks reconstructed in the same event. For both J/\u03c8 and \u03d2 reconstruction, we insist that any\nother reconstructed track to be combined with the identi\ufb01ed trigger muon has an opposite electric charge\nand is within a cone of \u2206R = 3.0 around the muon direction, so as to retain over 99% (91%) of the signal\nevents in the J/\u03c8 (\u03d2) case. As in the di-muon analysis, we require that both the identi\ufb01ed muon and the\ntrack are \ufb02agged as having come from the primary vertex. In addition, we impose a cut on the transverse\nimpact parameter d0, |d0| < 0.04 mm on the muon and |d0| < 0.10 mm on the track, in order to further\nsuppress the number of background pairs from B-decays.\nThe invariant mass distribution for the remaining pairings of a muon and a track is shown in Fig-\nure 17(a) for J/\u03c8 with pT larger than 9 GeV and in Figure 17(b) for J/\u03c8 with pT larger than 17 GeV.\nThe distributions are \ufb01tted using a single gaussian for the signal and a straight line for the background.\nClear J/\u03c8 peaks can be seen, with statistically insigni\ufb01cant mass shifts and the resolution close to that in\nthe di-muon sample. It\u2019s worth noting that the signal-to-background ratio around the J/\u03c8 peak improves\nslightly with increasing transverse momentum of J/\u03c8. At higher pT the cos\u03b8 \u2217acceptance also becomes\nbroader, which should help independent polarisation measurements.\nFor \u03d2 the situation is less favourable, due to the combination of a lower signal cross-section and\na higher background. Although the \u03d2 peak can be seen above the smooth background, its statistical\nsigni\ufb01cance is rather low. Hence, with this statistics, the use of the single muon sample for \u03d2 cannot be\njusti\ufb01ed, and in the following we will only rely on the di-muon sample.\nIn conclusion, we expect that the single muon trigger with a 10 GeV threshold can be successfully\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1097\n\nMass (GeV)\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n/dM [nb/(100 MeV)]\n\u03c3\nd\n-2\n10\n-1\n10\n1\n10\nMass (GeV)\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n/dM [nb/(100 MeV)]\n\u03c3\nd\n-2\n10\n-1\n10\n1\n10\n4X\n\u00b5\n6\n\u00b5\n\u2192\nbb\nDirect onia\nDrell-Yan\nFigure 16: The cumulative plot of the invariant mass of di-muons from various sources, recon-\nstructed with a \u00b56\u00b54 trigger, with the requirement that both muons are identi\ufb01ed as coming from\nthe primary vertex and with a pseudo-proper time cut of 0.2 ps. The dotted line shows the cumu-\nlative distribution without vertex and pseudo-proper time cuts.\nused to select prompt J/\u03c8 events. The expected background here, although much larger than in di-\nmuon case, is well under control. For \u03d2 however, the single muon sample is only likely to be useful at\nsigni\ufb01cantly higher statistics and higher transverse momenta.\n3.5\nSummary of cuts and ef\ufb01ciencies\nTable 4 summarises the ef\ufb01ciencies of all the selection and background suppression cuts described above,\nfor both the di-muon and single muon trigger samples. Not all cuts are applicable to all samples; those\nwhich are not are labelled accordingly. Numbers in italics are estimates in cases where no adequate\nfully simulated sample was available. The ef\ufb01ciencies for \u00b56\u00b54 samples are calculated relative to the\nMonte Carlo sample with generator-level cuts on the two highest muon transverse momenta of 6 and 4\nGeV. For the \u00b510 samples, the generator-level cut of 10 GeV was applied to the pT of the highest-pT\nmuon. Expected yields NS of quarkonia for 10 pb\u22121 are given at the bottom of the table, along with\nbackground yields NB within the invariant mass window of \u00b1300 MeV for J/\u03c8 and \u00b11 GeV for \u03d2, and\nthe signal-to-background ratios at respective J/\u03c8 and \u03d2 peaks for each sample.\nFor higher, excited quarkonium states with vector quantum numbers the ef\ufb01ciencies are expected to\nbe similar, but not necessarily identical. The biggest differences are expected for \u03c8 \u2032, where the produc-\ntion mechanisms as well as decay kinematics are signi\ufb01cantly different.\n4\nPolarisation and cross-section measurement\nThe Colour Octet Model predicts that prompt quarkonia produced in pp collisions are transversely po-\nlarised, with the degree of polarisation increasing as a function of the transverse momentum. Other\nproduction models predict different pT dependencies of the polarisation and so this quantity serves as an\nimportant measurement for discrimination of these models (see Figure 1(b)).\nQuarkonium polarisation can be assessed by measuring the angular distribution of the muons pro-\nduced in the decay. The relevant decay angle \u03b8 \u2217is de\ufb01ned in Figure 7. The spin alignment of the parent\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1098\n\nMass (GeV)\n2.4\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\nEvents / 50 MeV\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n6\n10\n\u00d7\nMass (GeV)\n2.4\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\nEvents / 50 MeV\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n6\n10\n\u00d7\n3 MeV\n\u00b1\nM = 3\n\u2206\n3 MeV\n\u00b1\n = 56\n\u03c3\n)>9 GeV\n\u03c8\n(J/\nT\np\nATLAS\n(a) J/\u03c8 with pT > 9 GeV\nMass (GeV)\n2.4\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\nEvents / 50 MeV\n0\n5\n10\n15\n20\n25\n3\n10\n\u00d7\nMass (GeV)\n2.4\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\nEvents / 50 MeV\n0\n5\n10\n15\n20\n25\n3\n10\n\u00d7\n5 MeV\n\u00b1\nM = 3\n\u2206\n5 MeV\n\u00b1\n = 54\n\u03c3\n)>17 GeV\n\u03c8\n(J/\nT\np\nATLAS\n(b) J/\u03c8 with pT > 17 GeV\nFigure 17: Prompt quarkonium signal and bb \u2192\u00b5X background events selected with the \u00b510\ntrigger, in the mass range around J/\u03c8 with (a) pT above 9 GeV, and (b) pT above 17 GeV,\ncorresponding to 10 pb\u22121 of data. The background from B decays is shown in light grey. Cuts\ndescribed in the text have been applied. The distributions were \ufb01tted using the sum of a linear\nbackground and a gaussian peak centered at M = 3097 MeV +\u2206M with resolution \u03c3.\nvector quarkonium state can be determined by measuring the polarisation parameter \u03b1 in the distribution\ndN\nd cos\u03b8 \u2217= C\n3\n2\u03b1 +6\n\u00001+\u03b1 cos2 \u03b8 \u2217\u0001\n.\n(2)\nThe choice of parameters in Equation 2 is such that the distribution is normalised to C. The parameter\n\u03b1, de\ufb01ned as \u03b1 = (\u03c3T \u22122\u03c3L)/(\u03c3T +2\u03c3L), is equal to +1 for transversely polarised production (helicity\n= \u00b11). For a longitudinal polarisation (helicity = 0), \u03b1 is equal to \u22121. Unpolarised production consists\nof equal fractions of helicity states +1, 0 and \u22121, and corresponds to \u03b1 = 0.\nThe dif\ufb01culty of quarkonium polarisation measurements is evidenced by the discrepancies between\nD\u00d8 and CDF results shown in Figure 1(b). The problem can be traced to the limited acceptance at high\n|cos\u03b8 \u2217|, and hence dif\ufb01culties in separating acceptance corrections from spin alignment effects (see,\ne.g., [7]).\nNote that the feed-down from \u03c7 state and b-hadron decays may lead to a different spin alignment\nand hence to a possible effective depolarisation which is hard to estimate. In addition, due to the lim-\nited statistics, the polarisation measurements at the Tevatron cannot reach the region of high pT, where\ntheoretical uncertainties are expected to be smaller.\nAt ATLAS we aim to measure the polarisation of prompt vector quarkonium states, in the transverse\nmomentum range up to \u223c50 GeV and beyond, with extended coverage in cos\u03b8 \u2217which will allow for\nimproved understanding of ef\ufb01ciency measurements and thus reduced systematics. The promptly pro-\nduced J/\u03c8 mesons and those that originated from B-hadron decays can be separated using the displaced\ndecay vertices, as explained above. With a high production rate of quarkonia at LHC, it will be possible\nto achieve a higher degree of purity of prompt J/\u03c8 in the analysed sample and reduce the depolarising\neffect from B-decays, whilst retaining high statistics.\nAs explained in Section 2.1.3, with the di-muon trigger signature such as \u00b56\u00b54, the acceptance\nat large values of |cos\u03b8 \u2217| (where the difference between various polarisation states is the biggest)\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1099\n\nQuarkonium\nJ/\u03c8\nJ/\u03c8\n\u03d2\n\u03d2\nTrigger type\n\u00b56\u00b54\n\u00b510\n\u00b56\u00b54\n\u00b510\nMC cross-section\n23 nb\n23 nb\n5.2 nb\n2.8 nb\n\u03b5L1\nLevel-1 trigger\n87%\n96%\n84%\n96%\n\u03b5L2\nLevel-2 trigger\n97%\n>99%\n66%\n>99%\n\u03b5Rec\nReconstruction\n89%\n96%\n93%\n96%\n\u03b5Vtx\nVertex \ufb01t\n99%\n99%\n99%\n99%\n\u03b51\n\u03b5L1 \u00b7\u03b5L2 \u00b7\u03b5Rec \u00b7\u03b5Vtx\n75%\n90%\n51%\n90%\n\u03b5t0\nPseudo-proper time cut\n93%\n93%\nn/a\nn/a\n\u03b5Flg\nOnly primary vertex tracks\n96%\n92%\n95%\n92%\n\u03b5\u2206R\nSecond track inside cone\nn/a\n99%\nn/a\n91%\n\u03b5d0\nImpact parameter cut\nn/a\n90%\nn/a\n90%\n\u03b52\n\u03b5t0 \u00b7\u03b5Flg \u00b7\u03b5\u2206R \u00b7\u03b5d0\n90%\n76%\n95%\n75%\n\u03b5\nOverall ef\ufb01ciency \u03b51 \u00b7\u03b52\n67%\n69%\n49%\n68%\nObserved signal cross-section\n15 nb\n16 nb\n2.5 nb\n2.0 nb\nNS for 10 pb\u22121\n150 000\n160 000\n25 000\n20 000\nNB in mass window for 10 pb\u22121\n7000\n700 000\n16 000\n2 000 000\nSignal/Background at peak\n60\n1.2\n10\n0.05\nTable 4: Predicted and observed cross-sections for prompt vector quarkonia, and ef\ufb01ciencies of\nvarious selection and background suppression cuts described in Section 3.\nis strongly reduced, especially at low transverse momenta of quarkonium. The kinematic acceptance\nA (pT,cos\u03b8 \u2217) of the \u00b56\u00b54 cuts applied at generator level, with respect to the full generator-level sample\nwith no cuts on muon transverse momenta, is shown by the solid lines in Figure 18 for various pT slices\nof J/\u03c8 . The acceptance is seen to be quite low at J/\u03c8 pT below 12 GeV, but in higher pT slices there\nis an area in the middle of cos\u03b8 \u2217range with essentially 100% acceptance, which becomes broader with\nincreasing pT of the J/\u03c8 , but does not go beyond |cos\u03b8 \u2217| \u22430.5.\nThe acceptance for the single muon trigger sample, shown with the dashed lines in Figure 18, is\ndifferent: here the areas of 100% acceptance are at high |cos\u03b8 \u2217|, and the dip in the middle gradually \ufb01lls\nup with increasing pT. This sample essentially has a full acceptance at pT > 20 GeV, apart from the drop\nat |cos\u03b8 \u2217| > 0.95 due to the cut of 0.5 GeV on the pT of the track of the second muon.\nThe plots in Figure 18 were obtained using a dedicated generator-level Monte Carlo sample. The er-\nror bars shown in the \ufb01gure re\ufb02ect both statistical errors and the uncertainties due to possible dependence\non \u03b7 coverage.\nThe simulated \u2018raw\u2019 measured distributions dNraw/d cos\u03b8 \u2217, for the same slices of J/\u03c8 transverse\nmomenta, are shown in Figure 19. Again, solid and dashed lines represent the events selected by the\ndi-muon \u00b56\u00b54 and the single muon \u00b510 triggers, respectively. The sample was generated with zero\npolarisation. The raw numbers of measured events in the \u00b510 sample were obtained by \ufb01tting the invari-\nant mass distributions with a gaussian peak and a linear background, for each bin of cos\u03b8 \u2217in each pT\nslice. With the estimated signal-to-background ratios shown in Figure 17(a), this causes an increase in\nthe statistical errors, typically by a factor of 2.\nThe corrected distributions dNcor/d cos\u03b8 \u2217are calculated according to the following formula:\ndNcor\nd cos\u03b8 \u2217=\n1\nA (pT,cos\u03b8 \u2217)\u00b7\u03b51 \u00b7\u03b52\n\u00b7\ndNraw\nd cos\u03b8 \u2217\n(3)\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1100\n\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\nATLAS\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nAcceptance\n0\n0.5\n1\nFigure 18: Generator-level kinematic acceptances of the \u00b56\u00b54 (solid lines) and \u00b510\u00b50.5 (dashed\nlines) cuts, calculated with respect to the sample with no muon pT cuts, in slices of J/\u03c8 transverse\nmomentum: left to right, top to bottom 9 \u221212 GeV, 12 \u221213 GeV, 13 \u221215 GeV, 15 \u221217 GeV,\n17\u221221 GeV, above 21 GeV.\nHere \u03b51 stands for the trigger and reconstruction ef\ufb01ciency, while \u03b52 denotes the ef\ufb01ciency of background\nsuppression cuts for each sample, as de\ufb01ned in Table 4. Their values have been averaged over the\naccessible phase space within the relevant pT slice. Studies have shown that while \u03b51 depend on pT (cf.\nFigure 10(a)), \u03b52 remain essentially constant over the phase space of interest. The ef\ufb01ciencies \u03b51 and \u03b52\nfor both samples are listed in Table 5, while the acceptances A (pT,cos\u03b8 \u2217) are shown in Figure 18.\npT, GeV\n9\u221212\n12\u221213\n13\u221215\n15\u221217\n17\u221221\n> 21\n\u03b51(\u00b56\u00b54), %\n67\u00b11\n75\u00b11\n77\u00b11\n78\u00b11\n79\u00b11\n80\u00b11\n\u03b52(\u00b56\u00b54), %\n90\u00b11\n90\u00b11\n90\u00b11\n90\u00b11\n90\u00b11\n90\u00b11\n\u03b51(\u00b510), %\n86\u00b11\n89\u00b11\n90\u00b11\n90\u00b11\n90\u00b11\n90\u00b11\n\u03b52(\u00b510), %\n76\u00b11\n76\u00b11\n76\u00b11\n76\u00b11\n76\u00b11\n76\u00b11\nTable 5: Ef\ufb01ciencies for the \u00b56\u00b54 and \u00b510 samples, averaged over each of the six pT slices.\nAt high pT the two samples increasingly overlap, thus allowing for a cross-check of acceptance and\nef\ufb01ciency corrections. However, for measurement purposes the \u00b56\u00b54 samples are used whenever pos-\nsible, complemented by \u00b510 samples at high cos\u03b8 \u2217. In order to achieve this, the distributions shown\nin Figure 19 were appropriately masked and combined. The combined distributions dNcor/d cos\u03b8 \u2217,\ncorrected according to Equation 3, are shown in Figure 20. The errors shown in the plots include the sta-\ntistical errors on the raw data, as well as the uncertainties on the acceptance and ef\ufb01ciencies. These cos\u03b8 \u2217\ndistributions are \ufb01tted using the Equation 2, with \u03b1 and C as free parameters for each pT slice. The \ufb01t\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1101\n\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n2\n4\n6\n3\n10\n\u00d7\nATLAS\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n1\n2\n3\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n1\n2\n3\n4\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.5\n1\n1.5\n2\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.5\n1\n1.5\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.2\n0.4\n0.6\n0.8\n1\n3\n10\n\u00d7\nFigure 19: Measured distributions for \u00b56\u00b54- (solid lines) and \u00b510- (dashed lines) triggered events,\nin the same pT slices of the J/\u03c8 candidate as in Figure 18. The simulated data sample is unpo-\nlarised. Statistics correspond to 10 pb\u22121.\nresults are presented in Table 6, with constant C rescaled to the measured cross-section \u03c3, corresponding\nto the integrated luminosity of 10 pb\u22121.\nTo further check our ability to measure the spin alignment of J/\u03c8 , the raw distributions shown in\nFigure 19 were reweighted to emulate transversely polarised (\u03b1gen = +1) and longitudinally polarised\n(\u03b1gen = \u22121) J/\u03c8 samples, and the analysis described above was repeated. The results are shown in\nFigure 21 and in the middle two sections of Table 6.\nA similar analysis can be done for measuring the polarisation and cross-section of \u03d2 , but at the\nintegrated luminosity of 10 pb\u22121 these measurements are expected to be far less precise than in J/\u03c8\ncase. The main reasons are lower \u03d2 cross-sections at high transverse momenta, and higher backgrounds\nfor the \u00b510 sample. The latter reason, as explained in Section 3.4, means that with these statistics the\n\u00b510 sample is essentially unusable, and the limited acceptance of the \u00b56\u00b54 sample at high |cos\u03b8 \u2217|\nmakes a precise measurement dif\ufb01cult.\nThe corrected |cos\u03b8 \u2217| distributions for unpolarised \u03d2 from the \u00b56\u00b54 sample are shown in Fig-\nure 22. The results of the \ufb01t using Equation 2, with normalisation matched to the integrated luminosity\nof 10 pb\u22121, are shown in the last section of Table 6. With the integrated luminosity increased by an\norder of magnitude, the \u00b510 sample should become useful and the estimated errors on \u03d2 polarisation\nmeasurement could be reduced by a factor of 5.\nThe errors shown in Figures 20 \u201422 and Table 6 include the statistical uncertainties on the measured\nnumbers of events as well as various systematic errors stemming from the uncertainties on acceptances\nand ef\ufb01ciencies described above.\nThe overall uncertainty on the integrated luminosity needs to be added to all measured cross-sections,\nand is expected to be rather large during the initial LHC runs. This uncertainty will not, however, affect\nthe relative magnitudes of the cross-sections measured in separate pT slices, or the measured values of\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1102\n\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n20\n40\n60\n3\n10\n\u00d7\nATLAS\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n2\n4\n6\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n2\n4\n6\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n1\n2\n3\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.5\n1\n1.5\n2\n2.5\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.5\n1\n1.5\n3\n10\n\u00d7\nFigure 20: Combined and corrected distributions in J/\u03c8 polarisation angle cos\u03b8 \u2217, for the same\npT slices as in Figure 18. The data sample is unpolarised (\u03b1gen = 0). The lines show the results of\nthe \ufb01t using Equation 2, where the \ufb01tted values of \u03b1 are given in Table 6. Statistics correspond to\n10 pb\u22121.\nSample\npT, GeV\n9\u221212\n12\u221213\n13\u221215\n15\u221217\n17\u221221\n> 21\nJ/\u03c8 , \u03b1gen = 0\n\u03b1\n0.156\n\u22120.006\n0.004\n\u22120.003\n\u22120.039\n0.019\n\u00b10.166\n\u00b10.032\n\u00b10.029\n\u00b10.037\n\u00b10.038\n\u00b10.057\n\u03c3, nb\n87.45\n9.85\n11.02\n5.29\n4.15\n2.52\n\u00b14.35\n\u00b10.09\n\u00b10.09\n\u00b10.05\n\u00b10.04\n\u00b10.04\nJ/\u03c8 , \u03b1gen = +1\n\u03b1\n1.268\n0.998\n1.008\n0.9964\n0.9320\n1.0217\n\u00b10.290\n\u00b10.049\n\u00b10.044\n\u00b10.054\n\u00b10.056\n\u00b10.088\n\u03c3, nb\n117.96\n13.14\n14.71\n7.06\n5.52\n3.36\n\u00b16.51\n\u00b10.12\n\u00b10.12\n\u00b10.07\n\u00b10.05\n\u00b10.05\nJ/\u03c8 , \u03b1gen = \u22121\n\u03b1\n\u22120.978\n\u22121.003\n\u22121.000\n\u22121.001\n\u22121.007\n\u22120.996\n\u00b10.027\n\u00b10.010\n\u00b10.010\n\u00b10.013\n\u00b10.014\n\u00b10.018\n\u03c3, nb\n56.74\n6.58\n7.34\n3.53\n2.78\n1.68\n\u00b12.58\n\u00b10.06\n\u00b10.06\n\u00b10.04\n\u00b10.03\n\u00b10.02\n\u03d2, \u03b1gen = 0\n\u03b1\n\u22120.42\n\u22120.38\n\u22120.20\n0.08\n\u22120.15\n0.47\n\u00b10.17\n\u00b10.22\n\u00b10.20\n\u00b10.22\n\u00b10.18\n\u00b10.22\n\u03c3, nb\n2.523\n0.444\n0.584\n0.330\n0.329\n0.284\n\u00b10.127\n\u00b10.027\n\u00b10.029\n\u00b10.016\n\u00b10.015\n\u00b10.012\nTable 6: J/\u03c8 and \u03d2 polarisation and cross-sections measured in slices of pT, for 10 pb\u22121.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1103\n\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n20\n40\n60\n80\n3\n10\n\u00d7\nATLAS\nATLAS\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n2\n4\n6\n8\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n2\n4\n6\n8\n10\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n1\n2\n3\n4\n5\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n1\n2\n3\n4\n3\n10\n\u00d7\n*\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/bin\n0\n0.5\n1\n1.5\n2\n2.5\n3\n10\n\u00d7\nFigure 21: Combined and corrected distributions in polarisation angle cos\u03b8 \u2217, for longitudinally\n(\u03b1gen = \u22121, dotted lines) and transversely (\u03b1gen = 1, dashed lines) polarised J/\u03c8 mesons, in the\nsame pT slices as in Figure 18. The lines show the results of the \ufb01t using Equation 2, where the\n\ufb01tted values of \u03b1 are given in Table 6. Statistics correspond to 10 pb\u22121.\nthe polarisation coef\ufb01cient \u03b1. Additional systematic effects have also been studied, such as the in\ufb02uence\nof \ufb01nite resolution in pT and cos\u03b8 \u2217, changes in binning, details of the functions used for \ufb01tting the\ninvariant mass distributions, and variations of cuts used for background suppression. Their respective\nuncertainties on the measured values of \u03b1 and \u03c3 have been found not to exceed a small fraction of the\nquoted errors, and have thus been deemed negligible.\nIn conclusion, with the integrated luminosity of 10 pb\u22121 it should be possible to measure the polari-\nsation of J/\u03c8 with the precision of order 0.02 \u22120.06, depending on the level of polarisation itself, in a\nwide range of transverse momenta, pT \u224310\u221220 GeV and beyond. In case of \u03d2, the expected precision\nis somewhat lower, of order 0.20. In both cases, however, the pT dependence of the cross-section should\nbe measured reasonably well.\n5\nAnalysis of \u03c7 production\nQuarkonium states with even C parity, such as \u03b7c,b and \u03c7c,b, have a strong coupling to the colour-singlet\ntwo-gluon state, and hence a signi\ufb01cantly higher production cross-section than vector quarkonia. Their\ndominant production mechanism for the phase space area accessible in ATLAS is via the subprocess\nshown in Figure 2(b) in Section 1. Their detection, however, is rather more dif\ufb01cult due to the absence\nof purely leptonic decays.\nAbout 30 to 40% of J/\u03c8 and \u03d2 are expected to come from decays \u03c7c \u2192J/\u03c8\u03b3 and \u03c7b \u2192\u03d2\u03b3. Un-\nfortunately, the energies of the radiated photons tend to be quite small. The ability of ATLAS to detect\nthese photons and resolve various \u03c7 states is analysed in Section 5.1. Another possibility of observing \u03c7b\nand possibly \u03b7b states is considered in Section 5.2, where the reconstruction of these states is attempted\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1104\n\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n3\n10\n\u00d7\nATLAS\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n50\n100\n150\n200\n250\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n50\n100\n150\n200\n250\n*\n\u03b8\ncos\n-1 -0.8-0.6-0.4-0.2 -0 0.2 0.4 0.6 0.8\n1\nEvents/bin\n0\n50\n100\n150\n200\n250\nFigure 22: Corrected distributions in polarisation angle cos\u03b8 \u2217, for unpolarised \u03d2 mesons, in\nthe same slices of \u03d2 transverse momentum as in Figure 18. Only \u00b56\u00b54 sample has been used.\nStatistics correspond to 10 pb\u22121.\nthrough their decay into a pair of J/\u03c8 , both of which subsequently decay into \u00b5 +\u00b5\u2212.\n5.1\nRadiative decays of \u03c7c,\u03c7b states\nReconstructing \u03c7c candidates requires associating a reconstructed J/\u03c8 with the photon emitted from the\n\u03c7c decay. The transverse momentum distribution for all identi\ufb01ed photon candidates in events with a\nprompt J/\u03c8 , as measured by the ATLAS electromagnetic calorimeter, is shown in Figure 23(a) (light\ngrey histogram).\nFor \u03c7c reconstruction, each selected quarkonium candidate is combined with every reconstructed\nand identi\ufb01ed photon candidate in the event, and the invariant mass of the \u00b5\u00b5\u03b3 system is calculated. No\nexplicit cut is applied to the pT of the photon. The \u00b5\u00b5\u03b3 system is considered to be a \u03c7 candidate, if the\ndifference \u2206M between the invariant masses of the \u00b5\u00b5\u03b3 and \u00b5\u00b5 systems lies between 200 and 700 MeV,\nand the cosine of the opening angle \u03b1 between the J/\u03c8 and \u03b3 momenta is larger than 0.97. The last\nrequirement comes from the observation that for the correct \u00b5\u00b5\u03b3 combinations, the angle \u03b1 is usually\nvery small (see reconstructed distribution in Figure 23(b)). By analysing Monte Carlo information, it was\nfound that all photons from generated \u03c7 decays were found in the peak near cos\u03b1 = +1, with the long\ntail in the reconstructed distribution representing the combinatorial background. The transverse energy\ndistribution for those photon candidates which satisfy the above requirements is presented in Figure 23(a)\nby the dark histogram. With these cuts, the combinatorial background is strongly reduced.\nFigure 24 shows the distribution in \u2206M for the selected \u03c7c decay candidates. The expected mean\npositions of the peaks corresponding to \u03c70, \u03c71 and \u03c72 signals (318, 412 and 460 MeV, respectively) are\nindicated by arrows. The grey histogram shows the contribution from the background process of J/\u03c8\nproduction from B-hadron decays, some of which survive the pseudo-proper time cut.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1105\n\n (GeV)\n\u03b3\nT\n p\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nEvents\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n3\n10\n\u00d7\nATLAS\n(a)\n\u03b1\ncos\n0.8 0.82 0.84 0.86 0 88 0.9 0 92 0.94 0 96 0.98\n1\nEvents\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n3\n10\n\u00d7\nATLAS\n(b)\nFigure 23: (a) Transverse momentum distribution of photons reconstructed in prompt J/\u03c8 events.\n(b) Distribution of cos\u03b1 for each reconstructed \u03b3 in an event. On both plots, the light grey (dark\ngrey) histograms show the distributions before (after) the cut on the opening angle \u03b1 between the\nphoton and the J/\u03c8 momentum direction. All photons from \u03c7 \u2192J/\u03c8\u03b3 decays have cos\u03b1 > 0.97,\nwhile the vast majority of background combinations fall outside the range shown in plot (b). The\nsample corresponds to the integrated luminosity of 6 pb\u22121.\nThe solid line in Figure 24 is the result of a simultaneous \ufb01t to the measured distribution, with the\nthree peak positions \ufb01xed at their expected values, and the common resolution function \u03c3(\u2206M). The\nresolution in \u03c3(\u2206M) is expected to increase with increasing \u2206M, and was empirically parameterised\nas \u03c3(\u2206M) = a \u00b7 \u2206M + b. The dashed lines show the shapes of individual peaks and of the background\ncontinuum. The \ufb01t parameters are the heights of the three gaussian peaks h0,h1,h2, the constants a\nand b, and the three parameters describing the smooth polynomial background. The systematic studies\ninclude the variation of the background parameterisation and the introduction of a mass shift common\nfor the three resonances. The true amplitudes of the peaks (15, 123 and 87, respectively) are reproduced\nreasonably well:\nh0\n=\n15\u00b13(stat.)\u00b110(syst.),\nh1\n=\n101\u00b14(stat.)\u00b112(syst.),\n(4)\nh2\n=\n103\u00b14(stat.)\u00b19(syst.),\nwith a strong negative correlation between the last two. The resolution is found to increase from about\n35 MeV at \u03c70 to about 48 MeV at \u03c72, while the overall reconstruction ef\ufb01ciency of \u03c7c states is estimated\nto be about 4%. It may be possible to signi\ufb01cantly improve the resolution by using photon conversions,\nbut this is unlikely to yield a big increase in ef\ufb01ciency.\nThe procedure of reconstructing \u03c7b decays into \u03d2+\u03b3 is the same as in the charmonium case, except\nthe di-muon pair is required to be an \u03d2 candidate. However, the higher di-muon mass and hence smaller\nexpected boost makes the photon much softer and hence more dif\ufb01cult to detect. With the available\nsimulated statistics (50 000 events corresponding to 10 pb\u22121), only 20 \u03c7b candidates have been found in\nthe appropriate mass window, which gives an ef\ufb01ciency estimate of 0.03%. In order to reliably observe\n\u03c7b \u2192\u03d2+\u03b3 decays, an integrated luminosity of at least 1 fb\u22121 will be needed.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1106\n\nM (MeV)\n\u2206\n100\n200\n300\n400\n500\n600\n700\n800\n900\nEvents/bin\n0\n50\n100\n150\n200\n250\nM (MeV)\n\u2206\n100\n200\n300\n400\n500\n600\n700\n800\n900\nEvents/bin\n0\n50\n100\n150\n200\n250\nATLAS\nFigure 24: Difference in invariant masses of \u00b5\u00b5\u03b3 and \u00b5\u00b5 systems in prompt J/\u03c8 events (light\ngrey) with bb \u2192\u00b56\u00b54X background surviving cuts (dark grey). The arrows represent the true\nsignal peak positions, and the lines show the results of the \ufb01t described in the text. Event yields\ncorrespond to an integrated luminosity of 10 pb\u22121.\n5.2\nAnalysis of \u03c7b \u2192J/\u03c8J/\u03c8\nAnother possibility for measuring \u03c7b production is through the decay \u03c7b \u2192J/\u03c8J/\u03c8 \u2192\u00b5\u00b5\u00b5\u00b5. The use\nof this decay for \u03c7b detection was proposed in [16], while in [17] the corresponding branching fraction\nwas calculated to be Br(\u03c7b0 \u2192J/\u03c8 J/\u03c8) = 2\u00d710\u22124.\nThe predicted total inclusive cross-section of \u03c7b0 production at LHC is estimated at around 1.5 \u00b5b\n[17], yielding the following theoretical estimate (without any momentum cuts on muons):\n\u03c3(pp \u2192\u03c7b0 +X)Br(\u03c7b0 \u2192J/\u03c8 J/\u03c8) = 330pb\n(5)\nWe use this cross-section in our study. It should, however, be considered as a lower bound, with higher\norder QCD corrections expected to increase it signi\ufb01cantly, especially within the COM approach. This\ncross-section also does not include other C-even states (\u03b7b,\u03c7b2 and radial excitations), meaning that the\noverall combined cross-section of resonant J/\u03c8 J/\u03c8 production in the \u03d2 mass region can be at least an\norder of magnitude higher.\nThe PYTHIA Monte Carlo generator, used to simulate this process, was modi\ufb01ed to include this\nparticular decay. Events for this study are triggered with a di-muon trigger \u00b56\u00b54, as for the J/\u03c8 and\n\u03d2 di-muon analysis. Out of 50 000 generated \u03c7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) events 815, or 1.6%, passed\nthe \u00b56\u00b54 trigger cuts. Taking into account di-muon branching fractions of the two J/\u03c8 mesons, this\ncorresponds to the cross-section \u03c3 = 20 fb after trigger.\nThe two triggered muons have the highest pT of the four. The two remaining muons, in many cases,\nhave transverse momenta too low to be identi\ufb01ed as muons (i.e. below 2.5 GeV), and sometimes too low\nto be even reconstructed (below 0.5 GeV).\nTwo classes of events, remaining after the trigger cuts, have been considered to be useful:\na) events where the two trigger muons came from the same J/\u03c8 . Then, the third muon has to be\nidenti\ufb01ed by the muon system, while the fourth must at least be reconstructed as a track (124\nevents);\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1107\n\nb) events where each trigger muon came from a different J/\u03c8 . The remaining two muons may or\nmay not be identi\ufb01ed, but their tracks still need to be reconstructed (330 events).\nThus, taking the trigger, muon identi\ufb01cation and track reconstruction ef\ufb01ciencies into account, one ex-\npects about 50% of triggered \u03c7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) decays to be observed, which amounts to 0.8%\nof the generated sample, corresponding to the cross-section of 10 fb. Hence, the observed statistics is\nexpected to be around 100 events for the integrated luminosity 10 fb\u22121.\nOnce the two J/\u03c8 candidates in the event have been reconstructed, a simultaneous \ufb01t of the four\nmuon tracks to the common vertex is performed, with J/\u03c8 mass constraints applied to the respective di-\nmuon invariant masses. The resulting distribution is presented in Figure 25(a). The resolution on the \u03c7b\nMass [GeV]\n9\n9 2\n9.4\n9.6\n9 8\n10\n10.2\n10.4\n10.6\n10.8\nEvents\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n = 1 MeV\n\u039c\n\u2206\n = 39 MeV\n\u03c3\nATLAS \n(a)\nLow mass\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nHigh mass\n1 5\n2\n2 5\n3\n3 5\n4\n4 5\n5\nATLAS \n(b)\nFigure 25: (a) Reconstructed \u03c7b invariant mass, with J/\u03c8 mass constraints applied on the respec-\ntive di-muon pair masses. (b) Higher di-muon invariant mass plotted versus the lower di-muon\ninvariant mass in \u03c7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) events.\nmass is estimated to be as good as 40 MeV. Similar resolution should be expected for the reconstructed\ninvariant mass in the decays of other \u03c7bJ states, while the resolution for \u03b7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) should\nbe slightly better.\nWith two pairs of muons in each signal event, there are two possible pairings of oppositely charged\nmuons. The plot of the invariant mass of one di-muon pair versus the invariant mass of the other is shown\nin Figure 25(b), using generator-level information. All correct pairings, and none of the incorrect pairings\nof di-muons fall within the circle of radius 200 MeV (about 3-4 \u03c3) from the point with coordinates\nMJ/\u03c8,MJ/\u03c8. The incorrect pairings are scattered over the whole area, so by selecting the pairings from\nthe circle de\ufb01ned above, the combinatorial background can be strongly reduced.\nThe main expected sources of background to \u03c7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) decays are the processes of\nbottom quark production, pp \u2192bbX, with each b either decaying into J/\u03c8 + X, or into a muon with\nadditional charged tracks. These backgrounds have been analysed with the same Monte Carlo samples\nused in our study of backgrounds for single J/\u03c8 and \u03d2 production. Within the available statistics, very\nfew background events have survived the signal selection cuts described above, and the background sup-\npression cuts on pseudo-proper time on secondary vertices. Extrapolating these results to the integrated\nluminosity of 10 fb\u22121 shows that the statistically signi\ufb01cant \u03c7b \u2192J/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) signal peak (or\npeaks) should be visible on top of the combinatorial continuum, with the expected signal-to-background\nratio of 10-20% or above.\nIn short, so far we have seen no major obstacles in an attempt to search for narrow resonances in the\nJ/\u03c8(\u00b5\u00b5)J/\u03c8(\u00b5\u00b5) invariant mass distributions. However, dedicated high statistics Monte Carlo samples\nare needed to draw more reliable conclusions.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1108\n\n6\nPhysics reach with early data\nDuring the initial run of the LHC, the integrated luminosity of 1 pb\u22121 with the \u00b56\u00b54 trigger would mean\nabout 15 000 J/\u03c8 \u2192\u00b5\u00b5 and 2 500 \u03d2\u2192\u00b5\u00b5 recorded events. If the \u00b54\u00b54 trigger is used, these numbers\nwould increase up to 17 000 and 20 000 respectively, with these additional events mainly concentrated at\nthe lower end of the quarkonium transverse momenta.\nAdditional, largely independent statistics will be provided by the \u00b510 trigger: 16 000 J/\u03c8 and\n2 000 \u03d2 with transverse momenta above about 10 GeV, with distributions similar to those from the\n\u00b56\u00b54 samples. Quite separate from these, another 7 000 of J/\u03c8 \u2192\u00b5\u00b5 events are expected from b-\ndecay events. All these events should be perfectly usable for detector alignment, acceptance and trigger\nef\ufb01ciency studies, as well as for understanding tracking and muon system performances.\nAt the integrated luminosity of about 10 pb\u22121 recorded numbers of J/\u03c8 \u2192\u00b5\u00b5 and \u03d2\u2192\u00b5\u00b5 will be\nroughly equal to the statistics used in this note. With these statistics, the pT dependence of the cross-\nsection for both J/\u03c8 and \u03d2 should be measured reasonably well, in a wide range of transverse momenta,\npT \u224310 \u221250 GeV. The precision of J/\u03c8 polarisation measurement can reach 0.02 \u22120.06 (depending\non the level of polarisation itself), while the expected error on \u03d2 polarisation is unlikely to be better than\nabout 0.2. At this stage, \ufb01rst attempts may be made to understand the performance of the electromagnetic\ncalorimetry at low photon energies, and to try and reconstruct \u03c7c states from their radiative decays.\nWith an integrated luminosity of 100 pb\u22121, the transverse momentum spectra are expected to reach\nabout 100 GeV and possibly beyond, for both J/\u03c8 and \u03d2 . With several million J/\u03c8 \u2192\u00b5\u00b5 and more\nthan 500 000 of \u03d2\u2192\u00b5\u00b5 decays, and a good understanding of the detector, high precision polarisation\nmeasurements, at the level of few percent, should become possible for both J/\u03c8 and \u03d2. \u03c7b \u2192\u03d2\u03b3 decays\ncould become observable, while other measurements mentioned above will become increasingly precise.\nFurther increase of the integrated luminosity should make it possible to observe the resonant produc-\ntion of J/\u03c8 meson pairs in the mass range of the \u03d2 system. During the future high luminosity running,\nthe need to keep event rates manageable will mean an increase of thresholds of relevant single- and di-\nmuon triggers, and the prescaling of lower threshold triggers. The higher luminosity will further expand\nthe range of reachable transverse momenta and allow further tests of the production mechanisms, as well\nas make \u03c7b reconstruction easier.\nReferences\n[1] See e.g. V. G. Kartvelishvili, A. K. Likhoded, S. R. Slabospitsky, Sov. J. Nucl. Phys. 28 (1978) 280;\nM. Gluck, J. F. Owens and E. Reya, Phys. Rev. D17 (1978) 2324; E. L. Berger and D. L. Jones,\nPhys. Rev. D23 (1981) 1521; V. G. Kartvelishvili, A. K. Likhoded, Sov. J. Nucl. Phys. 39 (1984)\n298; B. Humpert, Phys. Lett. B184 (1987) 105.\n[2] F. Abe et al. [CDF Collaboration], Phys. Rev. Lett. 69 (1992) 3704.\n[3] M. Kramer, Prog. Part. Nucl. Phys. 47 (2001) 141 [arXiv:hep-ph/0106120].\n[4] V. M. Abazov et al. [D\u00d8Collaboration], D\u00d8 Note 5089-conf.\n[5] G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D51 (1995) 1125 [Erratum-ibid. D55\n(1997) 5853] [arXiv:hep-ph/9407339]; E. Braaten and S. Fleming, Phys. Rev. Lett. 74 (1995) 3327\n[arXiv:hep-ph/9411365].\n[6] S. P. Baranov, Phys. Rev. D66 (2002) 114003.\n[7] A. Abulencia et al. [CDF Collaboration], Phys. Rev. Lett. 99 (2007) 132001.\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1109\n\n[8] J. P. Lansberg, J. R. Cudell and Yu. L. Kalinovsky, Phys. Lett. B633 (2006) 301 [arXiv:hep-\nph/0507060]; P. Artoisenet, J. P. Lansberg and F. Maltoni, Phys. Lett. B653 (2007) 60.\n[9] T. Sjostrand, S. Mrenna and P. Skands, PYTHIA 6.4: Physics and manual, JHEP 0605 (2006) 026\n[arXiv:hep-ph/0603175].\n[10] P. Nason et al., Bottom production, in CERN report 2000-004 [arXiv:hep-ph/0003142].\n[11] ATLAS Collaboration, Triggering on Low-pT Muons and Di-Muons for B-Physics, this volume.\n[12] F. Abe et al. [CDF Collaboration], Phys. Rev. Lett. 79 (1997) 572; D. E. Acosta et al. [CDF Col-\nlaboration], Phys. Rev. Lett. 88 (2002) 161802.\n[13] W.-M. Yao et al., Journal of Physics G33 (2006) 1.\n[14] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[15] D. E. Acosta et al. [CDF Collaboration], Phys. Rev. Lett. 96 (2006) 202001 [arXiv:hep-\nex/0508022].\n[16] V. G. Kartvelishvili and A. K. Likhoded, Yad. Fiz. 40 (1984) 1273.\n[17] V. V. Braguta, A. K. Likhoded and A. V. Luchinsky, Phys. Rev. D72 (2005) 094018 [arXiv:hep-\nph/0506009].\nB-PHYSICS \u2013 HEAVY QUARKONIUM PHYSICS WITH EARLY DATA\n1110\n\nProduction Cross-Section Measurements and Study of the\nProperties of the Exclusive B+ \u2192J/\u03c8K+ Channel\nAbstract\nIn the initial phase of the LHC operation at low luminosity several Standard\nModel physics analyses will be performed in order to validate the ATLAS\ndetector and trigger system. The B+\u2192J/\u03c8K+ channel can be observed with\nthe \ufb01rst ATLAS data at LHC and can be used for detector performance studies.\nThis channel will provide a reference in the search for rare B decays. It will\nalso be used to estimate the systematic uncertainties and ef\ufb01ciencies of \ufb02avor\ntagging algorithms, needed for CP violation measurements. The prospects to\nmeasure the B+ mass, its total and differential production cross sections and\nlifetime with the \ufb01rst ATLAS data, are described in this note.\n1\nIntroduction\nThe expected large hadronic cross-section for b-quark production and the high luminosity at the LHC\nleads to copious b-quark production, with the presence of a b\u00afb pair in about one percent of the collisions.\nQuantitatively, the expected inclusive production cross-section for pp \u2192b\u00afb + X at LHC is estimated\nto be \u03c3b\u00afb \u2248500 \u00b5b leading to more than 105 b\u00afb pairs per second at the LHC design luminosity of\nL \u22481033 cm\u22122s\u22121. However, the extrapolation of the b\u00afb cross-section measurement from the Tevatron\nenergy of 1.8\u20131.96 TeV [1, 2] to the LHC energy of 14 TeV suffers from large uncertainties. The theo-\nretical predictions are based on NLO QCD calculations with uncertainties smaller than 20 % [3] in the\nkinematical region of the LHC, originating mainly from scale uncertainties [4], as well as uncertainties\ndue to the parton density functions and the b-fragmentation.\nA precise measurement of the b\u00afb inclusive cross-section at the LHC can be used to constrain these\ntheoretical uncertainties. In addition, the large production rate allows for exclusive cross-section mea-\nsurements shortly after the LHC start up, which have different systematic uncertainties and model de-\npendencies (fragmentation models) from the inclusive ones. Furthermore, the b\u00afb represents the largest\nphysics background for many processes, therefore its measurement is a prerequisite to any discovery.\nIn this note the exclusive channel B+ \u2192J/\u03c8K+ is studied extensively and the procedure to measure\nthe differential and total cross-sections with the \ufb01rst 10 pb\u22121 is presented, with event selection based on\nthe identi\ufb01cation of the J/\u03c8 decay to two muons.\nThe exclusive B+ \u2192J/\u03c8K+ decay can be measured during the initial luminosity phase of the LHC,\nbecause of the clear event topology and rather large branching ratio. It can serve as a reference channel\nfor rare B decay searches, whose total and differential cross-sections will be measured relative to its\ncross-section, thus allowing the cancelation of common systematic uncertainties. Furthermore, it can be\nused to estimate the systematic uncertainties and ef\ufb01ciencies of \ufb02avour tagging algorithms, which are\nneeded for CP violation measurements. Finally, the relatively large statistics for this decay allow for\ninitial detector performance studies. In particular, the precise measurement of the well-known mass and\nlifetime [5] can be used for inner detector calibration and alignment studies.\nIn Section 2 of the note the Monte Carlo data sets used for this study are described. In Section 3 the\nJ/\u03c8 selection procedure is presented. The B+\u2192J/\u03c8K+ mass, cross-section and lifetime measurements\ncan be found in Section 4. The expected statistics during the early LHC luminosity phase are discussed\nin Section 5 together with estimates of the systematic uncertainties.\nAll the following studies have been done for luminosity of L = 1032 cm\u22122s\u22121. However, since pile-\nup does not play any role at this luminosity, it is straightforward to rescale the results of these studies to\nL = 1031 cm2s\u22121, in case this will be the luminosity at startup.\n1111\n\n2\nMonte Carlo Samples\nAll Monte Carlo (MC) data sets used for the studies presented in this note have been produced using\nPYTHIA-6.4 [6] without overlaying pileup events.\nProcess\nNgen\nL [pb\u22121]\nNgen(B+ \u2192J/\u03c8K+)\nbb \u2192J/\u03c8(\u00b56\u00b54)+X\n145 500\n13.2\n7 072\nTable 1: Monte Carlo data set used for the B+ study. The Ngen(B+ \u2192J/\u03c8K+) events are the ones\ncontained in the whole generated sample.\nAt the generator level, the ATLAS speci\ufb01c PYTHIA implementation for B-physics which provides an\ninterface to PYTHIA-6 [7] was used. The study of the B+ \u2192J/\u03c8K+ channel is done using the inclusive\nproduction cross-section of \u03c3(b\u00afb \u2192J/\u03c8(\u00b56\u00b54)X), where the numbers in the bracket denote the cuts\napplied on the muons from the J/\u03c8 decay in order for the generated event to be accepted (one muon\nwith pT > 6 GeV and the other with pT > 4 GeV). The cross-section at the generation level, after\nimplementing these cuts to the muons from the J/\u03c8 decay is 11.1 nb. The total number of generated\nevents and the number of the B+ \u2192J/\u03c8K+ decays found in the sample are given in Table 1. All\nef\ufb01ciencies presented in this note, are calculated relative to the generated number of events.\n3\nJ/\u03c8 Identi\ufb01cation Procedure\nA reliable identi\ufb01cation of the J/\u03c8 meson in the decay channel J/\u03c8 \u2192\u00b5 +\u00b5\u2212, as well as the recon-\nstruction of the primary and secondary vertices, are the prerequisites for the B+ \u2192J/\u03c8K+cross-section\nmeasurement. For the selection of the B+ candidates a further requirement of a positively charged track\n(K+ ) originating from the J/\u03c8 secondary vertex is imposed.\nThe distance \u20d7x between the pp interaction vertex and the secondary vertex of the B-decay in the\ntransverse plane is used for the J/\u03c8 identi\ufb01cation. In the ATLAS Inner Detector TDR [8], the deter-\nmination of the position of the primary vertex on an event-by-event basis was demonstrated, and for the\nB+ \u2192J/\u03c8K+ decay, a vertex resolution of \u03c3x = 29 \u00b5m and \u03c3y = 27 \u00b5m was estimated. For up-to-date\ninformation on the average primary vertex resolution with the staged ATLAS detector see [9].\nThe vector \u20d7x =\u20d7xprim \u2212\u20d7xB from the primary vertex \u20d7xprim to the secondary B-decay vertex \u20d7xB in the\nplane normal to the incoming proton beam [10] is used to de\ufb01ne the transverse decay length Lxy, which\nis actually the projection of\u20d7x onto the direction of the transverse momentum of the B meson:\nLxy = \u20d7x\u00b7 \u20d7pT\n|pT| .\n(1)\nThe transverse decay length Lxy is a signed variable, which is negative if the particle appears to decay\nbefore the secondary vertex of its production and positive otherwise. For a zero lifetime sample, a\nGaussian distribution peaked at Lxy = 0 is expected. For exclusive decays, the proper decay length is\ngiven by:\n\u03bb = Lxy \u00b7 mB\npB\nT\n.\n(2)\nFor the uncertainty of the transverse decay length Lxy, only the contribution arising from the uncertainties\non the primary and secondary vertex coordinates are taken into account:\n\u03c3 2\nLxy =\n1\n(pB\nT)2 \u00b7\n\u0010\n\u03c3 2\nx (pB\nx )2 +2\u03c3 2\nxypB\nx pB\ny +\u03c3 2\ny (pB\ny )2 +\u03c3 2\nx1(pB\nx )2 +\u03c3 2\ny1(pB\ny )2\u0011\n,\n(3)\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1112\n\nwhere \u03c3x, \u03c3xy, and \u03c3y are the covariance matrix elements of the secondary vertex \ufb01t, \u03c3x1 is the resolution\nof the primary vertex in x, \u03c3y1 is the resolution of the primary vertex in y, pB\nT is the transverse momentum\nof the B+ meson and \ufb01nally px and py are the x and y components of B+ momentum.\nSince the J/\u03c8 reconstruction relies on its decay into two muons: J/\u03c8 \u2192\u00b5 +\u00b5\u2212, the \ufb01rst step in the\nevent selection procedure is the identi\ufb01cation of the decay muons, which in general have low pT .\nIf a muon track reconstructed by the muon spectrometer has an inner detector track associated to\nit, it is considered to be a muon and is used to form the J/\u03c8 candidate. An inner detector track may\nalso be declared a muon candidate and used in the J/\u03c8 mass reconstruction, if it is has hits or track\nsegments in the innermost stations of the muon spectrometer. In either case the J/\u03c8 mass is calculated\nusing the momentum of the muon candidate provided by the inner detector, in order to exploit the better\nmomentum resolution of the inner detector in this pT\nregion. The main J/\u03c8\nselection cuts are as\nfollows:\n\u2022 All possible di-muons with pT,1 \u22653.0 GeV and pT,2 \u22656.0 GeV are formed;\n\u2022 The tracks of each muon pair are then \ufb01tted to a common vertex;\n\u2022 From the vertices found, only the ones with \u03c72/ndf < 10 are retained;\n\u2022 To select J/\u03c8\nmesons originating from the decay of a B+, a cut on the proper decay length,\n\u03bb > 0.1 mm, is imposed to reduce combinatorial background from prompt J/\u03c8 . If this cut is\nnot imposed, the algorithm identi\ufb01es all possible combinations consistent with J/\u03c8 decaying to\nmuons in the event;\n\u2022 J/\u03c8 candidates inside a mass window of 120 MeV around mJ/\u03c8 are retained.\nThe ef\ufb01ciency for all previously mentioned cuts is presented in Table 2, where the ef\ufb01ciency after each\ncut is computed with respect to the previous.\nGiven that the sample used does not contain any prompt J/\u03c8 , the effect of the cut on the proper\ndecay length \u03bb in the table indicates the loss in signal events. As it is explained in the following section,\nthis cut is not applied for the lifetime measurement. The J/\u03c8 reconstruction ef\ufb01ciency is also given for\nthe case of no cut on the J/\u03c8 proper decay length \u03bb.\nThe J/\u03c8 invariant mass distribution without a cut on \u03bb is shown in Figure 1. The shape can be\ndescribed by a Gaussian with exponential tails. The J/\u03c8\nmass and its resolution, obtained from a\nGaussian \ufb01t, is 3098 MeV and 57.4 MeV respectively.\ncut\nwith \u03bb cut\nno \u03bb cut\nJ/\u03c8 cut\nNJ/\u03c8\n\u03b5J/\u03c8 [%]\nNJ/\u03c8\n\u03b5J/\u03c8 [%]\nafter vertexing\n123 489\n84.8\n123 489\n84.8\nafter vtx \u03c72 cut\n115 156\n93.3\n115 156\n93.3\nafter \u03bb cut\n84 829\n73.6\n-\n-\nafter mass cut\n81 293\n95.8\n105 827\n91.9\nTotal eff\n55.8\n72.7\nTable 2: J/\u03c8 reconstruction ef\ufb01ciencies with and without \u03bb cut.\nIn order to study the effect of misalignment, displaced magnetic \ufb01eld and incorrect material map on\nthe J/\u03c8 observed mass position and resolution, a systematic study using different ATLAS geometry\ncon\ufb01gurations was performed, with different combinations of possible misalignments of the calorimeter\nand the muon spectrometer, as well as a displaced magnetic \ufb01eld map and distorted material in the inner\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1113\n\nInvariant mass [MeV]\n2800\n2900\n3000\n3100\n3200\n3300\n3400\nEntries\n0\n200\n400\n600\n800\n1000\n1200\n1400\nFigure 1: J/\u03c8 invariant mass distribution with a Gaussian \ufb01t superimposed.\ndetector and the calorimeter. These studies were performed using a dedicated B0\ns \u2192J/\u03c8\u03c6 dataset. It\nwas found that the width of the J/\u03c8 mass \ufb01t \u03c3(mJ/\u03c8) is rather stable, varying between 51 and 59 MeV.\nThe trigger ef\ufb01ciency is about 99 % and was computed from the J/\u03c8 candidates that have at least\none muon with pT > 6 GeV in the trigger. This is expected, since at the generation level it is required\nthat both muons from the J/\u03c8 have pT > 6 GeV and pT > 4 GeV.\n4\nAnalysis of the B+ \u2192J/\u03c8K+ Channel\nThe analysis that follows for the selection of B+ events can equally well be applied for the charge con-\njugate state. Negligible direct CP violation is expected in the B\u00b1 \u2192J/\u03c8K\u00b1 because for b \u2192c + \u00afcs\ntransitions the standard model predicts that the leading and higher order diagrams are characterized by\nthe same weak phase. A measurement of the asymmetry is given in [11]. The main source of asymmetry\nis the different interaction probabilities for K+ and K\u2212with the detector material. Other non-CP-\nviolating sources of asymmetry are expected to lead to a lepton energy asymmetry and estimated to be\nnegligible [12].\n4.1\nEvent selection\nThe B+ mesons are reconstructed from a J/\u03c8 and a K+ candidate. The J/\u03c8 selection is described in\nSection 3 and the K+ candidates are identi\ufb01ed using information from the inner detector. Speci\ufb01cally,\nthe procedure comprises the following steps:\n\u2022 The original collection of tracks is scanned once again (excluding those already denoted as muons)\nand those with pT > 1.5 GeV and |\u03b7| < 2.7 are retained;\n\u2022 From this collection, the tracks with positive charge and inconsistent with coming from the primary\nvertex at one standard deviation level (|d0|/\u03c3d0 > 1, where d0 is the impact parameter of the track)\nare considered to be K+ candidates;\n\u2022 The \u00b5+\u00b5\u2212pair considered to be originating from the J/\u03c8 \u2192\u00b5+\u00b5\u2212decay and the K+ candidate\nare \ufb01tted to a common vertex. The vector de\ufb01ned by the sum of the J/\u03c8 and K+ momentum\nvectors is required to point to the primary vertex, and the two muon tracks are constrained to mJ/\u03c8;\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1114\n\n\u2022 Only combinations with vertex \u03c72/ndf < 6 , pT(\u00b5) > 5 GeV and \u03bb > 0.1 mm are retained;\n\u2022 In case that more than two B+ candidates were found in the same event, the one with the smallest\nvertex \u03c72/ndf is accepted.\nInvariant mass (MeV)\n4600\n4800\n5000\n5200\n5400\n5600\n5800\nEntries\n0\n50\n100\n150\n200\n250\n300\nFigure 2: Invariant mass M(K+\u00b5+\u00b5\u2212) distribution with the B+ mass peak for signal (red) and combina-\ntorial b\u00afb -background (blue).\n4.2\nMass \ufb01t\nThe B+ mass determination has been performed using the sample of b\u00afb \u2192J/\u03c8X decays. The B+ in-\nvariant mass distribution m(K+\u00b5+\u00b5\u2212) of the candidates ful\ufb01lling all cuts is presented in Fig. 2. In the\nsame \ufb01gure the signal and background events can be seen separately, where the distinction between them\nis made using the Monte Carlo truth information. The \ufb01t to the mass distribution is done by using the\nmaximum-likelihood method, where the probability density function is a Gaussian for the signal region\nand a linear function for the background:\nL\n=\n\u03b1 fsig +(1\u2212\u03b1)fbkg\nfsig\n=\n1\n\u221a\n2\u03c0\u03c3 e\u22121\n2 ( mi\u2212m\n\u03c3\n)2 ,\n(4)\nfbkg\n=\nb(mi \u2212w\n2 )+ 1\nw ,\nwhere \u03b1 is the fraction of signal events in the \ufb01tted region, m the B+ mass, b is the slope of the back-\nground distribution and w de\ufb01nes the range of the \ufb01t. The mass range of the \ufb01t is taken from 5.15 GeV\nto 5.8 GeV. This is done in order to reduce contributions from partially reconstructed B meson de-\ncays that populate the left side of Fig. 2. The background at the right of the mass peak originates from\nmisidenti\ufb01ed \u03c0+ from B+ \u2192J/\u03c8\u03c0+ decays.\nThe result of the B+ mass \ufb01t is: M(B+) = (5279.3 \u00b1 1.1) MeV with a width of \u03c3(B+) = (42.2 \u00b1\n1.3) MeV. The relative errors scaled properly for an integrated luminosity of 10 pb\u22121 are about 0.02%\nand 3.5% respectively. The corresponding \ufb01t is presented in Fig. 3. The slight shoulder to the left of the\nmass distribution is due to the background shape.\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1115\n\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nmean = 5279.3 +/- 1.1 MeV\nsigma = 42.2 +/- 1.3 Mev\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nFigure 3: B+ mass \ufb01t with the both signal (red) and background (blue) contributions shown separately.\n4.3\nDifferential and total production cross-section\nThe feasibility of the measurement of the B+ \u2192J/\u03c8K+ total and differential production cross-sections\nat LHC, with the \ufb01rst 10 pb\u22121, is explored in this section. The dataset used is the b\u00afb \u2192J/\u03c8X and\nthe reconstructed B+ \u2192J/\u03c8K+ candidates were selected based on the event selection described in Sec-\ntion 4.1. The B+ mass \ufb01t method described previously was then used to extract the ef\ufb01ciencies in bins of\npT as well as the total ef\ufb01ciency.\nThe differential cross-section d\u03c3/d pT can be obtained from:\nd\u03c3(B+)\nd pT\n=\nNsig\n\u2206pT \u00b7L \u00b7A \u00b7BR\n(5)\nwhere Nsig is the number of reconstructed B+ mesons obtained from the mass \ufb01t. The size of the pT\nbin is denoted with \u2206pT. Furthermore, L is the total luminosity and A the overall ef\ufb01ciency. The\nbranching ratio BR is the product of the world average [5] branching ratios of BR(B+ \u2192J/\u03c8K+) =\n(10.0\u00b11.0)\u00d710\u22124 and BR(J/\u03c8 \u2192\u00b5+\u00b5\u2212) = (5.88\u00b10.10)\u00d710\u22122. The invariant mass spectra of the\nB+ candidates are \ufb01tted in each pT\nrange using an extended unbinned maximum likelihood \ufb01t. The\nprobability density function is a Gaussian for the signal and a linear function for the background region:\nL = Nsig\nNtotal\n\u00b7 fsig + Ntotal \u2212Nsig\nNtotal\n\u00b7 fbkg\n(6)\nwhere fsig and fbkg are the \ufb01t functions as described in Equation 4. For this \ufb01t, the B+ mass has been\n\ufb01xed to the value obtained from the mass \ufb01t in the previous Section 4.2, m = 5279.3 MeV. The results\nfor the overall ef\ufb01ciencies and the mass widths of the \ufb01ts, for the individual pT bins, are summarized in\nTable 3. The mass \ufb01ts in the various pT regions are presented in Figure 4 whereas the \ufb01t over the full\npT range is shown in Fig. 3.\nTo measure the B+ total cross-section a similar procedure to the one used for the calculation of the\ndifferential cross-section is followed, but in this case all B+ with pT > 10 GeV are used to calculate the\ntotal ef\ufb01ciency A . The B+ mass distribution is shown in Fig. 3. The results of the total ef\ufb01ciency and\nthe mass width from the \ufb01t, for the B+ total cross-section measurement, are presented in Table 4.\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1116\n\npT range [GeV]\npT \u2208[10,18]\npT \u2208[18,26]\npT \u2208[26,34]\npT \u2208[34,42]\nA [%]\n20.1\u00b11.0\n37.3\u00b11.7\n45.0\u00b13.1\n51.6\u00b14.7\n\u03c3(B+) [ MeV]\n38.5\u00b12.0\n42.3\u00b12.1\n46.1\u00b13.2\n46.6\u00b14.0\nTable 3: Ef\ufb01ciency A and B+ mass width \u03c3(B+) for the various pT bins.\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n10\n20\n30\n40\n50\n60\n70\nnbkg = 310 +/- 29\nnsig = 710 +/- 36\nsigma = 38.5 +/- 2.0 Mev\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n10\n20\n30\n40\n50\n60\n70\n(a) 10 \u2264pT < 18 GeV\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n10\n20\n30\n40\n50\n60\n70\nnbkg = 183 +/- 26\nnsig = 779 +/- 36\nsigma = 42.3 +/- 2.1 Mev\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n10\n20\n30\n40\n50\n60\n70\n(b) 18 \u2264pT < 26 GeV\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n5\n10\n15\n20\n25\n30\nnbkg = 51 +/- 16\nnsig = 335 +/- 23\nsigma = 46.1 +/- 3.2 Mev\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n5\n10\n15\n20\n25\n30\n(c) 26 \u2264pT < 34 GeV\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\nnbkg = 27.2 +/- 9.8\nnsig = 165 +/- 15\nsigma = 46.6 +/- 4.0 Mev\nB+ mass (MeV)\n5200\n5300\n5400\n5500\n5600\n5700\n5800\nEvents / ( 6.5 MeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\n(d) 34 \u2264pT < 42 GeV\nFigure 4: Fit of the B+ mass in various pT\nranges: pT \u2208[10,18] GeV (a), pT \u2208[18,26] GeV (b),\npT \u2208[26,34] GeV (c), pT \u2208[34,42] GeV (d).\ntotal cross-section\nA [%]\n29.8\u00b10.8\n\u03c3(B+) [ MeV]\n42.2\u00b11.3\nTable 4: Overall ef\ufb01ciency and B+ mass width for all B+ with pT > 10 GeV.\n4.4\nLifetime measurement\nThe measurement of the lifetime \u03c4 of the selected B+ candidates is a sensitive tool to con\ufb01rm the beauty\ncontents in a sample, in particular the number of the reconstructed B+ \u2192J/\u03c8K+ decays obtained in the\nb\u00afb \u2192J/\u03c8X dataset. The proper decay time is de\ufb01ned as t = \u03bb/c. For this analysis, no cut on the proper\ndecay length \u03bb (Equation 2) of the J/\u03c8 candidate or the B+ candidate should be applied.\nThe proper decay time distribution in the signal region B+ \u2192J/\u03c8K+ can be parametrised as a convo-\nlution of an exponential function with a Gaussian resolution function, while the background distribution\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1117\n\nparametrisation consists of two different exponential functions, where each is convoluted with a Gaus-\nsian resolution function. In the b\u00afb \u2192J/\u03c8X no additional zero lifetime events are expected because there\nare no prompt J/\u03c8 produced. In the realistic case, where zero lifetime events will be present, an extra\nGaussian centered at zero is needed in order to properly describe those events. With the model used here,\nthe Gaussian resolution functions depend on the reconstructed uncertainties on an event-by-event basis.\nIn addition, it is assumed, that the distribution of the uncertainties per event are different for the signal\nand the corresponding background probability density functions (pdf) [13]. The use of conditional pdfs\nwas required in order to take into account the proper decay time error per event. The exponential part of\nthe lifetime distribution has the usual form:\nFt(t) = e\n\u2212t\n\u03c4 ,\n(7)\nwhere t is the proper decay time and \u03c4 is the lifetime. Accordingly, the convoluted function is then\nFc(t) = e\n\u2212t\n\u03c4 \u2297G(t,\u00b5,s\u00b7\u03c3i),\n(8)\nwhere \u00b5 is the mean value of the Gaussian resolution function which parametrises the average bias in\neach proper decay time measurement. The scale factor of the error is s and \u03c3i is the per event proper\ndecay time error. The conditional pdf on the per event uncertainty is then:\nFt(t) = Fc(t|\u03c3i)\u00b7P(\u03c3i),\n(9)\nwhere P(\u03c3i) is the distribution of the proper decay time error. The distribution of the proper decay time\nuncertainty is approximated by a superposition of Gaussian functions. In order to separate between the\nsignal and the background, the proper decay time pdf is multiplied with the B+ mass pdf, described in\nSection 4.2. A two-dimensional \ufb01t to the B+ proper decay time and B+ mass is then performed.\nThe results of the lifetime \ufb01t are presented in Table 5 and shown in Figure 5. The background can\nbe best described with the two lifetime components (\u03c41 and \u03c42) which are also shown in Table 5. For\nthe events in the mass region of the signal within M(B+) \u2208[5.15,5.8] GeV the proper decay time found\nfrom the decay length is compared to the generated B+ lifetime. The result of the comparison is shown\nin Fig. 5. The differences are well centered at zero with a Gaussian distribution and sigma 0.088 ps. It\nshould be noted that the resolution as well as its \u03c3 in \u03b7 bins of 0.25 is found to be independent of \u03b7.\nB+ proper time (ns)\n0\n0.002 0.004 0 006 0 008\n0 01\n0 012 0.014\nEvents / ( 0.000155 ns )\n1\n10\n2\n10\nB+ proper time (ns)\n0\n0.002 0.004 0 006 0 008\n0 01\n0 012 0.014\nEvents / ( 0.000155 ns )\n1\n10\n2\n10\nEntries \n 2802\nConstant \n 122\nMean -2.508e-06\nSigma \n 8.75e-05\nLifetime resolution (nsec)\n0.5\n0.4\n0.3\n0.2\n0.1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n-\n10\n\u00d7\nEntries\n0\n20\n40\n60\n80\n100\n120\n140\n160\nEntries \n 2802\nConstant \n 122\nMean -2.508e-06\nSigma \n 8.75e-05\nFigure 5: B+ lifetime \ufb01t (left) with the signal (dashed red) and the background (dashed black) contribu-\ntions shown separately and B+ lifetime resolution (right).\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1118\n\nSignal lifetime \u03c4 [ps]\n1.637\u00b10.036\nBG lifetime \u03c41 [ps]\n1.320\u00b10.24\nBG lifetime \u03c42 [ps]\n0.370\u00b10.067\nTable 5: Results for the lifetime \ufb01t.\n5\nStatistical and Systematic Uncertainties\nFrom the analysis presented above, the expected number of reconstructed B+ candidates amounts to 160\nper pb\u22121 . This implies that suf\ufb01cient statistics can be collected for a reliable cross-section measurement,\nafter just a few months of data taking at the initial low luminosity phase of the LHC. This scenario is valid\nfor a luminosity less than L = 1032 cm\u22122s\u22121, since the analysis was performed without pileup events\nand contains no special trigger requirements or prescaling other than a single muon with p\u00b5\nT > 6 GeV at\nlevel-1.\nFor the measurements presented in this note the main sources of systematic uncertainties are the\nsame. The uncertainty from the luminosity in the initial phase is estimated to be 10 % and will be\nreduced to about 6.5 % after 0.3 fb\u22121 of data. The uncertainty from the PDF\u2019s is estimated to be 3 %,\nwhile the scale uncertainty of the NLO calculations is about 5 %. Finally, the uncertainty originating\nfrom the muon identi\ufb01cation is about 3 %. Assuming Gaussian distributions for the above mentioned\nuncertainties, the total systematic uncertainty of the signal varies from 9.2 % to 12 % and is dominated\nby the uncertainty in the luminosity.\nGiven that a statistical precision of O(1 %) will be reached with an integrated luminosity of 0.1 fb\u22121,\nthe contribution of the systematics will dominate the uncertainties of the \ufb01rst measurements. This is\nthe case even for the differential cross-section measurement. Although the statistics in each pT\nbin\nis limited, the total uncertainty is dominated by the systematic uncertainties in the branching ratio of\nthe B+ \u2192J/\u03c8K+ and in the luminosity, which are of the same order. For the exclusive cross-section\nmeasurement in the B+\u2192J/\u03c8K+ channel, the relative uncertainties of the differential and total cross-\nsections are given in Table 6. Therein, the \ufb01rst row of the table contains the quadratic sum of the\nstatistical uncertainty corresponding to an integrated luminosity of 0.01 fb\u22121 and the uncertainty in the\nef\ufb01ciency. The latter is based on the statistics of the Monte Carlo dataset used. The second row is\ncalculated by adding in quadrature the above uncertainty to the systematic uncertainty of the luminosity\nand the branching ratio for every pT bin.\nFor the high statistics pT\nbins as well as for the total cross-section, the total relative uncertainty\nis dominated by systematic errors, originating mainly from the uncertainty in the luminosity, which is\nassumed to be 10 % for the initial phase, and the 10 % uncertainty in the branching ratio of B+ \u2192J/\u03c8K+.\nThe effect of the assumed background shape on the measurements is estimated to be less than 1 %.\nFinally, the precision of the lifetime measurement, for the same integrated luminosity is 2.5 %, where no\nsystematic effects are taken into account.\npT range [GeV]\npT \u2208[10,18]\npT \u2208[18,26]\npT \u2208[26,34]\npT \u2208[34,42]\npT \u2208[10,inf)\nstat.+A [%]\n7.7\n6.9\n10.5\n13.9\n4.3\ntotal [%]\n16.1\n15.8\n17.6\n19.8\n14.8\nTable 6: Statistical and total uncertainties for the B+ \u2192J/\u03c8K+ differential and total cross-section mea-\nsurements for an integrated luminosity of 0.01 fb\u22121. Total uncertainties include luminosity and BR\nsystematic uncertainties.\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1119\n\n6\nSummary and Conclusions\nIn this note, the B+\u2192J/\u03c8K+ channel using an inclusive b\u00afb\u2192J/\u03c8(\u00b56\u00b54)X dataset has been studied by\ndeveloping the J/\u03c8 selection methods and understanding their ef\ufb01ciencies. A method for measuring\nthe B+ mass using a likelihood \ufb01t, in order to separate signal and background, is established. The B+\nselection ef\ufb01ciency A , both in pT bins and in the whole pT region, needed for the calculation of the\ndifferential and total cross-sections from real data, is extracted with \ufb01t methods similar to those used in\nthe B+ mass measurement case. Finally a likelihood \ufb01t, which takes into account the per-event primary\nvertex error, is performed for the measurement of the B+ lifetime.\nThe total B+\u2192J/\u03c8K+ production cross-section can be measured with a statistical precision better\nthan 5% with the \ufb01rst 10pb\u22121 of data. The differential cross-section with precision of the order of 10%.\nWith the same statistics, adequate detector performance studies can be realised using the B+ mass and\nlifetime measurements.\nReferences\n[1] F. Acosta et al., (CDF Collab.), Phys. Ref. D 71 (2005) 032001.\n[2] S. Abbott et al., (D0 Collab.), Phys. Lett. B 487 (2000) 264.\n[3] S. Alekhin et al., HERA and the LHC, Workshop Proceedings, Part B., CERN-2005-014, DESY-\nPROC-2005-01.\n[4] S.P. Baranov and M. Smizanska, CERN-ATL-PHYS-98-133.\n[5] W. -M. Yao et al, J. of Phys. G 33 (2006) 1.\n[6] T. Sjostrand, S. Mrenna and P. Skands, JHEP 0605 (2006) 026.\n[7] M. Smizanska,PythiaB an interface to Pythia6 dedicated to simulation of beauty events,ATL-COM-\nPHYS-2003-038, (2003).\n[8] The ATLAS Collaboration, ATLAS Inner Detector Technical Design Report, /CERN/LHCC/97-16,\n(30 April 1997).\n[9] The ATLAS Collaboration, The Expected Performance of the Inner Detector, this volume.\n[10] F. Abe et al, Phys. Rev. D 55 (1998) 5382.\n[11] B. Aubert et al, (BABAR Collab.), Phys. Rev. D 65 (2005) 091191.\n[12] C. Schmidt and M. Peskin, Phys. Rev. Lett. 69 (1992) 410.\n[13] G. Punzi, arXiv:physics/0401045v1 [physics.data-an], (2004).\nB-PHYSICS \u2013 PRODUCTION CROSS-SECTION MEASUREMENTS AND STUDY OF THE . . .\n1120\n\nPhysics and Detector Performance Measurements with the\nDecays B0\ns \u2192J/\u03c8\u03c6 and B0\nd \u2192J/\u03c8K0\u2217with Early Data\nAbstract\nThe decay processes B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6 are expected to be ob-\nserved in large numbers with the ATLAS experiment. During the early data\ntaking period, with an integrated luminosity of around \u223c10\u2212150 pb\u22121, it will\nbe possible to measure the masses and proper lifetimes for these decays with\nsuf\ufb01cient precision to allow them to be used for detector performance checks.\nMethods for the determination of the mass and lifetime when the performance\nof the detector and reconstruction software will not be fully understood are\npresented. A powerful simultaneous \ufb01tting technique is used. Understanding\nthe potential for \ufb02avour tagging methods will be one of the important goals\nfor B-physics with early data. The performance of the jet charge tagger for the\nself-calibrating decay, B0\nd \u2192J/\u03c8K0\u2217, is presented. The implications for the\njet charge tag in the B0\ns \u2192J/\u03c8\u03c6 decay are also discussed.\n1\nIntroduction\nThe decay B0\ns \u2192J/\u03c8\u03c6 is one of the most promising channels at the LHC due to its rich physics potential.\nThis will begin with the earliest data taken by ATLAS. Due to the high b\u00afb cross-section [1] and dedicated\nJ/\u03c8 trigger in ATLAS [2], large statistics data will be quickly accumulated. This will allow the channel\nto be used for basic measurements of the B mass and lifetime, which will provide a sensitive test of the\nunderstanding of the tracking system after only 150 pb\u22121 of data. After collecting only 1 fb\u22121 of data,\nATLAS will begin to improve world precisions for these measurements. A similar analysis will also be\nperformed for the channel B0\nd \u2192J/\u03c8K0\u2217, where the expected statistics are higher by about a factor of\n15.\nThe analysis methods to be used will evolve with increasing statistics and understanding of the detec-\ntor and backgrounds. This paper concentrates on the early phase of data taking. More advanced studies\nof the angular dependence of the decays and CP violation are not covered. In the very early data tak-\ning period, the low statistics will not allow an investigation of the full list of theoretical parameters, but\nrather will concentrate on the mass and lifetime. As the backgrounds will not be well understood either,\nno hard cuts will be made to reject them, but rather backgrounds topologically similar to the signal will\nbe admitted. This will also reduce the dependence on reconstruction algorithms and trigger behaviour,\nneither of which will be thoroughly tested when ATLAS starts to take data. In particular, no secondary\nvertex displacement cuts will be applied, and the dominant background admitted will be from direct J/\u03c8\nproduction.\nThe simulation of the decays and their backgrounds is described in Section 2, and the reconstruction\nof the events in Section 3. The methods developed to extract the B hadron mass and lifetime as well as the\nprecision expected to be reached with early data are described in Section 4. A study of the possibilities\nfor \ufb02avour-tagging with early data, an important initial step for the CP violation measurements to be\ndone later, is presented in Section 5.\n2\nMonte Carlo production\nTable 1 lists the Monte Carlo data samples used in this study. The beauty events were generated by\nPYTHIA 6.4 [3] using a method described in [4]. For the direct J/\u03c8 decays a special tuning of the\n1121\n\nColour Octet Model was prepared within PYTHIA [5]. In order to make the simulation studies more\nef\ufb01cient the initial cuts on the transverse momentum, pT, and the pseudorapidity, \u03b7, were applied at the\ngenerator level. To ensure that most of the generated events passed the trigger at the reconstruction stage,\nonly events containing decays of J/\u03c8 into dimuons, with pT larger than 6 GeV and 4 GeV, both detected\nwithin |\u03b7| < 2.4, were retained for detector simulations.\nTable 1: Monte Carlo samples used in this study. Cross sections are given by PYTHIA after applying\ncuts |\u03b7| < 2.4 and pT larger than 6 GeV and 4 GeV for the \ufb01rst and second muons from J/\u03c8 .\nProcess\nMC Statistics\nCross section\nb\u00afb \u2192J/\u03c8X\n150 000\n11.1 nb\npp \u2192J/\u03c8X\n150 000\n21.7 nb\nB0\ns \u2192J/\u03c8\u03c6\n50 000\n0.02 nb\nB0\nd \u2192J/\u03c8K0\u2217\n30 000\n0.24 nb\n3\nAnalysis of the decays B0\ns \u2192J/\u03c8\u03c6 and B0\nd \u2192J/\u03c8K0\u2217\n3.1\nStrategy for analysis of early data\nThe strategies deployed during the early period of the experiment will differ from those used later. In\nparticular, the low statistics available will not allow a determination of the complete list of physics\nvariables that can in principle be determined from the B0\ns \u2192J/\u03c8\u03c6 and B0\nd \u2192J/\u03c8K0\u2217decays [6]. During\nthe early phase, the compositions of the backgrounds will not be well understood. Furthermore, at\nthis time, the detector and reconstruction software performance will also not be fully understood, and\nrestrictive selection cuts to remove backgrounds may bias the signal in an uncontrolled way. The strategy\nin these early stages will therefore be to use loose cuts, which will admit more of the background decays.\nIn particular, omitting vertex selections allows a statistically meaningful contribution from prompt J/\u03c8\nevents. Most of these events fall outside the signal region of the study, and allow a better determination\nof the vertex resolution, which in turn allows a better overall B lifetime determination. This approach\nis consistent with the B trigger strategy for early data where no cut on secondary vertex displacement is\nrequired.\n3.2\nReconstruction\nMonte Carlo events of signal and background processes, as described in Table 1, were passed through\nfull detector simulation and reconstruction. Trigger algorithms were applied during the reconstruction.\nOnly events accepted by the J/\u03c8 \u2192\u00b5+\u00b5\u2212trigger [2] (with thresholds of pT > 6 GeV and pT > 4 GeV\nfor the fastest and second fastest muon) were retained for of\ufb02ine analysis. The reconstructed data objects\nwere then processed as follows.\nJ/\u03c8 \u2192\u00b5+\u00b5\u2212candidates were sought by forming all possible pairs of oppositely charged muon\ntracks passing the cuts pT > 4 GeV and |\u03b7| < 2.4. Pairs containing at least one muon track with pT >\n6 GeV were \ufb01tted to a common vertex. Pairs were assumed to be muons from J/\u03c8 decays if the vertex\n\ufb01t resulted in a \ufb01t \u03c72/n.d.f < 6 and the invariant mass of the muon pair fell within a 3 \u03c3 window around\nthe nominal J/\u03c8 mass, with \u03c3 = 58 MeV. This window was chosen by \ufb01tting a Gaussian distribution\nto the invariant mass of the muon pairs in the events pp \u2192J/\u03c8X and bb \u2192\u00b5 +\u00b5\u2212X, see Figure 1. The\nbackground from non resonant \u00b5+\u00b5\u2212pairs in the 3 \u03c3 window is 10%.\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1122\n\nEntries \n 80274\nMean \n 3087\nRMS \n 101.7\n / ndf \n2\n\u03c7\n 76.36 / -3\nConstant \n 11.2\n\u00b1\n 771.8 \nMean \n 0.7\n\u00b1\n 3099 \nSigma \n 0.72\n\u00b1\n 57.97 \nMass (MeV)\n2800\n2900\n3000\n3100\n3200\n3300\n3400\n0\n100\n200\n300\n400\n500\n600\n700\n800\nEntries \n 80274\nMean \n 3087\nRMS \n 101.7\n / ndf \n2\n\u03c7\n 76.36 / -3\nConstant \n 11.2\n\u00b1\n 771.8 \nMean \n 0.7\n\u00b1\n 3099 \nSigma \n 0.72\n\u00b1\n 57.97 \n Mass (MeV)\n970\n980\n990 1000 1010 1020 1030 1040 1050 1060 1070\n0\n20\n40\n60\n80\n100\n120\n140\n160\n Mass (MeV)\n600\n700\n800\n900\n1000\n1100\n0\n100\n200\n300\n400\n500\nFigure 1: Reconstructed invariant mass distributions of J/\u03c8 \u2192\u00b5+\u00b5\u2212(left), \u03c6 \u2192K+K\u2212(middle) and\nK0\u2217\u2192K\u00b1\u03c0\u2213(right) candidates.\nThe \u03c6 \u2192K+K\u2212candidates were reconstructed from all pairs of oppositely charged tracks, not iden-\nti\ufb01ed as muons, with pT > 0.5 GeV and |\u03b7| < 2.5, which were \ufb01tted to a common vertex. These tracks\nwere assumed to be kaons from \u03c6 decays if the vertex \ufb01t resulted in a \u03c7 2/n.d.f < 6, and the invari-\nant mass of the track pairs (under the assumption that they were left by kaons) fell within the interval\n1009.2\u22121029.6 MeV. This interval is based on a \ufb01t to the invariant mass distribution of the reconstructed\n\u03c6 \u2192K+K\u2212decay candidates shown in Figure 1. The signal \ufb01t used a Breit-Wigner correctly accounting\nfor phase space convoluted with a Gaussian to represent the detector resolution. The background was\napproximated by a linear function. (Additional terms up to quadratic have no signi\ufb01cant in\ufb02uence on the\n\ufb01t.)\nThe K0\u2217\u2192K\u00b1\u03c0\u2213candidates were reconstructed by selecting all tracks that had pT > 0.5 GeV and\n|\u03b7| < 2.5 that had not been previously identi\ufb01ed as muons, forming them into oppositely charged pairs\nand \ufb01tting them to a common vertex. These pairs were assumed to be K\u00b1\u03c0\u2213from K0\u2217decays if the \ufb01t\nresulted in a \u03c72/n.d.f < 6, the transverse momentum of the K0\u2217candidate was greater than 3 GeV, and\nthe invariant mass of the track pair fell within the interval 790-990 MeV, under the assumption that they\nwere left by K\u00b1\u03c0\u2213hadrons. In Figure 1, the signal has been \ufb01tted to a Breit-Wigner function convoluted\nwith a Gaussian and the background has been \ufb01tted to a second degree polynomial function.\nTo \ufb01nd the B0\nd \u2192J/\u03c8K0\u2217candidates, the tracks from each combination of J/\u03c8 \u2192\u00b5+\u00b5\u2212and K0\u2217\u2192\nK\u00b1\u03c0\u2213candidates were \ufb01tted to a common point. The two muon tracks were constrained to the PDG\nJ/\u03c8 mass. These quadruplets of tracks were assumed to be from B0\nd \u2192J/\u03c8K0\u2217decays if the transverse\nmomentum of the B0\nd candidate was greater than 10 GeV and the \ufb01t resulted in a \u03c72/n.d.f < 6. In the\ncase of more than one candidate per event, the candidate with the lowest \u03c7 2/n.d.f was retained.\nB0\ns \u2192J/\u03c8\u03c6 candidates were sought by \ufb01tting the tracks from each combination of J/\u03c8 \u2192\u00b5 +\u00b5\u2212\nand \u03c6 \u2192K+K\u2212candidates \ufb01tted to a common vertex. The two muon tracks were constrained to the PDG\nJ/\u03c8 mass. These quadruplets of tracks were assumed to be from B0\ns \u2192J/\u03c8\u03c6 decays if the transverse\nmomentum of the B0\ns candidate was greater than 10 GeV and the \ufb01t resulted in a \u03c72/n.d.f < 6. If there\nwas more than one candidate per event then the candidate with the lowest \u03c7 2/n.d.f was chosen.\nAccepted B0\ns and B0\nd candidates contain a negligible background from non-resonant \u00b5 +\u00b5\u2212pairs,\n0.1% and 0.2% respectively, and therefore the background from non-resonant bb \u2192\u00b5 +\u00b5\u2212X events are\nnot considered in this analysis.\nEvents were accepted in a wide invariant mass window of \u00b112 \u00b7 \u03c3 around B hadron mass, where\nthe mass resolution \u03c3 was determined from recontruction of the B0\nd and B0\ns masses for the two signal\nchannels. The mass resolutions were obtained from \ufb01tting a single Gaussian to the Monte Carlo signal.\nTable 2 shows the number of events that can be expected using the above procedure for an integrated\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1123\n\nTable 2: Signal and background statistics of B0\ns and B0\nd candidates expected with 10 pb\u22121.\nSelected candidates\nexpected with 10 pb\u22121\nSignal B0\nd \u2192J/\u03c8K0\u2217\n1024\npp \u2192J/\u03c8X background\n1419\nb\u00afb \u2192J/\u03c8X background\n3970\nSignal B0\ns \u2192J/\u03c8\u03c6\n76\npp \u2192J/\u03c8X background\n2449\nb\u00afb \u2192J/\u03c8X background\n1660\nAll events satifying B0\nd or B0\ns selections\n10323\nluminosity of 10 pb\u22121.\nBy the time the LHC reaches a luminosity of 1033 cm\u22122 s\u22121 and the detector is better understood,\nit will be safe to apply displaced secondary vertex cuts, which will remove most of the backgrounds.\nIn the studies of exclusive channels of B decays, vertex displacement selections are replaced by cuts on\nthe B hadron decay time. This method avoids any bias on the proper decay time measurements. Table\n3 shows the reconstruction ef\ufb01ciences with and without decay time cuts. In particular, by requiring that\nthe proper decay time of the B0\ns candidate is greater than 0.5 ps, additional rejection by a factor of 260\nfor the pp \u2192J/\u03c8X can be achieved while losing 25% of the signal.\nTable 3: B0\nd \u2192J/\u03c8K0\u2217(B0\ns \u2192J/\u03c8\u03c6) signal and background reconstruction ef\ufb01ciencies before and after\nthe cut on B0\nd (B0\ns) decay time t. The applied cut was t > 0.5 ps.\nef\ufb01ciency [%]\nbefore time cut\nafter time cut\nSignal B0\nd \u2192J/\u03c8K0\u2217\n42.0\n30.4\npp \u2192J/\u03c8X background\n0.67\n0.0064\nb\u00afb \u2192J/\u03c8X background\n3.05\n1.52\nSignal B0\ns \u2192J/\u03c8\u03c6\n40.5\n30.0\npp \u2192J/\u03c8X background\n1.5\n0.0058\nb\u00afb \u2192J/\u03c8X background\n1.1\n0.8\n4\nSimultaneous \ufb01t of mass and lifetime of B0\nd and B0\ns with early data\nWe now turn to methods for extracting physically interesting parameters from the decays of the B0\ns and\nB0\nd mesons. The \ufb01rst measurements with early data will comprise the mean lifetimes and masses of these\nmesons.\nWe perform a simultaneous maximum likelihood \ufb01t for each B0\ns and B0\nd mass and proper decay time\ndistributions. The likelihood function L is de\ufb01ned by:\nL =\nN\n\u220f\ni=1\n\u0014nsig\nN \u00d7 psig(ti,mi)+ nbck1\nN\n\u00d7pbkg1(ti,mi)+ N \u2212nsig \u2212nbck1\nN\n\u00d7pbkg2(ti,mi)\n\u0015\n(1)\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1124\n\nwhere the index i runs over the events, N = nsig +nbck1 +nbck2 is the total number of reconstructed events\nin the \ufb01t and nsig, nbck1 and nbck2 are the numbers of signal and background events. The terms psig, pbkg1\nand pbkg2 are products of two probability density functions that model the mass m and proper decay time\nt of the signal and the prompt and non-prompt backgrounds respectively (see Section 2). The number of\nexpected events for the prompt background is nbck1 and the corresponding probability density function\nin formula 1 is pbkg1. The probability density function for the non-prompt background is pbkg2.\nFor the signal, the mass distribution is modeled by a Gaussian distribution, whose mean value is the\nB hadron mass m(B) and its width \u03c3m is given by the detector mass resolution. Both m(B) and \u03c3m are\ndetermined from the \ufb01t. The reconstructed proper decay time distribution for the signal is parameterised\nby the function:\npsig(ti) =\nR \u221e\n0 e\u2212\u0393t\u03c1(t \u2212ti)dt\nR \u221e\n\u2212\u221e(\nR \u221e\n0 e\u2212\u0393t\u03c1(t \u2212t\u2032)dt)dt\u2032\n(2)\nwhere the decay time resolution function \u03c1(t \u2212ti) was approximated by a Gaussian of width \u03c3 which is\na free parameter of the \ufb01t.\nFor the background, the mass distribution of the prompt component is assumed to follow a \ufb02at dis-\ntribution as observed in simulated data (see Figure 2). The non-prompt component is modeled with a\nsecond order polynomial function where the coef\ufb01cient of the linear (quadratic) terms, denoted as c1 (c2)\nin Table 4, are determined from the \ufb01t.\nThe decay time distribution of the prompt background component is parametrised by a Gaussian of\nwidth \u03c3. The non-prompt component was modeled by the sum of two exponential functions, convoluted\nwith the decay time resolution function \u03c1. The two exponential functions are denoted as \u03931 and \u03932, the\nconstant coef\ufb01cient between them is b1.\npbck2(ti) =\nR \u221e\n0\n\u0000\u03931e\u2212\u03931t +b1 \u00d7\u03932e\u2212\u03932t\u0001\n\u03c1(t \u2212ti)dt\nR \u221e\n\u2212\u221e(\nR \u221e\n0 (\u03931e\u2212\u03931t +b1 \u00d7\u03932e\u2212\u03932t)\u03c1(t \u2212t\u2032)dt)dt\u2032\n(3)\n4.1\nB0\nd \u2192J/\u03c8K0\u2217decay\nThe likelihood function, \u22122lnL is minimised to extract the B0\nd lifetime \u03c4 = 1/\u0393 and mass m(B) from the\nreconstructed events containing a B0\nd \u2192J/\u03c8K0\u2217candidates and backgrounds. This \ufb01t corresponds to an\nintegrated luminosity of 10 pb\u22121. The distributions of the reconstructed masses and lifetimes are shown\nin Figure 2. Table 4 summarises the results of the likelihood \ufb01t. The values obtained from the \ufb01t agree\nwith the input values used in the simulation (given in the \ufb01rst column) within the statistical errors of the\n\ufb01t. The average lifetime of the B0\nd can be measured with an uncertainty of 10% for 10 pb\u22121.\n4.2\nB0\ns \u2192J/\u03c8\u03c6 decay\nThe B0\ns B0s system exhibits two mass eigenstates with two lifetimes; the lifetime difference \u2206\u0393s/\u0393s is\nexpected to be O(10\u22121). However, with early data (a few hundred pb\u22121), the statistics are insuf\ufb01cient to\ndetermine both lifetimes. For the initial period of LHC running, it is assumed that \u2206\u0393s = 0. The method\nfor the B0\ns \ufb01t is the same as for the B0\nd case, the main difference being the smaller fraction of signal events,\nas shown in the mass and lifetime distributions for the reconstructed events after cuts selecting the B0\ns\nsignal (Figure 3).\nStatistics of reconstructed events corresponding to an integrated luminosity of 150 pb\u22121 enables\nmeasurements to be made with relative precisions on the B0\ns lifetime of 10% (Table 5). In the \ufb01t the\nbackground events are weighted by factor of 15, since Monte Carlo statistics were limited to the equiva-\nlent of 10 pb\u22121 for the current study.\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1125\n\nTable 4: Results of the \ufb01t to reconstructed B0\nd candidates corresponding to 10 pb\u22121. The \ufb01rst column\nshows input values used in simulation.\nParameter\nSimulated value\nFit result with statitical error\n\u0393, ps\u22121\n0.651\n0.73 \u00b1 0.07\nm(B), GeV\n5.279\n5.284 \u00b1 0.006\n\u03c3, ps\n0.132 \u00b1 0.004\n\u03c3m, GeV\n0.054 \u00b1 0.006\nnsig/N\n0.16\n0.155 \u00b1 0.015\nnbck1/N\n0.062\n0.595 \u00b1 0.017\nb1\n1.08 \u00b1 0.27\n\u03931, ps\u22121\n0.67 \u00b1 0.05\n\u03932, ps\u22121\n2.4 \u00b1 0.3\nc1\n-2.75 \u00b1 0.28\nc2\n4.7 \u00b1 1.4\n Mass (MeV)\n4900 5000 5100 5200 5300 5400 5500 5600 5700\n0\n50\n100\n150\n200\n250\n300\n350\n400\n Mass (MeV)\n4900 5000 5100 5200 5300 5400 5500 5600 5700\n0\n50\n100\n150\n200\n250\n300\n350\n400\n Decay time (ps)\n-2\n0\n2\n4\n6\n8\n10\n1\n10\n2\n10\n3\n10\n X\n\u03c8\n J/\n\u2192\nbb \n X\n\u03c8\n J/\n\u2192\npp \n0*\n K\n\u03c8\n J/\n\u2192\n \nd\nB\nFigure 2: Distributions of the reconstructed B0\nd mass and decay time expected with integrated luminosity\nof 10 pb\u22121.\n5\nThe performance of the jet charge tagger with early data\nMost studies of CP-violation and mixing require the identi\ufb01cation of the \ufb02avour of the neutral B mesons;\nthis is known as \ufb02avour tagging. Understanding the potential for \ufb02avour tagging methods will be one of\nthe important goals with early data. In studies of CP-violation and mixing of neutral B mesons, one must\nknow the \ufb02avour of a B meson both at the time of production (t = 0) and at the time of decay.\nIn a small number of cases, the \ufb02avour at production can be inferred from the charge of the highest\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1126\n\nTable 5: Results from the \ufb01t to reconstructed B0\ns candidates corresponding to 150 pb\u22121.\nInput\nFit result with statistical error\n\u0393s, ps\u22121\n0.683\n0.743 \u00b1 0.051\nm(B), GeV\n5.343\n5.359 \u00b1 0.006\n\u03c3, ps\n0.152 \u00b1 0.001\n\u03c3m, GeV\n0.061 \u00b1 0.006\nnsig/N\n0.018\n0.031 \u00b1 0.005\nnbck1/N\n0.397\n0.379 \u00b1 0.006\nb1\n0.023 \u00b1 0.01\n\u03931, ps\u22121\n1.35 \u00b1 0.02\n\u03932, ps\u22121\n0.44 \u00b1 0.08\nc1\n-1.44 \u00b1 0.07\nc2\n2.14 \u00b1 0.49\n Mass (MeV)\n5000 5100 5200 5300 5400 5500 5600 5700\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n Mass (MeV)\n5000 5100 5200 5300 5400 5500 5600 5700\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n Decay time (ps)\n-2\n0\n2\n4\n6\n8\n10\n1\n10\n2\n10\n3\n10\n4\n10\n X\n\u03c8\n J/\n\u2192\nbb \n X\n\u03c8\n J/\n\u2192\npp \n\u03c6 \n\u03c8\n J/\n\u2192\n \ns\nB\nFigure 3: Plots to show the distributions of the reconstructed B0\ns mass and decay time expected with\n150 pb\u22121. Background distributions constructed from simulated events corresponding to 10 pb\u22121 were\nscaled by a factor of 15.\npT lepton unassociated with the signal decay, with the assumption that this tagging lepton originates\nfrom a semi-leptonic decay of the other B hadron in the event. For the majority of the events, one must\nuse the jet charge tagging method. According to fragmentation models, the particles are ordered in the\nmomentum component parrallel to the original quark direction, while charge conservation also imposes\ncharge ordering [7]. These two facts may be used to form a jet charge, which is related to the b-quark\ncharge at production. The jet used in this method consists of all tracks that are unassociated with the\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1127\n\nsignal decay with pT > 500 MeV, |\u03b7| < 2.5, inside a cone of opening angle \u2206R around the B meson in\nthe laboratory frame. The opening angle of the jet cone, \u2206R, is de\ufb01ned:\n\u2206R =\np\n\u2206\u03b72 +\u2206\u03d52\n(4)\nwhere \u2206\u03b7 and \u2206\u03d5 are the differences in pseudorapidity and azimuthal angle between the cone wall and\nthe B meson. The jet charge, Qjet, tends to be positive for \u00afb-jets and negative for b-jets, thus allowing the\nB0 meson \ufb02avour at production to be inferred. The jet charge is de\ufb01ned as:\nQjet = \u2211i qip\u03ba\ni\n\u2211i |pi|\u03ba\n(5)\nwhere the qi is the charge of the ith track in the jet and pi is a measure of the tracks momentum that can\nbe, for example, the transverse momentum of the track or a projection of the track\u2019s momentum along the\naxis of the B meson\u2019s direction. These are referred to as the pT method and the pL method respectively.\nThe parameter \u03ba controls the relative contribution of the hard and soft tracks in the jet charge. One\npossible improvement in the algorithm is to remove ambiguous cases such as events with Qjet close to\nzero; the smallest allowed value of |Q jet| is called the \u201cexclusion cut\u201d. The opening angle of the jet\ncone, the exclusion cut and \u03ba are free parameters and must be tuned to get the best performance from the\ntagger.\n5.1\nQuantifying the performance of a \ufb02avour tagger\nThe effectiveness of the discrimination between B0 and B0 mesons at production time is characterized by\ntwo quantities: its ef\ufb01ciency, \u03b5tag, and the dilution, Dtag. The ef\ufb01ciency is the fraction of B mesons that\nwere tagged either correctly or incorrectly and is described by:\n\u03b5tag = Nr +Nw\nNt\n(6)\nwhere Nr and Nw are the numbers of correctly and incorrectly tagged B mesons respectively, and Nt is\nthe total number of reconstructed B mesons. The dilution, also known as the purity, is given by:\nDtag = Nr \u2212Nw\nNr +Nw\n= 1\u22122wtag\n(7)\nwhere wtag is the wrong tag fraction:\nwtag =\nNw\nNr +Nw\n(8)\nIn a typical CP violation study, where the aim is to identify a difference in some property between a\nparticle and its anti-particle, the relationship between the true asymmetry of this property, Atrue, and the\nasymmetry as measured in the data, Ameas, will be\nAtrue =\n1\nDtag\nAmeas\n(9)\nwhich is derived in, for instance, [8]. For the small asymmetries expected in the B decays, the statistical\nuncertainty on Atrue is, to a good approximation:\n\u03c3A \u2248\n1\nq\n\u03b5tagD2tagNt\n(10)\nThe tag algorithm effectiveness is indicated by the quality factor or tagging power, Qtag:\nQtag = \u03b5tagD2\ntag\n(11)\nThe quality factor is used as a measure of success when optimising the \ufb02avour tagger.\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1128\n\n5.2\nUnderstanding the jet charge tagger using B0\nd \u2192J/\u03c8K0\u2217decays\nDuring the early data taking phase, there will be too few B0\ns \u2192J/\u03c8\u03c6 decays reconstructed to allow a\ndetailed comparison between the jet charge distribution obtained from the data and that predicted by the\nMonte Carlo. However, there will be a suf\ufb01cient number of the analogous B0\nd \u2192J/\u03c8K0\u2217decays to allow\nsuch a comparison to be made. Additionally, the \ufb01nal state of the B0\nd \u2192J/\u03c8K0\u2217, with a subsequent decay\nof K0\u2217to charged mesons, allows the initial \ufb02avour to be determined in a statistical way, and therefore\nthe decay mode is considered as self-calibrating. The jet charge tagger thus produced will be important\nfor the CP violation studies with B0\nd \u2192J/\u03c8KS, and the study of B0\nd \u2192J/\u03c8K0\u2217will allow us to gain\ncon\ufb01dence in the tagging performance for B0\ns \u2192J/\u03c8\u03c6.\nFor this study, the signal decays were reconstructed as described in the Section 3 for both B0\nd \u2192\nJ/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6 decays. A reconstructed sample of 15000 decays was used for each channel,\ncorresponding to 150 pb\u22121for B0\nd \u2192J/\u03c8K0\u2217and 1.5 fb\u22121for B0\ns \u2192J/\u03c8\u03c6; this de\ufb01nes our working point\nfor the two channels in this study. The quality factor was then maximised by systematically varying the\njet charge tagger input parameters \u2206R, \u03ba and exclusion cut. It was found that optimal results for both\nB0\ns and B0\nd mesons were obtained using the projection of the track momentum in the direction of the B\nmeson (the pL method) as the measure of momentum in Equation 5. The other optimal parameters are\nshown in Table 6. Using these optimised parameters, the jet charge distribution for both B0\nd \u2192J/\u03c8K0\u2217\nand B0\ns \u2192J/\u03c8\u03c6 are shown in Figure 4.\nTable 6: The optimised parameters of the \ufb02avour tagging algorithm for both B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192\nJ/\u03c8\u03c6.\nParameter\nB0\nd \u2192J/\u03c8K0\u2217\nB0\ns \u2192J/\u03c8\u03c6\n\u03ba\n0.9\n0.8\n\u2206R cut\n0.7\n0.6\nExclusion cut\n0.05\n0.2\nJet Charge\n-1\n-0.5\n0\n0.5\n1\n1\n10\n2\n10\n3\n10\n0*\n K\n\u03c8\n J/\n\u2192\n \nd\nB\nJet Charge\n-1\n-0.5\n0\n0.5\n1\n1\n10\n2\n10\n3\n10\nCorrectly Tagged\nIncorrectly Tagged\nNot Tagged\n0*\n K\n\u03c8\n J/\n\u2192\n \nd\nB\nJet Charge\n-1\n-0.5\n0\n0.5\n1\n10\n2\n10\n3\n10\n\u03c6\n \n\u03c8\n J/\n\u2192\n \ns\nB\nJet Charge\n-1\n-0.5\n0\n0.5\n1\n10\n2\n10\n3\n10\nCorrectly Tagged\nIncorrectly Tagged\nNot Tagged\n\u03c6\n \n\u03c8\n J/\n\u2192\n \ns\nB\nFigure 4: Plots of Qjet for B0\nd \u2192J/\u03c8K0\u2217(left) and B0\ns \u2192J/\u03c8\u03c6 (right) using their optimised parameters\nof Table 6 and the equivalent luminosity of Table 7.\nOne might expect that the different \ufb02avour content in the formation of the B mesons will result in a\ndifferent jet charge behavior for B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6. This is indeed what is observed, both\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1129\n\nin the optimisation of these jet charges and their distributions. However, one should also note that both\nthe shapes and the optimised parameters, except the exclusion cut, are similar.\nThe numbers in Table 7 characterise the expected performance of the jet charge tagger. With an\nintegrated luminosty of 150 pb\u22121, it will be possible to calibrate the jet charge tagger for the B0\nd, from\nthe data, with an ef\ufb01ciency of 87.0 \u00b1 0.3% and a wrong tag fraction of 38.0 \u00b1 0.4%. Calibrating with\nreal data for the B0\ns is more challenging as there is no readily availible and clean self-tagging mode. In\nthis case, the Monte Carlo dependent calibration will be used, but the agreement of the Monte Carlo with\nreal data will be tested indirectly though the B0\nd \u2192J/\u03c8K0\u2217channel.\nTable 7: Performance of the \ufb02avour tagging algorithm for the optimised values given in Table 6. The\nerrors given in the table are statistical.\nParameter\nB0\nd \u2192J/\u03c8K0\u2217\nB0\ns \u2192J/\u03c8\u03c6\nEquivalent luminosity\n150 pb\u22121\n1.5 fb\u22121\nNumber of Reconstructed Events\n13948\n15784\nEf\ufb01ciency, \u03b5tag\n0.870\u00b10.003\n0.625\u00b10.005\nWrong Tag Fraction, wtag\n0.380\u00b10.004\n0.374\u00b10.005\nDilution, Dtag\n0.240\u00b10.009\n0.251\u00b10.010\nQuality, Qtag\n0.050\u00b10.004\n0.039\u00b10.003\n6\nSummary and conclusion\nWith the early data, the decays B0\nd \u2192J/\u03c8K0\u2217and B0\ns \u2192J/\u03c8\u03c6 can be used to measure B hadron masses\nand lifetimes with suf\ufb01cient precision to permit sensitive tests of the detector performance. In particular,\nthe B0\nd lifetime can be determined with a relative statistical error of 10%, with an integrated luminosity of\n10 pb\u22121, and the same precision will be achieved for the B0\ns lifetime with 150 pb\u22121. The proposed method\nof a simultaneous \ufb01t of background and signal events allows a sensitive determination of the masses and\ndecay times of B mesons. With early data, the optimal overall precision will be obtained with no cuts\non the secondary vertex displacement. This is appropriate for the early data when the performance of\nthe detector and reconstruction algorithms may not be well understood. This strategy is consistent with\nthat of the early B-physics triggers, where no displacement cuts on the J/\u03c8 will be applied at the trigger\nlevel.\nIn the early data taking phase, the self-tagging decay B0\nd \u2192J/\u03c8K0\u2217will be used to calibrate the\njet charge tag for jets containing a B0\nd. This will be of use for physics studies involving B0\nd decays, but\nalso this good understanding for the tagging performance for B0\nd \u2192J/\u03c8K0\u2217will allow the fragmentation\nmodelling for B0\ns \u2192J/\u03c8\u03c6 decays to be improved.\nReferences\n[1] P.Nason, et al., Bottom Production, CERN-2000-004, pp.231-304, (2000).\n[2] S.Tarem et al., Triggering on Low-pTMuons and Di-Muons for B-Physics, this volume.\n[3] T. Sjostrand , S. Mrenna, P. Skands, PYTHIA 6.4 Physics and Manual, JHEP 0605:026, (2006).\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1130\n\n[4] S.P.Baranov, M.Smizanska, J.Hrivnac, E.Kneringer, Overview of Monte Carlo simulations for AT-\nLAS B-physics, ATL-PHYS-2000-025, CERN, (2000); S.P. Baranov, M.Smizanska, Beauty Pro-\nduction Overview from Tevatron to LHC, ATL-PHYS-98-133, CERN, (1998).\n[5] V. Kartvelishvili for the ATLAS coll, B physics in ATLAS, Nucl. Phys. Proc. Suppl. 164:161-168,\n(2007).\n[6] M. Smi\u02c7zansk\u00b4a for the ATLAS collaboration, ATLAS: Helicity Analyses In Beauty Hadron Decays,\nNucl. Instrum. Meth. A446:138-142, (2000); J. Catmore for the ATLAS collaboration, LHC sensi-\ntivity to new physics in B0\ns parameters, Nucl. Phys. Proc. Suppl. 167:181-184, (2007).\n[7] R. D. Field, R. P. Feynman, A Parameterization of the properties of Quark Jets, Nucl. Phys. B 136,\n1 (1978).\n[8] CDF Collaboration, Neural Network based Jet Charge Tagger in Semileptonic Samples, CDF note\n7285, (2005); C. Lecci, A Neural Jet Charge Tagger for the Measurement of the B0\ns \u2212B0\ns Oscillation\nFrequency at CDF, Ph.D. thesis, University of Karlsruhe (TH), (2005).\n[9] ATLAS\nCollaboration,\nDetector\nand\nphysics\nperformance\nTechnical\nDesign\nReport,\nCERN/LHCC/99-14, CERN, (1999); R. W. L. Jones for ATLAS collaboration, High precision\nmeasurements of B0\ns parameters in B0\ns \u2192J/\u03c8\u03c6 decays. Nucl. Phys. Proc. Suppl. 156:147-150,\n(2006); E. Bouhova-Thacker, Feasibility study for the Measuring of the CKM Phases \u03b3 and \u03b4\u03b3\nin Decays of Neutral B-Mesons with the ATLAS Detector, Ph.D. thesis, University of Shef\ufb01eld,\n(2000).\nB-PHYSICS \u2013 PERFORMANCE MEASUREMENTS FOR B0\nd \u2192J/\u03c8K0\u2217AND B0\ns \u2192J/\u03c8\u03c6 . . .\n1131\n\nPlans for the Study of the Spin Properties of the \u039bb Baryon\nUsing the Decay Channel \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212)\nAbstract\nThis note summarizes the results of a study of the feasibility of measuring\ncertain spin properties of \u039bb baryon in the ATLAS experiment. We present an\nassessment of approaches for extracting the inclusive \u039bb polarization and the\nparity violating \u03b1\u039bb parameter for the decay \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) from\nthe reconstructed four \ufb01nal state charged particles. As a key test, we generated\nMonte Carlo samples of \u039bb events of \ufb01xed polarization in the ATLAS detector\nand evaluated our ability to precisely extract the input polarization from the\nreconstructed events. The physics motivation for the planned measurements\nin ATLAS include the search for an explanation of the anomalous spin effects\nin hyperon inclusive production observed at lower energies, tests of various\ndecay models based on HQET, tests of CP in an area not yet directly explored,\nand the development of \u039bb polarimetry as a possible tool for spin analysis in\nfuture SUSY and other studies.\n1\nIntroduction\nWe report here plans for the measurement of spin parameters of the \u039bb hyperon. We utilize the decay\nmode \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) to extract the \u039bb signal from what is expected to be a low background\nenvironment, given that the \ufb01nal state has four charged particles and a displaced secondary vertex. The\npolarization and parity violating \u03b1\u039bb parameter will be determined from the relevant angular correla-\ntions between the \ufb01nal state particles. We expect to accumulate approximately 13000 \u039bb events (and a\nsimilar number of \u039bb) with an integrated luminosity of 30 fb\u22121 . This estimation is based on the latest\nreconstruction software and trigger simulation for the ATLAS experiment.\nThe \u039bb is the lightest baryon containing a b quark, and since its discovery in 1991 by the UA1 Col-\nlaboration [1] it has created a great deal of interest. Besides the so\u2212called \u039bb lifetime puzzle [2], the\n\u039bb has been the subject of various theoretical studies ranging from proposed tests of CP violation [3],\nT violation tests and new physics studies [4], measurement of top quark spin correlation functions [5]\nand the extraction of the weak phase \u03b3 of the CKM matrix [6]. Speci\ufb01c physics interest in the \u039bb parity\nviolating \u03b1\u039bb parameter studies derives from its ability to serve as a test for various heavy quark factor-\nization models and perturbative QCD (PQCD). \u039bb studies are also of interest because of the continuing\nmystery of why hyperons have consistently displayed large polarizations when produced at energies even\nup to several hundred GeV and at large pT where most models predict zero polarization. It is not known\nif these effects can be explained by some not yet understood effect of existing physics or if they point\nto new physics altogether. \u039bb polarization holds the possibility of illuminating just how polarized b\nquarks are produced and, indeed, it may have relevance to how fermions are produced in all pp induced\nprocesses.\nInterest in the studies of the \u039bb lifetime parameter derives from the current controversy from Tevatron\nexperiments concerning the question of how much longer the b quark lives in a meson vs. in a hyperon.\nWith an expected increase of a factor of 100 in the statistics at the LHC, we expect to make a de\ufb01nitive\nstatement on this puzzle. Again, this will further constrain the theoretical models which have as their\nbasis PQCD and the Heavy Quark Model. Lifetime measurements will not be examined in this article,\nsince it is not the focus of the current study, though many of the event selection issues, discussed here,\nmight be applicable in the \u039bb lifetime studies.\n1132\n\nWe have examined the primary technical challenges in the measurement of \u039bb polarization in ATLAS\nby generating large samples of \u039bb baryons with various known polarizations, allowing them to decay in\nthe detector using model\u2212predicted amplitudes, and then reconstructing these events using standard\nATLAS packages. These samples have permitted us to test our ability to reconstruct events and to\ncon\ufb01rm that we can recover the input polarization and the decay amplitudes. They also have allowed us\nto compare various polarization extraction methods and to assess the impact of detector corrections and\ndetector resolution effects. We provide here a report on the results of these studies, and on the work we\nundertook to adapt the EVTGEN [7] decay package to produce polarized \u039bb within the ATLAS software\nframework.\n2\nTheoretical overview\nIn the quark model the \u039bb is a fermion consisting of a b quark accompanied by a di\u2212quark (ud) of\ntotal spin zero. In this model the polarization of the \u039bb is thus expected to be totally due to the b quark\npolarization. QCD calculations suggest that the b quark polarization would be small. However, there\nare models of quark scattering [8], in which spin effects are expected to scale with the mass of the\nheavy quark, and where the possibility exists for \u039bb polarizations to be quite large. We further note that\nQCD has not been able to predict the very large polarizations that have been observed in the inclusive\nproduction of \u039b hyperons at energies of several hundred GeV. It is hoped that the huge mass difference\nin the b and s quarks will help elucidate the origin of these unexplained spin effects.\nInterest in the \u03b1\u039bb parameter for the \u039bb stems from the fact that HQET models [9] purport to calculate\nthis quantity from rather basic principles of PQCD and factorization. We have an interest in comparing\nour ultimate measurements of this quantity with these predictions and assessing what constraints they can\nprovide for these models. We provide below a brief overview of the theoretical basis for the polarization\nand \u03b1\u039bb measurements.\n2.1\nHeavy quark polarization in QCD\nIn the Standard Model heavy quark production is dominated by gluon\u2212gluon fusion and q \u00afq annihilation\nprocesses. A non\u2212zero polarization requires an interference between non\u2212\ufb02ip and spin\u2212\ufb02ip helicity\namplitudes for the \u039bb production, with the latter containing an imaginary part. In QCD this complex part\ncan only be generated through loop corrections, so that the relevant diagrams for polarized quarks are\nO(\u03b14\ns ). The polarization expected from all QCD sub\u2212processes (g \u2212g fusion, q \u00afq annihilation and q\u2212\nq, q\u2212g scattering) have been calculated [10]. The formulae for the polarization for each one of the four\nprocesses is directly proportional to \u03b1s, and it depends just on the ratio xQ = mQ/pQ and the scattering\nangle \u03b8Q, (all de\ufb01ned in the center of mass frame), and are thus valid for any \ufb01nal\u2212state quark Q. The\nexpected polarization in single b quark production by gluon\u2212gluon fusion and q \u00afq annihilation has been\nfound to be a maximum of 5% for gluon\u2212gluon fusion, and a maximum 10% for q \u00afq annihilation. When\nthese predictions are compared to the observed \u039b polarization (due to the s quark polarization) [11], they\nare found to be an order of magnitude too small. One might not be surprised if the \u039bb polarization is, as\nwell, greater than predicted in QCD.\nAn important result in [10] is the dependence of the polarization on the quark mass. The heaviest\nquark produced is the most polarized, and the maximum polarization is reached around xQ \u22430.3. The b\nquark polarization is predicted to be an order of magnitude greater than the s quark polarization, which\nfrom \u039b polarization measurements has been found to reach values over 20% at 400 GeV [12].\nThe measurement of the \u039bb polarization in ATLAS in the exclusive channel \u039bb \u2192J/\u03c8\u039b proposed\nhere would cover pT(\u039bb) > 8000 MeV (because of trigger and reconstruction constraints on the trans-\nverse momentum of the \ufb01nal\u2212state particles, see Table 2) and xF(\u039bb) < 0.1. It could make a signi\ufb01cant\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1133\n\ncontribution to testing different models of production of polarized baryons in this new kinematic region.\nAn idea that the heavy quark pre\u2212exists in the incoming proton before scattering and becomes po-\nlarized through a direct scattering from an incoming quark provides another pathway for the \u039bb to be\npolarized. This possibility has been discussed by Neal and Burelo [13]. If polarizations are observed in\ninclusive \u039bb production that exceed a few percent, such a mechanism should be given careful attention,\nsince no other existing models can account for such large values.\n2.2\n\u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) decay and angular distributions\nThe proposed study of \u039bb polarization would probe not only the production process but also explore the\ndecay of \u039bb. Decay models predict values for various quantities that can be experimentally observed,\nthus providing a test of speci\ufb01c HQET/Factorization model [14] assumptions.\nFigure 1: The weak decay of \u039bb: \u039bb \u2192J/\u03c8\u039b .\nThe fact that \u039bb has a signi\ufb01cant lifetime suggests that it decays weakly. The dominant decay process\nwould involve the emission of a W \u2212boson, as illustrated in Figure 1. The spin and parity of the particles\ninvolved in the \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) decay are well known. The \u039bb with JP = 1\n2\n+ decays to \u039b with\nJP = 1\n2\n+ and J/\u03c8 with JP = 1\u2212. The general amplitudes for the decay of \u039bb( 1\n2\n+) \u2192\u039b( 1\n2\n+)J/\u03c8(1\u2212) is\ngiven by:\nM = \u039b(p\u039b) \u03b5\u2217\n\u00b5(pJ/\u03c8)\n\"\nA1 \u03b3\u00b5\u03b35 +A2\np\u00b5\n\u039bb\nm\u039bb\n\u03b35 +B1 \u03b3\u00b5 +B2\np\u00b5\n\u039bb\nm\u039bb\n#\n\u039bb(p\u039bb),\n(1)\nwhich is parameterized by the four complex decay amplitudes A1, A2, B1, B2 and where \u03b5\u00b5 is the polar-\nization vector of the J/\u03c8 .\nGiven the general amplitude, we may compute the helicity amplitudes. We use helicity amplitudes,\nbecause they have a direct physical relationship to the spin parameters we wish to study. Four helicity\namplitudes are required to describe the decay completely. We will use the notation H\u03bb\u039b,\u03bbJ/\u03c8 for the\nhelicity amplitudes of the decay \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) , where \u03bb\u039b = \u00b11/2 is the helicity of \u039b and\n\u03bbJ/\u03c8 = +1, 0, -1 is the helicity of J/\u03c8 . These four helicity amplitudes: a+ = H1/2,0, a\u2212= H\u22121/2,0,\nb+ = H\u22121/2,1, b\u2212= H1/2,\u22121 are normalized to unity:\n|a+|2 +|a\u2212|2 +|b+|2 +|b\u2212|2 = 1.\n(2)\nIn this notation, the \u039bb decay asymmetry parameter \u03b1\u039bb is given by [15]:\n\u03b1\u039bb = |a+|2 \u2212|a\u2212|2 +|b+|2 \u2212|b\u2212|2\n|a+|2 +|a\u2212|2 +|b+|2 +|b\u2212|2 .\n(3)\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1134\n\nThe helicity amplitudes a+ , a\u2212, b+ , b\u2212are computed directly from the decay amplitudes A1, A2,\nB1, B2 according to the following equations:\na+ =\n1\nmJ/\u03c8\n\u001apQ+\n\u0014\n(m\u039bb \u2212m\u039b)A1 \u2212\nQ\u2212\n2m\u039bb A2\n\u0015\n+pQ\u2212\n\u0014\n(m\u039bb +m\u039b)B1 +\nQ+\n2m\u039bb B2\n\u0015\u001b\n,\na\u2212=\n1\nmJ/\u03c8\n\u001a\n\u2212pQ+\n\u0014\n(m\u039bb \u2212m\u039b)A1 \u2212\nQ\u2212\n2m\u039bb A2\n\u0015\n+pQ\u2212\n\u0014\n(m\u039bb +m\u039b)B1 +\nQ+\n2m\u039bb B2\n\u0015\u001b\n,\nb+ =\n\u221a\n2\n\u0012pQ+ A1 \u2213pQ\u2212B1\n\u0013\n,\nb\u2212= \u2212\n\u221a\n2\n\u0012pQ+ A1 \u2213pQ\u2212B1\n\u0013\n,\n(4)\nwhere Q\u00b1 = (m\u039bb \u00b1m\u039b)2 \u2212m2\nJ/\u03c8 and m\u039bb and m\u039b are the \u039bb and \u039b masses respectively [16, 17].\nThe polarization of the \u039bb can be determined from the angular correlations between the \u039bb \u2192J/\u03c8\u039b\n\ufb01nal decay products. The \u039bb polarization reveals itself in the asymmetry of the distribution of the angle\n\u03b8. This angle is de\ufb01ned as the angle between the normal to the beauty baryon production plane and the\nmomentum vector of the \u039b decay daughter, as seen in the \u039bb rest frame. The decay angular distribution\ncan be expressed as:\nw \u223c1+\u03b1\u039bbPcos(\u03b8),\n(5)\nwhere \u03b1\u039bb is the decay asymmetry parameter of \u039bb and P is the \u039bb polarization [18].\nUsing the method described in [17], it can be shown that the full decay angular distribution is:\nw(\u20d7\u03b8,\u20d7A,P) =\n1\n(4\u03c0)3\ni=19\n\u2211\ni=0\nf1i(\u20d7A) f2i(P,\u03b1\u039b) Fi(\u20d7\u03b8)\n(6)\nwhere the f1i(\u20d7A) are bilinear combinations of the helicity amplitudes and \u20d7A = (a+,a\u2212,b+,b\u2212). f2i stands\nfor P\u03b1\u039b, P, \u03b1\u039b, or 1, where \u03b1\u039b is \u039b decay asymmetry parameter. Fi are orthogonal angular functions\nde\ufb01ned in Table 1. The \u039bb decay asymmetry parameter \u03b1\u039bb is related to the helicity amplitudes as\nde\ufb01ned in Equation 3. The \ufb01ve angles \u20d7\u03b8 = (\u03b8,\u03b81,\u03b82,\u03d51,\u03d52) (see Figure 2) in this probability density\nfunction (p.d.f.) have the following meanings:\n\u2022 \u03b8 is the angle between the normal to the production plane and the direction of the \u039b in the rest\nframe of the \u039bb particle;\n\u2022 \u03b81 and \u03c61 are the polar and azimuthal angles that de\ufb01ne the direction of the proton in the \u039b rest\nframe with respect to the direction of the \u039b in the \u039bb rest frame;\n\u2022 \u03b82 and \u03c62, de\ufb01ne the direction of \u00b5+ in the J/\u03c8 rest frame with respect to the direction of the\nJ/\u03c8 in the \u039bb rest frame.\nThere are nine unknown parameters in Equation 6. They are the polarization P and four complex\nhelicity amplitudes: a+ = |a+|ei\u03b1+, a\u2212= |a\u2212|ei\u03b1\u2212, b+ = |b+|ei\u03b2+, b\u2212= |b\u2212|ei\u03b2\u2212. Using the normalization\ncondition (see Equation 2) and using the fact that the overall global phase is arbitrary, we can reduce the\nnumber of unknown independent parameters to seven.\n3\nMonte Carlo samples\nIn order to determine if it is feasible to detect polarized \u039bb\u2019s in the ATLAS experiment and to mea-\nsure their polarization, Monte Carlo samples of polarized \u039bb particles were generated using the standard\nATLAS software packages. The generation of polarized \u039bb particles and the propagation of their polar-\nization in the decay process required a special treatment, and EVTGEN was adapted for this purpose.\nThe next sections describe how this was implemented in the framework of the ATLAS experiment.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1135\n\ni\nf1i\nf2i\nFi\n0\na+a\u2217\n+ +a\u2212a\u2217\n\u2212+b+b\u2217\n+ +b\u2212b\u2217\n\u2212\n1\n1\n1\na+a\u2217\n+ \u2212a\u2212a\u2217\n\u2212+b+b\u2217\n+ \u2212b\u2212b\u2217\n\u2212\nP\ncos\u03b8\n2\na+a\u2217\n+ \u2212a\u2212a\u2217\n\u2212\u2212b+b\u2217\n+ +b\u2212b\u2217\n\u2212\n\u03b1\u039b\ncos\u03b81\n3\na+a\u2217\n+ +a\u2212a\u2217\n\u2212\u2212b+b\u2217\n+ \u2212b\u2212b\u2217\n\u2212\nP\u03b1\u039b\ncos\u03b8 cos\u03b81\n4\n\u2212a+a\u2217\n+ \u2212a\u2212a\u2217\n\u2212+ 1\n2b+b\u2217\n+ + 1\n2b\u2212b\u2217\n\u2212\n1\n1/2(3cos2 \u03b82 \u22121)\n5\n\u2212a+a\u2217\n+ +a\u2212a\u2217\n\u2212+ 1\n2b+b\u2217\n+ \u22121\n2b\u2212b\u2217\n\u2212\nP\n1/2(3cos2 \u03b82 \u22121) cos\u03b8\n6\n\u2212a+a\u2217\n+ +a\u2212a\u2217\n\u2212\u22121\n2b+b\u2217\n+ + 1\n2b\u2212b\u2217\n\u2212\n\u03b1\u039b\n1/2(3cos2 \u03b82 \u22121) cos\u03b81\n7\n\u2212a+a\u2217\n+ \u2212a\u2212a\u2217\n\u2212\u22121\n2b+b\u2217\n+ \u22121\n2b\u2212b\u2217\n\u2212\nP,\u03b1\u039b\n1/2(3cos2 \u03b82 \u22121) cos\u03b8 cos\u03b81\n8\n\u22123Re(a+a\u2217\n\u2212)\nP,\u03b1\u039b\nsin\u03b8 sin\u03b81 sin2 \u03b82 cos\u03d51\n9\n3Im(a+a\u2217\n\u2212)\nP\u03b1\u039b\nsin\u03b8 sin\u03b81 sin2 \u03b82 sin\u03d51\n10\n\u22123\n2Re(b\u2212b\u2217\n+)\nP\u03b1\u039b\nsin\u03b8 sin\u03b81 sin2 \u03b82 cos(\u03d51 +2\u03d52)\n11\n3\n2Im(b\u2212b\u2217\n+)\nP\u03b1\u039b\nsin\u03b8 sin\u03b81 sin2 \u03b82 sin(\u03d51 +2\u03d52)\n12\n\u22123\n\u221a\n2Re(b\u2212a\u2217\n+ +a\u2212b\u2217\n+)\nP\u03b1\u039b\nsin\u03b8 cos\u03b81 sin\u03b82 cos\u03b82 cos\u03d52\n13\n3\n\u221a\n2Im(b\u2212a\u2217\n+ +a\u2212b\u2217\n+)\nP\u03b1\u039b\nsin\u03b8 cos\u03b81 sin\u03b82 cos\u03b82 sin\u03d52\n14\n\u22123\n\u221a\n2Re(b\u2212a\u2217\n\u2212+a+b\u2217\n+)\nP\u03b1\u039b\ncos\u03b8 sin\u03b81 sin\u03b82 cos\u03b82 cos(\u03d51 +\u03d52)\n15\n3\n\u221a\n2Im(b\u2212a\u2217\n\u2212+a+b\u2217\n+)\nP\u03b1\u039b\ncos\u03b8 sin\u03b81 sin\u03b82 cos\u03b82 sin(\u03d51 +\u03d52)\n16\n3\n\u221a\n2Re(a\u2212b\u2217\n+ \u2212b\u2212a\u2217\n+)\nP\nsin\u03b8 sin\u03b82 cos\u03b82 cos\u03d52\n17\n\u22123\n\u221a\n2Im(a\u2212b\u2217\n+ \u2212b\u2212a\u2217\n+)\nP\nsin\u03b8 sin\u03b82 cos\u03b82 sin\u03d52\n18\n3\n\u221a\n2Re(b\u2212a\u2217\n\u2212\u2212a+b\u2217\n+)\n\u03b1\u039b\nsin\u03b81 sin\u03b82 cos\u03b82 cos(\u03d51 +\u03d52)\n19\n\u22123\n\u221a\n2Im(b\u2212a\u2217\n\u2212\u2212a+b\u2217\n+)\n\u03b1\u039b\nsin\u03b81 sin\u03b82 cos\u03b82 sin(\u03d51 +\u03d52)\nTable 1: The coef\ufb01cients f1i, f2i and Fi of the probability density function in Equation 6.\nFigure 2: Angles describing the \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) decay.\n3.1\nThe generation of polarized \u039bb particles\nTo generate \u039bb particles, the PYTHIA 6.4 generator [19] is used. Since PYTHIA does not incorporate\npolarization information from the decay of \u039bb particles, EVTGEN was used to generate the \u039bb decay.\nEVTGEN provides a general framework for implementation of B hadron decays using spinor algebra\nand decay amplitudes. This framework permits the proper management of spin correlations of very\ncomplicated decay processes. EVTGEN is a Monte Carlo generation package itself, but in this case it is\nused only to decay the \u039bb particles produced by PYTHIA.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1136\n\n3.1.1\nRe\u2212hadronization process and cuts at PYTHIA level\nPYTHIA provides mechanisms to produce b quarks, referred to as gluon\u2212gluon fusion, q-q annihilation,\n\ufb02avor excitation, and gluon splitting. If all these processes are taken into account, beauty quark events\nwould constitute only 1% of the total number of generated events. In addition, the fraction of b quarks\nhadronizing to \u039bb is less than 10%. These make the process of \u039bb generation computationally slow. To\noptimize the generation process, a re\u2212hadronization step of the same event in the b\u00afb pairs production is\nused. In order to avoid repetition of \u039bb events due to the re-hadronization process, a \u039bb pre\u2212selection\nis implemented at this stage to \ufb01lter on average only one of the re\u2212hadronized copies of the same event.\nAn additional reason that the \u039bb generation process is slow is that around 95% of \ufb01nal state particles\n(two muons, a proton, and a pion) of the generated \u039bb events are outside of the \u03b7 limits (|\u03b7| < 2.5)\nof the ATLAS detector. In addition, all events must pass the level\u22121 trigger of the ATLAS trigger\nsystem and some pre\u2212reconstruction requirements, such as having a minimum reconstructable transverse\nmomentum. We could not apply these cuts in the PYTHIA step since the kinematics information of\nthe \u039bb children is available only at a later stage, when EVTGEN decays the \u039bb particles. However, by\nanalyzing the pT and \u03b7 distributions of \u039bb particles before and after cuts (emulating level\u22121 and level\u22122\ntriggers, and requiring |\u03b7| < 2.5) on the \ufb01nal state particles, we estimated pT and \u03b7 limits, below which\nthe \u039bb can not be selected and then applied these cuts in the PYTHIA selection. Figure 3 shows the pT\nand \u03b7 distributions from which the pT(\u039bb) > 6000 MeV and |\u03b7(\u039bb)| < 3 cuts were selected to \ufb01lter \u039bb\nparticles in PYTHIA.\n(MeV)\nT\np\n0\n10000\n20000\n30000\n40000\nEntries/800\n2\n10\n3\n10\n4\n10\nATLAS\n\u03b7\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\nEntries/0.4\n2\n10\n3\n10\nATLAS\nFigure 3: Distributions of pT (left) and \u03b7 (right) for \u039bb particles generated using PYTHIA, without\ncuts (hollow circle), applying \u03b7 cuts only (cross) and applying all cuts (solid circle) from Table 2.\n3.1.2\nSetting \u039bb polarization in EVTGEN\nTo set the polarization of \u039bb particles we used the spin density matrix description of EVTGEN. For the\ncase of spin\u22121/2 particles like \u039bb the density matrix is de\ufb01ned as:\n\u03c1 = 1\n2(I +\u20d7P\u00b7\u20d7\u03c3)\n(7)\nwhere \u20d7P is the polarization vector, and \u20d7\u03c3 = (\u03c31,\u03c32,\u03c33), where \u03c3i is i-th Pauli matrix. In our case \u20d7P is\nde\ufb01ned as:\n\u20d7P = P\n\u0012 \u02c6z\u00d7\u20d7plab(\u039bb)\n|\u02c6z\u00d7\u20d7plab(\u039bb)|\n\u0013\n(8)\nwhere P is the magnitude of the polarization, \u20d7plab is the momentum of the \u039bb in the laboratory frame,\nand \u02c6z is the z - axis (along the beam direction) in the ATLAS reference system.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1137\n\nTo decay polarized \u039bb we use the HELAMP model of EVTGEN. This model is capable of simu-\nlating a generic two body decay with arbitrary spin con\ufb01guration, taking as input the helicity amplitudes\ndescribing the process. In the case of the decay \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) , as it has been shown in the\nprevious section, there are four complex helicity amplitudes: a+, a\u2212, b+, and b\u2212.\nThe \u039b decay into a proton and a pion has been simulated with the same model, using as input\nparameters the two helicity amplitudes H\u03bb\u039b,\u03bbp de\ufb01ned in terms of the \u039b helicity \u03bb\u039b and the proton \u03bbp\nhelicity as\nh\u2212= H\u22121\n2,\u22121\n2 ,\nh+ = H+ 1\n2 ,+ 1\n2 .\n(9)\nThe choice of h\u00b1 is constrained by the experimentally well known \u039b \u2192p\u03c0\u2212asymmetry parameter [20]\n\u03b1\u039b = |h+ |2 \u2212|h\u2212|2 = 0.642\u00b10.013.\n(10)\nFinally, the decay J/\u03c8 \u2192\u00b5+\u00b5\u2212has been described with the EVTGEN VLL (Vector into Lepton Lep-\nton) model [7].\n3.1.3\nFiltering of \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) events\nAs a last step in the generation process, we apply kinematic cuts on muons, pion and proton to emulate the\n\ufb01ducial acceptance, level\u22121 trigger, and pre\u2212reconstruction requirements. These cuts are summarized\nin Table 2.\nParticles\nMinimum pT [MeV ]\nMaximum |\u03b7|\nProtons and \u03c0\u2019s\n500\n2.7\nMost energetic muon\n4000\n2.7\nOther muon\n2500\n2.7\nTable 2: Cuts applied at the particle level.\n3.2\nMonte Carlo samples and input model for \u039bb decays\nAs input to the HELAMP class of EVTGEN, the result obtained within the framework of PQCD for-\nmalism and the factorization theorem [9] has been used to model the \u039bb decay. From the complex\namplitudes calculated in this model, A1, A2, B1, B2 in Equation 1, the helicity amplitudes a+ , a\u2212, b+ ,\nb\u2212are calculated by using Equation 4. This is summarized in Table 3. In this model, the \u039bb decay\nasymmetry parameter, de\ufb01ned in Equation 3, is \u03b1\u039bb = -0.457 1.\nA1 =\u221218.676\u2212185.036i\na+ =\u22120.0176\u22120.4229i\nA2 = \u22127.461\u2212351.242i\na\u2212= 0.0867+0.2425i\nB1 = 15.818\u2212162.663i\nb+ =\u22120.0810\u22120.2837i\nB2 = \u22124.252+266.653i\nb\u2212= 0.0296+0.8124i\nTable 3: PQCD model amplitudes Ai and Bi, are given in units of 10\u221210 and helicity amplitudes a\u00b1 and\nb\u00b1 are normalized to unity.\nBy using this decay model as input, two Monte Carlo samples were generated with polarizations\nof -25% and -75%. These Monte Carlo samples were generated, simulated, and fully reconstructed by\nusing the Athena framework [21].\n1There is an ERRATA in [9] in the reported value of \u03b1\u039bb [14].\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1138\n\nTo show how the angular distributions behave, fast Monte Carlo samples (see section 3.3) were\ngenerated using an accepted\u2212rejected method based on the p.d.f. de\ufb01ned in Equation 6. Figure 4 shows\nthe distributions of the \ufb01ve angles for helicity amplitudes from Table 3 and polarizations of 40%, 0%,\n-40%.\n)\n\u03b8\ncos(\n-0.5\n0\n0.5\nEntries/0.02\n0\n5000\n10000\n15000\nPolarization = 0\nPolarization = -0.4\nPolarization = 0.4\nATLAS\n)\n1\n\u03b8\ncos(\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\nEntries/0.02\n0\n5000\n10000\n15000\nPolarization = -0.4\nATLAS\n1\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEntries/0 063\n4000\n6000\n8000\n10000\n12000\n14000\nPolariza ion = 0\nPolariza ion = -0.4\nPolarization = 0.4\nATLAS\n)\n2\n\u03b8\ncos(\n-0.5\n0\n0.5\nEntries/0.02\n0\n5000\n10000\n15000\nPolarization = -0.4\nATLAS\n2\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEntries/0.063\n2000\n4000\n6000\n8000\n10000\n12000\n14000\nPolarization = -0.4\nATLAS\nFigure 4: Distributions of the \ufb01ve angles characterizing the decay \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) for differ-\nent polarization values. For cos(\u03b81), cos(\u03b82), and \u03c62, all three distributions for the different polarization\nvalues look similar, thus only one polarization case is presented.\n3.3\nFast Monte Carlo generation\nIn order to do fast tests of different \u039bb decay models and different polarization values, we need to generate\nlarge Monte Carlo samples. This represents a problem due to the computer time required to produce a\nfull chain simulated Monte Carlo data. In order to address this problem a fast Monte Carlo generator was\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1139\n\ndeveloped. This generator uses Equation 6 to generate angular distributions for the daughters of the \u039bb\nin the \u039bb rest frame, and then uses a (p,\u03b7) distribution derived from phase space of generated events in\nPYTHIA to compute the kinematic variables of the daughter particles in the laboratory frame. Detector\neffects are incorporated by using pT and \u03b7 cuts on \ufb01nal state particles to mimic di-muon triggers and\npre\u2212reconstruction requirements. Figure 5 illustrates the strong agreement between angular distributions\nproduced by using PYTHIA and EVTGEN Monte Carlo events and fast Monte Carlo events.\n)\n\u03b8\ncos(\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nEvents/0 04\n1000\n1500\n2000\n2500\n3000\n EvtGen \n Fast MC \nATLAS\n)\n1\n\u03b8\ncos(\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nEvents/0.04\n1000\n1500\n2000\n2500\n3000\n EvtGen \n Fast MC \nATLAS\n)\n2\n\u03b8\ncos(\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0 2\n0.4\n0.6\n0.8\n1\nEvents/0.04\n1500\n2000\n2500\n3000\n3500\n EvtGen \n Fast MC \nATLAS\n1\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEvents/0.1256\n1200\n1400\n1600\n1800\n2000\n2200\n2400\n2600\n2800\n3000\n EvtGen \n Fast MC \nATLAS\n2\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEvents/0.1256\n1500\n2000\n2500\n3000\n EvtGen \nFast MC \nATLAS\nFigure 5: Comparison of Monte Carlo events (PYTHIA + EVTGEN) with fast Monte Carlo generated\nevents. Solid dots represent the Monte Carlo events.\n4\n\u039bb reconstruction\nThe reconstruction of \u039bb candidates begins with a search for events with J/\u03c8 candidates. Among these\nevents we search for \u039b \u2192p\u03c0\u2212candidates, which are then combined with the J/\u03c8 to reconstruct the \u039bb.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1140\n\n4.1\nSelection of J/\u03c8 \u2192\u00b5+\u00b5\u2212candidates\nWe search for J/\u03c8 candidates which satisfy the following selection criteria:\n\u2022 The \u00b5+\u00b5\u2212candidates must originate at the same reconstructed vertex and the \u03c7 2 of the vertex\nmust be lower than 20;\n\u2022 The invariant mass of \u00b5+\u00b5\u2212candidates M(\u00b5+\u00b5\u2212) should be within 2800 MeV and 3400 MeV.\nThe invariant mass distribution of \u00b5+\u00b5\u2212candidates before applying the invariant mass cuts to select \u039bb\nis shown in Figure 6.\n \n \n \n \n \n Invariant mass (MeV)\n2800\n3000\n3200\n3400\nEntries/8\n0\n500\n1000\n1500\n2000\n2500\n3000\n \n \n \n \n \nEntries \n 43471\n \n1\nN\n 635\n\u00b1\n 2.766e+004 \n \n1\n\u00b5\n 0.3\n\u00b1\n 3095 \n \n1\n\u03c3\n 0.63\n\u00b1\n 45.65 \n \n2\nN\n 623\n\u00b1\n 1.554e+004 \n \n2\n\u03c3\n 1.5\n\u00b1\n 102.7 \nEntries \n 43471\n \n1\nN\n 635\n\u00b1\n 2.766e+004 \n \n1\n\u00b5\n 0.3\n\u00b1\n 3095 \n \n1\n\u03c3\n 0.63\n\u00b1\n 45.65 \n \n2\nN\n 623\n\u00b1\n 1.554e+004 \n \n2\n\u03c3\n 1.5\n\u00b1\nATLAS\n 102.7 \nFigure 6: Invariant mass of \u00b5+\u00b5\u2212candidates. The dark color represents all J/\u03c8\ncandidates after\nreconstruction and vertexing requirement. The circles represents J/\u03c8\ncandidates when level\u22121 and\nlevel\u22122 trigger signature are required.\n4.2\nSelection of \u039b \u2192p\u03c0\u2212candidates\nFrom the previously selected events containing a J/\u03c8 , \u039b candidates are selected by applying the follow-\ning requirements:\n\u2022 Two opposite charged tracks originating from the same reconstructed vertex.\n\u2022 The invariant mass of two tracks M(p\u03c0\u2212) should be within 1105 MeV and 1128 MeV range, where\nfor computing M(p\u03c0\u2212), the track with the highest transverse momentum was assumed to be the\nproton, as observed in 100% of the times in Monte Carlo generations, while the other track was\nassumed to be a pion.\nMany of the \u039b particles decay outside of the high\u2212precision part of the Inner Detector, which covers\na radius of about 40 cm from the beam line, and thus are lost in reconstruction. The decay vertex position\nof \u039b\u2019s in the RZ plane is presented in Figure 8. If the \u039b decays outside the 40 cm radius, the number\nof reconstructed space points (hits in the pixel or silicon layers) is not suf\ufb01cient for a successful track\nreconstruction. This effect reduces the fraction of reconstructible \u039b to around 60%. Figure 7 presents\nthe invariant mass distribution of the p\u03c0\u2212candidates before the invariant mass cuts have been applied.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1141\n\nEntries \n 105472\n \n1\nN\n 199.7\n\u00b1\n 8665 \n \n1\n\u00b5\n 0.1\n\u00b1\n 1116 \n \n1\n\u03c3\n 0.075\n\u00b1\n 2.904 \na \n 175\n\u00b1\n -2.006e+004 \nb \n 0.16\n\u00b1\n 18.81 \nInvariant mass [MeV]\n1090\n1100\n1110\n1120\n1130\n1140\n1150\nEntries/0.65\n0\n500\n1000\n1500\n2000\n2500\nATLAS\nFigure 7: Invariant mass of p\u03c0\u2212candidates.\nZ(mm)\n-2000\n-1000\n0\n1000\n2000\nR(mm)\n0\n500\n1000\n1500\n2000\n0\n200\n400\n600\n800\n1000\n1200\nATLAS\nZ(mm)\n-2000\n-1000\n0\n1000\n2000\nR(mm)\n0\n500\n1000\n1500\n2000\n0\n50\n100\n150\n200\n250\nATLAS\nFigure 8: Decay vertex position of \u039b\u2019s in the RZ plane at the generation level (left) and after reconstruc-\ntion (right)\n.\n4.3\nSelection of \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) candidates\nA previous study [22] based on early ATLAS simulation software estimated that the number of \u039bb and\n\u039bb events which we expect to collect for the integrated luminosity of 30 fb\u22121 is 75000. Using the new\nfully reconstructed sample we made a new estimation. We used the following expression to calculate the\nnumber of events:\nN = L \u03c3(\u039bb)E ,\n(11)\nwhere L is the integrated luminosity, \u03c3(\u039bb) = 7.4 pb is the cross section of \u039bb \u2192J/\u03c8(\u00b5(pT >\n4000 MeV)\u00b5(pT > 2500 MeV))\u039b(p(pT > 500 MeV)\u03c0(pT > 500 MeV)) , see details of the calculation\nin Table 4, and E is an overall \u039bb acceptance, which includes the level\u22121 and level\u22122 acceptance for\n\u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) .\nFor selecting events with b hadrons at a luminosity below about 1033cm\u22122s\u22121, the \ufb01rst level trigger\nwill require the presence of a muon with pT > 6000 MeV within the trigger geometric acceptance of\n|\u03b7| < 2.4. The effect of the level\u22121 trigger threshold on muon pT is not a sharp cut and a fraction of\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1142\n\n\u03c3(pp \u2192\u039bbX)\n0.00828113 mb\nBR ( \u039bb \u2192J/\u03c8\u039b )\n(4.7\u00b12.8)\u00d710\u22124 [20]\nBR ( \u039b \u2192p\u03c0\u2212)\n(63.9\u00b10.5)\u00d710\u22122 [20]\nBR ( J/\u03c8 \u2192\u00b5+\u00b5\u2212)\n(5.93\u00b10.06)\u00d710\u22122 [20]\nIncluding cuts\n0.05\nOverall cross-section\n7.4 pb\nTable 4: The cross-section calculation of \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) decay.\nmuons with pT lower than 6000 MeV will be collected. Figure 9 shows the ef\ufb01ciency of the level\u22121\nsimulation with nominal pT\nthreshold of 6000 MeV as function of pT . Around 69% of events with\nJ/\u03c8 \u2192\u00b5+\u00b5\u2212, where one muon has pT\n> 4000 MeV and the second muon has pT\n> 2500 MeV,\npassed the level\u22121 trigger simulation. Therefore a signal dataset with pT less than 6000 MeV has been\nchosen to study all possible triggered events with low pT muons instead of a usual sharp 6000 MeV cut.\n [MeV]\nT\np\n5000\n10000\n15000\nEfficiency\n0\n0 2\n0.4\n0.6\n0 8\n1\nlevel 1 threshold - 6000MeV/c\nATLAS\nFigure 9: The level\u22121 trigger simulation ef\ufb01ciency as a function of muon pT , obtained from the \u039bb\nsignal sample over the whole detector volume.\nFurther selections in the high level trigger are based on the Region of Interest (RoI) identi\ufb01ed at\nlevel\u22121, as follows: a search for a second muon close to the trigger muon is used to select channels\ncontaining two \ufb01nal state muons, for example from J/\u03c8 . It is based on expanding the level\u22121 muon RoI\nto \ufb01nd a second muon which was not triggered by level\u22121. This increases the ef\ufb01ciency of the di\u2212muon\ntrigger by extending the pT acceptance for the second muon down below 6000 MeV. The size of the\nincreased RoI is based on the distribution of angular distance in \u03b7 and \u03c6 between two muons decayed\nfrom J/\u03c8 . The Inner Detector tracks which are reconstructed within these RoI, are then extrapolated to\nthe muon system to \ufb01nd the corresponding hits within the window. The Inner Detector tracks associated\nwith the muon spectrometer hits can be identi\ufb01ed as muons. The level\u22122 trigger ef\ufb01ciency is found\nto be around 78% for \u039bb \u2192J/\u03c8(\u00b5(pT > 4000 MeV)\u00b5(pT > 2500 MeV))\u039b(p(pT > 500 MeV)\u03c0(pT >\n500 MeV)) .\nWe reconstruct the \u039bb by performing a constrained \ufb01t to a common vertex for the two muon tracks\nand \u039b , with the two muon tracks constrained to the J/\u03c8 mass of 3097 MeV [20]. The reconstruction ef-\n\ufb01ciency depends on the cuts which will be applied on all Inner Detector tracks in the reconstruction stage\nto reduce the fake rate. The overall ef\ufb01ciency is found to be around 6.1% if the pT threshold is 500 MeV,\nsee Table 5. Figure 10 shows the invariant mass distribution of \u039bb candidates. Simulation of the level\u22121\ntrigger with level\u22121 pT thresholds of 6000 MeV and 4000 MeV and level\u22122 trigger, explained above,\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1143\n\nincluded in the analysis. We expect to collect around 13500 (13100) \u039bb \u2192J/\u03c8(\u00b5+\u00b5\u2212)\u039b(p\u03c0\u2212) events\nusing 4000 MeV (6000 MeV) level\u22121 muon threshold for the integrated luminosity of about 30 fb\u22121 .\nlevel\u22121 trigger:\none muon\ntwo muons\nwith pT threshold\n4 GeV\n6 GeV\n4GeV\n6GeV\nlevel\u22122 trigger:\nTrigDiMuon\nTopological trigger\nJ/\u03c8 reconstruction ef\ufb01ciency\nincluding level-1 and\n42%\n39%\n27.5%\n10%\nlevel-2 triggers\n\u039b reconstruction ef\ufb01ciency\n15%\n\u039bb overall ef\ufb01ciency\n6.1%\n5.9%\n5.4%\n3.5%\nTable 5: The overall \u039bb ef\ufb01ciency depending on the trigger strategy.\nInvariant mass [MeV]\n5200\n5400\n5600\n5800\n6000\nEntries/10\n0\n100\n200\n300\n400\n500\n600\n700\n800\nEntries \n 7237\n \n1\nN\n 219.7\n\u00b1\n 3651 \n \n1\n\u00b5\n 0.6\n\u00b1\n 5641 \n \n1\n\u03c3\n 1.19\n\u00b1\n 33.15 \n \n2\nN\n 206.6\n\u00b1\n 2453 \n \n2\n\u03c3\n 3.81\n\u00b1\n 81.51 \na \n 7.69\n\u00b1\n 83.66 \nb \n 0.00137\n\u00b1\n -0.01318 \nATLAS\nFigure 10: \u00b5+\u00b5\u2212\n\u039b invariant mass distribution. The dark color represents all \u039bb candidates after\nreconstruction and vertexing requirement, and the light color represents the case when a level\u22121 and\nlevel\u22122 trigger signature is required in addition. Filled circles represents data after all selection cuts.\nThe \ufb01t is the result of using double Gaussian and Polynomial functions.\nWe need to acknowledge that there are other inef\ufb01ciencies that will appear when we analyze the real\ndata. For example, even if the individual track reconstruction ef\ufb01ciency is as high as 98%, we will have\nan overall reduction in event rate of about 10%. Even if such reductions occur, we still expect the \ufb01nal\nsample to be suf\ufb01cient for a meaningful measurement of the \u039bb polarization.\n4.4\nAngular distributions and angular resolutions\nThe reconstruction ef\ufb01ciency modi\ufb01es the angular distributions used in the polarization determination.\nFigure 11 shows how the angular distributions change due to detector acceptance for a Monte Carlo\nsample with polarization of -75%.\nThe angular resolution of the \ufb01ve angles is presented in Figure 12. We used this angular resolution\nin the statistical uncertainty study.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1144\n\nEntries 10000\np0 \n 500.9\np1 \n 168.4\n)\n\u03b8\ncos(\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\nEntries/0.1\n0\n100\n200\n300\n400\n500\n600\n700\n800 Entries 10000\np0 \n 500.9\np1 \n 168.4\nATLAS\n)\n1\n\u03b8\ncos(\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\nEntries/0.1\n0\n200\n400\n600\n800\n1000\nATLAS\n)\n2\n\u03b8\ncos(\n-0.8\n-0.6\n-0.4\n-0 2\n-0\n0.2\n0.4\n0.6\n0.8\nEntries/0.1\n0\n200\n400\n600\n800\n1000\nATLAS\n1\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEntries/0.31\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nATLAS\n2\n\u03c6\n-3\n-2\n-1\n0\n1\n2\n3\nEntries/0.31\n0\n100\n200\n300\n400\n500\n600\n700\n800\nATLAS\nFigure 11: Comparison of fast Monte Carlo events without kinematics and detector acceptance cuts\n(open circles) and Monte Carlo events after full detector simulation and reconstruction (solid circles).\n4.5\nBackground\nDue to its production rate the main background source for our \u039bb reconstruction will be the prompt pro-\nduction and decay of J/\u03c8 \u2192\u00b5+\u00b5\u2212which are then combined with \u039b candidates in the event. However,\nthe long lifetime of the \u039bb allows us to reduce signi\ufb01cantly this kind of background by applying a life-\ntime cut. After a \u039bb lifetime cut (a cut of 200 \u00b5m on the proper transverse decay length), this background\nwas found to be negligible and it is not considered in this study.\nIn order to investigate the different contributions of long\u2212lived background particles not removed by\nthe lifetime cut mentioned above, we used a inclusive J/\u03c8 Monte Carlo sample of b\u00afb \u2192J/\u03c8X requiring\nin addition to a J/\u03c8 , a \u039b in each event (b\u00afb \u2192J/\u03c8\u039bX). This \u039b could be produced along with the J/\u03c8\nfrom a B hadron decay or just be part of the event, and the invariant mass of the J/\u03c8 + \u039b combination\nshould be within 5100 - 6100 MeV. Figure 13 shows the invariant mass distributions of \u039bb candidates\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1145\n\nEntries \n 3915\n \n1\nN\n 1285\n \n1\n\u00b5\n -8.573e-005\n 1\n\u03c3\n 0.02388\n \n2\nN\n 2432\n \n2\n\u03c3\n 0.007839\n\u03b8\n\u2206\n-0.1\n-0 05\n0\n0.05\n0.1\nEvents\n0\n100\n200\n300\n400\n500\n600\nATLAS\nEntries \n 3915\n \n1\nN\n 2321\n \n1\n\u00b5\n 0 003007\n 1\n\u03c3\n 0 03301\n \n2\nN\n 1348\n \n2\n\u03c3\n 0.09718\n1\n\u03b8\n\u2206\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\nEntries \n 3915\n \n1\nN\n 1176\n \n1\n\u00b5\n -0.0003067\n 1\n\u03c3\n 0.03276\n \n2\nN\n 2582\n \n2\n\u03c3\n 0 0136\n2\n\u03b8\n\u2206\n-0.1\n-0.05\n0\n0 05\n0.1\nEvents\n0\n50\n100\n150\n200\n250\n300\n350\n400\nATLAS\nEntries \n 3915\n \n1\nN\n 2514\n \n1\n\u00b5\n -0 001766\n 1\n\u03c3\n 0.04384\n \n2\nN\n 1022\n \n2\n\u03c3\n 0.146\n1\n\u03c6\n\u2206\n-0 5 -0.4 -0.3 -0.2 -0.1\n0\n0.1\n0.2\n0.3\n0.4\n0 5\nEvents\n0\n100\n200\n300\n400\n500\nATLAS\nEntries \n 3915\n \n1\nN\n 1621\n \n1\n\u00b5\n 4.199e-005\n 1\n\u03c3\n 0.03354\n \n2\nN\n 1942\n \n2\n\u03c3\n 0.009608\n2\n\u03c6\n\u2206\n-0.1\n-0.05\n0\n0 05\n0.1\nEvents\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nATLAS\nFigure 12: Angular resolution from fully simulated Monte Carlo data. The \ufb01t is the result of using double\nGaussian distributions.\nreconstructed in this Monte Carlo sample. The observed level of background under the \u039bb signal is of\nfew percents, and it is considerably reduced after extra cuts like the lifetime cut mentioned above. In\nFigure 13 another wider distribution due to \u039bb \u2192J/\u03c8\u03a30(\u039b\u03b3) is observed very close to our \u039bb \u2192J/\u03c8\u039b\nsignal. This is due to the branching ratios of both decays channels being the same as set by default in\nPYTHIA. This behavior has not been observed at Tevatron experiments where hundreds of \u039bb \u2192J/\u03c8\u039b\nevents are reconstructed. Therefore we expect the branching ratio of the \u039bb \u2192J/\u03c8\u03a30(\u039b\u03b3) decay to be\nconsiderably smaller than the branching ratio of the \u039bb \u2192J/\u03c8\u039b, and that the resulting background will\nbe much smaller than shown.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1146\n\n Invariant Mass (MeV)\n5000\n5200\n5400\n5600\n5800\n6000\n0\n200\n400\n600\n800\n1000\n1200\nAll\n\u039b\n + \n\u03c8\n J/\n\u2192\nb\n\u039b\n)\n\u03b3 \n\u039b\n(\n0\n\u03a3\n + \n\u03c8\n J/\n\u2192\nb\n\u039b\n\u039b\n \n\u2295\n \n\u03c8\n J/\n\u2192\nB\nATLAS\n Invariant Mass (MeV)\n5100 5200 5300 5400 5500 5600 5700 5800 5900 6000 6100\nEvents / ( 50 )\n0\n50\n100\n150\n200\n250\n Invariant Mass (MeV)\n5100 5200 5300 5400 5500 5600 5700 5800 5900 6000 6100\nEvents / ( 50 )\n0\n50\n100\n150\n200\n250\n\u039b\n \n\u03c8\n J/\n\u2192\n \nb\n\u039b\n)\n\u03b3 \n\u039b\n(\n\u03a3\n \n\u03c8\n J/\n\u2192\nb\n\u039b\nATLAS\nFigure 13: Invariant mass distribution from \u039bb candidates identi\ufb01ed in b \u2192J/\u03c8\u039bX Monte Carlo sample.\nComposition at generation level with smearing from reconstruction (left) and \ufb01t to the fully reconstructed\nevents (right) after vertexing requirement are shown.\n5\nExtracting \u039bb polarization and decay parameters\n5.1\nFitting method\n5.1.1\nLikelihood function\nTo extract polarization and decay amplitudes we performed an un\u2212binned maximum likelihood \ufb01t to the\nangular distributions. The log\u2212likelihood function L is de\ufb01ned by:\nL = \u22122\nN\n\u2211\nj=1\nlog(wobs(\u20d7\u03b8\n\u2032,\u20d7A,P)),\n(12)\nwhere\nwobs(\u20d7\u03b8\n\u2032,\u20d7A,P) =\nR w(\u20d7\u03b8\n\u2032,\u20d7A,P)T(\u20d7\u03b8,\u20d7\u03b8\n\u2032)d\u20d7\u03b8\nR R w(\u20d7\u03b8\n\u2032,\u20d7A,P)T(\u20d7\u03b8,\u20d7\u03b8\n\u2032)d\u20d7\u03b8d\u20d7\u03b8\n\u2032 .\n(13)\nw(\u20d7\u03b8\n\u2032,\u20d7A,P) is the p.d.f de\ufb01ned in Equation 6, \u20d7\u03b8\n\u2032 are the measured angles, \u20d7\u03b8 are angles without detector\neffects, and T(\u20d7\u03b8,\u20d7\u03b8\n\u2032) is de\ufb01ned as\nT(\u20d7\u03b8,\u20d7\u03b8\n\u2032) = \u03b5(\u20d7\u03b8)R(\u20d7\u03b8,\u20d7\u03b8\n\u2032),\n(14)\nwhere \u03b5(\u20d7\u03b8) is the ef\ufb01ciency function and R(\u20d7\u03b8,\u20d7\u03b8\n\u2032) is the resolution function.\nIn the ideal case the resolution function is:\nR(\u20d7\u03b8,\u20d7\u03b8\n\u2032) = \u03b4(\u20d7\u03b8 \u2212\u20d7\u03b8\n\u2032),\n(15)\nthen we have\nwobs(\u20d7\u03b8\n\u2032,\u20d7A,P) =\nw(\u20d7\u03b8\n\u2032,\u20d7A,P)\u03b5(\u20d7\u03b8\n\u2032)\n\u2211i=19\ni=0 f1i(\u20d7A)f2i(P\u03b1\u039b)Fi\n,\n(16)\nwhere Fi =\nR Fi(\u20d7\u03b8)\u03b5(\u20d7\u03b8)d\u20d7\u03b8 are the acceptance corrections values, which have to be calculated in advance\nto perform the \ufb01t.\nThe \ufb01nal log\u2212likelihood may be re\u2212written as a sum of two terms:\nL = \u22122\nN\n\u2211\nj=1\n[log(\nw(\u20d7\u03b8\n\u2032,\u20d7A,P)\n\u2211i=19\ni=0 f1i(\u20d7A)f2i(P\u03b1\u039b)Fi\n)+log(\u03b5(\u20d7\u03b8\n\u2032))].\n(17)\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1147\n\nSince the second term does not depend on the parameters we want to measure, the main challenge is to\n\ufb01nd the acceptance function.\n5.1.2\nDetector acceptance corrections\nThe acceptance corrections integral Fi =\nR Fi(\u20d7\u03b8)\u03b5(\u20d7\u03b8)d\u20d7\u03b8 can be approximated by the following form,\nusing the Monte Carlo integration techniques\nFi \u2248\n1\nNgen\nj=Nacc\n\u2211\nj=0\nFi(\u20d7\u03b8)\nG(\u20d7\u03b8)\n,\n(18)\nwhere Ngen is the number of generated events, Nacc is the number of accepted events after the simulation\nof the \ufb01ducial acceptance and pT cut and G is the p.d.f which has been used to generate the \u03b8.\nIf the generation of the events is done using certain p.d.f (w), the acceptance can be calculated by the\nsimple expression:\nFi \u2248\n1\nNgen\nj=Nacc\n\u2211\nj=0\nFi(\u20d7\u03b8)\nw(\u20d7\u03b8,\u20d7A,P)\n.\n(19)\nWe used this expression to calculate the acceptance in the case when w is the p.d.f from Equation 6.\nThis method can be used under the assumption that the acceptance does not depend on the measured\nparameters, and that the angular resolutions are close enough to the ideal resolutions. In order to check\nthe \ufb01rst assumption we plotted the ratio\nR w(\u20d7\u03b8,\u20d7A,P)\u03b5(\u20d7\u03b8,\u20d7A,P)d\u20d7\u03b8\nR w(\u20d7\u03b8,\u20d7A,P)\u03b5(\u20d7\u03b8,\u20d7A,P = 0)d\u20d7\u03b8\n(20)\nfor the different polarization values (see Figure 14). No signi\ufb01cant dependence of the acceptance on the\npolarization is observed in this test.\nPolarization\n-1\n-0 5\n0\n0.5\n1\nRatio\n0\n0.5\n1\n1.5\n2\nATLAS\nFigure 14: Ratio de\ufb01ned in Equation 20 as a function of polarization.\nThe angular resolutions are shown in Figure 12. To test the effect of these resolutions, Monte Carlo\n\ufb01ts were performed including a smearing of the data based on the Gaussian \ufb01ts in Figure 12. Fit results\nwith and without smearing are consistent within the statistical uncertainty. Figure 15 shows, as an ex-\nample, a comparison of \ufb01t results for a sample of 2000 events with polarization of -75% when \ufb01ts are\nperformed on the sample of generated Monte Carlo events.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1148\n\nOutput - Input\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n-\u03b2\n - \n+\n\u03b1\n-\u03b2\n - \n-\n\u03b1\n-\u03b2\n - \n+\n\u03b1\n|\n+\n|b\n|-\n|a\n|\n+\n|a\nPolarization\nATLAS\nFigure 15: Comparison of \ufb01t outputs from generation level Monte Carlo with and without Gaussian\nsmearing due to \ufb01nite angular resolution. Error bars are statistical uncertainties from the \ufb01t with Gaussian\nsmearing included.\n5.2\nFits to fully simulated Monte Carlo data\nIn order to extract polarization and decay parameters from the Monte Carlo data samples, \ufb01nal \u039bb se-\nlection cuts were applied. A proper transverse decay length greater than 200 \u00b5m is required to remove\ncontamination from prompt produced J/\u03c8 events. The proper transverse decay length for the \u039bb candi-\ndate is given by:\n\u03bb =\nLxy\n(\u03b2\u03b3)\u039bb\nT\n= Lxy\ncM\u039bb\npT\n,\n(21)\nwhere (\u03b2\u03b3)\u039bb\nT and M\u039bb are the transverse boost and the mass of the \u039bb, and Lxy is a transverse decay\nlength. The transverse decay length is de\ufb01ned as Lxy = Lxy \u00b7 pT/pT where Lxy is the vector that points\nfrom the primary vertex to the \u039bb decay vertex and pT is the transverse momentum vector of the \u039bb. A\nminimum pT of 500 MeV is required for any track used in the \u039bb reconstruction. In addition, a pT >\n4000 MeV is required for the muon with larger pT , and pT > 2500 MeV for the second muon. These\ncuts reduce the \u039bb sample by 21%, mainly due to the lifetime cut.\nTable 6 shows the results of performing a likelihood \ufb01t to our fully simulated Monte Carlo data, for\na sample of 2000 \u039bb events, corresponding to around 5 fb\u22121 of collected data. Figure 16 shows the\ndifference between the input values in Monte Carlo and the extracted values of polarization and decay\nparameters by the likelihood \ufb01t. We used as \ufb01tting parameters: |a+|, |a\u2212|, |b+|, \u03b1+ \u2212\u03b2\u2212, \u03b1\u2212\u2212\u03b2\u2212,\n\u03b2+ \u2212\u03b2\u2212, and the polarization P.\nDetector acceptance corrections in Equation 19 were computed separately from the two Monte Carlo\nsamples with different polarizations which are used in this study. Corrections computed in the Monte\nCarlo sample of -75% polarization were used in the \ufb01t of the Monte Carlo sample of -25% polarization,\nand vice versa. Due to the limited statistics in the Monte Carlo samples used to calculate the acceptance\ncorrections de\ufb01ned in Equation 19, a bagging (from bootstrap aggregating) technique [23] was used to\ngenerate multiple samples in order to avoid the effect of statistical \ufb02uctuations. This technique consists\nof generating replicates of a data set by selecting at random events from the original data set allowing\nrepetition of events. We generated 1000 bootstrap replicates of the fully simulated Monte Carlo data\nsample. The Fi factors (Equation 19) were computed from each generated data sample and the average\nwas taken as the value for each of the twenty Fi correction factors. Systematic uncertainty due to the\nwidth of the correction factors distributions in these 1000 generated data sets was estimated by repeating\nthe \ufb01t to fully simulated Monte Carlo using the Fi values from the each of the generated samples, and\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1149\n\nParameter\nValue \u00b1 Uncertainty\nValue \u00b1 Uncertainty\nValue\n(Polarization = -25%)\n(Polarization = -75%)\n(Input at generation level)\nPolarization\n-0.213 \u00b1 0.069\n-0.882 \u00b1 0.064\n-0.25/-0.75\n|a+|\n0.461 \u00b1 0.051\n0.413 \u00b1 0.023\n0.429\n|a\u2212|\n0.289 \u00b1 0.058\n0.161 \u00b1 0.035\n0.260\n|b+|\n0.259 \u00b1 0.071\n0.370 \u00b1 0.027\n0.295\n\u03b1+ \u2212\u03b2\u2212\n-0.991 \u00b1 0.640\n-2.050 \u00b1 0.134\n-1.612\n\u03b1\u2212\u2212\u03b2\u2212\n0.856 \u00b1 0.364\n0.681 \u00b1 0.342\n1.231\n\u03b2+ \u2212\u03b2\u2212\n-1.442 \u00b1 0.666\n-2.624 \u00b1 0.187\n-1.849\nTable 6: Fit results from fully simulated and reconstructed Monte Carlo events with input polarization of\n-25% and -75%.\nassigning the width of the distribution of \ufb01tted parameters as a systematic uncertainty. This systematic\nerror (also shown in Figure 16) can be reduced with more Monte Carlo statistics for the Fi calculation.\nOutput - Input\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n-\u03b2\n - \n+\n\u03b2\n-\u03b2\n - \n-\n\u03b1\n-\u03b2\n - \n+\n\u03b1\n|\n+\n|b\n|-\n|a\n|\n+\n|a\nPolarization\nATLAS\n-1\n5fb\nP =-25%\nOutput - Input\n-1.5\n-1\n-0.5\n0\n0.5\n-\u03b2\n - \n+\n\u03b2\n-\u03b2\n - \n-\n\u03b1\n-\u03b2\n - \n+\n\u03b1\n|\n+\n|b\n|-\n|a\n|\n+\n|a\nPolarization\nATLAS\n-1\n5fb\nP =-75%\nFigure 16: Comparison of \ufb01t results for polarization of -25% (left) and -75% (right) with respect to input\nvalues from Monte Carlo generation. The statistical and systematic uncertainties are included.\n5.3\nEstimate of statistical uncertainties\nTo estimate statistical uncertainties as a function of polarization, we used a fast Monte Carlo probabilistic\napproach to generate polarized \u039bb particles. The fast Monte Carlo includes angular resolution from the\nfully reconstructed samples and detector acceptance simulation. We generated a large number of samples\nwith different values of polarization. A maximum likelihood \ufb01t was used to extract the decay parameters\nand the polarization. Detector acceptance corrections were calculated from high statistics fast Monte\nCarlo data simulated without polarization. Figure 17 presents the expected statistical uncertainty in the\npolarization P and in \u03b1\u039bb as a function of the polarization value for the integrated luminosity of 30 fb\u22121\n. The study was done for \u03b1\u039bb = -0.457 with the same input model as used in fully simulated Monte\nCarlo. In Figure 17 also the correlation between \u03b1\u039bb and P is shown as a function of polarization. The\ncorrelation values were extracted from the Maximum Likelihood \ufb01t results.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1150\n\nIn our study we used speci\ufb01c set of decay amplitudes, presented in Table 3, to demonstrate our ability\nto extract these parameters. To insure that the success of our analysis techniques did not depend on the\namplitudes chosen, we conducted a fast Monte Carlo study using a different model with \u03b1\u039bb = 0.1 [24]\nto test our procedure in a case of smaller \u03b1\u039bb value. We found that it is possible to satisfactorily extract\n\u03b1\u039bb and the polarization even with such a change in the amplitude values.\nPolarization\n-1\n-0.5\n0\n0.5\n1\nP\n\u03c3\n0.021\n0 022\n0.023\n0 024\n0.025\n0.026\n0.027\nATLAS\nPolarization\n-1\n-0 5\n0\n0 5\n1\nb\n\u03b1\n\u03c3\n0.02\n0.03\n0.04\nATLAS\nPolarization\n-1\n-0.5\n0\n0.5\n1\n)\nb\n\u03b1\nCorrelation(P,\n-0.6\n-0.4\n-0.2\n0\n0 2\n0.4\n0 6\nATLAS\nFigure 17: Expected statistical uncertainty on polarization (top) and on \u03b1\u039bb (center) as a function of the\npolarization P. Bottom plot shows the expected correlation between \u03b1\u039bb and the polarization P. All\nplots show results from the fast Monte Carlo study, obtained for the expected number of \u039bb events in\ndata sample of 30 fb\u22121 .\n6\nResults and conclusions\nIn this note we have presented the results from a series of studies to determine if polarized \u039bb baryons\ncan be reconstructed in ATLAS and have their polarization and \u03b1\u039bb parameter measured. Our results\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1151\n\nindicate that the answer is af\ufb01rmative. \u039bb events should be identi\ufb01able through the reconstruction of\ntheir four charged \ufb01nal state particles, and the angles between these particles can be measured with suf-\n\ufb01cient accuracy to determine the parent\u2019s polarization. With trigger constraints and detector cuts fully\nspeci\ufb01ed, our more complete analysis suggests that the number of events we should expect after 30 fb\u22121\nof data will only be 13,000, compared to the 37,500 noted in the ATLAS-TDR [22]. Different additional\ndetector and background effects, which are dif\ufb01cult to model at the current level of detector description,\ncan further reduce the signal sensitivity. These effects could include the detector and trigger inef\ufb01ciency,\nmisalignment, pile-up events and increased combinatorial background due to e.g. the fake tracks. Never-\ntheless, even with a reduction of 50%, a polarization measurement with a statistical uncertainty of several\npercent should be possible in a regime where polarization is larger than 25% as experimentally measured\nat lower energies. Efforts will continue to develop algorithms to improve the various reconstruction and\ntrigger ef\ufb01ciencies and in consequence providing an enhanced yield of reconstructed particles in data\nsamples.\nWe note that almost all models predict that the \u039bb polarization at the LHC at small Feynman x should\nbe vanishingly small. Measurement of a signi\ufb01cant polarization would have to be regarded as a signal of\nan unexplained effect, either from the domain of existing physics, or of new physics altogether.\nWe further note that the development of \u039bb polarimetry as a tool for studying spin effects at the LHC\ncould be important. For example, members for the SUSY community are quite interested in knowing\nwhat fraction of the b quark polarization ends up in the polarization of a \u039bb, since this could provide a\nway to test if b quark SUSY partners have the correct handedness. Only a few hundred \u039bb decays would\nbe required to, for example, determine if its polarization were 100% or -100%. Challenges clearly exist,\nhowever, in determining the polarization transfer fraction, which requires a source of b\u2019s such as from\nZ \u2192b\u00afb, and in dealing with the fact that only 10\u22125 of b\u2019s generate decay into the \u039bb channel we have\ndescribed here. Our work on this topic will continue.\nOther related studies that should continue include mechanisms for comparing the \u03b1\u039bb parameters\nfrom \u039bb and its antiparticle as a test of CP. We will accumulate data on both. If CP is conserved, the two\nparameters should be equal in magnitude but opposite in sign. While the precision of this test will not be\nhigh, and while models predict that any CP violation would be small in this sector, nevertheless, such a\ntest would be unique in this domain and should be made.\nFinally, as noted in Section 1, the lifetime of the \u039bb remains a topic of signi\ufb01cant interest. Such a\nmeasurement will be a natural by-product of our efforts to extract the \u039bb spin parameters.\nReferences\n[1] C. Albajar et al., Phys. Lett. B 243 (1991) 540.\n[2] F. Gabbiani et al., Phys. Rev. D 68 (2003) 114006.\n[3] I. Dunietz, Z. Phys. C 56 (1992) 129.\n[4] C. Q. Geng et al., Phys. Rev. D 65 (2002) 091502.\n[5] C. A. Nelson, Eur. Phys. J. C 19 (2001) 323.\n[6] A. K. Giri et al., Phys. Rev. D 65 (2002) 073029.\n[7] D. J. Lange, Nucl. Inst. Meth. A462 (2001) 152.\nhttp:://www.slac.stanford.edu/\u223clange/EvtGen/\n[8] J. Szwed, Phys. Lett. B 105 (1981) 403.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1152\n\n[9] C. Chou et al., Phys. Rev. D 65 (2002) 074030.\n[10] W. G. D. Dharmaratna and G. R. Goldstein, Phys. Rev. D 53 (1996) 1073.\n[11] W. G. D. Dharmaratna and G. R. Goldstein, Phys. Rev. D 41 (1990) 1731.\n[12] K. Heller, Proceedings of the 9th International Symposium on High Energy Spin Physics, Bonn,\nGermany, p. 97, Springer-Verlag (1990).\n[13] H. A. Neal and E. De La Cruz Burelo, AIP Conf. Proc. 915 (2007) 449 .\n[14] Chung-Hsien Chou et al., Phys. Rev. D 65 (2002) 074030; J. C. Collins, Phys. Rev. D 58 (1998)\n094002; Chung-Hsien Chou, Int. J. Mod. Phys. A 18 (2003) 1429.\n[15] J. Hrivnac et al., J. Phys. G: Nucl. Part. Phys 21 (1995) 629.\n[16] J. G. Korner and M. Kramer, Z. Phys. C 55 (1992) 659.\n[17] P. Bialas et al., Z. Phys. C 57 (1993) 115.\n[18] R. Lednicky, Jad. Fiz. 43 (1986) 1275.\n[19] T. Sjostrand et al., Comp. Phys. Comm. 135 (2001) 238, eprint hep-ph/0108264.\n[20] W. M. Yao et al., J. Phys. G: Nucl. Part. Phys. 33 (2006) 1-1232.\n[21] ATLAS-TDR-017; CERN-LHCC-2005-022.\n[22] ATLAS TDR, CERNLHC99-15, Vol. II (1999) 614.\n[23] A. C. Davison et al., Bootstrap methods and their application, Cambridge Univ. Press (1997).\n[24] H. Y. Cheng and B. Tseng, Phys. Rev. D 53 (1996) 1457.\nB-PHYSICS \u2013 PLANS FOR THE STUDY OF THE SPIN PROPERTIES OF THE \u039bb BARYON USING . . .\n1153\n\nStudy of the Rare Decay B0\ns \u2192\u00b5+\u00b5\u2212\nAbstract\nWe investigate the feasibility of measuring of the rare decay B0\ns \u2192\u00b5+\u00b5\u2212in\nATLAS. The contribution of inclusive and of the most important non\u2013combinatorial\nbackground is studied.\n1\nIntroduction\nThe rare decays, B0\ns \u2192\u2113+\u2113\u2212with \u2113\u00b1 = e\u00b1,\u00b5\u00b1, or \u03c4\u00b1, are mediated by \ufb02avour-changing neutral currents\nthat are forbidden in the Standard Model at tree level. The lowest-order contributions in the Standard\nModel involve weak penguin loops and weak box diagrams that are CKM suppressed. Examples of the\nlowest-order diagrams are shown in Figure 1. Since the B0\ns meson is a pseudoscalar that has positive C\nparity and the transition proceeds in an \u2113= 0 state, the electromagnetic penguin loop is forbidden. The\ntwo leptons are either both right-handed or both left-handed leading to additional helicity suppression.\nThus, branching fractions expected in the Standard Model are tiny.\ns\nt\n\u00afb\nW \u2212\nW +\nZ0\n\u00b5+\n\u00b5\u2212\ns\nt\n\u00afb\nW +\nW \u2212\n\u00b5+\n\u03bd\n\u00b5\u2212\nFigure 1: Lowest order Standard Model contributions to B0\ns \u2192\u00b5+\u00b5\u2212.\nThe early searches for rare B meson decays started with radiative penguin decays, \ufb01rst observed by\nCLEO in 1993, where they presented evidence for the exclusive decay B \u2192K\u2217\u03b3 and for the inclusive\ndecay B \u2192Xs\u03b3 a year later [1,2].\nThe B factory experiments, BaBar and Belle, have measured these decay modes with more precision.\nThe present world average for the inclusive mode is B(B \u2192Xs\u03b3) = (3.55 \u00b1 0.26) \u00d7 10\u22124 [3]. BaBar\nand Belle also observed the decays B \u2192K(\u2217)\u2113+\u2113\u2212and B \u2192Xs\u2113+\u2113\u2212that are two orders of magnitude\nsmaller than B \u2192Xs\u03b3 [4,5]. The decay B0\ns \u2192\u00b5+\u00b5\u2212is expected to be further reduced by three orders of\nmagnitude.\nIn extensions of the Standard Model, the B0\ns \u2192\u00b5+\u00b5\u2212\nbranching fraction may be enhanced by\nseveral orders of magnitude. Thus, several experiments have searched for these decays. The largest B0\ns\nsamples have been collected by CDF and D0 corresponding to a luminosity of 2 fb\u22121 but no signal has\nbeen observed. The lowest branching fraction upper limit was set recently by CDF yielding B(B0\ns \u2192\n\u00b5+\u00b5\u2212) < 5.8 \u00d7 10\u22128@95% con\ufb01dence level [6]. This is still about an order of magnitude higher than\nthe Standard Model prediction. As ATLAS has an elaborate muon system extended over a large region of\nthe solid angle, the dimuon \ufb01nal state is expected to be reconstructed with high ef\ufb01ciency and good mass\nresolution. Thus, there are good prospects for observing this decay in the dimuon channel and measuring\nits branching fraction with reasonable precision.\n2\nTheoretical description\nThe Standard Model amplitude for the process Bs,d \u2192\u2113+\u2113\u2212is calculated from the effective Hamiltonian\nHeff = \u2212GF\n\u221a\n2\n\u03b1\n\u03c0 sin2 \u03b8W\nV \u2217\ntbVtq(C10(\u00b5)O10(\u00b5)+CS(\u00b5)OS(\u00b5)+CP(\u00b5)OP(\u00b5))+h.c.,\n(1)\n1154\n\nwhere Ci(\u00b5) are Wilson coef\ufb01cients that present the perturbatively calculable short-distance effects and\nOi(\u00b5) are local operators that describe the non-perturbative long-distance effects of the transition. The\nscale parameter \u00b5 is of the order of the b-quark mass (\u223c5 GeV), \u03b8W is the weak mixing angle, \u03b1 is\nthe electromagnetic coupling constant and V \u2217\ntbVtq are CKM matrix elements for t \u2192b and t \u2192q = s,d\ntransitions, respectively.\nThe dominant contribution results from the axial-vector operator O10, [7]:\nO10 = (\u00afbL\u03b3\u00b5qL)( \u00af\u2113\u03b3\u00b5\u03b35\u2113).\n(2)\nThe Wilson coef\ufb01cient C10 has been determined in the next-to-leading order (NLO) of QCD. The NLO\ncorrections are in the percent range and higher-order corrections are not relevant [8]. In NLO an excellent\napproximation in terms of the MS mass of the top quark, \u00afmt, is given by:\nC10( \u00afmt) = 0.9636\n\u001480.4 GeV\nMW\n\u00afmt\n164 GeV\n\u00151.52\n.\n(3)\nThe measurements of the top quark mass at the Tevatron, mpole\nt\n= 171.4\u00b12.1 GeV [9], yield an MS mass\nof \u00afmt = 163.8\u00b12.0 GeV and the world average of the W-boson mass is mW = 80.403\u00b10.029 GeV. The\naccuracy of this approximation is 5\u00d710\u22124 for masses of 149 GeV < \u00afmt < 179 GeV.\nThe other two operators represent scalar and pseudoscalar couplings to the leptons:\nOS = mb(\u00afbRqL)( \u00af\u2113\u2113),OP = mb(\u00afbRqL)( \u00af\u2113\u03b35\u2113).\n(4)\nThe Wilson coef\ufb01cients, CS and CP, are determined from penguin diagrams that involve the Higgs boson\nor the neutral Goldstone boson, respectively. Although they are not helicity suppressed, their contribu-\ntions are tiny in the Standard Model and they may be safely neglected in Standard Model calculations.\nThe Bq \u2192\u00b5+\u00b5\u2212branching fractions including the scalar and pseudoscalar contributions are given\nby:\nB(B0\nq \u2192\u00b5+\u00b5\u2212) =\nG2\nF\u03b12\n64\u03c03 sin4 \u03b8W\n|V \u2217\ntbVtq|2\u03c4BqM3\nBq f 2\nBq\nv\nu\nu\nt1\u2212\n4m2\u00b5\nM2\nBq\n\u00d7\n\" \n1\u2212\n4m2\n\u00b5\nM2\nBq\n!\nM2\nBqC2\nS +\n\u0012\nMBqCP \u22122m\u00b5\nMBq\nC10\n\u00132#\n,\n(5)\nwhere MBq, \u03c4Bq, and fBq respectively are mass, lifetime and decay constants of the Bq meson. The decay\nconstant is determined in different models, including quark models, QCD sum rules and unquenched\nlattice theory. The accuracy is presently of the order of 10 \u221215%. Evaluating \u03b1 at the Z-mass scale,\n\u03b1(MZ) = 1/128, the following predictions were made for the Bq \u2192\u00b5+\u00b5\u2212branchings fractions in the\nStandard Model [8]:\nBr(B0\ns \u2192\u00b5+\u00b5\u2212) = (3.86 \u00b1 0.15) \u00d7\n\u03c4B0s\n1.527ps\n|V \u2217\ntsVtb|2\n1.7 \u00d7 10\u22123\nfBs\n240MeV \u00d7 10\u22129,\n(6)\nBr(B0\nd \u2192\u00b5+\u00b5\u2212) = (1.06 \u00b1 0.04) \u00d7\n\u03c4B0\nd\n1.527ps\n\f\fV \u2217\ntdVtb\n\f\f2\n6.7 \u00d7 10\u22125\nfBd\n200MeV \u00d7 10\u221210.\nIn extensions of the Standard Model, such as supersymmetry (SUSY), Higgs doublet models or\nmodels with extra gauge bosons, scalar-current, pseudoscalar-current or axial-vector current interactions\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1155\n\nmay arise with new particles in the loop. This yields new contributions in the Wilson coef\ufb01cients C10,CS,\nand CP. Since the scalar and pseudoscalar operators are not helicity suppressed, they may give rise\nto a large enhancement of the branching fraction. Furthermore, the contribution of the pseudoscalar\noperator may produce destructive or constructive interference with the axial vector operator. Thus, new\nphysics may increase or decrease the branching fraction with respect to the Standard Model value. For\nexample, in the minimal supersymmetric Standard Model (MSSM), the B0\ns \u2192\u00b5+\u00b5\u2212branching fractions\nare proportional to tan6(\u03b2) 1. The branching fraction of Bd \u2192\u00b5+\u00b5\u2212is expected to be a factor of 40\nlower than that for Bs \u2192\u00b5+\u00b5\u2212, hence, the latter is the focus of this note.\n3\nATLAS strategy for B0\ns \u2192\u00b5+\u00b5\u2212study\nMeasurements of the properties of B decays with such extremely low branching fractions in ATLAS\nis possible namely due to the large beauty cross-section and luminosity of the LHC machine. Thus at\nluminosity 1033 cm\u22122 s\u22121 1012 B hadron pairs will be produced each year. It is expected that ATLAS\nwill record 108 events with B decays each year by using B-physics triggers [10]. Triggers dedicated to\nrare dimuon B0\ns \u2192\u00b5+\u00b5\u2212decays will be described in the Section 4.2 of this document.\nSince the branching fraction is so small in the Standard Model, semileptonic B decays and even some\nrare B decays may yield substantial backgrounds. The key issue for B0\ns \u2192\u00b5+\u00b5\u2212discovery at the LHC\nis the suppression of the backgrounds. The ATLAS strategy for observing B0\ns \u2192\u00b5+\u00b5\u2212is as follows.\nThe \ufb01rst step is to trigger on events containing a B0\ns \u2192\u00b5+\u00b5\u2212candidate using dedicated trigger\nalgorithms which are described in this document. In the of\ufb02ine analysis the selections will be re\ufb01ned to\nreduce backgrounds. To achieve \ufb01nal separation of signal from background we will employ statistical\nmethods based on several variables. Both parts of the of\ufb02ine selection are described in this paper.\nOnce recorded data are available, the background in the signal region will be estimated using side-\nbands in the distribution of the muon pair invariant mass. In the current study the background was\nestimated using simulated events. Two categories of backgrounds were simulated: the so called com-\nbinatorial background from b\u00afb pairs producing two muons in the \ufb01nal state; and the exclusive back-\ngrounds, coming from two-body hadronic B decays and from the process B0\ns \u2192K\u2212\u00b5+\u03bd. The exclusive\nbackgrounds contribute to the signal region and the lower mass sideband only. They do not occur in the\nhigher mass sideband, so their contribution to the signal is estimated separately.\nAfter the number of background events in the signal region has been determined, the number of signal\nevents NB can be determined from a comparison of the total number of events found in the signal region,\nand the estimated background. For low statistics an upper limit on NB corresponding to certain con\ufb01-\ndence level is determined using appropriate statistical methods. Once NB is determined the B0\ns \u2192\u00b5+\u00b5\u2212\nbranching fraction, B(B0\ns \u2192\u00b5+\u00b5\u2212), can be calculated using a relative normalisation to the reference\nchannel B+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+.\nThis document presents a Monte Carlo simulation study which follows the strategy described above.\nWe start from the trigger level in Section 4.2. This is followed by the of\ufb02ine analysis, optimisation\nof discriminating variables and \ufb01nally the determination of background and signal contribution in the\nsignal regions, in Section 4.4. Systematic uncertainties are analysed in Section 5, followed by the start-\nup strategy in Section 6.\nIt should be stressed that due to large uncertainty in the predictions of the b\u00afb production cross-section\nat the LHC energy this paper cannot derive a precise sensitivity to B(B0\ns \u2192\u00b5+\u00b5\u2212) at ATLAS but rather\nto show the ATLAS potential for this study and its discovery capability under some assumptions.\n1tan(\u03b2) is the ratio of vacuum expectation values for charged and neutral Higgs bosons.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1156\n\n4\nMonte Carlo study\n4.1\nSimulation and event selection\nThe Monte Carlo simulation samples used in the analysis have been generated as part of the central AT-\nLAS Monte Carlo data production runs, and details of this simulation have been given in the introduction\nto this chapter.\nThe list of generated signal and background events is given in Table 1. To ensure that most of the\nProcess\n# Events\nB0\ns \u2192\u00b5+\u00b5\u2212\n47.5k\nbb \u2192\u00b5+\u00b5\u2212X\n146.5k\nB0\ns \u2192K\u2212\u03c0+\n50k\nB0\ns \u2192K\u2212\u00b5+\u03bd\n50k\nTable 1: List of processes and number of events analysed\ngenerated dimuon events passed the trigger, only events containing two muons with pT larger than 6\nGeV and 4 GeV, were retained for detector simulation. For the signal channel B0\ns \u2192\u00b5+\u00b5\u2212, multiply-\ning the cross-section reported by PYTHIA with the branching ratio 3.42 \u00d710\u22129 gave a cross-section of\n15 fb. 47.5k events have been generated and passed through the full detector simulation and reconstruc-\ntion. Simulation of pileup has not been available, thus it was not simulated for either the signal or the\nbackground events.\nThe sample of dominant background process events, b\u00afb decaying semileptonically giving two muons\nin the \ufb01nal state, were simulated with the same versions of the software, and with the same kinematic\ncuts as for the signal. The PYTHIA cross-section for such a sample is estimated to be 110 nb and a total\nof 146.5k background events that passed the reconstruction stage were used in the physics analysis.\nIn addition to the combinatorial background, there are several B backgrounds that may contribute to\nthe signal region. These include two and three body decays where two of the \ufb01nal state particles are K\u00b1,\n\u03c0\u00b1 or \u00b5\u00b1. Although the rate for misidenti\ufb01cation of kaons or pions as muons, due to punchthrough or\ndecay in \ufb02ight, is only of the order 0.5%, the small B(B0\ns \u2192\u00b5+\u00b5\u2212) requires investigation of the other\nrare B decays. The decay modes which we consider to be most important are summarised in Table 2.\nprocess\nbranching fraction\nRef.\nB0 \u2192K+\u03c0\u2212\n(1.82\u00b10.08)\u00d710\u22125\n[11]\nB0 \u2192\u03c0+\u03c0\u2212\n(4.6\u00b10.4)\u00d710\u22126\n[11]\nB0 \u2192K+K\u2212\n< 3.7\u00d710\u22127@90%CL\n[11]\nB0\ns \u2192\u03c0+\u03c0\u2212\n< 1.7\u00d710\u22124@90%CL\n[11]\nB0\ns \u2192\u03c0+K\u2212\n< 2.1\u00d710\u22124@90%CL\n[11]\nB0\ns \u2192K+K\u2212\n< 5.9\u00d710\u22125@90%CL\n[11]\nB0\ns \u2192K\u2212\u00b5+\u03bd\n\u223c1.36\u00d710\u22124\n* 2\nB0 \u2192\u03c0\u2212\u00b5+\u03bd\n(1.36\u00b10.15)\u00d710\u22124\n[11]\nTable 2: B meson decays contributing to the non-combinatorial background\n2An estimation based on isospin symmetry and the measurement of B0 \u2192\u03c0\u2212\u00b5+\u03bd.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1157\n\nWe have studied one of the two-body and one of the three-body decays with full simulation, namely\nB0\ns \u2192K\u2212\u03c0+ and B0\ns \u2192K\u2212\u00b5+\u03bd. Contributions from the other channels were estimated to be similar\nor smaller. To enable the production of a sizable event sample with decay in \ufb02ight, a special GEANT\nsimulation option which forces kaons and pions from selected B mesons to decay in the inner detector\nvolume was developed [12].The position of the decay is randomly selected from a uniform distribution\nbetween the origin and the exit point from the inner detector.\n4.2\nTrigger strategy\nWe describe trigger methods for selection of the B0\ns \u2192\u00b5+\u00b5\u2212channel developed by the B trigger group\nas part of the project presented in this document. The full description of the ATLAS B-physics triggers\nis given in the introduction to the B-physics chapter [10]. The \ufb01rst level trigger (L1) performance for\ndimuon channels can be found in [13] and details of the second level (L2) dimuon trigger implementation\nin [12].\nAt the LHC start-up, the luminosity level is expected to be of order 1031cm\u22122s\u22121 and a pT threshold\nas low as 4 GeV can be used at L1. The dimuon rate after L1 is expected to be only a few Hz. This\nadmits the possibility of applying L2 track reconstruction in the full volume of the inner detector. This\ndetailed approach allows the study of dimuon background features to understand of their composition.\nWith the subsequent rise of luminosity the L1 pT threshold will increase to 6 GeV. The dimuon rate\nafter L1 is expected to rise to about 360 Hz at L = 1033cm\u22122s\u22121 and the L2 track reconstruction in the\nfull volume of inner detector will be replaced by the Region of Interest (RoI) guided mode, documented\nin [12].\nThe simulation of the trigger in the current study is performed by applying the strategies for lumi-\nnosity L = 1033cm\u22122s\u22121. At L1 the threshold of pT > 6 GeV has been applied and events containing\ntwo L1 muon signatures are analysed further using the L2 topological dimuon trigger algorithm with a\nthreshold of pT > 6 GeV. Following the RoI de\ufb01ned at L1, the muon candidates are reconstructed in\nthe muon spectrometer, then matched to the tracks reconstructed in the inner detector (inside the RoI)\nand combined into one track. The invariant mass of two opposite sign muons is required to be less than\n7 GeV. These muons should also be successfully \ufb01tted to a common vertex. Only loose selection cri-\nteria are used at this step (\u03c72 < 10). Implementation of the third level trigger, the event \ufb01lter (EF), is\nnot \ufb01nalised yet and the of\ufb02ine reconstruction ef\ufb01ciency is used to estimate the EF ef\ufb01ciency (the same\nreconstruction algorithms are supposed to be used at EF).\nResults on the L1 and L2 ef\ufb01ciencies as well as an estimated EF ef\ufb01ciency for signal B0\ns \u2192\u00b5+\u00b5\u2212are\ngiven in Table 3. The L1 ef\ufb01ciency is de\ufb01ned as the ratio of the B0\ns \u2192\u00b5+\u00b5\u2212events passing the L1 trigger\nand the input events generated with pT > 6 GeV and |\u03b7| < 2.5 for both muons from the B0\ns \u2192\u00b5+\u00b5\u2212\ndecay. The L2 ef\ufb01ciency is de\ufb01ned as the fraction of events accepted by L1 satisfying the above L2\nreconstruction and selection cuts. The ef\ufb01ciency of the event \ufb01lter is estimated as the fraction of events\nthat both satisfy L2 and also are successfully reconstructed at EF. These values of the ef\ufb01ciency have\nbeen used in the subsequent analysis.\nVarious types of trigger algorithms and trigger thresholds will be used in the real experiment depend-\ning on the luminosity achieved, dedicated computing resources available for the online event processing\nand the actual beauty yield at LHC energies.\nTable 3: Trigger ef\ufb01ciency of signal B0\ns \u2192\u00b5+\u00b5\u2212. The methods of calculating ef\ufb01ciencies at L1, L2 and\nEF levels are given in the relevant place in the text.\nL1*L2 ef\ufb01ciency\nEF w.r.t L2\nOverall trigger eff.\n0.52\n0.88\n0.46\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1158\n\n4.3\nEvent reconstruction and analysis.\nMuon reconstruction quality is of high importance for the B0\ns \u2192\u00b5+\u00b5\u2212channel. The muon candidates\nproduced by the STACO [14] method were used. This method combines the independently reconstructed\ninner detector and muon spectrometer tracks. Figure 2 shows the muon reconstruction ef\ufb01ciency as a\nfunction of a true muon pT. The ef\ufb01ciency is de\ufb01ned as the number of muon candidates reconstructed and\nmatched to the Monte Carlo particle tracks in the corresponding pT bin divided by number of generated\nmuons. The pT spectrum of generated muons is superimposed on the ef\ufb01ciency plot.\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\n35\n40\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nT\n1/N dN/dp\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nATLAS\nFigure 2: Muon of\ufb02ine reconstruction ef\ufb01ciency as a function of pT. The superimposed histogram - pT\nspectrum of muons in the signal events (right scale).\nFor the physics analysis, we select events containing identi\ufb01ed muon pairs with opposite charges.\nAside of the kinematic cuts (p\u00b51(\u00b52)\nT\n> 6(4) GeV and |\u03b7\u00b51,\u00b52| < 2.5) no additional cuts have have been\napplied. These two muons then constitute a B meson candidate. The VKalVrt vertexing package [15] is\nused to \ufb01t tracks into a vertex. We require the vertex quality to have \u03c7 2 < 10. The momentum resolution\nis important as a narrow mass search window reduces the background contribution. Figure 3 shows\nthe dimuon mass distribution for the cases when both muons are in the barrel region (|\u03b7\u00b51,\u00b52| < 1.1) or\nin the end-cap (|\u03b7\u00b51,\u00b52| > 1.1). The Gaussian \ufb01t (using bins with contents > 10% of maximum) gives\n\u03c3 = 70 MeV for the barrel and \u03c3 = 124 MeV for the end-cap. We used 90 MeV as an estimate of the\ninvariant mass resolution for the signal events.\nIn this document we present a cut-based method for signal extraction and background rejection. For\nthe future, we are investigating another method using a boosted decision tree [16].\nIn the cut based analysis a set of discriminating variables is chosen and using the signal and back-\nground simulated events the optimal set of cuts is determined. The signal events are identi\ufb01ed by re-\nquiring that the dimuon invariant mass is consistent with the mass of Bs meson. To reduce background\nevents where two muons originate from different sources (e.g. independent semileptonic decays of b and\n\u00afb quarks), the following discriminating variables were chosen (values used in the \ufb01nal analysis are given\nin parentheses):\n\u2022 Transverse decay length of the Bs candidate Lxy (Lxy >0.5 mm )\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1159\n\n) [GeV]\n\u00b5 \n\u00b5\nInv.Mass(\n4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4\nNevents\n0\n500\n1000\n1500\n2000\n2500\n3000\n 1 MeV\n\u00b1\n = 70 \n\u03c3\n|<1.1\n1\n\u00b5\n\u03b7\n|\n|<1.1\n2\n\u00b5\n\u03b7\n|\nATLAS\n) [GeV]\n\u00b5 \n\u00b5\nInv.Mass(\n4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4\nNevents\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n|>1.1\n1\n\u00b5\n\u03b7\n|\n|>1.1\n2\n\u00b5\n\u03b7\n|\n 1 MeV\n\u00b1\n = 124 \n\u03c3\nATLAS\nFigure 3: Reconstructed Bs mass in barrel - when both muons have |\u03b7| < 1.1(left) and in the end-cap -\nboth muons have |\u03b7| > 1.1 (right)\n\u2022 The pointing angle \u03b1 between the dimuon pair summary momentum and the direction of the decay\nvertex as seen from the primary vertex (\u03b1 <0.017 rad )\n\u2022 Isolation I\u00b5\u00b5 = p\u00b5\u00b5\nT /(p\u00b5\u00b5\nT + \u03a3ipi\nT(\u2206R < 1)) , where the sum is over all tracks with pT > 1 GeV\n(excluding the muon pairs) within a cone of \u2206R < 1, where \u2206R =\np\n(\u2206\u03b7)2 +(\u2206\u03c6)2 and \u2206\u03b7 and\n\u2206\u03c6 are the pseudorapidity and azimuthal angle of track i with respect to the momentum vector of\nthe muon pair ( I\u00b5\u00b5 > 0.9 ).\n\u2022 An asymmetric search window for M\u00b5\u00b5,\u2208[MB0s \u2212\u03c3,MB0s +2\u03c3], is used to avoid a possible contri-\nbution from B0\nd \u2192\u00b5+\u00b5\u2212decay.\nFigures 4, 5 and 6 show distributions of discriminating variables for signal and background events.\nDue to the low Monte Carlo statistics, it is not feasible to perform a cut analysis as in a real experiment\n(i.e. applying all cuts simultaneously) since this will leave no events for the analysis. However, some\nof the discriminating variables show no (or small) correlations between each other. This allows the\nestimation of the rejection power of such variables separately. Then the product of all ef\ufb01ciencies can\nprovide a reasonable estimate of the total rejection. Table 4 shows a correlation matrix for the variables\nused in this study. The correlation between the pointing angle \u03b1 and the transverse decay length Lxy is\nhigher than among other variables so the pointing angle and the transverse decay length are examined\nsimultaneously to take their correlation into account. The systematic uncertainty due to this correlation\nis estimated as +50%.\nFigure 7 illustrates the rejection power of each cut. One cut is applied at a time to the combinato-\nrial background events and to the B0\ns \u2192K\u2212\u00b5\u03bd and B0\ns \u2192K\u2212\u03c0+ events where one or two hadrons are\nmisidenti\ufb01ed as a muon. The combinatorial background is effectively suppressed by these cuts while the\nnon-combinatorial events are less well rejected.\nTable 5 summarizes the output of this cut-based analysis. For the b\u00afb \u2192\u00b5\u00b5X background in the\nleft column the ef\ufb01ciencies are given separately for each cut, whilst in the right column the combined\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1160\n\nTransverse decay length [mm]\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nxy\n1/N dN/L\n-3\n10\n-2\n10\n-1\n10\nATLAS\nFigure 4: Transverse decay length of reconstructed B0\ns candidates. The signal is shown as closed circles,\nbackground as opened circles. Distributions are normalised to 1. The vertical line indicates the lowest\ntransverse decay length allowed for selected events.\n\u00b5\n\u00b5I\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u00b5\n\u00b5\n1/N dN/dI\n0\n0.05\n0.1\n0.15\n0.2\nATLAS\nFigure 5: Distribution of isolation variable I\u00b5\u00b5 for the reconstructed B0\ns candidates. The signal is shown\nas closed circles, background as opened circles. Distributions are normalised to 1. The vertical line\nindicates the lowest values of variable I\u00b5\u00b5 allowed for selected events.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1161\n\n\u03b1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n\u03b1\n1/N dN/d\n-3\n10\n-2\n10\n-1\n10\nFigure 6: Distribution of pointing angle \u03b1 for the reconstructed B0\ns candidates. The signal is shown as\nclosed circles, background as opened circles. Distributions is normalised to 1. The vertical line indicates\nthe highest values of \u03b1 allowed for selected events.\nM\u00b5\u00b5\nI\u00b5\u00b5\n\u03b1\nLxy\nM\u00b5\u00b5\n1\n-0.09\n0.04\n-0.03\nI\u00b5\u00b5\n1\n-0.07\n-0.03\n\u03b1\n1\n-0.17\nLxy\n1\nTable 4: The linear correlation coef\ufb01cients among the discriminating variables for background events.\nThe statistical uncertainty is about \u00b10.05 for each coef\ufb01cient.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1162\n\nef\ufb01ciency is given for the cuts on the pointing angle and on the transverse decay length. As one can see\nthe total rejection is largely overestimated if all cuts are treated separately, so the combined value is used\nto estimate a total yield of background events. The contribution from B0\ns \u2192K\u2212\u00b5\u03bd and B0\ns \u2192K\u2212\u03c0+ is\nfound to be negligible comparing to the combinatorial background contribution. The errors quoted for\nthe ef\ufb01ciencies are statistical only, so they represent only the size of the available Monte Carlo sample,\nbut not the expected accuracy of the experiment where the initial number of background events will be\nmuch higher. More details on uncertainties will be given in Section 5.\nFigure 8 shows the dimuon mass distribution for signal and background events after all selection cuts\nhave been applied. For the combinatorial background, the contribution for the left and right side of the\nsignal region is estimated in the same way as for the signal region (Table 5).\n) [GeV]\n\u00b5\n \n\u00b5\nMass(\n4.5\n5\n5.5\n6\n6.5\n7\ndN/dM\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n\u00b5 \n\u00b5\n->\nb\nb \n\u00b5 \n\u00b5\n->\n0\ns\nsignal B\n\u03c0\n->K \n0\ns\nB\n\u03bd \n\u00b5\n->K \n0\ns\nB\na)\n) [GeV]\n\u00b5 \n\u00b5\nMass(\n4.5\n5\n5.5\n6\n6.5\n7\ndN/dM\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n\u00b5 \n\u00b5\n->\nb\nb \n\u00b5 \n\u00b5\n->\n0\ns\nsignal B\n\u03c0\n->K \n0\ns\nB\n\u03bd \n\u00b5\n->K \n0\ns\nB\nLxy > 0.5 mm\nb)\n) [GeV]\n\u00b5\n \n\u00b5\nMass(\n4.5\n5\n5.5\n6\n6.5\n7\ndN/dM\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n\u00b5 \n\u00b5\n->\nb\nb \n\u00b5 \n\u00b5\n->\n0\ns\nsignal B\n\u03c0\n->K \n0\ns\nB\n\u03bd \n\u00b5\n->K \n0\ns\nB\n < 0.017\n\u03b1\nc)\n) [GeV]\n\u00b5 \n\u00b5\nMass(\n4.5\n5\n5.5\n6\n6.5\n7\ndN/dM\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n\u00b5 \n\u00b5\n->\nb\nb \n\u00b5 \n\u00b5\n->\n0\ns\nsignal B\n\u03c0\n->K \n0\ns\nB\n\u03bd \n\u00b5\n->K \n0\ns\nB\n > 0.9\n\u00b5\n\u00b5I\nd)\nFigure 7: The Monte Carlo di-muon mass distributions for signal B0\ns \u2192\u00b5+\u00b5\u2212(histogram), combinato-\nrial background (closed circles) and non-combinatorial background (open circles and triangles) for (a)\npreselected events, (b) after cuts on transverse decay length, (c) pointing angle and (d) isolation. The\nnumber of events has been scaled to 10 fb\u22121 of integrated luminosity.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1163\n\n) [GeV]\n\u00b5\n \n\u00b5\nMass(\n4.5\n5\n5.5\n6\n6.5\n]\n-1\ndN/dM [GeV\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n\u00b5\n \n\u00b5\n \n\u2192\nb\nb \n\u00b5\n \n\u00b5\n \n\u2192\n0\ns\nsignal B\n\u03c0\n K \n\u2192\n0\ns\nB\n\u03bd \n\u00b5\n K \n\u2192\n0\ns\nB\nATLAS\nFigure 8: Dimuon mass distribution for surviving events after applying all three cuts. The signal is\nshown as histogram, combinatorial background by closed circles and non-combinatorial backgrounds\nby opened circles and triangles. The combinatorial background is estimated assuming a factorisation of\napplied cuts. Statistics are given for an integrated luminosity 10 fb\u22121.\nTable 5: Selection ef\ufb01ciencies and number of signal and background events for integrated luminosity\nof 10 fb\u22121. Preselection criteria used: 4 GeV < M(\u00b5\u00b5) < 7.3 GeV , vertex \ufb01t \u03c72 < 10 , transverse\ndecay length Lxy < 20 mm. Numbers of expected events are computed according to the Standard Model\nexpectation. In the left column for the b\u00afb \u2192\u00b5\u00b5X background the ef\ufb01ciencies are given separately for\neach cut, in the right column the combined ef\ufb01ciency is given for the cuts on the pointing angle and on\nthe transverse decay length.\nSelection cut\nB0\ns \u2192\u00b5+\u00b5\u2212ef\ufb01ciency\nbb \u2192\u00b5+\u00b5\u2212X ef\ufb01ciency\nI\u00b5\u00b5 > 0.9\n0.24\n(2.6\u00b10.3)\u00b710\u22122\nLxy > 0.5mm\n0.26\n(1.4\u00b10.1)\u00b710\u22122\n(1.0\u00b10.7)\u00b710\u22123\n\u03b1 < 0.017 rad\n0.23\n(8.5\u00b10.2)\u00b710\u22123\nMass in [\u2212\u03c3,2\u03c3]\n0.76\n0.079\nTOTAL\n0.04\n0.24\u00b710\u22126\n(2.0\u00b11.4)\u00b710\u22126\nEvents yield\n5.7\n14+13\n\u221210\n5\nSystematic uncertainties\nThere are several sources of uncertainty in this analysis. Some of them are relevant only for the Monte\nCarlo study, whilst others should be taken into account with the real data analysis as well.\nIn this presented analysis, the expected number of signal and background events is estimated by\ncounting directly instead of the normalisation procedure described in Section 3, which is supposed to\nbe used in a real experiment. Consequently the dimuon trigger and reconstruction ef\ufb01ciencies, and\nacceptance, are not canceled by those from the reference channel and must explicitly be taken into\naccount. Using the methods developed by ATLAS [12] this systematic uncertainly is estimated to be of\nabout few percent.\nThere is a theoretical uncertainty of a factor of two in the b-production cross-section at LHC energies,\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1164\n\nwhich clearly affects the Monte Carlo predictions. Consequently all numbers of events from Table 5 scale\naccordingly.\nThe difference between the real and simulated kinematic properties of detected particles (e.g., due\nto not fully accounting for misalignment or material effects) can also introduce a bias in our predictions.\nHowever Figure 2 shows that the most of muons from B0\ns \u2192\u00b5+\u00b5\u2212have a pT\nin the region of the\nef\ufb01ciency plateau so the possible deformation of pT (as well as \u03b7) spectra could change the resulting\nef\ufb01ciency by not more than a few percent. The uncertainty from the cuts factorisation hypothesis is\nassumed to be approximately 50%.\nSome uncertainties will, to a large extent, cancel if we use a normalisation channel B+ \u2192J/\u03c8K+\nto estimate the B(B0\ns \u2192\u00b5+\u00b5\u2212) as the dimuon trigger conditions are similar for both channels. Without\nexperimental data, it is dif\ufb01cult to estimate the uncertainty in the number of background events in a\ngiven mass range. In the D0 analysis [17], the sideband extrapolation method is estimated to give an\nuncertainly of 20-30%. Indeed, this is the main source of uncertainty in the D0 analysis of B0\ns \u2192\u00b5+\u00b5\u2212.\nCorrections should also be made for the contribution of B0\nd \u2192\u00b5\u00b5 decay in the experimental sample.\nIn total, the uncertainty from the systematic errors discussed in this Section is approximately \u00b125%.\nIn addition, the procedure adopted to estimate backgrounds via cut factorisation has large uncertainties,\nwhich are estimated to be of the order of 50%, as discussed above. In addition, a 70% uncertainty arises\nfrom Monte Carlo statistics. Overall, we choose to combine these in quadrature to obtain an indicative\noverall uncertainty on the background of +90%/-75%.\n6\nStart-up strategy\nAlready at 1 fb\u22121of integrated luminosity, ATLAS can have O(106) of dimuon events in a mass window\n4 GeV < M(\u00b5\u00b5) < 7 GeV (after vertexing and quality cuts). It will allow tuning of the selection proce-\ndure either for the cut-based analysis or for the multivariate methods for the background discrimination.\nEvents that survive background suppression will be used to estimate the background contribution to the\nsignal search region. The contribution from combinatorial background will be estimated using the side-\nbands interpolation procedure. The contribution from exclusive backgrounds due to fake dimuons from\nhadronic two-body B decays or from B0\ns \u2192K\u2212\u00b5+\u03bd, will be determined on the basis of the study of the\nhadron/muon misidenti\ufb01cation probability. The background estimation will be compared with the num-\nber of events observed in the signal region. Following this information an upper limit on the number of\nsignal events NB corresponding to certain con\ufb01dence level will be determined, using appropriate statisti-\ncal methods. Finally, the value of NB will be used to extract the upper limit on the B0\ns \u2192\u00b5+\u00b5\u2212branching\nfraction, B(B0\ns \u2192\u00b5+\u00b5\u2212), using a reference channel B+ \u2192J/\u03c8K+. In this procedure a ratio of geomet-\nric and kinematical acceptances of the signal and the reference channels will be determined from the\nMonte Carlo simulation. Trigger and of\ufb02ine reconstruction ef\ufb01ciencies largely cancel for dimuons in\nthese channels. The reference channel B+ \u2192J/\u03c8K+ will also be used to check the Monte Carlo simu-\nlation. The ef\ufb01ciency of the \ufb01nal selection cuts on discriminating variables for the signal B0\ns \u2192\u00b5+\u00b5\u2212\nwill be determined using Monte Carlo simulation (validated with the reference channel).\n7\nConclusions\nWe have presented the strategy for searching for the rare decay B0\ns \u2192\u00b5+\u00b5\u2212with the ATLAS detector.\nWhilst we do not expect to observe this decay during the early stages of the LHC, as more luminosity\nbecomes available and our understanding of the backgrounds improves, it should be possible to identify\na signal for the process. There are uncertainties due to the relatively unknown beauty production cross-\nsection at the LHC, and also the limited Monte Carlo statistics available for this study. Within these\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1165\n\nlimitations, assuming the Standard Model, we expect a signal of 5.7 events with a background of 14+13\n\u221210\nevents for an integrated luminosity of 10 fb\u22121. It is evident that the background uncertainties are large\nin this study. However, background estimates based on real data will be able to make use of much\nhigher statistics and these will provide reduced uncertainties, as well as allowing the evaluation of more\nsophisticated methods of analysis.\nReferences\n[1] R.Ammar et.al., Phys. Rev. Lett. 71 (1993) 674.\n[2] M.S. Alam et.al., Phys. Rev. Lett. 74 (1995) 2885.\n[3] Heavy Flavor Averaging Group (HFAG) Collaboration, arXiv:hep-ex/0704.3575.\n[4] B.Aubert et.al. [BABAR Collaboration], Phys. Rev.D 73 (2006) 092001.\n[5] M.Iwasaki et.al.[Belle Collaboration], Phys. Rev. D 72 (2005) 092005.\n[6] CDF Collaboration, Search for B0\ns \u2192\u00b5+\u00b5\u2212and B0\nd \u2192\u00b5+\u00b5\u2212Decays in 2fb\u22121 of p \u00afp Collisions\nwith CDF II, CDF Public Note 8956, 2007.\n[7] Bobeth, C. and Ewerth, T. and Kruger, F. and Urban, J., Phys. Rev. D64 (2001) 074014.\n[8] M. Misiak and J. Urban, Phys. Lett. B 451, 161 (1999); G. Buchalla and A.J. Buras, Nucl. Phys. B\n548, 309 (1999).\n[9] The Tevatron Electroweak Working Group, For the CDF and D Collaborations, Combination of\nCDF and D0 Results on the Mass of the Top Quark, arXiv:hep-ex/0608.032v1.\n[10] ATLAS Collaboration, Introduction to B-Physics, this volume.\n[11] W.-M.Yao et al. (Particle Data Group), J. Phys. G 33 (2006).\n[12] ATLAS Collaboration, Triggering on Low-pTMuons and Di-Muons for B-Physics, this volume.\n[13] ATLAS Collaboration, Performance Study of the Level-1 Di-Muon Trigger, this volume.\n[14] S. Hassani et.al., Nuclear Instruments and Methods in Physics Research A572 (2007) 77\u201379.\n[15] V. Kostyukhin, VKalVrt - package for vertex reconstruction in ATLAS, ATLAS Note ATL-PHYS-\n2003-031, 2003.\n[16] Y. Freund and R. Schapire, Journal of Computer and System Science 55 (1997) 119\u2013139.\n[17] The D0 Collaboration, A new upper limit for the rare decay B0\ns \u2192\u00b5+\u00b5\u2212using 2fb\u22121 of Run II\ndata, D0 Note 5344-CONF, 2007.\nB-PHYSICS \u2013 STUDY OF THE RARE DECAY B0\ns \u2192\u00b5+\u00b5\u2212\n1166\n\nTrigger and Analysis Strategies for B0\ns Oscillation\nMeasurements in Hadronic Decay Channels\nAbstract\nThe capabilities of measuring B0\ns oscillations in proton-proton interactions with\nthe ATLAS detector at the Large Hadron Collider are evaluated. B0\ns candidates\nin the D\u2212\ns \u03c0+ and D\u2212\ns a+\n1 decay modes from semileptonic exclusive events are\nsimulated and reconstructed using a detailed detector description and the AT-\nLAS software chain. For the measurement of the oscillation frequency a \u2206ms\nsensitivity limit of 29.6 ps\u22121 and a \ufb01ve standard deviation measurement limit\nof 20.5 ps\u22121 are derived from unbinned maximum likelihood amplitude \ufb01ts\nfor an integrated luminosity of 10 fb\u22121 . The initial \ufb02avour of the B0\ns meson is\ntagged exclusively with opposite-side leptons. Trigger strategies are proposed\nfor scenarios of different instantaneous luminosities in order to maximise the\nsignal channel trigger ef\ufb01ciencies.\n1\nIntroduction\nAs tests of the Standard Model the CP\u2013violation parameter sin(2\u03b2) will be measured with high pre-\ncision (at the percent level) as well as properties of the B0\ns-meson system, like the mass difference of\nthe two mass eigenstates \u2206ms, the lifetime difference \u2206\u0393s/\u0393s and the weak mixing phase \u03c6s induced\nby CP-violation, with \u03c6s \u22482\u03bb 2 \u03b7 in the Wolfenstein parametrisation. The different masses of the CP\u2013\neigenstates BL\ns (CP\u2013even) and BH\ns (CP\u2013odd) give rise to Bs mixing. The observed B0\ns and \u00afB0\ns particles\nare linear combinations of these eigenstates, where transitions are allowed due to non\u2013conservation of\n\ufb02avour in weak\u2013current interactions and will occur with a frequency proportional to \u2206ms. B0\ns oscillations\nhave been observed at the Fermilab Tevatron collider by the CDF collaboration [1] measuring a value\nof \u2206ms = (17.77 \u00b1 0.10(stat) \u00b1 0.07(sys))ps\u22121 and D0 collaboration [2] reporting a two-sided bound\non the B0\ns oscillation frequency with a range of 17 ps\u22121 < \u2206ms < 21 ps\u22121. Both results are consistent\nwith Standard Model expectations [3]. In ATLAS, the \u2206ms measurement is an important baseline for the\nB-physics program and an essential ingredient for a precise determination of the phase \u03c6s. CP\u2013violation\nin B0\ns- \u00afB0\ns mixing is a prime candidate for the discovery of non\u2013standard\u2013model physics. For the channel\nB0\ns \u2192J/\u03c8\u03c6, which has a clean experimental signature, a very small CP-violating asymmetry is predicted\nin the Standard Model. The measurement of any sizeable effect of the weak\u2013interaction\u2013induced phase\n\u03c6s in the CKM matrix, which lies above the predicted value, would indicate that processes beyond the\nStandard Model are involved. Furthermore, the determination of important parameters in the B0\ns meson\nsystem will be valuable input for \ufb02avour dynamics in the Standard Model and its extensions.\nIn this note an estimation of the sensitivity to measure the B0\ns- \u00afB0\ns oscillation frequency with the AT-\nLAS detector is presented. The signal channels considered are the hadronic decay channels B0\ns \u2192D\u2212\ns \u03c0+\nand B0\ns \u2192D\u2212\ns a+\n1 with D\u2212\ns \u2192\u03c6\u03c0\u2212followed by \u03c6 \u2192K+K\u2212. In the case of B0\ns \u2192D\u2212\ns a+\n1 the a+\n1 decays\nas a+\n1 \u2192\u03c1\u03c0+ with \u03c1 \u2192\u03c0+\u03c0\u2212. Including the sub-decay D\u2212\ns \u2192K\u22170K\u2212[4] would increase the event\nstatistics by about 30%. However, for these sub-channels, which require an additional trigger signature,\nthe increase of the overall trigger rate would be unacceptable. Detailed information of the signal and the\nexclusive background channels is given in Section 2. The high event rate at the Large Hadron Collider\n(LHC) imposes very selective requirements onto the B-physics trigger strategies, reducing the rate by\nabout six orders of magnitude for recording events. Since an initial \u201clow-luminosity\u201d running period is\nscheduled with a luminosity starting at 1031 cm\u22122s\u22121 and rising to 2\u00b71033 cm\u22122s\u22121, followed later on by\nthe design luminosity of the LHC of 1034 cm\u22122s\u22121, the B-trigger must be \ufb02exible enough to cope with the\n1167\n\nincreasing luminosity conditions. The overall B-trigger strategy as well as the different strategies dealing\nwith the luminosity scenarios in the initial running periods are discussed in Section 3. An important part\nof the mixing measurement is to identify the \ufb02avour at production, i.e., whether the observed Bs meson\ninitially contained a b or a \u00afb quark. A detailed description of an opposite-side lepton \ufb02avour tag and of\nthe various sources of the wrong tag fractions is given in Section 4. The selection of B0\ns candidates with\nkinematic cuts as well as mass resolutions of the B0\ns, are explained and shown in Section 5. A luminosity\nof 1033 cm\u22122s\u22121 and no pileup is considered for the detailed analysis of signal and background channels.\nStrategies for lower and higher luminosities are also discussed in the same section. The results of the\nsignal-candidate selection are used as input to a toy Monte Carlo simulation generating a sample of B0\ns\ncandidates, which is used for the amplitude \ufb01t method [5] to obtain the \u2206ms measurement limits. The\nconstruction of the likelihood function, the Monte Carlo sample and the extraction of the \u2206ms sensitivity\nare discussed in Section 6.\n2\nSimulated Data Samples\nSimulated b-quark pairs are generated using PYTHIA [6], with the \u00afb-quark required to decay to one of\nthe speci\ufb01ed signal channels. The b-quark decays semileptonically producing a muon with pT > 6 GeV\nwithin |\u03b7| < 2.5. Details on generation, simulation and reconstruction of the simulated data samples are\ngiven in the introduction of the B-chapter [7].\nIn addition to the simulated signal samples B0\ns \u2192D\u2212\ns (\u03c6\u03c0\u2212)\u03c0+ and B0\ns \u2192D\u2212\ns (\u03c6\u03c0\u2212)a+\n1 , correspond-\ning exclusive background channels that give an irreducible contribution to the selected B0\ns signal were\ninvestigated. Two B0\nd decay channels, B0\nd \u2192D\u2212\u03c0+/a+\n1 and B0\nd \u2192D+\ns \u03c0\u2212/a\u2212\n1 , and one B0\ns channel,\nB0\ns \u2192D\u2217\u2212\ns \u03c0+/a+\n1 , were simulated for both hadronic decay channels. The dedicated trigger studies de-\nscribed in Section 3 require additional samples, such as the inclusive background channels b\u00afb \u2192\u00b56X,\nb\u00afb \u2192\u00b54X and c\u00afc \u2192\u00b54X containing semileptonic b or c decays requiring one muon with a generated\npT > 4 GeV (or 6 GeV) and further decay products (X). Also, one particular signal sample (as a choice\nB0\ns \u2192D\u2212\ns a+\n1 ) requiring one muon with a generated pT > 4 GeV (identi\ufb01ed by (\u00b54)) is used for the trig-\nger studies. A sample of minimum bias events is used for the determination of overall trigger rates. See\nTable 1 for the number of events generated and the cross-sections calculated from the values given by\nPYTHIA and the appropriate branching ratios [8]. Errors on the cross-sections include statistical errors\nand contributions from the uncertainties on the branching ratios.\nEffects of pileup and B-meson mixing were not included in the simulation of any of the samples.\n3\nTrigger Strategies\nThe trigger strategy used for the B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 channels is to identify the D\u00b1\ns decaying\nto \u03c6(\u2192K+K\u2212) \u03c0, which is common to both decay channels. At level one (LVL1) a muon is required to\nenrich the content of the triggered data sample with B-events. The high level trigger (HLT) is split into\nlevel two (LVL2) and Event Filter (EF). A search for a D\u00b1\ns is performed following one of two strategies.\nThe \ufb01rst method, the FullScan approach, performs reconstruction of tracks within the entire Inner De-\ntector. It is an ef\ufb01cient method, but time consuming and its feasibility depends on the background event\nrate. The second method performs track reconstruction in a limited volume of the Inner Detector only,\nwhich is de\ufb01ned by a low-pT jet region of interest (RoI) identi\ufb01ed at LVL1. This RoI-based method\nis faster but there is a loss in ef\ufb01ciency due to the requirement of a LVL1 jet RoI in the event and the\ngeometrical restriction to the RoI.\nThe increase of the luminosity after LHC startup affects the trigger in two ways: the trigger rates for\nthe jet and muon trigger will increase, seeding the HLT D\u00b1\ns algorithm more frequently, and combinatorial\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1168\n\nTable 1: Number of events generated and calculated cross-sections for the different signal and exclusive\nbackground simulated data samples for the B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 analysis and particular samples\nused for dedicated trigger studies. Branching ratios for particle decays into \ufb01nal states are included.\n\u2217)The branching fraction has not been measured yet, only an upper limit exists.\nChannel\nEvents\nCross-section [pb]\nSignal\nB0\ns \u2192D\u2212\ns \u03c0+\n88 450\n10.4 \u00b1 3.5\nB0\ns \u2192D\u2212\ns a+\n1\n98 450\n5.8 \u00b1 3.2\nBackground\nB0\nd \u2192D+\ns \u03c0\u2212\n43 000\n0.2 \u00b1 0.1\nB0\nd \u2192D\u2212\u03c0+\n41 000\n6.2 \u00b1 1.1\nB0\ns \u2192D\u2217\u2212\ns \u03c0+\n40 500\n9.1 \u00b1 2.8\nB0\nd \u2192D+\ns a\u2212\n1\n50 000\n< 8.9 \u2217)\nB0\nd \u2192D\u2212a+\n1\n50 000\n3.7 \u00b1 2.1\nB0\ns \u2192D\u2217\u2212\ns a+\n1\n100 000\n12.1 \u00b1 2.7\nTrigger\nB0\ns \u2192D\u2212\ns a+\n1 (\u00b54)\n50 000\n13.6 \u00b1 7.6\nb\u00afb \u2192\u00b56X\n242 150\n(6.14 \u00b1 0.02) \u00b7106\nb\u00afb \u2192\u00b54X\n98 450\n(19.08 \u00b1 0.30) \u00b7106\nc\u00afc \u2192\u00b54X\n44 750\n(26.28 \u00b1 0.09) \u00b7106\nminimum bias\n2 623 060\n70\u00b7109\nbackground from pileup affects the performance of the selection algorithm. Therefore, trigger menus\ncorresponding to different LHC luminosities are discussed in Sections 3.4 to 3.6.\nThe trigger ef\ufb01ciencies are presented for the B0\ns \u2192D\u2212\ns a+\n1 channel. Results for the B0\ns \u2192D\u2212\ns \u03c0+\nchannel are expected to be similar within a few percent (see Section 3.2).\n3.1\nLVL1 Trigger Selection\nThe ATLAS hardware allows three LVL1 low-pT muon trigger thresholds to be de\ufb01ned at once, which\ncan only be adjusted between runs by recon\ufb01guring the lookup tables implemented in the muon trigger\n\ufb01rmware. In order to study more than three thresholds we investigated the two available, pre-de\ufb01ned\nmenus (named A and B) with respect to the low-pT muon trigger thresholds1.\nThe three implemented low-pT thresholds for trigger menu A are: 0 GeV2 (named MU00), 5 GeV\n(MU05) and 6 GeV (MU06). For trigger menu B, the three low-pT thresholds are 6 GeV (MU06), 8 GeV\n(MU08), and 10 GeV (MU10). Figure 1 shows the ef\ufb01ciencies of the low-pT LVL1 muon trigger signatures\nas a function of the true pT of the muon with the highest pT in the event.\nThe LVL1 trigger ef\ufb01ciency depends strongly on the threshold chosen for the transverse momentum\nof the muon as shown in Table 2. Note that there is a discrepancy between the MU06 ef\ufb01ciencies from both\ntrigger menus, which will be taken as a systematic uncertainty of the current implementation. Although\nthese dedicated trigger studies have been performed with the B0\ns \u2192D\u2212\ns a+\n1 sample, the LVL1 ef\ufb01ciencies\nfor B0\ns \u2192D\u2212\ns \u03c0+(\u00b56) have been checked and agree well with those in Table 2.\nThe input to the LVL1 calorimeter trigger is a set of \u223c7 200 trigger towers with granularity \u2206\u03c6 \u00d7\n\u2206\u03b7 \u22480.1 \u00d7 0.1 formed by the analogue summation of calorimeter cells. There are separate sets of\ntrigger towers for the EM and hadronic calorimeters. The LVL1 jet algorithm employed here uses a\n1All presented trigger thresholds are meant to be inclusive, i.e. to include all events ful\ufb01lling a trigger signature with a pT\nthreshold equal to or higher than the indicated one.\n2This requires a coincidence between the muon chambers without an actual threshold applied. Due to the detector geometry\nthis corresponds to an effective transverse momentum threshold of about 4 GeV.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1169\n\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\nTrigger Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMU00\nMU05\nMU06\nATLAS\n(a) Thresholds for menu A [9]\n [GeV]\nT\np\n0\n5\n10\n15\n20\n25\n30\nTrigger Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMU06\nMU08\nMU10\nATLAS\n(b) Thresholds for menu B\nFigure 1: Muon trigger ef\ufb01ciency as a function of the true pT of the muon with the highest pT in the\nevent for the B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) for (a) trigger menu A and (b) trigger menu B.\nTable 2: LVL1 muon trigger ef\ufb01ciencies for the signal datasets B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) and B0\ns \u2192D\u2212\ns a+\n1 (\u00b56)\nand the exclusive background samples. The \ufb01rst three lines refer to trigger menu A [9], while the last\nthree lines refer to trigger menu B. For b\u00afb \u2192\u00b54X, b\u00afb \u2192\u00b56X and c\u00afc \u2192\u00b54X, the Monte Carlo data\nsamples are only available using trigger menu A.\nMenu\nThreshold\nEf\ufb01ciency [%]\nB0\ns \u2192D\u2212\ns a+\n1\nB0\ns \u2192D\u2212\ns a+\n1\nbb \u2192\u00b54X\nbb \u2192\u00b56X\nc\u00afc \u2192\u00b54X\n(\u00b54)\n(\u00b56)\nMU00\n75.65\u00b10.19\n86.77\u00b10.15\n71.74\u00b10.14\n86.60\u00b10.07\n70.42\u00b10.22\nA\nMU05\n68.41\u00b10.21\n82.60\u00b10.17\n63.51\u00b10.15\n81.91\u00b10.08\n62.05\u00b10.23\nMU06\n58.93\u00b10.22\n81.90\u00b10.17\n52.28\u00b10.16\n81.00\u00b10.08\n50.44\u00b10.24\nMU06\n61.15\u00b10.22\n83.83\u00b10.16\n\u2014\n\u2014\n\u2014\nB\nMU08\n44.78\u00b10.22\n77.64\u00b10.19\n\u2014\n\u2014\n\u2014\nMU10\n34.89\u00b10.21\n65.47\u00b10.21\n\u2014\n\u2014\n\u2014\ncluster of \u2206\u03c6 \u00d7\u2206\u03b7 of approximately 0.4\u00d70.4 (corresponding to 4\u00d74 trigger towers). The projections of\nthe vectors of the energy depositions onto the plane perpendicular to the beam axis (transverse energy,\nET) are summed over both the electromagnetic and the hadronic layers. The jet algorithm moves the\ncluster template in steps of 0.2 across the \u03c6 \u00d7\u03b7 plane. An RoI is produced if the 4\u00d74 cluster is a local\nET maximum (as de\ufb01ned in [10]) and the cluster ET sum is greater than the required threshold. The\njet RoI is usable if the average number of RoIs per event (RoI multiplicity, see Fig. 2 and Table 3) is\nsmall, ideally about 1-2. Clearly, a compromise is required as an increased threshold will reduce the\nmultiplicity, but will also give a reduced ef\ufb01ciency for \ufb01nding the B jet in an event.\nFor a transverse energy threshold of 4 GeV, which is implemented to initiate the LVL2 D\u00b1\ns trigger in\ntrigger menus A and B, the jet trigger has an acceptance of (98.36\u00b10.06)% based on all events in the\nB0\ns \u2192D\u2212\ns a+\n1 sample.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1170\n\nNumber of RoIs\n0\n2\n4\n6\n8\n10\n12\nEntries\n0\n10000\n20000\n30000\n40000\n50000\nJT06\nJT05\nJT04\nATLAS\n(a) b\u00afb \u2192\u00b54X\nNumber of RoIs\n0\n2\n4\n6\n8\n10\n12\nEntries\n0\n20\n40\n60\n80\n100\n3\n10\n\u00d7\nJT06\nJT05\nJT04\nATLAS\n(b) b\u00afb \u2192\u00b56X\nNumber of RoIs\n0\n2\n4\n6\n8\n10\n12\nEntries\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\nJT06\nJT05\nJT04\nATLAS\n(c) c\u00afc \u2192\u00b54X\nFigure 2: RoI multiplicity distributions for the background samples (a) for b\u00afb \u2192\u00b54X, (b) for b\u00afb \u2192\u00b56X\nand (c) for c\u00afc \u2192\u00b54X as a function of the jet RoI energy threshold [9]. Only RoIs with \u03b7 < 2.4 have\nbeen taken into account. This corresponds to the requirement that the RoI is to be contained within the\nsolid angle covered by the Inner Detector.\nTable 3: Mean and root mean square of the RoI multiplicity distributions (Figure 2) for the background\nsamples as a function of the jet RoI transverse energy (ET) threshold [9]. Only RoIs with \u03b7 < 2.4 have\nbeen taken into account. A strong anticorrelation between the ET threshold and the mean RoI multiplicity\nis observed.\nThreshold\nb\u00afb \u2192\u00b54X\nb\u00afb \u2192\u00b56X\nc\u00afc \u2192\u00b54X\n[ GeV]\nMean\nRMS\nMean\nRMS\nmean\nRMS\n4\n2.847\n1.746\n2.883\n1.754\n3.235\n1.759\n5\n1.301\n1.244\n1.441\n1.295\n1.643\n1.300\n6\n0.703\n0.952\n0.881\n1.046\n0.998\n1.048\n7\n0.454\n0.786\n0.634\n0.911\n0.703\n0.900\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1171\n\n3.2\nLVL2 Trigger Selection\nThe \ufb01rst step of LVL2 is to con\ufb01rm the LVL1 muon trigger decision using more precise muon momentum\nmeasurement. Secondly, information from Inner Detector and muon chambers are combined to give a\nfurther improvement in the momentum measurement.\nAs described above, the LVL2 tracking can be run in either FullScan or RoI-guided modes. In both\ncases, the same algorithm (named DsPhiPi) is used to combine the reconstructed tracks and search \ufb01rst\nfor a \u03c6 and then for a D\u00b1\ns . In the RoI-guided approach tracks are reconstructed in a region \u2206\u03c6 \u00d7 \u2206\u03b7 =\n1.5\u00d71.5 around all jet RoIs with ET above a certain programmable threshold [11]. A pT cut of 1.4 GeV\nis applied to all reconstructed tracks.\nOpposite sign track pairs are considered as a \u03c6 candidate if they pass the following cuts: |\u2206z| < 3 mm,\nwhere z is the distance along the beam line of the track\u2019s point of closest approach to the centre of the\ndetector, |\u2206\u03c6| < 0.2 and |\u2206\u03b7| < 0.2.\nThe tracks are combined using a K mass hypothesis and a cut around the \u03c6 mass m\u03c6(PDG) =\n1019.46 MeV [8] is applied. Track pairs passing the cut are then combined with all other tracks as-\nsuming a \u03c0 mass for the third track. An event is selected if the mass of the track triplet is close to the\nD\u00b1\ns mass mDs(PDG) = 1968.2 MeV. The mass cuts used are 1005 MeV < mKK < 1035 MeV for the \u03c6\ncandidates and 1908 MeV < mKK\u03c0 < 2028 MeV for the Ds candidates.\nThe LVL2 track \ufb01t masses are shown in Figure 3 and Table 4 for the RoI-guided approach and\nFullScan. The standard deviations obtained from the Gaussian \ufb01ts show that the mass cuts used corre-\nspond to 3.0 standard deviations for the \u03c6 mass distribution and 2.8 standard deviations for the D\u00b1\ns mass\ndistribution [9]. The results for the RoI-based approach and those for FullScan agree well.\n) [MeV]\n\u03c6\nm(\n1005\n1010\n1015\n1020\n1025\n1030\n1035\nEntries (normalized)\n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\nRoI\nFS\nATLAS\n(a) True \u03c6 candidates\n) [MeV]\n\u00b1\ns\nm(D\n1900\n1920\n1940\n1960\n1980\n2000\n2020\n2040\nEntries (normalized)\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nRoI\nFS\nATLAS\n(b) True D\u00b1s candidates\nFigure 3: LVL2 track \ufb01t mass distributions of (a) \u03c6 and (b) D\u00b1\ns candidates (corresponding to a \u03c6 or D\u00b1\ns\nparticle from the signal decay in the Monte Carlo truth information) for the FullScan- and RoI-based\nLVL2 trigger signatures from B0\ns \u2192D\u2212\ns a+\n1 events ful\ufb01lling the respective LVL2 D\u00b1\ns trigger signature and\nMU06 [9].\nThe acceptances of possible trigger strategies up to LVL2 are given in Table 5 for the signal samples\nand in Table 6 for the background datasets. The LVL2 trigger rates for the B0\ns \u2192D\u2212\ns \u03c0+ channel are\nexpected to be lower by a few percent since the average pT of the B0\ns candidates and consequently the\naverage pT of the Ds candidates is smaller for the B0\ns \u2192D\u2212\ns \u03c0+ channel than for the B0\ns \u2192D\u2212\ns a+\n1 channel\ndue to different track selections (see Fig. 5 and Section 5.1).\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1172\n\nTable 4: LVL2 track \ufb01t masses for the FullScan- and RoI-based LVL2 trigger signatures (only candidates\ncorresponding to a \u03c6 or D\u00b1\ns particle from the signal decay in the Monte Carlo truth information) from\nB0\ns \u2192D\u2212\ns a+\n1 events ful\ufb01lling the respective LVL2 D\u00b1\ns trigger and MU06. The table shows the results of\nGaussian \ufb01ts within the trigger mass windows to the mass distributions from Fig. 3. The results for both\ntrigger strategies agree within statistical errors.\nFullScan-based\nLVL2 trigger [9]\nRoI-based\nLVL2\ntrigger\nm(\u03c6): mean [MeV ]\n1019.55\u00b10.05\n1019.52\u00b10.05\nm(\u03c6): std. dev. [MeV ]\n5.07\u00b10.06\n5.04\u00b10.05\nm(D\u00b1\ns ): mean [MeV ]\n1966.9\u00b10.3\n1967.0\u00b10.3\nm(D\u00b1\ns ): std. dev. [MeV ]\n21.7\u00b10.3\n21.5\u00b10.3\nTable 5: Acceptances of LVL2 (RoI and FullScan, FS) for the B0\ns \u2192D\u2212\ns a+\n1 sample for trigger menus A\nand B.\nMenu A\nMenu B\nTrigger\nscenario\nPasses (in %)\n(\u00b56)\nPasses (in %)\n(\u00b54)\nTrigger\nscenario\nPasses (in %)\n(\u00b56)\nPasses (in %)\n(\u00b54)\nEvents\n50 000\n50 000\n50 000\n50 000\nL2 mu0\n85.19\u00b10.16\n72.05\u00b10.20\nL2 mu6\n77.13\u00b10.19\n35.03\u00b10.21\nL2 mu5\n79.65\u00b10.18\n49.39\u00b10.22\nL2 mu8\n45.54\u00b10.22\n18.96\u00b10.18\nL2 mu6\n75.66\u00b10.19\n34.41\u00b10.21\nL2 mu10\n26.04\u00b10.20\n10.91\u00b10.14\nFS & L2 mu0\n32.98\u00b10.21\n22.93\u00b10.19\nFS & L2 mu6\n29.99\u00b10.21\n12.71\u00b10.15\nFS & L2 mu5\n30.79\u00b10.21\n16.75\u00b10.17\nFS & L2 mu8\n19.14\u00b10.18\n10.91\u00b10.14\nFS & L2 mu6\n29.38\u00b10.20\n12.49\u00b10.15\nFS & L2 mu10\n11.83\u00b10.15\n4.92\u00b10.10\nRoI & L2 mu0\n28.74\u00b10.20\n19.14\u00b10.18\nRoI & L2 mu6\n26.19\u00b10.20\n11.10\u00b10.14\nRoI & L2 mu5\n26.88\u00b10.20\n14.26\u00b10.16\nRoI & L2 mu8\n17.09\u00b10.17\n7.05\u00b10.12\nRoI & L2 mu6\n25.68\u00b10.20\n10.91\u00b10.14\nRoI & L2 mu10\n10.80\u00b10.14\n4.56\u00b10.09\nTable 6: Acceptances of LVL2 (RoI and FullScan) for the background samples b\u00afb \u2192\u00b54X, b\u00afb \u2192\u00b56X\nand c\u00afc \u2192\u00b54X (trigger menu A).\nTrigger scenario\npasses\n(in\n%)\n(b\u00afb \u2192\u00b54X)\npasses\n(in\n%)\n(b\u00afb \u2192\u00b56X)\npasses\n(in\n%)\n(c\u00afc \u2192\u00b54X)\nevents\n98 450\n242 150\n44 750\nFS & L2 mu0\n2.00\u00b10.05\n3.73\u00b10.05\n2.71\u00b10.08\nFS & L2 mu5\n1.47\u00b10.04\n3.48\u00b10.05\n1.93\u00b10.06\nFS & L2 mu6\n1.11\u00b10.03\n3.32\u00b10.05\n1.43\u00b10.05\nRoI & L2 mu0\n1.73\u00b10.04\n3.34\u00b10.05\n2.34\u00b10.07\nRoI & L2 mu5\n1.30\u00b10.04\n3.12\u00b10.05\n1.73\u00b10.06\nRoI & L2 mu6\n1.01\u00b10.03\n2.99\u00b10.05\n1.32\u00b10.05\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1173\n\n3.3\nEvent Filter Selection\nThe muon con\ufb01rmation at the Event Filter (EF) employs a muon track reconstruction algorithm using\nmuon detector data only, similar to the algorithm used for of\ufb02ine reconstruction.\nThe EF D\u00b1\ns selection is very similar to that at LVL2. The track reconstruction can be performed in\nFullScan or RoI-guided modes, which share a common EF signature. The search for \u03c6 and D\u00b1\ns particles\ncurrently uses the same mass cuts as at LVL2, even though better mass resolutions are expected for the\nEF than for LVL2. In the future the mass cuts might be tightened and additional selection cuts will be\nadded as discussed in section 3.5. EF output rates, which are only available for the minimum bias sample,\nare discussed in the following subsections.\n3.4\nTrigger Strategies for Early Running\nAt the lowest luminosities (1031 cm\u22122s\u22121 and 1032 cm\u22122s\u22121), the trigger selection needs to be as ef\ufb01cient\nas possible, which means running a loose trigger. To estimate rates and perform timing studies a trigger\nmenu with a different set of muon thresholds [12] is applied to the minimum bias sample. Table 7\nshows the expected trigger rates for muons at LVL1 and after con\ufb01rmation at LVL2. The output rates\nof the DsPhiPi trigger at LVL2 and the EF are given in Table 8 for 1031 cm\u22122s\u22121. For a luminosity\nof 1033 cm\u22122s\u22121 and higher, the rates are expected to increase because of event pile-up and cavern\nbackground events.\nTable 7: Muon rates based on 2.6 \u00b7 106 minimum bias events. Rates set in italics are based on an inter-\npolation using an exponential approximation of the rate dependence on the muon threshold concerned.\nEffects caused by event pile-up and cavern-background events are not included.\nLuminosity\nLVL1\n[cm\u22122s\u22121]\nL1 MU00\nL1 MU06\nL1 MU10\n1031\n1.3 \u00b1 0.02 kHz\n480 \u00b1 10 Hz\n266 \u00b1 8 Hz\n1032\n13.0 \u00b1 0.2 kHz\n4.8 \u00b1 0.1 kHz\n2.7 \u00b1 0.1 kHz\n1\u00b71033\n130 \u00b1 2 kHz\n48 \u00b1 1 kHz\n27 \u00b1 1 kHz\n2\u00b71033\n260 \u00b1 4 kHz\n96 \u00b1 2 kHz\n54 \u00b1 2 kHz\nLVL2\nL2 mu0\nL2 mu5\nL2 mu6\nL2 mu8\nL2 mu10\n1031\n450 \u00b1 11 Hz\n213 Hz\n120 \u00b1 6 Hz\n50 Hz\n25 \u00b1 3 Hz\n1032\n4.5 \u00b1 0.1 kHz\n2.1 kHz\n1.20 \u00b1 0.06 kHz\n500 Hz\n250 \u00b1 30 Hz\n1\u00b71033\n45.0 \u00b1 1.1 kHz\n21 kHz\n12.0 \u00b1 0.6 kHz\n5 kHz\n2.5 \u00b1 0.3 kHz\n2\u00b71033\n90.0 \u00b1 2.2 kHz\n42 kHz\n24.0 \u00b1 1.2 kHz\n10 kHz\n5.0 \u00b1 0.6 kHz\nIn addition to the overall allowed output rate, the time constraints of the HLT system are limiting the\nDsPhiPi trigger. The maximum allowed average computing times are 40 ms at LVL2 and 1 s at the EF.\nMost of the time is taken in the tracking algorithms as can be seen in Table 9 which shows the average\nCPU time used by the tracking and hypothesis algorithms at LVL2 and EF.\nTable 10 summarises the LVL2 ef\ufb01ciencies and the expected numbers for B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) events\nbefore and after the application of event selection cuts in the analysis as well as the estimated LVL2 and\nEF trigger rates for different luminosity scenarios and different trigger choices. The L2 and EF output\nrates shown in this table are deduced from the rate information given in Tables 7 and 8. The LVL2\nmuon trigger ef\ufb01ciency estimates presented in Table 10 are based on the LVL2 results obtained with the\nB0\ns \u2192D\u2212\ns a+\n1 (\u00b54) sample shown in Table 5.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1174\n\nTable 8: Output rates for the DsPhiPi trigger based on 2.6\u00b7106 minimum bias events at 1031 cm\u22122s\u22121.\nRates set in italics are based on an interpolation using the results from Table 7.\nLVL2\nEF\nMuon input trigger\nRoI\nFullScan\nRoI\nFullScan\nL1 MU00\n23 \u00b1 3 Hz\n31 \u00b1 3 Hz\n14 \u00b1 2 Hz\n19 \u00b1 2 Hz\nL1 MU06\n11 \u00b1 2 Hz\n13 \u00b1 2 Hz\n6.4 \u00b1 1.3 Hz\n7.5 \u00b1 1.4 Hz\nL2 mu0\n15 \u00b1 2 Hz\n18 \u00b1 2 Hz\n6.1 \u00b1 1.3 Hz\n6.9 \u00b1 1.4 Hz\nL2 mu5\n9.5 Hz\n9.9 Hz\n4.5 Hz\n4.5 Hz\nL2 mu6\n6.7 \u00b1 1.3 Hz\n6.4 \u00b1 1.3 Hz\n3.5 \u00b1 1.0 Hz\n3.2 \u00b1 0.9 Hz\nL2 mu8\n3.9 Hz\n3.3 Hz\n2.1 Hz\n1.7 Hz\nL2 mu10\n2.5 Hz\n2.0 Hz\n1.2 Hz\n0.9 Hz\nTable 9: Average CPU times on an HLT computing node (Dual core Intel(R) Xeon(R) CPU 5160 @\n3.00 GHz) using 900 b\u00afb \u2192\u00b56X events.\nAlgorithm\nTime/RoI\nTime/event\nLVL2\ntracking\nIdscan RoI\n15 ms\n23 ms\nIdscan FullScan\n91 ms\nhypothesis\nDsPhiPi\n< 1 ms\nEvent Filter\ntracking\nRoI\n130 ms\n208 ms\nFullScan\n470 ms\nhypothesis\nDsPhiPi\n< 1 ms\nAt 1031 cm\u22122s\u22121, once the improvements discussed in Section 3.5 have been applied to the EF\nalgorithms, it should be possible to run the FullScan-based trigger at the LVL1 4 GeV muon rate and\nto remain within the constraints given by available trigger resources. As the luminosity is increased to\n1032 cm\u22122s\u22121, we will need to raise the muon threshold for the FullScan-based trigger or to move to a\nRoI-based trigger. However, the muon threshold should be kept as low as possible in order to achieve\nthe highest possible trigger ef\ufb01ciency and to allow for as many B0\ns \u2192D\u2212\ns a+\n1 events as possible to pass.\nCompared to earlier publications like [13] the b\u00afb cross-section as shown in [7] is at the upper limit of\nwhat is expected and therefore the muon rates are likely to be overestimated.\n3.5\nTrigger Strategies for Running at 1033 cm\u22122s\u22121\nAt 1033 cm\u22122s\u22121 the trigger needs to remain as ef\ufb01cient as possible while operating within the constraints\nof the trigger system\u2019s resources. The EF output rate is expected to be about 10-20 Hz for B-physics.\nThe muon rates expected at LVL1 and LVL2 for different thresholds and luminosities are included\nin Table 7. The LVL2 muon rates are the input rates for the LVL2 tracking algorithms. Using the\ninformation on jet RoI multiplicities from Figure 2 and Table 3, the computing times from Table 9 and\nthe muon rates in Table 7, trigger strategies are determined for different luminosities.\nFor a luminosity of 1033 cm\u22122s\u22121, a LVL1 trigger muon in combination with the RoI-based Ds trigger\nwill be used. It is planned to use thresholds of 6 GeV for the trigger muon and 5 GeV for the jet RoI\ntrigger. It is clear from Table 8 that in order to run such a trigger the LVL2 and EF selections will have\nto be tightened. This may be achieved by introducing vertex \ufb01tting and by reconstructing the B0\ns at the\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1175\n\nTable 10: LVL2 and EF output rates for minimum bias events, LVL2 trigger ef\ufb01ciencies and numbers\nof expected B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) events without or with selection cuts. Rates set in italics are estimates\nbased on the interpolated and extrapolated rates given in Table 7. LVL2 output rates marked by \u2020 are\ndownscaled by a factor two, the estimated rate reduction for a Ds vertex requirement at LVL2. For EF\noutput rates marked by \u2021, an estimated rate reduction factor of 60 accounting for EF B0\ns reconstruction is\napplied. (See section 3.5 for details.) The results in the columns \u201cLVL2 eff.\u201d and NB0\ns \u2192D\u2212\ns a+\n1\nLVL2 output (without\nand with selection cuts applied) are based on the B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) Monte Carlo data sample. Num-\nbers marked by # are corrected for the estimated ef\ufb01ciency loss by a Ds vertex requirement at LVL2.\nThe integrated luminosities and expected event numbers correspond to one year running at the given\ninstantaneous luminosity (107 seconds).\nL\nR L dt\nTrigger\nLVL2 eff.\nNB0\ns\u2192D\u2212\ns a+\n1\nLVL2 output\nNB0\ns \u2192D\u2212\ns a+\n1\nLVL2 output\nLVL2 rate\nEF rate\n[cm\u22122s\u22121]\n[pb]\u22121\nset\n[%]\nno sel. cuts\nincl. sel. cuts\n[Hz]\n[Hz]\n1031\n100\nL2mu0FS\n22.93\u00b10.19\n308\n63\n18 \u00b1 2\n6.9 \u00b1 1.4\nL2mu5FS\n16.75\u00b10.17\n225\n47\n9.9\n4.5\nL2mu6FS\n12.49\u00b10.15\n168\n35\n6.4 \u00b1 1.3\n3.2 \u00b1 0.9\n1032\n1 000\nL2mu6FS\n12.49\u00b10.15\n1 678\n351\n64 \u00b1 13\n32 \u00b1 9\nL2mu5RoI\n14.26\u00b10.16\n1 916\n267\n95\n45\nL2mu6RoI\n10.91\u00b10.14\n1 466\n322\n67 \u00b1 13\n35 \u00b1 10\n1033\n10 000\nL2mu5RoI\n12.01\u00b10.13#\n16 134#\n3 582#\n475\u2020\n7.5\u2021\nL2mu6RoI\n9.19\u00b10.12#\n12 344#\n2 709#\n335\u00b193\u2020\n5.8\u00b12.0\u2021\nL2mu8RoI\n5.94\u00b10.10#\n7 976#\n1 757#\n196\u2020\n3.5\u2021\nL2mu10RoI\n3.84\u00b10.08#\n5 159#\n1 132#\n126\u2020\n2.0\u2021\n2\u00b71033\n20 000\nL2mu6RoI\n9.19\u00b10.12#\n24 687#\n5 418#\n670\u00b1187\u2020\n11.7\u00b14.0\u2021\nL2mu8RoI\n5.94\u00b10.10#\n15 953#\n3 517#\n392\u2020\n7.1\u2021\nL2mu10RoI\n3.84\u00b10.08#\n10 318#\n2 264#\n252\u2020\n4.1\u2021\nEF level.\nPreliminary studies at LVL2 show that a requirement for a vertex \ufb01t to the 3 tracks of the Ds candidate\ncan achieve a factor 2 rate reduction for a drop in ef\ufb01ciency from 38% to 32%. This estimate is applied\nto cells marked by # and \u2020 in Table 10. Also, it might be an option to further reduce the rate by tightening\nthe acceptance windows for m\u03c6 and mDs on LVL2, but the resulting rate reduction and the expected signal\nef\ufb01ciency loss will need to be studied.\nA considerable rate reduction at the EF level may be achieved by reconstructing the B0\ns. A preliminary\nstudy using of\ufb02ine selection cuts (see Section 5.1), which have been relaxed to simulate wider mass\nwindow and vertexing requirements for the reconstructed particles, has been performed with the b\u00afb \u2192\n\u00b54X and c\u00afc \u2192\u00b54X samples. The resulting rate reduction factor, estimated to be approximately 60, is\napplied to cells marked by \u2021 in Table 10. According to this study, the overall trigger and reconstruction\nef\ufb01ciency for the B0\ns \u2192D\u2212\ns a+\n1 signal events will be reduced by about 55%. Although these estimates will\nneed to be con\ufb01rmed by an implementation of a simpli\ufb01ed B0\ns reconstruction at the EF level, reasonable\nEF output rates are expected to be achievable.\nThe numbers of expected B0\ns \u2192D\u2212\ns a+\n1 (\u00b54) events for 10 fb\u22121 of data for a luminosity of 1033 cm\u22122s\u22121\nare given in Table 10. It will be necessary to establish a muon trigger threshold as low as possible to\nmaximise the signal event yield.\n3.6\nTrigger Strategies for Higher Luminosities\nAs luminosity increases, it is necessary to stay within the limits of the LVL2 trigger processing times and\nallowable output rates. As Table 10 shows, this will require increasing the muon threshold to 8 GeV or\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1176\n\n10 GeV and to add additional trigger elements in the EF as discussed at the end of Section 3.5. Another\noption, however a less ef\ufb01cient one, is to prescale the 6 GeV rate before running the track reconstruction.\n4\nFlavour Tagging\nThe measurement of B0\ns oscillations needs the knowledge of the \ufb02avour of the B0\ns meson at production\ntime and at decay time in order to classify events as mixed or not mixed. The tagging algorithm tries\nto determine the \ufb02avour at production time, whereas the decay particles of the signal B0\ns determine the\n\ufb02avour at decay time. In this analysis soft muon tagging (see B-physics chapter of [4]) is used and\nthe general application on the simulated data samples is shown in Section 4.2 without applying trigger\nconditions or any selection cut. Tagging results speci\ufb01c for the hadronic channels under investigation\nincluding trigger and selection cuts for B0\ns candidates are given in Section 5.3.\n4.1\nSoft Muon Tagging\nIn proton-proton collisions b quarks are produced in pairs leaving the signal B0\ns and the opposite side b\nhadron with the opposite \ufb02avour. In the case of a semileptonic decay as shown in Fig. 4, the charge of\nthe produced lepton is correlated with the \ufb02avour of the signal B0\ns meson at production time. The charge\nof the muon with the highest reconstructed pT is used for the determination of the \ufb02avour. Because of\nthe muon trigger, in hadronic B0\ns decay channels soft muon tagging has a high tagging ef\ufb01ciency \u03b5tag =\nNtag/Nall limited by the muon reconstruction ef\ufb01ciency. Details on the aspects of muon reconstruction\nand identi\ufb01cation in ATLAS can be found in [14].\nFigure 4: In the case of a signal B0\ns, the associated opposite side b hadron decaying semileptonically\nproduces a negatively charged lepton.\nThe dilution factor is de\ufb01ned as Dtag = Nc\u2212Nw\nNc+Nw where Nc is the number of events correctly tagged\nand Nw is the number of events with a wrong tag. These wrong tags arise from mixing of the tagging\nb hadron, muons from decays b \u2192c \u2192\u00b5, additional c pairs and various particles decaying into muons.\nThe wrong tag fraction \u03c9 = Nw/(Nc +Nw) is the ratio of wrongly tagged events to all tagged events. As\nthe generation of the simulated data does not include B meson oscillations, mixing of the tagging side\nhadron is introduced arti\ufb01cially using the integrated mixing probabilities \u03c7d and \u03c7s [8]:\n\u03c7d = \u0393(B0\nd \u2192\u00afB0\nd \u2192\u00b5+X)\n\u0393(B0\nd \u2192\u00b5\u00b1X)\n= 0.188\u00b10.003\n\u03c7s = \u0393(B0\ns \u2192\u00afB0s \u2192\u00b5+X)\n\u0393(B0s \u2192\u00b5\u00b1X)\n= 0.49924\u00b10.00003\n4.2\nApplication to Signal Samples\nIn Fig. 5 the transverse momentum of the signal B0\ns mesons is compared for the two B0\ns decay channels,\nthe vertical lines show the mean values of the two distributions. This difference arises from the different\nkinematical con\ufb01guration due to the condition on all charged \ufb01nal state particles pT > 0.5 GeV at Monte\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1177\n\nCarlo generation. As B0\ns \u2192D\u2212\ns a+\n1 has a total number of six \ufb01nal state particles, the mean transverse\nmomentum of the signal B0\ns is higher compared to B0\ns \u2192D\u2212\ns \u03c0+ with a total number of four \ufb01nal state\nparticles. The difference in the B0\ns transverse momentum spectrum is also expected at of\ufb02ine reconstruc-\ntion level due to the different pT selection cuts for the \u03c0 and the a1 combinations (see Section 5.1). This\nleads in the case of the B0\ns \u2192D\u2212\ns \u03c0+ sample to an overall wrong tag fraction of \u03c9 = 20.29 \u00b1 0.14 %\nand in the case of the B0\ns \u2192D\u2212\ns a+\n1 channel to a wrong tag fraction \u03c9 = 21.05\u00b10.11 %, which is higher\ncompared to the B0\ns \u2192D\u2212\ns \u03c0+ channel (see all events in Table 11 in Section 5.3).\n) [GeV]\ns\n(B\nT\np\n0\n10\n20\n30\n40\n50\n [%]\nall\nN / N\n0\n1\n2\n3\n4\n\u03c0\n \ns\n D\n\u2192\n \ns\nB\n1\n a\ns\n D\n\u2192\n \ns\nB\nATLAS\nFigure 5: Normalised distributions of signal B0\ns transverse momentum pT of the two channels B0\ns \u2192\nD\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 . The vertical lines represent the mean values of the distributions, in the case of\nB0\ns \u2192D\u2212\ns \u03c0+ the mean is 14.80\u00b10.03 GeV, in the case of B0\ns \u2192D\u2212\ns a+\n1 17.68\u00b10.03 GeV. The observed\ndifference is due to the different particle selections.\nIn Fig. 6 the wrong tag fractions and the sources of these wrong tags are compared for both B0\ns decays\nchannels. The wrong tag fraction is shown as a function of the tagging muon\u2019s transverse momentum\npT(\u00b5), in Fig. 6(a) for B0\ns \u2192D\u2212\ns \u03c0+ and in Fig. 6(b) for B0\ns \u2192D\u2212\ns a+\n1 . In the regime pT(\u00b5) < 11 GeV the\nB0\ns \u2192D\u2212\ns a+\n1 wrong tag fraction is higher. As mentioned above this difference arises from the different\ntrack selections of the two decay channels. In both channels the two main sources of wrong tags are\nmixing of neutral B mesons on the tagging side and muons from cascade decays b \u2192c \u2192\u00b5. As the\noverall wrong tag fraction is decreasing with the muon pT, also the part with a wrong tag due to the\ncascade b \u2192c \u2192\u00b5 is decreasing at the same rate. A further source of mistags are additional c\u00afc-pairs.\nThe wrong tag fraction of this part stays about constant with increasing pT(\u00b5). A small part of the wrong\ntag fraction originates from J/\u03c8, \u03c6, \u03c1, \u03b7 or \u03c4 particles decaying into muons. Additional sources like\nmuons from kaons and pions or hadrons misidenti\ufb01ed as muons can be neglected [12].\nA b\u00afb pair produced in proton proton collisions has a transverse momentum equal to zero at \ufb01rst order.\nGoing through fragmentation and hadronisation, the pT of the signal B0\ns meson and the opposite side b\nhadron are still correlated, and therefore a muon coming from a semileptonic decay of the b hadron also\nis correlated with the signal B0\ns. Hence a muon from a cascade b \u2192c \u2192\u00b5 is more likely to pass the\nLVL1 muon trigger when B0\ns meson has a higher pT, leading to the increase in wrong tag fraction with\npT(B0\ns). This behaviour is shown in the Fig. 6(c) and 6(d).\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1178\n\n) [GeV]\n\u00b5\n(\nT\np\n4\n6\n8\n10\n12\n14\nwrong tag fraction [%]\n0\n5\n10\n15\n20\n25\n30\nall, mixing\nall, no mixing\n c\n\u2192\nchain b \nadd. c-pair\nother\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n) [GeV]\n\u00b5\n(\nT\np\n4\n6\n8\n10\n12\n14\nwrong tag fraction [%]\n0\n5\n10\n15\n20\n25\n30\nall, mixing\nall, no mixing\n c\n\u2192\nchain b \nadd. c-pair\nother\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\n) [GeV]\ns\n(B\nT\np\n0\n10\n20\n30\n40\n50\nwrong tag fraction [%]\n0\n5\n10\n15\n20\n25\n30\n35\nall, mixing\nall, no mixing\n c\n\u2192\nchain b \nadd. c-pair\nother\nATLAS\n(c) B0s \u2192D\u2212s \u03c0+\n) [GeV]\ns\n(B\nT\np\n0\n10\n20\n30\n40\n50\nwrong tag fraction [%]\n0\n5\n10\n15\n20\n25\n30\n35\nall, mixing\nall, no mixing\n c\n\u2192\nchain b \nadd. c-pair\nother\nATLAS\n(d) B0s \u2192D\u2212s a+\n1\nFigure 6: Wrong tag fraction as functions of tagging muons transverse momentum pT(\u00b5) in (a) and (b)\nand wrong tag fractions as functions of signal Monte Carlos B0\ns transverse momentum pT(B0\ns) in (c) and\n(d). The wrong tag fraction is shown with mixing of the tagging side b hadron and without mixing.\nWithout mixing, the different sources of wrong tags are shown. The main contribution is coming from\nb \u2192c \u2192\u00b5 followed by additional c pairs. Additional sources shown are muons coming from J/\u03c8, \u03c6,\n\u03c1, \u03b7 and \u03c4.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1179\n\n4.3\nSystematic Uncertainties of Soft Muon Tagging\nThe calibration of the soft muon tagger will be done with events from the exclusive decay channel\nB+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+ . The high branching ratio and the simple event topology allows the measurement\nof this channel during the initial luminosity phase at the LHC. Without mixing on the signal side, these\nevents can be used to estimate the systematic uncertainties of soft muon tagging.\nFor an integrated luminosity of 1 fb\u22121 160 000 events of the decay channel B+ \u2192J/\u03c8(\u00b5+\u00b5\u2212)K+ are\nexpected [15] at ATLAS. About 13.5 % events are estimated to have an additional third muon for \ufb02avour\ntagging. Requiring a minimum transverse momentum of 6 GeV for this additional muon, the number of\nevents will be reduced by a factor of three. Assuming that the wrong tag fraction in this channel behaves\nlike in the hadronic B0\ns decay channels, the expected statistical error of the wrong tag fraction would be\nof the order of 0.1 % for 1 fb\u22121 integrated luminosity.\n5\nEvent Selection\nFor the following analysis selecting Bs candidates the default trigger choices are to require MU06 and\nJT04 trigger elements at LVL1 and to perform a search for the Ds \u2192\u03c6(K+K\u2212)\u03c0 decay within a jet RoI\nat LVL2. Resulting event numbers and plots are given for 10 fb\u22121 unless indicated otherwise.\n5.1\nSignal Event Reconstruction\nFor the reconstruction of the Bs vertex only tracks with a pseudo-rapidity |\u03b7| < 2.5 are used proceeding\nvia the following steps. The \u03c6 decay vertex is \ufb01rst reconstructed by considering all pairs of oppositely-\ncharged tracks with pT > 1.5 GeV for both tracks. Kinematic cuts on the angles between the two tracks,\n\u2206\u03d5KK < 10\u25e6and \u2206\u03b8KK < 10\u25e6, are imposed, where \u03d5 denotes the azimuthal angle and \u03b8 the polar angle.\nThe two-track vertex is then \ufb01tted assigning the kaon mass to both tracks. Combinations passing a \ufb01t-\nprobability cut [16] of 1% (\u2243\u03c72/dof = 7/1) with the invariant mass within three standard deviations of\nthe nominal \u03c6 mass are selected as \u03c6 candidates. The plots in Fig. 7 show the invariant mass distribution\nfor all mKK combinations overlaid with the \u03c6 candidates matching a generated \u03c6 from the signal decay\n(grey \ufb01lled area) \ufb01tted with a single Gaussian function. For the B0\ns \u2192D\u2212\ns \u03c0+ channel the mass resolution\nis \u03c3\u03c6 = (4.30\u00b10.03) MeV and for the B0\ns \u2192D\u2212\ns a+\n1 channel \u03c3\u03c6 = (4.28\u00b10.03) MeV. This mass window\nfor accepted \u03c6 candidates is shown by the vertical lines. No trigger selections are applied for the mass\nplots shown in Fig. 7 to Fig. 9.\nFrom the remaining tracks, a third track with pT > 1.5 GeV is added to all accepted \u03c6 candidates.\nThe pion mass is assigned to the third track and a three-track vertex is \ufb01tted. Three-track vertex candi-\ndates which have a \ufb01t probability greater than 1% (\u2243\u03c72/dof = 12/3) and an invariant mass within three\nstandard deviations of the nominal Ds mass are selected as Ds candidates. The plots in Fig. 8 show\nthe invariant mass distribution for all mKK\u03c0 combinations overlaid with the Ds candidates matching a\ngenerated Ds from the signal decay (grey \ufb01lled area) \ufb01tted with a single Gaussian function. For the\nB0\ns \u2192D\u2212\ns \u03c0+ channel the mass resolution is \u03c3Ds = 17.81 \u00b1 0.13 MeV and for the B0\ns \u2192D\u2212\ns a+\n1 channel\n\u03c3Ds = 17.92\u00b10.13 MeV. The 3\u03c3Ds mass range for accepted Ds candidates is shown by the vertical lines.\nFor the B0\ns \u2192D\u2212\ns a+\n1 channel a search is performed for a\u00b1\n1 candidates using three-particle combina-\ntions of charged tracks for events with a reconstructed Ds meson. In a \ufb01rst step \u03c10 mesons are recon-\nstructed from all combinations of two tracks with opposite charges and with pT > 0.5 GeV, each particle\nin the combination being assigned a pion mass. A kinematic cut \u2206R\u03c0\u03c0 =\np\n\u2206\u03c6 2\u03c0\u03c0 +\u2206\u03b72\u03c0\u03c0 < 0.650 is\nused to reduce the combinatorial background. The two selected tracks are then \ufb01tted as originating from\nthe same vertex; from the combinations passing a \ufb01t probability cut of 1% (\u2243\u03c7 2/dof = 7/1), those with\nan invariant mass within 400 MeV of the nominal \u03c10 mass are selected as \u03c10 candidates. Next a third\ntrack with pT > 0.5 GeV from the remaining charged tracks is added to the \u03c10 candidate, assuming the\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1180\n\npion hypothesis for the extra track. A kinematic cut \u2206R\u03c1\u03c0 < 0.585 is applied. The three tracks are \ufb01tted\nto a common vertex without any mass constraints. Combinations with a \ufb01t probability greater than 1%\n(\u2243\u03c72/dof = 12/3) and with an invariant mass within 325 MeV of the nominal a1 mass are selected as a\u00b1\n1\ncandidates.\nThe B0\ns candidates are reconstructed combining the D\u00b1\ns candidates with a\u00b1\n1 candidates with opposite\ncharge and different tracks. A six-track vertex \ufb01t is performed with mass constraints for the tracks from\n\u03c6 and Ds; due to the large a1 natural width the three tracks from the a1 are not constrained to the a1 mass.\nThe total momentum of the B0\ns vertex is required to point to the primary vertex and the momentum of the\nDs vertex to the B0\ns vertex. Only six-track combinations with a vertex \ufb01t probability greater than 1% (\u2243\n\u03c72/dof = 27/12) are considered as B0\ns candidates.\nFor the B0\ns \u2192D\u2212\ns \u03c0+ channel for each reconstructed Ds meson a fourth track from the remaining\ntracks in the event is added. This track is required to have opposite charge with respect to the pion track\nfrom the Ds and pT > 1 GeV. The four-track decay vertex is \ufb01tted including \u03c6 and Ds mass constraints,\nand requiring that the total momentum of the B0\ns vertex points to the primary vertex and the momentum\nof Ds vertex points to the B0\ns vertex. In order to be selected as B0\ns candidates, the four-track combinations\nare required to have a vertex \ufb01t probability greater than 1% (\u2243\u03c72/dof = 20/8).\nFor both channels, B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 , the signed separation between the reconstructed\nB0\ns vertex and the primary vertex is required to be positive (the momentum should not point backward to\nthe parent vertex). To improve the purity of the sample, further cuts are imposed: the proper decay time\nof the B0\ns has to be greater than 0.4 ps, the B0\ns impact parameter (shortest distance of the reconstructed\nB0\ns trajectory from the primary vertex in the transverse plane to the reconstructed B0\ns decay vertex) is\nrequired to be smaller than 55 \u00b5m and pT of the B0\ns must be larger than 10 GeV. The plot in Fig. 9(a)\nshows the invariant mass distribution for all mKK\u03c0\u03c0 Bs candidates matching a generated Bs from the signal\ndecay for the B0\ns \u2192D\u2212\ns \u03c0+ channel \ufb01tted with a single Gaussian function and giving a mass resolution of\n\u03c3Bs = 52.80\u00b10.68 MeV. For the B0\ns \u2192D\u2212\ns a+\n1 channel Fig. 9(b) shows the invariant mass distribution for\nall mKK\u03c0\u03c0\u03c0\u03c0 Bs candidates matching a generated Bs and giving a mass resolution of \u03c3Bs = 40.82\u00b10.53\nMeV. The difference in the B0\ns mass resolutions is caused by the pT spectrum of the \u03c0 in the B0\ns \u2192D\u2212\ns \u03c0+\ndecay being harder than the pT spectra of the three pions in the B0\ns \u2192D\u2212\ns a+\n1 decay, as the pion momentum\nresolution is worse for higher pT. A \ufb01nal mass cut of two standard deviations on the B0\ns candidates is\napplied for further analysis (see vertical lines in Fig. 9). For some events more than one B0\ns candidate\nis reconstructed and in that case the candidate with the lowest \u03c72/dof from the vertex \ufb01t is selected for\nfurther analysis.\nNo relevant effects induced by the trigger selections on \ufb01t variables of the mass plots or the kinematic\ndistributions of the Bs candidates are found (discussed in Section 6.3). All differences are within the \ufb01t\nerrors.\n5.2\nBackground Channels\nTwo main sources of background are considered: irreducible background coming from a decay channel\nthat closely mimics the B0\ns signal and combinatorial background coming from random combination of\ntracks.\n5.2.1\nExclusive Background Channels\nThe exclusive samples listed in Table 1 are used as irreducible background sources. See Table 12 in Sec-\ntion 6 for the numbers of reconstructed candidates after applying the same selection cuts as for the signal\nsamples. The histograms in Fig. 10 show the invariant mass spectrum of reconstructed B0\ns candidates for\nthe B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 channel respectively (no trigger selection cut applied). The different\ncontributions are scaled with the cross-section given in Table 1.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1181\n\n [MeV]\nKK\nm\n980\n1000\n1020\n1040\n1060\n3\n(Entries / 1 MeV) x10\n0\n1\n2\n3\n4\n5\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [MeV]\n KK\nm\n980\n1000\n1020\n1040\n1060\n3\n(Entries / 1 MeV) x10\n0\n1\n2\n3\n4\n5\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 7: Reconstructed mass mKK for all combinations within the signal sample (black line) and KK\ncandidates corresponding to a \u03c6 particle from the signal decay in the Monte Carlo truth information (grey\n\ufb01lled). The standard deviation obtained from a \ufb01t within two standard deviations of a Gaussian function\n(dashed) to the distribution de\ufb01nes the three standard deviation cut range (vertical dashed). No trigger\nconditions are applied.\n [MeV]\n\u03c0\nKK\nm\n1800\n1900\n2000\n2100\n3\n(Entries / 3 MeV) x10\n0\n0.5\n1\n1.5\n2\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [MeV]\n\u03c0\n KK\nm\n1800\n1900\n2000\n2100\n3\n(Entries / 3 MeV) x10\n0\n0.5\n1\n1.5\n2\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 8: Reconstructed mass mKK\u03c0 for all combinations within the signal sample (black line) and KK\u03c0\ncandidates corresponding to a Ds particle from the signal decay in the Monte Carlo truth information\n(grey \ufb01lled). The standard deviation obtained from a \ufb01t within two standard deviations of a Gaussian\nfunction (dashed) to the distribution de\ufb01nes the three standard deviation cut range (vertical dashed). No\ntrigger conditions are applied.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1182\n\n [MeV]\n\u03c0\n\u03c0\nKK\nm\n5000\n5200\n5400\n5600\n5800\nEntries / 10 MeV\n0\n100\n200\n300\n400\n500\n600\n700\n800\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [MeV]\n\u03c0\n\u03c0\n\u03c0\n\u03c0\n KK\nm\n5000\n5200\n5400\n5600\n5800\nEntries / 10 MeV\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 9: mKK\u03c0\u03c0 (a) and mKK\u03c0\u03c0\u03c0\u03c0 (b) reconstructed mass and \ufb01t of a Gaussian function to the distribu-\ntion. Each KK\u03c0\u03c0 (KK\u03c0\u03c0\u03c0\u03c0) candidate displayed corresponds to a Bs particle in the Monte Carlo truth\ninformation. The two standard deviation cut range is shown by the vertical dashed lines. No trigger chain\napplied.\n [MeV]\n\u03c0\n\u03c0\nKK\nm\n5000\n5200\n5400\n5600\n5800\n / 10MeV \n-1\nEvents for 1 fb\n0\n10\n20\n30\n40\n50\n60\n70\n80\n\u03c0\ns\nD\n\u2192\ns\nB\n\u03c0\ns\nD\n\u2192\nd\nB\n\u03c0\n*\ns\nD\n\u2192\ns\nB\n\u03c0\nD\n\u2192\nd\nB\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [MeV]\n\u03c0\n\u03c0\n\u03c0\n\u03c0\nKK\nm\n5000\n5200\n5400\n5600\n5800\n / 10MeV \n-1\nEvents for 1 fb\n0\n10\n20\n30\n40\n50\n1\na\ns\nD\n\u2192\ns\nB\n1\na\ns\nD\n\u2192\nd\nB\n1\n*a\ns\nD\n\u2192\ns\nB\n1\nDa\n\u2192\nd\nB\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 10: mKK\u03c0\u03c0 (a) and mKK\u03c0\u03c0\u03c0\u03c0 (b) reconstructed mass for signal and background channels. In (b)\nthe upper limit for the branching fraction of the channel Bd \u2192Dsa1 is used.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1183\n\nIn the case of B0\nd \u2192D+\ns a\u2212\n1 , there is no measurement of the branching fraction available. The current\nupper limit is therefore used as a conservative estimate. The similarity to the B0\nd \u2192D+\ns \u03c0\u2212channel\nindicates that the B0\nd \u2192D+\ns a\u2212\n1 cross section could be in the same order as the one of the B0\nd \u2192D+\ns \u03c0\u2212\nchannel and therefore the B0\nd \u2192D+\ns a\u2212\n1 contribution in Fig. 10 (b) could be much smaller.\nThe Bs \u2192D\u2217\ns\u03c0 and Bs \u2192D\u2217\nsa1 channels are treated as a background source, since the momentum\nand hence the lifetime estimation for this decay is \ufb02awed due to the missing photon from the decay of\nthe D\u2217\ns.\n5.2.2\nCombinatorial Background\nThe limited statistics of the combinatorial background samples (e.g. 242 150 events for b\u00afb \u2192\u00b56X) do not\nallow us to give a reasonable estimate for the signal to background ratio. This ratio as well as kinematic\nproperties of the combinatorial background, like the shape of the proper time distribution will be studied\nonce early data are available.\n5.3\nTagging Results\nSoft muon tagging is applied on all available simulated data of the two hadronic signal channels B0\ns \u2192\nD\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 . Table 11 shows the number of events, the tagging ef\ufb01ciency and the wrong tag\nfractions. The tagging ef\ufb01ciency corresponds to the fraction of events where muon candidates have been\nsuccessfully reconstructed. The events with at least one muon are separated into events with a good tag\nand events with a wrong tag resulting in a wrong tag fraction.\nComparing the results for all simulated events between the two signal channels, the difference in\nthe wrong tag fraction is of the order 1 % due to the different kinematical topology. As the RoI trigger\napplies a pT cut of 1.4 GeV on all reconstructed tracks, low pT B0\ns mesons are rejected leading to an\nincreased wrong tag fraction for the triggered events (see Fig. 6(c) and 6(d)). After event reconstruction\noverall wrong tag fractions of \u03c9 = 22.30+0.56\n\u22120.55 % for the channel B0\ns \u2192D\u2212\ns \u03c0+ and \u03c9 = 23.31+0.56\n\u22120.55 % for\nthe channel B0\ns \u2192D\u2212\ns a+\n1 are observed. Effects of mixing are included as described in Section 4.1.\nTable 11: Tagging ef\ufb01ciencies and wrong tag fractions for the signal channels B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192\nD\u2212\ns a+\n1 are shown for three different stages: all simulated events, all triggered events passing the LVL1\nmuon trigger and the LVL2 RoI trigger, and \ufb01nally the numbers for the reconstructed events. The errors\nare statistical only.\nProcess\nType of\nNumber of\nTagging\nWrong Tag\nEvents\nEvents\nEf\ufb01ciency [%]\nFraction [%]\nB0\ns \u2192D\u2212\ns \u03c0+\nall events\n88450\n96.08\u00b10.07\n20.29\u00b10.14\ntriggered\n21613\n98.77\u00b10.07\n22.96\u00b10.29\nreconstructed\n5687\n98.79+0.14\n\u22120.15\n22.30+0.56\n\u22120.55\nB0\ns \u2192D\u2212\ns a+\n1\nall events\n98450\n95.93\u00b10.06\n21.05\u00b10.13\ntriggered\n27118\n98.55\u00b10.07\n23.91\u00b10.26\nreconstructed\n5757\n98.47+0.16\n\u22120.17\n23.31+0.56\n\u22120.55\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1184\n\n6\nDetermination of \u2206ms\n6.1\nMethods for the Determination of \u2206ms and its Measurement Limits\nFor the determination of the B0\ns oscillation frequency the maximum likelihood method is used. The\nlikelihood L is a function of the proper time t and the mixing state \u00b5, parametrised by \u2206ms and \u2206\u0393s,\napplied to \ufb01ve classes of events simultaneously: mixed and unmixed B0\ns, mixed and unmixed B0\nd, and\nbackground with lifetime but no mixing. The B0\ns and B0\nd classes have characteristic wrong tag fractions\n\u03c9, which are determined on event-by-event basis as described previously. By maximising the likelihood\nL for a given event sample one can then extract the model parameters.\nFor obtaining the 5 \u03c3 discovery and 95% exclusion measurement limits on \u2206ms the amplitude \ufb01t\nmethod is used because the maximum likelihood method was found to have some disadvantages in that\ncase [5]. The estimation of the maximum value of \u2206ms measurable with the ATLAS detector is using\nB0\ns candidates from the B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 hadronic channels. The numbers of reconstructed\nevents after applying the trigger selection (L1 MU06 and LVL2 RoI) and the B0\ns selection cuts as well\nas the expected numbers for an integrated luminosity of 10 fb\u22121are given in Table 12 for all signal and\nbackground channels. The effective cross-sections for the various processes can be found in Table 1.\nSigni\ufb01cant background comes from the \u00afB0\nd \u2192D\u2212\ns \u03c0+/a+\n1 and B0\ns \u2192D\u2217\u2212\ns \u03c0+/a+\n1 channels, and from the\ncombinatorial background. Due to limited sample size the estimation of the combinatorial background\nis very approximate.\nThe relative fractions of the signal and the background contributions will be determined by a \ufb01t of\nmass shape templates to the reconstructed B0\ns mass distribution employing a wider mass window than\nused here for the \ufb01nal extraction of \u2206ms, similar to the method used by CDF [1]. The mass shape tem-\nplates will be determined from Monte Carlo mass distributions of the individual channels. Uncertainties\nin the knowledge of the shapes will be taken into account as part of the systematical uncertainty.\nTable 12: Signal and background samples used for the study of B0\ns- \u00afB0\ns oscillations and number of events\nas obtained from the analysis as well as expected numbers for an integrated luminosity of 10 fb\u22121.\nProcess\nSimulated\nRec.\nRec. events\nevents\nevents\nfor 10 fb\u22121\nB0\ns \u2192D\u2212\ns \u03c0+\n88 450\n5 687\n6 657\nB0\nd \u2192D+\ns \u03c0\u2212\n43 000\n1 814\n99\nB0\nd \u2192D\u2212\u03c0+\n41 000\n23\n35\nB0\ns \u2192D\u2217\u2212\ns \u03c0+\n40 500\n495\n1 116\nB0\ns \u2192D\u2212\ns a+\n1\n98 450\n5 757\n3 368\nB0\nd \u2192D+\ns a\u2212\n1\n50 000\n1 385\n< 2454\nB0\nd \u2192D\u2212a+\n1\n50 000\n49\n36\nB0\ns \u2192D\u2217\u2212\ns a+\n1\n100 000\n870\n1 052\n6.2\nConstruction of the Likelihood Function\nThe probability density to observe an initial B0\nj meson (j = d, s) decaying at time t0 after its creation as\na \u00afB0\nj meson is given by\np j(t0, \u00b50) =\n\u03932\nj \u2212(\u2206\u0393 j/2)2\n2\u0393 j\ne\u2212\u0393 j t0\n\u0012\ncosh \u2206\u0393 jt0\n2\n+ \u00b50 cos(\u2206m jt0)\n\u0013\n(1)\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1185\n\nwhere \u2206\u0393 j = \u0393 j\nH \u2212\u0393 j\nL, \u0393 j = (\u0393 j\nH +\u0393 j\nL)/2 and \u00b50 = \u22121.\nFor the unmixed case (an initial B0\nj meson decaying as a B0\nj meson at time t0), the probability density\nis obtained by setting \u00b50 = +1 in Eq. 1. Here the small effects of CP violation are neglected. Unlike\n\u2206\u0393d, which can be safely set to zero, the width difference \u2206\u0393s in the B0\ns- \u00afB0\ns system could be as much as\n20% of the total width [17].\nHowever, the above probability is modi\ufb01ed by experimental effects. The probability as a function of\n\u00b50 and the reconstructed proper time t is obtained as the convolution of p j(t0, \u00b50) with the proper time\nresolution Res j(t |t0):\nq j(t,\u00b50) = 1\nN\nZ \u221e\n0 p j(t0,\u00b50) Res j(t | t0) dt0\n(2)\nwith the normalisation factor\nN =\nR \u221e\ntmin(\nR \u221e\n0 p j(t\u2032,\u00b50) Res j(t | t\u2032) dt\u2032) dt .\n(3)\nHere tmin = 0.4 ps is the cut on the B0\ns reconstructed proper decay time. Plots in Fig. 11 show the\nproper time resolutions, which are parametrised with the sum of two Gaussian functions around the\nsame mean value. The widths from the \ufb01t are \u03c31 = (68.4\u00b13.3) fs for the core fraction of 53.2% and\n\u03c32 = (157.2\u00b15.7) fs for the rest of the tail part of the distribution for the B0\ns \u2192D\u2212\ns \u03c0+ channel. The\nvalues for the B0\ns \u2192D\u2212\ns a+\n1 channel are \u03c31 = (72.5\u00b14.3) fs for the core fraction of (58.0\u00b16.8) % and\n\u03c32 = (144.7\u00b17.3) fs for the tail part.\nAssuming a fraction \u03c9 j of wrong tags occurring at production and/or decay, the probability becomes\n\u02dcq j(t,\u00b5) = (1\u2212\u03c9 j)q j(t,\u00b5)+\u03c9 jq j(t,\u2212\u00b5)\n(4)\nwhere \u00b50 has been replaced by \u00b5 in order to indicate that now we are talking about the experimental\nobservation of same or opposite \ufb02avour tags. For each signal channel, the background is composed of\noscillating B0\nd mesons, with probability given by Eq. 4, and of non-oscillating combinatorial background,\nwith probability given by Eq. 5, which results from Eq. 1 and Eq. 4 by setting \u2206m = 0 and \u2206\u0393 = 0 :\npcb(t,\u00b5) = \u0393cb\n2 e\u2212\u0393cbt [1+ \u00b5 (1\u22122\u03c9cb)]\n(5)\nFor a fraction fk j of the j component (j = s, d, and combinatorial background cb) in the total sample\nof type k, one obtains the probability density function\npdfk(t,\u00b5) = \u2211\nj=s,d,cb\nfk j \u02dcq j(t,\u00b5) .\n(6)\nThe index k = 1 denotes the B0\ns \u2192D\u2212\ns \u03c0+ channel and k = 2 the B0\ns \u2192D\u2212\ns a+\n1 channel. The likelihood of\nthe total event sample is written as\nL (\u2206ms,\u2206\u0393s) =\nNch\n\u220f\nk=1\nNk\nev\n\u220f\ni=1\npdfk(ti,\u00b5i)\n(7)\nwhere Nk\nev is the total number of events of type k, and Nch = 2. Each pdfk is properly normalised to unity.\nFigure 12 shows how the experimental effects, as parametrised in Eqs.\n2, 4, and 6, modify the\ndistribution of the proper time t of a Monte Carlo data sample.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1186\n\n [ps]\n0\n - t\nrec\nt\n-0.5-0.4-0.3-0.2 -0.1 0\n0.1 0.2 0.3 0.4 0.5\nEntries / 20 fs\n0\n100\n200\n300\n400\n500\n600\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [ps]\n0\n - t\nrec\nt\n-0.5-0.4-0.3-0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.5\nEntries / 20 fs\n0\n100\n200\n300\n400\n500\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 11: The resolution \u03c3t of the proper time of simulated B0\ns \ufb01tted with two Gaussian functions\n(dashed lines). Both Gaussian functions use a common mean value.\n0\n50\n100\n150\n200\n250\n300\n350\n0\n1\n2\n0\n25\n50\n75\n100\n125\n150\n175\n200\n0\n1\n2\n0\n50\n100\n150\n200\n250\n300\n350\n400\n0\n1\n2\nt0 [ps]\ntrec [ps]\ntrec [ps]\nMixed Events/0.025 ps\n(a)\n(b)\n(c)\nATLAS\nATLAS\nATLAS\nFigure 12: A sequence of plots showing how a true B0\ns oscillation signal with \u2206mgen\ns\n= 17.77 ps\u22121 (a)\nis diluted \ufb01rst by the effect of a \ufb01nite proper time resolution (b) and then by adding background events\nand including the effect of wrong tags (c). The plots contain samples of events equivalent to 10 fb\u22121 of\nintegrated luminosity. They were generated using the Monte Carlo method described in Section 6.3. Only\nthe case of mixed events is shown. For illustration a \u03c72-\ufb01t of the function Cexp(\u2212t/\u03c4)(1\u2212Dcos(\u2206mst))\nis overlaid to the solid histogram in (c), where D can be interpreted as the combined dilution factor:\nD \u22480.1 here. Note that this is different from the unbinned maximum likelihood \ufb01t to the total event\nsample of mixed and unmixed events which is actually used to derive results in this study. The dashed\nhistogram in (c) describes the contribution from all background sources.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1187\n\n6.3\nMonte Carlo Data Sample\nFor the amplitude \ufb01t method a simpli\ufb01ed Monte Carlo method is applied to generate a B0\ns sample using\nthe following input parameters: for each signal channel k the number of reconstructed signal events N(k)\nsig\nfor an integrated luminosity of 10 fb\u22121 and the number of background events N(k)\nB0\nd,s from B0\nd,s decays is\ngiven in Table 12. For the combinatorial background the ratio N(k)\nsig /N(k)\ncb is taken to be 1.\nThe wrong\ntag fraction is assumed to be the same for both B0\ns and B0\nd mesons in a speci\ufb01c signal channel (\u03c9s = \u03c9d),\nhowever, the values are slightly different for the two signal channels (see Table 11).\nA Monte Carlo sample with Nsig = N(1)\nsig +N(2)\nsig signal events oscillating with a given frequency \u2206ms\n(e.g. \u2206ms = 100 ps\u22121, which is far off the expected value for \u2206ms), together with NB0\nd,s = N(1)\nB0\nd,s + N(2)\nB0\nd,s\nbackground events oscillating with frequency \u2206md,s and Ncb = N(1)\ncb + N(2)\ncb combinatorial events (no\noscillations) is generated according to Eq. 1.\nThe uncertainty on the measurement of the transverse decay length, \u03c3dxy (see Fig. 13), and the true\nvalue of the g-factor g0 (g := m/pT) as seen in Fig. 14(a), are generated randomly according to the\ndistributions obtained from the simulated samples, \ufb01tted with appropriate combinations of Gaussian and\nexponential functions. For the B0\ns \u2192D\u2212\ns a+\n1 channel the true p0\nT distribution shown in Fig. 14(b) is \ufb01tted\nwith a combination of a parabola function in the low p0\nT region and a sum of two exponential functions\nin the high p0\nT region. The g0 values are obtained by converting generated p0\nT values at random.\nFrom the computed true decay length, d0\nxy = t0/g0, the corresponding reconstructed decay length\nis generated as dxy = d0\nxy + \u03c3dxy \u00b7 (\u00b5dxy + Sdxy\u2126). t0 is the proper time of the generated Bs. Sdxy is the\nwidth and \u00b5dxy the mean value of the Gaussian shape of the pull of the transverse decay length\ndxy\u2212d0\nxy\n\u03c3dxy\nshown in Fig. 15. The \ufb01tted values are Sdxy = 1.099 \u00b1 0.011 and \u00b5dxy = (8.76 \u00b1 1.47) \u00b7 10\u22122 for the\nB0\ns \u2192D\u2212\ns \u03c0+ channel respectively Sdxy = 1.113 \u00b1 0.011 and \u00b5dxy = (5.40 \u00b1 1.48) \u00b7 10\u22122 for the B0\ns \u2192\nD\u2212\ns a+\n1 channel. The reconstructed g-factor is generated as g = g0 + g0\u00b5g + g0Sg\u2126\u2032. The distribution\nof the fractional g-factor g\u2212g0\ng0\nas shown in Fig. 16 is \ufb01tted with a Gaussian resulting in a width of\nSg = (0.89 \u00b1 0.01) \u00b7 10\u22122 and a mean value of \u00b5g = (0.27 \u00b1 0.12) \u00b7 10\u22123 for the B0\ns \u2192D\u2212\ns \u03c0+ channel\nrespectively Sg = (0.82\u00b10.01)\u00b710\u22122 and \u00b5g = (0.56\u00b10.11)\u00b710\u22123 for the B0\ns \u2192D\u2212\ns a+\n1 channel. Both\n\u2126and \u2126\u2032 are random numbers distributed according to the normal distribution. From the transverse\ndecay length and g-factor, the reconstructed proper time is then computed as t = gdxy. The probability\nfor the event to be mixed or unmixed is determined from the t0 and \u2206ms (or \u2206md) values using the\nexpression (1\u2212cos(\u2206m jt0)/cosh(\u2206\u0393 jt0/2))/2 which is left from Eq. 1 after the exponential part has\nbeen separated.\nFor a fraction of the events, selected at random, the state is interchanged between mixed and unmixed,\naccording to the wrong tag fraction \u03c9tag. Half of the combinatorial events are added to the mixed events\nand half to the unmixed events.\nFor the exclusive B0\nd,s background channels as well as the combinatorial background, the recon-\nstructed proper time is generated assuming that it has the same distribution as the one for signal B0\ns mesons\ncoming from the D\u2212\ns \u03c0+ and D\u2212\ns a+\n1 sample respectively, no mixing included.\nThe \u2206ms measurement limits are obtained applying the amplitude \ufb01t method [5] to the sample gen-\nerated as described in the previous section. According to this method a new parameter, the B0\ns oscil-\nlation amplitude A , is introduced in the likelihood function by replacing the term \u2018\u00b50cos\u2206mst0\u2019 with\n\u2018\u00b50A cos\u2206mst0\u2019 in the B0\ns probability density function given by Eq. 1. The new likelihood function,\nsimilar to Eq. 7, again includes all experimental effects. For each value of \u2206ms, this likelihood function\nis minimized with respect to A , keeping all other parameters \ufb01xed, and a value A \u00b1 \u03c3 stat\nA\nis obtained.\nOne expects, within the estimated uncertainty, A = 1 for \u2206ms close to its true value, and A = 0 for \u2206ms\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1188\n\n [mm]\nxy\nd\n\u03c3\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nm\n\u00b5\nEntries / 7.5 \n0\n100\n200\n300\n400\n500\n600\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [mm]\nxy\nd\n\u03c3\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nm\n\u00b5\nEntries / 7.5 \n0\n100\n200\n300\n400\n500\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 13: The uncertainty on the measurement of the transverse decay length, \u03c3dxy including trigger\nselection.\n [ps/mm]\n0\ng\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8\n2\nEntries / 40 fs/mm\n0\n50\n100\n150\n200\n250\n300\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n [GeV]\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\nEntries / 1 GeV\n0\n50\n100\n150\n200\n250\n300\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 14: The true value of the g-factor g0 = t0/d0\nxy of simulated B0\ns from the B0\ns \u2192D\u2212\ns \u03c0+ sample\n(a) \ufb01tted with the sum of three Gaussian functions (dashed lines) and the true transverse momentum\ndistribution p0\nT of simulated B0\ns from the B0\ns \u2192D\u2212\ns a+\n1 sample (b) including trigger selection.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1189\n\nxy\nd\n\u03c3\n ) / \nxy truth\n - d\nxy\n( d\n-6\n-4\n-2\n0\n2\n4\n6\nEntries / 0.25\n0\n100\n200\n300\n400\n500\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\nxy\nd\n\u03c3\n ) / \nxy,truth\n - d\nxy\n( d\n-6\n-4\n-2\n0\n2\n4\n6\nEntries / 0.25\n0\n100\n200\n300\n400\n500\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 15: The pull of the measurement of the transverse decay length,\ndxy\u2212d0\nxy\n\u03c3dxy\nand \ufb01t of a Gaussian\nfunction (dashed) to the distribution including trigger selection.\n0\n ) / g\n0\n( g - g\n-0.06 -0.04 -0.02\n0\n0.02\n0.04\n0.06\nEntries / 0.002\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\n(a) B0s \u2192D\u2212s \u03c0+\n0\n ) / g\n0\n( g - g\n-0.06 -0.04 -0.02\n0\n0.02\n0.04\n0.06\nEntries / 0.002\n0\n100\n200\n300\n400\n500\n600\nATLAS\n(b) B0s \u2192D\u2212s a+\n1\nFigure 16: The fractional resolution of the g-factor g\u2212g0\ng0\nof simulated B0\ns \ufb01tted with a single Gaussian\nfunction including trigger selection.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1190\n\n]\n-1\n [ps\ns\n m\n\u2206\n5\n10\n15\n20\n25\n30\n35\nAmplitude\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n]\n-1\n [ps\ns\n m\n\u2206\n5\n10\n15\n20\n25\n30\n35\nAmplitude\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\nstat\n\u03c3\n \n\u00b1\ndata \nstat\n\u03c3\n1.645 \nstat\n\u03c3\n 1.645 \n\u00b1\ndata \n-1\n95% CL sensitivity = 29.6 ps\nATLAS\n(a) Amplitude vs. \u2206ms\n]\n-1\n [ps\ns\n m\n\u2206\n5\n10\n15\n20\n25\n30\n35\nSignificance\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n95 % CL sensitivity\n signal\n\u03c3\n> 5\n-1\n95 % CL sensitivity : 29.6 ps \n-1\n limit : 20.5 ps \n\u03c3\n5\nATLAS\n(b) Signi\ufb01cance vs. \u2206ms\nFigure 17: The B0\ns oscillation amplitude (a) and the measurement signi\ufb01cance (b) as a function of \u2206ms\nfor an integrated luminosity of 10 fb\u22121 for a speci\ufb01c Monte Carlo experiment with \u2206mgen\ns\n= 100 ps\u22121 .\nfar from the true value. A \ufb01ve standard deviation measurement limit is de\ufb01ned as the value of \u2206ms for\nwhich 1/\u03c3A = 5, and a sensitivity at 95% C.L. as the value of \u2206ms for which 1/\u03c3A = 1.645. Limits are\ncomputed with the statistical uncertainty \u03c3 stat\nA . A detailed investigation on the systematic uncertainties\n\u03c3 syst\nA , which affects the measurement of the B0\ns oscillation, is presented in [18].\n6.4\nExtraction of the \u2206ms Sensitivity\nFor the nominal set of parameters (as de\ufb01ned in the previous sections), \u2206\u0393s = 0 and an integrated lu-\nminosity of 10 fb\u22121, the amplitude \u00b11\u03c3 stat\nA\nis plotted as a function of \u2206ms in Fig. 17(a). The 95% C.L.\nsensitivity to measure \u2206ms is found to be 29.6 ps\u22121. This value is given by the intersection of the dashed\nline, corresponding to 1.645 \u03c3 stat\nA , with the horizontal line at A = 1.\nFrom Fig. 17(b), which shows the signi\ufb01cance of the measurement S(\u2206ms) = 1/\u03c3A as a function of\n\u2206ms, the 5\u03c3 measurement limit is found to 20.5 ps\u22121.\nThe dependence of the \u2206ms measurement limits on the integrated luminosity is shown in Fig. 18(a),\nwith the numerical values given in Table 13.\nTable 13: The dependence of \u2206ms measurement limits on the integrated luminosity L .\nL\n5 \u03c3 limit\n95% C.L. sensitivity\n[fb\u22121]\n[ps\u22121]\n[ps\u22121]\n3\n14.5\n25.0\n5\n17.0\n27.0\n10\n20.5\n29.6\n20\n23.7\n32.0\n30\n25.3\n33.2\n40\n26.4\n34.1\nThe dependence of the \u2206ms measurement limits on \u2206\u0393s/\u0393s is determined for an integrated luminosity\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1191\n\n]\n-1\n L dt [fb\n\u222b\n1\n10\n]\n-1\n limits [ps\ns\n m\n\u2206\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nsensitivity\n limit\n\u03c3\n5\nATLAS\n(a) \u2206ms limits vs.\nR Ldt\n [%]\ns\n\u0393\n / \ns\n\u0393\n\u2206\n0\n20\n40\n60\n80\n100\n]\n-1\n limits [ps\ns\n m\n\u2206\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nsensitivity\n limit\n\u03c3\n5\nATLAS\n(b) \u2206ms limits vs. \u2206\u0393s/\u0393s\nFigure 18: The dependence of \u2206ms measurement limits (a) on the integrated luminosity and (b) on\n\u2206\u0393s/\u0393s for an integrated luminosity of 10 fb\u22121. The dashed horizontal line in (a) denotes the CDF\nmeasurement.\nof 10 fb\u22121, other parameters having their nominal value. The \u2206\u0393s/\u0393s is used as a \ufb01xed parameter in the\namplitude \ufb01t method. As shown in Fig. 18(b) no sizeable effect is seen up to \u2206\u0393s/\u0393s \u223c30%.\n6.5\nExtraction of the \u2206ms Measurement Precision\nWhereas the \u2206ms measurement limits are obtained by using the amplitude method (see previous section),\nin case of the presence of an oscillation signal in the data the value of the oscillation frequency \u2206ms and\nits precision are determined by minimising the likelihood (given by Eq. 7) with respect to \u2206ms. In this\n\ufb01t \u2206\u0393s is \ufb01xed to 0, because a study has shown that the systematic uncertainties resulting from varying\n\u2206\u0393s/\u0393s in the range 0 to 0.2 (suggested by the present uncertainty) are practically negligible.\nAn example of the likelihood function is given in Fig. 19(a), in which the \u2206mgen\ns\nin the Monte Carlo\nsample has been set to the value measured by CDF for illustration. From this type of graphs the precision\nof the measurement of \u2206ms is extracted and plotted in Fig. 19(b) as a function of the integrated luminosity\nfor three values of \u2206mgen\ns\n.\n6.6\nDiscussion of Results\nIn this note it is shown that with an integrated luminosity of 10 fb\u22121 ATLAS is able to verify the CDF\nmeasurement of \u2206ms = (17.77 \u00b1 0.10(stat) \u00b1 0.07(sys))ps\u22121 at the \ufb01ve standard deviation level. For\nthese parameters the statistical error on \u2206ms is calculated to be about 0.065 ps\u22121.\nIn a preceding study [18] it was found that over a wide range of values for \u2206ms and integrated\nluminosity the systematic uncertainty on the measured value of \u2206ms was smaller by at least a factor of\n10 compared to the statistical uncertainty. The list of contributions to that systematic error estimation\nincluded the wrong tag fraction with a relative error of 5% compared to 2.5% found in this study. For\nthe reasons mentioned above, the evaluation of systematic effects has not been repeated here. The study\nof the effect of varying \u2206\u0393s (as explained in the previous section) is new, but the contribution to the\nsystematic uncertainty is also very small.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1192\n\n0\n200\n400\n600\n0\n10\n20\n30\n40\n\u2206ln(likelihood)\n\u2206ms [ps-1]\n0\n1\n2\n3\n17.65\n17.7\n17.75\n17 8\n17.85\n17.9\nATLAS\n(a) \u2206ln(likelihood) vs. \u2206ms\n]\n-1\nLdt [fb\n\u222b\n0\n10\n20\n30\n40\n50\n]\n-1\n statistical error [ps\ns\nm\n\u2206\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n-1\n = 20.0 ps\ns\nm\n\u2206\n-1\n = 17.77 ps\ns\nm\n\u2206\n-1\n = 15.0 ps\ns\nm\n\u2206\nATLAS\n(b) \u03c3stat(\u2206ms) vs.\nR Ldt\nFigure 19: (a) The negative natural logarithm of the likelihood for a speci\ufb01c Monte Carlo data sample\nfor an integrated luminosity of 10 fb\u22121 and a true value of \u2206mgen\ns\n= 17.77 ps\u22121. The inset shows a\nzoom around the minimum. (b) The statistical error \u03c3stat(\u2206ms) as a function of the integrated luminosity\nfor values of \u2206mgen\ns\nof 15, 17.77 and 20 ps\u22121. For comparison: the CDF statistical error on their \u2206ms\nmeasurement is 0.10 ps\u22121.\nSystematic uncertainties on the overall trigger ef\ufb01ciencies mainly effect the statistics available for\nthe analysis. However, an important systematic effect for the \u2206ms measurement would be introduced in\ncase different trigger ef\ufb01ciencies for positively and negatively charged muons are observed. In order to\nconstrain this effect, dimuon events from a calibration channel like B+ \u2192J/\u03c8 K+ with J/\u03c8 \u2192\u00b5+\u00b5\u2212\nwhich are triggered by a single muon trigger could be used.\nClearly LHCb can measure \u2206ms more precisely than ATLAS (\u03c3stat(\u2206ms) \u223c0.01 ps\u22121 with 2 fb\u22121 of\ndata [19]), but the \u2206ms measurement with ATLAS is needed for the simultaneous \ufb01t of all parameters of\nthe weak sector of the B0\ns- \u00afB0\ns system (weak mixing phase \u03c6s, \u2206ms, \u0393s and \u2206\u0393s). This will be performed by\na combined analysis of the channels described in this note and the B0\ns \u2192J/\u03c8 \u03c6 channel [20]. The ATLAS\nmeasurement is an independent cross-check of the measurements performed by other experiments.\n7\nSummary and Conclusions\nWe have studied the capabilities of the ATLAS detector to measure B0\ns oscillations in pp collisions\nat 14 TeV using the purely hadronic decay channels B0\ns \u2192D\u2212\ns (\u03c6\u03c0\u2212)\u03c0+ and B0\ns \u2192D\u2212\ns (\u03c6\u03c0\u2212)a+\n1 . For\nan integrated luminosity of 10 fb\u22121 a \u2206ms sensitivity limit of 29.6 ps\u22121 and a \ufb01ve standard deviation\nmeasurement limit of 20.5 ps\u22121 is obtained from a likelihood \ufb01t employing the amplitude \ufb01t method.\nThis result depends only weakly on the lifetime difference \u2206\u0393s. The trigger is based on a single muon\ntrigger with adjustable muon pT thresholds between 4 and 10 GeV on all trigger levels and an active\nsearch for Ds \u2192\u03c6\u03c0 decays by the High Level Trigger. For 1031 cm\u22122s\u22121 we will be able to afford a muon\ntrigger with the loosest pT threshold combined with a FullScan Ds \u2192\u03c6\u03c0 search. For 1032 cm\u22122s\u22121, we\nwill need to increase the muon pT threshold to 6 GeV and possibly employ the RoI-based LVL2 trigger.\nIn both cases, the trigger rates can be kept at an acceptable level. For higher luminosities, we need to\nimplement additional constraints in the HLT in order to reduce the event output rates further.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1193\n\nThe of\ufb02ine event reconstruction searches for the hadronic decay of the B0\ns and requires a muon with\na minimum pT of 6 GeV for each event. While the \ufb02avour of the B0\ns at decay time is determined from the\ncharge of the Ds particle, the identi\ufb01cation of the initial B0\ns \ufb02avour at production time is extracted from\nthe charge of the soft muon in the event, taking effects of B0\ns mixing into account. An overall tagging\nef\ufb01ciency of 98.8 \u00b1 0.2% and 98.5 \u00b1 0.2% as well as average wrong tag fractions of 22.3 \u00b1 0.6% and\n23.3\u00b10.6% for the B0\ns \u2192D\u2212\ns \u03c0+ and the B0\ns \u2192D\u2212\ns a+\n1 channels, respectively, are obtained.\nAbout 100000 Monte Carlo events of each sample have been produced without B0\ns oscillations.\nMonte Carlo events for several exclusive B0\ns and B0\nd background channels as well as for inclusive back-\nground like b\u00afb \u2192\u00b5X and c\u00afc \u2192\u00b5X have been used. The hadronic decay of the signal side B0\ns is recon-\nstructed constraining the masses of intermediate particles in the decay chain. A B0\ns mass resolution of\n52.8\u00b10.7 MeV and 40.8\u00b10.5 MeV is obtained and after the application of all analysis cuts, 6657 and\n3368 events are expected for an integrated luminosity of 10 fb\u22121 for the B0\ns \u2192D\u2212\ns \u03c0+ and the B0\ns \u2192D\u2212\ns a+\n1\ndecay channels, respectively. We have considered several exclusive background channels, contribut-\ning to the background inside the B0\ns mass window. The B0\nd \u2192D\u2212\u03c0+/a+\n1 channels hardly contribute\n(percent level of the signal), but the B0\ns \u2192D\u2217\u2212\ns \u03c0+/a+\n1 make a considerable contribution of about 16%\n(B0\ns \u2192D\u2212\ns \u03c0+) and 31% (B0\ns \u2192D\u2212\ns a+\n1 ). While the B0\nd \u2192D\u2212\ns \u03c0+ channel is expected to contribute with\nabout 1.5% relative to the B0\ns \u2192D\u2212\ns \u03c0+ signal, we can only estimate the B0\nd \u2192D\u2212\ns a+\n1 contribution to be\nless than about 70% of the B0\ns \u2192D\u2212\ns a+\n1 signal, given that this decay channel has not yet been observed.\nIn future, the B0\ns \u2192D\u2217\u2212\ns \u03c0+/a+\n1 channels may be considered signal rather than background. An\nestimate of the combinatorial background is severely limited by the available Monte Carlo event statistics.\nWe plan to use early data to obtain a realistic estimate. For an integrated luminosity of 100 pb\u22121 at\n1032 cm\u22122s\u22121 we only expect about 90 events in the B0\ns \u2192D\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns a+\n1 channels, while the\nB+ \u2192J/\u03c8(\u00b5\u00b5)K+ decay channel, which has a large branching ratio, may be used to calibrate the soft\nmuon tagging with early data. On LVL2 the processing time for the Ds \u2192\u03c6\u03c0 trigger may be reduced by\nrestricting the track reconstruction to Regions of Interest (RoI), seeded by a LVL1 jet energy trigger. This\ntypically leads to a reduction of the trigger ef\ufb01ciency by a few percent. At an instantaneous luminosity\nof 2 \u00b7 1033 cm\u22122s\u22121 several options will be considered to achieve acceptable Event Filter output rates.\nBesides further constraining the mass windows of the Ds \u2192\u03c6\u03c0 trigger, other improvements are obtained\nby checking for a good reconstruction quality of the Ds vertex or the implementation of a trigger element\nin the Event Filter which searches for the full B0\ns decay chain. However, there is an uncertainty of a factor\ntwo in the overall b\u00afb cross-section at the centre-of-mass energy of 14 TeV and therefore the trigger rates\nmay vary.\nDue to the achieved sensitivity limit to measure the B0\ns oscillations we expect to be able to verify the\nCDF measurement of \u2206ms = 17.77\u00b10.10(stat)\u00b10.07(sys) ps\u22121 at the \ufb01ve standard deviation level with\na statistical error on \u2206ms of about 0.065 ps\u22121. This will provide a reasonable precision which allows us\nto combine the measurement described in this note with the analysis of the B0\ns \u2192J/\u03c8\u03c6 channel [20] in\na simultaneous \ufb01t for all parameters of the weak sector of the B0\ns- \u00afB0\ns system.\nReferences\n[1] A. Abulencia et al. [CDF Collaboration], Phys. Rev. Lett. 97 (2006) 242003.\n[2] V.M. Abazov et al. [D0 Collaboration], Phys. Rev. Lett. 97 (2006) 021802.\n[3] M. Battaglia et al. arXiv:hep-ph/0304132 (2003).\n[4] ATLAS Collaboration,\nATLAS Detector and Physics Performance TDR 15,\nVol. 2,\n(CERN/LHCC/99-15, May 1999).\n[5] H.G. Moser and A. Roussarie, Nucl. Instr. Meth. A 384 (1997) 491.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1194\n\n[6] T. Sj\u00a8ostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[7] ATLAS Collaboration, Introduction to B-Physics, this volume.\n[8] W.-M. Yao et al., Journal of Physics G 33 (2006 and 2007 partial update for the 2008 edition) 1+.\n[9] H. v. Radziewski, Trigger Considerations for the Measurement of B0\ns \u2192D\u2212\ns a+\n1 with the ATLAS\nExperiment, Master\u2019s thesis, University of Siegen, 2007 (SI-HEP-2008-05).\n[10] ATLAS Collaboration, ATLAS Level-1 Trigger TDR 12, (CERN/LHCC/98-14, June 1998).\n[11] C. Schiavi, Real Time Tracking with ATLAS Silicon Detectors and its Applications to Beauty in\nHadron Physics, Ph.D. thesis, Genoa University and INFN Genoa, 2005 (CERN-THESIS-2008-\n028).\n[12] ATLAS Collaboration, Triggering on Low-pTMuons and Di-Muons for B-Physics, this volume.\n[13] P. Nason et al., arXiv:hep-ph/0003142v2 (2001).\n[14] ATLAS Collaboration, Muons in the Calorimeters: Energy Loss Corrections and Muon Tagging,\nthis volume.\n[15] ATLAS Collaboration, Production Cross-Section Measurements and Study of the Properties of the\nExclusive B+ \u2192J/\u03c8K+ Channel, this volume.\n[16] Upper Tail Probability of Chi-Squared Distribution, CERNLIB - CERN Program Library, routine\nentry PROB (G100), CERN.\n[17] M. Beneke, G. Buchalla and I. Dunietz, Phys. Rev. D 54 (1996), 4419, M. Beneke et al., Phys.\nLett. B459 (1999) 631.\n[18] B. Epp, V.M. Ghete, A. Nairz, EPJdirect CN3, SN-ATLAS-2002-015 (2002) 1\u201323.\n[19] S. Barsuk [LHCb Collaboration], LHCb 2005-068 (2005).\n[20] ATLAS Collaboration, Physics and Detector Performance Measurements for B0\nd \u2192J/\u03c8K0\u2217and\nB0\ns \u2192J/\u03c8\u03c6 with Early Data, this volume.\nB-PHYSICS \u2013 TRIGGER AND ANALYSIS STRATEGIES FOR B0\ns OSCILLATION . . .\n1195\n\n\nHiggs Boson\n1197\n\nIntroduction on Higgs Boson Searches\nAbstract\nThe investigation of the dynamics responsible for electroweak symmetry break-\ning is one of the prime tasks of experiments at present and future colliders.\nExperiments at the CERN Large Hadron Collider (LHC) will be able to dis-\ncover a Standard Model Higgs boson over the full mass range as well as Higgs\nbosons in extended models. In this introductory paper the Higgs boson produc-\ntion cross-section and decay branching ratios according to the Standard Model,\nand its Minimal Supersymmetric extension, are presented and discussed.\n1\nIntroduction\nThe Large Hadron Collider at CERN, almost ready to start colliding proton beams at \u221as=14 TeV, will\nplay an important role in the investigation of fundamental questions of particle physics. While the Stan-\ndard Model of electroweak [1] and strong [2] interactions is in excellent agreement with the numer-\nous experimental measurements, the dynamics responsible for electroweak symmetry breaking are still\nunknown. Within the Standard Model, the Higgs mechanism [3] is invoked to break the electroweak\nsymmetry. A doublet of complex scalar \ufb01elds is introduced, of which a single neutral scalar particle, the\nHiggs boson, remains after symmetry breaking [4]. Many extensions of this minimal version of the Higgs\nsector have been proposed, mostly discussed a scenario with two complex Higgs doublets as realized in\nthe Minimal Supersymmetric Standard Model (MSSM) [5].\nWithin the Standard Model, the Higgs boson is the only particle that has not been discovered so\nfar. The direct search at the e+e\u2212collider LEP has led to a lower bound on its mass of 114.4 GeV [6].\nIndirectly, high precision electroweak data constrain the mass of the Higgs boson via their sensitivity to\nloop corrections. Assuming the overall validity of the Standard Model, a global \ufb01t [7] to all electroweak\ndata leads to the 95% C.L. mH < 144 GeV. The 95 % C.L. lower limit obtained from LEP is not used in\nthe determination of this limit. Including it increases the limit to 182 GeV [7].\nOn the basis of the present theoretical knowledge, the Higgs sector in the Standard Model remains\nlargely unconstrained. While there is no direct prediction for the mass of the Higgs boson, an upper limit\nof \u223c1 TeV can be inferred from unitarity arguments [8].\nFurther constraints can be derived under the assumption that the Standard Model is valid only up to\na cutoff energy scale \u039b, beyond which new physics becomes relevant. Requiring that the electroweak\nvacuum is stable and that the Standard Model remains perturbative allows to set upper and lower bounds\non the Higgs boson mass [9, 10]. For a cutoff scale of the order of the Planck mass, the Higgs boson\nmass is required to be in the range 130 < MH < 180 GeV. If new physics appears at lower mass scales,\nthe bound becomes weaker, e.g., for \u039b = 1 TeV the Higgs boson mass is constrained to be in the range\n50 < MH < 800 GeV.\nDirect searches for the Standard Model Higgs boson at the Tevatron include looking for its production\nvia gluon fusion and subsequent decay to WW (\u2217) . The observed 95% C.L. limit by CDF (with an\nintegrated luminosity of 2.4 fb\u22121 analysed) is 0.85 pb for MH= 160 GeV, which is about 1.6 times the\nStandard Model prediction [11]. Similarly the D\u00d8 Collaboration excludes at 95% C.L. the production of\nthis boson with a cross-section about 2.4 times the one predicted by the Standard Model (\u03c3WW\nSM ). Searches\nat low mass are done studying Higgs bosons produced in association with the W and Z, and looking for\nH \u2192bb with leptonic W an Z decays (e,\u00b5). CDF sets a 95% C.L. limit to 8.2\u00d7\u03c3bb\nSM, while the one from\nD\u00d8 is 11\u00d7\u03c3bb\nSM, for MH= 115 GeV. Preliminary results on the combination of the results from these two\nexperiments lead to a 95% C.L. limit on the Higgs boson production cross-section to about 5.1\u00d7\u03c3SM for\nMH= 115 GeV, and 1.1\u00d7\u03c3SM for MH= 160 GeV [11].\n1198\n\nThe Minimal Supersymmetric Standard Model contains two complex Higgs doublets, leading to \ufb01ve\nphysical Higgs bosons after electroweak symmetry breaking: three neutral (two CP-even h and H, and\none CP-odd A) and a pair of charged Higgs bosons H\u00b1. At tree level, the Higgs sector of the MSSM\nis fully speci\ufb01ed by two parameters, generally chosen to be mA, the mass of the CP-odd Higgs boson,\nand tan\u03b2, the ratio of the vacuum expectation values of the two Higgs doublets. Radiative corrections\nmodify the tree-level relations signi\ufb01cantly. This is of particular interest for the mass of the lightest\nCP-even Higgs boson, which at tree level is constrained to be below the mass of the Z boson. Loop\ncorrections are sensitive to the mass of the top quark, to the mass of the scalar particles and in particular\nto mixing in the stop sector. The largest values for the mass of the Higgs boson h are reached for large\nmixing, characterized by large values of the mixing parameter Xt := At \u2212\u00b5 cot\u03b2, where At is the trilinear\ncoupling and \u00b5 is the Higgs mass parameter. If the full one-loop and the dominant two-loop contributions\nare included [12, 13], the upper bound on the mass of the light Higgs boson h is expected to be around\n135 GeV (mh-max scenario). While the light neutral Higgs boson may be dif\ufb01cult to distinguish from its\nStandard Model counterpart, the other heavier Higgs bosons are a distinctive signal of physics beyond\nthe Standard Model. The masses of the heavier Higgs bosons H, A and H\u00b1 are often almost degenerate.\nDirect searches at LEP have given lower bounds of 92.9 (93.3) GeV and 93.4 (93.3) GeV on the\nmasses of the lightest CP-even Higgs boson h and the CP-odd Higgs boson A within the mh-max (no-\nmixing) scenario. [14] In those scenarios, the mixing parameter in the stop sector is set to values of\nXt = 2 TeV and Xt = 0, respectively. Given the LEP results, the tan\u03b2 regions of 0.9 < tan\u03b2 < 1.5 and\n0.4 < tan\u03b2 < 5.6 are excluded at 95% con\ufb01dence level for the mh-max and the no-mixing scenarios,\nrespectively [14]. However, it should be noted that the exclusions in tan\u03b2 depend critically on the exact\nvalue of the top-quark mass. In the LEP analysis mt = 179.3 GeV has been assumed. With decreasing\ntop mass the theoretical upper bound on mh decreases and hence the exclusions in tan\u03b2 increase, while\nfor mt of about 183 GeV , or higher, the exclusions in tan\u03b2 vanish.\nDirect searches at the Tevatron have been performed looking to the tau-pair and b-pair production.\nWith an integrated luminosity of 1.8 fb\u22121 no excess of events has been observed, and exclusion limits on\nproduction cross-section times branching fraction to tau pairs for a Higgs boson mass in the range from\n90 to 250 GeV have been set. The expected reach of this search, assuming MSSM Higgs production,\nextends below tan\u03b2= 40 for MA in the mass range MA= 120 to 160 GeV [15].\nThe charged Higgs boson mass is related to mA via the tree-level relation m2\nH\u00b1 = m2\nW + m2\nA and it\nis less sensitive to radiative corrections [16]. Direct searches for charged Higgs bosons in the decay\nmodes H\u00b1 \u2192\u03c4\u03bd and H\u00b1 \u2192cs have been carried out at LEP, yielding a lower bound of 78.6 GeV on\nmH\u00b1 independent of the H\u00b1 \u2192\u03c4\u03bd branching ratio [17]. At the Tevatron, the CDF and D\u00d8 experiments\nhave performed direct and indirect searches for the charged Higgs boson through the process pp \u2192t\u00aft\nwith at least one top quark decaying via t \u2192H\u00b1b. These searches have excluded the small and large\ntan\u03b2 regions for H\u00b1 masses up to \u223c160 GeV [18]. Other experimental bounds on the charged Higgs\nboson mass can be derived using processes where the charged Higgs boson enters as a virtual particle.\nFor example, the measurement of the b \u2192s\u03b3 decay rate allows indirect limits to be set on the charged\nHiggs boson mass [19] which, however, are strongly model dependent [20].\nThe high collision energy of the LHC will allow the search for Higgs bosons to be extended into\nunexplored mass regions. The experiments have a large discovery potential for Higgs bosons in both the\nStandard Model and in the MSSM over the full parameter range. Should the Higgs boson be light, i.e.\nhave a mass in the range favoured by the precision electroweak measurements, the experiments at the\nTevatron might also get indications of the existence of a Higgs boson.\nIn this chapter, the potential for Higgs boson searches at the Large Hadron Collider with the ATLAS\nexperiment is reviewed, focussing on the investigation of the Higgs sectors in the Standard Model and in\nthe MSSM.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1199\n\nTable 1: Set of parameters used in the evaluation of the Higgs boson cross-sections (see text).\nMuds = 190 MeV\nMc = 1.40 GeV\nMb = 4.60 GeV\nMt = 172 GeV\nMZ =91.187 GeV\nMW = 80.41 GeV\nGF = 1.16639\u00d710\u22125 GeV\u22122\nNF = 5\n\u039bLO\nQCD = 165 MeV\n\u039bNLO\nQCD = 226 MeV\n\u03b1LO\ns (MZ) = 0.130\n\u03b1NLO\ns\n(MZ) = 0.118\nTable 2: Cross-sections for Higgs boson production via gluon fusion at LO and NLO in the mass range\n100 \u2264MH \u22641000 GeV. The \ufb01rst column gives the Higgs boson mass, the second the LO order cross-\nsection, the third and fourth column gives the NLO electroweak (EW) and QCD corrections respectively\n(see text), the last column presents the overall NLO cross-section.\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\n100\n27.788\n0.80\n0.04\n51.264\n105\n25.518\n0.80\n0.04\n47.189\n110\n23.519\n0.81\n0.05\n43.590\n120\n20.170\n0.81\n0.05\n37.579\n130\n17.491\n0.82\n0.06\n32.809\n140\n15.314\n0.82\n0.07\n28.886\n150\n13.521\n0.82\n0.08\n25.680\n160\n12.029\n0.83\n0.07\n22.854\n170\n10.776\n0.84\n0.03\n20.114\n180\n9.715\n0.84\n0.02\n18.080\n190\n8.812\n0.85\n-0.01\n16.212\n200\n8.038\n0.85\n-0.02\n14.760\n250\n5.490\n0.88\n-0.02\n10.231\n300\n4.286\n0.91\n-0.01\n8.143\n350\n4.414\n0.97\n-0.01\n8.666\n400\n4.124\n0.93\n0.00\n7.923\n450\n2.945\n0.91\n0.00\n5.622\n500\n1.975\n0.91\n0.00\n3.772\n550\n1.307\n0.92\n0.00\n2.505\n600\n0.869\n0.93\n0.00\n1.675\n650\n0.585\n0.94\n0.00\n1.134\n700\n0.398\n0.95\n0.00\n0.777\n750\n0.275\n0.97\n0.00\n0.541\n800\n0.193\n0.97\n0.00\n0.381\n850\n0.137\n0.99\n0.00\n0.272\n900\n0.098\n1.01\n0.00\n0.197\n950\n0.071\n1.03\n0.00\n0.144\n1000\n0.052\n1.06\n0.00\n0.107\n2\nProduction cross-sections and branching fractions for a Standard Model\nHiggs boson\n2.1\nProduction cross-sections\nThis section reports on the Standard Model Higgs boson production cross-section via gluon fusion, Vec-\ntor Boson Fusion (VBF), and the associated production with a Vector Boson (WH and ZH), to leading\norder (LO) and to next to leading order (NLO). The associated production with t\u00aft is also discussed.\nThe calculation is performed using the CTEQ6L1 and CTEQ6M Parton Distribution Functions (PDF)\nat LO and NLO respectively [21]. Single and two-loop calculations of the running strong coupling\nconstant \u03b1s are used for the LO and NLO computation respectively. Table 1 shows the values of the\nStandard Model parameters used in the computations.\nThe cross-section of the gluon fusion process is evaluated using the program HIGLU [22]. The\ncalculation is performed with exact NLO matrix element. The renormalization and factorization scales\nare set to the Higgs boson mass. The values of \u03b1s are calculated according to the values of \u039bQCD given\nin Table 1 with 5 \ufb02avors. This approach may overestimate the LO cross-section; however this effect is\nexpected to be negligible compared to the effect from the scale uncertainty.\nTable 2 reports the cross-sections for Higgs boson production via gluon fusion at LO and NLO in\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1200\n\nTable 3: Cross-sections for Higgs boson production via Vector Boson Fusion at LO and NLO in the\nmass range 100 \u2264MH\u22641000,GeV. The \ufb01rst column gives the Higgs boson mass, the second the LO\norder cross-section, the third and fourth column gives respectively the NLO electroweak (EW) and QCD\ncorrections (see text), the \ufb01fth column presents the overall NLO cross-section.\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\n100\n5.037\n0.04\n-0.05\n5.001\n105\n4.835\n0.04\n-0.05\n4.802\n110\n4.633\n0.04\n-0.05\n4.608\n120\n4.277\n0.04\n-0.05\n4.246\n130\n3.961\n0.04\n-0.05\n3.931\n140\n3.670\n0.04\n-0.05\n3.651\n150\n3.415\n0.04\n-0.05\n3.397\n160\n3.173\n0.05\n-0.05\n3.154\n170\n2.956\n0.05\n-0.04\n2.976\n180\n2.770\n0.04\n-0.04\n2.764\n190\n2.591\n0.05\n-0.03\n2.624\n200\n2.427\n0.04\n-0.04\n2.447\n250\n1.789\n0.04\n-0.04\n1.795\n300\n1.355\n0.05\n-0.04\n1.358\n350\n1.053\n0.04\n-0.06\n1.037\n400\n0.833\n0.04\n-0.03\n0.848\n450\n0.670\n0.04\n0.00\n0.694\n500\n0.542\n0.05\n0.01\n0.574\n550\n0.447\n0.04\n0.03\n0.477\n600\n0.371\n0.04\n0.04\n0.402\n650\n0.311\n0.04\n0.06\n0.341\n700\n0.262\n0.04\n0.08\n0.292\n750\n0.222\n0.04\n0.10\n0.252\n800\n0.190\n0.03\n0.13\n0.220\n850\n0.163\n0.03\n0.15\n0.193\n900\n0.140\n0.03\n0.19\n0.170\n950\n0.121\n0.03\n0.23\n0.152\n1000\n0.105\n0.03\n0.27\n0.136\nTable 4: Cross-sections for the associated Higgs boson production with W bosons at LO and NLO in the\nmass range 100 \u2264MH\u2264200 GeV.\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\n100\n2.476\n0.22\n-0.06\n2.877\n110\n1.855\n0.22\n-0.06\n2.154\n120\n1.414\n0.23\n-0.07\n1.641\n130\n1.095\n0.23\n-0.07\n1.269\n140\n0.860\n0.23\n-0.08\n0.995\n150\n0.684\n0.24\n-0.09\n0.787\n160\n0.550\n0.24\n-0.12\n0.615\n170\n0.447\n0.24\n-0.10\n0.511\n180\n0.366\n0.24\n-0.11\n0.417\n190\n0.303\n0.25\n-0.09\n0.349\n200\n0.252\n0.25\n-0.09\n0.292\nthe mass ranges 100 \u2264MH\u22641000 GeV. The NLO cross-section is obtained from the LO one as follows:\n\u03c3NLO = \u03c3LO \u00d7(1+\u03b4QCD +\u03b4EW).\nThe cross-section of VBF Higgs boson production is estimated with the package VV2H F [22]. The\nresults are reported in Table 3 as a function of the Higgs boson mass in the range 100 GeV\u2264MH\u22641000\nGeV. The renormalization and factorization scales are set to the Higgs boson mass.\nThe cross-sections for WH, ZH and t\u00aftH production are one to two orders of magnitude below the\ngluon and vector boson fusion cross-sections. The values are given in Tables 4, 5, and 6 respectively.\nThe cross-section for the Higgs boson produced in association with t\u00aft is estimated with the package\nHQQ [22]. The renormalization and factorization scales are set to (MH+ 2Mt)/2. The QCD corrections to\nthis process are known [23,24] and yield a K-factor of about 1.25. However it should be stressed that the\nmain backgrounds in this analysis (t\u00aftb\u00afb and t\u00aftjj) are known to LO only. Table 6 reports the cross-section\nof Higgs boson production associated to t\u00aft in the mass range 100 GeV\u2264MH\u2264200 GeV.\nThe package V2HV is used to estimate the Higgs boson production cross-section in association with\nthe W and Z bosons [22]. The renormalization and factorization scales are set to the sum of the invariant\nmasses of the weak boson and of the Higgs boson. Tables 4 and 5 report the cross-sections of these\nprocesses in the mass range 100 GeV\u2264MH\u2264200 GeV.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1201\n\nTable 5: cross-sections for the Higgs boson associated production with Z bosons at LO and NLO in the\nmass range 100 \u2264MH\u2264200 GeV.\nMH(GeV)\n\u03c3LO (pb)\n\u03b4QCD\n\u03b4EW\n\u03c3NLO (pb)\n100\n1.298\n0.22\n-0.05\n1.519\n110\n0.980\n0.22\n-0.05\n1.148\n120\n0.752\n0.23\n-0.05\n0.882\n130\n0.585\n0.23\n-0.05\n0.687\n140\n0.462\n0.23\n-0.06\n0.543\n150\n0.368\n0.23\n-0.06\n0.433\n160\n0.297\n0.24\n-0.09\n0.342\n170\n0.242\n0.24\n-0.06\n0.286\n180\n0.199\n0.24\n-0.07\n0.233\n190\n0.165\n0.24\n-0.06\n0.195\n200\n0.137\n0.25\n-0.06\n0.163\nTable 6: cross-sections for the associated Higgs boson production with t\u00aft to LO and NLO (courtesy of\nM. Spira) in the mass range 100\u2264MH\u2264200 GeV.\nMH(GeV)\n\u03c3LO (pb)\n\u03c3NLO (pb)\nK Factor\n100\n0.873\n1.088\n1.25\n110\n0.680\n0.848\n1.25\n120\n0.537\n0.669\n1.25\n130\n0.428\n0.534\n1.25\n140\n0.345\n0.431\n1.25\n150\n0.282\n0.352\n1.25\n160\n0.232\n0.291\n1.26\n170\n0.193\n0.243\n1.26\n180\n0.162\n0.204\n1.26\n190\n0.137\n0.174\n1.27\n200\n0.117\n0.149\n1.27\n2.2\nDecays branching ratios\nHiggs boson branching ratios are evaluated with the program HDECAY [25]. Here, the default settings\nde\ufb01ned by the authors are used (see Ref. [25]), except for the parameters speci\ufb01ed in Table 1.\nTables 7 and 8 report the most relevant Higgs boson branching ratios for 100 \u2264MH\u22641000 GeV:\nH \u2192bb,\u03c4+\u03c4\u2212,\u03b3\u03b3,ZZ(\u2217),WW (\u2217) and t\u00aft.\nFigure 1 (left) shows the branching fractions and the production cross-section (right) of the Standard\nModel Higgs boson as a function of its mass (Figures taken from Reference [26]).\n2.3\nStandard Model Higgs boson search in ATLAS\nThe Standard Model Higgs boson is searched for at the LHC in various decay channels, the choice of\nwhich depends by the signal rates and the signal to background ratios in the various mass regions.\nThe Standard Model Higgs boson channels considered in this volume are:\n\u2022 pp \u2192H \u2192\u03b3\u03b3\n\u2022 pp \u2192H \u2192ZZ(\u2217) \u21924l(l = e,\u00b5)\n\u2022 pp \u2192qqH \u2192qq\u03c4+\u03c4\u2212\n\u2022 pp \u2192H \u2192W +W \u2212\u2192l\u03bdl\u03bd,l\u03bdqq\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1202\n\nTable 7: Relevant Higgs boson branching ratios for the mass range 100 \u2264MH\u2264200 GeV.\nMH(GeV)\n\u0393H (GeV)\nH \u2192bb\nH \u2192\u03c4+\u03c4\u2212\nH \u2192\u03b3\u03b3\nH \u2192WW(\u2217)\nH \u2192ZZ(\u2217)\n100\n0.0026\n0.8117\n0.08002\n0.00157\n0.01019\n0.00106\n110\n0.0029\n0.7694\n0.07726\n0.00194\n0.04454\n0.00412\n120\n0.0036\n0.6773\n0.06915\n0.00223\n0.13310\n0.01520\n130\n0.0049\n0.5249\n0.05440\n0.00227\n0.28880\n0.03866\n140\n0.0080\n0.3414\n0.03587\n0.00197\n0.48540\n0.06781\n150\n0.0166\n0.1742\n0.01854\n0.00141\n0.68310\n0.08301\n160\n0.0772\n0.03960\n0.00426\n0.00056\n0.90150\n0.04334\n170\n0.3837\n0.00837\n0.00091\n0.00015\n0.96540\n0.02253\n180\n0.6282\n0.00536\n0.00059\n0.00010\n0.93460\n0.05750\n190\n1.038\n0.00339\n0.00038\n0.00007\n0.77610\n0.21870\n200\n1.426\n0.00257\n0.00029\n0.00005\n0.73470\n0.26130\nTable 8: Relevant Higgs boson branching ratios for the mass range 250 \u2264MH\u22641000 GeV.\nMH(GeV)\n\u0393H (GeV)\nH \u2192WW(\u2217)\nH \u2192ZZ(\u2217)\nH \u2192t\u00aft\n250\n4.046\n0.7003\n0.2977\n0.00000\n300\n8.505\n0.6911\n0.3075\n0.00007\n350\n15.60\n0.6722\n0.3078\n0.01878\n400\n29.30\n0.5787\n0.2703\n0.14990\n450\n46.55\n0.5489\n0.2600\n0.19030\n500\n67.56\n0.5446\n0.2606\n0.19420\n550\n92.55\n0.5500\n0.2652\n0.18430\n600\n122.3\n0.5591\n0.2711\n0.16940\n650\n157.7\n0.5692\n0.2773\n0.15310\n700\n199.7\n0.5793\n0.2832\n0.13710\n750\n249.2\n0.5889\n0.2887\n0.12210\n800\n307.7\n0.5977\n0.2937\n0.10840\n850\n376.5\n0.6057\n0.2982\n0.09586\n900\n457.4\n0.6129\n0.3023\n0.08458\n950\n552.5\n0.6195\n0.3059\n0.07445\n1000\n664.1\n0.6253\n0.3092\n0.06537\n\u2022 pp \u2192t\u00aftH \u2192t\u00aftb\u00afb\n\u2022 pp \u2192t\u00aftH \u2192t\u00aftW +W \u2212, and pp \u2192ZH \u2192\u2113+\u2113\u2212W +W \u2212\n3\nHiggs Bosons in the Minimal Supersymmetric Extension to the Stan-\ndard Model\nAs discussed in the Introduction, in the Minimal Supersymmetric Standard Model two Higgs doublets\nare required, resulting in three neutral and two charged observable Higgs bosons. The production of\nneutral Higgs bosons and their decays are different from those in the Standard Model. While decays into\nZZ or WW are dominant in the Standard Model for Higgs boson masses above MH> 2 MW, for high\nvalues of tan\u03b2 these decay modes are either suppressed in case of the h and H or even absent in the case\nof the A. Instead, the coupling of the Higgs bosons to third generation fermions are strongly enhanced\nfor large regions of the MSSM parameter space.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1203\n\n [GeV]\nH\nm\n2\n10\n3\n10\nBranching Ratio\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\nbb\n\u03c4\n\u03c4\n\u03b3 \n\u03b3\nWW\nZZ\ntt\n [GeV]\nH\nm\n2\n10\n3\n10\nCross-section [pb]\n-1\n10\n1\n10\n2\n10\nATLAS\n H\n\u2192\ngg \nqqH\nWH\nZH\nttH\nFigure 1: Left: Branching ratios for the relevant decay modes of the Standard Model Higgs boson as a\nfunction of its mass. Right: cross-sections for the \ufb01ve production channels of the Standard Model Higgs\nboson at the LHC at 14 TeV.\n3.1\nProduction and decays of neutral Higgs bosons\nThe Higgs boson production proceeds via two different mechanisms, the direct and the b quark associated\nproduction, as described below. In the following \u03c6 stands for either of the three neutral Higgs bosons: A,\nH, and h. Further details can be found in [27].\nDirect Production:\nThe diagram for this process is depicted in Fig. 2(a). It dominates in the range of\nlow tan\u03b2 and its rates are signi\ufb01cantly larger than for the Standard Model. For the range of higher tan\u03b2 it\nis still dominant for low mA. The cross-section for this process has been calculated at NLO accuracy [22]\nand the numerical values used here are listed under \u03c3direct\nh/H/A in Table 9.\nAssociated Production:\nDifferent approaches have been followed by theorists to calculate the cross-\nsection for Higgs boson production in association with b quarks, each of them assuming one of the\ndiagrams depicted in Fig. 2(b-d) as their leading order (LO) contribution. The implications connected\nwith this choice are brie\ufb02y discussed below.\n\u2022 gg \u2192b\u00afb\u03c6:\nThe cross-section for this process has been calculated at NLO accuracy for the case of both b\nquarks at high transverse momentum [28, 29], where this calculation is considered to be reliable.\ng\ng\n\u03c6\ng\ng\nb\n\u03c6\n\u00afb\nb\n\u00afb\n\u03c6\nb\ng\n\u03c6\nb\ng\nq\n\u00afq\nb\n\u03c6\n\u00afb\na)\nb)\nc)\nd)\ne)\nFigure 2: Feynman diagrams contributing to the MSSM Higgs boson production. Diagram a) is called\n\u2018direct production\u2019, diagrams b) to e) contribute to the b quark associated production. In the above\ndiagrams \u03c6 represents either of the neutral Higgs bosons in the MSSM, h, H, or A.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1204\n\nFor the cases where only one or zero b quarks with high pT are required in the \ufb01nal state, the\ncross-section has been calculated at NLO accuracy by integrating over the momentum of one or\nboth b quarks, respectively [28,30,31]. In these cases the predictions are considered less reliable\ndue to the occurrence of potentially large collinear logarithms of the form log(Q/mb) from the\ngluon splitting process, where Q is the factorization scale which is expected to be much larger than\nmb.\n\u2022 b\u00afb \u2192\u03c6:\nThe potentially large collinear logarithms can be dealt with by absorbing them into the parton\ndensity function (PDF) of the b quark and thus resumming them to all orders of perturbation theory.\nThe intrinsically still present b quarks from the gluon splitting process are given zero transverse\nmomentum at leading order. At higher order they can acquire transverse momentum. E.g. the\nprocess bg \u2192b\u03c6 is a NLO contribution leading to an observable b quark. The total cross-section\nfor this process has been calculated at NLO [32,33] and NNLO accuracy [34] and is considered to\nbe reliable when it is not required (but also not vetoed) to observe a b quark.\n\u2022 bg \u2192b\u03c6:\nThis process is a mixture of the two processes discussed above in a sense that one b quark is\ncoming from the matrix element description and the other from the b PDF. This process has been\ncalculated at NLO accuracy [35] and is considered to be reliable if one observes only one b quark\nwith high pT in the \ufb01nal state. In principle in this case one should also veto any additional b quark\nwhich is experimentally challenging due to the limited b-tagging ef\ufb01ciency.\n\u2022 qq \u2192b\u00afb\u03c6:\nCompared to gg \u2192b\u00afb\u03c6 this process only contributes at the 1%-level at LHC energies and is\ntherefore only mentioned for completeness.\nA comparison of the predicted cross-sections for both the inclusive and exclusive approach is shown\nin Figure 3. The blue band corresponds to the NNLO calculation of b\u00afb \u2192\u03c6, where the width of the\nband corresponds to the residual scale uncertainties when varying the default renormalization (\u00b5r = mH)\nand factorization (\u00b5f = mH/4) scales. The red band shows the corresponding NLO calculation of gg \u2192\nb\u00afb\u03c6. The scale uncertainty for gg \u2192b\u00afb\u03c6 is of the order 20 to 30%, while the scale uncertainty for\nb\u00afb \u2192\u03c6 is much smaller, in particular at high Higgs boson masses. This might be due to the remaining\ncollinear logarithms in the gg \u2192b\u00afb\u03c6 calculation. However, contributions from e.g. PDF-uncertainties,\nin particular for the b PDF have not been included here. Both methods agree within uncertainties. At\nlarger Higgs boson masses, the prediction from b\u00afb \u2192\u03c6 is slightly higher than that from gg \u2192b\u00afb\u03c6. One\nof the effects that might explain this is the inclusion of closed-top-loops in the gg \u2192b\u00afb\u03c6 calculation,\nabsent in the b\u00afb \u2192\u03c6 case. In conclusion, both predictions may be used to normalize an inclusive signal\nsample, where no cuts have been applied on the momenta of the b quarks at generator level.\nDue to the \ufb01nite integrated luminosity assumed to be available for the analyses discussed in this note,\nthe inclusive normalization is chosen. The cross-section were calculated using FeynHiggs-2.6.2 [36]\nyielding the cross-section for a Standard Model Higgs boson. The cross-sections in the MSSM were\nthen obtained by scaling them by the ratio of partial widths into b\u00afb:\n\u03c3\u03c6\nMSSM(mA, tan\u03b2) = \u03c3SM(m\u03c6)\u00b7\n\u0393MSSM\nb\u00afb\u03c6\n(mA, tan\u03b2)\n\u0393SM\nb\u00afb\u03c6(m\u03c6)\n.\n(1)\nThe production cross-sections for all Higgs boson masses considered here and their branching frac-\ntion into a \u03c4+\u03c4\u2212and \u00b5+\u00b5\u2212\ufb01nal states in the mmax\nh\nscenario are summarized in Table 9 for tan\u03b2 = 20.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1205\n\n\u03c3(pp \u2192bb\n_ h + X) [fb]\n\u221as = 14 TeV\n\u00b5 = (2mb + Mh)/4\nMh [GeV]\nbb\n_ \u2192h (NNLO)\ngg \u2192bb\n_ h (NLO)\n10\n10 2\n10 3\n100\n150\n200\n250\n300\n350\n400\n\u03c3(pp \u2192b/b\n_ +h + X) [fb]\n\u221as = 14 TeV\n|\u03b7b/b\n_| < 2.5\n\u00b5 = (2mb + MH)/4\npT\nb/b\n_\n> 20 GeV\ngg \u2192bb\n_ +H\ngb/b\n_ \u2192b/b\n_ +H\nMH [GeV]\n1\n10\n10 2\n100\n150\n200\n250\n300\n350\n400\n450\n500\nFigure 3: The inclusive cross-sections for the processes b\u00afb \u2192\u03c6/ (blue hatched region) and gg \u2192b\u00afb\u03c6\n(red hatched region) are shown on the right-hand side; the exclusive cross-sections for bg \u2192b\u03c6(blue\nhatched region) and gg \u2192b\u00afb\u03c6(red hatched region) are shown on the right-hand side. The width of the\nbands corresponds to the theoretical uncertainty due to the choice of renormalization and factorization\nscales.\n3.2\nProduction and decays of charged Higgs bosons\nThe search strategies for charged Higgs bosons depend on the charged Higgs boson mass, which dictates\nboth the production and the available decay modes. Below the top quark mass the main production\nmode is through top quark decays, t \u2192H+b, and in this range the H+ \u2192\u03c4+\u03bd decay mode is dominant.\nOnce above the top quark threshold, production mainly takes place through gb fusion (g\u00afb \u2192\u00aftH+).\nFor such high charged Higgs boson masses, the decay into a top and a b quark dominates, H+ \u2192t \u00afb,\nbut H+ \u2192\u03c4+\u03bd can still be sizeable and offers a much cleaner signature. The process gg \u2192\u00aftbH+ is\nimportant for charged Higgs boson production with mH+ around the top mass. Since the LHC will be\nthe \ufb01rst collider t\u00aft factory, \u201clight\u201d charged Higgs bosons may be copiously produced through the process\nq \u00afq, gg \u2192t\u00aft \u2192\u00aftbH+ [37]. While this is the dominant production mode, there are other processes which\nalso contribute to the light charged Higgs boson production, like single top events or diagrams with the\nsame \ufb01nal state as mentioned above (tbH+), but which do not proceed through t\u00aft production. H+ events\nthrough single top production are not considered in this volume.\nThe charged Higgs boson production cross-section is evaluated for two different MSSM scenarios.\nThey are chosen such that in Scenario A the decay of H+ into SUSY particlces is suppressed, and in\nScenario B (also known as the \u201cmh-max\u201d scenario) the mass of the lightest Higgs boson h0 is maximised.\nTable 9: Mass, cross-section for direct production, cross section for b-associated production, and branch-\ning fractions into \u03c4+\u03c4\u2212and \u00b5+\u00b5\u2212\ufb01nal states for Higgs bosons in the mmax\nh\nscenario and for tan\u03b2 = 20.\nAll values were obtained using FeynHiggs-2.6.2 and HIGLU.\nMass / GeV\n\u03c3direct\nh/H/A/fb\n\u03c3associated\nh/H/A\n/fb\nB(h/H/A \u2192\u03c4+\u03c4\u2212)/%\nB(h/H/A \u2192\u00b5+\u00b5\u2212)/%\nA\nH\nh\nA\nH\nh\nA\nH\nh\nA\nH\nh\nA\nH\nh\n110\n129.8\n109.0\n\u2013\n\u2013\n\u2013\n314810\n7579\n310707\n8.86\n9.11\n8.88\n0.031\n0.032\n0.031\n130\n134.2\n124.7\n92517\n93941\n43545\n189602\n92897\n99992\n9.11\n9.23\n9.00\n0.032\n0.033\n0.032\n160\n160.8\n128.0\n32148\n34706\n44561\n97480\n93102\n6650\n9.42\n9.46\n8.40\n0.033\n0.033\n0.030\n200\n200.5\n128.4\n9847\n11377\n45957\n45685\n45095\n2188\n9.57\n9.72\n7.49\n0.034\n0.034\n0.027\n300\n300.4\n128.6\n955\n1451\n46986\n10312\n10253\n979\n8.22\n9.51\n6.27\n0.029\n0.034\n0.022\n450\n449.8\n128.6\n\u2013\n\u2013\n\u2013\n2019\n2035\n723\n6.07\n6.24\n5.68\n0.021\n0.022\n0.020\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1206\n\nFor the two scenarios the following set of parameters have been used:\nScenario A:\n\u2022 mt = 175 GeV\n\u2022 MSUSY = 500 GeV\n\u2022 At = 1000 GeV\n\u2022 \u00b5 = 200 GeV\n\u2022 M2 = 1000 GeV\n\u2022 M3 = 1000 GeV\nScenario B (\u201cmh-max\u201d):\n\u2022 mt = 170 GeV\n\u2022 MSUSY = 1000 GeV\n\u2022 Xt = 2000 GeV, where At = Xt + \u00b5/tan\u03b2\n\u2022 \u00b5 = 200 GeV\n\u2022 M2 = 200 GeV\n\u2022 M3 = 800 GeV\nMSUSY denotes the soft SUSY-breaking mass parameter in the sfermion sector, mtXt is the off-\ndiagonal entry in the stop mass matrix, \u00b5 the Higgsino mixing paramter, and M2 and M3 the soft\nSUSY-breaking mass parameters in the SU(2) gaugino and the gluino sector, respectively. In the follow-\ning, numerical NLO cross-sections for the low-mass H+ region are calculated with FeynHiggs (version\n2.6.2 [36]). Heavy H+ NLO cross-sections are obtained with Ref. [38] and corrected with the dominant\nsupersymmetry loop corrections (re\ufb02ecting the altered relation between the bottom quark mass and its\nYukawa coupling, \u2206mb) as proposed in Ref. [39].\nFigure 4 shows the results for the tbH+ \ufb01nal state as a function of tan\u03b2 for the MSSM scenarios A\nand B. The production cross-section has a minimum at tan\u03b2 \u22487. This is caused by a mimimum in the\nH+tb Yukawa coupling and renders the so-called intermediate tan\u03b2 region (4 < tan\u03b2 < 10) which is\nexperimentally hard to reach.\n\u03b2\ntan\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nCross section (fb)\n\u22122\n10\n\u22121\n10\n1\n10\n2\n10\n+\n600 GeV H\n500 GeV H\n400 GeV H\n350 GeV H\n300 GeV H\n250 GeV H\n200 GeV H\n170 GeV H\n150 GeV H\n130 GeV H\n120 GeV H\n110 GeV H\n+\n90 GeV H\nScenario A\nATLAS\n\u03b2\ntan\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nCross section (fb)\n\u22122\n10\n\u22121\n10\n1\n10\n2\n10\n+\n600 GeV H\n500 GeV H\n400 GeV H\n350 GeV H\n300 GeV H\n250 GeV H\n200 GeV H\n170 GeV H\n150 GeV H\n130 GeV H\n120 GeV H\n110 GeV H\n+\n90 GeV H\nScenario B\nATLAS\nFigure 4: Expected charged Higgs boson production cross-section in the MSSM for scenarios A and B\nfor light [36] and heavy charged Higgs bosons [38].\nBelow the top quark mass, the charged Higgs boson predominantly decays into a \u03c4 lepton and a\nneutrino, and for values of tan\u03b2 >5 this branching ratio is close to 100%, as shown in Figures 5 and 6.\nDecay modes involving c\u00afs and Wh are also present, but depending on the value of tan\u03b2 they are one or\ntwo orders of magnitude smaller than \u03c4\u03bd. The decay of the W boson originating from the associated top\nquark adds variety to the possible charged Higgs boson signatures, but it also provides handles for signal\nreconstruction and, even more important, for background rejection.\nOnce above the top quark mass threshold, the H+ \u2192t \u00afb decay mode shows a rapid growth and soon\nbecomes an important decay mode as shown in Figure 5. Contrary to the light charged Higgs boson,\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1207\n\n mass (GeV)\n+\nH\n100\n200\n300\n400\n500\n600\n branching ratio\n+\nH\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n mass (GeV)\n+\nH\n100\n200\n300\n400\n500\n600\n branching ratio\n+\nH\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n\u03bd\n\u03c4 \n\u2192\n+\nH\n cs\n\u2192\n+\nH\n tb\n\u2192\n+\nH\n=2)\n\u03b2\nScenario B (tan\nATLAS\n mass (GeV)\n+\nH\n100\n200\n300\n400\n500\n600\n branching ratio\n+\nH\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n mass (GeV)\n+\nH\n100\n200\n300\n400\n500\n600\n branching ratio\n+\nH\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n\u03bd\n\u03c4 \n\u2192\n+\nH\n cs\n\u2192\n+\nH\n tb\n\u2192\n+\nH\n=35)\n\u03b2\nScenario B (tan\nATLAS\nFigure 5: Charged Higgs boson branching ratios as a function of mass for the mh-max scenario for\ntan\u03b2 = 2 and tan\u03b2 = 35 and three selected decay modes.\nfor which the H+ \u2192\u03c4+\u03bd decay mode is an almost exclusive decay mode, the heavy charged Higgs H+\nboson does not solely decay into t \u00afb, but a signi\ufb01cant fraction is allowed to decay into other decay modes\nlike \u03c4+\u03bd, W +h, c\u00afs or SUSY particles where kinematically allowed.\nThe calculations are performed with FeynHiggs [36], as it allows to calculate both the BR(t \u2192H+b)\nand the H+ decay branching in a consistent way, and includes important corrections to the tree level\nvalues. Figure 6 shows the calculated branching ratios for two different charged Higgs boson masses,\none light (130 GeV) and one heavy (600 GeV), as a function of tan\u03b2 .\n\u03b2\ntan\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n branching ratio\n+\nH\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n130\n\u03bd\n\u03c4\ncs130\ntb130\n600\n\u03bd\n\u03c4\ntb600\nScenario A\nATLAS\n\u03b2\ntan\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n branching ratio\n+\nH\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n130\n\u03bd\n\u03c4\ncs130\ntb130\n600\n\u03bd\n\u03c4\ntb600\nScenario B\nATLAS\nFigure 6: Expected charged Higgs boson branching ratios in the MSSM for scenarios A and B for the\nexample of a light (mH+ = 130 GeV) and a heavy (mH+ = 600 GeV) charged Higgs boson [36].\nReferences\n[1] S.L. Glashow, Nucl. Phys. 22 (1961) 579;\nS. Weinberg, Phys. Rev. Lett. 19 (1967) 1264;\nA. Salam, in Elementary Particle Theory, ed. N. 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D 67 (2003) 014018.\nHIGGS \u2013 INTRODUCTION ON HIGGS BOSON SEARCHES\n1211\n\nProspects for the Discovery of the Standard Model Higgs\nBoson Using the H\u2192\u03b3\u03b3 Decay\nAbstract\nThe discovery potential for the Standard Model Higgs boson through the H \u2192\n\u03b3\u03b3 decay in the ATLAS detector is reported. Various performance aspects\nof the Higgs boson mass reconstruction and the photon identi\ufb01cation are dis-\ncussed.\nTrigger issues are also considered.\nThe potential of an inclusive\nH \u2192\u03b3\u03b3 search and Higgs boson searches in association with one or two high\npT jets are evaluated. Studies of the associated WH, ZH and t\u00aftH produc-\ntion processes are also presented. Finally, the discovery potential is assessed\nusing an unbinned multivariate maximum-likelihood \ufb01t. These studies are per-\nformed for experimental conditions expected for an instantaneous luminosity\nof \u22481033 cm\u22122s\u22121.\n1\nIntroduction\nIn the mass range 110 < mH < 140 GeV the Higgs boson is expected to decay into two photons with a\nbranching fraction large enough to render the search feasible at the LHC [1]. The inclusive search for the\nHiggs boson in the diphoton decay channel has been studied in ATLAS for many years and constitutes\none of the benchmarks for the detector performance [2\u20134]. In this paper the sensitivity of ATLAS to this\nchannel is re-evaluated with an updated detector description and software. The impact of higher order\nQCD and electroweak corrections on the discovery potential is also evaluated.\nThe Higgs boson can be produced in association with hadronic jets of high transverse momentum, pT.\nGluons from initial-state radiation in the gg \u2192H and qq\u2192qqH Vector Boson Fusion (VBF) processes\nare the largest contributors to Higgs boson production in association with high pT hadronic jets. The\nsearch for a Higgs boson using the diphoton decay mode in association with one and two jets at the LHC\nhas been suggested [5\u20137] and a previous analysis reported on feasibility studies for these \ufb01nal states\nusing a fast detector simulation [8, 9]. This paper presents an update of these studies based on a more\ncomplete description of the detector simulation.\nIn addition to the diphoton invariant mass, other discriminating variables are incorporated into the\nanalysis and combined by means of an unbinned maximum-likelihood \ufb01t. Photon reconstruction proper-\nties and the event topology are used to separate the data sample into categories that are \ufb01t simultaneously.\nIn the search for a Standard Model Higgs boson, the associated production with W, Z, or t\u00aft can\nserve to complement the inclusive Higgs boson and Higgs boson + jets channels and help to determine\nthe Higgs boson coupling to the Standard Model gauge bosons and the Yukawa coupling to the top\nquark [10]. These measurements would provide consistency checks of the Standard Model. They could\nalso be interpreted in terms of Minimal Supersymmetric Standard Model couplings at high tan\u03b2 (for\nmH \u223c120 GeV) and high mA. Deviations from Standard Model rates could imply new physics such\nas gauge-Higgs uni\ufb01cation [11, 12] or the presence of resonances in models of little Higgs [13, 14],\nLeft-Right symmetry [15] or technicolour [16]. The feasibility of diphoton searches in association with\nweak vector bosons is evaluated using a full detector simulation. This involves searches for diphotons in\nassociation with either just missing transverse energy, Emiss\nT\n, or Emiss\nT\nand a charged lepton (electron or\nmuon), and updates earlier studies performed with a fast detector simulation [17,18].\n1212\n\n2\nMonte Carlo event generation\nThe Monte Carlo (MC) event generation required for this paper is split into two main groups. The \ufb01rst\ngroup corresponds to MC samples produced with a full detector simulation based on GEANT4 [19].\nThese are used for the evaluation of detailed detector effects relevant to the analyses. The second group\nof MC samples are processed with a fast detector simulation [20] and are used primarily for the evaluation\nof the analysis sensitivity. For example, the Higgs boson mass resolution, photon identi\ufb01cation ef\ufb01ciency\nand photon-jet rejection are evaluated with a full detector simulation. The resulting photon ef\ufb01ciency and\nphoton-jet rejection are parameterised as a function of the photon pT and these parameterisations are then\napplied to the fast detector simulation.\n2.1\nSignal processes\nSignal events are generated using PYTHIA [21]: this package implements Leading Order (LO) Matrix\nElement calculations for all the signal processes considered here. The gluon fusion process is also\nsimulated with the MC@NLO [22, 23] package. This package provides QCD Next-to-Leading-Order\n(NLO) Matrix Elements [24\u201327] in addition to a good description of multiple soft-gluon emission at next-\nto-next-to-leading logarithmic level (NNLL) [28\u201330]. This is relevant to evaluating the discriminating\npower of the diphoton pT and other relevant variables. All signal processes used here are processed\nthrough a full detector simulation. Signal events produced via the VBF mechanism are also modeled\nwith HERWIG [31]. All the generated samples for signal processes used here are normalized to the NLO\ncross-sections [32] taking into account only QCD corrections.\n2.2\nBackground processes\nBackground processes can be split into two main groups: backgrounds coming from the production of\ntwo isolated photons, which are usually referred to as irreducible, and reducible backgrounds coming\nfrom events with at least one fake photon. Fake photons are mostly due to the presence of a leading \u03c00\nresulting from the fragmentation of a quark or a gluon. Table 1 gives a summary of the MC packages\nand the cross-sections (in pb) for the irreducible and reducible backgrounds used here.\nIn this paper QCD corrections to both signal and background are considered in the inclusive analysis.\nThe irreducible background is mainly due to the qq,qg \u2192\u03b3\u03b3x processes at up to order \u03b12\u03b1s (namely\nthe Born and Bremsstrahlung contributions) and the gg \u2192\u03b3\u03b3 up to order \u03b12\u03b13\ns (referred to as the box\ncontribution). Contributions from photons produced collinear to quarks are also taken into account at\nNLO. The DIPHOX [33] and ResBos [34\u201336] programs are used to assess the irreducible background\ncomputation. DIPHOX includes all the processes to order \u03b12\u03b1s, including the Bremsstrahlung contribu-\ntion with the quasi collinear fragmentation of quarks and gluons which are computed at NLO. DIPHOX\ndoes not include resummation effects. ResBos includes the Born and box contributions at NLO as well\nas the bremsstrahlung contribution (but the fragmentation contribution is only at LO). ResBos includes\nresummation effects to NNLL.\nIn these computations, a parton level isolation cut of 15 GeV in a cone of \u2206R = 0.4 is used. This is\nchecked against the real photon identi\ufb01cation cuts using PYTHIA fully simulated events. DIPHOX and\nResBos predictions for the total irreducible background agree to better than 10% [37].\nTable 1 shows the cross-sections used to normalize the MC generation in the inclusive analysis.\nThe cross-sections for qq,qg \u2192\u03b3\u03b3x and gg \u2192\u03b3\u03b3 quoted in Table 1 were computed with ResBos for\n80 < m\u03b3\u03b3 < 150 GeV, where m\u03b3\u03b3 is the invariant mass of the diphoton system, and pT\u03b3 > 25 GeV, where\npT\u03b3 is the transverse momentum of the photons. Photons are required to lie in the central region of the\ndetector, |\u03b7| < 2.5. The factorization and renormalization scales are set dynamically as the invariant\nmass of the diphoton system.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1213\n\nTable 1: Details of the cross-section calculation and event generation for the irreducible and re-\nducible photonic backgrounds used in the H \u2192\u03b3\u03b3 analysis. The \ufb01rst three columns display the\ncross-section calculators, kinematic cuts and resulting cross-sections (in pb). The last two columns\nshow the MC packages used for event generation and the number of events generated with a full\nand fast detector simulations, respectively.\nProcess\n\u03c3 calculator\nCuts\n\u03c3(pb)\nFull simulation\nFast simulation\n# of events\n# of events\nqq,qg \u2192\u03b3\u03b3x\nResBos/\n80 < m\u03b3\u03b3 < 150 GeV\n20.9\nPYTHIA/ALPGEN\nALPGEN\nDIPHOX\npT\u03b3 > 25 GeV,|\u03b7| < 2.5\n200000/1300000\n1670000\ngg \u2192\u03b3\u03b3\nResBos\n80 < m\u03b3\u03b3 < 150 GeV\n8.0\nPYTHIA\nPYTHIA\npT\u03b3 > 25 GeV,|\u03b7| < 2.5\n200000\n850000\n\u03b3 j\nJETPHOX\npT\u03b3 > 25 GeV\n180\u00b7103\nPYTHIA\nALPGEN\n3000000\n36700000\nj j\nNLOJET++\npT > 25 GeV\n477\u00b7106\nPYTHIA\nALPGEN\n10000000\n37000000\nIn order to evaluate irreducible backgrounds for signal-signi\ufb01cance computations and to include the\neffect of high-pT jets, the ALPGEN MC generator is used [38, 39].1 This includes 2 \u2192N tree-level\nMatrix Elements, where N = 2 \u22125. The minimum parton pT and maximum pseudorapidity are set to\n20 GeV and |\u03b7| < 5, respectively. A prescription for the merging of matrix elements and parton showers\nis used [41]. The pT threshold for the merging of the parton shower and the Matrix Elements is set to\n20 GeV and \u2206R = 0.7.\nThe total cross-section of the ALPGEN samples of \u03b3\u03b3+jets events is normalized to the cross-section\ngiven in Table 1. The diphoton invariant mass and transverse momentum spectra are re-weighted to the\ncorresponding spectra obtained with ResBos for the Born and Bremsstrahlung contributions. This is mo-\ntivated by the fact that ResBos provides a NNLL description of the resummation effects that signi\ufb01cantly\naffects the pT spectrum of the diphoton system up to about 40 or 50 GeV.\nThe box contribution is simulated with the PYTHIA package using the leading order one loop Matrix\nElements with full and fast detector simulations. The cross-section of this sample is normalized to the\ncross-section given in Table 1. The diphoton invariant mass and momentum spectra are re-weighted to\nthe corresponding spectra obtained with ResBos.\nThe total inclusive cross-section for the \u03b3 j process is obtained using the package JETPHOX [42].\nThis package simulates direct and fragmentation single photon production. The distribution of the photon\npT that is obtained is compared with that for direct production predicted using the PYTHIA package. It\nis observed that the differential cross-section obtained with JETPHOX is a factor of 2.1 larger than that\nobtained with PYTHIA, with a weak pT dependence. Table 1 shows the cross-section for inclusive \u03b3 j\nproduction for pT\u03b3 > 25 GeV.\nThe inclusive dijet cross-section is computed with the help of the NLOJET++ package [43,44], which\ntakes into account QCD NLO corrections. The dijet cross-section obtained with this program is found to\nbe a factor of 1.3 larger than that obtained with PYTHIA. Table 1 shows the cross-section for inclusive\ndijet production for pT > 25 GeV.\nFor purposes of signal signi\ufb01cance computation the ALPGEN MC package is used to generate sam-\n1This generation does not include the box contribution nor the electroweak \u03b3\u03b3 j j process. The latter is generated with the\nMadGraph package [40] and it is used in the Higgs boson searches in association with hadronic jets only (see Sections 5.2\nand 5.3).\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1214\n\nTable 2: Event generators and cross-sections for backgrounds used in the analyses of associated\nproduction. Photons are required to be in |\u03b7| < 2.7 and to have pT > 20 GeV. For the W \u00b1(\u2192\ne\u00b1\u03bd)\u03b3 process the electron is required to pass the same cuts as the photons. The diphoton invariant\nmass should be in the interval 90 < m\u03b3\u03b3 < 150 GeV, when appropriate. For the b\u00afb\u03b3\u03b3 process the\npT of the b quark is required to be greater than 20 GeV.\nProcess\nGenerator\nCross-section\nNumber of events\nZ(\u2192\u2113\u2113)\u03b3\u03b3\nMadGraph\n2.4 fb\n17500\nZ(\u2192\u03bd\u03bd)\u03b3\u03b3\nMadGraph\n4.9 fb\n17500\nW +(\u2192\u2113\u03bd)\u03b3\u03b3\nMadGraph\n3.3 fb\n28200\nW \u2212(\u2192\u2113\u03bd)\u03b3\u03b3\nMadGraph\n3.1 fb\n31500\nW \u00b1(\u2192e\u00b1\u03bd)\u03b3\nPYTHIA\n5.9 pb\n218350\nc\u00afc\u03b3\u03b3\nMadGraph\n257 fb\n5000\nb\u00afb\u03b3\u03b3\nMadGraph\n24.41 fb\n5000\nt\u00aft\u03b3\u03b3\nMadGraph\n1.97 fb\n4900\nples of \u03b3+jets and multi-jets with a fast detector simulation. ALPGEN includes 2 \u2192N tree-level Matrix\nElements, where N = 2 \u22125. The minimum parton pT and pseudorapidity range are set to 20 GeV and\n|\u03b7| < 6, respectively. The same matching conditions as in the \u03b3\u03b3+jets sample are used. The samples\ngenerated with ALPGEN are normalized to cross-sections given in Table 1.\nA small background contribution is expected from Drell-Yan e+e\u2212faking a photon pair. For this\npurpose 420k events were generated using the PYTHIA package with a full detector simulation. The\ngenerator cross-section after requiring one lepton with pT > 10 GeV and |\u03b7| < 2.7 is 1.23 nb.\nSpeci\ufb01c backgrounds contributing to the Higgs boson plus lepton and Higgs boson plus missing\ntransverse energy channels are also produced. W/Z + diphoton backgrounds can produce the same\ntopology as the signal. To evaluate the contributions from these backgrounds, the MadGraph [40] gen-\nerator, which includes the Z and W bosons produced in association with two photons with tree-level\ndiagrams has been used. The cross-sections for these processes, including the leptonic branching ratios,\nare shown in Table 2, requiring that the photons have pT > 20 GeV and |\u03b7| < 2.7, and that the invariant\nmass of the two photons be between 90 and 150 GeV.\nThe c\u00afc\u03b3\u03b3, b\u00afb\u03b3\u03b3 and t\u00aft\u03b3\u03b3 cross-sections shown in Table 2 do not include the branching ratios of\nleptonic decays. For the b\u00afb\u03b3\u03b3 process the transverse momentum of the b quark is required to be greater\nthan 20 GeV. In the t\u00aft\u03b3\u03b3 events, also produced by MadGraph, the photons only come from the top\nquarks. The contribution from events in which photons arise from the decay products of the t\u00aft system\nwas roughtly evaluated. Events were generated with PYTHIA using the Matrix Elements for the t\u00aft\nprocess. The production of two additional high pT photons coming from the \ufb01nal state radiation of the\ntop quark decay products was evaluated. It was found that the t\u00aft\u03b3\u03b3 background needs to be multiplied by\na factor 7.5 to account for this effect: this factor was applied for the analysis of the associated channel.\nIt is probably conservative because the photons radiated by the quarks should not be isolated and would\nbe removed by the analysis cuts.\nThere is a contribution to the background from events with a W boson and a photon, where the W\nboson decays into an electron and a neutrino. In some events, the electron can be mis-reconstructed as a\nphoton. The PYTHIA generator is used for this background and the cross-section, including the leptonic\nbranching ratio, is given in Table 2 after requiring pT > 20 GeV and |\u03b7| < 2.7 for both the photon and\nthe electron. For all the processes in Table 2 a full detector simulation was used and QED radiative\ncorrections to the Z/W decays were treated with PHOTOS [45].\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1215\n\n3\nPhoton selection and \u03b3\u03b3 reconstruction\n3.1\nPhoton reconstruction and calibration\nPhotons in the calorimeter are reconstructed from clusters of different sizes: in the barrel region (|\u03b7| <\n1.37 ) a \u2206\u03b7x\u2206\u03c6 = 3x7 cluster (in units of middle sampling calorimeter cells) is used for converted\nphotons to recover as much as possible the energy that might be lost due to the opening of the two\nelectrons in the magnetic \ufb01eld. A 3x5 cluster is used for unconverted photons. In the endcap region\n(1.52 < |\u03b7| < 2.37 ) a 5x5 cluster has been used for both converted and unconverted photons. The chosen\ncluster sizes are a compromise between maximal energy containment and minimization of the noise. In\nthe simulation, all the effects that contribute to the calorimeter resolution constant term, which by design\nshould be kept below 0.7%, are taken into account by smearing the reconstructed cells energies. The\nenergy of the photons in the electromagnetic (EM) calorimeter has been reconstructed using appropriate\nweights for the presampler and back compartments of the calorimeter to correct for the energy lost in\nthe material in front of the calorimeter, for the longitudinal leakage and for the energy losses outside the\ncluster. Different weights for unconverted photons and electrons are used, as derived from the nominal\ndetector geometry (see Ref. [46] for details). Clusters are then corrected for a series of effects. The\nvariations of the energy with respect to the impact point inside each cell are corrected for. These effects\nare due to the fact that the shower is not fully contained inside the cluster (the effect is larger for small\ncluster sizes) and to the calorimeter material structure in \u03c6. The photon candidate position is de\ufb01ned as\nthe barycenter of the associated cluster: the fact that the cells have a \ufb01nite granularity introduces a bias in\nthe measured position which is corrected for as a function of the particle impact point within the central\ncell (more details in Ref. [46]).\n3.2\nPhoton identi\ufb01cation\nPowerful photon identi\ufb01cation is required to reduce the background from jets faking photons (from j j\nevents and \u03b3 j events) below the irreducible background. The photon identi\ufb01cation relies on the \ufb01ne\nsegmentation of the electromagnetic calorimeter, especially the \ufb01rst layer, allowing an event-by-event\nrejection of \u201cisolated\u201d \u03c00s, which are the main source of fake photons from jets. The details of the\nshower-shape variables and the cuts can be found in Ref. [47]. The shower-shape variables include the\nleakage in the \ufb01rst compartment of the hadronic calorimeter, variables characterizing the lateral size of\nthe shower in the second layer of the EM calorimeter, and variables related to the transverse size in\nthe \ufb01rst layer of the EM calorimeter, together with a search for a second maximum in \u03b7 in the energy\ndeposited in the strips of the \ufb01rst layer. The average ef\ufb01ciency of the calorimeter cuts for photons\nfrom Higgs boson decays with pT > 25 GeV has been found to be 83% when pile-up corresponding to\n1033cm\u22122s\u22121 instantaneous luminosity is added. A track isolation cut is also applied to reduce further\nthe fake background: the sum of the pT of tracks in a \u2206R = 0.3 cone around the cluster position is\ncomputed for tracks with pT > 1 GeV and a cut at 4 GeV is applied. For tracks with \u2206R < 0.1 of the\ncluster position additional cuts are applied to remove conversion tracks from the sum. The ef\ufb01ciency of\nthis cut for photons ful\ufb01lling all other identi\ufb01cation cuts is 98% [47]. The cuts have been optimized\nusing photons from Higgs boson decays as a signal sample and an inclusive jet sample for the fake rate\nstudy. The optimisation of the cuts has been done mostly in the ET range 25 \u221235 GeV and the same\ncuts are applied to converted and unconverted photons. Table 3 shows the rejection factors for inclusive\njets (normalized to jets found from the simulated particles without detector effects using a cone of size\n\u2206R = 0.4), as measured from the inclusive jet sample. The rejection is also given separately for quark\nand gluon jets. The difference in rejection comes from the different fragmentation. After all cuts, the\ndominant background comes from \u201csingle\u201d \u03c00s. The uncertainty on the rejection (uncertainty on the\nfragmentation, modeling of the detector response) is close to a factor of two [47].\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1216\n\nTable 3: Jet rejections expected for the inclusive jet sample for ET > 25 GeV. The results are\nshown before and after track isolation cuts for all jets and separately for quark and gluon jets. The\nerrors are statistical only.\nAll\nquark-jet\ngluon-jet\nRejection (before isolation)\n5070\u00b1120\n1770\u00b150\n15000\u00b1700\nRejection (after isolation)\n8160\u00b1250\n2760\u00b1100\n27500\u00b12000\n3.3\nConversion reconstruction\nConsidering Higgs boson decays with photons within |\u03b7| < 2.5, about 57% of the selected events have\nat least one true conversion with a radius smaller than 80 cm. Converted photons may start showering\nbefore the beginning of the calorimeter thereby degrading the energy resolution. In addition, the energy\ndeposition in the calorimeter from a converted photon is geometrically broader in \u03c6 than that from an\nunconverted photon due to the magnetic \ufb01eld in the Inner Detector cavity. On the other hand when a\nphoton from a Higgs boson decay converts, the measurement of the conversion radius can be used to\nimprove the accuracy on the measurement of the photon direction (see Section 3.4).\nConversions are reconstructed by a vertexing algorithm using the reconstructed particle tracks, as\nexplained in more detail in Ref. [48]. An electromagnetic cluster with an associated track which is one\nof the two tracks of a conversion, is classi\ufb01ed as a double track conversion. When a photon converts and\nonly one reconstructed track is associated to the corresponding cluster this photon may be mis-identi\ufb01ed\nas an electron: in order to increase the conversion reconstruction ef\ufb01ciency when an electromagnetic\ncluster has an associated track with no B-layer hit and the associated track does not belong to a recon-\nstructed double track conversion, this object is classi\ufb01ed as a single track conversion. Including single\ntrack conversions in the analysis increases by \u22486% the signal ef\ufb01ciency while the overall background\nis increased by approximately the same factor. The conversion reconstruction ef\ufb01ciency as a function of\nthe conversion radius is shown in Fig. 1: with the reconstruction software version used for this analysis,\nthe overall ef\ufb01ciency is \u224866.4% for conversions with a radius below 40 cm. The different contributions\nfrom single-track and double-track conversion reconstruction are also shown.\nConversion radius [mm]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nTotal conversions\nDouble track\nSingle track\nATLAS\nFigure 1: Ef\ufb01ciency of single-track and double-track conversion reconstruction as a function of the\nconversion radius.\nFor a given electromagnetic cluster, more than one associated reconstructed conversion can be found:\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1217\n\nmultiple conversions are due to secondary conversions or fake conversions. Fake conversions arise from\ntwo tracks that do not come from a conversion or with only one of the two tracks coming from a con-\nversion. In the case of multiple conversions, the conversion with the smallest radius is selected: the\nreconstructed conversion is then correctly associated to a converted photon from a Higgs boson decay in\n97.6% of simulated signal cases.\nThe jet contribution to the total background can be evaluated from the analysis of converted photons\n(see Ref. [48] for more details and updated results). The presence of tracks associated to the conversion\nprovides a measurement of the transverse momentum of the converted photon in the tracker and conse-\nquently an evaluation of the ratio pT/ET, where ET is the transverse energy of the calorimeter cluster.\nThis variable should be distributed between 0 and 1. As shown in Fig. 2, converted photons have val-\nues of pT/ET which populate the region around 1 with a large non Gaussian tail to lower values due to\nbremsstrahlung of the electrons. In contrast, the distribution expected for a converted photon from a \u03c00\nwith the same transverse energy peaks at much lower values since the cluster collects the full energy of\nboth photons from \u03c00 decay. It is particularly instructive to note that Fig. 2 also shows that the expected\ndistributions for pT/ET for jets passing all the photon identi\ufb01cation cuts is very similar to that obtained\nfrom single \u03c00\u2019s with the same transverse energy: this indicates that the residual background from jets is\ndominated by single \u03c00\u2019s. The shapes in Fig. 2 for converted photons coming from a jet and converted\nphotons from the direct process can be parametrized and used to discriminate between the two compo-\nnents in a data sample of conversion events, allowing an evaluation of the \u03b3 j and j j percentage in the\nbackground.\nT\n/E\nT\np\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n0.24\n=40GeV\nT\n, E\n\u03b3\nSingle \n=40GeV\nT\n, E\n0\n\u03c0\nSingle \n-jet sample\n\u03b3\n from \n\u03b3\n-jet sample\n\u03b3\njet from \nATLAS\nFigure 2: pT/ET ratio for conversions where both tracks were reconstructed in different event samples.\n3.4\nPrimary vertex reconstruction\nAmong the reconstructed photons passing the identi\ufb01cation cuts, the two with highest pT are assumed\nto come from the Higgs boson decay. The azimuthal angle \u03c6 is determined by the cluster barycenter in\nthe second layer of the EM calorimeter. The pseudorapidity \u03b7 relies on the knowledge of the position zH\nat which the Higgs boson is produced and decays.\nExploiting the multi-layer structure of the EM calorimeter, an estimate of the direction of each photon\ncan be achieved by \ufb01tting a straight line in the (R,z) plane through the cluster barycenters detected in the\npresampler and in the \ufb01rst and second samplings of the EM calorimeter. The intercept of these lines with\nthe ATLAS beam axis provides two independent measurements of the hard scattering vertex, z\u03b31 and z\u03b32\nwith their uncertainties. They are combined in a weighted average with the nominal interaction vertex\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1218\n\nat z0 = 0 which has a spread of \u00b156 mm to yield a calorimeter estimate, zcalo\nH , of the primary vertex.\nThe performance expected for H \u2192\u03b3\u03b3 events is displayed in Table 4 and Fig. 3 (left plot). The accuracy\n(RMS) of the primary vertex position reconstruction is 13 mm, 17 mm, 41 mm, when both photons are in\nthe barrel, one in the barrel and one in the endcap, and both in the endcap. In the simulation of the events\nused for this analysis a 4mm shift of the electromagnetic calorimeter along the z-axis was introduced\n(see Ref. [49] for more details) with respect to the nominal position. This effect has been taken into\naccount at the reconstruction level, recalculating the pseudorapidity of the cells in each calorimeter layer\nwith respect to the interaction point taking as a radial position reference the geometrical center (in the\nradial direction) of the cell. To compute the photon direction, the pointing algorithm makes use of the\nradial position of the barycenter of the shower instead of the geometrical center of the cell biasing the\ndistribution of the reconstructed primary vertex position obtained from calorimeter pointing with respect\nto the true position as shown in Fig. 3, left plot (see Ref. [50] for more details). When a conversion is\nreconstructed, its coordinates are added as an extra point to the straight line \ufb01t, thus improving the Higgs\nboson vertex position accuracy; the distribution exhibits large tails with an RMS of 8 mm and a narrow\nGaussian core with a width of 0.15 mm.\nBy adding the reconstructed primary vertex to the linear \ufb01t, the best Higgs boson position accuracy\nis achieved, with a Gaussian width of 0.07 mm (see Table 4 and Fig. 3, plot on the right). In the case of\npile-up, more than one primary vertex may be reconstructed by the inner detectors. The discrimination\nof the hard-scattering vertex from pile-up vertices is done using a likelihood that is a combination of the\ncalorimeter information and the sum of the squares of the pTs of the tracks originating from the vertex\n(named P2\nT in the following). So\nL = LP2\nT \u00d7Lcalo\n(1)\nwhere\nLP2\nT = pH(p2\nT)/pMB(p2\nT)\n(2)\nLcalo = e\u22121\n2\nz2\n562 \u00d7e\n\u22121\n2\n(z\u2212zcalo)2\n\u03c32zcalo /e\u22121\n2\nz2\n562 = e\n\u22121\n2\n(z\u2212zcalo)2\n\u03c32zcalo\n(3)\nThe \ufb01rst component of the likelihood, LPT2, is, for a certain value of P2\nT, the probability for the\nHiggs boson vertex to have this P2\nT divided by the same probability for a minimum bias vertex. The\nsecond component is the product of the probabilities that a measured vertex is that of the Higgs boson\nvertex divided by the probability that the measured vertex position is that of a minimum bias vertex. The\nvertex misidenti\ufb01cation due to pile-up is displayed by the columns labeled \u2018tail\u2019 in Table 4. When the\nvertex associated to the Higgs boson production is correctly identi\ufb01ed among the others, the impact of\nthe direction measurement on the invariant mass resolution becomes negligible with respect to that of the\nenergy measurement.\n3.5\nInvariant mass and signal acceptances\nThe invariant mass of diphoton pairs has been reconstructed for different signal samples using the tools\ndescribed in the previous Sections: the 2g17i trigger selection (see Section 4 for more details) is applied\nand two identi\ufb01ed photons are required to be reconstructed with pT > 40 GeV and pT > 25 GeV within\nthe \ufb01ducial region of 0 < |\u03b7| < 1.37 and 1.52 < |\u03b7| < 2.37. Fig. 4 presents the invariant mass distribu-\ntions of \u03b3\u03b3 pairs from Higgs boson decay with mH = 120 GeV. The shaded histograms correspond to\nevents with at least one true converted photon with a conversion radius smaller than 80 cm. The con-\nverted photons are currently calibrated at the electron scale and the unconverted ones at the photon scale:\nin the case of the geometry with additional material in front of the calorimeter, the observed difference\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1219\n\nTable 4: Performance of the Higgs boson longitudinal vertex position reconstruction, using\ncalorimeter pointing only (zcalo\nH ) and the reconstructed primary vertex (zcalo+vtx\nH\n): averages (\u27e8\u27e9)\nand RMS are displayed in mm. \u2018tail\u2019 shows the percentage of events which are outside the his-\ntogramme window (\u00b1100 mm and \u00b11 mm for zcalo\nH\nand zcalo+vtx\nH\nrespectively).\nLuminosity\nzcalo\nH\n\u2212ztrue\nH\n(mm)\nzcalo+vtx\nH\n\u2212ztrue\nH\n(mm)\n\u27e8\u27e9\nRMS\ntail(%)\n\u27e8\u27e9\nRMS\ntail(%)\nNo pileup\n2.3\n17.3\n0.09\n-0.008\n0.10\n1.2\n1033\n3.3\n17.4\n0.09\n-0.010\n0.10\n13.0\n2\u00b71033\n2.4\n17.1\n0.18\n-0.007\n0.10\n18.3\n [mm]\ntrue\n-z\nrec\nz\n-100-80 -60 -40 -20 0\n20 40 60 80 100\nArbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nATLAS\nNo pile-up\n-1\ns\n-2\ncm\n33\n10\n-1\ns\n-2\ncm\n33\n2*10\n [mm]\ntrue\n-z\nrec\nz\n-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8\n1\nArbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\nNo pile-up\n-1\ns\n-2\ncm\n33\n10\n-1\ns\n-2\ncm\n33\n2*10\nFigure 3: Difference between the reconstructed primary vertex position and the true position obtained\nfrom calorimetric pointing and conversion track information (when available) without/with the recon-\nstructed primary vertex (left/right plot), for events without pile-up (black plots) and with pile-up eval-\nuated for 1033 and 2 \u00b7 1033 cm\u22122s\u22121 (red, green plots). The narrow peak on top of the broader one is\ndue to events in which at least one photon has a reconstructed conversion vertex. In the right plots, the\nnon-Gaussian shape is due to the overlap of barrel-barrel, barrel-endcap and endcap-endcap topologies,\nwhich have different resolutions.\nbetween the peak of the distribution of events with no conversions and the one with at least one recon-\nstructed conversion is around 1 %. In the future a speci\ufb01c calibration will be implemented for converted\nphotons using the same prescription as that used for electrons and unconverted photons.\nTo be consistent with previous studies ( [4], [3]) the mass resolution obtained for the photon pairs\nhas been determined from an asymmetric Gaussian \ufb01t ([-2 \u03c3 , + 3 \u03c3]) of the invariant mass peak. The\nasymmetric window is used to reduce the impact of the residual low energy tails in the reported width.\nTable 5 shows the results for different Higgs boson masses with and without pileup at 1033 cm\u22122s\u22121 in\nthe case of simulations with additional dead material in front of the calorimeter (see Ref. [49] for more\ndetails). Since the energy calibration coef\ufb01cients have been calculated using the nominal geometry, the\npresence of additional dead material in front of the calorimeter affects the determination of the value\nof the invariant mass, moving the peak mean down by a few per mille. In addition it increases the\namount of low energy tails: the percentage of events with a reconstructed invariant mass more than 3\u03c3\nfrom the mean increases from 3.5 % for the nominal geometry to 6.8 % for the distorted geometry.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1220\n\n [GeV]\n\u03b3\n\u03b3\nM\n100\n105\n110\n115\n120\n125\n130\n135\n140\nArbitrary units\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n2400\n\u03b3\nAt least 1 converted \n0.01) GeV\n\u00b1\nMean=(119.72\n0 01) GeV\n\u00b1\n=(1.42\n\u03c3\nATLAS\n [GeV]\n\u03b3\n\u03b3\nM\n100\n105\n110\n115\n120\n125\n130\n135\n140\nArbitrary units\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n\u03b3\nAt least 1 converted \n0.03) GeV\n\u00b1\nMean=(119.46\n0.02) GeV\n\u00b1\n=(1.46\n\u03c3\nATLAS\nFigure 4: Invariant mass distributions for photons pairs from Higgs boson decays with mH = 120 GeV\nafter trigger and identi\ufb01cation cuts; on the left the invariant mass distribution obtained using the nominal\ngeometry simulation is reported while on the right plot the same invariant mass distribution is reported\nwhen additional dead material is included in the simulation. The shaded histograms correspond to events\nwith at least one converted photon.\nThe acceptances after trigger selection (see Section 4 for more details) and analysis cuts together with\nthe mass resolutions for the different values of mH are reported in Table 5. The mass window for the\nevaluation of the signal signi\ufb01cance (denoted mass bin) is de\ufb01ned as \u00b11.4\u03c3 around the central value.\nAs can be seen in Table 5 the fraction of signal events in the mass bin is 26 % for mH = 120 GeV slightly\nincreasing with the Higgs boson mass. The relative mass resolution \u03c3m/m is close to 1.2 % degrading\nby a few percent relative when the pileup is added.\nTable 5: Ef\ufb01ciencies after trigger, identi\ufb01cation and inclusive analysis cuts (see Section 5.1).\nReconstructed invariant mass peak positions and resolutions for different Higgs boson masses\nwith and without 1033 cm\u22122s\u22121 pileup are also reported. Distorted geometry has been used in all\ncases.\nmH = 120 GeV\nmH = 130 GeV\nmH = 140 GeV\nNo pileup\nPileup\nNo pileup\npileup\nNo pileup\nPileup\nL1\n0.66\n0.64\n0.69\n0.65\n0.68\n0.66\nL2\n0.54\n0.52\n0.55\n0.52\n0.56\n0.53\nEF\n0.50\n0.47\n0.52\n0.49\n0.52\n0.49\nAnalysis cuts\n0.36\n0.32\n0.38\n0.35\n0.39\n0.36\nMass bin\n0.26\n0.24\n0.28\n0.26\n0.29\n0.27\nMass Fitted (m)\n119.46\n119.47\n129.47\n129.41\n139.41\n139.41\n\u03c3m, GeV\n1.46\n1.52\n1.54\n1.62\n1.66\n1.69\n3.6\nBackground analysis on fully simulated samples\nLarge samples of \u03b3\u03b3 and \u03b3 j events as well as Drell-Yan Z \u2192e+e\u2212were generated with PYTHIA and\nfully simulated. The differential cross-section at LO as a function of the diphoton invariant mass for \u03b3 j\nand e+e\u2212events after the analysis procedure described in previous sections is reported in Fig. 5. For the\nj j background contribution evaluation not enough statistic was available in full simulation and it has been\nestimated only from fast simulated events using photon ef\ufb01ciency and the jet rejection parametrizations\nobtained from full simulation.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1221\n\n [GeV]\n\u03b3\n\u03b3\nM\n80\n90\n100\n110\n120\n130\n140\n150\n [pb/GeV]\n\u03b3\n\u03b3\n /dM\n\u03c3\nd\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n-jet contribution\n\u03b3\nATLAS\n [GeV]\n\u03b3\n\u03b3\nM\n80\n90\n100\n110\n120\n130\n140\n150\n [pb/GeV]\n\u03b3\n\u03b3\n /dM\n\u03c3\nd\n-3\n10\n-2\n10\n-1\n10\nDrell-Yan contribution\nATLAS\nFigure 5: Diphoton candidates invariant mass distribution for \u03b3 j (left) and Drell-Yan e+e\u2212(right) events\nafter photon identi\ufb01cation and analysis cuts with and without trigger selection.\nThe goodness of the photon ef\ufb01ciency and jet rejection parametrizations used in Section 5 on fast\nsimulated events to estimate the background contributions has been tested on the \u03b3 j sample in full sim-\nulation: the distribution of the cross-section as a function of the diphoton candidates invariant mass has\nfound to be in agreement within 15 % in the 110-150 GeV mass range with the distribution from the fast\nsimulated sample after photon ef\ufb01ciency and jet rejection parametrization used in Section 5.\n3.7\nJet tagging in simulation\nSection 5 presents two analyses which rely on tagging hadronic jets. Jet tagging is particularly relevant\nto Higgs boson searches in association with two high pT jets since such an analysis is intended to isolate\nHiggs boson production via VBF.\nIn the VBF production process, it is expected that the two quark-initiated jets are observed in opposite\nhemispheres and with a large separation in pseudorapidity. Tagging these jets further suppresses the\nbackground processes. Furthermore, since there is no colour exchange between the two quarks, the\nHiggs boson should be observed in a large rapidity gap, where additional activity from QCD jets is\nsmall. A central jet veto (CJV) which suppresses the background processes is therefore used in the event\nselection,\nThe relative ef\ufb01ciencies for jet tagging are summarized in Table 6. The following four conditions are\napplied:\n\u2022 two simulated quarks with pT > 40 GeV and pT > 20 GeV (|\u03b7| < 5) and in opposite hemispheres,\n\u2022 two reconstructed jets with pT > 40 GeV and pT > 20 GeV (|\u03b7| < 5),\n\u2022 the two reconstructed jets are in opposite hemispheres,\n\u2022 differences in \u03b7 between the simulated quarks and the reconstructed jets are smaller than 0.4 (this\nis referred to as matching).\nThe present tagging method selects correct tagging jets in 75.7% of the events. Under a pileup\ncondition of 1033cm\u22122s\u22121, a degradation of less than 5% is observed. The difference between HERWIG\nand PYTHIA is about 6%.\n4\nPerformance of the photon trigger on H \u2192\u03b3\u03b3 events.\nThere are two trigger selections which are foreseen for the H \u2192\u03b3\u03b3 analyses: 2g17i and g55. The 2g17i\ntrigger selects events with at least two isolated photons and is ef\ufb01cient for photon pT above 20 GeV. The\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1222\n\nTable 6: Relative ef\ufb01ciencies of the tagging method for VBF H \u2192\u03b3\u03b3 with mH = 120 GeV (see\ntext).\nSelection\nHERWIG (no pileup)\nHERWIG (Pileup 1033)\nPYTHIA (no pileup)\nstep 1 (quark level)\n0.618\u00b10.002\n0.613\u00b10.003\n0.632\u00b10.002\nstep 2 (rec level)\n0.914\u00b10.002\n0.911\u00b10.002\n0.943\u00b10.001\nstep 3 (rec level)\n0.801\u00b10.002\n0.774\u00b10.003\n0.771\u00b10.002\nstep 4 (matching)\n0.757\u00b10.003\n0.726\u00b10.003\n0.713\u00b10.003\ng55 trigger selects events with at least one photon and is ef\ufb01cient for photon pT above 60 GeV. No\nisolation is required in the g55 trigger. In the analyses presented in Section 5 only the 2g17i menu has\nbeen considered to avoid possible biases in the invariant mass reconstruction: a more detailed description\nof the photon selection at the High Level Trigger is available [51]. The photon reconstruction at the\ntrigger level relies only on calorimetric information. To calculate ET and shower shapes variables the\nHigh Level Trigger uses algorithms similar to those used for of\ufb02ine analysis using information from the\n\ufb01rst and second sampling of the calorimeter. For photon trigger menus the isolation is only applied at L1\ntrigger.\nThe trigger ef\ufb01ciency has been evaluated for Higgs boson events having two of\ufb02ine reconstructed\nphotons passing the following kinematic cuts: two photons with pT\u03b3 > 25 GeV and pT\u03b3 > 40 GeV re-\nspectively both in the region 0< |\u03b7| <1.37 and 1.52< |\u03b7| <2.37, passing the identi\ufb01cation cuts described\nin Section 3.2.\nTable 7: Ef\ufb01ciency for the 2g17i menu item to trigger on H \u2192\u03b3\u03b3 events with mH = 120 GeV,\nnormalized with respect to the of\ufb02ine selections.\nTrigger Level\n2g17i Trigger ef\ufb01ciency\nL1\n96.3\u00b10.3\nL2 Calo\n95.0\u00b10.4\nEF Calo\n93.6\u00b10.4\nTable 7 shows in the \ufb01rst column the ef\ufb01ciency of the 2g17i menu item to select H \u2192\u03b3\u03b3 events after\neach trigger level.\nThe 2g17i trigger menu item is expected to be \u223c94% ef\ufb01cient for triggering on Higgs boson decays\nwith two reconstructed photons. The ef\ufb01ciency loss is mainly due to the calorimeter isolation at L1\nwhich is not applied in the of\ufb02ine photon selection.\nTrigger rates for 2g17i are studied in the context of the ATLAS trigger development. This trigger is\nfound to be usable (unprescaled) up to luminosities of 1033 cm\u22122s\u22121 [51].\n5\nEvent selection\nIn this Section the analysis details of the various event selections are described. The event selection for\nthe inclusive analysis is given in Section 5.1 and for the Higgs boson search in association with jets are\ngiven in Sections 5.2 and 5.3. Finally, the event selections for diphoton searches in association with\nmissing transverse momentum and charged leptons are given in Sections 5.4 and 5.5. Here the various\nevent selections are presented as disjoint analyses. In Section 7 the statistical power of these channels is\ncombined and their impact on the Higgs boson discovery potential is evaluated.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1223\n\n5.1\nInclusive analysis\nThe inclusive analysis refers to the search for a resonance in events with two photons that pass certain\nquality criteria. The analysis reported here follows closely the event selection of past studies [3,4]. The\ndetector performance and optimization studies succinctly presented in Sections 3 and 4 are geared toward\nmaximizing the discovery potential of the inclusive analysis.\nThe following cuts are applied:\nIa At least two photon candidates (see Section 3.2) in the central detector region de\ufb01ned as |\u03b7| < 2.37\nexcluding the transition region between barrel and endcap calorimeters, 1.37 < |\u03b7| < 1.52 (crack in\nthe following). At this level it is required that the event passes the trigger selection (see Section 4).\nIb Transverse momentum cuts of 40,25 GeV on the leading and sub-leading photon candidates, re-\nspectively.\nThe \ufb01ducial cuts in Ia are motivated by the quality of the off-line photon identi\ufb01cation and the\nfake photon rate (see Section 3.2). The values of the cuts on the transverse momentum of the photon\ncandidates (cut Ib) are not varied and are obtained from previous optimization studies [3].\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n50\n100\n150\n200\n250\n300\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n50\n100\n150\n200\n250\n300\nSignal\nIrreducible bkg\nReducible bkg\nATLAS\nFigure 6: Diphoton invariant mass spectrum after the application of cuts of the inclusive analysis. Results\nare presented in terms of the cross-sections in fb. The contribution from various signal and background\nprocesses are presented in stacked histograms (see text).\nFigure 6 shows the expected diphoton mass spectrum after the application of cuts Ia and Ib. The\nhashed histogram in the bottom corresponds to the contributions from events with one and two fake\nphotons. The second hashed histogram corresponds to the irreducible backgrounds (see Section 2.2). The\nbackground contributions are obtained with MC samples with a fast detector simulation normalized to\nthe cross-sections speci\ufb01ed in Section 2.2. The fast detector simulation is corrected in order to reproduce\nthe aspects of the detector performance critical to the analysis, which are obtained with a full detector\nsimulation (see Sections 3 and 4). The expected contribution from a Higgs boson signal for mH =\n120 GeV, obtained with a full detector simulation, is also shown in Fig. 6.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1224\n\nTable 8: Expected cross-sections (in fb) for different signal (mH = 120 GeV) and background\nprocesses within a mass window of m\u03b3\u03b3 \u00b11.4 of the mass resolution in the no pileup case reported\nin Table 5. Cuts Ia and Ib were applied.\nSignal Process\nCross-section (fb)\nBackground Process\nCross-section (fb)\ngg \u2192H\n21\n\u03b3\u03b3\n562\nVBF H\n2.7\nReducible \u03b3 j\n318\nttH\n0.35\nReducible j j\n49\nVH\n1.3\nZ \u2192e+e\u2212\n18\nTable 9: Summary of the relative systematic uncertainties on the \u03b3\u03b3 and \u03b3 j processes.\nPotential sources\n\u03b3\u03b3\n\u03b3 j\nScale dependence\n14%\n20%\nFragmentation\n5%\n1%\nPDF\n6%\n7%\nTotal\n16%\n21%\nTable 8 shows the expected cross-sections (in fb) for background and signal in a mass window of\n\u00b11.4 of the mass resolution in the no pileup case reported in Table 5 around 120 GeV after the application\nof cuts Ia and Ib. Table 8 indicates that the relative contribution from events with at least one fake photon\nconstitutes 39% of the total background, about a factor of two larger than evaluated in Ref. [4]. This\nincrease is mostly attributed to three factors. Firstly, a different method for the parametrization of the\nfake photon background is used here. Secondly, the budget of inactive material in front of the \ufb01rst layer\nof the calorimeter has increased with respect to the one used in previous studies. Finally, the contribution\nfrom fragmentation in the \u03b3 j process (see Section 2.2) is allowed for here for the \ufb01rst time.\n5.1.1\nTheoretical uncertainties on background prediction\nIn this Section the theoretical uncertainties of the predictions for prompt single and double photon pro-\nduction used in the inclusive analysis are evaluated.\nThe irreducible background rate is evaluated using ResBos [34\u201336], which implements a full matrix\nelement calculation at NLO and the resummed formalism. It thus yields an accurate description of the\nlow pT\u03b3\u03b3 region, as corroborated by recent Tevatron results [52]. In the high diphoton transverse momen-\ntum, pT\u03b3\u03b3, domain the precision of its prediction needs to be assessed. To account for the incompleteness\nof the \ufb01xed order calculation two approaches are used: both the renormalisation and factorisation scales\n(\u00b5R,F) are varied, from 0.5\u00d7m\u03b3\u03b3 to 2\u00d7m\u03b3\u03b3, \ufb01rst assuming \u00b5R = \u00b5F then independently.\nResBos does not provide the most accurate description of the fragmentation of partons into pho-\ntons. In particular, it implements the single-photon fragmentation only at LO. An improved estimation\nof this contribution is given by the DIPHOX program [33] which implements single and double-photon\nfragmentation at NLO. The predictions of the fragmentation and direct contributions of the two afore-\nmentioned calculations agree to within 6%.\nThe systematic uncertainty related to the parton distribution functions is studied in Ref. [53] and esti-\nmated to be of the order of 6%. Systematic uncertainties related to the irreducible background evaluation\nare summarised in Table 9 they amount to an overall relative uncertainty of 16%.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1225\n\nA similar study has been performed with JETPHOX in order to evaluate theoretical uncertainties of\nthe \u03b3 j process. The second column of Table 9 reports the results from this study.2\n5.2\nHiggs boson plus one jet analysis\nIn this Section and in Section 5.3 two event selections are presented that take into account the presence\nand properties of high pT hadronic jets in association with the photon pair. This analysis follows earlier\nstudies in ATLAS using a fast detector simulation [8].\nParton level studies have indicated that searches for the Higgs boson in association with at least one\nhigh pT jet may have a strong discovery potential [5]. This analysis exploits mainly the fact that the\ngluon radiation pattern of the two leading Higgs boson production mechanisms differs strongly from the\none expected for the reducible and irreducible backgrounds. The leading jet in the gg \u2192H j and VBF\nmechanisms tends to be harder and be more separated from the diphoton system than in background\nevents. The invariant mass of the two photons and the jet system discriminates well the signal from the\nbackground.\nThe following event selection is chosen after the application of cut Ia:\nIIa Transverse momentum cuts of 45 and 25 GeV on the leading and sub-leading photon candidates,\nrespectively.\nIIb Presence of at least one hadronic jet with pT > 20 GeV in |\u03b7| < 5.\nIIc A cut on the invariant mass of the diphoton and the leading jet, m\u03b3\u03b3 j > 350 GeV.\nThe lower bound on the jet pT is dictated by the ability to calibrate hadronic jets in ATLAS [54].\nThe large hadronic activity due to the underlying events and multiple proton-proton interactions at the\nLHC, in conjunction to the signi\ufb01cant amount of inactive material before the calorimeter, may make it\ndif\ufb01cult to lower the pT threshold. The variable m\u03b3\u03b3 j is the main discriminator used here to improve the\nsignal-to-background ratio. Other discriminating variables could be used to further enhance the analysis\nsensitivity [5].\nFigure 7 displays the resulting diphoton invariant mass spectrum after the application of cuts Ia and\nIIa-IIc.\nTable 10: Expected cross-sections (in fb) for the Higgs boson plus one jet Analysis. Results are\ngiven after the application of cuts Ia and IIa-IIc (see Section 5.2). In the last row the expected\ncross-sections within a mass window of m\u03b3\u03b3 of \u00b12 GeV around 120 GeV are given.\nCut\ngg \u2192H\nVBFH\nVH\nttH\nTotal\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nIa-IIa\n28\n3.6\n1.7\n0.49\n34\nIIb\n13\n3.5\n1.5\n0.49\n19\nIIc\n3.2\n1.9\n0.22\n0.17\n5.5\nMass Window\n2.3\n1.4\n0.17\n0.13\n4.0\nTables 10 and 11 display the expected cross-sections for signal and background events in the range\n110 < m\u03b3\u03b3 < 150 GeV after the application of cuts Ia and IIa-IIc. Table 10 illustrates that the leading\n2It is important to note that the uncertainty of the contribution of the reducible background is dominated by the uncertainty\nin the determination of the fake photon rejection. This uncertainty may be signi\ufb01cantly larger than the uncertainties quoted in\nTable 9.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1226\n\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\nSignal\nIrreducible bkg\nReducible bkg\nATLAS\nFigure 7: Diphoton invariant mass spectrum in fb obtained with the Higgs boson plus one jet analysis\n(see Section 5.2). The same procedure as in Fig. 6 in Section 5.1 is used to obtain the histograms in\nFig. 7. The same codes for signal and backgrounds are used as in Fig. 6.\nTable 11: Expected cross-sections (in fb) of background for the Higgs boson plus one jet Analysis.\nResults are given after the application of cuts Ia and IIa-IIc (see Section 5.2). In the last row the\nexpected cross-sections within a mass window of m\u03b3\u03b3 of \u00b12 GeV around 120 GeV are given.\nCut\n\u03b3\u03b3\nReducible \u03b3 j\nReducible j j\nEW \u03b3\u03b3 j j\nTotal\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nIa-IIa\n9698\n8498\n937\n99\n19233\nIIb\n4786\n4438\n444\n99\n9768\nIIc\n501\n824\n89\n71\n1485\nMass Window\n28\n17\n2.0\n1.5\n49\nHiggs boson production mechanism after the application of cuts remains the gg \u2192H j process, closely\nfollowed by the VBF mechanism. It is important to note that the gg \u2192H j process has been evaluated at\nLO ignoring the large QCD NLO corrections.\n5.3\nHiggs boson plus two jets analysis\nThis Section considers an event selection comprising two photons in association with two high pT jets,\nor tagging jets. In this analysis the tagging jets are de\ufb01ned as the two leading jets in the event. The VBF\nHiggs boson process at LO produces two high pT and relatively forward jets in opposite hemispheres\n(backward-forward). The pseudorapidity gap and invariant mass of these jets tend to be signi\ufb01cantly\nlarger than those expected for background processes. The NLO description of the VBF process does not\nsigni\ufb01cantly distort this picture.3\n3About 10% of the VBF events display the feature that a radiated gluon coming from one of the quark lines happens to\nbecome a tagging jet. In this class of events the pseudorapidity gap and the invariant mass of the tagging jets appears similar to\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1227\n\nA number of variables are chosen that are sensitive to the different kinematics displayed by the signal\nand background processes [9]. The following is the optimized event selection after the application of cut\nIa:\nIIIa Transverse momentum cuts of 50 and 25 GeV on the leading and sub-leading photon candidates,\nrespectively.\nIIIb Presence of at least two hadronic jets in |\u03b7| < 5 with pT > 40,20 GeV for the leading and sub-\nleading jet, respectively. The tagging jets must be in opposite hemispheres, \u03b7j1\u00b7\u03b7 j2 < 0, where \u03b7j1\nand \u03b7j2 correspond to the pseudorapidity of the leading and sub-leading jets, respectively. Finally,\nit is required that the pseudorapidity gap between the tagging jets be large, \u2206\u03b7 j j > 3.6.\nIIIc Photons are required to have pseudorapidity between those of the tagging jets.\nIIId Invariant mass of the tagging jets, m j j > 500 GeV.\nIIIe Veto on events with a third jet with pT > 20 GeV and |\u03b7| < 3.2\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n [GeV]\n\u03b3\n\u03b3\n M\n110\n115\n120\n125\n130\n135\n140\n145\n150\n [fb/GeV]\n\u03b3\n\u03b3\n/dM\n\u03c3\nd\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nSignal\nIrreducible bkg\nReducible bkg\nATLAS\nFigure 8: Diphoton invariant mass spectrum obtained with the Higgs boson plus two jet analysis (see\nSection 5.3).\nFigure 8 displays the resulting diphoton invariant mass spectrum after the application of cuts Ia and\nIIIa-IIIe.\nTables 12 and 13 display the expected cross-sections for a Higgs boson signal with mH = 120 GeV\nand background events in the mass range \u00b12 GeV around 120 GeV after the application of cuts Ia and\nIIIa-IIIe. Table 12 shows that the dominant Higgs boson production mechanism surviving the events\nselection is the VBF mechanism. Unfortunately, the QCD NLO corrections to the main backgrounds\nincluded in Table 13 are not known and therefore these results suffer from large theoretical uncertainties.\nThe event selections presented in this and the previous Sections have a certain degree of overlap.\nThis is particularly relevant for the VBF Higgs boson production mechanism. In Section 7 the signal\nsigni\ufb01cance of a combined analysis is presented that takes into account the event overlap.\nthat displayed by a typical QCD background process. This effect is well reproduced by the HERWIG generator.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1228\n\nTable 12: Expected cross-sections (in fb) for the Higgs boson plus two jet analysis. Results are\ngiven after the application of cuts Ia and IIIa-IIIe (see Section 5.3). In the last row the expected\ncross-sections within a mass window of m\u03b3\u03b3 of \u00b12 GeV around 120 GeV are given.\nCut\ngg \u2192H\nVBFH\nVH\nttH\nTotal\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nIa-IIIa\n26.40\n3.53\n1.68\n0.50\n32.11\nIIIb\n0.63\n1.44\n0.02\n0.01\n2.10\nIIIc\n0.55\n1.39\n0.01\n0.01\n1.96\nIIId\n0.32\n1.16\n0.01\n0.00\n1.49\nIIIe\n0.25\n1.03\n0.00\n0.00\n1.28\nMass Window\n0.18\n0.79\n0.00\n0.00\n0.97\nTable 13: Expected cross-sections (in fb) of background for the Higgs boson plus two jet analysis\nfor mH = 120 GeV. Results are given after the application of cuts Ia and IIIa-IIIe (see Sec-\ntion 5.3). In the last row the expected cross-sections within a mass window of m\u03b3\u03b3 of \u00b12 GeV\naround 120 GeV are given.\nCut\n\u03b3\u03b3\nReducible \u03b3 j\nReducible j j\nEW \u03b3\u03b3 j j\nTotal\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nIa-IIIa\n7417\n6355\n710\n92\n14574\nIIIb\n94\n97\n13\n45\n249\nIIIc\n70\n69\n9.9\n41\n189\nIIId\n33\n34\n5.6\n38\n111\nIIIe\n17\n17\n2.5\n26\n63\nMass Window\n0.86\n0.42\n0.06\n0.59\n1.95\n5.4\nHiggs boson plus missing transverse energy and isolated leptons\nThe main signal production mechanism contributing to a category of events with two photons, missing\ntransverse energy and isolated leptons will be from WH \u2192\u2113\u03bd\u03b3\u03b3 and ttH. The basic selection requires the\npresence of two energetic photons, missing transverse momentum, and one high energetic lepton. The\nmain backgrounds for this channel are t\u00aft\u03b3\u03b3, W\u03b3\u03b3 where the W decays to \u2113\u03bd and W\u03b3 \u2192e\u03bd\u03b3 where the\nother photon is radiated by the electron or is a fake photon from an additional jet.4 This latter background\nis multiplied by a factor 2 to include the W\u03b3 \u2192\u00b5\u03bd\u03b3 contribution. Another important background turns\nout to be \u03b3\u03b3 and \u03b3 j, when fake electrons or muons are reconstructed. ALPGEN was used to produce\nthe diphoton background including a full simulation of the detector. The cross section was multiplied by\na factor 1.4 to account approximately for the box diagram (40% of the contribution, see Table 1). For\nreducible backgrounds (68% contribution, see Table 8), the cross-section of the diphoton background is\nscaled by a factor 1.68. It is dif\ufb01cult to evaluate the accuracy of this approximation but this diphoton\nprocess is not the leading background. A multivariate analysis based on various kinematical variables\nwould require very large Monte Carlo samples for the backgrounds. Here, a simple set of basic event\nselection criteria is chosen:\nIVa The \ufb01rst selection criterion sets minima on the transverse momenta of the two reconstructed pho-\n4Note that there is some double counting when both W\u03b3 and W\u03b3\u03b3 are included.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1229\n\ntons. The cut requires the pT of the most energetic photon to be higher than 60 GeV and the pT\nof the second more energetic photon to be above 30 GeV. Events where one of the two photons\nis reconstructed in the crack region are rejected. The cross-sections in the \ufb01rst line of the table 14\nare given in the mass range between 110 and 150 GeV.\nIVb Requiring a cut that the transverse momentum of the most energetic isolated lepton (electron or\nmuon) be higher than 30 GeV suppresses ef\ufb01ciently the diphoton and W\u03b3 backgrounds. Only the\nelectrons passing a tight electron identi\ufb01cation cut are selected.\nIVc The diphoton background can further be strongly suppressed by requiring missing transverse en-\nergy higher than 30 GeV.\nIVd When an electron is reconstructed, events are removed in with either of the invariant masses of\nthe electron and each of the photons is close to the Z mass (between 80 and 100 GeV): this cut\nremoves the events coming from the (Z/\u03b3\u2217) + \u03b3 \u2192e+e\u2212\u03b3 when an electron is reconstructed as a\nphoton.\nTable 14: Expected cross-sections (in fb) for the Higgs boson with missing transverse energy and\nlepton analysis for mH = 120 GeV. Results are given after the application of cuts IVa-IVc (see\nSection 5.4) in the mass range 110 < m\u03b3\u03b3 < 150 GeV. In the last row the expected cross-sections\nwithin a mass window of m\u03b3\u03b3 of \u00b12 GeV around 120 GeV are given.\nCut\nW \u00b1H \u2192\n\u2113\u03bd\u03b3\u03b3\nt\u00aftH \u2192\nx\u03b3\u03b3\nW \u00b1\u03b3\u03b3 \u2192\n\u2113\u03bd\u03b3\u03b3\nt\u00aft\u03b3\u03b3\nb\u00afb\u03b3\u03b3\nW \u00b1\u03b3 \u2192\ne\u03bd\u03b3\n(Z/\u03b3\u2217)+\u03b3 \u2192\ne+e\u2212\u03b3\n\u03b3\u03b3\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nIVa\n0.328\n0.467\n0.509\n2.53\n3.78\n18.0\n10.28\n2558\nIVb\n0.122\n0.103\n0.149\n0.582\n0.0098\n0.406\n2.60\n0.644\nIVc\n0.091\n0.086\n0.097\n0.474\n0\n0.263\n0.076\n0.091\nIVd\n0.084\n0.077\n0.090\n0.419\n0\n0.143\n0\n0.091\nMass Win.\n0.064\n0.062\n0.0092\n0.042\n0\n0.014\n0\n0.010\nTable 14 summarizes the expected cross-sections for the principal signal and backgrounds after the vari-\nous cuts used in the analysis. The uncertainty in the background level, due to Monte Carlo statistics only,\nis estimated to be 10%. However, the background contribution in this analysis can have larger sources of\nsystematic uncertainties. The resulting Higgs boson mass peak and background are shown in Fig. 9 after\nall cuts have been applied. The reconstructed mass resolution is 1.47 GeV.\n5.5\nHiggs boson plus missing transverse energy\nThis analysis is intended to select principally the ZH \u2192\u03bd\u03bd\u03b3\u03b3 events. In order to have an analysis\nindependent from that of Section 5.4, only events which do not have a reconstructed lepton with pT >\n30 GeV have been considered here. It should be noted that cases where the lepton is of low pT or did not\npass the tight selection criterion are included. Thus the WH signal contributes signi\ufb01cantly. The main\nfeatures are the presence of two energetic photons from the Higgs boson and a large transverse missing\nenergy. The dominant backgrounds for this channel are the t\u00aft\u03b3\u03b3, Z\u03b3\u03b3 and W\u03b3 \u2192e\u03bd\u03b3 channels where, in\nthe latter case, the electron can be mis-reconstructed as a photon or the second photon is either radiated\nby the electron or is a fake photon. Here, the diphoton background is multiplied by the same factors as\nin Section 5.4 and the t\u00aft\u03b3\u03b3 by the factor 7.5 as explained in Section 2.2.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1230\n\n110\n115\n120\n125\n130\n135\n140\n145\n150\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n110\n115\n120\n125\n130\n135\n140\n145\n150\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nSignal\nIrreducible bkg\nReducible bkg\n [GeV]\n\u03b3\n\u03b3\nM\n [fb/GeV]\n\u03b3\n\u03b3\n/ dM\n\u03c3\nd \nATLAS\nFigure 9: Expected distribution of the invariant mass of the two photons for the signals and main back-\ngrounds after applying the analysis cuts for events having one lepton reconstructed in the \ufb01nal state.\nDue to a lack of MC statistics for the diphoton and the W\u03b3 backgrounds, their expected distribution is\napproximated by showing an average of the number of events passing the analysis cuts in the m\u03b3\u03b3 mass\nrange shown.\nVa As in Section 5.4, a cut on the transverse momentum of the most energetic photon above 60 GeV\nand a cut on the second more energetic photon pT of 30 GeV are applied to suppress the diphoton\nbackground. Events where one of the two photons is reconstructed in the crack region are then\nremoved.\nVb The selection is then based mostly on the requirement of high missing transverse momentum. A\ncut of Emiss\nT\n> 80 GeV suppresses almost completely the \u03b3\u03b3 background while reducing the W\u03b3\nbackground by a factor 20 and the ZH \u2192\u03bd\u03bd\u03b3\u03b3 signal by a factor 2.\nVc In order to further suppress the W\u03b3 background, where the electron is often reconstructed as a\nconverted photon, events where either of the photons appears to have converted are rejected.\nVd At this point, because of potentially signi\ufb01cant background from QCD events, dif\ufb01cult to evaluate,\na cut requiring that the scalar sum of the pT of the jets in the event be larger than 150 GeV is\nimposed. It suppresses the contribution from the t\u00aft\u03b3\u03b3 and b\u00afb\u03b3\u03b3 backgrounds, as well as of the t\u00aftH\nsignal.\nTable 15 summarizes the expected cross-sections after the different cuts applied for this analysis for\nsignal and backgrounds. The expected mass distributions of diphotons from the associated W/Z plus\nHiggs boson and from the backgrounds are shown in Fig. 10, after the application of all cuts. To account\nfor the W\u03b3 \u2192\u00b5\u03bd\u03b3, the W\u03b3 \u2192e\u03bd\u03b3 background has been multiplied by two in the \ufb01gure although some\ndouble counting is introduced. The uncertainty in the background level, due to Monte Carlo statistics\nonly, is estimated to be 15%. The reconstructed mass resolution is 1.31 GeV. This result is expected to\nbe sensitive to uncertainties in the simulation and reconstruction of Emiss\nT\ntails.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1231\n\nTable 15: Expected cross-sections (in fb) for the Higgs boson with missing transverse energy\nanalysis. Results are given after the application of cuts Va-Vd (see Section 5.5) in the mass range\n110 < m\u03b3\u03b3 < 150 GeV. In the last row the expected cross-sections within a mass window of m\u03b3\u03b3\nof \u00b11.8 GeV around 120 GeV are given.\nCut\nZH \u2192\n\u03bd\u03bd\u03b3\u03b3\nWH \u2192\n\u2113\u03bd\u03b3\u03b3\nt\u00aftH \u2192\nx\u03b3\u03b3\nZ\u03b3\u03b3 \u2192\n\u03bd\u03bd\u03b3\u03b3\nW \u00b1\u03b3\u03b3 \u2192\n\u2113\u03bd\u03b3\u03b3\nt\u00aft\u03b3\u03b3\nb\u00afb\u03b3\u03b3\nW \u00b1\u03b3 \u2192\ne\u03bd\u03b3\n\u03b3\u03b3\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\n\u03c3 (fb)\nVa\n0.115\n0.207\n0.364\n0.325\n0.360\n1.95\n3.77\n17.55\n2558\nVb\n0.058\n0.062\n0.080\n0.126\n0.071\n0.461\n0.010\n0.789\n0.211\nVc\n0.046\n0.049\n0.064\n0.096\n0.056\n0.377\n0.010\n0.191\n0.141\nVd\n0.042\n0.042\n0.006\n0.093\n0.050\n0.021\n0.005\n0.120\n0.073\nMass Win.\n0.034\n0.033\n0.0056\n0.009\n0.006\n0.002\n0.0005\n0.012\n0.007\n110\n115\n120\n125\n130\n135\n140\n145\n150\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n110\n115\n120\n125\n130\n135\n140\n145\n150\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nSignal\nIrreducible bkg\nReducible bkg\n [GeV]\n\u03b3\n\u03b3\nM\n [fb/GeV]\n\u03b3\n\u03b3\n/ dM\n\u03c3\nd \nATLAS\nFigure 10: Expected distribution of the invariant mass of the two photons for the signals and main\nbackgrounds after applying all the diphoton and Emiss\nT\nanalysis cuts. Due to a lack of statistics for the\ndiphoton and the W\u03b3 backgrounds, their expected distribution is approximated by showing an average of\nthe number of events passing the analysis cuts in the m\u03b3\u03b3 mass range shown.\n6\nMaximum-likelihood \ufb01t\nAn unbinned extended multivariate maximum-likelihood \ufb01t to extract the H \u2192\u03b3\u03b3 signal and background\nevent yields is performed. With respect to the cut analysis presented in Section 5, the \ufb01t takes advantage\nof further discrimination information from the kinematic and topological properties of H \u2192\u03b3\u03b3 decays.\nIn addition to the diphoton invariant mass, m\u03b3\u03b3, the transverse momentum of the Higgs boson, PT,H,\nand the magnitude of the photon decay angle in the Higgs boson rest frame with respect to the Higgs\nboson lab \ufb02ight direction, |cos\u03b8 \u22c6|, are included. To reduce the model dependence, the most relevant\nparameters describing the probability density functions (PDF) for the dominant background are freely\nvaried and determined simultaneously with the event yields by the \ufb01t. Only the parametric shapes of the\nPDFs are obtained from Monte Carlo simulation. Suf\ufb01cient background statistics in the sidebands must\nbe retained to ensure that the \ufb02oating shape parameters do not increase the statistical errors on the signal\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1232\n\nyield. The m\u03b3\u03b3 resolution depends on the diphotons\u2019 pseudorapidities, with core Gaussian widths varying\nbetween 1.2 and 3 GeV. Disjoint pseudorapidity regions (denoted categories), are de\ufb01ned such that the\nm\u03b3\u03b3 resolution is similar for events belonging to the same category, and maximally different for events\nof different categories. The m\u03b3\u03b3 resolution also depends on whether or not photons have converted at an\nearly stage in the material in front of the calorimeter (see Section 3.3). H \u2192\u03b3\u03b3 events can have zero,\none or two reconstructed conversions, which are split into corresponding categories. Following Section 5\ndisjoint categories are also introduced for events accompanied by zero, one and two or more jets, where\nthe last category contains predominantly VBF events. The use of categories separates sub-populations\nof events with different properties and hence improves the accuracy of the likelihood model.\nThe signal and background samples used to build the likelihood model are selected with the criteria\ndescribed in Section 5. The full detector simulation is used for signal processes, while the background\nprocesses are generated with the fast simulation. The trigger and photon identi\ufb01cation ef\ufb01ciencies, and\nthe misidenti\ufb01cation in background events are parametrised using the full detector simulation. The prob-\nability of a photon to convert into an e+e\u2212pair with one or two tracks being reconstructed, and the energy\nresolution of the converted photon are parametrised using the full detector simulation.\n6.1\nLikelihood model\nThe probability density function, Pc\ni , for an event i in category c is the weighted sum of the probability\ndensities of all components, namely Pc\ni = NH f c\nHPc\nH,i +\u2211\nnbkg\nj=1 Nc\nBjPc\nB j,i, where NH is the number of H \u2192\u03b3\u03b3\nsignal events determined by the \ufb01t,5 f c\nH is the fraction of signal events in category c (c = 1,...,ncat,\nnote that \u2211c f c\nH = 1) taken from simulation, and Nc\nBj is the number of background events of type j\n(j = 1,...,nbkg) found in category c, which is determined from the \ufb01t. The signal and background PDFs\nPc\nU,i, with U = H,B j, are the products Pc\nU,i = \u220fnvar\nk=1 pc\nU(xk,i) of the PDFs pc\nU(xk,i) of the discriminating\nvariables xk,i, k = 1,...,nvar, used in the \ufb01t. The extended likelihood over all categories and events is\ngiven by L = \u220fncat\nc=1 e\u2212Nc\n\u220fNc\ni=1 Pc\ni , where Nc (Nc) is the total number of events expected (observed) in\ncategory c with c = 1,...,ncat. The PDFs Pc\nU,i depend on parameters (coef\ufb01cients) that may be freely\nvarying in the \ufb01t. The parametrisations and hence the adjustable parameters differ between categories in\ngeneral, but can also span over several categories.\n6.2\nFit variables\nThe H \u2192\u03b3\u03b3 distribution of m\u03b3\u03b3 forms a Gaussian peak with tails to lower values from photon energy\nlosses before the calorimeter. It is well modeled by a Crystal Ball (CB) function [55]\npH(m\u03b3\u03b3) = N \u00b7\n(\nexp\n\u0000\u2212t2/2\n\u0001\n,\nfor t > \u2212\u03b1 ,\n(n/|\u03b1|)n \u00b7exp\n\u0000\u2212|\u03b1|2/2\n\u0001\n\u00b7(n/|\u03b1|\u2212|\u03b1|\u2212t)\u2212n ,\notherwise,\n(4)\nwhere t = (m\u03b3\u03b3 \u2212mH \u2212\u03b4mH)/\u03c3(m\u03b3\u03b3), N is a normalisation parameter, mH is the Higgs boson mass, \u03b4mH\nis a category dependent offset, \u03c3 represents the diphoton invariant mass resolution, and where n and \u03b1\nparametrise the non-Gaussian tail. To catch outliers an additional broad tail Gaussian is added to Equa-\ntion 4, which is, however, only relevant for events falling into the \u201cbad\u201d m\u03b3\u03b3 category (see Section 6.3).\nWithin a suf\ufb01ciently narrow mass window, the background distribution of m\u03b3\u03b3 forms an exponential tail\ndescribed by a single slope parameter \u03be.\nBecause of the large available statistics for simulated signal samples, shape uncertainties due to de\ufb01-\nciencies in the functional description are negligible. Systematic effects are due to simulation inaccuracies\nand are discussed in Section 7. A high-\ufb01delity description of the background PDFs is mandatory because\n5Throughout this section the subscript S is iden\ufb01tied with the H \u2192\u03b3\u03b3 signal.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1233\n\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n] \n0.025\n / \nfb\n \n*| [\n\u03b8\nd|cos\n / \u03c3\nd\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n] \n0.025\n / \nfb\n \n*| [\n\u03b8\nd|cos\n / \u03c3\nd\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n, 0 jets category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\n, 1 jet category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\n, 2 jets category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\nATLAS\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n] \n0.01\n / \npb\n \n*| [\n\u03b8\nd|cos\n / \u03c3\nd\n0\n2\n4\n6\n8\n10\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n] \n0.01\n / \npb\n \n*| [\n\u03b8\nd|cos\n / \u03c3\nd\n0\n2\n4\n6\n8\n10\n*|\n\u03b8\n|cos\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n2\n4\n6\n8\n10\nBackground, 0 jets category (dots: MC, line: PDF)\nBackground, 1 jet category (dots: MC, line: PDF)\nATLAS\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120\n140\n GeV]\n \n1.5\n / \nfb\n \n [\nT,H\ndp\n / \n\u03c3\nd\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120\n140\n GeV]\n \n1.5\n / \nfb\n \n [\nT,H\ndp\n / \n\u03c3\nd\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120\n140\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120\n140\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n, 0 jets category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\n, 1 jet category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\n, 2 jets category (dots: MC, line: PDF)\n\u03b3\n\u03b3\n\u2192\nH\nATLAS\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120 140\n160 180\n200\n GeV]\n 2\n / \nfb\n \n [\nT,H\ndp\n / \u03c3\nd\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120 140\n160 180\n200\n GeV]\n 2\n / \nfb\n \n [\nT,H\ndp\n / \u03c3\nd\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n [GeV]\nT,H\np\n0\n20\n40\n60\n80\n100\n120 140\n160 180\n200\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nBackground, 0 jets category (dots: MC, line: PDF)\nBackground, 1 jet category (dots: MC, line: PDF)\nATLAS\nFigure 11: Signal (left) and background (right) distributions of the Higgs boson decay angle, |cos\u03b8 \u22c6|\n(top), and the diphoton transverse momentum (bottom) for events with zero jets (full dots), one jet (open\ncircles) and VBF topology (full triangles, not shown for background because of a too low relative cross-\nsection). The corresponding PDF parametrisations are overlaid (see text).\nthe large majority of the events entering the \ufb01t are of that type. It is achieved by \ufb02exible parametrisations\nwith a suf\ufb01cient number of parameters determined by the \ufb01t, ensuring a stable \ufb01t result with respect to\nshape rede\ufb01nitions.\nThe distribution of |cos\u03b8 \u22c6| for a scalar Higgs boson is uniform. However, acceptance effects, pri-\nmarily from the minimum pT requirements for the photons (See Section 5.1), suppress |cos\u03b8 \u22c6| values\ntowards one, where the photons are collinear with the Higgs boson lab frame momentum. The empirical\nsignal PDF is interpolated by a double Gaussian function. The phase space for background events from\nt-channel graphs and quark or gluon fragmentation at NLO is enhanced for photons collinear with the\ndiphoton lab momentum, so that the background |cos\u03b8 \u22c6| distribution exhibits some clustering towards\nlarge values. Acceptance suppression competes, however, with this enhancement thus reducing the dis-\ncrimination power of the variable. It is found that the |cos\u03b8 \u22c6| distributions differ signi\ufb01cantly between\nthe \u03b3\u03b3, \u03b3 j and j j backgrounds, with stronger enhancements at large |cos\u03b8 \u22c6| values for the backgrounds\noriginating from jet misidenti\ufb01cation. The inclusive shape of these backgrounds is parametrised by the\nsum of a positively de\ufb01ned third order polynomial and two Gaussian functions. The inclusive signal and\nbackground distributions of |cos\u03b8 \u22c6| for events with and without jets are shown in Fig. 11.\nThe Higgs boson transverse momentum exhibits a strong rise at low values and a long exponential\ntail beyond the maximum. The distribution is \ufb01tted by a sum of two bifurcated Gaussian functions\n(distributions where below and above the center half Gaussian distributions with different widths are\nused) and one symmetric Gaussian. The diphoton transverse momentum distribution for background is\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1234\n\n|1\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n|\n2\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n1.47 GeV\n(1) [22.6%]\n1.47 GeV\n(1) [22.6%]\n1.82 GeV\n(2) [22.6%]\n1.82 GeV\n(2) [22.6%]\n2.06 GeV\n(3) [12.4%]\n2.06 GeV\n(3) [12.4%]\n1.92 GeV\n(4) [10.4%]\n1.92 GeV\n(4) [10.4%]\n3.27 GeV\n(5) [10.8%]\n3 27 GeV\n(5) [10.8%]\n1.79 GeV\n(6) [15.1%]\n1.79 GeV\n(6) [15.1%]\n3.18 GeV\n(7) [3.4%]\n3.18 GeV\n(7) [3.4%]\n1.38 GeV\n(8) [2 8%]\n1.38 GeV\n(8) [2 8%]\n|1\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n|\n2\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n|1\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n|\n2\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n1.79 GeV\n(1) [13.2%]\n1.79 GeV\n(1) [13.2%]\n2.21 GeV\n(2) [14.1%]\n2.21 GeV\n(2) [14.1%]\n2.27 GeV\n(3) [10.2%]\n2.27 GeV\n(3) [10.2%]\n2.19 GeV\n(4) [8.7%]\n2.19 GeV\n(4) [8.7%]\n3.37 GeV\n(5) [14.6%]\n3 37 GeV\n(5) [14.6%]\n2.17 GeV\n(6) [24.3%]\n2.17 GeV\n(6) [24.3%]\n3.46 GeV\n(7) [8.0%]\n3.46 GeV\n(7) [8 0%]\n2.00 GeV\n(8) [7 0%]\n2.00 GeV\n(8) [7 0%]\n|1\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\n|\n2\n\u03b7\n |\n0\n0.5\n1\n1.5\n2\n2.5\nFigure 12: Regions of photon pseudorapidities with different invariant mass resolutions for unconverted\nphotons (left) and at least one converted photon (right). The text per box denotes the region number, the\npercentage of events occurring in the region and the RMS of the diphoton invariant mass for H \u2192\u03b3\u03b3\nevents. To simplify the likelihood model, events with photons in regions (1) and (8) are merged and\nrepresent category \u201cgood\u201d (signal fraction 24%), events in regions (2), (3), (4) and (6) correspond to\ncategory \u201cmedium\u201d (60%), and regions (5) and (7) are \u201cbad\u201d (15%).\nsofter than that for signal and can be described by the sum of three exponential polynomials (see Fig. 11).\n6.3\nFit categories\nEight photon pseudorapidity regions with different diphoton invariant mass resolution for H \u2192\u03b3\u03b3 events\nare identi\ufb01ed. They are illustrated in Fig. 12 for unconverted photon pairs (left plot) and events with\nat least one photon conversion (right plot). The regions are chosen to be symmetric with respect to an\ninterchange of the photons. The crack region is excluded from the photon selection. The m\u03b3\u03b3 RMS\nvalues vary between 1.3 GeV in the centre and large-\u03b7 regions to 3.1 GeV in the regions closely beyond\nthe crack. To simplify the likelihood model, the eight regions are merged into three categories that are\ndistinguished in the \ufb01t (see Fig. 12).\nTwo categories are introduced to separate events without and with at least one photon conversion\nto take account of the worse resolution of the latter events. Photon conversions reconstructed with one\nor two tracks are not explicitly distinguished. Additional categories are introduced for Higgs boson\nproduction with zero, one, and two or more accompanying jets, using the requirements described in\nSections 5.2 and 5.3. No separate categories are introduced in the present analysis to distinguish Higgs\nboson production in association with a W and Z boson or a t\u00aft quark pair; these are included in the\nprevious selections. Separating them would add some power, but would increase the complexity.\n6.4\nCorrelations\nThe likelihood product used to derive the event PDF Pc\nU ignores correlations between the discriminating\nvariables xk. The classi\ufb01cation in categories of events with distinct properties improves the accuracy\nof this assumption. The remaining (positive) linear correlation coef\ufb01cients is lower than 7% (10%) for\nsignal (background) events among the three \ufb01t variables tolerable.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1235\n\nTable 16: H \u2192\u03b3\u03b3 discovery potential for a Higgs boson mass of 120 GeV, various likelihood\nsetups and a simulated integrated luminosity of 10fb\u22121. The left column gives the discriminating\nvariables used in the \ufb01t, the second column the categories, the third (\ufb01fth) column the average\n\u2206lnL and its statistical uncertainty as derived from the toy MC samples, and the fourth (sixth)\ncolumn quotes the estimated Gaussian signal signi\ufb01cance in units of one standard deviation. Due\nto the background dominance, the variance of the signi\ufb01cance in the toy experiments is approxi-\nmately one. The \ufb01ts have been performed with \ufb01xed Higgs boson mass (Higgs boson mass \ufb02oating\nwithin [112,128] GeV). The signi\ufb01cance for \ufb02oating Higgs boson mass has been obtained with\ntoy MC simulation (the \u2206lnL cannot be directly interpreted in terms of signi\ufb01cance and is given\nfor completeness only). Due to the large number of required toy MC \ufb01ts it has not been computed\nfor the most involved \ufb01t with highest expected signi\ufb01cance.\nHiggs boson mass \ufb01xed\nHiggs boson mass \ufb02oating\nFit variables\nCategories\n\u27e8\u2206lnL \u27e9\nSigni\ufb01cance [\u03c3]\n\u27e8\u2206lnL \u27e9\nSigni\ufb01cance [\u03c3]\nm\u03b3\u03b3\n\u2013\n2.67\u00b10.04\n2.31\u00b10.02\n3.54\u00b10.05\n1.44\u00b10.02\nm\u03b3\u03b3\n\u03b7\n3.18\u00b10.05\n2.52\u00b10.02\n\u2212\n\u2212\nm\u03b3\u03b3\n\u03b7, Conversions\n3.32\u00b10.05\n2.58\u00b10.02\n\u2212\n\u2212\nm\u03b3\u03b3\n\u03b7, Conversions, Jets\n5.99\u00b10.07\n3.46\u00b10.02\n6.66\u00b10.07\n2.64\u00b10.02\nm\u03b3\u03b3, |cos\u03b8 \u22c6|\n\u03b7, Conversions, Jets\n7.33\u00b10.08\n3.83\u00b10.02\n\u2212\n\u2212\nm\u03b3\u03b3, PT,H\n\u03b7, Conversions, Jets\n7.03\u00b10.08\n3.75\u00b10.02\n\u2212\n\u2212\nm\u03b3\u03b3, PT,H, |cos\u03b8 \u22c6|\n\u03b7, Conversions, Jets\n8.49\u00b10.08\n4.12\u00b10.02\n9.25\u00b10.09\n\u2212\n6.5\nFit performance\nStudies are performed involving large samples of toy MC simulation to assess the discovery potential for\n\ufb01ts using likelihood models of increasing complexity.6 The abundance of signal and background events\nused in these \ufb01ts is tuned to the NLO expectation for 10fb\u22121 of integrated luminosity, taking into account\nthe trigger and reconstruction acceptance.\nThe results for \ufb01ts with \ufb01xed and \ufb02oating Higgs boson mass (the latter only done for the m\u03b3\u03b3-only\nand the full \ufb01ts) are summarised in Table 16. For each toy MC sample we perform two \ufb01ts, one with\n\ufb02oating signal yield and another with zero signal to test the background-only hypothesis. The log-\nlikelihood difference, \u2206lnL , found in these \ufb01ts, estimates the false discovery probability (p-value). The\n\u27e8\u2206lnL \u27e9values given in Table 16 are obtained from Gaussian \ufb01ts to well-behaved pull distributions.\nFor \ufb01xed Higgs boson mass, the signal signi\ufb01cance in terms of \u03c3 can be approximated by the quantity\n\u221a\n\u22122\u2206lnL . For \ufb02oating Higgs boson mass, the extra degree of freedom in the \ufb01t yields a higher value\nof \u27e8\u2206lnL \u27e9. However in this case the p-value and signi\ufb01cance must be evaluated with toy MC simulation\nof background-only samples. As expected, the obtained signi\ufb01cances are lower than in the \ufb01xed mass\ncase, in spite of the higher \u27e8\u2206lnL \u27e9values.\n7\nDiscovery potential\nThis Section reports on the potential for the discovery of a Higgs boson in the mass range 120 < mH <\n140 GeV using the event counting computation and the maximum likelihood \ufb01t formalism (see Sec-\n6Although required for real data the evaluation of goodness-of-\ufb01t estimators is not discussed here, because the generated\ntoy data is intrinsically consistent with the underlying model.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1236\n\ntion 6). The signal signi\ufb01cance is evaluated for each of the analyses presented in Section 5. The discov-\nery reach is given for a combined analysis including the utilization of additional discriminating variables.\nThe last signi\ufb01es the maximum discovery potential for a Standard Model Higgs boson in the mass range\nspeci\ufb01ed above.\nTable 17: Expected cross-sections (in fb) of signal (S) and background (B) for the different anal-\nyses presented in Section 5 within a mass window of \u00b11.4\u03c3\u03b3\u03b3 as a function of the Higgs boson\nmass (in GeV).\nInclusive\nH +1jet\nH +2jets\nH+Emiss\nT\n+\u2113\nH+Emiss\nT\nmH\nS\nB\nS\nB\nS\nB\nS\nB\nS\nB\n120\n25.4\n947\n4.0\n49\n0.97\n1.95\n0.134\n0.077\n0.075\n0.037\n130\n24.1\n755\n4.3\n47\n0.96\n1.72\n0.112\n0.076\n0.063\n0.037\n140\n19.3\n610\n3.9\n46\n0.81\n1.72\n0.079\n0.076\n0.045\n0.036\nTable 17 shows the signal and background effective cross-sections for the different analyses presented\nin Section 5 as a function of the Higgs boson mass.7 Table 18 displays the corresponding expected signal\nsigni\ufb01cances for 10fb\u22121 of integrated luminosity. The \ufb01rst sub-column under each analysis shows the\nsignal signi\ufb01cance based on event counting, \u03c3(S,B), where S and B correspond to the number of signal\nand background events in a mass window of \u00b11.4\u03c3\u03b3\u03b3 around mH, respectively, and where \u03c3\u03b3\u03b3 is the mass\nresolution (in the no pileup case reported in Table 5).8 The values of \u03c3(S,B) reported in Table 18 can be\ncompared with earlier studies performed by the ATLAS collaboration [2\u20134,8,9]. The inclusion of pileup\ndecreases the event counting signal signi\ufb01cance by at most 10%.\nThe signal signi\ufb01cances reported in the second and third sub-column under each analysis, \u03c3Fix\n1D and\n\u03c3Float\n1D\n, are obtained by means of a one dimensional \ufb01t using the diphoton invariant mass as a dis-\ncriminating variable by letting the Higgs boson mass \ufb01xed and \ufb02oated, respectively.9 Each analysis\nis treated independently from each other. In these \ufb01ts the Higgs boson mass is let free in the range\n110 < mH < 140 GeV (except for mH = 140 GeV for which the range was set to 120 < mH < 150 GeV)\nto take into account for the coverage of the analysis.10 The results in Table 18 do not take into account the\nevent overlap among the three analyses. The last column reports the event counting signal signi\ufb01cance\nof the three analyses combined, taking into account the event overlap.\nTable 18 illustrates that the inclusive search for a diphoton resonance is the most sensitive one for a\nsearch of a Standard Model Higgs boson. As reported in Section 2, the inclusive analysis is evaluated\nusing QCD corrections for both signal and background processes. This is not the case for the H + 1jet\nand other analyses. The discovery potential of H +1jet analysis could be further enhanced if QCD NLO\ncorrections were applied on both signal and reducible backgrounds [56,57].\nTable 19 shows two \ufb01t-based signal signi\ufb01cances compared to \u03c3Fix\n1D and \u03c3Float\n1D\nreported in Table 18.\nThe values of \u03c3Fix\nC13D and \u03c3Float\nC13D correspond to the signal signi\ufb01cance computed by means of a three di-\nmensional \ufb01t, including m\u03b3\u03b3,PT,H and |cos\u03b8 \u22c6| (see Section 6.2) by means of \ufb01xing and \ufb02oating the mass,\nrespectively. At this stage the event classi\ufb01cation according to |\u03b7| regions is used (see Section 6.3).11\n7The contribution from Drell-Yan is computed for the inclusive analysis only.\n8The event counting signi\ufb01cance for the inclusive and H + 1jet analyses are approximated by S/\n\u221a\nB. For the rest of the\nanalyses a Poisson-based computation is used due to the small expected number of background events for 10fb\u22121 of integrated\nluminosity.\n9For the sake of simplicity, the \ufb01t-based signal signi\ufb01cance does not include the Drell-Yan contribution.\n10The range of the \ufb01t to the background is set to 110 < mH < 150 GeV.\n11For the \ufb01nal results presented in this section, a simpli\ufb01ed \ufb01tting model as well as a more conservative classi\ufb01cation are\nused with respect to those considered for Table 16. In particular the diphoton category with two jets is not split into \u03b7 categories\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1237\n\nTable 18: Signal signi\ufb01cances (expressed in terms of Gaussian sigmas) for a Standard Model\nHiggs boson as a function of the mass (in GeV) using the different analyses reported in Sec-\ntions 5.1-5.3 for 10fb\u22121 of integrated luminosity. Results are reported in terms of the signal\nsigni\ufb01cance based on event counting, \u03c3(S,B), and a \ufb01t-based signal signi\ufb01cance, \u03c3Fix\n1D and \u03c3Float\n1D\n(see text).\nInclusive (with K-factors)\nH +1jet (no K-factors)\nH +2jet (no K-factors)\nCombined\nmH\n\u03c3(S,B)\n\u03c3Fix\n1D\n\u03c3Float\n1D\n\u03c3(S,B)\n\u03c3Fix\n1D\n\u03c3Float\n1D\n\u03c3(S,B)\n\u03c3Fix\n1D\n\u03c3Float\n1D\n\u03c3(S,B)\n120\n2.6\n2.4\n1.5\n1.8\n1.8\n1.3\n1.9\n2.0\n1.1\n3.3\n130\n2.8\n2.7\n1.8\n2.0\n2.1\n1.6\n2.1\n2.1\n1.2\n3.5\n140\n2.5\n2.2\n1.3\n1.8\n1.7\n1.2\n1.7\n2.0\n1.0\n3.0\nTable 19: Signal signi\ufb01cances (expressed in terms of Gaussian \u03c3s) for a Standard Model Higgs\nboson as a function of the mass for 10fb\u22121 of integrated luminosity. Different \ufb01t-based approaches\nare used. The signi\ufb01cances, \u03c3Fix\n1D , \u03c3Fix\nC13D and \u03c3Fix\nC23D correspond to a one dimensional \ufb01t, to a\nthree dimensional \ufb01t using the \ufb01rst type of event classi\ufb01cation and to a three dimensional \ufb01t (see\nSection 6.2) using all classi\ufb01cations considered in Section 6.3, respectively using a \ufb01x Higgs\nboson mass (see text). The signi\ufb01cances \u03c3Float\n1D\n, \u03c3Float\nC13D and \u03c3Float\nC23D , correspond to \ufb01t based results\nobtained with a \ufb02oating Higgs boson mass.\nmH[ GeV]\n\u03c3Fix\n1D\n\u03c3Float\n1D\n\u03c3Fix\nC13D\n\u03c3Float\nC13D\n\u03c3Fix\nC23D\n\u03c3Float\nC23D\n120\n2.4\n1.5\n3.1\n2.1\n3.6\n2.8\n130\n2.7\n1.8\n3.4\n2.4\n4.2\n3.4\n140\n2.2\n1.3\n3.2\n2.2\n4.0\n3.2\nThe values of \u03c3Fix\nC23D and \u03c3Float\nC23D correspond to the maximum achievable sensitivity of all the analyses\nreported in Section 5 combined. In addition to the procedure followed to obtain \u03c3Fix\nC13D and \u03c3Float\nC13D , a\nclassi\ufb01cation of events according to the presence of hadronic jets is used.\nFigure 13 displays a summary of the expected signal signi\ufb01cance for the inclusive and \ufb01nal combined\nanalysis for 10fb\u22121 of integrated luminosity as a function of the Higgs boson mass. The solid circles\ncorrespond to the sensitivity of the inclusive analysis reported in Section 5.1 using event counting with\nbackground and signal rates assumed. The solid triangles linked with solid and dashed lines correspond\nto the sensitivity of the inclusive analysis by means of one dimensional \ufb01ts, with a \ufb01xed and \ufb02oating\nHiggs boson mass, respectively. The solid squares linked with solid and dashed lines correspond to the\nvalues of \u03c3Fix\nC13D and \u03c3Float\nC13D given in Table 19, respectively.\nThe stability of the \ufb01ts are checked against changes in the composition of the background. The values\nof \u03c3Fix\n1D for the inclusive analysis are recomputed by increasing and decreasing the reducible background\nby a factor of two. The \ufb01ts are redone with the same functional forms as in the nominal analysis and the\nresults are consistent with the expectations obtained by using S/\n\u221a\nB.\nThe degradation of the Higgs boson discovery sensitivity due to systematic uncertainties is consid-\nered. Various sources of systematic errors are evaluated. The Higgs boson mass resolution has signi\ufb01cant\nimpact on the sensitivity. A large degradation of the Higgs boson mass resolution is chosen by the addi-\ntion of a 1% constant term in the photon energy resolution. The impact of Higgs boson mass resolution\nis evaluated for the inclusive analysis by means of one-dimensional \ufb01ts with a \ufb01xed Higgs boson mass.\nand the conversion categories are not used.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1238\n\nHiggs boson mass [GeV]\n120\n125\n130\n135\n140\nSignal Significance\n0\n1\n2\n3\n4\n5\n6\n7\n8\n fixed\nH\nCombined, fit based with M\n floated\nH\nCombined, fit based with M\n fixed\nH\nInclusive, fit based with M\n floated\nH\nInclusive, fit based with M\nInclusive, number counting\ncombined, number counting\n-1\nL = 10 fb\n\u222b\nATLAS\nFigure 13: Expected signal signi\ufb01cance for a Higgs boson using the H \u2192\u03b3\u03b3 decay for 10fb\u22121 of inte-\ngrated luminosity as a function of the mass. The solid circles correspond to the sensitivity of the inclusive\nanalysis reported in Section 5.1 using event counting. The open circles display the event counting signi\ufb01-\ncance when the Higgs boson plus jet analyses (see Sections 5.2 and 5.3) are included. The solid triangles\nlinked with solid and dashed lines correspond to the sensitivity of the inclusive analysis by means of\none dimensional \ufb01ts, with a \ufb01xed and \ufb02oating Higgs boson mass, respectively. The solid squares linked\nwith solid and dashed lines correspond to the maximum sensitivity that can be attained with a combined\nanalysis (see text and Table 19).\nIf the resolution is increased both in toy Monte Carlo experiments and in the \ufb01tting function a decrease\nof 8% in the signal sensitivity is observed. If, however, the resolution is only degraded in toy Monte\nCarlo experiments, so that the \ufb01tting model does not accommodate the Higgs boson mass resolution\ndegradation, then the effect is a 12% reduction in sensitivity.\nThe systematic uncertainty due to PT,H has been estimated by using PYTHIA signal events, reweighted\nto NLO using ResBos, and \ufb01tted with the nominal model based on MC@NLO event simulation. This\ninconsistency between generation and \ufb01t reduces the signi\ufb01cance of the full \ufb01t (including all categories\nand the variables m\u03b3\u03b3, PT,H, and |cos\u03b8 \u22c6|, see Table 16) by 5%.\nThe sensitivity of the associated production channels has been studied separately for the diphoton +\nEmiss\nT\n+ lepton and for the diphoton + Emiss\nT\nanalyses (see Sections 5.4-5.5). With 30 fb\u22121 these channels\nhave the potential to contribute to the overall discovery signal of a SM Higgs boson, but we choose\nnot to report the value of the signal signi\ufb01cance because the systematic uncertainties on the background\nnormalization are large given the present status of simulations.\n8\nConclusions\nThe feasibility of the search for a Standard Model Higgs boson in the H \u2192\u03b3\u03b3 decay with the ATLAS\ndetector at the LHC has been presented. The detector performance issues relevant to the search have\nbeen evaluated using a full detector simulation. Triggering effects and the impact of pile-up are also\nreported. A signal signi\ufb01cance based on event counting of 2.6 (4.6) can be obtained with 10 (30) fb\u22121 of\nintegrated luminosity for mH = 120 GeV in the case of inclusive analysis. Despite the slight degradation\nwith respect to previous studies, the feasibility of the search for a Standard Model Higgs boson in the\nH \u2192\u03b3\u03b3 decay is con\ufb01rmed. In addition to the inclusive analysis the search for diphotons in association\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1239\n\nwith jets is considered. The addition of these channels enhances the event counting signal signi\ufb01cance\nto 3.3 (5.7) with 10 (30) fb\u22121 of integrated luminosity for mH = 120 GeV. The expected sensitivity can\nbe enhanced by means of an unbinned maximum-likelihood \ufb01t dividing the data sample into categories\ndepending on the event topology and exploiting a number of discriminating variables: the increase in\nthe discovery potential increases up to 3.6 (2.8) in the case of \ufb01xed (\ufb02oating) mass \ufb01t for 10 fb\u22121 of\nintegrated luminosity.\nThe search for H \u2192\u03b3\u03b3 in association with Z/W or t\u00aft has been addressed, indicating that a good signal-\nto-background ratio can be achieved. However, the uncertainty on the background contribution in these\nanalyses is large given the present status of simulations.\nReferences\n[1] C. Aurenche and C. Seez, in Proc. Large Hadron Collider Workhsop, Aachen, edited by G. Jarlskog\nand D. Rein, CERN 90-10/ECFA 90-133 (1990).\n[2] L. Fayard and G. 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Gaiser, Charmonium Spectroscopy from Radiative Decays of the J/Psi and Psi-Prime, Ph.D.\nThesis, SLAC-R-255 (1982).\n[56] D. de Florian, M. Grazzini and Z. Kunszt, Phys. Rev. Lett. 82 (1999) 5209\u20135212.\n[57] V. Del Duca, F. Maltoni, Z. Nagy and Z. Trocsanyi, JHEP 04 (2003) 059.\nHIGGS \u2013 PROSPECTS FOR THE DISCOVERY OF THE STANDARD MODEL HIGGS BOSON . . .\n1242\n\nSearch for the Standard Model H \u2192ZZ\u2217\u21924l\nAbstract\nThe Standard Model Higgs boson discovery potential through its observation\nin the 4-lepton (electron and muon) \ufb01nal state using the ATLAS detector is\ninvestigated. Fully simulated signal and background samples were produced\nwith the latest simulation of the ATLAS detector. The samples were subse-\nquently digitized and reconstructed using the ATLAS of\ufb02ine software. The\nanalysis performance dependence on kinematic, lepton reconstruction and iso-\nlation cuts is studied for Higgs boson masses ranging from 120 to 600 GeV.\nThe statistical and systematic uncertainties on the background estimation are\nevaluated and their impact on the Higgs boson discovery potential and exclu-\nsion limits is discussed.\n1\nIntroduction\nThe search for the Standard Model Higgs boson is a major goal of the Large Hadron Collider (LHC).\nThe \ufb01rst proton-proton LHC data at 14 TeV center of mass energy are expected in 2009. The Higgs\nboson mass is a free parameter in the Standard Model, however there is strong expectation motivated by\nprecision electroweak data [1] and direct searches [2] that a low mass Higgs boson (114.4 \u2212199 GeV,\n95% con\ufb01dence level) should be discovered at the LHC. The experimentally cleanest signature for the\ndiscovery of the Higgs boson is its \u201cgolden\u201d decay to four leptons (electrons and muons): H \u2192ZZ \u2192\n4\u2113. The excellent energy resolution and linearity of the reconstructed electrons and muons leads to a\nnarrow 4-lepton invariant mass peak on top of a smooth background. The expected signal to background\nratio after all experimental cuts depends on the Higgs boson mass itself. The major component of the\nbackground consists of irreducible ZZ \u21924\u2113decays. The most challenging mass region is between 120-\n150 GeV where one of the Z bosons is off-shell giving low transverse momentum leptons. In this region\nbackgrounds from Zb\u00afb \u21924\u2113and t\u00aft \u21924\u2113are important and require tight lepton isolation cuts to keep\ntheir contribution well below the ZZ continuum.\n2\nDetector simulation, Monte-Carlo samples, trigger and event recon-\nstruction\nIn this section a brief summary of the detector simulation is presented and the Monte-Carlo (MC) sam-\nples used in the analysis are described. This includes an outline of the various cross-sections and the\ncorresponding theoretical uncertainties. Finally a brief description of the electron and muon trigger and\nof\ufb02ine reconstruction is presented.\n2.1\nDetector simulation and Monte-Carlo samples\nThe ATLAS detector is simulated by the GEANT4 [3] software. Simulation, digitization and reconstruc-\ntion are all performed within the ATLAS software framework ATHENA. The set of H\u21924\u2113samples\nused in this analysis covers the mass range from 120 to 600 GeV. Simulation of pileup, cavern back-\nground and minimum bias events is performed by mixing them with the Higgs boson signal at digiti-\nzation level [4], [5]. An instantaneous constant luminosity of 1033 cm\u22122 s\u22121 is assumed. The cavern\nbackground consists of thermalized slow neutrons and low energy photons escaping the calorimeters [6].\nThe expected level of cavern background is increased by an overall \u201csafety factor\u201d: in this analysis a\n1243\n\nsafety factor of 5 is used.\nThe H\u21924\u2113analysis is sensitive to uncertainties in the knowledge of the material distribution in ATLAS,\nto distortions of the magnetic \ufb01elds, and to the accuracy of the Inner Detector (ID) and of the Muon\nSpectrometer (MS) alignment. Some of these uncertainties have been taken into account by using geo-\nmetrical layouts including extra material. The layout used in this analysis includes additional material in\nthe ID, and between the barrel presampler and strips and barrel cryostat upstream and downstream the\ncalorimeter. The calibration of the LAr Electromagnetic Calorimeter (LAr EMC) is based on the nom-\ninal geometry without this extra material and its inclusion in our study provides a realistic systematic\neffect in the analysis. A detailed description of the layout used in simulation and reconstruction can be\nfound in [7]. In the analysis presented in this note, uncertainties due to misalignment corrections are not\nincluded: the same misaligned layout is used both in simulation and reconstruction.\nThe Higgs boson signal samples were generated exclusively by PYTHIA [8] (version 6.3 for mH =\n130 GeV and version 6.4 for the rest of the masses), while for the background samples various event\ngenerators were used. For the signal, PYTHIA calculates the cross-sections in leading order (LO) taking\ninto account both gluon and vector boson fusion (VBF) diagrams. Next-to-leading order (NLO) effects\nare considered by scaling the total PYTHIA cross-sections [9]. During generation, a 4-lepton \ufb01lter was\napplied to the samples, requiring 4 true leptons with pT > 5 GeV/c within |\u03b7| < 2.7. The \ufb01lter acceptance\nand the cross-section as a function of the Higgs boson mass is given in Table 1. The number of available\nMC events are shown in the last column.\nProcess\n\u03c3LO \u00b7BR [fb]\n\u03c3NLO \u00b7BR [fb]\nFilter acc.\nEvents\nH[120] \u21924l\n1.68\n2.81\n0.584\n40K\nH[130] \u21924l\n3.76\n6.25\n0.633\n40K\nH[140] \u21924l\n5.81\n9.72\n0.662\n40K\nH[150] \u21924l\n6.37\n10.56\n0.685\n10K\nH[160] \u21924l\n2.99\n4.94\n0.704\n40K\nH[165] \u21924l\n1.38\n2.29\n0.712\n40K\nH[180] \u21924l\n3.25\n5.38\n0.733\n40K\nH[200] \u21924l\n12.39\n20.53\n0.753\n50K\nH[300] \u21924l\n7.65\n13.32\n0.782\n10K\nH[400] \u21924l\n6.07\n10.78\n0.814\n40K\nH[500] \u21924l\n2.98\n5.12\n0.842\n40K\nH[600] \u21924l\n1.53\n2.53\n0.853\n40K\nTable 1: Monte Carlo signal data samples, 4-lepton (e,\u00b5) \ufb01lter acceptance, LO and NLO cross-sections,\nand number of events used in the analysis as a function of the Higgs boson mass in GeV (reported in\nsquare brackets). The cross-sections in the table include the branching ratio of the Higgs boson to ZZ\u2217\nand Z\u2192ll, l=e,\u00b5.\n2.1.1\nCorrections to leading order cross-sections for background processes\nThe backgrounds considered in this analysis, together with their cross-sections and K-factors, de\ufb01ned as\nthe ratio between the NLO and the LO cross-sections, are listed in Table 2. For the generation of these\nsamples several MC generators are employed. The t\u00aft background was generated using MC@NLO [10].\nThe QCD ZZ was generated with PYTHIA6.3, the Zb\u00afb background with AcerMC3.1 [11], and the WZ\nbackground with HERWIG 6.5 [12] interfaced to Jimmy [13] for simulation of the underlying event. The\ncross-sections listed in Table 2 are all at LO (except for the t\u00aft which is at NLO), and they do not include\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1244\n\nthe lepton \ufb01lter ef\ufb01ciency. The following corrections are applied to the cross-section of each process to\ncorrect for effects of subprocesses not originally included in the generators:\n\u2022 an additional 30% is applied to the QCD ZZ background cross-section to account for the missing\nquark box diagram in PYTHIA;\n\u2022 8.5 pb are added to the Zb\u00afb cross-section to account for the qq \u2192Zb\u00afb diagrams that are not included\nin the generation.\nThe last column in Table 2 shows the events available for each sample. Each Z boson in the QCD\nqq \u2192ZZ irreducible background is forced to decay into lepton pairs (including all three \ufb02avours).\nThe Zb\u00afb reducible background was generated using ACERMC3.1 [11] with Parton Density Func-\ntion (PDF) set CTEQ6L, QCD scales \u00b5R = \u00b5F = mZ, massive b-quark, interfaced to PYTHIA 6.3 for\nshowering and hadronization. The Z \u2192ll (l = e,\u00b5) decay is forced at generator level. The full Z/\u03b3\u2217\ninterference is taken into account, with a cut on the resonance mass at 30 GeV. The ACERMC dataset\nincludes only the gg \u2192Zb\u00afb process. The q \u00afq \u2192(Z/\u03b3\u2217)b\u00afb contribution, where q is a light quark, is not\nincluded; its contribution to the total LO Zb\u00afb cross-section is less than 15%. The AcerMC LO cross-\nsection, including the Z \u2192ll branching ratio (BR), evaluated with the above parameter choice, amounts\nto 52.03 \u00b1 0.03 pb for the gg \u2192(Z/\u03b3\u2217)b\u00afb and 8.64 \u00b1 0.01 pb for the q \u00afq \u2192(Z/\u03b3\u2217)b\u00afb.\nProcess\nGenerator\n\u03c3\u00b7 BR [fb]\nCorrections\nFA\nEvts [k]\nq \u00afq \u2192ZZ \u21924\u2113\nPYTHIA6.3\n158.8\n+47.64\n[4\u2113]0.219\n100\ngg \u2192Zb\u00afb \u21922\u2113b\u00afb\nAcerMC/PYTHIA6.3\n52030\n+8640 (q \u00afq \u2192Zb\u00afb)\n[4\u2113] 0.00942\n430\ngg \u2192Zb\u00afb \u21922\u2113b\u00afb\nAcerMC/PYTHIA6.3\n52030\n+8640 (q \u00afq \u2192Zb\u00afb)\n[3\u2113] 0.147\n200\ngg,q \u00afq \u2192t\u00aft\nMC@NLO/Jimmy\n833000\n[4\u2113] 0.00728\n400\nq \u00afq \u2192WZ\nJimmy\n26500\n[3\u2113] 0.0143\n70\nq \u00afq \u2192Z inclusive\nPYTHIA6.3\n1.5\u00b7106\n[1\u2113]0.89\n500\nTable 2: Background samples, generators used, acceptance of the multi-lepton \ufb01lter (FA), LO cross-\nsection (except for t\u00aft, which is NLO) and corrections applied. The number of events is given in the last\ncolumn. For ZZ, l = e,\u00b5,\u03c4 while for the rest l = e,\u00b5. The relative errors on the \ufb01lter acceptances (FA)\nare smaller than 0.4%.\n2.1.2\nNext-to-Leading-Order cross-sections for the background\nThe t\u00aft sample, generated by MC@NLO, is the only sample in Table 2 that already includes NLO pro-\ncesses. To evaluate the NLO cross-sections for the other background processes, the program MCFM [14]\nis used. The overall conditions for all MCFM NLO calculations are the following: CTEQ6M, \u00b5R = \u00b5F =\nmZ, mb = 0 full (Z/\u03b3\u2217) interference. Any two \ufb01nal state partons are merged in a single jet if their sepa-\nration \u2206R(j j) is smaller than 0.7.\nIn the case of the Zb\u00afb sample, the following additional selections are applied: mZ > 30 GeV; pT(b) >\n10 GeV, |\u03b7(b)| < 2.5. The NLO cross-section obtained from MCFM is:\n270.4+40.6\n\u221235.7(\u00b5R)+5.4\n\u22128.0(\u00b5F)\u00b112.5(PDF)\u00b11.0(stat) pb\nwhere the \ufb01rst two uncertainties come from the QCD renormalization and factorization scales, varying\nindependently the energy scale of the process from 0.5mZ to 2mZ, while the last one quotes the PDF\nuncertainty, calculated by making use of 40 sets of PDFs for CTEQ6M (20 plus and 20 minus). This\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1245\n\nq \u00afq \u2192Z/\u03b3\u2217Z/\u03b3\u2217\nmZ/Z\u2217> 12 GeV\nmZZ (GeV)\nK-factor\n[115,125]\n1.15\n[125,135]\n1.21\n[145,155]\n1.25\n[155,165]\n1.34\n[175,185]\n1.31\n[195,205]\n1.32\n[295,305]\n1.40\n[395,405]\n1.52\n[495,505]\n1.84\n[595,605]\n1.81\nTable 3: K-factors for the ZZ background. The error on the K-factors is dominated by the systematics\n(from PDF and renormalization and factorization scales) and amounts to 3.3%.\nresult has proved to be quite stable with respect to the variation of the cuts both on the minimum jet pT\nand the minimum jet separation \u2206R(j j). The LO cross-section evaluated with MCFM on the same phase\nspace is 189.9 \u00b1 0.2 pb, resulting in a K-factor of 1.42. The effective cross-section can be evaluated as\nfollows\n\u03c3ef f = \u03c3LO \u00b7BR(Z \u2192ee,\u00b5\u00b5)\u00b7FA\u00b7K = 812.1 fb,\nwhere \u03c3 \u00b7 BR(Z \u2192ee,\u00b5\u00b5) is the AcerMC cross-section listed in Table 2 rescaled to include the q \u00afq\ncontribution, and FA is the acceptance of the generator \ufb01lter, as reported in Table 2. The statistical error\non the \ufb01lter ef\ufb01ciency is 0.2% for this dataset.\nThe NLO cross-section for the q \u00afq \u2192ZZ\u2217process is calculated with MCFM, applying the same\nkinematic selection on the Z boson masses as in PYTHIA (mZ(\u2217) > 12 GeV):\n\u03c3NLO = 22.1+0.1\n\u22120.2(\u00b5R = \u00b5F)\u00b10.7(PDF) pb\nwhere the statistical error is much smaller than the systematic ones. The effective cross-section used in\nthe analysis can be evaluated according to\n\u03c3ef f = \u03c3LO \u00b7[BR(Z \u2192ll)]2 \u00b7FA\u00b7(K +0.3) = 34.82\u00b7(K(mZZ)+0.3) fb,\nwhere \u03c3LO \u00b7 [BR(Z \u2192ll)]2 is the LO cross-section, that includes the Z branching ratio to leptons from\nPYTHIA and amounts to 159\u00b10.05 (stat) fb. The additional 30% accounts for the correction coming\nfrom the gg \u2192ZZ\u2217due to the quark box, as listed in Table 2. The relative statistical error on the \ufb01lter\nacceptance FA is 0.3% for this process. The mass-dependent K-factors used in this analysis are shown\nin table 3.\nThe NLO cross-section for the WZ background is evaluated by applying the same cut on the boson\nmasses (mZ\u2217/W \u2217> 20 GeV) as in the HERWIG-Jimmy generator used for the LO process:\nW \u2212: \u03c3NLO = 21.7+0.5\n\u22120.9(\u00b5R = \u00b5F)\u00b10.9(PDF) pb\nW + : \u03c3NLO = 34.8+1.2\n\u22120.9(\u00b5R = \u00b5F)\u00b11.0(PDF) pb\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1246\n\nwhere the QCD scale uncertainties are included. The statistical error is negligible. The effective cross-\nsection can then be evaluated as follows:\n\u03c3ef f = \u03c3NLO(W +Z +W \u2212Z)\u00b7FA = 807 fb\nwhere \u03c3NLO(W +Z +W \u2212Z) refers to the sum of the two contributions. The relative statistical error on the\n\ufb01lter ef\ufb01ciency for this process is 0.4%.\n2.2\nTrigger\nThe simulation of the full ATLAS trigger chain allows to evaluate the impact of the on-line selection\non the Higgs boson search. Level-one (LVL1) trigger objects (Region-of-interest, ROI), available in the\nsimulation, correspond to small \u2206\u03b7\u00d7 \u2206\u03c6 regions where a lepton that satis\ufb01es the online selection criteria\nis found. LVL1 muon thresholds are programmable in the pT range from 4 GeV/c to about 40 GeV/c.\nSimilarly to the LVL1 muon Trigger, electron/photon ROIs can be of eight types, depending on the high-\nest ET threshold satis\ufb01ed. The settings in this case are also programmable. In this analysis, two types of\nelectron/photon ET thresholds are considered, ET thres=15 and 22 GeV. For both thresholds, cuts on iso-\nlation and on leakage in the hadronic calorimeter are also applied at LVL1. The LVL1 electrons/photons\nand muons are subsequently con\ufb01rmed by the High Level Trigger (HLT). The \ufb01rst step is the Level-2\ntrigger (LVL2) where fast algorithms are used to validate the selected lepton. Events with leptons of\na given quality and with energy above certain \ufb01xed thresholds are retained for a more accurate recon-\nstruction and selection by the Event Filter (EF), where algorithms based on the of\ufb02ine reconstruction\nsoftware are used for the \ufb01nal selection. The choice of HLT selection thresholds is optimized for physics\nperformance, assuring that trigger rates satisfy the system latency. The main aspects of the electron and\nmuon trigger systems are described in [15] and [16].\nThe acceptance of the muon trigger as a function of the generated pT for the threshold pT thres=20\nGeV/c, is shown in Fig. 1. The ef\ufb01ciency above threshold is explained by the geometrical coverage of\nthe muon LVL1 trigger detectors; in the barrel, the space occupied by detector feet, supports, services,\netc., limits the geometrical acceptance to about 80%, while the ef\ufb01ciency of the trigger algorithm itself\nis very close to 100%. The trigger ef\ufb01ciencies of electrons for a selection threshold of ET thres=22 GeV,\nincluding electron identi\ufb01cation and isolation cuts, is shown in Fig. 2.\n [GeV]\nT\np\n0\n10\n20\n30\n40\n50\n60\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nL1\nL2\nEF\nATLAS\nFigure 1: Muon trigger: selection ef\ufb01ciencies of the\nthree trigger levels as a function of the true muon\ntransverse momentum. The selection threshold is\npT thres=20 GeV/c.\n [GeV]\nT\nE\n0\n10\n20\n30\n40\n50\n60\nEfficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nL1\nL2\nEF\nATLAS\nFigure 2: Electron trigger: selection ef\ufb01ciencies of\nthe three trigger levels as a function of the true elec-\ntron transverse energy. The selection threshold is\nET thres=22 GeV.\nIn this paper, several trigger menus foreseen for the LHC running at luminosity L=1033 cm\u22122s\u22121, are\nconsidered. The trigger ef\ufb01ciency for single and double lepton triggers, for a signal sample with a Higgs\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1247\n\nUnbiased sample\nAfter event selection\nTrigger Menu\n4e\n4\u00b5\n2e2\u00b5\n4e\n4\u00b5\n2e2\u00b5\n1\u00b520\n0.1\n95.3\n71.3\n0.4\n98.2\n72.7\n1e22i\n94.7\n0.4\n68.6\n99.8\n0.1\n78.1\n2e15i\n76.3\n<0.2\n33.2\n98.9\n<0.2\n60.2\n1\u00b520 or 1e22i\n94.7\n95.3\n95.7\n99.8\n98.2\n98.9\n2\u00b510 or 2e15i or 1\u00b510 and 1e15i\n76.4\n93.3\n87.8\n98.9\n97.6\n96.9\nTable 4: Trigger selection ef\ufb01ciencies (in %) for various trigger menus, computed for H \u2192ZZ\u2217\u2192\n4l\n(mH=130 GeV), for the full trigger chain LVL1+HLT. The \ufb01rst three columns show the ef\ufb01ciencies\ncomputed on the full event sample. The last three columns show the ef\ufb01ciencies for events selected by\nthe H \u2192ZZ\u2217\u21924l\nanalysis. The absolute errors on the ef\ufb01ciencies are 0.4% for the unbiased samples,\nand 0.2% for events passing the of\ufb02ine selection.\nboson mass of 130 GeV, is shown in Table 4. The results are shown for two classes of events: those\n\ufb01ltered at generator level, requiring 4 leptons within pT> 5 GeV and |\u03b7| <2.7 (unbiased sample), and\nthose passing the signal selection of reconstructed events, described later in this note. A double-lepton\ntrigger with 10 GeV threshold for the muons and 15 GeV threshold for the electrons (isolation required),\nselects Higgs boson to four lepton decays with an ef\ufb01ciency higher than 97 %. In the following, the\nsingle-lepton menu requiring 1\u00b520 or 1e22i will be applied as trigger selection.\n2.3\nElectron and muon reconstruction\nThe leptons used for the ef\ufb01ciency studies are required to satisfy the generator level kinematic cuts\n|\u03b7| < 2.5,and pT> 5 GeV. The lepton ef\ufb01ciency is de\ufb01ned as the ratio of reconstructed to generated\nleptons originating from Z decays. The reconstructed leptons include leptons not originating from Z\ndecays (non-prompt leptons) and fakes, so it is important to study these candidates and to estimate the\nfraction of leptons coming from non-Z decays and fakes. The non-Z lepton fraction is de\ufb01ned as the\nnumber of reconstructed leptons matched to true leptons not originating from Z decays, divided by the\ntotal number of reconstructed leptons. The fraction of fakes is de\ufb01ned as the number of reconstructed\nleptons not matched to a true lepton, divided by the total number of reconstructed leptons.\n2.3.1\nElectron reconstruction\nThe details of electron reconstruction are described in [17] and [18]. Here the electron de\ufb01nitions used\nin this analysis are brie\ufb02y summarized. An electron is selected using the of\ufb02ine algorithm requiring:\n1. a cluster in the barrel and endcap LAr EMC, reconstructed by the ATLAS of\ufb02ine software;\n2. an inner detector track associated with the cluster;\n3. cluster containment in the LAr EMC;\n4. consistency of the lateral shower shape of the cluster with an electron isolated from hadronic\nactivity;\n5. the lateral shower shape to be inconsistent with a \u03c00 \u2192\u03b3\u03b3 decay, using the strip section of the LAr\nEMC;\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1248\n\n6. track quality requirements: a certain number of hits on the Pixel and SCT detector is required, and\na transverse impact parameter smaller than 0.1 cm.\nThe containment and isolation requirements (2,3,4) are satis\ufb01ed using the so-called LooseElectron de\ufb01-\nnition. This de\ufb01nition uses shower shape variables calculated with the middle sampling of the LAr EMC.\nThe addition of requirements 5 and 6 corresponds to the MediumElectron de\ufb01nition. In this analysis the\nMediumElectron de\ufb01nition with the addition of calorimetric isolation using all cells (EM and hadronic)\ninside a \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 = 0.2 cone (MediumElectron+CaloIso) has been used. The isolation cuts\nare \u03b7-dependent, as described in detail in [17].\nTrue electrons not originating from a Z boson decay represent a background to the H\n\u2192ZZ\u2217\u2192\n4l search. Typically they are not isolated and in most cases these electrons originate from heavy quark\ndecays. It should be stressed that leptons from B-mesons are more isolated than those coming from\nD-meson decays, and therefore are more dif\ufb01cult to reject. The isolation also depends on the event\ntopology. The non-Z electrons are a small fraction (less than 1%) of the total number of electrons in the\nH \u2192ZZ\u2217\u21924l events. The electron ef\ufb01ciency as a function of the pseudorapidity \u03b7 and the transverse\nmomentum pT for the Loose, MediumElectron and MediumElectron+CaloIso de\ufb01nitions is shown in\nFig. 4. A signi\ufb01cant drop in ef\ufb01ciency is observed at low pT. This is due to the loss of discrimination\npower of the shower shape cuts. A summary of electron ef\ufb01ciencies and fraction of fakes and non-Z\n|\n\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\nMedium+CALOISO\nMedium\nLoose\nATLAS\nFigure 3: Electron reconstruction ef\ufb01ciency as a\nfunction of \u03b7. The electron-id criteria are described\nin the text.\n (GeV)\nT\nE\n10\n20\n30\n40\n50\n60\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\nMedium+CALOISO\nMedium\nLoose\nATLAS\nFigure 4: Electron reconstruction ef\ufb01ciency as a\nfunction of pT. The electron-id criteria are described\nin the text.\nelectrons is presented in [17]. The total fraction of fakes depends on the isolation cut and is particularly\nhigh for lower pT. For low momenta, pT < 15GeV, the fraction of these electrons is about 8% of the\ntotal reconstructed electrons in this pT range. The contribution from electrons which do not come from\nZ decays is a fraction of the fake electrons dominated by heavy \ufb02avour (c,b) decays. The b-originated\nelectrons are a factor of 1.5-2 more than the c-originated electrons.\n2.3.2\nMuon reconstruction\nThe muon identi\ufb01cation in ATLAS relies on the Muon Spectrometer (MS) for standalone reconstruction\nas well as on the ID and Calorimeters for combined muon reconstruction. In order to combine the muon\ntracks reconstructed in the ID and the MS, the ATLAS of\ufb02ine muon identi\ufb01cation packages have been\ndeveloped. The purpose of these packages is to associate segments and tracks found in the MS with the\ncorresponding ID track in order to identify muons at their production vertex with optimum parameter\nresolution. Details on the muon system design and performance can be found in [19]. Details on the\nalgorithms of the muon identi\ufb01cation described here can be found in [20].\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1249\n\nThe standalone muon reconstruction algorithm measures the \ufb01ve parameters of the reconstructed\ntracks with their associated 5x5 covariance matrix at the entrance of the Muon Spectrometer. The muon\nmomentum is corrected using an energy loss parameterization. Overall, the reconstructed track param-\neters with their full covariance matrices are provided at three locations: 1) at the entrance to the muon\nspectrometer, 2) at the entrance to the calorimeters, 3) at the perigee of the track. Standalone tracks\nreconstructed in the MS are combined with tracks reconstructed in the ID in the region of \u03b7<2.5. This\ncombination improves the momentum resolution for tracks with momenta up to 100 GeV and suppresses\nthe rate of fake muons. A statistical combination of the two sets of track parameters is made, weighted\nby their corresponding covariance matrices. Given a certain \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 cone, all tracks from the\nID are combined with the ones from the MS and the pair giving the best \u03c72 is kept. The same procedure\nis repeated until no more combinations are possible.\nAn algorithm has been developed in order to recover muons which fail to be reconstructed in the MS\n(either because they are low pT muons or because the number of stations is insuf\ufb01cient). The principle\nof the algorithm is based on the extrapolation of ID tracks to the inner stations of the MS and their\nmatching to a segment reconstructed in these stations that was not yet associated to a combined track.\nThe extrapolation is also performed to medium stations, in the regions of \u03b7 between 1 < \u03b7 < 1.4, where\nthere is a type of inner stations missing, resulting in a drop of the reconstruction ef\ufb01ciency.\nThe reconstruction ef\ufb01ciency of muons from a 130 GeV Higgs boson sample as a function of their\ntransverse momentum and \u03b7, is shown in Figs. 5 and 6 respectively.\n (GeV)\nT\np\n10\n20\n30\n40\n50\n60\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nCombined Muons\nAll Muons\nATLAS\nFigure 5: Muon reconstruction ef\ufb01ciency as a func-\ntion of pT.\nEmpty (\ufb01lled) markers show the ef-\n\ufb01ciency of the combined (combined+extrapolated\nfrom the ID) algorithm. Reconstructed muons of a\nHiggs boson sample of 130 GeV mass decaying into\nfour muons are used.\n|\n\u03b7\n|\n0\n0 5\n1\n1.5\n2\n2.5\nEfficiency\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nCombined Muons\nAll Muons\nATLAS\nFigure 6: Muon reconstruction ef\ufb01ciency as a func-\ntion of \u03b7. Empty (\ufb01lled) markers show the ef\ufb01ciency\nof the combined (combined+extrapolated from the\nID) package. Reconstructed muons of a Higgs boson\nsample of 130 GeV mass decaying into four muons\nare used.\n3\nBackground Rejection\nThe large Zb\u00afb and t\u00aft background cross-sections compared to the Standard Model Higgs boson cross-\nsection, require further reduction of these processes by applying additional lepton identi\ufb01cation criteria.\nA reduction well below the irreducible ZZ\u2217background yield is a safeguard against large uncertainties\non the production cross-sections of these \ufb01nal states. One can exploit the fact that leptons originating\nfrom the Z boson decays are expected to be signi\ufb01cantly more isolated than the ones originating from\nheavy quark leptonic decays. These leptons are also expected to originate from the main interaction\npoint, while b,c-originating leptons should come from secondary displaced vertices.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1250\n\nIn this section, a set of isolation and impact parameter cuts for background rejection is described. In\nthis analysis the cuts have been chosen so that the expected rate for Zb\u00afb to 4-leptons (4e, 4\u00b5 and 2e2\u00b5) is\nno more than one third of the ZZ rate. For Higgs boson masses above 160GeV, the reducible background\ncontribution is expected to be less than 10% of the irreducible ZZ.\n3.1\nMuon Isolation\nFor the muon \ufb01nal state both calorimetric and track isolation criteria have been considered.\n\u2022 The calorimetric isolation discriminant is de\ufb01ned as the sum of the transverse energy deposited in\nthe calorimeter inside a cone of a given radius \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2, around the muon. The energy\ndeposition of the muon itself is subtracted from the isolation energy. The cone energy of the least\nisolated muon is used as a discriminant.\n\u2022 The track isolation discriminant is de\ufb01ned as the sum of the transverse momenta of the inner\ndetector tracks in a cone of radius \u2206R around the muon. The inner detector muon track is excluded\nfrom the sum. The least isolated track of all muons in the event, is used as discriminant.\nIn Figs. 7 and 8 the rejection of the Zb\u00afb background as a function of the 4\u00b5 signal ef\ufb01ciency (mH=130\nGeV) is presented, for different calorimetric and track isolation cones, respectively. A cone size of 0.2 is\nadopted for both calorimetric and track isolation as a conservative choice. Moreover, as shown in Figs. 9\nand 10, the background rejection improves when the isolation quantities are normalized to the transverse\nmomentum of the muon, thus the normalized isolation discriminants are used in the analysis.\nSignal\n\u2208\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nZbb\nR\n1\n10\n2\n10\nT\nCa o\n E\n\u03a3\nCalorimeter Isolation \n R 0.10\n\u2206\n R 0.20\n\u2206\n R 0.30\n\u2206\n R 0.40\n\u2206\n R 0.50\n\u2206\nATLAS\nFigure 7: Zb\u00afb rejection versus H \u21924\u00b5 ef\ufb01ciency,\nfor mH = 130GeV, for various calorimetric isolation\ncone sizes.\nSignal\n\u2208\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nZbb\nR\n1\n10\n2\n10\nT\n p\n\u03a3\nTrack Isolation \n R = 0.15\n\u2206\n R = 0.20\n\u2206\n R = 0.25\n\u2206\n R = 0.30\n\u2206\n R = 0.35\n\u2206\nATLAS\nFigure 8: Zb\u00afb rejection versus H \u21924\u00b5 ef\ufb01ciency,\nfor mH = 130GeV, for various track isolation cone\nsizes.\nThe distributions of the normalized calorimetric and track isolation variables calculated using the\ncones chosen in this analysis for the signal and the main backgrounds are presented in Figs. 11 and 12,\nrespectively. The cuts on the calorimetric and tracker isolation are chosen so that the ef\ufb01ciency for the\nsignal, after application of the two cuts, is close to 90%. The selection cuts are placed at 0.23 and 0.15\nfor the calorimetric and the tracker isolation, respectively.\n3.2\nElectron Isolation\nFor the electron \ufb01nal state both calorimetric and track isolation in the inner detector are considered.\nAlthough partial calorimetric isolation along the \u03b7 direction is already part of the electron-id require-\nments, an extra calorimetric isolation in a cone of \u2206R = 0.2 is applied. The de\ufb01nition of the electron\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1251\n\nSignal\n\u2208\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nZbb\nR\n1\n10\n2\n10\nCalorimeter Isolation\n R = 0.2\n\u2206\n, \nT\n E\n\u03a3\nAbsolute : \n R = 0.2\n\u2206\n, \nT\n\u00b5\n/p\nT\n E\n\u03a3\nNormalized : \nATLAS\nFigure 9: Zb\u00afb rejection versus H \u21924\u00b5 ef\ufb01ciency,\nfor mH = 130GeV, for standard and normalized\ncalorimetric isolation calculated in a \u2206R=0.2 cone\naround the muon track.\nSignal\n\u2208\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nZbb\nR\n1\n10\n2\n10\nTrack Isolation\n R = 0.20\n\u2206\n, \nT\n p\n\u03a3\nAbsolute : \n R = 0 20\n\u2206\n, \nT\n\u00b5\n/p\nT\n p\n\u03a3\nNormalized : \nATLAS\nFigure 10: Zb\u00afb rejection versus H \u21924\u00b5 ef\ufb01ciency,\nfor mH = 130GeV, for standard and normalized\ntrack isolation calculated in a \u2206R=0.2 cone around\nthe muon track.\nR=0.20\n\u2206\nfor\nT\n\u00b5\n/p\nT\nE\n\u03a3\nMaximum\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nEvents/0.1\n4\n10\n3\n10\n2\n10\n1\n10\n1\n\u00b5\n 4\n\u2192\n ZZ*\n\u2192\nH(130GeV)\nZbb\ntt\nATLAS\nFigure\n11:\nNormalized\ncalorimetric\nisolation\n(\u2206R=0.2) for the signal (mH = 130), the Zb\u00afb and t\u00aft\nbackgrounds for the 4\u00b5 channel.\nR=0.20\n\u2206\nfor\nT\n\u00b5\n/p\nT\np\n\u03a3\nMaximum\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nEvents/0.1\n4\n10\n3\n10\n2\n10\n1\n10\n1\n\u00b5\n 4\n\u2192\n ZZ*\n\u2192\nH(130GeV)\nZbb\ntt\nATLAS\nFigure 12:\nNormalized track isolation (\u2206R=0.2)\nfor the signal, the Zb\u00afb and t\u00aft backgrounds for the\n4\u00b5 channel.\ntrack isolation is the same as for the muons: it is the sum of the transverse momenta of inner detector\ntracks in a cone with radius \u2206R around the direction of the electron track. The pT of the electron track\nis excluded from the sum. In an attempt to remove from the sum tracks originating from conversions of\nbremsstrahlung photons, only tracks which have at least one hit in the B-layer (the innermost layer of\nthe Pixel detector) are considered in the sum. The track isolation is normalized to the electron pT. The\ndistribution of the electron track isolation is shown in Fig. 13, for a cone size \u2206R=0.2. For the analysis\nall leptons must satisfy a \u03a3pT/pT < 0.15 tracking isolation cut.\n3.3\nImpact parameter analysis\nLeptons from t\u00aft and Zb\u00afb backgrounds are most likely to originate from displaced vertices. Further\nrejection of these backgrounds can be achieved by placing a cut on the transverse impact parameter sig-\nni\ufb01cance (de\ufb01ned as d0/\u03c3d0, where d0 is the distance of closest approach in the transverse plane) of\nthe tracks associated to the leptons. For electrons, bremsstrahlung smears the impact parameter distribu-\ntion, hence reducing the discriminating power of this cut with respect to muons. The impact parameter\nis calculated with respect to the event vertex \ufb01tted using a set of tracks reconstructed in the ID. This\nallows to remove the effect of the spread of the vertex position, which at LHC is 15 \u00b5m along each of\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1252\n\n isolation\nT\nElectron p\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nSignal\nZbb\ntt\nATLAS\nFigure 13: Signal and background distributions for electron track isolation, normalized to the electron\ntrack pT, in a cone \u2206R <0.2.\nthe transverse x and y axes. In Figs. 14 and 15, the transverse impact parameter signi\ufb01cance for muons\nand electrons is shown. Tracks with d0 signi\ufb01cance greater than 3 are not included in the primary vertex\n\ufb01t, and this causes the shoulder visible in the distributions. The discriminating variable used in the event\nselection for Zb\u00afb and t\u00aft background rejection, is the maximum lepton impact parameter in the event.\nThis is shown in Figs. 16 and 17 for 4\u00b5 and 4e events, respectively. For electron tracks, the maximum\nimpact parameter normalized to its error is required to be less than 6, while for muons less than 3.5.\nd0 significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSignal\nZbb\ntt\nATLAS\nFigure 14: Transverse impact parameter signi\ufb01cance\nfor muons from signal and reducible background\nevents.\nd0 significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSignal\nZbb\ntt\nATLAS\nFigure 15: Transverse impact parameter signi\ufb01cance\nfor electrons from signal and reducible background\nevents.\n4\nEvent selection\nIn this section the full set of cuts performed in this analysis are summarized and the event kinematic\nreconstruction is described. These cuts including the isolation and vertexing cuts covered in the previous\nsection are summarized in Table 5.\n4.1\nEvent preselection\nEvents that pass the trigger selection are required to further satisfy certain lepton preselection criteria.\nAn electron must satisfy the LooseElectron requirement described in Section 2.3.1, and have an ET>5\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1253\n\nd0 significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSignal\nZbb\ntt\nATLAS\nFigure 16: Maximum impact parameter signi\ufb01cance\nin 4-muon events, for signal and reducible back-\ngrounds.\nd0 significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nArbitrary units\n-3\n10\n-2\n10\n-1\n10\nSignal\nZbb\nATLAS\nFigure 17: Maximum impact parameter signi\ufb01cance\nin 4-electron events, for signal and reducible back-\ngrounds.\nEvent Preselection\nFour leptons: LooseElectrons or muons.\npT>7 GeVand |\u03b7| < 2.5, at least two with pT>20 GeV\nEvent Selection\nKinematic Cuts\nLepton quality: 2 pairs of same \ufb02avour opposite charge leptons.\nElectrons must be MediumElectrons satisfying the CaloIso criterion.\nFor H masses of 200 GeV and higher, four LooseElectrons are required instead.\nZ, Z\u2217and Higgs boson reconstruction: single quadruplet with\n|mll1 \u2212mZ| < \u2206m12 GeV, mll2 > m34.\nIsolation and\nMuon Calorimetric isolation (\u03a3ET/pT < 0.23).\nvertexing cuts\nLepton Inner detector track isolation (\u03a3pT/pT < 0.15).\nCut on maximum lepton impact parameter\n(d0/\u03c3d0 < 3.5 for muons, d0/\u03c3d0 < 6.0 for electrons).\nTable 5: Summary of the analysis cuts for the H\u21924\u2113analysis. The two lepton pairs are denoted as mll1\nand mll2. The values of the mass window \u2206m12 and of the cut m34 are de\ufb01ned in Table 6.\nGeV and |\u03b7| < 2.5. Muons are selected by requiring pT>5 GeV and |\u03b7| < 2.5 (see section 2.3.2). The\n\ufb01nal stage of event preselection requires at least four leptons with pT>7 GeVand |\u03b7| < 2.5, with at least\nof two these leptons having pT>20 GeV.\n4.2\nEvent selection and kinematic reconstruction\nFollowing Table 5, in this section we review the kinematic cut part of the event selection. These cuts\nhave been optimized separately for each Higgs boson mass considered in this note.\nLepton quality requirements:\nEvents used in this analysis are required to have at least four leptons (e, \u00b5) which can be coupled in\npairs of opposite charge and same \ufb02avour. These leptons are required to satisfy the requirements:\n\u2022 Electrons: for Higgs boson masses below 200 GeV, electrons are required to satisfy the Medium-\nElectron quality requirement, and the calorimetric isolation in a \u2206R = 0.2 cone (CaloIsolation).\nFor masses above or equal to 200 GeV, due to the higher momentum of the decay electrons, the\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1254\n\nMediumElectron requirement is relaxed and these electrons are required to satisfy the LooseElec-\ntrons quality (see Section 2.3.1). This is a conservative choice, due to the fact that complete studies\non Z+jets background rejection were limited by the number of simulated events available.\n\u2022 Muons are required to be either reconstructed by the combined reconstruction algorithm, or by\nthe tagging algorithm which is matching tracks in the inner detector to hit patterns in the muon\nspectrometer (see Section 2.3.2).\nZ, Z(\u2217) and Higgs boson mass reconstruction\nThe 4-lepton Higgs boson candidate mass reconstruction proceeds after selecting one single lepton\nquadruplet in an event. When more than one quadruplet is found, the one with a dilepton mass closest to\nthe nominal Z mass, and with the highest pTleptons associated to the second Z, is chosen. The resolution\nof the dilepton mass can be improved by applying a Z-mass constraint to the pair with a mass closest\nto the Z invariant mass. When both Z\u2019s are on-shell (for Higgs boson masses of 200 GeV and above),\nthe Z-mass constraint can be applied to both lepton pairs. The constraint itself is a convolution between\nthe nominal Z Breit-Wigner distribution, and a gaussian distribution centered at the measured Z value\nwith \u03c3 equal to the experimental resolution. The distribution of the Higgs boson mass reconstructed in\nthe case of a 130 GeV Higgs boson is shown in Figs. 18, 19 and 20 for the 4e, 4\u00b5 and 2e2\u00b5 channels\nrespectively. Only the gaussian region of the distribution is considered in the \ufb01t in the case of the 4e\nchannel: the fraction of events falling within \u00b12\u03c3 from the mean value is 81.7% in this case. The tail of\nthe distribution is due to electron bremsstrahlung losses upstream the calorimeters.\n [GeV]\neeee\nm\n80\n90\n100\n110\n120\n130\n140\n150\nArbitrary units\n0\n20\n40\n60\n80\n100\n120\n 0.09) GeV\n\u00b1\nMean = (129.76 \n 0.07) GeV\n\u00b1\n = (2.16 \n\u03c3\nATLAS\nFigure 18: Reconstructed H(130 GeV)\u21924e mass\nafter application of the Z-mass constraint \ufb01t.\n [GeV]\n\u00b5\n\u00b5\n\u00b5\n\u00b5\nm\n80\n90\n100\n110\n120\n130\n140\n150\nArbitrary units\n0\n50\n100\n150\n200\n250\n300\n350\n400\n 0.04) GeV\n\u00b1\nMean = (129.94 \n 0.04) GeV\n\u00b1\n = (1.78 \n\u03c3\nATLAS\nFigure 19: Reconstructed H(130 GeV)\u21924\u00b5 mass\nafter application of the Z-mass constraint \ufb01t.\nThe Higgs boson mass resolution for masses for which the Higgs boson has a negligible intrinsic\nwidth, is shown in Figs. 21 and 22. In these \ufb01gures it is shown that the Z-mass constraint improves the\nmass resolution by 10% to 17%. The 4-lepton mass shifts after the Z-mass constraint are shown in Fig.\n23 for each of the three decay channels. Independently of the \ufb01t, the 4e mass is biased to lower values due\nto material effects (see Section 2.3.1). For this reason the electron energy has already been corrected by\n+1% based on the difference of the reconstructed Z mass and the PDG Z mass. The Z-mass constraint is\nonly slightly correcting for these effects. In the 4\u00b5 channel, the bias introduced by the Z-mass constraint\nis negligible.\nFinally, the set of kinematic cuts applied to the reconstructed Z invariant masses is shown in Table\n6. The cuts have been optimized using the expected distributions for signal and backgrounds, and the\nexpected dilepton resolution. In this table Z1 is the dilepton with a mass closest to the nominal Z mass,\nwhile Z2 is the lower mass dilepton pair. To estimate the signi\ufb01cance, the events in a \u00b12\u03c3 mass window\nare selected.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1255\n\n [GeV]\n\u00b5\n\u00b5\nee\nm\n80\n90\n100\n110\n120\n130\n140\n150\nArbitrary units\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n 0.04) GeV\n\u00b1\nMean = (129.90 \n 0 03) GeV\n\u00b1\n = (1.85 \n\u03c3\nATLAS\nFigure 20: Reconstructed H(130 GeV)\u21922e2\u00b5 mass after application of the Z-mass constraint \ufb01t.\nHiggs Mass [GeV] \n120\n130\n140\n150\n160\n170\n180\nResolution [GeV]\n1\n1.5\n2\n2.5\n3\n3.5\n4e no Z mass constraint\n4e with Z mass constraint\nATLAS\nFigure 21: Higgs\u21924e mass resolution as a func-\ntion of the Higgs boson mass. Open circles denote\nthe resolution obtained when no Z-mass constraint\nis applied, while full circles show the resolution in\nthe case of the Z-mass constraint.\nHiggs Mass [GeV] \n120\n130\n140\n150\n160\n170\n180\nResolution [GeV]\n1\n1.5\n2\n2.5\n3\n3.5\n no Z mass constraint\n\u00b5\n4\n with Z mass constraint\n\u00b5\n4\nATLAS\nFigure 22: Higgs\u21924\u00b5 mass resolution as a func-\ntion of the Higgs boson mass. Open circles denote\nthe resolution obtained when no Z-mass constraint\nis applied, while full circles show the resolution in\nthe case of the Z-mass constraint.\n4.3\nEvent selection results\nThe cut \ufb02ow for the selection of a 130 GeV Higgs boson is shown in Tables 7 and 8, for signal and\nbackgrounds respectively.\nThe same is shown for the t\u00aft background in Table 9. In this case, the\navailable MC statistics is not suf\ufb01cient to determine the number of expected events, and only upper\nlimits at 90% CL are set. The \ufb01nal selection ef\ufb01ciencies are shown in Figs. 24 and 25 The distributions\nof the reconstructed 4-lepton mass, obtained after all cuts, are shown in Figs. 26, 27, 28 for three of the\nlow-mass values (130, 150, and 180 GeV), and in Figs. 29, 30, and 31 for three of the high-mass ones\n(300, 400, and 600 GeV).\nThe number of expected events shown for the three decay channels combined is computed using NLO\ncross-sections (Section 2.1), for a luminosity of 30 fb\u22121. The NLO cross-sections after the full event\nselection, are shown in Table 10 for the three decay channels separately and combined. In this table,\nsignal events are selected within a mH \u00b12\u03c3mH mass window, and systematic errors are not yet taken into\naccount in the signi\ufb01cance calculation. Here \u03c3mH is the experimental 4-lepton mass resolution, shown in\nTable 6. The signi\ufb01cances for the each of the three channels, and their combination, are summarized in\nFig. 32.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1256\n\nHiggs Mass [GeV] \n120\n130\n140\n150\n160\n170\n180\nM/M (%)\n\u2206\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\n4e with Zmass constraint\n with Z mass constraint\n\u00b5\n4\n with Z mass constraint\n\u00b5\n2e2\nATLAS\nFigure 23: Shift of the mean 4-lepton mass for each of the three decay channels, with and without the\nZ-mass constraint on the dilepton mass.\nH Mass\nZ1 mass window\nZ2 mass cut\nH mass resolution (GeV)\n(GeV)\n(GeV)\n(GeV)\n4e\n4\u00b5\n2e2\u00b5\n120\n\u00b115\n>15\n2.0\n1.8\n1.9\n130\n\u00b115\n>20\n2.2\n1.8\n1.9\n140\n\u00b115\n>30\n2.2\n2.0\n2.1\n150\n\u00b115\n>30\n2.3\n2.1\n2.2\n160\n\u00b115\n>30\n2.4\n2.2\n2.3\n165\n\u00b115\n>35\n2.5\n2.4\n2.4\n180\n\u00b112\n>40\n2.8\n2.7\n2.8\n200\n\u00b112\n>60\n3.9\n3.7\n3.8\n300\n\u00b112\n\u00b112\n8.4\n8.4\n8.4\n400\n\u00b112\n\u00b112\n16.5\n17.3\n17.2\n500\n\u00b112\n\u00b112\n33.8\n34.4\n32.8\n600\n\u00b112\n\u00b112\n52.2\n57.2\n53.2\nTable 6: Cuts applied to the reconstructed leading and sub-leading Z masses, and the Higgs boson mass\nresolution values used to de\ufb01ne the signal region.\n4.4\nEstimates of WZ and Z+Jets backgrounds\nThe contribution of other potentially dangerous backgrounds have also been estimated. Examples are the\nWZ\u21923\u2113and the inclusive Z+X where the Z decays leptonically. In the WZ\u21923\u2113background pileup and\ncavern background are included. WZ is found to give a negligible contribution to the total background:\nthe upper limit on the expected number of events is lower than the limit on t\u00aft events. The Z+jets process\nprovides one of the most serious backgrounds to the 4e-channel at low masses. With the available MC\nstatistics (500K events, see Table 2), no event survives the lepton quality and pT selection cuts. An\nestimate based on cut factorization leads to an evaluation of the expected number of events after the full\nevent selection, that would correspond to one event after the initial lepton quality and pT cuts. This is at\nthe level of about twice the Zbb background, i.e. below the ZZ\u2217continuum. The available MC statistics\nis therefore not suf\ufb01cient to set stringent limits on the Z+jets background. However, the rejection based\non the lepton quality and pT cuts should guarantee the complete removal of this background.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1257\n\nSelection cut\nSelection step\nSignal\n4e\n4\u00b5\n2e2\u00b5\nTrigger selection\n1\n94.7\n95.3\n95.7\nLepton preselection\n2\n57.0\n73.8\n66.8\nLepton quality and pT\n3\n24.7\n60.5\n39.7\nZ\u2019s mass cuts\n4\n17.1\n42.9\n27.6\nCalo Isolation\n5\n17.1\n39.5\n25.4\nTracker Isolation\n6\n16.5\n38.1\n24.7\nIP cut\n7\n15.1\n36.5\n23.2\nH Mass cut\n8\n12.5\u00b10.3\n31.4\u00b10.5\n19.2\u00b10.4\nTable 7: Fraction of events (in %) selected after each event selection cut, for each of the three decay\nchannels, and for a 130 GeV Higgs boson. The ef\ufb01ciencies of each selection are calculated with respect\nto the fraction of events in which the Higgs boson decays into the corresponding channel, and that pass\nthe generator \ufb01lter described in Section 2.1.\nSelection cut\nZZ\nZbb\n4e\n4\u00b5\n2e2\u00b5\n4e\n4\u00b5\n2e2\u00b5\nTrigger\n1\n96.6\n96.6\n96.6\n91.4\n91.4\n91.4\nPreselection\n2\n13.8\n17.6\n31.4\n2.6\n9.4\n12.0\nLepton quality and pT\n3\n7.3\n16.0\n21.9\n1.1\u00b710\u22121\n2.1\n1.7\nZ mass cuts\n4\n6.9\n14.8\n20.2\n4.7\u00b710\u22122\n1.1\n8.4\u00b710\u22121\nCalo Isolation\n5\n6.9\n13.9\n19.5\n4.7\u00b710\u22122\n8.5\u00b710\u22122\n1.2\u00b710\u22121\nTrack Isolation\n6\n6.8\n13.6\n19.2\n1.3\u00b710\u22122\n3.3\u00b710\u22122\n4.4\u00b710\u22122\nIP cut\n7\n6.2\n13.0\n17.8\n5.6\u00b710\u22123\n1.1\u00b710\u22122\n1.8\u00b710\u22122\nH Mass window\n8\n5.2\u00b710\u22122\n11.3\u00b710\u22122\n12.0\u00b710\u22122\n1.6\u00b710\u22123\n1.2\u00b710\u22123\n3.0\u00b710\u22123\nTable 8: Fraction of events (in %) selected after each event selection cut for the background processes.\nThe 130 GeV Higgs boson mass selection cuts are applied.\n4.5\nEffects of pile-up and cavern background\nThe effects of pile-up and cavern background in the analysis are studied for the analysis for the Higgs\nboson mass of 130 GeV . The signal selection ef\ufb01ciencies are shown in Fig. 33, for the 4\u00b5 and 4e channel,\nas a function of the selection cuts listed in Table 7. Table 12 summarizes the results for the three decay\nchannels. The effect of pileup is to decrease the signal selection ef\ufb01ciency by about 10%, for all three\ndecay channels. This decrease is due to a slight decrease in the trigger ef\ufb01ciency, and of the calorimetric\nand tracker isolation cut ef\ufb01ciencies. Part of the loss can be recovered by reoptimizing these cuts.\n5\nSystematic uncertainties\nCentral to the H\u21924\u2113analysis is the estimate of the background in a candidate signal region. In this sec-\ntion the systematic uncertainties on quantities associated with the background estimation and the signal\nef\ufb01ciency are discussed. First the theoretical uncertainties are presented. Subsequently, the impact of\nexperimental systematic uncertainties on the event selection is discussed. Some of the systematics, like\nthe theoretical uncertainties and systematics on the signal ef\ufb01ciency, affect the estimate of the expected\nsensitivity. Signal signi\ufb01cance extraction from real data is affected by systematics on the knowledge of\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1258\n\nSelection cut\nt\u00aft\n4e\n4\u00b5\n2e2\u00b5\nTrigger\n1\n75.1\n75.1\n75.1\nPreselection\n2\n1.0\n4.7\n10.1\nLepton quality and pT\n3\n6.8\u00b710\u22123\n7.3\u00b710\u22121\n5.8\u00b710\u22121\nZ mass cuts\n4\n1.6\u00b710\u22123\n2.0\u00b710\u22121\n1.0\u00b710\u22121\nCalo Isolation\n5\n1.6\u00b710\u22123\n1.6\u00b710\u22123\n5.4\u00b710\u22123\nTrack Isolation\n6\n2.6\u00b710\u22124\n2.5\u00b710\u22124\n1.0\u00b710\u22123\nIP cut\n7\n2.6\u00b710\u22124\n< 6\u00b710\u22124\n2.6\u00b710\u22124\nH Mass window\n8\n< 6\u00b710\u22124\n< 6\u00b710\u22124\n< 6\u00b710\u22124\nTable 9: Fraction of events (in %) selected after each event selection cut for the t\u00aft background. For small\navailable statistics 90% CL limits are considered.\nHiggs Mass [GeV] \n120\n130\n140\n150\n160\n170\n180\nSelec ion Efficiency (%)\n0\n10\n20\n30\n40\n50\nH->ZZ*->4e\n\u00b5\nH->ZZ*->4\n\u00b5\nH->ZZ*->2e2\nATLAS\nFigure 24: Selection ef\ufb01ciency as a function of the\nHiggs boson mass, for each of the three decay chan-\nnels, for the case of only one on-shell Z.\nHiggs Mass [GeV] \n200\n250\n300\n350\n400\n450\n500\n550\n600\nSelec ion Efficiency (%)\n0\n10\n20\n30\n40\n50\n60\nH->ZZ*->4e\n\u00b5\nH->ZZ*->4\n\u00b5\nH->ZZ*->2e2\nATLAS\nFigure 25: Selection ef\ufb01ciency for as a function of\nthe Higgs boson mass, for each of the three decay\nchannels, for the case of two on-shell Z\u2019s.\nlepton energy scale and resolution, as determined for example from inclusive Z studies, lepton recon-\nstruction ef\ufb01ciency, and reducible background knowledge from control samples.\n5.1\nTheoretical uncertainties\nThe major theoretical uncertainties in the prediction of the inclusive background cross-sections are the\nPDF uncertainties and uncertainties related to the QCD renormalization and factorization scales. Scale\nuncertainties re\ufb02ect theoretical uncertainties due to the omission of higher order diagrams. PDF and\nscale uncertainties have already been discussed and evaluated for the main backgrounds and are only\nrecalled here (see Section 2.1). In summary, for the calculation of the NLO inclusive cross-sections, the\nQCD scales have been independently varied in the range (0.5-2)\u00d7 the energy scale of the process. The\nPDF uncertainty has been evaluated by making use of 40 sets of PDF\u2019s for CTEQ6M (20 plus and 20\nminus).\n5.2\nExperimental uncertainties\nSystematic effects on the H\u21924\u2113analysis arise from experimental uncertainties related to the lepton re-\nconstruction. The major contributions in the total systematic uncertainty in the H\u21924\u2113yield come from\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1259\n\n [GeV]\n4l\nm\n100\n110\n120\n130\n140\n150\n160\n170\n180\n190\n200\nEvents/(2 5 GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n [GeV]\n4l\nm\n100\n110\n120\n130\n140\n150\n160\n170\n180\n190\n200\nEvents/(2 5 GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 26: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 130 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\n [GeV]\n4l\nm\n120\n130\n140\n150\n160\n170\n180\n190\n200\n210\n220\nEvents/(2 5 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n [GeV]\n4l\nm\n120\n130\n140\n150\n160\n170\n180\n190\n200\n210\n220\nEvents/(2 5 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 27: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 150 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\n [GeV]\n4l\nm\n140\n150\n160\n170\n180\n190\n200\n210\n220\n230\n240\nEvents/(2.5 GeV)\n0\n5\n10\n15\n20\n25\n [GeV]\n4l\nm\n140\n150\n160\n170\n180\n190\n200\n210\n220\n230\n240\nEvents/(2.5 GeV)\n0\n5\n10\n15\n20\n25\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 28: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 180 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\n [GeV]\n4l\nm\n200\n220\n240\n260\n280\n300\n320\n340\n360\n380\n400\nEvents/(5 GeV)\n0\n10\n20\n30\n40\n50\n [GeV]\n4l\nm\n200\n220\n240\n260\n280\n300\n320\n340\n360\n380\n400\nEvents/(5 GeV)\n0\n10\n20\n30\n40\n50\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 29: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 300 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\nuncertainties in lepton energy scale, reconstruction and identi\ufb01cation ef\ufb01ciency. The impact of these un-\ncertainties on the analysis is studied by applying variations to of\ufb02ine reconstructed variables. The level\nof these variations has been provided by the performance groups.\nUncertainties in lepton energy scale\nUncertainties on the energy scale of electrons arise from the EM calibration. These are considered by\nvarying by \u00b10.5% the ET of the reconstructed electrons. Energy scale uncertainties for muons arise due\nto the imperfect knowledge of the magnetic \ufb01eld. Here the recostructed muon pT is varied by \u00b11%.\nThese values are assumed on the basis of the foreseen in-situ determination of the detector performance.\nUncertainties in lepton energy resolution\nThe level of knowledge of the material distributions in ATLAS affects the lepton energy reconstruction.\nTo properly evaluate the impact of this contribution on the analysis, the reconstructed electron energies\nare smeared with a Gauss function using a \u03c3ET = 0.0073\u00b7ET. This extra smearing deteriorates the trans-\nverse energy resolution of 50 GeV electrons by a relative 10%. In the muon system, an additional term\ncan be added to this smearing, to take into account misalignment uncertainties. The total muon smearing\nis \u03c31/pT = 0.011/pT \u22950.00017 (with pT in GeV). In the pT range of interest for Higgs boson searches,\nthe second term is negligible. The values of the corrections described above have been chosen so that the\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1260\n\n [GeV]\n4l\nm\n250\n300\n350\n400\n450\n500\n550\nEvents/(10 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n [GeV]\n4l\nm\n250\n300\n350\n400\n450\n500\n550\nEvents/(10 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 30: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 400 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\n [GeV]\n4l\nm\n400\n450\n500\n550\n600\n650\n700\n750\n800\nEvents/(20 GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n [GeV]\n4l\nm\n400\n450\n500\n550\n600\n650\n700\n750\n800\nEvents/(20 GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n4l\n\u2192\nZZ*\n\u2192\nH\nZZ\nZbb\ntt\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 31: Reconstructed 4-lepton mass for signal\nand background processes, in the case of a 600 GeV\nHiggs boson, normalized to a luminosity of 30 fb\u22121.\nHiggs mass [GeV] \n100\n200\n300\n400\n500\n600\nSignal significance\n1\n10\n4e\n\u00b5\n4\n\u00b5\n2e2\nTotal\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 32: Expected signal signi\ufb01cances computed\nusing Poisson statistics, for each of the three decay\nchannels, and their combination.\nSelection Cut\n2\n3\n4\n5\n6\n7\n8\nSelection Efficiency (%)\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nSignal 4e\nSignal 4e+pileup\n\u00b5\nSignal 4\n+pileup\n\u00b5\nSignal 4\nFigure 33: Fraction of selected events with and with-\nout pile-up and cavern background, for the cuts in\nTables 7 and 8 (130 GeV H\u21924e and 4\u00b5 analyses).\nnominal resolution on muon pT of 3% is increased to 3.3% after applying the extra smearing.\nUncertainties in lepton reconstruction ef\ufb01ciency\nThe impact of uncertainties in the lepton reconstruction ef\ufb01ciency can be estimated by discarding a \ufb01xed\nfraction of leptons before the analysis. The level of uncertainties considered here is 0.2% for electrons\nand 1% for muons, motivated by performance group studies.\nMaterial effects in electron ef\ufb01ciency\nUncertainties in electron ef\ufb01ciency receive a large contribution from uncertainties in the knowledge of\nmaterial upstream the LAr EMC. Systematic effects in\ufb02uence shower shape discriminants included in the\nelectron identi\ufb01cation criteria. Examples of such discriminants are the mean energy fraction in a core of\n3\u00d77 middle sampling cells normalized to a window of 7\u00d77 cells, and the mean energy fraction outside\na 3-strip core and inside a 7-strip window. As discussed in [17], the presence of extra material shifts\nand changes the shapes of these distributions, hence reducing the discrimination power of these cuts.\nThe integrated effect in electron ef\ufb01ciency is rather small (less than 2%). However the true systematic\nuncertainty in the ef\ufb01ciency due to the knowledge of the material depends on how well the material and\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1261\n\nMass (GeV)\n120\n130\n140\n150\n160\n165\n180\nSelection\nSignal\n0.043\n0.124\n0.239\n0.297\n0.162\n0.078\n0.205\nZZ\u2217/\u03b3\u2217\n0.028\n0.027\n0.020\n0.017\n0.033\n0.044\n0.196\n4e\nZbb\n0.006\n0.013\n0.004\n0.004\n< 0.004\n0.006\n0.002\nt\u00aft\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\nSigni\ufb01cance (30 fb\u22121)\n0.9\n2.4\n4.8\n6.1\n3.3\n1.4\n2.1\nSignal\n0.108\n0.311\n0.563\n0.707\n0.381\n0.177\n0.476\nZZ\u2217/\u03b3\u2217\n0.052\n0.059\n0.061\n0.017\n0.073\n0.080\n0.258\n4\u00b5\nZbb\n0.019\n0.009\n0.009\n0.008\n0.006\n0.004\n0.008\nt\u00aft\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\nSigni\ufb01cance (30 fb\u22121)\n1.7\n4.4\n7.0\n8.4\n5.1\n2.6\n4.1\nSignal\n0.130\n0.381\n0.709\n0.932\n0.485\n0.229\n0.642\nZZ\u2217/\u03b3\u2217\n0.063\n0.063\n0.081\n0.074\n0.102\n0.116\n0.483\n2e2\u00b5\nZbb\n0.030\n0.025\n0.013\n0.009\n0.009\n0.004\n0.004\nt\u00aft\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\nSigni\ufb01cance (30 fb\u22121)\n1.8\n4.8\n7.7\n9.8\n5.6\n2.8\n4.2\nSignal\n0.281\n0.816\n1.511\n1.94\n1.03\n0.484\n1.32\nZZ\u2217/\u03b3\u2217\n0.143\n0.150\n0.163\n0.151\n0.208\n0.240\n0.938\nAll\nZbb\n0.055\n0.047\n0.026\n0.021\n0.015\n0.013\n0.013\nt\u00aft\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\n<0.04\nSigni\ufb01cance (30 fb\u22121)\n2.8\n7.1\n11.5\n14.2\n8.2\n4.2\n6.2\nTable 10: Cross-sections (in fb) after the full event selection for the signal and irreducible and reducible\nbackgrounds. The cross-sections are given for each of three channels 4e ,4\u00b5 and 2e2\u00b5 , and for their\ncombination. When no event is passing the event selection, 90% C.L. limits on the cross-section are set.\nFor each channel and for their combination, the expected signi\ufb01cance is given for 30 fb\u22121. It is assumed\nthat the background in the signal region is known with negligible uncertainty. The t\u00aftbackground is\nassumed not to contribute to the sign\ufb01\ufb01cance,\nthe shower shapes can be measured using data.\n5.3\nSummary of the systematic uncertainties\nThe impact of the various lepton systematic uncertainties on the Higgs boson signal yield and background\nrejection is summarized in Table 13 for the various 4\u2113\ufb01nal states. Variations have been applied to both\nsignal and background samples, and the analysis algorithm ran with the hypothesis of mH = 130 GeV.\nA 3% uncertainty on the luminosity has been taken into account in the total systematic error calculation.\nThe total systematic error on the signal ef\ufb01ciency has been included in the calculation of the exclusion\nlimits described in the following.\n6\nBackground extraction from data and signi\ufb01cance estimation\nIn Section 4 the signi\ufb01cance has been obtained assuming that the background is known with a negligible\nuncertainty. In this section various methods to extract the background from data, evaluate the background\nuncertainties, and include them in the signi\ufb01cance calculation, are presented.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1262\n\nMass (GeV)\n200\n300\n400\n500\n600\nSelection\n4e\nSignal\n1.41\n0.917\n0.737\n0.370\n0.174\nZZ\u2217/\u03b3\u2217\n0.689\n0.342\n0.225\n0.228\n0.179\nSigni\ufb01cance (30 fb\u22121)\n7.4\n6.6\n6.3\n3.4\n1.9\n4\u00b5\nSignal\n1.94\n1.16\n0.918\n0.463\n0.206\nZZ\u2217/\u03b3\u2217\n0.867\n0.468\n0.379\n0.346\n0.296\nSigni\ufb01cance (30 fb\u22121)\n9.0\n7.2\n6.3\n3.6\n1.8\n2e2\u00b5\nSignal\n3.33\n2.13\n1.69\n0.825\n0.377\nZZ\u2217/\u03b3\u2217\n1.53\n0.836\n0.610\n0.570\n0.438\nSigni\ufb01cance (30 fb\u22121)\n11.7\n9.8\n9.0\n5.0\n2.7\nAll\nSignal\n6.68\n4.21\n3.34\n1.66\n0.76\nZZ\u2217/\u03b3\u2217\n3.09\n1.65\n1.21\n1.14\n0.914\nSigni\ufb01cance (30 fb\u22121)\n16.5\n13.8\n12.7\n7.1\n3.8\nTable 11: Cross-sections (in fb) after the full event selection for signal and irreducible background. For\nHiggs boson masses above 180 GeV the contribution of the reducible backgrounds to the total back-\nground cross-section is negligible. The cross-sections are given for each of three channels 4e, 4\u00b5 and\n2e2\u00b5 , and for their combination. When no event is passing the event selection, 90% C.L. limits on the\ncross-section are set. For each channel and for their combination, the expected signi\ufb01cance is given for\n30 fb\u22121. It is assumed that the background in the signal region is known with negligible uncertainty.\n4e\n4\u00b5\n2e2\u00b5\nNo Pileup and CB\n12.5\u00b10.3\n31.4\u00b10.5\n19.2\u00b10.4\nWith Pileup and CB\n12.1\u00b10.3\n28.4\u00b10.5\n17.0\u00b10.4\nTable 12: Selection ef\ufb01ciencies in %, after all cuts, for the signal at 130 GeV, and for each of the three\ndecay channels. The ef\ufb01ciencies are shown for the two cases: with and without the addition of minimum\nbias low-luminosity pileup and cavern background with safety factor 5.\nThe main challenge in measuring the background for the 4\u2113channel over a very wide mass range\n(from m4\u2113120 GeVto m4\u2113600 GeV), comes from the fact that signal and background shapes and cross-\nsections vary considerably. The dominant background comes from the ZZ(\u2217) continuum. While we\nexpect to measure the ZZ in the high mass region (M4\u2113> 180 GeV) where the reducible backgrounds\nbecome negligible, in the low mass region the signi\ufb01cant presence of Zb\u00afb and t\u00aft requires their knowledge.\nMeasurements of these backgrounds with early data will provide upper bounds in their expectation after\nall Higgs boson analysis cuts.\n6.1\nSigni\ufb01cance determination\nMost of the systematic uncertainties discussed in the previous section do not contribute to the signif-\nicance determination if the data distributions are \ufb01tted, and signal and background are extracted from\nthe \ufb01t. The resulting uncertainty in the knowledge of the background reduces the con\ufb01dence level for\nclaiming a discovery. In this section a \ufb01t-based approach for background and signi\ufb01cance extraction is\npresented. A \ufb01t of the selected 4-lepton invariant mass, using the signal hypothesis at a \ufb01xed mass and\napplying the pro\ufb01le likelihood ratio method to extract the signi\ufb01cance is considered. The \ufb01t method, and\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1263\n\nZbb\nZZ\nH\nZbb\nZZ\nH\nZbb\nZZ\nH\n4e\n4\u00b5\n2e2\u00b5\nScale +0.5% (+1%)\n+1.5\n+0.1\n+0.9\n+2.4\n+0.4\n+1.3\n+1.9\n+0.1\n+0.9\nScale -0.5% (-1%)\n-1.1\n-0.2\n-0.5\n-2.3\n-0.3\n-2.5\n-1.7\n-0.2\n-1.4\nResolution\n-0.5\n-0.1\n-0.4\n+0.1\n-0.1\n-2.6\n-0.2\n-0.1\n-0.5\nRec. ef\ufb01ciency\n-1.0\n-0.7\n-0.5\n-3.8\n-4.0\n-3.8\n-2.0\n-2.1\n-1.7\nLuminosity\n3\n3\n3\nTotal\n3.6\n3.1\n3.2\n5.4\n5.0\n6.0\n4.1\n3.7\n3.8\nTable 13: Impact, in %, of the systematic uncertainties on the overall selection ef\ufb01ciency, as obtained for\na mH = 130 GeVin the 4e,4\u00b5, and 2e2\u00b5 \ufb01nal states.\nthe results obtained after varying the background shape, the \ufb01t range and even including background-\nonly \ufb01ts without the signal hypothesis, are the main subject of this section. An alternative approach with\na global two-dimensional (2D) \ufb01t on the (mZ\u2217,m4\u2113) plane is also brie\ufb02y discussed.\nThe baseline method used as input to the combination of all ATLAS Standard Model Higgs boson\nsearches, is based on a \ufb01t of the 4-lepton invariant mass distribution over the full range from 110 to\n700 GeV. The method, whose details are described in [21], is summarized below.\nThe 4-lepton reconstructed invariant mass after the full event selection (except the \ufb01nal cut on the\n4-lepton reconstructed mass) is used as a discriminating variable to construct a likelihood function. The\nlikelihood is calculated on the basis of parametric forms of signal and background probability density\nfunctions (pdf) determined from the MC. For a given set of data, the likelihood is a function of the\npdf parameters \u20d7p and of an additional parameter \u00b5 de\ufb01ned as the ratio of the signal cross-section to\nthe Standard Model expectation (i.e. \u00b5 = 0 means no signal, and \u00b5 = 1 corresponds to the signal rate\nexpected for the Standard Model). To test a hypothesized value of \u00b5 the following likelihood ratio is\nconstructed:\n\u03bb(\u00b5) = L(\u00b5, \u02c6\u02c6\u20d7p)\nL( \u02c6\u00b5, \u02c6\u20d7p)\n(1)\nwhere \u02c6\u02c6\u20d7p is the set of pdf parameters that maximize the likelihood L for the analysed dataset and for\na \ufb01xed value of \u00b5 (conditional Maximum Likelihood Estimators), and ( \u02c6\u00b5, \u02c6\u20d7p) are the values of \u00b5 and\n\u20d7p that maximise the likelihood function for the same dataset (Maximum Likelihood Estimators). The\npro\ufb01le likelihood ratio is used to reject the background only hypothesis (\u00b5 = 0) in the case of discovery,\nand the signal+background hypothesis in the case of exclusion. The test statistic used is q\u00b5 = \u22122ln\u03bb(\u00b5),\nand the median discovery signi\ufb01cance and limits are approximated using expected signal and background\ndistributions, for different mH, luminosities and signal strength \u00b5. The MC distributions, with the content\nand error of each bin reweighted to a given luminosity (in the following referred to as \u201cAsimov data\u201d,\nsee [21]), are \ufb01tted to derive the pdf parameters: in the \ufb01t, mH is \ufb01xed to its true value, while \u03c3H is allowed\nto \ufb02oat in a \u00b120% range around the value obtained from the signal MC distributions. All parameters\ndescribing the background shape are \ufb02oating within sensible ranges. The irreducible background has\nbeen modelled using a combination of Fermi functions which are suitable to describe both the plateau\nin the low mass region and the broad peak corresponding to the second Z coming on shell. The chosen\nmodel is described by the following function:\nf(mZZ) =\np0\n(1+e\np6\u2212mZZ\np7\n)(1+e\nmZZ\u2212p8\np9\n)\n+\np1\n(1+e\np2\u2212mZZ\np3\n)(1+e\np4\u2212mZZ\np5\n)\n(2)\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1264\n\nThe \ufb01rst plateau, in the region where only one of the two Z bosons is on shell, is modelled by the \ufb01rst\nterm, and its suppression, needed for a correct description at higher masses, is controlled by the p8 and\np9 parameters. The second term in the above formula accounts for the shape of the broad peak and the\ntail at high masses. This function can describe with a negligible bias the ZZ background shape with good\naccuracy over the full mass range. The Zb\u00afb contribution is relevant to the background shape only when\nsearching for very light Higgs boson (in this study, only at mH = 120 GeV). In this case, an additional\nterm is added to the ZZ continuum, with a functional form similar to the second part of equation 2. For\nthe signal modelling a simple gaussian shape has been used for mH \u2264300 GeV, while a relativistic Breit-\nWigner formula is needed at higher values of the Higgs boson mass. In Figs. 34 and 35 two examples of\npseudo-experiments with the resulting \ufb01t functions for signal and background are shown.\n [GeV]\n4l\nm\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / ( 4.2 )\n0\n5\n10\n15\n20\n25\n30\n [GeV]\n4l\nm\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / ( 4.2 )\n0\n5\n10\n15\n20\n25\n30\nATLAS\n-1\n L = 30 fb\n\u222b\nFigure 34: A pseudo-experiment corresponding to\n30 fb\u22121 of data for a Higgs boson mass of 130 GeV.\nThe functions \ufb01tting the signal and the background\nare shown.\n [GeV]\n4l\nm\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / ( 4.2 )\n0\n10\n20\n30\n40\n50\n [GeV]\n4l\nm\n100\n150\n200\n250\n300\n350\n400\n450\n500\nEvents / ( 4.2 )\n0\n10\n20\n30\n40\n50\nATLAS\n-1\n L = 30 fb\n\u222b\nFigure 35: A pseudo-experiment corresponding to\n30 fb\u22121 of data for a Higgs boson mass of 180 GeV.\nThe functions \ufb01tting the signal and the background\nare shown.\nThe results presented in the following approximate the signi\ufb01cance from the test statistics as\np\n\u22122ln\u03bb(\u00b5).\nIn order for the results of the method to be valid, the test statistic q\u00b5 = \u22122ln\u03bb(\u00b5) should be distributed\nas a \u03c72 with one degree of freedom. The results obtained with the strategy described above must thus\nbe validated using toy MC. Such validation tests show a good agreement of the test statistic with the\nexpected \u03c72 distribution, as discussed in detail in [21]. This allows to approximate the signi\ufb01cance from\nthe test statistic as\np\n\u22122ln\u03bb(\u00b5). The signi\ufb01cances obtained as the square root of the median pro\ufb01le\nlikelihood ratios for discovery, \u22122ln\u03bb(\u00b5 = 0) are shown in Table 14 for all mH values considered in this\npaper, and for various luminosities. In Fig. 36, the signi\ufb01cance obtained from the pro\ufb01le likelihood ra-\ntio, after the \ufb01t of signal+background is shown. The signi\ufb01cance is compared to the Poisson signi\ufb01cance\nshown in Section 4. The slightly reduced discovery potential is due to the fact that several background\nshape and normalization parameters are derived from the data-like sample.\nConcerning exclusion, the median pro\ufb01le likelihood ratios are calculated under the background only\nhypothesis, and the integrated luminosity needed to exclude the signal at 95% C.L. is the one correspond-\ning to\n\u221a\n\u22122ln\u03bb=1.64. The integrated luminosity needed for exclusion is shown in Fig. 37.\nThe median signi\ufb01cance estimation with Asimov data can be validated using toy MC pseudo-exp-\neriments. For each mass point, 3000 background-only pseudo-experiments are generated. For each\nexperiment, the pro\ufb01le likelihood ratio method is used to \ufb01nd which \u00b5 value can be excluded at 95%\nCL. The resulting distributions are then analysed to \ufb01nd the median and \u00b11\u03c3 and \u00b12\u03c3 intervals. The\noutcome of this test is summarized in Fig. 38, where the 95% CL exclusion \u00b5 obtained from single \ufb01ts\non the full MC datasets is plotted as well. As shown, the agreement is good over the full mass range.\nFitting the 4-lepton mass distribution with all parameters left free in function 2 allows the \ufb01t to absorb\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1265\n\nL\nmH (GeV)\n(fb\u22121)\n120\n130\n140\n150\n160\n165\n180\n200\n300\n400\n500\n600\n1\n0.5\n1.1\n2.0\n2.3\n1.3\n0.7\n0.9\n2.6\n2.3\n1.9\n0.9\n0.6\n2\n0.7\n1.6\n2.8\n3.3\n1.8\n1.0\n1.3\n3.7\n3.2\n2.8\n1.3\n0.8\n5\n1.0\n2.4\n4.5\n5.2\n2.9\n1.6\n2.1\n5.9\n5.1\n4.2\n2.1\n1.2\n10\n1.5\n3.5\n6.3\n7.3\n4.1\n2.2\n2.9\n8.3\n7.2\n6.0\n2.9\n1.8\n30\n2.6\n6.0\n10.9\n12.7\n7.0\n3.8\n5.1\n14.4\n12.7\n10.4\n5.3\n3.3\nTable 14: The signi\ufb01cances obtained from the median pro\ufb01le likelihood ratios for discovery -2ln\u03bb(\u00b5 =\n0), for all Higgs boson masses considered and for various luminosities.\nHiggs mass [GeV] \n100\n200\n300\n400\n500\n600\nSignal significance\n1\n10\nProfile likelihood ratio\nPoisson probability\n-1\n L=30 fb\n\u222b\nATLAS\nFigure 36: Signi\ufb01cance obtained from the pro\ufb01le\nlikelihood ratio, as a function of the Higgs boson\nmass. The result is compared with the one shown\nin Section 4 where systematic errors on signal and\nbackground have not been included, and the signi\ufb01-\ncance has been calculated using Poisson statistics.\nHiggs mass [GeV] \n100\n200\n300\n400\n500\n600\n]\n-1\nLumi for exclusion [fb\n1\n10\nATLAS\nFigure 37: The luminosity needed for exclusion of\nthe Standard Model Higgs boson with the H\n\u2192\nZZ\u2217\u21924l channel alone, as a function of the Higgs\nboson mass.\npossible systematics. Inclusion of systematic effects on mass scale and resolution (see Section 5), and on\nthe knowledge of the reducible background, have a total effect smaller than 4% on the signi\ufb01cance from\nthe \ufb01t.\nIn addition to the baseline method described above, different \ufb01t assumptions have been studied and\nare discussed below for completeness.\nA background-only \ufb01t can be performed using pseudo-experiments corresponding to 30 fb\u22121 of\ndata, including both signal and backgrounds; the function described in formula 2 is used to describe the\nbackground, and the \ufb01t is performed over the full range 110-700 GeV, but in this case all the parameters\napart from the overall normalization are \ufb01xed to the values obtained from a \ufb01t of the full MC statistics\navailable. The signal mass window, de\ufb01ned for each value of the Higgs boson mass as described in\nSection 4, is excluded from the \ufb01t (sideband-\ufb01t), and the expected background in the signal region is\nobtained as the integral of the background function in the signal window. The pseudo-experiments \ufb01ts\nprovide an estimate of background statistical \ufb02uctuations and of possible biases introduced by the \ufb01t,\nthat must be taken into account in the signi\ufb01cance determination. The statistical uncertainty on the\nbackground resulting from the \ufb01t is no more than 6% over the full mass range.\nAnother method based on the sidebands consists of calculating, using the full MC statistics, the ratio\n\u03c4 = BMW\nBSB between the background events in the signal mass window (BMW) and those in the sidebands\n(BSB). In the pseudo-experiments, the background level in the signal mass window is estimated as:\nBMW(i) = \u03c4 \u00d7 Nobs\nSB (i) and the signal as: SMW(i) = Nobs\nMW(i) \u2212BMW(i). The resulting uncertainty on the\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1266\n\n [GeV]\nH\nm\n100\n200\n300\n400\n500\n600\n-1\n at 5fb\n\u00b5\n95% CL exclusion \n0\n0.5\n1\n1.5\n2\nToyMC median\n\u03c3\n 2 \n\u00b1\ntoyMC \n\u03c3\n 1 \n\u00b1\ntoyMC \nAsimov result\nATLAS\nFigure 38: Validation of the median signi\ufb01cance estimation with toy Monte-Carlo experiments. The \u00b5\nvalue corresponding to 95% CL exclusion obtained from Asimov data is compared to the one obtained\nusing the median pro\ufb01le likelihood ratio from the toy MC pseudo-experiments.\nbackground is no more than 5% over the full mass range. The signi\ufb01cance is then obtained, in both\ncases, using the pro\ufb01le likelihood ratio method applied to the case of a counting experiment, assuming\nthe background mean, and statistical error on the background as from the \ufb01t. The results for 130, 150\nand 180 GeV Higgs boson mass are summarized in Table 15. The sideband \ufb01t and the \u03c4-ratio method\nMethod\nBackground\n130\n150\n180\nerror\nGeV\nSideband\nfrom \ufb01t\n6.6\n14.0\n5.9\n\u03c4-ratio\nfrom \u03c4-ratio\n6.7\n14.0\n5.8\nTable 15: The signal signi\ufb01cance for various Higgs boson masses, obtained including the background\nuncertainties from the sideband \ufb01t and the \u03c4-ratio methods.\ncan be used to test the impact of some systematic effects, like the mass scale and resolution in the ZZ\nthreshold region at 180 GeV, and the uncertainties on the reducible Zb\u00afb background. The impact of a\n\u00b11% variation of the energy scale on the signi\ufb01cance from the \ufb01t with all parameters \ufb01xed apart from the\nnormalization is of 21% for a Higgs boson mass of 180 GeV, the most critical region. A \u00b120% variation\nof the mass resolution has a 7% effect on the signi\ufb01cance. Systematics connected to the knowledge\nof the reducible Zb\u00afb background have been tested removing this background from the samples used to\ncalculate the \ufb01t parameters or the \u03c4-ratio, and have been found to be at the level of 8%.\nThe presence of uncertainties in the shape of the m4\u2113distribution at low masses (m4\u2113< 180 GeV)\nand the potential dif\ufb01culty of predicting the shape in this region using the distribution at higher masses\nm4\u2113> 180 GeV, motivate studies where shape information is extracted from restricted \ufb01ts in this low\nmass region. Examples are \ufb01ts in the region from 110 to 170 GeV, where the background is expected\nto have a simple shape. In this range we perform both background-only \ufb01ts excluding the signal region,\nand \ufb01ts including the signal hypothesis, using the pro\ufb01le likelihood method but a simpler background\nparametrization (1st order polynomial). For the background-only \ufb01ts we extract the signi\ufb01cance cal-\nculating the p-value as de\ufb01ned in [21], using the method described in [22]. The extracted signi\ufb01cance\nhas also been calculated throwing large numbers of toy-MC experiments that were used to calculate the\np-value, in order to validate the method of [22]. The background-only \ufb01ts in the 110 to 170 GeV region\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1267\n\ngive a signi\ufb01cance of 5.6\u03c3 for a 130 GeV Higgs boson. When the signal hypothesis is included using the\npro\ufb01le likelihood method, a signi\ufb01cance of 5.8\u03c3 is found. The small increase in the signi\ufb01cance is due\nto the inclusion of the signal hypothesis which renders the statistical test more powerful. These results\nfor the 130 GeV Higgs boson are close to those obtained from the full mass range \ufb01t baseline method\n(Table 14). Independent measurements (e.g. Zb\u00afb background) are expected to provide constraints in the\nknowledge of the background thus improving the discovery potential.\nThe \ufb01tting approach discussed so far involves one-dimensional \ufb01ts of the m4\u2113distribution. This\napproach can be generalized to a global 2D \ufb01t on the (mZ\u2217,m4\u2113) plane. Such 2D \ufb01ts, in contrast to the\nbaseline approach, exploit correlations between mZ\u2217and m4\u2113, after a single set of cuts independent of\nthe Higgs boson mass. Having a single set of cuts allows the extraction of the signal through both \ufb01xed\nand \ufb02oating Higgs boson mass \ufb01ts. The 2D models on the (mZ\u2217,m4\u2113) plane, have been obtained for the\nZZ and Zb\u00afb backgrounds. All available signal samples (for masses from 120 to 600 GeV) have been\nused to develop a one-parameter family of surfaces (the parameter being mH) that adequately models\nthe signal for any intermediate value of the true Higgs boson mass. Table 16 summarizes the expected\nsigni\ufb01cance as a function of mH, for both \ufb01xed and \ufb02oating Higgs boson mass window \ufb01ts, and an\nintegrated luminosity of 30 fb\u22121. These results are obtained using toy MC pseudo-experiments using a\nmedian likelihood ratio for the \ufb01xed mass case, and a p-value for the \ufb02oating mass case, as described\nin [21]. The signi\ufb01cances shown in the \ufb01rst row of Table 16 are consistent with the corresponding results\nof the baseline analysis shown in Table 14.\nMass (GeV)\n120\n130\n140\n150\n160\n2D \ufb01t Fixed Higgs boson Mass\n2.0\n6.3\n11.6\n14.0\n8.3\n2D \ufb01t Floating Higgs boson Mass\n1.1\n5.6\n10.9\n13.2\n7.5\nTable 16: Median signi\ufb01cance from a 2D global \ufb01t on the (mZ\u2217,m4\u2113) plane for both \ufb01xed and \ufb02oating\nHiggs boson mass window and an integrated luminosity of 30 fb\u22121.\n7\nSummary and conclusion\nThe potential of ATLAS in observing the Higgs boson in its H \u2192ZZ\u2217\u21924\u2113decay mode was presented.\nFor an integrated luminosity of 30 fb\u22121, ATLAS will discover the Higgs boson in the 4\u2113channel-alone\nin the mass range from 130 \u2212500 GeV, with the exception of the region around 160 GeV of the WW\nturn on, where signi\ufb01cances of about 4\u03c3 were found. In the very low mass region of 120 GeV, just\nabove the LEP limit, a signi\ufb01cance close to 3\u03c3 is expected: this is a strong contribution to the combined\nsigni\ufb01cance of the various Standard Model decay modes [21]. The H \u2192ZZ \u21924\u2113channel is highly\nsensitive in the high mass region (400 GeV > m4\u2113> 200 GeV), and in the 150 GeV region, where the\nHiggs boson should be discovered with 5 fb\u22121.\nThe results obtained in this work include studies of the effect of systematic uncertainties on the\nsignal extraction. In parallel to these studies, several attempts to improve the sensitivity of the channel\nby increasing the signal yield and keeping the same level of background were performed. Examples are\nthe relaxing of the lepton-id criteria for one of the four leptons, the use of calorimeter for muon tagging,\nand application of multivariate techniques. Although the \ufb01rst results are encouraging, these studies are\nbeyond the scope of this note since they are still in their very early stages.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1268\n\nReferences\n[1] http://lepewwg.web.cern.ch/LEPEWWG/.\n[2] The ALEPH, DELPHI, L3 and OPAL Collaborations, Search for the Standard Model Higgs Boson\nat LEP, 2003, CERN-EP/2003-011.\n[3] Geant4 Collaboration, Geant4 - A simulation toolkit, Nuclear Instruments and Methods in Physics\nResearch Section A 506 (2003) 250-303.\n[4] Lampl, W.; Laplace, S.; Lechowski, M.; Rousseau, D.; Ma, H.; Menke, S.; Unal, G., Digitization\nof LAr Calorimeter for CSC simulations, ATL-LARG-PUB-2007-011.\n[5] Rebuzzi, D.; Assamagan, K.A.; Di Simone, A.; Hasegawa, Y.; Van Eldik, N.,\nGeant4 Muon\nDigitization in the ATHENA Framework, ATL-SOFT-PUB-2007-001.\n[6] Baranov, S.; Bosman, M.; Dawson, I.; Hedberg, V.; Nisati, A.; Shupe, M., Estimation of Radiation\nBackground, Impact on Detectors, Activation and Shielding Optimization in ATLAS, CERN-ATL-\nGEN-2005-001 (2005).\n[7] B. Kersevan et al., CSC note on Monte-Carlo, This volume.\n[8] T. Sjostrand, et al., Comput. Phys. Commun. 135 (2001) 238\u2013259.\n[9] The ATLAS Collaboration, Introduction on Higgs Boson Searches, this volume.\n[10] S. Frixione and B.R. Webber, The MC@NLO event generator, 2002, hep-ph/0207182.\n[11] B. Kersevan and E. Richter-Was, The MonteCarlo Event Generator AcerMC 2.0 with Interfaces to\nPYTHIA 6.2 and HERWIG 6.5, 2004, hep-ph/0405247.\n[12] G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M.H. Seymour\nand B.R. Webber, Herwig 6.5, JHEP 0101 (2001) 010 [hep-ph/0011363]; hep-ph/0210213.\n[13] J.M. Butterworth, Jeffrey R. Forshaw, M.H. Seymour, Multiparton interactions in photoproduction\nat HERA, Z.Phys.C72:637-646,1996..\n[14] J. Campbell, R.K. Ellis, F. Maltoni, S. Willenbrock, Phys. Rev. D 73:054007 (2006).\n[15] R. Goncalo et al.,\nOverview of the High-Level Trigger Electron and Photon Selection for the\nATLAS Experiment at LHC, CERN-ATL-DAQ-CONF-2005-036.\n[16] Muon Trigger Group, The Muon Trigger Slice, 2007, ATLAS Note ATL-PUB-MUON-2007-0.\n[17] The ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[18] The ATLAS Collaboration, Calibration and Performance of the Electromagnetic Calorimeter, this\nvolume.\n[19] ATLAS Muon Collaboration, ATLAS Muon TDR, 1997, CERN/LHCC/97-22.\n[20] S. Hassani et al.,\nA muon identi\ufb01cation and combined reconstruction procedure for the AT-\nLAS detector at the LHC using the (Muonboy, STACO, Mutag) reconstruction packages, 2007,\nNucl.Instrum.Meth.A572:77-79,2007.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1269\n\n[21] The ATLAS Collaboration, Statistical Combination of Several Important Standard Model Higgs\nBoson Search Channels, this volume.\n[22] S. Paganis, D.R. Tovey, Background and Signal Estimation for a low mass Higgs Boson at the\nLHC, Eur. Phys. Journal C, 10.1140/epjc/s10052-008-0637-z, 2008.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL H \u2192ZZ\u2217\u21924l\n1270\n\nSearch for the Standard Model Higgs Boson via Vector Boson\nFusion Production Process in the Di-Tau Channels\nAbstract\nWe outline a search for the Standard Model Higgs boson decaying into a \u03c4-\npair in association with two jets, which is produced dominantly by the Vector\nBoson Fusion (VBF) process. The results indicate signi\ufb01cant potential for a\ndiscovery in the low mass range. We consider fully leptonic, semi-leptonic,\nand, for the \ufb01rst time, fully hadronic tau decays. Mass reconstruction, central-\njet veto, and jet tagging are discussed, and we present an approach to estimate\nthe background from the data. Additional emphasis has been given to trigger\nissues and the impact of pileup. The results are based on an improved detector\ndescription, including misalignments, the most recent reconstruction software,\nand modern Monte Carlo event generators, including a revised prediction of\nthe underlying event activity.\n1\nIntroduction\nThe search for the Higgs boson and the source of electroweak symmetry breaking is a primary task of the\nLarge Hadron Collider (LHC). It has been shown [1] that the ATLAS detector is capable of discovering\nthe Standard Model Higgs boson with masses ranging from the LEP limit of 114 GeV [2] to about\n1 TeV. The low-mass region is preferred from electroweak precision measurements and in this region\n(mH < 130 GeV) the searches for Higgs bosons decaying to taus and photons are the most promising\nfor discovery [3\u20135]. Searches for the Higgs boson produced in Vector Boson Fusion (VBF) tend to have\nreasonably high signal-to-background ratios, making them more robust to systematic uncertainties.\nWithin the Standard Model, the ability to observe the Higgs boson in multiple production and decay\ncon\ufb01gurations makes it possible to measure the Higgs boson coupling to fermions and vector bosons [6].\nFurthermore, the VBF processes provide a tool for measuring the Higgs boson spin and CP properties [7,\n8]. In the context of the Minimal Supersymetric Standard Model, (MSSM), the branching ratio of a\nHiggs boson decaying to photons is generally suppressed, which makes the search for Higgs boson\ndecaying to taus very important. The complementarity of the coupling of the light and heavy CP-even,\nneutral Higgs bosons of the MSSM to taus makes it possible to cover most or all of the mA \u2212tan\u03b2 plane\nby reinterpreting the results for a Standard Model Higgs boson decaying into taus in the context of the\nMSSM [9,10].\nA previous ATLAS analysis outlined the sensitivity to a low mass Higgs boson including the \ufb01rst\nestimates for the VBF channels [4]. These results were primarily based on a fast simulation that parame-\nterized the results of key detector performance studies performed with a full GEANT simulation. In this\nnote we have considered three decay modes: the lepton-lepton (ll-channel), lepton-hadron (lh-channel)\nand the hadron-hadron (hh-channel) from VBF H \u2192\u03c4+\u03c4\u2212signature. The analysis has been done using\nstate-of-the art Monte Carlo generators, full GEANT-based simulation of the ATLAS detector with re-\nalistic misalignments and distortions applied to the expected material in the detector, utilization of our\ncurrent reconstruction algorithms, and, where possible, incorporation of pileup interactions.\nThis analysis requires excellent performance from every ATLAS detector subsystem; the presence\nof \u03c4 decays implies \ufb01nal states with electrons, muons, hadronic tau decays, and missing transverse\nmomentum, while the Vector Boson Fusion production process introduces jets that tend to be quite\nforward in the detector. Due to the small rate of signal production and large backgrounds, particle\nidenti\ufb01cation must be excellent and optimized speci\ufb01cally for this channel. Furthermore, triggering relies\n1271\n\non the lowest energy lepton triggers or exceptionally challenging tau trigger signatures. The detector\nperformance aspects so important to this analysis are described in Refs. [11\u201319].\n1.1\nMonte Carlo samples\nEstimating the sensitivity of ATLAS to this channel requires the state of the art in Monte Carlo tools.\nThe most challenging aspect of the theoretical calculations is the description of jet activity, an area in\nwhich the tools have evolved substantially since ATLAS \u2019 \ufb01rst publication on the sensitivity to the VBF\nprocesses. Details of the Monte Carlo samples are outlined in Ref. [20]. The signal samples were pro-\nduced with HERWIG [21] and PYTHIA [22]. The QCD Z+jets and W+jets samples were produced\nwith ALPGEN [23], which employs the MLM matching [24] between the hard process (calculated with\na leading-order matrix element for up to 5 jets) and the parton shower of HERWIG. The electroweak\n(ELWK) Z+jets background was simulated with SHERPA [25]. The t\u00aft+jets and diboson background\nsamples were generated with MC@NLO [26]. In all processes with taus, the tau decay was simulated\nusing TAUOLA [27]. Additional photon radiation from charged leptons was simulated with PHO-\nTOS [28]. The production cross-section for the signal is based on the next-to-leading order (NLO)\ncomputation and the k-factor (the ratio of the cross-section to that predicted by the lowest order calcu-\nlation) is around 5% in the target mass range of 100\u2212150 GeV. Note that the k-factor only involves the\nQCD corrections.\nBecause the GEANT-based detector simulation is computationally intensive, an event \ufb01lter was ap-\nplied to each sample after the parton shower and hadronization. Most processes were required to have\nat least one lepton in the \ufb01nal state. For background processes a VBF \ufb01lter was used to remove events\nthat would fail jet-related requirements. The \ufb01lter bias has been studied and well-validated, but it affects\nour ability to estimate background rates early in the analysis cut \ufb02ow. Furthermore, a signi\ufb01cant Monte\nCarlo sample was produced with the ATLAS fast simulation, ATLFAST [29], without any event \ufb01lter.\nThese ATLFAST samples are used for systematic studies and to aid in the estimation of background\nrates (see Section 3.4).\nThe effect of in-time pileup (i.e. other soft p-p collisions in the same bunch crossing), out-of-\ntime pileup (i.e. p-p collisions in neighboring bunch crossings), and the underlying event (i.e. multi-\nparton scattering and soft activity in the p-p collision of interest) are all important to this analysis.\nThe underlying event has substantial theoretical uncertainty, and different models\u2019 predictions for the\nunderlying event activity vary by large factors when extrapolating to the LHC energy range. Fortunately,\nthe underlying event activity will be one of the \ufb01rst measurements at the LHC and will be well measured\nby the time the analysis described in this Note is performed. The pileup interactions are incorporated\nearly in the simulation chain, at the time when the detector readout is simulated.\n2\nEvent selection\n2.1\nTriggering\nWhile the ATLAS trigger system provides several possibilities for triggering that take advantage of\nthe signal\u2019s complex \ufb01nal state, we restrict ourselves here to simple robust trigger signatures that are\nexpected to have a low rate and an acceptable selection ef\ufb01ciency [12,13]. For the lh and ll \ufb01nal states\nthe events are selected by an isolated electron with pT \u226522 GeV (e22i) or an isolated muon with pT \u2265\n20 GeV (mu20). The entire trigger chain has been simulated with the use of our current trigger algorithms\nand trigger menus; however, the dilepton triggers composed of isolated muons with pT \u226510 GeV and\nisolated electrons with pT \u226515 GeV considered in Ref. [4] were not used in this study. The trigger\nef\ufb01ciency for VBF H \u2192\u03c4\u03c4 (with mH = 120 GeV) is 9.0% for events selected by the electron trigger and\n9.9% in the case of muons. The trigger ef\ufb01ciencies include detector acceptance and are normalized with\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1272\n\nTable 1:\nThe product of ef\ufb01ciency and acceptance for the signal from the e22i, mu20,\nandL1 TAU30 xE40 softHLT triggers.\nTrigger menu\nEf\ufb01ciency \u00d7 Acceptance(%)\ne22i\n9.08 \u00b1 0.03\nmu20\n9.88 \u00b1 0.04\nL1 TAU30 xE40 softHLT\n3.67\u00b10.02\nrespect to the production cross-section for VBF H \u2192\u03c4\u03c4. Additional triggers for the lh and ll \ufb01nal states,\nfor instance the combined \u03c4 +e or \u03c4+\u00b5 triggers and triggers which take advantage of the tagging jets of\nthe VBF process, are under study.\nThe all hadronic mode, or hh-channel, utilizes a different triggering strategy. Unlike the clean sig-\nnature of the electron and muon triggers, the single tau trigger is expected to be exposed the large QCD\njets background. Therefore only tau trigger in combination with other signatures, like missing ET or\nanother tau in the event, can be considered. We use L1 TAU30 xE40 softHLT as the primary trigger\nmenu for the hh-channel in this study. It should be noted that unlike the high pT single lepton triggers,\nboth the hadronic tau and Emiss\nT\ntriggers are based on requirements from the \ufb01rst level of the trigger\nsystem with only a loose selection in the high-level trigger [30]. The expected trigger acceptance of\nL1 TAU30 xE40 softHLT is listed in Table 1 as well as those from e22i and mu20 menus. The trigger\nef\ufb01ciency for the signal events (for mH = 120 GeV) is 3.7% for L1 TAU30 xE40 softHLT. The disad-\nvantage of the missing ET trigger is the relatively low ef\ufb01ciency on signal; therefore, alternative menus\nlike double tau menus are now being developed.\n2.2\nElectron and muon reconstruction and identi\ufb01cation\nElectron candidates are formed from a cluster of cells in the electromagnetic calorimeter together with a\nmatched track. The electron identi\ufb01cation includes information from the shape of the shower, tracking\ninformation, and the consistency of the track and cluster. ATLAS provides multiple working points\nthat trade electron ef\ufb01ciency for improved rejection of fakes. In this analysis we use the Medium class\nelectron as it provides suf\ufb01cient fake rejection and provides a higher signal ef\ufb01ciency. In addition to\nthe standard electron identi\ufb01cation, we require that the energy in an isolation cone of radius \u2206R = 0.2\naround the electron contains less than 10% of the electron\u2019s ET 1. The isolation cut is imposed to reject\nthe contamination from hadronic jets.2 The reconstruction and identi\ufb01cation ef\ufb01ciency is fairly \ufb02at after\npT \u226515 GeV, where it achieves 69.4 \u00b1 0.2% ef\ufb01ciency while keeping the fake electron contamination\nat the order of 0.1%. In the VBF H \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 +4\u03bd signal sample, the probability to reconstruct a fake\nelectron was found to be slightly higher, 0.25\u00b10.03%, re\ufb02ecting some level of process-dependence.\nIn ATLAS, muon candidates can be seeded from either tracks in the inner detector or in the stand-\nalone muon spectrometer. In this analysis we required the highest quality muon candidates, which are\nformed by extrapolating the track in the muon spectrometer to the interaction point, \ufb01nding a matching\ninner detector track, and forming a combined track if the two tracks satisfy various quality require-\nments [15]. The muon identi\ufb01cation is composed of requirements on track quality and hit multiplicity\nin several muon stations. Similarly to the electrons, we require an isolation condition that the summed\nET within a radius \u2206R of 0.2 is less than 10% of the muon pT to reject the contamination from jets. The\nreconstruction and identi\ufb01cation ef\ufb01ciency is fairly \ufb02at after pT \u226510 GeV, and it achieves 91.9 \u00b1 0.1%\nwhile keeps the fake muon rejection under 0.005%.\n1Due to a problem with the reconstruction, a correction to the isolation energy in the Tile gap scintillator was required.\n2A track-based isolation requirement was also studied and shown to have similar performance.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1273\n\nThe electron and muon identi\ufb01cation criteria are summarized in Table 2. The pT thresholds for\nelectron and muon identi\ufb01cation are chosen to provide stable identi\ufb01cation ef\ufb01ciency and suf\ufb01cient fake\nrejection. In addition, we require that the pT of the of\ufb02ine reconstructed lepton must satisfy the pT\nthresholds of the corresponding trigger, which is not strictly enforced due to subtle differences between\nthe of\ufb02ine reconstruction and the trigger algorithms.\nTable 2: Summary of the identi\ufb01cation requirements for electrons and muons.\nLepton identi\ufb01cation\nElectron ID: Medium\nIsolation ET(\u2206R = 0.2)/pT \u22640.1\npT \u226525 GeV for trigger electron (e22i)\npT \u226515 GeV for other electrons\nMuon ID: Combined muon\nIsolation ET(\u2206R = 0.2)/pT \u22640.1\npT \u226520 GeV for trigger muon (mu20i)\npT \u226510 GeV for other muons\n2.3\nHadronic-tau reconstruction and identi\ufb01cation\nApproximately 65% of tau leptons decays produce hadrons. The majority of hadronic tau decays are\ncomposed of single-prong candidates with one charged pion, which provides a track and a hadronic\nshower, and potentially associated neutral pions that provide an additional electromagnetic sub-cluster.\nIn addition, three-prong tau decays are also reconstructed, but with a higher rate of fakes from QCD\njets. Due to the high momentum of the taus produced in this process, the decay products are collimated\ninto a narrow region. ATLAS currently employs two hadronic tau reconstruction algorithms [31]; both\nrequire a calorimeter cluster matching a track; however, one algorithm is seeded by calorimeter clusters\nand the other is seeded by the track. The two algorithms\u2019 ef\ufb01ciencies are complementary in different pT\nregimes, and provide rejection strategies for their energy measurement and rejection against jets. The\ncalorimeter-seeded algorithm was used for this analysis.\nThe calorimeter-seeded algorithm provides a log-likelihood ratio that distills discriminating power\nfrom a variety of track quality and shower shape information to discriminate between taus and jets [14].\nThe discriminating variable is designed to maintain a high tau ef\ufb01ciency while rejecting fake tau candi-\ndates from jets, leaving the precise working point to be optimized in the context of a speci\ufb01c analysis.\nThe cuts on the discriminating variable and pT of the tau candidates were optimized with respect to a\nsimple s/\n\u221a\ns+b performance measure. The background sample included Z+jets, W+jets, and t\u00aft+jets,\nwhich comprises a background sample with a representative mixture of real and fake taus. Our model-\ning of the jet fragmentation indicates that quark-initiated jets are more collimated and have a 6-8 times\nhigher fake rate than gluon-initiated jets. The relative abundance of real and fake tau candidates depends\non the kinematic requirements imposed on the sample, thus the optimization should be performed after\nthe \ufb01nal kinematic requirements described in Sections 2.8 and 2.9. However, the limited size of Monte\nCarlo samples requires that only a subset of the criteria used in the \ufb01nal event selection are applied dur-\ning the optimization. Several subsets of the \ufb01nal event selection criterion were evaluated, and the \ufb01nal\noptimization was found to be reasonably stable and nearly independent of pT. After the optimization, the\ncalorimeter-seeded algorithm\u2019s log-likelihood ratio was required to be greater than 4, corresponding to\nan identi\ufb01cation ef\ufb01ciency of 50.0\u00b10.2% and a fake jet selection ef\ufb01ciency of \u223c1% for gluon-initiated\njets and \u223c2.5% for quark-initiated jets.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1274\n\n(GeV)\nT\np\n0\n20\n40\n60\n80\n100 120 140\n\u03b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H\n+jets\n-\u03c4\n+\n\u03c4\n\u2192\nZ\ntt\nATLAS\n(GeV)\nT\np\n0\n20\n40\n60\n80\n100 120 140\n\u03b5\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\nQCD di-jet\n+jets\n\u03bd\n\u00b5\n\u2192\nW\n+jets\n-\n\u00b5\n+\n\u00b5\n\u2192\nZ\ntt\nATLAS\n(a)\n(b)\nFigure 1: Reconstruction and identi\ufb01cation ef\ufb01ciency of the hadronic tau (a) and the jet-fake rejection\nef\ufb01ciency (b) as a function of pT, respectively.\nIn addition to rejection against jets, an electron-veto was used to reject tau candidates which arise\nfrom electrons that have failed the electron identi\ufb01cation. This electron-veto was performed by requiring\nthat the tau candidate have at least 0.2% of its energy in the \ufb01rst sampling of the hadronic calorimeter and\nthat the ratio of high-threshold (HT) to low-threshold (LT) hits in the transition radiation tracker (TRT)\nbe less than 20% in the range |\u03b7\u03c4| < 1.7. This electron-veto procedure suppresses the electron fake rate\nby 82.5% while retaining 90% of the hadronic tau candidates selected without the veto.\nFinally, we present the hadronic tau reconstruction and identi\ufb01cation performance in Fig. 1 (a) and\nthe fake-jet tagging rate (b) as a function of pT, respectively. The selection criteria for the hadronic tau\nidenti\ufb01cation is summarized in Table 3.\nTable 3: Selection criteria for the hadronic tau identi\ufb01cation from the calorimeter-seeded recon-\nstruction algorithm.\nHadronic tau identi\ufb01cation\nTau ID: Calorimeter-seeded\npT \u226530 GeV\nTrack multiplicity : 1 or 3 tracks\n|charge| = 1\nLog Likelihood Ratio \u22654\nElectron Veto:\nminimum TRT HT/LT\u22640.2 if |\u03b7\u03c4|\u22641.7 and LT\u226510\nEHAD\nT\n/pT\u22650.002 in matched electron object\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1275\n\n2.4\nJet reconstruction\n2.4.1\nForward tagging jets\nThe jet activity of the vector boson fusion process is unique in several ways, providing many handles\nto suppress backgrounds and isolate a sample of signal events with high purity. The most important\nfeatures of the VBF process are the presence of two high-pT quark-initiated \u201ctagging jets\u201d, which tend\nto be relatively forward and well separated in rapidity. Furthermore, due to color coherence in this elec-\ntroweak process, additional QCD radiation between the tagging jets tends to be suppressed and motivates\na Central Jet Veto (CJV) [32]. This section outlines the choice of jet algorithms and their performance,\nthe de\ufb01nition of the tag jets, and several issues related to the CJV.\nFigure 2 shows the \u03b7 spectra of the highest and second highest pT jets in signal and various back-\nground samples. Because the VBF jets can be very forward, the jet \ufb01nding ef\ufb01ciency in this region is\nimportant in the analysis. Furthermore, the forward calorimeters (3.1\u2264|\u03b7| \u22644.9) do not have a pro-\njective geometry, which leads to different challenges for jet reconstruction. ATLAS currently provides\ncollections of jets based on two algorithms (a seeded cone algorithm with split-merge and a kT algo-\nrithm), each with two sets of parameters (the cone size and the kT cutoff scale), applied to two different\ninput representations of the energy deposits in the calorimeter (towers merged to avoid negative energy\n\ufb02uctuations from electronic noise and clusters based on the ATLAS TopoCluster algorithm) [18]. These\ndifferent jet algorithms and the different calorimeter pre-clustering result in different performances for\njets, especially at low pT and high |\u03b7|.\nJet identi\ufb01cation ef\ufb01ciency and purity are de\ufb01ned to give a quantitative measure of the jet identi\ufb01ca-\ntion. The ef\ufb01ciency and purity were calculated with respect to generator-level jets obtained by running\nthe same jet algorithm on the stable interacting particles after hadronization and before GEANT simula-\ntion. To ensure that only hadronic jets are considered, we only use dimuon events, where both taus decay\ninto a muon and neutrinos, or Z/W bosons directly decay into muons. This avoids any bias in the jet\nreconstruction produced by the presence of electrons. A reconstructed jet is considered to be matched if\nthe corresponding generator-level jet is within \u2206R \u22640.15 for jets with a cone size of 0.4. The matching\ncone size was chosen to avoid a single generator-level jet being matched to more than one reconstructed\njet; with the given parameters this effect is at the order of 10\u22123.\nThe jet reconstruction ef\ufb01ciency in different |\u03b7| regions and two different clustering algorithms is\nshown in Fig. 3 as a function of the generator-level jet pT and \u03b7. The reconstruction ef\ufb01ciency rises\nover 95% for jets with pT above 50 GeV. On the other hand, the ef\ufb01ciency drops at |\u03b7| \u223c1.5 and |\u03b7|\n\u223c3.2 for jets in the range of 20-30 GeV of pT. This drop in ef\ufb01ciency is due to the crack region in the\ncalorimeter or large amounts of dead material in the corresponding \u03b7 region. The jet collections based\non calorimeter towers show a drop in ef\ufb01ciencies in the forward region due to a higher seed threshold,\nwhile the jet collections based on TopoClusters do not show this loss of ef\ufb01ciency. For this reason, jets\nbased on TopoClusters have been chosen for this analysis.\nCorrectly identifying the quark-initiated tagging jets from the VBF process is very important for\nthe measurement of Higgs boson spin and CP properties and for making precise correspondence with\ntheoretical calculations [8]. Typically, the tagging jets are found in opposite hemispheres, but there are\ntwo approaches to incorporating this requirement in the analysis. One option is to de\ufb01ne the tagging jets\nas the two highest pT jets in the event, and reject the event from the signal candidates if they are in the\nsame hemisphere (e.g. require \u03b7j1 \u00d7\u03b7 j2 \u22640). A second option is to de\ufb01ne the \ufb01rst tagging jet to be the\nhighest pT jet in the event and the second tagging jet to be the highest pT jet in the opposite hemisphere.\nIn this second approach it is not required that the second tagging jet is the second highest pT jet in the\nevent. These two strategies were compared, and it was found that the \ufb01rst method more reliably matched\nthe quark-initiated tagging jets from the hard process.\nThe generator-level jets match the hard-scattered quarks nearly 100% of the time above a certain\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1276\n\n\u03b7\n-5 -4\n-3 -2\n-1\n0\n1\n2\n3\n4\n5\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n\u00b5\n\u00b5\n \n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\n) +jets\n\u00b5\n\u00b5\n\u2192\nZ(\n) +jets\n\u00b5\n\u00b5\n\u2192\n(tt\nATLAS\n\u03b7\n-5 -4\n-3 -2\n-1\n0\n1\n2\n3\n4\n5\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n\u00b5\n\u00b5\n \n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\n) +jets\n\u00b5\n\u00b5\n\u2192\nZ(\n) +jets\n\u00b5\n\u00b5\n\u2192\n(tt\nATLAS\n(a)\n(b)\nFigure 2: Pseudorapidity of the highest pT (a) and the second highest pT (b) jets for the Cone jet al-\ngorithm based on TopoClusters with R = 0.4 in VBF H \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 (mH=120 GeV) and background\nevents. Only pT cuts were applied to jets. Solid (black) histogram is for signal, dashed (red) histogram\nis for t\u00aft \u2192WW \u2192(\u00b5\u00b5), and dotted (blue) histogram is for Z\u2192\u00b5\u00b5+n jets.\n(GeV)\nT\np\n10 20 30 40 50 60 70 80 90 100 110\n\u03b5\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n ll\n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\nForward jet (TopoC4)\nCentral jet (TopoC4)\nATLAS\n\u03b7\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n\u03b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n ll\n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\nTopo C4 jet\nTower C4 jet\nATLAS\n(a)\n(b)\nFigure 3:\nJet reconstruction ef\ufb01ciency for the Cone jet algorithm with R = 0.4 as a function of the\ngenerator-level jet pT for the jets based on TopoClusters (a) and \u03b7 for Tower- and TopoCluster-based jets\n(b).\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1277\n\npT threshold. To estimate the purity of the tagging jets, we de\ufb01ne the ef\ufb01ciency with respect to the\ngenerator-level jets. The reconstructed tag jets have a high purity over the entire pT and \u03b7 range and\ndo not show a strong dependence on the jet algorithms. Integrated ef\ufb01ciencies and purities for jets with\npT \u226520 GeV indicate that the TopoCluster-based algorithm has better performance for this analysis.\nBecause additional jets often lie in the central detector region, where we wish to employ a central jet\nveto, jets with smaller cones are favored for the selection. Furthermore, calorimeter noise (including\neffects from pileup of minimum-bias events) increases with jet cone radius. Thus, we use the cone jet\nalgorithm with R = 0.4 running on TopoClusters as the primary jet algorithm in this analysis.\nHaving converged on a speci\ufb01c calorimeter pre-clustering and jet algorithm, we now present the\nkinematic properties of the jets that discriminate between the signal and backgrounds. The pT cuts on\nthe tagging jets are effective at reducing several backgrounds and Fig. 2 shows that the pseudorapidity\ndistributions are substantially different. Instead of relying directly on the pseudorapidity of the tagging\njets, Fig. 4 shows that the pseudorapidity gap (a) and invariant mass of the two tagging jets (b) provide\nsubstantial background rejection.\njj\n\u03b7\n\u2206\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\n\u00b5\n\u00b5\n \n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\n) +jets\n\u00b5\n\u00b5\n\u2192\nZ(\n) +jets\n\u00b5\n\u00b5\n\u2192\n(tt\nATLAS\n (GeV)\njj\nM\n0\n500\n1000\n1500\n2000\n2500\nArbitrary Units\n-3\n10\n-2\n10\n-1\n10\n\u00b5\n\u00b5\n \n\u2192\n-\u03c4\n+\n\u03c4\n\u2192\nVBF H(120)\n) +jets\n\u00b5\n\u00b5\n\u2192\nZ(\n) +jets\n\u00b5\n\u00b5\n\u2192\n(tt\nATLAS\n(a)\n(b)\nFigure 4: Pseudorapidity gap between tag jets (a) and invariant-mass distributions of tag jets (b) in VBF\nH \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 events (mH=120 GeV). A requirement \u03b71 \u00d7\u03b72 \u22640 is used in addition to the cuts on jet\npT. Solid (black) histogram is for signal, dashed (red) histogram is for t\u00aft \u2192WW \u2192(\u00b5\u00b5), and dotted\n(blue) histogram is for Z\u2192\u00b5\u00b5+n jets.\n2.4.2\nCentral jet veto\nAs mentioned above, the color coherence in the VBF Higgs boson production leads to a suppression of\nQCD radiation between the tagging jets. This color coherence is also found in the electroweak Z+jets\nbackground. In contrast, most of the other backgrounds have a much larger probability for additional\nQCD radiation in the central region. This is the physical motivation for a central jet veto (CJV). Figure 5\nshows the jet multiplicity distribution for the signal and backgrounds after requiring two tagged jets (with\npT \u226520 GeV) in opposite hemispheres. The fraction of signal events with three or more jets is small.\nThe experimental challenge for the CJV is to provide a cut that is robust against additional minimum\nbias events (in-time pileup events). The optimization for the central jet veto has been studied in terms\nof pT and \u03b7. The probability to have at least one reconstructed jet with pT \u226520 GeV within |\u03b7| \u22643.2\nis 1.6% from a single minimum-bias event. In Fig. 6, we present the trade-off of background rejection\nversus signal ef\ufb01ciency from varying the pT threshold on the third highest pT jet (markers indicate\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1278\n\nthresholds of 20 and 30 GeV). A veto based on a \ufb01xed \u03b7-window was compared to a dynamic \u03b7-\nwindow de\ufb01ned by the \u03b7 of the two tagging jets. We maintain the previous central jet veto requirement:\nno jets in |\u03b7| \u22643.2 with pT \u226520 GeV. Figure 7 shows the ef\ufb01ciency of the central jet veto for signal,\nirreducible, and reducible backgrounds at varying levels of pileup.\nThe CJV poses signi\ufb01cant theoretical challenges as well. At the parton-level, the CJV ef\ufb01ciency is\nexpected to be known quite well with little theoretical uncertainty. However, the current tools that allow\nfor the full parton-shower and hadronization (prerequisite for an analysis based on a GEANT-based\ndetector simulation) show signi\ufb01cant uncertainties. We have observed signi\ufb01cant differences between\nthe central jet activity in signal events generated with PYTHIA and those generated with HERWIG.\nKnowledge of the uncertainty on the CJV is needed for setting limits on the Higgs boson cross-section\nand for making coupling measurements; however, it is not needed directly in establishing a deviation\nfrom the background-only expectation (see Section 5.3).\nIn future studies we will also include a veto procedure using track information; in particular using\nvertexing information to reduce the impact of jets from in-time pileup. Furthermore, a track-based veto\nand the use of timing information in the calorimeter will also be studied to reduce the impact of out-of-\ntime pileup.\nNumber of jets\n0\n1\n2\n3\n4\n5\n6\n7\n8\nArbitrary Units\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nATLAS\n-l\nl \n\u2192\n-\u03c4\n+\n\u03c4 \n\u2192\nVBF H(120) \n) +jets\n-\u03c4\n+\n\u03c4\n\u2192\nZ(\ntt\nFigure 5: Jet multiplicity distribution for the sig-\nnal, Z+jets, and t\u00aft background after requiring the\ncuts up to the N jets \u22652 level in the list of cuts for\nthe ll channel (see Table 5).\nsignal\n\u03b5\n0.2\n0.4\n0.6\n0.8\n1\nbackground\n\u03b5\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n|<3 2\n\u03b7\n3rd jet in |\n Without pile-up\n-1\ns\n-2\ncm\n33\n L = 10\nt\n Only t\n3rd jet between VBF jets\n Without pile-up\n-1\ns\n-2\ncm\n33\n L = 10\nt\n Only t\n30 GeV\n20 GeV\n20 GeV\n30 GeV\nFigure 6: Background rejection versus signal sen-\nsitivity for the central jet veto with and without\npileup. Also shown is the case for t\u00aft-only back-\nground.\n2.4.3\nb-jet veto\nIn the ll-channel, the largest background contribution comes from t\u00aft(+jets) \u2192l\u03bdbl\u03bdb(+jets). By\nintroducing a veto on b-tagged forward jets it is possible to reduce this background [19]. Because the\ntagging jets are fairly forward in the detector, the b-tagging requirement is rather loose, i.e. ef\ufb01cient,\nand the t\u00aft background can be reduced by a factor 2\u223c3. Figure 8 demonstrates the ef\ufb01ciency of the b-jet\nveto as a function of the forward jet pT for the signal and t\u00aft background. The cut on the b-tag weight\nwas optimized to achieve 65.1% reconstruction ef\ufb01ciency for b-quark jets, while 9.4% mis-identi\ufb01cation\nef\ufb01ciency for the light \ufb02avor jets is retained. Note that the b-jet veto is only used in the ll-channel.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1279\n\n)\n-1\ns\n-2\nLuminosity(cm\nno pileup\n33\n10\n33\n2x10\nno pileup\n33\n10\n33\n2x10\n\u03b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nVBF H (lh-channel)\nVBF H (ll-channel)\n (lh-channel)\n\u03c4\n\u03c4\n\u2192\nZ\n (ll-channel)\n\u03c4\n\u03c4\n\u2192\nZ\n (lh-channel)\ntt\n (ll-channel)\ntt\nATLAS\nFigure 7: Central jet veto performance in the pres-\nence of varying levels of pileup for signal and back-\nground samples.\n(GeV)\nT\np\n0\n50\n100 150 200 250 300 350 400\n\u03b5\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nll\n\u2192\n\u03c4\n\u03c4\n\u2192\nH(120)\ntt\nFigure 8:\nEf\ufb01ciency of the b-jet veto as a func-\ntion of the forward jet pT in for the signal and t\u00aft\nbackground.\n2.5\nMissing transverse energy\nSigni\ufb01cant missing transverse energy (Emiss\nT\n) is present in H \u2192\u03c4+\u03c4\u2212events because neutrinos are\nalways associated with the \u03c4 decays. The performance of the Emiss\nT\nalgorithm plays a vital role in this\nanalysis because Emiss\nT\nis used in the mass reconstruction of the tau pair. Ultimately, the Emiss\nT\nresolution\nis what limits the m\u03c4\u03c4 resolution. Furthermore, the absolute scale of the Emiss\nT\nmust be well calibrated\nto correctly reconstruct the Higgs boson mass. In addition to the standard Emiss\nT\nalgorithm [17], we\nhave made a dedicated correction in the presence of hadronic tau decays. The correction is based on the\ncalibrated tau energy instead of the default treatment of the object that uses a jet calibration. This removes\na \u223c1 GeV bias in the Emiss\nT\ndistribution for the lh-channel. The sensitivity of the signal ef\ufb01ciency to the\nabsolute energy scale is presented in Section 5.2. By requiring a large Emiss\nT\n, it is possible to improve\nthe m\u03c4\u03c4 resolution and reject many backgrounds that do not contain neutrinos (e.g. Z \u2192ll). We require\nEmiss\nT\n\u226530 GeV for the lh-channel and Emiss\nT\n\u226540 GeV for the ll- and hh-channels.\n2.6\nMass reconstruction\nAlthough there are several neutrinos in the event, it is possible to reconstruct the \u03c4+\u03c4\u2212invariant mass\nby making the approximation that the decay products of the \u03c4 are collinear with the \u03c4 in the laboratory\nframe. This is a good approximation since mH/2 \u226bm\u03c4 and hence the taus are highly boosted. This\nleaves two unknown quantities and two equations: the fraction of each \u03c4\u2019s momentum carried away by\nneutrinos and the constraints from the two components of Emiss\nT\n. For notational simplicity, consider\nthe lh-channel and let l represent the momentum vector for the leptonic visible decay product and h\nrepresent the momentum vector for the hadronic visible decay products. By neglecting the \u03c4 rest mass\nand imposing the collinear approximation, we can write\nm\u03c4\u03c4 =\np\n2(Eh +E\u03bdh)(El +E\u03bdl)(1\u2212cos\u03b8lh)\n.\n(1)\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1280\n\nBy introducing the variables xh and xl, the fraction of the \u03c4\u2019s momentum carried away by the visible\ndecay products, we can re-write the invariant mass as\nm\u03c4\u03c4 =\nmlh\n\u221axlxh\nfor xl,h \u22650\n.\n(2)\nOne can easily solve for the x\u03c4 variables by requiring that the vector sum of the neutrinos coincides with\nthe two measured components of Emiss\nT\n:\nxh =\nEh\nEh +E\u03bdh\n=\nhxly \u2212hylx\nhxly +Emiss\nx\nly \u2212hylx \u2212Emiss\ny\nlx\n= N\nDh\n(3)\nand\nxl =\nEl\nEl +E\u03bdl\n=\nhxly \u2212hylx\nhxly \u2212Emiss\nx\nhy \u2212hylx +Emiss\ny\nhx\n= N\nDl\n,\n(4)\nwhere we have introduced N,Dh, and Dl for convenience. If the two \u03c4s are back-to-back, then these\nequations are linearly-dependent and one cannot solve for the x\u03c4s. For this reason, we require that\ncos\u2206\u03c6\u03c4\u03c4 \u2265\u22120.9. Typically the Higgs boson has signi\ufb01cant pT due to the tagging jets. Events that\ncome from the process X \u2192\u03c4\u03c4 with no other sources of missing energy should have 0 \u2264x\u03c4 \u22641, though\nresolution effects in Emiss\nT\nmay lead to unphysical solutions with either x\u03c4 < 0 or x\u03c4 \u22651. Equation 2\nshows explicitly that cuts on x\u03c4 will impose constraints on the reconstructed mass for a given event, viz.\nm\u03c4\u03c4 \u2265mlh, which results in an asymmetric distribution for m\u03c4\u03c4.\nThe sensitivity of m\u03c4\u03c4 to a mis-measurement of Emiss\nT\ndepends on the orientation of the \u03c4s. This sen-\nsitivity can be summarized by a Jacobian factor, J. Neglecting correlation between the mis-measurement\nof the x- and y-components of Emiss\nT\n, one can de\ufb01ne the Jacobian as follows\nJ =\n\u2206m\u03c4\u03c4\n\u2206Emiss\nT\nx/y\n=\nv\nu\nu\nt\n\u0012 \u2202m\u03c4\u03c4\n\u2202Emiss\nx\n\u00132\n+\n \n\u2202m\u03c4\u03c4\n\u2202Emiss\ny\n!2\n.\n(5)\nThus, we arrive at\nJ = 1\n2\nmlh\u221axlxh\n|N|3\nq\u0000xlhyD2\nh \u2212xhlyD2\nl\n\u00012 +\n\u0000xhlxD2\nl \u2212xlhxD2\nh\n\u00012\n.\n(6)\nThe \ufb01nal mass measurement is a result of a \ufb01t to the m\u03c4\u03c4 distribution, and it is important to incorporate\nboth the asymmetry and the fact that the width of the m\u03c4\u03c4 distribution is not common for all events. The\nmodeling of the asymmetry and Jacobian scaling of the m\u03c4\u03c4 distribution is described in Section 4.2.\n2.7\nSummary of the event selection for ll-channel\nThe event selection for ll-channel is summarized below, including some kinematic requirements speci\ufb01c\nto the ll-channel.\n\u2022 Trigger: electron trigger e22i or muon trigger mu20.\n\u2022 Trigger lepton: at least one lepton must have a reconstructed pT greater or equal to the correspond-\ning trigger requirement.\n\u2022 Dilepton: exactly two identi\ufb01ed leptons with opposite charge.\n\u2022 Missing ET: Emiss\nT\n\u226540 GeV.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1281\n\n\u2022 Collinear approximation: 0 \u2264xl1,l2 \u22640.75 and cos\u2206\u03c6ll \u2265\u22120.9.\nThe tighter cut on x\u03c4 \u22640.75 has been found to provide a better background rejection in the ll-\nchannel. The shape of the control samples used to estimate the signal sensitivity are obtained after\nthese cuts; additional details of the data-driven background estimation are given in Section 3. In\naddition to the cuts above, the signal candidates are also required to satisfy the following cuts.\n\u2022 Jet multiplicity: at least one jet with pT \u226540 GeV and at least one additional jet with\npT \u226520 GeV.\n\u2022 Forward jets: in opposite hemispheres \u03b7 j1 \u00d7\u03b7 j2 \u22640, with tau centrality min{\u03b7 j1,\u03b7 j2} \u2264\u03b7lep1,2 \u2264\nmax{\u03b7j1,\u03b7 j2} for the two highest pT jets.\n\u2022 b-jet veto: the event is rejected if either tag jet has b-tag weight greater than 1.\n\u2022 Jet kinematics: \u2206\u03b7 j j \u22654.4 and dijet mass m j j \u2265700 GeV for two forward jets.\n\u2022 Central jet veto: the event is rejected if there are any additional jets with pT \u226520 GeV in |\u03b7| \u22643.2.\n\u2022 Mass window: mH \u221215 GeV \u2264m\u03c4\u03c4 \u2264mH +15 GeV around the test mass mH.\nTable 4 summarizes the cross-section for signal events after each of the cuts described above.\nTable 4: Signal cross-section (fb) for the ll-channel for various Higgs boson masses.\nMass (GeV)\n105\n110\n115\n120\n125\n130\n135\n140\nCross section (fb)\n394.7\n372.0\n341.8\n309.1\n266.8\n225.4\n180.1\n135.8\nTrigger\n65.6(3)\n65.1(2)\n61.1(2)\n57.2(1)\n51.5(2)\n44.7(1)\n36.5(1)\n28.3(1)\nTrigger lepton\n56.4(3)\n56.2(2)\n53.2(2)\n49.5(1)\n44.7(2)\n38.9(1)\n31.8(1)\n24.7(1)\nDilepton\n5.73(7)\n5.86(6)\n5.80(6)\n5.46(3)\n4.94(5)\n4.30(4)\n3.61(4)\n2.88(4)\nEmiss\nT\n\u226540 GeV\n3.41(5)\n3.49(5)\n3.45(5)\n3.17(3)\n2.94(4)\n2.56(4)\n2.17(3)\n1.78(4)\nCollinear Approx.\n2.34(5)\n2.38(4)\n2.33(4)\n2.15(2)\n1.95(4)\n1.69(3)\n1.46(2)\n1.16(3)\nN jets \u22652\n1.96(4)\n1.97(4)\n1.95(4)\n1.77(2)\n1.61(3)\n1.41(3)\n1.20(2)\n0.95(3)\nForward jet\n1.48(4)\n1.49(4)\n1.48(3)\n1.34(2)\n1.21(3)\n1.08(3)\n0.91(2)\n0.73(3)\nb-jet veto\n1.26(3)\n1.30(3)\n1.25(3)\n1.16(2)\n1.04(3)\n0.94(2)\n0.77(2)\n0.64(2)\nJet kinematics\n0.70(3)\n0.69(2)\n0.70(2)\n0.63(1)\n0.58(2)\n0.52(2)\n0.43(1)\n0.37(2)\nCentral jet veto\n0.61(2)\n0.60(2)\n0.62(2)\n0.56(1)\n0.50(2)\n0.45(2)\n0.38(1)\n0.32(2)\nMass window\n0.52(2)\n0.50(2)\n0.51(2)\n0.45(1)\n0.39(2)\n0.34(1)\n0.29(1)\n0.23(1)\n2.8\nSummary of the event selection for lh-channel\nThe event selection for lh-channel is summarized below, including some kinematic requirements speci\ufb01c\nto the lh-channel.\n\u2022 Trigger: electron trigger e22i or muon trigger mu20.\n\u2022 Trigger lepton: at least one lepton must have a reconstructed pT greater or equal to the correspond-\ning trigger requirement.\n\u2022 Dilepton veto: exactly one identi\ufb01ed lepton (ensures this sample is disjoint from the ll-channel).\n\u2022 Hadronic \u03c4: exactly one identi\ufb01ed hadronic \u03c4 with opposite charge of the lepton.\n\u2022 Missing ET: Emiss\nT\n\u226530 GeV.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1282\n\n\u2022 Collinear approximation: 0 \u2264xl \u22640.75, 0 \u2264xh \u22641, and cos\u2206\u03c6lh \u2265\u22120.9.\nThe asymmetric treatment of xh and xl provides background rejection in the lh-channel.\n\u2022 Transverse mass: in order to further suppress the W + jets and t\u00aft backgrounds, a cut on the trans-\nverse mass of the lepton and Emiss\nT\nmT =\nq\n2 plep\nT\nEmiss\nT\n\u00b7(1\u2212cos\u2206\u03c6) \u226430 GeV\n(7)\nis required, where plep\nT\nis the transverse momentum of the lepton in the lh-channel and \u2206\u03c6 is the\nangle between that lepton and\n\u20d7\nEmiss\nT\nin the transverse plane. The shape of the control samples used\nto estimate the signal sensitivity are obtained after these cuts; additional details of the data-driven\nbackground estimation are given in Section 3. In addition to the cuts above, the signal candidates\nare also required to satisfy the following cuts.\n\u2022 Jet multiplicity: At least one jet with pT \u226540 GeV and at least one additional jet with\npT \u226520 GeV.\n\u2022 Forward jets: in opposite hemispheres \u03b7 j1 \u00d7\u03b7 j2 \u22640, with tau centrality min{\u03b7 j1,\u03b7j2} \u2264\u03b7lep,\u03c4 \u2264\nmax{\u03b7j1,\u03b7 j2} for the two highest pT jets.\n\u2022 Jet kinematics: \u2206\u03b7 j j \u22654.4 and dijet mass m j j \u2265700 GeV for two forward jets.\n\u2022 Central jet veto: the event is rejected if there are any additional jets with pT \u226520 GeV in |\u03b7| \u22643.2.\n\u2022 Mass window: mH \u221215 GeV \u2264m\u03c4\u03c4 \u2264mH +15 GeV around the test mass mH.\nTable 5 summarizes the cross-section for signal events after each of the cuts described above. With\n30 fb\u22121 integrated luminosity, about 20 signal events are expected in the mass window.\nTable 5: Signal cross-sections (fb) for the lh-channel for various Higgs boson masses.\nMass (GeV)\n105\n110\n115\n120\n125\n130\n135\n140\nCross section (fb)\n394.7\n372.0\n341.8\n309.1\n266.8\n225.4\n180.1\n135.8\nTrigger\n65.6(3)\n65.1(2)\n61.1(2)\n57.2(1)\n51.5(2)\n44.7(1)\n36.5(1)\n28.3(1)\nTrigger lepton\n56.4(3)\n56.2(2)\n53.2(2)\n49.5(1)\n44.7(2)\n38.9(1)\n31.8(1)\n24.7(1)\nDilepton veto\n50.0(3)\n49.6(2)\n46.7(2)\n43.4(1)\n38.9(2)\n34.0(1)\n27.6(1)\n21.3(1)\nHadronic \u03c4\n7.7(1)\n8.1(1)\n8.1(1)\n8.02(7)\n7.4(1)\n6.68(8)\n5.72(7)\n4.53(9)\nEmiss\nT\n\u226530 GeV\n4.8(1)\n5.1(1)\n5.08(9)\n4.96(5)\n4.63(8)\n4.16(7)\n3.51(6)\n2.82(8)\nCollinear Approx.\n3.19(9)\n3.50(8)\n3.51(8)\n3.34(5)\n3.14(7)\n2.77(6)\n2.37(5)\n1.91(6)\nTransverse mass\n2.53(8)\n2.70(7)\n2.67(7)\n2.46(4)\n2.26(6)\n1.98(5)\n1.64(4)\n1.29(5)\nN jets \u22652\n2.12(7)\n2.22(7)\n2.21(6)\n2.02(4)\n1.80(5)\n1.60(4)\n1.32(4)\n1.00(5)\nForward jet\n1.61(7)\n1.66(6)\n1.73(5)\n1.52(3)\n1.41(5)\n1.20(4)\n1.03(3)\n0.78(4)\nJet kinematics\n0.88(5)\n0.86(4)\n0.92(4)\n0.82(2)\n0.73(3)\n0.65(3)\n0.56(2)\n0.42(3)\nCentral jet veto\n0.77(5)\n0.77(4)\n0.81(4)\n0.72(2)\n0.63(3)\n0.55(2)\n0.50(2)\n0.38(3)\nMass window\n0.68(4)\n0.68(4)\n0.70(3)\n0.61(2)\n0.52(3)\n0.44(2)\n0.40(2)\n0.30(3)\n2.9\nSummary of the event selection for hh-channel\nThe event selection for hh-channel is summarized below, including some kinematic requirements speci\ufb01c\nto the hh-channel.\n\u2022 Trigger: a combination of the hadronic tau and missing ET trigger L1 TAU30 xE40 softHLT.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1283\n\n\u2022 Hadronic taus: two identi\ufb01ed hadronic taus are required pT above 35 GeV and 30 GeV with\nopposite charge.\n\u2022 Missing ET: Emiss\nT\n\u226540 GeV.\n\u2022 Collinear approximation: 0.2 \u2264xh1,h2 \u22641, and cos\u2206\u03c6hh \u2265\u22120.9.\n\u2022 Di-tau transverse mass: in order to further suppress fake-\u03c4 candidates from W + jets and t\u00aft back-\ngrounds, a cut on the di-tau transverse mass\nmhh\nT\n=\nq\n2 phh\nT Emiss\nT\n\u00b7(1\u2212cos\u2206\u03c6) \u226480 GeV\n(8)\nis required, where phh\nT is the transverse momentum of the two hadronic tau system and \u2206\u03c6 repre-\nsents the azimuthal angle between phh\nT and\n\u20d7\nEmiss\nT\n. This variable has been identi\ufb01ed as potentially\nuseful for the analysis. The optimal value of this cut depends heavily on the relative amount of the\nW+jets, t\u00aft and QCD backgrounds, therefore, the requirement is kept fairly loose.\n\u2022 Jet multiplicity, forward jets, angular cuts, and central jet veto in the case of the lh-channel.\n\u2022 Total pT: to reject events with many jets like t\u00aft, a cut on the total pT is applied:\n||\u20d7pT h1 + \u20d7pT h2 + \u20d7pT j1 + \u20d7pT j2 + \u20d7\nEmiss\nT\n|| \u226460 GeV\n.\n(9)\n\u2022 Jet kinematics: \u2206\u03b7 j j \u22654 and dijet mass mj j \u2265700 GeV for two forward jets.\n\u2022 Central jet veto: the event is rejected if there are any additional jets with pT \u226520 GeV in with\n|\u03b7| \u22643.2.\n\u2022 Mass window: mH \u221215 GeV \u2264m\u03c4\u03c4 \u2264mH +20 GeV around the test mass mH.\nTable 6 summarizes the cross-section for signal events after each of the cuts described above. The\nevents used in the analysis have been generated applying a \ufb01lter that requires two hadronic taus with\npT \u226512 GeV in the \ufb01nal state, produced in |\u03b7| \u22642.7 and with \u2206\u03c6 \u22642.9.\nTable 6:\nSignal cross-sections (fb) for the hh-channel for various Higgs boson masses. The\nevents used in the analysis had a \ufb01lter applied at generation that required two hadronic taus with\npT \u226512 GeV in the \ufb01nal state, produced in |\u03b7| \u22642.7 and with \u2206\u03c6 \u22642.9.\nMass (GeV)\n105\n110\n115\n120\n125\n130\n135\nCross section (fb)\n394.7\n372.0\n341.8\n309.1\n266.8\n225.4\n180.1\nTrigger tau & MET\n12.4(2)\n12.1(2)\n12.0(2)\n11.4(1)\n10.4(2)\n9.2(1)\n7.93(1)\n2 Hadronic \u03c4s\n1.73(8)\n1.80(8)\n1.93(8)\n1.83(4)\n1.67(7)\n1.52(5)\n1.29(5)\nEmiss\nT\n\u226540 GeV\n1.34(7)\n1.39(7)\n1.50(7)\n1.43(3)\n1.32(6)\n1.17(5)\n0.99(4)\nCollinear Approx.\n0.91(6)\n1.02(6)\n1.13(6)\n1.03(3)\n1.00(5)\n0.85(4)\n0.72(3)\nDi-tau Transverse mass\n0.91(6)\n1.02(6)\n1.13(6)\n1.03(3)\n1.00(5)\n0.85(4)\n0.72(3)\nN jets \u22652\n0.77(5)\n0.88(6)\n0.94(5)\n0.86(3)\n0.84(5)\n0.72(4)\n0.61(3)\nTotal pT\n0.72(5)\n0.84(5)\n0.91(5)\n0.83(3)\n0.80(5)\n0.69(4)\n0.58(3)\nForward jet\n0.62(5)\n0.73(5)\n0.75(5)\n0.72(2)\n0.68(4)\n0.58(3)\n0.50(3)\nJet kinematics\n0.37(4)\n0.43(4)\n0.41(4)\n0.45(2)\n0.41(3)\n0.36(3)\n0.28(2)\nCentral jet veto\n0.34(3)\n0.38(4)\n0.36(3)\n0.39(2)\n0.35(3)\n0.32(3)\n0.24(2)\nMass window\n0.25(3)\n0.35(4)\n0.33(3)\n0.34(2)\n0.29(3)\n0.27(2)\n0.20(2)\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1284\n\n3\nBackground estimation\n3.1\nOverview\nDespite the advances in theoretical tools and extraordinarily detailed simulation of the ATLAS detector,\nit is preferable to estimate backgrounds from data instead of relying entirely on Monte Carlo estimates.\nBelow we describe data-driven background estimation techniques for each of the major backgrounds\nand estimate the systematic uncertainty of the estimates. Each technique has been developed to address\nthe aspects of the background estimation which are most relevant for the analysis: the shape of the m\u03c4\u03c4\ntail from the irreducible Z \u2192\u03c4\u03c4, the fake tau contribution in the lh-channel, and the normalization of\nthe QCD backgrounds. Section 4 describes how these techniques are incorporated into the \ufb01nal signal\nextraction, signi\ufb01cance calculation, and mass measurement.\nWhile it is possible to use Monte Carlo to estimate the systematics associated with the data-driven\nbackground estimation techniques, we must wait for data until we can employ these methods to produce\nreliable estimates of the backgrounds. Thus, in a feasibility study such as this one we face the additional\nchallenge of predicting the expected backgrounds with Monte Carlo. The challenge of predicting our\nbackground and the associated uncertainties are distinct from the ones that we will face once we have\ncollected \u223c30 fb\u22121 of data.\nThe major challenge in background prediction is related to the limited size of our Monte Carlo\nsamples. Backgrounds from mis-identi\ufb01ed leptons are dif\ufb01cult to estimate due to the large rejection\nfactors of the identi\ufb01cation algorithms. Even the irreducible Z \u2192\u03c4\u03c4 backgrounds are suppressed by\nseveral orders of magnitude due to the kinematic requirements. The t\u00aft background requires particularly\nlarge sample sizes because it is suppressed by both identi\ufb01cation and kinematic requirements. Table 7\nsummarizes the size of the Monte Carlo samples used in this study and their corresponding luminosity.\nDespite the large computing investment and generator-level \ufb01lters3, many background samples were not\nsuf\ufb01ciently large to estimate rates deep in the analysis where rejection is at the order of 106 - 108. Thus,\nthe \u201cfull\u201d GEANT simulation was augmented with a fast simulation sample \u223c100 times larger and a\ncut factorization method was used to predict the \ufb01nal background rates. While these procedures have\nlarge uncertainties, they are only relevant to our ability to estimate our sensitivity and will not plague the\nanalysis once we have data.\n3.2\nZ + jets\nWhile there is some theoretical uncertainty in the Z \u2192\u03c4\u03c4+jets background [33], the most serious danger\nof this background comes from the high-side tail in the m\u03c4\u03c4 distribution, where we would expect to see\nthe signal. This tail is dominated by instrumental effects; particularly mis-measurement of Emiss\nT\n, which\nis correlated to instrumental effects related to jet energy mis-measurement. Thus, we have developed a\ndata-driven background estimation technique, which begins with a signal-free Z \u2192\u00b5\u00b5+jets sample and\ntransfers the dominant instrumental effects to the Z \u2192\u03c4\u03c4+jets sample. This is achieved by replacing\nthe muons with an equivalent tau, and carefully treating the decay of the tau. This technique is justi\ufb01ed\nbecause the Z \u2192\u00b5\u00b5+jets events have identical jet activity and kinematics as Z \u2192\u03c4\u03c4+jets (before the tau\ndecays) and because the relevant features of tau decays are well understood. We restrict the technique\nto the Z \u2192\u00b5\u00b5+jets control sample because muons lose only a small fraction of their energy in the\ncalorimeter, and the effect on Emiss\nT\nis easier to estimate. After creating the emulated Z \u2192\u03c4\u03c4+jets\ncontrol sample, the full event selection is applied. The normalization of the Z \u2192\u03c4\u03c4 background does not\n3VBFCut : Ne/\u00b5 \u22651 or 2, or N\u03c4 \u22651 with pT \u226510 GeV, |\u03b7| \u22642.7 for electron, muon and tau from W and Z, respectively. For\nthe hadron level jets with cone size 0.4, Njet \u22652 with p1\nT \u226520 GeV for the highest pT jet, p2\nT \u226515 GeV for the second highest\npT jet, and |\u03b7| \u22645, m j j \u2265300 GeV, \u2206\u03b7 j j \u22652.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1285\n\nTable 7: Details of the background samples used in this study. The VBFCut \ufb01lter is applied for\nZ/W+jets events at generator level. The corresponding luminosities for Z/W+jets and di-boson\nevents are estimated for 2 jets events for Z and 3 jets events for W, and WW events for di-boson\nprocess respectively. In t\u00aft samples, the actual physics events are approximately 70% to the total\nnumber of simulated events according to the treatment of the negative weighted events.\nProcess\ncross-section (pb)\nSimulated events\nLuminosity (fb\u22121)\nZ \u2192ll+jets\n35.1\n714,500\n63.1\nW \u2192l\u03bd+jets\n346.3\n765,000\n3.43\nt\u00aft+jets (full)\n450.0\n1,012,941\n1.65\nt\u00aft+jets (fast)\n833.0\n96,250,000\n84.3\nt\u00aft (2-muon, full)\n32.6\n904,000\n20.4\nWW/WZ/ZZ+jets\n174.2\n258,094\n0.57\nQCD di-jets (full)\n\u223c1.4\u00d7109\n1,503,250\n\u223c10\u22126\nQCD di-jets (fast)\n\u223c1.4\u00d7109\n80,000,000\n\u223c5 \u00d710\u22125\nrequire this emulation because it can be estimated directly from the height of the Z-peak in m\u03c4\u03c4 spectrum\nobtained with the signal candidates.\nThe \ufb01rst task is to obtain a signal-free dimuon control sample. Both loose and tight control samples\nhave been used in this data-driven estimation technique. The loose control sample is used to estimate\nthe ditau background not only from Z \u2192\u03c4\u03c4+jets events but also from t\u00aft or di-boson backgrounds, while\nthe tight control sample can be used for the Z \u2192\u03c4\u03c4 background estimation by obtaining relatively pure\nZ \u2192\u00b5\u00b5+jets events. The loose control sample requires only a minimum sets of cuts from the ll-channel,\nhence \u223c10% of this control sample includes other processes such as t\u00aft, diboson or even Z \u2192\u03c4\u03c4. The\ntight control sample, in contrast, selects pure Z \u2192\u00b5\u00b5 events with less than 1% contamination from the\nother processes. A tighter event selection is used to de\ufb01ne this control sample, it is identical to the \ufb01nal\nevent selection in the ll-channel but excludes of the Emiss\nT\n, collinear approximation, and mass window\ncuts. To improve the purity of Z events, a Z mass window cut is used: m\u00b5\u00b5 \u2265mZ \u221210 GeV. Due\nto a strong correlation between the m\u03c4\u03c4 and m\u00b5\u00b5 distributions before the \u00b5 \u2192\u03c4 conversion, the m\u03c4\u03c4\ndistribution is biased by a cut on m\u00b5\u00b5. The lower bound on m\u00b5\u00b5 \u2265mZ \u221210 GeV has little in\ufb02uence\nof the shape in the signal region; however, an upper mass cut causes a large bias. Therefore, no upper\nbound is placed on m\u00b5\u00b5. After obtaining the dimuon events, the reconstructed muons are replaced by\nthe Monte Carlo tau, then decayed and simulated in the ATLAS detector simulation and reconstruction\nsoftware.\nTwo different techniques for replacing the muon with the tau decay products were evaluated in this\nstudy. One uses the TAUOLA decay package [27] and the other uses a simple re-scaling of the mo-\nmentum and ef\ufb01ciency of taus, since the technical complexity of re-simulation by TAUOLA are rather\ndif\ufb01cult in the full detector simulation and reconstruction. A comparison of the two different methods\nprovides a quantitative validation of this procedure. Several comparisons of the Z \u2192\u03c4\u03c4+jets control\nsample emulated from Z \u2192\u00b5\u00b5 and the true Z \u2192\u03c4\u03c4 background were performed after imposing the\nfull event selection criteria for the ll- and lh-channels. Figure 9 shows the pT of the leptons and the\nEmiss\nT\ndistributions of the emulated sample compared to the true Z \u2192\u03c4\u03c4 \u2192ll + 4\u03bd process. Figure 10\n(a) depicts the reconstructed visible mass for the true and emulated samples in the lh-channel and (b)\nshows the bin-by-bin ratio of these distributions. Excellent agreement between the true and emulated\ndistributions are also observed in each of the ll-, lh-, and hh-channels in the region of interest. The gray\nhorizontal band in the \ufb01gure represents \u00b110% around a ratio of 1, which is used to re\ufb02ect the uncertainty\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1286\n\nin the shape from the tau modeling and sensitivity to the analysis cuts. With this method we are able to\naccurately model both the shape and normalization of the Z \u2192\u03c4\u03c4 backgrounds for all tau decays.\n (GeV)\nT\nLepton p\n0\n20\n40\n60\n80\n100\n120 140\n160 180\n200\nFraction of Events\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n ll\n\u2192\n \u03c4\n\u03c4 \n\u2192\nZ \n scaled \n\u00b5\n\u00b5 \n\u2192\nZ \n (GeV)\nT,miss\nE\n0\n50\n100\n150\n200\n250\n300\nFraction of Events\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n ll\n\u2192\n \u03c4\n\u03c4 \n\u2192\nZ \n scaled\n\u00b5\n\u00b5\n \n\u2192\nZ \n(a)\n(b)\nFigure 9: Transverse momentum of the leptons (a) and missing transverse energy (b) for the two pro-\ncesses rescaled Z \u2192\u00b5\u00b5 and true Z \u2192\u03c4\u03c4 \u2192ll +4\u03bd.\n (GeV)\n\u03c4\u03c4\nM\n0\n50\n100\n150\n200\n250\n300\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n\u03c4\u03c4\n\u2192\nFull-sim True Z\n\u03c4\u03c4\n\u2192\nFull-sim Emulated Z\nATLAS\n (GeV)\n\u03c4\u03c4\nM\n0\n50\n100\n150\n200\n250\n300\nRatio EMULATED / TRUE\n0 5\n0.6\n0.7\n0 8\n0 9\n1\n1.1\n1 2\n1.3\n1.4\n1 5\n (GeV)\n\u03c4\u03c4\nM\n0\n50\n100\n150\n200\n250\n300\nRatio EMULATED / TRUE\n0 5\n0.6\n0.7\n0 8\n0 9\n1\n1.1\n1 2\n1.3\n1.4\n1 5\nATLAS\n(a)\n(b)\nFigure 10: Reconstructed invariant mass distribution (a) and its bin-by-bin ratio (b) generated from the\ntrue and emulated Z \u2192\u03c4\u03c4 \u2192lh+3\u03bd events. The gray band represents \u00b110% around a ratio of 1.\n3.3\nQCD background in lh-channel\nThe method described above estimates the contribution of taus for all processes, including t\u00aft, but does\nnot estimate the contribution of the fake taus. The fake rate of leptons is much smaller as compared to\nthe contribution from real leptons from W and \u03c4 decays in the ll-channel. In contrast, in the lh-channel\nroughly half of the t\u00aft background come from fake hadronic-taus. In addition, the W+jets background is\ncomparable to t\u00aft in the lh-channel; therefore, estimating the QCD fake contribution to the lh-channel re-\nquires a dedicated procedure. Estimation of the QCD fake rate is determined from a data-driven method.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1287\n\nThe technique used here exploits the track multiplicity in a cone around the tau candidate. Real\ntaus typically have one or three tracks, with some spread due to tracking ef\ufb01ciency or the presence of\nspurious tracks. Electrons have dominantly a single track, while jets have a broad distribution with a\nhigher average multiplicity. Figure 11 shows the track multiplicity distribution for taus, electrons, and\njets in a cone of radius 0.7 after removing outlying tracks. It is clear that the track multiplicity can be\nused to constrain the relative abundance of the three components to the distribution. While Fig. 11 was\ncreated from Monte Carlo, the electron and jet track multiplicity distributions can easily be obtained\nfrom data.\nGiven a sample of tau candidates, the relative abundance of taus, electrons, and jets can be found by\n\ufb01tting the track multiplicity distribution with the extended likelihood function\nLtrack(rQCD,rtau) =\n\u220fN\ni Pois(ntot\nexp \u00d7(rtau f i\ntau +rQCD f i\njet +(1\u2212rtau \u2212rQCD)f i\nlep)|Ni\nobs)\n\u00d7 Gaus(Ntot\nobs|ntot\nexp,pntot\nexp)\n\u00d7Gaus(Nmeasured\nlep\n|ntot\nexp(1\u2212rtau \u2212rQCD),\u2206lepntot\nexp(1\u2212rtau \u2212rQCD))\n(10)\nwhere ntot\nexp is the total number of events estimated by the \ufb01t, rtau (rQCD) is the fraction of the tau (jet)\ncontribution with respect to the estimated total number of events, \u2206lep = 10% is the relative uncertainty\non lepton measurement, and f i is the normalized probability for the ith bin of the track multiplicity\ndistribution. The second term constrains the normalization, and the third term is an additional constraint\nterm for the lepton contribution estimated by an independent analysis. The \ufb01t is performed to \ufb01nd the\nmaximum likelihood estimate with MINUIT [34].\nThe track multiplicity distribution for the QCD jets is modeled from samples of QCD dijets that\nproduce tau candidates with pT in the range of 17- 280 GeV. No event level selections are applied at this\nstage. Similarly, the multiplicity distribution of the tau signal and lepton background are modeled with\nDrell-Yan Monte Carlo samples; however, all analysis requirements up to transverse mass cut are applied.\nPseudo-datasets were generated for various luminosities based on the corresponding cross-sections and\nmultiplicity distributions. The highly uncertain QCD multi-jet background was scaled to be \ufb01ve times\nlarger than the estimated rates of t\u00aft and W+jets after event selection. A \ufb01t was performed for each of the\n2000 pseudo-datasets and the results were used to estimate quantify the performance of the method. The\nexpected error on the fraction rtau is presented in Fig. 12 as a function of luminosity.\nThe fraction rtau in the signal candidates remaining after the transverse mass cut can be measured to\nwithin 5% accuracy with 1 fb\u22121 integrated luminosity. The largest uncertainty in this method comes from\nthe dependence of the track multiplicity on the jet pT. The systematics were estimated by dividing the\njet into two samples; those with pT \u226470 GeV and those with pT \u226570 GeV. Additionally, the presence\nof Emiss\nT\nin the pure QCD processes is strongly correlated to the event kinematics. Thus, we assign an\nadditional systematic associated with the variation observed when repeating the method with modi\ufb01ed\ntrack multiplicity distributions with and without the requirements on Emiss\nT\n. The systematics associated\nwith the QCD shape contribute about 2% to rtau measurement.\n3.4\nCut factorization method\nThe analysis cuts described in Section 2 have rejections against backgrounds of the order of 108. Only a\nfew tens of events are expected with 30 fb\u22121 of data, and the background Monte Carlo samples generally\ncorrespond to 5 fb\u22121 or less. The lack of suf\ufb01ciently large Monte Carlo samples requires an approxi-\nmate procedure to predict the background rate at the end of the analysis. We utilize a cut factorization\nmethod in which the analysis cuts are divided into three categories that are roughly uncorrelated so that\nthe rejection can be factorized. The \ufb01rst category are related to the tau decays from the Higgs boson\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1288\n\n# of tracks\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nArbitrary Units\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nLikelihood-seeded TauRec\n\u03c4\nelectron\njet\ndistance parameter=0.4\nATLAS\nFigure 11: Track multiplicity distribution for QCD\nfake events and electron-fake events as well as the\n\u03c4 signal.\n)\n-1\nLuminosity (pb\n0\n200\n400\n600\n800\n1000\n/r (%)\nr\u03c3\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nLikelihood-seeded TauRec\n+W) x 2\nt\nQCD(t\n+W) x 5\nt\nQCD(t\nATLAS\nFigure 12: Expected errors of the fraction rtau as a\nfunction of luminosity. The QCD events are scaled\nto \u00d72 and \u00d75.\ncandidate (trigger, lepton ID, hadronic tau ID, Emiss\nT\n, the collinear approximation, and the transverse\nmass) and the rejection is dominated by detector performance issues. The second category of cuts are\nrelated to the tagging jets (forward jets, jet separation, and dijet mass) and the rejection is dominated\nby the kinematic properties of the events. The third category consists of those cuts which are strongly\ncorrelated to both the forward tagging jets and the tau decay products (centrality, central jet veto, and\nmass window cut). The method itself is simple; the background rejection rate is determined for each of\nthe categories individually, and the product of these rejection rates is used to estimate the total rejection\nrate. Two variations on this cut factorization procedure were considered. In the \ufb01rst approach, the rejec-\ntion of the jet-related cuts were calculated without any tau-related cuts. The second approach differed\nin that it included the lepton and tau identi\ufb01cation in order to avoid bias effects from the contribution of\nfake leptons and taus. The residual correlations between the categories of cuts contributes to an uncer-\ntainty in this technique. The uncertainties were estimated with the use of larger samples produced with\nfast simulation and fully simulated samples with generator-level \ufb01lters, which enrich the backgrounds in\nthe signal-like region. The factorization process was used for all background processes except for the\nirreducible Z \u2192\u03c4\u03c4 background.\nFor the W \u2192l\u03bd+jets and Z \u2192ll+jets backgrounds, ALPGEN samples with up to 5-jets correspond-\ning to 4 fb\u22121 integrated luminosity were used. Table 8 shows the average of the jet rejection from the two\napproaches, which is used as our \ufb01nal prediction. The Z events in ll-channel indicate that the jet-related\ncuts are not strongly correlated with the tau-related cuts, since the rejection rate is the same in the electron\nand muon modes. The correlation between the categories of cuts was investigated with an ALPGEN Z\n\u2192\u03c4\u03c4 + n jets sample enriched with the VBFCut \ufb01lter. The production kinematics are the same, but the\nenhanced Emiss\nT\ndue to the \u03c4 decays lets a suf\ufb01cient number of events survive all the analysis cuts. The\nbackground predictions with and without cut factorization are consistent within the 20% statistical error.\nThus, we assign a 20% systematic uncertainty for this evaluation method on this process.\nThe t\u00aft background is the most complicated process in that it includes both irreducible and reducible\ncontributions in all channels. We use 106 t\u00aft events produced by the MC@NLO generator. The events do\nnot include the process in which both Ws decay hadronically, thus the sample corresponds to 1.6fb\u22121 of\nintegrated luminosity. While the rejection of the tau-related cuts can be reliably estimated, the rejection of\nthe jet-related cuts suffers from the limited sample sizes. The rejection of the jet-related cuts is expected\nto be very high (\u00d7104 for t\u00aft), resulting in a \u223c30% statistical error in the \ufb01nal background predictions.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1289\n\nTable 8 summarizes the rejection of the jet-related cuts subdivided into events with a real or fake hadronic\ntau for the lh-channel and by lepton \ufb02avor for the ll-channel. Again, the average of the two approaches is\nused for the \ufb01nal background prediction. Table 8 shows that there is a considerable contribution of fake-\ntau events for the lh-channel. In the ll-channel, the contribution from semi-leptonic decays of B-hadrons\nwas found to be very small. An estimate of the uncertainty in the method was found by comparing the\nprediction from cut-factorization to the direct estimate from an enriched sample \ufb01ltered to require at least\ntwo muons in the event. Furthermore, the cut-factorization results were compared to a sample produced\nwith the fast simulation that was approximately 100 times larger. Based on these comparisons, we assign\n50% uncertainty in the t\u00aft background prediction.\nThe diboson background contribution was predicted with the same cut-factorization procedure. Even\nafter using the cut-factorization procedure, the statistical uncertainty in the prediction is very large. For-\ntunately, the diboson production cross-section is much smaller than the t\u00aft processes, so the effect of this\nbackground is very small. The results of the cut factorization prediction are presented in Table 8, and we\nassign a large uncertainty of 50% for diboson background rate. While a number of tests were performed\nto validate the method, it is clear that this is an approximate procedure and that the limited size of the\nMonte Carlo samples fundamentally limits our ability to predict this background.\nTable 8: Rejection rates of the jet-related cuts for Z/W+jets, t\u00aft and diboson events in ll- and\nlh-channels, respectively.\nAcceptance\nll-channel\n(%)\nZ \u2192ee/\u00b5\u00b5+jets\nW \u2192e\u03bd/\u00b5\u03bd+jets\nt\u00aft (ee/\u00b5\u00b5/e\u00b5)\nWW/WZ/ZZ\nJet kinematics\n2.32(2) / 2.43(2)\n2.4(3) / 1.5(2)\n0.72(8) / 0.52(5) / 0.60(4)\n0.43(5) / 0.56(3) / 0.33(3)\nCentral jet veto\n1.00(1) / 1.02(1)\n1.1(3) / 0.8(2)\n0.11(3) / 0.04(1) / 0.10(1)\n0.26(5) / 0.26(4) / 0.10(2)\nMass window\n0.230(5) / 0.202(4)\n0.1(1) / 0.1(1)\n0.019(7) / 0.002(1) / 0.010(3)\n\u2013\n/ \u2013\n/ 0.03(1)\nRejection rate\nlh-channel\n(%)\nZ \u2192ee/\u00b5\u00b5\nW \u2192e\u03bd/\u00b5\u03bd\nt\u00aft (tau / non-tau)\nWW/WZ/ZZ\nJet kinematics\n2.60(5) / 2.8(1)\n2.7(1) / 2.6(1)\n0.93(6) / 1.11(6)\n0.2(2) / 0.6(1) / 0.50(3)\nCentral jet veto\n1.14(3) / 1.30(9)\n1.7(1) / 1.3(1)\n0.07(3) / 0.12(3)\n0.1(1) / 0.3(1) / \u2013\nMass window\n0.22(1) / 0.11(2)\n0.10(3) / 0.05(2)\n0.015(8) / \u2013\n\u2013\n/ 0.03(3) / \u2013\n3.5\nBackground for the hh-channel\nIn addition to the Z+jets, W+jets and t\u00aft backgrounds, the hh-channel also has a background from the pure\nQCD multi-jet process. The estimation of QCD multi-jets must be made from data. A few handles exist\nfor estimating the pure QCD background. First, one can utilize a sample of same-sign tau candidates to\nestimate the fake tau contribution since the sign of the tau candidate from QCD is approximately random.\nPotentially, one can utilize constraints from the track multiplicity distribution as described in Section 3.3.\nFurthermore, one can loosen the identi\ufb01cation requirements on the tau candidates to obtain a sample\ndominated by QCD fakes, and then extrapolate this background into the signal region using knowledge\nof the fake tau\u2019s likelihood distribution obtained with data. The ef\ufb01ciency of these techniques must also\nbe established with data, but here we assume that the same-sign sample will be able to estimate the QCD\nbackground with an uncertainty given by two components. The \ufb01rst component of this uncertainty is\nthe statistical error in the control sample, which scales like 1/\u221aNSS, where NSS is the size of same sign\nsample coming from QCD backgrounds. The second component is a systematic uncertainty associated\nwith using the same sign sample to estimate the opposite sign sample. Experience from the Tevatron\nshows that charge correlations can be of order 13% with an uncertainty of order 3% [35,36]. Given that\nthe \ufb01nal state requires two additional jets, which can alter the contribution of quark and gluon-initiated\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1290\n\njets, we assume a 10% systematic error associated with the charge correlation. In addition, the same sign\nsample will also include a contribution from W \u2192\u03c4\u03bd+jets, where the Tevatron experiments observed a\ncharge correlation that was much higher with a 40% uncertainty [35]. The experience from the Tevatron\nprovides some insight into this approach, but the results are not directly relevant because the LHC is not\na \u00afp-p machine.\nAs in the ll and lh-channels we do not have suf\ufb01ciently large Monte Carlo samples to predict the\nbackground for the hh-channel. We employ the same cut factorization method for the Z+jets, W+jets\nand t\u00aft backgrounds as described above. The prediction of the pure QCD multi-jet background from\nMonte Carlo is hopeless without factorizing the analysis even further. A sample of 80 million QCD\ndijet events (including c\u00afc and b\u00afb processes) were simulated with the fast detector simulation. The tau\nfake rate was parameterized from full simulation as a function of \u03b7 and pT and used to re-weight the\ndijet sample. In order for a pure QCD process to satisfy the event selection, there must be at least\nfour high-pT jets. Previous studies have shown that the parton shower underestimates the tagging jet\nrequirement by a factor of 2-3 [4]. Therefore, we multiply the prediction from QCD dijets after the\nforward jet requirement by a factor of 5 to include the underestimate from the parton shower and an\nadditional safety factor. Table 11 shows that the analysis cuts are extremely effective at rejecting QCD\nbackgrounds, but a realistic estimation of the remaining background requires data.\n3.6\nSummary of the background predictions\nTables 9, 10, and 11 summarize the background predictions for the ll-, lh-, and hh-channels, respectively.\nThe tables also indicate the statistical uncertainty on the estimates from the limited size of the Monte\nCarlo samples. Note that the mass window cut is set with respect to the test Higgs mass of 120 GeV.\nThe effective cross-sections estimated with the cut-factorization method are marked with an asterisk.\nFurthermore, the predictions from the t\u00aft sample simulated with the fast simulation are shown, where the\neffective cross-section was normalized to the fully simulated sample after the collinear approximation\nfor the ll-channel and after the transverse mass cut for the lh-channel.\nTable 9: Summary of the backgrounds for the ll-channel. An asterisk is used to indicate cross-\nsections estimated from the cut factorization method. Note that at least one of taus are decayed\nleptonically in QCD Z \u2192\u03c4+\u03c4\u2212+jets process.\nZ \u2192\u03c4+\u03c4\u2212+jets(\u22651)\nt\u00aft\nZ \u2192l+l\u2212+n jets\nW \u2192l\u03bd+n jets\ndiboson\nQCD\nELWK\nFull\nFast\n(n \u22651)\n(n \u22651)\nWW/ZZ/WZ\nCross section (fb)\n168.4\u00d7103\n1693\n833\u00d7103\n768.6\u00d7103\n8649\u00d7103\n174.1\u00d7103\nTrigger\n51.5(1)\u00d7103\n230(1)\n209.8(2)\u00d7103\n633.8(4)\u00d7103\n4411(9)\u00d7103\n32.0(1)\u00d7103\nTrigger lepton\n42.7(1)\u00d7103\n190(1)\n179.1(2)\u00d7103\n588.0(4)\u00d7103\n3815(9)\u00d7103\n28.0(1)\u00d7103\nDilepton\n4.25(5)\u00d7103\n19.2(4)\n21.7(1)\u00d7103\n369.9(5)\u00d7103\n2.5(2)\u00d7103\n3.95(6)\u00d7103\nEmiss\nT\n\u226540 GeV\n744(18)\n9.9(3)\n16847( 99)\n2683( 67)\n1148(176)\n1744( 49)\nCollinear Approx.\n454(14)\n6.2(2)\n1817( 33)\nAtlfast\n104( 12)\n46( 21)\n73( 9)\nN jets \u22652\n262( 8)\n5.8(2)\n1722( 32)\n1699(4)\n73( 8)\n14( 6)\n51( 8)\nForward jet\n39( 2)\n2.0(1)\n294( 13)\n324(1)\n10( 3)\n\u22651.2(2)\u2217\n8( 3)\nb-jet veto\n30( 2)\n1.5(1)\n89( 7)\n90.3(9)\n9( 3)\n\u22651.0(2)\u2217\n5( 2)\nJet kinematics\n2.71(5)\n0.57(5)\n11.8(3)\u2217\n26.7(5)\n0.66(3)\u2217\n0.19(4)\u2217\n0.33(5)\u2217\nCentral jet veto\n1.24(3)\n0.43(4)\n1.9(1)\u2217\n2.6(1)\n0.27(1)\u2217\n0.10(2)\u2217\n0.18(4)\u2217\nMass window\n0.23(1)\n0.04(1)\n0.10(2)\u2217\n0.06(2)\n0.058(3)\u2217\n0.01(1)\u2217\n0.002(1)\u2217\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1291\n\nTable 10: Summary of the backgrounds for the lh-channel. An asterisk is used to indicate cross-\nsections estimated from the cut factorization method. Note that at least one of taus are decayed\nleptonically in QCD Z \u2192\u03c4+\u03c4\u2212+jets process.\nZ \u2192\u03c4+\u03c4\u2212+jets(\u22651)\nt\u00aft\nZ \u2192l+l\u2212+n jets\nW \u2192l\u03bd+n jets\ndiboson\nQCD\nELWK\nFull\nFast\n(n \u22651)\n(n \u22651)\nWW/ZZ/WZ\nCross section (fb)\n168.4\u00d7103\n1693\n833\u00d7103\n768.6\u00d7103\n8649\u00d7103\n174.1\u00d7103\nTrigger\n51.5(1)\u00d7103\n230(1)\n209.8(2)\u00d7103\n633.8(4)\u00d7103\n4411(9)\u00d7103\n32.0(1)\u00d7103\nTrigger lepton\n42.7(1)\u00d7103\n190(1)\n179.1(2)\u00d7103\n588.0(4)\u00d7103\n3815(9)\u00d7103\n28.0(1)\u00d7103\nDilepton veto\n38.4(1)\u00d7103\n171(1)\n156.4(2)\u00d7103\n216.5(4)\u00d7103\n3811(9)\u00d7103\n23.7(1)\u00d7103\nHadronic \u03c4\n3062( 42)\n19.3(4)\n5224( 56)\n20250(156)\n32537(1012)\n704( 30)\nEmiss\nT\n\u226530 GeV\n850( 20)\n12.1(3)\n4251( 50)\n468(26)\n21001( 801)\n474( 26)\nCollinear Approx.\n514( 15)\n7.8(2)\n606( 19)\n17( 3)\n324( 46)\n32( 6)\nTransverse mass\n415( 13)\n6.5(2)\n176( 10)\nAtlfast\n11( 2)\n67( 18)\n14( 3)\nN jets \u22652\n235( 7)\n6.0(2)\n162(9)\n167(1)\n8( 1)\n49( 11)\n7( 1)\nForward jet\n40( 3)\n2.3(1)\n32(4)\n26.1(4)\n1.3(6)\n\u22652.9(3)\u2217\n3( 1)\nJet kinematics\n2.7(1)\n0.72(6)\n1.8(1)\u2217\n3.6(1)\n0.10(1)\u2217\n0.7(1)\u2217\n0.06(1)\u2217\nCentral jet veto\n1.2(1)\n0.49(5)\n0.25(4)\u2217\n0.43(5)\n0.047(6)\u2217\n0.43(6)\u2217\n0.02(1)\u2217\nMass window\n0.11(2)\n0.04(1)\n0.012(5)\u2217\n0.03(1)\n0.008(1)\u2217\n0.020(6)\u2217\n0.001(1)\u2217\nTable 11: Summary of the backgrounds for the hh-channel. An asterisk is used to indicate cross-\nsections estimated from the cut factorization method and/or an additional safety factor. Note that\nboth taus are decayed hadronically in QCD Z \u2192\u03c4+\u03c4\u2212+jets and W \u2192\u03c4\u03bd+jets processes. The t\u00aft\nsample is required to have at least one lepton in the top decay.\nZ \u2192\u03c4+\u03c4\u2212+jets(\u22651)\nt\u00aft\nW \u2192\u03c4\u03bd +n jets\nQCD di-jet\nQCD\nELWK\n(n \u22651)\n(\u00d7 5)\nCross section (fb)\n40.3\u00d7103\n1693\n833 \u00d7103\n922\u00d7103\n19.1 1012\nTrigger tau & MET\n1756(15)\n126(1)\n78177(232)\n39600(400)\n2 Hadronic \u03c4s\n161(4)\n4.9(2)\n373(16)\n317(33)\n2.756(3) 106*\nEmiss\nT\n\u226540 GeV\n108(4)\n3.7 (2)\n335(15)\n243(29)\n0.97(3) 103*\nCollinear Approx.\n72(3)\n2.3 (1)\n43(5)\n20(7)\n1.7(2) 102*\nDi-tau Transverse mass\n72(3)\n2.3(1)\n39(5)\n18(7)\n1.6(2) 102*\nN jets \u22652\n46(2)*\n2.1(1)\n34(5)*\n8(3)*\n0.86(4) 102*\nTotal pT\n40(2)*\n1.9(1)\n24(4)*\n8(3)*\n0.75(3) 102*\nForward jet\n17(1)*\n1.1(1)\n9(2)*\n3(1)*\n23(3)*\nJet kinematics\n1.4(1)*\n0.43(6)\n0.6(2)*\n0.5(4)*\n8(3)*\nCentral jet veto\n0.7(1)*\n0.36(6)\n0.16(9)*\n0.3(3)*\n4(1)*\nMass window\n0.08(3)*\n0.03(1)\n0.03(3)*\n0.1(1)*\n1(1)*\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1292\n\n4\nSignal sensitivity\n4.1\nOverview\nIn this section we outline the method for extracting the signal signi\ufb01cance from the data and measuring\nthe Higgs boson mass. In addition to a simple method based on counting the number of events in a\nmass window, we present a method based on \ufb01tting the m\u03c4\u03c4 spectrum. Particular care has been given to\nthe incorporation of uncertainty in both the rate and shape for the signal and backgrounds. The \ufb01tting\nstrategy constrains the shape of the Z \u2192\u03c4\u03c4 background from the data-driven techniques described in\nSection 3.2. The data-driven estimates for the t\u00aft and W+jets background are not \ufb01nalized, thus we rely\non Monte Carlo to constrain the shape of those backgrounds and allow for large variation in the shape. In\nthe lh-channel, the normalization of the fake-tau contribution is constrained from the track multiplicity\nmeasurement outlined in Section 3.3. Sections 4.2 and 4.3 describe the parameterization of the signal and\nbackgrounds, while Sections 4.4 and 4.5 describe how the control samples are incorporated to constrain\nthe normalization and shape uncertainties. The expected signal sensitivity is estimated by considering\na hypothetical data set given by the median of the signal-plus-background estimate. The normalization\nof the background predictions are described in Section 3.6. Due to the limited size of the Monte Carlo\nsamples, the shape of the m\u03c4\u03c4 spectrum for the t\u00aft and W+jets background was obtained from an earlier\npoint in the event selection, just after the collinear approximation requirement in the ll-channel and after\nthe transverse mass cut in the lh-channel (see Sections 2.7 and 2.8). Similarly, the shape of the Z \u2192\u03c4\u03c4\nbackground in the control sample, which can be estimated by the data-driven techniques described in\nSection 3.2, was obtained from a Z \u2192\u03c4\u03c4 Monte Carlo sample just after the same points in the event\nselection. Depending on how the analysis evolves, the shape of the m\u03c4\u03c4 spectrum from an earlier point\nin the event selection \u2013 which is dominated by backgrounds \u2013 may also provide a useful control sample\nto validate the data-driven background estimation techniques since it is fairly stable in the later stages of\nthe event selection.\nFor the \ufb01rst time ATLAS has investigated the hh-channel. While the signal ef\ufb01ciency and m\u03c4\u03c4 mass\nresolution are roughly comparable to the ll- and lh-channels, a reliable estimate of the QCD background\ncan only be provided with data. Therefore, we do not report on an estimated sensitivity for the hh-channel\nbelow.\n4.2\nShape parameterization for H \u2192\u03c4\u03c4 and Z \u2192\u03c4\u03c4\nThe shape of the m\u03c4\u03c4 distribution for signal and Z \u2192\u03c4\u03c4 events is dictated by the resolution of Emiss\nT\nand the kinematics of the collinear approximation. As discussed in Section 2.6, the width of the m\u03c4\u03c4\ndistributions is given by the Emiss\nT\nresolution scaled by a Jacobian factor and the cuts on the x\u03c4 variables\nintroduce an asymmetry in the m\u03c4\u03c4 distribution. A full solution would include an event-by-event Jacobian\nscaling of the width and truncation at m\u03c4\u03c4 \u2265mvis/\np\nxcut\n1 xcut\n2 . An approximate parameterization can be\nconstructed with these features in mind. First, we consider three sub-samples of events with J \u22642,\n2 < J \u22645, and J > 5. Let, \u27e8J\u27e9i and Ni denote the mean of the Jacobian and the number of events\nin the ith subsample, respectively. We account for the Jacobian scaling of the width by using a triple\nGaussian with identical mean, normalizations according to the ratios of the Ni and widths according\nto the ratios of \u27e8J\u27e9i. To account for the asymmetry introduced by the x\u03c4 cuts, we modulate the triple\nGaussian by an ef\ufb01ciency envelope derived from the mvis spectrum. The ef\ufb01ciency envelope re\ufb02ects\nthe probability that m\u03c4\u03c4 is greater than mvis and is parameterized as: 1/2+1/2erf{[m\u03c4\u03c4 \u2212\u27e8mvis\u27e9]/\n\u221a\n2\u03c3vis},\nwhere \u27e8mvis\u27e9and \u03c3vis are the mean and standard deviation of the spectrum for those events which fail\nthe x\u03c4 cuts. The parameter \u27e8mvis\u27e9depends on the Higgs boson mass and was linearly parameterized by\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1293\n\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nArbitrary Units\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nATLAS\nlh\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nArbitrary Units\n0\n10\n20\n30\n40\n50\n60\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\n0\n10\n20\n30\n40\n50\n60\nATLAS\nlh\n\u2192\n\u03c4\n\u03c4\n\u2192\nVBF H(120)\n(a)\n(b)\nFigure 13: Figures (a) and (b) show the result of a \ufb01t to a pure Monte Carlo samples of Z \u2192\u03c4\u03c4 and\nsignal (mH = 120 GeV) in the lh-channel, respectively. The dashed lines represent the three components\nof the model and the dotted curve represents the erf() ef\ufb01ciency envelope. These samples do not include\npileup.\n0.576mH +60 GeV; the width \u03c3vis was \ufb01xed at 10 GeV. We parametrize the m\u03c4\u03c4 distribution as\nLH/Z(m\u03c4\u03c4|m,\u03c3H/Z) = N\n\u00141\n2 + 1\n2 erf\n\u0012m\u03c4\u03c4 \u2212\u27e8mvis\u27e9\n\u221a\n2\u03c3vis\n\u0013\u0015\n\u00d7\n3\n\u2211\ni=1\nNi Gaus(m\u03c4\u03c4|m,\u03c3H/Z\u27e8J\u27e9i),\n(11)\nwhere the resulting function\u2019s normalization constant N was found by numerical integration with the\nROOFIT package [37].\nThe Z \u2192\u03c4\u03c4 control sample described in Section 3.2 is used to constrain the mean, mZ, and the overall\nwidth of the distribution, \u03c3Z, which are the only free parameters in the Z \u2192\u03c4\u03c4 background model. The\nerror bars in the control sample were scaled by 10% to account for the 10% shape uncertainty in the\n\u00b5 \u2192\u03c4 rescaling method and the extrapolation from the control region to the \ufb01nal signal region. Figure 13\nshows the result of the \ufb01t to the Z \u2192\u03c4\u03c4 and Higgs boson signal in the lh-channel.\nAn alternate parameterization was also considered. This parameterization was also composed of\nthree components, but the asymmetry in the shape was modeled with a \u201cbifurcated\u201d or \u201cdimidated\u201d\nGaussian [38], in which the width of the lower half was smaller than the width of the upper half of the\ndistribution. This alternate parameterization did not \ufb01x the ratio of the widths and normalizations for the\nthree components based on the distribution of the Jacobian; instead, these parameters were themselves\nparameterized as a piece-wise linear function of mH. Each of the three components required four param-\neters to model the widths, together with two parameters for normalization constants, and two parameters\nfor the linearity in the Higgs boson mass. In total the signal model was represented by 16 parameters.\nResults from these two parameterizations were in good agreement.\n4.3\nShape parameterization for t\u00aft and W+jets\nIn contrast to the irreducible Z \u2192\u03c4\u03c4+jets background, the W+jets background is dominated by situations\nin which one of the tau decay products comes from a W decay and the second tau decay product is a fake\nfrom a jet. The t\u00aft background is even more complicated because the decay products from top contain a\nreal tau contribution as well as a fake tau contribution. It is dif\ufb01cult to estimate this background using\nMonte Carlo because one must understand in detail both the jet kinematics for as well as the lepton or \u03c4\nfake rate as a function of pT and \u03b7. Instead, it is desirable to estimate this background with data. Since the\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1294\n\ndata-driven strategy for the W+jets background is under development, we simply rely on Monte Carlo to\nprovide a control sample for this background. Figure 14(a) shows the shape of the fully simulated W+jets\nbackground and the fast simulation t\u00aft background sample after the transverse mass cut. The shapes are\nconsistent within statistical errors. While the shapes from those backgrounds remain stable through the\n\ufb01nal stages of the event selection, a conservative 50% error is applied to each bin in the combined t\u00aft and\nW+jets control sample to re\ufb02ect uncertainty in how this shape changes as the remainder of the analysis\ncuts are applied.\nThe shape of the QCD background was parameterized with the following equation\nLQCD(m\u03c4\u03c4|a1,a2,a3) = N\n\u0012\n1\nm\u03c4\u03c4 +a1\n\u0013a2\nma3\n\u03c4\u03c4\n.\n(12)\nThe form is motivated by a competition between the parton distribution functions and the matrix element.\nIn the lh-channel, the normalization of the backgrounds with fake taus can be constrained by using\nthe track multiplicity constraint described in Section 3.3; however, there is an additional uncertainty\nassociated with how well the fake fraction can be extrapolated from the control sample to the signal\nlike region. We apply a conservative 50% systematic on this fraction associated with the extrapolation.\nFigure 14(b) and (c) show the result of the simultaneous \ufb01t to the fake tau background described in\nthe Section 4.5 with (solid) and without (dashed) the signal contribution for the ll- and lh-channel,\nrespectively. The variation re\ufb02ects the magnitude of the shape uncertainty.\n (GeV)\n\u03c4\n\u03c4\nm\n0\n100\n200\n300\n400\n500\n600\nArbitrary Units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nQCD shape w/ 50% syst.\n\u03c4\n l + \n\u2192\n tt\n l + jets\n\u2192\n tt\nW+jets\nATLAS\n100 200 300 400 500 600 700 800 900\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n (GeV)\n\u03c4\n\u03c4\nm\n100 200 300 400 500 600 700 800 900\nEvents / ( 5 GeV )\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\nATLAS\nQCD Control Sample\nll-channel\n-1\n = 14 TeV, 30 fb\ns\n=120GeV)\nH\ns+b fit (M\nb-only fit\n100 200 300 400 500 600 700 800 900\n0\n1\n2\n3\n4\n5\n6\n7\n (GeV)\n\u03c4\n\u03c4\nm\n100 200 300 400 500 600 700 800 900\nEvents / ( 5 GeV )\n0\n1\n2\n3\n4\n5\n6\n7\nATLAS\nQCD Control Sample\nlh-channel\n-1\n = 14 TeV, 30 fb\ns\n=120GeV)\nH\ns+b fit (M\nb-only fit\n(a)\n(b)\n(c)\nFigure 14: Figure (a) shows that the shapes are similar for these backgrounds and that the shape is stable\nin the \ufb01nal stages of the cut \ufb02ow. The m\u03c4\u03c4 spectrum for t\u00aft and W+jets backgrounds after all cuts for\nthe ll-channel (b) and lh-channel (c) with a \ufb01t to the spectrum. The solid and dashed curves show the\nresult of the simultaneous \ufb01t to the control sample and signal candidates with and without the signal\ncontribution, respectively.\n4.4\nSignal signi\ufb01cance neglecting shape uncertainty\nFor a given hypothesized Higgs boson mass, mH, the mass window has been de\ufb01ned as mH \u221215 GeV \u2264\nm\u03c4\u03c4 \u2264mH +15 GeV. A simple approach to estimating the expected signi\ufb01cance of the signal is to count\nevents in this range and calculate the probability for at least this many events from the background-only\nprediction. An alternate approach is to \ufb01t the m\u03c4\u03c4 spectrum and use the resulting signal yield as a test\nstatistic. Table 12 shows the signi\ufb01cance obtained from number counting assuming a 10% background\nuncertainty as was done in Ref. [4] and the result from the \ufb01tted signal yield. The next subsection\nprovides a \ufb01nal result indicating a more realistic treatment of both normalization and shape uncertanties.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1295\n\nTable 12: Expected signal signi\ufb01cance for several masses based on number counting in a mass\nwindow with 30 fb\u22121 of data. Results are shown neglecting uncertainty in the background rate\nand incorporating it with two methods (see text). These results do not include the impact of\npileup, which is discussed in Section 4.7.\nll-channel\nlh-channel\ncombined\nmH\nCounting\nFitted Yield\nCounting\nFitted Yield\nCounting\nFitted Yield\n105\n2.20\n2.43\n2.85\n3.46\n3.80\n4.17\n110\n2.46\n2.88\n3.45\n4.19\n4.46\n5.06\n115\n2.86\n3.26\n4.18\n4.96\n5.32\n5.96\n120\n2.80\n3.17\n4.23\n4.73\n5.36\n5.72\n125\n2.67\n2.96\n3.97\n4.32\n5.08\n5.28\n130\n2.42\n2.73\n3.54\n3.88\n4.62\n4.77\n135\n2.17\n2.37\n3.38\n3.60\n4.35\n4.25\n140\n1.74\n2.00\n2.66\n2.83\n3.55\n3.35\n4.5\nIncorporating control samples and shape uncertainty\nBy \ufb01tting the m\u03c4\u03c4 spectrum to a model that accurately describes the signal and various backgrounds\nit is possible to directly incorporate uncertainty in the background shape and take advantage of the\nshape of the signal within the mass window. In order to constrain the background rate and shape, we\nsimultaneously \ufb01t the signal candidates and the background control samples outlined in Section 3. The \ufb01t\nis performed twice, once letting the signal parameters \ufb02oat (the maximum likelihood estimates denoted\nwith a single \u02c6 ) and once constraining the signal normalization to be zero (the conditional maximum\nlikelihood estimates denoted with a double\u02c6\u02c6). The ratio of these likelihoods is referred to as the pro\ufb01le\nlikelihood ratio, \u03bb,\n\u03bb(\u00b5 = 0) = L(data|\u00b5, \u02c6\u02c6b(\u00b5), \u02c6\u02c6\u03bd(\u00b5))\nL(data| \u02c6\u00b5, \u02c6b, \u02c6\u03bd)\n,\n(13)\nwhere \u00b5 represents the signal strength in units of the Standard Model expectation and \u03bd represents the\nnuisance parameters needed to describe the shape. If the Higgs boson mass is speci\ufb01ed, the distribution of\n\u22122log\u03bb ratio asymptotically approaches a \u03c72 distribution with the number of degrees of freedom given\nby the number of parameters of interest4. The motivation for \u00b5 is that it enforces the relationship of\nthe Standard Model branching ratios when combining the individual channels, maintaining the property\nthat the distribution of \u22122log\u03bb is \u03c72 with one degree of freedom. This improves the power compared\nto a method which lets the signal in each channel vary independently. If the Higgs boson mass is not\n\ufb01xed, then one must take into account the \u201clook-elsewhere\u201d effect, which is discussed in more detail in\nSection 6. The likelihood function used in the simultaneous \ufb01t is simply a product of the likelihoods\nfrom the individual measurements:\nL(data|\u00b5,mH,\u03bd)\n=\nLtrack(track multiplicity|rQCD)\n(14)\n\u00d7\nLZ(Z+jets control|mZ,\u03c3Z)\n\u00d7\nLQCD(QCD control|a1,a2,a3)\n\u00d7\nLs+b(signal candidates|\u00b5,mH,\u03c3H,mZ,\u03c3Z,rQCD,a1,a2,a3),\nwhere the ai are the parameters used to parameterize the fake-tau background and \u03bd represents all nui-\nsance parameters of the model: \u03c3H,mZ,\u03c3Z,rQCD,a1,a2,a3. When using the alternate parameterization\n4When constraining \u00b5 \u22650, the distribution for the background-only hypothesis is modi\ufb01ed such that \u22122log\u03bb(\u00b5 = 0) \u223c\n1/2\u03b4(0)+1/2\u03c72\n1, and this is taken into account in computing the p-value.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1296\n\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nEvents / ( 5 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nATLAS\nlh\n\u2192\n\u03c4\n\u03c4\n\u2192\nVBF H(120)\n-1\n = 14 TeV, 30 fb\ns\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nEvents / ( 5 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nlh\n\u2192\n\u03c4\n\u03c4\n\u2192\nVBF H(120)\n-1\n = 14 TeV, 30 fb\ns\nATLAS\n(a)\n(b)\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nEvents / ( 5 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nATLAS\nll\n\u2192\n\u03c4\n\u03c4\n\u2192\nVBF H(120)\n-1\n = 14 TeV, 30 fb\ns\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n60\n80\n100\n120\n140\n160\n180\n0\n2\n4\n6\n8\n10\n12\n14\n (GeV)\n\u03c4\n\u03c4\nm\n60\n80\n100\n120\n140\n160\n180\nEvents / ( 5 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nll\n\u2192\n\u03c4\n\u03c4\n\u2192\nVBF H(120)\n-1\n = 14 TeV, 30 fb\ns\nATLAS\n(c)\n(d)\nFigure 15: Example \ufb01ts to a data sample with the signal-plus-background (a,c) and background only\n(b,d) models for the lh- and ll-channels at mH = 120 GeV with 30 fb\u22121 of data. Not shown are the\ncontrol samples that were \ufb01t simultaneously to constrain the background shape. The \ufb01ts are performed\nto the signal and background expectation (histograms), while the overlaid data with error bars are only\nindicative of a possible data set. These samples do not include pileup.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1297\n\nof the signal, the exact form of Equation 14 is modi\ufb01ed to coincide with parameters of that model.\nFigure 15 shows the \ufb01t to the signal candidates for mH = 120 GeV with (a,c) and without (b,d)\nthe signal contribution. It can be seen that the background shapes and normalizations are trying to\naccommodate the excess near m\u03c4\u03c4 = 120 GeV, but the control samples are constraining the variation.\nTable 13 shows the signi\ufb01cance calculated from the pro\ufb01le likelihood ratio for the ll-channel, the lh-\nchannel, and the combined \ufb01t for various Higgs boson masses with 30 fb\u22121 of data. Finally, we present\nthe expected signi\ufb01cance as a function of Higgs boson mass in Fig.16.\nTable 13: Expected signal signi\ufb01cance for sev-\neral masses based on \ufb01tting the m\u03c4\u03c4 spectrum with\n30 fb\u22121 of data. Background uncertainties are in-\ncorporated by utilizing the pro\ufb01le likelihood ratio.\nThese results do not include the impact of pileup,\nwhich is discussed in Section 4.7.\nmH\nll-channel\nlh-channel\ncombined\n105\n1.95\n2.41\n3.10\n110\n2.44\n3.35\n4.15\n115\n2.98\n4.07\n5.04\n120\n2.92\n3.87\n4.85\n125\n2.75\n3.75\n4.65\n130\n2.46\n3.38\n4.18\n135\n2.21\n3.32\n3.99\n140\n1.80\n2.70\n3.24\n (GeV)\nH\nm\n105 110 115 120 125 130 135 140\n)\n\u03c3\nExpected Significance (\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nATLAS\n-1\n = 14 TeV, 30 fb\ns\nll-channel\nlh-channel\ncombined\nFigure 16: Expected signal signi\ufb01cance for several\nmasses based on \ufb01tting the m\u03c4\u03c4 spectrum. Back-\nground uncertainties are incorporated by utilizing\nthe pro\ufb01le likelihood ratio. These results do not in-\nclude the impact of pileup.\n4.6\nMass determination\nThe mass parameter mH and its error can be determined from the \ufb01ts described above; however, the\nparameter in the model may not be the best estimate of the physical Higgs boson mass. Similarly, the\nerror on the mass parameter from the \ufb01t should be validated with a large number of pseudo-experiments.\nFigure 17 (a) shows the relationship of the input Higgs boson mass and the reconstructed Higgs boson\nmass (i.e. the parameter mH in Equation 11) obtained with 2000 pseudo-experiments per input mass\npoint. Figure 17 (b) shows the m\u03c4\u03c4 resolution for the signal as a function of the input Higgs boson mass.\nWhen scaling the deviation by the MINOS errors, the pull distribution of mH was found to be consistent\nwith the normal distribution N(0,1). The mass resolution is found to be in the range of 8\u223c10 GeV. A\nsimilar mass resolution was found in the hh-channel when analyzing signal Monte Carlo samples.\n4.7\nIn\ufb02uence of pileup\nThe presence of pileup has three major effects on the analysis. First, additional p-p interactions can\nproduce hadronic activity in the central region which causes events to fail the central jet veto. Secondly,\nthe presence of pileup generally degrades the Emiss\nT\nresolution, which, in turn, reduces the ef\ufb01ciency of\nthe collinear approximation cuts and degrades the m\u03c4\u03c4 resolution. Thirdly, pileup degrades the hadronic\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1298\n\ninput Mass (GeV)\n100 105 110 115 120 125 130 135 140\nreco. Mass (GeV)\n100\n105\n110\n115\n120\n125\n130\n135\n140\nlh-channel\n/ndf 4.418/5\n2\n\u03c7\np0 2.645, p1 0.976\nll-channel\n/ndf 4.922/5\n2\n\u03c7\np0 1.105, p1 0.988\nATLAS\ninput Mass (GeV)\n100 105 110 115 120 125 130 135 140\nreco. Mass (GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nlh-channel\n/ndf 7.177/5\n2\n\u03c7\np0 0.019, p1 0.094\nll-channel\n/ndf 17.401/5\n2\n\u03c7\np0 -3.099, p1 0.135\nATLAS\n(a)\n(b)\nFigure 17: The linearity of the \ufb01tted mass versus the input mass (a) and the mass resolution versus the\ninput mass (b). These results do not include the impact of pileup, which is discussed in Section 4.7.\ntau identi\ufb01cation. Fortunately, the electron and muon identi\ufb01cation have been shown to be quite robust\nagainst pileup [15, 16]. While the jet performance is affected by pileup, the analysis is fairly robust\nagainst those effects.\nThe simulation of pileup is technically very challenging since it is performed at a very low level\nin the detector simulation. Limited samples with pileup were available at the time of writing, and the\nEmiss\nT\nand hadronic tau identi\ufb01cation algorithms were not re-tuned in this context. The distribution of\nthe log likelihood ratio discriminant for the calorimeter-based hadronic tau identi\ufb01cation algorithm is\nshifted to lower values for both real taus and jet fakes. By simply adjusting the cut on the log likelihood\nratio to 0, the same signal ef\ufb01ciency can be maintained with approximately a 50% drop in jet rejection.\nBy re-tuning the discriminant in the context of pileup, improved jet rejection should be possible. In all\nthree channels, the mass resolution is degraded from \u223c9.5 to \u223c11.5 GeV for mH = 120 GeV due to the\ndegradation of the Emiss\nT\nresolution. Figure 8 shows that the central jet veto survival probability drops\nfrom \u223c88% to \u223c75% at 1033 cm\u22122 s\u22121 and \u223c65% at 2\u00d71033 cm\u22122 s\u22121. Studies indicate that the use of\ntracking and calorimeter timing information can be used to mitigate this loss in signal ef\ufb01ciency.\nGiven the lack of background samples simulated with pileup and the need to re-optimize the recon-\nstruction and analysis in that context, we do not report signal signi\ufb01cance estimates.\n5\nSystematic uncertainties\n5.1\nOverview\nThe data-driven background estimation methods described above have been developed so that uncer-\ntainty in the background shape and normalization are included directly into the signi\ufb01cance calculation.\nBecause the discovery criterion is simply testing the presence or absence of the signal, it is not sensitive\nto some of the sources of systematic uncertainty. In contrast, measurement of the Higgs boson mass is\nsensitive to the energy scale of electrons, muons, hadronic taus and Emiss\nT\n. Furthermore, measurement\nand exclusion of \u03c3(pp \u2192qqH) \u00d7 BR(H \u2192\u03c4\u03c4) are sensitive to the uncertainty on the signal selection\nef\ufb01ciency. Below we discuss the impact of these systematics on the analysis.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1299\n\n5.2\nSystematic mis-measurement of the signal\nFirst, we consider the purely experimental sources of systematics. The approach here is to assume that\nonce we have data, the estimates of the energy scales, resolutions, and ef\ufb01ciencies might be systemat-\nically biased. Estimates of the systematic uncertainty from various sources are given in Table 14. The\nuncertainty estimates are common for all this series of notes, except for the uncertainties on the central\njet veto and forward jet tagging ef\ufb01ciency. There is not yet a dedicated study of the expected uncertainty\non these ef\ufb01ciencies from data, thus we assume uncertainty on the reconstruction ef\ufb01ciency to be half the\ntau identi\ufb01cation ef\ufb01ciency and point out that most effects relevant to the jets have already been included\nin the jet energy scale uncertainty. We use the nominal detector performance as the central value and\nthen manipulate the Monte Carlo signal to re\ufb02ect these changes. For instance, in the case of the electron\nenergy scale uncertainty, we coherently change all electrons to have 0.5% higher ET, modify the Emiss\nT\nvector accordingly, and recalculate the signal ef\ufb01ciency. This is done individually for each source of\nsystematic and upward and downward \ufb02uctuations are treated separately. In the case of the jet energy\nscale, only some elements of the uncertainty are relevant for Emiss\nT\n. A study of Emiss\nT\nprojected onto\nthe direction of the reconstructed Z in Z \u2192ll+jets with a subset of the analysis cuts indicated that the\nEmiss\nT\nscale can be measured within 5%; thus we only manipulate the Emiss\nT\nvector according to a 5% jet\nenergy scale shift. In the case of systematic uncertainty on resolution, we only considered a degradation\nin the resolution by the tabulated amount. Finally, for systematics on reconstruction and identi\ufb01cation\nef\ufb01ciency we assume a 1-to-1 transfer to the uncertainty on the signal ef\ufb01ciency and include a factor\nof two when the signal ef\ufb01ciency scales as the square (e.g. the electron ef\ufb01ciency in the ll-channel).\nTable 14 summarizes the effect of systematic mis-measurement on the signal ef\ufb01ciency.\nTable 14: Estimated scale of systematic mis-measurements and their effect on the signal ef\ufb01ciency.\n\u2020 When varying the jet energy scale, only a 5% mis-measurement of the jet energy was used in\nmanipulating the Emiss\nT\nvector. See text for details.\nSource\nRelative uncertainty\nEffect on signal ef\ufb01ciency\nluminosity\n\u00b13%\n\u00b1 3%\nmuon energy scale\n\u00b1 1%\n\u00b1 1%\nmuon energy resolution\n\u03c3(pT)\u22950.011pT \u22951.7 10\u22124p2\nT\n\u00b1 0.5%\nmuon ID ef\ufb01ciency\n\u00b11 %\n\u00b1 2%\nelectron energy scale\n\u00b1 0.5%\n\u00b1 0.4 %\nelectron energy resolution\n\u03c3(ET)\u22957.3 10\u22123ET\n\u00b1 0.3 %\nelectron ID ef\ufb01ciency\n\u00b1 0.2%\n\u00b1 0.4%\ntau energy scale\n\u00b1 5%\n\u00b1 4.9%\ntau energy resolution\n\u03c3(E)\u22950.45\n\u221a\nE\n\u00b1 1.5%\ntau ID ef\ufb01ciency\n\u00b1 5%\n\u00b1 5%\n\u00b1 7% (|\u03b7| \u22643.2)\njet energy scale\u2020\n\u00b1 15% (|\u03b7| \u22653.2)\n+16%/\u221220%\n\u00b1 5% (on Emiss\nT\n)\njet energy resolution\n\u03c3(E)\u22950.45\n\u221a\nE (|\u03b7| \u22643.2)\n\u03c3(E)\u22950.67\n\u221a\nE (|\u03b7| \u22653.2)\n\u00b1 1%\nb-tagging ef\ufb01ciency\n\u00b1 5%\n\u00b1 5%\nforward tagging ef\ufb01ciency\n\u00b1 2 %\n\u00b1 2%\ncentral jet reconstruction ef\ufb01ciency\n\u00b1 2 %\n\u00b1 2%\ntotal summed in quadrature\n\u00b120%\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1300\n\n5.3\nTheoretical uncertainty\nIn addition to the effect of systematic mis-measurement on the signal ef\ufb01ciency, theoretical uncertain-\nties also limit our ability to estimate the signal ef\ufb01ciency. Next-to-leading order QCD calculations are\nnow available for the vector boson fusion process. A dedicated study [39] investigated the overall renor-\nmalization and factorization scale dependence (2%) as well as the parton distribution function (PDF)\nuncertainties (3.5%). Next-to-leading order electroweak corrections are also quite large for the vector\nboson fusion process, giving a 3% uncertainty for the full next-to-leading order calculation [40]. Re-\ncently, the dominant next-to-leading order QCD corrections to the Higgs boson plus three jets have been\ncalculated for vector boson fusion, providing a scale uncertainty on the parton-level central jet veto sur-\nvival probability of 1% [41].\nWhile the parton-level theoretical uncertainties are under very good control and below the level of\nboth the statistical error and measurement-related systematics, the same is not true for the theoretical\nuncertainty related to the parton-shower and underlying-event. We rely on Monte Carlo simulations that\nmodel the parton-shower, hadronization, and underlying event to simulate the detector response. The\nuncertainty in these calculations is not comparable to the accuracy of the parton-level predictions. The\ncentral jet veto ef\ufb01ciency was studied with the signal process generated with PYTHIA (with various\ntunings), HERWIG and SHERPA and the fast detector simulation. After the analysis cuts, the different\ngenerators differ by 41%. Studies focusing speci\ufb01cally on the matrix element\u2013parton shower matching\nindicate a substantially smaller uncertainty [33, 42]. We will measure the underlying event [43, 44] and\ntune the parton shower and hadronization with data, but it is likely that this contribution of the uncertainty\nwill remain signi\ufb01cant. Currently there is no estimate of the expected uncertainty related to the parton-\nshower, hadronization, and underlying event tuning. Clearly, this is an area that deserves attention as\nsuch a large uncertainty will hinder exclusions if a Higgs boson does not exist in this mass range and\ncross-section and coupling measurements if one does. After discussions with the authors of PYTHIA,\nHERWIG and SHERPA we feel that the residual uncertainty in the parton shower after tuning to the\ndata will be less than the 18% uncertainty quoted for the jet energy scale. Thus, the uncertainty in the\nsignal ef\ufb01ciency will be dominated by the jet energy / Emiss\nT\nscale uncertainty and the precise uncertainty\nin the parton shower is not relevant. Table 15 summarizes the theoretical uncertainties for the signal\nproduction.\nTable 15: Theoretical uncertainties which affect the estimation of the signal ef\ufb01ciency.\nSource\nRelative uncertainty\nEffect on signal ef\ufb01ciency\nPDF uncertanties\n\u00b13.5%\n\u00b13.5%\nscale dependence on cross-section\n\u00b13%\n\u00b1 3%\nscale dependence CJV ef\ufb01ciency\n\u00b1 1%\n\u00b1 1%\nparton-shower and underlying event\n\u00b1 \u226410%\n\u00b1 <10%\ntotal summed in quadrature\n\u00b1 < 10%\n6\nDiscussion\nThe expected signal signi\ufb01cances in Table 13 are qualitatively consistent with the results found in\nRef. [4]; however, the predicted cross-sections in Tables 9 and 10 are signi\ufb01cantly different. In particular,\nthe initial cross-section of the Z+jets background is smaller by nearly a factor of four and the t\u00aft back-\nground in the ll-channel is larger by nearly a factor of 2. Much of this difference re\ufb02ects the evolution\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1301\n\n (GeV)\nH\nm\n100 105 110 115 120 125 130 135 140 145\np(Mass Floated)/p(Mass Fixed)\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n5.5\n6\nll-channel\nlh-channel\ncombined\nATLAS\nFigure 18: The ratio of expected p-values for the\n\ufb02oating and \ufb01xed mass \ufb01ts as a function of the\nHiggs boson mass. This plot summarizes the im-\npact of the \u201clook-elsewhere\u201d effect in this analysis.\n (GeV)\nH\nm\n105 110 115 120 125 130 135 140\n\u00b5\nExpected 95% CL Exclusion for \n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nATLAS\n-1\n = 14 TeV, 10 fb\ns\nll-channel\nlh-channel\nFigure 19: Expected 95% exclusion of the signal\nrate in units of the Standard Model expectation, \u00b5,\nas a function of the Higgs boson mass for the ll and\nlh-channels with 10 fb\u22121 of data. The exclusion\ntakes into account the uncertainty on the signal\nef\ufb01ciency described in Section 5.\nin the Monte Carlo generators for these challenging backgrounds. In the case of the Z+jets background,\ndifferences in the choice of renormalization and factorization scales and parton density functions are the\nsource for part of the discrepancy; however, approximately a factor of two comes from the treatment of\nsoft and collinear divergences. After substantial investigation, we concluded that the Z+jets background\nestimate used in Ref. [4] was conservative. In the case of t\u00aft+jets, the necessary matching between ma-\ntrix elements and parton showers had not been developed when Ref. [4] was written. The recipe used to\nmerge the t\u00aft+0,1,2 jet samples at that time and the more realistic b-tagging performance limits our ability\nto understand in detail the source of the differences. We are con\ufb01dent that MC@NLO and our current\ndetector simulation and of\ufb02ine reconstruction provide a superior prediction of this background.\nFor the \ufb01rst time, ATLAS has investigated the potential of the hh-channel. Much of this work has\nbeen devoted to the development and study of tau and missing ET triggers. It now appears that the trigger\nis feasible, and the reconstruction of the signal maintains an ef\ufb01ciency and m\u03c4\u03c4 mass resolution compa-\nrable to the ll- and lh-channels. The open question for this channel is the size of the QCD background \u2013\na question that can only be answered with data.\nThe results shown in Section 4 are based on a \ufb01xed mass hypothesis. If one leaves the Higgs boson\nmass a free parameter in the likelihood \ufb01ts, then one must take into account the \u201clook-elsewhere\u201d ef-\nfect. Naively, one would expect the magnitude of the effect to be rather small for this channel given the\n\u223c10 GeV mass resolution and the \u223c30 GeV mass range of interest. Detailed study shows that it is a mix-\nture of two effects. First, the distribution of \u22122log\u03bb(\u00b5 = 0) is not \u03c72-distributed under the background-\nonly hypothesis; it has a longer tail which raises the p-value. Secondly, the median of \u22122log\u03bb(\u00b5 = 0)\nunder the signal-plus-background hypothesis is systematically larger in the \ufb02oating mass case because\nthe model can adapt to \ufb02uctuations in the signal mean. Figure 18 summarizes the impact of these two\neffects.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1302\n\nFuture work for this channel includes an extensive study of performance in the context of pileup,\nincluding optimization of the hadronic tau identi\ufb01cation and Emiss\nT\nreconstruction. The data-driven\nbackground estimation for the t\u00aft and W+jets backgrounds must be further developed. In order to measure\n\u03c3(pp \u2192qqH)\u00d7BR(H \u2192\u03c4\u03c4) at the desired level, the systematics associated with the signal ef\ufb01ciency\nmust be reduced. This requires a technique to measure the central jet veto and forward jet tagging\nef\ufb01ciency in data. Additionally, the use of the Emiss\nT\nprojection method should be further developed to\nmitigate the impact of the jet energy scale uncertainty.\nWhile the results shown in Section 4 only include the contribution of Higgs bosons produced via\nvector boson fusion, an additional 10% contribution from the gluon-fusion production process could\nbe expected at mH = 120 GeV. Finally, the theoretical uncertainty associated with the parton shower\nand underlying event, which currently gives the largest uncertainty on the signal ef\ufb01ciency, must be\naddressed. The tuning of the parton shower, hadronization, and underlying event model will be among\nthe earliest measurements at the LHC. If the residual theoretical uncertainty is not reduced suf\ufb01ciently, a\ndifferent strategy may need to be found for the central jet veto. The expected exclusion power based on\nthe uncertainty in the signal ef\ufb01ciency is shown in Fig. 19.\n7\nSummary and conclusion\nThe sensitivity of the ATLAS detector to a Standard Model Higgs boson produced via vector boson\nfusion with subsequent decay into taus has been investigated with state-of-the-art Monte Carlo genera-\ntors, a full GEANT-based simulation of the ATLAS detector and our current trigger and reconstruction\nalgorithms. Particular emphasis has been placed on data-driven background estimation strategies and the\nestimation of the associated uncertainties in normalization and shape. The impact of pileup has not been\nfully addressed; however, results without pileup indicate that a \u223c5\u03c3 signi\ufb01cance can be achieved for a\nHiggs boson mass in the range 115 \u2013 125 GeV after collecting 30 fb\u22121 of data and combining the ll- and\nlh-channels. The Higgs boson mass resolution is approximately 10 GeV, leading to approximately 3.5%\nmass measurement. The hh-channel has also been investigated and gives similar results for signal and\nnon-QCD backgrounds as the other channels; however due to the challenge of predicting the QCD back-\nground, we do not report on an estimated sensitivity for that channel. Currently, measurement-related\nsystematics and large theoretical uncertainties limit the ability for a measurement of the product of cross-\nsection and branching ratio. 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James and M. Roos, \u201cMINUIT, a System for Function Minimaization and Analysis of the Pa-\nrameter Errors and Correlations\u201d, Comput. Phys. Commun. 10 (1975) 343.\n[35] V.M. Abazov et al., The D0 Collaboration, \u201cFirst measurement of \u03c3( \u00afpp \u2192Z)Br(Z \u2192\u03c4\u03c4) at \u221as =\n1.96 TeV\u201d, Phys. Rev. D 71 (2005) 072004.\nFurther\ndiscussion\nin\npreliminary\ndraft\nof\n\u201cMeasurement\nof\n\u03c3( \u00afpp\n\u2192\nZ)Br(Z \u2192\u03c4\u03c4)\nwith\n1\nfb\u22121\nat\n\u221as\n=\n1.96\nTeV\n\u201d\nfound\nhere:\nhttp://www-\nd0.fnal.gov/Run2Physics/WWW/results/prelim/EW/E21/E21.pdf\n[36] S. Duensing, \u201cMeasurement of \u03c3( \u00afpp \u2192Z)Br(Z \u2192\u03c4\u03c4) at \u221as = 1.96-TeV using the D0 detector at\nthe Tevatron\u201d, FERMILAB-THESIS-2004-23.\n[37] W. Verkerke and D. Kirkby, \u201cThe RooFit Toolkit for data modeling\u201d, hep-ph/0306116.\n[38] R. Barlow, \u201cAsymmetric errors\u201d, In the Proceedings of PHYSTAT2003: Statistical Problems in Par-\nticle Physics, Astrophysics, and Cosmology, Menlo Park, California, 8-11 Sep 2003, pp WEMT002,\nhep-ph/0401042.\n[39] T. Figy, C. Oleari and D. Zeppenfeld, \u201cNext-to-leading order jet distributions for Higgs boson\nproduction via weak-boson fusion\u201d, Phys. Rev. D 68 (2003) 073005.\n[40] M. Ciccolini, A. Denner and S. Dittmaier, \u201cStrong and electroweak corrections to the production\nof Higgs+2jets via weak interactions at the LHC\u201d, Phys. Rev. Lett. 99 (2007) 161803.\n[41] T. Figy, V. Hankele and D. Zeppenfeld, \u201cNext-to-leading order QCD corrections to Higgs plus three\njet production in vector-boson fusion\u201d, hep-ph/0710.5621.\n[42] V. Del Duca et al., \u201cMonte Carlo studies of the jet activity in Higgs + 2jet events\u201d, J. High Energy\nPhys. 0610 (2006) 016.\n[43] The ATLAS Collaboration, \u201cA Study of Minimum Bias Events\u201d, this volume.\n[44] D. Acosta et al., The CDF Collaboration, Phys. Rev. D 70 (2004) 072002.\nHIGGS \u2013 SEARCH FOR THE STANDARD MODEL HIGGS BOSON VIA VECTOR BOSON FUSION . . .\n1305\n\nHiggs Boson Searches in Gluon Fusion and Vector Boson\nFusion using the H \u2192WW Decay Mode\nAbstract\nThe prospects for Higgs searches in the H +0j (H \u2192WW \u2192e\u03bd\u00b5\u03bd), H +2j\n(H \u2192WW \u2192e\u03bd\u00b5\u03bd), and H +2j (H \u2192WW \u2192\u2113\u03bdqq) channels at ATLAS are\npresented, including realistic effects such as trigger ef\ufb01ciencies and detector\nmisalignment, with an emphasis on practical methods to estimate the back-\ngrounds using control samples in data. With 10 fb\u22121 of integrated luminosity,\none would expect to be able to discover a Standard Model Higgs boson in the\nmass range 135 < mH < 190 GeV and to be able to measure its mass with a\nprecision of about 7 GeV if its true mass is 130 GeV or about 2 GeV if its true\nmass is 160 GeV.\n1\nIntroduction\nThe nature of the Electroweak symmetry breaking sector is arguably the most important unknown in\nparticle physics today. An introduction to the Higgs mechanism and an overview of the possible search\nchannels for a (standard model) Higgs boson at the LHC can be found in Ref. [1]. This note studies\nthe sensitivity of Higgs boson searches in the decay mode H \u2192WW to a Standard Model Higgs boson.\nSpecial emphasis is placed on in-situ control samples that can be used to estimate the background con-\ntributions using data and on the systematic uncertainties associated with these background determination\nmethods.\nThe note is organised as follows: Section 2 discusses the production mechanisms and \ufb01nal states\nunder study, the relevant backgrounds for each process and the Monte Carlo generators used to model\nthem. In Section 3, the performance of the reconstruction for the various \ufb01nal-state particles is described.\nIn Section 4, an overview of statistical issues common to most of the analyses is presented. Section 5\ndescribes the event selection and control samples for a search for H \u2192WW \u2192e\u03bd\u00b5\u03bd in events where no\nhard jets are reconstructed in the detector. In Section 6, the analysis of the H +2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd\nchannel is presented, and in Section 7, an analysis of events where one of the W bosons decays to two\njets is discussed. Finally, in Section 8, the combined sensitivity of the ATLAS detector to the presence\nof neutral scalar resonances in the W pair \ufb01nal state is presented.\n2\nPhysics Processes and Monte Carlo\nIn the Standard Model, there are two dominant production modes of the Higgs boson in the kinematic\nregion of interest for the H \u2192WW decay mode: gluon fusion and Vector Boson Fusion (VBF). In\nstudies of the former production mode, one must consider background processes that yield two leptons\nand signi\ufb01cant missing transverse energy in the \ufb01nal state; in the latter, the \ufb01nal state also includes two\nhard jets (from the struck quarks) which tend to be well-separated in pseudorapidity. This note considers\nthe following signal and background processes:\n\u2022 Higgs boson production via gluon fusion: This is the dominant production mechanism for the\nsignal considered in the analysis of Section 5; it is modeled with 48500 events generated by\nMC@NLO [2, 3]. A Higgs boson decay matrix element similar to the one used in Ref. [4] was\nused to reweight this Monte Carlo sample to include the complete spin correlations for the Higgs\ndecay.\n1306\n\n\u2022 Higgs boson production via Vector Boson Fusion: This is the dominant production mechanism\nfor the Higgs boson searches of Sections 6 and 7. This process is modeled with the generators\nprovided in PYTHIA [5] (14500 events), HERWIG [6] (18050 events), and SHERPA [7] (19950\nevents).\n\u2022 pp \u2192WW production. This is the dominant background contribution to the analysis studied in\nSection 5; in that analysis, it is modeled with 178450 events generated by MC@NLO. It is impor-\ntant to note that MC@NLO only calculates the O(\u03b10\ns ) and O(\u03b11\ns ) contributions to this process;\nit does not compute the O(\u03b12\ns ) contributions. Because of the large gluon luminosity expected at\nLHC it is important to include at least the gluon-initiated component (where the W pair production\nproceeds via a quark box) for the analysis of the fully jet-vetoed \ufb01nal state. This contribution is\nmodeled with 176300 events produced using the generator in Ref. [8].\nIn the Vector Boson Fusion searches, the contributions from processes like qq \u2192WWqq (mediated\nby the exchange of a weak boson or a gluon) become important. Therefore, a sample of 171250\nevents generated with ALPGEN [9,10] is used instead of MC@NLO to model the pp \u2192WW j j\nbackground in the analysis of Section 6.\n\u2022 tt production. The two top quarks decay into a pair of W bosons and two b jets. The cross-section\nis expected to be dominated by doubly resonant tt production in the Vector Boson Fusion searches\nof Sections 6 and 7; however, for the search of Section 5, one must also take care to handle the\nsingle-top background correctly. The absolute cross-section for the contribution from single top\nproduction is presently only known with leading-order uncertainties, but since the search presented\nin Section 5 normalises the top background using data, it is only necessary to consider its potential\nimpact on the extrapolation from the b-tagged to the b-vetoed region. In the estimation of the\nsensitivity of all channels under study, a sample of 538300 events generated with MC@NLO is\nused to model this background. Two MadEvent [11\u201313] samples are used to estimate the impor-\ntance of the contribution from single-top production in the H +0j channel: one contains all matrix\nelements for pp \u2192WWbb; the other contains only the doubly-resonant contribution.\n\u2022 Z \u2192ll production. In channels with two electrons or two muons, the direct decays of Z \u2192ee and\nZ \u2192\u00b5\u00b5 dominate, but this background can also contribute to e\u00b5 \ufb01nal states when the Z decays to\na pair of \u03c4 leptons which both decay leptonically. This background is modeled with a sample of\n163200 events generated with PYTHIA in the H +0j analysis of Section 5 and with a sample of\n38150 events produced using ALPGEN in the H +2j analysis of Section 6.\n\u2022 W+n jets production, with n \u22645. This is the dominant background for the lepton-hadron channel;\nhowever, it can also play a role in the dilepton channels as a source of fakes. This background is\nmodeled using a sample of 411424 events generated with ALPGEN.\nA special subset of this background is W+c+n jets, with n \u22644. The charm production in associa-\ntion with a W boson through processes like gs \u2192Wc is enhanced, due to the large parton density\nfunction of strange sea quarks and the large CKM matrix element |Vcs|. Decays of charm mesons\nare a potential source of leptons. Lepton isolation cuts are tuned on this kind of background, to\nreach the necessary rejection against leptons from semileptonic charm- or b- decays. [14].\n\u2022 bb, cc and QCD multi-jet. Due to the large cross section of these processes they could be a further\nsource of background. The large amount of CPU power needed makes a Monte Carlo simulation of\nthese backgrounds currently unrealistic. For the dilepton channels the requirement of two leptons\nand missing transverse energy should reduce these backgrounds to a negligible level.\nTable 1 gives an overview of the cross sections of the signal and background samples used in this\nnote. Detailed tables of the Higgs boson cross sections and branching ratios can be found in Ref. [1].\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1307\n\nProcess\nGenerator\nCross-section(pb)\ngg \u2192H \u2192WW (MH = 170 GeV)\nMC@NLO\n19.418\nVBF H \u2192WW (MH = 170 GeV)\nPYTHIA/Sherpa\n2.853\nVBF H \u2192WW (MH = 300 GeV)\nHERWIG\n0.936\nqq/qg \u2192WW\nMC@NLO/Alpgen\n111.6\ngg \u2192WW\nGG2WW\n5.26\npp \u2192tt\nMC@NLO\n833\nZ \u2192\u03c4\u03c4+jets\nPYTHIA/ALPGEN\n2015\nW+jets\nALPGEN\n20510\nTable 1: Overview of the Monte Carlo generators and cross sections for the Higgs boson signal and\nbackground processes used in this note. The W+jets cross-section listed is the cross-section per lepton\n\ufb02avor.\n3\nReconstruction\nThe \ufb01nal states considered here all include leptons. Section 3.1 brie\ufb02y describes the lepton selection\ncriteria and other central aspects of the reconstruction used in this note. Then, in Section 3.2, a few\nimportant details about jets, Emiss\nT\n, and pile-up are brie\ufb02y discussed. Note that the results presented in this\nnote were made using version 12 of the ATLAS software, whereas the results on detector performance\nin Refs. [15] and [16] are based on release 13.\n3.1\nLeptons\nThe electron selection consists of the following criteria :\n\u2022 Electrons are identi\ufb01ed using the standard ATLAS criteria described in Ref. [15]. In the H + 0j\n(H \u2192WW \u2192e\u03bd\u00b5\u03bd) and H + 2j (H \u2192WW \u2192\u2113\u03bdqq) channels, tight electrons are required. In\nthe case of the H + 2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd analysis of Section 6, a suf\ufb01ciently strong rejection\nagainst the W+jets background can be achieved by applying cuts on the VBF tagging jets that it is\npossible to use a medium electrons instead.\n\u2022 A track match is required. The transverse impact parameter signi\ufb01cance of the matched track,\nd0/\u03c3d0, is required to be less than 10.\n\u2022 Candidates are required to be well isolated. Calorimeter isolation in a \u2206R cone of 0.2 is required\nto be less than 5 GeV, and \u03a3pT of tracks in a cone of \u2206R < 0.4, excluding tracks from other lepton\ncandidates and tracks with pT < 1 GeV, is required to be less than 5 GeV.\n\u2022 Kinematic acceptance: pT > 15 GeV and |\u03b7| < 2.5 (The pT threshold is larger for the lepton-\nhadron channel). Electron candidates in the crack region, 1.37 < |\u03b7| < 1.52, are excluded.\nIt has been shown that similar isolation criteria can effectively suppress the background from W+c+jet\nevents, where a second lepton comes from charm decay, to negligible levels.\nW+jets is one of the main sources of fake backgrounds for the dilepton channels; it is crucial to\nachieve a good rejection against this background. The probability for a jet to be misreconstructed as\nan electron was derived from a W(\u2192\u00b5\u03bd)+jets sample which contains no true high pT electrons. The\naverage ef\ufb01ciency to reconstruct an electron candidate without isolation cuts in the gg \u2192H \u2192WW signal\nevents is 60.3\u00b10.5%; the additional isolation criteria reduce this to 50.0\u00b10.5% ef\ufb01ciency. With all cuts,\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1308\n\nthe average fake rate as determined from W \u2192\u00b5\u03bd+jets events is (1.7\u00b10.2)\u00d710\u22124 before isolation and\n(6.7+1.5\n\u22121.3)\u00d710\u22125 after isolation.\nThe muon selection consists of a similar set of cuts :\n\u2022 Combined muons and best match to an inner detector track [16].\n\u2022 Calorimeter Isolation based on the etcone20 variable [16] (etcone20 < 2.5 GeV) and track isola-\ntion (in a cone of \u2206R < 0.4) as for electrons, but with a different pT threshold, \u03a3pT < 3 GeV.\n\u2022 Transverse impact parameter signi\ufb01cance less than 10.\n\u2022 pT > 15 GeV and |\u03b7| < 2.5 (The pT threshold is larger for the lepton-hadron channel)\nAs for the electrons, similar isolation criteria were shown to be effective against the W+c+jet back-\nground. The performance for muons is better than for electrons. The average ef\ufb01ciency to reconstruct a\nmuon candidate in gg \u2192H \u2192WW signal events is 94.2 \u00b1 0.1% before isolation cuts and 77.1 \u00b1 0.2%\nafter applying cuts. The corresponding fake rate in W \u2192e\u03bd+jets events is (1.7+0.6\n\u22120.5)\u00d710\u22125 after isolation\ncuts are applied.\n3.2\nJets, Missing pT, and Pile-up\nIn the H +2j searches of Sections 6 and 7, the presence of at least two jets with pT > 20 GeV and a large\ndifference in pseudorapidity are required. It is frequently the case that at least one of these jets will land\nin the forward region of the detector. To minimise the effect of calorimeter noise and maximise ef\ufb01ciency\nfor the jets of interest to this study, jets reconstructed from topological clusters are used, rather than jets\nreconstructed from calorimeter towers [17]. For VBF Higgs boson signal processes the ef\ufb01ciency for jets\nwith a cone size of \u2206R = 0.4 from topological clusters is 94.3% in the central detector region and 95.3%\nin the forward region. For jets from calorimeter towers the ef\ufb01ciency is signi\ufb01cantly lower with 92.4%\nin the central detector region and 84.1% in the forward region.\nAll the searches considered in this note make use of analysis techniques that either select or give\na large weight to events without additional jets; in either case, events are effectively rejected if they\ncontain extra jets beyond those jets (if any) that are explicitly required by the analysis. Even in the \ufb01rst\nyears of \u201clow-luminosity\u201d data taking at the LHC, analyses will be affected by the pile-up of multiple\ncollisions per beam crossing. Low pT QCD interactions (minimum-bias) are present simultaneously to\na hard interaction. Such pile-up events will give rise to jet activity that can sometimes cause interesting\nsignal events to be erroneously rejected; in selecting a jet algorithm, it is necessary to consider this\neffect. Single minimum-bias events have a three times lower probability to be discarded by the central\njet veto cut when using jets reconstructed with a cone size of \u2206R = 0.4 instead of jets with a cone size\nof \u2206R = 0.7. Furthermore, in the presence of pile-up the jet calibration has to correct for the additional\nenergy that is not from the hard interaction. Due to the well de\ufb01ned jet area, this is much easier done\nwith a cone jet algorithm than with a kt jet algorithm.\nFor the reasons mentioned above, the analyses in this note have used jets reconstructed from topo-\nlogical clusters with a cone algorithm of \u2206R = 0.4 [17]. Jet ef\ufb01ciencies increase with ET and are rather\nstable with |\u03b7|. However it should be noted that the ef\ufb01ciency drops at |\u03b7| \u22654.8 near the boundary of\nthe forward calorimeter, as expected. Therefore this note uses only jets with |\u03b7| \u22644.8. Jets within a cone\nof \u2206R < 0.4 of any electron candidate are ignored.\nThere are other ways to minimise the impact of pile-up; the tracking system of the ATLAS detector\nis designed to separate the vertices of the different inelastic collisions in an event. Jets built of tracks\nemerging from the same vertex as the leptons from the Higgs boson decay should be insensitive to pile-up\nif the vertex reconstruction is working as expected.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1309\n\n(Standard Jet) [GeV]\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\nEntries /( 4.2 GeV )\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n WW (without pile-up)\n\u2192\nH \n WW (with pile-up)\n\u2192\nH \nATLAS\n(Track Jet) [GeV]\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\nEntries /( 4.2 GeV )\n0\n10\n20\n30\n40\n50\n WW (without pile-up)\n\u2192\nH \n WW (with pile-up)\n\u2192\nH \nATLAS\nFigure 1: Jet pT distributions (|\u03b7| < 2.5) for the H \u2192WW signal sample with (red line) and without\n(gray \ufb01lled area) pile-up. Left: Standard jets. Right: Track jets.\nWhile the H \u2192WW searches presented in this note use standard calorimeter jets for the jet veto, it\nis important to illustrate the potential of track jets. The H + 2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd analysis has been\nstudied as an example.\nTrack jets are reconstructed from only those tracks that have pT > 0.5 GeV and with at least 7 hits\nin the pixel and semiconductor tracker. The Higgs boson production vertex is taken to be the vertex for\nwhich the sum of the transverse energies of the emerging tracks is largest. All tracks that emerge from\nthis vertex and are not associated with an isolated lepton are fed into the standard ATLAS cone \u2206R = 0.4\njet algorithm. Leptons are considered isolated if the sum of the transverse energies of all tracks from the\nsame vertex as the lepton in a cone of 0.01< \u2206R < 0.2 around the lepton is less than 5 GeV.\nThe independence of the track jets to activity from pile-up is re\ufb02ected in the jet pT distributions in\nthe H \u2192WW signal sample without and with pile-up (pile-up was generated with an average of 2.3\nadditional events) in Figure 1. The additional pp collisions in presence of pile-up created additional\nstandard jets at low transverse energies while the multiplicities of track jets are unaffected by pile-up.\nA central jet veto cut is constructed using track jets in the acceptance region of the inner detector\nof |\u03b7| < 2.5 and standard jets at larger pseudorapidities (up to |\u03b7| < 3.2). The cut on the transverse\nmomentum of the track jets is chosen such that the same rejection ef\ufb01ciency is obtained for H \u2192WW\nevents without pile-up as for the jet veto based on standard jets. This requires a lowering of the pT cut\nfrom 20 GeV for standard jets to 12.3 GeV for track jets. Table 2 shows the fraction of events passing\nH \u2192WW\nt\u00aft\nno pile-up\nwith pile-up\nno pile-up\nwith pile-up\nstd jets (|\u03b7| < 2.5)\n72.0\u00b11.0\n63.0\u00b11.2\n28.6\u00b13.4\n19.7\u00b13.3\ntrack jets\n72.0\u00b11.0\n73.5\u00b11.1\n28.6\u00b13.4\n25.9\u00b13.6\nstd jets (|\u03b7| < 3.2)\n65.4\u00b11.0\n57.0\u00b11.2\n24.0\u00b13.2\n16.3\u00b13.0\ncombination\n65.8\u00b11.0\n65.9\u00b11.1\n24.0\u00b13.2\n23.1\u00b13.5\nTable 2: Fraction of events (%) passing the central jet veto\nthe different options for the central jet veto. The central jet veto based on standard jets is sensitive to\npile-up while the track jets show only small sensitivity to pile-up. The combination of the track jet veto\nin |\u03b7| < 2.5 and the standard jet veto in |\u03b7| > 2.5 shows robustness against pile-up.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1310\n\nlog Likelihood Ratio\n0\n10\n20\n30\n40\n50\n60\nProbability\n7\n10\n6\n10\n5\n10\n4\n10\n3\n10\n2\n10\n1\n10\n1\nBackground Only\n=200 GeV\nH\nS+B, M\n=350 GeV\nH\nS+B, M\n=550 GeV\nH\nS+B, M\n-1\n L dt=10 fb\n\u222b\nATLAS\nlog Likelihood Ratio\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nProbability\n6\n10\n5\n10\n4\n10\n3\n10\n2\n10\n1\n10\n1\nBackground Only\n=130 GeV\nH\nS+B, M\n=160 GeV\nH\nS+B, M\n=190 GeV\nH\nS+B, M\n1\n L dt=10 fb\n\u222b\nATLAS\nFigure 2: Left: The log Likelihood Ratio distributions for toy Monte Carlo corresponding to the\nH \u2192WW \u2192\u2113\u03bdqq analysis at 10 fb\u22121 for background-only outcomes (red) and signal-plus background\noutcomes with several values of the Higgs boson mass. Right: The same plot, but for the H + 2j,\nH \u2192WW \u2192e\u03bd\u00b5\u03bd analysis.\nThe performance of the missing transverse momentum reconstruction is strongly affected by the\npresence of pile-up. In this study, the cell based reconstruction algorithm described in Ref. [18] has been\nused.\nFortunately, the H \u2192WW \u2192\u2113\u03bd\u2113\u03bd searches are not very sensitive to the resolution of Emiss\nT\n. Since\nthe Higgs boson mass cannot be directly reconstructed in the 2\u21132\u03bd \ufb01nal state, a transverse mass is used;\nalthough this does have a peak centred around the true value of the Higgs boson mass, the distribution is\nvery broad (several tens of GeV). Therefore a degraded Emiss\nT\nresolution is unlikely to signi\ufb01cantly alter\nthe transverse mass shape unless the degradation is rather severe. The H +2j (H \u2192WW \u2192\u2113\u03bd\u2113\u03bd) anal-\nysis of Section 6 makes use only of this transverse mass and observables related to the leptons and the jet\nactivity in the event; the Emiss\nT\ncut in that analysis serves mostly to reject backgrounds like Z \u2192ee/\u00b5\u00b5\nwhich have no intrinsic Emiss\nT\n. The H +0j analysis of Section 5 does make use of the transverse momen-\ntum of the Higgs boson candidate, which is obviously very sensitive to the Emiss\nT\nresolution; however, that\nanalysis involves a \ufb01tting algorithm developed with exactly this concern in mind and includes checks that\ndemonstrate that the algorithm still works reliably in the presence of a degraded Emiss\nT\nmeasurement.\nIn the case of the H \u2192WW \u2192\u2113\u03bdqq analysis of Section 7, the Emiss\nT\nis used in the reconstruction of the\nHiggs boson candidate\u2019s invariant mass. In principle, then, a degraded Emiss\nT\nresolution does propagate\ninto the Higgs boson mass resolution, and so problems with the Emiss\nT\nreconstruction are more harmful to\nthe H \u2192WW \u2192\u2113\u03bdqq channel than to the dilepton channels. However, for a Standard Model-like Higgs\nboson with a mass above \u2248300 GeV, the natural width of the Higgs boson tends to become rather large,\nand the Emiss\nT\nresolution is again not the primary concern of the analysis.\nMismeasurements of jets and detector inef\ufb01ciencies can lead to instrumental Emiss\nT\n. It is very hard to\npredict such effects without real data and no cuts to reduce instrumental Emiss\nT\nare currently foreseen.\n4\nStatistical Formalism\nThe sensitivity estimates presented in this note use a \ufb01t-based hypothesis testing procedure. Unless\nstated otherwise, selection cuts are always independent of the Higgs boson mass hypothesis, no matter\nhow broad the range of masses where the search is sensitive. To take advantage of the discriminating\npower contained in variables for which the distribution depends signi\ufb01cantly on the Higgs boson mass\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1311\n\nSelection\nSelection cuts\ngg \u2192H\ntt\nWW\nZ \u2192\u03c4\u03c4\nW + jets\nLepton Selection+Mll\n166.4\n6501\n718.12\n4171\n209.1\npre-\npmiss\nT\n> 30 GeV\n147.7\n5617\n505.25\n526.3\n181.6\nselection\nZ \u2192\u03c4\u03c4 Rej.\n145.8\n5215\n485.12\n164.2\n150.4\nJet Veto\n61.80\n14.84\n238.35\n31.91\n76.12\nb-veto\n61.56\n6.85\n237.87\n30.76\n76.12\n\u2206\u03c6ll < 1.575,\nsignal region\nMT < 600 GeV\n50.6\u00b12.5\n2.3\u00b11.6\n85.4\u00b12.7\n<1.7\n38\u00b138\n\u2206\u03c6ll > 1.575,\ncontrol region\nMT < 600 GeV\n10.9\u00b11.1\n4.6\u00b12.3\n151.9\u00b13.6\n30.8\u00b14.2\n38\u00b138\nb-tagged\nsignal region\n\u2206\u03c6ll < 1.575\n-\n1.14\u00b11.14\n-\n-\n-\nb-tagged\ncontrol region\n\u2206\u03c6ll > 1.575\n-\n5.71\u00b12.55\n-\n-\n-\nTable 3: Cut \ufb02ows (in fb) for MH = 170 GeV in the H +0j, H \u2192WW \u2192e\u03bd\u00b5\u03bd channel. A \u2018-\u2019 indicates\nthat the corresponding contribution is ignored in the \ufb01t. The WW background contains the two processes\nq \u00afq \u2192WW and gg \u2192WW.\nhypothesis or is not precisely predicted by theory, a maximum-Likelihood \ufb01t to those variables is used.\nTo perform the hypothesis test itself, a Likelihood Ratio is used, \u03bb = Ls+b/Lbg\u2212only. The numerator and\ndenominator of this ratio are obtained from separate \ufb01ts to the data, with the number of signal \ufb02oating as\na free parameter (subject to the constraint Ns \u22650) in the \ufb01t for Ls+b, and with the number of signal \ufb01xed\nto zero in the \ufb01t for Lbg\u2212only. The sampling distributions of \u03bb at a given luminosity (in the presence of\nsignal and in its absence) are studied by generating pseudo-experimental outcomes and performing the\nfull \ufb01t to each outcome.\nThroughout this note, when a \ufb01t is performed, the Higgs boson mass mH is allowed to \ufb02oat as a free\nparameter in the \ufb01t. The resulting signi\ufb01cance estimates therefore represent the probability that, in the\nabsence of signal, a background \ufb02uctuation anywhere in the allowed mass range would produce an excess\nat least as signi\ufb01cant as the observed excess. This is slightly different from the convention adopted in\nsome other studies, where the signi\ufb01cance represents the probability that a background \ufb02uctuation would\nproduce an excess that is consistent with a speci\ufb01ed mass and at least as signi\ufb01cant as the observed\nexcess.\nFigure 2 shows two examples of the Likelihood Ratio probability distributions. The left plot shows\nthe sampling distribution of the Likelihood Ratio for the H \u2192WW \u2192\u2113\u03bdqq \ufb01t discussed in Section 7\n(assuming a negligible background from fakes), and the right plot shows the corresponding distributions\nfor the analysis of Section 6.2. A \ufb01t to the real data would yield one value of \u03bb; to obtain a p-value, one\nwould integrate the red distribution in the acceptance region, i.e. from the observed value of \u03bb to in\ufb01nity.\nIn the absence of data, the expected signi\ufb01cance is computed by taking the \u201cobserved\u201d value of \u03bb to\nbe the median of the signal-plus-background distribution for a given mass. The expected signi\ufb01cance Z\nreported here is one-sided, i.e., Z =\n\u221a\n2erfc\u22121(2p). When the number of pseudo-experimental outcomes\nin the acceptance region is too small, the background-only Likelihood Ratio distribution is extrapolated\nwith an exponential decay.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1312\n\n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\nNormalized to 1\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nSignal\nQCD WW\nATLAS\n(GeV)\nWW\nP\n0\n10\n20\n30\n40\n50\n60\nNormali ed to 1\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nSignal\nQCD WW\nATLAS\n(GeV)\nM\n0\n100\n200\n300\n400\n500\n600\nEvents / ( 10 )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n(GeV)\nM\n0\n100\n200\n300\n400\n500\n600\nEvents / ( 10 )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nW+jets\nWW\ntt\nSignal\nPseudodata\nATLAS\n1\n L dt=10 fb\n\u222b\nFigure 3: Left: transverse opening angle \u2206\u03c6ll of the two leptons after preselection cuts. Middle : trans-\nverse momentum pWW\nT\nof the WW system after preselection cuts. Right: transverse mass MT for events\nwith \u2206\u03c6ll < 1.575 and pWW\nT\n> 20 GeV, in a \ufb01tted toy Monte Carlo outcome containing a Standard Model\nHiggs boson with MH = 170 GeV, after 10 fb\u22121 of integrated luminosity. The Likelihood Ratio in this\noutcome is 30.69, which is typical for this value of MH and this luminosity.\n5\nLeptonic W Pair Production with No Hard Jets\nThe H + 0j, H \u2192WW \u2192\u2113\u03bd\u2113\u03bd channel has been shown to have a strong discovery potential. [19\u201322]\nThe basic event selection consists of only a few simple cuts:\n\u2022 Require that the event has exactly two isolated, opposite-sign leptons (electron or muon) with\npT > 15 GeV.\n\u2022 To suppress backgrounds from single-top production, backgrounds from dileptonic decays of bb\nand cc resonances, and lepton pairs from b \u2192c cascade decays, require that the invariant mass mll\nof the leptons is between 12 GeV and 300 GeV.\n\u2022 Require that the event has Emiss\nT\n> 30 GeV\n\u2022 To suppress backgrounds from Z \u2192\u03c4\u03c4, reconstruct the invariant mass of a hypothetical \u03c4 pair\nusing the collinear approximation [23]. If the energy fractions x1\n\u03c4 and x2\n\u03c4 are both positive and the\ninvariant mass of the \u03c4 pair M\u03c4\u03c4 is in the range |M\u03c4\u03c4 \u2212MZ| < 25 GeV, the event is rejected.\n\u2022 To suppress backgrounds from top quark decays, reject events that contain any hard jets with\npT > 20 GeV and |\u03b7 j| < 4.8.\n\u2022 To further suppress the top background, reject events with any jets with pT > 15 GeV and a b-\ntagging weight greater than 4.\nTable 3 shows the cross-sections in the e\u00b5 channel for signal and background after these cuts.\nThe trigger ef\ufb01ciency for signal is suf\ufb01ciently large for this analysis to be viable. Events are required\nto pass at least one of the ATLAS single-lepton or double-lepton triggers. The level-1 trigger menus\nused here are 2EM15I, EM25I, EM60I, MU20, and MU40. For the Level 2 trigger and the event \ufb01lter,\nevents are required to pass the e25i, 2e15i, e60, or mu20i triggers. Details on the trigger menus can be\nfound in Ref. [24]. For the e\u00b5 channel considered here the trigger ef\ufb01ciency for L1 is 99.0%; for L2\nit is 96.7%, and for the EF it is 95.2% The ef\ufb01ciency is quite high, and the trigger ef\ufb01ciency does not\ndistort the shapes of the kinematic variables of interest in the signal in a signi\ufb01cant way. Table 3 does\nnot include the trigger ef\ufb01ciency, but it is taken into account as an overall scale factor for the signal and\nbackground when generating toy Monte Carlo to test the \ufb01tting algorithm described in the next section\nand in the calculation of the expected statistical signi\ufb01cance for this channel.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1313\n\nAfter the basic event selection (all cuts from Table 3 including the cut on \u2206\u03c6ll), the signal to back-\nground ratio is only \u22481:4, but there is still a good deal of discriminating power in the \ufb01nal state. This\nanalysis focuses on three variables:\n\u2022 the transverse opening angle \u2206\u03c6ll; a cut on this variable exploits differences in the spin correlations\nin the WW system in the Higgs signal and the WW background,\n\u2022 the transverse mass MT, as de\ufb01ned in Ref. [25],\n\u2022 the transverse momentum of the WW system, pWW\nT\n, which tends to be slightly larger for signal than\nfor WW background because gluon-initiated processes tend to have more initial-state radiation\nthan quark-initiated processes.\nThe distributions of these variables are shown in Figure 3. To make use of the discriminating power of\nthese variables, a maximum-likelihood \ufb01t is performed.\n5.1\nFitting Algorithm\nThe \ufb01t is a 2-dimensional \ufb01t of transverse mass and pWW\nT\nin two bins of the dilepton opening angle \u2206\u03c6ll\nin the transverse plane. [26] The present study considers a \ufb01t to only those events with one electron\nand one muon, since an in-situ background extraction procedure for the Z \u2192ee/\u00b5\u00b5 background has\nnot yet been studied. After the preselection cuts and the additional requirement that MT < 600 GeV is\napplied, the remaining events are separated into two subsamples, one with \u2206\u03c6ll < 1.575 and the other\nwith \u2206\u03c6ll > 1.575. Table 3 shows the cross-sections for the signal and various backgrounds in these two\nregions. The region with large \u2206\u03c6ll (control region) is enriched in background and the region with small\n\u2206\u03c6ll (signal region) is enriched in signal.\nThe top background is estimated with the help of b-tagged control samples with the same kinematic\ncuts as the signal-enriched and background-enriched regions. Table 3 includes estimates of the top cross-\nsection in the b-tagged control regions. In the present study, the b-tagging ef\ufb01ciency is assumed to be\nwell-known (i.e., the ratio of cross-sections in the b-tagged and b-vetoed regions is taken from Monte\nCarlo), and the contamination from processes with only light jets in the b-tagged regions is ignored. The\ntt cross-section estimates in Table 3 are based on Monte Carlo samples that use MC@NLO to model\nthe top background; even if the b-tagging is well-understood, the ratio of the top cross-section in the b-\ntagged and b-vetoed regions is sensitive to the treatment of the single-top contribution to the background.\nMoreover, studies based on fast simulation samples have shown that there are also differences in the\nshape of the distributions of MT and pWW\nT\nbetween top background models based on doubly-resonant top\nproduction and models that include the singly-resonant and nonresonant processes. (For example, the\nsingle-top contribution leads to a larger number of events with large MT and small pWW\nT\n.) Nevertheless,\nin the present study, standalone \ufb01ts are performed on the b-tagged control samples before the \ufb01t to the\nb-vetoed regions begins, and the top background in the b-vetoed regions is estimated by extrapolating\nboth the shape and the normalization from the b-tagged region to the b-vetoed region based on ratios\nobtained from MC@NLO.\nThe Z \u2192\u03c4\u03c4 background is normalized and its shape is determined by studying a sample of Z \u2192\u00b5\u00b5\nevents taken from real data, where the reconstructed muons are replaced by simulated taus [23]. Two-\nmuon events with a dimuon invariant mass between 82 and 98 GeV are selected, and the same jet veto\nthat is used in the rest of this analysis is applied to the selected events. The effective cross-section after\nthese cuts is roughly 360 pb. The reconstructed muons in the event are replaced with simulated tau\nleptons, and the remaining event selection cuts are applied. The ef\ufb01ciency of those cuts is about 0.07%,\nleaving an effective cross-section of roughly 250 fb. To be conservative, the present study assumes that\nef\ufb01cency factors will lower this \ufb01gure to about 200 fb. A standalone \ufb01t to these \u201cdata-Monte-Carlo\u201d\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1314\n\nevents is performed to determine the shape and normalization of the Z \u2192\u03c4\u03c4 background; in the \ufb01nal\n\ufb01t, the shape parameters are \ufb01xed and the normalization is rescaled by a factor that is assumed in this\nstudy to be well-predicted. The parameters obtained from the \ufb01t to the Z \u2192\u03c4\u03c4 data-Monte-Carlo control\nsample are not allowed to \ufb02oat in the main \ufb01t.\nAt the time of this writing, an in-situ determination of fake backgrounds from processes such as\nW+jets has not yet been studied. For this study, a \ufb01xed probability distribution has been used to represent\nthe fake backgrounds, assuming for the moment that the shape and normalization of fake backgrounds\nare well-predicted. Because of the limited size of the available W+jets Monte Carlo sample, there are not\nenough Monte Carlo events remaining after cuts to provide a prediction of the shape of the transverse\nmass vs. pWW\nT\ndistribution for W+jets; the shape of this distribution is therefore taken from a set of\nevents with loosened isolation and shower shape cuts. This treatment ignores any potential systematic\nuncertainty on the W+jets background; future studies will attempt to address this in more detail.\nOnce the \ufb01ts to the control samples are completed, a simultaneous \ufb01t of the two \u2206\u03c6ll bins in the\nb-vetoed region is performed. A few of the parameters that describe the shape of the transverse mass\nand pWW\nT\ndistributions of the WW background are allowed to \ufb02oat in the \ufb01t. The pWW\nT\ndistributions for\nthe WW background in the two regions are taken to be the same up to a parabolic distortion factor. The\nnormalizations of the WW background are free to \ufb02oat independently; however, we add a penalty term\nof the form (R fit \u2212Rtrue)2/\u03c3 2\nR, where R fit is the ratio of the best-\ufb01t number of WW background events in\nthe small-\u2206\u03c6ll region over the number in the large-\u2206\u03c6ll region, Rtrue is the Monte Carlo prediction of the\nratio taken from the central-value calculation, and \u03c3R is the uncertainty in the prediction of Rtrue, taken\nto be 10%. This value of \u03c3R is chosen to be larger than the actual variation of R due to changes in the Q2\nscale de\ufb01nition (about 5%) so that the constraint term does not cause a large bias in the observed value\nof R; such a bias could be expected to lead to a degradation in the sensitivity of the hypothesis test. The\nvalue of \u03c3R has not been optimized; such a study may be performed in the future.\nIn order to demonstrate the robustness of the \ufb01t against systematic uncertainties, toy Monte Carlo has\nbeen used to compute the sampling distributions for the Likelihood Ratio in several scenarios where the\n\u201ctrue\u201d probability distribution has been distorted to model various sources of systematic error. Seven dis-\ntorted scenarios are considered: four altered Q2 scale choices (factorization and renormalization scales\nraised and lowered by factors of 8), two alternative top background models (based on leading-order\npp \u2192WWbb and leading-order pp \u2192tt \u2192WWbb), and one alternative model of all irreducible back-\ngrounds where the x and y components of Emiss\nT\nhave been independently smeared by 5 GeV each. These\nalternative models have been derived using fast simulation because large-statistics Monte Carlo samples\nare needed in order to be sure any change in the shape of the observables is actually due to the sys-\ntematic uncertainty under study and not merely a statistical \ufb02uctuation. In these systematic scenarios,\nthe background contribution from fakes is ignored. Figure 4 shows the Likelihood Ratio distribution for\nbackground-only outcomes (upper left) and the distribution of pulls of the \ufb01tted Higgs boson mass (upper\nright) for signal-plus-background outcomes with a true Higgs boson mass of 170 GeV. Both distributions\nare nearly independent of the systematic distortions.\nThe lower left plot in Figure 4 shows the linearity of the mass determination as a function of the true\nHiggs mass. The line shows the mean of a Gaussian \ufb01t to the region around the peak of the distribution\nof best-\ufb01t Higgs masses in the toy Monte Carlo sample for the case of nominal detector performance.\nThe green band shows the width of the Gaussian and is a direct measure of the variability of the mass\nestimate on repetition of the experiment; the error bars show the median \ufb01t error. The typical variability\nof the mass determination at 10 fb\u22121 ranges from 5.2 GeV at MH =130 GeV to 1.6 GeV at MH =160 GeV\nto 4.2 GeV at MH =190 GeV.\nFigure 4 also shows the expected signi\ufb01cance for an integrated luminosity of 10 fb\u22121. This channel\nis most promising for Higgs boson masses near the WW threshold.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1315\n\nlog Likelihood Ratio\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nProbability\n6\n10\n5\n10\n4\n10\n3\n10\n2\n10\n1\n10\nNominal\nmiss\nT\nSmeared P\n scale 1\n2\nQ\n scale 2\n2\nQ\n scale 3\n2\nQ\n scale 4\n2\nQ\nt\nLeading-order t\nb\nLeading-order WWb\nNominal\nmiss\nT\nSmeared P\n scale 1\n2\nQ\n scale 2\n2\nQ\n scale 3\n2\nQ\n scale 4\n2\nQ\nt\nLeading-order t\nb\nLeading-order WWb\nATLAS\n-1\n L dt=10 fb\n\u222b\nH\nPull on M\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\nNormalized to 1\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nNominal\n Scale 1\n2\nQ\n Scale 2\n2\nQ\n Scale 3\n2\nQ\n Scale 4\n2\nQ\nt\nLeading-order t\nb\nLeading-order WWb\nm ss\nT\nSmeared P\nATLAS\n=170 GeV\ntrue\nH\nM\nMean=-0.2385\nRMS=1.109\n(GeV)\ntrue\nH\nM\n130\n140\n150\n160\n170\n180\n190\n(GeV)\ntrue\nH\n-M\nrec\nH\nM\n-10\n-5\n0\n5\n10\n15\n20\nMedian Fit Error\nWid h of Gaus. fit to best-fit Mass dist.\nATLAS\n-1\n L dt=10 fb\n\u222b\n(GeV)\nH\nM\n130\n140\n150\n160\n170\n180\n190\nMedian Significance\n0\n2\n4\n6\n8\n10\n12\n14\nATLAS\n-1\n L dt = 10 fb\n\u222b\nFigure 4: Upper Left: The log Likelihood Ratio distributions for background-only toy Monte Carlo\noutcomes corresponding to 10 fb\u22121 in the H + 0j, H \u2192WW \u2192l\u03bdl\u03bd analysis. Upper Right: The cor-\nresponding pull distributions for MH=170 GeV. Lower Left: The linearity of the mass determination.\nLower Right: the expected signi\ufb01cance for an integrated luminosity of 10 fb\u22121.\nRegion\nSignal, MH = 170 GeV (fb)\ntt\nWW\nZ \u2192\u03c4\u03c4\nW+jets\nSignal-like\n28.65\u00b10.80\n1.14\u00b11.14\n29.35\u00b11.59\n<1.74\n38\u00b138\nControl\n1.47\u00b10.27\n5.71\u00b12.55\n61.13\u00b12.33\n4.06\u00b11.53\n<114\nb-tagged\n0\n6.85\u00b12.80\n0.11\u00b10.09\n1.16\u00b10.82\n<114\nTable 4: Cross-sections (in fb) after all cuts for a number-counting analysis with a test mass of MH =\n170 GeV in the H +0j, H \u2192WW \u2192e\u03bd\u00b5\u03bd channel.\n5.2\nCross-check with a Number-Counting Analysis\nA number counting analysis of this channel has been performed as a cross-check. The signal region is\nde\ufb01ned by the basic event selection in addition to the following few additional cuts: pWW\nT\n> 10 GeV,\nMll < 64 GeV, \u2206\u03c6ll < 1.5, and 50 < MT < 180 GeV. A control region is de\ufb01ned by the requirements\npWW\nT\n> 10 GeV, 80 < Mll < 300 GeV, and \u2206\u03c6ll > 1.5. In order to normalize the top background, it\nis also useful to de\ufb01ne a b-tagged region with similar kinematic cuts: pWW\nT\n> 10 GeV and \u2206\u03c6ll > 1.5.\nTable 4 shows the cross-sections for signal and backgrounds in these regions. Only one of the W+jets\nevents passes all the selection cuts for the signal-like region; it corresponds to a cross-section of 38\nfb. None of the W+jets events survives in either control region. Because this background is modeled\nwith Alpgen W +n jets, with n \u22645, and because the Monte Carlo was generated with different effective\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1316\n\nluminosities for different jet multiplicities, it is not straightforward to compute a meaningful upper bound\non the W+jets cross-section in the control regions. The quoted cross-section is simply three times the\ncross-section observed in the signal region (which is based on one Monte Carlo event).\nThe ratios of background cross-sections in the various regions have to come from a theoretical pre-\ndiction; in a number-counting approach there is no simple way to constrain them with data. A similar\nbackground normalization strategy was studied in Refs. [27] and [28]; in Ref. [27], the theoretical error\non the ratio of WW cross-sections in the signal-like region and the control region was 5%, the system-\natic error on the ratio of the top background cross-sections in the signal-like and b-tagged regions was\n9%, and the uncertainty on the ratio of the top background cross-sections in the control region and the\nb-tagged regions was also 9%. These systematic errors have not been re-evaluated in the context of this\nanalysis, nor have the relevant instrumental systematic errors been computed; this cross-check simply\nuses these values as the systematic uncertainties on the extrapolations.\nUsing the cross-sections for MH = 170 GeV in Table 4 and taking into account the additional 95.2%\ntrigger ef\ufb01ciency on signal and background, the luminosity-dependent errors on the normalizations of the\ncontrol samples (ignoring W+jets in the Control and b-tagged regions), and the systematic uncertainties\ndescribed above, the expected signi\ufb01cance of the number-counting analysis (in the Gaussian approxima-\ntion, for\nR L dt = 10 fb\u22121) is 8.5\u03c3. This \ufb01gure ignores the error on the W+jets background prediction; in\na future study, it will be important to normalize the W+jets background using data. In the interest of per-\nforming a meaningful comparison with the \ufb01t analysis, it is helpful to compute the signi\ufb01cance ignoring\nthe W+jets background altogether: 10.4\u03c3. This is comparable to the result from the \ufb01t; if the contribution\nfrom the W+jets background is ignored there, the signi\ufb01cance is 8.8\u03c3 at the same luminosity.\n6\nLeptonic W Pair Production with Two Hard Jets\nThis Section presents the analysis of events where a W pair is produced in association with two hard jets\nand both W bosons decay leptonically. [29\u201332] In Section 6.1, the main discriminators in this channel\nare reviewed. For background extraction and signi\ufb01cance estimation, two complementary approaches\nare considered; both of them are \ufb01t-based. In Section 6.2, an analysis that uses a Neural Network to\ncombine several jet variables into a single discriminator and \ufb01ts the Neural Network output and MT is\npresented. This method has the advantage that the correlations among variables related to jets (described\nin Section 6.1) are naturally taken into account by the Neural Network, and the weak correlations between\nthe jet variables and the lepton variables are largely taken into account by the way the control sample\nis used in the \ufb01t. However, it has the disadvantage that the Neural Network must be trained ahead of\ntime; in principle, this may introduce some model-dependence to the procedure. Ideally, one would like\nto directly model all kinematic variables in a maximum Likelihood \ufb01t; Section 6.3 describes an analysis\nthat takes this approach with a \ufb01t of \ufb01ve kinematic variables. This method has the advantage that there\nis no training stage and therefore has the potential to be more model independent than the analysis of\nSection 6.2. However, because of the dif\ufb01culty in constructing a fully correlated probability distribution\nfor a 5-dimensional space, the probability distributions used in the \ufb01t of Section 6.3 include only the\nlargest correlations among the kinematic variables and ignore some smaller correlations. It is possible\nto make some corrections to the shapes of the distributions to model correlations not inherently present\nin the \ufb01t model; Section 6.3 explores the prospects for extracting such corrections from b-tagged control\nsamples. The combined signi\ufb01cance estimate at the end of this note will be based on the analysis of\nSection 6.2, but further studies of both approaches are needed in order to converge on a \ufb01nal strategy for\nthe analysis of real data.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1317\n\nPseudorapidity gap between Tagjets\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nNormalized to 1\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nPYTHIA, VBF H\nAlpgen, Z+jets\nMC/NLO, ttbar\nMC/NLO, WW\nATLAS\nTagjet invariant mass (GeV)\n0\n500\n1000\n1500\n2000\n2500\nNormalized to 1\n-3\n10\n-2\n10\n-1\n10\nPYTHIA, VBF H\nAlpgen, Z+jets\nMC/NLO, t bar\nMC/NLO, WW\nATLAS\nAzimuthal angle between Tagjets\n0\n0.5\n1\n1.5\n2\n2.5\n3\nNormalized to 1\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n0.1\nPYTHIA, VBF H\nAlpgen, Z+jets\nMC/NLO, ttbar\nMC/NLO, WW\nATLAS\n (GeV)\nt\nThird Jet E\n0\n20\n40\n60\n80\n100\n120\n140\nNormalized to 1\n-2\n10\n-1\n10\n1\nPYTHIA, VBF H\nAlpgen, Z+jets\nMC/NLO, t bar\nMC/NLO, WW\nATLAS\nFigure 5: Pseudorapidity gap between tag jets (left top plot), invariant-mass distributions of tag jets\n(right top plot), azimuthal angle gap between tag jets (left bottom plot) and Et of the third jet in VBF\nH \u2192WW \u2192\u00b5\u03bd \u00b5\u03bd Pythia events (m(H)=170 GeV). A requirement \u03b71\u03b72 \u22640 is used in addition to the\nrequirement jet Et > 20 GeV.\n6.1\nHandles for Suppressing the Top Background\nIn both of the \ufb01t-based approaches under study, tt is the dominant background after the preselection\ncuts, and in both approaches, similar discriminators are used to suppress it. Two discriminators warrant\nspecial attention: jet kinematics, which is discussed in Section 6.1.1, and b-tagging, which is discussed\nin Section 6.1.2.\n6.1.1\nJet Kinematics\nOne of the main advantages of any search for a Higgs in association with two jets is the possibility to\nsuppress QCD backgrounds with cuts on jet kinematics. The Vector Boson Fusion Higgs signal features\nseveral distinctive characteristics:\n\u2022 The two jets arising from struck quarks (often referred to as \u201ctag\u201d jets) tend to be the highest-pT\njets in the event, and they tend to be well-separated in pseudorapidity;\n\u2022 they tend to have a large invariant mass;\n\u2022 there is very little jet activity in the region between the two tag jets.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1318\n\nLeading Jet Weight\n-15 -10 -5\n0\n5\n10 15 20 25 30 35\nSubleading Jet Weight\n-15\n-10\n-5\n0\n5\n10\n15\n20\n25\n30\n35\nRegion I: 85%\nRegion II: 14%\nRegion III: 0.48%\nIII\nII\nI\nCut 1\nCut 2\nATLAS\nLeading Jet Weight\n-15 -10 -5\n0\n5\n10 15 20 25 30 35\nSubleading Jet Weight\n-15\n-10\n-5\n0\n5\n10\n15\n20\n25\n30\n35\nRegion I: 85%\nRegion II: 14%\nRegion III: 0.48%\nIII\nII\nI\nCut 1\nCut 2\nATLAS\nFigure 6: The distribution of leading versus sub-leading jet weights in the events for signal (left plot)\nand the t\u00aft background (right plot). The plots are divided in three regions: (I) where there is a non-default\nb-tagging weight for more than one jet, (II) where there is only b-tagging information for one jet in the\nevent and (III) where there are no jets with b-tagging information in the event.\nFigure 5 shows the distributions of the pseudorapidity gap between the tag jets, their invariant mass, and\nthe pT of the third-highest pT jet in the event. The \ufb01gure also shows the distribution of the azimuthal\nangle between the tagjets, \u2206\u03c6 j j. It is possible to enhance the discrimination against backgrounds with\na cut on \u2206\u03c6 j j, but in this study no such cut is applied on the grounds that this angle is needed in a\nmeasurement of the spin and CP properties of the Higgs boson [33].\nOnly one Higgs boson mass is shown for the signal process in Figure 5, but it is worth noting that\nthe dependence of these variables on the Higgs boson mass is rather weak. It is also worth noting that\nPythia 6.4 predicts a somewhat harder pT spectrum for the third jet than Herwig and Sherpa do. This\nwould amount to a difference as large as a few tens of percent in the survival probability if a jet veto cut\nwere applied.\nIt has been shown in previous studies that hard cuts on the kinematic variables discussed here can\nprovide a strong rejection against the top background [25,34,35]. As part of the present study, it has been\nchecked that the high signal-to-background ratio that can be achieved in this channel is not sensitive to\ndegradations arising from detector alignment effects.\n6.1.2\nRejecting Top with B-tagging\nAnother effective way to reject a signi\ufb01cant fraction of the t\u00aft events while retaining a high ef\ufb01ciency for\nthe signal is to apply a veto on events containing jets with high b-tagging weights. The t\u00aft events naturally\ncontain two jets originating from b-quarks whereas the heavy \ufb02avor content in the signal events is limited\nat tree level to having c quarks in the tagging jets, and then typically in only one of the two tagging jets.\nThis makes vetoing against events with more than one jet with high b-tagging weight especially ef\ufb01cient.\nFigure 6 shows the distribution of leading versus sub-leading jet weights in the events for signal (left\nplot) and the t\u00aft background (right plot). The plots are divided in three regions: I where there is a non-\ndefault b-tagging weight for more than one jet, II where there is only b-tagging information for one jet in\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1319\n\nCut\nSignal (170 GeV)\ntt\nWW+jets\nZ \u2192\u03c4\u03c4\nW+jets\nLepton Selection\n30.20\n8317\n838.96\n(2096)\n1323\nForward Jet Tagging\n17.27\n946.6\n32.77\n79.30\n31.83\nLeptons Between Jets\n16.47\n617.8\n22.92\n55.13\n27.91\nZ \u2192\u03c4\u03c4 Rejection\n15.68\n561.8\n21.20\n39.03\n27.91\npmiss\nT\n, MT, mll\u03bd\nT\n12.78\n425.9\n15.28\n0\n13.96\nb-veto\n12.67\n206.72\n-\n-\n-\nsignal box, b-jet Veto\n9.28\u00b10.27\n28.5\u00b15.7\n4.75\u00b10.30\n-\n4.3\u00b14.3\nsignal box, no b-jet Veto\n9.65\n114.2\n4.99\n-\n6.07\nControl, b-jet Veto\n3.02\u00b10.15\n89\u00b110\n9.78\u00b10.43\n-\n7.9\u00b15.0\nControl, no b-jet Veto\n3.13\n311.7\n10.28\n-\n7.89\nTable 5: Cut \ufb02ows (in fb) for MH = 170 GeV in the H + 2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd channel. Numbers in\nparentheses are affected by generator-level \ufb01lter cuts.\nthe event and III where there are no jets with b-tagging information in the event1. The fraction of events\nin each of the three regions is:\n\u2022 38% of the events in region I, 48% of the events in region II and 14% of the events in region III\nfor the Higgs signal.\n\u2022 85% of the events in region I, 14% of the events in region II and 0.5% of the events in region III\nfor the t\u00aft background.\nThe selection in the leading versus sub-leading jet weights plane was optimized for the highest in-\ncrease in the number-counting signi\ufb01cance after the following cuts have been applied:\n\u2022 Two leptons, pT > 15 GeV\n\u2022 Missing transverse energy Emiss\nT\n> 30 GeV\n\u2022 At least two jets with pT > 20 GeV and |\u03b7| < 4.8\n\u2022 The two jets with highest transverse momentum are required to be in opposite hemispheres, with\n\u2206\u03b7(jet1, jet2) > 3\n\u2022 Require that both leptons are between the two leading jets in pseudorapidity.\nTwo cuts are applied on the b-tagging weights:\n\u2022 weight(jet1)+0.6\u00d7weight(jet2)<3 for events in region I\n\u2022 weight(jet1)<8 for events in region II\nThese cuts provide a strong rejection against the top background and a large acceptance for the Higgs\nsignal.\n6.2\nTwo-dimensional Fit\nTo select the events that are used in the two-dimensional \ufb01t, the same preselection cuts that were de-\nscribed in the previous section are applied, plus two additional cuts:\n1Jets can lack b-tagging information if they fall outside the acceptance of the inner tracker, or because there are no tracks\nwith high impact parameter signi\ufb01cance in the jet.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1320\n\nNeural Network Output\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEvents / ( 0.02 )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nNeural Network Output\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEvents / ( 0.02 )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nATLAS\n(GeV)\nT\nM\n0\n100\n200\n300\n400\n500\n600\nEvents / ( 10 )\n0\n2\n4\n6\n8\n10\n12\n(GeV)\nT\nM\n0\n100\n200\n300\n400\n500\n600\nEvents / ( 10 )\n0\n2\n4\n6\n8\n10\n12\n-1\n L dt=10 fb\n\u222b\nPseudodata, \nBest-fit Signal\n2-lepton Background\nFake BG (W+jets)\nATLAS\nFigure 7: An example \ufb01t to a toy Monte Carlo outcome corresponding to 10 fb\u22121 of integrated luminosity\nin the H +2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd channel. The pseudodata contains a Standard Model Higgs boson with\na true mass of 170 GeV. Left: The Neural Network output distribution in the signal box, for events with\n50 < MT < 180 GeV. Right: The transverse mass distribution for events in the signal box with Neural\nNetwork output larger than 0.8. The Likelihood Ratio for this outcome was 22.62, which is typical if the\nsignal model used as truth is derived from a Monte Carlo sample generated with SHERPA.\n\u2022 To reject backgrounds from Z \u2192\u03c4\u03c4, assume that the leptons are coming from \u03c4 decays and com-\npute x1\n\u03c4 and x2\n\u03c4, the fractions of the tau energies carried by the visible leptons in the collinear\napproximation. If x1\n\u03c4 and x2\n\u03c4 are positive and M\u03c4\u03c4 is close to the Z mass (|M\u03c4\u03c4 \u2212MZ| < 25 GeV),\nthe event is rejected.\n\u2022 Require that the transverse mass MT is between 50 GeV and 600 GeV, and that the transverse mass\nmll\u03bd\nT\n(as de\ufb01ned in Ref. [25]) is at least 30 GeV.\nIn this analysis, electrons are selected using the standared ATLAS medium electron selection. The de\ufb01-\nnition of muons, and the isolation cuts applied to both, are the same as in the H +0j, H \u2192WW \u2192e\u03bd\u00b5\u03bd\nanalysis in Section 5.\nEvents surviving the cuts above are used in the \ufb01t; they are partitioned into a signal box and a\ncontrol region de\ufb01ned by additional cuts on the pseudorapidity gap between the leptons and the dilepton\nopening angle in the transverse plane. An event lies in the signal box if it has \u2206\u03c6ll < 1.5 and \u2206\u03b7ll < 1.4;\notherwise, it lies in the control region. Table 5 shows the cross-sections for signal and background in\nthese two regions.\nThe trigger ef\ufb01ciency has been studied in the context of this analysis. The same trigger menus as in\nthe H +0j, H \u2192WW \u2192e\u03bd\u00b5\u03bd analysis are used, and the results are similar: a trigger ef\ufb01ciency of 99.0%\nafter Level 1, 96.8% after Level 2, and 94.5% after the Event Filter. These ef\ufb01ciencies are quite high, and\nas for the H + 0j analysis, it has been checked that the trigger ef\ufb01ciency does not signi\ufb01cantly change\nthe shape of the most important kinematic variables. Table 5 does not include the trigger ef\ufb01ciency, but\nit is taken into account as an overall scale factor for signal and background when generating toy Monte\nCarlo to test the 2-dimensional \ufb01t described in the next section.\nAfter the preselection described above, a four-variable Neural Network is used to further enhance the\nseparation between the signal and the background. The inputs to the Neural Network are:\n\u2022 \u2206\u03b7 j j, the pseudorapidity gap between the tagjets\n\u2022 Mj j, the invariant mass of the tagjets\n\u2022 pveto\nT\n, the transverse momentum of the leading non-tag jet in the region |\u03b7| < 3.2, and\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1321\n\n\u2022 \u03b7\u2217= \u03b73 \u2212(\u03b71 +\u03b72)/2, the pseudorapidity gap between the tag-tag system and the third jet. It is\nset to -9 if no third jet is present.\nThe Neural Network classi\ufb01es events as signal-like if they have large \u2206\u03b7 j j, large Mj j, low pveto\nT\n, and\nlarge |\u03b7\u2217|. Figure 7 shows the Neural Network output and transverse mass distributions in the signal\nbox. The \ufb01t is a two-dimensional \ufb01t to these two quantities; both the signal model and the background\nmodel are uncorrelated product probability density functions (PDFs). The \ufb01t does not distinguish among\nthe various types of background.\nAn in-situ normalization of fake backgrounds has not yet been implemented for this channel. For the\npresent study, a static model has been used to approximate the fake background from W+jets. The same\nfunctional form used for the irreducible backgrounds was \ufb01tted to a set of W+jets Monte Carlo events that\npass a loosened lepton selection, and its normalization was scaled to the cross-section obtained with the\ntighter selection cuts actually used in the analysis. In the present study, none of the parameters governing\nthe shape or normalization of the fake background are allowed to \ufb02oat in the \ufb01t; systematic errors on the\nshape and normalization of the W+jets background are ignored.\nThe Neural Network output distribution for the background in the signal box is taken to be the same\nas the distribution in the control region, but it is multiplied by a linear extrapolation factor. Apart from\nthe slope of this extrapolation factor, all parameters governing the shape of the Neural Network output\ndistribution in the two regions are required to be the same.\nA check on the impact of altered jet energy scales on the Neural Network output distributions for\nsignal and background has been performed; changing the jet energy scale by 5% in the region with\ntracking and 10% elsewhere does not change the Neural Network output shape in a meaningful way.\nThis is not surprising, since the Neural Network inputs are slowly varying functions of the jet energy.\nSimilarly, raising the jet pT thresholds from 20 GeV to 30 or 40 GeV to mimic a degraded ef\ufb01ciency for\nlow-pT jets does not have a large impact on the ratio of the Neural Network output distributions in the\nsignal box and the control regions.\nGiven the fact that the Neural Network output shape is insensitive to the jet energy scale, one would\nexpect that the ratio of distributions in the signal box and control region would be insensitive to the\njet energy scale as well. Other possible sources of uncertainty in the ratio of Neural Network output\ndistributions are underlying event activity and the Q2 scale uncertainty; these sources of uncertainty have\nnot been checked explicitly at this time. However, it is reasonable to think they might be small because\nthe cuts on jets in the signal box are the same as in the control region and because the distributions of\nvariables related to jets are not strongly correlated to the lepton angular variables. If the uncertainty in\nthe ratio of distributions is suf\ufb01ciently small, then one can \ufb01x the parameter governing the extrapolation\nfactor; if it is too large, one must allow it to \ufb02oat in the \ufb01t. In the latter case, it may be possible to\nconstrain it somewhat by looking into a b-tagged control sample; this possibility has been studied in the\ncontext of the \ufb01ve-dimensional \ufb01t discussed in the next section. All of these possibilities require further\nstudy in the context of the two-dimensional \ufb01t; this note will simply consider both scenarios: allowing\nthe slope of the extrapolation factor to \ufb02oat in the \ufb01t and \ufb01xing it to a predetermined value taken from\nMonte Carlo. In both cases, it is assumed that the transverse mass distributions are well-predicted, and\nthat the Neural Network output distribution is not; in practice this means that the MT parameters are set\nto \ufb01xed values while most of the parameters describing the Neural Network output shape are allowed to\n\ufb02oat in the \ufb01t.\nThe expected signi\ufb01cance is shown as a function of the true Higgs mass in Figure 8 for the two\ntreatments of the extrapolation factor considered in this study. The sensitivity is comparable to what\nwas quoted in previous studies of this channel, at least for the case where the extrapolation parameter is\nconstrained to a \ufb01xed value.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1322\n\n(GeV)\ntrue\nH\nM\n130\n140\n150\n160\n170\n180\n190\n(GeV)\ntrue\nH\n-M\nrec\nH\nM\n-15\n-10\n-5\n0\n5\n10\n15\n20\n25\nMedian Fit Error\nWidth of Gaus. fit to best-fit Mass dist.\nATLAS\n-1\n L dt=10 fb\n\u222b\n(GeV)\nH\nM\n130\n140\n150\n160\n170\n180\n190\nMedian Significance\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\nFixed Extrapolation\nFloating Extrapolation\nSherpa Signal\nPythia 6.4 Signal\nATLAS\n-1\n L dt=10 fb\n\u222b\nFigure 8: Left: The Neural Network output distribution for the H +2j, H \u2192WW \u2192e\u03bd\u00b5\u03bd channel in the\nsignal box. Right: The expected signi\ufb01cance at 10 fb\u22121. The blue and magenta triangles were computed\nusing a \ufb01xed extrapolation.\n6.3\nFive-dimensional Fit\nA conceptually simpler but more technically challenging strategy is to directly \ufb01t the most important\nkinematic variables. This section describes such an approach to the H +2j, H \u2192WW \u2192\u2113\u03bd\u2113\u03bd channel.\nThe selection cuts used in this analysis are similar to those used in section 6.2, with a few slight\ndifferences:\n\u2022 Either two or three jets with transverse momentum pT > 20 GeV and pseudorapidity |\u03b7| < 4.9 are\nallowed.\n\u2022 The missing transverse momentum Emiss\nT\nis greater than 20 GeV.\n\u2022 The pseudorapidity gap between the tagjets is required to satisfy |\u2206\u03b7 j j| > 2.5, and the invariant\nmass of the tagjets is required to lie in the range m j j \u2208[600,3000] GeV.\n\u2022 A b-tagged jet is de\ufb01ned as having a displaced vertex signi\ufb01cance greater than 4.5.\nThe values of the Higgs boson mass, mH, and the cross section, \u03c3(VBF H \u2192WW), are determined with\nan unbinned maximum likelihood \ufb01t to the distributions of x = (MT,\u2206\u03c6ll,\u2206\u03b7ll,\u2206\u03b7 j j,m j j), as obtained\nfrom the selected data sample. A multidimensional kernel estimation technique [36] has been used to\nhelp model the kinematic distributions in the control samples.\nEvents in the selected data sample are divided into categories based on four properties: the \ufb02avors of\nthe reconstructed lepton pair (\u00b5\u00b5, \u00b5e, and ee); the number of reconstructed good jets (2jet and 3jet);\nevents with and without a b-tagged jet (btag and bveto, where a b-tagged jet is de\ufb01ned as having a\ndisplaced vertex signi\ufb01cance greater than 4.5); and events that fall into the signal region, \u2018sigbox\u2019,\nhaving |\u2206\u03c6ll| < 1.5 and |\u2206\u03b7ll| < 1.4, and those that fall outside, into the \u2018sideband\u2019 region. The b-\nvetoed sigbox region is denoted as region 1, the b-vetoed sideband as region 2, the b-tagged sigbox\nregion as region 3, and the b-tagged sideband region as region 4.\nMost t\u00aft background events contain a b-tagged jet, whereas most WW background events fall into\nthe bveto category. The majority of Higgs boson events is expected to be found in physics region 1.\nEvents outside of this region are not considered as signal candidates. These regions are de\ufb01ned to be the\nbackground control samples.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1323\n\nFor t\u00aft, WW, and H \u2192WW events, the selected samples are mostly dominated by di-leptonic W\ndecays. For this reason, the relative fractions of \u00b5\u00b5, ee, and \u00b5e events (f\u00b5\u00b5, fee, 1\u2212f\u00b5\u00b5\u2212fee) are taken\nto be identical for background and signal events.\nThe signal model is obtained from fully simulated Monte Carlo events, and is factorized into four\nshapes, modelling MT, \u2206\u03c6ll, \u2206\u03b7ll and (\u2206\u03b7 j j,m j j) respectively. The signal shape is assumed to be inde-\npendent of the lepton pair category and the number of good jets per event.\nThe Higgs boson transverse mass distribution, MT, is described with a double-sided exponential,\nhaving two different lifetimes, convoluted with a Gaussian. The mean of the Gaussian is interpreted as\nthe Higgs boson mass, mH, and is left free in the \ufb01t. The left-handed lifetime, \u03c4L, comes from the missing\nz-component in the transverse mass calculation. The parameter \u03c4L is a linear function of mH, and equals\n25 GeV for a Higgs boson mass of 130 GeV, and 45 GeV for a Higgs boson mass of 170 GeV. The\nright-handed component, \u03c4R, is the result of the non-validity of the approximation ml \u00afl = m\u03bd \u00af\u03bd in the\nde\ufb01nition of MT, and is \ufb01xed to 20 GeV for all Higgs boson masses. The width of the Gaussian, \u03c3MET,\nis interpreted as the resolution on the missing transverse energy, and is \ufb01xed to 15 GeV.\nThe distributions of \u2206\u03c6ll and \u2206\u03b7ll in signal are described with single Gaussians, with means \ufb01xed to\nzero, and widths of \u03c3\u2206\u03c6 = 1.09 and \u03c3\u2206\u03b7 = 0.62 respectively.\nThe tagging jet observables \u2206\u03b7 j j and m j j in signal are strongly correlated, and are modeled with a\n2-dimensional (2D) kernel estimation function.\nFor these observables, the largest unmodelled correlation is between \u2206\u03c6ll and \u2206\u03b7ll, and is found to\nbe 14% from the available signal Monte Carlo sample.\nThe collection of background events in regions 2\u20134 serves as a data control sample for the determi-\nnation of: a) the probability density functions, and b) the number of background candidates in physics\nregion 1. The background shape is assumed to be independent of the lepton pair category and number of\ngood jets per event. The shape is factorized into two pieces, describing (MT,\u2206\u03c6ll,\u2206\u03b7ll) and (\u2206\u03b7 j j,m j j)\nrespectively.\nThe background distribution of (MT,\u2206\u03c6ll,\u2206\u03b7ll) \u2013 observables mostly independent of the jet charac-\nteristics \u2013 is modelled with a 3D kernel estimation function, using the events in physics region 3. A small\nef\ufb01ciency correction is applied to the observable MT, calculated as the ratio the distributions of MT in\nphysics regions 2 and 4, both determined using 1D kernel estimation functions.\nAccounting for the hard pT spectrum of the b-tagged jet sample, the distribution of (\u2206\u03b7 j j,m j j) is\nmodelled with a 2D kernel estimation function using the background events in physics region 2. A\ncorrection function is applied to \u2206\u03b7 j j, determined as the ratio the \u2206\u03b7 j j distributions in physics regions 3\nand 4, again determined using 1D kernel estimation functions.\nThe unmodelled correlations between these observables are found to be smaller than 10%, as ob-\ntained from the t\u00aft and WW background Monte Carlo samples.\nThe number of background events in physics region 1 is partially estimated from the number of\nbackground events in categories 2\u20134. For this we assume the ratio of events in the sideband to sigbox\nregions (fsigbox\u2212sideband) to be identical for the btag and bveto categories. Given the ratio of events of\nphysics regions 2 and 4 (fbveto\u2212btag), determined independently for the 2jet and 3jet samples, estimates\nfor the number of background events in physics region 1 can be obtained. These estimates are expressed\nas the total number of background events, nbkg, and the relative fraction of background event in the 3jet\ncategory, fbkg\u22123j.\nFinally, the \ufb01tted number of Higgs boson signal events, nH, is determined seperately for the 2jet\nand 3jet categories.\n6.3.1\nToy Monte Carlo Studies\nA \ufb01t example to approximately 1 fb\u22121 of fully simulated Monte Carlo events, including Higgs boson\nsignal events with a mass of 170 GeV, is demonstrated in the left side of Fig. 9. The plot shows the events\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1324\n\nHiggs transverse mass (GeV)\n50\n100\n150\n200\n250\n300\nEvents / ( 22500 )\n0\n5\n10\n15\n20\n25\nHiggs transverse mass (GeV)\n50\n100\n150\n200\n250\n300\nEvents / ( 22500 )\n0\n5\n10\n15\n20\n25\nATLAS\n]\n2\nHiggs mass [GeV/c\n120\n140\n160\n180\n200\nStat. significance [SD]\n0\n1\n2\n3\nWW (ll)\n\u2192\nVBF H\nLHC Data\n-1\n1 fb\nATLAS\nFigure 9: Left: The Higgs boson transverse mass distribution for events in the de\ufb01ned physics signal\nregion, corresponding to approximately 1 fb\u22121 of data, as obtained from fully simulated Monte Carlo\nevents. The solid (blue) curve is the total \ufb01t projection. The background contribution is represented\nby the dashed (red) curve. Right: The expected statistical sensitivity to Standard Model VBF H \u2192\nW +W \u2212\u2192l+\u03bd l\u2212\u00af\u03bd decays for 1 fb\u22121 of ATLAS data, using the \ufb01ve-dimensional \ufb01t of Section 6.3.\nFit parameter\nValue\nGlobal corr.\nParameter\nValue\nGlobal corr.\nfbveto\u2212btag;2jet\n0.89\u00b10.14\n72%\nnB\n90.5\u00b17.4\n93%\nfbveto\u2212btag;3jet\n3.02\u00b10.24\n88%\nnH;2jet\n18.6\u00b15.5\n25%\nfbkg\u22123 jet\n0.72\u00b10.03\n80%\nnH;3jet\n9.6\u00b17.9\n38%\nfsigbox\u2212sideband\n2.64\u00b10.19\n86%\n\u03c3MET\n15000\n\u2013\nfee\n0.11\u00b10.01\n34%\n\u03c3\u2206\u03c6ll\n0.62\u00b10.03 (\ufb01xed)\n\u2013\nf\u00b5\u00b5\n0.47\u00b10.01\n34%\n\u03c3\u2206\u03b7ll\n1.09\u00b10.06 (\ufb01xed)\n\u2013\nmH\n168\u00b18\n12%\n\u03c4R\n20000 (\ufb01xed)\n\u2013\nTable 6: The free parameters for the \ufb01ve-dimensional \ufb01t described in Section 6.3, and their best-\ufb01t values\nfor the example toy Monte Carlo outcome in the left side of Figure 9.\nin the de\ufb01ned physics region 1, with the total and background \ufb01t projections overlaid. Here the signal\nshape has been obtained from fully simulated Monte Carlo events. The background probability density\nfunction has been obtained using kernel estimation from the (Monte Carlo) events in the background\ncontrol samples.\nThe corresponding \ufb01t results are given in Table 6. The Higgs boson mass found is consistent with the\ngenerated value. The total numbers of Higgs boson and background events found are consistent with the\ninput values of 27 and 86 respectively. The \ufb01t is most sensitive to Higgs boson events in the 2jet signal\nregion \u2013 where most Higgs boson events are expected, and contributions from t\u00aft background events are\nminimal. For Higgs boson masses in the range [160,170] GeV, the signal to background ratio is this\ncategory is approximately 1 : 1. The error on the \ufb01tted number of background events in the signal region\nis found to be 7.4. When not including the estimated number of background event from the background\ncontrol samples in the \ufb01t, the error on the number \ufb01tted number of background events doubles. The error\non the \ufb01tted number of Higgs boson events rises by 25%, and the correlation of the \ufb01tted number of\nHiggs boson events with all other \ufb01t parameters \u2013 mostly correlated to the number of background events\n\u2013 rises from 25% to 45%. The correlation of the Higgs boson mass with all other \ufb01t parameters is 12%.\nThe statistical properties of this \ufb01tting algorithm have been studied with about 15k toy Monte Carlo\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1325\n\noutcomes like the one discussed in the previous paragraph. The toy outcomes have been generated with\nthe same number of events seen in, and the shapes obtained from, the fully simulated Monte Carlo signal\nand background samples remnant after the event selection, corresponding to 1 fb\u22121 of data. The mass of\nthe generated Higgs boson sample is varied between 110 and 200 GeV, in steps of 10 GeV. The Higgs\nboson cross-section is adjusted accordingly [1]. The \ufb01t algorithm described above has been performed\non each generated pseudo-experiment.\nThe \ufb01tted number of Higgs boson events in the 2jet signal region \u2013 most sensitive to the Higgs\nsignal \u2013 shows an average bias of less than 0.8 event over the entire generated mass range. Roughly 12\nHiggs boson events are needed in this region before a clear signal peak can be picked up by the \ufb01tter.\nThe error on the \ufb01tted number of 2jet Higgs boson events varies between 3.1 and 5.6 events for no\ngenerated Higgs boson events to the maximum cross-section between 160 and 170 GeV respectively.\nThe average \ufb01t error on the Higgs boson mass parameter is about 14.0 GeV in background-only\noutcomes, or about 9.4 GeV in outcomes containing both background and a 160 GeV Higgs signal with\ncross-section as given by the Standard Model. In Fig. 9, note that the background distribution, dominated\nby t\u00aft events, peaks at around 160 GeV. Pseudo-experiments with no generated signal events tend to peak\nat this mass, where statistical \ufb02uctuations are largest. For 1 fb\u22121 samples, starting from the generated\nHiggs boson mass of 110 GeV with a value of +1\u03c3, the \ufb01t show a decreasing bias in the mass pull\ndistribution, which is consistent with zero at 160 GeV, and becomes \u22121\u03c3 at 200 GeV. The width\nof the pull is consistent with one in the generated mass range of [150,190] GeV, and grows for lower\ncross-section, upto 1.7\u03c3 at 120 GeV.\nThe average statistical sensitivity derived from the toy Monte Carlo study is shown in the right side\nof Figure 9. At 1 fb\u22121 of data, the sensitivity to VBF H \u2192W +W \u2212\u2192l+\u03bd l\u2212\u00af\u03bd decays is greater than\none for Higgs boson masses greater than 120 GeV. (Below 120 GeV the H \u2192W +W \u2212branching ratio\nbecomes too small for this measurement to be effective.) It reaches a maximum of 2.5\u03c3 at the Higgs\nboson mass of 160 GeV.\n7\nW Pair Production with Two Hard Jets in the Lepton-Hadron Channel\nThis section describes the analysis of events where the W pair is produced in association with two hard\njets and one W boson decays leptonically (with the other W decaying to jets). [25,29,37\u201342] The dom-\ninant backgrounds to this \ufb01nal state are W+jets and tt production; it is possible that QCD multijets will\nalso play an important role. Because of the large jet multiplicity, there are large theoretical uncertainties\nin the predicted normalization of the backgrounds, especially for W+jets and QCD multijets. Therefore,\nthis section will emphasize studies of the signal, the W+jets background, and the tt background, with\ndiscussion of how to normalize the backgrounds given data. Quantitative predictions of the discovery\nsensitivity will not be included here.\nBecause there is only one neutrino in the \ufb01nal state, this channel permits a better estimate of the\nHiggs candidate invariant mass than the dilepton channels. Taken together with the large sensitivity of\nthe dilepton channels for Higgs masses near 160 GeV, this means that the H \u2192WW \u2192l\u03bdqq channel is\nmost interesting for the study of Higgs bosons with masses in excess of roughly 250-300 GeV.\nThe most obvious way to estimate the invariant mass of a H \u2192WW \u2192\u2113\u03bdqq candidate is to assume\nthat both W bosons are on-shell. One can then use the W mass constraint for the W \u2192\u2113\u03bd system to\nestimate the z momentum of the neutrino.2\nThe analysis of this channel uses reconstructed jets to measure the invariant masses of Higgs boson\ncandidates; it is therefore necessary to consider out-of-cone corrections to the jet energies that were\nnot important in the dilepton channels. Eventually, these corrections should be taken from real data;\n2The W mass constraint yields a quadratic equation which can have 0, 1, or 2 real solutions. If there are two solutions, the\none with smaller |p\u03bdz | is used; if there is no real solution, the imaginary term is ignored and only the real part is used.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1326\n\nCut\nW+jets\nttbar\nSignal (MH = 300 GeV)\nLeptonic W Selection\n2353291*\n128654\n174.27\nHadronic W Selection\n134483\n70872\n73.26\nForward Jet Tagging\n1076.8\n1929\n23.16\nLepton Between Jets\n867.0\n1679\n22.93\nMj j\n131.0\n367.7\n9.16\nCentral Jet Veto\n57.98\n58.24\n8.43\n\u2206\u03b7 j1,l\n16.07\n47.96\n6.93\nb-jet Veto\n16.07\n14.84\n6.06\nTrigger Selection\n13.06\n12.40\n5.08\n167 < Ml\u03bdqq < 1000 GeV\n13.1\u00b14.7\n12.4\u00b13.4\n5.08\u00b10.29\nControl Regions\nb-tagged\n0\n26\u00b15\n0.75\u00b10.12\nSmall-\u2206\u03b7 j j Control Region\n500.16\n778.76\n20.79\nSmall-\u2206\u03b7 j j Control Region(b-veto)\n441.64\n186.13\n19.95\nSmall-\u2206\u03b7 j j (b-veto and Trigger)\n369.38\n157.47\n15.06\nSmall-\u2206\u03b7 j j (167 < Ml\u03bdqq < 1000 GeV)\n358\u00b129\n154\u00b112\n15.1\u00b10.5\nSmall-\u2206\u03b7 j j Control Region(b-tag)\n37\u00b114\n493\u00b122\n2.3\u00b10.2\nTable 7: Cross-sections (in fb) for the signal and various backgrounds after successive cuts in the H \u2192\nWW \u2192l\u03bdqq channel. A \u2018*\u2019 indicates a number that is biased by generator-level cuts.\nhowever, such a study has not yet been performed. For the present study, the out-of-cone correction\nfrom ATLFAST-B [43] has been applied to all jets. After applying this correction to the reconstructed jet\nmomenta, the following cuts are applied:\n\u2022 Leptonic W selection. The event must contain exactly one hard lepton, with transverse momentum\npT > 25 GeV for electrons and pT > 20 GeV for muons. It is also required that the missing\ntransverse momentum, pmiss\nT\n, be larger than 30 GeV.\n\u2022 Hadronic W selection. Out of all jets with large transverse momentum, pT > 30 GeV, the two\nwhose invariant mass is closest to the known value of the W mass are selected. It is required that\nthe reconstructed invariant mass of these two jets be between 64 GeV and 90 GeV.\n\u2022 Forward Jet Tagging. Select the two jets (excluding those from the W decay) that have the highest\ntransverse momentum. These are labelled as the \u201ctagging\u201d jets; by construction, they are disjoint\nfrom the jets that form the W \u2192qq candidate. Require that they be high-pT (p j1\nT > 50 GeV,\np j2\nT > 30 GeV), that they lie in opposite hemispheres (\u03b7 j1\u00b7\u03b7 j2 < 0), and that they be well-separated\nin pseudorapidity (|\u03b7 j1 \u2212\u03b7 j2| > 4.4).\n\u2022 Require that the lepton be between the tagjets in pseudorapidity.\n\u2022 Mj j: require that the invariant mass of the two tagging jets be greater than 1500 GeV.\n\u2022 Central Jet Veto: reject the event if it contains any extra jets (in addition to the two jets from the\ndecay of the W and the two tagging jets) with pT > 30 GeV and |\u03b7| < 3.2.\n\u2022 b-jet veto: apply the b-jet veto cuts described in Section 6.1.2.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1327\n\nTrigger Level\nElectron Channel\nMuon Channel\nL1\n97.1%\n85.3%\nL2\n94.3%\n81.2%\nEF\n92.4%\n79.6%\nTable 8: Trigger ef\ufb01ciencies with respect to of\ufb02ine cuts for the H+2j lepton-hadron channel, for a Higgs\nboson mass of 170 GeV.\n\u2022 \u2206\u03b7 j1,l: require that the pseudorapidity gap between the leading jet from the decay of the W and\nthe lepton be no larger than 1.5.\n\u2022 Reconstruct the mass of the Higgs boson candidate, Ml\u03bdqq, by applying the W mass constraint to\nthe lepton-pmiss\nT\nsystem. The resolution is enhanced by performing a kinematic \ufb01t to the mass of\nthe hadronically decaying W, minimizing the function \u03c72 = (Mrec\nW \u2212Mtrue\nW )/\u0393W +(\u2206E j1)2/\u03c3 2\nj1 +\n(\u2206E j2)2/\u03c3 j2, where \u03c3, the energy resolution for the jets, is given for now by the parameterization\nused in ATLFAST, \u03c3/E j = 0.03 \u22950.5/\np\nE j/ GeV. The left plot in Figure 10 shows the distri-\nbution of the Higgs boson candidate invariant mass after all cuts for a representative Higgs boson\nmass of 300 GeV. The \ufb01gure includes the mass peak obtained in a few distorted scenarios.\nTable 7 shows the cut \ufb02ow for W+jets, for tt, and for signal at a representative Higgs boson mass of\n300 GeV. At the time of this writing, a detailed estimate of the background from QCD multijet events is\nnot available.\nThe trigger ef\ufb01ciency for this channel has been estimated, considering only the single-lepton triggers:\nEM25I, EM60, MU20, and MU40 at Level 1; e25i, e60, and mu20i for Level 2 and the Event Filter.\nTable 8 shows the trigger ef\ufb01ciency for signal (MH = 170 GeV) events that pass the of\ufb02ine cuts. Because\nthe present analysis relies only on single-lepton triggers, the trigger ef\ufb01ciency for this channel is not as\nhigh as for the two-lepton channels. However, it has been checked that the trigger ef\ufb01ciency does not\ndistort the Ml\u03bdqq shape for signal in a meaningful way. At the time of this writing, the trigger ef\ufb01ciency\nfor the backgrounds has not been explicitly computed; in Table 7, the trigger ef\ufb01ciency for background\nis assumed to be the same as the trigger ef\ufb01ciency for signal.\nThe control sample for this channel is a region with loosened cuts on \u2206\u03b7 j j and Mj j. In particular,\nthe event selection is the same as in the signal-like region, except that the pseudorapidity gap between\nthe tagjets is required to be less than 4 instead of larger than 4.4, and the lower bound on the invariant\nmass of the tagjets is lowered to 500 GeV. Table 7 shows the contributions from the various subprocesses\nafter these cuts are applied. Since both the signal-like region and the control region have a nontrivial\ncontribution from top events, it is necessary to de\ufb01ne b-tagged control samples to normalize the top\nbackground. These samples have the same kinematic cuts as the signal-like and control regions, but the\nb-veto cut is reversed. The cross-sections in these two regions are also shown in the table.\nThe shape of the W+jets background in the signal-like region is the same as the W+jets background\nin the control region to within the available Monte Carlo statistics. Likewise, the top background in the\nb-tagged region with the same kinematic cuts as the signal-like region has the same shape as the top\nbackground in the b-vetoed signal-like region. In fast simulation, there is a small difference between the\ntop background shapes in the control region and the b-tagged region with the same kinematic cuts as\nthe control region, but that distortion is small compared to the statistical errors expected at the luminosi-\nties considered here. These statements are robust against a variety of systematic uncertainties, namely\nchanges in the Q2 scale (a factor of 4 up and down for both top and W+jets) as well as altered jet energy\nscales (\u00b15% in the region with tracking, \u00b110% elsewhere), degraded jet energy resolution (Gaussian\nsmearing to roughly double the resolution), degraded Emiss\nT\nresolution (modeled by smearing the x and\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1328\n\n(GeV)\n qq\n\u03bd\nl\nM\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section(fb)\n0\n0.2\n0.4\n0.6\n0.8\n1\nNominal\nRaised jet E scale\nLowered jet E scale\nATLAS\nSmeared Jet Resolution\n(GeV)\n qq\n\u03bd\nl\nM\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\n0\n5\n10\n15\n20\n25\n30\n35\n40\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\nEvents / ( 15.1455 )\n0\n5\n10\n15\n20\n25\n30\n35\n40\nPseudodata\nSignal\ntt\nW+jets\n1\n L dt 10 fb\nATLAS\n\u222b\n(GeV)\n qq\n\u03bd\nl\nM\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\nEvents / ( 15.1455 )\n0\n00\n200\n300\n400\n500\n600\n150\n200\n250\n300\n350\n400\n450\n500\n550\n600\n0\n00\n200\n300\n400\n500\n600\nPseudodata\nSignal\ntt\nW+jets\n1\n L dt 10 fb\nATLAS\n\u222b\nFigure 10: Left: the reconstructed invariant mass of the Ml\u03bdqq system for fully simulated signal Monte\nCarlo events with a true Higgs boson mass of 300 GeV. The red dashed and black dotted curves show the\nmass peaks obtained when the jet energy scale is raised and lowered by 7% in the region with |\u03b7| < 2.5\nand 15% elsewhere. The blue dot-dashed curve shows the result obtained when the jet energy resolution\nis smeared by 45%/\n\u221a\nE in the region with |\u03b7| < 2.5 and 63%/\n\u221a\nE elsewhere. Middle: A toy Monte\nCarlo outcome corresponding to 10 fb\u22121 of integrated luminosity for the signal-like region of the H +2j,\nH \u2192l\u03bdqq analysis described in Section 7. Here, the background from QCD multijets is assumed to be\nnegligible. Right: the corresponding distribution in the control region.\ny components of Emiss\nT\nby 5 GeV each), and Emiss\nT\nreconstruction that has been degraded by arti\ufb01cially\ninducing a shift of 3% in the reconstructed Emiss\nT\n.\nThe background is normalized and the signal extracted with the help of a \ufb01tting algorithm which\nimplements a simultaneous binned \ufb01t in the signal-like region and the main control region in the range\n167< Ml\u03bdqq <1000 GeV. The \ufb01t proceeds in two steps: \ufb01rst, standalone \ufb01ts of the top background\nmodel to the b-tagged regions are performed. All parameters governing the shape of the top background\ndistributions are allowed to \ufb02oat in this \ufb01t. After the \ufb01ts to the b-tagged regions, these parameters are\n\ufb01xed, and the histograms are rescaled by the ratio of cross-sections in the b-tagged and b-vetoed regions\nto obtain estimates of the top background normalization and shape in both b-vetoed regions.\nThe main \ufb01t is a simultaneous \ufb01t of the Ml\u03bdqq distribution in the signal-like and control regions. All\nshape parameters for the W+jets background are free to \ufb02oat in the \ufb01t, but the parameters governing\nthe top background shape and normalization remain \ufb01xed. The W+jets background shape is assumed to\nbe the same in the signal-like region and the control region, but the normalizations in the two regions\nare independent. Likewise, the signal shape is assumed to be the same in both regions, but the ratio\nof signal cross-sections is parameterized as a function of Higgs boson mass based on Monte Carlo.\nFigure 10 shows the result of an example \ufb01t to a toy Monte Carlo outcome with a true Higgs boson mass\nof 300 GeV.\nThe performance of the \ufb01tting algorithm has been evaluated by generating pseudo-experimental out-\ncomes corresponding to a luminosity of 10 fb\u22121 with and without true signal events. However, because\nof the large theoretical uncertainty in the prediction of the W+jets background and the lack of a precise\nestimate of the QCD multijet background, an estimate of the expected signi\ufb01cance is omitted here.\n8\nConclusions\nThe prospects for a search for a Standard Model Higgs boson in the WW decay mode have been studied,\nusing a realistic model of the ATLAS detector, including effects such as trigger ef\ufb01ciencies, backgrounds\nfrom fakes, and realistic misalignments. Three channels have been considered: H +0j with H \u2192WW \u2192\ne\u03bd\u00b5\u03bd, H +2j with H \u2192WW \u2192e\u03bd\u00b5\u03bd, and H +2j with H \u2192\u2113\u03bdqq. In-situ background normalization\ntechniques for all three channels have been proposed, and their effectiveness and robustness has been\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1329\n\n(GeV)\ntrue\nH\nM\n130\n140\n150\n160\n170\n180\n190\n(GeV)\ntrue\nH\n-M\nrec\nH\nM\n-10\n-5\n0\n5\n10\n15\n20\nMedian Fit Error\nWid h of Gaus. fit to best-fit Mass dist.\nATLAS\n-1\n L dt=10 fb\n\u222b\n(GeV)\nH\nM\n130\n140\n150\n160\n170\n180\n190\nMedian Significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n\u00b5\n e\n\u2192\n WW\n\u2192\nH+2j, H\n\u00b5\n e\n\u2192\n WW\n\u2192\nH+0j, H\nCombined\nATLAS\n-1\n L dt = 10 fb\n\u222b\nFigure 11: Left: The linearity of the mass determination for the combined \ufb01t of H +0/2j, H \u2192WW \u2192\ne\u03bd\u00b5\u03bd. Right: The expected signi\ufb01cance at 10 fb\u22121.\ndemonstrated with detailed toy Monte Carlo studies.\nThe H +0j, H \u2192e\u03bd\u00b5\u03bd channel is very promising for Higgs boson masses in the region around the\nWW threshold. For other masses, this channel is still very promising, but the analysis is more dif\ufb01cult\nbecause of large systematic uncertainties in the background prediction. It has been shown that these\nuncertainties can be controlled, and that the background can be normalized, with a two-dimensional \ufb01t\nin the transverse mass and the pT of the WW system. With 10 fb\u22121 of integrated luminosity, one would\nexpect to be able to reach a 5\u03c3 discovery with the H \u2192WW \u2192e\u03bd\u00b5\u03bd channel alone if there is a Standard\nModel Higgs with a mass betwen \u223c140 GeV and \u223c185 GeV. A measurement of the mass of the Higgs\nboson at this luminosity would have a precision of less than 2 GeV for a Standard Model Higgs boson\nwith a mass of 160 GeV, or a precision of less than 4 GeV for a Standard Model Higgs boson with a mass\nof 140 GeV.\nThe H + 2j, H \u2192e\u03bd\u00b5\u03bd channel has a smaller event rate than the H + 0j channel but a similar\nsigni\ufb01cance. With 10 fb\u22121 of integrated luminosity, one would expect to be able to reach a 5\u03c3 discovery\nin the H \u2192WW \u2192e\u03bd\u00b5\u03bd channel alone if there is a Standard Model Higgs boson with a mass between\n150 GeV and 180 GeV. A measurement of the Standard Model Higgs boson mass at this luminosity\nwould typically return a precision less than \u223c4-5 GeV if the Higgs boson mass is 160 GeV, or less than\n8 GeV if the Higgs boson mass is 140 GeV.\nIn the range below MH = 200 GeV, both of the dilepton channels are important; it is therefore inter-\nesting to consider a combined \ufb01t of the two. In the combined \ufb01t, a shared mass parameter has been used\nfor the two channels, but the signal normalizations have been allowed to \ufb02oat independently to preserve\nmodel-independence. Figure 11 shows the linearity of the mass determination and the expected signi\ufb01-\ncance of a combined \ufb01t of the two dilepton channels as a function of the true Higgs boson mass. As in the\nother linearity plots in this note, the green band represents the width of a gaussian \ufb01t to the region around\nthe peak of the best-\ufb01t mass distribution and the error bars show the median \ufb01t error. The combined\nsigni\ufb01cance for a Standard Model Higgs is above the 5\u03c3 level for MH larger than about 140 GeV.\nThe H +2j, H \u2192\u2113\u03bdqq channel is most interesting for Higgs masses above \u223c250 GeV. It has been\nshown that the background normalization can be estimated from data, but it is dif\ufb01cult to make a strong\nstatement about the discovery potential of this analysis until a measurement of the W+4 jets background\ncan be obtained from \ufb01rst data.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1330\n\nReferences\n[1] ATLAS Collaboration, Introduction on Higgs Boson Searches, this volume.\n[2] S. Frixione and B. R. Webber, JHEP 06 (2002) 029.\n[3] S. Frixione, P. Nason, and B. R. Webber, JHEP 08 (2003) 007.\n[4] Anastasiou, Charalampos and Dissertori, Gunther and Stockli, Fabian and Webber, Bryan R., JHEP\n03 (2008) 017.\n[5] T. Sjostrand, S. Mrenna, and P. Skands, JHEP 05 (2006) 026.\n[6] G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Seymour\nand B. R. Webber, JHEP 0101 (2001) 010.\n[7] T. Gleisberg et al., JHEP 02 (2004) 056.\n[8] T. Binoth, M. Ciccolini, N. Kauer, and M. Kramer, JHEP 12 (2006) 046.\n[9] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. D. Polosa, JHEP 07 (2003) 001.\n[10] F. Caravaglios, M. L. Mangano, M. Moretti, and R. Pittau, Nucl. Phys. B539 (1999) 215\u2013232.\n[11] J. Alwall et al., JHEP 09 (2007) 028.\n[12] T. Stelzer and W.F. Long, Phys. Commun. 81 (1994) 357\u2013371.\n[13] H. Murayama, I. Watanabe, and K. Hagiwara, HELAS Manual, 1991.\n[14] M. Rast, Studie zum Entdeckungspotential im Prozess Higgs \u2192WW \u2192l\u03bdl\u03bd mit dem ATLAS-\nExperiment unter Beruecksichtigung des W+Jets-Untergrundes, available as BONN-IB-2007-09.\n[15] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[16] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[17] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[18] ATLAS Collaboration, Measurement of Missing Tranverse Energy, this volume.\n[19] V. Barger, G. Bhattacharya, T. Han, and B. A. Kniehl, Phys. Rev. D 43 (1991) 779\u2013788.\n[20] M. Dittmar and H. Dreiner, Phys. Rev. D55 (1997) 167.\n[21] ATLAS Collaboration, ATLAS Detector and Physics Performance, CERN/LHCC 99-15 (1999).\n[22] The CMS Collaboration, CMS Techical Design Report, J. Phys. G: Nucl. Part. Phys. 34.\n[23] ATLAS Collaboration,\nSearch for the Standard Model Higgs Boson via Vector Boson Fusion\nProduction Process in the Di-Tau Channels, this volume.\n[24] ATLAS Collaboration, Trigger for Early Running, this volume.\n[25] S. Asai et al., Eur. Phys. J. C32S2 (2004) 19\u201354.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1331\n\n[26] W. Quayle, Higgs Searches in the H \u2192WW Decay Mode Using the ATLAS Detector, CERN-\nTHESIS-2008-072.\n[27] C. Buttar et al., Les Houches physics at TeV colliders 2005, standard model, QCD, EW, and Higgs\nworking group: Summary report, 2006, hep-ph/0604120.\n[28] The CMS Collaboration, Journal of Physics G: Nuclear and Particle Physics 34 (2007) 995\u20131579.\n[29] R. N. Cahn, Sally and Dawson, Phys. Lett. B136 (1984) 196.\n[30] R. N. Cahn, S. D. Ellis, R. Kleiss, W. J. and Stirling, Phys. Rev. D 35 (1987) 1626\u20131632.\n[31] D. Rainwater, and D. Zeppenfeld, Phys. Rev. D 60 (1999) 113004.\n[32] N. Kauer, T. Plehn, D. Rainwater, and D. Zeppenfeld,, Phys. Lett. B503 (2001) 113\u2013120.\n[33] C. Ruwiedel, M. Schumacher, and N. Wermes, Eur. Phys. J. C (2006) 42 p, Accepted as Scienti\ufb01c\nNote SN-ATLAS-2007-060.\n[34] K. Cranmer, P. McNamara, B. Mellado, Y. Pan, W. Quayle, Sau Lan Wu, Neural Network Based\nSearch for Higgs Boson Produced via VBF with H \u2192W +W \u2212\u2192l+l\u2212Pmiss\nT\nfor 115 < 130 GeV,\nATLAS Internal note ATL-PHYS-2003-007.\n[35] K. Cranmer, Y. Fang, B. Mellado, S. Paganis, W. Quayle, Sau Lan Wu, Analysis of VBF H \u2192\nWW \u2192l\u03bdl\u03bd, ATLAS Internal Note ATL-PHYS-2004-019.\n[36] K. S. Cranmer, Comput. Phys. Commun. 136 (2001) 198\u2013207.\n[37] K. Iordanidis and D. Zeppenfeld, Phys. Rev. D 57 (1998) 3072\u20133083.\n[38] A. Erdogan, D. Froidveaux, S. Klioukhine, and S. V. Zmushko, Study of H \u2192WW \u2192l\u03bd j j and\nH \u2192ZZ \u2192ll j j decays for MH = 1 TeV, ATLAS internal note ATL-PHYS-92-008 (1992).\n[39] D. Froidevaux, Luc Poggioli, and S. V. Zmushko, H \u2192WW \u2192l\u03bd j j and H \u2192ZZ \u2192ll j j Particle\nlevel studies, ATLAS internal note ATL-PHYS-97-103.\n[40] V. Cavasinni, D. Costanzo, S. Lami, and F. Spano, Search for H to WW to l nu jj with the ATLAS\ndetector (mH = 300-600 GeV), ATLAS internal note ATL-PHYS-98-127.\n[41] V. Cavasinni, D. Costanzo, E. Mazzoni, I. Vivarelli, Search for a Intermediate Mass Higgs boson\nproduced via Vector Boson Fusion in the channel H \u2192WW \u2192l\u03bd j j with the ATLAS detector,\nATLAS internal note ATL-PHYS-2002-010 (2002).\n[42] C. Le Maner, Luc Poggioli, H. Przysiezniak, Elzbieta Richter-Was, ATLAS internal note ATL-\nPHYS-2004-003.\n[43] E. Richter-Was, D. Froidevaux, and L. Poggioli,\nATLFAST 2.0 a fast simulation package for\nATLAS, Internal Report ATL-PHYS-98-131, CERN, Geneva, Nov 1998.\nHIGGS \u2013 HIGGS BOSON SEARCHES IN GLUON FUSION AND VECTOR BOSON FUSION USING . . .\n1332\n\nSearch for t\u00aftH(H \u2192b\u00afb)\nAbstract\nFor a light Higgs boson, with mH\n\u2264135 GeV, the largest decay mode is\nH \u2192b\u00afb. Events where the Higgs boson is produced in association with a\nt\u00aft pair manifest a distinct signature due to the presence of two W bosons and\nfour b quarks. Topological and kinematical quantities are used to reconstruct\nthe t\u00aft system. The identi\ufb01cation of an additional b\u00afb pair from the Higgs boson\ndecay is used to further reduce the background.\nIn this analysis we focus on the sensitivity to a light Standard Model Higgs\nboson with the ATLAS detector in the channel t\u00aftH(H \u2192b\u00afb) using the semi-\nleptonic \ufb01nal state with 30 fb\u22121 of integrated luminosity. The relevant back-\ngrounds to the channel are investigated and the impact of their associated sys-\ntematic uncertainties is explored.\n1\nSignal\nAt the LHC t\u00aftH production is dominated (90%) by gluon fusion, as illustrated in Fig. 1. The remaining\n10% arises from quark-antiquark interactions. For a Higgs boson mass between 115 GeV and 130 GeV\nthe production cross-section times branching ratio to b\u00afb varies between roughly 0.4 and 0.2 pb at leading\norder. The top quarks decay almost exclusively to bW, and therefore the various \ufb01nal states can be\nclassi\ufb01ed according to the decays of the W bosons.\nThe all-hadronic channel is the one with the highest branching fraction, with a value of 43%. Un-\nfortunately, the large QCD multijet cross-section does not allow easy triggering with jets. Only tight\nrequirements on the jet pT and on the jet multiplicity could lead to reasonable rates in the \ufb01rst level of\nthe trigger, but these requirements come at the expense of signal ef\ufb01ciency. This is being studied for\nthis \ufb01nal state together with the use of b-tagging at the second level of the trigger to reduce the jet pT\nthreshold.\nThe fully-leptonic \ufb01nal state analysis is probably the least feasible, despite presenting a simpler\nsignature to trigger on, given the presence of two isolated leptons. The branching fraction (5%) is low\nand the two neutrinos prevent the reconstruction of the top quarks.\n\u0000\u0000\u0002\u0001\n\u0003\n\u0003\n\u0003\n\u0003\n\u0004\n\u0005\u0007\u0006\n\b\n\t\n\b\n\u0006\n\u000b\n\u000b\n\f\n\r\n\u000b\n\u000b\n\r\nFigure 1: One of the Feynman diagrams for t\u00aftH production in the semi-leptonic \ufb01nal state.\nThe semi-leptonic \ufb01nal state is a good compromise with a branching fraction of about 28% excluding\ntau leptons. The experimental signature consists of one energetic isolated lepton, a high jet multiplicity\nwith multiple b-tags, and missing transverse energy from the escaping neutrino, as shown in Fig. 1. The\n1333\n\ntrigger relies on the presence of the high-pT lepton. The non-b-tagged jets can be used for reconstructing\nthe hadronically decaying W boson, decreasing the possible combinatorial permutations.\n2\nPhysics backgrounds\nThe production of t\u00aft events is the main background for the t\u00aftH process. Given the high jet multiplicity\nin the signal process (\u22656 jets), only t\u00aft events produced together with at least two extra jets contribute to\nthe preselected data sample. Since most of these extra jets come from the hadronisation of light quarks,\nthis contribution is greatly reduced by asking for four jets to be identi\ufb01ed as b-jets.\n\u000e\n\u000e\n\u000f\n\u0010\n\u0010\n\u000f\n\u0010\n\u0010\n\u0010\n\u0010\n\u000f\n\u000f\n\u000f\n\u000f\n\u0011\n\u0011\n\u0011\n\u000f\n\u000e\n\u000e\n\u0010\n\u000f\n\u000f\nFigure 2: Example of Feynman diagrams for the t\u00aftb\u00afb QCD production.\nThe irreducible background comes from t\u00aftb\u00afb production. This can proceed via QCD or electroweak,\n(EW), interactions with a total cross-section of the order of 9 pb. Some of the Feynman diagrams involved\nin the two production mechanisms are shown in Fig. 2 and Fig. 3. While the QCD production cross-\nsection is ten times larger than the EW production, the latter is also important. The two b-jets not coming\nfrom the t\u00aft decay have large momenta and also have a total invariant mass which is typically close to the\nZ boson mass, and can therefore contaminate the signal region.\nFigure 3: Example of Feynman diagrams for the t\u00aftb\u00afb EW production.\nThe t\u00aftc\u00afc background cross-section is 60% higher than t\u00aftb\u00afb [1], so it could also play an important role.\nHowever, it is found upon investigation that due to the c-jet rejection factor, the t\u00aftc\u00afc background plays a\nnegligible part in comparison with the t\u00aftb\u00afb background. No dedicated sample is therefore simulated for\nthis study. Some t\u00aftc\u00afc events are however present in the inclusive t\u00aft +jets sample used.\nSeveral other backgrounds, such as W+jets, tW production and QCD multijet production, could also\nhave a non-negligible impact on the analysis. Even though the W plus two jets inclusive cross-section\nis about 1200 pb per lepton \ufb02avor [2], it has been shown [3] and con\ufb01rmed in this analysis that the\ncontribution can be reduced to a negligible level if the four b-tags requirement is applied. This is also\ntrue for the less abundant tW background, which has a cross-section of 9.5 pb [4]. Even when four b-jets\nare requested in the event, contamination via QCD b\u00afbb\u00afb production, which has a cross-section of a few\nhundred nb [5], is still possible. The reconstruction of the t\u00aft system allows a certain degree of safety\nagainst non-top background. None of these samples are presented in what follows.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1334\n\n3\nMonte Carlo samples and cross-sections\nThis study uses the leading order cross-sections for the signal and t\u00aftb\u00afb samples. No calculation has yet\nbeen performed for t\u00aftb\u00afb at next-to-leading order, (NLO). This study also uses a t\u00aft background, simulated\nat next-to-leading order. This is the only NLO Monte Carlo sample used, and the only t\u00aft large sample\navailable in ATLAS at the time this analysis was performed. No K-factors are applied to the samples\nsimulated at leading order in the signi\ufb01cance estimates.\nThe signal sample is generated for a Higgs boson mass of mH = 120 GeV with PYTHIA [6] 6.403.\nThe exact generated process was pp \u2192t\u00aftHX \u2192\u2113\u03bdbq \u00afq\u2032bb\u00afbX, with \u2113= e or \u00b5. The factorization and\nrenormalization scales used are identical and are listed in Table 1. The signal and the t\u00aftb\u00afb events are\ngenerated with a lepton \ufb01lter requiring at least one electron or one muon with pseudorapidity |\u03b7| < 2.7\nand transverse momentum above 10 GeV. The leading order production cross-section used is \u03c3(t\u00aftH) =\n537 fb [7]. The branching ratios H \u2192b\u00afb of 67.5% at 120 GeV [7], W\u2192\u2113\u03bd of 10.66% [8], and W\u2192\nhadrons of 67.6% [8] is applied. Finally the lepton \ufb01lter ef\ufb01ciency of \u03b5 = 0.953 is also applied. The\nresulting cross-section is 100 fb.\nFor both t\u00aftb\u00afb QCD and EW samples, the exact process generated is gg\u2192t\u00aftb\u00afbX\u2192\u2113\u03bdbq \u00afq\u2032bb\u00afbX,\nwith \u2113= e or \u00b5. Both processes can be initiated by a q \u00afq pair, but only the dominant gluon fusion is\nsimulated, with the cross-sections being increased to allow for the q \u00afq pair production. For the t \u00aftb\u00afb QCD\nsample, AcerMC 3.4 [9] is used and interfaced to PYTHIA 6.403 for the simulation of the initial and\n\ufb01nal state radiation, hadronisation and decay. The t\u00aftb\u00afb EW sample is generated using AcerMC 3.3 and\nPYTHIA 6.403. The leading order t\u00aftb\u00afb QCD cross-section is \u03c3(pp \u2192t\u00aftb\u00afb) = 8.2(gg)(+0.5(q \u00afq)) pb\nand the lepton \ufb01lter ef\ufb01ciency is \u03b5 = 0.946. For the t\u00aftb\u00afb EW sample, the leading order cross-section is\n\u03c3(pp \u2192t\u00aftb\u00afb) = 0.90(gg)(+0.04(q \u00afq)) pb and the lepton \ufb01lter ef\ufb01ciency is \u03b5 = 0.943.\nThe reducible t\u00aft background events are generated with the MC@NLO [10] program, interfaced\nto HERWIG [11] and Jimmy [12]. The events in this sample correspond to the processes pp \u2192t\u00aft \u2192\n(\u2113\u03bd,q \u00afq\u2032)b\u2113\u03bdb with \u2113= e,\u00b5,\u03c4. The generator versions used are MC@NLO 3.1 and HERWIG 6.510. For\nthe inclusive t\u00aft cross-section we use the NLO+NLL calculation of \u03c3(pp \u2192t\u00aft) = 833 pb. The t\u00aft sample\nis also produced using a \ufb01lter requiring one electron or one muon with pseudorapidity |\u03b7| < 2.7 and\ntransverse momentum above 14 GeV. The t\u00aft \ufb01lter also applies requirements on the jets in the generated\nevents which are reconstructed using a seeded \ufb01xed-cone algorithm with a cone size of \u2206R = 0.4 [13], by\nrequiring at least:\n\u2022 six jets with pT> 14 GeV and |\u03b7| < 5.2\n\u2022 four jets with pT> 14 GeV and |\u03b7| < 2.7\nThe ef\ufb01ciency of this generator \ufb01lter on inclusive t\u00aft events is 0.146.\nFor the t\u00aft sample, about 10% of events are t\u00aftb\u00afb and are removed following the overlap treatment\nexplained in Ref. [14] together with their associated cross-section.\nTable 1 summarizes the cross-sections, calculated using the Monte Carlo generators, of the different\nprocesses considered for this analysis, together with the corresponding numbers of generated events and\nthe equivalent integrated luminosity. All branching fractions and \ufb01lter ef\ufb01ciencies are included.\n4\nAnalysis overview\nThe analysis consists of an initial preselection requirement which is applied to the events to ensure that\nthe fundamental physics objects associated with t\u00aftH are reconstructed. Following preselection, three\ndifferent analysis techniques are implemented in order to reconstruct the top quark pairs and the Higgs\nboson through the identi\ufb01cation of their decay products.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1335\n\nTable 1: Summary of the different samples used for the analysis. The cross-sections are taken from\nthe generators and include all branching fractions and \ufb01lter ef\ufb01ciencies. The fourth column shows the\nequivalent integrated luminosity, taking into account all corrections (see text). For the scale calculations,\nmH = 120 GeV and mt = 175 GeV are used. max(pT 2t, pT 2\u00aft) corresponds to the higher of the two values\nof pT 2 when both the top and anti-top quarks are considered.\nProcess\n\u03c3 (fb)\nEvents\nL (fb\u22121)\nFact. & Renorm Scale\nPDF set\nt\u00aftH (LO)\n100\n92750\n931\nQ2 = m2\nt +max(pT 2t, pT 2\u00aft)\nCTEQ6L1\nt\u00aftb\u00afb QCD (LO)\n2371\n98350\n42\nQ = mH/2+mt = 235 GeV\nCTEQ6L1\nt\u00aftb\u00afb EW (LO)\n255\n24750\n97\nQ = mH/2+mt = 235 GeV\nCTEQ6L1\nt\u00aft \ufb01ltered (NLO)\n109487\n710321\n6.5\nQ2 = m2\nt + 1\n2(pT 2t + pT 2\u00aft)\nCTEQ6M\nThe identi\ufb01cation and association of decay products is directly related to the quality of the recon-\nstructed Higgs boson signal. It mainly suffers from the misassociation of the four b-tagged jets to the\noriginal partons. For this reason, the initial cut-based approach is complemented by two multivariate\nalgorithms, called the pairing likelihood and constrained mass \ufb01t.\n5\nPreselection\nAt the preselection level we require that the event passes the trigger requirement to identify at least one\nhigh-pT lepton (muon or electron) coming from the decay of one of the W bosons. We then require\nthat the event reconstruction identi\ufb01es exactly one isolated high-pT lepton (muon or electron). Vetoing\nthe presence of a second isolated lepton is intended to remove additional sources of background. After\nthe lepton requirements are met, we require at least six calorimeter jets, of which at least four must be\nloosely b-tagged jets from the decay of the top quarks and the Higgs boson.\n5.1\nTrigger requirements\nThe presence of one high-pT lepton, together with missing transverse momentum, is a distinct signature\nof W boson production. These leptons can generally be used to trigger on W production with high ef\ufb01-\nciency. A logical OR of the single isolated electron (e22i) [15], high-pT electron (e55) [15] and single\nmuon (mu20) [16] triggers is used. The inclusion of the e55 trigger is found to improve the ef\ufb01ciency\nfor high-pT electrons where the e22i trigger ef\ufb01ciency was reduced due to the isolation requirement.\nMissing energy triggers were not available at the time of writing, but could be used in future analysis.\nThe trigger ef\ufb01ciency is approximately 82% for the semileptonic top decays for those events which\nwould otherwise pass the of\ufb02ine analysis. This is included consistently in the following sections.\n5.2\nReconstructed high pT lepton selection\nIn this Section we explain the selection criteria used for reconstructed electrons and muons produced in\nthe semi-leptonic decay of the t\u00aft system. As previously mentioned, exactly one high-pT isolated electron\nor muon must be reconstructed for the event to pass the preselection.\nTo be considered for the analysis, reconstructed electrons must have transverse momentum pT >\n25 GeV and pseudorapidity |\u03b7| < 2.5. Further calorimeter-based cuts are applied to the loose elec-\ntron [17] de\ufb01nition. An isolation cut is also applied to the candidate electrons in the form of an upper\nlimit of 0.15 on the ratio of the pT of the additional tracks inside a cone of size 0.2 in \u2206R, (\np\n\u2206\u03b72 +\u2206\u03c6 2),\naround the electron track to the electron pT.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1336\n\nMuon candidates are reconstructed using a combination of the Inner Detector and Muon Spectrom-\neter [18]. They must pass the acceptance cuts pT > 20 GeV and |\u03b7| < 2.5. In order to remove poorly\nreconstructed muons, cuts are applied to the muon track \ufb01t quality and its transverse impact parameter,\nwhich helps to discriminate against muons generated by the decay of long-lived mesons.\nAn isolation cut of 0.30 on the ratio between the transverse energy deposited inside a cone of size\n0.2 in \u2206R around the muon track and the muon pT is applied.\n5.3\nJets\nTo reconstruct the energy of the partons produced in the original collision, calorimeter jets are recon-\nstructed using a seeded \ufb01xed-cone algorithm with a cone size of \u2206R = 0.4 [13]. Cuts on pT > 20 GeV\nand |\u03b7| < 5.0 are initially applied. Only events with at least 6 jets are kept for the analysis. All electrons\nreconstructed as jets are identi\ufb01ed and removed from the jet collection according to the electron overlap\nremoval procedure described in Section 5.3.1. Reconstructed muons which are not isolated are combined\ninto jets where applicable (see Section 5.3.3), and only after this step are the jet energies calibrated for\nresidual effects. The jet multiplicity is shown in Fig. 4, calculated after electron overlap removal and the\njet \u03b7 and pT cuts.\nIn the following analyses the concept of \u2018correct\u2019 jets is important. This is de\ufb01ned by \ufb01nding the\nclosest reconstructed jet to each parton, after \ufb01nal state radiation. This match is in \u2206R space and must\nbe closer than 0.4. A W or H boson is correctly matched if both the jets being used are associated to\nthe partons from its decay, while for a top quark the matching refers to the b quark jet only. Normally\n\u2018correct\u2019 is applied in this note only to one quark or boson at a time.\n5.3.1\nTreatment of overlaps between jets and electrons\nSince most electrons are also reconstructed by the jet algorithm it becomes necessary to identify them in\nthe jet collection in order to avoid double counting. The criteria for the jet-electron overlap removal is the\nfollowing: each jet matching a well-reconstructed electron (i.e. ful\ufb01lling the cuts de\ufb01ned in Section 5.2)\nwithin a \u2206R of 0.2, and for which the ratio of the electron to the jet transverse momenta is greater than\n0.75, is discarded from the jet collection. About 4% of the jets in the signal sample are removed by this\nselection, 99% of them being actual true electrons.\n5.3.2\nb-tagging\nb-jets are identi\ufb01ed using the IP3D+SV1 tagger [19], which exploits both the impact parameter of tracks\nand the properties of an inclusive secondary vertex, using a likelihood approach which leads to a single\ndiscriminating variable: the b-tagging weight. In order to allow for a projected decrease in light jet\nrejection of approximately 30%, the b-tagging weight for this study is increased by 0.9 for central jets\n(|\u03b7| < 2.5) having no associated (\u2206R < 0.3) heavy quark or lepton (b,c,\u03c4) in the Monte Carlo simulation\nhistory. The b-tag weight spectrum for b-, c-, and light jets in the signal sample is shown in Fig. 4. A cut\non the weight de\ufb01nes which jets will be eventually identi\ufb01ed as b-jets in the analysis. The rejection of c-\nand light jets versus the b-jet ef\ufb01ciency, obtained by varying the weight cut, is also shown in Fig. 5. The\ndifferent samples exhibit very similar behaviour. The rejection for \u201cpuri\ufb01ed\u201d jets is shown in the bottom\nrow of Fig. 5. Puri\ufb01ed jets are those which have no heavy \ufb02avor (b, c, \u03c4) quark or lepton within 0.8 in\n\u2206R.\nIn the preselection, a loose set of criteria are initially used to de\ufb01ne a sample of jets as a \ufb01rst step to\nidentifying b jets for the analyses. The requirements are that the jet is in the central region of the detector\n|\u03b7| < 2.5, and has b-tag weight \u22650. If there are fewer than four of these jets, the event is discarded.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1337\n\nThe cut-based analysis and the pairing likelihood (Sections 8 and 9) require that there are at least four\nb-jets having b-tag weight \u22655.5. The b-tag weight \u22650 working point implies a b-tagging ef\ufb01ciency of\nabout 85% and a rejection of light (c-) jets of about 8.6 (2.4), whereas the working point at b-tag weight\n\u22655.5 implies a b-tagging ef\ufb01ciency of about 65% and a rejection of light (c-) jets of about 60 (6).\nnumber of jets per event\n0\n2\n4\n6\n8\n10\n12\n14\n16\narbitrary units\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nb-tagging weight (SV1+IP3D)\n-20\n-10\n0\n10\n20\n30\n40\narbitrary units\n-3\n10\n-2\n10\n-1\n10\n1\nb jets\nc jets\nlight jets\nATLAS\nFigure 4: Left: Multiplicity of jets, inside pT and \u03b7 acceptance. Right: Distribution of b-tagging weight\nfor b-, c- and light jets in t\u00aftH events, using the IP3D+SV1 tagger.\nb-tag efficiency\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\nc jet rejection\n1\n10\n2\n10\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nb-tag efficiency\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\nlight jet rejection\n2\n10\n3\n10\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nb-tag efficiency\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\nc jet rejection\n1\n10\n2\n10\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nPurification\nATLAS\nb-tag efficiency\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\nlight jet rejection\n2\n10\n3\n10\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nPurification\nFigure 5: Rejection of light and c-jets versus b-tagging ef\ufb01ciency. Red open markers indicate the working\npoint (b-tag weight \u22655.5) used for the cut-based and paring likelihood analyses, open markers with a\ncentral dot (right plots) represent the performance when the 30% performance degradation is applied.\nThe lower plots show results for puri\ufb01ed jets, where no heavier quark existed within a wide cone of\n\u2206R < 0.8.\n5.3.3\nTreatment of low pT muons\nAbout 20% of the time a B-meson decay cascade gives rise to a muon. With a four b-jet signature in\nthis channel, these muons, also called soft muons are present in almost every event. In order to improve\nthe estimate of the momentum of the original b quark, these muons must be used to correct the jet four-\nmomenta by adding the muon four-momentum to a jet. Two different algorithms (high and low-pT [20])\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1338\n\nidentify the muons, which are required to be within \u2206R < 0.4 of the jet axis. Among the candidates\nfrom the high-pT algorithm which are separated from the selected hard lepton by \u2206R > 0.1, only the one\nwith the best track quality is considered for addition. All the neighbouring candidates from the low-pT\nalgorithm are considered for addition, provided they ful\ufb01l pT > 4 GeV and pT < 100 GeV, |\u03b7| < 2.5\nand chi-squared per degree of freedom \u03c72/n < 30 for the combined \ufb01t. In addition, a loose anti-isolation\ncut is applied, requiring that the energy reconstructed in the calorimeter within a cone of size 0.2 in\n\u2206R around the muon track divided by the muon pT is higher than 0.1. Table 2 shows that adding\nlow pT muons to jets improves both the mean jet pT and resolution. Fig. 6 shows that there is also an\nimprovement in the Higgs boson mass and resolution, when the correct jet combination is chosen.\n5.3.4\nCalibration\nA Monte Carlo based jet correction has been derived to take into account residual calibrations, e.g.\nout-of-cone effects and neutrinos. The parametrization was derived from full simulation, so that the\njet four-momentum is corrected by a \ufb02avor dependent rescaling factor which scales all components of\nthe four-momentum. Table 2 shows that for b-jets, the residual calibration brings the jet and associated\nparton pT into agreement from an offset of 5.4 to \u22120.5 GeV. Each of the analyses uses the light jet\ncorrection for those jets which are assigned to the W boson and corrects the other four jets as b quark\noriginated. The impact of the calibration on the Higgs boson mass peak where the correct jet combination\nis chosen is shown in Fig. 6. Both the mass peak location and the resolution are improved.\nTable 2: The true parton pT minus the measured jet pT with and without adding muons and making the\nout-of-cone correction. The quoted values are the results of a Gaussian \ufb01t in the region \u00b120 GeV.\nTreatment\nValue\nNo Calibration\nAdded muons\nCalibrated\nBoth corrections\nAll b jets\nMean, GeV\n5.7\u00b10.05\n5.4\u00b10.05\n-0.1\u00b10.04\n-0.5\u00b10.04\nSigma, GeV\n10.0\u00b10.05\n9.8\u00b10.05\n10.2\u00b10.05\n10.0\u00b10.04\nb jets with muons\nMean, GeV\n26\u00b12.6\n7.6\u00b10.2\n11.4\u00b10.5\n2.3\u00b10.2\nSigma, GeV\n18.2\u00b11.1\n11.8\u00b10.2\n13.6\u00b10.4\n12.0\u00b10.2\nAll light jets\nMean, GeV\n2.4\u00b10.04\n2.3\u00b10.04\n-1.4\u00b10.04\n-1.5\u00b10.04\nSigma, GeV\n8.4\u00b10.04\n8.4\u00b10.04\n8.9\u00b10.04\n8.3\u00b10.04\nLight jets with muons\nMean, GeV\n10.5\u00b10.9\n2.4\u00b10.4\n7.3\u00b10.7\n-1.0\u00b10.4\nSigma, GeV\n11.3\u00b10.8\n10.9\u00b10.5\n11.5\u00b10.6\n10.7\u00b10.4\n5.4\nResults of preselection on signal and background\nThe effect of the event preselection on signal and background samples is illustrated in Table 3. The\nef\ufb01ciency for the four b-tag cut is different in the signal and in the irreducible background because the\ntwo additional b-jets have different pT and |\u03b7| spectra. The preselection, at a level of four loose b-tags,\nremoves a large fraction of the signal, but also reduces the backgrounds to a level where they can be\nhandled more easily; for example 98% of the t\u00aftX background is removed. It also ensures that the selec-\ntions are a subset of the requirements placed at generator level. The selected sample has approximately\na 0.6% signal component, with a little more than 8% of the background being irreducible t\u00aftb\u00afb. Further\ntightening the b-tagging requirement to four jets with weights of at least 5.5 reduces the samples with\nfour b quarks by a further factor of four while removing 90% of the remaining t\u00aftX background.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1339\n\n) [GeV]\nb\nm(b\n40\n60\n80\n100\n120\n140\n160\n180\n200\narbitrary units\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n 0.34 GeV\n\u00b1\n : 16.16 \n\u03c3\n 0.31 GeV\n\u00b1\nmean: 117.7 \n 0.42 GeV\n\u00b1\n : 18.15 \n\u03c3\n 0.37 GeV\n\u00b1\nmean: 106.6 \nATLAS\n) [GeV]\nb\nm(b\n40\n60\n80\n100\n120\n140\n160\n180\n200\narbirary units\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n 0.15 GeV\n\u00b1\n : 15.61 \n\u03c3\n 0.14 GeV\n\u00b1\nmean: 119.82 \n 0.16 GeV\n\u00b1\n : 16.91 \n\u03c3\n 0.15 GeV\n\u00b1\nmean: 106.33 \nATLAS\nFigure 6: Effect of adding a reconstructed low pT muon to at least one of the b jets (left), and the effect\nof jet calibration (right) shown for the Higgs boson mass where the correct jet combination is chosen.\nRed solid (black open) markers and solid (dotted) line show the mass distribution and \ufb01tted values for\njets after (before) correction. The effect of the accidental wrong muon matches can be seen in the shape\ndistortion. All distributions are normalized to unity.\nTable 3: Cross-sections after each preselection cut for signal and background. The last row shows the\nfurther effect of tightening the b-tag requirements to the level of the \ufb01nal selection in the cut based and\npairing likelihood analyses. In the last column the contribution of t\u00aftb\u00afb has been removed. The errors are\nstatistical only.\nPreselection cut\nt\u00aftH(fb)\nt\u00aftb\u00afb(EW) (fb)\nt\u00aftb\u00afb(QCD) (fb)\nt\u00aftX (fb)\nlepton\n57. \u00b1 0.2\n141 \u00b1 1.0\n1356 \u00b1 6\n63710 \u00b1 99\n+ \u22656 jets\n36 \u00b1 0.2\n77 \u00b1 0.9\n665 \u00b1 4\n26214 \u00b1 64\n+ \u22654 loose b-tags\n16.2 \u00b1 0.2\n23 \u00b1 0.7\n198 \u00b1 3\n2589 \u00b1 25\n+ \u22654 tight b-tags\n3.8 \u00b1 0.06\n4.2 \u00b1 0.2\n30 \u00b1 0.8\n51 \u00b1 2\n6\nReconstruction of the hadronically decaying W bosons\nReconstructing the W boson four-momenta is necessary to reconstruct the top quarks. The reconstruction\nof the hadronically decaying W boson is done in different ways by the three analyses.\nFor the cut-based and pairing likelihood analyses (see Sections 8 and 9), the highest four b-tagged\njets (with b-jet weight \u22655.5) are excluded from the hadronically decaying W reconstruction, however\nall other jets are paired to form W candidates. Figure 7 shows the mass distribution and multiplicity of\nall W candidates for the cut-based analysis. Only candidates within 25 GeV of the true W mass are kept.\nEven with these cuts the hadronically decaying W candidate multiplicity is still very high. All jets used\nto form these W candidates are calibrated with the light-jet calibration. The likelihood analyses do not\nrequire an explicit cut upon this mass as the de\ufb01nition of the likelihood imposes it automatically, but the\nconstrained \ufb01t likelihood (Section 10) imposes a requirement that the mass be between 30 and 150 GeV\nto reduce the number of combinations to be evaluated.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1340\n\njj combinations per event\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\ncross section [fb]\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n 0.76\n\u00b1\nmean: 1.82 \n 0.54\n\u00b1\nRMS : 1.45 \nATLAS\nm(jj) [GeV]\n0\n50\n100\n150\n200\n250\narbirary units\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n 0.35 GeV\n\u00b1\nmean: 84 35 \n 0.36 GeV\n\u00b1\n : 10.34 \n\u03c3\nATLAS\nFigure 7: Cross-sections of hadronically decaying W combinations per event giving candidates within\n25 GeV of the true W mass in the signal sample. (left). Right: Invariant mass spectrum for hadronically\ndecaying W candidates normalized to unity. The dotted line shows combinations where the jets from the\nW are correctly matched.\n7\nReconstruction of the leptonically decaying W bosons\nWhen reconstructing the leptonically decaying W, we use the lepton four-momentum as measured in\nthe detector. The neutrino, transverse momentum can be inferred by measuring the imbalance of the\ntransverse energy in the event. This measured quantity is referred to as missing transverse energy.\n7.1\nNeutrino pz estimation\nOnce the missing transverse energy is identi\ufb01ed with pT \u03bd, the invariant mass of the sum of the lepton\nand neutrino four-momenta can be constrained to the W boson mass [21]. Because of the limited mea-\nsurement resolution on the transverse missing energy, for a signi\ufb01cant fraction of events the quadratic\nconstraint equation does not have a real solution. In this case the \u201c\u2206= 0 approximation\u201d can be made\nby dropping the imaginary part of those solutions with complex roots. Another method (the \u201ccollinear\napproximation\u201d) assumes that the W boson decay products are produced preferentially in the same direc-\ntion (due to the large top quark mass boosting the W boson). For the collinear approximation, one can\nassume that pz\u2113= pz\u03bd.\nConsidering t\u00aftH events where one lepton is reconstructed, 72% of the time pz\u03bd has real solutions. In\nthis case, both solutions are carried forward into the analyses, and the best performing \ufb01nal state solution\nis used. For these events the pz\u03bd resolution is 19.5 GeV. In the other 28% of cases where there are no\nreal pz\u03bd solutions, the \u2206= 0 approximation is used and the pz\u03bd resolution is 40 GeV. This performs\nbetter than the collinear approximation where the pz\u03bd resolution is 54 GeV. The quality of the W-boson\nreconstruction can be seen in Fig. 8. For the events where there is no real solution for pz\u03bd, the direction\nand the mass of the W boson is better represented by the \u2206= 0 approximation.\nSince the mass constraint is lost when using the \u2206= 0 approximation (the same would be true for\nthe collinear approximation) there is an actual cut for the reconstructed W boson mass. The cut-based\nand pairing likelihood analyses only consider W candidates having a mass less than 140 GeV, while\nthe constrained \ufb01t analysis does not make an explicit requirement on this but the poor \u03c7 2 will remove\nextreme cases.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1341\n\n)\nReco\n, W\ntrue\nR(W\n\u2206\n0\n0.2 0.4 0.6 0.8\n1\n1 2 1.4 1.6 1.8\n2\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n 0\n\u2265\n \n\u2206\n 0\n\u2248\n \n\u2206\nz\nl\n P\n\u2248\n \nz\n\u03bd\nP\nATLAS\n) [GeV]\n\u03bd\nm(l\n80\n100 120 140 160 180 200 220 240\narbitrary units\n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\n0 09\n 0\n\u2248\n \n\u2206\nz\nl\n P\n\u2248\n \nz\n\u03bd\nP\nATLAS\nFigure 8: Distributions of \u2206R between the true and the reconstructed W boson (left) and of the recon-\nstructed leptonically decaying W mass (right) for events where a solution for pz is found (solid black\nline) and events where an approximation is used (dotted red for \u2206= 0, dashed blue for the collinear\napproximation). All distributions are normalized to unity.\n8\nCut-based analysis\nThis section describes the algorithms used to reconstruct the t\u00aft system and the Higgs boson. The b-jets\nare associated with the leptonically and hadronically decaying W boson candidates, to build a list of\ntop quark candidates. The combination of b-jets resulting in the best reconstruction for the top quark\ncandidates is taken as the \ufb01nal choice. It is important to note that the b-jets themselves satisfy the cut\non b-tag weight \u22655.5 and that if there are more than four of these jets, then the four with the highest\nweight are treated as b-jets. Events where there is no combination giving a satisfactory top quark mass\nreconstruction are discarded. The two remaining b-jets are used to form the Higgs boson candidate.\n8.1\nTop-antitop quark system and combinatorial background\nIn each event, top quarks are reconstructed by pairing two b-jets with the W boson candidates in the way\nwhich minimizes the \u03c72 expressed as:\n\u03c72 =\n\u0012m j jb \u2212mtop\n\u03c3m j jb\n\u00132\n+\n\u0012ml\u03bdb \u2212mtop\n\u03c3ml\u03bdb\n\u00132\n,\n(1)\nwhere \u03c3m j jb and \u03c3ml\u03bdb are the reconstructed mass resolutions estimated in simulated signal events and are\n13 and 19 GeV respectively. Only combinations ful\ufb01lling |m j jb \u2212mtop| < 25 GeV and |ml\u03bdb \u2212mtop| < 25\nGeV are considered for the \u03c72 calculation. The top quark mass distributions for the chosen combination\nin the signal sample is shown in Fig. 9. The two remaining b-tagged jets are used to form the Higgs boson\ncandidates. The mass distribution for all Higgs boson candidates in the signal sample is shown in Fig. 10,\nand in the same plot the signal and physics background cross-sections are adjacent. Here the dif\ufb01culty of\nthe analysis is clearly shown, requiring dedicated studies to measure the background normalization and\nits shape in data.\nAs a \ufb01nal cut, to discriminate against t\u00aft events where no Higgs boson is produced, only events in\na mass window of 30 GeV from the nominal Higgs boson mass are used for the \ufb01nal estimation of the\ncut-based analysis signi\ufb01cance.\nThe effect of the \ufb01nal selection for the cut-based analysis on signal and background samples is shown\nin Table 4. The selections have reduced the signal by a factor of sixteen from the preselection, but the\nsignal to background has increased from 0.006 to 0.11. The irreducible t\u00aftb\u00afb background is 46% of the\ntotal.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1342\n\nTable 4: Accepted cross-section after each successive mass-window selection cut for signal and back-\nground in the cut-based analysis. In the last column the contribution of t\u00aftb\u00afb is removed. Errors are\nstatistical only.\ncut\nt\u00aftH(fb)\nt\u00aftbb(EW) (fb)\nt\u00aftbb(QCD) (fb)\nt\u00aftX (fb)\nWhad + Wlep\n2.49 \u00b1 0.05\n2.9 \u00b1 0.2\n18.2 \u00b1 0.7\n22.5 \u00b1 1.9\n+ t\u00aft+Higgs\n2.04 \u00b1 0.05\n2.2 \u00b1 0.2\n14.7 \u00b1 0.6\n14.3 \u00b1 1.5\n+ Higgs boson mass window\n1.00 \u00b1 0.03\n0.52 \u00b1 0.07\n3.6 \u00b1 0.3\n4.9 \u00b1 0.9\nb) [GeV]\n\u03bd\nm(l\n100 120 140 160 180 200 220 240\ncross section [fb/3GeV]\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n 0.28 GeV\n\u00b1\n : 11.22 \n\u03c3\n 0.28 GeV\n\u00b1\nmean: 174.84 \nATLAS\nm(jjb) [GeV]\n100 120 140 160 180 200 220 240\ncross section [fb/3GeV]\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n 0.24 GeV\n\u00b1\n : 9.38 \n\u03c3\n 0.22 GeV\n\u00b1\nmean: 174.93 \nATLAS\nFigure 9: Reconstructed invariant mass spectrum for selected leptonic (left) and hadronic (right) top\nquark candidates in the signal sample. The dotted red line indicates the candidates formed by assigning\nthe correct b-jet to the top quark being considered. All distributions are given in cross-section.\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/8GeV]\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\n 1.07 GeV\n\u00b1\nmean: 118.52 \n 1.64 GeV\n\u00b1\n : 22.85 \n\u03c3\nATLAS\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/30GeV]\n0\n1\n2\n3\n4\n5\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/30GeV]\n0\n1\n2\n3\n4\n5\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nFigure 10: Left: Reconstructed invariant mass spectrum for Higgs boson candidates in the signal sample.\nThe dotted red line indicates the candidates formed by assigning the correct b-jets. Right: Reconstructed\ninvariant mass spectrum for signal and backgrounds after the cut-based selection. All distributions are\ngiven in cross-section.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1343\n\n9\nPairing likelihood analysis\nIn the previous Section we used a cut-based approach to identify the top quark decay products. A\nstraightforward improvement to such an approach is to use several discriminating topological distribu-\ntions combined together in order to build a pairing likelihood. As a \ufb01rst step the analysis considers only\ntop quark properties as likelihood templates. Even though Higgs boson properties could help associating\nb-jets, if used, those could lead to bias in the background distributions. A correct combination is ob-\ntained when the objects used for the reconstructed variables match the Monte Carlo partons, regardless\nof whether other objects are correctly associated. On the other hand all the wrongly reconstructed objects\nare used to form the wrong combination templates. The variables used, shown in Fig. 11, are:\nm(jj) [GeV]\n0\n50\n100 150 200 250 300 350 400\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\nm(jjb) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\nATLAS\nb) [GeV]\n\u03bd\nm(l\n0\n100\n200\n300\n400\n500\n600\n700\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\n(j,j) [rad]\n\u2220\n0\n0.5\n1\n1 5\n2\n2.5\n3\n3.5\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nATLAS\nR(jj,b)\n\u2206\n0\n0 5\n1 1 5\n2\n2.5\n3\n3.5\n4\n4.5\n5\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nR(l,b)\n\u2206\n0\n0.5\n1\n1 5\n2\n2 5\n3\n3 5\n4\n4.5\n5\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nFigure 11: Pairing likelihood templates for top quark topological distributions, derived from the t \u00aftH sig-\nnal sample. Solid lines represent the correct combination while the dotted lines show the combinatorial\nbackground in the signal itself. See text for a description of the variables.\n\u2022 m j j: The invariant mass of the light jets from the hadronic W decay.\n\u2022 m j jb: The invariant mass of the hadronic top decay products.\n\u2022 ml\u03bdb: The invariant mass of the leptonic top decay products.\n\u2022 \u2220(j, j): The angle between the light jets from the hadronic W decay.\n\u2022 \u2206R(j j,b): The distance in R between the hadronic W and b jet from the hadronic top decay.\n\u2022 \u2206R(l,b): The distance in R between the lepton and the b jet from the leptonic top decay.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1344\n\nThe output of the pairing likelihood for the correct and wrong b-jet combinations is shown in Fig. 12.\nAs shown in this plot, even though the correct distributions are peaked at 1, the wrong combinations still\nhave a large probability of being selected. The only combination used is the one which maximizes\nthe likelihood output. In order to avoid the presence of a large combinatorial contribution a cut on the\nlikelihood output of 0.9 is used to select well-reconstructed events. After this cut, b-jets are associated\nto reconstruct the Higgs boson, as shown in Fig. 12, and the two top quarks, shown in Fig. 13. The\ninvariant mass distribution for the selected Higgs boson candidates for signal and backgrounds is shown\nin Fig. 14.\nLikelihood\n0\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9\n1\narbitrary units\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/8GeV]\n0.05\n0.1\n0.15\n0 2\n0.25\n 0.81 GeV\n\u00b1\nmean: 117.27 \n 1.05 GeV\n\u00b1\n : 20.08 \n\u03c3\nATLAS\nFigure 12: Left hand side: combinatorial likelihood output for t\u00aftH events. Black solid (red dotted)\nhistogram indicates the correct (wrong) combinations. Right hand side: invariant mass for the Higgs\nboson candidates reconstructed using the maximum likelihood con\ufb01guration, after applying a cut on the\nlikelihood. Dotted histogram indicates the correct combinations. The differential cross-section is shown\nin fb.\nb) [GeV]\n\u03bd\nm(l\n100 120 140 160 180 200 220 240\ncross section [fb/3GeV]\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n 0.39 GeV\n\u00b1\n : 13.43 \n\u03c3\n 0.37 GeV\n\u00b1\nmean: 173.44 \nATLAS\nm(jjb) [GeV]\n100 120 140 160 180 200 220 240\ncross section [fb/3GeV]\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n 0 25 GeV\n\u00b1\n : 11.28 \n\u03c3\n 0 29 GeV\n\u00b1\nmean: 173 83 \nATLAS\nFigure 13: On the left (right) hand side is shown the leptonic (hadronic) top quark candidates recon-\nstructed invariant mass using the maximum likelihood con\ufb01guration, after applying a cut on the likeli-\nhood output. The dotted histogram indicates the correct b quark jet for the top quark being considered.\nThe differential cross-section is shown in fb.\nA \ufb01nal cut on the reconstructed Higgs boson mass, requiring it to be within 30 GeV of the Higgs\nboson nominal mass is applied. The event yield for the whole analysis using the pairing likelihood is\nshown in Table 5. This analysis reduces the signal by a factor thirteen, and produces a sample which has\na signal to background ratio of 0.1. The irreducible t\u00aftb\u00afb background increases to 45% of the total.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1345\n\nTable 5:\nCross-sections after each selection cut for signal and backgrounds for the pairing likelihood\nanalysis. In the last column the contribution of t\u00aftb\u00afb has been removed. Errors are statistical only.\napplied cuts\nt\u00aftH(fb)\nt\u00aftb\u00afb(EW) (fb)\nt\u00aftb\u00afb(QCD) (fb)\nt\u00aftX (fb)\nLeptonic W\n3.6 \u00b1 0.06\n4.1 \u00b1 0.2\n29 \u00b1 0.8\n48 \u00b1 2.7\n+ Best likelihood > 0.9\n2.3 \u00b1 0.05\n2.5 \u00b1 0.2\n16 \u00b1 0.6\n19 \u00b1 1.7\n+ Higgs boson mass window\n1.2 \u00b1 0.04\n0.68 \u00b1 0.08\n4.6 \u00b1 0.3\n6.5 \u00b1 1.0\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/30GeV]\n0\n1\n2\n3\n4\n5\n6\n) [GeV]\nb\nm(b\n0\n50\n100 150 200 250 300 350 400\ncross section [fb/30GeV]\n0\n1\n2\n3\n4\n5\n6\nttH\nttbb (QCD)\nttbb (EW)\nttjj\nATLAS\nFigure 14: Reconstructed invariant mass spectrum for Higgs boson candidates for signal and back-\ngrounds after pairing likelihood selection. The differential cross-section is shown in fb.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1346\n\n10\nConstrained \ufb01t analysis\nAn alternative analysis uses a mass-constrained \ufb01t to the measured missing energy and jet and lepton\nfour-momenta to help with the jet combinatorics. There are six quarks produced from the top quark and\nHiggs boson decays, and these are matched to the reconstructed jets. The \u03c7 2 from this \ufb01t is used in a\nlikelihood technique together with kinematic variables, b-tagging and jet charge. Then, all jet combina-\ntions passing loose criteria are tested and the one with the best likelihood is chosen. The analysis starts\nfrom the preselection as described in Section 5. The signal events are then separated from background\nin a second likelihood step.\n10.1\nMass-Constrained \ufb01t technique\nThe \ufb01t varies a scale factor for the four-momenta of the jets and the z component of the neutrino mo-\nmentum. Adjustments to the jet momenta and masses through the scale parameters, f i, produce accom-\npanying changes in the missing energy and hence in the parameters used in the reconstruction of the\nleptonically decaying W as the transverse components of its neutrino are taken to be the missing energy.\nThe longitudinal component of the momentum of decaying W boson\u2019s neutrino pz\u03bd is the last \ufb01t parame-\nter. The parameters are constrained by the estimated jet errors and by the masses of the top quarks and W\nbosons. These later are included as approximate Gaussian \u03c72 contributions calculated using the masses\ninferred from the current parameters as indicated in the following equation:\n\u03c72 =\n6\n\u2211\ni=1\n \nf i\njet \u22121\n\u03c3 i\njet/Pi,initial\njet\n!2\n+ (mlep\nW \u221280.425)2\n\u03c3 2\nW\n+ (mlep\nt\n\u2212175)2\n\u03c3 2t\n(2)\nwhere the W and top quark widths \u03c3W and \u03c3t are 2.1 and 1.5 GeV respectively.\nTo simplify the \ufb01t, the hadronic top quark and W are forced to be exactly on mass shell. The scale\nfactor of the higher pT jet from the W is externally varied, while the other two scale factors are calculated\nto give the correct masses. The momenta of all six jets are varied, but these three are linked. There are\ntherefore \ufb01ve free parameters and not seven. This implies that these two particles are \ufb01xed to their\nnominal masses, while the leptonic top quark and W are given widths.\nThe calculation of the momentum of the neutrino from the leptonic W decay normally has two solu-\ntions, as discussed in Section 7. Both of these are used as starting points for the \ufb01t, to ensure that it does\nnot \ufb01nd only one local minimum, and the \ufb01t with the larger \u03c72 is discarded. If the W neutrino solutions\nhad complex roots then the real part of these is used as an initial value.\nThe jet momenta are calibrated as discussed in Section 5.3.4, and the following errors are used in the\n\ufb01t:\n\u03c3Plight/Plight = 0.988/\u221apT \u22950.035\n(3)\n\u03c3Pb/Pb = 0.888/\u221apT \u22950.125\n(4)\nwhere the momenta are measured in GeV. This form comes from comparing reconstructed jet pT with\nsimulated initial quark pT; in other words it includes not only detector effects but also fragmentation.\nBoth light and b-jet momentum errors are treated as Gaussian distributed; for b quark jets in particular\nthis is not a good description as the frequent presence of a neutrino gives tails to the measured energy\nresponse.\nThe \ufb01t adjusts the momenta of all the jets, including those from the Higgs boson, but the \ufb01tted Higgs\nboson mass is not used in the analysis, as it offers no improvement.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1347\n\n10.2\nb-tag information\nIn order to use the b-tagger output, as described in Section 5.3.2, for a likelihood, the distributions of\nweights expected for b-jets and non b-jets in this environment are required. This is done using jets taken\nfrom the signal simulation, where only jets with a parent quark within 0.4 in \u2206R and no second quark\nwithin 0.6 in \u2206R are used. The ratio of smoothed weight distributions with b-jet over light \ufb02avored jets\n(u,d,s) is shown in Fig. 15.\nB weight\n-10\n0\n10\n20\n30\n40\nRatio, b/light\n1\n10\n2\n10\nATLAS\nFigure 15: The b-tagging likelihood ratio extracted from signal simulation as the ratio of b-weight distri-\nbutions for b-jets and light jets. The degree of smoothing re\ufb02ects the statistical precision at each point.\nIn the analysis, four jets are taken to be from b quarks. For each jet we compute L i\nb, the ratio of\nb/light for jet i as shown in Fig. 15. In selecting combinations the sum \u03a3i log10 L i\nb is taken over the four\njets. There is no requirement made on the jets from the W boson.\n10.3\nJet charge\nThe assignment of jets to quarks can bene\ufb01t from the jet charge measurement as we know the expected\ncharges of the quarks involved. The jet charge is the momentum weighted sum of the charged particle\ncharges within the jet, and it shows some correlation with the initial quark charge. The \u00afb(b) quark\nhas only a charge of (-)1/3, and furthermore, after hadronisation there are oscillations which reduce the\nsensitivity, but there is some information.\nThe analysis requires exactly one high pT lepton which has charge Ql, and therefore we know the\nexpected charge of both of the b quarks associated to the top quarks via the relationship sign(Ql) =\nsign(Qtlept) = \u22121\u00d7sign(Qthad), and the sum of the charges of the jets from the hadronically decaying W\nboson QW had = \u22121\u00d7Ql. The measured values of these are then compared with the expectations using a\nlikelihood. The sum of the Higgs boson jet charges is much less sensitive because the expected value is\nzero, but it is also used.\nThe jet charge plots in Fig. 16 are calculated using jets from the signal sample. The W plots are made\nusing only true light jets which were tagged as light jets, and the b plots only from tagged b-jets associated\nwith a b quark. This is to ensure that the jet charge is independent of b-tag information. The W wrong\ncombinations distribution has spikes at integral values which generally involve at least one jet outside\nthe tracker acceptance contributing a charge of zero. These are less frequent in the correct combinations\nwhich tend to be central. The other distributions re\ufb02ect b-tagged jets which must therefore have charged\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1348\n\nq(W)\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\nATLAS\nq(b)\n-1\n-0.5\n0\n0.5\n1\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\nATLAS\nq(H)\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents, relative normalization\n1\n10\n2\n10\nATLAS\nFigure 16: Left: The jet charge of W boson candidates, based on the sum of the jet-charges of the two\njets signed by the high-pT lepton. Center: Jet charges of individual b-jets from top quarks; signed so\nthat those where quark charge agreeing with the lepton charge from W decay are positive. Right: The\nmagnitude of the sum of the jet charges of the jets assigned to the Higgs boson. Wrong b-jet combinations\nhave a somewhat \ufb02atter distribution. Correct combinations are solid (black) and wrong combinations are\ndashed (red).\nparticle tracks. It is assumed that the jet charge information can be calibrated from the plentiful top quark\npair events. The normalizations are arbitrary, as they offset every combination equally. The jet-charge is\nused as L jet\u2212charge = L hadronic top\nq(b)\n\u00d7L leptonic top\nq(b)\n\u00d7Lq(W) \u00d7Lq(H).\n10.4\nLikelihood analysis for jet assignment\nAll possible assignments of jets to quarks are evaluated in turn. Those combinations which fail a loose\nquality requirement are discarded. This quality requirement is that:\n\u2022 Both of the jets assigned to the Higgs boson must have a b-likelihood greater than zero. From\nFig. 15 that corresponds to a cut of about -2 on the b-tagging variable.\n\u2022 Selections on the mass of the W and top quark which decay to jets. The W mass calculated from\nthe jets without \ufb01tting must lie between 30 and 150 GeV, and the top quark mass between 100 and\n250 GeV. Note that the jet energy correction factor applied depends upon whether or not the jet is\nconsidered to originate from a b quark in this hypothesis.\n\u2022 Total b-likelihood greater than 8. This is the sum of the log-likelihoods of the four jets which are\nassigned to b-jets; this roughly corresponds to the mean b-weight of the jets being 4 or greater.\nIn the preselected signal sample there are a mean of 5811 combinations to be tested per event, but\nthe above quality requirement reduces this to 233; a considerable saving in time. 90% of the preselected\nsignal events have at least one combination passing the above requirements.\nEvents which pass these selections are processed by the t\u00aftH \ufb01tting code. Correct or wrong combina-\ntions are then used to de\ufb01ne a likelihood ratio.\nThe elements of that likelihood ratio are as follows:\n\u2022 The log10 of the \u03c72 from the \ufb01t.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1349\n\n2\n\u03c7 \n10\nlog\n-1\n-0.5\n0\n0.5\n1\n1.5\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nmin\njet . t|\n-1\n-0.5\n0\n0.5\n1\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n\u03b8\n cos \nlept\nbt\n-1\n-0.5\n0\n0.5\n1\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nFigure 17: Left: The \u03c72 of the \ufb01t. Center: jet\u00b7top|min. The cosine of the minimum angle between top\nquarks and their daughter jets. Correct combinations have more collimated tops. Right: The tlept\nb\ncos\u03b8 \u2217.\nThe decay angle in the rest frame of the leptonically decaying top quark of the b-jet relative to the top\nquark direction in the lab frame. Correct combinations are solid (black) and wrong combinations are\ndashed (red).\n\u2022 jet\u00b7top|min: The minimum cosine of the angle between the top quarks and any of their four jets in\nthe t\u00aftH center of mass frame.\n\u2022 tlept\nb\ncos\u03b8 \u2217: The decay angle in the rest frame of the leptonically decaying top quark of the b-jet\nrelative to the top quark direction in the lab frame.\n\u2022 tlept\nb \u2206R: the distance in \u2206R space between the lepton and the b quark assigned to the same top\nquark.\n\u2022 |\u03b7|max: The maximum |\u03b7| of the considered jets. Jets from the t\u00aftH system tend to be more central\nthan those from the underlying event.\n\u2022 cos\u03b8 \u2217\nH\u2212jet: Measured in the Higgs boson rest frame, this is the cosine of the angle between the\nhigher pT of the two jets from the Higgs boson and the boost applied to shift from the lab frame to\nthe Higgs boson rest frame.\n\u2022 mt: The hadronic top quark mass before the \ufb01t is performed.\nThe variables are displayed in Figs. 17 and 18 for correct and wrong combinations. In this case\n\u2018correct\u2019 implies that all six quarks are correctly assigned. Fig. 19 shows how each variable would\nperform if used individually to separate correct and incorrect pairings. For each variable combinations\nare selected by the likelihood ratio found using that variable alone. The Fig. shows the fraction of wrong\npairings which would be accepted as a function of the fraction of correct ones. The \ufb01t \u03c7 2 is the most\npowerful single variable over much of Fig. 19, but the masses of the hadronic top quark and W work\nwell at high ef\ufb01ciency while jet\u00b7top|min is also rather powerful. Clearly the variables have correlations,\nand these are taken into account by evaluating the likelihood in a 3D space de\ufb01ned by the three variables\nunder study. This explicitly includes the correlations, but is limited by the simulation statistics required to\npopulate the space. The combination of \u03c72, jet\u00b7top|min and tlept\nb\ncos\u03b8 \u2217was adopted as the most powerful\nset of three variables found.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1350\n\n R\n\u2206\n \nlept\nbt\n0 0.5\n1 1.5\n2 2.5 3 3.5 4 4.5 5\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nmax\n\u03b7\n0\n1\n2\n3\n4\n5\n6\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n [GeV]\nt\nm\n100 120 140 160 180 200 220 240\nEvents, relative normalization\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nFigure 18: Left: The distribution of distances, \u2206R, between the lepton and the b quark from the leptonic\ntop quark. Center: The maximum |\u03b7| of any jet in the combination being tested. Correct combinations\nare more central. Right: The reconstructed mass of the hadronically decaying top quark, before any \ufb01t is\nperformed. Correct combinations are solid (black) and wrong combinations are dashed (red).\nFraction of good combinations\n0\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9\n1\nFraction of bad combniations\n-2\n10\n-1\n10\n1\n*\u03b8\n cos\nl\nbt\n*\u03b8\n cos\nh\nbt\nH-jet\n*\u03b8\ncos\nR\n\u2206\n \nl\nb\nT\nmax\n\u03b7\nW\nm\nT\nm\n2\n\u03c7\nmin\n\uf8e6\n t \n\u2022\njet \nnull\nATLAS\nFigure 19: The performance of a range of possible variables if they are used individually to \ufb01nd the\ncorrect quark-jet pairing in a t\u00aftH event. For a given ef\ufb01ciency for selecting the correct pairing (x axis),\nwhat fraction of the incorrect pairings will also be chosen (y axis). The line labelled null shows the effect\nof selecting combinations at random.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1351\n\nThe remaining variables were tested to see whether their addition as uncorrelated likelihood contri-\nbutions made a signi\ufb01cant improvement, and those that did were included. The \ufb01nal likelihood is de\ufb01ned\nas follows:\nLpairing = logL 3D\nlog\u03c72,jet\u00b7top|min,tlept\nb\ncos\u03b8 \u2217+logLtlept\nb \u2206R +logL|\u03b7|max\n+logLcos\u03b8 \u2217\nH\u2212jet +logLmt +logLb\u2212tag +logL jet\u2212charge\n(5)\nThe combination which produces the largest likelihood for each event is adopted. The quality of the\nchosen combination is examined in Section 11.\n10.5\nSignal and background separation\nThe separation of signal from background is again done using the likelihood technique. There are two\nrather different backgrounds considered: the t\u00aft j j component for which b-tagging is the primary tool and\nthe \u2018irreducible\u2019 t\u00aftb\u00afb background which differs from the signal only in kinematic ways, which can be\nexploited to give some separation. The variables used to separate signal and background are:\n\u2022 Lpairing: From combinatorics.\n\u2022 \u03a3i log10 L i\nb: Sum of the log-likelihoods of the four jets used as b\u2019s in the combination chosen.\n\u2022 \u03a3H\nb\u2212tag: The sum of the b-tagging weight of the two jets from the Higgs boson.\n\u2022 \u2206\u03b7(H,top)min: The difference in \u03b7 between the Higgs boson and the closer top quark.\n\u2022 cos(tH)max: The higher of the two angles between top quarks and Higgs boson in the center of\nmass of the t\u00aftH system.\n\u2022 Hp in C.o.M: The Higgs boson momentum in the center of mass frame of the t\u00aftH system.\n\u2022 cos\u03b8 \u2217\nH\u2212jet: As de\ufb01ned in Section 10.4.\nPairing likelihood\n-30\n-25\n-20\n-15\n-10\n-5\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nPairing likelihood\n-30\n-25\n-20\n-15\n-10\n-5\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nsum of four b-tag likelihoods\n8\n10\n12\n14\n16\n18\n20\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nsum of four b-tag likelihoods\n8\n10\n12\n14\n16\n18\n20\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nsum of b-tags(H)\n0\n10\n20\n30\n40\n50\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nsum of b-tags(H)\n0\n10\n20\n30\n40\n50\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nFigure 20: Left: Distributions for signal and backgrounds of the likelihood used to \ufb01nd the combinatorics\nsolution. Center: The sum of the b-tag likelihoods of the four jets used as b\u2019s in the chosen combination.\nThere was cut at 8 in the combinatorics preselection. Right: The sum of the b-tags of the jets associated\nto the Higgs boson. This variable removes t\u00aft j j more than t\u00aftb\u00afb. Histograms are \ufb01lled for every event\nwhere there is a successful \ufb01t. In all histograms, the sum of the individual histograms is shown. They\nare stacked to indicate relative contributions.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1352\n\nmax\ncos(tH)\n-1 -0.8 -0 6 -0.4 -0 2 0\n0 2 0.4 0.6 0.8\n1\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nmax\ncos(tH)\n-1 -0.8 -0 6 -0.4 -0 2 0\n0 2 0.4 0.6 0.8\n1\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nCoM\np\nH\n0 100 200 300 400 500 600 700 800 9001000\n1\n\u00d7\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nCoM\np\nH\n0 100 200 300 400 500 600 700 800 9001000\n1\n\u00d7\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n S gnal\nATLAS\nH-jet\n*\u03b8\ncos\n-1 -0.8 -0.6 -0.4 -0.2 0\n0.2 0.4 0.6 0 8\n1\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\nH-jet\n*\u03b8\ncos\n-1 -0.8 -0.6 -0.4 -0.2 0\n0.2 0.4 0.6 0 8\n1\nCross-section [fb/bin]\n-1\n10\n1\n10\n2\n10\n tt j\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nFigure 21: Left: The maximum cosine of the angle between either top quark and the Higgs boson when\nboosted into the t\u00aftH center of mass frame. Center: The momentum of the Higgs boson candidate in the\ncenter of mass frame. Note that the true Higgs bosons have a lower momentum than the background.\nRight: The cos\u03b8 \u2217of the higher pT of the jets from the Higgs boson. This tends to be more central for\nsignal events. In all histograms, the sum of the individual histograms is shown. They are stacked to\nindicate relative contributions.\nFigures 20 and 21 show the data used to produce the likelihood ratio for most of the variables.\nThe backgrounds fall into two basic classes - the t\u00aft j j and the t\u00aftb\u00afb, and to deal with these two 3D\nlikelihoods are de\ufb01ned. The \ufb01rst includes the three quantities which contain b-tagging information:\nLpairing,\u03a3i log10 L i\nb,\u03a3H\nb\u2212tag. These are all powerful but are highly correlated and therefore bene\ufb01t from a\ncorrect treatment of those correlations. The second is cos(tH)max,Hp,cos\u03b8 \u2217\nH\u2212jet, which carries discrimi-\nnation based on event kinematics. It too has important correlations. These likelihoods are combined as\nif independent, with one further likelihood, derived from \u2206\u03b7(H,top)min, added as well. All the likeli-\nhoods have been smoothed so that the expected \ufb02uctuations are below 10%, and there is therefore little\nover-training, as separate test and training samples are maintained.\nThe distributions used to de\ufb01ne the likelihood are constructed using all events for which a constrained\n\ufb01t was made, and all the components are normalized to the cross-sections at that stage. The signal\nseparation likelihood is:\nLs/b = 1/3\n\u0012\nlogL 3D\nLpairing,\u03a3i log10 L i\nb,\u03a3h\nb\u2212tag +logL\u2206\u03b7(H,top)min +logL 3D\ncos(tH)max,Hp,cos\u03b8 \u2217\nH\u2212jet\n\u0013\n(6)\nThe factor of 3 makes this an average, rather than a sum, and is there purely for convenience. Note\nthat there is nothing in this de\ufb01nition to prefer correctly paired signal events.\nFigure 22 shows the distribution of the \ufb01nal likelihood. It is generally dominated by t\u00aft j j events, but\nat the largest likelihood values the t\u00aftb\u00afb and signal events are more prevalent. It can be seen that any\nt\u00aftH analysis will be selecting a tail of the signal, and controlling this will be important. The signal to\nbackground ratio, within the mass window, rises to about 25%, and any rise above that is in a region\naffected by lack of simulation statistics.\nThe \ufb01nal choice of working point will depend upon the details of the systematic error evaluation.\nThe tighter the selection on the likelihood the higher the signal to background ratio but the smaller the\nsamples in data and simulation; the latter is an important consideration.\nThe maximum signi\ufb01cance which might be expected in a measurement (evaluated as s/\n\u221a\nb) ignoring\nall systematic uncertainties, is obtained by cutting at a log likelihood of -4.44. This would yield a\nsigni\ufb01cance of 2.78\u03c3, but at low purity. Reducing the mass range by requiring that the candidate has a\nmass within the range 90 to 150 GeV does not appear to improve the results when systematic errors are\nnot considered.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1353\n\nSignal separation Like ihood\n-6\n-5.5\n-5\n-4.5\n-4\nCross-section [fb/bin]\n-2\n10\n-1\n10\n1\n10\n2\n10\nSignal separation Like ihood\n-6\n-5.5\n-5\n-4.5\n-4\nCross-section [fb/bin]\n-2\n10\n-1\n10\n1\n10\n2\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nSignal separation Like ihood\n-6\n-5.5\n-5\n-4.5\n-4\nCross-section [fb/bin]\n-2\n10\n-1\n10\n1\n10\nSignal separation Like ihood\n-6\n-5.5\n-5\n-4.5\n-4\nCross-section [fb/bin]\n-2\n10\n-1\n10\n1\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nSignal separation Likelihood\n-6\n-5.5\n-5\n-4.5\n-4\nIntegrated cross-section [fb]\n-1\n10\n1\n10\n2\n10\n3\n10\nSignal separation Likelihood\n-6\n-5.5\n-5\n-4.5\n-4\nIntegrated cross-section [fb]\n-1\n10\n1\n10\n2\n10\n3\n10\n ttjj\n ttbbEW\n ttbbQCD\n Signal\nATLAS\nSignal separation l kel hood\n-6\n-5.5\n-5\n-4.5\n-4\nSignal to background\n-2\n10\n-1\n10\n1\nATLAS\nFigure 22: Left: The total signal separation likelihood. The top \ufb01gure shows all events while the bottom\nshows only those within a Higgs boson candidate mass window of 90 to 150 GeV. Right: The integrated\nversion of the lower left plot, so the total event rates passing any cut can be seen. The bottom half of this\nplot is the signal to background ratio implied.\nIf an arbitrary ten per cent error on the background level is assumed then the signi\ufb01cance for this cut,\nevaluated as s/\np\nb+(\u03b4b)2, decreases to below 0.5\u03c3, while the highest signi\ufb01cance is around 1.8\u03c3 for a\ncut at -4.05. This is shown numerically in Table 6, where the expected event rates are shown for three\ndifferent cut values. No \ufb01nal choice is really possible without complete evaluation of systematic errors,\nbut -4.2 with the mass window cut applied does seem to be a plausible working point. The statistical\nsigni\ufb01cance for this selection is 2.18\u03c3. At this point the signal is reduced by a factor of twelve from the\npreselection, but signal to background ratio has become 0.125\u00b10.01. The irreducible t\u00aftb\u00afb background\nhas increased to 50% of the total.\nTable 6: The accepted cross-sections for signal and the main backgrounds at various stages of the\nanalysis. The t\u00aft j j cross-section suffers from limited statistics.\nSelection\nt\u00aftH(fb)\nt\u00aftb\u00afb(EW) (fb)\nt\u00aftb\u00afb(QCD) (fb)\nt\u00aftX (fb)\nInitial Sample\n100\n255\n2371\n109487\nPass preselection\n16\n23\n198\n2589\nFit quality requirements\n14\n20\n165\n1584\nLs/b > -4.40\n4.9\n5.1\n35\n58\nLs/b > -4.20\n2.5\n2.3\n13.9\n11.9\nLs/b > -4.10\n1.4\n0.96\n7.11\n4.5\nMass window 90 to 150 GeV.\nLs/b > -4.40\n2.3\u00b10.07\n1.4\u00b10.17\n10.8\u00b10.7\n22\u00b13.1\nLs/b > -4.20\n1.3\u00b10.05\n0.62\u00b10.12\n4.6\u00b10.5\n5.3\u00b11.5\nLs/b > -4.10\n0.71\u00b10.04\n0.23\u00b10.07\n2.5\u00b10.35\n2.2\u00b11.0\nThe distribution of the masses of the candidates can be seen in Fig. 23, at a cut of Ls/b > \u22124.2. The\nright hand side of Fig. 23 shows details of the mass distribution for signal only.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1354\n\nM(bb) [GeV]\n0\n50\n100 150 200 250 300 350 400\nCross-section [fb/30GeV]\n0\n1\n2\n3\n4\n5\n6\nM(bb) [GeV]\n0\n50\n100 150 200 250 300 350 400\nCross-section [fb/30GeV]\n0\n1\n2\n3\n4\n5\n6\n ttjj\n ttbbEW\n ttbbQCD\n Signal\n Signal\nATLAS\nM(bb) [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\nCross-section [fb/10GeV]\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\nMean=121.6GeV\nRMS=21.8GeV\nATLAS\nFigure 23: The mass distribution after cutting at -4.2 in Ls/b. Left: All samples, showing the contri-\nbutions stacked. The signal distribution is also shown separately at the bottom. Right: Signal only, the\ndashed (red) line equals events where the correct jets from the Higgs boson are selected.\n11\nComparison between the three analysis techniques\nThe performance of the cut-based, pairing likelihood and the constrained \ufb01t analyses in terms of purity\nversus selection ef\ufb01ciency can be seen in Fig. 24. For the likelihood analyses, the different working points\nare obtained by varying the \ufb01nal cut on the likelihood discriminant. In the case of the cut-based analysis,\nthe same variation is achieved by loosening or tightening the mass-window cuts on the hadronically\ndecaying W and the reconstructed top quarks. For this section the ef\ufb01ciency is de\ufb01ned as the selection\nef\ufb01ciency relative to the total events simulated. The purity is de\ufb01ned in terms of the correctness of the\nassignment of b-jets used to reconstruct the \ufb01nal objects. For instance, one has a pure hadronic top\nquark when the b-jet matches the true b parton from the top quark decay, regardless of whether the same\nhappens for the hadronic W boson decay products.\nFig. 24 clearly shows the increase of performance when using more information (likelihood) than\njust the mass of the reconstructed particles (cut-based).\nThe chosen working points are indicated with solid markers on Fig. 24. Those points have not been\noptimized in terms of statistical signi\ufb01cance, because of a lack of statistics for the t\u00aftX background and\nbecause due consideration of the systematic errors should also in\ufb02uence the decision. However, the\nsigni\ufb01cance does not change much with the choice of the cut on the pairing likelihood output since this\nlikelihood is not designed to discriminate signal from physics background events.\nThe ability of the three analyses to correctly identify objects in the event is compared in Table 7. The\nlikelihood-based assignments perform noticeably better than the cut-based analysis. The signal ef\ufb01ciency\nand statistical signi\ufb01cance are also improved.\n12\nBackground Shapes\nThe success of this analysis relies on the accurate knowledge of the background level and shape. Monte\nCarlo predictions are affected by large systematic uncertainties, as the background rejection depends\ncritically also on the jet \ufb02avor composition. For this reason it is mandatory to develop methods to\nmeasure background directly from real data.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1355\n\nEfficiency\n0.005\n0.01\n0.015\n0.02\n0.025\n0.03\n0.035\n purity\nb\nb\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\nCut-based\nLikelihood\nConstrained fit\nATLAS\nFigure 24: Comparison of the purity of reconstructed b\u00afb invariant mass before the \ufb01nal mass window cut\nversus selection ef\ufb01ciency for the cut-based, the pairing likelihood and the constrained \ufb01t analysis. The\nsolid markers show the selected working points.\nTable 7: A comparison of quality criteria for the three analyses at their working points. The mass window\nof 90 to 150 GeV is only applied for the last two rows.\nCut Based\nPairing likelihood\nConstrained \ufb01t\nb jet from Hadronic top correct\n44.4\u00b11.1%\n49.2\u00b11.1%\n51.0\u00b11.5%\nb jet from Leptonic top correct\n50.5\u00b11.2%\n57.4\u00b11.1%\n56.2\u00b11.5%\nHiggs boson jets correctly chosen\n29.4\u00b11.0%\n34.0\u00b11.0%\n32.0\u00b11.4%\nFour b quarks correct\n23.3\u00b11.0%\n27.5\u00b11.0%\n27.1\u00b11.3%\nHiggs boson mass peak resolution, GeV\n22.8\u00b11.6\n20.1\u00b11.1\n22.3\u00b12.1\nSignal Ef\ufb01ciency\n2.04\u00b10.05%\n2.32\u00b10.05%\n2.49\u00b10.07%\nSignal to background\n0.110\u00b10.014\n0.103\u00b10.014\n0.123\u00b10.019\ns/\n\u221a\nb, 30fb\u22121\n1.82\n1.95\n2.18\nOne important result of the present study is that the Higgs boson candidate mass spectrum depends\nweakly upon the b-tagging working point. This is shown in Fig. 25, which reports the difference in b\u00afb\ninvariant mass shape for the t\u00aftb\u00afb and t\u00aft+jets processes after applying the pairing likelihood analysis with\nthe loose and tight b-tagging requirement as de\ufb01ned in Section 5.3.2\nThe complete determination of the background shape from data depends crucially on the relative\ncontributions of the t\u00aftb\u00afb and t\u00aft+jets distributions, which in turn depends on the strength of the b-tagging\ncut applied. The b\u00afb invariant mass can be studied for a b-tag requirement, the \u201cmedium b-tag\u201d, between\nthe loose and tight, such that the possible presence of signal can be still neglected. We choose a medium\nworking point corresponding to a b-tagging weight cut of 3, such that the ratio of the contribution of t \u00aftb\u00afb\nwith respect to t\u00aft+jets goes from 11% to 30%, with a signal contamination of less than 3%.\nOne strategy contemplated is to use the t\u00aftb\u00afb/t\u00aft+jets fraction coming from the Monte Carlo prediction\nand the total number of events from the data to normalize the Monte Carlo at the loose working point\nwhere the signal level is less than 1%. Using the Monte Carlo jet \ufb02avor composition and the ratio of\nthe b-, c- and light jet ef\ufb01ciencies (\u03b5medium\nb, c, light(pT,\u03b7)/\u03b5loose\nb, c, light(pT,\u03b7)) at the loose and medium working\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1356\n\npoints, it is then possible to predict the shape and normalization at the medium working point.\nThe data reduction when moving the b-tag quality from \u201cloose\u201d to \u201cmedium\u201d is explained by the ratio\nof the b-tag ef\ufb01ciencies at these two working points applied to the t\u00aftb\u00afb and t\u00aft+jets data. With a 50 pb\u22121\ndata sample, the b-tagging ef\ufb01ciency of b- and c-jets will be known with an accuracy of 5% [19], while\nthe rejection of light quark jets will be measured with a 10% uncertainty. We expect a signi\ufb01cantly\nmore accurate knowledge of the b-tagging performance with a data sample of approximately 30 fb\u22121.\nThis will allow the measurement of the background level of t\u00aftb\u00afb and t\u00aft+jets as a function of the b\u00afb\ninvariant mass for the loose and medium b-tagging working points. These measurements can be used to\nverify and tune with data the background prediction given by the Monte Carlo simulation, which will be\nused to extrapolate the event yeld expectation of known processes when the b-tag quality is moved from\n\u201cmedium\u201d to \u201ctight\u201d. This extrapolation can be monitored, and eventually further corrected, by looking\nat the comparison with the measured data outside the mass window, where the number of signal events\nexpected is small (about 4%). If necessary, this procedure can be extended by asking for three b-tagged\njets to further constrain the background composition and its shape and absolute normalization, to achieve\nthe 5% systematic uncertainty necessary for the analysis of this processes.\nHiggs candiates mass [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\n+jets sample\ntt\n tight b-tag \n loose b-tag \nATLAS\n0\n50\n100\n150\n200\n250\n300\n350\nratio\n0\n0.5\n1\n1.5\n2\n2.5\nHiggs candiates mass [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n (QCD) \nb\nb\ntt\n tight b-tag \n loose b-tag \nATLAS\n0\n50\n100\n150\n200\n250\n300\n350\nratio\n0\n0.5\n1\n1.5\n2\n2.5\nFigure 25: Ratio of the invariant mass spectrum for Higgs boson candidates after combinatorial likeli-\nhood analysis and using a loose and tight cut on the b-tag weight. Left hand side: t\u00aft+jets, right hand side:\nt\u00aftb\u00afb. The signal region shows very consistent behaviour.\n13\nSystematic uncertainties\nThe evaluation of systematic uncertainties, especially in the background level, is of vital importance in\nthis analysis. Unfortunately it has not yet been brought to a satisfactory level and a robust method to\ninfer background shapes and normalization from data, vital for this channel, still needs to be developed.\nFollowing the estimation of systematic uncertainties due to the standard detector effects, Table 8 shows\nthe various contributions for all three analyses. It is noticeable how important the jet uncertainties are for\nboth signal and background. Indeed the knowledge of the jet energy and of the b-tagging performance\nhave a crucial impact on the kinematic quantities used for the reconstruction of the t\u00aft system and for the\ncorrect identi\ufb01cation of the b-jets used for the analysis. Large \ufb02uctuations on the background estimations\narise due to the lack of statistics for the t\u00aftX sample, giving rise to a relative statistical error up to 20%.\nWhile the theoretical uncertainties for the signal and background normalization are quite large, their\nimpact can be reduced by making direct measurements. This is certainly the case for the t\u00aft cross-section,\nwhere the theoretical uncertainties associated with the NLO+NLL calculation are around 12% [14] while\nwith only 100 pb\u22121 of data, a direct measurement of the cross-section for the semileptonic \ufb01nal state\nusing b-tagging could be performed with a much smaller error [22]. The t\u00aftb\u00afb background is only cal-\nculated at LO, the cross-section calculation has a strong scale dependence, a factor 4 when changing\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1357\n\nfrom Q2\nQCD = \u02c6s to Q2\nQCD =< p2\nT > [9]. Even though the signal cross-sections used for this work are\nLO, NLO calculations are already available with a theoretical uncertainty including errors coming from\nparton distribution functions of the order of 15-20% [23] (compared to the 100-200% uncertainty of the\nLO cross-section).\nTable 8: Effect of the various systematic uncertainties on the signal and background ef\ufb01ciencies.\nSource\nCut-based\nLikelihood\nConstrained \ufb01t\nsignal\nbackground\nsignal\nbackground\nsignal\nbackground\nElectron\nenergy scale\n\u00b1 0.5%\n\u00b1 2%\n\u00b1 0.3%\n\u00b1 3%\n\u00b1 1%\n\u00b1 3%\nresolution\n\u00b1 0.5%\n\u00b1 0.6%\n\u00b1 0%\n\u00b1 1%\n\u00b1 0.2%\n\u00b1 4%\nef\ufb01ciency\n\u00b1 0.2%\n\u00b1 2%\n\u00b1 0.2%\n\u00b1 1%\n\u00b1 0.5%\n\u00b1 0.2%\nMuon\nenergy scale\n\u00b1 0.7%\n\u00b1 3%\n\u00b1 0.6%\n\u00b1 0.2%\n\u00b1 0.4 %\n\u00b1 4%\nresolution\n\u00b1 0.8%\n\u00b1 0.6%\n\u00b1 0.3%\n\u00b1 0.4%\n\u00b1 1%\n\u00b1 3%\nef\ufb01ciency\n\u00b1 0.3%\n\u00b1 0.1%\n\u00b1 0.8%\n\u00b1 0.1%\n\u00b1 0.4%\n\u00b1 0.1%\nJet\nenergy scale\n\u00b1 9%\n\u00b1 5%\n\u00b1 9%\n\u00b1 14%\n\u00b1 9%\n\u00b1 8%\nresolution\n\u00b1 0.3%\n\u00b1 7%\n\u00b1 1%\n\u00b1 5.5%\n\u00b1 5%\n\u00b1 14%\nb-tag\n\u00b1 16%\n\u00b1 20 %\n\u00b1 18%\n\u00b1 20%\n\u00b1 16%\n\u00b1 20%\nb mis-tag\n\u00b1 0.8%\n\u00b1 5%\n\u00b1 1.1%\n\u00b1 3%\n\u00b1 3%\n\u00b1 10%\nsummed in quadrature\n\u00b1 18%\n\u00b1 22%\n\u00b1 20%\n\u00b1 25%\n\u00b1 19%\n\u00b1 28%\n13.1\nEffect of pile-up on signal\nThe portion of the semi-leptonic t\u00aftH signal sample used here is simulated a second time, but with the\nanticipated effects of pile-up and cavern background included. It is important to stress that the same\ngenerated events are used as input for both pile-up and non pile-up samples. The pile-up actually applied\nto the events is that expected for running at instantaneous luminosity L of 1033cm\u22121s\u22121.\nThe effect of pile-up on the preselection of events (applicable to all three analyses) is shown in\nTable 9, and as can be seen, the effect of the trigger requirement is the most signi\ufb01cant.\nTable 9: The effect of pile-up on the samples at successive stages of preselection with relative\nef\ufb01ciencies.\nt\u00aftH \u03c3 (fb)\nQuantity \\ Sample\nNo pile-up\npile-up\nStarting Sample Generated\n100\n100\nPass Trigger (e22i, e55, mu20)\n65 (65%)\n62 (62%)\nOne high-pT Lepton\n56 (87%)\n53 (86%)\n\u22656 jets (pT> 20 GeV, |\u03b7| < 5)\n36 (64%)\n34 (64%)\n\u22654 central b-jet candidates, (|\u03b7| < 2.5 & b-jet weight > 0)\n16 (45%)\n15 (44%)\nPreselected\n16 (45%)\n15 (44%)\nThe distribution of the number of high pT leptons in the events before preselection is shown in\nFig. 26 for the pile-up and non pile-up samples. They are very similar, suggesting that the electron and\nmuon reconstruction are not signi\ufb01cantly affected by pile-up; however the trigger requirement reduces\nthe number of events with pile-up available to the rest of the preselection.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1358\n\nHigh pT lepton multiplicity\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n0\n2000\n4000\n6000\n8000\n10000\n12000\nATLAS\nNo PileUp\nPileUp\nFigure 26: High pTlepton multiplicity (e\u00b1,\u00b5\u00b1)\nfor pile-up and non pile-up samples (before\npreselection).\nJet multiplicity\n0\n2\n4\n6\n8\n10\n12\n14\n0\n1000\n2000\n3000\n4000\n5000\nATLAS\nNo PileUp\nPileUp\nFigure 27: Jet multiplicity (before preselec-\ntion) for pile-up and non pile-up samples. The\ncuts pT< 20 GeV and |\u03b7| < 5 are applied to the\nindividual jets.\nb-jet mult. after preselection\n-0.5 0\n0.5\n1 1.5\n2\n2.5\n3\n3.5\n4\n4.5\n0\n200\n400\n600\n800\n1000\n1200\nATLAS\nNo PileUp\nPileUp\nFigure 28: b jet multiplicity (after preselection)\nfor pile-up and non pile-up samples. The cuts\npT< 20 GeV, |\u03b7| < 2.5 and bjet weight > 5.5\nare applied to the individual jets.\nm(bb) [GeV]\n0\n50\n100\n150\n200\n250\n300\n0\n10\n20\n30\n40\n50\nATLAS\nNo PileUp\nPileUp\nFigure 29: Reconstructed Higgs boson mass\npeak (mbb) for pile-up and non pile-up samples.\nFigure 27 shows the jet multiplicity before preselection. It can be seen that the number of events\nhaving exactly 6 jets is reduced by approximately 10%, and the number of events having more than 7\njets is increased. The net effect will be an increase in the combinatorial background, though the extra\njets will typically have a low pT.\nFor the cut-based and pairing likelihood analyses, candidate b-jets are designated as those jets lying\nin the central region of the detector (|\u03b7| < 2.5), with pT> 20 GeV and b-jet weight > 5.5, however, if\nthere are more than four of these then the jets with the highest b-jet weights are used.\nThe number of b-jets in the events both with and without pile-up after the other preselection cuts are\napplied can be seen in Fig. 28, where there is a reduction in the number of events having the requisite\nfour b-jets.\nThe extent of the reduction in events at the various stages of the cut-based analysis is shown in Table\n10. The most pronounced difference comes from the reduction in the number of b-jets, and the net\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1359\n\neffect of pile-up is a \u223c12% reduction in the number of events where it is possible to reconstruct a Higgs\nparticle, as shown in Fig. 29. This effect will also manifest itself in the backgrounds, since they all\nhave either two or four b-quarks. The most interesting background pile-up study would now be with the\nt\u00aft j j sample, since this relies on mis-tagging of light jets to create a physics background, however this is\nbeyond the scope of this study which only examines the signal.\nIt should be noted that in the course of this study, the b-jet ef\ufb01ciency and light-jet rejections were\nstudied, however no visible differences were observed. This can be explained by the fact that even a 1%\ndrop in ef\ufb01ciency from 50% to 49% causes almost an 8% drop in events having four b-jets.\nTable 10: The extent of the reduction in events for pile-up and non pile-up samples for the cut-\nbased analysis with relative ef\ufb01ciencies in parentheses. The harshest reduction comes from the\nfour b-jet requirement.\nt\u00aftH \u03c3 (fb)\nQuantity \\ Sample\nNo pile-up\npile-up\nPreselected events\n16.0\n14.8\n\u22654 b-jets (b-jet weight > 5.5)\n3.7 (23.1%)\n3.2 (21.5%)\nHad & Lep W inside mass-window\n2.5 (66.4%)\n2.1 (66.8%)\nt, \u00aft-quarks rec. in mass-window\n2.0 (81.6%)\n1.8 (83.1%)\n14\nSigni\ufb01cance estimates\nThe number of remaining events in the Higgs boson mass window (30 GeV around the nominal Higgs\nboson mass) have been used to compute a crude estimate of the statistical signi\ufb01cance for this channel\nwith 30 fb\u22121. For such a channel in which the signal and backgrounds are very alike, this naive estimate is\nnot the most relevant \ufb01gure of merit, but it is still useful to compare analyses. For the cut-based analysis,\na signi\ufb01cance of 1.8 is achieved with signal to background ratio of approximately 0.11. It is worth noting\nthat the addition of the low pT muons to jets and the residual jet calibrations performed in Sections 5.3.3\nand 5.3.4 improved the cut-based analysis signi\ufb01cance by 0.3. With the pairing likelihood approach\nthe signi\ufb01cance is 1.95 for a signal to background ratio of 0.1. Finally the constrained \ufb01t likelihood\ngives 2.2 (1.7) for a signal over background value of 0.12 (0.14), obtained with a cut on Ls/b of -4.2\n(-4.1). Figure 30 shows the total signi\ufb01cance S/\np\nB+(\u2206B)2 as a function of the systematic error on the\nbackground (\u2206B) for the different analyses. As is shown in the Fig., only a background uncertanity level\nbelow 10% allows exploitation of the statistical power of the mass constrained \ufb01t analysis with respect\nto the cut-based analysis, and even less for the case the pairing likelihood. Even for a robust analysis\nsuch as the cut-based approach, the large systematic uncertainties estimated in Table 8 provide a clear\nindication that a data driven background estimation is necessary.\n15\nConclusion\nWe performed a baseline sensitivity study for the detection of a Standard Model Higgs boson decaying to\nb\u00afb when produced together with a t\u00aft pair. After the de\ufb01nition of a common preselection, three different\ntechniques are used, all aimed at the reconstruction of the t\u00aft system. The \ufb01rst one is based on the\nreconstruction of the top quark and W candidate masses (cut-based analysis). The second one (pairing\nlikelihood analysis) uses a more complete description of the kinematic properties of the t\u00aft system to build\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1360\n\n B/B\n\u2206\n0\n0.05\n0.1 0.15\n0.2 0.25 0.3\n0.35 0.4 0.45\n0.5\ntotal significance\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\ncut-based\npairing likelihood\nconstrained mass fit\nATLAS\nFigure 30: Comparison of the total signi\ufb01cance as function of systematic uncertainties (\u2206B), for the\ncut-based, the pairing likelihood and the constrained \ufb01t analysis. Markers indicate the signi\ufb01cance cor-\nresponding to the background uncertainty estimated in Table 8.\na likelihood discriminant and isolate the jets coming from the Higgs boson decay. The third approach\n(constrained \ufb01t) uses the known masses and jet errors as constraints to produce a combinatoric likelihood,\nand a second likelihood to separate signal from background. While the cut-based analysis is certainly\nthe most stable one, relying only on the reconstructed invariant masses of the top quark candidates,\nit also performs worse with respect to the other two likelihood based analyses. On the other hand,\nthese likelihood based analyses can be used successfully only after all kinematical variables are well\nunderstood together with their correlations. Although beyond the scope of this work, the use of more\nadvanced multivariate techniques is foreseen to reduce both the combinatorial and physics background.\nThe statistical signi\ufb01cance obtained for the three approaches was 1.82 for the cut-based, 1.95 for\nthe pairing likelihood and 2.18 for the constrained mass \ufb01t at signal-to-background ratios of 0.11, 0.10\nand 0.12 respectively. All the analyses suffer drastic reduction in signi\ufb01cance as the overall systematic\nuncertainty increases. The most important individual uncertainties are those for the jet energy scale and\nb-tagging ef\ufb01ciency.\nFrom this study emerges the necessity of a strong b-tagging algorithm which is important not only\nto suppress the t\u00aft+jets physics background but also to help reduce the combinatorial background by\nimproving the hadronically decayingW reconstruction. It is also clear that the combinatorial background,\nresponsible for the dilution of the Higgs boson mass peak, needs to be further reduced, possibly using\nmultivariate techniques, in order to improve the statistical signi\ufb01cance of the channel. Improvements in\nthe mass peak resolution would also enhance the ability of a shape analysis from two perspectives; \ufb01rstly\nit would be easier to select a signal-depleted region for any shape \ufb01ts, and secondly the mass peak itself\nwould become more pronounced.\nThe results presented in this work can be compared with a previous ATLAS study [3] performed\nusing fast simulation with a parametrized b-tagging ef\ufb01ciency which had a higher performance than\nthe one used here and also used PYTHIA in order to simulate the t\u00aft+X background. It resulted in a\nsigni\ufb01cance of 1.9 and 2.6 respectively for the cut-based and likelihood analyses. The results presented\nin this note can also be compared with a recent CMS study [24] reporting a signi\ufb01cance of 1.8 for the\nelectron channel and 1.6 for the muon channel, in both cases for an integrated luminosity of 60 fb\u22121.\nWhile a detailed comparison between the two experiments is not attempted in this work, it is noteworthy\nthat the jet energy resolution quoted the CMS paper could be a key factor in explaining the improved\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1361\n\nsensitivity seen by ATLAS for this channel.\nThe measurement of the background normalization from data is vital for this channel. Subsequent\nstudies must be performed in this regard. Further methods of extracting shape information from data\nmust also be developed, in particular, the extraction of the signal in the presence of a quasi-signal-like\nbackground as is exhibited in the invariant mass plots at the ends of the analyses. The shape information\nand any estimate of the signi\ufb01cance obtained from it could be used in conjunction with the counting\nexperiment information to improve the overall signi\ufb01cance.\nReferences\n[1] M.L. Mangano et al., JHEP 0307 (2003) 001 (and updates).\n[2] J. Campbell, R. Ellis and D. Rainwater, Phys. Rev. D68 (2003) 094021.\n[3] J. Cammin and M. Schumacher, ATL-PHYS-2003-024.\n[4] ATLAS Collaboration, Prospect for Single Top Quark Cross-Section Measurements, this volume.\n[5] S. Tsuno et al., hep-ph/0204222v2.\n[6] T. Sjostrand, S. Mrenna and P. Skands, JHEP 0605 (2006) 26.\n[7] ATLAS Collaboration, Introduction on Higgs Boson Searches, this volume.\n[8] W.-M. Yao et al., Journal of Physics, G 33, 1 (2006).\n[9] B. Kersevan and E. Richter-Was, Comp. Phys. Comm.149 (2003) 142 (and updates).\n[10] S. Frixione and B.R. Webber, JHEP 0206 (2002) 029 (and updates).\n[11] G. Corcella et al., HERWIG 6.5 JHEP 0101 (2001) 010.\n[12] J. Butterworth et al., http://projects.hepforge.org/jimmy/.\n[13] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[14] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties, this\nvolume.\n[15] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[16] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this volume.\n[17] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[18] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[19] S. Corr\u00b4eard et al., b-tagging performance, ATL-PHYS-2004-006.\n[20] ATLAS Collaboration, Soft Muon b-Tagging, this volume.\n[21] ATLAS Collaboration, Top Quark Mass Measurements, this volume.\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1362\n\n[22] ATLAS Collaboration, Determination of the Top Quark Pair Production Cross-Section, this volume.\n[23] S. Dawson et al., Phys. Rev. D68 (2003) 034022.\n[24] CMS Collaboration, CMS Physics TDR, CERN-LHCC-2006-21 (2006).\nHIGGS \u2013 SEARCH FOR t\u00aftH(H \u2192b\u00afb)\n1363\n\nStudy of Signal and Background Conditions in\nt\u00aftH,H \u2192WW (\u2217) and WH,H \u2192WW (\u2217)\nAbstract\nIn this note we present Monte Carlo studies of the associated Standard Model\nHiggs boson production in the t\u00aftH and WH channels with the decay H \u2192\nWW (\u2217). These channels are intended to provide information on the Higgs bo-\nson\u2019s couplings. We study the two- and three lepton \ufb01nal states in t\u00aftH and\nthree lepton \ufb01nal states in WH, based on the full ATLAS detector simulation.\n1\nIntroduction\nThe discovery and subsequent study of the Higgs boson is one of the main aims of the Large Hadron\nCollider (LHC) at CERN. The possible mass range of the Standard Model Higgs boson is bounded by the\nlower limit set at LEP of 114 GeV and reaches to about 1000 GeV [1]. The ATLAS experiment will use\nall possible channels to extract information on it, because comparing the rates in the different channels\nwill allow information on the couplings to be extracted.\nThe sensitivity of ATLAS to a Higgs boson produced in gluon fusion or via vector boson fusion\nand decaying to W quark pairs has been discussed elsewhere in this volume [2]. This note contains the\nresults of studies of the Higgs boson in the same decay mode but produced in association with either top\nquarks, (t\u00aftH,H \u2192WW (\u2217)), or a W boson (WH,H \u2192WW (\u2217)). The cross-sections for these processes\nare signi\ufb01cantly lower than for inclusive Higgs production, and the additional activity makes them more\ncomplex to reconstruct, but the presence of extra signatures gives more possibilities for the reduction of\nthe background.\nThis note explores techniques to exploit these signatures, and the signal and background conditions\nare studied in both channels. A full simulation of the ATLAS experiment is employed to estimate these,\nwhich represents an improvement over the fast simulation used in previous studies of t\u00aftH [3] and WH\n[4,5]. The marginal production rates and numerous background sources, many with large cross-sections,\nmake this analysis dif\ufb01cult, and both the background and signal need to be established in some detail.\nNevertheless, if the background can be well estimated, then for integrated luminosities of several tens of\nfb\u22121 measurements should be possible.\nThe backgrounds considered in detail here arise from the inclusive t\u00aft process, from t\u00aft produced in\nassociation with gauge bosons, and from gauge bosons produced inclusively or in pairs. Unfortunately,\nit has not been possible to model all the relevant backgrounds with a complete simulation at the statis-\ntical level required; this is true for example of inclusive QCD multijet events. Section 2 describes the\nconsidered signal and background processes. Sections 3 and 4 give the details of t\u00aftH and WH anal-\nysis accordingly. Section 5 discusses the results, including the signal-to-background ratio that can be\nachieved in these two channels.\n2\nSignal and background Monte Carlo samples\nSignal and background were produced with various generators, through a realistic ATLAS detector sim-\nulation based on the GEANT 4 package [6].\n1364\n\n2.1\nSignal generation\nEvents with a Higgs boson decaying to a W pair produced in association with a t\u00aft pair or with a W boson\ncan be searched for at hadron colliders by requiring the presence of lepton pairs (\u2113= e,\u00b5).\nIn particular, for the two-lepton \ufb01nal states, like-sign leptons are selected; this allows a strong reduc-\ntion of the large background produced by the Z or t\u00aft leptonic decays. In order to improve the ef\ufb01ciency of\nthe Monte Carlo data sample production, generated events were \ufb01ltered before their processing through\nthe ATLAS detector simulation.\nFor the WH channel, only events with three leptons in the \ufb01nal state were selected. These leptons\nhad to pass loose \u03b7 and pT cuts.\nSamples of t\u00aftH with at least two leptons were generated and \ufb01ltered for different Higgs boson masses\nbetween 120 and 200 GeV using the PYTHIA 6.4 generator [7]. Results obtained with these samples\nwere normalized to the Next-to-Leading Order (NLO) cross-sections and branching ratios reported in\nRef. [1]. Only the mH = 170 GeV mass point was studied for the WH channel, where signal events were\ngenerated with the MC@NLO program [8].\nTable 1 summarizes the most important characteristics of the signal samples used for this note.\nTable 1: Signal samples generated for the t\u00aftH and WH,H \u2192WW (\u2217) analyses.\nProcess\nmH [GeV]\n\u03c3tot(NLO) [fb]\nFinal states\nGenerator\n\u03c3 \u00d7BR\u00d7\u03b5 filter [fb]\nN(events)\nt\u00aftH\n120, 130, 140\n669, 534, 431\nt\u00aftH \u21924W (2L)\nPYTHIA 6.4\n3.60, 6.25, 8.51\n\u223c40k\n150, 160, 170\n352, 291, 243\n9.68, 10.49,9.31\nper mH\n180, 190, 200\n204, 174, 149\n7.62, 5.50, 4.42\nt\u00aftH\n120, 130, 140\n669, 534, 431\nt\u00aftH \u21924W (3L)\nPYTHIA 6.4\n2.34, 4.05, 5.49\n\u223c40k\n150, 160, 170\n352, 291, 243\n6.31, 6.91, 6.15\nper mH\n180, 190, 200\n204, 174, 149\n5.00, 3.54, 2.86\nWH\n170\n511\nWH \u2192WWW (3L)\nMC@NLO\n3.42\n80k\n2.2\nBackground samples for t\u00aftH,H \u2192WW (\u2217)\nThe main backgrounds for the t\u00aftH,H \u2192WW (\u2217) \ufb01nal states are t\u00aft, t\u00aftW, t\u00aftZ, t\u00aftt\u00aft and t\u00aftb\u00afb. Single top\nevents have been neglected. Jets from QCD production and WZ production processes are also sources of\nbackground. However, lepton identi\ufb01cation with isolation and a jet multiplicity requirement are expected\nto reject a large fraction of these. The background from QCD multijet production has not been properly\nestimated so far and it is hoped that the selection requirements reduce it to an acceptable level.\nA special MC@NLO sample is \ufb01ltered for a pair of like-sign or more than two leptons with a\npT > 13 GeV and |\u03b7| < 2.6 at the generator level. It results in a \ufb01lter acceptance of 0.0384. In addition,\nwhen there are three or more generated leptons, events with oppositely charged leptons from W bosons\nfalling into a special domain ( pT \u226530 GeV and ||\u03b7|\u22121.5| \u22640.2 for electron, pT \u226515 GeV and ||\u03b7|\u2212\n1.25| \u22640.2 for muon ) were rejected. This results in a small bias, analysis dependent.\nThe Wb\u00afb sample was produced by the ALPGEN generator with only leptonic W boson, a generator\nlevel \ufb01lter led to an additional 0.02 acceptance, and a 2.57 K-factor [6] was also included. Leading\norder t\u00aftW + jets samples were produced with ALPGEN [9]. The minimum pT for the additional jets\nwas 15 GeV, while the maximum |\u03b7| was 6.0. The generated jets were also required to be separated\nby a distance \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 larger than 0.4. MLM matching [9] was performed to avoid double\ncounting of additional jets.\nSamples of t\u00aftZ, t\u00aftt\u00aft, t\u00aftb\u00afb and t\u00aftb\u00afb(EW) were produced with the leading order generator ACERMC [10].\nThe t\u00aftZ events are normalized to the total cross-section recently calculated at NLO [11], while other AC-\nERMC samples are normalized to LO. In the t\u00aftZ sample, the decay Z \u2192\u2113\u2113was forced. The t\u00aftb\u00afb(EW)\nsample contains the electroweak contribution to the production of t\u00aftb\u00afb. For both t\u00aftb\u00afb samples, the \ufb01nal\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1365\n\nstates containing four b-jets, two light jets and a lepton (muon or electron) were generated. Table 2\nsummarizes the characteristics of all background samples relevant for the t\u00aftH analysis.\nTable 2: The samples used to estimate the background contribution in the t\u00aftH,H \u2192WW (\u2217) analysis. L\ndenotes the effective integrated luminosity available from Monte Carlo statistics.\nProcess\nGenerator\n\u03c3tot [fb]\n\u03c3 \u00d7BR\u00d7\u03b5 filter [fb]\nN(events)\nL [fb\u22121]\nt\u00aft\nMC@NLO\n833000\n450000\n440k\n0.98\nt\u00aft pre-\ufb01ltered\nMC@NLO\n833000\n32000\n350k\n10.9\nt\u00aftb\u00afb(EW)\nACERMC 3.3\n900\n244\n6.5k\n26.6\nt\u00aftb\u00afb\nACERMC 3.3\n8200\n2244\n44k\n19.6\nWb\u00afb\nALPGEN\n2.1\u00d7105\n1387.8\n20k\n14.4\nt\u00aftW + 0 jets\nALPGEN\n189\n25.3\n20k\n790\nt\u00aftW + 1 jets\nALPGEN\n156\n20.7\n20k\n966\nt\u00aftW + \u22652 jets\nALPGEN\n237\n34.0\n18k\n529\nt\u00aftZ\nACERMC 3.4\n1090\n87.0\n19k\n218\ngg \u2192t\u00aftt\u00aft\nACERMC 3.4\n2.2\n1.44\n21k\n14583\nqq \u2192t\u00aftt\u00aft\nACERMC 3.4\n0.48\n0.31\n7k\n22580\n2.3\nBackground samples for WH,H \u2192WW (\u2217)\nThe t\u00aft and Wb\u00afb samples as given in Table 2 are used also in this analysis. For the irreducible diboson\nWZ/ZZ backgrounds only the fully leptonic decays were considered; this was done with the MC@NLO\ngenerator. The ALPGEN t\u00aftW+0 jet sample described in Section 2.2 was analyzed to account for the\nt\u00aftW background and as it gives a negligible accepted cross-section the samples with additional jets were\nnot considered. The huge W+jet background was generated with HERWIG [12] and was normalized to\nthe NLO production cross-section [6] with a \ufb01lter applied, requiring at least one electron (muon) with\npT \u226510 GeV and |\u03b7| \u22642.7 ( pT \u22655 GeV and |\u03b7| \u22642.8 ).\nAn overview of all background samples used for the WH analysis is given in Table 3.\nTable 3: List of background samples for the WH analysis. L denotes the effective integrated luminosity\navailable from Monte Carlo statistics.\nProcess\nGenerator\n\u03c3tot [fb]\n\u03c3 \u00d7BR\u00d7\u03b5 filter [fb]\nN(events)\nL [fb\u22121]\nt\u00aft no all-hadronic\nMC@NLO\n833000\n450000\n440k\n0.98\nt\u00aft pre-\ufb01ltered\nMC@NLO\n833000\n32000\n350k\n10.9\nWZ\nMC@NLO 3.10\n47760\n750\n36k\n48\nZZ\nMC@NLO 3.10\n14750\n72.5\n50k\n690\nW+jets\nHERWIG\n1.91\u00d7108\n2.8\u00d7107\n60k\n0.0214\nWb\u00afb\nALPGEN\n2.1\u00d7105\n1387.8\n20k\n14.4\nt\u00aftW + 0 jet\nALPGEN\n189\n25.3\n20k\n790\n3\nSelection of the t\u00aftH, H \u2192WW (\u2217) two and three-lepton \ufb01nal states\nIn this study, the high pT single lepton trigger is used for the t\u00aftH two-lepton (2L) events and three-\nlepton (3L) analyses, with a trigger ef\ufb01ciency larger than 96% for both channels at of\ufb02ine selection\nlevel. Cut-based analyses were performed, based on the standard ATLAS reconstruction of a medium\nquality electron [13], combined muons [14], and cone size of \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 = 0.4 (cone-0.4) tower\njets [15].\nSignal data sets for nine Higgs boson masses in the range between 120 and 200 GeV were analysed.\nIn the following, numbers will be given mainly for the most promising Higgs boson mass of 160 GeV\nincluding cut \ufb02ow information for the 120 and 200 GeV mass points.\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1366\n\n3.1\nEvent selection in t\u00aftH, H \u2192WW (\u2217)\nThe event selection is based on the analysis of \ufb01nal states with at least two reconstructed leptons and\njets; from now on we refer to this analysis as \u201cbasic selection\u201d. Each lepton or jet is required to have\ntransverse momentum pT > 15 GeV and to lie in the pseudorapidity region |\u03b7| < 2.5. Finally, two-lepton\n(2L) events are required to have at least six reconstructed jets, while events with three leptons (3L) must\nhave at least four jets.\nThe 2L(3L) selection retains 36.1% (35%) of the Higgs boson events with mH = 160 GeV, while\nreducing the various backgrounds (see Tables 4 and 5).\nFor both selections, further suppression of the main background sources can be done by isolation.\nThe isolation criteria require that the transverse energy deposited in the calorimeter around the lepton\nin a cone size \u2206R = 0.2 be below 10 GeV (calorimeter isolation), the maximum pT of extra tracks\nreconstructed in the Inner Detector around the lepton track in a cone size \u2206R = 0.2 be below 2 GeV\n(tracker isolation) and the angular separation \u2206Rlep\u2212cl j between the lepton and the closest jet be greater\nthan 0.2 for an electron or 0.25 for a muon (cone isolation). This is referred to as \u201cstandard isolation\u201d\nand it allows the reduction of the t\u00aft background by more than a factor of 10 (170) in the 2L (3L) analysis.\nThe t\u00aftZ/t\u00aftW backgrounds are suppressed by a factor 2 (t\u00aftZ, 2L) to 5 (t\u00aftW +2jets, 3L).\nFurther reduction of the t\u00aft background in the dilepton \ufb01nal state can be achieved by requiring exactly\ntwo like-sign isolated leptons. This requirement suppresses the large t\u00aft processes with two leptonic\nW-decays, as well as the contribution from the t\u00aftZ process.\n [GeV]\nl,l\nm\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nRate [1/4GeV]\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0 2\n0.22\nttH\nttZ\nATLAS\n(a) Dilepton invariant mass distributions\n [GeV]\n\u00b5\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nRate [1/4GeV]\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n from W-decays\n\u00b5\n-decays\n\u03c4\n not from W/\n\u00b5\nATLAS\n(b) pT-distributions of isolated and non-isolated muons\nFigure 1: (a) Dilepton invariant mass distributions in t\u00aftH (2L) and t\u00aftZ and (b) pT -distributions of muons\npassing the loose isolation criteria. The solid distribution shows electrons from W decays in the 160 GeV\nsignal sample, the dotted distribution shows muons in t\u00aft, which could not be matched to a generator-level\nmuon from a W- or \u03c4-decay. All distributions are normalized to unity.\nIn both \ufb01nal states, t\u00aftZ can be suppressed further by an explicit Z-veto: events that contain a lepton\npair of opposite charge and same \ufb02avour with an invariant mass between 75 GeV < m\u2113\u2113< 100 GeV are\nrejected. This veto includes all leptons passing the selection criteria and loose pT-cut, here set to 6 GeV.\nThe dilepton invariant mass distributions in t\u00aftH and t\u00aftZ are shown in Figure 1(a). The Z-veto decreases\nthe t\u00aftZ-contribution roughly by 75%, while 98% of the signal survive in the 2L analysis. In the 3L case,\n83% of the signal events pass the Z-veto, while 80% of the t\u00aftZ contribution is suppressed.\nAt this stage of the 2L selection, 73% of the remaining t\u00aft events have at least one muon from a\nsemi-leptonic heavy quark decay, while the fraction of events with electrons of this origin is only 20%\n(identi\ufb01cation of electrons embedded in jets is more dif\ufb01cult than that of muons).\nFurther rejection of these muons from t\u00aft events is achieved by requiring the reconstructed muon pT\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1367\n\nto be larger than 20 GeV, as leptons from heavy quark decays tend to be softer than leptons from W\ndecays (see Figure 1(b)). After this cut, the fraction of events with at least one muon from semileptonic\ndecay versus the one with at least one electron from semileptonic decay is respectively 46% and 41% .\nThe detailed cut \ufb02ows, with the corresponding accepted cross-sections, are listed in Tables 4 and 5.\nFrom now on the \u201cbasic selection\u201d is quoted with the \ufb01lter ef\ufb01ciency allowed for. In the 2L analysis we\nhave used the special MC@NLOt\u00aft sample described in Section 2.2 and a small bias has been computed\nat various stages of the cut \ufb02ow. The different values have been found to be compatible and a correction\nof 1.15 \u00b1 0.10 has been applied in the t\u00aft line in Table 4. In the 3L analysis the standard MC@NLOt\u00aft\nsample has been used, and therefore no correction has been applied.\nIn both cases, the largest background contribution is expected from t\u00aft events. The accuracy of the MC\nprediction of the total background expectation is limited by the available statistics and by the intrinsic\naccuracy of the simulation tools. In the case of t\u00aft the basic cross-section error is large, but the ALPGEN\npredictions for higher additional jet multiplicities suffer from even larger uncertainties. There may also\nbe background contributions from W bosons with multijets which have not been reliably estimated or\nQCD multijet production or other sources which it has not been possible to simulate.\nTable 4: Cut \ufb02ow and expected cross-sections [fb] for the t\u00aftH (2L) analysis. The errors presented are\nstatistical only. Some backgrounds, such as W+jets, b\u00afb and t\u00aft j j have not been included.\nSample\n\u03c3Total \u00b7BR\nBasic sel.\nCalo iso.\nTrack iso.\nCone iso.\nLike-sign\nZ-veto\np\u00b5\nT\nt\u00aftH (2Ltruth, 120 GeV)\n3.9\n1.05\n0.80\n0.65\n0.52\n0.52\n0.51\n0.45\u00b10.01\nt\u00aftH (2Ltruth, 160 GeV)\n11.1\n4.01\n3.02\n2.57\n2.09\n2.09\n2.04\n1.85\u00b10.03\nt\u00aftH (2Ltruth, 200 GeV)\n4.7\n1.83\n1.43\n1.24\n1.05\n1.04\n1.02\n0.95\u00b10.01\nt\u00aftbb (EW)\n259.0\n15.8\n4.1\n0.9\n0.3\n0.2\n0.2\n0.11\u00b10.07\nt\u00aftb\u00afb\n2360.\n177.\n31.7\n6.3\n1.8\n0.9\n0.9\n0.5\u00b10.2\nt\u00aft\n833000.\n6170.\n1970.\n870.\n500.\n16.0\n16.0\n7.4\u00b11.1\nt\u00aftt\u00aft\n2.68\n0.65\n0.33\n0.26\n0.20\n0.07\n0.07\n0.06\u00b10.00\nt\u00aftW+0j\n61.1\n1.17\n0.46\n0.30\n0.19\n0.10\n0.10\n0.09\u00b10.01\nt\u00aftW+1j\n50.5\n2.09\n0.93\n0.66\n0.48\n0.23\n0.23\n0.21\u00b10.02\nt\u00aftW+\u22652j\n76.9\n8.6\n4.9\n4.1\n3.3\n1.58\n1.54\n1.40\u00b10.05\nt\u00aftZ\n110.\n25.7\n20.5\n18.1\n13.7\n1.6\n1.2\n1.14\u00b10.07\nWb\u00afb\n66721.\n1.6\n0.14\n-\n-\n-\n-\n-\nTotal background\n10.3\u00b11.1\nTable 5: Cut \ufb02ow and expected cross-sections [fb] for the t\u00aftH (3L) analysis. The errors presented are\nstatistical only; systematic uncertainties are also important. Some backgrounds, such as W+jets, b\u00afb and\nt\u00aft j j have not been included.\nSample\n\u03c3Total \u00b7BR\nBasic sel.\nCalo iso.\nTrack iso.\nCone iso.\nZ-veto\np\u00b5\nT\nt\u00aftH (3Ltruth, 120 GeV)\n2.5\n0.66\n0.46\n0.38\n0.29\n0.24\n0.20\u00b10.00\nt\u00aftH (3Ltruth, 160 GeV)\n7.1\n2.53\n1.78\n1.47\n1.14\n0.95\n0.82\u00b10.02\nt\u00aftH (3Ltruth, 200 GeV)\n3.1\n1.16\n0.82\n0.70\n0.55\n0.43\n0.39\u00b10.01\nt\u00aft\n833000.\n1600.\n230.\n50.0\n9.3\n7.2\n2.1\u00b12.1\nt\u00aftW+0j\n61.1\n0.78\n0.17\n0.08\n0.04\n0.03\n0.03\u00b10.01\nt\u00aftW+1j\n50.5\n1.07\n0.28\n0.14\n0.08\n0.08\n0.06\u00b10.01\nt\u00aftW+\u22652j\n76.9\n2.77\n0.85\n0.60\n0.50\n0.42\n0.38\u00b10.03\nt\u00aftZ\n110.\n15.0\n8.6\n6.8\n5.3\n1.05\n0.86\u00b10.06\nTotal background\n3.4\u00b12.1\n3.2\nProjective likelihood estimator for electron isolation\nA projective likelihood estimator, called IsolationLikelihood [13], was developed in the course of the\nt\u00aftH,H \u2192WW (\u2217) (2L) analysis. Alternative to the standard isolation, this tool is meant to combine the\nseparation power of several isolation variables into a single, more powerful one. It uses the likelihood\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1368\n\nratio method to reject electrons from semi-leptonic heavy quark decays using a different set of isolation\nvariables than those described in Ref. [13]:\n\u2022 The additional transverse energy deposited in a cone of size \u2206R = 0.2 around the electron cluster.\n\u2022 The sum of the p2\nT of all additional tracks measured in a \u2206R = 0.2 cone around the electron cluster.\n\u2022 The transverse impact parameter signi\ufb01cance |Ip|/\u03b4(Ip) of the electron.\nIn addition, the \u201ccone isolation\u201d cut is also used as in the standard isolation analysis.\nWhen tuned to give the same electron isolation ef\ufb01ciency obtained with standard isolation in the\nt\u00aftH analysis, the IsolationLikelihood allows a higher rejection of non isolated electron background by\na factor 1.5 to 4, as shown in Figure 2. Using this projective likelihood estimator could suppress the\nt\u00aft background from 7.4 \u00b1 1.1 pb to 5.7 \u00b1 1.0 pb, while keep the same signal and other backgrounds\nselection ef\ufb01ciencies. It shows a potential improvement of this analysis which could be adopted at a\nsmall increase in complexity, but it has not been used in this document.\nsignal efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nsignal efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nbackground rejection\n1\n10\n2\n10\n3\n10\n4\n10\n WW / electron medium\n\u2192\nH(160GeV), H \ntt\n| < 1.37\n\u03b7\n < 19GeV; 0 < |\nT\n15GeV < p\n| < 1.37\n\u03b7\n < 43GeV; 0 < |\nT\n27GeV < p\n| < 2.47\n\u03b7\n < 19GeV; 1.52 < |\nT\n15GeV < p\n| < 2.47\n\u03b7\n < 43GeV; 1.52 < |\nT\n27GeV < p\nATLAS\nFigure 2: Non-isolated electron rejections vs. signal ef\ufb01ciencies obtained by the IsolationLikelihood\nestimator for four different pT and \u03b7 intervals. The large points mark the working point of the standard\nisolation cuts for comparison and indicate the size of the error bars, which are not shown for the curves.\n4\nWH analysis\nOnly the three lepton \ufb01nal state, W(H \u2192WW (\u2217)) \u21923 (l\u03bd) is described below. The analysis of the larger\ncross-section dilepton \ufb01nal state, which has an important W + jet background is currently ongoing.\nThe basic selection requires three leptons that satisfy the lepton identi\ufb01cation criteria, i.e. medium\nelectron [13] and standard muon [14]. The lepton pT-thresholds were set to 35 GeV for the leading\nand 15 GeV for the other lepton. As seen from Fig. 3(a) the cut on the leading lepton reduces the\nbackgrounds much more than the signal. The presence of these leptons also ensures that any signal is\nef\ufb01ciently recorded by the ATLAS trigger system\nIn addition to a 6 GeV calorimeter isolation and a 0.25 cone isolation as described in Section 3.1,\nptrack\nT\n/plepton\nT\n\u22640.05 were forced, where ptrack\nT\nis of the track with maximal pT in a cone of \u2206R=0.2\n(0.3) around the muon (electron). Furthermore, a cut on the lepton three-dimensional impact parameter\nI3D/\u03c3I \u22642.5 was employed to reject leptons from bottom quarks.\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1369\n\nIn order to reduce the WZ background, a Z veto is applied by requiring that no opposite sign and\nsame \ufb02avor lepton pair has an invariant mass between mass 65 and 105 GeV (Fig. 3(b)). In addition only\nevents with Emiss\nT\n\u226530 GeV were kept. To further reduce the backgrounds, we ask the sum of the pT\nof all the jets (which were preselected above 20 GeV from cone-0.7 tower jets [15]) to be smaller than\n120 GeV, as seen in Figure 3(c).\nFor additional rejection of t\u00aft and t\u00aftW, events having at least one jet ful\ufb01lling a loose b-tag [16]\nare removed. In order to exploit the spin correlations in the H \u2192WW (\u2217) signal, the minimum angular\nseparation ( \u2206R ) between lepton pairs is required to be in the range of [ 0.1 \u223c1.5 ] (so called \u201cH-S cut\u201d).\n [GeV]\nT\nLepton leading p\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nLeptons (arbitrary normalisation)\nWH\ntt \nWZ \nttW \nW + jets \nATLAS\n(a) Lepton pT\n [GeV] \nl\n m\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nMuons (arbitrary normalisation)\nWH\ntt \nWZ \nZZ \nttW \nATLAS\n(b) lepton-lepton invariant mass\n sum [GeV]\nT\nJet P\n0\n50\n100\n150\n200\n250\n300\n350\nJets (arbitrary normalisation)\nWH\ntt \nWZ \nttW \nW + jets \nATLAS\n(c) Jet pT-sum\nFigure 3:\npT-distribution for the leading leptons in the WH(3L) signal, t\u00aft, WZ, t\u00aftW and W+jet-\nproduction(a), invariant mass of all the lepton pairs (b) and sum of the pT of all jets (c) for the WH\n(3L) signal and the relevant backgrounds. All these plots are done after loose cut.\nTable 6 summarises the cross-sections after the cut \ufb02ow described above. The \ufb01ltered MC@NLOt\u00aft\nsample described in Section. 2.2 has been used here. In order to take into account the bias introduced\nby this sample, a correction of 2.36 \u00b1 0.6 has been applied. The background rate from W bosons with\nmultijets, QCD multijet production or other sources, which have not yet been possible to simulate, have\ntheir contribution still under study. The errors on the background are, at this stage, much larger than the\nsize of the expected signal.\n5\nDiscussion\n5.1\nUncertainties in the analyses\nSeveral systematic uncertainties affect the results presented in this paper. There are theory uncertainties\nassociated to the the choice of the Parton Distribution Functions (PDFs), to the choice of the renormal-\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1370\n\nTable 6: WH (3L) cut \ufb02ow and corresponding cross-sections. The errors presented are statistical only;\nsystematic uncertainties are also important. Some backgrounds, such as WWW, single top and t\u00aftZ have\nnot been included.\nInput [fb]\nBasic sel.\nIsolation\nZ-veto\nEmiss\nT\nH-S\n(b-) jet veto\nWH (3L)\n5.04\n1.18\n0.62\n0.53\n0.47\n0.36\n0.31 \u00b10.02\nWZ\n750.\n165.5\n1.41\n0.74\n0.63\n0.21\n0.10+0.08\n\u22120.06\nt\u00aft\n833000.\n3564.3\n6.45\n6.11\n5.10\n1.02\n0.34+0.70\n\u22120.3\nZZ\n72.5\n34.5\n0.13\n0.06\n0.013\n0.008\n0.005\u00b10.001\nt\u00aftW\n61.1\n1.35\n0.22\n0.21\n0.19\n0.07\n0.003+0.005\n\u22120.003\nWb\u00afb\n66721.\n3.1\n-\n-\n-\n-\n-\nW \u2192e\u03bd+jets\n2.05 \u00b7107\n17.6\n-\n-\n-\n-\n-\nW \u2192\u00b5\u03bd+jets\n2.05 \u00b7107\n27.6\n-\n-\n-\n-\n-\nTotal background\n0.45\u00b10.70\nization and factorization scales, to the description of the initial and \ufb01nal state radiation and to the model\nused to simulate the heavy quark fragmentation. In order to evaluate the size of these uncertainties, the\ntheory parameters above mentioned have been varied within intervals corresponding to sensible choices.\nConcerning the PDFs, the MRST2000-LO set was used at the place of the CTEQ6L1.\nFor the t\u00aftH analysis, the theory uncertainties have been found to induce a 9% change of the signal\ncross-section, dominated by the PDF choice. The impact to the t\u00aft process, which is the most important\nsource of background to this signal, has been found to be 12% in Ref. [6]. An additional 5%, found\nin study of the signal process, associated to the uncertainty of the initial and \ufb01nal state radiation, has\nbeen included in quadrature, giving an overall 13% uncertainty on the total cross-section. However, the\nbackground sample is dominated by t\u00aft with extra jets, and the uncertainty on this rate is of order a factor\ntwo. For WH, the PDF uncertainty was found to be less than 5%, and energy scale uncertainty even\nsmaller [17]. Including these effects and others (ISR,FSR) we get a total theoretical uncertainty of 9%.\nThe effect of experimental systematic uncertainties has been also investigated. The main sources of\nthese uncertainties are represented by the knowledge of the integrated luminosity, the energy scale and\nthe energy resolution of electrons, muons and jets, as well as the tag ef\ufb01ciency of b-jets and the rejection\nof light quarks. The level of these uncertainties and the impact on the overall event selection is presented\nin Tables 7 and 8. Pile-up events will decrease the detector performance and the impact needs to be\nproperly addressed in future studies. However, the relatively low jet transverse momentum threshold of\n15 GeV in the t\u00aftH analyses may be sensitive to this. The overall systematic uncertainty expected in the\nt\u00aftH analysis is 10% (10%) for the 2L (3L) signal and 15% (18%) for those backgrounds which have\nbeen quanti\ufb01ed. In the case of the WH analysis the overall systematic uncertainty is about 10% for the\nsignal, and about 20% for those background systematics which have been estimated. In each case the\ntotal background uncertainty is much larger than this at present.\n5.2\nConclusion\nThe t\u00aftH,H \u2192WW (\u2217) andWH,H \u2192WW (\u2217) processes have been studied using two- and three-lepton \ufb01nal\nstates. The signal and main backgrounds have been estimated using a full GEANT based simulation of\nthe detector. The estimated accepted cross-sections in fb of signal and background for these processes\nare 1.9:10 (t\u00aftH 2L), 0.8:3.4 (t\u00aftH 3L) and 0.3:0.4 (WH 3L) respectively. The signal is small and clear\ndistinguishing features such as resonance peaks have not been established. The backgrounds are larger\nand their uncertainties have not been fully controlled. The analysis is therefore very challenging.\nAccurate estimations of the background level using large simulation samples (made with more ef\ufb01-\ncient simulation packages) as well as direct measurements using control samples from real LHC data are\nessential if a good signal signi\ufb01cance is to be reached. For example the production of W bosons with\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1371\n\nTable 7: Overview of the experimental systematic uncertainties on the signal and background predictions\nrelated to the t\u00aftH channel in those channels studied. All numbers are in %.\nSource of the uncertainty\nt\u00aftH (2L)\nt\u00aftH (3L)\n\u2206signal (%)\n\u2206background (%)\n\u2206signal (%)\n\u2206background (%)\nLuminosity\n3\n3\n3\n3\n3\nElectron ID ef\ufb01ciency\n0.2\n0.2\n0.2\n0.3\n0.3\nMuon ID ef\ufb01ciency\n1\n1.0\n1.0\n1.5\n1.5\nElectron ET scale\n0.5\n0.1\n0.1\n0.2\n0.3\nMuon ET scale\n1\n0.5\n0.2\n0.7\n1.0\nElectron ET resolution\n0.1\n0.1\n0.1\n0.2\nMuon pT resolution\n0.6\n2.2\n0.3\n0.9\nJet energy scale\n7\n1.2\n4.9\n2.7\n10\nJet energy resolution\n1.0\n1.4\n1.9\n5.7\nElectron isolation ef\ufb01ciency\n1\n1\n1\n1.5\n1.5\nMuon isolation ef\ufb01ciency\n1\n1\n1\n1.5\n1.5\nExperimental uncertainty\n\u00b13.9\n\u00b16.6\n\u00b15.2\n\u00b112.3\nTable 8: Overview of the experimental uncertainties on the signal and background predictions related to\nthe WH channels in those channels studied. All numbers are in %.\nSource of the uncertainty\nWH 3L selection\n\u2206WH (3L) (%)\n\u2206WZ (%)\n\u2206t\u00aft (%)\n\u2206ZZ (%)\n\u2206t\u00aftW (%)\nLuminosity\n3\n3\n3\n3\n3\n3\nElectron ID ef\ufb01ciency\n0.2\n0.3\n0.3\n0.2\n0.9\n1.1\nMuon ID ef\ufb01ciency\n1\n1.5\n1.7\n1.9\n1.0\n1.7\nElectron energy scale\n0.5\n0.06\n0.06\n0.2\n0.02\n0.07\nMuon energy scale\n1\n0.2\n0.1\n1.0\n0.08\n0.7\nMuon pT resolution\n0.1\n0.03\n0.2\n0.02\n0.4\nJet energy scale\n7\n2.5\n2.6\n17.4\n2.3\n13.6\nJet energy resolution\n0.005\n0.03\n1.9\n0.5\n0.7\nb-tag eff. / light jet rej.\n5 / 32\n1.0\n1.0\n2.7\n0.8\n3.2\nExperimental uncertainty\n\u00b14.3\n\u00b114.5\nlarge numbers of jets need to be measured, as does the fake contribution from b-jets. These two channels\nshould then contribute to the measurement of the Standard Model Higgs boson properties, in particular\nthe couplings of this boson to top and to the W.\nReferences\n[1] ATLAS Collaboration, Introduction on Higgs Boson Searches at the Large Hadron Collider, this\nvolume.\n[2] ATLAS Collaboration, Higgs Boson Searches in Gluon Fusion and Vector Boson Fusion using the\nH \u2192WW Decay Mode, this volume.\n[3] J. Lev\u02c6eque, J. B. de Vivie, V. Kostioukhine and A. Rozanov, Search for the standard model Higgs\nBoson in the t\u00aftH, H \u2192WW (\u2217) channel, ATL-PHYS-2002-019 (2002).\n[4] K. Jakobs, A study of the associated production WH with, W \u2192l\u03bd and H \u2192WW (\u2217) \u2192l\u03bdl\u03bd,\nATL-PHYS-2000-008 (2000).\n[5] V. Cavasinni and D. Costanzo, Search for WH \u2192WWW \u2192l\u00b1\u03bd l\u00b1\u03bd jet-jet, using like-sign leptons.,\nATL-PHYS-2000-013 (2000).\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1372\n\n[6] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[7] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[8] S. Frixione B. R. and Webber, The MC@NLO 3.2 event generator, 2006, hep-ph/0601192.\n[9] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A. D. Polosa, JHEP 07 (2003) 001.\n[10] B. P. Kersevan and E. Richter-Was, The Monte Carlo event generator AcerMC version 2.0 with\ninterfaces to PYTHIA 6.2 and HERWIG 6.5, 2004, hep-ph/0405247.\n[11] Lazopoulos, Achilleas and McElmurry, Thomas and Melnikov, Kirill and Petriello, Frank,\n(arXiv:0804.2220[hep-ph]).\n[12] G. Corcella et al., HERWIG 6.5 release note, 2002, hep-ph/0210213.\n[13] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[14] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[15] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[16] ATLAS Collaboration, b-Tagging Performance, this volume.\n[17] O.Brein, A.Djouadi and R.Harlander, Phys.Lett B579 (2004) 149\u2013156.\nHIGGS \u2013 STUDY OF SIGNAL AND BACKGROUND CONDITIONS IN t\u00aftH,H \u2192WW \u2217AND . . .\n1373\n\nDiscovery Potential of h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\nAbstract\nThis note describes a study of the discovery potential for the supersymmetric\nHiggs bosons h/H/A in proton-proton collisions at a center-of-mass energy of\n14 TeV in \ufb01nal states with \u03c4 lepton pairs with the ATLAS detector at the LHC.\nThe Higgs bosons are produced in association with b quarks and decay into a\n\u03c4\u03c4 \ufb01nal state where both \u03c4 leptons decay leptonically. The signature of Higgs\nbosons with masses between 110 and 450 GeV is analyzed and the discovery\npotential is assessed. The analysis is based on an integrated luminosity of\n30fb\u22121.\nAll results are obtained using full simulation of the ATLAS detector. No pile-\nup or cavern background has been considered in this analysis. In addition a\nprocedure for estimating the shape and the normalization of the irreducible\nZ \u2192\u03c4+\u03c4\u2212background from data is investigated. The discovery potential as a\nfunction of mA and tan\u03b2 is shown for the mmax\nh\nMSSM benchmark scenario.\n1\nIntroduction\nIn the Minimal Supersymmetric Standard Model (MSSM), the minimal extension of the Standard Model,\ntwo Higgs doublets are required, resulting in \ufb01ve observable Higgs bosons. Three of them are electrically\nneutral (h, H, and A) while two of them are charged (H\u00b1). At tree level their properties like masses,\nwidths and branching fractions can be predicted in terms of only two parameters, typically chosen to be\nthe mass of the CP-odd Higgs boson, mA, and the tangent of the ratio of the vacuum expectation values\nof the two Higgs doublets, tan\u03b2.\nIn the MSSM the couplings of the Higgs bosons to fermions and bosons are different from those\nin the Standard Model resulting in different production cross-sections and decay rates. While decays\ninto ZZ or WW are dominant in the Standard Model for Higgs boson masses above mH \u223c160 GeV,\nin the MSSM these decay modes are either suppressed like cos(\u03b2 \u2212\u03b1) in the case of the H (where \u03b1\nis the mixing angle of the two CP-even Higgs bosons) or even absent in case of the A. Instead, the\ncoupling of the Higgs bosons to third generation fermions is strongly enhanced for large regions of the\nparameter space. The decay of the neutral Higgs bosons into a pair of \u03c4 leptons therefore constitutes\nan important discovery channel at the LHC. The production of the Higgs bosons can proceed via two\ndifferent processes: gluon-fusion or production in association with b quarks.\nIn this note, the discovery potential of neutral MSSM Higgs bosons, produced via associated produc-\ntion with b quarks and decaying into a pair of \u03c4 leptons in ATLAS at the LHC is discussed. Only \u03c4 lepton\ndecays into electrons and muons are considered here. Higgs bosons in the mass range between 110 and\n450 GeV are analyzed for an integrated luminosity of 30fb\u22121. Both the shape and the normalization of\nthe Z \u2192\u03c4\u03c4 background which is dominant for low Higgs boson masses are estimated from Z \u2192\u00b5\u00b5 and\nZ \u2192ee events in data. The results are interpreted in the mmax\nh\nscenario as a function of the two parameter\nof the model, mA and tan\u03b2 [1]. Studies concerning the semileptonic and the fully hadronic \ufb01nal state are\nnot included in this note. These studies are ongoing and will be published separately.\nThis note is organized as follows. In Section 2 the signal and background processes are introduced\nand their cross-sections are discussed. In Section 3 the analysis is discussed. After a description of\nthe selection, a procedure to estimate the shape and the normalization of the irreducible Z \u2192\u03c4 +\u03c4\u2212\nbackground from data is detailed before the discovery potential in the mA \u2212tan\u03b2 plane is assessed. In\nSection 4 the results are summarized.\n1374\n\n2\nSignal and background processes\n2.1\nHiggs boson production\nThe production mechanism of Higgs bosons in the MSSM is discussed in the introductory section of this\nchapter. The Higgs boson masses, their production cross-section and their branching fraction into a pair\nof \u03c4 leptons are summarized in Table 1.\nTable 1: Masses, cross-sections for b-associated production, and branching fractions into the \u03c4 +\u03c4\u2212\ufb01nal\nstate for Higgs bosons in the mmax\nh\nscenario and for tan\u03b2 = 20.\nMass / GeV\n\u03c3 associated\nh/H/A\n/fb\nB(h/H/A \u2192\u03c4+\u03c4\u2212)/%\nA\nH\nh\nA\nH\nh\nA\nH\nh\n110\n129.8\n109.0\n314810\n7579\n310707\n8.9\n9.1\n8.9\n130\n134.2\n124.7\n189602\n92897\n99992\n9.1\n9.2\n9.0\n160\n160.8\n128.0\n97480\n93102\n6650\n9.4\n9.5\n8.4\n200\n200.5\n128.4\n45685\n45095\n2188\n9.6\n9.7\n7.5\n300\n300.4\n128.6\n10312\n10253\n979\n8.2\n9.5\n6.3\n450\n449.8\n128.6\n2019\n2035\n723\n6.1\n6.2\n5.7\nThe theoretical uncertainty on the inclusive production cross-section, i.e. without imposing any re-\nquirements on the pT of the b jets at generator level, is estimated taking into account contributions from\nthe scale uncertainty and from the uncertainty on the parton distribution functions. The scale uncertainty\nis obtained from Ref. [2] as a function of the mass of the Higgs boson. The contribution from the Parton\nDensity Functions (PDFs) is estimated by exchanging MRST2002 for MRST2004 parton distribution\nfunctions. Since the cross-sections obtained with MRST2004 are smaller than that with MRST2002 they\nare considered conservative. Therefore, half of the difference observed with this variation is taken as a\nsystematic uncertainty.\nThe total uncertainty on the cross-section, obtained by adding the PDF and scale uncertainties in\nquadrature, is displayed in Fig. 1 as a function of the Higgs boson mass mA. For Higgs boson masses as\nlow as mA = 100 GeV the total theoretical uncertainty is of the order of 20%. This uncertainty decreases\nto values below 10% for mA = 400 GeV. For low Higgs boson masses the contribution from the scale\nuncertainty dominates over that from the parton distribution functions while for high Higgs boson masses\nthe situation is reversed.\n2.2\nBackground processes\nThe following background processes are relevant and have been considered in this analysis (for details\nsee Ref. [3]).\n\u2022 Z \u2192\u2113\u2113: The Drell-Yan production of Z bosons and their subsequent decay into a pair of leptons\nconstitutes an important source of background. The production cross-section has been calculated\nto NNLO accuracy and was found to be \u03c3Z\u2192\u2113\u2113= (2015\u00b160)pb1 .\nEvents with the Z boson decaying to a pair of \u03c4 leptons constitute an irreducible background. In\nparticular for low Higgs boson masses, due to the limited invariant mass resolution in the \u03c4 +\u03c4\u2212\n\ufb01nal state this background is problematic and needs therefore to be estimated directly from data.\n\u2022 t\u00aft production: The cross-section for this process has been calculated at NLO+NLL accuracy and\nwas found to be \u03c3t\u00aft = (833 \u00b1 100)pb. This background is dominant for Higgs boson masses\nbeyond mA = 200 GeV.\n1The cross-section is given for a cut on the invariant mass of the lepton pair of m\u2113\u2113> 60 GeV.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1375\n\nFigure 1: Systematic uncertainty on the signal cross-section for associated Higgs boson production as\na function of mA. The dashed line corresponds to the contribution from the scale uncertainty, the dash-\ndotted line to that introduced by the uncertainty on the parton distribution functions, and the solid line is\nthe sum of both contributions added in quadrature.\n\u2022 W+jets production: The production cross-section for this process has been calculated at NNLO\naccuracy and was found to be \u03c3W+Jets = 20510pb. This dataset was complemented by a Wb\u00afb\nsample whose cross-section has been calculated to NLO accuracy (\u03c3Wb\u00afb = 176.9pb).\n2.3\nEvent generation\nThe Monte Carlo samples have been generated using the SHERPA [4], PYTHIA [5], HERWIG [6], ALP-\nGEN [7], and MC@NLO [8] Monte Carlo generators. Except for SHERPA, all external matrix element\ngenerators are interfaced to HERWIG to produce the parton shower. The \u03c4 leptons are decayed using ei-\nther SHERPA or TAUOLA [9]. Initial and \ufb01nal state radiation of photons is simulated using PHOTOS [10].\nEvent \ufb01lters have been applied for all processes in order to increase the event generation ef\ufb01ciency.\nDetails on Monte Carlo simulation are given in Ref. [3].\n3\nAnalysis of the exclusive lepton lepton \ufb01nal state\nThe experimental signature consists of two leptons from the \u03c4 decays and missing transverse energy, /ET,\ndue to the neutrinos from the \u03c4 decays. At least one jet tagged as coming from a b quark is required in\nthe event and therefore the b quark associated production is dominant here.\n3.1\nPreselection\nThe preselection cuts are grouped into \u2018Trigger Selection\u2019, \u2018b-Tagging\u2019, \u2018Lepton Selection\u2019, and cuts\nrelated to the reconstruction of the invariant mass of the Higgs boson.\nTrigger selection:\nAn isolated muon (electron) with transverse momentum of at least 20 GeV (25 GeV)\nor two isolated electrons with pT \u226515 GeV, or one electron with pT \u226515 GeV and a muon with\npT \u226510 GeV are required.\nb-Tagging:\nSince the Higgs boson is produced in association with b quarks, at least one jet has to be\nidenti\ufb01ed as coming from a b quark in order to suppress backgrounds from processes involving light\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1376\n\nquarks. Jets are reconstructed using a cone algorithm with radius \u2206R = 0.42, and a b-tagging weight of\n\u22653 is required in order for the jet to be labeled as coming from a b quark [11].\nLepton selection:\nElectrons are required to have pT \u226510 GeV, be within |\u03b7| < 2.5 and pass the\nmedium electron selection [12]. No isolation criteria are applied. Muons are reconstructed using the\nalgorithm described in Ref. [13]. A minimum pT of 10 GeV and |\u03b7| < 2.5 are required. An isolation\ncone of opening angle \u2206R = 0.2 around the muon track is used with a maximum ET of 6 GeV deposited\nin the calorimeters. Two leptons of opposite charge are required if the event is to be considered for further\nanalysis. In case more than two leptons ful\ufb01ll the above requirements the lepton pair with the highest\nscalar sum of pT is selected.\nCollinear approximation:\nThe invariant mass of the Higgs boson candidate is reconstructed using the\ncollinear approximation [14]. In this approximation the masses of the particles involved in the decay of\nthe \u03c4 lepton are small compared to their momenta, so that the direction of the \u03c4 lepton can be approxi-\nmated by the direction of its observed visible decay products. The method assumes furthermore that the\nmissing energy observed in the event is entirely due to neutrinos from the \u03c4 lepton decays. In addition\nthe Higgs boson is required to have some amount of transverse momentum. If that is not the case the two\n\u03c4 leptons from the Higgs boson decay are back-to-back. An accurate reconstruction of the transverse\nmomenta of the \u03c4 leptons is not possible in that case and the resolution of the invariant mass of the \u03c4 pair\nwill be poor. Neglecting the masses of all leptons, the invariant mass of the Higgs boson candidate can\nbe reconstructed via\nm\u03c4+\u03c4\u2212=\nm\u2113\u2113\n\u221ax1x2\n.\n(1)\nThe quantity xi = pT \u2113i/pT \u03c4i is the fraction of the \u03c4 lepton momentum carried by its visible decay products.\nThey are calculated from /ET in the event and the transverse momentum of the visible leptons. For\nthis calculation /ET is decomposed into two components, each of them pointing along the direction of\nthe charged decay products of the \u03c4 lepton. This fraction is required to be within physical bounds\n(0 < xi < 1). In order for the solution to be numerically stable a cut on the angle between the visible\ndecay products of the \u03c4 lepton of \u2206\u03c6\u2113\u2113< 3 is imposed. This also improves the invariant m\u03c4\u03c4 resolution.\nThe accepted cross-section for the above preselection is detailed in Table 2 for the signal and the\ndominant background contributions.\nTable 2: Cross-section in fb passing the preselection criteria as described in the text. The numbers for\nthe signal samples are given assuming tan\u03b2 = 20.\nProcess\nTrigger\nLepton Selection\n1 or 2 jets\n> 0 b-tags\nColl. Approx\nmA = 110 GeV\n1837.6\n1154.8\n628.6\n175.7\n118.4\nmA = 130 GeV\n1511.8\n971.6\n544.6\n172.1\n115.7\nmA = 160 GeV\n987.4\n656.4\n374.9\n119.1\n80.8\nmA = 200 GeV\n497.9\n340\n199.3\n63.9\n44.9\nmA = 300 GeV\n139.4\n98.8\n60.2\n20.4\n13.9\nmA = 450 GeV\n25.3\n18.3\n11.2\n3.7\n2.4\nt\u00aft\n255114\n48045.9\n7804.8\n5479\n1096.2\nZ \u2192\u03c4\u03c4\n47026.8\n27654.4\n14053.2\n665.1\n440.6\nZ \u2192ee\n1.4 E6\n797747\n421393\n16197.8\n2848.43\nZ \u2192\u00b5\u00b5\n1.3 E6\n704275\n345491\n16811.5\n3223.43\nW+Jets\n17.2 E6\n91042.8\n44612.4\n1537.5\n122.43\n2The radius \u2206R of the cone is de\ufb01ned as \u2206R =\np\n\u2206\u03c62 +\u2206\u03b72\n3Results were obtained using cut factorization.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1377\n\n3.2\nEvent selection\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\nArbitrary Units\n0\n (130 GeV)\n\u03c4\n\u03c4\n\u2192\nH\nGaussian fit\n = 24.6 GeV\n\u03c3\nATLAS\n [GeV]\nT,Higgs\np\n0\n20\n40\n60\n80\n100\n120\n140\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\n0\n1\n2\n3\n4\n5\n6\n7\n8\nATLAS\nFigure 2: Invariant m\u03c4+\u03c4\u2212distribution for a Higgs boson of mass mA = 130 GeV (left) after preselection\ncuts. The width has been determined by a \ufb01t of a single Gaussian to the peak region of the distribution.\nThe right-hand plot shows the m\u03c4+\u03c4\u2212distribution as a function of the pT of the Higgs boson.\nCuts on kinematic variables have been optimized in an iterative procedure in order to maximize the\nstatistical signi\ufb01cance S/\n\u221a\nB for a potential Higgs boson signal. Since the composition of the background\ndepends on the signal mass hypothesis, this has been done separately for each mass point. In addition,\nthe optimization has been done separately for the ee, \u00b5\u00b5, and for the mixed e\u00b5 \ufb01nal states.\nThe following variables are considered: To suppress background from t\u00aft production only events\nwith less than three jets are selected. The invariant dilepton mass m\u2113\u2113has to be well below mZ in order\nto suppress Z \u2192ee and Z \u2192\u00b5\u00b5 events. Since there are neutrinos from the \u03c4 decays in the event,\nmissing transverse energy is required in the event. The transverse momentum of the jet tagged as coming\nfrom a b quark has to be above a certain value which depends on the Higgs boson mass under study.\nRequirements on the maximum pT of the leading lepton as well as on that of the lepton-lepton system\npT,\u2113\u2113are imposed. In addition, the angle \u2206\u03c6 between the two leptons is restricted. The cut values and\nthe accepted cross-section for a Higgs boson mass of mA = 130 GeV are given in Table 3.\nThe resolution of the m\u03c4+\u03c4\u2212distribution using the collinear approximation for a Higgs boson of mass\nmA = 130 GeV is illustrated in Fig. 2 (left) after applying preselection cuts. The width as extracted from a\n\ufb01t of a single Gaussian to the peak region is \u03c3 = 25 GeV compared to the natural width of a Higgs boson\nof that mass between less than 100 MeV up to a few GeV depending on tan\u03b2. The m\u03c4+\u03c4\u2212distribution\nversus the pT of the Higgs boson is illustrated on the right-hand side of Fig. 2, showing that the invariant\nmass resolution improves with pT of the Higgs boson.\n3.3\nSelection results\nThe accepted cross-sections after all cuts for different Higgs boson masses and the various backgrounds\nare summarized in Table 4 for tan\u03b2 = 20. The reconstructed \u03c4\u03c4 invariant mass distributions are dis-\nplayed in Fig. 3 for all masses considered. The vertical solid lines mark the mass window de\ufb01ned as\nm\u22121.65\u03c3 < m\u03c4+\u03c4\u2212< m+2\u03c3 where \u03c3 denotes the invariant m\u03c4+\u03c4\u2212resolution for a given mass hypoth-\nesis as determined from Monte Carlo simulations. All candidate events falling inside this mass window\nare used to calculate the signi\ufb01cances for a Higgs boson signal.\nIn the low mass range, the invariant mass resolution is of the order of 25 GeV. A potential signal for\na Higgs boson is nearly indistinguishable from the irreducible Z \u2192\u03c4 +\u03c4\u2212background which dominates\nin this mass range over the contribution from t\u00aft processes, which contribute at the (10\u221220)% level. This\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1378\n\nmakes it necessary to estimate the shape and the normalization of the Z \u2192\u03c4 +\u03c4\u2212background directly\nfrom data. A procedure has been developed and will be discussed in detail in Section 3.5.\nTable 3: Accepted cross-section in fb for optimized cuts for mA = 130 GeV and tan\u03b2 = 20. The values\nof the cuts applied are stated for the ee/\u00b5\u00b5 (upper row) and e\u00b5 (lower row) subchannels. In case only\none number is given it applies to all leptonic subchannels.\nVariable\nSelection\nH \u2192\u03c4\u03c4\nt\u00aft\nZ \u2192\u03c4\u03c4\nZ \u2192ee\nZ \u2192\u00b5\u00b5\nW+Jets\nPrecuts\n115.7\u00b15.1\n1096\u00b135\n441\u00b116\n3223\u00b1123\n2848\u00b1108\n122\u00b140\npT b-jet\n(15\u221266) GeV\n90.0\u00b14.5\n443\u00b122\n337\u00b114\n2756\u00b1113\n2481\u00b1101\n91\u00b135\nm\u2113\u2113\n(27\u221270) GeV\n(0\u221270) GeV\n72.6\u00b14.1\n138\u00b112\n326\u00b114\n134\u00b125\n92\u00b119\n60\u00b128\nx1 \u00b7x2\n(0.04\u22120.4)\n(0.0\u22120.5)\n64.1\u00b13.8\n108\u00b111\n251\u00b112\n47\u00b115\n36\u00b112\n40\u00b123\npmiss\nT\n(20\u2212\u221e) GeV\n(15\u2212\u221e) GeV\n52.2\u00b13.5\n102\u00b111\n171\u00b110\n4.3\u00b14.5\n5.1\u00b14.6\n33\u00b121\npH\nT\n(0\u2212\u221e) GeV\n(0\u221270) GeV\n47.7\u00b13.3\n57.9\u00b17.9\n159.4\u00b19.8\n4.3\u00b14.5\n4.6\u00b14.3\n28\u00b119\npT,\u2113\u2113\n(0\u221245) GeV\n(0\u221260) GeV\n46.5\u00b13.3\n38.2\u00b16.5\n155.8\u00b19.6\n3.9\u00b14.3\n2.5\u00b13.2\n23\u00b117\n\u2206\u03a6\u2113\u2113\n(2.24\u22123)\n(2\u22123)\n43.3\u00b13.1\n32.8\u00b16.0\n107.5\u00b18.0\n3.6\u00b14.1\n3.8\u00b14.0\n21\u00b117\npT leading \u2113\n(10\u221280) GeV\n43.3\u00b13.1\n32.8\u00b16.0\n107.5\u00b18.0\n3.6\u00b14.1\n3.8\u00b14.0\n21\u00b117\nMass Window\n(111\u2212198) GeV\n28.4\u00b12.6\n19.7\u00b14.6\n22.1\u00b13.6\n1.8\u00b12.9\n2.0\u00b12.8\n12\u00b112\nTable 4: Accepted cross-section for all Higgs boson mass hypotheses analyzed. The cross-section in fb\nfor signal and background after all selection cuts is given (except for the cut on the mass window) for\ntan\u03b2 = 20.\nH \u2192\u03c4+\u03c4\u2212\nt\u00aft\nZ \u2192\u03c4+\u03c4\u2212\nZ \u2192e+e\u2212\nZ \u2192\u00b5+\u00b5\u2212\nW+jets\nmA = 110 GeV\n34.4 \u00b1 2.9\n24.0 \u00b1 5.1\n62.1 \u00b1 6.1\n1.9 \u00b1 3.0\n2.7 \u00b1 3.3\n8 \u00b1 11\nmA = 130 GeV\n28.4 \u00b1 2.6\n19.7 \u00b1 4.6\n22.1 \u00b1 3.6\n1.8 \u00b1 2.9\n2.0 \u00b1 2.8\n12 \u00b1 12\nmA = 160 GeV\n18.7 \u00b1 1.2\n39.3 \u00b1 6.6\n8.4 \u00b1 2.2\n1.4 \u00b1 2.5\n2.0 \u00b1 2.9\n1.8 \u00b1 4.9\nmA = 200 GeV\n10.9 \u00b1 0.6\n28.4 \u00b1 5.6\n5.4 \u00b1 1.8\n2.0 \u00b1 3.1\n2.1 \u00b1 2.9\n3.7 \u00b1 7.0\nmA = 300 GeV\n2.7 \u00b1 0.1\n32.8 \u00b1 6.0\n3.0 \u00b1 1.3\n0.4 \u00b1 1.4\n1.7 \u00b1 2.6\n5.8 \u00b1 8.8\nmA = 450 GeV\n0.50 \u00b1 0.03\n50.2 \u00b1 7.4\n1.8 \u00b1 1.0\n0.4 \u00b1 1.4\n0.3 \u00b1 1.1\n4.1 \u00b1 7.3\nIn the medium mass range, the contributions from Z \u2192\u03c4+\u03c4\u2212events and from t\u00aft processes become\nequally important. The mass resolution for signal events is now of the order of (30\u221240) GeV leading to\na broad structure which is indistinguishable from that of background events.\nIn the high mass range (mA = 300 to 450 GeV), the cross-section for the signal process decreases\nrapidly. The invariant mass resolution for signal events is between (50 \u221280) GeV so that a discovery\nwith an integrated luminosity of L = 30fb\u22121 in this channel will not be possible.\n3.4\nSystematic uncertainties\nIn order to assess the impact of systematic uncertainties, each of these has been applied in turn and\nthe impact on the result of the analysis is evaluated. The uncertainties assumed on the energy and\nmomentum resolution of muons, electrons, photons, and jets are conservative estimates assuming non-\noptimal performance of the corresponding algorithms at the beginning of data taking.\n1. For muons the uncertainty on the reconstructed pT is \u03c3(1/pT) = (0.011/pT \u22970.00017) with pT\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1379\n\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\nCross Section (fb / 15 GeV)\n0\n10\n20\n30\n40\n50\n60\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\nCross Section (fb / 15 GeV)\n0\n10\n20\n30\n40\n50\n60\n=110 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nt bar\nW+jets\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\nCross Section (fb / 15 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100\n150\n200\n250\n300\nCross Section (fb / 15 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n=130 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nttbar\nW+jets\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100 150 200 250 300 350 400\nCross Section (fb / 40 GeV)\n0\n10\n20\n30\n40\n50\n60\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50\n100 150 200 250 300 350 400\nCross Section (fb / 40 GeV)\n0\n10\n20\n30\n40\n50\n60\n=160 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nttbar\nW+jets\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50 100 150 200 250 300 350 400 450\nCross Section (fb / 62 GeV)\n5\n10\n15\n20\n25\n30\n [GeV]\n\u03c4\n\u03c4\nm\n0\n50 100 150 200 250 300 350 400 450\nCross Section (fb / 62 GeV)\n5\n10\n15\n20\n25\n30\n=200 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nttbar\nW+jets\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n0\n100\n200\n300\n400\n500\nCross Section (fb / 90 GeV)\n10\n20\n30\n40\n50\n [GeV]\n\u03c4\n\u03c4\nm\n0\n100\n200\n300\n400\n500\nCross Section (fb / 90 GeV)\n10\n20\n30\n40\n50\n=300 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nttbar\nW+jets\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n0\n100 200 300 400 500 600 700 800\nCross Section (fb / 160 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n [GeV]\n\u03c4\n\u03c4\nm\n0\n100 200 300 400 500 600 700 800\nCross Section (fb / 160 GeV)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n=450 GeV\nA\nm\n=20\n\u03b2\ntan\n\u2192\n\u2190\n\u03c4\n\u03c4\n\u2192\nH\n\u03c4\n\u03c4\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nee\n\u2192\nZ\nttbar\nW+jets\nATLAS\nFigure 3: Invariant m\u03c4+\u03c4\u2212distribution for signal and background events. The distributions are shown\nafter all selection cuts with the nominal masses and tan\u03b2 values as indicated in the plots. The vertical\nlines indicate the mass window used for calculating the signal signi\ufb01cance.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1380\n\nTable 5: Effects of systematic uncertainties as described in the text for different Higgs boson masses\nfor tan\u03b2 = 20. The effects of the systematic uncertainties considered are listed in percent. The total\nuncertainty is obtained by adding the individual contributions in quadrature.\nmA = 110 GeV\nmA = 130 GeV\nmA = 160 GeV\nUncertainty / %\nSignal\nt\u00aft Bkg\nW+jets\nSignal\nt\u00aft Bkg\nW+jets\nSignal\nt\u00aft Bkg\nW+jets\nb-tagging ef\ufb01ciency\n2.8\n3.9\n0.8\n4.0\n4.1\n0.7\n6.6\n3.3\n0.5\nJet energy scale\n0.3\n6.0\n0.9\n< 0.1\n5.3\n1.6\n1.1\n4.0\n1.5\nJet resolution\n8.3\n0.8\n0.3\n< 0.1\n0.2\n1.2\n6.1\n0.4\n1.2\nElectron energy scale\n0.7\n0.5\n1.0\n0.4\n0.1\n1.0\n0.4\n0.5\n0.9\nElectron resolution\n0.7\n0.6\n1.0\n1.6\n0.2\n1.0\n0.4\n0.2\n0.4\nMuon energy scale\n0.7\n0.9\n0.7\n1.2\n0.6\n0.7\n0.4\n0.4\n0.7\nMuon resolution\n1.4\n0.6\n2.5\n0.8\n1.1\n2.4\n1.7\n0.4\n2.4\nElectron ef\ufb01ciency\n< 0.1\n0.5\n0.4\n< 0.1\n0.5\n0.4\n< 0.1\n0.4\n0.4\nMuon ef\ufb01ciency\n< 0.1\n0.8\n0.7\n0.8\n0.2\n0.7\n< 0.1\n0.9\n0.7\nLight jet rejection\n< 0.1\n< 0.1\n3.4\n0.4\n< 0.1\n3.4\n0.7\n< 0.1\n3.4\nTotal exp. uncertainty\n9\n7.4\n4.7\n4.6\n6.8\n4.9\n9.2\n5.3\n4.8\nmA = 200 GeV\nmA = 300 GeV\nmA = 450 GeV\nUncertainty / %\nSignal\nt\u00aft Bkg\nW+jets\nSignal\nt\u00aft Bkg\nW+jets\nSignal\nt\u00aft Bkg\nW+jets\nb-tagging ef\ufb01ciency\n4.8\n3.2\n0.5\n4.2\n3.1\n0.3\n4.8\n3.8\n0.1\nJet energy scale\n0.6\n3.6\n1.5\n0.9\n3.1\n0.6\n0.4\n2.1\n0.7\nJet resolution\n8.0\n1.6\n2.7\n0.8\n0.4\n2.7\n0.7\n0.5\n2.4\nElectron energy scale\n0.5\n0.5\n0.9\n< 0.1\n0.2\n0.8\n0.4\n0.2\n1.2\nElectron resolution\n0.3\n0.1\n0.4\n< 0.1\n< 0.1\n0.3\n< 0.1\n0.4\n0.3\nMuon energy scale\n0.5\n0.4\n0.7\n0.5\n0.4\n0.7\n0.9\n0.3\n0.9\nMuon resolution\n0.3\n0.1\n2.4\n0.8\n0.3\n2.3\n0.4\n0.7\n2.2\nElectron ef\ufb01ciency\n0.3\n0.3\n0.4\n0.8\n< 0.1\n0.4\n0.4\n0.1\n0.4\nMuon ef\ufb01ciency\n0.3\n1.0\n0.7\n0.8\n1.3\n0.7\n1.1\n1.0\n0.7\nLight jet rejection\n0.8\n< 0.1\n3.4\n0.4\n< 0.1\n3.4\n0.4\n< 0.1\n3.4\nTotal exp. uncertainty\n9.4\n5.3\n5.4\n4.6\n4.7\n5.1\n5.1\n4.6\n5.1\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1381\n\ngiven in GeV. The uncertainty on the energy scale is estimated to be \u00b11%, and that on the recon-\nstruction ef\ufb01ciency is assumed to be 1% and \ufb02at in pT.\n2. For electrons and photons the uncertainty on the reconstructed ET is \u03c3(ET) = 0.0073 \u00b7 ET. The\nuncertainty on the energy scale is estimated to be \u00b10.5%, and that on the reconstruction ef\ufb01ciency\nis assumed to be 0.2% and being \ufb02at in ET.\n3. For jets with |\u03b7| < 3.2 (|\u03b7| > 3.2) the uncertainty on the jet energy scale is taken to be \u00b13%\n(\u00b110%) and the jet energy resolution is assumed to be 45%\n\u221a\nE (63%\n\u221a\nE).\n4. For the b-tagging a degradation of the tagging ef\ufb01ciencies of 5% is taken as systematic uncertainty.\nFor the Z+light jets background an uncertainty on the rejection rate of \u00b110% is assumed.\nA detailed description of the sources of systematic uncertainties can be found in [3]. The impact of\nthe systematic uncertainties on the number of signal and t\u00aft background events4 inside the mass window\nis summarized in Table 5 for Higgs boson masses between mA = 110 and 450 GeV. A sample of 48M t\u00aft\nevents from fast simulation has been used for these studies. The Z \u2192\u03c4\u03c4 background in this analysis is\nestimated from sidebands in data as described in the next Section. The number of events from Z \u2192\u00b5\u00b5\nand Z \u2192ee processes after all selection cuts is small compared to that from t\u00aft. Their contribution to the\ntotal systematic uncertainty is small compared to that from t\u00aft processes.\n3.5\nEstimation of Z \u2192\u03c4+\u03c4\u2212shape and normalization from data\nDimuon mass [GeV]\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nNormalized to Unity\n\u22123\n10\n\u22122\n10\n\u22121\n10\n\u00b5\n\u00b5\n\u2192\nZ\n\u03c4\n\u03c4\n\u2192\nZ\n (130 GeV)\n\u03c4\n\u03c4\n\u2192\nH\nttbar\n\u2192\n\u2190\nATLAS\n [GeV]\nT,miss,calo\np\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nEvents / 2 GeV\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n\u00b5\n\u00b5\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\nFigure 4: Distribution of the invariant dilepton mass m\u2113\u2113(left). The shaded area illustrates the distribution\nfrom Z \u2192\u00b5\u00b5 events, and the solid line that from signal events. The contribution from Z \u2192\u03c4 +\u03c4\u2212and\nt\u00aft events is illustrated by the dashed and dotted lines, respectively. The cut on the invariant \u2113\u2113mass\nis indicated by the solid vertical lines. The distribution of pmiss\nT\nin the calorimeter for Z \u2192\u00b5\u00b5 and\nZ \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 +X events (right). All plots shown are after preselection cuts.\nAs discussed above the estimation of the shape and the normalization of the irreducible Z \u2192\u03c4 +\u03c4\u2212\nevents from data is of great importance in particular for low Higgs boson masses where this background\nis dominant. Procedures to estimate both the shape and the normalization of Z \u2192\u03c4 +\u03c4\u2212events from data\nare needed. This procedure is based on Z \u2192\u00b5\u00b5 and Z \u2192ee events selected from a sideband region\nwhich is free of Higgs boson events, in contrast to the signal region. The method proceeds in three steps:\n4The impact on the number of Z \u2192\u03c4+\u03c4\u2212events is not listed here since this background is estimated from data.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1382\n\n1. As a \ufb01rst step, a pure sample of Z \u2192\u00b5\u00b5 or Z \u2192ee events is selected from a sideband region as\ndescribed below.\n2. The shape of the m\u03c4\u03c4 spectrum is estimated by adapting the four-momenta of the muons such that\nthey appear like coming from Z \u2192\u03c4\u03c4 events.\n3. The normalization of the Z \u2192\u03c4\u03c4 background is estimated from a double-ratio comparing the\nnumber events found in data and in Monte Carlo in the sideband region as well as in the signal\nregion.\nThis procedure is described in detail below.\n3.5.1\nDe\ufb01nition of signal and sideband regions\nEvents of the type Z \u2192ee and Z \u2192\u00b5\u00b5 are selected from a sideband region (called region B) with very\nhigh purity and with an event topology similar to that from Z \u2192\u03c4+\u03c4\u2212events in the signal region (called\nregion A). The following cuts are applied in order to select Z \u2192ee and Z \u2192\u00b5\u00b5 events in region B:\n\u2022 The invariant mass of the lepton-lepton system is required to be within 75 GeV < m\u2113\u2113< 100 GeV,\nwhere \u2113\u2113is either a ee or a \u00b5\u00b5 \ufb01nal state.\n\u2022 At least one jet identi\ufb01ed as coming from a b quark has to be found in the event.\n\u2022 The number of jets allowed in the event has to be less than three.\nThe main cut de\ufb01ning region B is that on the invariant lepton-lepton mass. A distribution illustrating\nthe cut on m\u2113\u2113is displayed in Fig. 4 (left) showing the large amount of Z \u2192\u00b5\u00b5 events selected by\nthe cuts above that only have a small contamination of events coming from t\u00aft processes and events\ncontaining Higgs boson decays. The number of events from Z \u2192ee and Z \u2192\u00b5\u00b5 is around 500000 for\nan integrated luminosity of 30fb\u22121 and thus much larger than the number of Z \u2192\u03c4\u03c4 events expected in\nthe signal region. The purity of the Z \u2192\u00b5\u00b5 (Z \u2192ee) control sample in region B after all cuts mentioned\nabove is 99.1% (97.9%) with a contribution of 0.04% (0.05%) of events from the signal process5 with\nthe remainder coming from t\u00aft processes.\n3.5.2\nEstimation of the Z \u2192\u03c4+\u03c4\u2212shape from data\nThe method of estimating the shape of Z \u2192\u03c4+\u03c4\u2212events from data is based on the assumption that in\nthe calorimeter this type of events is indistinguishable from that of type Z \u2192\u00b5\u00b5. This method has been\nproven to work in a vector boson fusion H \u2192\u03c4+\u03c4\u2212analysis [15].\nThe muons are minimum ionizing particles and their energy deposit in the calorimeter only weakly\ndepends on their momentum. Therefore, the missing energy signatures of both types of events in this\ndetector component are very similar as illustrated on the right-hand side of Fig. 4. Altering the energy\nof muons in Z \u2192\u00b5\u00b5 events so that they correspond to those from Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5\u00b5 + 4\u03bd events leads\nto identical distributions of pT,\u00b5, pT,miss and m\u03c4+\u03c4\u2212for both classes of events. The following procedure\nis adopted:\n\u2022 Three dimensional reference histograms from Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5\u00b5 +4\u03bd events from Monte Carlo in\nregion A are created. The following variables calculated in the Z rest frame are used:\n5A Higgs boson mass of mA = 130 GeV and tan\u03b2 = 20 is assumed here. The contamination of Higgs boson events is even\nsmaller for the other signal masses considered in this analysis.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1383\n\n1. The absolute value of the Gottfried-Jackson angle \u03be between the Z boson and the negatively\ncharged muon.\n2. The energy of the muon with cos\u03be > 0.\n3. The energy of the muon with cos\u03be < 0.\n\u2022 The components of the momentum vector of the muons in Z \u2192\u00b5\u00b5 events from region B are altered\nin a way that they match those from Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5\u00b5 + 4\u03bd events using the above reference\nhistogram:\npi,altered = pi\n|\u20d7p| \u00b7E\u00b5,altered.\n(2)\nFor each event, the angle \u03be is calculated and then new energies for the muons are chosen randomly\nfrom the reference histogram. After applying this procedure, the muon momenta are boosted back\ninto the lab frame.\n\u2022 The missing energy in the event is re-calculated according to the new muon momenta:\n\u20d7pT,miss,altered = \u20d7pT,miss \u2212\u2211\n\u00b5\npT,altered +\u2211\n\u00b5\npT,old.\n(3)\nA comparison of pT,miss, of x1 \u00b7x2 from the collinear approximation and of the invariant m\u03c4+\u03c4\u2212mass\nfrom altered Z \u2192\u00b5\u00b5 in comparison with Z \u2192\u03c4+\u03c4\u2212\u2192\u00b5\u00b5 +4\u03bd events is shown on the left-hand side,\nmiddle and right-hand side of Fig. 5, respectively. Good agreement within the statistical uncertainties of\nthe samples used is observed.\n [GeV]\nT,miss\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\nEvents / Bin\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n altered\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n+4\n\u00b5\n\u00b5\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\n2\n*x\n1\nx\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nEvents / Bin\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n altered\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n+4\n\u00b5\n\u00b5\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\n [GeV]\n\u03c4\n\u03c4\nm\n50\n100\n150\n200\n250\nEvents / Bin\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n altered\n\u00b5\n\u00b5\n\u2192\nZ\n\u03bd\n+4\n\u00b5\n\u00b5\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\nFigure 5: Comparison of the pT,miss, x1 \u00b7 x1, and m\u03c4\u03c4 spectra for events of type Z \u2192\u00b5\u00b5 and Z \u2192\u03c4\u03c4.\nGood agreement within the statistical uncertainties is observed.\nThe same shape as extracted from region B using Z \u2192\u00b5\u00b5 events to estimate Z \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 + X\nevents in region A is also used for Z \u2192\u03c4\u03c4 \u2192ee+X and Z \u2192\u03c4\u03c4 \u2192\u00b5e+X events. As shown in Figure\n6, the m\u03c4\u03c4 shapes are identical within statistical uncertainties justifying this procedure.\n3.5.3\nEstimation of the background normalization from data\nIn order to estimate the number of background events from the Z \u2192\u03c4+\u03c4\u2212background process for this\nanalysis, the same de\ufb01nition of the sideband region has been used as described above.\nThe number of Z \u2192\u03c4+\u03c4\u2212background events in the signal region A can then be obtained by re-\nweighting the number of events found in data in region B by the predicted ratio of the number of events\nfound in Monte Carlo in region A relative to that found in region B. In order for this method to be valid,\nthe following two conditions have to hold:\n(Z \u2192\u2113\u2113)B\nData\n(Z \u2192\u2113\u2113)B\nMC\n=\n(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)B\nData\n(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)B\nMC\n(4)\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1384\n\n [GeV]\n\u03c4\n\u03c4\nm\n0\n100\n200\n300\n400\n500\n600\nEvents normalized to Unity\n-2\n10\n-1\n10\n\u03bd\nee+4\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\n\u03bd\n+4\n\u00b5\n\u00b5\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\n\u03bd\n+4\n\u00b5\ne\n\u2192\n\u03c4\n\u03c4\n\u2192\nZ\nATLAS\nFigure 6: Comparison of the m\u03c4\u03c4 shape for Z \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 +X, Z \u2192\u03c4\u03c4 \u2192ee+X, and Z \u2192\u03c4\u03c4 \u2192\u00b5e+X\nevents. Good agreement is observed within the statistical uncertainties of the samples used.\n(Z \u2192\u2113\u2113)B\nData\n(Z \u2192\u2113\u2113)B\nMC\n=\n(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)A\nData\n(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)A\nMC\n,\n(5)\nwhere the \ufb01rst condition means that Z \u2192\u2113\u2113events behave like Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd events, and when\ncombined with the second it implies that Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd events in region A and in region B behave\nidentically.\nThe calculation of the number of events from the Z \u2192\u03c4+\u03c4\u2212process in data is performed in bins of\npT of the leading lepton vs. the pT of the subleading lepton with a bin size of 2 \u00d7 2 GeV2 which was\nfound to give unbiased results in previous Monte Carlo based studies [16]. This ensures that the method\nis less dependent on the differences in pT in the signal and the sideband region. Once events from real\ndata are available the method has to be validated and the in\ufb02uence of a possible difference between data\nand the Monte Carlo prediction on the results has to be checked.\nThis procedure also allows to easily take into account differences in acceptance and trigger ef-\n\ufb01ciencies by simply applying the appropriate factors to the reweighting procedure. The number of\nZ \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd events in region A is then given by\n(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)A\nData = \u2211\ni, j\n\u0000(Z \u2192\u03c4+\u03c4\u2212\u2192\u2113\u2113+4\u03bd)A\nMC\n\u0001\ni j\n\u0000(Z \u2192\u2113\u2113)B\nMC\n\u0001\ni j\n\u00b7\n\u0000(Z \u2192\u2113\u2113)B\nData\n\u0001\ni j ,\n(6)\nwhere i and j indicate the corresponding bin in pT. The statistical uncertainty on this method is calculated\naccording to Gaussian error propagation. The method has been tested using two independent Monte\nCarlo samples, one to \ufb01ll the reference histogram and one to test the reweighting procedure. Good\nagreement within statistical uncertainties between the expected number of events in region A and that\nactually found was observed.\nThe application of this method is straight forward for the ee and the \u00b5\u00b5 \ufb01nal state. For the e\u00b5\n\ufb01nal state the procedure has to be adapted since there are no Z \u2192e\u00b5 decays. In order to estimate\nthe number of background events in that case, events from Z \u2192ee and Z \u2192\u00b5\u00b5 processes are used.\nAdditional correction factors are applied to account for the differences in trigger ef\ufb01ciencies and selection\nef\ufb01ciencies in that case.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1385\n\n3.5.4\nSystematic uncertainties of the background estimation procedure\nTable 6: The effects of systematic uncertainties on the calculation of the normalization.\nUncertainty Effect\nValue\nSystematic Uncertainty\nMuon resolution\n\u03c3\n\u0010\n1\npT\n\u0011\n=\nr\u0010\n0.011\npT\n\u00112\n+0.000172\n0.16 %\nMuon energy scale\n\u00b11%\n1.35 %\nMuon ef\ufb01ciency\n\u00b11%\n0.7 %\nElectron resolution\n\u03c3 (ET) = 0.0073\u00b7ET\n1.9 %\nElectron energy scale\n\u00b10.5%\n0.85 %\nElectron ef\ufb01ciency\n\u00b10.2%\n0.1 %\nThe impact of the systematic uncertainties on the estimation of the number of background events\nfrom Z \u2192\u03c4+\u03c4\u2212processes as described in Section 3.4 has been evaluated. The uncertainties on jet\nenergy scale and jet resolution, as well as on the b tagging ef\ufb01ciency are expected to be negligible since\nthe same effects would apply to the signal region as well as to the sideband region. The remaining\ncontributions to the systematic uncertainty on the background estimation procedure are coming from the\nenergy scale, ef\ufb01ciency and resolution connected with the electrons and muons in the \ufb01nal state. These\ncontributions as expected in 30fb\u22121 of data are summarized in Table 6.\nIn addition, systematic uncertainties due to the different acceptances and trigger ef\ufb01ciencies for the\nZ \u2192ee/\u00b5\u00b5 samples from the sideband region compared to Z \u2192\u03c4\u03c4 \u2192ee/\u00b5\u00b5/e\u00b5 + X samples in the\nsignal region need to be taken into account. Since the reweighting of events is done as a function of the\npT of the leading and the subleading lepton, these are easy to apply. Since this analysis is aimed at an\nintegrated luminosity of 30fb\u22121, it is assumed that by then these uncertainties are evaluated to a very\nhigh precision.\nThe overall systematic uncertainty has been evaluated to be 2.6% by dividing the available MC events\ninto two independent samples. This uncertainty has been taken into account for the \ufb01nal results.\n3.5.5\nSummary of the background estimate from data\nBoth methods described above are now combined to estimate the Z \u2192\u03c4\u03c4 background and thereby the\nsigni\ufb01cance of a possible Higgs boson signal in the low mass region. First, the number of events of\ntype Z \u2192\u03c4+\u03c4\u2212is estimated using the method described in Section 3.5.3. Then, the shape of this back-\nground is determined as described in Section 3.5.2. The background is then subtracted from the m\u03c4+\u03c4\u2212\ndistribution.\n3.6\nResults and discovery potential\nThe discovery potential for the h/H/A \u2192\u03c4+\u03c4\u2212\u2192\u2113\u21134\u03bd channel is now assessed. All sub-channels,\ni.e. ee, e\u00b5 and \u00b5\u00b5 are combined to calculate the signi\ufb01cance of a Higgs boson signal. A mass window\nm\u22121.65\u03c3 < m\u03c4+\u03c4\u2212< m+2\u03c3 is applied to calculate the \ufb01nal signi\ufb01cance where \u03c3 denotes the invariant\nmass resolution of the Higgs boson signal of the corresponding mass.\nThe shape and the normalization of the Z \u2192\u03c4+\u03c4\u2212background is estimated from the sideband region\nin data as described in Section 3.5. There is no corresponding procedure available yet for the t \u00aft back-\nground so that all experimental systematic uncertainties are taken into account for all calculations below.\nTheoretical uncertainties are treated separately. The signi\ufb01cance of a potential Higgs boson signal in the\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1386\n\n / GeV\nA\nm\n150\n200\n250\n300\n350\n400\n450\n\u03b2\ntan\n0\n10\n20\n30\n40\n50\n60\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\nATLAS\n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n\u03bd\n 2 l + 4 \n\u2192\n\u03c4\n\u03c4\n\u2192\nbb h/H/A\n Discovery\n\u03c3\n5 \n / GeV\nA\nm\n150\n200\n250\n300\n350\n400\n450\n\u03b2\ntan\n0\n10\n20\n30\n40\n50\n60\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\nATLAS\n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n\u03bd\n 2 l + 4 \n\u2192\n\u03c4\n\u03c4\n\u2192\nbb h/H/A\n95% CL. Exclusion\nFigure 7: The \ufb01ve \u03c3 discovery potential (left) and the 95% exclusion limit (right) as a function of mA and\ntan\u03b2. The solid line represents the main result of the analysis. The dashed lines indicate the discovery\npotential and exclusion limit including an addition 10% uncertainty on the t\u00aft cross-section. The bands\nrepresent the in\ufb02uence of the systematic uncertainty on the signal cross-section.\ngiven mass window is calculated as\nSign. =\nS\nq\nNt\u00aft +(\u2206t\u00aftsys)2 +NZ\u2192\u03c4\u03c4 +(\u2206Z\u2192\u03c4\u03c4\nsys\n)2 +NW\u2192\u2113\u03bd +(\u2206W\u2192\u2113\u03bd\nsys\n)2 +NZ\u2192ee +NZ\u2192\u00b5\u00b5\n,\n(7)\nwhere S is the number of signal events, Nt\u00aft and \u2206sys(t\u00aft) are the statistical and systematic uncertainties\non the t\u00aft background. The quantities NZ\u2192\u03c4+\u03c4\u2212and \u2206sys(Z \u2192\u03c4+\u03c4\u2212) are the statistical and systematic\nuncertainties on the Z \u2192\u03c4+\u03c4\u2212background, respectively. The term in the denominator is dominated\nby the contribution from t\u00aft events; the contributions from NZ\u2192ee and NZ\u2192\u00b5\u00b5 and their corresponding\nsystematic uncertainties are negligible.\nThe discovery potential and the 95% exclusion limit in the mmax\nh\nscenario as a function of tan\u03b2 and\nmA and for an integrated luminosity of 30fb\u22121 is displayed in Fig. 7 on the left-hand side and right-\nhand side, respectively. The uncertainty on the signal cross-section is indicated as bands in the plots.\nThe calculation of the signi\ufb01cance includes both statistical and experimental systematic uncertainties\non the background. The uncertainties on the background cross-sections are not taken into account in\nthe main results since they are assumed to be measured with high precision at the time of the analysis.\nHowever, since the cross-section for the t\u00aft background might not be measured at high precision in the\nregion of phase space relevant to this analysis, the discovery potential including a 10% uncertainty on\nthat background is displayed in addition (dashed line).\nThe discovery potential for Higgs bosons is shown in Fig. 8 as a function of tan\u03b2 for various mA\nvalues, and in Fig. 9 as a function of mA for various tan\u03b2 values.\n4\nConclusion\nIn this note a study of the discovery potential for the supersymmetric Higgs bosons h/H/A in proton-\nproton collisions at a center-of-mass energy of 14 TeV with the ATLAS detector at the LHC has been\npresented. The \ufb01nal state h/H/A \u2192\u03c4+\u03c4\u2212in b quark associated production has been investigated with\nat least one jet identi\ufb01ed as coming from a b quark and with both \u03c4 leptons decaying leptonically.\nA signi\ufb01cant improvement for the discovery potential can be achieved if this channel is combined\nwith the \u2113-had and had-had channel, where one \u03c4 lepton decays leptonically (either electron or muon)\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1387\n\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n1\n10\n2\n10\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 110 GeV\nA\nm\nATLAS\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n1\n10\n2\n10\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 130 GeV\nA\nm\nATLAS\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n1\n10\n2\n10\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 160 GeV\nA\nm\nATLAS\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n-1\n10\n1\n10\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheore ical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 200 GeV\nA\nm\nATLAS\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n-2\n10\n-1\n10\n1\n10\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 300 GeV\nA\nm\nATLAS\n\u03b2\ntan\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSignificance\n-3\n10\n-2\n10\n-1\n10\n1\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \n-1\n=14 TeV, 30 fb\ns\n scenario\nmax\nh\nm\n = 450 GeV\nA\nm\nATLAS\nFigure 8: The discovery potential as a function of tan\u03b2 and for Higgs boson masses as indicated in the\nplots. The solid lines indicate the discovery potential including experimental systematic uncertainties.\nThe dashed lines indicate the discovery potential including an additional systematic uncertainty on the t \u00aft\ncross-section. The bands indicate the impact of the systematic uncertainty on the signal cross-section.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1388\n\n / GeV\nA\nm\n100 150 200 250 300 350 400 450\nSignificance\n-1\n10\n1\n10\n2\n10\n scenario\nmax\nh\nm\n-1\n=14 TeV, 30 fb\ns\n = 20\n\u03b2\ntan\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \nATLAS\n / GeV\nA\nm\n100 150 200 250 300 350 400 450\nSignificance\n-1\n10\n1\n10\n2\n10\n scenario\nmax\nh\nm\n-1\n=14 TeV, 30 fb\ns\n = 35\n\u03b2\ntan\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \nATLAS\n / GeV\nA\nm\n100 150 200 250 300 350 400 450\nSignificance\n-1\n10\n1\n10\n2\n10\n scenario\nmax\nh\nm\n-1\n=14 TeV, 30 fb\ns\n = 45\n\u03b2\ntan\nExp. Systematics only\n(tt) Uncertainty\n\u03c3\n+10% \nTheoretical Uncertainty\n\u03c3\n5 \nATLAS\nFigure 9: The discovery potential as a function of mA. The solid lines indicate the discovery potential in-\ncluding experimental systematic uncertainties for tan\u03b2 values as indicated in the plots. The dashed lines\nindicate the discovery potential including an additional systematic uncertainty on the t\u00aft cross-section of\n10%. The bands indicate the impact of the systematic uncertainty on the signal cross-section.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1389\n\nand one hadronically, or both \u03c4 leptons decay hadronically [17].\nReferences\n[1] Carena, M. S. and Heinemeyer, S. and Wagner, C. E. M. and Weiglein, G., Eur. Phys. J. C26 (2003)\n601\u2013607.\n[2] Harlander, R. V. and Kilgore, W. B., Phys. Rev. D 68 (2003) 013001.\n[3] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties,\nthis volume.\n[4] Gleisberg, Tanju et al., JHEP 02 (2004) 056.\n[5] Sjostrand, T. et al., Comput. Phys. Commun. 135 (2001) 238\u2013259.\n[6] Marchesini, G. and Webber, B. R., Cavendish-HEP-87/9 (1987).\n[7] Mangano, M. L. and Moretti, M., and Piccinini, F. and Pittau, R. and Polosa, A. D., JHEP 07 (2003)\n001.\n[8] Frixione, S. and Webber, B. R., hep-ph/0207182 (2002).\n[9] Jadach, S. and Kuhn, J. H. and Was, Z., Comput. Phys. Commun. 64 (1990) 275\u2013299.\n[10] Barberio, E. and van Eijk, B. and Was, Z., Comput. Phys. Commun. 66 (1991) 115\u2013128.\n[11] ATLAS Collaboration, b-Tagging Performance, this volume.\n[12] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[13] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[14] Ellis, R. K. and Hinchliffe, I. and Soldate, M. and van der Bij, J. J., Nucl. Phys. B297 (1988) 221.\n[15] M. Schmitz, Studie zur Bestimmung des Untergrundes aus Daten und der Higgs-Boson-Masse in\nVektorbosonfusion mit H \u2192\u03c4\u03c4 \u2192\u00b5\u00b5 +4\u03bd mit dem ATLAS-Detektor, Internal Report BONN-IB-\n2006-07 (2006), Bonn University, 2006.\n[16] J. Schaarschmidt, A Study of b Quark Associated Higgs Production in the Decay Mode h/H/A \u2192\n\u03c4\u03c4 \u21922\u2113+4\u03bd with ATLAS at LHC, Internal report, Technische Universit\u00a8at Dresden, 2007.\n[17] ATLAS: Detector and physics performance technical design report. Volume 2, CERN-LHCC-99-\n15.\nHIGGS \u2013 DISCOVERY POTENTIAL OF h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\n1390\n\nSearch for the Neutral MSSM Higgs Bosons in the Decay\nChannel A/H/h \u2192\u00b5+\u00b5\u2212\nAbstract\nMotivated by the high muon momentum resolution and identi\ufb01cation ef\ufb01-\nciency achievable with the ATLAS detector, the observability of A/H/h \u2192\n\u00b5+\u00b5\u2212channel is explored. The high experimental resolution in this decay\nmode compensates to some extent for the suppression of the branching ratio,\nwith respect to the A/H/h \u2192\u03c4+\u03c4\u2212decays. The analyses are performed in\nthe Higgs mass range from 100 to 500 GeV. Two main analysis strategies are\napplied - the search for the dimuon \ufb01nal states resulting from the direct A/H/h\nproduction is combined with the search for the associated b\u00afbA/H/h production\nmode.\nThe studies are optimized for the early stage of data taking up to an integrated\nluminosity of 30 fb\u22121. All results are obtained combining the fast and the\nfull simulation of the ATLAS detector with the nominal detector layout and\nthe trigger ef\ufb01ciencies included. In addition, dedicated data samples are pro-\nduced to study the impact of the pile-up and cavern background on the analysis\nperformance. The estimation of the background contribution from the experi-\nmental data and the contribution of theoretical and experimental uncertainties\nare also addressed. The discovery potential is shown in the mA-tan\u03b2 plane in\ncontext of the mmax\nh\nMSSM benchmark scenario.\n1\nIntroduction\nIn the framework of the Standard Model, the observability of the Higgs boson in the decay channel\nH \u2192\u00b5+\u00b5\u2212is very unlikely, since the branching ratio for the Higgs decay into muons is very small and\nthe backgrounds from several Standard Model processes are large. As opposed to the Standard Model\npredictions, the decay of neutral MSSM Higgs bosons A, H and h into two muons is strongly enhanced\nin the MSSM for large values of tan\u03b2 and can be used either as a discovery channel or for the exclusion\nof a large region of the mA-tan\u03b2 parameter space (see Ref [1]).\nCompared to the dimuon channel, the A/H/h \u2192\u03c4+\u03c4\u2212decays have a substantially larger branching\nratio which scales as (m\u03c4/m\u00b5)2 and thus provide a promising discovery signature, as discussed in Ref [2].\nNevertheless, the \u03c4 identi\ufb01cation represents an experimental challenge. The \u00b5 +\u00b5\u2212\ufb01nal state, on the\nother hand, has the advantage of a very clear signature in the detector. Furthermore, a full reconstruction\nof the Higgs boson \ufb01nal state is possible, which allows for a direct mass measurement. The dimuon\nchannel provides for the most accurate Higgs boson mass measurement.\nIn this note, the potential for the discovery of the neutral MSSM Higgs bosons is evaluated in the\ndimuon decay channel. The study concentrates on the region of (mA \u2212tan\u03b2) plane with mA >110 GeV\nand intermediate tan\u03b2 values between 10 and 60, which is still uncovered by the current exprimental\nlimits [3, 4]. A detailed study of the ATLAS discovery potential for this channel has been recently\nperformed in the low mass region below 130 GeV [5]. The study includes also higher Higgs boson\nmasses up to 400 GeV.\nIn Section 2, the relevant production and decay rates of the MSSM Higgs boson are brie\ufb02y discussed\nin the context of the mmax\nh\nLHC scenario [6], as well as the production mechanisms of the major back-\nground processes. In Section 3, the Monte Carlo simulation and data samples used for the analysis are\ndescribed. Section 4 provides a short description of the detector performance obtained from the simu-\n1391\n\nlation, related to the reconstructed particles which will be present in the \ufb01nal state. The event selection\ncriteria, the resulting ef\ufb01ciency of the signal selection and the corresponding background rejection shall\nbe described in Section 5. Discussion of the systematic uncertainties is presented in Section 6. Sec-\ntion 7 describes the methods for the estimation of different background contributions from the the real\ndata. The obtained results are \ufb01nally represented by the discovery contours in the (mA-tan\u03b2) plane (see\nSection 9). The note concludes with Section 10.\n2\nSignal and background processes\nIn this Section, the properties of the signal shall be brie\ufb02y described, as well as the background processes\nrelevant for the MSSM Higgs boson searches in the dimuon \ufb01nal state at the LHC.\n2.1\nSignal production and decays\nThe characteristic production and decay properties of all MSSM Higgs bosons are determined at tree-\nlevel by the values of the two free parameters tan\u03b2 and the mass mA of the A boson. These properties\nhave been calculated at NNLO with the Feynhiggs 2.6.2 package [7] in the mmax\nh\nscenario, as summarized\nin Ref [1].\nThe direct gg \u2192A/H/h production via the gluon-gluon fusion is an analogue to the Standard Model\nHiggs boson production. This process is important in the region of low tan\u03b2 values (below 10), where the\nHiggs bosons couple most strongly to up-type quarks. For larger values of tan\u03b2, the rate of the b\u00afbA/H/h\nHiggs production in association with b-quarks becomes dominant, due to the enhanced couplings to the\nb-quarks.\nThere are two approaches to calculate the signal rates for the associated b\u00afbA/H/h production mode.\nIn the \ufb01rst approach, the production cross-section for the gg \u2192b\u00afbH process has been calculated at NLO\nin Ref [8, 9]. This calculation is most reliable in the case where both outgoing b-quarks have a high\ntransverse momentum (above \u223c15 GeV). The inclusive cross-section without any cut on the transverse\nmomenta of the b-quarks is less accurate, due to additional collinear logarithms which appear in the\ncalculation due to the presence of low-momentum b-quarks. An alternative approach is the calculation\nof the inclusive cross-section for the b\u00afb \u2192H process, for which the collinear logarithms can be absorbed\nin a parton density function for the b-quarks and resummed to all orders of perturbation theory [10,11].\nThis later calculation has been implemented in a parametrized way into the Feynhiggs package, which\nwas \ufb01nally used for the evaluation of the signal cross-sections, as mentioned previously.\nThe different higher-order calculations mentioned above have been extensively compared in Ref [12].\nThe two approaches agree within uncertainties. For the gg \u2192b\u00afbH calculation, the uncertainty related\nto the variation of the renormalization and the factorization scale amounts to 20-30%. For the b\u00afb \u2192H\ncalculation, which is used for the analysis, the scale uncertainty is much smaller, less than 10%. However,\nit should be noted that the uncertainty on the b parton density function has not been included here. In\norder to estimate this pdf-uncertainty, a calculation of the b\u00afb \u2192H cross-section is performed with two\ndifferent parton density functions, MRST2002 and MRST2004. The observed difference of \u223c14% is\ntaken as the estimate of the pdf-uncertainty. Adding the 10% scale uncertainty to this in quadrature, the\ntotal theory uncertainty for the signal is estimated to be \u223c17% for H boson masses up to 500 GeV.\nThe production cross-section of H and A bosons increases approximately quadratically with increas-\ning tan\u03b2, while the h boson production is tan\u03b2-dependent only for mA <130 GeV. Also the branching\nratio of H and A boson decays into \u00b5+\u00b5\u2212pairs become enhanced with increasing values of tan\u03b2. The\nh boson decay is rather insensitive to the two mentioned parameters. The increase of the cross-sections\nand branching ratios with tan\u03b2 make the A/H/h \u2192\u00b5+\u00b5\u2212decay channel a promising Higgs signature\nin MSSM.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1392\n\nAdditionally, the signal is enhanced due to the mass degeneracy of the neutral Higgs bosons. For A\nboson masses mA <130 GeV, the h and A bosons are degenerate in mass, while the heavy H boson mass\nis rather constant (\u223c130 GeV). In case of mA \u2248130 GeV, all three bosons have very similar masses. For\nmA >130 GeV, the h boson mass reaches its maximum value of \u223c130 GeV, independent of the A boson\nmass, while the A and H bosons become degenerate in mass. Thus the signal can be observed as the sum\nof all two or three degenerate mass states.\n2.2\nBackground processes\nThe processes with two muons in the \ufb01nal state, which give a major background contribution in the\nsearches for the A/H/h signal are depicted in Figure 1.\nZ/ *\n\u03b3\nq\nq\n\u00b5\n\u00b5\nQ\nQ\nZ\nZ\nq\nq\nW\nW\n\u00b5\n\u03bd\n\u00b5\n\u03bd\nq\nq\n\u00b5\n\u00b5\nQ\nQ\nq\nq\n\u00b5\n\u00b5\n\u00b5\ng\ng\nt\nt\nW\nW\n\u00b5\n\u03bd\n\u03bd\nb\nb\na)\nc)\nd)\ng\nq, Q\nq, Q\n\u00b5\n\u00b5\nZ\ng\nZ\nb)\nFigure 1: Tree-level Feynman diagrams of the dominant background processes with two isolated\nmuons in the \ufb01nal state: a) Drell-Yan Z boson production, b) Z boson production in association\nwith jets, c) t\u00aft production and d) ZZ and WW production. q is a general symbol for u and d quarks,\nwhile Q stands for the b and c quarks.\nThe dominant background process with a very large production rate of \u223c1 nb is the Drell-Yan Z\nboson production, with subsequent Z decay into two muons. The invariant dimuon mass peaks at the Z\nresonance, such that the search for the A/H/h becomes unfeasible for the Higgs masses below 100 GeV.\nEven for the higher Higgs boson masses, the tail of the Z resonance still provides an overwhelming\nbackground. The Drell-Yan background can be suppressed by requiring the presence of one or more\nadditional b-jets, originating from the associated b\u00afbA production. The major backgrounds remaining\nafter this requirement are the Z boson production in association with the light jets or b-jets and the t \u00aft \u2192\n(W +b)(W \u2212\u00afb) \u2192(\u00b5+\u03bdb)(\u00b5\u2212\u03bd \u00afb) background. The t\u00aft background can be distinguished from the signal\nby a higher jet activity and a large missing energy caused by the neutrinos from W decays. Additional\nbackground from WW and ZZ diboson productions is expected to be small, due to the much lower\nproduction rates.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1393\n\n3\nData samples\nTwo different Monte Carlo generators are used for the signal production. PYTHIA 6.4 [13] has been used\nto generate the direct gg \u2192\u03c6 \u2192\u00b5\u00b5 and associated gg \u2192b\u00afb\u03c6 \u2192b\u00afb\u00b5\u00b5 processes (where \u03c6 = A, H, h).\nThe SHERPA [14] event generator (version 1.0.9) combines all three associated production mechanisms,\ngg \u2192b\u00afb\u03c6, bg \u2192b\u03c6 and b\u00afb \u2192\u03c6, in a coherent way without double-counting. This is accomplished\nby the CKKW algorithm [15] for the matching of the parton showers to the quark emission from the\nmatrix elements. Both generators provide leading-order cross-sections, which have been rescaled to\nthe Feynhiggs NNLO values. The studies at the D0 experiment [16] have shown that the differential\nSHERPA distributions are in a good agreement with the real data and can simply be normalized to the\npreviously described inclusive higher-order cross-sections. The comparison of the samples produced by\nthe two generators will be described in Section 6.1. A generator \ufb01lter requiring at least two muons with\npT >5 GeV and |\u03b7| <2.7 is applied to each event for all signal data samples, after the showering and\nbefore writing out the events into permanent storage. The background samples are listed in Table 1,\ntogether with the corresponding NLO cross-sections. The details of the cross-section computation can\nbe found in Ref [17]. In addition to already mentioned generators, the MC@NLO 3.1 [18] and AcerMC\n3.4 packages [19] have been used for the event generation.\nFull simulation of the detector response has been performed for all signal and background event\ntopologies, within the ATHENA software framework which uses the GEANT4 [20] package for the\ndescription of the detector response. In addition, due to the large background production rates, it is nec-\nessary to increase the number of simulated events by means of the parametrized fast detector simulation\n(Atlfast [21]). The presented analyses are based on the combination of both simulation types. The sam-\nples obtained with the detailed simulation have been used for the tuning of the parametrized description\nof the detector performance in the fast simulation. The tuning procedure provides a very good agreement\nwith the full detector simulation. Any remaining differences are treated as systematic uncertainty.\nProcess\nGenerator\n\u03c3 \u00d7BR\nFilter\nNumber\nSimulation\n[pb]\nef\ufb01ciency\nof events\ntype\nt\u00aft; 2\u00b5-\ufb01lter\nMC@NLO\n833\n0.072\n500 000\nfull sim.\nt\u00aft; 1\u2113-\ufb01lter\nMC@NLO\n833\n0.556\n600 000\nfull sim.\n(Z \u2192\u00b5\u00b5)+0-3 light jets\nSHERPA\n2036\n0.490\n5 000\nfull sim.\n(Z \u2192\u00b5\u00b5)+1-3 b-jets\nSHERPA\n52.3\n0.914\n5 000\nfull sim.\nb\u00afb(Z \u2192\u00b5\u00b5)\nAcerMC/PYTHIA\n45\n0.788\n280 000\nfull sim.\nZZ \u2192b\u00afb\u00b5\u00b5\nPYTHIA\n0.151\n0.724\n10 000\nfull sim.\nWW\nPYTHIA\n116.8\n0.35\n50 000\nfull sim.\nt\u00aft, no \ufb01lter\nMC@NLO\n833.0\n1.0\n100 000 000\nAtlfast\n(Z \u2192\u00b5\u00b5)+0-3 light jets\nSHERPA\n1165.9\n0.855\n30 000 000\nAtlfast\n(Z \u2192\u00b5\u00b5)+0-3 b-jets\nSHERPA\n52.3\n0.914\n1 000 000\nAtlfast\nTable 1: Background data samples with corresponding NLO cross-sections.\nAll mentioned data samples have been simulated assuming there are no additional pp-interactions per\nevent. However, at luminosities of 1033 cm\u22122s\u22121 one expects to have 2-3 such pile-up interactions super-\nimposed to the hard scattering. In addition, the neutron and photon background of the muon spectrometer\n(so called cavern background) may increase the muon trigger rate and degrade the muon reconstruction\nperformance [22]. In order to study the impact of the pile-up and cavern background on the analysis\nperformance, dedicated b\u00afbA, t\u00aft and Zb\u00afb data samples have been simulated with the realistic pile-up and\ncavern background contribution. The simulated cavern background is assumed to be \ufb01ve times higher\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1394\n\nthan the prediction of GCALOR [23] and FLUKA [24] simulations, to account for the uncertainty of the\ncalculation.\n4\nDetector performance\nA detailed description of the ATLAS detector and its performance is given in Ref [25]. The details of\nthe detector layout, the software framework used for the Monte Carlo production, as well as the details\nof the reconstruction of fully simulated events can be found in Ref [26]. In this Section, the performance\nof the reconstruction algorithms is shortly described, concentrating on the key objects for the analyses:\nmuon identi\ufb01cation and momentum measurement, jet reconstruction, b-tagging and the measurement\nof the missing transverse energy (Emiss\nT\n). First, the results obtained in absence of pile-up and cavern\nbackground in the detector are shown. These are subsequently compared to the results obtained when\nboth pile-up and cavern background are taken into account.\n4.1\nReconstruction performance without pile-up and cavern background\nIn ATLAS, the muon reconstruction is performed by combining the information of the muon spectrom-\neter and the inner detector. Staco and MuTag [22] reconstruction packages are used for the study. The\naverage muon reconstruction ef\ufb01ciency is (97.15\u00b10.04)%. This is reduced to (95.44\u00b10.05)% if a match\nbetween the muon spectrometer track and the inner detector track is required. The momentum resolu-\ntion of low-pT muons is mostly dominated by the inner detector performance, while the high-pT muon\nreconstruction is more sensitive to the muon spectrometer performance. The average muon momentum\nresolution is better than 3%, which allows for an excellent dimuon mass resolution, as shown in Figure 2\nfor the A-boson (mA=200 GeV) produced via the associated b\u00afbA and the direct gg \u2192A production mode.\nAs expected, the experimental dimuon mass resolution does not depend on the Higgs production mode.\nTable 2 summarizes the dimuon mass resolutions obtained for different A boson masses.\nMean \n 4\n\u00b1\nSigma \n 4.8e\u221203\n\u00b1\n 6.3 \n (GeV)\n\u2212\n\u00b5\n+\n\u00b5\nm\n100\n150\n200\n250\n300\n350\n400\nEntries\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nMean \n 4e\u221203\n\u00b1\n 199.6 \nSigma \n\u00b1\n\u00b5\n\u00b5\nbbA \u2212> \n = 200 GeV\nA\nm\n) = 30\n\u03b2\ntan(\nMean \n 5e\u221203\n\u00b1\n 199.6 \nSigma \n 5.5e\u221203\n\u00b1\n 6.3\n (GeV)\n\u2212\n\u00b5\n+\n\u00b5\nm\n100\n150\n200\n250\n300\n350\n400\nEntries\n0\n100\n200\n300\n400\n500\n600\n700\n800\nMean \n\u00b1\nSigma \n\u00b1\n\u00b5\n\u00b5\ngg\u2212> A \u2212> \n = 200 GeV\nA\nm\n) = 30\n\u03b2\ntan(\nFigure 2: Dimuon mass distribution for the b\u00afbA and gg \u2192A signal samples with an A boson mass\nof 200 GeV and tan\u03b2=30. The distributions are \ufb01tted by the Gauss function.\nCharacteristic of the b\u00afbA signal are the b-jets with generally rather low transverse momenta, as shown\nin Figure 3(a). Since the ef\ufb01ciency of the b-jet reconstruction decreases with the pT, the number of\nreconstructed b-jets will in general be smaller for the signal than for the t\u00aft or ZZ \u2192b\u00afb\u00b5\u00b5 backgrounds,\nwhere the b-jets are more energetic (see Figure 3(b)). A detailed study was performed to identify the\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1395\n\nA boson mass (GeV)\n(GeV)\n110\n130\n150\n200\n300\n400\nNatural width\n2.16\n2.48\n2.80\n3.60\n5.61\n8.46\nReconstructed \u03c3\n2.59 \u00b1 0.02\n3.83 \u00b1 0.03\n4.11 \u00b1 0.04\n6.29 \u00b1 0.05\n10.2 \u00b1 0.2\n15.0 \u00b1 0.3\nReconstructed\n109.818\n129.738\n149.796\n199.589\n298.82\n399.37\nmass\n\u00b1 0.006\n\u00b1 0.005\n\u00b1 0.006\n\u00b1 0.005\n\u00b1 0.04\n\u00b1 0.04\nTable 2: The natural width of the A boson and the expected width of the dimuon resonance based\non Monte Carlo simulated data are shown for the b\u00afbA signal at different mass points and with\ntan\u03b2=30.\n(b-jet) (GeV)\nT\np\n0\n50\n100\n150\nNormalized to unity\n0.00\n0.05\n0.10\n0.15\n = 200 GeV \nA\nbbA, m\n \ntt \nZbb \nZZ \nATLAS\na)\nN(b-jet)\n0\n2\n4\n6\n8\n10\nNormalized to unity\n0 0\n0 5\n1 0\n = 200 GeV \nA\nbbA, m\n \ntt \nZbb \nZZ \nATLAS\nb)\nFigure 3: a) Transverse momentum pT of the b-jets in the b\u00afbA signal and the dominant background\nprocesses and b) the number of reconstructed b-jets per event. The selection criteria for the b-jets\nare described in the text.\noptimum b-jet selection criteria. The best jet reconstruction performance is observed for the jet cone\nalgorithms with the cone size of \u2206R =\np\n\u2206\u03b72 +\u2206\u03c6 2 = 0.4, compatible with the performance of the kT\nalgorithm for the same cone size. After a jet is selected as described, the b-tagging algorithm is performed\nto determine whether the jet originates from the b-quark. The minimum pT value of 20 GeV is required\nfor each b-jet in order to reduce the contribution of the calorimeter noise and of the mistagged light-\nor c-jets. The rejection of light- and c-jets is essential for the suppression of the Z + jet background.\nOne could extend the lower pT-bound down to \u223c15 GeV without a large change of the rejection rate.\nHowever, the impact on the \ufb01nal signal signi\ufb01cance will be rather small, while the agreement between\nthe full and the fast simulation is shown to decrease.\nSeveral b-tagging algorithms have been studied in order to de\ufb01ne the optimum selection of the low-\npT b-jets coming from the signal. The best rejection is obtained by IP3DSV1 [27], which is based on the\ninformation obtained from the transverse and longitudinal impact parameter signi\ufb01cances of the tracks\nand from the reconstructed secondary vertex. The distribution of the b-tagging weight obtained by this\nalgorithm is shown in Figure 4 for the b-jets and the light jets in the b\u00afbA signal sample at 200 GeV\nand in the t\u00aft background sample. The arrow indicates the optimum cut value of 4. Figure 5 shows the\nobtained b-tagging ef\ufb01ciency for the b\u00afbA signal sample, in dependence on the b-jet ET (Figure 5a)) and\n\u03b7 (Figure 5b)). The kinematic cuts of pT >20 GeV and |\u03b7| < 2.5, as well as the IP3DSV1 weight-cut\nof 4 have been applied for the b-jet selection. The resulting b-tagging ef\ufb01ciency is (64.1\u00b10.81)% for the\nb\u00afbA signal sample, with a light-jet rejection of (80\u00b11) for the Z+ jet sample. Systematic detector-related\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1396\n\n3D impact parameter + secondary vertex weight, IP3DSV1\n-20\n-10\n0\n10\n20\n30\n40\nNormalized to unity\n-3\n10\n-2\n10\n-1\n10\nlight jets from bbA\nb-jets from bbA\nlight jets from tt\nb-jets from tt\nATLAS\nFigure 4: Distribution of the b-tagging weight for the b-jets and the light jets in the b\u00afbA signal\nand t\u00aft background sample, obtained by the IP3DSV1 b-tagging algorithm. The arrow indicates\nthe optimum cut value of 4, which is used for the selection of the b-jets in the analyses.\n (GeV)\nb-jet\nT\nE\n0\n50\n100\n150\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\na)\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nb)\nFigure 5: B-tagging ef\ufb01ciency in dependence of b-jet transverse energy ET (a) and pseudorapidity\n\u03b7 (b), evaluated for the b\u00afbA signal sample at mA =200 GeV and tan\u03b2 =30. IP3DSV1 b-tagging\nweight cut of >4 has been applied.\nuncertainties are not included here.\nThe \ufb01nal important reconstruction object is the missing transverse energy (Emiss\nT\n), which allows for\nthe suppression of the t\u00aft background. In the signal processes, there is no neutrino contribution, such that\nthe measured Emiss\nT\nvalue is dominated by the experimental resolution. The reconstruction algorithm for\nthe calculation of the missing transverse energy is described in detail in Ref [28]. The distributions of\nEmiss\nT(x,y) components in the signal samples have a Gaussian part with a width \u03c3=(7.8\u00b10.1) GeV, while the\nnon-Gaussian tails (above 5\u03c3) are found to contribute less than 1.5% to the overall distribution. E miss\nT\nis\nsensitive to pile-up effects, as will be described in the next subsection.\n4.2\nReconstruction performance under in\ufb02uence of pile-up and cavern background\nIn the following, the detector performance related to the analysis is evaluated in dependence on the pile-\nup at luminosities of 1033 cm\u22122s\u22121 and cavern background (\ufb01ve times higher than the expectation). In\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1397\n\nFigure 6(left), the ef\ufb01ciency and the fake rate of the muon reconstruction is shown for the b\u00afbA signal\nsample simulated without and with the pile-up contribution as a function of the pseudorapidity. The\ncorresponding momentum resolution is shown in Figure 6(middle). Similar results are obtained also\nfor the background samples. As can be seen from the plots, muon reconstruction is only marginally\n|\u03b7\n|\n0\n0.5\n1\n1.5\n2\n2.5\nEfficiency and fake rate\n0\n0.2\n0.4\n0.6\n0.8\n1\nefficiency, w/o pile-up\nfake rate, w/o pile-up\n \nefficiency, with pile-up\nfake rate, with pile-up\nATLAS\n|\u03b7\n|\n0\n1\n2\n-resolution (%)\nT\nMuon p\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nw/o pile-up\nwith pile-up\nATLAS\n (GeV)\n\u00b5\n\u00b5\nm\n0\n100\n200\n300\n400\n500\nNormalized to unity\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nw/o pile-up\nwith pile-up\nATLAS\nFigure 6: Ef\ufb01ciency and the fake rate (left) and resolution (middle) of the muon reconstruction as\na function of the |\u03b7| (for pT >20 GeV), with and without the pile-up contribution in the b\u00afbA signal\nsample with mA=200 /GeV. The right plot shows the corresponding dimuon mass distribution.\nin\ufb02uenced by pile-up. Consequently, the dimuon invariant mass also remains unaffected, as shown in\nFigure 6(right) for mA=200 GeV.\nOn the contrary, the reconstruction of the missing transverse energy is substantially affected by pile-\nup in the calorimeter. The degradation of the Emiss\nT\n-resolution mainly affects the selection of events\nwith a small true missing energy (signal and the Z background) as shown in Figure 7(left); t\u00aft events,\ncharacterized by a large missing energy, are rather insensitive to pile-up (see Figure 7(right)). This\n (GeV)\nmiss\nT\nE\n0\n50\n100\n150\n200\nEntries\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nwithout pile-up\nwith pile-up\n=200 GeV\nA\nbbA, m\nATLAS\n (GeV)\nmiss\nT\nE\n0\n50\n100\n150\n200\nEntries\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nwithout pile-up\nwith pile-up\ntt background\nATLAS\nFigure 7: Missing transverse energy distribution for the b\u00afbA signal at 200 GeV (left) and the t\u00aft\nbackground (right),with and without pile-up.\neffect must be taken into account during the optimization of the event selection criteria. For instance, an\nevent selection cut at Emiss\nT\n<30 GeV, which is reasonable without pile-up, would reject too many signal\nevents, once the pile-up contribution is included. Therefore, this analysis cut should rather be set to at\nleast 40 GeV in the realistic LHC environment.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1398\n\nThe change of the calorimeter response under the in\ufb02uence of pile-up affects also the jet reconstruc-\ntion. Due to a higher calorimeter activity, one expects an increase in the number of reconstructed jets.\nThis can be observed in Figure 8(left), showing the jet multiplicity in the Zb\u00afb background events.\nNumber of jets per event\n0\n2\n4\n6\n8\n10\nEntries\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n1\n10\nwithout pile-up\nwith pile-up\nATLAS\nNumber of b-jets per event\n0\n1\n2\n3\n4\n5\nEntries\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nwithout pile-up\nwith pile-up\nATLAS\nFigure 8: Total number of jets per event (left) and the number of b-jets (right) in the Zb\u00afb back-\nground sample, with and without the pile-up contribution.\nNo signi\ufb01cant impact of the pile-up is observed on the b-tagging (see Figure 8(right)), due to the\nadditional tracking and vertex information.\n5\nEvent selection\nThe search for the MSSM Higgs bosons can be performed by several different approaches, related to the\nnumber of jets one requires to be present in the \ufb01nal state. As mentioned before, due to a large signal\nproduction rate in the associated production mode, the presence of the b-jets in the \ufb01nal state can help\nto suppress the Drell-Yan background. On the contrary, the remaining events with 0 b-jets provide for a\nhigh signal rate on top of the smoothly distributed background, even at low integrated luminosity.\nThe event selection methods are optimized separately for the two cases:\n\u2022 Signatures with 0 b-jets in the \ufb01nal state.\n\u2022 Signatures with at least one b-jet in the \ufb01nal state.\nThe two mentioned \ufb01nal states are uncorrelated and therefore complementary. In the case of 0 b-\njets in the \ufb01nal state, the dominant background is the Drell-Yan Z boson production, while in the case\nof at least one b-jet the t\u00aft background has the biggest contribution, especially for Higgs masses above\n130 GeV, which are further away from the Z resonance.\nBefore describing the selection criteria, the preselection of the events is discussed, common to the\ntwo signatures above. The preselection is de\ufb01ned by the kinematic cuts on muon pT and |\u03b7|, together\nwith the muon isolation criteria.\n5.1\nPreselection\nThe main characteristics of the signal signatures is the presence of two isolated muons of opposite charge\nin the \ufb01nal state. The pT-distribution of the muons is shown in Figure 9 for the signal and background\nprocesses. The signal is characterized by the relatively high-pT muons, while the background has muons\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1399\n\n (GeV)\nT\np\n0\n50\n100\n150\n200\n250\n300\nNormalized to unity\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\n0.14\n0.16\n0.18\n = 110 GeV \nA\nbbA, m\n = 200 GeV\nA\nbbA, m\n = 300 GeV \nA\nbbA, m\n = 400 GeV \nA\nbbA, m\nZ+light jets \nZ+ b jets \ntt \nZZ \nATLAS\nFigure 9: Distribution of the muon transverse momentum pT for the muons in the signal and\nbackground events.\nof lower momenta. The muon pT distribution in the signal is highly correlated to the Higgs boson mass.\nTherefore, the lower bound on the muon pT is kept at a relatively low value, in order to allow for a\ngeneral search in a broad Higgs mass range. At preselection level, both muons are required to have a\npT >20 GeV and to be in the pseudorapidity range |\u03b7| <2.7.\nThe selected high-pT muons are required to be isolated, in order to reject the processes in which the\nmuons originate from the hadronic decays. The applied isolation criteria require the calorimeter energy\nET deposited in a cone of size \u2206R = 0.4 around a given muon, divided by the muon pT to be lower\nthan 0.2. The distribution of this isolation variable is shown in Figure 10(left) for different signal and\nbackground processes.\nThe isolation criteria signi\ufb01cantly decrease the t\u00aft background, where one of the muons comes from\nthe b-decays. The power of rejection of the non-isolated muons originating from the b-quarks in the\nt\u00aft background is shown in Figure 10(right) for the standard calorimeter isolation (E cone0.4\nT\n), and for the\nisolation normalized by the muon pT.\nDue to the high muon momenta, the signal can be ef\ufb01ciently triggered by the single high-pT muon\ntrigger. The ef\ufb01ciency of the trigger selection for the dimuon signal events is shown to be around 95%\nfor all studied mass points. The detailed study of the trigger selection ef\ufb01ciency for events which pass all\nof\ufb02ine event selection criteria will be presented in Section 5.3. In the following, the results of the event\nselection without the trigger requirement are presented at \ufb01rst.\n5.2\nSignatures with 0 b-jets and with at least one b-jet in the \ufb01nal state\nThe large Z boson background contribution can be reduced by requiring that the jets which are present\nin the \ufb01nal state are tagged as b-jets. Therefore, assuming a fully performing b-tagging algorithm, the\nfollowing set of selection criteria can be applied:\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1400\n\n)\n\u00b5\n(\nT\n/p\ncone0.4\nT\nE\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nNormalized to unity\n-3\n10\n-2\n10\n-1\n10\n1\n = 200 GeV \nA\nbbA, m\n \ntt\nZbb\nZZ\nATLAS\nmuon isolation efficiency\n0.80\n0.85\n0.90\n0.95\n1.00\nrejection of non-isolated muons\n0\n500\n1000\n1500\n)\n\u00b5\n(\nT\n/p\ncone0.4\nT\nE\ncone0.4\nT\nE \nworking point\n)\n\u00b5\n(\nT\n/p\ncone0.4\nT\nE\ncone0.4\nT\nE \nworking point\nATLAS\nFigure 10: (left) Muon isolation variable Econe0.4\nT\n/pT(\u00b5), shown for different signal and back-\nground processes. Here, the Econe0.4\nT\nis the energy measured in the calorimeters in cone \u2206R = 0.4\naround a given muon. (right) Rejection of the non-isolated muons originating from the b-quarks\nin t\u00aft events as a function of the selection ef\ufb01ciency for isolated muons, shown for the two isolation\nvariables described in the text. The \ufb01lled circle indicates the working point with the isolation cut\nat Econe0.4\nT\n/pT(\u00b5) <0.2 .\n\u2022 Events are required to pass the preselection criteria and to have a missing transverse energy\nEmiss\nT\n<40 GeV. This cut is particularly effective in rejecting the t\u00aft and WW background, which\nare characterized by a high missing energy due to the presence of neutrinos in the \ufb01nal state (see\nFigure 11(left)).\n (GeV)\nmiss\nT\nE\n0\n50\n100\n150\n200\nNormalized to unity\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\n0.35\n = 200 GeV\nA\nbbA, m\nZ+light jets\nZ+ b jets\ntt\nZZ\nWW\nATLAS\nIP3DSV1 weight\n0\n20\n40\nNormalized to unity\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n 200 GeV\nA\nbbA, m\nZ+light jets\nZ+ b jets\ntt \nZZ\nATLAS\nNumber of b-jets / event\n0\n2\n4\n6\n8\n10\nNormalized to unity\n0\n0 2\n0.4\n0.6\n0 8\n1\n = 200 GeV \nA\nbbA, m\nZ+light jets \nZ+ b jets \ntt \nZZ \nWW \nATLAS\nFigure 11: (left) Missing transverse energy, (middle) distribution of the b-tagging IP3DSV1 weight\nafter requiring pT >20 GeV and |\u03b7| <2.5 and (right) the multiplicity of reconstructed b-jets per\nevent, after applying the pT- and \u03b7-cuts and requiring the b-tagging IP3DSV1 weight greater than\n4. Distributions for the b\u00afbA signal (mA=200 GeV) and for the major background processes are\nshown. Arrows indicate the cuts applied in the analysis.\n\u2022 Subsequently, the number of b-jets is counted in each event, requiring pT >20 GeV, |\u03b7| <2.5 and\nthe b-tagging IP3DSV1 weight greater than 4. The distribution of the b-tagging weights before\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1401\n\nand the b-jet multiplicity after applying the weight-cut are shown in Figure 11. As shown in the\nmiddle plot, the b-tagging weight is effective in reducing the background from Z+light jets, at the\nexpense of a signi\ufb01cant loss of the signal. This cut is scarcely effective against the t\u00aft background,\nwhich, however, can be reduced by the additional cuts discussed below. Therefore, the analysis\nis divided into a channel with 0 b-jets (in which the Z background is dominant) and the channel\nwith at least one b-jet (in which the t\u00aft background plays an important role and can be further\nsuppressed).\n\u2022 Further t\u00aft rejection criteria have been studied for the channel with at least one b-jet.\n\u2013 Two muons originating from the decay of the same particle (Higgs boson) tend to be emitted\nback-to-back, especially if this particle has a low transverse momentum. As opposed to that,\nthe muons originating from the two different particles (as in the t\u00aft events) are not correlated\nand can be separated by any angle. Therefore, the cut is applied on the angle \u2206\u03c6\u00b5\u00b5 between\nthe two muons by requiring |sin\u2206\u03c6\u00b5\u00b5| <0.75. The |sin\u2206\u03c6\u00b5\u00b5| distributions for the signal and\nbackground processes are shown in Figure 12(a).\n\u2013 In addition, several discriminating variables related to the hadronic activity in the events have\nbeen studied: the pT distribution of the b-jets, the number of jets per event, or a sum of the\ntransverse momenta of all jets in the event (\u2211p jet\nT ). The distributions of two of these variables\nare shown in Figure 12b) and c). The latter is shown to provide the highest rejection against\nthe t\u00aft background, while at the same time remaining relatively robust under the the in\ufb02uence\nof pile-up. A cut at \u2211p jet\nT <90 GeV is required.\n|\n\u00b5\n\u00b5\n\u03c6 \n\u2206\n|sin \n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nNormalized to unity\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\n0.14\n0.16\n = 200 GeV\nA\nbbA, m\nZ+light jets\nZ+ b jets\ntt\nZZ\nATLAS\n) (GeV)\nb\nT\nmax(p\n0\n50\n100\n150\n200\nNormalized to unity\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n = 200 GeV \nA\nbbA, m\nZ+ b jets \ntt \nZZ \nATLAS\n (GeV)\njet\nT\n p\n\u2211\n0\n100\n200\n300\n400\nNormalized to unity\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n = 200 GeV \nA\nbbA, m\nZ+ b jets\ntt\nZZ \nATLAS\nFigure 12: Discriminating variables against the t\u00aft background: a) |sin\u2206\u03c6| shown for the b\u00afbA signal\n(mA=200 GeV) and for the major background processes, b) the maximum pT of the b-jet, and c)\n\u2211p jets\nT\n-distribution for the signal and background processes. Arrows indicate the cuts applied in\nthe analysis.\n\u2022 The \ufb01nal number of events which is used for the calculation of the signal signi\ufb01cances is eval-\nuated in a mass window \u2206m=mA\u00b12\u03c3\u00b5\u00b5 around the A boson mass, where \u03c3\u00b5\u00b5 is the expected\nmA-dependent width of the dimuon resonance (see Table 2).\nThe signal and background event rates after each of the cuts described above are shown in Tables 3 and 4.\nA signal selection ef\ufb01ciency of 7-10% is reached for the channel with at least one b-jet in the \ufb01nal\nstate. The dominant background processes are almost equally the Z + jet and the t\u00aft events. The signal\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1402\n\nCut\nbbA (fb)\nbbA (fb)\nbbA (fb)\nbbA (fb)\nbbA (fb)\ngg \u2192A (fb)\n130 GeV\n150 GeV\n200 GeV\n300 GeV\n400 GeV\n200 GeV\nAll events\n13.4\u00b7101\n8.7\u00b7101\n31.5\u00b7100\n6.9\u00b7100\n19.3\u00b710\u22121\n32.3\u00b710\u22121\nmuon preselection\n8.8(2)\u00b7101\n5.9(1)\u00b7101\n22.3(3)\u00b7100\n5.0(1)\u00b7100\n14.4(3)\u00b710\u22121\n28.6(3)\u00b710\u22121\nEmiss\nT\n<40 GeV\n8.3(2)\u00b7101\n5.4(1)\u00b7101\n20.3(2)\u00b7100\n4.4(1)\u00b7100\n11.7(2)\u00b710\u22121\n25.9(3)\u00b710\u22121\nnr. of b-jets=0\n6.6(1)\u00b7101\n4.3(1)\u00b7101\n15.5(2)\u00b7100\n31.6(8)\u00b710\u22121\n8.2(2)\u00b710\u22121\n25.1(3)\u00b710\u22121\n\u2206m\n5.6(1)\u00b7101\n34.1(8)\u00b7100\n128.0(1)\u00b710\u22121\n26.4(8)\u00b710\u22121\n6.9(2)\u00b710\u22121\n204.2(1)\u00b710\u22122\nnr. of b-jets\u22651\n16.2(7)\u00b7100\n11.2(5)\u00b7100\n4.8(1)\u00b7100\n12.1(5)\u00b710\u22121\n3.5(1)\u00b710\u22121\n8.2(5)\u00b710\u22122\n|sin\u2206\u03c6\u00b5\u00b5| <0.75\n11.7(6)\u00b7100\n8.3(4)\u00b7100\n4.0(1)\u00b7100\n10.7(5)\u00b710\u22121\n3.2(1)\u00b710\u22121\n4.8(4)\u00b710\u22122\n\u2211pjets\nT\n< 90 GeV\n9.3(5)\u00b7100\n6.5(3)\u00b7100\n2.9(1)\u00b7100\n7.1(4)\u00b710\u22121\n1.7(1)\u00b710\u22121\n2.0(3)\u00b710\u22122\n\u2206m\n8.3(5)\u00b7100\n5.3(3)\u00b7100\n23.9(8)\u00b710\u22121\n5.9(4)\u00b710\u22121\n14.8(8)\u00b710\u22122\n1.7(3)\u00b710\u22122\nTable 3: \u03c3 \u00d7 BR for the signal processes at tan\u03b2=30 after each selection cut. Numbers in brackets\nrepresent the statistical error on the last digit.\nCut\nZ +light jet\nZ +b jet\nt\u00aft\nZZ \u2192bb\u00b5\u00b5\nWW\nTotal\n(fb)\n(fb)\n(fb)\n(fb)\n(fb)\nAll events\n2036.0\u00b7103\n52.3\u00b7103\n833.0\u00b7103\n151.0\n116.8\u00b7103\nmuon preselection\n727.7(2)\u00b7103\n333.8(4)\u00b7102\n57.6(1)\u00b7102\n61.3(8)\u00b7100\n6.7(2)\u00b7102\nEmiss\nT\n<40 GeV\n726.2(2)\u00b7103\n330.1(4)\u00b7102\n132.7(6)\u00b7101\n56.1(8)\u00b7100\n3.0(2)\u00b7102\nnr. of b-jets=0\n710.7(2)\u00b7103\n242.3\u00b7102\n25.6(3)\u00b7101\n22.3(5)\u00b7100\n2.9(2)\u00b7102\n\u2206m (130 GeV)\n35.4(1)\u00b7102\n8.8(2)\u00b7101\n20.2(8)\u00b7100\n1.5(4)\u00b710\u22121\n1.8(4)\u00b7101\n3.7(1)\u00b7103\n\u2206m (150 GeV)\n152.5(8)\u00b7101\n3.4(1)\u00b7101\n16.0(7)\u00b7100\n0.7(3)\u00b710\u22121\n2.6(5)\u00b7101\n15.9(1)\u00b7102\n\u2206m (200 GeV)\n58.9(5)\u00b7101\n8.4(7)\u00b7100\n11.6(6)\u00b7100\n0.6(1)\u00b710\u22121\n1.6(3)\u00b7101\n62.5(6)\u00b7101\n\u2206m (300 GeV)\n18.1(3)\u00b7101\n1.8(3)\u00b7100\n5.1(4)\u00b7100\n0.1(1)\u00b710\u22121\n0.2(2)\u00b7101\n19.0(4)\u00b7101\n\u2206m (400 GeV)\n7.8(2)\u00b7101\n0.8(2)\u00b7100\n2.0(2)\u00b7100\n0.1(1)\u00b710\u22121\n0.2(2)\u00b7101\n8.4(3)\u00b7101\nnr. of b-jets\u22651\n154.9(3)\u00b7102\n87.7(2)\u00b7102\n107.1(6)\u00b7101\n33.8(6)\u00b7100\n0.6(2)\u00b7101\n|sin\u2206\u03c6\u00b5\u00b5| <0.75\n84.3(2)\u00b7102\n49.8(2)\u00b7102\n61.7(4)\u00b7101\n19.0(5)\u00b7100\n0.3(2)\u00b7101\n\u2211pjets\nT\n<90 GeV\n44.3(1)\u00b7102\n33.0(1)\u00b7102\n8.9(2)\u00b7101\n10.7(3)\u00b7100\n0.3(2)\u00b7101\n\u2206m (130 GeV)\n3.1(1)\u00b7101\n15.1(9)\u00b7100\n7.7(5)\u00b7100\n0.7(3)\u00b7100\n<0.7\u00b7100\n5.5(2)\u00b7101\n\u2206m (150 GeV)\n14.8(8)\u00b7100\n6.0(6)\u00b7100\n6.2(4)\u00b7100\n0.2(1)\u00b710\u22121\n<0.7\u00b7100\n2.8(1)\u00b7101\n\u2206m (200 GeV)\n6.7(5)\u00b7100\n2.0(3)\u00b7100\n5.8(4)\u00b7100\n<0.1\u00b710\u22121\n<0.7\u00b7100\n1.5(1)\u00b7101\n\u2206m (300 GeV)\n2.2(3)\u00b7100\n0.6(2)\u00b7100\n2.3(3)\u00b7100\n<0.1\u00b710\u22121\n<0.7\u00b7100\n5.8(8)\u00b7100\n\u2206m (400 GeV)\n1.1(2)\u00b7100\n0.1(1)\u00b7100\n0.4(1)\u00b7100\n0.1(1)\u00b710\u22121\n<0.7\u00b7100\n2.3(7)\u00b7100\nTable 4: \u03c3 \u00d7BR for the background processes obtained after each event selection cut. The upper limits\nare evaluated at 90% CL. Numbers in brackets represent the statistical error on the last digit.\nevents are mainly lost due to the limited b-jet reconstruction ef\ufb01ciency, as discussed previously. This is\nin agreement with a much larger signal selection ef\ufb01ciency of 40-50% in the case of the channel with 0\nb-jets. Here, the Z background is observed to have a dominant contribution. The invariant dimuon mass\ndistributions obtained for the two channels are shown in Figure 13.\nIn the initial phase of the detector running, the b-tagging algorithms still may not have the optimum\nperformance. Therefore, the discovery potential has also been evaluated for the case where no b-tagging\nrequirement is imposed on the reconstructed jets. Due to the large Z background, the signatures with no\nb-tagging requirement will provide a similar discovery potential as the analysis with 0 b-jets in the \ufb01nal\nstate.\n5.3\nTrigger selection\nPreviously calculated event selection ef\ufb01ciencies have been obtained assuming that each analysed event\ncan be triggered. In this Section, a realistic trigger description is included to evaluate the effect of the\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1403\n\n (GeV)\n\u00b5\n\u00b5\nm\n150\n200\n250\n300\n350\nEntries / (4 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n150\n200\n250\n300\n350\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n bbA\n Z+l jets\n Z+b jets\n WW\n tt\n ZZ\n=150 GeV\nA\nm\n=200 GeV\nA\nm\n=300 GeV\nA\nm\na)\nATLAS\n (GeV)\n\u00b5\n\u00b5\nm\n150\n200\n250\n300\n350\nEntries / (4 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n150\n200\n250\n300\n350\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n bbA\n Z+l jets\n Z+b jets\n WW\n tt\n ZZ\n=150 GeV\nA\nm\n=200 GeV\nA\nm\n=300 GeV\nA\nm\nb)\nATLAS\nFigure 13: Invariant dimuon mass distributions of the main backgrounds and the A boson signal\nat masses mA=150, 200 and 300 GeV and tan\u03b2 = 30, obtained for the integrated luminosity of\n30 fb\u22121 . B-tagging has been applied for the event selection. The production rates of H and A\nbosons have been added together. a) for the 0 b-jet \ufb01nal state and b) for the \ufb01nal state with at least\n1 b-jet.\nlimited trigger ef\ufb01ciency on the \ufb01nal event selection.\nSince the signal processes are characterized by the two high-pT muons in the \ufb01nal state (see Fig-\nure 9), the most reliable trigger item is a single high-pT muon with pT >20 GeV. The single-muon\ntrigger ef\ufb01ciency is mostly limited by the geometrical acceptance of the trigger chambers in the muon\nspectrometer, as discussed in detail in [29]. The ef\ufb01ciency of the trigger selection for events passing\nall previously described event selection criteria is shown in Table 5 for the signal at 200 GeV and for\nthe background samples. A very similar trigger selection ef\ufb01ciency can be observed for all signal and\nDataset\nL1\nHigh level trigger\nbbA, 200 GeV\n97.2\n95.0\nt\u00aft\n97.1\n95.1\nb\u00afbZ\n97.1\n94.8\nTable 5: Trigger selection ef\ufb01ciency (%) of events which pass all event selection criteria described\nin Section 5.2. The results are listed for the signal and the two background processes.\nbackground samples. The relatively high \ufb01nal trigger selection ef\ufb01ciency of \u223c95% corresponds to the\ndecrease of the signal signi\ufb01cance by 2-3% compared to the previously shown results. It has been shown\nthat the observed ef\ufb01ciencies are effectively stable to a level of about \u00b10.5% at any level of the event\nselection, since the selection criteria are not affecting the muon kinematics. Furthermore, the trigger\nselection does not induce any bias to the dimuon invariant mass distribution.\nThe studies described above have been performed under the assumption that the trigger threshold for\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1404\n\na single high-pT muon is 20 GeV. If this threshold should be higher, some of the signal events might\nbe lost by the trigger selection. In order to evaluate the sensitivity of the signal selection on the varying\ntrigger thresholds, a dedicated study has been performed. New trigger thresholds of 20, 26 and 30 GeV\nare emulated by the requirement that at least one reconstructed muon with a pT above the given threshold\nexists in the event. This muon is also required to have a matching L1 region-of-interest in the muon\nspectrometer, in order to take into account the holes in the geometrical trigger acceptance. The trigger\nselection ef\ufb01ciencies for the new trigger thresholds are shown in Figure 14 for events remaining after\neach of the analysis cuts applied on the b\u00afbA signal with mass mA=200 GeV. No visible degradation of the\nanalysis cut\nn(b)>0\nacopl.\n\u03a3\nmuon\npreselection\nT\nE\np T\njet\n\u2206m\nmiss\nL1 trigger selection efficiency\n0.88\n0.90\n0.92\n0.94\n0.96\n0.98\n1.00\nATLAS\n\u2212threshold\nT\n 20 GeV p\n\u2212threshold\nT\n 26 GeV p\n\u2212threshold\nT\n 30 GeV p\nFigure 14: Trigger selection ef\ufb01ciency of the b\u00afbA signal events (mA=200 GeV) in dependence\non the of\ufb02ine analysis selection. Different curves show the results obtained for different trigger\nthresholds.\n\ufb01nal signal selection is observed for the trigger threshold variations of up to 30 GeV. Similar behavior\nis observed also for the signal at other mass points. This result can be explained by a rather high muon\nmomenta in the signal samples, such that there is only a small fraction of signal events in which both\nmuons have a pT below 30 GeV. The dependence of the t\u00aft and Zb\u00afb background selection on the trigger\nthreshold of up to 30 GeV is shown to be smaller than 2% after all analysis cuts.\n6\nSystematic uncertainties\nSeveral sources of systematic uncertainties can affect the total yields of both the signal and the back-\nground events after applying the selection criteria speci\ufb01ed in the previous Section. In this Section, the\nin\ufb02uence of the theoretical and the detector-related systematic uncertainties is evaluated.\n6.1\nTheoretical uncertainties\nAs mentioned previously, the Higgs boson production in association with the b-quarks has been simu-\nlated with PYTHIA and SHERPA Monte Carlo generators and the obtained differential distributions are\nscaled to the Feynhiggs NNLO cross-sections. It is important to remark that no cuts have been applied\non the transverse momenta of the generated b-quarks, since also the event topologies with less than two\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1405\n\nobserved b-jets are studied in the presented analyses. (An outgoing b-quark can be considered as observ-\nable if its momentum is above \u223c15 GeV). Therefore, the corresponding NNLO cross-sections also have\nto be calculated in an inclusive way, with no constraints on the kinematics of the b-quarks.\nAs discussed in Section 2, the total theoretical uncertainty on the inclusive cross-section amounts to\n\u223c17%, depending on the Higgs boson mass. In addition, since the experimental search distinguishes\nbetween the \ufb01nal states with 0 and those with 1 or more b-jets (with pT >20 GeV), it is important to\nshow that the proportion between the mentioned different event topologies which is obtained from the\nMonte Carlo generators also agrees with theory predictions. For this purpose, the fraction of generated\nevents is calculated which have exactly one b-quark with pT >15 GeV and |\u03b7| <2.5 in the \ufb01nal state\n(before hadronization). This number is then compared to the ratio of the MCFM cross-section calculated\nfor the bg \u2192bH process with the same cuts on the b-quarks, divided by the inclusive cross-section. The\nresult of the comparison is shown in Figure 15, being comparable to the 20% uncertainty. The SHERPA\n(GeV)\nH\nm\n100\n200\n300\n400\n500\ntotal\n1b \u03c3\n/\nATLAS\n\u03c3\n0.2\n0.25\n0.3\n0.35\n0.4\n0.4\n0.45\n0.5\n0.55\n0.6\nTheory, MRST2004\nTheory, MRST2002\nSherpa 1.0.9\nPythia 6.4\nFigure 15: Fraction of events \u03c31b with exactly one b-quark with pT >15 GeV and |\u03b7| <2.5,\nrelative to the total inclusive cross-section \u03c3total, shown in dependence on the Higgs boson mass\nMH. The lines show the theory prediction as the ratio between the MCFM bg \u2192Hb and b\u00afb \u2192H\ncross-sections. Solid line: MRST2004 pdf set, dashed line: MRST2002 pdf set. Circles: result\nfrom SHERPA 1.0.9. Triangles: PYTHIA 6.4 gg \u2192b\u00afbH process.\nprediction is about 20% higher than PYTHIA and agrees better with the theory calculation with the\nMRST2004 pdf set. The MRST2002 pdf set gives a better compatibility with PYTHIA. Taking into\naccount the theory uncertainties mentioned above, one can conclude that the samples produced with both\ngenerators can reproduce the NLO predictions from a single b-quark rate.\nThe observed differences between SHERPA and PYTHIA are visible also in the differential b-quark\ndistributions. The differential pT and \u03b7-distributions of the leading b-quark, as obtained by the PYTHIA\nand SHERPA generators are compared in Figure 16 for the signal at the mass of 200 GeV. The com-\nparison is performed on a parton level, before hadronization. A slightly harder transverse momentum\nspectrum and a more central pseudorapidity of the b-quarks is observed in the SHERPA events.\n6.2\nDetector-related systematic uncertainties\nSystematic uncertainties related to the muon and the jet reconstruction, as well as the uncertainties on\nthe b-tagging performance have been evaluated with rather conservative estimates on the level of under-\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1406\n\nATLAS\n (GeV)\nleading b\nT\np\n0\n20\n40\n60\n80\n100\n120\nnormalized\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nSherpa 1.0.9\nPythia 6.4\nleading b\n\u03b7\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\nnormalized\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\nATLAS\nFigure 16: Differential pT and \u03b7 distribution of the leading b-quark, obtained by SHERPA (gray\nhistogram) and by the PYTHIA gg \u2192b\u00afbH calculation (solid line). All histograms have been\nnormalized to unity.\nstanding of the detector performance. This level is assumed to correspond approximately to an integrated\nluminosity of 1 fb\u22121. For each of the above effects, the corresponding change of the reconstructed miss-\ning transverse energy is taken into account. Further more, systematic effects due to the differences\nbetween the fast and the full simulation are taken into account by means of the comparison between the\nfull and fast simulation.\nMuon reconstruction uncertainties are treated separately for the reconstruction ef\ufb01ciency, muon\nmomentum resolution and the muon momentum scale. The ef\ufb01ciency of the muon identi\ufb01cation is\nassumed to be known with an accuracy of \u00b11%, based on the results of the tag-and-probe method for the\nmuon ef\ufb01ciency measurement from the real data [30]. Systematic errors of the muon momentum scale\nare taken to be \u00b11%, arising for instance from the non-perfect knowledge of the magnetic \ufb01eld. The\nincomplete understanding of the material distributions inside the detector, as well as possible residual\ndetector misalignment can lead to an additional smearing of the muon momentum resolution. Based\non early detector calibration, the additional smearing is expected to be \u03c3( 1\npT ) = 0.011\npT\n\u22950.00017 (in\n1/(GeV)). The \ufb01rst term enhances the effect of the Coulomb scattering, while the second enhances the\ncontribution from the misalignment.\nJet reconstruction uncertainties are estimated by the jet performance group [25]. In the pseudo-\nrapidity region below |\u03b7|=3.2, the jet energy scale uncertainty of \u00b13% and a resolution uncertainty of\n\u03c3(E) = 0.45\u00b7\n\u221a\nE are assumed. For |\u03b7| >3.2, the corresponding values are \u00b110% and \u03c3(E) = 0.63\u00b7\n\u221a\nE\nrespectively.\nb-tagging ef\ufb01ciency and the fake rate are crucial for the described analysis. Conservative relative\nuncertainty of \u00b15% on the b-tagging ef\ufb01ciency and \u00b110% uncertainty on the rejection of the light jets\nhave been assumed.\nThe results obtained after implementing each of the above systematic uncertainties separately into\nthe analysis are shown in Table 6 for the signal at mA=150 GeV and for the backgrounds within the\ncorresponding mass window. Signals at different mass points are affected by a similar amount. The\nbackground uncertainties are also rather independent of the dimuon mass region, but from one exception.\nThe muon momentum scale mostly affects the background in the lower mass region, close to the Z\nresonance, while the deviations become smaller for the higher signal masses, i.e. one observes \u00b111%,\n\u00b15% and \u00b13% for the Higgs masses of 110, 130 and 200 GeV respectively.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1407\n\nSystematic uncertainty [%]\nSignal\nt\u00aft\nZ+ b jet\nZ+light jet\nMuon ef\ufb01ciency\n\u00b12\n\u00b11\n\u00b12\n\u00b12\nMuon pT scale\n\u00b12\n\u00b13\n\u00b13\n\u00b15\nMuon resolution\n-2\n-4\n3\n3\nJet energy scale\n\u00b11\n\u00b15\n\u00b12\n\u00b12\nJet energy resolution\n-1\n-3\n-1\n-1\nb-tagging ef\ufb01ciency\n\u00b14\n\u00b13\n\u00b14\n\u00b12\nb-tagging fake rate\n\u00b11\n\u00b10\n\u00b10\n\u00b16\nFull-Atlfast corrections\n0\n+8\n-10\n+5\nTotal\n\u00b15\n\u00b112\n\u00b112\n\u00b111\nTable 6: Relative deviation of the selection ef\ufb01ciency in % for the signal at mA=150 GeV and for\nthe background events after imposing each of the systematic uncertainties separately, as described\nin the text. The total deviation is given as quadratic sum of the separate contributions, including\nthe one-sided corrections.\n7\nBackground estimation based on the measured data\nAs previously discussed, theoretical and experimental uncertainties can lead to systematic errors in de-\ntermination of the background rates. Additional information on the shape and the size of the background\ncontributions can be collected from the real data. As shown before, two major backgrounds surviving all\nevent selection criteria are the Z + jet and the t\u00aft processes. Two strategies to estimate their contributions\nfrom the measured data shall now be described.\nThe \ufb01rst method makes use of the fact that the branching ratio for A/H boson decays into two\nelectrons is negligible compared to the dimuon decay channel. Therefore, since one doesn\u2019t expect\nany signal in the dielectron \ufb01nal state, one can use this signature to determine the total background\ncontribution. Additionally, the signatures with one electron and one muon in the \ufb01nal state provide\nthe contribution of the t\u00aft background alone, since the Z + jet processes do not contribute to this \ufb01nal\nstate. Thus, one can separately measure the two background contributions. The background estimation\nbased on the e+e\u2212-channel has been discussed in detail in [31]. Good agreement has been demonstrated\nbetween the dilepton invariant mass distributions for the Z \u2192\u00b5\u00b5 and the Z \u2192ee processes. In this paper,\nthe emphasis is given to a similar procedure for the determination of the t\u00aft background.\nThe goal of the second method is to de\ufb01ne a set of event selection criteria which allow for the\nhigher selection ef\ufb01ciency for the particular background process, while simultaneously rejecting all other\nsignal and background contributions. Such background-enriched control sample can be used to better\nunderstand the shape of the invariant dimuon mass distribution.\n7.1\nBackground estimation based on the e+e\u2212and \u00b5\u00b1e\u2213signatures\nThe estimation of the t\u00aft background is important for the analysis channel with at least one b-jet in the\n\ufb01nal state. A study is performed using fast simulation of the t\u00aft background, in order to obtain a reliable\nstatistical accuracy. The detector performance given by the fast simulation has been adjusted such to\nreproduce the performance obtained with the full simulation, as mentioned previously. Based on the\nstudies in [31], the shape of the dilepton invariant mass distribution obtained for the \u00b5 +\u00b5\u2212, e+e\u2212and\n\u00b5\u00b1e\u2213\ufb01nal state in the t\u00aft process are expected to be very similar. The total number of background events\nselected in each of the three \ufb01nal states will be different due to different reconstruction ef\ufb01ciencies for\nmuons and electrons. However, since these ef\ufb01ciencies can be experimentally measured with an accuracy\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1408\n\nof better than 1%, this effect can be corrected for rather precisely. Additional differences may occur due\nto an additional calorimeter activity in presence of electrons. This can be taken into account by rejecting\nall reconstructed jets which overlap with reconstructed electrons.\n (GeV)\n-l\n+l\nm\n100\n150\n200\n250\n300\nEntries / (32 GeV)\n3\n10\n-\n\u00b5\n+\n\u00b5\n+\ne\n-\n\u00b5\n, \n-e\n+\n\u00b5\n-e\n+\ne\na)\nATLAS\n (GeV)\n-l\n+l\nm\n100\n150\n200\n250\n300\nRatio of invariant mass distributions\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n\u00b5\n\u00b5\n / m\nee\nm\n\u00b5\n\u00b5\n / m\n\u00b5\ne\nm\nATLAS\nb)\nFigure 17: (a) The \u00b5+\u00b5\u2212invariant mass distribution (stars) of the t\u00aft background, and its estimates\nobtained from the e+e\u2212(triangles) and \u00b5\u00b1e\u2213(full circles) \ufb01nal states. (b) Corresponding ratios\nof estimated and actual \u00b5+\u00b5\u2212invariant mass distributions.\nFigure 17(a) shows the invariant mass distributions obtained for the \u00b5 +\u00b5\u2212, e+e\u2212and \u00b5\u00b1e\u2213\ufb01nal\nstates in t\u00aft events. The dielectron distribution has been scaled down by a factor 0.842, to account for\nthe difference between the electron and muon reconstruction ef\ufb01ciency. Similarly, the \u00b5 \u00b1e\u2213-distribution\nhas been scaled down by 0.5\u00d70.84. Figure 17(b) shows the corresponding ratios of estimated and actual\n\u00b5+\u00b5\u2212invariant mass distribution. The subtraction of the \u00b5\u00b1e\u2213sample from the total background is\nillustrated in Figure 18 for L =30 fb\u22121, for the analysis requiring identi\ufb01cation of at least one b-jet.\n (GeV)\n\u00b5\n\u00b5\nm\n150\n200\n250\n300\n350\nEntries / (4 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n150\n200\n250\n300\n350\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nbbA\nZ+l jets\nZ+b jets\nWW\ntt\nZZ\n=150 GeV\nA\nm\n=200 GeV\nA\nm\n=300 GeV\nA\nm\nATLAS\nFigure 18: Invariant dimuon mass as in Figure 13(b), after the subtraction of the t\u00aft background\nestimated in the \u00b5\u00b1e\u2213\ufb01nal state. The distributions correspond to an integrated luminosity of\nL =30 fb\u22121.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1409\n\n7.2\nBackground estimation from the control samples\nIn analyses with 0 b-jets in the \ufb01nal state the dominant background is the Z + jet process. Since the\ntopology of this process is very similar to the signal topology, it is rather dif\ufb01cult to de\ufb01ne a set of\nselection criteria which would allow for the extraction of the Z background and simultaneous rejection\nof the signal.\nContrary to that, the t\u00aft process is characterized by a relatively high missing transverse energy and a\nhigh jet activity. Since this background is important for the analysis with at least one jet in the \ufb01nal state,\nthe event selection criteria of this analysis are modi\ufb01ed by selecting only events with a missing transverse\nenergy above 60 GeV and by removing the cut on the \u2211p jet\nT -variable. All other selection criteria remain\nthe same. The purity of the t\u00aft control sample obtained after the described event selection is shown in\nFigure 19(a). All remaining processes are suppressed to a negligible amount. Figures 19(b) and (c)\n (GeV)\n\u00b5\n\u00b5\nm\n100\n150\n200\n250\n300\nEntries / (16 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n100\n150\n200\n250\n300\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nbbA\nZ+l jets\nZ+b jets\nWW\ntt\nZZ\na)\nATLAS\n (GeV)\n\u00b5\n\u00b5\nm\n100\n150\n200\n250\n300\nEntries normalized to unity\n-2\n10\n-1\n10\nb)\nATLAS\ntt control sample\ntt measured\n (GeV)\n\u00b5\n\u00b5\nm\n100\n150\n200\n250\n300\n (measuerd)\n\u00b5\n\u00b5\n (control) / N\n\u00b5\n\u00b5\nN\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\nc)\nATLAS\nFigure 19: (a) t\u00aft control sample (stacked histogram) obtained as described in text. Full circles indi-\ncate the actually measured \u00b5+\u00b5\u2212invariant mass distribution for the t\u00aft background, after applying\nthe standard analysis selection cuts. (b) The measured (full circles) and the control t\u00aft distributions\n(open squares), normalized to the same number of events. (c) The ratio of normalized distributions\nfrom (b).\nshow the t\u00aft background obtained with the selection criteria described in Section 5.2 for at least one\nb-jet in the \ufb01nal state (t\u00aft measured) compared to the distribution obtained from the t\u00aft control sample.\nBoth distributions are normalized to the same number of events. The shape of the t\u00aft background can be\nestimated by the described procedure with an accuracy of 10-20%.\n7.3\nFit function for the parametrization of the background\nThe background can be parametrized by the function fB consisting of a Breit-Wigner and an exponential\ncontribution,\nfB(x) = a1\nx \u00b7\n\u0014\n1\n(x2 \u2212M2\nZ)+M2\nZ\u03932\nZ\n+a2 \u00b7exp(\u2212a3 \u00b7x)\n\u0015\n,\n(1)\nwhere x is the running dimuon mass, while a1, a2 and a3 are the free parametrization parameters. The\nmean MZ and the width \u0393Z of the Breit-Wigner distribution describe the Z resonance. The parameters\na2,3 describing the exponential part can be determined by the \ufb01t on the background estimated from data,\nas described in the previous subsection. The overall normalization factor a1 is determined by the \ufb01t on\nthe side bands of the dimuon mass distribution. Figure 20 shows the result of the \ufb01t on the background\ndistribution obtained after all analysis cuts for the case with at least one b-jet in the \ufb01nal state. The\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1410\n\ntwo dashed lines correspond to the errors on the a2,3 parameters, as obtained from the e+e\u2212data at an\nintegrated luminosity of 10 fb\u22121.\nDimuon Mass (GeV)\n100\n150\n200\n250\n300\n350\n400\n450\n500\n\u22121\nEvents/4 GeV/30fb\n\u22121\n10\n1\n10\n2\n10\n3\n10\nFigure 20: Fit (full line) of the background function fbkg (see Eq. 1) on the background distribution\n(full circles) resulting from the analysis with at least one b-jet in the \ufb01nal state. The dashed lines\nrepresent the shape variations given by the errors on the a2 and a3 parameters, from the \ufb01t on the\ne+e\u2212data.\nThe accuracy of the background parametrization by the described method has been tested by means\nof large number of toy Monte Carlo experiments at different integrated luminosities L . Typical results\nof the background extraction in the mass window from 188-212 GeV are shown in Figure 21 for an inte-\ngrated luminosity of 15 fb\u22121 (left) and 3 fb\u22121 (right). The empirically evaluated expected uncertainty of\nMean \n 0.000032\n\u00b1\n \u22120.001012 \nSigma \n 0.00003\n\u00b1\n 0.02253 \nexpected\n)/BKG\nexpected\n\u2212BKG\nfitted\n(BKG\n\u22120 5 \u22120.4 \u22120 3 \u22120.2 \u22120.1\n\u22120\n0.1\n0.2\n0.3\n0.4\n0.5\nATLAS\nMC Toy Experiments\n0\n10000\n20000\n30000\n40000\n50000\n60000\n70000\n80000\n90000\nMean \n 0.000032\n\u00b1\n \u22120.001012 \nSigma \n 0.00003\n\u00b1\n 0.02253 \nMean \n 5.48e\u221204\n\u00b1\n 2.24e\u221205 \nSigma \n 0.00052\n\u00b1\n 0.04639 \nexpected\n)/BKG\nexpected\n\u2212BKG\nfitted\n(BKG\n\u22120 5 \u22120.4 \u22120.3 \u22120.2 \u22120.1\n\u22120\n0.1\n0 2\n0.3\n0.4\n0.5\nATLAS\nMC Toy Experiments\n0\n100\n200\n300\n400\n500\n600\n700\n800\nMean \n 5.48e\u221204\n\u00b1\n 2.24e\u221205 \nSigma \n 0.00052\n\u00b1\n 0.04639 \nFigure 21: Normalized difference of the expected number of background events (BKGexpected) in\nthe mass window from 188-212 GeV, and the number (BKG fitted) obtained from the \ufb01t method\ndescribed in the text (left) for an integrated luminosity of =15 fb\u22121 and (b) =3 fb\u22121.\nthe background determination from the \ufb01t to data is \u223c8%/\np\nL [fb\u22121]. The variation of the exponential\nshape, due to the errors on the \ufb01t parameters a2 and a3, plays a non-marginal role only for dimuon masses\nabove 300 GeV, decreasing the relative uncertainty to \u223c10%/\np\nL [fb\u22121]. Conservatively the latter ex-\npression will be used in the analyses discussed below. Similar \ufb01t procedure has been performed also for\nthe analysis with 0 b-jets in the \ufb01nal state. Due to the larger amount of background, a smaller background\nuncertainty of \u223c2%/\np\nL [fb\u22121] can be obtained in this case, including the systematic uncertainty on the\nshape parameters a2 and a3.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1411\n\n8\nEvaluation of the signal signi\ufb01cance\nTwo approaches have been applied to evaluate the statistical signi\ufb01cance of the observed signal. The\n\u201d\ufb01xed mass\u201d approach provides the signi\ufb01cance based on the number of signal and background events\nwhich are expected in a given range of the dimuon invariant mass. However, the location of the signal\nmass peak can be determined only if the signal rates are suf\ufb01ciently high, or if the signal is already\ndiscovered in the A/H/h \u2192\u03c4\u03c4 decay channel. In a more general \u201d\ufb02oating mass\u201d approach, no constraints\nare applied on the dimuon invariant mass.\nThe number of signal and background events can be determined from the \ufb01t of the function fSB to\nthe data,\nfSB(x) = p0 \u00b7 fB + p1 \u00b7 fS = p0 \u00b7 fB + p1 \u00b7\n1\n\u03c3A\n\u221a\n2\u03c0 \u00b7exp\n\u0012\n\u2212(x\u2212p2)2\n2\u03c3 2\nA\n\u0013\n,\n(2)\nwhere fS is the Gaussian distribution describing the signal. p2 is the mass of the signal (which can\nbe \ufb01xed or left as a free, \u201d\ufb02oating\u201d parameter) and \u03c3A is the width of the Higgs resonance. p0 is the\nbackground scale and p1 the total number of signal events. The number of signal (NS) and background\n(NB) events used for the calculation of the signal signi\ufb01cance is extracted from the \ufb01t, by integration in\na window of \u00b12\u03c3A. The signal signi\ufb01cance is evaluated by means of the pro\ufb01le likelihood method [32],\nusing the obtained number of signal and background events as an input and taking into account the\nbackground uncertainty (10%/\np\nL [fb\u22121]) as discussed in Section 7.3 above.\nThe results obtained for the signal signi\ufb01cance have been cross-checked by the large number of\nMonte Carlo pseudoexperiments for several different integrated luminosities. The pseudoexperiments\nare based on the Monte Carlo distributions and are divided into the \u201dbackground-only\u201d experiments\n(BO), containing only background contributions, and the \u201dsignal-plus-background\u201d experiments (SpB)\nhaving both the signal and the background contribution. In addition to the pro\ufb01le likelihood calculation\nin each of these experiments, the signal signi\ufb01cance can be estimated also from the log-likelihood ratios.\nThe log-likelihood ratio lnQBO and lnQSpB, both de\ufb01ned as (NS + NB)ln NS+NB\nNB\n\u2212NS, are evaluated for\neach BO- and SpB-pseudoexperiment. The signal signi\ufb01cance is obtained from the probability of a Type-\nII error, de\ufb01ned by the fraction of BO pseudoexperiments which have a log-likelihood ratio lnQBO larger\nthan the median of the lnQSpB-distribution. The probability of a Type-I error, i.e. the number of SpB-\npseudoexperiments which fall below the median of the lnQBO-distribution, was used to determine the\n95% CL limits.\nFigure 22(left) shows the comparison of the signal signi\ufb01cances obtained in the \ufb01xed-mass approach.\nThe solid line shows the results of the pro\ufb01le likelihood method, while the dots are the results given by\nthe Type-II error probabilities obtained in the pseudoexperiments. At very low luminosities, the pro\ufb01le-\nlikelihood estimation based on average values seems to slightly overestimate the signi\ufb01cance. However,\nat luminosities close to those needed for the 5\u03c3-signi\ufb01cance, the two calculations give equivalent re-\nsults. Figure 22(right) shows the degradation of the signal signi\ufb01cance observed once the \ufb02oating-mass\napproach is applied in which the Higgs mass is left as a free parameter of the \ufb01t (usually reffered to as\na look-elsewhere effect). In general, the ratio of the Type-II error probabilities obtained from the \ufb01xed-\nmass and the \ufb02oating-mass approaches is constant and approximatelly equal to the explored mass range\ndivided by the signal mass width. Correspondingly, the ratio of signal signi\ufb01cances is lower at low lu-\nminosities, while the difference between the two approaches is reduced to 5% or less at the luminosities\nclose to those needed for a 5\u03c3-discovery.\n8.1\nIn\ufb02uence of the systematic uncertainties on the signal signi\ufb01cance\nIn order to include the systematic uncertainties in the calculation of the signal signi\ufb01cance, one should\nperform additional large number of pseudoexperiments for each of the systematic effects. However, the\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1412\n\n)\n-1\nLuminosity (fb\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nSignificance\n0\n1\n2\n3\n4\n5\n6\nProfile L on average expectation\nFixed Mass Type II error\nATLAS\n)\n-1\nLuminosity (fb\n1\n10\n2\n10\nfixed mass\n/Significance\nfloat mass\nSignificance\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n=200 GeV, 0 bjets\nA\nm\n=200 GeV, >=1 bjets\nA\nm\n=110 GeV, >=1 bjets\nA\nm\n=150 GeV, >=1 bjets\nA\nm\n=300 GeV, >=1 bjets\nA\nm\nATLAS\nFigure 22:\n(left) Signal signi\ufb01cance obtained in the \ufb01xed-mass approach for the signal at\nmA=200 GeV and tan\u03b2=30, as a function of integrated luminosity. The full line corresponds to\nthe results obtained by the pro\ufb01le likelihood method using the average number of expected signal\nand background events, while the dots show the results obtained from the Type-II error probability\nfrom a large amount of pseudoexperiments. Both estimations include the background uncertainty\nfrom the fSB-\ufb01t. (right) Ratio of signal signi\ufb01cances obtained with the \ufb02oating- and the \ufb01xed-mass\napproach, as a function of the integrated luminosity.\ndifference between the signal signi\ufb01cance in the \ufb02oating-mass and in the \ufb01xed-mass approach is small\ncompared to the effect of the additional systematic uncertainties. Thus, in the following the \ufb01xed-mass\napproach is used and the full treatment of the look-elsewhere effect is left for the future studies.\nBy means of the background estimation from the data, the amount of the background events under-\nneath the signal can be determined with an accuracy of \u223c10%/\np\nL [fb\u22121], as described in Section 7.\nThis can be achieved independently of the systematic uncertainties discussed in Section 6.\nTherefore, the in\ufb02uence of the systematic uncertainties on the signal signi\ufb01cance is given by the\ncorresponding changes in the expected number of signal and background events. The numbers entering\nthe signi\ufb01cance calculation are therefore changed accordingly, taking into account that the systematic\nuncertainty is different for different background processes. The signal signi\ufb01cance is calculated sepa-\nrately for each systematic effect and the deviations from the original signal signi\ufb01cance are added in\nquadrature. Figure 23 shows the signal signi\ufb01cance obtained for two different masses mA, as a function\nof tan\u03b2. The contributions of the uncertainty in the background determination from the \ufb01t to data and of\nthe experimental systematic uncertainties to the expected signi\ufb01cance are shown separately.\n9\nDiscovery potential and the exclusion limits\nThe previously described methods for the evaluation of the signal signi\ufb01cance and of the exclusion limits\nhave been applied to all mass points studied. Table 7 summarizes the signal signi\ufb01cances obtained for\ndifferent signal mass points at tan\u03b2=30 and L =10 fb\u22121, for the analysis with 0 b-jets and with at least\none b-jet in the \ufb01nal state. The luminosities needed to reach the 5\u03c3 signal signi\ufb01cance and the 95%\nCL exclusion limit are given in Table 8, for different signal masses at tan\u03b2=30.\nThe results shown so\nfar do not include the possible degradation due to the in\ufb02uence of pile-up and cavern background. The\ndegraded resolution of the missing transverse energy is expected to cause a \u223c15% change in the \ufb01nal\nselection of the signal and the Z background. The t\u00aft background is characterized by a large Emiss\nT\nand is\ntherefore somewhat less sensitive to the Emiss\nT\nperformance under pile-up (\u223c10% change in the selection\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1413\n\ntan \u03b2\n0\n10\n20\n30\n40\n50\n60\n70\nSignificance\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n=150 GeV\nA\n, m\n\u22121\nL=10 fb\nNo background uncertainty\nBkg from the fit to data\nSystematics included\nATLAS\ntan \u03b2\n0\n10\n20\n30\n40\n50\n60\n70\nSignificance\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n=300 GeV\nA\n, m\n\u22121\nL=10 fb\nNo background uncertainty\nBkg from the fit to data\nSystematics included\nATLAS\nFigure 23: Signal signi\ufb01cance as a function of tan\u03b2 for the integrated luminosity of 10 fb\u22121 and\nmA=150 GeV (left) and mA=300 GeV (right). The dotted curves are obtained assuming a negligible\nerror of the background determination. The dashed curves show the result once the background\nuncertainty is taken into account, as obtained from the \ufb01t to the data. The solid curves additionally\ninclude the systematic uncertainties. The width of the solid curves indicates the errors in the\nbackground shape parametrization.\nSignal signi\ufb01cance\nmA\nNo background\nBackgr. uncertainty\nExperimental\nTheoretical\n(GeV)\nuncertainty\nof 10%/\np\nL [fb\u22121]\nsyst. uncertainty\nuncertainty\n0b\n\u22651b\n0b\n\u22651b\n0b\n\u22651b\n0b\n\u22651b\n110\n5.5\n6.4\n2.7\n4.5\n2.4 - 3.1\n3.8 - 5.3\n2.2 - 3.2\n3.7 - 5.3\n130\n5.6\n6.6\n3.6\n5.3\n3.4 - 3.8\n4.8 - 5.9\n3.1 - 4.1\n4.5 - 6.1\n150\n5.2\n5.8\n4.1\n5.2\n3.9 - 4.3\n4.8 - 5.6\n3.9 - 4.7\n4.5 - 5.9\n200\n3.1\n3.8\n2.8\n3.6\n2.7 - 2.9\n3.3 - 3.9\n2.5 - 3.1\n3.2 - 4.0\n300\n1.2\n1.8\n1.1\n1.8\n1.0 - 1.2\n1.6 - 2.0\n1.0 - 1.2\n1.7 - 1.9\n400\n0.5\n0.8\n0.5\n0.8\n0.4 - 0.5\n0.7 - 0.9\n0.4 - 0.5\n0.7 - 0.9\nTable 7: Signal signi\ufb01cance for signal at different mass points, with tan\u03b2=30 and L =10 fb\u22121.\nThe numbers are shown for different levels of the background uncertainty. For degenerate A, H\nand h boson states with the same mass, the production rates have been summed.\nef\ufb01ciency). Table 9 summarizes the results obtained with pile-up effects taken into account. Only small\nchanges are observed compared to the previous results.\nThe results shown in Tables 7 and 8 can be extrapolated to other tan\u03b2 values. The only difference\nwhich occurs for the a given signal mass point when changing the tan\u03b2 value is the change of the\nproduction rates and of the natural width of the A/H/h bosons. In the (mA \u2212tan\u03b2) plane which is of\ninterest for this analysis, the resolution of the mass measurement is mostly dominated by the experimental\nresolution. Nevertheless, the variation of the natural Higgs width is taken into account in the calculation\nby increasing the background contribution correspondingly to the expected change of the mass window.\nUsing the previously described production cross-sections and branching ratios, the 5\u03c3-discovery\ncurves are obtained as shown in Figure 24(left) separately for the analysis with 0 and with at least one b-\njet in the \ufb01nal state. The luminosity needed for the exclusion of the signal hypothesis at a 95% con\ufb01dence\nlevel is shown in Figure 24(right).\nThe signatures with the b-jets in the \ufb01nal state allow for the highest discovery potential. The 0 b-jet\n\ufb01nal state plays nevertheless an important role. Since the search in this \ufb01nal state is uncorrelated to the\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1414\n\nmA\nL [fb\u22121] for a 5\u03c3 discovery\nL [fb\u22121] for 95% C.L. exclusion\n(GeV)\n(No systematics)\nNo systematics\nWith systematics\n0b\n\u22651b\ncomb.\n0b\n\u22651b\ncomb.\n0b\n\u22651b\ncomb.\n110\n20.9\n12.2\n7.7\n1.8\n2.0\n0.9\n2.7\n2.8\n1.4\n130\n12.0\n8.9\n5.1\n1.9\n1.4\n0.8\n3.6\n1.9\n1.2\n150\n10.5\n9.3\n4.9\n1.6\n1.5\n0.8\n2.2\n2.0\n1.0\n200\n25.9\n19.1\n11.0\n3.7\n3.1\n1.7\n4.9\n3.8\n2.1\n300\n174.6\n81.6\n55.6\n38.6\n13.8\n10.2\n43.8\n16.4\n12.0\n400\n1124.0\n444.8\n318.7\n320.0\n75.1\n60.8\n361.0\n86.5\n69.8\nTable 8: Integrated luminosity (in fb\u22121) needed for a 5\u03c3 signal signi\ufb01cance and 95% CL exclusion\nof the signal hypothesis, shown for the signal at tan\u03b2=30. For degenerate A, H and h boson states\nwith the same mass, the production rates have been summed.\nmA (GeV)\nL [fb\u22121] for 5\u03c3 discovery\nL [fb\u22121] for 95% CL exclusion\n110\n8.7\n1.9\n130\n5.8\n1.6\n150\n5.6\n1.3\n200\n12.5\n2.6\n300\n62.9\n13.6\n400\n359.5\n87.5\nTable 9: Luminosity needed for the 5\u03c3 signal signi\ufb01cance (no systematics) and the 95% CL\nexclusion of the signal hypothesis (with systematics), obtained for the combined analyses, with\nthe pile-up effects taken into account. The results are shown for tan\u03b2=30.\n (GeV)\nA\nm\n50\n100\n150\n200\n250\n300\n350\n400\n450\n discovery\n\u03c3\n\u03b2\ntan for 5\n0\n10\n20\n30\n40\n50\n60\nmax\nh\n\u22121\nm\n\u2212 scenario\nL=10 fb\n>=1 b\u2212jet, With exp. systematics\n5 discovery contour\n\u03c3\n>=1 b\u2212jet, Theoretical uncertainty\n0 b\u2212jets, With exp. systematics\n0 b\u2212jets, Theoretical uncertainty\nATLAS\n (GeV)\nA\nm\n50\n100\n150\n200\n250\n300\n350\n400\n450\ntan for 95%CL Exclusion\n\u03b2\n0\n10\n20\n30\n40\n50\n60\n>=1 b\u2212jet, No systematics\n>=1 b\u2212jet, With systematics\nmax\nh\n\u22121\n0 b\u2212jets, No systematics\nm\n\u2212 scenario\nL=10 fb\n95% CL exclusion contour\n0 b\u2212jets, With systematics\nATLAS\nFigure 24: tan\u03b2 values needed for the 5\u03c3-discovery (left) and for the 95% CL exclusion of the\nsignal hypothesis (right), shown in dependence on the A boson mass.\nprevious one, one can quadratically add the signal signi\ufb01cances obtained from the two analyses. The\n5\u03c3-discovery curves obtained from the combination of both analyses, as well as the combined 95% CL\nexclusion limits are shown in Figure 25. At an integrated luminosity of 10 fb\u22121, the discovery can be\nreached for mA masses up to 350 GeV with tan\u03b2 values between 25 and 60. For mA masses below\n110 GeV the sensitivity drops rapidly as shown in Ref [5], due to the increasing Drell-Yan background\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1415\n\n (GeV)\n (GeV)\nA\nm\n50\n50\n100\n100\n150\n150\n200\n200\n250\n250\n300\n300\n350\n350\n400\n400\n450\n450\n discovery\n discovery\n\u03c3\n\u03b2\n\u03c3\n\u03b2\ntan for 5\n0\n10\n10\n20\n20\n30\n30\n40\n40\n50\n50\n60\n60\n\u22121\nL=10 fb\nmax\nh\n\u22121\nCombined Analysis\nCombined Analysis\nm\n\u2212 scenario\nWithout Systematics\nWithout Systematics\nL=30 fb\nWith Experimental Systematics\nWith Experimental Systematics\nTheoretical Uncertainty\nTheoretical Uncertainty\nATLAS\n discovery contour\n discovery contour\n\u03c3\n5\n (GeV)\nA\nm\n50\n100\n150\n200\n250\n300\n350\n400\n450\n\u03b2\ntan for 95% CL Exclusion\n0\n10\n20\n30\n40\n50\n60\nCombined Analysis\nNo Theore ical Uncertainty\nWith Theoretical Uncertainty\nATLAS\n\u22121\nL=10 fb\nmax\nh\n95% CL exclusion contour\n\u22121\nm\n\u2212 scenario\nL=30 fb\nFigure 25:\nCombined analyses results:\n(left) tan\u03b2 values needed for the 5\u03c3-discovery at\nL =10 fb\u22121 and L =30 fb\u22121, shown in dependence on the A boson mass and (right) combined\n95% CL exlucion limits.\nclose to the pole mass of the Z boson. The tan\u03b2 values above \u223c16 can be excluded already with 10 fb\u22121\nof integrated luminosity in case of the Higgs boson masses up to 200 GeV.\n10\nConclusions\nIn this note, the potential for the discovery of the neutral MSSM Higgs boson is evaluated in the dimuon\ndecay channel. As opposed to the Standard Model predictions, the decay of neutral MSSM Higgs bosons\nA, H and h into two muons is strongly enhanced in the MSSM. In addition, the \u00b5 +\u00b5\u2212\ufb01nal state provides\na very clean signature in the detector.\nThe event selection criteria are optimized in the signal mass range from 100 to 500 GeV, separately\nfor the signatures with 0 b-jets and with at least one b-jet in the \ufb01nal state. The obtained combined result\nshows that an integrated luminosity of 10 fb\u22121 allows for the discovery for mA masses up to 350 GeV\nwith tan\u03b2 values between 30 and 60. Three times higher luminosity allows for an increased sensitivity\ndown to tan\u03b2=20. The theoretical and detector-related systematic uncertainties are shown to degrade\nthe signal signi\ufb01cance by up to 20%. This takes into account that the background contribution can be\nestimated from the data with an accuracy of \u223c2-10%/L [fb\u22121].\nReferences\n[1] ATLAS Collaboration, \u201dIntroduction on Higgs Boson Searches\u201d, this volume.\n[2] ATLAS Collaboration, \u201dDiscovery Potential of h/A/H \u2192\u03c4+\u03c4\u2212\u2192\u2113+\u2113\u22124\u03bd\u201d, this volume.\n[3] ALEPH, DELPHI, L3 and OPAL Collaborations, The LEP Working Group for Higgs Boson\nSearches, \u201dSearch for neutral MSSM Higgs bosons at LEP\u201d, LHWG Note 2005-01.\n[4] J. Nielsen, The CDF and D0 Collaborations, \u201dTevatron searches for Higgs bosons beyond the Stan-\ndard Model\u201d, FERMILAB-CONF-07-415-E, Proceedings of the Hadron Collider Physics Sympo-\nsium 2007 (HCP 2007), La Biodola, Isola d\u2019Elba, Italy, May 20-26, 2007.\n[5] S. Gentile, H. Bilokon, V. Chiarella, G. Nicoletti, Eur.Phys.J.C 52 (2007) 229\u2013245.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1416\n\n[6] M. Carena, S. Heinemeyer, C.E.M. Wagner and G. Weiglein, Eur.Phys.J.C 26 (2003) 601\u2013607.\n[7] S. Heinemeyer, W. Hollik, G. Weiglein, Comput.Phys.Commun. 124 (2000) 76\u201389.\n[8] S. Dittmaier, M. Kramer and M. Spira, Phys.Rev.D 70 (2004) 074010.\n[9] S. Dawson, C.B. Jackson, L. Reina and D. Wackeroth, Phys.Rev.Lett. 94 (2005) 031802.\n[10] D. Dicus, T. Stelzer, Z. Sullivan and S. Willenbrock, Phys.Rev.D 59 (1999) 094016.\n[11] R.V. Harlander and W.B. Kilgore, Phys.Rev.D 68 (2003) 013001.\n[12] K.A. Assamagan et al., \u201dThe Higgs Working Group: Summary report 2003\u201d, Proceedings of the\n3rd Les Houches Workshop: Physics at TeV Colliders, Les Houches, France, 26 May - 6 Jun 2003,\narXiv:0406152 [hep-ph].\n[13] T. Sj\u00a8ostrand, P. Eden, C. Friberg, L. L\u00a8onnblad, G. Miu, S. Mrenna and E. Norrbin,\nCom-\nput.Phys.Commun. 135 (2001) 238\u2013259.\n[14] T. Gleisberg, S. H\u00a8oche, F. Krauss, A. Sch\u00a8alicke, S. Schumann, J. Winter, JHEP 0402 (2004) 056.\n[15] S. Catani, F. Krauss, R. Kuhn, and B. R. Webber, JHEP 11 (2001) 063.\n[16] F. Krauss, A. Sch\u00a8alicke, S. Schumann, G.Soff, Phys.Rev.D 70 (2004) 114009.\n[17] D. Rebuzzi, M. Schumacher et al., \u201dCross sections for Standard Model processes to be used in the\nATLAS CSC notes\u201d, ATL-COM-PHYS-2008-077, Geneva, CERN, 2008.\n[18] S. Frixione and B.R. Webber, JHEP 0206 (2002) 029;\nS. Frixione, P. Nason and B.R. Webber, JHEP 0308 (2003) 007.\n[19] B.P. Kersevan, E. Richter-Was, Preprint: TPJU-6-2004, arXiv:0405247 [hep-ph].\n[20] S. Agostinelli et al., Nucl.Instrum.Meth.A 506 (2003) 250-303;\nJ. Allison et al., IEEE Transactions on Nuclear Science 53 No.1 (2006) 270-278.\n[21] E. Richter-Was, D. Froidevaux, L. Poggioli, \u201dATLFAST 2.0 a fast simulation package for ATLAS\u201d,\nATL-PHYS-98-131, Geneva, CERN, 1998.\n[22] ATLAS Collaboration, \u201dMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples\u201d, this volume;\nS. Baranov et al., \u201dEstimation of radiation background, impact on detectors, activation and shielding\noptimization in ATLAS\u201d, ATLAS-GEN-2005-011, Geneva, CERN 2005.\n[23] C. Zeitnitz and T.A. Gabriel, Nucl.Instrum.Meth.A 349 (1994) 106\u2013111.\n[24] A. Fasso, A. Ferrari, J. Ranft, and P.R. Sala, \u201dFLUKA: a multi-particle transport code\u201d, CERN-\n2005-10, Geneva, CERN, 2005.\n[25] ATLAS Collaboration, \u201dThe ATLAS Experiment at the CERN Large Hadron Collider\u201d, JINST 3\n(2008) S08003.\n[26] ATLAS Collaboration, \u201dCross-Sections, Monte Carlo Simulations and Systematic Uncertainties\u201d,\nthis volume.\n[27] ATLAS Collaboration, \u201db-Tagging Performance\u201d, this volume.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1417\n\n[28] ATLAS Collaboration, \u201dMeasurement of Missing Tranverse Energy\u201d, this volume;\nATLAS Collaboration, \u201dDetector Level Jet Corrections\u201d, this volume.\n[29] ATLAS Collaboration, \u201dPerformance of the Muon Trigger Slice with Simulated Data\u201d, this volume.\n[30] ATLAS Collaboration, \u201dIn-Situ Determination of the Performance of the Muon Spectrometer\u201d, this\nvolume.\n[31] S. Gentile, H. Bilokon, V. Chiarella G. Nicoletti, \u201dData based method for Z \u2192\u00b5 +\u00b5\u2212background\nsubtraction in ATLAS detector at LHC\u201d, ATL-PHYS-PUB-2006-019, Geneva, CERN 2006.\n[32] W.A. Rolke, A.M. Lopez, J. Conrad, Nucl.Instrum.Meth.A 551 (2005) 493\u2013503.\nHIGGS \u2013 SEARCH FOR THE NEUTRAL MSSM HIGGS BOSONS IN THE DECAY CHANNEL . . .\n1418\n\nSensitivity to an Invisibly Decaying Higgs Boson\nAbstract\nMany extensions of the Standard Model include Higgs bosons decaying pre-\ndominantly or partially to non-interacting particles such as the SUSY Lightest\nSupersymmetric Particle (LSP). To set limits on the production cross-section\ntimes the branching fraction to invisible decay products of such Higgs bosons\nwith the ATLAS detector requires an examination of speci\ufb01c production modes\nsuch as the associated production (ZH) or the vector boson fusion (VBF) pro-\ncess. The predominant Standard Model backgrounds for these processes are\nZZ \u2192\u2113\u2113\u03bd\u03bd for the ZH channel and jets from QCD processes and W \u00b1 or Z\nbosons produced in association with jets for the VBF channel. The sensitivity\nto an invisibly decaying Higgs boson is investigated in this paper using fully\nsimulated ATLAS data for both signal and background. The ATLAS potential\nfor triggering these events is also discussed.\n1\nIntroduction\nSome extensions of the Standard Model predict that Higgs bosons could decay into stable neutral weakly\ninteracting particles, leading to invisible Higgs boson decays. The Higgs boson decay products could\nbe for example neutralinos, gravitinos, gravitons or Majorons [1-3]. In the case of the Minimal Su-\npersymmetric Standard Model (MSSM), if R-parity is conserved, Higgs bosons decaying into a pair of\nneutralinos may in some cases even dominate [1]. Being the lightest supersymmetric particles, neutrali-\nnos would be stable and would leave the detector without decaying, remaining invisible. If R-parity is\nviolated, then Higgs bosons could decay into Majorons, which would interact too weakly to allow detec-\ntion [2]. Some theories with extra dimensions also predict invisible Higgs boson decays, and have the\nadded advantage of generating neutrino masses [3]. This search is sensitive to any boson coupling to Z\nor W and decaying invisibly. The combined LEP Higgs boson mass limit in this channel is 114.4 GeV\n[4].\nAt the Large Hadron Collider, Higgs boson production could occur through several mechanisms.\nTo select and identify events with an invisibly decaying Higgs boson one must be able to trigger on a\nsignature that is visible in the event. This is possible for channels such as Vector Boson Fusion (VBF)\nqqH [5], t\u00aftH [6] and the associated production processes, ZH and W \u00b1H [7, 8]. Although gluon fusion\nhas a much higher Higgs boson production cross-section than these modes [9], it is not possible to trigger\non these events when the Higgs boson decays invisibly.\nIn this paper, the ATLAS sensitivity to an invisibly decaying Higgs boson is determined in a way that\ndoes not depend on a speci\ufb01c extension of the Standard Model. The analysis uses the variable \u03be 2 which\nis de\ufb01ned as,\n\u03be 2 = BR(H \u2192inv.)\u03c3BSM\n\u03c3SM\n(1)\nwhere \u03c3BSM represents the \u201cBeyond the Standard Model\u201d cross-section and \u03c3SM represents the Standard\nModel cross-section. In the case for which the Higgs boson decays entirely to the invisible mode, \u03be 2\nis the ratio between the non-Standard Model cross-section and the Standard Model cross-section. Only\ntwo of the three possible production modes are considered in this paper, VBF and associated production.\nIn addition, for associated production, only the ZH mode is considered as the background to the W \u00b1H\nsignal is overwhelming [10].\nIn this paper, the Monte Carlo samples, for both the VBF and the ZH channels, the trigger, the event\nselection, the systematic uncertainties and the results are discussed. We conclude by summarizing the\nlimits on \u03be 2 for an invisibly decaying Higgs boson.\n1419\n\nThis analysis compares signals and backgrounds that have been generated using Standard Model\nprocesses. The Higgs boson signal events are simulated to be invisible by changing the properties of the\nHiggs boson decay chain. In reality an invisibly decaying Higgs boson would be expected to result from\na process not contained within the Standard Model, and in this case backgrounds associated with this new\nphysics would be important. However, consideration of \u201cBeyond the Standard Model\u201d backgrounds is\nbeyond the scope of this paper as they would have to be considered in the context of each speci\ufb01c model.\nThis analysis assumes Standard Model backgrounds and serves as a limiting case for the indication of a\nparticle that behaves like a Higgs boson that is not consistent with the Standard Model.\n2\nThe Vector Boson Fusion qqH production channel\nThe vector boson fusion (VBF) channel has the second largest production mode after gluon fusion and\nhas the largest production cross-section for observable invisible Higgs boson decays. The VBF invisible\nHiggs boson production mode, Figure 1, is characterized by two outgoing jets resulting from the inter-\nacting quarks, and large missing transverse energy from the Higgs boson. The topology of the jets is\nparticularly useful in selecting the events as the jets are preferentially separated in pseudo-rapidity (\u03b7)\nand are correlated in the azimuthal angle \u03c6. In addition, the lack of colour \ufb02ow between the two jets leads\nto minimal jet activity between the two tagging jets which is potentially useful for selecting events. At\nhigh luminosity however, central jet activity resulting from overlapping events may become problematic\nfor cuts based on this event characteristic.\nFigure 1: Feynman diagram of the VBF process. The V represents either a Z or W boson.\nThe study of the VBF channel for this paper includes a mass scan with an estimate of the sensitivity to\nHiggs boson masses between 110 to 250 GeV. This is based on fully reconstructed signal and background\nevents. In addition to the sensitivity, the trigger acceptance for this channel has been investigated.\n2.1\nMonte Carlo generation for the VBF analysis\nSignal and background samples were generated using the standard version of ATLAS software used for\nthis set of papers. The samples were used to determine the sensitivity of ATLAS to an invisible Higgs\nboson, taking into account the trigger and analysis ef\ufb01ciencies. A number of backgrounds with signatures\nsimilar to the signal have been studied and are listed here. In all cases, \u2113represents e or \u00b5.\n1. Dijet production from QCD processes form a major background due to the very large cross-section\nfor these processes. Fake missing energy measurements can arise from poorly instrumented re-\ngions or inef\ufb01ciencies in the detector.\n2. W+jet processes with W \u2192\u2113\u03bd mimic the signal when the lepton is outside the detector acceptance.\nThe neutrino provides the missing energy signature.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1420\n\nHiggs boson Mass [GeV ]\nCross-section [pb]\n# Events\nGenerator\n110\n4.63\n10k\nJIMMY\n130\n3.96\n30k\nJIMMY\n130\n3.93\n10k\nPYTHIA6.4\n200\n2.41\n10k\nJIMMY\n250\n1.79\n10k\nJIMMY\nTable 1: Invisible Higgs boson samples generated for this analysis. Leading-order cross-sections\nfor the Higgs boson produced via Vector Boson Fusion were evaluated by the ATLAS Higgs\nWorking group [15].\n3. Z+jet processes with Z \u2192\u03bd\u03bd constitute an irreducible background.\n4. Z+jet with Z \u2192\u2113\u2113forms a background to the signal when the leptons are not within the acceptance\nof the detector.\nEvent generation for the VBF channel has proved challenging given that the predicted \u03b7 distributions\nof tagging jets differ greatly according to the event simulation model used. The HERWIG-JIMMY\npackage [11], [12], [13] represents an average response of the available models and has been used to\ngenerate data for the Higgs boson mass scan. Signal events have been generated with both HERWIG\nand PYTHIA [14] at a Higgs boson mass of 130 GeV to estimate the contribution of this effect to the\nsystematic uncertainty. To generate an invisible Higgs boson sample, the Higgs boson is forced to decay\ninto two Z bosons which are subsequently forced to decay into neutrinos. The set of data samples\nproduced for this analysis is summarized in Table 1. The VBF signal Monte-Carlo was produced to\nleading order. The difference between LO and NLO cross-section is negligible, \u223c1%[9], therefore the\nLO cross-sections were been used for the signal in this note. Table 1 includes the Standard Model VBF\nHiggs boson production cross-section that were used [9].\nFor an ideal detector, event selection cuts ef\ufb01ciently remove the QCD dijet background. However,\nthis background is considered because of the large cross-section for the process and the presence of\npoorly instrumented regions and dead regions generating false missing transverse energy (Emiss\nT\n) signals.\nIn order to provide enough statistics throughout the full transverse momentum (pT) spectrum, the QCD\nbackground was divided into several pT ranges to produce several sub-samples, of approximately equal\nnumber of events, as shown in Table 2 [16]. The surviving background comes from the high pT bins\nallowing reasonable statistics in the \ufb01nal sample. Thus the binning is used to generate the QCD back-\nground within a reasonable amount of computer time and allow for the very high rejection factor for this\nbackground in this analysis.\nIn previous ATLAS studies of the invisible Higgs boson produced via the VBF process, the PYTHIA\npackage has been used to generate both the W+jet and Z+jet backgrounds. However, the PYTHIA\nimplementation for these backgrounds only includes the matrix element term for the qq \u2192gV and qg \u2192\nqV processes. The PYTHIA implementation tends to underestimate the Z+2jets process because it does\nnot include a complete matrix element calculation. In contrast, ALPGEN [17] provides an exact matrix\ncalculation at tree level for up to 3 partons. For this reason, ALPGEN was used to produce both the W+jet\nand Z+jet backgrounds. Within ALPGEN, there are two different Z+jet implementations, one which only\nincludes QCD matrix element terms and the second which includes the QCD and EW matrix element\nterms. In the second case, only on-shell bosons are created without Z/\u03b3\u2217interference, in contrast, the \ufb01rst\ncase does include these effects. By comparing events generated with the two different implementations it\nwas found that the QCD-only process underestimates the background by \u223c25%. The effect of a non-zero\nZ boson width was checked by varying the Z boson mass. This showed that the result was insensitive to\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1421\n\nJet Sample\n\u03c3(pb)\npTrange [GeV ]\nJ0\n1.76\u00d71010\n8-17\nJ1\n1.38\u00d7109\n17-35\nJ2\n9.33\u00d7107\n35-70\nJ3\n5.88\u00d7106\n70-140\nJ4\n3.08\u00d7105\n140-280\nJ5\n1.25\u00d7104\n280-560\nJ6\n3.60\u00d7102\n560-1120\nJ7\n5.71\u00d7100\n1120-2240\nTable 2: Cross-section and pT range for the QCD dijet background samples generated with\nPYTHIA. The cross-sections given in the second column are for the speci\ufb01c pT range with no\nother cuts.\nthe use of on-shell bosons. Therefore, all ALPGEN samples used in this study were generated using the\noption that included both QCD+EW terms.\nFor the Z+jet background, three samples were produced for each of the two decay modes, Z \u2192\u03bd\u03bd and\nZ \u2192\u2113\u2113. Two exclusive samples were produced for the one and two parton \ufb01nal states and one inclusive\nsample was produced for three or more partons. Default ALPGEN settings were used to generate events\nexcept for a cut to remove very low Emiss\nT\nevents by setting Emiss\nT\n> 10 GeV and a change in acceptance\nto ensure complete \u03b7 coverage by opening the phase space setting for both jets and leptons (|\u03b7j| < 6 and\n|\u03b7\u2113| < 6).\nIn this study, only the leptonic decay of the W boson from the W+jet background was considered.\nThe Emiss\nT\narises from a combination of the Emiss\nT\nassociated with the neutrino and the lepton energy in\nthe case where the lepton escapes detection. The W+jet background was generated in the same manner\nas for the Z+jet background.\n2.2\nTrigger\nThe major challenge for triggering candidate events for the VBF invisible Higgs boson analysis is to\nretain signal events whilst reducing the very large QCD background to an acceptable level. These prob-\nlems are particularly acute with the \ufb01rst level trigger (L1) which can easily be overwhelmed by the QCD\nbackground. A trigger for these signal events is possible using a relatively high Emiss\nT\ncut while selecting\none or two jets of moderate transverse energy. For triggers of this type, QCD backgrounds dominate.\nIn order to produce an acceptable rate for the High Level Trigger (HLT), the trigger menu items used to\nselect invisible Higgs boson events should add no more than a few Hz of trigger rate, even at the highest\nluminosities.\nThe trigger study of this note is based on the standard full ATLAS simulation of the L1 trigger.\nThe HLT has not been considered, as at the time of the study HLT algorithms for Emiss\nT\nhad not been\nfully implemented and there had been no simulation of forward jets. Jets are classi\ufb01ed into central jets\n|\u03b7| < 3.2 and forward jets 3.2 < |\u03b7| < 5.\nData for the trigger study consisted of the sample of VBF Invisible Higgs boson events with a Higgs\nboson mass of 130 GeV produced using HERWIG and a sample of QCD dijet produced using PYTHIA\nas described in Section 2.1. The results of this study are shown in Table 3 for 1031 cm\u22122 s\u22121 luminosity.\nThe acceptances shown in Table 3 give the effect of the trigger on the VBF Higgs boson samples used\nin the VBF analysis. As such the acceptance is de\ufb01ned as the number of signal events that survive both\nthe trigger and the data selection cuts described in Section 2.3.1, divided by the number of events that\nsurvive the selection cuts alone. The trigger rates in Table 3 are the expected raw rates for the speci\ufb01c\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1422\n\nTrigger Menu\nAcceptance[%]\nRates[Hz] for\nnormalized\nL = 1031 cm\u22122 s\u22121\nto of\ufb02ine cuts\nL1 XE60\n99\n5.0 \u00b1 1.3\nL1 XE70\n98\n1.5 \u00b1 0.6\nL1 XE80\n96\n0.6 \u00b1 0.1\nL1 XE100\n84\n0.2 \u00b1 0.1\nL1 XE120\n70\n0.1 \u00b1 0.1\nL1 FJ23+XE70\n78\n0.9 \u00b1 0.6\nL1 J23+L1 XE70\n83\n1.4 \u00b1 0.6\nL1 J23+L1 XE100\n73\n0.2 \u00b1 0.1\nL1 FJ23+L1 XE100\n66\n0.0 \u00b1 0.0\nL1 FJ23+L1 J23+L1 XE70\n62\n0.9 \u00b1 0.6\nL1 FJ23+L1 J23+L1 XE100\n55\n0.0 \u00b1 0.0\nTable 3: Signal acceptance and level one trigger rates for the VBF invisible Higgs boson channel\nbased on full ATLAS simulations and with mH = 130 GeV . The L1 trigger menu items are Emiss\nT\n(L1 XE) central jet (L1 J) and forward jet (L1 FJ), see text. The number following the menu\nobject indicates the trigger threshold given in GeV. Both single and combined triggers are shown\nin this Table. The values are given for a luminosity of 1031 cm\u22122 s\u22121 and do not account for\npile-up effects.\ntrigger. One expects an overlap with other trigger signatures such that the additional rate produced by\nthese signatures will be less than the calculated raw rates.\nThe numbers given in Table 3 are the best estimation we currently have of the trigger rates. In reality\nbeam conditions and detector effects could lead to much higher values. It is clear that the trigger strategy\nwill depend on these background effects and on the luminosity. At low luminosities, (1031 cm\u22122 s\u22121) it\nis likely that a simple trigger based on Emiss\nT\nalone such as Emiss\nT\n> 70 GeV (L1 XE70) will be suf\ufb01cient.\nHowever if the trigger rate for this item is higher than expected, VBF invisible Higgs boson events\ncould still be triggered using a higher Emiss\nT\ntrigger such as Emiss\nT\n> 80 GeV (L1 XE80) or Emiss\nT\n> 100\nGeV (L1 XE100) whichever one can be used without pre-scaling. As the luminosity increases or if\nbackgrounds are worse than expected, it will be necessary to use a combined trigger for this channel.\nThe numbers in Table 3 suggest that triggers based on Emiss\nT\nand either a forward or central jet would be\nsuf\ufb01cient. However the addition of a single jet to an Emiss\nT\ntrigger provides a relatively small reduction in\nrate due to correlations that can occur when high energy jets are mis-measured. There is concern that this\ncould be ampli\ufb01ed by pile-up effects. Requiring a forward jet plus a central jet plus Emiss\nT\nis expected to\nsolve these problems albeit with a reduction of signal acceptance. For a luminosity of 1033 cm\u22122 s\u22121, the\nmost conservative trigger option is a combined trigger with Emiss\nT\n> 100 GeV and a forward and a central\njet each with a pT > 23 GeV. This trigger will have an acceptance rate for the signal of 55% as shown\nin Table 3. Note that the uncertainties shown in Table 3 are statistical only. A further major uncertainty\nin trigger rates are pile-up effects which have not been considered here. In practice, adjustments will be\nrequired to select the optimum trigger based on the experimental rates observed at the LHC.\nInvisibly decaying Higgs boson events produced via vector boson fusion can be selected using a\ncombination of Emiss\nT\nand jet triggers with a small impact on the overall L1 trigger rate. For low lumi-\nnosities (1031 cm\u22122 s\u22121) it is expected that a Emiss\nT\ntrigger of 70 GeV or greater will be suf\ufb01cient. For\nhigher luminosities such as 1033 cm\u22122 s\u22121, a trigger with Emiss\nT\n> 100 GeV and a forward and central jet\neach with pT > 23 GeV will be required.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1423\n\n2.3\nEvent selection for the VBF channel\nTwo separate methods are used to extract the signal: the \ufb01rst method is called the cut-based analysis, the\nsecond is the shape analysis. Both analyses are conducted by \ufb01rst applying the selection cuts described\nin the next sub-section. For the cut-based analysis, the signal is extracted using all the cuts including a\ncut on \u03c6j j, the angle between the two tagged jets in the transverse plane. This is described in Section\n2.5. For the shape analysis, this last cut is not applied. Instead, the shape of the \u03c6j j distribution is used\nto extract the fraction of signal events. This is described in Section 2.6. Results are derived separately\nwith these two methods.\nThe selection cuts described in this section were developed using a signal sample with mH = 130\nGeV.\n2.3.1\nSelection cuts\nThe event selection is based on standard ATLAS de\ufb01nitions for jets, leptons and missing transverse\nenergy [18]. A primary characteristic of a signal event is the presence of two jets from the VBF process.\nEvents are selected based on each of the two highest pT jets in the event which are referred to as the\n\u201ctagging jets\u201d. These tagging jets are required to have a pT > 40 GeV and be in the rapidity range\n|\u03b7j1,2| < 5. Cuts on the product and difference of the pseudorapidity of the two jets are used, \u03b7 j1 \u00b7\u03b7j2 < 0\nand \u2206\u03b7 > 4.4, respectively. Kinematic distributions of the tagged jets for the signal and background are\nshown in Figure 2. In the upper two plots of this Figure, it can be seen that signal events and the\nW+jet and Z+jet backgrounds have very similar pT distributions. When the W+jet and Z+jet events are\ngenerated with only one parton the pT distributions are much softer. When the two parton and three\nparton components are added the pT distribution becomes harder and similar to the signal.\nThe second major event characteristic used to select events is a large Emiss\nT\nfrom the invisible decay\nof the Higgs boson. A cut on this variable signi\ufb01cantly reduces the QCD background as no real Emiss\nT\nis\nexpected for QCD events. In this analysis there is a requirement that Emiss\nT\n> 100 GeV. The Emiss\nT\ndistri-\nbutions for the signal and backgrounds are shown in Figure 3.\nThe majority of QCD dijet background events will produce soft jets resulting in the tagging jets\nhaving a low invariant mass. This feature can be used to reject QCD events by requiring a minimum\ninvariant mass of 1200 GeV for the tagging jets. The invariant mass distribution of the tagging jets is\nshown in Figure 3. The QCD dijet background can be further reduced by requiring that the direction of\nthe measured Emiss\nT\nis not correlated with the tagging jets. A missing transverse energy isolation variable,\nI, is de\ufb01ned for this purpose as I = min[\u03c6(Emiss\nT\n)\u2212\u03c6(j1,2)]. Events with a small value of I are expected\nto result from mis-measured jets caused by dead material and cracks in the detector. This is illustrated\nin Figure 4 which shows that QCD dijet events preferentially have a small value of I. A selection of\nI < 1 rad has been used which is compatible with previous analyses. The W+jet and Z+jet backgrounds\ncan be reduced by rejecting events with any identi\ufb01ed lepton. For this reason, events with electrons or\nmuons with a pT > 20 GeV are rejected, as are events containing \u03c4-jets with a pT > 30 GeV. These cuts\nare based on an earlier ATLAS fast simulation study.\nA key aspect of the VBF Higgs boson search is the electroweak nature of the signal,and this can be\nused to suppress backgrounds by using the fact that the signal has no color \ufb02ow between the interact-\ning quarks at tree level. Although the W+jet and Z+jet backgrounds include both electroweak and QCD\nterms, the cross-section is dominated by the QCD contribution. Therefore, unlike the signal, the majority\nof background events have QCD activity in the central region. The presence of this extra QCD radiation\nbetween the two tagging jets provides, in principle, a powerful tool to suppress this background. In prac-\ntice the difference is diluted both by the underlying event and pile-up. The Underlying Event (UE) arises\nfrom interactions of the spectator partons and is not consistently modeled by the available event gener-\nators. For example, the ratio of the average jet multiplicity from the UE between HERWIG/PYTHIA is\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1424\n\nTagged Jet #1 Pt [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n\t VBF Inv. Higg\n\t Z+j\n\t W+j\n\t QCD Dij\nATLAS\nTagged Jet #2 Pt [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n\t VBF In . Higg\n\t Z+je\n\t W+j\n\t QCD Dij\nATLAS\nj2\n\u03b7\n \n\u00d7 \nj1\n\u03b7\n-10\n-5\n0\n5\n10\n0\n0 05\n0.1\n0.15\n0.2\n0 25\n0.3\n\t VBF n . Higg\n\t Z+j\n\t W+je\n\t QCD Dij\nATLAS\njj\n\u03b7\n \n\u2206\n0\n2\n4\n6\n8\n10\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n\t VBF n . Higg\n\t Z+j\n\t W+j\n\t QCD Dij\nATLAS\nFigure 2: Comparison of tagged jet properties for signal events (mH = 130 GeV) and the three\nmajor backgrounds. The upper left plot shows the pT of the leading tagged jet, the upper right\nplot shows the pT of the jet with the second highest pT. The lower left plot shows the product of\nthe directions of the two tagged jets in pseudo-rapidity (\u03b7j1 \u00d7\u03b7 j2), and the lower right plot shows\nthe difference in \u03b7 between the two tagged jets (\u2206\u03b7). The enhancement at \u2206\u03b7 of 0.5 in the VBF\nsignal results from a single high pT jet being reconstructed as two jets. The \ufb01lter cut described in\nSection 2.1 has been applied to the W+jet and Z+jet Monte-Carlo data, but no trigger cuts have\nbeen applied. The distributions are normalized to unity. The vertical dotted lines show the cut\nvalues used in the analysis.\nInvariant Tagged Jet Mass [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n\t VB Inv Higg\n\t Z+j\n\t W+j\n\t QCD Di\nATLAS\nMissing Transverse Energy [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-9\n10\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n\t VB nv H gg\n\t Z+\n\t W+\n\t QCD Dij\nATLAS\nFigure 3: The reconstructed invariant mass of the tagging jets (left) and the Emiss\nT\n(right) for the\ninvisible Higgs boson signal (mH = 130 GeV) and the three main backgrounds. Single events in\nthe high Emiss\nT\ntail of each individual sample (J0, J1 etc) can result in a spike with a large error.\nThe \ufb01lter cut described in Section 2.1 has been applied to the W+jet and Z+jet Monte-Carlo data,\nbut no trigger cuts have been applied. The distributions are normalized to unity.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1425\n\nMissing Transverse Energy Isolation [rad]\n0\n0.5\n1\n1.5\n2\n2.5\n3\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n\t VBF n . Higg\n\t Z+j\n\t W+je\n\t QCD Dij\n [rad]\njj\n\u03c6\n0\n0 5\n1\n1.5\n2\n2.5\n3\n0 02\n0 04\n0 06\n0 08\n0.1\n0.12\n\t VBF nv Higg\n\t Z+j\n\t W+j\n\t QCD Dij\nATLAS\nFigure 4: The distribution of the reconstructed Emiss\nT\nisolation variable (I) is shown in the right\nhand plot and the azimuthal angle between the tagging jets (\u03c6j j) is shown in the right hand plot for\nthe invisible Higgs boson signal (mH = 130 GeV) and the three main backgrounds. The \ufb01lter cut\ndescribed in Section 2.1 has been applied to the W+jet and Z+jet Monte-Carlo data, but no trigger\ncuts have been applied. The distributions are normalized to unity.\nbetween 1.38 and 1.85. Therefore PYTHIA generates events with fewer jets from the UE, but these jets\nhave on average a higher pT . If a cut is applied to remove events that have a central jet that exceed a\nspeci\ufb01c pT value, the so called Central Jet Veto (CJV) cut, fewer PYTHIA events will survive than HER-\nWIG events. Although there is a clear difference in the topology between the signal and background, the\nadded contribution from the UE has a large effect on the ef\ufb01ciency of this cut. In the same way pile-up,\nwhich results from central activity unrelated to the event of interest can also reduce the effectiveness of\nthis CJV cut. The effect of pile-up has not been studied, as suitable data samples were not available. For\nthis analysis, a central jet veto is used requiring that there are no additional jets with pT > 30 GeV for\n|\u03b7| < 3.2. It should be stressed that this cut is applied after the selection of the two tagging jets which can\nbe located anywhere within the full \u03b7 range including |\u03b7| < 3.2. So this cut does not bias the selection\nof the tagging jets, nor does it introduce a bias with respect to the trigger which has elements that allow\njets to be located within an |\u03b7| < 3.2.\nUnlike the signal which is uniquely produced via Vector Boson Fusion, the W+jet and Z+jet back-\ngrounds can be produced by the qq \u2192gV and qg \u2192qV processes in which the second jet comes from\na radiative process. Therefore, the difference in \u03c6 between the two tagged jets is different for the signal\nand the radiative background as can be seen in Figure 4. This difference provides additional discriminat-\ning power and is used in the analysis presented in Section 2.5 requiring \u03c6j j < 1 rad. Moreover, the \u03c6j j\nvariable motivates the shape analysis presented in Section 2.6.\nThe selection cuts along with the surviving cross-sections after each cut are shown in Table 4 for\na Higgs boson mass mH = 130 GeV and the three main backgrounds. Table 5 shows the effect of\nthe cuts for the four Higgs boson mass values considered in this study. The cross-sections for W+jet\nand Z+jet processes were calculated to LO but have been normalized to the results calculated with the\ngenerator FEWZ at NNLO which results in a value for the total cross-section which is known to within\n\u223c10%1 [16].\nThe \ufb01rst cut applied to the data simulates the effect of the L1 trigger with the most conservative menu\noption given in Table 3 and discussed in the previous section namely, a Emiss\nT\n> 100 GeV, a central jet\nwith pT > 23 GeV and a forward jet with pT > 23 GeV. This cut reduces the QCD dijet background rate\nby approximately 7 orders of magnitude. The effect of the trigger on the W+jet and Z+jet backgrounds\nis smaller with a reduction of two orders of magnitude, by contrast the signal is reduced by about 50%.\n1This includes the PDF and QCD scale uncertainties.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1426\n\nSelection Cuts\nHiggs boson mH = 130 GeV\nW+jet\nZ+jet\nQCD\nInitial \u03c3 (fb)\n3.93\u00d7103\n1.24\u00d7106\n4.08\u00d7105\n1.91\u00d71013\nL1 Trigger\n2.71\u00d7102 (0.07)\n1.42\u00d7104 (0.01)\n6.31\u00d7103 (0.02)\n1.52\u00d7106 (<0.01)\n+ Tagged jets\n1.47\u00d7102 (0.54)\n1.35\u00d7103 (0.10)\n6.16\u00d7102 (0.10)\n1.81\u00d7105 (0.12)\n+ Mj j\n1.11\u00d7102 (0.76)\n6.64\u00d7102 (0.49)\n3.76\u00d7102 (0.61)\n1.28\u00d7105 (0.71)\n+ Emiss\nT\n> 100 GeV\n1.08\u00d7102 (0.97)\n4.70\u00d7102 (0.71)\n2.69\u00d7102 (0.72)\n2.84\u00d7103 (0.02)\n+ Lepton veto\n1.07\u00d7102 (1.00)\n3.01\u00d7102 (0.64)\n2.62\u00d7102 (0.97)\n2.76\u00d7103 (0.97)\n+ I > 1 rad\n9.60\u00d7101 (0.89)\n1.49\u00d7102 (0.49)\n2.11\u00d7102 (0.81)\n3.61 (<0.01)\n+ Central jet veto\n8.93\u00d7101 (0.93)\n1.10\u00d7102 (0.74)\n1.32\u00d7102 (0.63)\n0.07 (0.02)\n+ \u03c6j j < 1 rad\n4.50\u00d7101 (0.50)\n1.94\u00d7101 (0.18)\n4.21\u00d7101 (0.32)\n0.07 (1.00)\nTable 4: Cross-section in fb for a Higgs boson (mH = 130 GeV) and background samples at each step of\nthe selection process. Initial cross-section for W/Z+jet are quoted after VBF \ufb01lter and NNLO corrections.\nThe \ufb01rst cut is the effect of the L1 trigger simulation with a Emiss\nT\nof 100 GeV, a central jet with pT > 23\nGeV and a forward jet with pT > 23 GeV (Table 3). The central jet veto is applied to jets other than the\ntwo tagging jets and does not bias any of the other cuts. Numbers in parentheses are the ef\ufb01ciencies for\neach cut.\nHiggs boson mass [GeV]\n100\n130\n200\n250\nInitial \u03c3(fb)\n4630\n3930\n2410\n1780\nL1 Trigger\n322\n271\n240\n168\n+ Tagged jets\n166\n147\n134\n93\n+ Mj j\n126\n111\n100\n73\n+ Emiss\nT\n> 100 GeV\n121\n108\n98\n70\n+ Lepton veto\n121\n107\n98\n70\n+ I > 1 rad\n108\n96\n86\n63\n+ Central jet veto\n94\n89\n79\n59\n+ \u03c6j j < 1 rad\n43\n45\n39\n30\nTable 5: Cross-section in fb for each signal mass at each step in the selection cuts. The \ufb01rst cut is the\neffect of the L1 trigger simulation with a Emiss\nT\nof 100 GeV, a central jet with pT > 23 GeV and a forward\njet with pT > 23 GeV.\nThe jet tagging cuts reduces all three backgrounds by a factor of 10. Although a L1 Emiss\nT\nis applied a\nlarge fraction of events still survive because of the the L1 Emiss\nT\nresolution. The other cuts that have a\nlarge impact on the QCD rate are the Emiss\nT\ncut and the Emiss\nT\nisolation cut. Together they reduce this\nbackground to a negligible level. The effect of these selection cuts on the Z+jet and W+jet backgrounds\nare less dramatic. The lepton veto reduces the W+jet and Z+jet by \u223c36% and \u223c3%, respectively. The\nlepton veto cut removes few events in the Z+jet channel as the Emiss\nT\ncut removes most of the Z\u2192\u2113\u2113de-\ncay mode. The remaining Z+jet events are dominated by the Z\u2192\u03bd\u03bd mode. Leptons are only identi\ufb01ed\nfor |\u03b7| < 2.5, so the lepton veto cut does not remove all the W+jet background events due to this limited\n\u03b7 range. Therefore, electrons and \u03c4-jet in the forward region (|\u03b7| > 2.5) are mis-identi\ufb01ed as jets most\nof the time. In a similar manner, muons in the forward direction are generally not identi\ufb01ed and result in\nfake Emiss\nT\n.\n2.4\nSystematic uncertainties\nThree major types of systematic uncertainties are considered. One arises from the implemention of the\nMonte Carlo generators, the second from the experimental systematic uncertainties and the third from\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1427\n\nSelection Cuts\nHERWIG 130 GeV\nPYTHIA 130 GeV\nInitial \u03c3(fb)\n3.93\u00d7103 (1.000)\n3.93\u00d7103 (1.000)\nPre-Cut (Emiss\nT\n> 80 GeV)\n1.76\u00d7103 (0.448)\n1.78\u00d7103 (0.453)\n+ Tagged Jets\n4.07\u00d7102 (0.231)\n4.10\u00d7103 (0.230)\n+ Mj j\n2.45\u00d7102 (0.602)\n2.45\u00d7103 (0.598)\n+ Emiss\nT\n> 100 GeV\n2.05\u00d7102 (0.837)\n2.14\u00d7103 (0.873)\n+ Lepton Veto\n2.05\u00d7102 (1.000)\n2.12\u00d7102 (0.991)\n+ I > 1 rad\n1.84\u00d7102 (0.898)\n1.80\u00d7102 (0.849)\n+ Central Jet Veto\n1.59\u00d7102 (0.864)\n1.07\u00d7101 (0.594)\n+ \u03c6j j < 1 rad\n7.43\u00d7101 (0.467)\n4.93\u00d7101 (0.461)\nTable 6: Comparison between HERWIG and PYTHIA generated samples on the selection cuts for\nthe 130 GeV Higgs boson mass. The cross-section results are quoted in fb and the cut ef\ufb01ciency\nis given in parenthesis. The major difference occurs in the last two rows of this table.\nthe theoretical knowledge of the production cross-sections.\nTwo event generator effects are discussed, the \ufb01rst is the treatment of the Underlying Event (UE) and\nthe second is the effect of using a \ufb01xed Z boson mass. To illustrate the effect of the UE, signal events\nhave been generated with two different event generators, HERWIG and PYTHIA that treat the UE in\ndifferent ways. Table 6 shows the ef\ufb01ciency of each selection cut used in the VBF analyses for the two\ngenerators. The difference in cross-sections between the two samples are within \u223c2% of each other\nfor cuts up to the Emiss\nT\nisolation cut. However, once the central jet veto is applied, fewer Pythia events\nsurvive resulting in a large difference of \u223c49%. This is believed to be the result of the difference in\nthe modeling of the UE in the two generators; Pythia tends to produce fewer but harder jets, resulting\nin more events being removed by the central jet veto cut, see Section 2.3. If the number of background\nevents is underestimated due to a combination of this cut and the choice of generator the sensisitivity to\nthe signal will be arti\ufb01cially enhanced. A systematic study of the effect of generator choice on the central\njet veto cut would require a large number of data and background samples to be produced with a variety\nof generators and this is beyond the scope of this paper. It is not clear which generator represents reality\nbest. For consistency both the background and signal samples were generated using HERWIG. When\nreal data becomes available it will be possible to measure the magnitude of central jet activity directly\nand use this to tune the generators.\nThe use of ALPGEN requires the use of a \ufb01xed Z mass. The effect of the missing off-shell terms\nfrom the background samples was checked using the Z \u2192\u03bd\u03bd analysis by adding a Emiss\nT\ncontribution\nrandomly generated by a Breit-Wigner distribution using the Z mass and width parameters. This study\nindicated that the effect of using a \ufb01xed mass Z boson was negligible.\nTwo methods are considered in this paper to extract the signal signi\ufb01cance. The \ufb01rst, a cut-based\nanalysis, relies on the number of signal and background events after all cuts have been made. The\nsecond, a shape analysis relies on the ratio of the number of background events contained in two regions\nof the \u03c6j jvariable distribution; namely the number of events for \u03c6j j < 1 divided by all events. The\nsystematic uncertainties of interest are the ones related to these three quantities; the number of signal\nand background events and the background shape ratio. They are shown in Table 7.\nThe event reconstruction variables that result in the largest systematic uncertainties are the jet reso-\nlution and the jet energy scale. For the jet energy resolution, the systematic uncertainty was estimated by\nsmearing the momentum of the jets using a Gaussian distribution with a width given by \u03c3(E) = 0.45\n\u221a\nE\nfor |\u03b7| < 3.2 and \u03c3(E) = 0.63\n\u221a\nE for |\u03b7| > 3.2. Changing the jet energy magnitude also affects the\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1428\n\nSystematics\nHiggs boson 130 GeV\nBackground\nCut-Based\nShape\nLuminosity\n3 %\n\u223c0%\nJet energy resolution:\n0.8 %\n5.3 %\n4.5 %\n\u03c3(E) = 0.45\n\u221a\nE for |\u03b7| < 3.2\n\u03c3(E) = 0.63\n\u221a\nE for |\u03b7| > 3.2\nJets energy scale:\n4.0 %\n3.2 %\n0.2 %\n+7% for |\u03b7| < 3.2\n+15% for |\u03b7| > 3.2\nJets energy scale:\n10.0 %\n19.5 %\n2.8 %\n\u22127% for |\u03b7| < 3.2\n\u221215% for |\u03b7| > 3.2\nTotal\n10.5 %\n20.4 %\n5.3 %\nTable 7: Experimental contributions to the systematic uncertainty. The systematic uncertainty on\nthe Jet Energy Scale (JES) is asymmetric. Only the largest (negative) JES systematic uncertainty\nis included in the total experimental uncertainty shown in the last row of the table.\nEmiss\nT\n, so for each event, Emiss\nT\nwas recalculated for the x- and y-components. The analysis was then\nrepeated to determine the change in the number of signal and background events and the shape ratio. In\nthe same way the effect of changes in the jet energy scale was investigated by shifting the overall scale\nby \u00b17% for |\u03b7| < 3.2 and \u00b115% for |\u03b7| > 3.2. Again this affects the Emiss\nT\n, and this change was taken\ninto account. As can be seen in Table 7, there is an asymmetric dependence on the Jet Energy Scale,\n(JES), so positive and negative deviations are considered separately. Lepton reconstruction was analyzed\nand found not to contribute to the \ufb01nal systematic uncertainty. The JES uncertainties used here are con-\nservative for 30 fb\u22121, but the impact of this choice on the sensitivity limits presented in this paper is\nsmall. Finally, 3% was assigned to the uncertainty in the luminosity. To get the experimental systematic\nuncertainty for each analysis the terms were added in quadrature giving an overall systematic uncertainty\nof 20% on the number of background events which applies to the cut-based analysis and an uncertainty\nof 5.3% on the background shape ratio that applies to the shape analysis.\nIn addition to the uncertainty in the UE and the reconstruction algorithms, there is a systematic un-\ncertainty which arises from the uncertainty in the absolute cross-section of the backgrounds. The main\nbackgrounds to the invisible Higgs boson channel are Z+jet and W+jet. The total cross-sections for\nthese processes have been corrected to NNLO and are known to \u223c10%, (see Section 2.3). However\nthe cuts used to select the VBF process, result in a very restricted phase space which makes it dif\ufb01cult\nto determine the systematic uncertainty on the cross-section for the \ufb01nal data samples. This means that\nthe systematic uncertainty on the number of background events due to the cross-section is currently un-\nknown, could be very large and is likely to dominate other uncertainties. The shape of the \u03c6 j j distribution\non the other hand is quite well constrained by theory and based on previous studies has a systematic un-\ncertainty of 10% [5]. At NLO it is expected to be 5%. In this analysis a conservative value of 10%\nis assumed for the uncertainty due to the cross-section which when combined with the much smaller\nexperimental effect leads to an overall systematic uncertainty of 11.3% on the background shape.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1429\n\n2.5\nCut-based analysis\nThis analysis uses the selection cuts summarized in Section 2.3.1. The signal signi\ufb01cance is calculated\nbased on the number of signal and background events that remain after all cuts. The limitation of this\nanalysis is that the systematic uncertainty on the background cross-sections described in the previous\nsection could be very large. One way of dealing with this uncertainty is to use experimental data of the\nZ+jet channel where the Z decays to two leptons. After correction for the detector acceptance, these\nevents can be used to infer the value of the cross-section for the irreducible background in which the\nZ decays to two neutrinos. A similar analysis can be done for the W+jet background. These so called\n\u201cdata driven\u201d corrections will be the subject of a future publication. In the next section we report on an\nalternative method which uses the shape of the azimuthal angle distribution between the jets to reduce\nthe dependence of the systematic error on the cross-section. In the current section the sensitivity to\nan invisible Higgs boson without systematic errors are calculated to provide baseline numbers for the\nsensitivity to an invisible Higgs boson produced via the VBF process.\nThe number of signal and background events after the \u03c6j j cut is shown in Tables 4 and 5. These\nnumbers can be used to calculate the 95 % CL sensitivity of \u03be 2 for the invisible Higgs boson, given the\nassumed backgrounds. This is done by calculating the number of signal events required to increase the\ntotal event count by a factor 1.64 times the uncertainty on the number of background events as shown in\nEquation 2.\n1.64\u03c3B = NS\u03be 2\n(2)\nHere NS is the number of signal events after the selection cuts and \u03c3B = \u221aNB . The results of this analysis\ngives a \u03be 2 for an integrated luminosity of 30 fb\u22121 at 95 % C.L. for Higgs mass between 110 GeV and 250\nGeV of \u223c5\u22128% in the case when systematic uncertainties are not included. An additional 6% statistical\nuncertainty2 arises from the limited number of events in the data samples.\n2.6\nShape analysis\nThe shape analysis is motivated by a marked difference in the \u03c6j j distribution between the signal and the\nW/Z+jet background as shown in Figure 5, which is taken from reference [5]. This plot shows that the\nbackgrounds peak above a \u03c6j j of 1 while the signal is higher at low \u03c6j j values. To characterize the shape\nof the \u03c6j j distribution the ratio R has been de\ufb01ned as the number of events with \u03c6j j < 1 divided by the\ntotal number of events as shown in Equation 3. As the proportion of signal in the sample increases the\nvalue of R increases.\nR =\nR 1\n0\nd\u03c3\nd\u03c6j j\nR \u03c0\n0\nd\u03c3\nd\u03c6j j\n(3)\nThe advantage of the shape analysis described in this section over other analyses is that it does\nnot require a knowledge of the absolute cross-section but rather the ratio of the number of events for\n(\u03c6 j j < 1) to all events. As such, the systematic error associated with the absolute cross-section is reduced\nto a negligible amount. However, as discussed in Section 2.4, there is a systematic uncertainty associated\nwith the knowledge of the \u03c6j j distribution which is known to \u223c10% or better. In addition, the systematic\nuncertainties due to detector effects are much smaller for this ratio than they are for the number of\nbackground events, which is the relevant variable for a pure cut-based analysis (Table 7). The overall\nsystematic uncertainty on the ratio R has been calculated to be 11.3%.\nEquation 3 can be re-written in the context of this analysis and expanded to provide a background-\n2Based on a binomial error calculation.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1430\n\nFigure 5: The \u03c6j j distribution for the signal and background in radians [5]. The solid and dash-\ndotted lines represent the expected distribution for the Higgs boson signal with Higgs boson\nmasses of mH = 120 and mH = 300 GeV respectively. The dotted and dashed lines represent the\ndistributions expected from the backgrounds. The plot shows the distributions after VBF selection\ncuts have been made. Note that for the \u03c6j j plot shown earlier did not have these cuts applied,\n(Figure 4).\nonly term, as shown in Equation 4.\nR = N1\nB\nN\u03c0\nB\n\u0014\n1+\u03be 2\n\u0012N1\nS\nN1\nB\n\u2212N\u03c0\nS\nN\u03c0\nB\n\u0013\n+\u00b7\u00b7\u00b7\n\u0015\n(4)\nHere N1\nB and N1\nS are the number of events within \u03c6j j < 1 and N\u03c0\nB and N\u03c0\nS are the number of events\nwithin the entire \u03c6j j range. The \ufb01rst term of Equation 4 provides the expected ratio for the background\ncontribution. However, since the ratio between the signal and background are not the same in the presence\nof a signal, a non-zero value is expected in the second term. The variation from the \u2018background only\u2019\nratio dictates the sensitivity to new physics. The ratio N1\nB/N\u03c0\nB can be determined using the Stndard Model\ntheoretical prediction or by a data driven technique.\nThe shape analysis applies the selection cuts discussed in Section 2.3.1 but not the \u03c6j j cut. Therefore,\nthe results from Table 4 before this last cut are used. The \ufb01rst term of Equation 4 is calculated to be\n0.254\u00b10.007. To determined the 95% C.L. sensitivity limit a variation of 1.64\u03c3R is required, where \u03c3R\nis the uncertainty on the ratio R from Equation 4. Therefore, the \ufb01rst order \u03be 2 terms from Equation 4 is\nset to the required 95% CL sensitivity limit, that is 1.64\u03c3R, as shown in Equation 5.\n1.64\u03c3R = \u03be 2\n\u0012N1\nS\nN1\nB\n\u2212N\u03c0\nS\nN\u03c0\nB\n\u0013\u0012 N1\nB\nN\u03c0\nB\n\u0013\n(5)\nSolving for \u03be 2 provides the 95 % CL sensitivity limit for the invisible Higgs boson. The results of this\nanalysis are shown in Figure 6. Without systematic errors, the shape analysis gives a value of \u03be 2 that\nranges from 11 to 19%. This can be compared with the simple cut-based analysis which gave a \u03be 2\nvalue that ranged from 5 to 8%. So although the shape analysis method removes the dependence on the\nabsolute cross-section of the backgrounds there is a reduction in the sensitivity to the signal. To include\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1431\n\nHiggs Mass [GeV]\n100\n120\n140\n160\n180\n200\n220\n240\n260\n [%]\n2\n\u03be\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nATLAS\n\tFull S mulat on Using Shape Analys s No Systematic\n\tFull S mulat on Using Shape Analys s W h Systematic\nFigure 6: Sensitivity for an invisible Higgs boson at 95% C.L. via the VBF channel using shape\nanalysis for an integrated luminosity of 30fb\u22121 with and without systematic uncertainties. The\nblack triangles (circles) are the results from this analysis with (without) systematic uncertainties.\nthe systematic uncertainties, the uncertainty on the background becomes \u03c3R =\np\n\u03c3R2 +\u03b12R2, where \u03b1\nis the fractional systematic uncertainty given in Table 7. The result obtained that includes systematic\nuncertainties gives value of \u03be 2 of around 60% for mH between 100 and 200 GeV. This sensitivity is\ndominated by the systematic uncertainty that arises from the theoretical knowledge of the shape of the \u03c6j j\ndistribution. Using calculations at NLO could reduce this uncertainty by a factor of 2 greatly enhancing\nthe sensitivity of this method of analysis.\n2.7\nSummary for the VBF invisible Higgs boson channel\nThe study described above has investigated the sensitivity of the ATLAS detector to a Higgs boson\nparticle produced by the VBF process that has an invisible decay mode. It should be stressed that these\nresults do not include pile-up which can reduce the sensitivity. It has been shown that with 30 fb\u22121\nof data it is possible to detect this process over a wide range of masses if the Beyond Standard Model\ncross-section is more than 60% of the Standard Model cross-section for a Higgs mass range of up to 200\nGeV and 100% of the Higgs boson decays are invisible. Triggering for this channel is possible using a\ntrigger requiring large Emiss\nT\nplus a forward and a central jet of moderate pT. Triggers of this kind would\nbe useful up to luminosities of at least 1033 cm\u22122 s\u22121.\n3\nThe associated ZH production channel\nThe Feynman diagram for associated production in the ZH channel is shown in Figure 7. The signal of\nan invisibly decaying Higgs boson in the ZH channel can be detected when the Z boson decays into two\nleptons, which can be used for triggering the event. The presence of an invisibly decaying Higgs boson\nis detected from the missing transverse energy.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1432\n\n\u03c70\n\u03c70\nl\nl\nFigure 7: (Left): The Feynman diagram for Higgs boson associated production with a Z boson. (Right):\nA representation of the decay of a Higgs boson into two invisible neutralinos represented by \u03c70 recoiling\nagainst the two leptons coming from the Z decay.\nVarious backgrounds with signatures similar to the signal have been studied and are listed here. In\nall cases, unless otherwise speci\ufb01ed, \u2113represents e or \u00b5.\n1. The ZZ \u2192\u2113\u2113\u03bd\u03bd \ufb01nal state gives the same signature as the signal (irreducible background) and is\nthe main background;\n2. The t\u00aft \u2192b\u2113+\u03bd \u00afb\u2113\u2212\u03bd process mimics the signal when the two b-jets are not reconstructed, or when\na second lepton results from a b quark decay;\n3. The W +W \u2212\u2192\u2113\u03bd\u2113\u03bd process mimics the signal but can be greatly reduced by cutting on the Z\nmass;\n4. The ZZ \u2192\u03bd \u00af\u03bd\u03c4 \u00af\u03c4 and \u03c4 \u2192\u2113\u03bd \u00af\u03bd can also mimic the signal.\n5. The ZZ \u2192\u2113\u00af\u2113\u03c4 \u00af\u03c4 and \u03c4 \u2192\u2113\u03bd \u00af\u03bd can pass the selection criteria if some particles are missed;\n6. The ZW \u2192\u2113\u2113\u2113\u03bd decay mode also simulates the signal when one lepton is not detected;\n7. The Z plus jets background, with Z \u2192\u2113\u00af\u2113(Drell-Yan process) \ufb01nal state can be mistaken for the\nsignal when poor jet reconstruction leads to missing transverse energy.\n3.1\nMonte Carlo generation for the ZH channel\nThe signal and the background events have been generated using different particle generators chosen\naccording to which process they simulate best. The events are fully simulated then reconstructed using\nATHENA. The diboson production cross-sections are taken from Ref. [16]. All events were passed\nthrough a \ufb01lter immediately after generation. The two \ufb01lters used are described in detail in Section\n3.2.2. Only the few samples generated with the simpler lepton \ufb01lter will be mentioned here. All other\nsamples were generated with the \ufb01lter containing mZ and Emiss\nT\ncuts.\nDetails on the generated events and pre-de\ufb01ned parameters are given below. All generators use the\nCTEQ6M structure functions to generate the processes.\n\u2022 Seven signal samples were generated using PYTHIA, with mH = 110, 120, 130, 140, 150, 200 and\n250 GeV. Only the samples with mH = 130 and 140 GeV used the lepton \ufb01lter. To generate the\ninvisibility of the Higgs boson, the H is produced as a stable particle, which goes undetected.\n\u2022 ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd is generated using PYTHIA. This is the main and irreducible background. One Z\ndecays to a lepton pair while the other is allowed to decay to any \ufb02avor of neutrino pairs.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1433\n\n\u2022 t\u00aft is produced with the MC@NLO generator with all top quark decay modes allowed. The \ufb01lter\ndescribed in detail in Section 3.2.2 retains mostly t\u00aft \u2192b\u2113+\u03bd \u00afb\u2113\u2212\u00af\u03bd events with \u2113= e or \u00b5 only.\nHadronic top quark decays with a subsequent b \u2192c\u2113\u03bd decay are also included.\n\u2022 W +W \u2212\u2192\u2113+\u03bd\u2113\u2212\u03bd is generated with MC@NLO.\n\u2022 ZZ \u2192\u03c4+\u03c4\u2212\u03bd\u03bd and ZZ \u2192\u2113\u2113\u03c4+\u03c4\u2212events are generated with PYTHIA. The \u03c4 was allowed to decay\nhadronically and leptonically in both samples.\n\u2022 ZW \u00b1 \u2192\u2113+\u2113\u2212\u2113\u00b1\u03bd samples are produced with the MC@NLO generator. Since the cross-sections\nfor ZW + and ZW \u2212production are different, two different datasets were generated. The ZW sam-\nples were not \ufb01ltered since MC@NLO does not include the Z width at generation, leading to\nproblems when trying to apply a cut on the Z mass at the generator level. For these datasets, we\nuse samples generated with the lepton \ufb01lter which selected events containing at least two leptons.\nThese events need to be reweighted after full reconstruction to account for the distorted Z mass\ndistribution.\n\u2022 Z \u2192\u2113+\u2113\u2212+ jet events are produced using the SHERPA generator.\n3.2\nEvent selection for ZH channel\nThe event selection is made in three stages:\n1. For simulated samples, a \ufb01lter is applied immediately after the event Monte Carlo generation to\navoid unnecessary simulation of a large fraction of the background which would otherwise be\nreadily rejected at the preselection level. The event \ufb01lter cuts are loose preselection cuts applied\non true Monte Carlo quantities.\n2. The preselection cuts use fully reconstructed variables and aim at rejecting most backgrounds,\nretaining only the most likely events to be used at the \ufb01nal selection level.\n3. The \ufb01nal selection uses a multivariate analysis (Boosted Decision Tree) to re\ufb01ne the selection cuts\nwhile retaining a high signal ef\ufb01ciency.\n3.2.1\nAnalysis framework for the ZH channel\nThe standard ATLAS selection criteria are used to identify these objects [18].\n3.2.2\nFilter for the ZH channel\nThe \ufb01lter decision is based on true Monte Carlo quantities. The \ufb01lter must not reject events that would\nhave passed the preselection cuts to avoid introducing biases, and must have a large rejection ef\ufb01ciency\nagainst background. To do so, the \ufb01lter uses cuts looser than, but similar to, the preselection cuts, namely:\n\u2022 The events must contain at least two leptons with pT >4.5 GeV of same \ufb02avor but opposite charge\nwithin \u03b7 < 2.7.\n\u2022 The reconstructed mass of these two leptons must be within \u00b125 GeV of the Z mass.\n\u2022 The events must satisfy Emiss\nT\n> 50 GeV. The Emiss\nT\nis computed from a vectorial sum over all\ninvisible, stable particles such as Higgs bosons and neutrinos, and all lost particles falling outside\nthe calorimeter \ufb01ducial region of pT > 5.0 GeV and \u03b7 > 5.0.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1434\n\nchannel\nZH\u2192\u2113\u2113inv.\nZZ\nt\u00aft\nWW\nZZ\nZZ\nZW\nZ+jet\nmH=130 GeV\n\u2113\u00af\u2113\u03bd\u03bd\n\u2113\u03bd\u2113\u03bd\n\u03c4\u03c4\u03bd\u03bd\n\u2113\u2113\u03c4\u03c4\n\u2113\u2113\u2113\u03bd\n\u2113\u2113+ jet\n# of generated events\n10 K\n50 K\n104 K\n70.4 K\n50 K\n50 K\n250 K\n27.25K\n\ufb01lter ef\ufb01ciency\n75.4%\n29.2%\n1.13%\n4.5%\n5.16%\n71.4%\n100%\n0.0154%\n\u03c3*BR (fb)\n46.2\n728.0\n833000.0\n5245.6\n364.0\n123.0\n820.0\n3105063\n\ufb01lter cuts\n34.9\n212.6\n9412.9\n236.5\n18.8\n87.8\n820.0\n478.4\nafter trigger\n32.5\n198.5\n8620.6\n217.1\n14.2\n77.8\n735.3\n460.6\nEmiss\nT\n> 90 GeV cut\n14.0\n83.8\n3254.5\n46.6\n1.9\n4.1\n85.9\n105.8\npT lepton cut\n10.1\n61.6\n1596.2\n30.5\n0.4\n1.5\n24.0\n46.2\nmZ \u00b120 GeV cut\n9.6\n60.2\n1187.4\n19.9\n0.0\n1.2\n19.7\n43.2\nb-tag cut\n9.3\n58.6\n358.0\n18.7\n0.0\n1.1\n19.0\n17.7\nTable 8: Monte Carlo estimates of the cross-section times branching ratio in (fb) for the signal\nwith mH = 130 GeV and background processes following successive preselection cuts described\nin Section 3.2.4 for the ZH analysis. The number of generated events refers to \ufb01ltered events. The\ncross-sections are given at NLO as calculated in Ref. [16] for Standard Model processes and from\nRef. [9] for the ZH production cross-sections.\nZH\u2192\u2113\u2113inv.\nmH (GeV)\n110\n120\n130\n140\n150\n200\n250\n# of generated events\n10 K\n50 K\n10 K\n10 K\n10 K\n10 K\n10 K\n\ufb01lter ef\ufb01ciency\n47.0%\n49.6%\n75.4%\n75.9%\n56.4%\n64.6%\n70.1%\n\u03c3\u00b7BR (fb)\n77.3\n59.4\n46.2\n36.6\n29.1\n11.0\n5.2\nafter \ufb01lter cuts\n36.3\n29.4\n34.9\n27.7\n16.4\n7.1\n3.6\nafter trigger cuts\n34.0\n27.8\n32.5\n26.0\n15.6\n6.8\n3.5\nafter Emiss\nT\n> 90 cut\n18.3\n15.6\n14.0\n12.5\n10.0\n4.9\n2.7\nafter pT lepton cut\n13.5\n11.6\n10.1\n9.3\n7.4\n3.7\n2.0\nafter mZ \u00b120 GeV cut\n13.2\n11.4\n9.6\n8.7\n7.3\n3.6\n2.0\nafter b-tag cut\n13.0\n11.1\n9.3\n8.5\n7.1\n3.5\n2.0\nTable 9: Monte Carlo estimates of the cross-section (fb) for the signal with seven different Higgs\nmass hypotheses following successive preselection cuts described in Section 3.2.4 for the ZH\nchannel analysis. The number of generated events refers to \ufb01ltered events. Two samples were\ngenerated using a simpler \ufb01lter that retained events containing at least two leptons, (mH = 130 and\n140 GeV) whereas all other samples used a \ufb01lter that required \ufb01nding two leptons forming a Z\nboson and large Emiss\nT\n, as described in Section 3.2.2. The ef\ufb01ciency for this \ufb01lter increases with\nthe Higgs mass hypothesis.\nA simpler lepton \ufb01lter with only the \ufb01rst selection cut was used for the ZW \u2192\u2113\u2113\u2113\u03bd samples, for two\nsignal samples with Higgs mass hypothesis mH = 130 and 140 GeV, and for the ZZ \u2192\u2113\u2113\u2113\u2113sample used\nfor a normalization study.\nThe \ufb01lter reduces the total CPU time needed for full reconstruction by more than a factor of 1000.\nThe results are summarized for a signal with a Higgs boson mass hypothesis of 130 GeV and the back-\nground samples in Table 8. In Table 9, the effect of the \ufb01lter, trigger and preselection cuts are shown for\nthe signal at other Higgs boson masses.\n3.2.3\nTrigger for ZH channel\nAn invisibly decaying Higgs boson in the ZH channel can be detected when the Z decays into two\nleptons. We trigger on such events using the full simulation of the trigger and by requiring either one or\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1435\n\ntwo isolated, high pT leptons satisfying any of the following trigger signatures:\n\u2022 single electron trigger: one isolated lepton with pT > 22 GeV.\n\u2022 single muon trigger: one muon with pT > 20 GeV.\n\u2022 di-electron trigger: two isolated electrons with pT > 15 GeV.\n\u2022 missing transverse energy trigger: Emiss\nT\n> 100 GeV.\nThe di-muon trigger with a lower pT momentum cut was not implemented in this analysis but will\nbe used in the future. The overall trigger ef\ufb01ciency of 92.8% compares well with what is retained\nwhen applying cuts on fully reconstructed variables, selecting events containing either one electron with\npT > 25 GeV, two electrons with pT > 15 GeV or one muon with pT > 20 GeV. The effect of the trigger\non all samples studied is given in Table 8.\n3.2.4\nEvent preselection\nA \ufb01rst preselection is applied to reject most backgrounds, in particular the t\u00aft and (Z+jet) backgrounds.\nThe following cuts are applied:\n\u2022 the event must satisfy one of the trigger signatures described in the previous section;\n\u2022 large missing transverse energy, i.e. Emiss\nT\n> 90 GeV.\n\u2022 the event must contain exactly two leptons of the same \ufb02avor but opposite charge with pT > 15\nGeV;\n\u2022 an anti-b-tag is applied to further suppress the t\u00aft background.\n\u2022 a loose cut on the invariant mass of the two leptons, namely |m\u2113\u2113\u2212mZ| < 20 GeV, is applied to\nreject some t\u00aft background without reducing the signal ef\ufb01ciency.\nThe \u03c3 \u00b7BR for the signal and the background processes listed in Section 3 are shown in Table 8. The\neffects of the \ufb01lter and preselection cuts are also shown in this table.\n3.2.5\nFinal event selection\nIn order to improve the sensitivity of this channel, the most discriminative variables are used to form a\nmultivariate analysis (Boosted Decision Tree or BDT). Sixteen different variables are used as inputs to\nthe BDT, namely:\n\u2022 the missing transverse energy Emiss\nT\n,\n\u2022 the transverse mass mT =\nq\n2p\u2113\u2113\nT \u00b7Emiss\nT\n(1\u2212cos\u2206\u03c6) where \u2206\u03c6 is the azimuthal angle between the\ndilepton system and \u20d7pT miss,\n\u2022 the cosine of the angle between \u20d7pT miss and the most energetic lepton,\n\u2022 the reconstructed Z mass,\n\u2022 the transverse momentum of each lepton,\n\u2022 the cosine of the angle between the two leptons in the transverse plane and in 3-dimensions,\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1436\n\n\u2022 the cosine of the angle between \u20d7pT miss and \u20d7pT Z,\n\u2022 the cosine of the angle between the most energetic jet and \u20d7pT miss,\n\u2022 the energy found in a cone \u2206R = 0.1 rad around each lepton; the lepton isolation variable is partic-\nularly useful for muons where very little energy is found around isolated muons but not so much\nfor electrons where the energy deposit is much wider,\n\u2022 the energy of each of the three most energetic jets, and\n\u2022 the total number of jets.\nThese variables are shown in Figures 8 to 11 for the signal and the background after applying the pres-\nelection cuts listed in Section 3.2.4. Each distribution has been normalized to unity. The various back-\ngrounds have been regrouped: the irreducible background, ZZ \u2192\u2113\u2113\u03bd\u03bd, the non-resonant background: t\u00aft\nand WW, and \ufb01nally all other backgrounds containing at least one Z boson: ZZ \u2192\u2113\u2113\u03c4\u03c4, ZZ \u2192\u03c4\u03c4\u03bd\u03bd,\nZW and (Z + jet).\nEach of the main backgrounds after the preselection cuts, namely t\u00aft \u2192b\u2113\u03bd b\u2113\u03bd, WW \u2192\u2113\u03bd\u2113\u03bd,\nZZ \u2192\u2113\u2113\u03c4\u03c4, ZW \u2192\u2113\u2113\u2113\u03bd and (Z+jet) are compared to the signal to train a Boosted Decision Tree\n(BDT) [19]. Each one of these backgrounds is trained separately. Nothing is gained from training a\nBDT against the irreducible background, ZZ \u2192\u2113\u2113\u03bd\u03bd, so this background is not used. An ensemble (for-\nest) of decision trees is successively generated from the training sample, where each new tree is trained\nby giving increased weights to the events that have been misclassi\ufb01ed in the previous tree. The classi\ufb01er\nresponse is obtained as the sum of the classi\ufb01cation results for each tree, weighted by the purity obtained\nfor all training events in that tree. The large number of decision trees in the forest increases the perfor-\nmance of the classi\ufb01er and stabilizes the response with respect to statistical \ufb02uctuations in the training\nsample.\nFor each background type, a set of weights is established. Half the Monte Carlo events contained in\neach \ufb01le is used for the training and the other half for the analysis. The \ufb01le containing the signal and\nall the backgrounds, including the less important ones, is then analyzed using these weights. Each event\nis assigned a weight corresponding to the likelihood of being identi\ufb01ed as signal or background. The\nBDT weight distributions are shown in Figure 12. Each plot shows the output variable distribution for\nBoosted Decision Trees trained against different backgrounds, namely, from top plot to bottom plot, the\nt\u00aft \u2192b\u2113\u03bdb\u2113\u03bd, WW \u2192\u2113\u03bd\u2113\u03bd, ZZ \u2192\u2113\u2113\u03c4\u03c4, ZW \u2192\u2113\u2113\u2113\u03bd and Z+jet. The ZZ \u2192\u03c4\u03c4\u03bd\u03bd background is not\nused to train a speci\ufb01c BDT since too few events survive the preselection cuts. The cuts on the \ufb01ve BDT\noutputs are adjusted to minimize the value of \u03be 2, de\ufb01ned in Equation 2.\nThe same procedure is repeated using different Higgs boson mass hypotheses ranging from mH = 110\nGeV to mH = 250 GeV, optimizing the cuts each time. The numbers of events surviving all Boosted\nDecision Trees cuts for each Monte Carlo sample and these seven Higgs boson mass hypotheses are\ngiven in Table 11. The BDT inputs variables are also ranked during each training against a particular\nbackground. Each time, the input variables are assigned a weight proportional to their importance in\nseparating power. The sum of these weights are given in Table 10, showing which variables offer the\nbest separation power. The order of importance varies for each of the trees but all variables are useful\nin at least one tree. The Z mass is the overall most discriminative variable, mostly due to its very high\nranking in the BDT trained against t\u00aft and WW backgrounds.\n3.3\nSystematic uncertainties\n3.3.1\nBackground cross-section\nSince this is a counting experiment, one is looking for events in excess of what is expected by the\nStandard Model. However, exactly what is expected from Standard Model backgrounds is not well\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1437\n\n)\nlepton 1\nT\n - p\nmiss\nT\ncos(E\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-3\n10\n-2\n10\n-1\n10\n)\nlepton 1\nT\n - p\nmiss\nT\ncos(E\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-3\n10\n-2\n10\n-1\n10\n (GeV)\nZ\nm\n75\n80\n85\n90\n95\n100\n105\n110\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n (GeV)\nZ\nm\n75\n80\n85\n90\n95\n100\n105\n110\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n (GeV)\nmiss\nT\nE\n50\n100 150\n200\n250\n300\n350\n400 450\n500\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n (GeV)\nmiss\nT\nE\n50\n100 150\n200\n250\n300\n350\n400 450\n500\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n HZ\n\u03bd \n\u03bd\n l l \n\u2192\n ZZ \n t\n WW, t\n, ZW, Z + jet\n\u03c4 \u03c4\n l l \n\u2192\n ZZ \n (GeV)\nT\nm\n0\n100\n200\n300\n400\n500\n600\n700\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n (GeV)\nT\nm\n0\n100\n200\n300\n400\n500\n600\n700\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\nATLAS\nFigure 8: Input variables used by the Boosted Decision Tree for the signal with mH = 130 GeV and the\nmain backgrounds. Top left: Missing ET. Top right: transverse mass, de\ufb01ned as the reconstructed mass\nin the transverse plane, namely m2\nT = E2\nT \u2212p2\nT. Bottom left: cosine of the angle between the missing ET\nand highest momentum lepton in the transverse plane. Bottom right: reconstructed Z mass. Each plot\nhas been normalized to unity. The combined samples had \ufb01rst been scaled to the same luminosity.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1438\n\n) in 2D\n2\n - l\n1\ncos(l\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n) in 2D\n2\n - l\n1\ncos(l\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n) in 3D\n2\n - l\n1\ncos(l\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n) in 3D\n2\n - l\n1\ncos(l\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\n0.09\n (GeV)\nlepton 1\nT\np\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n (GeV)\nlepton 1\nT\np\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n HZ\n\u03bd \u03bd\n l l \n\u2192\n ZZ \n t\n WW, t\n, ZW, Z + jet\n\u03c4 \u03c4\n l l \n\u2192\n ZZ \n \n (GeV)\nlepton 2\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n (GeV)\nlepton 2\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n \nATLAS\nFigure 9: Input variables used by the Boosted Decision Tree for the signal with mH = 130 GeV and the\nmain backgrounds. Top left: Transverse momentum of the most energetic lepton. Top right: Transverse\nmomentum of the second lepton. Bottom left: Cosine of the angle between the two leptons in the\ntransverse plane and, Bottom right: in 3-dimensions. Each plot has been normalized to unity. The\ncombined samples had \ufb01rst been scaled to the same luminosity.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1439\n\nenergy in cone around lepton 1 (GeV)\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nenergy in cone around lepton 1 (GeV)\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nenergy in cone around lepton 2 (GeV)\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nenergy in cone around lepton 2 (GeV)\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n)\nZ\n - p\nmiss\nT\ncos(E\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-3\n10\n-2\n10\n-1\n10\n1\n)\nZ\n - p\nmiss\nT\ncos(E\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-3\n10\n-2\n10\n-1\n10\n1\n HZ\n\u03bd \n\u03bd\n l l \n\u2192\n ZZ \n t\n WW, t\n, ZW, Z + jet\n\u03c4 \u03c4\n l l \n\u2192\n ZZ \n \n)\nmiss\nT\n - E\n1\ncos(jet\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-2\n10\n-1\n10\n)\nmiss\nT\n - E\n1\ncos(jet\n-1\n-0.5\n0\n0.5\n1\narbitrary units\n-2\n10\n-1\n10\nATLAS\nFigure 10: Input variables used by the Boosted Decision Tree for the signal with mH = 130 GeV and\nthe main backgrounds. Top left: The cosine of the angle between the direction of missing ET and the\nreconstructed Z transverse momentum. Top right: The cosine of the angle between the most energetic\njet and the direction of missing ET. Bottom left: The energy contained in a cone of 0.10 rad around\nthe most energetic lepton. Bottom right: The energy contained in a cone of 0.10 rad around the second\nlepton. Each plot has been normalized to unity. The combined samples had \ufb01rst been scaled to the same\nluminosity.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1440\n\n (GeV)\njet 3\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n (GeV)\njet 3\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nnumber of jets\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\narbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nnumber of jets\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\narbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n (GeV)\njet 1\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n (GeV)\njet 1\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n HZ\n\u03bd \u03bd\n l l \n\u2192\n ZZ \n t\n WW, t\n, ZW, Z + jet\n\u03c4 \u03c4\n l l \n\u2192\n ZZ \n (GeV)\njet 2\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n (GeV)\njet 2\nE\n0\n50\n100\n150\n200\n250\n300\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nATLAS\nFigure 11: Input variables used by the Boosted Decision Tree for the signal with mH = 130 GeV and the\nmain backgrounds. Top left: The energy distribution for the most energetic jet; Top right: for the second\nand, Bottom left: third most energetic jets. Bottom right: the number of jets in the event. Each plot has\nbeen normalized to unity. The combined samples had \ufb01rst been scaled to the same luminosity.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1441\n\n ll + jet) BDT output\n\u2192\n(Z \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n ll + jet) BDT output\n\u2192\n(Z \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n ll l\n\u2192\n(ZW \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n ll l\n\u2192\n(ZW \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03c4\n\u03c4\n ll \n\u2192\n(ZZ \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03c4\n\u03c4\n ll \n\u2192\n(ZZ \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n l\n\u03bd\n l\n\u2192\n(WW \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n l\n\u03bd\n l\n\u2192\n(WW \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n bl\n\u03bd\n bl\n\u2192\n(tt \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\n) BDT output\n\u03bd\n bl\n\u03bd\n bl\n\u2192\n(tt \n-2\n-1.5\n-1\n-0 5\n0\n0 5\n1\nentries\n-2\n10\n-1\n10\n1\n10\n2\n10\nHZ\n\u03bd \u03bd\n l l \n\u2192\nZZ \n t\nt\nWW\n\u03c4 \u03c4\n l l \n\u2192\nZZ \nZW\nZ+jets\nATLAS\nFigure 12: The Boosted Decision Tree (BDT) output variables obtained after comparing half the signal\nevents to \ufb01ve different backgrounds separately, namely, from top to bottom: t\u00aft \u2192b\u2113\u03bdb\u2113\u03bd, WW \u2192\u2113\u03bd\u2113\u03bd,\nZZ \u2192\u2113\u2113\u03c4\u03c4, ZW \u2192\u2113\u2113\u2113\u03bd and Z \u2192\u2113\u2113+ jets. The BDT assigns values close to +1 for a signal-like event and\n-1 for background-like events. The distributions are shown for the signal and all types of background\nwhen using the other half of the events for the analysis. The Boosted Decision Trees trained against\nthe ZW background offers the best separation power. The \u03be 2 decreases further once additional cuts on\nthe other BDT output variables are applied, namely the WW BDT output, then the ZZ \u2192\u2113\u2113\u03c4\u03c4 BDT\noutput, the (Z+jet) BDT output and \ufb01nally the t\u00aft BDT output. All BDT output cut values are indicated\nby a vertical dashed line. Nothing is gained from training a BDT against the irreducible background,\nZZ \u2192\u2113\u2113\u03bd\u03bd for all Higgs boson mass hypotheses, so it is not used.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1442\n\ninput variable to BDT\nsum of weights\nZ mass\n0.57\ncos\u2113\u2113(in 2D)\n0.46\ncos\u2113\u2113(in 3D)\n0.42\ncos(Emiss\nT\n\u2212\u20d7pZ)\n0.41\n# of jets\n0.40\ntransverse mass\n0.39\ncos(jet \u2212Emiss\nT\n)\n0.32\ncosEmiss\nT\n\u2212plepton#1\nT\n0.31\nEmiss\nT\n0.28\nplepton#1\nT\n0.27\nE jet#1\n0.26\nE jet#2\n0.23\nplepton#2\nT\n0.21\nenergy in a cone around lepton # 1\n0.17\nenergy in a cone around lepton # 2\n0.16\nE jet#3\n0.13\nTable 10: Order of importance for the 16 input variables used to train the separate Boosted Deci-\nsion Trees used for the analysis at mH = 130 GeV. The second column gives the sum of the weights\ngiven to each input variable by the \ufb01ve separate BDT used for the analysis. These weights are not\nused for the analysis per se but give an idea of the relative importance of each input variable. In\nparticular, the \ufb01rst four variables are used to mostly reject the non-resonant background.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1443\n\nchannel\nZH\nZZ\nt\u00aft\nWW\nZZ\nZZ\nZW\nZ+jet\n\u2113\u00af\u2113inv.\n\u2113\u00af\u2113\u03bd\u03bd\n\u2113\u03bd\u2113\u03bd\n\u03c4\u03c4\u03bd\u03bd\n\u2113\u2113\u03c4\u03c4\n\u2113\u2113\u2113\u03bd\n\u2113\u2113+jet\nexpressed as cross-sections given in fb\nmH = 110 GeV\n1.31\n3.44\n0.00\n0.01\n0.00\n0.02\n0.37\n0.03\nmH = 120 GeV\n2.99\n13.64\n0.18\n0.28\n0.00\n0.16\n2.16\n0.10\nmH = 130 GeV\n0.89\n2.93\n0.00\n0.00\n0.00\n0.02\n0.33\n0.00\nmH = 140 GeV\n0.98\n3.51\n0.00\n0.00\n0.00\n0.03\n0.48\n0.00\nmH = 150 GeV\n1.32\n6.37\n0.18\n0.00\n0.00\n0.06\n0.62\n0.00\nmH = 200 GeV\n0.62\n4.83\n0.18\n0.00\n0.00\n0.04\n0.42\n0.00\nmH = 250 GeV\n0.31\n2.50\n0.00\n0.00\n0.00\n0.03\n0.24\n0.02\n# of events corresponding to 30 fb\u22121\nmH = 110 GeV\n39.2\n103.1\n<2.7\n0.2\n<0.01\n0.8\n11.0\n0.8\nmH = 120 GeV\n89.6\n409.3\n5.4\n8.5\n0.1\n4.7\n64.7\n3.0\nmH = 130 GeV\n26.8\n87.9\n<2.7\n<0.06\n<0.01\n0.8\n9.9\n<0.36\nmH = 140 GeV\n39.5\n191.1\n5.4\n<0.06\n<0.01\n1.7\n18.7\n<0.36\nmH = 150 GeV\n36.5\n173.0\n5.4\n0.2\n<0.01\n1.8\n19.0\n<0.36\nmH = 200 GeV\n18.5\n145.0\n5.4\n<0.06\n<0.01\n1.3\n12.7\n<0.36\nmH = 250 GeV\n9.3\n74.9\n<2.7\n<0.06\n<0.01\n1.0\n7.2\n0.7\nTable 11: Monte Carlo estimates of the cross-sections in fb surviving the \ufb01nal Boosted Decision\nTree selection cuts for each background process and seven mass hypotheses for the ZH channel.\nThe corresponding numbers of events for 30 fb\u22121 of total integrated luminosity are also given.\nThe \ufb01nal cuts on the Boosted Decision Tree output variables were set separately for each BDT\noutput variable and for each mass hypothesis, each time optimizing the sensitivity \u03be 2.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1444\n\nknown, given the theoretical uncertainties on the Standard Model production cross-sections and this leads\nto the main source of systematic uncertainty. The current best estimates for each of these cross-sections\nfrom the next-to-leading order calculation is about 6% for ZZ and 5% for ZW [20]. The uncertainty on\nthe (Z+jet) cross-section has no impact on the \ufb01nal results since this background is negligible. Several\ncontrol samples can be used to constrain the ZZ and ZW cross-sections. For ZZ, one can use the four\nlepton \ufb01nal state (even including \u03c4) but this will require a large data sample (of the order of at least\n30 fb\u22121) to reduce the statistical uncertainty. For the ZW cross-section, one can use a ZW control\nsample with events containing three identi\ufb01ed leptons. Both these cross-sections will be measured in\nATLAS data. Uncertainties associated with kinematic distributions have not been taken into account at\nthis point. A combined theoretical uncertainty of 5.8% obtained from a weighted average is assigned to\nthe background production cross-section.\nOne could in principle use ZZ \u2192\u2113\u2113\u2113\u2113events from data to calibrate the number of events coming\nfrom ZZ \u2192\u2113\u2113\u03bd\u03bd decays. Such an approach was proposed in [21] where one would \ufb01rst select a pure\nsample of ZZ \u2192\u2113\u2113\u2113\u2113events by \ufb01nding two Z bosons, then declaring one Z to decay invisibly. This\nwould work in the absence of other backgrounds but it is not possible to completely eliminate the ZW \u2192\n\u2113\u2113\u2113\u03bd background. More importantly, such a technique has a very low ef\ufb01ciency: about 1.8% of all\nZZ \u2192\u2113\u2113\u2113\u2113survive the preselection cuts, with \u2113here being e,\u00b5 or \u03c4. Only a dozen of events would\nsurvive all of the BDT selection cuts for 30 fb\u22121 of data. Hence, it is deemed impossible to calibrate\nquantitatively the ZZ \u2192\u2113\u2113\u2113\u2113cross-section using this technique. However, one could still check the effect\nof the preselection cuts on ZZ \u2192\u2113\u2113\u2113\u2113events with two leptons declared invisible as described above to\nensure that the main and irreducible background, ZZ \u2192\u2113\u2113\u03bd\u03bd, behaves as expected under these cuts.\nAbout 85 ZZ \u2192\u2113\u2113\u2113\u2113events are expected to pass the preselection cuts, as opposed to 163 ZZ \u2192\u2113\u2113\u03bd\u03bd\nevents for 30 fb\u22121 of integrated luminosity. After the preselection cuts, the ZZ \u2192\u2113\u2113\u03bd\u03bd background\ncorresponds to about 36% of the total number of selected events in the absence of non Standard Model\ncontributions, as seen from Table 8. This method would provide a normalization of the cross-section\nusing data at about 11% uncertainty level.\n3.3.2\nEffect related to the training of the Boosted Decision Tree\nSince half the events are used for training the BDT, and the other half for testing, this arbitrary choice\nhas a slight effect on the outcome. For the central value of this analysis, we used every other event for\nthe training. To estimate the effect of this choice, the analysis was redone using the \ufb01rst half of the events\nfor training, and the second half for testing. Since we are only using Monte Carlo events, this second\nchoice does not introduce additional time-dependent effects that one would expect with real data. The\ndifference in the results, namely +0.2% signal events and +0.7% background events, is ascribed as a\ncontribution to the systematic uncertainty.\n3.3.3\nLepton momentum resolution effect and energy scale effect\nDifferent tests are done to assess the contributions to the systematic uncertainty from the lepton momen-\ntum resolution and the uncertainty on the lepton energy scale. Each time, new modi\ufb01ed input variables\nare used to retrain the BDT and assess the overall effect by comparing the new number of selected signal\nand background events to the original numbers of events selected. All contributions to the systematic\nuncertainty are summarized in Table 12.\nThe tests performed are:\n\u2022 The lepton momenta are smeared using a Gaussian distribution. A constant sigma of 0.73% is\nused for electrons. For muons, the sigma is calculated using the following formula: \u03c3(pT) =\n[(0.011 \u00b7 pT)2 + (0.00017 \u00b7 p2\nT)2]1/2/pT with pT in GeV. The smearing is applied to one type of\nleptons at a time.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1445\n\nsignal\nbackground\nelectron reconstruction ef\ufb01ciency\n\u00b10.2%\n\u00b10.2%\nelectron pT resolution (\u00b10.73%)\n+0.5%\n+1.7%\nelectron energy scale (\u00b10.5%)\n+1.1%\n+2.1%\nsub-total for electrons (43% of events)\n+1.2% -0.2%\n+2.7% - 0.2%\nmuon reconstruction ef\ufb01ciency\n\u00b11.0%\n\u00b11.0%\nmuon pT resolution (see formula in text)\n+1.1%\n+1.9%\nmuon energy scale (\u00b11%)\n+1.0%\n+2.2%\nsub-total for muons (57% of events)\n+1.8% - 1.0%\n+3.1% - 1.0%\ncombined contributions for leptons\n+1.5% - 0.7%\n+2.9% - 0.7%\njet energy scale (\u00b17% or \u00b115%)\n+0.8%\n+0.2% - 2.2%\njet energy resolution effect on Emiss\nT\n-2.2%\n-0.4%\nluminosity\n-\n\u00b13.0%\ncross-section\n-\n\u00b15.8%\n\ufb01lter effects\n\u00b11.4%\n\u00b11.4%\nBoosted Decision Tree training effects\n\u00b10.2%\n\u00b10.7%\ntotal\n+2.2% - 2.6 %\n+7.3% - 7.1%\nTable 12: Contributions to the systematic uncertainties. The Higgs boson mass was set to 130\nGeV to assess these uncertainties. The \ufb01nal background uncertainty is rounded-off to \u00b17.2%.\n\u2022 For each type of lepton, a multiplicative scaling factor is applied to simulate an energy scale\nuncertainty of \u00b10.5% for electrons and \u00b11.0% for muons.\n3.3.4\nJet momentum resolution effect and energy scale effect\nThree different modi\ufb01cations are done in turn to the jet energy to evaluate the contributions from the\njet energy scale and jet energy resolution to the missing energy evaluation. After each modi\ufb01cation, the\nmissing ET is recalculatedEach contribution is shown in Table 12. The three modi\ufb01cations made to the\njet energy are:\n\u2022 Jet energy scale: the jet energy is increased by \u00b17% for jets within \u03b7 \u22643.2 and \u00b115% for jets\nwithin \u03b7 > 3.2.\n\u2022 Jet energy resolution: the jet energy is smeared using a Gaussian by 0.45 \u00b7\n\u221a\nE for jets within\n\u03b7 \u22643.2 and 0.63\u00b7\n\u221a\nE for \u03b7 > 3.2.\n3.4\nResults for the ZH channel\nThe sensitivity with 30 fb\u22121 of data is evaluated in terms of \u03be 2 with \u03be 2 = 1.64\u03c3B/NS for a 95% CL as for\nthe VBF analysis where \u03c3B is the combined statistical and systematic uncertainty as detailed in Section\n2.5. The values of \u03be 2 are summarized in Table 13.\n3.5\nCross-checks with a cut-based analysis\nTo ensure that the Boosted Decision Tree performed as expected, we duplicated a previous ATLAS\nanalysis performed using a cuts-based approach [21]. The same cuts as were applied to our current\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1446\n\nmH\n# signal\n# background\n\u03c3B\n\u03be 2\n110 GeV\n39.2\n115.9\n13.6\n56.7%\n120 GeV\n82.5\n449.4\n38.3\n76.2%\n130 GeV\n26.8\n98.6\n12.2\n74.4%\n140 GeV\n39.5\n217.0\n21.3\n88.5%\n150 GeV\n36.5\n199.4\n20.0\n89.9%\n200 GeV\n18.5\n164.4\n17.3\n153.4%\n250 GeV\n9.3\n83.8\n10.9\n191.6%\nTable 13: The sensitivity with 30 fb\u22121 at 95% con\ufb01dence level calculated in terms of \u03be 2 for seven\ndifferent mass hypotheses for the ZH channel.\nMonte Carlo samples after the \ufb01lter and trigger cuts of this analysis, and using the signal generated with\nmH = 130 GeV. These cuts are:\n1. Filter cuts as in this analysis\n2. Trigger cuts as in this analysis\n3. Lepton cuts: select events containing no more than two leptons with pT > 7 GeV. Electrons must\nhave pT > 15 GeV within |\u03b7| < 2.5 and muons are selected if pT > 10 GeV and |\u03b7| < 2.4. Two\nleptons of the same \ufb02avor but opposite charge are required.\n4. Z mass: the recontructed Z mass must be within 10 GeV from the pole mass.\n5. Emiss\nT\n> 100 GeV.\n6. Jet veto: all events containing a jet having pT > 30 GeV within |\u03b7| < 4.9 are rejected.\n7. b-jet veto: all events containing a b-tagged jet having at pT > 15 GeV within |\u03b7| < 4.9 are rejected.\n8. Transverse mass: mT > 200 GeV.\nThe two analyses can be compared after the MET cut. The sensitivity with 30 fb\u22121 at 95% con\ufb01dence\nlevel calculated in terms of \u03be 2 for this cut-based analysis is 87.9% for mH = 130 GeV. This compares\nwell with what was obtained with the BDT technique (\u03be 2 = 74.4% for the same mass value with the BDT\napproach). The difference in sensitivity increases further for higher Higgs mass hypotheses. The results\nare given in Table 14.\n4\nComparison of results and summary\nThe sensitivity of ATLAS to an invisibly decaying Higgs boson produced via the VBF and ZH channel\nhas been examined. A comparison between the sensitivities of the two channels can be seen in Figure 13.\nThis plot shows that the channels have a similar sensitivity for low Higgs boson masses. It is possible\nto look at combined statistics for the ZH analysis and the VBF shape analyses although the analysis\ntechniques are different. Clearly the improvement in sensitivity by combining statistics is not large. Of\nfar greater signi\ufb01cance in the analysis of real ATLAS data would be the observation of a signi\ufb01cant\nexcess of events in two different and distinct channels. An observation of this kind would give credibility\nto the hypothesis that a particle is being generated that behaves like a Higgs boson and decays invisibly.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1447\n\nchannel\nZH\nZZ\nt\u00aft\nWW\nZZ\nZZ\nZW\nZ+jet\n\u2113\u00af\u2113inv.\n\u2113\u00af\u2113\u03bd\u03bd\n\u2113\u03bd\u2113\u03bd\n\u03c4\u03c4\u03bd\u03bd\n\u2113\u2113\u03c4\u03c4\n\u2113\u2113\u2113\u03bd\n\u2113\u2113+jet\n\u03c3*BR in fb\n46.2\n728.0\n833000.0\n5245.6\n364.0\n123.0\n820.0\n3105062.8\nafter \ufb01lter\n34.9\n212.6\n9412.9\n236.5\n18.8\n87.8\n820.0\n478.4\nafter trigger\n32.5\n198.5\n8620.6\n217.1\n14.2\n77.8\n735.3\n460.6\npT lepton +ID + charge cut\n23.8\n148.1\n4451.2\n158.4\n2.7\n37.6\n177.5\n221.6\nafter mZ \u00b110 GeV cut\n20.7\n133.0\n1654.7\n51.1\n0.0\n28.8\n125.4\n192.9\nafter Emiss\nT\n> 100 cut\n7.4\n44.9\n460.7\n7.3\n0.0\n0.8\n13.7\n27.9\nno jet with pT > 30 GeV\n4.2\n23.7\n5.8\n0.8\n0.0\n0.3\n4.2\n0.1\nb-tag cut for jet with pT > 15 GeV\n4.2\n23.6\n4.8\n0.8\n0.0\n0.3\n4.1\n0.1\nafter mT > 200 GeV cut\n3.9\n21.3\n0.5\n0.4\n0.0\n0.3\n3.4\n0.1\nTable 14: Monte Carlo estimates of the cross-sections in fb after applying simple cuts for each\nbackground process and one mass hypothesis of mH = 130 GeV for the ZH channel. The corre-\nsponding \u03be 2 would be 87.9%.\nHiggs Mass [GeV]\n100\n120\n140\n160\n180\n200\n220\n240\n260\n [%]\n2\n\u03be\n0\n50\n100\n150\n200\n250\nATLAS\n\tVBF Shape Analys\n\tZH Boosted Decision Tree Analys\nFigure 13: Sensitivity to an invisible Higgs boson with ATLAS for both the VBF and ZH channels\nwith 30 fb\u22121of data assuming only Standard Model backgrounds. The open crosses show the\nsensitivity for the ZH analysis and the solid triangles show the sensitivity for the VBF shape\nanalysis for 95 % CL. Both these results include systematic uncertainties.\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1448\n\nIn summary, a study using fully simulated ATLAS data has shown that the ATLAS experiment will\nbe sensitive to an invisibly decaying Higgs boson in both the VBF and ZH production channels assuming\nonly Standard Model backgrounds. It is clear that the analysis will require a good understanding of the\nexperimental systematic uncertainties. If the decay of a Higgs boson was entirely in the invisible mode,\nthis analysis has shown that with 30 fb\u22121of data, ATLAS will be sensitive to a situation in which the\nbeyond the Standard Model cross-section is of the order of 80% the Standard Model Higgs boson cross-\nsections for a Higgs Boson mass of less than 150 GeV. The VBF analysis has a sensitivity of better than\n90% up to a Higgs Boson mass of 250 GeV.\nReferences\n[1] K. Greist, H. E. Haber, Phys. Rev. D37 (1988) 719; A. Djouadi, J. Kalinowski, P. M. Zerwas, Z.\nPhys. C57 (1993) 569; A. Djouadi, P. Janot, J. Kalinowski, P. M. Zerwas, Phys. Lett. B376(1996)\n220; I. Antoniadis, M. Tuckmantel, F. Zwirner, Nucl. Phys. B707 (2005) 215.\n[2] J. C. Romao, F. de Campos, J. W. F. Valle, Phys. Lett. B292 (1992) 329; M. Hirsch, J. C. Romao,\nJ. W. F. Valle; A. V. Moral, Invisible Higgs Boson Decays in Spontaneously Broken R-Parity, hep-\nph/0407269.\n[3] N. Arkani-Hamed, S. Dimopoulos, G. Dvali, J. March-Russell, Phys. Rev. D024032 (2002) 1264;\nA. Datta, K. Huitu, J. Laamanen, B. Mukhopadhyaya, Phys. Rev. D70 (2004) 075003; K. M. Be-\nlotsky, V. A. Khoze, A. D. Martin, M. G. Ryskin, Eur. Phys. J. C36 (2004) 503; D. Dominici, hep-\nph/0408087 (2004); J. Laamanen, hep-ph/0505104 (2005); D. Dominici, hep-ph/0503216 (2005);\nM. Battaglia, D. Dominici, J. F. Gunion, J. D. Wells, hep-ph/0402062 (2004); A. Datta, K. Huitu,\nJ. Laamanen, B. Mukhopadhyaya, Phys. Rev. D70 (2004) 075003.\n[4] LEP Higgs Working Group, Searches for invisible Higgs bosons: Preliminary combined results\nusing LEP data collected at energies up to 209 GeV, hep-ex/0107032 (2001).\n[5] O. J. P. \u00b4Eboli, D. Zeppenfeld,, Phys. Lett. B 495 (2000) 147.\n[6] J. F. Gunion, Phys. Rev. Lett. 72 (1994) 199.\n[7] D. Choudhury, D. P. Roy, Phys. Lett. B 232 (1994) 368.\n[8] R. M. Godbole, M. Guchait, K. Mazumdar, S. Moretti, D.P. Roy, Phys. Lett. B 1571 (2003) 1284.\n[9] ATLAS Collaboration, Introduction on Higgs Boson Searches, this volume.\n[10] P. Gagnon, Invisible Higgs boson decays in the ZH and WH channels, ATL-PHYS-PUB-2005-011\n(2005).\n[11] G. Corcella et al., Herwig 6.5 Release Note, hep-ph/0210213v2 (2005).\n[12] J. M. Butterworth, J. R. Forshaw, M. H. Seymour, Z. Phys. C72 (1996) 637\u2013646.\n[13] J. M. Butterworth, M. H. Seymour, Jimmy4: Multiparton Interactions in Herwig for the LHC,\nhttp://projects.hepforge.org/jimmy/draft20051116.ps.\n[14] T. Sjostrand, S. Mrenna, P. Skands, PYTHIA 6.4 Physics and Manual, hep-ph/0603175 (2006).\n[15] B. Mellado, A. Nisati, D. Rebuzzi, S. Rosati, G. Unal, S. L. Wu, Higgs Production Cross-Sections\nand Branching Ratios for the ATLAS Higgs Working Group, ATL-COM-PHYS-2007-024 (2007).\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1449\n\n[16] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties, this\nvolume.\n[17] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, A. Polosa, JHEP 07 (2003) 001.\n[18] ATLAS Collaboration, Jets and Missing Transverse Energy Chapter, this volume;\nATLAS Collaboration, b-Tagging Chapter, this volume;\nATLAS Collaboration, Electrons and Photons Chapter, this volume;\nATLAS Collaboration, Muon Chapter, this volume.\n[19] A. H\u00a8ocker et al., TMVA - Toolkit for Multivariate Data Analysis, CERN-OPEN-2007-007, ACAT\n040, 2007, arXiv: physics/0703039, http://tmva.sf.net/.\n[20] ATLAS Collaboration, Diboson Physics Studies, this volume.\n[21] F. Meisel, M. Duhrssen, M. Heldmann, K. Jakobs, Study of the discovery potential for an invisibly\ndecaying Higgs boson via the associated ZH production in the ATLAS experiment, ATL-PHYS-\nPUB-2006-009 (2006).\nHIGGS \u2013 SENSITIVITY TO AN INVISIBLY DECAYING HIGGS BOSON\n1450\n\nCharged Higgs Boson Searches\nAbstract\nThe discovery of a charged Higgs boson would be tangible proof of physics\nbeyond the Standard Model. This note presents the ATLAS potential for dis-\ncovering a charged Higgs boson, utilizing \ufb01ve different \ufb01nal states of the signal\narising from the three dominating fermionic decay modes of the charged Higgs\nboson. The search covers the region below the top quark mass, taking into ac-\ncount the present experimental constraints, the transition region with a charged\nHiggs boson mass of the order of the top quark mass, and the high-mass region\nwith a charged Higgs boson mass up to 600 GeV. All studies are performed\nwith a realistic simulation of the detector response including all three trigger\nlevels and taking into account all dominant systematic uncertainties. Results\nare given in terms of discovery and exclusion contours for each channel indi-\nvidually and for all channels combined, showing that the ATLAS experiment\nis capable of detecting the charged Higgs boson in a signi\ufb01cant fraction of the\n(tan\u03b2, mH\u00b1) parameter space with its \ufb01rst 10 fb\u22121 of data. The so-called in-\ntermediate tan\u03b2 region (around tan\u03b2 = 7) is experimentally hard to reach but\nexclusion sensitivity is given in this area.\n1\nIntroduction\nCharged Higgs bosons (H\u00b1)1 are naturally predicted in many non-minimal Higgs scenarios, such as\nTwo Higgs Doublet Models (2HDM), and models with Higgs triplets including Little Higgs models.\nTheir discovery would be a de\ufb01nite signal for the existence of New Physics beyond the Standard Model,\npossibly the \ufb01rst experimental evidence for the Minimal Supersymmetric Standard Model (MSSM) if it\nis realised in nature, and the supersymmetry mass scale is high enough that sparticles escape discovery.\nThe following analyses will only consider the 2HDM, in particular the so-called type II-2HDM, which\nis the Higgs sector of the MSSM.\nThe search strategies for charged Higgs bosons depend on their hypothesized mass, which dictates\nboth the production rate and the available decay modes. Below the top quark mass, the main production\nmode is through top quark decays, t \u2192H+b, and in this range the H+ \u2192\u03c4\u03bd decay mode is dominant.\nAbove the top quark threshold, production mainly takes place through gb fusion (gb \u2192tH+), and for\nsuch high charged Higgs boson masses the decay into a top quark and a b quark dominates, H+ \u2192tb .\nA more detailed discussion of the different signal \ufb01nal states used for this study including backgrounds,\ncross-sections and branching ratios can be found in Reference [1].\nCharged Higgs boson searches involve several higher level reconstructed physics objects such as elec-\ntrons, muons, jets, jets tagged as b jets and \ufb01nally jets identi\ufb01ed as \u03c4 jets. These objects are reconstructed\nby dedicated ATLAS algorithms and details about their performance can be found in References [2\u20136].\nIn the following, only ef\ufb01ciencies will be quoted for the different objects.\nThe note is organized as follows: Section 2 summarizes the trigger menus used for the signatures\nunder investigation. The analysis sections are divided into light (Section 3) and heavy (Section 4) H+\nstudies, which are in turn divided according to the signal \ufb01nal state: First, t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq\nis discussed in Section 3.1, then t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq in Section 3.2. Section 3.3 addresses\nt\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd. Two studies for heavy H+ are described, namely for gg/gb \u2192t[b]H+ \u2192\nbqq[b]\u03c4(had)\u03bd (Section 4.1) and gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb (Section 4.2).\nIn Section 5, systematic uncertainties and their impact are discussed, followed by a description of the\n1In the following, the charged Higgs boson will be denoted H+ , but H\u2212is always implicitly included.\n1451\n\ndata-driven t\u00aft control sample method which is needed for the extraction of the background shape and\nnormalization in all H+ studies. Section 6 provides combined results from the different search topolo-\ngies. The charged Higgs boson results are summarized in Section 7.\n2\nTrigger\nThe production and decay modes of the charged Higgs boson studied here lead to \ufb01nal states containing\nthe following: two to four b jets, light jets from hadronic decays of W bosons, one or more neutrinos from\nW or H+ decays, and for most channels a tau lepton decaying either hadronically or into an electron or\nmuon plus neutrinos. These event characteristics suggest the following ATLAS Trigger [7] menus, one\nfor an instantaneous luminosity of L = 1031cm\u22122s\u22121, and two alternatives for L = 1033cm\u22122s\u22121, based\non these trigger signatures:\n\u2022 L = 1031cm\u22122s\u22121: xE70, e22i, mu20, xE30_L1_TAU13, xE20_3j20_L1_TAU13\n\u2022 L = 1033cm\u22122s\u22121: xE80, e55, mu40, xE50_L1_TAU30, xE40_3j20_L1_TAU30 or\nxE80, e22i_xE30, mu20_xE30, xE50_L1_TAU30, xE40_3j20_L1_TAU30\nwhere xE represents a missing transverse energy trigger selection, and e, mu, tau and j correspond to\nelectron, muon, tau, and jet triggers, respectively. A number before each symbol indicates the required\ntrigger multiplicity, as in 3j for three jets. Values after these symbols are the approximate trigger thresh-\nolds in transverse momentum, and a \ufb01nal i means that isolation requirements are applied. L1_ indicates\nthat the stated threshold for the following trigger selection is applied at the \ufb01rst trigger level while the\nhigh level trigger selection is softer. Combined triggers are indicated by the juxtaposition of two or more\nselections. Each analysis uses a subset of items of the two 1033 menus.\nThe menus were chosen based on a careful study of the signal event characteristics and the most\nrealistic trigger signature rates available. The chosen signatures meet the requirements of the trigger\nbandwidth budget [7] at all trigger levels. For each of the channels studied in the following sections, the\ntrigger ef\ufb01ciencies will be evaluated.\n3\nLight Charged Higgs Boson Searches\nIn this section, charged Higgs boson searches in the three light H+ channels (mH+ < mt) selected for\ninvestigation are presented:\n\u2022 t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq\n\u2022 t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq\n\u2022 t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd\nwhere for a tau lepton, \u03c4(had) indicates its hadronic decay and \u03c4(lep) its decay to an electron or muon\nplus neutrinos. If the charged Higgs boson is light, then BR(t \u2192bW) might not be close to unity, as it\nis in the Standard Model prediction. This means that the expected background from Standard Model t\u00aft\ndecays (the dominant background to all H+ searches) is reduced. Since the number of events after the\nevent selection is NSM\nt\u00aft\nfor the background-only hypothesis, and NH+ +NMSSM\nt\u00aft\nin the signal+background\ncase, the number of observable excess events is thus not simply the number of H+ events (NH+) \u2014 it is\ndecreased by the difference in the SM and the MSSM t\u00aft prediction: Nexcess = NH+ \u2212(NSM\nt\u00aft\n\u2212NMSSM\nt\u00aft\n).\nThis is taken into account consistently.\nAll plots, tables and results in this section are based on the trigger menu for an instantaneous lumi-\nnosity of L=1033cm\u22122s\u22121 presented in Section 2, on the signal cross-sections for the mh-max MSSM\nscenario (see Reference [1]) and the background cross-sections given in Reference [8].\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1452\n\n3.1\nt\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq\nThe channel in which both the \u03c4 and the W boson decay hadronically has a relatively high cross-section,\nmaking it a priori one of the most promising in searches for H+ lighter than the top quark. On the other\nhand, the absence of leptons, as well as the high hadronic activity, is a challenge, particularly for the\ntrigger. The events are characterised by a \u03c4 jet, four other jets, two of which are initiated by b quarks,\nand missing energy. The main expected backgrounds for this channel are t\u00aft events where one top quark\ndecays hadronically and the other to a hadronically decaying \u03c4. For this study all t\u00aft decay modes have\nbeen considered as background, as well as single top, W+jets and QCD dijet events. For ATLAS, this\nchannel has previously only been studied using fast simulation [9].\n3.1.1\nPreselection\nTrigger\nEither the xE50_L1_TAU30 or the xE40_3j20_L1_TAU30 trigger signature (see Section 2) is\nrequired for this study.\nCuts I\nFollowing the trigger, a set of cuts was used to preselect the signal and suppress the background.\nThis \ufb01rst cut set relates primarily to the multiplicity of the of\ufb02ine analysis objects (which are different\nfrom the trigger objects, leading in some cases to lower optimum cut values for the of\ufb02ine objects). These\nare given in Table 3.1.1.\nCuts II\nAfter the \ufb01rst set of cuts, the W is reconstructed from the pair of light jets with invariant mass\nm j j closest to the nominal W mass, mW. The parent top quark is then found by pairing the reconstructed\nW with the b quark which leads to an apparent top quark mass m j jb closest to the nominal value mt. Cuts\nare made both on the W and the top quark reconstructed masses. The top quark on the H+ side cannot\nbe fully reconstructed due to the presence of the neutrino, but information on its azimuthal angle, \u03c6, and\ntransverse momentum, pT, can still be extracted.\nAt this stage a large number of background events still remains, mainly from Standard Model t\u00aft as\nwell as from QCD and single-top production. In order to discriminate against the latter two, two cuts\n(items 8 and 9 in Table 3.1.1) are applied aiming to enhance the topology of t\u00aft decays.\nTable 1: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Applied precuts. A b-tagging cut is applied to all jets,\nyielding b jet reconstruction ef\ufb01ciency of about 70%. For \u03c4 jets, a cut on the \u03c4-tagging variable\nis applied such that a reconstruction ef\ufb01ciency of about 32% is obtained for a pseudorapidity\n|\u03b7| < 1.5, and a tighter cut (due to the high QCD jet fake-rate for large \u03b7) for |\u03b7| > 1.5 leads to an\nef\ufb01ciency of about 20% in this region. The Emiss\nT\ncut is increased to 50 GeV if only the signature\nxE50 L1 TAU30 has triggered the event.\nCuts I\nCuts II\n1. exactly 1 \u03c4-tagged jet with pT > 35 GeV\n6. |mrec\nW \u2212mW| < 30 GeV\n2. exactly 2 b-tagged jets with pT > 15 GeV\n7. |mrec\nt\n\u2212mt| < 40 GeV\n3. at least 2 non-tagged jets with pT > 15 GeV\n8. \u2206\u03c6(phardest top\nT\n, psoftest top\nT\n) > 2.5\n4. veto on isolated leptons with pT > 5 GeV\n9. phardest top\nT\n/psoftest top\nT\n< 2\n5. Emiss\nT\n> 40/50 GeV\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1453\n\n Likelihood Discriminant Value\n0\n0.2\n0.4\n0.6\n0.8\n1\nNumber of Events\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n Likelihood Discriminant Value\n0\n0.2\n0.4\n0.6\n0.8\n1\nNumber of Events\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nSignal\n no-all-hadronic\ntt\n all-hadronic\ntt\nSingle top\nW + jets\nATLAS\n candidate (GeV)\n+\n Transverse Mass of H\n0\n20\n40\n60\n80 100 120 140 160 180 200\nNumber of Events\n0\n50\n100\n150\n200\n250\n candidate (GeV)\n+\n Transverse Mass of H\n0\n20\n40\n60\n80 100 120 140 160 180 200\nNumber of Events\n0\n50\n100\n150\n200\n250\nSignal\n no-all-hadronic\ntt\nATLAS\n(a)\n(b)\nFigure 1: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Likelihood distribution (a) and transverse mass (b) for an H+\nmass of 130 GeV and the corresponding background, stacked and normalized to the cross-section with\ntan\u03b2 = 20. The hatched area shows what would be expected from a Standard Model only scenario. A\ncut at 0.6 is made on the likelihood and at 65 GeV on the transverse mass.\n3.1.2\nLikelihood Discriminant\nFollowing these cuts, the remaining background is dominated by t\u00aft events, particularly those in which one\nW decays hadronically and the other to a \u03c4 and a neutrino, and all reducible backgrounds are effectively\nsuppressed. In order to discriminate between this background and the signal, a Likelihood Discriminant\nmethod has been implemented. The variables used (listed in Table 2) have been selected to re\ufb02ect\nthe two characteristics which distinguish the signal from the background: the heavier mass of the H+\ncompared to the W, with its effects on the kinematics of the event; and the difference in \u03c4 polarization\ndepending on the parent. This difference, exploited in variable I, will cause the leading track within the\n\u03c4 jet to be harder [10]. Also selected combinations of variables have been included, as correlations are\nnot included in the de\ufb01nition of the likelihood used. Likelihood discriminants are constructed for the\n\ufb01ve different studied H+ mass points (90, 110,120,130 and 150 GeV). Figure 1a shows the resulting\nlikelihood distribution for an H+ mass of 130 GeV and the background.\nTable 2: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Variables used for the Likelihood Discriminant. \u03c4 denotes\nthe \u03c4 jet in the event, bH+ is the b jet coming from the same top as the presumed H+, and M(\u03c4, bH+)\nis the invariant mass of the \u03c4 jet and the bH+ jet. \u2206R =\np\n(\u2206\u03c6)2 +(\u2206\u03b7)2 represents a distance.\nI.\npleading \u03c4 track\nT\n/p\u03c4\nT\nV.\np\u03c4\nT/pbH+\nT\nII.\n1\u2212cos(\u2206\u03c6(\u03c4, pmiss\nT\n))\nVI.\nM(\u03c4,bH+)\nIII.\n1\u2212cos(\u2206\u03c6(H+,bH+))\nVII.\n\u2206R(\u03c4,bH+)\nIV.\nM(\u03c4,bH+)\u00b7\u2206R(\u03c4,bH+)\nA cut is applied on the obtained likelihood, requiring a value higher than 0.6 for an event to be\nretained (0.8 for a charged Higgs boson mass mH+ = 150 GeV, due to the better signal-background\nseparation). The transverse mass of the H+ is then calculated for the retained events (shown in Fig.\n1b). A \ufb01nal cut is then applied to this reconstructed transverse mass of the H+ candidate (at 50 GeV for\nmH+ = 90 GeV, at 60 GeV for mH+ = 110 and 120 GeV, at 65 GeV for mH+ = 130 GeV and at 75 GeV\nfor mH+ = 150 GeV). These cut values have been selected to optimize the signi\ufb01cance considering both\nsystematic and statistical uncertainties.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1454\n\n3.1.3\nResults\nTable 3: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Selection cut \ufb02ow. For each sample, the cross-sections\nafter cuts are given in fb and for tan\u03b2 = 20 in the \ufb01rst line and the relative cut ef\ufb01ciencies in the\nsecond line (in italics). Standard Model cross-sections are given for all the backgrounds. There\nare insuf\ufb01cient Monte Carlo statistics for the QCD events \u2013 see discussion in the text for a cross-\nsection estimate.\nChannel\nAll events\nTrigger\nCuts I\nCuts II\nH+\n90 GeV\n[fb]\n38388\n3384\n404\n136\n[/]\n0.088\n0.119\n0.337\nH+\n110 GeV\n[fb]\n27147\n2871\n286\n112\n[/]\n0.106\n0.100\n0.391\nH+\n120 GeV\n[fb]\n21363\n2563\n255\n94\n[/]\n0.120\n0.099\n0.368\nH+\n130 GeV\n[fb]\n15666\n2136\n217\n79\n[/]\n0.136\n0.102\n0.364\nH+\n150 GeV\n[fb]\n5869\n982\n88\n30\n[/]\n0.167\n0.089\n0.342\nt\u00aft \u22651 lepton\n[fb]\n4.52\u00b7105\n56287\n852\n307\n[/]\n0.125\n0.015\n0.360\nt\u00aft hadronic\n[fb]\n3.81\u00b7105\n1746\n37\n21\n[/]\n0.005\n0.021\n0.571\nsingle top\n[fb]\n112500\n7700\n63\n17\n[/]\n0.068\n0.008\n0.277\nW + jets\n[fb]\n277800\n15489\n73\n30\n[/]\n0.056\n0.005\n0.409\nQCD dijets\n[fb]\n3.2\u00b7108\n3.18\u00b7105\n5\n\u2013\n[/]\n0.001\n1.7\u00b710\u22124\n\u2013\nTable 3 shows the selection cut \ufb02ow for the \ufb01ve different signal mass points and all backgrounds\nstudied in this note. The expected cross-section after the trigger and after the \ufb01rst and second set of cuts\nis presented, as well as the relative ef\ufb01ciency of each step.\nIt is dif\ufb01cult to draw conclusions about the suppression of the QCD background, due to its very high\ncross-section at the LHC. This leads to large statistical uncertainties since no simulated event survives\nthe entire analysis chain. In fact already the expected cross-section after Cuts I (see Table 3) is governed\nby large statistical uncertainties. A very conservative upper limit for the expected number of QCD events\ncan be obtained by assuming that the expected ef\ufb01ciency of QCD events is limited from above by the\nef\ufb01ciency of the hadronic t\u00aft events for all cuts for which the number of simulated QCD events is not\nsuf\ufb01cient to draw de\ufb01nitive conclusions2. This assumption is very conservative since the second set of\ncuts have been speci\ufb01cally designed to identify the t\u00aft topology in order to reject QCD. Nevertheless,\nusing this assumption, the cross-section of surviving QCD events is limited by 55 fb after the likelihood\ncut (for mH+ = 130 GeV), while after the cut on the transverse mass this estimate is down to 50 fb.\nGiven the conservative nature of this estimate, the assumption that the background from QCD events is\nnegligible compared to the one from t\u00aft events is justi\ufb01ed.\nTable 4 shows the \ufb01nal expected cross-section following the cut on the likelihood discriminant and\nthe further cut on the transverse mass of the H+ candidate. The shape of the likelihood discriminant\n2After Cuts II, even more conservatively, this limit is taken from the ef\ufb01ciency for the t\u00aft \u22651 e/\u00b5/\u03c4 events, due to the\nlimited number of surviving hadronic t\u00aft events at this point.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1455\n\nTable 4: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Final event selection results. The cross-sections after all\ncuts are given in fb and for tan\u03b2 = 20 as well as the relative cut ef\ufb01ciencies. Standard Model\ncross-sections are given for t\u00aft . Backgrounds not tabulated have been found to be negligible.\nChannel\nCut\nSignal\nt\u00aft \u22651 e/\u00b5/\u03c4\n[fb]\n[/]\n[fb]\n[/]\nH+\n90 GeV\nLH > 0.6\n56.2\n0.413\n55.8\n0.182\nmT >50 GeV\n35.3\n0.628\n32.1\n0.574\nH+\n110 GeV\nLH > 0.6\n53.6\n0.478\n52.7\n0.172\nmT >60 GeV\n35.1\n0.655\n27.9\n0.529\nH+\n120 GeV\nLH > 0.6\n42.6\n0.455\n45.5\n0.148\nmT >60 GeV\n32.5\n0.764\n29.0\n0.636\nH+\n130 GeV\nLH > 0.6\n38.3\n0.483\n50.7\n0.165\nmT >65 GeV\n31.4\n0.819\n25.9\n0.510\nH+\n150 GeV\nLH > 0.8\n14.0\n0.467\n26.9\n0.088\nmT >75 GeV\n9.3\n0.662\n10.3\n0.385\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nScenario B\nATLAS\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nScenario B\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nATLAS\nFigure 2: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdbqq: Discovery (left) and exclusion contour (right) for Scenario\nB (mh-max) [1]. Systematic and statistical uncertainties are included. The systematic uncertainty is\nassumed to be 10% for the background, and 24% for the signal (see Sections 5.2 and 5.1). The lines\nindicate a 5\u03c3 signi\ufb01cance for the discovery and a 95% CL for the exclusion contour.\ndepends on the mass point for which the analysis is performed, i.e. one will need to run a separate\nanalysis using a different likelihood discriminant for each mass point. Therefore the background rejection\nwill naturally depend on the mass point for which it is evaluated.\nThe shape-based Pro\ufb01le Likelihood method (see Section 6) is applied on the entire transverse mass\nhistogram for each masspoint, in order to extract the signi\ufb01cance of the signal hypothesis. Fig. 2 shows\nthe discovery contour in the (tan\u03b2, mH+) plane for an integrated luminosity of L = 10 fb\u22121 as well as\nthe exclusion reach for L = 1 fb\u22121.\n3.2\nt\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq\nThe events of the leptonic \u03c4 channel are characterized by a single isolated lepton, and large missing\nenergy due to three neutrinos in the \ufb01nal state. A full reconstruction of the event is therefore impossible.\nInstead, kinematic properties of the event are used to discriminate between the signal and the main\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1456\n\nbackground, which is the Standard Model semi-leptonic t\u00aft process.\nThe branching ratio to \u03c4 leptons of a light charged Higgs boson is expected to be almost 100%,\nwhile the Standard Model W decay is universal with respect to lepton \ufb02avor. This means that the most\nprominent signature of the signal is an excess of kinematically \u03c4-like events.\nFurthermore, it is possible to construct a quantity that is bound by the charged Higgs boson mass\n(in analogy to the transverse mass in a W decay). This \u2019charged Higgs boson transverse mass\u2019 can be\nused to provide further discrimination power against the background, as well as a direct indication for\nthe charged Higgs boson mass.\n3.2.1\nPreselection\nTrigger\nThe trigger requirement is based on either an isolated lepton or missing transverse energy (xE).\nEvents are required to pass one of the following three trigger signatures (see Section 2): e22i_xE30,\nmu20_xE30, or xE80.\nOf\ufb02ine\nEvents that have passed the trigger are selected based on the following cuts:\n\u2022 Exactly one isolated lepton with pT > 5 GeV. If the event has not been triggered by the xe80\nsignature then the requirement is raised to 20 GeV or 25 GeV (for the e25i+xe30 and mu20i+xe30\nrequirement, respectively).\n\u2022 Missing transverse energy Emiss\nT\n> 120 GeV\n\u2022 At least 4 jets with pT > 40 GeV and |\u03b7| < 2.5\n\u2022 Exactly two out of the four leading jets are tagged as b jets\nEvents surviving these selection cuts are expected to be dominantly t\u00aft events.\n3.2.2\nMethod for \ufb01nal state reconstruction\nFirst, the hadronic W is reconstructed from the light (non b-tagged) jets. All possible pairs of light jets\nare considered and the one which gives an invariant mass closest to mW is selected.\nThe assignment of the two b jets to the hadronic & leptonic sides is done using the angular correlation\nbetween the b jets and their associated particles, i.e. the lepton and the reconstructed W. The charge\ncorrelation between the lepton and its associated b jet is also used. The charge of the b jet is de\ufb01ned in\nthe following way:\nQ jet = \u2211(pi\nL)\u03b1qi\n\u2211(pi\nL)\u03b1\n(1)\nwhere the sum is over tracks i belonging to the jet, qi is the charge associated to the track, and pi\nL is\nthe longitudinal component of the track momentum with respect to the jet direction. The parameter \u03b1 is\noptimized to give maximal separation between b and \u00afb jets. The value obtained from optimization with\nMC data is \u03b1 = 0.5.\nA likelihood ratio combining the angular and charge correlations is used. This likelihood ratio is\nde\ufb01ned between two hypotheses corresponding to the two possibilities of assigning the b jets. The\nhypothesis which achieves the higher likelihood ratio score is adopted. This algorithm selects the correct\nb jets assignment for about 70% of the events, when no cut is applied to the likelihood score of the\nselected hypothesis. Higher purity can be achieved at the cost of lower ef\ufb01ciency by placing such a cut,\nbut this is not done for this analysis.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1457\n\n\u22121\n\u22120.5\n0\n0.5\n1\n0\n0.5\n1\n1.5\n2\n2.5\ncos\u03c8\narbitrary units\n \n \nttbar background\nsignal mH+= 90 GeV\nsignal mH+= 130 GeV\nATLAS\n(a)\n0\n50\n100\n150\n0\n0.005\n0.01\n0.015\n0.02\n0.025\nmT\n(W) [GeV]\narbitrary units\n \n \nttbar background\nSignal, mH+ = 150 GeV\nSignal, mH+ = 90 GeV\nATLAS\n(b)\nFigure 3: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq: (a) cos\u03c8 distribution, (b) W transverse mass distribution, for\nsignal and background, after selection cuts, for charged Higgs boson masses of 90 and 150 GeV.\nOnce the b jets are assigned, the reconstructed top quark mass mrec\ntop on the hadronic side of the event\ncan be evaluated, and only those events which satisfy 100 GeV < mrec\ntop < 300 GeV are retained for further\nanalysis.\n3.2.3\nFurther reduction of t\u00aft background\nIn order to reduce the number of background events in which the lepton comes directly from a W decay,\nthe decay angle cos\u03c8 is used\ncos\u03c8 =\n2m2\n\u2113b\nm2top \u2212m2\nW\n\u22121.\n(2)\nIn such events, \u03c8 is the angle between the lepton and top quark directions in the W rest frame (In the\nlimit that the b quark is massless). The top quark, due to its large mass, couples mostly to the longitudinal\npolarization component of the W boson. As a result the cos\u03c8 distribution would have a large (\u224870%)\ncontribution that is symmetric around cos\u03c8 = 0 [11\u201313]. However, both the left-handed component of\nthe W boson and the indirect leptons coming from \u03c4 decays contribute to the lower cos\u03c8 region, and this\nregion is further enhanced by the selection cuts that favor events with large missing energy and therefore\nleptonic \u03c4 decays. The signal contribution is similar to that of the indirect leptons, and the less energetic\nb jets, due to the higher H+ mass, push cos\u03c8 to even lower values. This can be seen in Fig. 3 (a). As a\nfurther selection cut, events are required to have cos\u03c8 < \u22120.8.\nThe transverse mass of the W (in the hypothesis of a leptonic W decay), mW\nT , calculated using the\nmissing transverse momentum and the lepton transverse momentum, provides further discrimination\nagainst the t\u00aft background with a direct lepton from a W. The separation is most distinct for low charged\nHiggs boson masses and is shown for two different H+ masses in Fig. 3 (b).\nCharged Higgs Boson Transverse Mass\nA generalized transverse mass for the charged Higgs boson\n(in the hypothesis of a H+ \u2192\u03c4\u03bd decay) in this channel can be de\ufb01ned. The derivation and properties of\nthis variable are described in Reference [14].\n(mH+\nT )2 = (\nq\nm2top +(\u20d7plep\nT +\u20d7pb\nT +\u20d7pmiss\nT\n)2 \u2212pb\nT)2 \u2212(\u20d7pmiss\nT\n+\u20d7plep\nT )2\n(3)\nThis transverse mass satis\ufb01es mH+ < mH+\nT\n< mtop. Figure 4 shows the distributions of mH+\nT\nfor several\ncharged Higgs boson masses.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1458\n\n0\n50\n100\n150\n0\n5\n10\n15\n20\nmT [GeV]\narbitrary units\n0\n50\n100\n150\n0\n5\n10\n15\n20\n25\nmT [GeV]\n0\n50\n100\n150\n200\n0\n5\n10\n15\n20\nmT [GeV]\nmH+ = 90 GeV\nmH+ = 120 GeV\nmH+ = 150 GeV\nATLAS\nATLAS\nATLAS\nFigure 4: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq: mH+\nT\ndistribution, after selection cuts, for mH+ = 90, 120, and\n150 GeV. The dotted line represents the nominal simulated mass.\n3.2.4\nResults\nThe cross-sections of signal and background events surviving selection cuts are shown in Table 5.\nTable 5: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq: Selection cut \ufb02ow. For each sample, the cross-sections\nafter cuts (in fb) are given in the \ufb01rst line and the relative cut ef\ufb01ciencies in the second line (in\nitalics). The signal cross-sections correspond to tan\u03b2 = 20.\nChannel\nAll events\nTrigger\npre-selection\nreco. cuts\ncos\u03c8\nmW\nT\nH+\n90 GeV\n[fb]\n20760\n8408\n239\n190\n74\n70\n[/]\n0.405\n0.028\n0.79\n0.39\n0.94\n110 GeV\n[fb]\n14710\n6401\n138\n104\n42\n37\n[/]\n0.43\n0.021\n0.75\n0.40\n0.89\n120 GeV\n[fb]\n11560\n5305\n125\n82\n32\n23\n[/]\n0.46\n0.023\n0.66\n0.39\n0.71\n130 GeV\n[fb]\n8510\n4103\n75\n49\n23\n21\n[/]\n0.48\n0.018\n0.65\n0.47\n0.88\n150 GeV\n[fb]\n3180\n1747\n33\n23\n12\n10\n[/]\n0.55\n0.019\n0.70\n0.54\n0.79\nt\u00aft \u22651 e/\u00b5/\u03c4\n[fb]\n452000\n209339\n1963\n1317\n257\n144\n[/]\n0.46\n0.009\n0.67\n0.19\n0.56\nQCD dijet pT=280-1120 GeV\n[fb]\n12.9\u00b7106\n213000\n< 50\n< 50\n< 50\n< 50\n[/]\n0.017\n< 2.5\u00b710\u22124\n-\n-\n-\nW+jets\n[fb]\n31.2\u00b7106\n7.69\u00b7106\n173\n86.4\n< 80\n< 80\n[/]\n0.25\n2.2\u00b710\u22125\n0.50\n-\n-\nFigure 5 (a) shows the mW\nT differential cross-section for tan\u03b2 = 20. Figure 5 (b) shows the corre-\nsponding distributions for mH+\nT .\nThe statistical signi\ufb01cance of the signal is calculated from both the W transverse mass and the H+\ntransverse mass distributions, after event reconstruction and all selection cuts. The \ufb01nal signi\ufb01cance is\ntaken as the maximum of these two. In Fig. 6, the 5\u03c3 discovery contour is plotted in the (mH\u00b1,tan\u03b2)\nplane.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1459\n\n0\n50\n100\n150\n200\n0\n10\n20\n30\n40\n50\n60\n70\nmT(W) [GeV]\nCross\u2212section [fb]\n \n \nmH+=110GeV\ntan\u03b2 = 20\nsignal\nttbar\nSM ttbar\nATLAS\n(a)\n0\n50\n100\n150\n200\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nmT(H) [GeV]\nCross\u2212section [fb]\n \n \nmH+=110GeV\ntan\u03b2 = 20\nsignal\nttbar\nSM ttbar\nATLAS\n(b)\nFigure 5: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq: Transverse mass differential cross-section for signal and back-\nground, for tan\u03b2 = 20, and for the hypothesis of (a) W, and (b) H+ .\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario B\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario B\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nFigure 6: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq: Discovery (left) and exclusion contour (right) for Scenario\nB (mh-max) [1]. Systematic and statistical uncertainties are included. The systematic uncertainty is\nassumed to be 10% for the background, and 35% for the signal (see Sections 5.2 and 5.1). The lines\nindicate a 5\u03c3 signi\ufb01cance for the discovery and a 95% CL for the exclusion contour.\n3.3\nt\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd\nIn this channel a light charged Higgs boson is produced in t\u00aft decay. The W boson from one top quark\ndecays into leptons, while the \u03c4 lepton originating from the H+ decay results in a jet. At least three\nneutrinos are present in the event and thus the reconstruction of the complete event is impossible. Due to\nthe high branching ratio of this charged Higgs boson decay (BR(H+ \u2192\u03c4\u03bd ) \u2248100% for low mH+), the\nsignal can be observed as an excess of tau leptons in the \ufb01nal state over the main background of Standard\nModel t\u00aft production.\nDue to the production mechanism, the Standard Model t\u00aft events will be the most important back-\nground to this channel. However, signi\ufb01cant contributions from other backgrounds are still possible, and\nthus important to study: In the inclusive process pp \u2192W+jets, the \ufb01nal state is similar to the signal\nsignature if one of the jets is mis-tagged as a \u03c4 jet or a lepton and the W boson decays to the appropriate\nother object. Furthermore, the backgrounds constituted by single top quark events are considered. Single\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1460\n\ntop quarks can be produced with an associated W boson or b jet, and thus produce \ufb01nal states similar\nto the signal. Their contribution to the total background is however expected to be small due to the\nsmaller cross-sections. Finally, the overwhelming background of QCD dijet is expected to be completely\nsuppressed by demanding a high quantity of missing transverse energy and an isolated lepton.\n3.3.1\nEvent Selection\nTrigger:\nEvents are required to pass one of the following three trigger items (see Section 2):\ne22i_xE30, mu20_xE30, or xE40_3j20_L1_TAU30.\nSelection:\nTo select signal events and suppress the Standard Model t\u00aft background several small dif-\nferences between the processes are exploited. The following cuts are applied:\n1. Ne,\u00b5 \u22651: At least one isolated lepton with pT > 10 GeV; muons with |\u03b7| < 2.7 and electrons with\n|\u03b7| < 2.5 are considered.\n2. Njets=Nlight jets+Nb jets+N\u03c4 jets \u22653: At least three jets with pT > 20 GeV.\n3. N\u03c4 jet \u22651: At least one of the jets is required to be \u03c4-tagged. A \u03c4 jet quality cut is applied, leading\nto a \u03c4 jet reconstruction ef\ufb01ciency of about 30%.\n4. Nb jet \u22651: At least one b jet with pT > 20 GeV is required, and a b jet quality cut is applied,\nleading to a b jet ef\ufb01ciency of about 60%.\n5. p\u03c4\nT > 40 GeV\n6. pe\nT > 25 GeV or p\u00b5\nT > 20 GeV: This cut is only applied if the event was triggered by the appropriate\nlepton signature. If both lepton trigger requirements are met then only the cut on pe\nT is applied.\n7. q\u03c4 +ql = 0: The \u03c4 jet and the lepton are required to have opposite charge.\n8. Emiss\nT\n> 175 GeV\nFigure 7 (a) shows the jet multiplicity of the signal and the main t\u00aft background. While there are more jets\nfor the t\u00aft background than the signal a cut on jet multiplicity suppresses other backgrounds. Figure 7\n(b) displays the \u03c4 transverse momentum (p\u03c4\nT). Cut 6 is only applied, if the event was triggered by a\nlepton signature. For such events, a pT cut is applied to the reconstructed lepton according to the trigger\nthreshold.\n3.3.2\nResults\nIn Table 6 the cross-sections for signal and background after each cut are shown. The \ufb01rst two cuts select\nevents which include a lepton and three jets, assumed to be the two b jets and a \u03c4 jet. These cuts are\nmotivated by the \ufb01nal state under study, but do not reduce the most important leptonic t\u00aft background.\nRequiring one jet to be a \u03c4 jet removes more than 95% of the t\u00aft background while at least one quarter of\nthe signal remains, depending on the charged Higgs boson mass. Only one jet is required to be b-tagged,\nwhich is motivated by the fact that mH+ > mW and thus the b quark produced in t \u2192bH+ is in average\nsofter (the most probable value for pb\nT is about 55 GeV for t \u2192bW, and between 15 GeV for mH+ = 150\nGeV and 45 GeV for mH+ = 90 GeV for t \u2192bH+). The b-tagging ef\ufb01ciency decreases quickly for low\npb\nT [5] and thus the number of reconstructed b jets decreases with increasing mH+.\nDue to the mass difference mentioned above and the \u03c4 polarizations being different depending on\nwhether the \u03c4 jet originated from an H+ or W, the \u03c4-jet is expected to be harder for the signal than the\nbackground, motivating a cut on p\u03c4\nT. A harder \u03c4 jet in turn leads to more missing energy, thus making\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1461\n\nJet Multiplicity/Event\n0\n1\n2\n3\n4\n5\n6\n7\n8\narbitrary units\n0\n0.05\n0.1\n0.15\n0 2\n0.25\n0 3\nATLAS\n 90\n+\nH\n 150\n+\nH\ntt\n(a)\n [GeV]\n\u03c4\nT\np\n20\n40\n60\n80\n100\n120\n140\n160\n180\narbitrary units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nATLAS\n 90\n+\nH\n 150\n+\nH\ntt\n 90\n+\nH\n 150\n+\nH\ntt\n 90\n+\nH\n 150\n+\nH\ntt\n 90\n+\nH\n 150\n+\nH\ntt\n 90\n+\nH\n 150\n+\nH\ntt\n 90\n+\nH\n 150\n+\nH\ntt\n(b)\nFigure 7: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd: (a) Multiplicity of jets and (b) \u03c4 jet transverse momentum\n(p\u03c4\nT).\n [GeV]\nmiss\nT\nE\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb / 50 GeV]\n0\n10\n20\n30\n40\n50\n60\n70\n80\nATLAS\n90 GeV\n150 GeV\ntt\nFigure 8: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd: Emiss\nT\ndifferential cross-section after all cuts for tan\u03b2 = 20. The\nsignal contributions for the different mass hypothesis are individually stacked on top of the background\ndistribution.\nthe Emiss\nT\nan attractive variable to cut on. A high value is required for Emiss\nT\n. This is mainly needed to\noptimize the signi\ufb01cance with respect to the systematic error. Multidimensional optimization attempts\nhave shown that above respective thresholds, the signi\ufb01cance is not very sensitive to changes in the values\nof other continuous selection cuts (such as p\u03c4\nT).\nThe normalized number of events as a function of the missing transverse energy is shown in Fig. 8. A\nclear excess is observable for low charged Higgs boson masses, while close to the top quark mass there is\nonly sensitivity for very high values of tan\u03b2. Figure 9 shows the \ufb01nal discovery and exclusion contours\nfor the channel under investigation. A signi\ufb01cant region of the parameter space above tan\u03b2 = 30 is\ncovered by this decay mode, while the sensitivity for low and intermediate tan\u03b2 is limited.\n4\nHeavy Charged Higgs Boson Searches\nIn this chapter, charged Higgs boson searches in the two heavy H+ (mH+ \u2273mt) channels selected for\ninvestigation are presented:\n\u2022 gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd\n\u2022 gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb\nThe notation [b] implies the additional b given in the production mode gg \u2192tbH+, which is not produced\nin the mode gb \u2192tH+. All plots, tables and results in this section are based on the trigger menu for an\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1462\n\nTable 6: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd: Event selection cut \ufb02ow. For each sample, the cross-\nsections after cuts are given in fb and for tan\u03b2 = 20 in the \ufb01rst line and the relative cut ef\ufb01ciencies\nin the second line (in italics).\nChannel\nAll events\nTrigger\n\u22651 e,\u00b5\n\u22653 jets\n\u22651\u03c4\n\u22651 b\n\u03c4 pT\n\u2211q\nEmiss\nT\nH+\n90 GeV\n[fb]\n12098\n6219\n4972\n4248\n1092\n929\n586\n582\n44\n[/]\n0.51\n0.80\n0.85\n0.26\n0.85\n0.63\n0.99\n0.08\n110 GeV\n[fb]\n8570\n4510\n3534\n2986\n772\n650\n439\n431\n30\n[/]\n0.53\n0.78\n0.84\n0.26\n0.84\n0.67\n0.98\n0.07\n120 GeV\n[fb]\n6737\n3611\n2868\n2440\n654\n535\n360\n354\n23\n[/]\n0.54\n0.79\n0.85\n0.27\n0.82\n0.67\n0.98\n0.06\n130 GeV\n[fb]\n4954\n2670\n2112\n1730\n512\n399\n270\n265\n20\n[/]\n0.54\n0.79\n0.82\n0.30\n0.78\n0.67\n0.98\n0.07\n150 GeV\n[fb]\n1853\n1048\n836\n626\n177\n130\n94\n94\n7\n[/]\n0.57\n0.80\n0.75\n0.28\n0.74\n0.72\n1.00\n0.07\nt\u00aft \u22651 e/\u00b5/\u03c4\n[fb]\n452000\n169612\n137928\n122547\n4760\n4006\n1915\n1730\n78\n[/]\n0.37\n0.81\n0.89\n0.04\n0.84\n0.48\n0.90\n0.04\nsingle top\n[fb]\n112500\n30180\n25065\n18081\n271\n168\n47\n38\n0\n[/]\n0.27\n0.83\n0.72\n0.02\n0.61\n0.28\n0.81\n0.0\nW\u2192e\u03bd+jets\n[fb]\n476012\n144997\n114152\n53060\n780\n90\n40\n29\n0\n[/]\n0.30\n0.79\n0.46\n0.01\n0.12\n0.44\n0.74\n0.0\nW\u2192\u00b5\u03bd+jets\n[fb]\n157800\n48372\n43003\n41493\n582\n70\n40\n26\n0\n[/]\n0.31\n0.89\n0.96\n0.01\n0.12\n0.57\n0.64\n0.0\nW\u2192\u03c4\u03bd+jets\n[fb]\n277755\n23187\n9443\n6920\n187\n20\n12\n3\n0\n[/]\n0.08\n0.41\n0.73\n0.03\n0.10\n0.61\n0.22\n0.0\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario B\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\n90\n100\n110\n120\n130\n140\n150\n160\n170\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario B\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nFigure 9: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd: Discovery (left) and exclusion contour (right) for Scenario\nB (mh-max) [1]. Systematic and statistical uncertainties are included. The systematic uncertainty is\nassumed to be 10% for the background, and 41% for the signal (see Sections 5.2 and 5.1). The lines\nindicate a 5\u03c3 signi\ufb01cance for the discovery and a 95% CL for the exclusion contour.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1463\n\n / MeV)\n\u03c4\nT\nlog(p\n4.7\n4.8\n4.9\n5\n5.1\n5.2\n5.3\narbitrary unit\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\ntt\n 170\n+\nH\n 600\n+\nH\nATLAS\n / MeV)\nm ss\nT\nlog(E\n4.7\n4.8\n4.9\n5\n5.1\n5.2\n5.3\narbitrary unit\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\ntt\n 170\n+\nH\n 600\n+\nH\nATLAS\n)\n\u03c6\n\u2206\n1-cos(\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\narbitrary unit\n0\n0.1\n0.2\n0.3\n0.4\n0.5\ntt\n 170\n+\nH\n 600\n+\nH\nATLAS\nFigure 10: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: Probability density functions for t\u00aft and two signal mass\npoints. The plots show, from the upper left to the lower right, log(p\u03c4\nT), log(Emiss\nT\n), and 1\u2212cos(\u2206\u03c6).\ninstantaneous luminosity of L=1033cm\u22122s\u22121 presented in Section 2, on the signal cross-sections for the\nmh-max MSSM scenario (see Reference [1]) and the background cross-sections given in Reference [8].\n4.1\ngg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd\nThe following section describes the event selection for the H+ \u2192\u03c4\u03bd channel for the case mH+ \u2273mt.\nThe signal \ufb01nal state is characterised by a hard \u03c4 jet, large missing transverse momentum (due to the\nneutrino), one or two b jets, two light jets, a W boson and a top quark (the mass of which can be\nreconstructed) and has previously been investigated in Reference [15].\nThe main background to this signal channel are t\u00aft decays, in particular when one of the top quarks\ndecays to a \u03c4 jet, t \u2192b\u03c4(had)\u03bd, and the other one hadronically, t \u2192bqq. However, other t\u00aft modes\ncan also contribute when some of the objects in the event are not correctly reconstructed, e.g. a light\njet as a \u03c4 jet. Other backgrounds to be considered are single top, W+jets and QCD multi-jet events. A\nparametrized detector simulation has been used to evaluate the leptonic (e,\u00b5,\u03c4) t\u00aft background. The\nparametrization has been adjusted (using a smaller full detector simulation t\u00aft\nsample) such that the\ndistributions of all the quantities in the events agree with the full detector simulation.\n4.1.1\nPreselection\nTrigger:\nThe trigger selection employs items of the H+ trigger menu (see Section 2). Events are\nrequired to pass at least one of the two following trigger item combinations: xE40_3j20_L1_TAU30 or\nxE50_L1_TAU30.\n\u03c4 jet reconstruction:\nOnly \u03c4 jet candidates with transverse momenta greater than 15 GeV with a pseu-\ndorapidity outside of the crack region 1.4 < \u03b7 < 1.6 are considered, and a high cut on the \u03c4 quality\nvariable is placed yielding a \u03c4 reconstruction ef\ufb01ciency of about 20% and leading to a high rejection of\nparton jets. Exactly one \u03c4 jet is required in the event, followed by a cut of p\u03c4\nT > 50 GeV in order to\nreduce the QCD background at an early stage.\nJet reconstruction:\nAt least three more jets with pT > 15 GeV are required, and exactly one of them\nhas to be b-tagged. For this purpose, a b-tagging cut is applied to all jets with a b-tagging ef\ufb01ciency of\nabout 70%.\nMissing Transverse Energy:\nA soft cut of 40 GeV on the transverse missing energy Emiss\nT\nis applied\nto remove most of the QCD background already in the preselection, while it affects the t\u00aft background\nonly slightly (about 30% of the t\u00aft events with leptons are removed).\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1464\n\nlog-likelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\narbitrary unit\n0\n0.05\n0.1\n0.15\n0.2\n0.25\ntt\n 170\n+\nH\nATLAS\nlog-likelihood\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\narbitrary unit\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\ntt\n 600\n+\nH\nATLAS\nFigure 11: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: Likelihood distributions. The areas are normalized to\nunity. The background likelihood for 170 GeV does not peak at 0 because of the trigger selection (and to\na smaller degree the less stringent preselection cuts for the PDF determination) which already removes\nmost of the events in the \ufb01rst bins.\nW boson and top quark reconstruction:\nFor further discrimination of all backgrounds without hadron-\nically decaying top quarks, an attempt is made to reconstruct a W boson and a top quark. For all combi-\nnations of the b jet with two other jets, the minimum value of\n\u03c72 = (m j j \u2212mW)2\n\u03c32mW\n+ (mb(j j)r \u2212mt)2\n\u03c32mt\n(4)\nis calculated for each event (mW and mt are the nominal W and t masses, (j j)r are the two jets used in\nthe W reconstruction, rescaled to the W mass, and \u03c3mW and \u03c3mt represent the resolution of the W and t\nmass reconstruction, 10 GeV and 15 GeV). The resulting \u03c72 values are required to be smaller than 3.\nLepton veto:\nTo eliminate events with leptons (in particular leptonic t\u00aft modes), events with at least\none isolated lepton (e, \u00b5) with p\u2113\nT > 7 GeV are rejected.\nThe preselection aims at suppressing the reducible background such that only t\u00aft events involving\none hadronic and one semileptonic top quark decay survive. W+jets events are successfully removed by\nrequiring a b-tagged jet and a reconstructed top quark in the events, single top events by requiring a hard\n\u03c4 jet and high Emiss\nT\ntogether with a reconstructed hadronically decaying top quark, and QCD events by\nrequiring high Emiss\nT\n(and additionally by requiring b- and \u03c4-tags and a reconstructed top quark).\n4.1.2\nLikelihood for further reduction of the t\u00aft background\nAfter the preselection cuts, the background is dominated by t\u00aft events with one W decaying hadronically,\nand the other one to a hadronically decaying \u03c4 lepton and a neutrino (75% of the remaining background).\nAn uncorrelated likelihood approach has been chosen to reduce this background, employing the follow-\ning discriminant variables: (i) p\u03c4\nT, (ii) Emiss\nT\n, (iii) \u2206\u03d5 (azimuthal angle between the \u03c4 jet and the missing\nmomentum), (iv) HT (scalar sum of the pT of all jets in the event (excluding \u03c4 jets), and (v) pratio\nT\n(ratio\nbetween the transverse momenta of the \u03c4 jet and the hardest jet not used for the top quark reconstruction).\nThe probability density functions (PDFs) have been created for each signal mass point and for the\nt\u00aft sample (with at least one leptonic W decay) using full detector simulation. Slightly less stringent\npreselection cuts (p\u03c4\nT >40 GeV instead of 50 GeV, at least 1 b jet instead of exactly 1, and a maximum\nW/top reconstruction \u03c72 of 6 instead of 3) and no trigger selection are used to obtain the PDFs in order to\nkeep a suf\ufb01ciently high number of simulated events. The PDFs for two mass points and the t\u00aft background\nare shown in Fig. 10.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1465\n\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\nATLAS\n 170 GeV\n+\nH\ntt\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nATLAS\n 250 GeV\n+\nH\ntt\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1\n [GeV]\n+\nH\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nCross-section [fb/25 GeV]\n0\n0.2\n0.4\n0.6\n0.8\n1 ATLAS\n 400 GeV\n+\nH\ntt\nFigure 12: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: H+ transverse mass distributions for three signal mass\npoints and the corresponding background fortan\u03b2 = 35. The signal events are stacked on top of the\nbackground events.\nThe likelihood distributions for two example mass points are shown in Fig. 11. A cut requiring the\nlikelihood to be higher than 0.9 (mH+ = 400 and 600 GeV) or 0.95 (other mass cases) is applied and the\ncharged Higgs boson transverse mass of the remaining events is plotted as a \ufb01nal distribution to extract\nthe signi\ufb01cance of the H+ signal. These transverse mass distributions are shown in Fig. 12. A clear\nexcess can be observed for lower H+ masses, but the shapes are similar for signal and background.\nVarying cuts to change the signal-to-background ratio would be a quick way to establish the excess if it\nwas statistically unambiguous, followed by data-driven background estimation methods as described in\nSection 5.2. For higher H+ masses, sensitivity is only given for higher values of tan\u03b2, but the signal\nand background shapes are clearly distinguishable.\nEvent selection summary:\nThe following list summarizes the event selection:\n\u2022 Trigger: Trigger xE40_3j20_L1_TAU30 or xE50_L1_TAU30\n\u2022 Cut A: exactly one \u03c4 jet with p\u03c4\nT > 50 GeV, and Emiss\nT\n> 40 GeV\n\u2022 Cut B: at least three additional jets\n\u2022 Cut C: exactly one of the additional jets b-tagged\n\u2022 Cut D: veto on a lepton (e, \u00b5) with p\u2113\nT > 7 GeV\n\u2022 Cut E: W boson and top quark reconstructed with \u03c72 < 3\n\u2022 Cut F: likelihood value greater than 0.95 (0.9 for mH+ 400 and 600 GeV)\n\u2022 Cut G: mH+ in a certain mass window\n4.1.3\nResults\nThe cross-section of signal and background events surviving preselection cuts are shown in Table 7. All\nbackgrounds except for t\u00aft with at least one leptonic W decay mode are ef\ufb01ciently suppressed at this\nstage. The QCD dijet selection ef\ufb01ciency is too small to draw de\ufb01nite conclusions due to its high cross-\nsection, but assuming that dijet events in pT -bins lower than 140 GeV cannot produce a hard \u03c4 jet and\nthree jets with the top quark-invariant mass (plus large missing ET ), that the numbers presented for Cut\nB are of the right order of magnitude and that the relative ef\ufb01ciencies for the remaining cuts is smaller\nthan for t\u00aft events the conclusion can be drawn that the background from dijet events is negligible.\nThe ef\ufb01ciencies of the remaining Cuts F (likelihood) and G (mH+ ) are shown separately in Table 8;\nas for these cuts the background ef\ufb01ciencies depend on the H+ mass hypothesis. At this point, all other\nbackgrounds except for t\u00aft events with W decays to e, \u00b5 or \u03c4 are negligible.\nA signal-to-background ratio of the order of 1 has been achieved, resulting in robustness with respect\nto systematic uncertainties. The cross-section for very heavy H+ \u2192\u03c4\u03bd production is small but a very\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1466\n\nTable 7: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: Preselection cut \ufb02ow. For each sample, the cross-\nsections after cuts are given in fb and for tan\u03b2 = 35 in the \ufb01rst line and the relative cut ef\ufb01ciencies\nin the second line (in italics). The size of the QCD dijet sample is too small to draw accurate\nconclusions.\nChannel\nAll events\nTrigger\nCut A\nCut B\nCut C\nCut D\nCut E\nH+\n170 GeV\n[fb]\n1346\n280\n76\n67\n36\n35\n14.7\n[/]\n0.21\n0.27\n0.88\n0.54\n0.96\n0.42\n200 GeV\n[fb]\n551\n139\n40\n33\n19\n18\n7.4\n[/]\n0.25\n0.28\n0.83\n0.57\n0.97\n0.41\n250 GeV\n[fb]\n184\n58\n17\n15\n7.8\n7.6\n2.9\n[/]\n0.32\n0.30\n0.84\n0.54\n0.97\n0.38\n400 GeV\n[fb]\n28\n11\n3.3\n2.8\n1.5\n1.4\n0.58\n[/]\n0.39\n0.31\n0.84\n0.52\n0.98\n0.41\n600 GeV\n[fb]\n4.5\n1.7\n0.52\n0.46\n0.24\n0.23\n0.10\n[/]\n0.39\n0.30\n0.87\n0.52\n0.97\n0.43\nt\u00aft \u22651 e/\u00b5/\u03c4\n[fb]\n452000\n56300\n1669\n1532\n697\n518\n188\n[/]\n0.12\n0.03\n0.92\n0.46\n0.74\n0.36\nt\u00aft hadronic\n[fb]\n381000\n1746\n37\n37\n16\n16\n5\n[/]\n0.005\n0.02\n1.00\n0.43\n1.00\n0.33\nQCD dijet pT =140-1120 GeV\n[fb]\n3.2\u00b7108\n3.2\u00b7105\n1285\n1234\n106\n106\n-\n[/]\n0.001\n0.004\n0.96\n0.09\n1.00\n-\nW+jets\n[fb]\n341200\n19170\n2518\n1892\n314\n314\n13\n[/]\n0.06\n0.13\n0.75\n0.17\n1.00\n0.04\nsingle top\n[fb]\n112500\n7570\n161\n132\n39\n37\n12\n[/]\n0.07\n0.02\n0.81\n0.30\n0.93\n0.32\ngood discrimination against the background can be obtained with the likelihood method. The resulting\ndiscovery contours are presented in Fig. 13 and show that a sizable region of the MSSM space which\nhas not been explored experimentally before can be covered. Sensitivity is given for large tan\u03b2 and\nmH+ < 500 GeV.\n4.2\ngg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb\nIn this section the analysis strategy for the H+ \u2192tb channel is outlined. This is a particularly challenging\nsignal \ufb01nal state which includes 3 (or 4) b quarks, 2 light quarks, 1 high pT lepton and one neutrino. The\nchannel has previously been studied for ATLAS using fast detector simulation [16], and several aspects\nof the previous analysis have been adopted. However, the use of full simulation for the present study\nshowed the need to add several new cuts to improve the signal to background ratio.\n4.2.1\nTrigger\nEvents are required to pass one of the following trigger signatures (see Section 2): e22i_xE30, mu20_xE30,\nor xE40_3j20_L1_TAU30.\n4.2.2\nPreselection\nFollowing the trigger, the events are required to pass a set of preselection criteria which de\ufb01ne the mini-\nmum requirements needed for the event reconstruction:\n\u2022 exactly 1 isolated lepton (e or \u00b5) with pe\nT > 25 GeV, p\u00b5\nT > 20 GeV and |\u03b7| < 2.5.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1467\n\nTable 8: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: Event selection results. The cross-sections after cuts\nare given in fb and for tan\u03b2 = 35 as well as the relative cut ef\ufb01ciencies. The remaining background\nconsists only of t\u00aft events with at least one W decay to e, \u00b5 or \u03c4 plus \u03bd.\nChannel\nCut\nSignal\nBackground\n[fb]\n[/]\n[fb]\n[/]\nH+\n170 GeV\nLH>0.95\n3.8\n0.26\n2.3\n0.012\nmH+\nT\n> 100 GeV\n3.8\n0.99\n2.1\n0.91\n200 GeV\nLH>0.95\n3.1\n0.42\n3.2\n0.017\nmH+\nT\n> 120 GeV\n2.9\n0.92\n2.4\n0.74\n250 GeV\nLH>0.95\n1.4\n0.47\n3.1\n0.017\nmH+\nT\n> 150 GeV\n1.1\n0.77\n2.0\n0.63\n400 GeV\nLH>0.9\n0.47\n0.80\n4.5\n0.024\nmH+\nT\n> 250 GeV\n0.26\n0.56\n0.33\n0.074\n600 GeV\nLH>0.9\n0.075\n0.76\n2.5\n0.013\nmH+\nT\n> 300 GeV\n0.044\n0.58\n0.15\n0.062\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario B\n200\n250\n300\n350\n400\n450\n500\n550\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario B\n200\n250\n300\n350\n400\n450\n500\n550\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nFigure 13: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd: Discovery (left) and exclusion contour (right) for Sce-\nnario B (mh-max) [1]. Systematic and statistical uncertainties are included. The systematic uncertainty\nis assumed to be 10% for the background, and 44% for the signal (see Sections 5.2 and 5.1). The lines\nindicate a 5\u03c3 signi\ufb01cance for the discovery and a 95% CL for the exclusion contour.\n\u2022 at least 5 jets with pT > 20 GeV and |\u03b7| < 5.\n\u2022 at least 3 b-tagged jets with |\u03b7| < 2.5.\nLepton selection:\nElectron candidates that pass the cuts on transverse momentum and pseudorapidity\nmentioned above are required to pass further identi\ufb01cation and isolation criteria based on the shower\nshape in the electromagnetic calorimeter and the quality of the track in the inner detector. Concerning\nisolation, the energy in a cone of \u2206R = 0.20 around the electron is required to be less than 20% of the\nelectron transverse energy. The same isolation criteria is also applied to muon candidates.\nJet selection and b-tagging criteria:\nJet multiplicity is one of the main sources of combinatorial back-\nground and the b-tagging ef\ufb01ciency is the major factor reducing the overall ef\ufb01ciency of the preselection.\nFrom jets passing the preselection cuts mentioned above, those within the range |\u03b7| < 2.5 are considered\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1468\n\nb-tagged if passing a b-tagging quality cut leading to a b jet reconstruction ef\ufb01ciency of about 60%. Only\nevents with at least 3 b-tagged jets are accepted for the rest of the analysis.\n4.2.3\nReconstruction\nApart from the objects expected in the event \ufb01nal state, jets from the underlying event are also present\nleading to an increase of the jet multiplicity.\nReconstruction of the leptonic W:\nAfter the preselection is performed, all physics objects necessary\nfor the complete reconstruction of the event are present except for the neutrino coming from the leptoni-\ncally decaying W. In order to reconstruct the four-momentum of the neutrino, its transverse component\nis identi\ufb01ed with the missing transverse momentum, and the longitudinal component is computed using\nthe W mass constraint, leading to 0, 1 or 2 real solutions. In about 25% of the cases no real solution\ncan be found. In order to recover those events, the approximation of neglecting the imaginary part of the\nsolution is applied and has been found to have only a small effect on the top quark mass resolution.\nThe Combinatorial Likelihood:\nThe next step is to associate the reconstructed physics objects with\nobjects of the event, assuming a signal event topology. The number of possible combinations is very large\nand depends strongly on the number of light jets in the event. In order to overcome this combinatorial\nbackground, a likelihood function is de\ufb01ned. The likelihood formalism used in this analysis is based on\nm variables and should discriminate between n classes of events. For each of the m variables, \ufb01rst the\nprobability density functions f j\ni (xi) for each of the n classes are determined: Then the probability for an\nevent to be of class j when the value xi is measured for variable i is given by:\npj\ni (xi) =\nf j\ni (xi)\n\u2211n\nk=1 f k\ni (xi)\n(5)\nThe information about all m variables are combined, ignoring correlations, to de\ufb01ne the likelihood Lj\nthat an event belongs to class j when measuring the values xi for variables i = 1,...,m:\nLj =\n\u220fm\nl=1 pj\nl (xl)\n\u2211n\nk=1 \u220fm\nl=1 pk\nl (xl)\n(6)\nA combinatorial likelihood is used to discriminate between the two classes of events: the correct and the\nwrong combinations. The likelihood is based on 8 variables:\n\u2022 m j j: The invariant mass of two light jets.\n\u2022 m j jb: The invariant mass of two light jets and one b jet.\n\u2022 m\u2113\u03bdb: The invariant mass of the lepton, one of the two solutions of the neutrino and one b jet.\n\u2022 pT(bH): The transverse momentum of the b jet associated to the charged Higgs boson decay.\n\u2022 \u2206R(j, j): The distance in the azimuthal-pseudorapidity plane (\u2206R =\np\n\u2206\u03c6 2 +\u2206\u03b72) between two\nlight jets.\n\u2022 \u2206R(j j,b): \u2206R between the sum of two light jets and one b jet.\n\u2022 \u2206R(\u2113,b): \u2206R between the isolated lepton and one b jet.\n\u2022 \u2206R(bH,tH): \u2206R between the b jet and the top quark associated to the charged Higgs boson decay.\nThe likelihood is computed for each combination, and the combination with the highest likelihood in the\nevent is chosen. If the maximum likelihood in the event is found to be less than 0.7, the event is rejected.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1469\n\n4.2.4\nFinal Event Selection\nAfter the event reconstruction is complete the physical backgrounds must be suppressed, of which the\nlargest is t\u00aft + jets. In order to reduce this background requiring 4 b jets in the event is found to be crucial.\nThe events passing the 4 b jets requirements are then passed to a likelihood cut. The likelihood function\nused is based on 5 variables:\n\u2022 \u03b7bH: The pseudorapidity of the b jet associated to the charged Higgs boson decay.\n\u2022 \u2211b wb: The sum of the b-tagging weights of the 3 b jets associated to the top quark and charged\nHiggs boson decay.\n\u2022 < L >: The average combinatorial likelihood in the event.\n\u2022 \u2206R(bH,btbt): The distance in the (\u03c6,\u03b7) plane between the b jet associated to the charged Higgs\nboson decay and the system of the two b jets associated to the top quark decays.\n\u2022 pb1\nT /pb2\nT : The pT ratio of the two b jets not associated to the top quark decay, b1 being the one with\nthe lowest pT.\nA cut on the output of this likelihood is applied. Its value is optimized to maximize the charged Higgs\nboson signal signi\ufb01cance. This \ufb01nal step improves the signi\ufb01cance by only 10 to 15%. The limited\nnumber of simulated events at this stage of the analysis, especially for the backgrounds, made it very\ndif\ufb01cult to optimize the choice of variables to include in the likelihood. Larger background samples\nwill be needed to be able to de\ufb01ne a more performant likelihood as it was done in Reference [16] with\nparametrized detector simulation.\n4.2.5\nResults\nTable 9 shows the selection cut \ufb02ow after the different steps of the analysis for all simulated signal\nmasses, and for the background for one H+\nmass hypothesis. Table 10 presents the results for all\nsimulated H+ hypotheses. In Fig. 14, the reconstructed charged Higgs boson mass for signal and physics\nbackground is shown. Since the limited number of simulated events does not allow the construction of\na performing \ufb01nal selection likelihood, currently no H+ discovery or exclusion power can be extracted\nfrom this channel on its own and thus no contours are shown. It, however, contributes to the combined\nH+ sensitivity.\n5\nSystematic Uncertainties and Background Extraction From Data\nThe observation of a charged Higgs boson signal will be subject to statistical and systematic uncertainties.\nThe systematic uncertainties stem from two sources: theoretical and experimental, and both are discussed\nin Section 5.1. Section 5.2 addresses how to extract the dominating t\u00aft background from real data using\na novel technique with so-called control samples.\n5.1\nSystematic Uncertainties\n5.1.1\nTheoretical Systematic Uncertainties\nUncertainties in the expected production cross-sections for background and signal processes affect the\ndiscovery/exclusion potential of the channels under investigation. For all channels the uncertainty of the\nt\u00aft background is particularly interesting since this is the dominant background. A 12% uncertainty on\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1470\n\nTable 9: gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb: Selection cut \ufb02ow. The cross-\nsections in fb are given after each cut and for tan\u03b2 = 35 as well as the relative cut ef\ufb01ciencies.\nThe backgrounds are shown for a charged Higgs mass boson hypothesis of mH+ = 250 GeV.\nChannel\nAll events\nTrigger\nPreselection\nReconstruction\n4 b tags\nSelection\n200 GeV\n[fb]\n105\n64\n2.3\n2.2\n0.18\n0.16\n[/]\n0.61\n0.036\n0.93\n0.08\n0.89\n250 GeV\n[fb]\n170\n108\n8.1\n7.3\n1.06\n0.65\n[/]\n0.63\n0.075\n0.88\n0.11\n0.61\n400 GeV\n[fb]\n65\n45\n4.5\n3.9\n0.43\n0.26\n[/]\n0.69\n0.10\n0.88\n0.11\n0.59\n600 GeV\n[fb]\n22\n16\n1.8\n1.7\n0.27\n0.18\n[/]\n0.75\n0.12\n0.92\n0.16\n0.67\nt\u00aft + jets\n[fb]\n112000\n74400\n1040\n875\n35.0\n11.7\n[/]\n0.66\n0.014\n0.84\n0.04\n0.33\nt\u00aft b\u00afb (QCD)\n[fb]\n2240\n1575\n130\n117.8\n17.6\n6.8\n[/]\n0.70\n0.083\n0.90\n0.15\n0.38\nt\u00aft b\u00afb (EW)\n[fb]\n244\n155\n14.4\n13.0\n2.0\n0.39\n[/]\n0.63\n0.09\n0.90\n0.15\n0.19\nTable 10: gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb: Event selection results. The\ncross-sections after all cuts are given in fb and for tan\u03b2 = 35 as well as the global selection\nef\ufb01ciencies.\nChannel\nSignal\nt\u00aft + jets\nt\u00aft b\u00afb (QCD)\nt\u00aft b\u00afb (EW)\n[fb]\n[/]\n[fb]\n[/]\n[fb]\n[/]\n[fb]\n[/]\n200 GeV\n0.16\n0.0015\n21.0\n0.00019\n12.2\n0.0054\n1.05\n0.0043\n250 GeV\n0.65\n0.0038\n11.7\n0.00010\n6.76\n0.0030\n0.74\n0.0030\n400 GeV\n0.26\n0.0039\n15.9\n0.00014\n8.91\n0.0040\n1.05\n0.0043\n600 GeV\n0.18\n0.0084\n19.8\n0.00018\n10.5\n0.0047\n1.21\n0.0049\nthe NLL calculations is expected3 leading to \u03c3t\u00aft = 833 \u00b1 100 pb [17]. Other backgrounds considered\nhave similar or smaller uncertainties.\nThe branching ratios BR(t \u2192H+b) and BR(H+ \u2192\u03c4\u03bd,cs,tb) have been determined with the Feyn-\nHiggs package, and similar systematic uncertainties apply [18]:\n\u2022 \u2206BR(t \u2192H+b)/BR < 10%\n\u2022 \u2206BR(H+ \u2192\u03c4\u03bd)/BR < 5%\n\u2022 \u2206BR(H+ \u2192cs,tb)/BR < 10%\nIn the high-mass region, the dominant systematic uncertainties on the charged Higgs boson production\ncross-section stem from the renormalization scale and factorization scale dependence and are calculated\nto be smaller than 20% in the whole MSSM space. The decrease of the cross-section due to supersym-\nmetry loop corrections has been taken into account by adjusting the cross-sections with an additional\n3The t\u00aft cross-section will be measured in early LHC studies and transform this theoretical uncertainty into a much smaller\nexperimental uncertainty, despite possible H+ effects in the measurement.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1471\n\n [GeV]\nH\nm\n0\n100 200 300 400 500 600 700 800 900 1000\nCross Section [fb / 50 GeV]\n0\n2\n4\n6\n8\n10\n12\n = 200 GeV\n+\nH\nm\nSignal + Background\n + jets\ntt\n (QCD)\nb\n b\ntt\n (ElW)\nb\n b\ntt\nATLAS\n [GeV]\nH\nm\n0\n100 200 300 400 500 600 700 800 900 1000\nCross Section [fb / 50 GeV]\n0\n2\n4\n6\n8\n10\n12\n = 250 GeV\n+\nH\nm\nSignal + Background\n + jets\ntt\n (QCD)\nb\n b\ntt\n (ElW)\nb\n b\ntt\nATLAS\n [GeV]\nH\nm\n0\n100 200 300 400 500 600 700 800 900 1000\nCross Section [fb / 100 GeV]\n0\n2\n4\n6\n8\n10\n12\n = 400 GeV\n+\nH\nm\nSignal + Background\n + jets\ntt\n (QCD)\nb\n b\ntt\n (ElW)\nb\n b\ntt\nATLAS\n [GeV]\nH\nm\n0\n100 200 300 400 500 600 700 800 900 1000\nCross Section [fb / 100 GeV]\n0\n2\n4\n6\n8\n10\n12\n = 600 GeV\n+\nH\nm\nSignal + Background\n + jets\ntt\n (QCD)\nb\n b\ntt\n (ElW)\nb\n b\ntt\nATLAS\nFigure 14: gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb: Reconstructed H+ mass. The value\nof tan\u03b2 has been chosen such that the pure statistical signi\ufb01cance results in a value of 5.\nfactor as proposed in Reference [19], re\ufb02ecting the altered relation between the bottom quark mass and\nits Yukawa coupling, \u2206mb. Remaining supersymmetry loop corrections are shown to be negligible.\n5.1.2\nExperimental Systematic Uncertainties\nSeveral quantities are subject to experimental systematic uncertainties: Tagging and reconstruction ef-\n\ufb01ciencies, energy scales, energy resolutions and the luminosity determination. A detailed list of the\nsystematical uncertainties considered, including their numerical value, is given in Table 11. Each sys-\ntematic effect has been evaluated individually using the given uncertainty on an event-by-event basis.\nThe systematic uncertainty of the missing transverse energy is indirectly considered by taking the\neffects of the other systematic effects in the missing transverse momentum calculation into account.\nThe systematic uncertainty estimates are generally conservative, in particular for the results assuming an\nintegrated luminosity of 30 fb\u22121. However, due to the usage of control samples to estimate the t\u00aft back-\nground, the uncertainty values have a negligible impact on the H+ discovery sensitivity. Furthermore,\ntests have shown that even for the exclusion sensitivity the effect is very small: Assuming that the total\nexperimental systematic uncertainty on the results could be halved, the change in sensitivity would only\nbe of the order of 0.1 in tan\u03b2 for \ufb01xed values of mH+.\nThe dominant systematic uncertainty for all H+ channels is the jet energy scale, with values between\n10% and 30%. Similarly, channels with hadronic \u03c4 decays are strongly affected by the \u03c4 jet energy scale.\nThe channel H+ \u2192tb, requiring 4 b-tags, is strongly affected by uncertainties in b-tagging ef\ufb01ciency\nand rejection of light jets. The total experimental systematic uncertainty for the different H+ channels\nis between about 15% and 40% for the signal, affecting mainly the exclusion sensitivity. Similar values\napply for the main background, t\u00aft , which would remove most of the discovery potential. Thus a tech-\nnique for a data-driven estimation of the background has been developed, greatly reducing the systematic\nuncertainty on the background. These \u201ct\u00aft control samples\u201d are discussed in the following section.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1472\n\nTable 11: Effects of systematic uncertainties for all channels under investigation. The num-\nbers are given in terms of percentage changes in cross-section.\nThe channels are: 1: t\u00aft \u2192\nbH+bW \u2192b\u03c4(had)\u03bdbqq (see Section 3.1), 2: t\u00aft \u2192bH+bW \u2192b\u03c4(lep)\u03bdbqq (see Section 3.2),\n3: t\u00aft \u2192bH+bW \u2192b\u03c4(had)\u03bdb\u2113\u03bd (see Section 3.3), 4: gg/gb \u2192t[b]H+ \u2192bqq[b]\u03c4(had)\u03bd (see\nSection 4.1) and 5: gg/gb \u2192t[b]H+ \u2192t[b]tb \u2192bW[b]bWb \u2192b\u2113\u03bd[b]bqqb (see Section 4.2).\nUncertainty\nValue\n1\n2\n3\n4\n5\nS\nB\nS\nB\nS\nB\nS\nB\nS\nB\n\u03c4 E Resolution\n0.45\u00d7\n\u221a\nE\n-2\n+3\n-\n-\n+8\n-3\n-4\n-1\n-\n-\n\u03c4 E Scale\n\u22125%\n-2\n+5\n-\n-\n0\n-9\n-15\n-21\n-\n-\n+5%\n-5\n-5\n-\n-\n+8\n+1\n+4\n+28\n-\n-\n\u03c4-tag Ef\ufb01ciency\n\u00b15%\n-5\n-2\n-\n-\n-8\n-1\n-8\n-5\n-\n-\nJet E Resolution\n0.45\n\u221a\nE,|\u03b7| < 3.2\n-2\n-3\n-8\n+5\n+8\n+3\n-12\n-3\n-2\n-4\n0.63\n\u221a\nE,|\u03b7| > 3.2\nJet E Scale\n+7(15)%,|\u03b7| < (>)3.2\n-9\n+12\n+29\n+22\n+35\n+19\n+4\n-18\n+9\n+8\n-7(15)%,|\u03b7| < (>)3.2\n-5\n-5\n-21\n-12\n-19\n-17\n-31\n+15\n-8\n-6\nb-tag Ef\ufb01ciency\n\u00b15%\u03b5btag\n0\n-14\n+4\n-6\n0\n-3\n-7\n+3\n-8\n-10\nb-tag Rejection\n-10%\n-7\n+10\n0\n+1\n0\n0\n-2\n-3\n-4\n+6\n+10%\n+7\n-2\n0\n0\n0\n-1\n-3\n-1\n0\n-5\n\u00b5 E Resolution\n0.011/PT \u22950.00017\n0\n0\n-4\n+1\n0\n+1\n0\n0\n-4\n-5\n\u00b5 E Scale\n-1%\n0\n0\n0\n+1\n+4\n-1\n0\n0\n-4\n-6\n+1%\n0\n0\n-4\n-1\n0\n0\n0\n0\n+4\n+7\n\u00b5 Ef\ufb01ciency\n\u00b11%\n0\n0\n0\n-1\n0\n0\n0\n-2\n-2\n-1\ne E Resolution\n0.0073\u00d7ET\n0\n0\n0\n0\n0\n-1\n0\n0\n-4\n-4\ne E Scale\n-0.5%\n0\n0\n0\n+1\n0\n-1\n0\n0\n-4\n-5\n+0.5%\n0\n0\n0\n-1\n+4\n-1\n0\n0\n+4\n+6\ne Ef\ufb01ciency\n\u00b10.2%\n0\n0\n0\n0\n0\n0\n0\n0\n0\n-1\nLuminosity\n-3%\n-3\n-3\n-3\n-3\n-3\n-3\n-3\n-3\n-3\n-3\n+3%\n+3\n+3\n+3\n+3\n+3\n+3\n+3\n+3\n+3\n+3\n5.2\nt\u00aft Control Samples\nThe t\u00aft process, in particular with one or more \u03c4 leptons in the \ufb01nal state, is the dominant background\nto all analyses presented in this note. As the relative contributions from this background in different\njet multiplicities are not known, the subtraction of these backgrounds using a data-driven method is\nnecessary.\nThe method is data-driven in the sense that it uses t\u00aft \u2192WbWb \u2192\u00b5\u03bdb\u00b5\u03bdb and t\u00aft \u2192WbWb \u2192\n\u00b5\u03bdbqqb events collected by ATLAS to model the t\u00aft backgrounds with one or more taus in the \ufb01nal state.\nAfter applying a minimal set of event selection criteria on the data (optimized for both ef\ufb01ciency and\npurity), one or two leptons from the events are removed and the 4 momenta of the removed objects are\nscaled into tau leptons with corrections for the mass. The tau leptons are fed into TAUOLA [20] for decay\nand the decay products are passed to the ATLAS detector simulation and reconstruction software. Finally\nthe result is merged with the original event from which the leptons were removed to constitute a control\nsample.\nThe result is a data-driven control sample for each of the t\u00aft \ufb01nal states which potentially constitute\na background to one of the H+\nanalyses, using events from data that can be easily and ef\ufb01ciently\ntriggered. With this method both the shape and the normalization of these backgrounds for all \u03c4 decays\n(i.e., leptonic and hadronic decays, or in the case of analyses requiring two taus the lepton-hadron and\nhadron-hadron modes) can be modelled.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1473\n\n5.2.1\nObtaining t\u00aft Control Samples from Data\nTo extract the t\u00aft control samples from data a set of selection criteria is applied. These are designed to\noptimize the ef\ufb01ciency and purity of the samples.\nDimuonic channel\nIn order to extract the t\u00aft \u2192WbWb \u2192\u00b5\u03bdb\u00b5\u03bdb sample, events with at least two\nisolated muons with pT > 20 GeV are selected. To reject muons coming from Z decays, events with a\ndimuonic invariant mass in the range 70-110 GeV are rejected. A further requirement is that the missing\ntransverse energy in the event is larger than 40 GeV.\nTable 12 summarizes the result of the above selection. The ef\ufb01ciency of the signal (dimuonic t\u00aft\nevents) to survive this selection is 28% and the sample purity is estimated to be 71%.\nTable 12: Ef\ufb01ciency and purity for collecting t\u00aft dimuonic events. Each mu20 indicates a generator\nlevel cut requiring one muon with pT > 20 GeV.\nProcess\ncross-section [fb]\nef\ufb01ciency\nevents [fb-1]\nt\u00aft signal\n9310\n0.284\n2641\nt\u00aft background\n823690\n4.96\u00b710\u22124\n407\nW+Jets\n202400\n1.61\u00b710\u22124\n33\nZ+Jets\n210290\n1.45\u00b710\u22123\n305\nbb(mu20mu20)\n261000\n1.23\u00b710\u22123\n322\nTotal background\n-\n-\n1067\n\u00b5+jet channel\nThe selection criteria for the t\u00aft \u2192WbWb \u2192\u00b5\u03bdbqqb sample are designed to reject\nbb \u21921\u00b5 +X events which have a large cross-section. Events are accepted if an isolated muon is found\nand two jets in the event with transverse momenta above 40 GeV have an invariant mass within 20 GeV\nof the nominal W mass. Events with high pT muons in the jets are rejected. A missing transverse energy\ncut of 40 GeV is applied, as well as a requirements of least two more jets with transverse momenta above\n40 GeV. At least one of these jets is required to be a b-tagged. The overall transverse energy of the event\nis required to be larger than 250 GeV and events with a high pT isolated electron are rejected.\nThe results of the above selection are summarized in Table 13. The selection ef\ufb01ciency for signal\nevents is 8.6% and the signal purity is 74%.\nTable 13: Ef\ufb01ciency and purity for collecting t\u00aft muon+jets events.\nProcess\ncross-section [fb]\nef\ufb01ciency\nevents [fb-1]\nt\u00aft signal\n119040\n8.62\u00b710\u22122\n10263\nt\u00aft background\n713960\n1.80\u00b710\u22123\n1287\nW+Jets\n202400\n5.61\u00b710\u22123\n1134\nZ+Jets\n210290\n2.84\u00b710\u22124\n74\nbb(mu20)\n13600000\n8.40\u00b710\u22125\n1147\nTotal background\n-\n-\n3642\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1474\n\n5.2.2\nMethod Validation\nTo thoroughly test the t\u00aft control sample method, the produced events have to be run through the different\nanalyses and the obtained shapes and normalizations have to be compared to the ones obtained in these\nanalyses. However, a global check can be done by comparing various distributions from the two cases\n(a) \u201creal\u201d t\u00aft events and (b) \u201cscaled\u201d t\u00aft control sample events where muons have been replaced by \u03c4\nleptons. This has been done separately for three \ufb01nal states of interest.\nBasic preselection cuts on quantities like transverse momenta have been applied, lower than or at\nmost equal to the preselection cuts applied in the analyses which use the quantities plotted in the follow-\ning. The MC@NLO event weights have not been taken into account in order to increase the available\nstatistics since this has been shown not to bias the comparison.\n Transverse Mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\nATLAS\n bjj\n\u03bd\n\u03c4\n b\n\u2192\nt\nReal t\n bjj\n\u03bd\n\u03c4\n b\n\u2192\nt\nScaled t\n Transverse Mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\nRatio Scaled / Real\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n Transverse Mass [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\nRatio Scaled / Real\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nATLAS\nFigure 15: t\u00aft \u2192b\u03c4(lep)\u03bdbqq: Left: W \u2192\u03c4(lep)\u03bd transverse mass, both for the real and the scaled t\u00aft\nevents. Right: The corresponding bin-by-bin ratio. The gray band represents \u00b110% around a ratio of 1.\n Top Transverse Momentum [GeV] \n0\n50\n100\n150\n200\n250\n300\n350\n400\nArbitrary Units\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nATLAS\n bjj\n\u03bd\n\u03c4\n b\n\u2192\nt\nReal t\n bjj\n\u03bd\n\u03c4\n b\n\u2192\nt\nScaled t\n Top Transverse Momentum [GeV] \n0\n50\n100\n150\n200\n250\n300\n350\n400\nRatio Scaled / Real\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n Top Transverse Momentum [GeV] \n0\n50\n100\n150\n200\n250\n300\n350\n400\nRatio Scaled / Real\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nATLAS\nFigure 16: t\u00aft \u2192b\u03c4(had)\u03bdbqq: Left: t \u2192b\u03c4(had)\u03bd momentum, both for the real and the scaled t\u00aft events.\nRight: The corresponding bin-by-bin ratio. The gray band represents \u00b110% around a ratio of 1.\nIn Fig. 15, the W \u2192\u03c4(lep)\u03bd transverse mass is shown for the t\u00aft \u2192b\u03c4(lep)\u03bdbqq mode. Here, for the\nscaled events, a muon has been replaced by a leptonically decaying \u03c4. For the modes t\u00aft \u2192b\u03c4(had)\u03bdbqq\nand t\u00aft \u2192b\u03c4(had)\u03bdb\u2113\u03bd, in the scaled events a muon has been replaced by a hadronically decaying \u03c4. The\nt \u2192b\u03c4(had)\u03bd momentum is shown in Fig. 16, demonstrating the success of this replacement.\nThe presented plots demonstrate that the dominant background of all H+ studies, t\u00aft , can be mod-\nelled with the t\u00aft control sample method. Even without the intended further re\ufb01nement of the method, in\nthe regions of interest quantities of the H+ analyses can be modelled within a 10% error margin. This is\nremarkable in particular for complex quantities, i.e. variables extracted from the combination of several\nobjects (like the top quark mass), and gives con\ufb01dence that the t\u00aft control sample method allows to re-\nproduce the relevant correlations in the event. Thus for all results a systematic t\u00aft background uncertainty\nof 10% is assumed (while the signal systematic uncertainty is extracted from Monte Carlo events, see\nSection 5.1).\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1475\n\n6\nCombined Results\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario A\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario A\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nFigure 17: Scenario A: Combined Results. Left: Discovery contour, Right: Exclusion contour. System-\natic and statistical uncertainties are included.\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario B\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario B\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nFigure 18: Scenario B (mh-max): Combined Results. Left: Discovery contour, Right: Exclusion contour.\nSystematic and statistical uncertainties are included.\nThe sensitivities for discovery and exclusion are calculated with the Pro\ufb01le Likelihood method [21\u2013\n23], which includes statistical and systematic uncertainties. The results are summarized in combined\ndiscovery and exclusion contours for all H+\nchannels for two MSSM Scenarios A and B [1], and\nthree different integrated luminosities (1, 10, and 30 fb\u22121). Figure 17 shows the result for the MSSM\nScenario A. 5\u03c3 discovery contours and 95% CL exclusion contours are shown. Figure 18 shows the\nsame results for the MSSM Scenario B (mh-max). Previous studies have shown that the dependence of\nthe H+ discovery sensitivity on the speci\ufb01c choice of the MSSM parameter values is generally very\nsmall, with the exception of the Higgsino mixing parameter \u00b5 [24, 25]. The discovery signi\ufb01cance is\ncalculated for both cases assuming a systematic background uncertainty of 10% following the study of\nt\u00aft control samples (Section 5.2). The signal systematic uncertainties are discussed in Section 5.1. The\nstatistical uncertainties arising from the use of Monte Carlo samples with a \ufb01nite number of events have\nbeen consistently taken into account.\nA discovery sensitivity is given for a large part of the mH+ -tan\u03b2 space for both scenarios, but\nthe dif\ufb01cult intermediate tan\u03b2 region, where the H+ cross-section has its minimum, is not covered.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1476\n\nmH [GeV]\ntan\u03b2\n5\u03c3 discovery sensitivity\n \n \nATLAS\nScenario B\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nmH [GeV]\ntan\u03b2\n95% C.L. exclusion sensitivity \n \n \nATLAS\nScenario B\n90\n110\n130\n150\n170\n200\n250\n400\n600\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\n60\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II\nExcluded\n95% CL\nFigure 19: Scenario B (mh-max): Combined Results. Left: Discovery contour, Right: Exclusion contour.\nStatistical errors arising from simulation statistics are neglected.\n5\u03c3 discovery sensitivity \nmH [GeV]\nBR(t \u2192 H+b)\nATLAS\n \n \n90\n100\n110\n120\n130\n140\n150\n10\n2\n10\n1\n10\n0\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II Excluded 95% CL\n95% C.L. exclusion sensitivity \nmH [GeV]\nBR(t \u2192 H+b)\nATLAS\n \n \n90\n100\n110\n120\n130\n140\n150\n10\n2\n10\n1\n10\n0\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nCDF Run II Excluded 95% CL\nFigure 20: Model-independent: Combined light H+ results in the (mH+, BR(t \u2192H+b))-plane. Left:\nDiscovery contour, Right: Exclusion contour. Systematic uncertainties and statistical uncertainties are\nincluded. BR(H+ \u2192\u03c4\u03bd) = 1 is assumed.\nmH [GeV]\n\u03c3(t[b]H+)\u00d7BR(H+\u2192\u03c4\u03bd) [pb]\n5\u03c3 discovery sensitivity \n \n \nATLAS\n200\n250\n300\n350\n400\n450\n500\n550\n600\n10\n2\n10\n1\n10\n0\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nmH [GeV]\n\u03c3(t[b]H+)\u00d7BR(H+\u2192\u03c4\u03bd) [pb]\n95% C.L. exclusion sensitivity \n \n \nATLAS\n200\n250\n300\n350\n400\n450\n500\n550\n600\n10\n2\n10\n1\n10\n0\n30 fb\u22121\n10 fb\u22121\n1 fb\u22121\nFigure 21: Model-independent: Heavy H+ results in the (mH+, \u03c3)-plane. Left: Discovery contour,\nRight: Exclusion contour. Systematic uncertainties and statistical uncertainties are included.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1477\n\nHowever, a charged Higgs boson in this region could be excluded for values up to the top quark mass.\nAdditional integrated luminosity does not give any further H+ sensitivity for a low-mass H+ after a\nfew fb\u22121 have been recorded. The reason is the statistical error from the small t\u00aft Monte Carlo sample\nwhich is equivalent to about 1 fb\u22121 at the LHC and makes extrapolation to higher luminosities dif\ufb01cult.\nRepeating the low-mass H+\nstudies with larger Monte Carlo samples is thus expected to lead to a\nsigni\ufb01cantly larger discovery and exclusion reach, as can be seen in Fig. 19 in which the statistical\nuncertainty arising from simulation statistics is neglected (i.e. it is assumed that the number of simulated\nevents is much larger than the number of expected real-data events).\nFigure 20 shows the discovery and exclusion contour in terms of the branching ratio t \u2192H+b as a\nfunction of mH+. With one year of low luminosity data, it will be possible to discover the charged Higgs\nboson if BR(t \u2192H+b) is larger than about 1-3%, and to exclude it even if this branching ratio is well\nbelow the percent level. Similar contours for a heavy H+ are presented in Fig. 21; here the y-axis shows\nthe cross-section for the process gg/gb \u2192t[b]H+ \u2192t[b]\u03c4\u03bd. Sensitivity is given for a cross-section of\nthe order of 0.1pb. Both \ufb01gures are model-independent in the sense that they can be interpreted in the\ncontext of any MSSM, other SUSY, or even non-SUSY scenario.\n7\nConclusions\nThe ATLAS potential for discovering or excluding the existence of a charged Higgs boson in two dif-\nferent MSSM scenarios has been evaluated for \ufb01ve different \ufb01nal states of the H+ signal. Signi\ufb01cant\nimprovements of present day constraints can already be achieved with limited data (less than 1 fb\u22121,\nabout one month at low luminosity at the LHC) although it may not qualify as early physics due to its\ndependency on higher level reconstruction objects.\nBelow the top quark mass charged Higgs bosons are predominantly produced in top quark decays\nand the main decay mode is H+ \u2192\u03c4\u03bd . Three different signal \ufb01nal states have been studied and analyzed\nseparately, each of them separately outperforming the present sensitivity from the Tevatron experiments\nalready with 1 fb\u22121 of data. The combined performance of the three channels yields a discovery reach\nfor 10 fb\u22121 which covers tan\u03b2 values down to 20 and up to 4 for all charged Higgs boson masses up to\nabout 150 GeV. For intermediate tan\u03b2 region (around tan\u03b2 = 7), no discovery sensitivity is present, but\na charged Higgs boson could be excluded in this region. The current sensitivity is primarily limited by\nsimulation statistical uncertainties, it is thus expected that a larger production of simulated events will\ngreatly improve the situation and give access to the intermediate tan\u03b2 region.\nTwo analyses have been conducted in the search for a heavy charged Higgs boson (mH+ > mt), a\nregion presently uncovered in direct searches. Here, the main production mode is through gb fusion\n(gb \u2192tH+) and the decay into a top and a b quark dominates. However, the dominant tb decay mode\nsuffers from large irreducible backgrounds, and the combinatorial background. Consequently the dis-\ncovery potential for a heavy charged Higgs boson is dominated by the \u03c4\u03bd decay mode, which despite its\nsigni\ufb01cantly smaller branching ratio allows for more ef\ufb01cient background suppression. The discovery\nreach in the context of the MSSM (mh-max) strongly depends on the charged Higgs boson mass and\nreaches from (mH+ = 200 GeV, tan\u03b2 = 28) to (mH+ = 350 GeV, tan\u03b2 = 58) for an integrated luminosity\nof 30 fb\u22121. Additionally, the model-independent discovery reach for a charged Higgs boson as a function\nof its production cross-section has been evaluated. A light H+ sensitivity for a BR(t \u2192H+b) down to\nthe percent level is given for a discovery, and well below that level for an exclusion. For a heavy H+\ndecaying to \u03c4\u03bd, sensitivity is given for cross-sections of the order of 0.1pb.\nThe results presented in this note give con\ufb01dence that the LHC and the ATLAS detector will be\nable to probe an extended Higgs sector over a sizable region of the MSSM parameter space. For a high\nSUSY mass scale, the charged Higgs boson could be the \ufb01rst signal of New Physics (and indication for\nSupersymmetry) discovered.\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1478\n\nReferences\n[1] ATLAS Collaboration, Introduction on Higgs Boson Searches, this volume.\n[2] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons; Calibration and Performance\nof the Electromagnetic Calorimeter, this volume.\n[3] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[4] ATLAS Collaboration, Detector Level Jet Corrections; Measurement of Missing Transverse En-\nergy, this volume.\n[5] ATLAS Collaboration, b-Tagging Performance, this volume.\n[6] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[7] ATLAS Collaboration, Trigger for Early Running, this volume.\n[8] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties, this\nvolume.\n[9] C. Biscarat, M. Dosil, ATL-PHYS-2003-038 (2003).\n[10] D. P. Roy, Phys. Lett. B 459 (1999) 607\u2013614.\n[11] G. L. Kane, G. A. Ladinsky, C.-P. Yuan, Phys. Rev. D 45 (1992) 124.\n[12] C. A. Nelson, B. T. Kress, M. Lopes, T. McCauley, Phys. Rev. D 56 (1997) 5928.\n[13] R. H. Dalitz, G. R. Goldstein, Phys. Rev. D 45 (1992) 1531.\n[14] E. Gross, O. Vitells, arXiv:0801.1459v1 (2008).\n[15] B. Mohn, M. Flechl, J. Alwall, ATL-PHYS-PUB-2007-006 (2007).\n[16] K. Assamagan, N. Gollub, Acta Physica Polonica B 33 (2002) 707\u2013720.\n[17] R. Bonciani, S. Catani, M.L. Mangano, P. Nason, Nucl. Phys. B529 (1998) 424\u2013450.\n[18] S. Heinemeyer, private communication (2007).\n[19] T. Plehn, Phys. Rev. D 67 (2003) 014018.\n[20] S. Jadach, J. H. Kuhn, Z. Was, Comput. Phys. Commun. 64 (1990) 275.\n[21] S. S. Wilks, Ann. Math. Statist. 9 (1938) 60.\n[22] S. A. Murphy, A.W. Van Der Vaart, J. Am. Statist. Assoc. 95 (2000) 449.\n[23] ATLAS Collaboration, Statistical Combination of Several Important Standard Model Higgs Boson\nSearch Channels, this volume.\n[24] M. Carena, S. Heinemeyer, C. E. M. Wagner, G. Weiglein, Eur. Phys. J. C45 (2006) 797\u2013814.\n[25] M. Hashemi, S. Heinemeyer, R. Kinnunen, A. Nikitenko, G. Weiglein, arXiv:0804.1228 (2008).\nHIGGS \u2013 CHARGED HIGGS BOSON SEARCHES\n1479\n\nStatistical Combination of Several Important Standard\nModel Higgs Boson Search Channels\nAbstract\nIn this note we describe statistical procedures for combination of results from\nindependent searches for the Higgs boson. Here only the Standard Model\nHiggs is considered, although the methods can easily be extended to non-\nstandard Higgs models as well as to other searches. The methods are ap-\nplied to Monte Carlo studies of four important search channels: H \u2192\u03c4+\u03c4\u2212,\nH \u2192W +W \u2212\u2192e\u03bd\u00b5\u03bd, H \u2192\u03b3\u03b3 and H \u2192ZZ(\u2217) \u21924 leptons. The statistical\ntreatment relies on a large sample approximation that is expected to be valid\nfor an integrated luminosity of at least 2 fb\u22121. Results are presented for the\nexpected statistical signi\ufb01cance of discovery and expected exclusion limits.\n1\nIntroduction\nHiggs searches will exploit a number of statistically independent decay channels. One wishes to combine\nall of the information from them to provide a single measure of the signi\ufb01cance of a discovery or limits\non Higgs production. The approach taken in this paper is based on frequentist statistical methods, where\neffects of systematic uncertainties are incorporated by use of the pro\ufb01le likelihood ratio.\nThe statistical procedures used for establishing discovery and setting limits are described in Section 2.\nThese methods are very general and can be applied to the combination of results of essentially any search\nthat will be carried out at the LHC. Section 3 summarizes the four search channels for the Standard Model\nHiggs boson considered in this note: H \u2192\u03c4+\u03c4\u2212, H \u2192W +W \u2212\u2192e\u03bd\u00b5\u03bd, H \u2192\u03b3\u03b3 and H \u2192ZZ(\u2217) \u2192\n4 leptons.\nThe statistical treatment requires knowledge of the distribution of a test statistic based on the pro\ufb01le\nlikelihood ratio. To determine these distributions by Monte Carlo so as to establish discovery at a high\nlevel of signi\ufb01cance would require an enormous amount of simulated data, which is not practical at\npresent. Therefore the distributions have been estimated using the functional form expected to hold in\nthe large sample limit. Investigations shown in Section 3 indicate that this approximation should be\nreliable for an integrated luminosity above 2 fb\u22121.\nIn Section 4 we show the result of the combination. For different values of the integrated luminosity\nand hypothesized Higgs mass, we present the signal signi\ufb01cance expected assuming the Standard Model\nHiggs production rate, as well as expected upper limits on the Higgs production cross section, under the\nhypothesis of no Higgs signal.\nThe channels considered here focus on the search for a Higgs boson in the low-mass range. It is\nplanned to include other channels in the future, e.g., further \ufb01nal states from the W+W\u2212and ZZ modes.\nThis will improve sensitivity especially at higher Higgs mass values.\n2\nStatistical methods\nIn this section we describe the general statistical model and likelihood function, \ufb01rst for a single channel\nand then generalized to multiple channels. In Section 2.2 we give the procedure used to establish discov-\nery based on a frequentist signi\ufb01cance test, where the effects of systematic uncertainties are incorporated\nby use of the pro\ufb01le likelihood ratio. Section 2.3 covers the corresponding methods for setting limits. For\nboth discovery and exclusion one requires the sampling distribution of the statistic used in the test; this\n1480\n\nis described in Section 2.4. Section 2.5 discusses a series of approximations used to determine expected\nvalues of the discovery signi\ufb01cance and exclusion limits.\nThe approach taken in this note is to carry out tests for discovery and exclusion for \ufb01xed values of\nthe Higgs mass mH. In principle the entire procedure is then repeated for all masses, resulting in limits\non or a measurement of mH. In practice, an interpolation is made between \ufb01nite steps in mH.\n2.1\nThe statistical model and likelihood function\nFirst we consider the case of a single search channel. The measurement results in a set of numbers\nof events found in kinematic regions where signal could be present. These typically correspond to a\nhistogram of a variable such as the mass of the reconstructed Higgs candidate, with the numbers of\nentries denoted by n = (n1,...,nN). In some cases one may consider a histogram with only one bin, i.e.,\nthe measured outcome is simply a number of candidate events found. The number of entries in bin i, ni,\nis modeled as a Poisson variable with mean value\nE[ni] = \u00b5L\u03b5i\u03c3iB +bi \u2261\u00b5si +bi ,\n(1)\nwhere L is the integrated luminosity, \u03b5i, \u03c3i and B are the signal ef\ufb01ciency, Higgs cross section, and\nbranching ratio, and bi is the expected number of background events. Here \u00b5 is a signal strength parame-\nter de\ufb01ned such that \u00b5 = 0 corresponds to the absence of a signal; \u00b5 = 1 gives the signal rate si expected\nfrom the Standard Model. If we consider a \ufb01xed Higgs mass mH, the only parameter of interest is \u00b5. All\nother adjustable parameters needed to specify the model are called nuisance parameters.\nIn principle the expected background values bi can be predicted using Monte Carlo models for Stan-\ndard Model processes. In the measurements considered here, however, the systematic uncertainty in the\nStandard Model prediction is in many cases quite large, and this would severely limit the sensitivity of\nthe search. Therefore data regions where one expects only a very small amount of signal (control regions)\nare used to constrain the background in the signal region (see also below).\nFor the ith bin of a histogram of a discriminating variable x, the expected signal and background can\nbe written\nsi\n=\nstot\nZ\nbini fs(x;\u03b8s)dx ,\n(2)\nbi\n=\nbtot\nZ\nbini fb(x;\u03b8b)dx ,\n(3)\nwhere stot and btot are the total expected numbers of events in the histograms, fs(x;\u03b8 s) and fb(x;\u03b8 b) are\nthe probability density functions (pdfs) of x for signal and background, and \u03b8 s and \u03b8 b represent sets of\nshape parameters.\nThe parametric forms of the pdfs fs(x;\u03b8 s) and fb(x;\u03b8 b) are determined from Monte Carlo simula-\ntions or data control samples. In the following we will use \u03b8 = (\u03b8 s,\u03b8 b,btot) to refer to all of the nuisance\nparameters. The signal normalization stot here is not an adjustable parameter, but rather is \ufb01xed equal to\nthe Standard Model prediction.\nIn addition to the measured histogram n, some search channels also make use of a set of subsidiary\nmeasurements m = (m1,...,mM) in control regions where one expects mainly background events. These\ncan be modeled as being Poisson distributed with mean values\nE[mi] = ui(\u03b8) ,\n(4)\nwhere the ui are calculable quantities depending on a set of parameters, at least some of which are the\nsame as those entering into the predictions for si and bi above. In practice the subsidiary measurements\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1481\n\nare constructed so as to provide information on the background normalization btot and sometimes also\non its shape.\nIf the measurement is based on counting events in a given kinematic region, i.e., without using the\nshape of a distribution, in the formalism above the histograms have a single bin. The value s = stot is\nthen the Standard Model prediction for the signal and b = btot is the (unknown) expected background.\nThere are then no shape parameters, and b itself plays the role of \u03b8 as the single nuisance parameter. In\nthis case the subsidiary measurement m is made in a control region where signal is absent (or can to good\napproximation be neglected), and has an expectation value\nE[m] = u = \u03c4b ,\n(5)\nwhere \u03c4 is a scaling constant whose value can be estimated from a Monte Carlo simulation.\nThe likelihood function is the product of Poisson probabilities for all bins:\nL(\u00b5,\u03b8) =\nN\n\u220f\nj=1\n(\u00b5s j +b j)n j\nn j!\ne\u2212(\u00b5s j+b j)\nM\n\u220f\nk=1\numk\nk\nmk! e\u2212uk .\n(6)\nEquivalently the log-likelihood is\nlnL(\u00b5,\u03b8) =\nN\n\u2211\nj=1\n(n j ln(\u00b5s j +b j)\u2212(\u00b5s j +b j)) +\nM\n\u2211\nk=1\n(mk lnuk \u2212uk)+C ,\n(7)\nwhere C represents terms that do not depend on the parameters and thus can be dropped. Here and in (6)\nthe parameters \u03b8 enter through Eqs. (2), (3), and (4).\nIn the case where the presence of signal in the histogram n gives a peak sitting on a smooth back-\nground, one does not need a subsidiary measurement m. Rather, as long as the number of parameters in\nthe models for the signal and background distributions is smaller than the total number of bins measured,\none can determine the strength parameter \u00b5 from the histogram n alone. Here the regions away from\nthe peak (the sidebands) play the role of the subsidiary measurement by providing information on the\nbackground level. Of course if an additional subsidiary measurement is available, this will improve the\naccuracy of the background determination, which will increase the sensitivity of the analysis.\nIn the case of several independent search channels, the method described above is generalized in a\nstraightforward manner. For each channel i there is a likelihood function Li(\u00b5,\u03b8i). Its general form is\ngiven by Eq. (6), except that all quantities carry an additional index i to label the channel except the\nglobal strength parameter \u00b5, which is assumed to be the same for all channels. Since the channels are\nstatistically independent, the full likelihood function is given by the product\nL(\u00b5,\u03b8) = \u220f\ni\nLi(\u00b5,\u03b8 i) ,\n(8)\nwhere \u03b8 here represents all of the nuisance parameters.\nSystematic uncertainties are effectively included in the analysis through the nuisance parameters\n\u03b8. The model must be suf\ufb01ciently \ufb02exible, i.e., it must contain enough parameters, so that for at least\nsome point in its parameter space it can be regarded as representing the truth. One must exercise some\nrestraint in achieving this, however, as an increasing number of nuisance parameters leads to a decrease in\nsensitivity to the parameters of interest. Some of the components of \u03b8 may be common among different\nchannels, e.g., parameters relating to uncertainty in the integrated luminosity. These then represent a\ncommon (correlated) systematic uncertainty.\nAs an example, consider the signal ef\ufb01ciency \u03b5 that enters in the relation between the cross section\nand expected number of signal events. Suppose the ef\ufb01ciency has been estimated to have a value \u02c6\u03b5 and\nsystematic uncertainty \u03c3\u02c6\u03b5. To incorporate this uncertainty into the model, we can regard the measured\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1482\n\nvalue \u02c6\u03b5 as a random variable whose true value \u03b5 is treated as a nuisance parameter. For the pdf f\u03b5(\u02c6\u03b5;\u03b5,\u03c3\u02c6\u03b5)\none could use, e.g., a Gaussian distribution centred about \u03b5, or for a quantity such as the ef\ufb01ciency which\nmust lie in the range 0 \u2264\u03b5 \u22641 one could use a pdf that automatically satis\ufb01es this constraint (e.g., a beta\ndistribution). For whatever choice is deemed appropriate, the likelihood (6) is multiplied by f\u03b5(\u02c6\u03b5;\u03b5,\u03c3\u02c6\u03b5),\nevaluated with the best estimate \u02c6\u03b5, and the parameter \u03b5 is included in the set of nuisance parameters \u03b8.\nTo test a hypothesized value of \u00b5 we construct the pro\ufb01le likelihood ratio,\n\u03bb(\u00b5) = L(\u00b5, \u02c6\u02c6\u03b8)\nL( \u02c6\u00b5, \u02c6\u03b8) .\n(9)\nHere \u02c6\u02c6\u03b8 in the numerator denotes the value of \u03b8 that maximizes L for the speci\ufb01ed \u00b5, i.e., it is the\nconditional maximum-likelihood estimator (MLE) of \u03b8 (and thus is a function of \u00b5). The denominator\nis the maximized (full) likelihood function, i.e., \u02c6\u00b5 and \u02c6\u03b8 are the MLEs. The presence of the nuisance\nparameters broadens the pro\ufb01le likelihood ratio as a function of \u00b5 relative to what one would have if\ntheir values were \ufb01xed. This re\ufb02ects the loss of information about \u00b5 due to the systematic uncertainties.\nThe likelihood ratio (9) and procedures for incorporating systematic uncertainties applied here differ\nsomewhat from those used for the searches carried out at LEP. Some of these differences are discussed\nfurther in Appendix A.\nFrom the de\ufb01nition of the pro\ufb01le likelihood ratio one can see that 0 \u2264\u03bb \u22641, with \u03bb(\u00b5) = 1 implying\ngood agreement between the data and the hypothesized value of \u00b5. Equivalently it is convenient to work\nwith the quantity\nq\u00b5 = \u22122ln\u03bb(\u00b5) ,\n(10)\nso that high values of q\u00b5 correspond to poor agreement between the data and the hypothesized \u00b5. The\nstatistic q\u00b5 will have a sampling distribution f(q\u00b5|\u00b5\u2032). Here \u00b5 refers to the strength parameter used\nto de\ufb01ne the statistic q\u00b5, entering in the numerator of the likelihood ratio, and \u00b5\u2032 is the value used to\nde\ufb01ne the data generated to obtain the distribution (i.e., the \u2018true\u2019 value). For the special case \u00b5 \u2032 = \u00b5 and\nfor a suf\ufb01ciently large data sample, the pdf f(q\u00b5|\u00b5) approaches a limiting form related to the chi-square\ndistribution, discussed further in Section 2.4. For \u00b5\u2032 \u0338= \u00b5, the distribution of q\u00b5 is shifted to higher values,\nre\ufb02ecting the decreased agreement between the data generated with \u00b5 \u2032 and the hypothesis tested by q\u00b5,\nas indicated in Fig. 1. The two cases of particular interest are \u00b5 = 0, the background-only hypothesis,\nand \u00b5 = 1, the hypothesis of background plus signal present at the Standard Model rate.\nThe level of compatibility between data that give an observed value q\u00b5,obs for q\u00b5 and a hypothesized\nvalue of \u00b5 is quanti\ufb01ed by giving the p-value\np\u00b5 =\nZ \u221e\nq\u00b5,obs\nf(q\u00b5|\u00b5)dq\u00b5 .\n(11)\nThis is the probability, under the assumption of \u00b5, of seeing data with equal or greater incompatibility,\nas measured by q\u00b5, relative to the data actually obtained. This is illustrated in Fig. 1, where the shaded\narea indicates the p-value of the hypothesized \u00b5. The \ufb01gure also indicates the median value of q\u00b5 under\nthe assumption of a different value of the strength parameter \u00b5\u2032 used to generate the data. For \u00b5 and \u00b5\u2032\nvalues that are increasingly different, the median med[q\u00b5|\u00b5\u2032] moves further to the right. An observed\nvalue of q\u00b5 at this median would give a correspondingly small p-value for \u00b5.\n2.2\nEstablishing discovery\nTo establish discovery we try to reject the \u00b5 = 0 (background-only) hypothesis, i.e., that there is no\nHiggs signal present. To do this we use the statistic q0 = \u22122ln\u03bb(0). One expects to \ufb01nd a low value\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1483\n\n\u00b5\nq\n)\n\u00b5|\n\u00b5\nf(q\n,obs\n\u00b5\nq\n\u2019]\n\u00b5|\n\u00b5\nmed[q\n\u2019)\n\u00b5|\n\u00b5\nf(q\np-value\nFigure 1: Illustration of the determination of\nthe p-value of a hypothesized value of \u00b5. The\nleft-hand curve indicates the pdf of q\u00b5 for data\ngenerated with the same value of \u00b5 as was used\nto de\ufb01ne the statistic q\u00b5; this is used to deter-\nmine the p-value of \u00b5, shown as the shaded re-\ngion. The right-hand curve indicates the pdf of\nq\u00b5 for data generated with a different value of\nthe strength parameter, \u00b5\u2032.\nof \u03bb(0) (high q0) if the data include signal. Here even though one is testing the hypothesis that the\nHiggs does not exist, the de\ufb01nition of q0 depends on the hypothesized Higgs mass mH. It enters through\nthe denominator of the likelihood ratio (9), which contains the maximum-likelihood estimator \u02c6\u00b5 for the\nstrength of a Higgs signal at the mass mH. By de\ufb01ning the test statistic in this way one maximizes the\nprobability of rejecting the \u00b5 = 0 hypothesis if the Higgs boson exists at the speci\ufb01ed mass. This search\nprocedure is then carried out for all values of mH (in practice an interpolation is carried out between \ufb01nite\nsteps in mH).\nA given data set will result in an observed value q0,obs of q0. The level of compatibility between the\ndata and the no-Higgs hypothesis is quanti\ufb01ed by giving the p-value\np0 =\nZ \u221e\nq0,obs\nf(q0|0)dq0 .\n(12)\nThis is the probability, under the assumption of \u00b5 = 0 (background only), of seeing data as signal-like\nor more so relative to the data actually obtained. A small value is interpreted as evidence against \u00b5 = 0,\ni.e., a discovery of the signal.\nOne can de\ufb01ne the signi\ufb01cance corresponding to a given p-value as the number of standard deviations\nZ at which a Gaussian random variable of zero mean would give a one-sided tail area equal to p. That is,\nthe signi\ufb01cance Z is related to the p-value by\np =\nZ \u221e\nZ\n1\n\u221a\n2\u03c0 e\u2212x2/2 dx = 1\u2212\u03a6(Z) ,\n(13)\nwhere \u03a6 is the cumulative distribution for the standard (zero mean, unit variance) Gaussian. Equivalently\none has\nZ = \u03a6\u22121(1\u2212p) ,\n(14)\nwhere \u03a6\u22121 is the quantile of the standard Gaussian (inverse of the cumulative distribution). In (13) and\n(14) the subscript 0 was dropped as these relations hold for all p-values, not only those of the \u00b5 = 0\nhypothesis. The relation between Z and p is illustrated in Fig. 2.\nA signi\ufb01cance of Z = 5 corresponds to p = 2.87 \u00d7 10\u22127. For a suf\ufb01ciently large data sample, one\nwould obtain a p-value of 0.5 for data in perfect agreement with the expected background. With the\nde\ufb01nition of Z given above, this gives Z = 0. If the data \ufb02uctuate below the expected background, Z\nbecomes negative.\nNote that according to the de\ufb01nition (14), a p-value of 0.05 corresponds to Z = 1.64. This should not\nbe confused with a 1.96\u03c3 \ufb02uctuation of a Gaussian variable that gives 0.05 for the two-sided tail area.\nThe signi\ufb01cance of a discovery Z depends on the data obtained. To quantify our ability to discover a\nhypothesized signal in advance of seeing the data, we report the median signi\ufb01cance under the assump-\ntion that the signal is present at the Standard Model rate, \u00b5 = 1. Since Z is a monotonic function of p0,\nand p0 is also a monotonic function of q0, we have for the median signi\ufb01cance,\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1484\n\nx\n\u03c3\nZ\np-value\nFigure 2:\nIllustration of the corre-\nspondence between the signi\ufb01cance Z\nand a p-value.\nZmed = \u03a6\u22121(1\u2212p0med) = \u03a6\u22121(1\u2212p0(q0med)) .\n(15)\nThis can be obtained from the median value of q0 found using data generated under the assumption of\n\u00b5 = 1.\nA complete evaluation of the median signi\ufb01cance is computationally dif\ufb01cult, as it requires a large\nnumber of repeated simulations of the full set of experimental outputs and determination of Z(q0) from\nthe combination of all channels. Therefore in this note we have used the approximate methods described\nin Section 2.5, which allow one to estimate quickly the median signi\ufb01cance.\n2.3\nSetting limits\nIn addition to establishing discovery by rejecting the \u00b5 = 0 hypothesis, we can consider the alternative\nhypothesis of some non-zero \u00b5 and try to reject it. A p-value is computed for each \u00b5, and the set of \u00b5\nvalues for which the p-value is greater than or equal to a \ufb01xed value 1 \u2212CL form a con\ufb01dence interval\nfor \u00b5, where typically one takes a con\ufb01dence level CL = 95% . The upper end of this interval \u00b5up is the\nupper limit (i.e., \u00b5 \u2264\u00b5up at 95% CL).\nTo compute the p-value for a hypothesized \u00b5 we \ufb01rst consider again the test statistic q\u00b5 = \u22122ln\u03bb(\u00b5)\nas initially de\ufb01ned in (9) and (10). For purposes of computing limits, we introduce a modi\ufb01cation to this\nde\ufb01nition as described below.\nIf the data are incompatible with the hypothesized \u00b5, one expects a large value of \u22122ln\u03bb(\u00b5), i.e.,\n\u03bb(\u00b5) close to zero. If a data set generated according to the hypothesis \u00b5 gives a large value of \u22122ln\u03bb(\u00b5),\nthis can be the result of either an upward or downward \ufb02uctuation in \u02c6\u00b5 relative to \u00b5. This is illustrated\nin the scatterplot of \u02c6\u00b5 versus \u22122ln\u03bb(\u00b5) shown in Fig. 3(a), which is from a toy Monte Carlo study with\n\u00b5 = 0.8. The projection of the points on the \u02c6\u00b5 axis is shown in Fig. 3(b). Note that \u02c6\u00b5 \u22650 is imposed;\nthe reasons for and consequences of this requirement are discussed in Section 2.4.\nFor purposes of setting an upper limit, however, we want to determine the smallest \u00b5 such that there\nis a \ufb01xed small probability (one minus the con\ufb01dence level) to \ufb01nd data as compatible with that value of\n\u00b5 or less, relative to the degree of compatibility found with the real data. Therefore the data with upward\n\ufb02uctuations in \u02c6\u00b5 are not counted when computing the p-value, because they would be compatible with\nsome larger \u00b5. Therefore for purposes of computing limits we rede\ufb01ne q\u00b5 to be1\nq\u00b5 =\n(\n\u22122ln\u03bb(\u00b5)\n\u02c6\u00b5 \u2264\u00b5 ,\n0\notherwise.\n(16)\nThe distribution of the new q\u00b5 thus corresponds to the lower branch only of the U-shaped scatterplot\nshown in Fig. 3(a).\n1Equivalently, one could retain the de\ufb01nition q\u00b5 = \u22122ln(L(\u00b5, \u02c6\u02c6\u03b8)/L( \u02c6\u00b5, \u02c6\u03b8)) by placing an upper bound on \u02c6\u00b5 equal to \u00b5, i.e.,\nby imposing 0 \u2264\u02c6\u00b5 \u2264\u00b5. In this way, when \u02c6\u00b5 = \u00b5 then one has q\u00b5 = 0 just as in the case of discovery when testing \u00b5 = 0.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1485\n\n0\n2\n4\n6\n8\n10\n12\n14\n0\n0.5\n1\n1.5\n2\n2.5\n3\n\u00b5\n)\n\u00b5\n(\n\u03bb\n-2 ln \n0\n0.5\n1\n1 5\n2\n2.5\n3\n0\n100\n200\n300\n400\n500\n600\n\u00b5\n(a)\n(b)\nFigure 3: (a) Scatterplot of \u02c6\u00b5 versus \u22122ln\u03bb(\u00b5); (b) the distribution of \u02c6\u00b5 (see text).\nUsing the new de\ufb01nition (16), the p-value is given by the integral of f(q\u00b5|\u00b5) from the observed\nvalue q\u00b5,obs to in\ufb01nity as in Eq. (11) and as illustrated in Fig. 1. The p-value is computed in this manner\nfor all values of \u00b5, and the upper limit \u00b5up at 95% con\ufb01dence level is the largest value of \u00b5 for which the\np-value is at least 0.05.\nThe result can be summarized by giving the upper limit on \u00b5 as a function of the Higgs mass mH.\nSpeci\ufb01cally, if we can reject the hypothesis \u00b5 = 1 at a certain con\ufb01dence level, then the corresponding\nvalue of mH is regarded as excluded for a Standard Model Higgs. The lowest mass value not excluded is\nthe lower limit mlo.\nOne is also interested in the median limit under the assumption that there is no Higgs. As in the case\nof the discovery signi\ufb01cance, a full calculation of the median limit is dif\ufb01cult as it requires a large number\nof repeated simulations based on the full pro\ufb01le likelihood ratio. For purposes of this note, therefore, we\nuse the approximation techniques described in Section 2.5.\n2.4\nSampling distribution of the likelihood ratio\nTo determine the p-values required for both discovery and exclusion we need the sampling distribution,\nassuming data generated according to a given value of \u00b5, of the statistic q\u00b5, i.e., f(q\u00b5|\u00b5). For the case of\ndiscovery signi\ufb01cance we use q0 = \u22122ln\u03bb(0), and for setting limits we use q\u00b5 = \u22122ln\u03bb(\u00b5) for \u02c6\u00b5 \u2264\u00b5\nand q\u00b5 = 0, otherwise.\nTo claim discovery we require p-values for \u00b5 = 0 down to around 10\u22127, and therefore to do this with\na Monte Carlo simulation requires an extremely large number of simulated measurements. In practice\nthis is only carried out for simple test cases. Even for setting limits at 95% con\ufb01dence level, it is often\nnot practical to use Monte Carlo.\nUnder a set of regularity conditions and for a suf\ufb01ciently large data sample, Wilks\u2019 theorem says that\nfor a hypothesized value of \u00b5, the pdf of the statistic \u22122ln\u03bb(\u00b5) approaches the chi-square pdf for one\ndegree of freedom [2]. More generally, if there are n parameters of interest, i.e., those parameters that do\nnot get a double hat in the numerator of the likelihood ratio (9), then \u22122ln\u03bb(\u00b5) asymptotically follows\na chi-square distribution for n degrees of freedom. A proof and details of the regularity conditions can\nbe found in standard texts such as [3].\nIn the searches considered here, the data samples are generally large enough to ensure the validity of\nthe asymptotic formulae for the likelihood-ratio distributions. In our case, however, the distributions are\nmodi\ufb01ed because of constraints imposed on the expected number of events.\nUsually when searching for a new type of particle reaction one regards the mean number of events\ncontributed to any bin from any source, signal or background, to be greater than or equal to zero. In\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1486\n\nsome analyses it could be meaningful to consider a new effect that suppresses the expected number\nof events, e.g., the presence of a new decay channel could mean that the number of decays to known\nchannels is reduced. Here, however, we will regard any contribution to an expected number of events as\nnon-negative.\nAssuming only non-negative event rates, the maximum-likelihood estimators for the parameters are\nconstrained, e.g., \u02c6\u00b5 \u22650. As a consequence, if the observed number of events is below the level predicted\nby the background alone, then the maximum of the likelihood occurs for \u00b5 = 0, i.e., negative \u00b5 is not\nallowed. We can consider the effect of having \u02c6\u00b5 = 0 on the distribution of q\u00b5 for two cases: \u00b5 = 0 and\n\u00b5 > 0.\nFor \u00b5 = 0, i.e., when computing the discovery signi\ufb01cance, if \u02c6\u00b5 = 0 one has (see (9)),\n\u03bb(0) = L(0, \u02c6\u02c6\u03b8)\nL( \u02c6\u00b5, \u02c6\u03b8) = L(0, \u02c6\u02c6\u03b8)\nL(0, \u02c6\u03b8) = 1 ,\n(17)\nsince \u02c6\u00b5 = 0 and therefore \u02c6\u02c6\u03b8 = \u02c6\u03b8. The statistic q0 = \u22122ln\u03bb(0) is therefore equal to zero. This can be\nseen in the scatterplot of q0 versus \u02c6\u00b5 in Fig. 4(a). Figure 4(b) shows the corresponding q0 distribution\nwith the peak visible at q0 = 0. The superimposed curve is a chi-square distribution multiplied by one\nhalf, corresponding to the half of the events with \u02c6\u00b5 > 0.\n0\n2\n4\n6\n8\n10\n12\n14\n0\n0.5\n1\n1.5\n2\n2.5\n3\n\u00b5\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n1\n10\n2\n10\n3\n10\n0\nq\n(a)\n(b)\nFigure 4: (a) Scatterplot of \u02c6\u00b5 versus q\u00b5 from a Monte Carlo study with \u00b5 = 0; (b) the distribution of q0 (see text).\nFrom Fig. 4(b) one can see that except for the spike at q0 = 0 (when \u02c6\u00b5 = 0), the pdf of q0 can be well\napproximated by the chi-square pdf. Assuming a fraction w for the cases with \u02c6\u00b5 > 0 one has the pdf\nf(q0|0) = wf\u03c72\n1(q0)+(1\u2212w)\u03b4(q0) .\n(18)\nIn the usual case where upward and downward \ufb02uctuations of \u02c6\u00b5 are equally likely we have w = 1/2. The\np-value of the background-only hypothesis given an observation q0,obs greater than zero is therefore\np =\nZ \u221e\nq0,obs\nwf\u03c72\n1 (q0)dq0 = w(1\u2212F\u03c72\n1 (q0,obs)) ,\n(19)\nwhere F\u03c72\n1 is the cumulative chi-square distribution for one degree of freedom.\nThe second case to consider is \u00b5 > 0, e.g., when one wants to set an upper limit on \u00b5. Under the\nhypothesis \u00b5, one obtains \u02c6\u00b5 > \u00b5 and \u02c6\u00b5 \u2264\u00b5 with approximately equal probability. Figure 5 shows the\ndistributions of q\u00b5 for both cases \u02c6\u00b5 > \u00b5 and \u02c6\u00b5 \u2264\u00b5 obtained from the scatterplot Fig. 3(a), from a Monte\nCarlo study with \u00b5 = 0.8.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1487\n\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n1\n10\n2\n10\n3\n10\n\u00b5\n > \n\u00b5\n)\n\u00b5\n(\n\u03bb\n-2 ln \n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n1\n10\n2\n10\n3\n10\n)\n\u00b5\n(\n\u03bb\n-2 ln \n\u00b5\n \n\u2264\n \n\u00b5\n(a)\n(b)\nFigure 5: Distributions of \u22122ln\u03bb(\u00b5) for (a) \u02c6\u00b5 > \u00b5 and (b) \u02c6\u00b5 \u2264\u00b5. The superimposed curves are chi-square\ndistributions for one degree of freedom normalized to half the number of entries in the original distribution (see\nFig. 3(a)).\nFrom Fig. 5(a) one can see that for \u02c6\u00b5 > \u00b5, the data follow the chi-square pdf quite accurately. This\nportion of the distribution is ignored, however, when setting upper limits on \u00b5, because of the modi\ufb01ed\nde\ufb01nition of q\u00b5 (20) used for limits,\nq\u00b5 =\n(\n\u22122ln\u03bb(\u00b5)\n\u02c6\u00b5 \u2264\u00b5 ,\n0\notherwise.\n(20)\nSuppose now \u02c6\u00b5 \u2264\u00b5 with a probability w; in practice this is close to one half. (Note for the case of q0,\nw is the probability of \u02c6\u00b5 > \u00b5. The different de\ufb01nitions of w are used so as to give similar forms for\nf(q0|0) and f(q\u00b5|\u00b5).) Thus for \u02c6\u00b5 > \u00b5 one has from (20) q\u00b5 = 0, and therefore the distribution has a\ndelta function at q\u00b5 = 0 with weight 1\u2212w. The pdf of f(q\u00b5|\u00b5) can therefore be written\nf(q\u00b5|\u00b5) = wf(q\u00b5|\u00b5, \u02c6\u00b5 \u2264\u00b5)+(1\u2212w)\u03b4(q\u00b5) .\n(21)\nwhere f(q\u00b5|\u00b5, \u02c6\u00b5 \u2264\u00b5) is the conditional pdf for q\u00b5 given \u02c6\u00b5 \u2264\u00b5.\nFor \u02c6\u00b5 \u2264\u00b5, one may sometimes \ufb01nd \u02c6\u00b5 equal to zero, i.e., the lower edge of the allowed range, as can\nbe seen in the scatterplot of \u02c6\u00b5 versus q\u00b5 shown in Fig. 3(a). Although for the case \u00b5 = 0 this gave a peak\nat q0 = 0, here it gives\n\u03bb(\u00b5) = L(\u00b5, \u02c6\u02c6\u03b8)\nL( \u02c6\u00b5, \u02c6\u03b8) = L(\u00b5, \u02c6\u02c6\u03b8)\nL(0, \u02c6\u03b8) ,\n(22)\nwhich in contrast to (17) is not equal to unity. The effect of having \u02c6\u00b5 = 0 on the distribution of q\u00b5 is\ntherefore more complicated than was the case for q0.\nIn general for \u02c6\u00b5 \u2264\u00b5, the distribution of q\u00b5 falls off more steeply than the chi-square distribution.\nThis is seen in Fig. 5(b). Therefore a p-value based on the chi-square formula will be larger than the\ntrue p-value, and the corresponding signi\ufb01cance Z will be smaller. The upper limits obtained for \u00b5 are\ntherefore larger, i.e., a smaller set of \u00b5 values is excluded.\nIf \u00b5 is suf\ufb01ciently large, then \u02c6\u00b5 is very rarely pushed to zero and f(q\u00b5|\u00b5, \u02c6\u00b5 \u2264\u00b5) approaches a\nchi-square distribution for one degree of freedom. For purposes of the present study, the chi-square\napproximation is adequate, but gives somewhat conservative limits. That is, we take the distribution of\nq\u00b5 to be\nf(q\u00b5|\u00b5) = wf\u03c72\n1 (q\u00b5)+(1\u2212w)\u03b4(q\u00b5)\n(23)\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1488\n\nand use w = 0.5. One has therefore the same pdf for q\u00b5 using the modi\ufb01ed de\ufb01nition (20) as was found\nin (18) for q0 based on the original de\ufb01nition, q0 = \u22122ln\u03bb(0).\nTo summarize the result above, the pdf of q\u00b5 can be approximated by a mixture of a chi-square pdf\nfor one degree of freedom with weight w and a delta function at zero with weight 1\u2212w. This holds both\nfor discovery (\u00b5 = 0) and setting limits (\u00b5 > 0).\nConsider now the variable\nu = \u221aq\u00b5 =\np\n\u22122ln\u03bb(\u00b5) ,\n(24)\nwhich has the pdf\nf(u) = \u0398(u)w\nr\n2\n\u03c0 e\u2212u2/2 +(1\u2212w)\u03b4(u) ,\n(25)\nwhere \u0398(u) = 1 for u \u22650 and is zero otherwise. The second term in (25) follows from the fact that the\nvalues q0 = 0 and u = 0 occur with equal probability, 1 \u2212w. Furthermore if a variable x follows the\nstandard Gaussian distribution, then one can show x2 follows a chi-square distribution for one degree of\nfreedom. Therefore if x2 follows a \u03c72 distribution, then\n\u221a\nx2 follows a Gaussian scaled up by a factor of\ntwo for x > 0 so as to have a total area of unity.\nThe p-value of the hypothesis \u00b5 for a non-zero observation q\u00b5,obs is therefore\np = P(q\u00b5 \u2265q\u00b5,obs) = P(u \u2265\u221aq\u00b5,obs) = 2w\nZ \u221e\n\u221aq\u00b5,obs\n1\n\u221a\n2\u03c0 e\u2212u2/2 du = 2w(1\u2212\u03a6(\u221aq\u00b5,obs)) .\n(26)\nCombining this with Eq. (14) for the signi\ufb01cance Z gives\nZ = \u03a6\u22121(1\u22122w(1\u2212\u03a6(\u221aq\u00b5,obs))) .\n(27)\nIn the usual case where the weights of the chi-square and delta-function terms are equal, i.e., w = 1/2,\nEq. (27) reduces to to the simple formula\nZ = \u221aq\u00b5,obs .\n(28)\n2.5\nApproximate methods\nTo determine the discovery signi\ufb01cance or to set limits using a given data set, one must carry out the\nglobal \ufb01t described above. For this one needs \ufb01rst to combine the likelihood functions for the individual\nchannels into the full likelihood function containing a single strength parameter \u00b5, and use this to \ufb01nd\nthe pro\ufb01le likelihood ratio. It is possible, however, to \ufb01nd approximate values for the median discovery\nsigni\ufb01cance and limits in a way that only requires as input the separate pro\ufb01le likelihood ratio values\nfrom each of the channels. This is very useful especially in the planning phase of a search that combines\nmultiple channels.\nThe procedure relies on two separate approximations. First, we estimate the median value of the pro-\n\ufb01le likelihood ratio \u03bb(\u00b5) by evaluating the likelihood function with a single, arti\ufb01cial data set in which\nall statistical \ufb02uctuations are suppressed, as described in Section 2.5.1. Second, to determine the signif-\nicance values from the likelihood ratios, we use the asymptotic form of the distribution of \u22122ln\u03bb(\u00b5)\nvalid for suf\ufb01ciently large data samples. This is described in Section 2.5.2, and its validity is checked\nfor the individual channels in Section 3. Here the limitations of the approximation are investigated and\nfor one case where it is found to be insuf\ufb01ciently accurate (the discovery signi\ufb01cance for the channel\nH \u2192W +W \u2212plus no jets), an alternate procedure is followed.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1489\n\n2.5.1\nApproximation for the median likelihood ratio\nTo \ufb01nd the median discovery signi\ufb01cance and limits, the median likelihood ratios \u03bbi(\u00b5) are \ufb01rst found\nfor each channel separately, and then combined to give the full median likelihood ratio. One can estimate\nthe median \u03bbi(\u00b5) by the value of the likelihood ratio evaluated with a single arti\ufb01cially constructed data\nset, in which all statistical \ufb02uctuations are suppressed and the data values n and m are replaced by their\nexpectation values for a given integrated luminosity and a hypothesized strength parameter \u00b5A. We refer\nto this as an \u2018Asimov\u2019 data set.2 It replaces having to simulate a large number of experiments from which\none would determine the median.\nAs before, \u00b5A = 0 is the background only hypothesis and \u00b5A = 1 corresponds to background plus\nsignal present at the Standard Model rate. The median referred to thus pertains to what one would obtain\nwith a large number of experiments generated under the assumption of \u00b5A. The approximation is in fact\nmore accurate if one uses noninteger values for numbers of events in the log-likelihood (the factorial\nterms are in any case absent) so that the Asimov likelihood LA is found by substituting\nn j\n=\n\u00b5As j +b j\n(29)\nmk\n=\nuk ,\n(30)\ninto the likelihood function (6) for each channel. Here for s j, b j and uk, one needs in principle the\nexpectation values, i.e., these quantities should have no statistical errors. In practice they are estimated\nusing a Monte Carlo sample corresponding to an integrated luminosity substantially larger than what is\nconsidered for the data. The numbers of signal and background events are then scaled to the desired\nluminosity. The other nuisance parameters such as shape parameters are estimated as would be done\nwith any other data set; we refer below to the resulting values as \u03b8 A. Because the Asimov data set has\nno statistical \ufb02uctuations, the \u03b8 A are simply the values one would derive from a very large Monte Carlo\ndata sample.\nThe estimate of the median likelihood ratio used for the ith channel is therefore\n\u03bbA,i(\u00b5) = LA,i(\u00b5, \u02c6\u02c6\u03b8)\nLA,i( \u02c6\u00b5, \u02c6\u03b8) \u2248\nLA,i(\u00b5, \u02c6\u02c6\u03b8)\nLA,i(\u00b5A,\u03b8 A) ,\n(31)\nwhere LA,i denotes the likelihood function (6) evaluated with the Asimov data values (29) and (30). The\napproximation used for the \ufb01nal step in (31) exploits the fact that ML estimate of \u02c6\u00b5 is very close to the\ninput value \u00b5A when the likelihood function is constructed using the Asimov data set.\nNote that if the likelihood functions for the individual channels were to be constructed with data\ncontaining statistical \ufb02uctuations rather than with the arti\ufb01cial Asimov data, then the ML estimate of the\nstrength parameter, \u02c6\u00b5, would in general be different for each channel. The full likelihood function (8)\nused for the combination, however, contains a single global \u00b5. We can now exploit the fact that for the\nAsimov data one has \u02c6\u00b5 \u2248\u00b5A for all of the channels and thus obtain the median likelihood ratio for the\ncombination as the product of the individual \u03bbA,i(\u00b5),\n\u03bbA(\u00b5) = \u220f\ni\n\u03bbA,i(\u00b5) .\n(32)\nMonte Carlo studies show that Eq. (32) provides an excellent approximation to the median value one\nwould \ufb01nd from data generated with \u00b5A as the strength parameter.\n2The name of the Asimov data set is inspired by the short story Franchise, by Isaac Asimov [1]. In it, elections are held by\nselecting a single voter to represent the entire electorate.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1490\n\nFor purposes of quantifying how likely we are to discover the Higgs if it exists, we report the signif-\nicance obtained from the p-value of \u00b5 = 0 with an Asimov data set that corresponds to \u00b5A = 1,\n\u03bbs+b(0) = \u220f\ni\nLs+b,i(0, \u02c6\u02c6\u03b8)\nLs+b,i(1,\u03b8A) .\n(33)\nHere the subscript s+b refers to the Asimov data set; the argument 0 denotes the value of \u00b5 being tested.\nThat is, Eq. (33) approximates what one would obtain with data generated with signal and background\nfor the median value of \u03bb(0), which is used to test the background-only (\u00b5 = 0) hypothesis. Equation\n(33) provides the median q0med = \u22122ln\u03bbs+b(0), and from this the p-value and signi\ufb01cance Z are found\nusing equation (15).\nTo determine the limits on \u00b5 that we expect to set if the Higgs does not exist (or is beyond our\nreach), we \ufb01nd the p-value of a hypothesized \u00b5 using the likelihood ratio \u03bb(\u00b5) based on Asimov data\nfor background only (\u00b5A = 0),\n\u03bbb(\u00b5) = \u220f\ni\nLb,i(\u00b5, \u02c6\u02c6\u03b8)\nLb,i(0,\u03b8A) .\n(34)\nThat is, \u03bbb(\u00b5) approximates the median value of \u03bb(\u00b5) one would obtain from data generated according\nto the background-only hypothesis. The value of \u03bbb(\u00b5) is used to determine the median q\u00b5med, which is\nused to \ufb01nd the median p-value, p\u00b5med. This is computed for all \u00b5 and the point where p\u00b5med = 0.05 gives\nthe 95% CL upper limit.\nBecause \u02c6\u00b5 \u2248\u00b5A holds for each channel individually when using Asimov data, it is possible to de-\ntermine the values of the likelihood ratio entering into (32) separately for each channel, which simpli\ufb01es\ngreatly the task of estimating the median signi\ufb01cance that would result from the full combination. It\nshould be emphasized, however, that the discovery signi\ufb01cance or exclusion limits determined from real\ndata require one to construct the full likelihood function containing a single parameter \u00b5, and this must\nbe used in a global \ufb01t to \ufb01nd the pro\ufb01le likelihood ratio.\nFurthermore, some systematic errors, e.g., the uncertainty in the integrated luminosity, are common\nto all channels and correspond to a common nuisance parameter. When using Asimov data, the values of\nsuch parameters will be \ufb01tted to the same values in all channels. Thus the correlations between common\nsystematics are taken into account just as they would be in a global \ufb01t of all channels.\nA limitation of the procedure with Asimov data is that it only provides an estimate of the median\nlikelihood ratio. To obtain an uncertainty band on the expected (median) discovery and exclusion sensi-\ntivities as a function of mH one would have to simulate a large number of experiments.\n2.5.2\nApproximate relation between likelihood ratio and signi\ufb01cance\nTo compute the p-values we need the distribution f(q\u00b5|\u00b5) of q\u00b5 = \u22122ln\u03bb(\u00b5). For a suf\ufb01ciently large\ndata sample the pdf of q\u00b5 takes on a well de\ufb01ned limiting form related to the chi-square distribution, as\ndiscussed in Section 2.4. Assuming this form, the p-value of the hypothesis \u00b5 is found to be\np\u00b5 \u22481\u2212\u03a6(\u221aq\u00b5) ,\n(35)\nand the signi\ufb01cance Z is given by the formula\nZ = \u03a6\u22121(1\u2212p\u00b5) \u2248\np\n\u22122ln\u03bb(\u00b5) .\n(36)\nFor estimating the median discovery signi\ufb01cance we use equations (35) and (36) together with the equa-\ntion (33), the likelihood ratio based on Asimov data containing signal and background. To \ufb01nd the\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1491\n\nmedian limit on \u00b5, we use again equations (35) and (36) but with the likelihood ratio based on Asimov\nbackground data only, equation (34).\nThe validity of this approximation is investigated for each channel by generating distributions of\nq\u00b5 for \u00b5 = 0,1 using a fast Monte Carlo simulation and comparing the resulting histograms with the\nexpected asymptotic form. These comparisons are shown in Section 3.\n2.6\nConsequences of testing many Higgs mass values\nThe statistical signi\ufb01cance of a potential discovery is quanti\ufb01ed by giving the p-value of the no-Higgs\nhypothesis, i.e., the probability, under the assumption of background only, that that one would see data\nwith equal or less compatibility with this hypothesis relative to the data obtained. Finding this proba-\nbility below a speci\ufb01ed threshold (e.g., the 5\u03c3 threshold, or p < 2.87 \u00d7 10\u22127) corresponds to claiming\ndiscovery of a Higgs boson.\nThe approach taken in this analysis is to compute the p-value of the no-Higgs hypothesis separately\nas a function of the Higgs mass. The threshold p-value is thus the false discovery rate for Higgs boson\nof a given mass. Further one should also estimate the probability, under the assumption of background\nonly, that this p-value will fall below the discovery threshold for any mass within the range considered.\nBy searching for the Higgs within a broad range of hypothetical masses, one increases the probability of\nobserving what appears to be a signal at some mass, and so the effective signi\ufb01cance of the discovery is\nreduced. In HEP this is sometimes referred to as the \u201clook-elsewhere effect\u201d.\nTo \ufb01rst approximation the effective increase in the false-discovery rate is given by the number of\nstatistically separate mass ranges explored. If a certain data set would give a p-value of mH below the\ndiscovery threshold, then the same data would in general also indicate discovery for other masses very\nclose by. Roughly speaking, the mass range in which a given data set would indicate discovery is set by\nthe mass resolution for the Higgs candidate. So the factor by which the p-value is in\ufb02ated is given by the\nmass range explored divided by the average mass resolution. Monte Carlo studies can be used to validate\nand re\ufb01ne this approximation; this approach is planned for future analyses.\nAn alternative to considering \ufb01xed Higgs masses is to treat both the strength parameter \u00b5 and the\nHiggs mass mH as free parameters in the likelihood ratio. For example, to establish discovery one com-\nputes the p-value of the no-Higgs hypothesis. As before, this is the probability, under the assumption of\nno Higgs, of \ufb01nding data with equal or lesser compatibility with \u00b5 = 0 relative to the data obtained. In\ncontrast to the \ufb01xed-mass case, however, \u201cless compatible\u201d here means having a lower likelihood ratio\nfor any allowed value of the Higgs mass; the lowest value comes when the denominator contains the\n\ufb01tted maximum-likelihood estimator \u02c6mH. In practice the \ufb01tted value of the Higgs mass is restricted to\nlie within a stated range. This has been done for the Higgs searches using the \u03b3\u03b3 [4] and W+W\u2212[5]\nchannels, with the aim of extending this method to a combination of all channels.\n3\nCombination of Higgs search channels\nIn this section a brief description of each of the four search channels is given. For each channel, the\nmethod used to obtain the likelihood ratio is described, and values of the test variable q\u00b5 as de\ufb01ned\nby Eq. (10) for discovery and by Eq. (16) for limits are tabulated for several values of the integrated\nluminosity L and Higgs mass mH. For the discovery sensitivity where one tests \u00b5 = 0, the median value\nof q0 is given under the assumption of \u00b5 = 1; for exclusion sensitivity, the median of q1 is given under\nthe assumption of \u00b5 = 0.\nIn addition, for each channel we show distributions of q\u00b5 under the assumption of \u00b5 for the two\ncases \u00b5 = 0 and \u00b5 = 1. For the approximations used in this note to be valid, these should be close to the\nasymptotic form described in Section 2.4. This limiting form for the distribution f(q\u00b5|\u00b5) is a mixture of\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1492\n\na delta function at q\u00b5 = 0 and a chi-square distribution for one degree of freedom, where each component\nhas equal weight. We refer to this as a 1\n2\u03c72\n1 distribution. For the case of \u00b5 = 0 we compare directly the\nMonte Carlo distribution of q0 with the 1\n2\u03c72\n1 distribution and the delta-function term at q0 = 0 is clearly\nvisible. For \u00b5 = 1 we show the equivalent comparison but for reasons of convenience only the events\nwith \u02c6\u00b5 \u2264\u00b5 are shown, i.e., the events with \u02c6\u00b5 > \u00b5 that contribute to the delta function at q1 = 0 are left\noff. That is, for exclusion it is the conditional pdf f(q1|\u00b5 = 1, \u02c6\u00b5 \u22641) that is compared to a chi-square\ndistribution for one degree of freedom; there is no delta function term.\nAll channels use data driven background estimation methods. This way, the uncertainties in the back-\nground shape and normalization are treated within the framework of the pro\ufb01le likelihood as nuisance\nparameters. Using control samples the effect of many uncertainties like energy scales and fake rates on\nthe background estimate can be constrained by the control samples. Uncertainties on the signal ef\ufb01ciency\ndo not affect the discovery sensitivity which is testing the presence or absence of a signal; however, this\nis not the case for exclusion sensitivity. As one would expect, uncertainty in the signal ef\ufb01ciency does\nreduce the exclusion sensitivity. This uncertainty was incorporated into the pro\ufb01le likelihood calculation\nby adding an extra term to the likelihood function for every channel as described in Section 2.1: a Gaus-\nsian relating the nominal ef\ufb01ciency estimated in an auxiliary measurement, the true ef\ufb01ciency, and the\nuncertainty of that auxiliary measurement.\n3.1\nH \u2192\u03b3\u03b3\nDetails on the H \u2192\u03b3\u03b3 channel are given in Ref. [4]. We perform an unbinned maximum-likelihood\n\ufb01t to extract the signal and background event yields by using the diphoton invariant mass, m\u03b3\u03b3, as a\ndiscriminating variable. The H \u2192\u03b3\u03b3 distribution of m\u03b3\u03b3 forms a Gaussian peak with tails to lower\nvalues from photon energy losses before the calorimeter. It is well modelled by a Crystal Ball function.\nThe signal probability density function, pH(m\u03b3\u03b3), is given by\npH(m\u03b3\u03b3) = N \u00b7\n(\nexp\n\u0000\u2212t2/2\n\u0001\n,\nfor t > \u2212\u03b1 ,\n(n/|\u03b1|)n \u00b7exp\n\u0000\u2212|\u03b1|2/2\n\u0001\n\u00b7(n/|\u03b1|\u2212|\u03b1|\u2212t)\u2212n ,\notherwise,\n(37)\nwhere t = (m\u03b3\u03b3 \u2212mH \u2212\u03b4mH)/\u03c3(m\u03b3\u03b3), N is a normalisation parameter, mH is the Higgs boson mass,\n\u03b4mH is an offset and \u03c3 represents the diphoton invariant mass resolution. The non-Gaussian tail is\nparametrised by n and \u03b1. We include an additional, broader Gaussian term in Eq. 37 to improve the\ndescription of the tails of the distribution. Within a suf\ufb01ciently narrow mass window, the background of\nm\u03b3\u03b3 is modeled by an exponential distribution with a single slope parameter \u03be.\nThe resulting median pro\ufb01le likelihood ratios for discovery, \u03bb(\u00b5 = 0) (using toy s+b Monte Carlo\nexperiments and taking the median of the \u03bb(\u00b5 = 0) distribution ) are given in Table 1 for a few Higgs\nmasses at some given luminosities.\nThe distribution of the test statistic q0 under the null background only hypothesis, for mH = 120 GeV\nwith an integrated luminosity of 2 and 10 fb\u22121, is shown in Fig. 6. A 1\n2\u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\nThe median pro\ufb01le likelihood ratio for exclusion, \u22122ln\u03bb(\u00b5) (using toy background-only Monte\nCarlo experiments and taking the median of the \u03bb(\u00b5) distribution) is given in Table 2 for a few Higgs\nmasses at several integrated luminosities and for a signal strength \u00b5 = 1, corresponding to a Standard\nModel Higgs Boson.\nThe distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypotheses for mH = 150 GeV with\nan integrated luminosity of 2 and 10 fb\u22121 is shown in Figures 7. A \u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1493\n\nTable 1: Median values of \u22122ln\u03bb(\u00b5) (evaluated at \u00b5 = 0) obtained from \ufb01ts to simulated data generated with\nH \u2192\u03b3\u03b3 signal plus background (\u00b5 = 1) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n115\n120\n130\n140\n1\n0.35\n0.55\n0.75\n0.67\n2\n0.75\n1.07\n1.45\n0.95\n5\n1.95\n2.95\n3.65\n2.55\n10\n3.95\n5.86\n7.35\n5.05\n30\n11.85\n17.72\n21.99\n15.05\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n\u03b3 \u03b3 \n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n\u03b3 \u03b3 \n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 6: The distribution of the test statistic q0 (for H \u2192\u03b3\u03b3), under the null background only hypothesis, for\nmH = 120 GeV with an integrated luminosity of 2 (a) and 10 (b) fb\u22121. A 1\n2\u03c72\n1 distribution is superimposed.\nTable 2: Median values of \u22122ln\u03bb(\u00b5) (evaluated at \u00b5 = 1) obtained from H \u2192\u03b3\u03b3 background-only (\u00b5 = 0)\nsimulated data for several values of the Higgs mass and integrated luminosities.\nL\nmH (GeV)\n(fb\u22121)\n115\n120\n130\n140\n1\n0.72\n0.73\n0.91\n0.67\n2\n0.97\n1.21\n1.39\n0.97\n5\n2.11\n2.59\n3.13\n2.23\n10\n3.55\n4.87\n5.71\n4.04\n30\n8.47\n10.50\n11.63\n9.00\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1494\n\n1\nq\n0\n2\n4\n6\n8\n10\n12\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n\u03b3 \u03b3 \n\u2192\nH \n-1\nL = 2 fb\n1\nq\n0\n2\n4\n6\n8\n10\n12\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n\u03b3 \u03b3 \n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 7: The distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypothesis (for H \u2192\u03b3\u03b3), for mH = 120\nGeV with an integrated luminosity of (a) 2 fb\u22121 and (b) 10 fb\u22121. A \u03c72\n1 distribution is superimposed.\n3.2\nH \u2192W +W \u2212\nThe H \u2192W +W \u2212search is divided into two topologies, production of a Higgs with no jets (H +0j) and\nwith two additional jets (H +2j), using in both cases the decay mode H \u2192WW \u2192e\u03bd\u00b5\u03bd. The present\nstudy does not yet consider the \ufb01nal states e\u03bde\u03bd or \u00b5\u03bd\u00b5\u03bd, nor those with hadronic W decays. Future\ninclusion of these channels is expected to improve the search sensitivity particularly for the high Higgs\nmass region. The search is described in detail in Ref. [5].\n3.2.1\nH +0j\nThe analysis of the H + 0j channel uses a two dimensional maximum-likelihood \ufb01t of the transverse\nmass and the transverse momentum of the WW system in two bins of the dilepton opening angle in the\ntransverse plane. The \ufb01t includes control samples to measure the backgrounds from tt and Z \u2192\u03c4\u03c4.\nThe QCD WW background requires particular attention. Its distributions of Higgs-candidate trans-\nverse mass and pT are described with functions containing several adjustable (nuisance) parameters, and\nseveral others whose values are determined from a full Monte Carlo simulation and thereafter treated as\n\ufb01xed. The distribution of the test statistic q0 under the background-only (\u00b5 = 0) hypothesis is shown in\nFig. 8(a) for mH = 150 GeV for an integrated luminosity of 10 fb\u22121. The same \ufb01xed QCD WW shape\nparameters are used both to generate the data and for calculating the likelihood ratio. A 1\n2\u03c72\n1 distribution\nis superimposed, showing the level of agreement of the asymptotic approximation.\nFor this channel, further investigation of the systematic uncertainties was carried out. For the \ufb01xed\nshape parameters related to pT and transverse mass distributions for the QCD WW background, the val-\nues used to generate the data were varied relative to what was used when determining the likelihood ratio.\nThis was done in a manner that minimized the sensitivity of the resulting q0 distribution to variations in\nother \ufb01xed parameters such as the QCD Q2 scale. The resulting distributions of q0 are thus no longer\nexpected to follow the 1\n2\u03c72\n1 form, as can be seen in Fig. 8(b).\nBecause the chi-square approximation is not valid in this case, the p-values are calculated using the\nq0 distribution obtained directly from the Monte Carlo. An exponential is \ufb01tted to the tail region in\norder to extrapolate to large q0 values, and the median value of q0 under the hypothesis of signal plus\nbackground is determined using the same variation of the background parameters. It was found that the\nmedian p-value of the background-only hypothesis, with the median computed under assumption of the\ns+b hypothesis, is very similar to the original case where the QCD shape parameters are not varied and\nthe 1\n2\u03c72\n1 distribution is used.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1495\n\n0\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n (0 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 10 fb\n0\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n (0 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 10 fb\nAltered parameters\n(a)\n(b)\nFigure 8: The distribution of the test statistic q0 for H +0 j \u2192WW +0 j, under the background-only hypothesis,\nwith the same \ufb01xed QCD WW shape parameters used at both the generator and the \ufb01t level, for mH = 150 GeV\nand for an integrated luminosity of 10 fb\u22121 (a) with the same shape parameters for event generation and \ufb01tting; (b)\nwith altered shape parameters. A 1\n2 \u03c72\n1 distribution is superimposed.\nFor the combination of results for discovery (i.e., testing \u00b5 = 0), we have used the p-values as\ndescribed above for the case of the H + 0j channel. The same variation of QCD WW parameters was\nalso investigated for the case of exclusion (i.e., testing \u00b5 > 0, and in particular \u00b5 = 1), and it was done\nas well for the H + 2j channel. In those studies, however, the distributions, under the assumption of\n\u00b5, of the test statistic q\u00b5 were found to agree quite well with the expected 1\n2\u03c72\n1 distribution, even after\nthe parameter variation. Therefore for these cases we have based the combination of results on the\nasymptotic approximations for the q\u00b5 distributions (as done in this paper for the other Higgs channels).\nTo simplify the comparison with the other channels, the median p-values of the background-only\n(\u00b5 = 0) hypothesis for the H + 0j channel were converted into effective values of the variable q0 =\n\u22122ln\u03bb(0) according to q0 = Z2 =\n\u0000\u03a6\u22121(1\u2212p)\n\u00012. These are given in Table 3 for several Higgs masses\nand integrated luminosities.\nTable 3: Median values of \u22122ln\u03bb(\u00b5 = 0) obtained from H + 0 j \ufb01ts using data simulated under the assumption\nof signal plus background (\u00b5 = 1) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n130\n140\n150\n160\n170\n180\n190\n1\n1.64\n4.30\n9.56\n16.52\n15.39\n7.37\n3.17\n2\n2.87\n8.60\n19.36\n34.67\n30.58\n13.73\n5.63\n5\n6.55\n20.15\n42.77\n74.39\n63.58\n31.54\n13.54\n10\n11.52\n33.27\n70.67\n113.33\n103.44\n51.06\n22.78\nThe median pro\ufb01le likelihood ratio for exclusion, \u03bb(\u00b5) (using background-only MC experiments and\ntaking the median of the \u03bb(\u00b5) distribution), is given in Table 4 for several Higgs masses and integrated\nluminosities for the signal strength \u00b5 = 1.0, corresponding to a SM Higgs Boson.\nThe distribution of the statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypothesis is shown in Fig. 9 for mH = 150\nGeV and for an integrated luminosity of 2 and 10 fb\u22121. A \u03c72\n1 distribution is superimposed, showing the\nvalidity of the asymptotic approximation.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1496\n\nTable 4: Median values of \u22122ln\u03bb(\u00b5 = 1) obtained from H + 0 j \ufb01ts using simulated background-only (\u00b5 = 0)\ndata for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n130\n140\n150\n160\n170\n180\n190\n1\n1.37\n3.93\n8.69\n14.83\n14.23\n7.26\n3.26\n2\n2.57\n7.47\n15.59\n25.20\n23.65\n12.91\n5.84\n5\n5.85\n15.26\n30.05\n45.60\n41.13\n25.41\n12.02\n10\n10.01\n24.69\n45.24\n62.13\n57.69\n37.42\n20.03\n1\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-2\n10\n-1\n10\n1\nATLAS\n (0 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 2 fb\n1\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-2\n10\n-1\n10\n1\nATLAS\n (0 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 9: The distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypothesis for H +0 j \u2192WW +0 j, for\nmH = 150 GeV with an integrated luminosity of (a) 2fb\u22121 and (b) 10fb\u22121. A \u03c72\n1 distribution is superimposed.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1497\n\n3.2.2\nH +2j\nThe H +2j analysis uses a two-dimensional \ufb01t based on the transverse mass and the output of a Neural\nNetwork, which takes as input several kinematic variables related to the jet activity in the event. The \ufb01t is\nperformed simultaneously in signal-enriched and background-enriched regions distinguished by lepton\nangular variables, which are nearly uncorrelated to the jet variables used in the Neural Network.\nThe median pro\ufb01le likelihood ratios for discovery, \u22122ln\u03bb(\u00b5 = 0) (using toy s+b MC experiments\nand taking the median of the \u03bb(\u00b5 = 0) distribution), are given in Table 5 for several Higgs masses and\nintegrated luminosities.\nTable 5: Median values of \u22122ln\u03bb(\u00b5) for \u00b5 = 0 obtained from H + 2 j \ufb01ts to simulated data with signal plus\nbackground (\u00b5 = 1) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n130\n140\n150\n160\n170\n180\n190\n1\n0.39\n0.89\n1.61\n2.73\n2.89\n1.85\n1.23\n2\n0.70\n1.75\n3.22\n5.34\n5.67\n3.66\n2.07\n5\n2.01\n5.29\n8.87\n14.20\n14.58\n9.22\n5.71\n10\n3.82\n9.14\n16.56\n26.35\n26.05\n16.68\n9.93\nThe distribution of the statistic q0 under the background-only hypothesis is shown in Fig. 10 for\nmH = 150 GeV and for an integrated luminosity of 2 and 10 fb\u22121. A 1\n2\u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\n0\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n|0)\n0\nf(q\n-2\n10\n-1\n10\n1\n10\nATLAS\n (2 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n|0)\n0\nf(q\n-2\n10\n-1\n10\n1\n10\nATLAS\n (2 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 10: The distribution of the test statistic q0 (for H + 2 j \u2192WW + 2 j), under the null background only\nhypothesis, for mH = 150 GeV and for an integrated luminosity of 2 (a) and 10 (b) fb\u22121. A 1\n2\u03c72\n1 distribution is\nsuperimposed.\nThe median pro\ufb01le likelihood ratio for exclusion, \u22122ln\u03bb(\u00b5) with \u00b5 = 1, where the median is com-\nputed using background-only MC data, is given in Table 6 for several Higgs masses and integrated\nluminosities.\nThe distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s + b hypothesis is shown in Figures 11\nfor mH = 150 GeV with an integrated luminosity of 2 and 10fb\u22121. A \u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1498\n\nTable 6: Median values of \u22122ln\u03bb(\u00b5) for \u00b5 = 1 obtained from H +2 j \ufb01ts to simulated background-only (\u00b5 = 0)\ndata for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n130\n140\n150\n160\n170\n180\n190\n1\n0.37\n0.75\n1.31\n2.29\n2.44\n1.99\n0.95\n2\n0.87\n2.49\n5.06\n8.18\n7.74\n3.85\n1.90\n5\n1.40\n3.13\n5.86\n9.58\n9.90\n7.89\n4.59\n10\n2.80\n6.56\n10.72\n16.14\n16.62\n13.94\n8.74\n1\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-2\n10\n-1\n10\n1\nATLAS\n (2 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 2 fb\n1\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-2\n10\n-1\n10\n1\nATLAS\n (2 jet)\n-\nW\n+\n W\n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 11: The distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s + b (\u00b5 = 1) hypothesis (for H + 2 j \u2192\nWW + 2 j), for mH = 150 GeV with an integrated luminosity of (a) 2fb\u22121 and (b) 10fb\u22121. A \u03c72\n1 distribution is\nsuperimposed.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1499\n\n3.3\nH \u2192\u03c4+\u03c4\u2212\nThe sensitivity of the ATLAS detector to a Higgs boson produced via Vector Boson Fusion and decaying\nto tau leptons has been investigated [6].\nTwo tau decay channels are considered: ll and lh. Although there are several neutrinos in the event,\nit is possible to reconstruct the \u03c4+\u03c4\u2212invariant mass, m\u03c4\u03c4, by making the collinear approximation, in\nwhich the decay products of the \u03c4 are assumed to be collinear with the \u03c4 direction in the laboratory\nframe. After other event selection criteria are imposed, the spectrum of m\u03c4\u03c4 is used to extract the signal.\nParticular care has been given to the incorporation of uncertainty in both the rate and shape for the signal\nand backgrounds.\nA data-driven background estimation technique has been established for the major backgrounds.\nEach technique has been developed to address the aspects of the background estimation which are most\nrelevant for the analysis: the shape of the m\u03c4\u03c4 tail from the irreducible Z \u2192\u03c4\u03c4, the fake tau contribution\nin the lh-channel, and the normalization of the QCD backgrounds.\nIn addition to the m\u03c4\u03c4 spectrum from the Z \u2192\u03c4\u03c4 and QCD control samples, a track multiplicity\ndistribution is used to constrain the fraction of QCD events in the lh-channel. This likelihood term is\ndenoted Ltrack(rQCD,rtau), where rtau (rQCD) denotes the fraction of real taus (fakes from jets) in the\nsample. The track multiplicity distribution for the QCD jets is modelled from samples of QCD di-jets\nthat produce tau candidates.\nThe shape of the m\u03c4\u03c4 distribution for signal and Z \u2192\u03c4\u03c4 events is dictated by the resolution of /ET and\nthe kinematics of the collinear approximation. The parameterization of m\u03c4\u03c4 for the signal and Z \u2192\u03c4\u03c4\nbackground are based on the kinematics of the collinear approximation and reproduces an asymmetric\ndistribution with non-Gaussian tails. This distribution is dependent on the overall width width, \u03c3H/Z, and\na mean, mH/Z.\nA Z \u2192\u03c4\u03c4 control sample is used to constrain the mean, mZ, and the overall width of the distribution,\n\u03c3Z, which are the only free parameters in the Z \u2192\u03c4\u03c4 background model. The error bars in the control\nsample were scaled to 10% to account for the 10% shape uncertainty in the \u00b5 \u2192\u03c4 rescaling method.\nThe shapes for W+jets and t\u00aft are very similar and are modelled with a single distribution. A con-\nservative 50% error is applied to each bin in the combined QCD (i.e., t\u00aft and W+jets) control sample to\nre\ufb02ect uncertainty in how this shape changes as the remainder of the analysis cuts are applied.\nThe shape of the QCD background was parametrized with the following equation:\nLQCD(m\u03c4\u03c4|a1,a2,a3) = N\n\u0012\n1\nm\u03c4\u03c4 +a1\n\u0013a2\nma3\n\u03c4\u03c4 .\n(38)\nThe form is motivated by a competition between the parton distribution functions and the matrix element.\nIn the lh-channel, the normalization of the backgrounds with fake taus can be constrained by using the\ntrack multiplicity method described above. We apply a conservative 50% systematic on this fraction.\nBy \ufb01tting the m\u03c4\u03c4 spectrum to a model that accurately describes the signal and various backgrounds\nit is possible to directly incorporate uncertainty in the background shape and take advantage of the shape\nof the signal within the mass window. We utilize the pro\ufb01le likelihood ratio as our test statistic. The\nlikelihood function corresponding to the simultaneous \ufb01t is simply a product of the likelihoods from the\nindividual measurements:\nL(data|\u00b5,mH,\u03bd)\n=\nLtrack(track multiplicity|rQCD)\u00d7LZ(Z+jets control|mZ,\u03c3Z)\n\u00d7\nLQCD(QCD control|a1,a2,a3)\n\u00d7\nLs+b(signal candidates|\u00b5,mH,\u03c3H,mZ,\u03c3Z,rQCD,a1,a2,a3),\n(39)\nwhere the ai are the parameters used to parametrize the QCD background and \u03bd represents all nuisance\nparameters of the model: \u03c3H,mZ,\u03c3Z,rQCD,a1,a2,a3.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1500\n\nThe data-driven background estimation methods described above have been developed so that un-\ncertainty in the background shape and normalization are included directly into the signi\ufb01cance calcu-\nlation. Because the discovery criterion is simply testing the presence or absence of the signal, it is not\nsensitive to some of the sources of systematic uncertainty. In contrast, measurement and exclusion of\n\u03c3(pp \u2192qqH) \u00d7 BR(H \u2192\u03c4\u03c4) are sensitive to the uncertainty on the signal selection ef\ufb01ciency. Both\nexperimental and theoretical sources of uncertainty on the signal ef\ufb01ciency have been evaluated. The jet\nenergy scale uncertainty dominates in this channel, and a signal ef\ufb01ciency uncertainty of 18% was used\nwhen estimating the exclusion sensitivity.\nThe median pro\ufb01le likelihood ratios for discovery, \u03bb(\u00b5 = 0) (using the Asimov data sets with \u00b5A =\n1), are given in Table 7 for a few Higgs masses at some given luminosities. The distribution of the test\nstatistic q0 under the null background only hypothesis, for mH = 130 GeV with an integrated luminosity\nof 2 and 10fb\u22121, is shown in Figure 12. A 1\n2\u03c72\n1 distribution is superimposed, showing the validity of the\nasymptotic approximation.\nTable 7: Median values of \u22122ln\u03bb(\u00b5 = 0) obtained from H \u2192\u03c4 +\u03c4\u2212simulated data generated with signal plus\nbackground (\u00b5 = 1) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n110\n120\n130\n140\n1\n0.59\n0.88\n0.72\n0.46\n2\n1.18\n1.74\n1.40\n0.89\n5\n2.91\n4.43\n3.34\n2.08\n10\n5.81\n8.23\n6.37\n3.91\n30\n17.2\n23.6\n17.6\n10.6\nThe resulting median pro\ufb01le likelihood ratio for exclusion, \u03bb(\u00b5) (using the Asimov data sets, \u00b5A =\n0), is given in Table 8 for a few Higgs masses at some given luminosities and signal strength \u00b5 = 1.0\ncorresponding to a Standard Model Higgs Boson.\nThe distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypotheses for mH = 130GeV with\nan integrated luminosity of 2 and 10 fb\u22121 is shown in Figures 13. A \u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\nTable 8: Median values of \u22122ln\u03bb(\u00b5 = 1) obtained from H \u2192\u03c4 +\u03c4\u2212background-only (\u00b5 = 0) simulated data for\nseveral values of the Higgs mass and integrated luminosities.\nL\nmH (GeV)\n(fb\u22121)\n110\n120\n130\n140\n1\n0.64\n0.71\n0.52\n0.32\n2\n1.31\n1.41\n1.03\n0.64\n5\n3.30\n3.42\n2.52\n1.56\n10\n6.93\n7.79\n7.18\n3.48\n30\n15.3\n16.6\n12.8\n8.48\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1501\n\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 10 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\n1 - F(q\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\n1 - F(q\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\n(c)\n(d)\nFigure 12: The distribution of the test statistic q0 for H \u2192\u03c4+\u03c4\u2212under the null background-only hypothesis,\nfor mH = 130GeV with an integrated luminosity of 2 (a) and 10 (b) fb\u22121. A 1\n2\u03c72\n1 distribution is superimposed.\nFigures (c) and (d) show 1 \u2212F(q0) where F(q0) is the corresponding cumulative distribution. The small excess\nof events at high q0 is statistically compatible with the expected curves, as can be seen by comparison with the\ndotted histograms that show the 68.3% central con\ufb01dence intervals for p = 1 \u2212F(q0|0). The lower dotted line at\n2.87\u00d710\u22127 shows the 5\u03c3 discovery threshold.\n1\nq\n0\n1\n2\n3\n4\n5\n6\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 2 fb\n1\nq\n0\n1\n2\n3\n4\n5\n6\n7\n8\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-2\n10\n-1\n10\n1\nATLAS\n-\u03c4\n+\n\u03c4 \n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 13: The distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s + b hypothesis for H \u2192\u03c4+\u03c4\u2212, for\nmH = 130GeV with an integrated luminosity of (a) 2 fb\u22121 (b) and 10 fb\u22121. A \u03c72\n1 distribution is superimposed.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1502\n\n3.4\nH \u2192ZZ(\u2217) \u21924l\nDetails of the H \u2192ZZ(\u2217) \u21924l channel can be found in Ref. [7]. The main challenge of this channel\nfor what concerns statistical analysis is its relevance over a very wide mass range (from mH around\n120GeV up to 700GeV), over which the shapes and cross sections of both signal and background show\nconsiderable variations.\nWhile in principle it would be possible to divide the mass range in different regions and use sepa-\nrate models for each of them, using a unique background model for the whole phase space is a better\napproach, since it allows to estimate discovery and exclusion signi\ufb01cance at any mass, without having\nto worry about boundaries between different models. This will be needed of course when the analysis is\nperformed using real data, where mH is unknown.\nThe main background after event \ufb01ltering in this channel is the irreducible ZZ \u21924l process. Re-\nducible backgrounds such as Zb\u00afb \u21924l +X or t\u00aft give a negligible contribution to the overall shape, with\nthe only exception of the mH = 120GeV case, where Zb\u00afb \u21924l + X modi\ufb01es the background shape in\nthe low mass region, and it must therefore be taken into account.\nThe irreducible background has been modelled using a combination of Fermi functions which are suit-\nable to describe both the plateau in the low mass region and the broad peak corresponding to the second\nZ coming on shell. The chosen model is described by the following function:\np0\n(1+e\np6\u2212MZZ\np7\n)(1+e\nMZZ\u2212p8\np9\n)\n+\np1\n(1+e\np2\u2212MZZ\np3\n)(1+e\np4\u2212MZZ\np5\n)\n.\n(40)\nThe \ufb01rst plateau, in the region where only one of the two Z bosons is on shell, is modelled by the\n\ufb01rst term, and its suppression, needed for a correct description at higher masses, is controlled by the p8\nand p9 parameters. The second term in the above formula accounts for the shape of the broad peak and\nthe tail at high masses. This function can describe with a negligible bias the ZZ background shape with\ngood accuracy over the full mass range.\nAs already mentioned, the Zb\u00afb contribution is relevant only when searching for very light Higgs\nbosons (in this study, only mH = 120GeV). In this case, an additional term is added to the ZZ continuum,\nwith a functional form similar to the second part of equation 40. For what concerns signal modelling, a\nsimple Gaussian shape has been used for mH \u2264300GeV, while a relativistic Breit-Wigner formula was\nneeded to properly describe the big tails arising at higher values of the Higgs mass.\nIn the \ufb01ts to determine the pro\ufb01le likelihood ratio, mH is \ufb01xed to the hypothesized value, while \u03c3H\nis allowed to \ufb02oat in a \u00b120% range around the value obtained from the signal Monte Carlo distributions.\nAll the parameters describing the background shape are \ufb02oating within sensible ranges. Given the com-\nplexity of the model involved, the \ufb01t can from time to time get trapped into local minima. While there is\nno easy way to avoid this problem, the fake measurements obtained in this case are easy to distinguish\nfrom the correct ones, and a repetition of the \ufb01t from a different starting point is enough to solve the\nproblem.\nThe resulting median pro\ufb01le likelihood ratios for discovery, \u22122ln\u03bb(\u00b5 = 0), with the median com-\nputed using toy s+b MC data (i.e., with \u00b5 = 1), are given in Table 9 for several values of the Higgs mass\nand integrated luminosity.\nThe distribution of the test statistic q0 under the null background-only hypothesis, for mH = 200 GeV\nwith an integrated luminosity of 2 and 10fb\u22121, is shown in Fig. 14. A 1\n2\u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\nThe resulting median pro\ufb01le likelihood ratio for exclusion, \u03bb(\u00b5) (using toy background-only MC\nexperiments and taking the median of the \u03bb(\u00b5) distribution), is given in Table 10 for several Higgs\nmasses and luminosities using a signal strength \u00b5 = 1.0 corresponding to a Standard Model Higgs boson.\nThe distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypothesis for mH = 200 GeV with\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1503\n\nTable 9: Median values of \u22122ln\u03bb(\u00b5 = 0) obtained from H \u2192ZZ(\u2217) \u21924l simulated data generated with signal\nplus background (\u00b5 = 1) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n120\n130\n140\n150\n160\n165\n180\n200\n300\n400\n500\n600\n1\n0.22\n1.20\n3.98\n5.35\n1.65\n0.49\n0.86\n6.86\n5.20\n3.55\n0.88\n0.31\n2\n0.44\n2.40\n7.96\n10.7\n3.30\n0.98\n1.71\n13.7\n10.4\n7.68\n1.74\n0.62\n5\n1.05\n5.97\n19.9\n26.7\n8.26\n2.46\n4.27\n34.3\n25.8\n17.8\n4.34\n1.54\n10\n2.18\n12.0\n39.8\n53.5\n16.5\n4.9\n8.55\n68.7\n51.6\n35.5\n8.47\n3.11\n30\n6.56\n35.8\n120\n160\n48.9\n14.8\n25.6\n206\n162\n108\n27.9\n10.9\n60\n13.1\n71.6\n239\n321\n99.1\n29.5\n51.3\n407\n310\n213\n52.6\n18.6\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n|0)\n0\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 10 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n|0)\n0\n1 - F(q\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 2 fb\n0\nq\n0\n2\n4\n6\n8\n10\n12\n14\n16\n|0)\n0\n1 - F(q\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\n(c)\n(d)\nFigure 14: The distribution of the test statistic q0 (for H \u21924l), under the null background only hypothesis,\nfor mH = 200 GeV with an integrated luminosity of 2 (a) and 10 (b) fb\u22121. A 1\n2\u03c72\n1 distribution is superimposed.\nFigures (c) and (d) show 1 \u2212F(q0) where F(q0) is the corresponding cumulative distribution. The small excess\nof events at high q0 is statistically compatible with the expected curves, as can be seen by comparison with the\ndotted histograms showing the 68.3% central con\ufb01dence intervals for p = 1 \u2212F(q0|0). The lower dotted line at\n2.87\u00d710\u22127 shows the 5\u03c3 discovery threshold.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1504\n\nTable 10: Median values of \u22122ln\u03bb(\u00b5 = 1) obtained from H \u2192ZZ(\u2217) \u21924l simulated data generated with back-\nground only (\u00b5 = 0) for several values of the Higgs mass and integrated luminosity.\nL\nmH (GeV)\n(fb\u22121)\n120\n130\n140\n150\n160\n165\n180\n200\n300\n400\n500\n600\n1\n0.16\n0.93\n2.25\n3.12\n1.23\n0.39\n0.51\n4.86\n2.86\n2.36\n0.87\n0.28\n2\n0.33\n1.85\n4.50\n6.22\n2.4\n0.75\n1.90\n9.64\n5.68\n4.69\n1.74\n0.56\n5\n0.83\n4.60\n11.2\n15.4\n6.09\n2.28\n4.74\n23.5\n14.0\n11.6\n4.32\n1.39\n10\n1.60\n9.14\n22.0\n30.3\n12.1\n3.86\n5.05\n45.2\n27.3\n22.7\n8.57\n2.77\n30\n4.78\n26.8\n63.0\n85.3\n35.1\n11.4\n14.7\n105\n74.1\n63.0\n24.9\n8.22\n60\n8.90\n51.7\n117\n155\n66.9\n22.3\n28.0\n174\n129\n113\n47.6\n16.1\nan integrated luminosity of 2 and 10fb\u22121 is shown in Figures 15. A \u03c72\n1 distribution is superimposed,\nshowing the validity of the asymptotic approximation.\n1\nq\n0\n2\n4\n6\n8\n10\n12\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 2 fb\n1\nq\n0\n2\n4\n6\n8\n10\n12\n14\n 1)\n\u2264\n \n\u00b5\n=1, \n\u00b5|\n1\nf(q\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n 4l\n\u2192\nH \n-1\nL = 10 fb\n(a)\n(b)\nFigure 15: The distribution of the test statistic q1 for \u02c6\u00b5 \u22641 under the s+b hypothesis (for H \u21924l), for mH = 200\nGeV with an integrated luminosity of (a) 2fb\u22121 and (b) 10fb\u22121. A \u03c72\n1 distribution is superimposed.\n3.5\nLimitations of the approximations used\nThe distributions shown in Sections 3.1 through 3.4 show varying levels of agreement between the\nasymptotic chi-square form and the results of Monte Carlo simulations. For the WW (0 jet) channel\n(Fig. 8), the discrepancy in the distribution of q0 is very large, and this is understood to arise from the\nspecial manner in which the systematic uncertainties for this channel were treated. The distribution of q0\nfor the WW (0 jet) channel therefore does not use the asymptotic formula. This is the only channel for\nwhich the approximation was not applied.\nFor other cases such as the distribution of q1 for the H \u2192\u03b3\u03b3 channel shown in Fig. 7, the Monte Carlo\ndistribution falls off signi\ufb01cantly faster than the chi-square curve. This means that the signi\ufb01cance with\nwhich one excludes the tested hypothesis will be less when estimated from the chi-square curve, leading\nto conservative limits. As the integrated luminosity increases, one expects to the asymptotic formula to\nbecome more accurate.\nIn some of the distributions such as that of q0 for the H \u2192ZZ(\u2217) \u21924l channel shown in Fig. 14, the\nMonte Carlo simulation indicates a slight excess over the chi-square curve in the tail region. The level of\nthe excess is not statistically signi\ufb01cant in the part of the distribution that can be meaningfully assessed\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1505\n\ngiven the amount of Monte Carlo data available (out to q0 between around 9 to 16, i.e., to the level of a\n3 to 4\u03c3 discovery). At present it is not practical to verify directly that the chi-square formula remains\nvalid to the 5\u03c3 level (i.e., out to q0 = 25). Thus the results on discovery signi\ufb01cance presented here rest\non the assumption that the asymptotic distribution is a valid approximation to at least the 5\u03c3 level.\nThe validation exercises carried here out indicate that the methods used should be valid, or in some\ncases conservative, for an integrated luminosity of at least 2 fb\u22121. At earlier stages of the data taking,\none will be interested primarily in exclusion limits at the 95% con\ufb01dence level. For this the distributions\nof the test statistic q\u00b5 at different values of \u00b5 can be determined with a manageably small number of\nevents. It is therefore anticipated that we will rely on Monte Carlo methods for the initial phase of the\nexperiment.\n4\nResults of the combination\n4.1\nCombined discovery sensitivity\nThe full discovery likelihood ratio for all channels combined, \u03bbs+b(0), is calculated using Eq. 33. This\nuses the median likelihood ratio of each channel, \u03bbs+b,i(0), found either by generating toy experiments\nunder the s+b hypothesis and calculating the median of the \u03bbs+b,i distribution or by approximating the\nmedian likelihood ratio using the Asimov data sets with \u00b5A,i = 1. Both approaches were validated to\nagree with each other. The discovery signi\ufb01cance is calculated using Eq. 36, i.e., Z \u2248\np\n\u22122ln\u03bb(0),\nwhere \u03bb(0) is the combined median likelihood ratio.\nThe resulting signi\ufb01cances per channel and the combined one are shown in Fig. 16 for an integrated\nluminosity of 10 fb\u22121.\n (GeV)\nH\nm\n100\n120\n140\n160\n180\n200\n220\nexpected significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\nCombined\n 4l\n\u2192\n \n(*)\nZZ\n\u03b3 \n\u03b3\n\u03c4 \u03c4\n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW0j \n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW2j \nATLAS\n-1\nL = 10 fb\n (GeV)\nH\nm\n100\n200\n300\n400\n500\n600\nexpected significance\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\nCombined\n 4l\n\u2192\n \n(*)\nZZ\n\u03b3 \n\u03b3\n\u03c4 \u03c4\n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW0j \n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW2j \nATLAS\n-1\nL = 10 fb\n(a)\n(b)\nFigure 16: The median discovery signi\ufb01cance for the various channels and the combination with an integrated\nluminosity of 10 fb\u22121 for (a) the lower mass range (b) for masses up to 600 GeV.\nThe median discovery signi\ufb01cance as a function of the integrated luminosity and Higgs mass is shown\ncolour coded in Fig. 17. The full line indicates the 5\u03c3 contour. Note that the approximations used do\nnot hold for very low luminosities (where the expected number of events is low) and therefore the results\nbelow about 2fb\u22121 should be taken as indications only. In most cases, however, the approximations tend\nto underestimate the true median signi\ufb01cance.\n4.2\nCombined exclusion sensitivity\nThe full likelihood ratio of all channels used for exclusion for a signal strength \u00b5, \u03bbb(\u00b5), is calculated\nusing Eq. 34 with the median likelihood ratios of each channel, \u03bbb,i(\u00b5), calculated, either by generating\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1506\n\nmH [GeV]\nLuminosity [fb\u22121]\nsignificance\n \n \nATLAS\nH \u2192 \u03b3\u03b3\nH \u2192 ZZ* \u2192 4l\nH \u2192 \u03c4\u03c4\nH \u2192 WW \u2192 e\u03bd\u00b5\u03bd\n120\n140\n160\n180\n200\n220\n240\n260\n280\n300\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\nFigure 17: Signi\ufb01cance contours for different Standard Model Higgs masses and integrated luminosities. The\nthick curve represents the 5\u03c3 discovery contour. The median signi\ufb01cance is shown with a colour according to the\nlegend. The hatched area below 2 fb\u22121 indicates the region where the approximations used in the combination are\nnot accurate, although they are expected to be conservative.\ntoy experiments under the b-only hypothesis and calculating the median of the \u03bbb,i distribution or ap-\nproximating the median likelihood ratio using the Asimov data sets with \u00b5A,i = 0. Both approaches were\nchecked to agree with each other. A signal strength \u00b5 = 1 corresponds to the Standard Model Higgs\nboson.\nAny exclusion of \u00b5(mH) smaller than 1 corresponds to an exclusion of a Standard Model Higgs\nboson with a mass mH. To probe the median sensitivity for excluding a Standard Model Higgs boson we\nfollow Eq. 35 and calculate the corresponding p-value for \u00b5 = 1, p1 for a given luminosity at a given\nHiggs mass. A p-value of 0.05 corresponds to a signi\ufb01cance (Eq. 36) of 1.64. The resulting p1 for the\nvarious channels as well as for the combination, for a luminosity of 2fb\u22121, are shown in Fig. 18. Note\nthat any p-value below 0.05 indicates an exclusion. We therefore conclude that with a luminosity of 2\nfb\u22121 ATLAS has the median sensitivity to exclude a Standard Model Higgs boson heavier than 115 GeV\nat the 95% Con\ufb01dence Level. This can also be seen from Fig. 19, which shows the luminosity required\nto exclude a Higgs boson with a mass mH at a given con\ufb01dence level from the combination of the four\nchannels explored in this note.\nThe sharp increase in the required luminosity for lower mH seen in Fig. 17 re\ufb02ects the decrease in\nsensitivity to the Higgs when using only the set of channels considered here. Further developments will\nincrease the sensitivity in this region. For example, improved analysis methods for the H \u2192\u03b3\u03b3 channel\nare described in Ref. [4], including a separation of the events into those with zero or two accompanying\njets. Additional \ufb01nal states such as ttH with H \u2192bb will help somewhat, although the contribution to\nthe sensitivity will be small because of the large uncertainties in the background.\nFor the WW channel, the present study includes only the e\u03bd\u00b5\u03bd decay mode, but it is planned to\ninclude e\u03bde\u03bd, \u00b5\u03bd\u00b5\u03bd and qql\u03bd as well. The ZZ(\u2217) channel here only includes Z decays to ee and \u00b5\u00b5, but\nin future analyses qq\u03bd\u03bd will be included. The additional WW and ZZ(\u2217) modes have been found to have\nsensitivity for a high-mass Higgs. Finally, combination with the results from ATLAS with those of CMS\nwill of course result in an overall increase in sensitivity.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1507\n\n (GeV)\nH\nm\n100\n120\n140\n160\n180\n200\n220\n=1\n\u00b5\nexpected p-value of \n-10\n10\n-9\n10\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nCombined\n 4l\n\u2192\n \n(*)\nZZ\n\u03b3 \n\u03b3\n\u03c4 \u03c4\n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW0j \n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW2j \nATLAS\n-1\nL = 2 fb\nexpected\n95% CL exclusion\n (GeV)\nH\nm\n100\n200\n300\n400\n500\n600\n=1\n\u00b5\nexpected p-value of \n-10\n10\n-9\n10\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nCombined\n 4l\n\u2192\n \n(*)\nZZ\n\u03b3 \n\u03b3\n\u03c4 \u03c4\n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW0j \n\u03bd\n\u00b5\n\u03bd\n e\n\u2192\nWW2j \nATLAS\n-1\nL = 2 fb\nexpected 95% CL exclusion\n(a)\n(b)\nFigure 18: The median p-value obtained for excluding a Standard Model Higgs Boson for the various channels\nas well as the combination for (a) the lower mass range (b) for masses up to 600 GeV.\n0.99\n0.95\n0.90\n0.80\nmH [GeV]\nLuminosity [fb\u22121]\nCombined Exclusion CL\n \n \nATLAS\nH \u2192 \u03b3\u03b3\nH \u2192 ZZ* \u2192 4l\nH \u2192 \u03c4\u03c4\nH \u2192 WW \u2192 e\u03bd\u00b5\u03bd\n110\n115\n120\n125\n130\n135\n140\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0.55\n0.62\n0.70\n0.75\n0.80\n0.85\n0.90\n0.93\n0.95\n0.97\n0.98\nFigure 19: The expected luminosity required to exclude a Higgs boson with a mass mH at a con\ufb01dence level given\nby the corresponding colour. The hatched area below 2 fb\u22121 indicates the region where the approximations used\nin the combination are not accurate, although they are expected to be conservative.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1508\n\n5\nConclusions\nThe procedure for combination of search results based on the pro\ufb01le likelihood ratio has been applied\nto a study of the search for the Standard Model Higgs boson using four search channels: H \u2192\u03c4 +\u03c4\u2212,\nH \u2192W +W \u2212\u2192e\u03bd\u00b5\u03bd, H \u2192\u03b3\u03b3 and H \u2192ZZ(\u2217) \u21924 leptons. The combination method is very general\nand can be applied to essentially any search that will be carried out at the LHC.\nThe study here has not exploited all of the search channels that will be investigated and therefore the\ncurrent estimates of the sensitivity can be regarded as conservative. For example, using further decay\nmodes in the ZZ and WW channels will provide additional sensitivity especially for a Higgs boson in the\nhigher mass range.\nThe studies have exploited a series of useful approximations that allow one to determine the median\ndiscovery and exclusion sensitivities from a combined \ufb01t in a manner that only requires separate input\ningredients from the individual channels. The determination of the signi\ufb01cance for a given (e.g., real)\ndata set, however, will require a simultaneous \ufb01t of all of the channels.\nIt is not practical at present to generate enough Monte Carlo data to verify directly that the tail of\nthe pro\ufb01le likelihood distribution is well described to the level required for discovery at the 5\u03c3 level,\ncorresponding to an upper tail area of 2.87 \u00d7 10\u22127. The estimates of discovery signi\ufb01cance presented\nhere therefore rely on the assumption that the large-sample approximation used remains valid out to this\nlevel.\nThe validation studies shown in Section 3 indicate that the approximations used should be reasonably\naccurate or lead to conservative limits for an integrated luminosity of at least 2 fb\u22121. For the earlier\nstages of the experiment it is expected that one will need to rely on Monte Carlo methods, which should\nbe feasible for exclusion limits at the 95% con\ufb01dence level.\nThe pro\ufb01le likelihood ratio treats systematic errors by associating the uncertainties with adjustable\n(nuisance) parameters. Other methods for treating systematic uncertainties can also be considered. Us-\ning Bayesian methods, for example, one would associate a prior probability density with the nuisance\nparameters. We plan to develop and use this and other approaches in parallel with the pro\ufb01le likelihood\nmethod for searches at the LHC.\nThe study presented in this paper provides the discovery signi\ufb01cance for a Higgs boson of a speci\ufb01c\nmass. That is, the traditional discovery threshold p-value of 2.87 \u00d7 10\u22127 corresponding to a 5\u03c3 effect\nfor a given hypothesized Higgs mass refers to the false discovery rate for a Higgs of that mass. The false\ndiscovery rate for a Higgs of any mass is higher, and several approaches are being pursued to quantify this\n(the so-called \u2018look-elsewhere effect\u2019). The most mature of these methods involves using a simultaneous\n\ufb01t of the Higgs mass mH and the strength parameter \u00b5 (or equivalently the Higgs production rate), as has\nbeen discussed in the studies of H \u2192\u03b3\u03b3 [4] and H \u2192W +W \u2212[5].\nTo summarize, the studies based on the four channels considered in this note con\ufb01rm the good dis-\ncovery and exclusion sensitivities already shown in the ATLAS Technical Design Report (TDR) [10].\nFurthermore the results here are based on better knowledge and a more realistic simulation of the detec-\ntor than what is described in the TDR. Because of the approximations used, the present studies are valid\nonly for luminosities above 2fb\u22121. With a luminosity of 2fb\u22121 the expected (median) sensitivity is at the\n5\u03c3 level or greater for discovery of a Higgs boson in the mass range between 143 and 179 GeV, and the\nexpected upper limit at 95% con\ufb01dence level on the Higgs mass is 115 GeV.\nA\nComparison with procedures used at LEP\nIn this appendix we compare the procedures described in the present analysis with those used in searches\ncarried out at LEP. More details on these methods be found in [8]. The important differences involve\nthe de\ufb01nition of the test statistic used and the treatment of systematic uncertainties. In addition, the LEP\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1509\n\nanalyses adopted a special procedure to prevent spurious exclusion due to a downward \ufb02uctuation of the\nnumber of events (the CLs method, see below).\nIn the LEP Higgs searches, a hypothesized value of the Higgs mass mH was tested by constructing\nthe statistic\nQ = Ls+b\nLb\n= L(\u00b5 = 1)\nL(\u00b5 = 0) ,\n(41)\nwhere as before b (\u00b5 = 0) represents the background-only hypothesis and s+b (\u00b5 = 1) refers to back-\nground plus signal at the rate predicted by the Standard Model. For convenience the equivalent logarith-\nmic variable q = \u22122lnQ was used.\nThe sampling distribution of Q was determined by Monte Carlo simulation. The Monte Carlo was\nalso used to incorporate systematic errors by sampling values of the corresponding nuisance parameters\nfrom pdfs that re\ufb02ected their uncertainties. That is, one effectively integrated the product of the likelihood\nand prior pdfs for the nuisance parameters.\nFor a give observed value qobs = \u22122lnQobs, the p-values for the s and s+b hypotheses were deter-\nmined as\nps+b\n=\nZ \u221e\nqobs\nf(q|s+b)dq \u2261CLs+b ,\n(42)\npb\n=\nZ qobs\n\u2212\u221ef(q|b)dq \u22611\u2212CLb .\n(43)\nHaving determine the p-values, the LEP analyses then based exclusion of the s+b hypothesis not on the\np-value of s+b but rather on the ratio CLs, de\ufb01ned as\nCLs = CLs+b\nCLb\n= ps+b\n1\u2212pb\n.\n(44)\nThe signal-plus-background hypothesis was said to be excluded at con\ufb01dence level CL = 1\u2212\u03b1 = 0.95\nif one \ufb01nds\nCLs < \u03b1 .\n(45)\nSince CLb \u22641, one has CLs \u2265CLs+b. Therefore the CLs method will not exclude as large a region of\nparameter space as that based on the signal-plus-background p-value (CLs+b method). As the CLs+b\nmethod was designed to provide an interval that brackets the true value of the parameter with a proba-\nbility of at least 1 \u2212\u03b1, the CLs limit must cover the true parameter with a greater probability; it is in\nthis sense conservative. The CLs method was devised so as to avoid the problem where a downward\n\ufb02uctuation in the number of background events can lead to exclusion of the Higgs mass considered, even\nfor hypothesized mass values where one does not expect to be sensitive to Higgs production [9].\nIn contrast, in the present analysis we test a hypothesized value of the strength parameter \u00b5 using\nq\u00b5 = \u22122ln L(\u00b5, \u02c6\u02c6\u03b8)\nL( \u02c6\u00b5, \u02c6\u03b8) ,\n(46)\nas described in Section 2. With this de\ufb01nition, the sampling distribution of the test statistic f(q\u00b5|\u00b5)\napproaches a well de\ufb01ned form related to the chi-squared distribution for a suf\ufb01ciently large data sample.\nThe ability to exploit this approximate form is very useful as the relevant p-value for a 5\u03c3 discovery\nis 2.87 \u00d7 10\u22127, and therefore to determine this from Monte Carlo would require an extremely large\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1510\n\nnumber of simulated experiments. At LEP this was not a crucial issue as the statistical treatment focused\nprimarily on exclusion limits at 95% CL, not on discovery at the 5\u03c3 level.\nSystematic uncertainties here have been incorporated using the pro\ufb01le likelihood, rather than with\nthe integrated likelihoods used at LEP. For the uncertainties most relevant to the analyses at the LHC, the\nbroadening of the likelihood function obtained by both procedures is similar. It is the pro\ufb01le likelihood\nratio and not the ratio of integrated likelihoods, however, that approaches the chi-squared form in the\nlarge sample limit in accordance with Wilks\u2019 theorem.\nThe CLs method has not been applied in the present analysis but studies of its application to searches\nin ATLAS are ongoing.\nA \ufb01nal difference with the LEP procedures concerns the de\ufb01nition of signi\ufb01cance Z. Here we have\nde\ufb01ned its relation to the p-value as the number of standard deviations of a Gaussian variable that would\ngive a one-sided tail area of p, as described in Section 2.1. A signi\ufb01cance of Z = 5 corresponds to\np = 2.87\u00d710\u22127. The LEP Higgs group de\ufb01ned this relation using a two-sided \ufb02uctuation of a Gaussian\nvariable, i.e., a 5\u03c3 signi\ufb01cance corresponded to p = 5.7\u00d710\u22127.\nReferences\n[1] Isaac Asimov, Franchise, in Isaac Asimov: The Complete Stories, Vol. 1, Broadway Books, 1990.\n[2] S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses,\nAnn. Math. Statist. 9 (1938) 60-2.\n[3] A. Stuart, J.K. Ord, and S. Arnold, Kendall\u2019s Advanced Theory of Statistics, Vol. 2A: Classical In-\nference and the Linear Model 6th Ed., Oxford Univ. Press (1999), and earlier editions by Kendall\nand Stuart.\n[4] The ATLAS Collaboration, Prospects for the Discovery of the Standard Model Higgs Boson Using\nthe H \u2192\u03b3\u03b3 Decay, this volume.\n[5] The ATLAS Collaboration, Higgs Boson Searches in Gluon Fusion and Vector Boson Fusion\nusing the H \u2192WW Decay Mode, this volume.\n[6] The ATLAS Collaboration, Search for the Standard Model Higgs Boson via Vector Boson Fusion\nProduction Process in the Di-Tau Channels, this volume.\n[7] The ATLAS Collaboration, Search for the Standard Model H \u2192ZZ\u2217\u21924l, this volume.\n[8] ALEPH, DELPHI, L3 and OPAL Collaborations, Search for the Standard Model Higgs Boson at\nLEP, CERN-EP/2003-011, Phys. Lett. B565 (2003) 61-75.\n[9] Alex Read, Modi\ufb01ed frequentist analysis of search results (the CLs method), proceedings of the\nWorkshop on Con\ufb01dence Limits, CERN 2000-005.\n[10] The ATLAS Collaboration, ATLAS: Detector and physics performance technical design report,\nVolume 2, CERN-LHCC-99-15, ATLAS-TDR-15, May 1999.\nHIGGS \u2013 STATISTICAL COMBINATION OF SEVERAL IMPORTANT STANDARD MODEL HIGGS . . .\n1511\n\n\nSupersymmetry\n1513\n\nSupersymmetry Searches\nAbstract\nThis chapter serves as an introduction to a collection of six articles that detail\nthe strategy foreseen to search for Supersymmetry with the ATLAS detector\nat the Large Hadron Collider, concentrating on the initial data taking period\nwith an expected integrated luminosity of about 1 fb\u22121 . We review here the\nphenomenology of Supersymmetry with ATLAS and discuss how events are\nsimulated and reconstructed, concentrating on aspects related to Supersymme-\ntry searches. We also introduce many of the experimental variables that are\nused throughout this collection.\n1\nIntroduction\nSupersymmetry (SUSY) is one of the theoretically favoured candidates for physics beyond the Standard\nModel. The main motivation is to protect the Higgs boson mass from quadratically diverging radiative\ncorrections, in a theory where the Standard Model is valid only up to a high scale \u039b. The proposed\nsolution postulates the invariance of the theory under a symmetry which transforms fermions into bosons\nand vice-versa.\nThe basic prediction of SUSY is thus the existence, for each Standard Model particle degree of\nfreedom of a corresponding sparticle, with spin different by half a unit. The SUSY generators commute\nwith the SU(2) \u00d7U(1) \u00d7 SU(3) symmetries of the Standard Model, and with the Poincar\u00b4e group. It\nfollows that with unbroken SUSY the partner particles would have the same quantum numbers and\nmasses as the Standard Model particles. Since no superpartner has been observed to date, SUSY must be\nbroken. A common approach to the phenomenological study of SUSY is to assume the minimal possible\nparticle content, and to parametrise the SUSY-breaking Lagrangian as the sum of all the terms which\ndo not reintroduce quadratic divergences into the theory. The model thus obtained is called Minimal\nSupersymmetric Standard Model (MSSM) and is characterised by a large number of parameters (\u223c100).\nIn order to warrant the conservation of baryonic and leptonic quantum numbers, a new multiplicative\nquantum number, R-parity, is introduced, which is 1 for particles and -1 for the SUSY partners. Models\nwhere R-parity is violated can be formulated, but in the current volume we concentrate on models with\nR-parity conservation.\nThe consequences of R-parity conservation are that sparticles must be produced in pairs, and that\neach will decay to the lightest SUSY particle (LSP) which must be stable. Cosmological arguments\nsuggest that stable LSPs should be weakly interacting and so would escape direct detection at ATLAS,\nresulting in the characteristic feature expected for SUSY events \u2013 an imbalance of the transverse energy\nmeasured in the detector, abbreviated here as Emiss\nT\n. The associated signatures will provide sensitivity\nto a large class of models. The aim of the simulation studies is to ensure that the ATLAS experiment\nwill have rapid sensitivity to a large ensemble of SUSY models, and to develop a general search strategy.\nIt is not possible to explore in full the 100-dimensional parameter space of the MSSM. It is therefore\nnecessary to adopt some speci\ufb01c assumptions for the SUSY breaking, resulting in models de\ufb01ned by a\nsmall number of parameters at the SUSY breaking scale. Two models will be studied in detail:\n\u2022 mSUGRA, where SUSY breaking is mediated by gravitational interaction;\n\u2022 GMSB, where SUSY breaking is mediated by a gauge interaction through messenger gauge \ufb01elds.\nThese two models give quite different topologies, due to the different nature of the lightest SUSY particle,\nwhich is the lightest neutralino for the mSUGRA case and the gravitino for the GMSB case. For each\n1514\n\nof these models a set of benchmark points has been de\ufb01ned, on which full simulation studies have been\nperformed.\nThe analysis work presented in the different SUSY notes is a coherent body of work based on an\nagreement among the many groups performing the analyses on many subjects both theoretical and ex-\nperimental. All of the analyses are based on a common implementation of the SUSY model, common\nbackground datasets have been used, and all of the analyses apply a common de\ufb01nition of the physics\nobjects in the detectors, optimised for the speci\ufb01c environment of the SUSY searches. In the following\nsections a quick overview of these common issues will be given, which should be read before approach-\ning the detailed studies documented in the different notes.\n2\nSignal and Background generation\nThe simulated data used for the studies documented here have been produced by Monte Carlo simulation\ninside the of\ufb01cial ATLAS software and production frameworks, and for all of the samples a detailed\nsimulation of the detector has been performed.\n2.1\nSignal samples\nFor the detailed SUSY analysis a set of benchmark points in the mSUGRA and GMSB frameworks were\nchosen, with the aim of exploring sensitivity to a wide class of of \ufb01nal-state signatures.\nFor the mSUGRA points, the principle that the predicted cosmological relic density of neutralinos\nshould be consistent with the observed density of cold dark matter was used for guidance. In order\nto reproduce the observed relic density, the model parameters must result in a spectrum which ensures\nef\ufb01cient annihilation of the neutralinos in the early universe. In the mSUGRA scenario this is possible\nonly in restricted regions of the parameter space where annihilation is enhanced either by a signi\ufb01cant\nhiggsino components in the lightest neutralino or through mass relationships. The points chosen are\nde\ufb01ned in terms of the mSUGRA parameters at the uni\ufb01cation scale:\nSU1 m0 = 70 GeV, m1/2 = 350 GeV, A0 = 0, tan\u03b2 = 10, \u00b5 > 0. Coannihilation region where\n\u02dc\u03c70\n1 annihilate with near-degenerate \u02dc\u2113.\nSU2 m0 = 3550 GeV, m1/2 = 300 GeV, A0 = 0, tan\u03b2 = 10, \u00b5 > 0. Focus point region near\nthe boundary where \u00b52 < 0. This is the only region in mSUGRA where the \u02dc\u03c70\n1 has a high\nhiggsino component, thereby enhancing the annihilation cross-section for processes such\nas \u02dc\u03c70\n1 \u02dc\u03c70\n1 \u2192WW.\nSU3 m0 = 100 GeV, m1/2 = 300 GeV, A0 = \u2212300 GeV, tan\u03b2 = 6, \u00b5 > 0. Bulk region: LSP\nannihilation happens through the exchange of light sleptons.\nSU4 m0 = 200 GeV, m1/2 = 160 GeV, A0 = \u2212400 GeV, tan\u03b2 = 10, \u00b5 > 0. Low mass point\nclose to Tevatron bound.\nSU6 m0 = 320 GeV, m1/2 = 375 GeV, A0 = 0, tan\u03b2 = 50, \u00b5 > 0. The funnel region where\n2m \u02dc\u03c70\n1 \u2248mA. Since tan\u03b2 \u226b1, the width of the pseudoscalar Higgs boson A is large and \u03c4\ndecays dominate.\nSU8.1 m0 = 210 GeV, m1/2 = 360 GeV, A0 = 0, tan\u03b2 = 40, \u00b5 > 0. Variant of coannihilation\nregion with tan\u03b2 \u226b1, so that only m\u02dc\u03c41 \u2212m \u02dc\u03c70\n1 is small.\nSU9 m0 = 300 GeV, m1/2 = 425 GeV, A0 = 20, tan\u03b2 = 20, \u00b5 > 0. Point in the bulk region with\nenhanced Higgs production\nThe SUSY particle mass spectra for each of these points are listed in Table 2.\nThe leading-order and next-to-leading-order cross-sections at 14 TeV center of mass for the chosen\npoints are given in Table 1. These have been calculated with the program PROSPINO 2.0.6 [1\u20133], using\nthe default settings, and the parton distribution set CTEQ6M [4].\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1515\n\nTable 1: Production cross-sections at leading order (\u03c3LO) and next-to-leading order (\u03c3NLO), numbers\nof Monte Carlo events simulated (N) and corresponding integrated luminosity for the SUSY benchmark\npoints used by ATLAS.\nLabel\n\u03c3LO (pb)\n\u03c3NLO (pb)\nN\nL (fb\u22121)\nSU1\n8.15\n10.86\n200 K\n18.4\nSU2\n5.17\n7.18\n50 K\n7.0\nSU3\n20.85\n27.68\n500 K\n18.1\nSU4\n294.46\n402.19\n200 K\n0.50\nSU6\n4.47\n6.07\n30 K\n4.9\nSU8.1\n6.48\n8.70\n50 K\n5.7\nSU9\n2.46\n3.28\n40 K\n12.2\nTable 2: Particle mass spectrum (in GeV) for the SUSY benchmark points.\nParticle\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8.1\nSU9\n\u02dcdL\n764.90\n3564.13\n636.27\n419.84\n870.79\n801.16\n956.07\n\u02dcuL\n760.42\n3563.24\n631.51\n412.25\n866.84\n797.09\n952.47\n\u02dcb1\n697.90\n2924.80\n575.23\n358.49\n716.83\n690.31\n868.06\n\u02dct1\n572.96\n2131.11\n424.12\n206.04\n641.61\n603.65\n725.03\n\u02dcdR\n733.53\n3576.13\n610.69\n406.22\n840.21\n771.91\n920.83\n\u02dcuR\n735.41\n3574.18\n611.81\n404.92\n842.16\n773.69\n923.49\n\u02dcb2\n722.87\n3500.55\n610.73\n399.18\n779.42\n743.09\n910.76\n\u02dct2\n749.46\n2935.36\n650.50\n445.00\n797.99\n766.21\n911.20\n\u02dceL\n255.13\n3547.50\n230.45\n231.94\n411.89\n325.44\n417.21\n\u02dc\u03bde\n238.31\n3546.32\n216.96\n217.92\n401.89\n315.29\n407.91\n\u02dc\u03c41\n146.50\n3519.62\n149.99\n200.50\n181.31\n151.90\n320.22\n\u02dc\u03bd\u03c4\n237.56\n3532.27\n216.29\n215.53\n358.26\n296.98\n401.08\n\u02dceR\n154.06\n3547.46\n155.45\n212.88\n351.10\n253.35\n340.86\n\u02dc\u03c42\n256.98\n3533.69\n232.17\n236.04\n392.58\n331.34\n416.43\n\u02dcg\n832.33\n856.59\n717.46\n413.37\n894.70\n856.45\n999.30\n\u02dc\u03c70\n1\n136.98\n103.35\n117.91\n59.84\n149.57\n142.45\n173.31\n\u02dc\u03c70\n2\n263.64\n160.37\n218.60\n113.48\n287.97\n273.95\n325.39\n\u02dc\u03c70\n3\n466.44\n179.76\n463.99\n308.94\n477.23\n463.55\n520.62\n\u02dc\u03c70\n4\n483.30\n294.90\n480.59\n327.76\n492.23\n479.01\n536.89\n\u02dc\u03c7+\n1\n262.06\n149.42\n218.33\n113.22\n288.29\n274.30\n326.00\n\u02dc\u03c7+\n2\n483.62\n286.81\n480.16\n326.59\n492.42\n479.22\n536.81\nh0\n115.81\n119.01\n114.83\n113.98\n116.85\n116.69\n114.45\nH0\n515.99\n3529.74\n512.86\n370.47\n388.92\n430.49\n632.77\nA0\n512.39\n3506.62\n511.53\n368.18\n386.47\n427.74\n628.60\nH+\n521.90\n3530.61\n518.15\n378.90\n401.15\n440.23\n638.88\nt\n175.00\n175.00\n175.00\n175.00\n175.00\n175.00\n175.00\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1516\n\nEven though the SUSY benchmark points are all based on the mSUGRA scenario, they provide a\nrather wide range of possible decay topologies. They share some common features, for example for all\nthese points the gluino mass is less than 1 TeV, and the ratio m \u02dcg/m \u02dc\u03c70\n1 = 6\u20138. For all points except SU2,\nthe squark and gluino masses are comparable. Hence gluinos and squarks would be copiously produced\nand would decay giving relatively high pT jets, possibly leptons, and Emiss\nT\n. These features are relatively\ngeneral \u2013 although not guaranteed \u2013 but the cold dark matter density predictions are very speci\ufb01c to\nmSUGRA.\nThe signatures from GMSB models are often very different because the \u02dc\u03c70\n1 is no longer the lightest\nsupersymmetric particle, so it would be expected to decay, and (depending on its lifetime) may do so\nwithin the detector. Given its particular experimental signature, a dedicated article of this chapter is\ndevoted to the relevant signatures [5], where the GMSB benchmarks are discussed in detail.\n2.2\nBackgrounds\nThe Standard Model background processes most relevant to SUSY searches are t\u00aft, W +jets, Z +jets, jet\nproduction from QCD processes and diboson production.\nDifferent Monte Carlo generators were used for different processes, in the attempt of optimising\nthe reliability of the estimate for the Standard Model backgrounds. See Ref. [6] for a more detailed\ndescription.\nFor t\u00aft production, which is the dominant background for many of the signatures, the MC@NLO [7,8]\ngenerator was used. It includes full next-to-leading order QCD corrections, affording a quite stable\nabsolute cross-section prediction and a good description of the \ufb01nal state kinematics for events with up\nto one additional QCD jet. QCD showering and fragmentation are performed using the HERWIG [9,10]\nprogram. Single top production is expected to add a very small contribution [11], but has also been\ninvestigated.\nTypically SUSY analyses require large jet multiplicities. It is very important to simulate correctly\nthe kinematics of the additional jets for processes like W + jets and Z + jets. For these processes we\ntherefore used the ALPGEN [12] generator, which at leading order in QCD and electroweak interactions,\ncalculates the exact matrix elements for multiparton hard processes in hadronic collisions. Showering\nand hadronisation are provided through the HERWIG program. In order to achieve a correct description\nof the jet multiplicities, it is necessary to perform a correct match between the jets produced by the\nmatrix-element generator and the ones produced by parton showering. This topic is the subject of active\ntheoretical work. Background samples of W and Z containing at least four jets were produced with\nALPGEN, using MLM matching [13] and with the jet matching cut set at 40 GeV. Contributions from\nprocesses with matrix-element parton multiplicities between one and \ufb01ve were summed to produce the\nmulti-jet sample. A \ufb01lter was applied at the generator level requiring at least four jets with transverse\nmomentum above 40 GeV, with at least one of these having a transverse momentum above 80 GeV, and\nwith missing transverse energy above 80 GeV.\nThe leading-order cross-sections were normalised to the results from next-to-next-leading-order cal-\nculations by applying a k factor of 1.15 (1.27) for W (Z) production respectively. The k factor was\ncalculated by comparing the inclusive leading-order cross-section to the NNLO calculation of [14]. For\ntopologies involving fewer than four jets, the PYTHIA generator [15] was used for the generation of the\nW and Z boson backgrounds.\nFor the simulation of QCD multi-jet samples, ALPGEN would also be an appropriate choice. For\npractical reasons, however, it was impossible to generate ALPGEN samples with suf\ufb01ciently large num-\nbers of events to simulate the backgrounds for these studies. As a backup solution we have used a shower\nMonte Carlo, PYTHIA, for which adequate statistics could be generated by producing samples in slices\nthe of pT of the hard scattering. A \ufb01lter at generation level is applied to the PYTHIA events, requiring\nfor the hardest jet a transverse momentum above 80 GeV, for the second jet transverse momentum above\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1517\n\nTable 3: Kinematic boundaries, number of events and integrated luminosity of the PYTHIA QCD back-\nground samples.\nLabel\npT range (GeV)\nN\nInt. Lumi (pb\u22121 )\nJ4\n140-280\n18 k\n19.6\nJ5\n280-560\n60 k\n168.4\nJ6\n560-1120\n20 k\n296.6\nJ7\n1129-2240\n4 k\n754.7\nJ8\n>2240\n4 k\n181000\n40 GeV and missing transverse energy above 100 GeV. The numbers of events which were used for\ndetailed simulation, and the corresponding integrated luminosity for each pT slice are shown in Table 3.\nThe contributions of the diboson processes WW, ZZ and WZ are almost negligible for multi-jet\nanalyses as they are strongly suppressed by typical SUSY selections requiring a large number of jets\nwith high transverse momenta and large missing transverse energy. However they are very important\nwhen searching for direct gaugino production [16]. The corresponding data samples were generated at\nleading order with the HERWIG Monte Carlo, including the full off-shell structure for Z/\u03b3. The cross-\nsections were then normalised to the next-to-leading-order cross-sections calculated with the MCFM\ncode [17].\nFor all the samples except QCD jet production a sample corresponding to at least 1 fb\u22121 of integrated\nluminnosity was simulated.\nPile-up and cavern background simulations were generally not included in the signal and background\nsamples except in a few cases where this is speci\ufb01cally indicated.\n3\nObject Identi\ufb01cation for SUSY analysis\nSupersymmetric events are expected to be characterised by several high-momentum jets and missing\ntransverse energy. Leptons1 and taus are also present in a large fraction of the events for the benchmark\npoints considered. The analyses documented in this Chapter use common particle identi\ufb01cation criteria,\nwhich are brie\ufb02y described in this section.\n3.1\nJets\nBecause of the relatively large multiplicity of jets in SUSY events, a narrow cone is preferable in the\nreconstruction of jets. The algorithm used to reconstruct jets in the analysis documented here is the cone\nalgorithm [18] with a cone size of 0.4. Most analyses presented do not rely on secondary-vertex tagging\n(\u201cb tagging\u201d) but when it is applied, standard ATLAS algorithms [19] are used.\n3.2\nMissing transverse energy\nThe measurement of the transverse energy imbalance in the detector plays a crucial role in the searches\nfor Supersymmetry with R-parity conservation, and the requirement of a large value of Emiss\nT\nis a com-\nmon feature of all the analyses presented in this chapter.\n1Except where explicitly indicated, in this Chapter the word \u201clepton\u201d and the corresponding symbol \u2113should be understood\nto mean \u2113\u2208{e,\u00b5}, i.e. they do not include taus.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1518\n\nFor the studies presented here, the Emiss\nT\nis calculated from the calorimeter cells, with calibration\nweights derived separately for cells associated to different objects (jets, electrons, photons, taus, and\nnon-associated clusters due to the soft part of the event) [20]. Sources of fake missing energy, such as\ndead or noisy parts of the calorimeter, fake muons, beam-gas and beam-halo events, cosmic rays and\nelectronics problems are not considered here. A detailed discussion of the strategies to remove sources\nof fake Emiss\nT\nin early data and to measure the Emiss\nT\nresolution and scale can be found in [20].\nThe contribution from non-gaussian tails in the Emiss\nT\nmeasurement can be strongly suppressed by\nrequiring a minimum angular separation between the Emiss\nT\nvector and the jets in the event. This cut also\nsuppresses the contributions from jets containing hard neutrinos from the leptonic decays of charmed\nand beauty mesons. This issue is discussed in detail in Ref. [21].\n3.3\nElectrons\nIn SUSY searches, the requirement of a high pT electron is normally associated with additional require-\nments on jets and Emiss\nT\n. For typical SUSY analyses the background from the production of QCD jets\ncan be reduced by cuts other than those requiring any lepton(s). Therefore stringent rejection against jets\nis not needed in SUSY studies, and relatively mild electron identi\ufb01cation cuts can be applied, leading to\na signi\ufb01cant gain in ef\ufb01ciency especially for searches involving many leptons. Jets reconstructed within\na cone2 of \u2206R = 0.2 of an identi\ufb01ed electron are discarded from the jet list. This procedure prevents the\nsame object being reconstructed both as a jet and as an electron.\nA standard algorithm called \u201ceGamma\u201d [22] was used for the electron identi\ufb01cation and reconstruc-\ntion, using the \u201cmedium\u201d purity cuts.\nThe transverse isolation energy in a cone of \u2206R < 0.2 around the electron, computed using the calori-\nmetric information, is used to select isolated electrons. This quantity is required to be smaller than\n10 GeV. In the available data-sets this variable was incorrectly calculated, but a signi\ufb01cant bias is intro-\nduced by this problem only in the crack region 1.37 < |\u03b7| < 1.52. In this region the electron identi\ufb01cation\nand measurement are also degraded because of the large amount of material in front of the calorimeter\nand the crack between the barrel and extended barrel of the calorimeters [23]. Events with an electron\nreconstructed in this region are therefore rejected.\nFinally, an electron is rejected if it is found within a distance 0.2 < \u2206R < 0.4 of a jet, since such\ncandidates are likely to be associated with the decay of a particle within that jet.\n3.4\nMuons\nMuons were reconstructed using an algorithm (STACO), which performs a statistical combination of a\ntrack reconstructed in the muon spectrometer with its corresponding track in the inner detector [24]. A\nreasonable quality of combination was guaranteed with a loose requirement that the tracks should match\nwith \u03c72 < 100. If more than one Inner Detector track matched a track from the Muon Spectrometer, only\nthe one with best match (smallest distance \u2206R) was kept. The total calorimeter energy deposited in a\ncone of \u2206R < 0.2 around the muon was required to be less than 10 GeV. Finally, muons found within a\ndistance \u2206R < 0.4 of a jet were discarded.\n3.5\nTaus\nAs will be described in subsequent analyses, \ufb01nal states containing taus are one of the possible signatures\nto be expected within the SUSY rich phenomenology. Taus are challenging objects to identify. When taus\nundergo leptonic decays, their products can be detected in electron- or muon-speci\ufb01c analyses. However,\nin approximately 65% of cases, a tau decays hadronically and the resultant jet needs to be disentangled\n2The cone is de\ufb01ned by \u2206R2 = \u2206\u03b72 +\u2206\u03c62, where \u03b7 and \u03c6 are the pseudorapidity and azimuthal angle respectively.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1519\n\nfrom the overwhelming jet backgrounds expected in ATLAS. In addition, tau signatures always contain\nan important source of missing energy in the form of neutrinos which usually make it impossible to fully\nreconstruct the tau-jet energy.\nElsewhere in this volume [25] two tau reconstruction algorithms, one calorimeter-based and the\nother one track-based, are described. Unless otherwise stated, taus being used in this Chapter follow the\nrecommendations from [25], with a likelihood discriminant of 4, within the \ufb01ducial region |\u03b7| < 2.5 and\npT > 15 GeV. In addition, although not crucial for the results, an overlap removal procedure has been\napplied. Since the electron identi\ufb01cation ef\ufb01ciency is higher than the tau identi\ufb01cation ef\ufb01ciency, a tau\nobject found in a vicinity (\u2206R < 0.4) of an electron object (following the prescriptions de\ufb01ned in the\nelectron performance section of the present note) is considered to be a fake and is removed. Also, since\nhadronically decaying taus are also usually reconstructed as jets, when a calorimeter jet is found within\n\u2206R < 0.4 of a reconstructed tau-jet, then the non-tau jet is disregarded.\n3.6\nTreatment of systematic uncertainties\n3.6.1\nDetector uncertainties\nSupersymmetry searches and measurements will inevitably be subject to uncertainties due to the im-\nperfect understanding of the behaviour of the detector. Many of the performance characteristics of the\ndetector will be constrained from the data themselves, with an accuracy which will depend on the size\nof the data-set available. In this chapter, we have used estimations of these uncertainties based on the\nprecision which is likely to be achievable with 1 fb\u22121 of integrated luminosity. The detector systematics\n\u2013 energy scale, resolution, or ef\ufb01ciency variations \u2013 are applied both to the \u201ctrue\u201d backgrounds and to the\ncontrol samples; data-driven methods will therefore be less sensitive to detector systematics than purely\nMonte Carlo-driven estimates.\nJets and Emiss\nT\nWe assume an overall uncertainty on the jet energy scale of 5%. We apply this as a\nglobal uncertainty, independently of jet pT and \u03b7, and identically for light-quark jets and jets from b\nquarks.\nThe jet energy resolution will be studied on di-jet samples and jets from W boson decay in t\u00aft events.\nAfter such measurements we expect a residual uncertainty of 10% on the resolution.\nThe missing transverse energy of the event, Emiss\nT\n, is calculated from the transverse vector sum of\nhigh pT objects like leptons and jets with a further component from unclustered energy. Part of the\nuncertainty in Emiss\nT\nis thus correlated with jet energy scale uncertainties, but also a wrong calibration of\nunclustered energy can affect Emiss\nT\n. When jets are rescaled or smeared, the Emiss\nT\nis recalculated with\nthe new jets. This takes into account the part of the Emiss\nT\nuncertainty that is correlated with the jets. For\nthe low pT part related to the unclustered energy, we \ufb01rst subtract leptons and jets with pT > 20 GeV\nfrom the Emiss\nT\n, apply a 10% uncertainty on the remainder, and then add the leptons and jets back in.\nElectrons\nFor electrons we estimate an uncertainty on the identi\ufb01cation ef\ufb01ciency (including the trig-\nger) of 0.5%. Furthermore, we assume an uncertainty on the electron energy scale of 0.2%, and on the\nenergy resolution of 1%. All these uncertainties are assumed to be independent of pT and \u03b7.\nMuons\nFor muons we estimate an uncertainty on the identi\ufb01cation ef\ufb01ciency of 1% for muons with\npT < 100 GeV, plus a 3% extrapolation uncertainty to a pT of 1 TeV. Furthermore, we assume an uncer-\ntainty on the muon pT scale of 0.2%, and on the pT resolution of 4% below 100 GeV, whereas the pT\nresolution at 1 TeV is assumed to be 10\u00b11%. All these uncertainties are assumed to be independent of\n\u03b7.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1520\n\nHeavy-\ufb02avour tagging\nWhere b tagging is used, we assume a relative uncertainty of 5% on the b-\ntagging ef\ufb01ciency, and 10% on the light-quark rejection.\n3.6.2\nMonte Carlo uncertainties\nAlthough data-driven background estimation methods try to use Monte Carlo simulations as little as\npossible by construction, some dependence remains for example when trying to understand the compo-\nsition of control samples when Monte Carlo-based corrections, distribution shapes or redecay methods\nare used.\nWe estimate uncertainties from the use of Monte Carlo samples by comparing different event gen-\nerators, particularly Alpgen and MC@NLO, and by variation of generator parameters. For the vector\nboson (V \u2208W,Z) + jets Alpgen samples used in this note, the standard value for the renormalization and\nfactorization scales was Q2 = M2\n\u2113\u2113+ p2\nT(V) where the two leptons are the vector boson decay products.\nThe pT threshold of the partons in the matrix-element calculation was 40 GeV, the minimum distance\n\u2206Rj j between partons was 0.7, and the parton distribution function used was CTEQ6L.\nFor systematic studies we vary:\n\u2022 The renormalization and factorization scales between 0.5Q and Q as de\ufb01ned above. We have also\nused a sample with a different scale de\ufb01nition Q2 = \u2211p2\nT(partons).\n\u2022 The pT threshold of partons in the matrix-element calculation, between 15 and 40 GeV.\n\u2022 The distance in \u2206R between partons in the matrix-element calculation, between 0.35 and 0.7.\n\u2022 The parton distribution function, comparing CTEQ6L to MRST2001J.\n4\nGlobal Variables\nThe SUSY analyses use some global event variables, built out the momenta of jets, leptons and pmiss\nT\n,\nwhich have a good signal discriminating power. We give here a detailed de\ufb01nition of these variables as\nused in the work described in the SUSY notes.\n4.1\nEffective mass\nThe effective mass (Meff ) is a measure of the total activity in the event. It is de\ufb01ned as:\nMeff \u2261\n4\n\u2211\ni=1\npjet,i\nT\n+\u2211\ni=1\nplep,i\nT\n+Emiss\nT\nwhere the sums run respectively over the four highest pT jets within |\u03b7| < 2.5, and over all of the\nidenti\ufb01ed leptons. This variable is useful in discriminating SUSY from Standard Model events. It has\nalso the interesting properties that for SUSY events it the Meff distribution peaks at a value which is\nstrongly correlated with the mass of the pair of SUSY particles produced in the proton-proton interaction.\nIt can therefore be used to quantify the mass-scale of SUSY events [26].\n4.2\nTransverse sphericity\nThe transverse sphericity (ST) is de\ufb01ned as:\nST \u2261\n2\u03bb2\n(\u03bb1 +\u03bb2)\n(1)\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1521\n\nwhere \u03bb1 and \u03bb2 are the eigenvalues of the 2\u00d72 sphericity tensor Sij = \u2211k pkipk j . The tensor is computed\nusing all jets with |\u03b7| < 2.5 and pT > 20 GeV, and all selected leptons.\nSUSY events tend to be relatively spherical (ST \u223c1) since the initial heavy particles are usually\nproduced approximately at rest in the detector and their cascade decays emit particles in many different\ndirections. QCD events are dominated by back-to-back con\ufb01gurations (ST \u223c0).\n4.3\nTransverse mass\nThe transverse mass MT is de\ufb01ned by:\nM2\nT(p\u03b1\nT ,pmiss\nT\n,m\u03b1,m\u03c7) \u2261m2\n\u03b1 +m2\n\u03c7 +2\n\u0000E\u03b1\nT Emiss\nT\n\u2212p\u03b1\nT \u00b7pmiss\nT\n\u0001\n(2)\nwhere\nE\u03b1\nT \u2261\nq\n(p\u03b1\nT )2 +m2\u03b1 ,\nEmiss\nT\n\u2261\nq\n(pmiss\nT\n)2 +m2\u03c7 ,\n(3)\nm\u03b1 and p\u03b1\nT are the mass and transverse momentum of some visible particle and pmiss\nT\nis the missing-\ntransverse-energy two-vector. The parameter m\u03c7 is the mass of the invisible particle, which is usually\nassumed to be zero.\nThis variable is useful when one parent particle decays to one visible and one invisible daughter\nparticle, for example W \u2192e\u03bd where it is clear that the mass of the invisible particle (neutrino) can\nindeed be safely neglected.\n4.4\nStransverse mass\nThe stranverse mass mT2 variable can be de\ufb01ned in terms of the transverse mass (Eq. (2)) by:\nm2\nT2(p\u03b1\nT ,p\u03b2\nT,pmiss\nT\n,m\u03b1,m\u03b2,m\u03c7) \u2261\nmin\n/q(1)\nT +/q(2)\nT =pmiss\nT\nh\nmax\nn\nM2\nT(p\u03b1\nT , /q(1)\nT ;m\u03b1,m\u03c7), M2\nT(p\u03b2\nT, /q(2)\nT ;m\u03b2,m\u03c7)\noi\n(4)\nwhere m\u03c7 is the trial mass for the lightest SUSY particle and p\u03b1,\u03b2\nT\nare the transverse momenta of two\nvisible particles (each of which is a canididate decay product of one of the two SUSY parent particles).\nThe vector sum of the dummy variables q(1)\nT\nand q(2)\nT\nis constrained to equal the total pmiss\nT\n2-vector, so\nthe missing transverse momentum is required as an input to the mT2 calculation. One can consider mT2\nto be a variable formed from dividing pmiss\nT\ninto two parts in all possible combinations that satisfy the\nkinematics of the event (for some m\u03c7, which is here taken to be zero) and calculating the transverse mass\nfor each decay branch. The resulting value is the best lower limit on the mass of a pair-produced SUSY\nparticle that could have decayed to the observed \ufb01nal state with the given p\u03b1\nT , p\u03b2\nT and pmiss\nT\n.\nThe original purpose for mT2 was to provide information on the masses of pair-produced SUSY\nparticles, decaying semi-invisibly [27, 28]. The variable was \ufb01rst proposed to determine SUSY particle\nmasses in \u201csimple\u201d two-body decays, such as two-jet or two-lepton \ufb01nal states, but it can also be used\nin more complicated cases, especially if it is possible to unambiguously determine which particles came\nfrom which branch of the decay.\n5\nSUSY Studies in ATLAS\nIn this collection of papers we review the techniques that will be used to search for SUSY with ATLAS\nat the LHC turn-on. Most of the studies presented are based on a total integrated luminosity of 1fb\u22121 that\nmay be collected during the \ufb01rst year of operation of the LHC. Larger datasets are assumed for studies\nthat investigate SUSY models with a lower cross-section as an illustration of studies that can be carried\nout once the LHC is in full operation.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1522\n\nThe \ufb01rst two articles in this collection concentrate on the background estimation for SUSY searches:\n\u2022 \u201cData-driven determinations of W, Z, and top backgrounds to Supersymmetry\u201d [11],\n\u2022 \u201cEstimation of QCD backgrounds to Searches for Supersymmetry\u201d [21].\nThe following two articles discuss SUSY searches and measurements:\n\u2022 \u201cProspects for Supersymmetry Discovery Based on Inclusive Searches\u201d [29],\n\u2022 \u201cMeasurements from Supersymmetric events\u201d [30].\nThe last two papers focus on searches for speci\ufb01c signatures:\n\u2022 \u201cMulti-lepton Supersymmetry searches\u201d [16],\n\u2022 \u201cSupersymmetry signatures with high-pT photons or long-lived heavy particles\u201d [5].\nReferences\n[1] W. Beenakker, R. Hopker, M. Spira and P.M. Zerwas, Nucl. Phys. B492 (1997) 51\u2013103.\n[2] W. Beenakker and others, Phys. Rev. Lett. 83 (1999) 3780\u20133783.\n[3] Prospino2, http://www.ph.ed.ac.uk/ tplehn/prospino/.\n[4] D. Stump and others, JHEP 10 (2003) 046.\n[5] ATLAS Collaboration, Supersymmetry Signatures with High-pT Photons or Long-Lived Heavy\nParticles, this volume.\n[6] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties, this\nvolume.\n[7] S. Frixione and B.R. Webber, JHEP 06 (2002) 029.\n[8] S. Frixione, P. Naso and B.R. Webber, JHEP 08 (2003) 007.\n[9] G. Corcella and others, JHEP 01 (2001) 010.\n[10] G. Corcella and others, HERWIG 6.5 release note hep-ph/0210213, 2002.\n[11] ATLAS Collaboration, Data-Driven Determinations of W, Z and Top Backgrounds to Supersym-\nmetry, this volume.\n[12] M. Mangano et al., JHEP 07 (2003) 001.\n[13] J. Alwall et al., Eur. Phys. J. C53 (2008) 473\u2013500.\n[14] K. Melnikov and F. Petriello, Phys. Rev. D74 (2006) 114017.\n[15] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[16] ATLAS Collaboration, Multi-Lepton Supersymmetry Searches, this volume.\n[17] J. Campbell, J. Ellis and R. Keith, Phys. Rev. D60 (1999) 113006.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1523\n\n[18] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[19] ATLAS Collaboration, Vertex Reconstruction for b-Tagging, this volume.\n[20] ATLAS Collaboration, Measurement of Missing Tranverse Energy, this volume.\n[21] ATLAS Collaboration, Estimation of QCD Backgrounds to Searches for Supersymmetry, this vol-\nume.\n[22] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[23] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[24] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[25] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[26] D.R. Tovey, EPJ Direct 4 (2002) 4.\n[27] C. Lester, D. Summers, Phys. Lett. B463 (1999) 99.\n[28] A. Barr, C. Lester, P. Stephens, J. Phys. G. 29 (2003) 2343.\n[29] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[30] ATLAS Collaboration, Measurements from Supersymmetric Events, this volume.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SEARCHES\n1524\n\nData-Driven Determinations of W, Z and Top Backgrounds to\nSupersymmetry\nAbstract\nThe Standard Model processes of W boson, Z boson and top quark production\neach in association with jets constitute major backgrounds to searches for Su-\npersymmetry at the LHC. In this note, we estimate the contribution of these\nbackgrounds for a basic SUSY selection, and discuss methods to derive them\nfrom the initial 1 fb\u22121 of integrated luminosity at ATLAS.\n1\nIntroduction\n1.1\nMotivation\nThe Large Hadron Collider (LHC) will provide excellent opportunities to search for new physics beyond\nthe Standard Model, and the ATLAS detector [1] is a general purpose experiment to explore such new\nphysics. Supersymmetry (SUSY) is a theoretically attractive model for new physics beyond the Standard\nModel, and searching for Supersymmetry is one of the main objectives of ATLAS. The actual search\nstrategy is described elsewhere in this volume [2].\nIt is clear, however, that any discovery of new physics can only be claimed when the Standard Model\nbackgrounds are understood and are under control. It is expected that at the LHC, Monte Carlo pre-\ndictions will not be suf\ufb01cient to achieve this: the backgrounds will have to be derived from the data\nthemselves, possibly helped by Monte Carlo. The development and description of such data-driven\nbackground estimation is the topic of this note. We note that for a complete understanding of the back-\ngrounds, multiple, independent methods are desired. Each of these may be sensitive to a speci\ufb01c back-\nground source, and affected by speci\ufb01c systematic effects. Only their consistency in combination allows\nfor suf\ufb01cient con\ufb01dence in the control of the background to claim a discovery when a signal appears to\nbe present.\n1.2\nData-driven methods: scope of this note\nThe general aim of data-driven methods is to estimate from the data the Standard Model backgrounds\nand their uncertainties in a \u201csignal\u201d region, in which new physics may be present. Such a signal region is\ntypically obtained after applying selection cuts, or multivariate methods, and the new physics is searched\nfor as an excess in the number of selected events over background, or as an excess in certain regions of\ncertain distributions.\nThe background estimation is performed by selection of \u201ccontrol samples\u201d, from which predictions\nin the signal region are derived. Good control samples should be as close as possible to the signal\nregion, yet free of SUSY signal, give an unbiased estimate of background in the signal region, have\nsuf\ufb01cient statistics, and small theoretical uncertainties. This note intends to describe a number of ideas\non selection of such control samples for SUSY searches. Good control of the composition of control\nsamples is important for a correct extrapolation into the signal region.\nThe methods described in this note should not be regarded as the \ufb01nal word on these procedures, but\nrather present a number of ideas. Each of these ideas will have to be pursued further, and the effect of\nother systematic uncertainties will need to be studied. Furthermore, SUSY selection cuts will evolve, and\nso the methods will need to evolve too. We do believe, however, that a \ufb01rst indication of the uncertainties\nthat can be expected can be given.\n1525\n\nThis note deals with top, W and Z backgrounds to SUSY searches with primary squark or gluino\nproduction, and assuming R-parity conservation. The initial priority is to simulate results for 1 fb\u22121 of\nintegrated luminosity, and for the understanding of the detector expected. The other important QCD\nbackground of quark (other than top) and gluon jet production is treated elsewhere in this volume [3].\nBackgrounds to alternative production models are also described elsewhere: direct gaugino produc-\ntion [4], and photonic and long-lived particle (such as R hadron) signatures [5].\n1.3\nSUSY contamination\nIf SUSY is discoverable, it is likely that SUSY events will creep into the control samples, thereby affect-\ning the background estimates. In general, SUSY events, mistakenly regarded as Standard Model physics,\nwill lead to an overestimation of the background, and thus to a reduced SUSY event excess. The extent\nto which this happens will be analysis- and SUSY model-dependent.\nSince we do not know whether SUSY exists, we quote the SUSY contamination effects separately\nfrom the other systematics. We will do so by running each data-driven estimation method not only over\nbackground samples, but also on a number of SUSY signal samples [6]. The samples represent various\nregions of mSUGRA parameter space, and together give an impression of the effects. The SU1 sample is\na point in the stau coannihilation region, the SU2 sample in the focus point region, and the SU3 sample\nin the bulk region. The SU4 point is a low-mass point, just above the Tevatron limits. It has a very large\ncross-section, and kinematic distributions that are typically only slightly harder than the Standard Model\nbackground. As will be shown, this model has the largest SUSY contamination effect on the background\nestimates.\nThere are a number of ways that the data-driven methods can take the presence of SUSY into account:\n1. Iteration. The Standard Model background is evaluated under the assumption that there is no\nSUSY. This will overestimate the background if there is SUSY, and reduce any excess. Neverthe-\nless, if an excess is seen, the underlying assumption in the background estimation has been proven\nwrong, and a correction can be applied. This correction can be derived from the properties of the\nobserved excess, and will lead to a new background estimate. An example of such a procedure is\nthe \u201cnew MT method\u201d described in section 3.3.3. However, other implementations are possible,\nand perhaps necessary, as well.\n2. A combined \ufb01t determining the composition of the control sample, allowing for a possible SUSY\ncontribution.\nBoth methods are investigated in this note. Nevertheless it is clear that these are preliminary ideas\nthat require further investigation. Most likely, some form of iteration on the background determinations\nwill be necessary.\n1.4\nLayout of this note\nA number of important prerequisites for the studies presented here are described in an introductory\nnote [6]:\n\u2022 the physics processes that form the background to SUSY searches and how they are simulated, as\nwell as a few SUSY event samples (SU1\u2013SU8) that serve to estimate the effect of SUSY on our\nbackground estimates;\n\u2022 the de\ufb01nition of objects like electrons, muon, taus, jets and missing transverse energy, and common\nvariables like the effective mass Meff ;\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1526\n\n\u2022 the origin and common treatment of various systematic uncertainties, both from the simulation and\nfrom the performance of the detector.\nFurthermore, the trigger menu that was used is described elsewhere [7]. In this note we then discuss the\nW, Z, and top-quark backgrounds and their data-driven estimation for two different SUSY search modes:\n1. the mode with one isolated electron or muon (section 2);\n2. the no-lepton mode, with a veto against isolated leptons (section 3).\n2\nOne-lepton search mode\n2.1\nSelection\nThe one-lepton search mode is expected to play a major role in the SUSY search, since the requirement\nof an isolated lepton will be effective in suppressing QCD background. In this search mode, we require\none isolated electron or muon, with a pT of more than 20 GeV. We veto events with a second identi\ufb01ed\nlepton with a pT of more than 10 GeV, so that we have no overlap with the di-lepton search mode.\nWe demand at least four jets with |\u03b7| < 2.5 and pT > 50 GeV, at least one of which must have\npT > 100 GeV. The transverse sphericity ST should be larger than 0.2, and the missing transverse energy\nEmiss\nT\nshould be larger than 100 GeV and larger than 0.2Meff, where Meff is the effective mass1. The\ntransverse mass MT reconstructed from the lepton and Emiss\nT\nshould be larger than 100 GeV.\n2.2\nBackgrounds in Monte Carlo\nIn many SUSY models after the selection cuts have been applied clear excesses will be observed in the\nhigh Emiss\nT\nand high effective mass regions, as shown in Figure 1. The dominant background process\nfor the one-lepton mode is t\u00aft (90%), with W \u00b1 +jets (10%) being the subdominant process. The neutrino\nemitted from the W \u00b1 decays produces the Emiss\nT\nin the both processes. Smaller contributions come from\nZ +jets, diboson and single top events and from QCD processes. It is interesting to note that the major t \u00aft\nbackground does not come from the semileptonic (t\u00aft \u2192b\u00afb\u2113\u03bdq \u00afq\u2032) top pair events which are reduced by\nthe MT and Emiss\nT\ncuts, but rather from the double leptonic (t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd) top decay where one lepton is\nnot identi\ufb01ed.\n2.3\nData-driven estimation strategies\nWe discuss a variety of different methods to estimate the background from data. These methods differ\nin their approach and therefore are in\ufb02uenced by different systematic uncertainties, and they focus on\ndifferent aspects of the background:\n1. estimation of W and t\u00aft background from a control sample formed by reversing one of the selection\ncuts (on MT) (section 2.3.1);\n2. estimation of the semileptonic t\u00aft background by explicit kinematic reconstruction and selection on\ntop mass (\u201ctop box\u201d) (section 2.3.2);\n3. estimation of the double leptonic t\u00aft background, where one lepton is missed, by explicit kinematic\nreconstruction of a control sample of the same process with both leptons identi\ufb01ed (section 2.3.3);\n1The variables ST, Meff and MT are de\ufb01ned elsewhere in this volume [6].\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1527\n\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\nSU3\nSM BG\ntt\nW\nZ\nsingle top\nATLAS\nEffective Mass [GeV]\n500\n1000\n1500\n2000\n2500\n3000\n / 200GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\nSU3\nSM BG\ntt\nW\nZ\nsingle top\nATLAS\nFigure 1: The Emiss\nT\nand effective mass distributions for the background processes and for an example\nSUSY benchmark point (SU3) in the one-lepton mode for an integrated luminosity of 1 fb\u22121. The black\ncircles show the SUSY signal. The hatched histogram show the sum of all Standard Model backgrounds;\nalso shown in different colours are the various components of the background.\n4. estimation of that same double leptonic t\u00aft background from a control sample derived by a cut on a\nnew variable HT2 (section 2.3.4);\n5. estimation of t\u00aft background by Monte Carlo redecay methods (section 2.3.5);\n6. estimation of W and t\u00aft background using a combined \ufb01t to control samples (section 2.3.6).\n2.3.1\nCreating a control sample by reversing the MT cut\nThe transverse mass MT is constructed from the identi\ufb01ed lepton and the missing transverse energy. In\nthe narrow-width limit MT is constrained to be less than mW for the semileptonic t\u00aft and theW \u00b1 processes.\nFigure 2 shows that MT is only weakly dependent on Emiss\nT\n. This variable is therefore suitable for the\nestimation of the background distribution itself. Events with small MT (< 100 GeV) are selected as the\ncontrol sample, in which the t\u00aft (\u223c84%) and W \u00b1 (\u223c16%) processes are enhanced over the SUSY and\nthe other background processes. The large MT (> 100 GeV) region is referred to as the signal region.\nSince, for the control sample, the other selection criteria are identical to those for events in the signal\nregion, the same kinematic distributions including Emiss\nT\ncan be obtained. The number of events for the\nvarious processes in signal region and control sample is summarized in the Table 1.\nTable 1: Number of background events and estimated numbers for t\u00aft, W \u00b1 and QCD processes without\nSUSY signal, normalized to 1 fb\u22121.\nSignal Region\nControl Sample\nt\u00aft(\u2113\u03bdq \u00afq)\n51 (25%)\n1505 (77%)\nt\u00aft(\u2113\u03bd\u2113\u03bd)\n140 (70%)\n132 (7%)\nW \u00b1(\u2113\u03bd)\n10 (5%)\n305 (16%)\nSUSY(SU3)\n450\n317\nThe normalization factor is obtained from the event numbers of the signal region and the control\nsample (100 < Emiss\nT\n< 200 GeV), in which the SUSY signal contribution is expected to be relatively\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1528\n\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n1\n10\n2\n10\n3\n10\nSignal Region\nControl Region\nATLAS\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\nSignal Region\nControl Region\nATLAS\nFigure 2: The Emiss\nT\ndistribution for t\u00aft (left) and SUSY (SU3, right) signal. In both \ufb01gures, the solid and\ndashed histograms show the Emiss\nT\ndistribution for MT > 100 GeV and < 100 GeV, respectively. The\nnumbers are normalized to 1 fb\u22121.\nsmall. Figure 3 shows the Emiss\nT\nand Meff distributions which are obtained using this method to estimate\nthe size of these backgrounds, and, for comparison, the true background distributions. The numbers of\nevents with Emiss\nT\n> 100 GeV and > 300 GeV are listed in Table 2. The prediction and the true values\nagree within the uncertainties, although somewhat less well for high Emiss\nT\n.\nThe t\u00aft event composition of the control sample differs from that of the signal sample, since the MT\ncut removes a much larger proportion of the semileptonic t\u00aft events. The control sample is still able to\npredict the background in the signal sample within statistical uncertainties. Nevertheless, the resulting\nsystematic shift needs to be investigated, and would be desirable to obtain independent estimates of the\nfully-leptonic and semileptonic t\u00aft backgrounds separately.\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\nes imated BG\nSM BG\ntt\nW\nZ\nsingle top\nATLAS\nEffective Mass [GeV]\n500\n1000\n1500\n2000\n2500\n3000\n / 200GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\nestimated BG\nSM BG\ntt\nW\nZ\nsingle top\nATLAS\nFigure 3: The Emiss\nT\nand effective mass distributions of the background processes for the one-lepton\nmode with an integrated luminosity of 1 fb\u22121. The open circles show the estimated distributions with the\nMT method. The hatched histogram shows the true sum of all Standard Model backgrounds; different\nsymbols show the various contributions to the background.\nSUSY signal contamination\nIf supersymmetric particles are produced they are also likely to contribute\nto the control samples. The estimated Emiss\nT\ndistribution with the presence of a SUSY signal (SU3 point)\nis shown in Figure 4 (left), and the numbers are listed in Table 3. The background is overestimated due\nto the SUSY contamination, and the inferred Emiss\nT\ndistribution is biased towards larger values. However,\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1529\n\nTable 2: Numbers of background events and estimated numbers for the sum of all background processes\nwithout SUSY signal, normalized to 1 fb\u22121\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nTrue BG\n203 \u00b1 6\n12.4 \u00b1 1.6\nEstimated BG\n190 \u00b1 8\n9.4 \u00b1 0.7\nRatio(Est./True)\n0.93 \u00b1 0.05\n0.76 \u00b1 0.11\nthe amount of the over-estimation is smaller than the SUSY signal itself, and a clear excess can still be\nobserved, as shown in the \ufb01gure. The same exercise was repeated for other SUSY signal points, as also\nshown in Table 3.\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\ntruth BG\ntruth BG+SUSY\ntruth SUSY\nest. BG (old MT)\nATLAS\nTransverse Mass [GeV]\n0\n50\n100 150 200 250 300 350\n400 450 500\n / 20GeV\n\u22121\nEvents / 1fb\n1\n10\n2\n10\n3\n10\nSU1\nSU2\nSU3\nSM BG\ntt\nW\nZ\nDiboson\nATLAS\nFigure 4: Left: the Emiss\nT\ndistribution of the background processes for the one-lepton mode with an\nintegrated luminosity of 1 fb\u22121. The red dots show the estimated distributions with the MT method, with\nSUSY signal (SU3) present. The hatched histogram shows the sum of all Standard Model backgrounds,\nand the OPEN histogram shows the SUSY signal (SU3). Right: the transverse mass distributions of\nthe various SUSY signals (SU1, SU2 and SU3) with an integrated luminosity of 1 fb\u22121. Background\nprocesses are superimposed for comparison. The hatched histogram shows the sum of all Standard\nModel backgrounds.\nCorrecting for SUSY signal: \u201cNew MT method\u201d\nIf, even for overestimated backgrounds, the pres-\nence of a concrete SUSY excess is observed in data, we can try to correct the background estimates.\nOne possible procedure is described here, referred to as the \u201cnew MT method\u201d. More advanced\nimplementations of such a correction procedure are possible and should be studied.\nThe new MT method makes use of the observation that in the one-lepton search mode, the MT\ndistribution of backgrounds falls off steeply beyond \u223c100 GeV, whereas for many SUSY signal models\nthis distribution falls only slowly. This is illustrated in Figure 4 (right). By making a general ansatz for\nthe shape of the SUSY MT distribution, and neglecting to \ufb01rst order the Standard Model background\nat high MT, the SUSY contamination can be subtracted from the control sample. Obviously, remaining\nStandard Model background in the high MT region and variations in the MT shape for various SUSY\nsignals are to be treated as systematic uncertainties on the method. Nevertheless, the data itself will tell\nwhat the MT shape is.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1530\n\nTable 3: Number of background events and estimated numbers for all background processes with SUSY\nsignal, normalized to 1 fb\u22121. Also the total number of events (SUSY + background) is shown.\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nTrue BG\n203 \u00b1 6\n12.4 \u00b1 1.6\n203 \u00b1 6\n12.4 \u00b1 1.6\nSU1\nSU4\nEstimated BG\n225 \u00b1 9\n21.6 \u00b1 1.1\n2366 \u00b1 102\n165 \u00b1 12.7\nTrue BG+SUSY\n463 \u00b1 7\n194 \u00b1 4\n3177 \u00b1 79\n415 \u00b1 29\nSU2\nSU6\nEstimated BG\n200 \u00b1 9\n10.9 \u00b1 0.7\n213 \u00b1 9\n16.3 \u00b1 0.9\nTrue BG+SUSY\n249 \u00b1 7\n34 \u00b1 2\n365 \u00b1 9\n129 \u00b1 5\nSU3\nSU8\nEstimated BG\n296 \u00b1 10\n33.3 \u00b1 1.4\n206 \u00b1 9\n13.7 \u00b1 0.8\nTrue BG+SUSY\n653 \u00b1 8\n245 \u00b1 4\n354 \u00b1 8\n115 \u00b1 5\nIn the simplest ansatz used here, the ratio of SUSY signal between the control sample MT < 100\nGeV and signal region MT > 100 GeV is assumed to be constant for all SUSY signal samples. The\nnormalization factor is obtained from the number of events in the signal region and the corrected control\nsample in the interval 100 GeV < Emiss\nT\n< 150 GeV (instead of 100 \u2013 200 GeV) to suppress the SUSY\ncontribution in the normalization region. The statistical error becomes relatively larger when the narrow\nband is used for normalization, but the over-estimation of the normalization factor due to the SUSY\nsignal can be suppressed. A lower Emiss\nT\nregion, such as Emiss\nT\n= 70 \u2212100 GeV, could be used for the\nnormalization in future studies.\nFigure 5 shows the Emiss\nT\nand the effective mass distributions of the estimated background processes.\nThe true distributions of the background processes are also superimposed. The numbers in regions of\nEmiss\nT\n> 100 GeV and 300 GeV are listed in Table 4. A reasonable agreement between the prediction\nand the true values is observed. For high values of Emiss\nT\n, the method tends to subtract too much SUSY\ncontamination and underestimates the background. More study is needed. The SU4 benchmark point is\na special case because it has a particularly light SUSY particle spectrum.\n [GeV]\nT\nMissing E\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\ntruth BG\ntruth BG+SUSY\ntruth SUSY\nest. BG (new MT)\nATLAS\nEffective Mass [GeV]\n500\n1000\n1500\n2000\n2500\n3000\n / 200GeV\n\u22121\nEvents / 1fb\n\u22121\n10\n1\n10\n2\n10\ntruth BG\ntruth BG+SUSY\ntruth SUSY\nest. BG (new MT)\nATLAS\nFigure 5: The Emiss\nT\nand effective mass distributions of the background processes for one lepton mode\nwith an integrated luminosity of 1 fb\u22121. The red dots show the estimated distributions with the \u201cnew\nMT\u201d method. The hatched histogram show the sum of all Standard Model backgrounds. The open\ncircles indicate the SUSY (SU3) signal.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1531\n\nTable 4: Numbers of background events and estimated numbers for all background processes in the\npresence of various SUSY signals, using the new MT method. The numbers are normalized to 1 fb\u22121.\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nTrue BG\n203 \u00b1 6\n12.4 \u00b1 1.6\n203 \u00b1 6\n12.4 \u00b1 1.6\nSU1\nSU4\nEstimated BG\n186 \u00b1 11\n8.9 \u00b1 0.8\n1382 \u00b1 98\n48.3 \u00b1 12.7\nTrue BG+SUSY\n463 \u00b1 7\n194 \u00b1 4\n3177 \u00b1 79\n415 \u00b1 29\nSU2\nSU6\nEstimated BG\n183 \u00b1 11\n8.8 \u00b1 0.8\n185 \u00b1 11\n8.1 \u00b1 0.9\nTrue BG+SUSY\n249 \u00b1 7\n34 \u00b1 2\n365 \u00b1 9\n129 \u00b1 5\nSU3\nSU8\nEstimated BG\n212 \u00b1 11\n12.3 \u00b1 1.0\n180 \u00b1 11\n6.6 \u00b1 0.8\nTrue BG+SUSY\n653 \u00b1 8\n245 \u00b1 4\n354 \u00b1 8\n115 \u00b1 5\nThe systematic uncertainties2 for the MT method are summarized in Table 5. As well as variation\nof jet energy scale and lepton identi\ufb01cation ef\ufb01ciency, the ALPGEN Monte Carlo was compared to\nMC@NLO, and parameters in ALPGEN (minimum pT of partons and minimum \u2206R between partons)\nwere varied. This method is stable against these systematic uncertainties at the \u223c15% level. More work\nis needed to estimate the SUSY contamination effects.\nTable 5: Systematic uncertainties of the one-lepton background estimations with the MT method, ex-\ncluding those related to SUSY signal contamination. Numbers are normalized to 1 fb\u22121\nSyst. error\nJet energy scale\n< 5%\nLepton ID ef\ufb01ciency\n7%\nMC@NLO vs ALPGEN\n8%\nMonte Carlo parameter variation (ALPGEN)\n< 5%\n2.3.2\nTopbox: a control sample for semileptonic top-pair background\nTop mass reconstruction and \u201ctopbox\u201d cuts\nThis section describes a data-driven method, denoted\nthe \u201ctopbox method\u201d, for estimating the t\u00aft background where one top decays leptonically, and the other\nhadronically.\nFor semileptonic t\u00aft events, the invariant mass of the leptonically decaying W boson can usually\nbe reconstructed by assuming that the neutrino from the W decay is responsible for all missing energy.\nThis is a fair assumption; after removal of fake Emiss\nT\n(noisy/dead calorimeter cells etc.) in the event-\ncleaning procedure, the resolution on Emiss\nT\nis expected to be approximately equal to 0.55\u221a\n\u2211ET [1],\nwhich is much smaller in a typical t\u00aft event than the Emiss\nT\nfrom the escaping neutrino. The fact that the\nmass of the leptonically decaying top can be reconstructed satisfactorily (see below) further justi\ufb01es the\nassumption.\nThe core of the method is to construct both the semileptonic and the hadronic top decays in a t\u00aft event\nfollowing the procedure below:\n2Throughout this note systematic uncertainties have been calculated according to the procedures outlined in the introduction\nto this chapter [6].\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1532\n\n\u2022 The leptonic W is assumed to decay into the observed lepton and a neutrino which is responsible\nfor all missing energy. The px and py components of the neutrino momentum are hence taken to\nbe the x and y components of Emiss\nT\n. The pz component of the neutrino can be calculated using\na W mass (mW ) constraint. The four-vector of the leptonic W is the sum of the four-vectors of\nthe lepton and the reconstructed neutrino. For events with transverse mass MT less than mW , two\nsolutions can be found. In the case of MT > mW no real solution is possible and, in such cases,\nthe momentum of the leptonic W is taken from the transverse components of the lepton and Emiss\nT\n.\n\u2022 The leptonic top is then reconstructed by taking the solution with the best reconstructed top mass\n(mtop-lep ) from combinations of a jet and one of the above leptonic W solutions. The jet is taken\nfrom the pool of the four highest-pT jets in the event. The best reconstructed top mass is de\ufb01ned\nto the one that is closest to the nominal top mass mt .\n\u2022 The hadronic W is then taken to be formed from the best reconstructed W mass (mW-had ) among\nthe two-jet combinations from the remaining three jets in the pool. The best reconstructed W mass\nis de\ufb01ned to be the invariant closest to mW .\n\u2022 Finally, the hadronic top is taken to be the one with the best reconstructed top mass (mtop-had )\namong combinations of the hadronic W and one of the remaining jets.\nThe plots in Figure 6 show the distributions of the reconstructed masses mtop-lep , mW-had , and\nmtop-had after the mass reconstruction procedure described above. The distributions are made for t\u00aft ,\nSU3 and W + jets event samples with standard one-lepton cuts, except for a modi\ufb01ed MT requirement\n(see below in the control sample section). As expected, the topbox mass reconstruction procedure offers\na very good separating power between t\u00aft and other processes.\nThe topbox cuts are then de\ufb01ned as follows: |mtop-lep \u2212mt | < 25 GeV, |mW-had \u2212mW| < 15 GeV,\nand |mtop-had \u2212mt | < 25 GeV.\nTopbox control sample\nTo make the topbox control sample, events are selected with the standard\nSUSY search cuts in the one-lepton mode, with the exception that MT > 100 GeV is replaced by MT <\nmW. In addition, the above topbox cuts are applied.\nTable 6 shows the number of events of various processes in the topbox control sample. The t\u00aft +jets\nprocess makes up more than 95% of the topbox control sample if no SUSY signal is present.\nTable 6: Composition of the topbox control sample. Numbers shown correspond to an integrated lumi-\nnosity of 1 fb\u22121 . The last \ufb01ve columns show the numer of SUSY events which would enter into the\ntopbox control sample.\nProcess\nt\u00aft +jets\nW +Jets\nSU1\nSU2\nSU3\nSU4\nSU6\nEvents\n340.9\n6.8\n1.8\n0.4\n4.9\n243.6\n0.4\nSUSY signal contamination\nTable 6 also shows the number of SUSY events, for various signal sam-\nples, in the topbox control sample, for 1 fb\u22121. In this method, SUSY contamination is in general small.\nThis fact makes the topbox method a good supplement to the other methods (e.g. the MT method). The\nexception is the SU4 benchmark point, which has a larger contribution because its light spectrum makes\nit rather similar to the t\u00aft background.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1533\n\nLeptonic Top Mass (GeV)\n0\n50\n100\n150\n200\n250\n300\n350\n400\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0.22\nttbar\nW+jets\nSU3\na.u.\nATLAS\nHadronic W Mass (GeV)\n0\n50\n100\n150\n200\n250\n300\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nttbar\nW+jets\nSU3\na. u.\nATLAS\nHadronic Top Mass (GeV)\n0\n100 200 300 400 500 600 700 800 900 1000\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nttbar\nW+jets\nSU3\na.u.\nATLAS\nFigure 6: Normalized distributions for reconstructed mtop-lep , mW-had , and mtop-had for t\u00aft , W + jets,\nand SU3 SUSY events, using the \u201ctopbox\u201d method.\nEstimation of the t\u00aft background in the signal region\nThe t\u00aft contamination in the signal region is\nestimated by multiplying the number of events in the data topbox by a scaling factor Rtt . Rtt is de\ufb01ned\nas the ratio of the number of Monte Carlo t\u00aft events in the signal region (those that pass the one-lepton\ncuts) to that in the topbox control sample. The procedure is summarized by the following equations:\nNsignal-region\nt\u00aft\n(data) = Ntopbox\nt\u00aft\n(data)\u00b7Rtt\n(1)\nRtt \u2261Nsignal-region\nt\u00aft\n(MC)/Ntopbox\nt\u00aft\n(MC)\n(2)\nWith fully simulated Monte Carlo samples, Rtt is determined to be 0.386 . The model dependence\n(variation of Monte Carlo generator and generator parameters) of this number is treated as a systematic\nuncertainty.\nSystematics\nThe systematic uncertainties of the topbox method are summarized in Table 7. The largest\nsource of uncertainty is from the jet energy scale uncertainty; this is expected since the method relies\nheavily on the reconstruction of top and W masses. The Monte Carlo model dependency of Rtt\nis\nestimated by comparing MC@NLO and ALPGEN, and by variation of the ALPGEN parameters, and\namounts to 8%. Finally, it is expected that extra jets due to event pile-up may affect the mass recon-\nstruction resolution. However, this is relevant only in high luminosity scenarios, beyond the scope of this\nnote. The statistical uncertainty on the topbox control sample normalization is estimated to be 5% for\n1 fb\u22121 given that the effective cross-section of t\u00aft in the topbox is about 400 fb.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1534\n\nTable 7: Systematic uncertainties of the topbox method for 1 fb\u22121.\nSource\nContribution [%]\nJet energy scale\n20\nEmiss\nT\nscale\n2\nMonte Carlo Model dependence of Rtt\n8\nTotal\n22\n2.3.3\nDi-leptonic top with one lepton missed: kinematic reconstruction\nIntroduction\nFully leptonic t\u00aft events may contribute to the one-lepton SUSY search sample if one\nof the two leptons originating from the W decay is not identi\ufb01ed. Such events can be classi\ufb01ed as: (1)\nevents with one tau (51%); (2) events where one lepton is misidenti\ufb01ed due to inef\ufb01ciency of the lepton\nidenti\ufb01cation algorithms (20%); (3) events where one lepton is lost inside a jet (17%); (4) events where\none lepton is not in the pT or \u03b7 acceptance (9%); and (5) events with two tau leptons (3%).\nThe method discussed here is based on the selection of a sample enhanced in t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events\nby requiring that the events satisfy a set of kinematic constraints particular to the t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd process.\nThis sample, denoted as the control sample, with two isolated identi\ufb01ed leptons, is used to estimate the\ncontribution from the \ufb01rst two categories of events listed above. The contribution from category (1) is\nestimated by replacing one of the leptons in the control sample with a tau, and category (2) is estimated\nby removing one of the two leptons. The contribution from the categories (3)\u2013(5) is not estimated from\nthe control sample. Events were required to \ufb01re either the 4j50 multi-jet trigger or the j80 xE50 jet plus\nEmiss\nT\ntrigger [7].\nSelection of the control sample\nThe following requirements are imposed to select events in the control\nsample: two isolated oppositely-charged leptons (electron or muon), with pT > 10 GeV and at least one\nwith pT > 20 GeV; at least three jets with |\u03b7| < 2.5 and pT > 50 GeV at least one of which must have\npT > 100 GeV. Note that in contrast to the SUSY one-lepton search selection given in Sec. 2.1 only\nthree jets are required, since the misidenti\ufb01ed lepton or tau can produce the fourth jet.\nFor t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events the two leptons, two b jets and the x- and y-components of the Emiss\nT\n-vector\nsatisfy the following kinematic constraints:\n(p\u03bd + p\u2113+)2 = m2\nW,\n(p\u00af\u03bd + p\u2113\u2212)2 = m2\nW,\n(p\u03bd + p\u2113+ + pb)2 = m2\nt ,\n(p\u00af\u03bd + p\u2113\u2212+ p\u00afb)2 = m2\nt ,\np\u03bdx + p\u00af\u03bdx = Emiss\nT,x ,\np\u03bdy + p\u00af\u03bdy = Emiss\nT,y ,\n(3)\nwhere p\u2113\u00b1, p\u03bd/\u00af\u03bd, pb/\u00afb are the lepton, neutrino and b-quark momenta respectively and mW and mt are the\nW boson and top quark masses. We assume that the only source of Emiss\nT\nis a pair of neutrinos, which is\na fair assumption as shown in the previous section.\nThe \ufb01nal state contains two unknown neutrino momenta and the above system of equations has a two-\nor four-fold ambiguity, as the solution is given by a quartic equation which can be solved with standard\nanalytical techniques [8]. Since there are at least three jets in each event, all possible combinations of\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1535\n\njet pairs made from the three highest pT jets are considered. Jet pairs for which the above system of\nequations has real solutions are denoted as b-jet pairs3. Figure 7 (left) shows the number of b-jet pairs\nfor the various processes contributing to the control sample.\nb-jet pairs\nN\n0\n1\n2\n3\n4\n5\n6\n-1\nEvents / 1fb\n0\n100\n200\n300\n400\n500\n600\nATLAS\n\u03bdl\u03bd\n l\nb\nb\n\u2192\ntt\nq\nq\n\u03bd\n l\nb\nb\n\u2192\ntt\nW\nZ\nSU1\nSU3\n (GeV)\nT\nMissing E\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n / 50 GeV\n-1\nEvents / 1fb\n1\n10\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n1\n10\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n1\n10\n\u03c4\u03bd\n\u03c4\n\u03bd\n l\nb\nb\n\u2192\ntt\n, misid. lepton\n\u03bd\n l\n\u03bd\n l\nb\nb\n\u2192\ntt\n, total\n\u03bdl\u03bd\n l\nb\nb\n\u2192\ntt\ntau decay resimulation\nMisid. lepton resimulation\nATLAS\nFigure 7: Left: distribution of number of b-jet pairs for events passing the control sample requirements in\nthe kinematic reconstruction method. The fraction of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events with no b-jet pairs is dominated\nby events with at least one b jet which is not among the three highest-pT jets. Right: distribution of Emiss\nT\nfor t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd\nevents with one tau lepton and events with a misidenti\ufb01ed lepton compared to the\nestimation from resimulated events with an integrated luminosity of 1 fb\u22121. The requirement on the\nnumber of b-jet pairs is not applied to the resimulated events. The distribution of all t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events\nis also shown.\nReplacement procedure\nEach event in the control sample is used as a seed for producing a series of\nresimulated events. One of the two identi\ufb01ed leptons in the seed event is replaced by tau lepton and a set\nof 1000 tau decays are simulated using the TAUOLA package [9]. The same procedure is repeated for the\nsecond lepton in the seed event, yielding a total of 2000 events for every seed event. Each resimulated\nevent is weighted by a factor of 1/\u03b5, where \u03b5, the identi\ufb01cation ef\ufb01ciency for the replaced lepton, is\nestimated from simulations.\nThe contribution of events where one lepton evades identi\ufb01cation is estimated as follows. If the\nreplaced lepton is an electron then a jet with the same momentum is substituted instead of it. If the lepton\nis a muon it is replaced by a so-called stand-alone muon (de\ufb01ned as a track in the muon spectrometer\nwith no match to a track in the inner detector) justi\ufb01ed by the fact that most muons not passing the muon\nde\ufb01nition are stand-alone muons. This procedure is applied to each of the two leptons in the seed events,\nresulting in two resimulated events for each seed event. The resimulated events are re-weighted with\n1\u2212\u03b5\n\u03b5 .\nFor both kinds of resimulated events, the SUSY one-lepton search selection are subsequently applied.\nAs a closure test of the replacement procedures described above, the Emiss\nT\ndistribution for resim-\nulated t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd\nevents passing the control sample selection apart from the requirement of b-jet\npairs, is compared to the Monte Carlo prediction. The result is shown in Fig. 7 (right) and shows good\nagreement.\nNormalization\nThe number of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd\nevents in the signal region is estimated by scaling of\nthe sum of described above contributions with two scaling factors. The \ufb01rst factor takes into account\nthe other categories of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events that are not estimated by this method. This \ufb01rst factor is\n3Note that within this section only kinematical conditions have used to identify these b-jet pairs \u2013 no secondary-vertex\nrequirement is used.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1536\n\nTable 8: Estimated background corresponding to an integrated luminosity of 1 fb\u22121 for different\nmSUGRA benchmark points. The second column shows the relative increase of the estimated back-\nground with respect to the estimation without contamination from the SUSY signal. The third column\nshows the number of SUSY events. The Monte Carlo prediction of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd background in the one\nlepton search mode is 136 events. The errors in the \ufb01rst column are statistical only.\nSUSY point\nEstimated\nRelative change\nTrue Signal\nBackground\n[%]\nEvents\nNo signal\n120\u00b114\nSU1\n137\u00b115\n15\n260\nSU2\n127\u00b115\n5.9\n45\nSU3\n176\u00b118\n47\n454\nSU4\n604\u00b138\n405\n2960\nSU6\n129\u00b116\n7.8\n162\nSU8\n124\u00b114\n3.8\n100\nestimated from Monte Carlo to be RMC = 1.4 \u00b1 0.1. The second normalization factor, Rb-jetpair, takes\ninto account the ef\ufb01ciency of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events to pass the requirement on the number of b-jet pairs;\nit is de\ufb01ned as the ratio of resimulated events before and after the b-jet pair selection in a normalization\nregion, 80 \u2264Emiss\nT\n\u2264120 GeV, and found to have the value Rb-jetpair = 1.4\u00b10.1(stat)\u00b10.1(syst).\nPresence of SUSY\nA possible SUSY signal could have an effect on the background estimation in two\nways: 1) by satisfying the kinematic constraints in Eq. 3 and therefore enter the control sample and 2) by\nentering the normalization region giving a systematic contribution to the scale factor Rb-jetpair. In Fig. 8\nthe estimated t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd background is shown with and without the contamination of a SUSY signal\n(SU3) while Tab. 8 gives the estimated number of t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd events in the presence of different SUSY\nsignals.\n (GeV)\nT\nMissing E\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n / 50 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n1\n10\n2\n10\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n1\n10\n2\n10\nATLAS\n\u03bd\n l\n\u03bd\n l\nb\nb\n\u2192\ntt\nSU3 signal\nEstimate\nover-estimate due to SU3\nq\nq\n\u03bd\n l\nb\nb\n\u2192\nt\nover-estimate due to t\n (GeV)\neff\nM\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / 200 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n1\n10\n2\n10\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n1\n10\n2\n10\nATLAS\n\u03bd\n l\n\u03bd\n l\nb\nb\n\u2192\ntt\nSU3 signal\nEstimate\nover-estimate due to SU3\nq\nq\n\u03bd\n l\nb\nb\n\u2192\nt\nover-estimate due to t\nFigure 8: The Emiss\nT\n(left) and Meff (right) distributions for the estimated and true t\u00aft \u2192b\u00afb\u2113\u03bd\u2113\u03bd contri-\nbution for the one-lepton SUSY search. Black points (red area) represent the estimation without (with)\nthe presence of a signal from SUSY (SU3).\nSystematic Uncertainties\nThe systematic uncertainties for this method are summarized in Tab. 9. The\nuncertainty from the replacement procedure is estimated by comparing number of resimulated events\nto the Monte Carlo prediction, see Fig. 7(right). The uncertainty of RMC is estimated by comparing\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1537\n\nTable 9: Breakdown of systematic uncertainties in the kinematic reconstruction method.\nSource\nContribution [%]\nReplacement\n10\nRMC\n10\nJet Energy Scale\n9\nRb-jetpair stat.\n9\nRb-jetpair syst.\n8\nBackground Subtraction\n3\nJet Energy Resolution\n1\nEmiss\nT\nscale\n1\nTotal\n21\nMC@NLO and ALPGEN. The statistical uncertainty of Rb-jetpair is calculated using binomial errors.\nThe systematic uncertainty of this factor takes into account the difference in the shapes between E miss\nT\ndistribution of the resimulated samples with and without applying the kinematical constraints in Eq. 3.\nThe uncertainty due to background subtraction is dominated by the presence of t\u00aft \u2192b\u00afbq \u00afq\u2113\u03bd events\nin the control sample. The systematic effects resulting from uncertainties in the lepton identi\ufb01cation\nef\ufb01ciency, the trigger ef\ufb01ciencies and the energy scale and resolution are expected to be much smaller.\n2.3.4\nDileptonic top with one lepton missed: HT2\nIntroduction\nIn this section we describe a method, denoted the \u201cHT2 method\u201d, to estimate background\nfrom dileptonic t\u00aft production where one of the leptons is not identi\ufb01ed. It relies on the (near) indepen-\ndence of Emiss\nT\nand the variable HT2. This variable is de\ufb01ned as:\nHT2 \u2261\n4\n\u2211\ni=2\npjeti\nT + plepton\nT\n.\n(4)\nIn the HT2 method, the shape of the Emiss\nT\ndistribution is estimated from dileptonic t\u00aft events with low\nHT2. This distribution is then normalized to the number of events at large HT2, but with low missing ET\n, and can then be used to estimate the remaining backgrounds in the signal region of large HT2 and large\nEmiss\nT\n.\nFor this method to work, the shape of the Emiss\nT\ndistribution needs to be independent of HT2. Note\nthat in Equation 4, the leading jet pT was excluded from the sum in order to reduce the correlation with\nEmiss\nT\n. The correlation between the hightest-pT jet and Emiss\nT\nis likely to be due to simple kinematics, i.e.\nto \ufb01rst approximation, the rest of the event recoils against this leading jet. This is illustrated in Figure 9\nwhich shows the Emiss\nT\ndistribution (at Monte Carlo \u201ctruth level\u201d) in slices of leading and sub-leading jet\npT . The reduced dependence of the Emiss\nT\nshape on the jet pT in the second-leading jet case is apparent,\nand will be further diminished by detector resolution effects.\nTo further reduce the correlation between HT2 and Emiss\nT\n, the Emiss\nT\nsigni\ufb01cance was used. This is\nto remove the correlation which arises from the fact that the Emiss\nT\nresolution depends on \u2211ET, where\n\u2211ET is clearly related to HT2. A simple form of Emiss\nT\nsigni\ufb01cance was used here, de\ufb01ned as Emiss\nT\nsigni\ufb01cance = Emiss\nT\n/[0.49\u00b7\u221a\n\u2211ET].\nThe results shown here are from a data sample consisting of the sum of t\u00aft (semi-leptonic and dilep-\ntonic decay modes) plus W(l\u03bd)+jets (where l = e,\u00b5,\u03c4). The trigger used in this analysis was the logical\nOR of the 4j50 multi-jet, the e22i single electron and the mu20 single muon triggers [7].\nA control sample de\ufb01ned by HT2 < 300 GeV was used to estimate the shape of the Emiss\nT\nsigni\ufb01cance.\nThe assumption is that this shape is independent of HT2 so it can be used to predict the shape of the E miss\nT\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1538\n\nTruth Missing E_T [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\npt1 = [0,100] GeV \npt1 = [200,300] GeV \npt1 = [400,500] GeV \nATLAS\nTruth Missing E_T [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\nArbitrary units\n-4\n10\n-3\n10\n-2\n10\n-1\n10\npt2 = [0,100] GeV \npt2 = [200,300] GeV \npt2 = [400,500] GeV \nATLAS\nFigure 9: Missing ET distribution in \u201clepton+jet\u201d t\u00aft events with MT > 100 GeV at Monte Carlo \u201ctruth\u201d\nlevel. Left: as a function of truth leading-jet pT . Right: as a function of truth second-leading jet pT .\nTable 10: Predicted and actual background levels as a function of Emiss\nT\nsigni\ufb01cance cut for an integrated\nluminosity of 1 fb\u22121 in the HT2 analysis. A rough equivalent Emiss\nT\ncut is listed, but the Emiss\nT\ncut is not\nsharp.\nEmiss\nT\nsig. cut\nRough equivalent Emiss\nT\ncut [GeV]\nPredicted BG\nActual BG\n14\n180\n57.3 \u00b1 5.5\n60.6 \u00b1 3.2\n16\n200\n34.8 \u00b1 4.5\n39.2 \u00b1 2.6\n18\n220\n19.1 \u00b1 3.1\n23.6 \u00b1 2.0\n20\n240\n10.1 \u00b1 2.1\n15.1 \u00b1 1.5\n22\n260\n6.2 \u00b1 1.8\n9.8 \u00b1 1.2\n24\n280\n3.8 \u00b1 1.5\n6.2 \u00b1 0.9\n26\n300\n1.3 \u00b1 0.7\n3.5 \u00b1 0.6\nsigni\ufb01cance in the signal \u201cband\u201d de\ufb01ned by HT2 > 300 GeV. The normalization of the prediction in the\nsignal band was obtainined by the number of events with HT2 > 300 GeV, but at low Emiss\nT\n, speci\ufb01cally\n8 300 GeV, which corresponds\napproximately to a cut on the effective mass of Meff > 600 GeV.\nThe ratio of observed to predicted backgrounds for a Emiss\nT\nsigni\ufb01cance cut of 14 is 1.06\u00b10.12; while\nthe ratio is consistent with unity, we take the uncertainty on the ratio (12%) as a systematic uncertainty\ndue to possible correlations between HT2 and Emiss\nT\nsigni\ufb01cance. Monte Carlo samples with larger\nnumbers of events would provide one possible way to further study the potential for correlations.\nThe distribution of the \u201corthogonal\u201d variable, namely HT2, was predicted in a similar way. The HT2\ndistribution was measured in a control region de\ufb01ned by 8 < Emiss\nT\nsigni\ufb01cance < 14. This distribution\nwas then normalized to the number of events at large Emiss\nT\nsigni\ufb01cance and low HT2, speci\ufb01cally, Emiss\nT\nsigni\ufb01cance > 14, and 150 GeV < HT2 < 300 GeV. The results are shown in Fig. 10 (right).\nThe near independence of HT2 and Emiss\nT\nsigni\ufb01cance should provide an important tool in under-\nstanding jet energy and Emiss\nT\nperformance in the complex events that make up the background to SUSY\nsearches. After all the SUSY selection cuts have been applied, the jet energy performance can be studied\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1539\n\nMissing Et significance\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEvents/1 fb-1\n-1\n10\n1\n10\n2\n10\nHT2 < 300 GeV. Rescaled \nHT2 > 300 GeV\nATLAS\nHT2 [GeV]\n0\n200\n400\n600\n800\n1000\n1200\n1400\nEvents/1 fb-1/50 GeV\n-1\n10\n1\n10\nMETsig=[8,14]. Rescaled \nMETsig > 14 \nATLAS\nFigure 10: Left: Points: Predicted Emiss\nT\nsigni\ufb01cance distribution in a t\u00aft plus W + jets sample. His-\ntogram: actual Emiss\nT\nsigni\ufb01cance distribution. Right: Predicted HT2 distribution in the same sample.\nHistogram: actual HT2 distribution.\nTable 11: Predicted and actual background levels (for 1 fb\u22121, HT2 method) for Emiss\nT\nsigni\ufb01cance > 14\nas a function of systematic effects applied to the reconstructed objects.\nModi\ufb01cation\nPredicted BG\nActual BG\nActual/predicted\nBaseline\n57.3 \u00b1 5.5\n60.6 \u00b1 3.2\n1.05 \u00b1 0.12\nEnergy scaled up\n64.1 \u00b1 5.5\n79.3 \u00b1 3.7\n1.24 \u00b1 0.12\nEnergy scaled down\n45.5 \u00b1 4.5\n47.3 \u00b1 2.7\n1.04 \u00b1 0.12\nJet resolution smearing\n55.5 \u00b1 5.1\n65.3 \u00b1 3.4\n1.18 \u00b1 0.12\nby looking at the HT2 distribution for low Emiss\nT\nevents; conversely, the Emiss\nT\ndistribution can be studied\nby selecting events with low HT2. Events in the tails of these distributions can be examined for signs of\ndetector problems.\nSystematic uncertainties due to detector miscalibrations\nThe results of systematic uncertainties due\nto detector performance are summarized in Table 11. The energy scale variations change the background\nlevel by about 30% while the worsening jet energy resolution results in about a 10% increase in back-\nground. However the predictions tend to change in the same direction as the actual backgrounds, and\ngenerally continue to provide reasonable determinations. We assign a 20% systematic uncertainty due to\ndetector effects.\nSystematic uncertainties due to event generation parameters\nThe systematic uncertainties in the\nmethod due to changes in Monte Carlo event generation parameters were studied with ALPGEN. The\nparton pT cut in ALPGEN was changed from 40 to 15 GeV and the renormalization scale was reduced\nby a factor of 2. The results of the studies are summarized in Table 12. We assign a 20% systematic\nuncertainty due to event generation uncertainties.\nBackground estimation in the presence of SUSY\nIn this section, we repeat the background estimation\nin the presence of SUSY signal. Figure 11 (left) shows the Emiss\nT\nsigni\ufb01cance distributions for the true\nbackground, true signal, and the estimated background, as well as the observed distribution of signal plus\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1540\n\nTable 12: Predicted and actual background levels (for 1 fb\u22121, HT2 method) for Emiss\nT\nsigni\ufb01cance > 14\nas a function of changes in the Monte Carlo generation parameters.\nModi\ufb01cation\nt\u00aft\nW +jets\nPredicted BG\nActual BG\nActual/predicted\nPT40, scale 1.0\nPT40, scale 0.5\n73.3 \u00b1 5.8\n63.9 \u00b1 3.2\n0.87 \u00b1 0.11\nPT40, scale 0.5\nPT40, scale 0.5\n133.8 \u00b1 7.2\n109.2 \u00b1 3.6\n0.82 \u00b1 0.05\nPT15, scale 1.0\nPT40, scale 0.5\n91.1 \u00b1 12.6\n72.5 \u00b1 6.0\n0.80 \u00b1 0.13\nMissing Et significance\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEvents/1 fb-1\n1\n10\n2\n10\nobserved ttbar+Wjets+SUSY \ntrue SUSY \ntrue ttbar+Wjets \nestimated ttbar+Wjets \nATLAS\nMissing Et significance\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nEvents/1 fb-1\n0\n5\n10\n15\n20\n25\ntrue SUSY \nestimated SUSY \nATLAS\nFigure 11: Left: Histogram: observed Emiss\nT\nsigni\ufb01cance distribution for the sum of t\u00aft plus W + jets\nbackground plus SUSY signal. Open circles: SUSY signal. Blue triangles: true t\u00aft plus W +jets back-\nground. Black \ufb01lled circles: estimated background. The SUSY signal shown here is the \u201c1 TeV SUSY\u201d\npoint (see text). Right: Open circles: true SUSY signal as a function of Emiss\nT\nsigni\ufb01cance. Black: es-\ntimated SUSY yield, obtained from the difference of the observed Emiss\nT\nsigni\ufb01cance distribution minus\nthe estimated background distribution.\nbackground. The SUSY signal here is the so-called \u201c1 TeV SUSY\u201d point (m0 = m 1\n2 = 400 GeV, tan\u03b2 =\n10, A=0, \u00b5 > 0).\nBecause of the signal contamination in the control region, the background level is overestimated,\nleading to an underestimation in the excess of signal over background. Nevertheless, it is clear that by\ncutting harder on Emiss\nT\nsigni\ufb01cance, for example, the signal can still be clearly seen over the estimated\nbackground. A comparison of the estimated signal yield to the true signal is shown in Figure 11 (right).\nThe results for all the tested SUSY points are summarized in Table 13.\n2.3.5\nTop background estimation with top redecay simulation\nIntroduction\nIt is possible to isolate a pure biased sample of fully-leptonic t\u00aft events by selecting low\nEmiss\nT\n(to reduce SUSY signal) opposite sign dilepton events where one and only one pair of invariant\nmass combinations m\u2113j between the two leptons and two hardest jets (b jets if tagging available) gives\nvalues below the expected endpoint from t \u2192Wb \u2192\u2113\u03bdb decays: mmax\n\u2113j\n=\nq\nm2t \u2212m2\nW (neglecting mb).\nA possible use of such a sample is to estimate the background of fully-leptonic t\u00aft events to SUSY\nsearches. One can reconstruct the kinematics of the decaying particles (W\u2019s or top quarks), remove\ntheir inferred decay products from the reconstructed event (including the event Emiss\nT\n), redecay the re-\nconstructed W\u2019s or top quarks using an event generator (e.g. PYTHIA) and then merge the simulated\nre-decay products back into the parent (\u2018seed\u2019) event. By redecaying particles earlier in the decay chain\n(i.e. the top rather than the W) the kinematic bias obtained from the event selection can be minimised.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1541\n\nTable 13: True and estimated background and signal, using the HT2 method, when the background\nestimation is performed in the presence of SUSY signal. The numbers are for an integrated luminosity\nof 1 fb\u22121 except for the SU4 point where 100 pb\u22121 is used.\nSUSY\nEmiss\nT\nsig.\nTrue\nEstimated\npoint\ncut\nTrue BG\nEst. BG\nTrue signal\nEst. signal\nS/\n\u221a\nB\nS/\n\u221a\nB\nSU1\n16\n39.2 \u00b1 2.6\n100.5 \u00b1 10.4\n219.7 \u00b1 8.7\n158.4 \u00b1 13.8\n35.1\n15.8\n20\n15.1 \u00b1 1.5\n53.1 \u00b1 7.8\n167.0 \u00b1 7.6\n128.9 \u00b1 11.0\n43.0\n17.7\n24\n6.2 \u00b1 0.92\n33.1 \u00b1 6.5\n120.8 \u00b1 6.4\n93.8 \u00b1 9.2\n48.6\n16.3\nSU2\n14\n60.6 \u00b1 3.2\n69.1 \u00b1 6.4\n30.4 \u00b1 2.3\n21.9 \u00b1 7.5\n3.9\n2.6\n16\n39.2 \u00b1 2.6\n43.1 \u00b1 5.3\n24.0 \u00b1 2.1\n20.2 \u00b1 6.2\n3.8\n3.1\n18\n23.6 \u00b1 2.0\n24.1 \u00b1 3.7\n18.3 \u00b1 1.8\n17.9 \u00b1 4.6\n3.8\n3.6\n20\n15.1 \u00b1 1.5\n13.9 \u00b1 2.7\n13.5 \u00b1 1.6\n14.7 \u00b1 3.5\n3.5\n3.9\nSU3\n16\n39.2 \u00b1 2.6\n198.1 \u00b1 22.5\n328.1 \u00b1 14.9\n169.2 \u00b1 27.2\n52.4\n12.0\n20\n15.1 \u00b1 1.5\n119.9 \u00b1 18.5\n228.9 \u00b1 12.5\n124.1 \u00b1 22.4\n59.0\n11.3\n24\n6.2 \u00b1 0.92\n62.9 \u00b1 13.7\n144.7 \u00b1 9.9\n88.0 \u00b1 16.9\n58.3\n11.1\nSU4\n16\n3.92 \u00b1 0.26\n120.7 \u00b1 8.7\n76.4 \u00b1 4.0\n-40.4 \u00b1 9.6\n38.6\n-3.7\n20\n1.51 \u00b1 0.15\n47.4 \u00b1 5.5\n37.4 \u00b1 2.8\n-8.5 \u00b1 6.1\n30.4\n-1.2\n24\n0.62 \u00b1 0.09\n17.8 \u00b1 3.3\n18.8 \u00b1 2.0\n1.6 \u00b1 3.9\n23.9\n0.4\nSU6\n16\n39.2 \u00b1 2.6\n71.5 \u00b1 7.2\n140.5 \u00b1 5.3\n108.2 \u00b1 9.3\n22.4\n12.8\n20\n15.1 \u00b1 1.5\n36.5 \u00b1 5.0\n108.8 \u00b1 4.7\n87.4 \u00b1 7.0\n28.0\n14.5\n24\n6.2 \u00b1 0.92\n25.1 \u00b1 4.3\n79.3 \u00b1 4.0\n60.3 \u00b1 6.0\n31.9\n12.0\n1 TeV\n16\n39.2 \u00b1 2.6\n61.1 \u00b1 6.8\n155.0 \u00b1 5.7\n133.1 \u00b1 9.2\n24.7\n17.0\n20\n15.1 \u00b1 1.5\n27.6 \u00b1 4.4\n118.1 \u00b1 5.0\n105.6 \u00b1 6.8\n30.4\n20.1\n24\n6.2 \u00b1 0.92\n15.6 \u00b1 3.5\n84.5 \u00b1 4.2\n75.1 \u00b1 5.6\n34.0\n19.0\nThis technique has a number of advantages over conventional Monte Carlo techniques. In particular the\nevent generator is used purely for modelling relatively well-understood decay and hadronisation pro-\ncesses \u2013 initially poorly understood aspects of process generation, such as parton distributions and the\nunderlying event model, are effectively obtained from the data. In principle this technique is applicable\nalso to other background processes such as Z \u2192\u03c4+\u03c4\u2212, which could be modelled by replacing identi\ufb01ed\nelectrons or muons in Z \u2192\u2113+\u2113\u2212control sample events with redecayed taus.\nIt should be noted that this technique is at best an approximation, assuming as it does the factorisation\nof each t\u00aft event into two independent tops, and hence neglecting effects such as colour connection and\nspin correlations between the tops and other partons in the event. It is therefore unlikely to be competitive\nwith a detailed Monte Carlo study using a fully tuned generator and validated parton distribution func-\ntions. In the early days of data-taking however it potentially provides a route to a rapid direct estimate of\nt\u00aft background from data complementary to, and independent from, more conventional estimates.\nSeed event selection\nSeed events were selected from the \u2018data\u2019 with cuts designed to maximise the\nnumber of fully leptonic t\u00aft (\u20182\u2113-t\u00aft\u2019) events while minimising the number of Standard Model backgrounds\nor SUSY signal events. Events were required to pass the j45 xE50 jet + Emiss\nT\ntrigger [7]. Single\nand dilepton triggers were not included in this study, but are planned to be added in future analyses.\nSubsequently, the following criteria were applied: Njet \u22652, pT(jet2) > 20 GeV, two Opposite Sign (OS)\nisolated leptons should be present, pT(\u21132) > 10 GeV, if the two leptons are of the same \ufb02avour |m\u2113\u2113\u2212mZ|\n> 15 GeV and m\u2113\u2113> 10 GeV is required, |m\u03c4\u03c4 \u2212mZ| > 15 GeV, where m\u03c4\u03c4 is calculated assuming the\nneutrinos travel parallel to their parents, and Emiss\nT\n< 1\n2(pT(\u21131)+ pT(\u21132)). The upper limit on Emiss\nT\nas\na function of lepton pT rejects SUSY signal events. For the purposes of this early-data study b-tagging\nwas assumed to be either not available or not well-understood.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1542\n\n (GeV)\nlj\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n / 10 GeV\n\u22121\nNo. Entries / 1 fb\n0\n200\n400\n600\n800\n1000\n\u03bd\n l\n\u03bd\n bb l\n\u2192\n tt\n\u03bd\n bb qq l\n\u2192\n tt\nWW/WZ/ZZ/single\u2212top\n 10\n\u00d7\nSU3 signal \nEstimate\n (GeV)\nlj\nm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n / 10 GeV\n\u22121\nNo. Entries / 1 fb\n0\n200\n400\n600\n800\n1000\nATLAS\nFigure 12:\nDistributions of m\u2113j values for various different Standard Model backgrounds and SUSY\nsignal. The histograms show distributions of \u2018data\u2019 events selected with the 2\u2113-t\u00aft selection. The data-\npoints show the equivalent distribution estimated with redecay simulation, normalised to the peak.\nKinematic Reconstruction and Redecay Simulation\nThe m\u2113j distribution of selected events (the\nhistogram in Figure 12) contains a prominent edge at the expected position mmax\n\u2113j\n= 155.4 GeV (mt =\n175 GeV). Events were further selected in which one and only one of the two possible pairs of \u2113j com-\nbinations obtained from the two leptons and two hardest jets gave m\u2113j values which were both less than\nmmax\n\u2113j .\nFor 2\u2113-t\u00aft signal events the two (b) jets, two leptons and Emiss\nT\ncomponents satisfy the constraints of\nEq. 3 given in section 2.3.3. These constraints, assuming massless neutrinos, leptons and jets, may be\nsolved for the 8 unknown 4-momentum components of the neutrinos. The constraints together give a\nquartic equation which can be solved with standard analytical techniques. If no solution was obtained\nthen to maximise statistics the real part of the least imaginary solution was taken. If multiple solutions\nwere obtained the solution with the smallest mean |pz| of the reconstructed top was used.\nThis selection results in 2207 dileptonic t\u00aft events for 1 fb\u22121. The contamination by other Standard\nModel processes and SUSY signal events was 912 events, dominated by semileptonic t\u00aft events, as shown\nin Figure 12. The SUSY contamination in the sample is small, due to the tight selection cuts.\nFour-vectors of the two reconstructed top quarks from each event were passed to a modi\ufb01ed version\nof PYTHIA 6.4 [10]. 1000 redecayed tops were produced from each reconstructed seed top, with each W\nforced to decay to e, \u00b5 or \u03c4. This \u2018recycling\u2019 of seed events increases the statistics of decay resimulated\nevents for the \ufb01nal Emiss\nT\nestimation process but leads to correlations between resimulated events derived\nfrom the same seed event. These correlations were taken into account in the \ufb01nal uncertainties quoted\nbelow. Decay products were passed to the ATLAS fast simulation program, and then merged back into\ntheir parent seed events.\nAs a cross-check of the estimation procedure redecayed events were passed through the same selec-\ntion as their parent seed events and the distribution of m\u2113j constructed and normalised to the seed m\u2113j\ndistribution. This is shown in Fig. 12 and indicates good agreement below mmax\n\u2113j .\nUse in one-lepton search background estimate\nDecay resimulated events were subjected to the stan-\ndard one-lepton SUSY search selection described in section 2.1, with one modi\ufb01cation: MT(\u2113,Emiss\nT\n) >\n150 GeV.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1543\n\n (GeV)\nmiss\nT\nE\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-1\nNo. Events / 1 fb\n1\n10\n\u03bd\n l\n\u03bd\n bb l\n\u2192\n tt\n\u03bd\n bb qq l\n\u2192\n tt\nZ+jets\nW+jets\nWW/WZ/ZZ/tW/tg/tq\nSU3 signal\nEstimate\nATLAS\n (GeV)\neff\nM\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nNo. Events / 1 fb\n1\n10\n\u03bd\n l\n\u03bd\n bb l\n\u2192\n tt\n\u03bd\n bb qq l\n\u2192\n tt\nZ+jets\nW+jets\nWW/WZ/ZZ/single-top\nSU3 signal\nEstimate\nATLAS\nFigure 13:\nEmiss\nT\n(left) and Meff (right) distributions of events passing the basic one-lepton SUSY\nselection cuts described in the text. Note that Z +jet and W +jet backgrounds are under-represented in\nthese plots for Emiss\nT\n< 80 GeV or Meff < 350 GeV due to \ufb01lter requirements applied to the respective\nMonte Carlo samples.\nThe remaining background at high Emiss\nT\nfollowing such cuts is dominated by semi-leptonic t\u00aft events,\nand to a lesser extent leptonicW +jets, Z+jets, single-top and di-boson events. For all these backgrounds\none expects primarily a Jacobian peak in the event MT(\u2113,Emiss\nT\n) distribution near MW (MZ for Z +jets).\nThis 1\u2113-Jacobian background was estimated with the Emiss\nT\ndistribution of events selected with the same\ncuts, with the exception of the MT(\u2113,Emiss\nT\n) cut, which was reversed to require MT(\u2113,Emiss\nT\n) < 100 GeV.\nThe 1\u2113-Jacobian and the 2\u2113-t\u00aft background estimates were compared to \u2018data\u2019 events subjected to the\none-lepton selection criteria described above. The two estimates were simultaneously normalised to the\n\u2018data\u2019 Emiss\nT\ndistribution in two bins: 40 < Emiss\nT\n< 100 GeV and 100 < Emiss\nT\n< 140 GeV. The total (2\u2113-t\u00aft\n+ 1\u2113-Jacobian) normalised estimate is plotted in Fig. 13(left) together with the \u2018data\u2019 Emiss\nT\ndistribution.\nFor Emiss\nT\n> 200 GeV the agreement between the estimate and the \u2018data\u2019 is good: 30.7 \u00b1 9.8 (30%)\nestimated, versus 39 \u2018observed\u2019.\nIn Fig. 13(right), the Meff distribution is shown, with the estimate normalised with the same factors\nas used in Fig. 13(left). The semi-leptonic t\u00aft forms a larger fraction of the background at large Meff\ncompared to at large Emiss\nT\nbecause it produces a larger number of jets than fully-leptonic t\u00aft.\nSUSY contamination\nThe shape of the estimated distribution is effectively insensitive to the presence\nof SUSY signal, primarily due to the low Emiss\nT\nrequirement in the 2\u2113-t\u00aft selection.\nHowever, there may be SUSY signal in the normalisation region. The bias in the estimate will be\nproportional to the amount of SUSY in the normalization region, which is largest for the samples with\nthe highest SUSY cross-section: SU3 and SU4. The effect of admixture of SU3 or SU4 signal events is\nshown in Table 14. In case of SU3, the background estimate is 60% higher, in case of SU4 as large as a\nfactor 15. For both samples, however, the excess of signal events is still signi\ufb01cant.\nIn principle the contamination effect could be reduced by normalization to more signal-free re-\ngions. The 2\u2113-t\u00aft and 1\u2113-Jacobian estimates could be normalized for example to the tail and peak of\nthe MT(\u2113,Emiss\nT\n) distribution at low Emiss\nT\n.\n2.3.6\nCombined \ufb01t method\nThe \ufb01t-based method for measuring the background, as described in this section, aims to improve upon\nthe plain MT sideband subtraction method for the one-lepton SUSY search mode. By analysing data in\na L-shaped region at both low-Emiss\nT\nin the full MT range and at low MT in the full Emiss\nT\nrange, and\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1544\n\nTable 14: Estimated and true background with the redecay method, in case of no SUSY signal, or\npresence of SU3 or SU4 SUSY signals. For the latter, also the amount of observed signal plus background\nevents is shown, proving that although the background is overestimated, the excess is still present.\nSample\nEstimated BG\nTrue BG\nObserved signal + BG\nNo SUSY\n30.7\u00b19.8\n39\n39\nSU3\n50.8\u00b113.6\n39\n392\nSU4\n456\u00b1102\n39\n1230\nperforming a two-dimensional extrapolation into the SUSY signal region we hope to enhance the back-\nground estimation. In a \ufb01t, correlations between Emiss\nT\nand MT can be taken into account. Furthermore,\nan explicit assumption can be put in that there is a \ufb01nite SUSY contamination in the control sample.\nFor our purposes, we de\ufb01ne in this analysis a sideband (SB) region and a SUSY signal (SIG) region.\nFor both regions, we apply the standard SUSY one-lepton selection cuts de\ufb01ned in section 2.1, with the\nexception of the cut on MT. The SB region is de\ufb01ned by the following additional cut: Emiss\nT\n< 200 GeV\nor MT < 150 GeV. In this analysis, the SIG region is de\ufb01ned by: Emiss\nT\n> 200 GeV and MT > 150 GeV.\nThis classi\ufb01cation assumes that the mass scale of SUSY is much higher than 200 GeV, which is true for\nall SUSY points considered in this note except SU4.\nThe analysis described here has been applied to electron + jets events only, but we expect the muon\n+ jets analysis to be completely analogous.\nThe main Standard Model backgrounds we expect are single-leptonic t\u00aft decays, double-leptonic\nt\u00aft decays, and W + jets events. Other backgrounds, such as Z + jets, diboson production or single top\nare negligible for 1 fb\u22121. The trigger used was an OR of the e22i single electron trigger, and the 4j50\nmulti-jet trigger [7].\nShape of the backgrounds\nWe will try to \ufb01t the contributions of the backgrounds in three observables:\nMT, Emiss\nT\nand mtop. Here mtop is the invariant mass of the three jets in the event with the largest vector-\nsummed pT [11].\nWe construct probability density functions (p.d.f.\u2019s) that model the major contributing processes in\nthe three observables after the event selection. We have done this both with and without explicitly taking\ninto account correlations between the three observables. Most of these correlations are in any case\nconsistent with zero.\nFigure 14 shows the distribution of the three observables for each type of background we consider, as\nwell as for one SUSY signal sample (SU3). The empirical model that we use to describe each background\ntype is overlaid on the data. This comparison of shapes demonstrates that there is suf\ufb01cient information\nin these three observables to be able to measure each of them in a combined \ufb01t.\nWe perform the procedure of constructing an empirical model from Monte Carlo for multiple SUSY\ndata points. A striking feature of a comparison of Emiss\nT\nand MT distributions of these SUSY points in\nthe SB region is that, with the exception of lower mass SUSY point SU4, they are all quite similar in\nshape. We can thus construct a model-independent \u2019Ansatz\u2019 shape to describe the SUSY contamination\nat low energy.\nTo validate this procedure, we perform \ufb01ts to a \u201cdata\u201d sample consisting of either background only,\nor background plus SU3 SUSY signal. The yields we \ufb01nd in a \ufb01t to 1 fb\u22121 are listed in Table 15 and are\nin agreement within errors with the truth values of the \ufb01tted event mix. If, in contrast, a SU3 SUSY signal\nwould be present in data, but the \ufb01t would not allow for SUSY (see table), the \ufb01t would overestimate\ndileptonic t\u00aft and W +jets, and underestimate semileptonic t\u00aft . This is as expected, as the SUSY signal\nhas a long tail in MT, but no substantial peak in the top mass.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1545\n\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n20\n0\n60\n80\n100\n120\ntt -> bb lv qq\nATLAS\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n20\n0\n60\n80\n100\n120\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n0\n20\n0\n60\n80\n100\n120\ntt -> bb lv qq\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n0\n20\n0\n60\n80\n100\n120\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n50\n100\n150\n200\ntt -> bb lv qq\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n50\n100\n150\n200\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\ntt -> bb lv lv\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n-2\n0\n2\n6\n8\n10\n12\n1\ntt -> bb lv lv\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n-2\n0\n2\n6\n8\n10\n12\n1\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\ntt -> bb lv lv\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n5\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n0\n5\nW+jets\n [GeV]\nT\nmiss\nE\n100\n150\n200\n250\n300\n350\n00\n5\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n0\n5\n [GeV]\nT\nm\n0\n50\n100\n0\n5\n0\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\nW+jets\n [GeV]\nT\nm\n0\n50\n100\n0\n5\n0\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\nW+jets\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n1 00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n [GeV]\nT\nmiss\nE\n10\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\nSU3\n [GeV]\nT\nmiss\nE\n10\n150\n200\n250\n300\n350\n00\n50\n500\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\nSU3\n [GeV]\nT\nm\n0\n50\n100\n150\n200\n250\n300\n350\n00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n0\n5\nSU3\n [GeV]\ntop\nm\n0\n200\n00\n600\n800\n1000\n1200\n00\n-1\nEvents / 1fb\n0\n5\n10\n15\n20\n25\n30\n35\n0\n5\nFigure 14: Distributions in missing ET (left), MT (middle) and mtop (right) of single lepton t\u00aft (top row),\ndouble lepton t\u00aft (second row), W + jet events (third row) and SUSY SU3 (last row). Each distribution\nis overlaid with a projection of the three-dimensional model that is \ufb01tted to that sample.\nThe same table also lists the yields obtained from a \ufb01t in which all components are taken as a simple\nuncorrelated product of three one-dimensional p.d.f.\u2019s. The yields and their uncertainties are very similar\nto those from the \ufb01t with models that include correlations and indicates that the effect of correlations in\nthe description of the background components is minor.\nFitting the data\nThe \ufb01t with \ufb01xed shapes relies on simulated events to determine the shapes of the\nvarious background components, while all yields are \ufb01tted from the data. The next step is to release as\nmany of the shape parameters in the \ufb01t to the data; in total there are 15 of these parameters. In the limit\nthat all parameters can be \ufb02oated, with the exception of the SUSY ansatz shape, the method becomes\nalmost independent on simulation input and fully data driven. It turns out that on a 1 fb\u22121 sample we can\n\ufb02oat all but two of the W +jets and 1-lepton t\u00aft shape parameters. These two are the fraction of events\nthat give the correct top quark mass in mtop for single lepton t\u00aft and the fraction of events with a correctly\nconstructed W boson in MT in single lepton t\u00aft .\nFloating the 2-lepton t\u00aft shape parameters in addition causes the \ufb01t to become unstable because the\nshapes of the dilepton component and that of the SUSY ansatz model are very similar. We are currently\ninvestigating the possibility of introducing additional constraints on the shape of the di-lepton t \u00aft events\nin order to solve this.\nThe result of the 1 fb\u22121 \ufb01t with \ufb02oating parameters is shown in Figure 15.\nThe \ufb01nal step in the analysis is to extrapolate the yields of the standard model background compo-\nnents from the sideband region to the signal region. Table 16 shows the yields from the combined \ufb01t with\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1546\n\nTable 15: Yields from the combined \ufb01t with \ufb01xed shapes for the various modeled physics processes.\nThe leftmost column lists the yield \ufb01tted with models that include correlations in the model structure.\nThe middle column shows these yields for models in which correlation terms have been disabled. The\nrightmost column gives the true yields in the \ufb01tted event mix.\nComponent\nFitted Yield\nFitted Yield w/o correlations\nTrue Yield\nno SUSY in data, no SUSY component in \ufb01t\nW +jets\n186\u00b133\n200\u00b127\n173\n1-lepton t\u00aft\n507\u00b132\n482\u00b132\n502\n2-lepton t\u00aft\n53\u00b113\n55\u00b116\n70\nSUSY\n-\n-\n0\nno SUSY in data, SUSY component in \ufb01t\nW +jets\n185\u00b133\n201\u00b127\n173\n1-lepton t\u00aft\n507\u00b132\n482\u00b132\n502\n2-lepton t\u00aft\n52\u00b115\n56\u00b116\n70\nSUSY\n4.4\u00b13.0\n\u22127.1\u00b116.0\n0\nSU3 in data, no SUSY component in \ufb01t\nW +jets\n292\u00b135\n261\u00b134\n173\n1-lepton t\u00aft\n386\u00b130\n356\u00b131\n502\n2-lepton t\u00aft\n338\u00b125\n389\u00b134\n70\nSUSY\n-\n-\n271\nSU3 in data, SUSY component in \ufb01t\nW +jets\n181\u00b140\n194\u00b135\n173\n1-lepton t\u00aft\n521\u00b136\n509\u00b135\n502\n2-lepton t\u00aft\n35\u00b123\n15\u00b130\n70\nSUSY\n280\u00b122\n293\u00b124\n271\n\ufb02oating shapes extrapolated to the signal region while propagating all (correlated) parameter uncertain-\nties; for comparison the same table also shows the results with shapes kept \ufb01xed. The \ufb01ts describe the\ndata within the statistical uncertainties.\nTable 16: Yields from the combined \ufb01t with either \ufb01xed or \ufb02oating shapes in the sideband region extrap-\nolated to the full parameter space, the truth yields in full parameter space, the extrapolated yields into\nthe signal region and the truth yields in the signal region.\nComponent\nExtrap. Yield in FULL\nTrue\nExtrap. Yield in SIG\nTrue\nShape Fixed\nShape Floating\nFULL\nShape Fixed\nShape Floating\nSIG\nW +jets\n205\u00b145\n227\u00b168\n173\n0.5\u00b10.4\n\u22121.2\u00b12.7\n2\n1-lepton t\u00aft\n476\u00b135\n485\u00b159\n502\n0.4\u00b10.2\n\u22121.1\u00b13.9\n0\n2-lepton t\u00aft\n62\u00b138\n17\u00b154\n70\n4.5\u00b12.9\n4.7\u00b17.9\n5\nSUSY SU3\n273\u00b133\n287\u00b138\n271\n92.7\u00b12.8\n95.6\u00b14.0\n91\nEffect of SUSY signal\nWhile table 16 shows the results of the \ufb01t for the various backgrounds and the\nSUSY signal in the case of the SU3 sample, Table 17 shows results, for \ufb01ts with \ufb02oating shapes, for other\nSUSY signal samples.\nAs has been noted earlier, SU4 is a special case. It is too close to the background for the Ansatz of\nthe shape to be valid, and it can not be \ufb01tted very well.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1547\n\n [GeV]\nT\nmiss\nE\n100 150 200 250 300 350 400 450 500\n / 13.3 GeV\n-1\nEvents / 1fb\n0\n20\n40\n60\n80\n100\n120\n140\ntt -> bb lv qq\ntt -> bb lv lv\nW+jets\nSU3\nATLAS\n [GeV]\nT\nmiss\nE\n100 150 200 250 300 350 400 450 500\n / 13.3 GeV\n-1\nEvents / 1fb\n0\n20\n40\n60\n80\n100\n120\n140\n [GeV]\nT\nm\n0\n50\n100 150 200 250 300 350 400\n / 13.3 GeV\n-1\nEvents / 1fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\ntt -> bb lv qq\ntt -> bb lv lv\nW+jets\nSU3\n [GeV]\nT\nm\n0\n50\n100 150 200 250 300 350 400\n / 13.3 GeV\n-1\nEvents / 1fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n [GeV]\ntop\nm\n0\n200 400 600 800 1000 1200 1400\n / 50.0 GeV\n-1\nEvents / 1fb\n0\n50\n100\n150\n200\n250\ntt -> bb lv qq\ntt -> bb lv lv\nW+jets\nSU3\n [GeV]\ntop\nm\n0\n200 400 600 800 1000 1200 1400\n / 50.0 GeV\n-1\nEvents / 1fb\n0\n50\n100\n150\n200\n250\nFigure 15: Distribution of missing ET (left), MT (center) and mtop (right) of a 1 fb\u22121 mix of t\u00aft , W +\njets standard model events and SUSY SU3 events overlaid with projections of the combined model on\nthese observables that was \ufb01tted to this mix of events with \ufb02oating yield parameters and \ufb02oating shaped\nparameters. For each projection the contributions of the 1-lepton t\u00aft ttbar contribution (dark blue), 2-\nlepton t\u00aft ttbar contribution (light blue), W +jet contribution (red) and ansatz SUSY constribution (black)\nare shown.\nTable 17: Yields from the combined \ufb01t with \ufb02oating shapes in the sideband region extrapolated to the full\nparameter space, the truth yields in full parameter space, the extrapolated yields into the signal region\nand the truth yields in the signal region, for various SUSY samples.\nComponent\nExtrap. Yield in FULL\nTrue in FULL\nExtrapolated Yield in SIG\nTrue in SIG\nSU1\nW +jets\n215\u00b156\n173\n1.8\u00b12.0\n2\n1-lepton t\u00aft\n486\u00b154\n502\n0.6\u00b10.6\n0\n2-lepton t\u00aft\n19\u00b135\n70\n0.5\u00b11.7\n5\nSUSY SU1\n154\u00b130\n129\n50.1\u00b12.6\n46\nSU2\nW +jets\n226\u00b151\n173\n1.3\u00b11.0\n2\n1-lepton t\u00aft\n452\u00b149\n502\n0.7\u00b10.5\n0\n2-lepton t\u00aft\n81\u00b132\n70\n8.0\u00b15.0\n5\nSUSY SU2\n0\u00b110\n14\n1.0\u00b16.1\n4\nSU6\nW +jets\n215\u00b154\n173\n0.5\u00b10.8\n2\n1-lepton t\u00aft\n469\u00b152\n502\n0.2\u00b10.6\n0\n2-lepton t\u00aft\n29\u00b134\n70\n2.6\u00b12.7\n5\nSUSY SU6\n117\u00b129\n86\n38.8\u00b12.5\n35\nSU8\nW +jets\n239\u00b153\n173\n2.5\u00b12.4\n2\n1-lepton t\u00aft\n485\u00b151\n502\n1.0\u00b11.2\n0\n2-lepton t\u00aft\n66\u00b145\n70\n15.1\u00b112.0\n5\nSUSY SU8\n34\u00b126\n79\n34.5\u00b113.0\n46\nSystematics\nTable 18 summarizes the results of a series of systematic studies. These studies are quan-\nti\ufb01ed in terms of relative variations of the measured SUSY cross-section, which we de\ufb01ne as the counted\nnumber of events in the data in the SIG region minus the \ufb01tted and extrapolated number of SM model\nevents expected in that same region, and divided by the ef\ufb01ciency for the selection of SUSY events,\nincluding the SIG region cuts, as measured from a pure sample of simulated SU3 SUSY events.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1548\n\nThe second column of Table 18 lists the relative variation under the in\ufb02uence of each systematic\nvariation if no extrapolation is applied in the \ufb01t and the analysis is performed without the SIG region cut.\nThis column thus quanti\ufb01es the effect on the shape \ufb01t stability only. The third columns shows the effect\nof each systematic study on the \ufb01tted yield in the signal region using extrapolation. Most effects are here\nof the order of 5-7%. The uncertainties due to Monte Carlo statistics are explicitly listed in the table.\nTable 18: List of studied systematic uncertainties for the combined-\ufb01t method.\nSystematic variation\nw/o extrapolation \u00b1 MC-error [%]\nin SIG \u00b1 MC-error [%]\nJet energy scale\n1.9\u00b10.7\n3.1\u00b11.1\nJet energy resolution\n3.7\u00b10.5\n0.5\u00b10.1\nElectron energy scale\n4.8\u00b10.6\n5.6\u00b11.4\nElectron energy resolution\n9.0\u00b11.2\n7.2\u00b11.4\nElectron identi\ufb01cation ef\ufb01ciency\n0.5\u00b10.2\n3.6\u00b12.3\nSoft Emiss\nT\nscale\n8.1\u00b11.8\n7.4\u00b13.4\n3\nNo-lepton search mode\n3.1\nSelection\nIn the no-lepton search mode, we veto all events with an identi\ufb01ed electron or muon with a pT of more\nthan 20 GeV. We demand at least 4 jets with |\u03b7| < 2.5 and pT > 50 GeV, one of which must have\npT > 100 GeV. The transverse sphericity ST should be larger than 0.2, and the missing transverse energy\nEmiss\nT\nshould be larger than 100 GeV and larger than 0.2 Meff , where Meff is the effective mass. We\nadd one more cut against the QCD background: the minimum value of the difference in azimuthal angle\nbetween the Emiss\nT\nvector and the three highest-pT jets should be larger than 0.2. This cut is futher\ndiscussed in a dedicated note on QCD background estimation [3].\n3.2\nBackgrounds in Monte Carlo\nFigure 16 shows the distributions of Emiss\nT\nand Meff after all the selections are applied.\n3.3\nData-driven estimation strategies\nIn this section we discuss data-driven estimation strategies for the no-lepton search mode. The strategies\nwe have studied are:\n1. estimation of Z (\u2192\u03bd \u00af\u03bd) plus jets from Z (\u2192\u2113+\u2113\u2212) plus jets, purely from data (replace method,\nsection 3.3.1);\n2. estimation of Z and W in an analogous way, but also helped by Monte Carlo (section 3.3.2);\n3. estimation of W and t\u00aft background from a one-lepton control sample derived by reversing one of\nthe selection cuts (on MT) (section 3.3.3);\n4. estimation of the cross-section of the t\u00aft \u2192b\u00afbq \u00afq\u2032\u03c4\u03bd process with hadronic tau decay (section 3.3.4).\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1549\n\nMissing ET [GeV]\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n\u22121\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nSU3\nSM BG\ntt\nW\nZ\nQCD\nsingle top\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / 200GeV\n\u22121\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nSU3\nSM BG\ntt\nW\nZ\nQCD\nsingle top\nFigure 16: The Emiss\nT\nand effective mass distributions of the SUSY signal and background processes\nfor the no-lepton mode with an integrated luminosity of 1 fb\u22121. The open circles show the SUSY signal\n(SU3 point). The shaded histogram shows the sum of all Standard Model backgrounds; different symbols\nshow the various components.\n3.3.1\nReplace method: Z \u2192\u03bd \u00af\u03bd from Z \u2192\u2113+\u2113\u2212\nIntroduction\nThe Z \u2192\u03bd \u00af\u03bd background is one of the main background process in the no-lepton channel.\nIn order to estimate and reproduce the number of expected background events, as well as the shape of\nthe Emiss\nT\nand Meff distributions, Z \u2192\u2113+\u2113\u2212events are selected, and the charged leptons are replaced\nby neutrinos. However, as the ratio of branching-ratios Br(Z \u2192\u2113+\u2113\u2212)/Br(Z \u2192\u03bd \u00af\u03bd) is small, statistical\nuncertainties will tend to be relatively large. Two solutions are proposed :\n1. Taking the distribution shape from Z \u2192\u2113+\u2113\u2212data but constraining it via a \ufb01t plus the assumption\nof a smooth evolution of the \ufb01tting parameters when relaxing the cuts. This is the method described\nin this section.\n2. Taking the distribution shape from Monte Carlo simulation as described in the next section ( Sec-\ntion 3.3.2).\nThe Monte Carlo method is more sensitive to generator-level and detector systematic uncertainties, but\ndoes not suffer from the larger statistical uncertainties, whereas the replace method precision is limited\nby the number of events in the control sample, but less sensitive to systematic uncertainties from the\ndetector. Both methods have to account for the fact that the detected charged lepton pairs will not cover\nthe full phase space of the neutrinos.\nControl Sample Selection\nThe control sample selection is identical to the no-lepton SUSY search\nselection, except that two electrons or two muons are required, and that the missing ET (Emiss\nT\n) is replaced\nby pT(\u2113+\u2113\u2212) \u2243pT(Z). Thus it is assumed that neutrinos are the main contribution to Emiss\nT\nwhen the Z\nboson decays into two neutrinos, such that Emiss\nT\nis roughly equivalent to pT(Z) for this physics process.\nThe Emiss\nT\nresolution of ATLAS is suf\ufb01cient for this to be a good approximation. In addition to pairs of\nisolated charged leptons, a sample composed of Z \u2192e\u00b1X is added, where X is a non-isolated electron\nor an electron-like object with very loose cuts. This additional sample is used to increase the statistics\nand measure the electron identi\ufb01cation ef\ufb01ciency via the \u201ctag-and-probe\u201d method. The goal of the tag-\nand-probe method is to select on one side a good electron (tag) and look at the other side to the nature\nof the object (the probe) which matches the constraint on the Z mass. Two cuts are added to reject the\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1550\n\nremaining backgrounds : 81 < MZ(\u2113+\u2113\u2212) < 101 GeV, and Missing ET < 30 GeV. After all cuts the\nnumber of selected events is summarized in Table 19. In particular, Table 19 shows the effect of an\nupper cut on Emiss\nT\nin order to reject t\u00aft background in the Z \u2192e\u00b1X channel. It has been veri\ufb01ed that\nthe ef\ufb01ciencies measured with the tag-and-probe method agree with ef\ufb01ciencies obtained directly from\nMonte Carlo, con\ufb01rming that X is indeed dominated by electrons rather than hadronic jets.\nTable 19: Number of selected Z \u2192\u2113+\u2113\u2212+ \u22654 jets events in 1 fb\u22121 in the replace-method analysis.\nProcess\nNo Emiss\nT\ncut\nEmiss\nT\n< 30 GeV\nZ \u2192e+e\u2212+n jets\n18.2\n14.1\nZ \u2192e\u00b1X +n jets\n25.6\n19.6\nZ \u2192\u00b5+\u00b5\u2212+n jets\n33.2\n26.1\nZ \u2192\u03c4+\u03c4\u2212+n jets\n1.6\n0.\nt\u00aft \u2192bb\u2113\u03bd\u2113\u03bd +n jets\n56.2\n0.3\nt\u00aft \u2192bb\u2113\u03bdqq+n jets\n506.6\n2.5\nLepton identi\ufb01cation and acceptance corrections\nA number of correlations must be applied in order\nto derive Z \u2192\u03bd \u00af\u03bd distributions from Z \u2192\u2113+\u2113\u2212: (1) a \ufb01ducial correction, since we cannot detect e and\n\u00b5 leptons beyond |\u03b7| = 2.5; (2) a kinematics correction for the additional cuts used to select Z \u2192\u2113+\u2113\u2212,\nincluding the Z invariant-mass window, the pT cut on the leptons, and the Emiss\nT\ncut; and (3) a correction\nfor the lepton identi\ufb01cation ef\ufb01ciency. The \ufb01rst two effects have to be computed from simulation whereas\nthe lepton identi\ufb01cation ef\ufb01ciency can be measured from collision data using the tag-and-probe method.\nAfter all corrections, the distribution can be summarized by the following formula:\nNZ\u2192\u03bd \u00af\u03bd(Emiss\nT\n) = NZ\u2192\u2113+\u2113\u2212(pT(\u2113+\u2113\u2212))\u00d7cKin(pT(Z))\u00d7cFidu(pT(Z))\u00d7 Br(Z \u2192\u03bd \u00af\u03bd)\nBr(Z \u2192\u2113+\u2113\u2212),\n(5)\nwhere NZ\u2192\u03bd \u00af\u03bd(Emiss\nT\n) is the corrected number of events per bin of missing ET, NZ\u2192\u2113+\u2113\u2212(pT(\u2113+\u2113\u2212)) is\nthe raw number of control sample events as a function of pT(Z), cKin and cFidu are the kinematic and\n\ufb01ducial corrections. The Emiss\nT\nand Meff distributions of Z \u2192e+e\u2212+e\u00b1X and Z \u2192\u00b5+\u00b5\u2212events after\nall corrections are compared to Z \u2192\u03bd \u00af\u03bd distributions in Figure 17.\nFor very high values of Emiss\nT\nand Meff , statistics is low. In order to present a smooth prediction of\nthe background, for example as a function of Meff , a \ufb01t of the shape has been performed. Of course, the\n\ufb01t is also affected by the low statistics in the tail, but by relaxing the jet pT and Emiss\nT\ncuts and observing\nhow the \ufb01t parameters evolve with the cuts, a smooth prediction can be made.\nSystematic uncertainties\nThe effects of various Monte Carlo generator and detector systematic uncer-\ntainties are summarized in Table 20. The main generator systematic uncertainty is due to the variation of\nthe renormalization scale and affects the acceptance correction, whereas the principal detector systematic\nuncertainty is related to the soft part of the missing transverse energy which is not taken into account\nwhen replacing neutrinos by charged leptons.\nSUSY contamination in the control sample\nDue to the tight control sample selection cuts, in partic-\nular Emiss\nT\n< 30 GeV, the SUSY contamination in the control sample in 1 fb\u22121 is negligible: 0.1 events\nfor SU1, 0.4 events for SU2, 0.9 events for SU3, and < 0.07 events for SU6.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1551\n\nMissing ET [GeV]\n0\n200\n400\n600\n800\n1000\n-\nEvents/1fb /25GeV\n-2\n10\n-1\n10\n1\n10\n2\n10\nATLAS\n\u03bd\n\u03bd\n\u2192\nZ\neX\n\u2192\nee + Z\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nEvents/1fb /100GeV \n-2\n10\n-1\n10\n1\n10\n2\n10\nATLAS\n\u03bd\n\u03bd\n\u2192\nZ\neX\n\u2192\nee + Z\n\u2192\nZ\n\u00b5\n\u00b5\n\u2192\nZ\nFigure 17: (Left) Emiss\nT\ndistribution after all corrections for Z \u2192\u03bd \u00af\u03bd, Z \u2192e+e\u2212+e\u00b1X and Z \u2192\u00b5+\u00b5\u2212\nprocesses. The number of events corresponds to an integrated luminosity of 1 fb\u22121. (Right) Meff distri-\nbution for the same physics processes.\nTable 20: Summary of systematic uncertainties for the replace method.\nDescription\nRelative uncertainty \u2206N/N [%]\nMC generator systematics\nALPGEN parameter variation\n6.3\nDetector systematics\nElectron energy scale\n0.05\nElectron energy resolution\n0.03\nElectron id ef\ufb01ciency\n0.50\nMuon energy scale\n0.30\nMuon energy resolution\n0.39\nMuon id ef\ufb01ciency\n1.00\nEmiss\nT\nscale (soft part)\n4.5\nTotal systematics (quadratic sum)\n\u223c8\nTotal statistics\n\u223c13\nTotal uncertainties\n\u223c15\n3.3.2\nZ and W background estimates from Z \u2192\u2113+\u2113\u2212plus Monte Carlo shape\nA modi\ufb01cation of the method of the previous section is described here. Denoted the \u201cMC method\u201d, it\nuses only the number of events in the Z(\u2192\u2113+\u2113\u2212)+jets control sample for normalization, but otherwise\nrelies on Monte Carlo simulation of kinematical distributions of events. The same normalization factor is\nused for both the Z(\u2192\u03bd \u00af\u03bd) background and the W(\u2192\u2113\u03bd) background since the production mechanism\nis very simliar.\nControl sample\nThe event selection of the control sample demands: two opposite-sign same-\ufb02avour\nleptons with pT > 20 GeV; Emiss\nT\n< 40 GeV; a di-lepton mass M\u2113\u2113within \u00b1 10 GeV of mZ . Subsequently,\nthe standard no-lepton SUSY cuts are applied after replacing \u2113+\u2113\u2212with \u03bd \u00af\u03bd.\nThe number of events selected with 1 fb\u22121 is summarized in Table 21. The contamination from t\u00aft\nevents is about 10\u22122 and therefore not signi\ufb01cant. The number of events estimated by a full simulation\nsample (with event \ufb01lter pZ\nT > 80 GeV) is 72 \u00b1 3 for 1 fb\u22121, which leads to a statistical uncertainty on\nthe estimation of 12%.\nThe method has been tested with a pseudo data sample prepared with Monte Carlo parameters set\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1552\n\nTable 21: Number of events in the MC method control sample (for 1 fb\u22121).\nprocess\n\u00b5 mode\ne mode\n\u00b5 + e (sum)\nZ(\u2192\u2113+\u2113\u2212)\n51\u00b11\n34\u00b11\n85\u00b11\nZ(\u2192\u03c4+\u03c4\u2212)\n< 0.1\n< 0.1\n< 0.1\nt\u00aft\n1.0\u00b10.3\n0.5\u00b10.2\n1.5\u00b10.4\nTable 22: Systematic uncertainty from variation of Monte Carlo generator parameters (ALPGEN) for the\nMC method. The pseudo data sample is discussed in the text.\nZ(\u2192\u03bd \u00af\u03bd)\nEmiss\nT\n> 300 GeV\nMeff > 800 GeV\npseudo data sample\n5%\n3%\nhalf renormalization scale\n2%\n0%\nlower parton pT\n9%\n4%\nW(\u2192\u2113\u03bd)\nEmiss\nT\n> 300 GeV\nMeff > 800 GeV\npseudo data sample\n16%\n7%\nhalf renormalization scale\n4%\n2%\nlower parton pT\n12%\n15%\nTable 23: Systematic uncertainty from detector performance in the MC method.\nEmiss\nT\n> 300 GeV\nMeff > 800 GeV\nJet energy scale\n6%\n6%\nJet energy resolution\n1%\n1%\nEmiss\nT\nsoft component scale\n1%\n< 1%\nLepton energy scale\n< 1%\n< 1%\nLepton identi\ufb01cation ef\ufb01ciency\n2%\n2%\ndifferently from the standard Monte Carlo sample4. In this pseudo data sample, the shape of Emiss\nT\nand\nMeff distributions is not affected; only the normalization changes signi\ufb01cantly. The MC method is able\nto recover such a change and predict the background correctly.\nSystematic uncertainty\nThe MC method relies on Monte Carlo for the shapes of the background\ndistributions. The systematic uncertainty from the Monte Carlo is estimated by using samples with\ndifferent Monte Carlo parameters (pseudo real data, half renormalization scale sample, lower parton\nthreshold sample). The results are summarized in Table 22; the deviation of the samples is 16% at most.\nOther potential sources of systematic error in the background estimation from uncertainties in detec-\ntor performance are summarized in Table 23. Since Monte Carlo is used, an uncertainty in the experi-\nmental jet energy scale affects the MC method prediction signi\ufb01cantly more than for the replace method\n(Section 3.3.1).\nSUSY contamination of the control sample\nThe tight selection cuts of the control sample makes any\nSUSY contamination negligible (as was also the case for the replace method discussed in Section 3.3.1).\n4renormalisation and factorisation scale 0.8 times the default, a minimum parton pT of 30 GeV (rather than 40 GeV), and\nseparation between partons \u2206R j j = 0.6 (rather than 0.7).\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1553\n\n3.3.3\nControl sample constructed from an MT-selected one-lepton sample\nW and top backgrounds\nThe t\u00aft and W \u00b1 + jets processes contribute to the background in the no-\nlepton mode, when the lepton emitted in the W \u00b1 \u2192\u2113\u03bd process is not identi\ufb01ed. The reasons why the\nemitted lepton is missed are summarized in Table 24. Hadronic decay of \u03c4\u2019s and the lepton being out\nof acceptance (the pT of the lepton is required to be larger than 20 GeV) are the dominant reasons, and\nsimilar reasons/ratio\u2019s are observed in both t\u00aft and W \u00b1 +jets processes.\nTable 24: Numbers of events in which leptons are missed for various reasons in the semi-leptonic and\nleptonic decays of top and W \u00b1. The numbers are normalized to 1 fb\u22121 and listed after the SUSY no-\nlepton selection is applied.\nt\u00aft\nW \u00b1 +jets\nW \u00b1 \u2192\u03c4 \u2192hadron\n1993 (43%)\n773 (42%)\nOut of acceptance\n1805 (39%)\n762 (41%)\nIsolation (close to jet)\n807 (18%)\n322 (17%)\nThe production processes t\u00aft and W \u00b1 with W \u00b1 \u2192\u2113\u03bd where the lepton is identi\ufb01ed constitute good\ncontrol samples from which to estimate these background processes in the no-lepton mode, since similar\nkinematic distributions are expected except for the presence of the lepton. For the control sample, the\nsame kinematic selections as for the signal in the no-lepton mode are applied. In addition, exactly one\nisolated lepton (e or \u00b5 with pT larger than 20 GeV) is required and the transverse mass between this\nlepton and the Emiss\nT\nis required to be smaller than 100 GeV to enhance the t\u00aft and W \u00b1 processes. After\nthese selections, this identi\ufb01ed lepton is treated as if had been missed and all kinematic variables are\nrecalculated.\nThe distributions of t\u00aft and W \u00b1 +jets events differ after the SUSY selections are applied. The Emiss\nT\nfor W \u00b1 tends to be larger than for t\u00aft events, since the boost factor of the W \u00b1 is larger for W \u00b1 +jets after\nseveral high pT jets are required. Therefore the reproduced distributions are sensitive to the mixture of\nthe t\u00aft and W \u00b1 + jets events in the control sample. The fractions of the t\u00aft and W \u00b1 + jets processes in\nthe control sample are 81% and 19%, respectively, close to the actual backgrounds in the signal region,\nwhich are 73% and 27% respectively. The systematic errors due to the uncertainties in the cross-section\nof t\u00aft and W \u00b1 +jets will be discussed later.\nThe estimated distribution is normalized with the data at 100 GeV < Emiss\nT\n< 200 GeV, where the con-\ntribution of the SUSY signal is expected to be small. The estimated distributions are slightly harder than\nthe true distributions of the background processes, but similar distributions are obtained. The number of\nestimated background events is summarized in the two top rows in Table 25. Reasonable agreement is\nobserved at high Emiss\nT\n.\nQCD, W and top background without and with SUSY signal\nIn a dedicated note within this vol-\nume [3] various methods for the estimation of QCD background from data are discussed.\nIn this section, we include QCD background, and estimate it as follows. It has been shown that\nafter the removal of events with mismeasured Emiss\nT\n(e.g. noisy or dead calorimeter cells), as discussed\nelsewhere in this volume [12], semi-leptonic heavy quark (b,c) decays are the dominant contribution to\nlarge Emiss\nT\nin the QCD background. A function is derived to represent the momentum fraction taken\nby the neutrino in b and c quark decays. This function is then applied to a control sample taken from\ndata (at least four jets with pT larger than 50 GeV, pT of the leading jet larger than 100 GeV, Emiss\nT\nsmaller than 100 GeV) dominated by light-quark QCD events. The resulting distributions are normalized\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1554\n\nto data in the region of \u2206\u03c6min < 0.2, where \u2206\u03c6min is the minimum value of the difference in azimuthal\nangle between the Emiss\nT\nvector and any of the three highest pT jets, as discussed in section 3.1 and the\ndedicated note [3].\nTheW \u00b1 and t\u00aft background processes can also be estimated from the data, as discussed in the previous\nparagraph. Since all these processes are present in the data simultaneously, the background estimations\nshould be done together. The same holds true for the presence of SUSY signal, which would contaminate\nthe control samples.\nFigure 18 (top row) shows the estimated and true distributions of Emiss\nT\nand the effective mass for\nthe combined background processes, without SUSY signal. The background distributions are reproduced\nwell and the correct normalizations are obtained for all the background processes. The numbers of events\nare also summarized in Table 25.\nTable 25: Number of true and estimated (MT method) background events in the no-lepton mode, for t \u00aft,\nW \u00b1 and QCD processes without SUSY signal, normalized to 1 fb\u22121.\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nt\u00aft and W \u00b1 only\nTrue BG (top and W \u00b1)\n6894 \u00b1 83\n276 \u00b1 17\nestimated BG (top and W \u00b1)\n7018 \u00b1 269\n311 \u00b1 28\nQCD, t\u00aft and W \u00b1\nTrue BG (QCD, top and W \u00b1)\n8077 \u00b1 90\n300 \u00b1 17\nEstimated BG\n8158 \u00b1 273\n327 \u00b1 28\nRatio(Est./True)\n1.01 \u00b1 0.04\n1.09 \u00b1 0.11\nIf SUSY exists, SUSY signal can contaminate the background estimations. This is illustrated in\nFigure 18 (middle row) and Table 26. In the \ufb01gure, the SUSY SU3 signal point is used; the table shows\nthe variation over a number of SUSY samples. The \ufb01gure and the table show that SUSY contamination\ncauses a decrease of SUSY event excess by typically 30%, but that the considered points, with the\nexception of SU2, are still observable with 1 fb\u22121.\nTable 26: Number of background events and estimated (MT method) numbers for t\u00aft, W \u00b1 and QCD\nprocesses, as well as various SUSY signals, in the no-lepton mode, normalized to 1 fb\u22121.\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nEmiss\nT\n> 100 GeV\nEmiss\nT\n> 300 GeV\nTrue BG (QCD,top and W \u00b1)\n8077 \u00b1 90\n300 \u00b1 17\n8077 \u00b1 90\n300 \u00b1 17\nSU1\nSU4\nEstimated BG\n8493 \u00b1 283\n510 \u00b1 39\n27527 \u00b1 588\n1409 \u00b1 83\nTrue BG + SUSY signal\n9152 \u00b1 96\n1078 \u00b1 33\n34209 \u00b1 185\n3535 \u00b1 59\nSU2\nSU6\nEstimated BG\n8198 \u00b1 274\n329 \u00b1 30\n8362 \u00b1 279\n431 \u00b1 35\nTrue BG + SUSY signal\n8193 \u00b1 91\n351 \u00b1 19\n8930 \u00b1 95\n924 \u00b1 30\nSU3\nEstimated BG\n9188 \u00b1 299\n633 \u00b1 44\nTrue BG + SUSY signal\n11333 \u00b1 106\n2113 \u00b1 46\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1555\n\nMissing ET [GeV]\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n-1\nEvents / 1fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / 200GeV\n-1\nEvents / 1fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nATLAS\nMissing ET [GeV]\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n-1\nEvents / 1fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nTrue QCD/top/W BG + SU3\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / 200GeV\n-1\nEvents / 1fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nTrue QCD/top/W BG + SU3\nATLAS\nMissing ET [GeV]\n0\n100 200 300 400 500 600 700\n800 900 1000\n / 50GeV\n-1\nEvents / 1fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nTrue QCD/top/W BG + SU3\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n / 200GeV\n-1\nEvents / 1fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTrue QCD/top/W BG\nEstimated QCD/top/W BG\nTrue QCD/top/W BG + SU3\nATLAS\nFigure 18: The estimated distributions of Emiss\nT\nand the effective mass of the t\u00aft, W \u00b1 and QCD back-\ngrounds in the no-lepton mode with a luminosity of 1 fb\u22121. In the plots in the top row, no SUSY signal is\npresent in the data, and black/red histograms show the true/estimated (MT method) background distribu-\ntions. In the plots in the middle and bottom rows, a SUSY SU3 signal is present in the data, and the blue\nhistograms show the background plus the SUSY signal. In the two plots in the middle row, no correction\nwas applied. In the two bottom plots, a correction with the \u201cnew MT method\u201d was performed.\nNew MT method\nThe \u201cnew MT method\u201d, discussed in section 2.3.1, provides a \ufb01rst rough method to\ncorrect for the presence of SUSY signal in the control sample, once a SUSY excess has been observed\nin data. With this method, the distributions shown in the bottom row of Figure 18 are obtained. The\n\ufb01gure shows the estimated background distributions with the new MT method, compared to the true\nbackground distributions, when SU3 SUSY signal is present in data.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1556\n\nSystematic uncertainties\nThe systematic errors of this method are summarized in Table 27. The\nALPGEN parameter variation includes a variation of the relative fraction of t\u00aft\nand W + jets in the\nsample. Although the actual number of background events varies with jet energy scale and Monte Carlo\ngenerator parameters by some 25%, the data-driven MT method is able to predict the background in the\nsignal region to within an assigned systematic error of 15%.\nTable 27: Systematic uncertainties of the MT-method background estimations in the no-lepton mode\nwithout SUSY signal. Also changes of the absolute background numbers are listed. Numbers are nor-\nmalized to 1 fb\u22121.\nSyst. error\nChange in background level\nJet energy scale\n< 5%\n25%\nLepton energy scale\n< 5%\n0%\nLepton Ef\ufb01ciency\n< 5%\n< 1%\nMC@NLO vs ALPGEN\n< 5%\n16%\nALPGEN parameter variation\n< 5%\n8%\n3.3.4\nTop pairs with \u03c4 decay\nIntroduction\nThe precise determination of the cross-section for the process of top-pair production with\none tau that decays hadronically, t\u00aft \u2192W(q \u00afq\u2032)W(\u03c4had\u03bd\u03c4)b\u00afb, is relevant because it constitutes an important\nbackground to SUSY searches with no leptons and signi\ufb01cant Emiss\nT\n. In fact, if no tau veto is applied,\nabout 65% of the total t\u00aft background in the no-lepton mode corresponds to events containing one tau.\nEvent reconstruction and selection\nThe topology of t\u00aft \u2192W(qq\u2032)W(\u03c4had\u03bd)b\u00afb events consists of two\nlight\u2013quark jets, one tau, and two b jets.\nThe control of the tau fake rate is very important in a busy environment like t\u00aft where the purity\nof the reconstructed tau sample is low due to the large jet multiplicity. A high tau purity is needed\nin order to reduce the internal combinatorial background and the background from the semileptonic\n(t\u00aft \u2192W(\u2113\u03bd\u2113)W(q \u00afq\u2032)b\u00afb where \u2113\u2208{e,\u00b5}) decays of t\u00aft. In this analysis, we use a calorimeter-based tau\nreconstruction algorithm [1], and require a minimum visible pT of the identi\ufb01ed tau of 25 GeV.\nThe event is built independently on the hadronic side and the leptonic side, and topology variables\nuseful to identify t\u00aft events and reject QCD and W +jet background are extracted. On the hadronic side, a\nhadronic W invariant mass is built choosing, among all the combinatorial possibilities of di-jets, the pair\nof jets with closest invariant mass to its PDG value. The hadronic top is built combining this hadronic W\nwith the closest identi\ufb01ed b jet in \u2206R. The b-jet identi\ufb01cation is loose, with a 75% ef\ufb01ciency for b jets\nfrom top decay.\nThe Emiss\nT\nis combined with the identi\ufb01ed tau in order to build a leptonic W transverse mass. We\nassume a collinear approximation for the decay of the tau (the visible products of the hadronic decay of\nthe tau and the associated \u00af\u03bd\u03c4 are collinear), and determine the invariant transverse mass of the leptonic\nW. The resulting leptonic W is then combined with the closest (in \u2206R) b jet to constitute the leptonic top.\nFor each event, a reconstructed tau will build a leptonic W (and top) in combination with Emiss\nT\n, and\nwill have an associated hadronic W (and top). If there is more than one reconstructed tau we select the\none that is associated with the jet pair that gives the hadronic W invariant mass closest to its PDG value.\nOnce the event is built, topology variables suitable for t\u00aft selection are computed and selection cuts are\napplied: Emiss\nT\n> 35 GeV, no identi\ufb01ed electron or muon with pT > 15 GeV should be present in the event,\nthe angle \u2206\u03c6 between the two reconstructed top quarks should be larger than 2.5, the ratio between the\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1557\n\ntransverse momentum of the two reconstructed top quarks should be smaller than 2, the angular distance\n(\u2206R) between the reconstructed b jets should be larger than 1, and the angle \u2206\u03c6 between the missing\nmomentum vector and the hadronic b jet should be larger than 0.5.\n (GeV)\nT\nMissing E\n0\n100\n200\n300\n400\n500\n600\n700\n800\narbitrary normalization\n1\n10\n2\n10\n3\n10\n4\n10\nSUSY no lepton cuts\nttbar cuts\nFigure 19: Missing ET of t\u00aft events with (q \u00afq\u2032,\u03c4had) for (circles) t\u00aft selection as in this analysis (control\nsample) and (squares) for the SUSY no-lepton mode selection.\nWith the loose b tagging used here, 2910 t\u00aft(q \u00afq\u2032,\u03c4had) events are selected for 1 fb\u22121. The background\nconsists of QCD and W +jets, for which 110 and 100 events respectively are selected. Therefore, with\nloose b tagging a good signal-to-background ratio can already be reached, although the uncertainty on\nthe QCD background number is large. If one were to use tighter b tagging (60% ef\ufb01ciency), 1650\nt\u00aft(q \u00afq\u2032,\u03c4had) events would be selected, against 2 QCD events and no W +jet events.\nIn the presence of SUSY, the numbers of SUSY signal events that would pass the event selection\nwith the loose b tag for 1 fb\u22121 are given in Table 28. They are generally small, with the exception of the\nSU4 point.\nTable 28: The number of SUSY events remaining after t\u00aft(q \u00afq\u2032,\u03c4had) selection for different SUSY points,\nfor 1 fb\u22121.\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8\nNevt\n22 \u00b1 1\n5 \u00b1 1\n155 \u00b1 5\n1700 \u00b1 60\n70 \u00b1 4\n45 \u00b1 3\nEstimation of the t\u00aft with (q \u00afq\u2032,\u03c4had) background to SUSY.\nFigure 19 shows that the selection ap-\nplied in order to identify the t\u00aft events with (q \u00afq\u2032,\u03c4had) introduces little bias in the Emiss\nT\ndistribution, as\ncompared to the SUSY no-lepton mode selection.\nApplying the SUSY no-lepton mode cuts, we estimate 210 t\u00aft (q \u00afq\u2032,\u03c4had) events as remaining back-\nground to the SUSY no-lepton mode for 1 fb\u22121.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1558\n\nSystematic uncertainties\nIn the data-driven analysis of t\u00aft decays in the (q \u00afq\u2032,\u03c4had) \ufb01nal state, the most\nrelevant contributions to the detector uncertainties are the jet and Emiss\nT\nenergy scale, b-tagging ef\ufb01ciency\nand \u03c4 identi\ufb01cation ef\ufb01ciency.\nTable 29: Systematic variation of the t\u00aft(q \u00afq\u2032,\u03c4had) cross-section due to detector-related uncertainties.\nSystematic variation\nCross-section variation [%]\nJet energy scale\n2.5\nb-tagging ef\ufb01ciency\n7.5\nLight quark rejection in b-tag\n1.3\n\u03c4-identi\ufb01cation ef\ufb01ciency\n3.4\nLight quark rejection in \u03c4-identi\ufb01cation\n4.5\nThe b-tagging ef\ufb01ciency plays an important role in the t\u00aft(q \u00afq\u2032,\u03c4had) reconstruction, since one of the\nselection criteria is that the two b jets expected in the \ufb01nal state should be reconstructed and correctly\nidenti\ufb01ed5.\nThe systematic contribution to the measurement of the t\u00aft(q \u00afq\u2032,\u03c4had) cross-section due to the \u03c4 iden-\nti\ufb01cation ef\ufb01ciency has been estimated by varying the \u03c4 identi\ufb01cation ef\ufb01ciency and the light quark\nrejection factor by 10%.\nThe uncertainty on the QCD background in the t\u00aft(q \u00afq,\u03c4had) sample is large due to the limited number\nof Monte Carlo events which could be generated. Probably tight b tagging is required in this analysis.\nFurther study is needed on this topic.\n4\nMulti-lepton and tau search modes\nAs well as the one-lepton and no-lepton search modes described earlier, there is considerable SUSY\ndiscovery potential in the multi-lepton and tau search modes, as discussed elsewhere in this volume [2,4].\nThe data-driven estimation of backgrounds in these modes, particularly the opposite-sign dilepton\nand the tau modes, can use the methods that have been described earlier in the context of the one-\nlepton search mode have also proven to be useful. These include the MT method, the HT2 method,\nthe kinematic reconstruction method and the redecay method. Furthermore, for the same-sign dilepton\nmode, a technique based on lepton isolation, as described in the note on QCD backgrounds [3] could be\nfurther developed.\n5\nDiscussion\nThe methods presented in this note represent a number of ideas on how top, W and Z backgrounds to\nSUSY searches can be extracted from the data, with appropriately chosen control samples. The results\nindicate that we expect, with 1 fb\u22121, to be able to measure in the no-lepton mode:\n\u2022 the Z \u2192\u03bd \u00af\u03bd background with two different methods to 8\u201313% stat. error, 10\u201315% syst. error;\n\u2022 the t\u00aft background with hadronic tau decay to < 6% stat. error, 10\u201315% syst. error (but with a\ncaveat for the QCD background);\n\u2022 and the sum of top, W and QCD backgrounds with the MT method to 4\u20138% stat. error, and 15%\nsyst. error.\n5This is in fact the only analysis in this note where b tagging is used.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1559\n\nIn the one-lepton mode:\n\u2022 the MT method gives the sum of t\u00aft and W background to 4\u20138% stat. error, 15% syst. error;\n\u2022 the semileptonic t\u00aft background can be estimated to 5% stat. error, 22% syst. error;\n\u2022 we can determine the fully leptonic t\u00aft background to 10% stat. error, 20% syst. error in at least\nthree independent ways;\n\u2022 and we have a combined \ufb01t method to extract all components.\nThese methods can also be applied to the multi-lepton and tau search modes.\nThe results obtained with the MT method in this note are stable with respect to systematic variations\nin detector performance and Monte Carlo parameters and cross-sections to the 15% level. However, the\nMT method measures a sum of semileptonic and fully leptonic t\u00aft and W/Z +jets background; it relies\non a control sample with different composition than the signal sample, and there is a subtle interplay\nbetween the t\u00aft and W/Z + jets components of the background. More work is needed to understand\npossible systematic effects. It is desirable to understand the individual components of the backgrounds\nas well, and the various other methods discussed in this note appear to succeed in this.\nThe presence of SUSY signal would affect the background estimates, at a level that depends on the\nSUSY signal properties, as well as on the method. Methods with very tight control samples (replace\nmethod, topbox method) see almost no effect. For the other methods, the background is overestimated\nby typically 20\u201330% for samples like SU1, SU2, SU3 and SU6. If a SUSY excess is nevertheless\nobserved (which is possible with 1 fb\u22121), a correction for the background overestimation can be applied.\nFirst ideas have been presented in this note, using the MT method, and the combined \ufb01t method. More\nwork is needed in this area. The SU4 benchmark point is a special case because of its light spectrum.\nIt produces events with kinematics which are similar to the Standard Model backgrounds and its cross-\nsection is high, so many methods would struggle to provide background predictions. It would, however,\nnot be missed [11].\nReferences\n[1] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3\n(2008) S08003.\n[2] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[3] ATLAS Collaboration, Estimation of QCD Backgrounds to Searches for Supersymmetry, this vol-\nume.\n[4] ATLAS Collaboration, Multi-Lepton Supersymmetry Searches, this volume.\n[5] ATLAS Collaboration, Supersymmetry Signatures with High-pT Photons or Long-Lived Heavy\nParticles, this volume.\n[6] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[7] ATLAS Collaboration, Trigger for Early Running, this volume.\n[8] J. Sjolin, J. Phys. G : Nucl. Part. Phys. 29 (2003) 543\u2013560.\n[9] S. Jadach, Z. Was, R. Decker and J.H. Kuhn, Comput. Phys. Commun. 76 (1993) 361\u2013380.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1560\n\n[10] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[11] ATLAS Collaboration, Determination of the Top Quark Pair Production Cross-Section, this vol-\nume.\n[12] ATLAS Collaboration, Measurement of Missing Tranverse Energy, this volume.\nSUPERSYMMETRY \u2013 DATA-DRIVEN DETERMINATIONS OF W, Z AND TOP BACKGROUNDS . . .\n1561\n\nEstimation of QCD Backgrounds to Searches for\nSupersymmetry\nAbstract\nThis note deals with techniques for estimating QCD multijet backgrounds to\ninclusive jets + Emiss\nT\n+ leptons searches for Supersymmetry. The note doc-\numents how the backgrounds may be estimated using a data set with an in-\ntegrated luminosity of 1 fb\u22121 or less. The likely systematic and statistical\nuncertainties in such estimates are also discussed. Data-driven approaches dis-\ncussed include jet smearing with functions derived from data and techniques\nfor background estimation using control samples. Monte Carlo based tech-\nniques using a variety of generators and simulation tools are also discussed\nwith a view to establishing their likely precisions and hence the optimum sim-\nulation strategy.\n1\nIntroduction\nIn searches for supersymmetry in events containing jets and missing transverse energy (Emiss\nT\n) the biggest\nbackground-determination challenge will be in understanding QCD jet events. Although fast simulation\nstudies [1] indicate that such backgrounds should be sub-dominant in the high Emiss\nT\nand large jet mul-\ntiplicity region, the situation with real data is still uncertain, and likely to be less favourable for SUSY\nsearches. In particular non-Gaussian tails to the detector jet response function, which can be caused by\ndead material, jet punch-through, pile-up of machine backgrounds and other effects, can dramatically\nincrease the cross-section of high Emiss\nT\nQCD background. QCD jet events in which such processes have\noccurred shall be referred to in this note as \u201cfake\u201d Emiss\nT\nevents in what follows, since in such events the\nnet pT of non-interacting particles measured in a perfect detector is inherently small. Events in which\nthe Emiss\nT\nvector is dominated by contributions from non-interacting particles such as neutrinos or the\nLightest Supersymmetric Particle (in the case of SUSY signal) shall be referred to as \u201creal\u201d E miss\nT\nevents.\nAccurate estimation of QCD jet backgrounds is dif\ufb01cult for a number of reasons. Processes gener-\nating fake Emiss\nT\nfrom event mis-measurement are expected to be poorly modeled in current GEANT4 [2]\nsimulations \u2013 this situation will improve once validation has been performed with real data. Furthermore\ntheoretical and experimental uncertainties will conspire to decrease further the systematic precision of\nMonte Carlo estimates while the large QCD cross-section will limit statistical precision by rendering\nproduction of unbiased GEANT4 samples corresponding to more than a few pb\u22121 unfeasible. This note\naddresses these problems, assessing the relative magnitudes of some of the uncertainties, identifying\ntechniques for minimising the contribution of such backgrounds in the SUSY signal region and studying\nnovel Monte Carlo- and data-driven approaches to accurate background estimation. It should be under-\nstood that the background estimates presented here are not intended to be de\ufb01nitive; rather the focus is on\ndeveloping and evaluating the performance of tools for future use. This note should be read in conjunc-\ntion with the notes outlining ATLAS Emiss\nT\nperformance [3], data-driven estimation strategies for W, Z\nand top backgrounds [4] and inclusive SUSY searches [5]. The main variables sensitive to the presence\nof SUSY signal which have been considered in this note are Emiss\nT\nand the \u2018effective mass\u2019 de\ufb01ned by\nMeff = \u22114\ni=1 |pT(ji)|+Emiss\nT\n[5], where the sum runs over the four leading jets satisfying the conditions\ndescribed below.\nWherever possible events appearing in Emiss\nT\nor Meff distributions have been selected with a standard\njet selection requiring at least four jets with pT > 50 GeV and |\u03b7| < 2.5, at least one of which must have\n1562\n\npT > 100 GeV. In some sections describing studies of new simulation techniques with limited available\nsimulation statistics these cuts have been relaxed \u2013 these cases are highlighted in the text. In addition\nthe performance of the different background estimation techniques has been compared by assessing the\nuncertainties of the background estimates for events passing a standard baseline set of cuts for the jets +\nEmiss\nT\n+ 0-lepton (1-lepton for Section 5.2) channel described elsewhere in this volume [5].\n2\nFake Emiss\nT\nrejection\n2.1\nJet \ufb01ducialisation in \u03b7\nIn QCD multijet events the generation of large fake Emiss\nT\nfrom jets falling in poorly instrumented regions\nof the detector is a signi\ufb01cant mechanism by which such events mimic SUSY signal. Conversely the large\nnumber of such events means they can provide a useful in-situ probe of the the ability of the detector to\nmeasure Emiss\nT\n. Here we consider the use of such events for de\ufb01ning non-\ufb01ducial regions where jets may\nbe expected to be poorly measured and hence capable of generating signi\ufb01cant fake Emiss\nT\n.\nThe Emiss\nT\nresolution of the ATLAS detector is known to scale with \u221a\u03a3ET [6], where \u03a3ET is the\nscalar sum over the transverse energies of all calorimeter objects. For this reason the Emiss\nT\n-signi\ufb01cance\nde\ufb01ned by S = Emiss\nT\n/\u221a\n\u2211ET is frequently used to distinguish real Emiss\nT\nfrom fake Emiss\nT\n. Because QCD\nmultijet events typically have little energy in invisible particles the value of \u27e8S\u27e9is determined by the E miss\nT\nresolution of the detector. Much of the variance in S is due to intrinsic shower \ufb02uctuations, but because\nthe reconstructed Emiss\nT\nis dominated by the transverse energy near the highest-pT jets, some is due to\nthe non-uniformity in energy resolution of the detector. A measurement of \u27e8S\u27e9in a sample of events in\nwhich one of the highest-pT jets points into a particular region of the calorimeter can therefore be used\nas a measure of the relative performance of that region.\nIn this study, the Emiss\nT\n-signi\ufb01cance of QCD jet events was used to calculate \u27e8S\u27e9in \u03b7 bins across the\ncalorimeter. Each event S value was used in two \u03b7 bins \u2013 one for each of the two highest-pT jets. The\nsame techniques could be used generate a full (\u03b7,\u03c6) map of the calorimeter. A sample of PYTHIA [7]\nsimulated QCD jet events with pT > 280 GeV and corresponding to an integrated luminosity of 23.8 pb\u22121\nwas used for the study [8]. Events were required to pass the 160 GeV high-level single-jet trigger [9]\nand to possess at least two high-pT jets with pT(j1) > 100 GeV and pT(j2) > 50 GeV. These two jets\nwere required to be back-to-back in the transverse plane such that \u03c0 \u2212|\u2206\u03c6(j1, j2)| < 0.4. Events were\nvetoed if they contained an isolated lepton with pT > 10 GeV and |\u03b7| < 2.5 or if Emiss\nT\nwas greater than\n80 GeV. The \u2206\u03c6 and Emiss\nT\ncuts eliminate contamination from events with signi\ufb01cant true Emiss\nT\n, eg. Z\n(\u2192\u03bd \u00af\u03bd ) + jets and heavy quark jets. While the Emiss\nT\ncut does, in principle, prohibit the identi\ufb01cation of\ncatastrophically unresponsive regions with this method, regions with consistently poor response would\nbe readily identi\ufb01able via the relative de\ufb01ciency of events with jets pointing into them.\nThe resulting calorimeter map is shown in Fig. 1. The degraded response in the tile barrel and tile\nbarrel-extended barrel gaps (\u03b7 \u223c0 and 0.6 < |\u03b7| < 0.8) and the LAr barrel-endcap and hadronic LAr-\nforward calorimeter transition regions (1.3 < |\u03b7| < 1.5 and 3.1 < |\u03b7| < 3.3) are all clearly visible. The\nprincipal application of these data is to de\ufb01ne non-\ufb01ducial regions of the detector, such that events with\njets pointing into these regions can be rejected. De\ufb01ning a cut value \u27e8S\u27e9min on \u27e8S\u27e9, a region is de\ufb01ned\nto be non-\ufb01ducial if \u27e8S\u27e9> \u27e8S\u27e9min in all of the corresponding bins in the calorimeter map (Fig. 1) and if\n\u27e8S\u27e9\u2212\u27e8S\u27e9min > 3\u03b5 in at least one of those bins, where \u03b5 is the uncertainty on the mean \u27e8S\u27e9. Fig.1 also\nshows the non-\ufb01ducial regions obtained in this way with \u27e8S\u27e9min = 0.95.\nThe jet \ufb01ducialisation process has been tested on the QCD jet sample which was used to de\ufb01ne\nthe regions and also on SUSY events from model point SU3 [10]. Events were required to satisfy the\njet cuts listed in Section 1 and events with a jet with pT > 40 GeV pointing into one of the non-\ufb01ducial\nregions depicted in Fig.1 were rejected. The ef\ufb01ciency of these cuts for the QCD and SUSY samples was\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1563\n\n\u03b7\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\n]\n-1/2\n [GeV\n0.6\n0.8\n1\n1.2\n1.4\n1.6\nATLAS\nFigure 1: \u27e8Emiss\nT\n/\u221a\u03a3ET\u27e9vs. \u03b7 j, where j is the \ufb01rst or second highest-pT jet in each event (points). The\nnon-\ufb01ducial regions selected with a cut at 0.95 (dashed line) are also shown (shaded areas; see text).\nThese regions correspond to the LAr barrel-endcap and HEC-forward transition regions.\n(74.8\u00b10.4)% and (75.4\u00b10.6)% respectively for Emiss\nT\n> 0 GeV, and (67.5\u00b13.7)% and (75.5\u00b10.7)%\nfor Emiss\nT\n> 100 GeV. The effect of these cuts on the simulated data-samples is clearly small however\nthey may be of more use with real data acquired with an imperfect detector, and the technique could be\nused as an on-line monitor of calorimeter performance.\n2.2\nJet\u2013Emiss\nT\n\u03c6 correlations\nOne of the main methods used to reduce the QCD multijet background in Emiss\nT\n+ jets inclusive SUSY\nsearches at the Tevatron has been the elimination of events in which the Emiss\nT\nis closely associated with\none of the leading jets in the transverse plane [11, 12]. This section provides a brief exploration of this\nmethod of background elimination in ATLAS.\n)\nT\nE\n(j1, \n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n)\nT\nE\n(j2, \n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\nEvents / 0.1x0.1 / 23.8pb\n1\n10\nATLAS\n)\nT\nE\n(j1, \n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n)\nT\nE\n(j2, \n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\nEvents / 0.1x0.1 / 23.8pb\n-2\n10\n-1\n10\nATLAS\nFigure 2: The |\u2206\u03c6(j1,Emiss\nT\n)| \u2212|\u2206\u03c6(j2,Emiss\nT\n)| plane for QCD multijet (left) and SUSY SU3 events\n(right) passing SUSY jet cuts and Emiss\nT\n> 100 GeV.\nFig. 2 shows the |\u2206\u03c6(j1,Emiss\nT\n)| \u2212|\u2206\u03c6(j2,Emiss\nT\n)| plane for events from the QCD multijet sample\ndescribed in Section 2.1 which pass the jet cuts described in Section 1 and possess Emiss\nT\n> 100 GeV\n(note that this sample has at least one jet with pT > 280 GeV \u2013 signi\ufb01cantly higher than the SUSY\nleading-jet pT requirement of 100 GeV). Almost all events are con\ufb01ned to small regions around (\u03c0,0)\nand (0,\u03c0), with a small number of events in which the Emiss\nT\nis not associated with one of the two highest-\npT (reconstructed) jets lying outside these regions. For comparison, the |\u2206\u03c6(j1,Emiss\nT\n)|\u2212|\u2206\u03c6(j2,Emiss\nT\n)|\nplane for events from a SUSY (SU3 model) sample [8] passing the above cuts is shown in Fig. 2. No\nsuch correlation with Emiss\nT\nis observed for this SUSY benchmark point.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1564\n\nmin\n\u03c6\n\u2206\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\nEvents / 0.05 / 23.8pb\n1\n10\n2\n10\nQCD\nSU3\nATLAS\nFigure 3: The \u2206\u03c6min distribution for QCD multijet (solid line) and SU3 SUSY (dashed line) events\npassing the SUSY jet cuts and with Emiss\nT\n> 100 GeV, as described in the text. Good discrimination is\nachieved with a cut at \u2206\u03c6min = 0.2 (vertical dotted line).\nFor the purposes of background reduction, this technique can be generalised by considering three\ncorrelations between the Emiss\nT\nvector and the leading three jets by de\ufb01ning \u2206\u03c6min as:\n\u2206\u03c6min = min(\u2206\u03c6(j1,Emiss\nT\n),\u2206\u03c6(j2,Emiss\nT\n),\u2206\u03c6(j3,Emiss\nT\n)).\n(1)\nThe \u2206\u03c6min distribution for the QCD and SUSY samples passing the SUSY jet cuts and with Emiss\nT\n> 100\nGeV are shown in Fig. 3. Also shown is the position of a cut at \u2206\u03c6min > 0.2 used in Ref. [5].\n2.3\nCalorimeter and tracking cuts\nEvents in which jet reconstruction problems lead to fake Emiss\nT\ncan be identi\ufb01ed with several variables [3].\nCuts on the fraction of the total energy of the jet (ETotal) deposited in the outermost layers of the tile\ncalorimeter ETile2 and in the hadronic endcap calorimeter EHEC can be de\ufb01ned to veto events with likely\nproblems in jet containment. Additional cuts on the fraction of the jet energy deposited in the cryostat\nbetween the tile and the liquid argon (ECryo \u2013 estimated from the energy in the closest calorimeter layers)\nand in the gap and crack scintillators (EGap) can be used to reject events with large depositions in dead\nmaterial. It is also possible to identify events in which there have been problems reconstructing the\nmissing transverse momentum by comparing the value calculated from charged tracks (E miss\nT,Trk ) with the\nusual calorimetric Emiss\nT\n.\nTable 1: Cross-section of SUSY SU3 signal and QCD jet backgrounds before and after application of the\nselection and cleaning cuts proposed in the text. Quoted statistical uncertainties in cross-sections after\ncuts derive from statistics of the Monte Carlo samples used.\nSample\nNo cuts [pb]\nSelection cuts [pb]\nCleaning cuts [pb]\nSUSY SU3\n27.51\n9.654\u00b10.019\n6.792\u00b10.016\nQCD (280 GeV < pT < 560 GeV)\n1.25\u00d7104\n17.2\u00b11.3\n9.7\u00b11.0\nQCD (560 GeV < pT < 1120 GeV)\n360.0\n4.22\u00b10.13\n1.805\u00b10.082\nQCD (1120 GeV < pT < 2240 GeV)\n5.71\n0.434\u00b10.003\n0.130\u00b10.002\nTable 1 shows the cross-section of SU3 signal and multijet background following application of\nthe SUSY jet cuts described in Section 1 together with a cut requiring Emiss\nT\n>100 GeV, and in addition\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1565\n\napplying the fake Emiss\nT\ncleaning cuts discussed above. The latter cuts were applied to jets with pT > 150\nGeV with the following acceptance criteria : ETile2/ETotal < 0.1, ECryo/ETotal < 0.2, EGap/ETotal < 0.2,\nEHEC/ETotal < 0.5 and Emiss\nT,Trk \u2212Emiss\nT\n< 50 GeV. Note that the speci\ufb01c cut values are analysis dependent\nand should be adapted for other cases. The table shows that the cleaning cuts are effective at removing\nbetween 40% (low pT) and 70% (high pT) of the multijet background, while rejecting \u223c30% of the\nremaining signal after selection cuts.\n2.4\nCosmic backgrounds and rejection cuts\nSearches for supersymmetry must contend with backgrounds in which fake Emiss\nT\narises from a variety\nof sources. Examples in which the fake Emiss\nT\nis generated independently from a hard scatter include\ndead or noisy calorimeter channels, accelerator-related background and cosmic rays in which a muon\nundergoes a hard bremsstrahlung. A range of data-cleaning tools is being prepared to reject fake E miss\nT\nin\nATLAS; here we focus on timing information from the hadronic tile calorimeter (TileCal). As one gains\na better understanding of the \ufb01rst data, this will be combined with information from other subdetectors.\nCalorimeter timing can be a powerful tool to remove fake Emiss\nT\nbackgrounds from cosmic rays [13].\nTiming in ATLAS is de\ufb01ned such that particles from the nominal interaction point (x = 0, y = 0, z = 0)\nwill arrive in the calorimeter cells at time t = 0. Cosmic ray events, however, will arrive at random times\nwith no correlation to the LHC beam structure. One of the methods to reject cosmic rays is to calculate\nthe \u201cup-minus-down\u201d time, in which one divides the TileCal into two segments, an upper segment, with\n\u03c6 > 0 and a lower segment with \u03c6 < 0, where \u03c6 is the angle in the transverse plane. One then calculates\nthe average time of cells in each segment, weighted by the energy of each cell i:\ntup(down) = \u2211\ni\n(Eup(down)\ni\n\u00d7ti)/\u2211\ni\nEup(down)\ni\n.\n(2)\nThe difference between the two quantities tup and tdown, should re\ufb02ect the average time-of-\ufb02ight. The\nresulting \u201cup-minus-down\u201d time should be centered at t = 0 for particles from the interaction point, as\ndemonstrated in Fig. 4. In this \ufb01gure, the \u201cup-minus-down\u201d time is calculated for a simulated Monte\nCarlo QCD dijet sample. As expected, the signal distribution peaks near zero. Note that the simulation\nincludes electronic noise, and so the timing distribution has a spread of several ns.\nDepending on their trajectory, cosmic ray muons traveling from the top to the bottom of ATLAS\nat near the speed of light will have a time-of-\ufb02ight of typically 18-20 ns over their travel distance of\napproximately 6-7 m [14] in the TileCal. This is demonstrated in Fig. 5 for a simulated Monte Carlo\nsample of cosmic ray muons. In this case, the distribution peaks near -18 ns (the time of \ufb02ight is negative\nas expected for a particle traveling from the top to the bottom). The width of the simulated distribution is\n3 ns, allowing for a good separation of the background from the signal peaking at t = 0. Further details\nof calorimeter timing studies with cosmic rays in ATLAS can be found in Ref. [14].\n3\nMonte Carlo systematics\n3.1\nGenerator systematics: proton PDF and underlying event\nIn this section, uncertainties on the Monte Carlo generation of QCD events arising from proton parton\ndistribution functions (PDFs) and modeling of the underlying event are brie\ufb02y investigated. These un-\ncertainties provide a limit to the precision with which the novel detector simulation strategies described\nin Sections 4.1 and 4.2 can model QCD backgrounds to SUSY. Due to the large number of Monte Carlo\nsamples required for this study, each with different PDF or underlying event parameters, it was unfeasible\nto work with GEANT4 detector simulation samples. Therefore dedicated samples of events were gener-\nated in the same pT ranges as the GEANT4 samples used elsewhere in this note [8] and passed through\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1566\n\nUp minus Down Time [ns]\n-100 -80 -60 -40 -20\n0\n20\n40\n60\n80 100\nEvents\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nATLAS\nFigure 4: \u201cUp-minus-down\u201d timing distribu-\ntion in TileCal for a simulated Monte Carlo di-\njet sample. As expected, the distribution peaks\nnear 0.\nUp minus Down Time [ns]\n-100 -80 -60 -40 -20\n0\n20\n40\n60\n80 100\nEvents\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\nFigure 5: \u201cUp-minus-down\u201d timing distribu-\ntion in TileCal for a simulated Monte Carlo\ncosmic ray sample. As expected, the distribu-\ntion peaks near -18 ns.\nthe ATLAS fast detector simulation [15]. For all distributions shown in this section, QCD events were\nselected with the common jet cuts described in Section 1.\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n / 400 GeV\n-1\nEvents / 1 fb\n [GeV]\neff\nM\n CTEQ6.1M (NLO PDF)\n MRST2004 (NLO PDF)\n CTEQ6L1 (LO PDF)\n CTEQ6.1M (NLO PDF)\n MRST2004 (NLO PDF)\n CTEQ6L1 (LO PDF)\nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nratio w.r.t. CTEQ6.1M\n [GeV]\neff\nM\nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 6: The Meff distribution for simulated QCD events satisfying SUSY jet cuts described in Section 1.\nThe left plot shows the number of events per bin, scaled to 1fb\u22121 and the right plot shows the fractional\ndifference with respect to CTEQ6.1M. In each case, the solid histogram and shaded band shows the\nresults from the CTEQ6.1M proton PDF. The dashed and dotted histograms show the results from the\nMRST2004 and CTEQ6L1 PDFs, respectively. The error bars re\ufb02ect the Monte Carlo statistics.\nProton Parton Distribution Functions\nAll calculations of cross-sections at the LHC rely on a knowl-\nedge of the proton parton distribution functions (PDFs). High-pT QCD events will be particularly sensi-\ntive to the gluon PDF at large x which, in current global \ufb01ts [16\u201319], is relatively poorly known. In this\nsection, the impact of the PDF uncertainties on distributions of observables sensitive to the presence of\nSUSY signal is estimated.\nEvents were generated using PYTHIA 6.403 [7], with the following PDFs: CTEQ6L1 [20], CTEQ6.1M [17]\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1567\n\nand MRST2004nlo [21]. Note that CTEQ6L1 is a leading order (LO) PDF, while CTEQ6.1M and\nMRST2004nlo sets are both next-to-leading-order (NLO) sets. CTEQ6.1M provides a set of error PDFs\n(S\u00b1\ni ), corresponding to the N eigenvector directions. Note that the S\u00b1\ni only re\ufb02ect the experimental un-\ncertainties on the data, and do not include any information on theoretical assumptions used in the \ufb01t.\nThe total PDF uncertainty arising from experimental sources, on a given observable, \u03a3, can then be\nconstructed according to:\n\u2206\u03a3\u00b1 =\ns\nN\n\u2211\ni=1\n\u0000max\n\u0000\u00b1\u03a3(S+\ni )\u2213\u03a3(S0),\u03a3(\u00b1S\u2212\ni )\u2213\u03a3(S0),0\n\u0001\u00012;\n(3)\nwhere \u2206\u03a3+(\u2206\u03a3\u2212) are the upper (lower) uncertainties on the observable and S0 represents the central (best\n\ufb01t) PDF value. For CTEQ6.1M, there are 40 error PDF sets, S\u00b1\ni , corresponding to N = 20 eigenvector\ndirections. Since the uncertainty band obtained from CTEQ6.1M only re\ufb02ects the uncertainties of the\nexperimental data, the predictions of this PDF are also compared here to those from MRST2004nlo (an\nalternative, independent NLO PDF) and to CTEQ6L11.\nThe distribution of Meff for the different PDFs considered, and the fractional uncertainty with respect\nto the central prediction of CTEQ6.1M, is shown in Fig. 6. The CTEQ6.1M uncertainty band ranges from\n\u223c20\u221250%, as Meff increases. The largest contribution to this band comes from eigenvector 15, which is\nmainly sensitive to the gluon at large x. The results from MRST2004nlo lie well within the CTEQ6.1M\nuncertainty band across the whole range of the distribution. The prediction from CTEQ6L1, a LO PDF,\nlies below those of the NLO PDFs. For Meff \u22731 TeV, the difference is approximately constant and at\nthe level of \u223c20%. The validity of using NLO versus LO PDFs, with LO matrix-element generators,\nis discussed in a recent publication [22]. However, these results indicate that the difference between the\nresults from LO and NLO PDFs is smaller than the CTEQ6.1M uncertainty band.\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n / 400 GeV\n-1\nEvents / 1 fb\n [GeV]\neff\nM\n PYTHIA - \u2019ATLAS default\u2019\n PYTHIA - \u2019Tune A\u2019\n PYTHIA - \u2019no MPI\u2019\n JIMMY - \u2019ATLAS default\u2019\nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nratio w.r.t. PYTATLASD\n [GeV]\nM\nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 7: The Meff distribution for simulated QCD events satisfying SUSY jet cuts described in Section 1.\nThe left plot shows the number of events per bin and the right plot shows the fractional uncertainty\nwith respect to the \u201cPYTHIA \u2013 ATLAS default\u201d model for the underlying event. In each plot, the\nsolid histogram shows the results from the \u201cPYTHIA \u2013 ATLAS default\u201d, the dotted histogram shows\n\u201cPYTHIA \u2013 Tune A\u201d, the dashed histogram shows \u201cPYTHIA \u2013 no MPI\u201d and the dot-dashed histogram\nshows \u201cJIMMY \u2013 ATLAS default\u201d. The error bars re\ufb02ect the Monte Carlo statistics.\n1Note that the PYTHIA parameters used by default within ATLAS are tuned to the CTEQ6L1 proton PDF. Strictly, if a\ndifferent PDF is used, a retuning of the Monte Carlo parameters to data should be performed. This has not been done in the\ncurrent study, and this should be bourne in mind when interpreting the results.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1568\n\nUnderlying Event\nMonte Carlo generation of QCD events is also sensitive to the underlying event.\nMulti-parton interactions are modelled in several Monte Carlo generators. For this study, the PYTHIA\n6.403 [7], and HERWIG 6.507 [23] (used in conjunction with JIMMY v4 [24]) are used. Further details\nof the underlying-event models compared are summarised below. Note that, unless otherwise stated,\nCTEQ6L1 is used as the proton PDF.\nThe underlying event models considered are brie\ufb02y summarised below:\n\u2022 \u201cPYTHIA \u2013 ATLAS default\u201d : the ATLAS default underlying-event tune for PYTHIA 6.4 [8].\n\u2022 \u201cPYTHIA \u2013 Tune A\u201d : a model based on the \u201cPYTHIA-TuneA\u201d [25] to Tevatron data. Note that\nsince underlying-event tunes also depend on the PDFs, CTEQ5L [26], appropriate to Tune A, has\nbeen used here.\n\u2022 \u201cPYTHIA \u2013 no MPI\u201d : a model in which multi-parton interactions have been switched off. All\nother parameters were left at the PYTHIA 6.403 defaults. This model does not describe the Teva-\ntron data, but is included for comparison.\n\u2022 \u201cJIMMY \u2013 ATLAS default\u201d - the ATLAS default underlying event tune for HERWIG 6.5 + JIMMY\n4 [8].\nThe distribution of Meff is shown in Fig. 7. The left plot shows the number of events per bin (scaled\nto 1 fb\u22121) while the right plot shows the fractional ratio with respect to \u201cPYTHIA \u2013 ATLAS default\u201d.\nAs expected, the model with no underlying event contribution, \u201cPYTHIA \u2013 no MPI\u201d, lies below the\npredictions of all other PYTHIA models. The highest model prediction is given by the \u201cPYTHIA \u2013 Tune\nA\u201d model, based on \u201cPYTHIA-TuneA\u201d to Tevatron data. The ATLAS default tunes, \u201cPYTHIA \u2013 ATLAS\ndefault\u201d and \u201cJIMMY \u2013 ATLAS default\u201d, show differences of \u223c20%. However, some of this difference\nmay come from the different normalisations of PYTHIA and HERWIG and not totally due to the underlying\nevent model. The overall spread in predictions from these models, is \u223c40% and is approximately\nconstant across the range of Meff shown.\n3.2\nJet energy scale uncertainty\nA signi\ufb01cant source of irreducible experimental uncertainty in Monte Carlo QCD background estimates\nwill arise from the uncertainty in the jet-energy-scale (JES). In this section, a simple estimate of the\nimpact of the JES uncertainty is performed. For each event, the energy and momentum of each jet has\nbeen scaled by a constant factor, corresponding to a 10%, 5%, 3% and 1% uncertainty on the JES. The\nEmiss\nT\nhas also been adjusted accordingly, by an amount corresponding to the change in the sum of the\njet momenta in the x and y directions. All such scaling is performed prior to any selection cuts. For this\nstudy, the QCD dijet events generated with PYTHIA have been used, with a fake Emiss\nT\n\ufb01lter applied to\nenhance the rate of potentially mismeasured events [3,8].\nFigure 8 shows the resulting Meff distribution. The shaded bands show the uncertainties on the distri-\nbution for the four different values of the JES uncertainty considered. For a 10% value, the uncertainty\non the Meff distribution ranges from \u223c50\u2212150%. An improved understanding of the JES to a level of\n5% reduces the uncertainty on Meff by more than a factor of two, while a 3% value shows an improved\nuncertainty on Meff of between \u223c10\u221230%. If the challenging goal of a 1% JES uncertainty is achiev-\nable, the results indicate that the uncertainty on high-pT events could be much reduced, to a level of\n\u223c5\u221210%.\n3.3\nGenerator comparison: PS vs. ALPGEN\nThe recent development of event generators in which regions of phase-space populated by a multi-\nparton matrix-element calculation are matched to those populated by a parton shower algorithm offer\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1569\n\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n / 400 GeV\n-1\nEvents / 1 fb\n [GeV]\neff\nM\n Pythia 6.4 \n10% JES uncert. \n5% JES uncert. \n3% JES uncert. \n1% JES uncert. \nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n8\n10\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nfractional uncertainty\n [GeV]\neff\nM\nATLAS\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nFigure 8: The Meff distribution for simulated QCD events satisfying SUSY jet cuts described in Section 1.\nThe left plot shows the number of events per bin and the right plot shows the fractional uncertainty with\nrespect to the central prediction. The shaded bands show the estimated uncertainty on the observable for\nassumed JES uncertainties of 10% (light), 5% (medium-light), 3% (medium) and 1% (dark).\nthe prospect of improved simulation of high pT QCD jet events. In this section we compare the physics\nperformance of such a generator, namely the leading-order ALPGEN [27] code, with that of a conventional\nstand-alone parton-shower generator (PYTHIA 6.403 [7]).\nMultijet QCD events were generated with ALPGEN 2.05+JIMMY and with PYTHIA 6.403 and the re-\nsulting distributions of observables sensitive to SUSY signal events compared using fast simulation [15].\nPYTHIA events were generated in different pT ranges of the two leading partons to study the high energy\ntails with suf\ufb01cient statistics (see Ref. [8]). Such sliced-sample production is also possible in ALPGEN.\nOnly events satisfying the standard SUSY jet cuts described in Section 1 were studied. The number of\nPYTHIA events passing the jet selection cuts is 2.1 times larger than the number of ALPGEN events for the\nsame integrated luminosity2. To facilitate comparison of the two samples, they were both normalized\nto 1 fb\u22121 and ALPGEN samples were further multiplied by a factor of 2.1. Error bars on each histogram\nbelow are based on the Monte Carlo statistics used in this study.\nFigure 9 shows the pT distribution of the leading four jets for ALPGEN and PYTHIA events. The new\nparton shower scheme available in PYTHIA 6.403 can produce hard subleading jets with similar pT to\nthose produced by ALPGEN while the two leading jets are somewhat softer. Even though PYTHIA also\ngenerates 2 \u21922 scattering using matrix-element calculations, the two highest-pT jets are softer because\nadditional partons are emitted from the leading partons using splitting functions.\nThe use of fast detector simulation for the comparison of event generators described in this section\nprevents accurate study of the impact of generator differences on \u2018fake\u2019 Emiss\nT\ndistributions. Neverthe-\nless, \u2018real\u2019 Emiss\nT\nevents in which heavy quark decays generate neutrinos can potentially dominate in\nthe tail of the Emiss\nT\ndistribution following application of the cuts described in Section 2 and Ref. [3].\nFast detector simulation can legitimately be used to study this background permitting comparison of\nPYTHIA and ALPGEN predictions of Emiss\nT\nand Meff distributions. Figure 10(a) shows the Emiss\nT\ndistri-\nbutions obtained from PYTHIA and ALPGEN while Figure 10(a) shows the relative difference between the\ndistributions of the Emiss\nT\n.\n2No b\u00afb or c\u00afc pair production events where the heavy quark pair is produced in the hard scatter rather than through gluon\nsplitting were generated in PYTHIA. This contribution is 10 % of the total b\u00afb cross-section and negligible compared to the total\nmulti-jet cross-section.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1570\n\n [GeV]\nT\np\n0\n500\n1000\n1500\n2000\n / 25 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(a)\nATLAS\n Leading Jet\nALPGEN\nPYTHIA\n [GeV]\nT\np\n0\n500\n1000\n1500\n2000\n / 25 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(b)\nATLAS\n Second Jet\nALPGEN\nPYTHIA\n [GeV]\nT\np\n0\n500\n1000\n1500\n2000\n / 25 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(c)\nATLAS\n Third Jet\nALPGEN\nPYTHIA\n [GeV]\nT\np\n0\n500\n1000\n1500\n2000\n / 25 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(d)\nATLAS\n Fourth Jet\nALPGEN\nPYTHIA\nFigure 9: The pT distributions of the four highest-pT jets; (a) the leading, (b) the second (c) the\nthird and (d) the fourth jet for PYTHIA (open circles) and ALPGEN (open histogram) events.\nPYTHIA predicts somewhat larger Emiss\nT\nthan ALPGEN, although limited Monte Carlo statistics prevent\n\ufb01rm conclusions from being drawn at large Emiss\nT\n. This effect likely originates from the fact that multi-jet\nevents containing gluon splitting are not fully included in ALPGEN because of the requirements of matrix\nelement \u2013 parton shower matching.\n3 The equivalent Meff distributions and the relative differences\nbetween generators are shown in Figure 11. The Meff distribution of ALPGEN events is harder than that of\nPYTHIA events, as expected from Figure 9(a) and (b).\n4\nMonte Carlo estimates\n4.1\nJet smearing with Transfer Function\nIntroduction\nIn this section, a Monte Carlo based detector simulation technique is described which\nmodels the response function of the ATLAS calorimeter to jets as a function of energy and \u03b7 using\nMonte Carlo \u201ctruth\u201d information, and then uses this response function to smear the energies of jets and\nother objects in Monte Carlo QCD jet events. The truth-derived response function used here is referred\nto as the particle-jet transfer function (PJTF) and in principle may be measured also from data using\ntechniques such as those described in Section 5.1.\n3To avoid double counting of partons generated by the matrix element calculation and parton shower algorithm, the MLM\nmatching scheme employed by ALPGEN requires that matrix element partons satisfy cuts on pT (>40 GeV) and \u2206R between\npartons (> 0.7). As a result of these requirements, processes such as ggbb generating multiple partons with \u2206Rbb < 0.7 are\nrejected during matching. Events with gluon splitting generated in the parton shower algorithm are however kept.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1571\n\n [GeV]\nT\nMissing E\n0\n100\n200\n300\n400\n500\n / 10 GeV\n-1\nEvents / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(a)\nATLAS\nALPGEN\nPYTHIA\n [GeV]\nT\nMissing E\n0\n20\n40\n60\n80 100 120 140 160 180 200\nALPGEN\n) / N\nALPGEN\n-N\nPYTHIA\n(N\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n(b)\nATLAS\nFigure 10: (a) ATLFAST Emiss\nT\ndistribution for PYTHIA(circles) and ALPGEN (histogram) and (b)\nthe relative difference (NPYTHIA-NALPGEN)/NALPGEN of the Emiss\nT\ndistributions. The shaded band is\nthe Monte Carlo statistical error.\n [GeV]\neff\nM\n0\n1000\n2000\n3000\n4000\n-1\nNevent / 100 GeV/ 1fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n(a)\nATLAS\nALPGEN\nPYTHIA\n [GeV]\neff\nM\n0\n1000\n2000\n3000\n4000\nALPGEN\n) / N\nALPGEN\n-N\nPYTHIA\n(N\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n(b)\nATLAS\nFigure 11: (a) ATLFAST Meff distribution for PYTHIA(circles) and ALPGEN (histogram) and (b)\nthe relative difference (NPYTHIA-NALPGEN)/NALPGEN of the Meff distributions. The shaded band is the\nMonte Carlo statistical error.\nModeling jets \u2013 reconstruction of the PJTF\nIn this section we use the following terminology for\ntwo different types of jets formed from Monte Carlo events \u2013 \u201cparticle jets\u201d, made from all the generated\nparticles in the event except muons and neutrinos, and \u201ccalorimeter jets\u201d formed from topological clusters\nin the calorimeter.\nIn general there is a high ef\ufb01ciency for reconstructing jets in the calorimeter, even though their energy\ncan potentially be mis-measured by a large amount. Jet fragmentation to particles of different types and\nthe response of the detector material to these particles in different \u03b7 regions can produce tails in the\nPJTF. It is possible for there not to be a one-to-one match between generator-level jets and calorimeter\njets even though the same jet clustering algorithms are used.\nTo reconstruct the PJTF it is necessary to measure the response of the calorimeter to generator-level\njets. This is accomplished by matching these to calorimeter jets, and requiring a good jet isolation in\nboth jets (separation from nearest jet \u2206R > 0.8), to ensure that accidental jet overlaps do not contribute\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1572\n\nto the tails in the PJTF. Jet energy responses are modeled with double Gaussians. The ratio of the\n1st and 2nd Gaussian components is empirically known to follow the ratio of energy deposits in the\nelectromagnetic and hadron calorimeter and hence the 1st/2nd Gaussian ratio is \ufb01xed to the mean value\nof Ehad/(Eem + Ehad) with a \ufb01tting procedure. GEANT4 simulated PYTHIA dijet samples with pT > 17\nGeV [8] are used to estimate the PJTF. Reconstructed jet energies are corrected with an energy-density\nbased weighting scheme [28]. The \ufb01ts are performed before the jet energy corrections have been applied,\ni.e. the PJTF is obtained at the calorimeter cell energy calibration level. To use the PJTF on reconstructed\njets, cell-to-jet energy corrections are applied after the PJTF. For the Emiss\nT\ncalculation the cell-level\ncorrection is used directly to retain consistency with full GEANT4 simulation Emiss\nT\n.\nModeling Emiss\nT\nAll truth jets (formed from stable truth particles expected to shower in the calorimeter)\nwith energy greater than 10 GeV are smeared with the PJTF. This avoids double counting of interact-\ning particles (electron, photon, tau) due to the potentially different treatment of merging and splitting\nof objects, for example when the photon is close to a jet. This simpli\ufb01cation of reconstructing jets\nfrom all stable showering particles mis-measures the energy scale of isolated electrons, photons and\ntaus by a small amount, however the ATLAS procedure of identifying and calibrating electromagnetic\nand hadronic showers separately ensures that the resulting bias is minimised. This study is additionally\nfocussed on QCD jet events and hence any such bias is still less important. Muons in the event are\nsimulated with the ATLFAST fast simulation code [15] due to the prohibitive time overhead associated\nwith full simulation of the ATLAS tracking systems. Finally in order to account for the potentially large\n\ufb02uctuation in the underlying event, we vectorially sum all the particles that are not part of jets above\n10 GeV to form a \u201csoft jet\u201d. This soft jet is added to the above jet sum to compensate for the contribution\nfrom soft particles outside of the jet cones. Once all the objects in the event are de\ufb01ned, the E miss\nT\nin the\nevent is calculated by summing their four-vectors, enabling comparison of the performance of the PJTF\ntechnique with full GEANT4 simulation.\nPerformance\nThe performance of the PJTF technique was assessed by comparing PJTF predictions\nwith those obtained from full GEANT4 simulation using the pT > 17 GeV dijet samples described above.\nThe event-by-event comparison was performed using both ATLFAST and fully reconstructed objects in\nthe GEANT4 simulation samples.\nThe jet multiplicity difference between full GEANT4 simulation and PJTF, and between full GEANT4\nsimulation and ATLFAST are shown in Fig. 12. Only jets with pT > 50 GeV and |\u03b7| < 2.5 were used, but\nno event selection based on the jet multiplicity was performed.\nNjets (= Full - (Fast or TF))\n\u2206\nJ4 \n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\narbitrary units\n0\n50\n100\n150\n200\n250\n300\n350\n3\n10\n\u00d7\nTransfer Function Jets\nAtlfast Jets\nATLAS\nNjets (= Full - (Fast or TF))\n\u2206\nJ6 \n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\narbitrary units\n0\n50\n100\n150\n200\n250\n3\n10\n\u00d7\nTransfer Function Jets\nAtlfast Jets\nATLAS\nFigure 12: Event by event difference in number of jets between full GEANT4 simulation and PJTF\n(blue,solid) and between full GEANT4 simulation and ATLFAST (red,dashed).\nThe left plot is for\n140 GeV < pT < 280 GeV events, and the right one is for 560 GeV < pT < 1120 GeV events.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1573\n\nThere is good agreement in jet multiplicity between the full GEANT4 simulation and the PJTF events.\nThe ATLFAST events have a somewhat higher multiplicity due to the simpli\ufb01ed calorimeter map used for\njet reconstruction. For the PJTF technique to be effective, it is important that the multiplicity at recon-\nstruction level is not biased. This is clearly demonstrated in Fig. 12. Good agreement was found for jet\npT > 40 GeV, which can be explained as follows. The topological clustering jet algorithm has a \u223c100%\nef\ufb01ciency so if the transfer function is correctly scaling and smearing the energy the jet multiplicity could\nonly be biased by jets splitting and/or merging.\nAnother performance check is the comparison of the scalar pT sum of the four leading jets obtained\nfrom full GEANT4 simulation, PJTF, and ATLFAST events. Events passing the typical SUSY jet cuts listed\nin Section 1 are used. Fig. 13 shows the comparisons for 140 GeV < pT < 280 GeV and 560 GeV <\npT < 1120 GeV events. Good agreement is observed between the full GEANT4 simulation and PJTF\nevents, while ATLFAST events have signi\ufb01cant deviations for the same reasons as for Fig. 12.\nJ4 Sum of 4 leadingEt [GeV]\n0\n200\n400\n600\n800\n1000\n1200\n1400\narbitrary units\n1\n10\n2\n10\n3\n10\nTransfer Function Jets\nFull simulation Jets\nAtlfast Jets\nATLAS\nJ6 Sum of 4 leadingEt [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\narbitrary units\n1\n10\n2\n10\n3\n10\n4\n10\nTransfer Function Jets\nFull simulation Jets\nAtlfast Jets\nATLAS\nJ4 Sum of 4 leadingEt [GeV]\n0\n200\n400\n600\n800\n1000\n1200\n1400\nratio w.r.t full-sim\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nTransfer Function Jets\nA lfast Jets\nATLAS\nJ6 Sum of 4 leadingEt [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n350\nratio w.r.t full-sim\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\nTransfer Function Jets\nAtlfast Jets\nATLAS\nFigure 13: Top: distributions of the scalar pT sum of the four leading jets in PJTF (black, solid), ATLFAST\n(red, solid) and fully GEANT4 simulated jets (blue, points). The left plot is for 140 GeV < pT < 280 GeV\nevents, and the right plot is for 560 GeV < pT < 1120 GeV. Bottom: the ratio with respect to the fully\nGEANT4 simulated jets.\nIn order to check the performance of Emiss\nT\nmodeling the typical SUSY jet cuts described in Section 1\nwere applied, with no Emiss\nT\ncut applied initially. We de\ufb01ne fake Emiss\nT\nas follows:\nEmiss,fake\nT\n= |pmiss,reco\nT\n|\u2212|pmiss,true\nT\n|\nwhere pmiss,reco\nT\nis the missing transverse momentum vector reconstructed using either the PJTF tech-\nnique, GEANT4 simulation, or ATLFAST, and pmiss,true\nT\nis the transverse vector of the sum of the neutrino\nmomenta.\nFig. 14 shows the fake Emiss\nT\ndistribution obtained from the PJTF technique and from full GEANT4\nsimulation. Also shown are the ATLFAST results, and the PJTF results without the soft-jet corrections.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1574\n\nfake MET [GeV]\n-40\n-20\n0\n20\n40\n60\n80\n100\nnormalized to 1\n4\n10\n3\n10\n2\n10\n1\n10\nAtlfast\nTransfer function\nFullSimulation\nTF no soft comp.\nATLAS\nfake MET [GeV]\n-100\n-50\n0\n50\n100\n150\n200\n250\nnormalized to 1\n4\n10\n3\n10\n2\n10\n1\n10\nAtlfast\nTransfer function\nFullSimulation\nTF no soft comp.\nATLAS\nfake MET [GeV]\n40\n20\n0\n20\n40\n60\n80\n100\nratio w.r.t full sim\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nAtlfast\nTransfer function\nTF no soft comp.\nATLAS\nfake MET [GeV]\n100\n50\n0\n50\n100\n150\n200\n250\nratio w.r.t full sim\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nAtlfast\nTransfer function\nTF no soft comp.\nATLAS\nFigure 14: Fake Emiss\nT\ndistributions from ATLFAST (red hatched), PJTF technique (black, solid) and\nfull GEANT4 simulation (blue, points). Also shown with the dashed green line is the PJTF distribution\nwithout soft-jet correction. The left plot is for 140 GeV < pT < 280 GeV events, and right plot is for\n560 GeV < pT < 1120 GeV. Bottom plots are the ratio of each distribution with respect to the full\nGEANT4 simulation.\n Missing Et [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n/20GeV\n1\n Events/1fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nTransfer Function\nFull simulation\nAtlfast\nATLAS\n[GeV]\neff\n M\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\n/60GeV\n1\n Events/1fb\n1\n10\n2\n10\n3\n10\n4\n10\nTransfer Function\nFull simulation\nAtlfast\nATLAS\nFigure 15: Emiss\nT\n(left) and Meff (right) distributions of 560 < pT < 2240 GeV PYTHIA QCD jet events\nsimulated with ATLFAST (light/red solid), the PJTF technique (dark/black, solid) and full GEANT4 simu-\nlation (points). Events were required to pass the SUSY jet cuts described in Section 1.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1575\n\nTable 2: Numbers of 560 < pT < 2240 GeV PYTHIA QCD jet events passing cuts for 1 fb\u22121 data, starting\nfrom an original total of 3.5 \u00d7105 events. Errors are also normalized to 1 fb\u22121. The cut de\ufb01nitions are\ndescribed in the text.\nMethod\nCut 1\nCut 2\nCut 3\nFull simulation\n(103.8\u00b10.3)\u00d7103\n(65.7\u00b10.3)\u00d7103\n4.3\u00b12.1\nPJTF technique\n(104.9\u00b10.3)\u00d7103\n(62.3\u00b10.2)\u00d7103\n2.2\u00b11.5\nATLFAST\n(120.0\u00b10.3)\u00d7103\n(86.1\u00b10.3)\u00d7103\n2.1\u00b11.5\nIt can be seen from the \ufb01gure that Emiss\nT\nestimated with the PJTF technique and with full GEANT4\nsimulation agree at the 20% level for fake Emiss\nT\n< 80 GeV (200 GeV) for 140\u2013280 GeV (560\u20131120\nGeV) dijet events. The \ufb01gures highlight the improvement in performance relative to the naive ATLFAST\nestimate of Emiss\nT\n, with the agreement between PJTF and full GEANT4 simulation persisting down into\nthe tail region a factor 10\u22123 below the peak.\nFig. 15 shows the performance of the PJTF technique for estimating QCD backgrounds to the E miss\nT\nand Meff distributions obtained following application of the SUSY jet cuts described in Section 1. In\nthese plots the event-weights and errors are normalized to 1 fb\u22121. Good agreement is seen between the\nPJTF distributions and the full simulation distributions over the full pT range, while the naive ATLFAST\ndistributions show larger deviations from the full simulation results.\nAdditional cuts equivalent to the full SUSY cuts described in Section 1 were applied to assess further\nthe consistency between the PJTF results and those obtained with full GEANT4 simulation. In Table 2 the\nremaining numbers of events after each stage in the event selection are shown. Cut 1 is the standard\nSUSY jet cut applied above. Cut 2 adds the requirement \u2206\u03c6min > 0.2 (see Section 2.2) while Cut 3\nrequires additionally Emiss\nT\n> max(100 GeV, 0.2Meff) and Meff > 800 GeV. Despite limited statistics the\nresults show that the PJTF approach provides reduced event selection bias in comparison with the naive\nATLFAST simulation.\n4.2\nFast GEANT4 simulation\nIntroduction\nThe simulation of the ATLAS detector is currently based on GEANT4 v.4.8.3 [2].\nGEANT4 simulation is very time consuming however and so its use for QCD background simulation\nat moderate or low pT is not viable. The fully GEANT4-based approach (refered to as full simulation in\nthe following) is especially slow in the simulation of electromagnetic cascades in the calorimeters due\nto their complicated geometry. A fast simulation tool (ATLFAST [15]) based on Gaussian smearing is\nalso available, and is used for studies of systematic uncertainties elsewhere in this note, but it does not\nreproduce with suf\ufb01cient accuracy the tails of distributions interesting for SUSY analysis, i.e. E miss\nT\nor\nMeff. For this reason, an intermediate approach to the simulation of the ATLAS detector, based on the\nparameterisation of the calorimeters\u2019 response, is under study [29]. In the so-called \u2018fast\u2019 GEANT4 sim-\nulation, electrons entering the calorimeters may receive different treatments according to their energy.\nFor high energy particles a shower parameterisation is used while for medium energy particles (below 1\nGeV) the detector response is taken from a shower library (\u201cfrozen showers\u201d), and low energy particles\n(below 10 MeV) are \u201ckilled\u201d by depositing their energy in a single spot in the calorimeter.\nPerformance\nWe tested fast GEANT4 simulation algorithms by simulating PYTHIA [7] dijet events with\nmoderate transverse momentum (280 GeV < pT < 560 GeV). The fast GEANT4 simulation can be per-\nformed using different options, which differ in the treatment applied to electromagnetic particles (shower\nparameterization, frozen showers or \u201ckilling\u201d) in different parts of the calorimeters (for more details,\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1576\n\nsee [29]). In the following, the fast GEANT4 options are numbered from 1 to 3, the \ufb01rst one being the\nmost conservative option, i.e., the closest to full simulation, and the third one the fastest option currently\navailable. The measured fast GEANT4 simulation time is \u223c60% lower than that required for full simula-\ntion. The three fast GEANT4 options differ among themselves by only a few percent of the full simulation\ntime. To study the effect of the fast GEANT4 simulation algorithms in SUSY searches, we compared the\ndistributions of typical quantities, i.e. the jet multiplicity and transverse momentum, E miss\nT\n, transverse\nsphericity, and effective mass in 5000 fast GEANT4 simulated events with the ones obtained from full\nsimulation (see Figs. 16, 17 and 18). We reconstructed jets with pT > 50 GeV and |\u03b7| < 2.5. Due to\nthe limited number of Monte Carlo events, no requirement was applied to the jet multiplicity, except in\nthe Emiss\nT\nand Meff distributions, where the standard SUSY jet cuts described in Section 1 were applied.\nTransverse sphericity and effective mass quantities were calculated only for events with at least 2 jets.\nWhilst the largest jet transverse momentum is well reproduced in the fast simulated samples, the\naverage jet multiplicity is lower than that of the fully simulated sample by 1-2%. The most conservative\nsample (option 1) is in agreement with the full simulation distribution inside the statistical uncertainty.\nThe width of the jet pT resolution is consistent across the samples, however the jet energy scale is too\nlow by 1-2% (see Fig. 17). Due to the limited number of events available only a qualitative comparison\nis possible in regions of interest for SUSY searches for Emiss\nT\n(higher than 100 GeV) and transverse\nsphericity (larger than 0.2). Within the statistical precision possible the fast simulated distributions agree\nwell with those obtained from full GEANT4 simulation. The size of the available samples preclude a full\nassessment of performance for the baseline SUSY cuts described in the introduction, since no events pass\nall cuts when using any of the three options. Similarly, from an equivalent number of GEANT4-simulated\nevents, none pass all the cuts.\nnb. reconstructed jets\n0\n2\n4\n6\n8\n10\n-1\nnb. Evts / 0.32 pb\n1\n10\n2\n10\n3\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\n [GeV]\nT\nLeading Jet p\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nnb. Evts / 40 GeV / 0.32 pb\n1\n10\n2\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\nFigure 16: Reconstructed jet multiplicity (left) and highest jet pT (right) for PYTHIA dijet samples simu-\nlated with different options. The statistical uncertainty only is shown for the full simulation sample.\nOverall, the fast GEANT4 simulation has been shown to be a promising faster alternative to the full\nGEANT4 based simulation. The reconstructed quantities in fast GEANT4 simulated samples are in good\nagreement with full simulation. Work is on-going to further reduce the simulation time, and to improve\nthe modeling of the jet energy scale.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1577\n\nT, true\n ) / p\nT, true\n -p\nT\nLeading Jet ( p\n-0.4\n-0.3\n-0.2\n-0.1\n-0\n0.1\n0.2\n0.3\n0.4\n-1\n# Evts / 0.016 / 0.32 pb\n1\n10\n2\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\n [GeV]\nT\nMissing E\n0\n50\n100\n150\n200\n250\n300\n350\n400\n-1\nnb. Evts/ 8 GeV / 0.32 pb\n1\n10\n2\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\nFigure 17: Leading jet pT resolution (left) and Emiss\nT\n(right) for PYTHIA dijet samples simulated with\ndifferent options. The statistical uncertainty only is shown for the full simulation sample.\nTransverse sphericity\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nnb. Evts / 0.04 / 0.32 pb\n1\n10\n2\n10\n3\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\n [GeV]\neff\nM\n0\n200 400 600 800 100012001400160018002000\n-1\nnb. Evts / 60 GeV / 0.32 pb\n1\n10\n2\n10\nATLAS\nFull sim\nFast G4 sim 1\nFast G4 sim 2\nFast G4 sim 3\nFigure 18: Transverse sphericity (left) and Meff (right) for PYTHIA dijet samples simulated with different\noptions. The statistical uncertainty only is shown for the full simulation sample.\n5\nData-driven estimates\n5.1\nJet smearing in the zero-lepton mode\nIntroduction\nThe inherent systematic and statistical uncertainties in Monte Carlo based QCD back-\nground estimates will limit their use until suf\ufb01cient data have been acquired to understand both the\nATLAS detector and the underlying physics of QCD processes at 14 TeV. For this reason data-driven\nbackground estimates with minimal reliance on Monte Carlo simulation will be a priority for the early\nphase of data-taking.\nThe method described in this section reduces dependence on Monte Carlo simulation by smearing jet\ntransverse momenta in low Emiss\nT\nQCD multijet data with a data-measured jet response function R de\ufb01ned\nas the distribution of event-by-event ratios of measured jet pT to true jet pT. This response function could\npotentially be used inter-changeably with the Monte Carlo-truth derived Particle Jet Transfer Function\n(PJTF) discussed in Section 4.1. Consequently the method described below provides a route to practical\nrealisation of the PJTF technique for use with real data. The technique can be broken down into three\ndistinct parts which are outlined below.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1578\n\nStep 1: Gaussian response function measurement\nThe \u201cEmiss\nT\nprojection method\u201d [30] applied to \u03b3\n+ jet events allows a measurement of the Gaussian response RG of the ATLAS calorimeters to jets. The\nlimited number of events prevent the measurement of the non-Gaussian tail with this technique (see Step\n2). The method uses transverse momentum conservation to constrain the pT of all activity associated with\na reconstructed jet with the pT of a hard photon. RG is obtained from the distribution of the photon-jet\npT balance R1:\nR1 = 1+ pmiss\nT\n\u00b7pT(\u03b3)\n|pT(\u03b3)|2\n,\n(4)\nwhere pT(\u03b3) is the photon transverse momentum, and pmiss\nT\nis the missing-transverse-momentum two-\nvector.\nA GEANT4-simulated PYTHIA [7] sample equivalent to 23.8pb\u22121 of \u03b3 + jets events was used, with\nevents required to pass a 60 GeV single-photon trigger [9]. With the additional requirement that events\nshould contain one and only one reconstructed jet, the jet response was measured with the distribution\nof R1 values de\ufb01ned above. The R1 distribution was measured in a number of photon pT bins, and each\nwas \ufb01tted with a Gaussian function. The standard deviations from these \ufb01ts to the response distributions\nare shown in Fig. 19 with the statistical error bars derived from the \ufb01t errors. The pT dependence of the\nwidths of the R1 distributions was \ufb01tted with the parametric form\n\u03c3R = A+\nB\n\u221apT\n+ C\npT\n,\n(5)\nshown in the \ufb01gure to describe well the GEANT4 simulated data. The sampling (A) and stochastic (B)\nterms in the above formula were used to calculate the width of RG as a function of jet pT, while the\nconstant term (C) was used to estimate the additional smearing of Emiss\nT\nnot associated with jets (see\nStep 3 below).\n [GeV]\nT\np\n50\n100\n150\n200\n250\n \nR\n\u03c3\n0.07\n0.08\n0.09\n0.1\n0.11\n0.12\n0.13\n0.14\n0.15\n / ndf \n2\n\u03c7\n 37.43 / 30\nA \n 0.02189\n\u00b1\n 0.04636 \nB \n 0.2722\n\u00b1\n 0.6356 \nC \n 1.188\n\u00b1\n 5.583 \n / ndf \n2\n\u03c7\n 37.43 / 30\nA \n 0.02189\n\u00b1\n 0.04636 \nB \n 0.2722\n\u00b1\n 0.6356 \nC \n 1.188\n\u00b1\n 5.583 \nATLAS\nFigure 19: Standard deviations of Gaussian \ufb01ts to measured response distributions vs. p\u03b3\nT. The \ufb01t is of\nthe functional form \u03c3R(pT) = A+BpT \u22121/2 +CpT \u22121.\nStep 2: Full (Gaussian + non-Gaussian) response function measurement\nIn order to reproduce the\ntail of the QCD multijet Emiss\nT\ndistribution it is necessary to characterise the non-Gaussian response of\nthe calorimeters to jets. The next stage in the technique therefore uses events in which the E miss\nT\nvector\ncan be unambiguously associated in \u03c6 with a single jet J to measure that response. The response of the\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1579\n\nATLAS calorimeters to jet J if its pT lies in the non-Gaussian tail can be obtained from\nR2 = pT(J)\u00b7pT(J,true)\n|pT(J,true)|2\n,\n(6)\nwhere pT(J) denotes the reconstructed transverse momentum of jet J. If it is assumed that the Emiss\nT\nin\nthese events is dominated by \ufb02uctuations in pT(J) then pT(J,true) can be approximated by\npT(J,true) \u2243pT(J)+pmiss\nT\n.\n(7)\nThe non-Gaussian response of ATLAS, RNG, is measured with the distribution of event R2 values.\nQCD jet events from the sample described in Section 2.1 were required to pass one of the high-pT\nmultijet or Emiss\nT\ntriggers [9], and required to contain at least three jets with pT > 250, 50 and 25 GeV,\nrespectively. Events were also required to possess Emiss\nT\n> 60 GeV. Events were further required to\ncontain a jet unambiguously associated with the Emiss\nT\nvector - i.e. events with one and only one jet\nparallel or anti-parallel to the Emiss\nT\nvector. Of the remaining jets in each event, the two with the highest\npT were required to have pT > 250, 50 GeV. In this way, the selected events predominantly had a\n\u2018Mercedes\u2019 type con\ufb01guration, with Emiss\nT\nparallel or anti-parallel to the pT of one of the jets. The\npT of this jet was used in Eqn. 6 to measure R2. The estimate of the jet response non-Gaussian tail\nRNG obtained from the distribution of R2 values is plotted as the histogram in Fig. 20(right) with a\nnormalisation obtained with the procedure described below. Although not considered in detail here, the\nW(\u2192\u03c4\u03bd) + 2 jet background could have been removed with a cut on the multiplicity of inner detector\ntracks per jet.\nNext we combine the Gaussian and non-Gaussian components of the jet response R measured pre-\nviously. The relative normalisation of the Gaussian (RG) and non-Gaussian (RNG) components can be\nmeasured using the balance of transverse momenta of jets in dijet events. The relative normalisation can\nbe obtained from the ratio of the numbers of dijet events with respectively one and zero jets with pT lying\nin the non-Gaussian tail of the jet response function. We therefore need to de\ufb01ne a variable which can\nclassify dijet events according to the number of jets with pT lying in the non-Gaussian tail. A suitable\nvariable is provided by R3(j), de\ufb01ned as the projection of the transverse momentum of each jet j\u2032 in the\nevent onto the event Emiss\nT\n:\nR3(j) = 1+ pmiss\nT\n\u00b7pT(j\u2032)\n|pT(j\u2032)|2\n,\n(8)\nwhich measures the response to the other jet j in the event (cf. Eqn. 4). If R3(j) lies below some threshold\nthen jet j can be considered to lie in the non-Gaussian tail.\nEvents were selected from the QCD jet event sample used above with the requirement that they\npassed a 160 GeV single-jet trigger requirement [9] and contained two and only two jets, back-to-back in\nthe transverse plane. The distribution of R3(j) for these events is plotted as data-points in Fig. 20(right).\nThe ratio of the integral of the low tail of the R3(j) distribution to the integral of a Gaussian function \ufb01tted\nto the peak is used to obtain the relative normalisation of the non-Gaussian and Gaussian components of\nthe jet response function. The full jet response function including normalised Gaussian and non-Gaussian\ncomponents is plotted in Fig. 20 (left).\nAs a \u2018closure test\u2019 of the reconstruction of the full response function, jets in a subset of the selected\ndijet events with low Emiss\nT\n-signi\ufb01cance (see Section 2.1) were smeared to reproduce the R3(j) distribu-\ntion. The resulting distribution is shown in Fig. 20 (right) for comparison with \u2018data\u2019.\nStep 3: Seed event selection and jet pT smearing\nIn order to estimate the Emiss\nT\nand Meff distributions\nof QCD multijet events the jet response function R measured in Step 2 was used to smear jet transverse\nmomenta in multijet events with low Emiss\nT\n(referred to below as \u2018seed events\u2019). Seed events were\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1580\n\nR\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\narbitrary units\n10\n2\n10\n3\n10\n4\n10\nFull smearing function\nGaussian component\nNon-gaussian component\nATLAS\nR\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\nEvents / 0.05 / 23.8pb\n1\n10\n2\n10\n3\n10\n4\n10\nDijet balance (data)\nDijet balance (estimate)\nMeasured response tail\nGaussian fit\nATLAS\nFigure 20: Left \u2013 smearing function for a jet of 250 GeV (thick line), with Gaussian and non-Gaussian\ncomponents (right and left facing hatches respectively) shown separately. Right \u2013 dijet balance distribu-\ntion (points) compared with the equivalent estimated distribution obtained from the jet response function\nto provide a \u2018closure test\u2019 of the technique. Also shown are a Gaussian \ufb01t to the region 0.8 < R3(j) < 1.15\n(thick line), and the non-Gaussian tail distribution (dashed histogram) measured with \u2018Mercedes\u2019 events\nnormalised to the tail of the dijet balance distribution.\nselected from the same PYTHIA jet sample used in Step 2. Seed event candidates were required to pass\none of the ATLAS high-pT jet triggers [9] together with the standard SUSY jet selection cuts described\nin Section 1 with a reduced jet pT threshold (pT(ji) > 45 GeV for i = 2,3,4) in order to avoid biasing the\n\ufb01nal estimate after smearing. Both the Emiss\nT\nsigni\ufb01cance (see Section 2.1) and the equivalent quantity\nconstructed from Emiss\nT\nderived only from in-cone jet energy were required to be less than 0.5 GeV1/2\nand 0.7 GeV1/2, respectively. The latter of these two cuts ensures that the hadronic activity in the selected\nseed events is well contained in the jets that will be smeared.\nSmeared events were constructed from each selected seed event by smearing the transverse momenta\nof their constituent jets with the jet response function R determined in Step 2. The Emiss\nT\nof smeared\nevents was calculated by replacing the contribution to the Emiss\nT\nfrom the pT of seed jets with a contri-\nbution from the pT of the equivalent smeared jets. An additional contribution pmiss\nT,C to pmiss\nT\ngenerated\nby the constant term measured in Step 1 was also taken into account. The smeared Emiss\nT\nwas therefore\ngiven by the magnitude of\npmiss\nT\n\u2032 = pmiss\nT,C \u2212\u2211\ni\np\u2032\nT(ji)+\u2211\ni\npT(ji),\n(9)\nwhere primed quantities are smeared.\nFig. 21 shows the Emiss\nT\nand Meff distributions for 23.8pb\u22121 of GEANT4 simulated \u2018data\u2019 and smeared\nseed events passing the SUSY jet cuts listed in Section 1. The estimate was normalised to GEANT4\nsimulated PYTHIA QCD jet events (\u2018data\u2019) with Emiss\nT\n< 50 GeV and somewhat tighter jet cuts (pT(j4) >\n60 GeV) imposed to ensure a reasonable sample of \u2018data\u2019 events obtained with the multi-jet triggers [9].\nThe dominant sources of systematic uncertainty in the estimate were pT bias in the selection of events\nand \ufb01nite statistics in the non-Gaussian tail measurement. Uncertainties on the A, B, and C parameters in\nEqn. 5 and the relative normalisation of the Gaussian and non-Gaussian parts of the jet response function\nwere also considered.\nGood agreement can be seen between the estimated and GEANT4 \u2018data\u2019 Emiss\nT\nand Meff distributions.\nApplying the full SUSY cuts described in Section 1, 2.36\u00b10.09(stat)\u00b11.44(syst) events are estimated\nversus 1 \u2018observed\u2019. The uncertainty in the estimate is therefore \u223c60% for 23.8 pb\u22121. If these \ufb01gures\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1581\n\n [GeV]\nT\nE\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\n-1\nEvents / 50GeV / 23.8pb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nQCD estimate\nQCD \u2019data\u2019\nOther SM\nSU3\nATLAS\n [GeV]\neff\nM\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-1\nEvents / 200GeV / 23.8pb\n1\n10\n2\n10\n3\n10\n4\n10\nQCD estimate\nQCD \u2019data\u2019\nOther SM\nSU3\nATLAS\nFigure 21: Emiss\nT\n(left) and Meff (right) distributions for smeared events and GEANT4 \u2018data\u2019 passing 0-\nlepton SUSY jet cuts. Also included for comparison are 23.8 pb\u22121 of SUSY (SU3) and the summed\ncontribution from Z \u2192\u03bd \u00af\u03bd + jets, W \u2192\u2113\u03bd + jets and t\u00aft + jets.\nare extrapolated to 1 fb\u22121 then the equivalent calculated uncertainties are \u223c0.6% (stat.) and 12.6%\n(syst.), with the systematic uncertainty reduced through access to increased statistics at step 2. However,\nresidual Standard Model (e.g. W(\u2192\u03c4\u03bd) + 2 jets) contamination of the \u2018Mercedes\u2019 control sample has\nnot been included in these uncertainty estimates and therefore we conservatively assume the same 60%\nsystematic uncertainty for 1 fb\u22121 of data. Systematic bias in the background estimate caused by the\npresence of SUSY signal is expected to be small \u2013 in particular the fractional contribution of SUSY\nevents to the Emiss\nT\nnormalisation region is \u227210\u22124.\n5.2\nLepton isolation in the one-lepton mode\nIntroduction\nAlthough QCD multijet background is not expected to be signi\ufb01cant after application of\nSUSY signal cuts in the 1-lepton mode [5], it still must be estimated. This will be particularly impor-\ntant when preparing control samples for data-driven background estimates of other backgrounds; it is\nimportant to ensure that such samples (which will have looser cuts than the \ufb01nal SUSY selection) are not\nsigni\ufb01cantly contaminated by QCD background. The technique studied here is also relevant for QCD\nbackgrounds in other lepton+jets channels, such as W(\u2192l\u03bd)+jets or t\u00aft in the semileptonic channel, al-\nthough the kinematic cuts used in searches for Supersymmetry (e.g. lepton + Emiss\nT\ntransverse mass, MT\n> 100 GeV) might select different background mechanisms.\nThe method, which has been used at the Tevatron, relies on the (near) independence of Emiss\nT\nand\nlepton isolation. The shape of the Emiss\nT\ndistribution is estimated from multijet events containing a\nnon-isolated lepton. This distribution is then normalized to the number of events containing an isolated\nlepton, but with low Emiss\nT\n. The method, if valid, would be complementary to the jet-smearing technique\ndescribed in Section 5.1 applied to one-lepton events, thereby allowing an important crosscheck of the\nsystematic uncertainties of the two methods.\nIn evaluating this method, it is important to understand potential correlations between isolation and\nEmiss\nT\n. One possible mechanism can arise when there are multiple sources of leptons in QCD multijet\nevents; if the sources each have a different Emiss\nT\nshape, and the relative mixture of the sources changes\nwith lepton isolation, this will appear as a correlation between Emiss\nT\nand isolation. A possible example\ninvolves electrons arising from jet mis-identi\ufb01cation and electrons from heavy-\ufb02avour decay. Another\nexample might involve leptons from charm versus leptons from bottom quark decays. Another possible\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1582\n\nsource of correlation arises from the kinematics of the heavy quark itself; the pT of the lepton, the\nassociated neutrino, and the remainder of the heavy quark fragmentation (which will be related to the\nisolation) are all coupled.\nPreliminary indications from studies of GEANT4 simulated QCD dijet samples suggest that the pri-\nmary source of electrons is a jet faking an electron, while the muon case is dominated by the decay of\nB hadrons. Thus the issue of multiple background sources alluded to above is not a serious concern\naccording to these Monte Carlo studies, but should be kept in mind for real data.\nWe \ufb01rst study the applicability of the lepton isolation technique in a pure sample of b\u00afb + jets. We\nthen move to a more realistic sample containing a mixture of t\u00aft and W +jets events in addition to the b\u00afb\n+ jets sample, focussing on the muon channel. The dominant systematic is found to be contamination of\ncontrol samples by t\u00aft events.\nMissing Et [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/100 pb-1/10 GeV\n-1\n10\n1\n10\nEtcone = [10,20] GeV. Rescaled\nEtcone < 10 GeV\nATLAS\nFigure 22: Points: Emiss\nT\ndistribution for the non-isolated lepton sample. Histogram: Emiss\nT\ndistribution\nfor the isolated lepton sample. The two distributions have been normalized to the same area in the region\nEmiss\nT\n= [10,20] GeV.\nLepton isolation versus Emiss\nT\nfor b\u00afb + jets\nThe dependence of Emiss\nT\non lepton (e,\u00b5) isolation was\nstudied with a sample of b\u00afb + jets events generated with ALPGEN [27], corresponding to an integrated\nluminosity of about 200 pb\u22121. At the event generator level, one of the b quarks was forced to undergo\nsemileptonic decay to e or \u00b5; also applied at the event generator level were \ufb01lters requiring true E miss\nT\n> 30 GeV, four or more truth jets with pT > 40 GeV, a leading truth jet with pT > 80 GeV and truth\nlepton with pT > 10 GeV. In the of\ufb02ine analysis, the events were required to satisfy the SUSY jet cuts\ndescribed in Section 1. The events were required to have one and only one lepton with pT greater than 20\nGeV, where the lepton could be either an electron or muon. Events with additional leptons (with pT>10\nGeV) were rejected.\nA (non-isolated) control sample was de\ufb01ned by the requirement Econe\nT\n= [10,20] GeV, where Econe\nT\nis the ET inside an \u03b7 \u2212\u03c6 cone of radius 0.2 centered around the lepton, excluding the lepton pT. The\n(isolated) signal sample was de\ufb01ned as Econe\nT\n< 10 GeV. The Emiss\nT\ndistribution of the control sample was\nnormalized in the region Emiss\nT\n= [10,20] GeV to the signal sample. This normalized Emiss\nT\ndistribution\nwas used to estimate the Emiss\nT\ndistribution for isolated leptons. Fig. 22 shows the Emiss\nT\ndistribution for\nthe isolated and non-isolated samples. The agreement is good, suggesting that the correlation between\nEmiss\nT\nand lepton isolation in b\u00afb+jets events is small.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1583\n\nIt is also apparent from Fig. 22 that the absolute level of background is low, even though typical\nSUSY selection cuts on Emiss\nT\n, transverse mass and effective mass (typically Emiss\nT\n> 100 GeV, MT\n> 100 GeV, and Meff > 800 GeV) have not yet been applied. We will return to this point later. The\nMeff distribution after the jet and lepton selection cuts is shown in Fig. 23(left). Ideally, one would like\nto demonstrate that the lack of correlation between lepton isolation and Emiss\nT\nstill holds even after the\nother SUSY selection cuts, such as those on MT and Meff, have been applied. This was not possible in\nthis study with fully simulated data due to the limited number of events available.\nEffective Mass [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\nEvents/100 pb-1/80 GeV\n-1\n10\n1\n10\nATLAS\nMissing Et [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents/100 pb-1/10 GeV\n-2\n10\n-1\n10\n1\n10\n2\n10\nttbar. Etcone < 10 GeV\nttbar. Etcone [10,20] GeV\nW+jets. Etcone < 10 GeV\nW+jets. Etcone [10,20] GeV\nbbbar. Etcone < 10 GeV\nbbbar. Etcone [10 20] GeV\nATLAS\nFigure 23: Left: distribution of the effective mass in the b\u00afb +jets sample after the jet and lepton selection\ncuts. Right: Emiss\nT\ndistributions for t\u00aft isolated muon sample (black \ufb01lled circle), t\u00aft non-isolated muon\nsample (red \ufb01lled square), W +jets isolated muon sample (black open circle), W +jets non-isolated muon\nsample (black open square), b\u00afb isolated muon sample (blue open triangle), b\u00afb non-isolated muon sample\n(magenta \ufb01lled triangle).\nContamination from W + jets and t\u00aft\nAn important systematic effect comes from the contamination\nof the control samples by W +jets and t\u00aft events. This was studied with fast simulation samples which had\nno generator-level cuts. The sample sizes corresponded to integrated luminosities of approximately 200\npb\u22121, 6 fb\u22121 and 3 fb\u22121 for b\u00afb+jets, t\u00aft and W +jets, respectively. The Emiss\nT\ndistribution, after the event\nselection cuts described above is shown in Fig. 23(right) for the b\u00afb, t\u00aft and W +jets samples for isolated\nand non-isolated muons de\ufb01ned as above. Looking \ufb01rst just at the b\u00afb events, there is good agreement in\nthe shape of the Emiss\nT\ndistribution for the isolated and non-isolated samples; this reinforces the \ufb01ndings\nfrom the GEANT4-simulated b\u00afb+jets samples on the independence of muon isolation and Emiss\nT\n. It is also\nclear that the non-isolated sample is dominated by b\u00afb at low Emiss\nT\n. However, the Emiss\nT\ntail is dominated\nby t\u00aft and W + jets events, even in the non-isolated sample.4 This implies that the shape of the Emiss\nT\ndistribution in the control sample will be distorted by the high Emiss\nT\ntail. It is possible to increase the\nnumber of b\u00afb events in the control sample by further loosening the isolation requirement, however this\nhas the disadvantage of extrapolating into the isolated signal region over a large range, which could be\nsusceptible to correlations between isolation and Emiss\nT\n. Furthermore, even if the isolation requirement\nin the control sample were successfully loosened, there is the problem of normalization. In the isolated\nsample, t\u00aft and W +jets completely dominate, even at very low Emiss\nT\n; this means that the normalization\nof the Emiss\nT\ndistribution will be distorted when extrapolating from the control to the signal region.\nOne might consider correcting the event yields in the control regions for the presence of t\u00aft and\nW + jets events. An early CDF t\u00aft cross-section analysis from Run2 [31] made corrections based on an\nassumed t\u00aft cross-section. D0 [32] used the so-called \u201cmatrix method\u201d where additional input on the\n4As an added complication the shape of this tail will change after the application of the MT cut which selects primarily\ndileptonic t\u00aft decays.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1584\n\nef\ufb01ciency for t\u00aft and b\u00afb events to pass the isolation cuts was used to extract the multijet background. The\nutility of these methods for the SUSY search could be further studied.\nDespite the limitations of the technique in the presence of t\u00aft and W +jets events background it should\nbe noted that this study also indicates that QCD backgrounds are unlikely to be dominant in the 1-lepton\nchannel. Even with application of just the standard SUSY 4-jet and lepton selection cuts, the QCD mul-\ntijet background in the 1-lepton channel is signi\ufb01cantly smaller than the t\u00aft and W + jets backgrounds\nand applying the remaining SUSY selection cuts further suppresses the QCD multijet background. Con-\nsequently in the baseline analysis the accuracy of QCD multijet background estimates is less important\nthan that of the estimates other backgrounds described in Ref. [4]. It should be kept in mind however\nthat for some background studies the jet or lepton selection cuts may be further loosened, in which case\nthe the lepton isolation technique might be applicable without the problem of contamination from other\nbackgrounds.\nMissing Et [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\nEvents/100 pb-1/20 GeV\n-2\n10\n-1\n10\n1\nttbar + Wjets. Etcone < 10 GeV\nttbar + Wjets. Etcone = [10,20] GeV\nATLAS\nFigure 24: Black circles: Emiss\nT\ndistribution for t\u00aft plus W +jets samples where the lepton is non-isolated\n(Econe\nT\n= [10,20] GeV). Histogram: Emiss\nT\ndistribution for t\u00aft plus W +jets samples with isolated leptons\n(Econe\nT\n< 10 GeV).\nUpper limit on Emiss\nT\ndistribution for b\u00afb + jets\nIf the multijet background is large compared to the\nbackground from t\u00aft (either because the existing Monte Carlo simulation happens to underestimate the\ncontribution or because the selection cuts were further loosened), then issues of t\u00aft contamination will\nbecome negligible and the methods described in the previous sections should work well to estimate the\nmultijet background. On the other hand, if the multijet background is small compared to t\u00aft as expected,\none can obtain the Emiss\nT\ndistribution from the control region (Econe\nT\n= [10,20] GeV) as an upper limit on\nthe multijet background; the (reasonable) assumption here (con\ufb01rmed in Monte Carlo) is that the E cone\nT\ndistribution for multijet background is \ufb02at (or falling) as Econe\nT\napproaches zero. After the MT cut, this\ncontrol region is expected to be dominated by t\u00aft and W +jets events containing non-isolated leptons with\nthe QCD multijet contribution playing only a very small role. Thus this will be an upper limit on the\nmultijet background, but the number of events so obtained will in any case be many fewer than from the\nmain t\u00aft and W +jets backgrounds (with isolated leptons) and so are likely to be negligible.\nThe contribution from b\u00afb + jets has been compared to GEANT4-simulated ALPGEN t\u00aft and W + jets\nsamples (corresponding to integrated luminosities of about 3 fb\u22121). In addition to the event selection\ncuts listed above (jet and lepton selection), the events were required to have MT > 100 GeV and Meff >\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1585\n\n800 GeV. The Emiss\nT\ndistribution for the sum of t\u00aft and W + jets samples for events with non-isolated\n(Econe\nT\n= [10,20] GeV) leptons is shown in Fig. 24; the contribution of b\u00afb+jets cannot be seen compared\nto that from t\u00aft plusW +jets. Furthermore, all contributions are negligible compared to the t\u00aft plusW +jets\nbackground with isolated leptons. Counting the number of non-isolated t\u00aft plus W + jets with Emiss\nT\n>\n100 (200) GeV, one would \ufb01nd an upper limit on the multijet background in the lepton channel of 10\u00b12\n(5 \u00b1 1) events for an integrated luminosity of 1 fb\u22121. The true number of multijet background events\nwould be estimated to be roughly an order of magnitude lower.\n6\nSummary\nThis paper has examined a wide range of techniques for estimating QCD backgrounds in searches for\nSupersymmetry at ATLAS. The focus of the paper has been on outlining the strategies which could\nbe used and assessing the likely uncertainties associated with them. It is important to note that only\nby comparing uncorrelated results from a number of such independent techniques can a robust QCD\nbackground estimate be obtained.\nGiven the dif\ufb01culty of obtaining accurate estimates of QCD jet backgrounds generating fake E miss\nT\nit\nwill be essential to reduce this source of background using the techniques described in Section 2 and also\nthe more general cuts described in Ref. [3]. The remaining backgrounds can be estimated using Monte\nCarlo (Section 3 and 4) or data-driven (Section 5) techniques.\nAll Monte Carlo based estimates will be subject to systematic effects arising from parton distribution\nand underlying event uncertainties (Section 3.1), likely to be of order 20% in each case for events satis-\nfying the baseline SUSY cuts described in Ref. [5]. A jet energy scale uncertainty of 5% (Section 3.2)\nwill contribute a further \u223c30%. While the precision with which Monte Carlo generators model QCD jet\nphysics at 14 TeV is dif\ufb01cult to assess prior to data-taking, the difference (Section 3.3) between a \u2018tra-\nditional\u2019 parton shower dijet estimate and that obtained from one of the newer matched matrix-element\n+ parton-shower generators for the baseline SUSY cut set is of order 50% if an accurate normalisation\nto data can be obtained. To these effects must be added luminosity uncertainties ranging from 20\u201330%\nat start-up (from machine parameters) reducing to <3\u20135% (from total cross-section measurements and\nW/Z counting).\nIn addition to the above systematic effects, Monte Carlo simulation-based estimates will be subject\nto detector simulation uncertainties \u2013 due to the imperfect description of the response of ATLAS to QCD\njets, and statistical uncertainties caused by the large QCD cross-section and access to \ufb01nite computing\nresources. It is impossible to assess the accuracy of current full (GEANT4) or fast (ATLFAST, \u2018fast G4\u2019\u2013\nSection 4.2 or PJTF\u2013Section 4.1) detector simulations without recourse to data, however the results\nof Section 4.1 suggest that uncertainties \u223c100% in the understanding of the response of the ATLAS\ncalorimeters to jets may lead to similar uncertainties in the background estimate.\nData-driven background estimates have the advantage that they are less prone to input systemat-\nics, and can in some cases bene\ufb01t from large statistics in control channels used to measure detector\nperformance. However, additional systematic uncertainties have to be considered due to the potential\ncontamination of control samples with non-QCD events, and from relying on Monte Carlo simulation\nto extrapolate from the control into the signal region. The data-driven estimate for the jets + E miss\nT\n+\n0-leptons channel described in Section 5.1 could potentially give a combined uncertainty of \u227260% for\n1 fb\u22121 of integrated luminosity and the baseline SUSY cut set, although a precise \ufb01gure is dif\ufb01cult to\nobtain without further Monte Carlo data. In the jets + Emiss\nT\n+ 1-lepton channel the QCD jet background\nis potentially far less signi\ufb01cant, in which case the technique described in Section 5.2 is likely to generate\na very conservative upper limit on the background a factor \u223c10 above the true background for 1 fb\u22121.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1586\n\nReferences\n[1] ATLAS Collaboration, ATLAS detector and physics performance. Technical design report Vol. 2,\nCERN-LHCC-99-15 (1999).\n[2] S. Agostinelli et al., Nucl. Instrum. Meth. A506 (2003) 250\u2013303.\n[3] ATLAS Collaboration, Measurement of Missing Tranverse Energy, this volume.\n[4] ATLAS Collaboration, Data-Driven Determinations of W, Z and Top Backgrounds to Supersym-\nmetry, this volume.\n[5] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[6] ATLAS Collaboration, ATLAS detector and physics performance. Technical design report Vol. 1,\nCERN-LHCC-99-15 (1999).\n[7] T. Sjostrand, S. Mrenna and P. Skands, JHEP 05 (2006) 026.\n[8] ATLAS Collaboration, Cross-Sections, Monte Carlo Simulations and Systematic Uncertainties, this\nvolume.\n[9] ATLAS Collaboration, Trigger for Early Running, this volume.\n[10] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[11] A. Affolder et al., Phys. Rev. Lett. 88 (2002) 041801.\n[12] V. Abazov et al., Phys. Lett. B660 (2008) 449\u2013457.\n[13] R.J. Teuscher, The Rejection of Cosmic and Halo Muons in the ZEUS Third Level Trigger, Ph.D.\nthesis, DESY-F35D-97-01 (1997).\n[14] B.Meirose, R.J. Teuscher, Time of Flight analysis Using Cosmic Ray Muons in the ATLAS Tile\nCalorimeter, ATLAS public note ATL-TILECAL-PUB-2008-004 (2008).\n[15] Richter-Was, Elzbieta and Froidevaux, Daniel and Poggioli, Luc, ATLFAST 2.0 a fast simulation\npackage for ATLAS Atlas Note ATL-PHYS-98-131.\n[16] W. Tung et al., JHEP 02 (2007) 053.\n[17] D. Stump et al., JHEP 10 (2003) 046.\n[18] A. Martin, R. Roberts, W. Stirling and R. Thorne, Eur. Phys. J. C23 (2002) 73\u201387.\n[19] S. Chekanov et al., Eur. Phys. J. C42 (2005) 1\u201316.\n[20] J. Pumplin et al., JHEP 07 (2002) 012.\n[21] A. Martin, R. Roberts, W Stirling and R. Thorne, Phys. Lett. B604 (2004) 61\u201368.\n[22] A. Sherstnev and R. Thorne, Parton Distributions for LO Generators, arXiv:0711.2473.\n[23] G. Corcella and others, JHEP 01 (2001) 010.\n[24] J. Butterworth, J. Forshaw and M. Seymour, Z. Phys. C72 (1996) 637\u2013646.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1587\n\n[25] R. D. Field (CDF Coll.),\nContribution to the APS/DPF/DPB Summer Study on the Fu-\nture of Particle Physics (Snowmass 2001), Snowmass, Colorado, 30 June - 21 July [hep-\nph/0201192]; R.D. Field (CDF Coll.), presentations at the Matrix Element and Monte Carlo\nTuning Workshop, Fermilab, 4 October 2002 and 29-30 April 2003, talks available from\nwebpage http://cepa.fnal.gov/psm/MCTuning/;\nR. D. Field and R. C. Group (CDF\nColl.), hep-ph/0510198;\nR. D. Field (CDF Coll.), further talks available from webpage\nhttp://www.phys.ufl.edu/ rfield/cdf/..\n[26] H. Lai et al., Eur. Phys. J. C12 (2000) 375\u2013392.\n[27] M. Mangano et al., JHEP 07 (2003) 001.\n[28] ATLAS Collaboration, Detector Level Jet Corrections, this volume.\n[29] E. Barberio et al., The Geant4-Based ATLAS Fast Electromagnetic Shower Simulation, Proceedings\nof the 10th ICATPP Conference in Como, Italy (2007).\n[30] B. Abbott et al., Nucl. Instrum. Meth. A424 (1999) 352\u2013394.\n[31] A. Abulencia et al., Phys. Rev. D74 (2006) 072006.\n[32] V. Abazov et al., Phys. Rev. D74 (2006) 112004.\nSUPERSYMMETRY \u2013 ESTIMATION OF QCD BACKGROUNDS TO SEARCHES FOR . . .\n1588\n\nProspects for Supersymmetry Discovery Based on Inclusive\nSearches\nAbstract\nThis note describes searches for generic SUSY models with R-parity conser-\nvation in the ATLAS detector at the CERN Large Hadron Collider. SUSY\nparticles would be produced in pairs and decay to the lightest SUSY parti-\ncle, \u02dc\u03c70\n1, which escapes the detector, giving signatures involving jets, possible\nleptons, and Emiss\nT\n. The integrated luminosity simulated is 1 fb\u22121 . This arti-\ncle relies on work published elsewhere in this collection, where the Standard\nModel backgrounds for SUSY are discussed.\n1\nIntroduction\nThis note describes the search for generic SUSY with R parity, so that SUSY particles are produced in\npairs and decay to the lightest SUSY particle, \u02dc\u03c70\n1, which escapes the detector, giving signatures involving\njets, possible leptons and Emiss\nT\n, an imbalance in the transverse energy measured in the detector. Most of\nthe introductory information necessary to the understanding of this document is given in the introductory\nSUSY note [1], which should be read before this one. These include a brief description of the theoretical\nframework, a de\ufb01nition of the SUSY benchmark models SUn studied in the detailed analyses, a descrip-\ntion of the Monte Carlo samples used for signal and background. Common identi\ufb01cation criteria for jets,\ntaus and leptons have been adopted throughout the analyses in this note, and are also described in [1] as\nwell as the de\ufb01nition of a few global variables relevant for the analysis, such as effective mass (Meff),\nstransverse mass (mT2) and transverse sphericity (ST). The background uncertainties used throughout\nthis work are based on Standard Model background studies documented in [2, 3]. Special signatures\nassociated, e.g., with Gauge Mediated SUSY Breaking are treated elsewhere [4].\nTwo different approaches have been used to develop the inclusive search strategy described here.\nFirstly, detailed studies have been carried out for various signatures (jets + Emiss\nT\n+ 0 leptons, jets + Emiss\nT\n+ 1 lepton, ...) using data-sets fully simulated with Geant 4 for speci\ufb01c SUSY signal parameters and for\nthe relevant Standard Model backgrounds. These detailed studies are used to develop deeper understand-\ning of how best to reconstruct these relatively complex events and to de\ufb01ne strategies for separating the\nsignal from the Standard Model backgrounds. In order to simplify the procedure of combining the results\nfrom the different analyses, the various leptonic signatures have been de\ufb01ned so that they are exclusive.\nFor example the 1-lepton signature rejects all events in which more than one lepton is present. However,\nno attempt is made to combine the different analyses in the present document.\nSecondly, the insight gained from studying speci\ufb01c points has been applied to several scans over\nsubsets of the SUSY parameter space, Since large numbers of signal points must be studied, these scans\nare of necessity based on fast, parameterized simulation. The goal is to verify that the different sets of\nbasic cuts studied on benchmark points provide sensitivity to a broad range of SUSY models. The results\nshown in this document will be used as a basis for the development of a strategy for SUSY discovery\nwith early ATLAS data.\n1.1\nTrigger\nThe trigger ef\ufb01ciency for the inclusive SUSY signals at the benchmark points has been studied based on\nthe complete simulation of all three trigger levels of ATLAS. For all the analyses we adopted the trigger\nthresholds de\ufb01ned for 2\u00d71033 cm\u22122s\u22121 in the High Level Trigger TDR [5]. These triggers are discussed\n1589\n\nfuther elsewhere [6] in this volume, where a detailed explanation of the naming convention for the trigger\nmenu items appearing in Table 1 can be found.\nThe jet triggers, denoted by \u201cJETS\u201d, consist of the logical \u201cor\u201d of the following triggers:\n\u2022 j400: 1 jet with pT > 400 GeV;\n\u2022 3j165: 3 jets with pT > 165 GeV;\n\u2022 4j110: 4 jets with pT > 110 GeV.\nThe Emiss\nT\ntrigger \u201cj70 xE70\u201d, requires Emiss\nT\n> 70 GeV accompanied by a jet with pT > 70 GeV. The\nlepton triggers are \u201ce22i\u201d: an isolated electron ef\ufb01cient for pT > 25 GeV; \u201c2e12i\u201d: two isolated electrons\nef\ufb01cient for pT > 15 GeV, \u201cmu20\u201d: a muon with pT > 20 GeV and \u201c2mu10\u201d: two muons with pT >\n10 GeV.\nSince the goal of this note is to develop a generic SUSY search, only the basic trigger building blocks\nhave been considered. More complex triggers combining different objects can be easily implemented in\nthe trigger menus. Also, only triggers which are not prescaled have been used.\nThe trigger ef\ufb01ciencies for the signal events passing the the 0, 1, 2, and 3-lepton selections de\ufb01ned\nin the following sections are listed in Table 1 for different requirements on jet multiplicity. In general the\nj70 xE70 is highly ef\ufb01cient, although there is some loss for SU4, the low-mass point with a very large\ncross-section. The j70 xE70 trigger is also very ef\ufb01cient for the \u03c4 and b modes, described in Sections 6\nand 7 below.\nThe basic performance of the leptonic and j70 xE70 triggers will be determined from Standard Model\nevents such as Z and \u00aftt using the methods described in [6]. It may be useful to check that performance\nby comparing (Monte Carlo) samples of SUSY events selected with multiple triggers. For the 0-lepton\nselection, the ef\ufb01ciency for JETS trigger alone is in the range 30-70%, except for the very low mass point\nSU4. This provides a useful redundancy in the early phases, as the Emiss\nT\ntrigger may require a longer time\nthan the other triggers to be completely understood, but only j70 xE70 has an ef\ufb01ciency close to one. For\nthe topologies involving leptons, both the single lepton triggers and j70 xE70 have typical ef\ufb01ciencies in\nexcess of 80%, so comparing them should be quite effective.\n1.2\nSystematic uncertainties and statistical procedure\nTo assess the discovery potential of the different analyses it is necessary to take into account systematic\nuncertainties. SUSY searches will address very complex topologies, typically with many jets in the \ufb01nal\nstate. The prediction of the Standard Model backgrounds to these topologies will require a complex\ninterplay of Monte Carlo and data-driven methods. The development of these methods and the estimate\nof the corresponding uncertainties are described in detail in [2] and [3]. The approximate uncertainties\nfor an integrated luminosity of 1fb\u22121 are estimated to be:\n\u2022 50% for the background from QCD multijet events,\n\u2022 20% for the background from t\u00aft, W +jets, Z +jets, and W/Z pairs.\nThe limited Monte Carlo statistics is also taken into account and all systematic uncertainties are\nadded in quadrature. The background can never be known exactly. Uncertainties on the background are\nincorporated in the signi\ufb01cance by convoluting the Poisson probability that the background \ufb02uctuates to\nthe observed signal with a Gaussian background probability density function with mean Nb and standard\ndeviation \u03b4Nb (see e.g. [7,8] and references therein). Given these assumptions, the probability p that the\nbackground \ufb02uctuates by chance to the measured value Ndata or above is given by\np = A\nZ \u221e\n0 db G(b;Nb,\u03b4Nb)\n\u221e\n\u2211\ni=Ndata\ne\u2212bbi\ni!\n,\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1590\n\nTable 1: Average event trigger ef\ufb01ciency (in %) for events passing various lepton and jet selection criteria\ndescribed in detail in the indicated sections.\nTrigger\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8.1\n0-lepton, 4-jet selection [Section 2.1]\nJETS\n44.6\n51.0\n33.8\n7.7\n51.7\n48.2\nj70 xE70\n99.7\n98.7\n99.5\n97.2\n99.6\n99.7\n0-lepton, 3-jet selection [Section 2.2]\nJETS\n64.9\n71.1\n54.9\n34.3\n71.8\n66.8\nj70 xE70\n100.\n99.8\n100.\n99.9\n100.\n100.\n0-lepton, 2-jet selection [Section 2.2]\nJETS\n44.1\n39.9\n30.1\n8.8\n53.6\n47.6\nj70 xE70\n100.\n100.\n100.\n99.9\n100.\n100.\n1-lepton, selection [Section 3]\nJETS\n41.8\n50.5\n31.7\n8.1\n48.4\n45.6\nj70 xE70\n99.6\n99.0\n98.9\n95.6\n98.9\n99.1\n1LEP (mu20 OR e22i)\n81.2\n81.0\n79.9\n80.3\n80.4\n79.5\nOS 2-lepton, selection [Section 4.1]\nJETS\n36.7\n47.3\n34.0\n6.7\n47.2\n40.8\nj70 xE70\n99.2\n100.0\n98.9\n94.3\n99.6\n100.0\n1LEP (mu20 OR e22i)\n87.0\n90.0\n87.5\n84.8\n79.6\n86.4\n2LEP (2mu10 OR 2e15i)\n20.5\n35.5\n27.0\n18.0\n26.0\n14.6\nSS 2-lepton, selection [Section 4.2]\nJETS\n39.9\n48.8\n29.2\n1.6\n46.6\n34.5\nj70 xE70\n99.3\n100.0\n98.9\n84.1\n98.3\n100.0\n1LEP (mu20 OR e22i)\n94.2\n92.7\n95.9\n95.2\n89.7\n96.6\n2LEP (2mu10 OR 2e15i)\n32.6\n41.5\n32.2\n25.4\n25.9\n31.0\n3-lepton, selection [Section 5]\nJETS\n43.7\n60.2\n40.1\n17.6\n46.4\n48.3\nj70 xE70\n95.6\n85.4\n93.5\n79.8\n96.4\n98.3\n1LEP (mu20 OR e22i)\n95.2\n94.2\n95.8\n94.7\n94.6\n96.7\n2LEP (2mu10 OR 2e15i)\n49.1\n60.2\n51.0\n44.7\n47.3\n53.3\nwhere G(b;Nb,\u03b4Nb) is a Gaussian and the factor\nA =\n\uf8ee\n\uf8f0\n\u221e\nZ\n0\ndb G(b;Nb,\u03b4Nb)\n\u221e\n\u2211\ni=0\ne\u2212bbi/i!\n\uf8f9\n\uf8fb\n\u22121\nensures that the function is normalised to unity. If the Gaussian probability density function G is replaced\nby a Dirac delta function \u03b4(b\u2212Nb), the estimator p results in a usual Poisson probability.\nThe probability p is transformed into \u201cstandard-deviations\u201d, denoted in this note by the symbol Zn,\nusing the formula\nZn =\n\u221a\n2 erf\u22121(1\u22122p)\nThe Root [9] library provides functions to calculate p and Zn.\nIf many different data selections are considered, it becomes more likely that statistical \ufb02uctuations\nwould be misinterpreted as new phenomena if the number of selections is not considered in the statistical\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1591\n\nTable 2: Number of events surviving subsequent selection cuts as de\ufb01ned in the text for 4-jets analysis\nnormalized to 1fb\u22121 using NLO cross-sections.\nSample\nCut 1\nCut 2\nCut 3\nCut 4\nCut 5\nMeff Cut\nSU3\n9600\n7563\n5600\n5277\n4311\n3349\nSU1\n3485\n2854\n2004\n1907\n1401\n1229\nSU2\n604\n369\n308\n279\n169\n131\nSU4\n79618\n57803\n46189\n42408\n34966\n8507\nSU6\n2551\n2062\n1468\n1383\n1080\n956\nSU8.1\n3118\n2540\n1778\n1686\n1448\n1284\nMC@NLO t\u00aft\n12861\n8798\n6421\n5790\n4012\n305\nPythia QCD\n29230\n7044\n4667\n848\n848\n13\nAlpgen Z\n1626\n1045\n732\n660\n644\n162\nAlpgen W\n4066\n2393\n1654\n1499\n1147\n228\nHerwig WZ\n22\n15\n9\n8\n4\n1\nTotal Standard Model\n47805\n19294\n13483\n8806\n6655\n708\nSU3 S/B\n0.2\n0.4\n0.4\n0.6\n0.6\n4.7\nZn\n0.5\n1.3\n1.4\n2.6\n2.7\n13\nSU3 eff (excl)\n35.1%\n78.8%\n74.0%\n94.2%\n81.7%\n77.9%\nSU3 eff (incl)\n35.1%\n27.7%\n20.5%\n19.3%\n15.8%\n12.3%\nprocedure. This is known in statistics as the problem of \u201cmultiple comparisons\u201d. The probability values\nare therefore corrected for multiple comparisons via a Monte Carlo method. The effect is the reduction\nof approximately half a unit of Zn for Zn = 3, decreasing with increasing Zn. In the last section of the\nnote the signi\ufb01cance always corresponds to the corrected Zn.\n2\nZero-lepton mode\nA SUSY signal at the LHC is typically dominated by the production of squarks and gluinos. In the\nR-parity conserving case, at the end of each sparticle decay chain one \ufb01nds an undetected LSPs, which\ncan together generate large Emiss\nT\n. The least model-dependent SUSY signature is therefore the search\nfor events with multiple jets and Emiss\nT\n. Traditionally searches have been performed requiring at least\nfour jets; the high multiplicity helps to reduce the background from QCD and W/Z +jets. Both for this\ntopology and for the leptonic topologies in the following sections we adopt very simple sets of cuts,\nsimilar to the ones used in the ATLAS Physics TDR [10]. In addition to the four-jet signatures we have\nalso addressed signatures with lower jet multiplicity. These signatures have more backgrounds, but might\nbe favoured in some SUSY models, and should be more cleanly reconstructed in the detector, because of\ntheir less-complex topologies. This may be an advantage in the early phases of the experiment.\n2.1\nFour or more jets in \ufb01nal state\nThe basic selections applied for this channel are:\n1. At least four jets with pT > 50 GeV at least one of which must have pT > 100 GeV; and Emiss\nT\n>\n100 GeV.\n2. Emiss\nT\n> 0.2Meff.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1592\n\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nSU3\nSM BG\ntt\nW\nZ\nQCD\nDi-boson\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nSU3\nSM BG\ntt\nW\nZ\nQCD\nDi-boson\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\nSU3\nSM BG\ntt\nW\nZ\nQCD\nDi-boson\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8.1\nSM BG\nATLAS\nFigure 1: Meff distribution for events surviving successive selection cuts: cut 1 (top left), cut 2 (top\nright), and cuts 3-5 (bottom left). The open circles represent point SU3, and the different background\ncontributions are shown according to the legend. The last plot (bottom right) show all of the SUSY\nbenchmark points and the total Standard Model background after cuts 1-5. Open circles represent the\nSUSY SU3 signal as predicted by Monte Carlo simulation, while the shaded area shows the total Standard\nModel background.\n3. Transverse sphericity, ST > 0.2.\n4. \u2206\u03c6(jet1 \u2212Emiss\nT\n) > 0.2, \u2206\u03c6(jet2 \u2212Emiss\nT\n) > 0.2, \u2206\u03c6(jet3 \u2212Emiss\nT\n) > 0.2.\n5. Reject events with an e or a \u00b5.\n6. Meff > 800 GeV.\nMost of the background samples have been \ufb01ltered at generation level with various requirements on E miss\nT\nand jet multiplicity. The \ufb01rst cut in the analysis \ufb02ow applies harder requirements than any of the ones\napplied at the \ufb01lter level to minimise the bias to the study from the use of \ufb01ltered samples.\nThe main background at this point from QCD events where Emiss\nT\nis produced either by a \ufb02uctuation\nin the measurement of the energy of one or more jets, or by a real neutrino from the decay of a B hadron\nproduced in the fragmentation process. Since the statistical \ufb02uctuation on the Emiss\nT\nmeasurement grow\nwith increasing Meff, the second cut above eliminates the Gaussian part of the Emiss\nT\nmeasurement \ufb02uctu-\nations. In SUSY events the jets are produced from the decay of heavy particles produced approximately\nat rest, and are thence distributed isotropically in space, whereas for the QCD events the direction of the\ntwo partons from the hard scattering provides a privileged direction. The cut on sphericity is intended\nto exploit this fact. Both for jet mismeasurement and for b decays, the Emiss\nT\nvector will be close the\ndirection of one jets, and so the \u2206\u03c6 cuts are very ef\ufb01cient in reducing the QCD background. The lepton\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1593\n\nveto is applied in order to facilitate the combination with analyses requiring leptons, but it is not expected\nto signi\ufb01cantly modify the signal-to-background ratio.\nThe number of events surviving each of the cuts for an integrated luminosity of 1fb\u22121 is shown in\nTable 2 for all of the considered benchmark points and for the backgrounds. The number of events in the\nlast column includes the effect of the j70xE70 trigger, which, as shown in Table 1, has an ef\ufb01ciency in\nexcess of 97% for all considered signal benchmarks.\nThe distribution of the \ufb01nal selection variable Meff, for signal and background, is shown in Fig. 1\nfor point SU3 at different stages of the analysis. The QCD background is dominant after the \ufb01rst cut\nbut is reduced to a similar level to the backgrounds containing real neutrinos by subsequently requiring\nEmiss\nT\n> 0.2Meff (cut 2). The cuts on event sphericity and \u2206\u03c6 strongly reduce the QCD background, which\nbecomes concentrated in the region of low Meff. After all cuts t\u00aft is the dominant background, but there\nare also signi\ufb01cant contributions from W +jets and Z +jets. The \ufb01nal cut, Meff > 800 GeV, reduces the\nbackground to below the level of the signal for all considered benchmark points except for SU2. For this\npoint to be found in the 0-lepton channel, one would have to select larger values of Meff to enhance the\nsignal-to-background ratio, and a greater integrated luminosity would be required.\nThe statistical signi\ufb01cance Zn for 1fb\u22121 was calculated using the prescription in Section 1.2 including\nthe systematic uncertainty on the background [2, 3]. The signi\ufb01cance for point SU3 after each cut is\nshown in Table 2. The signi\ufb01cances Zn after all cuts are 13 for SU3, 6.3 for SU1, 0.9 for SU2, 25\nfor SU4, 6.3 for SU6, and 6.5 for SU8.1. Evidently only point SU2, for which the cross section is\ndominated by direct gaugino production (which is investigated elsewhere in this volume [11]), would not\nbe accessible for the assumed set of cuts, integrated luminosity and level of background understanding.\nThese numbers should be taken as indicative. The uncertainty on the background used in the calcu-\nlation is the estimate of what one would obtain using complicated procedures for background evaluation\nbased on a combination of data-driven and Monte Carlo methods. The absolute value of the backgrounds\nused for this study is derived only from Monte Carlo, and the present uncertainty on this value is much\nhigher. An idea of the robustness of the analysis can be obtained by studying the signi\ufb01cance for the\nbenchmark points if the background would be increased by a factor 2. In this case the signi\ufb01cance for\nSU3 would drop to 7.8, and the one for SU6 to approximately 3.1. The signi\ufb01cance for SU6 would be,\nin this situation, dominated by the systematic uncertainty on the background evaluation. Therefore an\nincrease in integrated luminosity would result in an increased reach only if it can be used to reduce the\nuncertainty on the background evaluation.\n2.2\nInclusive two-jet and three-jet \ufb01nal states\nThe analyses based on lower jet-multiplicities are based on very similar requirements to the 4-jet analysis\nabove. The differences are: higher pT requirements on the remaining jets to cope with the increased\nQCD background, and a slightly harder Emiss\nT\ncut. The sphericity cut is less relevant in the case of low\njet multiplicities and is dropped. For the two (three)-jet analysis the cuts are respectively:\n1. At least two (three) jets, the hardest with pT > 150 GeV and the second (and third) with pT >\n100 GeV; Emiss\nT\n> 100 GeV\n2. Emiss\nT\n> 0.3(0.25)Meff.\n3. \u2206\u03c6(jet1 \u2212Emiss\nT\n) > 0.2, \u2206\u03c6(jet2 \u2212Emiss\nT\n) > 0.2, (\u2206\u03c6(jet3 \u2212Emiss\nT\n) > 0.2)\n4. Reject events with an e or a \u00b5\n5. Meff > 800 GeV.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1594\n\nThe Meff variable is different from the one de\ufb01ned in [1] in that only the 2(3) highest pT jets for the\n2\u2013(3\u2013)jet analysis are used.\nSince the ALPGEN W +jets and Z +jets background samples have a \ufb01lter at generation level requir-\ning 4 jets, samples produced with the PYTHIA generator were used in this case.\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nSU3\nSM background\ntt\nW\nZ\nQCD\nDiboson\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8.1\nSM background\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n1\n10\n2\n10\n3\n10\n4\n10\nFigure 2: Meff distribution for the 0-lepton plus 2-jet analysis, after \ufb01nal cuts. Left: The open circles\nshow the SUSY (SU3) signal Monte Carlo prediction, while the total Standard Model background is\nshown by the shaded histogram. The individual background contributions are shown by the points, as\ndescribed in the legend. Right: The points show the distribution of the signal for a number of SUn points.\nTable 3: Number of events surviving the selection cuts de\ufb01ned in the text for the 2\u2013jet analysis. Entries\nare normalized to 1 fb\u22121 using next-to-leading-order cross-sections.\nSample\nCut 1\nCut 2\nCut 3\nCut 4\nMeff Cut\nSU3\n18660.7\n12519.8\n12217.5\n10055.2\n6432.2\nSU1\n7699.9\n5427.5\n5318.1\n3996.8\n3196.0\nSU2\n642.4\n319.7\n301.2\n185.1\n90.4\nSU4\n123219\n64502.4\n62172.9\n52108.0\n9434.4\nSU6\n4483.1\n3133.5\n3041.7\n2418.5\n1987.0\nSU8.1\n6384.7\n4482.5\n4381.8\n3804.5\n3067.7\nt\u00aft\n17666.6\n6273.8\n5778.6\n3556.7\n304.8\nQCD\n124513.9\n7341.7\n1983.7\n1983.7\n107.6\nZ +jets\n3222.5\n2192.2\n2109.5\n2056.1\n391.6\nW +jets\n8887.2\n4504.5\n4072.4\n2775.5\n395.1\nDiboson\n150.4\n71.2\n66.0\n32.1\n6.8\nStandard Model\n154440.5\n20383.4\n14010.1\n10404.1\n1205.8\nSU3 S/B\n0.12\n0.61\n0.87\n0.97\n5.3\nSU3 S/\n\u221a\nB\n47.5\n87.7\n103.2\n98.6\n185.2\nSU3 eff (cum)\n67.4%\n45.2%\n44.1%\n36.3%\n23.2%\nSU3 eff (excl)\n67.4%\n67.1%\n97.6%\n82.3%\n64.0%\nThe cut \ufb02ow for the 2-jet analysis is given in Table 3, and the Meff distributions before the Meff cut\nfor the different background contributions and for the different signal points are shown in Figure 2. The\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1595\n\nnumber of events after all cuts includes the effect of the j70xE70 trigger, which, as shown in Table 1,\nhas an ef\ufb01ciency in excess of 99% for all considered SUSY benchmark points. After the \u2206\u03c6 cuts the\nt\u00aft, W + jets, Z + jets and QCD all give comparable contributions to the background. After all cuts the\nsurviving events are approximately doubled both for signal and background, as compared to the 4-jet\nanalysis, except for the low-mass SU4 points for which the harder kinematic cuts reduce the signal\nef\ufb01ciency.\nAssuming the estimated systematic background errors are the same as for the 4\u2013jet case, the estimated\nsigni\ufb01cances are 13.3 for SU3, 8.0 for SU1, 17.2 for SU4, 5.5 for SU6, and 7.7 for SU8.1, for 1 fb\u22121\nof integrated luminosity. The signi\ufb01cance for SU2, for which direct gaugino production is dominant, is\nless than 1.0. The equivalent numbers for the 3\u2013jet analysis are: 17.0 for SU3, 9.5 for SU1, 25.7 for\nSU4, 7.3 for SU6 and 9.6 for SU8. Although the signal over background ratio is equivalent or better (for\nthe three-jet topology) than for the 4-jet analysis this is only partially re\ufb02ected in the signi\ufb01cances when\nthe systematic uncertainty is taken into account. This is due to the increased contribution of the QCD\nbackground, which has an estimated uncertainty on QCD is of 50%, as compared to 20% for the other\nbackgrounds. Therefore, since the uncertainties of the backgrounds were evaluated for a 4-jet analysis,\na dedicated background study would be needed to obtain a correct estimate of the discovery potential in\nthis topology.\nThe 2-, 3- and 4-jet analyses are based on very similar cuts and therefore have a large overlap in the\nselected events. About 40% of all 2-jet events are also contained in the 3-jet slection and about 35%\nin the 4-jet selection. The biggest overlap is for the 3 jet events: about 59% of all 3-jet events are also\ncontained in the 4-jet analysis and about 97% in the 2-jet analysis.\nAn alternative strategy was explored where cuts 2 and 3 of the Meff analysis are dropped, and a cut\non the mT2 variable [12,13], mT2 > 400 GeV, is applied as the only discriminating observable. The mT2\nvariable, has the interesting properties that it takes low values for events where either the visible pT or\nEmiss\nT\nare small, and in the case of small \u2206\u03c6. It can therefore replace these topological cuts. For semi-\ninvisibly decaying particles mT2 is related to the difference in mass between the particles produced in\nthe interactions and their invisible decay products. It can therefore take a larger value for SUSY events\nthan for top or W events. Taking the estimates of the systematic background errors into account, the\nsigni\ufb01cances for the 2-jet mT2 analysis are: 15.6 for SU3, 11.5 for SU1, 10.9 for SU4, 8.3 for SU6, and\n11.1 for SU8.1, somewhat better than the equivalent analysis based on Meff. The most effective strategy\nwill be ultimately de\ufb01ned by how well the systematic uncertainty on the background evaluation can be\ncontrolled in the different approaches.\n3\nOne-lepton mode\nWhile the 0-lepton mode with multiple jets plus Emiss\nT\nis probably the most generic search mode for\nSUSY with R-parity conservation, it is sensitive to backgrounds from mismeasured QCD multijet events.\nRequiring one lepton in addition to multiple jets and Emiss\nT\ngreatly reduces the potential QCD multijet\nbackground; the remaining backgrounds are under better control. Even if \u03c4 decays of gauginos are dom-\ninant, leptonic \u03c4 decays provide a signi\ufb01cant 1-lepton rate, at least for high masses. It is not surprising,\ntherefore, that the reach in the 1-lepton and 0-lepton modes are comparable.\nThe cuts in this analysis are similar to those used in the ATLAS Physics TDR [10] but also include\na cut on the transverse mass1, MT, formed from the lepton and Emiss\nT\nwhich has the role of suppressing\nthe W + jets and t\u00aft backgrounds. The ST cut is included for historical reasons, but its effectiveness is\nquestionable:\n1Note the distinction between the transverse mass, MT , which is a function of the momentum of one visible particle and the\nmissing transverse momentum and the stransverse mass which is a function of the momenta of two visible particles and the\nmissing transverse momentum.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1596\n\nTable 4: Number of events surviving the selection cuts de\ufb01ned in the text for the 1-lepton analysis.\nEntries are normalized to 1 fb\u22121 using NLO cross-sections. The last column reports a simple S/\n\u221a\nB\ncalculation of the corresponding signi\ufb01cance of an observation for the SUSY benchmark points (SUn).\nSample\nCuts 1\u20134\nCut 5\nCut 6\nCut 7\nS/\n\u221a\nB\nSU1\n571.7\n423.0\n259.9\n232.3\n36.0\nSU2\n86.7\n75.6\n46.1\n39.6\n6.1\nSU3\n995.7\n767.9\n450.5\n363.6\n56.4\nSU4\n7523.6\n6260.4\n2974.4\n895.8\n138.9\nSU6\n342.3\n250.9\n161.9\n147.9\n22.9\nSU8.1\n296.4\n214.4\n151.4\n136.3\n21.1\nt\u00aft\n2028.5\n1546.8\n131.7\n36.0\nW\n425.2\n314.8\n9.9\n5.4\nZ\n39.0\n27.3\n1.7\n0.2\nDiboson\n7.3\n5.1\n0.8\n0.0\nQCD\n0.0\n0.0\n0.0\n0.0\nStandard Model BG\n2500.1\n1894.0\n144.1\n41.6\n1. Exactly one isolated lepton with pT > 20 GeV satisfying the selection criteria described earlier.\n2. No additional leptons with pT > 10 GeV. This ensures no overlap with the 0-lepton, 2-lepton, and\n3-lepton analyses.\n3. At least four jets with pT > 50 GeV at least one of which must have pT > 100 GeV.\n4. Emiss\nT\n> 100 GeV and Emiss\nT\n> 0.2Meff.\n5. Transverse sphericity, ST > 0.2.\n6. Transverse mass, MT > 100 GeV.\n7. Meff > 800 GeV.\nCuts 1\u20132 de\ufb01ne the 1-lepton analysis, while Cuts 3\u20134 both reduce the Standard Model backgrounds and\nensure compatability with the Standard Model \ufb01lter cuts. Distributions without these four cuts are not\nmeaningful and so are not shown. Cut 5 reduces the Emiss\nT\nbackground from mismeasured dijet events;\nCut 6 reduces the background from events in which the Emiss\nT\ncomes from W \u2192\u2113\u03bd; and Cut 7 selects\nhigh-mass \ufb01nal states.\nThe cut \ufb02ow table for these cuts is shown in Table 4. The number of events after all cuts includes\nthe effect of the j70xE70 trigger, which, as shown in Table 1, has an ef\ufb01ciency of around 99% for all the\nbenchmark points considered other than the low mass SU4 point, for which the ef\ufb01ciency is still above\n95%. Note that the QCD background is reduced to a negligible level by the lepton and Emiss\nT\ncuts as\nexpected. The background after all cuts is dominated by t\u00aft and W +jets, both of which are expected to\nbe better understood than the QCD background. Therefore, while the 1-lepton mode may not have better\nreach than the 0-lepton mode given the calculated backgrounds, its reach seems more robust against\nbackground uncertainties.\nThe Meff distribution for point SU3 after each cut is shown in Figure 3. The Emiss\nT\nand Meff distri-\nbutions for all the SUn points after all cuts are shown in Figures 4. It is clear from these \ufb01gures and\nfrom Table 4 that the only signi\ufb01cant backgrounds to the 1-lepton mode are from t\u00aft and W +jets, as one\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1597\n\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\nSU3\nall BG\ntt\nW\nZ\nQCD\nDi-boson\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 200 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\nSU3\nall BG\ntt\nW\nZ\nQCD\nDi-boson\nATLAS\nFigure 3: Expected Meff distributions after Cuts 1\u20134 (left), and Cut 6 (right) for the 1-lepton analysis.\nCompare with Table 4.\nEffective Mass [GeV]\n500\n1000\n1500\n2000\n2500\n3000\n-1\nevents / 200 GeV / 1fb\n-1\n10\n1\n10\n2\n10\n3\n10\nSU1\nSU2\nSU3\nSU4\nSU6\nSU8.1\nSM BG\nATLAS\nFigure 4: The Meff distributions for each of the SUn benchmark points, and for the sum of the Standard\nModel backgrounds with 1fb\u22121 for the 1-lepton analysis. All the cuts except on Meff are applied.\nwould expect. The estimated error on both of these backgrounds using data-driven methods is \u00b120% [2].\nGiven this and the calculated signal and background rates in Table 4, it is evident that all the SUSY points\nconsidered except SU2 could be discovered with good signi\ufb01cance in the 1-lepton mode. For SU2, the\nproduction cross-section is dominated by gaugino pair production, so a different analysis [11] is required.\nTo make this conclusion more quantitative, the signi\ufb01cance Zn de\ufb01ned in Section 1.2 was calculated.\nThe central value of each background is taken from the current Monte Carlo simulation; the studies\nof data-driven background estimation [2, 3] provide estimated errors of \u00b150% for QCD multijet back-\ngrounds and \u00b120% for t\u00aft, W +jets, and all other backgrounds. The results of this calculation are shown\nin Table 5 for an integrated luminosity of 1fb\u22121. Each of these points except SU2 would have Zn > 5 for\njust 100pb\u22121 if the same 20% background uncertainty could be obtained with that luminosity.\nThe signi\ufb01cances, Zn, (Table 5) for 1fb\u22121 are much smaller than the S/\n\u221a\nB values in Table 4. This\nre\ufb02ects the fact that, unlike S/\n\u221a\nB, the Zn measure of signi\ufb01cance includes the estimated systematic\nuncertainty on the background. Table 5 also indicates that, provided the relative uncertainties in the\nbackground determiations did note increase, harder Meff cuts would lead to better signi\ufb01cances after\nsystematic uncertainties in the background are taken into account.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1598\n\nTable 5: Signi\ufb01cance Zn for the 1-lepton plus 4-jet analysis with 1fb\u22121 including the systematic uncer-\ntainty in the background estimation.\nSample\nMeff > 400 GeV\nMeff > 800 GeV\nMeff > 1200 GeV\nEvents\nZn\nEvents\nZn\nEvents\nZn\nStandard Model BG\n144\n42\n2\nSU1\n260\n7.6\n232\n12.3\n114\n18.0\nSU2\n46\n1.5\n40\n3.4\n15\n6.0\nSU3\n450\n9.5\n364\n16.7\n110\n17.7\nSU4\n2974\n33.7\n896\n29.4\n99\n16.6\nSU6\n162\n4.9\n148\n8.9\n76\n14.2\nSU8.1\n151\n4.6\n136\n8.4\n66\n13.1\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\nSM BG\nATLAS\nW\nATLAS\ntt\nATLAS\nD boson\nATLAS\nSU3\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\nSM BG\nATLAS\nATLAS\nATLAS\nATLAS\ntt\nATLAS\nATLAS\nSU3\nFigure 5: Meff distribution for events with one lepton and: 2 jets (left) or 3 jets (right) after all cuts were\napplied.\nSupersymmetry events need not contain large numbers of jets. For example, in mSUGRA the process\n\u02dcqL + \u02dcqR \u2192\u02dc\u03c7\u00b1\n1 q\u2032 + \u02dc\u03c70\n1q\n\u2212\u2212\u2212\u2192\u02dc\u03c70\n1\u2113\u00b1\u03bd\ncan have a large rate and gives one lepton and just two hard jets. An alternative 1-lepton analysis has\nbeen performed requiring just two or three jets rather than four. Because a 4-jet selection was applied to\nthe Alpgen samples at the generator level, Pythia was used for the W + jets backgrounds. The jet cuts\nemployed are harder: 150 GeV for the leading jet and 100 GeV for the others. The missing energy cut\nis also harder, Emiss\nT\n> max(100 GeV,0.3Meff) and max(100 GeV,0.25Meff) for the 2-jet and 3-jet case\nrespectively. The Meff distributions after all cuts are shown in Figure 5. Evidently an analysis requiring\na smaller number of jets with harder cuts also can be effective.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1599\n\nTable 6: The number of events surviving the selection cuts de\ufb01ned in the text for the opposite-sign\ndilepton analysis, normalized to 1fb\u22121 using next-to-leading-order cross-sections. The last two columns\ngive the S/B ratio and the Zn signi\ufb01cance, the latter of which includes the systematic uncertainties on the\nStandard Model backgrounds.\nSample\nCuts 1-3\nCut 4\nS/B\nZn\nSU3\n200.8\n159.8\n1.88\n3.55\nSU1\n91.0\n72.6\n0.86\n1.65\nSU2\n22.5\n18.8\n0.22\n0.43\nSU4\n948.0\n809.5\n9.56\n22.5\nt\u00aft\n111.1\n81.5\nW +jets\n2.47\n1.97\nZ +jets\n1.77\n1.20\nQCD (J3-J7)\n0\n0\nTotal Standard Model\n115.34\n84.67\n4\nTwo-lepton mode\n4.1\nOpposite sign dileptons\nSupersymmetry events with two opposite-sign leptons can arise from neutralino decays, especially \u03c7 0\n2 \u2192\nl\u00b1l\u2213\u03c70\n1, either directly or through an intermediate slepton. Such dileptons must have the same \ufb02avour to\navoid inducing \u00b5 \u2192e\u03b3 and other lepton-\ufb02avour-violating interactions at one loop. By contrast leptons\nproduced from independent decays can give either same-\ufb02avour (OSSF) or different-\ufb02avour (OSDF)\ndilepton pairs, again with \u2113\u2208{e,\u00b5}.\nThe opposite-sign dilepton analysis uses the following cuts:\n1. Two isolated, opposite-sign leptons with pT > 10 GeV and |\u03b7| < 2.5 which satisfy the cuts de-\nscribed in the introductory SUSY note [1]. Events containing additional leptons were vetoed.\n2. At least four jets with pT > 50 GeV at least one of which must have pT > 100 GeV.\n3. Emiss\nT\n> 100 GeV and Emiss\nT\n> 0.2Meff.\n4. Transverse sphericity, ST > 0.2.\nCut 1 de\ufb01nes the opposite-sign dilepton sample, while Cuts 2 and 3 both suppress the Standard Model\nbackgrounds and provide consistency with the Monte Carlo generator cuts on those backgrounds. After\nCuts 1\u20133 the dominant background by far is t\u00aft, as one would expect. The ST cut only increases the S/B\nratio by about 8% while reducing the signal by 20%.\nThe signals and backgrounds after the cuts, and the corresponding signi\ufb01cances, are shown in Table 6.\nThe number of events after all cuts includes the effect of the j70xE70 trigger, which, as shown in Table 1,\nhas an ef\ufb01ciency of around 99% for all considered signal benchmarks, except for the low mass SU4\npoint, for which the ef\ufb01ciency is above 95%. The benchmark points SU3 and SU4 both have high\ndiscovery potential in the dilepton channel. While SU1 has fairly large dilepton branching ratios, many\nof the leptons are soft because of the small mass gaps between supersymmetric particles. An improved\nanalysis based low-pT lepton reconstruction algorithms would help greatly for this point.\nIt is instructive to see how the signi\ufb01cances, Zn, vary with the cut on the leading jet and on Emiss\nT\n. This\nis shown in Figure 6 for each of the points SU1 \u2013 SU4. It can be seen that the signi\ufb01cance improves with\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1600\n\nETMISS (GeV)\n100\n150\n200\n250\n300\n350\nSignificance\n0\n5\n10\n15\n20\n25\n30\nSU1\nSU2\nSU3\nSU4\nTransverse momentum leading jet (GeV)\n100\n150\n200\n250\n300\nSignificance\n0\n5\n10\n15\n20\n25\n30\nSU1\nSU2\nSU3\nSU4\nFigure 6: Signi\ufb01cance of signal events for the four benchmark points, as a function of the cut on trans-\nverse missing energy (left) and the transverse momentum of the leading jet (right), for an integrated\nluminosity of 1fb\u22121.\nTable 7: The optimized cuts for each point and corresponding signal, background, and signi\ufb01cance.\nCompare with Table 6.\nSample\nEmiss\nT\ncut\nLeading jet cut\nsignal\nbackground\nSigni\ufb01cance\nSU1\n100 GeV\n320 GeV\n37.97\n6.30\n6.94\nSU2\n140 GeV\n200 GeV\n13.74\n22.68\n1.07\nSU3\n140 GeV\n200 GeV\n125.34\n22.68\n11.45\nSU4\n110 GeV\n100 GeV\n772.53\n66.80\n24.70\nharder cuts than those given in the above cut list even for the low-mass point SU4. The optimal cuts for\neach point and the signal, background and signi\ufb01cance are shown in Table 7. Systematic errors of 50%\non on all Standard Model backgrounds are included. Of course one should not optimize an analysis for\na single point, but the table suggests that, provided the systematic uncertainties on the Standard Model\nbackground determinations do not signi\ufb01cantly increase, harder cuts would be preferred. Optimization\nfor wider ranges of points is discussed in Section 8.\nObserving an non-resonant excess of OSSF dilepton events over OSDF events would be a clear\nindication of new physics. In SUSY leptonic \u02dc\u03c70\n2 decays can produce this excess, and have a charac-\nteristic endpoint set by the masses involved. The signi\ufb01cance of the difference, calculated as (NOSSF \u2212\nNOSDF)/\u221aNOSSF +NOSDF, is shown in Table 8. This signi\ufb01cance calculation assumes that the relative\ne and \u00b5 acceptances are well understood, which is not unreasonable given that all Standard Model pro-\ncesses satisfy e/\u00b5/\u03c4 universality. For SU1 the combined branching ratio for \u02dc\u03c70\n2 \u2192\u02dc\u2113\u00b1\nL,R\u2113\u2213is 11.7%, but\nthe acceptance is reduced by the small mass gaps. For SU2 gaugino pair production dominates, so the\njet cuts suppress the signal.\n4.2\nSame sign dileptons\nIn the Standard Model the rate for prompt, isolated, same-sign dileptons is small. Of course some\nleptons from hadronized heavy or light quarks can also pass the isolation cut and contribute like-sign\nbackgrounds. In SUSY, on the other hand, the gluino is a self-conjugate Majorana fermion, so events\ncontaining like-sign dileptons can be common. Thus, same-sign dileptons are a good signature for SUSY\nand a characteristic feature of it.\nThe cuts used for the same-sign dilepton analysis are:\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1601\n\nTable 8: The number of OSSF and OSDF dilepton events passing the optimized cuts and the correspond-\ning statistical signi\ufb01cance for 1fb\u22121.\nSample\nEmiss\nT\ncut\nLeading jet cut\nNOSSF\nNOSDF\nSigni\ufb01cance\nSU1\n220 GeV\n100 GeV\n90.69\n58.53\n2.63\nSU2\n140 GeV\n100 GeV\n31.64\n29.95\n0.22\nSU3\n160 GeV\n160 GeV\n93.75\n38.58\n4.80\nSU4\n120 GeV\n100 GeV\n392.45\n281.55\n4.27\nTable 9: The number of events surviving the selection cuts (as de\ufb01ned in the text) for the same-sign dilep-\ntons analysis, normalized to 1fb\u22121 using next-to-leading-order cross-sections. No background events\npass the \ufb01nal cut; the 90% upper limit for t\u00aft background is given.\nProcess\nCuts 1\u20133\nCut 4\nZn\nSU1\n30.1\n21.9\n7.2\nSU2\n13.0\n6.6\n1.9\nSU3\n37.9\n24.9\n7.7\nSU4\n251.8\n138.8\n19.9\nSU6\n18.0\n13.9\n4.5\nt\u00aft\n2.1\n< 2.3\nW +jets\n0.7\n0.0\nZ +jets\n0.0\n0.0\n1. Exactly 2 same-sign leptons with pT > 20 GeV satisfying the usual isolation and other cuts [1].\n2. At least four jets with pT > 50 GeV at least one of which must have pT > 100 GeV.\n3. Transverse missing energy Emiss\nT\n> 100 GeV.\n4. Emiss\nT\n> 0.2Meff.\nThe \ufb01rst cut de\ufb01nes the same-sign dilepton sample, while Cuts 2-4 suppress the Standard Model back-\ngrounds. Cuts 1 and 2 are used in the Monte Carlo generator \ufb01lters for some of the backgrounds.\nThe cut \ufb02ow table for these cuts is shown in Table 9. The number of events after all cuts includes\nthe effect of the j70xE70 trigger, which, as shown in Table 1, has an ef\ufb01ciency of around 99% for all\nconsidered signal benchmarks, except for the low mass SU4 point, for which the ef\ufb01ciency is 84%.\nSince the W + jets and Z + jets backgrounds have been \ufb01ltered at the generator level, the results\nfor these are biased until after Cut 3, but evidently they are small. A number of other backgrounds\nwere examined and found to be negligible compared to those listed in the table. None of the Monte\nCarlo events generated for the Standard Model background determination passed all the cuts. A 90%\ncon\ufb01dence upper limit of 2.3 Monte Carlo events gives the indicated upper limit on the t\u00aft background\nafter cut 4. This is used as the estimate of the total background since t\u00aft is expected to dominate; b jets\ncan produce a second lepton of the same sign and that lepton has a non-negligable probablility of being\nwell-isolated. The assumption of t\u00aft dominance is consistent with the results after Cut 3 in Table 9. Two\npossible backgrounds, W \u00b1W \u00b1 and t\u00aftt\u00aft, are probably small but have not been studied.\nThe Emiss\nT\ndistributions after the other cuts are shown in Figure 7. While the rates are small, the S/B\nratio is good and the signal is distinctive. The Emiss\nT\ncut was varied and the value in the cuts used here\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1602\n\n [GeV]\nT\nmiss\nE\n100\n200\n300\n400\n500\n600\n700\n-1\nevents/ 100 GeV / 1fb\n-1\n10\n1\n10\n2\n10\nATLAS\nAll BG.\nW jets\ntt jets\nSUSY SU3\nSUSY SU2\nSUSY SU4\nSUSY SU1\nSUSY SU6\nFigure 7: Emiss\nT\nin the same sign dilepton events after all cuts except the Emiss\nT\ncut.\nfound to be appropriate.\nIt is clear that the Standard Model same-sign dilepton background is small and is probably dominated\nby t\u00aft. A data-driven analysis of this background has not yet been done. It is expected that it will be\npossible to measure the background from processes such as t \u2192\u2113+X, \u00afb \u2192\u00b5+X as a function of the\nisolation cut and to extrapolate to the cut used here. For \u00afb \u2192e+X, where the e identi\ufb01cation cuts\nimpose an implicit isolation cut, it will be necessary to extrapolate from the \u00b5 result using Monte Carlo\ntechniques. In the absence of such studies the signi\ufb01cance for the same-sign dilepton analysis has been\ncalculated using the 90% upper limit for t\u00aft given in Table 9 with the standard systematic uncertainty of\n\u00b120%. This gives the Zn values listed in the same table. Although the systematic error on the background\nis uncertain, certainly SU4 and very likely SU1 and SU3 would be observable with a signi\ufb01cance greater\nthan 5\u03c3 with 1fb\u22121.\nMore work on the same-sign dilepton background, and more generally on estimates of leptons from\nb and c decays passing isolation cuts, is clearly needed.\n5\nThree-lepton mode\nThe trilepton signal from direct gaugino production [14] is perhaps the best search mode for SUSY at\nthe Tevatron [15,16]. The corresponding search with ATLAS is described elsewhere in this volume [11].\nThe analyses discussed here are aimed at trilepton production from all sources, not just from direct\nproduction. Two approaches have been followed. The \ufb01rst, the 3-leptons+ jet selection makes explicit\nuse of a high-pT jet, similar to the 1- and 2-lepton analyses described above. The second, the 3-leptons+\nEmiss\nT\nselection, relies on track isolation cuts to select prompt leptons and is similar to the exclusive\nanalysis [11]. The 1LEP trigger typically gives an ef\ufb01ciency of >\u223c95% for these modes (see Table 1).\n5.1\nThree-lepton + jet analysis\nThe 3-leptons+jet selection requires:\n1. At least three leptons with pT > 10 GeV satisfying the usual identi\ufb01cation and isolation cuts [1].\n2. At least one jet with pT > 200 GeV.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1603\n\nNo Emiss\nT\ncut is made, so this analysis could be used even if detector problems seriously degraded the\nEmiss\nT\nperformance. The jet cut is suf\ufb01cient to suppress the WZ and W\u03b3\u2217backgrounds, so cuts on the\ninvariant mass of opposite-sign same-family dilepton pairs are also not required.\nTable 10: The numbers of surviving SUSY and Standard Model events for the benchmark points SU2,\nSU3 and SU4, as the \u201c3-leptons+jet\u201d inclusive trilepton selection is applied. All numbers are nomalized\nto 1 fb\u22121 of integrated luminosity.\nSample\nCut 1\nCut 2\nS/B\nS/\n\u221a\nB\nZn\nSU2\n35\n13\n1.1\n3.7\n2.7\nSU3\n139\n94\n7.8\n27.1\n11.5\nSU4\n1284\n312\n26.0\n90.0\n24.4\nt\u00aft\n455\n11\n\u2013\n\u2013\n\u2013\nZZ\n59\n0\n\u2013\n\u2013\n\u2013\nZW\n193\n1\n\u2013\n\u2013\n\u2013\nWW\n3\n0\n\u2013\n\u2013\n\u2013\nZ +\u03b3\n9\n0\n\u2013\n\u2013\n\u2013\nZb\n656\n0\n\u2013\n\u2013\n\u2013\nThe cut \ufb02ow for this selection is shown in Table 10. The number of events after all cuts includes\nthe effect of the 1LEP trigger, which, as shown in Table 1, has an ef\ufb01ciency of around 95% for all of\nthe benchmark points considered. The jet cut (Cut 2) particularly reduces the ZW and Zb backgrounds\nin which the jets tend to be soft. The dominant background after all cuts is t\u00aft, but there is also a small\nremaining background from WZ. The same table shows the statistical signi\ufb01cance S/\n\u221a\nB and the signif-\nicance Zn including a background uncertainty of 20%. As has already been discussed for the same-sign\ndilepton selection, the key issue for background determination is the estimation of leptons from b \u2192\u2113X\npassing the isolation cut in t\u00aft events. We expect that this could be measured as a function of the isolation\ncut for \u00b5 and then applied to e using Monte Carlo simulation. Given the large S/B in Table 10, even a\n100% background uncertainty would yield Zn > 5 for points SU3 and SU4.\nAdding a cut on Emiss\nT\nto this analysis was investigated. The surviving background events after the\ntrilepton and jet cuts have a wide range of Emiss\nT\n, so a cut to reduce them would also reduce the already\nrather small signal.\n5.2\nThree-lepton + Emiss\nT\nanalysis\nThe 3-leptons+Emiss\nT\nselection does not require (or veto) jets, so it is sensitive to direct gaugino produc-\ntion as well as to trileptons produced in the decays of squarks and gluinos. The analysis cuts have been\nsomewhat optimized for SU2, for which gaugino pair production dominates. Since the dominant source\nof trileptons in SUSY includes a decay \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1\u2113+\u2113\u2212, at least one OSSF lepton pair is required among\nthe three leptons.\nThe cuts for this analysis are:\n1. N\u2113\u22653 leptons with pT > 10 GeV satisfying the usual identi\ufb01cation and isolation cuts [1].\n2. At least one OSSF dilepton pair with M > 20 GeV to suppress low-mass \u03b3 \u2217, J/\u03c8, \u03d2, and conver-\nsion backgrounds.\n3. Lepton track isolation: p0.2\nT,trk < 1 GeV for muons and < 2 GeV for electrons, where p0.2\nT,trk is the\nmaximum pT of any additional track within a cone R = 0.2 around the lepton.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1604\n\nTable 11: Expected event numbers for the 3-leptons + Emiss\nT\nanalysis for 1fb\u22121 for signal and background\nprocesses. The WW and Z\u03b3 backgrounds are small and so are not listed.\nProcess\nCuts 1-2\nCut 3\nCut 4\nCut 5\nSU1\n42.2\n33.0\n32.6\n24.1\nSU2\n29.8\n24.1\n21.1\n17.6\nSU3\n130.1\n101.2\n98.6\n63.9\nSU4\n968.1\n691.5\n654.3\n544.9\nSU8.1\n10.2\n8.0\n8.0\n5.3\nWZ\n188.3\n166.2\n122.5\n22.8\nZZ\n55.9\n46.4\n10.3\n1.6\nZb\n582.5\n221\n1.3\n0\nt\u00aft\n283.2\n59.9\n56.6\n47.9\nTable 12: Number of signal (S) and background (B) events surviving the 3-leptons+Emiss\nT\nselection and\nthe corresponding values for S/\n\u221a\nB and Zn. All numbers are normalized to 1 fb\u22121 .\nSU1\nSU2\nSU3\nSU4\nSU8\nS\n24.1\n17.6\n63.9\n544.9\n5.3\nB\n73.5\nS/\n\u221a\nB\n2.8\n2.1\n7.5\n63.5\n0.6\nZn\n1.3\n1.0\n3.5\n16.4\n0.3\n4. Emiss\nT\n> 30 GeV.\n5. M < MZ \u221210 GeV for any OSSF dilepton pair.\nCut 3 provides an additional rejection of leptons from b and c decays beyond the calorimeter isolation\ncut, while Cut 4 reduces Standard Model backgrounds containing a Z.\nThe signi\ufb01cances S/\n\u221a\nB and Zn for this second analysis are shown in Table 12, where the Zn signi\ufb01-\ncance includes the standard 20% background systematic uncertainty. A detailed study of the performance\nof the lepton isolation cuts is needed to understand the uncertainty on the t\u00aft background in particular.\nSince this analysis does not require jets, one might hope that it would be sensitive to the dominant gaug-\nino pair production for SU2, but only SU4 gives a signal with Zn > 5 for 1fb\u22121. For all of the benchmark\npoints studied the 3-leptons+jet analysis is more sensitive than the 3-leptons+Emiss\nT\none.\n6\nTau mode\nSUSY models generically violate e/\u00b5/\u03c4 universality; \u03c4 decays can even be dominant, especially for\ntan\u03b2 \u226b1. Hence it is worthwhile to look for signatures involving hadronic \u03c4 decays even though the\nfake background from jets is much larger than that for e or \u00b5. Leptonic \u03c4 decays are indistinguishable\nfrom prompt leptons and are already included in the previous analyses.\nThe cuts used in this analysis are:\n1. At least four jets with pT > 50 GeV and at least one with pT > 100 GeV.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1605\n\nTable 13: The number of signal (S) and background (B) events after tau selection and corresponding\nvalues of signi\ufb01cance, normalised to 1fb\u22121.\nSample\nS\nB\nS/B\nS/\n\u221a\nB\nZn\nSU3\n259\n51\n5.1\n36.3\n12\nSU6\n119\n51\n2.3\n16.7\n6.8\n2. Emiss\nT\n> 100 GeV.\n3. \u2206\u03c6(ji,Emiss\nT\n) > 0.2 for each of the three leading jets ji, i = 0,1,2.\n4. No isolated leptons using the standard cuts [1].\n5. At least one \u03c4 with pT > 40 GeV and |\u03b7| < 2.5 reconstructed by the high pT \u03c4 algorithm [17] with\na likelihood, L > 4.\n6. Emiss\nT\n> 0.2Meff.\n7. MT > 100 GeV, where MT is calculated using the visible momentum of the hardest \u03c4 and Emiss\nT\n.\nCuts 1, 2, and 6 are standard. Cut 3 requires a large \u2206\u03c6 between Emiss\nT\nand the leading jets, thus reducing\nthe background both from mismeasured jets and from b and c decays. Cut 4 makes this analysis disjoint\nfrom the 1, 2, and 3-lepton analyses described above. There is still overlap with the 0-lepton analysis\ndescribed in Section 2. Cut 5 de\ufb01nes the \u03c4 sample; these cuts give an ef\ufb01ciency of \u223c50% with a purity\nof \u223c80% for the SU3 sample. Finally, if the Emiss\nT\ncomes from one W \u2192\u03c4\u03bd decay, then MT used in\nCut 7 should satisfy MT < mW. The applied cuts are a superset of the basic cuts for the inclusive 4-jet\n0-lepton analysis, which does not employ a \u03c4 veto and therefore the events selected for this analysis will\nhave an almost complete overlap with the ones selected in the analysis described in the corresponding\nsection. For the same reason, the ef\ufb01ciency of the j70xE70 trigger is expected to be between 97% and\n\u223c100% for all the benchmark points, as was the case for the inclusive multi-jet analysis.\nThe effect of these cuts is indicated graphically in Figure 8. The requirement of a reconstructed \u03c4\n(Cut 5) eliminates the QCD background. After the MT cut the S/B ratio is high. The resulting signal,\nbackground, and signi\ufb01cance for points SU3 and SU6 are given in Table 13 assuming the usual 20%\nsystematic uncertainty for the background, which is dominated by t\u00aft with some contribution from W +\njets.\nThe data-driven uncertainty on \u03c4 SUSY backgrounds has not yet been studied. Clearly \u03c4 reconstruc-\ntion is dif\ufb01cult. However, it should be possible to simulate real \u03c4 backgrounds by selecting backgrounds\nwith reconstructed e and \u00b5 and replacing the leptons with simulated \u03c4 decays. Fake backgrounds can be\nsimilarly determined using reconstructed events combined with the measured jet \u2192\u03c4 fake rate. If the\nresulting uncertainty on the background is about 20%, as is assumed in Table 13, then both points SU3\nand SU6 would be observable in the \u03c4 mode.\n7\nb-jet mode\nSUSY signals are typically rich in b quarks because the \u02dcb and \u02dct tend to be lighter than \ufb01rst- and second-\ngeneration squarks and because Higgsino couplings enhance heavy \ufb02avour production. In the benchmark\npoints studied the fractions of events containing b jets range from 14.4% for SU2 to 72.8% for SU4. In\nQCD events b quarks typically occur at the percent level. Thus, requiring a b quark suppresses the QCD\nbackground, which may be dif\ufb01cult to control, just as requiring an e or \u00b5 does.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1606\n\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nSM BG\nATLAS\nQCD\nATLAS\nZ\nATLAS\nW\nATLAS\ntt\nATLAS\nDiboson\nATLAS\nSU3\nATLAS\nSU6\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nSM BG\nATLAS\nQCD\nATLAS\nZ\nATLAS\nW\nATLAS\ntt\nATLAS\nDiboson\nATLAS\nSU3\nATLAS\nSU6\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nSM BG\nATLAS\nQCD\nATLAS\nZ\nATLAS\nW\nATLAS\ntt\nATLAS\nDiboson\nATLAS\nSU3\nATLAS\nSU6\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n-1\nevents / 400 GeV / 1fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nSM BG\nATLAS\nQCD\nATLAS\nZ\nATLAS\nW\nATLAS\ntt\nATLAS\nDiboson\nATLAS\nSU3\nATLAS\nSU6\nFigure 8: The Meff distributions for SUSY signals and Standard Model backgrounds in the \u03c4 analysis\nafter Cuts 4, 5, 6, and 7.\nIn this section an analysis of signatures with b jets is performed for SUSY points SU1, SU3, SU4 and\nSU6 using full simulation both for the signal and for the Standard Model backgrounds. Isolated leptons\nmay also be present, and all channels with and without leptons are summed. SUSY processes almost\nalways will give b\u00afb pairs, and this is taken into account. No equivalent analysis was performed in the\nPhysics TDR.\nThe cuts used in this analysis are as follows:\n1. At least 4 jets in the event with pT > 50 GeV.\n2. Leading jet pT > 100 GeV.\n3. Missing transverse energy, Emiss\nT\n> 100 GeV.\n4. Missing transverse energy, Emiss\nT\n> 0.2Meff.\n5. Transverse sphericity, ST > 0.2.\n6. At least 2 jets are tagged as b jets, as described below.\n7. Meff > 600, 800, or 1000 GeV.\nNote that Cuts 1\u20133 are also used in Monte Carlo generator \ufb01lters for some of the background samples.\nCut 7 is used to optimize the signal-to-background ratio in the selected events.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1607\n\nTable 14: Number of events surviving selection cuts as de\ufb01ned in the text for the inclusive search with\nb jets normalized to 1fb\u22121 using NLO cross-sections. The results are shown for three different values of\nthe Meff cut (Cut 7).\nSample\nCuts 1\u20133\nCut 4\nCut5\nCut 6\nCut 7\n600 GeV\n800 GeV\n1000 GeV\nSU1\n3469\n2806\n1994\n456\n442\n375\n263\nSU2\n608\n358\n299\n170\n166\n141\n87\nSU3\n9357\n7279\n5474\n1158\n1086\n818\n425\nSU4\n79761\n56697\n45661\n16478\n10204\n3186\n926\nSU6\n2557\n2049\n1467\n505\n495\n436\n340\nt\u00aft\n12864\n8273\n6117\n2182\n836\n215\n61\nQCD\n29435\n7402\n5171\n740\n259\n79\n5\nW +jets\n4068\n2309\n1600\n23\n16\n7\n2\nZ +jets\n1249\n680\n432\n5\n3\n1\n1\nDiboson\n22\n13\n8\n2\n1\n0\n0\nBSM\n47527\n18676\n13328\n2950\n1115\n303\n69\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n-1\nevents / 200 GeV / 1 fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\ntt\nQCD\nW\nZ\nDIBOSON\nSM\nB\nATLAS\nEffective Mass [GeV]\n0\n500\n1000\n1500\n2000\n2500\n-1\nevents / 200 GeV / 1 fb\n10\n2\n10\n3\n10\n4\n10\nSU1\nSU2\nSU3\nSU4\nSU6\nSM\nB\nATLAS\nFigure 9: Meff distributions for b-jet analysis. Left: Standard Model backgrounds. Right: SUSY signals\nwith total background.\nJets with pT > 20 GeV are selected as b jets using the default tagging algorithm based on the 3-\ndimensional impact parameter and secondary vertex detection [18] with a cut weight > 6.75, giving a\nnominal ef\ufb01ciency of 60%. Above about pT = 100 GeV both the ef\ufb01ciency and the light-jet rejection\ndecrease as discussed in the introductory SUSY note [1] and references therein. Naively one would\nexpect that the increase of the B decay length with \u03b3 = EB/MB \u226b1 would offset the 1/\u03b3 decrease of\nthe angles since the multiple scattering angular errors also decrease similarly. There is also a substantial\ndependence of b tagging on the \u03b7 of the jet. Many of the b jets in SUSY events have high pT: the\ntypical pT of the leading jet in SU3 is about 300 GeV, for which the light-jet rejection during b tagging\nis O(100).\nEvents with zero or more leptons and at least two tagged b jets were combined in a single inclusive\nanalysis. Inevitably this means that there is overlap with the analyses in Sections 2\u20135. The cut \ufb02ow is\nshown in Table 14. After Cut 6 (Nb \u22652) the t\u00aft background is dominant, as one might expect, but the\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1608\n\nTable 15: S/B ratio and signal signi\ufb01cance Zn including systematic effects for the b-jet analysis with\n0.1fb\u22121 and 1fb\u22121 with Meff > 1000 GeV.\nS/B\nZn for 0.1fb\u22121\nZn for 1fb\u22121\nSU1\n3.8\n6.0\n9.3\nSU2\n1.3\n2.3\n5.0\nSU3\n6.2\n7.5\n13.0\nSU4\n13.4\n12.6\n21.7\nSU6\n4.9\n7.1\n11.2\nQCD background remains substantial. The b-tagging performance at high pT is clearly an important\nissue for this analysis. As the applied cuts are a superset of the basic cuts for the inclusive 4-jet analyses,\nthe ef\ufb01ciency of the j70xE70 trigger is, as quoted in the corresponding section, between 97% and \u223c100%\nfor all the considered benchmark points.\nTo calculate the signi\ufb01cance in this channel an uncertainty of 50% for the QCD background and 20%\nfor the other backgrounds is assumed for 1fb\u22121. The uncertainty on the b-tagging ef\ufb01ciency of 60% is\n5% [2, 18]. This is assumed to be included in the t\u00aft uncertainty and is ignored for the other, smaller\nbackgrounds.\nThe hardest effective mass cut, Meff > 1000 GeV, was found to be the most effective, so only results\nfor it are shown here. The resulting signi\ufb01cances, Zn, including the above systematic effects, are shown\nin Table 15, for two luminosities: 0.1 and fb\u22121, where the same systematic uncertainty is assumed to\nbe the same for both luminosities. All background uncertainties are added linearly. The low-mass point\nSU4 and perhaps also SU3 could be discovered using this analysis with only 0.1fb\u22121 assuming that the\nbackground could be understood adequately. All points except SU2 could be discovered with 1fb\u22121, for\nwhich the background uncertainties are realistic. This analysis seems to be particularly useful compared\nto some other analyses for point SU6.\n8\nScans and optimization\nThe SUSY points studied so far were chosen to give a variety of signatures, but there is no reason to\nthink that they are representative of what might be found at the LHC. This section uses scans over the\nparameters of several models for SUSY breaking \u2013 all with R parity conservation \u2013 in order to sample\na wider range of possibilities. The goal is to develop one or more search strategies covering as wide a\nsubset of the scanned models as possible. Since each scan includes hundreds of points, this section must\nrely on ATLFAST [19], the fast parameterized simulation of the ATLAS detector.\nData-driven methods [2,3] will be used to determine the Standard Model backgrounds to the possible\nSUSY signatures. For 1fb\u22121 the estimated errors [2,3] are typically 50% for QCD jets and 20% for the\nW, Z, and t backgrounds. Several approaches were considered to look for an excess above a cut on Meff\nor Emiss\nT\nafter basic jet and lepton selections. The signi\ufb01cance is corrected for multiple cuts as described\nin Section 1.2. Results are shown here only for the Meff cut, that yielded best performance. A multivariate\noptimization using TMVA [20] gave a minor improvement with the available Monte Carlo statistics. This\nand other cut procedures are still being studied.\nThe analyses described above in this note have used signal and background cross-sections normalized\nto next-to-leading-order calculations [1]. This was impractical for scans over many points, each involving\nmany subprocesses. The goal here is not to determine the exact limit or exclusion value but rather to test\nwhether the proposed approaches work for a wide range of models. It was therefore decided to normalize\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1609\n\nthe signal cross-sections for all scans to the leading-order HERWIG values but to use next-to-leading-\norder normalizations for the backgrounds. Since next-to-leading-order corrections generally increase\ncross-sections, the resulting reach estimates are conservative.\n8.1\nSUSY signal samples\nIt is impossible to scan the 105-dimensional parameter space of the MSSM or even the 19 dimensional\nsubspace with \ufb02avour and CP conservation and degeneracy of the \ufb01rst two generations. Hence a number\nof SUSY-breaking models with many fewer parameters were used.\nSeveral of these scans (e.g. the \ufb01rst two mSUGRA scans listed below) ignore dark matter and other\nexisting constraints. Of course any true theory must obey such constraints. It is possible, however,\nto modify the SUSY breaking model to satisfy the constraints while keeping the basic phenomenology\nunchanged. One such example, the non-universal-Higgs model (NUHM), is discussed below. Since there\nis no unique model of SUSY-breaking, all these scans should be viewed only as possible patterns of LHC\nsignatures, not as complete theories.\nmSUGRA \ufb01xed grid, tan\u03b2 = 10, A0 = 0, \u00b5 > 0:\nA 25\u00d725 grid was made varying m0 from 60 GeV\nto 2940 GeV in 25 steps of 120 GeV, and m1/2 from 30 GeV to 1470 GeV in 25 steps of 60 GeV. SUSY\nspectra were generated using ISAJET 7.75 [21] with a top quark mass of 175 GeV. Out of the 625\npossible points, a spectrum could be successfully generated for 600; the other 25 failed for theoretical\nreasons. For each good point 20k events were produced using ATLFAST. Constraints other than from\ndirect searches were ignored. While constraints such as the dark-matter relic density constrain speci\ufb01c\nSUSY-breaking models such as mSUGRA, they are much less restrictive for generic models.\nmSUGRA \ufb01xed grid: tan\u03b2 = 50, A0 = 0, \u00b5 < 0:\nLarge tan\u03b2 increases the mixing of \u02dcbL,R and \u02dc\u03c4L,R,\nleading to enhanced b and \u03c4 production. A grid of 25\u00d725 points with was generated with m0 varied from\n200 to 3000 GeV in steps of 200 GeV and with m1/2 varied from 100 to 1500 GeV in steps of 100 GeV.\nThe top mass was \ufb01xed at 175 GeV. Constraints other than from direct searches were again ignored.\nmSUGRA random grid with constraints:\nIn this sample all mSUGRA parameters were varied in two\nregions2 previously found [22] to be compatible with dark-matter and other constraints with \u00b5 > 0 and\nmt = 175 GeV.\nThe mSUGRA parameters were chosen randomly (with \u00b5 > 0) and their properties calculated using\nISAJET 7.75. All selected points satisfy the LEP Higgs mass limit, mh > 114.4 GeV [23]; the WMAP\ntotal dark matter limit, \u2126h2 < 0.14 [24]; within 3\u03c3 the branching ratio limits B(b \u2192s\u03b3) = (3.55 \u00b1\n0.26)\u00d710\u22124 [25] within 3\u03c3 and B(Bs \u2192\u00b5+\u00b5\u2212) < 1.5\u00b710\u22127 [26]; and with \u03b4a\u00b5 less than the 3\u03c3 upper\nlimit from the muon anomalous magnetic moment measurement a\u00b5 = (11659208\u00b16)\u00d710\u221210 [27].\nGMSB grid: Mmess = 500 TeV, Nmess = 5, Cgrav = 1:\nWith Nmess = 5 the NLSP is a slepton which\ndecays promptly to leptons or \u03c4\u2019s. A \ufb01xed grid was made varying \u039b was varied from 10 TeV to 80 TeV\nin steps of 10 TeV and tan\u03b2 from 5 to 40 in steps of 5.\nNUHM grid:\nThe NUHM model is similar to the mSUGRA model but does not assume that the Higgs\nmasses unify with the squark and slepton ones at the GUT scale. This allows more gaugino/Higgsino\nmixing at the weak scale and so relaxes the mSUGRA dark matter constraints. The scan uses a step size\n2The parameters are varied within {0 < m0 < 2 TeV, 0.5 < m1/2 < 1.3 TeV, \u22120.34 < A0 < 2.4 TeV, 39 < tan\u03b2 < 55} and\n{1 < m0 < 3 TeV , m1/2 < 0.5 TeV , \u22122.0 < A0 < 2.0 TeV, 20 < tan\u03b2 < 55}\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1610\n\n [GeV/c]\nT\np\n50\n100\n150\n200\n250\n300\n350\n400\nEfficiency\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n\u03b7\n-2\n-1\n0\n1\n2\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nFigure 10: Ef\ufb01ciencies for electrons as a function of pT for the SU3 sample (left) and \u03b7 for the ALPGEN\nsample Z \u2192ee (right). The solid red line corresponds to the Geant 4 simulation, the solid circles to\nuncorrected ATLFAST, and the open circles to the corrected version of ATLFAST used for the reach\nanalyses.\nof 100 GeV in both m0 and m1/2. For each point the values of \u00b5 and MA at the weak scale are adjusted\nto give acceptable cold dark matter.\n8.2\nATLFAST corrections\nATLFAST is a fast parameterized simulation of the ATLAS detector. The version used here is rather\nidealized. Corrections to the ef\ufb01ciency for e reconstruction were applied as a function of pT and \u03b7. An\nexample of the effect of these corrections is shown in Figure 10. In addition, the ATLFAST algorithm\n\ufb01nding reconstructed cone jets was missing the split-merge step, so jets matched to the same truth jet\nwere combined. With these corrections the ATLFAST and full simulations agree reasonably well. All\nresults shown here use ATLFAST with these corrections.\n8.3\nDiscovery reach\nThe reach plots in this subsection are all based on analyses that require a certain number of jets and\nleptons (e or \u00b5) and then \ufb01nd an optimal Meff cut (in steps of 400 GeV) to maximize the signi\ufb01cance Zn\ncorrected for multiple cuts of the signal over the Standard Model background, using background errors\nestimated from studies of data-driven methods [2,3]. Not all modes were studied because of limited time\nor Monte Carlo statistics.\nThe analysis most similar to that in the Physics TDR [10], requires four jets with pT > {100, 50, 50, 50}\nGeV and Emiss\nT\n> max(100 GeV,0.2Meff). The 5\u03c3 discovery reach for the analyses reqiring zero, one,\nor two opposite-sign leptons for mSUGRA with tan\u03b2 = 10 are shown in Figure 11. The plot also shows\nthe trilepton reach with just one jet. The 0-lepton mode has the best estimated reach, close to 1.5 TeV for\nthe smaller of m \u02dcg and m \u02dcq. The 1-lepton estimated reach is somewhat less, but it is more robust against\nQCD backgrounds which might result from detector problems. Figure 11 also shows that the reach for\ntan\u03b2 = 50 is similar for the zero- and one-lepton channels. Despite the enhanced \u03c4 decays for tan\u03b2 \u226b1,\nthe one-\u03c4 reach is slightly worse than the reach for zero and one leptons. This re\ufb02ects the lower ef\ufb01ciency\nand purity for \u03c4 reconstruction. Compared to \u03c4 + 4 jets, the reach for \u03c4 + 3 jets is slightly better, while\n\u03c4 +2 jets is about the same. The curves for the \u03c4 +2-jet and the \u03c4 +3-jet analyses are not shown.\nRequiring four jets is not necessarily the best choice. The 5\u03c3 reach contours for the 0-lepton plus\nEmiss\nT\nand the 1-lepton plus Emiss\nT\nanalyses for various jet multiplicities are shown in Figure 12, again for\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1611\n\n [GeV]\n0\nm\n0\n500\n1000\n1500\n2000\n2500\n3000\n [GeV]\n1/2\nm\n0\n200\n400\n600\n800\n1000\n4 jets 0 lepton\n4 jets 1 lepton\n4 jets 2 leptons OS\n1 jet 3 leptons\n (0.5 TeV)\nq~\n (1.0 TeV)\nq~\n (1.5 TeV)\nq~\n (2.0 TeV)\nq~\n (2.5 TeV)\nq~\n (0.5 TeV)\ng~\n (1.0 TeV)\ng~\n (1.5 TeV)\ng~\n (2.0 TeV)\ng~\nATLAS\n discovery\n\u03c3\n5 \n = 10 \n\u03b2\nMSUGRA tan \nNO EWSB\n LSP\n1\n\u03c4\u223c\n (103 GeV)\n1\n\u03c7\u223c\n [GeV]\n0\nm\n500\n1000\n1500\n2000\n2500\n3000\n [GeV]\n1/2\nm\n200\n400\n600\n800\n1000\n4 jets 0 lepton\n4 jets 1 lepton\n\u03c4\n4 jets 1 \nATLAS\n = 50 \n\u03b2\nMSUGRA tan \n discovery\n\u03c3\n5 \nNO EWSB\n LSP\n1\n\u03c4\u223c\n (0.5 TeV)\nq~\n (1.0 TeV)\nq~\n (1.5 TeV)\nq~\n (2.0 TeV)\nq~\n (0.5 TeV)\ng~\n (1.0 eV)\ng~\n (1.5 TeV)\ng~\n (2.0 TeV)\ng~\nFigure 11: The 1 fb\u22121 5\u03c3 reach contours for the 4-jet plus Emiss\nT\nanalyses with various lepton require-\nments for mSUGRA as a function of m0 and m1/2. Left: tan\u03b2 = 10. Right: tan\u03b2 = 50. The horizontal\nand curved grey lines indicate gluino and squark mass contours respectively in steps of 500 GeV.\n [GeV]\n0\nm\n0\n500\n1000\n1500\n2000\n2500\n3000\n [GeV]\n1/2\nm\n0\n200\n400\n600\n800\n1000\n4 jets 0 lepton\n3 jets 0 lepton\n2 jets 0 lepton\n (0.5 TeV)\nq~\n (1.0 TeV)\nq~\n (1.5 TeV)\nq~\n (2.0 TeV)\nq~\n (2.5 TeV)\nq~\n (0.5 TeV)\ng~\n (1.0 TeV)\ng~\n (1.5 TeV)\ng~\n (2.0 TeV)\ng~\n~\nATLAS\n discovery\n\u03c3\n5 \n = 10 \n\u03b2\nMSUGRA tan \nNO EWSB\n LSP\n1\n\u03c4\u223c\n (103 GeV)\n1\n\u03c7\u223c\n [GeV]\n0\nm\n0\n500\n1000\n1500\n2000\n2500\n3000\n [GeV]\n1/2\nm\n0\n200\n400\n600\n800\n1000\n4 jets 1 lepton\n3 jets 1 lepton\n2 jets 1 lepton\n (0.5 TeV)\nq~\n (1.0 TeV)\nq~\n (1.5 TeV)\nq~\n (2.0 TeV)\nq~\n (2.5 TeV)\nq~\n (0.5 TeV)\ng~\n (1.0 TeV)\ng~\n (1.5 TeV)\ng~\n (2.0 TeV)\ng~\n~\nATLAS\n discovery\n\u03c3\n5 \n = 10 \n\u03b2\nMSUGRA tan \nNO EWSB\n LSP\n1\n\u03c4\u223c\n (103 GeV)\n1\n\u03c7\u223c\nFigure 12: The 1 fb\u22121 5\u03c3 reach contours for the 0-lepton and 1-lepton plus Emiss\nT\nanalyses with various\njet requirements as a function of m0 and m1/2 for the tan\u03b2 = 10 mSUGRA scan. The horizontal and\ncurved grey lines indicate the gluino and squark masses respectively in steps of 500 GeV.\nthe tan\u03b2 = 10 mSUGRA scan. For the 0-lepton mode the choice of four jets seems best, while for the\n1-lepton mode the 2-jet, 3-jet and 4-jet reaches are all comparable. The reaches (not shown here) for the\nopposite-sign dilepton plus Emiss\nT\nsignature requiring at least 2, 3, or 4 jets are comparable and in all cases\nare less than the reaches for the 0-lepton and 1-lepton modes. Observing a signal in multiple channels\nwould provide further con\ufb01dence that the observed excesses were evidence for new physics.\nThe mSUGRA \u201crandom\u201d scan with low-energy constraints samples only a limited range of parame-\nters and hence of gluino and squark masses. The results of this scan are shown as a scatter plot of points\nin Figure 13 compared to those for the mSUGRA scans. The reach for those mSUGRA points which are\ncompatible with low-energy constraints is comparable to that for generic points. This is not surprising\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1612\n\n [GeV]\ng~\nm\n200 400 600 800 1000 12001400 16001800 2000\n) [GeV]\nsquark\nmin (m\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\nATLAS\n discovery\n\u03c3\n5 \n4j0l MSUGRA\n4j0l MSUGRA DM\nFigure 13: Reach for the \u201crandom with constraints\u201d mSUGRA scan plotted in the m \u02dcg,m \u02dcq plane. Solid\ntriangles represent points which are observable (Zn > 5) with 1fb\u22121, while open triangles show points\nwhich are not.\n [GeV]\n0\nm\n100\n200\n300\n400\n500\n600\n700\n800\n900\n [GeV]\n1/2\nm\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\n1100\n4 jets 0 lepton MSUGRA\n4 jets 1 lepton MSUGRA\n4 jets 0 lepton NUHM\n4 jet 1 lepton NUHM\nATLAS\n discovery\n\u03c3\n5 \nFigure 14: The 1 fb\u22121 reach for NUHM models with 4 jets, 0 or 1 leptons, and Emiss\nT\n. The masses for\nNUHM are similar to those shown in Figure 11.\ngiven that the SUSY production cross-sections are mainly controlled by the gluino and squark masses,\nbut it adds support to the approach used in this section.\nThe mSUGRA model is only one possible mechanism for SUSY breaking. The non-universal-Higgs\nmodel has qualitatively similar phenomenology but different patterns of masses and decay modes. The\nreach plots with four jets, zero or one leptons, and Emiss\nT\nfor the NUHM are shown in Figure 14. The\nreach with zero and one leptons is virtually identical to that for mSUGRA. This is as expected: adding\nsome Higgsino mixing allows \u02dc\u03c70\n1 annihilation but has a minor effect on the other decays.\nAnother alternative often considered, Anomaly Mediated SUSY Breaking (AMSB), is not examined\nhere. Previous studies [28] have found an overall reach comparable to mSUGRA with similar assump-\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1613\n\n [TeV]\n\u039b\n10\n20\n30\n40\n50\n60\n70\n80\n\u03b2\ntan \n5\n10\n15\n20\n25\n30\n35\n40\n45\n4 jets 2 lepton (OS)\n1 jet 3 lepton \n (0.5 TeV)\nq~\n ( .0 TeV)\nq~\n (1 5 TeV)\nq~\n (2.0 TeV)\nq~\n (1.0 TeV)\ng~\n (1 5 TeV)\ng~\n (2.0 TeV)\ng~\nATLAS\n discovery\n\u03c3\n5 \nGMSB\nTACHYONIC\nFigure 15: The 1 fb\u22121 5\u03c3 reach contours of the 2-lepton and 3-lepton analyses for the GMSB scan.\nThe vertical solid and dashed grey lines indicate the gluino and squark masses respectively in steps of\n500 GeV.\ntions. The reach in the one-lepton modes is less because the lightest chargino is almost degenerate with\nthe LSP and so does not give visible leptons.\nThe models considered in the GMSB scan all have at least two leptons or \u03c4\u2019s at the Monte Carlo\ngenerator level, so the signatures are easier to distinguish from Standard Model backgrounds. The reach\nplots for this scan are shown in Figure 15. The reach for three leptons is signi\ufb01cantly better than for two\nleptons and extends well beyond 2 TeV for gluinos for large tan\u03b2 and is close to 2 TeV for all tan\u03b2.\nSpecial signatures that can result from GMSB models are discussed elsewhere in this volume [4].\n8.4\nSummary\nThe results of the scans presented in this section together with the full simulation analyses presented ear-\nlier indicate that ATLAS should discover signals for R-parity conserving SUSY with gluino and squark\nmasses less than O(1 TeV) after having accumulated and understood an integrated luminosity of about\n1fb\u22121. For favorable models the mass reach could be greater. The luminosity required to discover a given\nSUSY scenario is greater than that estimated previously [29]. The main differences in this analysis are\nthat the uncertainty in the background (derived from data-driven methods) is taken into account and that\nthe signal and background simulations are more realistic. Given the admittedly qualitative naturalness\narguments about SUSY masses, it is plausible that SUSY could be found with 1fb\u22121 if it exists at the\nTeV scale. Conversely, if SUSY is not found with 1fb\u22121, it might still eventually be discovered at the\nLHC, but it will be dif\ufb01cult to study in detail.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1614\n\nReferences\n[1] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[2] ATLAS Collaboration, Data-Driven Determinations of W, Z and Top Backgrounds to Supersym-\nmetry, this volume.\n[3] ATLAS Collaboration, Estimation of QCD Backgrounds to Searches for Supersymmetry, this vol-\nume.\n[4] ATLAS Collaboration, Supersymmetry Signatures with High-pT Photons or Long-Lived Heavy\nParticles, this volume.\n[5] ATLAS Collaboration, ATLAS High-Level Trigger, Data Acquisition and Controls Technical Design\nReport, ATLAS TDR-016 (2003).\n[6] ATLAS Collaboration, Trigger for Early Running, this volume.\n[7] R.D. Cousins and V.L. Highland, Nucl. Instrum. Meth. A320 (1992) 331\u2013335.\n[8] J. T. Linnemann, Measures of signi\ufb01cance in HEP and astrophysics, 2003.\n[9] R. Brun, and F. Rademakers, Nucl. Instrum. Meth. A389 (1997) 81\u201386.\n[10] ATLAS Collaboration, ATLAS detector and physics performance. Technical design report Vol. 2,\nCERN-LHCC-99-15 (1999).\n[11] ATLAS Collaboration, Multi-Lepton Supersymmetry Searches, this volume.\n[12] C. Lester, D. Summers, Phys. Lett. B463 (1999) 99.\n[13] A.J. Barr, C.G. Lester, P. Stephens, J. Phys. G. 29 (2003) 2343.\n[14] H. Baer, K. Hagiwara and X. Tata, Phys. Rev. Lett 57, 294 (1986) and Phys. Rev. D35, 1598 (1987);\nR. Arnowitt and P. Nath, Mod. Phys. Lett. A2, 331 (1987); R. Barbieri, F. Caravaglios, M. Frigeni\nand M. Mangano, Nucl. Phys. B367, 28 (1991); H. Baer and X. Tata, Phys. Rev. D47, 2739 (1993);\nJ. Lopez, D. Nanopoulos, X. Wang and A. Zichichi, Phys. Rev. D48, 2062 (1993); H. Baer, C. Kao\nand X. Tata, Phys. Rev. D48, 5175 (1993); S. Mrenna, G. Kane, G. D. Kribs and J. D. Wells, Phys.\nRev. D53, q1168 (1996)..\n[15] CDF Collaboration, CDF/PUB/EXOTIC,PUBLIC/9176, http://www-cdf.fnal.gov/physics\n/exotic/r2a/20080110.trilepton dube/cdf9176.pdf.\n[16] D0 Collaboration, D0 Note 5348-Conf,\nhttp://www-d0.fnal.gov/Run2Physics/WWW/results/prelim/NP/N52/N52.pdf.\n[17] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[18] ATLAS Collaboration, Vertex Reconstruction for b-Tagging, this volume.\n[19] Richter-Was, Elzbieta and Froidevaux, Daniel and Poggioli, Luc, ATLFAST 2.0 a fast simulation\npackage for ATLAS Atlas Note ATL-PHYS-98-131.\n[20] A. Hocker et al., TMVA: Toolkit for multivariate data analysis, physics/0703039, 2007.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1615\n\n[21] F. Paige, S. Protopopescu, H. Baer and X. Tata, ISAJET 7.69: A Monte Carlo event generator for p\np, anti-p p, and e+ e- reactions hep-ph/0312045, 2003.\n[22] R.R. de Austri, R. Trotta and L. Roszkowski, JHEP 05 (2006) 002.\n[23] R. Barate et al., Phys. Lett. B565 (2003) 61\u201375.\n[24] D. Spergel et al., Astrophys. J. Suppl. 170 (2007) 377.\n[25] E. Barberio et al., Averages of b-hadron properties at the end of 2006. arXiv:0704.3575 [hep-ex],\n2007.\n[26] A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 94 (2005) 221805.\n[27] G.W. Bennett et al., Phys. Rev. Lett. 92 (2004) 161802.\n[28] A.J. Barr, C.G. Lester, M.A. Parker, B.C. Allanach and P. Richardson, JHEP 03 (2003) 045.\n[29] D.R. Tovey, Eur. Phys. J. Direct C4 (2002) N4.\nSUPERSYMMETRY \u2013 PROSPECTS FOR SUPERSYMMETRY DISCOVERY BASED ON INCLUSIVE . . .\n1616\n\nMeasurements from Supersymmetric Events\nAbstract\nWe review the techniques used to reconstruct the decay of supersymmetric par-\nticles and measure their properties with ATLAS at the LHC, concentrating on\nstrategies to be applied to a data set of integrated luminosity of 1 fb\u22121 that can\nbe expected after the \ufb01rst year of operation of the LHC. These techniques are\nillustrated using several benchmark points chosen in the mSUGRA parameter\nspace, but they are applicable to a broader range of supersymmetric (and other\nsimilar) models. The most appropriate methods will be selected and \ufb01ne-tuned\nonce (and if) signatures consistent with Supersymmetry are established. Su-\npersymmetric cascade decays typically have large transverse missing energy\ndue to the presence of undectected neutralinos, and have characteristic edges\nand thresholds in the dilepton, dijet and lepton-jet invariant mass distributions.\nThe reconstruction of such edges is the focus of the \ufb01rst part of the paper. The\nsecond part of the paper concentrates on the reconstruction of more speci\ufb01c de-\ncay channels, involving light stops, staus and Higgs bosons. The \ufb01nal section\nindicates how sparticle masses and other supersymmetric parameters could be\nconstrained using such measurements.\n1\nIntroduction\nSupersymmetry (SUSY) can be discovered by the ATLAS experiment at the LHC during the initial run-\nning period if some coloured sparticles have masses of the order hundreds of GeV and hence production\ncross-sections of the order of a few pb. A strategy to establish SUSY discovery is outlined in another\npaper in this collection [1], while here we concentrate on parameter measurements that can be performed\nwith the early data. The same particle identi\ufb01cation conventions and selection criteria as in [2] are used\nin this paper.\nOnce a signature consistent with Supersymmetry has been established, the experimental emphasis\nwill move on to measuring the sparticle mass spectrum and constraining the parameters of the model. In\nthe case of R-parity-conserving models, the decay chain of sparticles cannot be completely reconstructed,\nas sparticles eventually decay into LSPs that can not be detected. For this reason edge positions, rather\nthan mass peaks, are measured in the invariant mass distribution of sparticle decay products. In R-parity-\nviolating models sparticles can have long lifetimes and can be detected by studying their decay in-\ufb02ight\nwithin the detector. These types of signatures are discussed in [3].\nA complete coverage of all allowed SUSY models is impossible, so we limit this study to a subset\nof the models where SUSY breaking is mediated by gravity (mSUGRA), and to the points in parameter\nspace described in [2], however the measurement techniques and \ufb01t methods developed can be adapted\nfor many models. During initial data-taking, the error on such measurements will be limited by statistics,\nmaking measurements possible only for models with moderate (\u22721 TeV) values of the SUSY mass scale\nwhere enough events can be isolated. In this paper we study the cases of a total integrated luminosity\nof 0.5 fb\u22121 for the \u201cLow Mass\u201d point (SU4) and of 1 fb\u22121 for the \u201cBulk\u201d point (SU3), with the idea of\ndeveloping the experimental analyses which might be performed after the \ufb01rst year or so of data taking.\nSome benchmark points require somewhat larger datasets in order to perform kinematic measurements;\nas an example we show a measurement of the dilepton mass edges for the \u201cCoannihilation\u201d point (SU1)\nwith a dataset corresponding to 18 fb\u22121.\nIn sections 3 and 4 we study the decay chain:\n\u02dcqL \u2192\u02dc\u03c70\n2q(\u2192\u02dc\u2113\u00b1\u2113\u2213q) \u2192\u02dc\u03c70\n1\u2113+\u2113\u2212q\n(1)\n1617\n\nin events containing two opposite-sign isolated electrons or muons, hard jets and missing energy. Kine-\nmatic endpoints in the invariant mass spectra of lepton pairs and lepton+jet combinations are \ufb01tted and\nused to derive relations between the masses of sparticles. In the case of \ufb01rst- and second-generation\nsquarks, it will often not be possible to experimentally determine squark \ufb02avour, so we de\ufb01ne m \u02dcqL to be\nthe average of the masses of the \u02dcuL and \u02dcdL squarks, and m \u02dcqR, the average mass of \u02dcuR and \u02dcdR.\nEvents with tau leptons in the \ufb01nal state are studied in Section 5 and di-tau mass edges in the \u02dc\u03c70\n2\ndecay chain reconstructed. This signature is particularly important in the co-annihilation region where\nthe decay into tau stau pairs is favoured.\nIn Section 6 we analyse events with two hard jets and missing energy in order to to measure the jet\n\u201cstransverse mass\u201d. This variable is sensitive to the mass of the right-handed squark in events where a\npair of squarks are produced, each decaying as:\n\u02dcqR \u2192q \u02dc\u03c70\n1\n(2)\nA kinematical edge depending on the mass of the light stop is reconstructed in Section 7 by exploiting\nthe decay:\n\u02dcg \u2192\u02dct1t \u2192\u02dc\u03c7\u00b1\n1 bt\n(3)\nand reconstructing the tb invariant mass.\nThe reconstruction of the lightest Higgs bosons, produced by the \u02dc\u03c70\n2 decay followed by the Higgs\ndecay into a pair of b quarks, is investigated in Section 8. Simulations of the \u201cHiggs\u201d point (SU9) show\nthat if these decays are allowed, then the Standard Model Higgs boson may be initially detected as a\nSUSY decay product rather than by signatures that involve its production via Standard Model processes.\nIn Section 9 the parameters measured in sections 3 to 8 are combined to extract information about the\nSUSY model such as the sparticle mass spectrum and the mSUGRA parameters (under the hypothesis\nthat mSUGRA is realised).\nAll of these studies use a realistic detector geometry with residual misalignments, and all relevant\nStandard Model backgrounds are taken into account, as are the trigger ef\ufb01ciencies. The reconstruction of\n\ufb01nal state objects, the event selection criteria, the strategy used to simulate both signal and background\nevents, and the methods for estimating systematic uncertainties are common across all SUSY analyses\nand are discussed in the introduction to this chapter [2].\n2\nMeasurement of endpoints\nThe decay chain in Eq. (1) is particularly suited to measure the mass of SUSY particles, as the presence in\nthe \ufb01nal state of charged leptons, missing energy from the escaping neutralino and hadronic jets ensures\na large signal to background ratio. Thus, \ufb01t results are not very dependent on the precise measurement of\nthe Standard Model background. Although we discuss the reconstruction of edges and thresholds within\nthe mSUGRA framework, the same methodology can be applied to the large variety of SUSY models\nwhere the \u02dcqL decay channel in Eq. (1) is open. In the following we indicate with \u2113only electrons and\nmuons (with \u02dc\u2113being their superpartners) while \u03c4 leptons are indicated explicitly.\nThe endpoint in the di-lepton invariant mass distribution is a function of the masses of the particles\ninvolved in the decay. If the sleptons are heavier than the \u02dc\u03c70\n2 then the decay proceeds through the three\nbody channel \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1\u2113+\u2113\u2212as in the SU4 model. In this case, the distribution of the invariant mass of\nthe two leptons has a non-triangular shape described in [4,5] with an endpoint equal to the difference of\nthe mass of the two neutralinos:\nmedge\n\u2113\u2113\n= m \u02dc\u03c70\n2 \u2212m \u02dc\u03c70\n1\n(4)\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1618\n\nIf at least one of the sleptons is lighter than the \u02dc\u03c70\n2 then the two-body decay channel \u02dc\u03c70\n2 \u2192\u02dc\u2113\u00b1\u2113\u2213\u2192\n\u02dc\u03c70\n1\u2113+\u2113\u2212dominates. The distribution of the invariant mass of the two leptons is triangular with an endpoint\nat:\nmedge\n\u2113\u2113\n= m \u02dc\u03c70\n2\nv\nu\nu\nt1\u2212\n \nm \u02dc\u2113\nm \u02dc\u03c70\n2\n!2s\n1\u2212\n\u0012m \u02dc\u03c70\n1\nm \u02dc\u2113\n\u00132\n.\n(5)\nFor the SU3 point, where the \u02dc\u2113R and the \u02dc\u03c41 are lighter than the \u02dc\u03c70\n2, such an endpoint is expected in the\n\u2113+\u2113\u2212(\u03c4+\u03c4\u2212) distribution for medge\n\u2113\u2113\n= 100.2 GeV (medge\n\u03c4\u03c4\n= 98.3 GeV). For the SU1 point both \u02dc\u2113R and\n\u02dc\u2113L as well as \u02dc\u03c41 and \u02dc\u03c42 are lighter than \u02dc\u03c70\n2, resulting in a double triangular distribution for the dilepton\ninvariant mass with two edges.\nMeasuring the dilepton endpoint allows us to establish a relationship between the masses of the two\nlightest neutralinos and any sleptons that are lighter than the \u02dc\u03c70\n2. For a determination of the masses of\nall the particles involved in the decay chain Eq. (1), further mass distributions involving a jet are used:\nm\u2113\u2113q, mthr\n\u2113\u2113q, m\u2113q(low) and m\u2113q(high). Since it is not possible to identify the quark from the \u02dcqL decay, we\nmake the assumption that it generates one of the two highest pT jets in the event, as is normally the case\nif the \u02dcqL is much heavier than the \u02dc\u03c70\n2. Hence only the two leading jets are considered. For the m\u2113\u2113q\ndistribution a maximum value of the distribution is expected so the jet giving the lowest m\u2113\u2113q value is\nused. The mthr\n\u2113\u2113q distribution is de\ufb01ned by the additional constraint m\u2113\u2113> medge\n\u2113\u2113\n/\n\u221a\n2, giving a non-zero\nthreshold value [6, 7]. Since a minimum is sought, the jet giving the highest m\u2113\u2113q value is used in this\ndistribution. The distributions m\u2113q(low) and m\u2113q(high) are formed from the lower and higher mlq value of\neach event using the same jet as for m\u2113\u2113q. Both distributions have well-de\ufb01ned endpoints.\nThe theoretical values of the kinematic threshold and endpoints listed above can be calculated using\nthe analytical expressions given in [6, 7]. The theoretical positions of the end points for the SU1, SU3\nand SU4 models are summarised in Table 1.\nTable 1: Value of the end points of the invariant mass distributions for the three benchmark points\nconsidered in this section. For SU1 the two endpoints correspond to the two available decay chains of\nthe \u02dc\u03c70\n2 involving a right or left slepton.\nMass Distribution\nSU1 end point (GeV)\nSU3 end point (GeV)\nSU4 end point (GeV)\nmedge\n\u2113\u2113\n56.1, 97.9\n100.2\n53.6\nmedge\n\u03c4\u03c4\n77.7, 49.8\n98.3\n53.6\nmedge\n\u2113\u2113q\n611, 611\n501\n340\nmthr\n\u2113\u2113q\n133, 235\n249\n168\nmmax\nlq(low)\n180, 298\n325\n240\nmmax\nlq(high)\n604, 581\n418\n340\nAnother advantage of the decay chain in 1 is the possibility of estimating both the SUSY combina-\ntorial background and the Standard Model background from the data with high accuracy. The technique,\nknown as \ufb02avour subtraction, is based on the fact that the signal contains two opposite-sign same-\ufb02avour\n(OSSF) leptons, while the background leptons come from different decay chains, which can be of the\nsame \ufb02avour or of different \ufb02avour with the same probability. The background thus cancels in the sub-\ntraction:\nN(e+e\u2212)/\u03b2 +\u03b2N(\u00b5+\u00b5\u2212)\u2212N(e\u00b1\u00b5\u2213)\n(6)\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1619\n\nwhere \u03b2 = 0.86 is an ef\ufb01ciency correction factor equal to the ratio of the electron and muon reconstruc-\ntion ef\ufb01ciencies. The value of \u03b2 is taken from [8,9], and is assumed in the following to be known with\nan uncertainty of 10%.\n3\nDilepton edges\n3.1\nEvent Selection\nEvents with two or three isolated leptons (electrons or muons) with pT > 10 GeV and |\u03b7| < 2.5 are\nselected. If two leptons are selected, they are required to have opposite signs. If three leptons are\npresent, the two opposite-sign combinations are considered and treated independently in the rest of the\nanalysis.\nIn order to select SUSY events and reject the Standard Model background it is necessary to require\nthe presence of energetic jets and missing energy. The variables used to discriminate SUSY from the\nSM background are the transverse missing energy, the transverse momenta of the four leading jets, the\nratio between the transverse missing energy and the effective mass, and the transverse sphericity (ST). In\norder to optimise the cuts on these variables, the value of:\nS \u2261(NOSSF \u2212NOSDF)/\u221aNOSSF +NOSDF\n(7)\nis maximized for each SUSY point, where NOSSF and NOSDF are the number of same-\ufb02avour and different-\n\ufb02avour lepton pairs respectively.\nThe S variable can be computed from collider data, since no Monte Carlo information is used. By\nmaximizing the value of S we are maximizing the selection ef\ufb01ciency for signal events while suppressing\nthe Standard Model and the SUSY combinatorial backgrounds.\nIn order to improve the sensitivity to the signal, only lepton pairs with an invariant mass m\u2113\u2113<\nmedge\n\u2113\u2113\n+ 10 GeV are considered. Since the true value of the endpoint is a priori unknown, this choice\nimplies that the edge has already been observed, and that afterwards the selection cuts are optimised as\ndescribed here in order to improve the separation between signal and background and the measurement\nof the endpoint. We are thus focusing here on determining selection cuts that would allow a precise\nmeasurement of the endpoint with moderate statistics, rather than on \ufb01nding the \ufb01rst evidence for an\nexcess of different-\ufb02avour lepton pairs or the \ufb01rst evidence for the presence of the edge.\nIn Table 2 the optimal selection resulting from the scan is shown. For all three points a 2-jet selection\nis preferred, leaving out cuts on the third and fourth jets, on ST and on the ratio Emiss\nT\n/Meff. For the\n\u201cCoannihilation\u201d point (SU1) and the \u201cBulk\u201d point (SU3) the S-value is found to be stable in an interval\naround the maximum value. For the \u201cLow Mass\u201d point (SU4) the best S-value is found for the loosest\ncut allowed by the available Monte Carlo samples. Hence even looser cuts may be preferred as far as the\nvalue of S is concerned. The cuts on Emiss\nT\nand the pT of leading jet are however required in order to\nhave a high trigger ef\ufb01ciency1.\nThe number of signal and background lepton pairs passing the selection cuts is shown in Table 3. All\nnumbers are for 1 fb\u22121. The main Standard Model background is always t\u00aft accounting for about 95% of\nthe total background. The remaining background events are from W, Z and WW, WZ, ZZ production.\nThe background due to QCD jets is negligible. The fraction of SUSY events in the selected sample with\nOSSF leptons is 59% for SU1, 77% for SU3, and 80% for SU4.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1620\n\nTable 2: Results of the event-selection optimisation for the S-variable Eq. (7) for signal (s) and Standard\nModel background (b) with range limit m\u2113\u2113< medge\n\u2113\u2113\n+ 10 GeV, for SU1, SU3 and SU4 for 1 fb\u22121. The\nbest selection is shown.\npj1\nT\npj2\nT\npj3\nT\npj4\nT\nEmiss\nT\nEmiss\nT\n/Meff\nST\nsOSSF\nsOSDF\nbOSSF\nbOSDF\nS\nSU1\n200\n150\n-\n-\n120\n-\n-\n120\n64\n69\n53\n5.1\nSU3\n180\n100\n-\n-\n120\n-\n-\n615\n149\n93\n92\n15.1\nSU4\n100\n50\n-\n-\n100\n-\n-\n3048\n1574\n411\n419\n19.9\nTable 3: Number of lepton pairs passing the selection cuts optimized for the SUSY sample SU1 (above),\nSU3 (middle) and SU4 (below), for 1 fb\u22121 of integrated luminosity. The contribution from t\u00aft produc-\ntion is indicated separately as it constitutes most of the Standard Model background. The remaining\nbackground events are from W, Z and WW, WZ, ZZ production. The background due to QCD jets is\nnegligible.\nSample\ne+e\u2212\n\u00b5+\u00b5\u2212\nOSSF\nOSDF\nSUSY SU1\n56\n88\n144\n84\nStandard Model (t\u00aft)\n35 (35)\n65 (63)\n101 (99)\n72 (68)\nSUSY SU3\n274\n371\n645\n178\nStandard Model (t\u00aft)\n76 (75)\n120 (115)\n196 (190)\n172 (165)\nSUSY SU4\n1729\n2670\n4400\n2856\nStandard Model (t\u00aft)\n392 (377)\n688 (657)\n1081 (1035)\n1104 (1063)\n3.2\nReconstruction of the dilepton edge\nThe distribution of the invariant mass of same-\ufb02avour and different-\ufb02avour lepton pairs is shown in\nFig. 1 for the SUSY benchmark points and backgrounds, after the selection cuts optimized for SU3 (left\nplot) and SU4 (right plot), and for an integrated luminosity of 1 fb\u22121 and 0.5 fb\u22121 respectively. It can\nbe seen from regions where the signal does not contribute (i.e. for the Standard Model backgrounds\nand for m\u2113\u2113> medge\n\u2113\u2113\nfor SUSY) that the different-\ufb02avour distributions are similar to the same-\ufb02avour\nbackgrounds.\nThe invariant mass distribution after \ufb02avour subtraction is shown in the left plot of Fig. 2 in the\npresence of the SU3 signal and for an integrated luminosity of 1 fb\u22121. The distribution has been \ufb01tted\nwith a triangle smeared with a Gaussian. The value obtained for the endpoint is (99.7\u00b11.4\u00b10.3) GeV\nwhere the \ufb01rst error is due to statistics and the second is the systematic error on the lepton energy scale\nand on the \u03b2 parameter [2]. This result is consistent with the true value of 100.2 GeV calculated from\nEq. (5).\nThe right plot of Fig. 2 shows the \ufb02avour-subtracted distribution in the presence of the SU4 signal for\nan integrated luminosity of 0.5 fb\u22121. The \ufb01t was performed using the function from [5] which describes\nthe theoretical distribution for the 3-body decay in the limit of large slepton masses, smeared for the\nexperimental resolution. This function vanishes near the endpoint and is a better description of the true\ndistribution for SU4 than the triangle with a sharp edge. The endpoint from the \ufb01t is (52.7 \u00b1 2.4 \u00b1\n1For this channel, both the lepton triggers and the trigger based on Emiss\nT\nmay be relied upon. The latter are however less\nef\ufb01cient, and they would imply different pT thresholds for electrons and muons.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1621\n\nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries/ 4 GeV / 1 fb\n0\n10\n20\n30\n40\n50\nSU3 OSSF\nBKG OSSF\nSU3 OSDF\nBKG OSDF\nATLAS\nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries/ 4 GeV / 0.5 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nSU4 OSSF\nBKG OSSF\nSU4 OSDF\nBKG OSDF\nATLAS\nFigure 1: Left: distribution of the invariant mass of same-\ufb02avour and different-\ufb02avour lepton pairs for\nthe SUSY benchmark points and backgrounds after the cuts optimized from data in presence of the SU3\nsignal (left), and the SU4 signal (right). The integrated luminosities are 1 fb\u22121 and 0.5 fb\u22121 respectively.\nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries/4 GeV/ 1 fb\n-10\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 40.11 / 45\nProb \n 0.679\nEndpoint \n 1.399\n\u00b1\n 99.66 \nNorm. \n 0.02563\n\u00b1\n -0.3882 \nSmearing \n 1.339\n\u00b1\n 2.273 \n / ndf \n2\n\u03c7\n 40.11 / 45\nProb \n 0.679\nEndpoint \n 1.399\n\u00b1\n 99.66 \nNorm. \n 0.02563\n\u00b1\n -0.3882 \nSmearing \n 1.339\n\u00b1\n 2.273 \nATLAS\nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries/4 GeV/ 0.5 fb\n-40\n-20\n0\n20\n40\n60\n80\n100\n120\n / ndf \n2\n\u03c7\n 10.5 / 16\nProb \n 0.839\nNorm \n 8.971\n\u00b1\n 70.07 \nM1+M2 \n 8.267\n\u00b1\n 67.71 \nM2-M1 \n 2.439\n\u00b1\n 52.68 \n / ndf \n2\n\u03c7\n 10.5 / 16\nProb \n 0.839\nNorm \n 8.971\n\u00b1\n 70.07 \nM1+M2 \n 8.267\n\u00b1\n 67.71 \nM2-M1 \n 2.439\n\u00b1\n 52.68 \nATLAS\nFigure 2: Left: Distribution of invariant mass after \ufb02avour subtraction for the SU3 benchmark point with\nan integrated luminosity of 1 fb\u22121. Right: the same distribution is shown for the SU4 benchmark point\nand an integrated luminosity of 0.5 fb\u22121. The line histogram is the Standard Model contribution, while\nthe points are the sum of Standard Model and SUSY contributions. The \ufb01tting function is superimposed\nand the expected position of the endpoint is indicated by a dashed line.\n0.2) GeV, consistent with the theoretical endpoint of 53.6 GeV.\nSince the true distribution will not be known for data, the distribution was also \ufb01tted with the smeared\ntriangle expected for the 2-body decay chain. This also gives a good \u03c7 2 with an endpoint of (49.1 \u00b1\n1.5 \u00b1 0.2) GeV. A larger integrated luminosity will be required to use the shape of the distribution to\ndiscriminate between the two-body and the three-body decays.\nIn Fig. 3 the \ufb02avour-subtracted distribution of the dilepton mass is shown for the SU1 point at an\nintegrated luminosity of 1 fb\u22121 (left) and 18 fb\u22121 (right) 2. While there is already a clear excess of\nSF-OF entries at 1 fb\u22121 , a very convincing edge structure cannot be located. At 18 fb\u22121\nthe two\nedges are visible. A \ufb01t function consisting of a double triangle convoluted with a Gaussian, the latter\n2Only 1 fb\u22121 of simulated Standard Model background was available. To scale the Standard Model contribution to higher\nluminosities a probability density function for the m(ll) distribution was constructed by \ufb01tting a Landau function to the 1 fb\u22121\ndistribution, assuming statistically identical shapes for e+e\u2212, \u00b5+\u00b5\u2212and e\u00b1\u00b5\u2213and normalisation according to a \u03b2 of 0.86. The\nsystematic uncertainty on the endpoint determination from this procedure was estimated to be a small fraction of the statistical\nuncertainty.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1622\n\nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries / 4 GeV / 1 fb\n-5\n0\n5\n10\n15\nATLAS\n / ndf \n2\n\u03c7\n 25.08 / 26\nEndpoint1 \n 1.20\n\u00b1\n 55.76 \nNorm1 \n 241.2\n\u00b1\n 2125 \nEndpoint2 \n 1.31\n\u00b1\n 99.26 \nNorm2 \n 292.5\n\u00b1\n 2073 \nm(ll) [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-1\nEntries / 4 GeV / 18 fb\n-20\n0\n20\n40\n60\n80\n100\n / ndf \n2\n\u03c7\n 25.08 / 26\nEndpoint1 \n 1.20\n\u00b1\n 55.76 \nNorm1 \n 241.2\n\u00b1\n 2125 \nEndpoint2 \n 1.31\n\u00b1\n 99.26 \nNorm2 \n 292.5\n\u00b1\n 2073 \nATLAS\n / ndf \n2\n\u03c7\n 25.08 / 26\nEndpoint1 \n 1.20\n\u00b1\n 55.76 \nNorm1 \n 241.2\n\u00b1\n 2125 \nEndpoint2 \n 1.31\n\u00b1\n 99.26 \nNorm2 \n 292.5\n\u00b1\n 2073 \nFigure 3: Distribution of invariant mass after \ufb02avour subtraction for the SU1 point and for an integrated\nluminosity of 1 fb\u22121 (left) and 18 fb\u22121 (right). The points with error bars show SUSY plus Standard\nModel, the solid histogram shows the Standard Model contribution alone. The \ufb01tted function is super-\nimposed (right), the vertical lines indicate the theoretical endpoint values.\nhaving a \ufb01xed width of 2 GeV, returns endpoint values of 55.8 \u00b1 1.2 \u00b1 0.2 GeV for the lower edge and\n99.3 \u00b1 1.3 \u00b1 0.3 GeV for the upper edge, consistent with the true values of 56.1 and 97.9 GeV. As can\nbe seen from Fig. 3 (right) the m\u2113\u2113distribution also contains a noticeable contribution from the leptonic\ndecay of Z bosons present in SUSY events. Even though the upper edge is located close to the Z mass,\nadding a Z peak of \ufb01xed mass and width to the \ufb01t function only affects the endpoints at the 0.2-0.3 GeV\nlevel. However the Z peak changes the normalisation of the upper triangle so for considerations of\ncouplings and branching ratios it should be included.\n4\nLeptons+Jets edges\nIn events selected for the dilepton analysis in the previous section, jets are added to construct further\ndistributions as described in Sect. 2. Additional selection cuts are applied to re\ufb01ne the distributions:\nm\u2113\u2113< medge\n\u2113\u2113\n+\u22061\n(all distributions)\n(8)\nm\u2113\u2113q < medge\n\u2113\u2113q +\u22062\n(m\u2113q distributions)\n(9)\nHere medge\n\u2113\u2113\nand medge\n\u2113\u2113q refer to experimental values found in this and the previous section. The value \u22061\nis a small number, 10 (3.3) GeV for SU3 (SU4), to account for the fact that the edge stretches slightly\nbeyond the \ufb01tted endpoint. One can see from Fig. 1 that this cut should be very effective for SU4, but\nmuch less so for SU3. The value \u22062 serves a similar purpose, but since the determination of medge\n\u2113\u2113q is less\nreliable, a looser cut is used, 155 (37) GeV for SU3 (SU4).\nThe invariant mass distributions m\u2113\u2113q and m\u2113q are shown in Figures 4 and 5 for both the \u201cBulk\u201d point\n(SU3) and the \u201cLow Mass\u201d point (SU4) after ef\ufb01ciency-corrected \ufb02avour subtraction.\nWhile the Standard Model background causes considerable bin-by-bin \ufb02uctuations for integrated lu-\nminosities \u22721 fb\u22121, the net contribution of entries beyond the endpoints is mainly due to combinatorics\nfrom choosing the wrong jet in a true SUSY event. For the distributions where a clear tail is visible, a\nstraight line is assumed for the background, otherwise it is set to zero. (The statistics box of the plots\nindicates which background hypothesis is used.) Since the tail is due to SUSY events, it will not be\nknown beforehand and a data-driven approach (not described here) would be required.\nThe lepton+jet distributions have shapes which depend on the sparticle masses [10]. Depending on\nthe sparticle spectrum, the edge region may contain non-trivial features such as experimentally unde-\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1623\n\n / ndf \n2\n\u03c7\n 2.3 / 10\nEndpoint \n 30.1\n\u00b1\n 516.7 \nSlope \n 0.0424\n\u00b1\n -0.1563 \nbck p0 \n 19.96\n\u00b1\n 26.37 \nbck p1 \n 0.03387\n\u00b1\n -0.04149 \nm(llq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 1 fb\n-10\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 2.3 / 10\nEndpoint \n 30.1\n\u00b1\n 516.7 \nSlope \n 0.0424\n\u00b1\n -0.1563 \nbck p0 \n 19.96\n\u00b1\n 26.37 \nbck p1 \n 0.03387\n\u00b1\n -0.04149 \nATLAS\n / ndf \n2\n\u03c7\n 3.593 / 9\nEndp. \n 12.2\n\u00b1\n 343.1 \nSlope \n 0.1294\n\u00b1\n -0.6258 \nbck p0 \n 11.04\n\u00b1\n 22.44 \nbck p1 \n 0.0252\n\u00b1\n -0.0447 \nm(llq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 0.5 fb\n0\n20\n40\n60\n80\n / ndf \n2\n\u03c7\n 3.593 / 9\nEndp. \n 12.2\n\u00b1\n 343.1 \nSlope \n 0.1294\n\u00b1\n -0.6258 \nbck p0 \n 11.04\n\u00b1\n 22.44 \nbck p1 \n 0.0252\n\u00b1\n -0.0447 \nATLAS\n / ndf \n2\n\u03c7\n 3.593 / 9\nEndp. \n 12.2\n\u00b1\n 343.1 \nSlope \n 0.1294\n\u00b1\n -0.6258 \nbck p0 \n 11.04\n\u00b1\n 22.44 \nbck p1 \n 0.0252\n\u00b1\n -0.0447 \n / ndf \n2\n\u03c7\n 9.727 / 6\nEndpoint \n 17.4\n\u00b1\n 265.4 \nSlope \n 0.0766\n\u00b1\n 0.2114 \nm(llq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 1 fb\n-5\n0\n5\n10\n15\n20\n25\n / ndf \n2\n\u03c7\n 9.727 / 6\nEndpoint \n 17.4\n\u00b1\n 265.4 \nSlope \n 0.0766\n\u00b1\n 0.2114 \nATLAS\n / ndf \n2\n\u03c7\n 6.359 / 6\nEndp. \n 35.5\n\u00b1\n 160.9 \nSlope \n 0.2473\n\u00b1\n 0.3279 \nm(llq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 0.5 fb\n-10\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 6.359 / 6\nEndp. \n 35.5\n\u00b1\n 160.9 \nSlope \n 0.2473\n\u00b1\n 0.3279 \nATLAS\n / ndf \n2\n\u03c7\n 6.359 / 6\nEndp. \n 35.5\n\u00b1\n 160.9 \nSlope \n 0.2473\n\u00b1\n 0.3279 \nFigure 4: Ef\ufb01ciency-corrected \ufb02avour-subtracted distributions of m\u2113\u2113q (top) and mthr\n\u2113\u2113q (bottom) for SU3\n(left) for 1 fb\u22121 and SU4 (right) with 0.5 fb\u22121 of integrated luminosity. The points with error bars show\nSUSY plus Standard Model, the solid histogram shows the Standard Model contribution alone. The \ufb01tted\nfunction is superimposed, the vertical line indicates the theoretical endpoint value.\ntectable \u2018feet\u2019 containing very few events or vertical drops. For all the relevant distributions of two-body\nscenarios, analytic formulas describing the shape in terms of the sparticle masses are known [11, 12].\nWith low statistics a straight-line \ufb01t is likely to give to give a suf\ufb01ciently good description in many cases.\nAll the edges and thresholds were \ufb01tted with the following formula,\nf(m) =\n1\n\u221a\n2\u03c0\u03c3\nZ\nexp\n\u0010\n\u2212(m\u2212m\u2032)2\n2\u03c3 2\n\u0011\nmax{A(m\u2032 \u2212mEP),0} dm\u2032 +max{a+bm,0} ,\n(10)\nwhere mEP represents the endpoint (or threshold), A is the slope of the signal distribution, while a and\nb are the background parameters. The Gaussian smearing gives a smooth transition between the two\nstraight lines and mimics in a simple way the smearing of an edge due to mismeasurement of jet mo-\nmenta. The smearing parameter \u03c3 was \ufb01xed to 15 GeV. The \ufb01tted endpoint values were found not to be\nvery sensitive to the choice of \u03c3 in the range 0\u201320 GeV. For m\u2113\u2113q and the m\u2113q distributions the integration\nrange is (0, mEP). For the mthr\n\u2113\u2113q distribution the lower integration limit is mEP while some 100\u2013200 GeV\nabove the upper \ufb01t range is a safe upper integration limit. The endpoints resulting from the \ufb01ts to the\ndistributions in Figures 4 and 5 are summarised in Table 4.\nFor the \u201cBulk\u201d point (SU3) the edges are found to be suf\ufb01ciently well described by a straight line\nin Eq. (10) for the signal region, however describing the background region by a straight line results in\nlarge systematic uncertainties in the endpoint \ufb01t. In particular, the m\u2113\u2113q distribution does not have a clear\nedge. Even though the m\u2113\u2113q cut in Eq. (9) removes a considerable amount of background for the m\u2113q(low)\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1624\n\n / ndf \n2\n\u03c7\n 5.527 / 8\nEndpoint \n 11.1\n\u00b1\n 445.3 \nSlope \n 0.0823\n\u00b1\n -0.2895 \nm(lq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 1 fb\n-10\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 5.527 / 8\nEndpoint \n 11.1\n\u00b1\n 445.3 \nSlope \n 0.0823\n\u00b1\n -0.2895 \nATLAS\n / ndf \n2\n\u03c7\n 4.783 / 6\nEndp. \n 8.1\n\u00b1\n 319.8 \nSlope \n 0.0808\n\u00b1\n -0.5903 \nm(lq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 0.5 fb\n0\n20\n40\n60\n80\n100\n / ndf \n2\n\u03c7\n 4.783 / 6\nEndp. \n 8.1\n\u00b1\n 319.8 \nSlope \n 0.0808\n\u00b1\n -0.5903 \nATLAS\n / ndf \n2\n\u03c7\n 4.783 / 6\nEndp. \n 8.1\n\u00b1\n 319.8 \nSlope \n 0.0808\n\u00b1\n -0.5903 \n / ndf \n2\n\u03c7\n 7.896 / 9\nEndpoint \n 6.3\n\u00b1\n 332.9 \nSlope \n 0.0260\n\u00b1\n -0.2852 \nm(lq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 1 fb\n-10\n0\n10\n20\n30\n40\n50\n60\n70\n / ndf \n2\n\u03c7\n 7.896 / 9\nEndpoint \n 6.3\n\u00b1\n 332.9 \nSlope \n 0.0260\n\u00b1\n -0.2852 \nATLAS\n / ndf \n2\n\u03c7\n 6.302 / 4\nEndp. \n 8.6\n\u00b1\n 200.7 \nSlope \n 0.338\n\u00b1\n -1.458 \nbck p0 \n 19.47\n\u00b1\n 18.31 \nbck p1 \n 0.07749\n\u00b1\n -0.06395 \nm(lq) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEntries / 20 GeV / 0.5 fb\n-20\n0\n20\n40\n60\n80\n100\n120\n / ndf \n2\n\u03c7\n 6.302 / 4\nEndp. \n 8.6\n\u00b1\n 200.7 \nSlope \n 0.338\n\u00b1\n -1.458 \nbck p0 \n 19.47\n\u00b1\n 18.31 \nbck p1 \n 0.07749\n\u00b1\n -0.06395 \nATLAS\n / ndf \n2\n\u03c7\n 6.302 / 4\nEndp. \n 8.6\n\u00b1\n 200.7 \nSlope \n 0.338\n\u00b1\n -1.458 \nbck p0 \n 19.47\n\u00b1\n 18.31 \nbck p1 \n 0.07749\n\u00b1\n -0.06395 \nFigure 5: Ef\ufb01ciency-corrected \ufb02avour-subtracted distributions of m\u2113q(high) (top) and m\u2113q(low) (bottom) for\nSU3 (left) with 1 fb\u22121 and SU4 (right) with 0.5 fb\u22121 of integrated luminosity. The points with error bars\nshow SUSY plus Standard Model, the solid histogram shows the Standard Model contribution alone.\nThe \ufb01tted function is superimposed, the vertical line indicates the theoretical endpoint value.\ndistribution there is still some background left for the m\u2113q(high) distribution. A systematic uncertainty is\nassigned to account for the background estimation for both \ufb01ts. In case of m\u2113q(low) a background-free \ufb01t\ncan be made resulting in a few GeV uncertainty. The mthr\n\u2113\u2113q distribution is expected to be concave, so a\nsystematic uncertainty is added in the estimation when \ufb01tting the threshold by a straight line \ufb01t.\nFor SU4, the m\u2113\u2113q and both of the m\u2113q distributions have edges which are well described by the \ufb01t\nfunction Eq. (10). This is con\ufb01rmed by the dominance of the statistical errors over the systematics ones.\nThe mthr\n\u2113\u2113q \ufb01t is more problematic resulting in somewhat larger errors. This could be expected since the\ncontributions from different-family and non-signal same-family peaks in this mass region, whereas they\nare close to vanishing in the edge regions of the other distributions. Another reason (although probably\nof less importance at 0.5 fb\u22121 ) is that the threshold edge is concave and only moderately well described\nby a straight line.\nWhile the \ufb01t values of medge\n\u2113\u2113q and mthr\n\u2113\u2113q are compatible with the theoretical values, the \ufb01tted mmax\nlq(high)\nand mmax\nlq(low) are off by 2\u03c3 and 4\u03c3, respectively. This comes from the fact that in SU4 the decay of \u02dc\u03c70\n2 is a\nthree-body decay. In such scenarios the m\u2113q distributions, and in particular m\u2113q(low) are often so sparsely\npopulated towards the high mass values that the endpoints are not experimentally deducible from the\nedges. Note, however, that there is no hint from the \u03c72 of the m\u2113q(low) \ufb01t that we are in such a situation.\nThis topic is discussed further in Sect. 9.1 where endpoint relations are inverted to give sparticle masses.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1625\n\nTable 4: Endpoint positions for SU3 and SU4, in GeV. The \ufb01rst error is statistical, the second and third\nare the systematic and the jet energy scale uncertainty, respectively. The theoretical values are also given\nfor ease of comparison to the left of the \ufb01tted values. The integrated luminosity assumed is 1 fb\u22121 for\nSU3 and 0.5 fb\u22121 for SU4.\nEndpoint\nSU3 truth\nSU3 measured\nSU4 truth\nSU4 measured\nmedge\n\u2113\u2113q\n501\n517\u00b130\u00b110\u00b113\n340\n343\u00b112\u00b13\u00b19\nmthr\n\u2113\u2113q\n249\n265\u00b117\u00b115\u00b17\n168\n161\u00b136\u00b120\u00b14\nmmax\nlq(low)\n325\n333\u00b16\u00b16\u00b18\n240\n201\u00b19\u00b13\u00b15\nmmax\nlq(high)\n418\n445\u00b111\u00b111\u00b111\n340\n320\u00b18\u00b13\u00b18\n5\nTau signatures\n5.1\nDetermination of the di-tau endpoint position\nThe endpoint of the invariant mass distribution from two taus emerging from a \u02dc\u03c70\n2 decay,\n\u02dc\u03c70\n2 \u2192\u02dc\u03c41\u03c4 \u2192\u02dc\u03c70\n1\u03c4\u00b1\u03c4\u2213,\n(11)\ndepends on the masses of the \u02dc\u03c70\n2, the \u02dc\u03c70\n1 and the \u02dc\u03c41, and therefore can contribute to the determination of\nSUSY parameters.\nTaus play an important role in scenarios like mSUGRA where \u02dc\u03c70\n2 is mostly wino, and therefore\npreferentially couples to L-type sfermions. The large L-R mixing in the stau sector signi\ufb01cantly enhances\nthe branching ratio for the decay \u02dc\u03c70\n2 \u2192\u02dc\u03c4\u00b1\n1 \u03c4\u2213with respect to other leptons. In the scenarios SU1 and\nSU3 studied here, for example, the branching ratio for the decays into taus is a factor of 10 larger than\nfor decays into electrons or muons. Since in many models (including mSUGRA) the \u02dc\u03c41 is the lightest\nslepton, for certain values of the SUSY parameters the only allowed two body decay is \u02dc\u03c70\n2 \u2192\u02dc\u03c4\u03c4 as\n\u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1h, \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1Z, and \u02dc\u03c70\n2 \u2192\u02dcee or \u02dc\u00b5\u00b5 are kinematically forbidden.\nFinally, whereas mass information about \u02dc\u03c70\n1 and \u02dc\u03c70\n2 can often be obtained more precisely from \u02dc\u03c70\n2\ndecays into electrons and muons (if these decays are open), decays into taus are needed to probe the \u02dc\u03c4\nmass parameters.\nIn contrast to \u02dc\u03c70\n2 decays into electrons or muons, the di-tau invariant mass spectrum does not have a\nsharp endpoint at the maximum kinematic value. Due to the presence of neutrinos from the tau decays,\nthe m\u03c4\u03c4 distribution (where m\u03c4\u03c4 indicates the invariant mass of the visible decay products of the tau\npair) falls off smoothly below the maximum value given by either Eq. (4) or Eq. (5). Only hadronic tau\ndecays are considered for tau identi\ufb01cation: the tracking-seeded reconstruction algorithm [13] is used\nto reconstruct taus in the \u201cCoannihilation\u201d point (SU1), while the calorimeter-seeded algorithm [13] is\nused for the \u201cBulk\u201d point model (SU3). This choice is motivated by the higher ef\ufb01ciency of the former\nin reconstructing the low pT taus that are present in the SU1 model.\nThe SU1 point also has a considerably lower cross-section than the SU3 point, so different selection\nprocedures are used to maximize the signal signi\ufb01cance. For the SU3 point events are selected with two\ntaus, Emiss\nT\n> 230 GeV, and at least four jets with pT greater than 220, 50, 50, 30 GeV respectively. For\nthe SU1 point the cut on Emiss\nT\nis relaxed to 100 GeV and at least two jets with pT greater than 100 and\n50 GeV respectively. In addition, an elliptical cut in the space of Emiss\nT\nand the sum pT(1)+ pT(2) of the\ntwo highest pT jets is applied to SU1. The semi-axes of the ellipse are 450 GeV for Emiss\nT\nand 500 GeV\nfor the sum of jet pT. This cut exploits the anticorrelation between Emiss\nT\nand (pT(1) + pT(2)) which is\ndifferent for the signal and the Standard Model background.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1626\n\n [GeV]\n\u03c4\n\u03c4\nM\n0\n50\n100\n150\n200\n-1\nEvents / 8 GeV /18 fb\n0\n10\n20\n30\n40\n50\n60\n70\nReconstructed\nTruth\nReconstructed\nTruth\nReconstructed\nTruth\nATLAS\n [GeV]\n\u03c4\n\u03c4\nM\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n-1\nentries / 10GeV/ 1fb\n-5\n0\n5\n10\n15\n20\nATLAS\nFigure 6: Invariant mass distribution of opposite-sign tau pairs with same-sign tau distribution subtracted,\nfor the SU1 (18 fb\u22121, left) and SU3 scenarios (1 fb\u22121, right). The dashed histogram in the left plot shows\nthe distribution at the generator level, while points show the reconstruction-level distribution.\nThe invariant mass distribution emerging after the above cuts are applied is shown in Figure 6 for the\nSU1 and SU3 scenarios, where the corresponding distribution of two taus with the same sign of electric\ncharge is subtracted from tau pairs with opposite sign in order to reduce combinatorial background. This\nis possible because uncorrelated and fake taus should arise about as often with the same charge as with\nopposite charges. To decrease the SUSY background further, the two taus arising from the same decay\nchain are required to have a maximum separation \u2206R < 2 in the \u03b7-\u03c6-plane.\nThe following log normal function with three parameters, inspired by [14], is used to \ufb01t the m\u03c4\u03c4\ndistribution:\nf(x) = p0\nx \u00b7exp\n\u0012\n\u22121\n2p2\n2\n(ln(x)\u2212p1)2\n\u0013\n(12)\nThis function does not contain the endpoint position explicitly, but approaches the x-axis asymptotically.\nThe endpoint is then derived from the in\ufb02ection point mIP of the \ufb01t function:\nmIP = exp\n \n\u22121\n2 p2\n2\n \n3\u2212\ns\n1+ 4\np2\n2\n!\n+ p1\n!\n(13)\nusing a Monte Carlo-based calibration procedure.\nThe in\ufb02ection point obtained for 14 SU3-like models is plotted against the theoretical endpoint value\nfor each of these models. The SU3-like points are generated using the ATLAS fast simulation program\n[15] and varying the masses of the \u02dc\u03c70\n2, the \u02dc\u03c41 and the \u02dc\u03c70\n1 separately, while keeping the other two masses\n\ufb01xed. In Figure 7 the in\ufb02ection point is plotted as a function of the endpoint mEP and \ufb01tted with a straight\nline, yielding the following calibration function:\nmIP = (0.47\u00b10.02)mEP +(15\u00b12) GeV\n(14)\nThe covariance between the slope and the axis intercept is \u22120.034 GeV.\nThe \ufb01t using function Eq. (12) for the SU1 and SU3 models is shown in Fig. 6 giving an in\ufb02ection\npoint at mIP = 48\u00b13 GeV and mIP = 62\u00b18 GeV respectively, which translates into endpoints at mEP =\n(70\u00b16.5stat \u00b15syst) GeV (SU1) and (102\u00b117stat \u00b15.5syst) GeV (SU3) using the calibration relation in\nEq. (14). The systematic uncertainty is dominated by the \ufb01tting procedure and is evaluated by changing\nthe binning and \ufb01t ranges. The effects of 1% and 5% jet energy scale uncertainies have been tested and\nfound to introduce an additional systematic uncertainty on the endpoint measurement well below 3%, so\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1627\n\n / ndf \n2\n\u03c7\n 8.608 / 12\nProb \n 0.736\ny-axis intercept a \n 1.80\n\u00b1\n 14.87 \nslope b \n 0.0197\n\u00b1\n 0.4655 \nEndpoint [GeV]\n0\n20\n40\n60\n80\n100\n120\n140\nInflection point [GeV]\n0\n10\n20\n30\n40\n50\n60\n70\n80\n / ndf \n2\n\u03c7\n 8.608 / 12\nProb \n 0.736\ny-axis intercept a \n 1.80\n\u00b1\n 14.87 \nslope b \n 0.0197\n\u00b1\n 0.4655 \nATLAS\nFigure 7: Calibration curve showing the relation between the position of the in\ufb02ection point (measured\nand \ufb01tted with function Eq. (12) after ATLFAST based detector simulation) and the endpoint (calculated\nwith equation Eq. (5)) of the di-tau mass distribution. The SU3 point is not included.\nthey are negligible compared to the systematic error introduced by the \ufb01tting procedure. The theoretical\nexpectation for the SU1 (SU3) endpoint is 78 GeV (98 GeV). The difference between the theoretical\nand the extracted endpoint comes from the \ufb01tting and \ufb01t-calibration procedure rather than from detector\neffects. As Fig. 6 (left) shows, the generator-level distribution of the visible products is close to the\nreconstruction-level distribution and after \ufb01tting gives an endpoint value of 70 GeV for the SU1 scenario\nwhich is the same as for the reconstructed distribution.\n5.2\nImpact of the tau polarization on the di-tau mass spectrum\nThe method discussed in the previous section assumes a \ufb01xed polarization of the two taus from the \u02dc\u03c70\n2 and\ntherefore neglects the effect of the polarization on the invariant mass spectra. However, the polarization\nof the taus from the decay cascade can vary signi\ufb01cantly between different SUSY models. Polarization\neffects on the di-tau mass distribution are studied by simulating samples of events where the polarization\nof the two taus from the decay Eq. (11) is allowed to vary. The ATLAS fast simulation program [15] is\nused to simulate a data sample equivalent to 51 fb\u22121 of data.\nParity violation in weak interactions in conjunction with momentum and angular momentum conser-\nvation leads to a correlation between the visible tau energy and the polarization of the tau. In case of the\ndecay \u03c4\u2212> \u03bd\u03c4\u03c0\u2212, since the pion is a scalar particle the neutrino spin is forced to be parallel to that of\nthe tau and therefore the \ufb01xed neutrino helicity determines the neutrino momentum direction. Thus, to\nconserve momentum, the direction of the pion momentum is forced to be parallel or antiparallel to that of\nthe tau depending on the tau polarization. This leads to the pion getting a boost parallel or antiparallel to\nthe tau momentum resulting in harder and softer pions. This affects the di-tau mass spectrum, as shown\nin Fig. 8. The curves in the plot are theoretical predictions from [16]. The invariant masses of taus with\nleft chirality (LL) are on average smaller than for right (RR) taus.\nFor decays via the vector mesons \u03c1 and a1, the momentum of the vector meson has the same (oppo-\nsite) direction as in the case of pions for longitudinal (transverse) polarization of the vector meson.\nAdding all hadronic tau decay modes \ufb01nally yields the invariant mass distributions shown in Figure 8\nfor the chirality options LL, RR and LR/RL. The position of the trailing edge is clearly shifted for\ndifferent polarizations whereas the shape difference calculated in [16] is barely visible after detector\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1628\n\nsimulation.\n \n \n \n \n \n \n) [GeV]\n\u03c4\n\u03c4\nM(\n0\n20\n40\n60\n80\n100\n120\n / 4 GeV\n-1\nEvents / 51.7 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n \n \n \n \n \n \n]-spectra\n\u03c0\n \n\u03c0\n [\nLL generator level\nRR generator level\nLR generator level\n \n \n \n \n \n \n \n \n) [GeV]\n\u03c4\n\u03c4\nM(\n0\n20\n40\n60\n80\n100\n120\n / 4 GeV\n-1\nEvents / 51.7 fb\n0\n50\n100\n150\n200\n250\n \n \n \n \n \n \n \n \n all decays\nLL detector level\nLR detector level\nRR detector level\nFigure 8: Left: Di-tau invariant mass spectrum for \u03c4 \u2192\u03c0\u03bd\u03c4 decays as obtained from Monte Carlo truth\ninformation together with the expectation from theory. Right: Di-tau invariant mass spectrum for all\nhadronic decays after an ATLFAST based detector simulation. Both plots show the mass distributions\nfor the chirality states LL, RR and LR/RL.\nAs a consequence, the in\ufb02ection point of the distribution is shifted due to polarization effects. The\nmaximum difference in the in\ufb02ection point measurement \u2206mIPA(RR \u2212LL) has been found to be 7 GeV\nwhich is comparable to the statistical error on the position of the in\ufb02ection point presented in the previous\nsection. Without additional information on the tau polarization we might quickly reach a point where it\nis not possible to improve the di-tau endpoint measurement. In this case the achievable precision for an\nintegrated luminosity of 1 fb\u22121 for the SU3 model is:\nmmax\n\u03c4\u03c4\n= 102\u00b117stat \u00b15.5syst \u00b17pol\nThe uncertainty due to the polarization effects dominates over the other systematic uncertainties and\ntherefore needs special attention. A study of the different polarization dependencies of the decay kine-\nmatics for different decay modes of the tau might be helpful. As the emission direction of vector mesons\nis opposite for longitudinal and transversal states the net effect is determined by the branching ratio into\nthe two states. It turns out that for the a1 there are as many longitudinal as transverse polarized whereas\nfor the \u03c1 there are more longitudinal vector mesons, leading to different polarization dependencies.\n6\n\u02dcqR pair reconstruction\nEvents where a pair of \u02dcqR particles is produced, and where each decays through the process\n\u02dcqR \u2192\u02dc\u03c70\n1q\n(15)\nlead to a characteristic signature with two high-pT jets and large Emiss\nT\nfrom the escaping neutralinos. \u02dcqR\npair production represents about 10% (5%) of the total SUSY production cross-section for the \u201cBulk\u201d\npoint SU3 (\u201cLow Mass\u201d SU4). For both points (and more generally in most of mSUGRA parameter\nspace) the \u02dcqR decays almost entirely through the process in Eq. (15).\nEvents with large Emiss\nT\nand a pair of high-pT jets are selected by requiring:\n\u2022 Emiss\nT\n> max(200 GeV, 0.25Meff) and Meff > 500 GeV\n\u2022 Two jets with pT > max(200 GeV,0.25Meff), |\u03b7| < 1 and \u2206R > 1\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1629\n\nTable 5: The total event yield and the number of Standard Model background events satisfying selection\ncriteria for mT2 reconstruction, signal-to-background ratio and signal statistical signi\ufb01cance. Only errors\nfrom the detector systematic uncertainties are quoted.\nIntegrated luminosity (fb\u22121)\nEvent yield\nStandard Model\nS/BSM\nS/\u221aBSM\nSU3\n1.0\n282 \u00b1 20\n18\n14.7 \u00b11.1\n62.2 \u00b14.7\nSU4\n0.5\n258 \u00b1 65\n9\n27.7 \u00b17.2\n83.0 \u00b121.7\n\u2022 No additional jet with pT > min(200 GeV, 0.15Meff)\n\u2022 No isolated leptons and no jets tagged as b jets\n\u2022 Transverse sphericity ST > 0.2\nThese selection cuts are tuned using the information from the event generation to select \u02dcqR pair produc-\ntion.\nThe systematic uncertainty originating from the jet and Emiss\nT\nenergy scale and resolution [2] change\nthe event yield by 7% for the case of SU3 and by 25% for the case of SU4. The systematic effect on the\nenergy scale and resolution of leptons is negligible.\nThe total event yield and the number of Standard Model background events satisfying the selection\ncriteria for 1 fb\u22121 for SU3 and 0.50 fb\u22121 for SU4 are given in Table 5 together with the signal-to-\nbackground ratio and the signal statistical signi\ufb01cance.\nTo reconstruct the \u02dcqR mass we use the the mT2 variable [2, 17, 18], sometimes referred to as \u201cstran-\nverse\u201d mass. This variable uses the kinematic features of the \u02dcqR decays to reconstruct m \u02dcqR\n3 making the\nassumption that m \u02dc\u03c70\n1 is known from the measurements in Section 4. The mT2 distributions for the SU3\nand SU4 points are shown in Figure 9. As is common for SUSY measurements, the distribution is ex-\npected to have an edge at m \u02dcqR rather than a peak. A linear \ufb01t is applied to the right part of the distribution\nto determine the edge position at 590\u00b19(stat)+13\n\u22126 (sys) GeV for SU3 and 421\u00b117(stat)+10\n\u22123 (sys) GeV for\nSU4. This can be compared to the expected positions of m \u02dcqR = 611 GeV for SU3 and m \u02dcqR = 406 GeV\nfor SU4. The systematic error accounts for the choice of the \ufb01t limits as well as the jet energy scale\nsystematic.\n7\nLight stop signature\nIn the \u201cLow Mass\u201d benchmark point (SU4), the SUSY masses are all in the range m \u02dc\u03c70\n1 = 60 GeV < m <\nm\u02dct2 = 445 GeV. The stop \u02dct1 is light (m\u02dct1 = 206 GeV) and always decays by \u02dct1 \u2192\u02dc\u03c7\u00b1\n1 b. A detailed analysis\nof the phenomenology of this point can be found in [19].\nAt this SU4 benchmark point the light stop is produced in the gluino decay Eq. (3) which has a\nbranching ratio of 42%. Associated gluino production with a \u02dcqL or \u02dcqR followed by the decay in Eq. (3)\noccurs in \u223c18% of all SU4 events. In the decay Eq. (3) the \ufb01nal state tb invariant mass distribution has\n3For the benchmark point considered here, the effect of the SUSY background (i.e. events other than the \u02dcqR pair production\nwhich pass the event selection) on the position of the edge is small. This has also been shown to be true for other benchmark\npoints [10]. However, the identi\ufb01cation of the edge as a measurement of the \u02dcqR mass may not hold for all the SUSY parameter\nspace.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1630\n\nSM\nSU3 + B\nIntegral \n 281.7\n / ndf \n2\n\u03c7\n 7.304 / 3\nA \n 18.2\n\u00b1\n 138.8 \n \nmax\nM\n 9.3\n\u00b1\n 589.7 \n [GeV]\nT2\nm\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-1\nEvents / 40 GeV / 1 fb\n0\n10\n20\n30\n40\n50\nSM\nSU3 + B\nIntegral \n 281.7\n / ndf \n2\n\u03c7\n 7.304 / 3\nA \n 18.2\n\u00b1\n 138.8 \n \nmax\nM\n 9.3\n\u00b1\n 589.7 \nSM\nSU3 + B\nfit\nSM\nB\nATLAS\nSM\nSU4 + B\nIntegral \n 257.9\n / ndf \n2\n\u03c7\n 0.8511 / 1\nA \n 62.7\n\u00b1\n 203.7 \n \nmax\nM\n 16.7\n\u00b1\n 421.4 \n [GeV]\nT2\nm\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-1\nEvents / 20 GeV / 0.5 fb\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nSM\nSU4 + B\nIntegral \n 257.9\n / ndf \n2\n\u03c7\n 0.8511 / 1\nA \n 62.7\n\u00b1\n 203.7 \n \nmax\nM\n 16.7\n\u00b1\n 421.4 \nSM\nSU4 + B\nfit\nSM\nB\nATLAS\nFigure 9: Fit of the sum of the reconstructed mT2 distributions in the selected SUSY and the remaining\nStandard Model background events with 1 fb\u22121 for SU3 and 0.5 fb\u22121 for SU4.\nthe upper kinematic endpoint:\nMmax(tb) =\n\"\nm2\nt +\nm2\n\u02dct1 \u2212m2\n\u02dc\u03c7\u00b1\n1\n2m2\n\u02dct1\n\u0010\n(m2\n\u02dcg \u2212m2\n\u02dct1 \u2212m2\nt )+\nq\n(m2\n\u02dcg \u2212(m\u02dct1 \u2212mt)2)(m2\n\u02dcg \u2212(m\u02dct1 +mt)2)\n\u0011#1/2\n.\n(16)\nWith m \u02dcg = 413 GeV, m \u02dc\u03c7\u00b1\n1 = 113 GeVand a top mass of 175 GeV, Eq. (16) gives\nMmax(tb) \u223c300 GeV.\n(17)\nThe other signi\ufb01cant decays at this benchmark point which lead to the same \ufb01nal state are:\n\u02dcg\n\u2192\n\u02dcb1b \u2192\u02dc\u03c7\u00b1\n1 tb,\n(18)\n\u02dcg\n\u2192\n\u02dcb1b \u2192\u02dct1Wb \u2192\u02dc\u03c7\u00b1\n1 bbW,\n(19)\n\u02dcg\n\u2192\n\u02dcb2b \u2192\u02dc\u03c7\u00b1\n1 tb,\n(20)\n\u02dcg\n\u2192\n\u02dcb2b \u2192\u02dct1Wb \u2192\u02dc\u03c7\u00b1\n1 bbW.\n(21)\nThe \ufb01nal states from the decays Eq. (19) and Eq. (21) are equivalent to the \ufb01nal state from the decay\nEq. (3) if the bW invariant mass is close to the top mass. Associated gluino production with left or\nright squark followed by these decays occurs in 4% (Eq. (18)), 9% (Eq. (19)), 0.1% (Eq. (20)) and 0.9%\n(Eq. (21)) of all SU4 events. Due to the small mass difference between \u02dcg and the \u02dcb1 or \u02dcb2, the \ufb01nal states\nEq. (18) and Eq. (19) can be suppressed by imposing a minimum cut on the pT of the b jet, while the \ufb01nal\nstates Eq. (20) and Eq. (21) are suppressed because b jets originating from the gluino decay \u02dcg \u2192\u02dcb2b are\non the average below the detection threshold.\nIn order to extract light stop signal from the \u02dcg \u02dcq events where gluino decays to stop and top, the \ufb01nal\nstate tb invariant mass distribution in Eq. (3) is reconstructed for top quark decays into hadronic \ufb01nal\nstates only:\nt \u2192Wb \u2192qqb\n(22)\nmaking no assumptions about the \u02dc\u03c7\u00b1\n1 decay modes which dominantly produce two additional light-quark\njets. The hardest jet in the event is assumed to be the light-quark jet originating from the decay of the\nleft or right squark produced in association with the gluino.\nWe select jets with pT > 20 GeVand |\u03b7| < 2.5. In this range the b-tagging ef\ufb01ciency is about 60% [1].\nThe event selection requires the following:\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1631\n\n\u2022 At least 5 jets in the event with pT > 30 GeV, where\n\u2013 The hardest jet is a light-quark jet with pT > 100 GeV,\n\u2013 2 and only 2 jets are tagged as b jets and they have pT > 50 GeV and\n\u2013 At least 2 of the light-quark jets have pT > 30 GeV\n\u2022 Emiss\nT\n> 150 GeV, Meff > 400 GeV, Emiss\nT\n/Meff > 0.2\n\u2022 ST > 0.1 .\nOf the Standard Model backgrounds simulated, only events from our t\u00aft and QCD samples satisfy\nthese selection criteria. No W +jets or Z +jets events pass the cuts.\nThe dominant detector-performance systematic uncertainties come from the jet and Emiss\nT\nenergy\nscale and resolution. Assuming that the uncertainties for 200 pb\u22121 are the same as for 100 pb\u22121, i.e.\n10% uncertainties on the jet and Emiss\nT\nenergy scale and resolution [20], and including 5% uncertainty\non the b-tagging ef\ufb01ciency, the resulting systematic uncertainty in the number of selected events would\nbe \u223c40% for SU4 and \u223c50% for t\u00aft .\nThe top-bottom invariant mass is reconstructed for events satisfying the selection criteria for the light\nstop search:\n\u2022 Excluding the hardest jet, all light-quark jets with pjet\nT > 30 GeV are combined into dijet pairs.\n\u2022 All such pairs with invariant mass within the window |m j j \u2212mW| < 15 GeV are combined with\neach of the two b jets and the bj j combination with invariant mass closest to the top mass is\nselected.\n\u2022 The four-vectors of this dijet pair are rescaled such that m j j = mW and mb j j is recalculated and\naccepted as top candidate if |mb j j \u2212mtop| < 30 GeV.\n\u2022 The same bj j combination is combined with the other b jet and mtb calculated, with the require-\nment that the angle between top and bottom be \u2206R(t,b) < 2.\nThe W sideband method [21\u201323] is used to estimate SUSY combinatorial background originating\nfrom supersymmetric processes in which jet pairs accidentally have an invariant mass within our W-\nmass window, and so fake W bosons. The sidebands used are the regions of dijet invariant mass 30 GeV\nbelow and 30 GeV above our W-mass window. The fake W boson contribution to the mtb distribution is\nevaluated as the average contribution of the jet pairs from the W sidebands after they have been scaled\nlinearly to the W mass zone and the procedure of mtb reconstruction has been repeated.\nThe numbers of signal and the remaining Standard Model background events, together with the total\nevent yield at 200 pb\u22121, are listed in Table 6. The mtb distribution reconstructed in signal events without\nthe subtraction of the SUSY combinatorial background and the SUSY combinatorial background itself\nare plotted in Figure 10. The contribution of fake W bosons in SU4 is higher than the number of events\nremaining after subtraction.\nThe mtb distributions before and after the subtraction of the SUSY combinatorial background are\nshown in Figure 10. The background-subtracted distirbution is \ufb01tted in order to extract the endpoint.\nThe resulting mtb distribution is \ufb01tted with a triangular function smeared with a Gaussian:\nf(M) = A\nZ 1\n\u22121 e\u2212\n(M\u2212Mmax\u221a\n1+x\n2\n)2\n2\u03c32\ndx+(a+bM),\nwhere the kinematic endpoint, Mmax, and the smearing, \u03c3, are two of the \ufb01ve \ufb01t parameters. The smear-\ning, \u03c3, models the experimental resolution of the reconstructed mtb. The position of the upper kinematic\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1632\n\nTable 6: The number of signal and remaining Standard Model background events and the total event\nyield at 200 pb\u22121. The last row gives the signal-to-background ratio. The errors quoted are from detector\nsources of systematic uncertainty.\nL = 200 pb\u22121\nInitial selection\n|mb j j \u2212mt| < 30 GeV\n\u2206R(t,b) < 2\nwithout\nwith\nwithout\nwith\nW sub.\nW sub.\nW sub.\nW sub.\nSU4\n963\n537\n224\n267\n120\nt\u00aft\n99\n28\n13\n9\n4\nQCD\n6\n3\n2\n3\n2\nTotal\n1068 \u00b1 426\n568 \u00b1 225\n239 \u00b1 95\n279 \u00b1 109\n126 \u00b1 50\nSU4 / (t\u00aft +QCD)\n9.2 \u00b1 4.1\n17.3 \u00b1 7.3\n14.9 \u00b1 6.3\n22.3 \u00b1 9.1\n20.0 \u00b1 8.3\nendpoint obtained from the 5-parameter \ufb01t (Figure 10) is Mmax = 297 \u00b1 9 GeV with \u03c3 = 28 \u00b1 7 GeV\ncorresponding to \u223c10% of the Mmax value. The position of the upper kinematic endpoint obtained from\nthe 4 parameters \ufb01t is Mmax = 298 \u00b1 6(stat)+16\n\u221241(sys) GeV with \u03c3 set to 10% of Mmax. The expected\nvalue of mtb given by Eq. (17) is 300 GeV.\nM(tb) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-1\nEvents / 20 GeV / 200 pb\n0\n10\n20\n30\n40\n50\nSU4\nIntegral \n 266.6\nSUSY\nB\nIntegral \n 146.6\nSU4\n from W sidebands\nSUSY\nB\nATLAS\nSM\n + B\nSUSY\nSU4 - B\nIntegral \n 125.6\n / ndf \n2\n\u03c7\n 17.21 / 15\nA \n 6.31\n\u00b1\n 26.43 \n \nmax\nM\n 8.6\n\u00b1\n 297.1 \n \n\u03c3\n 7.30\n\u00b1\n 27.89 \na \n 1.225\n\u00b1\n 1.407 \nb \n 0.002290\n\u00b1\n -0.002533 \nM(tb) [GeV]\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900 1000\n-1\nEvents / 20 GeV / 200 pb\n0\n5\n10\n15\n20\n25\nSM\n + B\nSUSY\nSU4 - B\nIntegral \n 125.6\n / ndf \n2\n\u03c7\n 17.21 / 15\nA \n 6.31\n\u00b1\n 26.43 \n \nmax\nM\n 8.6\n\u00b1\n 297.1 \n \n\u03c3\n 7.30\n\u00b1\n 27.89 \na \n 1.225\n\u00b1\n 1.407 \nb \n 0.002290\n\u00b1\n -0.002533 \nATLAS\nSM\n + B\nSUSY\nSU4 - B\nfit 5 par.\nSM\nB\nFigure 10: Left: Reconstructed mtb distributions in signal and SUSY combinatorial background events.\nRight: The 5 parameters \ufb01t of the sum of the reconstructed mtb distributions in signal and the remaining\nStandard Model events after the subtraction of the SUSY combinatorial background; all at 200 pb\u22121.\n8\nHiggs signatures in SUSY events\nIn the context of supersymmetric models, Higgs bosons at the LHC can be produced in proton collisions\neither through direct interaction of Standard Model particles, such as gluon-gluon fusion, or through the\ndecay of a supersymmetric particle produced in the initial interaction.\nWe will consider the possibility of observing the lightest CP-even h boson via the second mechanism.\nIn this case, a missing transverse energy signature, typical of R-parity conserving SUSY scenarios, can\nbe reconstructed in association with the Higgs boson and exploited to reduce the background, making it\npossible to study the dominant decay channel h \u2192b\u00afb, which is otherwise hidden by the enormous QCD\ncontinuum.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1633\n\nWithin mSUGRA the most promising source of Higgs production is the decay of a second-lightest\nneutralino. Indeed, \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1h, if open, dominates the \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1Z mode, because the two lightest neu-\ntralinos are basically gauginos, so that the higgsino-gaugino-Higgs vertex is enhanced with respect to\nthe higgsino-higgsino-gauge one. However, if the sleptons are lighter than the \u02dc\u03c70\n2, the decay channels\n\u02dc\u2113\u00b1\u2113\u2213and \u02dc\u03bd\u2113\u00af\u03bd\u2113open up, dominating the \u02dc\u03c70\n2 width. As a consequence, we expect that mSUGRA points\ninteresting for Higgs searches will not show a clear di-lepton signature. The benchmark point chosen for\nthis analysis is SU9, at which BR( \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1h) \u223c87%.\nExploiting the capabilities of the ATLAS detector in missing transverse energy measurement and b\ntagging, the passage of weakly interacting particles may be revealed and a b\u00afb pair with invariant mass\npeaking around the Higgs mass can be reconstructed.\nStandard Model events with similar signatures which are backgrounds for this analysis, include\nevents with neutrino production causing a genuine Emiss\nT\nsignal and QCD events with fake Emiss\nT\ngen-\nerated by instrumental effects. SUSY events can themselves constitute a background, as they contain\nmany b-jet candidates, both true and mistagged. These can be divided into two categories: SUSY cas-\ncades without and with production of a Higgs decaying to b\u00afb. In the latter case potential signal events\nmay be incorrectly reconstructed as the selected b\u00afb pair is not the one coming from the Higgs decay.\nWe will refer to the former type simply as \u201cSUSY background\u201d and to the latter as \u201ccombinatorial back-\nground\u201d.\nThe following selection cuts are applied:\n1. Emiss\nT\n> 300 GeV;\n2. two light-\ufb02avoured jets with pT > 100 GeV;\n3. two b jets with pT > 50 GeV;\n4. no leptons with pT > 10 GeV.\nThe \ufb01rst two cuts are typical of SUSY analyses, while the pupose of the last cut is to suppress back-\ngrounds from t\u00aft and W production.\nWhen three or more b jets with transverse momentum greater than 50 GeV are found in a single event,\nthe second and third leading-pT b-jets are chosen as the candidate Higgs decay pair. This is because an\nimportant source of b jets is the decay of a bottom squark to \u02dc\u03c70\n2 and b and since m\u02dcb\u2212m \u02dc\u03c70\n2 \u223c500 GeV > mh\nthe sbottom daughters get more allowed phase space than the Higgs daughters and thus, in general, higher\npT.\nIn Figure 11 (left) the invariant mass of the selected b jet pairs is shown assuming 10 fb\u22121 of collected\nluminosity. The shaded histogram corresponds to the sum of the Standard Model backgrounds, the\ndashed and dotted lines are the SUSY and combinatorial backgrounds respectively. These last two,\ntogether with the t\u00aft production, are the most important backgrounds. The black curve is the result of\na least squares \ufb01t to a Gaussian function, representing the Higgs resonance, superimposed on a second\ndegree polynomial background. The estimated number of signal and background events is obtained by\ncounting the b pairs with invariant mass inside a \u00b125 GeV range around the \ufb01tted peak centre. The\nsignal signi\ufb01cance, computed in the Gaussian approximation as the number of signal events over the\nsquare root of the background, is about 14.\nTable 7 summarises the expected event rates after the application of the selection cuts and after the\nadditional mass window request.\nSUSY mass spectrum information is reconstructed in the SU9 model by studying the decay:\n\u02dcqL \u2192\u02dc\u03c70\n2q \u2192\u02dc\u03c70\n1hq.\n(23)\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1634\n\n (GeV)\nbb\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n)\n-1\nEvents (1/8 GeV/10 fb\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nATLAS\nSignal\nComb BG\nSusy BG\nStandard Model BG\nGauss+Pol2\n (GeV)\nMIN\nbbj\nM\n0\n200\n400\n600\n800\n1000\n1200\n)\n-1\nEvents (1/8 GeV/10 fb\n0\n2\n4\n6\n8\n10\n12\n14\n16\nATLAS\nSignal\nComb BG\nSusy BG\nStandard Model BG\n Gauss\n\u2297\nTriang \nFigure 11: Invariant mass of the selected b-jet pairs (left) and invariant mass of the system consisting of\nthe Higgs plus the jet minimising mhq (right) for 10 fb\u22121 of integrated luminosity.\nTable 7: Summary of the number of expected SUSY and Standard Model events after the application of\nthe different selection cuts, for 10 fb\u22121 of integrated luminosity.\nSU9\nSignal\nComb BG\nSusy BG\nNo cuts\n11050\n21950\nCut 1, 2, 3\n356\n946\n908\nCut 4\n230\n449\n433\n\u00b125 GeV mass window\n179\n76\n76\nStandard Model\nt\u00aft\nZ\nW\nb\u00afb\nCut 1, 2, 3\n133\n12\n22\n43\nCut 4\n53\n8\n10\n21\n\u00b125 GeV mass window\n11\n2\n4\n4\nAs a consequence of two-body kinematics, the invariant mass of the Higgs-quark system shows both a\nminimum and a maximum value, related to different combinations of the masses of the SUSY particles\ninvolved.\nThe events passing the previous selection cuts, including the mass window cut, are also required to\nhave at least one b jet with pT > 100 GeV. Furthermore, a veto is imposed on additional b-tagged jets\nwith pT > 50 GeV. This will result in fewer signal events, but also in a reduced background contamina-\ntion yielding a clear distribution shape, albeit with lower signal signi\ufb01cance. As in Section 4 the quark\nfrom the \u02dcqL is expected to produce one of the two highest-pT jets and the two distributions mmin\nhq and\nmmax\nhq\nare reconstructed using the jet that maximises and minimises the mhq value, respectively. Since\nthe background events will tend to concentrate toward low mass values, the mmin\nhq (Figure 11, right) is\nused to determine the mass upper limit mhq,edge. The mhq,threshold value can determined from the mmin\nhq\ndistribution.\nThe mass edge value is obtained by \ufb01tting a triangular shape convolved with a Gaussian:\nmhq,edge = 695\u00b115 (stat)\u00b13 (syst)\u00b135 (JES),\nto be compared to the true value of 732 GeV. The statistical uncertainty is the error on the \ufb01tted parameter,\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1635\n\nwhile the systematic comes from the parameter dependence on the \ufb01tting boundaries. An additional 5%\nsystematic error is expected from the jet energy scale (JES) uncertainty.\nThe mass threshold evaluation is more challenging, since background events tend to populate the low\nmass region. For an integrated luminosity of 10 fb\u22121, it was not possible to \ufb01t to the mass distribution.\nHowever, high-statistics studies performed with a fast simulation of the ATLAS detector show that a\nmass threshold value could be extracted from 300 fb\u22121 of collected data, expected after 3 years of LHC\nrunning at design luminosity.\n9\nMass and parameters measurement\nThis section is devoted to the extraction of SUSY mass spectra and parameters from the measurements\ndescribed in the previous sections of this note. As an example, the mSUGRA benchmark points SU3\n(with a luminosity of 1 fb\u22121) and SU4 (with 0.5 fb\u22121) are chosen to give a \ufb02avour of what might be\nexpected in the initial phase of the experiment in case of a rather optimistic SUSY scenario. The small\nluminosity at this stage results in a limited number of available measurements and rather large uncertain-\nties. In such a situation only models with few parameters can be \ufb01tted. In Section 9.1 the masses of the\ndecay chain Eq. (1) are derived from the measurement of the kinematic endpoints described in Section 3\nand 4. In Sections 9.2 to 9.4 the parameters of the mSUGRA model are derived instead.\n9.1\nMeasurement of masses from SUSY decays\nWe use the information from the experimentally measured endpoints to extract the masses of the SUSY\nparticles. As described earlier in this paper, in many cases analytic expressions have been deduced for\nthe endpoints expressed in terms of the masses. Examples are shown in Eq. (4) and Eq. (5). If suf\ufb01cient\nendpoints are known, then the masses can be deduced. Here we use a numerical \u03c7 2 minimization based\non the MINUIT package to extract the SUSY particle masses from a combination of endpoints. We\nde\ufb01ne the \u03c72 as\n\u03c72 =\nn\n\u2211\nk=1\n(mmax\nk\n\u2212tmax\nk\n(m \u02dc\u03c70\n1,m \u02dc\u03c70\n2 ,m \u02dc\u2113R,m \u02dcqL))2\n\u03c3 2\nk\n.\n(24)\nFor each of the n endpoint measurements, k, the quantities mmax\nk\nand \u03c3k denote the \ufb01t value and its\nuncertainty respectively. The tmax\nk\nare the theoretical endpoint expressions [6, 10], which contain as\nparameters the masses of the two lightest neutralinos, the scalar quark \u02dcqL , and (for the two-body decay\nchain only) the scalar lepton \u02dc\u2113R . As a starting point for the \ufb01t the generated masses are used. The masses\nare constrained to be positive in the \ufb01t and the mass hierarchies from the model input are enforced.\nWith the statistics expected for an integrated luminosity of 1 fb\u22121 (0.5 fb\u22121) for SU3 (SU4) we\nobserve instabilities in the \ufb01t. Depending on the \ufb02uctuation and precision of the endpoint measurements\nthe \ufb01t does not converge. Some of the measured endpoints have shown possible deviations from the\ngenerated values of up to several standard deviations. Systematic effects to explain such discrepancies\nare identi\ufb01ed in earlier sections of this article. Signi\ufb01cant deviations distort the results and also negatively\naffect the \ufb01t convergence, especially in the presence of degenerate kinematic endpoint equations. We also\nnote large correlations (typically larger than 95%) among the \ufb01tted parameters. This is expected, since\nthe endpoints are most sensitive to mass differences. The correlations can also lead to dif\ufb01culties with\nconvergence and result in larger uncertainties for the \ufb01tted masses.\nTo show a potential result with early data, we quote here the results from converging \ufb01ts for both\nthe SU3 and SU4 points. We use the endpoints from the lepton+jets edges summarized in Table 4 and\nthe dilepton edge \ufb01t from Section 3 (99.7\u00b11.4\u00b10.3 GeV for SU3 and 52.7\u00b12.4\u00b10.3 GeV for SU4).\nFor the SU3 \ufb01t, all dilepton+jets edges are used. In the SU4-\ufb01t, we discard the m\u2113q(low) measurement\nas it has been shown not to be very reliable and does not provide additional constraints in three-body\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1636\n\nTable 8: Resulting SUSY particle masses and mass differences within SU3 and SU4 from the \u03c7 2 mini-\nmization \ufb01t using the dilepton and lepton+jets edges. Shown are the measured masses mmeas and mass\ndifferences \u2206mmeas followed \ufb01rst by the parabolic errors as returned by MIGRAD and then by the jet\nenergy scale errors. When the measured parameter is anticorrelated with the jet energy scale variation,\nthis is indicated by a \u2213sign. The input Monte Carlo masses mMC and mass differences \u2206mMC are also\nshown. The integrated luminosity assumed is 1 fb\u22121 for SU3 and 0.5 fb\u22121 for SU4.\nObservable\nSU3 mmeas\nSU3 mMC\nSU4 mmeas\nSU4 mMC\n[GeV]\n[GeV]\n[GeV]\n[GeV]\nm \u02dc\u03c70\n1\n88\u00b160\u22132\n118\n62\u00b1126\u22130.4\n60\nm \u02dc\u03c70\n2\n189\u00b160\u22132\n219\n115\u00b1126\u22130.4\n114\nm \u02dcq\n614\u00b191\u00b111\n634\n406\u00b1180\u00b19\n416\nm \u02dc\u2113\n122\u00b161\u22132\n155\nObservable\nSU3 \u2206mmeas\nSU3 \u2206mMC\nSU4 \u2206mmeas\nSU4 \u2206mMC\n[GeV]\n[GeV]\n[GeV]\n[GeV]\nm \u02dc\u03c70\n2 \u2212m \u02dc\u03c70\n1\n100.6\u00b11.9\u22130.0\n100.7\n52.7\u00b12.4\u22130.0\n53.6\nm \u02dcq \u2212m \u02dc\u03c70\n1\n526\u00b134\u00b113\n516.0\n344\u00b153\u00b19\n356\nm \u02dc\u2113\u2212m \u02dc\u03c70\n1\n34.2\u00b13.8\u22130.1\n37.6\ndecay scenarios such as SU4. The m\u2113q(high) endpoint can be measured more reliably and its kinematic\nexpression only differs from the one of m\u2113q(low) by a constant factor. The di-tau edges are not used here.\nThe masses resulting from the \u03c72 \ufb01t are shown in Table 8 (upper part). The parabolic errors are the\n\ufb01rst errors shown in the table and the jet energy scale errors are the second. Asymmetric errors show\na large uncertainty on the positive side. The jet energy scale errors are determined by varying all the\nendpoints along with their fully correlated jet energy scale uncertainties and re\ufb01tting the masses. The\ndifference in the central values of the \ufb01t is taken as the jet energy scale uncertainty for Table 8. One can\nsee that the jet energy scale errors are small compared to the error on the masses, but might be relevant\nto the mass difference measurements.\nWe note that a \ufb01t with SU3 kinematic assumptions applied to the SU4 endpoints also returns consis-\ntent masses. The decision about the mass hierarchy would thus have to be based on additional information\nfrom collider data. A possible source is the shape of the dilepton edge as discussed in Section 3.\nBesides the masses we can also extract differences of SUSY particle masses. These are more directly\nrelated to the endpoints and we expect to be able to determine them more reliably than the masses of\nindividual sparticles. For mass differences, a \u03c72 similar to Eq. Eq. (24) is used, where the parameters are\nwritten in terms of mass differences to the neutralino \u02dc\u03c70\n1. We obtain the results shown in Table 8 (bottom\npart).\nWe conclude that a \ufb01rst look at sparticle masses is possible with early data, although with large\nuncertainties. Appropriate model assumptions and additional information will probably have to be used\nto constrain the \ufb01ts.\n9.2\nObservables and \ufb01t assumptions\nTo demonstrate the feasibility of parameter determination with initial data, we show the constraints one\nwould obtain for our benchmark points if one assumed an mSUGRA framework.\nThe SUSY parameter-\ufb01tting package Fittino version 1.4.1 [24] is used, interfaced to a beta version\nof SPheno3 [25] to perform the theoretical calculations for a given set of parameters.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1637\n\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n [GeV]\n1/2\nM\n280\n290\n300\n310\n320\n330\n340\n [GeV]\n0\nM\n80\n100\n120\n140\n160\n180\nSU3 values\nATLAS\n0\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\n0.007\n [GeV]\n0\nA\n-1500-1000-500\n0\n500 1000 1500 2000 2500 3000\n)\n\u03b2\ntan(\n0\n5\n10\n15\n20\n25\n30\n35\nSU3 values\nATLAS\nFigure 12: Two-dimensional Markov chain likelihood maps for mSUGRA parameters M0 and M1/2 (left)\nas well as tan\u03b2 and A0 (right) for sign \u00b5 = +1, for benchmark point SU3, with integrated luminosity of\n1 fb\u22121. The crosses indicate the actual values of the parameters for that benchmark point.\nThe \ufb01t is given the measurements presented in sections 3, 4 and 6. The lepton and the jet energy\nscale uncertainties are each considered to be 100% correlated between measurements. Uncertainties on\nthe theoretical predictions are not taken into account. For illustration purposes an additional parame-\nter determination is performed where \u2013 following a prescription used in [26] \u2013 1% (0.5%) uncertainty\non the theoretical calculation of the pole masses of coloured (un-coloured) sparticles is assumed. No\ncorrelations between the theoretical uncertainties on the pole masses are considered.\n9.3\nMarkov chain analysis\nTo obtain a \ufb01rst glimpse of the possible parameter space a Markov chain analysis is performed. With this\ntechnique it is possible to ef\ufb01ciently sample from a large-dimensional parameter spaces. This allows us\nto check whether there are several topologically disconnected parameter regions which are favoured by\nthe given measurements.\nFigure 12 shows two-dimensional likelihood maps for M0 and M1/2 (left) as well as tan\u03b2 and A0\n(right) for sign \u00b5 = +1 obtained for the given set of measurements. The plots demonstrate that for a\ngiven sign \u00b5 preferred parameters are found around the true parameter points independent of the starting\npoint. No further preferred regions occur. For M0 and M1/2 a clearly preferred region is found around\nthe SU3 values of 100 GeV and 300 GeV, respectively. As expected, given the measurements used, the\ndetermination of tan\u03b2 and A0 is more dif\ufb01cult. Nevertheless, here too the region around the nominal\nSU3 values is the preferred one.\n9.4\nParameter determination\nIn order to determine the derived central values of the parameters and their uncertainties, for each as-\nsumption of the sign of \u00b5 a set of 500 toy \ufb01ts are performed. For each \ufb01t the observables are smeared\nusing the full correlation matrix. Simulated annealing followed by a Minuit \ufb01t started with the best\nparameter estimates from simulated annealing is subsequently run using the smeared observables. The\nfour-dimensional distribution of parameters obtained from the toy \ufb01ts is used to derive the parameter\nuncertainties and their correlations. Figure 13 shows the one-dimensional projections of parameter dis-\ntributions for M0, M1/2, tan\u03b2 and A0. The mean and RMS values of the results of the \ufb01t are reported in\nTable 9. As already indicated by the Markov chain analysis M0 and M1/2 can be derived reliably with\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1638\n\nuncertainties \u00b1 9.3 GeV and \u00b1 6.9 GeV (RMS of the toy \ufb01t results), respectively whereas for tan\u03b2 and\nA0 only the order of magnitude can be derived from these measurements. The \u03c7 2 distribution of the toy\n / ndf \n2\n\u03c7\n 24.13 / 20\nProb \n 0.2366\nConstant \n 6.1\n\u00b1\n 102 \nMean \n 0.19\n\u00b1\n 97.02 \nSigma \n 0.157\n\u00b1\n 4.165 \n [GeV]\n0\nM\n60\n80\n100\n120\n140\n160\nNumber of toy fits/2.3 GeV\n0\n20\n40\n60\n80\n100\n120\n / ndf \n2\n\u03c7\n 24.13 / 20\nProb \n 0.2366\nConstant \n 6.1\n\u00b1\n 102 \nMean \n 0.19\n\u00b1\n 97.02 \nSigma \n 0.157\n\u00b1\n 4.165 \nATLAS\n / ndf \n2\n\u03c7\n 42.9 / 35\nProb \n 0.1687\nConstant \n 2.33\n\u00b1\n 36.01 \nMean \n 0.3\n\u00b1\n 318.4 \nSigma \n 0.261\n\u00b1\n 5.821 \n [GeV]\n1/2\nM\n290\n300\n310\n320\n330\n340\nNumber of toy fits/1.2 GeV\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 42.9 / 35\nProb \n 0.1687\nConstant \n 2.33\n\u00b1\n 36.01 \nMean \n 0.3\n\u00b1\n 318.4 \nSigma \n 0.261\n\u00b1\n 5.821 \nATLAS\n / ndf \n2\n\u03c7\n 191.6 / 25\nProb \n 1.238e-27\nConstant \n 6.11\n\u00b1\n 63.36 \nMean \n 0.09\n\u00b1\n 4.95 \nSigma \n 0.115\n\u00b1\n 1.465 \n\u03b2\ntan \n0\n5\n10\n15\n20\n25\n30\n35\nNumber of toy fits/0.77\n0\n20\n40\n60\n80\n100\n120\n / ndf \n2\n\u03c7\n 191.6 / 25\nProb \n 1.238e-27\nConstant \n 6.11\n\u00b1\n 63.36 \nMean \n 0.09\n\u00b1\n 4.95 \nSigma \n 0.115\n\u00b1\n 1.465 \nATLAS\n / ndf \n2\n\u03c7\n 231.5 / 29\nProb \n 1.894e-33\nConstant \n 2.7\n\u00b1\n 33.9 \nMean \n 20.8\n\u00b1\n 379.9 \nSigma \n 14.5\n\u00b1\n 295.7 \n [GeV]\n0\nA\n-1000\n0\n1000\n2000\n3000\nNumber of toy fits/96 GeV\n0\n50\n100\n150\n200\n250\n / ndf \n2\n\u03c7\n 231.5 / 29\nProb \n 1.894e-33\nConstant \n 2.7\n\u00b1\n 33.9 \nMean \n 20.8\n\u00b1\n 379.9 \nSigma \n 14.5\n\u00b1\n 295.7 \nATLAS\nFigure 13: Distributions of the mSUGRA parameters obtained with the \ufb01ts to pseudo-experiment results.\n\ufb01ts can be used to evaluate the toy \ufb01t performance. The observed mean \u03c7 2 = 12.6 \u00b1 0.2 for sign \u00b5 =\n+1 is compatible with the expected value of Ndo f = 11. The solutions for the wrong assumption sign\n\u00b5 = \u22121, also reported in Table 9, cannot however be ruled out as the observed mean \u03c7 2 = 15.4\u00b10.3 is\nalso acceptable.\n10\nConclusions\nIf the supersymmetric partners of quarks and gluons exist at a moderate mass scale (\u22721 TeV) they will\nbe abundantly produced in pp collisions at the LHC centre-of-mass energy of 14 TeV. In this scenario,\na few fb\u22121 of ATLAS data will allow the discovery of the new particles [1], once the commissioning of\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1639\n\nTable 9: Results of a \ufb01t of the mSUGRA parameters to the observables listed in Sections 3, 4 and 6 for\nthe SU3 point. The mean and RMS of the distribution of the results from the toy \ufb01ts is reported. The two\npossible assumptions for the digital parameter sign(\u00b5) = +1 sign(\u00b5) = \u00b11 have been used, resulting in\ndifferent preferred regions for the other parameters. The effect of different assumptions on theoretical\nuncertainties is also shown.\nParameter\nSU3 value\n\ufb01tted value\nexp. unc.\nsign(\u00b5) = +1\ntan\u03b2\n6\n7.4\n4.6\nM0\n100 GeV\n98.5 GeV\n\u00b19.3 GeV\nM1/2\n300 GeV\n317.7 GeV\n\u00b16.9 GeV\nA0\n\u2212300 GeV\n445 GeV\n\u00b1408 GeV\nsign(\u00b5) = \u22121\ntan\u03b2\n13.9\n\u00b12.8\nM0\n104 GeV\n\u00b118 GeV\nM1/2\n309.6 GeV\n\u00b15.9 GeV\nA0\n489 GeV\n\u00b1189 GeV\nthe detector has been completed and the Standard Model backgrounds have been well understood.\nThe next step after discovery will be to select speci\ufb01c supersymmetric decay chains to measure the\nproperties of the new particles. Here we have focused on those measurements that will be possible using\n1 fb\u22121 of integrated luminosity. Speci\ufb01c benchmarks in parameter space have been used to demonstrate\nthe precision that can be expected from these measurements, but the same (or similar) techniques can be\napplied to much of the SUSY parameter space accessible with early LHC data.\nFor the benchmark points considered, the most promising decay chain involves the leptonic decay\nof the next-to-lightest neutralino ( \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1\u2113+\u2113\u2212). The invariant mass of the two leptons shows a clear\nkinematic maximum (Section 3) which could already be measured with a precision of a few per cent with\nthe limited data set considered. The combination of one or both leptons with the hardest jets in the event\nwould allow observation of several other kinematic minima and maxima (Section 4).\nFor high values of tan\u03b2 the decays into taus will be far more abundant than those involving electrons\nor muons; the excellent performance expected for the identi\ufb01cation and measurement of hadronic \u03c4\ndecays in ATLAS will also allow observation of the dilepton edge in the \u03c4 +\u03c4\u2212invariant mass distribution\n(Section 5).\nThe leptonic decays will not be the only channel for early measurements with supersymmetric de-\ncays. The \u02dcqR \u2192q \u02dc\u03c70\n1 decay can be used to determine the \u02dcqR mass (Section 6). The combination of\nhadronically decaying top quarks and b-jets in supersymmetric events is also a promising possibility for\nlow-scale Supersymmetry with decay chains involving scalar top and bottom quarks, as shown by the\nreconstruction of the edge of the tb invariant mass discussed in Section 7.\nIf the \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1h decay is open, it will provide a substantial source of Higgs bosons. Since the\nStandard Model backgrounds can be suppressed by the usual SUSY cuts, it will then become possible to\nobserve the h \u2192b\u00afb decay with moderate (5 fb\u22121) integrated luminosity (Section 8).\nThe different channels will provide complementary information about the SUSY mass phenomenol-\nogy. The various measurements will have to be combined to reconstruct the SUSY mass spectrum and\nattempt to understand the SUSY-breaking mechanism. In Section 9 it is discussed how a selected set\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1640\n\nof early studies can be combined to obtain the \ufb01rst measurements of supersymmetric masses and of the\nparameters of the mSUGRA model. With 1 fb\u22121 the reconstruction of part of the supersymmetric mass\nspectrum will only be possible for favourable SUSY scenarios and with some assumptions about the\ndecay chains involved. Larger integrated luminosity will help to overcome these limitations, as more\nmeasurements become possible and the precision of each increases.\nReferences\n[1] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[2] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[3] ATLAS Collaboration, Supersymmetry Signatures with High-pT Photons or Long-Lived Heavy\nParticles, this volume.\n[4] M. N. Nojiri, Y. Yamada, Phys. Rev. D 60 (1999) 015006.\n[5] U. De Sanctis, T. Lari, S. Montesano, C. Troncon, Eur. Phys. J. C 52 (2007) 743.\n[6] B. C. Allanach, C. G. Lester, M. A. Parker and B. R. Webber, JHEP 0009 (2000) 004.\n[7] C. G. Lester, M. A. Parker and M. J. White, JHEP 0710 (2007) 0051.\n[8] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[9] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[10] B. K. Gjelsten, D. J. Miller, P. Osland, JHEP 0412 (2004) 003.\n[11] D. J. Miller and P. Osland and A. R. Raklev, JHEP 0603 (2006) 034.\n[12] C.G. Lester, Phys. Lett. B655 (2007) 39\u201344.\n[13] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Hadronic \u03c4 Decays, this volume.\n[14] D. J. Mangeol, U. Goerlach, Search for \u02dc\u03c70\n2 decays to \u02dc\u03c4\u03c4 and SUSY mass spectrum measurement\nusing di-\u03c4 \ufb01nal states, 2006, CMS NOTE 2006/096.\n[15] Richter-Was, Elzbieta and Froidevaux, Daniel and Poggioli, Luc, ATLFAST 2.0 a fast simulation\npackage for ATLAS Atlas Note ATL-PHYS-98-131.\n[16] S. Y. Choi, K. Hagiwara, Y. G. Kim, K. Mawatari and P. M. Zerwas, Phys. Lett. B 648 (2007).\n[17] A.J. Barr, C.G. Lester, P. Stephens, J.Phys.G 29 (2003) 2343.\n[18] C.G. Lester, D. Summers, Phys.Lett.B 463 (1999) 99.\n[19] J. Krstic, M. Milosavljevic and D. Popovic, Studies of a low mass SUSY model at ATLAS with full\nsimulation, ATL-PHYS-PUB-2006-028.\n[20] ATLAS Collaboration, Data-Driven Determinations of W, Z and Top Backgrounds to Supersym-\nmetry, this volume.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1641\n\n[21] J. Hisano, K. Kawagoe and M.M. Nojiri, Phys. Rev. D 68 (2003) 035007.\n[22] J. Hisano, K. Kawagoe and M.M. Nojiri, A Detailed Study of the Gluino Decay into the Third\nGeneration Squarks at the CERN LHC, ATL-PHYS-2003-29.\n[23] ATLAS Collaboration, ATLAS detector and physics performance. Technical design report Vol. 2,\nCERN-LHCC-99-15 (1999).\n[24] P. Bechtle, K. Desch, and P. Wienemann, Comput. Phys. Commun. 174 (2006) 47\u201370.\n[25] W. Porod, Comput. Phys. Commun. 153 (2003) 275\u2013315.\n[26] R. Lafaye, T. Plehn, M. Rauch and D. Zerwas, Eur. Phys. J. C54 (2008) 617\u2013644.\nSUPERSYMMETRY \u2013 MEASUREMENTS FROM SUPERSYMMETRIC EVENTS\n1642\n\nMulti-Lepton Supersymmetry Searches\nAbstract\nWe investigate the potential of the ATLAS detector to discover new physics\nevents containing three leptons and missing transverse momentum. Such \ufb01nal\nstates are predicted in a variety of extensions to the Standard Model. In the\ncontext of supersymmetric models, they could result from direct production of\ngaugino pairs. Using Monte Carlo simulations we present the discovery poten-\ntial for several benchmark Supersymmetry points. We pay particular attention\nto the case where all strongly interacting sparticles are heavy. We investigate\ntrigger and reconstruction ef\ufb01ciencies and discuss methods for measuring var-\nious systematic uncertainties. A solid discovery is expected with an integrated\nluminosity of the order of several inverse fb. If coloured particles are heavy\ndirect production of gauginos dominates. In such scenarios, discovery would\nrequire about an order of magnitude larger luminosity.\n1\nIntroduction\nIf supersymmetric (or other partner) particle production at the LHC is dominated by particles without\ncolour charge, then one of the most promising discovery channels is in multi-lepton + missing transverse\nmomentum (Emiss\nT\n) \ufb01nal states with little hadronic activity. In this section we investigate the ability of the\nATLAS experiment to discover new physics in events containing three (or more) leptons \u2013 either electrons\nor muons \u2013 of which two must have opposite signs but the same \ufb02avour (OSSF). We determine the\nsensitivity which would be obtained for discovery of \ufb01ve benchmark points with an integrated luminosity\nof 10 fb\u22121.\nWhile an analysis of this channel is clearly sensitive to other models, in this section we use Su-\npersymmetry as our example signature, we assume R-parity conservation, and that the lightest SUSY\nparticle (LSP) is the weakly interacting \u02dc\u03c70\n1, which provides the missing transverse energy signal.\nIn the supersymmetric case, the \ufb01nal states of interest could come from leptonic decay of pairs of\nheavy gauginos (such as \u02dc\u03c70\n2 and \u02dc\u03c7+\n1 ) through real or virtual W \u00b1, Z0 or sleptons to leptons and a pair of\nLSPs. The heavy gauginos may be produced directly, or in the decay of heavier partner particles.\nThe primary aim is to make the most realistic determination which is possible at this time of the\ndiscovery potential in this channel. We also wish to identify the most important Standard Model back-\ngrounds, so that analyses can be prepared to measure them in control regions with the ATLAS data.\nThroughout this study we use the inclusive Supersymmetry production Monte Carlo samples de-\nscribed in [1]. The points lie in various regions of mSUGRA parameter space in which the LSP relic\ndensity is broadly consistent with the observed cold dark matter density.\nThe Standard Model backgrounds simulated are listed in Table 1. The most important backgrounds\nare found to be t\u00aft , Zb and ZW. Fully leptonic ZW events represent one signi\ufb01cant source of events\ncontaining three leptons and missing energy. Their contribution can be reduced by rejecting OSSF lepton\npairs with invariant masses consistent with the Z mass. Leptonic decays of t\u00aft , and Zb are expected to\nproduce two leptons but can generate a third from leptonic b quark decay. These backgrounds have large\ncross-sections, but can be reduced by the introduction of stringent cuts on the isolation of the lepton\ntracks \u2013 as we will discuss in Section 3.\nA particularly important benchmark point for the trilepton analysis is the point SU2 [1]. This point\nlies within the \u2018focus point\u2019 region of mSUGRA parameter space which is characterised by very large\nmasses for squarks and sleptons and relatively light gauginos. The heavy squarks and sleptons (see\nFigure 1 and Table 2 for the SUSY mass hierarchy at SU2), will have very small production cross-sections\n1643\n\nTable 1: List of the background samples used, with Monte Carlo generator cross-sections (\u03c3), next-to-leading-\norder to leading-order k factors (where known for leading-order generators), average weights (\u27e8w\u27e9) and corre-\nsponding integrated luminosities. The cross-sections for WW, WZ, ZZ, Z\u03b3 and Zb are quoted after a \ufb01lter is\napplied on the generator output requiring at least one lepton with pseudorapidity, |\u03b7| < 2.8 and transverse momen-\ntum, pT > 10 GeV. The diboson (WW, WZ, ZZ) samples have a different cross-section than the diboson MC@NLO\nsamples (found elsewhere in this volume) because they also include contributions from (and interference with) the\nphoton pole.\nProcess\n\u03c3 [pb]\nk factor\n\u27e8w\u27e9\nRdt L [fb\u22121]\nWW\n24.5\n1.67\n1\n1.22\nWZ\n7.8\n2.05\n1\n2.98\nZZ\n2.1\n1.88\n1\n12.7\nZ\u03b3\n2.6\n1.30\n1\n2.98\nZb\n154\n1\n0.66\n0.75\nt\u00aft\n450\n-\n0.73\n0.92\nat the LHC and make it a dif\ufb01cult region in which to discover SUSY using the analyses described in [2]\nbased on the selection of hadronic jets and missing transverse momentum [3]. However, gaugino and\ngluino production will still be abundant, so we expect good discovery potential in multi-lepton events.\nThe branching ratios of gauginos for SU2 can be found in Table 31.\n0\n1\n2\n3\n4\n5\n6\nMass [GeV]\n2\n10\n3\n10\n4\n10\n0\n\u03c7\u223c\n\u00b1\n\u03c7\u223c\ng~\nq~\nl~\nh,H,A\nFigure 1: SU2 sparticle mass spectrum.\nTable 2: Particle masses for SU2.\nSparticle\nMass [GeV]\nSparticle\nMass [GeV]\n\u02dc\u03c70\n1\n103\n\u02dcg\n857\n\u02dc\u03c70\n2\n160\n\u02dcuL\n3563\n\u02dc\u03c70\n3\n180\n\u02dcuR\n3574\n\u02dc\u03c70\n4\n295\n\u02dcdL\n3564\n\u02dc\u03c7\u00b1\n1\n149\n\u02dcdR\n3576\n\u02dc\u03c7\u00b1\n2\n287\n\u02dcb1\n2925\n\u02dc\u2113L\n3548\n\u02dcb2\n3501\n\u02dc\u2113R\n3547\n\u02dct1\n2131\n\u02dc\u03bdL\n3546\n\u02dct2\n2935\nThe total cross-section times branching ratio for chargino-neutralino direct pair production and decay\nto a trilepton \ufb01nal state is 32.6 fb. Table 4 shows the contribution from each \u02dc\u03c7\u00b1 \u02dc\u03c70 pair production to a\ntrilepton \ufb01nal state. The contribution from \u02dc\u03c7\u00b1 \u02dc\u03c7\u2213and \u02dc\u03c70 \u02dc\u03c70 pair production to a trilepton \ufb01nal state\nis not tabulated, but also adds a small contribution to the signal. Exclusive trilepton signal for SU2 is\ndominated by the pair production \u02dc\u03c7\u00b1\n1\n\u02dc\u03c70\n2 followed by \u02dc\u03c7\u00b1\n1\n\u2192\u02dc\u03c70\n1 \u2113\u03bd and \u02dc\u03c70\n2 \u2192\u02dc\u03c70\n1 \u2113+\u2113\u2212decays.\nThe trilepton signal may include contributions both from direct gaugino pair events and from other\nSUSY events. The latter can lead to trilepton \ufb01nal states when cascades initiated by heavier sparticles\ndecay via gauginos or sleptons. In a search it is not necessary to distinguish between the various contri-\nbutions to new physics and so both classes of event form part of the signal. However in this study we are\nparticularly interested in the scenario in which all strongly interacting particles are heavy, since in those\ncases other analyses (requiring jets) will have more dif\ufb01culty making a discovery. Since we want to be\nsensitive to SUSY even in this harder case, we de\ufb01ne the signal in two different ways:\n1The masses and branching ratios were calculated using Isajet v7.71 [4] using a top mass of 175 GeV.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1644\n\nTable 3: Some important branching\nratios for the benchmark point SU2.\nSparticle\nDecay Mode\nB.R.\n\u02dc\u03c70\n2\n\u02dc\u03c70\n1\u2113+\u2113\u2212\n7%\n\u02dc\u03c70\n3\n\u02dc\u03c70\n1\u2113+\u2113\u2212\n7%\n\u02dc\u03c70\n4\n\u02dc\u03c7\u00b1\n1 W \u2213\n81%\n\u02dc\u03c70\n3Z\n12%\n\u02dc\u03c7\u00b1\n1\n\u02dc\u03c70\n1\u2113\u03bd\n22%\n\u02dc\u03c7\u00b1\n2\n\u02dc\u03c70\n2W \u00b1\n38%\n\u02dc\u03c70\n3W \u00b1\n18%\n\u02dc\u03c7\u00b1\n1 Z\n30%\nTable 4:\nLeading-order cross-sections and num-\nber of trilepton events for integrated luminosity of\n10 fb\u22121 for SU2.\nProduction\n\u03c3 [fb]\nTrilepton events /10 fb\u22121\n\u02dc\u03c7\u00b1\n1 \u02dc\u03c70\n2\n1138.0\n175\n\u02dc\u03c7\u00b1\n1 \u02dc\u03c70\n3\n679.3\n105\n\u02dc\u03c7\u00b1\n1 \u02dc\u03c70\n4\n51.4\n6\n\u02dc\u03c7\u00b1\n2 \u02dc\u03c70\n2\n58.5\n7\n\u02dc\u03c7\u00b1\n2 \u02dc\u03c70\n3\n61.6\n7\n\u02dc\u03c7\u00b1\n2 \u02dc\u03c70\n4\n310.3\n26\nTOTAL\n326\n\u2022 \u201cInclusive SUSY\u201d : Inclusive supersymmetric particle pair production (any sparticles)\n\u2022 \u201cDirect gaugino\u201d : Direct production of charginos and neutralinos only\nInclusive SUSY represents the signal we would obtain at the benchmark points. Direct gaugino rep-\nresents a more pessimistic scenario, where coloured sparticles are heavy so have no signi\ufb01cant LHC\ncross-section.\n2\nLepton selection\nThe \ufb01nal selection will require three leptons \u2013 electrons or muons \u2013 which must consist of an OSSF pair\nand a further third lepton. The initial lepton selection requirements are based on the ATLAS standard\ncriteria. The main de\ufb01nitions are summarised in Table 5, and are brie\ufb02y discussed below. The relatively\nlow pT threshold for electrons and muons of 10 GeV in these analyses is an attempt to increase the\nnumber of trilepton events, despite lower lepton reconstruction ef\ufb01ciencies at low pT .\n\u2022 Muons must satisfy pT > 10 GeV and |\u03b7| < 2.5, and tracks found in the muon spectrometer must\nmatch inner detector tracks. For each muon spectrometer track only the best matching track in the\ninner detector is taken. It is required that the \u03c72 for the match of the muon track to the points on\nthe track [5] is less than 100. A primary isolation criterion requires less than 10 GeV of transverse\nenergy2 in the calorimeter in a cone of radius \u2206R = 0.2 around the muon3.\n\u2022 Electrons must satisfy pT > 10 GeV and |\u03b7| < 2.5. They must satisfy shower shape and isolation\nrequirements as described in [6]. The entire event is rejected if any electron candidate is found\nin the barrel-endcap transition region (1.37< |\u03b7| < 1.52) due to the lower electron identi\ufb01cation\nperformance in this region. A primary isolation criterion is that electrons must have less than\n10 GeV of transverse energy in an annulus of radius \u2206R=0.2 surrounding the electron.\nElectrons and muons are then subject to further vetoes as follows: electrons and muons within \u2206R <\n0.4 of a jet are removed from the event, along with OSSF pairs with invariant mass MOSSF < 20 GeV,\nwhich are likely to have been produced from photon conversions or hadronic decays.\n2Transverse energy, ET = E sin\u03b8, where E is the energy and \u03b8 is the polar angle relative to the beam direction.\n3\u2206R \u2261\np\n\u2206\u03b72 +\u2206\u03c62 where \u2206\u03b7 is the pseudorapidity difference, with \u03b7 \u2261\u2212logtan(\u03b8/2), and \u2206\u03c6 is the difference in\nazimuthal angle.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1645\n\nTable 5: Selection criteria for muons, electrons and jets.\nMuon\nElectron\nJet\npT cut\n> 10 GeV\n> 10 GeV\n> 10 GeV\n\u03b7 cut\n|\u03b7| < 2.5\n|\u03b7| < 1.37\n|\u03b7| < 2.5\nor 1.52 < |\u03b7| < 2.5\nCalorimeter\n|E| < 10 GeV\n|E| < 10 GeV\n-\nIsolation\nin \u2206R = 0.2\nin \u2206R = 0.2\n-\n2.1\nSingle lepton selection ef\ufb01ciencies\nSearches for SUSY \ufb01nal states with three leptons require both a high lepton reconstruction ef\ufb01ciency\nand low fake rates. There are few Standard Model processes with similar signatures, but the high cross\nsection backgrounds t\u00aft and Zb can pass the trilepton requirement as there are both primary leptons in the\nevent and a number of jets, in particular b jets which can introduce secondary leptons. Good isolation\ncriteria are therefore important in order to reduce the fake rate and thus the background. This section\npresents a study of the lepton ef\ufb01ciency, fake rate and purity for the common object de\ufb01nition which\nincludes a calorimeter based isolation criterion as well as the performance of a track-based alternative.\nWhen collision data are available, the best determination of these quantities will be made from the\nATLAS data using the methods described in [7]. Since most of our events of interest will have a similar\nenvironment \u2013 isolated leptons and little jet activity \u2013 we may expect that the values found in those studies\nshould closely match the corresponding quantities in our search. However since those measurements\nrequire collision data, in this section we present the ef\ufb01ciencies, fake rates and purities as determined\nfrom Monte Carlo information only.\nThe following isolation criteria have been studied:\n\u2022 No isolation cut - showed as a reference;\n\u2022 Calorimeter-based isolation E\u2206R=0.2\ncal\n< 10 GeV. E\u2206R=0.2\ncal\nis the energy deposited in a cone with\n\u2206R = 0.2 around the lepton candidate;\n\u2022 Maximum-pT track-based isolation p\u2206R=0.2\nTtrack,max(\u2113) < 2/1 GeV for e/\u00b5, where p\u2206R=0.2\nTtrack,max(\u2113) is the\nmaximum pT of any track in a \u2206R = 0.2 cone around the lepton;\n\u2022 Sum-pT track-based isolation p\u2206R=0.3\nTtrack,\u03a3(\u2113) < 4 GeV, where p\u2206R=0.3\nTtrack,\u03a3 is the sum of the pT of all\ntracks above 1 GeV in a \u2206R = 0.3 cone around the lepton.\nThe lepton reconstruction ef\ufb01ciency is de\ufb01ned to be\nE\u2113\u2261nmatch\n\u2113\nnMC\n\u2113\n,\n(1)\nwhere nmatch\n\u2113\nis the number of generator-level leptons matched to a reconstructed candidate and nMC\n\u2113\nis\nthe total number of generator-level leptons.\nIn this study generator-level leptons are de\ufb01ned to be charged leptons (\u2113\u2208{e,\u00b5}) which have come\nfrom decays of SUSY particles (sleptons and gauginos), Standard Model gauge bosons and tau leptons,\nbut do not include leptons from other sources (such as hadronic decays, bremsstrahlung, or photon con-\nversions). No isolation cut has been applied on these generator-level leptons. Generator-level particles\nare matched to reconstructed candidates which have passed kinematics cuts and object selection accord-\ning to the de\ufb01nition in Section 2. A match is required to be found within \u2206R = 0.02. Figure 2 shows\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1646\n\n [GeV]\nT\ngenerator-level electron p\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nelectron efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSU2\nATLAS\n(a)\n\u03b7\ngenerator-level electron \n0\n0.5\n1\n1.5\n2\n2.5\nelectron efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSU2\nATLAS\nNo isolation \n < 10 GeV\nR=0.2\n\u2206\ncal\nI \n) < 2 GeV\nmax\nT\n(p\nR=0.2\n\u2206\ntrk\nI \n(b)\n [GeV]\nT\ngenerator-level muon p\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nmuon efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSU2\nATLAS\n(c)\n\u03b7\ngenerator-level muon \n0\n0.5\n1\n1 5\n2\n2.5\nmuon efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSU2\nATLAS\nNo isolation \n < 10 GeV\nR=0.2\n\u2206\ncal\nI \n) < 1 GeV\nmax\nT\n(p\nR=0.2\n\u2206\ntrk\nI \n(d)\nFigure 2: The ef\ufb01ciency for electrons (a,b) and muons (c,d) to be reconstructed and to pass various\nisolation criteria, for the SU2 sample. The plots are shown as a function of the pT (a,c) and \u03b7 (b,d) of\nthe matched Monte Carlo lepton.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1647\n\n [GeV]\nT\nfake electron p\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nelectron fake rate\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\nTop\nATLAS\nNo isolation \n < 10 GeV\nR=0.2\n\u2206\ncal\nI \n) < 2 GeV\nmax\nT\n(p\nR=0.2\n\u2206\ntrk\nI \n(a)\n\u03b7\nfake electron \n0\n0.5\n1\n1.5\n2\n2.5\nelectron fake rate\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\nTop\nATLAS\n(b)\n [GeV]\nT\nfake muon p\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nmuon fake rate\n0\n0.0005\n0.001\n0.0015\n0.002\n0.0025\n0.003\n0.0035\n0.004\nTop\nATLAS\nNo isolation \n < 10 GeV\nR=0.2\n\u2206\ncal\nI \n) < 1 GeV\nmax\nT\n(p\nR=0.2\n\u2206\ntrk\nI \n(c)\n\u03b7\nfake muon \n0\n0 5\n1\n1 5\n2\n2.5\nmuon fake rate\n0\n0.0005\n0.001\n0.0015\n0.002\n0.0025\n0.003\n0.0035\n0.004\nTop\nATLAS\n(d)\nFigure 3: The fake rate for electrons (a,b) and muons (c,d) in the t\u00aft sample as function of the pT (a,c)\nand \u03b7 (b,d) of the fake lepton.\nthe reconstruction ef\ufb01ciency for electrons and muons from the SU2 sample using different isolation\nrequirements as function of the pT and \u03b7 of the matched Monte Carlo lepton.\nThe requirement that leptons should be separated from selected jets by \u2206R > 0.4 (referred to as the\n\u2206R(\u2113,jet) > 0.4 cut) is already a strong isolation requirement which reduces the ef\ufb01ciency by \u223c5% for\nelectrons and \u223c15% for muons. For the case of t\u00aft events (not shown in the \ufb01gures) the effect is even\nlarger as there are more jets in the events.\nFor the muons, one can see that after introducing the \u2206R(\u2113,jet) > 0.4 cut, the ef\ufb01ciency decreases\nwith increasing pT , while the |\u03b7| distribution decreases in the central region |\u03b7| <\u223c1.4. A clear drop in\nelectron ef\ufb01ciency can be found near |\u03b7| \u22481.4 which is the barrel-endcap transition region.\nAfter applying only the \u2206R(\u2113,jet) > 0.4 cut (referred to as \u201cno isolation\u201d in the plots), the total\nef\ufb01ciency is (65.5 \u00b1 0.5)% and (75.2 \u00b1 0.5)% for electrons and muons respectively. The calorimeter-\nbased isolation E\u2206R=0.2\ncal\n< 10 GeV reduces the electron ef\ufb01ciency by \u22483% to (63.6\u00b10.5)% while leaving\nthe muon ef\ufb01ciency almost unchanged. The track-based alternative has similar effect on both lepton\n\ufb02avours causing a loss of about 7 to 8% with respect to the \u201cno isolation\u201d performance.\nThe fake rate is de\ufb01ned as\nF\u2113\u2261nMC,match\n\u2113\nnMC\njet\n,\n(2)\nwhere nMC,match\n\u2113\nis the number of reconstructed leptons which are not matched to a generator-level lepton\nand nMC\njet is the number of jets at the generator level4.\nOnly generator-level jets with |\u03b7| < 2.5 are considered. They are rejected if there is an overlap with\nan electrons within \u2206R < 0.2, but in general include photons, hadronic tau jets and b jets. The generator\n4i.e. jets found by running a jet algorithm over the Monte Carlo generator \ufb01nal state, before detector simulation.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1648\n\njet must have energy, E > 7 GeV. Asymmetric pT cuts are applied to the reconstructed objects compared\nto their Monte Carlo equivalents. For the ef\ufb01ciency calculation pTMC\n\u2113\n> 10 compared to pT\u2113> 5 GeV,\nwhile for the fake rate calculation pTMC > 5 and pT\u2113> 10 GeV. This reduces the number of mismatches\nwhich would be found near the edge of the \ufb01ducial region from small mismeasurements of pT .\nFigure 3 shows the fake rate as function of the pT and \u03b7 of the fake lepton for the t\u00aft sample (one\nof the major backgrounds). The pT distribution is clearly peaked at low values typical for leptons from\nb-jet decays. The \u03b7 distribution follows the detector layout with higher fake rate in the transition region\nbetween the barrel and end caps.\nThe \u2206R(\u2113,jet) > 0.4 requirement provides a reduction in the fake rate of about \u224880% for muons and\n\u22485% for electrons (as compared to leptons passing the standard selection with E\u2206R=0.2\ncal\n< 10). With no\nisolation other than the \u2206R(\u00b5,jet) > 0.4 requirement one obtains a fake rate of (4.1 \u00b1 0.1) \u00d7 10\u22123 and\n(1.1\u00b10.1)\u00d710\u22123 for electrons and muons respectively. The isolation criteria provide a similar relative\nsuppression of the electron and muon fake: \u224820% for I\u2206R=0.2\ncal\n< 10 and \u224874% for p\u2206R=0.2\nTtrack,max(\u2113) <\n2/1 GeV for e/\u00b5. The effect of the isolation cuts is very similar in the case of the SU2 sample, but the\nfake rates are almost an order of magnitude lower than in t\u00aft events.\nWe de\ufb01ne purity by:\nP\u2113= nmatch\n\u2113\nn\u2113\n,\n(3)\nwhere n\u2113is the number of reconstructed leptons, and the matching criteria are as described above. The\nlepton selection described in Section 2 provide samples with a purity of 92% (e) and 97% (\u00b5) with very\nsimilar results for both the SU2 and t\u00aft samples. However after requiring at least 3 leptons in the event\nthere is a clear difference between the two. The purity is almost unchanged for SU2, while, in t\u00aft trilepton\nevents the purity drops to \u223c50% for electrons and \u223c70% for muons.\n3\nEvent selection\nEvents are required to pass either of the two single-lepton triggers, labelled L2 e22i and L2 mu20, which\nare well-suited for the tri-lepton analysis at L = 1031\u221232 cm\u22122s\u22121. A more detailed discussion of the\nmotivation for using these triggers can be found in Section 5.\nDistributions of some important event variables for Standard Model backgrounds and for the bench-\nmark point SU2 (both for inclusive SUSY and direct gaugino) can be found in Figure 4. We show the pT\ndistributions of reconstructed leptons (electron or muon) and jets. Requiring at least three leptons in the\nevent results in mainly t\u00aft and Zb Standard Model backgrounds, with larger contributions from dibosons\nin four lepton events. It can seen in Figures 4a and 4b that pT distributions of the two hardest leptons\nin three lepton events are similar in SU2 and t\u00aft , with Zb adding a signi\ufb01cant contribution in the low pT\nregion. The pT distributions for the third-hardest leptons are plotted in Figure 4c where it can be seen\nthat whilst t\u00aft and Zb are the major backgrounds in the low pT region, there is a large contribution from\nthe dibosons across the entire pT range. This is because the third leptons from t\u00aft and Zb are soft leptons\nfrom leptonic b-quark decay, whereas all the leptons from dibosons are from Z/W \u00b1 boson decays. The\npT distributions of the reconstructed jets are plotted in Figure 4d for events with three or more leptons.\nSince an OSSF lepton pair is expected from the \u02dc\u03c70\n2 decay, a selection requiring two OSSF leptons is\napplied (i.e. we require e+e\u2212+ \u2113or \u00b5+\u00b5\u2212+ \u2113, where \u2113\u2208e,\u00b5)5. A further cut requires three or more\nleptons in the event.\nA stringent cut on the isolation of the tracks of the leptons is made next, using the p\u2206R=0.2\nTtrack,max variable\ndescribed in Section 2.1. The purpose is to reduce backgrounds from bremsstrahlung, hadron decays and\n5Trilepton events where all three leptons have the Same Sign, (SS, \u2113\u00b1\u2113\u00b1\u2113\u00b1, where \u2113\u2208e,\u00b5) have also been investigated,\nhowever due to the very low statistics associated with the channel in the signal samples investigated, it is not considered further\nhere.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1649\n\n leading lepton [GeV]\nT\np\n0\n50\n100\n150\n200\n250\n300\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\nt\nt \nZb\nDibosons\n\u03b3\nZ \ninclusive SUSY \ndirect gaugino \nATLAS\n(a)\n leading lepton [GeV]\nnd\n 2\nT\np\n0\n20\n40\n60\n80\n100\n120\n140\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\nATLAS\n(b)\n leading lepton [GeV]\nrd\n 3\nT\np\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n(c)\n leading jet [GeV]\nT\np\n0\n50\n100 150 200 250 300 350\n400 450 500\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\nATLAS\n(d)\nFigure 4: Transverse momentum of the leading three leptons (a-c) and leading-jet pT (d) after an initial\nthree-lepton requirement has made.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1650\n\n [GeV]\nR=0.2\n\u2206\nT trackmatch\np\n0\n2\n4\n6\n8\n10\n12\n14\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nt\nt \nZb\nDibosons\n\u03b3\nZ \ninclusive SUSY \ndirect gaugino \nATLAS\n(a)\n [GeV]\nR=0.2\n\u2206\nT trackmatch\np\n0\n2\n4\n6\n8\n10\n12\n14\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\n(b)\nFigure 5: p\u2206R=0.2\nTtrack,max for (a) electrons and (b) muons.\n [GeV]\nSFOS\nM\n0\n50\n100\n150\n200\n250\n300\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\n3\n10\nt\nt \nZb\nDibosons\n\u03b3\nZ \ninclusive SUSY \ndirect gaugino \nATLAS\n(a)\n [GeV]\nT\np\n0\n50\n100 150 200 250 300 350\n400 450 500\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\nATLAS\n(b)\n leading jet [GeV]\nT\np\n0\n50\n100 150 200 250 300 350\n400 450 500\n-1\nEvents/10 fb\n-1\n10\n1\n10\n2\n10\nATLAS\n(c)\nFigure 6: (a) OSSF dilepton invariant mass distribution. (b) Emiss\nT\ndistribution after the Z mass window\ncut. (c) The pT distribution of the leading jet after the Emiss\nT\ncut is applied.\nphoton conversions. The relevant distributions for electrons and muons are plotted in Figure 5a and 5b.\nThe plots contain negative entries when no track is found within \u2206R. We require p\u2206R=0.2\nTtrack,max < 1 GeV for\nmuons and < 2 GeV for electrons. This reduces the number of background events to 23% (t\u00aft ) and 37%\n(Zb) of their previous levels, whilst keeping 82% (inclusive SUSY), 86% (direct gaugino) of the signal\nfor our SU2 benchmark point.\nThe diboson and Zb backgrounds will produce the two OSSF leptons mainly from Z decays, which\nwill not be the case for three-body decays of neutralinos. The dilepton invariant mass distribution is\nshown in Figure 6a, (after applying the cuts already described) and shows the expected peak at the Z\nmass. A simple way to reduce the these backgrounds is to discard events which have any OSSF dilepton\npair with invariant mass in the mass window 81.2 GeV < MOSSF < 101.2 GeV. Note that this exclusion\nwindow also offers an excellent control region in which to measure the size of these backgrounds from\nthe data. It is however somewhat model-dependent. Some points in SUSY parameter space preferentially\ndecay through real Z bosons, rather than through three-body decays. At those points the OSSF dilepton\nmass distribution would also be strongly peaked at the Z mass.\nA large missing-transverse-momentum cut is used in most SUSY analyses, but in this analysis a\nsmaller cut at 30 GeV is applied since in direct gaugino production the two invisible \u02dc\u03c70\n1s are often almost\nback-to-back in the transverse plane, resulting in a lower overall Emiss\nT\n(Figure 6b). Missing transverse\nmomentum is calculated as described in [8].\nFinally there is the possibility of adding a cut can be made on the hadronic activity in the event. This\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1651\n\ncould be useful in the case where direct gaugino production dominates, since it can be expected to reduce\nthe t\u00aft background to a greater extent than the signal. Whether this cut is appropriate will depend on the\nSUSY scenario presented by nature, so analyses both with and without this cut will be necessary.\nSelected jets must satisfy pT > 10 GeV and |\u03b7| < 2.5, and are reconstructed based on calorimeter\ntower signals [9] using a seeded cone algorithm with radius \u2206R = 0.4. Jets are initially selected with\npT > 10 GeV and |\u03b7| < 2.5. Jets are not considered if they overlap with a reconstructed electron within\n\u2206R < 0.2.\nThe pT distribution of the leading jet in the event is plotted in Figure 6c, where it is seen that the\ndirect gaugino production has jets with lower pT than the Standard Model backgrounds. The level of\nthis cut is chosen at pT > 20 GeV.\nThe complete event selection is then:\n1. At least one pair of OSSF leptons (e+e\u2212or \u00b5+\u00b5\u2212)\n2. N\u2113>= 3 (\u2113\u2208{e,\u00b5}), and where all \u2113i satisfy the requirements in Section 2\n3. p\u2206R=0.2\nTtrack,max < 2 GeV for electrons, p\u2206R=0.2\nTtrack,max < 1 GeV for muons\n4. No OSSF dilepton pair has invarint mass in the range 81.2 GeV < MOSSF < 102.2 GeV\n5. Emiss\nT\n> 30 GeV\n6. Optional \u2013 no jet with pT > 20 GeV\nIn Figure 7 we show distributions of the invariant mass of the dilepton pair after all cuts. The\ndistributions have been \ufb02avour subtracted; the quantity plotted is\nnOSSF \u2212nOSSF ,\n(4)\nwhere nOSSF is the number of events in the signal selection (containing OSSF dilepton pairs) as described\nearlier in this section, and nOSSF is the number of events in which there are three leptons, but no OSSF\npair. The non-OSSF events give an indication of the expected background size since many background\nsources do not necessarily produce OSSF pairs.\n4\nDiscovery potential\nThe numbers of events and the resulting signi\ufb01cance at each stage of the analysis are listed in Table 6 for\nthe benchmark point SU2. We use the following de\ufb01nition of signal sign\ufb01cance,\nS =\nS\n\u221aS+B\n(5)\nwhere S is the number of signal events and B is the number of background events. After applying the\nevent selection above (including the jet veto), 29 events remain for SU2 inclusive SUSY all of which are\ndirect gaugino, with an expected background of 210 events (mainly ZW production). This corresponds\nto S of 1.87 for 10 fb\u22121 . This yields a 5\u03c3 discovery signal after \u223c80 fb\u22121 of integrated luminsity.\nWith the jet veto selection, ZW is the dominant remaining Standard Model background. Without the jet\nveto, 177 signal events (95 of them direct gaugino) remain. Statistical signi\ufb01cances of 5.94 and 3.34 are\nfound for the inclusive SUSY and direct gaugino signals respectively.\nThe expected statistical signi\ufb01cances for various mSUGRA benchmark points are summarised in\nTable 7 excluding the jet veto unless indicated otherwise by \u201cSUx+JV\u201d.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1652\n\n [GeV]\nSFOS\nM\n0\n50\n100\n150\n200\n250\n300\n-1\nEvents/10 fb\n-50\n0\n50\n100\n150\nAll\nt\nt \nDibosons\ninclusive SUSY \ndirect gaugino \nATLAS\n(a)\n [GeV]\nSFOS\nM\n0\n50\n100\n150\n200\n250\n300\n-1\nEvents/10 fb\n-20\n-10\n0\n10\n20\n30\n40\n50\nATLAS\n(b)\nFigure 7: Distributions of the OSSF dilepton invariant mass after all selections have been applied\n(a) without the jet veto and (b) including a jet veto.\nTable 6: Numbers of events and statistical signi\ufb01cance as selection is applied for the benchmark point\nSU2, for integrated luminosity of 10 fb\u22121.\nKinematic Cut\nNo Cuts\nNL >= 2\nOSSF\nNL >= 3\nTrackIsol\nm\u2113\u2113\nEmiss\nT\nJetVeto\nSU2 gauginos\n64.0k\n1647\n1108\n178\n153\n120\n95\n29\nSU2 other\n7081\n776\n353\n127\n95\n85\n82\n0\nt\u00aft\n4.41M\n234k\n104k\n2812\n634\n507\n476\n42\nZZ\n38.2k\n10.4k\n9984\n580\n476\n57\n13\n6\nZW\n156k\n17.2k\n14.5k\n1910\n1682\n322\n218\n154\nWW\n400k\n22.7k\n10.7k\n25\n8\n8\n8\n8\nZ\u03b3\n32.8k\n7184\n6970\n91\n27\n7\n3\n0\nZb\n1.59M\n57.4k\n559k\n6523\n2409\n386\n0\n0\ninclusive SUSY S\n2.60\n1.74\n2.76\n3.36\n5.31\n5.94\n1.87\ndirect gaugino S\n1.77\n1.32\n1.61\n2.09\n3.20\n3.34\n1.87\nThe discovery prospects for inclusive SUSY, re\ufb02ected in columns titled \u201cSUx\u201d, are rather encourag-\ning: a 5\u03c3 discovery can be expected with several fb\u22121 of integrated luminosity6. The direct gaugino pair\nproduction is highlighted in columns marked as SU2\u03c7 and SU3\u03c7. Both for SU2 and SU3 we see a drop\nin signi\ufb01cance which roughly corresponds to the fraction of the direct gaugino production compared to\nthe total SUSY cross-section. In fact, the drop is somewhat higher, since the pT spectrum tends to be\nsofter for direct gaugino pair production compared to strong SUSY production with its characteristic\ndecay chains. Here, a discovery can be expected with several tens of fb\u22121.\n5\nLepton trigger study\nUnlike most SUSY searches, in this channel we cannot rely on jet or Emiss\nT\ntriggers. We have studied a\nvariety of triggers at the second level7, after the \ufb01rst level trigger has been applied. Other studies [10,11]\n6Taking into account statistical errors only. Systematic uncertainties are discussed in Section 6.5.\n7ATLAS has three trigger levels: a \ufb01rst level (L1) hardware trigger, a software-based second level trigger (L2) that examines\nregions of interest within the decector, and \ufb01nally a software-based event \ufb01lter (EF). More details about the electromagnetic [10]\nand muon [11] triggers may be found elsewhere in this volume.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1653\n\nTable 7: Discovery potential, and integrated luminosity required for 5\u03c3 discovery. The jet veto is only applied in\ncolumns headed \u2018+JV\u2019. For a fuller description of the notation, see the text.\nSU1\nSU2\nSU3\nSU4\nSU8\nSU2\u03c7\nSU3\u03c7\nSU2+JV\nSU3+JV\nS ,10 fb\u22121\n7.7\n5.9\n17.2\n69.3\n1.9\n3.3\n1.6\n1.9\n1.4\nRdt L for 5\u03c3\n4.2\n7.1\n0.8\n0.1\n70.5\n22.4\n92.9\n66.9\n119.3\nTable 8: Fraction of events triggered at L2 at three selection stages of the selection for the heavy coloured\nsparton scenario in SU2 (\ufb01rst block), the direct gaugino production in SU3 (second block), and the\ninclusive SU3 signal (third block). \u201cS\u201d stands for the OR-combination of L2 e22i and L2 mu20.\nSelection\nSU2\u03c7\nSU3\u03c7\nSU3 incl.\nStage\nL2 e22i\nL2 mu20\nS\nL2 e22i\nL2 mu20\nS\nL2 e22i\nL2 mu20\nS\nOSSF pair\n41%\n54%\n89%\n42%\n54%\n92%\n51%\n51%\n94%\nOSSF+3rd\u2113\n58%\n67%\n93%\n59%\n63%\n95%\n66%\n68%\n98%\nafter all cuts\n57%\n66%\n92%\n58%\n57%\n94%\n66%\n64%\n97%\ndemonstrate that objects passing L2 have a high ef\ufb01ciency for passing EF.\nAs a \ufb01gure of merit, the fractions of triggered events\n\u2022 after selecting for an OSSF pair;\n\u2022 after requiring a further third lepton;\n\u2022 after all cuts, including the jet veto;\nare studied.\nWe have identi\ufb01ed two single-lepton triggers, labelled L2 e22i and L2 mu20, that are well-suited for\nthe tri-lepton analysis at L = 1031\u221232 cm\u22122s\u22121. At high luminosity it is planned to have corresponding\ntriggers with additional isolation criteria (e22i tight and mu20i) which will remain unprescaled. The\nresulting event-triggering ef\ufb01ciencies are listed in Table 8. OR-combined, they have \u224892% probability\nfor direct gaugino production for the benchmark point SU2. They have suf\ufb01ciently high pT thresholds\nto be easily studied with leptonic Z decays.\nThe same trigger set was studied for the direct gaugino and inclusive SUSY for another bechmark\npoint, SU3, that has lighter squarks than SU2. Again the OR-combination of L2 e22i and L2 mu20\nshows a good performance of \u223c92, 95, 94%. Their individual L2 event ef\ufb01ciencies are summarised in\nthe middle block of Table 8.\nIn addition we have studied the performance of the L2 e22i and L2 mu20 triggers for the tri-lepton\nanalysis, outside of the heavy coloured sparton scenario, for inclusive SU3 production. Again in this\ncase we \ufb01nd L2 event ef\ufb01ciencies of around \u223c94, 98, 97%.\nThe ef\ufb01ciency is relatively high for lepton triggers even though the trigger thresholds are fairly high\ncompared to the of\ufb02ine cuts on lepton transverse momenta. The reason for that is simple combinatorics:\nsince the 3 leptons are ordered by their transverse momenta, it is likely that the leading lepton has a high\npT if the third one passes the of\ufb02ine threshold. On the other hand, cases where all the three leptons are\nbelow 20\u221230 GeV but above 10 GeV are unlikely.\nWe have investigated how the leptonic trigger ef\ufb01ciencies for the inclusive SUSY and direct gaugino\nfor the benchmark point SU2 change as a function of the progressive event selection stages described\nin Section 3. In both cases, the trigger ef\ufb01ciencies reach their approximate maxima after the three-\nlepton selection stage. Beyond this cut stage, the ef\ufb01ciency values plateau, indicating that our event\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1654\n\nselection requirements should not bias signal trigger ef\ufb01ciencies. It can be concluded that the L2 e22i and\nL2 mu20 single lepton triggers provide a good performance for the tri-lepton analysis in the early days\nof ATLAS running at L = 1031 cm\u22122s\u22121. Di-leptonic triggers with lower thresholds like 2e12i, 2mu10,\nand e15i mu10 can be used to recover events where all three leptons have low transverse momenta around\n20 GeV.\n6\nSystematic uncertainties\nThe dominant sources of systematic uncertainty for this search are different to other SUSY search chan-\nnels that focus on \ufb01nal states containing jets. For our multi-lepton search the main sources of uncertainty\nin the backgrounds are described below.\n6.1\nBackground rates\nThe production rates for the majority of background processes such as diboson production and t \u00aft are\nknown at the parton level at better than next-to-leading order. However, it is generally better to deter-\nmine the rate of these backgrounds from the ATLAS data themselves, reducing any uncertainty from\nluminosity, PDFs and other systematics (e.g. from acceptances, ef\ufb01ciencies etc). The background rate\nmeasurements should be made in \u201ccontrol regions\u201d in which they dominate. For the WZ background a\nsensible control region is the region of phase space where the OSSF lepton pair has an invariant mass\nnear the mZ [12]. For the t\u00aft background, one would examine single lepton and OSSF dilepton chan-\nnels [13]. Any statistical uncertainty in the background measurements forms a systematic uncertainty\nin our analysis. The expected integrated luminosities for cleanly measuring each background and the\nresulting statistical uncertainties can be found in Table 9.\nAny further systematic uncertainties in the background rates are not considered here so as not to\ndouble-counting their effects8. One must be careful that the extrapolation from the \u2018control\u2019 to the\n\u2018measurement\u2019 region of parameter space is well understood. The extrapolation for the backgrounds\ninvolving the Z peak relies on the Z line-shape, which is theoretically well-known. The extrapolation\nfrom dilepton to trilepton \ufb01nal states for t\u00aft relies on a good knowledge of the rate at which b quarks\n(from top decays) produce isolated leptons. A method of determining this rate from the ATLAS data is\npresented in Section 6.3.\nTable 9: Expected rates to cleanly select background samples in control regions, and the corresponding\nstatistical uncertainties.\nBackground\nStatistical uncertainty\nReference\nafter 10 fb\u22121 [%]\nWW\n1.3\n[12]\nWZ\n2.6\n[12]\nZZ\n6.6\n[12]\nt\u00aft\n\u226a1\n[13]\nOne can see from Table 6 that, after event selection and jet veto, the WZ and t\u00aft backgrounds are most\nsigni\ufb01cant in the signal region. The systematic uncertainty in measuring the rate of the backgrounds in\n8In fact, uncertainties on background rates that positively correlate between the selection region and the control region will\nactually tend to cancel.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1655\n\nthe control regions is expected to be of the order of a few percent maximum for the WZ and even smaller\nfor the t\u00aft (Table 9). Our estimate for the total systematic uncertainty due to statistical \ufb02uctuations in\nthe background control sample is therefore dominated by the WZ background. When multiplied by the\nfraction of the \ufb01nal background that comes from WZ, this generates 1.9% (0.8%) uncertainty in the\nbackground rate for the analysis with (without) the jet veto.\n6.2\nTrigger and reconstruction ef\ufb01ciencies\nLepton trigger and reconstruction ef\ufb01ciencies can be determined using the \u201ctag-and-probe\u201d method for\nelectrons and muons coming from Z \u2192\u2113\u2113[7].\nTable 10: Expected systematic uncertainties on background rates from other ATLAS measurements using\nthe tag-and-probe method, and resultant estimated uncertainties for this analysis. The label \u2018reco\u2019 refers\nto combined reconstruction and selection ef\ufb01ciencies.\nSource\nTag-and-probe [7]\nThis analysis (10 fb\u22121)\n(1\u2113\u00b1, 1fb\u22121)\n1\u2113\u00b1\n3\u2113\u00b1\ne (trigger)\n\u226a1%\n\t\n0.5 %\n\uf8fc\n\uf8fd\n\uf8fe2.3%\n\u00b5 (trigger)\n0.4 %\ne (reco)\n0.5 %\n1 %\n\u00b5 (reco)\n\u226a1%\n\u226a1%\nThe precision with which lepton trigger and reconstruction ef\ufb01ciency can be determined has been\nstudied in [7] for an integrated luminosity scaled to 1 fb\u22121. The statistical uncertainty on the trigger\nef\ufb01ciency for 1 fb\u22121 is very small (\u226a1%) and is negligible for 10 fb\u22121. The systematic uncertainties\nin determining the trigger ef\ufb01ciencies are shown in Table 10. The trigger ef\ufb01ciency uncertainty for our\nanalysis, for which the highest-pT lepton has similar kinematics to the sample used in [7], is therefore\nestimated to be <\u223c0.5% for\nRdt L = 10 fb\u22121.\nReconstruction and selection ef\ufb01ciencies have also been studied using a similar method [7]. The\nestimates of the uncertainties in the ef\ufb01ciencies are also contained in Table 10. We have increased the\nexpected uncertainty in the electron reconstruction ef\ufb01ciency from the \u201ctag-and-probe\u201d value of 0.5% to\nour own estimate of 1% to re\ufb02ect a somewhat larger uncertainty for our lower pT electrons.\nIn the \ufb01nal column of Table 10 we estimate the resulting systematic uncertainty for the trilepton\nselection ef\ufb01ciency of this analysis. Since we propose using single lepton triggers (Section 5), only\nthe highest pT lepton contributes, and our event trigger uncertainties are the same as the single-lepton\ntrigger ones. All three leptons are assumed to contribute to reconstruction and selection uncertainties,\nwith equal contributions from electrons and muons. Our resulting uncertainty from combined trigger,\nreconstruction and selection ef\ufb01ciencies is 2.3%.\nFor this study we assume that similar uncertainties will apply with and without the jet veto, but we\nnote that there may be larger systematic uncertainties in lepton ef\ufb01ciencies if jets are permitted in the\n\ufb01nal state.\n6.3\nLepton fake rates\nThe t\u00aft\nand Z + b backgrounds contribute to the trilepton \ufb01nal state when (along with a lepton pair\nfrom dileptonic t\u00aft decay or Z decay) a B hadron decays leptonically, producing a third isolated lepton.\nThe third lepton requirement reduces each of these backgrounds by a large factor \u2013 about two orders\nof magnitude in each case. About one order of magnitude of reduction can be accounted for by the\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1656\n\nbranching ratio of B hadrons to leptons, while the other factor of about ten arises from our rejection\nof non-isolated leptons. We are therefore sensitive to the rate at which leptons from b decays pass the\nisolation criteria, which we denote Rb\u2192\u2113(it should be understood to include leptons both from direct\nb \u2192\u2113and also from b \u2192c \u2192\u2113).\nWe hereby propose a method by which Rb\u2192\u2113could be measured in the ATLAS data, and estimate\nthe remaining systematic uncertainty after that measurement. The control sample we suggest is semi-\nleptonic t\u00aft decays in which a lepton from one (probe) b decay generates a same-sign dilepton pair. To\ncleanly select the control sample we would require events with t\u00aft kinematics (e.g. consistent invariant\nmasses for t and W) and one clean vertex tag from the other (probe) b jet. This sample has the further\nadvantage that the b quarks have the correct kinematical distributions for the background of interest\n(dileptonic t\u00aft ). The same-sign dilepton requirement removes contamination from normal dileptonic t\u00aft\ndecays since the latter will produce opposite-sign lepton pairs.\nDedicated studies [13] suggest that we can expect to cleanly select about nt\u00aft\u2212>\u2113= 5 \u00d7 104 semi-\nleptonic t\u00aft events (e and \u00b5 combined) for\nRdt L =10 fb\u22121. The fractional statistical uncertainty, \u03b4, that\nwe could expect from the proposed measurement of Rb\u2192\u2113is then,\n\u03b4(Rb\u2192\u2113) =\n1\n\u221aRb\u2192\u2113\u00d7nt\u00aft\u2212>\u2113\n.\n(6)\nFrom examination of the event record in our Monte Carlo samples, we found Rb\u2192\u2113to be approximately\n5\u00d710\u22123. If a similar rate were to be found from measurements of the semi-leptonic t\u00aft events, then the\ncorresponding value for \u03b4(Rb\u2192\u2113) would be 6%.\nWith a jet veto, t\u00aft forms about 20% of the background after full selection (and Z + b a very small\ncontribution), and there is a resulting \u22481.2% uncertainty in the total background. Without the jet veto,\nthe t\u00aft contribution is much larger (about 66%) and a 4% systematic uncertainty results.\n6.4\nJet and missing energy scales\nThe global uncertainty on the jet energy scale is currently conservatively expected to be about 5%, but\nthe true value is dif\ufb01cult to determine without collision data. In events in which the missing transverse\nmomentum is dominated by hadronic activity, the fractional uncertainty in Emiss\nT\nwill be of a similar\nsize, since the two measurements will be highly correlated. We therefore determined the effect of a 5%\nsystematic uncertainty in the missing energy when no jet veto is used.\nFor the analysis which includes a jet veto, we expect missing energy scale uncertainty to be rather\nsmaller than 5%, since the majority of the missing energy will recoil against the (well-measured) leptons.\nWe also assume that in this case the systematic uncertainties in the jet energy scale and the missing energy\nshould also be largely uncorrelated (for the same reason). Measurements of recoil of jets against Z bosons\nand photons allow the missing energy resolution to be well-determined as a function of jet energy [8].\nAny residual uncertainty in the missing energy scale is estimated by us to be about 2% at low hadronic\nenergies (based on systematic differences between methods in [8]).\nFor the jet-veto analysis, we determined the effects of a 5% variation in the hadronic energy scale\nand (an independent) 2% variation in the missing energy scale. The results are shown along with the\nsystematic uncertainties from other sources in Table 11.\nAs well as the uncertainty from the energy scales, there can be some contribution to the uncertainty\nin the number of events failing the jet veto from our lack of knowledge of initial-state radiation (ISR) in\nelectro-weak processes (such as WZ production). However the ISR spectrum can be readily determined\nfrom other electroweak production control regions (as described in [14] for single electroweak gauge\nboson production). The resulting statistical uncertainties in those control measurements will be small,\nand the systematic effects tend to cancel with those described in this section, so no additional systematic\nuncertainty is added here.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1657\n\n6.5\nSummary of systematic uncertainties\nTable 11: Estimates of the dominant uncertainties in the background determination for\nRdt L = 10 fb\u22121.\nSource\nUncertainty\nNo jet veto\nWith jet veto\nBackground production rates\n0.8%\n1.9%\nLepton Ef\ufb01ciency\n2.3%\n2.3%\nFakes (Rb\u2192\u2113)\n4.0%\n1.2%\nHadronic energy scale\n\u2013\n1.8%\nMissing energy scale\n1.5%\n1.0%\nTotal systematic\n4.9%\n3.8%\nStatistical\n3.7%\n6.9%\nStatistical + Systematic\n6.2%\n7.9%\nOur best current estimates of the various sources of uncertainty are summarised in Table 11. One can\nsee that with the full selection, including the jet veto, and if the supporting measurements can be made\nwith the precision expected, then the SUSY-search analysis will be limited by statistical \ufb02uctuations in\nthe background samples (about 6.9%) rather than by systematic sources of uncertainty (about 3.8%).\nWithout the jet veto, the statistical uncertainty is smaller, however the systematic contribution to the\ntotal uncertainty increases to 4.9%, largely because we have an increased sensitivity to Rb\u2192\u2113since the\ntop background is much larger if no jet veto is applied.\n7\nConclusions\nThe ATLAS experiment will have sensitivity to new physics, including supersymmetry, in events with\nthree leptons in association with missing transverse momentum. For most of the SUSY benchmark\npoints studied, a discovery of new physics could be made in this channel with integrated luminosity of\nseveral fb\u22121 . Models in which all strongly interacting partner particles are heavy would have smaller\ncross-sections, but could also be discovered with integrated luminosity of the order of several tens of\nfb\u22121 .\nThe major sources of systematic uncertainty were indicated and methods for determining these from\ndata discussed. While the actual sizes of these uncertainties can only be estimated reliably with collision\ndata, estimates based on existing information were presented. In particular, knowledge of the rate at\nwhich which b jets lead to seemingly-isolated leptons was found to be an important element in under-\nstanding Standard Model backgrounds. A method of measuring this rate from the data using t\u00aft events\nwas proposed.\nReferences\n[1] ATLAS Collaboration, Supersymmetry Searches, this volume.\n[2] ATLAS Collaboration, Prospects for Supersymmetry Discovery Based on Inclusive Searches, this\nvolume.\n[3] U. De Sanctis, T. Lari, S. Montesano and C. Troncon, Eur. Phys. J. C52 (2007) 743\u2013758.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1658\n\n[4] F. Paige, S. Protopopescu, H. Baer and X. Tata, ISAJET 7.69: A Monte Carlo event generator for p\np, anti-p p, and e+ e- reactions hep-ph/0312045, 2003.\n[5] ATLAS Collaboration, Muon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples, this volume.\n[6] ATLAS Collaboration, Reconstruction and Identi\ufb01cation of Electrons, this volume.\n[7] ATLAS Collaboration, Electroweak Boson Cross-Section Measurements, this volume.\n[8] ATLAS Collaboration, Measurement of Missing Tranverse Energy, this volume.\n[9] ATLAS Collaboration, Jet Reconstruction Performance, this volume.\n[10] ATLAS Collaboration, Physics Performance Studies and Strategy of the Electron and Photon Trig-\nger Selection, this volume.\n[11] ATLAS Collaboration, Performance of the Muon Trigger Slice with Simulated Data, this volume.\n[12] ATLAS Collaboration, Diboson Physics Studies, this volume.\n[13] ATLAS Collaboration, Determination of the Top Quark Pair Production Cross-Section, this vol-\nume.\n[14] ATLAS Collaboration, Production of Jets in Association with Z Bosons, this volume.\nSUPERSYMMETRY \u2013 MULTI-LEPTON SUPERSYMMETRY SEARCHES\n1659\n\nSupersymmetry Signatures with High-pT Photons or\nLong-Lived Heavy Particles\nAbstract\nIn certain Supersymmetry breaking scenarios, characteristic signatures can be\nexpected which would not necessarily be found in generic SUSY searches for\nevents containing high pT multi-jets and large missing transverse energy. This\npaper describes the expected response of the ATLAS detector to four signa-\ntures: high-pT photons which may or may not appear to point back to the\nprimary collision vertex and long-lived charged sleptons and R hadrons. Such\nprocesses often have the advantage of small Standard Model backgrounds\nand their observation could provide unique constraints on the different SUSY\nbreaking scenarios. Using these signatures discovery potentials are estimated\nfor either Gauge-Mediated Supersymmetry Breaking or Split-Supersymmetry\nscenarios. Using Monte Carlo samples of SUSY and background processes\ncorresponding to integrated luminosity of about 1 fb\u22121 we study all aspects\nof the analysis, including the expected trigger response and of\ufb02ine data recon-\nstruction.\n1\nIntroduction\nSupersymmetry (SUSY) is one of the most widely investigated theories of physics beyond the Standard\nModel [1\u20134]. Searches for signatures of new physics processes predicted within SUSY models are thus\ncentral to the physics program of the ATLAS experiment [5], which will be sensitive to the production\nof SUSY particles with masses up to several TeV [6]. To facilitate the exploitation of early LHC data,\na number of preparatory studies have been undertaken by the ATLAS SUSY group to estimate the re-\nsponse of the ATLAS detector to a variety of physics processes and to optimise and test the software\nwhich is necessary for the analysis of collider data. As a part of this exercise, the ATLAS SUSY group\nhas performed a number of studies. Techniques to estimate Standard Model backgrounds have been de-\nveloped [7, 8] and calculations have been made of the discovery potential for generic inclusive SUSY\nsignatures [9], based largely on the minimal SUGRA model [10\u201314] for which the principal observables\nare high-pT jets and missing transverse energy. However, there exist a number of SUSY scenarios which\npredict speci\ufb01c \ufb01nal state topologies which may not be observed by generic searches, such as prompt\nphotons and long-lived stable massive particles. In this work, the response of the ATLAS detector to\nsuch signatures is studied and, where appropriate, calculations are made of discovery potentials for early\nLHC running for which an integrated luminosity of around 1 fb\u22121 is assumed. Although the work is\nperformed within the framework of SUSY searches, the techniques which have been developed are more\ngenerally applicable to searches for new phenomena.\nThe theoretical models used in this work are based on the minimal Gauge Mediated Supersymmetry\nBreaking (GMSB) model [6,15\u201321] , the Split-SUSY model [22\u201325] and the gravitino LSP model [26].\nA description of the models is given in Section 2.1 while speci\ufb01c choices of parameters are found in the\nsections devoted to each of the studied signatures. Four signatures are investigated and are described\nbelow.\nTwo high-pT photons + Emiss\nT\n: In a GMSB scenario in which the next lightest supersymmetric particle\n(NLSP) is the \u02dc\u03c70\n1 , two high-pT photons are expected in each signal event each arising from the decay\nof a \u02dc\u03c70\n1\nto a \u02dcG and photon. Such events with two isolated high-pT photons plus large Emiss\nT\nhave\nsmall Standard Model backgrounds and a high mass discovery reach is expected even in the early LHC\n1660\n\nrunning. In the high mass regime, however, the production cross-section for SUSY events and the signal\nis of the same order as the instrumental background which includes misidenti\ufb01ed photons arising from\nelectrons or jets, and the irreducible background of radiation from leptons. Earlier experiments have\nexclusions limits of 93 GeV in \u02dc\u03c70\n1 mass and 167 GeV in \u02dc\u03c7\u00b1\n1\nmass [27].\nNon-pointing photons: In certain GMSB scenarios, the \u02dc\u03c70\n1 could be relatively long-lived. When the\ndecay length is comparable to the size of ATLAS inner-detector, high-pT photons could enter the elec-\ntromagnetic calorimeter surface at large incident angles with respect to a pointing direction to the beam\ninteraction point. An estimation of how the photon reconstruction and identi\ufb01cation ef\ufb01ciency is de-\ngraded for such non-pointing photons is essential in any measurement of the \u02dc\u03c70\n1 lifetime, which is di-\nrectly connected to the SUSY breaking scale. Current lower limits on the mass and lifetime are 101 GeV\nand 5 ns, respectively [28].\nStable sleptons: Stable1 heavy charged sleptons appear in certain regions of parameter space in GMSB\nscenarios. This signature consists of a penetrating charged track. Since interactions with detectors are\nionizations only, the observed tracks will look more like muons, except for their higher energy deposition\nand longer time of \ufb02ight than muons. The ATLAS muon system provides a time of \ufb02ight measurement\nwith an excellent time resolution (\u03c3to f \u22480.7ns) [29], which allows for a precise particle mass mea-\nsurements for slow particles. Owing to the very high LHC bunch crossing rate, the development of an\nappropriate triggering scheme is critical to the ensuring the detection of such particles. Previous experi-\nments have provided a lower limit of around 105 GeV in slepton mass [30]\nStable R hadrons: Stable massive supersymmetric hadrons (R hadrons) are predicted in Split-SUSY\nmodels or in the gravitino LSP scenario of SUGRA models [26]. The signature of R hadrons is sim-\nilar to that of stable sleptons although multiple nuclear interactions before reaching the muon system\nlead to characteristic event topologies, such as the appearence of high-pT tracks in the muon system\nwith no matching track in the inner-detector, or the electric charge \ufb02ipping between the inner-detector\nand the muon system. Lower mass limits of around 200 GeV have already been established by other\nexperiments [31].\nThis paper is organized as follows. Section 2 provides an overview of the different models and a\ndescription of the Monte Carlo datasets which were used in this work. Sections 3-6 describe the studies\nof signatures described above. Finally, a conclusion is given in Section 7.\n2\nOverview of the SUSY models and Monte Carlo datasets\nThe signal Monte Carlo data samples used in this paper are based on the speci\ufb01c supersymetry breaking\nscenarios. These models are described in Section 2.1. Some technical details and parameter values used\nin individual datasets are summarized in Section 2.2. Common background samples are used which\nare described in the introduction to this chapter [32]. In some cases, fast simulation (ATLFAST-I [33])\nsamples are also used when estimating the background contributions.\n2.1\nSUSY scenarios considered in this paper\n\u2022 GMSB (Gauge-Mediated Supersymmetry Breaking) scenarios: in GMSB, SUSY breaking which\ntakes place in hidden sector is transmitted to visible MSSM \ufb01elds through a messenger sector\nwhose mass scale is much below the Planck scale (Mm \u226aMP) via the ordinary Standard Model\ngauge interactions. The gravitino is very light (in general \u226a1 GeV) and is always the LSP. In\nthe minimal model of GMSB, all Supersymmetry breaking interactions are determined by a few\n1The term stable is used throughout this chapter to refer to particles which, although they may possess \ufb01nite lifetimes, do\nnot decay during their traversal of the ATLAS detector.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1661\n\nparameters. The phenomenologies studied in this paper are based on this minimal model. Discus-\nsions of the non-minimal GMSB models are found elsewhere [34,35].\nThe squarks, the sleptons, and the gauginos obtain their masses radiatively from the gauge inter-\nactions with the massive messengers; their masses therefore depend on the number of messenger\ngenerations, N5 (the index 5 comes from the fact that the messenger \ufb01elds form complete SU(5)\nrepresentations).\nThe gaugino masses scale like N5 while the scalar masses scale like \u221aN5. Hence for N5 = 1, the\nNLSP is the lightest neutralino ( \u02dc\u03c70\n1 ) which decays into photon and a gravitino ( \u02dcG ). For N5 \u22652,\nthe NLSP is a charged stau ( \u02dc\u03c41). When tan\u03b2 is not too large, the mass splitting between the \u02dc\u03c41\nand the right-handed selectrons, smuons (\u02dceR, \u02dc\u00b5R) is small, rendering them co-NLSP\u2019s which decay\ninto leptons and gravitinos. In contrast, in the large tan\u03b2 region, the stau is the sole NLSP.\nThe effective SUSY breaking order parameter FS, felt by the messengers, may not coincide with the\nintrinsic underlying SUSY breaking order parameter F, which determines the coupling strength.\nWhen FS is smaller, the NLSP decay length becomes longer. The dimensionless factor CG =\nF/FS(\u22651) is introduced to control the NLSP decay length with all the other parameters \ufb01xed. The\ndecay length is proportional to the square of the control parameter, i.e. scales as C2\nG.\nThe effective visible sector SUSY breaking parameter, \u039b(= FS/Mm) sets the overall mass scale for\nall the MSSM superpartners, which scales linearly with \u039b. On the other hand, these masses only\ndepend logarithmically on the messenger scale Mm. The MSSM masses are therefore predomi-\nnantly determined by the scale \u039b.\n\u2022 Split-SUSY scenario: Stable exotic hadrons feature in a number of SUSY scenarios. Split-SUSY is\none such model. Within this approach the hierarchy problem and the \ufb01ne tuning of the Higgs mass\nis accepted, or assumed to be set by another, as yet unknown, mechanism. Phenomenologically,\nwithin Split-SUSY scenarios the gauginos and higgsinos have light masses of order the weak\nscale, which are protected by the chiral symmetry while the scalars have a mass scale ms which\ncan be near the GUT scale. Since gluino decays proceed via internal squark lines, gluinos can be\nmeta-stable. A meta-stable gluino will form a bound state, a so-called R \u02dcg-hadron.\n\u2022 A gravitino LSP and a stop NLSP scenario: in addition to stable gluinos, meta-stable stops are also\nfeatures of some SUSY models. Here, the stops are usually the NLSP and decay to a gravitino LSP\nwith gravitational strength interactions. The generic possible candidate for NLSP is the lightest\nstop \u02dct1, which, like the gluino case in split SUSY scenario, would form stable bound states, denoted\nR\u02dct.\n2.2\nParameter values used in this work\nThe basic feature of the samples used in this paper are similar to those introduced in [32]. However,\nour studies also investigate sparticles which decay with a measurable decay length, and new techniques\nhave been introduced to allow these to be simulated. As in Ref. [32], ISAJET7.74 [36] was used to\ngenerate the sparticle mass spectrum in the context of minimal GMSB scenarios. The leading order (LO)\nand the next-to-leading order (NLO) cross-sections were assessed independently using PROSPINO2.0\n[37\u201339]. The mass spectrum tables from ISAJET were used by HERWIG/JIMMY [40,41] to generate\nthe sparticle cascade decays, parton showers, hadronisations, and underlying events. The HERWIG\noption pltcut (lifetime threshold above which the Herwig does not decay the particles) was set to 3.3 \u00d7\n10\u221211 s, hence sparticles with \ufb01nite decay length are not decayed at event generator level2. In the detector\n2the value is set in order not to decay K0 and \u039b at event generator level, but at detector simulation level.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1662\n\nTable 1: Summary of the neutralino NLSP samples. Dataset GMSB1 is a prompt photon decay sample,\nwhile dataset GMSB2 and GMSB3 are the non-pointing photon samples. N5 = 1,tan\u03b2 = 5,sgn(\u00b5) = +\nare used at each point.\nname\nNLO (LO) \u03c3 [pb]\n\u039b [TeV]\nMm [TeV]\nCG\nc\u03c4 [mm]\nM \u02dc\u03c70\n1 [GeV]\nGMSB1\n7.8 (5.1)\n90\n500\n1.0\n1.1\n118.8\nGMSB2\n7.8 (5.1)\n90\n500\n30.0\n9.5\u00b7102\n118.8\nGMSB3\n7.8 (5.1)\n90\n500\n55.0\n3.2\u00b7103\n118.8\nTable 2: Summary of the slepton NLSP sample. N5 = 3,tan\u03b2 = 5,sgn(\u00b5) = +, and no decay of slepton\nis assumed.\nname\nNLO (LO) \u03c3 [pb]\n\u039b [TeV]\nMm [TeV]\nM\u02dc\u03c41 [GeV]\nGMSB5\n21.0 (15.5)\n30\n250\n102.3\nTable 3: R-hadron samples. Dataset R-Hadron1 \u2013 R-Hadron6 are the R \u02dcg samples, while dataset R-\nHadron7 \u2013 R-Hadron9 are the R\u02dct samples.\nname\nNLO (LO) cross-section [pb]\nsparticle\nMass [GeV]\nR-Hadron1\n567 (335)\n\u02dcg\n300\nR-Hadron2\n12.2 (6.9)\n\u02dcg\n600\nR-Hadron3\n0.43 (0.23)\n\u02dcg\n1000\nR-Hadron4\n0.063 (0.033)\n\u02dcg\n1300\nR-Hadron5\n0.011 (0.006)\n\u02dcg\n1600\nR-Hadron6\n0.0014 (0.00075)\n\u02dcg\n2000\nR-Hadron7\n11.4 (7.8)\n\u02dct\n300\nR-Hadron8\n0.27 (0.18)\n\u02dct\n600\nR-Hadron9\n0.010 (0.0064)\n\u02dct\n900\nsimulation phase, the \u02dc\u03c70\n1 decaying into \u02dcG and \u03b3, decay length was passed to the ATLAS interface to\nGEANT4 and the sleptons ( \u02dc\u03c41, \u02dceR and \u02dc\u00b5R), interaction with detector materials, i.e. ionization loss was\nimplemented.\nIn R-hadrons scenarios, the masses of the stable sparticles (M \u02dcg,M\u02dct) fully determine the phenomenol-\nogy and other supersymmetric parameters (other sparticle masses) do not enter into any calculation. The\ngenerated samples are therefore highly model independent, and the only parameter that varies is the mass\nof the stable sparticle.\nTables 1-2 summarize the properties of the Monte Carlo signal samples used in this note. Tables\n1 and 2 describe the GMSB samples with a neutralino or slepton NLSP, respectively, while Table 3\nsummarizes the R-hadron samples.\n3\nDiscovery potential of GMSB SUSY with photon signatures\nIn GMSB models with N5 = 1 and low tan\u03b2 the lightest neutralino e\u03c70\n1 is the NLSP and decays to a grav-\nitino eG and, in scenarios where the neutralino is mainly a photino, to a photon. Therefore the standard\nSUSY decay cascade of squarks and gluinos is extended by the decay e\u03c70\n1 \u2192\u03b3 eG, as shown in Figure 1.\nDepending on the branching ratios of the squarks and gluinos decaying to various types of SUSY parti-\ncles, this decay chain may also contain multiple jets. Events with two high energy photons are expected\nin pp collisions, if the NLSP lifetime is not too long (Cgrav \u223c1). These photons originate close to the\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1663\n\n\u02dc\u03c702\n\u02dcl\n\u02dc\u03c701\n\u02dcg, \u02dcq\nl\nl\njet\n\u03b3\n\u02dcG\n1\nFigure 1: Typical SUSY decay chain for a neutralino NLSP decaying to a photon and a gravitino.\nprimary interaction vertex (\u201cprompt photons\u201d). The corresponding event signatures and the discovery\npotential for these models are discussed in this section. The case of large Cgrav and therefore long lived\nneutralinos, resulting in non-pointing photons, is discussed in Section 3.3. For detailed reconstruction\nand trigger studies we consider the GMSB1 model point as a typical example (see Table 1). For this\npoint the branching ratio of the decay of the lightest neutralino to a photon and a gravitino is \u223c97%, and\nthe total SUSY production cross-section is \u223c7.8pb.\nIn the following we discuss the optimisation of the signal selection, including the trigger selection,\nthe expected background from Standard Model processes and a detailed study of the discovery potential\nwith early data. Since for the latter a fast simulation approach is used, a comparison of fast and full\nsimulation results is also presented.\n3.1\nGMSB1 full simulation studies\n3.1.1\nSignal trigger strategy\nThe signal events studied here possess the standard SUSY event properties at the LHC: large E miss\nT\nand\nmultiple jets with high pT. These can be used for triggering the events. In addition, the feature of two\nhigh energy photons gives an additional way to trigger on these events independently of Emiss\nT\nand jet\ntriggers. In the following we consider two different trigger menus:\n\u2022 The \ufb01rst menu is the ATLAS initial menu foreseen for data-taking at a luminosity of 1031 cm\u22122s\u22121\n[42]. This menu includes various combinations of jet (J) and Emiss\nT\ntriggers (XE) and photon\ntriggers (EM) as shown in Table 4. No prescale values are foreseen for these triggers, whereas\nthe selection of the EM100 trigger is based entirely on the Level-1 (L1) trigger, with no selections\nenvisaged at the Level-2 (L2) trigger or in the event \ufb01lter. In the following, the trigger ef\ufb01ciency is\nde\ufb01ned as the ratio of the number of events without any preselection passing a trigger item divided\n[GeV]\n1\n\u03b3\nT,\np\n0\n50\n100\n150\n200\nEfficiency\n0\n0.5\n1\nATLAS\ng55 EF trigger efficiency\n spectrum\nT\nLeading photon p\nFigure 2: The g55 event \ufb01lter trigger ef\ufb01ciency (see text) for the GMSB1 sample as a function of the\nreconstructed pT of the leading photon.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1664\n\nby the total number of events. The total ef\ufb01ciencies for the L1 trigger for the various triggers of\nthis initial menu are summarised in Table 4. It can be seen, that in addition to the standard SUSY\ntriggers based on jets and Emiss\nT\n, the photon triggers have very high ef\ufb01ciencies for selecting\nGMSB1 events and can be used for initial running.\n\u2022 The second menu investigated here is the standard ATLAS trigger menu foreseen for the stable\nrunning at a luminosity of L = 1033 cm\u22122s\u22121. In this menu all three trigger levels are used in the\nselection. The triggers investigated are combinations of jet (j), Emiss\nT\n(xE) and photon (g) signa-\ntures, see Table 5. Again, no prescale values are foreseen for these items. The trigger ef\ufb01ciencies\nfor the signal at L1, L2 and event \ufb01lter are summarised in Table 5, where the L2 and event \ufb01lter\nef\ufb01ciencies also contain the ef\ufb01ciencies of the previous levels. It can be seen that for both of the\nplanned running phases the photon triggers are as ef\ufb01cient as the Emiss\nT\nand jet triggers for the\ncase of GMSB1 signal events. The ef\ufb01ciency for the g55 photon trigger after the event \ufb01lter as a\nfunction of the reconstructed pT of the leading photon is shown in Figure 2. As expected, after a\nsteep turn on around 55 GeV a plateau is reached. The integrated ef\ufb01ciency above the threshold of\n55 GeV is \u223c98%.\nTable 4: Trigger ef\ufb01ciencies and statistical errors for the GMSB1 event sample for (L = 1031 cm\u22122s\u22121).\nTrigger item\nEf\ufb01ciency\nTrigger item\nEf\ufb01ciency\n2EM13\n98.71 \u00b1 0.11\nXE70\n81.39 \u00b1 0.39\nEM100\n83.00 \u00b1 0.38\nJ70+XE30\n93.64 \u00b1 0.25\nEM18+XE15\n98.79 \u00b1 0.12\n2J42+XE30\n93.98 \u00b1 0.24\nJ100\n91.43 \u00b1 0.28\n4J23\n92.27 \u00b1 0.27\nTable 5: Trigger ef\ufb01ciencies and statistical errors for the GMSB1 event sample for (L = 1033 cm\u22122s\u22121).\nTrigger item\nL1\nL1+L2\nL1+L2+EF\ng55\n97.18\u00b10.60\n84.47\u00b11.32\n80.47\u00b11.44\n2g17i\n71.13\u00b11.65\n55.07\u00b11.81\n47.91\u00b11.81\nj65+xE70\n80.66\u00b10.40\n80.63\u00b10.40\n69.53\u00b10.46\n3j65\n83.63\u00b10.37\n83.55\u00b10.37\n83.37\u00b10.37\nIn summary it can be said that in the GMSB1 scenario the use of photon triggers is possible for initial\nrunning conditions, as well as at a higher luminosity. The ef\ufb01ciencies are as high as for the triggers based\non jets and Emiss\nT\nand can thus provide good redundancy.\n3.1.2\nSignal selection\nAt the benchmark point GMSB1, 48.9% (16.4%) of the signal events have one (two) photons with\npT > 20 GeV in the \ufb01ducial acceptance (|\u03b7| < 2.5) used for photon identi\ufb01cation. For the reconstruction\nof photons a standard cut-based photon selection [43] is used. This is mainly based on variables using\ninformation of the \ufb01rst and second samplings of the electromagnetic calorimeter. The photons are re-\nquired to be isolated and those located in the transition regions between barrel and endcap calorimeters\nare excluded. No track veto is applied. After a full GEANT4 simulation of the ATLAS detector, the\nselection ef\ufb01ciency for photons with pT > 20 GeV is about 65%.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1665\n\nTable 6: ALPGEN Background samples used in this section. The corresponding integrated luminosities\nis shown.\nProcess\nIntegrated luminosity (fb\u22121)\nTop\nleptonic\n\u223c13.4\nsemi-leptonic\n\u223c3.5\nhadronic\n\u223c17.1\nElectroweak\nZ \u2192e+e\u2212\n\u223c4.8\n+ jets\nZ \u2192\u00b5+\u00b5\u2212\n\u223c8.3\nZ \u2192\u03c4+\u03c4\u2212\n\u223c21.6\nZ \u2192\u03bd\u03bd\n\u223c9.1\nW \u2192e\u03bd\n\u223c3.4\nW \u2192\u00b5\u03bd\n\u223c4.7\nW \u2192\u03c4\u03bd\n\u223c3.9\nQCD\nmultiple jet production\n\u223c0.03\nAs background to the signal, events with QCD jets, single gauge boson (W and Z) production and t\u00aft\nproduction are simulated using the ALPGEN generator. The speci\ufb01c processes are listed in Table 6 and\nthe corresponding integrated luminosities are given for each process. In order to separate the signal from\nthe Standard Model background a standard preselection for SUSY-like signatures is \ufb01rst performed:\n\u2022 At least four jets must be found with pT > 50 GeV (pT > 100 GeV for the leading jet).\n\u2022 Missing transverse energy Emiss\nT\n> 100 GeV and Emiss\nT\n> 20%\u00b7Meff, where the effective mass Meff\nis de\ufb01ned as the scalar sum of Emiss\nT\nand the transverse momenta of the four leading jets.\n [GeV]\nmiss\nT\nE\n0\n500\n1000\n]\n-1\nNumber of events [1 fb\n1\n10\n2\n10\n3\n10\n4\n10\n [GeV]\nmiss\nT\nE\n0\n500\n1000\n]\n-1\nNumber of events [1 fb\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nGMSB1\nZ\nW\ntt\nJets\n [GeV]\neff\nM\n0\n500\n1000\n1500\n2000\n]\n-1\nNumber of events [1 fb\n10\n2\n10\n3\n10\n [GeV]\neff\nM\n0\n500\n1000\n1500\n2000\n]\n-1\nNumber of events [1 fb\n10\n2\n10\n3\n10\nATLAS\nGMSB1\nZ\nW\ntt\nJets\nFigure 3: Distributions after preselection for 1fb\u22121. Left: Missing transverse energy. Right: Effective\nmass for signal and Standard Model background.\nThe distributions of Emiss\nT\nand Meff after this selection are shown in Figure 3 for the Standard Model\nbackground (histograms) and the signal (open symbols) for an integrated luminosity of 1 fb\u22121. No large\nexcess of events is seen over the Standard Model background. However, as shown in Figure 4, a cut\non the number of reconstructed photons with pT > 20 GeV and |\u03b7| < 2.5 provides an effective way to\nfurther suppress the backgrounds. Figure 3.1.2 shows the pT distribution of the leading photon after\nthe initial preselection. Table 7 shows the number of selected events for signal (S) and background (B)\nafter requiring 0, 1 or 2 photons passing the cuts described above and either the g55 or the 2g17i trigger.\nThis combination of triggers has a combined ef\ufb01ciency for the signal of \u223c85% (\u223c99%) before (after)\napplying these selection cuts. The number of events is normalized to an integrated luminosity of 1fb\u22121.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1666\n\nIn addition, the signal signi\ufb01cance de\ufb01ned as Sig = S/\n\u221a\nB is given in the table. In the calculation of Sig\nit is assumed, that there is at least one background event left. With the requirement of two high-energy\nphotons the selection is mainly free from Standard Model background and the signi\ufb01cance becomes very\nlarge.\nIn addition to the selection criteria listed above, checks were made to see weather a better signal\nsigni\ufb01cance can be achieved by requiring an opposite sign same \ufb02avour (OSSF) lepton pair, which orig-\ninates in the squark/gluino decay cascade from a e\u03c70\n2 to e\u03c70\n1 decay via a slepton, as depicted in Figure 1.\nHere, only electrons and muons are accepted as leptons. The requirement of at least one OSSF lepton\npair reduces the number of selected signal and background events. The suppression factor for the signal\nfor the combination of one photon and one OSSF pair is larger than for the combination of two photons.\nHence, although the background is reduced to a very low level, just using the requirement of two photons\ngives the largest signi\ufb01cance. Requiring an OSSF pair in addition to two photons just reduces the signal,\nbecause the background is already very low.\n\u03b3\nN\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n]\n-1\nNumber of events [1 fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n\u03b3\nN\n0\n1\n2\n3\n4\n0\n1\n2\n3\n4\n]\n-1\nNumber of events [1 fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nATLAS\nGMSB1\nZ\nW\ntt\nJets\nFigure 4: Distributions after preselection for 1fb\u22121: Number of reconstructed photons with pT > 20 GeV\nand |\u03b7| < 2.5 (left) and transverse momentum of the leading photon for signal and Standard Model\nbackground. (right)\n3.2\nGMSB parameter scan with fast simulation\nTo investigate the discovery potential of the selection described above, over a wider range of the GMSB\nparameter space, it is necessary to make use of a fast detector simulation to obtain adequate statistics\nfor signal event reconstruction at various points in the parameter space. The computing requirements of\nthe full simulation make it impractical for this study, so for this part of the analysis the fast simulation\npackage ATLFAST [44] has been used instead. ATLFAST performs no detailed simulation of particle\ninteractions with the detector material, but instead parameterizes the detector response. It has two main\nfeatures relevant to the analysis discussed here:\n\u2022 every generated particle is reconstructed.\n\u2022 there is no distinction between electromagnetic and hadronic calorimeter compartments and the\nenergy of a particle is obtained by smearing the energy of the generated particle with a resolution\nfunction. No shower development is simulated.\nNote that ATLFAST does not simulate either reconstruction inef\ufb01ciencies nor particle misidenti\ufb01cation\nfor any particles.\nFigure 5(a) shows the Meff distributions of the GMSB1 event sample for full and fast simulation. In\nthe low energy region a small deviation of the fast simulation with respect to the full simulation can be\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1667\n\nTable 7: Number of selected signal and background events for 1fb\u22121 for different cuts on the number of\nphotons and opposite sign same \ufb02avour (OSSF) lepton pairs.\nN\u03b3\nNOSSF\nSignal\n\u2211Background\nSig\nNW\nNZ\nNt\u00aft\n0\n0\n1287.4\n929.6\n42.3\n274.4\n21.0\n632.8\n0\n1\n283.6\n73.0\n33.2\n8.7\n1.4\n63.0\n1\n0\n902.9\n51.7\n126.1\n19.5\n2.0\n30.1\n1\n1\n189.1\n1.4\n161.4\n0.2\n0.0\n1.2\n2\n0\n252.9\n0.1\n252.9\n0.0\n0.0\n0.1\n2\n1\n37.0\n0.0\n37.0\n0.0\n0.0\n0.0\n [GeV]\neff\nM\n0\n500\n1000\n1500\n2000\n2500\n]\n1\nNumber of events [1 fb\n0\n100\n200\n300\n400\n500\n600\n700\nATLAS\nfull simulation\nfast simulation\n(a)\n [GeV]\n 1\n\u03b3\nT,\np\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n]\n1\nNumber of events [1 fb\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nATLAS\nfull simulation\nfast simulation\nfast simulation corrected\n(b)\nFigure 5: Signal distributions for full and fast simulation: a) effective mass, b) transverse momentum of\nthe leading photon.\nobserved, which is due to a slightly higher jet momentum in ATLFAST in the low energy region. How-\never, of more importance for this analysis is the simulation of the photon identi\ufb01cation and it is important\nthat the fast simulation provides a reliable modelling. The transverse momentum of the leading photon is\nshown in Figure 5(b) for full and fast simulation. It can clearly be seen that some signi\ufb01cant discrepan-\ncies between both simulation approaches exist. This is a result of the photon detection ef\ufb01ciency, which\nis not included in the fast simulation. The fast simulation assumes a 100% detection ef\ufb01ciency for all\ntruth photons which pass a certain isolation criterion. This effect is taken into account in the analysis\nby imposing a realistic reconstruction probability on each photon by hand, depending on the transverse\nmomentum of the photon. The corrected pT distribution is also shown in Figure 5(b).\nIn Table 8 the numbers of selected signal events for full and fast simulation are shown and good\nagreement can be observed after each step of the selection. The level of agreement of the fast simulation\nwith the full simulation is of the order of 10% which is considered to be suf\ufb01cient for a rough estimation\nof the discovery potential via a scan of the GMSB model parameters using ATLFAST.\nTable 8: Number of selected signal events normalised to L = 1fb\u22121 for full and fast simulation for\nGMSB1.\nN\u03b3\nNOSSF\nSignal (full)\nSignal (fast)\n0\n0\n1287.4\n1597.7\n1\n0\n902.9\n1029.5\n2\n0\n252.9\n275.3\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1668\n\nIn order to estimate the selection ef\ufb01ciency and the discovery potential of the two photon chan-\nnel in a more model independent way, a scan of some GMSB model parameters has been performed.\nThe mass spectrum and branching fractions of the different GMSB model points have been calculated\nusing ISASUGRA 7.74 [36]. For each point 12500 signal events have been generated using the HER-\nWIG/JIMMY [40,41]. As discussed above, ATLFAST is used for the detector simulation of the signal\nwith a correction applied to the photon reconstruction ef\ufb01ciency. The estimates for the Standard Model\nbackground are taken from the full simulation as described in Section 3.1.2.\nFor the scan, the SUSY breaking scale parameter \u039b has been varied from 60 to 200 TeV in steps\nof 10 TeV and tan\u03b2 has been varied from 2 to 50 in steps of 2. The other model parameters are \ufb01xed\nto N5 = 1, Mmes = 500 TeV, sgn\u00b5 = +1 and Cgrav = 1, as for the GMSB1 model point. In this part of\nthe parameter space the neutralino is usually the NLSP, which is most often not the case for larger N5\nor larger tan\u03b2. For these regions, other channels need to be used to discover GMSB SUSY. These are\ndiscussed in Section 5. The discovery potential for the case of different Cgrav and hence non-pointing\nphotons is brie\ufb02y discussed in Section 3.3.\nFigure 6 shows the contour lines where the signi\ufb01cance reaches Sig = 5\u03c3 for the default selection cuts\nas described above for different integrated luminosities. Since it is assumed that there is 1 background\nevent left, these contour lines represent the lines with 5 signal events. In the regions below and left of the\nlines a 5\u03c3 discovery can be made with the corresponding amount of data. In the high tan\u03b2 region above\nthe solid line no sensitivity is quoted for the two photon channel, since in this region the \u02dc\u03c4 is the NLSP\nand so no signi\ufb01cant excess of photons is expected from the SUSY decay chains. Due to the fact that the\nSUSY cross section decreases with increasing \u039b, the signi\ufb01cance decreases as a function of \u039b for a given\nintegrated luminosity. In general the discovery potential in most parts of the GMSB model parameter\nspace is high, giving con\ufb01dence that GMSB SUSY can be discovered in the two photon channel with\nearly data, if it is realised in nature.\n [TeV]\n\u039b\n100\n150\n200\n\u03b2\ntan \n20\n40\n NLSP\n\u03c4\u223c\n-1\n1 pb\n-1\n10 pb\n-1\n100 pb\n-1\n1 fb\n NLSP\n1\n0\n\u03c7\u223c\nATLAS\nFigure 6: 5\u03c3 discovery potential contour lines for GMSB SUSY in the \u039b - tan\u03b2 plane for different\nintegrated luminosities.\n3.3\nGMSB3 (non-pointing photon) full simulation studies\nIf the gravitino mass parameter Cgrav is larger than unity, the NLSP will not decay promptly. In the\ncase where the NLSP is a light neutralino, the resulting photons in the \ufb01nal state will not point back\nto the interaction point and may therefore be reconstructed and triggered with lower ef\ufb01ciency. The\nreconstruction ef\ufb01ciency is discussed in greater detail in Section 4.1. Here, the standard photon selection\nwill be used to estimate the discovery potential.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1669\n\nTable 9: Trigger ef\ufb01ciencies and statistical errors for the GMSB3 event sample for (L = 1033 cm\u22122s\u22121).\nTrigger item\nL1\nL1+L2\nL1+L2+EF\ng55\n90.19\u00b11.08\n46.04\u00b11.81\n36.88\u00b11.75\n2g17i\n34.13\u00b11.72\n17.77\u00b11.39\n12.87\u00b11.22\nj65+xE70\n80.38\u00b10.56\n80.24\u00b10.56\n71.18\u00b10.64\n3j65\n79.80\u00b10.57\n79.66\u00b10.57\n79.62\u00b10.57\nTable 10: Number of selected signal (GMSB3) and background events for 1fb\u22121 for different cuts on the\nnumber of photons and opposite sign same \ufb02avour (OSSF) lepton pairs.\nN\u03b3\nNOSSF\nSignal\n\u2211Background\nSig\nNW\nNZ\nNt\u00aft\n0\n0\n825.2\n929.6\n27.1\n274.4\n21.0\n632.8\n0\n1\n265.2\n73.0\n33.2\n8.7\n1.4\n63.0\n1\n0\n255.8\n51.7\n35.7\n19.5\n2.0\n30.1\n1\n1\n68.6\n1.4\n58.6\n0.2\n0.0\n1.2\n2\n0\n12.5\n0.1\n12.5\n0.0\n0.0\n0.1\n2\n1\n4.7\n0.0\n4.7\n0.0\n0.0\n0.0\nA suitable model point to study is the GMSB3 point, which has the same parameters as GMSB1, but\nwith Cgrav = 55. The e\u03c70\n1 decay length in this point is therefore \u03b3\u03b2c\u03c4 \u22483 m. Although only 12.4% (0.6%)\nof the reconstructed events contain one (two) photons with pT > 20 GeV in the detector acceptance\nregion, this well exceeds the number of background photons. This suggests that one could also use the\nabove de\ufb01ned selection, which is based on the requirement of two hard photons.\nTable 9 shows the trigger ef\ufb01ciencies for the same items listed in Table 5. For the L1 trigger, the\nmain source of inef\ufb01ciency for the g55 trigger is from neutralino decaying to photons outside the inner-\ndetector volume. The larger the Cgrav parameter is, the greater is the number of neutralinos that will decay\noutside the inner-detector. This effect is more pronounced for the 2g17i trigger, which is optimized for\nthe production of both photons within the inner-detector volume. At L2 trigger and at the event \ufb01lter,\ncuts are placed on the shape of the electromagnetic showers, which are less ef\ufb01cient for non-pointing\nphotons due to their wider shower shape in the \u03b7 direction compared to prompt photons. The small\ndifference in jet trigger ef\ufb01ciencies between GMSB1 and GMSB3 is again due to the difference in the\nnumber of photons produced within the inner-detector volume. Photons in the event are treated as jets\nup to the event \ufb01lter, so that GMSB1 has effectively a larger number of jets, compared to the GMSB3\nsample, which makes a small but signi\ufb01cant difference in jet trigger ef\ufb01ciency.\nThe resulting numbers of selected events for 1 fb\u22121 are shown in Table 10. It can clearly be seen\nthat, although the signi\ufb01cance, again de\ufb01ned as Sig = S/\n\u221a\nB, is smaller than in the GMSB1 case, there\nare enough photons to select a large number of signal events. The difference to the prompt photon case is\nthat with the requirement of an OSSF lepton pair one could obtain a larger signi\ufb01cance, which is largest\nfor a combination of one hard photon and one OSSF pair.\n3.4\nConclusion of GMSB SUSY with photon signatures\nIn certain regions of the GMSB parameter space the NLSP is a light neutralino, decaying to a gravitino\nvia the emission of hard photons. These photons can be used to ef\ufb01ciently reject the Standard Model\nbackground and to discover GMSB SUSY, if it is realized in nature. Attention must be payed to the\nfact that the photons might not point back to the interaction point leading to losses in reconstruction and\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1670\n\nFigure 7: Schematic diagram of a non-pointing photon in the barrel section of the electromagnetic\ncalorimeter. A long lived neutralino can travel a signi\ufb01cant distance before decaying into a photon\nand a gravitino. The gravitino will escape the detector without interacting. A photon produced in this\nmanner can enter the calorimeter at a signi\ufb01cantly different angle (\u03b7\u03b3) than a photon produced at the\nprimary vertex (\u03b71).\ntrigger ef\ufb01ciencies.\n4\nProspects for neutralino lifetime determination\nIf GMSB SUSY is discovered, the ATLAS calorimeter can be used to \ufb01rst establish whether the neu-\ntralino has a long mean lifetime, and then to quantify it. The calorimeter can be used to both measure the\ndirection and the time of the electromagnetic shower. Both the capabilities can be utilised to determine\nthe mean lifetime of the neutralino.\nIf the neutralino has a signi\ufb01cant decay length, a photon can be observed3 that will not \u201cpoint-back\u201d\nto the primary interaction point. This is shown schematically in Figure 7. The neutralino ( \u02dc\u03c70\n1) travels\na signi\ufb01cant distance before decaying into a photon (\u03b3) and a gravitino ( \u02dcG). Due to the \ufb01nite opening\nangle between the photon and \u02dcG, the path taken by the photon does not extrapolate back to the primary\ninteraction point.\nThe \ufb01rst sampling layer can measure the \u03b7 position (Cluster 1 in Figure 7) whereas the second\nsampling layer can measure both \u03b7 and \u03c6 (Cluster 2 in Figure 7). A vector corresponding to the path of\nthe photon can therefore be constructed in the r \u2212z plane. Although we can not measure the exact decay\npoint of the neutralino based on these two measurements, we can extrapolate the path of the photon back\nto the beam axis, and measure the distance between this point and the primary vertex (Z\u2032 in Figure 7).\nSince the ATLAS calorimeter has a pointing geometry, if a photon enters the calorimeter at a signif-\nicant angle, the resulting electromagnetic shower can be spread out over a larger number of calorimeter\ncells. This wider shower-shape can result in issues for photon reconstruction algorithms and identi\ufb01ca-\ntion criteria. The effects of the reconstruction and identi\ufb01cation of the non-pointing photons are discussed\nin Section 4.1.\nIf the neutralino has a mean lifetime greater than 0.05 ns4, the Z\u2032 value associated with the photon\ncan be used to establish that the neutralino has a \u201clong\u201d lifetime. Once this observation has been made,\nthe Z\u2032 distance can also be used to measure the mean lifetime. This is discussed in Section 4.2.\nThe neutralino is a massive particle. This means that photons produced from long-lived neutralinos\nwill arrive at the calorimeter later than prompt photons from the primary vertex. A method which uses\nthe calorimeter timing information to calculate the mean neutralino lifetime is discussed in Section 4.3.\n3As long as the neutralino decays before the calorimeter.\n4For typical values assumed for the neutralino energy and mass of 200 and 100 GeV respectively, photons with a Z\u2032 of at\nleast 1cm from the primary vertex were observed.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1671\n\nneutralino decay length (mm)\n0\n500\n1000\n1500\n2000\n2500\nNumber of photons in data sample\n2\n10\n3\n10\n4\n10\nGMSB1\nGMSB2\nGMSB3\nATLAS\n (GeV/c)\nT\np\n0\n50 100 150 200 250 300 350 400 450 500\nNumber of photons in data sample\n0\n500\n1000\n1500\n2000\n2500\nGMSB1\nGMSB2\nGMSB3\nATLAS\nFigure 8: Left: The distributions of the decaylength of the neutralino in the z direction. Right: The\ntransverse momentum of the photons they produce.\n4.1\nReconstruction and identi\ufb01cation of non-pointing photons\n4.1.1\n\u03b7 de\ufb01nitions\nDue to the nature of the non-pointing photons, two de\ufb01nitions of \u03b7 are used in this section. The \u2018truth\n\u03b7\u2019 refers to the \u03b7 from the particle vector from the Monte Carlo event record (shown as \u03b7\u03b3 in Figure 7).\nThe term \u2018detector \u03b7\u2019 refers to the \u03b7 as measured by constructing a vector from (0,0,0) to the barycenter\nof the electromgnetic shower(shown as \u03b72 in Figure 7).\n4.1.2\nPhoton reconstruction ef\ufb01ciency\nThe photon reconstruction ef\ufb01ciency is de\ufb01ned as the fraction of photons, produced from the decay of a\nneutralino, that are reconstructed as a photon candidate. Using information from the Monte Carlo event\nrecord, photons are selected to be used in the ef\ufb01ciency calculation if they satisfy the following criteria:\n\u2022 originate from a neutralino decay occuring inside the outer envelope of the inner detector,\n\u2022 pT > 20 GeV,\n\u2022 |detector \u03b7| < 2.5.\nPhotons are declared as successfully reconstructed if a photon candidate is found within \u2206R < 0.2 of the\nposition of the truth photon in the calorimeter.\nThe z-component of the decay length and the momentum of the photon in the GMSB samples, as\nshown in Figure 8 and 8, depend upon the Cgrav parameter of the sample.\nThe overall ef\ufb01ciency for a photon to be reconstructed in the long-lived neutralino data samples,\nGMSB2 and GMSB3, is 88.3\u00b10.2% and 83.3\u00b10.4% respectively. This ef\ufb01ciency includes the recon-\nstruction of photons which have converted to an electron-position pair. This occurs approximately 30%\nof the time and is dependent on how much material the photon travels through the inner-detector. This\nmeans that a photon from a long-lived neutralino will have a smaller probability of converting than a pho-\nton produced at the primary vertex. The reconstruction ef\ufb01ciency of a photon which does not convert, is\n89.3\u00b10.2% for the GMSB2 sample and 84.2\u00b10.5% for the GMSB3 sample.\nThe difference in overall reconstruction ef\ufb01ciency measured between the GMSB2 and GMSB3 sam-\nples is due to the distribution of neutralino lifetimes in the sample, and hence the proportion of photons\nwhich are signi\ufb01cantly \u201cnon-pointing\u201d.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1672\n\n\u03b7\n\u2206\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\nReconstruction Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nGMSB2\nGMSB3\nGMSB2: fit\nGMSB3: fit\nATLAS\nFigure 9: Reconstruction ef\ufb01ciency as a function of \u2206\u03b7 for the GMSB2 and GMSB3 samples.\nThe reconstruction ef\ufb01ciency is measured independently from the sample parameters as a function\nthe variable \u2206\u03b7 = detector \u03b7 - truth \u03b7 as shown in Figure 9.\nThere is excellent agreement between the two cases.\nThe ef\ufb01ciency is approximately 90% for\n\u2206\u03b7 < 0.25, and falls steadily to 75% for \u2206\u03b7 \u22480.5. It is clear that the reconstruction ef\ufb01ciency could\nbias any measured neutralino lifetime distribution. This ef\ufb01ciency distribution is parameterised with an\napproximation to the top-hat function:\nReff(\u2206\u03b7) =\nb\n1+e\n|\u2206\u03b7|+a\nc\n+d\n(1)\nwith a = 4.7(6.9), b = 174(229), c = 0.779(1.16) and d = 0.545(0.351) for GMSB2 (GMSB3). The\nGMSB2 \ufb01t result is used in Sections 4.2 and 4.3 (due to greater statistics) to account for any bias in the\nneutralino lifetime determination due to inef\ufb01ciency.\n4.1.3\nStudy of photon identi\ufb01cation ef\ufb01ciency\nThe dependence of the photon ef\ufb01ciency on the neutralino decay length has been studied for all of\nthe standard photon selection variables [43]. The ef\ufb01ciency for each cut is de\ufb01ned as the fraction of\nreconstructed photons with pT > 20 GeV and |detector \u03b7| < 2.5 that pass the standard select requirement\nfor the given variable. Only photons that are successfully identi\ufb01ed with true photons that come from the\ndecay of a SUSY particle are used.\nFigure 10 shows the ef\ufb01ciency of these cuts as a function of the component of the neutralino decay\nlength parallel to the beam axis. From this \ufb01gure it can be seen that the hadronic leakage (Had/Em) is\nindependent of the neutralino decay length. Of the cuts forming the standard selection from the second\nsampling layer of the electromagnetic calorimeter, only the ratio of energy in the 3\u00d73 / 3\u00d77 cells (R33)\nis shown to be \ufb02at with respect to the neutralino decay length. The ef\ufb01ciency of the cuts on the ratio\nof energy in the 3\u00d77 / 7\u00d77 cells (R37) and the the lateral width of the shower (weta2) are shown to\nhave a clear dependence on the decay length. These two cuts are removed to form an \u2018unbiased photon\nselection\u2019 in the second sampling layer.\nFor the cuts forming the standard cut selection in the \ufb01rst sampling layer of the electromagnetic\ncalorimeter, the fraction of energy (f1) and the cuts on the search for a second minima in the \ufb01rst sampling\nlayer (DeltaE and DeltaEmax2) are shown to be relatively stable with respect to the neutralino decay\nlength. There is however, a signi\ufb01cant dependence of the ef\ufb01ciency on the decay length for the fraction\nof energy outside the shower core (fracm), the shower width in three strips (weta1) and the total width\nof the shower (wtot). These three cuts are removed to form an \u2018unbiased photon selection\u2019 in the \ufb01rst\nsampling layer.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1673\n\nneutralino decay length in Z (mm)\n0\n500\n1000\n1500\n2000\ncut efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nATLAS\nATLAS\nATLAS\nHad/Em\nR37 cut\nR33 cut\nweta2 cut\nf1 cut\nATLAS\nneutralino decay length in Z (mm)\n0\n500\n1000\n1500\n2000\ncut efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nDeltaEmax2 cut\nDeltaE cut\nWtot cut\nFracm cut\nweta1 cut\nATLAS\nFigure 10: Photon identi\ufb01cation cut ef\ufb01ciencies as a function of neutralino decay length in Z\nTable 11 shows the effect on the overall ef\ufb01ciency as the \ufb01ve cuts which have been shown to be\ndependent on the neutralino decay length cuts are excluded from the standard photon selection to form\nan \u2018unbiased photon selection\u2019. For simplicity the cuts are seperated according to which calorimeter\nsampling layer they are based upon.\nTable 11: Summary of photons identi\ufb01cation ef\ufb01ciencies for the three different signal samples. The\nhadronic, second sampling and \ufb01rst sampling cuts are applied sequentially.\nStandard photon selection\nhadronic\n2nd sampling\n1st sampling\nGMSB1\n(94.1\u00b10.2)%\n(75.7\u00b10.4)%\n(64.1\u00b10.4)%\nGMSB2\n(94.2\u00b10.1)%\n(56.4\u00b10.3)%\n(41.9\u00b10.3)%\nGMSB3\n(94.4\u00b10.3)%\n(49.8\u00b10.6)%\n(36.1\u00b10.6)%\nUnbiased selection\nhadronic\n2nd sampling\n1st sampling\nGMSB1\n(94.1\u00b10.2)%\n(93.4\u00b10.2)%\n(85.7\u00b10.3)%\nGMSB2\n(94.2\u00b10.1)%\n(92.2\u00b10.1)%\n(82.5\u00b10.1)%\nGMSB3\n(94.4\u00b10.3)%\n(92.1\u00b10.3)%\n(80.7\u00b10.5)%\nThe relative effect of loosening cuts on the background is shown in Table 12, which shows the\nfraction of jets, from a di-jet Monte Carlo data sample, that are reconstructed as photons, that also pass\nthe two different photon selections.\nTable 12: The fraction of jets reconstructed as photons and passing all photon criteria. The hadronic,\nsecond sampling and \ufb01rst sampling cuts are applied sequentially.\nHadronic\n2nd sampling\n1st sampling\nDefault photon selection\n(3.4\u00b10.1)%\n(0.57\u00b10.06)%\n(0.19\u00b10.03)%\nUnbiased selection\n(3.4\u00b10.1)%\n(2.7\u00b10.1)%\n(0.70\u00b10.07)%\n4.2\nProjected impact-parameter method for neutralino mean lifetime measurement\nThe distribution of the photon\u2019s projected longitudinal impact parameter Z\u2032 arising from GMSB signal\nevents can be used to estimate the mean neutralino lifetime.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1674\n\nt [ns]\n0\nATLAS\n2\n4\n6\n8\n10\n12\nExponential slope par\n-0.008\n-0.0075\n-0.007\n-0.0065\n-0.006\n-0.0055\nFigure 11: Fitted slope parameters of the projected intersection distributions versus mean neutralino\nlifetime from the custom-built Monte Carlo simulation for an integrated luminosity of 30 fb\u22121.\nA distribution of the intersection points of the z-axis with the projected photon path is then created\nfor all reconstructed photons. Each intersection point is corrected for the vertex displacement. An\nexponential function is \ufb01tted to the intersection distribution in order to extract the slope parameter which\nis sensitive to the mean neutralino lifetime. The range for the \ufb01t was chosen to be 50 to 500 mm, to\nremove any possible vertex effects, and to ensure that the decay occured within the volume of the inner-\ndetector.\nPlotting the resulting slope parameters versus the mean neutralino lifetime reveals a clear correlation\n(Figure 11) between the slope parameter and the neutralino lifetime. These results were obtained using\na custom-built Monte Carlo program which provides a detailed parameterisation of the response of the\ntransition radiation tracker and the electromagnetic calorimeter. It is envisaged that a calibration curve\nsuch as this, created using full simulation, could be used to determine the mean neutralino lifetime from\na measurement of the slope of the Z\u2032 distribution. In reality this slope will also be a function of the \u03b2 of\nthe neutralino.\nFor the GMSB2 data set, a slope of \u22124.35(6) \u00d7 10\u22123 was measured and for the GMSB3 data set,\na slope of \u22123.8(2) \u00d7 10\u22123 was measured. These slopes were obtained before any photon identi\ufb01cation\ncuts were applied. To estimate the effect of bias due to the reconstruction ef\ufb01ciency, a weight (=\n1\nReff(\u2206\u03b7))\nis applied to the events, see Section 4.1.2. By comparing the effect of applying this correction on the\nresultant Z\u2032 slope, a \u22125\u00d710\u22125 systematic error was obtained. Table 13 shows the values obtained when\ndifferent photon identi\ufb01cation cuts are used.\nThe results from the GMSB2 and GMSB3 samples shown in Table 13 demonstrate very clearly how\nthe slope of the Z\u2032 distribution can be affected by photon identi\ufb01cation cuts which are based on width\nmeasurements of the electromagnetic shower.\n4.3\nCalorimeter timing\nA comparison has been made of the timing of the electromagnetic shower in the calorimeter, compared\nto the lifetime of the generated neutralino (in its rest frame). A Gaussian is \ufb01tted to this distribution for\ndifferent bins of true lifetime, and the resultant mean cluster-time per generated neutralino mean lifetime\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1675\n\nTable 13: The slope of the projected-impact-parameter (Z\u2032) distributions of the photon, \ufb01tted from 50\nto 500 mm and measured in two different fully simulated Monte Carlo samples with different photon\nidenti\ufb01cation cuts.\nGMSB2: Generated mean lifetime of 3.17 ns\ndataset\nhadronic\n2nd Sampling\n1st Sampling\ndefault photon selection\n\u22124.35(6)\u00d710\u22123\n\u22127.00(9)\u00d710\u22123\n\u22128.3(1)\u00d710\u22123\nunbiased selection\n\u22124.35(6)\u00d710\u22123\n\u22124.39(6)\u00d710\u22123\n\u22124.54(7)\u00d710\u22123\nGMSB3: Generated mean lifetime of 10.7ns\ndataset\nhadronic\n2nd Sampling\n1st Sampling\ndefault photon selection\n\u22123.8(2)\u00d710\u22123\n\u22126.6(2)\u00d710\u22123\n\u22127.7(3)\u00d710\u22123\nunbiased selection\n\u22123.8(2)\u00d710\u22123\n\u22123.9(2)\u00d710\u22123\n\u22124.1(2)\u00d710\u22123\nTable 14: The mean lifetimes, measured using the calibrated calorimeter time, in two different full\nsimulation Monte Carlo samples with different photon identi\ufb01cation cuts. Also shown is the generated\nmean lifetime of the samples used.\nGMSB2: Generated mean lifetime of 3.17ns\ndataset\nhadronic\n2nd Sampling\n1st Sampling\ndefault photon selection\n2.9\u00b10.2 ns\n1.1\u00b10.07 ns\n1.33\u00b10.05 ns\nunbiased selection\n2.9\u00b10.2 ns\n2.9\u00b10.2 ns\n3.0\u00b10.2 ns\nGMSB3: Generated mean lifetime of 10.7ns\ndataset\nhadronic\n2nd Sampling\n1st Sampling\ndefault photon selection\n9\u00b14 ns\n3.4\u00b10.7 ns\n2.9\u00b10.6 ns\nunbiased selection\n9\u00b14 ns\n8\u00b13 ns\n19\u00b119 ns\nis plotted in Figure 12. This \ufb01t to this plot is used to calibrate the calorimeter time. It has been shown that\nthis method is robust against photon reconstruction or identi\ufb01cation ef\ufb01ciency biases. This is because it\nis independent of the angle of incidence of the photon on the calorimeter. The arrival time of the photon\nat the calorimeter is a function of the \u03b2 = v/c of the neutralino as well as its lifetime.\nUsing this calibrated calorimeter time, the neutralino lifetime is plotted for each photon. This dis-\ntribution has the expected exponential shape modi\ufb01ed by acceptance and resolution effects. In order to\nremove these effects, an exponential is \ufb01tted between 0.2 and 1 ns. The mean lifetime of the sample (\u03c4)\nwas calculated from \u03c4 =\n1\nslope where slope is the slope of the exponential \ufb01tted.\nTo calculate the effect of bias due to the reconstruction ef\ufb01ciency, a weight (=\n1\nReff(\u2206\u03b7)) was applied\nto the events (see Section 4.1.2). The systematic error on the lifetime determination due to uncertainties\non the reconstruction ef\ufb01ciency was determined to be 2%.\nTo study the effect of the photon identi\ufb01cation on this method, the mean lifetime deduced from the\nslope of the exponential is measured after different identi\ufb01cation cuts are applied to the photon sample.\nThese mean lifetimes are shown in Table 14. The large errors on the calculated lifetimes from the\nGMSB3 sample are due to lack of statistics available for the \ufb01t, over the limited range.\nIn order to obtain estimates for the systematic uncertainty due to the predicted \u03b2 distribution of the\nGMSB sample (or an error in the timing calibration), the calibration curve (Figure 12) was scaled up and\ndown by 5% corresponding to the difference in mean \u03b2 value between the GMSB2 and GMSB3 samples.\nThe effect on the measured mean lifetime determination corresponds to a systematic error of 0.4(2) ns\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1676\n\ngen time(ns)\n0\n1\n2\n3\n4\n5\n6\ncluster time(ns)\n0\n1\n2\n3\n4\n5\n6\nGMSB2\nGMSB3\nATLAS\nFigure 12: The measured cluster time as a function of the generated neutralino lifetime, for individual\nneutralinos in the Monte Carlo samples.\nfor the GMSB2(3) samples.\nIn order to obtain estimates for the systematic uncertainty in the mean lifetime determination from\nthe choice of \ufb01tting region or a global shift in the timing calibration, the \ufb01t range of the exponetial\ndistributions was shifted by 100 ps. A systematic error of 1(10) ns was obtained for the GMSB2(3)\nsamples.\nThe shape of the observed neutralino lifetime distribution is strongly affected by geometric accep-\ntance and event kinematics. To obtain a lifetime measurement unaffected by these issues, a very limited\n\ufb01tting range has been used. A more accurate \ufb01t could be achieved by \ufb01tting the entire distribution. A full\nacceptance correction, including model dependent effects, would then be required to relate this distribu-\ntion to the mean neutralino lifetime. This work, beyond the scope of this publication, should produce a\nmore accurate measurement of the mean neutralino lifetime.\n4.4\nConclusion of the neutralino lifetime determination\nTwo independent methods for determining the mean neutralino lifetime have been discussed. The two\nmethods are independent with different issues. For the Z\u2032 method of Section 4.2, a study using a simple\ncustom-built Monte Carlo program shows that there is a good correlation between the Z\u2032 parameter and\nthe mean neutralino lifetime. However, full simulation of a range of lifetime samples will be required to\nget the correct parameterisation of the relationship. The calorimeter timing study (Section 4.3), shows\nthere is a good correlation between the calorimeter time and lifetime of the associated neutralino. The\nlargest errors from this studies are due to the limited statistics in the range of the measured neutralino\nlifetime distribution, used for the exponential \ufb01t.\nIn both methods, one has to take care that the biases introduced by the reconstruction and identi-\n\ufb01cation of the photons are both measured and reduced, in order to prevent a distortion of the lifetime\ndistribution.\nBoth of these methods are signal dependent and rely on simulation calibration, either to produce the\nZ\u2032 calibration curve, or the timing calibration. This is because both the Z\u2032 value and the arrival time of the\nphoton in the calorimeter are functions of the \u03b2 of the neutralino as well as its lifetime. One can assume\na distribution of \u03b2 from Monte Carlo simulation (as has been done here), but constraints on the both\nparameters can in principle be achieved by combining the methods. It is proposed that, if non-pointing\nphotons are observed, a multivariate analysis method could be used to combine information from the\ncalorimeter timing and Z\u2032 together with information from the primary vertex and cluster positions and\nenergy to place model-independent constraints on the \u03b2 and lifetime of the parent of the non-pointing\nphoton.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1677\n\n5\nTrigger and reconstruction for searches of long-lived heavy particles\nHeavy, charged, long-lived particles are predicted in many models of physics beyond the Standard Model.\nOne example is GMSB where for high tan\u03b2 the \u02dc\u2113is the NLSP which couples weakly to the gravitino.\nThe signal is a heavy long-lived charged particle with velocity signi\ufb01cantly smaller than the speed of\nlight, \u03b2 < 1. The momentum (and therefore \u03b2) spectrum of these particles is model dependent. Those\nwhich have \u03b2 close to unity are indistinguishable from ordinary muons. Those with \u03b2 signi\ufb01cantly lower\nthan 1 could be identi\ufb01ed and their mass determined.\nIn ATLAS event fragments from different parts of the detector are assiged to a particular bunch\ncrossing (BC) using the BC identi\ufb01er (BCID). The usual assumption is that the particles traverse the\ndetector at nearly at the speed of light (\u03b2 \u22481). Hits from a slower particle may be lost during data\ncollection, or may be marked with the wrong BCID. The implications of low particle speed in the ATLAS\ntrigger and data acquisition design are considered below.\nThis note does not address the case where the decay length of heavy charged NLSP is such that a\nsigni\ufb01cant number of particles will decay inside the tracking volume.\n5.1\nDatasets used\nThis analysis is based on a data sample of 10,000 events from the CSC production generated with the\ncharacteristics of GMSB point 5: \u039b = 30 TeV , Mm = 250 TeV, N5 = 3, tan\u03b2 = 5, sgn(\u00b5) = +, Cgrav =\n5000. At this point the squarks and gluinos have masses around 700 GeV, the neutralino has a mass of\n114 GeV and the \u02dc\u03c4 and \u02dc\u2113have masses of 102 and 100 GeV respectively. The cross-section for this point\nis 23 pb and the \u02dc\u03c4 , \u02dce and \u02dc\u00b5 are co-NLSPs and are produced in the decay \u02dc\u03c70 \u2192\u02dc\u2113\u00b1\u2113\u2213. Because of the\nsmall mass difference between the neutralino and the slepton, the \u02dc\u2113and lepton are nearly collinear. The\npT and \u03b2 spectra of the sleptons and accompanying leptons are shown in Figure 13.\n [GeV/c]\nT\nP\n0\n50 100 150 200250 300 350 400 450 500\n0\n100\n200\n300\n400\n500\n600\n700\n800\nslepton\nmuon\nATLAS\n\u03b2\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1\n10\n2\n10\n3\n10\nslepton\nmuon\nATLAS\nFigure 13: Transverse momentum and velocity spectra for sleptons and accompanying leptons from the\nGMSB5 sample.\nGMSB5 is a single benchmark point and cannot be taken to represent all the possibilities of long-\nlived particle production. Some issues that impact our ability to discover long-lived new particles, if\nthey exist, depend on the mass and \u03b2 spectrum of these particles. In order to make our study less model\ndependent we also used for this study additional samples of events containing a single \u02dc\u03c4 each, generated\nat different \u03b2 with a uniform \u03b7 distribution between \u03b7 = \u22123 and \u03b7 = +3.\nSplit-SUSY events containing long-lived gluinos with masses of 300 GeV and 1000 GeV were also\nused to assess the ef\ufb01ciency of the slow particle trigger, as discussed below. The generation and simula-\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1678\n\ntion of these Split-SUSY events is described in Section 6.\nFor the background study we used single muon events from the CSC production. They were produced\nat constant pT with a uniform \u03b7 distribution, like the single \u02dc\u03c4 samples. We used cross-section estimates\nof 1000 pb (200 pb) for muons with pT > 40 GeV (> 100 GeV) inside the ATLAS acceptance of |\u03b7| < 2.5\n[45].\nThe simulation of a long-lived heavy sleptons in the ATLAS detector required a special patch to\nGEANT4 [46].\n5.2\nTrigger and DAQ issues\nWhen trying to identify slow particles [47, 48] one must pay special attention to the dimensions of AT-\nLAS. Since the detector extends over 20m in length from the interaction point to each detector side and\nthe bunch crossing period is 25ns, this means that particles from three separate bunch crossings can\nco-exist in the detector at the same time.\nAs described above, the matching of event fragments from different subdetectors is achieved using\nthe BCID. This is calibrated so that particles originating together at the interaction point and traveling at\nthe speed of light will have the same BCID assigned to them in all detector elements.\nWhen \u03b2 is suf\ufb01ciently small, the particle will take longer to reach the detectors (especially those far\nfrom the interaction point) and hits may be assigned a wrong BCID and thus not be read-out. Figure 14\nshows the ef\ufb01ciency with which slepton hits in the muon trigger chambers are associated to the correct\nbunch crossing as a function of \u03b2. This \ufb01gure was produced using the single \u02dc\u03c4 events described above.\nIt can be seen that ef\ufb01ciency drops sharply below \u03b2 = 0.8(0.7) in the endcap (barrel). In order to \ufb01nd\nparticles with \u03b2 < 0.7 (\u03b2 < 0.6) in the endcap (barrel), ATLAS must collect hits from the following\nbunch crossing (BC). Fortunately the MDT chambers collect data over a 700 ns interval, and thus hits\nfrom many BCs will be present. The RPC and TGC data acquisition can be set up to read out data from\n\u00b17 and \u00b11 BCs around the triggered BC respectively. The option to read out the information about extra\nBC, which was originally intended for debugging, must be switched on during routine ATLAS operation\nif we want to increase our ef\ufb01ciency for long-lived charged particles.\n\u03b2\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nefficiency to be in the correct BC\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03b2\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nefficiency to be in the correct BC\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nATLAS\nFigure 14: The ef\ufb01ciency, as a function of \u03b2, for all slepton hits in the muon trigger chambers to be\nincluded in the same BC with fast particles, for the barrel (right)and the endcap (left).\nThe hits from a slow particle may fall outside the correct BC, either for all trigger stations (e.g. if the\nparticle is very slow and the trigger was produced by another feature in the event) or hits in the low-pT\nstations in the barrel may arrive in the correct BC, but the hits in the outer station may be late. In such a\ncase, even if the pT of the particle was high, it would produce a low pT trigger.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1679\n\nTable 15: The L1 trigger ef\ufb01ciencies for GMSB5 simulated events for items from the trigger menu for\nL = 1033cm\u22122s\u22121. The description of the trigger items is in [42]\nTrigger label\nDescription & Ef\ufb01ciency in GMSB5\nMU40\n95%\nxE200\n63%\nEM25i\n46%\nIn GMSB5 the two sleptons are produced with different \u03b2\u2019s, and since most of the sleptons have high\n\u03b2, at least one of the two produced sleptons will have \u03b2 > 0.7 in 99% of the events. The level-1 [49]\nmuon trigger ef\ufb01ciency in the correct BC is very high, either from a slepton with high \u03b2, or from one of\nthe accompanying leptons. Table 15 shows the level-1 trigger ef\ufb01ciencies for GMSB5 events, based on\nthe Level-1 thresholds de\ufb01ned in the standard ATLAS menu for a luminosity of 1033.\nNevertheless, a low \u03b2 slepton, one with good potential for a mass measurement, could arrive to the\nmuon spectrometer, or more likely the outer muon station, in the next BC. In such a case the slow slepton\nwill not be found by the trigger, or be identi\ufb01ed as a low pT muon. In order to identify such a slow\nparticle muon trigger chamber data from the next BC has to be collected.\nIn Split SUSY, the gluinos are produced directly, and there are few other features in the event. There-\nfore the R hadrons themselves must trigger the event. Since both of the R hadrons may be slow, the muon\ntrigger may correspond to the wrong BC for the central parts of the detector. As a result, other event\ninformation such as that from the inner detector may be lost in the previous BC. This problem may be\nsolved by also collecting data from the previous BC in the inner detector, but the feasibility of doing this,\nfrom the point of view of increased data volume, has not been investigated in this work. Additional data\nfrom the calorimeter is not required in order to \ufb01nd long lived heavy charged particles.\n5.3\nA L2 trigger for heavy sleptons\n\u03b2\ngenerated \n0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95\n1\n\u03b2\nmeasured \n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nFigure 15: The \u03b2 measured for sleptons in the barrel at L2 for different values of true \u03b2. The error bar\nrepresents the \ufb01tted sigma of the measured \u03b2 distribution.\nAt L2 [50], algorithms are activated based on the Region of Interest (RoI) identi\ufb01ed at L1. Each\nalgorithm has a reconstruction stage which processes the data from the relevant parts of the subdetectors,\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1680\n\nand a hypothesis stage which makes the decision to keep or reject the reconstructed feature. L2 and the\nEvent Filter run in \u201dtrigger chains\u201d which de\ufb01ne the order in which algorithms are called and the input\nand output of each processing stage.\nThe role of the L2 muon trigger is to con\ufb01rm muon candidates \ufb02agged by the L1 and to give more\nprecise physics quantities of the muon candidate.\nThe L2 muon selection is performed in two stages. The \ufb01rst stage is performed by the muFast\nalgorithm [51], which starts from a L1 muon RoI and reconstructs the muon in the spectrometer, giving\na new pT estimate. The hypothesis cuts on the estimated pT are set so that 90% of the muons with pT\nabove the nominal threshold would pass the selection. The resulting trigger element is then passed to the\nnext algorithm.\nTrack \ufb01nding in the inner-detector is performed based on the region of interest found by muFast. The\nmuFast candidate and inner-detector tracks then pass to the next algorithm, muComb, which matches an\ninner-detector track to the muon spectrometer track and re\ufb01nes the pT estimate [50].\nIn the muon barrel, the excellent time resolution (about 3 ns) of the RPC allows measurements of the\ntime of \ufb02ight (TOF). A method for \ufb01nding the slepton and measuring its mass at L2 has been developed.\nWe will show that, in the barrel, a slow particle may already be selected effectively at L2. Figure 15\nshows the mean value and error of the \u03b2 reconstructed at the L2 as a function of generated \u03b2. This \ufb01gure\nwas produced using the single \u02dc\u03c4 events described above.\nA selection based only on the \u03b2 measurement would leave too many muons in the sample. At the hy-\npothesis stage, we select using pT(candidate)> 40 GeV, \u03b2(candidate)< 0.97 and m(candidate)> 40 GeV.\nThe mass is calculated from the measured \u03b2 and the candidate\u2019s pT and \u03b7 estimated by muFast. Fig-\nure 16 show the mass distribution of signal and background resulting from the selection for an integrated\nluminosity of 500 pb\u22121. It can be seen that the signal to background ratio is already good at the L2.\nAt a luminosity of 1033, a slow particle trigger without further trigger selection would produce a rate\nlower than 1 Hz coming from muons. Further re\ufb01nement of the slow particle selection using subsequent\nmuon trigger stages can reduce this rate to 0.2 Hz. The measurement of \u03b2 for high pT muon candidates is\nmass (GeV)\n40\n60\n80\n100\n120\n140\n160\n180\n200\nentries/4GeV\n100\n200\n300\n400\n500\n600\n700\n800\n900\nATLAS\nFigure 16: Mass distribution of signal and background resulting from the L2 selection for an integrated\nluminosity of 500 pb\u22121. The shaded area is the GMSB5 signal, the dashed line is the muon background,\nand the full line is the sum.\nalready part of the standard ATLAS L2 program MuFast, and a program to make the selection described\nabove is part of the ATLAS L2 trigger.\nMeasuring \u03b2 in the muon spectrometer at the second level trigger could be particularly useful for R\nhadrons, which have a L2 trigger ef\ufb01ciency of about 50% for a mass of 300 GeV. The ef\ufb01ciency loss\ncomes mainly from events where the R hadron is neutral in the inner detector (and undergoes charge\nexchange before the muon spectrometer), which then fail the second stage of the L2 trigger requiring\nmatching between the candidate found in the muon spectrometer and a track in the inner detector. An-\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1681\n\n\u03b2\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nReconstruction Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nMuid\nStaco\nATLAS\nFigure 17: The ef\ufb01ciency to reconstruct sleptons as muons as a function of \u03b2 for two ATLAS muon\nreconstruction packages.\nother source of loss (probably less well simulated) is the assignment of inner detector hits from the\ncharged R hadron to the incorrect bunch crossing.\nIf the R hadron is identi\ufb01ed in the muon spectrometer as a slow particle candidate, it could be ac-\ncepted without the requirement of a matching inner detector track. The slow particle selection at L2\nresults in an ef\ufb01ciency of 92% to select events with R hadrons in the barrel. The corresponding muon\nrate is expected to be completely negligible since all muons have an inner detector track.\nThe limitations of the L2 slow particle trigger should be noted. Firstly, this selection is performed\nonly in the barrel of the muon spectrometer, where the RPCs are the trigger chambers. The timing\ninformation from the endcap is in BC granularity and cannot be used to measure \u03b2. Secondly, a slow\nparticle which does not produce a RoI in the correct BC will not cause the muFast algorithm to be called,\nand the selection will not be performed. Therefore, slow particles in the endcap, as well as very slow\nsleptons in events triggered by other objects such as high pT leptons, can only be identi\ufb01ed of\ufb02ine.\nThe \ufb01nal trigger decision in ATLAS is made in the event \ufb01lter, which uses algorithms adapted from\nthe of\ufb02ine reconstruction. As will be shown in the next section, the standard muon reconstruction is\nnot ef\ufb01cient for slow particles; therefore many would be rejected at this stage. The combined trigger\nef\ufb01ciency of L2 and the event \ufb01lter for sleptons with velocity \u03b2 = 0.6 is 39%.\nTo avoid the ef\ufb01ciency loss at the event \ufb01lter, a speci\ufb01c reconstruction algorithm for slow particles,\nlike the one we describe below for reconstruction, is being implemented at the event \ufb01lter.\nSlow particle candidates found at L2 that do not have a matching inner-detector track (such as charge\n\ufb02ipped R-hadron candidates) should be accepted without further event \ufb01lter selection. This will increase\nthe combined trigger ef\ufb01ciency of the L2 and the event \ufb01lter for R hadrons with a mass of 300 GeV from\n25% to 92% in the barrel. The muon rate for this selection is completely negligible since all muons have\nan inner-detector track, but the effect of cavern background on this selection has not been studied yet.\n5.4\nReconstruction of heavy sleptons with the current muon reconstruction packages\nIn the standard ATLAS reconstruction [52], stable sleptons are expected to be reconstructed as muons.\nThe ef\ufb01ciency to reconstruct slow sleptons is compromised due to the following issues: muons are\nreconstructed by forming track segments in the three stations of the Muon Spectrometer. Segments in\nthe \u03c6 direction are found using the trigger chamber data. The data may not be collected if the hits from\na slepton are in the next bunch crossing instead of the collision BC. The lack of a \u03c6 segment hinders the\nreconstruction of the precision segment in \u03b7 using the MDT data. Furthermore, the radii of MDT hits\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1682\n\nare distorted by late arrival of the slepton and may not \ufb01t well to a segment.\nThe ef\ufb01ciency of reconstructing the slepton as a muon depends on the reconstruction technique.\nFigure 17 shows the reconstruction ef\ufb01ciency for sleptons with the two ATLAS combined reconstruction\npackages, Staco and Muid which are based on the muon standalone packages MuonBoy and MOORE\nrespectively. It can be seen that reconstruction ef\ufb01ciency starts dropping sharply for \u03b2 < 0.8. This\nindicates that special reconstruction techniques will be required for the slow particles. This is discussed\nin the next subsection.\n5.5\nIdentifying heavy long-lived particles at reconstruction\nEstimating the velocity and mass in the event reconstruction allows us to identify heavy long lived\ncharged particles, as well as to avoid the ef\ufb01ciency losses suffered when reconstructing them as muons.\nWe do this with the MuGirl package [53], which enables us to select candidates also when the segment\nreconstruction is imperfect. Of\ufb02ine, the velocity can be also determined using the MDTs, the ATLAS\nprecision muon chambers. In the MDT detectors, the hit position is obtained from the particle drift time.\nThe drift distance is calculated assuming the particle passed the chamber with \u03b2 = 1, which is wrong\nfor the slow slepton. Minimizing the \u03c72 of \ufb01t with respect to the time of arrival to the muon detectors\nyields an estimate of \u03b2 and of the particle mass. This information is combined with estimates of \u03b2 from\nthe muon trigger chambers. Figure 18 shows the \u03b2 resolution and reconstructed mass of sleptons from\nGMSB5 obtained from the reconstruction with MuGirl.\n\u03b2\n - true \n\u03b2\n-0.5 -0.4 -0.3 -0.2 -0.1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nevents/bin\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nreconstructed mass (GeV)\n0\n20\n40\n60\n80\n100 120 140 160 180 200\nevents/bin\n0\n100\n200\n300\n400\n500\n600\n700\n800\nATLAS\nFigure 18: \u03b2 resolution and reconstructed mass for sleptons from the GMSB5 sample.\n5.6\nConclusion of strategies for the long-lived heavy particle search\nHeavy, long-lived charged particles can be discovered in ATLAS, should they exist. However, this can-\nnot be done effectively using the standard ATLAS muon reconstruction tools. Furthermore, much of\nthe discovery must be done before the analysis stage, in the data acquisition, high level trigger and re-\nconstruction. We have added to the standard ATLAS software components which can identify sleptons\neffectively.\nThe ef\ufb01ciency to discover slow long-lived charged particles depends on collecting extra data from\nthe bunch crossing following the one in which the interaction occurred. This is most important for data\nfrom the muon trigger chambers, where this possibility is included in the data acquisition design.\nFor the GMSB5 model, discovery would assured with low integrated luminosity, once the MDT and\nRPC time calibrations are established. The discovery methods are largely independent of the model\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1683\n\ncharacteristics, with discovery for a given integrated luminosity depending primarily on the production\ncross-section of the slow particles.\n6\nSearch strategies for R hadrons at ATLAS\n6.1\nIntroduction\nThe presence (or absence) of massive exotic stable hadrons will be an important observable in the search\nfor and quanti\ufb01cation of any new physics processes seen at the LHC. Stable exotic coloured particles are\npredicted in a range of SUSY scenarios (see, for example, Refs. [22\u201326, 31]). Such particles could be\ncopiously produced at the LHC and sensitivity to particle masses substantially beyond those excluded by\nearlier collider searches (<\u223c200 GeV) [31] could be achieved at ATLAS even with rather modest amounts\nof integrated luminosity (\u223c1fb\u22121). This section outlines a strategy for the detection of exotic massive,\nlong-lived hadrons (so-called R hadrons) formed from either stable gluinos or stops (R \u02dcg and R\u02dct hadrons,\nrespectively). As described in section 2.1, the R \u02dcg hadrons (R\u02dct hadrons) are considered in the context of a\nSplit-SUSY (stop NLSP/gravitino LSP) scenario. Although this work is performed in the framework of\nSUSY, the techniques presented here may be used in generic searches for stable heavy exotic hadrons.\nAs in the heavy lepton studies presented in section 4, this work relies on a signature of high-pT muon-\nlike track, although the distributions presented in this section provide a means of discriminating between\nlepton and hadron hypotheses for any observed stable massive particle.\nThis section is organised as follows. First a description is given of the simulation of R hadrons at\nATLAS, including both the event generation and scattering of R hadrons in matter. Final state observ-\nables associated with R \u02dcg and R\u02dct hadrons are then presented and it is shown how it may be possible to\nexperimentally distinguish between these two types of particles should a discovery be made of stable\nmassive exotic hadrons. Finally, the discovery potential for R \u02dcg and R\u02dct hadrons is presented.\n6.2\nPhysics and detector simulation\n6.2.1\nEvent generation\nThe leading-order event generator PYTHIA [54] was used to produce samples of pair-produced gluino\nand stop-antistop events for a range of gluino and stop masses, as summarised in Table 16. Production\nmechanisms of stops and gluinos are illustrated in Figure 19, which shows leading-order Feynman dia-\ngrams. The effects of higher orders, which are important for the jet selection used later in section 6.3.3,\nare computed within PYTHIA using the parton shower technique.\nThe processes studied were selected such that they provide conservative estimates of likely rates at\nthe LHC, which depend principally on the mass of the heavy object under study and not other free SUSY\nparameters.\nFor the gluino generation a Split-SUSY scenario was used in which squarks masses were set to\n4 TeV. To ensure the results presented here are as model-independent as possible, only the PYTHIA\nsub-process gg \u2192\u02dcg \u02dcg was considered whilst neglecting the quark annihilation process q \u00afq \u2192\u02dcg \u02dcg, which is\nsensitive to the squark mass. The former process is anyway the dominant production channel for gluino\nmasses up to \u223c1.5 TeV.\nFor the stable stop sample, the diagonal production of pairs of the lighter stop state ( \u02dct1) were assumed\nand the following sub-processes modelled: gg \u2192\u02dct1\u02dct1 q \u00afq \u2192\u02dct1\u02dct1. All sparticle masses except that of the \u02dct1\nquark were set to 4 TeV although, at leading-order, the masses of other sparticles are not relevant for the\ncross-section calculations [55].\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1684\n\nTable 16: Expected number of gluino and stop pair-production events for 1fb\u22121 of integrated luminosity\nand the equivalent luminosity of signal samples.\nsparticle\nMass (GeV)\nEvents/fb\u22121\nL (fb\u22121)\n\u02dcg\n300\n2.69\u00d7105\n3.72\u00d710\u22122\n\u02dcg\n600\n4.84\u00d7103\n2.07\n\u02dcg\n1000\n138\n72.5\n\u02dcg\n1300\n16.4\n610\n\u02dcg\n1600\n2.12\n4.72\u00d7103\n\u02dcg\n2000\n0.230\n4.35\u00d7104\n\u02dct\n300\n7.82\u00d7103\n1.12\n\u02dct\n600\n1.76\u00d7102\n35.2\n\u02dct\n1000\n6.4\n1.5\u00d7103\n\u0000\u0000\u0001\n\u0000\u0001\n\u0000\u0002\n\u0002\n\u0001\n\u0003\n\u0001\n\u0003\n\u0000\u0000\u0001\n\u0003\n\u0001\n\u0003\n\u0004\nFigure 19: Selection of leading-order processes illustrating the production of gluino and stop particles.\nString fragmentation [56] was used to model the momenta of the R hadrons. A Peterson fragmenta-\ntion function [57],\nD(z) \u221d1\nz (1\u22121\nz \u2212\u03b5 \u02dcq \u02dcg\n1\u2212z)\u22122 ,\n(2)\nfor which the \u03b5 parameter for the heavy coloured object (\u03b5 \u02dcq \u02dcg) has a value extrapolated from its value for\nb-quarks (\u03b5 \u02dcq \u02dcg/\u03b5b = m2\nb/m2\n\u02dcq \u02dcg) [58] was used to model the momentum distribution of the R hadron.\nFollowing hadronisation, and based on calculations of the mass hierarchy of the lowest-lying R-\nhadron states [59], around 55% (40%) of the stable R \u02dcg (R\u02dct) hadrons are predicted to have zero electric\ncharge. This difference arises principally due to the possible existence of gluino-gluon states, for which\nthe production probability is set to 10% here, and which are treated as mesons when propagating through\nmatter (Section 6.2.2).\nTo complement the signal samples, various background samples were used, each corresponding to\nan integrated luminosity of at least \u223c1 fb\u22121. The generated and reconstructed number of events, and\nthe equivalent luminosity of each sample is given in Table 17. As the simulated trigger used for this\nanalysis requires a hard muon-like track, only events which could give rise to a high pT-muon (pT > 150\nGeV) were simulated. The following processes were considered. Leading-order 2-to-2 QCD processes,\nwhich include all quark \ufb02avours except top, and which differ in the values of the internal matrix el-\nement cut-offs ( \u02c6pT) were generated with PYTHIA, the predictions of which are denoted QCD when\ndiscussed in section 6.3.2. In addition, backgrounds arising from diboson (HERWIG [40]) and single\nboson (PYTHIA) production, denoted electroweak, were produced, again with matrix element cut-offs\nin order to produce hard muons. A sample of t\u00aft pair-production events, termed top, was also prepared\nusing the MC@NLO [60] program.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1685\n\nTable 17: Background samples used in this work. The number of generated and reconstructed events\nare shown along with the equivalent integrated luminosity.Event weighting accounts for the non-integer\nnumber of generated and reconstructed t\u00aft events.\nSample\nDataset ID\nGen. Events\nRec. Events\nL (fb\u22121)\nQCD: (PYTHIA)\n(140 GeV < \u02c6pT < 280GeV)\n5013\n3.125\u00d7108\n2572\n0.98\n(280GeV < \u02c6pT < 560 GeV)\n5014\n2.5\u00d7107\n4800\n1.12\n(560GeV < \u02c6pT < 1120 GeV)\n5015\n3.5\u00d7105\n738\n1.01\n(1120GeV < \u02c6pT < 2240GeV)\n5016\n5\u00d7104\n241\n9.46\n(2240GeV < \u02c6pT\n5017\n1\u00d7104\n42\n442.29\nElectroweak\nZZ (HERWIG)\n5985\n2.5\u00d7104\n53\n9.82\nWW (HERWIG)\n5986\n2\u00d7104\n50\n1.21\nWZ (HERWIG)\n5987\n1.5\u00d7104\n29\n2.32\nZ \u2192\u00b5\u00b5 (PYTHIA)\n5145\n1.3\u00d7104\n600\n1.29\nZ \u2192\u03c4\u03c4 (PYTHIA)\n5106\n3\u00d7103\n108\n9.94\nW \u2192\u00b5\u03bd (PYTHIA)\n5105\n3\u00d7104\n600\n0.94\nW \u2192\u03c4\u03bd (PYTHIA)\n5146\n3\u00d7104\n120\n7.82\nTop\ntt: (MC@NLO)\n5200\n1\u00d7106\n4065.08\n0.98\n6.2.2\nSimulation of R-hadron scattering in matter\nA model of R-hadron scattering [61,62] recently implemented in Geant4 [63] is used in this work. This is\nan update of earlier work [59] which, in view of the inherent uncertainties associated with modelling such\nprocesses, adopts a pragmatic approach in which the scattering rate is estimated with the geometric cross-\nsection and phase space arguments are used to predict the different 2-to-2 and 2-to-3 reactions. Other\napproaches to modelling R-hadron scattering have been proposed, based on Regge phenomenology [24,\n25, 64]. These yield predictions of energy loss and scattering cross-sections which are qualitatively\nsimilar to those given by the model used here and any differences would not be expected to change the\nconclusions of this paper.\nThe typical energy loss per interaction is predicted to be low (around several GeV [61]) since only the\nlight quarks within the R hadron should participate in interactions with matter, leaving the heavy squark\nor gluino as a spectator. This implies that the fraction of R hadrons which would be triggered (\u03b2 >\u223c0.6,\nsee Section 6.3.1) and which would then be stopped during their traversal of the detector is negligible5.\nIn addition to energy loss, another feature of R-hadron scattering, which has implications for experi-\nmental searches, is the possibility of charge and baryon number exchange. Following repeated scattering\nR \u02dcg hadrons and R\u02dct hadrons not containing an anti-stop should enter the muon system predominantly as\nbaryons. This is due to the occurence of meson-to-baryon conversion processes for which the inverse\nreaction is suppressed [59]. Anti-baryons, however, would be expected to quickly annihilate in matter\nand R\u02dct hadrons containing anti-stops would thus largely remain as mesons.\nThe material budget of the part of the ATLAS detector enclosed by the muon system varies as a\nfunction of pseudorapidity between 11 and 21 interaction lengths [5,29], with the calorimeters providing\nthe largest contribution. It is estimated that a R \u02dcg hadron (R\u02dct hadron) will typically undergo 10-20 (7-15)\n5Although it does not form a part of this work, the possibility of observing the decay of R hadrons which would be stopped\noffers a promising and complementary means of searching for R hadrons at the LHC [65,66].\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1686\n\nnuclear interactions before reaching the muon system [62]. The difference in scattering rates is due to the\nsmaller number of light valence quarks present in R\u02dct hadrons. Owing to the large number of interactions\na substantial rate of events is thus expected in which a R hadron appears to possess different values of\nthe electric charge in the inner detector and muon system.\nWhile such topologies represent a challenge for track reconstruction software, they also provide\nobservables useful for the discovery and characterisation of R hadrons, something which is explored in\nsection 6.3. For example, a R \u02dcg hadron can reverse the sign of its charge. R\u02dct hadrons [31] can only show\nthis behaviour in the case where an intermediate neutral state oscillates into its anti-particle [67,68]. Since\nthe expected rates of such are processes are essentially unconstrained by experimental limits on SUSY\nscenarios, they are not included in the simulation used here. Instead, a conservative, zero oscillation\nscenario is considered.\n6.3\nEvent selection\n6.3.1\nTrigger\nThe selected level 1 trigger is the mu6 trigger [29], which has been considered in previous studies of\nR hadrons at ATLAS as the most promising trigger for this type of work [69]. This trigger is sensitive\nto the \u2018classic\u2019 stable massive particle signature of a high transverse momentum muon-like track. The\ntrigger ef\ufb01ciency after the level 2 selection for both R \u02dcg and R\u02dct hadrons falls from around 30% at masses\nof several hundred GeV to around 20% at 2 TeV. The variation of ef\ufb01ciency with mass is due to the\nslowness of the R hadron. Here, we consider events in which a R-hadron track in the muon system\nmust be associated with the correct bunch crossing 6. This leads to a rapid fall in ef\ufb01ciency for \u03b2<\u223c0.6.\nA gradual decrease in ef\ufb01ciency would therefore naively be expected for increasing R-hadron mass.\nAfter including requirements that the event \ufb01lter is passed and the muon-like track is well-reconstructed,\nthere is little mass-dependence in the overall ef\ufb01ciency for R \u02dcg hadrons (around 10-15%) or R\u02dct hadrons\n(20-30%). This difference arises due to the stringent track cuts in the event \ufb01lter which, at low masses\n(\u223c300 GeV) reject a substantial proportion of tracks which have reversed the sign of their charge, which,\nas explained in section 6.2.2, occurs only for R \u02dcg hadrons. At higher masses, corresponding to higher\ntransverse momentum, the poorer momentum resolution allows more \u2018charge \ufb02ippers\u2019 to pass. As shown\nin section 6.3.3 this source of inef\ufb01ciency has little effect on the discovery potential owing to the large\npredicted cross-section for low mass R \u02dcg hadrons. However, future work could involve the development\nof triggers which do not rely on linked inner detector-muon chamber tracks. Should such a trigger\ncon\ufb01guration be introduced which is based on the mu40 [29] trigger at level 1, this could potentially\nimprove the overall ef\ufb01ciency by a factor of 2\u22123 for \u03b2>\u223c0.6.\n6.3.2\nR-hadron \ufb01nal state observables\nFollowing the trigger selection, reconstructed \ufb01nal state quantities were used to select R-hadron events\nand suppress background. A number of variables are presented which were found to provide discrimi-\nnation between R-hadron and Standard Model background processes. Since observables associated with\nR \u02dcg hadrons and R\u02dct hadrons are mostly very similar, generally only the R \u02dcg-hadron spectra are presented\nin this section. Where there is a substantial difference in the spectra of the two particle species, separate\ndistributions are shown.\nFigure 20 shows the expected transverse momenta distributions,\ndn\ndpT , of muon-like tracks in R \u02dcg and\nR\u02dct-hadron events, for an integrated luminosity of 1fb\u22121. Distributions from background events are also\nshown. As expected, the R-hadron spectra become harder with larger mass, extending up to \u223c1 TeV at\nthe largest mass values, while the background events are comparatively softer.\n6Section 5 explores possibilities of probing the lower \u03b2 region\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1687\n\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n10\n2\n10\n3\n10\nGluino masses: (GeV)\n300\n)\n2\n 10\n\u00d7\n600 (\n)\n4\n 10\n\u00d7\n1000 (\n)\n6\n 10\n\u00d7\n2000 (\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n10\n2\n10\n3\n10\nATLAS\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n-\n10\n1\n10\nStop masses: (GeV)\n300\n)\n2\n 10\n\u00d7\n600 (\n)\n4\n 10\n\u00d7\n1000 (\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n-\n10\n1\n10\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n-\n10\n1\n10\nBackgrounds :\nelectroweak\nQCD\nttbar\n (GeV)\nT\nP\n500\n1000\n1500\n2000\n )\n-1\n (GeV\nT\ndn/dP\n-\n10\n1\n10\nFigure 20: Distributions of transverse momenta\ndn\ndpT of hard tracks (pT > 50 GeV) as reconstructed in\nthe ID (left) and muon (right) system. The top, middle, and bottom plots show tracks from R \u02dcg, R\u02dct, and\nbackground events, respectively. As labelled, R-hadron spectra are scaled according to R-hadron mass.\nThe spectra correspond to an equivalent integrated luminosity of 1fb\u22121.\nThe ratio of high and low threshold HT/LT TRT hit multiplicities is shown in Fig 21 (top left) for\nR \u02dcg hadrons of mass 1000 GeV and muon candidates from background events. The different thresholds\ncorrespond to low (\u223c200 eV) and high (\u223c6.5 keV) amounts recorded of ionisation energy for a hit.\nOwing to the large mass and restricted \u03b2 range the simulated R-hadron data peak at lower values of\nHT/LT than the background tracks.\nSince R hadrons will typically suffer only several GeV energy loss per interaction through scatter-\ning in the calorimeter, it is unlikely they will be associated with a hard calorimeter jet. Figure 21 (top\nright) shows the distance R = (\u2206\u03b72 +\u2206\u03c6 2)1/2 between a R \u02dcg-hadron track and a jet (de\ufb01ned with the kT\nalgorithm) with pT > 100 GeV. Clearly for the R hadrons, the spectrum is typically larger than around\n1, unlike the background sources which peak at lower values. The QCD background peaks around zero\nsince a large proportion of muons in this sample are produced in the decay of heavy quarks. The top\ndistribution peaks at values around 0.4 re\ufb02ecting the higher jet multiplicity in such events compared to\nR-hadron events. The distribution is not shown for the electroweak backgrounds owing to the statisti-\ncal imprecision of the Monte Sample sample (very few events with high pT jets arise in the selected\nkinematic region under study here).\nIn a leading-order picture, R hadrons will be produced approximately back-to-back, unlike a number\nof background sources, as can be seen in Figure 21 (bottom left), which shows the cosine of the angle\nbetween two R \u02dcg-hadron candidates which both leave hard tracks in the muon system (cos\u2206\u03a6\u00b5,\u00b5); the\nR \u02dcg-hadron sample peaks strongly at (cos\u2206\u03a6\u00b5,\u00b5) \u223c\u22121. Figure 21 (bottom right) shows the distribution of\nthe cosine of the angle between hard tracks in the inner detector and muon system (cos\u2206\u03a6ID,\u00b5), which,\nfor pair production events, would be expected to display peaks at \u223c\u00b11.\nAs described in section 6.2.2, charge exchange processes can give rise to events in which a linked\ntrack is assigned different values of electric charge in the inner detector and muon systems. This is\nshown in Figure 22 which shows the variable qIDpT,ID\nq\u00b5 pT \u00b5 , where qID ,q\u00b5, pT,ID, and pT\u00b5 are the charge as\nreconstructed in the inner detector and muon system, and the reconstructed transverse momentum in\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1688\n\n# HT / # LT\n0\n0.2\n0.4\n0.6\nArbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n, 1 TeV\ng~\nEW\nQCD\ntt\nR\n0\n0.5\n1\n1.5\n2\nArbitrary units\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\n)\n\u00b5\n,\n\u00b5\n\u03c6\n\u2206\ncos(\n-1\n-0.5\n0\n0.5\n1\nArbitrary units\n-3\n10\n-2\n10\n-1\n10\n1\n)\n\u00b5\nID,\n\u03c6\n\u2206\ncos(\n-1\n-0.5\n0\n0.5\n1\nArbitrary units\n-3\n10\n-2\n10\n-1\n10\n1\nFigure 21: Ratio of the number of high to low threshold hits in the TRT (top left); distance between a\nR-hadron candidate and a jet (top right); cosine of the angle between two high pT tracks in the muon\nsystem (bottom left); and cosine of the angle between high pT tracks in the ID and muon systems (bottom\nright). Distributions are shown for R \u02dcg hadrons of mass 1000 GeV and three background sources.\nthe inner detector and muon system, respectively. The gluino distributions show a two peak structure,\nwith the peak at negative values of qIDpT,ID\nq\u00b5 pT \u00b5 arising from charge \u2018\ufb02ipping\u2019 processes. R\u02dct-hadron spectra\nindicate a very small rate (several per cent) of candidates with oppositely signed charge in the muon\nand ID systems which is due to charge misidenti\ufb01cation in the muon and ID systems. Both the stop\nand gluino distributions become broader with increasing mass; this re\ufb02ects the commensurate increase\nin pT and hence degraded resolution of the tracking systems, which has the effect of allowing a greater\nproportion of charge-\u2018\ufb02ipping\u2019 R \u02dcg hadrons to satisfy the event \ufb01lter.\n\u00b5\nT,\nP\n\u00b5\n/q\nT,ID\nP\nID\nq\n-2\n0\n2\n Arbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nGluino masses (GeV)\n300\n600\n1000\n2000\n\u00b5\nT,\nP\n\u00b5\n/q\nT, D\nP\nD\nq\n-2\n0\n2\n Arbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nStop masses (GeV)\n300\n600\n1000\nATLAS\nFigure 22: Distributions of qIDpT,ID\nq\u00b5 pT \u00b5 for R \u02dcg (left) and R\u02dct hadrons (right). Predictions for a range of R-hadron\nmasses are shown.\n6.3.3\nR-hadron selection criteria\nUsing the information presented in section 6.3.2 R-hadron selection criteria were developed following an\noptimisation procedure [62]. First, no hard muon-like track (pT > 250 GeV) can come within a distance\nR < 0.36 of a hard jet (pT > 100 GeV). Furthermore a candidate R hadron must satisfy at least one of\nthe following conditions listed below. For consistency the same selection is applied both for R \u02dcg and\nR\u02dct hadrons though criteria 3-4 are only relevant for R \u02dcg hadrons. However, these have a negligible impact\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1689\n\non the study of the stop discovery potential.\n1. The event contains at least one hard muon track with no linked inner detector track. A linked track\nis de\ufb01ned such that the distance R = (\u2206\u03b72 + \u2206\u03c6 2)1/2 between the measurements in the ID and\nmuon systems is less than 0.1.\n2. The event contains two hard back-to-back ID tracks with the TRT hit distribution satisfying HT/LT <\n0.05. A back-to-back con\ufb01guration is de\ufb01ned such that the cosine of the angle between the two\nmuon tracks is less than -0.85.\n3. The event contains two hard back-to-back (as de\ufb01ned above) like-sign muon tracks.\n4. The event contains at least one hard muon track with a hard matching ID track of opposite charge\nful\ufb01lling the condition pT,ID > 0.5pT\u00b5.\nTable 18 shows the acceptance numbers and rates for the various samples. It can be seen that for\nR-hadron masses below 1 TeV ATLAS opens up a discovery window with integrated luminosity of the\norder of 1 fb\u22121. For masses above 1 TeV the rate of signal events is small, and is comparable to the\nexpected background rate, so even discovery would be challenging even with larger data-sets.\nTable 18: Number of events selected for the given samples. Background samples not mentioned here are\nrejected by the selection.\nSample\nAccepted events\nRate (Events / fb\u22121)\n300 GeV gluino\n235\n6.44\u00d7103\n600 GeV gluino\n551\n2.70\u00d7103\n1000 GeV gluino\n774\n10.7\n1300 GeV gluino\n732\n1.20\n1600 GeV gluino\n685\n0.147\n2000 GeV gluino\n546\n1.26\u00d710\u22122\n300 GeV stop\n78\n70.0\n600 GeV stop\n134\n3.9\n1000 GeV stop\n170\n0.1\nJ5\n1\n0.893\nJ8\n1\n2.26\u00d710\u22123\nZ \u2192\u00b5\u00b5\n1\n0.776\n6.4\nConclusion of R-hadron search strategies\nStable massive exotic hadrons (R hadrons) are predicted in a number of SUSY scenarios. By exploiting\nthe signature of a hard penetrating particle which may undergo charge exchange in the calorimeter and\nseemingly does not fall within a jet, ATLAS will be able to discover R hadrons for masses below 1 TeV\nwith relatively low amounts of integrated luminosity (\u223c1fb\u22121).\n7\nConclusion\nSearch strategies at ATLAS have been developed for a range of signatures of new physics processes\nexpected within SUSY models. Studies were made of high transverse momentum photons, which may or\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1690\n\nmay not have been produced at the primary collision point, and of slow moving stable massive interacting\nparticles (sleptons and R-hadrons).\nIt was shown that with early LHC data, corresponding to an integrated luminosity of around 1fb\u22121,\nATLAS opens up a discovery window for those SUSY scenarios giving rise to the aforementioned sig-\nnatures. 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C49 (2007) 623\u2013640.\nSUPERSYMMETRY \u2013 SUPERSYMMETRY SIGNATURES WITH HIGH-pT PHOTONS OR LONG- . . .\n1693\n\n\nExotic Processes\n1695\n\nDilepton Resonances at High Mass\nAbstract\nWe present the discovery potential of a heavy new resonance decaying into a\npair of leptons with early LHC data with the ATLAS detector. The dilepton\n\ufb01nal states are robust channels to analyze because of the simplicity of the event\ntopology. The unprecedented available center-of-mass energy will allow one\nto probe regions that are inaccessible at previous experiments even with mod-\nest amounts of data. After studying the Standard Model predictions and the\nassociated uncertainties one can then look for signi\ufb01cant deviations as indica-\ntion of beyond the Standard Model physics (BSM). The focus of the note is\nto study the prospects for discovering BSM physics in the dilepton \ufb01nal states\nwith an integrated luminosity ranging from 100 pb\u22121 to 10 fb\u22121.\n1\nIntroduction\nNew heavy states forming a narrow resonance decaying into opposite sign dileptons are predicted in\nmany extensions of the Standard Model: grand uni\ufb01ed theories, Technicolor, little Higgs models, and\nmodels including extra dimensions [1\u20134]. The discovery of a new heavy resonance would open a new era\nin our understanding of elementary particles and their interactions. Because of the historic importance\nof the dilepton channel as a discovery channel and the simplicity of the \ufb01nal state, these channels will\nbe very important to study with early ATLAS data. The strictest direct limits on the existence of heavy\nneutral particles are from direct searches at the Tevatron [5\u20137]; the highest excluded mass is currently\nalmost 1 TeV. The LHC will have a center-of-mass energy of 14 TeV which should ultimately increase\nthe search reach for new heavy particles to the 5 - 6 TeV range. Many exotic models can be tested at the\nLHC, but analyzing all the existing models is impossible. Instead we choose to take a different approach,\ngrouping the early-data analysis by their \ufb01nal state topologies. There have been several other ATLAS\nstudies evaluating the potential for discovery of a heavy resonance [8]. However, this is the \ufb01rst study\nto include full trigger simulation, misalignments, and data driven methods. Including these experimental\nissues is important to realistically estimate the analysis potential. We focus on the early data phase of the\nexperiment, de\ufb01ned roughly to include the accumulation of up to 10 fb\u22121 of ATLAS data.\nIn the remaining of this introduction, the investigated models are reviewed. In sections 2 and 3,\nwe explore the detector performance concerning the electron, muon and tau reconstruction abilities at\nhigh energies and the corresponding trigger ef\ufb01ciencies. In section 4 we investigate the Standard Model\npredictions and associated uncertainties, as well as the signal cross-section. In section 5, we proceed to\nsearch for Exotic resonances.\n1.1\nModels Predicting a Z\u2032\nSeveral models [1,3] predict the existence of additional neutral gauge bosons. In particular, grand uni\ufb01ed\ntheories, as well as \u201clittle Higgs\u201d models, predict their existence as a manifestation of an extended sym-\nmetry group. Generically, there are no predictions for the mass of these particles. Since the experimental\nconsequences are very similar in the dilepton \ufb01nal state, we examine only some representative models:\nthe Sequential Standard Model (SSM)1, the E6 and the Left-Right Symmetric models [9]. The partial\nwidth of the Z\u2032 boson is given by \u0393(Z\u2032 \u2192\u2113+\u2113\u2212) \u2248[(gR\n\u2113)2 +(gL\n\u2113)2] mZ\u2032\n24\u03c0 where gR\n\u2113and gL\n\u2113are the right and\nleft handed couplings of the charged leptons to the Z\u2032 boson and mZ\u2032 is the mass of the Z\u2032 boson. For\n1The Sequential Standard Model includes a new heavy gauge boson with exactly the same couplings to the quarks and\nleptons as the Standard Model Z boson.\n1696\n\nZ\u2032 Model\nIndirect Searches (GeV)\nDirect Searches (GeV)\ne+e\u2212Colliders\np+p\u2212Colliders\nZ\u2032\n\u03c7\n680\n781\n864\nZ\u2032\n\u03c8\n481\n366\n853\nZ\u2032\n\u03b7\n619\n515\n933\nZ\u2032\nLRSM\n804\n518\n\u2013\nZ\u2032\nSSM\n1787\n1018\n966\nTable 1: 95% C.L. limits on various Z\u2032 models.\nthe masses and couplings considered here the natural width is typically around 1% of the mass of the\nresonance.\nThe strictest limits from direct searches come from the D0 and CDF experiments at the Tevatron [5\u2013\n7]. Indirect searches have also been undertaken by the LEP experiments [10]. The direct limits range\nfrom several hundred GeV to approximately 1 TeV and are shown in Table 1. These limits are not\nexpected to improve much beyond 1 TeV [11]. It should be noted that for models where the Z\u2032 couples\npreferentially to the third generation the limits are lower, therefore we consider it important to look at a\nlower invariant mass region in this channel.\n1.2\nRandall-Sundrum Graviton\nThe Randall-Sundrum model [4] addresses the hierarchy problem by adding one extra-dimension linking\ntwo branes, the Standard Model brane and the Planck brane. The hierarchy is solved by assuming for the\n\ufb01fth dimension a warped geometry in which the size of the ordinary coordinates decreases exponentially\nfrom the Planck scale to the TeV scale. The Randall-Sundrum model predicts the existence of a tower\nof Kaluza-Klein excitations of the graviton. These should be observable as resonances which decay into\nlepton pairs at the LHC. The current limits depend on the parameters of the model, and range from several\nhundred GeV to one TeV [5]. We consider the observability of a Randall-Sundrum graviton decaying into\nelectron pairs. The width of the graviton resonance would be very small. For the parameters considered\nhere it ranges from 10\u22124 to a few 10\u22123 times the mass.\n1.3\nTechnicolor\nStrongly interacting theories, like Technicolor and Extended Technicolor, provide a dynamical solution\nto the problem of Electroweak Symmetry Breaking. Many new technifermions which are bound together\nby a QCD-like force are predicted. One of the most promising search channels is the dilepton decay\nof the \u03c1TC and \u03c9TC. We study the \u201cTechnicolor Strawman Model\u201d or TCSM [12, 13] as a benchmark\nmodel for generic strongly interacting theories. The most stringent limits on technihadrons in the TCSM\nframework come from the CDF collaboration, who rules out \u03c1TC and \u03c9TC with masses below 280 GeV\nfor a particular choice of the TCSM parameters [14]. The width of the techni-mesons depends on the\nnumber of technicolors, but is generally assumed to be small, of the order of a few percent of their mass.\nMore details on the exact values of the parameters considered are discussed in a later section.\n2\nObject Identi\ufb01cation and Performance\nThis section describes the requirements used to select objects for the analyses and summarizes \ufb01ndings on\nthe performance using Monte Carlo simulations of the production and decay of new dilepton resonances.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1697\n\n2.1\nElectron Identi\ufb01cation\nThe electron identi\ufb01cation and performance is described in detail elsewhere [15]; here we summarize\nthe results concerning very high transverse momentum2 (pT). electron identi\ufb01cation and reconstruction.\nThe background to very high pT electron pairs is expected to be low, therefore only minimal selection\ncriteria need to be applied, in order to maximize ef\ufb01ciency. These minimal criteria are called loose. On\nthe other hand, when trying to select very high pT \u03c4 lepton pairs, where one \u03c4 decays hadronically, a\ntighter selection on the electron from the other \u03c4 decay is needed.\nOn top of the minimal requirements that the reconstructed clusters should have an absolute pseudo-\nrapidity (\u03b7) less than 2.5 and should be associated with a track reconstructed in the inner detector, two\nelectron selections were studied (both described in detail in [15]):\n\u2022 A loose selection based on hadronic leakage and shower shape variables. This selection achieves\nvery high ef\ufb01ciency while maintaining rejection against highly energetic pions with wide showers.\n\u2022 A medium selection, which makes further requirements to obtain better rejection against \u03c00 \u2192\u03b3\u03b3\nbackground by exploiting the very \ufb01ne granularity of the \ufb01rst compartment of the electromagnetic\ncalorimeter, and tighter requirements on the associated track.\nFigure 1 shows the reconstruction ef\ufb01ciency together with the ef\ufb01ciency of the two selections in a\nsample Z\u2032 \u2192e+e\u2212events with mZ\u2032 = 1 TeV as a function of transverse momentum and pseudo-rapidity,\nnormalized to truth electrons with pT greater than 50 GeV and |\u03b7| smaller than 2.5. The ef\ufb01ciency of the\nreconstruction is dominated by the ef\ufb01ciency of the cluster to track association and is on average slightly\nbelow 80%. It must be noted that this ef\ufb01ciency has improved in the more recent software version used\nin [15]. The loose selection criteria have a relative ef\ufb01ciency close to 1, whereas the medium selection\nleads to an overall average ef\ufb01ciency between 65% and 70%.\nThe energy resolution for electrons at high pT is about 1% except in the crack region between the\nforward and central calorimeters where the resolution is about 5% . The probability to assign the wrong\ncharge to an electron ranges from 1% to at most 5% as the transverse momentum goes from 100 GeV to\n1 TeV [16]. For a 1 TeV Z\u2032 a dielectron mass resolution of (0.80\u00b10.02)% is obtained.\n2.2\nMuon Identi\ufb01cation\nHere we discuss the requirements used to select muons, as well as a method to extract the identi\ufb01cation\nef\ufb01ciency from data. The ATLAS detector has an excellent standalone muon spectrometer: muon tracks\ncan be found both in the inner detector and the muon spectrometer. A \u201ccombined\u201d muon track consists\nin matched tracks from both the muon spectrometer and inner detector. We require that a muon, with\npT \u226530 GeV,\n\u2022 forms a combined track (inner detector and muon spectrometer) with |\u03b7| \u22642.5,\n\u2022 has a match \u03c72 < 100.0 (5 D.O.F) between the parameters of the inner detector and muon spec-\ntrometer tracks.\nThe muons in the 1 TeV Z\u2032 sample have a most probable pT of about 500 GeV. An ef\ufb01ciency of (95 \u00b1\n0.2)% with a resolution of approximately 5% is found with this selection. The results are consistent with\nprevious studies [17,18].\nThe muon identi\ufb01cation ef\ufb01ciency as a function of pT has been determined using two methods. The\n\ufb01rst method is the \u2019tag and probe\u2019 method, which has been used successfully at the Tevatron. In this\nmethod one uses a \u2019standard candle\u2019 as an in situ calibration point. It involves selecting Z \u2192\u00b5\u00b5 events\n2The transverse momentum is de\ufb01ned as the momentum projected on the plane transverse to the beam axis.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1698\n\n(GeV)\nT\np\n200\n400\n600\n800\n1000\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nReconstructed electron\nLoose selection\nMedium selection\n|\u03b7|\n0\n1\n2\nEfficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\nATLAS\nReconstructed electron\nLoose selection\nMedium selection\nFigure 1:\nEf\ufb01ciency of the loose and medium selection criteria in Z\u2032 \u2192e+e\u2212events with mZ\u2032 = 1 TeV as\na function of pT (left) and \u03b7 (right). The reconstruction ef\ufb01ciency is normalized to truth electrons inside the\ngeometrical acceptance |\u03b7| < 2.5 and with pT > 50 GeV.\nand evaluating the reconstruction ef\ufb01ciency from data on these events. One combined muon is used as\nthe tag while an inner detector track is used as a probe track. One can then study how often the probe\nmuon also has a combined track to get an unbiased measurement of the combined muon reconstruction\nef\ufb01ciency. The reconstruction ef\ufb01ciency was measured by \ufb01tting to the dimuon invariant mass spectrum\nand \ufb01nding the fraction of events where the probe track was found as a combined track. A comparison\nbetween this tag and probe method and Monte Carlo truth is shown in Fig. 2. The Monte Carlo truth\nef\ufb01ciency is determined by counting the number of generated muons with successfully reconstructed\ninner detector tracks that also have a combined muon track. This study demonstrates that we should be\nable to use this method to extrapolate into the very high pT range.\n2.3\nTau Identi\ufb01cation\nThe algorithm to reconstruct hadronically decaying \u03c4 lepton candidates is described in [19].\nIt is\ncalorimeter based; it starts from a reconstructed cluster with a transverse energy3 ET > 15 GeV and\nthen builds identi\ufb01cation variables based on information both from the electromagnetic and hadronic\ncalorimeters, as well as the inner tracker. Finally, an electron and a muon veto are applied, which means\nthat hadronically decaying \u03c4 candidates which are matched (which \u201coverlap\u201d) with an identi\ufb01ed electron\nor muon are removed.\nThe reconstruction ef\ufb01ciency, de\ufb01ned as the probability of a true hadronically decaying \u03c4 to be\nreconstructed as a cluster, and normalized to all true hadronically decaying \u03c4 leptons with ET >15 GeV\ninside the \u03b7 acceptance, is \ufb02at as a function of \u03b7 and \u03c6. The average ef\ufb01ciencies are summarized in\nTable 2. Ef\ufb01ciencies for electron and muon vetoes are given with respect to all reconstructed \u03c4 leptons.\nA likelihood is computed for each \u03c4 candidate. The \u03c4 likelihood combines information from the\ncalorimeter describing the shower shape and tracking information in a multivariate likelihood to maxi-\nmize the discrimination from background. Detailed studies were done to optimize the \u03c4 lepton ef\ufb01ciency\n3The transverse energy is de\ufb01ned as the energy multiplied by sin\u03b8, where \u03b8 is the angle between the beam axis and the\ndirection from the interaction point to the cluster.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1699\n\n (GeV)\nT\np\n30\n40\n50 60\n100\n200\n300\n400\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\nMCtruth\nTag/Probe\nFigure 2: Ef\ufb01ciency of muon reconstruction and identi\ufb01cation as a function of pT from two different\nmethods (see text).\nEvents in |\u03b7| \u22642.5\n(87.1 \u00b1 0.1) %\nEvents in |\u03b7| \u22642.5 AND ET >15 GeV\n(85.6 \u00b1 0.2) %\nReconstruction\n(98.8 \u00b1 0.1) %\nElectron veto\n(99.3 \u00b1 0.1) %\nMuon veto\n(99.9 \u00b1 0.0) %\nTable 2: Reconstruction ef\ufb01ciency, ef\ufb01ciency of e/\u00b5-\u03c4-jet overlap removal for hadronically decaying \u03c4\nleptons from Z\u2032 boson decays. The ef\ufb01ciencies for kinematic requirements are also given.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1700\n\nRequirement\nEf\ufb01ciency (%)\nET > 60 GeV\n89.8 \u00b1 0.2\nAND 1\u2264Ntrk \u22643\n79.2 \u00b1 0.3\nAND likelihood requirement\n51.0 \u00b1 0.3\nTable 3: Preselection and identi\ufb01cation ef\ufb01ciency for Z\u2032 \u2192\u03c4\u03c4 (m = 600 GeV). Ef\ufb01ciency is given with respect to\nreconstructed hadronically decaying \u03c4 leptons (after removal of overlap with electrons or muons).\nand jet rejection for the Z\u2032 boson search. The result (shown in Table 3) was to impose a pT-dependent\nlikelihood requirement, a requirement on the number of tracks, and a requirement on the transverse\nenergy.\n3\nTrigger\nThe aim of the trigger system is to reduce the rate of events \ufb02owing through the data acquisition to 200\nHz while maintaining a highly ef\ufb01cient selection for rare signal processes. Even at the initial luminosity\nof L = 1031 cm\u22122s\u22121, it will be a challenge to keep the trigger highly ef\ufb01cient for all important \ufb01nal\nstates. Several detailed trigger studies were undertaken for the dilepton \ufb01nal state. In this section we\nsummarize those results.\n3.1\nElectron Triggers\nThere are several proposed triggers which in principle can be used for the dielectron analysis. We studied\nfour triggers: e55 - requiring one electron with pT \u226560 GeV, e22i - requiring one isolated electron with\npT \u226525 GeV, 2e12 - requiring two electrons with pT \u226515 GeV, and 2e12i - requiring two isolated\nelectrons with pT \u226515 GeV.\nTable 4 shows the ef\ufb01ciency at the three ATLAS trigger levels [20]: level 1 (L1), level 2 (L2), and\nthe event \ufb01lter (EF) for a sample of graviton events. As can be seen in this table, the most ef\ufb01cient\ntriggers are the high pT triggers that do not require isolation. The low pT triggers (2e12, 2e12i) will\nnot be considered any further.\nSignature\nEf\ufb01ciency (L1/L2/EF) (%)\nTotal Trigger Ef\ufb01ciency (%)\ne55\n99.9\u00b10.0\n95.9\u00b10.2\n94.6\u00b10.3\n90.8\u00b10.3\ne22i\n85.9\u00b10.3\n96.4\u00b10.4\n83.9\u00b10.3\n80.9\u00b10.4\n2e12\n99.9\u00b10.1\n84.9\u00b10.5\n85.5\u00b10.3\n72.6\u00b10.6\n2e12i\n59.1\u00b10.7\n86.1\u00b10.7\n86.2\u00b10.3\n43.9\u00b10.7\nTable 4: Trigger level ef\ufb01ciencies on G\u2192e+e\u2212(m = 500GeV) events with respect to loose electron of\ufb02ine selec-\ntion. The last column shows the overall trigger ef\ufb01ciency after all levels.\n3.2\nMuon Triggers\nFor the dimuon channel we investigated the trigger ef\ufb01ciency for dimuon events using the single muon\n20 GeV pT trigger mu20 [20] . Results for various signal samples are shown in Table 5. Detailed studies\non ways to estimate the trigger ef\ufb01ciency were carried out and presented in [21]. It was found that a tag\nand probe method, similar to the method described for the of\ufb02ine muon reconstruction, could be used to\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1701\n\nSample\nmu20 Ef\ufb01ciency (L1/L2/EF) (%)\nTotal Trigger Ef\ufb01ciency (%)\nm = 400 GeV \u03c1T/\u03c9T\n97.6 \u00b1 0.1\n98.8 \u00b1 0.1\n99.5 \u00b1 0.1\n96.0 \u00b1 0.1\nm = 600 GeV \u03c1T/\u03c9T\n98.1 \u00b1 0.1\n98.5 \u00b1 0.1\n99.2 \u00b1 0.1\n95.9 \u00b1 0.1\nm = 800 GeV \u03c1T/\u03c9T\n97.6 \u00b1 0.1\n98.7 \u00b1 0.1\n99.2 \u00b1 0.1\n95.6 \u00b1 0.1\nm = 1 TeV \u03c1T/\u03c9T\n97.6 \u00b1 0.1\n98.7 \u00b1 0.1\n99.2 \u00b1 0.1\n95.6 \u00b1 0.1\nm = 1 TeV Z\u2032\n\u03c7\n97.8 \u00b1 0.1\n98.9 \u00b1 0.1\n99.5 \u00b1 0.0\n96.3 \u00b1 0.1\nm = 2 TeV Z\u2032\nSSM\n97.6 \u00b1 0.1\n98.7 \u00b1 0.1\n98.9 \u00b1 0.1\n95.3 \u00b1 0.2\nTable 5: Simulated trigger level ef\ufb01ciencies of dimuon resonance samples with respect to of\ufb02ine selec-\ntion. The last column shows the overall trigger ef\ufb01ciency after all levels.\nextrapolate Z \u2192\u00b5\u00b5 results to high pT. In addition, ef\ufb01ciencies were obtained using orthogonal triggers,\ngiving a sample which was minimally biased with respect to the muon triggers. It was found in [21] that\nthese estimates agreed with both the tag and probe method and the results from the simulated samples\nshown here. As can be seen from Table 5 the single muon triggers are highly ef\ufb01cient for any of our\nsignal samples with a total trigger ef\ufb01ciency around 95%.\n3.3\nTriggers for Taus\nThe \u03c4 lepton decays to hadronic states in 65% of the cases, and the rest of the time to lighter leptons (e or\n\u00b5). In our studies of ditau \ufb01nal states we select events triggered with a single lepton (e/\u00b5) trigger. Thus,\nwe consider two true \ufb01nal states, which we denote e\u03c4h and \u00b5\u03c4h.\nFor the e\u03c4h channel we consider two triggers: e22i and e55, as studied in section 3.1. The \u00b5\u03c4h\nevents are selected using the mu20 trigger already used in section 3.2. Note that the ef\ufb01ciencies shown\nhere are lower than for the dimuon or dielectron channel. This arises because there is only one electron or\nmuon in the \ufb01nal state considered here while in the dielectron or dimuon \ufb01nal state either electron/muon\ncan satisfy trigger requirements. Table 6 summarizes the trigger ef\ufb01ciencies.\nSignature\nEf\ufb01ciency (L1/L2/EF) (%)\nTotal Trigger Ef\ufb01ciency (%)\ne22i\n85.2 \u00b10.5\n89.8 \u00b10.4\n90.2 \u00b10.3\n69.1 \u00b10.6\ne55\n90.0 \u00b10.3\n74.2 \u00b10.4\n78.7 \u00b10.6\n52.6 \u00b10.8\ne22i or e55\n96.7 \u00b10.1\n88.7 \u00b10.4\n88.9 \u00b10.3\n75.5 \u00b10.5\nmu20\n79.8 \u00b10.6\n90.7 \u00b10.4\n97.5 \u00b10.4\n70.6 \u00b10.5\nTable 6: Trigger level ef\ufb01ciencies for different triggers for \u03c4 leptons from m = 600 GeV Z\u2032 bosons\ndecaying to e\u03c4h and \u00b5\u03c4h \ufb01nal states with respect to of\ufb02ine selection. The last column shows the overall\ntrigger ef\ufb01ciency after all levels.\n4\nStandard Model Predictions and Other Sources of Systematic Uncer-\ntainties\nIn this section, we investigate the main background sources and we show the dominance of the neutral\nDrell-Yan process. Then we investigate the uncertainties in the Standard Model predictions for Drell-Yan\nproduction, as well as for an extra neutral gauge boson. Finally, we discuss the experimental sources of\nuncertainties, including a dedicated study of the effect of the muon spectrometer alignment.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1702\n\n4.1\nBackground Sources\nThe neutral Drell-Yan (DY) process constitutes the irreducible background in the search for new heavy\ndilepton resonances.\nThe dielectron reducible background results from events in which one or two electrons come from\nthe jet\u2192electron or photon\u2192electron contamination. In addition, true isolated electrons can produced\nby W \u2192e\u03bd or Z \u2192ee decays. By combining these effects in the dielectron case, one can list the re-\nducible background sources: inclusive jets, W+jets, W+photon, Z+jets, Z+photon, photon+jet and pho-\nton+photon. For a \ufb01rst estimation of these backgrounds, we have used the event generator PYTHIA [22]\nto compute the differential cross-sections as a function of the invariant mass of the object pair. The re-\nsults are shown on the left of Fig. 3. The neutral Drell-Yan process has a much lower cross-section than\nmost of the backgrounds. For each electron-candidate leg originating from a jet (photon), we then apply\na rejection factor4 of Re\u2212jet = 4\u00d7103 (Re\u2212\u03b3 = 10) [15]. We apply an additional requirement to take into\naccount the geometrical acceptance in which the electrons are identi\ufb01ed, i.e. |\u03b7| < 2.5, and require at\nleast one object with pT \u226565 GeV. The resulting differential cross-sections are shown on the right of\nFig. 3. One can see that each contribution represents at most 25% of the neutral Drell-Yan process. The\nsum of all contributions does not exceed 30%. Both the transverse momentum and the rapidity require-\nments play an important role in reducing the QCD-jet background because it is produced mainly in the\nt-channel resulting in jets with high rapidities. Further reduction of these backgrounds may be obtained\nby requiring opposite electric charges.\nThe WW, WZ, ZZ and top pair processes can also produce two opposite sign electrons. Whereas\nthe cross-sections of the diboson processes are of the same order as the smallest backgrounds above,\nthe top pair cross-section is not negligible. As the topology of the events is not as simple as in the\nabove backgrounds, no conclusion can be drawn without a full simulation study. Using a sample of fully\nleptonic and semi-leptonic t\u00aft events, it was checked that the t\u00aft background was of the order of 10% of\nthe Drell-Yan contribution for di-object masses above 500 GeV after applying electron identi\ufb01cation and\nthe same rejection factor as above to the most energetic jet.\nM (GeV)\n500\n1000\n1500\n2000\n2500\n3000\n]\n-1\n/dm [fb GeV\n\u03c3\nd\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\njj \n \n\u03b3\nj+\nW+j \nZ+j \n \u03b3\n+\n\u03b3\n \n\u03b3\nW+\nDY \n \n\u03b3\nZ+\nM (GeV)\n500\n1000\n1500\n2000\n2500\n3000\n]\n-1\n/dm [fb GeV\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nDY \njj \n \n\u03b3\nW+\n \n\u03b3\n+\n\u03b3\nW+j \n \n\u03b3\nj+\n \n\u03b3\nZ+\nZ+j \nFigure 3: Background contribution to the e+e\u2212invariant mass spectrum: before selection requirements (left) and\nafter selection requirements (right).\n4This number is given for the medium selection while the loose selection was used here. However, this corresponds to an\nef\ufb01ciency of (80.6 \u00b1 0.2)%, which is higher than our average ef\ufb01ciency using loose criteria, due to the better performance of\nthe more recent release used in [15].\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1703\n\nThe rejection factors \u00b5-jet and \u00b5-photon are higher than the ones corresponding to the electrons and\nthe resulting reducible backgrounds are lower.\nAll these assumptions will have to be checked with the real data. One can use for instance electron-\nmuon or same charge samples, in which no signal is expected.\nIn the following, only the neutral Drell-Yan is considered as a source of background in the dilepton\nchannel. The ditau case is treated later.\n4.2\nControlling the Dilepton Cross-Section\nThe background estimations in the last section were performed with the PYTHIA event generator which\nuses tree-level calculations of the cross-sections. The tree-level dilepton cross-sections are subject to\nlarge higher order electroweak and QCD corrections. These are known at least to next-to-leading order\n(NLO) of perturbation theory, not only for the Standard Model Drell-Yan process, but also for a number\nof new physics processes. They have the additional bene\ufb01t of reducing the uncertainty induced by the a\npriori unknown renormalization and factorization scales \u00b5R,F. In the following, we discuss in detail the\nvarious known radiative corrections and the remaining theoretical uncertainties, focusing on the Standard\nModel Drell-Yan process and the corrections to the tree-level cross-section.\n4.2.1\nNLO Electroweak Corrections\nThe electroweak corrections to the Drell-Yan process are known to NLO in the \ufb01ne-structure constant\n\u03b1 [23, 24]. Initial-state photon radiation must be factorized into the parton density functions (PDFs),\nwhich in principle modi\ufb01es the DGLAP evolution of quarks and gluons, but has in practice little effect\non the quality of the global \ufb01t [25]. Only at very large x and \u00b52\nF can the correction become of the order\nof 1%. Multiple initial-state photon emission can also be resummed, leading to a 0.3% modi\ufb01cation of\nthe cross-section [26], or matched to parton showers [27]. The remaining initial-state QED contributions\nare also small, whereas the photon radiation emitted by the \ufb01nal state leptons can have a signi\ufb01cant\nimpact on their mass (M) and transverse momentum spectra as well as the forward-backward asymmetry\nAFB [28].\nIn the vector-boson resonance region(s) these and the universal parts of the weak corrections, which\ncan amount to +80 (+40) % for muon (electron) pairs below and \u221218 (\u221210) % above the resonance,\ncan be taken into account by using a running value of \u03b1(M2) or, more generally, effective vector and\naxial vector couplings in the Effective Born Approximation. The corrections are then reduced to +6\n(+2) % for muon (electron) pairs below and +1 (< +1) % above the resonance. While the presence of\nnew physics can modify the running of the weak parameters, the QED corrections remain unaffected.\nThe electroweak corrections coming from non-factorisable box diagrams with double-boson ex-\nchange are small in the Z (and Z\u2032) resonance region(s), but they can be quite large away from these\nresonances (\u22124 to \u221216 % for electron pairs, \u221212 to \u221238 % for muon pairs of invariant mass 300 GeV\nto 2 TeV at the LHC, see Fig. 4).\n4.2.2\nNLO QCD Corrections\nThe QCD corrections to the Standard Model Drell-Yan process are known at NLO [29] and next-to-\nnext-to-leading order (NNLO) [30,31] in the strong coupling constant \u03b1s. The latter include in principle\nnon-factorisable corrections through qq and gg initial states, which remain, however, smaller than 1% in\npractice, even at small values of x, where the gluon density is large. The effects of multiple soft-gluon\nradiation have been resummed simultaneously in the low-pT and high-mass (above 500 GeV) regions\nat next-to-leading logarithmic (NLL) accuracy not only for Standard Model Z-bosons [32], but also for\nZ\u2032 bosons [33]. They were shown to be in good agreement with the NNLO result as well as the one\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1704\n\nFigure 4: NLO electroweak corrections in the high-mass region for Standard Model electron and muon\npair production at the LHC [23]. In the presence of a new resonance, these relative corrections would be\nlargely reduced (see text).\nobtained by matching NLO QCD to parton showers in MC@NLO [33, 34]. In contrast, the match-\ning of tree-level matrix elements to parton showers in PYTHIA [22] requires the ad hoc application of\na (slightly) mass-dependent correction (K) factor and leads to an unsatisfactory description of the pT\nspectrum. For resonant spin-2 graviton production, which involves not only color-triplet quark, but also\ncolor-octet gluon initial states, the NLO QCD corrections are substantially larger (K \u22431.6) [35,36] than\nthose for Standard Model or extra neutral gauge bosons (K \u22431.26, see Fig. 5). In this case, the matching\nof matrix elements to parton showers has only been performed at the tree-level [37], and resummation\nhas only been performed in the low-pT region [36].\nWhile the NLO total cross-sections for vector bosons and gravitons still change substantially when\nthe renormalization and factorization scales are varied simultaneously around the resonance mass M by\na factor of two (\u00b19%) [33,36], the scale uncertainty is reduced to the percent-level at NNLO [30,31] or,\nalternatively, to +6 and \u22123 % after joint resummation at the NLL order [33].\nThe theoretical uncertainty coming from different parameterizations of parton densities is estimated\nin Fig. 5 [33] for invariant masses above 500 GeV. Since the invariant mass of the lepton pair is corre-\nlated with the momentum fractions of the partons in the external protons, the normalized mass spectra\n(left) are indicative of the different shapes of the quark and gluon densities in the CTEQ6M5 parameter-\nization [38]. The latter also in\ufb02uence the transverse-momentum spectra (right). The shaded bands show\nthe uncertainty induced by variations, added in quadrature, along the 20 independent directions that span\nthe 90% con\ufb01dence level of the data sets entering the CTEQ6 global \ufb01t [39]. With about \u00b15% at 1 TeV\n(\u00b111% at 3 TeV), the PDF uncertainty is slightly larger than the scale uncertainty [33,40].\n5CTEQ collaboration has recently proposed new sets of PDFs. Using them, both the central values and uncertainties may\nchange by several percents.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1705\n\n500\n1000\n1500\n2000\n2500\n3000\n1\n1.05\n1.1\n1.15\n1.2\n1.25\n1.3\n1.35\nCTEQ\n0\n10\n20\n30\n40\n50\n60\n70\n0\n1\n2\n3\n4\n5\n6\n7\n8\nCTEQ\n-1\n(fb GeV )\nT\nd\ndp\n\u03c3\n(GeV)\nM\n(GeV)\nTp\nLO\nd\ndM d\ndM\n\u03c3\n\u03c3\nFigure 5: Mass (left) and transverse-momentum (right) spectra after matching the NLO QCD corrections\nto joint resummation with CTEQ6M parton densities. The mass spectra have been normalized to the LO\nQCD prediction using CTEQ6L parton densities. The shaded bands indicate the deviations allowed by\nthe up and down variations along the 20 independent directions that span the 90% con\ufb01dence level of the\ndata sets entering the CTEQ6 global \ufb01t.\nThe uncertainty at low transverse momenta coming from non-perturbative effects in the PDFs is usu-\nally parameterized with a Gaussian form factor describing the intrinsic transverse momentum of partons\nin the proton. Three different parameterizations of this form factor have been proposed [41\u201343]. In\nall three cases the transverse-momentum distribution is changed by less than +3 and \u22126 % for pT >\n5 GeV [33].\nCombining the three contributions (from the scales, the PDFs and the non-perturbative form factor),\nthe total theoretical QCD uncertainty is \u00b18.5% at 1 TeV, \u00b114% at 3 TeV. It must be noted that these\nuncertainties are common to the signal (heavy resonance) and background (Standard Model Drell-Yan).\n4.3\nEffect of Muon Spectrometer Misalignment\nAt large pT (\u2265100 GeV), an important contribution to the muon momentum resolution is the alignment\nof the muon spectrometer. In the early data period, the resolution is expected to be dominated by the\nalignment. The ultimate goal of the alignment system is to determine the position of the chambers in the\nmuon spectrometer to about 40 \u00b5m and \u03c3rot(mrad) = 0.5\u03c3trans(mm).\nA detailed study was carried out in order to determine the effect of possible larger uncertainties in the\nposition of the chambers to the Z\u2032 search. For the analysis, in addition to the ideal case of no misalignment\nat all, we have chosen 7 different hypotheses of misalignment: (40\u00b5m,20\u00b5rad), corresponding to the\ntarget value of the alignment system, (100 \u00b5m, 50 \u00b5rad), (200 \u00b5m, 100 \u00b5rad), (300 \u00b5m, 150 \u00b5rad),\n(500 \u00b5m, 250 \u00b5rad), (700 \u00b5m, 350 \u00b5rad) and (1000 \u00b5m, 500 \u00b5rad). In the last two cases, the alignment\nresolution is of the same order or greater than the track sagitta we want to measure.\nAs shown in Fig. 6, the dominant effect leading to a wash out of the signal is the resolution loss6. The\n6The slight excess of events around 600 GeV is due to mis-reconstructed Z bosons. In later versions of the software, this\neffect is not present anymore.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1706\n\nloss of resolution due to misalignment will deteriorate our ability to determine the charge of the muon.\nThis was also studied as a function of the misalignment and is summarized in Table 7.\n \n \n \n \n (GeV)\n\u00b5\n\u00b5\nM\n0\n500\n1000\n1500\n2000\n2500\n3000\n-1\nEvents/60GeV/100pb\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n \n \n \n \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nATLAS\nDrell-Yan invariant mass spectrum\n \n \n \n \n \n \n (GeV)\n\u00b5\n\u00b5\nM\n0\n500\n1000\n1500\n2000\n2500\n3000\n-1\nEvents/30GeV/100pb\n0\n1\n2\n3\n4\n5\n \n \n \n \n \n \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nIdeal\nm\n\u00b5\n100 \nm\n\u00b5\n300 \nm\n\u00b5\n1000 \nATLAS\n model mass spectrum\n\u03c7\nZ\u2019 \nFigure 6: Left: reconstructed invariant mass distribution of Drell-Yan events for different misalignment\nhypotheses. The numbers corresponds to an integrated luminosity of 100 pb\u22121. Right: reconstructed\ninvariant mass of the Z\u2032\n\u03c7 model for the seven misalignment scenarios.\nMisalignment (\u00b5m)\nIdeal\n40\n100\n200\n300\n500\n700\n1000\nRelative ef\ufb01ciency\n0.984\n0.984\n0.984\n0.98\n0.973\n0.948\n0.918\n0.877\nTable 7: Loss in signal ef\ufb01ciency due to the charge misidenti\ufb01cation for seven misalignment hypotheses.\n4.4\nOther Systematic Uncertainties\nAdditional experimental systematic uncertainties must be taken into account, listed as follows:\n\u2022 the uncertainty in the ef\ufb01ciency of object identi\ufb01cation was assumed to be 5% for muons, 1% for\nelectrons, and 5% for \u03c4 leptons;\n\u2022 the uncertainty in the energy scale was assumed to be 1% for muons, 1% for electrons, and 5% for\n\u03c4 leptons;\n\u2022 the uncertainty in the resolution of the objects is as follows: \u03c3( 1\npT ) = 0.011\npT \u22950.00017 for muons,\n20 % for electrons, and 45% for \u03c4 leptons.\n\u2022 the uncertainty in the luminosity was assumed to be 20% with an integrated luminosity of 100 pb\u22121\nof data and 3% for 10 fb\u22121.\nThe effect of all the above on the discovery potential is discussed in the next section for individual\nchannels.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1707\n\n5\nSearch for Exotic Physics\nIn this section we present the discovery potential for several resonant signatures in the early running of\nATLAS. We focus on the reach with an integrated luminosity of up to 10 fb\u22121 of data.\nThe statistical signi\ufb01cance of an expected signal can be evaluated in several ways. The simplest\napproach, \u201cnumber counting\u201d is based on the expected rate of events for the signal and background\nprocesses. From these rates, and assuming Poisson statistics, one can determine the probability that\nbackground \ufb02uctuations produce a signal-like result according to some estimator; e.g. the likelihood\nratio. In the \u201cshape analysis\u201d approach, a detailed knowledge of the expected spectrum of the signal and\nbackground for one observable (like the invariant mass distribution for example) can be used to improve\nthe sensitivity of the search by treating each mass bin as an independent search channel, and combining\nthem accordingly.\nThe resulting sensitivity is in general higher in the shape analysis than the estimation given in the\nnumber counting approach. In the shape analysis, the data is \ufb01tted or compared to two models: a\nbackground-only model and a signal-plus-background model. These are also called \u201cnull hypothesis\u201d,\nnoted H0 and \u201ctest hypothesis\u201d, noted H1, respectively. The input signal and background shapes are\ngiven to the \ufb01tting algorithms either as histograms in the non-parameterized approach [44] or as func-\ntions in the parameterized approach. For each of the models, a likelihood or a \u03c72 distribution is computed\nand the log of the ratio of the two likelihoods (LLR) or the difference of two \u03c72s are estimated and used\nto compute the con\ufb01dence levels. Either CLb = CLHO alone, or CLs = CLH1/CLH0 (in the \u201cmodi\ufb01ed\nfrequentist approach\u201d [44]) can then be used to compute the signi\ufb01cance S:\nS =\n\u221a\n2\u00d7Er f \u22121(1\u2212CLb)\nor\nS =\n\u221a\n2\u00d7Er f \u22121(1\u22121\nCLs\n)\n(1)\nin the double tail convention7.\nA convenient way to compute the LLR is to use the Fast Fourier Transform (FFT) method presented\nin [45]. The advantage of this method is that it does not require the generation of millions of pseudo-\nexperiments needed for high signi\ufb01cances and which can be time consuming. The sources of systematic\nuncertainties can then be incorporated as nuisance parameters.\nThe above methods have been used to investigate the discovery potential of the Z\u2032 boson in the\ndilepton (e, \u00b5, \u03c4) channels, of the graviton in the dielectron channel, and of Technicolor in the dimuon\nchannel. This is presented in the following sections.\n5.1\nBackground Estimation\nAs discussed in the previous section, neutral Drell-Yan production of lepton pairs is expected to be the\ndominant background for all the analyses (but \u03c4+\u03c4\u2212) and other contribution will be neglected here. Since\ndifferent techniques are used to estimate the signal signi\ufb01cance we also treat the Drell-Yan background\nin a few different but entirely consistent ways:\n\u2022 In the \u201cnumber counting\u201d approach, we simply count the expected number of events under the\nresonance peak from various background sources, including the Drell-Yan process.\n\u2022 In the non-parameterized CLs method, we use the number and shape of the mass distribution by\nproducing a histogram for the background.\n\u2022 For several analyses, we perform a \ufb01t to the Drell-Yan background parameterizing the shape which\nallows to estimate the number of background events and extrapolate it to higher masses.\n7In this convention, 1\u2212CLb has to be lower than 2.87\u00d710\u22127 to correspond to a 5\u03c3 signi\ufb01cance.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1708\n\nEach of these methods produces a complementary and consistent approach to estimating the main\nbackground. When the Drell-Yan \ufb01t is needed, we parametrize the shape of the background by the for-\nmula ae\u2212bMc, where M is the invariant mass of the lepton pair and a,b,c are parameters of the \ufb01t. Fits to\nthe Drell-Yan spectrum presented in section 4.2 suggest that the parameterization exp(\u22122.2M0.3) used\nby [46] describes the background shape well. It is this one which is used in the Z\u2032 \u2192\u00b5\u00b5, G \u2192ee and\ntechnicolor analyses. In the Z\u2032 \u2192ee analysis, these parameters are allowed to vary in the individual en-\nsemble tests. The \ufb01t to the entire spectrum letting all parameters \ufb02oat is consistent with this prescription.\n5.2\nZ\u2032 \u2192ee Using a Parameterized Fit Approach\n5.2.1\nEvent Selection\nThe selection of events with two electrons coming from a Z\u2032 has been studied in samples of fully simu-\nlated Z\u2032\n\u03c7 \u2192e+e\u2212events with Z\u2032 boson masses of 1, 2 and 3 TeV, corresponding respectively to integrated\nluminosities of 21 fb\u22121, 204 fb\u22121 and 2392 fb\u22121.\nThe \ufb01rst requirement is that the two highest pT clusters in the event be in the geometrical acceptance.\nThe next requirement is that these clusters be associated with a track; its ef\ufb01ciency is 67% at 1 TeV and\ndecreases for higher masses. The third requirement is that these two reconstructed electron candidates\nbe identi\ufb01ed as loose electrons. The relative ef\ufb01ciency of such a selection is at least 94% and increases\nwith invariant mass. The trigger studies have been normalized to events with two loose electrons. As\nshown in section 3.1, the highest trigger ef\ufb01ciency is obtained with a non-isolated single electron trigger\n(e55). Its ef\ufb01ciency is 90.8% per event. The last requirement is that the two electrons have opposite\nelectric charges. The requirement \ufb02ow is presented in Table 8, where the events are counted in a window\nof \u00b14 \u0393Z\u2032 around the center of the resonance. Although the opposite charge requirement is optional in\nthe absence of a large background, especially at very high invariant mass, it allows to have a control\nsample (made of same sign dielectrons) for the background. The resulting overall ef\ufb01ciency is 48% at\nm = 1 TeV, 42% at m = 2 TeV and about 34% at m = 3 TeV.\nSelection\nSignal\nDY\nSignal\nDY\nSignal\nDY\nat 1 TeV\nat 1 TeV\nat 2 TeV\nat 2 TeV\nat 3 TeV\nat 3 TeV\n347.\n3.56\n14.7\n0.16\n1.22\n0.015\n2 generated e\u00b1, |\u03b7| < 2.5\n299.\n3.07\n13.7\n0.15\n1.16\n0.013\n2 clusters with a track\n201.\n2.06\n8.0\n0.09\n0.62\n0.009\n2 loose electrons\n190.\n1.96\n7.2\n0.08\n0.52\n0.008\nAt least one pT > 65 GeV\n190.\n1.96\n7.2\n0.08\n0.52\n0.008\nEvent triggered\n173.\n1.77\n6.6\n0.07\n0.47\n0.007\n2 opposite charges\n166.\n1.70\n6.2\n0.07\n0.43\n0.007\nTable 8: Requirement \ufb02ow table for the Z\u2032 \u2192e+e\u2212analysis: cross-sections in fb. The events are counted\nin a window of \u00b14 \u0393Z\u2032 around the resonance.\nThe above ef\ufb01ciencies, normalized to events in the geometrical acceptance (|\u03b7| < 2.5), are shown in\nFig. 7 (left) as a function of the invariant mass of the electrons. They do not depend on the model used\nto generate the Z\u2032 samples. Only the requirement that the two electrons be in the geometrical acceptance\ndepend on the model. Indeed, the relative proportions of initial quark \ufb02avors depend on the couplings of\nthe Z\u2032 to the quarks. The PDF of the up quarks being harder than that of the down quarks, Z\u2032 produced\nby a u \u00afu pair tend to be slightly more boosted, and therefore the electrons stemming from their decay\ntend to be produced at slightly higher pseudo-rapidities. This effect is visible in Fig. 7 (right) showing\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1709\n\n(GeV)\ne+e-\nGen\nM\n1000\n2000\n3000\n4000\nE\ufb03ciency\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n2 reconstruted electrons\n2 loose electrons\nevent triggered\nopposite charges\nATLAS\n1000\n2000\n3000\n4000\n0.84\n0.86\n0.88\n0 9\n0.92\n0.94\n0.96\nATLAS\nEfficiency\n(GeV)\ne+e-\nGen\nM\nSSM\nLR\n'\n'\n'\n'\n'\nDY\nZ\nZ\nZ\nZ\nZ\n\u03c8\n\u03c7\n'\n'\nZ\nZ\n\u03b7\ndd \u2192\nuu \u2192\nqq \u2192\nqq \u2192\nqq \u2192\nqq \u2192\nqq \u2192\nqq \u2192\nFigure 7:\nZ\u2032\n\u03c7 \u2192e+e\u2212selection ef\ufb01ciency as a function of the generated invariant mass. Left: all selections,\nnormalized to events in the geometrical acceptance; right: |\u03b7| < 2.5 criteria for u \u00afu and d \u00afd events separately and\nfor different Z\u2032 models (generator level).\nthe ef\ufb01ciency of the |\u03b7| selection for u \u00afu and d \u00afd events separately, and for a number of benchmark Z\u2032\nmodels: the Sequential Standard Model (Z\u2032\nSSM), the E6 models Z\u2032\n\u03c8, Z\u2032\n\u03c7, Z\u2032\n\u03b7, and the left-right symmetric\nmodel (Z\u2032\nLR). It is therefore possible to generalize the ef\ufb01ciencies that have been measured in the fully\nsimulated samples to models which haven\u2019t been simulated as well as to intermediate masses.\n5.2.2\nDiscovery Potential\nModeling of the dilepton invariant mass spectrum.\nIn order to compute the signi\ufb01cance for several\nZ\u2032 models, a parameterization of the mass spectrum of the signal and of the background has been used.\nThe differential cross-section can be factorized with a good precision in a parton-level term d \u02c6\u03c3\ndm and a\nPDF-dependent term GPDF(m):\nd\u03c3\ndm(m) = d \u02c6\u03c3\ndm(m)\u00d7GPDF(m)\n(2)\nUsing this factorization, one can write:\nd\u03c3\ndm\n\f\f\f\f\nDY\n(m) = 1\nm2 \u00d7GPDF(m)\n(3)\nd\u03c3\ndm\n\f\f\f\f\nSignal\n(m)\n=\n1\nm2 \u00d7GPDF(m)\n+\nApeak \u00d7 \u03932\nZ\u2032\nm2\nZ\u2032\nm2\n(m2 \u2212m2\nZ\u2032)2 +m2\nZ\u2032\u03932\nZ\u2032\n\u00d7GPDF(m)\n(4)\n+\nAinterf \u00d7 \u03932\nZ\u2032\nm2\nZ\u2032\nm2 \u2212m2\nZ\u2032\n(m2 \u2212m2\nZ\u2032)2 +m2\nZ\u2032\u03932\nZ\u2032\n\u00d7GPDF(m)\nwhere Apeak is the amplitude of the Z\u2032 process and Ainterf is the amplitude of the interference Z\u2032/Z and\nZ\u2032/\u03b3, both normalized to the Drell-Yan process. This parameterization only depends on four parameters:\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1710\n\nmZ\u2032, \u0393Z\u2032, Apeak and Ainterf. The differential cross-section is then multiplied by the appropriate K-factor\n(see section 4.2). The detector performance is accounted for as follows: the differential cross-section\nis multiplied by the ef\ufb01ciency computed above and convoluted by the invariant mass resolution (see\nsection 2.1). The agreement between this parameterization and the full simulation is shown in Fig. 8\n(left) for a Z\u2032\n\u03c7 at 1 TeV.\nLLR\n0\n20\n40\n60\n80\n100\nFrequency\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nSigni\ufb01cance = 6.45\nH0\nH1\n-1\nLuminosity = 1 fb\nATLAS\nM (GeV)\n500\n600\n700\n800\n900\n1000 1100 1200 1300 1400 1500\n)\n-1\n/dm (fb GeV\n\u03c3\nd\n-2\n10\n-1\n10\n1\nATLAS\n1 TeV Z'\n- parameterization\nDrell-Yan - parameterization\n1 TeV Z'\n- ATLAS simulation\n\u03c7\n\u03c7\nFigure 8:\nLeft: mass spectrum for a m = 1 TeV Z\u2032\n\u03c7 \u2192e+e\u2212obtained with ATLAS full simulation (histogram)\nand the parameterization (solid line). The dashed line corresponds to the parameterization of the Drell-Yan process\n(irreducible background). Right: Log-likelihood ratio densities with 1 fb\u22121 for a m = 2 TeV Z\u2032\n\u03c7 for the signal and\nbackground hypotheses. The vertical line is the median experiment in the H1 hypothesis.\nResults\nUsing the parameterization presented above to generate mass spectra for signal (\u03b3/Z/Z\u2032 \u2192\ne+e\u2212) and background (\u03b3/Z \u2192e+e\u2212), one can compute the distributions of the log-likelihood ratio of\nthe signal (H1) and background (H0) hypotheses.\nFigure 8 (right) shows the LLR distributions obtained for a 2 TeV Z\u2032\n\u03c7 with 1 fb\u22121 as well as the median\nsignal experiment used to calculate CLs. The FFT method [45] was used in the computation of the LLR\ndistributions. It is important to note that the mass window used to perform the analysis does not affect\nthe result.\nFigure 9 (left) shows the integrated luminosity needed for a 5\u03c3 discovery of the usual benchmark\nZ\u2032 models as a function of the Z\u2032 mass. Only statistical uncertainties were taken into account. The\nsystematic uncertainties are discussed in the next paragraph. A \ufb01xed mass window of [500 GeV\u22124 TeV]\nwas used to compute the signi\ufb01cance. Roughly speaking, less than 100 pb\u22121 are needed to discover a\n1 TeV Z\u2032, about 1 fb\u22121 are needed to discover a 2 TeV Z\u2032, and about 10 fb\u22121 are needed to discover a\n3 TeV Z\u2032.\nSystematic Uncertainties\nThe sources of systematic uncertainties were listed in section 4. Since the\nmain background is the Drell-Yan process, the systematic uncertainties from both the ef\ufb01ciencies and\nthe theoretical predictions on the cross-section will affect the number of signal and background events\nin the same way, and can be added in quadrature. The uncertainties in the event selection ef\ufb01ciency\nmainly come from the electron identi\ufb01cation and the geometrical acceptance. The former amounts to\n2 \u00d7 \u00b11% = \u00b12% for two electrons. Taking the extreme ef\ufb01ciencies for pure u \u00afu and d \u00afd events as a\nconservative estimate, the latter goes from \u00b13 to \u00b10.5%. Overall, this represents a systematic uncertainty\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1711\n\n1000\n1500\n2000\n2500\n3000\n-2\n10\n-1\n10\n1\n10\nSSM\nLR\n'\n'\n'\n'\n'\nZ\nZ\nZ\nZ\nZ\n\u03c8\n\u03c7\n\u03b7\nATLAS\n(GeV)\nZ\u2019\nM\nL (fb )\n-1\n1000\n1500\n2000\n2500\n3000\n-2\n10\n-1\n10\n1\n10\n(GeV)\nZ\u2019\nM\nL (fb )\n-1\nATLAS\n'\nZ \u03c7\nSystematic uncertainty\nFigure 9:\nIntegrated luminosity needed for a 5\u03c3 discovery of Z\u2032 \u2192e+e\u2212as a function of the Z\u2032 mass. Left:\nfor various benchmark models with statistical uncertainties only; right: for the Z\u2032\n\u03c7 with systematic uncertainties\nincluded.\nof \u00b13.6% to \u00b10.6% from the event selection. This is small as compared to the theoretical uncertainties,\nwhich range from \u00b18.5% to \u00b114%. The effect of these combined uncertainties on the luminosity needed\nto discover 1, 2 and 3 TeV Z\u2032s is +9\n\u221210%, +14\n\u221210%, +15\n\u221213% (respectively).\nThe uncertainty in backgrounds other than the Drell-Yan process is another type of uncertainty. How-\never, given that the Drell-Yan contribution is at the level of about 1% of the signal, any variation of the\nlevel of non-Drell-Yan background, which is more than ten times smaller, is negligible.\nThe uncertainty in the electron energy resolution is another type of uncertainty. In addition to the\nexpected uncertainties in the energy resolution as measured in the calorimeter (see section 4), we have\nconservatively assumed that there was no increase in precision on the measured dielectron invariant mass\ncoming from the angle measurement provided by the tracker. In this case, the resolution of invariant\nmass increases from about 1% (see section 2.1) to about 1.5%. The effect of these uncertainties on the\nluminosity needed for a discovery is +5\n\u22122%, independent of the Z\u2032 mass.\nThe last type of uncertainty which has been considered is the electron energy scale. When varied\nwithin the expected uncertainties, the discovery luminosity varies by +2.5\n\u22120 %, independent of the Z\u2032 mass.\nCombining all the above systematic uncertainties, the luminosity needed to discover, for example, a\nZ\u2032\n\u03c7 is shown in Fig. 9 (right). It must be noted that the systematic effect coming from the fact that we\ndo not know a priori the mass of the signal was not taken into account. This is adressed separately in\nappendix A.\n5.3\nZ\u2032 \u2192\u00b5\u00b5 Using a Parameterized Fit Approach\nThe dimuon channel represents an important complement to the dielectron channel. Although the reso-\nlution is expected to be up to an order of magnitude worse in the kinematic regime of interest, reducible\nbackgrounds are expected to be considerably lower as discussed in Section 4.1. This feature makes the\ndimuon channel competitive, especially with early data where the design background rejection may not\nbe achieved. In this section we consider two signal models decaying into dimuons - the Z\u2032\nSSM and the Z\u2032\n\u03c7\nboson.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1712\n\n5.3.1\nEvent Selection\nTo select events from the Z\u2032 \u2192\u00b5\u00b5 process we require two muons of opposite charge. The muons are\nrequired to ful\ufb01ll the muon identi\ufb01cation criteria studied in Section 2.2, including pT \u226530 GeV and\n|\u03b7| \u22642.5 . Events are triggered using the mu20 trigger described in Section 3.2. As seen in Section 4.1,\nthis should select a sample which consists mainly of Z/\u03b3 \u2192\u00b5\u00b5 with limited contamination from other\nsources of the order of a few percent. Table 9 indicates the effects of the various requirements on both\nthe signal and background samples.\nSample\nZ\u2032\nSSM (1 TeV)\nZ\u2032\n\u03c7 (1 TeV)\nDrell-Yan\nGenerated\n508.6\n380.6\n13.5\n|\u03b7| \u22642.5\n366.8\n271.5\n10.8\npT \u226530 GeV\n364.0\n270.1\n10.7\nMuon identi\ufb01cation\n342.3\n256.0\n10.0\nTrigger\n325.2\n243.2\n9.5\nOpposite charge\n324.8\n243.0\n9.5\nTable 9: Selection requirement \ufb02ow for the Z\u2032 \u2192\u00b5\u00b5 analysis - cross-sections in fb. Events are counted\nin a mass window of \u00b150 GeV of the resonance mass (signal) and for m\u00b5\u00b5 > 800 GeV (background).\n5.3.2\nDiscovery Potential\nTo evaluate the discovery potential, we use the FFT method [45], as in section 5.2. The amount of\ndata required to discover a Z\u2032 boson is computed from the log-likelihood ratio (LLR) of the signal (H1)\nand background (H0) hypotheses. Figure 10 shows the 1\u2212CLb obtained as a function of the integrated\nluminosity for the two studied Z\u2032 boson models at m = 1 TeV. The largest expected systematic uncertainty\n(from misalignment of the muon spectrometer) is shown separately. One can see that the amount of\nluminosity needed for a 5\u03c3 discovery ranges from 20 to 40 pb\u22121, which is competitive with the dielectron\nchannel.\n)\n-1\nLuminosity (pb\n5\n10\n15\n20\n25\nb\n1-CL\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nNo systematics\nTrigger\nTrigger + DY (9% nuisance parameter)\nm misalignment\n\u00b5\n300\nm nuisance parameter)\n\u00b5\nm (+-150 \n\u00b5\n300\nAll systematics\nATLAS\n discovery potential\n\u03c3\n5 \n)\n-1\nLuminosity (pb\n5\n10\n15\n20\n25\n30\n35\n40\n45\nb\n1-CL\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nNo systematics\nTrigger\nTrigger + DY (9% nuisance parameter)\nm misalignment\n\u00b5\n300\nm nuisance parameter)\n\u00b5\nm (+-150 \n\u00b5\n300\nAll systematics\nATLAS\n discovery potential\n\u03c3\n5 \nFigure 10: Results of the FFT computation of 1\u2212CLb for m = 1 TeV Z\u2032\nSSM (left) and Z\u2032\n\u03c7 (right) bosons.\nThe horizontal line indicates the 1\u2212CLb value corresponding to 5\u03c3.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1713\n\nSystematic Uncertainties\nSection 4 describes the systematic uncertainties that were considered. As\ncan be seen from Fig. 10 the effect of the nominal systematic uncertainties is modest in this channel.\nThe largest theoretical uncertainty entering this study is the knowledge of the Standard Model Drell-\nYan cross-section. In the dimuon channel, the largest experimental uncertainty is the resolution for high\npT muons which will be initially dominated by the alignment of the muon spectrometer. As already dis-\ncussed, the nominal alignment precision may not be achievable with the integrated luminosities presented\nhere and hence could signi\ufb01cantly alter the conclusions. Figure 10 shows that the integrated luminosity\nneeded to reach 5\u03c3 increases from 13 to 20 pb\u22121 if the muon spectrometer is aligned with a precision of\n300 \u00b5m. This takes into account an uncertainty of 150 \u00b5m on the alignment precision estimate, which\nwill have to be measured in data (e.g. from the Z \u2192\u00b5\u00b5 sample) and which is treated as a nuisance\nparameter in the sensitivity computation.\n5.4\nZ\u2032 \u2192\u03c4\u03c4 Using a Number Counting Approach\nThe ditau signature is an important component to the high mass resonance search. In particular, there\nare models in which a hypothetical new resonance couples preferentially to the third generation [47].\nFor these models the branching ratios are such that the dielectron and dimuon channels are not viable -\nhence it is critical that we consider all possible channels including ditaus. In this section we discuss the\ndiscovery potential for such a resonance. Because of \ufb01nite resources we restrict ourselves to the process\nZ\u2032 \u2192\u03c4\u03c4 with a single mass point m = 600 GeV although much of the discussion generalizes to a generic\nditau resonance search. The ditau \ufb01nal state can be divided into three \ufb01nal states: hadron-hadron (where\nboth \u03c4 leptons decay hadronically), hadron-lepton (where one \u03c4 lepton decays hadronically and one\ndecays leptonically), and lepton-lepton (where both decay leptonically). Here we consider the hadron-\nlepton (h \u2212\u2113) \ufb01nal state. The possibility of observing the hadron-hadron \ufb01nal state using a hadronic \u03c4\ntrigger will be examined later.\n5.4.1\nEvent Selection\nTo select events in the hadron-lepton \ufb01nal state, we select events with a \u201chadronic \u03c4\u201d candidate, a charged\nlepton (muon or electron), and missing transverse energy 8 (/ET). As opposed to the dielectron or dimuon\nchannel, the backgrounds to the ditau channel are considerably larger and include Drell-Yan production,\nW+jets, t\u00aft and dijet events. After the initial object selection several additional requirements are needed\nto maximize the expected signal signi\ufb01cance.\nWe consider hadronic \u03c4 candidates with pT > 60 GeV and impose a requirement on the likelihood as\na function the \u03c4 transverse energy as described in Section 2.3. Candidates which overlap with an electron\nor muon are removed.\nFor electron candidates we require medium electron selection criteria in this analysis (see Section\n2.1). The initial muon selection is the same as described in Section 2.2. Since this channel only requires\none high pT lepton the backgrounds are considerably higher than for the dielectron or dimuon \ufb01nal\nstates. To address this we impose additional requirements on the isolation of the lepton. The isolation\nrequirement imposed on electron candidates is \u2211E\u2206R<0.2\nTEM\n/pT < 0.1 where \u2211E\u2206R<0.2\nTEM\nis the sum of the\nenergy deposits in the electromagnetic calorimeter within a cone of \u2206R = 0.2 from the location in \u03b7-\u03c6 of\nthe electron, less the electron candidate energy. Isolated electrons are required to have pT > 27 GeV. We\nimpose an isolation requirement similar to that of electrons on muon candidates: \u2211E\u2206R<0.2\nTEM\n< 0.1. For\nisolated muons we require that the \u03c72 lie between 0 and 20 and to be considered by the analysis muons\nmust have pT > 22 GeV.\n8The missing transverse energy was reconstructed using the cell based algorithm described in [48].\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1714\n\nSelection\nSignal\nt\u00aft\nDrell-Yan\nMultijet\nW+jet\nTrigger\n1356.\n213600.\n2.3950 107\n4.19000 106\n6.69400 106\nLepton\n905.\n150900.\n1.2600 107\n1.08230 106\n120400.\n\u03c4 selection\n368.\n7818.\n145680\n40080\n4587.\nOpposite charge\n315.\n2498.\n5306\n23240\n771.\n/ET>30 GeV\n270.\n2040.\n2562\n835\n162.\nmT < 35 GeV\n203.2\n302.4\n388.0\n436.4\n83.8\nptot\nT < 70 GeV\n155.0\n106.7\n331.5\n221.6\n28.4\nmvis > 300 GeV\n132.5\n26.2\n105.6\n33.8\n15.0\ncos\u2206\u03c6\u2113h > \u22120.99\n13.3\n2.1\n5.5\n2.3\n2.7\nTable 10: Requirement \ufb02ow table for the m = 600 GeV Z\u2032\nSSM \u2192\u03c4\u03c4 \u2192\u2113h analysis - cross-sections given\nin fb. The Drell-Yan process includes all \ufb02avors of leptons (e+e\u2212, \u00b5+\u00b5\u2212, \u03c4+\u03c4\u2212) with an invariant mass\nof at least 60 GeV.\nAfter making the \u03c4 candidate selection we make several further requirements to maximize the signal\nsigni\ufb01cance. First, we require that /ET\u226530 GeV. To greatly help with the rejection of the t\u00aft backgrounds\nwe employ a requirement on the total event pT which is de\ufb01ned as the sum of /ETand the vector sum of\nthe hadronic \u03c4 with the lepton transverse momentum. We require ptot\nT < 70 GeV.\nThe transverse mass of the event is determined by using the lepton kinematics and the event /ET.\nDe\ufb01ning a four-vector for the missing energy: /pT = (/ET x, /ET y,0,|/ET|), the transverse mass is calculated\nas:\nmT =\nq\n2pT,\u2113/pT(1\u2212cos\u2206\u03c6\u2113,/pT ).\nWe require that mT < 35 GeV.\nIn the case of the lepton-hadron channel one cannot simply reconstruct the invariant mass of the\nresonance as energy is taken away from the event by the neutrinos. However, two quantities can be\nconstructed\n\u2022 A visible mass variable is calculated as de\ufb01ned by CDF [49] using the hadronic \u03c4 and the lepton\nfour-vector information:\nmvis =\nq\n(p\u2113+ ph + /pT)2\n\u2022 The collinear approximation is used to build up the event-by-event invariant mass. The fraction\nof the \u03c4 momentum carried by the visible decay daughters, x\u2113and xh, are calculated with the\nfollowing formulas:\nx\u2113=\npx,\u2113py,h \u2212px,hpy,\u2113\npy,hpx,\u2113+ py,h p/x \u2212px,hpy,\u2113\u2212px,hp/y\n, xh =\npx,\u2113py,h \u2212px,hpy,\u2113\npy,hpx,\u2113+ px,\u2113p/y \u2212px,hpy,\u2113\u2212py,\u2113p/x\n.\nThe reconstructed mass is then calculated as m\u03c4\u03c4 =\nm\u2113,h\n\u221ax\u2113xh .\nTo greatly help the background rejection and to restrict our search to the region of interest we require\nmvis > 300 GeV. Since the collinear approximation breaks down when the two \u03c4 leptons are back-to-\nback, we impose the requirement that cos\u2206\u03c6\u2113h > \u22120.99. Of course, since a very heavy particle tends\nto be produced at rest, the decay objects are mostly back-to-back, leading to a highly inef\ufb01cient mass\nreconstruction.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1715\n\nVisible Mass GeV\n0\n200\n400\n600\n800\n1000\n1200 1400\n-1\nEvents/fb\n0\n20\n40\n60\n80\n100\n120\nVisible Mass GeV\n0\n200\n400\n600\n800\n1000\n1200 1400\n-1\nEvents/fb\n0\n20\n40\n60\n80\n100\n120\n\u03c4\n\u03c4\n\u2192\nZ\u2019\nttbar\nQCD\nW+jets\nDrell-Yan\nATLAS\nCollinear Mass GeV\n0\n200\n400\n600\n800\n1000\n1200\n1400\n-1\nEvents/fb\n0\n1\n2\n3\n4\n5\n6\n7\n8\nCollinear Mass GeV\n0\n200\n400\n600\n800\n1000\n1200\n1400\n-1\nEvents/fb\n0\n1\n2\n3\n4\n5\n6\n7\n8\n\u03c4\n\u03c4\n\u2192\nZ\u2019\nttbar\nQCD\nW+jets\nDrell-Yan\nATLAS\nFigure 11: Left: the visible mass distribution in the Z\u2032 \u2192\u03c4\u03c4 \u2192\u2113h analysis for signal and background pro-\ncesses (1 fb\u22121 of data is assumed). Right: the reconstructed invariant mass obtained using the collinear\napproximation.\n5.4.2\nDiscovery Potential for 1 fb\u22121 of Data\nTable 10 shows the effect of the various selection requirements for the signal as well as all background\nprocesses considered. Distributions of the visible and reconstructed masses for signal and background\nare shown in Fig. 11. Here we assume a 600 GeV Z\u2032 and the SSM cross-section. In 1 fb\u22121 of ATLAS\ndata we estimate 132. signal events and 181. background events after imposing the event selection up to\nthe requirement on visible mass. Using S/\n\u221a\nB we estimate the signal signi\ufb01cance to be 9.9. The collinear\napproximation breaks down when the two \u03c4 leptons are back-to-back, so that even a loose requirement\n(such as cos\u2206\u03c6\u2113h > \u22120.99) reduces the signal by a large factor. Hence, we expect that the search will\nproceed by looking at the visible mass. If a signi\ufb01cant excess over background is seen, the collinear\napproximation will then be used to help establish the presence of a new resonance.\nSystematic uncertainties\nThe systematic uncertainties that were considered are described in Section 4.\nFor an analysis of 1 fb\u22121 of data the dominant systematic source on the signal, just over \u00b118%, comes\nfrom the uncertainty in the luminosity. The second most dominant systematic, the hadronic \u03c4 energy\nscale, affects the signal at the \u00b110% level. Summing in quadrature the effect of all systematic uncer-\ntainties on the signal Monte Carlo sample results in a total systematic uncertainty of about \u00b120%. The\ncurrent Monte Carlo samples available for the backgrounds to the ditau analysis are statistically limited\nand hence prevent a rigorous evaluation of the systematics at this time. As a conservative estimate, we\nassume that the total systematic uncertainty in the backgrounds is identical to that observed in the signal\nMonte Carlo. This is a conservative estimate because the majority of the backgrounds in the data have\nvery large cross-sections (dijets, W+jets, etc.) and in principle the evaluation of systematic uncertain-\nties there should be less sensitive to statistical \ufb02uctuations than for the signal events. Summing these\nsystematic uncertainties in quadrature and using the formula S/\n\u221a\nB+\u03b4B2 gives a signi\ufb01cance of 3.4 in\n1 fb\u22121.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1716\n\n5.5\nG \u2192e+e\u2212in a Parameterized Fit Approach\nIn this section we present a sensitivity study for the Randall-Sundrum G \u2192ee \ufb01nal state. In this channel,\nit is assumed that there is no interference between the G and the dilepton background. Table 11 shows\nthe parameters of the different G samples used in this analysis. \u0393G is the simulated graviton resonance\nwidth and \u03c3m stands for the width of the observed resonance after convolution with detector resolutions.\nFor k/ \u00afMpl < 0.06 the resonance is narrow compared to the experimental resolution.\nThe main Standard Model background is neutral Drell-Yan production. Other backgrounds such as\ndijets with both jets misidenti\ufb01ed as electrons are expected to be small and neglected at this time.\nModel Parameters\n\u0393G\n\u03c3m\n\u03c3 \u00b7BR(G \u2192e+e\u2212)\nmG\nk/ \u00afMpl\n[GeV]\n[GeV]\n[fb]\n500 GeV\n0.01\n0.08\n4.6\n187.4\n750 GeV\n0.01\n0.10\n6.4\n27.7\n1.0 TeV\n0.02\n0.57\n7.9\n26.0\n1.2 TeV\n0.03\n1.62\n10.3\n22.4\n1.3 TeV\n0.04\n2.98\n11.4\n25.3\n1.4 TeV\n0.05\n5.02\n13.1\n26.8\nTable 11: Parameters of the G \u2192ee samples used: natural width (\u0393G), Gaussian width after detector\neffects (\u03c3m) and leading order cross-section.\n5.5.1\nEvent Selection\nIn reconstructing the resonance mass, we require a pair of electrons \u2013 we do not make any charge re-\nquirements \u2013 with pT \u226565 GeV using the loose electron selection criteria described in Section 2.1. We\nrequire that the events pass the e55 single electron trigger (see section 3.1). Finally we require that\nthe two electrons are roughly back-to-back in \u03c6 with cos\u2206\u03c6ee < 0 between the two electrons. Table 12\nshows the remaining cross-section at each stage of the selection and the total e\ufb01ciency for different mass\npoints. The ef\ufb01ciency decreases at high graviton masses, due to the track match requirement, which is\nconsistent with the Z\u2032 boson analysis (see section 5.2). Table 13 shows the same requirement \ufb02ow for\nthe Drell-Yan.\nThe Drell-Yan background distribution after this event selection is shown in Fig. 12 along with signal\nat mG = 1 TeV and coupling k/ \u00afMpl = 0.02. The exponential described in Section 5.1 has been used to\nmodel the shape of the background.\n5.5.2\nDiscovery Potential\nWe search for an excess of events in the mass range from 300 GeV up to 2 TeV and study the signal\nsensitivity by use of \u201cextended maximum likelihood\u201d \ufb01tting. We consider two hypotheses. The null\nhypothesis, H0, is the hypothesis that the data are described by the Standard Model. The test hypothesis,\nH1, is that the data are described by the sum of the background and a narrow Gaussian resonance.\nTo investigate the potential for discovery pseudo-experiments are generated from both the null and\ntest hypothesis. Each pseudo-experiment is \ufb01t twice. The \ufb01rst \ufb01t assumes the data are described by\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1717\n\nSelection / Sample\n500 GeV\n750 GeV\n1.0 TeV\n1.2 TeV\n1.3 TeV\n1.4 TeV\nGenerated\n187.4\n27.7\n26.0\n22.4\n25.3\n26.8\nAcceptance\n172.4\n25.9\n24.7\n21.2\n24.0\n25.4\nTrigger\n168.7\n25.0\n22.6\n19.1\n21.4\n22.3\nElectron Id.\n127.9\n18.3\n16.4\n12.8\n14.6\n14.7\npT \u226565 GeV\n125.7\n18.2\n16.3\n12.7\n14.5\n14.6\ncos\u2206\u03c6ee < 0\n123.0\n17.8\n16.0\n12.6\n14.3\n14.4\nSelection ef\ufb01ciency (%)\n65.6\u00b11.1\n64.4\u00b11.1\n61.7\u00b11.1\n56.3\u00b11.1\n56.4\u00b11.1\n53.9\u00b11.1\nTable 12: Requirement \ufb02ow for the G \u2192ee analysis. The remaining cross-section (in fb) is given at each\nstage. The mass window is chosen as \u00b14\u03c3m around the signal peak.\nSelection/Sample\n500 GeV\n750 GeV\n1.0 TeV\n1.2 TeV\n1.3 TeV\n1.4 TeV\nGenerated\n20.33\n4.91\n1.43\n0.90\n0.51\n0.51\nAcceptance\n18.53\n4.50\n1.36\n0.87\n0.48\n0.49\nTrigger\n18.45\n4.25\n1.16\n0.80\n0.45\n0.44\nElectron Id.\n14.13\n3.18\n0.88\n0.58\n0.38\n0.33\npT \u226565 GeV\n13.85\n3.15\n0.88\n0.57\n0.38\n0.33\ncos\u2206\u03c6ee < 0\n13.41\n3.09\n0.85\n0.56\n0.36\n0.33\nTable 13: Remaining Drell-Yan cross-section (in fb) at each stage of the G \u2192ee analysis. The mass\nwindow is chosen as \u00b14\u03c3m around the signal peak.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1718\n\n (GeV)\nee\nM\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n-1\nEvents / (20GeV) / 1.0fb\n-2\n10\n-1\n10\n1\n10\nATLAS\nhistogram - expected\nfull circles - \"observed\"\nLog LR\n0\n20\n40\n60\n80\n100\n120\n140\n160\npseudoevents / 0.64\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nB\nS+B\nATLAS\nFigure 12: Left: expected (histogram) and \u201cobserved\u201d (\ufb01lled circles) Drell-Yan spectrum from full sim-\nulation. The observed distribution includes a graviton with mass of 1 TeV and coupling k/ \u00afMpl = 0.02.\nNote that for the purposes of this plot the vertical axis has been rescaled: the error bars correspond to an\nintegrated luminosity of 100 fb\u22121. Right: Log likelihood ratio curves for one million pseudo-experiments\ngenerated with background only (\ufb01lled circles), and signal plus background (empty circles) for the same\nm = 1 TeV signal point.\nthe Standard Model using the function described in Section 5.1. The second \ufb01t assumes the data are\ndescribed by the sum of a Gaussian and the shape describing the Drell-Yan background. During this\nsecond \ufb01t the mean of the Gaussian is allowed to \ufb02oat throughout the entire mass region considered, and\nthe width is \ufb01xed to the detector resolution.\nGraviton M (GeV)\n400\n600\n800\n1000\n1200\n1400\n1600\nee) fb\n\u2192\n x BR(G*\n\u03c3\n1\n10\n2\n10\n3\n10\n1.6)\n\u00d7\n=0.01 (\npl\nM\nk/\n1.6)\n\u00d7\n=0.02 (\npl\nM\nk/\n1.6)\n\u00d7\n=0.03 (\npl\nM\nk/\n1.6)\n\u00d7\n=0.04 (\npl\nM\nk/\n1.6)\n\u00d7\n=0.05 (\npl\nM\nk/\n Discovery\n\u03c3\n5\n Evidence\n\u03c3\n3\n=14TeV\ns\n-1\n L dt=1.0fb\n\u222b\nATLAS\nGraviton M (GeV)\n600\n800\n1000\n1200\n1400\npl\nM\nk/\n0.005\n0.01\n0.015\n0.02\n0.025\n Discovery Limits\n\u03c3\n5\n Evidence Limits\n\u03c3\n3\n-1\n L dt=1.0fb\n\u222b\n=14TeV\ns\nATLAS\nFigure 13: 5\u03c3 discovery potential (full squares) as a function of the graviton mass. The 3\u03c3 evidence\npotential is also shown (full circles). Left: shown with cross-sections as calculated by PYTHIA (LO) and\nmultiplied by a K factor of 1.6 for several values of the coupling; right: dependence of the discovery\npotential on the coupling.\nWe can then compare the likelihood of the signal and background hypotheses. The distribution of\nthe logarithm of the likelihood ratio between H0 and H1 is constructed, and shown for one signal point\nin Fig. 12. Based on this, we calculate the average expected discovery potential from the fraction of\nthe likelihood ratio distribution for background-only pseudo-experiments that extends beyond the mean\nof the distribution for signal plus background experiments. Figure 13 shows the 5\u03c3 discovery and 3\u03c3\nevidence reach in cross-section and k/ \u00afMpl coupling constant as a function of graviton mass, estimated\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1719\n\nfor an integrated luminosity of 1 fb\u22121.\nThe LO cross-sections are multiplied by the K-factors discussed in section 4.2.2 for both signal and\nDrell-Yan background. Various sources of systematic uncertainties for signal and background are con-\nsidered in the evaluation of the experimental sensitivity, including luminosity, energy scale, energy reso-\nlution, electron identi\ufb01cation ef\ufb01ciency and Drell-Yan background uncertainties as listed in section 4.4.\nThe combined effect of the systematic uncertainties is to increase the amount of integrated luminosity\nneeded for discovery between 10 and 15 percent for the different parameter sets.\n5.6\nTechnicolor Using a Non-Parameterized Approach\nTopcolor-assisted Technicolor models with walking gauge coupling predict new technihadron states that\nwould be copiously produced at the LHC. The lowest mass states are the scalar technipions (\u03c0\u00b1,0\nT\n) and\nthe vector technirho and techniomega (\u03c1\u00b1,0\nT\nand \u03c90\nT). The vector mesons decay into a gauge boson plus\ntechnipion (\u03b3\u03c0T, W\u03c0T or Z\u03c0T,) and fermion-antifermion pairs. This analysis searches for the decays\n\u03c1T \u2192\u00b5+\u00b5\u2212and \u03c9T \u2192\u00b5+\u00b5\u2212. The dimuon mode has a lower branching fraction than the modes involv-\ning technipions but the signal is clean, straightforward to trigger on, and can be readily observed with\nearly ATLAS data.\nThe particular model studied here is the \u201cTechnicolor Strawman Model\u201d or TCSM [12, 13]. In the\nTCSM, it is expected that techni-isospin is an approximate good symmetry and therefore the isotriplet\n\u03c1T and isosinglet \u03c9T will be nearly degenerate. We will assume for what follows that m\u03c1T = m\u03c9T .\nThe technipions are also expected to be nearly degenerate. In the TCSM, the technipion masses are\ngenerically not small. In particular, if m\u03c0T > m\u03c1T /2 the decays of the \u03c1T and \u03c9T to technipions would\nbe kinematically forbidden [50]. The dimuon rate is expected to come dominantly from the \u03c9T with a\nsmaller contribution from the \u03c1T.\nThe event selection is summarized in Table 14. The technivector meson natural widths are less than\na GeV, so the observed width \u03c3(m) is entirely due to detector resolution.\nIn principle, the best search sensitivity is not obtained by examining the entire dimuon mass distribu-\ntion for a bump all at once but by using an optimized mass window that maximizes the signal signi\ufb01cance\nfor a given assumed signal mass. A prescription for the optimal window size is taken from an analytic\ncalculation in Ref. [51]. Assuming a narrow Gaussian peak on a linear background, the optimal window\nwas found to be \u00b11.4\u03c3 about the peak mass. Since we are not really in the narrow resonance regime,\nwe did a study using full-simulation ATLAS Monte Carlo for a Technicolor signal on a Drell-Yan back-\nground. Taking S/\n\u221a\nB as our measure of signi\ufb01cance, Fig. 14 (left) shows that a window size of \u00b1 \u223c1.5\u03c3\nor a bit larger is optimal. For this study, a window size of \u00b11.5\u03c3 about the peak mass is used.\nFigure 14 (right) shows the integrated luminosity necessary to observe either 3\u03c3 evidence or a 5\u03c3\ndiscovery, using the modi\ufb01ed frequentist approach [44], of technimesons in this channel. The systematic\nuncertainties summarized in section 4.4 were included in this calculation of technimeson search sensitiv-\nity. It should be noted that the integrated luminosity needed for 5\u03c3 discovery will be affected by the level\nof misalignment of the muon spectrometer. The contours in Fig. 14 were computed assuming the level\nof alignment we expect to achieve. The studies in sections 4.3 and 5.3 show that for an initial precision\nof 300 \u00b5m with an uncertainty of 150 \u00b5m the amount of data needed to reach 5\u03c3 would increase by\napproximately 50%.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1720\n\nm\u03c1T ,\u03c9T (GeV)\n400\n600\n800\n1000\nPeak mass (GeV)\n403\n603\n804\n1004\n\u03c3(m) (GeV)\n13\n22\n34\n46\nRequirement\nGenerated\n201\n60.8\n23.0\n10.1\n|\u03b7| < 2.5\n116\n39.8\n15.8\n7.3\npT > 30 GeV\n114\n39.5\n15.7\n7.2\nL1 MU20\n112\n38.7\n15.3\n7.0\nL2 mu20\n110\n38.0\n15.1\n6.9\nEF mu20\n109\n37.5\n14.9\n6.8\nMatch \u03c72 < 100\n104\n35.7\n14.0\n6.4\nOpposite charge\n104\n35.7\n14.0\n6.4\nMass window\n78.2\n26.3\n10.3\n4.7\nDrell-Yan background\n46.9\n14.1\n6.1\n2.8\nSelection ef\ufb01ciency (%)\n38.9\u00b10.5\n43.2\u00b10.5\n44.8\u00b10.5\n46.8\u00b10.5\nTable 14: Selection requirement \ufb02ow for the analysis - cross-section in fb.\n)\n\u03c3\nWindow Size (\n1\n2\n3\n4\n5\n6\nB\nS/ \n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n)\n\u03c3\nWindow Size (\n1\n2\n3\n4\n5\n6\nB\nS/ \n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\nM = 400 GeV\nM = 600 GeV\nATLAS\n0\n700\n0\n1\n) (GeV)\nT\n\u03c9\n,\nT\n\u03c1\nMass(\n400\n500\n600\n700\n800\n900\n1000\n)\n-1\nIntegrated Luminosity (fb\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n) (GeV)\nT\n\u03c9\n,\nT\n\u03c1\nMass(\n400\n500\n600\n700\n800\n900\n1000\n)\n-1\nIntegrated Luminosity (fb\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nATLAS\n Evidence\n\u03c3\n3 \n Discovery\n\u03c3\n5 \nFigure 14: Left: for two different \u03c1T,\u03c9T signal masses, S/\n\u221a\nB is plotted as a function of mass-\nwindow size for windows centered on the peak mass. Right: integrated luminosity needed for 3\u03c3\nevidence or 5\u03c3 discovery as a function of \u03c1T,\u03c9T mass. The dashed lines include only statistical\nuncertainties while the solid lines contain the systematic uncertainties as well.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1721\n\n6\nSummary and Conclusions\nSeveral models which lead to resonances in the dilepton \ufb01nal state have been studied. Various systematic\nstudies have been undertaken which estimate the effect of uncertainties from both theoretical knowledge\nof Standard Model processes as well as expected and assumed early detector performance. Data-driven\nmethods have been developed to evaluate ef\ufb01ciencies, backgrounds, and uncertainties. It has been shown\nthat even with early data the discovery potential can be dramatically increased from current limits. The\ndiscovery potential with an integrated luminosity of 10 fb\u22121 depends on the particular model and varies\nin the m = 1.0 to 3.5 TeV range. It should be noted that resonance masses above 1 TeV which are\nunreachable by the Tevatron experiments could be discovered with 100 pb\u22121 of data already.\nA\nEffect of the Unknown Location and Rate\nWhen estimating the signi\ufb01cance of a local excess of events, the size of the region considered and un-\ncertainties in the shape of the background can signi\ufb01cantly reduce the sensitivity of the search. This\nappendix presents an assessment of the size of this effect for the Z\u2032 boson to dilepton searches. If an\nexcess is found in the dilepton invariant mass, its signi\ufb01cance needs to be evaluated in a way that takes\ninto account the possibility of background \ufb02uctuations of different masses, cross-sections and widths.\nOne possible way to do this is through the use of maximum likelihood \ufb01ts, where these quantities are\nfree parameters.\nTo estimate the effect on the sensitivity of the unknown rate and location of a dilepton resonance,\nthe decay Z\u2032\nSSM \u2192ee and Z\u2032\nSSM \u2192\u00b5\u00b5 were both generated for 16 true Z\u2032 masses between 1 and 4 TeV\n(evenly spaced every 200 GeV), with a lower cut on the true dilepton mass of 0.5 TeV in all cases. Each\nsample was simulated and reconstructed using fast simulation, and events were required to have two\nback-to-back (\u2206\u03c6 > 2.9) leptons of opposite charge with pT > 20 GeV and within |\u03b7| < 2.5. For an\nestimation of the expected background, Standard Model Drell-Yan production was used.\nThe dilepton resonance was modeled using an ad-hoc parameterization that models appropriately the\nshapes of both the Z\u2032 \u2192ee and Z\u2032 \u2192\u00b5\u00b5 modes, consisting of a product between a Breit-Wigner and a\nLandau distribution with a common mean, and where the width of the Landau was parameterized as a\nfunction of the width of the Breit-Wigner9. The common mean, the width parameter and the amplitude\nof the signal are allowed to \ufb02oat in the \ufb01ts.\nFigure 15 shows the likelihood ratio distributions for an m = 3 TeV Z\u2032\nSSM \u2192ee \ufb01t-based signi\ufb01-\ncance, where the signal rate, the peak\u2019s width and the mean mass all \ufb02oat in the \ufb01t, corresponding to\nan integrated luminosity of 4 fb\u22121. The distributions of the log-likelihood ratio for \ufb01ts to H0 pseudo-\nexperiments and for \ufb01ts to H1 pseudo-experiments are shown. The fraction p of the H0 distribution\nthat has a likelihood ratio larger than the mean of the H1 distribution is shaded. The value of p is then\ntransformed into a signi\ufb01cance following the convention under which p = 2.87 \u00d7 10\u22127 corresponds to\n5\u03c3 (see section 5). The fraction shown in the plot corresponds to a signi\ufb01cance of 4.29\u03c3.\nSeveral million pseudo-experiments were generated and \ufb01t, covering different masses and luminosi-\nties. Figure 16 shows the signi\ufb01cance for different approaches in the case of an m = 3 TeV Z\u2032\nSSM for\nboth the dielectron (left) and the dimuon (right) cases. The plots compare the signi\ufb01cance as obtained\nfrom number counting (circles), \ufb01xed mass \ufb01ts (dots) and \ufb02oating mass \ufb01ts (squares). The \ufb02oating-mass\nsigni\ufb01cances are on average 20% lower than the \ufb01xed-mass calculations for Z\u2032 \u2192ee, and about 15%\nlower in the dimuon case (in obtaining these numbers, we exclude the region below 2.25 fb\u22121, which is\naffected by low statistics effects).\n9The best motivated shape is a Breit-Wigner convoluted with a Gaussian resolution. Unfortunately, the convolution \ufb01t is\nvery time consuming and for this study millions of \ufb01ts were performed. Empirically the combination of a Breit-Wigner and a\nLandau were found to give essentially identical results.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1722\n\n \n \n \n \n \nLikelihood Ratio\n0\n10\n20\n30\n40\n50\n60\n70\n80\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n \n \n \n \n \nSignal+Background\nBackground only\nATLAS\nPseudo-experiments\nFigure 15: Likelihood ratio distribution for an m = 3 TeV Z\u2032\nSSM \u2192ee; the distribution on the left corre-\nsponds to background-only pseudo-experiments; the one on the right, to signal plus background.\n]\n-1\nIntegrated Luminosity [fb\n1\n2\n3\n4\n]\n\u03c3\nSignificance [\n0\n2\n4\n6\nNumber Counting\nFixed Mass\nFloating Mass\nATLAS\n]\n-1\nIntegrated Luminosity [fb\n1\n2\n3\nSignificance [ ]\n\u03c3\n0\n2\n4\n6\nNumber Counting\nFixed Mass\nFloating Mass\nATLAS\nFigure 16: Comparison of the \ufb01t-based signi\ufb01cance for \ufb01xed-mass (dots) and \ufb02oating-mass (squares) \ufb01ts\nfor both cases, Z\u2032 \u2192ee (left) and Z\u2032 \u2192\u00b5\u00b5 (right). Circles show the estimation from number counting.\nReferences\n[1] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32 (1974) 438\u2013441.\n[2] K. D. Lane and E. Eichten, Phys. Lett. B222 (1989) 274.\n[3] N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Phys. Lett. B513 (2001) 232\u2013240.\n[4] L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 3370\u20133373.\n[5] D0 Collaboration, V. M. Abazov et al., Phys. Rev. Lett. 95 (2005) 091801.\n[6] CDF Collaboration, A. Abulencia et al., Phys. Rev. Lett. 96 (2006) 211801.\n[7] CDF Collaboration, \u201cHigh-Mass Dielectron Resonance Search in p \u00afp Collisions at \u221as = 1.96\nTeV.\u201d CDF/PUB/EXOTIC/PUBLIC/9160, 2008.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1723\n\n[8] F. Ledroit, J. Morel, and B. Trocm\u00b4e, \u201cZ\u2032 at the LHC.\u201d ATL-PHYS-PUB-2006-024, 2006.\n[9] M. Cvetic, P. Langacker, and B. Kayser, Phys. Rev. Lett. 68 (1992) 2871\u20132874.\n[10] Particle Data Group Collaboration, W. M. Yao et al., J. Phys. 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Altarelli, B. Mele, and M. Ruiz-Altaba, Z. Phys. C45 (1989) 109.\n[48] ATLAS Collaboration, \u201cMeasurement of Missing Tranverse Energy.\u201d This volume.\n[49] CDF Collaboration, D. E. Acosta et al., Phys. Rev. Lett. 95 (2005) 131801.\n[50] E. Eichten and K. Lane, arXiv:0706.2339 [hep-ph].\n[51] K.-M. Cheung and G. L. Landsberg, Phys. Rev. D62 (2000) 076003.\nEXOTICS \u2013 DILEPTON RESONANCES AT HIGH MASS\n1725\n\nLepton plus Missing Transverse Energy Signals at High Mass\nAbstract\nThe prospects for the discovery of heavy lepton-neutrino resonances with the\nATLAS detector are evaluated using full detector simulation. The performance\nof large missing transverse momentum measurement is studied. Its impact on\nthe lepton-neutrino transverse mass reconstruction, and on the backgrounds\nrejection, is then discussed. As benchmark, the sensitivity to a Standard Model\nlike W \u2032 is evaluated. Emphasis is put on the discovery potential of ATLAS with\nearly data, namely with an integrated luminosity of 10 pb\u22121 to 10 fb\u22121.\n1\nIntroduction\nThe Standard Model of particle physics has been able to predict or describe, within errors, almost all\nmeasurements performed within its domain. However, several fundamental questions remain unresolved.\nIts mechanism for electroweak symmetry breaking has not been experimentally con\ufb01rmed. The model\nparameters still lack a theoretical explanation. There are indications, therefore, that the Standard Model\nis not a fundamental theory, but a good approximation of nature at the energy ranges that have been so far\naccessible to experiment. Thus, the search for physics beyond the Standard Model is an important part\nof the ATLAS physics program. In this document, a study is presented of the potential for the search of\n\ufb01nal states comprised of one electron or muon (lepton, in what follows) plus missing transverse energy.\nA large variety of theories beyond the Standard Model, predict additional gauge bosons.\nAny\ncharged, spin 1 gauge boson which is not included in the Standard Model is called W \u2032 boson and accord-\ning to several predictions there is at least one W \u2032 boson detectable at the LHC. These theories and mod-\nels which predict new charged gauge bosons range from the Grand Uni\ufb01ed Theories [1\u20133], the various\nLeft-Right Symmetric Models [1, 4\u201310], Kaluza-Klein theories [11\u201315], Little Higgs models [16\u201318],\ndynamical symmetry breaking models [19] and even models inspired from superstrings [20\u201322]. As an\nexample, the 45 decompositions of the SO(10) gauge group, which is a candidate for large GUT sym-\nmetries, under the SU(3)C \u00d7 SU(2)L \u00d7 SU(2)R \u00d7U(1)B\u2212L gives rise to a (1,1,3,0) triplet coming from\nthe SU(2)R group. That is, a triplet of right-handed W \u00b1,0 \ufb01elds, which carry weak (V+A) interactions.\nA theoretical model, based on the gauge group SU(3)C \u00d7 SU(2)L \u00d7 SU(2)R \u00d7U(1)B\u2212L which is called\na Left-Right Symmetric Model (LRSM), after spontaneous symmetry breaking, predicts a right-handed\nWR gauge boson mixes with the left-handed WL boson of the Standard Model. The WR gauge boson is\na very attractive W \u2032 boson candidate. The search for these particles is an important part of the studies\nfor new physics to be performed at LHC. Studies presented here are based on predictions of a \u201cStan-\ndard Model-like\u201d W \u2032 boson from so-called extended gauge models [23]. This W \u2032 boson has Standard\nModel-like couplings to fermions and its decays to WZ bosons are suppressed.\nThe D0 experiment, at Fermilab, has set the present lower limit for the W \u2032 boson mass [24] to\nmW \u2032 > 1 TeV at 95% C.L. The LHC, with a centre-of-mass energy of 14TeV, is expected to increase\nthe search reach even at early stages of data taking. Other ATLAS studies have evaluated the potential\nfor discovery of W \u2032 \u2192\u2113\u03bd\u2113where \u2113= \u00b5,e [25]. This study is based on the most recent realistic detector\ndescription, including a complete simulation of the trigger chain.\nThe remaining of this paper is organized as follows. The Monte Carlo samples which were used\nare summarized in section 2. Section 3 discusses the expected performance on lepton reconstruction,\nas well as on missing transverse energy. Section 4 brie\ufb02y describes the triggers which were used in this\nstudy. The event selection is discussed in section 5. The discovery potential of a W \u2032 with Standard Model\ncouplings is assessed in section 7, after examining the systematic uncertainties in section 6.\n1726\n\n2\nMonte Carlo Samples\nTable 1 summarizes the samples used in this study; a detailed account of the procedures, generators and\nsettings used is given in [26]. Signal samples for masses other than 1 and 2 TeV were produced locally\nand validated against central production samples.\nFor the signal, samples of W \u2032 \u2192\u2113\u03bd events were generated with PYTHIA v6.403 [27], based on the\nleading order cross sections and the parton distribution functions CTEQ6 [28], where \u2113can be any type\nof lepton (\u03c4 included), for true W \u2032 boson masses ranging from 1 to 4 TeV.\nThe main background for a W \u2032-type state is the high-mass tail of Standard Model W boson produc-\ntion; in order to provide enough background to study also the higher W \u2032 boson masses, two samples of\nStandard Model W boson events were produced, with different requirements on the true invariant mass\nof the W boson: one with 200 GeV < mW < 500 GeV, and one with mW > 500 GeV. In these stud-\nies, the alignment and calibration of the detector is assumed to be well described in the reconstruction\nalgorithms.\nProcess\nGenerator\n\u03c3 \u00d7BR [fb]\nComments\nEvents\n1 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n9430.\n30K\n1.5 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n1786.\n2.8K\n2 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n437.\n30K\n2.5 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n146.\n2K\n3 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n54.\n10K\n3.5 TeV W \u2032 \u2192\u2113\u03bd\nPYTHIA\n20.\n2.8K\nStandard Model W \u2192\u2113\u03bd\nPYTHIA\n18721.1\n200 GeV< mW <500 GeV\n20K\nStandard Model W \u2192\u2113\u03bd\nPYTHIA\n708.26\nmW >500 GeV\n20K\nt\u00aft\nMC@NLO\n452000\n340K\nDijet J0\nPYTHIA\n1.76\u00d71013\n\u02c6pT = 8\u221217 GeV\n380K\nDijet J1\nPYTHIA\n1.38\u00d71012\n\u02c6pT = 17\u221235 GeV\n380K\nDijet J2\nPYTHIA\n9.33\u00d71010\n\u02c6pT = 35\u221270 GeV\n390K\nDijet J3\nPYTHIA\n5.88\u00d7109\n\u02c6pT = 70\u2212140 GeV\n380K\nDijet J4\nPYTHIA\n3.08\u00d7108\n\u02c6pT = 140\u2212280 GeV\n390K\nDijet J5\nPYTHIA\n1.25\u00d7107\n\u02c6pT = 280\u2212560 GeV\n370K\nDijet J6\nPYTHIA\n3.60\u00d7105\n\u02c6pT = 560\u22121120 GeV\n380K\nDijet J7\nPYTHIA\n5.71\u00d7103\n\u02c6pT = 1120\u22122240 GeV\n430K\nTable 1: Monte Carlo samples used for the study of W \u2032 bosons.\n\u02c6pT represents the transverse\nmomentum of the partons in their rest frame. The t\u00aft sample includes only fully leptonic and\nsemi-leptonic channels.\n3\nReconstruction Performance\n3.1\nMuon Reconstruction\nMuon reconstruction in ATLAS uses all main detector subsystems. The Muon Spectrometer (MS) is\ndesigned to provide ef\ufb01cient and precise stand-alone momentum measurement for muons of transverse\nmomentum up to O(pT= 1 TeV). During the back-tracking of the muon to the production vertex, energy\nloss \ufb02uctuations can be measured with the use of the calorimeters, which can also provide independent\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1727\n\n) [%]\ntruth\nT\n - 1/p\nreco\nT\n(1/p\ntruth\nT\np\n-100\n-50\n0\n50\n100\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n 0.09\n\u00b1\nMean: -0.30 \n 0.10\n\u00b1\n: 5.23 \n\u03c3\nATLAS\nProbability\n) [%]\ntruth\nT\n - 1/p\nreco\nT\n(1/p\ntruth\nT\np\n-100\n-50\n0\n50\n100\n-3\n10\n-2\n10\n-1\n10\n 0.26\n\u00b1\nMean: 0.70 \n 0.28\n\u00b1\n: 11.33 \n\u03c3\nATLAS\nProbability\nFigure 1: Inverse pT resolution for muons from W \u2032 boson decays; left: pT < 400 GeV (muons\nfrom m = 1 TeV W \u2032 bosons), right: pT > 800 GeV (muons from m = 2 TeV W \u2032 bosons).\n|\u03b7|\n0\n1\n2\n resolution [%]\nT\np\n0\n2\n4\n6\n8\n10\nATLAS\n1 TeV W\u2019\n2 TeV W\u2019\n [TeV]\nT\np\n0.2\n0.4\n0.6\n0.8\n resolution [%]\nT\np\n0\n2\n4\n6\n8\n10\nATLAS\n1 TeV W\u2019\n2 TeV W\u2019\nFigure 2: Muon transverse momentum resolution as a function of \u03b7 (left) and pT (right) in W \u2032\nboson decays. Filled circles represent muons from m = 1 TeV W \u2032 bosons, while open circles\ncorrespond to muons from m = 2 TeV W \u2032 bosons.\nmuon tagging to increase the identi\ufb01cation ef\ufb01ciency. For optimum performance in momentum resolu-\ntion, the MS information is combined with the track information obtained in the Inner Detector (ID). A\nfull description of the algorithms for muon performance and identi\ufb01cation can be found in [29] and [30].\nFigure 1 shows the inverse transverse momentum (1/pT) resolution for muons from decays of a W \u2032\nboson for muons below pT = 400 GeV and above pT = 800 GeV. Especially relevant for the analysis\nare the negative tails in these plots, since they correspond to reconstructed muon candidates that have\na pT larger than that of the true particle. The relative contribution of these tails can be assessed by the\nfraction of muon candidates separated by more than 2\u03c3 from the mean of the distribution (which in\nboth cases is consistent with zero, as it should). The fraction in that negative tail is (4.9 \u00b1 0.3)% for\nmuons with pT < 400 GeV, and (3.8 \u00b1 0.4)% for pT > 800 GeV (to be compared with 2.275% for\na gaussian distribution). The transverse momentum resolution achieved is shown as a function of the\npseudo-rapidity \u03b7 and pT in Fig. 2. On average a resolution of 4.5 and 5.5% is recorded for muons from\nW \u2032 bosons of m = 1 TeV and 2 TeV respectively.\nFigures 3 and 4 show the ef\ufb01ciency for combined muon reconstruction as a function of pseudo-\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1728\n\n\u03b7\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\nATLAS\n0\n0.2\n0.4\n0.6\n0.8\n1\n1 TeV W\u2019\n2 TeV W\u2019\n\u03c6\nATLAS\n-3\n-2\n-1\n0\n1\n2\n3\nEfficiency\n0\n0 2\n0.4\n0.6\n0 8\n1\n1 TeV W\u2019\n2 TeV W\u2019\nFigure 3: Combined muon reconstruction ef\ufb01ciency as a function of \u03b7 and \u03c6 for muons from W \u2032\nboson decays.\n [TeV]\n\u00b5\nT\np\n0.0\n0.5\n1.0\n1.5\nEfficiency\n0.0\n0.5\n1.0\nATLAS\n1 TeV W\u2019\n2 TeV W\u2019\nFigure 4: Combined muon reconstruction ef\ufb01ciency as a function of pT for muons from W \u2032 boson\ndecays.\nrapidity (\u03b7), azimuthal angle (\u03c6) and transverse momentum (pT) for muons from fully simulated W \u2032\nboson decays. An overall ef\ufb01ciency of 93.6% and 92.4% is measured for m = 1 TeV and 2 TeV W \u2032\nboson samples, respectively. The regions with lower ef\ufb01ciency in muon reconstruction are observed, as\nexpected, in the middle plane (\u03b7 = 0) and in the transition regions between the barrel and the end-cap\nsections of the MS (at |\u03b7| \u223c1.2). The regions with low ef\ufb01ciency in \u03c6 correspond to the feet of the\ndetector (\u03c6 \u2243\u22122, \u22121) and to passages for services.\nOne important issue in this study concerns the background that can rise from badly reconstructed\nmuons. Their momentum being wrongly estimated upwards, can cause both the presence of a high\npT muon and, correspondingly, large missing transverse energy. In the de\ufb01nition of the muon, extra\nquality criteria may be imposed in order to diminish this probability. In this study, the following mild\nrequirements are adopted:\n\u2022 A matching \u03c72, between MS and ID tracks, smaller than 100 (further discussed in [30]).\n\u2022 An impact parameter in the z-axis (i.e. the beam axis) smaller than 200 mm.\n\u2022 An impact parameter signi\ufb01cance in the transverse (R-\u03c6) plane smaller than 10.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1729\n\n|\n\u03b7|\n0\n1\n2\n ) [%]\ntrue\n)/E\ntrue\n-E\nreco\n( (E\n\u03c3\n0\n2\n4\nATLAS\n1 TeV W\u2019\n2 TeV W\u2019\n [TeV]\ne\nE\n0.2\n0.4\n0.6\n0.8\n1.0\n ) [%]\ntrue\n)/E\ntrue\n-E\nreco\n( (E\n\u03c3\n0.0\n0.5\n1.0\n1.5\nATLAS\n1 TeV W\u2019\n2 TeV W\u2019\nFigure 5: Electron energy resolution as a function of pseudo-rapidity (left) and energy (right) in\nW \u2032 boson decays. Filled circles represent electrons from m = 1 TeV W \u2032 bosons, while open circles\ncorrespond to m = 2 TeV W \u2032 bosons.\n [%]\ntruth\nT\n)/p\ntruth\nT\n - p\nreco\nT\n(p\n-20\n-10\n0\n10\n20\nProbability\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n 0.03\n\u00b1\nMean: 0.09 \n 0.03\n\u00b1\n: 1.28 \n\u03c3\nATLAS\n [%]\ntruth\nT\n)/p\ntruth\nT\n - p\nreco\nT\n(p\n-20\n-10\n0\n10\n20\nProbability\n-3\n10\n-2\n10\n-1\n10\n 0.03\n\u00b1\nMean: 0.07 \n 0.02\n\u00b1\n: 1.06 \n\u03c3\nATLAS\nFigure 6: Electron pT resolution in W \u2032 boson decays; left: pT < 400 GeV (muons from m =\n1 TeV W \u2032 bosons), right: pT > 800 GeV (muons from m = 2 TeV W \u2032 bosons).\n3.2\nElectron Reconstruction\nElectron candidates are built starting from clusters of calorimeter cell energy depositions, which are\nmatched to a track from the inner detector. Electron identi\ufb01cation and reconstruction are described in\ndetail in [31] and [32], where three standard selections were developed to be used in physics searches.\nThe present study uses the medium set of selection requirements, which consists in several requirements\non the clusters used (size, containment, association with a track, shower shapes and quality of the track\nmatch).\nFigure 5 shows the electron energy resolution (in percentage) as a function of pseudo-rapidity (|\u03b7|)\nand true energy. The average energy resolution for electrons in this energy range is close to 1%, and is\nworse in the transition region between the two calorimeter systems. Figure 6 shows the relative differ-\nence between reconstructed and true transverse momenta of isolated electrons with true pT lower than\n400 GeV and higher than 800 GeV. The fractions of events in the upper tails (more than 2\u03c3 over the\n\ufb01tted mean) are (11.8 \u00b1 0.6)% and (5.3 \u00b1 0.5)%, respectively. These non-Gaussian tails are due to the\namount of material in the inner detector and are, therefore, \u03b7-dependent.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1730\n\n (reco - truth) [GeV]\nmiss\nT\nE\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.02\n0.04\n0.06\n 0.28\n\u00b1\nMean: 0.40 \n 0.30\n\u00b1\n: 18.25 \n\u03c3\nATLAS\n (reco - truth) [GeV]\nmiss\nT\nE\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.01\n0.02\n0.03\n 0.62\n\u00b1\nMean: -2.49 \n 0.89\n\u00b1\n: 25.01 \n\u03c3\nATLAS\nFigure 7: /ET resolution in muonic W \u2032 boson decays. mW \u2032 = 1 TeV (left) and 2 TeV (right).\n (reco - truth) [GeV]\nmiss\nT\nE\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.05\n0.10\n 0.15\n\u00b1\nMean: 0.13 \n 0.16\n\u00b1\n: 10.05 \n\u03c3\nATLAS\n (reco - truth) [GeV]\nmiss\nT\nE\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.05\n0.10\n 0.20\n\u00b1\nMean: 0.30 \n 0.21\n\u00b1\n: 13.74 \n\u03c3\nATLAS\nFigure 8: /ET resolution in W \u2032 boson decays to electrons. mW \u2032 = 1 TeV (left) and 2 TeV (right).\n3.3\nReconstruction of the Missing Transverse Energy\nThe \ufb01nal state under consideration includes a neutrino, whose momentum information can be inferred\nonly partially from the energy imbalance in the detector (since the total transverse momentum of the\nevent has to add up to zero). The reconstruction of the missing transverse energy (/ET) in ATLAS is\ndescribed in detail in [33].\nThe resolution of /ET reconstruction in W \u2032 boson events containing muons can be seen in Fig. 7. An\naverage resolution of about 18 GeV is observed for mW \u2032 = 1 TeV (25 GeV for mW \u2032 = 2 TeV). In the\ncase of mW \u2032 = 2 TeV the non-Gaussian tails in the resolution are more pronounced, and come from the\ndegraded performance of muon reconstruction at high pT.\nFigure 8 shows the /ET resolution for events that contain one high-pT electron from a W \u2032 boson\ndecay. The left plot corresponds to the m =1 TeV W \u2032 boson, and the right plot to 2 TeV; the resolutions\nare around 10 and 14GeV, respectively. These values agree well with the expected /ET resolution from\nthe mean of the scalar sum of transverse energy (< \u2211ET >) in each case; for the m = 1 TeV sample,\n< \u2211ET > for the selected events is 439GeV, which yields an estimated \u03c3(/ET) \u223c0.5\u221a\n\u2211ET = 10.5 GeV;\nfor m = 2 TeV, the expected value (based on < \u2211ET >) is 13.3GeV.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1731\n\n) [TeV]\n\u03bd\n(e\nT\nM\n0\n1\n2\n3\n [pb/25GeV]\nT\n/dM\n\u03c3\nd\n0.0\n0.1\n0.2\nATLAS\n\u2019True\u2019\nReconstructed\n) [TeV]\n\u03bd\n\u00b5\n(\nT\nM\n0\n1\n2\n3\n [pb/25GeV]\nT\n/dM\n\u03c3\nd\n0.0\n0.1\n0.2\nATLAS\n\u2019True\u2019\nReconstructed\nFigure 9: Transverse mass distribution for m = 1 TeV W \u2032 bosons, as obtained from the true\nparticles\u2019 momenta (\ufb01lled histograms), and from reconstructed information after basic selection\n(black outline). Left: electron mode; right: muon mode.\n) [TeV]\n\u03bd\n(e\nT\nM\n0\n1\n2\n3\n [pb/25GeV]\nT\n/dM\n\u03c3\nd\n0\n2\n4\n6\n-3\n10\n\u00d7\nATLAS\n\u2019True\u2019\nReconstructed\n) [TeV]\n\u03bd\n\u00b5\n(\nT\nM\n0\n1\n2\n3\n [pb/25GeV]\nT\n/dM\n\u03c3\nd\n0\n2\n4\n6\n-3\n10\n\u00d7\nATLAS\n\u2019True\u2019\nReconstructed\nFigure 10: As Fig. 9, for m = 2 TeV W \u2032 bosons, \ufb01lled: from true information; outline: recon-\nstructed transverse mass.\n3.4\nTransverse Mass Reconstruction\nIn the W \u2032 boson search, the transverse momentum pT of the single lepton in the event and the missing\ntransverse energy /ET are combined to obtain the transverse mass as follows:\nmT =\nq\n2pT /ET(1\u2212cos\u2206\u03c6\u2113,/ET )\n(1)\nwhere \u2206\u03c6\u2113,/ET is the angle between the momentum of the lepton and the missing momentum, in the\ntransverse plane. Figures 9 and 10 show the transverse mass distributions for m = 1 and 2 TeV signals,\nrespectively, as obtained from truth information (light gray \ufb01lled histograms) and the degradation due to\ndetector resolution and ef\ufb01ciency (black hollow histograms). As can be expected from Figs. 2 and 5, the\nshape of the transverse mass spectrum has a larger distortion in the muon channel than in the electron\nchannel, with larger tails for higher W \u2032 boson masses. On the other hand, the reconstruction ef\ufb01ciency is\nhigher in the muon channel (over 86% for each mass) than in the electron channel (about 72%).\nFigures 11 and 12 show the distribution of the difference between the \u201ctrue\u201d transverse mass (i.e. as\nobtained from the true momenta of the lepton and the neutrino) and its reconstructed value, for electron\nand muon modes, and for m = 1 and 2 TeV W \u2032 boson masses. In Fig. 11, single Gaussian \ufb01ts are shown;\na \ufb01tted width of about 12 GeV is obtained for the electron channel, while the muon channel, besides\nhaving much larger non-Gaussian tails, has a \ufb01tted width of about 23 GeV.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1732\n\n) [GeV]\n\u03bd\n (e\ntruth\nT\n - M\nreco\nT\nM\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.05\n0.10\n 0.19\n\u00b1\nMean: 1.70 \n 0.19\n\u00b1\n: 12.30 \n\u03c3\nATLAS\n) [GeV]\n\u03bd\n\u00b5\n (\ntruth\nT\n - M\nreco\nT\nM\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.01\n0.02\n0.03\n0.04\n 0.49\n\u00b1\nMean: 1.27 \n 0.68\n\u00b1\n: 23.28 \n\u03c3\nATLAS\nFigure 11: Distribution of the event-by-event difference between the reconstructed and \u201ctrue\u201d\ntransverse mass for the electron and muon channel, for m = 1 TeV W \u2032 bosons.\n) [GeV]\n\u03bd\n (e\ntruth\nT\n - M\nreco\nT\nM\n-200\n-100\n0\n100\n200\nProbability\n0.00\n0.02\n0.04\n0.06\n 0.28\n\u00b1\nMean: 2.05 \n 0.29\n\u00b1\n: 18.43 \n\u03c3\nATLAS\n) [GeV]\n\u03bd\n\u00b5\n (\ntruth\nT\n - M\nreco\nT\nM\n-200\n-100\n0\n100\n200\nProbability\n0.000\n0.005\n0.010\n0.015\n0.020\nATLAS\nFigure 12: As Fig. 11, for m = 2 TeV W \u2032 bosons.\nFigure 12 shows the corresponding comparison for a 2 TeV signal; however, in this case, the muon\nchannel (on the right) has a stronger non-Gaussian character, which is why no \ufb01t was performed. The\nquadratic mean of the distribution is about 84 GeV.\n4\nTrigger\nThe ATLAS trigger [34] has three levels: events passed by the L1 (level 1) hardware trigger are partially\nreconstructed in L2 (level 2) processors and, if accepted there, are fully processed in the EF (event \ufb01lter)\nprocessor farm. Only events accepted by the EF (and thus also by L1 and L2) are recorded for later\nreconstruction and analysis.\nTrigger rates are estimated in separate studies of the electron [35] and muon [36] trigger systems.\nHowever, this studies were performed with a more recent version of the software than the one used here1.\nTherefore, we have measured some of the rates directly in simulation using the dijet and top samples\ndescribed earlier in this note. We additionally measured L1 rates and ef\ufb01ciencies for single-electron and\nsingle-muon triggers with thresholds higher than those de\ufb01ned in the simulated trigger menu. The errors\nwe assign to our rate estimates are purely statistical.\n1Especially for electrons, the trigger menu and algorithms in the simulated samples are quite different from those in the\nabove notes which are much closer to those expected to be used during actual data acquisition.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1733\n\n4.1\nElectron trigger\nFor a single electron trigger with an ET threshold of 100 GeV, we measure a L1 rate of 14 \u00b1 1 Hz at\nan instantaneous luminosity of 1032 cm\u22122s\u22121, similar to the electron trigger study estimate of 10 Hz.\nThe ef\ufb01ciency to trigger on W \u2032 \u2192e\u03bd events for |\u03b7| < 2.5 is 98% for a mass of either 1 or 2 TeV. If the\nthreshold is raised to 250 GeV, we measure a rate of 25\u00b14 Hz at 1033 cm\u22122s\u22121 and an ef\ufb01ciency of 96%\nfor the 2 TeV mass.\nLoose requirements in L2 and EF can further reduce these rates with a moderate degradation of\nthe ef\ufb01ciency. For de\ufb01niteness in the calculations in the following sections, we assume that a trigger\nef\ufb01ciency (applied after all requirements) of 0.90 \u00b1 0.10 is achieved with an acceptable rate for all W \u2032\nboson masses.\n4.2\nMuon trigger\nThe trigger menu and algorithms in the simulation samples are similar to those in the muon trigger study\nand those expected for data acquisition. In contrast to the electron case, lower thresholds can be applied\nthanks to the lower fake rates. A signi\ufb01cant decrease in rate is then obtained thanks to an improved\nmeasurement of pT at each level. Applying a threshold of 20 GeV at each trigger level, we obtain an\nEF rate of 20\u00b110 Hz for an instantaneous luminosity of 1032 cm\u22122s\u22121, consistent with the muon study\nprediction of 13 Hz. We measure a W \u2032 \u2192\u00b5\u03bd trigger ef\ufb01ciency for |\u03b7| < 2.5 of 74% for m = 1 TeV and\n73% at 2 TeV. At 1033 cm\u22122s\u22121, we apply a pT threshold of 40 GeV, the maximum L1 value, and obtain\na trigger rate of 4.1\u00b10.7 Hz close to the 5.6 Hz obtained in the trigger study. The corresponding trigger\nef\ufb01ciency for the m = 2 TeV W \u2032 boson is 69%.\nIt should be noted that most of the ef\ufb01ciency loss comes from holes in the coverage of the muon\nsystem, where the reconstruction is also inef\ufb01cient.\n5\nEvent Selection\nThe decay W \u2032 \u2192\u2113\u03bd provides a rather clean signature consisting of a high-energy isolated lepton and\nlarge missing transverse energy. The largest backgrounds are the high-pT tail of the W \u2192\u2113\u03bd decays and\nt\u00aft production. Both these \ufb01nal states are accompanied by signi\ufb01cant jet activity, but contain also leptons\nthat are as isolated as those expected from W \u2032 \u2192\u2113\u03bd decays.\nA potentially dangerous background is the one arising from fake leptons; since this issue is more\nlikely to be signi\ufb01cant for electrons than for muons, the backgrounds will be presented separately for\nW \u2032 \u2192e\u03bd and W \u2032 \u2192\u00b5\u03bd \ufb01nal states.\n5.1\nEvent Preselection\nIn addition to the electron and muon identi\ufb01cation criteria described above, events are required to have:\n\u2022 Only one reconstructed lepton with pT > 50 GeV within |\u03b7| < 2.5.\n\u2022 Missing transverse energy /ET > 50 GeV.\nFigure 13 shows, on top, differential cross-section as a function of the lepton pT for the m = 1\nTeV and 2 TeV signal samples, Standard Model W boson, t\u00aft and dijet production. The dashed vertical\nline shows the requirement value (50 GeV). The bottom plots in Fig. 13 show the /ET distributions for\nthe same processes after requiring only one lepton with pT > 50GeV; again, the requirement value (at\n50 GeV) is shown with the dashed vertical line. This selection provides a relatively clean signal in the\nhigh transverse mass region, as shown in Fig. 14, which shows the differential cross-section as a function\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1734\n\n [TeV]\nT\nP\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n[pb/0.05TeV]\nT\n/dP\n\u03c3\nd\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \u03bd\n e \n\u2192\nW \nt\nt \nDiJets\nATLAS\n [TeV]\nT\nP\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n[pb/0.05TeV]\nT\n/dP\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\n [TeV]\nmiss\nT\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n[pb/0.05TeV]\nmiss\nT\n/dE\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \u03bd\n e \n\u2192\nW \nt\nt \nDiJets\nATLAS\n \n \n \n \n \n \n \n \n [TeV]\nmiss\nT\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n[pb/0.05TeV]\nmiss\nT\n/dE\n\u03c3\nd\n\u22125\n10\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n10\n2\n10\n3\n10\n \n \n \n \n \n \n \n \nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\nFigure 13: Top: leading lepton pT distributions (left: electron events, right: muon events). Bottom:\n/ET distribution of events with only one reconstructed lepton with pT > 50 GeV (left: electron\nevents, right: muon events).\nof the transverse mass after the requirements on pT and /ET. The background can be further rejected\nby exploiting additional observables, described in next sections: lepton isolation, lepton fraction and jet\nveto criteria.\n5.2\nBackground Rejection\nAfter the kinematic requirements are applied, the t\u00aft and dijets backgrounds are still larger than the high-\nmass tail of the Standard Model W boson close to the threshold value on the lepton pT and on /ET.\nSince the uncertainties on the rate of these backgrounds are large, it is desirable to bring them below the\nirreducible background from W bosons. To achieve this, additional requirements are imposed on lepton\nisolation and on the lepton fraction, described below. A simpler selection strategy, based on a jet veto, is\nalso explored, since it could prove useful during the \ufb01rst stages of data taking.\n5.2.1\nLepton Isolation\nAs the lepton from a W \u2032 boson decay is expected to be isolated, only events without high energy tracks\naround the lepton trajectory are accepted. The tracking isolation is done by requiring that the sum of the\npT of tracks in a \u2206R-cone around the lepton be below a threshold; \u2206R is de\ufb01ned as\n\u2206R \u2261\nq\n(\u2206\u03c6)2 +(\u2206\u03b7)2,\nwhere \u2206\u03c6 and \u2206\u03b7 are the distances in azimuthal angle and in pseudo-rapidity, respectively, from the\nlepton under consideration.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1735\n\n[TeV]\nT\nM\n0.5\n1\n1 5\n2\n2.5\n3\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \u03bd\n e \n\u2192\nW \nt\nt \nDiJets\nATLAS\n [TeV]\nT\nM\n0.5\n1\n1.5\n2\n2 5\n3\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\nFigure 14: Transverse mass spectrum after the basic kinematic requirements for background and\nsignal (mW \u2032 = 1 and 2 TeV). Left: electron mode; right: muon mode.\nSignal Efficiency\n0.6\n0.7\n0.8\n0.9\n1.0\nBackground Rejection\n1.0\n1.5\n2.0\n2.5\n3.0\n R=0.1, normalized\n\u2206\n R=0.3, normalized\n\u2206\n R=0.5, normalized\n\u2206\n R=0.1\n\u2206\n R=0 3\n\u2206\n R=0 5\n\u2206\nATLAS\nFigure 15: t\u00aft background rejection and signal ef\ufb01ciency for different requirement values on the\n\u2211pT (open markers) and (\u2211pT)/pTlepton (\ufb01lled markers), for the muon channel. Each marker type\ncorresponds to a different value for \u2206R, from 0.1 to 0.5.\nCalorimeter isolation was also explored (the calorimetric energy deposited within the volume be-\ntween two \u2206R-cones is required to be below a threshold).\nBesides requiring a maximum value of \u2211pTtracks (of 10 GeV to 1 GeV), the use of a normalized\nisolation requirement was also explored, in which the requirement is applied to the \u2211pTtracks/pTlepton\nratio. This ratio is required to be smaller than 0.1 to 0.01. Five different \u2206R values were used in both\ncases; as shown in Fig. 15 for muons, the normalized isolation selection achieves a higher t\u00aft rejection for\nthe same ef\ufb01ciencies. The ef\ufb01ciencies and rejections achieved for electrons are similar.\nThe calorimeter energy difference in two cones is not only of use in the electron case, but also in\nthe muon one. High pT muons coming from W \u2032 boson decays can also radiate a lot inside the material\npreceding the MS. This radiation appears as energy depositions close to the muon in the calorimeters.\nAs can be seen in Fig. 16 (right), the energy deposition in a cone of \u2206R < 0.1 around the muon is much\nhigher, around 30 GeV on average, than the deposition in a cone of \u2206R < 0.5 when the inner cone is\nsubtracted (in this case the average is aboout 7 GeV). Moreover, in Fig. 16 (left) it is shown that in the\nmajority of the cases, a high reconstructed energy deposition indicates the existence of high \ufb01nal state\nradiation. Therefore, the energy deposition in an inner cone (e.g. \u2206R < 0.1) must be subtracted also in\nthe case of muons when isolation criteria based on calorimetry are applied. Also on track based isolation\ncriteria an inner cone containing the muon track itself must be subtracted. In this case however, the\ninner cone can be much narrower, since it only needs to be able to exclude the track associated with the\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1736\n\nATLAS\nReconstructed E in cone [GeV]\n0\n100\n200\n300\n400\n500\n600\nTrue E in cone [GeV]\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nATLAS\n in cone (GeV)\nT\nE\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nEvents\n1\n10\n2\n10\n3\n10\nR=0.1\n\u2206\nR=0.5, after subtraction\n\u2206\nFigure 16: Left: the true energy deposition as a function of the reconstructed one in a cone of\n\u2206R=0.1 for muons coming from decays of m = 2 TeV W \u2032 bosons. Right: the solid histogram\nshows the energy recorded in a cone of \u2206R=0.1 around the muon. The dashed histogram shows\nthe energy recorded in a cone of \u2206R=0.5 after the subtraction of the inner cone deposition.\n in cone dR=0.3 \ntracks\nSum p_T\n0\n5\n10\n15\n20\n25\nProbability\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nW\u2019 [1TeV]\nW\u2019 [2TeV]\nSM W\ntt\n \nmuon\nSum E_T in cone dR=0.3 /p_T\n0\n0.2\n0.4\n0.6\n0.8\n1\nProbability\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nATLAS\nW\u2019 [1TeV]\nW\u2019 [2TeV]\nSM W\ntt\nFigure 17: Left: distribution of an absolute track based isolation variable for muons. Right:\ndistribution of a relative calorimetry based isolation variable for muons. In both cases the inner\ncone of \u2206R=0.1 is subtracted.\nlepton under consideration. Figure 17 shows the distributions of the isolation energy for different event\ncategories. For these plots, muons with pT > 20 GeV are considered.\nFor the analysis, a loose requirement of 0.05 is used on the normalized track-based isolation for\nboth channels (electron and muon), and no requirement on the calorimeter-based isolation is applied.\nTracks are included in the sum if 0.02 < \u2206R(track,lepton) < 0.3. This requirement keeps about 99% of\nthe signal for both masses (mW \u2032 = 1 and 2 TeV), rejects about 10% of the t\u00aft events left after the basic\nselection and rejects over 99% of the dijet background.\n5.2.2\nLepton Fraction\nAnother variable that can be used to reduce the dijet and t\u00aft backgrounds is the \u201dlepton fraction\u201d of the\nevent, which can be expressed as \u2211pleptons\nT\n/(\u2211pleptons\nT\n+ \u2211ET), where the scalar sum on the lepton pT\nsums over /ET as well. Essentially this variable measures the fraction of energy that can be attributed to\nleptons (including neutrinos, which are assumed to be the main contribution to /ET) in an event. Here,\nout of the visible leptons, only the most energetic one is included in the sum (its pT is added to the /ET to\nform \u2211pleptons\nT\n). The distribution of this variable is shown for different event categories in Fig. 18 (left).\nAs expected, it shows a much lower value for t\u00aft events (in pink) than for the rest of the samples used\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1737\n\n \njets\nT\n+p\nleptons\nT\n /Sum p\nleptons\nT\nSum p\n0\n0.1\n0 2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nProbability\n0\n0.005\n0 01\n0.015\n0.02\n0.025\n0.03\n0.035\nATLAS\nW\u2019 [1TeV]\nW\u2019 [2TeV]\nSM W\ntt\nEfficiency W\u2019\nATLAS\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0 8\n0.9\n1\n-\nEfficiency tt\n-3\n10\n-2\n10\n-1\n10\n1\nFigure 18: Left: distribution of the lepton fraction variable (see text) for different event categories.\nRight: signal ef\ufb01ciency versus t\u00aft ef\ufb01ciency for different requirement values on the lepton fraction\nvariable.\n(W \u2032 boson signals and Standard Model W bosons). The ef\ufb01ciency for signal versus t\u00aft events for different\nvalues of the variable, is shown in Fig. 18 (right). A requirement at 0.5 results in a signal ef\ufb01ciency of\n\u223c96% in both channels and a rejection factor of \u223c45 against the t\u00aft background, and it suppresses all the\nremaining dijet events. This value will be used subsequently.\n5.2.3\nJet Veto and Jet Multiplicity Requirements\nA selection procedure based solely on veto-ing events with high jet activity could provide an alternative\nway to extract a signal in this search. Several requirements on jet activity were explored; in some, events\nare rejected if they include any jet over an energy threshold, in others, jet multiplicity information is used.\nThe jet veto was applied just after the basic selection (i.e., lepton identi\ufb01cation, pT and /ET requirements).\nFigure 19 shows the distribution of the pT of the leading jet after the basic selection; the distribution\non the left corresponds to the electron channel and the one on the right to the muon channel. Tables 2\nand 3 show the expected rates for several jet veto criteria .\nFigure 20 shows how after a 200GeV jet veto requirement (and without isolation or lepton fraction\nrequirements), most of the t\u00aft and dijet background is rejected, and the signal to background ratio is good\nfor high transverse mass values. Although the signal is reduced by between 5 and 10% with respect to\nselecting on isolation and lepton fraction, a jet veto requirement may be a good tool if the calibration of\nthe \u2211ET (used to compute the lepton fraction) is not well understood in early data. However, in what\nfollows, this requirement is not used.\n5.3\nEvent Selection Results\nFigure 21 shows the expected transverse momentum spectra for signal and background for both channels\nafter all requirements (preselection, isolation, and lepton fraction). The selection requirement \ufb02ow is\nshown in Tables 4 and 5. The transverse mass requirement has been chosen by minimizing the luminosity\nneeded to get a 5\u03c3 excess. The initial cross-sections for the W \u2032 boson signals and for the high mass W\nboson tail include the K-factor obtained in section 6.1.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1738\n\n \n \n \n \n \n \n \n \n [TeV]\nLeadingJet\nT\np\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n[pb/0.05TeV]\nLeadingJet\nT\n/dp\n\u03c3\nd\n\u22125\n10\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n10\n2\n10\n \n \n \n \n \n \n \n \nATLAS\n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \u03bd\n e \n\u2192\nW \nt\nt \nDiJets\n \n \n \n \n \n \n \n \n [TeV]\nLeadingJet\nT\np\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n[pb/0.05TeV]\nLeadingJet\nT\n/dp\n\u03c3\nd\n\u22125\n10\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n10\n2\n10\n3\n10\n \n \n \n \n \n \n \n \nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\nFigure 19: Distributions for the pT of the leading jet after the basic selection. Left: electron\nselection. Right: muon selection.\n \n \n \n \n \n \n \n \n [TeV]\nT\nM\n0.5\n1.0\n1 5\n2.0\n2.5\n3.0\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n\u22125\n10\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n10\n \n \n \n \n \n \n \n \n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \n\u03bd\n e \n\u2192\nW \nt\nt \nDiJets\nATLAS\n \n \n \n \n \n \n \n \n [TeV]\nT\nM\n0.5\n1 0\n1.5\n2.0\n2 5\n3 0\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n\u22124\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n1\n10\n \n \n \n \n \n \n \n \nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\nFigure 20: mT spectrum after preselection requirements and a jet veto of ET < 200 GeV. Left:\nevents with a high-pT electron; right: events with a high pT muon.\n [TeV]\nT\nM\n0.5\n1\n1 5\n2\n2.5\n3\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\n \n\u03bd\n e \n\u2192\nW \nt\nt \nDiJets\nATLAS\n [TeV]\nT\nM\n0.5\n1\n1.5\n2\n2 5\n3\n[pb/0.05TeV]\nT\n/dM\n\u03c3\nd\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nATLAS\n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n \u03bd \n\u00b5\n \n\u2192\nW \nt\nt \nDiJets\nFigure 21: Expected transverse mass spectra after all requirements. Left: electron channel; right:\nmuon channel.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1739\n\n\u03c3 [pb]\nRequirement\nW \u2032 1TeV\nW \u2032 2TeV\nW\nt\u00aft\nDijets\nNo jets with pT > 100GeV\n2.71(4)\n0.112(2)\n4.74(5)\n7.07(7)\n17\u00b116\nNo jets with pT > 200GeV\n3.13(4)\n0.132(2)\n5.09(5)\n15.7(1)\n27\u00b116\nNo jets with pT > 500GeV\n3.38(4)\n0.146(2)\n5.18(5)\n18.7(1)\n44\u00b117\nLess than 4 jets with pT > 40GeV\n3.38(4)\n0.148(2)\n5.18(5)\n14.0(1)\n43\u00b117\nLess than 3 jets with pT > 100GeV\n3.39(4)\n0.148(2)\n5.18(5)\n17.8(1)\n44\u00b117\nLess than 2 jets with pT > 200GeV\n3.38(4)\n0.148(2)\n5.18(5)\n18.4(1)\n44\u00b117\n200GeV veto, mT > 0.7TeV\n1.73(3)\n0.0290(8)\n\u2013\n\u2013\n200GeV veto, mT > 1.4TeV\n0.066(1)\n0.0013(1)\n\u2013\n\u2013\nTable 2: Cross-sections for signal and backgrounds for dijets, t\u00aft, W and W \u2032 boson samples for different\nrequirements on jet content for the electron channel. The number in brackets is the error on the least\nsigni\ufb01cant digit.\n\u03c3 [pb]\nRequirement\nW \u2032 1TeV\nW \u2032 2TeV\nW\nt\u00aft\nDijets\nNo jets with pT > 100GeV\n3.22(4)\n0.141(2)\n5.50(5)\n8.77(8)\n2(1)\nNo jets with pT > 200GeV\n3.70(4)\n0.166(2)\n5.92(5)\n19.1(1)\n17(4)\nNo jets with pT > 500GeV\n3.96(4)\n0.182(2)\n6.04(5)\n22.7(1)\n39(5)\nLess than 4 jets with pT > 40GeV\n3.98(4)\n0.184(2)\n6.03(5)\n16.9(1)\n53(5)\nLess than 3 jets with pT > 100GeV\n3.98(4)\n0.185(2)\n6.04(5)\n21.5(1)\n73(5)\nLess than 2 jets with pT > 200GeV\n3.98(4)\n0.185(2)\n6.04(5)\n22.3(1)\n73(5)\n200GeV veto, mT > 0.7TeV\n2.07(3)\n0.040(1)\n0.005(2)\n\u2013\n200GeV veto, mT > 1.4TeV\n0.084(1)\n0.0033(8)\n0.0008(8)\n\u2013\nTable 3: Cross-sections for signal and backgrounds for dijets, t\u00aft, W and W \u2032 boson samples for different\nrequirements on jet content for the muon channel. The number in brackets is the error on the least\nsigni\ufb01cant digit.\n6\nSystematic Uncertainties\n6.1\nGenerator-level Systematic Uncertainties\nThe input for the full simulation studies described in earlier sections was obtained by generatingW \u2032 boson\nevents using PYTHIA [27]. Events in the high-mass tail of the W boson were generated using PYTHIA\nas well. Both use the default PYTHIA parton distribution functions (PDFs), CTEQ6l, the CTEQ6 [37]\nLO (leading-order) \ufb01t with NLO (next-to-leading-order) \u03b1S. Here we report on generator-level studies\nwhich examine the effects of making use of the NLO matrix elements and varying the PDFs.\n6.1.1\nHigher Orders\nTo evaluate contributions from higher order diagrams, we used MC@NLO [38] input to the HER-\nWIG [39] event generator. Both W and W \u2032 boson events were generated using the W boson production\nprocess with the W boson mass set to the W \u2032 boson value for the latter. The W \u2032 boson widths were set\nto the values calculated by PYTHIA. The masses and widths used are listed in Table 6. Both MC@NLO\nand HERWIG were run using the default HERWIG PDFs, MRST2004nlo, the MRST 2004 \ufb01t using the\nstandard MS scheme at NLO [40].\nOne million events were generated for each generator at each of the masses. The cross-section is\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1740\n\n\u03c3 [pb]\nRequirement\nW \u2032 (1 TeV)\nW \u2032 (2 TeV)\nW tail\nt\u00aft\nDijets[1-7]\n(No requirement)\n4.99\n0.231\n10.28\n452\n1.91\u00d71010\nPreselection\n3.67\u00b10.04\n0.160\u00b10.002\n6.80\u00b10.06\n150.57\u00b10.40\n(13.6\u00b10.2)\u00d7106\npT > 50 GeV\n3.43\u00b10.04\n0.150\u00b10.002\n5.53\u00b10.05\n51.13\u00b10.23\n(7.23\u00b10.6)\u00d7103\n/ET > 50 GeV\n3.40\u00b10.04\n0.149\u00b10.002\n5.19\u00b10.05\n25.78\u00b10.16\n45.33\u00b116.65\nIsolation\n3.36\u00b10.04\n0.148\u00b10.002\n5.01\u00b10.05\n23.30\u00b10.16\n0.65\u00b10.13\nLepton fraction\n3.25\u00b10.04\n0.145\u00b10.002\n4.10\u00b10.04\n0.50\u00b10.02\n\u2013\nmT > 700 GeV\n1.86\u00b10.03\n0.0317\u00b10.0008\n0\n\u2013\nmT > 1400 GeV\n0.0740\u00b10.001\n0.0014\u00b10.0002\n0\n\u2013\nTable 4: Cross-section for signal and backgrounds after each requirement. Electron mode.\n\u03c3 [pb]\nRequirement\nW \u2032 (1 TeV)\nW \u2032 (2 TeV)\nW tail\nt\u00aft\nDijets[1-7]\n(No requirement)\n4.99\n0.231\n10.28\n452\n1.91\u00d71010\nPreselection\n4.28\u00b10.05\n0.199\u00b10.002\n7.77\u00b10.06\n205.30\u00b10.46\n(11.2\u00b10.19)\u00d7106\npT > 50 GeV\n4.03\u00b10.04\n0.187\u00b10.002\n6.40\u00b10.06\n61.71\u00b10.25\n(1.24\u00b10.26)\u00d7103\n/ET > 50 GeV\n4.00\u00b10.04\n0.186\u00b10.002\n6.04\u00b10.05\n31.34\u00b10.18\n74.32\u00b123.28\nIsolation\n3.95\u00b10.04\n0.185\u00b10.002\n5.99\u00b10.05\n28.70\u00b10.17\n1.00\u00b10.82\nLepton fraction\n3.81\u00b10.04\n0.181\u00b10.002\n4.85\u00b10.05\n0.64\u00b10.03\n(1.96\u00b11.38)\u00d710\u22123\nmT > 700 GeV\n2.20\u00b10.03\n0.043\u00b10.002\n0.007\u00b10.003\n0.001\u00b10.001\nmT > 1400 GeV\n0.094\u00b10.0001\n0.0031\u00b10.0006\n0.001\u00b10.001\n0.001\u00b10.001\nTable 5: Cross-section for signal and backgrounds after each requirement. Muon mode.\ncalculated for transverse mass above 70% of the W \u2032 boson mass, i.e. above the values listed in Table 6.\nWe de\ufb01ne the K-factor to be the ratio of the MC@NLO cross-section to that from PYTHIA. These\nare shown as functions of \u03b7 in Fig. 22.\nIntegrals of the W \u2032 boson and W boson tail differential cross-sections are given in Table 7. The NLO\npredictions are 30-40% higher than those from PYTHIA, with little change with the variations in scale.\nAlthough the NLO/LO cross-section and acceptance ratios are of order 40%, the uncertainties on the\nNLO values are expected to be signi\ufb01cantly smaller. Also, the QED corrections are partially included\nthrough PHOTOS [41] for FSR, and should have a small impact on the measurements in case of the\nobservation of a signal.\n6.1.2\nParton Distribution Functions\nThe LHC will take data in a new energy regime and so we expect signi\ufb01cant uncertainty in signal and\nbackground predictions due to our uncertainty in knowledge of the PDFs.\nThe CTEQ6.1 \ufb01ts include 40 error PDFs corresponding to the two limits on each of 20 eigenvectors.\nM (GeV)\n\u0393 (GeV)\nMinimum mT (GeV)\n1000\n34.739\n700\n2000\n70.540\n1400\n3000\n106.390\n2100\nTable 6: Masses and widths used as input to MC@NLO/HERWIG generation of W \u2032 boson events.\nThe third column gives the lower limit for the masses used to calculate cross-sections.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1741\n\n\u03b7\n-2 5\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n1 TeV W\u2019-\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n1 TeV W\u2019+\n\u03b7\n-2 5\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n2 TeV W\u2019-\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n2 TeV W\u2019+\n\u03b7\n-2 5\n-2\n-1 5\n-1\n-0.5\n0\n0 5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n3 TeV W\u2019-\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\nK-factor\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nS=1.0\nS=0.5\nS=2.0\n3 TeV W\u2019+\nFigure 22: W \u2032 boson K-factors (ratios of MC@NLO and PYTHIA cross-sections) as functions of \u03b7\nfor positive (left) and negative (right) charge for masses of 1 (top), 2 (middle) and 3 TeV (bottom).\nS is the common scale factor. The errors are statistical.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1742\n\nProcess\nMin. mT\nPYTHIA \u03c3 (fb)\nNLO \u03c3 (fb)\nK-factor\nS=0.5\nS=2.0\nW \u2032(m = 1 TeV)+\n700\n534.\n(1)\n742.\n(1)\n1.389 (4)\n1.8% (2)\n-1.8% (2)\nW \u2032(m = 1 TeV)-\n700\n1204.\n(1)\n1644.\n(2)\n1.365 (3)\n1.7% (2)\n-1.8% (2)\nW \u2032(m = 2 TeV)+\n1400\n62.6\n(1)\n83.0\n(1)\n1.327 (3)\n2.7% (2)\n-1.6% (2)\nW \u2032(m = 2 TeV)-\n1400\n20.3\n(6)\n27.7\n(4)\n1.362 (4)\n3.0% (2)\n-1.4% (2)\nW \u2032(m = 3 TeV)+\n2100\n6.73 (1)\n8.69 (1)\n1.292 (3)\n3.7% (2)\n4.4% (2)\nW \u2032(m = 3 TeV)-\n2100\n1.791 (6)\n2.540 (4)\n1.370 (5)\n3.7% (2)\n4.4% (2)\nW+\n700\n20.22\n(7)\n27.66\n(8)\n1.368 (6)\n2.2% (4)\n-0.6% (4)\nW-\n700\n8.93\n(5)\n12.56\n(4)\n1.407 (9)\n2.6% (5)\n-0.8% (5)\nW+\n1400\n1.042 (4)\n1.424 (4)\n1.366 (7)\n2.2% (5)\n-1.5% (5)\nW-\n1400\n0.354 (2)\n0.499 (2)\n1.41 (1)\n1.8% (6)\n-1.6% (5)\nW+\n2100\n0.1231 (3)\n0.1657 (3)\n1.346 (4)\n3.0% (3)\n2.4% (3)\nW-\n2100\n0.0346 (1)\n0.0492 (1)\n1.421 (6)\n3.1% (3)\n2.5% (3)\nTable 7: Integrated W \u2032 boson and W boson tail cross-sections for PYTHIA and MC@NLO with\ncommon scale factor S=1. Integral is over the full \u03b7 range \u22122.5 < \u03b7 < 2.5. The listed K-factors\nare the ratios of the integrated MC@NLO and PYTHIA cross-sections. The last two columns give\nthe change in the MC@NLO cross-section when the common scale factor is changed by a factor\nof two. The statistical error in the last digit of each calculated quantity is shown in parentheses.\nThese can be used to estimate the uncertainty in predictions obtained with the \ufb01t. Figure 23 shows the\nPYTHIA prediction for the m = 1 TeV W \u2032 boson differential cross-section as a function of \u03b7 for the\nCTEQ6.1 central value and each of the 40 error sets. Events are required to have transverse mass above\nthe threshold in Table 6. The difference in shape between the positively and negatively charged bosons is\na consequence of the parton distribution functions since W \u2032+ are from u \u00afd fusion and W \u2032\u2212from d \u00afu fusion.\n\u03b7\n-2.5\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\n2.5\n (fb)\n\u03b7\n/d\n\u03c3\nd\n0\n100\n200\n300\n400\n500\nplus\nError sets\nminus\nError sets\nFigure 23: Muon \u03b7 distributions for positively- and negatively-charged m = 1 TeV W \u2032 bosons\nusing the CTEQ 6.1 PDF central value (black) and 40 error sets.\nWe calculated cross sections for W \u2032 boson production with mass of 1 TeV using the CTEQ6.1 cen-\ntral value and error PDFs by integrating over the full \u03b7 range (|\u03b7| < 2.5) in Fig. 23. To estimate the\noverall uncertainty, the positive and negative deviations for each eigenvector were summed separately in\nquadrature for each charge sign. Where both deviations for an eigenvector had the same sign, only the\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1743\n\nlarger magnitude was included in the sums. Table 8 shows the results.\nProcess\nMin. mT\nW+\nW-\nW \u2032 (m = 1 TeV)\n700\n-4.1% (5), +8.2% (5)\n-11.1% (7), +3.5% (8)\nTable 8: CTEQ6.1 combined error set deviations for W \u2032 boson cross-sections. The statistical error\non the last digit is shown in parentheses.\nCombining all the above, we assign a common K-factor of 1.37 for all masses and charges and assign\nan 8% uncertainty on this factor.\n6.2\nInstrumental Uncertainties\nDetector related uncertainties for these studies can be divided in two categories: the ones related to the\nreconstruction of the leptons and the ones corresponding to the global event activity as the /ET and the\njet characteristics. However, the lepton reconstruction uncertainties can be the dominant factor in the /ET\nresolution.\n6.2.1\nLepton Reconstruction\nThree main contributions can be identi\ufb01ed in this category. The ef\ufb01ciency of lepton identi\ufb01cation, as\nwell as the fake rates associated with this, the pT or ET scale and its measurement resolution.\nSystematic errors on the momentum scale of the muons can arise for instance due to the non-perfect\nknowledge of the magnetic \ufb01eld. To take into account such effects, a variation of \u00b11% is applied to the\npT of the reconstructed muons. Positive and negative variations are considered separately. In a similar\nway but for energy, a variation of \u00b10.5% was made for electrons.\nAn incomplete understanding of the material distributions inside the detector as well as possible mis-\nalignments in the MS can lead to an additional smearing of the momentum measurement resolution of\nmuons. To evaluate the impact of such contributions on the analysis, a smearing, based on early cali-\nbrations of \u03c3(1/pT) = 0.011/pT \u22950.00017 is applied. The \ufb01rst term enhances the Coulomb scattering\nsmearing, while the second enhances the alignment contribution, and is the crucial factor in this study.\nFor the energy measurement resolution for electrons, the total \u03c3(ET) is smeared by 0.0073 \u00d7 ET,\nwhich enhances the constant term only.\nLepton identi\ufb01cation ef\ufb01ciency is obviously important for this analysis. The identi\ufb01cation ef\ufb01ciency\ncan be estimated from the data, using the tag-and-probe method described in [42] for muons in the region\n20 < pT < 50 GeV and extrapolated to higher pT using simulated data. A value of \u00b15% has been chosen\nfor the evaluation of this uncertainty, corresponding to the early running period of integrated luminosities\nL < 100 pb\u22121. In the case of electrons a \u00b11% variation has been applied.\n6.2.2\nJet Reconstruction\nAn uncertainty on the jet energy scale of \u00b17% was imposed, together with an uncertainty on its resolution\nof \u03c3(ET) = 0.45\u00d7\u221aET \u22955%.\n6.2.3\nMissing Energy\nIf jets or leptons are systematically shifted, then missing transverse energy should be systematically\nshifted in a known direction. Based on the jet and leptons performance, the missing energy is shifted as\nfollows:\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1744\n\n\u2022 /ET (shi fted)(x) = /ET(x)+Elepton/jet(x)\u2212Elepton/jet\nshifted\n(x)\n\u2022 /ET (shi fted)(y) = /ET(y)+Elepton/ jet(y)\u2212Elepton/jet\nshifted\n(y)\n\u2022 \u2211ET(shifted) = \u2211ET +Elepton/jet\nT\n\u2212Elepton/ jet\nT(shifted)\nIn the case of muons, momentum is used instead of energy.\n6.2.4\nSummary of Experimental Systematic Uncertainties\nThe effects of the experimental uncertainties are summarized in Tables 9 and 10. In the high-pT range\nelectrons\nmuons\nDescription of systematic\n\u03b4s [%]\n\u03b4b [%]\n\u03b4s [%]\n\u03b4b [%]\nLepton energy scale +\n+0.8\n+1.8\n+1.2\n+4.6\nLepton energy scale -\n-0.7\n-2.1\n-1.2\n-4.4\nLepton energy resolution\n+0.1\n+0.2\n-1.0\n+3.7\nLepton identi\ufb01cation ef\ufb01ciency +\n+1.0\n+1.0\n+5.\n+5.\nLepton identi\ufb01cation ef\ufb01ciency -\n-1.0\n-1.0\n-5.\n-5.\nJet energy scale +\n+0.1\n-0.2\n-0.1\n+0.1\nJet energy scale -\n+0.1\n-0.2\n+0.1\n+0.7\nJet energy resolution\n+0.0\n+0.1\n-0.1\n+0.3\nLuminosity\n\u00b13.\n\u00b13.\nTable 9: Effect of the detector systematics in percentage for mW \u2032 = 1 TeV. \u03b4s is the uncertainty on\nthe signal, \u03b4b is the uncertainty on the background.\nelectrons\nmuons\nDescription of systematic\n\u03b4s [%]\n\u03b4b [%]\n\u03b4s [%]\n\u03b4b [%]\nLepton energy scale +\n+0.7\n+1.2\n+1.5\n+3.4\nLepton energy scale -\n-0.4\n-3.7\n-1.7\n-2.5\nLepton energy resolution\n-0.03\n0.0\n-4.2\n+6.8\nLepton identi\ufb01cation ef\ufb01ciency +\n+1.0\n+1.0\n+5.\n+5.\nLepton identi\ufb01cation ef\ufb01ciency -\n-1.0\n-1.0\n-5.\n-5.\nJet energy scale +\n+0.1\n1.2\n+0.1\n+0.8\nJet energy scale -\n-0.1\n0\n-0.3\n-0.1\nJet energy resolution\n-0.1\n0\n+0.1\n-0.1\nLuminosity\n\u00b13.\n\u00b13.\nTable 10: Effect of the detector systematics in percentage for mW \u2032 = 2 TeV. \u03b4s is the uncertainty\non the signal, \u03b4b is the uncertainty on the background.\nunder consideration, the systematic uncertainties on the quality of single lepton reconstruction have a\nstronger effect on the muon channel, for which there are comparable contributions from energy scale,\nresolution and identi\ufb01cation ef\ufb01ciency (with the resolution uncertainty becoming more important for a\nhigher W \u2032 mass); out of these three, the energy scale uncertainty dominates in the electron channel for\nmW \u2032 = 1 TeV, but becomes less important for mW \u2032 = 2 TeV. Jet uncertainties do not play a strong role\non either channel.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1745\n\n7\nDiscovery Potential\nIn order to assess the ATLAS discovery potential in the search for a W \u2032 \u2192\u2113+ /ET signal, the luminosity\nneeded for a 5\u03c3 excess is obtained as a function of the mass of the W \u2032 boson.\nThe signi\ufb01cance is obtained from the expected number of signal and background events in the region\nmT > 0.7mW \u2032, where mW \u2032 is the mass of the hypothesized W \u2032 boson. Calling these expected numbers s\nand b, respectively, the signi\ufb01cance S is obtained as\nS =\np\n2((s+b)ln(1+s/b)\u2212s)\nwhich gives a good approximation to the likelihood-ratio based signi\ufb01cance in the low statistics regime.\nFigure 24 shows the expected integrated luminosity needed for a 5-sigma excess as a function of the\nmass of the W \u2032 boson.\nHigher order corrections for W \u2032/W \u2192\u2113\u03bd processes are taken into account as stated in section 6.1.\nSystematic uncertainties listed in Tables 9 and 10 are taken into account by increasing the expected\nbackground by the sum in quadrature of its positive expected variations, and by reducing the signal by\nthe sum in quadrature of its expected negative variations; this assumes no correlations of the expected\nsignal and background expectations and, as a result, produces a conservative estimate.\nFor comparison, the integrated luminosity values for a 5\u03c3 signi\ufb01cance were also obtained taking\ninto account the shape of the signal and background mT distributions. This was done using a technique\nin which, instead of an ensemble of Monte Carlo pseudo-experiments [43], a Fast Fourier Transform\n(FFT) is used to calculate the experimental estimator distributions [44]. This method allows a fast de-\ntermination of the probability that background \ufb02uctuations produce a signal-like result, but it depends\non the assumption that both the location of the signal and its shape are well known. Treating each bin\nof the transverse mass distribution as an independent search channel, and combining them accordingly,\nthe resulting sensitivity is in general higher than the estimation given in the number counting approach.\nWith this method, the luminosity required for a 5\u03c3 effect was reduced between 20 and 35% with respect\nto the values shown in Fig. 24.\nEven for very low integrated luminosities (of the order of picobarns), a W \u2032 boson with a mass above\nthe current experimental limits could be found with a signi\ufb01cance in excess of 5\u03c3, while, with 1 fb\u22121,\nmasses of the order of 3 TeV can be reached. As an illustration, Figs 25 and 26 show Monte Carlo\noutcomes of pseudo-experiments corresponding to 10 pb\u22121 and 100 pb\u22121, respectively, for both channels.\nThe solid line histograms depict the expected background, those in dotted lines the m = 1 TeV W \u2032 boson\nsignal and the dashed-dotted line histograms show possible m = 2 TeV W \u2032 boson signals.\n8\nSummary and Conclusion\nThe potential for the ATLAS experiment to reconstruct and identify the decay of a heavy, charged gauge\nboson into a lepton and a neutrino has been studied. Various systematic and theoretical uncertainties\nhave been considered, as well as plausible estimations of our uncertainties about the performance of the\ndetector in the early stages of data taking. These studies show that, even with integrated luminosities\nas low as 10 pb\u22121 of data, it would be possible to discover this type of bosons, should they exist not\nfar beyond the current experimental limits and have Standard Model like couplings. With an integrated\nluminosity of a few fb\u22121, ATLAS has the potential to discover these particles for masses up to 4 TeV.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1746\n\nM(W\u2019) [TeV]\n1\n2\n3\n]\n-1\nLuminosity [pb\n1\n10\n2\n10\n3\n10\nATLAS\n\u03bd\n e \n\u2192\nW\u2019\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\ncombined\n (systematics)\n\u03bd\n e \n\u2192\nW\u2019\n (systematics)\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\ncombined (systematics)\nFigure 24: Integrated luminosity needed to have a 5\u03c3 discovery as a function of the mass of the\nW \u2032 bosons; triangles correspond to the e\u03bd search, squares to \u00b5\u03bd, circles to the combined search.\nFilled markers include the effect of systematic uncertainties.\n [TeV]\nT\nM\n0 2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n1 8\nExpected Events\n0\n1\n2\n3\n4\n5\n6\n \n \n \n \n \n \n \n \n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\nbackground\nATLAS\n [TeV]\nT\nM\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n1.8\nExpected Events\n0\n2\n4\n6\n8\n10\n \n \n \n \n \n \n \n \n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\nbackground\nATLAS\nFigure 25: Monte Carlo pseudo-experiment for 10 pb\u22121. Left: electron channel; right: muon\nchannel.\n [TeV]\nT\nM\n0 5\n1.0\n1.5\n2.0\n2.5\nExpected Events\n1\n10\n2\n10\n \n \n \n \n \n \n \n \n [1TeV]\n\u03bd\n e \n\u2192\nW\u2019\n [2TeV]\n\u03bd\n e \n\u2192\nW\u2019\nbackground\nATLAS\n [TeV]\nT\nM\n0.5\n1 0\n1.5\n2.0\n2.5\nExpected Events\n1\n10\n2\n10\n \n \n \n \n \n \n \n \n [1TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\n [2TeV]\n\u03bd \n\u00b5\n \n\u2192\nW\u2019\nbackground\nATLAS\nFigure 26: Monte Carlo pseudo-experiment for 100 pb\u22121. Left: electron channel; right: muon\nchannel.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1747\n\nReferences\n[1] P. Langacker, R. W. Robinett, and J. L. Rosner, Phys. Rev. D30 (1984) 1470.\n[2] F. Buccella, G. Mangano, O. Pisanti, and L. Rosa, Phys. Atom. Nucl. 61 (1998) 983\u2013990.\n[3] R. W. Robinett, Phys. Rev. D26 (1982) 2388.\n[4] J. C. Pati and A. Salam, Phys. Rev. D10 (1974) 275\u2013289.\n[5] R. N. Mohapatra and J. C. Pati, Phys. Rev. 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Pumplin et al., JHEP 07 (2002) 012.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1748\n\n[29] ATLAS Collaboration, CERN/LHCC 97-22 (1997) .\n[30] ATLAS Collaboration, \u201cMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples.\u201d This volume.\n[31] ATLAS Collaboration, \u201cReconstruction and Identi\ufb01cation of Electrons.\u201d This volume.\n[32] ATLAS Collaboration, \u201cCalibration and Performance of the Electromagnetic Calorimeter.\u201d This\nvolume.\n[33] ATLAS Collaboration, \u201cMeasurement of Missing Tranverse Energy.\u201d This volume.\n[34] ATLAS Collaboration, \u201cThe ATLAS Experiment at the CERN Large Hadron Collider.\u201d JINST 3\n(2008) S08003.\n[35] ATLAS Collaboration, \u201cPhysics Performance Studies and Strategy of the Electron and Photon\nTrigger Selection.\u201d This volume.\n[36] ATLAS Collaboration, \u201cPerformance of the Muon Trigger Slice with Simulated Data.\u201d This\nvolume.\n[37] J. Pumplin, A. Belyaev, J. Huston, D. Stump, and W. K. Tung, JHEP 02 (2006) 032.\n[38] S. Frixione, P. Nason, and B. R. Webber, JHEP 08 (2003) 007.\n[39] G. Corcella et al., arXiv:hep-ph/0210213.\n[40] A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Phys. Lett. B604 (2004) 61\u201368.\n[41] P. Golonka and Z. Was, Eur. Phys. J. C45 (2006) 97\u2013107.\n[42] ATLAS Collaboration, \u201cIn-Situ Determination of the Performance of the Muon Spectrometer.\u201d\nThis volume.\n[43] T. Junk, Nucl. Instrum. Meth. A434 (1999) 435\u2013443.\n[44] H. Hu and J. Nielsen, arXiv:physics/9906010.\nhttp://www.citebase.org/abstract?id=oai:arXiv.org:physics/9906010.\nEXOTICS \u2013 LEPTON PLUS MISSING TRANSVERSE ENERGY SIGNALS AT HIGH MASS\n1749\n\nSearch for Leptoquark Pairs and Majorana Neutrinos from\nRight-Handed W Boson Decays in Dilepton-Jets Final States\nAbstract\nFinal states with high-pT leptons and jets are predicted by many Beyond the\nStandard Model scenarios. Two prominent models are used here as guides\nto understanding the event topologies: the scalar leptoquarks and the Left-\nRight Symmetry. In contrast to many SUSY signatures, their topologies rarely\ncontain missing energy. Their discovery potential with early ATLAS data,\ncorresponding to an integrated luminosity of a few hundred inverse picobarns,\nis discussed.\n1\nIntroduction\nGrand Uni\ufb01cation has inspired many extensions of the Standard Model. Such models introduce new,\nusually very heavy particles, and previous searches for Grand Uni\ufb01cation Theory (GUT) signatures have\nplaced limits on masses and interaction strengths of the new particles. The LHC will probe new regions\nof parameter space, allowing for a direct search for these particles. Decays characterized by \ufb01nal states\nwith two highly energetic leptons, two jets and no missing transverse energy are studied in this note.\nThe models for new physics considered for this note are described below. The simulation of signal and\nbackground processes is described in section 2. In section 4 the baseline selection that is used for all\nanalyses is explained. After the trigger requirements are given (section 3), section 5 details the speci\ufb01cs\nof each of the analyses. The systematics are described in section 6 and the \ufb01nal sensitivity estimates are\ngiven in section 7.\n1.1\nLeptoquarks\nThe experimentally observed symmetry between leptons and quarks has motivated the search for lepto-\nquarks (LQ), hypothetical bosons carrying both quark and lepton quantum numbers, as well as fractional\nelectric charge [1\u20135]. Leptoquarks could, in principle, decay into any combination of a lepton and a\nquark. Experimental limits on lepton number violation, \ufb02avor-changing neutral currents, and proton de-\ncay favour three generations of leptoquarks. In such a scenario, each leptoquark couples to a lepton and\na quark from the same Standard Model generation [6]. Leptoquarks can either be produced in pairs by\nthe strong interaction or in association with a lepton via the leptoquark-quark-lepton coupling. Figure 1\nshows the Feynman diagrams for leptoquark production processes accessible at the LHC.\nThis note describes the search for leptoquarks decaying to either an electron and a quark or a muon\nand a quark. The branching ratio of a leptoquark to a charged lepton and a quark is denoted as \u03b2.\nDecays to neutrinos are not considered, and events are not explicitly selected based on the \ufb02avor of the\nquark. The experiments at the Tevatron have searched for \ufb01rst (decaying to eq), second (decaying to \u00b5q),\nand third (decaying to \u03c4q) generation scalar leptoquarks. For \u03b2 = B(LQ \u2192\u2113\u00b1q) = 1, the D\u00d8 [7] and\nCDF [8] collaborations have set 95%CL limits for \ufb01rst generation scalar leptoquarks of mLQ1 > 256 GeV\nand mLQ1 > 236 GeV, respectively. These limits are based on integrated p \u00afp luminosities of approxi-\nmately 250 pb\u22121 and 200 pb\u22121. The results for second generation leptoquarks, mLQ2 > 251 GeV and\nmLQ2 > 226 GeV, were obtained with 300 pb\u22121 and 200 pb\u22121 by the D\u00d8 [9] and CDF [10] experiments,\nrespectively.\nThe Tevatron exclusion limits are expected to reach 300-350 GeV in the near future.\n1750\n\ng\ng\ng LQ\nLQ\nl\nq\nl\nq\ng\nLQ\nLQ\ng\nLQ\nl\nq\nl\nq\nq\nq\ng LQ\nLQ\nl\nq\nl\nq\nq\nq\nl\nLQ\nLQ\nl\nq\nl\nq\ng\nq\nq\nLQ\nl\nq\nl\nq\nLQ\ng\nLQ\nl\nq\nl\nFigure 1: Feynman diagrams for leptoquark production.\n1.2\nLeft-Right Symmetry\nLeft-Right Symmetric Models (LRSMs) of the weak interaction address two important topics: the\nnonzero masses of the three known left-handed neutrinos [11] and baryogenesis. LRSMs conserve parity\nat high energies by introducing three new heavy right-handed Majorana neutrinos Ne, N\u00b5 and N\u03c4. The\nsmallest gauge group that implements an LRSM is SU(2)L \u00d7 SU(2)R \u00d7U(1)B\u2212L. At low energies, the\nleft-right symmetry is broken and parity is violated. The Majorana nature of the new heavy neutrinos\nexplains the masses of the three left-handed neutrinos through the see-saw mechanism [12]. The lepton\nnumber L could be violated in processes that involve the Majorana neutrinos. This opens a window to the\nvery attractive theoretical scenario for baryogenesis via leptogenesis, where baryon and lepton numbers\nB and L are violated but B\u2212L is conserved.\nIn addition to the Majorana neutrinos, most general LRSMs also introduce the new intermediate\nvector bosons WR and Z\u2032, Higgs bosons, and a left-right mixing parameter. The most restrictive lower\nlimit on the mass of the WR boson comes from the KL \u2212KS mass difference which requires mWR >\n1.6 TeV. This lower limit is subject to large corrections from higher-order QCD effects. Heavy right-\nhanded Majorana neutrinos with masses of about a few hundred GeV would be consistent with the data\nfrom supernova SN1987A. Such heavy neutrinos would allow for a WR boson at the TeV mass scale.\nThis scenario would also be consistent with LEP data on the invisible width of the Z boson. Present\nexperimental data on neutral currents imply a lower limit on the mass of a Z\u2032 boson of approximately\n400 GeV. Recent direct searches [13] for the WR boson at D\u00d8 give a lower mass limit of 739 GeV and\n768 GeV, assuming the WR boson could decay to both lepton pairs and quark pairs, or only to quark pairs,\nrespectively. However, heavy Majorana neutrinos decaying to a lepton and a pair of quarks (detected as\njets) were not searched for in those analyses.\nThe new intermediate vector bosons WR and Z\u2032 would be produced at the LHC via the Drell-Yan\n(DY) process like Standard Model W and Z bosons. Their decays would be a source of new Majorana\nneutrinos. The Feynman diagram for WR boson production and its subsequent decay to a Majorana\nneutrino is shown in Fig. 2. This note describes an analysis of WR boson production and its decays\nWR \u2192eNe and WR \u2192\u00b5N\u00b5, followed by the decays Ne \u2192eq\u2032 \u00afq and N\u00b5 \u2192\u00b5q\u2032 \u00afq, which can be detected in\n\ufb01nal states with (at least) two leptons and two jets.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1751\n\nq\nl-\nq-'\nW\nR\nNl\nW\nR\n*\nl or l\n-\nq\nq-'\ntwo jets\nFigure 2: Feynman diagram for WR boson production and its decay to a Majorana neutrino N\u2113.\nmLQ in GeV\n\u03c3(pp \u2192LQLQ) (NLO) in pb\n300\n10.1 \u00b1 1.5\n400\n2.24 \u00b1 0.38\n600\n0.225 \u00b1 0.048\n800\n0.0378 \u00b1 0.0105\nTable 1: NLO cross-sections for scalar leptoquark pair production at the LHC [16].\n2\nSimulation of Physics Processes\n2.1\nLeptoquarks\nThe signals have been studied using samples of \ufb01rst generation (1st gen.) and second generation (2nd gen.)\nscalar leptoquarks simulated with the Monte Carlo (MC) generator PYTHIA [14] and using the CTEQ6L1\nparameterization [15] of the parton density functions (PDFs). A leptoquark-lepton-quark coupling \u03bb =\n0.8 was used in the event generation leading to a natural width of the leptoquarks of 0.63 GeV and\n1.3 GeV for leptoquark masses of 400 GeV and 800 GeV respectively.\nThe next to leading order\n(NLO) cross-sections for leptoquark pair production at 14 TeV pp centre-of-mass energy were taken\nfrom Ref. [16] and are shown in Table 1 for the four simulated leptoquark masses.\n2.2\nLeft-Right Symmetry\nStudies of the discovery potential for WR bosons and the Majorana neutrinos, Ne and N\u00b5 produced in their\ndecays, were performed using datasets simulated with the MC generator PYTHIA according to a particu-\nlar implementation [17] of an LRSM described in [18]. The Standard Model axial and vector couplings,\nthe CKM matrix for the quark sector, no mixing between the new and Standard Model intermediate vector\nbosons, and phase space isotropic decays of Majorana neutrinos are assumed for the right-handed sec-\ntor in this model. The products of leading-order production cross-sections \u03c3(pp \u2192WRX) and branching\nfractions to studied \ufb01nal statesWR \u2192\u2113N\u2113\u2192\u2113\u2113j j are 24.8 pb for mWR = 1800 GeV,mNe = mN\u00b5 = 300 GeV\nand 47.0 pb for mWR = 1500 GeV,mNe = mN\u00b5 = 500 GeV. In the rest of this note, these samples are re-\nferred to as LRSM 18 3 and LRSM 15 5, respectively. The Majorana nature of the new heavy neutrinos\nallows for same-sign and opposite-sign dileptons.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1752\n\n2.3\nBackground Processes\nThe main sources of background for the analyses presented here are t\u00aft and inclusive Z/\u03b3\u2217production pro-\ncesses. Multijet production, where two jets are misidenti\ufb01ed as leptons, represents another background.\nIn addition, minor contributions arise from diboson production. Other potential background sources,\nsuch as single-top production, were also studied. Their contribution was found to be insigni\ufb01cant.\n\u2022 Z/\u03b3\u2217background was studied using a combination of two MC samples with generator-level dilep-\nton invariant mass preselections of m\u2113\u2113> 60 GeV and m\u2113\u2113> 150 GeV, the latter sample corre-\nsponding to a much larger integrated luminosity than the former. The samples were normalized to\nthe given luminosity using their partial cross-sections and the NLO estimate \u03c3(pp \u2192Z)\u00d7B(Z \u2192\n\u2113+\u2113\u2212) = 2032 pb, obtained with the MC generator FEWZ [19,20]. A lepton \ufb01lter was applied at\nthe event generation, requiring at least one electron or muon with transverse momentum greater\nthan 10 GeV and absolute pseudo-rapidity smaller than 2.7, resulting in an effective cross-section\nof 1808 pb.\nFor logistical reasons, the sample with the lower mass preselection was generated using the MC\ngenerator PYTHIA [14], and the sample with higher mass preselection was generated using HER-\nWIG [21]. In both cases, the CTEQ6L1 [15] parton distribution functions were used. The consis-\ntency between the two samples was veri\ufb01ed at high dilepton masses.\n\u2022 t\u00aft background was simulated using the MC generator MC@NLO [22] using the CTEQ6M [15]\nparton distribution functions. It was normalized to the given integrated luminosity using a produc-\ntion cross-section of 833 pb estimated to the next-to-leading order (NLO+NLL) [23]. In addition,\na lepton \ufb01lter was applied, requiring at least one electron or muon with transverse momentum\ngreater than 1 GeV, which resulted in an effective cross-section of 450 pb.\n\u2022 The diboson samples were generated using HERWIG with a generator-level preselection on the\ninvariant mass of Z/\u03b3\u2217> 20 GeV. With this requirement, the NLO partial cross-sections for WW,\nWZ and ZZ boson pair production processes were numerically estimated (using MC@NLO) to be\n117.6 pb, 56.4 pb, 17.8 pb, respectively. The CTEQ6L1 parton distribution functions were used\nfor event generation. Again, a lepton \ufb01lter was applied, with a transverse momentum threshold\nof 10 GeV and a maximum absolute pseudo-rapidity of 2.8. This resulted in a total effective\ncross-section of 60.9 pb.\n\u2022 The multijet background was simulated using PYTHIA with the CTEQ6L1 structure functions.\nThe normalization was based on PYTHIA cross-section estimates. The statistics of these samples\nare very limited, such that no reliable estimate of this background could be made at this time.\n3\nTrigger Requirements\nThe trigger system [24] of the ATLAS experiment has three levels, L1, L2 and the Event Filter (EF). To\nensure high overall trigger ef\ufb01ciencies, our analyses rely on single lepton trigger streams with relatively\nlow thresholds. The dielectron analyses rely on the single electron-based trigger called e55 which has a\nthreshold of around 60 GeV [24]. When selected events fail this trigger, the analyses rely on the lower-\nthreshold (about 25 GeV) single electron trigger called e22i [24] in which the electron is required to be\nisolated. A single muon trigger with threshold about 20 GeV (mu20 [24]) is used in the dimuon analyses.\nFinal states studied in this note always contain two high-pT leptons. While the baseline selection\ndescribed in section 4 requires two leptons with pT > 20 GeV, most signal events contain at least one\nlepton with signi\ufb01cantly higher pT. As a result, the overall trigger ef\ufb01ciency for events that satisfy all\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1753\n\nanalysis selection criteria (section 5) exceeds 95%. The trigger ef\ufb01ciencies for signal MC events that\nsatisfy all selection criteria are shown in Table 2.\nProcess\nL1\nL2\nEF\nL1*L2*EF\n1st gen. leptoquarks mLQ = 400 GeV\n100.0%\n99.4%\n97.6%\n97.0%\n2nd gen. leptoquarks mLQ = 400 GeV\n97.7%\n99.1%\n99.7%\n96.5%\nLRSM (ee) mWR = 1800 GeV, mNe = 300 GeV\n100.0%\n99.2%\n97.2%\n96.4%\nLRSM (\u00b5\u00b5) mWR = 1800 GeV, mN\u00b5 = 300 GeV\n96.8%\n98.7%\n98.9%\n94.5%\nTable 2: Overall trigger ef\ufb01ciencies for signal events that satisfy all selection criteria.\n4\nBaseline Event Selection\nThe baseline event selection, common for all analyses presented in this note, requires two leptons and\ntwo jets. All analyses use the same selection criteria for signal electron, muon, and jet candidates. The\nbaseline selection criteria for these reconstructed objects are summarized below. Performance studies\nare described elsewhere [25\u201328].\nElectron candidates are identi\ufb01ed as energy clusters reconstructed in the liquid argon electromagnetic\ncalorimeter that match tracks reconstructed in the inner tracking detector and satisfy the medium electron\nidenti\ufb01cation requirements [25].\nMuon candidates are identi\ufb01ed as tracks reconstructed in the muon spectrometer [26] that, when\nextrapolated to the beam axis, match a track reconstructed in the inner detector, and satisfy relative\nisolation energy requirements Eiso\nT /p\u00b5\nT \u22640.3. p\u00b5\nT is the muon candidate\u2019s transverse momentum and Eiso\nT\nis the energy detected in the calorimeters in a cone of \u2206R=\np\n\u2206\u03b72 +\u2206\u03c6 2=0.2 around the muon candidate\u2019s\nreconstructed trajectory, corrected for the expected energy deposition by a muon.\nJets are identi\ufb01ed as energy clusters reconstructed in the calorimeters using a \u2206R=0.4 cone algo-\nrithm [27]. \u2206R between a jet and any electron candidate (as de\ufb01ned above) must be larger than 0.1. This\nveto is imposed to avoid electrons being misidenti\ufb01ed as jets. It is applied in all analyses, regardless of\nwhether electrons are explicitly considered in the \ufb01nal states or not. The jet energy scale calibration is\nperformed using full MC simulation and requires that the average reconstructed jet energy agrees with the\naverage energy of the jets reconstructed with the Monte Carlo truth particles. The same jet reconstruction\nalgorithm, with cone size \u2206R = 0.4, is used for both reconstruction and calibration.\nAll objects are required to have pT \u226520 GeV, the leptons must have an absolute pseudo-rapidity |\u03b7|\nsmaller than 2.5 and jets must have |\u03b7| \u22644.5.\nTo suppress contributions from Drell-Yan backgrounds, the dilepton invariant mass is required to be\nat least 70 GeV. Tighter analysis-speci\ufb01c requirements are later applied to this and other variables in\norder to achieve the best sensitivities in individual studies, as described in the following section.\n5\nIndividual Analyses\n5.1\nSearch for Leptoquark Pair Production\nFollowing the baseline object identi\ufb01cation criteria described above, the leptoquark pair analyses require\nevents to have at least two oppositely charged leptons of the same \ufb02avour and at least two jets. Signal\nsensitivity and discovery potential are estimated using a sliding mass window algorithm: only events in\nthe mass region around the assumed mass of the leptoquark are analyzed.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1754\n\nFor large leptoquark masses, signal leptons and jets have, on average, larger transverse momenta\nthan background particles. The following kinematic quantities are used to separate the signal from back-\ngrounds: the transverse momentum of the leptons (pT ), the scalar sum of the transverse momenta of\nthe two most energetic jets and leptons (ST = \u2211|\u20d7pT|jet + \u2211|\u20d7pT|lep), the dilepton invariant mass (m\u2113\u2113),\nand lepton-jet invariant mass. The lepton-jet invariant mass represents the mass of the leptoquark if the\ncorrect lepton-jet combination is chosen. Since there are two leptons and two jets there are two possible\ncombinations, and we choose the combination which gives the smallest difference between the masses\nof the \ufb01rst and second leptoquark candidates.\nPhysics\nBefore\nBaseline\nST \u2265\nmee \u2265\nm1\nl j - m2\nl j window (GeV)\nsample\nselection\nselection\n490 GeV\n120 GeV\n[320-480] -\n[700-900] -\n[320-480]\n[700-900]\nLQ (m = 400 GeV)\n2.24\n1.12\n1.07\n1.00\n0.534\n-\nLQ (m = 800 GeV)\n0.0378\n0.0177\n0.0177\n0.0174\n-\n0.0075\nZ/\u03b3\u2217\u226560 GeV\n1808.\n49.77\n0.722\n0.0664\n0.0036\n0.00045\nt\u00aft\n450.\n3.23\n0.298\n0.215\n0.0144\n< 0.0012\nVector Boson pairs\n60.9\n0.610\n0.0174\n0.00384\n< 0.002\n< 0.0014\nMultijet\n108\n20.51\n0.229\n0.184\n0.0\n0.0\nTable 3: 1st generation leptoquark analysis. Partial cross-sections (pb) that survive selection criteria.\nThe upper limits are given at 68% con\ufb01dence level.\nPhysics\nBefore\nBaseline\np\u00b5\nT\u226560 GeV\nST \u2265\nm\u00b5\u00b5 \u2265\nml j window (GeV)\nsample\nselection\nselection\npjet\nT \u226525 GeV\n600 GeV\n110 GeV\n[300-500]\n[600-1000]\nLQ (400 GeV)\n2.24\n1.70\n1.53\n1.27\n1.23\n0.974\n-\nLQ (800 GeV)\n0.0378\n0.0313\n0.0306\n0.0304\n0.030\n-\n0.0217\nZ/\u03b3\u2217\u226560 GeV\n1808.\n79.99\n2.975\n0.338\n0.0611\n0.021\n0.014\nt\u00aft\n450.\n4.17\n0.698\n0.0791\n0.0758\n0.0271\n0.0065\nVB pairs\n60.9\n0.876\n0.0654\n0.00864\n0.00316\n0.00185\n0.00076\nMultijet\n108\n0.0\n0.0\n0.0\n0.0\n0.0\n0.0\nTable 4: 2nd generation leptoquark analysis. Partial cross-sections (pb) that survive selection criteria.\nIn both channels, the values of these selection criteria are optimized1 to achieve discovery with 5\u03c3\nsigni\ufb01cance at the lowest luminosity possible. Tables 3 and 4 show the values of the selection criteria\nand resulting signal and background cross-sections for 1st and 2nd generation channels, respectively.\nOne important difference between the two channels is the background due to jets being misidenti\ufb01ed\nas electrons. This background can be signi\ufb01cantly reduced by requiring both reconstructed jet-electron\nmasses, (m1\nl j, m2\nl j), to be close to the tested leptoquark mass. However, such a selection in the 2nd gen-\neration analysis would signi\ufb01cantly reduce the signal ef\ufb01ciency, especially for larger leptoquark masses.\nTherefore, a less strigent selection is applied, and only the average of the two muon-jet masses (mav\nl j ) is\nrequired to be near the tested leptoquark mass.\nFigure 3 shows the ST variable distribution with mLQ = 400 GeV, along with the main backgrounds,\nDrell-Yan and t\u00aft production, after baseline selection plus, for the 2nd generation case, the requirements\n1At this stage, only statistical uncertainties are taken into account.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1755\n\n [GeV]\nT\nS\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n-1\nEvents / 50 GeV / 100 pb\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nATLAS\nFirst generation\n [GeV]\nT\nS\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n-1\nEvents / 50 GeV / 100 pb\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\nATLAS\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nSecond generation\nFigure 3: ST in leptoquark MC events (mLQ = 400 GeV) after baseline selection. Left: 1st generation, right: 2nd\ngeneration with the additional requirements p\u00b5\nT > 60 GeV and pjet\nT > 25 GeV.\np\u00b5\nT > 60 GeV and pjet\nT > 25 GeV.\n [GeV] \nee\nM\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEvents / 20 GeV / 100 pb\n0\n1\n2\n3\n4\n5\n6\n7\n8\nATLAS\nFirst generation\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\n [GeV] \n\u00b5\n\u00b5\nM\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEvents / 20 GeV / 100 pb\n0\n1\n2\n3\n4\n5\n6\n7\n8\nATLAS\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nSecond generation\nFigure 4: m\u2113\u2113of the selected lepton pair after ST selection in leptoquark 1st generation (left) and 2nd generation\n(right) events (mLQ = 400 GeV).\nThe dilepton mass distribution after the ST selection is shown in Figure 4.\nFigures 5 and 6 show the reconstructed invariant mass of leptoquark candidates (mLQ=400 GeV) in\nsignal events and the main backgrounds, Drell-Yan and t\u00aft production, after the subsequent selections\non dimuon mass and ST. Due to gluon radiation, quarks produced in the decays of heavy particles are\nnot equivalent to standard jets. This shifts the peak of the jet energy resolution function towards smaller\nenergies and results in a low-mass shoulder in the distribution of reconstructed masses of heavy particles.\nFigure 5 shows two entries per event corresponding to the two reconstructed electron-jet objects obtained\nby adding x and y mass projections of (m1\nl j, m2\nl j) on a common axis, ml j.\nAll \ufb01gures show predicted distributions for an integrated luminosity of 100 pb\u22121.\nThe trigger ef\ufb01ciency is not included in the plots and tables shown in this section. However events\nsatisfying all selection criteria would trigger with an ef\ufb01ciency exceeding 95%, as discussed in Section 3.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1756\n\n [GeV]\nlj\nM\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\n2 * events / 10 GeV / 100 pb\n-1\n10\n1\n10\n2\n10\n3\n10\nATLAS\nFirst generation\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\n [GeV]\nlj\nM\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\n2 * events / 10 GeV / 100 pb\n0\n5\n10\n15\n20\n25\nATLAS\nFirst generation\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nFigure 5:\nReconstructed electron-jet invariant mass in the 1st generation leptoquark (mLQ=400 GeV) analysis\nfor signal and background MC events after baseline selection (left) and after all selection criteria (right). All\ndistributions are given for 100 pb\u22121 of integrated luminosity.\n [GeV]\nlj\nM\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEvents / 20 GeV / 100 pb\n-1\n10\n1\n10\n2\n10\n3\n10\nATLAS\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nSecond generation\n [GeV]\nlj\nM\n0\n100\n200\n300\n400\n500\n600\n700\n800\n-1\nEvents / 20 GeV / 100 pb\n0\n5\n10\n15\n20\n25\nATLAS\nSignal - 400 GeV\nDrell-Yan\ntt\nWW,ZZ,WZ\nSecond generation\nFigure 6: Reconstructed muon-jet invariant mass for 2nd generation leptoquarks (mLQ = 400 GeV) in signal and\nbackground MC events after baseline selection (left) and after all selection criteria (right). All distributions are\ngiven for 100 pb\u22121 of integrated luminosity.\n5.2\nSearch for New Particles from Left-Right Symmetric Models\nSignal event candidates are required to contain (at least) two electron or muon candidates and two or\nmore jets that pass the baseline selection criteria. As previously described, the minimum separation\nbetween a jet and an electron candidate \u2206R \u22650.1 is required. The two leading pT lepton candidates and\nthe two leading pT jets are assumed to be the decay products of the WR boson. The signal jet candidates\nare combined with each signal lepton, and the combination that gives the smallest invariant mass is\nconsidered as the heavy neutrino (N\u2113in Fig. 2). This assignment is correct in more than 99% of signal\nMC events. The other lepton is assumed to come directly from the decay of the WR boson.\nWhen the WR boson is at least twice as heavy as the Majorana neutrino, the daughter lepton from the\nneutrino\u2019s decay often begins to partially merge with one of the daughter jets. In the dielectron analysis,\nwhen the separation between this lepton and a signal jet candidate is in the range 0.1 \u2264\u2206R \u22640.4, using\nall three reconstructed objects to estimate the invariant mass of the neutrino would often result in double-\ncounting. To solve this problem, signal event candidates in the dielectron analysis are divided into two\ngroups. When the separation is outside the discussed range, i.e. \u2206R > 0.4, all three objects are used.\nHowever, when the separation is in the critical range, i.e. 0.1 \u2264\u2206R \u22640.4, only jets are used to estimate\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1757\n\nthe mass of the Ne neutrino. It must be noted that this procedure has little effect on the Ne neutrino mass\nresolution, because it is dominated by the resolution on the jets energy. The fraction of events falling in\nthe critical range depends on the ratio of WR boson and Majorana neutrino masses, and increases with\nthis ratio, being 8% for the 1500 GeV to 500 GeV ratio and 26% for the 1800 GeV to 300 GeV ratio\nconsidered here. No such problem exists in the dimuon analysis because muon reconstruction is possible\neven when the reconstructed trajectory\u2019s projection into the calorimeters randomly coincides with jet\nactivity. The mass of the Majorana neutrino can be reconstructed with a relative resolution of about\n6%, and the mass of the WR boson can be reconstructed with a relative resolution of 5% to 8%; better\nresolution on the latter is achieved in the dielectron analyses because the muon spectrometer resolution\nis degraded at high transverse momenta.\n0\n500\n1000\n1500\n2000\n2500\nST [ GeV ], dielectron channel\n10-1\n1\n101\n102\n103\nEvents / 60 GeV per 100 pb-1\nATLAS\n0\n500\n1000\n1500\n2000\n2500\nST [ GeV ], dimuon channel\n10-1\n1\n101\n102\n103\nEvents / 60 GeV per 100 pb-1\nATLAS\nFigure 7:\nLRSM analysis. ST distributions for signals and backgrounds normalized to 100 pb\u22121 of integrated\nluminosity after baseline selection in dielectron (left) and dimuon (right) analyses. Vertical lines indicate the region\nused in the analysis.\nWhile the main background sources in LRSM analyses are t\u00aft, Z/\u03b3\u2217, and vector boson pair production\nprocesses, multijets were also identi\ufb01ed as a source of potentially dangerous background in the dielectron\nanalysis. The distributions of the scalar sum of signal object candidates\u2019 transverse momenta ST, and the\nreconstructed dilepton invariant mass m\u2113\u2113for signal and background events, normalized to an integrated\nluminosity of 100 pb\u22121, are shown in Figs. 7 and 8.\nThe choice of the selection criteria ST \u2265700 GeV and m\u2113\u2113\u2265300 GeV is made in order to maintain\ngood ef\ufb01ciency not only for mass values used in this study, but also for signals with mWR \u22651000 GeV.\nPartial cross-sections for signal and background processes passing the selection criteria are shown\nin Tables 5 and 6. Some remarks are in order concerning the selection criteria\u2019s ef\ufb01ciencies. First, the\ndimuon channel is more ef\ufb01cient than the dielectron channel. This is due to the jet-electron merging\ndiscussed previously. This issue becomes especially important for a larger ratio of masses mWR/mNe.\nHowever, for a very heavy WR boson, the dielectron channel could become more signi\ufb01cant because the\nWR boson mass resolution does not become as wide in the dielectron channel as it does in the dimuon\nchannel. Also, because of its heavy mass, the potential to discover the WR boson and the heavy neutrino\ntogether is much better than in the inclusive search for the new heavy neutrino (assuming the same\nproduction mechanism) because of backgrounds.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1758\n\n100\n600\n1100\n1600\nM(ee) [ GeV ]\n10-1\n1\n101\n102\nEvents / 40 GeV per 100 pb-1\nATLAS\n100\n600\n1100\n1600\nM(\u00b5\u00b5) [ GeV ]\n10-1\n1\n101\n102\nEvents / 40 GeV per 100 pb-1\nATLAS\nFigure 8:\nLRSM analysis. The distributions of m\u2113\u2113for signals and backgrounds normalized to 100 pb\u22121 of\nintegrated luminosity after baseline selection in dielectron (left) and dimuon (right) analyses. Vertical lines indicate\nthe region used in the analysis.\nPhysics\nBefore\nBaseline\nmej j\nmee j j\nmee\nST\nsample\nselection\nselection\n\u2265100 GeV\n\u22651000 GeV\n\u2265300 GeV\n\u2265700 GeV\nLRSM 18 3\n0.248\n0.0882\n0.0882\n0.0861\n0.0828\n0.0786\nLRSM 15 5\n0.470\n0.220\n0.220\n0.215\n0.196\n0.184\nZ/\u03b3\u2217,m \u226560 GeV\n1808.\n49.77\n43.36\n0.801\n0.0132\n0.0064\nt\u00aft\n450.\n3.23\n3.13\n0.215\n0.0422\n0.0165\nVB pairs\n60.9\n0.610\n0.522\n0.0160\n0.0016\n0.0002\nMultijet\n108\n20.51\n19.67\n0.0490\n0.0444\n0.0444\nTable 5: LRSM dielectron analysis. Partial cross-sections (pb) that survive the selection criteria.\nFigures 9 and 10 show the distributions of the reconstructed invariant masses of the heavy neutrino\nand WR boson candidates for signal and background MC samples before and after the selection criteria\nare applied. All distributions are normalized to 100 pb\u22121 of integrated luminosity. It should be remarked\nthat the trigger ef\ufb01ciency is not included in the plots and tables shown in this section. However, events\nsatisfying all selection criteria would trigger with an ef\ufb01ciency exceeding 95%, as discussed in Section 3.\nBackground contributions to signal invariant mass spectra could also arise from jets that are misiden-\nti\ufb01ed as signal electrons. In principle, such misidenti\ufb01ed jets are ef\ufb01ciently suppressed because at least\ntwo signal electron candidates are required, but at present this background remains poorly understood be-\ncause larger statistics of multijet MC, or better, real data, would be necessary to evaluate its contribution\nreliably. If needed, a better suppression of events with multijets that are misidenti\ufb01ed as electrons is pos-\nsible by applying a more sophisticated isolation energy requirement. The multijet background does not\npose a problem in the dimuon analysis, where estimates of the misidenti\ufb01cation rate predict a vanishing\ncontribution from multijet to dimuon events.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1759\n\nPhysics\nBefore\nBaseline\nm\u00b5 j j\nm\u00b5\u00b5 j j\nm\u00b5\u00b5\nST\nsample\nselection\nselection\n\u2265100 GeV\n\u22651000 GeV\n\u2265300 GeV\n\u2265700 GeV\nLRSM 18 3\n0.248\n0.145\n0.145\n0.141\n0.136\n0.128\nLRSM 15 5\n0.470\n0.328\n0.328\n0.319\n0.295\n0.274\nZ/\u03b3\u2217,m \u226560 GeV\n1808.\n79.99\n69.13\n1.46\n0.0231\n0.0127\nt\u00aft\n450.\n4.17\n4.11\n0.275\n0.0527\n0.0161\nVB pairs\n60.9\n0.876\n0.824\n0.0257\n0.0047\n0.0015\nMultijet\n108\n0.0\n0.0\n0.0\n0.0\n0.0\nTable 6: LRSM dimuon analysis. Partial cross-sections (pb) that survive selection criteria.\nFinally, the analyses described in this note do not discriminate between same-sign and opposite-sign\ndileptons. Same-sign dileptons, however, are a very important signature of Majorana neutrinos, which,\nbeing their own anti-particles, could decay to a lepton of either charge. The background contribution to\nsame-sign dileptons is much smaller than to opposite-sign dileptons. Of course, both channels would\nhave to be studied if the discovery is made. The studies of charge misidenti\ufb01cation performed in the\nframework of the presented analyses, predict a rate as high as 5% for high-pT leptons which is strongly\n\u03b7-dependent.\n6\nSystematic Uncertainties\nThe following sources of systematic uncertainties have been considered in the described analyses:\n\u2022 20% uncertainty was assumed on the integrated luminosity.\n\u2022 In the dielectron analyses, 1% was used for the uncertainty in overall trigger ef\ufb01ciency.\n\u2022 For electron identi\ufb01cation and reconstruction ef\ufb01ciency, an uncertainty of 1% was assumed.\n\u2022 For muon identi\ufb01cation, including trigger and reconstruction ef\ufb01ciencies, an uncertainty of 5%\nwas assumed.\n\u2022 The uncertainty on the electron energy scale was assumed to be \u00b11%.\n\u2022 The uncertainty on the muon momentum scale was assumed to be \u00b11%.\n\u2022 The uncertainty on the jet energy scale was estimated by changing the energies of all jets simulta-\nneously by \u00b110% and \u00b120%, for |\u03b7 jet| \u22643.2 and |\u03b7jet| > 3.2, respectively.\n\u2022 The 20% uncertainty in electron pT resolution was estimated using a Gaussian smearing of pT\nwith a relative width of 0.66\u2217(0.10/\u221apT\nL0.007), where pT is in GeV.\n\u2022 The uncertainty due to muon 1/pT resolution was estimated using a Gaussian smearing of 1/pT\nwith a width of 0.011/pT\nL0.00017, where pT is in GeV.\n\u2022 The uncertainty due to jet energy resolution was estimated using a Gaussian smearing of jet\nenergies in such a way that the relative jet energy resolution widens from 0.60/\n\u221a\nE L0.05 to\n0.75/\n\u221a\nE L0.07 for |\u03b7 jet| \u22643.2, and from 0.90/\n\u221a\nE L0.07 to 1.10/\n\u221a\nE L0.10 for |\u03b7jet| > 3.2,\nwhere E is in GeV.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1760\n\n100\n350\n600\n850\n1100\nM(ejj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 20 GeV per 100 pb-1\nATLAS\n100\n350\n600\n850\n1100\nM(ejj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 20 GeV per 100 pb-1\nATLAS\n100\n350\n600\n850\n1100\nM(\u00b5jj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 20 GeV per 100 pb-1\nATLAS\n100\n350\n600\n850\n1100\nM(\u00b5jj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 20 GeV per 100 pb-1\nATLAS\nFigure 9: LRSM analysis. The distributions of the reconstructed invariant masses for Ne (top) and N\u00b5 (bottom)\ncandidates in background and signal (LRSM 18 3 and LRSM 15 5) events before (left) and after (right) back-\nground suppression is performed in dielectron and dimuon analyses. All distributions are normalized to 100 pb\u22121\nof integrated luminosity. LRSM 15 5 and LRSM 18 3 refer to two sets of LRSM mass hypotheses. See the text\nfor more information.\n\u2022 Statistical uncertainties on the number of background MC events were considered as systematic\nuncertainties on the number of background events.\n\u2022 The systematic uncertainty on the leptoquark cross-section (NLO) [16] was calculated by taking\nthe 40 PDF CTEQ6M tables (two per eigenvector of PDF variations, provided by the CTEQ group\nfor calculating uncertainties [15]), recalculating the leptoquark cross-section with each of these\ntables, and taking the largest difference of the two variations for each of the 20 eigenvectors to\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1761\n\n500\n1000\n1500\n2000\n2500\nM(eejj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 50 GeV per 100 pb-1\nATLAS\n500\n1000\n1500\n2000\n2500\nM(eejj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 50 GeV per 100 pb-1\nATLAS\n500\n1000\n1500\n2000\n2500\nM(\u00b5\u00b5jj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 50 GeV per 100 pb-1\nATLAS\n500\n1000\n1500\n2000\n2500\nM(\u00b5\u00b5jj) [ GeV ]\n10-1\n1\n101\n102\nEvents / 50 GeV per 100 pb-1\nATLAS\nFigure 10:\nLRSM analysis. The distributions of the reconstructed invariant masses for WR \u2192eNe (top) and\nWR \u2192\u00b5N\u00b5 (bottom) candidates in background and signal (LRSM 18 3 and LRSM 15 5) events before (left)\nand after (right) background suppression is performed in dielectron and dimuon analyses. All distributions are\nnormalized to 100 pb\u22121 of integrated luminosity. Notice that the invariant mass of theWR boson is shown before the\nrequirement m\u2113\u2113j j \u22651000 GeV is imposed. This variable is strongly correlated with the background-suppressing\nvariables ST and m\u2113\u2113. LRSM 15 5 and LRSM 18 3 refer to two sets of LRSM mass hypotheses. See the text for\nmore information.\nthe cross-section calculated with the standard CTEQ6M table. The estimate shown is the sum in\nquadrature of these 20 differences and the relative difference in cross-section obtained by varying\nrenormalization and factorization scales by a factor of 2. The systematic uncertainty is between\n15% and 28% for the tested leptoquark masses.\n\u2022 The uncertainty of the jet modeling in Z/\u03b3\u2217events was estimated by comparing the background\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1762\n\npredictions obtained using MC samples produced with PYTHIA to MC samples produced with\nALPGEN. For the leptoquark pair analysis, this results in an uncertainty of about 30% on the\nbackground from Z/\u03b3\u2217events.\n\u2022 Background cross-sections for t\u00aft and Z/\u03b3\u2217processes were assumed to have uncertainties of 12%\nand 10%, respectively.\nSystematic uncertainties affect both signal and background ef\ufb01ciencies, however the signi\ufb01cance compu-\ntation (next section) is mainly affected by the uncertainty on the background. The dominant systematic\neffects on the background are due to the uncertainties in integrated luminosity (20%), the jet energy\nscale (16%-35%), jet energy resolution (6%-28%), and the limited statistics of background MC samples\n(15%-30%). Possible other sources of systematic uncertainties such as initial and \ufb01nal state radiation\nmodeling, or pile-up, were not evaluated. The total systematic uncertainties for signals and backgrounds\nare summarized in Table 7.\nanalysis\neffect on signal events\neffect on background events\n1st gen.\n2nd gen.\n1st gen.\n2nd gen.\nleptoquark\n\u00b127%\n\u00b129%\n\u00b153%\n\u00b151%\nLRSM\n\u00b123%\n\u00b125%\n\u00b145%\n\u00b140%\nTable 7: Summary of total systematic uncertainties (%) for 100 pb\u22121 luminosity.\n7\nResults\nThe program Scp [29] is used to calculate the signi\ufb01cances of possible observations of the signals studied\nin this note. The signi\ufb01cance is de\ufb01ned in units of Gaussian standard deviations, corresponding to the\n(one-sided) probability of observing a certain number of events exceeding the MC-predicted background\nNb at a given integrated luminosity. This probability is usually referred to as CLb(N), where N is the\nnumber of observed events. We report the 5\u03c3 discovery potential evaluated in terms of CLb(Ns + Nb),\nwhere Ns is the expected number of signal events. Systematic uncertainties in the number of background\nevents were also included in the signi\ufb01cance calculations. For second generation leptoquarks, the signal\nselection was optimized at each mass point to minimize the cross-section times branching ratio needed\nto reach a 5\u03c3 discovery, while for all other analyses the selection cuts presented in earlier sections were\nused.\nThe overall reconstruction and trigger ef\ufb01ciencies discussed earlier are used to estimate ATLAS\u2019\nsensitivity and discovery potential for the studied \ufb01nal states below. These estimates include the trigger\nef\ufb01ciency for signal and background events, as discussed in Section 5, Table 2.\n7.1\nLeptoquarks\nThe integrated luminosities needed for a 5\u03c3 discovery of the 1st and 2nd generation scalar leptoquark\nsignals are shown in Table 8 as function of leptoquark mass, assuming \u03b2 = 1. Also, Fig. 11 predicts the\nintegrated luminosities needed for a 400 GeV leptoquark mass discovery, with various values of \u03b2 2, at a\n5\u03c3 level.\nFinally, Fig. 12 shows the minimum \u03b2 2 that can be probed with ATLAS with 100 pb\u22121 of integrated\nluminosity as a function of leptoquark mass. Lighter leptoquark masses can be probed with a smaller \u03b2\nbecause of their larger cross-section. It is evident from this \ufb01gure that ATLAS is sensitive to leptoquark\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1763\n\nLeptoquark mass\nExpected luminosity needed for a 5\u03c3 discovery\n1st gen.\n2nd gen.\n300 GeV\n2.8 pb\u22121\n1.6 pb\u22121\n400 GeV\n11.8 pb\u22121\n7.7 pb\u22121\n600 GeV\n123 pb\u22121\n103 pb\u22121\n800 GeV\n1094 pb\u22121\n664 pb\u22121\nTable 8: The integrated luminosities needed for a 5\u03c3 discovery of 1st and 2nd gen. scalar leptoquarks for different\nmass hypotheses.\n]\n-1\nIntegrated luminosity [pb\n0\n50\n100\n150\n200\n2\n\u03b2\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n1st gen.\n2nd gen.\n1st gen. (no syst. unc.)\n2nd gen. (no syst. unc.)\n discovery contours\n\u03c3\n5 \nFigure 11: 5\u03c3 discovery potential for 1st and 2nd\ngen.\nm = 400 GeV scalar leptoquarks versus \u03b2 2\nwith and without background systematic uncertainty\nincluded.\nLeptoquark mass [GeV]\n300\n350\n400\n450\n500\n550\n2\n\u03b2\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\n1st gen.\n2nd gen.\nFigure 12: Minimum \u03b2 2 of scalar leptoquarks versus\nleptoquark mass for 100 pb\u22121 of integrated luminosity\nat 5\u03c3 (background systematic uncertainty included.)\nmasses of about 565 GeV and 575 GeV for 1st gen. and 2nd gen., respectively, at the given integrated\nluminosity, provided leptoquarks always decay into charged leptons and quarks.\n7.2\nLeft-Right Symmetry\nThe signi\ufb01cances of studied signals versus integrated luminosity are shown in Fig. 13. Figure 14 shows\nthe product of signal cross-section and dilepton branching fraction versus the integrated luminosity nec-\nessary for a 5\u03c3 discovery.\nThe overall relative systematic uncertainties on Drell-Yan and t\u00aft backgrounds are approximately\n45% and 40% in the dielectron and dimuon analyses, respectively. These estimates are dominated by\ncontributions from jet reconstruction, uncertainty in integrated luminosity and insuf\ufb01cient MC statis-\ntics. Currently, multijet background is poorly understood and is not included in the presented sensitivity\nestimates for the dielectron channel.\n8\nSummary and Conclusions\nStudies of \ufb01nal states with two leptons and multiple jets have been discussed, considering both electrons\nand muons. The early-data discovery potential for Beyond the Standard Model physics predicted by two\nprominent GUT-inspired models has been investigated.\nBoth 1st and 2nd generation scalar leptoquark pair production could be discovered with less than\n100 pb\u22121 of integrated luminosity, provided that the mass of the leptoquarks is smaller than 500 GeV\nand the branching ratio into a charged lepton and a quark is 100%.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1764\n\n0\n100\n200\n300\nIntegrated pp luminosity [ pb-1 ]\n0.0\n2.5\n5.0\n7.5\n10.0\nSignificance (dielectron channel)\nATLAS\n0\n100\n200\n300\nIntegrated pp luminosity [ pb-1 ]\n0.0\n2.5\n5.0\n7.5\n10.0\nSignificance (dimuon channel)\nATLAS\nFigure 13: LRSM analysis. Expected signal signi\ufb01cances versus integrated luminosity for Ne, N\u00b5 neutrino and\nWR boson mass hypotheses, according to signal MC samples LRSM 18 3 and LRSM 15 5. Open symbols show\nsensitivities without systematic uncertainties. Sensitivities shown with closed symbols include an overall relative\nuncertainty of 45% (40%) estimated for background contributions in the dielectron (dimuon) analysis. LRSM 15 5\nand LRSM 18 3 refer to two sets of LRSM mass hypotheses. See the text for more information.\nTwo LRSM mass points (mWR = 1.8 TeV,mN\u2113= 300 GeV and mWR = 1.5 TeV,mN\u2113= 500 GeV) for\nthe right-handed WR boson and Majorana neutrinos N\u2113have been studied in the dielectron and dimuon\nchannels. It was found that discovery of these new particles at these mass points would require integrated\nluminosities of 150 pb\u22121 and 40 pb\u22121, respectively.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1765\n\n0\n100\n200\n300\n400\n500\nIntegrated pp luminosity [ pb-1 ]\n10-1\n1\n5\u03c3 signal discovery cross section * Br(ee) [ pb ]\nATLAS\n0\n100\n200\n300\n400\n500\nIntegrated pp luminosity [ pb-1 ]\n10-1\n1\n5\u03c3 signal discovery cross section * Br(\u00b5\u00b5) [ pb ]\nATLAS\nFigure 14: LRSM analysis. The product of signal cross-section and branching fraction to dielectron and dimuon\n\ufb01nal states versus integrated luminosity necessary for a 5\u03c3 discovery. Ne, N\u00b5 neutrino and WR boson mass hypothe-\nses are for signal MC samples LRSM 18 3 and LRSM 15 5. Horizontal lines indicate nominal cross-sections for\ntwo signal MC samples, according to the LRSM implementation in the MC simulation. Open symbols show dis-\ncovery potentials without systematic uncertainties. Discovery potentials shown with closed symbols include an\noverall relative uncertainty of 45% (40%) assumed for the background contribution in the dielectron (dimuon)\nanalysis. LRSM 15 5 and LRSM 18 3 refer to two sets of LRSM mass hypotheses. See the text for more infor-\nmation.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1766\n\nReferences\n[1] J. C. Pati and A. Salam, Phys. Rev. D10 (1974) 275\u2013289.\n[2] E. Eichten, I. Hinchliffe, K. D. Lane, and C. Quigg, Phys. Rev. D34 (1986) 1547.\n[3] E. Eichten, K. D. Lane, and M. E. Peskin, Phys. Rev. Lett. 50 (1983) 811\u2013814.\n[4] W. Buchmuller and D. Wyler, Phys. Lett. B177 (1986) 377.\n[5] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32 (1974) 438\u2013441.\n[6] M. Leurer, Phys. Rev. D49 (1994) 333\u2013342, arXiv:hep-ph/9309266.\n[7] D0 Collaboration, V. M. Abazov et al., Phys. Rev. D71 (2005) 071104, arXiv:hep-ex/0412029.\n[8] CDF Collaboration, D. E. Acosta et al., Phys. Rev. D72 (2005) 051107,\narXiv:hep-ex/0506074.\n[9] D0 Collaboration, V. M. Abazov et al., Phys. Lett. B636 (2006) 183\u2013190,\narXiv:hep-ex/0601047.\n[10] CDF Collaboration, A. Abulencia et al., Phys. Rev. D73 (2006) 051102,\narXiv:hep-ex/0512055.\n[11] T. Ahrens, Boston, USA, Kluwer Acad. Publ. (2000) . 177p.\n[12] R. N. Mohapatra and P. B. Pal, World Sci. Lect. Notes Phys. 60 (1998) 1\u2013397.\n[13] D0 Collaboration, V. M. Abazov et al., arXiv:0803.3256 [hep-ex].\n[14] T. Sjostrand, S. Mrenna, and P. Skands, JHEP 05 (2006) 026, arXiv:hep-ph/0603175.\n[15] J. Pumplin et al., JHEP 07 (2002) 012, arXiv:hep-ph/0201195.\n[16] M. Kramer, T. Plehn, M. Spira, and P. M. Zerwas, Phys. Rev. D71 (2005) 057503,\narXiv:hep-ph/0411038.\n[17] A. Ferrari et al., Phys. Rev. D62 (2000) 013001.\n[18] K. Huitu, J. Maalampi, A. Pietila, and M. Raidal, Nucl. Phys. B487 (1997) 27\u201342,\narXiv:hep-ph/9606311.\n[19] K. Melnikov and F. Petriello, Phys. Rev. Lett. 96 (2006) 231803, arXiv:hep-ph/0603182.\n[20] C. Anastasiou, L. J. Dixon, K. Melnikov, and F. Petriello, Phys. Rev. D69 (2004) 094008,\narXiv:hep-ph/0312266.\n[21] G. Corcella et al., JHEP 01 (2001) 010, arXiv:hep-ph/0011363.\n[22] S. Frixione and B. R. Webber, JHEP 06 (2002) 029, arXiv:hep-ph/0204244.\n[23] R. Bonciani, S. Catani, M. L. Mangano, and P. Nason, Nucl. Phys. B529 (1998) 424\u2013450,\narXiv:hep-ph/9801375.\n[24] ATLAS Collaboration, \u201cTrigger for Early Running.\u201d This volume.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1767\n\n[25] ATLAS Collaboration, \u201cReconstruction and Identi\ufb01cation of Electrons.\u201d This volume.\n[26] ATLAS Collaboration, \u201cMuon Reconstruction and Identi\ufb01cation: Studies with Simulated Monte\nCarlo Samples.\u201d This volume.\n[27] ATLAS Collaboration, \u201cJet Reconstruction Performance.\u201d This volume.\n[28] ATLAS Collaboration, \u201cb-tagging performance.\u201d This volume.\n[29] S. I. Bityukov, S. E. Erofeeva, N. V. Krasnikov, and A. N. Nikitenko. Prepared for PHYSTATO5:\nStatistical Problems in Particle Physics, Astrophysics and Cosmology, Oxford, England, United\nKingdom, 12-15 Sep 2005.\nEXOTICS \u2013 SEARCH FOR LEPTOQUARK PAIRS AND MAJORANA NEUTRINOS FROM RIGHT- . . .\n1768\n\nVector Boson Scattering at High Mass\nAbstract\nIn the absence of a light Higgs boson, the mechanism of electroweak symme-\ntry breaking will be best studied in processes of vector boson scattering at high\nmass. Various models predict resonances in this channel. Here, we investigate\nWWscalar and vector resonances, WZ vector resonances and a ZZ scalar reso-\nnance over a range of diboson centre-of-mass energies. Particular attention is\npaid to the application of forward jet tagging and to the reconstruction of dijet\npairs with low opening angle resulting from the decay of highly boosted vector\nbosons. The performances of different jet algorithms are compared. We \ufb01nd\nthat resonances in vector boson scattering can be discovered with a few tens of\ninverse femtobarns of integrated luminosity.\n1\nIntroduction\nIn the absence of a light Higgs boson, an alternative scenario to the Standard Model, Supersymmetry,\nor Little Higgs models must be invoked. In particular, Electroweak Symmetry Breaking (EWSB) could\nresult from a strong coupling interaction. Here, we will make no assumptions about the underlying dy-\nnamics of EWSB; we treat the Standard Model as a low energy effective theory, and evaluate the potential\nfor measuring vector boson scattering. In the Standard Model, perturbative unitarity is violated [1] in\nvector boson scattering at high energy for a Higgs mass mH > 870 GeV or, if there is no Higgs (mH \u2192\u221e),\nfor a centre-of-mass energy above a critical value of around 1.7 TeV. The only way to avoid a light Higgs\nboson is therefore to presume new physics at high energy [2], possibly in the form of vector boson pair\nresonances. Such resonances are predicted in many models such as QCD-like technicolour models with\nthe required Goldstone bosons resulting from chiral symmetry breaking [3]; Higgsless extra dimension\nmodels [4], where Kaluza-Klein states of gauge bosons are exchanged in the s-channel [5]; as well as in\nmodels with extra vector bosons, from GUT or from strong interaction (BESS models [6]) mixing with\nthe Standard Model vector bosons. The present search for resonances in vector boson scattering can be\nconsidered generic and may be interpreted in terms of any of these models.\n1.1\nThe Chiral Lagrangian Model\nThe Chiral Lagrangian (ChL) model is an effective theory valid up to 4\u03c0v \u223c3 TeV, where v = 246 GeV\nis the vacuum expectation value of the Standard Model Higgs \ufb01eld. It can provide a description of longi-\ntudinal gauge boson scattering at the TeV scale when no light scalar Higgs boson is present. Electroweak\nsymmetry breaking is realised non-linearly. A set of dimension-4 effective operators describe the low\nenergy interactions (see for example [7]). Since, at the LHC, vector boson scattering can occur at the\nTeV energy scale where the interaction becomes strong, it is necessary to unitarise the scattering am-\nplitudes. One popular unitarisation prescription is the so-called Pad\u00b4e prescription, or Inverse Amplitude\nMethod [8]. This is based on meson scattering in QCD, where it gives an excellent description [9],\nreproducing observed resonances. Among the terms of the Lagrangian which describe vector boson\nscattering, under some basic assumptions (custodial symmetry and CP conservation), only 2 parameters\n(namely \u03b14 and \u03b15) are important for this process. Depending on the values of these two parameters, one\ncan obtain Higgs-like scalar resonances and/or technicolour-like vector resonances [10]. The resulting\nproperly-unitarised amplitudes for vector boson scattering may therefore give information in a higher\nenergy range. They yield poles for certain values of \u03b14 and \u03b15 that can be interpreted as resonances, as\nshown in Fig. 1. The hashed region in the \ufb01gure is forbidden by causality arguments [11].\n1769\n\n5\n\u03b1\n-0.01\n-0.005\n0\n0.005\n0.01\n4\n\u03b1\n-0.01\n-0.005\n0\n0.005\n0.01\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\nForbidden\nVector Resonance\nVector & Scalar Resonance\nScalar Resonance\n(GeV)\nWW\nm\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\n-1\nevents / 1 fb\n-2\n10\n-1\n10\n1\n10\nATLAS\n500 GeV scalar\n800 GeV vector\n1 1 TeV vector\nnon resonant\nFigure 1: Left: regions in the (\u03b15,\u03b14) parameter space indicating which values exhibit vector and/or\nscalar resonances in the Pad\u00b4e unitarisation scheme. Right: number of events per fb\u22121 as a function of the\ndi-boson invariant mass for different resonance masses studied here.\nOther unitarisation procedures are possible, such as the K-matrix method [12] or the N/D method [13].\nIn general, resonances are not necessarily produced. In non-resonant cases, it remains vital to measure\nthe vector boson scattering cross section, but high luminosity and a very good understanding of back-\ngrounds will be required in order to measure the regularisation of the cross section.\n1.2\nCharacteristic Signatures of Vector Boson Scattering\nDiscovery of the physics signals studied here will, in general, require high integrated luminosity. It\nwill require also extremely large samples of simulated backgrounds, \ufb01ne tuning of all reconstruction\nalgorithms, and a good understanding of the detector performance, which will only gradually develop\nafter the \ufb01rst few years of LHC running. The main purpose of this note is not, therefore, to evaluate\nwith precision the discovery potential of ChL resonances, but to establish a strategy for the search of this\nimportant signal. The main emphasis will be put on those aspects most particular to the high mass vector\nboson scattering process; that is, the reconstruction of hadronically decaying vector bosons at high pT\nand the reconstruction of the high rapidity tag jets.\nThe decay of a high mass ChL resonance will produce two highly boosted vector bosons in the central\nrapidity region of the detector. For transverse momenta greater than about 250 GeV, a hadronically\ndecaying vector boson will be seen as one single wide and heavy jet. Methods of distinguishing such jets\nfrom single-parton jets will be investigated with different jet algorithms.\nA characteristic signature of vector boson scattering is the presence of two high rapidity and high\nenergy \u201ctag\u201d jets [14], arising from the quarks which radiate the incoming vector bosons. The process can\nthus be ef\ufb01ciently distinguished from contributions to the production of (mostly transversely polarised)\n\ufb01nal state vector bosons due to bremsstrahlung of these vector bosons from the quarks. In that case, the\naccompanying jets are softer and more central. A further component of the signature is the suppression\nof QCD radiation in the rapidity interval between the tag jets due to the fact that no colour is exchanged\nbetween the protons in these processes [15]. This characteristic feature allows for ef\ufb01cient use of central\njet veto to suppress backgrounds.\nThe high QCD background at the LHC naturally leads us to focus on \u201csemi-leptonic\u201d vector boson\nevents; that is, those events when one W or Z boson decays leptonically, and the other decays hadron-\nically. These channels represent the best compromise in that there is only at most one neutrino, so the\ndiboson mass may be reconstructed with reasonable resolution, and the backgrounds can be reduced to\na manageable level by the requirement of leptons and/or missing transverse energy (/ET). Fully-leptonic\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1770\n\nevents are also useful in cases where clear resonances are present, where a kinematic edge may be visible\nand the backgrounds may be reduced even further. The case of resonant ZZ \u2192\u2113+\u2113\u2212\u03bd \u00af\u03bd can also lead to a\nclean signature. Fully hadronic events may be useable at very high diboson energies, but this possibility\nis not considered further here. Thus, the study of vector boson scattering events will also require a good\nunderstanding of detector performance for electrons, muons and /ET. Although many ATLAS analyses\nwill depend on the reconstruction of these objects, the quality of such reconstruction is evaluated here\nfor the case of high energy leptons.\nThe note is organised as follows. In the next section (2) we describe the Monte Carlo simulations and\nthe samples used. Next, the trigger is discussed (Section 3), then the detector performance with particular\nfocus on the challenges of this analysis (Section 4). After this, the event selections, ef\ufb01ciencies and\npurities for the various \ufb01nal states are given (Section 5). An attempt to evaluate the expected sensitivity\nis made (Section 6), and the systematic uncertainties are discussed (Section 7), before a \ufb01nal summary\nand conclusion.\n2\nSignals and Background Simulation\n2.1\nDe\ufb01nition of Signal\nIn order to have a gauge invariant set of diagrams for the background, in spite of a Higgsless scenario, a\nlow mass Higgs will be assumed. A resonance signal will be de\ufb01ned here as an excess of events in the\nresonance mass region over the number expected from the Standard Model continuum when the Higgs\nboson mass is set at 100 GeV. This ensures that longitudinal vector boson scattering will contribute\nnegligibly to the process. This de\ufb01nition follows the prescription of [16]. We note that measurement\nof even a continuum cross section for this process at such high energies would be of great importance,\nbut will not be considered here as it should require high luminosity and a very good understanding of\nbackgrounds.\n2.2\nOverview of Generators\nThe Monte Carlo (MC) generators used in the main analysis are as follows.\n\u2022 PYTHIA [17] version 6.4.0.3 was used for the signal, with the CTEQ6L parton distribution function\nand the renormalisation and factorisation scale Q2 = m2\nW. The hard process was modi\ufb01ed to include\nnew vector boson scattering amplitudes (see below).\n\u2022 MADGRAPH [18], version 3.95, with PYTHIA for parton shower, hadronisation and underlying\nevent, was used for W+jets and Z+jets backgrounds. The default values of \ufb01xed renormalisation\nand factorisation scales of Q2 = m2\nZ were set and CTEQ6L1 parton distribution functions were\nused.\n\u2022 MC@NLO [19], with HERWIG [20], for parton shower and hadronisation and JIMMY [21,22] for\nunderlying event, was used for t\u00aft background.\nThe underlying event samples were tuned to data from previous experiments [22]. All samples use\nPHOTOS [23] to simulate \ufb01nal state radiation. WHIZARD [24] and ALPGEN [25, 26] are also used for\nsome generator level comparisons. WHIZARD uses PYTHIA for parton showering, hadronisation, and\nunderlying event. ALPGEN uses HERWIG/JIMMY.\nThe different choice of scales for MADGRAPH and PYTHIA is not ideal, but retained for histori-\ncal reasons since large samples were generated with these choices. However, studies showed that the\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1771\n\nSample name\nGenerator\n\u03c3 \u00d7Br, fb\nqqWZ \u2192qq j j\u2113\u2113, m = 500 GeV\nPYTHIA-73\n25.2\nqqWZ \u2192qq\u2113\u03bd j j, m = 500 GeV\nPYTHIA-73\n83.9\nqqWZ \u2192qq\u2113\u03bd\u2113\u2113, m = 500 GeV\nPYTHIA-73\n8.0\nqqWZ \u2192qq j j\u2113\u2113, m = 800 GeV\nPYTHIA-ChL\n10.5\nqqWZ \u2192qq\u2113\u03bd j j, m = 800 GeV\nPYTHIA-ChL\n35.2\nqqWZ \u2192qq\u2113\u03bd\u2113\u2113, m = 800 GeV\nPYTHIA-ChL\n3.4\nqqWZ \u2192qq j j\u2113\u2113, m = 1.1 TeV\nPYTHIA-ChL\n3.7\nqqWZ \u2192qq\u2113\u03bd j j, m = 1.1 TeV\nPYTHIA-ChL\n12.3\nqqWZ \u2192qq\u2113\u03bd\u2113\u2113, m = 1.1 TeV\nPYTHIA-ChL\n1.18\nqqWW \u2192qq\u2113\u03bd j j, m = 499 GeV (s)\nPYTHIA-ChL\n66.5\nqqWW \u2192qq\u2113\u03bd j j, m = 821 GeV (s)\nPYTHIA-ChL\n27.5\nqqWW \u2192qq\u2113\u03bd j j, m = 1134 GeV (s)\nPYTHIA-ChL\n17.0\nqqWW \u2192qq\u2113\u03bd j j, m = 808 GeV (v)\nPYTHIA-ChL\n29.8\nqqWW \u2192qq\u2113\u03bd j j, m = 1115 GeV (v)\nPYTHIA-ChL\n17.9\nqqWW \u2192qq\u2113\u03bd j j, non-resonant\nPYTHIA-ChL\n10.0\nqqZZ \u2192qq\u03bd\u03bd\u2113\u2113, m = 500 GeV\nPYTHIA-ChL\n4.0\nj jWZ \u2192j j\u2113\u03bd\u2113\u2113, background\nMADGRAPH\n96\nj jZZ \u2192j j\u03bd\u03bd\u2113\u2113, background\nMADGRAPH\n45.5\n\u03c3 (no Br), pb\nW + + 4 jets\nMADGRAPH\n165 \u00b1 0.1\nZ + 4 jets\nMADGRAPH\n87 \u00b1 0.7\nW + + 3 jets\nMADGRAPH\n6.2 \u00b1 0.02\nZ + 3 jets\nMADGRAPH\n3.8 \u00b1 0.02\nt\u00aft\nMC@NLO\n833\u00b1100\nTable 1: Data samples and generators used in the present study\nmajor effect is on the cross section rather than on event shapes, and the cross section normalisation is\ndetermined independently as described below.\nFurther details speci\ufb01c to the samples are given below.\n2.3\nList of samples\nTable 1 lists the Monte Carlo samples, produced with full detector simulation, used in the present analy-\nsis.\nThe \ufb01rst set of samples represents different reference cases of vector boson scattering signals:\n\u2022 PYTHIA-73: For the samples labelled \u201cPYTHIA-73\u201d, the process 73 (longitudinal WZ scattering)\nwas selected, with MSTP(46)=5 (QCD-like model of [27] with Pad\u00b4e unitarisation). All other\nswitches were left as default. This is meant to represent a generic narrow WZ resonance.\n\u2022 PYTHIA-ChL: datasets with generator labelled \u201cPYTHIA-ChL\u201d in the table use a modi\ufb01ed version\nof PYTHIA routine PYSGHG. The modi\ufb01cation involves replacing the scattering amplitudes cal-\nculated for processes 73\u201377 by those given by Dobado et al [10] with parameters a4 and a5. These\nparameters were chosen so as to produce a vector or scalar (indicated by a (v) or an (s) in the table)\nresonance at the desired mass, or signal with no resonances at all. Note that only vector WZ and\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1772\n\nscalar ZZ resonances are possible, but both scalar and vector WW resonances can be produced. A\ncontinuum sample was also generated using this model.\nBackground samples include events with two vector bosons and two jets in the \ufb01nal state, arising\nfrom gluon or electroweak vector boson exchange between incoming quarks. The vector bosons are here\nmostly transverse and emitted more centrally than in the case of longitudinal vector boson pair scattering.\n\u2022 j jWZ \ufb01nal state, where j is a quark or gluon: The decays of the vector bosons are performed in\nPYTHIA. Note that the semi-leptonic cases are already included in samples W+jets and Z+ jets\n(see below). Only the purely leptonic cases make use of this background.\n\u2022 The background process: \u2113\u2113\u03bd\u03bd with a pair of jets (quark or gluons). The cross section shown in\nTable 1 is for non-hadronic decay of the ZZ\u2019s, with a \ufb01lter requiring two leptons with pT > 5 GeV\nand |\u03b7| < 2.8.\n\u2022 W/Z +3 jets and W/Z +4 jets: they constitute backgrounds for the cases of high mass and lower\nmass resonances respectively since, in the former case, we expect that most of the vector bosons\nwhich decay hadronically will be reconstructed as a single jet. A correction factor of 1.38 is ap-\nplied to the W ++jets cross sections to account for the W \u2212+j process. These datasets include all\ntree level diagrams leading to W+4j, Z+4j, W+3j and Z+3j, with the vector bosons decaying lep-\ntonically, including all QCD and electroweak contributions. To keep the cross section manageable,\npreselection cuts were applied at MADGRAPH level. For the W,Z +4 jets case, we tag the highest\nrapidity jet (fjet), backward jet (bjet) and 2 central jets by requiring that |\u03b7 f jet| > 1.5, |\u03b7bjet| > 1.5,\nthat the forward and backward jet candidates be on different hemispheres: \u03b7f jet\u03b7bjet < 0, that at\nleast one forward jet have energy E > 300 GeV, and that the invariant mass of the combined for-\nward jets be mj j > 250 GeV. We further require pT of at least one of the central jets to be pj\nT > 50\nGeV, the pT of the vectorial addition of the central jets to be pj j\nT > 60 GeV and the invariant mass\nof the combined central jets m j j > 60 GeV. We note that the forward jet preselection suppresses\nthis background by a factor of 3.5.\nFor the case W,Z + 3 jets, we add the requirements: pT of the W or Z boson pT > 200 GeV,\n|\u03b7W/Z| < 2, and pT of one jet (central) pj\nT > 200GeV, |\u03b7j| < 2.\nAdditional samples were produced with fast detector simulation to improve background statistics.\n2.4\nComparative studies of generators\n2.4.1\nParton shower matching to matrix elements\nHere, MADGRAPH was used to generate the W+jets background. A better evaluation of this background\nwould be obtained using a generator for which W+n partons, n=0, 1, 2, 3 or 4 inclusive, are combined in a\nmanner which avoids double counting of jets produced by the parton shower in PYTHIA. ALPGEN is one\nsuch generator (and in fact such matching is now implemented in more recent versions of MADGRAPH).\nHowever, due to time constraints, and in order to have a manageable size of background samples, it was\nnot practical to use this technique. In order to validate the use of MADGRAPH, a comparison was made\nof the W + 4jets sample with an appropriate ALPGEN sample, with same analysis cuts applied. The\nALPGEN samples are not used in the \ufb01nal analysis since they lack suf\ufb01cient statistics.\nDistributions of the vector bosons and jets were compared. As an example, the distributions for\nthe forward jets are shown in Fig. 2. The overall conclusion is that the shapes of the distributions are\nin reasonable agreement. Therefore, neglecting the effect of parton shower double counting does not\nsigni\ufb01cantly affect the event topology. To the extent that such an error is made, the tag jets in the\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1773\n\n of tag jets [GeV]\nT\np\n0\n50 100 150200 250 300 350400 450 500\nArbitrary Units \n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nMadgraph\nAlpgen\nATLAS\na\n of tag jets\n\u03b7\n-5\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n5\nArbitrary Units \n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\n0 08\nMadgraph\nAlpgen\nATLAS\nb\nEnergy of tag jets [GeV]\n0\n500\n1000\n1500\n2000\n2500\n3000\nArbitrary Units \n-4\n10\n-3\n10\n-2\n10\n-1\n10\nMadgraph\nAlpgen\nATLAS\nc\nMass of tag jets [GeV]\n0\n10 20 30 40 50 60 70 80 90 100\nArbitrary Units \n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\nMadgraph\nAlpgen\nATLAS\nMadgraph\nAlpgen\nd\nFigure 2: Distributions of the forward jets in the W +4jet background for MADGRAPH (red) and ALP-\nGEN (black) samples (area normalised). The error bars show the statistical error in each sample.\nALPGEN sample have a lower energy (leading to a depletion with respect to the MADGRAPH samples at\nhigh energies of a few %) and so the backgrounds in this analysis can be considered to be conservatively\noverestimated. The sensitivity of such backgrounds to the scales has been discussed, for example, in [28,\n29]. The difference in Q2 scale of the two samples (ALPGEN uses Q2 = m2\nW + pT(W)2) leads to about a\nfactor two discrepancy in cross section. This was con\ufb01rmed by running MADGRAPH on a small sample\nwith the same scale as ALPGEN, yielding cross sections smaller by factors 2.05 and 1.77 for the QCD\nand QED processes respectively. These factors will be applied in the present analysis.\n2.4.2\nEffective W Approximation\nWHIZARD [24] is a relatively new event generator originally developed for the ILC. It is able to calculate\nthe full 2 \u21926 matrix element needed for the vector boson scattering processes and it implements the\nChiral Lagrangian model with the K-Matrix unitarisation scheme [27] which does not lead to vector\nboson resonances. Further unitarisation schemes in the form of arbitrary resonances are planned.\nThe generator does not assume an effective W approximation, whereby the bosons emitted from\nthe quarks are treated as partons, allowing vector boson scattering diagrams to form a gauge-invariant\nsubset. This approximation is made in the PYTHIA signal samples, and might be expected to particularly\naffect the tag jet kinematics. Comparisons between the tag jet distributions from WHIZARD and PYTHIA\nare shown in Fig. 3. The two samples are not strictly comparable since here, WHIZARD simulates\nthe 2 \u21924 processes including non-scattering electroweak diagrams and applies K-matrix unitarisation.\nAlthough there are differences (e.g. the tag jets from WHIZARD are somewhat harder than those from\nPYTHIA) they do not strongly depend upon the vector boson centre-of-mass, and thus the effective W\napproximation is unlikely to be the culprit. The harder tag jets in WHIZARD mean that if the signal looks\nmore like WHIZARD than PYTHIA, it would be more likely to pass the selection cuts, thus improving the\nsensitivity. The potential size of the effect was investigated and estimated to be at the few per cent level.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1774\n\n of tag jets [GeV]\nT\np\n0\n100\n200\n300\n400\n500\n600\nArbitrary Units\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nPythia\nWhizard\nATLAS\n(a)\n of tag jets\n\u03b7\n-4\n-2\n0\n2\n4\nArbitrary Units\n0\n0 01\n0 02\n0 03\n0 04\n0 05\n0 06\n0 07\nPythia\nWhizard\nATLAS\n(b)\nE of tag jets [GeV]\n0\n500\n1000\n1500\n2000\nArbitrary Units\n-2\n10\nPythia\nWhizard\nATLAS\n(c)\n of tag jets\n\u03b7\n\u2206\n4\n5\n6\n7\n8\n9\n10\nArbitrary Units\n0\n0 01\n0 02\n0 03\n0 04\n0 05\nPythia\nWhizard\nATLAS\n(d)\nFigure 3: Differences between WHIZARD (red) and PYTHIA (black) for vanishing anomalous couplings\nfor tag jet distributions of: transverse momentum (a), pseudo rapidity (b), energy (c) and pseudo rapidity\ndifference (d).\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1775\n\n3\nTrigger\nAs a \ufb01rst step in the analysis, it is important to evaluate the ef\ufb01ciency of the basic trigger menus for\na luminosity of 1033 cm\u22122s\u22121. The triggers chosen were based on an early menu [30] as an example,\nand the real physics menu is likely to be very different. However, since the signal is at relatively high\npT, and triggering on vector bosons is a high priority, this is not likely to have a large impact. To\nevaluate this ef\ufb01ciency, we apply the following cuts: for electrons and muons we require single leptons\nto have pT greater than the value corresponding to the threshold dictated by the trigger signature and\n|\u03b7| < 2.5; similarly for jets, but with a pseudorapidity cut of |\u03b7| < 3.2. This is necessary because trigger\nsignatures for forward jets exist separately, but unfortunately that trigger information was not available\nin the simulation version used for this study. The trigger ef\ufb01ciency is de\ufb01ned as the number of times\nthe trigger passed (with the corresponding cuts applied) divided by the number of truth events in the\nsamples (with the same cuts applied). In Table 2 we present a detailed list of ef\ufb01ciencies for the signals\nqqWZ \u2192qq j j\u2113\u2113(m = 1.1 TeV) in the left column and qqWW \u2192qq j j\u2113\u03bd (non-resonant) in the right1.\nThe poor ef\ufb01ciency of the e25i (see Fig. 4, left) and 2e12i triggers is understood to be due to the\nisolation criterion, which was not optimised for high energy electrons.\nelectron\nT\nP\n[GeV]\n50\n100\n150\n200\n250\n300\n350\n400\nEfficiency for e25i\n0\n0 1\n0 2\n0 3\n0 4\n0 5\n0 6\n0 7\n0 8\n[GeV]\nHadronic W\nP\n50\n100\n150\n200\n250\n300\n350\n400\nEfficiency\n0\n0 2\n0 4\n0 6\n0 8\n1\nj160 || 2j120\nj160\nFigure 4: Trigger ef\ufb01ciencies computed with the WW continuum signal. Left: ef\ufb01ciency of the e25i\ntrigger as a function of the pT of electrons from the true leptonically-decayingW boson. Right: ef\ufb01ciency\nof the j160 trigger (black triangles) as a function of the pT of the true hadronically-decaying W boson.\nAlso shown with blue circles is the ef\ufb01ciency when the j160 and 2j120 triggers are logically OR\u2019ed.\nIt is worth mentioning that the ef\ufb01ciency for the 2j120 trigger (Fig. 4, right), which requires two jets\nwith pT > 120 GeV suffers partly from the fact that the two jets from the vector boson decay are merged\ndue to the boost as described in Section 4.1. It is also signi\ufb01cantly higher for events with true electrons\nthan for those with true muons, probably because the electrons themselves are also reconstructed as jets\nin the calorimeter.\nFinally, various combinations of the trigger signatures might be explored in the future to improve\nthe ef\ufb01ciency. For instance, the e60 trigger might be used in conjunction with the e25i to compensate\nthe low ef\ufb01ciency of the latter for high-momentum electrons (Fig. 4). Likewise, the 2j120 trigger might\nbe used together with j160, since the ef\ufb01ciency of the latter drops signi\ufb01cantly when the hadronically-\ndecaying vector boson has pT < 300 GeV and decays into two distinctly resolvable jets.\n1Triggers 2j120 and j160 have been removed from the menu as they are expected to give too high a rate. However, forward\njet triggering will be available, and more recent developments in the electron trigger has resulted in improved ef\ufb01ciency.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1776\n\nWZ signal\nWW signal\nTrigger Signature\nCut Loss\nEf\ufb01ciency\nCut Loss\nEf\ufb01ciency\nElectrons\n2e12i\n13%\n36%\n> 99%\n\u2014\ne25i\n1%\n78%\n11%\n65%\ne60\n5%\n82%\n29%\n73%\nMuons\nmu6\n5%\n95%\n6%\n80%\nmu20\n5%\n92%\n9%\n73%\nJets\n2j120\n67%\n73%\n50%\n80%\nj160\n34%\n96%\n30%\n86%\nTable 2: Table of high level trigger ef\ufb01ciencies for qqWZ \u2192qq j j\u2113\u2113(m = 1.1 TeV) and qqWW \u2192\nqq j j\u2113\u03bd (non-resonant). The \u201cCut Loss\u201d columns indicate the fraction of true events that would be lost\nby applying the pT requirements of each trigger signature on the true electrons, muons and jets. Since\nsuch events are unlikely to satisfy the trigger conditions, they are not taken into account when the trigger\nef\ufb01ciencies are evaluated.\n4\nReconstruction Challenges\nIn this section, we focus on those parts of the reconstruction which are most particular to vector boson\nfusion at high masses. We discuss the following:\n\u2022 Reconstruction of hadronically-decaying vector bosons. In our regime these typically have high\npT and the decay products are very collimated. We discuss two alternative methods, using k\u22a5jets\nand subjets, and using cone jets with different radii.\n\u2022 Leptonically decaying vector bosons. These require good lepton and /ET measurement, but the\nchallenges here are not unique to these channels.\n\u2022 Forward \u2018tag\u2019 jets. Measuring jets close to the edge of the detector rapidity acceptance is a chal-\nlenge in common with low mass Higgs searches in vector boson fusion.\n\u2022 Central jet veto. Since the vector boson scattering process involves no colour exchange between\nthe protons, a suppression of QCD radiation is expected. This can be used to distinguish between\nsignal and background, but is sensitive to underlying event and pile-up.\n\u2022 Top veto. t\u00aft production is a major background for the channels which do not contain leptonic Z\nboson decays. A large fraction of this is removed by explicitly rejecting events containing top\ncandidates.\n4.1\nHadronic Vector Boson Identi\ufb01cation\nAt lower masses and pT, the hadronically-decaying vector bosons are identi\ufb01ed as dijet pairs. However,\nfor events where a hadronically-decaying vector boson is highly boosted, the decay products are often\ncollimated into a single jet. Cuts such as a dijet invariant mass window are no longer applicable in this\nscenario, but a single jet mass cut can be used.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1777\n\nThe single jet mass is de\ufb01ned as the invariant mass evaluated from the 4-vectors of the constituents of\nthe jet. In the ATLAS detector, these constituents are at present calorimeter objects, either topologically\nde\ufb01ned clusters with some local hadronic calibration, called here topoclusters, or calorimeter towers.\nFor jets containing the decay products of a boosted vector boson, this single jet mass is near the mass of\nthe parent boson. For light quark and gluon jets this mass is generally much lower. Since the background\nto hadronic vector boson identi\ufb01cation is so severe, further cuts may be applied on the subjet structure of\nthe candidate jet.\nIn addition, the transition between the dijet and single jet case as pT increases needs to be dealt with.\nTwo methods are used, as follows;\n1. Dynamically select the appropriate method. To do this, we \ufb01rst look at the highest pT jet. If this\npasses the mass window cut, then the single jet selection is applied, as described below. If it does\nnot, then combinations of jet pairs in the event are considered. The vector boson is still expected\nto be the highest pT hadronic system, and so the pT of all jet pairs is evaluated, and the highest\npT pair is taken to be the vector boson candidate. A mass window cut (dependent upon the jet\nalgorithm) is then applied to this pair. Thus a single analysis can be used to scan the data for signs\nof resonances without bias.\n2. When the single jet and jet pair cases yield very different signal to background ratios, it is prefer-\nable to choose a priori which mass region is being investigated, and to use the single jet recon-\nstruction for high masses and the dijet reconstruction for low masses. This approach is used in the\ncone algorithm analysis. For the m = 800 GeV resonance, both the dijet and single jet approaches\nare tried independently.\n4.1.1\nK\u22a5Algorithm\nThe k\u22a5algorithm is run with an R-parameter (which determines the \u201cjet size\u201d) of 0.6 on calibrated\ntopoclusters. The algorithm [31] merges pairs of constituents.\nThe k\u22a5analysis uses the dynamic selection technique described above to decide whether to use a\ndijet or a single jet for the vector boson candidate. The fraction of vector bosons reconstructed as a\nsingle jet, as a function of pT of the vector boson candidate, is given in Fig. 5. The transition between\ndijet and single jet takes place between pT = 200 and 300 GeV for this algorithm.\nof W [GeV\nT\nP\n100\n150\n200\n250\n300\n350\n400\n450\nFraction of single-jet W candidates\n0\n0 2\n0 4\n0 6\n0 8\n1\nATLAS\nFigure 5: Fraction of W boson candidates reconstructed from a single jet, as a function of the transverse\nmomentum of the reconstructed vector boson, for the WW m = 1.1 TeV signal sample.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1778\n\nJet Mass (Reco - True) GeV\n-50 -40 -30 -20 -10\n0\n10 20 30 40 50\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nFast Simulation\nFull Simulation\nATLAS\nPythia 6 403\nScalar 1 1 eV\nWW Signal\nY Scale (Reco - True) GeV\n-50 -40 -30 -20 -10\n0\n10 20 30 40 50\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\n0 14\n0 16\n0 18\n0 2\nFast Simulation\nFull Simulation\nATLAS\nPythia 6 403\nScalar 1 1 eV\nWW Signal\nFigure 6: Single jet mass residuals (left) and Y scale residuals (right) from different detector simulations,\nusing the k\u22a5algorithm. The truth is de\ufb01ned by running the jet algorithm on the hadronic \ufb01nal state of\nthe MC generator.\nSingle jet mode\nThe resolution of the single jet mass for the k\u22a5algorithm has been evaluated for both detector simulations\n(full and fast) for several samples. For the sample with a WW resonance at m = 1.1 TeV (Fig. 6 left)\nfor example, the W boson singlet jet mass resolution was found to be 7.4\u00b10.2% GeV from full and fast\ndetector simulation.\nA mass cut around the window from m = 68.4 GeV to 97.2 GeV is applied to W boson candidates,\nand from m = 68.7 GeV to 106.3 GeV for hadronic Z boson candidates reconstructed in the single jet\nmode. These mass windows are determined by considering the resolution, the tails, and the background\ncontamination.\nThe k\u22a5merging is intrinsically ordered in scale, making the \ufb01nal merging the hardest. The algorithm\nprovides a y value for this \ufb01nal merging, which is a measure of the highest scale at which a jet can be\nresolved into two subjets. The y value can be converted into a \u201cY scale\u201d in GeV using the relation Y scale\n= ET \u00d7\u221ay, where ET is the jet transverse energy. This Y scale is expected to be O(mV/2) (where mV is\nthe mass of the vector boson) for boosted vector boson jets, and much lower than ET for light jets [32].\nAt the truth and fast simulation levels this variable has been shown to have discriminating power even\nafter a single jet mass cut [32\u201335]. The resolution of the ATLAS detector for this variable is presented in\nFig. 6 (right). The resolutions, for the same sample as above, are 12.3\u00b10.3% and 8.8\u00b10.2% with full\nand fast detector simulation, respectively.\nBased on the resolution, the tails, and the background contamination, a Y scale cut around the win-\ndow from 30 GeV to 100 GeV is applied to W and Z boson candidates reconstructed in the single jet\nmode. To evaluate the bene\ufb01t of cutting on Y scale, a sample of single jet vector boson candidates is\nselected in signal and background by applying a pT > 300 GeV cut, motivated by Fig. 5, and a mass\nwindow cut. Starting from this sample, the ef\ufb01ciency of the Y scale cut is given in Table 3 for full and\nfast simulation. The numbers suggest that for the W+jets background, an additional rejection factor of\napproximately 2 is provided by the Y scale cut even after a single jet mass cut has been applied. This is\nachieved with a signal ef\ufb01ciency of approximately 80%.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1779\n\nDijet Mass (Reco - True) [GeV]\n-30 -25 -20 -15 -10 -5\n0\n5\n10 15 20\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\n0 14\n0 16\nFast Simulation\nFull Simulation\nATLAS\nPythia 6 403\nScalar 800GeV\nWW Signal\n(Reco - True)\n12\nDijet y\n-0.1\n-0.05\n0\n0.05\n0.1\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\n0 14\n0 16\n0 18\n0 2\nFast Simulation\nFull Simulation\nATLAS\nPythia 6 403\nScalar 800GeV\nWW Signal\nFigure 7: Dijet mass residuals (left) and y residuals (right) from different detector simulations, using the\nk\u22a5algorithm. The truth is de\ufb01ned by running the jet algorithm on the hadronic \ufb01nal state of the MC\ngenerator.\n1.1 TeV Vector Resonance\nW+4 jets\nt\u00aft\nJet Mass\n68% (67%)\n14% (14%)\n28% (28%)\nY Scale\n77% (84%)\n29% (40%)\n63% (70%)\nTable 3: Ef\ufb01ciency of the jet mass cut and of the Y scale cut in the one-jet case for full (fast) simulation.\nThe Y scale cut is applied after the mass cut.\n800 GeV Scalar Resonance\nW+4 jets\nt\u00aft\nJet Mass\n17% (20%)\n6% ( 7%)\n14% (14%)\nY Scale\n79% (83%)\n48% (49%)\n84% (82%)\nTable 4: Ef\ufb01ciency of the jet mass cut and of the Y scale cut in the two-jet case for full (fast) simulation.\nThe Y scale cut is applied after the mass cut.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1780\n\nDijet mode\nA mass cut around the window from m = 62 GeV to 94 GeV is applied to W boson candidates, and from\nm = 66.6 GeV to 106.2 GeV for hadronic Z boson candidates reconstructed in the dijet mode.\nA variable analogous to the y may be calculated, using the pT of the softer jet relative to the harder\none. This variable is required to be in the range 0.1 < \u221ay < 0.45. The ef\ufb01ciency is shown in Table 4.\nThe mass and y windows are again determined by considering the resolution, the tails, and the back-\nground contamination.\nThe resolutions of the dijet mass and the y variable for dijet vector boson candidates are shown in\nFig. 7. They are found to be approximately 5% for the mass and for the y variable, and are comparable\nin fast and full simulation.\n4.1.2\nCone Algorithm\nThe problem of the two jets from a boosted hadronically decaying vector boson merging into a single\njet has also been studied for jets reconstructed using the Cone Algorithm. With this algorithm, jet re-\nconstruction starts from seeds i.e. constituents (clusters) with pT > 1 GeV. The algorithm collects all\nconstituents around a seed within \u2206R =\np\n(\u2206\u03b7)2 +\u2206\u03c6)2 < R0 (where R0 can be, for instance 0.4) and\nadds their momenta vectorially. Then it repeats the procedure over the collection around the direction of\nthe sum, and computes a new sum. It continues repeating this operation until the resulting sum direction\nis stable.\nSingle jet hadronic W boson candidates are identi\ufb01ed with the highest pT object in the central region,\nafter having removed overlaps with all electrons in the event within a \u2206R of 0.1. A mass cut in a window\naround the reconstructed W boson mass is applied.\nFigure 8 shows an example of W boson reconstruction using the cone algorithm for the jet-pair case\n(m = 500 GeV resonance) and single jet case (m = 800 GeV resonance). A cone size of 0.8 is used\nfor selecting a single jet W boson and 0.4 for the case of a jet pair. The low mass tail is due to events\nwhere the two jets from the W are well separated. There is a small difference in the W boson mass peak\nreconstruction for the two cases. The jets chosen for this selection have a minimum pT cut of 20 GeV,\nand those overlapping with electrons have been removed.\nmass [GeV]\n20\n30\n40\n50\n60\n70\n80\n90\n100\n110\n120\n/5GeV\n-1\nEvents/fb\n0\n0.1\n0 2\n0 3\n0.4\n0 5\n0 6\n0.7\n0 8\n(500GeV)\nll\nZ\njj\nW\n(800GeV)\nll\nZ\nj\nW\nATLAS\nFigure 8: Reconstructed W boson for cases where it forms two separated jets (500 GeV) and a single jet\n(800 GeV). The samples used are the m = 500 GeV resonance (in green) and m = 800 GeV resonance\n(in red).\nThe exploration of the substructure of a wide jet (typically of size 0.8) is done by searching for 2\nnarrow jets (size \u223c0.2) \ufb01tting inside the big jet. Various variables can then be studied, among which\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1781\n\n1.1 TeV Vector Resonance\nW+4jets (QCD)\nt\u00aft\nZ+3jets (QED)\nsmall jets cut\n76.3%\n15.2%\n38.6%\n13.8%\nTable 5: Comparison of ef\ufb01ciencies for the jet sub-structure selection for a typical signal and back-\ngrounds. Ef\ufb01ciencies are relative to the selection of a single jet as described in the Y scale method (Table\n3). For the subjet selection, we require 2 small jets with pT > 15 GeV and invariant mass > 60 GeV (see\ntext).\n\u0001\u0002\n\u0001\u0003\n\u0004\u0002\n\u0004\u0003\n\u0005\u0002\n\u0005\u0003\n\u0006\u0002\n\u0006\u0003\n\u0007\u0002\u0002\n\u0001\n\u0002\n\u0003\n\u0007\u0002\n\u0007\u0003\n\b\u0002\n\b\u0003\n\t\u0002\n\t\u0003\n\n\u0002\n\u0002\n\u0007\u0002\n\b\u0002\n\t\u0002\n\n\u0002\n\u0003\u0002\n\u0001\n\u0002\n\u0002\u000b\u0002\u0002\u0003\n\u0002\u000b\u0002\u0007\n\u0002\u000b\u0002\u0007\u0003\n\u0002\u000b\u0002\b\n\u0002\u000b\u0002\b\u0003\n\u0002\u000b\u0002\t\n\u0002\u000b\u0002\t\u0003\nWide jet invariant Mass [GeV]\nNarrow jet transverse P [GeV]\nNarrow jet transverse P [GeV]\nWZ signal\nZ+3jets\nATLAS\nATLAS\nFigure 9: Pro\ufb01le histogram of the momentum of the narrow jet orthogonal to the wide jet direction vs\nthe invariant mass of the wide jet, for W boson hadronic decay of the resonance signal qqWj jZ\u2113\u2113of m =\n1.1 TeV (red) and for Z+3 jets sample (black). Lower graph : normalized distributions of narrow jet\northogonal momentum.\nare the energy ratio of the narrow jets, their invariant mass, the distance \u2206R between the leading narrow\njet and the wide jet, or the momentum component of this narrow jet transverse to the wide jet direction.\nThe discriminating power is illustrated for the WZ \u2192\u2113\u2113j j channel (1.1 TeV resonance) and its principal\nbackground in Fig. 9 which shows the latter variable (called here \u2018p transverse\u2019) versus the invariant mass\nreconstructed from two narrow jets. Cutting in the (pT, invariant mass) plane gives results comparable\nto those obtained with the Y scale method above, as illustrated in Table 5. Similarly, Fig. 10 shows the\npT versus \u2206R between the leading narrow jet and the wide jet.\n4.2\nLeptonic Vector Boson Identi\ufb01cation\n4.2.1\nLepton Reconstruction Ef\ufb01ciencies\nAll the signals studied in this note involve at least one leptonic vector boson decay. Electrons and muons\nare selected using standard ATLAS criteria [36, 37] for the case of a resonance m(WZ) of 800 MeV.\nFigure 11 shows the ef\ufb01ciency for W boson daughter leptons, where the trigger consition has not been\napplied. The results for different electron selection criteria are given. The loss of ef\ufb01ciency occurs in the\nforward regions, near the limits of the tracking detectors and at pT values close to the applied cut. The\nef\ufb01ciencies for the leptonic Z boson channels have been found to be similar.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1782\n\n\u0001\u0002\n\u0001\u0003\n\u0004\u0002\n\u0004\u0003\n\u0005\u0002\n\u0005\u0003\n\u0006\u0002\n\u0006\u0003\n\u0007\u0002\u0002\n\u0002\n\u0002\b\u0002\t\n\u0002\b\u0002\n\u0002\b\u0002\u0001\n\u0002\b\u0002\u0005\n\u0002\b\u0007\n\u0002\b\u0007\t\n\u0002\b\u0007\n\u0002\b\u0007\u0001\n\u0002\b\u0007\u0005\n\u0002\b\t\n\u0002\n\u0002\b\u0007\n\u0002\b\t\n\u0002\b\u000b\n\u0002\b\n\u0002\b\u0003\n\u0002 \u0001\n\u0002\n\u0002\b\u0002\u0007\n\u0002\b\u0002\t\n\u0002\b\u0002\u000b\n\u0002\b\u0002\n\u0002\b\u0002\u0003\n\u0002\b\u0002\u0001\n\u0002\b\u0002\u0004\n\u0002\b\u0002\u0005\n\u0002\b\u0002\u0006\n\u0002\b\u0007\nDe taR(w de jet narrow jet)\nDeltaR(wide jet, narrow jet)\nWZ signal\nZ+3jets\nATLAS\nATLAS\nWide jet invariant Mass [GeV]\nFigure 10: Pro\ufb01le histogram of the distance (narrow jets, wide jet) versus the invariant mass of the wide\njet, for W boson hadronic decay of the resonance signal qqWj jZ\u2113\u2113of m = 1.1 TeV (red) and for Z+3 jets\nsample (black). Lower graph : normalized distributions of distance (narrow jets, wide jet).\n[GeV]\ne\nP\n0\n100\n200\n300\n400\n500\n600\nElectron efficiency\n0\n0 1\n0 2\n0 3\n0 4\n0 5\n0 6\n0 7\n0 8\n0 9\n1\nATLAS\nloose EM criteria\nmedium EM criteria\nall candidates\ntight EM criteria\n [GeV]\n\u00b5\nT\nP\n0\n100\n200\n300\n400\n500\n600\nMuon efficiency\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nATLAS\ne\n!\n-3\n-2\n-1\n0\n1\n2\n3\nElectron efficiency\n0\n0 1\n0 2\n0 3\n0 4\n0 5\n0 6\n0 7\n0 8\n0 9\n1\nATLAS\nall candidates\nloose EM criteria\nmedium EM criteria\ntight EM criteria\n!\n!\n-3\n-2\n-1\n0\n1\n2\n3\nMuon efficiency\n0\n0 1\n0 2\n0 3\n0 4\n0 5\n0 6\n0 7\n0 8\n0 9\n1\nATLAS\nFigure 11: Ef\ufb01ciency of reconstructing and identifying W-daughter electrons (left) and muons (right)\nas functions of true lepton momentum (top) and pseudo-rapidity (bottom). The electron plots show the\nef\ufb01ciency for 4 different electron selection criteria: All candidate objects (green), loose (black circles),\nmedium (red squares), and tight (blue triangles).\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1783\n\nmass [GeV]\n60\n70\n80\n90\n100\n110\n120\nNumber of events\n0\n10\n20\n30\n40\n50\n60\n(800GeV)\nll\nZ\nj,jj\nW\n mean = 90.3 GeV\n sigma = 2.7 GeV\nATLAS\n-e\n+\nReconstructed Z from e\nmass [GeV]\n60\n70\n80\n90\n100\n110\n120\nNumber of events\n0\n5\n10\n15\n20\n25\n(800GeV)\nll\nZ\nj,jj\nW\n mean = 91.0 GeV\n sigma = 3.6 GeV\nATLAS\n-\n\u00b5\n+\n\u00b5\nReconstructed Z from \nFigure 12: Reconstructed Z boson from electron pairs (left) and muon pairs (right).\n4.2.2\nLeptonic Z Boson Reconstruction\nThe Z boson candidates are reconstructed from pairs of e+e\u2212or \u00b5+\u00b5\u2212. In the electron case, the mass\nresolution is about 2.7 GeV as is shown in Fig. 12 left, suggesting a mass window selection between\nm = 85 GeV and 97 GeV for mee. In the case of muons, the resolution for the Z mass reconstruction is\n3.6 GeV (see Fig. 12 right), so the mass requirement is loosened to be between m = 83 GeV and 99 GeV.\nFurthermore, to reduce the backgrounds (particularly the background from t\u00aft events), the pT of one of\nthe leptons is required to be pT > 50 GeV, and that of the other pT > 35 GeV. In the unlikely case that\nmore than one combination of leptons satisfy all these requirements, we choose the composite Z\u2113+\u2113\u2212with\nthe mass closest to the actual Z boson mass.\n4.2.3\nLeptonic W Boson Reconstruction\nFor the signal, after reconstruction of the hadronic vector boson candidate, the highest pT lepton corre-\nsponds to the lepton from the W boson decay in 96% of cases. Attributing the missing momentum to the\nneutrino, and taking the nominal W boson mass (mW = 80.42 GeV) as a constraint, a quadratic equation\nis obtained for the z-component of the neutrino\u2019s momentum. The z component is required in order to\nreconstruct the diboson mass in the \ufb01nal analysis. Only events for which at least one real solution exists\nfor this quadratic equation are retained. When there are two possible solutions, one is chosen at random\nto avoid kinematic bias on the resonance mass. Options such as selecting the reconstructed W boson\nwhich is more central have also been considered, and little difference was found in the purity of the\nreconstruction. In the fully leptonic case, the leptonic Z boson is reconstructed and its daughter leptons\nremoved before applying the above procedure.\n4.3\nTagged Forward Jets\nOne of the well known characteristic features of vector boson scattering is the presence of high energy\nforward jets [14], resulting from the primary quarks from which the vector bosons have radiated (see\nFig. 13). Such forward jets are expected to be much less prominent in processes involving gluon or\nelectroweak boson exchange with bremsstrahlung of vector bosons. In the latter case, these vector bosons\nare mostly transverse and have a harder pT spectrum than in WLWL scattering. Correspondingly, the\noutgoing primary quarks have a harder pT and are therefore less forward.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1784\n\ntag quarks\n!\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n!\n1/N dN/d\n0\n0.01\n0.02\n0.03\n0.04\n0.05\nATLAS\nFigure 13: Pseudo-rapidities of the forward and backward quarks in signal events after they radiate the\nvector bosons, obtained from PYTHIA before any showering, fragmentation, etc.\nMany different strategies are possible for implementing a tag-jet selection. A number of these were\ncompared, and the best rejection factors for a given ef\ufb01ciency were obtained as follows:\n1. Require two jets with\n\u2022 |\u03b7(jet)| > \u03b7cut and pT(jet) > pTcut\n\u2022 opposite signed rapidity\n\u2022 at least one of them has an energy greater than a critical value Ecut\n2. If more than one jet with the same sign rapidity satis\ufb01es the above cuts, choose the most energetic,\nlabelled FJ1. The next one is labelled FJ2.\n\u2022 Require the tag-jet with the opposite sign of rapidity to satisfy \u2206\u03b7(FJ1,FJ2) > \u2206\u03b7cut and\nE(FJ2) > E2cut\nIn addition a dijet mass cut is currently applied in the cone algorithm analyses. The speci\ufb01c values of the\ncuts in each case are to be optimised depending upon the kinematic region under study.\n4.4\nCentral Jet Veto\nA useful analysis strategy to suppress backgrounds such as t\u00aft is to apply a central jet veto [15, 38, 39].\nFor vector boson scattering, one expects little QCD radiation in the central region since only colourless\nelectroweak vector bosons are produced and the forward jets are not colour connected. Given the forward\njet cut de\ufb01nition, we unambiguously de\ufb01ne the central region of the event as the \u03b7 region between them.\nThe central jet veto then simply requires that no other high pT jet (here taken as pT > 30 GeV) other\nthan those resulting from the hadronically decaying vector boson lie in the central region.\nSpeci\ufb01cally, in the analyses where it is applied, the central jet veto rejects events if there are any\nadditional jets with a chosen maximum value for |\u03b7| and minimum value for pT.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1785\n\n4.5\nTop Quark Rejection\nWhile the \ufb01nal states from a leptonically decaying Z boson are mostly free of background from top\nprocesses, t\u00aft and tW events form an important source of background for the WW signals. To suppress\nthem, events can be vetoed if a reconstructed W boson candidate, combined with another jet in the event\n(excluding those overlapping with an identi\ufb01ed electron or within \u2206R < 0.8 of a W candidate), leads to\nan invariant mass close to that of the top quark [32]. A typical mass window is 130 < mt < 240 GeV.\nIn a future analysis it is likely that this cut can be improved using b-tag information and better jet\nmass reconstruction, but this has not been investigated here.\n5\nEvent Selection\nUsing the tools outlined in the previous section, we now characterise the samples and outline the speci\ufb01c\ncuts applied for each \ufb01nal state considered.\n5.1\nW +W \u2212\u2192\u2113\u00b1\u03bd j j and W \u00b1Z \u2192\u2113\u00b1\u03bd j j\nThe hadronic vector boson candidates and the tag jets are obtained using the k\u22a5algorithm as discussed\nin Section 4.1. The leptonic W is identi\ufb01ed as described in Section 4.2.3. Both vector boson candidates\nare required to have pT > 200 GeV, |\u03b7| < 2. Tag jet cuts are made as described in Section 4.3, with\npTcut = 10 GeV, Ecut = E2cut = 300 GeV and \u2206\u03b7cut = 5. The top veto (Section 4.5) and the the central\njet veto (Section 4.4) are applied.\nThe kinematic distributions for the WW channel are shown in Fig. 14. Note that these are signi\ufb01-\ncantly biased by the generator-level cuts. The selection ef\ufb01ciencies of the cuts on WW events from four\nexample scenarios are summarised in Table 6, along with the ef\ufb01ciency of the combined trigger selection\ndescribed in Section 3. No signi\ufb01cant differences are observed between the scalar and vector resonances,\nnor between the WZ and WW channels, except for the m = 500 GeV-resonant samples, where the pT re-\nquirements are found to be less ef\ufb01cient for the WZ sample. The QCD-like model of [27] tends to predict\nsofter vector bosons.\nDue to the small background statistics available with full simulation, the full-simulation signal sam-\nples are used together with fast-simulation background samples in obtaining the \ufb01nal results. The mod-\nelling of the kinematics is good, as shown in Fig. 14 2. However, in general the ef\ufb01ciency for selecting\nboth signal and background is higher in fast simulation by about 25% compared to full simulation. To\naccount for this, a constant scaling factor is applied to the fast-simulation samples in estimating the\nsigni\ufb01cance of the signal over the background (Section 6).\nFigure 15 shows a comparison of the \ufb01nal WW mass for the signal samples using fast and full\nsimulation.\nThe \ufb01nal WW mass spectra obtained using this analysis are shown in Fig. 16. The backgrounds\nshown have been obtained from the fast-simulation samples and the above mentioned scaling factor has\nbeen applied.\n5.2\nW \u00b1Z \u2192j j \u2113+\u2113\u2212\nThis channel bene\ufb01ts from a very good resolution on the Z boson leptonic reconstruction, which allows\ngood suppression of the t\u00aft background.\n2To achieve this agreement it was necessary to correct the lepton-\ufb01nding ef\ufb01ciency in the fast simulation by \ufb01tting a function\nto the ef\ufb01ciency from fast and full simulation as a function of lepton pT and correcting the fast simulation by the ratio of the\nfunctions.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1786\n\n[GeV]\nHadronic W\nT\nP\n0\n200\n400\n600\n800\nArbitrary Units\n0\n0 05\n0 1\n0 15\n0 2\n0 25\n0 3\n0 35\nWW S gna (Fu s m.)\nWW S gna (Fast s m.)\nW+jets (Fu s m.)\nW+jets (Fast s m.)\n(Fu s m.)\ntt\n(Fast s m.)\ntt\nATLAS\nHadronic W\n!\n4\n2\n0\n2\n4\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\n0 14\n0 16\nATLAS\n[GeV]\nLeptonic W\nT\nP\n0\n200\n400\n600\n800\nArbitrary Units\n0\n0 1\n0 2\n0 3\n0 4\n0 5\nATLAS\nLeptonic W\n!\n2\n1\n0\n1\n2\nArbitrary Units\n0\n0 02\n0 04\n0 06\n0 08\n0 1\n0 12\n0 14\n0 16\nATLAS\nJets\n!\n5\n0\n5\nArbitrary Units\n0\n0 1\n0 2\n0 3\n0 4\n0 5\n0 6\nATLAS\n[GeV]\nHardest Central Jet\nT\nP\n0\n50\n100\n150\nArbitrary Units\n-2\n10\n-1\n10\n1\nATLAS\nFigure 14: Kinematic distributions for the generated signal and backgrounds (t\u00aft and W+4 jets QCD) in\nthe 1.1 TeV W +W \u2212\u2192\u2113\u00b1\u03bd j(j) channel. The top two plots show the pT and \u03b7 for the hadronic W boson\ncandidate. The middle two show the same variables for the leptonic W boson candidate. The bottom\ntwo plots show the \u03b7 distribution of all jets which are at higher rapidity than the W boson candidates,\nand the pT distribution of the highest-pT central jet. In each plot, the full-simulation histograms (solid\nlines) have been normalised to unit area and the fast-simulation histograms (dashed lines) have been\nnormalised to the same cross section as their full-simulation counterparts.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1787\n\nCut\nm = 500 GeV Scalar Resonance\nm = 800 GeV Scalar Resonance\nm = 1.1 TeV Vector Resonance\nEf\ufb01ciency (%)\n\u03c3 (fb)\nEf\ufb01ciency (%)\n\u03c3 (fb)\nEf\ufb01ciency (%)\n\u03c3 (fb)\nStarting sample\n\u2013\n66\n\u2013\n28\n\u2013\n18\n\u22611 Hadronic W\n32.1\u00b10.5 ( 34)\n21 ( 23)\n40.0\u00b10.5 ( 45)\n11 ( 13)\n39.5\u00b10.7 ( 43)\n7.1 (7.8)\n\u22611 Leptonic W\n45.4\u00b10.9 ( 54)\n9.6 ( 12)\n48.5\u00b10.8 ( 57)\n5.4 (7.1)\n48.8\u00b11.2 ( 55)\n3.5 (4.3)\npT (Had. W) > 200 GeV\n57.6\u00b11.3 ( 69)\n5.5 (8.5)\n88.2\u00b10.7 ( 90)\n4.8 (6.4)\n86.6\u00b11.1 ( 88)\n3.0 (3.8)\n|\u03b7| (Had. W) < 2\n91.9\u00b10.9 ( 93)\n5.1 (7.9)\n95.3\u00b10.5 ( 95)\n4.6 (6.1)\n93.4\u00b10.9 ( 92)\n2.8 (3.5)\npT (Lep. W) > 200 GeV\n43.8\u00b11.8 ( 42)\n2.2 (3.3)\n91.3\u00b10.7 ( 89)\n4.2 (5.4)\n92.4\u00b11.0 ( 89)\n2.6 (3.1)\n|\u03b7| (Lep. W) < 2\n95.5\u00b11.1 ( 94)\n2.1 (3.1)\n95.3\u00b10.6 ( 95)\n4.0 (5.1)\n92.8\u00b11.0 ( 93)\n2.4 (2.9)\n\u22612 tag jets\n32.0\u00b12.6 ( 37)\n0.7 (1.1)\n42.4\u00b11.3 ( 49)\n1.7 (2.5)\n43.7\u00b12.0 ( 55)\n1.1 (1.6)\n\u22610 top candidates\n50.0\u00b15.0 ( 40)\n0.3 (0.5)\n52.0\u00b12.1 ( 41)\n0.9 (1.0)\n51.4\u00b13.0 ( 44)\n0.5 (0.7)\nCentral jet veto\n100.0\u00b10.0 ( 98)\n0.3 (0.4)\n96.7\u00b11.0 ( 97)\n0.8 (1.0)\n91.6\u00b12.3 ( 93)\n0.5 (0.7)\nTrigger ef\ufb01ciency\n96\u00b13\n0.3 (0.4)\n98\u00b11\n0.8 (1.0)\n98\u00b11\n0.5 (0.7)\nCut\nNon-resonant Signal\nt\u00aft Background\nW+jets Backgrounds\nEf\ufb01ciency (%)\n\u03c3 (fb)\nEf\ufb01ciency (%)\n\u03c3 (fb)\nEf\ufb01ciency (%)\n\u03c3 (fb)\nStarting sample\n\u2013\n10\n\u2013\n450000\n\u2013\n21365\n\u22611 Hadronic W\n38.0\u00b10.7 ( 41)\n3.8 (4.1)\n18.9\u00b10.1 (19)\n85000 ( 84000)\n8.3\u00b10.1 (9)\n1760 ( 1820)\n\u22611 Leptonic W\n48.2\u00b11.1 ( 55)\n1.8 (2.3)\n22.1\u00b10.2 (29)\n19000 ( 25000)\n23.3\u00b10.7 (31)\n410 ( 570)\npT (Had. W) > 200 GeV\n82.1\u00b11.3 ( 86)\n1.5 (1.9)\n16.8\u00b10.4 (20)\n3200 ( 5000)\n34.4\u00b11.7 (43)\n140 ( 240)\n|\u03b7| (Had. W) < 2\n94.4\u00b10.8 ( 94)\n1.4 (1.8)\n90.3\u00b10.7 (90)\n2900 ( 4500)\n80.1\u00b12.4 (77)\n110 ( 190)\npT (Lep. W) > 200 GeV\n90.4\u00b11.1 ( 87)\n1.3 (1.6)\n34.5\u00b11.3 (29)\n990 ( 1300)\n48.5\u00b13.3 (40)\n55 ( 75)\n|\u03b7| (Lep. W) < 2\n96.0\u00b10.8 ( 96)\n1.2 (1.5)\n94.6\u00b11.0 (90)\n930 ( 1200)\n80.4\u00b13.9 (79)\n44 ( 59)\n\u22612 tag jets\n45.1\u00b12.0 ( 54)\n0.6 (0.8)\n8.1\u00b11.3 (10)\n76 ( 120)\n13.9\u00b13.5 (22)\n6 ( 13)\n\u22610 top candidates\n56.5\u00b13.0 ( 47)\n0.3 (0.4)\n7.9\u00b14.4 ( 2)\n5 ( 2)\n60.5\u00b113.1 (23)\n4 ( 3)\nCentral jet veto\n91.1\u00b12.3 ( 94)\n0.3 (0.4)\n< 50 (< 25)\n< 5 ( < 1)\n84.9\u00b113.7 (91)\n3 ( 3)\nTrigger ef\ufb01ciency\n98\u00b11\n0.3 (0.4)\n\u223c100\n< 5 ( < 1)\n82\u00b116\n3 ( 3)\nTable 6: Ef\ufb01ciencies of the cuts for four different qqWW \u2192qq\u2113\u03bdqq signal samples and the backgrounds. The trigger ef\ufb01ciency row shows the ef\ufb01ciency\nof the logical OR of mu20i, e25i and jet160 signatures on the samples after all the cuts have been consecutively applied. The numbers in brackets\nare from the fast simulation.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1788\n\n[GeV]\nWW\nm\n200\n400\n600\n800 1000 1200 1400 1600 1800\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0 05\n0 1\n0 15\n0 2\n0 25\n0 3\n0 35\n0 4\nFull WW s500\nFast WW s500\nFull WW s800\nFast WW s800\nFull WW v1150\nFast WW v1150\nATLAS\nMC Errors Only\n[GeV]\nWZ\nm\n200\n400\n600\n800 1000 1200 1400 1600 1800\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0 05\n0 1\n0 15\n0 2\n0 25\n0 3\n0 35\n0 4\nFull WZ 500\nFull WZ 800\nFull WZ 1150\nATLAS\nMC Errors Only\nFigure 15: WW (left) and WZ (right) invariant mass spectra in the \u2113\u03bd j(j) semileptonic channel for the\nthree resonant signal samples. The WW plot shows a comparison of the fast- and full-simulation results.\nFor the m = 1.1 TeV WZ resonance, only the case of a single heavy jet from the W boson decay will\nbe considered as it constitutes the majority of the events. For the m = 800 GeV resonance, not all W\nbosons are boosted suf\ufb01ciently to produce a single jet. We therefore consider separately the cases of a\nW boson from a single heavy jet and from a jet pair. Finally, for the m = 500 GeV resonance, we only\nconsider the jet pair case. In this section, the cone algorithm will be used and compared with an analysis\nusing the k\u22a5jet algorithm.\n5.2.1\nW boson from a single jet\nThe main backgrounds will here be Z+ 3 jets and t\u00aft.\nTable 7 shows the cut \ufb02ow for the electron-based and the muon-based analyses for the ChL WZ\nresonances of mass m = 1.1 TeV and m = 800 GeV. The m = 500 GeV case is not considered here since\nthe W and Z bosons will not be suf\ufb01ciently boosted, in general, to produce a single jet. The Z \u2192e+e\u2212\nand Z \u2192\u00b5+\u00b5\u2212selections are shown, which correspond each to about 50% of the sample events. After\napplying electron quality cuts (medium electrons) we select the two highest pT leptons which should\nsatisfy respectively: pT(e,\u00b5) > 50 GeV and pT(e,\u00b5) > 35 GeV. The low ef\ufb01ciency of the lepton pair\ncut is approximately consistent with the expected selection ef\ufb01ciency per lepton, as shown in Fig. 11,\nas well as the detector acceptance. As can be seen in Fig. 17, the pT cut suppresses mostly the t\u00aft\nbackground. A leptonic Ze+e\u2212or Z\u00b5+\u00b5\u2212is afterwards reconstructed as described in Section 4.2.2, almost\neliminating completely this background. The ef\ufb01ciency of this cut is somewhat poorer for the signal\nthan for the background because most of the background events have Z bosons of relatively low pT, with\ndifferent lepton pair energies and opening angle.\nUsing the cone algorithm, size 0.8, the hadronic W boson candidate is identi\ufb01ed as a heavy single jet\nhaving a mass between 70 and 100 GeV, and separated in azimuthal angle from the Z boson candidate\nby \u2206\u03c6(W,Z) > 2, as described in Section 4.1 (see Fig. 18). At this stage, considering that the fraction\nof single jet W bosons becomes important for pT > 250 GeV (see Fig. 5), and in order to be consistent\nwith the preselection cuts on the Z+3 jets background, we apply the following cuts to the reconstructed\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1789\n\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nScalar 500 GeV\ntt\n\u0005\n\u0005\u0003\u0005\n\u0005\n\u0005\n\u0005\nW+jets\n\u0006\n\u0006\u0003\u0006\n\u0006\n\u0006\n\u0006\nSignal\n\u0007\n\u0007\u0001\u0007\u0001\u0007\n\u0007\n\u0007\u0001\u0007\u0001\u0007\n\u0007\n\u0007\u0001\u0007\u0001\u0007\nATLAS\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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03\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\n\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nScalar 800 GeV\ntt\n\u000b\n\u000b\n\u000b\n\u000b\nW+jets\n\f\n\f\n\f\n\f\nSignal\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\nATLAS\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nVector 1.1 TeV\ntt\n\u0011\n\u0011\u0003\u0011\n\u0011\n\u0011\n\u0011\nW+jets\n\u0012\n\u0012\u0003\u0012\n\u0012\n\u0012\n\u0012\nSignal\n\u0013\n\u0013\u0001\u0013\u0001\u0013\n\u0013\n\u0013\u0001\u0013\u0001\u0013\n\u0013\n\u0013\u0001\u0013\u0001\u0013\nATLAS\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\n\u0014\n\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u0001\u0014\u00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0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\u0003\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n\u0016\n[GeV]\nWW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nContinuum\ntt\n\u0017\n\u0017\n\u0017\n\u0017\nW+jets\nSignal\n\u0001\u0001\n\u0001\u0001\n\u0001\u0001\nATLAS\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u00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0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0004\n\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\u0003\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n\u0004\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nQCD-like 500 GeV\ntt\n\u0005\n\u0005\u0003\u0005\n\u0005\n\u0005\n\u0005\nW+jets\n\u0006\n\u0006\u0003\u0006\n\u0006\n\u0006\n\u0006\nSignal\n\u0007\n\u0007\u0001\u0007\u0001\u0007\n\u0007\n\u0007\u0001\u0007\u0001\u0007\n\u0007\n\u0007\u0001\u0007\u0001\u0007\nATLAS\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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03\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\n\t\n\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\n\t\n\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\n\t\n\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\u0003\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\n\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\u0003\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nEWChL 800 GeV\ntt\n\u000b\n\u000b\n\u000b\n\u000b\nW+jets\n\f\n\f\n\f\n\f\nSignal\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\nATLAS\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\u0003\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u000f\n\u0010\n\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\u0003\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n\u0010\n[GeV]\nWZ\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.2\n0.4\n0.6\n0.8\n1\nEWChL 1.1 TeV\ntt\n\u0011\n\u0011\u0003\u0011\n\u0011\n\u0011\n\u0011\nW+jets\n\u0012\n\u0012\u0003\u0012\n\u0012\n\u0012\n\u0012\nSignal\n\u0013\n\u0013\u0001\u0013\u0001\u0013\n\u0013\n\u0013\u0001\u0013\u0001\u0013\n\u0013\n\u0013\u0001\u0013\u0001\u0013\nATLAS\nFigure 16: WW (top 4) and WZ (bottom 3) invariant mass spectra in the \u2113\u03bd j(j) semileptonic channel,\nshowing the total W+jets and t\u00aft backgrounds and the signal for the three resonant signal samples and the\ncontinuum sample. The error bars re\ufb02ect the uncertainty from the Monte Carlo statistics.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1790\n\n [GeV]\nT\nLepton P\n100\n200\n300\n400\n500\nNumber of Events\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\ntt\nZ+3j\n(1.1TeV)\nll\nZ\nj,jj\nW\n [GeV]\nT\nLepton P\n50\n100\n150\n200\n250\n300\nArbitrary Units\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\ntt\nZ+3j\n(1.1TeV)\nll\nZ\nj,jj\nW\nFigure 17: pT of the highest pT and second highest pT electrons from reconstructed Z bosons in the m =\n1.1 TeV resonance sample. Distributions are arbitrarily normalised. The line indicates the cut value.\nmass [GeV]\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n/5GeV\n-1\nEvents/fb\n-3\n10\n-2\n10\n-1\n10\n1\n mean = 83.8 GeV\n sigma = 8.2 GeV\nZ+3j\n(1.1TeV)\nll\nZ\nj\nW\nATLAS\nFigure 18: Mass of the heavy jet for the m =\n1.1 TeV ChL resonance and corresponding back-\ngrounds. No t\u00aft event is left.\nmass [GeV]\n20\n30\n40\n50\n60\n70\n80\n90\n100\n110\n120\n/5GeV\n-1\nEvents/fb\n-2\n10\n-1\n10\n1\n10\n mean = 76 0 GeV\n sigma = 6.9 GeV\nZ+4j\ntt\n(800GeV)\nll\nZ\njj\nW\nATLAS\nFigure 19: Reconstructed W boson mass from a\njet pair for the m = 800 GeV resonance.\nW and Z bosons: pW,Z\nT\n> 250 GeV and |\u03b7W,Z| < 2.0.\nAfter a forward jet selection, (see Section 4.3, pTcut = 20 GeV, Ecut = E2cut = 300 GeV, \u03b7cut = 1.5,\n|\u03b7 f jet| > \u03b7central jet, \u2206\u03b7cut = 4.5), the invariant mass of these two jets is required to be greater than 700\nGeV. Note that the ef\ufb01ciency of the forward jet cuts appearing in Table 7 appears arti\ufb01cially good for the\nbackground because a preselection was already applied.\nA central jet veto was found to be unnecessary, as no t\u00aft event survived the selection. Because of\nthe lack of statistics for the t\u00aft sample, it is not possible to exclude completely a contribution from this\nbackground. The normalisation factor is 4.9, meaning that t\u00aft is excluded, over the whole mass range,\nat the level of 11.3 fb at 90% C.L. To have an estimate of the ef\ufb01ciency of the last two cuts at rejecting\nthis background, the mass window for the cut on the Z boson mass was loosened: 60 < mZ < 120 GeV,\nallowing 44 events (215 fb) to pass for the Z \u2192ee channel and 38 events (185 fb) for the Z \u2192\u00b5\u00b5\nchannel. The W boson mass cut alone is found to have an ef\ufb01ciency of 12% and the forward jet cut alone\nlets no event survive. Assuming that the cuts are independent, the overall ef\ufb01ciency of the heavy jet mass\ncut and forward jet tagging combined is higher than 0.15%. The exclusion limit at 95% C.L. (1.64 \u03c3) for\nthe t\u00aft background is shown in Table 7 and it will be assumed that this is negligible in the mass window of\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1791\n\nmass [GeV]\n400\n600\n800\n1000\n1200\n1400\n/100GeV\n-1\nEvents/fb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nZ+3j\n(1.1TeV)\nll\nZ\nj\nW\nATLAS\nmass [GeV]\n400\n500\n600\n700\n800\n900\n1000\n1100\n/100GeV\n-1\nEvents/fb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n(800GeV)\nll\nZ\nj\nW\nZ+3j\nATLAS\nFigure 20: Reconstruction of ChL resonance at m = 1.1 TeV (left) and m = 800 GeV (right) in the\nchannel qqWjZ\u2113\u2113(with \u2113= e,\u00b5), where a single jet cone 0.8 has been used to reconstruct the W.\nthe resonance. The Z+4 jets background was not included here because it may be double-counting with\nZ+3 jets with parton shower. In order to evaluate the level of this background, an average over the high\nmass region was taken because of the relatively poor Monte Carlo statistics, yielding about 0.03 fb/100\nGeV.\nFor the m = 1.1 TeV case, it was found that the trigger ef\ufb01ciency, based on the OR of e60, mu20\nand j160, was 100% at the end of the selection.\nFigure 20 shows the resonance mass resulting when the Z boson has been reconstructed from elec-\ntrons or muons and the W boson from a single jet of size 0.8.\n5.2.2\nW boson from a jet pair\nAs above, after applying electron quality cuts, the lepton transverse momenta are required to satisfy\npT(e1,\u00b51) > 50 GeV and pT(e2,\u00b52) > 35 GeV, and a Ze+e\u2212(Z\u00b5+\u00b5\u2212) boson having a mass between 85\nand 97 GeV (83 and 99 GeV) is then reconstructed. Considering all pairs of jets with pT > 30 GeV in\nthe central region (|\u03b7| < 3.0) not overlapping with the electron jets from the Z decay, the one yielding\nan invariant mass closest to the mass of a W boson will be the W boson candidate (see Fig. 19). The low\nef\ufb01ciency of this cut can be explained in part by the fact that a good fraction of events are constituted of\na single jet W boson. Forward and backward jet selection proceeds as in 5.2.1. A central jet veto is also\napplied: we exclude events with an extra jet, having a pT > 30 GeV, not corresponding to the jets from\nthe W boson or the forward and backward jets and we require the W and Z directions to be in the central\nregion |\u03b7| < 2. Figure 21 show the resulting reconstructed resonance masses. Table 7 summarizes the\ncut \ufb02ow for this analysis. Here, by using the technique of widening the Z boson mass window as in\nSect. 5.2.1, it is estimated that the t\u00aft background could be approximately 0.13 fb and it will be assumed\nthat this is negligible in the mass window of the resonance.\n5.2.3\nComparison to k\u22a5analysis\nThis channel was also studied with the analysis techniques described in Section 5.1, with the k\u22a5algorithm\nbut using the leptonic Z boson identi\ufb01cation (Section 4.2.2) instead of the leptonic W boson identi\ufb01cation\n(Section 4.2.3). The hadronically-decaying W boson is reconstructed dynamically from one or two jets\n(Section 4.1).\nThe signal mass distributions for fast and full simulation are shown in Fig. 22. The \ufb01nal mass\ndistributions are shown in Fig. 23, and are comparable to the results from the cone algorithm method for\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1792\n\nm = 1.1 TeV\nm = 800 GeV\nm = 500 GeV\nZ +3 j\nZ +4 j\nt\u00aft\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\nZ \u2192e+e\u2212\npT(e1) > 50 GeV, pT(e2) > 35 GeV\n0.79\n22%\n2.14\n20%\n4.15\n16%\n22.2\n20%\n195\n7.9%\n1055\n29%\n85 GeV < mZ < 97 GeV\n0.63\n80%\n1.69\n79%\n3.34\n80%\n18.5\n87%\n176\n90%\n39\n3.7%\nZ \u2192\u00b5+\u00b5\u2212\npT(\u00b51) > 50 GeV, pT(\u00b52) > 35 GeV\n0.60\n16%\n1.67\n16%\n3.11\n12.4%\n17.2\n16%\n170\n7.0%\n821\n22%\n83 GeV < mZ < 99 GeV\n0.48\n81%\n1.40\n84%\n2.68\n86%\n15.8\n90%\n163\n95%\n64\n7.8%\nZ \u2192e+e\u2212and Z \u2192\u00b5+\u00b5\u2212\nWjZll\nHeavy jet mass W \u2192j\n0.57\n51%\n0.75\n24%\n\u2013\n\u2013\n2.99\n8.7%\n\u2013\n\u2013\n0\n0%\nForward jet tagging\n0.22\n39%\n0.29\n39%\n\u2013\n\u2013\n0.67\n22%\n\u2013\n\u2013\n< 0.25\n\u2013\nWj jZll\n65 GeV < mj j < 90 GeV\nand \u2206\u03c6(Wj j,Z) > 2.0\n\u2013\n\u2013\n1.51\n25%\n2.21\n37%\n\u2013\n\u2013\n37.6\n11%\n9.8\n9.5%\nForward jet tagging\n\u2013\n\u2013\n0.62\n41%\n0.68\n31%\n\u2013\n\u2013\n9.57\n25%\n\u2013\n\u2013\nCentral jet veto\n\u2013\n\u2013\n0.29\n47%\n0.32\n47%\n\u2013\n\u2013\n4.85\n51%\n\u2013\n\u2013\nTable 7: Cut \ufb02ow for the Wj jZ\u2113\u2113, m = 1.1 TeV, 800 and 500 GeV signals. For each process, the cross section (fb) surviving the successive application\nof the cuts is shown, as well as the ef\ufb01ciency of each cut. The upper limit for t\u00aft in the last lines is for 95% C.L.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1793\n\nmass [GeV]\n500\n600\n700\n800\n900\n1000\n1100\n/50GeV\n-1\nEvents/fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nZ+4j\n(800GeV)\nll\nZ\njj\nW\nATLAS\nmass [GeV]\n200\n300\n400\n500\n600\n700\n800\n/50GeV\n-1\nEvents/fb\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nZ+4j\n(500GeV)\nll\nZ\njj\nW\nATLAS\nFigure 21: Reconstructed ChL resonance at m = 800 GeV (left) and m = 500 GeV (right) in the channel\nqqWj jZ\u2113\u2113(with \u2113= e,\u00b5) where two jets of cone size 0.4 have been used to reconstruct the W boson. No\nt\u00aft events survive the selection.\nW\u2113\u03bdZ\u2113\u2113(m = 500 GeV)\nW\u2113\u03bdZ\u2113\u2113(m = 1.1 TeV)\nW\u2113\u03bdZ\u2113\u2113j j(SM)\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\nZee\n1.47\n18%\n0.23\n20%\n20.7\n16%\nZ\u00b5\u00b5\n1.09\n14%\n0.18\n15%\n16.7\n13%\nW reconstruction\n1.43\n56%\n0.25\n61%\n18.9\n51%\nForward jet tagging\n0.63\n44%\n0.14\n56%\n1.6\n8.5%\nTable 8: Cut \ufb02ow for the W\u2113\u03bdZ\u2113\u2113(m = 500 GeV and 1.1 TeV) signals. All the cuts are described in detail\nin this section.\nthe 1.1 TeV case which is not sensitive to the cut on the pT of the VB\u2019s of 200 GeV.\n5.3\nW \u00b1Z \u2192\u2113\u00b1\u03bd \u2113+\u2113\u2212\nThis purely leptonic channel consists of four different signatures: W\u2113\u00b1\u03bdZ\u2113\u00b1\u2113\u2213with \u2113= e,\u00b5. The main\nbackground will be WZ j j production from the Standard Model. The analysis starts by identifying lep-\ntonic Ze+e\u2212(Z\u00b5+\u00b5\u2212) bosons as described in Section 4.2.2, after requiring two leptons with pT greater than\n50 and 35 GeV.\nAs a second step, we proceed to reconstruct the W boson from the highest pT lepton among those\nremaining in the event, if there is one, and the measured missing transverse energy, as described in\nSection 4.2.3. The solution which yields the highest pT W boson is kept.\nThe forward and backward jet selection follows the prescription of the Section 4.3 (pTcut = 20 GeV,\nEcut = E2cut = 300 GeV, \u03b7cut = 1.5, |\u03b7 f jet| > \u03b7central jet), \u2206\u03b7cut = 4.5).\nIn Table 8 we present the cut \ufb02ow of the reconstruction of the resonances for 1.1 TeV and 500 GeV.\nAlso in Fig. 24 and Fig. 25 we present the reconstructed resonance and the background WZ j j for the\nsame resonance mass.\n5.4\nZZ \u2192\u03bd\u03bd \u2113+\u2113\u2212\nThis scalar resonance can be interpreted as a Standard Model Higgs boson produced by vector boson\nfusion. At leading order, the cross section times branching ratio would be 6 fb, compared to 4 fb obtained\nfor the ChL model. This signal is characterised by a leptonic Z boson accompanied by large /ET, yielding\na large transverse mass. The backgrounds considered are: ZZ j j \u2192\u2113\u2113\u03bd\u03bd j j and WZ j j \u2192\u2113\u03bd\u2113\u2113j j. Other\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1794\n\n[GeV]\nZW\nm\n200\n400\n600\n800 1000 1200 1400 1600 1800\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nFull ZW 500\nFast ZW 500\nFull ZW 800\nFast ZW 800\nFull ZW 1150\nFast ZW 1150\nATLAS\nMC Errors Only\nFigure 22: WZ invariant mass spectrum in the \u2113+\u2113\u2212j(j) channel for the three resonant signal samples\nobtained using k\u22a5algorithm approach. Dotted lines indicate the fast simulation results.\nZ\u03bd\u03bdZ\u2113\u2113qq (m = 500GeV)\nW\u2113\u03bdZ\u2113\u2113j j (SM)\nZ\u03bd\u03bdZ\u2113\u2113j j (SM)\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\n\u03c3 (fb)\neff.\nZee\n0.72\n17.6%\n20.78\n22%\n9.1\n20%\nZ\u00b5\u00b5\n0.58\n15%\n16.7\n17%\n6.6\n15%\nForward jet tagging\n0.58\n45%\n3.2\n8.6%\n0.47\n3%\n/ET > 150 GeV\n0.44\n75%\n0.46\n14%\n0.12\n26%\nTable 9: Cut \ufb02ow for the Z\u03bd\u03bdZ\u2113\u2113qq (m = 500 GeV) signal. All the cuts are described in detail in this\nsection.\nbackground can result from Z+jets production, where the tail of the missing transverse energy distribution\ncan fake a signal.\nAfter selecting the leptonically decaying Ze+e\u2212(Z\u00b5+\u00b5\u2212) boson as usual, with mass between 85 and\n97 GeV (83 and 99 GeV), a minimum /ET of 150 GeV is required. For this high value of /ET, Z+jets\nbackground is expected to be negligible for a Standard Model Higgs boson signal [39]. The forward jet\nselection is applied (see Section 4.3, pTcut = 20 GeV, Ecut = E2cut = 300 GeV, \u03b7cut = 1.5, \u2206\u03b7cut =\n4.5).\nThe transverse mass, de\ufb01ned as:\nm2\nT = (\nq\npT(Z)2 +m2\nZ + /ET)2 \u2212(\u20d7pT(Z)+ \u20d7/pT)2\n(1)\nis shown in Fig. 26 and the cut \ufb02ow can be found in Table 9.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1795\n\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\u0001\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\u0003\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n\u0002\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nQCD-like 500 GeV\nZ+jets\n\u0004\n\u0004\u0003\u0004\n\u0004\n\u0004\u0003\u0004\n\u0004\n\u0004\n\u0004\nSignal\n\u0005\n\u0005\u0001\u0005\u0001\u0005\n\u0005\n\u0005\u0001\u0005\u0001\u0005\n\u0005\n\u0005\u0001\u0005\u0001\u0005\n\u0005\n\u0005\u0001\u0005\u0001\u0005\nATLAS\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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07\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\n\u0007\n\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\n\u0007\n\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\n\u0007\n\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\u0003\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n\u0007\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nEWChL 800 GeV\nZ+jets\n\b\n\b\n\b\n\b\n\b\n\b\nSignal\n\t\n\t\u0001\t\u0001\t\n\t\n\t\u0001\t\u0001\t\n\t\n\t\u0001\t\u0001\t\n\t\n\t\u0001\t\u0001\t\nATLAS\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 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0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\n\u000b\n\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\n\u000b\n\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\u0003\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n\u000b\n[GeV]\nZW\nm\n500\n1000\n1500\n2000\n/ 100 GeV\n-1\nEvents / 1 fb\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nEWChL 1.1 TeV\nZ+jets\n\f\n\f\u0003\f\n\f\n\f\u0003\f\n\f\n\f\n\f\nSignal\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\n\r\n\r\u0001\r\u0001\r\nATLAS\nFigure 23: WZ invariant mass spectrum in the \u2113+\u2113\u2212j(j) channel for the three resonant signal samples\nobtained using k\u22a5algorithm approach. Z+jet histogram (in red) represents a direct sum of all Z+3 or 4\njets backgrounds with no matching, and hence is a conservative estimate. The background from t\u00aft events\nhas been found to be negligible.\nmass [GeV]\n200\n400\n600\n800\n1000\n1200\n1400\n/100GeV\n-1\nEvents/fb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n (1.1TeV)\nll\nZ\n\u03bdl\nW\n jj (SM)\nll\nZ\n\u03bdl\nW\nATLAS\nResonance mass\nFigure 24: Full reconstruction of ChL resonance\nm \u223c1.1 TeV (W\u2113\u00b1\u03bdZ\u2113\u00b1\u2113\u2213).\nmass [GeV]\n200\n300\n400\n500\n600\n700\n800\n/50GeV\n-1\nEvents/fb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n (500GeV)\nll\nZ\n\u03bdl\nW\n jj (SM)\nll\nZ\n\u03bdl\nW\nATLAS\nResonance mass\nFigure 25: Full reconstruction of QCD-like reso-\nnance m \u223c500 GeV (W\u2113\u00b1\u03bdZ\u2113\u00b1\u2113\u2213).\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1796\n\nmass [GeV]\n200\n300\n400\n500\n600\n700\n800\n/50GeV\n-1\nEvents/fb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\nqq (SM)\nll\nZ\n\u03bd\n\u03bd\nZ\nqq (SM)\nll\nZ\n\u03bdl\nW\nqq (500GeV)\nll\nZ\n\u03bd\n\u03bd\nZ\nATLAS\nResonance transverse mass\nFigure 26: Transverse mass of the m = 500 GeV resonance Z\u03bd\u03bdZ\u2113\u2113.\n6\nResults\nThe signi\ufb01cance of the signals and the luminosity required for a possible discovery is estimated here.\nFrom the reconstructed resonance mass distributions in Section 5 one can evaluate the size of the signal\nand background in the resonance mass window. Table 10 summarises the approximate cross sections\nexpected after the analyses described above. The table also gives the luminosity required to observe a\nsigni\ufb01cant excess over the background, showing the uncertainty from MC statistics only, and the signi\ufb01-\ncance of a signal for an integrated luminosity of 100 fb\u22121. Because of the large statistical and systematic\nuncertainties (see Section 7), the numbers given here must be taken as an only an approximate indication\nof the reach of the LHC for such resonances.\nThe signi\ufb01cance is calculated as\nsigni\ufb01cance =\np\n2((S+B)ln(1+S/B)\u2212S)\n,\n(2)\nwhere S (B) is the number of expected signal (background) events in the signal peak region, which is\nde\ufb01ned as the three consecutive bins (of size given in the \ufb01gures, chosen to represent the resolution),\nwith the highest total number of signal events. The background is averaged over this region.\nIn the WW case, only the semileptonic channel is accessible. Thus, as shown in Table 10, around 25\nfb\u22121 is needed to start seeing indications of a resonance even in the most optimistic case studied here,\nand around 70 fb\u22121 is needed for a discovery.\nIn the continuum case, the \u201csignal\u201d is spread over an extended mass region with a total of about 0.3\nevents expected for each fb\u22121 in the mass range m = 400\u20131900 GeV, compared to about 2.5 background\nevents. Measuring this cross-section with any accuracy using the techniques developed here would re-\nquire an integrated luminosity of several hundred fb\u22121.\nSince the mass windows for hadronic W and Z boson decays overlap, in practice these scenarios\ncan probably not be distinguished in this channel, and a combined analysis would in reality have to be\nperformed, which would then be compared to those channels containing a leptonic Z boson decay.\nFor each of the WZ resonances, results of the different channels, W\u2113\u03bdZ\u2113\u2113, Wj jZ\u2113\u2113and W\u2113\u03bdZ j j can,\nin principle, be combined. From Table 10, one can conclude that for two of three mass regions, m =\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1797\n\nProcess\nCross section (fb)\nLuminosity (fb\u22121)\nSigni\ufb01cance\nsignal\nbackground\nfor 3\u03c3\nfor 5\u03c3\nfor 100 fb\u22121\nWW/WZ \u2192\u2113\u03bd j j,\nm = 500 GeV\n0.31\u00b10.05\n0.79\u00b10.26\n85\n235\n3.3\u00b10.7\nWW/WZ \u2192\u2113\u03bd j j,\nm = 800 GeV\n0.65\u00b10.04\n0.87\u00b10.28\n20\n60\n6.3\u00b10.9\nWW/WZ \u2192\u2113\u03bd j j,\nm = 1.1 TeV\n0.24\u00b10.03\n0.46\u00b10.25\n85\n230\n3.3\u00b10.8\nWj jZ\u2113\u2113, m = 500 GeV\n0.28\u00b10.04\n0.20\u00b10.18\n30\n90\n5.3\u00b11.9\nW\u2113\u03bdZ\u2113\u2113, m = 500 GeV\n0.40\u00b10.03\n0.25\u00b10.03\n20\n55\n6.6\u00b10.5\nWj jZ\u2113\u2113, m = 800 GeV\n0.24\u00b10.02\n0.30\u00b10.22\n60\n160\n3.9\u00b11.2\nWjZ\u2113\u2113, m = 800 GeV\n0.27\u00b10.02\u00b10.05\n0.23\u00b10.07\u00b10.05\n38\n105\n4.9\u00b11.1\nWjZ\u2113\u2113, m = 1.1 TeV\n0.19\u00b10.01\u00b10.04\n0.22\u00b10.07\u00b10.05\n68\n191\n3.6\u00b11.0\nW\u2113\u03bdZ\u2113\u2113, m = 1.1 TeV\n0.070\u00b10.004\n0.020\u00b10.009\n70\n200\n3.6\u00b10.5\nZ\u03bd\u03bdZ\u2113\u2113, m = 500 GeV\n0.32\u00b10.02\n0.15\u00b10.03\n20\n60\n6.6\u00b10.6\nTable 10: Approximate signal and background cross sections expected after the analyses. An approxi-\nmate value of the luminosity required for 3\u03c3 and 5\u03c3 signi\ufb01cance, and the expected signi\ufb01cance for 100\nfb\u22121 are shown. The uncertainties, when given, are due to Monte Carlo statistics only.\n500 GeV and 800 GeV, a chiral Lagrangian vector resonance can be discovered with less than 100 fb\u22121.\nThe expectations with the alternative k\u22a5analysis described in Section 5.2.3 are not far from the values\nin Table 10. As an example, the integrated luminosity needed for 3\u03c3 observation of the m = 800 GeV\nsignal is 63 fb\u22121, and of the m = 1.1 TeV signal is 81 fb\u22121.\nA scalar resonance at m = 500 GeV will require about 60 fb\u22121 to be seen in the ZZ \u2192\u03bd\u03bd\u2113\u2113channel.\n7\nSystematic Uncertainties\nA number of large systematic uncertainties affect the signals studied here. Because of the small cross\nsections and the important backgrounds, it is dif\ufb01cult to estimate them with precision from Monte Carlo\nsimulations. Data driven tests will be required to understand better the systematic effects. Some discus-\nsion of the most signi\ufb01cant effects is given here.\n7.1\nBackground Cross sections\nAs was discussed in Section 2, the renormalisation and factorisation scales, Q2, can affect the cross\nsection by as much as a factor of two. This is especially true at high centre of mass energies, where\nthe degree of virtuality of partons and choice of scale for \u03b1s are quite critical [28, 29]. At present\nthis represents a theoretical uncertainty on the current sensitivity estimate. While the predictions may\nimprove in future, in an eventual analysis, the backgrounds would have to be measured from data and\nthe eventual size of the associated systematic uncertainty has not been studied here.\nAnother consideration is that for the analyses which dynamically move between the dijet and single\njet reconstruction technique for the hadronically decaying vector boson (see Section 4.1), to evaluate\nthe background with the samples available both W+3 jet and W+4 jet samples must be used. This\nimplies some double-counting due to the lack of parton-shower matching in these samples, and so the\nbackground will be overestimated. This is in addition to the fact that as shown in Section 2.4.1, the\nMADGRAPH samples used overestimate slightly the energy of the tag jets. The effect is expected to be\nat the few per cent level.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1798\n\n7.2\nSignal Cross sections\nThe PYTHIA signal generation produces softer tag jets than the more exact WHIZARD MC, and thus the\nsignal ef\ufb01ciencies are likely to be underestimated.\n7.3\nMonte Carlo Statistics\nWe are limited by the very large size of the background samples required. Fast MC simulation was\nshown to be in good agreement with full simulation and was used to evaluate t\u00aft background for the\nWW signals. In some cases, only upper limits on the backgrounds can be given, although it is expected\nthat these limits are very conservative. Again, this represents a systematic uncertainty on the current\nsensitivity estimates, but will not be present in a \ufb01nal data analysis, assuming suf\ufb01cient simulated data\nwill eventually be available.\n7.4\nPile-up and Underlying Event\nPile-up and underlying event are separate effects which have potentially similar and crucial impact on\nthe ef\ufb01ciency of the forward jet cuts, the central jet veto and the top veto, as well as on the jet mass\nresolution.\nOf particular concern is the fact that the top veto in the WW analysis uses jets down to pT = 10 GeV,\nexpected to be strongly affected by these effects [40]. Simply raising the cut to 20 GeV admits signif-\nicantly larger background. Some of this can be removed for the higher mass resonances by raising the\npT cut on the vector boson. However, a more promising approach is likely to be to exploit b-tagging and\nimproved jet mass reconstruction to improve the veto.\n7.4.1\nPile-up\nFully simulated samples with pile-up at low luminosity (1033cm\u22122s\u22121) were available, but with much\nlower statistics: we restricted the analysis to one signal sample and one background sample. However\npile-up effects should be approximately independent of the underlying physics sample, and we assume\nwe can safely generalise the results obtained here.\nWe compared the same events of the Wj jZ\u2113\u2113at m = 1.1 TeV sample reconstructed with and without\npile-up simulation. This allows computation of the fraction of events with pile-up having tagged forward\njets with respect to corresponding non-pile-up events which fail the tagged jet criterion, thus de\ufb01ning a\n\u2018fake\u2019 rate. The reciprocal fraction de\ufb01nes a \u2018miss\u2019 rate. The effect of pile-up increases with increasing\njet radius and decreasing energy threshold, as would be expected. We found that both \u2018fake\u2019 and \u2018miss\u2019\neffects are essentially due to the degradation of energy resolution in presence of pile-up and that their\ncombination contributes to an uncertainty on the ef\ufb01ciency of the order of 5%.\n7.4.2\nUnderlying Event\nCurrent simulations use underlying event models tuned to Tevatron and other data [22], but there is a\nlarge extrapolation needed to 14 TeV. The underlying event would be have to be measured in LHC data,\nand its level is not currently known.\n7.5\nOther Systematic Effects\nSystematic effects, such as uncertainties in the luminosity, in ef\ufb01ciencies and resolutions, jet energy\nscale, etc. are of the order of a few percent and will therefore be completely dominated by the above\neffects and by statistical uncertainties.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1799\n\n8\nSummary and Conclusion\nThe Chiral Lagrangian model with Pad\u00b4e unitarisation provides a framework for studying vector boson\nscattering at high mass, in case a light Higgs boson is not found at the LHC in the \ufb01rst years of running.\nWith full detector simulation, the search for vector and scalar resonances of masses m = 500, 800 and\n1100 GeV is studied. To suppress the very high backgrounds from W+jets and Z+jets to acceptable levels\nrequires special techniques investigated here. In particular, at these high masses, hadronic vector boson\ndecay results in a single jet. The reconstruction of the jet mass is found to be generally quite ef\ufb01cient\nat rejecting QCD jets. The k\u22a5and the cone algorithms can be applied to this heavy jet to resolve it into\ntwo light jets, suppressing further the background. Other conventional techniques for the study of vector\nboson fusion are also found essential for the present analysis: forward jet tagging, central jet veto and\ntop-jet veto.\nThe cut-based analysis presented here is performed with realistic simulation and reconstruction of\nleptons and jets. Improvements can be expected by more sophisticated analysis and, with real data and a\ngood understanding of the detector, further gains can be achieved by improvements in the reconstruction\nef\ufb01ciencies.\nThe discovery of resonances in vector boson scattering at high mass will take a few tens of fb\u22121, but\nthe different decay channels of the vector boson pairs allow a cross-check of the presence of a resonance.\nThese results can be considered generic of vector boson scattering and can therefore be interpreted in\nterms of other theoretical models with possibly different cross-sections.\nReferences\n[1] S. Dawson, hep-ph/9901280.\n[2] M. S. Chanowitz. Presented at the 23rd International Conference on High Energy Physics,\nBerkeley, Calif., Jul 16-23, 1986.\n[3] K. Lane and S. Mrenna, Phys. Rev. D67 (2003) 115011, hep-ph/0210299.\n[4] C. Csaki, C. Grojean, H. Murayama, L. Pilo, and J. Terning, Phys. Rev. D69 (2004) 055006,\nhep-ph/0305237.\nC. Csaki, C. Grojean, L. 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C32S2 (2004) 19\u201354, hep-ph/0402254.\nEXOTICS \u2013 VECTOR BOSON SCATTERING AT HIGH MASS\n1802\n\nDiscovery Reach for Black Hole Production\nAbstract\nModels with extra space dimensions, in which our Universe exists on a 4-\ndimensional brane embedded in a higher dimensional bulk space-time, offer a\nnew way to address outstanding problems in and beyond the Standard Model.\nIn such models the Planck scale in the bulk can be of the order of the elec-\ntroweak symmetry breaking scale. This allows the coupling strength of gravity\nto increase to a size similar to the other interactions, opening the way to the\nuni\ufb01cation of gravity and the gauge interactions. The increased strength of\ngravity in the bulk space-time means that quantum gravity effects would be\nobservable in the TeV energy range reachable by the LHC. The most spectac-\nular phenomenon would be the production of black holes, which would decay\nsemi-classically by Hawking radiation emitting high energy particles. In this\nnote, we discuss the potential for the ATLAS experiment to discover such black\nholes in the early data (1\u20131000 pb\u22121)\n1\nIntroduction\nIn this study we simulate the search for black holes in the \ufb01rst 100 pb\u22121 of LHC data with the ATLAS\ndetector and software framework.\nThe document\u2019s structure is as follows: Section 2 gives an overview of the extra dimension models,\npresent limits on the size of the extra dimensions and a discussion of black hole production and decay. In\nSection 3 the Monte Carlo simulation samples are described. Section 4 presents basic event properties,\nand is followed by Sections 5 and 6 dealing with the triggering and analysis selection, respectively. The\nexpected systematic uncertainties are given in Section 7. Finally, the extraction of model parameters,\nespecially of black hole properties, is covered in Section 8. A summary is given in Section 9.\n2\nTheory\n2.1\nTheoretical Motivation\nThe electroweak energy scale and the Planck scale, at which gravitational interactions become strong,\ndiffer by about sixteen orders of magnitude. This large difference between the scales of the two funda-\nmental interactions is known as the hierarchy problem. Explaining the hierarchy problem is one of the\noutstanding challenges in particle physics.\nArkani-Hamed, Dimopoulos and Dvali (ADD) [1\u20133], and Randall and Sundrum (RS) [4, 5] have\npioneered approaches to solving the hierarchy problem by using extra-dimensional space. The hierarchy\nis generated by the geometry of the additional spatial dimensions. ADD models postulate additional \ufb02at\nextra dimensions, while RS models invoke a single warped extra dimension. The observed weakness of\ngravity is thus due to the gravitational \ufb01eld being allowed to expand into the higher-dimensional space\n(bulk), while the Standard Model particles are con\ufb01ned to our familiar three-dimensional space (3-brane).\nExtra-dimensional models can also be motivated by string theory.\nIn extra-dimensional models, the D-dimensional Planck scale MD is the fundamental scale from\nwhich the Planck scale MPl = 1.22\u00d71019 GeV in four dimensions is derived1. The relationship between\n1Several conventions exist for the D-dimensional Planck scale in the ADD model. We denote by MD the parameter de\ufb01ned\nby Giudice, Rattazzi and Wells [6] and used by the PDG [7]: MD\u22122\nD\n= (2\u03c0)D\u22124/(8\u03c0GD), where GD is the D-dimensional\nNewton gravity constant. In an alternative convention given by Dimopoulos and Landsberg [8] the D-dimensional Planck scale\n1803\n\nthe two scales is determined by the volume of the extra dimensions in ADD models or by the warp factor\nin RS models. For large extra dimensions or a strongly warped extra dimension, the fundamental scale\nof gravity can be as low as the electroweak scale. If the Planck scale is low enough, black holes could be\nproduced at the Large Hadron Collider (LHC) [9,10]. Detecting them will not only test general relativity\nand probe extra dimensions, but would also teach us about quantum gravity.\n2.2\nExperimental Limits\nAssuming that low-scale gravity is due to the existence of extra dimensions2, most experimental searches\nfor unusual low-scale gravity effects have focused on detecting evidence for extra dimensions. Current\nexperimental limits allow the fundamental scale of gravity to be as low as about 1 TeV. In testing the\nADD models and deriving limits in these models, the compacti\ufb01cation radius of all extra dimensions is\nassumed to be the same. ADD models have been tested at length scales comparable to the radius of the\ncompacti\ufb01ed (i.e. curled-up) dimensions R. Were the effective number of large extra dimensions to be\nn = D \u22124, the inverse-square law would smoothly change from the 1/r2 form for r \u226bR to a 1/r2+n\nform for r \u226aR. Searches have been performed and constraints on the Planck scale have been set by\ntabletop and particle accelerator experiments, astrophysical observations, cosmic-ray measurements and\ncosmological considerations. Direct searches for black holes at collider experiments have not yet been\nperformed. The only direct limits on black hole production in high energy interactions were obtained\nusing cosmic-ray data. Table top experiments lead to an upper bound of R \u226444 \u00b5m, at the 95% con\ufb01dence\nlevel [12]. The LEP bounds obtained with direct searches vary from 1.5 TeV for n = 2 extra dimensions\nto 0.75 TeV for 5 extra dimensions [13]. The latest direct search result from the CDF collaboration has\nset lower bounds with 1.1 fb\u22121 of Run II data on MD of 1.33 TeV for n = 2 to 0.88 TeV for n = 6 [14]. All\nfour LEP experiments combined set a lower limit on MD of 1.2 TeV for positive interference, or 1.1 TeV\nfor negative interference between Standard Model diagrams and graviton exchange [15, 16]. Indirect\nsearches by the D\u00d8 [17] collaboration set lower limits around 1.28 TeV3. Astrophysics places the most\nstringent lower limits on MD in ADD models which however fall sharply with increasing number of\nextra dimension [18\u201324]. Considerations of neutron star dynamics imposes the strongest constraints:\nMD > 1760, 77, 9 and 2 TeV for n = 2, 3, 4 and 5 extra dimensions, respectively [18]. One should\nnote that all astrophysical and cosmological constraints are based on a number of assumptions, whose\nuncertainties are not included in the limit derivations, so the results are reliable only as order of magnitude\nestimates. Ultra high-energy cosmic-ray particles, through their interaction with the Earth\u2019s atmosphere,\noffer a complementary probe of extra dimensions. Cosmic-rays interact with the atmosphere and earth\u2019s\ncrust with centre-of-mass energies of the order of 100 TeV. The particles can produce black holes deep\nin the atmosphere, leading to quasi-horizontal giant air showers. So far a lower bound on MD in the\nADD model, ranging from 1.0 to 1.4 TeV for scenarios with 4 to 7 extra dimensions has been set at 95%\ncon\ufb01dence level [25]. It is expected that the Pierre Auger Observatory will be able to set more stringent\nlimits during the \ufb01rst \ufb01ve years of operation; the estimates place MD \u22733 TeV for n \u22654 [26].\n2.3\nWorking Model\nOur working model for black holes uses the black disk cross-section, which depends only on the horizon\nradius. The (4+n)-dimensional Myers-Perry solution [27], similar to the 4-dimensional Schwarzschild\nradius, is chosen for the horizon radius rh. It depends only on the number of dimensions and the Planck\nMDL is de\ufb01ned via MD\u22122\nDL\n= 1/GD.\n2See Ref. [11] for a model of TeV gravity in four dimensions.\n3This lower limit uses the Hewett approach for the calculation of MD and implies a positive interference term \u03bb with the\nStandard Model diagrams.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1804\n\nscale. The classical black hole cross-section at the parton level is\n\u02c6\u03c3ab\u2192BH = \u03c0r2\nh ,\n(1)\nwhere a and b are the parton types. In most cases, we work with initial black hole masses at least \ufb01ve\ntimes higher than the Planck scale at which the expression for the cross section should be valid.\nThe total cross-section is obtained by convoluting the parton-level cross-section with the parton dis-\ntribution functions (PDFs), integrating over the phase space, and summing over the parton types.\nThroughout this study we use the CTEQ6L1 (leading order with leading order \u03b1s) parton distribution\nfunctions [28] within the LHAPDF framework [29]. The momentum scale for the PDFs is set equal to\nthe black hole mass for convenience.\nThe transition from the parton-level to the hadron-level cross-section is based on a factorisation\nansatz. The validity of this formula for the energy region above the Planck scale is unclear. Even if\nfactorisation is valid, the extrapolation of the parton distribution functions into this transplanckian region\nbased on Standard Model evolution from present energies is questionable, since the evolution equations\nneglect gravity and possible KK states in the proton.\nThe details of horizon formation, and the balding and spin-down phases have been ignored4. The\nimportant effects of angular momentum in the production and decay of the black hole in extra dimen-\nsions are not accounted for in the Monte Carlo event generator. The black holes are considered as\nD-dimensional Schwarzschild solutions. Only the Hawking evaporation phase is generated by the simu-\nlation.\nWe can view the Hawking evaporation phase as consisting of two parts: determination of the particle\nspecies and assigning energy to the decay products. A particle species is selected randomly with a\nprobability determined by its number of degrees of freedom and the ratio of emissivities5. The degrees\nof freedom take into account polarisation, charge and colour. The emitted charge is chosen such that the\nmagnitude of the black hole charge decreases. All Standard Model particles are considered, including a\nHiggs boson6. The particles are treated as massless, including the gauge bosons and heavy quarks.\nGravitons have not been included in the simulation, which is another drawback of the current model.\nBecause the graviton lives in the bulk, the number of degrees of freedom of the graviton becomes sig-\nni\ufb01cant for high numbers of dimensions. In addition, the graviton emissivity is highly enhanced as the\nspace-time dimensionality increases. Therefore the black hole may lose a signi\ufb01cant fraction of its mass\ninto the bulk, resulting in missing transverse energy.\nThe energy assignment to the decay particles in the Hawking evaporation phase has been imple-\nmented as follows. The particle species selected by the model described above is given an energy ran-\ndomly according to its extra-dimensional decay spectrum. A different decay spectrum is used for scalars,\nfermions and vector bosons, i.e. the spin statistics factor is taken into account. Grey-body spectra are\nused without approximations [30]. The grey-body factors depend on the number of dimensions. The\nHawking temperature is updated after each decay. It is assumed the decay is quasi-stationary in the sense\nthat the black hole has time to come into equilibrium at each new temperature before the next particle is\nemitted. The energy of the particle given by the spectrum must be constrained to conserve energy and\nmomentum at each step.\nThe evaporation phase ends when the chosen energy for the emitted particle is ruled out by the\nkinematics of a two-body decay. At this point an isotropic two-body phase-space decay is performed. In\nour simulation, the decay is performed totally to Standard Model particles and no stable exotic remnants\nsurvive.\n4The main effects of these are to reduce the black hole production cross-section, possibly by as much as a few orders of\nmagnitude. Work is underway to try to estimate the magnitude of this.\n5Here emissivity is the fractional emission rate per degree of freedom. Mathematically it is ratio of dE/dt for different\nspecies, or roughly speaking the area under the black body distribution for a particular type of particle.\n6Including a scalar Higgs boson is not signi\ufb01cant since it has only one degree of freedom.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1805\n\nName\nDescription\nValue\nMINMSS\nMinimum mass of black holes\n5 TeV\nMAXMSS\nMaximum mass of black holes\n14 TeV\nMPLNCK\nPlanck scale\n1 TeV\nMSSDEF\nConvention for Planck scale\n2\nTOTDIM\nTotal number of dimensions\n6\nNBODY\nNumber of particles in remnant decay\n2\nGTSCA\nBlack hole mass used as PDF momentum scale\nTrue\nTIMVAR\nAllow TH to change with time\nTrue\nMSSDEC\nUse all Standard Model particles as decay products\nTrue\nGRYBDY\nInclude grey-body effects\nTrue\nKINCUT\nUse a kinematic cut-off on the decay\nTrue\nTable 1: Default parameters used in the CHARYBDIS generator.\nBaryon number, colour and electric charge are conserved in the black hole production and decay in\nthis model. Missing transverse energy in the generator comes only from the neutrinos, while in reality\nmissing transverse energy is also possible due to the lost energy in inelastic production, graviton emis-\nsion, a non-detectable black hole remnant and the possibility that the black hole can leave the Standard\nModel brane. For the black holes we consider, only a small amount of energy, on average, is lost due to\nneutrinos. If gravitons were considered, the average energy loss would be approximately 9% [31].\n3\nMonte Carlo Simulations\n3.1\nProduction of Signal and Background Events\nThe event generator CHARYBDIS [32, 33] version 1.003 was used within the ATLAS software frame-\nwork to generate Monte Carlo signal samples. It was interfaced via the Les Houches accord [29] to\nHERWIG [34, 35] which provides the parton evolution and hadronisation, as well as Standard Model\nparticle decays.\nTable 1 shows the default CHARYBDIS parameters used, for which approximately 25000 events\nwere generated. Three other black hole signal samples were generated with variations in the number of\ndimensions and in the black hole minimum mass. In all simulations, the parameter MSSDEF was set\nequal to 2, setting the Planck scale MPLNCK to be the D-dimensional Planck scale MDL in the con-\nvention of Ref. [8]. The above samples subsequently underwent the full ATLAS detector simulation\nand reconstruction. Fast simulation using ATLFAST [36] was employed to widen the range of signal\nsamples studied, enabling investigation of the many theoretical uncertainties modelled by generator pa-\nrameter switches (see Table 2).\nBlack holes decay democratically to all particles of the Standard Model, so few Standard Model\nprocesses should produce the same particle spectrum. Black hole decays are characterised by a number\nof high energy and transverse momentum objects, so the primary Standard Model backgrounds are states\nwith high multiplicity or high energy jets. The predominant backgrounds to our signal are described\nbelow and their datasets and cross-sections are listed in Table 3. Sizeable samples are required due to\ntheir large cross-sections at the LHC.\n\u2022 t\u00aft leptonic and hadronic decay modes. This process yields the largest contribution to the back-\nground due to its large cross-section at the LHC and the large branching ratio to hadronic \ufb01nal\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1806\n\nn\nmBH ( TeV)\n\u03c3 ( pb)\nNote\n2\n5-14\n40.7\n2\n8-14\n0.34\n4\n5-14\n24.3\n7\n5-14\n22.3\n2\n5-14\n6.4\nMPLNCK=2\n3\n5-14\n28.5\n5\n5-14\n22.7\n2\n5-14\n40.7\nKINCUT=0\n7\n5-14\n22.3\nKINCUT=0\n2\n5-14\n40.7\nTIMEVAR=0\n7\n5-14\n22.3\nTIMEVAR=0\n2\n5-14\n40.7\nNBODY=4\n7\n5-14\n22.3\nNBODY=4\nTable 2: Monte Carlo datasets and their respective cross-sections used in this analysis. The \ufb01rst four\nsamples were simulated using both full and fast simulations; the lower nine samples were simulated using\nthe fast simulation ATLFAST. The \ufb01nal column shows the CHARYBDIS parameter that was changed\nwith respect to the reference set shown in Table 1.\nstates. The matrix element calculation is done with MC@NLO [37] and HERWIG is used to\nperform the parton shower evolution, parton decay and their hadronisation.\n\u2022 QCD dijet production. The requirements placed on the hadronic part of the signal events reduces\nthe contribution from low-pTQCD jets. This background is generated using PYTHIA 6.4 [38].\nNote that the complete QCD inclusive jet production is not fully modelled by the PYTHIA dijet\nsimulation due to the lack of higher-order QCD contributions. Very low-statistics samples of\nmultijet samples generated by ALPGEN [39] were also used.\n\u2022 W \u2192\u2113\u03bd + jets production. These backgrounds, though coming from the hard process, have cross-\nsections that rapidly become small compared to the signal as more jets are added. Vector boson\nplus jets samples were generated using ALPGEN.\n\u2022 Z \u2192\u2113\u2113+ jets production.\n\u2022 \u03b3(\u03b3) + jets production.\n3.2\nDetector Simulation\nThe detector simulation and reconstruction of both signal and background Monte Carlo events were\nperformed within the ATLAS of\ufb02ine framework.\nFast simulation (ATLFAST) was used to widen the range of signal samples studied. The primary\nadvantage of this is one of processing rate: since no detector interactions are modelled it requires less than\none second per event. In contrast, full simulation requires approximately 15 minutes for typical Standard\nModel events, and over 30 minutes per black hole event. Despite this advantage, there are drawbacks:\nthe fast simulation does not include a complete treatment of lepton isolation and misidenti\ufb01cation nor of\nphoton conversion.\nThe same generator signal samples were passed through the full and fast simulations in order to\nunderstand the differences in black hole events. Variables ranging from simple multiplicities to event\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1807\n\nProcess\n\u03c3 ( pb)\nSemi/Fully Leptonic t\u00aft\n463\nHadronic t\u00aft\n370\nQCD dijets\n12.84\u00d7103\nW \u2192e\u03bde + jets\n281\nW \u2192\u00b5\u03bd\u00b5 + jets\n279\nZ \u2192ee + jets\n25.8\nZ \u2192\u00b5\u00b5 + jets\n26.0\n\u03b3 + jets\n5.00\u00d7103\n\u03b3\u03b3 + jets\n67.6\nTable 3: Background Monte Carlo datasets and their respective branching ratio times cross-sections.\nParticle Multiplicity\n0\n5\n10\n15\n20\n25\n30\nNumber / 1/ Event\n-4\n10\n-3\n10\n-2\n10\n-1\n10\nFull n=2\nFull n=7\nFast n=2\nFast n=7\nATLAS\nMET [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\nNumber / 50 GeV / Event\n-3\n10\n-2\n10\n-1\n10\nFull n=2\nFull n=7\nFast n=2\nFast n=7\nATLAS\nFigure 1: Total particle multiplicity and missing transverse energy distributions for signal samples from\nfast and full simulation.\nshapes were compared. Sample distributions of particle multiplicity and /ETare shown in Figure 1. The\nmultiplicity difference is due to differing default jet algorithms; we use a cone algorithm with radius\n\u2206R = 0.4 in the full simulation, whereas ATLFAST uses a k\u22a5algorithm. Using the same algorithm for\nboth samples gives very close agreement, nonetheless this discrepancy will have an effect in analyses\ndependent purely upon multiplicity information. All other variables investigated showed concordant\nresults.\n4\nEvent Properties\nThe high mass scale, and the thermal nature of the decay process, result in black hole events being\ncharacterised by a large number of high-pT\ufb01nal state particles, including all the Standard Model \ufb01elds.\nGraviton emission is also expected, but is not simulated in CHARYBDIS. Of the \ufb01nal state particles, the\ndetector can measure jets, electrons, muons and photons well, and will be able to reconstruct some of the\nZ and W bosons. The missing transverse energy, produced mainly by neutrino and graviton emission,\ncan also be measured. In this section, the data sample with two extra dimensions and black hole masses\nabove 5 TeV is used as the reference signal sample.\nA key feature of black hole decays is that the Hawking temperature is higher for larger n, for a given\nblack hole mass. A higher temperature produces higher energy emissions, with the consequence that the\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1808\n\nPdgId\n-30\n-20\n-10\n0\n10\n20\n30\n-1\nEvent\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n>5TeV \nBH\nn=2,M\nn=4\nn=7\n>8TeV \nBH\nn=2,M\nATLAS\nFigure 2: PDG code of particles emitted from black hole decay for a minimum black hole mass of 5 TeV\nand n = 2, 4 and 7 and for a minimum black hole mass of 8 TeV and n = 2 (|PdgId| = 1 \u2013 6 are quarks,\n11 \u2013 16 leptons, and 21 \u2013 25 gauge and Higgs bosons). The vertical axis shows multiplicity per black\nhole decay.\nenergy is shared between fewer particles. This has a signi\ufb01cant effect on the multiplicity and event shape\ndistributions. Similarly, the samples with a higher black hole low-mass cutoff produce more high energy\n\ufb01nal state particles.\n4.1\nParticle Types and Multiplicities\nFigure 2 shows the types of particles produced directly by black hole decay. The vertical axis shows\nthe average number of particles per black hole decay. From this \ufb01gure, we see that a heavier black hole\nhas more decay products. The particle-antiparticle balance is broken by the initial state of two protons\ncolliding. Moreover, due to conservation of energy and momentum, colour connection etc., a perfect\ndemocratic decay cannot be achieved, e.g., the number of top quarks is smaller than that of ligher quarks.\nThe possibility of identifying fermions and bosons and determining their branching ratios in black hole\ndecays was studied in [40].\nFigure 3 shows pT and pseudorapidity (\u03b7) distributions of particles produced directly from black\nhole decays. As expected, the shape depends little on particle type. Figure 4 shows the reconstructed\nmultiplicity of \ufb01nal-state jets, leptons and photons. Four signal samples are shown for n = 2, 4 and 7\nwith a minimum black hole mass of 5 TeV, and for n = 2 with a minimum black hole mass of 8 TeV. The\n\ufb01gure also compares the reference signal to the backgrounds. The multiplicity in the signal falls as n\nrises, because the black holes decay at a higher temperature.\n4.2\nEvent Shape\nAt \ufb01rst sight, one would expect black hole events to be very different from the background in event\nshape variables [38,41,42] such as sphericity, because of the high multiplicity thermal decay. However,\nthe event shape of the black hole events varies considerably with n, making such variables less useful\nthan could be hoped. Though the background distributions show less variation, when these are scaled\nby their large cross sections, there is a large degree of overlap, disfavouring their use as a cut variable.\nAdditionally, our ignorance of the decay modes of the \ufb01nal black hole remnant introduces a signi\ufb01cant\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1809\n\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\nNormalized Unit\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n>5TeV\nBH\nn=2,M\nn=4\nn=7\n>8TeV\nBH\nn=2,M\nATLAS\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\nNormalized Unit\n0\n0 01\n0 02\n0 03\n0 04\n0.05\n0 06\n0 07\n0 08\n0 09\n>5TeV\nBH\nn=2,M\nn=4\nn=7\n>8TeV\nBH\nn=2,M\nATLAS\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\nNormalized Unit\n0\n0 01\n0.02\n0.03\n0.04\n0 05\n0.06\n0.07\n0.08\n0.09\n>5TeV\nBH\nn=2,M\nn=4\nn=7\n>8TeV\nBH\nn=2,M\nATLAS\nEta\n-4\n-2\n0\n2\n4\nNormalized Unit\n0\n0 02\n0 04\n0 06\n0 08\n0.1\n>5TeV\nBH\nn=2,M\nn=4\nn=7\n>8TeV\nBH\nn=2,M\nATLAS\nFigure 3: Generator pT distributions (top row): leptons (left) and Z bosons (right) emitted from the black\nhole. The bottom row shows pT and \u03b7 spectra for all particles emitted from the black hole.\nMultiplicity\n0\n5\n10\n15\n20\n25\n-1\nEvents / 1/ fb\n1\n10\n2\n10\n3\n10\n4\n10\nn=2, m>5TeV\nn=4\nn=7\nn=2, m>8TeV\nATLAS\nMul iplicity\n0\n5\n10\n15\n20\n25\n-1\nEvents / 1/ fb\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 4: Multiplicities of reconstructed objects for (left) black hole samples and (right) backgrounds.\nThey are normalised to the integrated luminosity of 1 fb\u22121.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1810\n\nCircularity\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nEvents / 0.05/ fb\n1\n10\n2\n10\n3\n10\n4\n10\nn=2, m>5TeV\nn=4\nn=7\nn=2, m>8TeV\nATLAS\nCircularity\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nEvents / 0.05/ fb\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 5: Circularity calculated from reconstructed objects for (left) black hole samples and (right)\nbackgrounds.\nThrust\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n-1\nEvents /0 025/ fb\n1\n10\n2\n10\n3\n10\n4\n10\nn=2, m>5TeV\nn=4\nn=7\nn=2, m>8TeV\nATLAS\nThrust\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n-1\nEvents /0 025/ fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 6: Thrust calculated from reconstructed objects for (left) black hole samples and (right) QCD\ndijet and t\u00aft backgrounds.\nsystematic effect. In our version of CHARYBDIS, once the mass of the black hole has dropped below\nthe Planck scale, the remnant decays to either 2 or 4 bodies. We have selected the two-body option for\nour standard samples. This means that at high n, where events can reach this stage after few emissions,\nthe circularity of the events is reduced, and the thrust increased.\nThe distinguishing power between signal and backgrounds of a selection of event shape variables was\nstudied; Figure 5 shows the circularity distribution for the same samples as Figure 4; similarly Figs. 6\nand 7 show their thrust distributions, sphericity and aplanarity. The expected bias towards more \u201cjet-\nlike\u201d events is clearly seen at high n. For this reason, we choose not to use event shape variables as a\ndiscriminant in this analysis.\n5\nTrigger\nThe ATLAS trigger and data-acquisition system consists of three levels (L1, L2, EF) of online event\nselection [43]. Each subsequent trigger level re\ufb01nes the decisions made at the previous level and may\napply additional selection criteria. The ATLAS trigger is described in detail in ref. [44].\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1811\n\n(a) Thrust major\n(b) Thrust minor\nThrust Major\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nEvents / 0.05/ fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nBH n=2\nBH n=7\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nThrust Minor\n0\n0.1\n0 2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nEvents / 0.05/ fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nBH n=7\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\n(c) Sphericity\n(d) Aplanarity\nSphericity\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n-1\nEvents / 0.05/ fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\nBH n=2\nBH n=7\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nAplanarity\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n-1\nEvents /0.025/ fb\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nBH n=7\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 7: Different event shape variables for black hole samples and backgrounds. They are normalised\nto the integrated luminosity of 1 fb\u22121.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1812\n\n [GeV]\nrec\nT\np\n0\n200 400 600 800 1000 1200 1400 1600 1800 2000\n \n \n \nEfficiency\n0.2\n0.4\n0.6\n0.8\n1\n150GeV\n300GeV\n400GeV\n600GeV\n800GeV\nATLAS\na)\n [GeV]\nrec\nT\np\n0\n200 400 600 800 1000 1200 1400 1600 1800 2000\n \n \n \nEfficiency\n0\n0 2\n0.4\n0.6\n0 8\n1\n150GeV\n300GeV\n400GeV\n600GeV\n800GeV\nATLAS\nb)\n [GeV]\nrec\nT\np\n0\n200 400 600 800 1000 1200 1400 1600 1800 2000\n \n \n \nEfficiency\n0.2\n0.4\n0.6\n0.8\n1\n150GeV\n300GeV\n400GeV\n600GeV\n800GeV\nATLAS\nc)\nFigure 8: Simulated jet trigger ef\ufb01ciencies as functions of the of\ufb02ine reconstructed jet pTfor a) L1, b) L2\nand c) EF. The ef\ufb01ciencies are determined for different pT-thresholds: 150 GeV (black), 300 GeV (red),\n400 GeV (blue), 600 GeV (magenta) and 800 GeV (cyan).\n5.1\nTriggering on Black Holes\nEach black hole produces multiple decay products, including hadronic jets, leptons and photons, as\ndescribed in Section 4. The jets typically carry a dominant fraction of the visible decay energy and hence\nprovide the best option for triggering black hole events.\nThe response of the jet trigger, as simulated in the current version of the ATLAS detector simulation,\nis demonstrated in Figure 8. The plots show the trigger ef\ufb01ciencies for various pT-thresholds as functions\nof the jet pT reconstructed of\ufb02ine. For these plots, a match between the jet reconstructed of\ufb02ine and at\nthe respective trigger level is required. The matching consists of searching for the closest of\ufb02ine jet in\n\u2206R =\np\n(\u2206\u03b7)2 +(\u2206\u03c6)2, where \u2206\u03b7 and \u2206\u03c6 are the distances between the reconstructed jet and the trigger\njet in pseudorapidity \u03b7 and azimuth \u03c6, respectively. To avoid incorrect matching for L1 jets, a modi\ufb01ed\ncriterion is applied: the L1 jet closest in energy to the reconstructed jet is chosen among the jets found\nwithin the \u2206R = 0.5 distance around the reconstructed jet. The shape of the L1 ef\ufb01ciency distribution\nfor the 800 GeV threshold is due to the saturation of the L1 trigger tower energies at 255 GeV. Events in\nwhich the transverse energy in one trigger tower exceeds 255 GeV are automatically accepted, as larger\nvalues \ufb01ll up the memory of the L1 trigger analog-to-digital converters.\nThe ef\ufb01ciency at each trigger level is determined independently of the decisions at the other levels.\nWere the trigger chain to have the same threshold on all levels, the total ef\ufb01ciency would be the con-\nvolution of the respective functions. The L2 algorithms are based on regions of interest provided by\nL1, hence it is not possible to determine their ef\ufb01ciency completely independently of the L1 decisions.\nThe L2 algorithms were run on all L1 jet RoI starting from the lowest L1 jet pTthreshold of 35 GeV.\nThis is much lower than the thresholds studied, making the L2 decision (shown in Figure 8b) virtually\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1813\n\nTrigger Threshold [GeV]\n100\n200\n300\n400\n500\n600\n700\n800\n900\nEfficiency\n0 5\n0.6\n0.7\n0 8\n0 9\n1\nLevel 1\nLevel 2\nEvent Filter\nATLAS\na)\nTrigger Threshold [GeV]\n100\n150\n200\n250\n300\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLevel 1\nLevel 2\nEvent Filter\nATLAS\nb)\nTrigger Threshold [GeV]\n100\n150\n200\n250\n300\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nLevel 1\nLevel 2\nEvent Filter\nATLAS\nc)\nFigure 9: Simulated jet trigger ef\ufb01ciencies for black hole events from the signal sample with n = 2 and\nm > 5 TeV as functions of the jet pTthreshold for a) single-jet trigger, b) 3-jet trigger and c) 4-jet trigger.\nThe ef\ufb01ciencies are determined for L1 (black), L2 (red) and EF (blue).\nindependent of the L1 ef\ufb01ciency.\nThe total trigger ef\ufb01ciencies are listed in Table 4 for three signal samples and demonstrated in Fig-\nure 9 for the signal sample with n = 2 and m > 5 TeV. The highest ef\ufb01ciency is provided by the single-jet\ntrigger, which we consider to be the master trigger for the black hole events. The presence of multiple\nhigh-pT jets per event, each of which is likely to pass the trigger, results in very high total ef\ufb01ciencies.\nSetting this trigger threshold at 400 GeV will provide greater than 99% ef\ufb01ciency at all trigger levels.\nThe Standard Model process rate at this threshold is expected to be less than 0.1 Hz at an instantaneous\nluminosity of 1031 cm\u22122s\u22121, which should allow this trigger to run at this threshold without prescaling\nfor the \ufb01rst few years of LHC data taking. The rate of black hole events is expected to be less than 5 mHz\nat the 1031 cm\u22122s\u22121 luminosity. For the start-up running at the luminosity of 1031 cm\u22122s\u22121, it is planned\nto set the highest threshold for the single-jet trigger at 120 GeV, guaranteeing an ef\ufb01ciency of almost\n100% for black hole events.\nAlternatively, a trigger based on the scalar sum of transverse energies of all recorded decay products\n(\u201csum-ET trigger\u201d) can be used. No simulation of this trigger is available in the samples used in this\nstudy. Looking at this sum in the of\ufb02ine reconstruction suggests that this trigger would collect nearly\n100% of black hole events for Planck scales above 1 TeV. It is foreseen to run this trigger in the start-up\ndata taking, unprescaled at the threshold of 650 GeV.\nBased on experience from previous collider experiments, one may expect detector hardware problems\nat the beginning of data taking. In particular, noisy channels in the calorimeter or trigger electronics may\ncause high trigger rates for the single-jet trigger and for the sum-ET trigger, such that even the highest\nthreshold triggers have to be prescaled. In such cases, a multijet (3- or 4-jet) trigger is considered for use\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1814\n\na) CHARYBDIS: n = 2,m > 5 TeV\nTrigger\nL1\nL2\nEF\nj100\n1\n1\n1\nj400\n0.997\n0.997\n0.997\n3j100\n0.998\n0.998\n0.998\n3j250\n0.972\n0.971\n0.971\n4j100\n0.985\n0.985\n0.985\n4j250\n0.865\n0.862\n0.862\nb) CHARYBDIS: n = 4,m > 5 TeV\nTrigger\nL1\nL2\nEF\nj100\n1\n1\n1\nj400\n0.997\n0.997\n0.996\n3j100\n0.952\n0.952\n0.952\n3j250\n0.886\n0.885\n0.885\n4j100\n0.807\n0.806\n0.806\n4j250\n0.612\n0.607\n0.607\nc) CHARYBDIS: n = 7,m > 5 TeV\nTrigger\nL1\nL2\nEF\nj100\n1\n1\n1\nj400\n0.990\n0.987\n0.985\n3j100\n0.807\n0.806\n0.805\n3j250\n0.710\n0.704\n0.704\n4j100\n0.525\n0.522\n0.522\n4j250\n0.343\n0.341\n0.341\nTable 4: Simulated jet trigger ef\ufb01ciencies for black hole events as functions of the jet-pTthreshold for\ndifferent simulation samples.\nuntil the detector problems are resolved. The ef\ufb01ciencies of such triggers are listed in Table 4.\nIn the present study, the minimum mass of a black hole is set at 5 TeV or more in order to be safely\nabove the Planck scale. At lower masses one may expect an increased rate of dijet events described by\na contact interaction. The single-jet trigger or the sum-ET trigger at the thresholds considered above are\nwell suited for detecting such signatures. Such events may not, however, be selected by multijet triggers.\nThe trigger ef\ufb01ciencies, studied here in the simulation, have to be determined from data. An unbiased\ndetermination requires an \u201corthogonal\u201d trigger, e.g. a trigger based on fully independent information\nfrom that used by the master trigger. A muon trigger which is based solely on signals in the muon\ndetector should be well suited for such studies.\n6\nSignal Selection and Background Rejection\n6.1\nEvent Selection\nSince all types of Standard Model particles are produced from black hole decay, we make full use of\nparticle identi\ufb01cation information (PID) from our detectors. First we select muons, electrons, photons\nand jets, which are called objects in this section. Table 5 shows the details of their selection criteria.\nThe identi\ufb01cation of objects is sometimes ambiguous: e.g., an electron could be simultaneously\nreconstructed as a jet. To resolve this, we apply PID to each object, selecting muons, electrons, photons\nand jets in that order of priority. Once an object passes the PID criteria in a given category, any remaining\nambiguous assignments are removed if they match the chosen object within a \u2206R of less than 0.1.\nNext we select black hole events using these objects as described below. Then we reconstruct a\nblack hole from all the identi\ufb01ed objects for the selected event. The mass of the black hole in an event\nis calculated from the four-momenta of the reconstructed \ufb01nal state objects and missing ET, which is\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1815\n\nincluded in the calculation to improve the reconstructed mass resolution:\npBH = \u2211\ni=objects\npi +(/ET, /ET x, /ET y,0) ,\n(2)\nmBH =\nq\np2\nBH .\n(3)\nWe present two methods to select black hole events. One is based on the scalar summation of pT\nand the other on the multiplicity of high-pT objects. Both make use of the characteristic of a black hole\nhaving large mass. After that, we require a high-pT lepton to reject backgrounds further.\nFigure 10 shows the scalar summation of the pT of each object, \u2211|pT|, which demonstrates good\nbackground discrimination and high signal ef\ufb01ciency for all black hole samples. We require \u2211|pT| to be\nlarger than 2.5 TeV to reject backgrounds. This requirement is relatively unaffected by changes in the\nmodel, in particular by changes to the number of extra dimensions n. Figure 11 shows mBH distributions\nafter this requirement. The QCD dijet background is already well suppressed, but we also investigated\nthe effect of a further selection, requiring a lepton with a pT > 50 GeV. This resulted in the QCD dijet\nbackground being rejected by a factor greater than 106 as shown in Table 6, which summarises the event\nnumbers for an integrated luminosity of 1 fb\u22121. Though the high statistics QCD samples used were\ngenerated with PYTHIA, a leading order generator, there were also pT-sliced small ALPGEN multijet\nsamples available. When investigated using the \u2211|pT| and lepton cut method, a very similar, marginally\nlower number of background events was predicted according to the very limited statistics available.\nLarger scale studies would be needed to conclude anything more concrete. Poisson con\ufb01dence limits are\nused for samples where fewer than 20 events passed the requirements. Signal cross-section errors are\nstatistical only; the theoretical uncertainties are large as discussed in Section 2. 7\nAn alternative selection procedure was also used. Figure 12 shows the pT distributions of the leading,\n2nd-, 3rd- and 4th-leading objects out of all the selected objects. The 4th-leading object still has larger pT\nin the signal events than in the background events. We require the number of objects with pT > 200 GeV\nto be equal to or greater than four. Figure 14 (left) shows mBH distributions after this requirement. Since\nQCD processes still remain large, a lepton requirement is again used to decrease it. Figure 13 shows the\ndistribution of the highest pT lepton (muon or electron). As expected, the number of leptons from QCD\nprocesses is small. Requiring the number of leptons (muons or electrons) with pT > 200 GeV to be equal\nto or greater than one results in the mBH distributions shown in Figure 14(right).\nThe shape of the background in the region of high mBH was \ufb01tted with a gaussian plus an asymmetric\ngaussian (Figure 15) and that function is used to estimate the number of background events.\nCHARYBDIS does not include graviton emission. In practice this, and the energy lost in gravita-\ntional interactions during the balding phase, would be another source of /ET. Consequently we expect\n7In the case of two hadronic subsamples (tt and dijets) where very few events passed the \u2211|pT | requirement, the lepton\nrequirement rejection factor was applied to the \u2211|pT | requirement\u2019s Poisson bound to estimate the background distribution\nerror.\n(a) muon\n(b) electron\n|\u03b7| < 2.5, pT > 15 GeV\nCentral track match (0 \u2264\u03c72 < 100)\nIsolation ET,cone0.2 < min(100,0.2pT +20) GeV\n|\u03b7| < 2.5 except for 1.00< |\u03b7| <1.15, 1.37< |\u03b7| <1.52\npT > 15 GeV\nmedium selection [45]\n(c) photon\n(d) jet\n|\u03b7| < 2.5, pT > 15 GeV\ntight selection [45]\nIsolation ET,cone0.2 < 0.2pT +20 GeV\nCone algorithm (R = 0.4) based on calorimeter towers\n|\u03b7| < 2.5, pT > 20 GeV\nTable 5: Particle selection\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1816\n\n| [GeV]\nT\nSum |P\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n-1\nEvents / 200 GeV / fb\n1\n10\n2\n10\n3\n10\nn=2, m>5TeV\nn=4\nn=7\nn=2, m>8TeV\nATLAS\n| [GeV]\nT\nSum |P\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n-1\nEvents / 200 GeV / fb\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 10: \u2211|pT| distributions for (left) black hole samples and (right) backgrounds (QCD dijet, t\u00aft and\nvector boson plus jets), along with one signal sample for reference. They are normalised to an integrated\nluminosity of 1 fb\u22121.\nReconstructed BH Mass [GeV]\n0\n1000 2000 3000 4000 5000 6000 7000 8000 900010000\n-1\nEvents / 200 GeV / fb\n-1\n10\n1\n10\n2\n10\n3\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nReconstructed BH Mass [GeV]\n0\n1000 2000 3000 4000 5000 6000 7000 8000 900010000\n-1\nEvents / 200 GeV / fb\n-1\n10\n1\n10\n2\n10\n3\n10\nBH n=2\nQCD\nZ+jets\nW+jets\nttbar\nATLAS\nFigure 11: Black hole mass distribution with a requirement \u2211|pT| >2.5 TeV (left), and black hole mass\ndistribution with an additional requirement on the lepton-pT of pT > 50 GeV (right). The signal sample\nwith n = 2 and m > 5 TeV and backgrounds are shown.\nDataset\nBefore selection\n\u2211|pT| > 2.5 TeV\nAfter requiring a lepton\nacceptance\n(fb)\n(fb)\n(fb)\nn = 2,m > 5 TeV\n40.7\u00b10.1\u00d7103\n39.2\u00b10.3\u00d7103\n18.6\u00b10.2\u00d7103\n0.46\nn = 4,m > 5 TeV\n24.3\u00b10.1\u00d7103\n22.6\u00b10.2\u00d7103\n6668\u00b183\n0.27\nn = 7,m > 5 TeV\n22.3\u00b10.1\u00d7103\n20.1\u00b10.2\u00d7103\n3574\u00b160\n0.17\nn = 2,m > 8 TeV\n338.2\u00b11\n338.1\u00b12.5\n212\u00b116\n0.63\nt\u00aft\n833\u00b1100\u00d7103\n23.6+12.2\n\u22126.7\n8.2+2.43\n\u22122.43\n9.8\u00d710\u22126\nQCD dijets\n12.8\u00b13.7\u00d7106\n5899+1773\n\u22121771\n5.37+3.25\n\u22122.02\n4.3\u00d710\u22127\nW\u2113\u03bd + \u22652 jets\n1.9\u00b10.04\u00d7106\n12.3+9.0\n\u22121.8\n4.67+8.75\n\u22120.93\n2.4\u00d710\u22126\nZ\u2113\u2113+ \u22653 jets\n51.8\u00b11\u00d7103\n2.75+2.02\n\u22122.01\n2.57+0.95\n\u22120.64\n5.0\u00d710\u22125\nTable 6: Acceptance for each signal and background dataset in fb after requiring \u2211|pT| >2.5 TeV, and a\nlepton with pT > 50 GeV.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1817\n\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n-1\nEvents/50GeV/fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nOther BG\nATLAS\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n-1\nEvents/50GeV/fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nOther BG\nATLAS\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n-1\nEvents/50GeV/fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nOther BG\nATLAS\nPt[GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n-1\nEvents/50GeV/fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nBH n=2\nQCD\nOther BG\nATLAS\nFigure 12: pT distributions of leading (top left), 2nd- (top right), 3rd- (bottom left) and 4th-leading\n(bottom right) objects out of all the selected objects for the signal sample with n = 2 and m > 5 TeV and\nbackgrounds (see Table 7).\nP [GeV]\n0\n200\n400\n600\n800\n1000 1200 1400 1600 1800 2000\n-1\nEvents/50GeV/fb\n1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nBH n=2\nQCD\nOther BG\nATLAS\nFigure 13: pT distributions of the leading lepton (electron or muon) after requiring the number of ob-\njects (electron, muon, photon or jet) with pT > 200 GeV to be larger than 3 for the signal sample with\nn = 2 and m > 5 TeV and backgrounds (see Table 7).\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1818\n\n[GeV]\nBH\nM\n0\n1000 2000 3000 4000 5000 6000 7000 8000 9000 10000\n-1\nEvents/100GeV/fb\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nBH n=2\nQCD\nOther BG\nATLAS\n[GeV]\nBH\nM\n0\n1000 2000 3000 4000 5000 6000 7000 8000 9000 10000\n-1\nEvents/100GeV/fb\n1\n10\n1\n10\n2\n10\n3\n10\nBH n=2\nQCD\nOther BG\nATLAS\nFigure 14: Black hole mass distribution for the signal sample with n = 2 and m > 5 TeV and backgrounds\n(see Table 7) after multiplicity requirement of at least 4 objects with pT > 200 GeV (left plot) and an\nadditional requirement of a lepton (electron or muon) with pT > 200 GeV (right plot).\nDataset\nBefore selection\nAfter multi-object\nAfter lepton requirement\nAcceptance\n(fb)\nrequirement (fb)\n(fb)\nn = 2,m > 5 TeV\n40.7\u00d7103\n38.9\u00b10.4\u00d7103\n14.0\u00b10.2\u00d7103\n0.34\nn = 4,m > 5 TeV\n24.3\u00d7103\n17.9\u00b10.3\u00d7103\n4521\u00b1126\n0.19\nn = 7,m > 5 TeV\n22.3\u00d7103\n9953\u00b1185\n1956\u00b182\n0.087\nn = 2,m > 8 TeV\n338\n338\u00b14\n164\u00b13\n0.49\nt\u00aft\n833\u00d7103\n129\u00b127\n36+12\n\u22129\n4.3\u00d710\u22125\nQCD dijets\n12.8\u00d7106\n38.9\u00b11.9\u00d7103\n6+107\n\u22123\n5.6\u00d710\u22127\nW+jets\n560\u00d7103\n99+28\n\u221222\n56+24\n\u221213\n1\u00d710\u22123\nZ+jets\n51.8\u00d7103\n29+90\n\u22124\n19+90\n\u22123\n4\u00d710\u22124\n\u03b3(\u03b3)+jets\n5.1\u00d7106\n285+87\n\u221276\n0+40\n\u22120\n< 10\u22125\nTable 7: Acceptance of the 4-object requirements for each dataset in fb. 90% con\ufb01dence limits are used\nwhen no events passed the requirements.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1819\n\nGeV\nBH\nM\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n9000 10000\n-1\nEvents/200GeV/fb\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\ngaussian\nasymmetric gaussian\nsum of both\nATLAS\nFigure 15: The background shape after the 4-object and lepton requirements is shown (data points). The\npoints were \ufb01tted by the sum (black line) of a gaussian (red line) and an asymmetric gaussian (green\nline).\nCHARYBDIS to underestimate this for black hole events. Nonetheless, each of the black hole samples\nstudied in this analysis often have very wide distributions of /ET, with tails extending out to several TeV.\nThis property of models with black holes is most unusual and hard to reproduce in other new physics\nscenarios, and should make it possible to distinguish between Black Holes and the majority of SUSY\nmodels for example.\nA requirement on /ET above \u223c500 \u2212600 GeV was studied as an alternative to a lepton require-\nment for black hole signal selection. Figure 16 shows the potential of this method, and contrasts these\nmodels with three common supersymmetric models of different cross-section and mass scale. Despite\nthe possibility of early evidence for the presence of black holes, there are disadvantages to relying on\nsuch a selection. Firstly, our ability to reconstruct the black hole\u2019s mass is aided by limiting /ET to be\nunder 100 GeV (Figure 22). Such a signal from high /ET events would be dominated by those events\nreconstructed most poorly, limiting their use for cross-section measurement and discovery. The theo-\nretical uncertainties are large and dif\ufb01cult to quantify, and \ufb01nally there are experimental dif\ufb01culties in\ncalibrating and accurately measuring this variable across a wide energy range.\n6.2\nDiscovery Reach\nMaking a robust discovery potential for black hole events is dif\ufb01cult, because the semi classical assump-\ntions used to model them are only valid well above the Planck scale. Close to the Planck scale, events\nmay occur due to gravitational effects with lower multiplicities, but without the signatures anticipated\nby our event selections. As the energy rises above the threshold needed for black hole creation, our\nrequirements should become more ef\ufb01cient. Lack of theoretical understanding makes it impossible to\nmodel this threshold region.\nTo account for this, we impose a lower requirement on the true mass of black holes created in our\nsimulated samples, BHthresh, normally set at 5 TeV, and we do not attempt to account for any additional\nsignal from lower masses. In order to estimate the discovery potential, two methods have been consid-\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1820\n\nMET [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\n-1\nEvents / 50 GeV / fb\n10\n2\n10\n3\n10\n4\n10\nn=2, m>5TeV\nn=4\nn=7\nn=2, m>8TeV\nBkg\nATLAS\nMET [GeV]\n0\n200\n400\n600\n800 1000 1200 1400 1600 1800 2000\n-1\nEvents / 50 GeV / fb\n1\n10\n2\n10\n3\n10\n4\n10\nn=2, m>5TeV\nn=7\nSU3 Bulk\nSU4 Low Mass\nSU6 Funnel\nBkg\nATLAS\nFigure 16: The left hand plot shows the missing transverse energy distributions after a \u2211|pT| > 2.5 TeV\nrequirement. A requirement of /ET> 500 GeV would leave negligible background and a large number of\nsignal events for all samples. The right hand plot compares two black hole samples with three supersym-\nmetric models with a range of mass scales; the two classes of models can easily be distinguished by their\ndiffering cross-sections and the extent of the /ET tail.\nered:\n1. we keep our signal selection requirements constant, and increase the value of BHthresh. Since the\nanalysis requirements are unchanged, the background remains constant, while the signal drops as\nthe production of events occurs at higher mass. We then evaluate the luminosity required to detect\na minimum of 10 signal events, with S/\n\u221a\nB > 5, assuming the production cross-section is as high\nas predicted. Such a study is shown in Figure 17, using the \u03a3|pT| and lepton requirements. This\nmethod produces conservative limits, taking some account of the uncertainty in the production\ncross-section near the threshold.\n2. We keep the production model unchanged with BHthresh = 5 TeV, but apply an additional require-\nment on the reconstructed black hole mass. This requirement reduces substantially background\nevents, while allowing the higher mass signal to pass unchanged. This is less conservative, since it\nallows black hole signal events to be produced at low mass, but to migrate above the reconstructed\nmass requirement because of the detector mass resolution, hence increasing the signal. As be-\nfore, we use the nominal value of the production cross-section, and evaluate the luminosity needed\nto meet our discovery criteria, this time as a function of reconstructed mass. A study using this\nmethod is shown in Figure 18 using the 4-object and lepton requirements.\nThe two approaches are complementary and illustrate the uncertainties in different ways. We observe\nthat the search reach is limited eventually at high mass by the falling production cross-section, re\ufb02ecting\nthe falling parton luminosity and the limited energy of the LHC. We conclude that, if the semi classical\ncross-section estimates are valid, black holes can be discovered above a 5 TeV threshold with a few pb\u22121\nof data, while 1 fb\u22121 would allow a discovery to be made even if the production threshold was at 8 TeV.\n7\nSystematic Uncertainties\n7.1\nSignal uncertainties\nWe have investigated the systematic uncertainties using fast simulation runs, having checked that the full\nand fast simulations agree well for this purpose.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1821\n\nBH Mass Threshold [TeV]\n5\n5.5\n6\n6.5\n7\n7.5\n8\n8.5\n9\n9.5\n]\n-1\nIntegrated Luminosity [fb\n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\n4\n10\nATLAS\nn=2\nn=4\nn=7\nFigure 17: Discovery potential using \u2211|pT| and lepton selections: required luminosity as a function of\nblack hole mass threshold. Error bars re\ufb02ect statistical uncertainties only.\nTeV\nBH cut\nM\n5\n5.5\n6\n6.5\n7\n7.5\n8\n8.5\n9\n-1\nfb\nIntegrated Luminosity \n-4\n10\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\nn=2\nn=4\nn=7\nATLAS\nFigure 18: Discovery potential for black holes using four-object and lepton requirements. The required\nluminosity is shown as a function of the requirement on the reconstructed black hole mass. The error\nbars correspond to experimental systematic uncertainties. (See text for constraints.)\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1822\n\nThere are a number of theoretical parameters associated with CHARYBDIS which can generate\nsystematic errors in the estimates of the acceptance for signal events. These are:\n\u2022 The kinematic cutoff. This parameter is normally true, and causes the generator to end thermal\nemission if an unphysical emission is randomly selected. The generator moves immediately to the\n\ufb01nal remnant decay phase. This approximation deteriorates at high numbers of extra dimensions\nbecause of the high temperature and emitted particle energies. We have investigated the alternative,\nwhere a new emission is selected until a physical one is chosen. In this case, thermal emission will\ncontinue until the black hole mass falls below MDL.\n\u2022 Temperature variation. The Hawking temperature of the black hole is normally allowed to increase\nas its mass decreases, as expected if the black hole has time to equilibrate between decays. We\nhave investigated the alternative of keeping the temperature \ufb01xed at the initial value, as would be\nthe case if the black hole decayed very quickly or \u201csuddenly\u201d (see Table 8).\n\u2022 Number of extra dimensions. In addition to our full simulation samples with n = 2, 4 and 7, we\nhave simulated n = 3 and 5 with the fast simulation. As noted above, the events become more\njet-like at high n and the particle multiplicity drops (see Figure 20), due to the increased Hawking\ntemperature. Our signal selection remains robust, as shown in Table 8.\n\u2022 Planck scale. We have investigated changing the Planck scale from its default value of MDL =\n1 TeV to 2 TeV. We note that, since the model is only valid for black hole masses much larger than\nthe Planck scale, this scenario is not well modelled in the range of masses accessible at the LHC.\n\u2022 Remnant decay. We have investigated changing the remnant decay model from a two-body to a\nfour-body mode (see Figure 20).\nFigure 19 shows the effect of changing the kinematic cutoff on the particle multiplicity and \u2211|pT|\ndistributions. Since the black hole is forced to decay thermally until it falls below MDL, the multiplicity\nis higher, and the events have lower energy emissions. The total energy remains constant, however so the\n\u2211|pT| distribution is relatively stable.\nParticle Multiplicity\n0\n5\n10\n15\n20\n25\nNumber / Event\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nn=2, kincut true\nn=7, kincut true\nn=2, kincut false\nn=7, kincut false\nATLAS\n| [GeV]\nT\nSum |P\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\nNumber / 200 GeV / Event\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nn=2, kincut true\nn=7, kincut true\nn=2, kincut false\nn=7, kincut false\nATLAS\nFigure 19: Particle multiplicity and \u2211|pT| distributions, showing the variation when the kinematic cut-off\nparameter is changed.\nThe acceptance of the signal for various parameter choices are shown in Table 8. Compared to the\nstandard full simulation, the largest effect is observed for high n, when the kinematic cut-off parameter\nis changed. This is as expected, since this parameter has a large effect on the evolution of the black hole\nduring its decay. Similarly changing the remnant decay from 2 to 4 bodies has a large effect at high n;\nthe effect of this, and of changing number of extra dimensions is shown in Figure 20.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1823\n\nParticle Multiplicity\n0\n5\n10\n15\n20\n25\nNumber / Event\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nn=2\nn=3\nn=4\nn=5\nn=7\nATLAS\nPar icle Multiplicity\n0\n5\n10\n15\n20\n25\nNumber / Event\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nn=2, 2-body remnant\nn=7, 2-body remnant\nn=2, 4-body remnant\nn=7, 4-body remnant\nATLAS\nFigure 20: Particle multiplicity distributions, showing the variation produced by a change in the number\nof extra dimensions, or the number of particles produced by remnant decay.\nn\nFull Sim\nFast Sim\nKin. Cut off\nTH-variation off\n4-body remnant\n2\n45.8\n42.9\n47.2\n48.7\n47.9\n3\n-\n33.2\n-\n-\n-\n4\n27.4\n26.6\n-\n-\n-\n5\n-\n21.7\n-\n-\n-\n7\n16.1\n15.9\n29.2\n16.6\n27.4\nTable 8: Signal acceptance (%) for different model assumptions.\n7.2\nUncertainties on detector performance\nTwo kinds of systematic uncertainties on detector performance were studied. One is an uncertainty on\nlepton identi\ufb01cation ef\ufb01ciency. To estimate this effect, we loosened and tightened particle identi\ufb01cation\nselections, by changing the hadronic leakage for electrons and the isolation cut for muons. The changes\nin signal ef\ufb01ciencies are around 2%.\nThe effect of a 5% error in the jet energy scale (JES) was also considered. The effect of these\nuncertainties on the discovery potential is shown in Figure 18.\n8\nResults\n8.1\nSearch Reach for Black Hole Production at the LHC\nThe studies presented show that the ATLAS detector is capable of discovering the production of black\nholes up to the kinematic limit of the LHC, assuming that the signal is correctly modelled. This con-\nclusion is largely based on the predicted huge production cross-section, and the small background from\nQCD dijets at very high-pT, especially when the presence of a high energy lepton is required. How-\never, both of these assumptions are suspect. The high production cross-section is subject to considerable\ndiscussion in the literature, as discussed in Section 2. Moreover, until the LHC has measured the QCD\ncross-section at 14 TeV, we cannot be certain of the tails of the QCD distributions. The Monte Carlo\nsimulations of these tails are working at the limit of their validity, given the high energies and large\nmultiplicities involved.\nFor these reasons, we prefer not to place too much weight on the detailed search reach limits. In-\nstead, we con\ufb01ne ourselves to the statement that, with current understanding, the black hole signature\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1824\n\nconsidered should be clearly visible if it exists.\n8.2\nDetermination of Model Parameters\nWe have considered the possibility of extracting model parameters from the data, should a signal be\nobserved. There are two key parameters: the Planck scale MD (or MDL depending on the convention)\nand the number of extra dimensions n. In Ref. [46, 47] a method was proposed to extract MD from the\ncross-section data, which \ufb01xes the Planck scale (within the model assumptions), and from events with\nhigh energy emissions.\nThe Hawking temperature TH of the black hole depends on n. If we detect events with emissions\nnear mBH/2, the energy of those emissions is a measure of the initial TH. Hence, over the sample of\nblack holes, the probability of such emissions is a measure of the characteristic temperature, and can\nbe used to extract n. This method was \ufb01rst put forward in Ref. [46], and here is made compatible\nwith the need for background rejection requirements. The requirements described in Section 6 are not\nappropriate: the lepton requirement biases the selected events in favour of \ufb01nal states with many particles,\nand hence against those events with a single high energy emission. A suitable requirement was found to\nbe \u2211|pT| > 3.5 TeV; this removes the background without biasing the signal events selected.\nFigure 21 shows the probability of a hard emission for two samples, compared to the predictions.\nThe method requires accurate mass resolution, and so an additional requirement on /ET< 100 GeV is\napplied. The addition of this requirement lowers the ef\ufb01ciency noticeably, but does improve the black\nhole mass reconstruction; details of the resolution and ef\ufb01ciency can be found in Figure 22. The data are\nconsistent with the expected value of n, but due to this reduction in signal ef\ufb01ciency, more data would\nbe required to make a de\ufb01nitive measurement. It should be noted that this measurement requires the\nPlanck scale to be known. If this cannot be determined from the production cross-section, it is likely that\nthe threshold behaviour near the Planck scale would provide an indication of its value. At present, no\ntheoretical model exists to allow us to make predictions in this region.\nReconstructed BH Mass [GeV]\n5000\n6000\n7000\n8000\n9000\n10000\nProb\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nn=7 BH Signal\nn=6 Upper Limit\nn=6 Lower Limit\nn=7 Upper Limit\nn=7 Lower Limit\nATLAS\nReconstructed BH Mass [GeV]\n5000\n6000\n7000\n8000\n9000\n10000\nProb\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\nn=4 BH Signal\nn=4 Upper Limit\nn=4 Lower Limit\nn=5 Upper Limit\nn=5 Lower Limit\nATLAS\nFigure 21: The probability of a hard emission near mBH/2 for n = 7 and n = 4. The bands show the ex-\npected range for n = 7 and n = 6, and for n = 5 and n = 4, respectively, for a luminosity of approximately\n0.75 fb\u22121.\n9\nSummary\nThe search for black holes in the \ufb01rst 100 pb\u22121 of LHC data with the ATLAS detector and software\nframework was simulated.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1825\n\nNormalisation\nMean (GeV)\nResolution (GeV)\nWithout\nNarrow\n1018\u00b126\n\u2212217\u00b15\n276\u00b19\n/ETrequirement\nWide\n276\u00b130\n\u2212148\u00b19\n722\u00b113\nWith\nNarrow\n318\u00b112\n\u2212116\u00b18\n215\u00b19\n/ETrequirement\nWide\n108\u00b17\n118\u00b118\n635\u00b116\nReconstructed Mass - True Mass [GeV]\n-4000 -3000 -2000 -1000\n0\n1000\n2000\n3000\n4000\n-1\nEvents / 80 GeV / fb\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nFigure 22: Black hole mass resolution distributions and their \ufb01ts to double Gaussian functions, using a\n\u2211|pT| and lepton requirement (1 fb\u22121). 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Harris et al., JHEP 05 (2005) 053, arXiv:hep-ph/0411022.\n[47] J. Tanaka, T. Yamamura, S. Asai, and J. Kanzaki, Eur. Phys. J. C41 (2005) 19\u201333,\narXiv:hep-ph/0411095.\nEXOTICS \u2013 DISCOVERY REACH FOR BLACK HOLE PRODUCTION\n1828\n", "DRAFT VERSION JULY 18, 2022\nTypeset using LATEX twocolumn style in AASTeX61\nSEARCH FOR HIGH-ENERGY NEUTRINOS FROM BINARY NEUTRON STAR MERGER GW170817 WITH ANTARES,\nICECUBE, AND THE PIERRE AUGER OBSERVATORY\nA. ALBERT,1 M. ANDR\u00b4E,2 M. ANGHINOLFI,3 M. ARDID,4 J.-J. AUBERT,5 J. AUBLIN,6 T. AVGITAS,6 B. BARET,6 J. BARRIOS-MART\u00b4I,7\nS. BASA,8 B. BELHORMA,9 V. BERTIN,5 S. BIAGI,10 R. BORMUTH,11, 12 S. BOURRET,6 M.C. BOUWHUIS,11 H. BR \u02c6ANZAS\u00b8,13\nR. BRUIJN,11, 14 J. BRUNNER,5 J. BUSTO,5 A. CAPONE,15, 16 L. CARAMETE,13 J. CARR,5 S. CELLI,15, 16, 17\nR. CHERKAOUI EL MOURSLI,18 T. CHIARUSI,19 M. CIRCELLA,20 J.A.B. COELHO,6 A. COLEIRO,6, 7 R. CONIGLIONE,10\nH. COSTANTINI,5 P. COYLE,5 A. CREUSOT,6 A. F. D\u00b4IAZ,21 A. DESCHAMPS,22 G. DE BONIS,15 C. DISTEFANO,10 I. DI PALMA,15, 16\nA. DOMI,3, 23 C. DONZAUD,6, 24 D. DORNIC,5 D. DROUHIN,1 T. EBERL,25 I. EL BOJADDAINI,26 N. EL KHAYATI,18 D. ELS \u00a8ASSER,27\nA. ENZENH \u00a8OFER,5 A. ETTAHIRI,18 F. FASSI,18 I. FELIS,4 L.A. FUSCO,19, 28 P. GAY,29, 6 V. GIORDANO,30 H. GLOTIN,31, 32\nT. GR\u00b4EGOIRE,6 R. GRACIA RUIZ,6, 33 K. GRAF,25 S. HALLMANN,25 H. VAN HAREN,34 A.J. HEIJBOER,11 Y. HELLO,22\nJ.J. HERN \u00b4ANDEZ-REY,7 J. H \u00a8OSSL,25 J. HOFEST \u00a8ADT,25 G. ILLUMINATI,7 C.W. JAMES,25 M. DE JONG,11, 12 M. JONGEN,11\nM. KADLER,27 O. KALEKIN,25 U. KATZ,25 D. KIESSLING,25 A. KOUCHNER,6, 32 M. KRETER,27 I. KREYKENBOHM,35\nV. KULIKOVSKIY,5, 36 C. LACHAUD,6 R. LAHMANN,25 D. LEF`EVRE,37 E. LEONORA,30, 38 M. LOTZE,7 S. LOUCATOS,39, 6\nM. MARCELIN,8 A. MARGIOTTA,19, 28 A. MARINELLI,40, 41 J.A. MART\u00b4INEZ-MORA,4 R. MELE,42, 43 K. MELIS,11, 14 T. MICHAEL,11\nP. MIGLIOZZI,42 A. MOUSSA,26 S. NAVAS,44 E. NEZRI,8 M. ORGANOKOV,33 G.E. P \u02d8AV \u02d8ALAS\u00b8,13 C. PELLEGRINO,19, 28 C. PERRINA,15, 16\nP. PIATTELLI,10 V. POPA,13 T. PRADIER,33 L. QUINN,5 C. RACCA,1 G. RICCOBENE,10 A. S \u00b4ANCHEZ-LOSA,20 M. SALDA \u02dcNA,4\nI. SALVADORI,5 D. F. E. SAMTLEBEN,11, 12 M. SANGUINETI,3, 23 P. SAPIENZA,10 F. SCH \u00a8USSLER,39 C. SIEGER,25 M. SPURIO,19, 28\nTH. STOLARCZYK,39 M. TAIUTI,3, 23 Y. TAYALATI,18 A. TROVATO,10 D. TURPIN,5 C. T \u00a8ONNIS,7 B. VALLAGE,39, 6 V. VAN ELEWYCK,6, 32\nF. VERSARI,19, 28 D. VIVOLO,42, 43 A. VIZZOCA,15, 16 J. WILMS,45 J.D. ZORNOZA,7 AND J. Z \u00b4U \u02dcNIGA7\n(ANTARES COLLABORATION)\nM. G. AARTSEN,46 M. ACKERMANN,47 J. ADAMS,48 J. A. AGUILAR,49 M. AHLERS,50 M. AHRENS,51 I. AL SAMARAI,52\nD. ALTMANN,53 K. ANDEEN,54 T. ANDERSON,55 I. ANSSEAU,49 G. ANTON,53 C. ARG \u00a8UELLES,56 J. AUFFENBERG,57 S. AXANI,56\nH. BAGHERPOUR,48 X. BAI,58 J. P. BARRON,59 S. W. BARWICK,60 V. BAUM,61 R. BAY,62 J. J. BEATTY,63, 64 J. BECKER TJUS,65\nK.-H. BECKER,66 S. BENZVI,67 D. BERLEY,68 E. BERNARDINI,47 D. Z. BESSON,69 G. BINDER,70, 62 D. BINDIG,66 E. BLAUFUSS,68\nS. BLOT,47 C. BOHM,51 M. B \u00a8ORNER,71 F. BOS,65 D. BOSE,72 S. B \u00a8OSER,61 O. BOTNER,73 E. BOURBEAU,50 J. BOURBEAU,74\nF. BRADASCIO,47 J. BRAUN,74 L. BRAYEUR,75 M. BRENZKE,57 H.-P. BRETZ,47 S. BRON,52 J. BROSTEAN-KAISER,47 A. BURGMAN,73\nT. CARVER,52 J. CASEY,74 M. CASIER,75 E. CHEUNG,68 D. CHIRKIN,74 A. CHRISTOV,52 K. CLARK,76 L. CLASSEN,77 S. COENDERS,78\nG. H. COLLIN,56 J. M. CONRAD,56 D. F. COWEN,55, 79 R. CROSS,67 M. DAY,74 J. P. A. M. DE ANDR\u00b4E,80 C. DE CLERCQ,75\nJ. J. DELAUNAY,55 H. DEMBINSKI,81 S. DE RIDDER,82 P. DESIATI,74 K. D. DE VRIES,75 G. DE WASSEIGE,75 M. DE WITH,83\nT. DEYOUNG,80 J. C. D\u00b4IAZ-V\u00b4ELEZ,74 V. DI LORENZO,61 H. DUJMOVIC,72 J. P. DUMM,51 M. DUNKMAN,55 E. DVORAK,58\nB. EBERHARDT,61 T. EHRHARDT,61 B. EICHMANN,65 P. ELLER,55 P. A. EVENSON,81 S. FAHEY,74 A. R. FAZELY,84 J. FELDE,68\nK. FILIMONOV,62 C. FINLEY,51 S. FLIS,51 A. FRANCKOWIAK,47 E. FRIEDMAN,68 T. FUCHS,71 T. K. GAISSER,81 J. GALLAGHER,85\nL. GERHARDT,70 K. GHORBANI,74 W. GIANG,59 T. GLAUCH,57 T. GL \u00a8USENKAMP,53 A. GOLDSCHMIDT,70 J. G. GONZALEZ,81\nD. GRANT,59 Z. GRIFFITH,74 C. HAACK,57 A. HALLGREN,73 F. HALZEN,74 K. HANSON,74 D. HEBECKER,83 D. HEEREMAN,49\nK. HELBING,66 R. HELLAUER,68 S. HICKFORD,66 J. HIGNIGHT,80 G. C. HILL,46 K. D. HOFFMAN,68 R. HOFFMANN,66\nB. HOKANSON-FASIG,74 K. HOSHINA,74, 86 F. HUANG,55 M. HUBER,78 K. HULTQVIST,51 M. H \u00a8UNNEFELD,71 S. IN,72 A. ISHIHARA,87\nE. JACOBI,47 G. S. JAPARIDZE,88 M. JEONG,72 K. JERO,74 B. J. P. JONES,89 P. KALACZYNSKI,57 W. KANG,72 A. KAPPES,77 T. KARG,47\nA. KARLE,74 U. KATZ,53 M. KAUER,74 A. KEIVANI,55 J. L. KELLEY,74 A. KHEIRANDISH,74 J. KIM,72 M. KIM,87 T. KINTSCHER,47\nJ. KIRYLUK,90 T. KITTLER,53 S. R. KLEIN,70, 62 G. KOHNEN,91 R. KOIRALA,81 H. KOLANOSKI,83 L. K \u00a8OPKE,61 C. KOPPER,59\nS. KOPPER,92 J. P. KOSCHINSKY,57 D. J. KOSKINEN,50 M. KOWALSKI,83, 47 K. KRINGS,78 M. KROLL,65 G. KR \u00a8UCKL,61 J. KUNNEN,75\nS. KUNWAR,47 N. KURAHASHI,93 T. KUWABARA,87 A. KYRIACOU,46 M. LABARE,82 J. L. LANFRANCHI,55 M. J. LARSON,50\nF. LAUBER,66 M. LESIAK-BZDAK,90 M. LEUERMANN,57 Q. R. LIU,74 L. LU,87 J. L \u00a8UNEMANN,75 W. LUSZCZAK,74 J. MADSEN,94\nG. MAGGI,75 K. B. M. MAHN,80 S. MANCINA,74 R. MARUYAMA,95 K. MASE,87 R. MAUNU,68 F. MCNALLY,74 K. MEAGHER,49\nM. MEDICI,50 M. MEIER,71 T. MENNE,71 G. MERINO,74 T. MEURES,49 S. MIARECKI,70, 62 J. MICALLEF,80 G. MOMENT\u00b4E,61\nT. MONTARULI,52 R. W. MOORE,59 M. MOULAI,56 R. NAHNHAUER,47 P. NAKARMI,92 U. NAUMANN,66 G. NEER,80\nH. NIEDERHAUSEN,90 S. C. NOWICKI,59 D. R. NYGREN,70 A. OBERTACKE POLLMANN,66 A. OLIVAS,68 A. O\u2019MURCHADHA,49\nT. PALCZEWSKI,70, 62 H. PANDYA,81 D. V. PANKOVA,55 P. PEIFFER,61 J. A. PEPPER,92 C. P\u00b4EREZ DE LOS HEROS,73 D. PIELOTH,71\nE. PINAT,49 M. PLUM,54 D. PRANAV,96 P. B. PRICE,62 G. T. PRZYBYLSKI,70 C. RAAB,49 L. R \u00a8ADEL,57 M. RAMEEZ,50 K. RAWLINS,97\nI. C. REA,78 R. REIMANN,57 B. RELETHFORD,93 M. RELICH,87 E. RESCONI,78 W. RHODE,71 M. RICHMAN,93 S. ROBERTSON,46\nM. RONGEN,57 C. ROTT,72 T. RUHE,71 D. RYCKBOSCH,82 D. RYSEWYK,80 T. S \u00a8ALZER,57 S. E. SANCHEZ HERRERA,59\nA. SANDROCK,71 J. SANDROOS,61 M. SANTANDER,92 S. SARKAR,50, 98 S. SARKAR,59 K. SATALECKA,47 P. SCHLUNDER,71\nT. SCHMIDT,68 A. SCHNEIDER,74 S. SCHOENEN,57 S. SCH \u00a8ONEBERG,65 L. SCHUMACHER,57 D. SECKEL,81 S. SEUNARINE,94\nJ. SOEDINGREKSO,71 D. SOLDIN,66 M. SONG,68 G. M. SPICZAK,94 C. SPIERING,47 J. STACHURSKA,47 M. STAMATIKOS,63\narXiv:1710.05839v2 [astro-ph.HE] 9 Nov 2017\n\n2\nT. STANEV,81 A. STASIK,47 J. STETTNER,57 A. STEUER,61 T. STEZELBERGER,70 R. G. STOKSTAD,70 A. ST \u00a8OSSL,87\nN. L. STROTJOHANN,47 T. STUTTARD,50 G. W. SULLIVAN,68 M. SUTHERLAND,63 I. TABOADA,96 J. TATAR,70, 62 F. TENHOLT,65\nS. TER-ANTONYAN,84 A. TERLIUK,47 G. TE\u02c7SI\u00b4C,55 S. TILAV,81 P. A. TOALE,92 M. N. TOBIN,74 S. TOSCANO,75 D. TOSI,74\nM. TSELENGIDOU,53 C. F. TUNG,96 A. TURCATI,78 C. F. TURLEY,55 B. TY,74 E. UNGER,73 M. USNER,47 J. VANDENBROUCKE,74\nW. VAN DRIESSCHE,82 N. VAN EIJNDHOVEN,75 S. VANHEULE,82 J. VAN SANTEN,47 M. VEHRING,57 E. VOGEL,57 M. VRAEGHE,82\nC. WALCK,51 A. WALLACE,46 M. WALLRAFF,57 F. D. WANDLER,59 N. WANDKOWSKY,74 A. WAZA,57 C. WEAVER,59 M. J. WEISS,55\nC. WENDT,74 J. WERTHEBACH,71 S. WESTERHOFF,74 B. J. WHELAN,46 K. WIEBE,61 C. H. WIEBUSCH,57 L. WILLE,74\nD. R. WILLIAMS,92 L. WILLS,93 M. WOLF,74 J. WOOD,74 T. R. WOOD,59 E. WOOLSEY,59 K. WOSCHNAGG,62 D. L. XU,74\nX. W. XU,84 Y. XU,90 J. P. YANEZ,59 G. YODH,60 S. YOSHIDA,87 T. YUAN,74 AND M. ZOLL51\n(ICECUBE COLLABORATION)\nA. AAB,99 P. ABREU,100 M. AGLIETTA,101, 102 I.F.M. ALBUQUERQUE,103 J.M. ALBURY,104 I. ALLEKOTTE,105 A. ALMELA,106, 107\nJ. ALVAREZ CASTILLO,108 J. ALVAREZ-MU \u02dcNIZ,109 G.A. ANASTASI,110, 111 L. ANCHORDOQUI,112 B. ANDRADA,106 S. ANDRINGA,100\nC. ARAMO,113 N. ARSENE,114 H. ASOREY,105, 115 P. ASSIS,100 G. AVILA,116, 117 A.M. BADESCU,118 A. BALACEANU,119\nF. BARBATO,120 R.J. BARREIRA LUZ,100 J.J. BEATTY,121 K.H. BECKER,122 J.A. BELLIDO,104 C. BERAT,123 M.E. BERTAINA,124, 102\nX. BERTOU,105 P.L. BIERMANN,125 J. BITEAU,126 S.G. BLAESS,104 A. BLANCO,100 J. BLAZEK,127 C. BLEVE,128, 129 M. BOH \u00b4A\u02c7COV \u00b4A,127\nC. BONIFAZI,130 N. BORODAI,131 A.M. BOTTI,106, 132 J. BRACK,133 I. BRANCUS,119 T. BRETZ,134 A. BRIDGEMAN,135\nF.L. BRIECHLE,134 P. BUCHHOLZ,136 A. BUENO,137 S. BUITINK,99 M. BUSCEMI,138, 139 K.S. CABALLERO-MORA,140\nL. CACCIANIGA,141 A. CANCIO,107, 106 F. CANFORA,99 R. CARUSO,138, 139 A. CASTELLINA,101, 102 F. CATALANI,142 G. CATALDI,129\nL. CAZON,100 A.G. CHAVEZ,143 J.A. CHINELLATO,144 J. CHUDOBA,127 R.W. CLAY,104 A.C. COBOS CERUTTI,145\nR. COLALILLO,120, 113 A. COLEMAN,146 L. COLLICA,102 M.R. COLUCCIA,128, 129 R. CONCEIC\u00b8 \u02dcAO,100 G. CONSOLATI,147, 148\nF. CONTRERAS,116, 117 M.J. COOPER,104 S. COUTU,146 C.E. COVAULT,149 J. CRONIN,150, \u2217S. D\u2019AMICO,151, 129 B. DANIEL,144\nS. DASSO,152, 153 K. DAUMILLER,132 B.R. DAWSON,104 J.A. DAY,104 R.M. DE ALMEIDA,154 S.J. DE JONG,99, 155 G. DE MAURO,99\nJ.R.T. DE MELLO NETO,130, 156 I. DE MITRI,128, 129 J. DE OLIVEIRA,154 V. DE SOUZA,157 J. DEBATIN,135 O. DELIGNY,126\nM.L. D\u00b4IAZ CASTRO,144 F. DIOGO,100 C. DOBRIGKEIT,144 J.C. D\u2019OLIVO,108 Q. DOROSTI,136 R.C. DOS ANJOS,158 M.T. DOVA,159\nA. DUNDOVIC,160 J. EBR,127 R. ENGEL,132 M. ERDMANN,134 M. ERFANI,136 C.O. ESCOBAR,161 J. ESPADANAL,100\nA. ETCHEGOYEN,106, 107 H. FALCKE,99, 162, 155 J. FARMER,150 G. FARRAR,163 A.C. FAUTH,144 N. FAZZINI,161 F. FELDBUSCH,164\nF. FENU,124, 102 B. FICK,165 J.M. FIGUEIRA,106 A. FILIP\u02c7CI\u02c7C,166, 167 M.M. FREIRE,168 T. FUJII,150 A. FUSTER,106, 107 R. GA\u00a8IOR,169\nB. GARC\u00b4IA,145 F. GAT\u00b4E,170 H. GEMMEKE,164 A. GHERGHEL-LASCU,119 P.L. GHIA,126 U. GIACCARI,130, 171 M. GIAMMARCHI,147\nM. GILLER,172 D. G\u0141AS,173 C. GLASER,134 G. GOLUP,105 M. G \u00b4OMEZ BERISSO,105 P.F. G \u00b4OMEZ VITALE,116, 117 N. GONZ \u00b4ALEZ,106, 132\nA. GORGI,101, 102 M. GOTTOWIK,122 A.F. GRILLO,111, \u2020 T.D. GRUBB,104 F. GUARINO,120, 113 G.P. GUEDES,174 R. HALLIDAY,149\nM.R. HAMPEL,106 P. HANSEN,159 D. HARARI,105 T.A. HARRISON,104 V.M. HARVEY,104 A. HAUNGS,132 T. HEBBEKER,134 D. HECK,132\nP. HEIMANN,136 A.E. HERVE,135 G.C. HILL,104 C. HOJVAT,161 E. HOLT,132, 106 P. HOMOLA,131 J.R. H \u00a8ORANDEL,99, 155 P. HORVATH,175\nM. HRABOVSK \u00b4Y,175 T. HUEGE,132 J. HULSMAN,106, 132 A. INSOLIA,138, 139 P.G. ISAR,114 I. JANDT,122 J.A. JOHNSEN,176\nM. JOSEBACHUILI,106 J. JURYSEK,127 A. K \u00a8A \u00a8AP \u00a8A,122 K.H. KAMPERT,122 B. KEILHAUER,132 N. KEMMERICH,103 J. KEMP,134\nR.M. KIECKHAFER,165 H.O. KLAGES,132 M. KLEIFGES,164 J. KLEINFELLER,116 R. KRAUSE,134 N. KROHM,122 D. KUEMPEL,122\nG. KUKEC MEZEK,167 N. KUNKA,164 A. KUOTB AWAD,135 B.L. LAGO,177 D. LAHURD,149 R.G. LANG,157 M. LAUSCHER,134\nR. LEGUMINA,172 M.A. LEIGUI DE OLIVEIRA,178 A. LETESSIER-SELVON,169 I. LHENRY-YVON,126 K. LINK,135 D. LO PRESTI,138, 139\nL. LOPES,100 R. L \u00b4OPEZ,179 A. L \u00b4OPEZ CASADO,109 R. LOREK,149 Q. LUCE,126 A. LUCERO,106 M. MALACARI,150\nM. MALLAMACI,141, 147 D. MANDAT,127 P. MANTSCH,161 A.G. MARIAZZI,159 I.C. MARIS\u00b8,180 G. MARSELLA,128, 129\nD. MARTELLO,128, 129 H. MARTINEZ,181 O. MART\u00b4INEZ BRAVO,179 J.J. MAS\u00b4IAS MEZA,153 H.J. MATHES,132 S. MATHYS,122\nJ. MATTHEWS,182 G. MATTHIAE,183, 184 E. MAYOTTE,122 P.O. MAZUR,161 C. MEDINA,176 G. MEDINA-TANCO,108 D. MELO,106\nA. MENSHIKOV,164 K.-D. MERENDA,176 S. MICHAL,175 M.I. MICHELETTI,168 L. MIDDENDORF,134 L. MIRAMONTI,141, 147\nB. MITRICA,119 D. MOCKLER,135 S. MOLLERACH,105 F. MONTANET,123 C. MORELLO,101, 102 G. MORLINO,110, 111 M. MOSTAF \u00b4A,146\nA.L. M \u00a8ULLER,106, 132 G. M \u00a8ULLER,134 M.A. MULLER,144, 185 S. M \u00a8ULLER,135, 106 R. MUSSA,102 I. NARANJO,105 L. NELLEN,108\nP.H. NGUYEN,104 M. NICULESCU-OGLINZANU,119 M. NIECHCIOL,136 L. NIEMIETZ,122 T. NIGGEMANN,134 D. NITZ,165 D. NOSEK,186\nV. NOVOTNY,186 L. NO\u02c7ZKA,175 L.A. N \u00b4U \u02dcNEZ,115 F. OIKONOMOU,146 A. OLINTO,150 M. PALATKA,127 J. PALLOTTA,187\nP. PAPENBREER,122 G. PARENTE,109 A. PARRA,179 T. PAUL,112 M. PECH,127 F. PEDREIRA,109 J. PE\u00b8 KALA,131 R. PELAYO,188\nJ. PE \u02dcNA-RODRIGUEZ,115 L.A.S. PEREIRA,144 M. PERLIN,106 L. PERRONE,128, 129 C. PETERS,134 S. PETRERA,110, 111 J. PHUNTSOK,146\nT. PIEROG,132 M. PIMENTA,100 V. PIRRONELLO,138, 139 M. PLATINO,106 M. PLUM,134 J. POH,150 C. POROWSKI,131 R.R. PRADO,157\nP. PRIVITERA,150 M. PROUZA,127 E.J. QUEL,187 S. QUERCHFELD,122 S. QUINN,149 R. RAMOS-POLLAN,115 J. RAUTENBERG,122\nD. RAVIGNANI,106 J. RIDKY,127 F. RIEHN,100 M. RISSE,136 P. RISTORI,187 V. RIZI,189, 111 W. RODRIGUES DE CARVALHO,103\nG. RODRIGUEZ FERNANDEZ,183, 184 J. RODRIGUEZ ROJO,116 M.J. RONCORONI,106 M. ROTH,132 E. ROULET,105 A.C. ROVERO,152\nP. RUEHL,136 S.J. SAFFI,104 A. SAFTOIU,119 F. SALAMIDA,189, 111 H. SALAZAR,179 A. SALEH,167 G. SALINA,184 F. S \u00b4ANCHEZ,106\nP. SANCHEZ-LUCAS,137 E.M. SANTOS,103 E. SANTOS,127 F. SARAZIN,176 R. SARMENTO,100 C. SARMIENTO-CANO,106 R. SATO,116\nM. SCHAUER,122 V. SCHERINI,129 H. SCHIELER,132 M. SCHIMP,122 D. SCHMIDT,132, 106 O. SCHOLTEN,190, 191 P. SCHOV \u00b4ANEK,127\nF.G. SCHR \u00a8ODER,132 S. SCHR \u00a8ODER,122 A. SCHULZ,135 J. SCHUMACHER,134 S.J. SCIUTTO,159 A. SEGRETO,192, 139 A. SHADKAM,182\nR.C. SHELLARD,171 G. SIGL,160 G. SILLI,106, 132 R. \u02c7SM\u00b4IDA,132 G.R. SNOW,193 P. SOMMERS,146 S. SONNTAG,136 J.F. SORIANO,112\nR. SQUARTINI,116 D. STANCA,119 S. STANI\u02c7C,167 J. STASIELAK,131 P. STASSI,123 M. STOLPOVSKIY,123 F. STRAFELLA,128, 129\n\n3\nA. STREICH,135 F. SUAREZ,106, 107 M. SUAREZ DUR \u00b4AN,115 T. SUDHOLZ,104 T. SUOMIJ \u00a8ARVI,126 A.D. SUPANITSKY,152 J. \u02c7SUP\u00b4IK,175\nJ. SWAIN,194 Z. SZADKOWSKI,173 A. TABOADA,132 O.A. TABORDA,105 C. TIMMERMANS,155, 99 C.J. TODERO PEIXOTO,142\nL. TOMANKOVA,132 B. TOM\u00b4E,100 G. TORRALBA ELIPE,109 P. TRAVNICEK,127 M. TRINI,167 M. TUEROS,159 R. ULRICH,132\nM. UNGER,132 M. URBAN,134 J.F. VALD\u00b4ES GALICIA,108 I. VALI \u02dcNO,109 L. VALORE,120, 113 G. VAN AAR,99 P. VAN BODEGOM,104\nA.M. VAN DEN BERG,190 A. VAN VLIET,99 E. VARELA,179 B. VARGAS C \u00b4ARDENAS,108 R.A. V \u00b4AZQUEZ,109 D. VEBERI\u02c7C,132\nC. VENTURA,156 I.D. VERGARA QUISPE,159 V. VERZI,184 J. VICHA,127 L. VILLASE \u02dcNOR,143 S. VOROBIOV,167 H. WAHLBERG,159\nO. WAINBERG,106, 107 D. WALZ,134 A.A. WATSON,195 M. WEBER,164 A. WEINDL,132 M. WIEDE \u00b4NSKI,173 L. WIENCKE,176\nH. WILCZY \u00b4NSKI,131 M. WIRTZ,134 D. WITTKOWSKI,122 B. WUNDHEILER,106 L. YANG,167 A. YUSHKOV,127 E. ZAS,109\nD. ZAVRTANIK,167, 166 M. ZAVRTANIK,166, 167 A. ZEPEDA,181 B. ZIMMERMANN,164 M. ZIOLKOWSKI,136 Z. ZONG,126 AND\nF. ZUCCARELLO138, 139\n(THE PIERRE AUGER COLLABORATION)\nB. P. ABBOTT,196 R. ABBOTT,196 T. D. ABBOTT,197 F. ACERNESE,198, 199 K. ACKLEY,200, 201 C. ADAMS,202 T. ADAMS,203\nP. ADDESSO,204 R. X. ADHIKARI,196 V. B. ADYA,205 C. AFFELDT,205 M. AFROUGH,206 B. AGARWAL,207 M. AGATHOS,208\nK. AGATSUMA,209 N. AGGARWAL,210 O. D. AGUIAR,211 L. AIELLO,212, 213 A. AIN,214 P. AJITH,215 B. ALLEN,205, 216, 217 G. ALLEN,207\nA. ALLOCCA,218, 219 P. A. ALTIN,220 A. AMATO,221 A. ANANYEVA,196 S. B. ANDERSON,196 W. G. ANDERSON,216 S. V. ANGELOVA,222\nS. ANTIER,223 S. APPERT,196 K. ARAI,196 M. C. ARAYA,196 J. S. AREEDA,224 N. ARNAUD,223, 225 K. G. ARUN,226 S. ASCENZI,227, 228\nG. ASHTON,205 M. AST,229 S. M. ASTON,202 P. ASTONE,230 D. V. ATALLAH,231 P. AUFMUTH,217 C. AULBERT,205 K. AULTONEAL,232\nC. AUSTIN,197 A. AVILA-ALVAREZ,224 S. BABAK,233 P. BACON,234 M. K. M. BADER,209 S. BAE,235 P. T. BAKER,236\nF. BALDACCINI,237, 238 G. BALLARDIN,225 S. W. BALLMER,239 S. BANAGIRI,240 J. C. BARAYOGA,196 S. E. BARCLAY,241\nB. C. BARISH,196 D. BARKER,242 K. BARKETT,243 F. BARONE,198, 199 B. BARR,241 L. BARSOTTI,210 M. BARSUGLIA,234 D. BARTA,244\nJ. BARTLETT,242 I. BARTOS,245, 200 R. BASSIRI,246 A. BASTI,218, 219 J. C. BATCH,242 M. BAWAJ,247, 238 J. C. BAYLEY,241\nM. BAZZAN,248, 249 B. B\u00b4ECSY,250 C. BEER,205 M. BEJGER,251 I. BELAHCENE,223 A. S. BELL,241 B. K. BERGER,196 G. BERGMANN,205\nJ. J. BERO,252 C. P. L. BERRY,253 D. BERSANETTI,254 A. BERTOLINI,209 J. BETZWIESER,202 S. BHAGWAT,239 R. BHANDARE,255\nI. A. BILENKO,256 G. BILLINGSLEY,196 C. R. BILLMAN,200 J. BIRCH,202 R. BIRNEY,257 O. BIRNHOLTZ,205 S. BISCANS,196, 210\nS. BISCOVEANU,258, 201 A. BISHT,217 M. BITOSSI,225, 219 C. BIWER,239 M. A. BIZOUARD,223 J. K. BLACKBURN,196 J. BLACKMAN,243\nC. D. BLAIR,196, 259 D. G. BLAIR,259 R. M. BLAIR,242 S. BLOEMEN,260 O. BOCK,205 N. BODE,205 M. BOER,261 G. BOGAERT,261\nA. BOHE,233 F. BONDU,262 E. BONILLA,246 R. BONNAND,203 B. A. BOOM,209 R. BORK,196 V. BOSCHI,225, 219 S. BOSE,263, 214\nK. BOSSIE,202 Y. BOUFFANAIS,234 A. BOZZI,225 C. BRADASCHIA,219 P. R. BRADY,216 M. BRANCHESI,212, 213 J. E. BRAU,264\nT. BRIANT,265 A. BRILLET,261 M. BRINKMANN,205 V. BRISSON,223 P. BROCKILL,216 J. E. BROIDA,266 A. F. BROOKS,196\nD. A. BROWN,239 D. D. BROWN,267 S. BRUNETT,196 C. C. BUCHANAN,197 A. BUIKEMA,210 T. BULIK,268 H. J. BULTEN,269, 209\nA. BUONANNO,233, 270 D. BUSKULIC,203 C. BUY,234 R. L. BYER,246 M. CABERO,205 L. CADONATI,271 G. CAGNOLI,221, 272\nC. CAHILLANE,196 J. CALDER \u00b4ON BUSTILLO,271 T. A. CALLISTER,196 E. CALLONI,273, 199 J. B. CAMP,274 M. CANEPA,275, 254\nP. CANIZARES,260 K. C. CANNON,276 H. CAO,267 J. CAO,277 C. D. CAPANO,205 E. CAPOCASA,234 F. CARBOGNANI,225 S. CARIDE,278\nM. F. CARNEY,279 J. CASANUEVA DIAZ,223 C. CASENTINI,227, 228 S. CAUDILL,216, 209 M. CAVAGLI `A,206 F. CAVALIER,223\nR. CAVALIERI,225 G. CELLA,219 C. B. CEPEDA,196 P. CERD \u00b4A-DUR \u00b4AN,280 G. CERRETANI,218, 219 E. CESARINI,281, 228\nS. J. CHAMBERLIN,258 M. CHAN,241 S. CHAO,282 P. CHARLTON,283 E. CHASE,284 E. CHASSANDE-MOTTIN,234 D. CHATTERJEE,216\nB. D. CHEESEBORO,236 H. Y. CHEN,285 X. CHEN,259 Y. CHEN,243 H.-P. CHENG,200 H. CHIA,200 A. CHINCARINI,254 A. CHIUMMO,225\nT. CHMIEL,279 H. S. CHO,286 M. CHO,270 J. H. CHOW,220 N. CHRISTENSEN,266, 261 Q. CHU,259 A. J. K. CHUA,208 S. CHUA,265\nA. K. W. CHUNG,287 S. CHUNG,259 G. CIANI,200, 248, 249 R. CIOLFI,288, 289 C. E. CIRELLI,246 A. CIRONE,275, 254 F. CLARA,242\nJ. A. CLARK,271 P. CLEARWATER,290 F. CLEVA,261 C. COCCHIERI,206 E. COCCIA,212, 213 P.-F. COHADON,265 D. COHEN,223\nA. COLLA,291, 230 C. G. COLLETTE,292 L. R. COMINSKY,293 M. CONSTANCIO JR.,211 L. CONTI,249 S. J. COOPER,253 P. CORBAN,202\nT. R. CORBITT,197 I. CORDERO-CARRI \u00b4ON,294 K. R. CORLEY,245 N. CORNISH,295 A. CORSI,278 S. CORTESE,225 C. A. COSTA,211\nM. W. COUGHLIN,266, 196 S. B. COUGHLIN,284 J.-P. COULON,261 S. T. COUNTRYMAN,245 P. COUVARES,196 P. B. COVAS,296\nE. E. COWAN,271 D. M. COWARD,259 M. J. COWART,202 D. C. COYNE,196 R. COYNE,278 J. D. E. CREIGHTON,216 T. D. CREIGHTON,297\nJ. CRIPE,197 S. G. CROWDER,298 T. J. CULLEN,224, 197 A. CUMMING,241 L. CUNNINGHAM,241 E. CUOCO,225 T. DAL CANTON,274\nG. D \u00b4ALYA,250 S. L. DANILISHIN,217, 205 S. D\u2019ANTONIO,228 K. DANZMANN,217, 205 A. DASGUPTA,299 C. F. DA SILVA COSTA,200\nV. DATTILO,225 I. DAVE,255 M. DAVIER,223 D. DAVIS,239 E. J. DAW,300 B. DAY,271 S. DE,239 D. DEBRA,246 J. DEGALLAIX,221\nM. DE LAURENTIS,212, 199 S. DEL\u00b4EGLISE,265 W. DEL POZZO,253, 218, 219 N. DEMOS,210 T. DENKER,205 T. DENT,205 R. DE PIETRI,301, 302\nV. DERGACHEV,233 R. DE ROSA,273, 199 R. T. DEROSA,202 C. DE ROSSI,221, 225 R. DESALVO,303 O. DE VARONA,205 J. DEVENSON,222\nS. DHURANDHAR,214 M. C. D\u00b4IAZ,297 L. DI FIORE,199 M. DI GIOVANNI,304, 289 T. DI GIROLAMO,245, 273, 199 A. DI LIETO,218, 219\nS. DI PACE,291, 230 I. DI PALMA,291, 230 F. DI RENZO,218, 219 Z. DOCTOR,285 V. DOLIQUE,221 F. DONOVAN,210 K. L. DOOLEY,206\nS. DORAVARI,205 I. DORRINGTON,231 R. DOUGLAS,241 M. DOVALE \u00b4ALVAREZ,253 T. P. DOWNES,216 M. DRAGO,205\nC. DREISSIGACKER,205 J. C. DRIGGERS,242 Z. DU,277 M. DUCROT,203 P. DUPEJ,241 S. E. DWYER,242 T. B. EDO,300\nM. C. EDWARDS,266 A. EFFLER,202 H.-B. EGGENSTEIN,233, 205 P. EHRENS,196 J. EICHHOLZ,196 S. S. EIKENBERRY,200\nR. A. EISENSTEIN,210 R. C. ESSICK,210 D. ESTEVEZ,203 Z. B. ETIENNE,236 T. ETZEL,196 M. EVANS,210 T. M. EVANS,202\nM. FACTOUROVICH,245 V. FAFONE,227, 228, 212 H. FAIR,239 S. FAIRHURST,231 X. FAN,277 S. FARINON,254 B. FARR,285 W. M. FARR,253\nE. J. FAUCHON-JONES,231 M. FAVATA,305 M. FAYS,231 C. FEE,279 H. FEHRMANN,205 J. FEICHT,196 M. M. FEJER,246\nA. FERNANDEZ-GALIANA,210 I. FERRANTE,218, 219 E. C. FERREIRA,211 F. FERRINI,225 F. FIDECARO,218, 219 D. FINSTAD,239 I. FIORI,225\n\n4\nD. FIORUCCI,234 M. FISHBACH,285 R. P. FISHER,239 M. FITZ-AXEN,240 R. FLAMINIO,221, 306 M. FLETCHER,241 H. FONG,307\nJ. A. FONT,280, 308 P. W. F. FORSYTH,220 S. S. FORSYTH,271 J.-D. FOURNIER,261 S. FRASCA,291, 230 F. FRASCONI,219 Z. FREI,250\nA. FREISE,253 R. FREY,264 V. FREY,223 E. M. FRIES,196 P. FRITSCHEL,210 V. V. FROLOV,202 P. FULDA,200 M. FYFFE,202\nH. GABBARD,241 B. U. GADRE,214 S. M. GAEBEL,253 J. R. GAIR,309 L. GAMMAITONI,237 M. R. GANIJA,267 S. G. GAONKAR,214\nC. GARCIA-QUIROS,296 F. GARUFI,273, 199 B. GATELEY,242 S. GAUDIO,232 G. GAUR,310 V. GAYATHRI,311 N. GEHRELS,274, \u2020\nG. GEMME,254 E. GENIN,225 A. GENNAI,219 D. GEORGE,207 J. GEORGE,255 L. GERGELY,312 V. GERMAIN,203 S. GHONGE,271\nABHIRUP GHOSH,215 ARCHISMAN GHOSH,215, 209 S. GHOSH,260, 209, 216 J. A. GIAIME,197, 202 K. D. GIARDINA,202 A. GIAZOTTO,219\nK. GILL,232 L. GLOVER,303 E. GOETZ,313 R. GOETZ,200 S. GOMES,231 B. GONCHAROV,201 G. GONZ \u00b4ALEZ,197\nJ. M. GONZALEZ CASTRO,218, 219 A. GOPAKUMAR,314 M. L. GORODETSKY,256 S. E. GOSSAN,196 M. GOSSELIN,225 R. GOUATY,203\nA. GRADO,315, 199 C. GRAEF,241 M. GRANATA,221 A. GRANT,241 S. GRAS,210 C. GRAY,242 G. GRECO,316, 317 A. C. GREEN,253\nE. M. GRETARSSON,232 P. GROOT,260 H. GROTE,205 S. GRUNEWALD,233 P. GRUNING,223 G. M. GUIDI,316, 317 X. GUO,277 A. GUPTA,258\nM. K. GUPTA,299 K. E. GUSHWA,196 E. K. GUSTAFSON,196 R. GUSTAFSON,313 O. HALIM,213, 212 B. R. HALL,263 E. D. HALL,210\nE. Z. HAMILTON,231 G. HAMMOND,241 M. HANEY,318 M. M. HANKE,205 J. HANKS,242 C. HANNA,258 M. D. HANNAM,231\nO. A. HANNUKSELA,287 J. HANSON,202 T. HARDWICK,197 J. HARMS,212, 213 G. M. HARRY,319 I. W. HARRY,233 M. J. HART,241\nC.-J. HASTER,307 K. HAUGHIAN,241 J. HEALY,252 A. HEIDMANN,265 M. C. HEINTZE,202 H. HEITMANN,261 P. HELLO,223\nG. HEMMING,225 M. HENDRY,241 I. S. HENG,241 J. HENNIG,241 A. W. HEPTONSTALL,196 M. HEURS,205, 217 S. HILD,241\nT. HINDERER,260 D. HOAK,225 D. HOFMAN,221 K. HOLT,202 D. E. HOLZ,285 P. HOPKINS,231 C. HORST,216 J. HOUGH,241\nE. A. HOUSTON,241 E. J. HOWELL,259 A. HREIBI,261 Y. M. HU,205 E. A. HUERTA,207 D. HUET,223 B. HUGHEY,232 S. HUSA,296\nS. H. HUTTNER,241 T. HUYNH-DINH,202 N. INDIK,205 R. INTA,278 G. INTINI,291, 230 H. N. ISA,241 J.-M. ISAC,265 M. ISI,196\nB. R. IYER,215 K. IZUMI,242 T. JACQMIN,265 K. JANI,271 P. JARANOWSKI,320 S. JAWAHAR,257 F. JIM\u00b4ENEZ-FORTEZA,296\nW. W. JOHNSON,197 D. I. JONES,321 R. JONES,241 R. J. G. JONKER,209 L. JU,259 J. JUNKER,205 C. V. KALAGHATGI,231\nV. KALOGERA,284 B. KAMAI,196 S. KANDHASAMY,202 G. KANG,235 J. B. KANNER,196 S. J. KAPADIA,216 S. KARKI,264\nK. S. KARVINEN,205 M. KASPRZACK,197 M. KATOLIK,207 E. KATSAVOUNIDIS,210 W. KATZMAN,202 S. KAUFER,217 K. KAWABE,242\nF. K\u00b4EF\u00b4ELIAN,261 D. KEITEL,241 A. J. KEMBALL,207 R. KENNEDY,300 C. KENT,231 J. S. KEY,322 F. Y. KHALILI,256 I. KHAN,212, 228\nS. KHAN,205 Z. KHAN,299 E. A. KHAZANOV,323 N. KIJBUNCHOO,220 CHUNGLEE KIM,324 J. C. KIM,325 K. KIM,287 W. KIM,267\nW. S. KIM,326 Y.-M. KIM,286 S. J. KIMBRELL,271 E. J. KING,267 P. J. KING,242 M. KINLEY-HANLON,319 R. KIRCHHOFF,205\nJ. S. KISSEL,242 L. KLEYBOLTE,229 S. KLIMENKO,200 T. D. KNOWLES,236 P. KOCH,205 S. M. KOEHLENBECK,205 S. KOLEY,209\nV. KONDRASHOV,196 A. KONTOS,210 M. KOROBKO,229 W. Z. KORTH,196 I. KOWALSKA,268 D. B. KOZAK,196 C. KR \u00a8AMER,205\nV. KRINGEL,205 B. KRISHNAN,205 A. KR \u00b4OLAK,327, 328 G. KUEHN,205 P. KUMAR,307 R. KUMAR,299 S. KUMAR,215 L. KUO,282\nA. KUTYNIA,327 S. KWANG,216 B. D. LACKEY,233 K. H. LAI,287 M. LANDRY,242 R. N. LANG,329 J. LANGE,252 B. LANTZ,246\nR. K. LANZA,210 A. LARTAUX-VOLLARD,223 P. D. LASKY,201 M. LAXEN,202 A. LAZZARINI,196 C. LAZZARO,249 P. LEACI,291, 230\nS. LEAVEY,241 C. H. LEE,286 H. K. LEE,330 H. M. LEE,331 H. W. LEE,325 K. LEE,241 J. LEHMANN,205 A. LENON,236\nM. LEONARDI,304, 289 N. LEROY,223 N. LETENDRE,203 Y. LEVIN,201 T. G. F. LI,287 S. D. LINKER,303 T. B. LITTENBERG,332 J. LIU,259\nR. K. L. LO,287 N. A. LOCKERBIE,257 L. T. LONDON,231 J. E. LORD,239 M. LORENZINI,212, 213 V. LORIETTE,333 M. LORMAND,202\nG. LOSURDO,219 J. D. LOUGH,205 C. O. LOUSTO,252 G. LOVELACE,224 H. L \u00a8UCK,217, 205 D. LUMACA,227, 228 A. P. LUNDGREN,205\nR. LYNCH,210 Y. MA,243 R. MACAS,231 S. MACFOY,222 B. MACHENSCHALK,205 M. MACINNIS,210 D. M. MACLEOD,231\nI. MAGA \u02dcNA HERNANDEZ,216 F. MAGA \u02dcNA-SANDOVAL,239 L. MAGA \u02dcNA ZERTUCHE,239 R. M. MAGEE,258 E. MAJORANA,230\nI. MAKSIMOVIC,333 N. MAN,261 V. MANDIC,240 V. MANGANO,241 G. L. MANSELL,220 M. MANSKE,216, 220 M. MANTOVANI,225\nF. MARCHESONI,247, 238 F. MARION,203 S. M \u00b4ARKA,245 Z. M \u00b4ARKA,245 C. MARKAKIS,207 A. S. MARKOSYAN,246 A. MARKOWITZ,196\nE. MAROS,196 A. MARQUINA,294 F. MARTELLI,316, 317 L. MARTELLINI,261 I. W. MARTIN,241 R. M. MARTIN,305 D. V. MARTYNOV,210\nK. MASON,210 E. MASSERA,300 A. MASSEROT,203 T. J. MASSINGER,196 M. MASSO-REID,241 S. MASTROGIOVANNI,291, 230\nA. MATAS,240 F. MATICHARD,196, 210 L. MATONE,245 N. MAVALVALA,210 N. MAZUMDER,263 R. MCCARTHY,242\nD. E. MCCLELLAND,220 S. MCCORMICK,202 L. MCCULLER,210 S. C. MCGUIRE,334 G. MCINTYRE,196 J. MCIVER,196\nD. J. MCMANUS,220 L. MCNEILL,201 T. MCRAE,220 S. T. MCWILLIAMS,236 D. MEACHER,258 G. D. MEADORS,233, 205 M. MEHMET,205\nJ. MEIDAM,209 E. MEJUTO-VILLA,204 A. MELATOS,290 G. MENDELL,242 R. A. MERCER,216 E. L. MERILH,242 M. MERZOUGUI,261\nS. MESHKOV,196 C. MESSENGER,241 C. MESSICK,258 R. METZDORFF,265 P. M. MEYERS,240 H. MIAO,253 C. MICHEL,221\nH. MIDDLETON,253 E. E. MIKHAILOV,335 L. MILANO,273, 199 A. L. MILLER,200, 291, 230 B. B. MILLER,284 J. MILLER,210\nM. MILLHOUSE,295 M. C. MILOVICH-GOFF,303 O. MINAZZOLI,261, 336 Y. MINENKOV,228 J. MING,233 C. MISHRA,337 S. MITRA,214\nV. P. MITROFANOV,256 G. MITSELMAKHER,200 R. MITTLEMAN,210 D. MOFFA,279 A. MOGGI,219 K. MOGUSHI,206 M. MOHAN,225\nS. R. P. MOHAPATRA,210 M. MONTANI,316, 317 C. J. MOORE,208 D. MORARU,242 G. MORENO,242 S. R. MORRISS,297 B. MOURS,203\nC. M. MOW-LOWRY,253 G. MUELLER,200 A. W. MUIR,231 ARUNAVA MUKHERJEE,205 D. MUKHERJEE,216 S. MUKHERJEE,297\nN. MUKUND,214 A. MULLAVEY,202 J. MUNCH,267 E. A. MU \u02dcNIZ,239 M. MURATORE,232 P. G. MURRAY,241 K. NAPIER,271\nI. NARDECCHIA,227, 228 L. NATICCHIONI,291, 230 R. K. NAYAK,338 J. NEILSON,303 G. NELEMANS,260, 209 T. J. N. NELSON,202\nM. NERY,205 A. NEUNZERT,313 L. NEVIN,196 J. M. NEWPORT,319 G. NEWTON,241, \u2021 K. K. Y. NG,287 T. T. NGUYEN,220 D. NICHOLS,260\nA. B. NIELSEN,205 S. NISSANKE,260, 209 A. NITZ,205 A. NOACK,205 F. NOCERA,225 D. NOLTING,202 C. NORTH,231 L. K. NUTTALL,231\nJ. OBERLING,242 G. D. O\u2019DEA,303 G. H. OGIN,339 J. J. OH,326 S. H. OH,326 F. OHME,205 M. A. OKADA,211 M. OLIVER,296\nP. OPPERMANN,205 RICHARD J. ORAM,202 B. O\u2019REILLY,202 R. ORMISTON,240 L. F. ORTEGA,200 R. O\u2019SHAUGHNESSY,252\nS. OSSOKINE,233 D. J. OTTAWAY,267 H. OVERMIER,202 B. J. OWEN,278 A. E. PACE,258 J. PAGE,332 M. A. PAGE,259 A. PAI,311, 340\nS. A. PAI,255 J. R. PALAMOS,264 O. PALASHOV,323 C. PALOMBA,230 A. PAL-SINGH,229 HOWARD PAN,282 HUANG-WEI PAN,282\n\n5\nB. PANG,243 P. T. H. PANG,287 C. PANKOW,284 F. PANNARALE,231 B. C. PANT,255 F. PAOLETTI,219 A. PAOLI,225 M. A. PAPA,233, 216, 205\nA. PARIDA,214 W. PARKER,202 D. PASCUCCI,241 A. PASQUALETTI,225 R. PASSAQUIETI,218, 219 D. PASSUELLO,219 M. PATIL,328\nB. PATRICELLI,341, 219 B. L. PEARLSTONE,241 M. PEDRAZA,196 R. PEDURAND,221, 342 L. PEKOWSKY,239 A. PELE,202 S. PENN,343\nC. J. PEREZ,242 A. PERRECA,196, 304, 289 L. M. PERRI,284 H. P. PFEIFFER,307, 233 M. PHELPS,241 O. J. PICCINNI,291, 230 M. PICHOT,261\nF. PIERGIOVANNI,316, 317 V. PIERRO,204 G. PILLANT,225 L. PINARD,221 I. M. PINTO,204 M. PIRELLO,242 M. PITKIN,241 M. POE,216\nR. POGGIANI,218, 219 P. POPOLIZIO,225 E. K. PORTER,234 A. POST,205 J. POWELL,241, 344 J. PRASAD,214 J. W. W. PRATT,232\nG. PRATTEN,296 V. PREDOI,231 T. PRESTEGARD,216 M. PRIJATELJ,205 M. PRINCIPE,204 S. PRIVITERA,233 G. A. PRODI,304, 289\nL. G. PROKHOROV,256 O. PUNCKEN,205 M. PUNTURO,238 P. PUPPO,230 M. P \u00a8URRER,233 H. QI,216 V. QUETSCHKE,297\nE. A. QUINTERO,196 R. QUITZOW-JAMES,264 F. J. RAAB,242 D. S. RABELING,220 H. RADKINS,242 P. RAFFAI,250 S. RAJA,255\nC. RAJAN,255 B. RAJBHANDARI,278 M. RAKHMANOV,297 K. E. RAMIREZ,297 A. RAMOS-BUADES,296 P. RAPAGNANI,291, 230\nV. RAYMOND,233 M. RAZZANO,218, 219 J. READ,224 T. REGIMBAU,261 L. REI,254 S. REID,257 D. H. REITZE,196, 200 W. REN,207\nS. D. REYES,239 F. RICCI,291, 230 P. M. RICKER,207 S. RIEGER,205 K. RILES,313 M. RIZZO,252 N. A. ROBERTSON,196, 241 R. ROBIE,241\nF. ROBINET,223 A. ROCCHI,228 L. ROLLAND,203 J. G. ROLLINS,196 V. J. ROMA,264 R. ROMANO,198, 199 C. L. ROMEL,242\nJ. H. ROMIE,202 D. ROSI \u00b4NSKA,345, 251 M. P. ROSS,346 S. ROWAN,241 A. R \u00a8UDIGER,205 P. RUGGI,225 G. RUTINS,222 K. RYAN,242\nS. SACHDEV,196 T. SADECKI,242 L. SADEGHIAN,216 M. SAKELLARIADOU,347 L. SALCONI,225 M. SALEEM,311 F. SALEMI,205\nA. SAMAJDAR,338 L. SAMMUT,201 L. M. SAMPSON,284 E. J. SANCHEZ,196 L. E. SANCHEZ,196 N. SANCHIS-GUAL,280 V. SANDBERG,242\nJ. R. SANDERS,239 B. SASSOLAS,221 P. R. SAULSON,239 O. SAUTER,313 R. L. SAVAGE,242 A. SAWADSKY,229 P. SCHALE,264\nM. SCHEEL,243 J. SCHEUER,284 J. SCHMIDT,205 P. SCHMIDT,196, 260 R. SCHNABEL,229 R. M. S. SCHOFIELD,264 A. SCH \u00a8ONBECK,229\nE. SCHREIBER,205 D. SCHUETTE,205, 217 B. W. SCHULTE,205 B. F. SCHUTZ,231, 205 S. G. SCHWALBE,232 J. SCOTT,241 S. M. SCOTT,220\nE. SEIDEL,207 D. SELLERS,202 A. S. SENGUPTA,348 D. SENTENAC,225 V. SEQUINO,227, 228, 212 A. SERGEEV,323 D. A. SHADDOCK,220\nT. J. SHAFFER,242 A. A. SHAH,332 M. S. SHAHRIAR,284 M. B. SHANER,303 L. SHAO,233 B. SHAPIRO,246 P. SHAWHAN,270\nA. SHEPERD,216 D. H. SHOEMAKER,210 D. M. SHOEMAKER,271 K. SIELLEZ,271 X. SIEMENS,216 M. SIENIAWSKA,251 D. SIGG,242\nA. D. SILVA,211 L. P. SINGER,274 A. SINGH,233, 205, 217 A. SINGHAL,212, 230 A. M. SINTES,296 B. J. J. SLAGMOLEN,220 B. SMITH,202\nJ. R. SMITH,224 R. J. E. SMITH,196, 201 S. SOMALA,349 E. J. SON,326 J. A. SONNENBERG,216 B. SORAZU,241 F. SORRENTINO,254\nT. SOURADEEP,214 A. P. SPENCER,241 A. K. SRIVASTAVA,299 K. STAATS,232 A. STALEY,245 M. STEINKE,205 J. STEINLECHNER,229, 241\nS. STEINLECHNER,229 D. STEINMEYER,205 S. P. STEVENSON,253, 344 R. STONE,297 D. J. STOPS,253 K. A. STRAIN,241\nG. STRATTA,316, 317 S. E. STRIGIN,256 A. STRUNK,242 R. STURANI,350 A. L. STUVER,202 T. Z. SUMMERSCALES,351 L. SUN,290\nS. SUNIL,299 J. SURESH,214 P. J. SUTTON,231 B. L. SWINKELS,225 M. J. SZCZEPA \u00b4NCZYK,232 M. TACCA,209 S. C. TAIT,241\nC. TALBOT,201 D. TALUKDER,264 D. B. TANNER,200 M. T \u00b4APAI,312 A. TARACCHINI,233 J. D. TASSON,266 J. A. TAYLOR,332\nR. TAYLOR,196 S. V. TEWARI,343 T. THEEG,205 F. THIES,205 E. G. THOMAS,253 M. THOMAS,202 P. THOMAS,242 K. A. THORNE,202\nE. THRANE,201 S. TIWARI,212, 289 V. TIWARI,231 K. V. TOKMAKOV,257 K. TOLAND,241 M. TONELLI,218, 219 Z. TORNASI,241\nA. TORRES-FORN\u00b4E,280 C. I. TORRIE,196 D. T \u00a8OYR \u00a8A,253 F. TRAVASSO,225, 238 G. TRAYLOR,202 J. TRINASTIC,200 M. C. TRINGALI,304, 289\nL. TROZZO,352, 219 K. W. TSANG,209 M. TSE,210 R. TSO,196 L. TSUKADA,276 D. TSUNA,276 D. TUYENBAYEV,297 K. UENO,216\nD. UGOLINI,353 C. S. UNNIKRISHNAN,314 A. L. URBAN,196 S. A. USMAN,231 H. VAHLBRUCH,217 G. VAJENTE,196 G. VALDES,197\nN. VAN BAKEL,209 M. VAN BEUZEKOM,209 J. F. J. VAN DEN BRAND,269, 209 C. VAN DEN BROECK,209, 354 D. C. VANDER-HYDE,239\nL. VAN DER SCHAAF,209 J. V. VAN HEIJNINGEN,209 A. A. VAN VEGGEL,241 M. VARDARO,248, 249 V. VARMA,243 S. VASS,196\nM. VAS \u00b4UTH,244 A. VECCHIO,253 G. VEDOVATO,249 J. VEITCH,241 P. J. VEITCH,267 K. VENKATESWARA,346 G. VENUGOPALAN,196\nD. VERKINDT,203 F. VETRANO,316, 317 A. VICER\u00b4E,316, 317 A. D. VIETS,216 S. VINCIGUERRA,253 D. J. VINE,222 J.-Y. VINET,261\nS. VITALE,210 T. VO,239 H. VOCCA,237, 238 C. VORVICK,242 S. P. VYATCHANIN,256 A. R. WADE,196 L. E. WADE,279 M. WADE,279\nR. WALET,209 M. WALKER,224 L. WALLACE,196 S. WALSH,233, 205, 216 G. WANG,212, 317 H. WANG,253 J. Z. WANG,258 W. H. WANG,297\nY. F. WANG,287 R. L. WARD,220 J. WARNER,242 M. WAS,203 J. WATCHI,292 B. WEAVER,242 L.-W. WEI,205, 217 M. WEINERT,205\nA. J. WEINSTEIN,196 R. WEISS,210 L. WEN,259 E. K. WESSEL,207 P. WESSELS,205 J. WESTERWECK,205 T. WESTPHAL,205 K. WETTE,220\nJ. T. WHELAN,252 B. F. WHITING,200 C. WHITTLE,201 D. WILKEN,205 D. WILLIAMS,241 R. D. WILLIAMS,196 A. R. WILLIAMSON,260\nJ. L. WILLIS,196, 355 B. WILLKE,217, 205 M. H. WIMMER,205 W. WINKLER,205 C. C. WIPF,196 H. WITTEL,205, 217 G. WOAN,241\nJ. WOEHLER,205 J. WOFFORD,252 K. W. K. WONG,287 J. WORDEN,242 J. L. WRIGHT,241 D. S. WU,205 D. M. WYSOCKI,252 S. XIAO,196\nH. YAMAMOTO,196 C. C. YANCEY,270 L. YANG,356 M. J. YAP,220 M. YAZBACK,200 HANG YU,210 HAOCUN YU,210 M. YVERT,203\nA. ZADRO\u02d9ZNY,327 M. ZANOLIN,232 T. ZELENOVA,225 J.-P. ZENDRI,249 M. ZEVIN,284 L. ZHANG,196 M. ZHANG,335 T. ZHANG,241\nY.-H. ZHANG,252 C. ZHAO,259 M. ZHOU,284 Z. ZHOU,284 S. J. ZHU,233, 205 X. J. ZHU,201 M. E. ZUCKER,196, 210 AND J. ZWEIZIG196\n(LIGO SCIENTIFIC COLLABORATION AND VIRGO COLLABORATION)\n1GRPHE - Universit\u00b4e de Haute Alsace - Institut universitaire de technologie de Colmar, 34 rue du Grillenbreit BP 50568 - 68008 Colmar, France\n2Technical University of Catalonia, Laboratory of Applied Bioacoustics, Rambla Exposici\u00b4o, 08800 Vilanova i la Geltr\u00b4u, Barcelona, Spain\n3INFN - Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy\n4Institut d\u2019Investigaci\u00b4o per a la Gesti\u00b4o Integrada de les Zones Costaneres (IGIC) - Universitat Polit`ecnica de Val`encia. C/ Paranimf 1, 46730 Gandia, Spain\n5Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n6APC, Univ Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cit\u00b4e, France\n\n6\n7IFIC - Instituto de F\u00b4\u0131sica Corpuscular (CSIC - Universitat de Val`encia) c/ Catedr\u00b4atico Jos\u00b4e Beltr\u00b4an, 2 E-46980 Paterna, Valencia, Spain\n8LAM - Laboratoire d\u2019Astrophysique de Marseille, P\u02c6ole de l\u2019 \u00b4Etoile Site de Ch\u02c6ateau-Gombert, rue Fr\u00b4ed\u00b4eric Joliot-Curie 38, 13388 Marseille Cedex 13, France\n9National Center for Energy Sciences and Nuclear Techniques, B.P.1382, R. P.10001 Rabat, Morocco\n10INFN - Laboratori Nazionali del Sud (LNS), Via S. So\ufb01a 62, 95123 Catania, Italy\n11Nikhef, Science Park, Amsterdam, The Netherlands\n12Huygens-Kamerlingh Onnes Laboratorium, Universiteit Leiden, The Netherlands\n13Institute of Space Science, RO-077125 Bucharest, M\u02d8agurele, Romania\n14Universiteit van Amsterdam, Instituut voor Hoge-Energie Fysica, Science Park 105, 1098 XG Amsterdam, The Netherlands\n15INFN - Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy\n16Dipartimento di Fisica dell\u2019Universit`a La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy\n17Gran Sasso Science Institute, Viale Francesco Crispi 7, 00167 L\u2019Aquila, Italy\n18University Mohammed V in Rabat, Faculty of Sciences, 4 av. Ibn Battouta, B.P. 1014, R.P. 10000 Rabat, Morocco\n19INFN - Sezione di Bologna, Viale Berti-Pichat 6/2, 40127 Bologna, Italy\n20INFN - Sezione di Bari, Via E. Orabona 4, 70126 Bari, Italy\n21Department of Computer Architecture and Technology/CITIC, University of Granada, 18071 Granada, Spain\n22G\u00b4eoazur, UCA, CNRS, IRD, Observatoire de la C\u02c6ote d\u2019Azur, Sophia Antipolis, France\n23Dipartimento di Fisica dell\u2019Universit`a, Via Dodecaneso 33, 16146 Genova, Italy\n24Universit\u00b4e Paris-Sud, 91405 Orsay Cedex, France\n25Friedrich-Alexander-Universit\u00a8at Erlangen-N\u00a8urnberg, Erlangen Centre for Astroparticle Physics, Erwin-Rommel-Str. 1, 91058 Erlangen, Germany\n26University Mohammed I, Laboratory of Physics of Matter and Radiations, B.P.717, Oujda 6000, Morocco\n27Institut f\u00a8ur Theoretische Physik und Astrophysik, Universit\u00a8at W\u00a8urzburg, Emil-Fischer Str. 31, 97074 W\u00a8urzburg, Germany\n28Dipartimento di Fisica e Astronomia dell\u2019Universit`a, Viale Berti Pichat 6/2, 40127 Bologna, Italy\n29Laboratoire de Physique Corpusculaire, Clermont Universit\u00b4e, Universit\u00b4e Blaise Pascal, CNRS/IN2P3, BP 10448, F-63000 Clermont-Ferrand, France\n30INFN - Sezione di Catania, Viale Andrea Doria 6, 95125 Catania, Italy\n3131, Aix Marseille Universit\u00b4e CNRS ENSAM LSIS UMR 7296 13397 Marseille, France; Universit\u00b4e de Toulon CNRS LSIS UMR 7296, 83957 La Garde, France\n32Institut Universitaire de France, 75005 Paris, France\n33Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n34Royal Netherlands Institute of Sea Research (NIOZ) and Utrecht University, Landsdiep 4, 1797 SZ \u2019t Horntje (Texel), the Netherlands\n35Dr. Remeis-Sternwarte and ECAP, Friedrich-Alexander-Universit\u00a8at Erlangen-N\u00a8urnberg, Sternwartstr. 7, 96049 , Germany\n36Moscow State University, Skobeltsyn Institute of Nuclear Physics, Leninskie gory, 119991 Moscow, Russia\n37Mediterranean Institute of Oceanography (MIO), Aix-Marseille University, 13288, Marseille, Cedex 9, France; Universit\u00b4e du Sud Toulon-Var, CNRS-INSU/IRD\nUM 110, 83957, La Garde Cedex, France\n38Dipartimento di Fisica ed Astronomia dell\u2019Universit`a, Viale Andrea Doria 6, 95125 Catania, Italy\n39Direction des Sciences de la Mati`ere - Institut de recherche sur les lois fondamentales de l\u2019Univers - Service de Physique des Particules, CEA Saclay, 91191\nGif-sur-Yvette Cedex, France\n40INFN - Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy\n41Dipartimento di Fisica dell\u2019Universit`a, Largo B. Pontecorvo 3, 56127 Pisa, Italy\n42INFN - Sezione di Napoli, Via Cintia 80126 Napoli, Italy\n43Dipartimento di Fisica dell\u2019Universit`a Federico II di Napoli, Via Cintia 80126, Napoli, Italy\n44Dpto. de F\u00b4\u0131sica Te\u00b4orica y del Cosmos & C.A.F.P.E., University of Granada, 18071 Granada, Spain\n45Dr. Remeis-Sternwarte and ECAP, Friedrich-Alexander-Universit\u00a8at Erlangen-N\u00a8urnberg, Sternwartstr. 7, 96049 Bamberg, Germany\n46Department of Physics, University of Adelaide, Adelaide, 5005, Australia\n47DESY, D-15738 Zeuthen, Germany\n48Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand\n49Universit\u00b4e Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium\n50Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark\n51Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden\n52D\u00b4epartement de physique nucl\u00b4eaire et corpusculaire, Universit\u00b4e de Gen`eve, CH-1211 Gen`eve, Switzerland\n53Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universit\u00a8at Erlangen-N\u00a8urnberg, D-91058 Erlangen, Germany\n54Department of Physics, Marquette University, Milwaukee, WI, 53201, USA\n55Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA\n56Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n57III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany\n58Physics Department, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA\n\n7\n59Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1\n60Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA\n61Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany\n62Dept. of Physics, University of California, Berkeley, CA 94720, USA\n63Dept. of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH 43210, USA\n64Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA\n65Fakult\u00a8at f\u00a8ur Physik & Astronomie, Ruhr-Universit\u00a8at Bochum, D-44780 Bochum, Germany\n66Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany\n67Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA\n68Dept. of Physics, University of Maryland, College Park, MD 20742, USA\n69Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA\n70Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA\n71Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany\n72Dept. of Physics, Sungkyunkwan University, Suwon 440-746, Korea\n73Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden\n74Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA\n75Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium\n76SNOLAB, 1039 Regional Road 24, Creighton Mine 9, Lively, ON, Canada P3Y 1N2\n77Institut f\u00a8ur Kernphysik, Westf\u00a8alische Wilhelms-Universit\u00a8at M\u00a8unster, D-48149 M\u00a8unster, Germany\n78Physik-department, Technische Universit\u00a8at M\u00a8unchen, D-85748 Garching, Germany\n79Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA\n80Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA\n81Bartol Research Institute and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA\n82Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium\n83Institut f\u00a8ur Physik, Humboldt-Universit\u00a8at zu Berlin, D-12489 Berlin, Germany\n84Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA\n85Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA\n86Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032, Japan\n87Dept. of Physics and Institute for Global Prominent Research, Chiba University, Chiba 263-8522, Japan\n88CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA\n89Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA\n90Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA\n91Universit\u00b4e de Mons, 7000 Mons, Belgium\n92Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA\n93Dept. of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA\n94Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA\n95Dept. of Physics, Yale University, New Haven, CT 06520, USA\n96School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA\n97Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA\n98Dept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK\n99IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands\n100Laborat\u00b4orio de Instrumentac\u00b8\u02dcao e F\u00b4\u0131sica Experimental de Part\u00b4\u0131culas \u2013 LIP and Instituto Superior T\u00b4ecnico \u2013 IST, Universidade de Lisboa \u2013 UL, Lisboa, Portugal\n101Osservatorio Astro\ufb01sico di Torino (INAF), Torino, Italy\n102INFN, Sezione di Torino, Torino, Italy\n103Universidade de S\u02dcao Paulo, Instituto de F\u00b4\u0131sica, S\u02dcao Paulo, SP, Brazil\n104University of Adelaide, Adelaide, S.A., Australia\n105Centro At\u00b4omico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, Argentina\n106Instituto de Tecnolog\u00b4\u0131as en Detecci\u00b4on y Astropart\u00b4\u0131culas (CNEA, CONICET, UNSAM), Buenos Aires, Argentina\n107Universidad Tecnol\u00b4ogica Nacional \u2013 Facultad Regional Buenos Aires, Buenos Aires, Argentina\n108Universidad Nacional Aut\u00b4onoma de M\u00b4exico, M\u00b4exico, D.F., M\u00b4exico\n109Universidad de Santiago de Compostela, Santiago de Compostela, Spain\n110Gran Sasso Science Institute (INFN), L\u2019Aquila, Italy\n111INFN Laboratori Nazionali del Gran Sasso, Assergi (L\u2019Aquila), Italy\n112Department of Physics and Astronomy, Lehman College, City University of New York, Bronx, NY, USA\n\n8\n113INFN, Sezione di Napoli, Napoli, Italy\n114Institute of Space Science, Bucharest-Magurele, Romania\n115Universidad Industrial de Santander, Bucaramanga, Colombia\n116Observatorio Pierre Auger, Malarg\u00a8ue, Argentina\n117Observatorio Pierre Auger and Comisi\u00b4on Nacional de Energ\u00b4\u0131a At\u00b4omica, Malarg\u00a8ue, Argentina\n118University Politehnica of Bucharest, Bucharest, Romania\n119\u201cHoria Hulubei\u201d National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania\n120Universit`a di Napoli \u201dFederico II\u201d, Dipartimento di Fisica \u201cEttore Pancini\u201c, Napoli, Italy\n121Ohio State University, Columbus, OH, USA\n122Bergische Universit\u00a8at Wuppertal, Department of Physics, Wuppertal, Germany\n123Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit\u00b4e Grenoble-Alpes, CNRS/IN2P3, Grenoble, France\n124Universit`a Torino, Dipartimento di Fisica, Torino, Italy\n125Max-Planck-Institut f\u00a8ur Radioastronomie, Bonn, Germany\n126Institut de Physique Nucl\u00b4eaire d\u2019Orsay (IPNO), Universit\u00b4e Paris-Sud, Univ. Paris/Saclay, CNRS-IN2P3, Orsay, France\n127Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic\n128Universit`a del Salento, Dipartimento di Matematica e Fisica \u201cE. De Giorgi\u201d, Lecce, Italy\n129INFN, Sezione di Lecce, Lecce, Italy\n130Universidade Federal do Rio de Janeiro, Instituto de F\u00b4\u0131sica, Rio de Janeiro, RJ, Brazil\n131Institute of Nuclear Physics PAN, Krakow, Poland\n132Karlsruhe Institute of Technology, Institut f\u00a8ur Kernphysik, Karlsruhe, Germany\n133Colorado State University, Fort Collins, CO\n134RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany\n135Karlsruhe Institute of Technology, Institut f\u00a8ur Experimentelle Kernphysik (IEKP), Karlsruhe, Germany\n136Universit\u00a8at Siegen, Fachbereich 7 Physik \u2013 Experimentelle Teilchenphysik, Siegen, Germany\n137Universidad de Granada and C.A.F.P.E., Granada, Spain\n138Universit`a di Catania, Dipartimento di Fisica e Astronomia, Catania, Italy\n139INFN, Sezione di Catania, Catania, Italy\n140Universidad Aut\u00b4onoma de Chiapas, Tuxtla Guti\u00b4errez, Chiapas, M\u00b4exico\n141Universit`a di Milano, Dipartimento di Fisica, Milano, Italy\n142Universidade de S\u02dcao Paulo, Escola de Engenharia de Lorena, Lorena, SP, Brazil\n143Universidad Michoacana de San Nicol\u00b4as de Hidalgo, Morelia, Michoac\u00b4an, M\u00b4exico\n144Universidade Estadual de Campinas, IFGW, Campinas, SP, Brazil\n145Instituto de Tecnolog\u00b4\u0131as en Detecci\u00b4on y Astropart\u00b4\u0131culas (CNEA, CONICET, UNSAM), and Universidad Tecnol\u00b4ogica Nacional \u2013 Facultad Regional Mendoza\n(CONICET/CNEA), Mendoza, Argentina\n146Pennsylvania State University, University Park, PA, USA\n147INFN, Sezione di Milano, Milano, Italy\n148Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali , Milano, Italy\n149Case Western Reserve University, Cleveland, OH, USA\n150University of Chicago, Enrico Fermi Institute, Chicago, IL, USA\n151Universit`a del Salento, Dipartimento di Ingegneria, Lecce, Italy\n152Instituto de Astronom\u00b4\u0131a y F\u00b4\u0131sica del Espacio (IAFE, CONICET-UBA), Buenos Aires, Argentina\n153Departamento de F\u00b4\u0131sica and Departamento de Ciencias de la Atm\u00b4osfera y los Oc\u00b4eanos, FCEyN, Universidad de Buenos Aires and CONICET, Buenos Aires,\nArgentina\n154Universidade Federal Fluminense, EEIMVR, Volta Redonda, RJ, Brazil\n155Nationaal Instituut voor Kernfysica en Hoge Energie Fysica (NIKHEF), Science Park, Amsterdam, The Netherlands\n156Universidade Federal do Rio de Janeiro (UFRJ), Observat\u00b4orio do Valongo, Rio de Janeiro, RJ, Brazil\n157Universidade de S\u02dcao Paulo, Instituto de F\u00b4\u0131sica de S\u02dcao Carlos, S\u02dcao Carlos, SP, Brazil\n158Universidade Federal do Paran\u00b4a, Setor Palotina, Palotina, Brazil\n159IFLP, Universidad Nacional de La Plata and CONICET, La Plata, Argentina\n160Universit\u00a8at Hamburg, II. Institut f\u00a8ur Theoretische Physik, Hamburg, Germany\n161Fermi National Accelerator Laboratory, USA\n162Stichting Astronomisch Onderzoek in Nederland (ASTRON), Dwingeloo, The Netherlands\n163New York University, New York, NY, USA\n164Karlsruhe Institute of Technology, Institut f\u00a8ur Prozessdatenverarbeitung und Elektronik, Karlsruhe, Germany\n\n9\n165Michigan Technological University, Houghton, MI, USA\n166Experimental Particle Physics Department, J. Stefan Institute, Ljubljana, Slovenia\n167Center for Astrophysics and Cosmology (CAC), University of Nova Gorica, Nova Gorica, Slovenia\n168Instituto de F\u00b4\u0131sica de Rosario (IFIR) \u2013 CONICET/U.N.R. and Facultad de Ciencias Bioqu\u00b4\u0131micas y Farmac\u00b4euticas U.N.R., Rosario, Argentina\n169Laboratoire de Physique Nucl\u00b4eaire et de Hautes Energies (LPNHE), Universit\u00b4es Paris 6 et Paris 7, CNRS-IN2P3, Paris, France\n170SUBATECH, \u00b4Ecole des Mines de Nantes, CNRS-IN2P3, Universit\u00b4e de Nantes, France\n171Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, Brazil\n172University of \u0141\u00b4od\u00b4z, Faculty of Astrophysics, \u0141\u00b4od\u00b4z, Poland\n173University of \u0141\u00b4od\u00b4z, Faculty of High-Energy Astrophysics,\u0141\u00b4od\u00b4z, Poland\n174Universidade Estadual de Feira de Santana, Feira de Santana, Brazil\n175Palacky University, RCPTM, Olomouc, Czech Republic\n176Colorado School of Mines, Golden, CO, USA\n177Centro Federal de Educac\u00b8\u02dcao Tecnol\u00b4ogica Celso Suckow da Fonseca, Nova Friburgo, Brazil\n178Universidade Federal do ABC, Santo Andr\u00b4e, SP, Brazil\n179Benem\u00b4erita Universidad Aut\u00b4onoma de Puebla, Puebla, M\u00b4exico\n180Universit\u00b4e Libre de Bruxelles (ULB), Brussels, Belgium\n181Centro de Investigaci\u00b4on y de Estudios Avanzados del IPN (CINVESTAV), M\u00b4exico, D.F., M\u00b4exico\n182Louisiana State University, Baton Rouge, LA, USA\n183Universit`a di Roma \u201cTor Vergata\u201d, Dipartimento di Fisica, Roma, Italy\n184INFN, Sezione di Roma \u201dTor Vergata\u201d, Roma, Italy\n185also at Universidade Federal de Alfenas, Bras\u00b4\u0131lia, Brazil\n186Charles University, Faculty of Mathematics and Physics, Institute of Particle and Nuclear Physics, Prague, Czech Republic\n187Centro de Investigaciones en L\u00b4aseres y Aplicaciones, CITEDEF and CONICET, Villa Martelli, Argentina\n188Unidad Profesional Interdisciplinaria en Ingenier\u00b4\u0131a y Tecnolog\u00b4\u0131as Avanzadas del Instituto Polit\u00b4ecnico Nacional (UPIITA-IPN), M\u00b4exico, D.F., M\u00b4exico\n189Universit`a dell\u2019Aquila, Dipartimento di Scienze Fisiche e Chimiche, L\u2019Aquila, Italy\n190KVI \u2013 Center for Advanced Radiation Technology, University of Groningen, Groningen, The Netherlands\n191also at Vrije Universiteit Brussels, Brussels, Belgium\n192INAF \u2013 Istituto di Astro\ufb01sica Spaziale e Fisica Cosmica di Palermo, Palermo, Italy\n193University of Nebraska, Lincoln, NE, USA\n194Northeastern University, Boston, MA, USA\n195School of Physics and Astronomy, University of Leeds, Leeds, United Kingdom\n196LIGO, California Institute of Technology, Pasadena, CA 91125, USA\n197Louisiana State University, Baton Rouge, LA 70803, USA\n198Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy\n199INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy\n200University of Florida, Gainesville, FL 32611, USA\n201OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n202LIGO Livingston Observatory, Livingston, LA 70754, USA\n203Laboratoire d\u2019Annecy-le-Vieux de Physique des Particules (LAPP), Universit\u00b4e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France\n204University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n205Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n206The University of Mississippi, University, MS 38677, USA\n207NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA\n208University of Cambridge, Cambridge CB2 1TN, United Kingdom\n209Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands\n210LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n211Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n212Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n213INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n214Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n215International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n216University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n217Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n218Universit`a di Pisa, I-56127 Pisa, Italy\n\n10\n219INFN, Sezione di Pisa, I-56127 Pisa, Italy\n220OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n221Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France\n222SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n223LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit\u00b4e Paris-Saclay, F-91898 Orsay, France\n224California State University Fullerton, Fullerton, CA 92831, USA\n225European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n226Chennai Mathematical Institute, Chennai 603103, India\n227Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n228INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n229Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n230INFN, Sezione di Roma, I-00185 Roma, Italy\n231Cardiff University, Cardiff CF24 3AA, United Kingdom\n232Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n233Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany\n234APC, AstroParticule et Cosmologie, Universit\u00b4e Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cit\u00b4e, F-75205 Paris Cedex 13,\nFrance\n235Korea Institute of Science and Technology Information, Daejeon 34141, Korea\n236West Virginia University, Morgantown, WV 26506, USA\n237Universit`a di Perugia, I-06123 Perugia, Italy\n238INFN, Sezione di Perugia, I-06123 Perugia, Italy\n239Syracuse University, Syracuse, NY 13244, USA\n240University of Minnesota, Minneapolis, MN 55455, USA\n241SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n242LIGO Hanford Observatory, Richland, WA 99352, USA\n243Caltech CaRT, Pasadena, CA 91125, USA\n244Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl\u00b4os \u00b4ut 29-33, Hungary\n245Columbia University, New York, NY 10027, USA\n246Stanford University, Stanford, CA 94305, USA\n247Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n248Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n249INFN, Sezione di Padova, I-35131 Padova, Italy\n250Institute of Physics, E\u00a8otv\u00a8os University, P\u00b4azm\u00b4any P. s. 1/A, Budapest 1117, Hungary\n251Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n252Rochester Institute of Technology, Rochester, NY 14623, USA\n253University of Birmingham, Birmingham B15 2TT, United Kingdom\n254INFN, Sezione di Genova, I-16146 Genova, Italy\n255RRCAT, Indore MP 452013, India\n256Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia\n257SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n258The Pennsylvania State University, University Park, PA 16802, USA\n259OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n260Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands\n261Artemis, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France\n262Institut FOTON, CNRS, Universit\u00b4e de Rennes 1, F-35042 Rennes, France\n263Washington State University, Pullman, WA 99164, USA\n264University of Oregon, Eugene, OR 97403, USA\n265Laboratoire Kastler Brossel, UPMC-Sorbonne Universit\u00b4es, CNRS, ENS-PSL Research University, Coll`ege de France, F-75005 Paris, France\n266Carleton College, North\ufb01eld, MN 55057, USA\n267OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n268Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n269VU University Amsterdam, 1081 HV Amsterdam, The Netherlands\n270University of Maryland, College Park, MD 20742, USA\n271Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA\n\n11\n272Universit\u00b4e Claude Bernard Lyon 1, F-69622 Villeurbanne, France\n273Universit`a di Napoli \u2018Federico II,\u2019 Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy\n274NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n275Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n276RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.\n277Tsinghua University, Beijing 100084, China\n278Texas Tech University, Lubbock, TX 79409, USA\n279Kenyon College, Gambier, OH 43022, USA\n280Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n281Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, I-00184 Roma, Italy\n282National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China\n283Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n284Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA\n285University of Chicago, Chicago, IL 60637, USA\n286Pusan National University, Busan 46241, Korea\n287The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n288INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n289INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n290OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n291Universit`a di Roma \u2018La Sapienza,\u2019 I-00185 Roma, Italy\n292Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n293Sonoma State University, Rohnert Park, CA 94928, USA\n294Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n295Montana State University, Bozeman, MT 59717, USA\n296Universitat de les Illes Balears, IAC3\u2014IEEC, E-07122 Palma de Mallorca, Spain\n297The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n298Bellevue College, Bellevue, WA 98007, USA\n299Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n300The University of Shef\ufb01eld, Shef\ufb01eld S10 2TN, United Kingdom\n301Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n302INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n303California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA\n304Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n305Montclair State University, Montclair, NJ 07043, USA\n306National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan\n307Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada\n308Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n309School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom\n310University and Institute of Advanced Research, Koba Institutional Area, Gandhinagar Gujarat 382007, India\n311IISER-TVM, CET Campus, Trivandrum Kerala 695016, India\n312University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n313University of Michigan, Ann Arbor, MI 48109, USA\n314Tata Institute of Fundamental Research, Mumbai 400005, India\n315INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy\n316Universit`a degli Studi di Urbino \u2018Carlo Bo,\u2019 I-61029 Urbino, Italy\n317INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n318Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n319American University, Washington, D.C. 20016, USA\n320University of Bia\u0142ystok, 15-424 Bia\u0142ystok, Poland\n321University of Southampton, Southampton SO17 1BJ, United Kingdom\n322University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA\n323Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n324Korea Astronomy and Space Science Institute, Daejeon 34055, Korea\n325Inje University Gimhae, South Gyeongsang 50834, Korea\n\n12\n326National Institute for Mathematical Sciences, Daejeon 34047, Korea\n327NCBJ, 05-400 \u00b4Swierk-Otwock, Poland\n328Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n329Hillsdale College, Hillsdale, MI 49242, USA\n330Hanyang University, Seoul 04763, Korea\n331Seoul National University, Seoul 08826, Korea\n332NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n333ESPCI, CNRS, F-75005 Paris, France\n334Southern University and A&M College, Baton Rouge, LA 70813, USA\n335College of William and Mary, Williamsburg, VA 23187, USA\n336Centre Scienti\ufb01que de Monaco, 8 quai Antoine Ier, MC-98000, Monaco\n337Indian Institute of Technology Madras, Chennai 600036, India\n338IISER-Kolkata, Mohanpur, West Bengal 741252, India\n339Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA\n340Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India\n341Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy\n342Universit\u00b4e de Lyon, F-69361 Lyon, France\n343Hobart and William Smith Colleges, Geneva, NY 14456, USA\n344OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n345Janusz Gil Institute of Astronomy, University of Zielona G\u00b4ora, 65-265 Zielona G\u00b4ora, Poland\n346University of Washington, Seattle, WA 98195, USA\n347King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n348Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India\n349Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n350International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n351Andrews University, Berrien Springs, MI 49104, USA\n352Universit`a di Siena, I-53100 Siena, Italy\n353Trinity University, San Antonio, TX 78212, USA\n354Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands\n355Abilene Christian University, Abilene, TX 79699, USA\n356Colorado State University, Fort Collins, CO 80523, USA\nSubmitted to ApJ\nABSTRACT\nThe Advanced LIGO and Advanced Virgo observatories recently discovered gravitational waves from a binary neutron star\ninspiral. A short gamma-ray burst (GRB) that followed the merger of this binary was also recorded by the Fermi Gamma-ray Burst\nMonitor (Fermi-GBM), and the Anticoincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics\nLaboratory (INTEGRAL), indicating particle acceleration by the source. The precise location of the event was determined by\noptical detections of emission following the merger. We searched for high-energy neutrinos from the merger in the GeV\u2013EeV\nenergy range using the ANTARES, IceCube, and Pierre Auger Observatories. No neutrinos directionally coincident with the\nsource were detected within \u00b1500 s around the merger time. Additionally, no MeV neutrino burst signal was detected coincident\nwith the merger. We further carried out an extended search in the direction of the source for high-energy neutrinos within the\n14-day period following the merger, but found no evidence of emission. We used these results to probe dissipation mechanisms\nin relativistic out\ufb02ows driven by the binary neutron star merger. The non-detection is consistent with model predictions of short\nGRBs observed at a large off-axis angle.\nKeywords: neutrinos \u2014 gravitational waves \u2014 gamma-ray burst: individual\n\u2217Deceased, August 2016.\n\u2020 Deceased, February 2017.\n\u2021 Deceased, December 2016.\n\n13\n1. INTRODUCTION\nThe observation of binary neutron star mergers with mul-\ntiple cosmic messengers is a unique opportunity that enables\nthe detailed study of the merger process, and provides in-\nsight into astrophysical particle acceleration and high-energy\nemission (e.g., Faber & Rasio 2012; Berger 2014; Bartos\net al. 2013; Abbott et al. 2017a). Binary neutron star merg-\ners are prime sources of gravitational waves (GWs; e.g.,\nAbadie et al. 2010), which provide information on the neu-\ntron star masses and spins (e.g., Veitch et al. 2015). Kilo-\nnova/macronova observations of the mergers provide further\ninformation on the mass ejected by the disruption of the neu-\ntron stars (e.g., Metzger 2017; Abbott et al. 2017b).\nParticle acceleration and high-energy emission by com-\npact objects are currently not well understood (e.g., M\u00b4esz\u00b4aros\n2013; Kumar & Zhang 2015), and could be deciphered by\ncombined information on the neutron star masses, ejecta\nmass, and gamma-ray burst (GRB) properties, as expected\nfrom multimessenger observations. In particular, the obser-\nvation of high-energy neutrinos would reveal the hadronic\ncontent and dissipation mechanism in relativistic out\ufb02ows\n(Waxman & Bahcall 1997). A quasi-diffuse \ufb02ux of high-\nenergy neutrinos of cosmic origin has been identi\ufb01ed by\nthe IceCube observatory (Aartsen et al. 2013; Aartsen et al.\n2013). The source population producing these neutrinos is\ncurrently not known.\nOn August 17, 2017, the Advanced LIGO (Aasi et al.\n2015) and Advanced Virgo (Acernese et al. 2015) obser-\nvatories recorded a GW signal, GW170817, from a bi-\nnary neutron star inspiral (Abbott et al. 2017c). Soon af-\nterwards, Fermi-GBM and INTEGRAL detected a short\nGRB, GRB170817A, from a consistent location (Gold-\nstein et al. 2017; Savchenko et al. 2017; Abbott et al.\n2017a).\nSubsequently, ultra-violet, optical, and infrared\nemission was observed from the merger, consistent with kilo-\nnova/macronova emission. Optical observations allowed the\nprecise localization of the merger in the galaxy NGC 4993,\nat\nequatorial\ncoordinates\n\u03b1(J2000.0) = 13h09m48.s085,\n\u03b4(J2000.0) = \u221223\u25e622\u203253.\u2032\u2032343 (Coulter et al. 2017b,a; Ab-\nbott et al. 2017d), and at a distance of \u223c40 Mpc. At later\ntimes, X-ray and radio emissions were also observed (Abbott\net al. 2017d), consistent with the expected afterglow of a\nshort GRB at high viewing angles (e.g., Abbott et al. 2017a).\nHigh-energy neutrino observatories continuously monitor\nthe whole sky or a large fraction of it, making them well\nsuited to study emission from GW sources, even for un-\nknown source locations or for emission prior to or after the\nGW detection (Adri\u00b4an-Mart\u00b4\u0131nez et al. 2016a; Albert et al.\n2017). It is also possible to rapidly analyze the recorded data\nand inform other observatories in case of a coincident de-\ntection, signi\ufb01cantly reducing the source localization uncer-\ntainty compared to that provided by GW information alone.\nIn this Letter we present searches for high-energy neu-\ntrinos in coincidence with GW170817/GRB170817A by\nthe three most sensitive high-energy neutrino observa-\ntories:\n(1) the ANTARES neutrino telescope (hereafter\nANTARES; Ageron et al. 2011), a ten megaton-scale un-\nderwater Cherenkov neutrino detector located at a depth of\n2500 m in the Mediterranean Sea; (2) the IceCube Neu-\ntrino Observatory (hereafter IceCube; Aartsen et al. 2017),\na gigaton-scale neutrino detector installed 1500 m deep in\nthe ice at the geographic South Pole, Antarctica; and (3)\nthe Pierre Auger Observatory (hereafter Auger; Aab et al.\n2015), a cosmic-ray air-shower detector consisting of 1660\nwater-Cherenkov stations spread over an area of \u223c3000 km2.\nAll three detectors joined the low-latency multimessenger\nfollow-up effort of LIGO-Virgo starting with LIGO\u2019s second\nobservation run, O2.\nUpon the identi\ufb01cation of the GW signal GW170817, pre-\nliminary information on this event was rapidly shared with\npartner observatories (Abbott et al. 2017d).\nIn response,\nIceCube (Bartos et al. 2017b,a,c), ANTARES (Ageron et al.\n2017a,b), and Auger (Alvarez-Muniz et al. 2017) promptly\nsearched for a neutrino counterpart, and shared their initial\nresults with partner observatories. Subsequently, the three\nfacilities carried out a more in-depth search for a neutrino\ncounterpart using the precise localization of the source.\nThis Letter is organized as follows.\nIn Section 2, we\npresent the neutrino searches carried out by ANTARES, Ice-\nCube, and Auger, as well as the results obtained. In Section\n3, we present constraints on processes in the merger that can\nlead to neutrino emission. We summarize our \ufb01ndings and\nconclude in Section 4.\n2. SEARCHES AND RESULTS\nNeutrino observatories detect secondary charged parti-\ncles produced in neutrino interaction with matter. Surface\ndetectors, such as Auger, use arrays of widely-spaced wa-\nter Cherenkov detectors to observe the air-shower parti-\ncles created by high-energy neutrinos. In detectors such as\nANTARES and IceCube, three-dimensional arrays of optical\nmodules deployed in water or ice detect the Cherenkov radia-\ntion from secondary charged particles that travel through the\ninstrumented detector region. For these detectors, the sec-\nondary particles can create two main event classes: track-like\nevents from charged-current interactions of muon neutrinos\nand from a minority of tau neutrino interactions; and shower-\nlike events from all other interactions (neutral-current in-\nteractions and charged-current interactions of electron and\ntau neutrinos). While energy deposition in track-like events\ncan happen over distances of O(km), shower-like events are\ncon\ufb01ned to much smaller regions.\nFor all detectors, neutrino signals must be identi\ufb01ed on top\nof a persistent background of charged particles produced by\n\n14\nFigure 1. Localizations and sensitive sky areas at the time of the GW event in equatorial coordinates: GW 90% credible-level localization\n(red contour; Abbott et al. 2017c), direction of NGC 4993 (black plus symbol; Coulter et al. 2017a), directions of IceCube\u2019s and ANTARES\u2019s\nneutrino candidates within 500 s of the merger (green crosses and blue diamonds, respectively), ANTARES\u2019s horizon separating down-going\n(north of horizon) and up-going (south of horizon) neutrino directions (dashed blue line), and Auger\u2019s \ufb01elds of view for Earth-skimming (darker\nblue) and down-going (lighter blue) directions. IceCube\u2019s up-going and down-going directions are on the northern and southern hemispheres,\nrespectively. The zenith angle of the source at the detection time of the merger was 73.8\u25e6for ANTARES, 66.6\u25e6for IceCube, and 91.9\u25e6for\nAuger.\nthe interaction of cosmic ray particles with the atmosphere\nabove the detectors. This discrimination is done by consid-\nering the observed direction and energy of the charged par-\nticles. Surface detectors focus on high-energy (\u22731017eV)\nshowers created close to the detector by neutrinos from near-\nhorizontal directions. In-ice and in-water detectors can select\nwell-reconstructed track events from the up-going direction\nwhere the Earth is used as a natural shield for the dominant\nbackground of penetrating muons from cosmic ray showers.\nBy requiring the neutrino interaction vertex to be contained\ninside the instrumented volume, or requiring its energy to\nbe suf\ufb01ciently high to be incompatible with the down-going\nmuon background, even neutrino events originating above\nthe horizon are identi\ufb01able. Neutrinos originating from cos-\nmic ray interactions in the atmosphere are also observed and\nconstitute the primary background for up-going and vertex-\ncontained event selections.\nAll three observatories, ANTARES, IceCube, and Auger,\nperformed searches for neutrino signals in coincidence with\nthe binary neutron star merger event GW170817, each us-\ning multiple event selections. Two different time windows\nwere used for the searches. First, we used a \u00b1500 s time\nwindow around the merger to search for neutrinos associated\nwith prompt and extended gamma-ray emission (Baret et al.\n2011; Kimura et al. 2017). Second, we searched for neutrinos\nover a longer 14-day time window following the GW detec-\ntion, to cover predictions of longer-lived emission processes\n(e.g., Gao et al. 2013; Fang & Metzger 2017).\n2.1. ANTARES\nThe ANTARES neutrino telescope has been continuously\noperating since 2008. Located deep (2500 m) in the Mediter-\nranean Sea, 40 km from Toulon (France), it is a 10 Mt-\nscale array of photosensors, detecting neutrinos with energies\nabove O(100) GeV.\nBased on the originally communicated locations of the\nGW signal and the GRB detection, high-energy neutrino can-\ndidates were initially searched for in the ANTARES online\ndata stream, relying on a fast algorithm which selects only\nup-going neutrino track candidates (Adri\u00b4an-Mart\u00b4\u0131nez et al.\n2016b). No up-going muon neutrino candidate events were\nfound in a \u00b1500 s time window centered on the GW event\ntime \u2013 for an expected number of atmospheric background\nevents of \u223c10\u22122 during the coincident time window. An ex-\ntended online search during \u00b11 h also resulted in no up-going\nneutrino coincidences.\nAs it subsequently became clear, the precise direction of\norigin of GW170817 in NGC 4993 was above the ANTARES\nhorizon at the detection time of the binary merger (see Fig. 1).\nThus, a dedicated analysis looking for down-going muon\nneutrino candidates in the online ANTARES data stream was\nalso performed. No neutrino counterparts were found in this\nanalysis.\nThe results of these low-latency searches were\nshared with follow-up partners within a few hours for the\nup-going search and a few days for the down-going search\n(Ageron et al. 2017a,b).\nHere, ANTARES used an updated high-energy neutrino fol-\nlow up of GW170817 that includes the shower channel. It\n\n15\nwas performed with the of\ufb02ine-reconstructed dataset, that in-\ncorporates dedicated calibration in terms of positioning, tim-\ning and ef\ufb01ciency (Adri\u00b4an-Mart\u00b4\u0131nez et al. 2012; Aguilar et al.\n2011; Aguilar et al. 2007). The analysis has been optimized\nto increase the sensitivity of the detector and extended to the\nlonger time window of 14 days.\nThe search for down-going neutrino counterparts to\nGW170817 was made feasible as the large background af-\nfecting this dataset can be drastically suppressed by requiring\na time and space coincidence with the GW signal. It was op-\ntimized, independently for tracks and showers, such that a\ndirectional coincidence with NGC 4993 within the search\ntime window of \u00b1500 s would have 3\u03c3 signi\ufb01cance. Muon\nneutrino candidates were selected by applying cuts on the\nestimated angular error and the track quality reconstruction\nparameter. While ANTARES is sensitive to neutrino events\nwith energy as small as O(100 GeV), the energy range corre-\nsponding to the 5% \u221295% quantiles of the neutrino \ufb02ux for\na E\u22122 signal spectrum is equal to [32 TeV; 22 PeV]. For such\na \ufb02ux, the median angular uncertainty, de\ufb01ned as the median\nvalue of the distribution of angles between the reconstructed\ndirection of the event and the true neutrino direction, is equal\nto 0.5\u25e6.\nShower events were selected by applying a set of cuts\nprimarily devoted to reducing the background rate (Albert\net al. 2017). The energy range corresponding to the 5%\u201395%\nquantiles of the neutrino \ufb02ux for a E\u22122 signal spectrum is\nequal to [23 TeV; 16 PeV], while the median angular error is\n6\u25e6with this set of relaxed cuts.\nNo events temporally coincident with GW170817 were\nfound.\nFive background track events (likely atmospheric\nmuons), not compatible with the source position, were de-\ntected (see Fig. 1). We used this non-detection to constrain\nthe neutrino \ufb02uence (see Fig. 2) which was computed as in\nAdri\u00b4an-Mart\u00b4\u0131nez et al. (2016a).\nThe search over 14 days is restricted to up-going events,\nbut includes all neutrino \ufb02avors (tracks and showers). We ap-\nplied quality cuts optimized for point-source searches which\ngive a median pointing accuracy of 0.4\u25e6and 3\u25e6respectively\nfor track and shower events (Albert et al. 2017). No events\nspatially coincident with GRB170817A were found.\nCompared to the upper limits obtained for the short time\nwindow of \u00b1500 s, those limits are signi\ufb01cantly less stringent\nabove 1 PeV, where the absorption of neutrinos by the Earth\nbecomes important for up-going events. Below 10 TeV, the\nconstraints computed for the 14-day time window are stricter\ndue to the better acceptance in this energy range for up-\ngoing neutrino candidates compared to down-going events\n(see Fig. 2).\n2.2. IceCube\nIceCube is a cubic-kilometer size neutrino detector (Aart-\nsen et al. 2017) installed in the ice at the geographic South\nPole in Antarctica between depths of 1450 m and 2450 m.\nDetector construction was completed in 2010, and the de-\ntector has operated with a \u223c99% duty cycle since. IceCube\nsearched for neutrino signals from GW170817 using two dif-\nferent event selection techniques.\nThe \ufb01rst search used an online selection of through-\ngoing muons, which is used in IceCube\u2019s online analyses\n(Kintscher & the IceCube Collaboration 2016; Aartsen et al.\n2016) and follows an event selection similar to that of point\nsource searches (Aartsen et al. 2014). This event selection\npicks out primarily cosmic-ray-induced background events,\nwith an expectation of 4.0 events in the northern sky (pre-\ndominantly generated by atmospheric neutrinos) and 2.7\nevents in the southern sky (predominantly muons generated\nby high energy cosmic rays interactions in the atmosphere\nabove the detector) per 1000 seconds. For source locations\nin the southern sky, the sensitivity of the down-going event\nselection for neutrinos below 1 PeV weakens rapidly with\nenergy due to the rapidly increasing atmospheric muon back-\nground at lower energies. Events found by this track selection\nin the \u00b1500 s time window are shown in Fig. 1. No events\nwere found to be spatially and temporally correlated with\nGW170817.\nA second event selection, described in Wandkowski et al.\n(2017), was employed of\ufb02ine. This uses the outermost op-\ntical sensors of the instrumented volume to veto incoming\nmuon tracks from atmospheric background events. Above\n60 TeV, this event selection has the same performance as\nthe high-energy starting event selection (Aartsen et al. 2014).\nBelow this energy, additional veto cuts similar to those de-\nscribed in Aartsen et al. (2015) are applied, in order to main-\ntain a low background level at energies down to a few TeV.\nBoth track- and cascade-like events are retained. The event\nrate for this selection varies over the sky, but is overall much\nlower than for the online track selection described above.\nBetween declinations \u221213\u25e6and \u221233\u25e6, the mean number of\nevents in a two-week period is 0.4 for tracks and 2.5 for cas-\ncades. During the \u00b1500 s time-window, no events passed this\nevent selection from anywhere in the sky.\nA combined analysis of the IceCube through-going track\nselection and the starting-event selection allows upper limits\nto be placed on the neutrino \ufb02uence from GW170817 be-\ntween the energies of 1 TeV and 1 EeV, shown in Fig. 2.\nIn the central range from 10 TeV to 100 PeV, the upper\nlimit for an E\u22122 power-law spectral \ufb02uence is F(E) =\n0.19 (E/GeV)\u22122 GeV\u22121 cm\u22122.\nBoth the through-going track selection and the starting\nevent selection were applied to data collected in the 14-\nday period following the time of GW170817. Because of\nIceCube\u2019s location at the South Pole and 99.88% on-time\n\n16\nduring the 14-day period, the exposure to the source loca-\ntion is continuous and unvaried. No spatially and tempo-\nrally coincident events were seen in either selection dur-\ning this follow-up period.\nThe resulting upper limits are\npresented in Fig. 2. At most energies these are unchanged\nfrom the short time-window. At the lowest energies, where\nmost background events occur, the analysis effectively re-\nquires stricter criteria for a coincident event than were re-\nquired in the short time window; the limits are correspond-\ningly higher. In the central range from 10 TeV to 100 PeV,\nthe upper limit on an E\u22122 power-law spectral \ufb02uence is\nF(E) = 0.23 \u00d7 (E/GeV)\u22122 GeV\u22121 cm\u22122.\nThe IceCube detector is also sensitive to outbursts of MeV\nneutrinos via a simultaneous increase in all photomultiplier\nsignal rates. A neutrino burst signal from a galactic core-\ncollapse supernova would be detected with high precision\n(Abbasi et al. 2011). The detector global dark rate is mon-\nitored continuously, the in\ufb02uence of cosmic ray muons is\nremoved and low-level triggers are formed when deviations\nfrom the nominal rate exceed pre-de\ufb01ned levels. No alert\nwas triggered during the \u00b1500 second time-window around\nthe GW candidate. This is consistent with our expectations\nfor cosmic events such as core-collapse supernovae or com-\npact binary mergers that are signi\ufb01cantly farther away than\nGalactic distances.\n2.3. Pierre Auger Observatory\nWith the surface detector (SD) of the Pierre Auger Obser-\nvatory in Malarg\u00a8ue, Argentina (Aab et al. 2015), air showers\ninduced by ultra-high energy (UHE) neutrinos can be iden-\nti\ufb01ed for energies above \u223c1017 eV in the more numerous\nbackground of UHE cosmic rays (Aab et al. 2015).\nThe\nSD consists of 1660 water-Cherenkov stations spread over\nan area of \u223c3000 km2 following a triangular arrangement of\n1.5 km grid spacing (Aab et al. 2015). The signals produced\nby the passage of shower particles through the SD detectors\nare recorded as time traces in 25 ns intervals.\nCosmic rays interact shortly after entering the atmosphere\nand induce extensive air showers. For highly inclined direc-\ntions their electromagnetic component gets absorbed due to\nthe large grammage of atmosphere from the \ufb01rst interaction\npoint to the ground. As a consequence, the shower front\nat ground level is dominated by muons that induce sharp\ntime traces in the water-Cherenkov stations.\nOn the con-\ntrary, showers induced by downward-going neutrinos at large\nzenith angles can start their development deep in the atmo-\nsphere producing traces that spread over longer times. These\nshowers have a considerable fraction of electrons and pho-\ntons which undergo more interactions than muons in the at-\nmosphere, spreading more in time as they pass through the\ndetector. This is also the case for Earth-skimming showers,\nmainly induced by tau neutrinos (\u03bd\u03c4) that traverse horizon-\ntally below the Earth\u2019s crust, and interact near the exit point\ninducing a tau lepton that escapes the Earth and decays in\n\ufb02ight in the atmosphere above the SD.\nDedicated and ef\ufb01cient selection criteria based on the\ndifferent time pro\ufb01les of the signals detected in showers\ncreated by hadronic and neutrino primaries, enable the\nsearch for Earth-skimming as well as downward-going\nneutrino-induced showers (Aab et al. 2015).\nDeeply-\nstarting downward-going showers initiated by neutrinos of\nany \ufb02avor can be ef\ufb01ciently identi\ufb01ed for zenith angles of\n60\u25e6< \u03b8 < 90\u25e6(Aab et al. 2015). For the Earth-skimming\nchannel typically only \u03bd\u03c4-induced showers with zenith an-\ngles 90\u25e6< \u03b8 < 95\u25e6can trigger the SD. This is the most\nsensitive channel to UHE neutrinos, mainly due to the larger\ngrammage and higher density of the target (the Earth) where\nneutrinos are converted and where tau leptons can travel tens\nof kilometers (Aab et al. 2015). The angular resolution of the\nAuger SD for inclined showers is better than 2.5\u25e6, improving\nsigni\ufb01cantly as the number of triggered stations increases\n(Bonifazi & Pierre Auger Collaboration 2009).\nAuger performed a search for UHE neutrinos with its SD\nin a time window of \u00b1500 s centered at the merger time of\nGW170817 (Abbott et al. 2017d), as well as in a 14-day pe-\nriod after it (Murase et al. 2009; Gao et al. 2013; Fang &\nMetzger 2017).\nThe sensitivity to UHE neutrinos in Auger is limited to\nlarge zenith angles, so that at each instant they can be ef-\n\ufb01ciently detected only from a speci\ufb01c fraction of the sky\n(Abreu et al. 2012; Aab et al. 2016). Remarkably, the po-\nsition of the optical counterpart in NGC 4993 (Coulter et al.\n2017b,a; Abbott et al. 2017d) is visible from Auger in the\n\ufb01eld of view of the Earth-skimming channel during the whole\n\u00b1500 s window as shown in Fig. 1. In this time period the\nsource of GW170817 transits from \u03b8 \u223c93.3\u25e6to \u03b8 \u223c90.4\u25e6\nas seen from the center of the array. The performance of the\nAuger SD array (regularly monitored every minute) is very\nstable in the \u00b1500 s window around GW170817, with an av-\nerage number of active stations amounting to \u223c95.8 \u00b1 0.1 %\nof the 1660 stations of the SD array.\nNo inclined showers passing the Earth-skimming selection\n(neutrino candidates) were found in the time window \u00b1500 s\naround the trigger time of GW170817. The estimated num-\nber of background events from cosmic rays in a 1000 s period\nis \u223c6.3 \u00d7 10\u22127 for the cuts applied in the Earth-skimming\nanalysis (Aab et al. 2015).\nThe absence of candidates in the \u00b1500 s window allows us\nto constrain the \ufb02uence in UHE neutrinos from GW170817,\nassuming they are emitted steadily in this interval and with\nan E\u22122 spectrum (Aab et al. 2016).\nSingle-\ufb02avor differ-\nential limits to the spectral \ufb02uence are shown in Fig. 2, in\nbins of one decade in energy.\nThe sensitivity of the ob-\nservatory is largest in the energy bin around 1018 eV. The\n\n17\nsingle-\ufb02avor upper limit to the spectral \ufb02uence is F(E) =\n0.77 (E/GeV)\u22122 GeV\u22121 cm\u22122 over the energy range from\n1017 eV to 2.5 \u00d7 1019 eV.\nIn the 14-day search period, as the Earth rotates, the posi-\ntion of NGC 4993 transits through the \ufb01eld of view of the\nEarth-skimming and downward-going channels.\nAs seen\nfrom the Pierre Auger Observatory, the zenith angle of the\noptical counterpart oscillates daily between \u03b8 \u223c11\u25e6and\n\u03b8 \u223c121\u25e6.\nThe source is visible in the Earth-skimming\nchannel for \u223c4% of the day, and in the downward-going\nchannel for \u223c10.5 % (\u223c11.1 %) in the zenith angle range\n60\u25e6< \u03b8 < 75\u25e6(75\u25e6< \u03b8 < 90\u25e6). No neutrino candi-\ndates were identi\ufb01ed in the two-week search period. Single-\n\ufb02avor differential limits to the spectral \ufb02uence are shown in\nFig. 2. The corresponding upper limit to the spectral \ufb02uence\nis F(E) = 25 (E/GeV)\u22122 GeV\u22121 cm\u22122 over the same en-\nergy interval as for the \u00b1500 s time window, where the dif-\nference is due to the relatively long periods of time when the\nsource of GW170817 is not visible in the inclined directions.\n3. DISCUSSION\nThe nature of high-energy emission from the binary merger\nand its aftermath is not yet clear. We compared the expected\nspectral \ufb02uence for different emission scenarios to our ob-\nservational upper limits to probe the properties of the merger\nand its aftermath. Here we brie\ufb02y outline the relevant infor-\nmation from electromagnetic observations, and present our\nresults for the different emission scenarios.\nThe merger occurred at a distance of \u223c40 Mpc, which is\nthe distance of its host galaxy NGC 4993, identi\ufb01ed through\nelectromagnetic observations (Coulter et al. 2017b,a; Abbott\net al. 2017d).\nThe prompt gamma-ray emission from the\nsource, GRB170817A, had an observed isotropic-equivalent\nenergy of Eiso \u22484 \u00d7 1046 erg, as recorded by Fermi-GBM\n(Abbott et al. 2017a). This is orders of magnitude below typ-\nical observed short-GRB energies (Berger 2014; Abbott et al.\n2017a).\nPrompt gamma-ray emission in at least some short GRBs\nis followed by a weaker, extended emission that can last for\nhundreds of seconds (Norris & Bonnell 2006; Kimura et al.\n2017).\nFermi-GBM did not detect a temporally extended\nemission following GRB170817A, placing a constraint of\n\u223c2\u00d71046 erg s\u22121 for a 10 s long emission period over 1 keV\u2013\n10 MeV (Abbott et al. 2017a), signi\ufb01cantly below typical lu-\nminosities observed for extended emission.\nThe very faint gamma-ray emission, along with its ob-\nserved, delayed afterglow, are consistent with a typical short\nGRB viewed off-axis (Granot et al. 2017; Ioka & Naka-\nmura 2017; Fraija et al. 2017; Troja et al. 2017; Hallinan\net al. 2017; Murguia-Berthier et al. 2017; Fong et al. 2017;\nMargutti et al. 2017; Haggard et al. 2017; Kim et al. 2017;\nMurguia-Berthier et al. 2017). A GRB is viewed off-axis\nif its viewing angle \u03b8obs, de\ufb01ned as the angle between the\njet axis and the line of sight, is greater than the jet opening\nhalf-angle \u03b8j (Granot et al. 2002). The viewing angle in-\nferred from the data is \u03b8obs \u227320\u25e6, while typical opening\nhalf-angles for short GRBs are within \u03b8j \u22483\u25e6\u221210\u25e6(Berger\n2014).\nGW data combined with the measured redshift of the host\ngalaxy further provide constraints on \u03b8obs. Here we assume\nthat the jet axis is aligned with the binary\u2019s total angular mo-\nmentum vector. Adopting the Hubble constant from cosmic\nmicrowave background measurements by the Planck satellite\n(Ade et al. 2016), these data are consistent with \u03b8obs = 0, but\nalso allow for a misalignment of \u03b8obs \u226428\u25e6at 90% credible\nlevel. Adopting the Hubble constant from Type Ia supernova\nmeasurements (Riess et al. 2016) gives a similar result with\nmaximum misalignment of \u03b8obs \u226436\u25e6at 90% credible level\n(LIGO Scienti\ufb01c and Virgo Collaborations et al. 2017).\nConsidering this off-axis scenario, we examined the ex-\npected high-energy neutrino emission from a typical GRB\nobserved at different viewing angles.\nThe most promis-\ning neutrino production mechanism from GRBs is related\nto the extended gamma emission, due to its relatively low\nLorentz factor resulting in high meson production ef\ufb01ciency\n(Kimura et al. 2017). In Fig. 2 we compared our observa-\ntional constraints with the expected neutrino \ufb02uence from the\nGRB\u2019s extended emission. For the on-axis (i.e. \u03b8obs \u2272\u03b8j)\nspectral \ufb02uence Fon, we assumed the results of Kimura\net al. (2017), rescaled to 40 Mpc.\nWe approximated the\nobserved off-axis spectral \ufb02uence, Fo\ufb00(E) for these mod-\nels using Fo\ufb00(E) = \u03b7Fon(E/\u03b7), where the scaling fac-\ntor \u03b7 = \u03b4(\u03b8obs)/\u03b4(0) accounts for different Doppler factors\n\u03b4(\u03b8obs) = [\u0393(1 \u2212\u03b2 cos(\u03b8obs \u2212\u03b8j))]\u22121 (Granot et al. 2002).\nFor comparison, we also examined the expected neutrino\n\ufb02ux associated with the prompt GRB emission (e.g., ]Moha-\nrana et al. 2016; Kimura et al. 2017). This emission phase\nis less favorable for neutrino production than the extended\nemission. We see in Fig. 2 that prompt emission from a sin-\ngle merger event is unlikely to produce a detected neutrino\nfor the considered observatories, even if viewed on-axis.\nAnother proposed explanation for the faintness of gamma-\nray emission is the interaction of the GRB jet with ejecta ma-\nterial from the merger (Kasliwal et al. 2017; Gottlieb et al.\n2017; Piro & Kollmeier 2017). Energy deposition by the jet\ninto the neutron star ejecta can form a cocoon that expands\noutwards at mildly relativistic speeds over a wide opening\nangle. Faint gamma-ray emission is then expected during the\nbreakout of this cocoon from the outer tail of the ejecta (Got-\ntlieb et al. 2017).\nHigh-energy neutrino production in this scenario may sig-\nni\ufb01cantly exceed the observed gamma-ray emission as neu-\ntrinos can escape through the ejecta even before it becomes\ntransparent to gamma-rays. This scenario resembles that of a\n\n18\njet burrowing through the stellar envelope in a core-collapse\nevent (M\u00b4esz\u00b4aros & Waxman 2001; Razzaque et al. 2003; Bar-\ntos et al. 2012; Murase & Ioka 2013). Nevertheless, if the\nobserved gamma-rays come from the outbreak of a wide co-\ncoon, it is less likely that the relativistic jet, which is more\nnarrowly beamed than the cocoon outbreak, also pointed to-\nwards Earth.\nWe further considered an additional neutrino-production\nmechanism related to ejecta material from the merger. If a\nrapidly rotating neutron star forms in the merger and does not\nimmediately collapse into a black hole, it can power a rela-\ntivistic wind with its rotational energy, which may be respon-\nsible for the sometimes observed extended emission (Met-\nzger et al. 2008). Optically thick ejecta from the merger can\nattenuate the gamma-ray \ufb02ux, while allowing the escape of\nhigh-energy neutrinos. Additionally, it may trap some of the\nwind energy until it expands and becomes transparent. This\nprocess can convert some of the wind energy to high-energy\nparticles, producing a long-term neutrino radiation that can\nlast for days (Murase et al. 2009; Gao et al. 2013; Fang &\nMetzger 2017).\nThe properties of ejecta material around\nthe merger can be characterized from its kilonova/macronova\nemission.\nConsidering the possibility that the relative weakness of\ngamma-ray emission from GRB170817A may be partly due\nto attenuation by the ejecta, we compared our neutrino con-\nstraints to neutrino emission expected for typical GRB pa-\nrameters. For the prompt and extended emissions, we used\nthe results of Kimura et al. (2017) and compared these to\nour constraints for the relevant \u00b1500 s time window. For\nextended emission we considered source parameters corre-\nsponding to both optimistic and moderate scenarios in Ta-\nble 1 of Kimura et al. (2017). For emission on even longer\ntimescales, we compared our constraints for the 14-day time\nwindow with the relevant results of Fang & Metzger (2017),\nnamely emission from approximately 0.3 to 3 days and from\n3 to 30 days following the merger. Predictions based on \ufb01du-\ncial emission models and neutrino constraints are shown in\nFig. 2.\nWe found that our limits would constrain the op-\ntimistic extended-emission scenario for a typical GRB at\n\u223c40 Mpc, viewed at zero viewing angle.\n4. CONCLUSION\nWe searched for high-energy neutrinos from the \ufb01rst bi-\nnary neutron star merger detected through GWs, GW170817,\nin the energy band of [\u223c1011 eV, \u223c1020 eV] using the\nANTARES, IceCube, and Pierre Auger Observatories, as well\nas for MeV neutrinos with IceCube. This marks an unprece-\ndented joint effort of experiments sensitive to high-energy\nneutrinos. We have observed no signi\ufb01cant neutrino counter-\npart within a \u00b1500 s window, nor in the subsequent 14 days.\n10 3\n10 2\n10 1\n100\n101\n102\n103\nE 2F [GeVcm 2]\n\u00b1500 sec time-window\nAuger\nIceCube\nANTARES\nKimura et al.\nEE optimistic\n0\n4\n8\nKimura et al.\nEE moderate\n0\n4\nKimura et al.\nprompt\n0\nGW170817 Neutrino limits (fluence per flavor: x +\nx)\n102\n103\n104\n105\n106\n107\n108\n109\n1010 1011\nE/GeV\n10 3\n10 2\n10 1\n100\n101\n102\n103\nE 2F [GeVcm 2]\n14 day time-window\nAuger\nIceCube\nANTARES\nFang &\nMetzger\n30 days\nFang &\nMetzger\n3 days\nFigure 2. Upper limits (at 90 % con\ufb01dence level) on the neutrino\nspectral \ufb02uence from GW170817 during a \u00b1500 s window centered\non the GW trigger time (top panel), and a 14-day window follow-\ning the GW trigger (bottom panel). For each experiment, limits are\ncalculated separately for each energy decade, assuming a spectral\n\ufb02uence F(E) = Fup \u00d7 [E/GeV]\u22122 in that decade only. Also\nshown are predictions by neutrino emission models. In the upper\nplot, models from Kimura et al. (2017) for both extended emission\n(EE) and prompt emission are scaled to a distance of 40 Mpc, and\nshown for the case of on-axis viewing angle (\u03b8obs \u2272\u03b8j) and se-\nlected off-axis angles to indicate the dependence on this parameter.\nThe shown off-axis angles are measured in excess of the jet opening\nhalf angle \u03b8j. GW data and the redshift of the host-galaxy constrain\nthe viewing angle to \u03b8obs \u2208[0\u25e6, 36\u25e6] (see Section 3). In the lower\nplot, models from Fang & Metzger (2017) are scaled to a distance\nof 40 Mpc. All \ufb02uences are shown as the per \ufb02avor sum of neutrino\nand anti-neutrino \ufb02uence, assuming equal \ufb02uence in all \ufb02avors, as\nexpected for standard neutrino oscillation parameters.\nThe three detectors complement each other in the energy\nbands in which they are most sensitive (see Fig. 2).\nThis non-detection is consistent with our expectations from\na typical GRB observed off-axis, or with a low-luminosity\nGRB. Optimistic scenarios for on-axis gamma-attenuated\nemission are constrained by the present non-detection.\nWhile the location of this source was nearly ideal for\nAuger, it was well above the horizon for IceCube and\nANTARES for prompt observations. This limited the sensitiv-\nity of the latter two detectors, particularly below \u223c100 TeV.\n\n19\nFor source locations near, or below the horizon, a factor of\n\u223c10 increase in \ufb02uence sensitivity to prompt emission from\nan E\u22122 neutrino spectrum is expected.\nWith the discovery of a nearby binary neutron star merger,\nthe ongoing enhancement of detector sensitivity (Abbott\net al. 2016) and the growing network of GW detectors (Aso\net al. 2013; Iyer et al. 2011), we can expect that several binary\nneutron star mergers will be observed in the near future. Not\nonly will this allow stacking analyses of neutrino emission,\nbut it will also bring about sources with favorable orientation\nand direction.\nThe ANTARES, IceCube, and Pierre Auger Collaborations\nare planning to continue the rapid search for neutrino can-\ndidates from identi\ufb01ed GW sources. A coincident neutrino,\nwith a typical position uncertainty of \u223c1 deg2 could signi\ufb01-\ncantly improve the fast localization of joint events compared\nto the GW-only case. In addition, the \ufb01rst joint GW and high-\nenergy neutrino discovery might thereby be known to the\nwider astronomy community within minutes after the event,\nopening a rich \ufb01eld of multimessenger astronomy with parti-\ncle, electromagnetic, and gravitational waves combined.\nACKNOWLEDGMENTS\n(ANTARES) The ANTARES authors acknowledge the \ufb01-\nnancial support of the funding agencies: Centre National de\nla Recherche Scienti\ufb01que (CNRS), Commissariat `a l\u2019\u00b4energie\natomique et aux \u00b4energies alternatives (CEA), Commission\nEurop\u00b4eenne (FEDER fund and Marie Curie Program), In-\nstitut Universitaire de France (IUF), IdEx program and Uni-\nvEarthS Labex program at Sorbonne Paris Cit\u00b4e (ANR-10-\nLABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU\n(ANR-11-LABX-0060) and the A*MIDEX project (ANR-\n11-IDEX-0001-02), R\u00b4egion \u02c6Ile-de-France (DIM-ACAV),\nR\u00b4egion Alsace (contrat CPER), R\u00b4egion Provence-Alpes-\nC\u02c6ote d\u2019Azur, D\u00b4epartement du Var and Ville de La Seyne-sur-\nMer, France; Bundesministerium f\u00a8ur Bildung und Forschung\n(BMBF), Germany; Istituto Nazionale di Fisica Nucleare\n(INFN), Italy; Nederlandse organisatie voor Wetenschap-\npelijk Onderzoek (NWO), the Netherlands; Council of the\nPresident of the Russian Federation for young scientists and\nleading scienti\ufb01c schools supporting grants, Russia; Na-\ntional Authority for Scienti\ufb01c Research (ANCS), Romania;\nMinisterio de Econom\u00b4\u0131a y Competitividad (MINECO): Plan\nEstatal de Investigaci\u00b4on (refs.\nFPA2015-65150-C3-1-P, -\n2-P and -3-P, (MINECO/FEDER)), Severo Ochoa Centre\nof Excellence and MultiDark Consolider (MINECO), and\nPrometeo and Grisol\u00b4\u0131a programs (Generalitat Valenciana),\nSpain; Ministry of Higher Education, Scienti\ufb01c Research\nand Professional Training, Morocco. We also acknowledge\nthe technical support of Ifremer, AIM and Foselev Marine\nfor the sea operation and the CC-IN2P3 for the computing\nfacilities.\n(IceCube) The IceCube collaboration acknowledges the\nsupport from the following agencies: U.S. National Science\nFoundation-Of\ufb01ce of Polar Programs, U.S. National Sci-\nence Foundation-Physics Division, University of Wisconsin\nAlumni Research Foundation, the Grid Laboratory Of Wis-\nconsin (GLOW) grid infrastructure at the University of Wis-\nconsin - Madison, the Open Science Grid (OSG) grid infras-\ntructure; U.S. Department of Energy, and National Energy\nResearch Scienti\ufb01c Computing Center, the Louisiana Optical\nNetwork Initiative (LONI) grid computing resources; Natu-\nral Sciences and Engineering Research Council of Canada,\nWestGrid and Compute/Calcul Canada; Swedish Research\nCouncil, Swedish Polar Research Secretariat, Swedish Na-\ntional Infrastructure for Computing (SNIC), and Knut and\nAlice Wallenberg Foundation, Sweden; German Ministry for\nEducation and Research (BMBF), Deutsche Forschungs-\ngemeinschaft (DFG), Helmholtz Alliance for Astroparti-\ncle Physics (HAP), Initiative and Networking Fund of the\nHelmholtz Association, Germany; Fund for Scienti\ufb01c Re-\nsearch (FNRS-FWO), FWO Odysseus programme, Flanders\nInstitute to encourage scienti\ufb01c and technological research\nin industry (IWT), Belgian Federal Science Policy Of\ufb01ce\n(Belspo); Marsden Fund, New Zealand; Australian Research\nCouncil; Japan Society for Promotion of Science (JSPS);\nthe Swiss National Science Foundation (SNSF), Switzer-\nland; National Research Foundation of Korea (NRF); Vil-\nlum Fonden, Danish National Research Foundation (DNRF),\nDenmark.\n(Auger) The successful installation, commissioning, and\noperation of the Pierre Auger Observatory would not have\nbeen possible without the strong commitment and effort from\nthe technical and administrative staff in Malarg\u00a8ue. We are\nvery grateful to the following agencies and organizations for\n\ufb01nancial support:\nArgentina \u2013 Comisi\u00b4on Nacional de Energ\u00b4\u0131a At\u00b4omica;\nAgencia Nacional de Promoci\u00b4on Cient\u00b4\u0131\ufb01ca y Tecnol\u00b4ogica\n(ANPCyT); Consejo Nacional de Investigaciones Cient\u00b4\u0131\ufb01cas\ny T\u00b4ecnicas (CONICET); Gobierno de la Provincia de Men-\ndoza; Municipalidad de Malarg\u00a8ue; NDM Holdings and\nValle Las Le\u02dcnas; in gratitude for their continuing coop-\neration over land access; Australia \u2013 the Australian Re-\nsearch Council; Brazil \u2013 Conselho Nacional de Desen-\nvolvimento Cient\u00b4\u0131\ufb01co e Tecnol\u00b4ogico (CNPq); Financiadora\nde Estudos e Projetos (FINEP); Fundac\u00b8\u02dcao de Amparo `a\nPesquisa do Estado de Rio de Janeiro (FAPERJ); S\u02dcao Paulo\nResearch Foundation (FAPESP) Grants No. 2010/07359-\n6 and No. 1999/05404-3; Minist\u00b4erio da Ci\u02c6encia, Tecnolo-\ngia, Inovac\u00b8\u02dcoes e Comunicac\u00b8\u02dcoes (MCTIC); Czech Republic\n\u2013 Grant No. MSMT CR LG15014, LO1305, LM2015038\nand CZ.02.1.01/0.0/0.0/16 013/0001402;\nFrance \u2013 Cen-\ntre\nde\nCalcul\nIN2P3/CNRS;\nCentre\nNational\nde\nla\nRecherche Scienti\ufb01que (CNRS); Conseil R\u00b4egional Ile-de-\n\n20\nFrance; D\u00b4epartement Physique Nucl\u00b4eaire et Corpusculaire\n(PNC-IN2P3/CNRS); D\u00b4epartement Sciences de l\u2019Univers\n(SDU-INSU/CNRS); Institut Lagrange de Paris (ILP) Grant\nNo. LABEX ANR-10-LABX-63 within the Investisse-\nments d\u2019Avenir Programme Grant No. ANR-11-IDEX-\n0004-02;\nGermany \u2013 Bundesministerium f\u00a8ur Bildung\nund Forschung (BMBF); Deutsche Forschungsgemeinschaft\n(DFG); Finanzministerium Baden-W\u00a8urttemberg; Helmholtz\nAlliance for Astroparticle Physics (HAP); Helmholtz-\nGemeinschaft Deutscher Forschungszentren (HGF); Min-\nisterium f\u00a8ur Innovation, Wissenschaft und Forschung des\nLandes Nordrhein-Westfalen; Ministerium f\u00a8ur Wissenschaft,\nForschung und Kunst des Landes Baden-W\u00a8urttemberg; Italy\n\u2013 Istituto Nazionale di Fisica Nucleare (INFN); Istituto\nNazionale di Astro\ufb01sica (INAF); Ministero dell\u2019Istruzione,\ndell\u2019Universit\u00b4a e della Ricerca (MIUR); CETEMPS Center\nof Excellence; Ministero degli Affari Esteri (MAE); Mexico\n\u2013 Consejo Nacional de Ciencia y Tecnolog\u00b4\u0131a (CONACYT)\nNo. 167733; Universidad Nacional Aut\u00b4onoma de M\u00b4exico\n(UNAM); PAPIIT DGAPA-UNAM; The Netherlands \u2013 Min-\nisterie van Onderwijs, Cultuur en Wetenschap; Nederlandse\nOrganisatie voor Wetenschappelijk Onderzoek (NWO);\nStichting voor Fundamenteel Onderzoek der Materie (FOM);\nPoland \u2013 National Centre for Research and Develop-\nment, Grants No. ERA-NET-ASPERA/01/11 and No. ERA-\nNET-ASPERA/02/11;\nNational Science Centre,\nGrants\nNo.\n2013/08/M/ST9/00322,\nNo.\n2013/08/M/ST9/00728\nand No. HARMONIA 5\u20132013/10/M/ST9/00062, UMO-\n2016/22/M/ST9/00198; Portugal \u2013 Portuguese national funds\nand FEDER funds within Programa Operacional Factores\nde Competitividade through Fundac\u00b8\u02dcao para a Ci\u02c6encia e a\nTecnologia (COMPETE); Romania \u2013 Romanian Authority\nfor Scienti\ufb01c Research ANCS; CNDI-UEFISCDI partner-\nship projects Grants No. 20/2012 and No. 194/2012 and\nPN 16 42 01 02; Slovenia \u2013 Slovenian Research Agency;\nSpain \u2013 Comunidad de Madrid; Fondo Europeo de Desar-\nrollo Regional (FEDER) funds; Ministerio de Econom\u00b4\u0131a y\nCompetitividad; Xunta de Galicia; European Community\n7th Framework Program Grant No. FP7-PEOPLE-2012-IEF-\n328826; USA \u2013 Department of Energy, Contracts No. DE-\nAC02-07CH11359, No. DE-FR02-04ER41300, No. DE-\nFG02-99ER41107 and No. DE-SC0011689; National Sci-\nence Foundation, Grant No. 0450696; The Grainger Foun-\ndation; Marie Curie-IRSES/EPLANET; European Particle\nPhysics Latin American Network; European Union 7th\nFramework Program, Grant No. PIRSES-2009-GA-246806;\nEuropean Union\u2019s Horizon 2020 research and innovation\nprogramme (Grant No. 646623); and UNESCO.\n(LIGO and Virgo) The authors gratefully acknowledge\nthe support of the United States National Science Foundation\n(NSF) for the construction and operation of the LIGO Labo-\nratory and Advanced LIGO as well as the Science and Tech-\nnology Facilities Council (STFC) of the United Kingdom,\nthe Max-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO600 detec-\ntor. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucle-\nare (INFN), the French Centre National de la Recherche\nScienti\ufb01que (CNRS) and the Foundation for Fundamental\nResearch on Matter supported by the Netherlands Organi-\nsation for Scienti\ufb01c Research, for the construction and op-\neration of the Virgo detector and the creation and support\nof the EGO consortium.\nThe authors also gratefully ac-\nknowledge research support from these agencies as well as\nby the Council of Scienti\ufb01c and Industrial Research of In-\ndia, the Department of Science and Technology, India, the\nScience & Engineering Research Board (SERB), India, the\nMinistry of Human Resource Development, India, the Span-\nish Agencia Estatal de Investigaci\u00b4on, the Vicepresid`encia i\nConselleria d\u2019Innovaci\u00b4o, Recerca i Turisme and the Consel-\nleria d\u2019Educaci\u00b4o i Universitat del Govern de les Illes Balears,\nthe Conselleria d\u2019Educaci\u00b4o, Investigaci\u00b4o, Cultura i Esport\nde la Generalitat Valenciana, the National Science Centre of\nPoland, the Swiss National Science Foundation (SNSF), the\nRussian Foundation for Basic Research, the Russian Science\nFoundation, the European Commission, the European Re-\ngional Development Funds (ERDF), the Royal Society, the\nScottish Funding Council, the Scottish Universities Physics\nAlliance, the Hungarian Scienti\ufb01c Research Fund (OTKA),\nthe Lyon Institute of Origins (LIO), the National Research,\nDevelopment and Innovation Of\ufb01ce Hungary (NKFI), the\nNational Research Foundation of Korea, Industry Canada\nand the Province of Ontario through the Ministry of Eco-\nnomic Development and Innovation, the Natural Science and\nEngineering Research Council Canada, the Canadian Insti-\ntute for Advanced Research, the Brazilian Ministry of Sci-\nence, Technology, Innovations, and Communications, the In-\nternational Center for Theoretical Physics South American\nInstitute for Fundamental Research (ICTP-SAIFR), the Re-\nsearch Grants Council of Hong Kong, the National Natural\nScience Foundation of China (NSFC), the Leverhulme Trust,\nthe Research Corporation, the Ministry of Science and Tech-\nnology (MOST), Taiwan and the Kavli Foundation. 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Lett., 78, 2292\n", "Draft version September 24, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nGWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n(See the end matter for the full list of authors)\nABSTRACT\nThe Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-\nwave signals identified by the LIGO\u2013Virgo\u2013KAGRA Collaboration in gravitational-wave data produced by the\neponymous detectors. The catalog provides information about the identified candidates, such as the arrival time\nand amplitude of the signal and properties of the signal\u2019s source as inferred from the observational data. GWTC\nis the data release of this dataset and version 4.0 extends the catalog to include observations made during the\nfirst part of the fourth LIGO\u2013Virgo\u2013KAGRA observing run up until 2024 January 31. This paper marks an\nintroduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of\narticles accompanying the catalog provides documentation of the methods used to analyze the data, summaries\nof the catalog of events, observational measurements drawn from the population, and detailed discussions of\nselected candidates.\nKeywords: Gravitational wave astronomy (675); Gravitational wave detectors (676); Gravitational wave sources\n(677); Stellar mass black holes (1611); Neutron stars (1108)\n1. OVERVIEW\nThe Laser Interferometer Gravitational-Wave Observatory\n(LIGO; Aasi et al. 2015a) and the Virgo (Acernese et al.\n2015) and KAGRA (Akutsu et al. 2021) observatories form\nan international network of ground-based gravitational-wave\n(GW) detectors. This paper is an introduction to the collec-\ntion of articles describing the contents of the LIGO\u2013Virgo\u2013\nKAGRA Collaboration (LVK) Gravitational-Wave Transient\nCatalog (GWTC) version 4.0, hereafter GWTC-4.0, along\nwith reviews of the methods used in various aspects in the\nconstruction of this catalog, astrophysical and cosmological\nimplications of the observations, and tests of general relativ-\nity (GR) that are performed on the observed transients. This\npaper provides details on the network of GW detectors, the\nobserving runs, observatory evolution, and a review of the\ntransient signals that have been identified. In addition, we\ndescribe conventions and notations that are used throughout\nthe collection of papers accompanying the catalog.\n1.1. The GWTC Sources and Science\nTransient GW signals may be produced by a variety of as-\ntrophysical sources, including compact binary coalescences\n(CBCs) of compact objects such as black holes (BHs) and\nneutron stars (NSs), core-collapse supernovae, and other ex-\nCorresponding author: LSC P&P Committee, via LVK Publications as\nproxy\nlvc.publications@ligo.org\nplosive phenomena (Abbott et al. 2020a).\nThe first ob-\nserved GW transient, GW150914, was a binary black hole\n(BBH) coalescence (Abbott et al. 2016a), and we have since\nobserved a binary neutron star (BNS) coalescence (Abbott\net al. 2017a) that had associated electromagnetic counter-\nparts (Abbott et al. 2017b), and neutron star\u2013black hole bi-\nnary (NSBH) coalescences (Abbott et al. 2020d).\nThis GWTC-4.0 collection of papers describes the GW\ntransient candidates observed by the LVK from the first ob-\nserving run (O1) through the end of the first part of the fourth\nobserving run (O4a) and the astrophysical implications of\nthese observations. The paper collection includes:\n\u2022 \u201cGWTC-4.0: Methods for Identifying and Charac-\nterizing Gravitational-wave Transients\u201d (Abac et al.\n2025a) reviews the procedures used to go from the cal-\nibrated output of the detectors to a list of transient can-\ndidates that includes measurements of the statistical\nsignificance and inferences on each of the correspond-\ning astrophysical sources.\n\u2022 \u201cGWTC-4.0: GWTC-4.0: Updating the Gravitational-\nWave Transient Catalog with Observations from the\nFirst Part of the Fourth LIGO\u2013Virgo\u2013KAGRA Observ-\ning Run\u201d (Abac et al. 2025b) describes the primary\nobservational results contained in GWTC-4.0: the sig-\nnificant GW transient candidates observed through the\nend of the O4a observing run and the inferred source\nparameters under the hypothesis that these transients\narise from GWs emitted by CBCs (Section 5.2).\narXiv:2508.18080v2 [gr-qc] 23 Sep 2025\n\n2\n\u2022 \u201cGWTC-4.0: Population Properties of Merging Com-\npact Binaries\u201d (Abac et al. 2025c) describes the under-\nlying population of CBCs inferred using GWTC-4.0\ndata, and related astrophysical implications.\n\u2022 \u201cGWTC-4.0:\nTests of General Relativity I \u2014\nOverview and General Tests\u201d (Abac et al. 2025d)\npresents an overview of the methods and tests of gen-\neral relativity performed on the subset of signals suit-\nable for such tests, and focuses on the general and con-\nsistency tests.\n\u2022 \u201cGWTC-4.0: Tests of General Relativity II \u2014 Parame-\nterized Tests\u201d (Abac et al. 2025e) describes the param-\neterized tests of GR performed on the signals.\n\u2022 \u201cGWTC-4.0: Tests of General Relativity III \u2014 Tests\nof the Remnant\u201d (Abac et al. 2025f) describes the tests\nof the coalescence remnants.\n\u2022 \u201cGWTC-4.0: Constraints on the Cosmic Expansion\nRate and Modified Gravitational-wave Propagation\u201d\n(Abac et al. 2025g) describes the methods used to de-\ntermine the Hubble constant and related parameters,\nincluding parameterized deviations from GR on cos-\nmological scales, using GWTC-4.0 candidates.\n\u2022 \u201cGWTC-4.0: Searches for Gravitational Wave Lensing\nSignatures\u201d (Abac et al. 2025h) describes the searches\nfor lensed GW signals in the geometric and wave op-\ntics regime in the GWTC-4.0 dataset. It also sets con-\nstraints on the merger rate at high redshift and the rel-\native rate of strongly lensed signals compared to un-\nlensed ones.\n\u2022 \u201cOpen Data from LIGO, Virgo, and KAGRA through\nthe First Part of the Fourth Observing Run\u201d (Abac\net al. 2025i) describes the publicly accessible data\nand other science products that can be freely accessed\nthrough the Gravitational Wave Open Science Center\n(GWOSC). These datasets include the raw GW strain\ntime series, details of the calibration and cleaning pro-\ncess, efforts to remove instrumental noise artifacts, and\ndetails of the online GWTC-4.0.\n\u2022 \u201cGW230814: Investigation of a Loud Gravitational-\nwave Signal Observed with a Single Detector\u201d (Abac\net al. 2025j) describes the analysis of the loudest event\nin the GWTC-4.0 catalog, GW230814_230901, which\nwas detected on 2023 August 14. This event is notable\nfor its high signal-to-noise ratio (SNR) and its potential\nimplications for our understanding of GW signals and\nGR.\n\u2022 \u201cGW231123: a Binary Black Hole Merger with To-\ntal Mass 190\u2013265 M\u2299\u201d (Abac et al. 2025k) describes\nthe analysis of the candidate GW231123_135430, de-\ntected on 2023 November 23. The candidate\u2019s source\nis exceptional, having the highest inferred total mass\nof any high-confidence BBH observations to date.\nTo reference the whole GWTC-4.0 collection, we encour-\nage citing this introductory paper.\n1.2. The Electronic Catalog: GWTC\nAbac et al. (2025i) documents the released open data, in-\ncluding the GWTC dataset. The catalog contains candidates\n(sometimes called events) identified in observational data\nthat are deemed likely to be caused by GW signals, as well\nas triggers corresponding to times selected by searches of the\ndata for GW transient signals that potentially contain an iden-\ntifiable signal but with lower confidence of being caused by\na GW.\n1.2.1. The Catalog Naming Convention\nThe LVK GWTC is a cumulative dataset containing data\non all transient candidates reported by the LVK. Released\nversions of the catalog have major and minor numbers in the\nformat:\nGWTC-.\nThe major number is determined by the span of time contain-\ning all candidates in the catalog as described below.\nPrior to GWTC-4.0, the minor number was routinely omit-\nted when describing a catalog version when that minor num-\nber was 0, so GWTC-1.0, GWTC-2.0, and GWTC-3.0 were\nreferred to as GWTC-1, GWTC-2, and GWTC-3 in the pa-\npers that described those catalog versions. In this paper, and\nin the future, we will include the .0 when referring to those\ncatalog versions. We also say that GWTC- can refer\nto GWTC-. for any minor version having\nthat major version number.\nEach catalog version is a superset of the previous (apart\nfrom retracted candidates), so that, for example, GWTC-3.0\n(Abbott et al. 2023) contains all the candidates in GWTC-2.1\n(Abbott et al. 2024). Since GWTC-2.1 provided a deeper list\nof candidates observed over the same period as GWTC-2.0\n(Abbott et al. 2021b), the minor version numbers of these\ntwo releases differ while their major version numbers remain\nthe same. In general:\n\u2022 The major number is incremented when the span of\ntime over which observational data were searched for\ntransients is increased.\n\u2022 The minor version resets to 0 when the major version\nnumber is increased.\n\u2022 The minor version is incremented when there is a\nchange in the data describing the transients (additional\ndata, modified data, or removed data) contained in the\ncatalog within the current timespan covered.\nThe time span covering the transient candidates in the cat-\nalog indicated by the major number is as follows:\nGWTC-1: Contains candidates occurring in data taken be-\nfore 2018 October 01 00:00:00.\nThe GWTC-1.0\ndataset is described in Abbott et al. (2019a).\n\n3\nGWTC-2: Contains candidates occurring in data taken be-\nfore 2019 October 01 15:00:00.\nThe GWTC-2.0\ndataset is described in Abbott et al. (2021b) and the\nGWTC-2.1 dataset in Abbott et al. (2024).\nGWTC-3: Contains candidates occurring in data taken be-\nfore 2020 May 01 00:00:00. The GWTC-3.0 dataset is\ndescribed in Abbott et al. (2023).\nGWTC-4: Contains candidates occurring in data taken be-\nfore 2024 January 31 00:00:00.\nThe GWTC-4.0\ndataset is described in Abac et al. (2025b).\nIn addition to GWTC, other catalogs of GW transients in-\nclude the Open Gravitational-wave Catalog (OGC), the most\nrecent version 4-OGC includes observations from 2015 to\n2020 (Nitz et al. 2023), as well as catalogs of candidate sig-\nnals identified by the IAS pipeline (Venumadhav et al. 2019;\nOlsen et al. 2022; Wadekar et al. 2024; Cheung et al. 2025).\nCompanion paper Abac et al. (2025i) provides details on the\nGWOSC event portal,1 a database of published GW transient\nevents, including Community Catalogs (Kanner et al. 2025)\ncontaining catalog results from communities outside of the\nLVK.\n1.2.2. Candidate Naming Conventions\nThe naming of our GW candidates follows the format\nGW

_\nencoding the date and Coordinated Universal Time (UTC) of\nthe signal. For example, GW200105_162426 was the tran-\nsient observed on 2020 January 5 at 16:24:26 UTC. For tran-\nsients signals spanning multiple second intervals, the time\nassigned to a signal is an estimate of the time of peak GW\namplitude.\nGW candidates reported prior to the release of GWTC-2.0\nwere designated by the abbreviated form\nGW
\nincluding candidates first appearing in GWTC-1.0 (Abbott\net al. 2019a) as well as GW190412 (Abbott et al. 2020e),\nGW190425 (Abbott et al. 2020b), GW190521 (Abbott et al.\n2020f), and GW190814 (Abbott et al. 2020d). These candi-\ndates retain their legacy names.\n1.3. Outline\nAn outline of the remainder of this article is: We briefly\ndescribe the network of ground-based GW detectors in Sec-\ntion 2 and their observing runs that have contributed to the\nGWTC-4.0 in Section 3. These sections are followed by short\nreviews of the evolution of the various observatories in Sec-\ntion 4 and of the nature of the transient sources observed in\nSection 5. A list of common acronyms is provided in Ap-\npendix A. Mathematical conventions used throughout the ar-\nticles in this compendium are described in Appendix B.\n1 GWOSC event portal https://gwosc.org/eventapi\n2. THE INTERNATIONAL GW OBSERVATORY\nNETWORK\nThe international ground-based GW observatory network\ncurrently comprises four primary observatories employing\nlaser interferometric GW detectors.\nThe four observato-\nries are the two US-based LIGO detectors, LIGO Hanford\nObservatory (LHO) in Washington and LIGO Livingston\nObservatory (LLO) in Louisiana (Aasi et al. 2015a), the\nEuropean Virgo detector (Acernese et al. 2015), and the\nJapanese KAGRA detector (Akutsu et al. 2021; Aso et al.\n2013; Somiya 2012).\nAll these detectors are enhanced\nMichelson interferometers that sense relative changes in the\nlengths L1 and L2 of their two 3 km to 4 km long arms\ncaused by passing GWs in the high-frequency band \u223c10 Hz\nto \u223c1000 Hz (Thorne 1987). Other GW frequency bands in-\nclude the very-low-frequency band \u223c1 nHz to \u223c100 nHz ob-\nserved by pulsar timing arrays such as the European Pulsar\nTiming Array (EPTA; Desvignes et al. 2016), the North\nAmerican Nanohertz Observatory for Gravitational Waves\n(NANOGrav; Brazier et al. 2019), the Parkes Pulsar Tim-\ning Array (PPTA; Kerr et al. 2020), the Indian Pulsar Timing\nArray (InPTA; Joshi et al. 2018), and their combined con-\nsortium the International Pulsar Timing Array (IPTA; Ver-\nbiest et al. 2016); and the low-frequency band \u223c0.1 mHz to\n\u223c10 mHz that will be observed by the Laser Interferometer\nSpace Antenna (LISA; Colpi et al. 2024).\nThe fractional change in the relative lengths of the two op-\ntical paths of interferometric detectors, \u2206(L1 \u2212L2), induced\nby a GW is known as the detector strain, h = \u2206(L1 \u2212L2)/L,\nwhere L is the average arm length (Section 5.1). The sensitiv-\nity of ground-based detectors is fundamentally limited below\n\u223c1 Hz by ground motion noise (Saulson 1984) and at high\nfrequencies by shot noise (Forward 1978; Krolak et al. 1991).\nSignificant noise sources at intermediate frequencies include\nthermal noise in the optics and their suspensions and quan-\ntum readout noise (Weiss 2022; Saulson 2017; Buonanno &\nChen 2001). In the frequency domain, the overall detector\nsensitivity is characterized by the (one-sided) noise power\nspectral density in strain-equivalent units, S n(f), with dimen-\nsions of time (Appendix B).\nThe GEO 600 GW detector (GEO) is a British\u2013German in-\nstrument with 600 m arms located near Hannover, Germany\n(Luck et al. 2010; Affeldt et al. 2014; Dooley et al. 2016).\nThis instrument is a laboratory for prototyping advanced in-\nterferometry techniques, but also is operated in data-taking\nastrowatch mode when not being used for instrument-science\nresearch (Grote 2010; Dooley et al. 2016). Astrowatch pro-\nvides GW observing coverage for times when the larger de-\ntectors are not observing between observing runs and when\nthe detectors are not taking scientific data; e.g., GEO data\nwas used to constrain post-merger signals following the first\nBNS detection (Abbott et al. 2017c).\n3. OBSERVING RUNS\nThe GW observing schedule is divided into observing runs,\ndown time for construction and commissioning, and transi-\ntional engineering runs between commissioning and observ-\n\n4\ning runs (Abbott et al. 2020a). Figure 1 shows a timeline of\nGW observations up to the end date of the time period cov-\nered by GWTC-4.0. Indicated are the observing periods of\neach observing run, and the times when each detector was\nin operation. Also shown are the times when GW transient\nsignals were detected.\nIn order to quickly compare sensitivities of detectors, the\nGW community uses a fiducial range, to which a typical BNS\ncan generally be detected. This fiducial distance assumes that\na SNR of at least 8 is needed for a detection, and it approx-\nimates the BNS inspiral waveform at Newtonian order (Sec-\ntion 5.2). The BNS inspiral range is a volume-averaged mea-\nsure of sensitivity to a signal from two 1.4 M\u2299bodies in a\nquasi-circular inspiral at a single-detector SNR threshold of\n8 (Finn & Chernoff 1993; Chen et al. 2021). When a ho-\nmogeneous BNS population of is assumed and cosmological\neffects are ignored, the BNS inspiral range for a detector is\ndetermined by its noise power spectrum as\nR = 1.016 \u00d7 10\u221220 Mpc s\u22121/6\nsZ \u221e\n0\nf \u22127/3\nS n(f) d f ,\n(1)\nand the sensitive volume of the detector (also when neglect-\ning cosmological effects) is given by V = (4\u03c0/3)R3 (Ap-\npendix B). (This measure is taken as a simple figure of merit\nof sensitivity to CBCs; it does not attempt to account for\nthe true underlying astrophysical distribution describing such\nsystems.) If the number of BNS mergers per unit time per\nunit volume of space, the merger rate density of BNSs, is\nR, then the expected number of BNS signals seen with SNR\ngreater than 8 in time T would be RVT. Figure 1 also gives\nthe typical BNS inspiral range, as given in Equation (1), for\neach detector during each observing run.\nThe amplitude strain noise spectra is the square-root of the\n(one-sided) noise power spectral density in strain equivalent\nunits S 1/2\nn ( f) having dimensions of time1/2. The amplitude\nstrain noise spectra of LHO, LLO, and Virgo during the var-\nious observing runs are shown in Figure 2. There is an over-\nall reduction in the detector noise levels with successive ob-\nserving runs resulting in increased sensitivity. Figure 2 also\nshows the fraction of the run duration during which different\ncombinations of detectors were observing.\nFigure 3 shows the cumulative number of candidates de-\ntected vs. the estimated effective time\u2013volume hypervolume\nVT for the detector network.\nFor the first two observing\nruns (described below), only data when two detectors were\noperating were searched for GWs. In this case the rate at\nwhich VT is accumulated at any observing time is given by\nthe sensitive volume V for the second most sensitive instru-\nment observing at that time. Beginning with the third ob-\nserving run, periods during which only a single detector was\nobserving were included in the search. During such time, the\nrate at which VT is accumulated is again given by the sen-\nsitive volume V = (4\u03c0/3)R3 but where R is computed from\nEquation (1) divided by 1.5, representing an effective SNR\nthreshold for detection of 12 rather than 8 for single-detector\nobservation (Abbott et al. 2021b). This simple estimate of\nVT, derived from the BNS inspiral range, is an approximate\none done for a quick and convenient overview. In particu-\nlar, it makes a crude approximation of whether a signal is\ndetectable and its numerical value is only representative of\nsensitivity to sources in a small region of mass space. Ac-\ntual measured sensitive hypervolume \u27e8VT\u27e9values for various\nCBC mass regions and search methods are reported in Abac\net al. (2025b).\n3.1. O1: The First Observing Run\nO1 consists of the time-period from 2015 September 12 to\n2016 January 19. O1 includes short time-periods which were\noriginally planned to be engineering time (2015 Septem-\nber 12 to 2015 September 18 and 2016 January 12 to\n2016 January 19), but which were of sufficient quality to be\nincluded in O1. This was the first observing run with the\nAdvanced LIGO (aLIGO) interferometers, in progress to-\nward full aLIGO design sensitivity (Abbott et al. 2016b,c),\nLHO achieving a BNS range of 80 Mpc and LLO a range of\n70 Mpc.\nOf the 129.7 d duration of O1, there were only 49.0 d\n(38%) when both LHO and LLO were observing jointly, and\nthere were 36.2 d (28%) when neither detector was observ-\ning. The largest non-observing periods were due to locking,\nthe time spent bringing the interferometers from an uncon-\ntrolled state to their low-noise configuration (Staley et al.\n2014), and environmental issues such as earthquakes, wind,\nand microseismic noise arising from ocean storms (Effler\net al. 2015; Abbott et al. 2016d). Wind and microseismic\nnoise have seasonal variation as storms are more prevalent\nin winter months; LLO was more susceptible to these than\nLHO, mainly due to its local geophysical environment (Daw\net al. 2004).\nOverall,\na\ntotal\neffective\nhypervolume\nVT\n=\n1.59 \u00d7 10\u22124 Gpc3 yr was accumulated during joint LHO\u2013\nLLO observing during O1.\n3.2. O2: The Second Observing Run\nThe O2 run from 2016 November 30 to 2017 August 25. It\nwas preceded by an engineering run that began on 2016 Oc-\ntober 31 at LLO and on 2016 November 14 at LHO. The\nLHO and LLO detectors achieved a typical BNS range sen-\nsitivity of 80 Mpc and 100 Mpc respectively (Abbott et al.\n2017d, 2019a). However, on 2017 July 06 LHO was severely\naffected by a 5.8 magnitude earthquake in Montana result-\ning in a post-earthquake sensitivity drop of approximately\n10 Mpc in BNS range for the remainder of the run (Abbott\net al. 2019a).\nThe Advanced Virgo (AdV) interferometer (Acernese et al.\n2015) joined O2 on 2017 August 01, forming a three-detector\nnetwork for the last month of the run. A vacuum contamina-\ntion issue required AdV to use steel wires rather than fused\nsilica fibers to suspend the test masses, limiting the sensitiv-\nity of AdV (Abbott et al. 2019a). In O2, a 30 Mpc BNS range\nwas achieved.\nThe LIGO detectors saw some improvement in duty factors\nduring non-winter months with an almost 50% reduction in\n\n5\n2015\n2016\n2017\n2018\n2019\n2020\n2021\n2022\n2023\n2024\nGEO\nLHO\nKAGRA\nLLO\nVirgo\nFigure 1. The timeline of observing runs covering a timespan starting from 2015 and lasting up to the beginning of O4b on 2024 April 10. The\nperiods in which the various detectors in the network were observing are shown in this timeline, along with the typical BNS inspiral ranges for\nthose detectors during the observing run. GEO astrowatch observing periods are shown in light gray. KAGRA observing periods during O4a,\nalso shown in light gray, were not used for GW observational analyses. In O1 and O4a, only LHO and LLO were participating. Virgo joined\nthese two detectors for the last month of O2 and was observing alongside them throughout O3a and O3b. At the end of O3 there was a short\njoint observing run, O3GK, which included GEO and KAGRA. Also shown is a timeline of the observed candidates contained in GWTC-1.0,\nGWTC-2.1, GWTC-3.0, and GWTC-4.0 with a probability of astrophysical origin greater than or equal to 50%. The time intervals covered by\nthe various versions of the GWTC are bounded from above but not from below, as indicated by the arrows pointing left (see Section 1.2.1).\ndowntime due to environmental effects at both sites, though\nLLO lost over twice as much observing time as LHO to earth-\nquakes, microseismic noise, and wind. O2 had a planned\nmid-run engineering break to effect needed repairs and to at-\ntempt improvements to the sensitivity. The Virgo instrument\noperated with a duty factor of approximately 85% after join-\ning O2. There were 15 d of all three detectors observing si-\nmultaneously.\nOverall,\na\ntotal\neffective\nhypervolume\nVT\n=\n3.52 \u00d7 10\u22124 Gpc3 yr was accumulated during O2; of this,\n3.27\u00d710\u22124 Gpc3 yr was accumulated during joint LHO\u2013LLO\nobserving, 2.41 \u00d7 10\u22125 Gpc3 yr was accumulated while all\nthree detectors were observing, and only 3.62 \u00d7 10\u22127 Gpc3 yr\nand 4.80\u00d710\u22127 Gpc3 yr were accumulated during joint LHO\u2013\nVirgo and LLO\u2013Virgo observing respectively.\n3.3. O3: The Third Observing Run\nO3 started on 2019 April 01, with a commissioning break\nfrom 2019 October 01 to 2019 November 01. This observ-\ning run was planned to continue to 2020 April 30 but the\nCOVID-19 pandemic resulted in a suspension of observing\non 2020 March 27 (Abbott et al. 2023). The period of O3\nprior to the commissioning break is referred to as O3a while\nthe period after the break is referred to as O3b. KAGRA had\nintended to join LIGO and Virgo at the end of O3 but the\nearly end made this impossible. Instead, KAGRA and GEO\njointly observed for a two week period from 2020 April 07\nto 2020 April 21 after LIGO and Virgo had suspended their\nobserving. This joint GEO\u2013KAGRA run (distinct from the\nO3 run described previously) is referred to as O3GK (Abbott\net al. 2022).\nIn O3, the LHO and LLO detectors achieved a BNS range\nof 110 Mpc and 140 Mpc respectively (Buikema et al. 2020).\nThis increase in sensitivity arose from a variety of improve-\nments, chief among them an increase in the input laser power,\nthe addition of a squeezed vacuum source at the interferom-\neter output (Tse et al. 2019), and mitigation of noise aris-\ning from scattered light (Soni et al. 2020). In addition, end\ntest-mass optics with lower-loss coatings, along with new re-\naction masses, were installed in each LIGO interferometer\n(Granata et al. 2020; Aston et al. 2012).\nThe steel wires in AdV were replaced with fused silica\nfibers in preparation for O3. Along with other improvements\nsuch as reduction of technical noises, an increase in laser\npower, and the installation of a squeezed vacuum source,\nVirgo achieved a BNS range of 60 Mpc (Acernese et al.\n2019).\nOver all of O3a and O3b, 361.1 d combined, there were\n154.3 d (43%) of three-detector observation and only 42.1 d\n(12%) during which no detector was observing.\nThe to-\ntal effective hypervolume VT accumulated was 3.21 \u00d7\n10\u22123 Gpc3 yr. Of this, 2.27 \u00d7 10\u22123 Gpc3 yr was accumulated\nduring three-detector observations, 7.20\u00d710\u22124 Gpc3 yr when\nLHO and LLO were observing, 4.09 \u00d7 10\u22125 Gpc3 yr when\nLHO and Virgo were observing, 5.03 \u00d7 10\u22125 Gpc3 yr when\nLLO and Virgo were observing. The amount accumulated\n\n6\n10 24\n10 23\n10 22\n10 21\n10 20\n10 19\n10 18\nStrain (1/ Hz)\nO1 (129.7 d)\nLHO (80 Mpc)\nLLO (70 Mpc)\nO2 (268.3 d)\nLHO (80 Mpc)\nLLO (100 Mpc)\nVirgo (30 Mpc)\n101\n102\n103\nFrequency (Hz)\n10 24\n10 23\n10 22\n10 21\n10 20\n10 19\n10 18\nStrain (1/ Hz)\nO3 (361.1 d)\nLHO (110 Mpc)\nLLO (140 Mpc)\nVirgo (60 Mpc)\n101\n102\n103\nFrequency (Hz)\nO4a (237.0 d)\nLHO (160 Mpc)\nLLO (160 Mpc)\n38%\n21%\n13%\n28%\n6%\n38%\n 1%\n1% \n14%\n12%\n1%\n27%\n43%\n14%\n9%\n11%\n3%\n3%\n7%\n12%\n53%\n14%\n16%\n17%\nFigure 2.\nRepresentative noise amplitude spectral densities for LHO, LLO, and Virgo during O1 (LHO, LLO: 2015 October 24), O2\n(LHO: 2017 June 10, LLO: 2017 August 06, Virgo: from Acernese et al. (2023a)), O3 (LHO: 2020 January 04, LLO: 2019 April 29, Virgo:\n2020 February 09), and O4a (LHO: 2024 January 11, LLO: 2023 November 19). The BNS inspiral ranges, defined by Equation (1), for these\nnoise curves are given in the legend. Inset sunburst charts show the fraction of the run duration during which different combinations of detectors\nwere observing. Gray regions in each ring indicates portions when a detector is not operating. The segments of the sunburst chart, clockwise\nfrom 12 o\u2019clock, are: LHO\u2013LLO, LHO alone, LLO alone, and neither for observing runs involving only LHO and LLO; and LHO\u2013LLO\u2013Virgo,\nLHO\u2013LLO, LHO\u2013 Virgo, LLO\u2013Virgo, LHO alone, LLO alone, Virgo alone, and none for observing runs involving LHO, LLO, and Virgo.\nwith only a single detector observing was 4.47\u00d710\u22125 Gpc3 yr,\n7.47 \u00d7 10\u22125 Gpc3 yr, and 9.72 \u00d7 10\u22126 Gpc3 yr for LHO, LLO,\nand Virgo, respectively.\nThe first operation of the KAGRA detector in an initial\nconfiguration with a simple Michelson interferometer oc-\ncurred in March 2016 (Akutsu et al. 2018). In August 2019,\nthe first lock of the Fabry\u2013Perot Michelson interferometer\nwas achieved, with power recycling accomplished in Jan-\nuary 2020. By the end of March 2020, KAGRA obtained\na BNS range of approximately 1 Mpc (Abe et al. 2023) and,\nalthough the LIGO and Virgo instruments had ended their\nO3 run, KAGRA was operated jointly with GEO, which had\na comparable BNS range, in O3GK yielding 6.4 d of joint\nobserving time.\n3.4. O4: The Fourth Observing Run\nO4 began on 2023 May 24 at 15:00:00 UTC. This run is\nagain divided into parts: the first part of the fourth observ-\ning run (O4a) ended on 2024 January 16 at 16:00:00 UTC\nand was followed by a commissioning break; the second part\nof the fourth observing run (O4b) started on 2024 April 10\nat 15:00:00 UTC. The O4b period continued until 2025 Jan-\nuary 28 17:00:00 UTC, the original intended end of O4; how-\never it was decided to continue observing into a third part\nof the fourth observing run (O4c). The period covered by\n\n7\n0.000\n0.002\n0.004\n0.006\n0.008\nCumulative effective hypervolume (Gpc\u00b3 yr)\n0\n50\n100\n150\n200\n250\nCumulative number of detections\nO1 O2\nO3a\nO3b\nO4a\nFigure 3. The number of CBC detection candidates with a probability of astrophysical origin greater than or equal to 50% versus the detector\nnetwork\u2019s effective surveyed hypervolume for BNS coalescences (Abbott et al. 2021b). The BNS effective surveyed hypervolume is a valid\nproxy for overall sensitivity to CBCs, though its scale is set to the case of canonical BNS signals. The colored bands indicate the different\nobserving runs. The final data sets for O1, O2, O3a, O3b, and O4a consist of 49.0 d, 122.2 d, 149.6 d (177.1 d), 124.6 d (141.9 d), and 126.5 d\n(196.8 d) with at least two detectors (one detector) observing, respectively. The cumulative number of probable candidates is indicated by the\nsolid black line, while the blue line, dark blue band and light blue band are the median, 50% confidence interval and 90% confidence interval\nfor a Poisson distribution fit to the number of candidates at the end of O4a.\nGWTC-4.0 contains events that occurred in O4a and earlier\nobserving runs only (see Section 1.2.1). O4b and O4c anal-\nyses are underway and will be included in future versions of\nthe GWTC.\nThe two LIGO detectors were observing during O4a, both\nhaving a BNS range of approximately 160 Mpc. During the\n237.0 d there were 126.5 d (53%) of two-detector joint obser-\nvation and 40.2 d (17%) when neither of the LIGO detectors\nwere observing. Virgo did not join joint observation until\nO4b in order to continue commissioning to address a dam-\naged mirror that limited performance and to improve sensi-\ntivity. KAGRA also continued commissioning to improve\nsensitivity with the goal of joining O4 toward the end of the\nrun.\nDuring O4a, the total effective hypervolume VT accu-\nmulated was 5.28 \u00d7 10\u22123 Gpc3 yr.\nThis is divided into\n3.85 \u00d7 10\u22124 Gpc3 yr during which LHO alone was observing,\n4.57 \u00d7 10\u22124 Gpc3 yr during which LLO alone was observing,\nand 4.44 \u00d7 10\u22123 Gpc3 yr during which both detectors were\nobserving.\nAt the time of writing, O4 is expected to continue until\n2025 November 18 at 16:00 UTC with no further planned\nbreaks in observing. The timeline for a fifth observing run\n(O5) is being assessed in order to maximize the scientific\noutput of the global network. Updates to the planned ob-\nserving schedule will be provided as soon as such decisions\nare made.2\n4. OBSERVATORY EVOLUTION\nThe advanced detector era is characterized by a series of\ntechnological improvements from the initial detectors that\ndeliver higher sensitivity and greater BNS range that made\npossible the era of GW observation. Some of the key instru-\nment science elements of the advanced era detectors are: (i)\nincreases in the input laser power entering the interferome-\nter, and to the circulating power in the interferometer cavities\n(a higher power in the arms produced a lower quantum shot\nnoise limited sensitivity above \u223c200 Hz); (ii) increases in test\nmass mirror size to accommodate larger beams which miti-\ngates coating thermal noise and heavier masses to reduce in-\nertial and quantum back-action effects; (iii) implementation\nof signal recycling (Meers 1988) in addition to power recy-\ncling (Drever 1983), which alters the frequency band of the\ndetectors\u2019 sensitivity (typically to give broader-band sensi-\ntivity); (iv) implementation of monolithic test-mass suspen-\nsions, which reduces the suspension thermal noise in the de-\ntectors\u2019 sensitivity band by using the same low mechanical\nloss material (fused silica for LIGO and Virgo) for the sus-\npension fibers as for the mirror substrate, and low loss joint-\ning techniques and thermo-elastic nulling (Aston et al. 2012;\nTravasso 2018); (v) improved passive and active seismic iso-\n2 LVK observing run plans https://observing.docs.ligo.org/plan\n\n8\nlation systems, and sensors to reduce ground motion coupling\nto the detector and to damp suspension modes (Braccini et al.\n2005; Matichard et al. 2015; Cooper et al. 2023); (vi) im-\nproved low-thermal-noise, low-absorption, high-reflectivity\nmirror coatings (Harry et al. 2007; Granata et al. 2020).\nThroughout the advanced-detector era of GW observation,\nthe LIGO and Virgo detectors have undergone a series of\nperformance-improving detector upgrades and commission-\ning activities of which detail is given in this section. De-\ntector upgrades include the installation of new hardware or\nupgrades to existing hardware in a detector. Examples of\ndetector upgrades include the installation of new laser sys-\ntems to provide higher power into the interferometer, instal-\nlation of baffles to mitigate scattered light and the injection\nof squeezed light to manipulate the quantum-noise limited\nsensitivity of the detectors (Tse et al. 2019; Acernese et al.\n2019). Commissioning activities cover a range of improve-\nments to sensitivity and observing uptime of the instruments\nfrom targeted noise-hunting activities to remove glitches,\nlines and broadband noise, and improved control schemes to\nmitigate instabilities and improve detector robustness.\nAlongside this has been the effort to build and commission\nthe KAGRA detector utilizing advanced technologies such as\ncryogenic cooling of the test-masses and an underground lo-\ncation. This schedule of planned upgrades and commission-\ning activities between observing runs ensures that the max-\nimal science output is achieved from the network. In terms\nof valuable scientific output, a successful upgraded detector\nthat has been offline for a period of time rapidly overtakes a\nnon-upgraded detector in continuous observational mode in\nterms of number of significant detections, and the resolution\nand sky-localization of high interest signals.\nThe aLIGO and AdV detectors are designed to be dual-\nrecycled Fabry\u2013Perot Michelson interferometers with or-\nthogonal kilometer-scale arms (Aasi et al. 2015a; Acernese\net al. 2015). Each arm contains a Fabry\u2013Perot optical cav-\nity, and a beam splitter at the corner between the arms forms\na Michelson interferometer that measures the change in the\nrelative phase of the light induced by changes in the lengths\nof these cavities (Thorne 1987; Vinet et al. 1988). Additional\npower-recycling and signal-recycling cavities are created by\nadding mirrors in the symmetric and antisymmetric ports of\nthe interferometer. These improve sensitivity by building up\nthe light power on the beam splitter and beneficially modi-\nfying the response of the interferometer respectively (Meers\n1988). The input and end mirrors on each of the Fabry\u2013Perot\ncavities are the test masses whose separations are affected by\nGWs. The mirrors are isolated by multistage pendulums that\nsuppress the ground motion by more than 10 orders of mag-\nnitude at frequencies around 10 Hz. Monolithic fused-silica\nfibers are used on the bottom stage of the suspension sys-\ntem to suppress thermal noise and the mirrors themselves are\nfused-silica substrates with low-loss, highly reflective coat-\nings (Aston et al. 2012).\nGround-based interferometers generally have the same\nfundamental limiting noise sources (Weiss 2022; Saulson\n2017), with the response of each detector and the exact ex-\ntent to which each noise limits sensitivity being specific to\nthe detailed design of each detector. At low observational\nfrequency below \u223c10 Hz the detectors are limited by a com-\nbination of seismic noise, gravity-gradient noise, suspension\nthermal noise and quantum radiation-pressure noise. Ther-\nmal noise in the mirror optical coatings is a significant noise\nsource at mid frequencies \u223c50 Hz to \u223c200 Hz (Harry et al.\n2007), and at high frequencies above \u223c200 Hz, sensitivity is\nlimited by the quantum shot noise.\nIn addition to these fundamental noise sources the de-\ntectors are also limited by technical noise.\nThis includes\nscattered-light noise, which occurs when some fraction of\nlight is deflected from the interferometer beam path and is\nincident on another moving surface varying the phase of the\nlight; this couples noise into the interferometer readout if part\nof this light is reflected back into the main beam (Accadia\net al. 2010; Ottaway et al. 2012). Interferometer controls-\nsystem noise is when signals couple between the multi-\nple feedback loops that control the degrees of freedom of\nthe interferometer and requires complicated optimization of\ncontrol-loop parameters to mitigate (Buikema et al. 2020).\nLaser noise due to fluctuations in the frequency, intensity and\npointing of the laser beam entering the interferometer is re-\nduced with dedicated multi-stage stabilization systems to a\nlevel such that is does not impact the sensitivity of the detec-\ntors, however suboptimal tuning of these stabilization sys-\ntems can lead to laser noise affecting sensitivity (Cahillane\net al. 2021). Environmental noise is caused when environ-\nmental effects in the vicinity of the interferometer (e.g., seis-\nmic activity) couple into the measurement of the interferom-\neter strain signal (Acernese et al. 2006; Effler et al. 2015;\nFiori et al. 2020; Nguyen et al. 2021; Helmling-Cornell et al.\n2024). Detector commissioning seeks to mitigate such non-\nfundamental noise sources.\nThe key parameters of the LIGO, Virgo, KAGRA and GEO\ndetectors across the advanced era observing runs are given\nin Table 1. The specific evolution of each detector in terms\nof detector upgrades and improvements is detailed in the re-\nmainder of this section.\n4.1. LIGO Hanford & Livingston Observatories\nLIGO is a US national facility comprising two US-based\ninterferometric detectors in Hanford, Washington (LHO),\nand Livingston, Louisiana (LLO), each with 4 km arms.\nLIGO construction began in 1994. From 2002 to 2010, initial\npower-recycled Fabry\u2013Perot Michelson interferometers were\noperated at these sites in a series of science runs S1 through\nS6 (Abbott et al. 2009; Aasi et al. 2015b). During this period,\nLIGO also operated a second interferometer with 2 km arms\nat the Hanford site. Subsequently the aLIGO project resulted\nin a major overhaul of the interferometers to improve the ca-\npabilities of the detectors (Aasi et al. 2015a) leading up to O1\nand the first observation of GWs.\nAcross the observing runs certain areas have been the main\nfocus of much of the detector improvement effort: (i) increas-\n\n9\nTable 1. Selected optical and physical parameters of the LIGO Hanford (LHO), LIGO Livingston (LLO), Virgo, KAGRA, and\nGEO 600 (GEO) interferometers throughout the advanced-detector era. The input laser power is the power that would be measured\nat the power recycling mirror (after the input mode cleaner) and is an estimate of the maximum level typically achieved during an\nobserving period. Suspension types are monolithic fused silica fibers, sapphire fibers, or steel wires.\nObserving period\nInterferometer\nInput laser power\nPower recycling gain\nSignal recycling\nSqueezing\nSuspension type\nO1\nLHO\n21 W\n38\n\u2713\n\u00d7\nSilica\nLLO\n22 W\n38\n\u2713\n\u00d7\nSilica\nO2\nLHO\n26 W\n40\n\u2713\n\u00d7\nSilica\nLLO\n25 W\n36\n\u2713\n\u00d7\nSilica\nVirgo\n10 W\n38\n\u00d7\n\u00d7\nSteel\nO3a\nLHO\n34 W\n44\n\u2713\n\u2713\nSilica\nLLO\n44 W\n47\n\u2713\n\u2713\nSilica\nVirgo\n18 W\n36\n\u00d7\n\u2713\nSilica\nO3b\nLHO\n34 W\n44\n\u2713\n\u2713\nSilica\nLLO\n40 W\n42\n\u2713\n\u2713\nSilica\nVirgo\n26 W\n34\n\u00d7\n\u2713\nSilica\nO3GK\nGEO\n3 W\n1000\n\u2713\n\u2713\nSilica\nKAGRA\n5 W\n12\n\u00d7\n\u00d7\nSapphire\nO4a\nLHO\n57 W\n50\n\u2713\n\u2713\nSilica\nLLO\n64 W\n35\n\u2713\n\u2713\nSilica\ning the arm cavity power by increasing the injected laser\npower and the power-recycling gain while achieving stable\noperation; (ii) mitigation of scattered-light sources and cou-\npling mechanisms; (iii) reduction of quantum noise with ad-\ndition of a squeezed-light system for O3 and the following\nimprovements to the quantum-enhancement factor.\nBoth aLIGO detectors are operated with a lower injected\nlaser power and lower power-recycling gain than the design\ngoal (Aasi et al. 2015a). The full amount of available laser\npower cannot be fully utilized due to issues with maintain-\ning long-duration stable locking of the interferometer due\nto angular instabilities and point absorbers in the test-mass\nmirrors (Brooks et al. 2021). This issue was the focus of\ncommissioning efforts to continually improve the operating\npower in the cavity by optimizing the interferometer con-\ntrol loops (Buikema et al. 2020) and reducing the presence\nof point absorbers in the mirrors. Stray-light control can be\nachieved by the addition of baffles to block unwanted beam\npaths and with active control of known scattered-light paths.\nThe addition of a squeezed vacuum source at the interferome-\nter\u2019s output alters the quantum noise in the interferometer and\nwith the inclusion of a filter cavity can produce frequency de-\npendent squeezing which can be used to surpass the standard\nquantum limit on sensitivity of a laser interferometer (Tse\net al. 2019; Ganapathy et al. 2023).\n4.1.1. O1\nThe sensitivity and limiting noise sources of the LIGO de-\ntectors during O1 is described in Abbott et al. (2016c). Fig-\nure 2 shows a representative amplitude spectral density of\nthe strain noise and the BNS range. In O1, the typical input\npower entering the power-recycling cavity was 21 W in LHO\nand 22 W in LLO, circulation of laser light in the power re-\ncycling cavity increases the power on the beam splitter to be\na factor of 38 times greater (the power recycling gain), and\na further increase in circulating power by a factor of 144 is\nachieved in the arms by the Fabry\u2013Perot cavities. The laser\ninput power and power-recycling gain during O1 and the later\nobserving runs is given in Table 1 alongside other detector\nparameters. An example of commissioning improvement is\nthe investigation at LLO during O1 of recurring changes in\nthe BNS range from 65 Mpc to 60 Mpc. By searching for\ncorrelation between the detector range and the hundreds of\ndata channels recorded by aLIGO it was found that the issue\nwas caused by a malfunctioning temperature sensor. This\nsensor was replaced resulting in\na more stable increased\nrange (Walker et al. 2018).\n4.1.2. O2\nAfter O1, several improvements were made to both LIGO\ninstruments (Abbott et al. 2017d).\nDetector upgrades in-\ncluded installation of new mass dampers on the end test-\nmass suspensions to dampen mechanical modes, improving\nthe stabilization of laser intensity, and installing a new out-\nput Faraday isolator and higher quantum-efficiency photodi-\nodes at the output port to improve signal-detection efficiency\nin the readout system. Mitigation of scattered light sources\nand other improvements to the detector sensitivity through-\n\n10\nout O2 resulted in a BNS range improvement to 100 Mpc\nby the end of the run (Davis et al. 2021). Commissioning\ntests during O2 on the LHO detector to increase in the laser\npower to 50 W did not result in an overall improvement in\nperformance of 80 Mpc BNS range at the end of O1, ow-\ning to point absorbers on one of the input test-mass optics,\nso the detector operated with 30 W input power. After O2, it\nwas demonstrated that the use of witness channels to perform\nnoise subtraction on the strain data was able to increase the\nBNS range by 20% (Davis et al. 2019; Driggers et al. 2019).\n4.1.3. O3\nLeading up to O3, several upgrades were made to the\nLIGO instruments (Buikema et al. 2020). The most signif-\nicant was the installation of an in-vacuum squeezed-light in-\njection system at each site to inject squeezed vacuum into\nthe interferometers to reduce shot noise at frequencies above\n50 Hz (Tse et al. 2019). The squeezer works by optically\npumping a non-linear crystal to modify the distribution of the\nquantum vacuum state that enters the interferometer (Caves\n1981; Barsotti et al. 2019).\nBetween O3a and O3b, adjustments to the squeezing sub-\nsystem produced large sensitivity improvements.\nAmong\nthese were the installation of higher power laser amplifiers\nwith stable operation and output power over 70 W (Bode\net al. 2020). A program of installation of optical baffles was\ncompleted to improve stray light control. The correlation\nof microseismic activity with scattered-light noise was deter-\nmined to be primarily caused by a scattered-light path aris-\ning from large relative motion between the end test mass and\nthe reaction mass that is immediately behind it (Soni et al.\n2020). A control loop that makes the reaction mass follow\nthe end mass, implemented on 2024 January 07 at LLO and\n2024 January 14 2024 at LHO, reduced the relative motion\nand mitigated the scattered-light noise (Davis et al. 2021).\nAt LHO, wind fences were installed to mitigate ground tilt\ninduced by wind on the buildings (Nguyen et al. 2021).\n4.1.4. O4a\nSeveral upgrades were implemented at LHO and LLO to\nimprove the quantum-limited sensitivity of the detectors via\nimproved quantum squeezing and higher intracavity power\n(Abac et al. 2024a). Further upgrades to the laser amplifi-\ncation system were implemented with stable operation and\noutput power over 140 W (Bode et al. 2020). A new vac-\nuum system to house a 300 m filter cavity was built at both\ndetectors along with an upgraded squeezing injection system\nto allow the injection of frequency-dependent squeezed vac-\nuum to achieve quantum noise reduction across the detec-\ntion frequency band (Ganapathy et al. 2023; Jia et al. 2024).\nSqueezing levels in O4a reached 5.8 dB at LLO and 4.6 dB at\nLHO, compared to the 2 dB to 3 dB achieved in O3 (Capote\net al. 2025). Test-mass mirrors were replaced at both ob-\nservatories to remove point defects on the mirrors that con-\ntributed to controls challenges and excess noise (Buikema\net al. 2020). This involved a replacement of both end test\nmasses at LLO and the input y-arm test mass at LHO. Re-\nplacing these test masses allowed both observatories to ap-\nproximately double the input power compared to O3, further\nimproving the quantum-limited sensitivity of the detectors\ndue to higher circulating power in the Fabry\u2013Perot arm cavi-\nties (Capote et al. 2025; Buikema et al. 2020).\nOther upgrades to the LIGO detectors include improve-\nments to the electronics in the GW signal readout chain,\ndamping of baffles to mitigate scattered light, and improve-\nments to electronics grounding (Capote et al. 2025; Soni et al.\n2025). The photodetector transimpedance amplifiers were\nimproved ahead of O4a using a design tested at GEO, re-\nsulting in a factor of ten reduction in dark noise compared to\nO3 (Grote et al. 2016). At both LIGO detectors, a septum\nwindow separating two vacuum volumes housing the output\noptics was removed, significantly reducing the coupling of\nacoustic noise. Baffles along the arm cavity and around vac-\nuum pumps were previously identified to couple excess scat-\ntered light in O3, and were damped to reduce their motion\nand therefore shift the frequency of up-converted scattered\nlight out of the sensitive band. Finally, injections into the\nbuilding electronics ground demonstrated that many spectral\nfeatures in the strain at LHO were the result of a fluctuating\nground potential (Capote et al. 2025; Soni et al. 2025). The\nresistance to ground was reduced for several electronics chas-\nsis around the detector. Additionally, the voltage biases of the\ntest-mass electrostatic drives were adjusted to minimize the\nelectronics noise coupling further (Capote et al. 2025).\nDetector commissioning ahead of O4a also focused on op-\ntimization of the auxiliary controls to reduce technical noise\nthat limited the detectors at low frequency in O3 (Buikema\net al. 2020).\nAlignment controls noise was reduced by a\nfactor of ten and length controls noise by a factor of two\nat both detectors near 20 Hz (Capote et al. 2025; Buikema\net al. 2020). Significant improvements to the controls in-\ncluded the upgrade to a camera servo system that requires\nno line injection to sense the alignment of the main detector\noptics (Capote et al. 2025). Suspension local control loops\nwere re-optimized to focus on noise suppression above 5 Hz,\nreducing both noise directly coupled to the strain, and noise\nthat couples indirectly through the length and alignment con-\ntrols (Capote et al. 2025).\nBoth detectors were also lim-\nited by unmitigated beam-jitter noise that was well-witnessed\nby auxiliary sensors (Capote et al. 2025). As such, front-\nend infrastructure using the non-stationary estimation and\nnoise subtraction (NonSENS) code (Vajente 2018) was im-\nplemented to perform noise cleaning in low latency, increas-\ning detector sensitivity by up to 5 Mpc in BNS range (Vajente\net al. 2020; Vajente 2022; Capote et al. 2025).\n4.1.5. Beyond O4\nLooking to the future there is ongoing construction of\nLIGO-India (Souradeep et al. 2017), a third LIGO interfer-\nometer to be built in the Hingoli district of Maharashtra, In-\ndia. This facility will be based on aLIGO hardware and de-\nsign, and its location will provide a significant improvement\n\n11\nin the sky localization of GW sources (Pankow et al. 2020;\nSaleem et al. 2022; Pandey et al. 2025).\nIn parallel, there are plans underway to upgrade the\nexisting LIGO detectors (and eventually LIGO-India) to\nAdvanced+ LIGO (A+) sensitivity (Abbott et al. 2020a;\nCooper et al. 2023). The A+ upgrade to the LIGO detectors\nis a series of detector upgrades utilizing improved technol-\nogy that has been developed in parallel to the observing runs.\nThe inclusion of frequency dependent squeezing was origi-\nnally planned as an A+ upgrade but was implemented ahead\nof O4a at both sites (Capote et al. 2025). Other A+ upgrades,\nwhich will be implemented for future observing runs, include\nnew optics with lower noise and loss, improved sensors for\ncontrolling the mirrors, a new pre-mode cleaner to reduce\nbeam-jitter noise, improved output mode cleaners with lower\nloss, and a balanced homodyne readout system that allows\nfor better readout control of the interferometer signal.\nA post-O5 upgrade, referred to as LIGO A\u266f(A\u266f), explores\nmore transformative changes in detector design with the goal\nof increasing the sensitivity to the limits of what is possi-\nble with the existing infrastructure of the LIGO detectors\n(Fritschel et al. 2024). Detector improvements that facili-\ntate the achievement of the A\u266fsensitivity include the upgrade\nof the laser injection system to deliver more power into the\ninterferometer, and an improved system for the thermal com-\npensation of the test-mass mirrors. The test-mass mirrors will\nbe replaced with heavier masses with improved optical coat-\nings, and A\u266ftargets an improved exploitation of the quan-\ntum noise reduction from the squeezed-light system. The A\u266f\nconfigurations are natural outgrowths of A+ configurations,\nand will serve as pathfinders for the next-generation Cosmic\nExplorer concept (Evans et al. 2021). Additionally, it has\nmuch technological overlap with Advanced Virgo+ (AdV+)\nand Virgo_nEXT (Section 4.2), which presents the possibil-\nity of collaborating on developing these technologies.\n4.2. Virgo Observatory\nThe Virgo interferometer, located in Cascina (Italy), is the\nlargest European GW detector, designed in its AdV phase I\nas a 3 km dual-recycled Fabry\u2013Perot Michelson interferom-\neter (Acernese et al. 2015). Construction of Virgo started\nin 1997 and was completed in 2003 (Acernese et al. 2005).\nFour science runs of the initial Virgo interferometer, VSR1\nthrough VSR4, took place between 2007 and 2011. These\nwere followed by upgrades leading to the AdV design op-\nerated during O2 and O3. Subsequently, further upgrades\nleading to AdV+ were planned to take place in two phases,\nthe first for operation during O4 and the second for opera-\ntion during O5. A proposed next-generation upgrade planned\npost-O5, Virgo_nEXT, would provide further sensitivity by\npushing current facilities to their limit and would serve as a\npathfinder for future ground-based GW detectors.\nThe first-generation Virgo detector (Accadia et al. 2012a)\nobserved jointly with the initial LIGO detector\u2019s fourth and\nfifth science runs.\nAfter several years of commissioning,\nfrom 2007 May to 2007 October the first scientific data run\nVSR1 (along with LIGO) took place, for which a BNS range\nof 4 Mpc was achieved (Acernese et al. 2008). At this stage,\nVirgo was a power-recycled Fabry\u2013Perot Michelson inter-\nferometer with a 20 W laser source. The second Virgo sci-\nence run, VSR2 (also along with LIGO), from 2009 July to\n2010 January (Accadia & Swinkels 2010), was preceded by\nset of major improvements to mitigate scattered light and to\nimprove the light-injection system.\nThe replacement of the four payloads in the Fabry\u2013Perot\ncavities was the major improvement in preparation for the\nthird Virgo science run VSR3 from 2010 July to 2010 Oc-\ntober (Accadia et al. 2012b). Issues arising from thermal\nnoise due to improperly-aligned suspension wires and de-\ngraded contrast resulting from differing radii of mirror cur-\nvature were addressed leading up to VSR4, from 2011 June\nto 2011 October, during which Virgo achieved a BNS range\nof 12 Mpc. While the three previous VSR were aligned with\ninitial LIGO science runs, Virgo took data during this run\ntogether with GEO. The main upgrade consisted on the in-\nstallation of the central heating radius of curvature correc-\ntion (CHRoCC) on both end mirrors, which allowed to con-\ntrol the radius of curvature of the mirrors in real-time (Ac-\ncadia et al. 2013). This system was designed to correct the\nthermal lensing effect in the mirrors, which had been a sig-\nnificant source of noise in the interferometer. Virgo stopped\nobserving in 2011 for the AdV upgrade.\n4.2.1. O2\nAfter these four science runs, major modifications were\nmade to the optical layout to increase the broadband sensi-\ntivity by up to an order of magnitude (Abbott et al. 2017e).\nThese upgrades marked the transition from Virgo, a first-\ngeneration interferometer, to AdV, a second-generation GW\ndetector (Acernese et al. 2015).\nThe installation of AdV\nstarted in 2011 and was completed in 2016.\nAdV was\nplanned as a dual-recycled interferometer with 125 W en-\ntering the interferometer, though signal recycling was not\nimplemented until O4.\nThe main improvements included\na \u223c10-fold increase in the arm-cavity finesse (a measure of\nhow long light stays within the cavity), 42 kg fused silica test\nmasses with ultra low absorption and high homogeneity, new\nstray light control using diaphragm baffles and a vibration\nisolation system, an improved thermal compensation system\nwith double axicon CO2 laser projectors and ring heaters, an\nimproved output mode cleaner with two cascaded monolithic\nbow-tie resonators, and a new design of payloads triggered\nby the need to suspend heavier mirrors, baffles and compen-\nsation plates.\nThe several months of commissioning that started at the\nend of 2016 October achieved the target early-stage BNS\nrange of 8 Mpc in 2017 April with 13 W input laser power.\nAfter an intense campaign of noise investigations, AdV sen-\nsitivity was considered sufficient to join aLIGO during the O2\nobserving run in 2017 August (Acernese et al. 2018). Dur-\ning O2, the AdV BNS range reached 30 Mpc. As noted in\nSection 3.2, the low-frequency Virgo sensitivity during O2\nwas limited by thermal noise from metallic suspension wires,\nwhich were implemented as a fallback option due to the fre-\n\n12\nquent failure of monolithic suspensions after the installation\nof the main AdV upgrades.\n4.2.2. O3\nThe most important Virgo upgrades for O3 were the miti-\ngation of suspension thermal noise by installation of mono-\nlithic suspensions, and the mitigation of quantum noise by\nincrease of input laser power and by injection of frequency-\nindependent squeezing. An in-air optical parametric ampli-\nfier was implemented in the Virgo interferometer before the\nstart of O3a, and squeezing injections were maintained dur-\ning the whole of O3, with a 3 dB gain in sensitivity at high\nfrequency (Acernese et al. 2019, 2020).\nThroughout O3, work was continuously carried out to im-\nprove the Virgo sensitivity in parallel with the ongoing data\ntaking. Dedicated tests were made during planned breaks\nin operation (commissioning, calibration and maintenance),\nin-depth data analysis of these tests was performed between\nbreaks to ensure continual improvement. In particular, the\none-month commissioning break between the O3a and O3b\nobserving periods was used to get a better understanding of\nthe Virgo sensitivity and of some of its main limiting noises\n(Abbott et al. 2023). This effort culminated during the last\nthree months of O3b.\nThe most significant change to the Virgo configuration be-\ntween O3a and O3b was the increase of the input power from\n18 W to 26 W. As with the LIGO detectors, it was found that\nthe optical losses of the arms increased following the increase\nof the input power.\nNew high quantum-efficiency photodiodes that had been\ninstalled at the output (detection) port of the interferometer\nprior to the start of O3a were found to increase the electron-\nics noise at low frequency. These were improved at the end\nof 2020 January during a maintenance period, by replacing\npre-amplifiers. The electronic noise disappeared completely,\nleading to a BNS inspiral range gain of \u223c2 Mpc.\nFinally, in the period between the end of 2020 January to\nthe beginning of 2020 February the alignment was improved\nfor the injection of the squeezed light into the interferometer\n(Acernese et al. 2019, 2020), a critical parameter of the low-\nfrequency sensitivity. By mitigating scattered-light noise, the\nBNS range increased by 1 Mpc to 2 Mpc.\n4.2.3. O4\nThe AdV+ interferometer layout (Acernese et al. 2023b)\nwas designed as a two-step project, for O4 (Phase I) and O5\n(Phase II), with the aim to reduce quantum and thermal noise,\nrespectively. The main upgrades for O4 included: a new\nhigh-power fiber laser amplifier replacing the former solid\nstate amplifier, to reach 125 W; the implementation of an ad-\nditional recycling cavity at the output of the interferometer,\nthe signal recycling cavity, to broaden the sensitivity band;\nan output mode cleaner with increased finesse; a frequency-\ndependent squeezing system to reduce quantum noise at all\nfrequencies; a network of seismic and acoustic sensors for\nNewtonian noise monitoring; and a Newtonian calibrator for\nimproved calibration accuracy. These upgrades, while meant\nto improve the detector sensitivity, also increased the diffi-\nculties in controlling the interferometer in presence of opti-\ncal defects (both from thermal aberration and cold defects),\ndue to the marginal stability of the Virgo recycling cavities\n(Acernese et al. 2023b). Efforts were put forward to con-\ntrol the dual-recycled interferometer\u2019s sensitivity to small de-\nfects. For instance, a CHRoCC (Accadia et al. 2013) was in-\nstalled in 2022 to create a thermal lens on the pick-off plate\nso as to match the power recycling cavity to the arm cavities.\nThese turned out not to be enough to have a stable interferom-\neter working at the targeted laser power. High-order modes\nwere resonant in the cavities, and these strongly complicated\nstable operations. The laser input power was decreased to\n18 W to improve interferometer control and stability. The\nvarious changes on the configuration and attempts to reach\nstable operations prolonged the anticipated commissioning\nperiod between runs. Thus, AdV+ could not join for the O4a\nobserving run. Instead, continued commissioning allowed\nAdV+ to reach a BNS range of 54 Mpc, with which it joined\nO4b.\n4.3. KAGRA Observatory\nThe KAGRA interferometer, situated in Japan\u2019s Kamioka\nmine, is the only large-scale GW detector in East Asia.\nIt is designed as a cryogenic, 3 km, dual-recycled Fabry\u2013\nPerot Michelson interferometer. The KAGRA project was\nfunded in 2010, construction begin in 2012 and tunnel ex-\ncavation was completed in 2014 (Akutsu et al. 2021). Fol-\nlowing installation and assembly in the tunnel, two opera-\ntions using temporary detector configurations served as key\nproject milestones: the initial-phase KAGRA (iKAGRA) op-\neration in 2016 April (Akutsu et al. 2018) and the baseline-\ndesign KAGRA (bKAGRA) phase-1 operation in 2018 April.\nDuring the bKAGRA phase-1 operation, both cryogenic\ntechnology and the large-scale vibration isolation systems\nof KAGRA were successfully demonstrated (Akutsu et al.\n2019). By the summer of 2019, the primary installation of in-\nstruments was completed, allowing for the commissioning of\nthe detector to begin immediately. In 2019 October, a mem-\norandum of agreement forming the LVK was signed and the\nLVK international observation network was launched (Brady\net al. 2019). After that the commissioning phase continued\nuntil 2020 March, marking the commencement of the detec-\ntor\u2019s scientific operation.\n4.3.1. O3GK\nO3GK was a joint observation conducted with the GEO de-\ntector in 2020 April (Abe et al. 2023) just after the early ter-\nmination of O3b. The O3GK operation marked the first joint\nobservation between KAGRA and GEO. This collaboration\naimed to improve the detection capabilities by combining\ndata from both detectors. The optical configuration used dur-\ning O3GK was a power-recycled Fabry\u2013Perot Michelson in-\nterferometer, with one room-temperature sapphire test mass\nand the others set around 250 K.\nDuring the O3GK operation, KAGRA observed for ap-\nproximately 7.3 d, with a strain sensitivity of 3.0 \u00d7 10\u221222 Hz\n\n13\nat 250 Hz. The BNS range was about 0.7 Mpc (Abbott et al.\n2022).\nThe sensitivity of KAGRA during O3GK was in-\nfluenced by various noise sources, including sensor noise\nfrom local controls of the vibration isolation systems, acous-\ntic noise, shot noise, and laser frequency noise (Abe et al.\n2023). Understanding these noise contributions was crucial\nfor planning future improvements to the detector\u2019s sensitiv-\nity. To enhance its performance, KAGRA plans to implement\nhardware upgrades and refine its noise mitigation strategies.\nThese improvements aim to extend the detection range and\nincrease the precision of GW observations.\n4.3.2. O4\nOn 2024 January 01 a 7.5 magnitude earthquake struck\nnear the KAGRA site, marking the most significant seis-\nmic event in the area in the past century.\nAs a result,\n10 seismic noise isolators sustained damage but have since\nbeen restored. While further investigation and improvements\nwere still needed for some vacuum and facility-related com-\nponents, partial commissioning began in 2024 July.\nBy\n2024 October, all earthquake-related repairs were completed,\nfollowed by noise-reduction efforts across multiple domains.\nDuring the October commissioning, KAGRA achieved a\nsignificant improvement on the BNS range using a power-\nrecycled Fabry\u2013Perot Michelson interferometer configura-\ntion with DC readout.\nFurther commissioning tasks have\nbeen performed, including: reduction of suspension local\ncontrol noise through updates to the control filters; reduc-\ntion of photodiode dark noise below the shot noise level\nby mitigating electrical coupling from other electronic de-\nvices; reduction of quantum shot noise by increasing the laser\npower to above 10 W; reduction of thermal noise by cooling\nthe mirrors and their suspensions to below 100 K; and re-\nduction of frequency noise and acoustic noise through hard-\nware improvements and control system updates. Following\nthese improvements, KAGRA began operating in O4c on\n2025 June 11.\n4.4. GEO Observatory\nThe GEO detector is a Michelson interferometer with two\nnearly-orthogonal 600 m arms (Willke et al. 2002). Rather\nthan Fabry\u2013Perot cavities, GEO uses folding in the arms, in\nwhich the light traverses each arm twice, to give an optical\nlength of 1200 m for each arm. GEO is sensitive to GWs in\nthe 50 Hz to 1.5 kHz frequency range. GEO began operation\nin 2001. From 2009 to 2014, it underwent a series of up-\ngrades, the GEO-HF program, that resulted in a factor of 4\nimprovement in sensitivity at high frequencies (Grote 2010;\nDooley et al. 2016). In 2010, squeezed vacuum injection was\nfirst applied in GEO (Abadie et al. 2011), and the first long-\nterm application of squeezing was demonstrated in GEO in\n2011 (Grote et al. 2013). Subsequently, 6 dB of squeezing\n(equivalent to a factor of 4 increase in light power) has been\nachieved (Lough et al. 2021).\nGEO has served as an advanced development center and\ntestbed for technologies that were subsequently incorporated\nin larger detectors (Affeldt et al. 2014) such as dual-recycling\n(Heinzel et al. 2002), monolithic suspension (Go\u00dfler 2004),\nthermal compensation (Luck et al. 2004), homodyne detec-\ntion (DC readout) (Hild et al. 2009), and squeezed-light in-\njection (Abadie et al. 2011).\n4.4.1. Astrowatch\nFollowing the first-generation LIGO and Virgo science\nruns, GEO embarked on an astrowatch program of near con-\ntinual data collection (when the detector is not being used for\ninstrument science research) as the sole observing detector\n(Dooley 2015). This mode of operation has continued since\n2007 and allows for searches for GWs associated with ex-\nternal events such as gamma-ray bursts, neutrino detections,\nor nearby supernovae, occurring outside of other detectors\u2019\nobserving periods (e.g., Abac et al. 2024b).\n4.4.2. O3GK\nAs described in Section 3.3, a two-week-long joint observ-\ning run with the GEO and KAGRA detectors took place in\n2020 April, during which GEO operated with a 80% duty\ncycle (10.9 d of operation) and a BNS range of 1.1 Mpc (Ab-\nbott et al. 2022). The laser power injected was about 3 W,\nwhich led to about 3 kW of circulating power in the power re-\ncycling cavity, or 1.5 kW circulating power per arm (Affeldt\net al. 2014; Dooley et al. 2016). Bilinear noise subtraction re-\nsulted in modest improvement in sensitivity and data quality\n(Mukund et al. 2020). Since GEO and KAGRA had similar\nsensitivity during O3GK, this joint run enabled searches for\nGW transient signals occurring simultaneously in both de-\ntectors, though no significant events were observed (Abbott\net al. 2022).\n5. REVIEW OF OBSERVED TRANSIENT SOURCES\nThe GWTC includes all observed transient GW candidates\nreported by the LVK. It is most likely that the significant can-\ndidates in GWTC-4.0 have an astrophysical origin and were\nproduced by CBC sources (the remaining less-significant\ncandidates are largely non-astrophysical). This section pro-\nvides a foundational overview of transient GW signals, espe-\ncially those from CBCs, for use in interpreting the catalog\u2019s\ncontents and for reference in companion papers. We first pro-\nvide a short overview of the basic physics of GWs and then\nprovide an introduction to the CBC sources to be used as a\nreference for other papers in the collection of articles. Addi-\ntional detail can also be found in Maggiore (2007, 2018) and\nCreighton & Anderson (2011).\n5.1. Gravitational Waves\nIn metric theories of gravity, such as GR, the local gravi-\ntational field can be described in terms of 6 independent de-\ngrees of freedom that represent the relative accelerations of\na collection of nearby freely-falling observers (Pirani 1956;\nMisner et al. 1973). Plane wave solutions to the linearized\ngravitational field equations (Einstein 1916) represent the\nweak GWs in the far-field region (where the observer is far\nfrom the source, and the gravitational field is treated as a per-\nturbation to Minkowski spacetime) that are observed by GW\n\n14\ndetectors. The vacuum Einstein field equations of GR then\nfurther restrict the degrees of freedom of the plane wave solu-\ntions to 2 transverse polarizations that propagate at the speed\nof light (Eddington 1922). These are called the plus (+) po-\nlarization and the cross (\u00d7) polarization. In a suitably-chosen\nset of coordinates, known as the transverse-traceless gauge\n(Misner et al. 1973; Thorne 1987) which is akin to the radia-\ntion gauge in classical electromagnetism, the perturbation to\nthe Minkowski metric for these two polarizations is given by\nthe two functions of spacetime h+ and h\u00d7, respectively. These\npolarizations represent two spin-2 purely-transverse tensor\nmodes (Weinberg 1972). The transverse-traceless gauge is\na useful choice because worldlines that are the histories of\nfixed points in these spatial coordinates are geodesics of the\nperturbed spacetime (Hartle 2021). Thus, changes in time\nin the metrical distance between fixed spatial coordinate lo-\ncations, which is described by the time derivatives of h+ and\nh\u00d7, represent the deviation of the geodesics at these locations.\nTherefore, h+ and h\u00d7 are the physical (observable) degrees of\nfreedom of a GW.\nFrom an observational point of view, GW signals are\nbroadly classified as persistent or transient. The main classes\nof persistent GWs include quasi-monochromatic signals,\ne.g., as produced by rotating NSs having a non-axisymmetric\nmass distribution (Zimmermann & Szedenits 1979), and con-\ntinuous stochastic superpositions of GWs from numerous un-\nresolved independent sources (Romano & Cornish 2017).\nHere we focus on the transient signals that are cataloged in\nGWTC.\n5.1.1. Transient GW Signals\nA transient GW is one that registers a signal of short dura-\ntion (much less than the duration of the observing run) within\nthe sensitivity band of the GW detectors. Such GWs can be\ncharacterized by their geocentric arrival time tgeo, the time at\nwhich some fiducial point in the GW\u2019s waveform (such as its\npeak amplitude, for example) passes through the Earth\u2019s cen-\nter. We expect that transient GWs will be observed as plane\nwaves originating from a particular point in the sky, usually\ngiven in terms of the equatorial celestial coordinate system\nof right ascension \u03b1 and declination \u03b4, with a normal vector\n\u2212N along this line of sight. A key task for multimessenger\nastronomy with GWs is the reconstruction of the source lo-\ncation, which facilitates follow-up with other astronomical\nfacilities (Abbott et al. 2020a).\nA network of detectors spaced at different locations on\nthe Earth can observe the difference in the time of arrival of\nthe fiducial point in the waveform arising from the propaga-\ntion of the plane wave across the Earth, and thereby recon-\nstruct the direction of propagation N (Fairhurst 2009, 2011;\nCreighton & Anderson 2011; Singer & Price 2016). Such tri-\nangulation is the main way in which the source of transient\nGWs are localized. Hence, uncertainty in the sky location of\nthe source, \u2206\u2126, partially results from the measurement un-\ncertainty of the arrival time in each detector (Fairhurst 2011).\nA single detector provides no ability to determine the sky\nlocation of a source for transient signals lasting much less\nX\nNCP\nN\n\u03c8\n\u03b1\n\u2212\u03b4\nsource\nGST\nGHA\nequa\nto\nr\nial \npla\nne\nwav\ne \npl\nan\ne\nprime \nme\nridi\nan\n\u2648\nFigure 4. Relationship between the sky location in equatorial coor-\ndinates, the polarization angle, and the GW coordinate frame. The\ndirection from the source to the Earth is N and the vector X de-\nfines a reference direction on the transverse plane called the wave\nplane. The location on the source on the sky in the equatorial co-\nordinate system is given by its right ascension \u03b1 and declination \u03b4.\nThe polarization angle \u03c8 is the angle counterclockwise about N be-\ntween the equatorial plane and X. Also shown is the Greenwich\nsidereal time (GST), the angle between the first point of Aries \u0017\nand the prime meridian, and the Greenwich hour angle (GHA) of\nthe source, GHA = GST \u2212\u03b1. NCP is the North celestial pole.\nthan a day and having wavelengths much longer than the\nsize of the detector (as is the case for all candidates reported\nin GWTC-4.0); however, with two detectors, the difference\nin times of arrival identifies a circle on the celestial sphere,\ncentered on the axis separating the detectors, on which the\nwave\u2019s origin may lie. The presence of a third detector whose\nlocation is not colinear with the other two then identifies the\nsource position to one of two points on the sky mirrored\nacross the plane containing these three detectors. A fourth\ndetector, not coplanar with the other three, finally resolves\nthe location of the source to a single point on the sky. Addi-\ntional localization information can be provided by coherently\ncombining the observed GW signals from an array of detec-\ntors as described below. For some types of transient sources\nhaving known GW emission, such as CBCs, it is also possi-\nble to estimate the distance to the source from measurements\nof the wave amplitude (Cutler & Flanagan 1994). In such\ncases, there is a volume-localization uncertainty \u2206V as well\n(Singer et al. 2016; Del Pozzo et al. 2018).\nGW detectors such as the LIGO, Virgo, and KAGRA de-\ntectors are designed to sense changes in the difference of the\nlengths of their orthogonal arms, \u2206L = \u2206(L1 \u2212L2), caused\n\n15\nby GWs, via laser interferometry. These\n-shaped Michel-\nson interferometers measure the difference in phase of coher-\nent light, split at a beam-splitter located at the vertex of the\n, after traversing the arms and recombining at the beam-\nsplitter \u2206\u03d5 = 2\u03c0\u2206L/\u03bb\u2217, where \u03bb\u2217is the wavelength of the\nlaser light (Moss et al. 1971; Weiss 2022; Forward 1978).\nFor GW transients having durations much less than a day\nand wavelengths much greater than the length L of the de-\ntector arms, the strain induced on the arms is a linear combi-\nnation of plus- and cross-polarizations of the metric pertur-\nbation (Forward 1978; Rudenko & Sazhin 1980; Schutz &\nTinto 1987; Thorne 1987)\nh = \u2206L\nL = F+h+ + F\u00d7h\u00d7.\n(2)\nHere, F+ and F\u00d7 are the detector\u2019s beam pattern functions,\nwhich depend on the position on the sky from which the\nGW source is located, a polarization angle that defines the\naxes of the plus- and cross-polarization in the wave frame,\nthe Earth rotation angle at the time of the signal\u2019s arrival,\nand the location, orientation, and geometry of the detector on\nthe Earth\u2019s surface (Anderson et al. 2001). Figure 4 shows\nthe sky coordinate conventions used. For long-duration sig-\nnals, effects of the Earth\u2019s rotation need to be included; for\nshort-wavelength signals, the beam pattern functions also\ndepend on the wavelength of the GWs (Rakhmanov 2009;\nRakhmanov et al. 2008). Neither of these effects are signif-\nicant in any of the transient signals detected to date. The\namplitudes of the strains measured in a network of detec-\ntors provide additional information about the location of the\nsource of the GW if the polarization of the GW is known\nowing to the dependence of the beam pattern functions on\nthe position of the source on the sky (e.g., Singer & Price\n2016). This information helps to break degeneracies in sky\nlocalization; for instance, with only two detectors, the source\nis typically localized to an extended arc or ring on the sky,\nbut the amplitude response can help reduce this uncertainty\nto specific regions along that ring.\nTable 2 summarizes the parameters associated with a gen-\neral transient plane GW, a detector\u2019s response to such a GW,\nand the accuracy of localization of the wave\u2019s source.\nLVK Catalog of Observed Transient GW Signals \u2014In the com-\npanion paper Abac et al. (2025b), we describe the significant\ntransient GWs candidates in GWTC-4.0, highlighting those\nobserved in O4a. GWTC-4.0 also provides the inferred prop-\nerties of the GWs as well as their sources, e.g., the masses\nand spins of the binary components under the assumption\nthan the GWs were produced by CBCs. The GWTC dataset,\nalong with other open data products, is detailed in the com-\npanion paper Abac et al. (2025i).\n5.1.2. Gravitational Lensing of GWs\nLike electromagnetic waves, GWs can be gravitationally\nlensed by massive objects, e.g., galaxies, interposed between\nthe GW source and the observer. The GW polarization tensor\nis parallel-propagated along geodesics (Misner et al. 1973)\nand is little affected by the gravitational potential of the lens-\ning mass so it is sufficient to consider scalar diffraction the-\nory (Takahashi & Nakamura 2003). In a thin-lens approxi-\nmation, the bending of the trajectory of the GW propagation\noccurs on a lens plane orthogonal to the line of sight and at\nthe distance of the lensing body. With \u03be1 and \u03be2 as the coor-\ndinates of the lens plane, at each point on this plane there is\nan observed time delay T(\u03be1, \u03be2) relative to straight-line mo-\ntion with no lens, corresponding to the path from the source\nto that point on the lens plane to the observer. This delay\naccounts for the gravitational field of the lens. GWs are de-\nflected by a gravitational lens with the time delay field on\nthe lens plane determining the complex phases of the inter-\nfering partial waves used to compute a frequency-dependent\ncomplex-valued magnification factor. This factor is given by\nthe Fresnel\u2013Kirchhoff diffraction formula\nF(f) = i\nDOS\nDOLDLS\n(1 + zL)f\nc\n\"\nexp \u0002\u22122\u03c0ifT(\u03be1, \u03be2)\u0003 d\u03be1 d\u03be2 ,\n(3)\nwhere the integral is over the lens plane, f is the observed\nGW frequency, (1 + zL)f is the blue-shifted frequency of the\nGW on the lens plane (zL is the redshift of the lens), and\nthe distances DOS, DOL, and DLS are the distances between\nthe observer (us) and the GW source, between the observer\nand the gravitational lensing object, and between the lensing\nobject and the source respectively (Schneider et al. 1992).\nIn a cosmological setting, these are angular diameter dis-\ntances (Hogg 1999). The geometric optics limit corresponds\nto Fermat\u2019s principle in which the geodesic paths taken by\nGWs are those passing through the lens plane at extrema of\nthis two-dimensional time-delay field T(\u03be1, \u03be2), which may\nbe local minima, which produce Type I images, local max-\nima, which produce Type III images, or saddle points, which\nproduce Type II images (Schneider et al. 1992). Equation (3)\nis evaluated in this high-frequency limit by use of the station-\nary phase approximation to obtain\nF j(\u00b1|f|) = \u221a\u00b5j exp\n\u0010\n\u22132\u03c0i|f|t j \u00b1 i\u03c0n j\n\u0011\n,\n(4)\nwhere \u221a\u00b5j and tj are the magnification amplitude and ob-\nserved time delay of image j, and nj is 0, 1/2, or 1 for Type I,\nType II, and Type III images respectively. Therefore, such\nimages are magnified or demagnified by a factor that is posi-\ntive for Type I images and negative for Type III images, while\nthe gravitational waveform of Type II images is additionally\ndistorted, appearing as the Hilbert transform of the original\nwaveform (Dai & Venumadhav 2017; Ezquiaga et al. 2021).\nFor GW transients, the images are a set of repeated signals\nfrom the same event observed at different times, the delays\ndetermined by the differences in the time-delay field on the\nlens plane of the different images. These delays are typically\nminutes to months for galaxy lenses (Li et al. 2018; Ng et al.\n2018; Oguri 2018) and up to years for galaxy cluster lenses\n(Smith et al. 2017, 2018; Robertson et al. 2020; Ryczanowski\net al. 2020). The images also appear at different points on the\n\n16\nTable 2. Parameters describing a transient plane GW, a detector\u2019s instantaneous antenna response in the long-wavelength\nlimit, and measures of inferred localization of the signal on the sky.\nParameter name\nSymbol\nNotes [Dimensions]\nPlus (+) and cross (\u00d7) polarizations\nh+, h\u00d7\nFunctions describing the plus polarization (h+) and cross polarization\n(h\u00d7) of the metric perturbation [dimensionless]\nGeocentric arrival time\ntgeo\nTime of arrival at the center of the Earth of some fiducial point in the\nGW\u2019s waveform, normally close to the peak amplitude of the\nwaveform [time]\nPropagation direction\nN\nDirection of propagation of the GW, the unit vector normal to the\nplanar wavefronts; the direction to the source of the wave is \u2212N\n[dimensionless]\nRight ascension\n\u03b1\nAzimuth of the sky location of the source of the GW in the equatorial\ncoordinate system (see Figure 4) [angle]\nDeclination\n\u03b4\nLatitude of the sky location of the source of the GW in the equatorial\ncoordinate system (see Figure 4) [angle]\nPolarization angle\n\u03c8\nOrientation of the axes defining the plus- and cross-polarization on the\ntransverse plane of the GW relative to the line-of-nodes of this plane\nand the Earth\u2019s equatorial plane (see Figure 4) [angle]\nPlus and cross beam patterns\nF+, F\u00d7\nAntenna response of a detector to the plus-polarization (F+) and the\ncross-polarization (F\u00d7), functions of the sky location of the source, the\npolarization angle, the geocentric arrival time of the signal, and the\nlocation, orientation, and geometry of the detector on the Earth\n(Anderson et al. 2001) [dimensionless]\nDetector strain\nh\nGravitational-wave induced strain on a detector, Equation (2); the GW\nreadout of the detector is proportional to this quantity [length/length]\nSky area\n\u2206\u2126\nLocalization area, typically taken as the 90% credible area; if results at\ndifferent CLs are quoted, these are indicated with a subscript, e.g.,\n\u2206\u212650 is the 50% credible area [solid angle]\nVolume localization\n\u2206V\nLocalization volume (for signals where the distance to the source can\nbe estimated), typically taken as the 90% credible volume; if results at\ndifferent CLs are quoted, these are indicated with a subscript, e.g.,\n\u2206V50 is the 50% credible volume [volume]\nsky, with arcminute-scale separation, but GW detectors have\ninsufficient sky-localization capabilities to distinguish them\nin this way. When gravitational lensing can be described in\nthis geometric optics limit it is referred to as strong lensing.\nHowever, when the wavelength of the GW is compara-\nble to the Schwarzschild radius of the gravitational lens,\nthe geometric optics limit of Fermat\u2019s principle is no longer\nvalid, and the Fresnel\u2013Kirchhoff diffraction formula of Equa-\ntion (3) must be used to determine the complex-valued and\nfrequency dependent magnification factor. Such lensing ef-\nfects can result from objects having masses up to 105 M\u2299and\nsearches can be done in a modeled (e.g., Wright & Hendry\n2021) or phenomenological (Liu et al. 2023) way.\nSearches for Gravitational-lensing Signatures in GW Signals \u2014\nIn the companion paper Abac et al. (2025h), we present\nsearches for gravitational-lensing signatures in GWTC-4.0.\nSuch signatures sought include multiple images from strong\nlensing, individual Type-II strongly lensed images, and\nwaveform distortions induced by point-mass lensing.\n5.1.3. GW Polarization and Propagation in Alternative Theories\nof Gravity\nIn GR, plane GW perturbations to flat spacetime propa-\ngate at the speed of light and contain two transverse polariza-\ntions. However, in modified theories of gravity extending be-\nyond GR, additional polarizations may be present, including\ntwo transverse-longitudinal spin-1 vector modes, a transverse\nspin-0 scalar mode, and a longitudinal spin-0 scalar mode\n(Eardley et al. 1973a,b; Will 2018). With multiple detectors,\nit is possible to test for such additional polarizations (Schutz\n1986). A linear combination of strain data from three detec-\ntors can be formed in which any GW signal from a known sky\nlocation and containing only plus- and cross-polarizations is\ncanceled (Guersel & Tinto 1989; Klimenko et al. 2008; Sut-\nton et al. 2010; Creighton & Anderson 2011; Wong et al.\n2021). Any residual GW signal found in such a null-space\n\n17\nwould provide evidence for the presence of vector or scalar\nnon-GR polarizations.\nIn addition, in alternative Lorentz invariance violating the-\nories of gravity or in which the graviton is massive, GWs\nare dispersive. Certain theories of dark energy also result\nin dispersive GW propagation (de Rham & Melville 2018;\nBaker et al. 2022; Harry & Noller 2022). The GW disper-\nsion relation between the frequency f and the wavelength \u03bb\n(one where they are not inversely proportional) leads to phase\nspeeds and/or group speeds that differ from the speed of light.\nSuch propagation effects can be measured for a known wave-\nform by the anomalous arrival times of different frequency\ncomponents. A common parameterized dispersion relation-\nship is motivated by a modified energy\u2013momentum relation-\nship for the graviton of the form (Mirshekari et al. 2012)\nE2 = (pc)2 + A\u03b1(pc)\u03b1 ,\n(5)\nwhere A\u03b1 is a GR-violating parameter having dimensions\nof (energy)2\u2212\u03b1. For de Broglie waves, E = 2\u03c0\u210ff and p =\n2\u03c0\u210f/\u03bb, where 2\u03c0\u210fis the Planck constant. Such a modified\nenergy\u2013momentum relation leads to a dispersion relation in\nwhich the phase velocity vp is given by\n\u0012vp\nc\n\u00132\n= 1 + A\u03b1\n 2\u03c0\u210fc\n\u03bb\n!\u03b1\u22122\n,\n(6)\nwhere the phase velocity is related to the frequency and the\nwavelength of the GW, vp = \u03bbf. The group velocity, vg =\nvp \u2212dvp/d ln \u03bb, determines the difference in arrival times of\ndifferent frequency components of the GW after propagation\nfrom its source to the observer. For small deviations from\nGR (vp \u2248c), the group velocity is frequency dependent with\nvg \u2212c\nc\n\u22481\n2(\u03b1 \u22121)A\u03b1(2\u03c0\u210ff)\u03b1\u22122 .\n(7)\nSpecial cases include (i) a graviton of mass mg , 0 for which\n\u03b1 = 0, A0 = m2\ngc4, and\nvg \u2212c\nc\n\u2248\u22121\n2\n \u03bbg f\nc\n!\u22122\n,\n(8)\nwhere \u03bbg = 2\u03c0\u210f/(mgc) is the Compton wavelength of the\ngraviton, and (ii) the case in which GWs are non-dispersive\nbut propagate at a speed different than the speed of light for\nwhich \u03b1 = 2 and\nvg = c\np\n1 + A2 .\n(9)\nStringent bounds on the latter are provided by the close\ntemporal association of the BNS signal GW170817 and the\ngamma-ray burst GRB 170817A (the gamma rays arriving\nless than 2 s after the BNS GW merger signal), resulting in\n|A2| \u227210\u221214 (Abbott et al. 2017f).\nThe Einstein\u2013Hilbert action of GR contains second deriva-\ntives of the spacetime metric (Weinberg 1972; Misner et al.\n1973; Wald 1984; Carroll 2019). Standard model extensions\nhaving modified actions containing third derivatives of the\nmetric can produce CPT-violating terms in the gravitational\nfield equations, which can produce birefringence effects in\nwhich different GW helicities propagate with different phase\nvelocities (Kostelecky 2004; Kosteleck\u00fd & Mewes 2016;\nMewes 2019; Haegel et al. 2023). Other theories of gravita-\ntion also have GWs with birefringent propagation (Zhu et al.\n2024). Such birefringence leads to a frequency-dependent\nrotation of the GW polarization angle.\nBoth GW birefringence and the modified GW dispersion\nrelation can potentially be anisotropic, where the magnitude\nof the observed effect depends on the direction to the source.\nTests of GR: GW Polarization and Propagation \u2014In the compan-\nion paper Abac et al. (2025d), we test the GR prediction of\nthe polarizations of GWs by searching for evidence of vector-\nor scalar-polarization modes in observed GW signals. Mean-\nwhile, Abac et al. (2025e) presents tests of a modified dis-\npersion relation and of anisotropic birefringence using GW\nsignals from CBCs, for which it is assumed that the GW near\nthe source is described by GR to a good approximation, but\nthe waveform is affected during propagation.\n5.2. Compact Binary Coalescence\nBinaries consisting of two BHs (BBH systems), two NSs\n(BNS systems), or in which one component is a NS and the\nother a BH (NSBH systems), have all been observed by the\nLVK (Abbott et al. 2016a, 2017a, 2021c). The detectable\nsignal produced by such systems arises from the late stage\nof orbital decay, driven by GW emission, and by the ensu-\ning merger of the binary components and the settling of the\nresulting object (a NS or BH) to a final, stationary configura-\ntion (Chatziioannou et al. 2024).\nTable 3 provides a list of parameters used to describe\nCBCs.\n5.2.1. Newtonian Inspiral\nAt early stages of the inspiral, when the magnitude of the\ndifference in velocity vectors of the two components of the\nbinary, v, is much smaller than the speed of light, the orbit\nis determined approximately by Newtonian mechanics while\nthe gravitational radiation is described by the quadrupole\nformula (Einstein 1916, corrected by Eddington 1922, page\n279). For a quasi-circular orbit that is inclined an angle \u03b9 rel-\native to the direction to an observer, h+ and h\u00d7 are sinusoidal\nand are 90\u25e6out of phase,\nh+ = \u22122(1 + cos2 \u03b9)GM\u03b7\nc2r\n\u0012v\nc\n\u00132\ncos 2\u03d5\n(10a)\nand\nh\u00d7 = \u22124 cos \u03b9GM\u03b7\nc2r\n\u0012v\nc\n\u00132\nsin 2\u03d5 ,\n(10b)\nwhere r is the distance between the source and the observer,\nM = m1 + m2 is the total mass of the system, \u03b7 = m1m2/M2\nis the symmetric mass ratio, M\u03b7 is the reduced mass of the\nsystem, and \u03d5 is the orbital phase relative to the ascending\n\n18\nnode (Peters & Mathews 1963; Thorne 1987; Finn & Cher-\nnoff 1993; Will & Wiseman 1996). See Figure 5. When \u03b9 = 0\nor \u03b9 = \u03c0 (face on and face off respectively), the amplitudes of\nthe sinusoidal functions h+ and h\u00d7 are equal and the GW is\ncircularly polarized; when \u03b9 = \u03c0/2 (edge on), h\u00d7 = 0, and the\nGW is linearly polarized.\nThe GW luminosity of such a system, i.e., the power in\ngravitational radiation, is\n\u02d9EGW = 32\n5\nc5\nG \u03b72 \u0012v\nc\n\u001310\n.\n(11)\nThis radiation gives rise to a secular orbital decay. Since\nthe (Newtonian) energy of the bound system is Eorb\n=\n\u2212(1/2)\u03b7Mv2, and equating \u02d9EGW = \u2212\u02d9Eorb, we deduce that\nthe period of the orbit, P = 2\u03c0GM/v3 by Kepler\u2019s third law,\nevolves according to\n\u02d9P = \u2212192\u03c0\n5\n\u03b7\n\u0012v\nc\n\u00135\n.\n(12)\nAt fixed orbital period (or orbital frequency), the orbital ve-\nlocity is proportional to the cube root of the total mass,\nv \u221dM1/3. It can be seen then that h+, h\u00d7 \u221d\u03b7M5/3, \u02d9EGW \u221d\n(\u03b7M5/3)2, Eorb \u221d\u03b7M5/3 and \u02d9P \u221d\u03b7M5/3. At the Newtonian\nlevel of approximation, a single combination of the compo-\nnent masses,\nM = \u03b73/5M =\n(m1m2)3/5\n(m1 + m2)1/5 ,\n(13)\nknown as the chirp mass, solely determines both the ampli-\ntude of a GW at fixed orbital frequency and its frequency\nevolution (Kafka 1988; Cutler et al. 1993; Finn & Chernoff\n1993).\nThis chirp mass is normally the most accurately-\nmeasured mass parameter for low-mass systems in which\nmost of the signal observed arises from the pre-merger phase.\n5.2.2. Post-Newtonian Inspiral and Other Effects\nAdditional terms in the GW amplitude and frequency evo-\nlution appear at higher orders in v/c in a post-Newtonian\n(PN) expansion in the equations of motion and in the gravi-\ntational emission (Blanchet 2014). At the Newtonian order,\nthe frequency of the GW is twice the frequency of the orbital\nmotion, f = 2 forb = 2/P, and\nv3 = \u03c0GM f .\n(14)\nAt O(v/c) beyond this, additional components to the GW at\nfrequencies at one and three times the orbital frequency arise\nfrom current quadrupole and mass octupole radiation, and\nother components occur at O(v2/c2) beyond Newtonian or-\nder from current octupole and mass hexadecapole radiation\n(Thorne 1980); the amplitudes of these higher-order multi-\npole moments of radiation are proportional to a different com-\nbination of component masses (Kidder 2008). The frequency\nevolution also gains additional terms at O(v2/c2) beyond the\n\u2126\n\u03c9\nrp\n\u00a0L\nN\nX\np\nlane of\n s\nky\norb\nit\nal p\nlan\ne\n\u03b9\n\u03c6\nFigure 5. Relationship between the orbital elements and the GW\ncoordinate frame. The direction from the source to the Earth is\nN and the vector X defines a reference direction on the transverse\nplane (the plane of the sky). The inclination \u03b9 is the angle between\nN and the orbital angular momentum vector L. The longitude of the\nascending node of the orbit \u2126is the angle on the plane of the sky\nbetween X the ascending node \u0013, N\u00d7 L. The angle \u2126is degenerate\nwith the polarization angle \u03c8. The orbit of the primary about the\ncenter of mass of the system is shown. The orbital phase \u03d5 is the\nangle on the orbital plane between the ascending node and position\nvector of the primary relative to the center of mass. For an eccentric\norbit, the distance of the primary from the center of mass at peri-\napsis is rp and the argument of the periapsis \u03c9 for the primary is\nthe angle on the orbital plane between the ascending node and the\nposition vector of the primary at periapsis.\nleading-order Newtonian term, again having a different de-\npendence on the component masses from the leading New-\ntonian order (Wagoner & Will 1976). Spin effects from ro-\ntating binary components also appear in post-Newtonian cor-\nrections to the quadrupole waveform due to O(v3/c3) spin\u2013\norbit and O(v4/c4) spin\u2013spin effects (Kidder et al. 1993), and\nto precession of the orbital plane if the spin angular momen-\ntum vectors of the bodies are not aligned (or anti-aligned)\nwith the orbital angular momentum vector (Apostolatos et al.\n1994). The dimensionless parameter \u03c7eff,\n\u03c7eff =\nc\nGM\nL \u00b7 (S1/m1 + S2/m2)\n|L|\n(15)\nwhere S1 and S2 are the spins of the two binary components\nand L is the orbital angular momentum about the center of\nmass, is an effective inspiral spin parameter that is conserved\nunder the orbit-averaged precession equations of motion at\nO(v4/c4) (Damour 2001; Racine 2008; Ajith et al. 2011; San-\ntamaria et al. 2010; Kesden et al. 2010). Whereas \u03c7eff de-\n\n19\npends on the spin components aligned with the orbital angu-\nlar momentum, a dimensionless effective precession spin pa-\nrameter that depends on in-orbital-plane components of the\nspins,\n\u03c7p =\nc\nGm1\nmax\n(|L \u00d7 S1/m1|\n|L|\n, 3m1 + 4m2\n3m2 + 4m1\n|L \u00d7 S2/m2|\n|L|\n)\n,\n(16)\ncaptures the dominant precession effects (Schmidt et al.\n2015).\nDeformable binary components (NSs but not BHs) suf-\nfer an induced quadrupole deformation Qij under an external\ntidal field Ei j, where these quadrupole tensors are those ap-\npearing in a multipole expansion of the Newtonian potential\ncentered on the body of mass m as (Thorne 1998)\n\u03a6(x) = \u2212Gm\n|x| \u22121\n2GQij\n3xix j \u2212|x|2\u03b4ij\n|x|5\n+ 1\n2Eijxix j+\u00b7 \u00b7 \u00b7 . (17)\nThe dimensionless tidal deformability, \u039b, of a body of mass\nm is defined in terms of the ratio of the induced deformation\nto the external tidal field as\nGQij\n(Gm/c2)5 = \u2212\u039bEij ,\n(18)\nwhere BHs have \u039b = 0. Newtonian tidal interactions of de-\nformable components appear as effective O(v10/c10) correc-\ntions to the binding energy and GW luminosity (Flanagan &\nHinderer 2008). At this order, the dimensionless combina-\ntion of tidal parameters given by (Favata 2014)\n\u02dc\u039b = 16\n13\n(m1 + 12m2)m4\n1\u039b1 + (m2 + 12m1)m4\n2\u039b2\n(m1 + m2)5\n(19)\nappears, where \u039b1 and \u039b2 are the dimensionless tidal de-\nformabilities of the two bodies, and it is this parameter that\nis most measurable in the waveforms produced by binaries\nwith deformable companions (Poisson 2021). Spinning bod-\nies experience quadrupole deformation of the form\nQi j = diag\n \n\u22121\n3Q, \u22121\n3Q, 2\n3Q\n!\n,\n(20)\nwhere Q is the spin-induced mass quadrupole moment scalar.\nThe quadrupole deformations induced by an object\u2019s spin re-\nsults in Newtonian quadrupole\u2013monopole effects as an ef-\nfective O(v4/c4) correction, the same order as the spin\u2013spin\ncoupling relativistic effects (Poisson 1998). The size of the\nspin-induced deformation depends on the nature of the body,\nwhere the ratio of the quadrupole scalar to the square of the\nbody\u2019s spin magnitude is given by the dimensionless param-\neter \u03ba as\nQ = \u2212\u03ba |S|2\nmc2 ,\n(21)\nwhere m is the mass of the body. For a BH, \u03ba = 1 (Thorne\n1980).\nBinaries detected by ground-based observatories are com-\nmonly assumed to have negligibly small orbital eccentric-\nity remaining by the time the orbital period has decayed to\nthe point that the GW frequencies have entered the high-\nfrequency sensitivity band of the detectors. This decay in ec-\ncentricity happens because orbital eccentricity is efficiently\nreduced by GW emission during the orbital decay (Peters\n1964). However, there are channels of compact binary for-\nmation that could result in non-negligible orbital eccentric-\nity being present even at the last stages of inspiral observed\nby ground-based detectors (e.g., Mapelli 2020). The lead-\ning order effects of orbital eccentricity would appear at the\nNewtonian level (Peters & Mathews 1963). Two additional\nparameters are needed to describe an eccentric binary sys-\ntem, the eccentricity e, and the argument of the periapsis \u03c9.\nAlthough these are well defined for Newtonian two-body sys-\ntems, there are different ways to generalize their definitions\nfor relativistic systems, and there is not yet a settled conven-\ntion for these parameters (Shaikh et al. 2023).\nTests of GR from CBC Inspiral \u2014PN theory in GR predicts\nthe relative amplitudes of subdominant modes of GW radi-\nation (Blanchet 2014), which depend on the binary\u2019s masses\nand spins (e.g., Arun et al. 2009). Thus, allowing for free-\ndom in these amplitudes and checking if they are consistent\nwith those predicted by GR provides a consistency test of\nthe agreement of the signal with the waveform model used\nto analyze it (Puecher et al. 2022). In the companion pa-\nper Abac et al. (2025d), this test is carried out for BBH sig-\nnals, considering deviations, \u03b4A\u2113m, in the amplitude of the\n(\u2113= 2, m = \u00b11) or (\u2113= 3, m = \u00b13) subdominant multipole\nmoments relative to the dominant (\u2113= 2, m = \u00b12) and other\nmultipole moments.\nThe PN expansion of the orbital energy and GW energy\nloss makes a prediction of how the GW phase evolves with\ntime as the orbit decays (Blanchet 2014). The PN formal-\nism expresses this phase evolution with a set of coefficients\nin a series expansion of the GW phase in terms of powers\n(v/c)n\u22125 and (v/c)n\u22125 log(v/c) for integer n (with n = 0 for\nthe leading-order Newtonian inspiral) that depend on the bi-\nnary components\u2019 masses and spins for point particles. Vio-\nlations of GR can lead to differences in the values of the PN\ncoefficients from those predicted by GR (e.g., Yunes & Pre-\ntorius 2009; Tahura & Yagi 2018) which could be observed\nin a GW signal (Blanchet & Sathyaprakash 1994, 1995; Arun\net al. 2006; Mishra et al. 2010; Li et al. 2012). In the com-\npanion paper Abac et al. (2025e), we present parameterized\ntests for such violations.\nEffects arising from the finite size of the component\nmasses of a binary include spin-induced multipole moments,\nmost importantly their spin-induced quadrupole moments Q,\nwhich also affect the orbital evolution. For a BH, there is a\nfixed relation between its spin-induced quadrupole moment\nand its mass and spin (Poisson 1998). Deviations from this\npredicted value, as observed in the phase evolution of a GW\nsignal, can be used to distinguish a BBH from a compact\nbinary containing exotic, non-BH components. Some exam-\nples of exotic alternatives to BHs, being compact objects ca-\npable of having masses greater than the maximum mass of\na NS, include boson stars (Kaup 1968; Ruffini & Bonaz-\n\n20\nzola 1969), gravastars (Mazur & Mottola 2004), fuzzballs\n(Mathur 2005), and firewalls (Almheiri et al. 2013).\nThe\ncompanion paper Abac et al. (2025e) presents such param-\neterized tests of the nature of the components of CBCs.\n5.2.3. Compact Binary Merger and Ringdown\nThe final stages of GW emission from CBCs that result in\na BH remnant can be modeled as a linear gravitational per-\nturbation to a Kerr BH spacetime (Press & Teukolsky 1973).\nRemarkably, the partial differential equations for the outgo-\ning GW content of such a perturbation decouple from the\nother gravitational modes, and those decoupled equations are\nseparable into a radial equation, an angular equation, and\nan exponential function of time with a complex frequency\n(Teukolsky 1972, 1973). The separation results in a spec-\ntrum of complex eigenfrequencies of the GW perturbations\nto the BH spacetime indexed by integer degree \u2113and order\nm numbers, \u2113\u22652 and |m| \u2264\u2113, and integer overtone n with\nn \u22651 (Leaver 1985; Berti et al. 2006). The angular eigen-\nfunctions, which depend on \u2113and m, also depend on the di-\nmensionless complex frequency and the dimensionless spin\nparameter of the remnant BH. The complex eigenfrequen-\ncies describe the spectrum of exponentially-decaying sinu-\nsoidal GW quasinormal modes that make up what is called\nthe BH ringdown. GR therefore provides a prediction for the\nrelationship between the frequency and the decay constant\nfor the spectrum of such quasinormal modes which depend\nsolely on the mass and spin of the final BH, and thus the BH\nringdown radiation can be used to test these predictions of\nGR.\nSpanning the region between the portion of the waveform\nthat can be computed by PN calculations at early time and\nby a superposition of quasinormal modes at late time is what\nis known as the merger phase of the compact binary. Due\nto the non-perturbative nature of this phase, numerical rela-\ntivity (NR) solutions to Einstein\u2019s field equations are sought\n(Lehner & Pretorius 2014; Duez & Zlochower 2019). Such\nsolutions both interpolate these early and late phases and also\nprovide the information about the quasinormal mode ampli-\ntudes and phases excited as well as the mass and spin of the\nremnant BH (Hofmann et al. 2016; Healy & Lousto 2017;\nJim\u00e9nez-Forteza et al. 2017).\nWhen at least one component of the binary in the compact\nbinary coalescence is not a BH (i.e., a NS), the merger and\nringdown phases might be considerably more complex due\nto the presence of matter in the system. NR is typically re-\nquired to compute the entire post-inspiral phase of the GWs\nemitted from such systems (Faber & Rasio 2012; Kyutoku\net al. 2021). One important piece of such simulations is to\ndetermine if disruption of a NS component occurs, particu-\nlarly in the case of NSBH systems in which the NS might\nbe swallowed whole by the BH (typical for large mass and\nlow spin BHs) or might be tidally disrupted by the BH (typ-\nical for small mass or high spin BHs). Such NS disruption\nwould be expected to produce electromagnetic emission that\ncould be observed by electromagnetic astronomical observa-\ntories. Guided by numerical simulations, one can estimate\nwhether a system having particular parameters inferred from\nthe inspiral phase will be electromagnetically bright and so a\ncandidate for electromagnetic follow-up observations (Fou-\ncart et al. 2018; Chatterjee et al. 2020; Berbel et al. 2024).\nDepending on the masses of the initial components, the\nproduct of the merger of two NSs might be another NS,\na supramassive NS (a uniformly-spinning NS that is more\nmassive than the highest allowed mass for non-spinning NS,\nwhich remains a NS until its angular momentum is dissi-\npated, resulting in its collapse to a BH), a hypermassive NS\n(a NS more massive that would be allowed for any stationary,\nspinning, configuration, but which is temporarily supported\nby differential rotation, and which will ultimately collapse to\na BH), or there might be a direct collapse on a dynamical\ntimescale to form a BH after the merger (Baumgarte et al.\n2000; Piro et al. 2017). Both the electromagnetic and GW\nemission from these different scenarios are expected to vary\nconsiderably (Abbott et al. 2017c).\nTests of GR from CBC Merger \u2014NR simulations of BBHs in\nGR provide predictions for the GW waveform spanning the\ninspiral, merger, and final ringdown phases of evolution.\nTests for violations of GR can be performed by subtracting\nthe best-fit GR waveform from the observed data and test-\ning whether the remaining residual is consistent with detec-\ntor noise or if there is remaining signal present. Alternatively,\nsince NR predicts how a final BH mass and spin are related\nto the initial BH masses and spins for a BBH CBC (Hof-\nmann et al. 2016; Healy & Lousto 2017; Jim\u00e9nez-Forteza\net al. 2017), a test of consistency between the initial orbital\nparameters and the final BH mass and spin can be performed.\nHere, the initial component BH masses and spins can be de-\ntermined from the early inspiral phase of the GW signal,\nwhile the mass and the spin of the final BH are found from the\nlate-time ringdown radiation. In practice, such a consistency\ntest divides the GW signal into low- and high-frequency por-\ntions (below and above a given cutoff frequency) that are\nindependently modeled with full inspiral\u2013merger\u2013ringdown\nwaveforms (Ghosh et al. 2016, 2018).\nCompanion paper\nAbac et al. (2025d) presents results from such residual and\ninspiral\u2013merger\u2013ringdown consistency tests.\nIn GR, a BH remnant produced by a CBC will rapidly set-\ntle to a stationary Kerr BH (Kerr 1963), uniquely character-\nized by its mass and spin (Israel 1967; Carter 1971), through\nemission of ringdown radiation in a spectrum of quasinormal\nmodes, as described earlier. These quasinormal modes have\na discrete spectrum of complex-valued eigenfrequencies (the\nimaginary part of which determines the decay timescale), so\na possible non-BH remnant (e.g., Macedo et al. 2013), or\nmodifications of the spectrum in alternative theories of GR\n(e.g., Cano et al. 2024), can be tested by looking for devia-\ntions in the observed ringdown radiation from the anticipated\nspectrum of quasinormal modes (Berti et al. 2025).\nFurthermore, if the remnant object does not possess an\nevent horizon, ingoing GW radiation can be reflected off of\na surface or scattered off of an inner potential and reemerge\nas an echo signal observed within ~seconds after the merger\n\n21\n(Cardoso et al. 2016; Cardoso & Pani 2019; Siemonsen\n2024). The companion paper Abac et al. (2025f) presents\ntests of the nature of the remnant resulting from CBC through\nobserved quasinormal mode spectra and searches for GW\nechoes.\nThe post-inspiral portion of a BBH signal can be phe-\nnomenologically modeled with various parameters that are\nfitted to NR simulations (Pratten et al. 2020). The compan-\nion paper Abac et al. (2025e) explores possible deviations of\nthese parameters from their nominal values (Meidam et al.\n2018; Roy et al. 2025).\n5.2.4. Redshift and Cosmological Effects\nGWs can be redshifted, just as electromagnetic waves are.\nThese changes are caused by the Doppler effect due to rela-\ntive motion of the emitter and the observer (often described\nin terms of peculiar velocities relative to the rest frame of the\ncosmological microwave background radiation), the expan-\nsion of space between the emitter and the observer, or due to\ngravitational redshift if the emitter and observer have differ-\nent gravitational potentials. For sources beyond the nearby\nuniverse (having redshifts \u22730.1), cosmological expansion is\nthe dominant source of redshift (Peterson et al. 2022).\nThe redshift is the fractional difference between the fre-\nquency of a wave at emission at its source fsrc, and its ob-\nserved frequency at a detector fdet, z = (fsrc \u2212fdet)/fdet (Hogg\n1999). Thus, the observed frequency of a wave is related to\nits emitted frequency by fdet = fsrc/(1+z). Similarly, an inter-\nval in time in the source-frame dtsrc is related to an observed\ninterval in time by a detector dtdet by dtdet = (1 + z)dtsrc.\nEquation (10) and (12) are both parameterized in terms of\nthe orbital velocity v, which is related to the GW frequency f\nin the dominant mode by Equation (14). At a fixed moment\nin a GW waveform, where the binary has some instantaneous\nvalue of v, we have\nv3 = \u03c0GM fsrc = \u03c0GM(1 + z)fdet.\n(22)\nThat is: a redshifted signal, observed at frequency fdet, pro-\nduced by a system with intrinsic mass M has identical mor-\nphology to an un-redshifted signal produced by a system with\nintrinsic mass (1 + z)M (Krolak & Schutz 1987). If the red-\nshift is unknown, then the observable mass parameters are\nthe various combinations of (1 + z)m1 and (1 + z)m2, e.g.,\n(1 + z)M and (1 + z)M. These mass parameters with the\n1 + z scale factor are referred to as detector-frame masses,\nmdet\n1\n= (1 + z)m1, mdet\n2\n= (1 + z)m2, Mdet = (1 + z)M, and\nMdet = (1 + z)M. PN corrections to the waveform preserve\nthis degeneracy for point particles (and BHs). However, for\nNSs, a functional relationship between the mass of a NS and\nits tidal deformability means that a measurement of \u02dc\u039b can\nbreak the degeneracy between mass and redshift, allowing\nthe two to be independently measured (Messenger & Read\n2012).\nThe amplitudes of h+ and h\u00d7 given in Equation (10) also\ndepend on the total mass through the factor M/r. If the factor\n(1 + z)M is determinable from the rate of decay of the or-\nbital period, Equation (12), then the amplitude factor can be\nwritten [(1 + z)M]/[(1 + z)r] suggesting that the measurable\namplitude distance parameter is (1 + z)r.\nThe parameter r that appears in inverse proportion to the\nGW amplitude in Equation (10) represents the areal radius,\ni.e., spheres centered on the GW source have area 4\u03c0r2.\nWithin a cosmological setting, this parameter is the trans-\nverse comoving distance DM (Hogg 1999). Then, if the red-\nshift is entirely due to the cosmological expansion of space-\ntime, the combination (1 + z)DM is equal to the luminosity\ndistance of the source, and this becomes the observable dis-\ntance parameter from the GW amplitude. In this sense, then,\ngiven a known cosmology (i.e., the values of the Hubble con-\nstant, matter density, and the spatial curvature) the functional\nrelationship between luminosity distance and redshift allows\nthe determination of the latter from the former, and the intrin-\nsic masses, e.g., M, can then be deduced from the observed\nmass\u2013redshift combined parameters, e.g., Mdet = (1 + z)M.\nHowever, if other redshift effects are present, e.g., due to pe-\nculiar motion of the source or the observer relative to the\nHubble flow, the combination (1+z)DM is no longer equal to\nthe luminosity distance.\nNevertheless, when reporting the parameters of a CBC, we\nnormally assume that cosmological expansion is the only sig-\nnificant source of redshift, and so the observed amplitude pa-\nrameter (1 + z)DM is referred to as luminosity distance DL,\nwhile a dimensionful intrinsic mass parameter such as the\nprimary mass m1 is derived from observed detector frame\nmass parameters as m1 = mdet\n1 /[1 + z(DL)], where the re-\nlationship between the redshift and the luminosity distance,\nz(DL), is obtained by some standard cosmological model.\nThe only case where this was not done was for GW170817\nwhere the measured geocentric redshift to its host galaxy\nNGC 4993 was used (Abbott et al. 2019b). The main un-\ncertainty in the chirp mass of the system comes from the\nunknown peculiar velocity of the system relative to its host\ngalaxy. Unless otherwise specified, the reference cosmology\nused to relate luminosity distance to redshift throughout the\nworks is a \u039bCDM model (Peebles & Ratra 2003) correspond-\ning to a spatially-flat Friedman\u2013Lema\u00eetre\u2013Robertson\u2013Walker\nspacetime (Friedmann 1999a,b; Lemaitre 1931; Robertson\n1935a,b, 1936; Walker 1937; Weinberg 1972; Misner et al.\n1973) with Hubble constant H0 = 67.9 km s\u22121 Mpc\u22121, matter\ndensity parameter \u2126m = 0.3065, and cosmological constant\ndensity parameter \u2126\u039b = 1 \u2212\u2126m = 0.6935 (Ade et al. 2016,\ncolumn TT+lowP+lensing+ext of Table 4).\nConstraints on Cosmic Expansion from GW Observations \u2014If the\nredshift of a GW source can be determined independently\nof its distance then a distance-redshift relationship can be\nobtained and used to infer cosmological parameters (Schutz\n1986; Krolak & Schutz 1987). Here, the CBC is called a\nstandard siren (akin to the standard candles such as Cepheid\nvariables and Type Ia supernovae used to measure distances\nto their galaxy hosts), where the luminosity distance of the\nCBC is inferred from the amplitude of the GWs (Holz &\nHughes 2005). The most direct method of determining the\nredshift of a GW source is if there is an electromagnetic\n\n22\ncounterpart in which spectroscopic measurements of the red-\nshift of its host galaxy can be made (Krolak & Schutz 1987;\nHolz & Hughes 2005; Dalal et al. 2006; Chen et al. 2018).\nThis method is known as the bright sirens method.\nFor\nexample, the BNS coalescence GW170817 (Abbott et al.\n2017a) was associated with the optical kilonova AT 2017gfo\nin the galaxy NGC 4993 (Abbott et al. 2017b), which al-\nlowed for a measurement of the maximum a posteriori value\nof the Hubble constant with 68.3% CL highest density inter-\nval 69+17\n\u22128 km s\u22121 Mpc\u22121 (Abbott et al. 2021a).\nIf no electromagnetic counterpart to a GW is observed, var-\nious methods are available to deduce the associated redshift\n(BBHs are not normally expected to produce any electromag-\nnetic radiation, unless there is matter present in their environ-\nment). One such method, the galaxy catalog method, also\ncalled the dark siren method, is to obtain statistical associa-\ntion of GW sources with potential host galaxies observed in\nsurveys (Schutz 1986; MacLeod & Hogan 2008). This is usu-\nally done simultaneously with information obtained from an-\nother method, the spectral siren method. In the spectral siren\nmethod, a known feature in the mass distribution of the pop-\nulation of CBCs is used to statistically infer the redshift of a\nnumber of sources at a given distance by how the observed\ndetector-frame mass distribution is shifted with respect to the\nlocal (zero redshift) distribution (Chernoff & Finn 1993; Tay-\nlor et al. 2012; Farr et al. 2019; Mastrogiovanni et al. 2021).\nFinally, future observations of BNS mergers may be capable\nof directly inferring the redshift of the source from the GW\nsignal alone through measurements of the NS tidal deforma-\ntions (Messenger & Read 2012; Chatterjee et al. 2021).\nThe companion paper Abac et al. (2025g) reports on con-\nstraints on the cosmic expansion history based on combined\nCBC bright- and dark-sirens, including both the galaxy cata-\nlog method and the spectral siren approach. If GWs prop-\nagate through cosmological backgrounds differently from\nelectromagnetic waves in a manner that produces a different\ndistance\u2013amplitude relation, the modified propagation effects\ncan be observed using standard siren methods (Belgacem\net al. 2018). The companion paper Abac et al. (2025g) also\nreports on constraints on such effects of modified GW prop-\nagation.\n5.2.5. Populations of compact binaries\nWith a multitude of observed CBCs, one can infer the un-\nderlying population of these sources. In doing so, one needs\nto account for the detector selection effects, e.g.\nthe fact\nthat farther away events are less probable to be detected as\ncompared to events that are nearby. One key element of the\npopulation that can be measured is the local merger rate den-\nsity, R, representing the number of compact binary coales-\ncences occurring per unit time per unit volume in the local\nuniverse (Phinney 1991; Kim et al. 2003; Brady et al. 2004;\nBiswas et al. 2009; Farr et al. 2015; Abbott et al. 2016e), or\nits evolution with cosmic redshift R(z), which is the number\nof coalescences per unit source-frame time per unit comov-\ning volume at a cosmological redshift of z (Fishbach et al.\n2018). Another is the population distribution of masses and\nspins of merging compact binaries, p(m1, m2, S1, S2), which\nmight also evolve over cosmic history, p(m1, m2, S1, S2|z).\nThe measurement uncertainty in single-event parameters and\nthe total number of detected events dictate the measurability\nof features in the population. These inferences are impor-\ntant in understanding the underlying astrophysical formation\nchannels of compact binaries (e.g., Stevenson et al. 2017;\nFarr et al. 2017; Zevin et al. 2021; Mandel & Broekgaarden\n2022).\nInference of the Population of CBCs \u2014In the companion paper\nAbac et al. (2025c), we present measurements of the local\nrate of BNS, NSBH, and BBH mergers, inference of the evo-\nlution of the CBC rate over cosmological time, and inference\nof the distribution of masses and spins of CBCs.\nTable 3. Parameters describing a CBC system with quasi-circular orbits.\nParameter name\nSymbol\nNotes [Dimensions]\nPrimary and secondary masses\nm1, m2\nMass of the more massive (m1) and less massive (m2) body in system,\nm1 \u2265m2 [mass]\nChirp mass\nM\nSee Equation (13) [mass]\nTotal mass\nM\nM = m1 + m2 [mass]\nFinal mass\nMf\nMass of the remnant [mass]\nMass ratio\nq\nq = m2/m1 \u22641 [dimensionless]\nSymmetric mass ratio\n\u03b7\n\u03b7 = m1m2/(m1 + m2)2 \u22641/4 [dimensionless]\nEnergy radiated\nErad\nErad = (M \u2212Mf)c2 [energy]\nPeak luminosity\n\u2113peak\nPeak GW luminosity, typically 0.1% of the Planck luminosity\n(\u2113Planck = c5/G) for BBH coalescences [power]\nTable 3 continued\n\n23\nTable 3 (continued)\nParameter name\nSymbol\nNotes [Dimensions]\nPrimary and secondary spin vectors\nS1, S2\nSpin angular momentum of the primary (S1) and secondary (S2)\n[angular momentum]\nPrimary and secondary dimensionless spin\nmagnitudes\n\u03c71, \u03c72\n\u03c71,2 = c|S1,2|/(Gm2\n1,2); \u03c71,2 \u22641 for Kerr BHs primary/secondary\n[dimensionless]\nRemnant dimensionless spin magnitude\n\u03c7f\n\u03c7f = cS f/(GM2\nf ) where S f is the magnitude of the remnant\u2019s spin\nangular momentum; \u03c7f \u22641 for a Kerr BH remnant [dimensionless]\nNewtonian orbital angular momentum\nL\nInstantaneous orbital angular momentum about the center of mass;\ndefines z-direction for spin coordinates [angular momentum]\nTotal angular momentum\nJ\nJ = L + S1 + S2 [angular momentum]\nPrimary and secondary tilt angle\n\u03b81, \u03b82\nAngle between S1,2 and L [angle]\nSpin azimuthal angle difference\n\u03d512\nAngle between L \u00d7 (S1 \u00d7 L) and L \u00d7 (S2 \u00d7 L) [angle]\nEffective inspiral spin parameter\n\u03c7eff\nSee Equation (15) [dimensionless]\nEffective precession spin parameter\n\u03c7p\nSee Equation (16) [dimensionless]\nOrbital inclination angle\n\u03b9\nAngle between L and the direction to the Earth N (see Figure 5) [angle]\nSource inclination angle\n\u03b8JN\nAngle between J and the direction to the Earth N [angle]\nViewing angle\n\u0398\n\u0398 = min{\u03b8JN, \u03c0 \u2212\u03b8JN} [angle]\nOrbital phase\n\u03d5\nPhase of a binary\u2019s orbit, the angle on the orbital plane between the\nseparation vector (the position vector of the primary minus the position\nvector of the secondary) and the line of nodes, L \u00d7 N (see Figure 5)\n[angle]\nCoalescence phase\n\u03d5c\nOrbital phase, the angle on the orbital plane between the separation\nvector (the position vector of the primary minus the position vector of\nthe secondary) and the line of nodes, L \u00d7 N, at a point in the evolution\ncorresponding to the point in the waveform used to define tgeo (see\nTable 2) [angle]\nAngular diameter distance\nDA\nAn object of transverse length x is observed to subtend an angle in\nradians of x/DA when both the object and observer are at rest relative\nto a homogeneous cosmology (Hogg 1999) [length]\nTransverse comoving distance\nDM\nAreal radius of a sphere centered on a point in an isotropic cosmology,\ndefined so the sphere has area 4\u03c0D2\nM (Hogg 1999) [length]\nLuminosity distance\nDL\nA source of isotropic radiation having luminosity \u2113iso is observed to\nhave flux \u2113iso/(4\u03c0D2\nL) when both the source and observer are at rest\nrelative to a homogeneous cosmology (Hogg 1999) [length]\nRedshift\nz\nThe fractional difference between the frequency of a wave at emission\nat its source fsrc, and its observed frequency at a detector fdet,\nz = ( fsrc \u2212fdet)/ fdet; the reference cosmology for the relationship\nbetween distance and the cosmological redshift is given in the text\n[dimensionless]\nPrimary and secondary dimensionless\ntidal deformabilities\n\u039b1, \u039b2\nSee Equation (18); \u039b1,2 = 0 for a BH primary/secondary\n[dimensionless]\nEffective tidal deformability\n\u02dc\u039b\nSee Equation (19); \u02dc\u039b = 0 for a BBH [dimensionless]\nPrimary and secondary dimensionless\nspin-induced quadrupole moments\n\u03ba1, \u03ba2\nSee Equation (21); \u03ba1,2 = 1 for a BH primary/secondary\n[dimensionless]\nPrimary and secondary radii\nR1, R2\nAreal radii of primary and secondary and objects, defined so their\nsurface areas are 4\u03c0R2\n1,2; used in defining NS compactness [length]\nTable 3 continued\n\n24\nTable 3 (continued)\nParameter name\nSymbol\nNotes [Dimensions]\nPrimary and secondary compactness\nC1, C2\nDimensionless mass-to-radius ratios C1,2 = Gm1/(c2R1,2) of\nprimary/secondary; 1/C1,2 = 1 +\n\u221a\n1 + \u03c72\n1,2 for Kerr BH\nprimary/secondary [dimensionless]\nMerger rate density\nR\nRate of binary mergers per unit volume in the local universe; may be\nexpressed as a function of cosmological redshift, R(z); the rate in the\nlocal Universe R(z = 0) can be notated R0; subscripts can be used if\nconsidering different populations, e.g., RBNS, RNSBH, and RBBH [time\u22121\nvolume\u22121]\n6. SYNOPSIS\nThis paper serves as an introduction to the collection of\npapers accompanying the LVK\u2019s GWTC-4.0. We have pro-\nvided an overview of the GW detectors and observing runs of\nthe LVK network and of the observed GWs from CBCs. The\nprimary sequels to this introduction are a description of the\nmethods used to perform searches for GWs in LVK data and\nto characterize source properties of identified signals (Abac\net al. 2025a), and a summary of the main observations of\nGWTC-4.0, highlighting new CBC candidates and their esti-\nmated estimated masses and spins (Abac et al. 2025b). Other\ncompanion papers presenting science results from the analy-\nsis of the GWTC-4.0 candidates were described in Section 1.\nGWTC provides a prodigious census of over 200 merging\nBHs and NSs spanning two orders of magnitude in mass from\n\u223c1 M\u2299NSs to remnant BHs exceeding 100 M\u2299. Study of\nthese observations will provide new insight into the nature\nof these objects, their population distribution, and their for-\nmation channels. These GW observations allow for sensitive\ntests of GR and provide information about the cosmological\nexpansion history.\nData availability: Event data used within this work is\nopenly available in the GWTC-4.0 online catalog, which\nis hosted at https://gwosc.org/GWTC-4.0 and documented\nfurther in Abac et al. (2025i).\nData behind Figures 1, 2,\nand 3 can be found in LIGO\u2013Virgo\u2013KAGRA Collaboration\n(2025).\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded by\nthe National Science Foundation. The authors also grate-\nfully acknowledge the support of the Science and Technol-\nogy Facilities Council (STFC) of the United Kingdom, the\nMax-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO 600 de-\ntector. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucle-\nare (INFN), the French Centre National de la Recherche\nScientifique (CNRS) and the Netherlands Organization for\nScientific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and support of\nthe EGO consortium. The authors also gratefully acknowl-\nedge research support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India, the\nDepartment of Science and Technology, India, the Science\n& Engineering Research Board (SERB), India, the Ministry\nof Human Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00f3n (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00f3n y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC - Cen-\ntroNazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the European\nUnion NextGenerationEU, the Comunitat Auton\u00f2ma de les\nIlles Balears through the Conselleria d\u2019Educaci\u00f3 i Universi-\ntats, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia i So-\ncietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Science\nCentre of Poland and the European Union - European Re-\ngional Development Fund; the Foundation for Polish Sci-\nence (FNP), the Polish Ministry of Science and Higher Ed-\nucation, the Swiss National Science Foundation (SNSF), the\nRussian Science Foundation, the European Commission, the\nEuropean Social Funds (ESF), the European Regional De-\nvelopment Funds (ERDF), the Royal Society, the Scottish\nFunding Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scientific Research Fund (OTKA), the French\nLyon Institute of Origins (LIO), the Belgian Fonds de la\nRecherche Scientifique (FRS-FNRS), Actions de Recherche\nConcert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek\n- Vlaanderen (FWO), Belgium, the Paris \u00cele-de-France Re-\ngion, the National Research, Development and Innovation\nOffice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of Sci-\nence, Technology, and Innovations, the International Center\nfor Theoretical Physics South American Institute for Funda-\nmental Research (ICTP-SAIFR), the Research Grants Coun-\ncil of Hong Kong, the National Natural Science Foundation\nof China (NSFC), the Israel Science Foundation (ISF), the\nUS-Israel Binational Science Fund (BSF), the Leverhulme\n\n25\nTrust, the Research Corporation, the National Science and\nTechnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The authors\ngratefully acknowledge the support of the NSF, STFC, INFN\nand CNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific Re-\nsearch (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for\nTransformative Research Areas (A) 20A203: JP20H05854,\nthe joint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and the\nNational Science and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research Pro-\ngram, the Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the pur-\npose of open access, the authors have applied a Creative\nCommons Attribution (CC BY) license to any Author Ac-\ncepted Manuscript version arising. We request that citations\nto this article use \u2019A. G. Abac et al. (LIGO-Virgo-KAGRA\nCollaboration), ...\u2019 or similar phrasing, depending on journal\nconvention.\nFacilities:\nEGO:Virgo, GEO600, Kamioka:KAGRA,\nLIGO\nSoftware: Plots were prepared with Matplotlib (Hunter\n2007) and seaborn (Waskom 2021). Astropy (Price-\nWhelan et al. 2022), GWpy (Macleod et al. 2021), LAL-\nSuite (LIGO\u2013Virgo\u2013KAGRA Collaboration 2018; Wette\n2020), NumPy (Harris et al. 2020), SciPy (Virtanen et al.\n2020) were used for data processing in generating the figures\nand quantities in the manuscript.\nA. ACRONYMS AND GLOSSARY\nThis is a reference of frequently-used terms and acronyms.\nA+: Advanced+ LIGO refers to a configuration of LIGO following a series of upgrades, some in advance of O4 (such as the\naddition of a new 300 m filter cavity for frequency-dependent vacuum squeezing), and some planned in advance of O5,\nsuch as installation of new optics with lower noise and loss (Abbott et al. 2020a; Cooper et al. 2023).\nA\u266f: LIGO A\u266f(A-sharp) is a proposed upgrade of the Advanced+ LIGO interferometers anticipated on a post-O5 timeline. The\nbaseline A\u266fdesign is a room-temperature 1 \u00b5m laser wavelength interferometer upgrade with larger test masses having\ncoatings with lower thermal noise, higher laser power, and increased levels of vacuum squeezing (Fritschel et al. 2024).\nAdV: Advanced Virgo refers to an upgraded Virgo detector (Acernese et al. 2015) with an advanced interferometer. Virgo\noperated with the AdV configuration during O2 and O3.\nAdV+: Advanced Virgo+ is an upgrade to the AdV detector to take place in two phases: the first phase for operation during O4\nand the second phase for operation during O5.\naLIGO: Advanced LIGO refers to an upgraded LIGO configuration with advanced interferometers installed at both LHO and\nLLO. LIGO operated with the aLIGO configuration during O1, O2, O3, and O4 (Aasi et al. 2015a).\nBBH: Binary black hole. A binary system where both components are BHs.\nBH: Black hole.\nBHNS: Black hole\u2013neutron star binary specifically refers to systems in which the BH formed before the NS. See also NSBH.\nbKAGRA: Baseline-design KAGRA is a configuration of the KAGRA detector as a cryogenic dual-recycled Fabry\u2013Perot\nMichelson interferometer. bKAGRA phase-1 operation without power- or signal-recycling took place from 2018 April 28\nto 2018 May 06 2018 (Akutsu et al. 2019).\nBNS: Binary neutron star. A binary system where both components are NSs.\nCBC: Compact binary coalescence. The gravitational-radiation-driven orbital decay resulting in merger of a binary system made\nof two compact objects (NSs or BHs).\nCI: Credible interval. See CL.\n\n26\nCL: Credible level. Given a n = 1 univariate or n-dimensional multivariate random variable x having probability density\nfunction (PDF) p(x) and a n-dimensional region Rn\n\u03b1, then the CL \u03b1 of the region Rn\n\u03b1 is the probability of x lying in Rn\n\u03b1,\n\u03b1 = P(x \u2208Rn\n\u03b1) =\nR\nRn\u03b1 p(x) dnx. The region Rn\n\u03b1 is then known as a 100\u03b1% CL credible region, with special cases: credible\ninterval (CI) if n = 1, credible area if n = 2, or credible volume if n = 3. When n > 1 we normally take Rn\n\u03b1 to be the region\nhaving the smallest volume that has CL \u03b1 (the highest density region). When n = 1 (CI), R1\n\u03b1 is normally chosen to be an\nequal-tailed interval (also known as a symmetric interval), from the \u03b1/2 quantile to the 1 \u2212\u03b1/2 quantile, but sometimes\nthe smallest highest density interval is used instead.\nEoS: Equation of state of a neutron star. For cold neutron stars (having temperature below the Fermi temperature), the equation\nof state (EoS) is of a barotropic fluid, a relationship between the energy density of the fluid and its pressure.\nFAR: False alarm rate. Often used as a detection threshold, the probability of any one or more of a sequence of statistical tests\nperformed over a duration T erroneously rejecting a null hypothesis is 1 \u2212exp(\u2212T \u00d7 FAR). FAR therefore has dimensions\nof time\u22121. When interpreted as a measure of a detection significance of a candidate detection, this is the rate at which noise\nalone would produce more significant candidates.\nGEO: The GEO 600 GW detector is a British\u2013German\n-shaped interferometric GW detector with 600 m arms located near\nHannover, Germany (Willke et al. 2002).\nGR: General relativity. Einstein\u2019s theory of gravitation.\nGW: Gravitational wave. See Sections 1 and 5.1.\nGWOSC: The Gravitational Wave Open Science Center (formerly known as the LIGO open science center) was created to\nprovide public access to GW data products (Abbott et al. 2021d). The GWOSC online data and resources can be found at\nhttps://gwosc.org.\nGWTC: The Gravitational-Wave Transient Catalog is the electronic catalog of GW transients observed by LIGO, Virgo, and\nKAGRA detectors produced by the LVK.\nIFAR: Inverse false alarm rate. The reciprocal of FAR, IFAR = (FAR)\u22121, having dimensions of time. A larger IFAR implies a\nmore significant candidate, while a larger FAR implies a less significant candidate.\nIFO: Interferometer, a type of detector that uses laser interferometry to measure changes in the lengths of optical paths induced\nby GWs.\nIGWN: The International GW Observatory Network is a self-governing consortium using ground-based GW interferometers to\nexplore the fundamental physics of gravity and to observe the Universe. The observatory network includes the KAGRA,\nLHO, LLO, and Virgo detectors. In addition, the GEO detector serves as a technology testbed and operates in an astrowatch\nmode outside of other detectors\u2019 observing periods.\niKAGRA: Initial-phase KAGRA is a configuration of the KAGRA detector as a simple Michelson interferometer that consists\nof two end test masses and a beam splitter. iKAGRA was operated from 2016 March 25 to the 2016 March 31 and from\n2016 April 11 to 2016 April 25 (Akutsu et al. 2018).\nIMBH: Intermediate-mass black hole. A BH in the mass range \u223c102 M\u2299to \u223c105 M\u2299.\nKAGRA: KAGRA is a Japanese\n-shaped interferometric GW detector with 3 km arms located underground at the Kamioka\nObservatory in Japan (Akutsu et al. 2021).\nKAGRA Collaboration: The KAGRA Collaboration manages the building, operation, and development of the KAGRA detec-\ntor.\nLHO: The LIGO Hanford Observatory, one of the two LIGO observatories, located in Hanford, Washington, is an\n-shaped\ninterferometric GW detector with 4 km arms.\nLIGO: The Laser Interferometer Gravitational-Wave Observatory consists of two widely spaced installations within the United\nStates: one in Hanford, Washington (LHO) and the other in Livingston, Louisiana (LLO). LIGO is operated by the LIGO\nLaboratory, a consortium of the California Institute of Technology and the Massachusetts Institute of Technology funded\nby the U.S. National Science Foundation.\nLLO: The LIGO Livingston Observatory, one of the two LIGO observatories, located in Livingston, Louisiana, is an\n-shaped\ninterferometric GW detector with 4 km arms.\n\n27\nLSC: The LIGO Scientific Collaboration, founded in 1997, is a group of more that 1000 scientists that carries out science related\nto the LIGO detectors and their observations.\nLV: The LIGO\u2013Virgo Collaboration. Prior to O3b, all observational results were published by the LV.\nLVC: The LIGO\u2013Virgo Collaboration. The acronym LV is now preferred.\nLVK: The LIGO\u2013Virgo\u2013KAGRA Collaboration.\nNS: Neutron star.\nNSBH: The general term for a neutron star\u2013black hole binary: a binary system in which one component is a NS and the other is\na BH. If used in distinction with BHNS, it refers to such systems in which the NS formed before the BH.\nNR: Numerical relativity, the use of numerical methods to solve relativistic field equations.\nO1: The first observing run began on 2015 September 12 and ended on 2016 January 19. The LHO and LLO detectors partici-\npated in this observing run.\nO2: The second observing run began on 2016 November 30 and ended on 2016 August 25 during which the LHO and the LLO\ndetectors were operating. On 2017 August 1, the AdV detector joined the observing run, forming a three-detector network.\nO3: The third observing run began on 2019 April 1 and ended on 2020 March 27 during which the LHO, LLO, and Virgo\ndetectors were operating. A commissioning break from 2019 October 1 to 2019 November 1 divided O3 into two parts,\nO3a and O3b. A subsequent short run, O3GK, from 2020 April 7 to 2020 April 21 with GEO and KAGRA observing\nfollowed O3b.\nO3a: The first, pre-commissioning-break, part of O3, from 2019 April 1 until 2019 October 1, during which the LHO, LLO, and\nVirgo detectors were operating.\nO3b: The second, post-commissioning-break, part of O3, from 2019 November 1 until 2020 March 27, during which the LHO,\nLLO, and Virgo detectors were operating. O3b was planned to continue until 2020 April 30, but ended early due to the\nCOVID-19 pandemic.\nO3GK: A short observing run after O3b from 2020 April 7 to 2020 April 21, during which the KAGRA and GEO detectors were\nobserving. KAGRA had intended to join LIGO and Virgo at the end of O3 but the early end of O3b made this impossible.\nO4: The fourth observing run began on 2023 May 24 and is planned to continue into late 2025. It is divided into parts, the first\nof which, O4a, covered the period from 2023 May 24 until a commissioning break from 2024 January 16 until 2024 April\n10. During O4a, LHO and LLO were observing. Following the break, observing continued in O4b from 2024 April 10\nuntil an original intended end date of 2025 January 23, with LHO, LLO, and Virgo observing. It was decided to continue\nO4 observing in a third period O4c, beginning 2025 January 23, lasting until late 2025.\nO4a: The first part of the fourth observing run including data from 2023 May 24 until a commissioning break that began on 2024\nJanuary 16. During O4a, LHO and LLO were observing.\nO4b: The second part of the fourth observing run starting at the end of a commissioning break on 2024 April 10 and ending\non the originally-planned O4 end date of 2025 January 23. During O4b, LHO, LLO, and Virgo were observing. It was\ndecided to continue O4 observations with a third part, O4c, immediately following the end of O4b on 2025 January 23.\nO4c: The third part of the fourth observing run, extending the run beyond its intended end date of 2025 January 23 through late\n2025. A commissioning break in O4c took place between 2025 April 01 and 2025 June 11.\nO5: The fifth observing run is the planned future observing run to follow O4.\nPDF: Probability density function. Given a n = 1 univariate or n-dimensional multivariate random variable x, the probability of\nx lying in a n-dimensional region Rn is P(x \u2208Rn) =\nR\nRn p(x) dnx, where p(x) is the PDF.\nPE: Parameter estimation, the process of measuring the parameters that describe the source of a signal, e.g., the masses and spins\nof the binary components of a CBC, from the observational data.\nPN: Post-Newtonian, a perturbative method of obtaining solutions to relativistic field equations based on slow-motion and weak-\nfield expansion of the spacetime metric and the stress\u2013energy source.\n\n28\nPSD: Power spectral density. See Appendix B.\nSNR: Signal-to-noise ratio. See Appendix B.\nVirgo: The Virgo detector is a European\n-shaped interferometric GW detector with 3 km arms located near Cascina, Italy (near\nPisa).\nVirgo_nEXT: Virgo_nEXT is a planned, post-O5, major upgrade of Virgo to fill the gap between the current phase, AdV+, and\nnext-generation detectors.\nVirgo Collaboration: The Virgo Collaboration manages the building, operation, and development of the Virgo detector.\nB. CONVENTIONS FOR DATA ANALYSIS\nThis appendix serves to define the data analysis conventions that will be used throughout the GWTC-4.0 companion papers.\nFor a general introduction to data analysis we refer the reader to Abbott et al. (2020c) and references therein.\nTime series a(t) and frequency series \u02dca(t) are related to each other by our conventions for the Fourier transform\n\u02dca(f) =\nZ +\u221e\n\u2212\u221e\na(t) exp (\u22122\u03c0ift) dt\n(23)\nand its inverse transform\na(t) =\nZ +\u221e\n\u2212\u221e\n\u02dca(f) exp (+2\u03c0ift) d f .\n(24)\nWith these conventions, the dimension of \u02dca are [\u02dca] = [a] \u00d7 time.\nDetector noise is often taken to be a stochastic Gaussian process. If n(t) is a real-valued stochastic Gaussian process then the\none-sided power spectral density (PSD) S n(f) is formally defined by\n\u27e8\u02dcn\u2217(f \u2032)\u02dcn(f)\u27e9= 1\n2S n(f)\u03b4(f \u2212f \u2032) ,\n(25)\nwhere \u27e8\u00b7\u27e9is a statistical ensemble average of realizations of n(t) and \u02dcn\u2217is the complex conjugate of \u02dcn. The one-sided PSD is\ndefined only for f \u22650. With these conventions, the dimensions of S n are [S n] = [n]2 \u00d7 time. Real detector noise is neither\nentirely stationary nor Gaussian (Abbott et al. 2020c). However, it is often sufficient to assume n(t) is ergodic such that\nS n(f) = lim\nT\u2192\u221e\n2\nT\n\f\f\f\f\f\f\nZ T/2\n\u2212T/2\nn(t) exp (\u22122\u03c0ift) dt\n\f\f\f\f\f\f\n2\n.\n(26)\nThe factor of two in the one-sided PSD ensures that the integrated power is\nZ \u221e\n0\nS n(f) d f = lim\nT\u2192\u221e\n1\nT\nZ T/2\n\u2212T/2\nn2(t) dt .\n(27)\nThe amplitude spectral density is defined to be the square-root of the power spectral density, S 1/2\nn (f).\nWe often use a detector-noise-weighted inner product between two real-valued time series, a(t) and b(t), which is defined as\n\u27e8a|b\u27e9= 4 Re\nZ +\u221e\n0\n\u02dca\u2217(f)\u02dcb(f)\nS n(f)\nd f\n(28a)\n=\nZ +\u221e\n\u2212\u221e\n\u02dca\u2217(f)\u02dcb(f)\n(1/2)S n(|f|) d f ,\n(28b)\nwhere S n( f) is the detector\u2019s one-sided PSD for the readout noise from that detector. The second form, Equation (28b), is an\nappropriate generalization of the inner product for complex-valued time series.\nSince GW detectors are insensitive at very low frequencies, the mean of the detector readout is arbitrary and so we take the\ndetector noise to have zero-mean, \u27e8n(t)\u27e9= 0. Gaussian noise is then entirely characterized by its PSD and its distribution is given\nby the probability density\np(n) = 1\nW exp\n \n\u22121\n2\u27e8n|n\u27e9\n!\n,\n(29)\nwhere W is a usually-neglected normalizing constant, the path integral W =\nR\nexp (\u2212\u27e8n|n\u27e9/2) Dn.\n\n29\nConsider a template waveform u(t) that is unit-normalized, \u27e8u|u\u27e9= 1, which is expected to match a hypothetical signal in\ndetector data d(t). The matched filter signal-to-noise ratio (SNR) is\n\u03c1mf = \u27e8u|d\u27e9.\n(30)\nIf data d(t) = n(t) + h(t) contains Gaussian noise n(t) plus a signal h(t) that is perfectly matched by the template waveform,\nh(t) \u221du(t), then \u03c1mf is a random variable having a normal distribution with unit variance and mean equal to the optimal SNR\n\u03c1opt =\np\n\u27e8h|h\u27e9.\n(31)\nThe likelihood that detector data d(t) contains a signal h(t) is given by Equation (29) with n(t) = d(t) \u2212h(t),\np(d|h) = 1\nW exp\n \n\u22121\n2\u27e8d \u2212h|d \u2212h\u27e9\n!\n(32a)\n= exp (\u2212\u27e8d|d\u27e9\u27e9/2)\nW\nexp\n \n\u27e8h|d\u27e9\u22121\n2\u27e8h|h\u27e9\n!\n(32b)\n= p(d|\u2205) exp\n \n\u03c1mf\u03c1opt \u22121\n2\u03c12\nopt\n!\n,\n(32c)\nwhere \u03c1mf is the matched-filter SNR with unit-normalized template u(t) \u221dh(t) and p(d|\u2205) = W\u22121 exp (\u2212\u27e8d|d\u27e9/2) is the likelihood\nunder the no-signal hypothesis, d(t) = n(t). The likelihood is viewed as a functional of h(t) for a given realization of detector data\nd(t). The second factor in Equation (32c) is the signal-to-noise likelihood ratio p(d|h)/p(d|\u2205). Note that the likelihood ratio is a\nmonotonically-increasing function of the matched-filter SNR and so \u03c1mf is the uniformly most powerful test for a known signal\nin Gaussian detector noise (Neyman & Pearson 1933). If the amplitude of the signal is unknown, h(t) = \u03c1optu(t) with unknown\n\u03c1opt, then the likelihood is maximized for \u03c1opt = \u03c1mf and\nmax\n\u03c1opt p(d|\u03c1optu) = p(d|\u2205) exp\n 1\n2\u03c12\nmf\n!\n.\n(33)\nFor the Newtonian inspiral of Section 5.2.1, the signal observed in a detector can be obtained in the frequency domain under\nthe stationary phase approximation as (Sathyaprakash & Dhurandhar 1991; Cutler et al. 1993)\n\u02dch(f) = \u2212\nr\n5\u03c0\n24\nGM\nc3\nGM\nc2Deff\n \u03c0GMf\nc3\n!\u22127/6\nexp (\u2212i\u03a8(f)) ,\n(34)\nwhere \u03a8( f) is the stationary phase function and\nDeff = r\n\uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0F2\n+(\u03d1, \u03c6, \u03c8)\n 1\n2 + 1\n2 cos2 \u03b9\n!2\n+ F2\n\u00d7(\u03d1, \u03c6, \u03c8) cos2 \u03b9\n\uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb\n\u22121/2\n.\n(35)\nis the effective distance (Allen et al. 2012), which is related to the distance to the binary r by a factor that accounts for the\norientation angles that describe the position of the source on the sky (\u03d1, \u03c6), its inclination \u03b9, and polarization angle \u03c8. Since\nF2\n+ + F2\n\u00d7 \u22641 (with equality for a source on the zenith or nadir of an\n-shaped interferometric detector), Deff \u2265r (with equality\nonly if \u03b9 = 0 or \u03b9 = \u03c0). The optimal SNR for such a signal is\n\u03c1opt =\nr\n5\n6\u03c0\nGM\nc2Deff\n \u03c0GM\nc3\n!\u22121/6 sZ +\u221e\n0\nf \u22127/3\nS n(f) d f .\n(36)\nThe horizon distance Dhor (Allen et al. 2012) of a source is the effective distance of a signal from such a source that has SNR \u03c1opt\nequal to some detection threshold \u03c1th. Such sources would not be expected to be detected beyond the horizon distance, but not all\nnearer sources will be detected either. The sensitive volume (Finn & Chernoff 1993; Chen et al. 2021) is a measure of the effective\nvolume of space in which randomly isotropically-oriented and homogeneously-distributed identical sources will produce signals\nin the detector with SNR \u03c1opt greater than the threshold \u03c1th,\nV =\nR\n\u03c1opt>\u03c1th r2 sin \u03d1 sin \u03b9 dr d\u03d1 d\u03c6 d\u03b9 d\u03c8\nR\nsin \u03b9 d\u03b9 d\u03c8\n(37a)\n= 0.086 084 \u00d7 4\n3\u03c0D3\nhor .\n(37b)\n\n30\nIf the merger rate density is R then the expected number of detections in time T is RVT. For a standard measure of detector\nsensitivity, a binary source of two 1.4 M\u2299objects (M = 2\u22121/5 \u00d7 1.4 M\u2299\u22481.22 M\u2299) is considered and a threshold SNR of \u03c1th = 8\nis adopted (Chen et al. 2021). The sensitive volume is converted into an equivalent spherical radius as V = (4\u03c0/3)R3 to obtain the\nBNS range R = Dhor/2.264 78, Equation (1).\nREFERENCES\nAasi, J., et al. 2015a, Class. Quant. 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Akcay\n,23\nT. Akutsu\n,24, 25\nS. Albanesi\n,26, 27\nR. A. Alfaidi\n,28\nA. Al-Jodah\n,29\nC. All\u00b4en\u00b4e,30\nA. Allocca\n,31, 4\nS. Al-Shammari,32\nP. A. Altin\n,33\nS. Alvarez-Lopez\n,34\nO. Amarasinghe,32\nA. Amato\n,35, 36\nC. Amra,37\nA. Ananyeva,10\nS. B. Anderson\n,10\nW. G. Anderson\n,10\nM. Andia\n,38\nM. Ando,39, 40\nT. Andrade,41\nM. Andr\u00b4es-Carcasona\n,42\nT. Andri\u00b4c\n,7, 8, 43\nJ. Anglin,44\nS. Ansoldi\n,45, 46\nJ. M. Antelis\n,47\nS. Antier\n,48\nM. Aoumi,49\nE. Z. Appavuravther,50, 51\nS. Appert,10\nS. K. Apple\n,52\nK. Arai\n,10\nA. Araya\n,53\nM. C. Araya\n,10\nM. Arca Sedda,43\nJ. S. Areeda\n,54\nL. Argianas,55\nN. Aritomi,2\nF. Armato\n,56, 57\nS. Armstrong\n,58\nN. Arnaud\n,38, 59\nM. Arogeti\n,60\nS. M. Aronson\n,11\nG. Ashton\n,61\nY. Aso\n,24, 62\nM. Assiduo,63, 64\nS. Assis de Souza Melo,59\nS. M. Aston,65\nP. Astone\n,66\nF. Attadio\n,67, 66\nF. Aubin\n,68\nK. AultONeal\n,69\nG. Avallone\n,70\nS. Babak\n,71\nF. Badaracco\n,56\nC. Badger,72\nS. Bae\n,73\nS. Bagnasco\n,27\nE. Bagui,74\nL. Baiotti\n,75\nR. Bajpai\n,24\nT. Baka,76\nT. Baker\n,77\nM. Ball,78\nG. Ballardin,59\nS. W. Ballmer,79\nS. Banagiri\n,80\nB. Banerjee\n,43\nD. Bankar\n,14\nT. M. Baptiste,11\nP. Baral\n,9\nJ. C. Barayoga,10\nB. C. Barish,10\nD. Barker,2\nN. Barman,14\nP. Barneo\n,41, 81\nF. Barone\n,82, 4\nB. Barr\n,28\nL. Barsotti\n,34\nM. Barsuglia\n,71\nD. Barta\n,83\nA. M. Bartoletti,84\nM. A. Barton\n,28\nI. Bartos,44\nS. Basak\n,22\nA. Basalaev\n,85\nR. Bassiri\n,86\nA. Basti\n,87, 88\nD. E. Bates,32\nM. Bawaj\n,89, 50\nP. Baxi,90\nJ. C. Bayley\n,28\nA. C. Baylor\n,9\nP. A. Baynard II,60\nM. Bazzan,91, 92\nV. M. Bedakihale,93\nF. Beirnaert\n,94\nM. Bejger\n,95\nD. Belardinelli\n,20\nA. S. Bell\n,28\nD. S. Bellie,80\nL. Bellizzi\n,88, 87\nW. Benoit\n,96\nI. Bentara\n,97\nJ. D. Bentley\n,85\nM. Ben Yaala,58\nS. Bera\n,98\nF. Bergamin\n,7, 8\nB. K. Berger\n,86\nS. Bernuzzi\n,26\nM. Beroiz\n,10\nC. P. L. Berry\n,28\nD. Bersanetti\n,56\nA. Bertolini,36\nJ. Betzwieser\n,65\nD. Beveridge\n,29\nG. Bevilacqua\n,99\nN. Bevins\n,55\nR. Bhandare,100\nS. A. Bhat\n,14\nR. Bhatt,10\nD. Bhattacharjee\n,101, 102\nS. Bhaumik\n,44\nS. Bhowmick,103\nV. Biancalana\n,99\nA. Bianchi,36, 104\nI. A. Bilenko,105\nG. Billingsley\n,10\nA. Binetti\n,106\nS. Bini\n,107, 108\nC. Binu,109\nO. Birnholtz\n,110\nS. Biscoveanu\n,80\nA. Bisht,8\nM. Bitossi\n,59, 88\nM.-A. Bizouard\n,48\nS. Blaber,111\nJ. K. Blackburn\n,10\nL. A. Blagg,78\nC. D. Blair,29, 65\nD. G. Blair,29\nF. Bobba,70, 112\nN. Bode\n,7, 8\nG. Boileau\n,48\nM. Boldrini\n,66, 67\nG. N. Bolingbroke\n,113\nA. Bolliand,114, 37\nL. D. Bonavena\n,44, 91\nR. Bondarescu\n,41\nF. Bondu\n,115\nE. Bonilla\n,86\nM. S. Bonilla\n,54\nA. Bonino,116\nR. Bonnand\n,30, 114\nP. Booker,7, 8 A. Borchers,7, 8 S. Borhanian,6 V. Boschi\n,88 S. Bose,117 V. Bossilkov,65 A. Boudon,97 A. Bozzi,59 C. Bradaschia,88\nP. R. Brady\n,9\nA. Branch,65\nM. Branchesi\n,43, 118\nI. Braun,101\nT. Briant\n,119\nA. Brillet,48\nM. Brinkmann,7, 8\nP. Brockill,9\nE. Brockmueller\n,7, 8\nA. F. Brooks\n,10\nB. C. Brown,44\nD. D. Brown,113\nM. L. Brozzetti\n,89, 50\nS. Brunett,10\nG. Bruno,13\nR. Bruntz\n,120\nJ. Bryant,116\nY. Bu,121\nF. Bucci\n,64\nJ. Buchanan,120\nO. Bulashenko\n,41, 81\nT. Bulik,122\nH. J. Bulten,36\nA. Buonanno\n,123, 1\nK. Burtnyk,2\nR. Buscicchio\n,124, 125\nD. Buskulic,30\nC. Buy\n,126\nR. L. Byer,86\nG. S. Cabourn Davies\n,77\nG. Cabras\n,45, 46\nR. Cabrita\n,13\nV. C\u00b4aceres-Barbosa\n,6\nL. Cadonati\n,60\nG. Cagnoli\n,127\nC. Cahillane\n,79\nA. Calafat,98\nJ. Calder\u00b4on Bustillo,128\nT. A. Callister,129\nE. Calloni,31, 4\nM. Canepa,57, 56\nG. Caneva Santoro\n,42\nK. C. Cannon\n,40\nH. Cao,34\nL. A. Capistran,130\nE. Capocasa\n,71\nE. Capote\n,2\nG. Capurri\n,88, 87\nG. Carapella,70, 112\nF. Carbognani,59\nM. Carlassara,7, 8\nJ. B. Carlin\n,121\nT. K. Carlson,131\nM. F. Carney,101\nM. Carpinelli\n,124, 132, 59\nG. Carrillo,78\nJ. J. Carter\n,7, 8\nG. Carullo\n,133\nJ. Casanueva Diaz,59\nC. Casentini\n,134, 19, 20\nS. Y. Castro-Lucas,103\nS. Caudill,131, 36, 76\nM. Cavagli`a\n,102\nR. Cavalieri\n,59\nG. Cella\n,88\nP. Cerd\u00b4a-Dur\u00b4an\n,135, 136\nE. Cesarini\n,20\nW. Chaibi,48\nP. Chakraborty\n,7, 8\nS. Chakraborty,100\nS. Chalathadka Subrahmanya\n,85\nJ. C. L. Chan\n,137\nM. Chan,111\nR.-J. Chang,138\nS. Chao\n,139, 140\nE. L. Charlton,120\nP. Charlton\n,141\nE. Chassande-Mottin\n,71\nC. Chatterjee\n,142\nDebarati Chatterjee\n,14\nDeep Chatterjee\n,34\nM. Chaturvedi,100\nS. Chaty\n,71\nK. Chatziioannou\n,10\nC. Checchia\n,99\nA. Chen\n,15\nA. H.-Y. Chen,143\nD. Chen\n,144\nH. Chen,139\nH. Y. Chen\n,145\nS. Chen,142\nY. Chen,139\nYanbei Chen,146\nYitian Chen\n,147\nH. P. Cheng,148\nP. Chessa\n,89, 50\nH. T. Cheung\n,90\nS. Y. Cheung,149\nF. Chiadini\n,150, 112\nG. Chiarini,92\nR. Chierici,97\nA. Chincarini\n,56\nM. L. Chiofalo\n,87, 88\nA. Chiummo\n,4, 59\nC. Chou,143\nS. Choudhary\n,29\nN. Christensen\n,48\nS. S. Y. Chua\n,33\nP. Chugh,149\nG. Ciani\n,107, 108\nP. Ciecielag\n,95\nM. Cie\u00b4slar\n,122\nM. Cifaldi\n,20\nR. Ciolfi\n,151, 92\nF. Clara,2\nJ. A. Clark\n,10, 60\nJ. Clarke,32\nT. A. Clarke\n,149\nP. Clearwater,152\nS. Clesse,74\nS. M. Clyne,153\nE. Coccia,43, 118, 42\nE. Codazzo\n,154\nP.-F. Cohadon\n,119\nS. Colace\n,57\nE. Colangeli,77\nM. Colleoni\n,98\nC. G. Collette,155\nJ. Collins,65\nS. Colloms\n,28\nA. Colombo\n,156, 125\nC. M. Compton,2\nG. Connolly,78\nL. Conti\n,92\nT. R. Corbitt\n,11\nI. Cordero-Carri\u00b4on\n,157\nS. Corezzi,89, 50\nN. J. Cornish\n,158\nA. Corsi\n,159\nS. Cortese\n,59\nR. Cottingham,65\nM. W. Coughlin\n,96\nA. Couineaux,66\nJ.-P. Coulon,48\nJ.-F. Coupechoux,97\nP. Couvares\n,10, 60\nD. M. Coward,29\nR. Coyne\n,153\nK. Craig,58\nJ. D. E. Creighton\n,9\nT. D. Creighton,160\nP. Cremonese\n,98\nA. W. Criswell\n,96\nS. Crook,65\nR. Crouch,2\nJ. Csizmazia,2\nJ. R. Cudell\n,161\nT. J. Cullen\n,10\nA. Cumming\n,28\nE. Cuoco\n,162, 163\nM. Cusinato\n,135\nP. Dabadie,127\nL. V. Da Concei\u00b8c\u02dcao,164\nT. Dal Canton\n,38\nS. Dall\u2019Osso\n,66\nS. Dal Pra\n,165\nG. D\u00b4alya\n,126\nB. D\u2019Angelo\n,56\nS. Danilishin\n,35, 36\nS. D\u2019Antonio\n,20\nK. Danzmann,8, 7, 8\nK. E. Darroch,120\nL. P. Dartez,65\nA. Dasgupta,93\nS. Datta\n,166\nV. Dattilo\n,59\nA. Daumas,71\nN. Davari,167, 132\nI. Dave,100\nA. Davenport,103\nM. Davier,38\nT. F. Davies,29\nD. Davis\n,10\nL. Davis,29\nM. C. Davis\n,96\nP. Davis\n,168, 169\nM. Dax\n,1\nJ. De Bolle\n,94\nM. Deenadayalan,14\nJ. Degallaix\n,170\nU. Deka\n,22\nM. De Laurentis\n,31, 4\nS. Del\u00b4eglise\n,119\nF. De Lillo\n,21\nD. Dell\u2019Aquila\n,167, 132\nF. Della Valle\n,99\nW. Del Pozzo\n,87, 88\nF. De Marco\n,67, 66\nG. Demasi,171, 64\nF. De Matteis\n,19, 20\nV. D\u2019Emilio\n,10\nN. Demos,34\nA. Depasse\n,13\nN. DePergola,55\nR. De Pietri\n,172, 173\nR. De Rosa\n,31, 4\nC. De Rossi\n,59\nM. Desai,34\nR. DeSalvo\n,174\n\n38\nA. DeSimone,175\nR. De Simone,150\nA. Dhani\n,1\nR. Diab,44\nM. C. D\u00b4iaz\n,160\nM. Di Cesare\n,31, 4\nG. Dideron,176\nN. A. Didio,79\nT. Dietrich\n,1\nL. Di Fiore,4\nC. Di Fronzo\n,29\nM. Di Giovanni\n,67, 66\nT. Di Girolamo\n,31, 4\nD. Diksha,36, 35\nA. Di Michele\n,89\nJ. Ding\n,34, 71, 177\nS. Di Pace\n,67, 66\nI. Di Palma\n,67, 66\nF. Di Renzo\n,97\nDivyajyoti\n,178\nA. Dmitriev\n,116\nZ. Doctor\n,80\nN. Doerksen,164\nE. Dohmen,2\nD. Dominguez,179\nL. D\u2019Onofrio\n,66\nF. Donovan,34\nK. L. Dooley\n,32\nT. Dooney,76\nS. Doravari\n,14\nO. Dorosh,180\nM. Drago\n,67, 66\nJ. C. Driggers\n,2\nJ.-G. Ducoin,181, 71\nL. Dunn\n,121\nU. Dupletsa,43\nD. D\u2019Urso\n,167, 154\nH. Duval\n,182\nS. E. Dwyer,2\nC. Eassa,2\nM. Ebersold\n,30\nT. Eckhardt\n,85\nG. Eddolls\n,79\nB. Edelman\n,78\nT. B. Edo,10\nO. Edy\n,77\nA. Effler\n,65\nJ. Eichholz\n,33\nH. Einsle,48\nM. Eisenmann,24\nR. A. Eisenstein,34\nA. Ejlli\n,32\nM. Emma\n,61\nK. Endo,183\nR. Enficiaud\n,1\nA. J. Engl,86\nL. Errico\n,31, 4\nR. Espinosa,160\nM. Esposito,4, 31\nR. C. Essick\n,184\nH. Estell\u00b4es\n,1\nT. Etzel,10\nM. Evans\n,34\nT. Evstafyeva,185\nB. E. Ewing,6\nJ. M. Ezquiaga\n,137\nF. Fabrizi\n,63, 64\nF. Faedi,64, 63\nV. Fafone\n,19, 20\nS. Fairhurst\n,32\nA. M. Farah\n,129\nB. Farr\n,78\nW. M. Farr\n,186, 187\nG. Favaro\n,91\nM. Favata\n,188\nM. Fays\n,161\nM. Fazio,58\nJ. Feicht,10\nM. M. Fejer,86\nR. Felicetti\n,189\nE. Fenyvesi\n,83, 190\nD. L. Ferguson\n,145\nT. Fernandes\n,191, 135\nD. Fernando,109\nS. Ferraiuolo\n,192, 67, 66\nI. Ferrante\n,87, 88\nT. A. Ferreira,11\nF. Fidecaro\n,87, 88\nP. Figura\n,95\nA. Fiori\n,88, 87\nI. Fiori\n,59\nM. Fishbach\n,184\nR. P. Fisher,120\nR. Fittipaldi,193, 112\nV. Fiumara\n,194, 112\nR. Flaminio,30\nS. M. Fleischer\n,195\nL. S. Fleming,18\nE. Floden,96\nH. Fong,111\nJ. A. Font\n,135, 136\nC. Foo,1\nB. Fornal\n,196\nP. W. F. Forsyth,33\nK. Franceschetti,172\nN. Franchini,197\nS. Frasca,67, 66\nF. Frasconi\n,88\nA. Frattale Mascioli\n,67, 66\nZ. Frei\n,198\nA. Freise\n,36, 104\nO. Freitas\n,191, 135\nR. Frey\n,78\nW. Frischhertz,65\nP. Fritschel,34\nV. V. Frolov,65\nG. G. Fronz\u00b4e\n,27\nM. Fuentes-Garcia\n,10\nS. Fujii,199\nT. Fujimori,200\nP. Fulda,44\nM. Fyffe,65\nB. Gadre\n,76\nJ. R. Gair\n,1\nS. Galaudage\n,201\nV. Galdi,174\nH. Gallagher,109\nB. Gallego,202\nR. Gamba\n,6, 26\nA. Gamboa\n,1\nD. Ganapathy\n,34\nA. Ganguly\n,14\nB. Garaventa\n,56, 57\nJ. Garc\u00b4ia-Bellido\n,203\nC. Garc\u00b4ia N\u00b4u\u02dcnez,18\nC. Garc\u00b4ia-Quir\u00b4os\n,204\nJ. W. Gardner\n,33\nK. A. Gardner,111\nJ. Gargiulo\n,59\nA. Garron\n,98\nF. Garufi\n,31, 4\nP. A. Garver,86\nC. Gasbarra\n,19, 20\nB. Gateley,2\nF. Gautier\n,205\nV. Gayathri\n,9\nT. Gayer,79\nG. Gemme\n,56\nA. Gennai\n,88\nV. Gennari\n,126\nJ. George,100 R. George\n,145 O. Gerberding\n,85 L. Gergely\n,206 Archisman Ghosh\n,94 Sayantan Ghosh,207 Shaon Ghosh\n,188\nShrobana Ghosh,7, 8\nSuprovo Ghosh\n,14\nTathagata Ghosh\n,14\nJ. A. Giaime\n,11, 65\nK. D. Giardina,65\nD. R. Gibson,18\nD. T. Gibson,185\nC. Gier\n,58\nS. Gkaitatzis\n,87, 88\nJ. Glanzer\n,10\nF. Glotin,38\nJ. Godfrey,78\nP. Godwin\n,10\nA. S. Goettel\n,32\nE. Goetz\n,111\nJ. Golomb,10\nS. Gomez Lopez\n,67, 66\nB. Goncharov\n,43\nY. Gong,208\nG. Gonz\u00b4alez\n,11\nP. Goodarzi,209\nS. Goode,149\nA. W. Goodwin-Jones\n,10, 29\nM. Gosselin,59\nR. Gouaty\n,30\nD. W. Gould,33\nK. Govorkova,34\nS. Goyal\n,1\nB. Grace\n,33\nA. Grado\n,89, 50\nV. Graham\n,28\nA. E. Granados\n,96\nM. Granata\n,170\nV. Granata\n,70\nS. Gras,34\nP. Grassia,10\nA. Gray,96\nC. Gray,2\nR. Gray\n,28\nG. Greco,50\nA. C. Green\n,36, 104\nS. M. Green,77\nS. R. Green\n,210\nA. M. Gretarsson,69\nE. M. Gretarsson,69\nD. Griffith,10\nW. L. Griffiths\n,32\nH. L. Griggs\n,60\nG. Grignani,89, 50\nC. Grimaud\n,30\nH. Grote\n,32\nS. Grunewald\n,1\nD. Guerra\n,135\nD. Guetta\n,211\nG. M. Guidi\n,63, 64\nA. R. Guimaraes,11\nH. K. Gulati,93\nF. Gulminelli\n,168, 169\nA. M. Gunny,34\nH. Guo\n,212\nW. Guo\n,29\nY. Guo\n,36, 35\nAnchal Gupta\n,10\nAnuradha Gupta\n,213\nI. Gupta\n,6\nN. C. Gupta,93\nP. Gupta,36, 76\nS. K. Gupta,44\nT. Gupta\n,158\nV. Gupta\n,96\nN. Gupte,1\nJ. Gurs,85\nN. Gutierrez,170\nF. Guzman\n,130\nD. Haba,179\nM. Haberland\n,1\nS. Haino,214\nE. D. Hall\n,34\nR. Hamburg\n,215\nE. Z. Hamilton\n,98\nG. Hammond\n,28\nW.-B. Han\n,216\nM. Haney\n,36, 204\nJ. Hanks,2\nC. Hanna,6\nM. D. Hannam,32\nO. A. Hannuksela\n,217\nA. G. Hanselman\n,129\nH. Hansen,2\nJ. Hanson,65\nR. Harada,40\nA. R. Hardison,175\nS. Harikumar,180\nK. Haris,36, 76\nT. Harmark\n,133\nJ. Harms\n,43, 118\nG. M. Harry\n,218\nI. W. Harry\n,77\nJ. Hart,101\nB. Haskell,95\nC.-J. Haster\n,219\nK. Haughian\n,28\nH. Hayakawa,49\nK. Hayama,220\nR. Hayes,32\nM. C. Heintze,65\nJ. Heinze\n,116\nJ. Heinzel,34\nH. Heitmann\n,48\nA. Heffernan\n,98\nF. Hellman\n,221\nA. F. Helmling-Cornell\n,78\nG. Hemming\n,59\nO. Henderson-Sapir\n,113\nM. Hendry\n,28\nI. S. Heng,28\nM. H. Hennig\n,28\nC. Henshaw\n,60\nM. Heurs\n,7, 8\nA. L. Hewitt\n,185, 222\nJ. Heyns,34\nS. Higginbotham,32\nS. Hild,35, 36\nS. Hill,28\nY. Himemoto\n,223\nN. Hirata,24\nC. Hirose,224\nS. Hochheim,7, 8\nD. Hofman,170\nN. A. Holland,36, 104\nD. E. Holz\n,129\nL. Honet,74\nC. Hong,86\nS. Hoshino,224\nJ. Hough\n,28\nS. Hourihane,10\nN. T. Howard,142\nE. J. Howell\n,29\nC. G. Hoy\n,77\nC. A. Hrishikesh,19\nH.-F. Hsieh\n,139\nH.-Y. Hsieh,139\nC. Hsiung,225\nW.-F. Hsu\n,106\nQ. Hu\n,28\nH. Y. Huang\n,140\nY. Huang\n,6\nY. T. Huang,79\nA. D. Huddart,226\nB. Hughey,69\nD. C. Y. Hui\n,227\nV. Hui\n,30\nS. Husa\n,98\nR. Huxford,6\nL. Iampieri\n,67, 66\nG. A. Iandolo\n,35\nM. Ianni,20, 19\nA. Ierardi,43\nA. Iess\n,228, 88\nH. Imafuku,40\nK. Inayoshi\n,229\nY. Inoue,140\nG. Iorio\n,91\nP. Iosif\n,189, 46\nM. H. Iqbal,33\nJ. Irwin\n,28\nR. Ishikawa,230\nM. Isi\n,186, 187\nY. Itoh\n,231, 200\nH. Iwanaga,231\nM. Iwaya,199\nB. R. Iyer\n,22\nC. Jacquet,126\nP.-E. Jacquet\n,119\nS. J. Jadhav,232\nS. P. Jadhav\n,152\nT. Jain,185\nA. L. James\n,10\nP. A. James,120\nR. Jamshidi,155\nA. Jan\n,145\nK. Jani\n,142\nJ. Janquart\n,13\nK. Janssens\n,21, 48\nN. N. Janthalur,232\nS. Jaraba\n,203\nP. Jaranowski\n,233\nR. Jaume\n,98\nW. Javed,32\nA. Jennings,2\nW. Jia,34\nJ. Jiang\n,148\nS. J. Jin\n,29\nC. Johanson,131\nG. R. Johns,120\nN. A. Johnson,44\nN. K. Johnson-McDaniel\n,213\nM. C. Johnston\n,219\nR. Johnston,28\nN. Johny,7, 8\nD. H. Jones\n,33\nD. I. Jones,234\nE. J. Jones,11\nR. Jones,28\nS. Jose,178\nP. Joshi\n,6\nS. K. Joshi,14\nJ. Ju,235\nL. Ju\n,29\nK. Jung\n,236\nJ. Junker\n,33\nV. Juste,74\nH. B. Kabagoz\n,65\nT. Kajita\n,237\nI. Kaku,231\nV. Kalogera\n,80\nM. Kalomenopoulos\n,219\nM. Kamiizumi\n,49\nN. Kanda\n,200, 231\nS. Kandhasamy\n,14\nG. Kang\n,238\nN. C. Kannachel,149\nJ. B. Kanner,10\nS. J. Kapadia\n,14\nD. P. Kapasi\n,33\nS. Karat,10\nR. Kashyap\n,6\nM. Kasprzack\n,10\nW. Kastaun,7, 8\nT. Kato,199\nE. Katsavounidis,34\nW. Katzman,65\nR. Kaushik\n,100\nK. Kawabe,2\nR. Kawamoto,231\nA. Kazemi,96\nD. Keitel\n,98\nJ. Kennington\n,6\nR. Kesharwani\n,14\nJ. S. Key\n,239\nR. Khadela,7, 8\nS. Khadka,86\nF. Y. Khalili\n,105\nF. Khan\n,7, 8\nI. Khan,240, 37\nT. Khanam,159\nM. Khursheed,100\nN. M. Khusid,186, 187\nW. Kiendrebeogo\n,48, 241\nN. Kijbunchoo\n,113\nC. Kim,242\nJ. C. Kim,243\nK. Kim\n,244\nM. H. Kim\n,235\nS. Kim\n,227\nY.-M. Kim\n,244\nC. Kimball\n,80\nM. Kinley-Hanlon\n,28\nM. Kinnear,32\nJ. S. Kissel\n,2\nS. Klimenko,44\nA. M. Knee\n,111\nN. Knust\n,7, 8\nK. Kobayashi,199\nP. Koch,7, 8\nS. M. Koehlenbeck\n,86\nG. Koekoek,36, 35\nK. Kohri\n,245, 246\nK. Kokeyama\n,32\nS. Koley\n,43\nP. Kolitsidou\n,116\nK. Komori\n,40, 39\nA. K. H. Kong\n,139\nA. Kontos\n,247\nM. Korobko\n,85\nR. V. Kossak,7, 8\nX. Kou,96\nA. Koushik\n,21\n\n39\nN. Kouvatsos\n,72\nM. Kovalam,29\nD. B. Kozak,10\nS. L. Kranzhoff,35, 36\nV. Kringel,7, 8\nN. V. Krishnendu\n,116\nA. Kr\u00b4olak\n,248, 180\nK. Kruska,7, 8\nJ. Kubisz\n,249\nG. Kuehn,7, 8\nS. Kulkarni\n,213\nA. Kulur Ramamohan\n,33\nA. Kumar,232\nPraveen Kumar\n,128\nPrayush Kumar\n,22\nRahul Kumar,2\nRakesh Kumar,93\nJ. Kume\n,250, 251, 40\nK. Kuns\n,34\nN. Kuntimaddi,32\nS. Kuroyanagi\n,203, 252\nS. Kuwahara\n,40\nK. Kwak\n,236\nK. Kwan,33\nJ. Kwok,185\nG. Lacaille,28\nP. Lagabbe\n,30, 107\nD. Laghi\n,126\nS. Lai,143\nE. Lalande,253\nM. Lalleman\n,21\nP. C. Lalremruati,254\nM. Landry,2\nB. B. Lane,34\nR. N. Lang\n,34\nJ. Lange,145\nR. Langgin\n,219\nB. Lantz\n,86\nA. La Rana\n,66\nI. La Rosa\n,98\nJ. Larsen,195\nA. Lartaux-Vollard\n,38\nP. D. Lasky\n,149\nJ. Lawrence\n,160, 255\nM. N. Lawrence,11\nM. Laxen\n,65\nC. Lazarte\n,135\nA. Lazzarini\n,10\nC. Lazzaro,256, 154\nP. Leaci\n,67, 66\nL. Leali,96\nY. K. Lecoeuche\n,111\nH. M. Lee\n,243\nH. W. Lee\n,257\nJ. Lee,79\nK. Lee\n,235\nR.-K. Lee\n,139\nR. Lee,34\nSungho Lee\n,258\nSunjae Lee,235\nY. Lee,140\nI. N. Legred,10\nJ. Lehmann,7, 8\nL. Lehner,176\nM. Le Jean\n,170\nA. Lema\u02c6itre,259\nM. Lenti\n,64, 171\nM. Leonardi\n,107, 108, 24\nM. Lequime,37\nN. Leroy\n,38\nM. Lesovsky,10\nN. Letendre,30\nM. Lethuillier\n,97\nY. Levin,149\nK. Leyde\n,71, 77\nA. K. Y. Li,10\nK. L. Li\n,138\nT. G. F. Li,106\nX. Li\n,146\nY. Li,80\nZ. Li,28\nA. Lihos,120\nC-Y. Lin\n,260\nE. T. Lin\n,139\nL. C.-C. Lin\n,138\nY.-C. Lin\n,139\nC. Lindsay,18\nS. D. Linker,202\nT. B. Littenberg,261\nA. Liu\n,217\nG. C. Liu\n,225\nJian Liu\n,29\nF. Llamas Villarreal,160\nJ. Llobera-Querol\n,98\nR. K. L. Lo\n,137\nJ.-P. Locquet,106\nM. R. Loizou,131\nL. T. London,72, 34\nA. Longo\n,63, 64\nD. Lopez\n,161, 204\nM. Lopez Portilla,76\nA. Lorenzo-Medina\n,128\nV. Loriette,38\nM. Lormand,65\nG. Losurdo\n,228, 88\nE. Lotti,131\nT. P. Lott IV\n,60\nJ. D. Lough\n,7, 8\nH. A. Loughlin,34\nC. O. Lousto\n,109\nN. Low,121\nM. J. Lowry,120\nN. Lu\n,33\nL. Lucchesi\n,88\nH. L\u00a8uck,8, 7, 8\nD. Lumaca\n,20\nA. P. Lundgren,77\nA. W. Lussier\n,253\nL.-T. Ma\n,139\nS. Ma,176\nR. Macas\n,77\nA. Macedo\n,54\nM. MacInnis,34\nR. R. Maciy,7, 8\nD. M. Macleod\n,32\nI. A. O. MacMillan\n,10\nA. Macquet\n,38\nD. Macri,34\nK. Maeda,183\nS. Maenaut\n,106\nS. S. Magare,14\nR. M. Magee\n,10\nE. Maggio\n,1\nR. Maggiore,36, 104\nM. Magnozzi\n,56, 57\nM. Mahesh,85\nM. Maini,153\nS. Majhi,14\nE. Majorana,67, 66\nC. N. Makarem,10\nD. Malakar\n,102\nJ. A. Malaquias-Reis,17\nU. Mali\n,184\nS. Maliakal,10\nA. Malik,100\nL. Mallick\n,164, 184\nA. Malz\n,61\nN. Man,48\nV. Mandic\n,96\nV. Mangano\n,66, 67\nB. Mannix,78\nG. L. Mansell\n,79\nG. Mansingh,218\nM. Manske\n,9\nM. Mantovani\n,59\nM. Mapelli\n,91, 92, 262\nF. Marchesoni,51, 50, 263\nC. Marinelli\n,99\nD. Mar\u00b4in Pina\n,41, 81, 264\nF. Marion\n,30\nS. M\u00b4arka\n,265\nZ. M\u00b4arka\n,265\nA. S. Markosyan,86\nA. Markowitz,10\nE. Maros,10\nS. Marsat\n,126\nF. Martelli\n,63, 64\nI. W. Martin\n,28\nR. M. Martin\n,188\nB. B. Martinez,130\nM. Martinez,42, 266\nV. Martinez\n,127\nA. Martini,107, 108\nJ. C. Martins\n,17\nD. V. Martynov,116\nE. J. Marx,34\nL. Massaro,35, 36\nA. Masserot,30\nM. Masso-Reid\n,28\nM. Mastrodicasa,66, 67\nS. Mastrogiovanni\n,66\nT. Matcovich\n,50\nM. Matiushechkina\n,7, 8\nM. Matsuyama,231\nN. Mavalvala\n,34\nN. Maxwell,2\nG. McCarrol,65\nR. McCarthy,2\nD. E. McClelland\n,33\nS. McCormick,65\nL. McCuller\n,10\nS. McEachin,120\nC. McElhenny,120\nG. I. McGhee\n,28\nJ. McGinn,28\nK. B. M. McGowan,142\nJ. McIver\n,111\nA. McLeod\n,29\nT. McRae,33\nD. Meacher\n,9\nQ. Meijer,76\nA. Melatos,121\nM. Melching\n,7, 8\nS. Mellaerts\n,106\nC. S. Menoni\n,103\nF. Mera,2\nR. A. Mercer\n,9\nL. Mereni,170\nK. Merfeld,159\nE. L. Merilh,65\nJ. R. M\u00b4erou\n,98\nJ. D. Merritt,78\nM. Merzougui,48\nC. Messenger\n,28\nC. Messick\n,9\nB. Mestichelli,43\nM. Meyer-Conde\n,267\nF. Meylahn\n,7, 8\nA. Mhaske,14\nA. Miani\n,107, 108\nH. Miao,268\nI. Michaloliakos\n,44\nC. Michel\n,170\nY. Michimura\n,10, 40\nH. Middleton\n,116\nS. J. Miller\n,10\nM. Millhouse\n,60\nE. Milotti\n,189, 46\nV. Milotti\n,91\nY. Minenkov,20\nN. Mio,269\nLl. M. Mir\n,42\nL. Mirasola\n,154, 256\nM. Miravet-Ten\u00b4es\n,135\nC.-A. Miritescu\n,42\nA. K. Mishra,22\nA. Mishra,22\nC. Mishra\n,178\nT. Mishra\n,44\nA. L. Mitchell,36, 104\nJ. G. Mitchell,69\nS. Mitra\n,14\nV. P. Mitrofanov\n,105\nR. Mittleman,34\nO. Miyakawa\n,49\nS. Miyamoto,199\nS. Miyoki\n,49\nG. Mo\n,34\nL. Mobilia,63, 64\nS. R. P. Mohapatra,10\nS. R. Mohite\n,6\nM. Molina-Ruiz\n,221\nC. Mondal\n,168\nM. Mondin,202\nM. Montani,63, 64\nC. J. Moore,185\nD. Moraru,2\nA. More\n,14\nS. More\n,14\nE. A. Moreno\n,34\nG. Moreno,2\nS. Morisaki\n,40, 199\nY. Moriwaki\n,183\nG. Morras\n,203\nA. Moscatello\n,91\nM. Mould\n,34\nP. Mourier\n,98, 270\nB. Mours\n,68\nC. M. Mow-Lowry\n,36, 104\nF. Muciaccia\n,67, 66\nD. Mukherjee\n,261\nSamanwaya Mukherjee,14\nSoma Mukherjee,160\nSubroto Mukherjee,93\nSuvodip Mukherjee\n,12, 176, 271\nN. Mukund\n,34\nA. Mullavey,65\nH. Mullock,111\nJ. Munch,113\nJ. Mundi,218\nC. L. Mungioli,29\nY. Murakami,199\nM. Murakoshi,230\nP. G. Murray\n,28\nS. Muusse\n,33\nD. Nabari\n,107, 108\nS. L. Nadji,7, 8\nA. Nagar,27, 272\nN. Nagarajan\n,28\nK. Nakagaki,49\nK. Nakamura\n,24\nH. Nakano\n,273\nM. Nakano,10\nD. Nanadoumgar-Lacroze,42\nD. Nandi,11\nV. Napolano,59\nP. Narayan\n,213\nI. Nardecchia\n,20\nT. Narikawa,199\nH. Narola,76\nL. Naticchioni\n,66\nR. K. Nayak\n,254\nA. Nela,28\nA. Nelson\n,130\nT. J. N. Nelson,65\nM. Nery,7, 8\nA. Neunzert\n,2\nS. Ng,54\nL. Nguyen Quynh\n,274, 275\nS. A. Nichols,11\nA. B. Nielsen\n,276\nG. Nieradka,95\nY. Nishino,24, 277\nA. Nishizawa\n,278\nS. Nissanke,271, 36\nE. Nitoglia\n,97\nW. Niu\n,6\nF. Nocera,59\nM. Norman,32\nC. North,32\nJ. Novak\n,114, 279, 280\nJ. F. Nu\u02dcno Siles\n,203\nL. K. Nuttall\n,77\nK. Obayashi,230\nJ. Oberling\n,2\nJ. O\u2019Dell,226\nM. Oertel\n,279, 114, 281, 280\nA. Offermans,106\nG. Oganesyan,43, 118\nJ. J. Oh,282\nK. Oh\n,227\nT. O\u2019Hanlon,65\nM. Ohashi\n,49\nM. Ohkawa\n,224\nF. Ohme\n,7, 8\nR. Oliveri\n,114, 281, 280\nR. Omer,96\nB. O\u2019Neal,120\nK. Oohara\n,283, 284\nB. O\u2019Reilly\n,65\nR. Oram,10\nN. D. Ormsby,120\nM. Orselli\n,50, 89\nR. O\u2019Shaughnessy\n,109\nS. O\u2019Shea,28\nY. Oshima\n,39\nS. Oshino\n,49\nC. Osthelder,10\nI. Ota\n,11\nD. J. Ottaway\n,113\nA. Ouzriat,97\nH. Overmier,65\nB. J. Owen\n,285\nA. E. Pace\n,6\nR. Pagano\n,11\nM. A. Page\n,24\nA. Pai\n,207\nL. Paiella,43\nA. Pal,286\nS. Pal\n,254\nM. A. Palaia\n,88, 87\nM. P\u00b4alfi,198\nP. P. Palma,67, 19, 20\nC. Palomba\n,66\nP. Palud\n,71\nJ. Pan,29\nK. C. Pan\n,139\nR. Panai\n,154, 91\nP. K. Panda,232\nShiksha Pandey,6\nSwadha Pandey,34\nP. T. H. Pang,36, 76\nF. Pannarale\n,67, 66\nK. A. Pannone,54\nB. C. Pant,100\nF. H. Panther,29\nF. Paoletti\n,88\nA. Paolone,66, 287\nA. Papadopoulos,28\nE. E. Papalexakis,209\nL. Papalini\n,88, 87\nG. Papigkiotis\n,288\nA. Paquis,38\nA. Parisi\n,89, 50\nB.-J. Park,258\nJ. Park\n,289\nW. Parker\n,65\nG. Pascale,7, 8\nD. Pascucci\n,94\nA. Pasqualetti,59\nR. Passaquieti\n,87, 88\nL. Passenger,149\nD. Passuello,88\nO. Patane\n,2\nD. Pathak,14\nL. Pathak\n,14\nA. Patra,32\nB. Patricelli\n,87, 88\nA. S. Patron,11\nB. G. Patterson,32\nK. Paul\n,178\nS. Paul\n,78\nE. Payne\n,10\nT. Pearce,32\nM. Pedraza,10\nA. Pele\n,10\nF. E. Pe\u02dcna Arellano\n,290\nS. Penn\n,291\nM. D. Penuliar,54\nA. Perego\n,107, 108\nZ. Pereira,131\nJ. J. Perez,44\nC. P\u00b4erigois\n,151, 92, 91\nG. Perna\n,91\nA. Perreca\n,107, 108\nJ. Perret,71\nS. Perri`es\n,97\nJ. W. Perry,36, 104\nD. Pesios,288\nS. Petracca,174\nC. Petrillo,89\n\n40\nH. P. Pfeiffer\n,1\nH. Pham,65\nK. A. Pham\n,96\nK. S. Phukon\n,116\nH. Phurailatpam,217\nM. Piarulli,126\nL. Piccari\n,67, 66\nO. J. Piccinni\n,33\nM. Pichot\n,48\nM. Piendibene\n,87, 88\nF. Piergiovanni\n,63, 64\nL. Pierini\n,66\nG. Pierra\n,97\nV. Pierro\n,292, 112\nM. Pietrzak,95\nM. Pillas\n,161\nF. Pilo\n,88\nL. Pinard,170\nI. M. Pinto\n,292, 112, 293, 31\nM. Pinto,59\nB. J. Piotrzkowski\n,9\nM. Pirello,2\nM. D. Pitkin\n,185, 222\nA. Placidi\n,50\nE. Placidi\n,67, 66\nM. L. Planas\n,98\nW. Plastino\n,294, 20\nC. Plunkett\n,34\nR. Poggiani\n,87, 88\nE. Polini\n,34\nL. Pompili\n,1\nJ. Poon,217\nE. Porcelli,36\nE. K. Porter,71\nC. Posnansky\n,6\nR. Poulton\n,59\nJ. Powell\n,152\nM. Pracchia\n,161\nB. K. Pradhan\n,14\nT. Pradier\n,68\nA. K. Prajapati,93\nK. Prasai,86\nR. Prasanna,232\nP. Prasia,14\nG. Pratten\n,116\nG. Principe\n,189, 46\nM. Principe,174\nG. A. Prodi\n,107, 108\nL. Prokhorov\n,116\nP. Prosperi,88\nP. Prosposito,19, 20\nA. C. Providence,69\nA. Puecher,36, 76\nJ. Pullin\n,11\nM. Punturo\n,50\nP. Puppo,66\nM. P\u00a8urrer\n,153\nH. Qi\n,15\nJ. Qin\n,33\nG. Qu\u00b4em\u00b4ener\n,169, 114\nV. Quetschke,160\nP. J. Quinonez,69\nF. J. Raab\n,2\nI. Rainho,135\nS. Raja,100\nC. Rajan,100\nB. Rajbhandari\n,109\nK. E. Ramirez\n,65\nF. A. Ramis Vidal\n,98\nA. Ramos-Buades,36, 1\nD. Rana,14\nS. Ranjan\n,60\nK. Ransom,65\nP. Rapagnani\n,67, 66\nB. Ratto,69 A. Ray\n,9 V. Raymond\n,32 M. Razzano\n,87, 88 J. Read,54 M. Recaman Payo,106 T. Regimbau,30 L. Rei\n,56 S. Reid,58\nD. H. Reitze\n,10\nP. Relton\n,32\nA. I. Renzini\n,10, 124\nB. Revenu\n,295, 38\nR. Reyes,202\nA. S. Rezaei\n,66, 67\nF. Ricci,67, 66\nM. Ricci\n,66, 67\nA. Ricciardone\n,87, 88\nJ. W. Richardson\n,209\nM. Richardson,113\nA. Rijal,69\nK. Riles\n,90\nH. K. Riley,32\nS. Rinaldi\n,262, 91\nJ. Rittmeyer,85\nC. Robertson,226\nF. Robinet,38\nM. Robinson,2\nA. Rocchi\n,20\nL. Rolland\n,30\nJ. G. Rollins\n,10\nA. E. Romano\n,296 R. Romano\n,3, 4 A. Romero\n,30 I. M. Romero-Shaw,185 J. H. Romie,65 S. Ronchini\n,6, 43, 118 T. J. Roocke\n,113\nL. Rosa,4, 31 T. J. Rosauer,209 C. A. Rose,60 D. Rosi\u00b4nska\n,122 M. P. Ross\n,52 M. Rossello-Sastre\n,98 S. Rowan\n,28 S. Roy\n,13\nS. K. Roy\n,186, 187\nD. Rozza\n,124, 125\nP. Ruggi,59\nN. Ruhama,236\nE. Ruiz Morales\n,297, 203\nK. Ruiz-Rocha,142\nS. Sachdev\n,60\nT. Sadecki,2\nJ. Sadiq\n,128\nP. Saffarieh\n,36, 104\nS. Safi-Harb,164\nM. R. Sah\n,12\nS. Saha\n,139\nT. Sainrat\n,68\nS. Sajith Menon\n,211, 67, 66\nK. Sakai,298\nM. Sakellariadou\n,72\nS. Sakon\n,6\nO. S. Salafia\n,156, 125, 124\nF. Salces-Carcoba\n,10\nL. Salconi,59\nM. Saleem\n,96\nF. Salemi\n,67, 66\nM. Sall\u00b4e\n,36\nS. U. Salunkhe,14\nS. Salvador\n,169, 168\nA. Samajdar\n,76, 36\nA. Sanchez,2\nE. J. Sanchez,10\nJ. H. Sanchez\n,80\nL. E. Sanchez,10\nN. Sanchis-Gual\n,135\nJ. R. Sanders,175\nE. M. S\u00a8anger\n,1\nF. Santoliquido,43\nF. Sarandrea,27\nT. R. Saravanan,14\nN. Sarin,149\nP. Sarkar,7, 8\nS. Sasaoka\n,179\nA. Sasli\n,288\nP. Sassi\n,50, 89\nB. Sassolas\n,170\nB. S. Sathyaprakash\n,6, 32\nR. Sato,224\nY. Sato,183\nO. Sauter\n,44\nR. L. Savage\n,2\nT. Sawada\n,49\nH. L. Sawant,14 S. Sayah,30 V. Scacco,19, 20 D. Schaetzl,10 M. Scheel,146 A. Schiebelbein,184 M. G. Schiworski\n,79 P. Schmidt\n,116\nS. Schmidt\n,76\nR. Schnabel\n,85\nM. Schneewind,7, 8\nR. M. S. Schofield,78\nK. Schouteden,106\nB. W. Schulte,7, 8\nB. F. Schutz,32, 7, 8\nE. Schwartz\n,86\nM. Scialpi,299\nJ. Scott\n,28\nS. M. Scott\n,33\nR. M. Sedas\n,65\nT. C. Seetharamu,28\nM. Seglar-Arroyo\n,42\nY. Sekiguchi\n,300\nD. Sellers,65\nA. S. Sengupta\n,301\nD. Sentenac,59\nE. G. Seo\n,28\nJ. W. Seo\n,106\nV. Sequino,31, 4\nM. Serra\n,66\nG. Servignat\n,71, 281\nA. Sevrin,182\nT. Shaffer,2\nU. S. Shah\n,60\nM. S. Shahriar\n,80\nM. A. Shaikh\n,243\nL. Shao\n,229\nA. Sharma\n,301\nA. K. Sharma,22\nP. Sharma,100\nS. Sharma Chaudhary,102\nM. R. Shaw,32\nP. Shawhan\n,123\nN. S. Shcheblanov\n,302, 259\nY. Shikano\n,303, 304\nM. Shikauchi,40\nK. Shimode\n,49\nH. Shinkai\n,305\nJ. Shiota,230\nS. Shirke,14\nD. H. Shoemaker\n,34\nD. M. Shoemaker\n,145\nR. W. Short,2\nS. ShyamSundar,100\nA. Sider,155\nH. Siegel\n,186, 187\nD. Sigg\n,2\nL. Silenzi\n,50, 51\nM. Simmonds,113\nL. P. Singer\n,306\nA. Singh,213\nD. Singh\n,6\nM. K. Singh\n,22\nN. Singh\n,98\nS. Singh,179, 62\nA. Singha\n,35, 36\nA. M. Sintes\n,98\nV. Sipala,167, 154\nV. Skliris\n,32\nB. J. J. Slagmolen\n,33\nD. A. Slater,195\nT. J. Slaven-Blair,29\nJ. Smetana,116\nJ. R. Smith\n,54\nL. Smith\n,28, 189\nR. J. E. Smith\n,149\nW. J. Smith\n,142\nK. Somiya\n,179\nI. Song\n,139\nK. Soni\n,14\nS. Soni\n,34\nV. Sordini\n,97\nF. Sorrentino,56\nH. Sotani\n,307\nA. Southgate,32\nF. Spada\n,88\nV. Spagnuolo\n,35, 36\nA. P. Spencer\n,28\nM. Spera\n,46, 308\nP. Spinicelli\n,59\nC. A. Sprague,274\nA. K. Srivastava,93\nF. Stachurski\n,28\nD. A. Steer\n,309\nN. Steinle\n,164\nJ. Steinlechner,35, 36\nS. Steinlechner\n,35, 36\nN. Stergioulas\n,288\nP. Stevens,38\nS. P. Stevenson,152\nF. Stolzi\n,99\nM. StPierre,153\nG. Stratta\n,310, 134, 66, 311\nM. D. Strong,11\nA. Strunk,2\nR. Sturani,312\nA. L. Stuver,55, \u2217\nM. Suchenek,95\nS. Sudhagar\n,95\nN. Sueltmann,85\nL. Suleiman\n,54\nJ.M. Sullivan\n,60\nK. D. Sullivan,11\nJ. Sun,238\nL. Sun\n,33\nS. Sunil,93\nJ. Suresh\n,48\nB. J. Sutton,72\nP. J. Sutton\n,32\nT. Suzuki\n,224\nY. Suzuki,230\nB. L. Swinkels\n,36\nA. Syx,68\nM. J. Szczepa\u00b4nczyk\n,313, 44\nP. Szewczyk\n,122\nM. Tacca\n,36\nH. Tagoshi\n,199\nS. C. Tait\n,10\nH. Takahashi\n,267\nR. Takahashi\n,24\nA. Takamori\n,53\nT. Takase,49\nK. Takatani,231\nH. Takeda\n,314\nK. Takeshita,179\nC. Talbot,129\nM. Tamaki,199\nN. Tamanini\n,126\nD. Tanabe,140\nK. Tanaka,49\nS. J. Tanaka\n,230\nT. Tanaka\n,314\nD. Tang,29\nS. Tanioka\n,79\nD. B. Tanner,44\nW. Tanner,7, 8\nL. Tao\n,209\nR. D. Tapia,6\nE. N. Tapia San Mart\u00b4in\n,36\nR. Tarafder,10\nC. Taranto,19, 20\nA. Taruya\n,315\nJ. D. Tasson\n,316\nJ. G. Tau\n,109\nR. Tenorio\n,98\nH. Themann,202\nA. Theodoropoulos\n,135\nM. P. Thirugnanasambandam,14\nL. M. Thomas\n,10\nM. Thomas,65\nP. Thomas,2\nJ. E. Thompson\n,234\nS. R. Thondapu,100\nK. A. Thorne,65\nE. Thrane,149\nS. Tibrewal\n,145\nJ. Tissino\n,43\nA. Tiwari,14\nP. Tiwari,43\nS. Tiwari\n,204\nV. Tiwari\n,116\nM. R. Todd,79\nA. M. Toivonen\n,96\nK. Toland\n,28\nA. E. Tolley\n,77\nT. Tomaru\n,24\nK. Tomita,231\nV. Tommasini,10\nT. Tomura\n,49\nH. Tong\n,149\nC. Tong-Yu,140\nA. Toriyama,230\nN. Toropov\n,116\nA. Torres-Forn\u00b4e\n,135, 136\nC. I. Torrie,10\nM. Toscani\n,126\nI. Tosta e Melo\n,317\nE. Tournefier\n,30\nM. Trad Nery,48\nA. Trapananti\n,51, 50\nF. Travasso\n,51, 50\nG. Traylor,65\nC. Trejo,10\nM. Trevor,123\nM. C. Tringali\n,59\nA. Tripathee\n,90\nG. Troian\n,189, 46\nA. Trovato\n,189, 46\nL. Trozzo,4\nR. J. Trudeau,10\nT. T. L. Tsang\n,32\nS. Tsuchida\n,318\nL. Tsukada\n,219\nK. Turbang\n,182, 21\nM. Turconi\n,48\nC. Turski,94\nH. Ubach\n,41, 81\nN. Uchikata\n,199\nT. Uchiyama\n,49\nR. P. Udall\n,10\nT. Uehara\n,319\nM. Uematsu,231\nS. Ueno,230\nV. Undheim\n,276\nT. Ushiba\n,49\nM. Vacatello\n,88, 87\nH. Vahlbruch\n,7, 8\nG. Vajente\n,10\nA. Vajpeyi,149\nG. Valdes\n,320\nJ. Valencia\n,98\nA. F. Valentini,11\nM. Valentini\n,104, 36\nS. A. Vallejo-Pe\u02dcna\n,296\nS. Vallero,27\nV. Valsan\n,9\nN. van Bakel,36\nM. van Beuzekom\n,36\nM. van Dael\n,36, 321\nJ. F. J. van den Brand\n,35, 104, 36\nC. Van Den Broeck,76, 36\nD. C. Vander-Hyde,79\nM. van der Sluys\n,36, 76\nA. Van de Walle,38\nJ. van Dongen\n,36, 104\nK. Vandra,55\nH. van Haevermaet\n,21\nJ. V. van Heijningen\n,36, 104\nP. Van Hove\n,68\nJ. Vanier,253\nM. VanKeuren,101\nJ. Vanosky,2\nM. H. P. M. van Putten\n,16\nZ. Van Ranst\n,35, 36\nN. van Remortel\n,21\n\n41\nM. Vardaro,35, 36\nA. F. Vargas,121\nJ. J. Varghese,69\nV. Varma\n,131\nA. N. Vazquez,86\nA. Vecchio\n,116\nG. Vedovato,92\nJ. Veitch\n,28\nP. J. Veitch\n,113\nS. Venikoudis,13\nJ. Venneberg\n,7, 8\nP. Verdier\n,97\nM. Vereecken,13\nD. Verkindt\n,30\nB. Verma,131\nP. Verma,180\nY. Verma\n,100\nS. M. Vermeulen\n,10\nF. Vetrano,63\nA. Veutro\n,66, 67\nA. M. Vibhute\n,2\nA. Vicer\u00b4e\n,63, 64\nS. Vidyant,79\nA. D. Viets\n,84\nA. Vijaykumar\n,184\nA. Vilkha,109\nV. Villa-Ortega\n,128\nE. T. Vincent\n,60\nJ.-Y. Vinet,48\nS. Viret,97\nA. Virtuoso\n,46\nS. Vitale\n,34\nA. Vives,78\nH. Vocca\n,89, 50\nD. Voigt\n,85\nE. R. G. von Reis,2\nJ. S. A. von Wrangel,7, 8\nL. Vujeva,137\nS. P. Vyatchanin\n,105\nJ. Wack,10\nL. E. Wade,101\nM. Wade\n,101\nK. J. Wagner\n,109\nA. Wajid,56, 57\nM. Walker,120\nG. S. Wallace,58\nL. Wallace,10\nE. J. Wang,86\nH. Wang\n,39\nJ. Z. Wang,90\nW. H. Wang,160\nY. F. Wang\n,1\nZ. Wang,140\nG. Waratkar\n,207\nJ. Warner,2\nM. Was\n,30\nT. Washimi\n,24\nN. Y. Washington,10\nD. Watarai,40\nK. E. Wayt,101\nB. R. Weaver,32\nB. Weaver,2\nC. R. Weaving,77\nS. A. Webster,28\nN. L. Weickhardt\n,85\nM. Weinert,7, 8\nA. J. Weinstein\n,10 R. Weiss,34 F. Wellmann,7, 8 L. Wen,29 P. Wessels\n,7, 8 K. Wette\n,33 J. T. Whelan\n,109 B. F. Whiting\n,44\nC. Whittle\n,10\nE. G. Wickens,77\nJ. B. Wildberger,1\nD. Wilken\n,7, 8, 8\nD. J. Willadsen,84\nK. Willetts,32\nD. Williams\n,28\nM. J. Williams\n,77\nN. S. Williams,116\nJ. L. Willis\n,10\nB. Willke\n,8, 7, 8\nM. Wils\n,106\nC. W. Winborn,102\nJ. Winterflood,29\nC. C. Wipf,10\nG. Woan\n,28\nJ. Woehler,35, 36\nN. E. Wolfe,34\nH. T. Wong\n,140\nI. C. F. Wong\n,217, 106\nJ. L. Wright,33\nM. Wright\n,28\nC. Wu\n,139\nD. S. Wu\n,7, 8\nH. Wu\n,139\nE. Wuchner,54\nD. M. Wysocki\n,9\nV. A. Xu\n,34\nY. Xu\n,204\nN. Yadav\n,95\nH. Yamamoto\n,10\nK. Yamamoto\n,183\nT. S. Yamamoto\n,40\nT. Yamamoto\n,49\nS. Yamamura,199\nR. Yamazaki\n,230\nT. Yan,116\nF. W. Yang\n,322\nF. Yang,265\nK. Z. Yang\n,96\nY. Yang\n,143\nZ. Yarbrough\n,11\nH. Yasui,49\nS.-W. Yeh,139\nA. B. Yelikar\n,109\nX. Yin,34\nJ. Yokoyama\n,323, 40, 39\nT. Yokozawa,49\nJ. Yoo\n,147\nH. Yu\n,146\nS. Yuan,29\nH. Yuzurihara\n,49\nA. Zadro\u02d9zny,180\nM. Zanolin,69\nM. Zeeshan\n,109\nT. Zelenova,59\nJ.-P. Zendri,92\nM. Zeoli\n,13\nM. Zerrad,37\nM. Zevin\n,80\nA. C. Zhang,265\nL. Zhang,10\nR. Zhang\n,148\nT. Zhang,116\nY. Zhang\n,33\nC. Zhao\n,29\nYue Zhao,322\nYuhang Zhao\n,71\nY. Zheng\n,102\nH. Zhong\n,96\nR. Zhou,221\nX.-J. Zhu\n,324\nZ.-H. Zhu\n,324, 208\nA. B. Zimmerman\n,145\nM. E. Zucker34, 10\nAnd J. Zweizig\n10\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6The Pennsylvania State University, University Park, PA 16802, USA\n7Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n8Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n9University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n10LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n11Louisiana State University, Baton Rouge, LA 70803, USA\n12Tata Institute of Fundamental Research, Mumbai 400005, India\n13Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n14Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n15Queen Mary University of London, London E1 4NS, United Kingdom\n16Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n17Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n18SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n19Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n20INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n21Universiteit Antwerpen, 2000 Antwerpen, Belgium\n22International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n23University College Dublin, Belfield, Dublin 4, Ireland\n24Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n25Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n27INFN Sezione di Torino, I-10125 Torino, Italy\n28SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n29OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n30Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n31Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n32Cardiff University, Cardiff CF24 3AA, United Kingdom\n33OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n\n42\n34LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n35Maastricht University, 6200 MD Maastricht, Netherlands\n36Nikhef, 1098 XG Amsterdam, Netherlands\n37Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n38Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n39Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n40University of Tokyo, Tokyo, 113-0033, Japan.\n41Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n42Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n43Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n44University of Florida, Gainesville, FL 32611, USA\n45Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n46INFN, Sezione di Trieste, I-34127 Trieste, Italy\n47Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, Monterrey 64849, Mexico\n48Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n49Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n50INFN, Sezione di Perugia, I-06123 Perugia, Italy\n51Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n52University of Washington, Seattle, WA 98195, USA\n53Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n54California State University Fullerton, Fullerton, CA 92831, USA\n55Villanova University, Villanova, PA 19085, USA\n56INFN, Sezione di Genova, I-16146 Genova, Italy\n57Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n58SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n59European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n60Georgia Institute of Technology, Atlanta, GA 30332, USA\n61Royal Holloway, University of London, London TW20 0EX, United Kingdom\n62Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n63Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n64INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n65LIGO Livingston Observatory, Livingston, LA 70754, USA\n66INFN, Sezione di Roma, I-00185 Roma, Italy\n67Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n68Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n69Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n70Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n71Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n72King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n73Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n74Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n75International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n76Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n77University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Northwestern University, Evanston, IL 60208, USA\n81Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n82Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n83HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n84Concordia University Wisconsin, Mequon, WI 53097, USA\n85Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n86Stanford University, Stanford, CA 94305, USA\n87Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n88INFN, Sezione di Pisa, I-56127 Pisa, Italy\n89Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n90University of Michigan, Ann Arbor, MI 48109, USA\n\n43\n91Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96University of Minnesota, Minneapolis, MN 55455, USA\n97Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Universit\u00e0 di Siena, I-53100 Siena, Italy\n100RRCAT, Indore, Madhya Pradesh 452013, India\n101Kenyon College, Gambier, OH 43022, USA\n102Missouri University of Science and Technology, Rolla, MO 65409, USA\n103Colorado State University, Fort Collins, CO 80523, USA\n104Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n105Lomonosov Moscow State University, Moscow 119991, Russia\n106Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n107Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n108INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n109Rochester Institute of Technology, Rochester, NY 14623, USA\n110Bar-Ilan University, Ramat Gan, 5290002, Israel\n111University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n112INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n113OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n114Centre national de la recherche scientifique, 75016 Paris, France\n115Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n116University of Birmingham, Birmingham B15 2TT, United Kingdom\n117Washington State University, Pullman, WA 99164, USA\n118INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n119Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n120Christopher Newport University, Newport News, VA 23606, USA\n121OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n122Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n123University of Maryland, College Park, MD 20742, USA\n124Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n125INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n126L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00e9 de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n127Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n128IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n132INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n135Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n136Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n137Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n138Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n139National Tsing Hua University, Hsinchu City 30013, Taiwan\n140National Central University, Taoyuan City 320317, Taiwan\n141OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n142Vanderbilt University, Nashville, TN 37235, USA\n143Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n144Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n145University of Texas, Austin, TX 78712, USA\n146CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n147Cornell University, Ithaca, NY 14850, USA\n\n44\n148Northeastern University, Boston, MA 02115, USA\n149OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n150Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n151INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n152OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n153University of Rhode Island, Kingston, RI 02881, USA\n154INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n155Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n156INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n157Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n158Montana State University, Bozeman, MT 59717, USA\n159Johns Hopkins University, Baltimore, MD 21218, USA\n160The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n161Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n162DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n163Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2, Bologna, Italy\n164University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n165INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n166Chennai Mathematical Institute, Chennai 603103, India\n167Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n168Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n169Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n170Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n171Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n172Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n173INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n174University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n175Marquette University, Milwaukee, WI 53233, USA\n176Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n177Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n178Indian Institute of Technology Madras, Chennai 600036, India\n179Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n180National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n181Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00e9, CNRS, UMR 7095, 75014 Paris, France\n182Vrije Universiteit Brussel, 1050 Brussel, Belgium\n183Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n184Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n185University of Cambridge, Cambridge CB2 1TN, United Kingdom\n186Stony Brook University, Stony Brook, NY 11794, USA\n187Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n188Montclair State University, Montclair, NJ 07043, USA\n189Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n190HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n191Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n192Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n193CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n194Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n195Western Washington University, Bellingham, WA 98225, USA\n196Barry University, Miami Shores, FL 33168, USA\n197Centro de Astrof\u00edsica e Gravita\u00e7\u00e3o, Departamento de F\u00edsica, Instituto Superior T\u00e9cnico - IST, Universidade de Lisboa - UL, Av. Rovisco Pais 1, 1049-001\nLisboa, Portugal\n198E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n199Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n200Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n201Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n202California State University, Los Angeles, Los Angeles, CA 90032, USA\n\n45\n203Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n204University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n205Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n206University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n207Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n208School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n209University of California, Riverside, Riverside, CA 92521, USA\n210University of Nottingham NG7 2RD, UK\n211Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n212University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n213The University of Mississippi, University, MS 38677, USA\n214Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n215Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA\n216Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n217The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n218American University, Washington, DC 20016, USA\n219University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n220Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n221University of California, Berkeley, CA 94720, USA\n222University of Lancaster, Lancaster LA1 4YW, United Kingdom\n223College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n224Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n225Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n226Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n227Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n228Scuola Normale Superiore, I-56126 Pisa, Italy\n229Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n230Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,\nJapan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n234University of Southampton, Southampton SO17 1BJ, United Kingdom\n235Sungkyunkwan University, Seoul 03063, Republic of Korea\n236Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n237Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n238Chung-Ang University, Seoul 06974, Republic of Korea\n239University of Washington Bothell, Bothell, WA 98011, USA\n240Aix Marseille Universit\u00e9, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n241Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n242Ewha Womans University, Seoul 03760, Republic of Korea\n243Seoul National University, Seoul 08826, Republic of Korea\n244Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n245Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n246Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n247Bard College, Annandale-On-Hudson, NY 12504, USA\n248Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n249Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n250Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n251Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n252Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n253Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n254Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n255Texas Tech University, Lubbock, TX 79409, USA\n256Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n257Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n\n46\n258Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,\nRepublic of Korea\n259NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n260National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science Park, Hsinchu City 30076,\nTaiwan\n261NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n262Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n263School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n264Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n265Columbia University, New York, NY 10027, USA\n266Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n267Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa\n224-8551, Japan\n268Tsinghua University, Beijing 100084, China\n269Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n270School of Physical & Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand\n271GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n272Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n273Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n274Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n275Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, To Huu street Yen Nghia Ward, Ha Dong District, Hanoi, Vietnam\n276University of Stavanger, 4021 Stavanger, Norway\n277Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n278Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima\n903-0213, Japan\n279Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n280Observatoire de Paris, 75014 Paris, France\n281Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n282National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n283Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n289Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n290Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n291Hobart and William Smith Colleges, Geneva, NY 14456, USA\n292Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n295Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n296Universidad de Antioquia, Medell\u00edn, Colombia\n297Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n298Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n299Dipartimento di Fisica e Scienze della Terra, Universit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n300Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n301Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n302Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n303University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n304Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n305Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n306NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n307iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n308Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n309Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS, Universit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n310Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n\n47\n311INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n312Universidade Estadual Paulista, 01140-070 S\u00e3o Paulo, Brazil\n313Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n314Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n315Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n316Carleton College, Northfield, MN 55057, USA\n317University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n318National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n319Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n320Texas A&M University, College Station, TX 77843, USA\n321Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n322The University of Utah, Salt Lake City, UT 84112, USA\n323Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n324Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n", "Ultralight vector dark matter search using data from the KAGRA O3GK run\nA. G. Abac,1 R. Abbott,2 H. Abe,3 I. Abouelfettouh,4 F. Acernese,5, 6 K. Ackley\n,7 C. Adamcewicz\n,8\nS. Adhicary,9 N. Adhikari\n,10 R. X. Adhikari\n,2 V. K. Adkins,11 V. B. Adya,12 C. Affeldt,13, 14 D. Agarwal\n,15\nM. Agathos\n,16 O. D. Aguiar\n,17 I. Aguilar,18 L. Aiello\n,19 A. Ain\n,20 P. Ajith\n,21 T. Akutsu\n,22, 23\nS. Albanesi,24, 25 R. A. Alfaidi\n,26 A. Al-Jodah\n,27 C. All\u00b4en\u00b4e,28 A. Allocca\n,29, 6 S. Al-Shammari,19\nP. A. Altin\n,12 S. Alvarez-Lopez\n,30 A. Amato\n,31, 32 L. Amez-Droz,33 A. Amorosi,33 C. Amra,34 S. Anand,2\nA. Ananyeva,2 S. B. Anderson\n,2 W. G. Anderson\n,2 M. Andia\n,35 M. Ando,36 T. Andrade,37 N. Andres\n,28\nM. Andr\u00b4es-Carcasona\n,38 T. Andri\u00b4c\n,1, 39 J. Anglin,40 S. Ansoldi,41, 42 J. M. Antelis\n,43 S. Antier\n,44\nM. Aoumi,45 E. Z. Appavuravther,46, 47 S. Appert,2 S. K. Apple,48 K. Arai\n,2 A. Araya\n,49 M. C. Araya\n,2\nJ. S. Areeda\n,50 N. Aritomi\n,4 F. Armato,51 N. Arnaud\n,35, 52 M. Arogeti\n,53 S. M. Aronson\n,11 K. G. Arun\n,54\nG. Ashton\n,55 Y. Aso\n,22, 56 M. Assiduo,57, 58 S. Assis de Souza Melo,52 S. M. Aston,59 P. Astone\n,60\nF. Aubin\n,61 K. AultONeal\n,43 G. Avallone\n,62 S. Babak\n,63 F. Badaracco\n,51 C. Badger,64 S. Bae\n,65\nS. Bagnasco\n,25 E. Bagui,66 Y. Bai,2 J. G. Baier\n,67 R. Bajpai\n,22 T. Baka,68 M. Ball,69 G. Ballardin,52\nS. W. Ballmer,70 S. Banagiri\n,71 B. Banerjee\n,39 D. Bankar\n,15 P. Baral\n,10 J. C. Barayoga,2 B. C. Barish,2\nD. Barker,4 P. Barneo\n,37, 72 F. Barone\n,73, 6 B. Barr\n,26 L. Barsotti\n,30 M. Barsuglia\n,63 D. Barta\n,74\nS. D. Barthelmy,75 M. A. Barton\n,26 I. Bartos,40 S. Basak\n,21 A. Basalaev\n,76 R. Bassiri\n,18 A. Basti\n,77, 20\nM. Bawaj\n,78, 46 P. Baxi,79 J. C. Bayley\n,26 A. C. Baylor\n,10 M. Bazzan,80, 81 B. B\u00b4ecsy\n,82 V. M. Bedakihale,83\nF. Beirnaert\n,84 M. Bejger\n,85 D. Belardinelli\n,86 A. S. Bell\n,26 V. Benedetto,87 D. Beniwal,88 W. Benoit\n,89\nJ. D. Bentley\n,76 M. Ben Yaala,90 S. Bera\n,91 M. Berbel\n,92 F. Bergamin\n,13, 14 B. K. Berger\n,18\nS. Bernuzzi\n,93 M. Beroiz\n,2 D. Bersanetti\n,51 A. Bertolini,32 J. Betzwieser\n,59 D. Beveridge\n,27 N. Bevins\n,94\nR. Bhandare,95 U. Bhardwaj\n,96, 32 R. Bhatt,2 D. Bhattacharjee\n,67, 97 S. Bhaumik\n,40 S. Bhowmick,98\nA. Bianchi,32, 99 I. A. Bilenko,100 G. Billingsley\n,2 A. Binetti\n,101 S. Bini\n,102, 103 O. Birnholtz\n,104\nS. Biscoveanu\n,71, 30 A. Bisht,14 M. Bitossi\n,52, 20 M.-A. Bizouard\n,44 J. K. Blackburn\n,2 C. D. Blair,27, 59\nD. G. Blair,27 F. Bobba,62, 105 N. Bode\n,13, 14 G. Bogaert,44 G. Boileau\n,106, 44 M. Boldrini\n,107, 60\nG. N. Bolingbroke\n,88 A. Bolliand,108, 34 L. D. Bonavena\n,80 R. Bondarescu\n,37 F. Bondu\n,109 E. Bonilla\n,18\nM. S. Bonilla\n,50 A. Bonino,110 R. Bonnand\n,28 P. Booker,13, 14 A. Borchers,13, 14 V. Boschi\n,20 S. Bose,15\nV. Bossilkov,59 V. Boudart\n,111 A. Boumerdassi,19 A. Bozzi,52 C. Bradaschia,20 P. R. Brady\n,10 M. Braglia\n,112\nA. Branch,59 M. Branchesi\n,39, 113 M. Breschi\n,93 T. Briant\n,114 A. Brillet,44 M. Brinkmann,13, 14\nP. Brockill,10 E. Brockmueller\n,13, 14 A. F. Brooks\n,2 D. D. Brown,88 M. L. Brozzetti\n,78, 46 S. Brunett,2\nG. Bruno,115 R. Bruntz\n,116 J. Bryant,110 F. Bucci,58 J. Buchanan,116 O. Bulashenko\n,37, 72 T. Bulik,117\nH. J. Bulten,32 A. Buonanno\n,118, 1 K. Burtnyk,4 R. Buscicchio\n,119, 120 D. Buskulic,28 C. Buy\n,121\nR. L. Byer,18 G. S. Cabourn Davies\n,122 G. Cabras\n,41, 42 R. Cabrita\n,115 L. Cadonati\n,53 G. Cagnoli\n,123\nC. Cahillane\n,70 J. Calder\u00b4on Bustillo,124 J. D. Callaghan,26 T. A. Callister,125 E. Calloni,29, 6 J. B. Camp,75, 51\nG. Caneva Santoro\n,38 M. Cannavacciuolo\n,62 K. C. Cannon\n,36 H. Cao,126 Z. Cao\n,127 L. A. Capistran,128\nE. Capocasa\n,63 E. Capote,70 G. Carapella,62, 105 F. Carbognani,52 M. Carlassara,13, 14 J. B. Carlin\n,129\nM. Carpinelli\n,119, 130, 52 G. Carrillo,69 J. J. Carter\n,13, 14 G. Carullo\n,131 J. Casanueva Diaz,52 C. Casentini,132, 86\nG. Castaldi,133 S. Y. Castro-Lucas,98 S. Caudill,134, 32, 68 M. Cavagli`a\n,97 R. Cavalieri\n,52 G. Cella\n,20\nP. Cerd\u00b4a-Dur\u00b4an\n,135, 136 E. Cesarini\n,86 W. Chaibi,44 P. Chakraborty\n,13, 14 S. Chalathadka Subrahmanya\n,76\nC. Chan,36 J. C. L. Chan\n,125 K. H. M. Chan\n,137 M. Chan,138 W. L. Chan,137 K. Chandra,139\nR.-J. Chang,140 P. Chanial\n,63 S. Chao\n,141, 142 C. Chapman-Bird\n,26 E. L. Charlton,116 P. Charlton\n,143\nE. Chassande-Mottin\n,63 C. Chatterjee\n,27 Debarati Chatterjee\n,15 Deep Chatterjee\n,30 M. Chaturvedi,95\nS. Chaty\n,63 K. Chatziioannou\n,2 A. Chen,144 A. H.-Y. Chen,145 D. Chen\n,146 H. Chen,141 H. Y. Chen\n,147\nK. H. Chen,142 X. Chen,27 Yi-Ru Chen,141 Yanbei Chen,148 Yitian Chen\n,149 H. P. Cheng,40 P. Chessa\n,77, 20\nH. T. Cheung,79 H. Y. Chia,40 F. Chiadini\n,150, 105 C. Chiang,142 G. Chiarini,81 A. Chiba,151 R. Chiba,152\nR. Chierici,153 A. Chincarini\n,51 M. L. Chiofalo\n,77, 20 A. Chiummo\n,6, 52 C. Chou,145 S. Choudhary\n,27\nN. Christensen\n,44 S. S. Y. Chua\n,12 K. W. Chung,64 G. Ciani\n,80, 81 P. Ciecielag\n,85 M. Cie\u00b4slar\n,85 M. Cifaldi,86\nA. A. Ciobanu,88 R. Ciolfi\n,154, 81 F. Clara,4 J. A. Clark\n,2, 53 T. A. Clarke\n,8 P. Clearwater,155 S. Clesse,66\nF. Cleva,44 E. Coccia,39, 113, 38 E. Codazzo\n,39 P.-F. Cohadon\n,114 M. Colleoni\n,91 C. G. Collette,33 J. Collins,59\nS. Colloms,26 A. Colombo\n,119, 120, 156 M. Colpi\n,119, 120 C. M. Compton,4 L. Conti\n,81 S. J. Cooper\n,110\nT. R. Corbitt\n,11 I. Cordero-Carri\u00b4on\n,157 S. Corezzi,78, 46 N. J. Cornish\n,82 A. Corsi\n,158 S. Cortese\n,52\nC. A. Costa,17 R. Cottingham,59 M. W. Coughlin\n,89 A. Couineaux,60 J.-P. Coulon,44 S. T. Countryman\n,159\nJ.-F. Coupechoux,153 B. Cousins\n,9 P. Couvares\n,2, 53 D. M. Coward,27 M. J. Cowart,59 D. C. Coyne\n,2\nR. Coyne\n,160 K. Craig,90 R. Creed,19 J. D. E. Creighton\n,10 T. D. Creighton,161 P. Cremonese\n,91\narXiv:2403.03004v1 [astro-ph.CO] 5 Mar 2024\n\n2\nA. W. Criswell\n,89 J. C. G. Crockett-Gray,11 M. Croquette\n,114 R. Crouch,4 S. G. Crowder,162 J. R. Cudell\n,111\nT. J. Cullen,2 A. Cumming\n,26 E. Cuoco,52, 163, 20 M. Cusinato\n,135 P. Dabadie,123 T. Dal Canton\n,35\nS. Dall\u2019Osso\n,60 G. D\u00b4alya\n,84 B. D\u2019Angelo\n,51 S. Danilishin\n,31, 32 S. D\u2019Antonio,86 K. Danzmann,14, 13, 14\nK. E. Darroch,116 L. P. Dartez,4 A. Dasgupta,83 S. Datta\n,54 V. Dattilo,52 A. Daumas,63 N. Davari,164, 130\nI. Dave,95 A. Davenport,98 M. Davier,35 T. F. Davies,27 D. Davis\n,2 L. Davis,27 M. C. Davis\n,94 E. J. Daw\n,165\nM. Dax\n,1 J. De Bolle\n,84 M. Deenadayalan,15 J. Degallaix\n,166 M. De Laurentis\n,29, 6 S. Del\u00b4eglise\n,114\nV. Del Favero\n,75 F. De Lillo\n,115 D. Dell\u2019Aquila\n,164, 130 W. Del Pozzo\n,77, 20 F. De Marco\n,60, 107\nF. De Matteis\n,132, 86 V. D\u2019Emilio\n,19 N. Demos,30 T. Dent\n,124 A. Depasse\n,115 N. DePergola,94\nR. De Pietri\n,167, 168 R. De Rosa\n,29, 6 C. De Rossi\n,52 R. De Simone,150 A. Dhani,1 S. Dhurandhar,15 R. Diab,40\nM. C. D\u00b4\u0131az\n,161 M. Di Cesare\n,29 G. Dideron,169 N. A. Didio,70 T. Dietrich\n,1 L. Di Fiore,6 C. Di Fronzo\n,33\nF. Di Giovanni\n,135 M. Di Giovanni,107, 60 T. Di Girolamo\n,29, 6 D. Diksha,32, 31 A. Di Michele\n,78 J. Ding\n,63, 170\nS. Di Pace\n,107, 60 I. Di Palma\n,107, 60 F. Di Renzo\n,153 Divyajyoti\n,171 A. Dmitriev\n,110 Z. Doctor\n,71\nE. Dohmen,4 P. P. Doleva,116 L. Donahue,172 L. D\u2019Onofrio\n,60 F. Donovan,30 K. L. Dooley\n,19 T. Dooney,68\nS. Doravari\n,15 O. Dorosh,173 M. Drago\n,107, 60 J. C. Driggers\n,4 Y. Drori,2 J.-G. Ducoin,174, 63 L. Dunn\n,129\nU. Dupletsa,39 D. D\u2019Urso\n,164, 130 H. Duval\n,175 P.-A. Duverne,35 S. E. Dwyer,4 C. Eassa,4 M. Ebersold\n,176, 28\nT. Eckhardt\n,76 G. Eddolls\n,26 B. Edelman\n,69 T. B. Edo,2 O. Edy\n,122 A. Effler\n,59 J. Eichholz\n,12\nH. Einsle,44 M. Eisenmann,22 R. A. Eisenstein,30 A. Ejlli\n,19 M. Emma\n,55 E. Engelby,50 A. J. Engl,18\nL. Errico,29, 6 R. C. Essick\n,177 H. Estell\u00b4es\n,1 D. Estevez\n,61 T. Etzel,2 M. Evans\n,30 T. Evstafyeva,16\nB. E. Ewing,9 J. M. Ezquiaga\n,125 F. Fabrizi\n,57, 58 F. Faedi,58, 57 V. Fafone\n,132, 86 S. Fairhurst\n,19\nP. C. Fan\n,172 A. M. Farah\n,125 B. Farr\n,69 W. M. Farr\n,178, 179 G. Favaro\n,80 M. Favata\n,180 M. Fays\n,111\nM. Fazio,90 J. Feicht,2 M. M. Fejer,18 E. Fenyvesi\n,74, 181 D. L. Ferguson\n,147 I. Ferrante\n,77, 20 T. A. Ferreira,11\nF. Fidecaro\n,77, 20 A. Fiori\n,20, 77 I. Fiori\n,52 M. Fishbach\n,177 R. P. Fisher,116 R. Fittipaldi,182, 105\nV. Fiumara,183, 105 R. Flaminio,28 S. M. Fleischer\n,184 L. S. Fleming,185 E. Floden,89 E. M. Foley,89 H. Fong,138\nJ. A. Font\n,135, 136 B. Fornal\n,186 P. W. F. Forsyth,12 K. Franceschetti,167 N. Franchini,63 S. Frasca,107, 60\nF. Frasconi\n,20 A. Frattale Mascioli\n,107, 60 Z. Frei\n,187 A. Freise\n,32, 99 O. Freitas\n,188, 135 R. Frey\n,69\nW. Frischhertz,59 V. V. Frolov,59 G. G. Fronz\u00b4e\n,25 M. Fuentes-Garcia\n,2 S. Fujii,152 I. Fukunaga,189 P. Fulda,40\nM. Fyffe,59 W. E. Gabella\n,190 B. Gadre\n,68 J. R. Gair\n,1 S. Galaudage\n,8, 191 S. Gallardo,192 B. Gallego,192\nR. Gamba\n,93 A. Gamboa\n,1 D. Ganapathy\n,30 A. Ganguly\n,15 S. G. Gaonkar,15 B. Garaventa\n,51, 193\nJ. Garcia-Bellido\n,112 C. Garc\u00b4\u0131a-N\u00b4u\u02dcnez,185 C. Garc\u00b4\u0131a-Quir\u00b4os\n,176 J. W. Gardner\n,12 K. A. Gardner,138\nJ. Gargiulo\n,52 A. Garron\n,91 F. Garufi\n,29, 6 C. Gasbarra\n,132, 86 B. Gateley,4 V. Gayathri\n,10\nG. Gemme\n,51 A. Gennai\n,20 J. George,95 R. George,147 O. Gerberding\n,76 L. Gergely\n,194 N. Ghadiri,50\nArchisman Ghosh\n,84 Shaon Ghosh\n,180 Shrobana Ghosh,13, 14 Suprovo Ghosh\n,15 Tathagata Ghosh\n,15\nL. Giacoppo,107, 60 J. A. Giaime\n,11, 59 K. D. Giardina,59 D. R. Gibson,185 D. T. Gibson,16 C. Gier\n,90\nP. Giri\n,20, 77 F. Gissi,87 S. Gkaitatzis\n,77, 20 J. Glanzer,11 A. E. Gleckl,50 F. Glotin,35 J. Godfrey,69 P. Godwin,2\nN. L. Goebbels\n,76 E. Goetz\n,138 J. Golomb,2 S. Gomez Lopez\n,107, 60 B. Goncharov\n,39 G. Gonz\u00b4alez\n,11\nP. Goodarzi,126 A. W. Goodwin-Jones\n,27 M. Gosselin,52 A. S. G\u00a8ottel\n,19 R. Gouaty\n,28 D. W. Gould,12\nS. Goyal\n,21 B. Grace,12 A. Grado\n,195, 6 V. Graham\n,26 A. E. Granados\n,89 M. Granata\n,166 V. Granata\n,62\nL. Granda Argianas,94 S. Gras,30 P. Grassia,2 C. Gray,4 R. Gray\n,26 G. Greco,46 A. C. Green\n,32, 99\nS. M. Green,122 S. R. Green\n,1 A. M. Gretarsson,43 E. M. Gretarsson,43 D. Griffith,2 W. L. Griffiths\n,19\nH. L. Griggs\n,53 G. Grignani,78, 46 A. Grimaldi\n,102, 103 C. Grimaud,28 H. Grote\n,19 A. S. Gruson,50\nD. Guerra\n,135 D. Guetta\n,196, 60 G. M. Guidi\n,57, 58 A. R. Guimaraes,11 H. K. Gulati,83 F. Gulminelli\n,197, 198\nA. M. Gunny,30 H. Guo\n,186 W. Guo\n,27 Y. Guo\n,32, 31 Anchal Gupta\n,2 Anuradha Gupta\n,199 Ish Gupta\n,9\nN. C. Gupta,83 P. Gupta,32, 68 S. K. Gupta,40 T. Gupta\n,82 N. Gupte,1 R. Gurav,126 J. Gurs,76 N. Gutierrez,166\nF. Guzman\n,128 D. Haba,3 M. Haberland,1 L. Haegel\n,63 G. Hain,116 S. Haino,200 E. D. Hall\n,30\nE. Z. Hamilton,176 G. Hammond\n,26 W.-B. Han\n,201 M. Haney\n,176, 32 J. Hanks,4 C. Hanna,9 M. D. Hannam,19\nO. A. Hannuksela\n,137 A. G. Hanselman\n,125 H. Hansen,4 J. Hanson,59 R. Harada,36 T. Harder,44 K. Haris,32, 68\nT. Harmark\n,131 J. Harms\n,39, 113 G. M. Harry\n,202 I. W. Harry\n,122 B. Haskell,85 C.-J. Haster\n,203\nJ. S. Hathaway,204 K. Haughian\n,26 H. Hayakawa,45 K. Hayama,205 J. Healy\n,204 A. Heffernan\n,91\nA. Heidmann\n,114 M. C. Heintze,59 J. Heinze\n,110 J. Heinzel,30 H. Heitmann\n,44 F. Hellman\n,206 P. Hello,35\nA. F. Helmling-Cornell\n,69 G. Hemming\n,52 M. Hendry\n,26 I. S. Heng\n,26 E. Hennes\n,32 J.-S. Hennig,31, 32\nM. Hennig,31, 32 C. Henshaw\n,53 A. Hernandez,180 T. Hertog,101 M. Heurs\n,13, 14 A. L. Hewitt\n,16, 207\nS. Higginbotham,19 S. Hild,31, 32 P. Hill,90 S. Hill,26 Y. Himemoto\n,208 A. S. Hines,128 N. Hirata,22 C. Hirose,209\nJ. Ho,142 S. Hoang,35 S. Hochheim,13, 14 D. Hofman,166 N. A. Holland,32, 99 K. Holley-Bockelmann,190\n\n3\nI. J. Hollows\n,165 Z. J. Holmes\n,88 D. E. Holz\n,125 C. Hong,18 J. Hornung,69 S. Hoshino,209 S. Hourihane,2\nE. J. Howell\n,27 C. G. Hoy\n,122 D. Hoyland,110 C. A. Hrishikesh,132 H.-F. Hsieh\n,141 C. Hsiung,210 H. C. Hsu,142\nS.-C. Hsu\n,48, 141 W.-F. Hsu\n,101 P. Hu,190 Q. Hu\n,26 H. Y. Huang\n,142 Y.-J. Huang\n,9 Y. Huang,30\nY. T. Huang,48 A. D. Huddart,211 B. Hughey,43 D. C. Y. Hui\n,212 V. Hui\n,28 R. Hur,69 S. Husa\n,91 R. Huxford,9\nT. Huynh-Dinh,59 A. Iakovlev\n,213 G. A. Iandolo,31 A. Iess\n,163, 20 K. Inayoshi\n,214 Y. Inoue,142\nG. Iorio\n,80 J. Irwin\n,26 M. Isi\n,178, 179 M. A. Ismail\n,142 Y. Itoh\n,189, 215 M. Iwaya,152 B. R. Iyer\n,21\nV. JaberianHamedan\n,27 P.-E. Jacquet\n,114 S. J. Jadhav,216 S. P. Jadhav\n,155 T. Jain,16 A. L. James\n,19\nP. A. James,116 R. Jamshidi,33 A. Z. Jan\n,147 K. Jani\n,190 L. Janiurek,26 J. Janquart,68, 32 K. Janssens\n,106, 44\nN. N. Janthalur,216 S. Jaraba\n,112 P. Jaranowski\n,217 P. Jasal,37 R. Jaume\n,91 W. Javed,19 A. Jennings,4\nW. Jia,30 J. Jiang\n,40 H.-B. Jin\n,218, 219 K. Johansmeyer,180 G. R. Johns,116 N. A. Johnson,40 R. Johnston,26\nN. Johny,13, 14 D. H. Jones\n,12 D. I. Jones,220 R. Jones,26 S. Jose,171 P. Joshi,9 L. Ju\n,27 K. Jung\n,221\nJ. Junker\n,13, 14 V. Juste,61 T. Kajita\n,222 C. Kalaghatgi,68, 32, 223 V. Kalogera\n,71 M. Kamiizumi\n,45\nN. Kanda\n,215, 189 S. Kandhasamy\n,15 G. Kang\n,224 J. B. Kanner,2 S. J. Kapadia,15 D. P. Kapasi\n,12\nS. Karat,2 C. Karathanasis\n,38 S. Karki\n,97 R. Kashyap,9 M. Kasprzack\n,2 W. Kastaun,13, 14 J. Kato,151\nT. Kato,152 S. Katsanevas,52, \u2217E. Katsavounidis,30 W. Katzman,59 T. Kaur,27 R. Kaushik\n,95 K. Kawabe,4\nD. Keitel\n,91 J. Kelley-Derzon,40 J. Kennington\n,9 R. Kesharwani,15 J. S. Key\n,225 S. Khadka,18\nF. Y. Khalili\n,100 F. Khan\n,13, 14 I. Khan,226, 34 T. Khanam,158 E. A. Khazanov,213 M. Khursheed,95\nW. Kiendrebeogo\n,44, 227 N. Kijbunchoo\n,88 C. Kim,228 J. C. Kim,229 K. Kim\n,230 M. H. Kim,231 S. Kim\n,212\nW. S. Kim,232 Y.-M. Kim\n,230 C. Kimball\n,71 N. Kimura,45 M. Kinley-Hanlon\n,26 M. Kinnear,19\nJ. S. Kissel\n,4 T. Kiyota,189 S. Klimenko,40 T. Klinger,19 A. M. Knee\n,138 N. Knust\n,13, 14 P. Koch,13, 14\nS. M. Koehlenbeck\n,18 G. Koekoek,32, 31 K. Kohri\n,233 K. Kokeyama\n,19 S. Koley\n,39 P. Kolitsidou\n,110\nM. Kolstein\n,38 K. Komori\n,36 A. K. H. Kong\n,141 A. Kontos\n,234 M. Korobko\n,76 R. V. Kossak,13, 14 X. Kou,89\nA. Koushik,106 N. Kouvatsos\n,64 M. Kovalam,27 N. Koyama,209 D. B. Kozak,2 S. L. Kranzhoff,31, 32 V. Kringel,13, 14\nN. V. Krishnendu\n,21 A. Kr\u00b4olak\n,235, 173 G. Kuehn,13, 14 P. Kuijer\n,32 S. Kulkarni\n,199 A. Kulur Ramamohan\n,12\nA. Kumar,216 Praveen Kumar\n,124 Prayush Kumar\n,21 Rahul Kumar,4 Rakesh Kumar,83 J. Kume\n,80, 81, 36\nK. Kuns\n,30 S. Kuroyanagi\n,112, 236 S. Kuwahara,36 K. Kwak\n,221 K. Kwan,12 G. Lacaille,26 P. Lagabbe,28\nD. Laghi\n,121 S. Lai,145 A. H. Laity,160 M. H. Lakkis,33 E. Lalande,237 M. Lalleman\n,106 M. Landry,4 B. B. Lane,30\nR. N. Lang\n,30 J. Lange,147 B. Lantz\n,18 A. La Rana\n,60 I. La Rosa\n,91, 107, 28 A. Lartaux-Vollard\n,35\nP. D. Lasky\n,8 J. Lawrence,158 M. Laxen\n,59 A. Lazzarini\n,2 C. Lazzaro,80, 81 P. Leaci\n,107, 60 S. LeBohec,186\nY. K. Lecoeuche\n,138 H. M. Lee\n,229 H. W. Lee\n,238 K. Lee\n,231 R.-K. Lee\n,141 R. Lee,30 S. Lee\n,230 Y. Lee,142\nI. N. Legred,2 J. Lehmann,13, 14 L. Lehner,169 A. Lema\u02c6\u0131tre,239 M. Lenti\n,58, 240 M. Leonardi\n,241, 22 E. Leonova\n,96\nM. Lequime,34 N. Leroy\n,35 M. Lesovsky,2 N. Letendre,28 M. Lethuillier\n,153 C. Levesque,237 Y. Levin,8\nK. Leyde,63 A. K. Y. Li,2 K. L. Li\n,140 T. G. F. Li,137, 101 X. Li\n,148 Chien-Yu Lin,142, 141 Chun-Yu Lin\n,242\nE. T. Lin\n,141 F. Lin,142 H. Lin,142 L. C.-C. Lin\n,140 F. Linde,223, 32 S. D. Linker,133, 192 T. B. Littenberg,243\nA. Liu\n,137 G. C. Liu\n,210 Jian Liu\n,27 F. Llamas,161 J. Llobera-Querol\n,91 R. K. L. Lo\n,2 J.-P. Locquet,101\nL. London,96 A. Longo\n,57, 58 D. Lopez,176 M. Lopez Portilla,68 M. Lorenzini\n,132, 86 V. Loriette,35 M. Lormand,59\nG. Losurdo\n,20 T. P. Lott IV\n,53 J. D. Lough\n,13, 14 H. A. Loughlin,30 C. O. Lousto\n,204 M. J. Lowry,116\nH. L\u00a8uck,14, 13, 14 D. Lumaca\n,86 A. P. Lundgren,122 A. W. Lussier\n,237 L.-T. Ma,141 S. Ma,148 M. Ma\u2019arif\n,142\nR. Macas\n,122 M. MacInnis,30 R. R. Maciy,13, 14 D. M. Macleod\n,19 I. A. O. MacMillan\n,2 A. Macquet\n,38\nD. Macri,30 K. Maeda,151 S. Maenaut\n,101 I. Maga\u02dcna Hernandez,10 S. S. Magare,15 C. Magazz`u\n,20\nR. M. Magee\n,2 E. Maggio\n,1 R. Maggiore,32, 99 M. Magnozzi\n,51, 193 M. Mahesh,76 S. Mahesh,244 M. Maini,160\nS. Majhi,15 E. Majorana,107, 60 C. N. Makarem,2 J. A. Malaquias-Reis,17 S. Maliakal,2 A. Malik,95 N. Man,44\nV. Mandic\n,89 V. Mangano\n,60, 107 B. Mannix,69 G. L. Mansell\n,70, 30 M. Manske\n,10 M. Mantovani\n,52\nM. Mapelli\n,80, 81 F. Marchesoni,47, 46, 245 D. Mar\u00b4\u0131n Pina\n,37, 72, 246 F. Marion\n,28 S. M\u00b4arka\n,159 Z. M\u00b4arka\n,159\nC. Markakis\n,144 A. S. Markosyan,18 A. Markowitz,2 E. Maros,2 A. Marquina\n,157 S. Marsat\n,121\nF. Martelli\n,57, 58 I. W. Martin\n,26 R. M. Martin\n,180 B. B. Martinez,128 M. Martinez,38, 247 V. Martinez\n,123\nA. Martini,102 K. Martinovic,64 J. C. Martins\n,17 D. V. Martynov,110 E. J. Marx,30 L. Massaro,31, 32 A. Masserot,28\nM. Masso-Reid\n,26 M. Mastrodicasa,60 S. Mastrogiovanni\n,60 M. Mateu-Lucena\n,91 M. Matiushechkina\n,13, 14\nM. Matsuyama,189 N. Mavalvala\n,30 N. Maxwell,4 G. McCarrol,59 R. McCarthy,4 D. E. McClelland\n,12\nS. McCormick,59 L. McCuller\n,2 G. I. McGhee,26 K. B. M. McGowan,190 M. Mchedlidze,180 C. McIsaac\n,122\nJ. McIver\n,138 K. McKinney,162 A. McLeod\n,27 T. McRae,12 S. T. McWilliams,244 D. Meacher\n,10\nA. K. Mehta,1 Q. Meijer,68 A. Melatos,129 S. Mellaerts\n,101 A. Menendez-Vazquez\n,38 C. S. Menoni\n,98\nR. A. Mercer\n,10 L. Mereni,166 K. Merfeld,69 E. L. Merilh,59 J. R. M\u00b4erou\n,91 J. D. Merritt,69 M. Merzougui,44\n\n4\nC. Messenger\n,26 C. Messick,10 M. Meyer-Conde\n,189 F. Meylahn\n,13, 14 A. Mhaske,15 A. Miani\n,102, 103\nH. Miao,248 I. Michaloliakos\n,40 C. Michel\n,166 Y. Michimura\n,2, 36 H. Middleton\n,110 A. L. Miller\n,32\nS. Miller,2 M. Millhouse\n,53 E. Milotti\n,249, 42 Y. Minenkov,86 N. Mio,250 Ll. M. Mir\n,38 L. Mirasola,251, 60\nM. Miravet-Ten\u00b4es\n,135 C.-A. Miritescu\n,38 A. K. Mishra,21 A. Mishra,15 C. Mishra\n,171 T. Mishra\n,40\nA. L. Mitchell,32, 99 J. G. Mitchell,43 S. Mitra\n,15 V. P. Mitrofanov\n,100 G. Mitselmakher\n,40 R. Mittleman,30\nO. Miyakawa\n,45 S. Miyamoto,152 S. Miyoki\n,45 G. Mo\n,30 L. Mobilia,57, 58 L. M. Modafferi\n,91\nS. R. P. Mohapatra,2 S. R. Mohite\n,10 M. Molina-Ruiz\n,206 C. Mondal,197 M. Mondin,192 M. Montani,57, 58\nC. J. Moore,110 M. Morales,50 D. Moraru,4 F. Morawski,85 A. More\n,15 S. More\n,15 C. Moreno\n,43 G. Moreno,4\nS. Morisaki\n,36, 152 Y. Moriwaki\n,151 G. Morras\n,112 A. Moscatello\n,80 P. Mourier\n,91 B. Mours\n,61\nC. M. Mow-Lowry\n,32, 99 S. Mozzon\n,122 F. Muciaccia\n,107, 60 D. Mukherjee\n,243 Samanwaya Mukherjee,15\nSoma Mukherjee,161 Subroto Mukherjee,83 Suvodip Mukherjee\n,252, 169, 96 N. Mukund\n,30 A. Mullavey,59\nJ. Munch,88 C. L. Mungioli,27 M. Munn,4 W. R. Munn Oberg,253 M. Murakoshi,254 P. G. Murray\n,26 S. Muusse,12\nS. L. Nadji,13, 14 A. Nagar,25, 255 N. Nagarajan\n,26 K. N. Nagler,43 K. Nakamura\n,22 H. Nakano\n,256 M. Nakano,2\nD. Nandi,11 V. Napolano,52 P. Narayan,199 I. Nardecchia\n,132, 86 H. Narola,68 L. Naticchioni\n,60 R. K. Nayak\n,257\nB. F. Neil,27 J. Neilson,87, 105 A. Nelson,128 T. J. N. Nelson,59 M. Nery,13, 14 A. Neunzert\n,4 S. Ng,50 C. Nguyen\n,63\nP. Nguyen,69 L. Nguyen Quynh\n,258 S. A. Nichols,11 A. B. Nielsen\n,259 G. Nieradka,85 A. Niko\n,142\nY. Nishino,22, 260 A. Nishizawa\n,36 S. Nissanke,96, 32 E. Nitoglia\n,153 W. Niu,9 F. Nocera,52 M. Norman,19\nC. North,19 J. Novak\n,108, 261, 262, 263 J. F. Nu\u02dcno Siles\n,112 G. Nurbek,161 L. K. Nuttall\n,122 K. Obayashi,254\nJ. Oberling\n,4 J. O\u2019Dell,211 M. Oertel\n,108, 261, 262, 264, 263 A. Offermans,101 G. Oganesyan,39, 113 J. J. Oh\n,232\nK. Oh\n,212 S. H. Oh\n,232 T. O\u2019Hanlon,59 M. Ohashi\n,45 M. Ohkawa\n,209 F. Ohme\n,13, 14 H. Ohta,36\nA. S. Oliveira\n,159 R. Oliveri\n,108, 261, 262 V. Oloworaran,27 B. O\u2019Neal,116 K. Oohara\n,265, 266 B. O\u2019Reilly\n,59\nN. D. Ormsby,116 M. Orselli\n,46, 78 R. O\u2019Shaughnessy\n,204 Y. Oshima\n,267 S. Oshino\n,45 S. Ossokine\n,1\nC. Osthelder,2 D. J. Ottaway\n,88 A. Ouzriat,153 H. Overmier,59 B. J. Owen\n,158 A. E. Pace,9 R. Pagano\n,11\nM. A. Page\n,22 A. Pai,139 S. A. Pai,95 A. Pal,268 S. Pal\n,257 M. A. Palaia\n,20, 77 O. Palashov,213 M. P\u00b4alfi,187\nP. P. Palma,132, 86 C. Palomba\n,60 K. C. Pan\n,141 P. K. Panda,216 L. Panebianco,57, 58 P. T. H. Pang,32, 68\nF. Pannarale\n,107, 60 B. C. Pant,95 F. H. Panther,27 C. D. Panzer\n,89 F. Paoletti\n,20 A. Paoli,52 A. Paolone,60, 269\nE. E. Papalexakis,126 L. Papalini\n,20, 77 G. Papigkiotis,270 A. Parisi\n,32, 96 J. Park\n,230 W. Parker\n,59\nG. Pascale,13, 14 D. Pascucci\n,84 A. Pasqualetti,52 R. Passaquieti\n,77, 20 D. Passuello,20 O. Patane\n,4 M. Patel,116\nD. Pathak,15 M. Pathak,88 A. Patra,19 B. Patricelli\n,77, 20 A. S. Patron,11 S. Paul\n,69 E. Payne\n,2 T. Pearce,19\nM. Pedraza,2 R. Pegna\n,20 A. Pele\n,2 F. E. Pe\u02dcna Arellano\n,45 S. Penn\n,253 M. D. Penuliar,50 A. Perego\n,102, 103\nA. Pereira,123 J. J. Perez,40 C. P\u00b4erigois\n,154, 81, 80 C. C. Perkins,40 G. Perna\n,80 A. Perreca\n,102, 103 J. Perret,63\nS. Perri`es\n,153 J. W. Perry,32, 99 D. Pesios,270 C. Petrillo,78 H. P. Pfeiffer\n,1 H. Pham,59 K. A. Pham\n,89\nK. S. Phukon\n,110, 32, 223 H. Phurailatpam,137 O. J. Piccinni\n,38 M. Pichot\n,44 M. Piendibene\n,77, 20\nF. Piergiovanni\n,57, 58 L. Pierini\n,60 G. Pierra\n,153 V. Pierro\n,87, 105 M. Pietrzak,85 M. Pillas,35 F. Pilo\n,20\nL. Pinard,166 C. Pineda-Bosque,192 I. M. Pinto\n,87, 105, 271, 29 M. Pinto,52 B. J. Piotrzkowski\n,10 M. Pirello,4\nM. D. Pitkin\n,16, 207 A. Placidi\n,46, 78 E. Placidi\n,107, 60 M. L. Planas\n,91 W. Plastino\n,272, 273 R. Poggiani\n,77, 20\nE. Polini\n,28 L. Pompili\n,1 J. Poon,137 E. Porcelli,32 J. Portell\n,37, 72, 246 E. K. Porter,63 C. Posnansky,9\nR. Poulton\n,52 J. Powell\n,155 M. Pracchia,28 B. K. Pradhan\n,15 T. Pradier,61 A. K. Prajapati,83 K. Prasai,18\nR. Prasanna,216 P. Prasia,15 G. Pratten\n,110 M. Principe,133, 87, 271, 105 G. A. Prodi\n,274, 103 L. Prokhorov,110\nP. Prosposito,132, 86 L. Prudenzi,1 A. Puecher,32, 68 J. Pullin\n,11 M. Punturo\n,46 F. Puosi,20, 77 P. Puppo,60\nM. P\u00a8urrer\n,160 H. Qi\n,144 J. Qin\n,12 G. Qu\u00b4em\u00b4ener\n,198, 108, 197 V. Quetschke,161 C. Quigley,19 P. J. Quinonez,43\nR. Quitzow-James,97 F. J. Raab\n,4 G. Raaijmakers,96, 32 N. Radulesco,44 P. Raffai\n,187 S. X. Rail,237\nS. Raja,95 C. Rajan,95 B. Rajbhandari\n,204, 158 D. S. Ramirez,43 K. E. Ramirez\n,59 F. A. Ramis Vidal\n,91\nA. Ramos-Buades\n,1 D. Rana,15 E. Randel,98 S. Ranjan\n,53 P. Rapagnani\n,107, 60 B. Ratto,43 S. Rawat,89\nA. Ray\n,10 V. Raymond\n,19 M. Razzano\n,77, 20 J. Read,50 M. Recaman Payo,101 T. Regimbau,28 L. Rei\n,51\nS. Reid,90 S. W. Reid,116 D. H. Reitze\n,2 P. Relton\n,19 A. Renzini,2 P. Rettegno\n,25 B. Revenu\n,63, 275\nA. Reza,32 M. Rezac,50 A. S. Rezaei\n,60, 107 F. Ricci,107, 60 M. Ricci,60 D. Richards,211 C. J. Richardson\n,43\nJ. W. Richardson\n,126 A. Rijal,43 K. Riles\n,79 H. K. Riley,19 S. Rinaldi\n,77, 20 J. Rittmeyer,76 C. Robertson,211\nF. Robinet,35 M. Robinson,4 A. Rocchi\n,86 L. Rolland\n,28 J. G. Rollins\n,2 M. Romanelli,109 A. E. Romano,276\nR. Romano\n,5, 6 A. Romero\n,175 I. M. Romero-Shaw,16 J. H. Romie,59 S. Ronchini\n,39, 113 T. J. Roocke\n,88\nL. Rosa,6, 29 T. J. Rosauer,126 C. A. Rose,10 D. Rosi\u00b4nska\n,117 M. P. Ross\n,48 M. Rossello\n,91 S. Rowan\n,26\nS. K. Roy,178, 179 S. Roy,68 D. Rozza\n,164, 130 P. Ruggi,52 E. Ruiz Morales\n,277, 112 K. Ruiz-Rocha,190\nS. Sachdev\n,53 T. Sadecki,4 J. Sadiq\n,124 P. Saffarieh,32, 99 M. R. Sah,252 S. S. Saha\n,141 T. Sainrat,61\n\n5\nS. Sajith Menon,196, 107, 60 K. Sakai,278 M. Sakellariadou\n,64 T. Sako,151 S. Sakon\n,9 O. S. Salafia\n,156, 120, 119\nF. Salces-Carcoba\n,2 L. Salconi,52 M. Saleem\n,89 F. Salemi\n,107, 60 M. Sall\u00b4e\n,32 S. Salvador\n,198, 197, 108\nA. Sanchez,4 E. J. Sanchez,2 J. H. Sanchez\n,71 L. E. Sanchez,2 N. Sanchis-Gual\n,279, 135 J. R. Sanders,280\nE. M. S\u00a8anger,1 T. R. Saravanan,15 N. Sarin,8 A. Sasli\n,270 P. Sassi\n,46, 78 B. Sassolas\n,166 H. Satari,27\nR. Sato,209 S. Sato,151 Y. Sato,151 O. Sauter\n,40 R. L. Savage\n,4 T. Sawada\n,45 H. L. Sawant,15 S. Sayah,28\nD. Schaetzl,2 M. Scheel,148 J. Scheuer,71 M. G. Schiworski\n,88 P. Schmidt\n,110 S. Schmidt\n,68 R. Schnabel\n,76\nM. Schneewind,13, 14 R. M. S. Schofield,69 K. Schouteden,101 H. Schuler,9 B. W. Schulte,13, 14 B. F. Schutz,19, 13, 14\nE. Schwartz\n,19 J. Scott\n,26 S. M. Scott\n,12 T. C. Seetharamu,26 M. Seglar-Arroyo\n,38 Y. Sekiguchi\n,281\nD. Sellers,59 A. S. Sengupta\n,282 D. Sentenac,52 E. G. Seo\n,26 J. W. Seo\n,101 V. Sequino,29, 6 A. Sergeev,213\nM. Serra\n,60 G. Servignat\n,261 Y. Setyawati\n,68 T. Shaffer,4 U. S. Shah\n,53 M. S. Shahriar\n,71\nM. A. Shaikh\n,229 B. Shams,186 L. Shao\n,214 A. K. Sharma,21 P. Sharma,95 S. Sharma-Chaudhary,97\nP. Shawhan\n,118 N. S. Shcheblanov\n,283, 239 B. Shen,118 Y. Shikano\n,284, 285 M. Shikauchi,36 K. Shimode\n,45\nH. Shinkai\n,286 J. Shiota,254 D. H. Shoemaker\n,30 D. M. Shoemaker\n,147 R. W. Short,4 S. ShyamSundar,95\nA. Sider,33 H. Siegel\n,159, 178, 179 M. Sieniawska,115 D. Sigg\n,4 L. Silenzi\n,46, 47 M. Simmonds,88 L. P. Singer\n,75\nA. Singh,199 D. Singh\n,9 M. K. Singh\n,21 A. Singha\n,31, 32 A. M. Sintes\n,91 V. Sipala,164, 130 V. Skliris\n,19\nB. J. J. Slagmolen\n,12 T. J. Slaven-Blair,27 J. Smetana,110 J. R. Smith\n,50 L. Smith\n,26 R. J. E. Smith\n,8\nW. J. Smith,190 J. Soldateschi\n,240, 287, 58 S. N. Somala\n,288 K. Somiya\n,3 K. Soni\n,15 S. Soni\n,30 V. Sordini,153\nF. Sorrentino,51 N. Sorrentino\n,77, 20 R. Soulard,44 T. Souradeep,15, 289 A. Southgate,19 E. Sowell,158\nV. Spagnuolo,31, 32 A. P. Spencer\n,26 M. Spera\n,80, 81 P. Spinicelli,52 A. K. Srivastava,83 F. Stachurski\n,26\nD. A. Steer\n,63 J. Steinlechner,31, 32 S. Steinlechner\n,31, 32 N. Stergioulas\n,270 P. Stevens,35 M. StPierre,160\nL. C. Strang,129 G. Stratta\n,290, 291, 60, 292 M. D. Strong,11 A. Strunk,4 R. Sturani,293 A. L. Stuver\n,94\nM. Suchenek,85 S. Sudhagar\n,15, 85 N. Sueltmann,76 A. G. Sullivan\n,159 K. D. Sullivan,11 L. Sun\n,12 S. Sunil,83\nA. Sur\n,85 J. Suresh\n,36, 115 P. J. Sutton\n,19 Takamasa Suzuki\n,209 Takanori Suzuki,3 B. L. Swinkels\n,32\nA. Syx,61 M. J. Szczepa\u00b4nczyk\n,40 P. Szewczyk\n,117 M. Tacca\n,32 H. Tagoshi\n,152 S. C. Tait\n,26\nH. Takahashi\n,294 R. Takahashi\n,22 A. Takamori\n,49 K. Takatani,189 H. Takeda\n,295 M. Takeda,189\nC. J. Talbot,90 C. Talbot,30 M. Tamaki,152 N. Tamanini\n,121 D. Tanabe,142 K. Tanaka,296 S. J. Tanaka\n,254\nT. Tanaka\n,295 A. J. Tanasijczuk,115 D. Tang,27 S. Tanioka\n,70 D. B. Tanner,40 L. Tao\n,40 R. D. Tapia,9\nE. N. Tapia San Mart\u00b4\u0131n\n,32 R. Tarafder,2 C. Taranto,132, 86 A. Taruya\n,297 J. D. Tasson\n,172 M. Teloi,33\nR. Tenorio\n,91 H. Themann,192 A. Theodoropoulos,135 M. P. Thirugnanasambandam,15 L. M. Thomas\n,110\nM. Thomas,59 P. Thomas,4 J. E. Thompson\n,148 S. R. Thondapu,95 K. A. Thorne,59 E. Thrane,8 J. Tissino\n,39\nA. Tiwari,15 Shubhanshu Tiwari\n,176 Srishti Tiwari\n,15 V. Tiwari\n,110 M. R. Todd,70 A. M. Toivonen\n,89\nK. Toland\n,26 A. E. Tolley\n,122 T. Tomaru\n,22 K. Tomita,189 T. Tomura\n,45 C. Tong-Yu,142 A. Toriyama,254\nN. Toropov\n,110 A. Torres-Forn\u00b4e\n,135, 136 C. I. Torrie,2 M. Toscani\n,121 I. Tosta e Melo\n,298 E. Tournefier\n,28\nA. A. Trani\n,36 A. Trapananti\n,47, 46 F. Travasso\n,47, 46 G. Traylor,59 J. Trenado\n,37 M. Trevor,118\nM. C. Tringali\n,52 A. Tripathee\n,79 L. Troiano,299, 105 A. Trovato\n,42, 249 L. Trozzo,6 R. J. Trudeau,2\nT. T. L. Tsang\n,19 R. Tso,148, \u2020 S. Tsuchida\n,300 L. Tsukada,9 T. Tsutsui\n,36 K. Turbang\n,175, 106 M. Turconi\n,44\nC. Turski,84 H. Ubach\n,37, 72 A. S. Ubhi,110 T. Uchiyama\n,45 R. P. Udall\n,2 T. Uehara\n,301 K. Ueno\n,36\nC. S. Unnikrishnan,252 T. Ushiba\n,45 A. Utina\n,31, 32 M. Vacatello\n,20, 77 H. Vahlbruch\n,13, 14 N. Vaidya\n,2\nG. Vajente\n,2 A. Vajpeyi,8 G. Valdes\n,128 J. Valencia,91 M. Valentini\n,99, 32 S. A. Vallejo-Pe\u02dcna,276 S. Vallero,25\nV. Valsan\n,10 N. van Bakel,32 M. van Beuzekom\n,32 M. van Dael\n,32, 302 J. F. J. van den Brand\n,31, 99, 32\nC. Van Den Broeck,68, 32 D. C. Vander-Hyde,70 M. van der Sluys\n,32, 68 A. Van de Walle,35 J. van Dongen\n,32, 99\nK. Vandra,94 H. van Haevermaet\n,106 J. V. van Heijningen\n,115 J. Vanosky,2 M. H. P. M. van Putten\n,303\nZ. van Ranst\n,31, 32 N. van Remortel\n,106 M. Vardaro,31, 32 A. F. Vargas,129 V. Varma\n,1 M. Vas\u00b4uth\n,74\nA. Vecchio\n,110 G. Vedovato,81 J. Veitch\n,26 P. J. Veitch\n,88 S. Venikoudis,115 J. Venneberg\n,13, 14 P. Verdier\n,153\nD. Verkindt\n,28 B. Verma,134 P. Verma,173 Y. Verma\n,95 S. M. Vermeulen\n,2 D. Veske\n,159 F. Vetrano,57\nA. Veutro,60 A. M. Vibhute\n,4 A. Vicer\u00b4e\n,57, 58 S. Vidyant,70 A. D. Viets\n,304 A. Vijaykumar\n,21 A. Vilkha,204\nV. Villa-Ortega\n,124 E. T. Vincent\n,53 J.-Y. Vinet,44 S. Viret,153 A. Virtuoso\n,249, 42 S. Vitale\n,30 H. Vocca,78, 46\nD. Voigt\n,76 E. R. G. von Reis,4 J. S. A. von Wrangel,13, 14 S. P. Vyatchanin\n,100 L. E. Wade,67 M. Wade\n,67\nK. J. Wagner\n,204 R. C. Walet,32 M. Walker,116 G. S. Wallace,90 L. Wallace,2 H. Wang\n,267 J. Z. Wang,79\nW. H. Wang,161 Z. Wang,142 G. Waratkar\n,139 R. L. Ward,12 J. Warner,4 M. Was\n,28 T. Washimi\n,22\nN. Y. Washington,2 D. Watarai,36 K. E. Wayt,67 B. Weaver,4 C. R. Weaving,122 S. A. Webster,26 M. Weinert,13, 14\nA. J. Weinstein\n,2 R. Weiss,30 C. M. Weller,48 R. A. Weller\n,190 F. Wellmann,13, 14 L. Wen,27 P. We\u00dfels,13, 14\nK. Wette\n,12 J. T. Whelan\n,204 D. D. White,50 B. F. Whiting\n,40 C. Whittle\n,30 J. B. Wildberger,1 O. S. Wilk,67\n\n6\nD. Wilken\n,13, 14, 14 K. Willetts,19 D. Williams\n,26 M. J. Williams\n,26 N. S. Williams,110 J. L. Willis\n,2\nB. Willke\n,14, 13, 14 M. Wils\n,101 C. C. Wipf,2 G. Woan\n,26 J. Woehler,31, 32 J. K. Wofford\n,204 N. E. Wolfe,30\nD. Wong,138 H. T. Wong\n,142 H. W. Y. Wong\n,137 I. C. F. Wong\n,137 J. L. Wright,12 M. Wright\n,26\nC. Wu\n,141 D. S. Wu\n,13, 14 H. Wu\n,141 D. M. Wysocki\n,10 L. Xiao\n,2 V. A. Xu\n,30 Y. Xu\n,176 N. Yadav\n,85\nH. Yamamoto\n,2 K. Yamamoto\n,151 M. Yamamoto,151 T. S. Yamamoto\n,236 T. Yamamoto\n,45 S. Yamamura,152\nR. Yamazaki\n,254 S. Yan,18 T. Yan,110 F. W. Yang\n,186 F. Yang,159 K. Z. Yang\n,89 L.-C. Yang,145 Y. Yang\n,145\nZ. Yarbrough\n,11 S.-W. Yeh,141 A. B. Yelikar\n,204 S. M. C. Yeung,10 X. Yin,30 J. Yokoyama\n,36 T. Yokozawa,45\nJ. Yoo\n,149 H. Yu\n,148 H. Yuzurihara\n,45 A. Zadro\u02d9zny,173 A. J. Zannelli,116 M. Zanolin,43 M. Zeeshan\n,204\nT. Zelenova,52 J.-P. Zendri,81 M. Zeoli,111, 115 M. Zerrad,34, 226 M. Zevin\n,71 A. C. Zhang,159 J. Zhang\n,12\nL. Zhang,2 R. Zhang\n,40 T. Zhang,110 Y. Zhang\n,12 C. Zhao\n,27 Yue Zhao,186 Yuhang Zhao\n,152, 22, 63\nY. Zheng\n,97 H. Zhong\n,89 S. Zhong,27 R. Zhou,206 Z.-H. Zhu\n,127, 305 M. E. Zucker,30, 2 and J. Zweizig\n2\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\nT. Fujimori,189 H. Fujimoto\n,267 T. Fujita\n,306, 36 Y. Manita\n,295 I. Obata\n,307 and H. Takidera267\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3Graduate School of Science, Tokyo Institute of Technology,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n4LIGO Hanford Observatory, Richland, WA 99352, USA\n5Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n6INFN, Sezione di Napoli, I-80126 Napoli, Italy\n7University of Warwick, Coventry CV4 7AL, United Kingdom\n8OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n9The Pennsylvania State University, University Park, PA 16802, USA\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11Louisiana State University, Baton Rouge, LA 70803, USA\n12OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n13Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n14Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n15Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n16University of Cambridge, Cambridge CB2 1TN, United Kingdom\n17Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n18Stanford University, Stanford, CA 94305, USA\n19Cardiff University, Cardiff CF24 3AA, United Kingdom\n20INFN, Sezione di Pisa, I-56127 Pisa, Italy\n21International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n22Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n23Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n24Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n25INFN Sezione di Torino, I-10125 Torino, Italy\n26SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n27OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n28Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n29Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n30LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n31Maastricht University, 6200 MD Maastricht, Netherlands\n32Nikhef, 1098 XG Amsterdam, Netherlands\n33Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n34Institut Fresnel, Aix Marseille Universit\u00b4e, CNRS, Centrale Marseille, F-13013 Marseille, France\n35Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n36University of Tokyo, Tokyo, 113-0033, Japan.\n37Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n38Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n39Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n40University of Florida, Gainesville, FL 32611, USA\n41Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n42INFN, Sezione di Trieste, I-34127 Trieste, Italy\n\n7\n43Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n44Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n45Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n46INFN, Sezione di Perugia, I-06123 Perugia, Italy\n47Universit`a di Camerino, I-62032 Camerino, Italy\n48University of Washington, Seattle, WA 98195, USA\n49Earthquake Research Institute, The University of Tokyo,\n1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n50California State University Fullerton, Fullerton, CA 92831, USA\n51INFN, Sezione di Genova, I-16146 Genova, Italy\n52European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n53Georgia Institute of Technology, Atlanta, GA 30332, USA\n54Chennai Mathematical Institute, Chennai 603103, India\n55Royal Holloway, University of London, London TW20 0EX, United Kingdom\n56The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n57Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n58INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n59LIGO Livingston Observatory, Livingston, LA 70754, USA\n60INFN, Sezione di Roma, I-00185 Roma, Italy\n61Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n62Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n63Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n64King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n65Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n66Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n67Kenyon College, Gambier, OH 43022, USA\n68Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n69University of Oregon, Eugene, OR 97403, USA\n70Syracuse University, Syracuse, NY 13244, USA\n71Northwestern University, Evanston, IL 60208, USA\n72Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n73Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n74Wigner RCP, RMKI, H-1121 Budapest, Hungary\n75NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n76Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n77Universit`a di Pisa, I-56127 Pisa, Italy\n78Universit`a di Perugia, I-06123 Perugia, Italy\n79University of Michigan, Ann Arbor, MI 48109, USA\n80Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n81INFN, Sezione di Padova, I-35131 Padova, Italy\n82Montana State University, Bozeman, MT 59717, USA\n83Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n84Universiteit Gent, B-9000 Gent, Belgium\n85Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n86INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n87Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n88OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n89University of Minnesota, Minneapolis, MN 55455, USA\n90SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n91IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n92Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n93Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n94Villanova University, Villanova, PA 19085, USA\n95RRCAT, Indore, Madhya Pradesh 452013, India\n96GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n97Missouri University of Science and Technology, Rolla, MO 65409, USA\n98Colorado State University, Fort Collins, CO 80523, USA\n99Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n\n8\n100Lomonosov Moscow State University, Moscow 119991, Russia\n101Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n102Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n103INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n104Bar-Ilan University, Ramat Gan, 5290002, Israel\n105INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n106Universiteit Antwerpen, 2000 Antwerpen, Belgium\n107Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n108Centre national de la recherche scientifique, 75016 Paris, France\n109Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n110University of Birmingham, Birmingham B15 2TT, United Kingdom\n111Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n112Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n113INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n114Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n115Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n116Christopher Newport University, Newport News, VA 23606, USA\n117Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n118University of Maryland, College Park, MD 20742, USA\n119Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n120INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n121L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse,\nCNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n122University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n123Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n124IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n125University of Chicago, Chicago, IL 60637, USA\n126University of California, Riverside, Riverside, CA 92521, USA\n127Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n128Texas A&M University, College Station, TX 77843, USA\n129OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n130INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n131Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n132Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n133University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n136Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n137The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n138University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n139Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n140Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142National Central University, Taoyuan City 320317, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Queen Mary University of London, London E1 4NS, United Kingdom\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n146Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Cornell University, Ithaca, NY 14850, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n153Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS,\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n\n9\n154INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n157Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n158Texas Tech University, Lubbock, TX 79409, USA\n159Columbia University, New York, NY 10027, USA\n160University of Rhode Island, Kingston, RI 02881, USA\n161The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n162Bellevue College, Bellevue, WA 98007, USA\n163Scuola Normale Superiore, I-56126 Pisa, Italy\n164Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n165The University of Sheffield, Sheffield S10 2TN, United Kingdom\n166Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n167Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n168INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n169Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n170Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n171Indian Institute of Technology Madras, Chennai 600036, India\n172Carleton College, Northfield, MN 55057, USA\n173National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n174Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n175Vrije Universiteit Brussel, 1050 Brussel, Belgium\n176University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n177Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n178Stony Brook University, Stony Brook, NY 11794, USA\n179Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n180Montclair State University, Montclair, NJ 07043, USA\n181Institute for Nuclear Research, H-4026 Debrecen, Hungary\n182CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n183Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n184Western Washington University, Bellingham, WA 98225, USA\n185SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n186The University of Utah, Salt Lake City, UT 84112, USA\n187E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n188Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n189Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n190Vanderbilt University, Nashville, TN 37235, USA\n191Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n192California State University, Los Angeles, Los Angeles, CA 90032, USA\n193Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n194University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n195INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n196Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n197Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n198Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n199The University of Mississippi, University, MS 38677, USA\n200Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n201Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n202American University, Washington, DC 20016, USA\n203University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n204Rochester Institute of Technology, Rochester, NY 14623, USA\n205Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n206University of California, Berkeley, CA 94720, USA\n207University of Lancaster, Lancaster LA1 4YW, United Kingdom\n208College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n\n10\n209Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n210Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n211Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n212Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n213Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n214Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n215Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n216Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n217University of Bia lystok, 15-424 Bia lystok, Poland\n218National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n219School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n220University of Southampton, Southampton SO17 1BJ, United Kingdom\n221Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n222Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n223Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n224Chung-Ang University, Seoul 06974, Republic of Korea\n225University of Washington Bothell, Bothell, WA 98011, USA\n226Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n227Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n228Ewha Womans University, Seoul 03760, Republic of Korea\n229Seoul National University, Seoul 08826, Republic of Korea\n230Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n231Sungkyunkwan University, Seoul 03063, Republic of Korea\n232National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n233Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n234Bard College, Annandale-On-Hudson, NY 12504, USA\n235Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n236Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n237Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n238Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n239NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n240Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n241Department of Physics, University of Trento, via Sommarive 14, Povo, 38123 TN, Italy\n242National Center for High-performance computing,\nNational Applied Research Laboratories, No.\n7, R&D 6th Rd.,\nHsinchu Science Park, Hsinchu City 30076, Taiwan\n243NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n244West Virginia University, Morgantown, WV 26506, USA\n245School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n246Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n247Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n248Tsinghua University, Beijing 100084, China\n249Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n250Institute for Photon Science and Technology, The University of Tokyo,\n2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n251INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n252Tata Institute of Fundamental Research, Mumbai 400005, India\n253Hobart and William Smith Colleges, Geneva, NY 14456, USA\n254Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n\n11\n255Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n256Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n257Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n258Department of Physics and Astronomy, University of Notre Dame,\n225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n259University of Stavanger, 4021 Stavanger, Norway\n260Department of Astronomy, The University of Tokyo,\n7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n261Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n262Observatoire de Paris, 75014 Paris, France\n263Universit\u00b4e PSL, 75006 Paris, France\n264Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n265Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n266Niigata Study Center, The Open University of Japan, 754 Ichibancho,\nAsahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan\n267Department of Physics, The University of Tokyo,\n7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n268CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n269Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n270Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n271Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n272Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n273INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n274Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n275Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n276Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n277Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n278Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n279Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research\nand Development in Mathematics and Applications, 3810-183 Aveiro, Portugal\n280Marquette University, Milwaukee, WI 53233, USA\n281Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n282Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n283Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n284Graduate School of Science and Technology, Gunma University,\n4-2 Aramaki, Maebashi, Gunma 371-8510, Japan\n285Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n286Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n287INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n288Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n289Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n290Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at,\nMax-von-Laue-Str.\n1, 60438 Frankfurt am Main, Germany\n291Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n292INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n293Universidade Estadual Paulista, 01140-070 Campinas, S\u02dcao Paulo, Brazil\n294Research Center for Space Science, Advanced Research Laboratories,\nTokyo City University, 8-15-1 Todoroki, Setagaya, Tokyo 158-0082, Japan\n295Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n296Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n297Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n298University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n\n12\n299Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n300National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n301Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n302Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n303Department of Physics and Astronomy, Sejong University,\n209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n304Concordia University Wisconsin, Mequon, WI 53097, USA\n305School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n306Waseda Institute for Advanced Study, Waseda University,\n1-6-1 Nishi-Waseda, Shinjuku, Tokyo 169-8050, Japan\n307Kavli Institute for the Physics and Mathematics of the Universe,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\nAmong the various candidates for dark matter (DM), ultralight vector DM can be probed by laser\ninterferometric gravitational wave detectors through the measurement of oscillating length changes\nin the arm cavities. In this context, KAGRA has a unique feature due to differing compositions\nof its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels.\nHere we present the result of a search for U(1)B\u2212L gauge boson DM using the KAGRA data from\nauxiliary length channels during the first joint observation run together with GEO600. By applying\nour search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds\non the coupling strength between the U(1)B\u2212L gauge boson and ordinary matter are obtained for\na range of DM masses. While our constraints are less stringent than those derived from previous\nexperiments, this study demonstrates the applicability of our method to the lower-mass vector DM\nsearch, which is made difficult in this measurement by the short observation time compared to the\nauto-correlation time scale of DM.\nI.\nINTRODUCTION\nRecently, a number of novel dark matter (DM) searches\nusing laser interferometric gravitational wave (GW) de-\ntectors have been proposed [1\u20136] and conducted [7\u201311].\nBecause of their extremely high sensitivity to the dif-\nferential length changes of their arms in the frequency\nrange O(10 \u2212103) Hz, they can probe the interaction\nbetween the detector and DMs, which have masses of\nO(10\u221214\u221210\u221211) eV/c2 and therefore oscillate coherently\nwithin this frequency band. Vector DM (or so-called dark\nphoton DM) interacts with test masses of the interfer-\nometer, for example, via a coupling to the baryon (B) or\nbaryon minus lepton (B\u2212L) number current. Because of\nthe non-relativistic dispersion (under the standard halo\nmodel [12, 13]), the vector DM field exerted on the test\nmasses behave as an oscillating dark electric force, in-\nducing a measurable change in the differential length of\nthe arm cavity. Vector DMs of this type, which we re-\nfer to as U(1)B and U(1)B\u2212L gauge boson, were previ-\nously searched in Ref. [9] by using the latest observational\ndata from the Advanced LIGO [14\u201316] and Virgo [17, 18]\ndetectors. Remarkably, the constraint on the coupling\nstrength of vector DM to baryons from GW interfer-\nometers surpasses those from existing experiments such\nas the E\u00a8ot-Wash torsion balance [19, 20] and MICRO-\nSCOPE [21\u201323], by orders of magnitude for certain fre-\n\u2217Deceased, November 2022.\n\u2020 Deceased, July 2023.\nquency bands. Similarly, dilatonic DM, whose interac-\ntion alters the apparent electron mass or the fine struc-\nture constant, was probed with data from the GEO600\ninterferometer [10, 24, 25]. These searches highlight the\npotential of GW detectors as direct probes of ultralight\nDM.\nA Japanese laser interferometric GW detector, KA-\nGRA [26\u201328], can also probe the vector DM interaction,\nbut in a relatively unique way compared to the previ-\nous searches.\nFor the Advanced LIGO and Virgo de-\ntectors, all the mirrors (including test masses) are made\nof the same material (fused silica), in other words, they\nhave a common charge-to-mass ratio with respect to the\ndark electric field.\nBecause the spatial variation scale\n(so-called coherence length) of the ultralight DM field\nis O(105 \u2212108)km in our target mass range, all mirrors\nof each detector, which are separated only a few kilo-\nmeters, respond to the vector field nearly identically. In\ncontrast, KAGRA employs sapphire for cryogenic test\nmasses and fused silica for room temperature auxiliary\nmirrors. Therefore, owing to the difference in the charge-\nto-mass ratios, those mirrors respond differently to the\nvector field, and the vector DM signal in the (differential)\nlength change can be enhanced for auxiliary length moni-\ntors [3, 29]. Especially in the case of U(1)B\u2212L, where the\ndifference in charge-mass ratio is relatively large, these\nchannels are shown to have better sensitivity to vector\nDM than existing experiments in certain low frequency\nbands, when KAGRA reaches design sensitivity [3].\nIn this work, we conduct an ultralight vector DM\nsearch with KAGRA using the data of its auxiliary length\n\n13\nchange monitors during the first joint observation run\ntogether with GEO600 (O3GK) [30]. Although the de-\ntector was in operation for two weeks during O3GK,\nthe durations of the contiguous data segments were at\nmost about 7 hours [31]. For our target mass range, this\nduration can be comparable to or smaller than the so-\ncalled coherence time, within which the amplitude and\nthe phase of DM can be regarded as a constant. Since\neach such measurement is one realization of a random\nfield, their stochasticity needs to be taken into account,\nespecially when setting the upper bound on the coupling\nstrength of the ultralight DM. Therefore, our pipeline\nis constructed based on a recent study [32], which thor-\noughly investigates the stochastic nature of the ultra-\nlight vector DM. Using the detection statistic discussed\nin Ref. [32], we numerically derive upper limits on the\ncoupling strength incorporating the stochastic nature of\nthe DM. On the other hand, various noise lines [31] re-\nsult in a false detection as a DM signal. In order to dis-\ntinguish outliers, we have implemented veto procedures\nmaking use of expected features of ultralight DM signals.\nThe rest of the paper is organized as follows. We first\nintroduce our model of ultralight vector DM and discuss\nits stochastic nature in Sec. II. After describing our search\nmethod in Sec. III, the results of our analysis using O3GK\ndata are presented in Sec. IV. Sec. V provides a discussion\nof these results and of the prospects for future searches.\nII.\nDARK MATTER SEARCH WITH KAGRA\nA.\nVector Dark Matter Model\nIn this work, we consider a ultralight vector dark mat-\nter field A\u00b5(t, x), which is regarded as a gauge boson of\nU(1)D gauge symmetry with D being a label for a charge,\nsuch as B and B \u2212L. We assume it interacts with ordi-\nnary matter through the coupling to the U(1)D current\nJ\u00b5\nD. The Lagrangian density L is then given as\nL = \u2212\u03b50c2\n4 F \u00b5\u03bdF\u00b5\u03bd + \u03b50\n2\n\u0012mAc2\n\u210f\n\u00132\nA\u00b5A\u00b5 \u2212\u03f5DeJ\u00b5\nDA\u00b5,\n(1)\nwhere F\u00b5\u03bd = \u2202\u00b5A\u03bd \u2212\u2202\u03bdA\u00b5 is the field strength, c is the\nspeed of light, \u210fis the reduced Planck constant, mA is the\nmass of the vector field, \u03b50 is the permittivity of vacuum\nand \u03f5D is the gauge coupling constant normalized by the\nelectromagnetic coupling constant. Since the temporal\ncomponent of the vector field A0 is negligibly small, we\nconsider only its spatial components \u20d7A = (Ax, Ay, Az) in\nthe following discussion.\nAssuming the standard halo model, the local density\nof DM is \u03c1DM \u223c0.4 GeV/cm3, and its virial velocity\nis vvir \u2243220 km/sec around the solar system in our\nGalaxy [12, 13].\nThese profiles imply that DM would\nhave an extremely large number density for the mass\nrange 10\u221222eV/c2 \u2272m \u22721eV/c2 and behave as a clas-\nsical wave oscillating at about the Compton frequency\nfc = mAc2/2\u03c0\u210f. Then, one can describe it as the super-\nposition of plane waves with different velocities \u20d7v(i,n) and\nphases \u03b8(i,n) as\nAi(t, \u20d7x) =\nA\n\u221a\nN\nN\nX\nn=1\ncos\n\u0010\n2\u03c0fc\n\u0010\n1 + v2\n(i,n)/2c2\u0011\nt\n\u2212\u210f\u22121mA\u20d7v(i,n) \u00b7 \u20d7x + \u03b8(i,n)\n\u0011\n,\n(2)\nwhere \u03b8(i,n) is a random variable following a uniform dis-\ntribution over [0, 2\u03c0] and A \u2261\np\n2\u03c1DM\u210f2/\u03b503m2\nAc4. Note\nthat, for simplicity, the absence of correlation between\nthe direction of \u20d7A and \u20d7v is assumed.\nHere \u20d7v(i,n) fol-\nlows the DM velocity distribution of the standard halo\nmodel [13]:\nfSHM(\u20d7v) d3\u20d7v =\n1\n(\u03c0v2\nvir)3/2 exp\n\u0014\n\u2212(\u20d7v + \u20d7v\u2299)2\nv2\nvir\n\u0015\nd3\u20d7v,\n(3)\nwith the solar velocity |\u20d7v\u2299| \u2243232 km/sec.\nThis dis-\ntribution results in the velocity dispersion of the DM\nas \u00afv2 = v2\n\u2299+ (3/2)v2\nvir \u2243O(10\u22126c2).\nIn such a non-\nrelativistic regime, the time derivative of the field dom-\ninates over the spatial derivative. Hence, it can be re-\ngarded as a oscillating dark \u201celectric\u201d field, which induces\ndisplacements of the test masses in GW interferometers\nas \u03b4\u00a8xi = \u03f5De(Q/M) \u02d9Ai.\nAnother feature is that there appears a length scale,\ncalled \u201ccoherence length\u201d, which is evaluated as L =\n2\u03c0\u210f/mA\n\u221a\n\u00afv2 \u223c107km (10\u221213eV \u00b7 c\u22122/mA). This scale\ncharacterizes the spatial variation of the ultralight DMs.\nAs we will see below, the separation of test masses here is\nmuch shorter than L, we can take \u20d7x = 0 in Eq. (2) with-\nout loss of generality and hereafter neglect the position\ndependence of the vector field.\nB.\nAuxiliary length channels of KAGRA\nFrom 2020 April 7 to 2020 April 21, KAGRA con-\nducted its first joint observation run (O3GK) [30, 31],\ntogether with GEO600. The configuration of KAGRA\ninterferometer during O3GK is shown in Fig. 1. Similarly\nto that of LIGO and Virgo, it is based on a Michelson in-\nterferometer with a Fabry-P\u00b4erot cavity in two perpendic-\nular arms. Each arm cavity is formed by the input test\nmass (ITM) and the end test mass (ETM). The main\nchannel to monitor the differential changes caused by\nGWs is called the differential arm length (DARM). The\ndifferential length between the beam splitter (BS) and\ntwo ITMs are controlled so that the Michelson fringe will\nbe at the dark fringe at the anti-symmetric port, and the\nchannel to monitor the differential Michelson interferom-\neter length is called MICH. The power recycling mirror\n(PRM) and two ITMs form a power recycling cavity to\neffectively enhance the input power. The channel to mon-\nitor the power recycling cavity length is called PRCL.\n\n14\nlaser\nPRM\nBS\nITMX\nETMX\nITMY\nETMY\nSRM\nsignal\nrecycling\ncavity\nY-arm cavity\nX-arm cavity\npower\nrecycling\ncavity\nanti-symmetric port\nFIG. 1. The schematic of the KAGRA interferometer. ITM\n(ETM): input (end) test mass, BS: beam splitter, PRM:\npower recycling mirror, SRM: signal recycling mirror.\nDuring O3GK, a signal recycling mirror (SRM) was\ntilted, and the signal recycling cavity was not formed [33].\nInstead, this tilted SRM introduced an optical loss of\n70%, which led to degraded shot noise for the DARM\nreadout. Two auxiliary channels, MICH and PRCL were\nrecorded using different interferometer sensing ports, and\nwere not affected by this optical loss. Using the length\nsymbols in Fig. 1, changes in DARM, MICH and PRCL\ncan be written as\n\u03b4LDARM = \u03b4(Lx \u2212Ly),\n(4)\n\u03b4LMICH = \u03b4(lx \u2212ly),\n(5)\n\u03b4LPRCL = \u03b4[(lx + ly)/2 + lp],\n(6)\nrespectively. Note that each length parameter is given\nas Lx = Ly = 3000m, lx = 26.7m, ly = 23.3m and lp =\n41.6m, all of which are much shorter than the coherence\nlength of DM.\nPrevious vector DM searches using LIGO and Virgo fo-\ncused on DARM channels with the highest displacement\nsensitivity. This sensitivity is equivalent to the sensitiv-\nity to vector DM interactions for both LIGO and Virgo\nemploying room temperature fused silica mirrors for all\nthe mirrors. This situation, however, drastically changes\nfor KAGRA, which employs cryogenic sapphire mirrors\nfor the test masses. As pointed out in Ref. [3], MICH\nand PRCL contain both the fused silica mirrors such as\nPRM and BS, and the sapphire test masses that respond\ndifferently to the vector DM due to the different charge-\nto-mass ratio.\nThis results in the enhancement of the\n(differential) length change caused by vector DM in those\nchannels. Since the difference becomes larger especially\nfor the U(1)B\u2212L gauge boson, hereafter we focus on the\nD = B \u2212L case.\nC.\nSignal in the KAGRA\u2019s auxiliary length\nchannels\nSince the frequency of each plane wave is localized near\nthe Compton frequency as fi = fc\np\n1 + v2\ni /c2 \u223cfc(1 +\nO(10\u22126)), it is convenient to work in the Fourier space.\nLet us consider the Fourier transform of the signal in X\nchannel with duration T and center time t0:\n\u02dchX(f; t0) \u2261\nZ t0+T/2\nt0\u2212T/2\ndt hX(t)e\u22122\u03c0if(t\u2212t0+T/2).\n(7)\nTo simplify the discussion, T is taken to be much shorter\nthan the time scale of Earth\u2019s rotation.\nAs discussed\nin [32], the oscillating length changes of an arm cavity\ncan be decomposed into three contributions referred to\nas charge asymmetry, spatial difference and finite light\ntraveling time [8]. For auxiliary length monitors of in-\nterest here, the dominant contribution is the one from\ncharge asymmetry expressed as\n\u02dchX(f; t0) = i \u03f5De\n2\u03c0f \u2206\n\u0012QD\nM\n\u0013\nli\nX(t0) \u02dcAi(f; t0),\n(8)\nwhere \u2206(QD/M) is the difference of charge to mass ra-\ntio between two mirrors (BS and ITMX/Y) and in our\ncase, it is \u2206(QB\u2212L/M) \u223c0.009/mn with mn being the\nneutron mass [3]. The vector li\nX(t0) is given as\nli\nX(t) =\n\uf8f1\n\uf8f2\n\uf8f3\nni(t) \u2212mi(t),\n(X = MICH)\n1\n2\n\u0000ni(t) + mi(t)\n\u0001\n,\n(X = PRCL),\n(9)\nwhere ni and mi are unit vectors pointing along the or-\nthogonal arm axes depicted in Fig. 1. Here \u02dcAi(f; t0) is\nthe Fourier transform of the field amplitude. Since it is\na superposition of a huge number of partial waves, the\ncentral limit theorem assures that \u02dcAi(f; t0) and conse-\nquently \u02dchX(f; t0) follow a Gaussian distribution. Note\nthat, when the DM density and the distance between the\ntest masses are fixed, this type of contribution results\nin a larger field amplitude and hence in a larger signal\nfor the lower frequencies [3, 32]. This is the reason why\nMICH and SRCL (not available in O3GK) has, under\nthe design sensitivity, the capability of limiting the DM\ncoupling beyond existing limits in the lower frequency\nband.\nAt this point, it is convenient to introduce the so-called\ncoherence time\n\u03c4 \u22612\u03c0/mAv2\nvir \u223c0.3 day\n\u001210\u221213 eV \u00b7 c\u22122\nmA\n\u0013\n,\n(10)\nwhich quantifies the characteristic correlation lifetime of\nthe DM field at different times \u27e8\u02dch\u2217\nX(f; t0)\u02dchX(f; t1)\u27e9. Let\nT be the duration of a single chunk of data and Nch\nbe the number of equal-length chunks. For higher mass\nranges, in general, the coherence time becomes shorter\nthan the duration of each chunk as \u03c4 < T. In this case,\n\n15\nthe amplitude and phase of the DM randomly evolve\nwithin the chunks. While this decoherence reduces the\ngrowth of the signal-to-noise (SNR) ratio in amplitude as\n\u221d(NchT)1/4 [32], each data chunk can be regarded as an\nindependent measurement of DM, and in fact the statis-\ntical treatment can be simplified [32]. For a lower mass\nrange (\u03c4 > T), however, the correlation of the DM field\nbetween different data chunks cannot be neglected. This\nissue will be addressed in the following section describing\nthe search pipeline.\nFinally, let us give a concrete expression of the signal\ncovariance \u27e8\u02dch\u2217\nX(f; t0)\u02dchX(f; t1)\u27e9used in our analysis. By\ncombining Eqs. (2) and (3), it is derived as\nD\n\u02dch\u2217\nX(f; t0)\u02dchX(f; t1)\nE\n= \u03f52\nDe2A2T 2v3\nvir\n32\u03c0\n5\n2 f 2v3\n\u2299\n\u001a\n\u2206\n\u0012QD\nM\n\u0013\u001b2\n\u00d7\nli\nX(t0)lX,i(t1)e\n\u2212\nv2\n\u2299\nv2\nvir\n+2\u03c0ifDM(t1\u2212t0) (I(x+) \u2212I(x\u2212)) .\n(11)\nHere I(x) is a function of the DM frequency and the time\nI(x) = X2\n8\n\u0014\u221a\u03c0XeX2/4\n\u001a\nerf\n\u0012 x\nX \u2212X\n2\n\u0013\n+ erf\n\u0012 x\nX + X\n2\n\u0013\u001b\n\u22124e\u2212x2/X2 sinh(x)\n\u0015\n,\n(12)\nwhere we use the following parametrization,\nx = 2v\u2299\nv2\nvir\nv,\nX =\n2v\u2299\nvvir\np\n1 \u2212i\u03c0v2\nvirc\u22122fDM(t1 \u2212t0)\n, (13)\nand\nv\u00b1\nc \u2261\ns\n2\n\u0012f \u00b1 1/(2T)\nfDM\n\u22121\n\u0013\n,\nx\u00b1 \u22612v\u2299\nv2\nvir\nv\u00b1.\n(14)\nFor t0 = t1, our I(x) coincides with the function \u2206s(fn)\nin Ref. [32], which gives the deterministic part of the\nspectral shape.\nIII.\nSEARCH METHOD\nA.\nDetection statistics\nHere we introduce, and slightly extend, the detection\nstatistic discussed in Ref. [32].\nIt is based on the ex-\nisting methods of continuous GW searches [34\u201336] that\nalso look for a narrow band signal similarly to our case.\nFor comprehensive reviews of those method, see e.g.\nRefs. [37\u201339] The search method discussed in Ref. [32]\nis generally applicable to the ultralight DM searches us-\ning a single detector and interested readers could refer to\nRef. [40] for the application of this detection statistic to\nthe ultralight axion search.\nAs we discussed in Sec. II, the spectrum of the DM\nsignal is localized within the narrow frequency band fc \u2264\nf \u2272fc(1+\u03ba2v2\nvir/c2) where \u03ba is O(1) constant and we set\n\u03ba = 3.17 to guarantee that the fractional loss of signal\npower becomes less than 1%. For each single data chunk,\nwe sum up the spectra over this frequency range:\n\u03c1i(fc) \u2261\nX\nfc\u2264fn\u2264fc(1+\u03ba2v2\nvir/c2)\n4| \u02dcd(fn; ti)|2\nTS(fn; ti) ,\n(15)\nwhere T again is the duration of the data chunks, \u02dcd(fn; ti)\nrepresents the Fourier transform of the i-th data chunk\nand S(fn; ti) is the one-sided noise power spectral density\n(PSD) around t = ti. Note that in order to neglect the\neffect of Earth\u2019s rotation as in Sec. II, T should be small\nenough and hereafter we take T = 30 min.\nIn our pipeline, S(fn; ti) is estimated from \u02dcd(fn; ti)\nby applying the running median and then converting it\nto the mean value by multiplying a correction factor (see\nApp.A of Ref. [41]). In the median estimation, 180 neigh-\nboring frequency bins corresponding to 0.1Hz band width\nare involved so that the effect of DM signal with narrow\nbandwidth can be smeared out. The number of bins in-\nvolved in \u03c1i(fc) is given as\nNbin =\n\u0018\u03ba\u00afv2fc\n\u2206f\n\u0019\n=\n\u0018\n\u03baT\n\u03c4\n\u0019\n,\n(16)\nwhere \u2308x\u2309represents the minimum integer larger than x.\nBy performing the summation over all chunks, we can\ndefine the detection statistics \u03c1 as\n\u03c1(fc) \u2261\nNch\nX\ni\n\u03c1i(fc),\n(17)\nwhere Nch represents the number of chunks. Under the\nassumption of the stationarity and Gaussian distribution\nof noise, \u03c1 follows a \u03c72 distribution with 2NbinNch de-\ngrees of freedom in the absence of signal. We chose the\nthreshold to be the 95% percentile of this distribution.\nB.\nUpper limit estimation\nIn this study, we derive upper limits based on the fre-\nquentist\u2019s method where \u03b2 % confidence level upper limit\nis derived through the integration of the likelihood func-\ntion L(\u03c1(fc); \u03f5\u03b2%\nD ) as\n1 \u2212\u03b2\n100 =\nZ \u03c1obs\n0\nd\u03c1L(\u03c1(fc); \u03f5\u03b2%\nD ).\n(18)\nOne might expect the central limit theorem to be applica-\nble to \u03c1(fc) since the number of chunks is relatively large.\nThere is, however, a non-vanishing cross-correlation be-\ntween different segments \u27e8\u03c1i\u03c1j\u27e9|i\u0338=j \u0338= 0 for |ti \u2212tj| < \u03c4.\nThis correlation prevents the convergence to a Gaussian\ndistribution especially for lower-mass DM and makes the\nanalytical expression of L(\u03c1(fc); \u03f5D) complicated [32]. In\nfact, this analytical expression suffers from numerical in-\nstability for intermediate regimes where the coherence\n\n16\ntime and the duration of chunks are comparable. In our\npipeline, therefore, the 95% upper limit on the coupling\nconstant was numerically derived as follows.\nAssuming that only Gaussian noise \u02dcn(fn; ti) and ul-\ntralight DM signals are present in the data, it can be\nexpressed as \u02dcd(fn; ti) = \u02dcn(fn; ti) + \u02dchX(fn; ti). Therefore,\ndependence of \u03c1 on the coupling constant can be decom-\nposed as\n\u03c1(fc; \u03f5D) =\nX\nti,fn\n4\nTS\n\u0010\n|\u02dcn|2 + 2Re\nh\n\u02dcn\u2217\u02dchX\ni\n+ |\u02dchX|2\u0011\n= N 2 + \u03f5DN \u00b7 S + \u03f52\nDS2.\n(19)\nHere N 2 represents contributions from 2NbinNch unit\nGaussian variables since the noise component in \u03c1 is nor-\nmalized by the PSD. On the other hand, S2 represents\ncontributions solely from the Gaussian signal \u02dchX(fn; ti)\n(also normalized by noise PSD) whose correlation func-\ntion is given as Eq. (11) under the standard halo model\nassumption. N \u00b7S is the contribution from the cross term\nof the unit Gaussian and the normalized signal. For a\nfixed DM mass (or fc), we simulated 105 realizations of\nN 2, S2, N \u00b7S from the covariance of the DM signal (11)\nand the estimated noise PSD Sn(fn; ti). Then we can\nobtain a histogram of \u03c1 that approximates the likelihood\nL(\u03c1(fc); \u03f5D) and depends on the value of \u03f5D. Then the\nvalue of \u03f5D, for which the observed value of the detec-\ntion statistics \u03c1obs(fc) coincides with the 5% percentile of\nthis realization, is identified as the 95% upper limit. We\nwould like to emphasize that our method does not suffer\nfrom the numerical instability mentioned above and that\nit is applicable to arbitrary masses of DM.\nIV.\nANALYSIS\nA.\nData\nWe analyzed the O3GK data collected from the KA-\nGRA detector in the observation mode, and the data\nfrom GEO600 is not used. During the O3GK run, the\nKAGRA detector had duty factors, the fraction of time\nthe detector is in the observing mode to the total time, of\n\u223c53%. The length channels considered in this study are\nthe differential Michelson interferometer length (MICH)\nand the power recycling cavity length (PRCL). For both\nthe MICH and PRCL channels, calibrations of data were\nperformed offline for this study, whose parameters and\ninformation will be summarized in Ref. [42].\nFor the\nfrequency band we used for the analysis, calibration un-\ncertainty in MICH and PRCL channels are 20-30% in\namplitude.\nThe amplitude spectral densities (ASDs), derived from\nS(fn; ti), of these channels during O3GK are plotted in\nFig 2.\nWe should note that, for the last few days of\nO3GK, alignments of mirrors were dithered at signifi-\ncantly large amplitude for the beam position control [31].\nThese injected lines were accompanied by a large number\nof sidebands. Since our pipeline simply searches power\nexcesses within narrow bandwidth, it is not straightfor-\nward to distinguish those noise lines from the DM sig-\nnals.\nHence the segments from the last three days of\nthe O3GK, where the efficiency of the DM search was\nspoiled, were not included in our analysis. Consequently,\nthe number of 30 minute chunks subject to our pipeline\nwas 217.\nFIG. 2. ASDs of the MICH and PRCL estimated from the\nfirst 30 min chunk during O3GK.\nAnother limitation is that the vibration isolation sys-\ntems for mirrors in MICH and PRCL were simplified\ncompared to those in the full-design [31]. Consequently,\nthere are many noise peaks in the lower frequency range,\nwhere the KAGRA\u2019s auxiliary degrees of freedom become\nmore and more sensitive. Although our pipeline can be\nused in the lower frequency range \u227210Hz, the analysis\nwas performed over the frequency range from 15 Hz to\n1015 Hz for this demonstration analysis.\nB.\nCandidates and veto procedure\nIn Fig. 3, the detection statistics \u03c1(fc) computed in our\npipeline are shown respectively for MICH and PRCL. As\nexpected from the many lines in ASDs shown in Fig. 2,\nmore non-Gaussian power excess within an expected sig-\nnal bandwidth is observed in the PRCL data.\nUnder\nthe 5% False-Alarm-Probability derived from \u03c72 distri-\nbution for Gaussian noise, 1944 and 4133 lines are iden-\ntified as candidates for MICH and PRCL, respectively.\nThese candidates are then subject to the veto analysis\nas follows. First, according to the expected narrow band\nfeature of DM signal, the peak of \u03c1(fc) should also have\na comparable width if it has DM origin. As illustrated\nin the top panel of Fig. 4, candidates with a width more\nthan two times broader than the expected DM signal\nwidth were vetoed. We also vetoed lines that were less\nthan the peak width away from the vetoed peaks of \u03c1, as\n\n17\nFIG. 3. The detection statistics \u03c1 computed from 217 half-\nhour chunks during O3GK with MICH (top panel) and PRCL\n(bottom panel) channel. A step appears about every 200 Hz\nbecause of the increase in Nbin, which varies from 1 to 6. The\nstep height depends on the number of chunks.\nthere is a possibility that they originated from the same\nsource as those broad peaks.\nSecond, in contrast to transient noise, expected to pro-\nduce outliers in the O3GK data, DM signals should be\nmore persistent on average, albeit with random statisti-\ncal fluctuations. In the analysis, we chronologically di-\nvide the whole data chunks into two subsets and perform\nthe same analyses within the first half 108 chunks and\nthe second half 108 chunks. Then we take a coincidence\nbetween the candidates found in those two subsets to\nexclude transients that only appear during a limited du-\nration. However, it must be noted that this procedure\ninevitably vetoes weaker DM signals with which \u03c1(fc)\nexceeds the detection threshold only after summing over\nall the chunks. Furthermore, unless the signal coherence\ntime is sufficiently shorter than the data length of the\nsubset, the field amplitude (and therefore the value of\n\u03c1(fc)) can be significantly different for each subset. By\nexamining the spectrum, we found that in the case of\npresent data, such lines with the values of \u03c1 close to the\nthreshold are mostly sidebands of more intense lines, but\nthis issue must be considered in future studies. For pos-\nsible improvements to this veto procedure, see the dis-\ncussion below.\nFIG. 4. A schematic picture of the veto procedure. For both\ncases, the vertical red lines denote surviving candidates after\ntwo veto procedure. (Top panel) Green vertical bands indicate\nthe broad peak structures vetoed by the bandwidth criterion.\n(Bottom panel) The yellow vertical lines represent candidates\nwith power excess that fails coincidence requirements.\nAfter applying these two veto procedures, 77 lines re-\nmain as candidates in the MICH data while 202 lines\nremain in the PRCL data.\nMany of them are in the\nlow frequency range below 100 Hz, where there are many\nlines due to injected signals and the suspension noise. By\nreferring to, for example, the Appendix A. of Ref [31] dis-\ncussing the noise lines of DARM during O3GK, we found\nthat 57 out of 77 lines in the MICH data and 54 out of\n202 lines in the PRCL data come from known lines. Note\nthat there were few dedicated studies of the line identi-\nfication for MICH and PRCL channels during O3GK,\nand lines of unknown origin still remain. Therefore, for\nour future reference, the candidate lines identified in this\nstudy are listed in Ref. [43].\nC.\nUpper limit\nThere are several lines that have passed our pipeline\ndetection criteria, but they cannot be claimed as DM\nsignals given the current level of displacement sensitivity\nshown in Fig. 2 and the much shorter total observation\ntime, compared to those assumed in Ref. [3]. With the\n\n18\nscaling of SNR \u221d(NchT)1/4, their prediction on upper\nlimits derived by setting SNR = 1 can be scaled to give\nan order of magnitude estimate of the upper limits we\ncan derive from \u03c1. By comparing the design sensitivity\n(Fig. 2 in Ref. [3]) with our Fig. 2 and considering another\nsuppression factor of (Nch \u00b7 30min/1yr)1/4 \u223c0.011/4 that\ncomes from the difference between the real and assumed\nobservation time, we expect that the upper limit on \u03f5B\u2212L\nfrom O3GK data will be at best O(10\u221220). This is much\nweaker than those derived from the E\u00a8ot-Wash torsion\nbalance [19, 20] and MICROSCOPE [21\u201323], predicting\n10\u221224 to 10\u221223 in the frequency band of our interest.\nTherefore, the upper limit estimation here should be\nconsidered as a demonstration of our pipeline, which\ncan accurately analyze low-frequency regions and high-\nfrequency regions as well. As such a demonstration, up-\nper limits on the coupling constant are derived over the\nwhole frequency range analyzed in this study. Note that\nin principle, upper limits can be derived even for \u03c1(fc)\nthat exceed the detection threshold.\nFIG. 5. 95% upper limit on the B\u2212L gauge coupling constant\nderived from MICH data (blue line) and PRCL data (orange\nline). Many narrow peaks observed in lower mass range are\ndue to unknown line artifacts in the lower frequency range.\nIn Fig. 5, 95% upper limits on the coupling constant\n\u03f5B\u2212L are shown.\nHere the constraint is smoothed by\ncollecting the maximum value of \u03c1(fc) within a 0.1Hz\nbandwidth. For clarity, uncertainty of the calibration is\nnot displayed. Let us stress that the stochastic nature of\nDM is properly taken into account in deriving this bound,\nby using the covariance of DM signal (11) for simulating\nthe realization of \u03c1(fc). As demonstrated in Ref. [32],\nfor example, incorrect deterministic treatment predicts\na non-central \u03c72 distribution of \u03c1(fc) and overestimates\nthe upper bound by up to a factor of 3 in low mass (or\nlong coherence time) regions.\nWe also found that our\nresult is consistent with the above rough estimate on the\nupper limit based on the SNR scaling, which is also a\nconsequence of the stochastic nature of ultralight DMs [3,\n32].\nAs expected, these upper limits derived from the KA-\nGRA O3GK data are weaker than previous published\nlimits by several orders of magnitude. Again, this is ow-\ning to both the current noise level of the KAGRA detec-\ntor and the limited duration of the measurement time.\nIn order to reach the unexplored parameter space, re-\nduction of the dominant low-frequency noise and longer\nstable detector operation are indispensable.\nV.\nDISCUSSION\nIn this work, an ultralight vector DM search with KA-\nGRA was conducted for the first time by using the KA-\nGRA data from the O3GK run. Our pipeline design is\nguided by a recent study on the stochastic nature of the\nultralight vector DM [32].\nConsequently, the KAGRA\nO3GK data, which has a relatively short measurement\ntime compared to the DM coherence time for low DM\nmasses, can be analyzed.\nWe found that our pipeline can discriminate candidates\nfor vector DM signal from the broad peaks and transient\nlines, which are expected to have an instrumental ori-\ngin. Nonetheless, there are several lines with unspecified\norigin meeting our criteria, especially for the lower fre-\nquency range. We expect that the number of such lines\nwill decrease in upcoming observations because of, for\nexample, an updated system for the suspension control\nand an improved understanding of the noise. Although\nthe upper limits derived in this analysis are weaker than\nprevious ones, they are found to be consistent with the\nprediction given in prior studies [3, 32]. Achieving the\ndesigned sensitivity and future upgrades of the KAGRA\ndetector [44] will allow us to fully appreciate its unique\nfeature as a vector DM detector exploiting the mirrors\nmade of different materials to yield new constraints.\nThere are several directions for improving our DM\nsearch pipeline. First, as outlined in Sec. II, our anal-\nysis is performed assuming the equilibration of vector\npolarization. Depending on the production mechanism,\nhowever, only a specific polarization mode might be pro-\nduced. Therefore, the formalism beyond this assumption\nmay allow us to probe the cosmological origin of vector\nDM. Second, while the bandwidth criterion for the veto\nanalysis is quite robust, the appropriateness of taking co-\nincidence between subsets of whole data should depend\non the strength and coherence time of the signal being\nsearched for. Since the covariance of the vector DM sig-\nnal is known, it is possible to implement a test to check\nwhether the candidates follow a distribution consistent\nwith the given covariance. This could provide a more ro-\nbust way to distinguish a DM signal from the noise lines.\nFinally, our pipeline can be extended to include the anal-\nysis of the DARM channel data, which has been used in\nDM searches in other GW detectors.\n\n19\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO), for the construction and operation of the Virgo\ndetector and the creation and support of the EGO consor-\ntium. The authors also gratefully acknowledge research\nsupport from these agencies as well as by the Council\nof Scientific and Industrial Research of India, the De-\npartment of Science and Technology, India, the Science\n& Engineering Research Board (SERB), India, the Min-\nistry of Human Resource Development, India, the Span-\nish Agencia Estatal de Investigaci\u00b4on (AEI), the Span-\nish Ministerio de Ciencia e Innovaci\u00b4on and Ministerio de\nUniversidades, the Conselleria de Fons Europeus, Uni-\nversitat i Cultura and the Direcci\u00b4o General de Pol\u00b4\u0131tica\nUniversitaria i Recerca del Govern de les Illes Balears,\nthe Conselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Soci-\netat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Na-\ntional Science Centre of Poland and the European Union\n\u2013 European Regional Development Fund; Foundation for\nPolish Science (FNP), the Swiss National Science Foun-\ndation (SNSF), the Russian Foundation for Basic Re-\nsearch, the Russian Science Foundation, the European\nCommission, the European Social Funds (ESF), the Eu-\nropean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish Uni-\nversities Physics Alliance, the Hungarian Scientific Re-\nsearch Fund (OTKA), the French Lyon Institute of Ori-\ngins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek \u2013 Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Science and Engineering Re-\nsearch Council Canada, Canadian Foundation for Innova-\ntion (CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoretical\nPhysics South American Institute for Fundamental Re-\nsearch (ICTP-SAIFR), the Research Grants Council of\nHong Kong, the National Natural Science Foundation of\nChina (NSFC), the Leverhulme Trust, the Research Cor-\nporation, the National Science and Technology Council\n(NSTC), Taiwan, the United States Department of En-\nergy, and the Kavli Foundation. The authors gratefully\nacknowledge the support of the NSF, STFC, INFN and\nCNRS for provision of computational resources.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-inAid for Scientific Research on Innovative Ar-\neas 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grantin-Aid for Scientific Research (S)\n17H06133 and 20H05639 , JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cosmic\nRay Research, University of Tokyo, National Research\nFoundation (NRF), Computing Infrastructure Project of\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, Korea Astronomy and Space Science Institute\n(KASI), and Ministry of Science and ICT (MSIT) in Ko-\nrea, Academia Sinica (AS), AS Grid Center (ASGC) and\nthe National Science and Technology Council (NSTC)\nin Taiwan under grants including the Rising Star Pro-\ngram and Science Vanguard Research Program, Ad-\nvanced Technology Center (ATC) of NAOJ, and Mechan-\nical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied a\nCreative Commons Attribution (CC BY) license to any\nAuthor Accepted Manuscript version arising. 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D 102, 022008 (2020).\n", "DRAFT VERSION AUGUST 26, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nGWTC-4.0: Methods for Identifying and Characterizing Gravitational-wave Transients\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n(SEE THE END MATTER FOR THE FULL LIST OF AUTHORS)\nABSTRACT\nThe Gravitational-Wave Transient Catalog (GWTC) is a collection of candidate gravitational-wave transient\nsignals identified and characterized by the LIGO\u2013Virgo\u2013KAGRA Collaboration. Producing the contents of the\nGWTC from detector data requires complex analysis methods. These comprise techniques to model the signal;\nidentify the transients in the data; evaluate the quality of the data and mitigate possible instrumental issues; infer\nthe parameters of each transient; compare the data with the waveform models for compact binary coalescences;\nand handle the large amount of results associated with all these different analyses. In this paper, we describe the\nmethods employed to produce the catalog\u2019s fourth release, GWTC-4.0, focusing on the analysis of the first part\nof the fourth observing run of Advanced LIGO, Advanced Virgo and KAGRA.\nKeywords: Gravitational wave astronomy (675); Gravitational wave detectors (676); Gravitational wave sources\n(677); Stellar mass black holes (1611); Neutron stars (1108)\n1. INTRODUCTION\nInterferometric gravitational-wave (GW) detectors pro-\nduce a calibrated discrete digital time series h(t) known as\nthe strain (a dimensionless measure of the relative difference\nin arm length of the interferometers). The Advanced Laser\nInterferometer Gravitational-Wave Observatory (LIGO; Aasi\net al. 2015) and Advanced Virgo (Acernese et al. 2015) de-\ntectors are the most sensitive to date. Alongside the develop-\ning KAGRA detector (Akutsu et al. 2019) the LIGO\u2013Virgo\u2013\nKAGRA Collaboration (LVK) has recently undertaken the\nfourth observing run (O4) observing run. However, the data\nproduced are dominated by detector noise, with only occa-\nsional occurrences of detectable transient GW signals (Ab-\nbott et al. 2020a,b); to date, all such observed signals likely\narise from compact binary coalescences (CBCs) involving\nblack holes (BHs) and neutron stars (NSs). This paper de-\nscribes the methodology used to analyze the calibrated strain\ndata up to the first part of the fourth observing run (O4a)\nand produce version 4.0 of the Gravitational Wave Transient\nCatalog (GWTC), hereafter referred to as GWTC-4.0. For a\ngeneral introduction to GWTC-4.0, see Abac et al. (2025a)\nwhich also contains a description of the observed source\nclasses and data analysis nomenclature which should be read\nas a background to this methodology paper. The scientific re-\nsults of GWTC-4.0 are presented in Abac et al. (2025b). Data\nCorresponding author: LSC P&P Committee, via LVK Publications as\nproxy\nlvc.publications@ligo.org\nanalysis methods not directly related to producing catalog re-\nsults, such as searches for continuous GWs or subsolar-mass\nCBCs, will be described elsewhere.\nThere are many interconnected elements to the data pro-\ncessing methodology described in this work. To provide a\nvisual guide and summary, Figure 1 shows a diagram of the\ndata-processing workflow. In Section 2, we introduce the\nfundamental concepts behind modeling GW waveforms from\nCBC sources and describe the waveform approximants used\nin later analyses. The data analysis process then starts with\nthe calibrated strain data h(t) and associated auxiliary data,\nwhich is produced by the LVK detectors and is the input\nto the analysis. The strain data and auxiliary data are in-\nputs to the process of searching for signals and compiling a\nlist of candidates from the strain data which we describe in\nSection 3. Section 4 discusses how we assess data quality\naround candidates and mitigate the impact of potential in-\nstrumental issues. The strain data, candidate lists, and data-\nquality information are then inputs into the methods used to\ninfer the properties of the signals and their sources which\nwe describe in Section 5.\nIn Section 6 we detail consis-\ntency tests performed on selected candidates to evaluate how\nwell CBC waveform models match the data. Section 7 de-\nscribes the technologies used to manage the flow of informa-\ntion throughout the analysis process as shown in Figure 1.\nFinally, we conclude in Section 8.\n2. MODELING COMPACT BINARY COALESCING\nSIGNALS\nIn this section, we will describe the modeling of CBC\nwaveform signals, including binary black hole (BBH), binary\narXiv:2508.18081v1 [gr-qc] 25 Aug 2025\n\n2\nh(t)+\nTransient Searches (Section 3)\nOnline/Offline\nOffline\nGraceDB (Section 7)\nPublic Alerts/\nCatalog Search Table\nOnline Parameter Estimation (Section 5)\nOnline Parameter Estimation\nData Quality (Section 4)\nEvent Validation\nGlitch Subtraction\ncbcflow (Section 7)\ncbcflow Data\nCatalog Parameter Estimation (Section 5)\nPSD Generation\nAuto-Configuration\nProduction Parameter Estimation\nCatalog Pipeline (Section 7)\nCatalog Data\nData Product\nFigure 1. A high-level rendering of the flow of data from the strain and auxiliary data, denoted h(t)+, to the production of GWTC-4.0\ndescribed in this work. In this work, we use the terms downstream and upstream to refer to the flow of information in the analysis process (e.g.\nthe parameter estimation is downstream of the compilation of search results since it depends on their outputs). This complex process enables\nthe use of the most complete set of information for the final results while also leveraging preliminary studies to parallelise and reduce the\noverall analysis time. The term online (also referred to as low-latency in the literature) refers to analyses run on live data with a goal to upload\ncandidates to GRACEDB immediately and enable rapid public alerts, while offline refers to analyses run with the goal to identify candidates for\nthe GWTC. In each box, we provide references to the sections of this paper where the methods are explained in more detail.\n\n3\nneutron star (BNS), and neutron star\u2013black hole binary\n(NSBH) systems. This modeling is a crucial aspect for the\ndetection and astrophysical interpretation of these systems\nand is used by modeled search algorithms (described in Sec-\ntion 3) and parameter estimation (PE; described in Section 5).\nThe focus of this section is on the waveform models used in\nGWTC-4.0, although we include models employed in analy-\nses of previous GWTC versions that have been superseded in\nnewer versions, in particular the PE analyses performed for\nGWTC-1.0 and GWTC-2.0. For an introduction to waveform\nmodeling in general, see Section 5 of Abac et al. (2025a).\nSeveral different modeling approaches have been followed\nin the development of CBC waveform models for the com-\nplete inspiral\u2013merger\u2013ringdown (IMR) stages of the signal.\nInspiral-only models have been developed based on post-\nNewtonian (PN) theory (Blanchet 2014), using different PN-\nexpansions of the balance equations for the two-body dynam-\nics, under the TAYLOR family (Buonanno et al. 2009) for\nnon-spinning systems and the SPINTAYLOR family (Sturani\n2015; Isoyama et al. 2020) for spinning systems. The IMR-\nPHENOM approach (Ajith et al. 2007) focuses on the descrip-\ntion of the GW signal, traditionally in Fourier domain for an\nefficient implementation in the data analysis pipelines, com-\nbining PN and numerical relativity (NR) information into\nclosed-form expressions for describing the inspiral, merger\nand ringdown stages of the signal. The effective-one-body\n(EOB) approach (Buonanno & Damour 1999, 2000) focuses\non accurately describing the dynamics and resulting wave-\nform of the system in the time-domain, using a combination\nof resummed analytical information and calibration to NR.\nInside this approach, two main different development effort\nhave been followed, the SEOBNR (Buonanno et al. 2007)\nand TEOB (Damour & Nagar 2014; Nagar & Shah 2016)\napproaches. The NRSURROGATE approach (Blackman et al.\n2017a) focuses on producing efficient surrogate models of\nthe NR data, with or without hybridization with analytical\nwaveforms, to deliver highly accurate waveform in a valid-\nity region limited by the input numerical data, both in the\nnumber of cycles and in the coverage of parameter space.\nThese modeling approaches provide the waveform models\ndescribed in this section.\nThe majority of waveform models that we describe in this\nsection correspond to CBC systems on quasi-circular or-\nbits (also called quasi-spherical orbits when spin precession\nis present), therefore neglecting orbital eccentricity effects,\nsince at the moment all models employed in the analysis of\nGWTC candidates have this restriction.\nOne of the main\nreasons for this limitation is that mature eccentric waveform\nmodels have only been developed recently, and reviewed ver-\nsions were not yet ready at the time of starting the analyses\ndescribed in this work. This limitation can lead to biases\nin the mass parameters (Martel & Poisson 1999; Lower et al.\n2018; Lenon et al. 2020; O\u2019Shea & Kumar 2023; Favata et al.\n2022), and also influence the inferred spins (Lenon et al.\n2020; Romero-Shaw et al. 2020a; O\u2019Shea & Kumar 2023;\nFavata et al. 2022; Morras et al. 2025a,b). For high-mass\nsystems, where few orbits are observed, neglecting eccen-\ntricity can also lead to incorrectly identifying spin-precessing\neffects due to possible degeneracies of both effects in this\nregime (Ramos-Buades et al. 2020a; Calder\u00f3n Bustillo et al.\n2021; Romero-Shaw et al. 2023).\nDuring a binary inspi-\nral, the energy loss from GW emission rapidly circularizes\nan eccentric orbit, generally reducing expectation of signifi-\ncant eccentricity (Peters 1964) by the time the signal enters\nthe sensitive frequency band of the interferometers (Tucker\n& Will 2021).\nRate estimations (Wen 2003; Samsing &\nRamirez-Ruiz 2017; Gupte et al. 2024) constrain the fraction\nof events with observable eccentricity to a small percentage.\nNevertheless, recent independent analyses have shown evi-\ndence of nonzero eccentricity in a few previously detected\nsignals (Romero-Shaw et al. 2020a; Gamba et al. 2023a;\nGayathri et al. 2022; Gupte et al. 2024; Planas et al. 2025b;\nMorras et al. 2025b; Planas et al. 2025a). Therefore, we can-\nnot exclude a priori that a few candidates in GWTC-4.0 may\npresent nonzero eccentricity.\nIn the following subsections, we will describe chronolog-\nically the relevant waveform modeling efforts that lead to\nmodels employed in GWTC analyses.\nFor consulting the\nspecific set of waveform models employed in each GWTC\nversion, we refer the reader to Table 1, while a summary of\nthe physics of each model is displayed in Table 2. Their us-\nage on specific pipelines will be described in the correspond-\ning sections of this work.\n2.1. BBH Models\nWithin the IMRPHENOM and SEOBNR families, the first\ncomplete IMR models calibrated to NR were produced for\nthe dominant spin-weighted spherical harmonic multipole\nof nonspinning systems (Ajith et al. 2007; Buonanno et al.\n2007), and then extended to aligned-spin systems (Ajith et al.\n2011; Santamaria et al. 2010; Taracchini et al. 2014b). Im-\nproved versions were developed for GWTC analyses: IMR-\nPHENOMD (Husa et al. 2016; Khan et al. 2016) and SEOB-\nNRV4 (Boh\u00e9 et al. 2017), increasing the amount of analytical\ninformation included in the models, the number and coverage\nof the calibration dataset, specific details of the model ex-\npressions and better accuracy with NR. A highly optimized\nversion of SEOBNRV4 was produced to reduce its compu-\ntational cost in the time domain, SEOBNRV4_OPT (Devine\net al. 2016), and reduced-order model (ROM) techniques\nwere applied to obtain a fast Fourier-domain version of\nthe original model, SEOBNRV4_ROM (Boh\u00e9 et al. 2017).\nWithin the TEOB approach, a version of the model for the\ndominant multipole of BBH systems was developed, TEO-\nBRESUMS (Nagar et al. 2018), including a post-adiabatic\napproximation for the dynamics that increases its computa-\ntional efficiency (Nagar & Rettegno 2019). Additionally, the\ninspiral-only models TAYLORF2 (Damour et al. 2001; Buo-\nnanno et al. 2009; Vines et al. 2011), which is an analytical\nFourier-domain model, and SPINTAYLORT4 (Sturani 2015;\nIsoyama et al. 2020), a time-domain model, have also been\nemployed for searching GW signals.\nModeling spin-precession effects is crucial for precise\nmeasurements of spins (Vitale et al. 2014; Pratten et al.\n\n4\n2020b; Johnson-McDaniel et al. 2022b; Biscoveanu et al.\n2021; Steinle & Kesden 2022), providing key information\nabout the formation channels of the observed systems (Ro-\ndriguez et al. 2016; Stevenson et al. 2017; Talbot & Thrane\n2017; Zhu et al. 2018), and breaking degeneracies in param-\neter inference (Vecchio 2004; Lang & Hughes 2006; Chatzi-\nioannou et al. 2015; Krishnendu & Ohme 2022).\nSpin-\nprecession can significantly increase the complexity of the\nsignal, and modeling efforts focused first on applying the\ntwisting-up approach (Buonanno et al. 2003; Schmidt et al.\n2011; Boyle et al. 2011; O\u2019Shaughnessy et al. 2012; Schmidt\net al. 2012) to the dominant-multipole models, differing on\nthe description of the spin dynamics of the system. The IM-\nRPHENOM approach incorporated a closed-form solution of\nthe next-to-next-to-leading order spin-precessing evolution\nequations for single-spin configurations (Marsat et al. 2013;\nBohe et al. 2013), mapping then the expressions effectively\nto double-spin systems (Schmidt et al. 2015), and employ-\ning the twisting-up technique first to IMRPHENOMC (San-\ntamaria et al. 2010) to obtain IMRPHENOMP (Hannam et al.\n2014), and then to the more accurate model IMRPHENOMD\nto obtain IMRPHENOMPV2 (Hannam et al. 2014; Boh\u00e9 et al.\n2016). On the SEOBNR approach, spin-dynamics were in-\ncorporated via evolution of the EOB equations of motion\nfor a quasi-circular spin-precessing Hamiltonian, construct-\ning the spin-precessing polarizations from the quadrupolar\nmultipoles in the co-precessing frame for producing SEOB-\nNRV3 (Pan et al. 2014).\nSubdominant harmonics in the signal were shown to be\nimportant for reducing several degeneracies in the analy-\nsis of signals (Capano et al. 2014; Graff et al. 2015; Ab-\nbott et al. 2021a, 2024), in particular in inclination\u2013distance\ndegeneracy and modeling efforts focused on their inclu-\nsion into current models. IMRPHENOMHM (London et al.\n2018) incorporated a set of the most important subdomi-\nnant harmonics to the IMRPHENOMD model, although with-\nout additional calibration of these harmonics to numeri-\ncal data.\nSEOBNRV4HM (Cotesta et al. 2018) incorpo-\nrated a similar list of harmonics to SEOBNRV4, with ex-\nplicit calibration of the waveform modes to NR and test-\nparticle waveforms, and provided an efficient ROM version\nin Fourier-domain, SEOBNRV4HM_ROM (Cotesta et al.\n2020). Spin-precessing versions of these multipolar wave-\nform models were developed in parallel, with some improve-\nments in the spin-dynamics description in the IMRPHENOM\napproach, resulting in IMRPHENOMPV3HM (Khan et al.\n2020) and SEOBNRV4PHM (Ossokine et al. 2020). Addi-\ntionally, the NRSURROGATE approach started producing the\nfirst surrogate models for multipolar spin-precessing signals,\nfirst with NRSUR7DQ2 (Blackman et al. 2017b) and then\nextending the parameter space coverage with NRSUR7DQ4\n(Varma et al. 2019a).\nInside the IMRPHENOM approach, a new generation of\nwaveform models was developed improving substantially the\naccuracy of the previous generation, providing a new model\nfor the dominant harmonic of aligned-spin signal, IMRPHE-\nNOMXAS (Pratten et al. 2020a), a model for subdominant\nharmonics explicitly calibrated to NR simulations, IMR-\nPHENOMXHM (Garc\u00eda-Quir\u00f3s et al. 2020) and its extension\nto spin-precessing signals through the twisting-up technique\nand the employment of the multiscale expression for the spin\ndynamics (Klein et al. 2013; Chatziioannou et al. 2013; Klein\net al. 2014), IMRPHENOMXPHM (Pratten et al. 2021). This\ngeneration also reduced substantially the computational cost\nof waveform generation via an implementation of the multi-\nbanding method (Vinciguerra et al. 2017; Garc\u00eda-Quir\u00f3s et al.\n2021). On a parallel effort, a new phenomenological fam-\nily of models was developed in the time domain, IMRPhe-\nnomTPHM (Estell\u00e9s et al. 2021, 2022b,a), with the aim of\novercoming the limitations of the stationary-phase approxi-\nmation (SPA) in the modeling of precessing signals, and in-\ncluding for the first time in a phenomenological model accu-\nrate numerical solutions of the spin-precession equations.\nFurther improvements for spin-precessing signals were re-\ncently introduced in the IMRPHENOMXPHM model, in-\ntroducing for the first time explicit calibration with spin-\nprecessing NR simulations in IMRPHENOMXO4A (Hamil-\nton et al. 2021; Thompson et al. 2024) as well as the inclu-\nsion of the dominant multipole equatorial asymmetry (Ghosh\net al. 2024), a key effect for accurately describing systems\nwith large remnant recoil (Varma et al. 2020; Borchers et al.\n2024) and improving accuracy of spin-precessing models\n(Ramos-Buades et al. 2020b). This effect has been shown\nin several recent studies to be relevant for the correct infer-\nence of spin-precessing signals (Kolitsidou et al. 2024; Estel-\nl\u00e9s et al. 2025). Additionally, improvements in the descrip-\ntion of the spin dynamics during the inspiral were incorpo-\nrated in IMRPHENOMXPHM_SPINTAYLOR (Colleoni et al.\n2025b), performing numerically the integration of the PN\nspin dynamic equations and enhancing the accuracy for the\ninspiral stage of the signal.\nThe SEOBNR approach has recently been developed with\na new and more accurate generation of BBH waveform mod-\nels, SEOBNRV5HM (Pompili et al. 2023) for aligned-spin\nsystems and SEOBNRV5PHM (Ramos-Buades et al. 2023)\nfor spin-precessing systems. Improvements include more an-\nalytical PN information (Henry 2023; Khalil et al. 2023) and\nrecent developments from second-order gravitational self-\nforce for the flux and gravitational modes (Warburton et al.\n2021; van de Meent et al. 2023), increasing the coverage of\nparameter space employed in the calibration with NR and\ntest-mass limit simulations (Barausse et al. 2012; Taracchini\net al. 2014a). These are also substantial improvements to the\ncomputational efficiency of the models via the implementa-\ntion of the post-adiabatic technique (Nagar & Rettegno 2019;\nMihaylov et al. 2021) and the release of the modular and\nhighly optimized Python package pySEOBNR (Mihaylov\net al. 2023). The dominant and multipolar spin-aligned mod-\nels SEOBNRV5 and SEOBNRV5HM also provide efficient\nROM versions in the Fourier domain, SEOBNRV5_ROM\nand SEOBNRV5HM_ROM (Pompili et al. 2023).\n2.2. BNS Models\n\n5\nWhen modeling BNS mergers, the inclusion of tidal in-\nteractions is critical for accurately describing the two-body\ndynamics and the corresponding GW emission. These inter-\nactions are characterized by the dimensionless tidal deforma-\nbility parameter \u039b, which encodes the response of a NS to the\ngravitational field of its companion and is directly related to\nthe equation of state (EoS) of dense nuclear matter (Flana-\ngan & Hinderer 2008; Hinderer 2008). Measurements of the\ntidal deformability through GW observations can constrain\nthe EoS of dense nuclear matter (Chatziioannou 2020). Tidal\ninteractions in BNS systems are first captured at 5 PN order\n(Flanagan & Hinderer 2008; Vines et al. 2011) in the veloc-\nity expansion and have been extended up to 7.5 PN order\n(Damour et al. 2012; Henry et al. 2020). Tidal corrections\nhave been added to the GW phase of the PN inspiral Taylor\nFourier-domain model TAYLORF2 (Vines et al. 2011).\nBesides being tidally deformed by their companions,\nrapidly-spinning NSs acquire an intrinsic oblateness where\nthe NS mass-quadrupole moment depends on the dimen-\nsionless spin and encodes information about the EoS. The\ninteraction between this quadrupole and the monopole of\nthe companion generates an additional conservative poten-\ntial, usually termed quadrupole\u2013monopole coupling, enter-\ning the two-body dynamics at the same 2 PN order as the\nspin\u2013spin term and contributing corrections to both the bind-\ning energy and the GW flux (Poisson 1998). Neglecting the\nquadrupole-monopole term can bias tidal-deformability and\nspin measurements once spins approach millisecond-pulsar\nvalues (Agathos et al. 2015; Samajdar & Dietrich 2018).\nIn addition to PN-based tidal corrections and quadrupole-\nmonopole interaction, NR simulations play an essential role\nin accurately modeling the merger and post-merger phases\nof BNS coalescence, where nonlinear effects become sig-\nnificant, and several catalogs of BNS simulations have been\nproduced (Dietrich et al. 2018; Gonzalez et al. 2023b; Ki-\nuchi et al. 2017). The NRTIDAL approach (Dietrich et al.\n2017) has been developed to incorporate tidal effects into the\nfrequency-domain BBH waveform models, maintaining the\ncomputational efficiency of the BBH model baseline. The\ntidal phase in frequency domain is modeled by employing\nthe PN-expanded phase and calibrating it to NR BNS sim-\nulations. The original NRTIDAL model included PN-phase\ncorrections augmented with calibration in the time domain\nusing a non-spinning set of equal-mass BNS NR simulations,\nand then transformed to frequency-domain using the SPA. It\nwas incorporated (Dietrich et al. 2019b) in the construction\nof the BNS models IMRPHENOMD_NRTIDAL and SEOB-\nNRV4_ROM_NRTIDAL, for aligned-spin systems, IMR-\nPHENOMPV2_NRTIDAL, for precessing systems, which\nwas employed in the analysis of GW170817 (Abbott et al.\n2017a) together with SEOBNRV4_ROM_NRTIDAL.\nNRTIDALVTWO (Dietrich et al. 2019a) improved upon\nthe previous model by the employment of improved NR\ndata, the incorporation of spin effects, and the addi-\ntion of amplitude corrections to the GW signal.\nIt\nwas incorporated to several BBH baselines models, in-\ncluding IMRPHENOMPV2_NRTIDALV2 (Dietrich et al.\n2019a) and more recently IMRPHENOMXP_NRTIDALV2\n(Colleoni et al. 2025a), for precessing systems, and SEOB-\nNRV4_ROM_NRTIDALV2 for aligned-spin systems.\nWithin the EOB framework, the SEOBNRV4T (Hin-\nderer et al. 2016; Steinhoff et al. 2016) and TEOBRESUMS\n(Bernuzzi et al. 2015; Nagar et al. 2018; Akcay et al. 2019)\nmodels aim to provide a more accurate description of the in-\nspiral phase, particularly in regimes where tidal interactions\nbecome significant. SEOBNRV4T includes tidally-induced\nmultipole moments (up to \u2113= 3), the effect of dynamical\ntides from f-mode resonances (Hinderer et al. 2016; Stein-\nhoff et al. 2016), and the spin-induced quadrupole moment\n(Poisson 1998; Harry & Hinderer 2018). An efficient sur-\nrogate version of the model in the frequency domain, based\non Gaussian process regression, was developed to reduce the\ncost of its employment in data-analysis applications (Lackey\net al. 2019).\nSimilarly, TEOBRESUMS incorporates tidally-induced\nquadrupole moments using a different resummation and new\ninformation from gravitational self-force, with the lack of\nf-mode resonances but the addition of calibration to NR\nBNS simulations in a more recent version of the model\n(Gamba et al. 2023b).\nIn order to improve its efficiency\nin data-analysis applications, a combination of the post-\nadiabatic technique and the SPA is employed to produce\nfast frequency-domain inspiral templates (Nagar & Rettegno\n2019; Gamba et al. 2021).\n2.3. NSBH Models\nModeling NSBH mergers presents distinct challenges\ncompared to BNS systems, primarily because the NS may be\nfully disrupted and accreted by the BH without producing a\npost-merger remnant. As in BNS systems, the tidal response\nof the NS affects the phase evolution of the inspiral, requiring\nthe inclusion of tidal corrections in the waveform phase (Pan-\nnarale et al. 2011). Additionally, in an EoS-dependent region\nof parameter space, typically involving unequal masses or\nhighly-spinning BHs, the NS can be tidally disrupted before\nreaching the innermost stable circular orbit. In such cases,\nthe signal amplitude is strongly suppressed at high frequen-\ncies (Kyutoku et al. 2011; Foucart et al. 2014; Kawaguchi\net al. 2015). While tidal disruption and post-merger rem-\nnants can also occur in BNS mergers, disrupted NSBH sys-\ntems may lack a distinct merger signature altogether if the\nNS is fully disrupted before crossing the BH\u2019s horizon.\nCurrent NSBH models employed to analyse the NSBH\ncandidate signals from GWTC-2.0 onwards are the SEOB-\nNRV4_ROM_NRTIDALV2_NSBH (Matas et al. 2020)\nmodel and IMRPHENOMNSBH (Thompson et al. 2020)\nmodel. Both models incorporate tidal information into the\nphase of the respective Fourier-domain BBH baseline model\nusing the NRTIDALVTWO phase model described in Sec-\ntion 2.2.\nDisruptive and non-disruptive mergers are han-\ndled by adding tidal correction to the GW amplitude, as\nwell as establishing a parameter-space dependent cut-off fre-\nquency for suppressing the GW amplitude in the case of dis-\nruptive events. In particular, IMRPHENOMNSBH employs\n\n6\nan NR-calibrated amplitude model (Pannarale et al. 2013,\n2015),\nwhile\nSEOBNRV4_ROM_NRTIDALV2_NSBH\nimplements NR-calibrated correction factors to the underly-\ning BNS NRTIDAL model. Both the amplitude model of\nSEOBNRV4_ROM_NRTIDALV2_NSBH and the correc-\ntion factors in SEOBNRV4_ROM_NRTIDALV2_NSBH\nincorporate disruptive events by establishing a cut-off fre-\nquency and tapering the waveform at frequencies above this\ncut-off.\nOne of the main limitations of current NSBH models is\nthat they are restricted to the dominant multipole and as-\nsume spin-aligned configurations. Including only the dom-\ninant mode can lead to degeneracies in distance and incli-\nnation, as well as to a non-negligible loss in signal-to-noise\nratio (SNR) for unequal-mass NSBH systems, since higher-\norder multipoles can contain a significant fraction of the sig-\nnal power for asymmetric binaries. Therefore, future models\nwill need to address this limitation, and there is active devel-\nopment towards this (Gonzalez et al. 2023a).\n2.4. Luminosity and Remnant Properties\nBesides modeling the GW waveform, accurate predictions\nof the mass and spin of the final remnant BH, as well as es-\ntimations of the peak luminosity, are also crucial for popu-\nlation studies and tests of general relativity (GR). Several\nanalytical fits have been developed using the remnant prop-\nerties from NR BBH simulations (Hofmann et al. 2016; Kei-\ntel et al. 2017; Healy & Lousto 2017; Jim\u00e9nez-Forteza et al.\n2017), and recently accurate Gaussian process regression sur-\nrogate models have been developed (Varma et al. 2019b; Is-\nlam et al. 2023). For NSBH systems, dependency on the\ntidal deformability of the NS have been included (Zappa et al.\n2019). These fitting formulae generally depend on the com-\nponent masses and spins, typically specified at some refer-\nence frequency in the inspiral stage of the signal. For estimat-\ning these quantities from the inferred source properties (see\nSection 5.9), the input spin values are evolved forward until\na fiducial orbital frequency near merger is achieved, and then\nresults from different fitting formulae are averaged to provide\nthe final estimates. For precessing systems, these formulae\nare often augmented with in-plane spin contribution before\nthe average procedure is applied (Johnson-McDaniel et al.\n2016).\n3. SIGNAL IDENTIFICATION\nThe GW strain time series produced by advanced-era inter-\nferometric detectors can be treated as a linear superposition\nof continuous non-astrophysical noise and occasional tran-\nsient astrophysical signals. On timescales of tens of seconds,\nthe noise is generally well approximated by colored station-\nary Gaussian processes, allowing for relatively stable model-\ning and analysis. However, on longer timescales, the noise\nbecomes non-stationary, exhibiting time-dependent statisti-\ncal properties. It is frequently contaminated by transient non-\nGaussian artifacts, known as glitches (Nuttall 2018; Glanzer\net al. 2023; Soni et al. 2025), and is also affected by slowly\ntime-varying broadband disturbances (Abbott et al. 2020b).\nOn the other hand, the signals in the data are presently rel-\natively rare, occurring at a rate of just a few per week. GW\nsearches are thus required to perform statistical data reduc-\ntion, taking in the kilohertz-sampled strain data and produc-\ning a list of astrophysical candidates. This marks the begin-\nning of the data-analysis workflow illustrated in Figure 1.\nThe search for GW transient candidates is carried out\nthrough two distinct phases. Initially, online analyses en-\nable prompt follow-up observations by the global astronom-\nical community (Abbott et al. 2019b, 2023a; LIGO Scien-\ntific Collaboration et al. 2025). Later, offline analyses are\nconducted to produce a more accurate list of candidates by\nre-evaluating the significance of the initial online candidates\nand identifying new ones. Some of the factors responsible for\nthe differences in the online and offline analyses are the use\nof the final strain data, improved data quality, enhanced algo-\nrithms, and a better understanding of the noise background\nin the data.\nTwo broad families of detection algorithms are used:\nsearch pipelines for minimally-modeled transient sources\nthat do not rely on specific waveform predictions and search\npipelines that, conversely, aim to maximize sensitivity to\nCBCs by using sets of template waveforms (a subset of the\nmodels described in Section 2). For the GWTC, we use mul-\ntiple pipelines concurrently and combine their results. This\napproach minimizes the risk of missing astrophysical signals\nand allows us to cover a wider range of the CBC parameter\nspace.\nTemplate-based pipelines target specific regions of the\nCBCs parameter space, usually defined by the redshifted\n(detector-frame) masses (Krolak & Schutz 1987) and spins\nof the two compact objects, which are arranged into template\nbanks.\nTemplate waveforms are currently calculated ne-\nglecting several physical effects, specifically non-dominant\nmultipole emission, orbital precession, eccentricity and tidal\ndeformability.\nThe templates thus only model the domi-\nnant multipole emission from quasi-circular BBH coales-\ncences with spins parallel to the orbital angular momen-\ntum. This simplification reduces the dimensionality of the\nparameter space to be covered, and therefore the number\nof templates.\nSeveral studies have shown that this has a\nlimited impact on the detection rate while offering a sig-\nnificant reduction in computational cost (Dal Canton et al.\n2015; Calder\u00f3n Bustillo et al. 2016; Harry et al. 2016;\nCalder\u00f3n Bustillo et al. 2017; Dietrich et al. 2019b; Ramos-\nBuades et al. 2020c; Phukon et al. 2025; Chia et al. 2024;\nMehta et al. 2025).\nIn modeled searches, we search the data from each detector\nby matched filtering each template u(f|\u03b8int) (where \u03b8int is a\nvector over a subset of intrinsic CBC parameters), to produce\na SNR time series defined as (Maggiore 2007; Allen et al.\n2012)\n\u03c1(t) = 4\n\f\f\f\f\f\nZ fhigh\nflow\nh(f)u\u2217(f|\u03b8int)\nSn(f)\ne2i\u03c0ftdf\n\f\f\f\f\f ,\n(1)\n\n7\nTable 1. A summary of waveform models used in each release of the GWTC. Since the catalog is cumulative, later releases (e.g., GWTC-3.0,\nGWTC-4.0) include all previous candidates. In most cases, PE results from earlier releases remain unchanged. An exception is GWTC-2.1,\nwhich reanalyzed O1 and O2 data using updated waveform models, replacing the original PE results from GWTC-1.0 and GWTC-2.0. As a\nresult, the PE analyses with the waveform approximants listed for GWTC-1.0 and GWTC-2.0 are not part of GWTC-4.0. The models employed\nin GWTC-4.0 are discussed in Section 2, and their use within specific pipelines is described in the following sections. Special candidate analyses\nmight employ additional waveform models not listed here, but discussed for those particular signals.\nCatalog release\nData analysed\nSearch templates\nSensitivity estimates\nParameter estimation\nGWTC-1.0\n(Abbott et al. 2019a)\nO1, O2\nSEOBNRV4_ROM,\nTAYLORF2\n-\nIMRPHENOMPV2, IMRPHENOMPV2_NRTIDAL,\nSEOBNRV3, SEOBNRV4_ROM_NRTIDAL,\nSEOBNRV4T, TAYLORF2, TEOBRESUMS\nGWTC-2.0\n(Abbott et al. 2021a)\nO3a\nSEOBNRV4_ROM,\nTAYLORF2\nSEOBNRV4_OPT\nIMRPHENOMD, IMRPHENOMD_NRTIDAL,\nIMRPHENOMHM, IMRPHENOMPV2,\nIMRPHENOMPV2_NRTIDAL,\nIMRPHENOMPV3HM,\nIMRPHENOMNSBH, NRSUR7DQ4,\nSEOBNRV4_ROM_NRTIDALV2_NSBH,\nSEOBNRV4_ROM, SEOBNRV4HM_ROM,\nSEOBNRV4P, SEOBNRV4PHM,\nSEOBNRV4T_SURROGATE, TAYLORF2,\nTEOBRESUMS\nGWTC-2.1\n(Abbott et al. 2024)\nO1\u2013O3a\nSEOBNRV4_OPT,\nSEOBNRV4_ROM,\nSPINTAYLORT4,\nTAYLORF2\nSEOBNRV4P,\nSEOBNRV4PHM,\nSPINTAYLORT4\nIMRPHENOMPV2_NRTIDAL,\nIMRPHENOMXPHM,\nSEOBNRV4PHM,\nGWTC-3.0\n(Abbott et al. 2023a)\nO3b\nSEOBNRV4_OPT,\nSEOBNRV4_ROM,\nSPINTAYLORT4,\nTAYLORF2\nSEOBNRV4P,\nSEOBNRV4PHM,\nSPINTAYLORT4\nIMRPHENOMNSBH,\nIMRPHENOMXPHM,\nSEOBNRV4_ROM_NRTIDALV2_NSBH,\nSEOBNRV4PHM\nGWTC-4.0\n(Abac et al. 2025b)\nO4a\nIMRPHENOMD,\nSEOBNRV4_OPT,\nSEOBNRV4_ROM,\nSEOBNRV5_ROM,\nSPINTAYLORT4, TAYLORF2\nIMRPHENOMXPHM\nIMRPHENOMNSBH,\nIMRPHENOMPV2_NRTIDALV2,\nIMRPHENOMXO4A\nIMRPHENOMXPHM_SPINTAYLOR,\nNRSUR7DQ4,\nSEOBNRV4_ROM_NRTIDALV2_NSBH,\nSEOBNRV5PHM\nwhere h represents the strain data, and Sn is the power spec-\ntral density (PSD) of the detector noise (see Appendix B of\nAbac et al. 2025a). The lower integration limit frequency\nflow is determined by considerations of computational cost,\ndata quality, and calibration reliability. The upper limit fhigh\nis predominantly based on considerations of computational\ncost. Both limits may vary with search implementations and\ntemplates.\nModeled search pipelines produce triggers by looking for\npeaks exceeding a given threshold in the SNR time series.\nThis same procedure is applied to the calibrated data pro-\nvided by all available detectors. All search pipelines attempt\nto pair candidates from one detector with coincident candi-\ndates from others. In such cases, under the assumption of\nindependent detector noise, the network SNR is computed as\nthe root-sum-square of the individual detector SNRs (Mag-\ngiore 2007). Some pipelines also consider signals detected\nby a single interferometer. Each pipeline has its own ap-\nproach for combining the SNR values it measures with its\nown signal consistency tests to rank its candidates. Based on\ntheir ranking, search pipelines assign each candidate a false\nalarm rate (FAR) value, which quantifies the expected rate of\nnon-astrophysical candidates produced with a rank at least as\nhigh as the candidate under consideration.\nIn addition to the measure of detection significance pro-\nvided by the FAR of a candidate, we have also provided the\nprobability pastro that a candidate is of astrophysical rather\nthan terrestrial (noise) origin. The calculation of pastro ac-\ncounts for both the rate of noise events corresponding to the\nFAR and an estimated rate of astrophysical signals under\nsome prior model of the CBC population (Farr et al. 2015;\nKapadia et al. 2020). It is formally defined as (Abbott et al.\n2016a)\npastro(x) =\nRastrof(x)\nRastrof(x) + Rnoiseb(x),\n(2)\nwhere Rastro is the total rate of astrophysical candidates in\na given pipeline, Rnoise is the total rate of candidates due\nto noise, and f(x) and b(x) are the probability density func-\ntion (PDF) of signal and noise events, respectively, at the can-\ndidate ranking value x. Each pipeline estimates these rates\nand calculates a pastro value for the candidates it identifies\nusing its own method. Since O4a, most pipelines use a com-\nmon signal model based on a distribution of simulated sig-\nnals (injections) over source masses, spins and distance (see\n\n8\nTable 2. Waveform models used in GWTC analyses. We indicate if the model includes spin-precession, matter effects and which multipoles\nare included for each model. For spin-precessing models, the multipoles correspond to those available in the coprecessing frame. We indicate\nthe most relevant reference for each model, additional references are given in the main text of Section 2. Special candidate analyses might\nemploy additional waveform models not listed here, but discussed for those particular signals.\nModel\nPrecession\nMultipoles (\u2113, |m|)\nMatter\nReference\nSPINTAYLORT4\n\u2713\n\u2113\u22644\n\u2713\nIsoyama et al. (2020)\nTAYLORF2\n\u00d7\n(2, 2)\n\u2713\nDamour et al. (2001)\nIMRPHENOMD\n\u00d7\n(2, 2)\n\u00d7\nKhan et al. (2016)\nIMRPHENOMD_NRTIDAL\n\u00d7\n(2, 2)\n\u2713\nDietrich et al. (2019b)\nIMRPHENOMHM\n\u00d7\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4), (4, 3)\n\u00d7\nLondon et al. (2018)\nIMRPHENOMNSBH\n\u00d7\n(2, 2)\n\u2713\nThompson et al. (2020)\nIMRPHENOMPV2\n\u2713\n(2, 2)\n\u00d7\nBoh\u00e9 et al. (2016)\nIMRPHENOMPV2_NRTIDAL\n\u2713\n(2, 2)\n\u2713\nDietrich et al. (2019b)\nIMRPHENOMPV2_NRTIDALV2\n\u2713\n(2, 2)\n\u2713\nDietrich et al. (2019a)\nIMRPHENOMPV3HM\n\u2713\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4), (4, 3)\n\u00d7\nKhan et al. (2020)\nIMRPHENOMXPHM\n\u2713\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4)\n\u00d7\nPratten et al. (2021)\nIMRPHENOMXPHM_SPINTAYLOR\n\u2713\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4)\n\u00d7\nColleoni et al. (2025b)\nIMRPHENOMXO4A\n\u2713\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4)\n\u00d7\nThompson et al. (2024)\nNRSUR7DQ4\n\u2713\n\u2113\u22644\n\u00d7\nVarma et al. (2019a)\nSEOBNRV3\n\u2713\n(2, 2), (2, 1)\n\u00d7\nPan et al. (2014)\nSEOBNRV4_OPT\n\u00d7\n(2, 2)\n\u00d7\nDevine et al. (2016)\nSEOBNRV4_ROM\n\u00d7\n(2, 2)\n\u00d7\nBoh\u00e9 et al. (2017)\nSEOBNRV4HM_ROM\n\u00d7\n(2, 2), (2, 1), (3, 3), (4, 4), (5, 5)\n\u00d7\nCotesta et al. (2020)\nSEOBNRV4_ROM_NRTIDAL\n\u00d7\n(2, 2)\n\u2713\nDietrich et al. (2019b)\nSEOBNRV4_ROM_NRTIDALV2_NSBH\n\u00d7\n(2, 2)\n\u2713\nMatas et al. (2020)\nSEOBNRV4P\n\u2713\n(2, 2), (2, 1)\n\u00d7\nOssokine et al. (2020)\nSEOBNRV4PHM\n\u2713\n(2, 2), (2, 1), (3, 3), (4, 4), (5, 5)\n\u00d7\nOssokine et al. (2020)\nSEOBNRV4T\n\u00d7\n(2, 2)\n\u2713\nSteinhoff et al. (2016)\nSEOBNRV4T_SURROGATE\n\u00d7\n(2, 2)\n\u2713\nLackey et al. (2019)\nSEOBNRV5_ROM\n\u00d7\n(2, 2)\n\u00d7\nPompili et al. (2023)\nSEOBNRV5PHM\n\u2713\n(2, 2), (2, 1), (3, 3), (3, 2), (4, 4), (4, 3), (5, 5)\n\u00d7\nRamos-Buades et al. (2023)\nTEOBRESUMS\n\u00d7\n(2, 2), (2, 1), (3, 3), (3, 2), (3, 1)\n\u2713\nAkcay et al. (2019)\nEssick et al. 2025, and Section 3.7) to calculate the signal\nPDF f(x); a slightly different model used by one analysis is\ndescribed in Section 3.2.\nThe total astrophysical probability pastro is then dis-\ntributed between three mutually-exclusive source categories:\na BNS class corresponding to both component (source-\nframe) masses ranging between 1 M\u2299and 3 M\u2299; a NSBH\nclass for one mass between 1 M\u2299and 3 M\u2299and the other\nabove; and a BBH class corresponding to both masses above\n3 M\u2299. The associated probabilities for each category thus\nsum to pastro:\npBNS + pNSBH + pBBH = pastro.\n(3)\nThe complementary probability that the candidate is of ter-\nrestrial origin, i.e. caused by noise rather than a CBC, is no-\ntated as pterr = 1 \u2212pastro.\nTransient search methods used to compile our catalog for\ndata from the first observing run (O1) and second observing\n\n9\nrun (O2) are described in Section 3 of Abbott et al. (2019a),\nand for data from third observing run (O3), in Section 4\nof Abbott et al. (2021a), Section 3 of Abbott et al. (2024)\nand Section 4 of Abbott et al. (2023a). We describe here\nthe methods used for data from O4a, in the context of this\ncumulative catalog. In the coming subsections, we present\ndetails of the different pipelines used to identify transient\nGW candidates, including coherent WaveBurst (CWB) for\nminimally-modeled sources (Klimenko et al. 2016; Mishra\net al. 2022, 2025), and GStreamer LIGO Algorithm Li-\nbrary (GSTLAL; Cannon et al. 2012a; Messick et al. 2017;\nSachdev et al. 2019; Hanna et al. 2020; Cannon et al. 2020;\nSakon et al. 2024; Ray et al. 2023; Tsukada et al. 2023; Ew-\ning et al. 2024; Joshi et al. 2025a,b), Multi-Band Template\nAnalysis (MBTA; All\u00e9n\u00e9 et al. 2025), PYCBC (Dal Canton\net al. 2021), and Summed Parallel Infinite Impulse Response\n(SPIIR; Chu et al. 2022) for model-based search analyses.\nEach pipeline analyzed strain data from the available detec-\ntors, using the data summarized in Table 3.\nFor offline analyses, a set of Category 1 (CAT1) flags are\ndetermined, which flag periods of severe data-quality or tech-\nnical issues affecting the interferometers during the observa-\ntion time. During CAT1 periods (detailed in Section 4.1 of\nSoni et al. 2025), the data are considered too contaminated\nby noise to be analyzable within realistic computational or\nhuman resources.\nDuring the O1 to O3 observing runs, short-duration Cate-\ngory 2 (CAT2) flags were also provided for transient searches\n(Abbott et al. 2020b). CAT2 flags are based on statistical cor-\nrelations found between excess noise transients in auxiliary\nchannels and in the strain data. As of O4, these CAT2 flags\nare no longer used in CBC searches, though they continue to\nbe used for minimally-modeled transient searches (Soni et al.\n2025).\nAs an extra input for CBC searches, a timeseries is gen-\nerated by the IDQ pipeline (Essick et al. 2020). This time-\nseries contains statistical data-quality information based on\nthe activity of auxiliary channels deemed safe (i.e., chan-\nnels that should not be influenced by GWs). Observation\ntimes marked with IDQ flags are likely to be contaminated\nby glitches. Unlike CAT1 flags, which are mandatory ve-\ntoes prior to any analysis, IDQ flags are optional and may\nbe used either as vetoes, or as input in the ranking statis-\ntic of the candidates. CAT1 vetoes and the IDQ timeseries\nare created from the strain data and auxiliary channels as a\npre-processing step and ingested by the offline searches (see\nFigure 1).\n3.1. CWB\nThe CWB algorithm is designed to detect transient GW\nsignals using networks of GW detectors without requiring\na specific waveform model. It identifies coincident excess\npower events by analyzing multi-resolution time\u2013frequency\n(TF) representations of detector strain data (Klimenko et al.\n2008, 2016). Once potential GW signals or noise events are\nidentified, CWB reconstructs the source sky location and the\nsignal waveforms recorded by the detectors using the con-\nTable 3.\nThe O4a data processed by search pipelines.\nAs\ndescribed in Abac et al. (2025c), different levels of processing\nproduce different channels of data.\nFull Frames refers to the\nGDS-CALIB_STRAIN_CLEAN channel, while Analysis Ready\nrefers to the GDS-CALIB_STRAIN_CLEAN_AR channel; these\nchannels are identical other than that the Analysis Ready channel\ncontains only data for times ready to be analysed.\nPipeline\nOnline\nOffline\nCWB\nFull Frames\nFull Frames\nGSTLAL\nFull Frames\nFull Frames\nMBTA\nFull Frames\nAnalysis Ready\nPYCBC\nFull Frames\nAnalysis Ready\nSPIIR\nFull Frames\nno offline analysis\nstrained maximum-likelihood method (Klimenko et al. 2005,\n2016). This analysis is performed on detector strain data, ac-\ncommodating signal frequencies up to a few kilohertz and\ndurations up to a few seconds.\nThe CWB detection statistic relies on coherent energy Ec,\nwhich is derived from cross-correlating the reconstructed sig-\nnal waveforms in the detectors and normalizing them by the\nspectral amplitude of the detector noise. The square root of\nEc provides a lower bound on the signal network SNR and is\nused for the initial selection of candidates identified by CWB.\nAs the production rate of CWB candidates is primarily driven\nby glitches, additional post-production vetoes are applied to\nfurther reduce the background rates.\nOne primary signal-independent veto statistics is the net-\nwork correlation coefficient, defined as cc = Ec/(Ec + En),\nwhere En represents the normalized residual noise energy\nafter the reconstructed signal has been subtracted from the\ndata. Typically, for glitches cc \u226a1. Consequently, candi-\ndates with cc < 0.6 are rejected as potential glitches. For\nauthentic GW signals, the residual energy En is expected to\nfollow the \u03c72 distribution with the number of degrees of free-\ndom NDoF proportional to the number of TF data samples\ncomprising the signal. The reduced \u02dc\u03c72 = \u03c72/NDoF statis-\ntic serves as a powerful signal-independent veto, effectively\nidentifying and removing glitches where \u02dc\u03c72 is significantly\ngreater than 1. To enhance the search for CBC signals, CWB\nperforms analysis in the frequency band below 512 Hz and\nalso employs weak signal-dependent vetoes. These vetoes\nare based on the central frequency fc and the detector-frame\nchirp mass (1 + z)M, both of which are estimated from the\nTF evolution of the signal power (Tiwari et al. 2016).\nAll candidates identified by CWB are ranked by the re-\nduced coherent network SNR\n\u03c1cWB =\ns\nEc\n1 + \u02dc\u03c72[max(1, \u02dc\u03c72) \u22121] .\n(4)\nTo estimate the statistical significance of the GW candidates,\nthey are ranked against background events generated by the\n\n10\n1\n552\n3\n200\nPrimary mass [M ]\n1\n3\n200\n10\n268\nSecondary mass [M ]\nGstLAL search space\nz\n1\n(\n0.05, 0.05)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.99, 0.99)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.99, 0.99)\nz\n2\n(\n0.99, 0.99)\nz\n1\n(\n0.7, 0.99)\nz\n2\n(\n0.7, 0.99)\n1\n2\n100\n10\n500\nPrimary mass [M ]\n1\n2\n100\n10\n500\nSecondary mass [M ]\nMBTA search space\nz\n1\n(\n0.05, 0.05)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.998, 0.998)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.998, 0.998)\nz\n2\n(\n0.998, 0.998)\n1\n2\n100\n10\n500\nPrimary mass [M ]\n1\n2\n100\n10\n500\nSecondary mass [M ]\nPyCBC search space\nz\n1\n(\n0.05, 0.05)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.997, 0.997)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.997, 0.997)\nz\n2\n(\n0.997, 0.997)\n1.1\n10.0\n3.0\n100.0\nPrimary mass [M ]\n1.1\n10.0\n3.0\n100.0\nSecondary mass [M ]\nSPIIR search space\nz\n1\n(\n0.05, 0.05)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.99, 0.99)\nz\n2\n(\n0.05, 0.05)\nz\n1\n(\n0.99, 0.99)\nz\n2\n(\n0.99, 0.99)\nFigure 2. Regions of the CBC parameter space explored by our different template-based search pipelines. Individual masses are given in the\ndetector frame, i.e. they are redshifted. The spin parameters \u03c7z\n1,2 are the spin projections along the orbital angular momentum.\n\n11\ndetector noise. A comprehensive background data sample,\nequivalent to approximately 1000 years of observation time,\nis obtained by repeating the CWB analysis on time-shifted\ndata. To ensure that astrophysical signals are excluded from\nthe background data, the time shifts are selected to be much\nlarger than the expected signal time delay between the de-\ntectors. The statistical significance of each CWB candidate\nis quantified by its FAR. The FAR is defined as the rate of\nbackground events that exhibit a larger \u03c1cWB value than the\nGW candidate in question. To account for potential long-\nterm variations in detector noise, the candidate significance\nis estimated using nearby data intervals, typically one to two\nweeks in length.\nSince the publication of GWTC-3.0, the CWB algorithm\nused in the previous observing runs (Klimenko et al. 2016;\nDrago et al. 2020), i.e., CWB-2G, has undergone signifi-\ncant improvements, and a new version, CWB-BBH, has been\nadopted for CBC searches: it incorporates two major changes\ncompared to CWB-2G.\nThe\nfirst\nchange\ninvolves\nreplacing\nthe\nWilson\u2013\nDebauchies\u2013Meyer (WDM) wavelet transform (Necula et al.\n2012) with the multi-resolution WaveScan transform, which\nis based on the Gabor wavelets (Klimenko 2022). This up-\ndate effectively reduces temporal and spectral leakage in the\nTF data, potentially leading to more accurate signal repre-\nsentation.\nSecondly, in addition to the traditional excess-power statis-\ntic, the algorithm now incorporates the cross-power statis-\ntic (Klimenko 2022) for identifying transient signals. The\nexcess-power represents the total power of a TF data sam-\nple (or WaveScan pixel) integrated over the detector network.\nThe cross-power represents the correlation of power in the\ndetectors. Both statistics are maximized over possible time-\nof-flight delays of a GW signal across the detector network.\nThe excess-power and the cross-power amplitudes, ae and\na\u00d7, respectively, follow a predictable half-normal distribu-\ntion with unity variance assuming quasi-stationary detector\nnoise (Klimenko 2022).\nFor analysis, TF pixels with the\nexcess-power amplitude exceeding 2.3 standard deviations\nare selected.\nSpatially and temporally adjacent TF pixels\nare then clustered to form the initial CWB-BBH candidates\n(clusters).\nThe clustered excess-power PI\ni=1 a2\ne[i] and the cross-\npower PI\ni=1 a2\n\u00d7[i] are used to calculate the upper bounds on\nthe signal network SNR \u03c1p and the coherent network SNR\n\u03c1\u00d7 respectively (Mishra et al. 2025), where I is the number\nof the TF pixels comprising the cluster. The \u03c1e is optimized\nfor identification of clusters due to fluctuations of the quasi-\nstationary detector noise dominating the initial CWB-BBH\nrate on the order of 100 Hz. All clusters with \u03c1p > 4 are\naccepted for further analysis. The accepted CWB-BBH clus-\nters are mostly produced by glitches with a typical rate of\n0.1 Hz. After selection, the initial TF clusters are aggregated\nif they fall within the time and frequency intervals of 0.23 s\nand 64 Hz respectively. It improves the energy collection for\ntransient candidates that can be fragmented into clusters by\nthe TF transform. The glitch rate is further reduced by requir-\ning \u03c1\u00d7 > 7, where the upper bound of the coherent network\nSNR is calculated for the defragmented candidates.\nThe above conditions on the \u03c1e and \u03c1\u00d7 require that the GW\nsignal clusters with SNR > 4 and defragmented GW candi-\ndates with SNR > 7 are accepted for the analysis. The result-\ning reduced candidates rate, on the order of 1 mHz, makes\nthe subsequent likelihood analysis and reconstruction of the\nremaining candidates computationally feasible. At this stage,\nthe sky location of each candidate is determined and the\nsignal waveforms are reconstructed with the inverse WaveS-\ncan transform (Klimenko 2022). The CWB-BBH candidates\nwith \u03c1cWB > 7 are stored for the post-production analysis.\nMoreover, the post-production veto analysis has been re-\nplaced by the XGBoost machine-learning algorithm (Mishra\net al. 2021, 2022, 2025), based on an ensemble of deci-\nsion trees. It performs a classification of CWB-BBH can-\ndidates by using a subset of 25 summary statistics including\n\u03c1cWB, cc, \u02dc\u03c7, \u03c1e, \u03c1\u00d7, fc, and (1 + z)M. To improve the dis-\ntinction between astrophysical GW signals and glitches, the\nCWB-BBH detection statistic is modified as\n\u03c1r = \u03c1cWBWXGB,\n(5)\nwhere WXGB is the XGBoost classification factor (Mishra\net al. 2021) ranging from 0 (indicating a glitch) to 1 (indi-\ncating a signal). The XGBoost response is trained using a\nsubset of background candidates and a representative set of\nsimulated BBH signals, which are injected into the detector\ndata and recovered with CWB-BBH. Due to a weak depen-\ndence of the CWB-BBH summary statistics on the CBC pop-\nulation and signal models, the algorithm is robust to a variety\nof CBC features, including higher multipoles, unequal com-\nponent masses, misaligned spins, eccentric orbits, and possi-\nble deviations from GR (Mishra et al. 2022; Bhaumik et al.\n2025).\n3.2. GSTLAL\nGSTLAL is a stream-based time-domain matched-filtering\nsearch pipeline (Cannon et al. 2012a; Messick et al. 2017;\nSachdev et al. 2019; Hanna et al. 2020; Cannon et al. 2020;\nSakon et al. 2024; Ray et al. 2023; Tsukada et al. 2023; Ew-\ning et al. 2024; Joshi et al. 2025a,b). All previous GWTC ver-\nsions included results produced by GSTLAL (Abbott et al.\n2019a, 2021a, 2024, 2023a).\nFor this analysis, multiple\nGSTLAL configurations were used: an online configura-\ntion whose results were re-evaluated using the full back-\nground, an offline configuration that processed data dropped\nby the online configuration, and another offline configuration\nthat targeted intermediate-mass black hole (IMBH) mergers\n(Joshi et al. 2025a). The primary configuration was an online\nsearch, which identified CBC signals in near real-time, en-\nabling rapid alerts and follow-up. The online search dropped\n\u223c3% of the observing run data due to, e.g., computer down-\ntime. The dropped data were processed in an offline con-\nfiguration, methodologically identical to the online configu-\nration, but executed post O4a. The online configuration did\n\n12\nnot cover the high-mass region of the parameter space, so an\nadditional offline configuration was run to target the IMBH\nregion, shown in grey in Figure 2. All configurations (on-\nline, dropped-data and IMBH) were used to evaluate search\nsensitivity by injecting simulated signals into the detector\nstrain data and analyzing the effectiveness of signal recov-\nery. Final candidate ranking and significance estimation in-\ncorporated the collective results from all configurations. An\nadditional early-warning configuration, designed to identify\nBNS mergers prior to coalescence, was also deployed during\nO4a. However, results from the early-warning configuration\nare not part of GWTC-4.0.\nThe analysis begins by constructing a template bank to\ncover the targeted astrophysical parameter space.\nStrain\ndata are then pre-processed to prepare for matched-filtering,\nwhich correlates the pre-processed strain with templates from\nthe bank. Peaks in the matched-filter output are identified\nas triggers and subsequently ranked using a likelihood ra-\ntio (LR) statistic that incorporates signal consistency and de-\ntector network properties (Tsukada et al. 2023). The back-\nground LR distribution from noise triggers is used to esti-\nmate the FAR and the significance of each GW candidate. In\nthe following paragraphs, we describe each component of the\nanalysis in detail, beginning with the template bank.\nFor O4a, the template bank targeted CBCs with detector-\nframe total masses between 1.95 M\u2299and 610 M\u2299, and mass\nratios from 0.05 to 1 (Sakon et al. 2024; Joshi et al. 2025a). It\nwas divided into two disjoint regions: stellar-mass (compo-\nnent masses up to 200 M\u2299) and IMBH (primary component\nmass between 200 M\u2299and 552 M\u2299and secondary compo-\nnent mass below 268 M\u2299). While no BBHs with total mass\nabove 400 M\u2299have been observed so far, cosmological red-\nshifting of source-frame masses can shift distant stellar-mass\nbinaries into the IMBH region in the detector frame, moti-\nvating an extended search (Abbott et al. 2023a). Templates\nin both regions were spin aligned, i.e. spin components in\nthe orbital plane are zero.\nAligned spin values were al-\nlowed in [\u22120.99, +0.99] for stellar-mass templates, with ad-\nditional restriction to [\u22120.05, +0.05] for component-masses\nbelow 3 M\u2299, consistent with observations for BNSs (Sto-\nvall et al. 2018). In the IMBH region, spins were restricted\nto [\u22120.70, +0.99] to mitigate triggers from noise transients\nwith similar time\u2013frequency structure as high-mass wave-\nforms with large anti-aligned spins (Hanna et al. 2022). The\nsearch space is illustrated in Figure 2.\nDuring template bank creation, templates were placed\nusing a metric based on the IMRPHENOMD approximant\n(Husa et al. 2016; Khan et al. 2016), with a lower frequency\ncutoff of 10 Hz and a maximum duration of 128 s, ensuring\ncoverage of the detector\u2019s sensitive band while limiting com-\nputational cost. The duration constraint led to a template-\ndependent low-frequency cutoff for low-mass systems. For\nexample, a 1.4 M\u2299\u20131.4 M\u2299binary would have a waveform\nduration of over 1000 s starting from 10 Hz. To stay within\nthe 128 s constraint, its corresponding lower frequency cutoff\nmust be raised to \u223c22 Hz (Peters & Mathews 1963).\nTemplate placement was performed using MANIFOLD\n(Hanna et al. 2023), an algorithm based on a geometric bi-\nnary tree that tiles the parameter space dictated by the mini-\nmal match constraints. A minimal match of 97% was applied\nin the stellar-mass region, corresponding to a 10% expected\nloss in detection rate (Owen 1996), while the IMBH region\nused 99%, resulting in a total of \u223c1.8 \u00d7 106 templates.\nTo improve fault tolerance of the online configuration, the\nstellar-mass bank was interleaved into two complementary\nhalves, each independently covering the stellar-mass region\nand analyzed independently at separate data centers (God-\nwin 2020; Sakon et al. 2024). Each half was subdivided into\ntemplate bins and each bin was decomposed into filters using\nsingular value decomposition (SVD; Cannon et al. 2012b;\nSakon et al. 2024).\nAfter template bank construction, the detector strain data\nwere preprocessed to ensure compatibility with the tem-\nplates and to reduce noise contamination. Data were resam-\npled to 2048 Hz and whitened. To suppress short-duration\nhigh-amplitude noise transients that can mimic astrophysi-\ncal signals, especially at high masses where template wave-\nforms are short, amplitude-based gating was applied to the\nwhitened data. The gating threshold was a linear function of\nthe chirp-mass, with values computed per template bin and\nexpressed in units of the standard deviation of the whitened\nstrain data. This adaptive approach balances glitch suppres-\nsion with sensitivity to real signals across the mass range\n(Sachdev et al. 2019; Ewing et al. 2024).\nIn parallel with gating, accurate whitening of strain data\nand template waveforms required careful PSD estimation to\ncharacterize frequency-dependent noise. In the online con-\nfiguration, PSDs were estimated using a 4 s fast Fourier trans-\nform (FFT) computed continuously on incoming data and\nused to whiten the strain in real time.\nTo account for longer-term noise variations that could im-\npact the SVD, template waveforms were re-whitened weekly\nusing updated PSDs derived from recent data. For template\nwhitening, the analysis period was divided into continuous\nsegments of up to 8 h, with each segment producing a PSD\nusing a 8 s FFT.\nThe final PSD was constructed by tak-\ning the median power in each frequency bin across segments\n(Messick et al. 2017). The SVD basis for each template bin\nwere then recomputed weekly using the same PSD. Weekly\ncadence balanced the need to track gradual detector noise\nevolution with the high computational cost of recomputing\nSVDs (Ewing et al. 2024).\nAfter whitening the strain data using the PSD, matched-\nfiltering was performed in the time domain, using the SVD\nbasis, starting at 15 Hz for the stellar-mass region (10 Hz for\nthe IMBH region). The output, an SNR time series, was\nscanned for peaks exceeding a threshold of 4, which were\ndefined as triggers. A signal-consistency statistic, \u03be2, was\ncomputed for each trigger to quantify the deviation between\nobserved and expected SNR values across a fixed number of\npoints centered on the peak. Only the highest SNR trigger in\neach 1 s window per template bin was kept. Templates with\nchirp masses up to 1.73 M\u2299used the TAYLORF2 approxi-\n\n13\nmant and 701 samples to compute \u03be2. Higher-mass templates\nused the SEOBNRV4_ROM approximant and 351 samples\nto compute \u03be2 (Messick et al. 2017). The resulting triggers\nwere used to form candidates for further processing.\nCandidates were classified as either single-detector or co-\nincident. Coincident candidates are defined as triggers from\nthe same template in two or more detectors and occurring\nwithin the light-travel time between detectors, plus a 5 ms\nwindow to account for timing uncertainties. Single-detector\ncandidates had no corresponding trigger in another detec-\ntor within the window (Sachdev et al. 2019).\nCandidates\nfrom the IMBH region were excluded if they were a single-\ndetector candidate. Each candidate was ranked using a LR\nquantifying the probability of astrophysical versus noise ori-\ngin.\nThe LR incorporated per-detector SNRs, the signal-\nconsistency statistic \u03be2, local trigger rates, detector sensitiv-\nities, and prior assumptions about the CBC population. For\ncoincident candidates, the relative arrival times and phases\nat the different detectors were included, with probabilities\ncomputed assuming isotropically-distributed sources. In con-\ntrast, single-detector candidates were down-weighted using a\nsingles-penalty, empirically tuned via signal simulation cam-\npaigns, in order to suppress false positives while retaining\nsensitivity (Sachdev et al. 2019).\nThe LR was computed independently for each template bin\nto account for variations in how templates interact with de-\ntector noise. Background distributions for each template bin\nwere built from single-detector triggers occurring during co-\nincident observing time. Candidates were clustered in an 8 s\nwindow, and the candidate with the highest LR across all\ntemplate bins was selected for further processing. Further\ndetails on the LR calculation can be found in Cannon et al.\n(2015); Messick et al. (2017); Tsukada et al. (2023).\nCandidate significance was quantified using FAR, defined\nas the rate at which detector noise could produce a candidate\nwith equal or higher LR than the candidate under considera-\ntion. FAR was estimated by populating the background LR\ndistribution via Monte Carlo sampling of SNR and \u03be2 values\ndrawn from the empirical background, smoothed via kernel\ndensity estimation (KDE). Samples were assigned coales-\ncence times, phases, and templates from uniform distribu-\ntions (Cannon et al. 2013; Joshi et al. 2025a). To reduce con-\ntamination of the background by astrophysical signals, a 10 s\nwindow around each GW candidate is vetted and excluded\nfrom the background, but only for candidates identified on-\nline by the online configuration (Joshi et al. 2023).\nDropped data from the online configuration was processed\nin an offline configuration, yielding additional candidates.\nResults from both configurations were merged, and FARs re-\ncomputed using the full background collected by the online\nconfiguration (Joshi et al. 2025b). The combined set of can-\ndidates and background defined the stellar-mass search anal-\nysis. To produce the final GWTC-4.0 results, candidates and\nbackground from the stellar-mass and IMBH search-analysis\nregions were combined into a unified analysis.\nEach re-\ngion was assigned a weight, determined from injection cam-\npaigns (Essick et al. 2025), reflecting its relative sensitivity\nand the expected number of detectable astrophysical signals.\nThe stellar-mass and IMBH search analyses were assigned\nweights of 0.94 and 0.06, respectively. The weights account\nfor the fact that different analyses contribute unequally to\nthe final set of candidates under the assumption of a given\nprior source population. FARs were rescaled by the inverse\nof these weights, and LRs were recomputed to provide a uni-\nfied, unbiased ranking (Joshi et al. 2025a).\nIn addition to FAR, the total probability of astrophysi-\ncal origin pastro, and the classification probability for the\nmutually-exclusive BNS, NSBH, or BBH source classes,\nwere calculated for each candidate. Unlike other pipelines,\nGSTLAL adopts a signal model that assumes the Salpeter\nprimary mass function (Salpeter 1955) for each source\nclass, with uniform distributions in mass ratio and spin.\nThe source-specific probabilities were computed using a\nBayesian framework that models the posterior probability\ndistribution of the rates associated with each class.\nThe\nframework treats GW triggers as realizations of independent\nPoisson processes, with rate estimates derived from previous\nobserving runs and the population properties of each source\nclass (Ray et al. 2023).\nO3 differed from O4a in search configuration, template\nbank design, and candidate ranking. While GWTC-4.0 re-\nsults were produced by using online results supplemented\nwith offline analyses to avoid redundant processing, the\nGWTC-3.0 results were produced entirely from a post-run\noffline analysis (Abbott et al. 2023a).\nThe O3 template\nbank extended to detector-frame total masses of 758 M\u2299,\nwith aligned-spin parameters in [\u22120.999, 0.999] for compo-\nnents more massive than 3 M\u2299, and was constructed using a\nstochastic placement algorithm (Abbott et al. 2021a). No du-\nration constraint was imposed during matched filtering with\nthe O3 template bank. Ranking of candidates identified by\nmatched-filtering used an LR similar to O4a, but also incor-\nporated the IDQ glitch likelihood (Godwin et al. 2020; Ab-\nbott et al. 2021a). The IDQ glitch likelihood was used only\nfor single-detector candidates prior to GWTC-2.1, and the\nsingles-penalty parameter, used to down-weight such trig-\ngers, was tuned differently than in O4a. Additionally, the\nLR term modeling the distribution of \u03be2 used an empirically-\ntuned analytical function in O3, rather than being directly\ninformed by the statistical properties of \u03be2 as done in O4a.\nFurthermore, data near vetted GW candidates were not ex-\ncluded from background estimation before O4a.\nThe GSTLAL pipeline used during O2 differed from\nO3 primarily in the template bank construction and can-\ndidate ranking methodology.\nThe O2 template bank cov-\nered detector-frame total masses up to 400 M\u2299and mass\nratios from 1/98 to 1, with aligned-spin parameters in\n[\u22120.999, 0.999] for components above 2 M\u2299(Abbott et al.\n2019a; Mukherjee et al. 2021). The LR in O2 assumed uni-\nform signal recovery across the template bank, ignoring the\nnon-uniform template density and any astrophysical prior on\nthe source population (Abbott et al. 2021a; Fong 2018).\nThe O2 GSTLAL pipeline differed from O1 in its template\nbank construction, candidate ranking methodology and data\n\n14\nconditioning. The O1 template bank covered detector-frame\ntotal masses from 2 M\u2299to 100 M\u2299(Mukherjee et al. 2021).\nIn O1, the LR was computed only for coincident candidates\nand excluded time and phase differences between detectors\n(Hanna et al. 2020). The LR included the joint probability of\nobserved SNRs but assumed equal horizon distances across\ndetectors: an approximation that neglected how detector-\nspecific noise characteristics impact the horizon distance. It\nwas improved in O2 by pre-computing joint SNR distribu-\ntions for a discrete set of horizon-distance ratios. Addition-\nally, the O1 pipeline also lacked a template-mass-dependent\nglitch excision threshold (Sachdev et al. 2019).\n3.3. MBTA\nMBTA (Abadie et al. 2012a; Adams et al. 2016; Aubin\net al. 2021; All\u00e9n\u00e9 et al. 2025) has performed online searches\nfor CBCs since the initial-detector era science runs (Abadie\net al. 2012b).\nMBTA analyzes each detector indepen-\ndently using matched-filtering, before searching for candi-\ndates seen in coincidence. To reduce the computational cost,\nthe pipeline splits the matched-filtering process over several\nfrequency bands (typically two). Since O3, MBTA runs of-\nfline search analyses as well, with the aim of more accurately\nassessing the significance of candidates and contributing to\nthe GWTC (Abbott et al. 2024, 2023a).\nThe parameter space explored by MBTA\u2019s template bank\nis entirely defined by the detector-frame masses and spins\n(assumed parallel to the orbital angular momentum) of the bi-\nnary components. The O4a analysis covers individual masses\ngreater than 1 M\u2299, total masses up to 500 M\u2299, and mass ra-\ntios ranging from 1/50 to 1. In line with astrophysical ex-\npectations for NSs (Stovall et al. 2018), spin magnitudes are\nrestricted to 0.05 for objects with masses below 2 M\u2299, while\nmore massive objects are allowed to have spin magnitudes\nof up to 0.998. Very short templates, which tend to gener-\nate a background excess, are removed by introducing a cut-\noff of 200 ms on the template duration, calculated starting\nfrom 18 Hz. A visual representation of the parameter space\ncovered by the O4a MBTA stellar-mass bank is given in the\nupper-right part of Figure 2.\nThe template banks used for O4a are generated with dif-\nferent algorithms. The stellar-mass search space is first di-\nvided into two regions, corresponding to BNS and symmet-\nrical BBH (no more than a factor 3 between the two com-\nponent masses). Templates in the BNS region are geomet-\nrically placed according to a local metric estimate (Brown\net al. 2013), aiming for SNR recovery of at least 98%. Sym-\nmetrical BBH template placement uses a hybrid algorithm\n(Roy et al. 2017, 2019), with a similar expected SNR recov-\nery. The rest of the bank is then completed using the same\nalgorithm, with the objective of limiting the maximum SNR\nloss to 3.5%. As MBTA filters data in two disjoint frequency\nbands, a bank has been created for each of them, as well as\none for the whole frequency range. Each template from the\nlatter bank is associated with a template from other banks,\nmaximizing their overlap in their common frequency band.\nMBTA uses a total of almost 825000 different templates,\nwhich are almost entirely described by approximately 55000\nlow-frequency-band templates and 20000 high-frequency-\nband templates. Templates use the SPINTAYLORT4 approx-\nimant (Klein et al. 2014) for total masses below 4 M\u2299and\nSEOBNRV4_OPT (Boh\u00e9 et al. 2017) above.\nBefore matched filtering, MBTA applies multiple pre-\nprocessing steps to the calibrated strain data delivered by the\ndetectors. Data are first resampled to 4096 Hz. Next, a gat-\ning procedure is applied, designed to remove short and high-\namplitude glitches. The gating used for O4 is similar to the\nversion deployed for O3 and is triggered by drops in the de-\ntector sensitivity (Aubin et al. 2021). It is also applied to\nperiods of poor quality data identified by data-quality vetoes\n(Abbott et al. 2020b). Less than 0.1% of the data provided\nby each detector was removed by MBTA gating during O4a\n(All\u00e9n\u00e9 et al. 2025). An ungated search analysis is also per-\nformed for part of the parameter space, with the aim of find-\ning the massive, intense CBCs that are likely to trigger the\ngating (Aubin et al. 2021).\nMBTA regularly re-estimates the noise PSD of each de-\ntector by taking the median over thousands of seconds of\ndata from several FFTs, whose lengths range from seconds\nto hundreds of seconds, depending on the targeted region of\nthe parameter space (Aubin et al. 2025).\nFor most templates, the matched-filter calculation is car-\nried out in two disjoint frequency bands, starting at 24 Hz and\nseparated at 80 Hz. When a sufficiently high SNR is detected,\nbands are then coherently recombined to produce a unified\nsingle-detector trigger from the two bands. The shortest tem-\nplates, however, are processed using a single band starting at\n20 Hz due to their intrinsically narrower frequency band.\nTriggers retrieved with an SNR above 4.4 (9 for the un-\ngated analysis) are recorded. MBTA then applies several\ntools to reject triggers produced by transient noise. A ba-\nsic \u03c72 test rejects any trigger whose SNR is not distributed\nas expected between the filtered bands (Adams et al. 2016).\nSince O3, a \u03c72 statistic is used to measure the discrepancy\nbetween the measured SNR time series and the template au-\ntocorrelation. The test is used to reweight the SNR, defining\na single-detector ranking statistic (Aubin et al. 2021).\nSince O3, MBTA has been downgrading the ranking\nstatistics of triggers occurring during periods when detectors\nshow signs of poor data quality. In the O4a offline analysis,\nthis task is performed by a new technique called SNR-Excess.\nIt builds a \u03c72 statistic from the differences between the time-\nseries of the maximum SNR observed around each trigger,\nand models based on a large population of simulated signals\n(All\u00e9n\u00e9 et al. 2025). This new procedure was motivated by\nthe desire to automate and standardize a data-quality test that\nwas performed manually online at the beginning of O4 in\ncase of detection. Candidates such as S230622ba, which trig-\ngered an automatic alert and was manually retracted after hu-\nman verification (LIGO Scientific Collaboration et al. 2023),\ncan now be vetoed before being released from the pipeline.\nMBTA looks for coincident triggers between detectors\nsharing the same templates, within a limited time window.\nA combined ranking statistic is computed as the quadrature\n\n15\nsum of single detector ranking statistics. Since O3, this statis-\ntic also includes a term measuring the consistency of arrival\ntimes, phases and amplitudes across the detectors (Aubin\net al. 2021). In addition to the search for coincident trig-\ngers between the two LIGO detectors, since the start of O4,\nMBTA now also produces single-detector candidates. In or-\nder to limit the risk of false alarms, while maximizing the\nchances of detecting electromagnetically-bright sources, the\nMBTA search for single-detector candidates is restricted to\nchirp masses below 7 M\u2299.\nThe significance of the candidates obtained by the stellar-\nmass search analysis is evaluated based on their probable ori-\ngin, quantified by pastro. These probabilities are obtained us-\ning a method similar to the O3 method (Andres et al. 2022).\nFor a given astrophysical source, the ratio of expected num-\nber of foreground triggers to the total number of triggers\n(foreground + background) is calculated. The foreground is\nestimated using population models similar to those used to\nestimate search sensitivity (see Section 3.7) and by fitting\nthe rate observed by MBTA. The background is obtained\nby fitting the distribution of the ranking statistic measured\nby MBTA, after eliminating confidently-detected astrophys-\nical signals. In the case of coincidences, the statistic is in-\ncreased by considering fake coincidences between noise trig-\ngers, regardless of the time of arrival. These operations are\nperformed over several bins in the mass and spin parameter\nspace covered by the search.\nThe pipeline associates a FAR to candidates using a\nmethod similar to the pastro background estimation. In order\nto make the values of pastro and FAR consistent with each\nother, and to include an astrophysical prior in the FAR defi-\nnition, pastro is used since O4a as a new ranking statistic.\nMBTA performed several online search analyses during\nO4a using a pipeline version similar to the offline analysis de-\nscribed above, with a few differences documented in All\u00e9n\u00e9\net al. (2025). All coincident candidates, as well as single-\ndetector candidates with chirp mass below 7 M\u2299, from the\nfull-bandwidth analysis with a FARs below 2 h\u22121 were sub-\nmitted to GRACEDB with a median latency of 21 s. In the ab-\nsence of prior realistic O4 data, the online pastro calculation\nperformed by the pipeline during O4a used the same model\nas for the offline second half of the third observing run (O3b)\nanalysis (Abbott et al. 2023a), adjusting the signal rates to\naccount for the increased sensitivity. MBTA was also con-\nducting early-warning searches for CBCs with component\nmasses between 1 M\u2299and 2.5 M\u2299and aligned spins below\n0.05, with the aim of rapidly identifying high-SNR signals.\nMBTA also conducted offline search analyses during the\nO3 period, and thus participated in the production of the pre-\nvious catalog versions GWTC-2.1 (Abbott et al. 2024) and\nGWTC-3.0 (Abbott et al. 2023a). At that time, the pipeline\nprocessing was slightly different. The O3 stellar-mass search\ntemplate bank was created using a purely stochastic method\n(Privitera et al. 2014), guaranteeing a SNR loss below 3%,\ncompared with 2% for parts of the O4 bank. During O3,\nthe pipeline only searched for CBCs with (detector-frame)\ntotal mass below 200 M\u2299, but no constraints on waveform\nduration were applied. Prior to the introduction of the SNR-\nExcess method, re-ranking of triggers occurring during peri-\nods of poor data quality was handled by comparing the trig-\nger rate before and after the application of various other re-\njection criteria. Before O4, MBTA only calculated signifi-\ncance for candidates seen in at least two detectors. The FAR\nvalues were based on a ranking that assumed all templates\nwere equiprobable, which was responsible for some inconsis-\ntencies with the associated pastro values. Trials factors were\nused to account for the various coincidence types and param-\neter space regions (Aubin et al. 2021).\n3.4. PYCBC\nThe PYCBC search pipeline (Dal Canton et al. 2014; Us-\nman et al. 2016; Nitz et al. 2017) is a descendant of the\nIHOPE pipeline (Allen et al. 2012; Babak et al. 2013), which\nwas used to search LIGO\u2013Virgo data during the initial detec-\ntor era up to 2010 (Abadie et al. 2012b; Aasi et al. 2013). The\ninput to PYCBC is the calibrated strain data from the detec-\ntors, which undergo a series of conditioning steps to prepare\nfor analysis. After removing invalid or contaminated strain\ndata flagged by CAT1 vetoes, we then apply high-pass filter-\ning to suppress low-frequency noise (below 15 Hz), down-\nsampling from 16 kHz to 2 kHz to reduce data volume, and\ngating (windowing out) to remove loud glitches (Usman et al.\n2016). The pipeline is also limited to analyze data segments\nwith a minimum length of 500 s, to ensure a sufficiently pre-\ncise PSD estimate.\nAfter data selection and input conditioning, data from each\ndetector are filtered using a fixed template bank. The tem-\nplates are placed in a four-dimensional parameter space of\ncomponent detector-frame masses and orbit-aligned spins.\nFor O4, the template bank is generated with a hybrid\ngeometric-random placement algorithm (Roy et al. 2017),\nimposing a minimum template waveform duration of 70 ms\nwhich allows coverage of systems with IMBHs, and applying\na dynamic minimal match criterion to ensure smooth tem-\nplate density across the mass range (Roy et al. 2017, 2019).\nThe match is calculated assuming the projected LIGO O4\nsensitivity that predicts a 160 Mpc BNS range (LIGO Scien-\ntific Collaboration et al. 2022). The waveform model used\nis SEOBNRV5_ROM (Pompili et al. 2023) for total mass\nabove 4 M\u2299, and TAYLORF2 (Vines et al. 2011) below. A\nfixed lower cutoff frequency of 15 Hz is applied for systems\nwith total mass above 100 M\u2299. The bank covers a total mass\nrange of 2 M\u2299to 500 M\u2299, with mass ratios from 1/97.989\nto 1, and aligned spin ranges from \u22120.997 to 0.997 for BH\ncomponents and from \u22120.05 to 0.05 for NS components, as\nshown in Figure 2.\nData from each detector are independently matched fil-\ntered against the template bank, producing an SNR time\nseries for each template: triggers, corresponding to poten-\ntial signals, are then identified as local SNR maxima above\na given threshold within predefined time windows. A \u03c72\ntest is applied to assess whether the time\u2013frequency distri-\nbution of power in the data matches the expected distribu-\ntion from the template waveform (Allen 2005). The pipeline\n\n16\nre-weights the matched-filter SNR using the reduced \u03c72 nor-\nmalized such that the expected value in Gaussian noise for a\nsignal matching the template is unity (Abadie et al. 2012b;\nUsman et al. 2016). Triggers with re-weighted SNR below a\nthreshold of 4 are discarded as they are likely to correspond\nto noise transients. Since short-duration blip glitches (Cabero\net al. 2019) may pass the time\u2013frequency \u03c72 test for some\ntemplates, a high-frequency sine-Gaussian \u03c72 test is used to\nfurther identify such glitches (Nitz 2018). A single-detector\nranking statistic \u02c6\u03c1 is then calculated, incorporating the time\u2013\nfrequency and sine-Gaussian \u03c72 tests, as well as a correction\nto the SNR due to short-term PSD variability (Mozzon et al.\n2020).\nThe next step of the pipeline is to identify candidates con-\nsistent with potential GW signals by comparing the coales-\ncence times and template parameters of triggers from mul-\ntiple detectors. Coincident candidates are found if triggers\nfrom two or more detectors, associated with the same tem-\nplate, occur within a time window that accounts for the light\ntravel time between detectors and a small margin for timing\nerrors. If data from more than two detectors are analyzed, co-\nincident candidates may be formed across multiple combina-\ntions of two and three detectors via the same process. Start-\ning in O4, candidates consisting of triggers in only a single\ndetector are also included (Davies & Harry 2022).\nFollowing this, the pipeline calculates the statistical sig-\nnificance of candidates by estimating their FAR. A ranking\nstatistic is assigned to each candidate, reflecting its likeli-\nhood of being a true GW signal versus background noise.\nThe FAR is computed for a coincident candidate by com-\nparing its ranking statistic to a set of artificially generated\nbackground candidates created by time-shifting triggers in\none detector relative to another. In O4a, where only LIGO\nHanford Observatory (LHO) and LIGO Livingston Obser-\nvatory (LLO) data are available, background candidates are\ngenerated by repeatedly shifting triggers in one detector with\nrespect to the other by a fixed interval. To ensure these candi-\ndates are statistically independent, clustering is performed on\nboth coincident (un-shifted) and time-shifted analyses: only\nthe candidate with the highest detection value within a set\ntime window is kept. To reduce background contamination\ndue to loud signals, any candidate detected with FAR below a\nthreshold of 1 per 100 yr is removed from the background es-\ntimation for less significant candidates (Abbott et al. 2016b;\nNitz et al. 2019).\nFor single-detector candidates in O4, since their FARs\ncannot be estimated from time-shifted analysis, the ranking\nstatistic distribution is fitted with a falling exponential, and\nextrapolated with a maximum possible inverse false alarm\nrate (IFAR) assignment of 1000 yr (Davies & Harry 2022).\nIn times when multiple detectors are active, FAR estimates\nfrom all candidate types at the ranking statistic value of the\ncandidate are added to give the final FAR estimate.\nThe ranking statistic assigned to both coincident and\nsingle-detector candidates is designed to optimize the de-\ntection rate by reflecting the relative densities of signal\nvs. noise over the binary source parameter space.\nTo ac-\ncount for noise variations across different templates, the\nsingle-detector background distributions are fitted, with the\nfit parameters allowed to vary over the template parameter\nspace (Nitz et al. 2017). We define an intermediate expres-\nsion R3, which is the basis for both the multi-detector and\nsingle-detector statistic:\nR3 = ln\n \n\u03c33\nmin,i/\u00af\u03c33\nHL,i\nAN{d}\nP\nd rd,i(\u02c6\u03c1d)\np(\u2126|S)\np(\u2126|N)\n!\n= ln p(\u2126|S) \u2212ln p(\u2126|N) \u2212ln AN{d}\n\u2212\nX\nd\nln rd,i(\u02c6\u03c1d) + 3(ln \u03c3min,i \u2212ln \u00af\u03c3HL,i).\n(6)\nHere p(\u2126|S) and p(\u2126|N) are the probabilities of a signal or\nnoise candidate, respectively, to have extrinsic parameters \u2126,\ncomprising relative phases, arrival times and amplitudes be-\ntween detectors (Nitz et al. 2017). We consider the noise\ndistribution p(\u2126|N) as uniform for a given combination of\ndetectors, absorbing this constant factor into the normaliza-\ntion of p(\u2126|S). The rate of noise events is predicted from the\nallowed time window AN{d} for coincident events involving\ndetectors {d} and the expected rate of noise triggers rd,i(\u02c6\u03c1d)\nin template i at re-weighted SNR \u02c6\u03c1d. The last term accounts\nfor the time-dependent rate of signals, which is proportional\nto the network sensitive volume for a given template, and\nscales with the cube of the minimum sensitive distance \u03c3min,i\nover triggering detectors, normalized to an average LIGO\nsensitive distance \u00af\u03c3HL,i.\nThe ranking statistic used in O4 includes two additional\nterms beyond Equation (6). First, an explicit model of the\nsignal distribution over binary masses and spins is incorpo-\nrated, intended to optimize the detection rate of the known\nCBC population while remaining sensitive to so far unpopu-\nlated parameter regions (Kumar & Dent 2024). Second, the\nnoise event rate model is updated to account for variations in\nthe rate of noise artifacts, correlated with auxiliary channels\nthat monitor the detector state or environmental disturbances,\nas measured by IDQ (Essick et al. 2020). We then have:\nRO4 = R3 + ln dS(\u03b8int) \u2212ln dN(\u03b8int)\n\u2212\nX\nd\nln \u03b4d (\u2206d(t), Bd(\u03b8int)) ,\n(7)\nwhere dS(\u03b8int) and dN(\u03b8int) represent a KDE-based model\ndistribution of signals over template parameter space \u03b8int,\nand the distribution of template points, respectively.\nThe\ntime-dependent excess rate of non-Gaussian triggers is no-\ntated as \u03b4d(\u2206d(t), Bd(\u03b8int)) \u22651 for a detector d. Our esti-\nmate of \u03b4d depends on a discrete detector state variable \u2206d(t)\nand on an index Bd(\u03b8int) labelling template bins. We con-\nsider three possible detector states, corresponding to (i) aux-\niliary channels indicating significant likelihood of noise arte-\nfacts; (ii) presence of loud gated glitches nearby in time, or\n(iii) neither. In the case of single-detector candidates, the\nranking statistic omits terms that depend on multi-detector\ncoincidence quantities (Davies & Harry 2022); specifically,\n\n17\nthe terms AN{d}, p(\u2126|S), and p(\u2126|N) present in Equa-\ntion (6) are omitted.\nThe probability of astrophysical origin pastro is estimated\nby a Poisson mixture inference (Abbott et al. 2016a,c), for\nwhich the distribution of signal events over the ranking statis-\ntic is estimated via histograms from a set of simulated signals\nand distributions of noise events are estimated via histograms\nof time-shifted background for coincident candidates, or\nvia exponential fits for single-detector candidates (Davies\n& Harry 2022). Such histograms are generated separately\nfor each type of (single-detector or coincident) candidate\nin single-detector or multi-detector observing time to allow\nfor differences in event rates and distributions (Dent 2025).\nMarginalization over the unknown rate of astrophysical sig-\nnals is performed by generalized Gauss\u2013Laguerre quadra-\nture (Creighton 2019). The resulting candidate pastro values\nare apportioned between different astrophysical categories\nusing an estimate of the source chirp mass based on search\noutputs (Dal Canton et al. 2021; Villa-Ortega et al. 2022).\nSeveral features of the PYCBC online search analysis\n(Dal Canton et al. 2021; Nitz et al. 2018) differ from the of-\nfline search analysis described above. The main differences\nin O4a, and their consequences for online results, are:\n\u2022 To reduce latency, multiple overlapping matched-filter\nanalysis segments with a stride of 8 s are used, in con-\ntrast to a typical stride of hundreds of seconds for of-\nfline search.\n\u2022 The bank construction is comparable to the offline\nsearch except that templates with duration below 0.15 s\nare not included, increasing robustness to loud, short-\nduration noise transients.\nThe SEOBNRV4_ROM\nmodel is used instead of the more recent SEOB-\nNRV5_ROM.\n\u2022 The ranking statistic for multi-detector candidates is\nsimpler than for the offline search (Nitz et al. 2017,\nEquation 2): in addition to the quadrature sum of re-\nweighted SNRs over detectors, it includes only the net-\nwork consistency term ln(p(\u2126|S)/p(\u2126|N)).\n\u2022 The significance of multi-detector candidates is ini-\ntially calculated using only the two most sensitive de-\ntectors, with other detectors (if available) incorporated\nvia a follow-up procedure.\n\u2022 To account for possible short-term changes in detec-\ntor behaviour, the background for multi-detector can-\ndidates is estimated from the preceding \u223c5 hours of\ndata in each of the two most sensitive detectors. The\nFAR estimate is limited in precision by this restricted\ndata extent, to a minimum of 1 per 100 yr in the two-\ndetector case.\n\u2022 Single-detector candidates are generated only for tem-\nplates with duration above 7 s, as these correspond to\nsystems with potential electromagnetic emission (Fou-\ncart et al. 2018).\n\u2022 The probability of astrophysical origin is estimated via\nsimple approximations to the densities of signal and\nbackground events (Dent 2023), in contrast to the de-\ntailed histogram estimates used by the offline calcula-\ntion.\n\u2022 After the initial candidate upload to GRACEDB, a\nfollow-up analysis is performed to maximize the net-\nwork SNR over template masses and aligned spin com-\nponents using all available detector data, and thus to\noptimize the resulting spatial localization, within min-\nutes.\n\u2022 An early-warning search algorithm is also operated,\ntargeting nearby mergers only, with component masses\nbetween 1 M\u2299and 3 M\u2299and zero spins (Nitz et al.\n2020a).\nThe above descriptions concern PYCBC-based analyses\nin the first part of O4. Here, for completeness, we summa-\nrize significant changes in search methods used for archival\ncatalog (offline) results since the GWTC-1.0 release. The\nO3 template bank was constructed using the same hybrid\ngeometric-random method as in O4 to ensure efficient cover-\nage of the parameter space (Roy et al. 2017). Three different\nindependent search analyses (PyCBC-BBH, PyCBC-Broad,\nand PyCBC-IMBH) were used, with each covering distinct\nregions of the parameter space (Abbott et al. 2023a; Chan-\ndra et al. 2021). The waveform model SEOBNRV4_ROM\nwas used for systems above 4 M\u2299, and TAYLORF2 for lower-\nmass systems (Roy et al. 2019). Templates with durations\nbelow 0.15 s were excluded to reduce false alarms from short\nglitches, thereby also placing an upper limit on the mass\nof the systems, unlike in O4, where shorter-duration tem-\nplates are included to improve coverage of high-mass sys-\ntems.\nThe template bank used in the earlier O2 and O1\nanalyses (Dal Canton & Harry 2017) spanned total masses\nfrom 2 M\u2299to 500 M\u2299, with mass ratios from 1/98 to 1, and\nspin limits based on component mass: 0.05 for masses be-\nlow 2 M\u2299and up to 0.998 for higher masses (Abbott et al.\n2019a). For O3, the background estimation was extended to a\nthree-detector network by using fixed relative time shifts be-\ntween detectors (Davies et al. 2020), whereas in earlier runs,\na two-detector method (also used in O4a) was employed. Un-\nlike in O4, single-detector candidates were not included in\nO3 or previous runs. The O3 broad search statistic is given\nby Equation (6), i.e., the O4 statistic without the additional\nKDE and data-quality terms. For the O3-BBH search, an al-\nternate ranking statistic was adopted, incorporating an addi-\ntional term in the broad search statistic dependent on the tem-\nplate chirp mass to enhance sensitivity to the observed BBH\npopulation (Nitz et al. 2020b). In earlier runs, only one type\nof event (LHO\u2013LLO) was considered, and sensitivity varia-\ntions across the parameter space, such as those described by\n\u03c3i, were neglected. As a result, many terms in the O3 statistic\nin Equation (6) either disappeared or became constants and\nwere omitted (Nitz et al. 2017).\n\n18\n3.5. SPIIR\nSPIIR is a coherent search pipeline developed primarily\nfor the online detection of GW signals from CBCs (Hooper\net al. 2012; Luan et al. 2012; Chu et al. 2022). It became\noperational during O3, during which it registered 38 out of\nthe 56 non-retracted public alerts (Abbott et al. 2021a, 2024;\nChu et al. 2022). The design of SPIIR focuses on efficiency\nand rapid processing, enabling it to provide detections with\nlatencies around 11 s. This capability makes SPIIR particu-\nlarly useful for issuing early warning alerts for electromag-\nnetic follow-ups of GW candidates (Kovalam et al. 2022).\nWhile an offline version of SPIIR is under development, it\nhas not yet participated in any of the offline searches through\nthe end of O4a.\nThe SPIIR pipeline employs infinite impulse-response\n(IIR) filters as template banks to perform matched filtering\ndirectly in the time domain (Hooper et al. 2012). Unlike\ntraditional methods, which can be time-consuming, the IIR\nfiltering approach allows SPIIR to execute matched filter-\ning rapidly.\nThe primary advantage of IIR filters is their\nability to approximate matched-filtering SNR in a way that\ncan be efficiently parallelized and executed on graphics pro-\ncessing units (GPUs), which significantly accelerate high-\nperformance computing tasks (Liu et al. 2012; Guo et al.\n2018). The SPIIR template-bank generation is a two-step\nprocess.\nThe first step is to generate the template points\nin the CBC parameter space using the stochastic placement\nalgorithm (Privitera et al. 2014; Harry et al. 2009) with a\nminimum match of 0.97. The approximant SPINTAYLORT4\n(Klein et al. 2014) is used for chirp mass below 1.73 M\u2299\nand SEOBNRV4_ROM for larger masses. In the second\nstep, each corresponding waveform is decomposed into ap-\nproximately 350 IIR filters (Hooper et al. 2012; Liu et al.\n2012; Guo et al. 2018). These IIR filters are then utilized for\nmatched filtering using GPU parallelization.\nThe real-time data analysis process begins by retrieving\nstrain data from a shared directory at the Caltech comput-\ning cluster for all detectors in observing mode. The data\nare then conditioned, applying data-quality vetoes, down-\nsampling from 16 384 Hz to 2048 Hz, and whitening, which\nrequires real-time PSD calculation.\nThe PSD calculation\ntakes place using the Welch method with tens of 4 s over-\nlapping data blocks. This method prevents sporadic transient\nsignals from biasing the PSD estimate. The data are also\nsubjected to gating to mitigate the effects of loud transient\nnoises. Once conditioned, the whitened data from each de-\ntector is passed through a set of IIR filters that span the pa-\nrameter space of CBC templates, generating corresponding\nSNR time series for each template.\nA key distinguishing feature of the SPIIR pipeline is\nits coherent search algorithm (Bose et al. 2011; Harry &\nFairhurst 2011). The coherent search algorithm looks for\ntime and phase consistency across all detectors. SPIIR cal-\nculates a maximum network likelihood ratio statistic to eval-\nuate the likelihood of a coherent GW signal being present\nin the data. This approach enhances the pipeline\u2019s sensitiv-\nity, particularly to weaker signals, and improves localization\naccuracy by combining data from multiple detectors.\nThe coherent analysis can be computationally demanding.\nTo address this challenge, SPIIR uses SVD (Wen 2008),\nwhich allows for efficient calculation of the coherent statistic\nby focusing on the most significant signal components. This\noptimization reduces the complexity of the search and en-\nables rapid scanning across different sky positions to localize\nthe source.\nAfter determining the coherent SNR, SPIIR applies a \u03be2\nsignal-consistency test (Messick et al. 2017) to asses the mor-\nphological consistency between data and template and com-\nbines it with the coherent SNR into a multidimensional rank-\ning statistic. FARs are assigned by comparing candidates\nwith background distributions generated from time-shifted\nanalyses. To ensure robust estimation, the pipeline collects\nat least one million background candidates, typically accu-\nmulated over several hours.\nA minimum of one week of\nbackground data are used to assign FARs, which is extrap-\nolated using a k-nearest-neighbor (KNN) KDE method with\nk = 11, smoothing the probability density using neighboring\nbins. This approach allows accurate FAR estimation even\nfor rare, high-significance candidates. To account for non-\nstationary noise, SPIIR additionally maintains shorter-term\nbackground sets over 2 h and 1 d. Furthermore, it stores in-\ndividual single-detector SNR and \u03be2 values and applies the\nsame KNN-based extrapolation method to estimate single-\ndetector FARs used in veto stages before making the final\ndecision about the trigger\u2019s validity.\nIn preparation for O4, SPIIR has undergone several up-\ngrades, with some already implemented and others still in\ntesting and review. These improvements include: automated\nsignal trigger removal from the background estimation, pre-\nventing astrophysical triggers from affecting the background\ncalculation; fine tuning of the signal consistency test \u03be2, aim-\ning to improve sensitivity to BNS and NSBH; and a dynamic\napproach to background collection. Furthermore, SPIIR has\nimplemented the necessary infrastructure to process KAGRA\ndata.\n3.6. Criteria for Inclusion in the Catalog\nSearch pipelines can in principle produce a rate of candi-\ndates as high as one every few seconds, depending on their\nconfiguration choices. With the sensitivity of current detec-\ntors, however, the vast majority of such candidates would\nhave low significance and would be unlikely to have an as-\ntrophysical origin. For practical consideration, we therefore\nselect a smaller number of candidates to report in the GWTC.\nThe criterion for selecting which candidates to include has\nevolved with the observing runs and GWTC versions. In\nGWTC-1.0 (Abbott et al. 2019a), we published all candidates\nfrom O1 and O2 for which at least one matched-filtering\npipeline (PYCBC or GSTLAL at the time) estimated a FAR\nbelow 1 per 30 d.\nGWTC-2.1 (Abbott et al. 2024) and\nGWTC-3.0 (Abbott et al. 2023a) respectively added candi-\ndates from first half of the third observing run (O3a) and O3b\nwith a FAR below 1 per 2 d in any pipeline. Following this\n\n19\nlogic, we now add candidates from O4a whose FAR is less\nthan 1 per 2 d in any of the pipelines described in Section 3,\nwith the exception of SPIIR.\nStricter candidate selection criteria are typically applied\nwhen performing downstream analyses and for the purpose\nof displaying lists and properties of the candidates. Stricter\ncriteria might, for example, be motivated by computational\nor person-power considerations. Furthermore, downstream\nanalyses might not necessarily have the same requirements;\nfor instance, a sufficiently large SNR might be necessary, as\nopposed to a sufficiently low FAR. Such considerations, and\nconsequently the corresponding selection criteria, might in\nturn evolve as data-analysis methods become more efficient.\nStricter criteria will therefore be described wherever neces-\nsary.\n3.7. Search sensitivity\nApart from the candidates themselves, an important prod-\nuct of search pipelines is a measurement of their sensitivity,\nwhich is necessary to diagnose the behavior of the pipelines\nand to infer the rate density of the astrophysical sources.\nWe quantify the sensitivity of the search pipelines described\nabove by their estimated time\u2013volume product or hypervol-\nume \u27e8V T\u27e9(Abbott et al. 2023a). The hypervolume repre-\nsents the sensitivity of a given search to a set of sources as-\nsumed uniformly distributed in both comoving volume and\nsource-frame time. An estimate of the total number of sig-\nnals \u02c6N that a pipeline is likely to detect during a period of\nobservation is given by\n\u02c6N = \u27e8V T\u27e9R,\n(8)\nwith R the rate of CBCs per unit comoving volume and\nsource-frame time (Abbott et al. 2016a). In practice, hyper-\nvolumes are obtained through weighted Monte Carlo simula-\ntions, which use simulated GW signals referred to as injec-\ntions.\nAt this time, the population of injected signals focuses on\nCBCs only, as no transient GW signal so far detected is in-\nconsistent with a CBC source at high confidence. The pa-\nrameter ranges and distribution models were chosen to rep-\nresent CBC signals the detectors were possibly sensitive to,\nbased on previous releases of GWTC (Abbott et al. 2023b).\nThe rate of injections was chosen to be much higher than\nthe astrophysical rate in order to reach a sufficient precision\nin \u27e8V T\u27e9. As the production of injections required detector\nPSDs to be measured over each month of observation, in-\njection analysis was performed offline. To ensure consis-\ntency in the \u27e8V T\u27e9measurements, all pipelines contributing\nGWTC candidates (GSTLAL, MBTA, PYCBC, and CWB-\nBBH) analyzed the same sets of injections. The pipelines\nprocessed data with injections using methods equivalent to\nthose used to produce candidates from injection-free data, de-\nscribed earlier in this section. All pipelines used background\ndata collected by their injection-free analyses to assign sig-\nnificances to the recovered injections. The choice of popula-\ntion priors and the injection generation process are detailed in\nEssick et al. (2025), while results from the injection analysis\nare described in Abac et al. (2025b).\nThe sensitive \u27e8V T\u27e9differs between pipelines, reflecting\ntheir abilities to detect CBCs within a given range of param-\neters as well as their different effective live times. Further-\nmore, as CWB-BBH is designed to search for BBH signals\nas described in Section 3.1, we calculate \u27e8V T\u27e9for the corre-\nsponding masses for this pipeline.\nThere are differences in how pipelines process injections\ncompared to injection-free data, which arise from computa-\ntional efficiency or technical considerations and do not af-\nfect the sensitivity estimation. The CWB-BBH pipeline per-\nformed injection generation in a 5 s time window around the\ntime of the injections. The GSTLAL and PYCBC pipelines\nprocessed data with injection using subsets of their template\nbanks based on the known chirp mass of the injections, in\norder to limit the computational cost. In addition, GSTLAL\nhad two other major differences for its injection processing\ncompared to its injection-free data processing. First, injec-\ntion processing was done entirely in an offline configuration,\nas opposed to reassigning significances to triggers obtained\nin online analysis, due to injection data not being available at\nthe time of the online analysis. Meanwhile, other pipelines\nprocessed both injection-free and injection data in their of-\nfline configurations to produce the GWTC-4.0 results and\n\u27e8V T\u27e9estimations. Second, the SNR time series were only\ncomputed for a short time window around the time of the in-\njections to limit the computational cost, as opposed to com-\nputing the SNR time series for all available data in O4a.\n4. DATA QUALITY AND CANDIDATE VETTING\nA subset of the candidates produced by the search algo-\nrithms described in Section 3 undergo studies to understand\nthe quality of the interferometric data surrounding the can-\ndidates with a goal to characterise and, if required, mitigate\nagainst any departures from stationary Gaussian noise such\nas glitches. This is vital to ensure that downstream analyses,\nparticularly PE (see Figure 1 and Section 5), which typically\nassume stationary Gaussian noise, produce unbiased results\n(Pankow et al. 2018; Powell 2018; Ghonge et al. 2024)\nEvent validation is the process of identifying and exam-\nining potential data-quality issues in the vicinity of a GW\ncandidate. We apply the process to all candidates reported\nby online search pipelines and labeled as significant, with\nan internationally-coordinated team who can provide rapid\nvetting and aided by an automated data-quality report frame-\nwork (Soni et al. 2025).\nIn contrast to O3, where LIGO and Virgo conducted sep-\narate validation processes (Davis et al. 2022; Acernese et al.\n2023), O4 employs a unified infrastructure across all ac-\ntive detectors. This uniformity in validation improves effi-\nciency, streamlines information flow between different anal-\nysis groups, and reduces the demand on human resources.\nOnce the initial online vetting is completed, all significant\ncandidates undergo further scrutiny to determine a final as-\nsessment of the data quality status.\n\n20\nIf data-quality issues such as glitches are identified around\na candidate and these issues are not severe enough to war-\nrant a retraction, we quantify if further action is required\nby comparing the PSD variance in the relevant region with\nexpected Gaussian noise and computing a p-value (Mozzon\net al. 2020). Until November 2023, a conservative thresh-\nold of 0.1 was adopted.\nThis threshold was then relaxed\nto 0.05. For p-values greater than this threshold, we con-\nclude the data are consistent with Gaussian noise, and the\ncandidates are ready for downstream analyses. On the other\nhand, if p \u22640.05, we attempt to subtract the noise using\neither a modeled Bayesian inference approach implemented\nin BAYESWAVE (Pankow et al. 2018; Cornish et al. 2021;\nChatziioannou et al. 2021; Hourihane et al. 2022), or a linear\nnoise subtraction based on auxiliary witness channels (Davis\net al. 2022). For all candidates in O4a, BAYESWAVE was\nused and applied to the GDS-CALIB_STRAIN_CLEAN_AR\nchannel as described in Abac et al. (2025c). For past ob-\nserving runs, BAYESWAVE has predominantly been applied,\nexcept in cases where a witness channel was available (Ab-\nbott et al. 2023a). However, if the noise is extended in time\nor frequency, as is often the case for certain glitch classes\n(e.g., Soni et al. 2020, 2024), making subtraction difficult, or\nif the data remains insufficiently stationary after subtraction,\nwe instead restrict the time and frequency analysis window\nto avoid the afflicted region. For badly afflicted candidates,\npreliminary parameter-estimation studies are routinely per-\nformed to validate the mitigation technique and understand\nthe impact on parameter estimates. Once a satisfactory miti-\ngation approach has been identified, the candidates are ready\nfor downstream analyses.\n5. PARAMETER ESTIMATION FOR CBC\nFor a selection of candidates identified by the search al-\ngorithms (see Section 3) and either having passed valida-\ntion or with appropriate mitigation (see Section 4), we use\nBayesian inference to estimate the source parameters \u03b8 of\nthe GW signal (see Figure 1), which includes both the intrin-\nsic parameters of the CBC source and the extrinsic param-\neters that localize and orient the source in spacetime (Abac\net al. 2025a). These inferences come in the form of posterior\ndistributions p(\u03b8|d) over the source parameters. The posteri-\nors represent our best understanding of the properties of the\nsource and its location, including all correlations and degen-\neracies in the measured parameters. The posteriors for the se-\nlected GW candidates from O4a are reported for the first time\nin (Abac et al. 2025b). We have not updated our inferences\nfor candidates identified in previous observing runs. Thus,\nour preferred parameter inferences for candidates identified\nbefore O4a remain the same as previously reported in Abbott\net al. (2024, 2023a), with the exception of the BNS candi-\ndate GW170817 whose preferred parameter inferences are\nreported in Abbott et al. (2019a).\nIn Sections 5.2 to 5.8, we describe the broad elements of\nGW PE and discuss the particular choices made in each ver-\nsion of the catalog in Section 5.9, noting that configuration\nfiles to reproduce the analysis of individual candidates are\nprovided with the data release.\n5.1. Bayesian Formalism\nTo carry out Bayesian PE, we assume the data d con-\ntains colored Gaussian noise and an astrophysical GW signal\nwhich is well-approximated by a quasi-circular CBC wave-\nform model (see Section 2), consistent with GR and absent\nof environmental effects. These assumptions determine the\nform of our likelihood p(d|\u03b8), which for a single detector is\nGaussian in the residuals between data and waveform (Finn\n1992; Cutler & Flanagan 1994; Abac et al. 2025a). We use\nthe standard formulation for this likelihood and the associ-\nated frequency-domain noise-weighted inner product (e.g.,\nVeitch et al. 2015b; Thrane & Talbot 2019). Given the likeli-\nhood and a prior distribution \u03c0(\u03b8), we compute the posterior\ndistribution from Bayes\u2019 theorem\np(\u03b8|d) = p(d|\u03b8)\u03c0(\u03b8)\np(d)\n,\n(9)\nwhere p(d) is the normalizing evidence:\np(d) =\nZ\np(d|\u03b8)\u03c0(\u03b8) d\u03b8 .\n(10)\nThe evidence is not required in most approaches to PE, but\ncan be used for model comparison.\nIn our baseline analyses the joint likelihood also includes\nadditional parameters to account for the calibration state\nof the detector and the uncertainty in this calibration (Sec-\ntion 5.4). The full likelihood is evaluated coherently across\nthe detector network by multiplying the individual interfer-\nometer likelihoods, under the assumption that the noise is\nindependent in each.\n5.2. Preliminary PE\nAfter initial identification of a candidate by a search algo-\nrithm (Section 3), we carry out preliminary PE in order to\nunderstand the properties of the source and guide our anal-\nysis settings. We choose our initial settings and waveform\nmodel using the output of the search pipelines, e.g., the point\nestimates of the source masses. As needed, we carry out fur-\nther analyses with modified priors or configuration settings,\nin some cases utilizing multiple waveform models to under-\nstand systematic modeling errors. If there are data-quality is-\nsues, this preliminary estimation is iterated alongside glitch-\nmitigation studies, as described in Section 4.\nPreliminary PE also guides our choice of waveform models\nfor inference (Section 2). Specifically, since 3 M\u2299provides a\nstringent upper limit on the maximum mass of a NS (Rhoades\n& Ruffini 1974; Kalogera & Baym 1996), candidates where\nboth source masses are > 3 M\u2299are classified as unambigu-\nous BBH candidates. Otherwise the source potentially con-\ntains a NS, and may be a NSBH or BNS. For sources which\nmay include a NS we carry out PE with waveforms that in-\nclude the imprint of matter onto the GW signal in order to\nconstrain such effects.\n\n21\n5.3. Likelihood Calculation: Elements of the Inner Product\nThe integration of the inner product that defines the like-\nlihood is carried out in the frequency domain (Abac et al.\n2025a; Veitch et al. 2015b; Thrane & Talbot 2019). Fol-\nlowing our standard conventions (Abac et al. 2025a), given\na discrete raw time-series data d(t) with a duration T and\nsampling frequency fs, we first apply a FFT and divide by\nthe sampling frequency to produce the discrete frequency se-\nries \u02dcd. Similarly, time-domain waveforms are transformed\ninto frequency series, while frequency-domain models can\nbe evaluated directly for use in the inner product.\nThe amount of data analyzed for each candidate depends\non the estimated mass of the system as determined by pre-\nliminary PE analyses, with lower mass signals in the sensi-\ntive band for longer periods of time. The segment of data\nused in PE is selected with the estimated time of coalescence\nset 2 s before the end of the segment, with the total duration\nset to powers of 2 ranging from 4 s up to 128 s such that the\nevolution of the signal starting from flow is included. This\nchoice sets the discrete frequency spacing \u2206f = 1/T in the\ninner product. Before transforming time-domain data to the\nfrequency domain to evaluate the likelihood, we apply a sym-\nmetric Tukey window function (Harris 1978) with a roll-on\ntime that balances how much data in the segment is affected\nby the windowing and the impact of spectral leakage of the\nnoise, especially at the lowest frequencies analyzed where\nthe noise is steeply varying.\nWe compute the required integral from a lower frequency\nflow to fhigh and discard the data outside this range. Gen-\nerally, flow is set to 20 Hz, below which the detector noise\nsteeply increases. The upper frequency fhigh is chosen to be\nthe Nyquist frequency, half the discrete sampling rate fs of\nthe data, with further modifications to account for power lost\ndue to applying a low-pass Butterworth filter when down-\nsampling the data to the desired sampling rate (Veitch et al.\n2015a; Romero-Shaw et al. 2020b). The result is fhigh =\n\u03b1roll-offfs/2, with the particular choice of \u03b1roll-off = 0.875\nselected to limit power loss to 1% (Abbott et al. 2023a). The\ndata are downsampled to limit the computational cost of the\nlikelihood evaluation, and fs is chosen for each candidate to\nensure that selected higher multipolar modes are resolved for\ncandidates which coalesce in the sensitive frequency band of\nthe detectors, or else set to a high enough value where noise\ndominates the signal power for low-mass candidates that co-\nalesce out of the sensitive band. This upper limit is generally\nfs = 4096 Hz or fs = 8192 Hz.\nA key ingredient in the likelihood evaluation is an esti-\nmate of the noise PSD for the analyzed data. In order to\nmitigate the effects of the nonstationary nature of the instru-\nmental noise, for PE results presented in the GWTC, we\nuse an on-source estimate for the PSD generated with the\nBAYESWAVE algorithm (Cornish & Littenberg 2015; Litten-\nberg & Cornish 2015; Cornish et al. 2021). This approach\nuses Bayesian inference to construct a posterior distribution\nover PSD realizations, and we take the median PSD value\nat each frequency (Chatziioannou et al. 2019) for the point-\nestimate used in the inner product.\n5.4. Calibration Marginalization\nIn order to account for the uncertain calibration of the\nstrain data, we allow for independent frequency-dependent\nshifts of the amplitude and phase of the waveform in each\ninterferometer (Farr et al. 2014). The frequency-dependent\nshifts are modeled using additional free parameters in our\nwaveform model, which we call calibration parameters. We\nmarginalize over the calibration parameters when reporting\nPE results (Abbott et al. 2016d).\nThe strain data are produced in near-real time using an ini-\ntial calibration model, which may be subsequently updated\nin order to recalibrate the data (Abac et al. 2025c). For the\nLIGO detectors the methods used to calibrate the strain data\nprovide a measured distribution of frequency-dependent cor-\nrection factors \u02dc\u03b7R(f) (Cahillane et al. 2017; Sun et al. 2020,\n2021; Dartez et al. 2025). These factors correct the calibrated\nstrain data d in each detector to the strain that would be mea-\nsured with perfect calibration d\u22c6,\n\u02dcd\u22c6= \u02dc\u03b7R \u02dcd .\n(11)\nFor the Virgo detector the methods used for calibration give\nan estimate of the inverse of the correction factor 1/\u02dc\u03b7R\n(which has been unity through O3) and the corresponding\nfrequency-dependent uncertainties (Accadia et al. 2014; Ac-\nernese et al. 2018, 2022).\nThe likelihood used in PE relies on knowledge of the noise\nproperties of the imperfectly calibrated data d through the\nestimated PSD. The likelihood p(d|\u03b8) is evaluated in the fre-\nquency domain using \u02dcd,\n\u02dcd = 1\n\u02dc\u03b7R\n[\u02dch(\u03b8) + \u02dcn\u22c6] =\n\u02dch(\u03b8)\n\u02dc\u03b7R\n+ \u02dcn ,\n(12)\nwhere \u02dcn\u22c6is the true noise in the detector, assumed to be\nGaussian, and \u02dcn = \u02dcn\u22c6/\u02dc\u03b7R is the noise in the calibrated strain,\nalso assumed to be Gaussian. The PSD describes the prop-\nerties of \u02dcn, so the correction factors \u02dc\u03b7R must be applied to\ncorrect the GW model \u02dch to account for imperfect calibration.\nThe corrections 1/\u02dc\u03b7R are approximated by small frequency-\ndependent amplitude and phase corrections, which are mod-\neled using splines (Farr et al. 2014). The values of these\nsplines at fixed frequency nodes are the calibration param-\neters, and for PE we use Gaussian priors on these additional\nparameters. For LIGO data we use the median and standard\ndeviation of the measured distribution of \u02dc\u03b7R (Cahillane et al.\n2017; Sun et al. 2020, 2021; Dartez et al. 2025) to set the\nmean and standard deviation of the priors over the calibration\nparameters describing 1/\u02dc\u03b7R. For Virgo data, the priors on the\ncalibration parameters through O3 are zero-mean Gaussians\nwith standard deviations corresponding to the directly mea-\nsured uncertainties in 1/\u02dc\u03b7R.\nUp to O3, the data from LHO and LLO were recalibrated\nprior to final analysis in order to approximately remove the\n\n22\nsystematic miscalibration arising from the initial model. For\nPE of these candidates, we used final calibrated data as de-\nscribed in Table 4 of Abac et al. (2025c). Because of this\nrecalibration, the errors and uncertainty on the calibration\nparameters are small, such that the priors for the calibration\nparameters are nearly centered at zero (corresponding to no\ncalibration correction). However, in O4a the data in LHO and\nLLO are no longer recalibrated (Abac et al. 2025c). Never-\ntheless, recalibration during PE can be effectively carried out\nusing calibration priors centered away from zero. For this\nreason the priors associated with the new GW candidates pre-\nsented in GWTC-4.0 may lie more than a standard deviation\naway from zero for GWTC-4.0 at various frequency points.\n5.5. Priors\nTo estimate the posterior distribution, Equation (9), we\nmust select an appropriate prior distribution over the binary\nparameters \u03b8. Since our inferences are made over a catalog\nof CBC systems with a wide range of properties and using\na variety of waveform models, our prior ranges are selected\nto be appropriate for each candidate. The priors chosen are\nagnostic and wide enough to cover the region of parameter\nspace where the posteriors have support, while ensuring a\nreasonable amount of analysis time and accounting for the\nparameter ranges over which our waveform models are cal-\nibrated. Prior ranges (e.g., on the component masses) are\nselected during preliminary PE analysis and adjusted after-\nward as needed, for example to ensure that an arbitrary prior\nboundary does not affect the posterior.\nFor all candidates we use priors that are uniform over the\n(redshifted) detector-frame component masses (1 + z)mi,\nwith boundaries in detector-frame total mass, detector-frame\nchirp mass, and mass ratio appropriate for each candidate and\napplied model (see Section 2). The priors are uniform on the\nspin magnitudes and isotropic in spin orientations. We use\nisotropic priors on the binary orientation, and priors that are\nuniform in comoving volume and comoving time so that the\npriors on the sky location are isotropic. For this we carry out\nsampling in a reference cosmology (Abac et al. 2025a) and\nreweight our final samples to priors appropriate for the cos-\nmological model of Ade et al. (2016), which is a flat-\u039bCDM\nmodel with H0 = 67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065,\nfollowing our approach in past versions of the GWTC.\n5.6. Sampling from the Posterior\nDue to the high dimensionality of the source parameters\n\u03b8, brute-force evaluation of the posteriors is intractable. In-\nstead we represent the posteriors for each candidate with dis-\ncrete samples \u03b8i which represent fair draws from the pos-\nterior distribution. The challenge then reduces to the prob-\nlem of stochastically sampling from the posterior distribution\np(\u03b8|d).\nA number of algorithms exist to tackle this sampling chal-\nlenge.\nThese include nested sampling (Skilling 2006), a\nMonte Carlo technique to estimate the evidence and which\nproduces samples as a byproduct, and Markov chain Monte\nCarlo (MCMC; Hastings 1970), which samples through ran-\ndom walks and forms the core of many sampling algorithms.\nThe evidence can be computed with MCMC methods by e.g.,\nthermodynamic integration (Goggans & Chi 2004; Litten-\nberg & Cornish 2009) via parallel tempering (Earl & Deem\n2005; van der Sluys et al. 2008; Veitch et al. 2015b). For\nthe new candidates presented in GWTC-4.0, we use the\nDYNESTY (Speagle 2020) nested-sampling algorithm, and\naccessed through the BILBY package (Ashton et al. 2019;\nRomero-Shaw et al. 2020b) which includes a custom step-\nping method optimized for use on parallelized computing re-\nsources, specifically large-core-count CPUs.\nFor PE results presented with previous catalog releases,\nwe have made use of additional, highly parallelized sam-\npling techniques to tackle computationally expensive anal-\nyses. These include PARALLELBILBY (Smith et al. 2020)\nand the RIFT algorithm (Pankow et al. 2015; Lange et al.\n2017; Wysocki et al. 2019). PARALLELBILBY is optimized\nto use distributed computing to perform nested sampling.\nRIFT is a highly parallel, iterative sampling algorithm that\nuses adaptive, grid-based explorations of the likelihood while\nmarginalizing over the extrinsic parameters, followed by a fi-\nnal stage of Monte Carlo sampling of the intrinsic and extrin-\nsic parameters. For a small number of candidates, parame-\nter inference was carried out using LALINFERENCE (Veitch\net al. 2015b), which provides an implementation of MCMC\nand nested sampling, as well as tailored methods for propos-\ning new sample points.\nTo improve sampling performance, certain parameters\nin the waveform model can be marginalized out of the\nposterior during sampling.\nDepending on the waveform\nmodel employed and the GW candidate, any of the coales-\ncence phase (Veitch et al. 2015b; Farr 2014), coalescence\ntime (Farr 2014; Romero-Shaw et al. 2020b), or luminosity\ndistance (Singer & Price 2016) have been marginalized over,\nas discussed in Section 5.9. This can be done analytically\nor numerically depending on the parameter and the details of\nthe waveform model. When marginalization is carried out,\nthe full posterior distributions are reconstructed in postpro-\ncessing (Thrane & Talbot 2019).\nThe method of marginalizing over calibration uncer-\ntainties varies depending on the sampling method used.\nFor inferences carried out using RIFT, the marginaliza-\ntion over the calibration model parameters is carried out\nin post-processing, by reweighting the likelihood of sam-\nples produced first without utilizing the spline calibration\nmodel (Payne et al. 2020; Abbott et al. 2023a). Meanwhile,\nfor PE using BILBY, PARALLELBILBY, and LALINFER-\nENCE, the parameters of the calibration model are inferred\nalongside the intrinsic and extrinsic binary parameters dur-\ning sampling.\nA large number of PE analyses and steps within each\nanalysis is required to produce the inferences included in\nGWTC-4.0. These analyses were managed using the ASI-\nMOV software library (Williams et al. 2023). Postprocessing\nof the samples is carried out with the PESUMMARY software\nlibrary (Hoy & Raymond 2021). This includes the compu-\ntation of derived parameters such as the remnant properties\n\n23\nfollowing BBH merger and the evolution of the spin compo-\nnents to large binary separations as described in Section 2.4.\nThese are implemented with routines in LALSUITE (LIGO\nScientific Collaboration et al. 2018; Wette 2020) and used\nby PESUMMARY. For reweighting of samples, e.g., to our\npreferred cosmological model or to incorporate calibration\nmarginalization with RIFT, either routines in PESUMMARY\nor simple custom routines (as in the case for new candidates\nin GWTC-4.0) are used and provided with our data release.\n5.7. Posterior Samples\nFollowing sampling, our measurements of the binary pa-\nrameters \u03b8 for each candidate are represented by a discrete\nset of parameter values \u03b8i sampled from the posterior distri-\nbution. These samples can be used to compute expectation\nvalues over quantities of interest, e.g., through Monte Carlo\nintegration. Marginalization is achieved by only consider-\ning the dependence of the samples on the quantities that are\nnot marginalized out. Each sample includes the fifteen in-\ntrinsic and extrinsic parameters required to describe the GW\nstrain from quasi-circular BBHs (systems which include NSs\nrequire an additional tidal parameter per NS) as well as the\nparameters required to describe the inferred calibration state.\nIn addition to these a number of quantities can be derived\nfrom the intrinsic parameters of the binary using the meth-\nods described in Section 2.4. These include the final mass\nMf and final dimensionless spin \u03c7f of the remnant compact\nobject following coalescence, the peak luminosity \u2113peak and\ntotal energy radiated Erad, as well as the final kick velocity of\nthe remnant vk when the relevant waveform model supports\nsuch estimates.\nSome intrinsic properties of the binaries vary over the\ncourse of the binary coalescence, i.e., the orientations of the\ndimensionless spins \u03c71 and \u03c72 in precessing systems. Our\ninitial inferences report these quantities at a reference fre-\nquency fref, taken to be 20 Hz, corresponding to a variable\nreference time before coalescence. The spin tilt angles with\nrespect to the orbital angular momentum, \u03b81 and \u03b82, in partic-\nular carry valuable information about the formation mecha-\nnism of the binary. These angles approach well-defined lim-\nits at infinite binary separation (Gerosa et al. 2015), where\nthey can be used in population inferences (e.g., Mould &\nGerosa 2022), and so we report the spin tilts and derived\nquantities such as \u03c7eff and \u03c7p in this limit. The spins are\nevolved from their reference values (Johnson-McDaniel et al.\n2022b) using PN expressions for the precession-averaged dy-\nnamics (Gerosa et al. 2015; Chatziioannou et al. 2017) to for-\nmally infinite separations (cf. Gerosa et al. 2023). Wherever\npossible, the more accurate hybrid evolution using a combi-\nnation of orbit-averaged precession followed by precession-\naverage evolution is employed, but for a small number can-\ndidates only the computationally faster precession-averaging\napproach is used. We report these evolved spin quantities in\nour final samples for BBH candidates, and for NSBH candi-\ndates when analyzing them with waveform models that ne-\nglect the imprint of matter onto the GW signal.\nIn reporting and plotting the inferred parameters for each\ncandidate, we marginalize out all but one or two parameters\nat a time, and report the median value and credible inter-\nvals (CIs) of the marginalized posteriors for those param-\neters.\nUnless otherwise noted, we report the median and\n90% CI of each binary parameter, marginalizing over the\nothers. Generally we use symmetric CIs for single param-\neters, so that 5% of the posterior density lies below the lower\nbound of the 90% CI and 5% of the density lies above the\nupper bound. In some instances where the posteriors have\nsupport near a physical prior boundary, the symmetric CI\ngives the appearance of excluding the boundary value even\nif there is high probability there. In such cases we may re-\nport the 90% highest posterior density (HPD), the smallest\ninterval containing 90% of the posterior density. When plot-\nting marginalized densities we make use of one- and two-\ndimensional KDE to produce continuous densities from sam-\nples. Our two-dimensional credible regions are constructed\nusing the HPD method.\nOur inferences on the location of GW candidates are avail-\nable in two formats. The samples themselves represent our\nfull posterior over the source parameters, including the sky\nlocation and distance of the detected GW sources. In addi-\ntion, we provide three-dimensional localizations in the same\nformat as the localizations included in our public GW alerts,\nby applying KDE to the samples. These localizations are\ncreated using LIGO.SKYMAP (Singer & Price 2016; Singer\net al. 2016a,b), which includes the BAYESTAR package\nused to localize GW candidates from modeled online and of-\nfline searches.\n5.8. Approximate Spatial Localization\nWe do not carry out full PE for all candidates which meet\nthe criteria for inclusion in GWTC-4.0 (Section 3.6). Simi-\nlar to the criteria for inclusion in our past catalog releases,\nthe criteria for full PE analysis has evolved with GWTC\nversions (Section 5.9). However, we provide approximate\nspatial localization for all candidates in GWTC-4.0 to en-\nable multimessenger analyses of large samples of weak GW\ncandidates using the same methods as for our public GW\nalerts. Such methods are computationally much cheaper than\nfull PE, and already integrated into the candidate manage-\nment system. In particular, for candidates produced by mod-\neled CBC searches, the approximate localization is carried\nout with BAYESTAR (Singer & Price 2016; Singer et al.\n2016a,b). For candidates produced by CWB-BBH, the lo-\ncalization method is directly part of CWB and described in\nSection 3.1.\n5.9. Analysis Settings and Details\nHere we describe the particular analysis settings which\nvary across the inferences carried out for each candidate in\nGWTC-4.0.\n5.9.1. New Candidates Found in O4a\nWe perform full Bayesian PE on a high-purity subset of the\ncandidates (Section 3.6), namely those with FARs < 1 yr\u22121\n\n24\nand pastro > 0.9, which is the least strict threshold we set for\nuse in further downstream analyses. For this subset, the anal-\nysis settings depend on the nature of the binary as inferred\nusing preliminary PE and confirmed in our final analysis. As\ndescribed in Abac et al. (2025b) these candidates include a\nlarge number of BBHs as well as new NSBHs, but no signif-\nicant BNS candidates.\nBased on preliminary PE and any input from data vali-\ndation (cf. Section 4), we categorize the signals and deter-\nmine an appropriate prior, waveform model, and data seg-\nment to analyze (in all cases, the data product is based on the\nGDS-CALIB_STRAIN_CLEAN_AR channel, as described\nin Abac et al. (2025c)). For nearly all cases, the durations\nare selected so that the \u2113= 3, |m| = 3 higher harmonic is\nfully captured within the frequency range integrated over in\nour likelihood. In each case it is possible that at the start-\ning frequency of the waveform, even higher harmonics be-\ngin in band, which may cause aliasing in the case of time-\ndomain waveform models. Due to the small amplitude of\nsuch higher harmonics relative to the lower-frequency mul-\ntipole moments, the effect is expected to be negligible. Fur-\nther, we adopt the additional prior during sampling such that\nthe \u2113= 3 mode is resolved in band, given the chosen sam-\npling rate. This only modifies the prior for a small number\nof candidates, and we have checked that in these cases, the\nprior makes no discernible difference in the final posterior\nsamples.\nFor all candidates the Tukey window applied before trans-\nforming time-domain data to the frequency domain has a roll-\non of 1 s. This is longer than the 0.4 s roll-on used in prior\nPE analyses. The longer window is chosen to reduce spectral\nleakage, because for the first time the instrumental noise near\nflow is sufficiently low that the small amount of leakage from\neven lower frequencies into frequency range integrated over\nin our likelihood made noticeable impact on our analyses.\nThe analysis of the initial PE results to determine our final\nsettings is carried out using the PECONFIGURATOR software\npackage. The resulting information is also used to determine\nthe appropriate waveform models to use to capture system-\natic uncertainties across waveform models.\nFor BBH candidates, we use both the phenomenological\nIMRPHENOMXPHM_SPINTAYLOR (Garc\u00eda-Quir\u00f3s et al.\n2020; Pratten et al. 2020a; Colleoni et al. 2025b) model\nand the effective one body model SEOBNRV5PHM (Khalil\net al. 2023; Pompili et al. 2023; Ramos-Buades et al. 2023)\nfor all candidates. In addition, we use NRSUR7DQ4 (Varma\net al. 2019a) for those candidates whose parameters lie within\nthe range of total mass and mass ratio values supported by the\nmodel, as determined by preliminary PE. In the case of NR-\nSUR7DQ4 we use a fixed duration of 10000(G/c3)M(1+z)\nfor the waveform model when evaluating the likelihood, with\nM(1 + z) the total detector-frame mass of the source. For\na subset of the candidates that are inferred to have unequal\nmasses or orbital precession, we additionally use IMRPHE-\nNOMXO4A (Hamilton et al. 2021; Thompson et al. 2024),\nsince these are cases where systematic differences between\nwaveform models are largest. In the case of the exceptional\nBBH candidate GW231123_135430 (Abac et al. 2025d), we\nadditionally employed the time-domain phenomenological\nmodel IMRPHENOMTPHM (Estell\u00e9s et al. 2022a).\nFor potential NSBHs (where the secondary has posterior\nsupport in the range m2 < 3M\u2299as expected for NSs, and\nthe primary has posterior support in the range m1 > 3M\u2299\nas expected for BHs), we perform additional analyses with\nand without matter effects. For our baseline results we em-\nploy our BBH models IMRPHENOMXPHM_SPINTAYLOR\nand SEOBNRV5PHM in the case of GW230529_181500;\nAbac et al. 2024 which include higher-multipolar emis-\nsion and precession but neglect matter effects.\nWe addi-\ntionally use IMRPHENOMNSBH (Thompson et al. 2020)\nand SEOBNRV4_ROM_NRTIDALV2_NSBH (Matas et al.\n2020) which include matter effects tuned to NSBH sys-\ntems but which neglect precession.\nWe also apply IMR-\nPHENOMPV2_NRTIDALV2 (Dietrich et al. 2019a), which\nincludes precession and tidal effects.\nSince these latter\nthree models do not incorporate higher multipolar emis-\nsion, we analytically marginalize over the coalescence phase.\nThese three models also differ in the ranges over which\nthe primary spin has been calibrated, and thus we enforce\n\u03c71 < 0.5 for IMRPHENOMNSBH, \u03c71 < 0.9 for SEOB-\nNRV4_ROM_NRTIDALV2_NSBH, and allow nearly max-\nimal spins \u03c71 < 0.99 for IMRPHENOMPV2_NRTIDALV2.\nIn all three cases we adopt the bound \u03c72 < 0.05, correspond-\ning to the largest projected spins near merger for Galactic\nBNSs which will merge in a Hubble time (Burgay et al. 2003;\nStovall et al. 2018). Depending on the model, multiple meth-\nods to accelerate the likelihood were employed, including\nmultibanding for IMRPHENOMXPHM (Garc\u00eda-Quir\u00f3s et al.\n2021; Morisaki 2021), heterodyning (also called relative bin-\nning; Cornish 2010, 2021; Zackay et al. 2018; Krishna et al.\n2023) for models including matter effects, and reduced-\norder quadrature (Canizares et al. 2015; Smith et al. 2016;\nMorisaki et al. 2023) for some analyses involving IMRPHE-\nNOMPV2_NRTIDALV2.\nFinally, for GW230529_181500,\nwe employ additional models with reduced physical content\nin order to test for the presence of effects such as preces-\nsion (Abac et al. 2024).\nFor all new candidates presented in GWTC-4.0, the lumi-\nnosity distance is marginalized over during sampling. For\nsampling we use a distance prior uniform in comoving vol-\nume and comoving time with the default cosmological model\nof the ASTROPY software package, a flat-\u039bCDM cosmology\nwith H0 = 67.66 km s\u22121 Mpc\u22121 and \u2126m = 0.30966. The\ncosmology assumed during sampling is not the default cos-\nmology we present our results in. Instead, the final samples\nare reweighted to our preferred cosmology (Ade et al. 2016)\nas described in Section 5.5.\n5.9.2. Candidates found in O1, O2 and O3\nAs a cumulative catalog, GWTC-4.0 includes candidates\ndetected during the first three observing runs of the advanced\ndetector network. As discussed in Section 3.6, GWTC-3.0\nincluded GW candidates identified during these runs with\nFARs less than a threshold value, which is 1 per 30 d for O1\n\n25\nand O2 and 1 per 2 d for O3. We have previously performed\nfull PE for the subset of these candidates having pastro > 0.5\nplus the NSBH candidate GW200105_162426 (Abbott et al.\n2021b), and our PE results for these candidates remain the\nsame in GWTC-4.0. These inferences were first presented\nin GWTC-2.1 (Abbott et al. 2024, for candidates found in\nO1, O2, and O3a) and GWTC-3.0 (Abbott et al. 2023a, for\ncandidates found in O3b). The exception is the BNS candi-\ndate GW170817, for which the PE results were not updated\nin GWTC-2.1, and so remain the same as those presented in\nGWTC-1.0 (Abbott et al. 2019a). Both sets of analyses from\nGWTC-2.1 and GWTC-3.0 used the same methods and set-\ntings which we now summarize.\nFor\neach\ncandidate,\nPSDs\nwere\ngenerated\nusing\nBAYESWAVE (Cornish & Littenberg 2015; Littenberg &\nCornish 2015; Cornish et al. 2021; Hourihane et al. 2022)\nas described in Section 5.3. For these candidates the roll-on\nof Tukey window applied to the time domain-data before\ntransforming to the frequency domain was 0.4 s. Multiple\nwaveform models were used in each case in order to under-\nstand systematic uncertainties in the inferences.\nFor BBH candidates, PE was carried out using two wave-\nform models which include higher harmonics and the effects\nof orbital precession. The phenomenological model IMR-\nPHENOMXPHM (Garc\u00eda-Quir\u00f3s et al. 2020; Pratten et al.\n2020a) was used with a multiscale prescription for the pre-\ncession dynamics (Chatziioannou et al. 2017) and sampling\nwas carried out with BILBY.\nThe EOB model SEOB-\nNRV4PHM (Ossokine et al. 2020) was also used for each\nBBH candidate, using RIFT to carry out PE.\nFor the NSBH candidates, multiple waveform models\nwere also used for PE.\nOur baseline results are drawn\nfrom the same models as for BBH candidates, namely\nIMRPHENOMXPHM and SEOBNRV4PHM. These mod-\nels include higher harmonics and precession but neglect\nmatter effects such as the tidal deformation or disruption\nof the NS on the waveform.\nThis is because such ef-\nfects are negligible for the NSBH candidates identified\nin O3b (Abbott et al. 2021b).\nIn order to assess the\nimportance of matter effects on the GW signal, models\nwhich include the effects to tidal deformation and mod-\nels which are specifically tailored for NSBH systems were\nalso used for inference. These were IMRPHENOMNSBH\nand SEOBNRV4_ROM_NRTIDALV2_NSBH. As with the\nnew NSBH candidates from O4a, we analytically marginal-\nize over the coalescence phase of these latter models which\nneglect higher multipolar emission. For each model two anal-\nyses were performed, one restricting the dimensionless spin\nmagnitude on the secondary to \u03c72 \u22640.05, and the second\nallowing it to range to \u03c72 \u22640.99 or the largest value al-\nlowed by the model. These inferences are computationally\nexpensive, and a number of samplers were employed depend-\ning on the waveform model, including DYNESTY as accessed\nthrough BILBY, RIFT, PARALLELBILBY, and LALINFER-\nENCE.\nUp to GWTC-4.0, two BNS candidates have been identi-\nfied, GW170817 and GW190425. Multiple models are used\nfor PE of GW170817 (Abbott et al. 2019a). GW170817 was\nanalysed with three frequency-domain models using LAL-\nINFERENCE:\nTAYLORF2 including tidal effects (Sturani\n2015; Isoyama et al. 2020; Flanagan & Hinderer 2008; Vines\net al. 2011), IMRPHENOMPV2_NRTIDAL, and SEOB-\nNRV4_ROM_NRTIDAL, and with two time-domain models\nusing RIFT: SEOBNRV4T (Hinderer et al. 2016; Steinhoff\net al. 2016), and TEOBRESUMS (Nagar et al. 2018). For\nthis candidate we marginalize over the phase analytically for\nmodels that assume spins aligned with the orbital plane. As\nwith our other analyses on candidates including NSs, multi-\nple analyses are carried out allowing only for relatively small\nspin magnitudes \u03c7i \u22640.05 and allowing for spin magni-\ntudes up to the maximum allowed for a given model, as large\nas \u03c7i \u22640.99. The second BNS candidate, GW190425 (Ab-\nbott et al. 2020c), was detected during O3a and its PE re-\nsults updated in GWTC-2.1. For this candidate we present\nresults using the precessing, tidal approximant IMRPHE-\nNOMPV2_NRTIDAL using DYNESTY through BILBY, and\nboth relatively low- and high-spin prior limits on the compo-\nnent spins. To accelerate inference we employ reduced-order\nquadrature.\nWhen using BILBY or PARALLELBILBY to analyze can-\ndidates from the first three observing runs, the posteriors are\nmarginalized over luminosity distance and geocenter time,\nwith the exception of the BILBY analysis of GW190425\nwhich only used distance marginalization. For these candi-\ndates, initial sampling was carried out with a distance prior\nuniform in Euclidean volume. During postprocessing, the\nposterior samples were then reweighted to the cosmological\nmodel described in Section 5.5 (Ade et al. 2016).\n5.9.3. Calibration Prior Settings for Candidates from O1, O2,\nand O3\nWe marginalized over the calibration uncertainties when\nproducing the PE results from GWTC-1.0, GWTC-2.0,\nGWTC-2.1 and GWTC-3.0, as discussed in Section 5.4. Due\nto an error in implementation, an incorrect prior on the cal-\nibration parameters for LHO and LLO was used for these\nresults. The priors were set using the median and CIs of \u02dc\u03b7R\nfrom Equation (11) for data from the LIGO detectors, rather\nthan those of 1/\u02dc\u03b7R as required by the method. In the limit of\nsmall calibration uncertainties, this amounts to a sign error in\nthe means of the Gaussian priors for the calibration parame-\nters. In the case that the means of the priors are zero the error\nhas no effect. However, the calibration uncertainties for LHO\nand LLO have nonzero means. Meanwhile, the priors on the\ncalibration parameters were set correctly for Virgo data.\nFor candidates detected in O1, O2, and O3 the means are\ngenerally small relative to the standard deviation of the pri-\nors on the calibration parameters. Further the absolute sizes\nof the standard deviations of these parameters are small in the\nsensitive band of the detectors, of the order of a few percent\nin amplitude and a few degrees in phase for the two LIGO\ninterferometers (Abbott et al. 2019a, 2021a, 2024, 2023a),\nand so a priori the impact of this error on our inferences\nis expected to be small. We have verified this expectation\n\n26\nthrough preliminary re-analysis of the potentially impacted\ncandidates, carried out by repeating PE with corrected pri-\nors and by reweighting the likelihood values of existing PE\nsamples in order to correct for the erroneous calibration pri-\nors. None of the scientific conclusions reported in previous\nstudies is affected by the error. In addition, the error does not\nimpact the significance of any of our candidates, since the\nGW searches described in Section 3 do not incorporate the\neffect of uncertain strain calibration.\nThe typical change in the posteriors following preliminary\nre-analysis is within statistical sampling error, as quantified\nby the Jensen\u2013Shannon divergence (Lin 1991) between one-\ndimensional marginal distributions before and after correc-\ntion (cf. Romero-Shaw et al. 2020b; Abbott et al. 2021a, Ap-\npendix A). As a particular case, the localization of the source\nof GW170817 receives only a small correction when re-\nanalyzed, and its association with the electromagnetic coun-\nterpart emission from AT 2017gfo (Abbott et al. 2017b) is\nunaffected by the error.\nAnother case is GW150914, which displays visible differ-\nences in the sky location posteriors when re-analyzed (al-\nthough the bounds of the 90% CI of the right ascension and\ndeclination remain nearly unchanged). Meanwhile, our in-\nferences of the intrinsic parameters of GW150914 remain\nunchanged to within sampling errors.\nWhile the impact on individual candidates is small, a pos-\nsible concern is that this error can bias analyses that ag-\ngregate data from multiple candidates, such as population\nstudies and cosmological inferences.\nWe are investigat-\ning the impact of the calibration marginalization error on\nthese analyses, but the effects are expected to be negligi-\nble compared to other sources of systematic error. This er-\nror does not impact the PE of new candidates observed in\nO4a (Abac et al. 2025b), and we have updated the PE results\nfor GW230529_181500 (Abac et al. 2024) to correct for the\nerror.\n5.10. On the Likelihood used for Inference\nLate in the preparation of this manuscript, we discovered\na normalization error in the likelihood used for the inference\ncodes BAYESWAVE, BILBY, LALINFERENCE, PARALLEL-\nBILBY, and RIFT. The error arises due to the incorrect ap-\nplication of a window factor that was intended to account for\nthe power lost in the noise residuals due to the Tukey win-\ndow applied to the data before transforming them to the fre-\nquency domain. This error causes the likelihood to be overly\nconstrained by a factor depending on the window function\nused to mitigate spectral leakage. The incorrect likelihood\n\u02c6p(d|\u03b8) is related to the correct likelihood p(d|\u03b8) via the av-\nerage power in the Tukey window \u02c6p(d|\u03b8) = p(d|\u03b8)\u03b2 with\n\u03b2 =\n\u0012\n1 \u22125Tw\n4T\n\u0013\u22121\n,\n(13)\nwhere Tw is the roll-off time of the Tukey window to one\nside, and T is the segment duration. The window factor is\napplied when computing the PSD via standard methods, but\nshould not be applied to the data when the signal has sup-\nport only where the window function is unity, as is the case\nin our analyses. Although accounting for the windowing us-\ning a single window factor in PSD estimation is still an ap-\nproximation when computing the likelihood, multiple inves-\ntigations and the use of probability\u2013probability tests (Veitch\net al. 2015b; Romero-Shaw et al. 2020b) have confirmed its\naccuracy. Further, these tests have confirmed the normaliza-\ntion error in our inference codes and the correctness of our\nupdated likelihood. More details on the error and validation\nof the updated likelihood can be found in Talbot et al. (2025).\nWe have reanalysed the O4a candidates presented in\nGWTC-4.0 using the correct likelihood and we find that the\ndifferences in the posteriors are small, but systematically\nwiden the posterior distributions. For the reanalyses, we use\nrejection sampling to reweight the samples from the original\nposteriors, which were produced using the incorrect likeli-\nhood. The acceptance ratio is the ratio of the likelihoods us-\ning the correct and incorrect likelihoods, p(d|\u03b8)/\u02c6p(d|\u03b8). In\nsome cases the rejection efficiency is poor, and so for all can-\ndidates we resample with replacement until we achieve the\noriginal number of samples. This procedure produces a new\nset of unbiased samples, but the samples are not independent.\nFor the worst cases, Tw = 1 s and T = 4 s, and so \u03b2 = 1.45,\nwhich also corresponds to overestimated SNRs from PE by\na factor 1.21. The impact is less for lower-mass candidates\nwhose durations are larger, so that for BBH candidates with\nTw = 1 s and T = 8 s, \u03b2 = 1.19 and the SNRs are overes-\ntimated by a factor of 1.09. The error also impacts previous\nanalyses from O1 through O3, but the impact is reduced be-\ncause of the smaller Tukey window applied when performing\nPE for candidates from those observing runs, and we have not\ncorrected these past inferences. For results from these previ-\nous runs, the worst cases have Tw = 0.4 s and T = 4 s, and\nso \u03b2 = 1.14 and the SNRs are overestimated by a factor of\n1.07. However, these new posteriors were not created in time\nto be included in the downstream analyses. Therefore, for\nO4a candidates, we release both the original posteriors using\nthe incorrect likelihood and the new reweighted posteriors\nusing the correct likelihood.\n6. WAVEFORM CONSISTENCY TESTS\nAs we have seen in the earlier Sections, a common as-\nsumption made so far for GWTC candidates is that the\nsignal source is a quasi-circular CBC, in vacuum, as pre-\ndicted by GR.\nAlthough no candidates have yet been\nproven to violate this assumption, GW190521 (Abbott et al.\n2020d), GW200105_042309 (Abbott et al. 2021b), and\nGW231123_135430 (Abac et al. 2025d) highlight the impor-\ntance of continuously checking its validity, in order to ensure\nthe reliability of astrophysical interpretations. One way of\nchecking this assumption is to perform waveform consistency\ntests. These tests compare different waveform reconstruction\ntechniques to assess their agreement and identify any unex-\npected features in the reconstructed signals. Waveform re-\nconstruction techniques can be minimally modeled (as seen\nfor CWB in Section 3.1) or template based (Sections 3 and 5).\n\n27\nMinimally-modeled techniques use time\u2013frequency wavelets\nto identify coherent features in the data of a network of multi-\nple detectors. This generic approach enables the discovery of\nunexpected phenomena (which might be present if the signal\nsource violates the assumption of a quasi-circular CBC) but\ndoes not provide a direct mapping between the reconstructed\nwaveform and the source\u2019s physical properties, such as the\nmasses and spins of a binary system and the distance to the\nsource.\nTo evaluate the consistency between template-based and\nminimally-modeled reconstructions, we implement a sys-\ntematic injection study (Abbott et al. 2019a, 2021a, 2023a;\nSalemi et al. 2019; Ghonge et al. 2020; Johnson-McDaniel\net al. 2022a). This involves injecting CBC waveform sam-\nples from the posterior parameter distributions (Section 5)\ninto detector data at times near but distinct from the candi-\ndate (off-source injections). These injections are then recon-\nstructed using minimally-modeled methods. By comparing\nthe reconstructed waveforms from off-source injections (wi)\nwith the reconstruction of the candidate ( \u02c6w), we can assess\nhow well the CBC PE posteriors align with the minimally-\nmodeled reconstruction. We quantify the agreement between\nwaveform reconstructions using the overlap, defined as\nO(h1, h2) =\n\u27e8h1|h2\u27e9\np\n\u27e8h1|h1\u27e9\u27e8h2|h2\u27e9\n,\n(14)\nwhere h1 and h2 are the waveforms being compared and \u27e8\u00b7|\u00b7\u27e9\ndenotes the noise-weighted inner product (Abac et al. 2025a,\nAppendix B). The overlap, O(h1, h2), is bounded between\n[\u22121, +1].\nFor each candidate, we compute two types of overlap mea-\nsurements and compare them to assess waveform consistency\nin terms of p-values:\n1. The off-source overlaps O(wi, hi) between injected\nwaveforms and their minimally-modeled reconstruc-\ntions, forming a reference distribution O;\n2. The on-source overlap O( \u02c6w, hmaxL) between the\nmaximum-likelihood posterior sample and the actual\nminimally-modeled reconstruction.\nThis comparison has an inherent asymmetry:\nfor off-\nsource cases, we calculate the overlap between known wave-\nforms and their minimally-modeled reconstructions, while\nfor on-source cases, we compare the maximum-likelihood\ntemplate from PE with the minimally-modeled reconstruc-\ntion. This asymmetry typically results in off-source matches\nbeing systematically lower than what would be expected\nfrom a true null distribution (Abbott et al. 2023a). Conse-\nquently, the derived p-values are conservative by construc-\ntion. Despite this limitation, the on-source p-value remains\na useful indicator for identifying unexpected signal features,\nthough with reduced statistical power compared to an unbi-\nased test.\nTo ensure reliable waveform consistency tests, we selected\nall O4a candidates that meet four key criteria: (i) data avail-\nability from both LIGO detectors, (ii) presence of PE re-\nsults using the NRSUR7DQ4 waveform family, (iii) detector-\nframe chirp mass (1 + z)M > 15M\u2299, and (iv) a network\nSNR > 10. These criteria reflect that minimally-modeled\nmethods require multi-detector data, and that they are partic-\nularly effective for high-mass CBCs with high SNR signals.\nThe candidates satisfying these criteria are analyzed\nin\na\ncompanion\npaper\n(Abac\net\nal.\n2025b)\nusing\nthree minimally-modeled waveform reconstruction methods:\nBAYESWAVE (Cornish & Littenberg 2015; Cornish et al.\n2021; Ghonge et al. 2020), and two configurations of the\nCWB pipeline described in Section 3.1. Specifically, CWB-\n2G (Klimenko et al. 2016; Drago et al. 2020) which employs\nthe WDM wavelet transform and an excess power statis-\ntic to identify coherent features and CWB-BBH (Klimenko\n2022) which uses the WaveScan transform and a cross-power\nstatistic. Both BAYESWAVE and CWB-2G are designed for\ngeneric GW transients, whereas CWB-BBH is optimized for\nCBC signals, also adopting specialized frequency bands and\ntime\u2013frequency resolutions.\nFor each selected candidate, our injection campaign used\nfor\n\u2022 BAYESWAVE approximately 400 random posterior\nsamples injected within \u00b18192 s of the candidate time,\n\u2022 CWB-2G and CWB-BBH several thousand random\nposterior samples injected across a 2\u20133 week period\nsurrounding the candidate time.\nThis analysis provides a robust statistical baseline to quan-\ntify the degree of agreement between template-based and\nminimally-modeled reconstructions for a relatively large sub-\nset of the candidates from GWTC-4.0. By comparing the on-\nsource overlap to the distribution from off-source injections,\nwe can verify their consistency with the quasi-circular CBC\nhypothesis, as well as identify those that may exhibit unex-\npected features.\n7. DATA MANAGEMENT\nThe workflow of data analyses described in this paper out-\nlines a complex chain of disparate analyses required to find\nand characterize GW transients (see Figure 1). In addition to\nthe internal complexity of each analysis, coordinating each\nstage of this analysis and effectively tracking that input and\noutput data is a significant challenge. This challenge grows\nwith the number of GW candidates observed, necessitating\nthe development of tools to manage these tasks with little to\nno human intervention. For O4a, this development included\nthe augmentation of existing infrastructure and the develop-\nment of new software packages including CBCFLOW and the\ncatalog data-product pipeline.\nThe online and offline analysis results from the search\npipelines described in Section 3 are stored in GRACEDB\n(Moe et al. 2014). For offline results, GRACEDB is also\nused to generate the final candidate list for the catalog. To\nfacilitate the tracking of these offline results, GRACEDB has\nbeen augmented to provide version-controlled snapshots of\n\n28\nthe state of the catalog during the progression of the offline\nanalyses.\nAs in GWTC-2.0, GWTC-2.1, and GWTC-3.0, the PE\nanalyses described in Section 5 are managed with the ASI-\nMOV software package (Williams et al. 2023).\nASIMOV\ningests data-quality recommendations and preliminary PE\nanalyses, and uses this to automatically determine appropri-\nate configuration for PE analyses, as well as automating the\nproduction of PSD estimates. Once all desired PE is com-\nplete, ASIMOV packages results into a standard format in-\ncluding all inputs and configuration required for reproduction\nusing PESUMMARY (Hoy & Raymond 2021) .\nThe CBCFLOW (Ashton et al. 2022) software package is\nused to manage the flow of data between the various analy-\nses and to track metadata about each stage of the analysis.\nA monitor process fetches search metadata from GRACEDB\nand preliminary PE results from a shared directory on the\nCaltech computing cluster. Data-quality information about\ncandidates is updated following the studies described in Sec-\ntion 4. ASIMOV reads CBCFLOW for search, data-quality,\nand preliminary-PE metadata, which is used to configure pro-\nduction analyses. Upon completion of those analyses, meta-\ndata about them are written back to CBCFLOW. All other\ndownstream analyses such as searches for lensed pairs of\ncandidates (Abac et al. 2025e) and tests of GR (Abac et al.\n2025f,g,h) also utilize CBCFLOW to track their progress and\nresults.\nFinally, the release data product is assembled by a collec-\ntion of scripts. These read CBCFLOW to identify the preferred\nsearch and PE results, as well as tracking their finalization\nstatus. These are then collated into the data product itself,\nand tables of summary information are generated to facilitate\ndownstream use.\n8. CONCLUSION\nLeading on from the introduction presented in Abac et al.\n(2025a), this article describes the analysis methods used to\ntransform the interferometric strain data from the LVK de-\ntectors into version 4.0 of the GWTC; the results of these\nanalyses are presented in Abac et al. (2025b). We began in\nSection 2 with a description of the waveform models used\nto describe the GW signals from CBCs involving BHs and\nNSs. In Section 3, we described the search methods we use\nto filter the strain data to identify candidate transient GW sig-\nnals (sensitive to both CBC sources as well as minimally-\nmodeled bursts of GW radiation), and how these candidates\nare then ranked to identify the most significant ones. Likely\nGW candidates are then studied to understand the quality of\ndata and identify any transient non-Gaussian noise that may\nbias later analyses (see Section 4). Section 5 described how\na subset of likely GW candidates are then characterized us-\ning computational Bayesian inference methods to estimate\nthe parameters of the GW source, such as the masses and\nspins of the compact objects involved. The PE results how-\never assume that the GW source is a quasi-circular CBC in\nvacuum as modeled in Section 2. To check this assumption,\nwe described in Section 6 how waveform consistency tests\ncompare different waveform reconstruction techniques to as-\nsess their agreement and identify any unexpected features in\nthe reconstructed signals. Finally, in Section 7, we described\nthe data management and workflow tools used to coordinate\nthe various analyses and track the input and output data.\nThe methods described in this work are continually devel-\noped to improve the capabilities of the LVK network to de-\ntect and characterize GW transients. Specifically, as the de-\ntectors evolve towards higher sensitivity, and more detectors\nare added to the network, we continue to see a greater num-\nber of signals and more high-fidelity signals at larger SNR\n(Abbott et al. 2020a). This necessitates efficiency improve-\nments across all the methods to avoid computational bottle-\nnecks and to ensure that the GW transient candidates can be\nprocessed in a timely manner. Moreover, the increased SNR\nrequires refinements to the waveform models to reduce sys-\ntematic biases as much as possible. The evolution of the de-\ntectors also necessitates continual improvements to the data\nanalysis methods to ensure optimal data processing (e.g., as\nthe noise floor of the detectors lowers, new glitch classes\nmay become relevant, requiring development to searches and\ndata-quality studies). Finally, as the time\u2013volume explored\nincreases, we hope to further expand the range of astrophys-\nical sources that can be detected and characterized, which in\nturn requires the development of new models, search, and PE\nmethods.\nData Availability: The data products generated by the\nmethods described within this work are openly available\nin the GWTC-4 online catalog, which is hosted at https://\ngwosc.org/GWTC-4.0 and documented further in Abac et al.\n(2025c).\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded by\nthe National Science Foundation. The authors also grate-\nfully acknowledge the support of the Science and Technol-\nogy Facilities Council (STFC) of the United Kingdom, the\nMax-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO 600 de-\ntector. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucle-\nare (INFN), the French Centre National de la Recherche\nScientifique (CNRS) and the Netherlands Organization for\nScientific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and support of\nthe EGO consortium. The authors also gratefully acknowl-\nedge research support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India, the\nDepartment of Science and Technology, India, the Science\n& Engineering Research Board (SERB), India, the Ministry\nof Human Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00f3n (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00f3n y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC - Cen-\n\n29\ntroNazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the European\nUnion NextGenerationEU, the Comunitat Auton\u00f2ma de les\nIlles Balears through the Conselleria d\u2019Educaci\u00f3 i Universi-\ntats, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia i So-\ncietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Science\nCentre of Poland and the European Union - European Re-\ngional Development Fund; the Foundation for Polish Sci-\nence (FNP), the Polish Ministry of Science and Higher Ed-\nucation, the Swiss National Science Foundation (SNSF), the\nRussian Science Foundation, the European Commission, the\nEuropean Social Funds (ESF), the European Regional De-\nvelopment Funds (ERDF), the Royal Society, the Scottish\nFunding Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scientific Research Fund (OTKA), the French\nLyon Institute of Origins (LIO), the Belgian Fonds de la\nRecherche Scientifique (FRS-FNRS), Actions de Recherche\nConcert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek\n- Vlaanderen (FWO), Belgium, the Paris \u00cele-de-France Re-\ngion, the National Research, Development and Innovation\nOffice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of Sci-\nence, Technology, and Innovations, the International Center\nfor Theoretical Physics South American Institute for Funda-\nmental Research (ICTP-SAIFR), the Research Grants Coun-\ncil of Hong Kong, the National Natural Science Foundation\nof China (NSFC), the Israel Science Foundation (ISF), the\nUS-Israel Binational Science Fund (BSF), the Leverhulme\nTrust, the Research Corporation, the National Science and\nTechnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The authors\ngratefully acknowledge the support of the NSF, STFC, INFN\nand CNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific Re-\nsearch (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for\nTransformative Research Areas (A) 20A203: JP20H05854,\nthe joint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and the\nNational Science and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research Pro-\ngram, the Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the pur-\npose of open access, the authors have applied a Creative\nCommons Attribution (CC BY) license to any Author Ac-\ncepted Manuscript version arising. We request that citations\nto this article use \u2019A. G. Abac et al. (LIGO-Virgo-KAGRA\nCollaboration), ...\u2019 or similar phrasing, depending on journal\nconvention.\nSoftware:\nPlots\nwere\nprepared\nwith\nMAT-\nPLOTLIB (Hunter 2007), NUMPY (Harris et al. 2020), and\nTIKZ (Tantau 2023).\nREFERENCES\nAasi, J., et al. 2013, Phys. Rev. D, 87, 022002,\ndoi: 10.1103/PhysRevD.87.022002\n\u2014. 2015, Class. Quant. Grav., 32, 074001,\ndoi: 10.1088/0264-9381/32/7/074001\nAbac, A. G., et al. 2024, Astrophys. J. 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K. ADKINS,11\nS. AFROZ\n,12\nD. AGARWAL\n,13, 14\nM. AGATHOS\n,15\nM. AGHAEI ABCHOUYEH\n,16\nO. D. AGUIAR\n,17\nS. AHMADZADEH,18\nL. AIELLO\n,19, 20\nA. AIN\n,21\nP. AJITH\n,22\nS. AKCAY\n,23\nT. AKUTSU\n,24, 25\nS. ALBANESI\n,26, 27\nR. A. ALFAIDI\n,28\nA. AL-JODAH\n,29\nC. ALL\u00c9N\u00c9,30\nA. ALLOCCA\n,31, 4\nS. AL-SHAMMARI,32\nP. A. ALTIN\n,33\nS. ALVAREZ-LOPEZ\n,34\nO. AMARASINGHE,32\nA. AMATO\n,35, 36\nC. AMRA,37\nA. ANANYEVA,10\nS. B. ANDERSON\n,10\nW. G. ANDERSON\n,10\nM. ANDIA\n,38\nM. ANDO,39, 40\nT. ANDRADE,41\nM. ANDR\u00c9S-CARCASONA\n,42\nT. ANDRI \u00b4C\n,7, 8, 43\nJ. ANGLIN,44\nS. ANSOLDI\n,45, 46\nJ. M. ANTELIS\n,47\nS. ANTIER\n,48\nM. AOUMI,49\nE. Z. APPAVURAVTHER,50, 51\nS. APPERT,10\nS. K. APPLE\n,52\nK. ARAI\n,10\nA. ARAYA\n,53\nM. C. ARAYA\n,10\nM. ARCA SEDDA,43\nJ. S. AREEDA\n,54\nL. ARGIANAS,55\nN. ARITOMI,2\nF. ARMATO\n,56, 57\nS. ARMSTRONG\n,58\nN. ARNAUD\n,38, 59\nM. AROGETI\n,60\nS. M. ARONSON\n,11\nG. ASHTON\n,61\nY. ASO\n,24, 62\nM. ASSIDUO,63, 64\nS. ASSIS DE SOUZA MELO,59\nS. M. ASTON,65\nP. ASTONE\n,66\nF. ATTADIO\n,67, 66\nF. AUBIN\n,68\nK. AULTONEAL\n,69\nG. AVALLONE\n,70\nS. BABAK\n,71\nF. BADARACCO\n,56\nC. BADGER,72\nS. BAE\n,73\nS. BAGNASCO\n,27\nE. BAGUI,74\nL. BAIOTTI\n,75\nR. BAJPAI\n,24\nT. BAKA,76\nT. BAKER\n,77\nM. BALL,78\nG. BALLARDIN,59\nS. W. BALLMER,79\nS. BANAGIRI\n,80\nB. BANERJEE\n,43\nD. BANKAR\n,14\nT. M. BAPTISTE,11\nP. BARAL\n,9\nJ. C. BARAYOGA,10\nB. C. BARISH,10\nD. BARKER,2\nN. BARMAN,14\nP. BARNEO\n,41, 81\nF. BARONE\n,82, 4\nB. BARR\n,28\nL. BARSOTTI\n,34\nM. BARSUGLIA\n,71\nD. BARTA\n,83\nA. M. BARTOLETTI,84\nM. A. BARTON\n,28\nI. BARTOS,44\nS. BASAK\n,22\nA. BASALAEV\n,85\nR. BASSIRI\n,86\nA. BASTI\n,87, 88\nD. E. BATES,32\nM. BAWAJ\n,89, 50\nP. BAXI,90\nJ. C. BAYLEY\n,28\nA. C. BAYLOR\n,9\nP. A. BAYNARD II,60\nM. BAZZAN,91, 92\nV. M. BEDAKIHALE,93\nF. BEIRNAERT\n,94\nM. BEJGER\n,95\nD. BELARDINELLI\n,20\nA. S. BELL\n,28\nD. S. BELLIE,80\nL. BELLIZZI\n,88, 87\nW. BENOIT\n,96\nI. BENTARA\n,97\nJ. D. BENTLEY\n,85\nM. BEN YAALA,58\nS. BERA\n,98\nF. BERGAMIN\n,7, 8\nB. K. BERGER\n,86\nS. BERNUZZI\n,26\nM. BEROIZ\n,10\nC. P. L. BERRY\n,28\nD. BERSANETTI\n,56\nA. BERTOLINI,36\nJ. BETZWIESER\n,65\nD. BEVERIDGE\n,29\nG. BEVILACQUA\n,99\nN. BEVINS\n,55\nR. BHANDARE,100\nR. BHATT,10\nD. BHATTACHARJEE\n,101, 102\nS. BHAUMIK\n,44\nS. BHOWMICK,103\nV. BIANCALANA\n,99\nA. BIANCHI,36, 104\nI. A. BILENKO,105\nG. BILLINGSLEY\n,10\nA. BINETTI\n,106\nS. BINI\n,107, 108\nC. BINU,109\nO. BIRNHOLTZ\n,110\nS. BISCOVEANU\n,80\nA. BISHT,8\nM. BITOSSI\n,59, 88\nM.-A. BIZOUARD\n,48\nS. BLABER,111\nJ. K. BLACKBURN\n,10\nL. A. BLAGG,78\nC. D. BLAIR,29, 65\nD. G. BLAIR,29\nF. BOBBA,70, 112\nN. BODE\n,7, 8\nG. BOILEAU\n,48\nM. BOLDRINI\n,66, 67\nG. N. BOLINGBROKE\n,113\nA. BOLLIAND,114, 37\nL. D. BONAVENA\n,44, 91\nR. BONDARESCU\n,41\nF. BONDU\n,115\nE. BONILLA\n,86\nM. S. BONILLA\n,54\nA. BONINO,116\nR. BONNAND\n,30, 114\nP. BOOKER,7, 8\nA. BORCHERS,7, 8\nS. BORHANIAN,6\nV. BOSCHI\n,88\nS. BOSE,117\nV. BOSSILKOV,65\nA. BOUDON,97\nA. BOZZI,59\nC. BRADASCHIA,88\nP. R. BRADY\n,9\nA. BRANCH,65\nM. BRANCHESI\n,43, 118\nI. BRAUN,101\nT. BRIANT\n,119\nA. BRILLET,48\nM. BRINKMANN,7, 8\nP. BROCKILL,9\nE. BROCKMUELLER\n,7, 8\nA. F. BROOKS\n,10\nB. C. BROWN,44\nD. D. BROWN,113\nM. L. BROZZETTI\n,89, 50\nS. BRUNETT,10\nG. BRUNO,13\nR. BRUNTZ\n,120\nJ. BRYANT,116\nY. BU,121\nF. BUCCI\n,64\nJ. BUCHANAN,120\nO. BULASHENKO\n,41, 81\nT. BULIK,122\nH. J. BULTEN,36\nA. BUONANNO\n,123, 1\nK. BURTNYK,2\nR. BUSCICCHIO\n,124, 125\nD. BUSKULIC,30\nC. BUY\n,126\nR. L. BYER,86\nG. S. CABOURN DAVIES\n,77\nG. CABRAS\n,45, 46\nR. CABRITA\n,13\nV. C\u00c1CERES-BARBOSA\n,6\nL. CADONATI\n,60\nG. CAGNOLI\n,127\nC. CAHILLANE\n,79\nA. CALAFAT,98\nJ. CALDER\u00d3N BUSTILLO,128\nT. A. CALLISTER,129\nE. CALLONI,31, 4\nG. CANEVA SANTORO\n,42\nK. C. CANNON\n,40\nH. CAO,34\nL. A. CAPISTRAN,130\nE. CAPOCASA\n,71\nE. CAPOTE\n,2\nG. CAPURRI\n,88, 87\nG. CARAPELLA,70, 112\nF. CARBOGNANI,59\nM. CARLASSARA,7, 8\nJ. B. CARLIN\n,121\nT. K. CARLSON,131\nM. F. CARNEY,101\nM. CARPINELLI\n,124, 132, 59\nG. CARRILLO,78\nJ. J. CARTER\n,7, 8\nG. CARULLO\n,133\nJ. CASANUEVA DIAZ,59\nC. CASENTINI\n,134, 19, 20\nS. Y. CASTRO-LUCAS,103\nS. CAUDILL,131, 36, 76\nM. CAVAGLI\u00c0\n,102\nR. CAVALIERI\n,59\nG. CELLA\n,88\nP. CERD\u00c1-DUR\u00c1N\n,135, 136\nE. CESARINI\n,20\nW. CHAIBI,48\nP. CHAKRABORTY\n,7, 8\nS. CHAKRABORTY,100\nS. CHALATHADKA SUBRAHMANYA\n,85\nJ. C. L. CHAN\n,137\nM. CHAN,111\nR.-J. CHANG,138\nS. CHAO\n,139, 140\nE. L. CHARLTON,120\nP. CHARLTON\n,141\nE. CHASSANDE-MOTTIN\n,71\nC. CHATTERJEE\n,142\nDEBARATI CHATTERJEE\n,14\nDEEP CHATTERJEE\n,34\nM. CHATURVEDI,100\nS. CHATY\n,71\nK. CHATZIIOANNOU\n,10\nC. CHECCHIA\n,99\nA. CHEN\n,15\nA. H.-Y. CHEN,143\nD. CHEN\n,144\nH. CHEN,139\nH. Y. CHEN\n,145\nS. CHEN,142\nY. CHEN,139\nYANBEI CHEN,146\nYITIAN CHEN\n,147\nH. P. CHENG,148\nP. CHESSA\n,89, 50\nH. T. CHEUNG\n,90\nS. Y. CHEUNG,149\nF. CHIADINI\n,150, 112\nG. CHIARINI,92\nR. CHIERICI,97\nA. CHINCARINI\n,56\nM. L. CHIOFALO\n,87, 88\nA. CHIUMMO\n,4, 59\nC. CHOU,143\nS. CHOUDHARY\n,29\nN. CHRISTENSEN\n,48\nS. S. Y. CHUA\n,33\nP. CHUGH,149\nG. CIANI\n,107, 108\nP. CIECIELAG\n,95\nM. CIE \u00b4SLAR\n,122\nM. CIFALDI\n,20\nR. CIOLFI\n,151, 92\nF. CLARA,2\nJ. A. CLARK\n,10, 60\nJ. CLARKE,32\nT. A. CLARKE\n,149\nP. CLEARWATER,152\nS. CLESSE,74\nS. M. CLYNE,153\nE. COCCIA,43, 118, 42\nE. CODAZZO\n,154\nP.-F. COHADON\n,119\nS. COLACE\n,57\nE. COLANGELI,77\nM. COLLEONI\n,98\nC. G. COLLETTE,155\nJ. COLLINS,65\nS. COLLOMS\n,28\nA. COLOMBO\n,156, 125\nC. M. COMPTON,2\nG. CONNOLLY,78\nL. CONTI\n,92\nT. R. CORBITT\n,11\nI. CORDERO-CARRI\u00d3N\n,157\nS. COREZZI,89, 50\nN. J. CORNISH\n,158\nA. CORSI\n,159\nS. CORTESE\n,59\nR. COTTINGHAM,65\nM. W. COUGHLIN\n,96\nA. COUINEAUX,66\nJ.-P. COULON,48\nJ.-F. COUPECHOUX,97\nP. COUVARES\n,10, 60\nD. M. COWARD,29\nR. COYNE\n,153\nK. CRAIG,58\nJ. D. E. CREIGHTON\n,9\nT. D. CREIGHTON,160\nP. CREMONESE\n,98\nA. W. CRISWELL\n,96\nS. CROOK,65\nR. CROUCH,2\nJ. CSIZMAZIA,2\nJ. R. CUDELL\n,161\nT. J. CULLEN\n,10\nA. CUMMING\n,28\nE. CUOCO\n,162, 163\nM. CUSINATO\n,135\nP. DABADIE,127\nL. V. DA CONCEI\u00c7\u00c3O,164\nT. DAL CANTON\n,38\nS. DALL\u2019OSSO\n,66\nS. DAL PRA\n,165\n\n39\nG. D\u00c1LYA\n,126\nB. D\u2019ANGELO\n,56\nS. DANILISHIN\n,35, 36\nS. D\u2019ANTONIO\n,20\nK. DANZMANN,8, 7, 8\nK. E. DARROCH,120\nL. P. DARTEZ,65\nA. DASGUPTA,93\nS. DATTA\n,166\nV. DATTILO\n,59\nA. DAUMAS,71\nN. DAVARI,167, 132\nI. DAVE,100\nA. DAVENPORT,103\nM. DAVIER,38\nT. F. DAVIES,29\nD. DAVIS\n,10\nL. DAVIS,29\nM. C. DAVIS\n,96\nP. DAVIS\n,168, 169\nM. DAX\n,1\nJ. DE BOLLE\n,94\nM. DEENADAYALAN,14\nJ. DEGALLAIX\n,170\nU. DEKA\n,171\nM. DE LAURENTIS\n,31, 4\nS. DEL\u00c9GLISE\n,119\nF. DE LILLO\n,21\nD. DELL\u2019AQUILA\n,167, 132\nF. DELLA VALLE\n,99\nW. DEL POZZO\n,87, 88\nF. DE MARCO\n,67, 66\nG. DEMASI,172, 64\nF. DE MATTEIS\n,19, 20\nV. D\u2019EMILIO\n,10\nN. DEMOS,34\nT. DENT\n,128\nA. DEPASSE\n,13\nN. DEPERGOLA,55\nR. DE PIETRI\n,173, 174\nR. DE ROSA\n,31, 4\nC. DE ROSSI\n,59\nM. DESAI,34\nR. DESALVO\n,175\nA. DESIMONE,176\nR. DE SIMONE,150\nA. DHANI\n,1\nR. DIAB,44\nM. C. D\u00cdAZ\n,160\nM. DI CESARE\n,31, 4\nG. DIDERON,177\nN. A. DIDIO,79\nT. DIETRICH\n,1\nL. DI FIORE,4\nC. DI FRONZO\n,29\nM. DI GIOVANNI\n,67, 66\nT. DI GIROLAMO\n,31, 4\nD. DIKSHA,36, 35\nA. DI MICHELE\n,89\nJ. DING\n,34, 71, 178\nS. DI PACE\n,67, 66\nI. DI PALMA\n,67, 66\nF. DI RENZO\n,97\nDIVYAJYOTI\n,179\nA. DMITRIEV\n,116\nZ. DOCTOR\n,80\nN. DOERKSEN,164\nE. DOHMEN,2\nD. DOMINGUEZ,180\nL. D\u2019ONOFRIO\n,66\nF. DONOVAN,34\nK. L. DOOLEY\n,32\nT. DOONEY,76\nS. DORAVARI\n,14\nO. DOROSH,181\nM. DRAGO\n,67, 66\nJ. C. DRIGGERS\n,2\nJ.-G. DUCOIN,182, 71\nL. DUNN\n,121\nU. DUPLETSA,43\nD. D\u2019URSO\n,167, 154\nH. DUVAL\n,183\nS. E. DWYER,2\nC. EASSA,2\nM. EBERSOLD\n,30\nT. ECKHARDT\n,85\nG. EDDOLLS\n,79\nB. EDELMAN\n,78\nT. B. EDO,10\nO. EDY\n,77\nA. EFFLER\n,65\nJ. EICHHOLZ\n,33\nH. EINSLE,48\nM. EISENMANN,24\nR. A. EISENSTEIN,34\nA. EJLLI\n,32\nM. EMMA\n,61\nK. ENDO,184\nR. ENFICIAUD\n,1\nA. J. ENGL,86\nL. ERRICO\n,31, 4\nR. ESPINOSA,160\nM. ESPOSITO,4, 31\nR. C. ESSICK\n,185\nH. ESTELL\u00c9S\n,1\nT. ETZEL,10\nM. EVANS\n,34\nT. EVSTAFYEVA,186\nB. E. EWING,6\nJ. M. EZQUIAGA\n,137\nF. FABRIZI\n,63, 64\nF. FAEDI,64, 63\nV. FAFONE\n,19, 20\nS. FAIRHURST\n,32\nA. M. FARAH\n,129\nB. FARR\n,78\nW. M. FARR\n,187, 188\nG. FAVARO\n,91\nM. FAVATA\n,189\nM. FAYS\n,161\nM. FAZIO,58\nJ. FEICHT,10\nM. M. FEJER,86\nR. FELICETTI\n,190\nE. FENYVESI\n,83, 191\nD. L. FERGUSON\n,145\nT. FERNANDES\n,192, 135\nD. FERNANDO,109\nS. FERRAIUOLO\n,193, 67, 66\nI. FERRANTE\n,87, 88\nT. A. FERREIRA,11\nF. FIDECARO\n,87, 88\nP. FIGURA\n,95\nA. FIORI\n,88, 87\nI. FIORI\n,59\nM. FISHBACH\n,185\nR. P. FISHER,120\nR. FITTIPALDI,194, 112\nV. FIUMARA\n,195, 112\nR. FLAMINIO,30\nS. M. FLEISCHER\n,196\nL. S. FLEMING,18\nE. FLODEN,96\nH. FONG,111\nJ. A. FONT\n,135, 136\nC. FOO,1\nB. FORNAL\n,197\nP. W. F. FORSYTH,33\nK. FRANCESCHETTI,173\nN. FRANCHINI,198\nS. FRASCA,67, 66\nF. FRASCONI\n,88\nA. FRATTALE MASCIOLI\n,67, 66\nZ. FREI\n,199\nA. FREISE\n,36, 104\nO. FREITAS\n,192, 135\nR. FREY\n,78\nW. FRISCHHERTZ,65\nP. FRITSCHEL,34\nV. V. FROLOV,65\nG. G. FRONZ\u00c9\n,27\nM. FUENTES-GARCIA\n,10\nS. FUJII,200\nT. FUJIMORI,201\nP. FULDA,44\nM. FYFFE,65\nB. GADRE\n,76\nJ. R. GAIR\n,1\nS. GALAUDAGE\n,202\nV. GALDI,175\nH. GALLAGHER,109\nB. GALLEGO,203\nR. GAMBA\n,6, 26\nA. GAMBOA\n,1\nD. GANAPATHY\n,34\nA. GANGULY\n,14\nB. GARAVENTA\n,56, 57\nJ. GARC\u00cdA-BELLIDO\n,204\nC. GARC\u00cdA N\u00da\u00d1EZ,18\nC. GARC\u00cdA-QUIR\u00d3S\n,205\nJ. W. GARDNER\n,33\nK. A. GARDNER,111\nJ. GARGIULO\n,59\nA. GARRON\n,98\nF. GARUFI\n,31, 4\nP. A. GARVER,86\nC. GASBARRA\n,19, 20\nB. GATELEY,2\nF. GAUTIER\n,206\nV. GAYATHRI\n,9\nT. GAYER,79\nG. GEMME\n,56\nA. GENNAI\n,88\nV. GENNARI\n,126\nJ. GEORGE,100\nR. GEORGE\n,145\nO. GERBERDING\n,85\nL. GERGELY\n,207\nARCHISMAN GHOSH\n,94\nSAYANTAN GHOSH,208\nSHAON GHOSH\n,189\nSHROBANA GHOSH,7, 8\nSUPROVO GHOSH\n,14\nTATHAGATA GHOSH\n,14\nJ. A. GIAIME\n,11, 65\nK. D. GIARDINA,65\nD. R. GIBSON,18\nD. T. GIBSON,186\nC. GIER\n,58\nS. GKAITATZIS\n,87, 88\nJ. GLANZER\n,10\nF. GLOTIN,38\nJ. GODFREY,78\nP. GODWIN\n,10\nA. S. GOETTEL\n,32\nE. GOETZ\n,111\nJ. GOLOMB,10\nS. GOMEZ LOPEZ\n,67, 66\nB. GONCHAROV\n,43\nY. GONG,209\nG. GONZ\u00c1LEZ\n,11\nP. GOODARZI,210\nS. GOODE,149\nA. W. GOODWIN-JONES\n,10, 29\nM. GOSSELIN,59\nR. GOUATY\n,30\nD. W. GOULD,33\nK. GOVORKOVA,34\nS. GOYAL\n,1\nB. GRACE\n,33\nA. GRADO\n,89, 50\nV. GRAHAM\n,28\nA. E. GRANADOS\n,96\nM. GRANATA\n,170\nV. GRANATA\n,70\nS. GRAS,34\nP. GRASSIA,10\nA. GRAY,96\nC. GRAY,2\nR. GRAY\n,28\nG. GRECO,50\nA. C. GREEN\n,36, 104\nS. M. GREEN,77\nS. R. GREEN\n,211\nA. M. GRETARSSON,69\nE. M. GRETARSSON,69\nD. GRIFFITH,10\nW. L. GRIFFITHS\n,32\nH. L. GRIGGS\n,60\nG. GRIGNANI,89, 50\nC. GRIMAUD\n,30\nH. GROTE\n,32\nS. GRUNEWALD\n,1\nD. GUERRA\n,135\nD. GUETTA\n,212\nG. M. GUIDI\n,63, 64\nA. R. GUIMARAES,11\nH. K. GULATI,93\nF. GULMINELLI\n,168, 169\nA. M. GUNNY,34\nH. GUO\n,213\nW. GUO\n,29\nY. GUO\n,36, 35\nANCHAL GUPTA\n,10\nANURADHA GUPTA\n,214\nI. GUPTA\n,6\nN. C. GUPTA,93\nP. GUPTA,36, 76\nS. K. GUPTA,44\nT. GUPTA\n,158\nV. GUPTA\n,96\nN. GUPTE,1\nJ. GURS,85\nN. GUTIERREZ,170\nF. GUZMAN\n,130\nD. HABA,180\nM. HABERLAND\n,1\nS. HAINO,215\nE. D. HALL\n,34\nR. HAMBURG\n,216\nE. Z. HAMILTON\n,98\nG. HAMMOND\n,28\nW.-B. HAN\n,217\nM. HANEY\n,36, 205\nJ. HANKS,2\nC. HANNA,6\nM. D. HANNAM,32\nO. A. HANNUKSELA\n,218\nA. G. HANSELMAN\n,129\nH. HANSEN,2\nJ. HANSON,65\nR. HARADA,40\nA. R. HARDISON,176\nS. HARIKUMAR,181\nK. HARIS,36, 76\nT. HARMARK\n,133\nJ. HARMS\n,43, 118\nG. M. HARRY\n,219\nI. W. HARRY\n,77\nJ. HART,101\nB. HASKELL,95\nC.-J. HASTER\n,220\nK. HAUGHIAN\n,28\nH. HAYAKAWA,49\nK. HAYAMA,221\nR. HAYES,32\nM. C. HEINTZE,65\nJ. HEINZE\n,116\nJ. HEINZEL,34\nH. HEITMANN\n,48\nA. HEFFERNAN\n,222\nF. HELLMAN\n,223\nA. F. HELMLING-CORNELL\n,78\nG. HEMMING\n,59\nO. HENDERSON-SAPIR\n,113\nM. HENDRY\n,28\nI. S. HENG,28\nM. H. HENNIG\n,28\nC. HENSHAW\n,60\nM. HEURS\n,7, 8\nA. L. HEWITT\n,186, 224\nJ. HEYNS,34\nS. HIGGINBOTHAM,32\nS. HILD,35, 36\nS. HILL,28\nY. HIMEMOTO\n,225\nN. HIRATA,24\nC. HIROSE,226\nS. HOCHHEIM,7, 8\nD. HOFMAN,170\nN. A. HOLLAND,36, 104\nD. E. HOLZ\n,129\nL. HONET,74\nC. HONG,86\nS. HOSHINO,226\nJ. HOUGH\n,28\nS. HOURIHANE,10\nN. T. HOWARD,142\nE. J. HOWELL\n,29\nC. G. HOY\n,77\nC. A. HRISHIKESH,19\nH.-F. HSIEH\n,139\nH.-Y. HSIEH,139\nC. HSIUNG,227\nW.-F. HSU\n,106\nQ. HU\n,28\nH. Y. HUANG\n,140\nY. HUANG\n,6\nY. T. HUANG,79\nA. D. HUDDART,228\nB. HUGHEY,69\nD. C. Y. HUI\n,229\nV. HUI\n,30\nS. HUSA\n,98\nR. HUXFORD,6\nL. IAMPIERI\n,67, 66\nG. A. IANDOLO\n,35\nM. IANNI,20, 19\nA. IERARDI,43\nA. IESS\n,230, 88\nH. IMAFUKU,40\nK. INAYOSHI\n,231\nY. INOUE,140\nG. IORIO\n,91\nP. IOSIF\n,190, 46\nM. H. IQBAL,33\nJ. IRWIN\n,28\nR. ISHIKAWA,232\nM. ISI\n,187, 188\nY. ITOH\n,233, 201\n\n40\nH. IWANAGA,233\nM. IWAYA,200\nB. R. IYER\n,22\nC. JACQUET,126\nP.-E. JACQUET\n,119\nS. J. JADHAV,234\nS. P. JADHAV\n,152\nT. JAIN,186\nA. L. JAMES\n,10\nP. A. JAMES,120\nR. JAMSHIDI,155\nK. JANI\n,142\nJ. JANQUART\n,13\nK. JANSSENS\n,21, 48\nN. N. JANTHALUR,234\nS. JARABA\n,204\nP. JARANOWSKI\n,235\nR. JAUME\n,98\nW. JAVED,32\nA. JENNINGS,2\nW. JIA,34\nJ. JIANG\n,148\nS. J. JIN\n,29\nC. JOHANSON,131\nG. R. JOHNS,120\nN. A. JOHNSON,44\nN. K. JOHNSON-MCDANIEL\n,214\nM. C. JOHNSTON\n,220\nR. JOHNSTON,28\nN. JOHNY,7, 8\nD. H. JONES\n,33\nD. I. JONES,236\nE. J. JONES,11\nR. JONES,28\nS. JOSE,179\nP. JOSHI\n,6\nS. K. JOSHI,14\nJ. JU,237\nL. JU\n,29\nK. JUNG\n,238\nJ. JUNKER\n,33\nV. JUSTE,74\nH. B. KABAGOZ\n,65\nT. KAJITA\n,239\nI. KAKU,233\nV. KALOGERA\n,80\nM. KALOMENOPOULOS\n,220\nM. KAMIIZUMI\n,49\nN. KANDA\n,201, 233\nS. KANDHASAMY\n,14\nG. KANG\n,240\nN. C. KANNACHEL,149\nJ. B. KANNER,10\nS. J. KAPADIA\n,14\nD. P. KAPASI\n,33\nS. KARAT,10\nR. KASHYAP\n,6\nM. KASPRZACK\n,10\nW. KASTAUN,7, 8\nT. KATO,200\nE. KATSAVOUNIDIS,34\nW. KATZMAN,65\nR. KAUSHIK\n,100\nK. KAWABE,2\nR. KAWAMOTO,233\nA. KAZEMI,96\nD. KEITEL\n,98\nJ. KENNINGTON\n,6\nR. KESHARWANI\n,14\nJ. S. KEY\n,241\nR. KHADELA,7, 8\nS. KHADKA,86\nF. Y. KHALILI\n,105\nF. KHAN\n,7, 8\nI. KHAN,242, 37\nT. KHANAM,159\nM. KHURSHEED,100\nN. M. KHUSID,187, 188\nW. KIENDREBEOGO\n,48, 243\nN. KIJBUNCHOO\n,113\nC. KIM,244\nJ. C. KIM,245\nK. KIM\n,246\nM. H. KIM\n,237\nS. KIM\n,229\nY.-M. KIM\n,246\nC. KIMBALL\n,80\nM. KINLEY-HANLON\n,28\nM. KINNEAR,32\nJ. S. KISSEL\n,2\nS. KLIMENKO,44\nA. M. KNEE\n,111\nN. KNUST\n,7, 8\nK. KOBAYASHI,200\nP. KOCH,7, 8\nS. M. KOEHLENBECK\n,86\nG. KOEKOEK,36, 35\nK. KOHRI\n,247, 248\nK. KOKEYAMA\n,32\nS. KOLEY\n,43\nP. KOLITSIDOU\n,116\nK. KOMORI\n,40, 39\nA. K. H. KONG\n,139\nA. KONTOS\n,249\nM. KOROBKO\n,85\nR. V. KOSSAK,7, 8\nX. KOU,96\nA. KOUSHIK\n,21\nN. KOUVATSOS\n,72\nM. KOVALAM,29\nD. B. KOZAK,10\nS. L. KRANZHOFF,35, 36\nV. KRINGEL,7, 8\nN. V. KRISHNENDU\n,116\nA. KR\u00d3LAK\n,250, 181\nK. KRUSKA,7, 8\nJ. KUBISZ\n,251\nG. KUEHN,7, 8\nS. KULKARNI\n,214\nA. KULUR RAMAMOHAN\n,33\nA. KUMAR,234\nPRAVEEN KUMAR\n,128\nPRAYUSH KUMAR\n,22\nRAHUL KUMAR,2\nRAKESH KUMAR,93\nJ. KUME\n,252, 253, 40\nK. KUNS\n,34\nN. KUNTIMADDI,32\nS. KUROYANAGI\n,204, 254\nS. KUWAHARA\n,40\nK. KWAK\n,238\nK. KWAN,33\nJ. KWOK,186\nG. LACAILLE,28\nP. LAGABBE\n,30, 107\nD. LAGHI\n,126\nS. LAI,143\nE. LALANDE,255\nM. LALLEMAN\n,21\nP. C. LALREMRUATI,256\nM. LANDRY,2\nB. B. LANE,34\nR. N. LANG\n,34\nJ. LANGE,145\nR. LANGGIN\n,220\nB. LANTZ\n,86\nA. LA RANA\n,66\nI. LA ROSA\n,98\nJ. LARSEN,196\nA. LARTAUX-VOLLARD\n,38\nP. D. LASKY\n,149\nJ. LAWRENCE\n,160, 257\nM. N. LAWRENCE,11\nM. LAXEN\n,65\nC. LAZARTE\n,135\nA. LAZZARINI\n,10\nC. LAZZARO,258, 154\nP. LEACI\n,67, 66\nL. LEALI,96\nY. K. LECOEUCHE\n,111\nH. M. LEE\n,245\nH. W. LEE\n,259\nJ. LEE,79\nK. LEE\n,237\nR.-K. LEE\n,139\nR. LEE,34\nSUNGHO LEE\n,260\nSUNJAE LEE,237\nY. LEE,140\nI. N. LEGRED,10\nJ. LEHMANN,7, 8\nL. LEHNER,177\nM. LE JEAN\n,170\nA. LEMA\u00ceTRE,261\nM. LENTI\n,64, 172\nM. LEONARDI\n,107, 108, 24\nM. LEQUIME,37\nN. LEROY\n,38\nM. LESOVSKY,10\nN. LETENDRE,30\nM. LETHUILLIER\n,97\nY. LEVIN,149\nK. LEYDE\n,71, 77\nA. K. Y. LI,10\nK. L. LI\n,138\nT. G. F. LI,106\nX. LI\n,146\nY. LI,80\nZ. LI,28\nA. LIHOS,120\nC-Y. LIN\n,262\nE. T. LIN\n,139\nL. C.-C. LIN\n,138\nY.-C. LIN\n,139\nC. LINDSAY,18\nS. D. LINKER,203\nT. B. LITTENBERG,263\nA. LIU\n,218\nG. C. LIU\n,227\nJIAN LIU\n,29\nF. LLAMAS VILLARREAL,160\nJ. LLOBERA-QUEROL\n,98\nR. K. L. LO\n,137\nJ.-P. LOCQUET,106\nM. R. LOIZOU,131\nL. T. LONDON,72, 34\nA. LONGO\n,63, 64\nD. LOPEZ\n,161, 205\nM. LOPEZ PORTILLA,76\nA. LORENZO-MEDINA\n,128\nV. LORIETTE,38\nM. LORMAND,65\nG. LOSURDO\n,230, 88\nE. LOTTI,131\nT. P. LOTT IV\n,60\nJ. D. LOUGH\n,7, 8\nH. A. LOUGHLIN,34\nC. O. LOUSTO\n,109\nN. LOW,121\nM. J. LOWRY,120\nN. LU\n,33\nL. LUCCHESI\n,88\nH. L\u00dcCK,8, 7, 8\nD. LUMACA\n,20\nA. P. LUNDGREN,77\nA. W. LUSSIER\n,255\nL.-T. MA\n,139\nS. MA,177\nR. MACAS\n,77\nA. MACEDO\n,54\nM. MACINNIS,34\nR. R. MACIY,7, 8\nD. M. MACLEOD\n,32\nI. A. O. MACMILLAN\n,10\nA. MACQUET\n,38\nD. MACRI,34\nK. MAEDA,184\nS. MAENAUT\n,106\nS. S. MAGARE,14\nR. M. MAGEE\n,10\nE. MAGGIO\n,1\nR. MAGGIORE,36, 104\nM. MAGNOZZI\n,56, 57\nM. MAHESH,85\nM. MAINI,153\nS. MAJHI,14\nE. MAJORANA,67, 66\nC. N. MAKAREM,10\nD. MALAKAR\n,102\nJ. A. MALAQUIAS-REIS,17\nU. MALI\n,185\nS. MALIAKAL,10\nA. MALIK,100\nL. MALLICK\n,164, 185\nA. MALZ\n,61\nN. MAN,48\nV. MANDIC\n,96\nV. MANGANO\n,66, 67\nB. MANNIX,78\nG. L. MANSELL\n,79\nG. MANSINGH,219\nM. MANSKE\n,9\nM. MANTOVANI\n,59\nM. MAPELLI\n,91, 92, 264\nF. MARCHESONI,51, 50, 265\nC. MARINELLI\n,99\nD. MAR\u00cdN PINA\n,41, 81, 266\nF. MARION\n,30\nS. M\u00c1RKA\n,267\nZ. M\u00c1RKA\n,267\nA. S. MARKOSYAN,86\nA. MARKOWITZ,10\nE. MAROS,10\nS. MARSAT\n,126\nF. MARTELLI\n,63, 64\nI. W. MARTIN\n,28\nR. M. MARTIN\n,189\nB. B. MARTINEZ,130\nM. MARTINEZ,42, 268\nV. MARTINEZ\n,127\nA. MARTINI,107, 108\nJ. C. MARTINS\n,17\nD. V. MARTYNOV,116\nE. J. MARX,34\nL. MASSARO,35, 36\nA. MASSEROT,30\nM. MASSO-REID\n,28\nM. MASTRODICASA,66, 67\nS. MASTROGIOVANNI\n,66\nT. MATCOVICH\n,50\nM. MATIUSHECHKINA\n,7, 8\nM. MATSUYAMA,233\nN. MAVALVALA\n,34\nN. MAXWELL,2\nG. MCCARROL,65\nR. MCCARTHY,2\nD. E. MCCLELLAND\n,33\nS. MCCORMICK,65\nL. MCCULLER\n,10\nS. MCEACHIN,120\nC. MCELHENNY,120\nG. I. MCGHEE\n,28\nJ. MCGINN,28\nK. B. M. MCGOWAN,142\nJ. MCIVER\n,111\nA. MCLEOD\n,29\nT. MCRAE,33\nD. MEACHER\n,9\nQ. MEIJER,76\nA. MELATOS,7, 269, 121\nM. MELCHING\n,7, 269, 121\nS. MELLAERTS\n,106\nC. S. MENONI\n,103\nF. MERA,2\nR. A. MERCER\n,9\nL. MERENI,170\nK. MERFELD,159\nE. L. MERILH,65\nJ. R. M\u00c9ROU\n,98\nJ. D. MERRITT,78\nM. MERZOUGUI,48\nC. MESSENGER\n,28\nC. MESSICK\n,9\nB. MESTICHELLI,43\nM. MEYER-CONDE\n,270\nF. MEYLAHN\n,7, 8\nA. MHASKE,14\nA. MIANI\n,107, 108\nH. MIAO,271\nI. MICHALOLIAKOS\n,44\nC. MICHEL\n,170\nY. MICHIMURA\n,10, 40\nH. MIDDLETON\n,116\nS. J. MILLER\n,10\nM. MILLHOUSE\n,60\nE. MILOTTI\n,190, 46\nV. MILOTTI\n,91\nY. MINENKOV,20\nN. MIO,272\nLL. M. MIR\n,42\nL. MIRASOLA\n,154, 258\nM. MIRAVET-TEN\u00c9S\n,135\nC.-A. MIRITESCU\n,42\nA. K. MISHRA,22\nA. MISHRA,22\nC. MISHRA\n,179\nT. MISHRA\n,44\nA. L. MITCHELL,36, 104\nJ. G. MITCHELL,69\nS. MITRA\n,14\nV. P. MITROFANOV\n,105\nR. MITTLEMAN,34\nO. MIYAKAWA\n,49\nS. MIYAMOTO,200\nS. MIYOKI\n,49\nG. MO\n,34\nL. MOBILIA,63, 64\nS. R. P. MOHAPATRA,10\nS. R. MOHITE\n,6\nM. MOLINA-RUIZ\n,223\nC. MONDAL\n,168\nM. MONDIN,203\nM. MONTANI,63, 64\nC. J. MOORE,186\nD. MORARU,2\nA. MORE\n,14\nS. MORE\n,14\nE. A. MORENO\n,34\nG. MORENO,2\nS. MORISAKI\n,40, 200\nY. MORIWAKI\n,184\n\n41\nG. MORRAS\n,204\nA. MOSCATELLO\n,91\nM. MOULD\n,34\nP. MOURIER\n,222, 273\nB. MOURS\n,68\nC. M. MOW-LOWRY\n,36, 104\nF. MUCIACCIA\n,67, 66\nD. MUKHERJEE\n,263\nSAMANWAYA MUKHERJEE,14\nSOMA MUKHERJEE,160\nSUBROTO MUKHERJEE,93\nSUVODIP MUKHERJEE\n,12, 177, 274\nN. MUKUND\n,34\nA. MULLAVEY,65\nH. MULLOCK,111\nJ. MUNCH,113\nJ. MUNDI,219\nC. L. MUNGIOLI,29\nY. MURAKAMI,200\nM. MURAKOSHI,232\nP. G. MURRAY\n,28\nS. MUUSSE\n,33\nD. NABARI\n,107, 108\nS. L. NADJI,7, 8\nA. NAGAR,27, 275\nN. NAGARAJAN\n,28\nK. NAKAGAKI,49\nK. NAKAMURA\n,24\nH. NAKANO\n,276\nM. NAKANO,10\nD. NANADOUMGAR-LACROZE,42\nD. NANDI,11\nV. NAPOLANO,59\nP. NARAYAN\n,214\nI. NARDECCHIA\n,20\nT. NARIKAWA,200\nH. NAROLA,76\nL. NATICCHIONI\n,66\nR. K. NAYAK\n,256\nA. NELA,28\nA. NELSON\n,130\nT. J. N. NELSON,65\nM. NERY,7, 8\nA. NEUNZERT\n,2\nS. NG,54\nL. NGUYEN QUYNH\n,277, 278\nS. A. NICHOLS,11\nA. B. NIELSEN\n,279\nG. NIERADKA,95\nY. NISHINO,24, 280\nA. NISHIZAWA\n,281\nS. NISSANKE,274, 36\nE. NITOGLIA\n,97\nW. NIU\n,6\nF. NOCERA,59\nM. NORMAN,32\nC. NORTH,32\nJ. NOVAK\n,114, 282, 283\nJ. F. NU\u00d1O SILES\n,204\nL. K. NUTTALL\n,77\nK. OBAYASHI,232\nJ. OBERLING\n,2\nJ. O\u2019DELL,228\nM. OERTEL\n,282, 114, 284, 283\nA. OFFERMANS,106\nG. OGANESYAN,43, 118\nJ. J. OH,285\nK. OH\n,229\nT. O\u2019HANLON,65\nM. OHASHI\n,49\nM. OHKAWA\n,226\nF. OHME\n,7, 8\nR. OLIVERI\n,114, 284, 283\nR. OMER,96\nB. O\u2019NEAL,120\nK. OOHARA\n,286, 287\nB. O\u2019REILLY\n,65\nR. ORAM,10\nN. D. ORMSBY,120\nM. ORSELLI\n,50, 89\nR. O\u2019SHAUGHNESSY\n,109\nS. O\u2019SHEA,28\nY. OSHIMA\n,39\nS. OSHINO\n,49\nC. OSTHELDER,10\nI. OTA\n,11\nD. J. OTTAWAY\n,113\nA. OUZRIAT,97\nH. OVERMIER,65\nB. J. OWEN\n,288\nA. E. PACE\n,6\nR. PAGANO\n,11\nM. A. PAGE\n,24\nA. PAI\n,208\nL. PAIELLA,43\nA. PAL,289\nS. PAL\n,256\nM. A. PALAIA\n,88, 87\nM. P\u00c1LFI,199\nP. P. PALMA,67, 19, 20\nC. PALOMBA\n,66\nP. PALUD\n,71\nJ. PAN,29\nK. C. PAN\n,139\nR. PANAI\n,154, 91\nP. K. PANDA,234\nSHIKSHA PANDEY,6\nSWADHA PANDEY,34\nP. T. H. PANG,36, 76\nF. PANNARALE\n,67, 66\nK. A. PANNONE,54\nB. C. PANT,100\nF. H. PANTHER,29\nF. PAOLETTI\n,88\nA. PAOLONE,66, 290\nA. PAPADOPOULOS,28\nE. E. PAPALEXAKIS,210\nL. PAPALINI\n,88, 87\nG. PAPIGKIOTIS\n,291\nA. PAQUIS,38\nA. PARISI\n,89, 50\nB.-J. PARK,260\nJ. PARK\n,292\nW. PARKER\n,65\nG. PASCALE,7, 8\nD. PASCUCCI\n,94\nA. PASQUALETTI,59\nR. PASSAQUIETI\n,87, 88\nL. PASSENGER,149\nD. PASSUELLO,88\nO. PATANE\n,2\nD. PATHAK,14\nL. PATHAK\n,14\nA. PATRA,32\nB. PATRICELLI\n,87, 88\nA. S. PATRON,11\nB. G. PATTERSON,32\nK. PAUL\n,179\nS. PAUL\n,78\nE. PAYNE\n,10\nT. PEARCE,32\nM. PEDRAZA,10\nA. PELE\n,10\nF. E. PE\u00d1A ARELLANO\n,293\nS. PENN\n,294\nM. D. PENULIAR,54\nA. PEREGO\n,107, 108\nZ. PEREIRA,131\nJ. J. PEREZ,44\nC. P\u00c9RIGOIS\n,151, 92, 91\nG. PERNA\n,91\nA. PERRECA\n,107, 108\nJ. PERRET,71\nS. PERRI\u00c8S\n,97\nJ. W. PERRY,36, 104\nD. PESIOS,291\nS. PETRACCA,175\nC. PETRILLO,89\nH. P. PFEIFFER\n,1\nH. PHAM,65\nK. A. PHAM\n,96\nK. S. PHUKON\n,116\nH. PHURAILATPAM,218\nM. PIARULLI,126\nL. PICCARI\n,67, 66\nO. J. PICCINNI\n,33\nM. PICHOT\n,48\nM. PIENDIBENE\n,87, 88\nF. PIERGIOVANNI\n,63, 64\nL. PIERINI\n,66\nG. PIERRA\n,97\nV. PIERRO\n,295, 112\nM. PIETRZAK,95\nM. PILLAS\n,161\nF. PILO\n,88\nL. PINARD,170\nI. M. PINTO\n,295, 112, 296, 31\nM. PINTO,59\nB. J. PIOTRZKOWSKI\n,9\nM. PIRELLO,2\nM. D. PITKIN\n,186, 224\nA. PLACIDI\n,50\nE. PLACIDI\n,67, 66\nM. L. PLANAS\n,98\nW. PLASTINO\n,297, 20\nC. PLUNKETT\n,34\nR. POGGIANI\n,87, 88\nE. POLINI\n,34\nL. POMPILI\n,1\nJ. POON,218\nE. PORCELLI,36\nE. K. PORTER,71\nC. POSNANSKY\n,6\nR. POULTON\n,59\nJ. POWELL\n,152\nM. PRACCHIA\n,161\nB. K. PRADHAN\n,14\nT. PRADIER\n,68\nA. K. PRAJAPATI,93\nK. PRASAI,86\nR. PRASANNA,234\nP. PRASIA,14\nG. PRATTEN\n,116\nG. PRINCIPE\n,190, 46\nM. PRINCIPE,175\nG. A. PRODI\n,107, 108\nL. PROKHOROV\n,116\nP. PROSPERI,88\nP. PROSPOSITO,19, 20\nA. C. PROVIDENCE,69\nA. PUECHER,36, 76\nJ. PULLIN\n,11\nM. PUNTURO\n,50\nP. PUPPO,66\nM. P\u00dcRRER\n,153\nH. QI\n,15\nJ. QIN\n,33\nG. QU\u00c9M\u00c9NER\n,169, 114\nV. QUETSCHKE,160\nP. J. QUINONEZ,69\nF. J. RAAB\n,2\nI. RAINHO,135\nS. RAJA,100\nC. RAJAN,100\nB. RAJBHANDARI\n,109\nK. E. RAMIREZ\n,65\nF. A. RAMIS VIDAL\n,98\nA. RAMOS-BUADES,36, 1\nD. RANA,14\nS. RANJAN\n,60\nK. RANSOM,65\nP. RAPAGNANI\n,67, 66\nB. RATTO,69\nA. RAY\n,9\nV. RAYMOND\n,32\nM. RAZZANO\n,87, 88\nJ. READ,54\nM. RECAMAN PAYO,106\nT. REGIMBAU,30\nL. REI\n,56\nS. REID,58\nD. H. REITZE\n,10\nP. RELTON\n,32\nA. I. RENZINI,10\nA. RENZINI\n,124\nB. REVENU\n,298, 38\nR. REYES,203\nA. S. REZAEI\n,66, 67\nF. RICCI,67, 66\nM. RICCI\n,66, 67\nA. RICCIARDONE\n,87, 88\nJ. W. RICHARDSON\n,210\nM. RICHARDSON,113\nA. RIJAL,69\nK. RILES\n,90\nH. K. RILEY,32\nS. RINALDI\n,264, 91\nJ. RITTMEYER,85\nC. ROBERTSON,228\nF. ROBINET,38\nM. ROBINSON,2\nA. ROCCHI\n,20\nL. ROLLAND\n,30\nJ. G. ROLLINS\n,10\nA. E. ROMANO\n,299\nR. ROMANO\n,3, 4\nA. ROMERO\n,30\nI. M. ROMERO-SHAW,186\nJ. H. ROMIE,65\nS. RONCHINI\n,6, 43, 118\nT. J. ROOCKE\n,113\nL. ROSA,4, 31\nT. J. ROSAUER,210\nC. A. ROSE,60\nD. ROSI \u00b4NSKA\n,122\nM. P. ROSS\n,52\nM. ROSSELLO-SASTRE\n,98\nS. ROWAN\n,28\nS. ROY\n,13\nS. K. ROY\n,187, 188\nD. ROZZA\n,124, 125\nP. RUGGI,59\nN. RUHAMA,238\nE. RUIZ MORALES\n,300, 204\nK. RUIZ-ROCHA,142\nS. SACHDEV\n,60\nT. SADECKI,2\nJ. SADIQ\n,128\nP. SAFFARIEH\n,36, 104\nS. SAFI-HARB,164\nM. R. SAH\n,12\nS. SAHA\n,139\nT. SAINRAT\n,68\nS. SAJITH MENON\n,212, 67, 66\nK. SAKAI,301\nM. SAKELLARIADOU\n,72\nS. SAKON\n,6\nO. S. SALAFIA\n,156, 125, 124\nF. SALCES-CARCOBA\n,10\nL. SALCONI,59\nM. SALEEM\n,96\nF. SALEMI\n,67, 66\nM. SALL\u00c9\n,36\nS. U. SALUNKHE,14\nS. SALVADOR\n,169, 168\nA. SAMAJDAR\n,76, 36\nA. SANCHEZ,2\nE. J. SANCHEZ,10\nJ. H. SANCHEZ\n,80\nL. E. SANCHEZ,10\nN. SANCHIS-GUAL\n,135\nJ. R. SANDERS,176\nE. M. S\u00c4NGER\n,1\nF. SANTOLIQUIDO,43\nF. SARANDREA,27\nT. R. SARAVANAN,14\nN. SARIN,149\nP. SARKAR,7, 8\nS. SASAOKA\n,180\nA. SASLI\n,291\nP. SASSI\n,50, 89\nB. SASSOLAS\n,170\nB. S. SATHYAPRAKASH\n,6, 32\nR. SATO,226\nY. SATO,184\nO. SAUTER\n,44\nR. L. SAVAGE\n,2\nT. SAWADA\n,49\nH. L. SAWANT,14\nS. SAYAH,30\nV. SCACCO,19, 20\nD. SCHAETZL,10\nM. SCHEEL,146\nA. SCHIEBELBEIN,185\nM. G. SCHIWORSKI\n,79\nP. SCHMIDT\n,116\nS. SCHMIDT\n,76\nR. SCHNABEL\n,85\nM. SCHNEEWIND,7, 8\nR. M. S. SCHOFIELD,78\nK. SCHOUTEDEN,106\nB. W. SCHULTE,7, 8\nB. F. SCHUTZ,32, 7, 8\nE. SCHWARTZ\n,86\nM. SCIALPI,302\nJ. SCOTT\n,28\nS. M. SCOTT\n,33\nR. M. SEDAS\n,65\nT. C. SEETHARAMU,28\nM. SEGLAR-ARROYO\n,42\nY. SEKIGUCHI\n,303\nD. SELLERS,65\nA. S. SENGUPTA\n,304\nD. SENTENAC,59\nE. G. SEO\n,28\nJ. W. SEO\n,106\nV. SEQUINO,31, 4\nM. SERRA\n,66\nG. SERVIGNAT\n,71, 284\nA. SEVRIN,183\nT. SHAFFER,2\nU. S. SHAH\n,60\nM. S. SHAHRIAR\n,80\nM. A. SHAIKH\n,245\nL. SHAO\n,231\nA. SHARMA\n,305\nA. K. SHARMA,22\nP. SHARMA,100\n\n42\nS. SHARMA CHAUDHARY,102\nM. R. SHAW,32\nP. SHAWHAN\n,123\nN. S. SHCHEBLANOV\n,306, 261\nY. SHIKANO\n,307, 308\nM. SHIKAUCHI,40\nK. SHIMODE\n,49\nH. SHINKAI\n,309\nJ. SHIOTA,232\nS. SHIRKE,14\nD. H. SHOEMAKER\n,34\nD. M. SHOEMAKER\n,145\nR. W. SHORT,2\nS. SHYAMSUNDAR,100\nA. SIDER,155\nH. SIEGEL\n,187, 188\nD. SIGG\n,2\nL. SILENZI\n,50, 51\nM. SIMMONDS,113\nL. P. SINGER\n,310\nA. SINGH,214\nD. SINGH\n,6\nM. K. SINGH\n,22\nN. SINGH\n,98\nS. SINGH,180, 62\nA. SINGHA\n,35, 36\nA. M. SINTES\n,98\nV. SIPALA,167, 154\nV. SKLIRIS\n,32\nB. J. J. SLAGMOLEN\n,33\nD. A. SLATER,196\nT. J. SLAVEN-BLAIR,29\nJ. SMETANA,116\nJ. R. SMITH\n,54\nL. SMITH\n,28, 190\nR. J. E. SMITH\n,149\nW. J. SMITH\n,142\nK. SOMIYA\n,180\nI. SONG\n,139\nK. SONI\n,14\nS. SONI\n,34\nV. SORDINI\n,97\nF. SORRENTINO,56\nH. SOTANI\n,311\nA. SOUTHGATE,32\nF. SPADA\n,88\nV. SPAGNUOLO\n,35, 36\nA. P. SPENCER\n,28\nM. SPERA\n,46, 312\nP. SPINICELLI\n,59\nC. A. SPRAGUE,277\nA. K. SRIVASTAVA,93\nF. STACHURSKI\n,28\nD. A. STEER\n,313\nN. STEINLE\n,164\nJ. STEINLECHNER,35, 36\nS. STEINLECHNER\n,35, 36\nN. STERGIOULAS\n,291\nP. STEVENS,38\nS. P. STEVENSON,152\nF. STOLZI\n,99\nM. STPIERRE,153\nG. STRATTA\n,314, 134, 66, 315\nM. D. STRONG,11\nA. STRUNK,2\nR. STURANI,316\nA. L. STUVER,55, \u2217\nM. SUCHENEK,95\nS. SUDHAGAR\n,95\nN. SUELTMANN,85\nL. SULEIMAN\n,54\nJ.M. SULLIVAN\n,317\nK. D. SULLIVAN,11\nJ. SUN,240\nL. SUN\n,33\nS. SUNIL,93\nJ. SURESH\n,48\nB. J. SUTTON,72\nP. J. SUTTON\n,32\nT. SUZUKI\n,226\nY. SUZUKI,232\nB. L. SWINKELS\n,36\nA. SYX,68\nM. J. SZCZEPA \u00b4NCZYK\n,318, 44\nP. SZEWCZYK\n,122\nM. TACCA\n,36\nH. TAGOSHI\n,200\nS. C. TAIT\n,10\nH. TAKAHASHI\n,270\nR. TAKAHASHI\n,24\nA. TAKAMORI\n,53\nT. TAKASE,49\nK. TAKATANI,233\nH. TAKEDA\n,319\nK. TAKESHITA,180\nC. TALBOT,129\nM. TAMAKI,200\nN. TAMANINI\n,126\nD. TANABE,140\nK. TANAKA,49\nS. J. TANAKA\n,232\nT. TANAKA\n,319\nD. TANG,29\nS. TANIOKA\n,79\nD. B. TANNER,44\nW. TANNER,7, 8\nL. TAO\n,210\nR. D. TAPIA,6\nE. N. TAPIA SAN MART\u00cdN\n,36\nR. TARAFDER,10\nC. TARANTO,19, 20\nA. TARUYA\n,320\nJ. D. TASSON\n,321\nJ. G. TAU\n,109\nR. TENORIO\n,98\nH. THEMANN,203\nA. THEODOROPOULOS\n,135\nM. P. THIRUGNANASAMBANDAM,14\nL. M. THOMAS\n,10\nM. THOMAS,65\nP. THOMAS,2\nJ. E. THOMPSON\n,236\nS. R. THONDAPU,100\nK. A. THORNE,65\nE. THRANE,149\nS. TIBREWAL\n,145\nJ. TISSINO\n,43\nA. TIWARI,14\nP. TIWARI,43\nS. TIWARI\n,205\nV. TIWARI\n,116\nM. R. TODD,79\nA. M. TOIVONEN\n,96\nK. TOLAND\n,28\nA. E. TOLLEY\n,77\nT. TOMARU\n,24\nK. TOMITA,233\nV. TOMMASINI,10\nT. TOMURA\n,49\nH. TONG\n,149\nC. TONG-YU,140\nA. TORIYAMA,232\nN. TOROPOV\n,116\nA. TORRES-FORN\u00c9\n,135, 136\nC. I. TORRIE,10\nM. TOSCANI\n,126\nI. TOSTA E MELO\n,322\nE. TOURNEFIER\n,30\nM. TRAD NERY,48\nA. TRAPANANTI\n,51, 50\nF. TRAVASSO\n,51, 50\nG. TRAYLOR,65\nC. TREJO,10\nM. TREVOR,123\nM. C. TRINGALI\n,59\nA. TRIPATHEE\n,90\nG. TROIAN\n,190, 46\nA. TROVATO\n,190, 46\nL. TROZZO,4\nR. J. TRUDEAU,10\nT. T. L. TSANG\n,32\nS. TSUCHIDA\n,323\nL. TSUKADA\n,220\nK. TURBANG\n,183, 21\nM. TURCONI\n,48\nC. TURSKI,94\nH. UBACH\n,41, 81\nN. UCHIKATA\n,200\nT. UCHIYAMA\n,49\nR. P. UDALL\n,10\nT. UEHARA\n,324\nM. UEMATSU,233\nS. UENO,232\nV. UNDHEIM\n,279\nT. USHIBA\n,49\nM. VACATELLO\n,88, 87\nH. VAHLBRUCH\n,7, 8\nG. VAJENTE\n,10\nA. VAJPEYI,149\nG. VALDES\n,325\nJ. VALENCIA\n,98\nA. F. VALENTINI,11\nM. VALENTINI\n,104, 36\nS. A. VALLEJO-PE\u00d1A\n,299\nS. VALLERO,27\nV. VALSAN\n,9\nN. VAN BAKEL,36\nM. VAN BEUZEKOM\n,36\nM. VAN DAEL\n,36, 326\nJ. F. J. VAN DEN BRAND\n,35, 104, 36\nC. VAN DEN BROECK,76, 36\nD. C. VANDER-HYDE,79\nM. VAN DER SLUYS\n,36, 76\nA. VAN DE WALLE,38\nJ. VAN DONGEN\n,36, 104\nK. VANDRA,55\nH. VAN HAEVERMAET\n,21\nJ. V. VAN HEIJNINGEN\n,36, 104\nP. VAN HOVE\n,68\nJ. VANIER,255\nM. VANKEUREN,101\nJ. VANOSKY,2\nM. H. P. M. VAN PUTTEN\n,16\nZ. VAN RANST\n,35, 36\nN. VAN REMORTEL\n,21\nM. VARDARO,35, 36\nA. F. VARGAS,121\nJ. J. VARGHESE,69\nV. VARMA\n,131\nA. N. VAZQUEZ,86\nA. VECCHIO\n,116\nG. VEDOVATO,92\nJ. VEITCH\n,28\nP. J. VEITCH\n,113\nS. VENIKOUDIS,13\nJ. VENNEBERG\n,7, 8\nP. VERDIER\n,97\nM. VEREECKEN,13\nD. VERKINDT\n,30\nB. VERMA,131\nP. VERMA,181\nY. VERMA\n,100\nS. M. VERMEULEN\n,10\nF. VETRANO,63\nA. VEUTRO\n,66, 67\nA. M. VIBHUTE\n,2\nA. VICER\u00c9\n,63, 64\nS. VIDYANT,79\nA. D. VIETS\n,84\nA. VIJAYKUMAR\n,185\nA. VILKHA,109\nV. VILLA-ORTEGA\n,128\nE. T. VINCENT\n,60\nJ.-Y. VINET,48\nS. VIRET,97\nA. VIRTUOSO\n,46\nS. VITALE\n,34\nA. VIVES,78\nH. VOCCA\n,89, 50\nD. VOIGT\n,85\nE. R. G. VON REIS,2\nJ. S. A. VON WRANGEL,7, 8\nL. VUJEVA,137\nS. P. VYATCHANIN\n,105\nJ. WACK,10\nL. E. WADE,101\nM. WADE\n,101\nK. J. WAGNER\n,109\nA. WAJID,56, 57\nM. WALKER,120\nG. S. WALLACE,58\nL. WALLACE,10\nE. J. WANG,86\nH. WANG\n,39\nJ. Z. WANG,90\nW. H. WANG,160\nY. F. WANG\n,1\nZ. WANG,140\nG. WARATKAR\n,208\nJ. WARNER,2\nM. WAS\n,30\nT. WASHIMI\n,24\nN. Y. WASHINGTON,10\nD. WATARAI,40\nK. E. WAYT,101\nB. R. WEAVER,32\nB. WEAVER,2\nC. R. WEAVING,77\nS. A. WEBSTER,28\nN. L. WEICKHARDT\n,85\nM. WEINERT,7, 8\nA. J. WEINSTEIN\n,10\nR. WEISS,34\nF. WELLMANN,7, 8\nL. WEN,29\nP. WESSELS\n,7, 8\nK. WETTE\n,33\nJ. T. WHELAN\n,109\nB. F. WHITING\n,44\nC. WHITTLE\n,10\nE. G. WICKENS,77\nJ. B. WILDBERGER,1\nD. WILKEN\n,7, 8, 8\nD. J. WILLADSEN,84\nK. WILLETTS,32\nD. WILLIAMS\n,28\nM. J. WILLIAMS\n,77\nN. S. WILLIAMS,116\nJ. L. WILLIS\n,10\nB. WILLKE\n,8, 7, 8\nM. WILS\n,106\nC. W. WINBORN,102\nJ. WINTERFLOOD,29\nC. C. WIPF,10\nG. WOAN\n,28\nJ. WOEHLER,35, 36\nN. E. WOLFE,34\nH. T. WONG\n,140\nI. C. F. WONG\n,218, 106\nJ. L. WRIGHT,33\nM. WRIGHT\n,28\nC. WU\n,139\nD. S. WU\n,7, 8\nH. WU\n,139\nE. WUCHNER,54\nD. M. WYSOCKI\n,9\nV. A. XU\n,34\nY. XU\n,205\nN. YADAV\n,95\nH. YAMAMOTO\n,10\nK. YAMAMOTO\n,184\nT. S. YAMAMOTO\n,40\nT. YAMAMOTO\n,49\nS. YAMAMURA,200\nR. YAMAZAKI\n,232\nT. YAN,116\nF. W. YANG\n,327\nF. YANG,267\nK. Z. YANG\n,96\nY. YANG\n,143\nZ. YARBROUGH\n,11\nH. YASUI,49\nS.-W. YEH,139\nA. B. YELIKAR\n,109\nX. YIN,34\nJ. YOKOYAMA\n,328, 40, 39\nT. YOKOZAWA,49\nJ. YOO\n,147\nH. YU\n,146\nS. YUAN,29\nH. YUZURIHARA\n,49\nA. ZADRO \u02d9ZNY,181\nM. ZANOLIN,69\nM. ZEESHAN\n,109\nT. ZELENOVA,59\nJ.-P. ZENDRI,92\nM. ZEOLI\n,13\nM. ZERRAD,37\nM. ZEVIN\n,80\nA. C. ZHANG,267\nL. ZHANG,10\nR. ZHANG\n,148\nT. ZHANG,116\nY. ZHANG\n,33\nC. ZHAO\n,29\nYUE ZHAO,327\nYUHANG ZHAO\n,71\nY. ZHENG\n,102\nH. ZHONG\n,96\nR. ZHOU,223\nX.-J. ZHU\n,329\nZ.-H. ZHU\n,329, 209\nA. B. ZIMMERMAN\n,145\nM. E. ZUCKER34, 10 AND J. ZWEIZIG\n10\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n\n43\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6The Pennsylvania State University, University Park, PA 16802, USA\n7Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n8Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n9University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n10LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n11Louisiana State University, Baton Rouge, LA 70803, USA\n12Tata Institute of Fundamental Research, Mumbai 400005, India\n13Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n14Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n15Queen Mary University of London, London E1 4NS, United Kingdom\n16Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n17Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n18SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n19Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n20INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n21Universiteit Antwerpen, 2000 Antwerpen, Belgium\n22International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n23University College Dublin, Belfield, Dublin 4, Ireland\n24Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n25Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n27INFN Sezione di Torino, I-10125 Torino, Italy\n28SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n29OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n30Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n31Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n32Cardiff University, Cardiff CF24 3AA, United Kingdom\n33OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n34LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n35Maastricht University, 6200 MD Maastricht, Netherlands\n36Nikhef, 1098 XG Amsterdam, Netherlands\n37Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n38Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n39Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n40University of Tokyo, Tokyo, 113-0033, Japan.\n41Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n42Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n43Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n44University of Florida, Gainesville, FL 32611, USA\n45Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n46INFN, Sezione di Trieste, I-34127 Trieste, Italy\n47Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, Monterrey 64849, Mexico\n48Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n49Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n50INFN, Sezione di Perugia, I-06123 Perugia, Italy\n51Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n52University of Washington, Seattle, WA 98195, USA\n53Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n54California State University Fullerton, Fullerton, CA 92831, USA\n55Villanova University, Villanova, PA 19085, USA\n\n44\n56INFN, Sezione di Genova, I-16146 Genova, Italy\n57Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n58SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n59European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n60Georgia Institute of Technology, Atlanta, GA 30332, USA\n61Royal Holloway, University of London, London TW20 0EX, United Kingdom\n62Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n63Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n64INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n65LIGO Livingston Observatory, Livingston, LA 70754, USA\n66INFN, Sezione di Roma, I-00185 Roma, Italy\n67Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n68Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n69Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n70Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n71Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n72King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n73Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n74Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n75International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n76Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n77University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Northwestern University, Evanston, IL 60208, USA\n81Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n82Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n83HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n84Concordia University Wisconsin, Mequon, WI 53097, USA\n85Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n86Stanford University, Stanford, CA 94305, USA\n87Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n88INFN, Sezione di Pisa, I-56127 Pisa, Italy\n89Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96University of Minnesota, Minneapolis, MN 55455, USA\n97Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Universit\u00e0 di Siena, I-53100 Siena, Italy\n100RRCAT, Indore, Madhya Pradesh 452013, India\n101Kenyon College, Gambier, OH 43022, USA\n102Missouri University of Science and Technology, Rolla, MO 65409, USA\n103Colorado State University, Fort Collins, CO 80523, USA\n104Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n105Lomonosov Moscow State University, Moscow 119991, Russia\n106Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n107Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n108INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n109Rochester Institute of Technology, Rochester, NY 14623, USA\n110Bar-Ilan University, Ramat Gan, 5290002, Israel\n111University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n112INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n\n45\n113OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n114Centre national de la recherche scientifique, 75016 Paris, France\n115Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n116University of Birmingham, Birmingham B15 2TT, United Kingdom\n117Washington State University, Pullman, WA 99164, USA\n118INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n119Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n120Christopher Newport University, Newport News, VA 23606, USA\n121OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n122Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n123University of Maryland, College Park, MD 20742, USA\n124Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n125INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n126L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00e9 de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n127Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n128IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n132INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n135Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n136Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n137Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n138Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n139National Tsing Hua University, Hsinchu City 30013, Taiwan\n140National Central University, Taoyuan City 320317, Taiwan\n141OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n142Vanderbilt University, Nashville, TN 37235, USA\n143Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n144Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n145University of Texas, Austin, TX 78712, USA\n146CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n147Cornell University, Ithaca, NY 14850, USA\n148Northeastern University, Boston, MA 02115, USA\n149OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n150Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n151INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n152OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n153University of Rhode Island, Kingston, RI 02881, USA\n154INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n155Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n156INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n157Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n158Montana State University, Bozeman, MT 59717, USA\n159Johns Hopkins University, Baltimore, MD 21218, USA\n160The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n161Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n162DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n163Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2, Bologna, Italy\n164University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n165INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n166Chennai Mathematical Institute, Chennai 603103, India\n167Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n168Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n169Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n\n46\n170Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n171International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India\n172Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n173Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n174INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n175University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n176Marquette University, Milwaukee, WI 53233, USA\n177Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n178Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n179Indian Institute of Technology Madras, Chennai 600036, India\n180Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n181National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n182Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00e9, CNRS, UMR 7095, 75014 Paris, France\n183Vrije Universiteit Brussel, 1050 Brussel, Belgium\n184Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n185Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n186University of Cambridge, Cambridge CB2 1TN, United Kingdom\n187Stony Brook University, Stony Brook, NY 11794, USA\n188Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n189Montclair State University, Montclair, NJ 07043, USA\n190Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n191HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n192Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n193Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n194CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n195Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n196Western Washington University, Bellingham, WA 98225, USA\n197Barry University, Miami Shores, FL 33168, USA\n198Centro de Astrof\u00edsica e Gravita\u00e7\u00e3o, Departamento de F\u00edsica, Instituto Superior T\u00e9cnico - IST, Universidade de Lisboa - UL, Av. Rovisco Pais 1, 1049-001\nLisboa, Portugal\n199E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n200Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n201Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n202Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n203California State University, Los Angeles, Los Angeles, CA 90032, USA\n204Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n205University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n206Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n207University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n208Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n209School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n210University of California, Riverside, Riverside, CA 92521, USA\n211University of Nottingham NG7 2RD, UK\n212Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n213University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n214The University of Mississippi, University, MS 38677, USA\n215Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n216Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA\n217Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n218The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n219American University, Washington, DC 20016, USA\n220University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n221Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n222IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n223University of California, Berkeley, CA 94720, USA\n224University of Lancaster, Lancaster LA1 4YW, United Kingdom\n\n47\n225College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n226Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n227Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n228Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n229Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n230Scuola Normale Superiore, I-56126 Pisa, Italy\n231Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n232Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n233Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,\nJapan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n236University of Southampton, Southampton SO17 1BJ, United Kingdom\n237Sungkyunkwan University, Seoul 03063, Republic of Korea\n238Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n239Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n240Chung-Ang University, Seoul 06974, Republic of Korea\n241University of Washington Bothell, Bothell, WA 98011, USA\n242Aix Marseille Universit\u00e9, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n243Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245Seoul National University, Seoul 08826, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n248Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n249Bard College, Annandale-On-Hudson, NY 12504, USA\n250Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n251Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n252Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n253Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n254Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n255Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n256Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n257Texas Tech University, Lubbock, TX 79409, USA\n258Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n259Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n260Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055,\nRepublic of Korea\n261NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n262National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science Park, Hsinchu City 30076,\nTaiwan\n263NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n264Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n265School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n266Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n267Columbia University, New York, NY 10027, USA\n268Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n269Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n270Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa\n224-8551, Japan\n271Tsinghua University, Beijing 100084, China\n272Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n273School of Physical & Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand\n274GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n\n48\n278Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, To Huu street Yen Nghia Ward, Ha Dong District, Hanoi, Vietnam\n279University of Stavanger, 4021 Stavanger, Norway\n280Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n281Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima\n903-0213, Japan\n282Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n283Observatoire de Paris, 75014 Paris, France\n284Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n285National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n286Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n287Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan\n288University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n289CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n290Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n291Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n292Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n293Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n294Hobart and William Smith Colleges, Geneva, NY 14456, USA\n295Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n296Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n297Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n298Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n299Universidad de Antioquia, Medell\u00edn, Colombia\n300Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n301Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n302Dipartimento di Fisica e Scienze della Terra, Universit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n303Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n304Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n305Department of Physics, Indian Institute of Technology Gandhinagar, Gujarat 382055, India\n306Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n307University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n308Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n309Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n310NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n311iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n312Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n313Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS, Universit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n314Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n315INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n316Universidade Estadual Paulista, 01140-070 S\u00e3o Paulo, Brazil\n317School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA\n318Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n319Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n320Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n321Carleton College, Northfield, MN 55057, USA\n322University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n323National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n324Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n325Texas A&M University, College Station, TX 77843, USA\n326Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n327The University of Utah, Salt Lake City, UT 84112, USA\n328Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n329Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n", "Draft version March 28, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nSwift-BAT GUANO follow-up of gravitational-wave triggers in the third LIGO\u2013Virgo\u2013KAGRA\nobserving run\nGayathri Raman,1 Samuele Ronchini,1 James Delaunay,2, 1 Aaron Tohuvavohu,3, 4 Jamie A. Kennea,1\nTyler Parsotan,5 Elena Ambrosi,6 Maria Grazia Bernardini,7 Sergio Campana,7 Giancarlo Cusumano,6\nAntonino D\u2019A`\u0131,6 Paolo D\u2019Avanzo,7 Valerio D\u2019Elia,8, 9 Massimiliano De Pasquale,10 Simone Dichiara,1\nPhil Evans,11 Dieter Hartmann,12 Paul Kuin,13 Andrea Melandri,14 Paul O\u2019Brien,11 Julian P. Osborne,11\nKim Page,11 David M. Palmer,15 Boris Sbarufatti,16 Gianpiero Tagliaferri,7 Eleonora Troja,17\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\nA. G. Abac,18 R. Abbott,19 H. Abe,20 I. Abouelfettouh,21 F. Acernese,22, 23 K. Ackley,24 C. Adamcewicz,25\nS. Adhicary,26 N. Adhikari,27 R. X. Adhikari,19 V. K. Adkins,28 V. B. Adya,29 C. Affeldt,30, 31 D. Agarwal,32\nM. Agathos,33 O. D. Aguiar,34 I. Aguilar,35 L. Aiello,36 A. Ain,37 T. Akutsu,38, 39 S. Albanesi,40, 41 R. A. Alfaidi,42\nA. Al-Jodah,43 C. All\u00b4en\u00b4e,44 A. Allocca,45, 23 S. Al-Shammari,36 P. A. Altin,29 S. Alvarez-Lopez,46 A. Amato,47, 48\nL. Amez-Droz,49 A. Amorosi,49 C. Amra,50 S. Anand,19 A. Ananyeva,19 S. B. Anderson,19 W. G. Anderson,19\nM. Andia,51 M. Ando,52 T. Andrade,53 N. Andres,44 M. Andr\u00b4es-Carcasona,54 T. Andri\u00b4c,18, 55 J. Anglin,56\nS. Ansoldi,57, 58 J. M. Antelis,59 S. Antier,60 M. Aoumi,61 E. Z. Appavuravther,62, 63 S. Appert,19 S. K. Apple,64\nK. Arai,19 A. Araya,65 M. C. Araya,19 J. S. Areeda,66 N. Aritomi,21 F. Armato,67 N. Arnaud,51, 68 M. Arogeti,69\nS. M. Aronson,28 G. Ashton,70 Y. Aso,38, 71 M. Assiduo,72, 73 S. Assis de Souza Melo,68 S. M. Aston,74 P. Astone,75\nF. Aubin,76 K. AultONeal,59 G. Avallone,77 S. Babak,78 F. Badaracco,67 C. Badger,79 S. Bae,80 S. Bagnasco,41\nE. Bagui,81 Y. Bai,19 J. G. Baier,82 R. Bajpai,38 T. Baka,83 M. Ball,84 G. Ballardin,68 S. W. Ballmer,85\nS. Banagiri,86 B. Banerjee,55 D. Bankar,32 P. Baral,27 J. C. Barayoga,19 B. C. Barish,19 D. Barker,21\nP. Barneo,53, 87 F. Barone,88, 23 B. Barr,42 L. Barsotti,46 M. Barsuglia,78 D. Barta,89 S. D. Barthelmy,90\nM. A. Barton,42 I. Bartos,56 S. Basak,91 A. Basalaev,92 R. Bassiri,35 A. Basti,93, 37 M. Bawaj,94, 62 P. Baxi,95\nJ. C. Bayley,42 A. C. Baylor,27 M. Bazzan,96, 97 B. B\u00b4ecsy,98 V. M. Bedakihale,99 F. Beirnaert,100 M. Bejger,101\nD. Belardinelli,102 A. S. Bell,42 V. Benedetto,103 D. Beniwal,104 W. Benoit,105 J. D. Bentley,92 M. Ben Yaala,106\nS. Bera,107 M. Berbel,108 F. Bergamin,30, 31 B. K. Berger,35 S. Bernuzzi,109 M. Beroiz,19 C. P. L. Berry,42\nD. Bersanetti,67 A. Bertolini,48 J. Betzwieser,74 D. Beveridge,43 N. Bevins,110 R. Bhandare,111\nU. Bhardwaj,112, 48 R. Bhatt,19 D. Bhattacharjee,82, 113 S. Bhaumik,56 S. Bhowmick,114 A. Bianchi,48, 115\nI. A. Bilenko,116 G. Billingsley,19 A. Binetti,117 S. Bini,118, 119 O. Birnholtz,120 S. Biscoveanu,86, 46 A. Bisht,31\nM. Bitossi,68, 37 M.-A. Bizouard,60 J. K. Blackburn,19 C. D. Blair,43, 74 D. G. Blair,43 F. Bobba,77, 121 N. Bode,30, 31\nG. Bogaert,60 G. Boileau,122, 60 M. Boldrini,123, 75 G. N. Bolingbroke,104 A. Bolliand,124, 50 L. D. Bonavena,96\nR. Bondarescu,53 F. Bondu,125 E. Bonilla,35 M. S. Bonilla,66 A. Bonino,126 R. Bonnand,44 P. Booker,30, 31\nA. Borchers,30, 31 V. Boschi,37 S. Bose,32 V. Bossilkov,74 V. Boudart,127 A. Boumerdassi,36 A. Bozzi,68\nC. Bradaschia,37 P. R. Brady,27 M. Braglia,128 A. Branch,74 M. Branchesi,55, 129 M. Breschi,109 T. Briant,130\nA. Brillet,60 M. Brinkmann,30, 31 P. Brockill,27 E. Brockmueller,30, 31 A. F. Brooks,19 D. D. Brown,104\nM. L. Brozzetti,94, 62 S. Brunett,19 G. Bruno,131 R. Bruntz,132 J. Bryant,126 F. Bucci,73 J. Buchanan,132\nO. Bulashenko,53, 87 T. Bulik,133 H. J. Bulten,48 A. Buonanno,134, 18 K. Burtnyk,21 R. Buscicchio,135, 136\nD. Buskulic,44 C. Buy,137 R. L. Byer,35 G. S. Cabourn Davies,138 G. Cabras,57, 58 R. Cabrita,131 L. Cadonati,69\nG. Cagnoli,139 C. Cahillane,85 J. Calder\u00b4on Bustillo,140 J. D. Callaghan,42 T. A. Callister,141 E. Calloni,45, 23\nJ. B. Camp,90 M. Canepa,142, 67 G. Caneva Santoro,54 M. Cannavacciuolo,77 K. C. Cannon,52 H. Cao,143 Z. Cao,144\nL. A. Capistran,145 E. Capocasa,78 E. Capote,85 G. Carapella,77, 121 F. Carbognani,68 M. Carlassara,30, 31\nJ. B. Carlin,146 M. Carpinelli,135, 147, 68 G. Carrillo,84 J. J. Carter,30, 31 G. Carullo,148 J. Casanueva Diaz,68\nC. Casentini,149, 102 G. Castaldi,150 S. Y. Castro-Lucas,114 S. Caudill,151, 48, 83 M. Cavagli`a,113 R. Cavalieri,68\nG. Cella,37 P. Cerd\u00b4a-Dur\u00b4an,152, 153 E. Cesarini,102 W. Chaibi,60 P. Chakraborty,30, 31\nS. Chalathadka Subrahmanya,92 C. Chan,52 J. C. L. Chan,141 K. H. M. Chan,154 M. Chan,155 W. L. Chan,154\nK. Chandra,156 R.-J. Chang,157 P. Chanial,78 S. Chao,158, 159 C. Chapman-Bird,42 E. L. Charlton,132\nP. Charlton,160 E. Chassande-Mottin,78 C. Chatterjee,43 Debarati Chatterjee,32 Deep Chatterjee,46\nM. Chaturvedi,111 S. Chaty,78 A. Chen,161 A. H.-Y. Chen,162 D. Chen,163 H. Chen,158 H. Y. Chen,164 K. H. Chen,159\nX. Chen,43 Yi-Ru Chen,158 Yanbei Chen,165 Yitian Chen,166 H. P. Cheng,56 P. Chessa,93, 37 H. T. Cheung,95\nH. Y. Chia,56 F. Chiadini,167, 121 C. Chiang,159 G. Chiarini,97 A. Chiba,168 R. Chiba,169 R. Chierici,170\nA. Chincarini,67 M. L. Chiofalo,93, 37 A. Chiummo,23, 68 C. Chou,162 S. Choudhary,43 N. Christensen,60\nS. S. Y. Chua,29 K. W. Chung,79 G. Ciani,96, 97 P. Ciecielag,101 M. Cie\u00b4slar,101 M. Cifaldi,102 A. A. Ciobanu,104\nR. Ciolfi,171, 97 F. Clara,21 J. A. Clark,19, 69 T. A. Clarke,25 P. Clearwater,172 S. Clesse,81 F. Cleva,60\nE. Coccia,55, 129, 54 E. Codazzo,55 P.-F. Cohadon,130 M. Colleoni,107 C. G. Collette,49 J. Collins,74 S. Colloms,42\nA. Colombo,135, 136, 173 M. Colpi,135, 136 C. M. Compton,21 L. Conti,97 S. J. Cooper,126 T. R. Corbitt,28\nI. Cordero-Carri\u00b4on,174 S. Corezzi,94, 62 N. J. Cornish,98 A. Corsi,175 S. Cortese,68 C. A. Costa,34\nR. Cottingham,74 M. W. Coughlin,105 A. Couineaux,75 J.-P. Coulon,60 S. T. Countryman,176 J.-F. Coupechoux,170\narXiv:2407.12867v2 [astro-ph.HE] 27 Mar 2025\n\n2\nB. Cousins,26 P. Couvares,19, 69 D. M. Coward,43 M. J. Cowart,74 D. C. Coyne,19 R. Coyne,177 K. Craig,106\nR. Creed,36 J. D. E. Creighton,27 T. D. Creighton,178 P. Cremonese,107 A. W. Criswell,105\nJ. C. G. Crockett-Gray,28 M. Croquette,130 R. Crouch,21 S. G. Crowder,179 J. R. Cudell,127 T. J. Cullen,19\nA. Cumming,42 E. Cuoco,68, 180, 37 M. Cusinato,152 P. Dabadie,139 T. Dal Canton,51 S. Dall\u2019Osso,75 G. D\u00b4alya,100\nB. D\u2019Angelo,67 S. Danilishin,47, 48 S. D\u2019Antonio,102 K. Danzmann,31, 30, 31 K. E. Darroch,132 L. P. Dartez,21\nA. Dasgupta,99 S. Datta,181 V. Dattilo,68 A. Daumas,78 N. Davari,182, 147 I. Dave,111 A. Davenport,114 M. Davier,51\nT. F. Davies,43 D. Davis,19 L. Davis,43 M. C. Davis,110 E. J. Daw,183 M. Dax,18 J. De Bolle,100 M. Deenadayalan,32\nJ. Degallaix,184 M. De Laurentis,45, 23 S. Del\u00b4eglise,130 V. Del Favero,90 F. De Lillo,131 D. Dell\u2019Aquila,182, 147\nW. Del Pozzo,93, 37 F. De Marco,75, 123 F. De Matteis,149, 102 V. D\u2019Emilio,36 N. Demos,46 T. Dent,140 A. Depasse,131\nN. DePergola,110 R. De Pietri,185, 186 R. De Rosa,45, 23 C. De Rossi,68 R. De Simone,167 A. Dhani,18\nS. Dhurandhar,32 R. Diab,56 M. C. D\u00b4\u0131az,178 M. Di Cesare,45 G. Dideron,187 N. A. Didio,85 T. Dietrich,18\nL. Di Fiore,23 C. Di Fronzo,49 F. Di Giovanni,152 M. Di Giovanni,123, 75 T. Di Girolamo,45, 23 D. Diksha,48, 47\nA. Di Michele,94 J. Ding,78, 188 S. Di Pace,123, 75 I. Di Palma,123, 75 F. Di Renzo,170 Divyajyoti,189 A. Dmitriev,126\nZ. Doctor,86 E. Dohmen,21 P. P. Doleva,132 L. Donahue,190 L. D\u2019Onofrio,75 F. Donovan,46 K. L. Dooley,36\nT. Dooney,83 S. Doravari,32 O. Dorosh,191 M. Drago,123, 75 J. C. Driggers,21 Y. Drori,19 J.-G. Ducoin,192, 78\nL. Dunn,146 U. Dupletsa,55 D. D\u2019Urso,182, 147 H. Duval,193 P.-A. Duverne,51 S. E. Dwyer,21 C. Eassa,21\nM. Ebersold,194, 44 T. Eckhardt,92 G. Eddolls,42 B. Edelman,84 T. B. Edo,19 O. Edy,138 A. Effler,74 J. Eichholz,29\nH. Einsle,60 M. Eisenmann,38 R. A. Eisenstein,46 A. Ejlli,36 M. Emma,70 E. Engelby,66 A. J. Engl,35 L. Errico,45, 23\nR. C. Essick,195 H. Estell\u00b4es,18 D. Estevez,76 T. Etzel,19 M. Evans,46 T. Evstafyeva,33 B. E. Ewing,26\nJ. M. Ezquiaga,141 F. Fabrizi,72, 73 F. Faedi,73, 72 V. Fafone,149, 102 S. Fairhurst,36 P. C. Fan,190 A. M. Farah,141\nB. Farr,84 W. M. Farr,196, 197 G. Favaro,96 M. Favata,198 M. Fays,127 M. Fazio,106 J. Feicht,19 M. M. Fejer,35\nE. Fenyvesi,89, 199 D. L. Ferguson,164 I. Ferrante,93, 37 T. A. Ferreira,28 F. Fidecaro,93, 37 A. Fiori,37, 93 I. Fiori,68\nM. Fishbach,195 R. P. Fisher,132 R. Fittipaldi,200, 121 V. Fiumara,201, 121 R. Flaminio,44 S. M. Fleischer,202\nL. S. Fleming,203 E. Floden,105 E. M. Foley,105 H. Fong,155 J. A. Font,152, 153 B. Fornal,204 P. W. F. Forsyth,29\nK. Franceschetti,185 N. Franchini,78 S. Frasca,123, 75 F. Frasconi,37 A. Frattale Mascioli,123, 75 Z. Frei,205\nA. Freise,48, 115 O. Freitas,206, 152 R. Frey,84 W. Frischhertz,74 P. Fritschel,46 V. V. Frolov,74 G. G. Fronz\u00b4e,41\nM. Fuentes-Garcia,19 S. Fujii,169 I. Fukunaga,207 P. Fulda,56 M. Fyffe,74 W. E. Gabella,208 B. Gadre,83\nJ. R. Gair,18 S. Galaudage,25, 209 S. Gallardo,210 B. Gallego,210 R. Gamba,109 A. Gamboa,18 D. Ganapathy,46\nA. Ganguly,32 S. G. Gaonkar,32 B. Garaventa,67, 142 J. Garcia-Bellido,128 C. Garc\u00b4\u0131a-N\u00b4u\u02dcnez,203\nC. Garc\u00b4\u0131a-Quir\u00b4os,194 J. W. Gardner,29 K. A. Gardner,155 J. Gargiulo,68 A. Garron,107 F. Garufi,45, 23\nC. Gasbarra,149, 102 B. Gateley,21 V. Gayathri,27 G. Gemme,67 A. Gennai,37 J. George,111 R. George,164\nO. Gerberding,92 L. Gergely,211 N. Ghadiri,66 Archisman Ghosh,100 Shaon Ghosh,198 Shrobana Ghosh,30, 31\nSuprovo Ghosh,32 Tathagata Ghosh,32 L. Giacoppo,123, 75 J. A. Giaime,28, 74 K. D. Giardina,74 D. R. Gibson,203\nD. T. Gibson,33 C. Gier,106 P. Giri,37, 93 F. Gissi,103 S. Gkaitatzis,93, 37 J. Glanzer,28 A. E. Gleckl,66 F. Glotin,51\nJ. Godfrey,84 P. Godwin,19 N. L. Goebbels,92 E. Goetz,155 J. Golomb,19 S. Gomez Lopez,123, 75 B. Goncharov,55\nG. Gonz\u00b4alez,28 P. Goodarzi,143 A. W. Goodwin-Jones,43 M. Gosselin,68 A. S. G\u00a8ottel,36 R. Gouaty,44\nD. W. Gould,29 S. Goyal,91 B. Grace,29 A. Grado,212, 23 V. Graham,42 A. E. Granados,105 M. Granata,184\nV. Granata,77 L. Granda Argianas,110 S. Gras,46 P. Grassia,19 C. Gray,21 R. Gray,42 G. Greco,62\nA. C. Green,48, 115 S. M. Green,138 S. R. Green,18 A. M. Gretarsson,59 E. M. Gretarsson,59 D. Griffith,19\nW. L. Griffiths,36 H. L. Griggs,69 G. Grignani,94, 62 A. Grimaldi,118, 119 C. Grimaud,44 H. Grote,36 A. S. Gruson,66\nD. Guerra,152 D. Guetta,213, 75 G. M. Guidi,72, 73 A. R. Guimaraes,28 H. K. Gulati,99 F. Gulminelli,214, 215\nA. M. Gunny,46 H. Guo,204 W. Guo,43 Y. Guo,48, 47 Anchal Gupta,19 Anuradha Gupta,216 Ish Gupta,26\nN. C. Gupta,99 P. Gupta,48, 83 S. K. Gupta,56 T. Gupta,98 N. Gupte,18 R. Gurav,143 J. Gurs,92 N. Gutierrez,184\nF. Guzman,145 D. Haba,20 M. Haberland,18 L. Haegel,78 G. Hain,132 S. Haino,217 E. D. Hall,46 R. Hamburg,51\nE. Z. Hamilton,194 G. Hammond,42 W.-B. Han,218 M. Haney,194, 48 J. Hanks,21 C. Hanna,26 M. D. Hannam,36\nO. A. Hannuksela,154 A. G. Hanselman,141 H. Hansen,21 J. Hanson,74 R. Harada,52 T. Harder,60 K. Haris,48, 83\nT. Harmark,148 J. Harms,55, 129 G. M. Harry,219 I. W. Harry,138 B. Haskell,101 C.-J. Haster,220 J. S. Hathaway,221\nK. Haughian,42 H. Hayakawa,61 K. Hayama,222 J. Healy,221 A. Heffernan,107 A. Heidmann,130 M. C. Heintze,74\nJ. Heinze,126 J. Heinzel,46 H. Heitmann,60 F. Hellman,223 P. Hello,51 A. F. Helmling-Cornell,84 G. Hemming,68\nM. Hendry,42 I. S. Heng,42 E. Hennes,48 J.-S. Hennig,47, 48 M. Hennig,47, 48 C. Henshaw,69 A. Hernandez,198\nT. Hertog,117 M. Heurs,30, 31 A. L. Hewitt,33, 224 S. Higginbotham,36 S. Hild,47, 48 P. Hill,106 S. Hill,42\nY. Himemoto,225 A. S. Hines,145 N. Hirata,38 C. Hirose,226 J. Ho,159 S. Hoang,51 S. Hochheim,30, 31 D. Hofman,184\nN. A. Holland,48, 115 K. Holley-Bockelmann,208 I. J. Hollows,183 Z. J. Holmes,104 D. E. Holz,141 C. Hong,35\nJ. Hornung,84 S. Hoshino,226 J. Hough,42 S. Hourihane,19 E. J. Howell,43 C. G. Hoy,138 D. Hoyland,126\nC. A. Hrishikesh,149 H.-F. Hsieh,158 C. Hsiung,227 H. C. Hsu,159 S.-C. Hsu,64, 158 W.-F. Hsu,117 P. Hu,208 Q. Hu,42\nH. Y. Huang,159 Y.-J. Huang,26 Y. Huang,46 Y. T. Huang,64 A. D. Huddart,228 B. Hughey,59 D. C. Y. Hui,229\nV. Hui,44 R. Hur,84 S. Husa,107 R. Huxford,26 T. Huynh-Dinh,74 G. A. Iandolo,47 A. Iess,180, 37 K. Inayoshi,230\nY. Inoue,159 G. Iorio,96 J. Irwin,42 M. Isi,196, 197 M. A. Ismail,159 Y. Itoh,207, 231 M. Iwaya,169 B. R. Iyer,91\nV. JaberianHamedan,43 P.-E. Jacquet,130 S. J. Jadhav,232 S. P. Jadhav,172 T. Jain,33 A. L. James,36 P. A. James,132\nR. Jamshidi,49 A. Z. Jan,164 K. Jani,208 L. Janiurek,42 J. Janquart,83, 48 K. Janssens,122, 60 N. N. Janthalur,232\nS. Jaraba,128 P. Jaranowski,233 P. Jasal,53 R. Jaume,107 W. Javed,36 A. Jennings,21 W. Jia,46 J. Jiang,56\nH.-B. Jin,234, 235 K. Johansmeyer,198 G. R. Johns,132 N. A. Johnson,56 R. Johnston,42 N. Johny,30, 31 D. H. Jones,29\n\n3\nD. I. Jones,236 R. Jones,42 S. Jose,189 P. Joshi,26 L. Ju,43 K. Jung,237 J. Junker,30, 31 V. Juste,76 T. Kajita,238\nC. Kalaghatgi,83, 48, 239 V. Kalogera,86 M. Kamiizumi,61 N. Kanda,231, 207 S. Kandhasamy,32 G. Kang,240\nJ. B. Kanner,19 S. J. Kapadia,32 D. P. Kapasi,29 S. Karat,19 C. Karathanasis,54 S. Karki,113 R. Kashyap,26\nM. Kasprzack,19 W. Kastaun,30, 31 J. Kato,168 T. Kato,169 S. Katsanevas,68, \u2217E. Katsavounidis,46 W. Katzman,74\nT. Kaur,43 R. Kaushik,111 K. Kawabe,21 D. Keitel,107 J. Kelley-Derzon,56 J. Kennington,26 R. Kesharwani,32\nJ. S. Key,241 S. Khadka,35 F. Y. Khalili,116 F. Khan,30, 31 I. Khan,242, 50 T. Khanam,175 M. Khursheed,111\nW. Kiendrebeogo,60, 243 N. Kijbunchoo,104 C. Kim,244 J. C. Kim,245 K. Kim,246 M. H. Kim,247 S. Kim,229 W. S. Kim,248\nY.-M. Kim,246 C. Kimball,86 N. Kimura,61 M. Kinley-Hanlon,42 M. Kinnear,36 J. S. Kissel,21 T. Kiyota,207\nS. Klimenko,56 T. Klinger,36 A. M. Knee,155 N. Knust,30, 31 P. Koch,30, 31 S. M. Koehlenbeck,35 G. Koekoek,48, 47\nK. Kohri,249 K. Kokeyama,36 S. Koley,55 P. Kolitsidou,126 M. Kolstein,54 K. Komori,52 A. K. H. Kong,158\nA. Kontos,250 M. Korobko,92 R. V. Kossak,30, 31 X. Kou,105 A. Koushik,122 N. Kouvatsos,79 M. Kovalam,43\nN. Koyama,226 D. B. Kozak,19 S. L. Kranzhoff,47, 48 V. Kringel,30, 31 N. V. Krishnendu,91 A. Kr\u00b4olak,251, 191\nG. Kuehn,30, 31 P. Kuijer,48 S. Kulkarni,216 A. Kulur Ramamohan,29 A. Kumar,232 Praveen Kumar,140\nPrayush Kumar,91 Rahul Kumar,21 Rakesh Kumar,99 J. Kume,52 K. Kuns,46 S. Kuroyanagi,128, 252 S. Kuwahara,52\nK. Kwak,237 K. Kwan,29 G. Lacaille,42 P. Lagabbe,44 D. Laghi,137 S. Lai,162 A. H. Laity,177 M. H. Lakkis,49\nE. Lalande,253 M. Lalleman,122 M. Landry,21 B. B. Lane,46 R. N. Lang,46 J. Lange,164 B. Lantz,35 A. La Rana,75\nI. La Rosa,107, 123, 44 A. Lartaux-Vollard,51 P. D. Lasky,25 J. Lawrence,175 M. Laxen,74 A. Lazzarini,19\nC. Lazzaro,96, 97 P. Leaci,123, 75 S. LeBohec,204 Y. K. Lecoeuche,155 H. M. Lee,245 H. W. Lee,254 K. Lee,247\nR.-K. Lee,158 R. Lee,46 S. Lee,246 Y. Lee,159 I. N. Legred,19 J. Lehmann,30, 31 L. Lehner,187 A. Lema\u02c6\u0131tre,255\nM. Lenti,73, 256 M. Leonardi,257, 38 E. Leonova,112 M. Lequime,50 N. Leroy,51 M. Lesovsky,19 N. Letendre,44\nM. Lethuillier,170 C. Levesque,253 Y. Levin,25 K. Leyde,78 A. K. Y. Li,19 K. L. Li,157 T. G. F. Li,154, 117 X. Li,165\nChien-Yu Lin,159, 158 Chun-Yu Lin,258 E. T. Lin,158 F. Lin,159 H. Lin,159 L. C.-C. Lin,157 F. Linde,239, 48\nS. D. Linker,150, 210 T. B. Littenberg,259 A. Liu,154 G. C. Liu,227 Jian Liu,43 F. Llamas,178 J. Llobera-Querol,107\nR. K. L. Lo,19 J.-P. Locquet,117 L. London,112 A. Longo,72, 73 D. Lopez,194 M. Lopez Portilla,83 M. Lorenzini,149, 102\nV. Loriette,51 M. Lormand,74 G. Losurdo,37 T. P. Lott IV,69 J. D. Lough,30, 31 H. A. Loughlin,46 C. O. Lousto,221\nM. J. Lowry,132 H. L\u00a8uck,31, 30, 31 D. Lumaca,102 A. P. Lundgren,138 A. W. Lussier,253 L.-T. Ma,158 S. Ma,165\nM. Ma\u2019arif,159 R. Macas,138 M. MacInnis,46 R. R. Maciy,30, 31 D. M. Macleod,36 I. A. O. MacMillan,19\nA. Macquet,54 D. Macri,46 K. Maeda,168 S. Maenaut,117 I. Maga\u02dcna Hernandez,27 S. S. Magare,32 C. Magazz`u,37\nR. M. Magee,19 E. Maggio,18 R. Maggiore,48, 115 M. Magnozzi,67, 142 M. Mahesh,92 S. Mahesh,260 M. Maini,177\nS. Majhi,32 E. Majorana,123, 75 C. N. Makarem,19 J. A. Malaquias-Reis,34 S. Maliakal,19 A. Malik,111 N. Man,60\nV. Mandic,105 V. Mangano,75, 123 B. Mannix,84 G. L. Mansell,85, 46 M. Manske,27 M. Mantovani,68 M. Mapelli,96, 97\nF. Marchesoni,63, 62, 261 D. Mar\u00b4\u0131n Pina,53, 87, 262 F. Marion,44 S. M\u00b4arka,176 Z. M\u00b4arka,176 C. Markakis,161\nA. S. Markosyan,35 A. Markowitz,19 E. Maros,19 A. Marquina,174 S. Marsat,137 F. Martelli,72, 73 I. W. Martin,42\nR. M. Martin,198 B. B. Martinez,145 M. Martinez,54, 263 V. Martinez,139 A. Martini,118 K. Martinovic,79\nJ. C. Martins,34 D. V. Martynov,126 E. J. Marx,46 L. Massaro,47, 48 A. Masserot,44 M. Masso-Reid,42\nM. Mastrodicasa,75 S. Mastrogiovanni,75 M. Mateu-Lucena,107 M. Matiushechkina,30, 31 M. Matsuyama,207\nN. Mavalvala,46 N. Maxwell,21 G. McCarrol,74 R. McCarthy,21 D. E. McClelland,29 S. McCormick,74\nL. McCuller,19 G. I. McGhee,42 K. B. M. McGowan,208 M. Mchedlidze,198 C. McIsaac,138 J. McIver,155\nK. McKinney,179 A. McLeod,43 T. McRae,29 S. T. McWilliams,260 D. Meacher,27 A. K. Mehta,18 Q. Meijer,83\nA. Melatos,146 S. Mellaerts,117 A. Menendez-Vazquez,54 C. S. Menoni,114 R. A. Mercer,27 L. Mereni,184\nK. Merfeld,84 E. L. Merilh,74 J. R. M\u00b4erou,107 J. D. Merritt,84 M. Merzougui,60 C. Messenger,42 C. Messick,27\nM. Meyer-Conde,207 F. Meylahn,30, 31 A. Mhaske,32 A. Miani,118, 119 H. Miao,264 I. Michaloliakos,56 C. Michel,184\nY. Michimura,19, 52 H. Middleton,126 A. L. Miller,48 S. Miller,19 M. Millhouse,69 E. Milotti,265, 58 Y. Minenkov,102\nN. Mio,266 Ll. M. Mir,54 L. Mirasola,267, 75 M. Miravet-Ten\u00b4es,152 C.-A. Miritescu,54 A. K. Mishra,91 A. Mishra,32\nC. Mishra,189 T. Mishra,56 A. L. Mitchell,48, 115 J. G. Mitchell,59 S. Mitra,32 V. P. Mitrofanov,116\nG. Mitselmakher,56 R. Mittleman,46 O. Miyakawa,61 S. Miyamoto,169 S. Miyoki,61 G. Mo,46 L. Mobilia,72, 73\nL. M. Modafferi,107 S. R. P. Mohapatra,19 S. R. Mohite,27 M. Molina-Ruiz,223 C. Mondal,214 M. Mondin,210\nM. Montani,72, 73 C. J. Moore,126 M. Morales,66 D. Moraru,21 F. Morawski,101 A. More,32 S. More,32\nC. Moreno,59 G. Moreno,21 S. Morisaki,52, 169 Y. Moriwaki,168 G. Morras,128 A. Moscatello,96 P. Mourier,107\nB. Mours,76 C. M. Mow-Lowry,48, 115 S. Mozzon,138 F. Muciaccia,123, 75 D. Mukherjee,259 Samanwaya Mukherjee,32\nSoma Mukherjee,178 Subroto Mukherjee,99 Suvodip Mukherjee,268, 187, 112 N. Mukund,46 A. Mullavey,74\nJ. Munch,104 C. L. Mungioli,43 M. Munn,21 W. R. Munn Oberg,269 M. Murakoshi,270 P. G. Murray,42 S. Muusse,29\nS. L. Nadji,30, 31 A. Nagar,41, 271 N. Nagarajan,42 K. N. Nagler,59 K. Nakamura,38 H. Nakano,272 M. Nakano,19\nD. Nandi,28 V. Napolano,68 P. Narayan,216 I. Nardecchia,149, 102 H. Narola,83 L. Naticchioni,75 R. K. Nayak,273\nB. F. Neil,43 J. Neilson,103, 121 A. Nelson,145 T. J. N. Nelson,74 M. Nery,30, 31 A. Neunzert,21 S. Ng,66 C. Nguyen,78\nP. Nguyen,84 L. Nguyen Quynh,274 S. A. Nichols,28 A. B. Nielsen,275 G. Nieradka,101 A. Niko,159 Y. Nishino,38, 276\nA. Nishizawa,52 S. Nissanke,112, 48 E. Nitoglia,170 W. Niu,26 F. Nocera,68 M. Norman,36 C. North,36\nJ. Novak,124, 277, 278, 279 J. F. Nu\u02dcno Siles,128 G. Nurbek,178 L. K. Nuttall,138 K. Obayashi,270 J. Oberling,21\nJ. O\u2019Dell,228 M. Oertel,124, 277, 278, 280, 279 A. Offermans,117 G. Oganesyan,55, 129 J. J. Oh,248 K. Oh,229 S. H. Oh,248\nT. O\u2019Hanlon,74 M. Ohashi,61 M. Ohkawa,226 F. Ohme,30, 31 H. Ohta,52 A. S. Oliveira,176 R. Oliveri,124, 277, 278\nV. Oloworaran,43 B. O\u2019Neal,132 K. Oohara,281, 282 B. O\u2019Reilly,74 N. D. Ormsby,132 M. Orselli,62, 94\nR. O\u2019Shaughnessy,221 Y. Oshima,283 S. Oshino,61 S. Ossokine,18 C. Osthelder,19 D. J. Ottaway,104 A. Ouzriat,170\n\n4\nH. Overmier,74 B. J. Owen,175 A. E. Pace,26 R. Pagano,28 M. A. Page,38 A. Pai,156 S. A. Pai,111 A. Pal,284 S. Pal,273\nM. A. Palaia,37, 93 M. P\u00b4alfi,205 P. P. Palma,149, 102 C. Palomba,75 K. C. Pan,158 P. K. Panda,232 L. Panebianco,72, 73\nP. T. H. Pang,48, 83 F. Pannarale,123, 75 B. C. Pant,111 F. H. Panther,43 C. D. Panzer,105 F. Paoletti,37 A. Paoli,68\nA. Paolone,75, 285 E. E. Papalexakis,143 L. Papalini,37, 93 G. Papigkiotis,286 A. Parisi,48, 112 J. Park,246 W. Parker,74\nG. Pascale,30, 31 D. Pascucci,100 A. Pasqualetti,68 R. Passaquieti,93, 37 D. Passuello,37 O. Patane,21 M. Patel,132\nD. Pathak,32 M. Pathak,104 A. Patra,36 B. Patricelli,93, 37 A. S. Patron,28 S. Paul,84 E. Payne,19 T. Pearce,36\nM. Pedraza,19 R. Pegna,37 A. Pele,19 F. E. Pe\u02dcna Arellano,61 S. Penn,269 M. D. Penuliar,66 A. Perego,118, 119\nA. Pereira,139 J. J. Perez,56 C. P\u00b4erigois,171, 97, 96 C. C. Perkins,56 G. Perna,96 A. Perreca,118, 119 J. Perret,78\nS. Perri`es,170 J. W. Perry,48, 115 D. Pesios,286 C. Petrillo,94 H. P. Pfeiffer,18 H. Pham,74 K. A. Pham,105\nK. S. Phukon,126, 48, 239 H. Phurailatpam,154 O. J. Piccinni,54 M. Pichot,60 M. Piendibene,93, 37 F. Piergiovanni,72, 73\nL. Pierini,75 G. Pierra,170 V. Pierro,103, 121 M. Pietrzak,101 M. Pillas,51 F. Pilo,37 L. Pinard,184\nC. Pineda-Bosque,210 I. M. Pinto,103, 121, 287, 45 M. Pinto,68 B. J. Piotrzkowski,27 M. Pirello,21 M. D. Pitkin,33, 224\nA. Placidi,62, 94 E. Placidi,123, 75 M. L. Planas,107 W. Plastino,288, 289 R. Poggiani,93, 37 E. Polini,44 L. Pompili,18\nJ. Poon,154 E. Porcelli,48 J. Portell,53, 87, 262 E. K. Porter,78 C. Posnansky,26 R. Poulton,68 J. Powell,172\nM. Pracchia,44 B. K. Pradhan,32 T. Pradier,76 A. K. Prajapati,99 K. Prasai,35 R. Prasanna,232 P. Prasia,32\nG. Pratten,126 M. Principe,150, 103, 287, 121 G. A. Prodi,290, 119 L. Prokhorov,126 P. Prosposito,149, 102 L. Prudenzi,18\nA. Puecher,48, 83 J. Pullin,28 M. Punturo,62 F. Puosi,37, 93 P. Puppo,75 M. P\u00a8urrer,177 H. Qi,161 J. Qin,29\nG. Qu\u00b4em\u00b4ener,215, 124, 214 V. Quetschke,178 C. Quigley,36 P. J. Quinonez,59 R. Quitzow-James,113 F. J. Raab,21\nG. Raaijmakers,112, 48 N. Radulesco,60 P. Raffai,205 S. X. Rail,253 S. Raja,111 C. Rajan,111 B. Rajbhandari,221, 175\nD. S. Ramirez,59 K. E. Ramirez,74 F. A. Ramis Vidal,107 A. Ramos-Buades,18 D. Rana,32 E. Randel,114 S. Ranjan,69\nP. Rapagnani,123, 75 B. Ratto,59 S. Rawat,105 A. Ray,27 V. Raymond,36 M. Razzano,93, 37 J. Read,66\nM. Recaman Payo,117 T. Regimbau,44 L. Rei,67 S. Reid,106 S. W. Reid,132 D. H. Reitze,19 P. Relton,36 A. Renzini,19\nP. Rettegno,41 B. Revenu,78, 291 A. Reza,48 M. Rezac,66 A. S. Rezaei,75, 123 F. Ricci,123, 75 M. Ricci,75 D. Richards,228\nC. J. Richardson,59 J. W. Richardson,143 A. Rijal,59 K. Riles,95 H. K. Riley,36 S. Rinaldi,93, 37 J. Rittmeyer,92\nC. Robertson,228 F. Robinet,51 M. Robinson,21 A. Rocchi,102 L. Rolland,44 J. G. Rollins,19 M. Romanelli,125\nA. E. Romano,292 R. Romano,22, 23 A. Romero,193 I. M. Romero-Shaw,33 J. H. Romie,74 T. J. Roocke,104 L. Rosa,23, 45\nT. J. Rosauer,143 C. A. Rose,27 D. Rosi\u00b4nska,133 M. P. Ross,64 M. Rossello,107 S. Rowan,42 S. K. Roy,196, 197\nS. Roy,83 D. Rozza,182, 147 P. Ruggi,68 E. Ruiz Morales,293, 128 K. Ruiz-Rocha,208 S. Sachdev,69 T. Sadecki,21\nJ. Sadiq,140 P. Saffarieh,48, 115 M. R. Sah,268 S. S. Saha,158 T. Sainrat,76 S. Sajith Menon,213, 123, 75 K. Sakai,294\nM. Sakellariadou,79 T. Sako,168 S. Sakon,26 O. S. Salafia,173, 136, 135 F. Salces-Carcoba,19 L. Salconi,68\nM. Saleem,105 F. Salemi,123, 75 M. Sall\u00b4e,48 S. Salvador,215, 214, 124 A. Sanchez,21 E. J. Sanchez,19 J. H. Sanchez,86\nL. E. Sanchez,19 N. Sanchis-Gual,295, 152 J. R. Sanders,296 E. M. S\u00a8anger,18 T. R. Saravanan,32 N. Sarin,25\nA. Sasli,286 P. Sassi,62, 94 B. Sassolas,184 H. Satari,43 R. Sato,226 S. Sato,168 Y. Sato,168 O. Sauter,56\nR. L. Savage,21 T. Sawada,61 H. L. Sawant,32 S. Sayah,44 D. Schaetzl,19 M. Scheel,165 J. Scheuer,86\nM. G. Schiworski,104 P. Schmidt,126 S. Schmidt,83 R. Schnabel,92 M. Schneewind,30, 31 R. M. S. Schofield,84\nK. Schouteden,117 H. Schuler,26 B. W. Schulte,30, 31 B. F. Schutz,36, 30, 31 E. Schwartz,36 J. Scott,42 S. M. Scott,29\nT. C. Seetharamu,42 M. Seglar-Arroyo,54 Y. Sekiguchi,297 D. Sellers,74 A. S. Sengupta,298 D. Sentenac,68\nE. G. Seo,42 J. W. Seo,117 V. Sequino,45, 23 M. Serra,75 G. Servignat,277 Y. Setyawati,83 T. Shaffer,21 U. S. Shah,69\nM. S. Shahriar,86 M. A. Shaikh,245 B. Shams,204 L. Shao,230 A. K. Sharma,91 P. Sharma,111\nS. Sharma-Chaudhary,113 P. Shawhan,134 N. S. Shcheblanov,299, 255 B. Shen,134 Y. Shikano,300, 301 M. Shikauchi,52\nK. Shimode,61 H. Shinkai,302 J. Shiota,270 D. H. Shoemaker,46 D. M. Shoemaker,164 R. W. Short,21\nS. ShyamSundar,111 A. Sider,49 H. Siegel,176, 196, 197 M. Sieniawska,131 D. Sigg,21 L. Silenzi,62, 63 M. Simmonds,104\nL. P. Singer,90 A. Singh,216 D. Singh,26 M. K. Singh,91 A. Singha,47, 48 A. M. Sintes,107 V. Sipala,182, 147 V. Skliris,36\nB. J. J. Slagmolen,29 T. J. Slaven-Blair,43 J. Smetana,126 J. R. Smith,66 L. Smith,42 R. J. E. Smith,25\nW. J. Smith,208 J. Soldateschi,256, 303, 73 S. N. Somala,304 K. Somiya,20 K. Soni,32 S. Soni,46 V. Sordini,170\nF. Sorrentino,67 N. Sorrentino,93, 37 R. Soulard,60 T. Souradeep,32, 305 A. Southgate,36 E. Sowell,175\nV. Spagnuolo,47, 48 A. P. Spencer,42 M. Spera,96, 97 P. Spinicelli,68 A. K. Srivastava,99 F. Stachurski,42\nD. A. Steer,78 J. Steinlechner,47, 48 S. Steinlechner,47, 48 N. Stergioulas,286 P. Stevens,51 M. StPierre,177\nL. C. Strang,146 G. Stratta,306, 307, 75, 308 M. D. Strong,28 A. Strunk,21 R. Sturani,309 A. L. Stuver,110\nM. Suchenek,101 S. Sudhagar,32, 101 N. Sueltmann,92 A. G. Sullivan,176 K. D. Sullivan,28 L. Sun,29 S. Sunil,99\nA. Sur,101 J. Suresh,52, 131 P. J. Sutton,36 Takamasa Suzuki,226 Takanori Suzuki,20 B. L. Swinkels,48 A. Syx,76\nM. J. Szczepa\u00b4nczyk,56 P. Szewczyk,133 M. Tacca,48 H. Tagoshi,169 S. C. Tait,42 H. Takahashi,310 R. Takahashi,38\nA. Takamori,65 K. Takatani,207 H. Takeda,311 M. Takeda,207 C. J. Talbot,106 C. Talbot,46 M. Tamaki,169\nN. Tamanini,137 D. Tanabe,159 K. Tanaka,312 S. J. Tanaka,270 T. Tanaka,311 A. J. Tanasijczuk,131 D. Tang,43\nS. Tanioka,85 D. B. Tanner,56 L. Tao,56 R. D. Tapia,26 E. N. Tapia San Mart\u00b4\u0131n,48 R. Tarafder,19\nC. Taranto,149, 102 A. Taruya,313 J. D. Tasson,190 M. Teloi,49 R. Tenorio,107 H. Themann,210\nA. Theodoropoulos,152 M. P. Thirugnanasambandam,32 L. M. Thomas,126 M. Thomas,74 P. Thomas,21\nJ. E. Thompson,165 S. R. Thondapu,111 K. A. Thorne,74 E. Thrane,25 J. Tissino,55 A. Tiwari,32\nShubhanshu Tiwari,194 Srishti Tiwari,32 V. Tiwari,126 M. R. Todd,85 A. M. Toivonen,105 K. Toland,42\nA. E. Tolley,138 T. Tomaru,38 K. Tomita,207 T. Tomura,61 C. Tong-Yu,159 A. Toriyama,270 N. Toropov,126\nA. Torres-Forn\u00b4e,152, 153 C. I. Torrie,19 M. Toscani,137 I. Tosta e Melo,314 E. Tournefier,44 A. A. Trani,52\nA. Trapananti,63, 62 F. Travasso,63, 62 G. Traylor,74 J. Trenado,53 M. Trevor,134 M. C. Tringali,68 A. Tripathee,95\n\n5\nL. Troiano,315, 121 A. Trovato,58, 265 L. Trozzo,23 R. J. Trudeau,19 T. T. L. Tsang,36 R. Tso,165, \u2020 S. Tsuchida,316\nL. Tsukada,26 T. Tsutsui,52 K. Turbang,193, 122 M. Turconi,60 C. Turski,100 H. Ubach,53, 87 A. S. Ubhi,126\nN. Uchikata,169 T. Uchiyama,61 R. P. Udall,19 T. Uehara,317 K. Ueno,52 C. S. Unnikrishnan,268 T. Ushiba,61\nA. Utina,47, 48 M. Vacatello,37, 93 H. Vahlbruch,30, 31 N. Vaidya,19 G. Vajente,19 A. Vajpeyi,25 G. Valdes,145\nJ. Valencia,107 M. Valentini,115, 48 S. A. Vallejo-Pe\u02dcna,292 S. Vallero,41 V. Valsan,27 N. van Bakel,48\nM. van Beuzekom,48 M. van Dael,48, 318 J. F. J. van den Brand,47, 115, 48 C. Van Den Broeck,83, 48\nD. C. Vander-Hyde,85 M. van der Sluys,48, 83 A. Van de Walle,51 J. van Dongen,48, 115 K. Vandra,110\nH. van Haevermaet,122 J. V. van Heijningen,131 J. Vanosky,19 M. H. P. M. van Putten,319 Z. van Ranst,47, 48\nN. van Remortel,122 M. Vardaro,47, 48 A. F. Vargas,146 V. Varma,18 M. Vas\u00b4uth,89 A. Vecchio,126 G. Vedovato,97\nJ. Veitch,42 P. J. Veitch,104 S. Venikoudis,131 J. Venneberg,30, 31 P. Verdier,170 D. Verkindt,44 B. Verma,151\nP. Verma,191 Y. Verma,111 S. M. Vermeulen,19 D. Veske,176 F. Vetrano,72 A. Veutro,75 A. M. Vibhute,21\nA. Vicer\u00b4e,72, 73 S. Vidyant,85 A. D. Viets,320 A. Vijaykumar,91 A. Vilkha,221 V. Villa-Ortega,140 E. T. Vincent,69\nJ.-Y. Vinet,60 S. Viret,170 A. Virtuoso,265, 58 S. Vitale,46 H. Vocca,94, 62 D. Voigt,92 E. R. G. von Reis,21\nJ. S. A. von Wrangel,30, 31 S. P. Vyatchanin,116 L. E. Wade,82 M. Wade,82 K. J. Wagner,221 R. C. Walet,48\nM. Walker,132 G. S. Wallace,106 L. Wallace,19 H. Wang,283 J. Z. Wang,95 W. H. Wang,178 Z. Wang,159\nG. Waratkar,156 R. L. Ward,29 J. Warner,21 M. Was,44 T. Washimi,38 N. Y. Washington,19 D. Watarai,52\nK. E. Wayt,82 B. Weaver,21 C. R. Weaving,138 S. A. Webster,42 M. Weinert,30, 31 A. J. Weinstein,19 R. Weiss,46\nC. M. Weller,64 R. A. Weller,208 F. Wellmann,30, 31 L. Wen,43 P. We\u00dfels,30, 31 K. Wette,29 J. T. Whelan,221\nD. D. White,66 B. F. Whiting,56 C. Whittle,46 J. B. Wildberger,18 O. S. Wilk,82 D. Wilken,30, 31, 31 K. Willetts,36\nD. Williams,42 M. J. Williams,42 N. S. Williams,126 J. L. Willis,19 B. Willke,31, 30, 31 M. Wils,117 C. C. Wipf,19\nG. Woan,42 J. Woehler,47, 48 J. K. Wofford,221 N. E. Wolfe,46 D. Wong,155 H. T. Wong,159 H. W. Y. Wong,154\nI. C. F. Wong,154 J. L. Wright,29 M. Wright,42 C. Wu,158 D. S. Wu,30, 31 H. Wu,158 D. M. Wysocki,27 L. Xiao,19\nV. A. Xu,46 Y. Xu,194 N. Yadav,101 H. Yamamoto,19 K. Yamamoto,168 M. Yamamoto,168 T. S. Yamamoto,252\nT. Yamamoto,61 S. Yamamura,169 R. Yamazaki,270 S. Yan,35 T. Yan,126 F. W. Yang,204 F. Yang,176 K. Z. Yang,105\nL.-C. Yang,162 Y. Yang,162 Z. Yarbrough,28 S.-W. Yeh,158 A. B. Yelikar,221 S. M. C. Yeung,27 X. Yin,46\nJ. Yokoyama,52 T. Yokozawa,61 J. Yoo,166 H. Yu,165 H. Yuzurihara,61 A. Zadro\u02d9zny,191 A. J. Zannelli,132\nM. Zanolin,59 M. Zeeshan,221 T. Zelenova,68 J.-P. Zendri,97 M. Zeoli,127, 131 M. Zerrad,50, 242 M. Zevin,86\nA. C. Zhang,176 J. Zhang,29 L. Zhang,19 R. Zhang,56 T. Zhang,126 Y. Zhang,29 C. Zhao,43 Yue Zhao,204\nYuhang Zhao,169, 38, 78 Y. Zheng,113 H. Zhong,105 S. Zhong,43 R. Zhou,223 Z.-H. Zhu,144, 321 A. B. Zimmerman,164\nM. E. Zucker,46, 19 J. Zweizig,19\n1Department of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA\n2Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA\n3Department of Astronomy & Astrophysics, University of Toronto, Toronto, ON M5S 3H4\n4Dunlap Institute for Astronomy & Astrophysics, University of Toronto, Toronto, ON M5S 3H4\n5Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n6INAF \u2013 IASF-Palermo, via Ugo La Malfa 153, 90146 Palermo PA, Italy\n7INAF-Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, LC, Italy\n8Space Science Data Center (SSDC) \u2013 Agenzia Spaziale Italiana (ASI), 00133 Roma, Italy\n9INAF \u2013 Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone, Italy\n10MIFT Department, Polo Papardo, University of Messina, Viale Ferdinando Stagno d\u2019Alcontres, 31, 98166 Messina, Italy\n11School of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK\n12Department of Physics & Astronomy, Clemson University, Kinard Lab of Physics, Clemson, SC 29634, USA\n13Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking, Surrey RH5 6NT, UK\n14INAF-Osservatorio Astronomico di Roma, Via di Frascati 33, 00040 Monte Porzio Catone, RM, Italy\n15Los Alamos National Laboratory, PO Box 1663, Los Alamos New Mexico 87545\n16INAF - Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, Italy\n17University of Rome Tor Vergata, via Cracovia 50, 00100 Roma, Italy\n18Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n19LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n20Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n21LIGO Hanford Observatory, Richland, WA 99352, USA\n22Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n23INFN, Sezione di Napoli, I-80126 Napoli, Italy\n24University of Warwick, Coventry CV4 7AL, United Kingdom\n25OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n26The Pennsylvania State University, University Park, PA 16802, USA\n27University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n28Louisiana State University, Baton Rouge, LA 70803, USA\n29OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n\n6\n30Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n31Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n32Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n33University of Cambridge, Cambridge CB2 1TN, United Kingdom\n34Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n35Stanford University, Stanford, CA 94305, USA\n36Cardiff University, Cardiff CF24 3AA, United Kingdom\n37INFN, Sezione di Pisa, I-56127 Pisa, Italy\n38Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n39Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n40Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n41INFN Sezione di Torino, I-10125 Torino, Italy\n42SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n43OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n44Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n45Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n46LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n47Maastricht University, 6200 MD Maastricht, Netherlands\n48Nikhef, 1098 XG Amsterdam, Netherlands\n49Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n50Institut Fresnel, Aix Marseille Universit\u00b4e, CNRS, Centrale Marseille, F-13013 Marseille, France\n51Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n52University of Tokyo, Tokyo, 113-0033, Japan.\n53Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n54Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n55Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n56University of Florida, Gainesville, FL 32611, USA\n57Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n58INFN, Sezione di Trieste, I-34127 Trieste, Italy\n59Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n60Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n61Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n62INFN, Sezione di Perugia, I-06123 Perugia, Italy\n63Universit`a di Camerino, I-62032 Camerino, Italy\n64University of Washington, Seattle, WA 98195, USA\n65Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n66California State University Fullerton, Fullerton, CA 92831, USA\n67INFN, Sezione di Genova, I-16146 Genova, Italy\n68European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n69Georgia Institute of Technology, Atlanta, GA 30332, USA\n70Royal Holloway, University of London, London TW20 0EX, United Kingdom\n71The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n72Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n73INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n74LIGO Livingston Observatory, Livingston, LA 70754, USA\n75INFN, Sezione di Roma, I-00185 Roma, Italy\n76Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n77Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n78Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n79King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n80Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n81Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n82Kenyon College, Gambier, OH 43022, USA\n83Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n84University of Oregon, Eugene, OR 97403, USA\n\n7\n85Syracuse University, Syracuse, NY 13244, USA\n86Northwestern University, Evanston, IL 60208, USA\n87Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n88Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n89Wigner RCP, RMKI, H-1121 Budapest, Hungary\n90NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n91International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n92Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n93Universit`a di Pisa, I-56127 Pisa, Italy\n94Universit`a di Perugia, I-06123 Perugia, Italy\n95University of Michigan, Ann Arbor, MI 48109, USA\n96Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n97INFN, Sezione di Padova, I-35131 Padova, Italy\n98Montana State University, Bozeman, MT 59717, USA\n99Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n100Universiteit Gent, B-9000 Gent, Belgium\n101Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n102INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n103Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n104OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n105University of Minnesota, Minneapolis, MN 55455, USA\n106SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n107IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n108Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n109Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n110Villanova University, Villanova, PA 19085, USA\n111RRCAT, Indore, Madhya Pradesh 452013, India\n112GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n113Missouri University of Science and Technology, Rolla, MO 65409, USA\n114Colorado State University, Fort Collins, CO 80523, USA\n115Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n116Lomonosov Moscow State University, Moscow 119991, Russia\n117Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n118Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n119INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n120Bar-Ilan University, Ramat Gan, 5290002, Israel\n121INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n122Universiteit Antwerpen, 2000 Antwerpen, Belgium\n123Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n124Centre national de la recherche scientifique, 75016 Paris, France\n125Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n126University of Birmingham, Birmingham B15 2TT, United Kingdom\n127Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n128Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n129INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n130Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n131Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n132Christopher Newport University, Newport News, VA 23606, USA\n133Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n134University of Maryland, College Park, MD 20742, USA\n135Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n136INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n137L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n138University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n139Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n\n8\n140IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n141University of Chicago, Chicago, IL 60637, USA\n142Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n143University of California, Riverside, Riverside, CA 92521, USA\n144Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n145Texas A&M University, College Station, TX 77843, USA\n146OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n147INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n148Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n149Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n150University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n151University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n152Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n153Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n154The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n155University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n156Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n157Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n158National Tsing Hua University, Hsinchu City 30013, Taiwan\n159National Central University, Taoyuan City 320317, Taiwan\n160OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n161Queen Mary University of London, London E1 4NS, United Kingdom\n162Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n163Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n164University of Texas, Austin, TX 78712, USA\n165CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n166Cornell University, Ithaca, NY 14850, USA\n167Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n168Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n169Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n170Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n171INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n172OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n173INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n174Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n175Texas Tech University, Lubbock, TX 79409, USA\n176Columbia University, New York, NY 10027, USA\n177University of Rhode Island, Kingston, RI 02881, USA\n178The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n179Bellevue College, Bellevue, WA 98007, USA\n180Scuola Normale Superiore, I-56126 Pisa, Italy\n181Chennai Mathematical Institute, Chennai 603103, India\n182Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n183The University of Sheffield, Sheffield S10 2TN, United Kingdom\n184Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n185Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n186INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n187Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n188Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n189Indian Institute of Technology Madras, Chennai 600036, India\n190Carleton College, Northfield, MN 55057, USA\n191National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n192Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n193Vrije Universiteit Brussel, 1050 Brussel, Belgium\n194University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n\n9\n195Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n196Stony Brook University, Stony Brook, NY 11794, USA\n197Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n198Montclair State University, Montclair, NJ 07043, USA\n199Institute for Nuclear Research, H-4026 Debrecen, Hungary\n200CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n201Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n202Western Washington University, Bellingham, WA 98225, USA\n203SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n204The University of Utah, Salt Lake City, UT 84112, USA\n205E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n206Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n207Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n208Vanderbilt University, Nashville, TN 37235, USA\n209Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n210California State University, Los Angeles, Los Angeles, CA 90032, USA\n211University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n212INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n213Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n214Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n215Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n216The University of Mississippi, University, MS 38677, USA\n217Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n218Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n219American University, Washington, DC 20016, USA\n220University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n221Rochester Institute of Technology, Rochester, NY 14623, USA\n222Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n223University of California, Berkeley, CA 94720, USA\n224University of Lancaster, Lancaster LA1 4YW, United Kingdom\n225College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n226Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n227Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n228Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n229Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n230Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n231Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233University of Bia lystok, 15-424 Bia lystok, Poland\n234National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n235School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n236University of Southampton, Southampton SO17 1BJ, United Kingdom\n237Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n238Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n239Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n240Chung-Ang University, Seoul 06974, Republic of Korea\n241University of Washington Bothell, Bothell, WA 98011, USA\n242Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n243Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245Seoul National University, Seoul 08826, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n\n10\n247Sungkyunkwan University, Seoul 03063, Republic of Korea\n248National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n249Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n250Bard College, Annandale-On-Hudson, NY 12504, USA\n251Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n252Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n253Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n254Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n255NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n256Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n257Department of Physics, University of Trento, via Sommarive 14, Povo, 38123 TN, Italy\n258National Center for High-performance computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n259NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n260West Virginia University, Morgantown, WV 26506, USA\n261School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n262Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n263Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n264Tsinghua University, Beijing 100084, China\n265Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n266Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n267INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n268Tata Institute of Fundamental Research, Mumbai 400005, India\n269Hobart and William Smith Colleges, Geneva, NY 14456, USA\n270Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n271Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n272Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n273Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n274Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n275University of Stavanger, 4021 Stavanger, Norway\n276Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n277Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n278Observatoire de Paris, 75014 Paris, France\n279Universit\u00b4e PSL, 75006 Paris, France\n280Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n281Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n282Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n283Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n284CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n285Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n286Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n287Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n288Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n289INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n290Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n291Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n292Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n293Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n294Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n295Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\n3810-183 Aveiro, Portugal\n296Marquette University, Milwaukee, WI 53233, USA\n297Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n298Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n\n11\n299Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n300Graduate School of Science and Technology, Gunma University, 4-2 Aramaki, Maebashi, Gunma 371-8510, Japan\n301Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n302Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n303INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n304Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n305Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n306Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n307Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n308INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n309Universidade Estadual Paulista, 01140-070 Campinas, S\u02dcao Paulo, Brazil\n310Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya, Tokyo\n158-0082, Japan\n311Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa\nCity, Chiba 277-8582, Japan\n313Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n314University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n315Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n316National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n317Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n318Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n319Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n320Concordia University Wisconsin, Mequon, WI 53097, USA\n321School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nABSTRACT\nWe present results from a search for X-ray/gamma-ray counterparts of gravitational-wave (GW)\ncandidates from the third observing run (O3) of the LIGO\u2013Virgo\u2013KAGRA (LVK) network using the\nSwift Burst Alert Telescope (Swift-BAT). The search includes 636 GW candidates received in low\nlatency, 86 of which have been confirmed by the offline analysis and included in the third cumulative\nGravitational-Wave Transient Catalogs (GWTC-3). Targeted searches were carried out on the entire\nGW sample using the maximum\u2013likelihood NITRATES pipeline on the BAT data made available\nvia the GUANO infrastructure. We do not detect any significant electromagnetic emission that is\ntemporally and spatially coincident with any of the GW candidates. We report flux upper limits in\nthe 15\u2013350 keV band as a function of sky position for all the catalog candidates. For GW candidates\nwhere the Swift-BAT false alarm rate is less than 10\u22123 Hz, we compute the GW\u2013BAT joint false\nalarm rate. Finally, the derived Swift-BAT upper limits are used to infer constraints on the putative\nelectromagnetic emission associated with binary black hole mergers.\n1. INTRODUCTION\nThe discovery of gravitational waves (GWs) from co-\nalescing binary black holes (BBH) by the Laser Interfer-\nometer Gravitational-Wave Observatory (LIGO) opened\na new window to the Universe (Abbott et al. 2016a). In\naddition to GWs, compact binary mergers with at least\none neutron star (NS) component are likely to gener-\n\u2217Deceased, November 2022.\n\u2020 Deceased, July 2023.\nate electromagnetic (EM) radiation (e.g., Nakar 2020a;\nKyutoku et al. 2021). Coincident detection of EM emis-\nsion from compact binary mergers provides a complete\npicture of the merger process and can have huge im-\nplications for our understanding of the Universe. Such\ncoincidences play a crucial role in tracing the properties\nof the source host galaxy (Troja et al. 2017; Alexander\net al. 2017), mitigating degeneracies in GW parameter\nestimation (Abbott et al. 2017a; Hughes & Holz 2003;\nWang & Giannios 2021), placing constraints on the NS\nequation of state (Bauswein et al. 2017; Radice et al.\n\n12\n2018), and investigating the expansion rate of the Uni-\nverse, thereby testing cosmological models (Abbott et al.\n2017a,b; Hotokezaka et al. 2019; Nissanke et al. 2013;\nSchutz 1986). Additionally, they allow for the measure-\nment of arrival time differences between photons and\ngravitons, providing limits to the mass of a graviton,\nexploring potential violations to the equivalence princi-\nple and Lorentz invariance (Abbott et al. 2017e).\nThe joint detection of the first GW event consistent\nwith a binary NS (BNS) coalescence GW170817 (Ab-\nbott et al. 2017a), and a coincident short gamma-ray\nburst GRB 170817A (Goldstein et al. 2017a; Savchenko\net al. 2017), accompanied by the optical/infrared kilo-\nnova counterpart AT 2017gfo (Arcavi et al. 2017; Coul-\nter et al. 2017; Tanvir et al. 2017; Evans et al. 2017;\nPian et al. 2017; Smartt et al. 2017; Drout et al. 2017;\nCowperthwaite et al. 2017) and the GRB afterglow (in\nthe X-rays: Troja et al. 2017; Margutti et al. 2017 and\nradio: Hallinan et al. 2017), together ushered in a new\nera in the field of multi-messenger astrophysics and for-\never impacted our comprehension of compact binary co-\nalescences (CBC) involving an EM counterpart. Mas-\nsive coordinated EM follow-up efforts were dedicated\nto deeply monitor the error regions derived from the\njoint sky localization of GW detectors and high-energy\nsatellites, helping to reduce the initial three detector\nnetwork sky localization from 28 deg2 to within a few\narcseconds of the host galaxy NGC 4993 (Abbott et al.\n2017d,a). The spectacular spectral and light curve evo-\nlution of this transient (Abbott et al. 2017d; Villar et al.\n2017) suggested that this explosive event was an ac-\ntive site for r-process nucleosynthesis (Pian et al. 2017;\nSmartt et al. 2017; Coulter et al. 2017; Drout et al. 2017)\n(for a detailed review of the multimessenger observa-\ntions of GW170817, see, e.g., Nakar 2020b; Margutti &\nChornock 2021).\nThe expected EM counterpart emission from BNS\nor neutron star\u2013black hole (NSBH) mergers can poten-\ntially be weak due to various factors such as consider-\nable source distances, an off-axis viewing angle, or lim-\nited amount of ejected mass.\nFor the specific case of\nGW170817, despite a coincident GRB detection, it took\nnearly half a day to localize the host galaxy and be-\ngin observations of the kilonova (Abbott et al. 2017a).\nPrompt targeted searches around the GW trigger times,\nleveraging facilities with enhanced localization capabil-\nities, can refine search strategies and assist optical or\ninfrared (IR) facilities in correctly identifying and pursu-\ning transient candidates for subsequent follow-up stud-\nies. In addition to prompt searches, Fermi-GBM anal-\nysis of triggers from the first and second LIGO\u2013Virgo\nobserving runs showed that targeted offline searches are\ncapable of recovering additional candidate joint events\nthat may be of astrophysical relevance (Hamburg et al.\n2020; Pillas et al. 2023). Temporal and spatial coinci-\ndence information can be used to derive the joint false\nalarm rate (FAR). These estimates have the potential to\nelevate subthreshold triggers in either the GW or GRB\ndomains to the status of an above-threshold candidate\ndetection (Nitz et al. 2019).\nUnlike Fermi, Swift has been for a long time inca-\npable of relaying a continuous stream of event mode data\nto the ground in real time. Such a capability was en-\nabled through GUANO (Gamma-ray Urgent Archiver\nfor Novel Opportunities, described in Section 2) (To-\nhuvavohu et al. 2020), which recovers event data from\nthe Swift Burst Alert Telescope (BAT, Barthelmy et al.\n2005), that then get processed by the Non-Imaging\nTransient Reconstruction And TEmporal Search (NI-\nTRATES, DeLaunay & Tohuvavohu 2022) pipeline (see\nSection 4) to search for subthreshold transient candi-\ndates.1\nIn addition to other astronomical transients,\nsuch as GRBs, fast radio bursts (FRBs), and high-\nenergy neutrinos, the GUANO-NITRATES infrastruc-\nture performs targeted searches on GW events commu-\nnicated by the LVK Collaboration, to detect possible\nGRBs associated with CBCs.\nThe impact and potential of Swift-BAT subthreshold\nsearches are crucial for multi-messenger related goals.\nIndeed, deeper targeted searches increase the joint de-\ntection horizon, thus enhancing the probability of find-\ning weak EM counterparts of CBCs in the hard X-ray\ndomain. Moreover, thanks to the high spatial accuracy\nenabled by the BAT coded mask, subthreshold searches\nopen the possibility of recovering the position of the\ncandidate EM event at the precision level of a few arc-\nminutes, fundamental to drive the subsequent follow-up\nwith ground and space-based EM facilities.\nCurrently, the targeted search analysis carried out\nthanks to GUANO, has enabled the discovery of more\nthan 35 GRBs with arcminute localization. A total of 7\nof the detected GRBs have a duration < 2 s (e.g., De-\nLaunay et al. 2020; Tohuvavohu et al. 2022a), hence they\nare potentially associated with CBCs containing at least\none NS. GUANO data have also been used for the local-\nization of 29 long GRBs through imaging (e.g., DeLau-\nnay et al. 2021a) and non-imaging analysis techniques\n(e.g., DeLaunay et al. 2021b; Tohuvavohu et al. 2022b).\nGRB 220107A, detected during BAT slew and localized\n1 Live reporting of the status of the real time Swift-BAT subthresh-\nold analysis can be found at https://guano.swift.psu.edu, where\nthe user can monitor all the triggers ingested by GUANO and\nvisualize the main results of the NITRATES analysis.\n\n13\nwith arcminute precision, enabled the first optical red-\nshift measured using GUANO data (DeLaunay et al.\n2022a).\nThe arcminute localization of GRB 211106A\nenabled prompt multiband follow up and led to the dis-\ncovery of the first afterglow in the millimeter band from\na short GRB (Tohuvavohu et al. 2021a). With GUANO,\none can additionally recover coarse localization informa-\ntion on GRB-like transients that originate from outside\nthe BAT field of view (FOV; e.g., DeLaunay et al. 2023).\nIn addition to the application to real-time analysis,\nthe availability of BAT data enables us to perform a\nsystematic, deeper targeted search focused on archival\nLVK triggers.\nThe goal of this study is to perform\nsuch an analysis on all the LVK triggers received dur-\ning the third LIGO\u2013Virgo observing run, during which\nthe GUANO pipeline started to be fully operational.\nThe run duration was comprised of two segments: O3a,\nwhich operated from April 1, 2019, 15:00 UTC to Oc-\ntober 1, 2019, 15:00, and O3b which operated from\nNovember 1, 2019, 15:00 UTC, to March 27, 2020, 17:00\nUTC. The alerts distributed during O3 were reporting\nthe following parameters: FAR, the signal classification\n(CBC or unmodeled Burst), and the associated astro-\nphysical probabilities.\nThe results of O3 are summa-\nrized in Gravitational-Wave Transient Catalog data re-\nleases GWTC-2 (Abbott et al. 2021), GWTC-2.1 (Ab-\nbott et al. 2024), and GWTC-3 (Abbott et al. 2023).\nIn this work, we use Swift-BAT observations to carry\nout offline targeted subthreshold searches for EM coun-\nterparts of the GW triggers obtained during O3. The\nrest of the paper is organized as follows: In Section 2,\nwe describe the Swift-BAT instrument and its new ca-\npabilities, and in Section 3, we provide details about the\nGW trigger sample used for the analysis. In Section 4\nwe summarize the targeted search method adopted for\nthe analysis. We present the results from our targeted\nsearch analysis on the various subcategories of triggers\nin Section 5, and discuss the scientific interpretation in\nSection 6.\n2. Swift-BAT\nThe Neil Gehrels Swift\nObservatory (henceforth,\nSwift) is a GRB-focused mission launched in 2004, with\nthree onboard payloads \u2013 the Burst Alert Telescope\n(BAT), the X-ray Telescope (XRT), and the UltraVio-\nlet/Optical Telescope (UVOT) \u2013 covering the EM spec-\ntrum from hard X-rays and gamma-rays all the way to\nthe optical (Gehrels et al. 2004). The BAT instrument\n(Barthelmy et al. 2005) is a hard X-ray coded mask im-\nager with a wide FOV that operates in the broad energy\nband of 15\u2013350 keV. It is the primary instrument that\ndetects GRBs and performs an onboard imaging anal-\nysis via a cross-correlation between the spatial pattern\nof the counts across the detector array and the pattern\nof the coded mask. The sensitivity of BAT is capable\nof providing arcminute localizations of GRBs triggered\nonboard (Gehrels et al. 2004). Due to the lack of con-\ntinuous downlinking of timing, spatial, and energy in-\nformation for each detector count (event mode data),\ncarrying out targeted searches offline has not been pos-\nsible in the past. A new infrastructure, called GUANO,\nwas incorporated into the Swift-BAT operations in 2019.\nDetails of the GUANO operations can be found in To-\nhuvavohu et al. (2020). From the outset, GUANO has\ndemonstrated that recovering event mode data from as-\ntrophysically compelling time windows can enhance the\noverall transient detection rate and sensitivity of BAT\n(Tohuvavohu et al. 2020).\n3. GRAVITATIONAL-WAVE TRIGGER SAMPLE\nThis paper focuses on the Swift-BAT subthreshold\nanalysis of a sample of GW triggers with a FAR<2\nper day, distributed by the LVK Collaboration dur-\ning O3. The subthreshold GW alerts were received by\nthe EM follow-up groups that were part of a Memo-\nrandum of Understanding with the LVK Collaboration.\nFor candidates found with CBC search pipelines (Dal\nCanton et al. 2021; Sachdev et al. 2019; Messick et al.\n2017; Aubin et al. 2021; Nitz et al. 2018; Hooper et al.\n2012) and Burst search pipelines (Klimenko et al. 2005,\n2016), the alerts contain basic information about the\nGW FAR, the probability of the candidate being astro-\nphysical (pastro) and trigger time. In the case of CBC\ncandidates, the alerts received in low latency report the\npastro split in the four CBC classes: BBH, BNS, NSBH,\nand Mass Gap. The Mass Gap category includes CBC\ncandidates in which at least one component has a mass\nin the range [3\u20135] M\u2299. Using the GW trigger informa-\ntion received in low latency, we can further perform a\nsearch for associations in BAT data.\nFrom the list of 1552 alerts that were communi-\ncated via low latency channels, we obtained successful\nGUANO data dumps for 636 triggers. The GW infor-\nmation of the candidates received in low latency are re-\nported in Table 1. The FAR and the pastro classification\nreported here correspond to the preferred event, namely\nthe one with the highest SNR. Swift-BAT event mode\ndata coincident with the GW trigger time were made\navailable for these triggers in real time via the GUANO\ndata dumps. Post-processing on the data was carried\nout on this sample from O3 using the NITRATES anal-\nysis pipeline (see Section 4).\nOut of the 636 low-latency alerts, a total of 86 GW\ncandidates have been confirmed by the offline analysis\n\n14\nand included in the GWTC-2.1 and GWTC-3 data re-\nleases (Abbott et al. 2024; Abbott et al. 2023). Among\nthe 86 confirmed candidates, 14 triggers have pastro >\n0.5 and 72 triggers have pastro < 0.5. We indicate the\ndetails of the confirmed candidates with pastro > 0.5\nand pastro < 0.5 in Table 2 and Table 3, respectively.\nThe values of FAR, pastro and CBC Class given in Ta-\nble 2 and Table 3 are derived from offline analyses,\nas reported in GWTC-2.1 and GWTC-3 data releases,\nhence are considered more reliable than the values ob-\ntained in low latency, reported in Table 1. The FAR\nand the pastro classification reported in Tables 2 and 3\ncome from the pipeline that gives the highest value of\npastro. For high significance events, if multiple pipelines\nderive a pastro \u22431, we select the one with highest SNR.\nAccording to these rules, in the case of S200225q, re-\nported in Table 2, the selected pipeline is cWB, but the\nevent is classified as CBC. The CBC class is determined\nby the highest among pBBH, pNSBH and pBNS. In Ta-\nbles 2 and 3 we report the value of pClass defined as\nmax[pBBH, pNSBH, pBNS]. It is possible that some candi-\ndates marked as \u201cBurst\u201d in Table 1 are then re-classified\nas \u201cCBC\u201d by the offline analysis. Therefore, for each\ncatalog event the most updated group is the one re-\nported in Tables 2 and 3.\nIn Figure 1 we show the histograms of the pastro prob-\nabilities for all the low-latency CBC candidates pro-\ncessed by GUANO, for a total of 424 candidates, di-\nvided into 67 BBH, 130 BNS, 148 NSBH, and 79 Mass\nGap events (Fig.\n2, left panel).\nIn the offline post-\nprocessing of GW candidates, the Mass Gap classifica-\ntion was removed, classifying an object with M > 3M\u2299\nas a black hole. This implies that all the CBC events\nwith at least one component mass in the range [3\u22125]M\u2299\nare re-distributed into the BBH and NSBH classes. The\ndistribution of the updated pastro classification released\nby LVK is over-plotted in Figure 1, and the classes are\ndivided in 39 BBH, 22 BNS and 17 NSBH candidates\n(Fig. 2, right panel).\n3.1. GW sky localization\nFor the selection of the GW sky localization for each\ncandidate we adopt the following scheme:\n1. Above\u2013threshold GW candidate: The GW can-\ndidate is contained in the list of high-probability\n(pastro > 0.5) candidates reported in Table 2 of\nGWTC-2.1 (Abbott et al. 2024) or Table 1 of\nGWTC-3 (Abbott et al. 2023). The GW sky lo-\ncalizations are downloaded from the parameter es-\ntimation data releases of GWTC-2.1 and GWTC-\n3.2\nWe use the results derived from a combina-\ntion of IMRPhenomXPHM (Pratten et al. 2021)\nand SEOBNRv4PHM (Ossokine et al. 2020) wave-\nforms (labeled as \u2018Mixed\u2019 in the release).\n2. Subthreshold GW candidate: The GW candidate\nis classified as low-probability (pastro < 0.5) in\nthe offline analysis. The GW sky localization is\nproduced by BAYESTAR (Singer & Price 2016;\nSinger et al. 2016) and is taken from the GWTC-3\nrelease, which contains both O3b events and up-\ndated O3a events. If multiple events are present\nfor a single GW candidate, the pipeline with the\nhighest pastro is considered for the selection of the\nsky localization.\n3. Non-confirmed low-latency GW candidate: The\nGW candidate has an associated low-latency alert,\nbut the event has not been confirmed by the offline\nanalysis. The GW sky localization is downloaded\nfrom GraceDB, selecting the preferred event.\n4. TARGETED SEARCHES USING\nGUANO-NITRATES\nTargeted searches are carried out in real time for\nall types of transients such as GRBs, FRBs, neutrino\nevents as well as GW triggers, on the event mode data\nobtained using GUANO. The targeted search pipeline\nthat is currently operational is NITRATES. This is\na maximum\u2013likelihood framework that forward models\nsignals through the entire instrument response (DeLau-\nnay & Tohuvavohu 2022). The BAT responses are cre-\nated by simulating the photon paths through all detector\nsegments using Geant4, which is a particle-interaction\nsimulator software toolkit (Allison et al. 2016). Unlike\nthe standard BAT responses, the NITRATES responses\naccount for all the detectors on the focal plane, regard-\nless of their coding by the mask. The responses also en-\ncode details on the gamma-ray interactions inside the in-\nstrument, which carry additional information. This ap-\nproach enables substantial sensitivity gain compared to\nthe conventional technique of cross-correlation imaging,\nwhich translates to a 50% increase in the detection hori-\nzon distance for a GRB 170817A-like burst compared\nto the onboard imaging. Details of the NITRATES re-\nsponse generation and the analysis pipeline are provided\nin DeLaunay & Tohuvavohu (2022).\nA GRB-like transient signal is described using the sky\nlocalization and parameters that are specific to the as-\nsumed spectral model (the peak energy and spectral\n2 GWTC-2.1\nrelease\nhttps://doi.org/10.5281/zenodo.6513631,\nGWTC-3 release https://doi.org/10.5281/zenodo.8177023\n\n15\nReceived in low-latency\nCon\ufb01rmed by o\ufb04ine analysis\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10[pBBH]\n5\n10\n15\n20\n25\n30\n35\n40\nFrequency\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10[pNSBH]\n5\n10\n15\n20\n25\n30\n35\n40\nFrequency\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10[pMass Gap]\n5\n10\n15\n20\n25\n30\n35\n40\nFrequency\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10[pBNS]\n5\n10\n15\n20\n25\n30\n35\n40\nFrequency\nFigure 1. Distribution of the pastro values for the CBC triggers detected during O3, with available GUANO data dumps. We\ndistinguish with different colors the triggers received in low latency and the ones confirmed by offline analysis.\nBBH\n67\n(15.8%)\nBNS\n130\n(30.7%)\nNSBH\n148\n(34.9%)\nMass Gap\n79\n(18.6%)\nLow latency (online)\nBBH\n39\n(50.0%)\nBNS\n22\n(28.2%)\nNSBH\n17\n(21.8%)\nPost processing (o\ufb04ine)\nFigure 2. Left: distribution of the CBC triggers from O3 received in low latency, which had successful GUANO data dumps,\ndivided in the BBH, NSBH, BNS, and Mass Gap classes. Right: analogous distribution for the CBC candidates confirmed by\nthe offline analysis. In the post-processing, the Mass Gap classification has been subsumed into BBH and NSBH.\n\n16\nslope). This framework then computes the significance\nof each signal using a test statistic (TS) by maximiz-\ning the log-likelihood (LLH) as a function of signal pa-\nrameters. The likelihood ratio test statistic \u039b is used\nto compare the source signal+background model (de-\nscribed using a set of parameters, \u0398sig that maximizes\nthe LLH) to a background-only model (described by the\nset of parameters \u0398off\nbkg, that maximizes the LLH in the\noff-time window) and is defined as follows (DeLaunay &\nTohuvavohu 2022):\n\u039b = \u22122[LLH(\u0398off\nbkg|Non) \u2212LLH(\u0398sig, \u0398off\nbkg|Non)],\n(1)\nwhere N on is on-time data.\nThe search pipeline workflow can be summarized as\nfollows:\n1. The event mode data is cleaned and filtered to\ndiscard potential glitches and artifacts from cosmic\nrays, and to flag poorly behaving detectors. Good\ntime intervals (GTIs) are determined, where there\nis quality data for the analysis.\n2. A time window of 50 s (from the pre- and post-\ntrigger intervals) is identified as the background\ninterval. It is then utilized to model contributions\nto the background from known bright sources and\ndiffuse sources.\n3. To narrow down the search parameter space, a set\nof simple analyses are performed to select a list\nof interesting start times and durations (hereafter\nreferred to as time seeds) as well as portions of the\nBAT FOV (position seeds).\n4. Finally, the log-likelihoods are computed for all\nparameters corresponding to the shortlisted time\nand position seeds.\nIn essence, the set of signal parameters that maximizes\nthe log-likelihood is the most preferred set of parame-\nters.\nThe NITRATES likelihood analysis outperforms the\nonboard mask-weighted imaging analysis by delivering\nsuperior sensitivity, given the increased effective area\n(see Fig. 2 in DeLaunay & Tohuvavohu 2022). At the\ncost of a significantly increased computational time, this\nmethod is capable of delivering arcminute scale localiza-\ntion for events that fall inside the BAT FOV, even when\nthe transient event does not trigger Swift-BAT onboard\n(Tohuvavohu et al. 2021b; Tohuvavohu 2023; DeLaunay\net al. 2022b).\nThe NITRATES pipeline has the abil-\nity to distinguish between bursts that come from in and\noutside the BAT FOV. NITRATES has also accurately\nlocalized sufficiently bright bursts outside the FOV (De-\nLaunay & Tohuvavohu 2022).\nSwift-BAT GUANO was operating during the O3 and\nwas successfully procuring event mode information in re-\nsponse to GW subthreshold triggers (Tohuvavohu et al.\n2020).\nWe describe the targeted search analysis that\nhas been carried out using the NITRATES version 0.0.1\nwhich was available in early 2022.3 The targeted search\nanalysis that was operational in O3 corresponded to a\npreliminary version of the NITRATES code, that has\nsince undergone several stages of development.\nThe\nmost updated version is publicly available on GitHub.4\nDuring O3, for a total of 636 GW triggers, GUANO\ndumped either 200 s or 90 s of event mode data, for\npublic triggers and for privately communicated triggers,\nrespectively. The choice of the width of the temporal\nwindow is made to avoid an overload of downlink data in\nthe process of GUANO data dump. The targeted search\npipeline was run in a time window of \u00b120 s centered\naround the trigger time. The search was carried out on\n8 time bins (0.128 s, 0.256 s, 0.512 s, 1.024 s, 2.048 s,\n4.096 s, 8.192 s and 16.384 s) and 9 energy bins (between\n15\u2013350 keV). The results from the search are reported\nusing the following set of parameters: 1) the maximum\n\u221a\nTS describes the statistical significance of a potential\ndetection (see Section 5); 2) \u2206LLHout indicates the pref-\nerence of the search to a location inside or outside the\nBAT FOV, and 3) \u2206LLHpeak indicates the confidence of\nthe search in localizing the source to arcminute scales.\nThe maximum\n\u221a\nTS is empirically mapped to a FAR\nusing the distribution of\n\u221a\nTS values found from analyz-\ning 51 ks of random data (see sec. 7.6 in DeLaunay &\nTohuvavohu 2022).\nThe NITRATES search was performed on the ROAR\nsupercomputing cluster on a set of 200 virtual cores for\na total of \u223c600 \u00d7 800 CPU hours for the entire GW\nsample.\n5. RESULTS FROM NITRATES\nThe targeted search analysis provides a list of top can-\ndidates whose spatial, temporal, and spectral parame-\nters maximize the log-likelihood. In order for a candi-\ndate to be qualified as a confident detection, we require\nthat the resulting detection significance parameter\n\u221a\nTS\nmust exceed the threshold value of 8, corresponding to\na FAR \u223c4 \u00d7 10\u22125 Hz. Being a targeted search, the NI-\nTRATES analysis can give a false positive with\n\u221a\nTS > 8\nwith a probability which follows a Poissionian distribu-\n3 https://github.com/Swift-BAT/NITRATES/tree/py2\n4 https://github.com/Swift-BAT/NITRATES\n\n17\ntion:\nP(Ndet \u22651) = 1 \u2212P(Ndet = 0) = 1 \u2212e\u2212FAR\u00d7\u2206t, (2)\nwith \u2206t = 40 s being the width of the search window.\nThis leads to a pre-trial p-value of 1.6 \u00d7 10\u22123. Since the\nNITRATES analysis is performed on all GW triggers\nwith a FAR < 2 day\u22121, and considering that there are\nNGW\u2212search = 5 independent GW pipelines, the rate of\nexpected false positive candidates falling within the tem-\nporal search window around a GW trigger with\n\u221a\nTS > 8\nis \u223c5 \u00d7 2 \u00d7 1.6 \u00d7 10\u22123 /day \u223c1/(60 day).5\nFor the entire sample of 636 low-latency triggers pro-\ncessed using NITRATES, we have no candidates that\nqualify as detection of a signal of astrophysical origin.\nNone of the top candidates within the \u00b120 s search win-\ndow are coincident with the GW triggers.\nA tempo-\nral coincidence with a GW trigger is claimed if the NI-\nTRATES search finds a candidate with\n\u221a\nTS > 8 and\n|t0 \u2212tstart| < 20 s, where t0 is the GW trigger time\nand tstart is the starting time of the temporal bin with\nhighest ranking statistics. A detailed list of all the NI-\nTRATES results for the entire sample analyzed during\nO3 is provided in Table 1. We discuss specific false pos-\nitive candidates in Section 5.1.\nIf the GW trigger time is included in the time window\ncorresponding to slew mode of BAT, the analysis can-\nnot be performed using NITRATES since the targeted\nsearch requires stable attitude information to compute\nthe background. Similarly, some triggers have insuffi-\ncient exposure time, preventing the NITRATES analy-\nsis. In this case neither TS results nor flux upper limits\ncan be computed.\nAs a cut to narrow down the pa-\nrameter space, the targeted search selects time seeds as\ndescribed in Section 4. If there are no time seeds that\npass the preliminary cuts then there will be no final like-\nlihood computations. Results for these types of triggers\nare indicated as NFL (No Final Likelihood) in Table 1.\nIn the case of NFL triggers, though, the flux upper limit\ncan be computed, since a full likelihood analysis is not\nrequired.\n5.1. False positives\nWe did not find any candidate associations from any\nof the triggers with BAT. However, the targeted search\npipeline did result in the detection of six candidates with\na significance above the NITRATES detection thresh-\nold of\n\u221a\nTS = 8.\nThese candidates were examined\nto understand our false positive population. S200327j\n5 Since the GW pipelines are not totally independent, a realistic\nvalue of NGW\u2212search is likely below 5, leading to an overall rate\nof false NITRATES candidate below 1/(60 day).\n(\n\u221a\nTS \u223c22), S200324ax (\n\u221a\nTS \u223c11), and S200225af\n(\n\u221a\nTS \u223c10.5) are triggers that occurred during the\npassage of Swift in the proximity of the South Atlantic\nAnomaly (SAA). The background characterization be-\ncomes unreliable when the spacecraft is either entering\nor leaving the SAA on account of increased background\ncontamination. Analyses close to the SAA are not con-\nsidered to be during good data times and are not ac-\ncounted for in the NITRATES FAR distribution. The\npipeline expanded into these not good data times to\nsearch for any exceptional signals.\nS200130ai corresponds to a subthreshold GW trigger\nat T0 = 2020-01-30T09:59:58 that was identified by the\nCBC search as a NSBH candidate with a pastro = 0.008\nand a GW FAR \u223c1.8\u00d710\u22125 Hz. It was detected us-\ning NITRATES at a significance of\n\u221a\nTS \u223c16.3 with\na \u2206LLHout = \u221219.68 and \u2206LLHpeak = 2.14, consis-\ntent with a sky localization outside the BAT-FOV. The\nhighest log-likelihood candidate, was identified to arise\n1.5 s prior to the GW trigger time.\nDue to the low\nvalue of \u2206LLHpeak, we do not have an arcminute-level\nprecision on the sky localization. The candidate was as-\nsociated with a Fermi trigger 602071201 (GCN 26944,\nFermi GBM Team 2020) and was classified as a long\nGRB. The Fermi localization is RA = 137.5 deg, Dec\n= \u221251.3 deg, with a statistical uncertainty of 3.5 de-\ngrees.\nThe Interplanetary Gamma-Ray Burst Timing\nNetwork (IPN) further localized the event in a 3-sigma\nerror box with an area of 1487 arcmin2 and centered at\nan RA = 134.742 deg and Dec = \u221249.627 deg (Hurley\net al. 2020). Although this event presents a temporal\ncoincidence with the GW trigger, on account of the lack\nof spatial coincidence with the GW location, this event\nis discarded from being associated with the GW sub-\nthreshold trigger.\nAdditionally, this low-latency GW\ncandidate has not been confirmed by offline analyses.\nIn S190919au, a peculiar dip (\u223c20 s) in the back-\nground may have contributed to a false elevation in the\nsignal detection statistic, by causing an under represen-\ntation of the background rate. For S190919u, we obtain\na\n\u221a\nTS \u223c8.0, which corresponds to a FAR of \u223c4\u00d710\u22125\nHz. Including the two events confirmed to be unrelated\nto their corresponding GW trigger, the search identi-\nfied three events with\n\u221a\nTS > 8 during good data times.\nThis is compatible with the Poissonian error bars of the\nexpected number of false positives, which corresponds\nto (4 \u00d7 10\u22125 Hz) \u00d7(40 s)\u00d7 636 GW triggers \u223c1. Addi-\ntionally, there is substantial uncertainty on the empir-\nically derived NITRATES FAR at\n\u221a\nTS \u22738.0 due to\nlow statistics (see Fig. 16 in DeLaunay & Tohuvavohu\n2022). Including the finite statistics used to determine\n\n18\nthe NITRATES FAR, the 90% confidence interval on\nthe expected number of false positives is 0.1 - 3.1.\n5.2. Computation of flux upper limits\nSince each GW trigger processed in this analysis re-\nsulted in a non-detection in Swift-BAT, we estimate\nthe flux upper limits in the following manner.\nThe\nNITRATES analysis generates rates curves in the 15\u2013\n350 keV energy band from the GTIs of the filtered event\nlist. The number of active detectors corresponding to\neach trigger is read out from its respective detector mask\nfile. A linear fit is carried out to the background window\nof duration 50 s. We then estimate the 5\u03c3 count rate\nand the corresponding uncertainty over the full signal\nwindow which has a \u00b120 s duration. This is computed\nfor all the 8 time bins (see Section 4). We further con-\nvert the 5\u03c3 count rates to flux upper limits, as a function\nof sky position, in the 15\u2013350 keV band, by convolving\ndifferent spectral models with the NITRATES responses\nfor each time bin iteration. We select 929 grid points on\nthe sky and interpolate upper limit values for locations\nin between. We assume the following different spectral\ntemplates:\n1. Band function (Band et al. 1993) with a soft tem-\nplate (Epeak = 70 keV, \u03b1 = \u22121.9, \u03b2 = \u22123.7)\n2. Band function with a normal template (Epeak =\n230 keV, \u03b1 = \u22121.0, \u03b2 = \u22122.3)\n3. Cutoff power law function with a hard template\n(Epeak = 1500 keV, \u03b1 = 1.5)\n4. Cutoff power law function that has been used to\ndescribe GRB 170817A (Epeak = 185 keV, \u03b1 =\n0.62) (Goldstein et al. 2017b)\nThe parameters \u03b1 and \u03b2 correspond to the low-energy\nand high-energy photon indices of the spectrum, respec-\ntively. The first three spectral templates are identical\nto the ones that are routinely adopted by Fermi-GBM\n(Goldstein et al. 2016a). In the rest of the paper, all the\nresults are reported assuming a Normal spectral tem-\nplate.\nCalling \u2126= (RA, Dec) the coordinates variable, for\neach temporal bin and spectral template we convert the\nupper limit map \u03d5UL(\u2126) into a unique marginalized up-\nper limit value:\n\u03d5UL =\nZ\n\u2126/\u2208\u2126\u2295\n\u03d5UL(\u2126)PGW(\u2126)d\u2126,\n(3)\nwhere PGW(\u2126) is the posterior probability distribution\nof the GW sky position. The notation \u2126/\u2208\u2126\u2295means\nthat the integral is limited to the region of the sky\nnot occulted by the Earth. We report in Table 1 the\nmarginalized flux upper limits for a 1 s time bin, assum-\ning the normal spectral template. In Fig. 3, we provide\nthe sky maps reporting both the flux upper limits as\na function of sky position and the GW contours (50%\nand 90% credible levels) for the GW candidates with\npastro > 0.5.\nAs additional information, we also report the quantity\n\u03b5in BAT, which quantifies the probability that the GW\nsource is inside the BAT coded FOV and corresponds to\n\u03b5in BAT =\nZ\n\u2126\u2208\u2126in\nPGW(\u2126)d\u2126,\n(4)\nwhere the integral is limited to the solid angle \u2126in,\nnamely the portion of the sky where the BAT partial\ncoding fraction is larger than 0.01. The location of \u2126in,\ni.e., the BAT FOV, is identified by the yellow region in\nthe sky maps of Figure 3. The higher the \u03b5in BAT, the\nbetter the BAT covering of the GW error region, and\nthe more constraining the derived upper limit. The flux\nupper limits as a function of \u03b5in BAT for all GW trigger\ncandidates is shown in Fig. 4. We also indicate with\ndifferent markers the sample of low-latency triggers, the\nconfirmed list of subthreshold candidates (pastro < 0.5),\nand the above-threshold candidates (pastro > 0.5). In\nTable 1 we also report the probability that the GW\nsource is occulted by the Earth, defined as:\n\u03b5\u2295=\nZ\n\u2126\u2208\u2126\u2295\nPGW(\u2126)d\u2126,\n(5)\nwhere \u2126\u2295is the solid angle subtended by the Earth from\nthe Swift reference system.\n5.3. Computation of luminosity upper limits\nWe further convert the flux upper limits into luminos-\nity upper limits for all the GW triggers with available\ninformation about the distance posterior distribution,\nnamely only triggers identified by CBC searches. The\nluminosity upper limit in the rest frame band 1 keV\u2013\n10 MeV is estimated as\nLUL = \u27e84\u03c0D2\nLk\u03d5UL\u27e9,\n(6)\nwhere DL is extracted from the posterior probability\nP(DL) reported in the GW sky localization files, while\nk is the k-correction and corresponds to\nk = I[1 keV/(1 + z), 10 MeV/(1 + z)]\nI[15 keV, 350 keV]\n,\n(7)\nwhere\nI[a, b] =\nZ b\na\nE dN\ndE (E)dE,\n(8)\n\n19\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S190701ah ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S190915ak ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S191204r ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S191216ap ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200128d ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200129m ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\nFigure 3. Flux upper limit maps are shown for all the O3 catalog events with a pastro > 0.5 that were processed successfully\nusing NITRATES. The color bar indicates the upper limit in the 15\u2013350 keV Swift-BAT band as a function of the sky position.\nThe part of the sky in white corresponds to the area covered by the Earth. The solid and dashed contours are the GW 90%\nand 50% credible levels, respectively.\nand dN/dE is the assumed photon spectrum. The band\n1 keV\u201310 MeV is chosen since it is usually adopted to\nreport the bolometric luminosity of GRBs.\nThe luminosity upper limits as a function of the mean\nvalue of the luminosity distance is reported in Figure 5.\nSimilar to what was shown previously, we demarcate the\nvarious samples. Candidates with a low latency classi-\nfication of Mass Gap were later re-distributed to other\ncategories as part of post-processing, which is evident\nfrom the Mass Gap panel in Figure 5. As expected and\nas evident already from Figure 4, we see a clear corre-\nlation between the luminosity upper limit and \u03b5in BAT\nin Figure 5, indicating that the inferred constraints on\nthe EM counterpart are more stringent when the GW\nprobability integrated inside the BAT FOV is higher.\nSince \u03d5UL is an upper limit and not a measure coming\nfrom a detection, Eq. (6) is an approximated method\nto convert \u03d5UL in a luminosity upper limit, averaging\nover the P(DL) distribution provided by the GW anal-\nysis. In Appendix A we show a more accurate way to\nestimate the luminosity upper limit, but we find no rel-\nevant differences with respect to the method reported\nin this section.\nThe Eq. (6) is used only to produce\nthe plots of Fig. 5, but this approximation is not used\nin Section 6 to perform inference about the EM model\nparameters. Instead, in Section 6 a reverse process is\nfollowed, namely the EM model is used to predict the\nluminosity, which is then convolved with P(DL) to ob-\ntain a probability distribution of the flux in the BAT\nenergy band.\n5.4. Computation of joint FAR\n\n20\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200208q ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200216br ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200220ad ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200225q ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22126\n10\u22125\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200302c ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\n0\u25e6\n315\u25e6\n270\u25e6\n225\u25e6\n180\u25e6\n135\u25e6\n90\u25e6\n45\u25e6\n0\u25e6\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n0\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nevent = S200322ab ,\ntemporal bin = 1.024 s, spectrum = normal\n10\u22127\n10\u22126\nFlux upper limit (erg cm\u22122 s\u22121)\nFigure 3. (continued)\nTo calculate the joint GW\u2013BAT FARs for each GW\ntrigger, we elaborate on the methods used to compute\nthe individual FARs and subsequently combine them.\nTo derive the sensitivity of the NITRATES search, time-\ntagged event data assembled from intervals correspond-\ning to calibration runs and data from before and after\nknown GRB signal times (total exposure time of \u223c51 ks)\nwere analyzed. The behavior of the background popula-\ntion and its associated FAR were then identified (see\nSection 7.6 and Fig. 16 in DeLaunay & Tohuvavohu\n2022). We further compute the joint Swift-BAT\u2013GW\nFAR by combining the BAT FAR (calculated using the\nmethod described above) with the GW FAR. A tar-\ngeted joint FAR threshold routine is constructed as part\nof the Rapid, on-source VOEvent Coincident Monitor\n(RAVEN; Abbott et al. 2017c; Urban 2016), which com-\nbines the FARs obtained from GWs along with those\nfrom BAT and computes the joint temporal as well as\nthe joint spatial FAR. We also specify details of the\nsearch pipeline used in the process, Burst or CBC. The\njoint FAR prescription as reported in the RAVEN doc-\numentation,6 is computed as\nFARGRB+GW = Z\nI\u2126\n\u0014\n1 + ln(Zmax\nZ\n)\n\u0015\n(9)\nwhere Z is the joint ranking statistic given by,\nZ = FARGWFARGRB\u2206t,\n(10)\nZmax = FARGW,maxFARGRB,max\u2206t,\n(11)\nand we adopt \u2206t = 30 s, FARGW,max = 2 day\u22121 and\nFARGRB,max = 10\u22123 Hz. I\u2126is an integral that quan-\ntifies the spatial overlap between the GW localization\nand the GRB localization (Ashton et al. 2018). Even\nif the search of subthreshold candidates in NITRATES\n6 https://lscsoft.docs.ligo.org/raven/joint far.html\n\n21\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b5in BAT\n\u22127.2\n\u22127.0\n\u22126.8\n\u22126.6\n\u22126.4\n\u22126.2\n\u22126.0\n\u22125.8\nlog10[\u03c6UL (erg cm\u22122 s\u22121)]\n50%\n90%\nLow-latency events\nCatalog events with pastro < 0.5\nCatalog events with pastro > 0.5\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n\u03b5\u2295\nFigure 4. The 15\u2013350 keV flux upper limit \u03d5UL derived with NITRATES as a function of \u03b5in BAT, namely the probability that\nthe GW candidate is contained inside the BAT FOV. The plot includes all the GW candidates received during O3, including\nboth Burst and CBC events. With different symbols we distinguish the GW candidates received in low latency and the ones\nconfirmed and included in the O3 catalog, separated in pastro > 0.5 and pastro < 0.5. The dashed and solid red lines are the 50%\nand 90% containment regions of the scatter plot, respectively. The one-dimensional histograms of \u03d5UL and \u03b5in BAT are reported\non the sides. The color bar indicates the value of \u03b5\u2295, the probability that the GW candidate is occulted by the Earth.\nis done in a temporal window [t0 \u221220 s, t0 + 20 s]\naround the trigger time t0, for the RAVEN joint alert\nthe adopted temporal window is [t0 \u221210 s, t0 + 20 s].\nSince none of the BAT candidates analyzed in this work\nhas a confident estimation of the sky localization, we\nadopt a uniform posterior probability on the full sky\nfor the EM candidate.\nHence, by definition, we set\nI\u2126= 1. The candidate triggers a RAVEN alert when the\nFARGRB+GW \u00d7 Nt < FARmax, with Nt being the trials\nfactor of the joint search and FARmax = (1/30) day\u22121\nfor CBC events and FARmax = 1 yr\u22121 for Burst events.\nThe trials factor corresponds to Nt = SGW(SGW + 1),\nwhere SGW is the number of search GW pipelines, 4 for\nCBC events and 3 for Burst events (Piotrzkowski 2022).\nSince the GW pipelines are not fully independent, a re-\nalistic value of the trials factor is smaller than the one\nadopted here, therefore the RAVEN threshold can be\nconsidered as a conservative estimate for the significance\nof a joint detection.\nWe quote the derived joint FARs along with other\ntrigger-specific details only for those triggers with a\nFARGRB,max < 10\u22123 Hz in Table 4.\nWe find that,\nafter rejecting false positives, 2 CBC events pass the\njoint FAR detection threshold to trigger a RAVEN\nalert. Specifically, S191110x (\n\u221a\nTS = 7.2) and S200108p\n(\n\u221a\nTS = 7.4) have a joint FAR of 3.02 \u00d7 10\u22124 yr\u22121\nand 21.3 yr\u22121, respectively. These values are obtained\nconsidering the GW FAR received with the low-latency\nalert. In the offline analysis of the GW candidates, nei-\nther S191110x or S200108p have been confirmed. We\ntherefore conclude that, considering the offline joint\nanalysis of GW and Swift-BAT data, none of the candi-\ndates is eligible to claim a significant joint detection.\nIn Fig. 6 we report the location in the GW FAR -\n\u221a\nTS plane of all the candidates that pass the condi-\ntion FARGW,max <2 day\u22121 and FARGRB,max < 10\u22123\nHz (i.e.,\n\u221a\nTS \u22737), to be considered for a potential\njoint alert. The astrophysical origin of all the candidates\nwith\n\u221a\nTS > 8 has been rejected as discussed in Section\n5.1, and therefore they are not reported in Fig. 6. The\ndashed black and red lines mark the separation line for\nthe event to pass the RAVEN alert threshold, for CBC\nand Burst candidates, respectively. Candidates below\nthose lines would have triggered a RAVEN alert.\n6. SCIENCE DISCUSSION\nIn this section, we describe how the upper limits de-\nrived from the joint subthreshold search can be used to\n\n22\nLow-latency events\nCatalog events with pastro < 0.5\nCatalog events with pastro > 0.5\n102\n103\n104\nDL (Mpc)\n1047\n1048\n1049\n1050\n1051\n1052\nLUL (erg s\u22121)\nBBH\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b5in BAT\n101\n102\n103\nDL (Mpc)\n1046\n1047\n1048\n1049\n1050\nLUL (erg s\u22121)\nNSBH\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b5in BAT\n102\n103\nDL (Mpc)\n1047\n1048\n1049\n1050\n1051\nLUL (erg s\u22121)\nMass Gap\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b5in BAT\n102\n103\nDL (Mpc)\n1047\n1048\n1049\n1050\nLUL (erg s\u22121)\nBNS\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b5in BAT\nFigure 5. Upper limits on the luminosity computed in the rest frame 1 keV\u201310 MeV energy band, as a function of the mean\nluminosity distance extracted from the sky localization map of each GW candidate. The color bar indicates the quantity \u03b5in BAT,\nnamely the probability that the GW candidate is located inside the BAT coded FOV. With different symbols, we distinguish\nthe GW candidates received in low latency and the ones confirmed and included in the O3 catalog, separated in pastro > 0.5\nand pastro < 0.5.\ninfer constraints about possible EM emission from the\nGW candidates. Starting from a model of the EM emis-\nsion, the luminosity in the BAT band can be estimated,\nwhose value will depend on some internal parameters\nof the model (\u03bb1, ..., \u03bbk).\nThe goal is to explore the\nmodel parameter space and test if the estimated flux is\nin agreement with the upper limit constraints derived in\nthis paper.\nFor this purpose, a knowledge of the distance of the\nGW candidate is needed, and the GW sky localization is\nused to extract the posterior distribution P(DL). Since\nonly CBC events have such information, Burst events\nare not considered in this discussion.\nFor the CBC\nevents, we consider a phenomenological model which de-\nscribes the probability distribution of the luminosity L\n(in the 15\u2013350 keV rest-frame)\nP(L) = (1 \u2212f)\u03b4(L = 0) + f\u03a0(L).\n(12)\nHere, the f parameter is a proxy for the EM-bright na-\nture of the event, i.e., given a CBC source described by a\nset of GW parameters \u20d7\u03b8GW, f(\u20d7\u03b8GW) corresponds to the\nprobability that the EM luminosity of the source is non-\nzero. On the other hand, \u03a0(L) is the intrinsic luminosity\nfunction of the EM transient associated with the specific\nCBC class. In the case of BNS and NSBH candidates,\nthe assumption on \u03a0(L) should be informed by our prior\nknowledge of the luminosity function of merger-driven\nGRBs. A detailed study of the impact of this work on\nour knowledge of merger-driven GRBs luminosity func-\ntion will be reported in a follow-up paper. In this sec-\n\n23\n7.0\n7.2\n7.4\n7.6\n7.8\n8.0\n\u221a\nTS\n\u221211\n\u221210\n\u22129\n\u22128\n\u22127\n\u22126\n\u22125\n\u22124\nlog10[GW FAR (Hz)]\nCBC\nCBC - RAVEN alert\nBurst\nFigure 6. Distribution in the GW FAR\u2013\n\u221a\nTS plane of all\nthe triggers which passed the threshold FARGRB < 10\u22123 Hz.\nTriggers in the regions below the black and red dashed\nlines (marked with a green cross) would have triggered the\nRAVEN alert system, for CBC and Burst events, respec-\ntively. The plot does not include all the triggers that have a\n\u221a\nTS > 8 which turned out to be spurious artifacts.\ntion, instead, we focus only on the BBH class, for which\nno strong prior exists for \u03a0(L). For simplicity and in\norder to show the constraining power of our joint sub-\nthreshold search, we assume that the EM process associ-\nated with BBH, if present, produces a universal, viewing\nangle-independent luminosity L0. Therefore, in the sce-\nnario specified above, we have (\u03bb1, ..., \u03bbk) = (f, L0) and\nP(L) = (1 \u2212f)\u03b4(L = 0) + f\u03b4(L \u2212L0) = P(L; f, L0).\n(13)\nOnce the model for the EM emission is specified, the\nprobability distribution of the predicted flux is\nP(\u03d5) = (1 \u2212f)\u03b4(\u03d5 = 0) + fPEM(\u03d5),\n(14)\nwhere PEM(\u03d5) = P(L0/4\u03c0kD2\nL) is the flux probability\ndistribution in the assumption that the source is EM\nbright. Hence, for the i-th candidate, the probability\nthat the predicted flux is below the estimated upper\nlimit \u03d50,i corresponds to\nPi(\u03d5 < \u03d50,i) = (1 \u2212f) + f\nZ \u03d50,i\n0\nPi(\u03d5)d\u03d5,\n(15)\nvalid in the limit in which the GW candidate is assumed\nto be real.\nTherefore, given a candidate GW with a\nprobability of being astrophysical pastro,i = \u03c0i, there are\nonly three possibilities to have a non-detection in BAT:\n1. The source is not astrophysical, with a probability\n1 \u2212\u03c0i;\n2. The source is astrophysical, but it is occulted by\nthe Earth, with a probability \u03c0i\u03b5\u2295;\n3. The source is astrophysical, it is not occulted by\nthe Earth and the predicted flux by the EM model\nis below the BAT upper limit, with a probability\n\u03c0i(1 \u2212\u03b5\u2295)Pi(\u03d5 < \u03d50,i).\nThis allows us to define a non-detection likelihood cor-\nresponding to\nLi = (1 \u2212\u03c0i) + \u03c0i[\u03b5\u2295+ (1 \u2212\u03b5\u2295)Pi(\u03d5 < \u03d50,i)].\n(16)\nAdditionally, there is also the possibility that the GW\nsource is astrophysical, but mis-classified.\nAs we dis-\ncuss later, this has a negligible impact on our analysis.\nIn the case of L0 \u21920, Pi(\u03d5 < \u03d50,i) \u21921, so Li \u21921.\nFor very large values of L0, instead, Pi(\u03d5 < \u03d50,i) \u21920\nand therefore Li \u2192(1 \u2212\u03c0i) + \u03c0i\u03b5\u2295.\nThis last re-\nsult shows how, even if the luminosity predicted by the\nmodel is exceedingly large, a non-detection can occur\nif the GW source is not real (1 \u2212\u03c0i), or if it is real\nbut occulted by the Earth (\u03c0i\u03b5\u2295).\nSince the analy-\nsis is focused only on BBH events, we consider only\nthose candidates that have pBBH > pNSBH, pBNS.\nBy\ndefinition, pBBH + pNSBH + pBNS = pastro and typi-\ncally for the candidates classified as BBH we have that\npBBH \u226bpNSBH, pBNS. The last condition allows us to\nconsider Eq. (16) still valid if we replace \u03c0i with pBBH,i,\nsince the contribution of pNSBH,i and pBNS,i to the non-\ndetection probability is negligible. For all the excluded\ncases that have pBBH < pNSBH, pBNS, we verified that\npBBH \u226a10\u22124, therefore their inclusion in the analysis\nwould contribute minimally to our results.\nGiven the definition of Eq. (16), Li indicates the prob-\nability, given a set of (\u03bb1, ..., \u03bbk) EM parameters, that\nthe BAT upper limit is not violated, taking into account\nthe possible non-astrophysical origin of the candidate\nand also the probability that, even if astrophysical, the\nsource is occulted by the Earth and therefore not de-\ntectable by Swift. Having a collection of E1, ..., EN GW\ncandidates, the posterior distribution of the model pa-\nrameters can be obtained following the Bayes theorem\nP(L0, f|E1, ..., EN)\n(17)\n=\nN\nY\ni=1\nLi\u03c0(L0)\u03c0(f)\n. Z\nN\nY\ni=1\nLi\u03c0(L0)\u03c0(f)dL0df,\nwhere \u03c0(L0) and \u03c0(f) are the prior distributions of L0\nand f. We assume a log-uniform prior for both L0 and f\nin the respective intervals 46 < log10[L0(erg s\u22121)] < 53\n\n24\nand \u22123 < log10(f) < 0. The choice of the prior bound-\naries are poorly informed by theoretical expectations,\nwhich are still affected by large uncertainties. Instead,\nthe priors are chosen on the basis of the typical range\nof upper limit luminosity derived in this work for BBH\nevents and the total number of candidates considered in\nthis analysis. The constraints reported in the following\nmay strongly depend on the choice of the prior bound-\naries. Therefore, the final goal of this simulation, more\nthan deriving strong limits on the putative EM model,\nis to show the predictive power of the present analysis\nin the context of model inference and how this analysis\ncan improve with the addition of more GW events in\nthe future.\nIn the specific case of our simulation, we consider all\nthe GW candidates released in GWTC-3 (Abbott et al.\n2023), including both the above threshold (pastro > 0.5)\nand the subthreshold (pastro < 0.5) candidates. For the\nlatter, we emphasize that the classification of the CBC\ncandidate as BBH merger is valid under the condition\nthat the subthreshold GW event is of astrophysical ori-\ngin. The simulation described in this section is set up in\nsuch a way that this assumption is taken into account\nfor the final constraints of the physical parameters. All\nthe low-latency candidates not confirmed by the offline\nanalysis are not included in the simulation. The con-\nsidered BBH sample with full NITRATES results and\navailable flux upper limits consists of 32 events, 12 of\nwhich with pastro > 0.5.\nIn order to compute numerically the functional behav-\nior of the likelihood, we set up a simulation to evaluate\nP(L0, f|E1, ..., EN) in the full [L0, f] plane defined by\nthe prior boundaries. The details of the simulation setup\nare reported in Appendix B. The results of the simula-\ntion for the sample of above threshold BBH candidates\nare reported in Fig. 7, where the color map indicates\nthe value of L = Q Li, normalized by the maximum\nmax (L) over the full domain. The contour levels defin-\ning the 50% and 90% exclusion regions are reported as\nwell. For comparison, in Fig. 7 we include also the same\ncontour levels obtained with an analysis that considers\nall the BBH candidates without imposing any cut on\nthe pastro. The level of constraining power of the anal-\nysis can be quantified by defining the fraction of the\nfull parameter space excluded with a credibility level \u03b7,\ncorresponding to:\nR\u03b7 = I\u03b7/Itot,\n(18)\nwhere Itot =\nR\ndfdL0, being the integral extended to\nthe full parameters domain, and with\nI\u03b7 =\nZ\nS\ndfdL0,\n(19)\n46\n47\n48\n49\n50\n51\n52\n53\nlog10[L0(erg s\u22121)]\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10(f)\n90%\n50%\n90%\n50%\nAll catalog events\nCatalog events with pastro > 0.5\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nL/max(L)\nFigure 7. Constraints on the two parameters L0 and f of\nthe model for the putative EM counterpart of BBH mergers.\nThe color map reports the likelihood L, for the full analysis\nincluding all the O3 catalog events with pastro > 0.5. L0 is\nin units of erg s\u22121. The thick blue solid and dashed contours\nindicate the exclusion regions in the [L0, f] plane at 90% and\n50% credibility levels, respectively. The magenta solid and\ndashed lines report the same contours, but for an analysis\nthat includes all O3 catalog events, with no cut in pastro.\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10(f)\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nP(log10(f))\nAll catalog events\nCatalog events with pastro > 0.5\nFigure 8. Posterior distribution of log10(f), including the\n50% and 90% upper limits with dot-dashed and dashed lines,\nrespectively. The function is derived from Fig. 7, marginal-\nizing over L0.\ncorresponding to the dimension of the region S of the pa-\nrameter space excluded with a credibility level \u03b7. The\nanalysis performed using only BBH with pastro > 0.5\ngives a R90% = 26.0%, while the analysis performed\nwith the inclusion of subthreshold BBH candidates gives\nR90% = 26.5%. This result indicates that with the in-\n\n25\n46\n47\n48\n49\n50\n51\n52\n53\nlog10[L0(erg s\u22121)]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nP(log10(L0))\nAll catalog events\nCatalog events with pastro > 0.5\nFigure 9. Posterior distribution of log10(L0), including the\n50% and 90% upper limits with the dot-dashed and dashed\nlines, respectively.\nThe function is derived from Fig. 7,\nmarginalizing over f.\nclusion of GW subthreshold events, the analysis allows\nus to exclude a slightly larger portion of the parameter\nspace, with respect to an analysis carried out using only\nevents with high pastro.\nFigs. 8 and 9 report the posterior distribution of P(f)\nand P(L0), respectively, obtained as:\nP(f) =\nZ\nP(L0, f|E1, ..., EN)dL0\n(20)\nand\nP(L0) =\nZ\nP(L0, f|E1, ..., EN)df.\n(21)\nBoth\nP(L0)\nand\nP(f)\nare\nnormalized\nsuch\nthat\nmax[P(L0)] = max[P(f)] = 1. The posterior is reported\nin magenta and blue for both samples, with and with-\nout cut in pastro, respectively. The 50% and 90% upper\nlimits are reported as well. From the shape of the pos-\nteriors, it is evident that both the L0 and f posteriors\nchange slightly if no cut in pastro is applied.\nFor the\nsample with pastro > 0.5, the 50% and 90% upper lim-\nits for f are log10(f50%) = \u22121.76 and log10(f90%) =\n\u22120.48, while for L0 are log10[L0,50%(erg s\u22121)] = 47.6\nand log10[L0,90%(erg s\u22121)] = 48.8, respectively.\nIn the limit of a collection of triggers which correspond\nonly to non-astrophysical events, i.e., all with \u03c0i = 0,\nthe likelihood is constant in the full parameter space,\nnot allowing to infer any constraints on the EM model\nparameters. On the other hand, if we increase the frac-\ntion of confident GW events and we keep fixed the total\nnumber N, their distance distribution P(DL) and the\nderived upper limits, then we obtain that L decreases\naccordingly. This implies that increasing the number of\nevents with \u03c0i close to 1, the overall exclusion region in\nthe (\u03bb1, ..., \u03bbk) parameter space increases as well. This\ndemonstrates that with the collection of more data, in\nthe limit of a GW detector horizon constant in time,\nthis method allows us to improve incrementally our con-\nstraints on the EM models of CBC events. Although,\nrealistically the GW detection horizon will increase with\ntime (Abbott et al. 2020), implying an overall increase of\nthe median values of DL of the candidate events. Such\nan effect increases in turn the values of the luminosity\nupper limits, increasing as well the values of Pi(\u03d5 < \u03d50)\nand hence of L. This effect tends to decrease the dimen-\nsion of the exclusion region of the (\u03bb1, ..., \u03bbk) parameter\nspace. Overall, the final outcome of the inclusion of ad-\nditional GW data, in terms of the constraining power of\nthis analysis, will depend on the simultaneous combined\neffect of increasing the number of confident events and\nof increasing the detection horizon.\nIn order to show how the inclusion of more significant\nGW candidates can improve the constraining power of\nthe present analysis, we carried out the following simu-\nlation. We repeated the same procedure adopted to pro-\nduce the exclusion regions of Fig. 7, but replacing the\nreal \u03c0i with \u03c0i = 1 for all the confirmed BBH candidates,\nhence imposing that they are all significant events. All\nthe values of \u03d5UL, \u03b5\u2295and P(DL) of each candidate are\nleft unchanged. The resulting 50% and 90% exclusion\nregions are reported in Fig. 10, with black dashed and\nsolid lines, respectively.\nThe fraction of the 90% ex-\ncluded region increases to a value of R90% = 34.2%,\nclearly demonstrating that, even if the BAT flux upper\nlimit are the same, the increase of confidence about the\nastrophysical nature of the GW improves our final con-\nstraints on the model parameter space.\nFurthermore,\nFig. 10 reports also the 50% and 90% exclusion regions\n(with red dashed and solid lines, respectively), obtained\nas before, but imposing both \u03c0i = 1 and \u03b5\u2295= 0 for\neach candidate. This combination corresponds to simu-\nlate all real BBH candidates, whose sky localization does\nnot overlap with the sky region covered by the Earth.\nIn this case R90% = 35.4%, showing that the fraction of\nGW sky posterior occulted by Earth has a slight impact\non our final results.\n7. CONCLUSIONS\nIn this work we report the systematic search of signals\njointly detected by the LIGO\u2013Virgo interferometers and\nthe Swift-BAT telescope, during the third LVK observ-\ning run. Thanks to the prompt availability of BAT data\nusing GUANO and the sensitive targeted search capa-\nbilities of the NITRATES pipeline, we conducted deep\nfollow-up searches for EM signals on a sample of 636 GW\n\n26\n46\n47\n48\n49\n50\n51\n52\n53\nlog10[L0(erg s\u22121)]\n\u22123.0\n\u22122.5\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\nlog10(f)\n90%\n50%\n90%\n50%\npastro=1\npastro=1, \u03f5\u2295=0\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nL/max(L)\nFigure 10. Same as Fig. 7, but simulating all the O3 catalog\ncandidates with an associated pastro = \u03c0i = 1. The black\ndashed and solid lines identify the 50% and 90% exclusion\nregions, respectively. The red dashed and solid lines have\nthe same meaning, but derived imposing both \u03c0i = 1 and\n\u03b5\u2295= 0.\ntriggers. The search results did not yield any confident\njoint detection, allowing us to derive upper limits in the\n15\u2013350 keV band. We provide comprehensive details on\nall analyzed GW triggers along with their NITRATES\nsearch statistics. This information can be valuable for\ncalibrating and comparing with other offline targeted\nsearch pipelines that are currently operational or may\nbe developed in the future.\nIn the specific case of the BBH class, the BAT flux up-\nper limits have been used to perform a stacking analysis\nand to derive constraints on the possible nature of an\nassociated EM emission. As illustrated in Section 6, the\npresence of several BBH candidates with large values of\npastro in our sample, enhances our ability to better con-\nstrain the parameter space for EM emission from BH\nmergers, with minimal assumptions on our prior knowl-\nedge of the nature of the emission.\nThe prospect of\ndetecting EM emission from BBH mergers has been de-\nbated and discussed in detail in recent times. Particu-\nlarly, the GBM trigger that accompanied the first BBH\nmerger event, GW150914, has served as a case study to\ntest possible association and potential implications (Ab-\nbott et al. 2016b; Connaughton et al. 2016; Goldstein\net al. 2016b). Though not likely, there are a number of\nphysical models that have been proposed that could give\nrise to detectable emission in the gamma-ray band. A\nsummary of the various different models has been dis-\ncussed in Fletcher et al. (2023) and Veres et al. (2019).\nThe models involve parameters pertaining to potential\nremnant accretion effects, magnetic field strength, black\nhole charge and spin, among others (e.g., Loeb 2016; Dai\net al. 2017; Woosley 2016; Zhang 2016). The method\ndescribed in Section 6 can be easily extended to any\nof these models, provided that the luminosity function\n\u03a0(L) of the putative BBH EM emission is known. Ad-\nditionally, effects possibly related to the viewing angle\ndependency of the EM emission can be easily included in\nthis approach. Regarding CBCs containing at least one\nNS (BNS and NSBH), it was not possible to conduct a\nsimilar stacking analysis as the one described for BBH in\nSection 6, due to the paucity of such events with a large\nenough value of pastro. Further observations, including\nthe fourth LVK observing run (O4), could lead to the\ncollection of a larger number of BNS and NSBH candi-\ndates with moderate values of pastro, giving the possibil-\nity to repeat the analysis performed in this paper and\nto derive informative constraints on the EM emission of\nthese classes and the properties of the associated GRB\npopulations. Data products associated with the present\nanalysis are reported in a separate data release.7\nO4 commenced on the 24th of May, 2023. The num-\nber of significant detections is expected to increase by\nseveral times during the entire duration of O4 (Abbott\net al. 2018; Petrov et al. 2022). Targeted search results\nusing the GUANO-NITRATES infrastructure are pub-\nlicly available in real-time8. In the case of non-detection\nof an EM counterpart, the GUANO team reports the\n15\u2013350 keV flux upper limit for all the GW triggers clas-\nsified as significant, via GCN Circulars. Additional en-\nhancements to the likelihood search code have reduced\nthe search latency by a factor of 2, with respect to O3.\nThanks to its sensitivity in the hard X-ray band and\nthe possibility to localize EM transients down to a pre-\ncision of an arcminute, Swift represents one of the main\ndiscovery machines for the detection of EM counterparts\nof GW transients. This paper shows how the GUANO\ninfrastructure has a deep impact on the multi-messenger\nscience case, in particular for optimally exploiting the\nsensitivity of the Swift-BAT instrument for the detec-\ntion of EM counterparts of CBCs detected by the LVK\nCollaboration.\nThe deep subthreshold search enabled\nby the NITRATES pipeline sensibly increases the de-\ntection horizon of Swift, giving the chance to detect\ntransients also outside the BAT FOV and allowing us\nto possibly detect faint X-ray/gamma-ray transients as-\nsociated to relativistic jets observed off-axis, as in the\ncase of GW170817.\nIn the case of a confident joint\nSwift-GW detection, the GUANO team will promptly\n7 https://doi.org/10.5281/zenodo.10600302\n8 https://guano.swift.psu.edu\n\n27\ndisseminate all the information about the EM candidate\nvia GCN Circulars, providing an estimate of the sky lo-\ncalization when available. Moreover, also in the case of\nnon-detection, this paper shows how the upper limits de-\nrived from the NITRATES analysis can be combined to\nhave the most sensitive constraints on the EM emission\nfrom all the CBC classes. The cumulative collection of\nnon-detection will gradually improve our knowledge of\nthe EM nature of CBCs.\nACKNOWLEDGMENTS\nGayathri Raman,\nSamuele Ronchini,\nand Jamie\nKennea acknowledge the support of NASA grants\n80NSSC19K0408 and 80NSSC22K1498 awarded as part\nof the NASA Neil Gehrels Swift Observatory Guest In-\nvestigator program. Jamie Kennea and James Delaunay\nacknowledge the support of NASA contract NAS5-0136.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO), for the construction and oper-\nation of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agencies\nas well as by the Council of Scientific and Industrial Re-\nsearch of India, the Department of Science and Technol-\nogy, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource Devel-\nopment, India, the Spanish Agencia Estatal de Investi-\ngaci\u00b4on (AEI), the Spanish Ministerio de Ciencia, Inno-\nvaci\u00b4on y Universidades, the European Union NextGen-\nerationEU/PRTR (PRTR-C17.I1), the ICSC - CentroN-\nazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the Eu-\nropean Union NextGenerationEU, the Comunitat Au-\nton`oma de les Illes Balears through the Direcci\u00b4o General\nde Recerca, Innovaci\u00b4o i Transformaci\u00b4o Digital with funds\nfrom the Tourist Stay Tax Law ITS 2017-006, the Con-\nselleria d\u2019Economia, Hisenda i Innovaci\u00b4o, the FEDER\nOperational Program 2021-2027 of the Balearic Islands,\nthe Conselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i So-\ncietat Digital de la Generalitat Valenciana and the\nCERCA Programme Generalitat de Catalunya, Spain,\nthe National Science Centre of Poland and the European\nUnion \u2013 European Regional Development Fund; Foun-\ndation for Polish Science (FNP), the Polish Ministry\nof Science and Higher Education, the Swiss National\nScience Foundation (SNSF), the Russian Science Foun-\ndation, the European Commission, the European So-\ncial Funds (ESF), the European Regional Development\nFunds (ERDF), the Royal Society, the Scottish Fund-\ning Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scientific Research Fund (OTKA), the\nFrench Lyon Institute of Origins (LIO), the Belgian\nFonds de la Recherche Scientifique (FRS-FNRS), Ac-\ntions de Recherche Concert\u00b4ees (ARC) and Fonds Weten-\nschappelijk Onderzoek \u2013 Vlaanderen (FWO), Belgium,\nthe Paris \u02c6Ile-de-France Region, the National Research,\nDevelopment and Innovation Office Hungary (NKFIH),\nthe National Research Foundation of Korea, the Natu-\nral Science and Engineering Research Council Canada,\nCanadian Foundation for Innovation (CFI), the Brazil-\nian Ministry of Science, Technology, and Innovations,\nthe International Center for Theoretical Physics South\nAmerican Institute for Fundamental Research (ICTP-\nSAIFR), the Research Grants Council of Hong Kong, the\nNational Natural Science Foundation of China (NSFC),\nthe Leverhulme Trust, the Research Corporation, the\nNational Science and Technology Council (NSTC), Tai-\nwan, the United States Department of Energy, and the\nKavli Foundation. The authors gratefully acknowledge\nthe support of the NSF, STFC, INFN and CNRS for\nprovision of computational resources.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-in-Aid for Scientific Research on Innovative Ar-\neas 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grant-in-Aid for Scientific Research (S)\n17H06133 and 20H05639 , JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cos-\nmic Ray Research, University of Tokyo, National Re-\nsearch Foundation (NRF), Computing Infrastructure\nProject of Global Science experimental Data hub Cen-\nter (GSDC) at KISTI, Korea Astronomy and Space\nScience Institute (KASI), and Ministry of Science and\nICT (MSIT) in Korea, Academia Sinica (AS), AS Grid\nCenter (ASGC) and the National Science and Technol-\nogy Council (NSTC) in Taiwan under grants includ-\ning the Rising Star Program and Science Vanguard Re-\n\n28\nsearch Program, Advanced Technology Center (ATC) of\nNAOJ, and Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individ-\nual authors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising. We\nrequest that citations to this article use \u2019A. G. Abac et\nal. (LIGO-Virgo-KAGRA Collaboration), ...\u2019 or similar\nphrasing, depending on journal convention.\nMatplotlib\n(Hunter\n2007),\nSEABORN\n(Waskom\n2021), NumPy (Harris et al. 2020) and SciPy (Virta-\nnen et al. 2020) were used in the preparation of the\nmanuscript.\n\n29\nREFERENCES\nAbbott B. P., et al., 2016a, Physical Review X, 6, 041015\nAbbott B. P., et al., 2016b, PhRvL, 116, 061102\nAbbott B. P., et al., 2017a, PhRvL, 119, 161101\nAbbott B. P., et al., 2017b, Nature, 551, 85\nAbbott B. P., et al., 2017c, ApJ, 841, 89\nAbbott B. P., et al., 2017d, ApJL, 848, L12\nAbbott B. P., et al., 2017e, ApJL, 848, L13\nAbbott B. P., et al., 2018, Living Reviews in Relativity, 21,\n3\nAbbott B. P., et al., 2020, Living Reviews in Relativity, 23,\n3\nAbbott R., et al., 2021, PhRvX, 11, 021053\nAbbott R., et al., 2023, PhRvX, 13, 041039\nAbbott R., et al., 2024, PhRvD, 109, 022001\nAlexander K. 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LUMINOSITY UPPER LIMIT\nA more accurate method to derive the luminosity upper limit should be based on the knowledge of P(DL) and P(\u03d5),\nwhere \u03d5 is the flux measured in the BAT energy band. Having only an upper limit, P(\u03d5) can be approximated as\nP(\u03d5) \u221d\n\uf8f1\n\uf8f2\n\uf8f3\n\u03a0(\u03d5),\n\u03d5 < \u03d5UL\n0,\n\u03d5 > \u03d5UL\n,\n(A1)\nwhere \u03a0(\u03d5) is our prior distribution for the flux.\nUsing the conversion from flux to luminosity L = 4\u03c0D2\nL\u03d5, the\nprobability distribution of the luminosity can be computed as\nP(L) = P(4\u03c0D2\nL\u03d5) \u221d\nZ 1\n\u03d5P\u03d5(\u03d5)PD2\nL\n\u0012 L\n4\u03c0\u03d5\n\u0013\nd\u03d5,\n(A2)\nwhere P\u03d5 is the flux probability distribution and PD2\nL is the probability distribution of D2\nL. In the conversion from\nflux to luminosity, the k-correction has been omitted, since it introduces a mild dependence on the redshift, which is\nnot relevant for the purposes of this section. The 5\u03c3 luminosity upper limit LUL can be found imposing that\nZ LUL\n0\nP(L)dL = 1 \u2212\u03b55\u03c3,\n(A3)\nwith \u03b55\u03c3 = 3 \u00d7 10\u22127. The value of LUL has been computed adopting two different assumptions for the flux prior,\ncorresponding to \u03a0(\u03d5) \u221dconst. and \u03a0(\u03d5) \u221d\u03d5\u22123/2, with the latter being inspired by the usual trend followed by GRBs\n(e.g., Salafia et al. 2023). In both cases, we find that LUL \u223c3 \u00d7 4\u03c0\u27e8D2\nL\u27e9\u03d5UL.\nB. SIMULATION SETUP\nIn this section we specify the details of the simulation used to compute numerically the L(L0, f|E1, ..., EN) function.\nFor each simulated GW candidate, the single Li is computed for each pairs of values (L0,n, fm). The flux predicted\nby the EM model is predicted injecting 1000 sources whose luminosity distance is distributed according to P(DL),\nderived from the GW localization. The probability Pi(\u03d5 < \u03d50,i) is derived computing the fraction of cases that have a\nflux below the sky-averaged BAT upper limit, defined by Eq. (3). The computation of L is performed on a 100 \u00d7 100\ngrid of (L0,n, fm). Once the previous steps are performed for all the GW candidates, the final combined likelihood is\ncomputed as\nL(L0, f|E1, ..., EN) =\nY\ni\nLi(L0, f).\n(B4)\nIn order to produce the credibility contours in the [L0,n, fm] plane, we adopt the following steps:\n1. L is normalized such that\nX\nn,m\nL(L0,n, fm) = 1.\n(B5)\n2. A one-dimensional array L[xn] is created flattening the two-dimensional grid L(L0,n, fm), then L[xn] is sorted\nin ascending order.\n3. We find the element [\u02c6L0, \u02c6f] = [xn\u2217] such that\nn\u2217\nX\nn=0\nL[xn] = \u03bb,\n(B6)\nwhere \u03bb is the credibility level of the contour.\n4. The contour is drawn imposing L = L(\u02c6L0, \u02c6f).\n\n32\nC. FLUX UPPER LIMIT DERIVATION\nIn this appendix we show an alternative method to compute the non-detection likelihood presented in Section 6.\nThe NITRATES analysis allows us to derive a flux upper limit at a given confidence level for each pixel of the GW\nsky localization, corresponding to the function \u03d5UL(RA, Dec) defined in Eq. (3). Then combined probability of being\nlocated in the pixel xi and to have a non-detectable EM emission is\nP(non-det, xi) \u221dPGW(xi)P[\u03d5 < \u03d5UL(xi)]\u2206\u2126i,\n(C7)\nwhere\nP[\u03d5 < \u03d5UL(xi)] = (1 \u2212f) + f\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5,\n(C8)\nand \u2206\u2126i is the area of the pixel. Here we express P(\u03d5|xi) as the conditional flux probability distribution, namely the\nflux probability distribution assuming that the GW source is contained in the pixel xi. To compute the P(\u03d5|xi), for\na fixed luminosity L, the luminosity distance is extracted from the the conditional probability distribution P(DL|xi),\nwhich is derived from the GW sky localization. Finally the overall non-detection probability is obtained integrating\nEq. (C7) over the full sky:\nP(non-det|f, L0) =\nX\nxi\nPGW(xi)P[\u03d5 < \u03d5UL(xi)]\u2206\u2126i = (1\u2212f)+f\nh\n\u03b5\u2295+\nX\nxi /\u2208\u2126\u2295\nPGW(xi)\u2206\u2126i\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5\ni\n, (C9)\nwhere we have used that\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5 = 1 if xi \u2208\u2295,\nand\nX\nxi\u2208\u2126\u2295\nPGW(xi)\u2206\u2126i = \u03b5\u2295.\n(C10)\nThe resulting probability of non-detecting any EM emission in correspondence to a GW trigger with a given pastro = \u03c0i\nis\nP(non-det|f, L0, \u03c0i) = (1 \u2212\u03c0i) + \u03c0iP(non-det|f, L0).\n(C11)\nEq. (C9) has to be compared with the method used in Section 6, where instead we used the approximation:\nP(non-det|f, L0) = (1 \u2212f) + f\nZ \u03d5UL\n0\nP(\u03d5)d\u03d5,\n(C12)\nwith\n\u03d5UL =\nZ\n\u2126/\u2208\u2126\u2295\n\u03d5UL(\u2126)PGW(\u2126)d\u2126,\n(C13)\nand P(\u03d5) is obtained extracting DL from the full sky marginalized distribution P(DL), corresponding to\nP(DL) =\nX\nxi\nPGW(xi)P(DL|xi)\u2206\u2126i.\n(C14)\nThe two methods give comparable results in the assumption that the following approximation is valid:\nZ \u03d5UL\n0\nP(\u03d5)d\u03d5 \u2248\u03b5\u2295+\nX\nxi /\u2208\u2126\u2295\nPGW(xi)\u2206\u2126i\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5.\n(C15)\nFor completeness, we clarify here the main differences in the two methods.\nMETHOD 1:\nThis is the method used in Section 6 and is based on the following steps:\n1. The marginalized upper limit \u03d5UL is computed over the full sky, weighting by the GW sky localization.\n2. Once L0 is fixed, the flux probability distribution P(\u03d5) is computed extracting randomly DL from the P(DL),\nthe latter corresponding to the posterior distribution of the GW luminosity distance, marginalized over the full\nsky (excluding the part occulted by the Earth).\n3. The integral\nR \u03d5UL\n0\nP(\u03d5)d\u03d5 which appears in Eq. (C12) is evaluated counting the fraction of simulated events that\nhave a predicted flux below the sky-averaged upper limit \u03d5UL.\n\n33\nMETHOD 2:\nThis is the method presented in this appendix and summarized by Eqs. (C9) and (C11), consisting in the following\nprocedure:\n1. A set of sources is injected in space and the distribution follows the volumetric probability distribution of the GW\ncandidate. First the coordinates of the injected source are extracted from the sky localization PGW(RA, Dec),\nthen for each position the distance is extracted according to the conditional probability P(DL|RA, Dec).\n2. For each injected source, once the luminosity L0 is fixed, the predicted flux is compared with the coordinates-\ndependent BAT upper limit map \u03d5UL(RA, Dec).\n3. We define \u03c1/\u2208\u2295the fraction of all the sources injected which are not occulted by the Earth and also have a\npredicted flux below \u03d5UL(RA, Dec). Given this definition, we have:\nX\nxi /\u2208\u2126\u2295\nPGW(xi)\u2206\u2126i\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5 = (1 \u2212\u03b5\u2295)\u03c1/\u2208\u2295.\n(C16)\nThe last equality can be justified considering that, if for each pixel i we inject Ntot,i sources, we can define \u03c1i =\nNND,i/Ntot,i, where NND,i is the fraction of injected sources that are not detected, i.e., with a predicted flux below\n\u03d5UL(xi). Therefore:\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5 = \u03c1i.\n(C17)\nLet us call Ntot the total number of sources injected on the full sky. Then we have\nNtot,i = NtotPGW(xi)\u2206\u2126i,\n(C18)\nand therefore\nX\nxi /\u2208\u2126\u2295\nPGW(xi)\u2206\u2126i\nZ \u03d5UL(xi)\n0\nP(\u03d5|xi)d\u03d5 =\nX\nxi /\u2208\u2126\u2295\nNtot,i\nNtot\n\u03c1i =\n1\nNtot\nX\nxi /\u2208\u2126\u2295\nNND,i.\n(C19)\nSince the total number of injected sources not occulted by Earth are Ntot,/\u2208\u2295= (1 \u2212\u03b5\u2295)Ntot, and using that\n\u03c1/\u2208\u2295=\n1\nNtot,/\u2208\u2295\nX\nxi /\u2208\u2126\u2295\nNND,i,\n(C20)\nwe finally recover Eq. (C16).\nIn order to quantify the difference between the two methods, the following test is performed. Having fixed the two\nparameters f and L0, we compute the likelihood L for the two methods and we derive the quantity\n\u03b5L = 2abs(L1 \u2212L2)\nL1 + L2\n.\n(C21)\nHere we use the subscripts 1 and 2 for the respective methods. Both likelihoods are computed considering only BBH\ncandidates with pastro > 0.5. In both cases, the total number of injected sources for each BBH candidate is Ntot = 1000.\nThe distribution of \u03b5L is evaluated sampling randomly f and L0, for a total of 100 sampled pairs (f, L0). We obtain\nthat the median value of \u03b5L is 0.04 and that in \u223c80% of the sampled cases \u03b5L < 0.2. Since the difference between the\ntwo methods is limited and since the Method 2 is more computationally expensive, all the results are used adopting\nMethod 1.\n\n34\nTable 1. List of 636 low latency GW triggers analyzed using NITRATES is shown along with their respective pastro values\nand 15\u2013350 keV band flux upper limits.\nThe maximum\n\u221a\nTS is indicated for all the triggers with successful NITRATES\nresults. Observations corresponding to triggers with insufficient exposure time during the BAT pointing mode do not have valid\nNITRATES results or flux upper limits. For those triggers that do have NITRATES results but fail to meet the criterion for\na full likelihood analysis, the max\n\u221a\nTS is indicated as NFL (No Final Likelihood). The GW triggers from the Burst pipeline\ndo not have associated pastro values and are therefore left blank. The fraction of the GW sky posterior distribution inside the\nBAT coded FOV and the fraction of the GW posterior occulted by the Earth are denoted by \u03b5in BAT and \u03b5\u2295, respectively.\nSID\nTime\nGW FAR\ngroup\npastro\nClass\n\u221a\nTS\nFlux UL\n\u03b5in BAT\n\u03b5\u2295\n(UTC)\n(Hz)\n(erg cm\u22122 s\u22121)\n(%)\n(%)\nS190701ah\n2019-07-01T20:33:07\n1.92\u00d710\u22128\nCBC\n0.934\nBBH\n6.4\n1.58\u00d710\u22127\n99.42\n0\nS190816i\n2019-08-16T13:04:31\n1.44\u00d710\u22128\nCBC\n0.833\nNSBH\n-\n-\n-\n-\nS190828af\n2019-08-28T17:51:02\n1.83\u00d710\u22125\nCBC\n0.012\nBNS\n-\n-\n-\n-\nS190829p\n2019-08-29T13:49:01\n2.59\u00d710\u22126\nCBC\n0.062\nMass Gap\n5.8\n2.05\u00d710\u22127\n58.03\n0.94\nS190830y\n2019-08-30T15:07:04\n7.70\u00d710\u22128\nCBC\n0.382\nMass Gap\n5.7\n1.45\u00d710\u22127\n78.14\n5.94\nS190831ai\n2019-08-31T18:31:02\n8.85\u00d710\u22126\nCBC\n0.064\nNSBH\n5.7\n8.38\u00d710\u22127\n1.46\n41.91\nS190901al\n2019-09-01T21:01:03\n8.78\u00d710\u22126\nCBC\n0.015\nNSBH\n6.6\n1.82\u00d710\u22127\n80.18\n1.08\nS190901d\n2019-09-01T02:56:47\n1.01\u00d710\u22125\nCBC\n0.018\nBNS\n6.5\n5.33\u00d710\u22127\n13.86\n43.34\nS190901h\n2019-09-01T04:38:54\n5.26\u00d710\u22126\nBurst\n-\n-\n6.3\n4.14\u00d710\u22127\n24.56\n43.03\nS190902ao\n2019-09-02T20:56:00\n7.21\u00d710\u22126\nCBC\n0.016\nNSBH\n6.1\n5.41\u00d710\u22127\n9.78\n24.09\nS190904c\n2019-09-04T02:59:52\n3.64\u00d710\u22126\nCBC\n0.037\nMass Gap\n5.2\n5.35\u00d710\u22127\n11.35\n17.04\nS190904p\n2019-09-04T12:32:03\n3.75\u00d710\u22126\nCBC\n0.026\nNSBH\n-\n-\n-\n-\nS190904w\n2019-09-04T17:49:01\n1.56\u00d710\u22126\nBurst\n-\n-\n5.8\n4.53\u00d710\u22127\n27.01\n0\nS190906ad\n2019-09-06T18:33:04\n1.41\u00d710\u22125\nCBC\n0.010\nBNS\n5.9\n5.43\u00d710\u22127\n15.61\n46.69\nS190906ag\n2019-09-06T19:35:03\n3.22\u00d710\u22126\nBurst\n-\n-\n5.5\n5.73\u00d710\u22127\n24.48\n28.62\nS190906ah\n2019-09-06T20:05:00\n8.90\u00d710\u22127\nCBC\n0.101\nNSBH\n5.7\n5.47\u00d710\u22127\n12.62\n19.27\nS190906s\n2019-09-06T15:20:02\n4.71\u00d710\u22126\nBurst\n-\n-\n6.4\n3.65\u00d710\u22127\n51.54\n6.26\nS190907n\n2019-09-07T14:29:05\n2.71\u00d710\u22126\nBurst\n-\n-\nNFL\n5.91\u00d710\u22127\n16.71\n10.63\nS190908az\n2019-09-08T21:34:01\n4.26\u00d710\u22127\nBurst\n-\n-\n5.7\n7.04\u00d710\u22127\n8.59\n23.3\nS190908e\n2019-09-08T02:34:06\n4.52\u00d710\u22126\nBurst\n-\n-\n5.5\n2.50\u00d710\u22127\n21.39\n77.13\nS190909ac\n2019-09-09T14:13:01\n4.54\u00d710\u22126\nBurst\n-\n-\n5.9\n3.43\u00d710\u22127\n16.23\n21.97\nS190909aw\n2019-09-09T19:41:05\n1.07\u00d710\u22126\nBurst\n-\n-\n5.8\n2.29\u00d710\u22127\n70.87\n2.4\nS190909bd\n2019-09-09T21:26:03\n8.85\u00d710\u22126\nCBC\n0.023\nMass Gap\n-\n-\n-\n-\nS190909y\n2019-09-09T12:49:01\n1.66\u00d710\u22126\nCBC\n0.134\nNSBH\n-\n-\n-\n-\nS190915ak\n2019-09-15T23:57:02\n9.74\u00d710\u221210\nCBC\n0.990\nBBH\n5.4\n1.33\u00d710\u22127\n87.31\n0.17\nS190915q\n2019-09-15T16:03:01\n2.66\u00d710\u22126\nBurst\n-\n-\n5.8\n4.81\u00d710\u22127\n11.92\n13.01\nS190916y\n2019-09-16T15:55:01\n9.70\u00d710\u22127\nCBC\n0.143\nBNS\n6.9\n5.58\u00d710\u22127\n10.2\n27.57\nS190917ad\n2019-09-17T19:14:00\n1.47\u00d710\u22125\nCBC\n0.013\nMass Gap\n6.4\n4.47\u00d710\u22127\n4.18\n3.5\nS190918aa\n2019-09-18T19:38:04\n6.68\u00d710\u22127\nCBC\n0.023\nBNS\n7.2\n1.09\u00d710\u22127\n64.36\n16.27\nS190919ag\n2019-09-19T17:58:02\n3.42\u00d710\u22126\nBurst\n-\n-\n7.2\n2.77\u00d710\u22127\n14.79\n56.16\nS190919ak\n2019-09-19T18:34:03\n1.06\u00d710\u22125\nCBC\n0.089\nBNS\n5.8\n3.11\u00d710\u22127\n28.36\n35.45\nS190919au\n2019-09-19T20:39:00\n3.24\u00d710\u22126\nBurst\n-\n-\n9.4\n6.34\u00d710\u22127\n0.04\n42.88\nS190919u\n2019-09-19T12:13:02\n8.18\u00d710\u22126\nBurst\n-\n-\n8.0\n3.84\u00d710\u22127\n20.56\n23.68\nS190920an\n2019-09-20T19:09:05\n2.77\u00d710\u22127\nBurst\n-\n-\n5.7\n3.16\u00d710\u22127\n15.6\n36.74\nS190920ap\n2019-09-20T19:27:04\n5.51\u00d710\u22126\nBurst\n-\n-\n5.8\n2.95\u00d710\u22127\n11.49\n46.04\nS190920z\n2019-09-20T12:55:04\n6.08\u00d710\u22126\nBurst\n-\n-\n6.1\n1.02\u00d710\u22127\n52.58\n38.59\nS190922ag\n2019-09-22T15:22:01\n2.89\u00d710\u22126\nBurst\n-\n-\n5.4\n3.02\u00d710\u22127\n50.45\n9.47\nS190922aq\n2019-09-22T18:08:05\n1.63\u00d710\u22125\nCBC\n0.013\nMass Gap\n6.2\n-\n-\n-\nS190923aj\n2019-09-23T17:04:04\n1.91\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS190923ak\n2019-09-23T17:06:03\n2.70\u00d710\u22126\nCBC\n0.216\nBBH\n-\n-\n-\n-\nS190923x\n2019-09-23T12:19:00\n2.10\u00d710\u22126\nCBC\n0.036\nBNS\n-\n-\n-\n-\n\n35\nS190923y\n2019-09-23T12:55:59\n4.78\u00d710\u22128\nCBC\n0.670\nNSBH\n-\n-\n-\n-\nS190926z\n2019-09-26T16:47:02\n1.27\u00d710\u22126\nBurst\n-\n-\n6.2\n3.37\u00d710\u22127\n1.81\n72.24\nS190927an\n2019-09-27T14:58:00\n3.60\u00d710\u22126\nCBC\n0.038\nBNS\n6.6\n4.59\u00d710\u22127\n0.02\n58.85\nS190928c\n2019-09-28T02:11:45\n6.73\u00d710\u22129\nBurst\n-\n-\n6.9\n2.84\u00d710\u22127\n0.04\n1.53\nS190928j\n2019-09-28T06:30:16\n2.51\u00d710\u22126\nCBC\n0.092\nBNS\n6.4\n5.64\u00d710\u22127\n8.9\n27.8\nS190930s\n2019-09-30T13:35:41\n3.00\u00d710\u22129\nCBC\n0.950\nMass Gap\n-\n-\n-\n-\nS190930t\n2019-09-30T14:34:07\n1.54\u00d710\u22128\nCBC\n0.74\nNSBH\n5.9\n5.15\u00d710\u22127\n11.69\n21.15\nS191105d\n2019-11-05T13:40:51\n6.63\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191106r\n2019-11-06T18:41:51\n3.31\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191107o\n2019-11-07T16:05:23\n5.62\u00d710\u22126\nBurst\n-\n-\n5.6\n6.00\u00d710\u22127\n3.02\n17.27\nS191107t\n2019-11-07T18:03:55\n4.14\u00d710\u22126\nCBC\n0.020\nNSBH\n6.0\n4.35\u00d710\u22127\n0.06\n17.98\nS191110w\n2019-11-10T16:48:32\n4.43\u00d710\u22126\nBurst\n-\n-\n6.6\n1.55\u00d710\u22127\n27.57\n47.27\nS191110x\n2019-11-10T18:08:42\n2.93\u00d710\u221211\nCBC\n0.999\nMass Gap\n7.2\n1.75\u00d710\u22127\n15.22\n56.88\nS191112n\n2019-11-12T04:43:25\n1.76\u00d710\u22125\nBurst\n-\n-\n5.3\n1.09\u00d710\u22126\n38.68\n17.28\nS191113aj\n2019-11-13T14:28:49\n2.31\u00d710\u22125\nCBC\n0.005\nBNS\n6.5\n2.18\u00d710\u22127\n16.07\n0.01\nS191114ad\n2019-11-14T12:58:04\n1.36\u00d710\u22125\nCBC\n0.065\nBBH\n6.0\n2.05\u00d710\u22127\n30.58\n22\nS191114am\n2019-11-14T15:39:15\n1.57\u00d710\u22125\nCBC\n0.021\nBBH\n6.3\n5.12\u00d710\u22127\n0\n1.97\nS191114at\n2019-11-14T16:16:17\n8.13\u00d710\u22126\nCBC\n0.008\nNSBH\n6.7\n3.66\u00d710\u22127\n15.85\n50.49\nS191115be\n2019-11-15T23:07:27\n1.05\u00d710\u22125\nCBC\n0.010\nNSBH\n6.0\n9.94\u00d710\u22127\n3\n0.64\nS191116ac\n2019-11-16T14:21:55\n9.04\u00d710\u22126\nCBC\n0.015\nNSBH\nNFL\n4.95\u00d710\u22127\n8.53\n1.28\nS191118n\n2019-11-18T07:59:05\n5.88\u00d710\u22126\nCBC\n0.018\nNSBH\n6.8\n8.70\u00d710\u22128\n85.8\n6.04\nS191118z\n2019-11-18T16:49:55\n7.31\u00d710\u22127\nCBC\n0.164\nBNS\n6.2\n1.17\u00d710\u22127\n38.57\n54.47\nS191121bf\n2019-11-21T13:13:24\n3.70\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191121bq\n2019-11-21T15:54:12\n2.72\u00d710\u22126\nBurst\n-\n-\n5.7\n2.73\u00d710\u22127\n38.34\n29.35\nS191121bt\n2019-11-21T16:45:42\n2.03\u00d710\u22125\nCBC\n0.004\nNSBH\n5.5\n3.06\u00d710\u22127\n6.25\n7.14\nS191123q\n2019-11-23T09:01:14\n1.07\u00d710\u22125\nBurst\n-\n-\n5.4\n5.84\u00d710\u22127\n2.04\n14.18\nS191127p\n2019-11-27T05:02:27\n2.63\u00d710\u22126\nCBC\n0.037\nMass Gap\n-\n-\n-\n-\nS191130q\n2019-11-30T07:52:23\n8.69\u00d710\u22126\nCBC\n0.005\nNSBH\n5.0\n5.55\u00d710\u22127\n1.24\n28.9\nS191202af\n2019-12-02T18:42:26\n2.36\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191204o\n2019-12-04T14:17:13\n1.16\u00d710\u22125\nCBC\n0.009\nNSBH\n-\n-\n-\n-\nS191204r\n2019-12-04T17:15:26\n3.06\u00d710\u221225\nCBC\n1.000\nBBH\nNFL\n1.21\u00d710\u22127\n86.69\n0\nS191204t\n2019-12-04T18:34:16\n1.67\u00d710\u22126\nBurst\n-\n-\n5.1\n3.73\u00d710\u22127\n15.06\n24.91\nS191205ae\n2019-12-05T20:56:37\n2.83\u00d710\u22127\nBurst\n-\n-\n5.7\n6.07\u00d710\u22127\n7.73\n3.8\nS191205ah\n2019-12-05T21:52:08\n1.25\u00d710\u22128\nCBC\n0.932\nNSBH\n5.2\n3.43\u00d710\u22127\n31.7\n7.85\nS191206ab\n2019-12-06T14:05:21\n6.19\u00d710\u22126\nCBC\n0.024\nMass Gap\n6.2\n2.82\u00d710\u22127\n34.03\n8.59\nS191206an\n2019-12-06T17:38:57\n1.01\u00d710\u22126\nBurst\n-\n-\n5.7\n3.14\u00d710\u22127\n5.28\n7.69\nS191207o\n2019-12-07T10:16:32\n1.42\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS191207u\n2019-12-07T12:29:56\n1.00\u00d710\u22125\nBurst\n-\n-\n6.1\n3.61\u00d710\u22127\n28.24\n32.09\nS191208b\n2019-12-08T02:02:15\n9.14\u00d710\u22126\nCBC\n0.017\nBNS\n5.0\n4.92\u00d710\u22127\n0.03\n41.23\nS191209ao\n2019-12-09T13:58:21\n1.02\u00d710\u22126\nCBC\n0.097\nMass Gap\n5.6\n4.34\u00d710\u22127\n0.37\n39.42\nS191209ar\n2019-12-09T14:32:42\n1.08\u00d710\u22126\nBurst\n-\n-\n6.2\n2.61\u00d710\u22127\n56.27\n8.52\nS191212ad\n2019-12-12T16:57:39\n2.55\u00d710\u22126\nBurst\n-\n-\n7.0\n5.43\u00d710\u22126\n0.17\n17.49\nS191212ap\n2019-12-12T19:59:21\n1.31\u00d710\u22126\nCBC\n0.080\nBNS\n6.0\n4.98\u00d710\u22127\n0.67\n4.94\nS191212b\n2019-12-12T00:31:07\n9.49\u00d710\u22126\nBurst\n-\n-\n4.9\n4.94\u00d710\u22127\n7.29\n39.35\nS191212l\n2019-12-12T07:57:05\n9.31\u00d710\u22126\nCBC\n0.021\nMass Gap\n7.2\n4.24\u00d710\u22127\n11.14\n69.95\nS191213al\n2019-12-13T16:09:04\n1.27\u00d710\u22127\nCBC\n0.518\nNSBH\n6.3\n3.61\u00d710\u22127\n16.31\n35.94\nS191213an\n2019-12-13T16:58:32\n8.60\u00d710\u22127\nBurst\n-\n-\n6.2\n2.92\u00d710\u22127\n50.3\n30.27\nS191213au\n2019-12-13T18:44:42\n7.84\u00d710\u22127\nBurst\n-\n-\n6.0\n1.47\u00d710\u22127\n9.88\n87.84\nS191213ay\n2019-12-13T19:16:25\n2.93\u00d710\u22126\nBurst\n-\n-\n6.3\n5.88\u00d710\u22127\n0.26\n11.37\nS191213be\n2019-12-13T19:54:22\n1.72\u00d710\u22126\nBurst\n-\n-\n5.6\n6.80\u00d710\u22127\n1.1\n79.01\n\n36\nS191213c\n2019-12-13T01:17:45\n6.71\u00d710\u22128\nCBC\n0.395\nNSBH\n5.9\n4.87\u00d710\u22128\n98.61\n0\nS191215r\n2019-12-15T19:57:29\n5.46\u00d710\u22126\nCBC\n0.023\nBNS\n6.3\n9.51\u00d710\u22128\n73.13\n12.09\nS191216ap\n2019-12-16T21:33:38\n1.13\u00d710\u221223\nCBC\n1.000\nMass Gap\n6.6\n6.61\u00d710\u22127\n0.56\n4.99\nS191219ak\n2019-12-19T17:49:47\n1.22\u00d710\u22126\nBurst\n-\n-\n7.2\n1.40\u00d710\u22127\n83.49\n3.23\nS191219an\n2019-12-19T18:36:24\n2.26\u00d710\u22126\nBurst\n-\n-\n6.0\n4.64\u00d710\u22127\n0.01\n38.33\nS191219ap\n2019-12-19T19:52:52\n3.14\u00d710\u22126\nCBC\n0.067\nMass Gap\n6.3\n3.05\u00d710\u22127\n21.87\n42.93\nS191220af\n2019-12-20T12:24:14\n3.96\u00d710\u221210\nCBC\n0.996\nBNS\n6.4\n4.93\u00d710\u22127\n4.63\n41.78\nS191220al\n2019-12-20T14:46:02\n1.92\u00d710\u22126\nCBC\n0.026\nBNS\n-\n-\n-\n-\nS191220aw\n2019-12-20T17:49:42\n9.31\u00d710\u22128\nCBC\n0.522\nNSBH\n-\n-\n-\n-\nS191221aa\n2019-12-21T10:31:37\n1.02\u00d710\u22125\nCBC\n0.018\nBNS\n5.6\n5.73\u00d710\u22127\n52.7\n1.74\nS191221al\n2019-12-21T14:41:21\n2.92\u00d710\u22126\nBurst\n-\n-\n5.8\n4.53\u00d710\u22127\n5.41\n24.69\nS191221ar\n2019-12-21T17:12:28\n1.22\u00d710\u22125\nCBC\n0.011\nNSBH\n6.7\n7.21\u00d710\u22127\n0.72\n7.38\nS191221v\n2019-12-21T08:51:06\n1.43\u00d710\u22126\nCBC\n0.003\nNSBH\n6.3\n1.33\u00d710\u22127\n97.95\n0\nS191221w\n2019-12-21T09:02:03\n1.76\u00d710\u22125\nCBC\n0.055\nMass Gap\n4.6\n5.28\u00d710\u22127\n8.91\n6.08\nS191222a\n2019-12-22T01:34:42\n8.95\u00d710\u22126\nCBC\n0.020\nBNS\n6.6\n9.11\u00d710\u22127\n0.03\n13.45\nS191222af\n2019-12-22T13:57:46\n1.94\u00d710\u22125\nCBC\n0.006\nNSBH\n-\n-\n-\n-\nS191222an\n2019-12-22T16:30:03\n1.79\u00d710\u22125\nCBC\n0.037\nMass Gap\n-\n-\n-\n-\nS191223aj\n2019-12-23T15:55:41\n2.23\u00d710\u22125\nCBC\n0.006\nBNS\n5.9\n2.57\u00d710\u22127\n51.53\n7.48\nS191223p\n2019-12-23T08:22:49\n1.54\u00d710\u22125\nCBC\n0.008\nNSBH\n5.7\n1.22\u00d710\u22126\n3.89\n6.33\nS191224p\n2019-12-24T05:03:59\n8.31\u00d710\u22126\nBurst\n-\n-\n6.1\n5.61\u00d710\u22127\n10.96\n17.7\nS191224x\n2019-12-24T11:23:11\n1.98\u00d710\u22125\nCBC\n0.011\nBNS\n6.3\n5.16\u00d710\u22127\n22.09\n8.42\nS191225aq\n2019-12-25T21:57:15\n1.27\u00d710\u22128\nCBC\n0.390\nMass Gap\n5.7\n1.78\u00d710\u22127\n55.64\n0.05\nS191225e\n2019-12-25T02:11:26\n9.64\u00d710\u22126\nCBC\n0.017\nBNS\n6.0\n2.49\u00d710\u22127\n37.71\n36.13\nS191225q\n2019-12-25T10:30:40\n1.69\u00d710\u22125\nCBC\n0.006\nNSBH\n6.0\n4.39\u00d710\u22127\n19.53\n13.61\nS191226ad\n2019-12-26T13:31:05\n1.19\u00d710\u22125\nCBC\n0.011\nBNS\n5.8\n3.58\u00d710\u22127\n9.16\n13.79\nS191226ae\n2019-12-26T14:39:20\n1.99\u00d710\u22126\nCBC\n0.026\nNSBH\n5.6\n2.49\u00d710\u22127\n21.45\n4.19\nS191226ai\n2019-12-26T17:35:27\n2.96\u00d710\u22127\nCBC\n0.602\nBBH\n-\n-\n-\n-\nS191226aj\n2019-12-26T18:10:18\n2.46\u00d710\u22126\nCBC\n0.073\nMass Gap\n6.6\n4.71\u00d710\u22127\n0.26\n65.36\nS191226ap\n2019-12-26T20:33:18\n5.04\u00d710\u22126\nBurst\n-\n-\n6.0\n4.36\u00d710\u22127\n14.53\n51.45\nS191226d\n2019-12-26T01:40:51\n2.24\u00d710\u22126\nBurst\n-\n-\n5.7\n4.80\u00d710\u22127\n0.01\n43.14\nS191226u\n2019-12-26T10:24:57\n9.17\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191227aa\n2019-12-27T11:47:25\n1.60\u00d710\u22125\nCBC\n0.006\nNSBH\n-\n-\n-\n-\nS191227af\n2019-12-27T13:06:49\n2.79\u00d710\u22126\nBurst\n-\n-\n6.6\n9.85\u00d710\u22128\n57.79\n35.03\nS191227aj\n2019-12-27T14:54:31\n5.45\u00d710\u22126\nCBC\n0.030\nMass Gap\n5.9\n2.56\u00d710\u22127\n22.12\n13.71\nS191227al\n2019-12-27T15:49:54\n1.62\u00d710\u22125\nCBC\n0.010\nBNS\n6.2\n2.71\u00d710\u22127\n41.93\n20.28\nS191227am\n2019-12-27T15:51:27\n6.04\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191227an\n2019-12-27T16:10:45\n8.60\u00d710\u22126\nCBC\n0.014\nNSBH\n6.3\n7.13\u00d710\u22127\n29.95\n0.15\nS191227ap\n2019-12-27T16:35:12\n1.68\u00d710\u22125\nBurst\n-\n-\n5.9\n2.18\u00d710\u22127\n44.6\n27.51\nS191227as\n2019-12-27T17:29:03\n1.32\u00d710\u22125\nBurst\n-\n-\n6.1\n2.87\u00d710\u22127\n21.77\n35.26\nS191227az\n2019-12-27T21:55:49\n1.21\u00d710\u22125\nCBC\n0.008\nNSBH\n6.9\n5.10\u00d710\u22127\n4.48\n0.34\nS191227bb\n2019-12-27T23:04:40\n3.86\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS191227h\n2019-12-27T02:58:36\n1.94\u00d710\u22125\nCBC\n0.034\nBBH\n6.5\n8.67\u00d710\u22127\n9.06\n26.08\nS191227o\n2019-12-27T04:55:18\n1.17\u00d710\u22125\nBurst\n-\n-\n6.8\n5.77\u00d710\u22127\n14.35\n1.91\nS191228ac\n2019-12-28T13:17:16\n1.44\u00d710\u22125\nCBC\n0.007\nNSBH\n7.0\n2.43\u00d710\u22127\n16.91\n65.16\nS191228am\n2019-12-28T18:51:01\n7.20\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS191228an\n2019-12-28T20:07:11\n1.83\u00d710\u22126\nBurst\n-\n-\n6.4\n2.49\u00d710\u22127\n48.48\n0.41\nS191228at\n2019-12-28T23:57:39\n8.92\u00d710\u22126\nBurst\n-\n-\n4.6\n2.99\u00d710\u22127\n36.08\n31.05\nS191228i\n2019-12-28T05:44:50\n2.27\u00d710\u22125\nCBC\n0.008\nMass Gap\n6.5\n3.47\u00d710\u22127\n38.65\n34.86\nS191228q\n2019-12-28T08:14:37\n5.18\u00d710\u22126\nBurst\n-\n-\n5.8\n4.05\u00d710\u22127\n27.39\n34.8\nS191228u\n2019-12-28T09:08:39\n9.00\u00d710\u22126\nBurst\n-\n-\n5.4\n4.01\u00d710\u22127\n10.1\n41.03\n\n37\nS191228w\n2019-12-28T09:49:35\n1.01\u00d710\u22125\nBurst\n-\n-\n6.4\n4.10\u00d710\u22127\n20.77\n26.8\nS191229ah\n2019-12-29T21:50:21\n1.23\u00d710\u22126\nBurst\n-\n-\n8.9\n7.45\u00d710\u22127\n22.06\n23.56\nS191229ai\n2019-12-29T22:11:21\n7.60\u00d710\u22126\nCBC\n0.015\nNSBH\n6.4\n1.56\u00d710\u22127\n30.56\n60.52\nS191229ak\n2019-12-29T23:16:09\n9.76\u00d710\u22126\nBurst\n-\n-\n5.7\n5.81\u00d710\u22127\n7.89\n40.58\nS191229o\n2019-12-29T12:02:34\n1.07\u00d710\u22125\nCBC\n0.011\nNSBH\n-\n-\n-\n-\nS191230aa\n2019-12-30T13:51:30\n1.07\u00d710\u22125\nCBC\n0.011\nNSBH\n6.6\n4.68\u00d710\u22127\n55.93\n0.06\nS191230ae\n2019-12-30T14:19:12\n1.44\u00d710\u22125\nCBC\n0.011\nMass Gap\n5.8\n1.89\u00d710\u22127\n34.17\n54.3\nS191230at\n2019-12-30T21:24:48\n1.64\u00d710\u22125\nCBC\n0.011\nBNS\n6.1\n5.52\u00d710\u22127\n0.09\n48.46\nS191230au\n2019-12-30T22:04:37\n2.12\u00d710\u22126\nBurst\n-\n-\n7.0\n2.54\u00d710\u22127\n40.47\n20.44\nS191230e\n2019-12-30T02:40:45\n1.09\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS191230k\n2019-12-30T04:10:08\n3.17\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS191230v\n2019-12-30T11:19:08\n8.75\u00d710\u22126\nCBC\n0.013\nNSBH\n6.8\n5.44\u00d710\u22127\n0.36\n1.48\nS191230y\n2019-12-30T13:08:19\n1.01\u00d710\u22125\nBurst\n-\n-\n5.7\n4.53\u00d710\u22127\n2.13\n52.59\nS191231ad\n2019-12-31T11:45:12\n1.33\u00d710\u22126\nBurst\n-\n-\n6.9\n1.21\u00d710\u22127\n51.96\n34.52\nS191231an\n2019-12-31T16:59:30\n1.67\u00d710\u22125\nCBC\n0.009\nNSBH\n6.2\n5.52\u00d710\u22127\n11.42\n7.79\nS200101o\n2020-01-01T14:18:13\n1.66\u00d710\u22125\nCBC\n0.012\nBNS\n7.4\n5.29\u00d710\u22127\n1.52\n61.15\nS200102ah\n2020-01-02T15:04:48\n1.70\u00d710\u22125\nCBC\n0.007\nNSBH\n5.3\n5.99\u00d710\u22127\n0\n38.48\nS200102an\n2020-01-02T18:05:23\n1.45\u00d710\u22125\nBurst\n-\n-\n6.5\n5.94\u00d710\u22127\n1.94\n32.62\nS200102ar\n2020-01-02T19:39:36\n2.24\u00d710\u22125\nCBC\n0.005\nNSBH\n6.4\n1.77\u00d710\u22127\n73.19\n2.04\nS200102au\n2020-01-02T21:01:56\n1.77\u00d710\u22125\nCBC\n0.009\nMass Gap\n5.6\n5.10\u00d710\u22127\n6.1\n8.29\nS200102k\n2020-01-02T06:17:35\n5.93\u00d710\u22126\nCBC\n0.016\nNSBH\n-\n-\n-\n-\nS200102y\n2020-01-02T11:15:25\n8.42\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200103aa\n2020-01-03T12:32:22\n6.00\u00d710\u22126\nBurst\n-\n-\n5.7\n9.42\u00d710\u22127\n1.26\n26.1\nS200103am\n2020-01-03T16:46:33\n1.68\u00d710\u22125\nCBC\n0.007\nNSBH\n-\n-\n-\n-\nS200103ao\n2020-01-03T18:29:37\n1.12\u00d710\u22125\nCBC\n0.013\nNSBH\n7.0\n3.23\u00d710\u22126\n1.05\n67.67\nS200103aw\n2020-01-03T22:34:12\n2.00\u00d710\u22125\nCBC\n0.002\nBBH\n5.2\n5.28\u00d710\u22127\n0.22\n25.17\nS200103az\n2020-01-03T23:31:11\n1.32\u00d710\u22126\nCBC\n0.078\nNSBH\n6.6\n2.58\u00d710\u22127\n1.42\n97.64\nS200103r\n2020-01-03T09:42:24\n1.57\u00d710\u22126\nBurst\n-\n-\n6.4\n2.60\u00d710\u22127\n27.35\n36.86\nS200103t\n2020-01-03T10:31:18\n4.10\u00d710\u22126\nBurst\n-\n-\n5.9\n7.13\u00d710\u22127\n10.63\n21.96\nS200103v\n2020-01-03T10:55:34\n1.18\u00d710\u22125\nBurst\n-\n-\n6.4\n3.68\u00d710\u22127\n24.33\n31.88\nS200103z\n2020-01-03T11:55:03\n1.49\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200104aa\n2020-01-04T10:04:38\n9.99\u00d710\u22126\nBurst\n-\n-\n6.1\n4.74\u00d710\u22127\n6.58\n43.27\nS200104ar\n2020-01-04T19:50:42\n3.13\u00d710\u22126\nCBC\n0.024\nNSBH\n6.7\n5.16\u00d710\u22127\n0.4\n26.15\nS200104d\n2020-01-04T04:13:54\n2.99\u00d710\u22126\nBurst\n-\n-\n6.2\n3.78\u00d710\u22127\n8.92\n44.22\nS200104r\n2020-01-04T08:05:48\n1.70\u00d710\u22125\nCBC\n0.010\nBNS\n6.0\n4.83\u00d710\u22127\n0.03\n12.34\nS200105aj\n2020-01-05T18:00:59\n1.43\u00d710\u22125\nCBC\n0.010\nBNS\n-\n-\n-\n-\nS200105p\n2020-01-05T09:03:23\n9.27\u00d710\u22126\nCBC\n0.019\nBNS\n6.0\n2.87\u00d710\u22127\n18.21\n77.63\nS200105u\n2020-01-05T12:01:59\n2.26\u00d710\u22125\nCBC\n0.005\nNSBH\n6.8\n8.27\u00d710\u22127\n1.99\n41.47\nS200105w\n2020-01-05T12:48:13\n6.15\u00d710\u22126\nCBC\n0.012\nNSBH\n5.6\n5.22\u00d710\u22127\n1.4\n69.28\nS200106ar\n2020-01-06T17:48:06\n3.03\u00d710\u22126\nBurst\n-\n-\n6.4\n1.54\u00d710\u22127\n58.45\n21.4\nS200106az\n2020-01-06T18:50:35\n1.39\u00d710\u22125\nBurst\n-\n-\n6.5\n3.42\u00d710\u22127\n13.15\n69.28\nS200106bd\n2020-01-06T22:24:59\n1.76\u00d710\u22125\nCBC\n0.005\nBNS\n5.8\n8.99\u00d710\u22127\n0.02\n99.56\nS200106f\n2020-01-06T01:36:45\n1.76\u00d710\u22126\nBurst\n-\n-\n6.0\n6.32\u00d710\u22127\n4.58\n18.82\nS200106i\n2020-01-06T03:07:57\n1.82\u00d710\u22125\nCBC\n0.015\nMass Gap\n5.5\n4.44\u00d710\u22127\n14.62\n28.82\nS200106k\n2020-01-06T04:37:09\n1.86\u00d710\u22125\nCBC\n0.009\nMass Gap\n7.0\n3.30\u00d710\u22127\n17.36\n36.7\nS200106s\n2020-01-06T08:37:45\n8.19\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200107i\n2020-01-07T03:16:26\n5.14\u00d710\u22126\nBurst\n-\n-\n5.4\n5.52\u00d710\u22127\n0.1\n23.85\nS200107j\n2020-01-07T03:22:04\n3.44\u00d710\u22127\nBurst\n-\n-\n6.5\n6.19\u00d710\u22127\n0\n7.88\nS200107m\n2020-01-07T04:08:28\n4.26\u00d710\u22126\nCBC\n0.022\nNSBH\n5.6\n4.71\u00d710\u22127\n13.51\n34.62\nS200107o\n2020-01-07T05:11:52\n1.05\u00d710\u22125\nCBC\n0.006\nNSBH\n5.3\n6.16\u00d710\u22127\n0.77\n24.76\n\n38\nS200108ag\n2020-01-08T18:30:05\n2.24\u00d710\u22125\nCBC\n0.009\nBNS\n6.6\n3.40\u00d710\u22127\n37.19\n28.06\nS200108ah\n2020-01-08T18:42:57\n2.16\u00d710\u22125\nCBC\n0.008\nNSBH\n7.1\n3.15\u00d710\u22127\n25.82\n29.67\nS200108an\n2020-01-08T23:51:51\n1.66\u00d710\u22125\nCBC\n0.011\nBNS\n6.8\n4.67\u00d710\u22127\n34.39\n12.38\nS200108j\n2020-01-08T03:42:27\n2.24\u00d710\u22125\nCBC\n0.007\nNSBH\n5.7\n5.72\u00d710\u22127\n15.67\n30.15\nS200108l\n2020-01-08T04:13:13\n2.13\u00d710\u22126\nCBC\n0.092\nBNS\n6.4\n3.53\u00d710\u22127\n10.23\n41.69\nS200108p\n2020-01-08T05:20:09\n1.93\u00d710\u22127\nCBC\n0.470\nBNS\n7.4\n7.83\u00d710\u22127\n2.39\n46.3\nS200109m\n2020-01-09T08:48:21\n1.94\u00d710\u22125\nCBC\n0.006\nNSBH\n5.9\n4.91\u00d710\u22127\n11.43\n3.39\nS200109o\n2020-01-09T13:51:35\n1.44\u00d710\u22125\nBurst\n-\n-\n5.8\n1.09\u00d710\u22127\n77.72\n9.11\nS200109r\n2020-01-09T15:30:31\n3.14\u00d710\u22126\nBurst\n-\n-\n7.0\n5.56\u00d710\u22127\n0\n99.4\nS200109s\n2020-01-09T15:44:38\n4.34\u00d710\u22126\nBurst\n-\n-\n7.0\n4.75\u00d710\u22127\n22.85\n20.23\nS200110aa\n2020-01-10T11:01:48\n2.12\u00d710\u22125\nBurst\n-\n-\n7.1\n2.92\u00d710\u22127\n47.55\n21.69\nS200110d\n2020-01-10T01:23:11\n1.45\u00d710\u22125\nBurst\n-\n-\n7.3\n5.40\u00d710\u22127\n7.42\n39.3\nS200110e\n2020-01-10T02:01:40\n6.32\u00d710\u22126\nBurst\n-\n-\n5.8\n3.77\u00d710\u22127\n0.77\n14.67\nS200110m\n2020-01-10T05:25:05\n1.21\u00d710\u22126\nBurst\n-\n-\n6.7\n6.61\u00d710\u22127\n1.48\n5.31\nS200110q\n2020-01-10T05:46:19\n4.45\u00d710\u22126\nBurst\n-\n-\n6.4\n4.99\u00d710\u22127\n0.76\n61.25\nS200110s\n2020-01-10T06:46:45\n1.51\u00d710\u22125\nBurst\n-\n-\n6.9\n1.35\u00d710\u22127\n79.96\n3.4\nS200110t\n2020-01-10T07:50:59\n1.79\u00d710\u22125\nBurst\n-\n-\n6.5\n4.70\u00d710\u22127\n11.22\n28.08\nS200110v\n2020-01-10T08:40:52\n1.56\u00d710\u22125\nBurst\n-\n-\n6.5\n2.89\u00d710\u22127\n25.33\n9.06\nS200110z\n2020-01-10T10:33:06\n6.50\u00d710\u22126\nBurst\n-\n-\n5.8\n2.03\u00d710\u22127\n56.99\n10.49\nS200111ae\n2020-01-11T22:02:00\n1.61\u00d710\u22125\nCBC\n0.009\nNSBH\n6.2\n7.87\u00d710\u22127\n11.26\n25.72\nS200111j\n2020-01-11T06:51:45\n2.70\u00d710\u22126\nBurst\n-\n-\n6.9\n5.25\u00d710\u22127\n12.19\n27.34\nS200111s\n2020-01-11T15:23:44\n1.04\u00d710\u22125\nCBC\n0.019\nBNS\n-\n-\n-\n-\nS200111w\n2020-01-11T19:00:59\n1.36\u00d710\u22125\nCBC\n0.011\nNSBH\n5.7\n2.70\u00d710\u22127\n60.18\n0.99\nS200112ac\n2020-01-12T21:29:08\n1.60\u00d710\u22125\nCBC\n0.004\nNSBH\n6.0\n6.91\u00d710\u22127\n1.12\n79.05\nS200112e\n2020-01-12T09:44:25\n1.61\u00d710\u22125\nCBC\n0.009\nBNS\n6.2\n6.47\u00d710\u22127\n0.01\n58.06\nS200113f\n2020-01-13T02:14:20\n1.79\u00d710\u22125\nCBC\n0.010\nBNS\n5.3\n3.12\u00d710\u22127\n18.59\n56.9\nS200113g\n2020-01-13T02:20:40\n1.81\u00d710\u22125\nCBC\n0.009\nBNS\n5.6\n4.69\u00d710\u22127\n3.35\n0.16\nS200113n\n2020-01-13T09:59:40\n1.57\u00d710\u22125\nCBC\n0.013\nMass Gap\n6.4\n6.05\u00d710\u22127\n0.52\n68.21\nS200113u\n2020-01-13T14:59:11\n1.13\u00d710\u22128\nBurst\n-\n-\n6.4\n5.70\u00d710\u22127\n7.56\n1.52\nS200114e\n2020-01-14T01:51:22\n1.88\u00d710\u22125\nCBC\n0.006\nNSBH\n6.0\n4.80\u00d710\u22127\n0.19\n95.25\nS200114f\n2020-01-14T02:08:18\n1.23\u00d710\u22129\nBurst\n8.8\n4.80\u00d710\u22128\n99.74\n0.0\nS200114m\n2020-01-14T05:47:08\n1.94\u00d710\u22125\nCBC\n0.035\nBBH\n6.4\n3.90\u00d710\u22127\n30.04\n0.06\nS200114p\n2020-01-14T06:50:05\n1.27\u00d710\u22125\nCBC\n0.009\nNSBH\n-\n-\n-\n-\nS200114w\n2020-01-14T13:17:40\n2.76\u00d710\u22126\nCBC\n0.238\nBBH\n6.2\n4.37\u00d710\u22127\n25.85\n0.22\nS200115ab\n2020-01-15T13:47:04\n1.07\u00d710\u22125\nBurst\n-\n-\n6.7\n4.82\u00d710\u22127\n6.56\n15.38\nS200115ak\n2020-01-15T21:00:55\n1.14\u00d710\u22125\nCBC\n0.014\nMass Gap\n4.3\n8.80\u00d710\u22128\n85.4\n11.91\nS200116ab\n2020-01-16T10:11:59\n1.67\u00d710\u22125\nCBC\n0.011\nBNS\n4.5\n1.17\u00d710\u22127\n42.05\n49.47\nS200116am\n2020-01-16T13:27:34\n3.02\u00d710\u22126\nCBC\n0.046\nBNS\n5.8\n1.64\u00d710\u22127\n44.69\n36.94\nS200116ay\n2020-01-16T20:55:30\n4.83\u00d710\u22126\nCBC\n0.028\nBNS\n6.4\n1.50\u00d710\u22127\n77.03\n7.07\nS200116b\n2020-01-16T00:08:17\n2.85\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200116ba\n2020-01-16T22:20:08\n6.77\u00d710\u22126\nCBC\n0.059\nBNS\n5.7\n7.51\u00d710\u22127\n31.22\n2.16\nS200116d\n2020-01-16T00:31:07\n1.59\u00d710\u22125\nCBC\n0.019\nBNS\n6.8\n4.59\u00d710\u22127\n32.04\n6.68\nS200116k\n2020-01-16T05:12:12\n3.30\u00d710\u22126\nBurst\n-\n-\n5.2\n2.91\u00d710\u22127\n34.49\n36.85\nS200116o\n2020-01-16T06:43:19\n1.46\u00d710\u22126\nBurst\n-\n-\n6.5\n3.25\u00d710\u22127\n10.6\n28.01\nS200117ag\n2020-01-17T15:45:58\n1.55\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200117ao\n2020-01-17T19:43:02\n1.05\u00d710\u22125\nCBC\n0.017\nBNS\n5.9\n3.21\u00d710\u22127\n0.08\n38.99\nS200117aq\n2020-01-17T20:18:33\n1.56\u00d710\u22125\nCBC\n0.007\nNSBH\n-\n-\n-\n-\nS200117as\n2020-01-17T20:57:03\n1.99\u00d710\u22125\nBurst\n-\n-\n6.3\n5.93\u00d710\u22127\n3.32\n25.36\nS200117j\n2020-01-17T07:36:50\n1.86\u00d710\u22125\nBurst\n-\n-\n6.2\n4.51\u00d710\u22127\n19\n37.3\nS200117z\n2020-01-17T13:25:54\n1.88\u00d710\u22125\nCBC\n0.005\nNSBH\n7.3\n4.93\u00d710\u22127\n18.54\n30.53\n\n39\nS200118ap\n2020-01-18T16:45:38\n5.77\u00d710\u22126\nCBC\n0.020\nNSBH\n-\n-\n-\n-\nS200118as\n2020-01-18T19:10:51\n2.01\u00d710\u22126\nCBC\n0.060\nNSBH\n6.6\n3.31\u00d710\u22127\n67.28\n0.84\nS200118d\n2020-01-18T01:15:36\n1.56\u00d710\u22125\nCBC\n0.019\nNSBH\n-\n-\n-\n-\nS200118e\n2020-01-18T01:14:04\n1.76\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200118k\n2020-01-18T02:27:04\n2.95\u00d710\u22126\nBurst\n-\n-\n6.3\n2.78\u00d710\u22127\n19.81\n11.16\nS200118p\n2020-01-18T05:07:50\n6.22\u00d710\u22126\nCBC\n0.027\nBNS\n5.7\n2.65\u00d710\u22127\n32.81\n44.11\nS200118z\n2020-01-18T08:30:55\n1.87\u00d710\u22125\nCBC\n0.011\nBNS\n6.0\n4.27\u00d710\u22127\n14.37\n32.28\nS200119g\n2020-01-19T05:29:43\n5.41\u00d710\u22126\nCBC\n0.026\nBNS\n5.7\n5.73\u00d710\u22127\n0.09\n96\nS200119h\n2020-01-19T05:52:36\n2.00\u00d710\u22125\nCBC\n0.009\nBNS\n6.5\n1.44\u00d710\u22127\n59.9\n18.67\nS200120e\n2020-01-20T20:51:02\n1.37\u00d710\u22126\nBurst\n-\n-\n6.5\n4.84\u00d710\u22127\n0\n75.71\nS200121h\n2020-01-21T04:24:28\n3.33\u00d710\u22126\nCBC\n0.026\nNSBH\n6.6\n4.67\u00d710\u22127\n2.84\n10.67\nS200121i\n2020-01-21T06:14:01\n9.81\u00d710\u22126\nCBC\n0.019\nMass Gap\n6.2\n2.85\u00d710\u22127\n8.61\n43.99\nS200121q\n2020-01-21T12:26:48\n3.38\u00d710\u22126\nCBC\n0.036\nBNS\n6.5\n4.09\u00d710\u22127\n0.8\n11.98\nS200122a\n2020-01-22T01:00:57\n3.03\u00d710\u22126\nBurst\n-\n-\n5.5\n5.80\u00d710\u22127\n9.99\n63.39\nS200122d\n2020-01-22T02:11:17\n8.91\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200122m\n2020-01-22T06:15:00\n1.59\u00d710\u22125\nCBC\n0.007\nNSBH\n5.6\n2.49\u00d710\u22127\n29.58\n42.92\nS200122n\n2020-01-22T06:14:09\n3.35\u00d710\u22126\nBurst\n-\n-\n5.8\n3.99\u00d710\u22127\n1.05\n61.04\nS200124n\n2020-01-24T08:50:58\n2.28\u00d710\u22125\nCBC\n0.006\nBNS\n-\n-\n-\n-\nS200124z\n2020-01-24T15:18:12\n2.20\u00d710\u22125\nCBC\n0.005\nNSBH\n7.0\n8.27\u00d710\u22127\n1.41\n3.93\nS200126ab\n2020-01-26T21:05:59\n9.92\u00d710\u22126\nCBC\n0.020\nBNS\n-\n-\n-\n-\nS200126ad\n2020-01-26T22:58:49\n4.32\u00d710\u22126\nCBC\n0.036\nBNS\n5.8\n1.82\u00d710\u22127\n29.24\n43.96\nS200126b\n2020-01-26T01:03:12\n1.55\u00d710\u22125\nBurst\n-\n-\n5.5\n4.20\u00d710\u22127\n13.58\n8.72\nS200126q\n2020-01-26T12:12:11\n2.11\u00d710\u22125\nCBC\n0.011\nMass Gap\n-\n-\n-\n-\nS200126s\n2020-01-26T12:44:32\n6.16\u00d710\u22126\nCBC\n0.022\nBNS\nNFL\n3.58\u00d710\u22127\n27.08\n4.78\nS200127c\n2020-01-27T00:49:50\n5.48\u00d710\u22127\nCBC\n0.042\nNSBH\n5.8\n2.64\u00d710\u22127\n0.36\n67.07\nS200127o\n2020-01-27T11:43:05\n2.50\u00d710\u22126\nCBC\n0.058\nBNS\n-\n-\n-\n-\nS200127s\n2020-01-27T15:27:19\n1.89\u00d710\u22125\nCBC\n0.012\nBNS\n-\n-\n-\n-\nS200128d\n2020-01-28T02:20:11\n1.64\u00d710\u22128\nCBC\n0.968\nBBH\n7.0\n2.07\u00d710\u22127\n26.25\n53\nS200128f\n2020-01-28T04:54:04\n1.37\u00d710\u22126\nBurst\n-\n-\n5.8\n4.76\u00d710\u22127\n4.67\n17.22\nS200128p\n2020-01-28T09:54:07\n5.35\u00d710\u22126\nCBC\n0.024\nNSBH\n6.1\n5.62\u00d710\u22127\n13.76\n23.17\nS200129ab\n2020-01-29T11:10:15\n5.74\u00d710\u22126\nCBC\n0.026\nBNS\n6.3\n4.95\u00d710\u22127\n0.02\n70.01\nS200129ad\n2020-01-29T11:57:52\n1.87\u00d710\u22126\nCBC\n0.035\nNSBH\n5.3\n6.48\u00d710\u22127\n0.01\n0.71\nS200129ai\n2020-01-29T13:01:06\n1.99\u00d710\u22125\nCBC\n0.009\nBNS\n-\n-\n-\n-\nS200129ap\n2020-01-29T15:39:24\n1.95\u00d710\u22125\nBurst\n-\n-\n6.6\n5.53\u00d710\u22127\n0.20\n37.41\nS200129bb\n2020-01-29T19:36:46\n1.60\u00d710\u22125\nCBC\n0.006\nNSBH\n5.3\n2.13\u00d710\u22127\n29.97\n45.18\nS200129i\n2020-01-29T05:07:00\n6.89\u00d710\u22126\nCBC\n0.022\nBNS\n6.3\n2.93\u00d710\u22127\n6.78\n0.01\nS200129k\n2020-01-29T06:26:01\n1.57\u00d710\u22125\nCBC\n0.008\nBNS\n5.9\n5.75\u00d710\u22127\n5.58\n2.87\nS200129m\n2020-01-29T06:54:58\n6.70\u00d710\u221232\nCBC\n1.000\nBBH\n5.8\n9.44\u00d710\u22127\n0\n0\nS200129q\n2020-01-29T08:50:16\n2.20\u00d710\u22126\nCBC\n0.040\nNSBH\n5.8\n5.38\u00d710\u22127\n1.52\n83.06\nS200129v\n2020-01-29T10:18:47\n8.13\u00d710\u22127\nCBC\n0.109\nNSBH\n5.7\n6.64\u00d710\u22127\n0\n41.39\nS200130ac\n2020-01-30T07:40:34\n3.08\u00d710\u22126\nCBC\n0.056\nMass Gap\n5.4\n1.73\u00d710\u22126\n4.79\n25.29\nS200130ai\n2020-01-30T09:59:58\n1.78\u00d710\u22125\nCBC\n0.008\nNSBH\n16.4\n1.86\u00d710\u22127\n36.48\n0.01\nS200130aq\n2020-01-30T13:16:21\n2.19\u00d710\u22125\nBurst\n-\n-\n5.1\n4.24\u00d710\u22127\n8.56\n32.34\nS200130at\n2020-01-30T14:33:37\n2.65\u00d710\u22126\nCBC\n0.052\nBNS\n5.7\n6.78\u00d710\u22127\n13.85\n0.5\nS200130j\n2020-01-30T04:27:50\n3.69\u00d710\u22126\nBurst\n-\n-\n6.0\n3.04\u00d710\u22127\n35.45\n31.31\nS200130z\n2020-01-30T07:10:21\n1.48\u00d710\u22125\nCBC\n0.009\nNSBH\n5.9\n4.44\u00d710\u22127\n0.29\n39.17\nS200131ap\n2020-01-31T19:39:35\n1.39\u00d710\u22125\nCBC\n0.013\nBNS\n6.4\n6.54\u00d710\u22127\n23\n57.25\nS200131c\n2020-01-31T01:15:08\n2.14\u00d710\u22125\nCBC\n0.020\nBNS\n5.4\n3.11\u00d710\u22127\n21.02\n1.03\nS200201b\n2020-02-01T01:35:45\n4.03\u00d710\u22126\nCBC\n0.036\nMass Gap\n5.8\n5.20\u00d710\u22127\n5.04\n29.4\nS200201c\n2020-02-01T01:39:17\n9.88\u00d710\u22126\nCBC\n0.017\nBNS\n5.7\n2.23\u00d710\u22127\n0.26\n56.09\n\n40\nS200204ak\n2020-02-04T21:52:56\n1.86\u00d710\u22125\nCBC\n0.006\nNSBH\n6.8\n3.76\u00d710\u22127\n1.98\n94.09\nS200205ab\n2020-02-05T07:30:51\n3.45\u00d710\u22126\nCBC\n0.040\nMass Gap\n5.9\n6.29\u00d710\u22127\n0.04\n1.56\nS200205ag\n2020-02-05T09:43:05\n1.64\u00d710\u22126\nCBC\n0.042\nNSBH\n-\n-\n-\n-\nS200205as\n2020-02-05T17:02:05\n1.15\u00d710\u22125\nBurst\n-\n-\n6.4\n5.83\u00d710\u22127\n5.46\n4.09\nS200205ax\n2020-02-05T22:44:49\n1.58\u00d710\u22125\nBurst\n-\n-\n5.8\n1.92\u00d710\u22127\n38.29\n30.69\nS200205e\n2020-02-05T01:59:16\n1.59\u00d710\u22125\nCBC\n0.007\nNSBH\n5.7\n2.00\u00d710\u22127\n55.33\n8.32\nS200206ao\n2020-02-06T11:38:22\n5.32\u00d710\u22126\nCBC\n0.024\nBNS\n-\n-\n-\n-\nS200206at\n2020-02-06T17:45:55\n1.91\u00d710\u22125\nCBC\n0.010\nBNS\n6.2\n6.37\u00d710\u22127\n1.16\n64.96\nS200206bc\n2020-02-06T21:24:22\n8.73\u00d710\u22127\nCBC\n0.124\nNSBH\n6.8\n2.27\u00d710\u22127\n47.65\n0.05\nS200206bg\n2020-02-06T23:07:15\n5.99\u00d710\u22127\nBurst\n-\n-\n6.0\n2.49\u00d710\u22127\n38.9\n29.45\nS200206r\n2020-02-06T05:16:09\n6.24\u00d710\u22126\nBurst\n-\n-\n6.5\n9.68\u00d710\u22127\n0.19\n79.89\nS200206v\n2020-02-06T05:40:04\n5.90\u00d710\u22126\nBurst\n-\n-\n6.3\n3.51\u00d710\u22127\n10.08\n55.9\nS200207aq\n2020-02-07T16:46:26\n3.38\u00d710\u22126\nCBC\n0.001\nMass Gap\n-\n-\n-\n-\nS200207t\n2020-02-07T07:53:06\n2.21\u00d710\u22125\nCBC\n0.005\nNSBH\n5.5\n3.37\u00d710\u22127\n37.1\n2.7\nS200208ac\n2020-02-08T18:57:11\n2.70\u00d710\u22126\nBurst\n-\n-\n5.7\n2.03\u00d710\u22127\n33.49\n40.16\nS200208l\n2020-02-08T09:01:03\n1.76\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200208q\n2020-02-08T13:01:17\n2.52\u00d710\u22129\nCBC\n0.993\nBBH\n6.2\n5.33\u00d710\u22127\n0\n0.76\nS200208v\n2020-02-08T15:32:25\n2.40\u00d710\u22126\nCBC\n0.045\nNSBH\n5.0\n3.36\u00d710\u22127\n18.52\n67.4\nS200209al\n2020-02-09T12:55:21\n1.25\u00d710\u22126\nBurst\n-\n-\n5.6\n3.53\u00d710\u22127\n23.45\n26.32\nS200209am\n2020-02-09T13:14:49\n8.41\u00d710\u22126\nCBC\n0.021\nBNS\n-\n-\n-\n-\nS200209au\n2020-02-09T16:44:05\n1.21\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200209aw\n2020-02-09T17:00:21\n1.40\u00d710\u22126\nBurst\n-\n-\n6.6\n4.63\u00d710\u22127\n0.1\n0.61\nS200209az\n2020-02-09T17:56:15\n6.13\u00d710\u22126\nCBC\n0.020\nBNS\nNFL\n3.45\u00d710\u22127\n1.95\n36.71\nS200209ba\n2020-02-09T17:58:01\n1.58\u00d710\u22125\nCBC\n0.009\nBNS\n5.3\n3.71\u00d710\u22127\n7.77\n80.29\nS200209bc\n2020-02-09T18:16:45\n1.14\u00d710\u22125\nBurst\n-\n-\n6.2\n1.83\u00d710\u22127\n49.17\n29.45\nS200209h\n2020-02-09T02:11:42\n2.10\u00d710\u22125\nCBC\n0.009\nBNS\nNFL\n6.73\u00d710\u22127\n0\n0.01\nS200209i\n2020-02-09T02:17:13\n1.16\u00d710\u22125\nBurst\n-\n-\n6.4\n5.82\u00d710\u22127\n5.95\n10.37\nS200209v\n2020-02-09T07:08:38\n8.58\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS200209w\n2020-02-09T07:28:45\n6.43\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS200210ab\n2020-02-10T10:48:37\n1.66\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200210ah\n2020-02-10T13:05:01\n2.11\u00d710\u22126\nBurst\n-\n-\n6.9\n5.10\u00d710\u22127\n0.71\n19.31\nS200210an\n2020-02-10T16:13:46\n1.22\u00d710\u22125\nCBC\n0.040\nBBH\n6.7\n4.31\u00d710\u22127\n2.56\n10.46\nS200210b\n2020-02-10T00:55:44\n8.04\u00d710\u22126\nBurst\n-\n-\n4.5\n2.54\u00d710\u22127\n13.89\n11.39\nS200211k\n2020-02-11T03:15:00\n5.56\u00d710\u22126\nCBC\n0.036\nBNS\n-\n-\n-\n-\nS200212aa\n2020-02-12T10:18:23\n3.52\u00d710\u22126\nCBC\n0.157\nBBH\n5.6\n3.85\u00d710\u22127\n19.75\n0.88\nS200212ai\n2020-02-12T12:09:01\n8.97\u00d710\u22126\nCBC\n0.018\nNSBH\n5.3\n5.81\u00d710\u22127\n1.33\n45.09\nS200212s\n2020-02-12T08:36:40\n8.70\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200213p\n2020-02-13T03:31:54\n1.37\u00d710\u22125\nCBC\n0.007\nNSBH\n5.7\n3.93\u00d710\u22127\n49.08\n3.09\nS200213q\n2020-02-13T03:43:44\n2.18\u00d710\u22125\nCBC\n0.008\nBNS\n6.5\n6.14\u00d710\u22127\n18.76\n0.02\nS200213z\n2020-02-13T06:07:16\n6.36\u00d710\u22126\nCBC\n0.052\nBBH\n6.2\n5.15\u00d710\u22127\n13.91\n10.38\nS200214ah\n2020-02-14T10:24:52\n2.26\u00d710\u22126\nBurst\n-\n-\n4.7\n6.11\u00d710\u22127\n1.18\n13.1\nS200214av\n2020-02-14T14:04:55\n2.50\u00d710\u22127\nBurst\n-\n-\n5.9\n6.70\u00d710\u22127\n0.11\n56.56\nS200214bd\n2020-02-14T16:49:01\n2.08\u00d710\u22125\nCBC\n0.006\nBNS\n5.8\n2.87\u00d710\u22127\n57.29\n1.98\nS200214bn\n2020-02-14T19:56:24\n9.25\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS200214bo\n2020-02-14T20:35:29\n1.93\u00d710\u22125\nCBC\n0.011\nBNS\n7.2\n4.64\u00d710\u22127\n10.09\n17.62\nS200214bp\n2020-02-14T22:14:40\n8.48\u00d710\u22126\nCBC\n0.021\nNSBH\n5.3\n1.79\u00d710\u22127\n17.92\n60.62\nS200214bq\n2020-02-14T22:33:07\n3.08\u00d710\u22126\nCBC\n0.005\nMass Gap\n5.4\n2.37\u00d710\u22127\n3.03\n53.35\nS200214br\n2020-02-14T22:45:26\n7.01\u00d710\u22128\nBurst\n-\n-\n5.2\n8.21\u00d710\u22127\n0.12\n78.46\nS200214m\n2020-02-14T04:36:51\n1.03\u00d710\u22125\nCBC\n0.033\nBBH\n5.3\n8.45\u00d710\u22127\n3.54\n3.01\nS200214p\n2020-02-14T05:11:32\n1.17\u00d710\u22125\nCBC\n0.015\nBNS\n5.4\n5.44\u00d710\u22127\n0.02\n28.5\n\n41\nS200215ah\n2020-02-15T19:59:56\n1.02\u00d710\u22126\nCBC\n0.126\nBNS\n-\n-\n-\n-\nS200215t\n2020-02-15T12:23:33\n8.20\u00d710\u22126\nCBC\n0.021\nBNS\n-\n-\n-\n-\nS200215z\n2020-02-15T16:38:59\n1.86\u00d710\u22125\nCBC\n0.010\nBNS\n-\n-\n-\n-\nS200216ae\n2020-02-16T10:33:58\n7.56\u00d710\u22127\nBurst\n-\n-\n5.5\n4.85\u00d710\u22127\n10.17\n19.3\nS200216aj\n2020-02-16T11:51:34\n9.95\u00d710\u22126\nCBC\n0.015\nBNS\n5.9\n5.46\u00d710\u22127\n0.9\n21.46\nS200216be\n2020-02-16T18:39:33\n5.80\u00d710\u22127\nBurst\n-\n-\n-\n-\n-\n-\nS200216br\n2020-02-16T22:08:05\n1.68\u00d710\u22125\nCBC\n0.021\nBBH\n6.6\n2.34\u00d710\u22127\n22.38\n0.03\nS200216h\n2020-02-16T03:24:11\n4.34\u00d710\u22126\nBurst\n-\n-\n5.2\n5.73\u00d710\u22127\n1.3\n31.24\nS200217ar\n2020-02-17T12:22:07\n2.27\u00d710\u22125\nCBC\n0.002\nMass Gap\n-\n-\n-\n-\nS200217bd\n2020-02-17T16:05:11\n1.80\u00d710\u22125\nCBC\n0.009\nBNS\n-\n-\n-\n-\nS200217bh\n2020-02-17T16:46:46\n1.20\u00d710\u22125\nCBC\n0.029\nBBH\n-\n-\n-\n-\nS200217c\n2020-02-17T03:10:33\n2.12\u00d710\u22126\nBurst\n-\n-\n6.4\n1.57\u00d710\u22127\n49.36\n29.59\nS200217cg\n2020-02-17T22:52:12\n7.45\u00d710\u22126\nCBC\n0.014\nNSBH\n4.9\n2.61\u00d710\u22127\n0.32\n1.31\nS200217k\n2020-02-17T04:53:17\n7.52\u00d710\u22126\nCBC\n0.020\nMass Gap\n6.4\n6.12\u00d710\u22127\n0.56\n1.74\nS200217v\n2020-02-17T07:30:47\n1.53\u00d710\u22125\nBurst\n-\n-\n5.7\n3.55\u00d710\u22127\n26.82\n18.2\nS200217w\n2020-02-17T07:37:44\n3.05\u00d710\u22127\nCBC\n0.431\nBBH\n5.9\n4.27\u00d710\u22127\n9.19\n28.12\nS200218al\n2020-02-18T10:05:22\n6.19\u00d710\u22128\nBurst\n-\n-\n6.0\n4.84\u00d710\u22127\n13.96\n10.77\nS200218am\n2020-02-18T10:39:25\n1.28\u00d710\u22126\nCBC\n0.131\nMass Gap\n6.3\n5.47\u00d710\u22127\n2.47\n5.86\nS200218ay\n2020-02-18T14:03:56\n8.63\u00d710\u22126\nCBC\n0.019\nBNS\n6.2\n3.55\u00d710\u22127\n0.02\n97.23\nS200218f\n2020-02-18T00:39:55\n1.01\u00d710\u22125\nCBC\n0.014\nBNS\n5.7\n5.31\u00d710\u22127\n3.5\n14.09\nS200218i\n2020-02-18T01:25:25\n2.61\u00d710\u22126\nCBC\n0.191\nBBH\n5.2\n5.28\u00d710\u22127\n0.01\n29.17\nS200218k\n2020-02-18T01:28:26\n2.23\u00d710\u22125\nCBC\n0.010\nNSBH\n-\n-\n-\n-\nS200218u\n2020-02-18T04:17:54\n7.26\u00d710\u22127\nBurst\n-\n-\n5.9\n5.04\u00d710\u22127\n8.13\n19.83\nS200219a\n2020-02-19T00:05:16\n8.84\u00d710\u22126\nCBC\n0.002\nBBH\n5.8\n1.36\u00d710\u22127\n79.35\n5.25\nS200219ao\n2020-02-19T14:33:42\n7.08\u00d710\u22126\nCBC\n0.027\nBNS\n-\n-\n-\n-\nS200219ap\n2020-02-19T14:47:34\n8.93\u00d710\u22126\nCBC\n0.025\nMass Gap\n6.4\n4.21\u00d710\u22127\n0.15\n1.07\nS200219aq\n2020-02-19T14:50:02\n2.91\u00d710\u22126\nCBC\n0.081\nBBH\n5.9\n5.52\u00d710\u22127\n0\n39.72\nS200219az\n2020-02-19T18:30:38\n2.27\u00d710\u22126\nCBC\n0.022\nNSBH\n-\n-\n-\n-\nS200219ba\n2020-02-19T18:42:03\n7.65\u00d710\u22126\nCBC\n0.034\nBBH\n-\n-\n-\n-\nS200219bg\n2020-02-19T19:45:29\n7.09\u00d710\u22126\nCBC\n0.128\nMass Gap\n5.3\n3.87\u00d710\u22127\n27.73\n26.67\nS200219f\n2020-02-19T03:09:19\n1.32\u00d710\u22125\nCBC\n0.021\nBBH\nNFL\n1.23\u00d710\u22127\n78.19\n0.04\nS200219q\n2020-02-19T07:07:00\n1.47\u00d710\u22125\nCBC\n0.023\nBBH\n-\n-\n-\n-\nS200220ac\n2020-02-20T06:20:14\n4.14\u00d710\u22126\nCBC\n0.061\nBBH\n5.8\n3.28\u00d710\u22127\n24.26\n16.25\nS200220ad\n2020-02-20T06:19:28\n4.86\u00d710\u22127\nBurst\n-\n-\n4.7\n5.08\u00d710\u22127\n0.32\n54.14\nS200220au\n2020-02-20T11:04:01\n4.01\u00d710\u22126\nCBC\n0.056\nBNS\n5.8\n5.28\u00d710\u22127\n9.19\n25.92\nS200220b\n2020-02-20T00:24:32\n1.86\u00d710\u22125\nCBC\n0.009\nBNS\n6.6\n6.10\u00d710\u22127\n0.04\n96.77\nS200220bt\n2020-02-20T22:11:49\n1.03\u00d710\u22126\nCBC\n0.155\nBNS\n4.8\n3.44\u00d710\u22127\n17.69\n24\nS200220bw\n2020-02-20T22:55:31\n1.14\u00d710\u22125\nCBC\n0.012\nNSBH\nNFL\n4.53\u00d710\u22127\n11.26\n25.74\nS200220k\n2020-02-20T02:45:26\n1.55\u00d710\u22125\nCBC\n0.011\nBNS\n-\n-\n-\n-\nS200220l\n2020-02-20T02:48:31\n7.95\u00d710\u22126\nCBC\n0.022\nMass Gap\n5.4\n5.49\u00d710\u22127\n0\n46.11\nS200220u\n2020-02-20T04:01:28\n1.95\u00d710\u22125\nCBC\n0.007\nNSBH\n5.6\n1.75\u00d710\u22127\n33.48\n50.49\nS200220v\n2020-02-20T04:25:03\n1.20\u00d710\u22125\nCBC\n0.015\nMass Gap\n6.2\n1.31\u00d710\u22127\n58.52\n24.14\nS200220w\n2020-02-20T04:51:22\n2.30\u00d710\u22125\nCBC\n0.008\nBNS\n6.3\n2.47\u00d710\u22127\n17.67\n32.86\nS200220x\n2020-02-20T04:52:44\n1.73\u00d710\u22125\nCBC\n0.006\nNSBH\n5.5\n3.81\u00d710\u22127\n28.03\n1.27\nS200221ai\n2020-02-21T09:28:19\n2.37\u00d710\u22126\nCBC\n0.036\nNSBH\n-\n-\n-\n-\nS200221ar\n2020-02-21T11:08:44\n1.86\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200221at\n2020-02-21T11:26:18\n1.77\u00d710\u22125\nBurst\n-\n-\n6.5\n4.27\u00d710\u22127\n6.49\n34.14\nS200221ax\n2020-02-21T13:19:12\n1.83\u00d710\u22125\nCBC\n0.052\nMass Gap\n5.6\n3.76\u00d710\u22127\n14.66\n33.62\nS200221b\n2020-02-21T00:59:26\n1.63\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200221bc\n2020-02-21T14:07:05\n2.99\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\n\n42\nS200221bh\n2020-02-21T15:19:18\n2.10\u00d710\u22125\nCBC\n0.008\nMass Gap\n4.9\n5.06\u00d710\u22127\n0.00\n31.34\nS200221bl\n2020-02-21T16:59:59\n1.20\u00d710\u22125\nBurst\n-\n-\n5.3\n3.15\u00d710\u22127\n22.76\n35.58\nS200221bu\n2020-02-21T20:14:38\n9.12\u00d710\u22126\nBurst\n-\n-\n5.4\n6.43\u00d710\u22127\n5.72\n33.06\nS200221c\n2020-02-21T01:13:57\n6.13\u00d710\u22126\nCBC\n0.028\nBNS\n6.1\n3.91\u00d710\u22127\n33.59\n6.07\nS200221z\n2020-02-21T06:41:32\n8.29\u00d710\u22127\nBurst\n-\n-\n5.8\n8.20\u00d710\u22127\n0\n44.14\nS200222ax\n2020-02-22T16:46:05\n2.36\u00d710\u22126\nCBC\n0.072\nMass Gap\n6.6\n1.09\u00d710\u22125\n33.39\n51.13\nS200222h\n2020-02-22T02:29:19\n2.84\u00d710\u22126\nBurst\n-\n-\n6.6\n2.44\u00d710\u22127\n26.95\n39.1\nS200222j\n2020-02-22T02:42:18\n7.70\u00d710\u22126\nCBC\n0.012\nNSBH\n6.2\n1.27\u00d710\u22127\n77.7\n11.1\nS200222u\n2020-02-22T04:48:17\n1.33\u00d710\u22125\nCBC\n0.004\nMass Gap\n5.6\n3.81\u00d710\u22127\n12.98\n6.12\nS200223aj\n2020-02-23T13:50:49\n1.35\u00d710\u22125\nCBC\n0.005\nBNS\n5.4\n7.01\u00d710\u22127\n0.02\n72.95\nS200223ao\n2020-02-23T14:28:21\n6.04\u00d710\u22126\nCBC\n0.054\nBBH\n5.4\n6.81\u00d710\u22127\n0.02\n0.04\nS200223aw\n2020-02-23T18:06:59\n8.01\u00d710\u22128\nCBC\n0.647\nBBH\n6.7\n2.97\u00d710\u22127\n34.45\n6.1\nS200223az\n2020-02-23T20:01:24\n1.36\u00d710\u22125\nCBC\n0.004\nNSBH\n5.1\n5.68\u00d710\u22127\n3.36\n18.7\nS200223l\n2020-02-23T05:17:44\n1.77\u00d710\u22125\nCBC\n0.008\nNSBH\n-\n-\n-\n-\nS200223u\n2020-02-23T08:09:27\n5.54\u00d710\u22126\nCBC\n0.054\nBBH\n-\n-\n-\n-\nS200224ab\n2020-02-24T05:45:46\n2.12\u00d710\u22125\nCBC\n0.040\nMass Gap\n5.8\n5.95\u00d710\u22127\n4.78\n6.01\nS200224ac\n2020-02-24T05:52:07\n2.64\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200224ag\n2020-02-24T06:30:15\n1.61\u00d710\u22125\nCBC\n0.030\nMass Gap\n-\n-\n-\n-\nS200224ak\n2020-02-24T06:55:12\n1.08\u00d710\u22125\nCBC\n0.009\nNSBH\n-\n-\n-\n-\nS200224as\n2020-02-24T09:34:32\n1.91\u00d710\u22125\nCBC\n0.003\nNSBH\n-\n-\n-\n-\nS200224cb\n2020-02-24T22:32:38\n1.36\u00d710\u22125\nCBC\n0.027\nBBH\n5.7\n4.30\u00d710\u22127\n0.59\n78.05\nS200224cd\n2020-02-24T23:13:13\n1.33\u00d710\u22125\nCBC\n0.010\nNSBH\n6.4\n5.34\u00d710\u22127\n0.09\n99.28\nS200224f\n2020-02-24T01:45:03\n7.47\u00d710\u22126\nCBC\n0.037\nBBH\n6.0\n8.83\u00d710\u22127\n3.55\n63.38\nS200224j\n2020-02-24T02:01:47\n1.93\u00d710\u22125\nCBC\n0.011\nMass Gap\n5.2\n4.77\u00d710\u22127\n2.08\n0.32\nS200224o\n2020-02-24T03:05:24\n1.33\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200225ac\n2020-02-25T09:12:05\n1.65\u00d710\u22125\nCBC\n0.015\nBBH\n5.4\n3.89\u00d710\u22127\n9.9\n60.86\nS200225af\n2020-02-25T10:00:45\n1.64\u00d710\u22126\nCBC\n0.104\nBNS\n10.6\n3.94\u00d710\u22127\n30.89\n25.81\nS200225ag\n2020-02-25T11:02:37\n2.21\u00d710\u22125\nCBC\n0.008\nNSBH\n5.8\n3.82\u00d710\u22127\n31.76\n0.04\nS200225an\n2020-02-25T12:57:00\n1.90\u00d710\u22125\nCBC\n0.002\nNSBH\n6.0\n5.91\u00d710\u22127\n15.64\n26.36\nS200225as\n2020-02-25T14:28:07\n6.23\u00d710\u22126\nCBC\n0.037\nBBH\n7.3\n3.53\u00d710\u22126\n0.33\n58.56\nS200225av\n2020-02-25T21:11:26\n1.44\u00d710\u22125\nCBC\n0.014\nBNS\n5.5\n3.62\u00d710\u22127\n10.72\n81.55\nS200225az\n2020-02-25T21:59:37\n9.58\u00d710\u22126\nCBC\n0.013\nNSBH\n-\n-\n-\n-\nS200225ba\n2020-02-25T22:09:01\n9.84\u00d710\u22126\nCBC\n0.018\nBNS\n5.9\n6.72\u00d710\u22127\n0.45\n88.36\nS200225k\n2020-02-25T03:41:20\n1.18\u00d710\u22125\nCBC\n0.008\nNSBH\n5.7\n9.43\u00d710\u22127\n0.12\n90.13\nS200225q\n2020-02-25T06:04:21\n9.19\u00d710\u22129\nCBC\n0.956\nBBH\n8.2\n4.63\u00d710\u22126\n2.2\n1.44\nS200225u\n2020-02-25T08:22:49\n1.47\u00d710\u22125\nCBC\n0.008\nNSBH\n-\n-\n-\n-\nS200226ac\n2020-02-26T07:57:51\n1.68\u00d710\u22125\nCBC\n0.014\nNSBH\n-\n-\n-\n-\nS200226ai\n2020-02-26T09:22:07\n2.02\u00d710\u22125\nCBC\n0.014\nBBH\n-\n-\n-\n-\nS200226bp\n2020-02-26T18:09:01\n1.73\u00d710\u22125\nCBC\n0.012\nBNS\n5.5\n6.21\u00d710\u22127\n8.22\n12.38\nS200226o\n2020-02-26T03:25:47\n2.21\u00d710\u22125\nCBC\n0.007\nBNS\n-\n-\n-\n-\nS200226z\n2020-02-26T07:18:43\n7.77\u00d710\u22126\nCBC\n0.017\nNSBH\n-\n-\n-\n-\nS200227d\n2020-02-27T01:01:17\n1.16\u00d710\u22125\nCBC\n0.009\nNSBH\n5.6\n4.29\u00d710\u22127\n4.75\n41.94\nS200227x\n2020-02-27T06:49:08\n1.12\u00d710\u22125\nCBC\n0.054\nMass Gap\n6.0\n5.80\u00d710\u22127\n12.56\n24.34\nS200228ai\n2020-02-28T12:49:29\n1.65\u00d710\u22125\nCBC\n0.009\nNSBH\n-\n-\n-\n-\nS200228bi\n2020-02-28T23:11:26\n1.24\u00d710\u22125\nCBC\n0.026\nBBH\n6.8\n4.64\u00d710\u22127\n18.36\n27.31\nS200228bl\n2020-02-28T23:44:54\n9.17\u00d710\u22126\nCBC\n0.017\nMass Gap\n5.9\n5.99\u00d710\u22127\n5.01\n32.9\nS200229ae\n2020-02-29T08:04:03\n1.26\u00d710\u22125\nBurst\n-\n-\n5.7\n7.33\u00d710\u22127\n1.37\n66.16\nS200229ag\n2020-02-29T08:43:31\n6.74\u00d710\u22126\nCBC\n0.003\nNSBH\n-\n-\n-\n-\nS200229al\n2020-02-29T10:32:00\n2.19\u00d710\u22125\nCBC\n0.005\nNSBH\n-\n-\n-\n-\nS200229bc\n2020-02-29T15:40:15\n7.92\u00d710\u22126\nCBC\n0.014\nNSBH\n5.7\n3.72\u00d710\u22127\n32.31\n0\n\n43\nS200229x\n2020-02-29T06:39:21\n1.85\u00d710\u22125\nCBC\n0.024\nBNS\n6.4\n8.77\u00d710\u22127\n0.47\n33.3\nS200301ae\n2020-03-01T09:42:26\n7.67\u00d710\u22126\nCBC\n0.017\nMass Gap\n6.8\n1.52\u00d710\u22127\n82.21\n1.41\nS200301an\n2020-03-01T17:37:42\n2.54\u00d710\u22126\nBurst\n-\n-\n7.0\n5.07\u00d710\u22127\n11.63\n26.94\nS200301ax\n2020-03-01T21:57:02\n5.68\u00d710\u22126\nCBC\n0.011\nBNS\n5.4\n2.70\u00d710\u22127\n35.19\n32.86\nS200301o\n2020-03-01T06:54:34\n9.21\u00d710\u22128\nBurst\n-\n-\n6.5\n1.39\u00d710\u22127\n57.81\n27.38\nS200301q\n2020-03-01T07:45:14\n1.09\u00d710\u22125\nCBC\n0.015\nMass Gap\n5.7\n1.63\u00d710\u22127\n61.29\n0.53\nS200301u\n2020-03-01T08:14:42\n2.08\u00d710\u22126\nBurst\n-\n-\n6.3\n2.52\u00d710\u22127\n27.83\n47.03\nS200302b\n2020-03-02T00:58:11\n2.06\u00d710\u22125\nCBC\n0.006\nNSBH\n6.5\n1.10\u00d710\u22127\n83.73\n0.06\nS200302bg\n2020-03-02T21:53:08\n9.31\u00d710\u22126\nCBC\n0.021\nBNS\n-\n-\n-\n-\nS200302c\n2020-03-02T01:58:11\n9.35\u00d710\u22129\nCBC\n0.889\nBBH\n5.7\n3.69\u00d710\u22127\n29.48\n27.98\nS200302m\n2020-03-02T06:14:02\n1.61\u00d710\u22125\nCBC\n0.018\nBBH\n6.0\n3.65\u00d710\u22127\n31.8\n14.56\nS200303ad\n2020-03-03T07:47:20\n1.94\u00d710\u22125\nCBC\n0.008\nNSBH\n5.4\n9.99\u00d710\u22127\n0.01\n52.01\nS200303ae\n2020-03-03T08:08:40\n4.06\u00d710\u22126\nCBC\n0.181\nBNS\n-\n-\n-\n-\nS200303aj\n2020-03-03T08:36:14\n1.47\u00d710\u22125\nCBC\n0.016\nMass Gap\n-\n-\n-\n-\nS200303ba\n2020-03-03T12:15:48\n1.32\u00d710\u22128\nCBC\n0.864\nBBH\n5.8\n5.30\u00d710\u22127\n4.42\n16.8\nS200303bf\n2020-03-03T13:14:32\n2.12\u00d710\u22125\nCBC\n0.014\nBBH\n-\n-\n-\n-\nS200303bl\n2020-03-03T14:42:16\n1.75\u00d710\u22125\nCBC\n0.016\nBBH\n6.6\n3.27\u00d710\u22127\n1.97\n31.14\nS200303f\n2020-03-03T01:19:35\n6.23\u00d710\u22126\nCBC\n0.015\nNSBH\n5.8\n5.79\u00d710\u22127\n1.01\n0.19\nS200303i\n2020-03-03T01:44:47\n1.48\u00d710\u22125\nCBC\n0.051\nBBH\n-\n-\n-\n-\nS200303p\n2020-03-03T03:11:58\n1.91\u00d710\u22125\nCBC\n0.002\nNSBH\n-\n-\n-\n-\nS200303r\n2020-03-03T03:34:34\n2.22\u00d710\u22125\nCBC\n0.013\nBBH\n-\n-\n-\n-\nS200304ao\n2020-03-04T14:46:28\n8.26\u00d710\u22126\nCBC\n0.029\nBBH\n5.0\n4.85\u00d710\u22127\n13.64\n29.69\nS200304ay\n2020-03-04T18:04:42\n1.89\u00d710\u22125\nCBC\n0.008\nNSBH\n7.1\n-\n-\n-\nS200304bg\n2020-03-04T20:03:56\n1.88\u00d710\u22125\nCBC\n0.005\nNSBH\n-\n-\n-\n-\nS200304bi\n2020-03-04T20:03:19\n1.30\u00d710\u22125\nBurst\n-\n-\n5.4\n2.81\u00d710\u22127\n33.15\n37.91\nS200304bj\n2020-03-04T20:23:27\n2.16\u00d710\u22125\nCBC\n0.053\nMass Gap\n6.0\n4.88\u00d710\u22127\n16.78\n30.41\nS200304d\n2020-03-04T02:36:34\n2.21\u00d710\u22125\nCBC\n0.001\nNSBH\n7.1\n2.47\u00d710\u22127\n39.05\n12.81\nS200305f\n2020-03-05T01:01:14\n1.98\u00d710\u22125\nCBC\n0.008\nMass Gap\n6.6\n1.14\u00d710\u22127\n71.25\n13.45\nS200305h\n2020-03-05T01:05:29\n2.68\u00d710\u22126\nBurst\n-\n-\n6.2\n2.92\u00d710\u22127\n25.95\n39.5\nS200305q\n2020-03-05T03:00:17\n2.24\u00d710\u22125\nCBC\n0.014\nBBH\n5.7\n1.93\u00d710\u22127\n0.57\n99.23\nS200305r\n2020-03-05T03:09:11\n2.26\u00d710\u22125\nCBC\n0.006\nBNS\n6.2\n4.11\u00d710\u22127\n31.05\n16.42\nS200306ar\n2020-03-06T11:18:22\n9.75\u00d710\u22126\nBurst\n-\n-\n6.9\n7.59\u00d710\u22127\n4.26\n20.08\nS200306aw\n2020-03-06T12:03:00\n1.97\u00d710\u22125\nCBC\n0.015\nBNS\n6.6\n1.93\u00d710\u22127\n32.37\n31.1\nS200306az\n2020-03-06T12:37:37\n3.53\u00d710\u22126\nBurst\n-\n-\n5.5\n3.75\u00d710\u22126\n13.1\n26.61\nS200306bj\n2020-03-06T14:16:31\n9.39\u00d710\u22126\nCBC\n0.009\nNSBH\n4.7\n1.87\u00d710\u22127\n9.13\n76.94\nS200306bq\n2020-03-06T15:03:01\n1.37\u00d710\u22125\nCBC\n0.011\nBNS\n6.1\n2.46\u00d710\u22127\n2.12\n1.64\nS200306by\n2020-03-06T16:21:06\n1.31\u00d710\u22127\nBurst\n-\n-\n5.4\n6.74\u00d710\u22127\n0.78\n12.25\nS200306cc\n2020-03-06T16:58:29\n1.42\u00d710\u22126\nBurst\n-\n-\n5.6\n6.07\u00d710\u22127\n11.21\n7.81\nS200306ci\n2020-03-06T19:39:14\n5.85\u00d710\u22126\nCBC\n0.021\nBNS\n6.2\n3.61\u00d710\u22127\n22.35\n33.5\nS200306cv\n2020-03-06T21:15:25\n2.48\u00d710\u22126\nCBC\n0.097\nBBH\n5.8\n4.63\u00d710\u22127\n6.64\n21.1\nS200306dc\n2020-03-06T23:07:39\n1.40\u00d710\u22125\nCBC\n0.024\nBBH\n-\n-\n-\n-\nS200307ac\n2020-03-07T07:36:20\n9.58\u00d710\u22126\nCBC\n0.027\nBBH\n7.0\n3.04\u00d710\u22127\n29.64\n25.63\nS200307ae\n2020-03-07T08:33:25\n1.59\u00d710\u22125\nCBC\n0.013\nBNS\n6.1\n2.71\u00d710\u22127\n18.12\n50.75\nS200307ak\n2020-03-07T10:01:25\n1.24\u00d710\u22129\nBurst\n-\n-\n5.2\n3.69\u00d710\u22127\n20.01\n0.08\nS200307ao\n2020-03-07T11:07:37\n2.02\u00d710\u22125\nBurst\n-\n-\n5.7\n5.42\u00d710\u22127\n10.88\n63.59\nS200307ap\n2020-03-07T12:01:25\n1.19\u00d710\u22129\nBurst\n-\n-\n6.5\n6.53\u00d710\u22127\n0\n23.59\nS200307aq\n2020-03-07T12:44:02\n1.96\u00d710\u22125\nCBC\n0.014\nBBH\n6.4\n6.14\u00d710\u22127\n18.03\n28.33\nS200307ar\n2020-03-07T12:51:04\n1.24\u00d710\u22125\nBurst\n-\n-\n6.3\n4.82\u00d710\u22127\n7.93\n16.88\nS200307aw\n2020-03-07T15:25:33\n9.31\u00d710\u22127\nBurst\n-\n-\n5.9\n3.10\u00d710\u22127\n29.13\n21.97\nS200307ay\n2020-03-07T16:08:24\n4.11\u00d710\u22126\nCBC\n0.021\nNSBH\n-\n-\n-\n-\n\n44\nS200307ba\n2020-03-07T17:53:38\n1.90\u00d710\u22126\nCBC\n0.095\nBBH\n5.4\n4.02\u00d710\u22127\n10.03\n1.74\nS200307bc\n2020-03-07T18:40:01\n9.05\u00d710\u22127\nCBC\n0.090\nBNS\n5.6\n3.40\u00d710\u22127\n27.17\n18.28\nS200307bk\n2020-03-07T23:36:32\n2.20\u00d710\u22125\nCBC\n0.006\nNSBH\n6.4\n7.47\u00d710\u22127\n4.42\n0.39\nS200307c\n2020-03-07T02:34:37\n2.22\u00d710\u22125\nCBC\n0.013\nBBH\n6.6\n7.64\u00d710\u22127\n0.02\n65.51\nS200307r\n2020-03-07T06:08:57\n1.27\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200307s\n2020-03-07T06:10:11\n2.60\u00d710\u22126\nBurst\n-\n-\n6.3\n2.17\u00d710\u22127\n5.58\n91.2\nS200307t\n2020-03-07T06:39:12\n1.20\u00d710\u22125\nCBC\n0.008\nNSBH\n6.3\n5.87\u00d710\u22127\n1.25\n56.02\nS200308af\n2020-03-08T11:46:48\n5.85\u00d710\u22126\nCBC\n0.016\nNSBH\nNFL\n2.62\u00d710\u22127\n31.77\n36.97\nS200308aj\n2020-03-08T12:43:22\n3.89\u00d710\u22126\nBurst\n-\n-\n6.0\n6.00\u00d710\u22127\n1.14\n31.23\nS200308au\n2020-03-08T14:31:49\n1.82\u00d710\u22125\nCBC\n0.016\nBBH\n6.0\n6.93\u00d710\u22127\n0.03\n99.26\nS200308av\n2020-03-08T14:28:38\n1.25\u00d710\u22125\nBurst\n-\n-\n5.3\n3.86\u00d710\u22127\n25.35\n23.97\nS200308bp\n2020-03-08T17:54:08\n7.08\u00d710\u22126\nBurst\n-\n-\n6.4\n3.87\u00d710\u22127\n8.65\n31.83\nS200308bz\n2020-03-08T20:24:27\n1.21\u00d710\u22125\nCBC\n0.009\nNSBH\n6.6\n7.08\u00d710\u22127\n1.94\n74.72\nS200308cc\n2020-03-08T21:26:18\n6.91\u00d710\u22126\nCBC\n0.019\nMass Gap\n5.4\n4.54\u00d710\u22127\n0.3\n0.64\nS200308e\n2020-03-08T01:19:27\n3.62\u00d710\u22129\nCBC\n0.830\nNSBH\n6.2\n4.97\u00d710\u22127\n1.91\n92.48\nS200308g\n2020-03-08T01:38:18\n7.01\u00d710\u22126\nCBC\n0.005\nNSBH\n5.7\n2.20\u00d710\u22127\n28.96\n50.22\nS200308h\n2020-03-08T01:45:05\n7.82\u00d710\u22126\nBurst\n-\n-\n5.5\n2.04\u00d710\u22127\n43.87\n19.8\nS200308i\n2020-03-08T02:19:35\n1.46\u00d710\u22125\nCBC\n0.003\nNSBH\n5.6\n1.33\u00d710\u22127\n62.07\n9.03\nS200308z\n2020-03-08T09:11:16\n1.08\u00d710\u22126\nCBC\n0.087\nNSBH\n6.2\n2.94\u00d710\u22127\n36.66\n46.02\nS200309ag\n2020-03-09T14:45:45\n5.47\u00d710\u22126\nCBC\n0.031\nBNS\n5.4\n2.96\u00d710\u22127\n23.37\n5.03\nS200309ai\n2020-03-09T15:35:45\n1.18\u00d710\u22125\nCBC\n0.025\nMass Gap\n-\n-\n-\n-\nS200309av\n2020-03-09T17:57:10\n2.15\u00d710\u22125\nCBC\n0.014\nBBH\n5.9\n5.55\u00d710\u22128\n95.56\n0.07\nS200309bh\n2020-03-09T21:28:42\n1.69\u00d710\u22125\nCBC\n0.006\nNSBH\n6.5\n6.71\u00d710\u22127\n0.02\n29.24\nS200309bj\n2020-03-09T22:30:15\n2.17\u00d710\u22125\nCBC\n0.036\nMass Gap\n6.8\n3.65\u00d710\u22127\n16.3\n26.46\nS200309bk\n2020-03-09T22:36:27\n9.07\u00d710\u22126\nCBC\n0.015\nBNS\n6.1\n5.75\u00d710\u22127\n5.45\n3.48\nS200309bm\n2020-03-09T23:14:58\n2.29\u00d710\u22125\nCBC\n0.016\nBBH\n-\n-\n-\n-\nS200309bu\n2020-03-09T23:59:07\n4.84\u00d710\u22126\nCBC\n0.041\nBBH\n5.7\n5.00\u00d710\u22127\n0.5\n1.53\nS200309d\n2020-03-09T01:26:51\n2.18\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200310ab\n2020-03-10T07:58:59\n2.30\u00d710\u22126\nCBC\n0.027\nMass Gap\n6.8\n3.02\u00d710\u22127\n27.19\n25.38\nS200310az\n2020-03-10T22:54:14\n1.69\u00d710\u22125\nCBC\n0.014\nMass Gap\n5.9\n3.96\u00d710\u22127\n2.08\n1.34\nS200310b\n2020-03-10T00:20:05\n2.02\u00d710\u22125\nCBC\n0.002\nNSBH\n6.4\n7.47\u00d710\u22127\n0.09\n15.25\nS200310f\n2020-03-10T01:02:19\n7.31\u00d710\u22126\nCBC\n0.051\nMass Gap\n-\n-\n-\n-\nS200310s\n2020-03-10T05:59:46\n9.75\u00d710\u22127\nBurst\n-\n-\n6.0\n8.05\u00d710\u22127\n0.17\n76.04\nS200310t\n2020-03-10T06:11:59\n3.41\u00d710\u22126\nCBC\n0.053\nBNS\n5.9\n1.03\u00d710\u22127\n85.57\n0.03\nS200310u\n2020-03-10T06:21:24\n1.06\u00d710\u22126\nCBC\n0.115\nBNS\n5.6\n4.94\u00d710\u22127\n0\n32.14\nS200311ba\n2020-03-11T10:31:22\n6.56\u00d710\u22126\nCBC\n0.026\nBNS\n-\n-\n-\n-\nS200311bb\n2020-03-11T10:34:04\n1.41\u00d710\u22126\nCBC\n0.115\nBNS\n5.9\n5.97\u00d710\u22127\n11.26\n32.65\nS200311bp\n2020-03-11T14:05:25\n9.06\u00d710\u22126\nCBC\n0.015\nBNS\n6.4\n3.19\u00d710\u22127\n39.53\n31.29\nS200311h\n2020-03-11T01:48:40\n8.12\u00d710\u22126\nBurst\n-\n-\n5.7\n3.49\u00d710\u22127\n26.74\n1.72\nS200311r\n2020-03-11T04:04:20\n2.06\u00d710\u22126\nCBC\n0.049\nNSBH\n-\n-\n-\n-\nS200311v\n2020-03-11T04:37:19\n1.27\u00d710\u22125\nCBC\n0.042\nMass Gap\n5.8\n4.98\u00d710\u22127\n0.42\n53.43\nS200311w\n2020-03-11T04:50:30\n1.40\u00d710\u22125\nCBC\n0.018\nNSBH\n-\n-\n-\n-\nS200311y\n2020-03-11T04:53:03\n7.61\u00d710\u22126\nBurst\n-\n-\n6.5\n3.11\u00d710\u22127\n20.96\n34.03\nS200312aa\n2020-03-12T07:36:08\n3.63\u00d710\u22126\nCBC\n0.023\nNSBH\n6.2\n3.20\u00d710\u22127\n52.44\n0\nS200312b\n2020-03-12T00:34:15\n1.93\u00d710\u22125\nCBC\n0.008\nMass Gap\n-\n-\n-\n-\nS200312ba\n2020-03-12T15:41:49\n9.85\u00d710\u22126\nBurst\n-\n-\n6.8\n3.93\u00d710\u22127\n11.22\n22.2\nS200312br\n2020-03-12T22:06:08\n1.72\u00d710\u22125\nCBC\n0.008\nNSBH\n6.4\n4.39\u00d710\u22127\n16.91\n19.47\nS200312d\n2020-03-12T01:16:51\n1.09\u00d710\u22125\nCBC\n0.131\nBBH\n6.4\n1.55\u00d710\u22127\n33.13\n56.29\nS200312i\n2020-03-12T01:43:29\n2.29\u00d710\u22127\nCBC\n0.187\nMass Gap\n5.6\n3.77\u00d710\u22127\n8.03\n69.57\nS200313aa\n2020-03-13T06:54:23\n8.17\u00d710\u22126\nBurst\n-\n-\n5.8\n2.66\u00d710\u22127\n43.35\n9.32\n\n45\nS200313ag\n2020-03-13T07:50:28\n9.62\u00d710\u22126\nBurst\n-\n-\n4.2\n1.47\u00d710\u22127\n24.9\n71.5\nS200313aw\n2020-03-13T12:33:04\n2.11\u00d710\u22125\nCBC\n0.010\nMass Gap\n-\n-\n-\n-\nS200313ba\n2020-03-13T13:31:50\n8.59\u00d710\u22126\nCBC\n0.007\nBNS\n5.8\n3.77\u00d710\u22127\n70.07\n0\nS200313bb\n2020-03-13T13:32:17\n1.84\u00d710\u22126\nCBC\n0.039\nNSBH\n5.8\n5.09\u00d710\u22127\n0.04\n64.3\nS200313be\n2020-03-13T14:45:42\n8.23\u00d710\u22126\nCBC\n0.015\nNSBH\n6.6\n5.98\u00d710\u22127\n5.5\n43.16\nS200313bf\n2020-03-13T15:06:31\n9.69\u00d710\u22126\nCBC\n0.020\nMass Gap\n5.6\n6.52\u00d710\u22127\n0\n42.72\nS200313bs\n2020-03-13T20:08:46\n1.92\u00d710\u22125\nCBC\n0.006\nBNS\n-\n-\n-\n-\nS200313by\n2020-03-13T21:40:33\n2.39\u00d710\u22126\nBurst\n-\n-\n6.8\n2.18\u00d710\u22127\n35.94\n42.59\nS200313cd\n2020-03-13T22:39:09\n1.18\u00d710\u22125\nCBC\n0.009\nNSBH\n5.4\n6.30\u00d710\u22127\n8.44\n44.62\nS200313h\n2020-03-13T01:46:59\n4.04\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200313j\n2020-03-13T02:17:18\n6.90\u00d710\u22126\nBurst\n-\n-\n-\n-\n-\n-\nS200313l\n2020-03-13T02:32:04\n2.14\u00d710\u22125\nCBC\n0.005\nNSBH\n6.4\n3.90\u00d710\u22127\n62.51\n0.02\nS200313n\n2020-03-13T03:33:07\n2.26\u00d710\u22125\nCBC\n0.006\nMass Gap\n7.0\n9.18\u00d710\u22127\n0.35\n7.04\nS200314ay\n2020-03-14T17:23:01\n2.26\u00d710\u22125\nCBC\n0.005\nNSBH\n5.4\n5.15\u00d710\u22127\n0.01\n26.18\nS200314be\n2020-03-14T19:47:18\n8.92\u00d710\u22126\nCBC\n0.033\nBBH\n6.3\n5.98\u00d710\u22127\n4.68\n31.97\nS200314bg\n2020-03-14T19:51:02\n1.86\u00d710\u22125\nCBC\n0.007\nNSBH\n-\n-\n-\n-\nS200314bn\n2020-03-14T21:12:48\n7.14\u00d710\u22127\nBurst\n-\n-\n5.8\n3.00\u00d710\u22127\n39.1\n8.05\nS200314bt\n2020-03-14T22:36:02\n1.28\u00d710\u22125\nCBC\n0.074\nMass Gap\n5.7\n4.80\u00d710\u22127\n3.78\n41.95\nS200314bx\n2020-03-14T23:29:35\n1.63\u00d710\u22127\nCBC\n0.189\nNSBH\n6.2\n1.19\u00d710\u22127\n81.51\n3.68\nS200314m\n2020-03-14T04:21:10\n1.04\u00d710\u22125\nCBC\n0.012\nBNS\n6.9\n7.35\u00d710\u22126\n0.11\n0.29\nS200314r\n2020-03-14T06:10:33\n1.34\u00d710\u22125\nCBC\n0.008\nNSBH\n5.5\n4.47\u00d710\u22127\n7.22\n20.9\nS200314x\n2020-03-14T07:26:14\n2.05\u00d710\u22125\nCBC\n0.005\nNSBH\n5.6\n2.42\u00d710\u22127\n10.07\n0.01\nS200315ac\n2020-03-15T11:07:32\n9.83\u00d710\u22126\nCBC\n0.002\nNSBH\n6.6\n5.28\u00d710\u22127\n2.8\n19.02\nS200315ba\n2020-03-15T20:48:52\n1.62\u00d710\u22125\nCBC\n0.022\nBBH\n5.8\n3.05\u00d710\u22127\n14.75\n21.12\nS200316ad\n2020-03-16T10:26:06\n1.24\u00d710\u22125\nCBC\n0.024\nMass Gap\n6.5\n3.47\u00d710\u22127\n31.9\n1.31\nS200316aj\n2020-03-16T11:39:17\n3.69\u00d710\u22126\nCBC\n0.034\nNSBH\n6.3\n6.66\u00d710\u22128\n99.29\n0.01\nS200316bk\n2020-03-16T22:16:22\n9.73\u00d710\u22126\nCBC\n0.013\nBNS\n5.8\n3.18\u00d710\u22127\n28.02\n33.66\nS200316f\n2020-03-16T01:37:07\n6.27\u00d710\u22126\nBurst\n-\n-\n5.8\n4.04\u00d710\u22127\n18.78\n39.79\nS200316u\n2020-03-16T06:28:34\n1.56\u00d710\u22125\nCBC\n0.006\nNSBH\n5.5\n1.73\u00d710\u22127\n95.27\n85.21\nS200316w\n2020-03-16T06:55:03\n1.40\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200317ad\n2020-03-17T11:52:19\n1.22\u00d710\u22125\nCBC\n0.014\nNSBH\n5.8\n8.61\u00d710\u22127\n0.01\n32.78\nS200317ag\n2020-03-17T13:31:35\n3.35\u00d710\u22127\nBurst\n-\n-\n7.4\n4.95\u00d710\u22127\n0.2\n11.09\nS200317ah\n2020-03-17T14:00:01\n9.02\u00d710\u22126\nCBC\n0.076\nMass Gap\n6.5\n5.40\u00d710\u22127\n6.56\n36.73\nS200317ai\n2020-03-17T14:14:06\n9.12\u00d710\u22126\nCBC\n0.021\nBNS\n5.7\n6.33\u00d710\u22127\n2.88\n76.18\nS200317b\n2020-03-17T00:19:00\n4.79\u00d710\u22126\nBurst\n-\n-\n5.0\n4.76\u00d710\u22127\n15.23\n11.1\nS200317c\n2020-03-17T02:24:40\n7.27\u00d710\u22126\nCBC\n0.081\nBNS\n6.3\n2.79\u00d710\u22127\n42.36\n20.62\nS200317d\n2020-03-17T02:33:58\n1.34\u00d710\u22125\nCBC\n0.025\nBBH\n6.4\n3.22\u00d710\u22127\n19.1\n5.8\nS200318af\n2020-03-18T08:02:54\n1.43\u00d710\u22125\nCBC\n0.007\nBNS\n-\n-\n-\n-\nS200318ak\n2020-03-18T10:21:25\n1.31\u00d710\u22125\nCBC\n0.008\nNSBH\n5.2\n2.64\u00d710\u22127\n7.52\n97.84\nS200318av\n2020-03-18T15:35:18\n1.16\u00d710\u22125\nBurst\n-\n-\n6.7\n5.22\u00d710\u22127\n11.87\n20.62\nS200318be\n2020-03-18T17:57:32\n3.22\u00d710\u22126\nCBC\n0.048\nBNS\n6.7\n4.11\u00d710\u22127\n0.01\n75.66\nS200318bf\n2020-03-18T18:04:09\n4.75\u00d710\u22126\nCBC\n0.035\nBNS\n6.2\n3.36\u00d710\u22127\n29.71\n27.94\nS200318n\n2020-03-18T03:20:11\n1.06\u00d710\u22125\nCBC\n0.010\nNSBH\n5.9\n5.68\u00d710\u22127\n3.38\n3.54\nS200318s\n2020-03-18T04:56:32\n1.79\u00d710\u22125\nBurst\n-\n-\n6.6\n3.93\u00d710\u22127\n31.15\n13.41\nS200318z\n2020-03-18T06:34:52\n6.40\u00d710\u22126\nBurst\n-\n-\n5.9\n5.94\u00d710\u22127\n5.89\n57.22\nS200319aq\n2020-03-19T13:50:32\n1.21\u00d710\u22125\nCBC\n0.020\nBBH\n6.3\n6.57\u00d710\u22127\n6.6\n67.54\nS200319ax\n2020-03-19T15:50:57\n1.93\u00d710\u22125\nCBC\n0.011\nBNS\n5.6\n4.90\u00d710\u22127\n0.01\n28.26\nS200319bh\n2020-03-19T22:27:38\n4.08\u00d710\u22126\nBurst\n-\n-\n6.8\n5.57\u00d710\u22127\n13.01\n24.54\nS200319d\n2020-03-19T01:38:23\n6.70\u00d710\u22126\nCBC\n0.053\nBNS\n6.2\n3.44\u00d710\u22127\n49.34\n0.28\nS200320af\n2020-03-20T08:35:13\n1.65\u00d710\u22125\nBurst\n-\n-\n5.9\n6.95\u00d710\u22127\n1.24\n25.73\n\n46\nS200320bm\n2020-03-20T22:34:05\n5.16\u00d710\u22127\nCBC\n0.193\nMass Gap\nNFL\n6.95\u00d710\u22127\n3.09\n0.4\nS200320p\n2020-03-20T04:36:30\n1.23\u00d710\u22126\nCBC\n0.075\nNSBH\n5.8\n2.35\u00d710\u22127\n49.27\n35.71\nS200320q\n2020-03-20T04:37:11\n1.49\u00d710\u22125\nBurst\n-\n-\n6.0\n5.27\u00d710\u22127\n20.22\n24.6\nS200320w\n2020-03-20T06:15:52\n1.51\u00d710\u22126\nBurst\n-\n-\n5.4\n6.25\u00d710\u22127\n4.29\n30.47\nS200321ak\n2020-03-21T14:34:50\n2.09\u00d710\u22125\nBurst\n-\n-\n5.8\n4.99\u00d710\u22127\n10.79\n43.72\nS200321bb\n2020-03-21T22:32:26\n2.45\u00d710\u22126\nCBC\n0.058\nBNS\n6.7\n6.93\u00d710\u22128\n39.15\n59.12\nS200321h\n2020-03-21T03:46:57\n5.11\u00d710\u22126\nBurst\n-\n-\n6.5\n4.66\u00d710\u22127\n27.21\n20.06\nS200321n\n2020-03-21T05:03:14\n2.21\u00d710\u22125\nCBC\n0.009\nMass Gap\n5.6\n9.15\u00d710\u22127\n0\n5.69\nS200321z\n2020-03-21T10:08:10\n1.67\u00d710\u22125\nCBC\n0.005\nMass Gap\n5.4\n7.36\u00d710\u22127\n3.83\n2.07\nS200322ab\n2020-03-22T09:11:33\n9.98\u00d710\u22126\nCBC\n0.072\nBBH\n6.2\n5.51\u00d710\u22127\n0.06\n24.67\nS200322at\n2020-03-22T14:59:58\n1.37\u00d710\u22126\nBurst\n-\n-\n4.8\n3.75\u00d710\u22127\n8.31\n44.23\nS200322ax\n2020-03-22T16:35:09\n6.07\u00d710\u22126\nBurst\n-\n-\n6.4\n5.71\u00d710\u22127\n1.29\n33.95\nS200322bh\n2020-03-22T19:11:57\n5.66\u00d710\u22126\nCBC\n0.035\nMass Gap\n6.8\n1.99\u00d710\u22127\n46.19\n3.33\nS200322bs\n2020-03-22T22:32:58\n2.23\u00d710\u22125\nBurst\n-\n-\n6.4\n1.39\u00d710\u22127\n61.44\n1\nS200322bv\n2020-03-22T23:06:07\n1.81\u00d710\u22127\nCBC\n0.300\nNSBH\n-\n-\n-\n-\nS200322by\n2020-03-22T23:34:00\n5.92\u00d710\u22127\nCBC\n0.133\nNSBH\n-\n-\n-\n-\nS200322n\n2020-03-22T04:11:26\n2.32\u00d710\u22126\nCBC\n0.037\nNSBH\nNFL\n4.87\u00d710\u22127\n65.29\n4.61\nS200322q\n2020-03-22T04:24:47\n4.55\u00d710\u22126\nCBC\n0.027\nBNS\n5.4\n2.69\u00d710\u22127\n65.73\n11.29\nS200322z\n2020-03-22T07:51:55\n8.31\u00d710\u22126\nCBC\n0.017\nMass Gap\n6.1\n1.96\u00d710\u22127\n61\n7.99\nS200323ah\n2020-03-23T11:31:55\n1.82\u00d710\u22125\nBurst\n-\n-\n6.1\n5.75\u00d710\u22127\n9.2\n15.61\nS200323aj\n2020-03-23T11:59:25\n1.65\u00d710\u22125\nBurst\n-\n-\n5.9\n5.11\u00d710\u22127\n8.89\n36.02\nS200323aq\n2020-03-23T13:33:24\n4.12\u00d710\u22126\nCBC\n0.017\nMass Gap\n5.8\n2.81\u00d710\u22127\n31.38\n31.42\nS200323as\n2020-03-23T13:53:52\n7.47\u00d710\u22126\nCBC\n0.013\nMass Gap\n5.9\n1.30\u00d710\u22127\n24.74\n68.22\nS200323ax\n2020-03-23T14:56:35\n1.43\u00d710\u22125\nCBC\n0.009\nBNS\n6.3\n8.59\u00d710\u22127\n0.86\n1.88\nS200323bf\n2020-03-23T19:37:34\n6.60\u00d710\u22127\nBurst\n-\n-\n8.3\n7.72\u00d710\u22127\n2.7\n77.62\nS200323n\n2020-03-23T05:20:05\n2.08\u00d710\u22125\nCBC\n0.010\nBNS\n6.2\n7.74\u00d710\u22127\n52.37\n28.86\nS200324a\n2020-03-24T01:46:44\n6.30\u00d710\u22126\nCBC\n0.021\nBNS\n6.5\n2.39\u00d710\u22127\n32.95\n36.47\nS200324ax\n2020-03-24T22:46:32\n1.85\u00d710\u22125\nCBC\n0.006\nNSBH\n10.6\n-\n-\n-\nS200325au\n2020-03-25T23:58:52\n2.28\u00d710\u22125\nCBC\n0.008\nMass Gap\nNFL\n1.24\u00d710\u22126\n1.94\n90.04\nS200325j\n2020-03-25T07:23:35\n2.81\u00d710\u22126\nCBC\n0.105\nBBH\n6.4\n5.41\u00d710\u22127\n1.33\n92.1\nS200325s\n2020-03-25T11:06:27\n9.84\u00d710\u22126\nCBC\n0.011\nMass Gap\n6.4\n4.11\u00d710\u22127\n7.56\n57.29\nS200325w\n2020-03-25T12:33:00\n9.84\u00d710\u22126\nBurst\n0.011\n-\n5.4\n6.61\u00d710\u22127\n0.33\n9.94\nS200326af\n2020-03-26T11:25:01\n2.09\u00d710\u22127\nBurst\n-\n-\n6.3\n4.21\u00d710\u22127\n12.18\n31.76\nS200326ax\n2020-03-26T16:10:49\n1.10\u00d710\u22125\nCBC\n0.017\nBNS\nNFL\n1.70\u00d710\u22127\n26.39\n55.04\nS200326ay\n2020-03-26T16:15:13\n8.90\u00d710\u22126\nCBC\n0.020\nBNS\n5.8\n6.29\u00d710\u22128\n29.72\n69.63\nS200326az\n2020-03-26T16:15:06\n4.02\u00d710\u22126\nBurst\n-\n-\n5.8\n5.02\u00d710\u22127\n3.33\n11.8\nS200326d\n2020-03-26T02:36:25\n1.57\u00d710\u22125\nCBC\n0.008\nNSBH\n-\n-\n-\n-\nS200326k\n2020-03-26T04:25:22\n1.01\u00d710\u22125\nBurst\n-\n-\n-\n-\n-\n-\nS200326x\n2020-03-26T09:10:40\n2.30\u00d710\u22125\nBurst\n-\n-\n6.2\n5.18\u00d710\u22127\n8.15\n31.08\nS200327am\n2020-03-27T12:53:52\n2.18\u00d710\u22125\nCBC\n0.020\nBBH\n5.9\n4.80\u00d710\u22127\n0.76\n59.11\nS200327as\n2020-03-27T14:00:08\n1.24\u00d710\u22125\nCBC\n0.027\nBBH\n6.2\n4.54\u00d710\u22127\n23.93\n34.74\nS200327az\n2020-03-27T16:01:26\n1.51\u00d710\u22125\nCBC\n0.009\nBNS\n7.0\n3.04\u00d710\u22127\n51.95\n12.82\nS200327g\n2020-03-27T02:34:28\n8.28\u00d710\u22127\nCBC\n0.111\nBNS\n5.7\n4.27\u00d710\u22127\n10.82\n3.53\nS200327i\n2020-03-27T03:12:11\n1.20\u00d710\u22125\nCBC\n0.033\nBBH\n5.8\n4.18\u00d710\u22127\n38.79\n17.17\nS200327j\n2020-03-27T03:15:27\n1.66\u00d710\u22125\nCBC\n0.006\nMass Gap\n22.4\n5.80\u00d710\u22127\n26.32\n0.13\n\n47\nTable 2. Details of the O3 candidates confirmed by the offline analysis and with a pastro > 0.5, for which GUANO data dumps\nare available. The reported pastro and FAR are relative to the pipeline with the highest pastro. If two pipelines have equal pastro,\nwe select the one with the highest SNR. The GW FAR, pastro and Class details are quoted from Abbott et al. (2024) and Abbott\net al. (2023).\nSID\nGW name\nFAR\nGroup\npastro\nClass\npClass\nPipeline\n(Hz)\nS190701ah\nGW190701 203306\n1.79 \u00d7 10\u22128\nCBC\n>0.99\nBBH\n1.00\nPyCBC-BBH\nS190915ak\nGW190915 235702\n2.22 \u00d7 10\u221212\nCBC\n>0.99\nBBH\n1.00\nPyCBC-BBH\nS190930s\nGW190930 133541\n3.81 \u00d7 10\u221210\nCBC\n>0.99\nBBH\n0.85\nPyCBC-BBH\nS191127p\nGW191127 050227\n1.29 \u00d7 10\u22127\nCBC\n0.74\nBBH\n0.74\nPyCBC-BBH\nS191204r\nGW191204 171526\n1.86 \u00d7 10\u221213\nCBC\n>0.99\nBBH\n1.00\nMBTA\nS191216ap\nGW191216 213338\n2.96 \u00d7 10\u221211\nCBC\n>0.99\nBBH\n1.00\nMBTA\nS200128d\nGW200128 022011\n1.36 \u00d7 10\u221210\nCBC\n>0.99\nBBH\n1.00\nPyCBC-BBH\nS200129m\nGW200129 065458\n9.03 \u00d7 10\u221241\nCBC\n>0.99\nBBH\n1.00\nGstLAL\nS200208q\nGW200208 130117\n9.84 \u00d7 10\u221212\nCBC\n>0.99\nBBH\n1.00\nPyCBC-BBH\nS200216br\nGW200216 220804\n1.11 \u00d7 10\u22128\nCBC\n0.77\nBBH\n0.77\nGstLAL\nS200220ad\nGW200220 061928\n2.16 \u00d7 10\u22127\nCBC\n0.62\nBBH\n0.62\nPyCBC-BBH\nS200225q\nGW200225 060421\n2.79 \u00d7 10\u221211\nCBC\n>0.99\nBBH\n1.00\ncWB\nS200302c\nGW200302 015811\n3.54 \u00d7 10\u22129\nCBC\n0.91\nBBH\n0.91\nGstLAL\nS200322ab\nGW200322 091133\n1.44 \u00d7 10\u22125\nCBC\n0.62\nBBH\n0.62\nMBTA\n\n48\nTable 3. List of the O3 candidates confirmed by the offline analysis with pastro < 0.5, for which GUANO data dumps were\navailable. GW FAR, pastro, Class and pClass are reported from Abbott et al. (2023). CBC or Burst group categories are quoted\nas per the offline analysis and not from the low-latency information.\nSID\nTime\nGroup\nGW FAR\npastro\nClass\npClass\nPipeline\n(UTC)\n(Hz)\nS190906ah\n2019-09-06T20:05:00\nCBC\n5.66 \u00d7 10\u22126\n2.38 \u00d7 10\u22123\nBBH\n1.51 \u00d7 10\u22123\nGstLAL\nS191106r\n2019-11-06T18:41:51\nCBC\n1.18 \u00d7 10\u22125\n1.97 \u00d7 10\u22122\nBBH\n1.97 \u00d7 10\u22122\nPyCBC-BBH\nS191116ac\n2019-11-16T14:21:55\nCBC\n8.25 \u00d7 10\u22126\n2.10 \u00d7 10\u22124\nNSBH\n1.67 \u00d7 10\u22124\nPyCBC-broad\nS191121bt\n2019-11-21T16:45:42\nCBC\n5.44 \u00d7 10\u22126\n4.13 \u00d7 10\u22123\nBBH\n4.13 \u00d7 10\u22123\nGstLAL\nS191208b\n2019-12-08T02:02:15\nCBC\n2.10 \u00d7 10\u22125\n4.26 \u00d7 10\u22124\nBNS\n4.26 \u00d7 10\u22124\nPyCBC-broad\nS191213be\n2019-12-13T19:54:22\nCBC\n5.78 \u00d7 10\u22126\n5.40 \u00d7 10\u22122\nBBH\n5.40 \u00d7 10\u22122\nPyCBC-BBH\nS191225aq\n2019-12-25T21:57:15\nCBC\n1.57 \u00d7 10\u22126\n1.30 \u00d7 10\u22122\nBBH\n1.30 \u00d7 10\u22122\nGstLAL\nS191229o\n2019-12-29T12:02:34\nCBC\n4.17 \u00d7 10\u22126\n1.15 \u00d7 10\u22121\nBBH\n6.13 \u00d7 10\u22122\nPyCBC-broad\nS191230at\n2019-12-30T21:24:48\nCBC\n1.72 \u00d7 10\u22125\n7.01 \u00d7 10\u22124\nBNS\n7.01 \u00d7 10\u22124\nPyCBC-broad\nS191231ad\n2019-12-31T11:45:12\nBurst\n4.31 \u00d7 10\u22127\n8.30 \u00d7 10\u22123\n-\n-\ncWB\nS200103az\n2020-01-03T23:31:11\nCBC\n5.09 \u00d7 10\u22126\n3.02 \u00d7 10\u22124\nNSBH\n2.98 \u00d7 10\u22124\nPyCBC-broad\nS200105aj\n2020-01-05T18:00:59\nCBC\n3.61 \u00d7 10\u22126\n5.88 \u00d7 10\u22124\nBNS\n5.85 \u00d7 10\u22124\nMBTA\nS200106k\n2020-01-06T04:37:09\nCBC\n1.00 \u00d7 10\u22125\n5.03 \u00d7 10\u22124\nBNS\n3.83 \u00d7 10\u22124\nMBTA\nS200109m\n2020-01-09T08:48:21\nCBC\n9.82 \u00d7 10\u22126\n1.44 \u00d7 10\u22123\nNSBH\n1.34 \u00d7 10\u22123\nPyCBC-broad\nS200112e\n2020-01-12T09:44:25\nCBC\n2.01 \u00d7 10\u22126\n3.10 \u00d7 10\u22123\nBNS\n3.02 \u00d7 10\u22123\nMBTA\nS200113f\n2020-01-13T02:14:20\nCBC\n2.23 \u00d7 10\u22125\n4.20 \u00d7 10\u22125\nBNS\n4.20 \u00d7 10\u22125\nMBTA\nS200113g\n2020-01-13T02:20:40\nCBC\n8.02 \u00d7 10\u22126\n1.48 \u00d7 10\u22123\nNSBH\n1.06 \u00d7 10\u22123\nPyCBC-broad\nS200114f\n2020-01-14T02:08:18\nBurst\n5.04 \u00d7 10\u22127\n2.10 \u00d7 10\u22123\n-\n-\ncWB\nS200114w\n2020-01-14T13:17:40\nCBC\n2.89 \u00d7 10\u22126\n9.44 \u00d7 10\u22122\nBBH\n4.98 \u00d7 10\u22122\nPyCBC-BBH\nS200118p\n2020-01-18T05:07:50\nCBC\n1.75 \u00d7 10\u22125\n6.41 \u00d7 10\u22124\nBNS\n6.41 \u00d7 10\u22124\nPyCBC-broad\nS200127o\n2020-01-27T11:43:05\nCBC\n1.57 \u00d7 10\u22125\n1.38 \u00d7 10\u22124\nBNS\n1.37 \u00d7 10\u22124\nMBTA\nS200127s\n2020-01-27T15:27:19\nCBC\n1.31 \u00d7 10\u22125\n1.34 \u00d7 10\u22124\nBNS\n1.33 \u00d7 10\u22124\nMBTA\nS200128f\n2020-01-28T04:54:04\nBurst\n2.34 \u00d7 10\u22127\n1.49 \u00d7 10\u22121\n-\n-\ncWB\nS200128p\n2020-01-28T09:54:07\nCBC\n1.40 \u00d7 10\u22126\n1.06 \u00d7 10\u22122\nNSBH\n1.02 \u00d7 10\u22122\nPyCBC-broad\nS200129ap\n2020-01-29T15:39:24\nBurst\n5.57 \u00d7 10\u22127\n1.50 \u00d7 10\u22123\n-\n-\ncWB\nS200129i\n2020-01-29T05:07:00\nCBC\n9.03 \u00d7 10\u22126\n1.13 \u00d7 10\u22123\nBNS\n1.13 \u00d7 10\u22123\nPyCBC-broad\nS200208l\n2020-02-08T09:01:03\nCBC\n1.33 \u00d7 10\u22125\n2.75 \u00d7 10\u22123\nBBH\n2.75 \u00d7 10\u22123\nPyCBC-BBH\nS200209am\n2020-02-09T13:14:49\nCBC\n2.10 \u00d7 10\u22125\n7.40 \u00d7 10\u22125\nBNS\n7.40 \u00d7 10\u22125\nMBTA\nS200210an\n2020-02-10T16:13:46\nCBC\n1.06 \u00d7 10\u22125\n2.47 \u00d7 10\u22122\nBBH\n2.47 \u00d7 10\u22122\nPyCBC-BBH\nS200212aa\n2020-02-12T10:18:23\nCBC\n4.82 \u00d7 10\u22126\n1.55 \u00d7 10\u22121\nBBH\n1.55 \u00d7 10\u22121\nMBTA\nS200213q\n2020-02-13T03:43:44\nCBC\n1.06 \u00d7 10\u22125\n3.58 \u00d7 10\u22124\nBNS\n2.79 \u00d7 10\u22124\nMBTA\nS200214bq\n2020-02-14T22:33:07\nCBC\n8.68 \u00d7 10\u22127\n2.61 \u00d7 10\u22121\nBBH\n2.61 \u00d7 10\u22121\nPyCBC-BBH\nS200214br\n2020-02-14T22:45:26\nBurst\n4.17 \u00d7 10\u22129\n9.10 \u00d7 10\u22121\n-\n-\ncWB\nS200218al\n2020-02-18T10:05:22\nBurst\n6.84 \u00d7 10\u22128\n4.88 \u00d7 10\u22121\n-\n-\ncWB\nS200218i\n2020-02-18T01:25:25\nCBC\n2.03 \u00d7 10\u22125\n3.59 \u00d7 10\u22123\nBBH\n3.59 \u00d7 10\u22123\nGstLAL\nS200219f\n2020-02-19T03:09:19\nCBC\n3.91 \u00d7 10\u22126\n1.34 \u00d7 10\u22122\nBBH\n1.34 \u00d7 10\u22122\nGstLAL\nS200220v\n2020-02-20T04:25:03\nCBC\n8.19 \u00d7 10\u22126\n1.25 \u00d7 10\u22123\nBNS\n9.78 \u00d7 10\u22124\nMBTA\nS200220w\n2020-02-20T04:51:22\nCBC\n2.28 \u00d7 10\u22125\n7.00 \u00d7 10\u22126\nBNS\n7.00 \u00d7 10\u22126\nMBTA\nS200221bh\n2020-02-21T15:19:18\nCBC\n4.51 \u00d7 10\u22126\n1.29 \u00d7 10\u22123\nNSBH\n1.29 \u00d7 10\u22123\nMBTA\nS200223aj\n2020-02-23T13:50:49\nCBC\n1.18 \u00d7 10\u22125\n4.41 \u00d7 10\u22124\nBNS\n4.41 \u00d7 10\u22124\nGstLAL\nS200223ao\n2020-02-23T14:28:21\nCBC\n1.47 \u00d7 10\u22125\n4.31 \u00d7 10\u22122\nBBH\n4.31 \u00d7 10\u22122\nPyCBC-broad\nS200223aw\n2020-02-23T18:06:59\nCBC\n1.53 \u00d7 10\u22127\n2.33 \u00d7 10\u22121\nBBH\n2.33 \u00d7 10\u22121\nGstLAL\nS200223u\n2020-02-23T08:09:27\nCBC\n3.37 \u00d7 10\u22127\n1.39 \u00d7 10\u22121\nBBH\n1.39 \u00d7 10\u22121\nGstLAL\nS200224cd\n2020-02-24T23:13:13\nCBC\n1.45 \u00d7 10\u22125\n1.50 \u00d7 10\u22124\nNSBH\n1.19 \u00d7 10\u22124\nPyCBC-broad\nS200224o\n2020-02-24T03:05:24\nBurst\n1.04 \u00d7 10\u22127\n4.00 \u00d7 10\u22121\n-\n-\ncWB\n\n49\nS200225as\n2020-02-25T14:28:07\nCBC\n1.37 \u00d7 10\u22125\n3.87 \u00d7 10\u22123\nBBH\n3.87 \u00d7 10\u22123\nGstLAL\nS200225az\n2020-02-25T21:59:37\nCBC\n4.85 \u00d7 10\u22126\n2.65 \u00d7 10\u22124\nNSBH\n1.83 \u00d7 10\u22124\nPyCBC-broad\nS200225k\n2020-02-25T03:41:20\nCBC\n1.07 \u00d7 10\u22125\n4.48 \u00d7 10\u22124\nNSBH\n4.48 \u00d7 10\u22124\nGstLAL\nS200225u\n2020-02-25T08:22:49\nCBC\n1.39 \u00d7 10\u22125\n4.46 \u00d7 10\u22122\nNSBH\n3.50 \u00d7 10\u22122\nPyCBC-broad\nS200226z\n2020-02-26T07:18:43\nCBC\n4.22 \u00d7 10\u22126\n3.34 \u00d7 10\u22123\nNSBH\n2.90 \u00d7 10\u22123\nPyCBC-broad\nS200302m\n2020-03-02T06:14:02\nCBC\n3.42 \u00d7 10\u22126\n1.40 \u00d7 10\u22122\nBBH\n1.40 \u00d7 10\u22122\nGstLAL\nS200303aj\n2020-03-03T08:36:14\nCBC\n2.16 \u00d7 10\u22125\n5.14 \u00d7 10\u22123\nBBH\n4.85 \u00d7 10\u22123\nMBTA\nS200304ao\n2020-03-04T14:46:28\nCBC\n7.87 \u00d7 10\u22126\n6.56 \u00d7 10\u22123\nBBH\n6.56 \u00d7 10\u22123\nGstLAL\nS200307ba\n2020-03-07T17:53:38\nCBC\n7.90 \u00d7 10\u22126\n1.04 \u00d7 10\u22122\nBBH\n1.04 \u00d7 10\u22122\nPyCBC-BBH\nS200307c\n2020-03-07T02:34:37\nCBC\n1.97 \u00d7 10\u22125\n2.71 \u00d7 10\u22123\nBBH\n2.71 \u00d7 10\u22123\nGstLAL\nS200308g\n2020-03-08T01:38:18\nCBC\n2.97 \u00d7 10\u22126\n2.43 \u00d7 10\u22123\nNSBH\n2.43 \u00d7 10\u22123\nGstLAL\nS200310b\n2020-03-10T00:20:05\nCBC\n1.58 \u00d7 10\u22125\n2.29 \u00d7 10\u22122\nNSBH\n1.67 \u00d7 10\u22122\nPyCBC-BBH\nS200310u\n2020-03-10T06:21:24\nCBC\n7.18 \u00d7 10\u22128\n4.79 \u00d7 10\u22123\nBNS\n4.79 \u00d7 10\u22123\nMBTA\nS200311ba\n2020-03-11T10:31:22\nCBC\n4.10 \u00d7 10\u22128\n1.94 \u00d7 10\u22121\nBNS\n1.94 \u00d7 10\u22121\nPyCBC-broad\nS200311r\n2020-03-11T04:04:20\nCBC\n1.78 \u00d7 10\u22125\n7.42 \u00d7 10\u22124\nNSBH\n4.67 \u00d7 10\u22124\nPyCBC-broad\nS200314be\n2020-03-14T19:47:18\nCBC\n2.30 \u00d7 10\u22126\n1.42 \u00d7 10\u22121\nBBH\n1.36 \u00d7 10\u22121\nPyCBC-BBH\nS200314x\n2020-03-14T07:26:14\nCBC\n1.54 \u00d7 10\u22125\n4.20 \u00d7 10\u22124\nNSBH\n4.00 \u00d7 10\u22124\nMBTA\nS200316aj\n2020-03-16T11:39:17\nCBC\n9.52 \u00d7 10\u22126\n9.08 \u00d7 10\u22124\nNSBH\n9.08 \u00d7 10\u22124\nMBTA\nS200318be\n2020-03-18T17:57:32\nCBC\n2.34 \u00d7 10\u22126\n1.97 \u00d7 10\u22124\nBNS\n1.97 \u00d7 10\u22124\nMBTA\nS200320p\n2020-03-20T04:36:30\nCBC\n7.49 \u00d7 10\u22127\n1.61 \u00d7 10\u22122\nNSBH\n1.55 \u00d7 10\u22122\nPyCBC-broad\nS200321bb\n2020-03-21T22:32:26\nCBC\n1.82 \u00d7 10\u22127\n3.55 \u00d7 10\u22123\nBNS\n3.53 \u00d7 10\u22123\nMBTA\nS200323as\n2020-03-23T13:53:52\nCBC\n3.02 \u00d7 10\u22126\n1.72 \u00d7 10\u22122\nBBH\n1.72 \u00d7 10\u22122\nGstLAL\nS200325j\n2020-03-25T07:23:35\nCBC\n9.14 \u00d7 10\u22126\n1.02 \u00d7 10\u22122\nBBH\n1.02 \u00d7 10\u22122\nPyCBC-BBH\nS200326af\n2020-03-26T11:25:01\nBurst\n7.51 \u00d7 10\u22128\n4.57 \u00d7 10\u22121\n-\n-\ncWB\nS200326ax\n2020-03-26T16:10:49\nCBC\n1.39 \u00d7 10\u22125\n3.60 \u00d7 10\u22125\nBNS\n3.60 \u00d7 10\u22125\nMBTA\nS200327g\n2020-03-27T02:34:28\nCBC\n8.91 \u00d7 10\u22127\n2.80 \u00d7 10\u22123\nBNS\n2.80 \u00d7 10\u22123\nMBTA\nS200327j\n2020-03-27T03:15:27\nCBC\n1.00 \u00d7 10\u22125\n9.57 \u00d7 10\u22124\nBNS\n9.34 \u00d7 10\u22124\nPyCBC-broad\n\n50\nTable 4.\nDetails of the joint FAR computed according to the procedure detailed in Section 5.4 for all the triggers with\nFARGRB,max < 10\u22123 Hz. The RAVEN alert is, by definition, evaluated considering only information received in low latency.\nThe events marked with a (*) are GW candidates with pastro > 0.5.\nName\nGW FAR\nGroup\nClass\n\u221a\nTS\nJoint FAR\nRaven Alert\n(Hz)\n(Hz)\nS190919ag\n3.42 \u00d7 10\u22126\nBurst\n-\n7.23\n2.16 \u00d7 10\u22127\nno\nS190919au\n3.24 \u00d7 10\u22126\nBurst\n-\n9.44\n7.36 \u00d7 10\u22129\nno\nS190919u\n8.18 \u00d7 10\u22126\nBurst\n-\n8.00\n8.56 \u00d7 10\u22128\nno\nS190930t\n1.54 \u00d7 10\u22128\nCBC\nNSBH\n14.60\n5.97 \u00d7 10\u221211\nyes\nS191110x\n2.93 \u00d7 10\u221211\nCBC\nMass Gap\n7.17\n9.59 \u00d7 10\u221212\nyes\nS191212l\n9.31 \u00d7 10\u22126\nCBC\nMass Gap\n7.16\n4.62 \u00d7 10\u22127\nno\nS191219ak\n1.22 \u00d7 10\u22126\nBurst\n-\n7.15\n1.19 \u00d7 10\u22127\nno\nS191226ae\n1.99 \u00d7 10\u22126\nCBC\nNSBH\n10.70\n4.81 \u00d7 10\u22129\nyes\nS191229ah\n1.23 \u00d7 10\u22126\nBurst\n-\n8.87\n3.15 \u00d7 10\u22129\nno\nS200101o\n1.66 \u00d7 10\u22125\nCBC\nBNS\n7.44\n4.15 \u00d7 10\u22127\nno\nS200108ah\n2.16 \u00d7 10\u22125\nCBC\nNSBH\n7.12\n6.77 \u00d7 10\u22127\nno\nS200108p\n1.93 \u00d7 10\u22127\nCBC\nBNS\n7.35\n1.71 \u00d7 10\u22128\nyes\nS200110aa\n2.12 \u00d7 10\u22125\nBurst\n-\n7.06\n6.91 \u00d7 10\u22127\nno\nS200110d\n1.45 \u00d7 10\u22125\nBurst\n-\n7.29\n4.84 \u00d7 10\u22127\nno\nS200114f\n1.23 \u00d7 10\u22129\nBurst\n-\n8.82\n5.70 \u00d7 10\u221212\nyes\nS200117z\n1.88 \u00d7 10\u22125\nCBC\nNSBH\n7.27\n5.63 \u00d7 10\u22127\nno\nS200130ai\n1.78 \u00d7 10\u22125\nCBC\nNSBH\n16.40\n3.13 \u00d7 10\u22128\nno\nS200214bo\n1.93 \u00d7 10\u22125\nCBC\nBNS\n7.20\n6.15 \u00d7 10\u22127\nno\nS200225af\n1.64 \u00d7 10\u22126\nCBC\nBNS\n10.57\n4.06 \u00d7 10\u22129\nyes\nS200225as\n6.23 \u00d7 10\u22126\nCBC\nBBH\n7.30\n2.86 \u00d7 10\u22127\nno\nS200225q*\n9.19 \u00d7 10\u22129\nCBC\nBBH\n8.21\n1.40 \u00d7 10\u221210\nno\nS200303bl\n1.75 \u00d7 10\u22125\nCBC\nBBH\n10.10\n3.09 \u00d7 10\u22128\nno\nS200304ay\n1.89 \u00d7 10\u22125\nCBC\nNSBH\n7.08\n6.74 \u00d7 10\u22127\nno\nS200304d\n2.21 \u00d7 10\u22125\nCBC\nNSBH\n7.08\n6.90 \u00d7 10\u22127\nno\nS200317ag\n3.35 \u00d7 10\u22127\nBurst\n-\n7.36\n2.66 \u00d7 10\u22128\nno\nS200323bf\n6.60 \u00d7 10\u22127\nBurst\n-\n8.27\n1.81 \u00d7 10\u22129\nno\nS200324ax\n1.85 \u00d7 10\u22125\nCBC\nNSBH\n10.60\n3.24 \u00d7 10\u22128\nno\nS200327j\n1.66 \u00d7 10\u22125\nCBC\nMass Gap\n22.46\n2.96 \u00d7 10\u22128\nno\n", "Draft version March 13, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nSearch for gravitational waves emitted from SN 2023ixf\nA. G. Abac,1 R. Abbott,2 I. Abouelfettouh,3 F. Acernese,4, 5 K. Ackley,6 S. Adhicary,7 N. Adhikari,8\nR. X. Adhikari,2 V. K. Adkins,9 D. Agarwal,10, 11 M. Agathos,12 M. Aghaei Abchouyeh,13 O. D. Aguiar,14\nI. Aguilar,15 L. Aiello,16, 17, 18 A. Ain,19 T. Akutsu,20, 21 S. Albanesi,22, 23, 24 R. A. Alfaidi,25 A. Al-Jodah,26\nC. All\u00b4en\u00b4e,27 A. Allocca,28, 5 S. Al-Shammari,18 P. A. Altin,29 S. Alvarez-Lopez,30 A. Amato,31, 32 L. Amez-Droz,33\nA. Amorosi,33 C. Amra,34 A. Ananyeva,2 S. B. Anderson,2 W. G. Anderson,2 M. Andia,35 M. Ando,36\nT. Andrade,37 N. Andres,27 M. Andr\u00b4es-Carcasona,38 T. Andri\u00b4c,39, 40, 1, 41 J. Anglin,42 S. Ansoldi,43, 44\nJ. M. Antelis,45 S. Antier,46 M. Aoumi,47 E. Z. Appavuravther,48, 49 S. Appert,2 S. K. Apple,50 K. Arai,2\nA. Araya,36 M. C. Araya,2 J. S. Areeda,51 L. Argianas,52 N. Aritomi,3 F. Armato,53, 54 N. Arnaud,35, 55\nM. Arogeti,56 S. M. Aronson,9 G. Ashton,57 Y. Aso,20, 58 M. Assiduo,59, 60 S. Assis de Souza Melo,55 S. M. Aston,61\nP. Astone,62 F. Attadio,63, 62 F. Aubin,64 K. AultONeal,65 G. Avallone,66 S. Babak,67 F. Badaracco,53\nC. Badger,68 S. Bae,69 S. Bagnasco,22 E. Bagui,70 J. G. Baier,71 L. Baiotti,72 R. Bajpai,20 T. Baka,73 M. Ball,74\nG. Ballardin,55 S. W. Ballmer,75 S. Banagiri,76 B. Banerjee,41 D. Bankar,11 P. Baral,8 J. C. Barayoga,2\nB. C. Barish,2 D. Barker,3 P. Barneo,37, 77 F. Barone,78, 5 B. Barr,25 L. Barsotti,30 M. Barsuglia,67 D. Barta,79\nA. M. Bartoletti,80 M. A. Barton,25 I. Bartos,42 S. Basak,81 A. Basalaev,82 R. Bassiri,15 A. Basti,83, 84\nD. E. Bates,18 M. Bawaj,85, 48 P. Baxi,86 J. C. Bayley,25 A. C. Baylor,8 P. A. Baynard II,56 M. Bazzan,87, 88\nV. M. Bedakihale,89 F. Beirnaert,90 M. Bejger,91 D. Belardinelli,17 A. S. Bell,25 V. Benedetto,92 W. Benoit,93\nJ. D. Bentley,82 M. Ben Yaala,94 S. Bera,95 M. Berbel,96 F. Bergamin,39, 40 B. K. Berger,15 S. Bernuzzi,23\nM. Beroiz,2 D. Bersanetti,53 A. Bertolini,32 J. Betzwieser,61 D. Beveridge,26 N. Bevins,52 R. Bhandare,97\nU. Bhardwaj,98, 32 R. Bhatt,2 D. Bhattacharjee,71, 99 S. Bhaumik,42 S. Bhowmick,100 A. Bianchi,32, 101\nI. A. Bilenko,102 G. Billingsley,2 A. Binetti,103 S. Bini,104, 105 O. Birnholtz,106 S. Biscoveanu,76 A. Bisht,40\nM. Bitossi,55, 84 M.-A. Bizouard,46 J. K. Blackburn,2 L. A. Blagg,74 C. D. Blair,26, 61 D. G. Blair,26 F. Bobba,66, 107\nN. Bode,39, 40 G. Boileau,19, 46 M. Boldrini,63, 62 G. N. Bolingbroke,108 A. Bolliand,109, 34 L. D. Bonavena,87\nR. Bondarescu,37 F. Bondu,110 E. Bonilla,15 M. S. Bonilla,51 A. Bonino,111 R. Bonnand,27 P. Booker,39, 40\nA. Borchers,39, 40 V. Boschi,84 S. Bose,112 V. Bossilkov,61 V. Boudart,113 A. Boudon,114 A. Bozzi,55\nC. Bradaschia,84 P. R. Brady,8 M. Braglia,115 A. Branch,61 M. Branchesi,41, 116 J. Brandt,56 I. Braun,71\nM. Breschi,23 T. Briant,117 A. Brillet,46 M. Brinkmann,39, 40 P. Brockill,8 E. Brockmueller,39, 40 A. F. Brooks,2\nB. C. Brown,42 D. D. Brown,108 M. L. Brozzetti,85, 48 S. Brunett,2 G. Bruno,10 R. Bruntz,118 J. Bryant,111\nF. Bucci,60 J. Buchanan,118 O. Bulashenko,37, 77 T. Bulik,119 H. J. Bulten,32 A. Buonanno,120, 1 K. Burtnyk,3\nR. Buscicchio,121, 122 D. Buskulic,27 C. Buy,123 R. L. Byer,15 G. S. Cabourn Davies,124 G. Cabras,43, 44 R. Cabrita,10\nV. C\u00b4aceres-Barbosa,7 L. Cadonati,56 G. Cagnoli,125 C. Cahillane,75 J. Calder\u00b4on Bustillo,126 T. A. Callister,127\nE. Calloni,28, 5 J. B. Camp,128 M. Canepa,54, 53 G. Caneva Santoro,38 K. C. Cannon,36 H. Cao,108\nL. A. Capistran,129 E. Capocasa,67 E. Capote,75 G. Carapella,66, 107 F. Carbognani,55 M. Carlassara,39, 40\nJ. B. Carlin,130 M. Carpinelli,121, 131, 55 G. Carrillo,74 J. J. Carter,39, 40 G. Carullo,132 J. Casanueva Diaz,55\nC. Casentini,133, 16, 17 S. Y. Castro-Lucas,100 S. Caudill,134, 32, 73 M. Cavagli`a,99 R. Cavalieri,55 G. Cella,84\nP. Cerd\u00b4a-Dur\u00b4an,135, 136 E. Cesarini,17 W. Chaibi,46 P. Chakraborty,39, 40 S. Chalathadka Subrahmanya,82\nJ. C. L. Chan,137 M. Chan,138 K. Chandra,7 R.-J. Chang,139 S. Chao,140, 141 E. L. Charlton,118 P. Charlton,142\nE. Chassande-Mottin,67 C. Chatterjee,143 Debarati Chatterjee,11 Deep Chatterjee,30 M. Chaturvedi,97\nS. Chaty,67 A. Chen,12 A. H.-Y. Chen,144 D. Chen,145 H. Chen,140 H. Y. Chen,146 J. Chen,30 K. H. Chen,141\nY. Chen,140 Yanbei Chen,147 Yitian Chen,148 H. P. Cheng,149 P. Chessa,85, 48 H. T. Cheung,86 S. Y. Cheung,150\nF. Chiadini,151, 107 G. Chiarini,88 R. Chierici,114 A. Chincarini,53 M. L. Chiofalo,83, 84 A. Chiummo,5, 55 C. Chou,144\nS. Choudhary,26 N. Christensen,46 S. S. Y. Chua,29 P. Chugh,150 G. Ciani,87, 88 P. Ciecielag,91 M. Cie\u00b4slar,119\nM. Cifaldi,17 R. Ciolfi,152, 88 F. Clara,3 J. A. Clark,2, 56 J. Clarke,18 T. A. Clarke,150 P. Clearwater,153\nS. Clesse,70 E. Coccia,41, 116, 38 E. Codazzo,41 P.-F. Cohadon,117 S. Colace,54 M. Colleoni,95 C. G. Collette,33\nJ. Collins,61 S. Colloms,25 A. Colombo,121, 122, 154 M. Colpi,121, 122 C. M. Compton,3 G. Connolly,74 L. Conti,88\nT. R. Corbitt,9 I. Cordero-Carri\u00b4on,155 S. Corezzi,85, 48 N. J. Cornish,156 A. Corsi,157 S. Cortese,55 C. A. Costa,14\nR. Cottingham,61 M. W. Coughlin,93 A. Couineaux,62 J.-P. Coulon,46 S. T. Countryman,158 J.-F. Coupechoux,114\nP. Couvares,2, 56 D. M. Coward,26 M. J. Cowart,61 R. Coyne,159 K. Craig,94 R. Creed,18 J. D. E. Creighton,8\nT. D. Creighton,160 P. Cremonese,95 A. W. Criswell,93 J. C. G. Crockett-Gray,9 S. Crook,61 R. Crouch,3\nJ. Csizmazia,3 J. R. Cudell,113 T. J. Cullen,2 A. Cumming,25 E. Cuoco,55, 84 M. Cusinato,135 P. Dabadie,125\nT. Dal Canton,35 S. Dall\u2019Osso,62 S. Dal Pra,62 G. D\u00b4alya,123 B. D\u2019Angelo,53 S. Danilishin,31, 32 S. D\u2019Antonio,17\nK. Danzmann,40, 39, 40 K. E. Darroch,118 L. P. Dartez,3 A. Dasgupta,89 S. Datta,161 V. Dattilo,55 A. Daumas,67\nN. Davari,162, 131 I. Dave,97 A. Davenport,100 M. Davier,35 T. F. Davies,26 D. Davis,2 L. Davis,26 M. C. Davis,93\nP. J. Davis,163, 164 M. Dax,1 J. De Bolle,90 M. Deenadayalan,11 J. Degallaix,165 M. De Laurentis,28, 5\nS. Del\u00b4eglise,117 F. De Lillo,10 D. Dell\u2019Aquila,162, 131 W. Del Pozzo,83, 84 F. De Marco,63, 62 F. De Matteis,16, 17\nV. D\u2019Emilio,2 N. Demos,30 T. Dent,126 A. Depasse,10 N. DePergola,52 R. De Pietri,166, 167 R. De Rosa,28, 5\nC. De Rossi,55 R. DeSalvo,168 R. De Simone,151 A. Dhani,1 R. Diab,42 M. C. D\u00b4\u0131az,160 M. Di Cesare,28 G. Dideron,169\narXiv:2410.16565v2 [astro-ph.HE] 11 Mar 2025\n\n2\nN. A. Didio,75 T. Dietrich,1 L. Di Fiore,5 C. Di Fronzo,33 M. Di Giovanni,63, 62 T. Di Girolamo,28, 5 D. Diksha,32, 31\nA. Di Michele,85 J. Ding,67, 170 S. Di Pace,63, 62 I. Di Palma,63, 62 F. Di Renzo,114 Divyajyoti,171 A. Dmitriev,111\nZ. Doctor,76 E. Dohmen,3 P. P. Doleva,118 D. Dominguez,172 L. D\u2019Onofrio,62 F. Donovan,30 K. L. Dooley,18\nT. Dooney,73 S. Doravari,11 O. Dorosh,173 M. Drago,63, 62 J. C. Driggers,3 J.-G. Ducoin,174, 67 L. Dunn,130\nU. Dupletsa,41 D. D\u2019Urso,162, 131 H. Duval,175 P.-A. Duverne,35 S. E. Dwyer,3 C. Eassa,3 M. Ebersold,27\nT. Eckhardt,82 G. Eddolls,75 B. Edelman,74 T. B. Edo,2 O. Edy,124 A. Effler,61 J. Eichholz,29 H. Einsle,46\nM. Eisenmann,20 R. A. Eisenstein,30 A. Ejlli,18 R. M. Eleveld,176 M. Emma,57 K. Endo,177 A. J. Engl,15\nE. Enloe,56 L. Errico,28, 5 R. C. Essick,178 H. Estell\u00b4es,1 D. Estevez,64 T. Etzel,2 M. Evans,30 T. Evstafyeva,179\nB. E. Ewing,7 J. M. Ezquiaga,137 F. Fabrizi,59, 60 F. Faedi,60, 59 V. Fafone,16, 17 S. Fairhurst,18 A. M. Farah,127\nB. Farr,74 W. M. Farr,180, 181 G. Favaro,87 M. Favata,182 M. Fays,113 M. Fazio,94 J. Feicht,2 M. M. Fejer,15\nR. Felicetti,183 E. Fenyvesi,79, 184 D. L. Ferguson,146 S. Ferraiuolo,185, 63, 62 I. Ferrante,83, 84 T. A. Ferreira,9\nF. Fidecaro,83, 84 P. Figura,91 A. Fiori,84, 83 I. Fiori,55 M. Fishbach,178 R. P. Fisher,118 R. Fittipaldi,186, 107\nV. Fiumara,187, 107 R. Flaminio,27 S. M. Fleischer,188 L. S. Fleming,189 E. Floden,93 E. M. Foley,93 H. Fong,138\nJ. A. Font,135, 136 B. Fornal,190 P. W. F. Forsyth,29 K. Franceschetti,166 N. Franchini,67 S. Frasca,63, 62\nF. Frasconi,84 A. Frattale Mascioli,63, 62 Z. Frei,191 A. Freise,32, 101 O. Freitas,192, 135 R. Frey,74 W. Frischhertz,61\nP. Fritschel,30 V. V. Frolov,61 G. G. Fronz\u00b4e,22 M. Fuentes-Garcia,2 S. Fujii,193 T. Fujimori,194 P. Fulda,42\nM. Fyffe,61 B. Gadre,73 J. R. Gair,1 S. Galaudage,195 V. Galdi,168 H. Gallagher,196 S. Gallardo,197\nB. Gallego,197 R. Gamba,23 A. Gamboa,1 D. Ganapathy,30 A. Ganguly,11 B. Garaventa,53, 54 J. Garc\u00b4\u0131a-Bellido,115\nC. Garc\u00b4\u0131a N\u00b4u\u02dcnez,189 C. Garc\u00b4\u0131a-Quir\u00b4os,198 J. W. Gardner,29 K. A. Gardner,138 J. Gargiulo,55 A. Garron,95\nF. Garufi,28, 5 C. Gasbarra,16, 17 B. Gateley,3 V. Gayathri,8 G. Gemme,53 A. Gennai,84 V. Gennari,123 J. George,97\nR. George,146 O. Gerberding,82 L. Gergely,199 Archisman Ghosh,90 Sayantan Ghosh,200 Shaon Ghosh,182\nShrobana Ghosh,39, 40 Suprovo Ghosh,11 Tathagata Ghosh,11 L. Giacoppo,63, 62 J. A. Giaime,9, 61 K. D. Giardina,61\nD. R. Gibson,189 D. T. Gibson,179 C. Gier,94 P. Giri,84, 83 F. Gissi,92 S. Gkaitatzis,83, 84 J. Glanzer,9 F. Glotin,35\nJ. Godfrey,74 P. Godwin,2 N. L. Goebbels,82 E. Goetz,138 J. Golomb,2 S. Gomez Lopez,63, 62 B. Goncharov,41\nY. Gong,201 G. Gonz\u00b4alez,9 P. Goodarzi,202 S. Goode,150 A. W. Goodwin-Jones,26 M. Gosselin,55 A. S. G\u00a8ottel,18\nR. Gouaty,27 D. W. Gould,29 K. Govorkova,30 S. Goyal,1 B. Grace,29 A. Grado,203, 5 V. Graham,25\nA. E. Granados,93 M. Granata,165 V. Granata,66 S. Gras,30 P. Grassia,2 A. Gray,93 C. Gray,3 R. Gray,25\nG. Greco,48 A. C. Green,32, 101 S. M. Green,124 S. R. Green,204 A. M. Gretarsson,65 E. M. Gretarsson,65\nD. Griffith,2 W. L. Griffiths,18 H. L. Griggs,56 G. Grignani,85, 48 A. Grimaldi,104, 105 C. Grimaud,27 H. Grote,18\nD. Guerra,135 D. Guetta,205, 62 G. M. Guidi,59, 60 A. R. Guimaraes,9 H. K. Gulati,89 F. Gulminelli,163, 164\nA. M. Gunny,30 H. Guo,190 W. Guo,26 Y. Guo,32, 31 Anchal Gupta,2 Anuradha Gupta,206 Ish Gupta,7\nN. C. Gupta,89 P. Gupta,32, 73 S. K. Gupta,42 T. Gupta,156 N. Gupte,1 J. Gurs,82 N. Gutierrez,165 F. Guzman,129\nH.-Y. H,140 D. Haba,172 M. Haberland,1 S. Haino,207 E. D. Hall,30 E. Z. Hamilton,95 G. Hammond,25 W.-B. Han,208\nM. Haney,32 J. Hanks,3 C. Hanna,7 M. D. Hannam,18 O. A. Hannuksela,209 A. G. Hanselman,127 H. Hansen,3\nJ. Hanson,61 R. Harada,36 A. R. Hardison,210 K. Haris,32, 73 T. Harmark,132 J. Harms,41, 116 G. M. Harry,211\nI. W. Harry,124 J. Hart,71 B. Haskell,91 C.-J. Haster,212 J. S. Hathaway,196 K. Haughian,25 H. Hayakawa,47\nK. Hayama,213 R. Hayes,18 A. Heffernan,95 A. Heidmann,117 M. C. Heintze,61 J. Heinze,111 J. Heinzel,30\nH. Heitmann,46 F. Hellman,214 P. Hello,35 A. F. Helmling-Cornell,74 G. Hemming,55 O. Henderson-Sapir,108\nM. Hendry,25 I. S. Heng,25 E. Hennes,32 C. Henshaw,56 T. Hertog,103 M. Heurs,39, 40 A. L. Hewitt,179, 215 J. Heyns,30\nS. Higginbotham,18 S. Hild,31, 32 S. Hill,25 Y. Himemoto,216 N. Hirata,20 C. Hirose,217 S. Hoang,35 S. Hochheim,39, 40\nD. Hofman,165 N. A. Holland,32, 101 K. Holley-Bockelmann,143 Z. J. Holmes,108 D. E. Holz,127 L. Honet,70\nC. Hong,15 J. Hornung,74 S. Hoshino,217 J. Hough,25 S. Hourihane,2 E. J. Howell,26 C. G. Hoy,124\nC. A. Hrishikesh,16 H.-F. Hsieh,140 C. Hsiung,218 H. C. Hsu,141 W.-F. Hsu,103 P. Hu,143 Q. Hu,25 H. Y. Huang,141\nY.-J. Huang,7 A. D. Huddart,219 B. Hughey,65 D. C. Y. Hui,220 V. Hui,27 S. Husa,95 R. Huxford,7 T. Huynh-Dinh,61\nL. Iampieri,63, 62 G. A. Iandolo,31 M. Ianni,17, 16 A. Iess,221, 84 H. Imafuku,36 K. Inayoshi,222 Y. Inoue,141 G. Iorio,87\nM. H. Iqbal,29 J. Irwin,25 R. Ishikawa,223 M. Isi,180, 181 M. A. Ismail,141 Y. Itoh,194, 224 H. Iwanaga,194 M. Iwaya,193\nB. R. Iyer,81 V. JaberianHamedan,26 C. Jacquet,123 P.-E. Jacquet,117 S. J. Jadhav,225 S. P. Jadhav,153 T. Jain,179\nA. L. James,2 P. A. James,118 R. Jamshidi,33 J. Janquart,73, 32 K. Janssens,19, 46 N. N. Janthalur,225 S. Jaraba,115\nP. Jaranowski,226 R. Jaume,95 W. Javed,18 A. Jennings,3 W. Jia,30 J. Jiang,42 J. Kubisz,227 C. Johanson,134\nG. R. Johns,118 N. A. Johnson,42 M. C. Johnston,212 R. Johnston,25 N. Johny,39, 40 D. H. Jones,29 D. I. Jones,228\nR. Jones,25 S. Jose,171 P. Joshi,7 L. Ju,26 K. Jung,229 J. Junker,29 V. Juste,70 T. Kajita,230 I. Kaku,194\nC. Kalaghatgi,73, 32, 231 V. Kalogera,76 M. Kamiizumi,47 N. Kanda,224, 194 S. Kandhasamy,11 G. Kang,232\nJ. B. Kanner,2 S. J. Kapadia,11 D. P. Kapasi,29 S. Karat,2 C. Karathanasis,38 R. Kashyap,7 M. Kasprzack,2\nW. Kastaun,39, 40 T. Kato,193 E. Katsavounidis,30 W. Katzman,61 R. Kaushik,97 K. Kawabe,3 R. Kawamoto,194\nA. Kazemi,93 D. Keitel,95 J. Kelley-Derzon,42 J. Kennington,7 R. Kesharwani,11 J. S. Key,233 R. Khadela,39, 40\nS. Khadka,15 F. Y. Khalili,102 F. Khan,39, 40 I. Khan,234, 34 T. Khanam,157 M. Khursheed,97 N. M. Khusid,180, 181\nW. Kiendrebeogo,46, 235 N. Kijbunchoo,108 C. Kim,236 J. C. Kim,237 K. Kim,238 M. H. Kim,239 S. Kim,220 Y.-M. Kim,238\nC. Kimball,76 M. Kinley-Hanlon,25 M. Kinnear,18 J. S. Kissel,3 S. Klimenko,42 A. M. Knee,138 N. Knust,39, 40\nK. Kobayashi,193 P. Koch,39, 40 S. M. Koehlenbeck,15 G. Koekoek,32, 31 K. Kohri,240, 241 K. Kokeyama,18 S. Koley,41\nP. Kolitsidou,111 M. Kolstein,38 K. Komori,36 A. K. H. Kong,140 A. Kontos,242 M. Korobko,82 R. V. Kossak,39, 40\nX. Kou,93 A. Koushik,19 N. Kouvatsos,68 M. Kovalam,26 D. B. Kozak,2 S. L. Kranzhoff,31, 32 V. Kringel,39, 40\nN. V. Krishnendu,81 A. Kr\u00b4olak,243, 173 K. Kruska,39, 40 G. Kuehn,39, 40 P. Kuijer,32 S. Kulkarni,206\n\n3\nA. Kulur Ramamohan,29 A. Kumar,225 Praveen Kumar,126 Prayush Kumar,81 Rahul Kumar,3 Rakesh Kumar,89\nJ. Kume,87, 88, 36 K. Kuns,30 N. Kuntimaddi,18 S. Kuroyanagi,115, 244 N. J. Kurth,9 S. Kuwahara,36 K. Kwak,229\nK. Kwan,29 J. Kwok,179 G. Lacaille,25 P. Lagabbe,27 D. Laghi,123 S. Lai,144 A. H. Laity,159 M. H. Lakkis,33\nE. Lalande,245 M. Lalleman,19 P. C. Lalremruati,246 M. Landry,3 B. B. Lane,30 R. N. Lang,30 J. Lange,146\nB. Lantz,15 A. La Rana,62 I. La Rosa,95 A. Lartaux-Vollard,35 P. D. Lasky,150 J. Lawrence,157 M. N. Lawrence,9\nM. Laxen,61 A. Lazzarini,2 C. Lazzaro,87, 88 P. Leaci,63, 62 Y. K. Lecoeuche,138 H. M. Lee,237 H. W. Lee,247\nK. Lee,239 R.-K. Lee,140 R. Lee,30 S. Lee,238 Y. Lee,141 I. N. Legred,2 J. Lehmann,39, 40 L. Lehner,169 M. Le Jean,165\nA. Lema\u02c6\u0131tre,248 M. Lenti,60, 249 M. Leonardi,104, 105, 20 M. Lequime,34 N. Leroy,35 M. Lesovsky,2 N. Letendre,27\nM. Lethuillier,114 S. E. Levin,202 Y. Levin,150 K. Leyde,67 A. K. Y. Li,2 K. L. Li,139 T. G. F. Li,209, 103 X. Li,147\nZ. Li,25 A. Lihos,118 C-Y. Lin,250 C.-Y. Lin,141 E. T. Lin,140 F. Lin,141 H. Lin,141 L. C.-C. Lin,139 Y.-C. Lin,140\nF. Linde,231, 32 S. D. Linker,197 T. B. Littenberg,251 A. Liu,209 G. C. Liu,218 Jian Liu,26 F. Llamas Villarreal,160\nJ. Llobera-Querol,95 R. K. L. Lo,137 J.-P. Locquet,103 L. T. London,68, 30, 98 A. Longo,59, 60 D. Lopez,113\nM. Lopez Portilla,73 M. Lorenzini,16, 17 A. Lorenzo-Medina,126 V. Loriette,35 M. Lormand,61 G. Losurdo,84\nT. P. Lott IV,56 J. D. Lough,39, 40 H. A. Loughlin,30 C. O. Lousto,196 M. J. Lowry,118 N. Lu,29 H. L\u00a8uck,40, 39, 40\nD. Lumaca,17 A. P. Lundgren,124 A. W. Lussier,245 L.-T. Ma,140 S. Ma,169 M. Ma\u2019arif,141 R. Macas,124\nA. Macedo,51 M. MacInnis,30 R. R. Maciy,39, 40 D. M. Macleod,18 I. A. O. MacMillan,2 A. Macquet,35 D. Macri,30\nK. Maeda,177 S. Maenaut,103 I. Maga\u02dcna Hernandez,8 S. S. Magare,11 C. Magazz`u,84 R. M. Magee,2 E. Maggio,1\nR. Maggiore,32, 101 M. Magnozzi,53, 54 M. Mahesh,82 S. Mahesh,252 M. Maini,159 S. Majhi,11 E. Majorana,63, 62\nC. N. Makarem,2 E. Makelele,71 J. A. Malaquias-Reis,14 U. Mali,178 S. Maliakal,2 A. Malik,97 N. Man,46\nV. Mandic,93 V. Mangano,62, 63 B. Mannix,74 G. L. Mansell,75, 30 G. Mansingh,211 M. Manske,8 M. Mantovani,55\nM. Mapelli,87, 88, 253 F. Marchesoni,49, 48, 254 D. Mar\u00b4\u0131n Pina,37, 77, 255 F. Marion,27 S. M\u00b4arka,158 Z. M\u00b4arka,158\nA. S. Markosyan,15 A. Markowitz,2 E. Maros,2 S. Marsat,123 F. Martelli,59, 60 I. W. Martin,25 R. M. Martin,182\nB. B. Martinez,129 M. Martinez,38, 256 V. Martinez,125 A. Martini,104, 105 K. Martinovic,68 J. C. Martins,14\nD. V. Martynov,111 E. J. Marx,30 L. Massaro,31, 32 A. Masserot,27 M. Masso-Reid,25 M. Mastrodicasa,62, 63\nS. Mastrogiovanni,62 T. Matcovich,48 M. Matiushechkina,39, 40 M. Matsuyama,194 N. Mavalvala,30 N. Maxwell,3\nG. McCarrol,61 R. McCarthy,3 D. E. McClelland,29 S. McCormick,61 L. McCuller,2 S. McEachin,118\nC. McElhenny,118 G. I. McGhee,25 J. McGinn,25 K. B. M. McGowan,143 J. McIver,138 A. McLeod,26 T. McRae,29\nD. Meacher,8 Q. Meijer,73 A. Melatos,130 S. Mellaerts,103 A. Menendez-Vazquez,38 C. S. Menoni,100 F. Mera,3\nR. A. Mercer,8 L. Mereni,165 K. Merfeld,157 E. L. Merilh,61 J. R. M\u00b4erou,95 J. D. Merritt,74 M. Merzougui,46\nC. Messenger,25 C. Messick,8 M. Meyer-Conde,194 F. Meylahn,39, 40 A. Mhaske,11 A. Miani,104, 105 H. Miao,257\nI. Michaloliakos,42 C. Michel,165 Y. Michimura,2, 36 H. Middleton,111 A. L. Miller,32 S. Miller,2 M. Millhouse,56\nE. Milotti,183, 44 V. Milotti,87 Y. Minenkov,17 N. Mio,36 Ll. M. Mir,38 L. Mirasola,258, 62 M. Miravet-Ten\u00b4es,135\nC.-A. Miritescu,38 A. K. Mishra,81 A. Mishra,11 C. Mishra,171 T. Mishra,42 A. L. Mitchell,32, 101 J. G. Mitchell,65\nS. Mitra,11 V. P. Mitrofanov,102 R. Mittleman,30 O. Miyakawa,47 S. Miyamoto,193 S. Miyoki,47 G. Mo,30\nL. Mobilia,59, 60 S. R. P. Mohapatra,2 S. R. Mohite,7 M. Molina-Ruiz,214 C. Mondal,163 M. Mondin,197\nM. Montani,59, 60 C. J. Moore,179 D. Moraru,3 A. More,11 S. More,11 G. Moreno,3 C. Morgan,18 S. Morisaki,36, 193\nY. Moriwaki,177 G. Morras,115 A. Moscatello,87 P. Mourier,95 B. Mours,64 C. M. Mow-Lowry,32, 101\nF. Muciaccia,63, 62 Arunava Mukherjee,259 D. Mukherjee,251 Samanwaya Mukherjee,11 Soma Mukherjee,160\nSubroto Mukherjee,89 Suvodip Mukherjee,260, 169, 98 N. Mukund,30 A. Mullavey,61 J. Munch,108 J. Mundi,211\nC. L. Mungioli,26 W. R. Munn Oberg,261 Y. Murakami,193 M. Murakoshi,223 P. G. Murray,25 S. Muusse,29\nD. Nabari,104, 105 S. L. Nadji,39, 40 A. Nagar,22, 262 N. Nagarajan,25 K. N. Nagler,65 K. Nakagaki,47 K. Nakamura,20\nH. Nakano,263 M. Nakano,2 D. Nandi,9 V. Napolano,55 P. Narayan,206 I. Nardecchia,17 T. Narikawa,193\nH. Narola,73 L. Naticchioni,62 R. K. Nayak,246 J. Neilson,92, 107 A. Nelson,129 T. J. N. Nelson,61 M. Nery,39, 40\nA. Neunzert,3 S. Ng,51 L. Nguyen Quynh,264 S. A. Nichols,9 A. B. Nielsen,265 G. Nieradka,91 A. Niko,141\nY. Nishino,20, 36 A. Nishizawa,266 S. Nissanke,98, 32 E. Nitoglia,114 W. Niu,7 F. Nocera,55 M. Norman,18 C. North,18\nJ. Novak,109, 267, 268, 269 J. F. Nu\u02dcno Siles,115 L. K. Nuttall,124 K. Obayashi,223 M. Obergaulinger,135 J. Oberling,3\nJ. O\u2019Dell,219 M. Oertel,109, 267, 268, 270, 269 A. Offermans,103 G. Oganesyan,41, 116 J. J. Oh,271 K. Oh,220 T. O\u2019Hanlon,61\nM. Ohashi,47 M. Ohkawa,217 F. Ohme,39, 40 A. S. Oliveira,158 R. Oliveri,109, 267, 268 B. O\u2019Neal,118 K. Oohara,272, 273\nB. O\u2019Reilly,61 N. D. Ormsby,118 M. Orselli,48, 85 R. O\u2019Shaughnessy,196 S. O\u2019Shea,25 Y. Oshima,36 S. Oshino,47\nS. Ossokine,1 C. Osthelder,2 I. Ota,9 D. J. Ottaway,108 A. Ouzriat,114 H. Overmier,61 B. J. Owen,157 A. E. Pace,7\nR. Pagano,9 M. A. Page,20 A. Pai,200 A. Pal,274 S. Pal,246 M. A. Palaia,84, 83 M. P\u00b4alfi,191 P. P. Palma,63, 16, 17\nC. Palomba,62 P. Palud,67 H. Pan,140 J. Pan,26 K. C. Pan,140 R. Panai,258, 87 P. K. Panda,225 S. Pandey,7\nL. Panebianco,59, 60 P. T. H. Pang,32, 73 F. Pannarale,63, 62 K. A. Pannone,51 B. C. Pant,97 F. H. Panther,26\nF. Paoletti,84 A. Paolone,62, 275 E. E. Papalexakis,202 L. Papalini,84, 83 G. Papigkiotis,276 A. Paquis,35 A. Parisi,85, 48\nB.-J. Park,238 J. Park,277 W. Parker,61 G. Pascale,39, 40 D. Pascucci,90 A. Pasqualetti,55 R. Passaquieti,83, 84\nL. Passenger,150 D. Passuello,84 O. Patane,3 D. Pathak,11 M. Pathak,108 A. Patra,18 B. Patricelli,83, 84\nA. S. Patron,9 K. Paul,171 S. Paul,74 E. Payne,2 T. Pearce,18 M. Pedraza,2 R. Pegna,84 A. Pele,2\nF. E. Pe\u02dcna Arellano,45 S. Penn,261 M. D. Penuliar,51 A. Perego,104, 105 Z. Pereira,134 J. J. Perez,42\nC. P\u00b4erigois,152, 88, 87 G. Perna,87 A. Perreca,104, 105 J. Perret,67 S. Perri`es,114 J. W. Perry,32, 101 D. Pesios,276\nS. Petracca,168 C. Petrillo,85 H. P. Pfeiffer,1 H. Pham,61 K. A. Pham,93 K. S. Phukon,111, 32, 231\nH. Phurailatpam,209 M. Piarulli,123 L. Piccari,63, 62 O. J. Piccinni,38 M. Pichot,46 M. Piendibene,83, 84\nF. Piergiovanni,59, 60 L. Pierini,62 G. Pierra,114 V. Pierro,92, 107 M. Pietrzak,91 M. Pillas,46 F. Pilo,84 L. Pinard,165\n\n4\nI. M. Pinto,92, 107, 278, 28 M. Pinto,55 B. J. Piotrzkowski,8 M. Pirello,3 M. D. Pitkin,179, 215 A. Placidi,60\nE. Placidi,63, 62 M. L. Planas,95 W. Plastino,279, 17 R. Poggiani,83, 84 E. Polini,27 L. Pompili,1 J. Poon,209\nE. Porcelli,32 E. K. Porter,67 C. Posnansky,7 R. Poulton,55 J. Powell,153 M. Pracchia,113 B. K. Pradhan,11\nT. Pradier,64 A. K. Prajapati,89 K. Prasai,15 R. Prasanna,225 P. Prasia,11 G. Pratten,111 G. Principe,183, 44\nM. Principe,168, 92, 278, 107 G. A. Prodi,104, 105 L. Prokhorov,111 P. Prosposito,16, 17 A. Puecher,32, 73 J. Pullin,9\nM. Punturo,48 P. Puppo,62 M. P\u00a8urrer,159 H. Qi,12 J. Qin,29 G. Qu\u00b4em\u00b4ener,164, 109 V. Quetschke,160 C. Quigley,18\nP. J. Quinonez,65 F. J. Raab,3 S. S. Raabith,9 G. Raaijmakers,98, 32 S. Raja,97 C. Rajan,97 B. Rajbhandari,196\nK. E. Ramirez,61 F. A. Ramis Vidal,95 A. Ramos-Buades,32 D. Rana,11 S. Ranjan,56 K. Ransom,61\nP. Rapagnani,63, 62 B. Ratto,65 S. Rawat,93 A. Ray,8 V. Raymond,18 M. Razzano,83, 84 J. Read,51\nM. Recaman Payo,103 T. Regimbau,27 L. Rei,53 S. Reid,94 D. H. Reitze,2 P. Relton,18 A. I. Renzini,2\nP. Rettegno,22 B. Revenu,280, 67 R. Reyes,197 A. S. Rezaei,62, 63 F. Ricci,63, 62 M. Ricci,62, 63 A. Ricciardone,83, 84\nJ. W. Richardson,202 M. Richardson,108 A. Rijal,65 K. Riles,86 H. K. Riley,18 S. Rinaldi,253, 87 J. Rittmeyer,82\nC. Robertson,219 F. Robinet,35 M. Robinson,3 A. Rocchi,17 L. Rolland,27 J. G. Rollins,2 A. E. Romano,281\nR. Romano,4, 5 A. Romero,175 I. M. Romero-Shaw,179 J. H. Romie,61 S. Ronchini,41, 116 T. J. Roocke,108 L. Rosa,5, 28\nT. J. Rosauer,202 C. A. Rose,8 D. Rosi\u00b4nska,119 M. P. Ross,50 M. Rossello,95 S. Rowan,25 S. K. Roy,180, 181 S. Roy,73\nD. Rozza,121, 122 P. Ruggi,55 N. Ruhama,229 E. Ruiz Morales,282, 115 K. Ruiz-Rocha,143 S. Sachdev,56 T. Sadecki,3\nJ. Sadiq,126 P. Saffarieh,32, 101 M. R. Sah,260 S. S. Saha,140 S. Saha,140 T. Sainrat,64 S. Sajith Menon,205, 63, 62\nK. Sakai,283 M. Sakellariadou,68 S. Sakon,7 O. S. Salafia,154, 122, 121 F. Salces-Carcoba,2 L. Salconi,55\nM. Saleem,93 F. Salemi,63, 62 M. Sall\u00b4e,32 S. Salvador,164, 163, 109 A. Sanchez,3 E. J. Sanchez,2 J. H. Sanchez,76\nL. E. Sanchez,2 N. Sanchis-Gual,135 J. R. Sanders,210 E. M. S\u00a8anger,1 F. Santoliquido,41 T. R. Saravanan,11\nN. Sarin,150 S. Sasaoka,172 A. Sasli,276 P. Sassi,48, 85 B. Sassolas,165 H. Satari,26, 18 R. Sato,217 Y. Sato,177\nO. Sauter,42 R. L. Savage,3 T. Sawada,47 H. L. Sawant,11 S. Sayah,27 V. Scacco,16, 17 D. Schaetzl,2 M. Scheel,147\nA. Schiebelbein,178 M. G. Schiworski,108 P. Schmidt,111 S. Schmidt,73 R. Schnabel,82 M. Schneewind,39, 40\nR. M. S. Schofield,74 K. Schouteden,103 B. W. Schulte,39, 40 B. F. Schutz,18, 39, 40 E. Schwartz,18 M. Scialpi,284\nJ. Scott,25 S. M. Scott,29 T. C. Seetharamu,25 M. Seglar-Arroyo,38 Y. Sekiguchi,285 D. Sellers,61\nA. S. Sengupta,286 D. Sentenac,55 E. G. Seo,25 J. W. Seo,103 V. Sequino,28, 5 M. Serra,62 G. Servignat,267\nA. Sevrin,175 T. Shaffer,3 U. S. Shah,56 M. A. Shaikh,237 L. Shao,222 A. K. Sharma,81 P. Sharma,97\nS. Sharma-Chaudhary,99 M. R. Shaw,18 P. Shawhan,120 N. S. Shcheblanov,287, 248 E. Sheridan,143 Y. Shikano,288, 289\nM. Shikauchi,36 K. Shimode,47 H. Shinkai,290 J. Shiota,223 D. H. Shoemaker,30 D. M. Shoemaker,146 R. W. Short,3\nS. ShyamSundar,97 A. Sider,33 H. Siegel,180, 181 M. Sieniawska,10 D. Sigg,3 L. Silenzi,48, 49 M. Simmonds,108\nL. P. Singer,128 A. Singh,206 D. Singh,7 M. K. Singh,81 S. Singh,20, 58 A. Singha,31, 32 A. M. Sintes,95 V. Sipala,162, 131\nV. Skliris,18 B. J. J. Slagmolen,29 T. J. Slaven-Blair,26 J. Smetana,111 J. R. Smith,51 L. Smith,25 R. J. E. Smith,150\nW. J. Smith,143 J. Soldateschi,249, 291, 60 K. Somiya,172 I. Song,140 K. Soni,11 S. Soni,30 V. Sordini,114\nF. Sorrentino,53 N. Sorrentino,83, 84 H. Sotani,292 R. Soulard,46 A. Southgate,18 V. Spagnuolo,31, 32\nA. P. Spencer,25 M. Spera,44, 293 P. Spinicelli,55 J. B. Spoon,9 C. A. Sprague,264 A. K. Srivastava,89\nF. Stachurski,25 D. A. Steer,67 J. Steinlechner,31, 32 S. Steinlechner,31, 32 N. Stergioulas,276 P. Stevens,35\nM. StPierre,159 G. Stratta,294, 133, 62, 295 M. D. Strong,9 A. Strunk,3 R. Sturani,296 A. L. Stuver,52, \u2217\nM. Suchenek,91 S. Sudhagar,91 N. Sueltmann,82 L. Suleiman,51 K. D. Sullivan,9 L. Sun,29 S. Sunil,89 J. Suresh,10\nP. J. Sutton,18 T. Suzuki,217 Y. Suzuki,223 B. L. Swinkels,32 A. Syx,64 M. J. Szczepa\u00b4nczyk,297, 42 P. Szewczyk,119\nM. Tacca,32 H. Tagoshi,193 S. C. Tait,2 H. Takahashi,298 R. Takahashi,20 A. Takamori,36 T. Takase,47\nK. Takatani,194 H. Takeda,299 K. Takeshita,172 C. Talbot,127 M. Tamaki,193 N. Tamanini,123 D. Tanabe,141\nK. Tanaka,47 S. J. Tanaka,223 T. Tanaka,299 D. Tang,26 S. Tanioka,75 D. B. Tanner,42 L. Tao,42 R. D. Tapia,7\nE. N. Tapia San Mart\u00b4\u0131n,32 R. Tarafder,2 C. Taranto,16, 17, 63 A. Taruya,300 J. D. Tasson,176 M. Teloi,33\nR. Tenorio,95 H. Themann,197 A. Theodoropoulos,135 M. P. Thirugnanasambandam,11 L. M. Thomas,2\nM. Thomas,61 P. Thomas,3 J. E. Thompson,147 S. R. Thondapu,97 K. A. Thorne,61 E. Thrane,150 J. Tissino,41\nA. Tiwari,11 P. Tiwari,41 S. Tiwari,198 V. Tiwari,111 M. R. Todd,75 A. M. Toivonen,93 K. Toland,25\nA. E. Tolley,124 T. Tomaru,20 K. Tomita,194 T. Tomura,47 C. Tong-Yu,141 A. Toriyama,223 N. Toropov,111\nA. Torres-Forn\u00b4e,135, 136 C. I. Torrie,2 M. Toscani,123 I. Tosta e Melo,301 E. Tournefier,27 A. Trapananti,49, 48\nF. Travasso,49, 48 G. Traylor,61 M. Trevor,120 M. C. Tringali,55 A. Tripathee,86 G. Troian,183 L. Troiano,302, 107\nA. Trovato,183, 44 L. Trozzo,5 R. J. Trudeau,2 T. T. L. Tsang,18 R. Tso,147, \u2020 S. Tsuchida,303 L. Tsukada,7\nT. Tsutsui,36 K. Turbang,175, 19 M. Turconi,46 C. Turski,90 H. Ubach,37, 77 N. Uchikata,193 T. Uchiyama,47\nR. P. Udall,2 T. Uehara,304 M. Uematsu,194 K. Ueno,36 S. Ueno,223 V. Undheim,265 T. Ushiba,47 M. Vacatello,84, 83\nH. Vahlbruch,39, 40 N. Vaidya,2 G. Vajente,2 A. Vajpeyi,150 G. Valdes,129 J. Valencia,95 M. Valentini,101, 32\nS. A. Vallejo-Pe\u02dcna,281 S. Vallero,22 V. Valsan,8 N. van Bakel,32 M. van Beuzekom,32 M. van Dael,32, 305\nJ. F. J. van den Brand,31, 101, 32 C. Van Den Broeck,73, 32 D. C. Vander-Hyde,75 M. van der Sluys,32, 73\nA. Van de Walle,35 J. van Dongen,32, 101 K. Vandra,52 H. van Haevermaet,19 J. V. van Heijningen,32, 101\nP. Van Hove,64 M. VanKeuren,71 J. Vanosky,2 M. H. P. M. van Putten,13 Z. van Ranst,31, 32 N. van Remortel,19\nM. Vardaro,31, 32 A. F. Vargas,130 J. J. Varghese,65 V. Varma,134 M. Vas\u00b4uth,79, \u2021 A. Vecchio,111 G. Vedovato,88\nJ. Veitch,25 P. J. Veitch,108 S. Venikoudis,10 J. Venneberg,39, 40 P. Verdier,114 D. Verkindt,27 B. Verma,134\nP. Verma,173 Y. Verma,97 S. M. Vermeulen,2 F. Vetrano,59 A. Veutro,62, 63 A. M. Vibhute,3 A. Vicer\u00b4e,59, 60\nS. Vidyant,75 A. D. Viets,80 A. Vijaykumar,178 A. Vilkha,196 V. Villa-Ortega,126 E. T. Vincent,56 J.-Y. Vinet,46\nS. Viret,114 A. Virtuoso,183, 44 S. Vitale,30 A. Vives,74 H. Vocca,85, 48 D. Voigt,82 E. R. G. von Reis,3\n\n5\nJ. S. A. von Wrangel,39, 40 S. P. Vyatchanin,102 L. E. Wade,71 M. Wade,71 K. J. Wagner,196 A. Wajid,53, 54\nM. Walker,118 G. S. Wallace,94 L. Wallace,2 H. Wang,36 J. Z. Wang,86 W. H. Wang,160 Z. Wang,141\nG. Waratkar,200 J. Warner,3 M. Was,27 T. Washimi,20 N. Y. Washington,2 D. Watarai,36 K. E. Wayt,71\nB. R. Weaver,18 B. Weaver,3 C. R. Weaving,124 S. A. Webster,25 M. Weinert,39, 40 A. J. Weinstein,2 R. Weiss,30\nF. Wellmann,39, 40 L. Wen,26 P. We\u00dfels,39, 40 K. Wette,29 J. T. Whelan,196 B. F. Whiting,42 C. Whittle,2\nJ. B. Wildberger,1 O. S. Wilk,71 D. Wilken,39, 40, 40 A. T. Wilkin,202 D. J. Willadsen,80 K. Willetts,18\nD. Williams,25 M. J. Williams,124 N. S. Williams,111 J. L. Willis,2 B. Willke,40, 39, 40 M. Wils,103 J. Winterflood,26\nC. C. Wipf,2 G. Woan,25 J. Woehler,31, 32 J. K. Wofford,196 N. E. Wolfe,30 H. T. Wong,141 H. W. Y. Wong,209\nI. C. F. Wong,209 J. L. Wright,29 M. Wright,25 C. Wu,140 D. S. Wu,39, 40 H. Wu,140 E. Wuchner,51 D. M. Wysocki,8\nV. A. Xu,30 Y. Xu,198 N. Yadav,91 H. Yamamoto,2 K. Yamamoto,177 T. S. Yamamoto,244 T. Yamamoto,47\nS. Yamamura,193 R. Yamazaki,223 S. Yan,15 T. Yan,111 F. W. Yang,190 F. Yang,158 K. Z. Yang,93 Y. Yang,144\nZ. Yarbrough,9 H. Yasui,47 S.-W. Yeh,140 A. B. Yelikar,196 X. Yin,30 J. Yokoyama,306, 36 T. Yokozawa,47 J. Yoo,148\nH. Yu,147 S. Yuan,26 H. Yuzurihara,47 A. Zadro\u02d9zny,173 M. Zanolin,65 M. Zeeshan,196 T. Zelenova,55 J.-P. Zendri,88\nM. Zeoli,113, 10 M. Zerrad,34 M. Zevin,76 A. C. Zhang,158 L. Zhang,2 R. Zhang,42 T. Zhang,111 Y. Zhang,29\nC. Zhao,26 Yue Zhao,190 Yuhang Zhao,67 Y. Zheng,99 H. Zhong,93 R. Zhou,214 X.-J. Zhu,307 Z.-H. Zhu,307, 201\nA. B. Zimmerman,146 M. E. Zucker,30, 2 J. Zweizig,2\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3LIGO Hanford Observatory, Richland, WA 99352, USA\n4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n5INFN, Sezione di Napoli, I-80126 Napoli, Italy\n6University of Warwick, Coventry CV4 7AL, United Kingdom\n7The Pennsylvania State University, University Park, PA 16802, USA\n8University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n9Louisiana State University, Baton Rouge, LA 70803, USA\n10Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n11Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n12Queen Mary University of London, London E1 4NS, United Kingdom\n13Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n14Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n15Stanford University, Stanford, CA 94305, USA\n16Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n17INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n18Cardiff University, Cardiff CF24 3AA, United Kingdom\n19Universiteit Antwerpen, 2000 Antwerpen, Belgium\n20Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n21Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n22INFN Sezione di Torino, I-10125 Torino, Italy\n23Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n24Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n25SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n26OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n27Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n28Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n29OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n30LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n31Maastricht University, 6200 MD Maastricht, Netherlands\n32Nikhef, 1098 XG Amsterdam, Netherlands\n33Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n34Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n35Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n36University of Tokyo, Tokyo, 113-0033, Japan.\n37Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n38Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n\n6\n39Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n40Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n41Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n42University of Florida, Gainesville, FL 32611, USA\n43Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n44INFN, Sezione di Trieste, I-34127 Trieste, Italy\n45Tecnol\u00b4ogico de Monterrey Campus Guadalajara, 45201 Zapopan, Jalisco, Mexico\n46Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n47Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n48INFN, Sezione di Perugia, I-06123 Perugia, Italy\n49Universit`a di Camerino, I-62032 Camerino, Italy\n50University of Washington, Seattle, WA 98195, USA\n51California State University Fullerton, Fullerton, CA 92831, USA\n52Villanova University, Villanova, PA 19085, USA\n53INFN, Sezione di Genova, I-16146 Genova, Italy\n54Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n55European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n56Georgia Institute of Technology, Atlanta, GA 30332, USA\n57Royal Holloway, University of London, London TW20 0EX, United Kingdom\n58Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n59Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n60INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n61LIGO Livingston Observatory, Livingston, LA 70754, USA\n62INFN, Sezione di Roma, I-00185 Roma, Italy\n63Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n68King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n69Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n70Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n71Kenyon College, Gambier, OH 43022, USA\n72International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n73Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n74University of Oregon, Eugene, OR 97403, USA\n75Syracuse University, Syracuse, NY 13244, USA\n76Northwestern University, Evanston, IL 60208, USA\n77Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n78Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n79HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n80Concordia University Wisconsin, Mequon, WI 53097, USA\n81International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n82Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n83Universit`a di Pisa, I-56127 Pisa, Italy\n84INFN, Sezione di Pisa, I-56127 Pisa, Italy\n85Universit`a di Perugia, I-06123 Perugia, Italy\n86University of Michigan, Ann Arbor, MI 48109, USA\n87Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n88INFN, Sezione di Padova, I-35131 Padova, Italy\n89Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n90Universiteit Gent, B-9000 Gent, Belgium\n91Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n92Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n93University of Minnesota, Minneapolis, MN 55455, USA\n\n7\n94SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n95IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n96Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n97RRCAT, Indore, Madhya Pradesh 452013, India\n98GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n99Missouri University of Science and Technology, Rolla, MO 65409, USA\n100Colorado State University, Fort Collins, CO 80523, USA\n101Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n102Lomonosov Moscow State University, Moscow 119991, Russia\n103Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n104Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n105INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n106Bar-Ilan University, Ramat Gan, 5290002, Israel\n107INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n108OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n109Centre national de la recherche scientifique, 75016 Paris, France\n110Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n111University of Birmingham, Birmingham B15 2TT, United Kingdom\n112Washington State University, Pullman, WA 99164, USA\n113Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n114Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n115Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n116INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n117Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n118Christopher Newport University, Newport News, VA 23606, USA\n119Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n120University of Maryland, College Park, MD 20742, USA\n121Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n122INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n123L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n124University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n125Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n126IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n127University of Chicago, Chicago, IL 60637, USA\n128NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n129Texas A&M University, College Station, TX 77843, USA\n130OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n131INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n132Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n133Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n136Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n137Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n138University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n139Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n140National Tsing Hua University, Hsinchu City 30013, Taiwan\n141National Central University, Taoyuan City 320317, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n145Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n146University of Texas, Austin, TX 78712, USA\n147CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n148Cornell University, Ithaca, NY 14850, USA\n149Northeastern University, Boston, MA 02115, USA\n\n8\n150OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n151Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n153OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n154INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n155Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n156Montana State University, Bozeman, MT 59717, USA\n157Texas Tech University, Lubbock, TX 79409, USA\n158Columbia University, New York, NY 10027, USA\n159University of Rhode Island, Kingston, RI 02881, USA\n160The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n161Chennai Mathematical Institute, Chennai 603103, India\n162Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n163Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n164Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n165Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n166Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n167INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n168University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n169Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n170Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n171Indian Institute of Technology Madras, Chennai 600036, India\n172Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n173National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n174Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n175Vrije Universiteit Brussel, 1050 Brussel, Belgium\n176Carleton College, Northfield, MN 55057, USA\n177Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n178Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n179University of Cambridge, Cambridge CB2 1TN, United Kingdom\n180Stony Brook University, Stony Brook, NY 11794, USA\n181Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n182Montclair State University, Montclair, NJ 07043, USA\n183Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n184HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n185Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n186CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n187Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n188Western Washington University, Bellingham, WA 98225, USA\n189SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n190The University of Utah, Salt Lake City, UT 84112, USA\n191E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n192Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n193Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n194Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n195Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n196Rochester Institute of Technology, Rochester, NY 14623, USA\n197California State University, Los Angeles, Los Angeles, CA 90032, USA\n198University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n199University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n200Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n201School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n202University of California, Riverside, Riverside, CA 92521, USA\n203INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n\n9\n204University of Nottingham NG7 2RD, UK\n205Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n206The University of Mississippi, University, MS 38677, USA\n207Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n208Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n209The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n210Marquette University, Milwaukee, WI 53233, USA\n211American University, Washington, DC 20016, USA\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n214University of California, Berkeley, CA 94720, USA\n215University of Lancaster, Lancaster LA1 4YW, United Kingdom\n216College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n217Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n218Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n219Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n220Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n221Scuola Normale Superiore, I-56126 Pisa, Italy\n222Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n223Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n224Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n225Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n226University of Bia lystok, 15-424 Bia lystok, Poland\n227Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n228University of Southampton, Southampton SO17 1BJ, United Kingdom\n229Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n230Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n231Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n232Chung-Ang University, Seoul 06974, Republic of Korea\n233University of Washington Bothell, Bothell, WA 98011, USA\n234Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n235Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n236Ewha Womans University, Seoul 03760, Republic of Korea\n237Seoul National University, Seoul 08826, Republic of Korea\n238Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n241Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n242Bard College, Annandale-On-Hudson, NY 12504, USA\n243Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n244Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n245Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n246Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n247Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n248NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n249Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n250National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n251NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n252West Virginia University, Morgantown, WV 26506, USA\n253Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n254School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n255Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n\n10\n256Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n257Tsinghua University, Beijing 100084, China\n258INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n259Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n260Tata Institute of Fundamental Research, Mumbai 400005, India\n261Hobart and William Smith Colleges, Geneva, NY 14456, USA\n262Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n263Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n264Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n265University of Stavanger, 4021 Stavanger, Norway\n266Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 903-0213, Japan\n267Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n268Observatoire de Paris, 75014 Paris, France\n269Universit\u00b4e PSL, 75006 Paris, France\n270Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n271National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n272Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n273Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n274CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n275Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n276Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n277Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n278Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n279Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n280Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n281Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n282Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n283Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n284Universit`a Degli Studi Di Ferrara, Via Savonarola, 9, 44121 Ferrara FE, Italy\n285Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n286Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n287Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n288Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n289Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n290Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n291INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n292iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n293Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n294Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n295INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n296Universidade Estadual Paulista, 01140-070 S\u02dcao Paulo, Brazil\n297Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n298Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n299Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n300Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n301University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n302Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n303National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n304Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n\n11\n305Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n306Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City,\nChiba 277-8583, Japan\n307Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\nABSTRACT\nWe present the results of a search for gravitational-wave transients associated with core-collapse\n1\nsupernova SN 2023ixf, which was observed in the galaxy Messier 101 via optical emission on 2023 May\n2\n19th, during the LIGO-Virgo-KAGRA 15th Engineering Run. We define a five-day on-source window\n3\nduring which an accompanying gravitational-wave signal may have occurred. No gravitational waves\n4\nhave been identified in data when at least two gravitational-wave observatories were operating, which\n5\ncovered \u223c14 % of this five-day window. We report the search detection efficiency for various possible\n6\ngravitational-wave emission models. Considering the distance to M101 (6.7 Mpc), we derive constraints\n7\non the gravitational-wave emission mechanism of core-collapse supernovae across a broad frequency\n8\nspectrum, ranging from 50 Hz to 2 kHz where we assume the gravitational-wave emission occurred\n9\nwhen coincident data are available in the on-source window. Considering an ellipsoid model for a\n10\nrotating proto-neutron star, our search is sensitive to gravitational-wave energy 1 \u00d7 10\u22124 M\u2299c2 and\n11\nluminosity 2.6 \u00d7 10\u22124 M\u2299c2/s for a source emitting at 82 Hz. These constraints are around an order\n12\nof magnitude more stringent than those obtained so far with gravitational-wave data. The constraint\n13\non the ellipticity of the proto-neutron star that is formed is as low as 1.08, at frequencies above 1200\n14\nHz, surpassing past results.\n15\nKeywords: SN 2023ixf \u2014 Gravitational-waves\n1. INTRODUCTION\nThe direct detection of gravitational waves (GWs)\nfrom a binary black hole merger (Abbott et al. 2016a)\nstarted the field of GW astronomy, and was followed by\nsimilar mergers (Abbott et al. 2019, 2021a, 2024, 2023a).\nTwo years later, the merger of two neutron stars was ob-\nserved both with GWs and across the electromagnetic\nspectrum (Abbott et al. 2017a,b), leading to the birth\nof GW multi-messenger astronomy. More recently, the\nobservation of mergers of mixed systems (Abbott et al.\n2021b; Abac et al. 2024) is allowing measurement of the\nmerger rates of all types of compact binary systems (Ab-\nbott et al. 2023b).\nCore-collapse supernovae (CCSNe) are the explosions\nof massive stars \u2013 masses above 8 M\u2299at the end of\ntheir evolution \u2013 leading to the production of neutron\nstars and black holes (Burrows et al. 1995; Kotake et al.\n2006; Janka 2012).\nCCSNe are astrophysical sources\nwith multi-messenger emission, having historically been\nobserved over the electromagnetic spectrum and, for SN\n1987A, also with low-energy neutrinos (Hirata et al.\n1987; Bionta et al. 1987; Alekseev et al. 1987). How-\n\u2217Deceased, September 2024.\n\u2020 Deceased, July 2023.\n\u2021 Deceased, February 2024.\never, the GW emission of CCSNe is still undetected.\nThe combination of GW and neutrino observations can\nprovide information about the collapse and the onset of\nthe explosion, since both messengers are emitted from\nthe core very soon after the collapse and have negli-\ngible interactions with the surrounding matter (Janka\n2012). On the other hand, electromagnetic emission is\nproduced in the outer layers of the star and is delayed.\nThe GW emission from CCSNe is weaker than the\nemission from compact binary mergers, making it de-\ntectable by the advanced generation of detectors only\nfor nearby supernovae (Gossan et al. 2016; Szczepa\u00b4nczyk\net al. 2021; Abbott et al. 2021c). The most likely op-\nportunity for observations are Galactic CCSNe, but the\nexpected rate is of the order of one or two per cen-\ntury (Bergh & Tammann 1991; Cappellaro et al. 1993;\nTammann et al. 1994; Diehl et al. 2006; Li et al. 2011;\nAdams et al. 2013). However, due to the large uncer-\ntainties of the progenitors and GW emission models,\nwe carry out searches for GW emission from CCSNe\nout to distances of 20 Mpc (Abbott et al. 2016b, 2020;\nSzczepa\u00b4nczyk et al. 2024).\nSN 2023ixf was identified in Messier 101 (M101) dur-\ning its rise, making it one of the closest type II CCSNe\nobserved. The two LIGO observatories were in observ-\ning mode during the fifteenth Engineering Run (ER15)\nof the LIGO-Virgo-KAGRA network (Aasi et al. 2015;\n\n12\nAcernese et al. 2015; Akutsu et al. 2021). In this article,\nwe report the results of the search for GWs and the new\nconstraints on GW emission obtained with SN 2023ixf.\n2. SN 2023IXF AND ER15 DATA\n2.1. Summary of SN 2023ixf multi-messenger\nobservations\nSN 2023ixf (RA = 14:03:38.562, DEC = +54:18:41.94,\nJ2000) was discovered on 2023 May 19 by Itagaki (2023)\nwith a clear (unfiltered) magnitude of 14.9 in the host\ngalaxy M101 (NGC 5457, Pinwheel Galaxy). M101 is\nat a distance of about 6.7 Mpc (see Sec. 2.3), making\nSN 2023ixf one of the nearest CCSNe observed in re-\ncent years. In addition, this galaxy is a well-observed\nobject with an extensive set of pre-discovery observa-\ntions. SN 2023ixf was quickly classified as a type II su-\npernova a few hours after the discovery (Perley et al.\n2023). Due to the prompt discovery and the close dis-\ntance, SN 2023ixf was the target of extensive electro-\nmagnetic coverage.\nThe optical light curve shows a\nrise to a maximum at about five days, followed by a\nplateau lasting for about one month, and a slow de-\ncline later (Hiramatsu et al. 2023; Hosseinzadeh et al.\n2023; Li et al. 2024; Sgro et al. 2023; Teja et al. 2023;\nYamanaka et al. 2023).\nThe early spectroscopic ob-\nservations show flash ionization features of hydrogen,\nhelium, nitrogen, carbon and a temperature increase\nnot explained by pure shock cooling, suggesting a de-\nlayed shock breakout in a dense circumstellar medium\n(Berger et al. 2023; Bersten, M. C. et al. 2024; Bostroem\net al. 2023; Grefenstette et al. 2023; Chandra et al. 2024;\nGuetta et al. 2023; Hiramatsu et al. 2023; Hosseinzadeh\net al. 2023; Koenig 2023; Jacobson-Galan et al. 2023;\nKilpatrick et al. 2023; Li et al. 2024; Martinez, L. et al.\n2024; Murase 2024; Niu et al. 2023; Pledger & Shara\n2023; Qin et al. 2024; Smith et al. 2023; Teja et al.\n2023; Van Dyk et al. 2023; Vasylyev et al. 2023; Xiang\net al. 2024; Yamanaka et al. 2023; Zimmerman et al.\n2024). The earliest detections of X-ray and radio emis-\nsion occurred four days (Grefenstette et al. 2023) and\none month (Matthews et al. 2023) after the discovery,\nrespectively. The hard X-ray (Grefenstette et al. 2023)\nand soft X-ray (Chandra et al. 2024; Panjkov et al. 2024)\nobservations suggest a high and decreasing neutral hy-\ndrogen column density close to SN 2023ixf. SN 2023ixf\nwas not detected in gamma-rays (Marti-Devesa 2023) or\nin neutrinos (Thwaites et al. 2023; Nakahata & Super-\nKamiokande Collaboration 2023; Abbasi et al. 2023).\n2.2. Nature and mass of progenitor\nA large set of M101 pre-discovery imaging observa-\ntions from ground-based telescopes, Hubble Space Tele-\nscope and Spitzer Space Telescope suggest the nature of\nthe SN 2023ixf progenitor to be a dusty and variable red\nsupergiant, with an estimated mass ranging from 8 to\n20 M\u2299(Dong et al. 2023; Flinner et al. 2023; Hiramatsu\net al. 2023; Jencson et al. 2023; Neustadt et al. 2023;\nNiu et al. 2023; Pledger & Shara 2023; Ransome et al.\n2024; Soraisam et al. 2023; Van Dyk et al. 2023; Xiang\net al. 2024; Ferrari, Luc\u00b4\u0131a et al. 2024; Moriya & Singh\n2024).\nThe circumstellar medium could have been produced\nby an enhancement in the mass loss before the SN ex-\nplosion, but several archival investigations did not find\nany pre-explosion outburst in the years before the dis-\ncovery (Dong et al. 2023; Flinner et al. 2023; Jencson\net al. 2023; Neustadt et al. 2023; Ransome et al. 2024;\nSoraisam et al. 2023), while detecting amplitude pulsa-\ntions (Kilpatrick et al. 2023; Soraisam et al. 2023).\n2.3. M101 distance\nThe distance of the supernova host galaxy is rele-\nvant to constrain the GW energy emission. Since as-\ntronomical distances are estimated using a broad range\nof methods, we have considered the available published\nvalues to estimate the distance to M101. More precisely,\nwe have considered the distance estimations reported in\nthe NASA Extragalacic Database (Helou et al. 1991),\na total number of 115 measurements using 12 differ-\nent methods: Cepheids, Planetary Nebulae Luminosity\nFunction, Supernova Ia, Tip of Red Giant Branch, SN II\noptical, Brightest Stars, Tully-Fisher relation, M Stars,\nRSV Stars, S Dor stars, H II region diameter and SN II\nradio. We adopt the median to the remaining 115 data\npoints, 6.7 Mpc, with a standard deviation of 0.9 Mpc,\nas the estimated distance of SN 2023ixf.\n2.4. On-source window\nThe on-source window is the time interval containing\nthe core bounce and the following GW emission. We\ndenote the start and end times of this interval as t1 and\nt2, respectively. Due to the availability of well-sampled\npublic photometric data of SN 2023ixf, the on-source\nwindow could be estimated using the early photomet-\nric observations that include the non-detections before\nthe rise to peak brightness as shown in Fig. 1. The first\ndetection is MJD = 60082.82611, at a CV magnitude of\n18.76\u00b10.25 (Chufarin et al. 2023), following the last pre-\ndiscovery observation at MJD = 60082.66041667, clear\nmagnitude > 20.4 (Mao et al. 2023). For SN 2023ixf,\nt2 is well approximated by the first detection, while t1\ninvolves the delay between collapse and shock breakout,\nwhose time falls between t2 and the latest pre-discovery\nobservation. The time delay depends on many proper-\nties of the progenitor, including its mass. Considering\n\n13\n-2.0\n-1.5\n-1.0\n-0.5\n0.0\n0.5\n1.0\nt \u2212t2 [days]\n13\n14\n15\n16\n17\n18\n19\n20\n21\n22\nMagnitude\nt2\nSN 2023ixf\ng, N.D.\no, N.D.\nclear, N.D.\nCV, N.D.\nB\nV\nR\nCV\ng\nr\nclear\n0\n\u22121\n\u22122\n\u22123\n\u22124\n\u22125\nt \u2212t2 [days]\nH1\nL1\n28.34%\n26.93%\nIFO Duty Factor\nFigure 1.\nEarly evolution of SN 2023ixf covering different photometric bands (B, V, R, g, o) and unfiltered observations\n(CV, clear); N.D. marks non detections; inset: LIGO Hanford (H1) and Livingston (L1) detectors duty cycle within the OSW\ndescribed in the text. Photometric data sources: Transient Name Server Astronotes, Astronomical Telegrams, AAVSO, Sgro\net al. (2023); Li et al. (2024).\n.\nthe large spread in mass estimations and the relation\nbetween mass and time delay found by Barker et al.\n(2022) (Fig. 6), we have adopted a conservative maxi-\nmal on-source window duration of five days, from 2023-\n05-13T19:49:35 to 2023-05-18T19:49:35 UTC.\n2.5. ER15 data\nER15 took place at the LIGO Livingston and Han-\nford Observatories from 2023 April 7 to 2023 May 24\nfollowing a period of upgrades and commissioning that\nimproved the detectors\u2019 sensitivity from the previous ob-\nserving run. During ER15, the observatories collect data\nas if it were a normal observing run with the excep-\ntion that calibration, commissioning, and noise investi-\ngations are performed. These studies are concentrated\nnear the beginning of ER15 and taper to an as-needed\nbasis towards the last week. The collapse of SN 2023ixf\nlikely happened during this end period of ER15 as did\nthe time period spanned by this search.\nThe uncertainty in the strain calibration has been\nfound to be similar to previous observing runs (Sun et al.\n2021). Its effect on the search is marginal and thus ig-\nnored.\nWithin the on-source window, the two LIGO\nobservatories were operating jointly for \u223c0.8 days.\nTransient\ndata\nartifacts,\nreferred\nto\nas\nglitches,\ncontaminate\nthe\ndata\nand\ncan\naffect\nthe\nconfidence\nestimation\nof\ncandidate\nevents.\nThe\nsearch\nhas\nbeen\ncarried\nout\nwith\nstrain\nchannels\nL1:GDS-CALIB STRAIN CLEAN AR\nand\nH1:GDS-CALIB STRAIN CLEAN AR where CLEAN means\nsome of the well identified noise sources have been re-\nmoved (Abbott et al. 2023c). Data quality studies reveal\nauxiliary channels that are insensitive to GWs and have\na strong correlation to the glitches in the output of the\ndetector.\nThese times of poor data quality are then\nremoved (vetoed) (Davis et al. 2021), representing 15\n% of the coincident time within the on-source window.\nThis gives the analysis time of \u223c0.68 days.\n3. SEARCH\n3.1. Coherent WaveBurst\nWe use coherent WaveBurst (cWB), a model-agnostic\nsearch algorithm, for the detection and reconstruction\nof transient GW signals (Klimenko et al. 2016).\nThe\nalgorithm identifies GW transients by searching for\nexcess power in spectrograms and reconstructs coher-\nent signals in multiple detectors.\nIn previous CCSN\nsearches (Szczepa\u00b4nczyk et al. 2023), spectrograms were\nobtained with the Wilson-Daubechies-Meyer wavelet\ntransform (Necula et al. 2012).\nThe SN 2023ixf anal-\nysis uses the high-resolution wavescan transform (Kli-\nmenko 2022) that utilizes both the excess-power and\ncross-power statistics for the identification of GW sig-\nnals and enables more accurate reconstruction of the\nsignal waveforms Mishra et al. (2025). The signal de-\ntection statistic \u03b70 is defined as \u03b70 = \u221aEc where Ec is\nthe total coherent energy across the detector network\n(Klimenko et al. 2016). To further separate GW signals\nfrom the noise, the triggers are then re-ranked with a\nreduced statistic \u03b7r = \u03b70 \u00b7 WXGB, where WXGB is the\nXGBoost classification penalty factor which ranges be-\ntween 0 (noise-like) and 1 (signal-like) (Szczepa\u00b4nczyk\net al. 2023; Mishra et al. 2021).\nFor this search, the\nXGBoost algorithm uses the SN 2023ixf sky location to\nimprove detection sensitivity.\n3.2. CCSN models\nTo test the sensitivity of the search, we use a range\nof different waveforms from numerical simulations, that\nspan the expected progenitor parameter space. For non-\n\n14\n0.1\n1\n10\nDistance [Mpc]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nDetection E\ufb03ciency\nGC\nLMC\nM 101\n82 Hz, 0.1s (NaN kpc)\n82 Hz, 1s (1.8 kpc)\n272 Hz, 0.001s (NaN kpc)\n272 Hz, 0.01s (6.9 kpc)\n272 Hz, 0.1s (20.0 kpc)\n272 Hz, 1s (35.1 kpc)\n2000 Hz, 0.001s (30.8 kpc)\n2000 Hz, 0.01s (120.9 kpc)\n2000 Hz, 0.1s (377.9 kpc)\n2000 Hz, 1s (625.6 kpc)\n1044\n1045\n1046\n1047\nIzz\u03f5 [g cm2]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nDetection E\ufb03ciency\n82 Hz, 0.1s\n82 Hz, 1s\n272 Hz, 0.001s\n272 Hz, 0.01s\n272 Hz, 0.1s\n272 Hz, 1s\n2000 Hz, 0.001s\n2000 Hz, 0.01s\n2000 Hz, 0.1s\n2000 Hz, 1s\nFigure 2. Detection efficiency of a GW source in the direction of M101, and within the on-source window of SN 2023ixf, for a\nFAR of less than 1 event in 10 years. The long-lasting bar-mode GW emission model is considered for various peak frequencies\nand durations. On the left panel Izz\u03f5 is fixed to 0.1\u00d71045 g cm2 and the detection efficiency is shown as function of the distance\nto the source. Horizontal dashed lines show 10%, 50%, and 90% detection efficiencies and the Galactic Center (GC), Large\nMagellanic Cloud (LMC) and M101 distances are shown as references. On the right panel, the distance is fixed to M101 and\nthe detection efficiency is shown as function of Izz\u03f5.\nrotating sources we use the 15 M\u2299SFHx s15 model\nfrom Kuroda et al. (2016) [Kur+16 s15], the 15 M\u2299\nD15 model from Mezzacappa et al. (2023) [Mez+23\nD15], the 20 M\u2299mesa20 pert model from O\u2019Connor &\nCouch (2018) [Oco+18 m20p], the 18 M\u2299s18 model\nfrom Powell & M\u00a8uller (2019) [Pow+19 s18], the 40 M\u2299\nNR model from Pan et al. (2021) [Pan+21 NR], and\nthe 25 M\u2299s25 model from Radice et al. (2019) [Rad+19\ns25]. For examples of progenitors at the lower mass end,\nwe include model he3.5 from Powell & M\u00a8uller (2019)\n[Pow+19 he3.5], which is an ultra-stripped progenitor\nwith a 3.5 M\u2299helium core, and the 13 M\u2299s13 model\nfrom Radice et al. (2019) [Rad+19 s13].\nWe also include waveforms from more energetic types\nof explosions.\nWe include the 50 M\u2299s50 model from\nKuroda et al. (2022) [Kur+22 s50], as an example of\na CCSN explosion powered by a first-order quantum-\nchromodynamics phase transition. We include several\nrotating models, as the rotation can significantly in-\ncrease the GW amplitude. They are the 40 M\u2299model\nSR from Pan et al. (2021) [Pan+21 SR], the 15 M\u2299s15fr\nmodel from Andresen et al. (2019) [And+19 s15fr], and\nthe 39 M\u2299helium star model m39 from Powell & M\u00a8uller\n(2020) [Pow+20 m39].\nWe also include a few models\nthat include both rapid rotation and magnetic fields,\nas this can result in powerful magnetorotational explo-\nsions. They are the 39 M\u2299m39 B12 model from Powell\net al. (2023) [Pow+23 B12], and model 3d signal O from\nObergaulinger & Aloy (2020) [Obe+20 signal O].\nWe also consider a phenomenological emission model\nrelated to the development of long-lasting bar-mode\ninstabilities inside the proto-neutron star (PNS) (Ott\n2010; Gossan et al. 2016). Assuming the PNS is well\nmodelled as a triaxial ellipsoid rotating around the z\naxis, one can approximate the GW emission with sine-\nGaussian waveforms\nh+(t) = 1\n2 h0 [1 + cos2 \u03b9] e\n\u2212t2\n\u03c42\ncos(2\u03c0f0t) ,\nh\u00d7(t) = h0 cos \u03b9 e\n\u2212t2\n\u03c42\nsin(2\u03c0f0t) ,\n(1)\nwhere\nh0 = 2\nD\nG\nc4\nIzz\u03f5\n2\n(2\u03c0f0)2 ,\n(2)\nIzz and \u03f5 are the moment of inertia and ellipticity of\nthe ellipsoid, f0 is twice the rotation frequency, D is the\nsource distance and \u03b9 is the inclination angle of the z axis\nwith respect to the line of sight. Izz\u03f5 is a free param-\neter. Throughout the paper, we consider the canonical\nvalue for neutron stars Izz = 1045 g cm2 (Paschalidis &\nStergioulas 2017) and keep \u03f5 as a free parameter.\n4. RESULTS\n4.1. Search result and background estimation\nThe detector data contains a variety of transient noise\nsources that contribute to the search background. To\nassess the significance of each trigger, we compute the\nfalse-alarm rate (FAR), which estimates the frequency\nof noise triggers mistakenly identified as potential GW\nevents. Within the on-source window, the trigger with\nthe lowest FAR is considered a GW event candidate.\nIn this search, the lowest FAR event candidate has a\nFAR of 2.11 per day, giving a false-alarm probability of\n1 \u2212e\u2212Tobs\u00d7FAR = 0.75; i.e., a probability of 0.75 that\nnoise alone would produce a trigger of this FAR or lower\n(Tobs = 0.68 days).\nThis suggests that this trigger is\nlikely due to noise.\n\n15\n4.2. Detection efficiency\nTo evaluate the search sensitivity, we take the signal\nmodels described in Sec. 3.2 and randomize the source\norientation such that it is uniformly distributed over a\nsphere. Then we add waveforms to the detector coinci-\ndent data within the on-source window for the sky lo-\ncation of SN 2023ixf. We compute the search detection\nefficiency, defined as the fraction of detected signals with\nFAR lower than 1 event in 10 years. This FAR corre-\nsponds to a false alarm probability of 1.9 \u00d7 10\u22124. At\nthe distance of SN 2023ixf none of the 14 models from\nnumerical simulations are detected. In Table 1 we re-\nport the distance at which we recover 90% of the added\nsignals for all 14 CCSN models.\nThe distances reach\nup to 6.9 kpc for the non-rotating explosions, which\nmeans that signals from non-rotating or slow-rotating\nprogenitor CCSN could be missed within the Galaxy\nfor sources further than the Galactic Center. The dis-\ntances for the more extreme models are around a fac-\ntor 4 larger than for the non-rotating explosions, ex-\nceeding the Galaxy boundaries \u2013 29.9 kpc for Pow+23\nB12 model \u2013 but without reaching the large Magellanic\nCloud distance. Finally, for the explosion driven by a\nfirst-order quantum-chromodynamics phase transition,\na detection of 90% is never achieved because only one\npolarization is extracted from the 2D numerical simula-\ntions.\nFig. 2 shows the detection efficiency for long-lasting\nbar-mode waveforms with frequencies between 82 Hz\nand 2 kHz and signal durations between 1 ms and 1 s.\nThe right plot is as a function of Izz\u03f5 for a source at\nthe location of SN 2023ixf. The left plot is as a function\nof distance for Izz\u03f5 \u223c0.1 \u00d7 1045 g cm2. The sensitivity\nincreases with the signals peak frequency and duration.\nFor instance, we could detect at 90% confidence level\na signal lasting 1 s at 2 kHz for Izz\u03f5 \u223c1045 g cm2. For\nlower frequencies, if we assume the canonical value Izz \u223c\n1045 g cm2, the source would need to be highly deformed\n(\u03f5 \u226b1).\n5. CONSTRAINTS\nAssuming the GW emission occurred when coincident\ndata are available in the on-source window, we estab-\nlish constraints on several quantities characterizing a\ncore collapse, including emitted GW energy, luminos-\nity, and PNS ellipticity, considering the long-lasting bar-\nmode model.\nThese bar-mode instabilities are some-\ntimes present in simulations at low rotational kinetic en-\nergy over gravitational potential energy ratio (T/|W|).\n5.1. Constraints on GW energy and luminosity\nTable 1. Distance of the 90% detection efficiency reached\nwith CCSN waveform models for a FAR of 1 event in 10\nyears. Values in bold represent the farthest distance reached\nfor each family of models. For the 2D Kur+22 s50 model,\ndetection efficiency remains lower than 90% whatever the\ndistance because there is only one polarization. We report\nthe 50% detection efficiency instead that is marked with \u2217.\nWaveform Models\nDistance [kpc]\nNon-\nrotating\nmodels\nKur+16 s15\n6.9\nMez+23 D15\n2.9\nOco+18 m20p\n1.0\nPow+19 s18\n5.5\nPow+19 he3.5\n2.8\nRad+19 s13\n0.6\nRad+19 s25\n5.8\nPan+21 NR\n6.6\nRotating\nmodels\nAnd+19 s15fr\n1.8\nObe+20 Signal O\n13.4\nPan+21 SR\n18.2\nPow+20 m39\n19.6\nPow+23 B12\n29.9\nPhase\nKur+22 s50\n8.9\u2217\ntransition\nmodel\nAssuming a rotating core, the emitted GW energy\nis (Sutton 2013)\nEGW = 2\n5\n\u03c02c3\nG D2f 2\n0\nZ \u221e\n\u2212\u221e\n[h2\n+(t) + h2\n\u00d7(t)] dt\n= 2\n5\n\u03c02c3\nG\nr\u03c0\n2 \u03c4D2f 2\n0 h2\n0\n(3)\nwhere the GW strain squared integral is computed for\nan optimally oriented source.\nThe GW luminosity is the ratio between the emitted\nGW energy and the duration of the emission. We define\nthe duration as the time interval \u03c490 that contains 90%\nof the energy such that the GW average luminosity is\ngiven by\nPGW = 0.9 EGW\n\u03c490\n.\n(4)\nFor the sine-Gaussians of Eq. (1) \u03c490 = 1.65 \u03c4. Consid-\nering the h0 value corresponding to 90% detection effi-\nciency we derive constraints on EGW and PGW shown\nin Fig. 3. The shaded region contains results from all\nlong-lasting bar-mode models. At 82 Hz the more strin-\ngent energy constraints are \u223c1 \u00d7 10\u22124 M\u2299c2.\nFig. 3\nalso shows the constraints derived from GW searches\ntargetting CCSNe during the third observing run (O3)\n\n16\n100\n1000\nFrequency [Hz]\n10\u22124\n10\u22123\n10\u22122\n0.1\n1\n10\nEGW [M\u2299c2]\nSN 2023ixf \u03c4 = 0.001 s\nSN 2023ixf \u03c4 = 0.01 s\nSN 2023ixf \u03c4 = 0.1 s\nSN 2023ixf \u03c4 = 1 s\nConstraints from O3 CCSNe\nMost stringent constraints\n1050\n1051\n1052\n1053\n1054\n1055\nEGW [erg]\n100\n1000\nFrequency [Hz]\n10\u22124\n10\u22123\n10\u22122\n0.1\n1\n10\n100\nPGW [M\u2299c2/s]\nSN 2023ixf \u03c4 = 0.001 s\nSN 2023ixf \u03c4 = 0.01 s\nSN 2023ixf \u03c4 = 0.1 s\nSN 2023ixf \u03c4 = 1 s\nConstraints from O3 CCSNe\nMost stringent constraints\n1052\n1054\n1056\nPGW [erg/s]\nFigure 3.\nGW energy (EGW) and luminosity (PGW) as\na function of the frequency for bar-mode signals with a de-\ntection efficiency of 90% and a FAR of 1 event in 10 years.\nThe shaded region contains combined results from all ana-\nlyzed models for SN 2023ixf.\nof the LIGO-Virgo-KAGRA network. The constraints\nwith SN 2023ixf are \u223c49 times more stringent than for\nO3 CCSNe over the whole frequency range.\nFor the\nemitted GW average luminosity shown in the bottom\npanel, the constraints are 2.6 \u00d7 10\u22124 M\u2299c2/s for signals\nat 82 Hz and 1 s long. They are a factor of \u223c36 more\nstringent compared to the O3 CCSNe over the whole\nfrequency range. This upper limit is between 2 and 5\norders of magnitude larger than the GW average lumi-\nnosity predicted by numerical simulations for the dif-\nferent explosion mechanisms (Szczepa\u00b4nczyk et al. 2021)\nshowing that we could soon exclude some of the most\noptimistically luminous models with a closer CCSN. It is\nalso \u223c7 orders of magnitude larger than the bolometric\nluminosity reported in Zimmerman et al. (2024).\n5.2. Constraints on PNS ellipticity\nAs shown in Sec. 3.2, the amplitude of the GW signal\nemitted by a rotating PNS can be parametrized by its\nellipticity and its moment of inertia given by the relation\nIzz\u03f5 =\nDc4\nG(2\u03c0f0)2 h0\n(5)\n100\n1000\nFrequency [Hz]\n1\n10\n102\n103\n104\n\u03f5\nSN 2023ixf \u03c4 = 0.001 s\nSN 2023ixf \u03c4 = 0.01 s\nSN 2023ixf \u03c4 = 0.1 s\nSN 2023ixf \u03c4 = 1 s\nConstraints from O3 CCSNe\nMost stringent constraints\nFigure 4. PNS ellipticity as a function of the frequency for\nbar-mode signals with a detection efficiency of 90% and a\nFAR of 1 per 10 years. The moment of inertia Izz is fixed\nto 1045 g cm2. The shaded region contains combined results\nfrom all analyzed bar-mode models for SN 2023ixf.\nFig. 4 reports the ellipticity for a range of bar-mode\nGW signal frequencies and durations for a detection ef-\nficiency of 90%. The most stringent constraints on ellip-\nticity are obtained for the signals with \u03c4 = 1 s, ranging\nfrom 3.6\u00d7102 at the lowest search frequency to 1.08 at\n2 kHz. The \u03f5 constraints get stricter with longer signals.\nOver the whole frequency range, the constraints given\nby SN 2023ixf on the ellipticity are \u223c6.8 more stringent\nthan for O3 CCSNe.\n6. SUMMARY AND DISCUSSION\nWe present the results of a search for GW signals coin-\ncident with SN 2023ixf, which was observed during the\nLIGO-Virgo-KAGRA Engineering Run 15, 2023 April\n24 to 2023 May 24. No significant GW candidates were\nidentified within the \u223c14 % of the on-source window\nwhere coincident good quality GW data are available.\nWith different CCSN waveform models, we quantify the\nsearch sensitivity by estimating the distances at which\n90% of the GW simulated signals are detected. The re-\nported distances are up to 6.9 kpc for non-rotating ex-\nplosions, and up to 29.9 kpc for rapidly rotating mod-\nels. These distance sensitivities have been obtained us-\ning the FAR of 1 event in 10 years . We derive con-\nstraints on the GW energy, luminosity, and PNS elliptic-\nity, which are the most stringent that GW detector data\nhave achieved to date. Assuming the PNS is well mod-\nelled as a rotating triaxial ellipsoid whose moment of in-\nertia along the rotation axis is fixed to Izz=1045 g cm2,\nwe find that the ellipticity should be lower than 1.08.\nThis value, obtained for an hypothetical 1 s-long signal\nat 2 kHz, is one order of magnitude larger than plau-\nsible estimates (\u223c0.1) derived from simulations where\nbar-mode instabilities are present (Shibagaki et al. 2021;\nObergaulinger & Aloy 2021; Bugli et al. 2023).\n\n17\nDespite the large distance of SN 2023ixf, this event\nprobes regions of the bar-mode instabilities parame-\nter space that are physically interesting. On the other\nhand, in the case of a neutrino-driven, magnetorota-\ntional or more exotic explosion model such as first-order\nquantum-chromodynamics phase transition, we show\nthat for detecting GWs from CCSNe, events within the\nLocal group are still the best prospect.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO), for the construction and oper-\nation of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies as well as by the Council of Scientific and Indus-\ntrial Research of India, the Department of Science and\nTechnology, India, the Science & Engineering Research\nBoard (SERB), India, the Ministry of Human Resource\nDevelopment, India, the Spanish Agencia Estatal de\nInvestigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comuni-\ntat Auton`oma de les Illes Balears through the Direcci\u00b4o\nGeneral de Recerca, Innovaci\u00b4o i Transformaci\u00b4o Digi-\ntal with funds from the Tourist Stay Tax Law ITS\n2017-006, the Conselleria d\u2019Economia, Hisenda i Inno-\nvaci\u00b4o, the FEDER Operational Program 2021-2027 of\nthe Balearic Islands, the Conselleria d\u2019Innovaci\u00b4o, Uni-\nversitats, Ci`encia i Societat Digital de la Generalitat\nValenciana and the CERCA Programme Generalitat de\nCatalunya, Spain, the Polish National Agency for Aca-\ndemic Exchange, the National Science Centre of Poland\nand the European Union \u2013 European Regional Develop-\nment Fund; the Foundation for Polish Science (FNP),\nthe Polish Ministry of Science and Higher Education,\nthe Swiss National Science Foundation (SNSF), the Rus-\nsian Science Foundation, the European Commission,\nthe European Social Funds (ESF), the European Re-\ngional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the\nNational Research, Development and Innovation Office\nHungary (NKFIH), the National Research Foundation\nof Korea, the Natural Science and Engineering Research\nCouncil Canada, Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoreti-\ncal Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council\nof Hong Kong, the National Natural Science Founda-\ntion of China (NSFC), the Leverhulme Trust, the Re-\nsearch Corporation, the National Science and Technol-\nogy Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, the JSPS\nLeading-edge\nResearch\nInfrastructure\nProgram,\nJSPS Grant-in-Aid for Specially Promoted Research\n26000005, JSPS Grant-in-Aid for Scientific Research on\nInnovative Areas 2905: JP17H06358, JP17H06361 and\nJP17H06364, JSPS Core-to-Core Program A, Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific\nResearch (S) 17H06133 and 20H05639, JSPS Grant-\nin-Aid for Transformative Research Areas (A) 20A203:\nJP20H05854, the joint research program of the Institute\nfor Cosmic Ray Research, the University of Tokyo, the\nNational Research Foundation (NRF), the Computing\nInfrastructure Project of Global Science experimental\nData hub Center (GSDC) at KISTI, the Korea Astron-\nomy and Space Science Institute (KASI), the Ministry\nof Science and ICT (MSIT) in Korea, Academia Sinica\n(AS), the AS Grid Center (ASGC) and the National Sci-\nence and Technology Council (NSTC) in Taiwan under\ngrants including the Rising Star Program and Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineer-\ning Center of KEK.\nWe would like to thank all of the essential workers who\nput their health at risk during the COVID-19 pandemic,\nwithout whom we would not have been able to complete\nthis work.\n\n18\nREFERENCES\nAasi, J., et al. 2015, Class. 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Branch,62 M. Branchesi,42, 116 J. Brandt,57 I. Braun,72\nM. Breschi,24 T. Briant,117 A. Brillet,47 M. Brinkmann,40, 41 P. Brockill,8 E. Brockmueller,40, 41 A. F. Brooks,2\nB. C. Brown,43 D. D. Brown,108 M. L. Brozzetti,85, 49 S. Brunett,2 G. Bruno,10 R. Bruntz,118 J. Bryant,111\nF. Bucci,61 J. Buchanan,118 O. Bulashenko,38, 78 T. Bulik,119 H. J. Bulten,33 A. Buonanno,120, 1 K. Burtnyk,3\nR. Buscicchio,121, 122 D. Buskulic,28 C. Buy,123 R. L. Byer,15 G. S. Cabourn Davies,124 G. Cabras,44, 45 R. Cabrita,10\nV. C\u00b4aceres-Barbosa,7 L. Cadonati,57 G. Cagnoli,125 C. Cahillane,76 J. Calder\u00b4on Bustillo,126 T. A. Callister,127\nE. Calloni,29, 5 J. B. Camp,128 M. Canepa,55, 54 G. Caneva Santoro,39 K. C. Cannon,37 H. Cao,108\nL. A. Capistran,129 E. Capocasa,68 E. Capote,76 G. Carapella,67, 107 F. Carbognani,56 M. Carlassara,40, 41\nJ. B. Carlin,130 M. Carpinelli,121, 131, 56 G. Carrillo,75 J. J. Carter,40, 41 G. Carullo,132 J. Casanueva Diaz,56\nC. Casentini,133, 16, 17 S. Y. 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Fisher,118 R. Fittipaldi,186, 107\nV. Fiumara,187, 107 R. Flaminio,28 S. M. Fleischer,188 L. S. Fleming,189 E. Floden,93 E. M. Foley,93 H. Fong,138\nJ. A. Font,135, 136 B. Fornal,190 P. W. F. Forsyth,30 K. Franceschetti,166 N. Franchini,68 S. Frasca,64, 63\nF. Frasconi,84 A. Frattale Mascioli,64, 63 Z. Frei,191 A. Freise,33, 101 O. Freitas,192, 135 R. Frey,75 W. Frischhertz,62\nP. Fritschel,31 V. V. Frolov,62 G. G. Fronz\u00b4e,23 M. Fuentes-Garcia,2 S. Fujii,193 T. Fujimori,194 P. Fulda,43\nM. Fyffe,62 B. Gadre,74 J. R. Gair,1 S. Galaudage,195 V. Galdi,168 H. Gallagher,196 S. Gallardo,197\nB. Gallego,197 R. Gamba,24 A. Gamboa,1 D. Ganapathy,31 A. Ganguly,11 B. Garaventa,54, 55 J. Garc\u00b4\u0131a-Bellido,115\nC. Garc\u00b4\u0131a N\u00b4u\u02dcnez,189 C. Garc\u00b4\u0131a-Quir\u00b4os,198 J. W. Gardner,30 K. A. Gardner,138 J. Gargiulo,56 A. Garron,95\nF. Garufi,29, 5 C. Gasbarra,16, 17 B. Gateley,3 V. Gayathri,8 G. Gemme,54 A. Gennai,84 V. Gennari,123 J. George,97\nR. George,146 O. Gerberding,82 L. Gergely,199 Archisman Ghosh,90 Sayantan Ghosh,200 Shaon Ghosh,182\nShrobana Ghosh,40, 41 Suprovo Ghosh,11 Tathagata Ghosh,11 L. Giacoppo,64, 63 J. A. Giaime,9, 62 K. D. Giardina,62\nD. R. Gibson,189 D. T. Gibson,179 C. Gier,94 P. Giri,84, 83 F. Gissi,92 S. Gkaitatzis,83, 84 J. Glanzer,9 F. Glotin,36\nJ. Godfrey,75 P. Godwin,2 N. L. Goebbels,82 E. Goetz,138 J. Golomb,2 S. Gomez Lopez,64, 63 B. Goncharov,42\nY. Gong,201 G. Gonz\u00b4alez,9 P. Goodarzi,202 S. Goode,150 A. W. Goodwin-Jones,27 M. Gosselin,56 A. S. G\u00a8ottel,18\nR. Gouaty,28 D. W. Gould,30 K. Govorkova,31 S. Goyal,1 B. Grace,30 A. Grado,203, 5 V. Graham,26\nA. E. Granados,93 M. Granata,165 V. Granata,67 S. Gras,31 P. Grassia,2 A. Gray,93 C. Gray,3 R. Gray,26\nG. Greco,49 A. C. Green,33, 101 S. M. Green,124 S. R. Green,204 A. M. Gretarsson,66 E. M. Gretarsson,66\nD. Griffith,2 W. L. Griffiths,18 H. L. Griggs,57 G. Grignani,85, 49 A. Grimaldi,104, 105 C. Grimaud,28 H. Grote,18\nD. Guerra,135 D. Guetta,205, 63 G. M. Guidi,60, 61 A. R. Guimaraes,9 H. K. Gulati,89 F. Gulminelli,163, 164\nA. M. Gunny,31 H. Guo,190 W. Guo,27 Y. Guo,33, 32 Anchal Gupta,2 Anuradha Gupta,206 Ish Gupta,7\nN. C. Gupta,89 P. Gupta,33, 74 S. K. Gupta,43 T. Gupta,156 N. Gupte,1 J. Gurs,82 N. Gutierrez,165 F. Guzman,129\nH.-Y. H,140 D. Haba,172 M. Haberland,1 S. Haino,207 E. D. Hall,31 E. Z. Hamilton,95 G. Hammond,26 W.-B. Han,208\nM. Haney,33 J. Hanks,3 C. Hanna,7 M. D. Hannam,18 O. A. Hannuksela,209 A. G. Hanselman,127 H. Hansen,3\nJ. Hanson,62 R. Harada,37 A. R. Hardison,210 K. Haris,33, 74 T. Harmark,132 J. Harms,42, 116 G. M. Harry,211\nI. W. Harry,124 J. Hart,72 B. Haskell,91 C.-J. Haster,212 J. S. Hathaway,196 K. Haughian,26 H. Hayakawa,48\nK. Hayama,213 R. Hayes,18 A. Heffernan,95 A. Heidmann,117 M. C. Heintze,62 J. Heinze,111 J. Heinzel,31\nH. Heitmann,47 F. Hellman,214 P. Hello,36 A. F. Helmling-Cornell,75 G. Hemming,56 O. Henderson-Sapir,108\nM. Hendry,26 I. S. Heng,26 E. Hennes,33 C. Henshaw,57 T. Hertog,103 M. Heurs,40, 41 A. L. Hewitt,179, 215 J. Heyns,31\nS. Higginbotham,18 S. Hild,32, 33 S. Hill,26 Y. Himemoto,216 N. Hirata,21 C. Hirose,217 W. C. G. Ho,218 S. Hoang,36\nS. Hochheim,40, 41 D. Hofman,165 N. A. Holland,33, 101 K. Holley-Bockelmann,143 Z. J. Holmes,108 D. E. Holz,127\nL. Honet,71 C. Hong,15 J. Hornung,75 S. Hoshino,217 J. Hough,26 S. Hourihane,2 E. J. Howell,27 C. G. Hoy,124\nC. A. Hrishikesh,16 H.-F. Hsieh,140 C. Hsiung,219 H. C. Hsu,141 W.-F. Hsu,103 P. Hu,143 Q. Hu,26 H. Y. Huang,141\nY.-J. Huang,7 A. D. Huddart,220 B. Hughey,66 D. C. Y. Hui,221 V. Hui,28 S. Husa,95 R. Huxford,7 T. Huynh-Dinh,62\nL. Iampieri,64, 63 G. A. Iandolo,32 M. Ianni,17, 16 A. Iess,222, 84 H. Imafuku,37 K. Inayoshi,223 Y. Inoue,141 G. Iorio,87\nM. H. Iqbal,30 J. Irwin,26 R. Ishikawa,224 M. Isi,180, 181 M. A. Ismail,141 Y. Itoh,194, 225 H. Iwanaga,194 M. Iwaya,193\nB. R. Iyer,20 V. JaberianHamedan,27 C. Jacquet,123 P.-E. Jacquet,117 S. J. Jadhav,226 S. P. Jadhav,153 T. Jain,179\nA. L. James,2 P. A. James,118 R. Jamshidi,34 J. Janquart,74, 33 K. Janssens,19, 47 N. N. Janthalur,226 S. Jaraba,115\nP. Jaranowski,227 R. Jaume,95 W. Javed,18 A. Jennings,3 W. Jia,31 J. Jiang,43 Hong-Bo Jin,228, 229 J. Kubisz,230\nC. Johanson,134 G. R. Johns,118 N. A. Johnson,43 M. C. Johnston,212 R. Johnston,26 N. Johny,40, 41 D. H. Jones,30\nD. I. Jones,231 R. Jones,26 S. Jose,171 P. Joshi,7 L. Ju,27 K. Jung,232 J. Junker,30 V. Juste,71 T. Kajita,233\nI. Kaku,194 C. Kalaghatgi,74, 33, 234 V. Kalogera,77 M. Kamiizumi,48 N. Kanda,225, 194 S. Kandhasamy,11 G. Kang,235\nJ. B. Kanner,2 S. J. Kapadia,11 D. P. Kapasi,30 S. Karat,2 C. Karathanasis,39 R. Kashyap,7 M. Kasprzack,2\nW. Kastaun,40, 41 T. Kato,193 E. Katsavounidis,31 W. Katzman,62 R. Kaushik,97 K. Kawabe,3 R. Kawamoto,194\nA. Kazemi,93 D. Keitel,95 J. Kelley-Derzon,43 J. Kennington,7 R. Kesharwani,11 J. S. Key,236 R. Khadela,40, 41\nS. Khadka,15 F. Y. Khalili,102 F. Khan,40, 41 I. Khan,237, 35 T. Khanam,157 M. Khursheed,97 N. M. Khusid,180, 181\nW. Kiendrebeogo,47, 238 N. Kijbunchoo,108 C. Kim,239 J. C. Kim,240 K. Kim,241 M. H. Kim,242 S. Kim,221 Y.-M. Kim,241\nC. Kimball,77 M. Kinley-Hanlon,26 M. Kinnear,18 J. S. Kissel,3 S. Klimenko,43 A. M. Knee,138 N. Knust,40, 41\nK. Kobayashi,193 P. Koch,40, 41 S. M. Koehlenbeck,15 G. Koekoek,33, 32 K. Kohri,243, 244 K. Kokeyama,18 S. Koley,42\nP. Kolitsidou,111 M. Kolstein,39 K. Komori,37 A. K. H. Kong,140 A. Kontos,245 M. Korobko,82 R. V. Kossak,40, 41\nX. Kou,93 A. Koushik,19 N. Kouvatsos,69 M. Kovalam,27 D. B. Kozak,2 S. L. Kranzhoff,32, 33 V. Kringel,40, 41\n\n3\nN. V. Krishnendu,20 A. Kr\u00b4olak,246, 173 K. Kruska,40, 41 G. Kuehn,40, 41 P. Kuijer,33 S. Kulkarni,206\nA. Kulur Ramamohan,30 A. Kumar,226 Praveen Kumar,126 Prayush Kumar,20 Rahul Kumar,3 Rakesh Kumar,89\nJ. Kume,87, 88, 37 K. Kuns,31 N. Kuntimaddi,18 S. Kuroyanagi,115, 247 N. J. Kurth,9 S. Kuwahara,37 K. Kwak,232\nK. Kwan,30 J. Kwok,179 G. Lacaille,26 P. Lagabbe,28 D. Laghi,123 S. Lai,144 A. H. Laity,159 M. H. Lakkis,34\nE. Lalande,248 M. Lalleman,19 P. C. Lalremruati,249 M. Landry,3 B. B. Lane,31 R. N. Lang,31 J. Lange,146\nB. Lantz,15 A. La Rana,63 I. La Rosa,95 A. Lartaux-Vollard,36 P. D. Lasky,150 J. Lawrence,157 M. N. Lawrence,9\nM. Laxen,62 A. Lazzarini,2 C. Lazzaro,87, 88 P. Leaci,64, 63 Y. K. Lecoeuche,138 H. M. Lee,240 H. W. Lee,250\nK. Lee,242 R.-K. Lee,140 R. Lee,31 S. Lee,241 Y. Lee,141 I. N. Legred,2 J. Lehmann,40, 41 L. Lehner,169 M. Le Jean,165\nA. Lema\u02c6\u0131tre,251 M. Lenti,61, 252 M. Leonardi,104, 105, 21 M. Lequime,35 N. Leroy,36 M. Lesovsky,2 N. Letendre,28\nM. Lethuillier,114 S. E. Levin,202 Y. Levin,150 K. Leyde,68 A. K. Y. Li,2 K. L. Li,139 T. G. F. Li,209, 103 X. Li,147\nZ. Li,26 A. Lihos,118 C-Y. Lin,253 C.-Y. Lin,141 E. T. Lin,140 F. Lin,141 H. Lin,141 L. C.-C. Lin,139 Y.-C. Lin,140\nF. Linde,234, 33 S. D. Linker,197 T. B. Littenberg,254 A. Liu,209 G. C. Liu,219 Jian Liu,27 F. Llamas Villarreal,160\nJ. Llobera-Querol,95 R. K. L. Lo,137 J.-P. Locquet,103 L. T. London,69, 31, 98 A. Longo,60, 61 D. Lopez,113\nM. Lopez Portilla,74 M. Lorenzini,16, 17 A. Lorenzo-Medina,126 V. Loriette,36 M. Lormand,62 G. Losurdo,84\nT. P. Lott IV,57 J. D. Lough,40, 41 H. A. Loughlin,31 C. O. Lousto,196 M. J. Lowry,118 N. Lu,30 H. L\u00a8uck,41, 40, 41\nD. Lumaca,17 A. P. Lundgren,124 A. W. Lussier,248 L.-T. Ma,140 S. Ma,169 M. Ma\u2019arif,141 R. Macas,124\nA. Macedo,52 M. MacInnis,31 R. R. Maciy,40, 41 D. M. Macleod,18 I. A. O. MacMillan,2 A. Macquet,36 D. Macri,31\nK. Maeda,177 S. Maenaut,103 I. Maga\u02dcna Hernandez,8 S. S. Magare,11 C. Magazz`u,84 R. M. Magee,2 E. Maggio,1\nR. Maggiore,33, 101 M. Magnozzi,54, 55 M. Mahesh,82 S. Mahesh,255 M. Maini,159 S. Majhi,11 E. Majorana,64, 63\nC. N. Makarem,2 E. Makelele,72 J. A. Malaquias-Reis,14 U. Mali,178 S. Maliakal,2 A. Malik,97 N. Man,47\nV. Mandic,93 V. Mangano,63, 64 B. Mannix,75 G. L. Mansell,76, 31 G. Mansingh,211 M. Manske,8 M. Mantovani,56\nM. Mapelli,87, 88, 256 F. Marchesoni,50, 49, 257 D. Mar\u00b4\u0131n Pina,38, 78, 258 F. Marion,28 S. M\u00b4arka,158 Z. M\u00b4arka,158\nA. S. Markosyan,15 A. Markowitz,2 E. Maros,2 S. Marsat,123 F. Martelli,60, 61 I. W. Martin,26 R. M. Martin,182\nB. B. Martinez,129 M. Martinez,39, 259 V. Martinez,125 A. Martini,104, 105 K. Martinovic,69 J. C. Martins,14\nD. V. Martynov,111 E. J. Marx,31 L. Massaro,32, 33 A. Masserot,28 M. Masso-Reid,26 M. Mastrodicasa,63, 64\nS. Mastrogiovanni,63 T. Matcovich,49 M. Matiushechkina,40, 41 M. Matsuyama,194 N. Mavalvala,31 N. Maxwell,3\nG. McCarrol,62 R. McCarthy,3 D. E. McClelland,30 S. McCormick,62 L. McCuller,2 S. McEachin,118\nC. McElhenny,118 G. I. McGhee,26 J. McGinn,26 K. B. M. McGowan,143 J. McIver,138 A. McLeod,27 T. McRae,30\nD. Meacher,8 Q. Meijer,74 A. Melatos,130 S. Mellaerts,103 A. Menendez-Vazquez,39 C. S. Menoni,100 F. Mera,3\nR. A. Mercer,8 L. Mereni,165 K. Merfeld,157 E. L. Merilh,62 J. R. M\u00b4erou,95 J. D. Merritt,75 M. Merzougui,47\nC. Messenger,26 C. Messick,8 Z. Metzler,120, 128, 260 M. Meyer-Conde,194 F. Meylahn,40, 41 A. Mhaske,11\nA. Miani,104, 105 H. Miao,261 I. Michaloliakos,43 C. Michel,165 Y. Michimura,2, 37 H. Middleton,111 A. L. Miller,33\nS. Miller,2 M. Millhouse,57 E. Milotti,183, 45 V. Milotti,87 Y. Minenkov,17 N. Mio,37 Ll. M. Mir,39\nL. Mirasola,262, 63 M. Miravet-Ten\u00b4es,135 C.-A. Miritescu,39 A. K. Mishra,20 A. Mishra,11 C. Mishra,171\nT. Mishra,43 A. L. Mitchell,33, 101 J. G. Mitchell,66 S. Mitra,11 V. P. Mitrofanov,102 R. Mittleman,31\nO. Miyakawa,48 S. Miyamoto,193 S. Miyoki,48 G. Mo,31 L. Mobilia,60, 61 S. R. P. Mohapatra,2 S. R. Mohite,7\nM. Molina-Ruiz,214 C. Mondal,163 M. Mondin,197 M. Montani,60, 61 C. J. Moore,179 D. Moraru,3 A. More,11\nS. More,11 G. Moreno,3 C. Morgan,18 S. Morisaki,37, 193 Y. Moriwaki,177 G. Morras,115 A. Moscatello,87\nP. Mourier,95 B. Mours,65 C. M. Mow-Lowry,33, 101 F. Muciaccia,64, 63 Arunava Mukherjee,263 D. Mukherjee,254\nSamanwaya Mukherjee,11 Soma Mukherjee,160 Subroto Mukherjee,89 Suvodip Mukherjee,264, 169, 98 N. Mukund,31\nA. Mullavey,62 J. Munch,108 J. Mundi,211 C. L. Mungioli,27 W. R. Munn Oberg,265 Y. Murakami,193\nM. Murakoshi,224 P. G. Murray,26 S. Muusse,30 D. Nabari,104, 105 S. L. Nadji,40, 41 A. Nagar,23, 266 N. Nagarajan,26\nK. N. Nagler,66 K. Nakagaki,48 K. Nakamura,21 H. Nakano,267 M. Nakano,2 D. Nandi,9 V. Napolano,56\nP. Narayan,206 I. Nardecchia,17 T. Narikawa,193 H. Narola,74 L. Naticchioni,63 R. K. Nayak,249 J. Neilson,92, 107\nA. Nelson,129 T. J. N. Nelson,62 M. Nery,40, 41 A. Neunzert,3 S. Ng,52 L. Nguyen Quynh,268 S. A. Nichols,9\nA. B. Nielsen,269 G. Nieradka,91 A. Niko,141 Y. Nishino,21, 37 A. Nishizawa,270 S. Nissanke,98, 33 E. Nitoglia,114\nW. Niu,7 F. Nocera,56 M. Norman,18 C. North,18 J. Novak,109, 271, 272, 273 J. F. Nu\u02dcno Siles,115 L. K. Nuttall,124\nK. Obayashi,224 J. Oberling,3 J. O\u2019Dell,220 M. Oertel,109, 271, 272, 274, 273 A. Offermans,103 G. Oganesyan,42, 116\nJ. J. Oh,275 K. Oh,221 T. O\u2019Hanlon,62 M. Ohashi,48 M. Ohkawa,217 F. Ohme,40, 41 A. S. Oliveira,158\nR. Oliveri,109, 271, 272 B. O\u2019Neal,118 K. Oohara,276, 277 B. O\u2019Reilly,62 N. D. Ormsby,118 M. Orselli,49, 85\nR. O\u2019Shaughnessy,196 S. O\u2019Shea,26 Y. Oshima,37 S. Oshino,48 S. Ossokine,1 C. Osthelder,2 I. Ota,9\nD. J. Ottaway,108 A. Ouzriat,114 H. Overmier,62 B. J. Owen,157 A. E. Pace,7 R. Pagano,9 M. A. Page,21 A. Pai,200\nA. Pal,278 S. Pal,249 M. A. Palaia,84, 83 M. P\u00b4alfi,191 P. P. Palma,64, 16, 17 C. Palomba,63 P. Palud,68 H. Pan,140\nJ. Pan,27 K. C. Pan,140 R. Panai,262, 87 P. K. Panda,226 S. Pandey,7 L. Panebianco,60, 61 P. T. H. Pang,33, 74\nF. Pannarale,64, 63 K. A. Pannone,52 B. C. Pant,97 F. H. Panther,27 F. Paoletti,84 A. Paolone,63, 279\nE. E. Papalexakis,202 L. Papalini,84, 83 G. Papigkiotis,280 A. Paquis,36 A. Parisi,85, 49 B.-J. Park,241 J. Park,281\nW. Parker,62 G. Pascale,40, 41 D. Pascucci,90 A. Pasqualetti,56 R. Passaquieti,83, 84 L. Passenger,150\nD. Passuello,84 O. Patane,3 D. Pathak,11 M. Pathak,108 A. Patra,18 B. Patricelli,83, 84 A. S. Patron,9 K. Paul,171\nS. Paul,75 E. Payne,2 T. Pearce,18 M. Pedraza,2 R. Pegna,84 A. Pele,2 F. E. Pe\u02dcna Arellano,46 S. Penn,265\nM. D. Penuliar,52 A. Perego,104, 105 Z. Pereira,134 J. J. Perez,43 C. P\u00b4erigois,152, 88, 87 G. Perna,87 A. Perreca,104, 105\nJ. Perret,68 S. Perri`es,114 J. W. Perry,33, 101 D. Pesios,280 S. Petracca,168 C. Petrillo,85 H. P. Pfeiffer,1\nH. Pham,62 K. A. Pham,93 K. S. Phukon,111, 33, 234 H. Phurailatpam,209 M. Piarulli,123 L. Piccari,64, 63\n\n4\nO. J. Piccinni,39 M. Pichot,47 M. Piendibene,83, 84 F. Piergiovanni,60, 61 L. Pierini,63 G. Pierra,114 V. Pierro,92, 107\nM. Pietrzak,91 M. Pillas,47 F. Pilo,84 L. Pinard,165 I. M. Pinto,92, 107, 282, 29 M. Pinto,56 B. J. Piotrzkowski,8\nM. Pirello,3 M. D. Pitkin,179, 215 A. Placidi,61 E. Placidi,64, 63 M. L. Planas,95 W. Plastino,283, 17 R. Poggiani,83, 84\nE. Polini,28 L. Pompili,1 J. Poon,209 E. Porcelli,33 E. K. Porter,68 C. Posnansky,7 R. Poulton,56 J. Powell,153\nM. Pracchia,113 B. K. Pradhan,11 T. Pradier,65 A. K. Prajapati,89 K. Prasai,15 R. Prasanna,226 P. Prasia,11\nG. Pratten,111 G. Principe,183, 45 M. Principe,168, 92, 282, 107 G. A. Prodi,104, 105 L. Prokhorov,111 P. Prosposito,16, 17\nA. Puecher,33, 74 J. Pullin,9 M. Punturo,49 P. Puppo,63 M. P\u00a8urrer,159 H. Qi,12 J. Qin,30 G. Qu\u00b4em\u00b4ener,164, 109\nV. Quetschke,160 C. Quigley,18 P. J. Quinonez,66 F. J. Raab,3 S. S. Raabith,9 G. Raaijmakers,98, 33 S. Raja,97\nC. Rajan,97 B. Rajbhandari,196 K. E. Ramirez,62 F. A. Ramis Vidal,95 A. Ramos-Buades,33 D. Rana,11 S. Ranjan,57\nK. Ransom,62 P. Rapagnani,64, 63 B. Ratto,66 S. Rawat,93 A. Ray,8 V. Raymond,18 M. Razzano,83, 84 J. Read,52\nM. Recaman Payo,103 T. Regimbau,28 L. Rei,54 S. Reid,94 D. H. Reitze,2 P. Relton,18 A. I. Renzini,2\nP. Rettegno,23 B. Revenu,284, 68 R. Reyes,197 A. S. Rezaei,63, 64 F. Ricci,64, 63 M. Ricci,63, 64 A. Ricciardone,83, 84\nJ. W. Richardson,202 M. Richardson,108 A. Rijal,66 K. Riles,86 H. K. Riley,18 S. Rinaldi,256, 87 J. Rittmeyer,82\nC. Robertson,220 F. Robinet,36 M. Robinson,3 A. Rocchi,17 L. Rolland,28 J. G. Rollins,2 A. E. Romano,285\nR. Romano,4, 5 A. Romero,175 I. M. Romero-Shaw,179 J. H. Romie,62 S. Ronchini,42, 116 T. J. Roocke,108 L. Rosa,5, 29\nT. J. Rosauer,202 C. A. Rose,8 D. Rosi\u00b4nska,119 M. P. Ross,51 M. Rossello,95 S. Rowan,26 S. K. Roy,180, 181 S. Roy,74\nD. Rozza,121, 122 P. Ruggi,56 N. Ruhama,232 E. Ruiz Morales,286, 115 K. Ruiz-Rocha,143 S. Sachdev,57 T. Sadecki,3\nJ. Sadiq,126 P. Saffarieh,33, 101 M. R. Sah,264 S. S. Saha,140 S. Saha,140 T. Sainrat,65 S. Sajith Menon,205, 64, 63\nK. Sakai,287 M. Sakellariadou,69 S. Sakon,7 O. S. Salafia,154, 122, 121 F. Salces-Carcoba,2 L. Salconi,56\nM. Saleem,93 F. Salemi,64, 63 M. Sall\u00b4e,33 S. Salvador,164, 163, 109 A. Sanchez,3 E. J. Sanchez,2 J. H. Sanchez,77\nL. E. Sanchez,2 N. Sanchis-Gual,135 J. R. Sanders,210 E. M. S\u00a8anger,1 F. Santoliquido,42 T. R. Saravanan,11\nN. Sarin,150 S. Sasaoka,172 A. Sasli,280 P. Sassi,49, 85 B. Sassolas,165 H. Satari,27 R. Sato,217 Y. Sato,177\nO. Sauter,43 R. L. Savage,3 T. Sawada,48 H. L. Sawant,11 S. Sayah,28 V. Scacco,16, 17 D. Schaetzl,2 M. Scheel,147\nA. Schiebelbein,178 M. G. Schiworski,108 P. Schmidt,111 S. Schmidt,74 R. Schnabel,82 M. Schneewind,40, 41\nR. M. S. Schofield,75 K. Schouteden,103 B. W. Schulte,40, 41 B. F. Schutz,18, 40, 41 E. Schwartz,18 M. Scialpi,288\nJ. Scott,26 S. M. Scott,30 T. C. Seetharamu,26 M. Seglar-Arroyo,39 Y. Sekiguchi,289 D. Sellers,62\nA. S. Sengupta,290 D. Sentenac,56 E. G. Seo,26 J. W. Seo,103 V. Sequino,29, 5 M. Serra,63 G. Servignat,271\nA. Sevrin,175 T. Shaffer,3 U. S. Shah,57 M. A. Shaikh,240 L. Shao,223 A. K. Sharma,20 P. Sharma,97\nS. Sharma-Chaudhary,99 M. R. Shaw,18 P. Shawhan,120 N. S. Shcheblanov,291, 251 E. Sheridan,143 Y. Shikano,292, 293\nM. Shikauchi,37 K. Shimode,48 H. Shinkai,294 J. Shiota,224 D. H. Shoemaker,31 D. M. Shoemaker,146 R. W. Short,3\nS. ShyamSundar,97 A. Sider,34 H. Siegel,180, 181 M. Sieniawska,10 D. Sigg,3 L. Silenzi,49, 50 M. Simmonds,108\nL. P. Singer,128 A. Singh,206 D. Singh,7 M. K. Singh,20 S. Singh,21, 59 A. Singha,32, 33 A. M. Sintes,95 V. Sipala,162, 131\nV. Skliris,18 B. J. J. Slagmolen,30 T. J. Slaven-Blair,27 J. Smetana,111 J. R. Smith,52 L. Smith,26 R. J. E. Smith,150\nW. J. Smith,143 J. Soldateschi,252, 295, 61 K. Somiya,172 I. Song,140 K. Soni,11 S. Soni,31 V. Sordini,114 F. Sorrentino,54\nN. Sorrentino,83, 84 H. Sotani,296 R. Soulard,47 A. Southgate,18 V. Spagnuolo,32, 33 A. P. Spencer,26\nM. Spera,45, 297 P. Spinicelli,56 J. B. Spoon,9 C. A. Sprague,268 A. K. Srivastava,89 F. Stachurski,26 D. A. Steer,68\nJ. Steinlechner,32, 33 S. Steinlechner,32, 33 N. Stergioulas,280 P. Stevens,36 M. StPierre,159 G. Stratta,298, 133, 63, 299\nM. D. Strong,9 A. Strunk,3 R. Sturani,300 A. L. Stuver,53, \u2217M. Suchenek,91 S. Sudhagar,91 N. Sueltmann,82\nL. Suleiman,52 K. D. Sullivan,9 L. Sun,30 S. Sunil,89 J. Suresh,10 P. J. Sutton,18 T. Suzuki,217 Y. Suzuki,224\nB. L. Swinkels,33 A. Syx,65 M. J. Szczepa\u00b4nczyk,301, 43 P. Szewczyk,119 M. Tacca,33 H. Tagoshi,193 S. C. Tait,2\nH. Takahashi,302 R. Takahashi,21 A. Takamori,37 T. Takase,48 K. Takatani,194 H. Takeda,303 K. Takeshita,172\nC. Talbot,127 M. Tamaki,193 N. Tamanini,123 D. Tanabe,141 K. Tanaka,48 S. J. Tanaka,224 T. Tanaka,303 D. Tang,27\nS. Tanioka,76 D. B. Tanner,43 L. Tao,43 R. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n,33 R. Tarafder,2 C. Taranto,16, 17, 64\nA. Taruya,304 J. D. Tasson,176 M. Teloi,34 R. Tenorio,95 H. Themann,197 A. Theodoropoulos,135\nM. P. Thirugnanasambandam,11 L. M. Thomas,2 M. Thomas,62 P. Thomas,3 J. E. Thompson,147 S. R. Thondapu,97\nK. A. Thorne,62 E. Thrane,150 J. Tissino,42 A. Tiwari,11 P. Tiwari,42 S. Tiwari,198 V. Tiwari,111 M. R. Todd,76\nA. M. Toivonen,93 K. Toland,26 A. E. Tolley,124 T. Tomaru,21 K. Tomita,194 T. Tomura,48 C. Tong-Yu,141\nA. Toriyama,224 N. Toropov,111 A. Torres-Forn\u00b4e,135, 136 C. I. Torrie,2 M. Toscani,123 I. Tosta e Melo,305\nE. Tournefier,28 A. Trapananti,50, 49 F. Travasso,50, 49 G. Traylor,62 M. Trevor,120 M. C. Tringali,56\nA. Tripathee,86 G. Troian,183 L. Troiano,306, 107 A. Trovato,183, 45 L. Trozzo,5 R. J. Trudeau,2 T. T. L. Tsang,18\nR. Tso,147, \u2020 S. Tsuchida,307 L. Tsukada,7 T. Tsutsui,37 K. Turbang,175, 19 M. Turconi,47 C. Turski,90 H. Ubach,38, 78\nT. Uchiyama,48 R. P. Udall,2 T. Uehara,308 M. Uematsu,194 K. Ueno,37 S. Ueno,224 V. Undheim,269 T. Ushiba,48\nM. Vacatello,84, 83 H. Vahlbruch,40, 41 N. Vaidya,2 G. Vajente,2 A. Vajpeyi,150 G. Valdes,129 J. Valencia,95\nM. Valentini,101, 33 S. A. Vallejo-Pe\u02dcna,285 S. Vallero,23 V. Valsan,8 N. van Bakel,33 M. van Beuzekom,33\nM. van Dael,33, 309 J. F. J. van den Brand,32, 101, 33 C. Van Den Broeck,74, 33 D. C. Vander-Hyde,76\nM. van der Sluys,33, 74 A. Van de Walle,36 J. van Dongen,33, 101 K. Vandra,53 H. van Haevermaet,19\nJ. V. van Heijningen,33, 101 P. Van Hove,65 M. VanKeuren,72 J. Vanosky,2 M. H. P. M. van Putten,13\nZ. van Ranst,32, 33 N. van Remortel,19 M. Vardaro,32, 33 A. F. Vargas,130 J. J. Varghese,66 V. Varma,134\nM. Vas\u00b4uth,80, \u2021 A. Vecchio,111 G. Vedovato,88 J. Veitch,26 P. J. Veitch,108 S. Venikoudis,10 J. Venneberg,40, 41\nP. Verdier,114 D. Verkindt,28 B. Verma,134 P. Verma,173 Y. Verma,97 S. M. Vermeulen,2 F. Vetrano,60\nA. Veutro,63, 64 A. M. Vibhute,3 A. Vicer\u00b4e,60, 61 S. Vidyant,76 A. D. Viets,81 A. Vijaykumar,178 A. Vilkha,196\nV. Villa-Ortega,126 E. T. Vincent,57 J.-Y. Vinet,47 S. Viret,114 A. Virtuoso,183, 45 S. Vitale,31 A. Vives,75\n\n5\nH. Vocca,85, 49 D. Voigt,82 E. R. G. von Reis,3 J. S. A. von Wrangel,40, 41 S. P. Vyatchanin,102 L. E. Wade,72\nM. Wade,72 K. J. Wagner,196 A. Wajid,54, 55 M. Walker,118 G. S. Wallace,94 L. Wallace,2 H. Wang,37 J. Z. Wang,86\nW. H. Wang,160 Z. Wang,141 G. Waratkar,200 J. Warner,3 M. Was,28 T. Washimi,21 N. Y. Washington,2\nD. Watarai,37 K. E. Wayt,72 B. R. Weaver,18 B. Weaver,3 C. R. Weaving,124 S. A. Webster,26 M. Weinert,40, 41\nA. J. Weinstein,2 R. Weiss,31 F. Wellmann,40, 41 L. Wen,27 P. We\u00dfels,40, 41 K. Wette,30 J. T. Whelan,196\nB. F. Whiting,43 C. Whittle,2 J. B. Wildberger,1 O. S. Wilk,72 D. Wilken,40, 41, 41 A. T. Wilkin,202\nD. J. Willadsen,81 K. Willetts,18 D. Williams,26 M. J. Williams,124 N. S. Williams,111 J. L. Willis,2\nB. Willke,41, 40, 41 M. Wils,103 J. Winterflood,27 C. C. Wipf,2 G. Woan,26 J. Woehler,32, 33 J. K. Wofford,196\nN. E. Wolfe,31 H. T. Wong,141 H. W. Y. Wong,209 I. C. F. Wong,209 J. L. Wright,30 M. Wright,26 C. Wu,140\nD. S. Wu,40, 41 H. Wu,140 E. Wuchner,52 D. M. Wysocki,8 V. A. Xu,31 Y. Xu,198 N. Yadav,91 H. Yamamoto,2\nK. Yamamoto,177 T. S. Yamamoto,247 T. Yamamoto,48 S. Yamamura,193 R. Yamazaki,224 S. Yan,15 T. Yan,111\nF. W. Yang,190 F. Yang,158 K. Z. Yang,93 Y. Yang,144 Z. Yarbrough,9 H. Yasui,48 S.-W. Yeh,140 A. B. Yelikar,196\nX. Yin,31 J. Yokoyama,310, 37 T. Yokozawa,48 J. Yoo,148 H. Yu,147 S. Yuan,27 H. Yuzurihara,48 A. Zadro\u02d9zny,173\nM. Zanolin,66 M. Zeeshan,196 T. Zelenova,56 J.-P. Zendri,88 M. Zeoli,113, 10 M. Zerrad,35 M. Zevin,77\nA. C. Zhang,158 L. Zhang,2 R. Zhang,43 T. Zhang,111 Y. Zhang,30 C. Zhao,27 Yue Zhao,190 Yuhang Zhao,68\nY. Zheng,99 H. Zhong,93 R. Zhou,214 X.-J. Zhu,311 Z.-H. Zhu,311, 201 A. B. Zimmerman,146 M. E. Zucker,31, 2\nJ. Zweizig,2 S.B. Araujo Furlan,312 Z. Arzoumanian,313 A. Basu,314 A. Cassity,315 I. Cognard,316, 317\nK. Crowter,315 S. del Palacio,312, 318 C. M. Espinoza,319, 320 E. Fonseca,321, 322 C. M. L. Flynn,153 G. Gancio,312\nF. Garc\u00b4\u0131a,312, 323 K. C. Gendreau,313 D. C. Good,324, 325 L. Guillemot,316, 317 S. Guillot,326, 327 M. J. Keith,314\nL. Kuiper,328 M. E. Lower,329, 153 A. G. Lyne,314 J. W. McKee,330 B. W. Meyers,315, 331 J. L. Palfreyman,332\nA. B. Pearlman,333, 334, \u00a7 G. E. Romero,312, 323 R. M. Shannon,153 B. Shaw,314 I. H. Stairs,315 B. W. Stappers,314\nC. M. Tan,333, 334, 331 G. Theureau,316, 317, 335 M. Thompson,315 P. Weltevrede,314 and E. Zubieta312, 323\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3LIGO Hanford Observatory, Richland, WA 99352, USA\n4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n5INFN, Sezione di Napoli, I-80126 Napoli, Italy\n6University of Warwick, Coventry CV4 7AL, United Kingdom\n7The Pennsylvania State University, University Park, PA 16802, USA\n8University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n9Louisiana State University, Baton Rouge, LA 70803, USA\n10Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n11Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n12Queen Mary University of London, London E1 4NS, United Kingdom\n13Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n14Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n15Stanford University, Stanford, CA 94305, USA\n16Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n17INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n18Cardiff University, Cardiff CF24 3AA, United Kingdom\n19Universiteit Antwerpen, 2000 Antwerpen, Belgium\n20International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n21Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n22Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n23INFN Sezione di Torino, I-10125 Torino, Italy\n24Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n25Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n26SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n27OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n28Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n29Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n30OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n31LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n32Maastricht University, 6200 MD Maastricht, Netherlands\n33Nikhef, 1098 XG Amsterdam, Netherlands\n34Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n35Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n36Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n\n6\n37University of Tokyo, Tokyo, 113-0033, Japan.\n38Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n39Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n40Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n41Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n42Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n43University of Florida, Gainesville, FL 32611, USA\n44Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n45INFN, Sezione di Trieste, I-34127 Trieste, Italy\n46Tecnol\u00b4ogico de Monterrey Campus Guadalajara, 45201 Zapopan, Jalisco, Mexico\n47Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n48Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n49INFN, Sezione di Perugia, I-06123 Perugia, Italy\n50Universit`a di Camerino, I-62032 Camerino, Italy\n51University of Washington, Seattle, WA 98195, USA\n52California State University Fullerton, Fullerton, CA 92831, USA\n53Villanova University, Villanova, PA 19085, USA\n54INFN, Sezione di Genova, I-16146 Genova, Italy\n55Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n56European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62LIGO Livingston Observatory, Livingston, LA 70754, USA\n63INFN, Sezione di Roma, I-00185 Roma, Italy\n64Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n65Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n66Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n67Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n68Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n69King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n70Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n71Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n72Kenyon College, Gambier, OH 43022, USA\n73International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n74Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n75University of Oregon, Eugene, OR 97403, USA\n76Syracuse University, Syracuse, NY 13244, USA\n77Northwestern University, Evanston, IL 60208, USA\n78Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n79Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n80HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n81Concordia University Wisconsin, Mequon, WI 53097, USA\n82Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n83Universit`a di Pisa, I-56127 Pisa, Italy\n84INFN, Sezione di Pisa, I-56127 Pisa, Italy\n85Universit`a di Perugia, I-06123 Perugia, Italy\n86University of Michigan, Ann Arbor, MI 48109, USA\n87Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n88INFN, Sezione di Padova, I-35131 Padova, Italy\n89Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n90Universiteit Gent, B-9000 Gent, Belgium\n\n7\n91Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n92Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n93University of Minnesota, Minneapolis, MN 55455, USA\n94SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n95IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n96Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n97RRCAT, Indore, Madhya Pradesh 452013, India\n98GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n99Missouri University of Science and Technology, Rolla, MO 65409, USA\n100Colorado State University, Fort Collins, CO 80523, USA\n101Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n102Lomonosov Moscow State University, Moscow 119991, Russia\n103Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n104Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n105INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n106Bar-Ilan University, Ramat Gan, 5290002, Israel\n107INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n108OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n109Centre national de la recherche scientifique, 75016 Paris, France\n110Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n111University of Birmingham, Birmingham B15 2TT, United Kingdom\n112Washington State University, Pullman, WA 99164, USA\n113Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n114Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n115Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n116INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n117Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n118Christopher Newport University, Newport News, VA 23606, USA\n119Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n120University of Maryland, College Park, MD 20742, USA\n121Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n122INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n123L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n124University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n125Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n126IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n127University of Chicago, Chicago, IL 60637, USA\n128NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n129Texas A&M University, College Station, TX 77843, USA\n130OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n131INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n132Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n133Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n136Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n137Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n138University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n139Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n140National Tsing Hua University, Hsinchu City 30013, Taiwan\n141National Central University, Taoyuan City 320317, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n145Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n146University of Texas, Austin, TX 78712, USA\n\n8\n147CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n148Cornell University, Ithaca, NY 14850, USA\n149Northeastern University, Boston, MA 02115, USA\n150OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n151Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n153OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n154INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n155Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n156Montana State University, Bozeman, MT 59717, USA\n157Texas Tech University, Lubbock, TX 79409, USA\n158Columbia University, New York, NY 10027, USA\n159University of Rhode Island, Kingston, RI 02881, USA\n160The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n161Chennai Mathematical Institute, Chennai 603103, India\n162Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n163Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n164Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n165Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n166Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n167INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n168University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n169Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n170Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n171Indian Institute of Technology Madras, Chennai 600036, India\n172Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n173National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n174Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n175Vrije Universiteit Brussel, 1050 Brussel, Belgium\n176Carleton College, Northfield, MN 55057, USA\n177Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n178Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n179University of Cambridge, Cambridge CB2 1TN, United Kingdom\n180Stony Brook University, Stony Brook, NY 11794, USA\n181Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n182Montclair State University, Montclair, NJ 07043, USA\n183Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n184HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n185Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n186CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n187Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n188Western Washington University, Bellingham, WA 98225, USA\n189SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n190The University of Utah, Salt Lake City, UT 84112, USA\n191E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n192Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n193Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n194Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n195Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n196Rochester Institute of Technology, Rochester, NY 14623, USA\n197California State University, Los Angeles, Los Angeles, CA 90032, USA\n198University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n199University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n200Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n\n9\n201School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n202University of California, Riverside, Riverside, CA 92521, USA\n203INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n204University of Nottingham NG7 2RD, UK\n205Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n206The University of Mississippi, University, MS 38677, USA\n207Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n208Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n209The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n210Marquette University, Milwaukee, WI 53233, USA\n211American University, Washington, DC 20016, USA\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n214University of California, Berkeley, CA 94720, USA\n215University of Lancaster, Lancaster LA1 4YW, United Kingdom\n216College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n217Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n218Department of Physics and Astronomy, Haverford College, 370 Lancaster Avenue, Haverford, PA 19041, USA\n219Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n220Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n221Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n222Scuola Normale Superiore, I-56126 Pisa, Italy\n223Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n224Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n225Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n226Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n227University of Bia lystok, 15-424 Bia lystok, Poland\n228National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n229School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n230Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n231University of Southampton, Southampton SO17 1BJ, United Kingdom\n232Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n233Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n234Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n235Chung-Ang University, Seoul 06974, Republic of Korea\n236University of Washington Bothell, Bothell, WA 98011, USA\n237Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n238Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n239Ewha Womans University, Seoul 03760, Republic of Korea\n240Seoul National University, Seoul 08826, Republic of Korea\n241Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n242Sungkyunkwan University, Seoul 03063, Republic of Korea\n243Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n244Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n245Bard College, Annandale-On-Hudson, NY 12504, USA\n246Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n247Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n248Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n249Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n250Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n251NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n252Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n\n10\n253National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n254NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n255West Virginia University, Morgantown, WV 26506, USA\n256Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n257School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n258Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n259Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n260Center for Research and Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD 20771\n261Tsinghua University, Beijing 100084, China\n262INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n263Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n264Tata Institute of Fundamental Research, Mumbai 400005, India\n265Hobart and William Smith Colleges, Geneva, NY 14456, USA\n266Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n267Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n268Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n269University of Stavanger, 4021 Stavanger, Norway\n270Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 903-0213, Japan\n271Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n272Observatoire de Paris, 75014 Paris, France\n273Universit\u00b4e PSL, 75006 Paris, France\n274Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n275National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n276Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n277Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n278CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n279Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n280Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n281Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n282Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n283Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n284Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n285Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n286Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n287Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n288Universit`a Degli Studi Di Ferrara, Via Savonarola, 9, 44121 Ferrara FE, Italy\n289Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n290Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n291Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n292Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n293Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n294Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n295INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n296iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n297Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n298Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n299INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n300Universidade Estadual Paulista, 01140-070 S\u02dcao Paulo, Brazil\n301Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n302Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n\n11\n303Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n304Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n305University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n306Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n307National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n308Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n309Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n310Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City,\nChiba 277-8583, Japan\n311Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n312Instituto Argentino de Radioastronom\u00b4\u0131a (CCT La Plata, CONICET; CICPBA; UNLP), C.C.5, (1894) Villa Elisa, Buenos Aires,\nArgentina\n313X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n314Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester, UK, M13 9PL\n315Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1 Canada\n316LPC2E, OSUC, Univ Orleans, CNRS, CNES, Observatoire de Paris, F-45071 Orleans, France\n317Observatoire Radioastronomique de Nan\u00b8cay, Observatoire de Paris, Universit\u00b4e PSL, Universit\u00b4e d\u2019Orl\u00b4eans, CNRS, 18330 Nan\u00b8cay,\nFrance\n318Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden\n319Departamento de F\u00b4\u0131sica, Universidad de Santiago de Chile (USACH), Av. V\u00b4\u0131ctor Jara 3493, Estaci\u00b4on Central, Chile\n320Center for Interdisciplinary Research in Astrophysics and Space Sciences (CIRAS), Universidad de Santiago de Chile, Chile\n321Department of Physics and Astronomy, West Virginia University, PO Box 6315, Morgantown, WV 26506, USA\n322Center for Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge Research Building, Morgantown, WV, USA\n323Facultad de Ciencias Astron\u00b4omicas y Geof\u00b4\u0131sicas, Universidad Nacional de La Plata, Paseo del Bosque, B1900FWA La Plata, Argentina\n324Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, New York, 10010, USA\n325Department of Physics, University of Connecticut, 196 Auditorium Road, U-3046, Storrs, CT 06269-3046, USA\n326IRAP, CNRS, 9 avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France\n327Universit\u00b4e de Toulouse, CNES, UPS-OMP, F-31028 Toulouse, France\n328SRON-Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA, Leiden, Netherlands\n329CSIRO, Space and Astronomy, PO Box 76, Epping, NSW 1710, Australia\n330Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada\n331International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia\n332School of Natural Sciences, University of Tasmania, Hobart, Australia\n333Department of Physics, McGill University, 3600 rue University, Montr\u00b4eal, QC H3A 2T8, Canada\n334McGill Space Institute, McGill University, 3550 rue University, Montr\u00b4eal, QC H3A 2A7, Canada\n335LUTH, Observatoire de Paris, PSL Research University, CNRS, Universit\u00b4e Paris Diderot, Sorbonne Paris Cit\u00b4e, F-92195 Meudon,\nFrance\nABSTRACT\nContinuous gravitational waves (CWs) emission from neutron stars carries information about their\ninternal structure and equation of state, and it can provide tests of General Relativity. We present a\nsearch for CWs from a set of 45 known pulsars in the first part of the fourth LIGO\u2013Virgo\u2013KAGRA\nobserving run, known as O4a. We conducted a targeted search for each pulsar using three independent\nanalysis methods considering the single-harmonic and the dual-harmonic emission models. We find no\nevidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude\nand on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the\nsingle-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical\nspin-down limit. The lowest upper limit on the amplitude is 6.4\u00d710\u221227 for the young energetic pulsar\nJ0537\u22126910, while the lowest constraint on the ellipticity is 8.8\u00d710\u22129 for the bright nearby millisecond\npulsar J0437\u22124715. Additionally, for a subset of 16 targets we performed a narrowband search that is\nmore robust regarding the emission model, with no evidence of a signal. We also found no evidence of\nnon-standard polarizations as predicted by the Brans-Dicke theory.\n\n12\n1. INTRODUCTION\nSince their discovery in 1967, pulsars have been cru-\ncial in advancing our understanding of fundamental\nphysics.\nThese extremely dense and compact objects\npossess strong magnetic fields and rotate rapidly, emit-\nting beams of electromagnetic (EM) radiation from hot\nspots near the poles or from the higher magnetosphere\n(Philippov & Kramer 2022).\nEM observations across\nvarious wavelengths (radio, X-rays, and gamma rays)\nhave provided detailed insights into pulsar properties,\nallowing precise measurements of pulsar parameters.\nGiven their stability and predictability, pulsars present\nan excellent opportunity for the search of continuous\ngravitational waves (CWs) in the LIGO\u2013Virgo\u2013KAGRA\n(LVK) data.\nIn contrast to transient gravitational waves (GWs)\nemitted by binary black hole (and neutron star) mergers\n(Abbott et al. 2021a,b, 2023), CWs have yet to be ob-\nserved. These signals should be nearly monochromatic,\nwith amplitude and frequency exhibiting small varia-\ntions over year-long timescales.\nCWs\nare\nexpected\nfrom\na\ntime-varying\nnon-\naxisymmetric mass distribution in rotating neutron stars\n(Zimmermann & Szedenits 1979).\nThis could be the\nresult of strain in the elastic crust (Ushomirsky et al.\n2000), accretion from a companion star (Bildsten 1998;\nMelatos & Payne 2005; Gittins & Andersson 2021), or\na strong inner magnetic field (Bonazzola & Gourgoul-\nhon 1996; Cutler 2002). Alternatively, the deformation\ncould be caused by fluid oscillations, such as those due to\nr-modes (Andersson 1998; Friedman & Morsink 1998).\nHowever, the sources of CWs are likely to possess smaller\nmass quadrupoles compared to the sources of transient\nGWs, resulting in a weaker signal. Therefore, for signals\nto be detectable with current detectors, we need to con-\nsider nearby sources integrating long stretches (months\nor years worth) of detector data.\nObservation of CWs from a neutron star would yield\ncrucial insights into the star\u2019s structure and its equation\nof state (Haskell & Bejger 2023; Gittins 2024). More-\nover, the form of the signal can be employed to test gen-\neral relativity by measuring (or constraining) the pres-\nence of non-standard polarizations (Isi et al. 2017; Ab-\nbott et al. 2019a). Possible mechanisms of CW emission\n\u2217Deceased, September 2024.\n\u2020 Deceased, July 2023.\n\u2021 Deceased, February 2024.\n\u00a7 Banting Fellow, McGill Space Institute (MSI) Fellow,\nand FRQNT Postdoctoral Fellow.\nfrom neutron stars are discussed in greater detail by\nRiles (2023) and Glampedakis & Gualtieri (2018).\nThe primary challenge for CW searches lies in accu-\nrately accounting for the various modulations that af-\nfect the signal received on the Earth. These include the\nDoppler effect due to the Earth\u2019s motion, the pulsar\u2019s\nrotational evolution (i.e., the slow spin-down) and rela-\ntivistic effects. EM observations provide accurate mea-\nsurements of the sky position and rotation parameters\nthat allow us to predict and correct these modulations,\nthereby enhancing the search sensitivity.\nBased on the knowledge of the source parameters,\ndifferent strategies can be used to search for CW sig-\nnals in LVK data (see Wette 2023, for a complete re-\nview of search methods). Targeted searches, the primary\nsubject of this paper, aim to detect CWs from known\npulsars, whose timing solutions can be calculated from\nknown rotation phases and spin-down rates. Targeted\nsearches use full-coherent methods that integrate data\nover long observation times maintaining phase coherence\nover time. By assuming that the GW phase evolution\nfollows the EM solution, the parameter space can be re-\nduced to the unknown signal amplitude and polarization\nparameters. This assumption is relaxed in narrowband\nsearches, which are performed in a narrow band around\nthe frequency and spin-down rate (e.g., Abbott et al.\n2017a, 2019b; Abbott et al. 2022).\nHowever, because\nthese searches decrease the sensitivity and increase the\ncomputational cost, they are often performed on fewer\ntargets.\nAlthough several CW searches have been conducted in\nthe last years targeting both isolated pulsars and those\nin binary systems, so far none of these searches have pro-\nduced evidence of CWs (e.g., Abbott et al. 2017b, 2019c,\n2020, 2021c, 2022; Ashok et al. 2021; Nieder et al. 2019,\n2020). In the absence of a signal, these searches set up-\nper limits on the GW amplitude and on the ellipticity,\nthe physical parameter that quantifies the asymmetry\nin the mass distribution.\nIn many cases, these limits\nare more stringent than (it is said to have \u201csurpassed\u201d)\nthe so-called spin-down limit; the theoretical limit calcu-\nlated by assuming 100% of each pulsar\u2019s spin-down lumi-\nnosity to be radiated through GWs. In the most recent\ntargeted search (Abbott et al. 2021c, 2022) considering\nO3 data, 24 pulsars surpassed their spin-down limits, in-\ncluding the Crab and Vela pulsars, J0537\u22126910 and two\nmillisecond pulsars, J0437\u22124715 and J0711\u22126830. Ad-\nditionally, searches for an r-mode emission are described\nin Rajbhandari et al. (2021) for the Crab and in Fesik\n& Papa (2020); Rajbhandari et al. (2021); Abbott et al.\n(2021d) for J0537\u22126910. Continuous improvements in\n\n13\ndetector sensitivity and data analysis techniques are pro-\ngressively enhancing our ability to detect these faint sig-\nnals.\nIn this paper, we present a targeted search for CWs\nfrom a set of 45 known pulsars, considering LIGO data\nfrom the initial part, O4a, of the most recent LVK ob-\nserving run. Pulsar selection is based on the available\nEM observations (see Section 4.2) and on the anticipated\nsensitivity for targeted searches near or below the spin-\ndown limit. Considering two different emission models,\nwe find no evidence of CW signals in the data, and we\nset upper limits on the amplitude and on the ellipticity\nfor each target. Additionally, we perform a narrowband\nsearch for a subset of 16 targets and a search for non-\nstandard polarizations as predicted by the Brans-Dicke\ntheory (Brans & Dicke 1961).\nThe paper is structured as follows.\nIn Section 2,\nwe briefly describe the expected signal for the emission\nmodels that we considered. The data analysis methods\nused in the paper are discussed in Section 3, while in\nSection 4 we describe the EM and GW data used for\nthe analysis. The results are summarized and discussed\nin detail in Sections 5 and 6. Conclusions are reported\nin Section 7.\n2. SIGNAL MODEL\n2.1. Standard signal\nFor the targeted search, we assume that the GW signal\nis locked to the rotational phase of the pulsar obtained\nthrough EM observations. For an isolated triaxial star,\nrotating steadily about one of its principal axes of in-\nertia, the GW emission frequency is twice the pulsar\u2019s\nspin frequency, frot. For the single-harmonic emission\nmodel, we search for signals at 2frot. However, there are\nadditional mechanisms which could emit GWs at other\nfrequencies. A superfluid component beneath the crust,\nrotating with a spin axis misaligned to the star\u2019s rotation\naxis would produce an additional emission at the rota-\ntion frequency, so that overall we have a dual-harmonic\nemission at both once and twice the rotation frequency\n(Jones 2010). This would not impact the EM signature.\nTherefore, a dual-harmonic search is performed at both\nfrot and 2frot. Additionally, a single-harmonic narrow-\nband search is performed around 2frot, allowing for the\npossibility of a difference in rotation rate between the\npulsation-producing magnetosphere and the part of the\nstar responsible for the CW emission.\nFor the general dual-harmonic emission model, the sig-\nnals h21 and h22 at frot and 2frot can be defined as\n(Pitkin et al. 2015):\nh21 = \u2212C21\n2\nh\nF D\n+ (\u03b1, \u03b4, \u03c8; t) sin \u03b9 cos \u03b9 cos\n\u0000\u03a6(t) + \u03a6C\n21\n\u0001\n+\nF D\n\u00d7 (\u03b1, \u03b4, \u03c8; t) sin \u03b9 sin\n\u0000\u03a6(t) + \u03a6C\n21\n\u0001i\n,\n(1)\nh22 = \u2212C22\nh\nF D\n+ (\u03b1, \u03b4, \u03c8; t)(1 + cos2 \u03b9) cos\n\u00002\u03a6(t) + \u03a6C\n22\n\u0001\n+\n2F D\n\u00d7 (\u03b1, \u03b4, \u03c8; t) cos \u03b9 sin\n\u00002\u03a6(t) + \u03a6C\n22\n\u0001i\n,\n(2)\nwhere C21 and C22 are the dimensionless constants that\ngive the component amplitudes, the angles (\u03b1, \u03b4) are the\nright ascension and declination of the source, the angles\n(\u03b9, \u03c8) describe the orientation of the source\u2019s spin axis\nwith respect to the observer in terms of inclination and\npolarization, \u03a6C\n21 and \u03a6C\n22 are phase angles at a defined\nepoch and \u03a6(t) is the rotational phase of the source.\nThe antenna functions F D\n+ and F D\n\u00d7 describe how the two\npolarization components (plus and cross) are projected\nonto the detector. These waveforms are detailed in Jones\n(2010) and used in Abbott et al. (2022).\nFor the triaxial star described earlier, which only emits\nGWs at 2frot, C21 in Equation (1) is 0, which leaves\nonly Equation (2) which contains C22. The amplitude\nh0 is defined as the amplitude of the circularly polarized\nsignal observable for a source directly above or below the\nplane of the detector with its spin axis pointed directly\ntoward or away from the detector. It can be calculated\nas:\nh0 = 2C22 = 16\u03c02G\nc4\nIzz\u03b5f 2\nrot\nd\n,\n(3)\nwhere d is the distance of the source. The equatorial\nellipticity \u03b5 for the triaxial star emitting GWs at only\n2frot is defined as\n\u03b5 \u2261|Ixx \u2212Iyy|\nIzz\n,\n(4)\nwhere Ixx, Iyy and Izz are the source\u2019s principle mo-\nments of inertia, with the star rotating about the z-axis.\nFrom the ellipticity, the pulsar\u2019s mass quadrupole, Q22\ncan be calculated using (Owen 2005)\nQ22 = Izz\u03b5\nr\n15\n8\u03c0 .\n(5)\nThe spin-down limit hsd\n0 of a source is given by:\nhsd\n0 = 1\nd\n \n5GIzz\n2c3\n| \u02d9frot|\nfrot\n!1/2\n(6)\nwhere \u02d9frot is the rotation frequency derivative, or spin-\ndown rate. This limit is the maximum GW amplitude\nallowed assuming all the lost rotational energy of the\n\n14\nstar is due to conversion into GW energy. It should be\nnoted that there are two types of spin-down rates: ob-\nserved, which can be affected by the transverse velocity\nof the source (e.g.\nthe Shklovskii effect, described in\nShklovskii (1970)), and intrinsic. Therefore, where pos-\nsible, the intrinsic spin-down rate is used in calculating\nthe spin-down limit.\n2.2. Non-standard polarization signal\nIn this paper, similar to the analysis in Abbott et al.\n(2022), we search for gravitational waves (GWs) with\npolarizations predicted by the Brans-Dicke modifica-\ntion of General Relativity (GR). Brans-Dicke theory in-\ncludes two tensor polarizations, like in GR, and an ad-\nditional scalar polarization. The dominant scalar radia-\ntion stems from the time-dependent dipole moment D.\nThe dipole radiation occurs at the pulsar\u2019s rotational\nfrequency frot. Assuming the dipole moment is along\nthe x-axis the amplitude hd\n0 of the signal is given by\nhd\n0 = 4\u03c0G\nc3 \u03b6 Dfrot\nd\n,\n(7)\nwhere \u03b6 is the parameter of the Brans-Dicke theory (see\nVerma 2021, for details).\n3. METHODS\nIn this Section, we describe the data analysis meth-\nods used in this work: three independent pipelines for\nthe targeted searches, one pipeline for the narrowband\nsearches and one pipeline for the non-standard polariza-\ntions searches. We use three targeted pipelines to com-\npare independent results as our methods rely on different\nstatistical approaches (Bayesian or frequentist) and on\ndifferent pre-processings and handling of non-stationary\nor non-gaussian noise disturbances in the data.\n3.1. Time-domain Bayesian Method\nThe Continuous (gravitational) Wave Inference in\nPython (CWInPy) package is used to perform the\nBayesian analysis (Pitkin 2022) following the method\ndescribed in Abbott et al. (2019c) and summarized here.\nFirst, a complex, slowly evolving heterodyne is used to\nremove the phase evolution of the source. This includes\ncorrections for the relative motion of the source with\nrespect to the detector and relativistic effects (Dupuis\n& Woan 2005). Then, a low-pass anti-aliasing filter is\napplied to the data to remove the upper sideband pro-\nduced from the heterodyne and limit the possibility of\ndisturbances from spectral lines. Next, the data is down-\nsampled, centered about the expected signal frequency\nwhich has been shifted to 0 Hz by the heterodyne. For\nthe dual-harmonic search, this method is repeated so\nthat time series centered at both frot and 2frot are ob-\ntained.\nThere are several unknown signal parameters, with\nthe amplitude being of primary interest. Bayesian infer-\nence is used to estimate these parameters as well as the\nevidence for the signal model. The priors used are the\nsame as those detailed in Appendix 2 of Abbott et al.\n(2017b) except for the amplitude priors, for which we\nuse flat priors with an upper cut off much higher than\nthe detector sensitivity.\nThis value is 1.0 \u00d7 10\u221221 for\nall pulsars. The Bayesian stochastic sampling algorithm\nused is dynesty (Skilling 2004, 2006), as wrapped with\nbilby (Ashton et al. 2019), with 1024 live points (the\nnumber of points drawn from the prior). In the absence\nof a signal, we calculate 95% credible upper bounds de-\nrived from the posterior probability distributions.\n3.1.1. Restricted priors\nFor some pulsars, there is sufficient information to re-\nstrict our uninformative prior assumptions on their in-\nclination and polarisation angles, for example if we have\nEM observations of their pulsar wind nebulae or, in the\ncase of J1952+3252, from proper motion measurements\nand observations of H\u03b1 lobes bracketing the bow shock\n(Ng & Romani 2004). In these cases, the parameter esti-\nmation is repeated and used along with the results from\nthe original uninformed priors. Table 1 shows the pul-\nsars for which we could restrict the priors and the values\nused for the restrictions. These values were obtained us-\ning the data from Table 2 of Ng & Romani (2008) and\nthe methods described in Appendix B of Abbott et al.\n(2017b). Each prior range is assumed to be Gaussian\nabout the given mean and standard deviation. The two\nvalues for \u03b9 are to incorporate the unknown rotation di-\nrection in the search by using a bimodal distribution.\nThe additional \u03b92 is simply \u03c0 \u2212\u03b91 radians.\n3.1.2. Glitches\nGlitches are transient events, where the normally sta-\nble pulsar spin suddenly increases in both rotation fre-\nquency and spin-down rate (Espinoza et al. 2011; Yu\net al. 2013; Basu et al. 2022). These events are most\ncommon in younger, non-recycled pulsars with rarer\nglitches seen in some millisecond pulsars (Cognard &\nBacker 2004; McKee et al. 2016). Some searches (e.g.,\nKeitel et al. 2019; Abbott et al. 2022; Abac et al. 2024a)\nlook for transient GWs in the aftermath of glitches.\nWhen a glitch occurs in a pulsar during the course of a\nGW observing run, we assume that the GW phase is af-\nfected in the same way as the EM phase. However, since\nthe phase offset is unknown at the time of the glitch,\nit is incorporated into the parameter inference for the\nBayesian method. This adjustment is not necessary for\n\n15\nTable 1. Pulsars for which we can restrict their orientation priors using electromagnetic observations. \u03a8 is the polarisation\nangle and \u03b9 is the inclination angle, with \u03b92 = \u03c0 \u2212\u03b91.\nPSR\n\u03a8 (rad)\n\u03b91 (rad)\n\u03b92 (rad)\nJ0205+6449\n1.5760 \u00b1 0.0078\n1.5896 \u00b1 0.0219\n1.5519 \u00b1 0.0219\nJ0534+2200 (Crab)\n2.1844 \u00b1 0.0016\n1.0850 \u00b1 0.0149\n2.0566 \u00b1 0.0149\nJ0537\u22126910\n2.2864 \u00b1 0.0383\n1.6197 \u00b1 0.0165\n1.5219 \u00b1 0.0165\nJ0540\u22126919\n2.5150 \u00b1 0.0144\n1.6214 \u00b1 0.0106\n1.5202 \u00b1 0.0106\nJ0835\u22124510 (Vela)\n2.2799 \u00b1 0.0015\n1.1048 \u00b1 0.0105\n2.0368 \u00b1 0.0105\nJ1952+3252\n0.2007 \u00b1 0.1501\n...\n...\nJ2021+3651\n0.7854 \u00b1 0.0250\n1.3788 \u00b1 0.0390\n1.7628 \u00b1 0.0390\nJ2229+6114\n1.7977 \u00b1 0.0454\n0.8029 \u00b1 0.1100\n2.3387 \u00b1 0.1100\npulsars that glitch before or after the observation pe-\nriod. Only two of the pulsars in our sample experienced\nglitches during the length of O4a: J0537\u22126910 with an\nepoch of \u223cMJD 60223 and J0540\u22126919 with an epoch\nof \u223cMJD 60150 (see, e.g., Espinoza et al. (2024); Tuo\net al. (2024)).\n3.2. 5-vector targeted pipeline\nThe 5-vector method is a frequentist data-analysis ap-\nproach (Astone et al. 2010), which has been used in the\nlast decade in several LVK searches (Abbott et al. 2022,\n2020, 2019c, 2017b). The 5-vector targeted pipeline re-\nlies on the Band-Sample Data (BSD) (Piccinni et al.\n2018) framework, i.e. a database of sub-sampled com-\nplex time-domain files (so-called BSD files) that covers\n10 Hz and spans 1 month of the original dataset that al-\nlows to reduce the computational cost of the analysis.\nTo correct for the signal phase modulations due to, for\nexample, the pulsar spin-down and the Doppler effect, a\nheterodyne method is used. Recently (D\u2019Onofrio et al.\n2023), the 5-vector method has been also applied to pul-\nsars in binary systems with the implementation of the\nDoppler correction due to the orbital motion (Leaci &\nPrix 2015; Leaci et al. 2017). After the spin-down and\nDoppler/relativistic corrections, there is a residual mod-\nulation at the detector due to the Earth sidereal motion\nthat splits the frequency of the expected CW signal.\nAssuming the single-harmonic emission scenario, the\ncentral peak at twice the pulsar rotation frequency has\nfour sidebands whose distance to the central peak is\n\u00b11, \u00b12f\u2295where f\u2295is the Earth\u2019s sidereal rotation fre-\nquency. A 5-vector consists of a complex array with five\ncomponents corresponding to the Fourier transform of\nthe detector\u2019s data (data 5-vector) or of the antenna pat-\nterns (template 5-vectors for the plus and cross compo-\nnent) at the five signal frequencies. The 5-vector method\ndefines two matched filters in the frequency domain, de-\nfined by the normalized scalar product between the data\n5-vector and the two template 5-vectors. To extend the\nanalysis to n detectors, the data 5-vector from each de-\ntector are combined together with coefficients that take\ninto account the detector\u2019s sensitivity and observation\ntime to construct the 5n-vectors (D\u2019Onofrio et al. 2024).\nThe two matched filters are linearly combined to define\na detection statistic (D\u2019Onofrio et al. 2023). To assess\nthe significance of a candidate, a p-value is computed\nfrom the noise distribution of the detection statistic us-\ning off-source frequencies as the noise background in the\nanalyzed frequency bands.\nIn case of no detection, a\nmixed Bayesian-frequentist upper limit procedure (de-\nscribed in Abbott et al. (2019c)) is used to set the up-\nper limit on the amplitude, assuming a uniform prior\nand considering informative priors on the polarization\nparameters, if present (see Table 1).\nIt is not straightforward to generalize the 5-vector\nmethod to the dual-harmonic emission model due to the\ncomplexity of the expected CW signal. In this case, an\nadditional analysis considering the emission at only the\nrotation frequency is performed; this would be a good\napproximation if the star\u2019s moment of inertia tensor is\nbiaxial, with a small misalignment angle between its\nsymmetry axis and the rotation axis (see Jones (2010)).\n3.3. F/G/D-statistic method\nThe time-domain F/G/D-statistic method utilizes the\nF-statistic derived in Jaranowski et al. (1998) and the\nG-statistic derived in Jaranowski & Kr\u00b4olak (2010). The\ninput data for this analysis are the heterodyned data\nused in time-domain Bayesian analysis. The F-statistic\nis employed when the amplitude, phase, and polariza-\ntion of the signal are unknown, whereas the G-statistic\nis applied when only the amplitude and phase are un-\nknown, and the polarization is known (as described in\nSection 3.1.1). These methods have been used in several\nanalyses of LIGO and Virgo data (Abadie et al. 2011;\nAasi et al. 2014; Abbott et al. 2017b, 2020, 2022). Ad-\nditionally, the method incorporates the D-statistic de-\nveloped in Verma (2021) to search for dipole radiation\nin Brans-Dicke theory. The D-statistic search was first\n\n16\nperformed in the LIGO and Virgo analysis presented in\nAbbott et al. (2022).\nThe three statistics are derived by calculating the\nmaximum likelihood estimators of the signal\u2019s constant\namplitude parameters. This is done by maximizing the\nlikelihood function and then substituting the amplitude\nvalues with their respective maximum likelihood esti-\nmators. As a result, we obtain statistics that are inde-\npendent of the amplitudes. In this method, a signal is\ndetected if the value of the F-, G- or D statistic exceeds\na certain threshold corresponding to an acceptable false-\nalarm probability. We consider a false-alarm probability\nof 1% for a signal to be deemed significant. The F-, G-,\nand D-statistics are computed for each detector and each\ninter-glitch period separately. The results from different\ndetectors or inter-glitch periods are then combined in-\ncoherently by summing the respective statistics. When\nthe values of the statistics are not statistically signifi-\ncant, we set an upper limit with a frequentist approach\non the amplitude of the GW signal.\n3.4. 5n-vector narrowband pipeline\nThe 5n-vector narrowband pipeline makes use of the\n5n-vector as in Astone et al. (2014a) and follows the\nsame principle of the method described in Section 3.2.\nWhile the former searches for a CW tightly locked to\nthe EM emission, this assumption is here relaxed search-\ning for CWs in a narrow frequency and spin-down range\naround twice the values inferred from EM observations,\nnamely\nf \u22082frot[1 \u2212\u03b4, 1 + \u03b4]\n(8)\nwith \u03b4 = 10\u22123 (Abbott et al. 2022), and an analogous\nexpression for \u02d9f.\nThe method makes use of the Short Fourier Data Base\n(SFDB) (Astone et al. 2005), which is a collection of\nshort-duration (2048 s) Fast Fourier Transforms (FFTs)\noverlapped by half.\nFor every target, data are Doppler corrected in the\ntime domain with a non-uniform resampling that is inde-\npendent of the CW frequency, then they are subsampled\nat 1 Hz. At this point, the time series are match-filtered\n(using 5-vectors as for the targeted search) to estimate\nthe two CW polarizations using a template bank in the\nf \u2212\u02d9f space. We build the template bank considering bin\nwidths equal to the inverse of the time series duration\nfor the frequency, while its inverse squared for the spin-\ndown grid. Higher-order spin-down terms, if provided in\nthe ephemerides, are fixed at twice the rotation terms\nto track the GW frequency evolution over time, without\nexploring any additional template (Astone et al. 2014b).\nThen, the matched filter results from different de-\ntectors are coherently combined (Mastrogiovanni et al.\n0\u00b0\n315\u00b0\n270\u00b0\n225\u00b0\n180\u00b0\n135\u00b0\n90\u00b0\n45\u00b0\n0\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n60\u00b0\n30\u00b0\n0\u00b0\n-30\u00b0\n-60\u00b0\n-60\u00b0\n-30\u00b0\nnarrowband targets\nFigure 1. Sky location in equatorial coordinates of the ana-\nlyzed targets. All targets are selected for the targeted search,\nwhile the triangles are the targets analyzed also with the nar-\nrowband search.\n2017) to evaluate the detection statistic.\nFrom the\ncollection of statistic values, we order them along the\nfrequency axis to select the maximum every 10\u22124 Hz,\nmarginalizing over the spin-down.\nWe use a p-value\nthreshold (i.e., the tail probability of the noise-only dis-\ntribution) of 1% to determine whether a selected point\nhas to be considered an outlier. The noise-only distribu-\ntion is inferred from the tail of the histogrammed non-\nmaxima values which is fitted with an exponential (Sing-\nhal et al. 2019). We use here a threshold of 1%, similar\nto previous searches (e.g., Abbott et al. (2022)), after\ntaking into account the trial factor.\nIf CW detection is not claimed, we set the 95% confi-\ndence level upper limit h95%\n0\nthrough software-injection\ncampaigns.\n4. DATASETS\n4.1. GW dataset\nThe considered dataset is the first part of the fourth\nobserving run, known as O4a, of the LIGO Livingston\n(L1) and LIGO Hanford (H1) detectors1. The O4a run\ntook place between May 24, 2023 15:00:00 UTC and\nended January 16, 2024 16:00:00 UTC. The duty factors\nfor L1 and H1 were 69.0% and 67.5%, respectively. The\nVirgo detector has not been considered since it joined\nthe O4 run on April 10, 2024 while the KAGRA detec-\ntor is planned to join O4 by the end of the run. For\na description of the upgrades to the Advanced LIGO\n(Capote et al. 2024), Advanced Virgo, and KAGRA de-\ntectors in preparation to the O4 run, we refer to Ap-\npendix A in Abac et al. (2024b).\nThe LIGO detectors are calibrated using photon\nradiation pressure actuation,\nwhere an amplitude-\n1 We\nconsidered\nL1:GDS\u2013CALIB STRAIN CLEAN AR\nand\nH1:GDS\u2013CALIB STRAIN CLEAN AR frame channels with\nCAT1 vetoes for L1 and H1, respectively.\n\n17\nmodulated laser beam is directed onto the end test\nmasses, causing a known change in the arm length from\nthe equilibrium position (Karki et al. (2016), Viets et al.\n(2018)).\nFor the O4a data used in this analysis, the\nworst 1\u03c3 calibration uncertainty is within 10% in am-\nplitude, and 10 degrees in phase, over the range 10\u20132000\nHz. The uncertainty at specific frequencies or times can\nbe significantly smaller.\nThe dataset used underwent cleaning processes de-\npending on the data framework used by each pipeline\n(we refer to Soni et al. (2024) for more details on data\nquality for CW searches).\nFor the Bayesian pipeline,\noutliers are removed before the heterodyne using a\nmedian-absolute-deviation (MAD) method as described\nin Chapter 3 of Iglewicz & Hoaglin (1993) with a thresh-\nold of 3.5. Concerning the 5-vector targeted pipeline,\ntwo cleaning steps are applied.\nFirst, short duration\ntime-domain disturbances are identified and substracted\nfrom the data when the SFDB database - from which\nBSD files are built - are created (this cleaning step is\nshared with the 5-vector narrowband search, which also\nstarts from the SFDB Astone et al. (2005)). A second\ncleaning step is applied on the BSD files (Piccinni et al.\n2018), removing large time-domain outliers, which were\nnot visible in the full band time series, with quadratic\nvalue larger than ten times the quadratic sum of the\nmedians of the data real and imaginary parts (com-\nputed over non-zero samples). The F-, G- or D statistic\nmethod performs further cleaning of the fine heterodyne\ndata through the Grubbs test (see Appendix D of Abadie\net al. (2011)).\n4.2. EM dataset\nThe timing solutions used as inputs for the GW search\nwere produced with EM data in the gamma rays, X-rays\nand radio wavelengths. The gamma ray timing solutions\nwere obtained from Fermi-LAT (Atwood et al. 2009); X-\nray timing solutions were obtained from Chandra (Weis-\nskopf et al. 2002) and the Neutron Star Interior Com-\nposition Explorer (NICER, Gendreau et al. 2016), while\nthe radio timing solutions were obtained from the Nan-\ncay Radio Telescope (NRT, Guillemot, L. et al. 2023),\nthe Jodrell Bank Observatory (JBO), the Argentine In-\nstitute of Radio astronomy (IAR, Gancio et al. 2020),\nthe Mount Pleasant Radio Observatory (Lewis et al.\n2003), the Five-hundred-meter Aperture Spherical Tele-\nscope (FAST, Smits et al. 2009) and the Canadian Hy-\ndrogen Intensity Mapping Experiment (CHIME, Amiri\net al. 2021).\nFor the radio-emitting pulsars, we used pazi or\nrfifind tasks in PSRCHIVE (van Straten et al. 2012)\nand PRESTO (Ransom 2011) packages respectively to\nmitigate Radio-frequency interferences (RFIs).\nNext,\nwe folded observations with prepfold or fold psrfits\ntasks in PRESTO and PSRFITS UTILS (Hotan et al.\n2004) packages. We then cross-correlated the folded pro-\nfiles with a noise-free template profile with high signal-\nto-noise ratio to obtain the Times of Arrivals (ToAs).\nNext, we select ToAs during the course of O4a run,\nso the solutions are valid for this time range. We use\nTEMPO (Nice et al. 2015), TEMPO2 (Edwards et al.\n2006; Hobbs et al. 2006, 2009) or PINT (Luo et al. 2019,\n2021) to characterise the rotation of each pulsar by fit-\nting the ToAs to a Taylor series expansion:\n\u03d5(t) = \u03d50+frot(t\u2212t0)+ 1\n2\n\u02d9frot(t\u2212t0)2+ 1\n6\n\u00a8frot(t\u2212t0)3+... ,\n(9)\nwhere t0 is the reference epoch and \u03d50 is the phase at t0,\nand frot, \u02d9frot, and \u00a8frot are the rotation frequency of the\npulsar, and its first and second derivatives, respectively.\nIf higher-order derivatives are measured, we also include\nthe corresponding terms in the Taylor expansion.\nDuring a glitch, the rotation frequency abruptly in-\ncreases. This glitch-induced alteration in the rotational\nphase can be taken into account in the timing model as\n(Yu et al. 2013):\n\u03d5g(t) = \u2206\u03d5 + \u2206f p\nrot(t \u2212tg) + 1\n2\u2206\u02d9f p\nrot(t \u2212tg)2+\n1\n6\u2206\u00a8f p\nrot(t \u2212tg)3 +\nX\ni\n\u0014\n1 \u2212exp\n\u0012\n\u2212t \u2212tg\n\u03c4 i\nd\n\u0013\u0015\n\u2206f d,i\nrot \u03c4 i\nd.\n(10)\nThe uncertainty on the glitch epoch tg is counteracted\nhere by \u2206\u03d5, and the step changes in frot, \u02d9frot and \u2206\u00a8frot\nat tg are represented by \u2206f p\nrot, \u2206\u02d9f p\nrot, and \u2206\u00a8f p\nrot. Finally,\n\u2206f d,i\nrot denotes temporal frequency increases that decay\nin \u03c4 i\nd days.\nThe ToA fitting process also provides the astrometric\nparameters of each pulsar and the orbital parameters for\nbinary pulsars (Lorimer & Kramer 2004). Uncertainties\nin the values of the pulsar and orbital parameters de-\nrived from fitting the ToAs are not taken into account\nin targeted/narrowband searches.\nFor many pulsars, their distances (Hobbs et al. 2004)\nare based on the observed dispersion measure using the\nGalactic electron density distribution model YMW16\n(Yao et al. 2017). The uncertainties in these measure-\nments can be as large as a factor of two.\nFor other\npulsars, the distance can be determined by measuring\nthe parallax with the timing solution (Smits et al. 2011)\nor, if the pulsar is in a binary system, the orbital period\nderivative (Verbiest et al. 2008). The first method usu-\nally results in an uncertainty ranging from 5% to 50%\n\n18\n(Shamohammadi et al. 2024).\nThe second one offers\nsignificantly higher accuracy, achieving uncertainties as\nlow as 0.1% (Verbiest et al. 2008; Reardon et al. 2016).\nOther methods such as Very Long Baseline Interferom-\netry (Lin et al. 2023) were also used to determine pulsar\ndistances.\nFor this analysis, we selected pulsars with a rota-\ntion frequency close to or greater than 10 Hz, to lie in\nthe bandwidth of the LIGO detectors, and with an ex-\npected targeted search sensitivity for the strain ampli-\ntude within a factor 3 of the spin-down limit (see Figure\n1 for the pulsars\u2019 sky locations and Table 2 for the list\nof analyzed pulsars). Out of the 45 pulsars analyzed in\nthis work, 11 pulsars belong to binary systems and there\nare 10 millisecond pulsars with frequencies higher than\n100 Hz.\n5. RESULTS\n5.1. Targeted searches\nWe found no statistical evidence of a CW signal in the\nO4a data for any of the analyzed targets. In this section,\nwe present the results of the targeted search conducted\nusing three different analysis methods across the full set\nof 45 pulsars.\nThe results are shown in Table 2.\nThe 95% upper\nlimit h95%\n0\nis given for the single-harmonic search along\nwith the mass quadrupole Q95%\n22\nand ellipticity \u03b595% up-\nper limits calculated using the distance listed in the ta-\nble and a fiducial moment of inertia Izz = 1038 kg m2.\nUncertainties on these parameters are not taken into\naccount, and for reference, we report the used best-fit\ndistance values in Table 2 provided by the EM obser-\nvation. However, for pulsars that did not surpass their\nspin-down limits, these Q22 and \u03f5 upper limits are un-\nphysical since they would lead to spin-down rates that\nare greater than their measured values. From the upper\nlimit on the amplitude, we also compute the spin-down\nratio as h95%\n0\n/hsd\n0 with hsd\n0 defined in Equation (6). The\nupper limits for the dual-harmonic search are included\nas C95%\n21\nand C95%\n22 . Finally, for the Bayesian method,\nthe odds of a coherent signal versus incoherent noise\nare given for both the single Ol=2\nm=2 and dual-harmonic\nOl=2\nm=1,2 searches. For the F-statistic and for the 5-vector\nmethod, to assess the statistical significance of a candi-\ndate and quantify the consistency with the assumption\nof just noise, we report the p-value.\nFor the two\nglitching pulsars,\nJ0537\u22126910\nand\nJ0540\u22126919, the Bayesian results are produced when\nincorporating an additional phase offset in the parame-\nter inference while for the F-statistic and the 5-vector\nmethod, an incoherent approach is used summing the\nstatistics from the inter-glitch periods.\nIn cases with\nsufficient observations of the pulsar wind nebulae, re-\nsults using restricted priors of inclination and polarisa-\ntion angles are listed in parentheses.\nFigure 2 shows the upper limits from the Bayesian\nanalysis for the single-harmonic search against an esti-\nmate of the sensitivity of the search using both detec-\ntors during O4a. The results for each pulsar are com-\npared with the corresponding spin-down limit. The re-\nsults from this analysis for each pulsar are represented\nby the blue dots, with their corresponding spin-down\nlimit shown by the grey triangles at the same frequency.\nThe sensitivity curve is shown as a pink line.\nSome\nhighlighted results for individual pulsars include the\nCrab pulsar (J0534+2200) which had the lowest spin-\ndown ratio of 0.00783, the Vela pulsar (J0835\u22124510),\nJ2021+3651 which had the highest odds of coherent\nsignal versus incoherent noise with \u22123.1, J0537\u22126910\nwhich had the most constraining amplitude upper limit\nof 6.38\u00d710\u221227, and J0437\u22124715 which had the most\nconstraining ellipticity upper limit of 8.8\u00d710\u22129. The dis-\ntribution of spin-down ratios for these results is shown\nin Figure 3 with 29 targets that surpass the spin-down\nlimit and the remaining targets, which all have a spin-\ndown ratio below 5.\nIn Figure 4, the ellipticity \u03b595% and mass quadrupole\nQ95%\n22\nupper limits are plotted against the GW frequency\nand compared with the corresponding spin-down limits\nfor the ellipticity. The contours of equal characteristic\nage have been calculated using \u03c4 = P/4 \u02d9P which can be\nderived with the assumption that GW emission alone is\ndriving the spin-down.\nAs shown in Table 2, there is broad agreement among\nthe different pipelines, despite these pipelines being\nlargely independent, and the statistical procedures used\nto derive the upper limits are different.\nThe data\nframeworks and pre-processing procedures used by each\npipeline account for the differences found in the upper\nlimit results.\n5.2. Narrowband results\nIn this section, we detail the results obtained with\nthe narrowband pipeline, presented in Section 3.4. The\nsearch did not highlight, for any of the 16 considered\ntargets, outliers with a False-Alarm Probability FAP<\n10\u22122 after taking into account the trial factor.\nFor the narrowband search, we consider only those\ntargets with hsd\n0\nabove the expected sensitivity that is\ntypically worse by a factor of two (Astone et al. 2014a)\nthan that of targeted pipelines due to the trial factor. In\nthis way, we selected 16 pulsars out of which 8 have not\nbeen analyzed in O3 (Abbott et al. 2022). Our dataset\nincludes the two pulsars that glitched, J0537-6910 and\n\n19\n102\n103\nGravitational-wave Frequency (Hz)\n10\u221227\n10\u221226\n10\u221225\n10\u221224\nh0 Strain Sensitivity\nJ0537-6910\nJ0437-4715\nCrab pulsar\nVela pulsar\nJ2021+3651\nSensitivity estimate\nResults\nbelow spin-down limit\nspin-down limits\nFigure 2. Upper limits on h0 for the 45 pulsars in this analysis using the time-domain Bayesian method and considering\nthe single-harmonic emission model. The blue stars show 95% credible upper limits on the amplitudes of h0. Grey triangles\nrepresent the spin-down limits for each pulsar (based on the distance measurement stated in Table 2 and assuming the canonical\nmoment of inertia). The pink curve gives an estimate of the expected strain sensitivity of both detectors combined during the\ncourse of O4a. The upper limits from the other two pipelines are broadly consistent, as shown in Table 2.\n10\u22123\n10\u22122\n10\u22121\n100\n101\nSpin-down Ratio (h95%\n0\n/hsd\n0 )\n0\n1\n2\n3\n4\n5\n6\n7\nNumber of Pulsars\nFigure 3. A histogram of the spin-down ratio considering\nthe single-harmonic emission model for 45 pulsars from the\nBayesian analysis.\nJ0540-6919. Similar to O3, for these pulsars we split O4a\ndata into two segments that exclude from the analysis\nthe period around [tg-1 d, tg+2 d], with tg the glitch\nepoch. The segments are then analyzed independently.\nThe search did not highlight any statistically signifi-\ncant outlier since the measured p-values are well above\nthe threshold set by a FAP of 10\u22122 corrected for the trial\nfactor. In Table 3, we report for each target the lowest\np-value found during the analysis and the threshold.\nIn the absence of any detections, we have calculated\nupper limits at the 95% CL for each of the analyzed\ntargets. Our results are listed in Table 3 and shown in\nFigure 5 comparing them with the expected sensitivity.\n5.3. Brans-Dicke theory\nTable 4 shows the results for the analyses on 45 pul-\nsars using the D-statistic to search for dipole radiation\npredicted by Brans-Dicke theory. No outliers have been\nfound in the analysis and we set upper limits on the ex-\n\n20\n102\n103\nGravitational-wave Frequency (Hz)\n10\u22129\n10\u22127\n10\u22125\n10\u22123\nEllipticity \u03b5\n\u03c4 = 103 y\n\u03c4 = 105 y\n\u03c4 = 107 y\n\u03c4 = 109 y\nResults\nbelow spin-down limit\nspin-down limits\n1029\n1030\n1031\n1032\n1033\n1034\n1035\nl = m = 2 Quadrupole Moment, Q22 (kg m2)\nFigure 4. 95% credible upper limits on ellipticity \u03b595% and mass quadrupole Q95%\n22\nfor all 45 pulsars using the Bayesian analysis\nmethod and considering the single-harmonic emission model. The upper limits for each pulsar are represented by blue circles\nwhile their spin-down limits are shown as grey triangles. Also included are purple contour lines of equal characteristic age\n\u03c4 = P/4 \u02d9P assuming that GW emission alone is causing spin-down. Only the results for pulsars which surpassed their spin-down\nare physically meaningful. The histogram on the right shows the distribution of the ellipticities obtained from the results (blue\nfilled bars) and in the spin-down limit (grey bars).\npected amplitude defined in Equation (7). The upper\nlimits in brackets shows the results using informative\npriors on the polarization parameters for the pulsars in\nTable 1.\n6. DISCUSSION\nIn this section, we discuss the results in Table 2.\nMotivated by the comparable results among the three\npipelines, we consider the Bayesian pipeline as a refer-\nence. As described in the previous section, we have no\nevidence of a CW signal in any of the searches we con-\nducted.\nWe compare the O4a results with previous targeted\nsearches by the LVK Collaboration (Abbott et al. 2022,\n2020, 2019c, 2017b), considering the first three observing\nruns. The ratio between the O4a upper limits on h0 and\nC21 and the corresponding upper limits set in previous\nsearches is shown in Figure 6.\n34 pulsars out of the 45 considered targets in Table\n2 have been already analyzed in the joint O2 plus O3\nanalysis (Abbott et al. 2022). Overall the corresponding\nupper limits on the GW amplitude are comparable for\nthe single-harmonic search, with some targets showing\nbetter results in O4a and some targets having worse re-\nsults than those in Abbott et al. (2022), see Figure 6.\nThis is expected since the targeted search sensitivity of\nthe O2\u2013O3 dataset is comparable to the O4a one, except\nat very low frequencies. The targeted search sensitivity\ncan be expressed in terms of minimum detectable ampli-\ntude (D\u2019Onofrio et al. 2024), hmin. For a multi-detector\nanalysis considering n detectors and averaging over the\nsky position and polarization parameters,\nhmin \u2248C\nv\nu\nu\nt\n n\nX\ni=1\nTi\nSi\n!\u22121\n,\n(11)\nwhere the factor C \u224311 (the exact value depending on\nthe considered pipeline), while Ti and Si are respectively\nthe effective observation time and the average power\nspectral density (PSD) for the i-th detector. For the O4a\ntargeted search sensitivity (with an observation time of\napproximately 1.3\u00d7107 seconds for both detectors), see\nthe pink curve in Figure 2.\n\n21\n101\n102\nGravitational-wave Frequency [Hz]\n10\u221226\n10\u221225\n10\u221224\n10\u221223\nh0 Strain Sensitivity\nSensitivity estimate\nSpin-down limits\nBelow Spin-down limits\nResults\nFigure 5. Expected sensitivity of the narrowband search using O4a (shaded pink region) dataset from the two LIGO detectors\nconsidering the single-harmonic emission model. The curve is compared with the spin-down limits (triangles) and the upper\nlimits (stars) averaged over all the 10\u22124 Hz bands for each source. Upper limits below the spin-down limit are highlighted with\norange circles.\n101\n102\n103\n0\n0.5\n1\n1.5\n2\n2.5\nFigure 6. Blue stars show the ratio between the O4a h0 upper limits for the analyzed targets (excluding the glitching pulsars)\nassuming the single-harmonic model divided by the corresponding h0 upper limits in Abbott et al. (2022) for the Bayesian method\nas a function of the corresponding frequency at twice the rotation frequency (red circles refer instead to the C21 parameter at\nthe rotation frequency assuming the dual-harmonic model). Blue filled stars show the h0 upper limit ratios considering the\ntargets (J0205+6449, J0737\u22123039A, J1813\u22121246, J1831\u22120952, J1837\u22120604) analyzed using O2 (Abbott et al. 2019c) and O1\ndata (blue asterisk for J1826\u22121334, Abbott et al. (2017b)).\n\n22\nThe O4 targeted searches have a sensitivity depth D =\nSh/Hz\nh0\nof around 500; here, Sh is the power spectrum\ntaking the harmonic mean of the data over time and\nover detectors, and h0 the upper limit on the pulsar\namplitude [Wette, Behnke+, Dreissigacker+].\nThe O4a PSDs for the two LIGO detectors are gener-\nally better, by almost a factor of 1.5 to 2, compared to\nthe corresponding O3 PSD2 depending on the consid-\nered frequency band. However, the effective observation\ntime for O4a is reduced by a factor of approximately 1.6,\nwhich diminishes the benefit of the improved detector\nsensitivity in O4a. As a result, we expect the sensitiv-\nity of the O4a search to be comparable to that of the\ncombined O2+O3 search. Upper limits on C21, on the\nother hand, are lower on average than the correspond-\ning O2+O3 results due to a better search sensitivity at\nfrequencies below 20 Hz.\nFor the remaining targets, 5 pulsars (J0205+6449,\nJ0737\u22123039A,\nJ1813\u22121246,\nJ1831\u22120952,\nand\nJ1837\u22120604) have been analyzed in the O2 search\n(Abbott et al. 2019c), and J1826\u22121334 has been an-\nalyzed in the O1 search (Abbott et al. 2017b).\nFor\nthese pulsars, we have a clear improvement in the upper\nlimits, as shown in Figure 6.\nThe remaining targets\n(J0058\u22127218, J1811\u22121925, J2016+3711, J2021+3651,\nJ2022+3842) have not been analyzed in recent targeted\nsearches and we surpass the spin-down limit for all these\ntargets.\nMany studies have been dedicated to illustrate how a\nfuture successful detection of CW will provide a wealth\nof information about neutron stars (see e.g. Sieniawska\n& Jones (2022); Lu et al. (2023)), and even help to con-\nstrain the nuclear equation of state (see e.g. Idrisy et al.\n(2015); Ghosh et al. (2023); Ghosh (2023)).\nIt is in-\nteresting to note that with improving sensitivity of the\nsearches with each observing run, even non-detection\nof a CW signal sets more and more stringent upper\nlimits on the ellipticity and possible sources of non-\naxisymmetric deformations in rotating neutron stars.\nThis may lead to a better understanding of properties of\nthe crust, internal magnetic fields, and accretion physics\n(Bildsten 1998; Melatos & Payne 2005; Ciolfi & Rezzolla\n2013), and even rule out certain scenarios related to r-\nmodes or limit their maximum saturation amplitudes\n(Abbott et al. 2021d).\nTheoretical estimates of the maximum mountain sizes\nthat an elastically deformed neutron star can sustain are\nsubject to significant uncertainties, with estimates for\nthe ellipticity \u03f5 ranging from \u223c10\u22126 for conventional\n2 For this estimation, we only consider the O3 run for simplicity\nsince it dominates the combined datasets.\nneutron stars, to as large as \u223c10\u22123 for stars with ex-\notic solid phases (see e.g. Ushomirsky et al. (2000); Owen\n(2005); Haskell et al. (2007); Johnson-McDaniel & Owen\n(2013); Gittins & Andersson (2021); Morales & Horowitz\n(2022)). Comparison with the results given in Figure 4\nand Table 2 show that our observationally-obtained up-\nper limits overlap with these ranges, confirming we are\ncontinuing to push into the regime of astrophysical in-\nterest. Estimates for magnetically-induced ellipticities\nare similarly uncertain (see e.g. Haskell et al. (2008);\nGlampedakis et al. (2012); Fujisawa et al. (2022)). Nev-\nertheless, to give a concrete example, Dall\u2019Osso & Perna\n(2017) (see however Lander & Jones (2018)) have sug-\ngested that the apparent gradual increase in the angle\nbetween the spin axis and magnetic axis of the Crab\npulsar provides evidence for a magnetically-induced el-\nlipticity \u03f5 \u223c(3\u201310) \u00d7 10\u22126. This to be compared with\nour upper limit of \u03f5 \u22486 \u00d7 10\u22126 for the Crab, again\nconfirming we are probing a regime for astrophysical in-\nterest.\nTheoretical estimates of the minimum mountain sizes\nare presented in Woan et al. (2018), which provides\npopulation-based evidence for millisecond pulsars hav-\ning a minimum ellipticity of \u03f5 \u224810\u22129.\nWe stress that our upper limits are subject to the un-\ncertainties from the detector calibration as described in\nSection 4.1, as well as statistical uncertainties that are\ndependent on the particular analysis method.\nThe narrowband results in Table 3 and in Figure 5\nshow no evidence of a CW signal for the considered sub-\nset of pulsars. No outlier was found for any of the tar-\ngets.\nOut of the 16 analyzed targets, 12 searches re-\nport an upper limit below the corresponding spin-down\nlimit (see Table 3), ranging from a factor of 1.16 for\nJ2021+3651 to 33 for J0534+2200. As for other meth-\nods, the targets analyzed with O3 data (Abbott et al.\n2022) report upper limits comparable to those in Ta-\nble 3. We stress that the narrowband search sensitivity\nis worse by at least a factor of 2 compared to the tar-\ngeted search sensitivity as it depends on the number of\ntemplates explored for each target (Mastrogiovanni et al.\n2017).\nThe search for non-GR polarizations as predicted\nby the Brans-Dicke theory shows no evidence of a\ndipole radiation. The most constraining upper limit for\ndipole radiation is obtained for the millisecond pulsar\nJ1719\u22121438.\nTogether with results from the O3 tar-\ngeted search analysis (Abbott et al. 2022) the obtained\nupper limits constitute the first constraints on the dipole\nradiation from the pulsar gravitational wave observa-\ntions.\n\n23\n7. CONCLUSION\nIn this work, we present a search for CW signals from\na set of 45 known pulsars using O4a data from the two\nLIGO detectors. Pulsars are chosen considering an ex-\npected sensitivity for the amplitude below or slightly\nabove the theoretical spin-down limit with a rotation\nfrequency close to or greater than 10 Hz. EM observa-\ntions were employed to constrain the pulsars\u2019 sky posi-\ntions and rotational parameters covering the O4a data\nperiod.\nWe performed a targeted search utilizing three inde-\npendent data analysis methods and two different emis-\nsion models. No evidence of a CW signal was found for\nany of the targets. The upper limit results show that\n29 targets surpass the theoretical spin-down limit. For\n11 of the 45 pulsars not analyzed in the last LVK tar-\ngeted search, we have a notable improvement in detec-\ntion sensitivity compared to previous searches. For these\ntargets, we surpass or equal the theoretical spin-down\nlimit for the single-harmonic emission model. We also\nhave, on average, an improvement in the upper limits\nfor the low frequency component of the dual-harmonic\nsearch for all analyzed pulsars. For the remaining tar-\ngets, the O4a upper limits are comparable to the results\nof the joint O2\u2013O3 analysis described in Abbott et al.\n(2022), which considered data with lower sensitivity but\na longer observation time.\nWe also conducted a narrowband search for 16 pulsars\nand a search for non-GR polarization as predicted by\nBrans-Dicke theory. No evidence of a CW signal was\nfound in any of these searches.\nThe analysis of the full O4 dataset will improve the\nsensitivity of targeted/narrowband searches for some of\nthe pulsars analyzed in Abbott et al. (2022) and here,\nincluding the Crab and Vela pulsars.\nACKNOWLEDGEMENT\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies as well as by the Council of Scientific and Indus-\ntrial Research of India, the Department of Science and\nTechnology, India, the Science & Engineering Research\nBoard (SERB), India, the Ministry of Human Resource\nDevelopment, India, the Spanish Agencia Estatal de\nInvestigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comunitat\nAuton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Com-\nmission, the European Social Funds (ESF), the Euro-\npean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish\nUniversities Physics Alliance, the Hungarian Scientific\nResearch Fund (OTKA), the French Lyon Institute\nof Origins (LIO), the Belgian Fonds de la Recherche\nScientifique (FRS-FNRS), Actions de Recherche Con-\ncert\u02dcA\u00a9es (ARC) and Fonds Wetenschappelijk Onder-\nzoek \u02c6a\u20ac\u201c Vlaanderen (FWO), Belgium, the Paris \u02c6Ile-de-\nFrance Region, the National Research, Development and\nInnovation Office of Hungary (NKFIH), the National\nResearch Foundation of Korea, the Natural Sciences and\nEngineering Research Council of Canada (NSERC), the\nCanadian Foundation for Innovation (CFI), the Brazil-\nian Ministry of Science, Technology, and Innovations,\nthe International Center for Theoretical Physics South\nAmerican Institute for Fundamental Research (ICTP-\nSAIFR), the Research Grants Council of Hong Kong, the\nNational Natural Science Foundation of China (NSFC),\nthe Israel Science Foundation (ISF), the US-Israel Bina-\ntional Science Fund (BSF), the Leverhulme Trust, the\nResearch Corporation, the National Science and Tech-\nnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\n\n24\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, the JSPS\nLeading-edge\nResearch\nInfrastructure\nProgram,\nJSPS Grant-in-Aid for Specially Promoted Research\n26000005, JSPS Grant-in-Aid for Scientific Research on\nInnovative Areas 2905: JP17H06358, JP17H06361 and\nJP17H06364, JSPS Core-to-Core Program A, Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific\nResearch (S) 17H06133 and 20H05639, JSPS Grant-\nin-Aid for Transformative Research Areas (A) 20A203:\nJP20H05854, the joint research program of the Institute\nfor Cosmic Ray Research, the University of Tokyo, the\nNational Research Foundation (NRF), the Computing\nInfrastructure Project of Global Science experimental\nData hub Center (GSDC) at KISTI, the Korea Astron-\nomy and Space Science Institute (KASI), the Ministry\nof Science and ICT (MSIT) in Korea, Academia Sinica\n(AS), the AS Grid Center (ASGC) and the National Sci-\nence and Technology Council (NSTC) in Taiwan under\ngrants including the Rising Star Program and Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineer-\ning Center of KEK.\nC.M.E. acknowledges support from ANID/FONDECYT,\ngrant 1211964. S.G. acknowledges the support of the\nCNES. W.C.G.H. acknowledges support through grant\n80NSSC22K1305 from NASA. This work is supported\nby NASA through the NICER mission and the As-\ntrophysics Explorers Program and uses data and soft-\nware provided by the High Energy Astrophysics Sci-\nence Archive Research Center (HEASARC), which\nis a service of the Astrophysics Science Division at\nNASA/GSFC and High Energy Astrophysics Division\nof the Smithsonian Astrophysical Observatory.\nThe Nan\u00b8cay radio Observatory is operated by the\nParis Observatory, associated with the French Centre\nNational de la Recherche Scientifique (CNRS), and par-\ntially supported by the Region Centre in France. We\nacknowledge financial support from \u201cProgramme Na-\ntional de Cosmologie and Galaxies\u201d (PNCG), and \u201cPro-\ngramme National Hautes Energies\u201d (PNHE) funded by\nCNRS/INSU-IN2P3-INP, CEA and CNES, France.\nA.B.P. is a Banting Fellow, a McGill Space Insti-\ntute (MSI) Fellow, and a Fonds de Recherche du Quebec\n\u2013 Nature et Technologies (FRQNT) postdoctoral fellow.\nE.F. is supported by the NSF grant AST-2407399.\nThe activities at the Instituto Argentino de Radioas-\ntronom\u00b4\u0131a (IAR) are supported by the national agency\nCONICET, the Province of Buenos Aires agency CIC,\nand the National University of La Plata (UNLP).\nSoftware:\nThe 5-vector method is based on the\nBSD framework (Piccinni et al. 2018) while the narrow-\nband method makes use of the SFDB framework (As-\ntone et al. 2005), both of them are based on the\nVirgo Rome Snag software. The Bayesian analysis uses\nCWInPy (Pitkin 2022), which uses dynesty (Skilling 2004,\n2006) within bilby (Ashton et al. 2019). Plots are pro-\nduced using matplotlib (Hunter 2007). Many pulsar\nephemerides are produced with Tempo (Nice et al. 2015),\nTempo2 (Hobbs et al. 2006).\n\n25\nTable 2. Table of the results for the targeted search on the set of 45 known pulsars for the three considered pipelines described in Section 3.\nPulsar Name\nfrot\n\u02d9Prot\nDistance\nhsd\n0\nAnalysis\nh95%\n0\n\u03b595%\nQ95%\n22\nh95%\n0\nhsd\n0\nC95%\n21\nC95%\n22\nStatistic@\nStatistic#\n(J2000)\n(Hz)\n(s s\u22121)\n(kpc)\nMethod\n(kg m2)\nl=2,m=1,2\nl=2,m=2\nJ0030+0451\u03b1\n205.5 \u22124.2\u00d710\u221216\n0.3a\n3.5\u00d710\u221227\nBayesian\n1.0\u00d710\u221226\n1.9\u00d710\u22128\n1.5\u00d71030\n2.9\n1.1\u00d710\u221226\n5.2\u00d710\u221227\n-5.1\n-10\nF-statistic 1.4\u00d710\u221226\n2.7\u00d710\u22128\nJ0537 2.1\u00d71030\n4.1\n1.6\u00d710\u221226\n6.5\u00d710\u221227\n0.47\n0.04\n5n-vector\n9.3\u00d710\u221227\n1.7\u00d710\u22128\n1.3\u00d71030\n2.6\n5.8\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.61\n0.038\nJ0058\u22127218\u03b2\n45.94 \u22126.1\u00d710\u221211\n59.70b\n1.56\u00d710\u221226\nBayesian\n8.8\u00d710\u221227\n5.9\u00d710\u22125\n4.5\u00d71033\n0.56\n2.4\u00d710\u221226\n4.4\u00d710\u221227\n-5.3\n-10\nF-statistic 4.9\u00d710\u221227\n3.3\u00d710\u22125\n2.5\u00d71033\n0.31\n3.5\u00d710\u221226\n6.2\u00d710\u221227\n0.32\n0.86\n5n-vector\n6.5\u00d710\u221227\n4.4\u00d710\u22125\n3.4\u00d71033\n0.41\n9.4\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n1\n0.80\nJ0117+5914\u03b3\n9.86 \u22125.69\u00d710\u221213\n1.77c\n1.1\u00d710\u221225\nBayesian\n1.7\u00d710\u221225\n7.4\u00d710\u22124\n5.8\u00d71034\n1.6\n7.7\u00d710\u221223\n8.8\u00d710\u221226\n-3.8\n-4.9\nF-statistic 2.3\u00d710\u221225\n1.0\u00d710\u22123\n7.8\u00d71034\n2.2\n8.4\u00d710\u221223\n1.2\u00d710\u221225\n0.39\n0.06\n5n-vector\n3.2\u00d710\u221225\n1.4\u00d710\u22123\n1.1\u00d71035\n2.9\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n0.87\nJ0205+6449\u03b3\n15.22 \u22124.49\u00d710\u221211\n3.20d\n4.33\u00d710\u221225\nBayesian\n3.2(4.2)\u00d710\u221226\n1.0(1.4)\u00d710\u22124\n8.0(10)\u00d71033\n0.073(0.096)\n5.6(4.8)\u00d710\u221225\n1.5(2.0)\u00d710\u221226\n-4.7(-4.5)\n-8.3(-8.3)\nF-statistic 2.4(4.4)\u00d710\u221226\n0.8(1.5)\u00d710\u22124\n6.0(10)\u00d71033\n0.055(0.10)\n1.3(0.56)\u00d710\u221224\n1.1(2.2)\u00d710\u221226\n0.24(0.44)\n0.75(0.47)\n5n-vector\n2.2(3.4)\u00d710\u221226\n0.72(1.1)\u00d710\u22124\n5.6(8.6)\u00d71033\n0.051(0.078)\n(5.7)\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.86\n0.84\nJ0437\u22124715\u03b4\n173.69 \u22124.15\u00d710\u221216\n0.16e\n7.95\u00d710\u221227\nBayesian\n7.2\u00d710\u221227\n8.8\u00d710\u22129\n6.8\u00d71029\n0.90\n1.1\u00d710\u221226\n3.4\u00d710\u221227\n-5.4\n-10\nF-statistic 9.0\u00d710\u221227\n1.1\u00d710\u22128\n8.5\u00d71029\n1.1\n1.5\u00d710\u221226\n4.4\u00d710\u221227\n0.31\n0.26\n5n-vector\n5.8\u00d710\u221227\n7.1\u00d710\u22129\n5.5\u00d71029\n0.32\n5.1\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.75\n0.38\nJ0534+2200\u03b3\n29.95 \u22123.78\u00d710\u221210\n2.00f\n1.43\u00d710\u221224\nBayesian\n1.1(0.9)\u00d710\u221226\n5.9(5.0)\u00d710\u22126\n4.6(3.9)\u00d71032\n0.0078(0.0067) 6.6(6.0)\u00d710\u221226\n5.4(4.5)\u00d710\u221227\n-5.1(-5.2)\n-9.5(-9.2)\nF-statistic 1.5(1.2)\u00d710\u221226\n8.0(6.3)\u00d710\u22126\n6.3(4.9)\u00d71032\n0.011(0.0085)\n9.4(7.0)\u00d710\u221226\n8.8(6.1)\u00d710\u221227\n0.19(0.18)\n0.30(0.36)\n5n-vector\n1.1(1.1)\u00d710\u221226\n5.7(5.8)\u00d710\u22126\n4.3(4.4)\u00d71032\n0.0074(0.0075) 2.6(2.6)\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.97\n0.44\nJ0537\u22126910\u03b2\n62.03 \u22121.99\u00d710\u221210\n49.70g\n2.91\u00d710\u221226\nBayesian\n6.4(8.9)\u00d710\u221227\n2.0(2.7)\u00d710\u22125\n1.5(2.1)\u00d71033\n0.22(0.31)\n2.4(1.4)\u00d710\u221226\n3.0(4.7)\u00d710\u221227\n-5.5(-5.3)\n-10.2(-10.4)\nF-statistic 8.8(4.5)\u00d710\u221227\n2.7(1.4)\u00d710\u22125\n2.0(1.0)\u00d71033\n0.29(0.15)\n3.2(9.0)\u00d710\u221226\n2.0(2.9)\u00d710\u221227\n0.24(0.25)\n1.00(0.92)\n5n-vector\n0.79(1.2)\u00d710\u221226\n2.4(3.7)\u00d710\u22125\n1.9(2.8)\u00d71033\n0.27(0.41)\n0.98(1.5)\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.45\n0.34\nJ0540\u22126919\u03b2\n19.77 \u22121.87\u00d710\u221210\n49.70g\n4.99\u00d710\u221226\nBayesian\n2.7(3.4)\u00d710\u221226\n8.1(10)\u00d710\u22124\n6.3(7.9)\u00d71034\n0.54(0.69)\n1.9(1.6)\u00d710\u221225\n1.4(1.7)\u00d710\u221226\n-4.6(-4.2)\n-8.5(-8.4)\nF-statistic 2.9(2.9)\u00d710\u221226\n8.6(8.6)\u00d710\u22124\n6.7(6.7)\u00d71034\n0.58(0.58)\n2.9(8.8)\u00d710\u221225\n1.4(1.5)\u00d710\u221226\n0.53(0.34)\n0.32(0.45)\n5n-vector\n1.6(2.4)\u00d710\u221226\n4.8(7.3)\u00d710\u22124\n3.7(5.6)\u00d71034\n0.27(0.41)\n3.7(5.7)\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.66\n0.76\nJ0614\u22123329\u03b1\n317.59 \u22121.76\u00d710\u221215\n0.63h\n3.01\u00d710\u221227\nBayesian\n1.1\u00d710\u221226\n1.6\u00d710\u22128\n1.2\u00d71030\n3.6\n8.9\u00d710\u221227\n5.4\u00d710\u221227\n-5.1\n-10\nF-statistic 1.1\u00d710\u221226\n3.1\u00d710\u22128\n2.4\u00d71030\n3.6\n1.0\u00d710\u221226\n5.3\u00d710\u221227\n0.66\n0.31\n5n-vector\n8.0\u00d710\u221227\n1.2\u00d710\u22128\n9.1\u00d71029\n2.7\n7.3\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.15\n0.21\nJ0737\u22123039A\u03b1\n44.05 \u22123.41\u00d710\u221215\n1.10i\n6.45\u00d710\u221227\nBayesian\n8.9\u00d710\u221227\n1.2\u00d710\u22126\n9.2\u00d71031\n1.4\n1.8\u00d710\u221226\n4.3\u00d710\u221227\n-5.3\n-10\nF-statistic 7.5\u00d710\u221227\n1.0\u00d710\u22126\n7.6\u00d71031\n1.2\n1.7\u00d710\u221225\n6.4\u00d710\u221227\n0.99\n0.87\n5n-vector\n6.2\u00d710\u221227\n8.3\u00d710\u22127\n6.4\u00d71031\n0.96\n1.4\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.49\n0.92\nJ0835\u22124510\u03f5\n11.19 \u22121.57\u00d710\u221211\n0.28i\n3.41\u00d710\u221224\nBayesian\n9.0(7.7)\u00d710\u221226\n4.7(4.1)\u00d710\u22125\n3.7(3.1)\u00d71033\n0.026(0.023)\n2.9(2.4)\u00d710\u221224\n4.1(3.7)\u00d710\u221226\n-4.1(-4.1)\n-7.1(-7.1)\nF-statistic 8.2(8.2)\u00d710\u221226\n4.4(4.3)\u00d710\u22125\n3.4(3.3)\u00d71033\n0.024(0.024)\n3.5(2.3)\u00d710\u221224\n4.0(3.9)\u00d710\u221226\n0.65(0.81)\n0.45(0.19)\n5n-vector\n8.5(8.7)\u00d710\u221226\n4.5(4.6)\u00d710\u22125\n3.5(3.6)\u00d71033\n0.025(0.025)\n2.7(2.8)\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.66\n0.17\nJ1231\u22121411\u03b1\n271.45 \u22125.92\u00d710\u221216\n0.42c\n2.83\u00d710\u221227\nBayesian\n1.2\u00d710\u221226\n1.6\u00d710\u22128\n1.2\u00d71030\n4.1\n1.2\u00d710\u221226\n5.9\u00d710\u221227\n-4.6\n-9.9\nF-statistic 1.2\u00d710\u221226\n1.6\u00d710\u22128\n1.2\u00d71030\n4.1\n1.7\u00d710\u221226\n5.9\u00d710\u221227\n0.14\n0.14\n5n-vector\n6.6\u00d710\u221227\n8.9\u00d710\u22129\n6.9\u00d71029\n1.4\n5.4\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.68\n0.51\nTable 2 continued\n\n26\nTable 2 (continued)\nPulsar Name\nfrot\n\u02d9Prot\nDistance\nhsd\n0\nAnalysis\nh95%\n0\n\u03b595%\nQ95%\n22\nh95%\n0\nhsd\n0\nC95%\n21\nC95%\n22\nStatistic@\nStatistic#\n(J2000)\n(Hz)\n(s s\u22121)\n(kpc)\nMethod\n(kg m2)\nl=2,m=1,2\nl=2,m=2\nJ1412+7922\u03b2\n17.18 \u22129.72\u00d710\u221213\n3.30j\n5.81\u00d710\u221226\nBayesian\n3.1\u00d710\u221226\n8.2\u00d710\u22125\n6.3\u00d71033\n0.53\n9.9\u00d710\u221225\n1.4\u00d710\u221226\n-4.7\n-8.0\nF-statistic 2.5\u00d710\u221226\n6.6\u00d710\u22125\n5.1\u00d71033\n0.43\n1.2\u00d710\u221224\n1.3\u00d710\u221226\n0.17\n0.57\n5n-vector\n2.3\u00d710\u221226\n6.4\u00d710\u22125\n4.9\u00d71033\n0.4\n4.0\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n1\n0.44\nJ1537+1155\u03b1\n26.38 \u22121.65\u00d710\u221215\n0.93k\n6.82\u00d710\u221227\nBayesian\n1.3\u00d710\u221226\n4.0\u00d710\u22126\n3.1\u00d71032\n1.8\n8.5\u00d710\u221226\n5.6\u00d710\u221227\n-5.2\n-9.6\nF-statistic 1.3\u00d710\u221226\n4.0\u00d710\u22126\n3.1\u00d71032\n1.8\n7.1\u00d710\u221226\n6.4\u00d710\u221227\n0.62\n0.91\n5n-vector\n1.6\u00d710\u221226\n5.0\u00d710\u22126\n3.9\u00d71032\n2.3\n3.3\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.90\n0.22\nJ1623\u22122631\u03b3\n90.29 \u22125.26\u00d710\u221215\n1.85l\n3.33\u00d710\u221227\nBayesian\n8.5\u00d710\u221227\n4.6\u00d710\u22127\n3.5\u00d71031\n2.6\n1.4\u00d710\u221226\n4.1\u00d710\u221227\n-5.2\n-10\nF-statistic 1.0\u00d710\u221226\n5.4\u00d710\u22127\n4.1\u00d71031\n3.1\n1.2\u00d710\u221226\n5.2\u00d710\u221227\n0.79\n0.19\n5n-vector\n5.6\u00d710\u221227\n3.0\u00d710\u22127\n2.3\u00d71031\n1.2\n6.8\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.78\n0.68\nJ1719\u22121438\u03b1\n172.71 \u22122.22\u00d710\u221216\n0.34c\n2.72\u00d710\u221227\nBayesian\n8.7\u00d710\u221227\n2.3\u00d710\u22128\n1.8\u00d71030\n3.2\n1.3\u00d710\u221226\n3.7\u00d710\u221227\n-5.3\n-10\nF-statistic 7.4\u00d710\u221227\n2.0\u00d710\u22128\n1.6\u00d71030\n2.8\n2.0\u00d710\u221226\n3.5\u00d710\u221227\n0.20\n0.51\n5n-vector\n7.4\u00d710\u221227\n2.0\u00d710\u22128\n1.5\u00d71030\n2.6\n7.0\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.33\n0.14\nJ1744\u22121134\u03b1\n245.43 \u22124.34\u00d710\u221216\n0.40e\n2.72\u00d710\u221227\nBayesian\n9.2\u00d710\u221227\n1.4\u00d710\u22128\n1.1\u00d71030\n3.4\n1.1\u00d710\u221226\n4.4\u00d710\u221227\n-5.0\n-10\nF-statistic 1.4\u00d710\u221226\n2.1\u00d710\u22128\n1.7\u00d71030\n5.2\n1.2\u00d710\u221226\n7.1\u00d710\u221227\n0.34\n0.02\n5n-vector\n5.7\u00d710\u221227\n8.8\u00d710\u22129\n6.8\u00d71029\n1.9\n8.8\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.11\n0.69\nJ1745\u22120952\u03b1\n51.61 \u22122.3\u00d710\u221216\n0.23c\n7.5\u00d710\u221227\nBayesian\n1.1\u00d710\u221226\n2.1\u00d710\u22127\n1.6\u00d71031\n1.4\n2.6\u00d710\u221226\n5.0\u00d710\u221227\n-5.3\n-9.7\nF-statistic 8.6\u00d710\u221227\n1.6\u00d710\u22127\n1.3\u00d71031\n1.4\n1.6\u00d710\u221226\n4.4\u00d710\u221227\n0.66\n0.62\n5n-vector\n1.2\u00d710\u221226\n2.5\u00d710\u22127\n1.9\u00d71031\n1.6\n1.1\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.91\n0.023\nJ1756\u22122251\u03b3\n35.14 \u22121.26\u00d710\u221215\n0.73m\n6.6\u00d710\u221227\nBayesian\n1.1\u00d710\u221226\n1.5\u00d710\u22126\n1.2\u00d71032\n1.6\n5.6\u00d710\u221226\n5.4\u00d710\u221227\n-5.1\n-9.4\nF-statistic 1.6\u00d710\u221226\n2.2\u00d710\u22126\n1.7\u00d71032\n2.3\n6.3\u00d710\u221226\n7.1\u00d710\u221227\n0.17\n0.22\n5n-vector\n1.0\u00d710\u221226\n1.5\u00d710\u22126\n1.1\u00d71032\n1.6\n3.1\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.031\n0.31\nJ1809\u22121917\u03b3\n12.08 \u22123.73\u00d710\u221212\n3.27c\n1.37\u00d710\u221225\nBayesian\n8.1\u00d710\u221226\n4.3\u00d710\u22124\n3.3\u00d71034\n0.59\n3.0\u00d710\u221224\n3.9\u00d710\u221226\n-4.2\n-7.0\nF-statistic 7.9\u00d710\u221226\n4.7\u00d710\u22124\n3.6\u00d71034\n0.65\n4.3\u00d710\u221224\n3.9\u00d710\u221226\n0.52\n0.05\n5n-vector\n4.0\u00d710\u221226\n2.1\u00d710\u22124\n1.6\u00d71034\n0.28\n2.7\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.079\n0.64\nJ1811\u22121925\u03b2\n15.46 \u22121.05\u00d710\u221211\n5.00n\n1.33\u00d710\u221225\nBayesian\n2.6\u00d710\u221226\n1.3\u00d710\u22124\n1.0\u00d71034\n0.20\n7.3\u00d710\u221225\n1.3\u00d710\u221226\n-4.8\n-8.1\nF-statistic 3.3\u00d710\u221226\n1.7\u00d710\u22124\n1.3\u00d71034\n0.25\n4.3\u00d710\u221225\n1.7\u00d710\u221226\n0.67\n0.85\n5n-vector\n3.3\u00d710\u221226\n1.6\u00d710\u22124\n1.2\u00d71034\n0.24\n6.1\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.23\n0.23\nJ1813\u22121246\u03ba\n20.80 \u22127.6\u00d710\u221212\n2.63o\n1.85\u00d710\u221225\nBayesian\n1.5\u00d710\u221226\n2.2\u00d710\u22125\n1.7\u00d71033\n0.082\n1.4\u00d710\u221225\n7.8\u00d710\u221227\n-5.0\n-9.1\nF-statistic 3.1\u00d710\u221226\n4.7\u00d710\u22125\n3.4\u00d71033\n0.055\n1.3\u00d710\u221225\n1.5\u00d710\u221226\n0.72\n0.07\n5n-vector\n1.6\u00d710\u221226\n2.3\u00d710\u22125\n1.8\u00d71033\n0.087\n7.7\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.73\n0.50\nJ1813\u22121749\u03b8\n22.35 \u22126.34\u00d710\u221211\n6.15c\n2.21\u00d710\u221225\nBayesian\n2.4\u00d710\u221226\n6.9\u00d710\u22125\n5.3\u00d71033\n0.11\n8.8\u00d710\u221226\n1.2\u00d710\u221226\n-4.4\n-8.7\nF-statistic 3.1\u00d710\u221226\n8.9\u00d710\u22125\n6.8\u00d71033\n0.14\n5.3\u00d710\u221226\n1.5\u00d710\u221226\n0.91\n0.02\n5n-vector\n1.8\u00d710\u221226\n5.3\u00d710\u22125\n4.1\u00d71033\n0.083\n6.6\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.53\n0.12\nJ1823\u22123021A\u03b3\n183.82 \u22121.14\u00d710\u221213\n8.02l\n2.5\u00d710\u221227\nBayesian\n7.5\u00d710\u221227\n4.2\u00d710\u22127\n3.3\u00d71031\n3.0\n1.6\u00d710\u221226\n4.0\u00d710\u221227\n-5.2\n-9.7\nF-statistic 4.9\u00d710\u221227\n2.7\u00d710\u22127\n2.2\u00d71031\n2.0\n2.3\u00d710\u221226\n3.5\u00d710\u221227\n0.12\n0.78\n5n-vector\n4.5\u00d710\u221227\n2.5\u00d710\u22127\n1.9\u00d71031\n1.8\n6.5\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.40\n0.91\nTable 2 continued\n\n27\nTable 2 (continued)\nPulsar Name\nfrot\n\u02d9Prot\nDistance\nhsd\n0\nAnalysis\nh95%\n0\n\u03b595%\nQ95%\n22\nh95%\n0\nhsd\n0\nC95%\n21\nC95%\n22\nStatistic@\nStatistic#\n(J2000)\n(Hz)\n(s s\u22121)\n(kpc)\nMethod\n(kg m2)\nl=2,m=1,2\nl=2,m=2\nJ1824\u22122452A\u03b1\n327.41 \u22121.73\u00d710\u221213\n5.37l\n3.45\u00d710\u221227\nBayesian\n8.1\u00d710\u221227\n9.6\u00d710\u22128\n7.4\u00d71030\n2.4\n1.5\u00d710\u221226\n3.7\u00d710\u221227\n-5.2\n-10.0\nF-statistic 7.0\u00d710\u221227\n8.3\u00d710\u22128\n6.4\u00d71030\n2.4\n2.2\u00d710\u221226\n3.3\u00d710\u221227\n0.10\n0.70\n5n-vector\n6.3\u00d710\u221227\n7.4\u00d710\u22128\n5.8\u00d71030\n1.8\n7.2\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.17\n0.64\nJ1826\u22121334\u03b3\n9.85 \u22127.31\u00d710\u221212\n3.61c\n1.93\u00d710\u221225\nBayesian\n1.5\u00d710\u221225\n1.3\u00d710\u22123\n1.0\u00d71035\n0.79\n4.9\u00d710\u221223\n7.0\u00d710\u221226\n-3.8\n-5.7\nF-statistic 1.5\u00d710\u221225\n1.3\u00d710\u22123\n1.0\u00d71035\n0.79\n3.7\u00d710\u221223\n7.6\u00d710\u221226\n0.42\n0.39\n5n-vector\n4.3\u00d710\u221225\n3.7\u00d710\u22123\n2.9\u00d71035\n2.2\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n0.42\nJ1828\u22121101\u03b3\n13.88 \u22122.85\u00d710\u221212\n4.77c\n7.67\u00d710\u221226\nBayesian\n4.2\u00d710\u221226\n2.5\u00d710\u22124\n1.9\u00d71034\n0.55\n5.3\u00d710\u221224\n2.1\u00d710\u221226\n-4.6\n-7.4\nF-statistic 3.5\u00d710\u221226\n2.1\u00d710\u22124\n1.6\u00d71034\n0.46\n3.1\u00d710\u221224\n2.1\u00d710\u221226\n0.98\n0.75\n5n-vector\n5.9\u00d710\u221226\n3.5\u00d710\u22124\n2.7\u00d71034\n0.78\n3.8\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.66\n0.19\nJ1831\u22120952\u03b3\n14.87 \u22121.84\u00d710\u221212\n3.68c\n7.7\u00d710\u221226\nBayesian\n4.2\u00d710\u221226\n1.6\u00d710\u22124\n1.3\u00d71034\n0.54\n6.4\u00d710\u221225\n1.9\u00d710\u221226\n-4.6\n-8.0\nF-statistic 3.2\u00d710\u221226\n1.2\u00d710\u22124\n0.99\u00d71034\n0.41\n9.1\u00d710\u221225\n2.1\u00d710\u221226\n0.44\n0.64\n5n-vector\n2.9\u00d710\u221226\n1.2\u00d710\u22124\n9.0\u00d71033\n0.38\n5.2\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.85\n0.77\nJ1833\u22120827\u03b3\n11.72 \u22121.26\u00d710\u221212\n4.50i\n5.88\u00d710\u221226\nBayesian\n6.2\u00d710\u221226\n4.8\u00d710\u22124\n3.7\u00d71034\n1.0\n2.7\u00d710\u221224\n3.0\u00d710\u221226\n-4.4\n-7.2\nF-statistic 5.4\u00d710\u221226\n4.2\u00d710\u22124\n3.2\u00d71034\n0.87\n3.5\u00d710\u221224\n2.8\u00d710\u221226\n0.40\n0.66\n5n-vector\n6.4\u00d710\u221226\n4.9\u00d710\u22124\n3.8\u00d71034\n1.1\n2.4\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.43\n0.35\nJ1837\u22120604\u03b3\n10.38 \u22124.84\u00d710\u221212\n4.78c\n1.15\u00d710\u221225\nBayesian\n7.8\u00d710\u221226\n8.2\u00d710\u22124\n6.3\u00d71034\n0.68\n5.6\u00d710\u221224\n3.6\u00d710\u221226\n-4.4\n-7.0\nF-statistic 8.8\u00d710\u221226\n9.3\u00d710\u22124\n7.1\u00d71034\n0.77\n1.2\u00d710\u221224\n3.6\u00d710\u221227\n0.97\n0.95\n5n-vector\n9.3\u00d710\u221226\n9.8\u00d710\u22124\n7.6\u00d71034\n0.80\n4.7\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.98\n0.43\nJ1838\u22120655\u03b2\n14.18 \u22129.9\u00d710\u221212\n6.60p\n1.02\u00d710\u221225\nBayesian\n6.6\u00d710\u221226\n5.1\u00d710\u22124\n4.0\u00d71034\n0.65\n1.3\u00d710\u221224\n3.4\u00d710\u221226\n-3.8\n-6.7\nF-statistic 7.1\u00d710\u221226\n5.5\u00d710\u22124\n4.3\u00d71034\n0.70\n2.6\u00d710\u221224\n3.6\u00d710\u221226\n0.15\n0.04\n5n-vector\n4.2\u00d710\u221226\n3.3\u00d710\u22124\n2.5\u00d71034\n0.41\n8.3\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.69\n0.29\nJ1849\u22120001\u03b2\n25.96 \u22129.54\u00d710\u221212\n7.00q\n6.98\u00d710\u221226\nBayesian\n1.4\u00d710\u221226\n3.3\u00d710\u22125\n2.6\u00d71033\n0.19\n1.3\u00d710\u221225\n6.0\u00d710\u221227\n-5.2\n-9.1\nF-statistic 1.7\u00d710\u221226\n4.0\u00d710\u22125\n3.2\u00d71033\n0.23\n1.4\u00d710\u221225\n8.1\u00d710\u221227\n0.18\n0.47\n5n-vector\n1.4\u00d710\u221226\n3.4\u00d710\u22125\n2.6\u00d71033\n0.2\n6.3\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.078\n0.77\nJ1856+0245\u03b3\n12.36 \u22129.49\u00d710\u221212\n6.32c\n1.12\u00d710\u221225\nBayesian\n5.8\u00d710\u221226\n5.7\u00d710\u22124\n4.4\u00d71034\n0.52\n1.3\u00d710\u221224\n2.9\u00d710\u221226\n-4.4\n-7.8\nF-statistic 5.3\u00d710\u221226\n5.2\u00d710\u22124\n4.0\u00d71034\n0.48\n1.8\u00d710\u221224\n2.5\u00d710\u221226\n0.69\n0.66\n5n-vector\n5.2\u00d710\u221226\n5.1\u00d710\u22124\n4.0\u00d71034\n0.47\n1.4\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.85\n0.40\nJ1913+1011\u03b3\n27.85 \u22122.62\u00d710\u221212\n4.61c\n5.36\u00d710\u221226\nBayesian\n1.1\u00d710\u221226\n1.6\u00d710\u22125\n1.2\u00d71033\n0.21\n6.5\u00d710\u221226\n5.2\u00d710\u221227\n-5.2\n-9.7\nF-statistic 1.2\u00d710\u221226\n1.7\u00d710\u22125\n1.3\u00d71033\n0.23\n4.0\u00d710\u221226\n5.8\u00d710\u221227\n0.96\n0.60\n5n-vector\n1.2\u00d710\u221226\n1.8\u00d710\u22125\n1.4\u00d71033\n0.23\n3.6\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.89\n0.35\nJ1925+1720\u03b3\n13.22 \u22121.83\u00d710\u221212\n5.05c\n5.94\u00d710\u221226\nBayesian\n5.9\u00d710\u221226\n4.1\u00d710\u22124\n3.1\u00d71034\n1.0\n2.2\u00d710\u221224\n2.8\u00d710\u221226\n-4.2\n-6.2\nF-statistic 5.4\u00d710\u221226\n3.8\u00d710\u22124\n2.8\u00d71034\n0.92\n4.2\u00d710\u221224\n2.9\u00d710\u221226\n0.03\n0.33\n5n-vector\n6.8\u00d710\u221226\n4.6\u00d710\u22124\n3.6\u00d71034\n1.1\n1.5\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.29\n0.014\nJ1935+2025\u03b3\n12.48 \u22129.47\u00d710\u221212\n4.60c\n1.53\u00d710\u221225\nBayesian\n5.5\u00d710\u221226\n3.8\u00d710\u22124\n3.0\u00d71034\n0.36\n1.5\u00d710\u221224\n2.6\u00d710\u221226\n-4.6\n-7.8\nF-statistic 4.8\u00d710\u221226\n3.3\u00d710\u22124\n2.6\u00d71034\n0.31\n7.7\u00d710\u221225\n2.3\u00d710\u221226\n0.98\n0.69\n5n-vector\n3.7\u00d710\u221226\n2.6\u00d710\u22124\n2.0\u00d71034\n0.24\n1.6\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.57\n0.81\nTable 2 continued\n\n28\nTable 2 (continued)\nPulsar Name\nfrot\n\u02d9Prot\nDistance\nhsd\n0\nAnalysis\nh95%\n0\n\u03b595%\nQ95%\n22\nh95%\n0\nhsd\n0\nC95%\n21\nC95%\n22\nStatistic@\nStatistic#\n(J2000)\n(Hz)\n(s s\u22121)\n(kpc)\nMethod\n(kg m2)\nl=2,m=1,2\nl=2,m=2\nJ1952+3252\u03b3\n25.30 \u22123.74\u00d710\u221212\n3.00i\n1.03\u00d710\u221225\nBayesian\n1.1(1.0)\u00d710\u221226\n1.2(1.1)\u00d710\u22125\n9.2(8.2)\u00d71032\n0.10(0.09)\n1.9(68)\u00d710\u221225\n4.2(2.8)\u00d710\u221227\n-5.3(-5.4)\n-8.6(-8.2)\nF-statistic 1.0\u00d710\u221226\n1.1\u00d710\u22125\n8.4\u00d71032\n0.091\n2.2\u00d710\u221225\n4.4\u00d710\u221227\n0.03\n0.77\n5n-vector\n1.1(1.1)\u00d710\u221226\n1.2(1.2)\u00d710\u22125\n9.1(9.5)\u00d71032\n0.1(0.11)\n5.1(5.1)\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.54\n0.72\nJ2016+3711\u03b6\n19.68 \u22122.81\u00d710\u221211\n6.10r\n1.58\u00d710\u221225\nBayesian\n2.0\u00d710\u221226\n7.4\u00d710\u22125\n5.7\u00d71033\n0.13\n1.6\u00d710\u221225\n8.8\u00d710\u221227\n-5.0\n-9.1\nF-statistic 3.2\u00d710\u221226\n1.2\u00d710\u22124\n9.1\u00d71033\n0.21\n1.2\u00d710\u221225\n1.7\u00d710\u221226\n0.84\n0.07\n5n-vector\n3.0\u00d710\u221226\n2.4\u00d710\u22124\n1.9\u00d71034\n0.41\n3.8\u00d710\u221225\n\u00b7 \u00b7 \u00b7\n0.62\n0.020\nJ2021+3651\u03b3\n9.64 \u22128.89\u00d710\u221212\n1.80s\n4.3\u00d710\u221225\nBayesian\n2.3(2.2)\u00d710\u221225\n1.0(1.0)\u00d710\u22123\n8.0(7.7)\u00d71034\n0.53(0.51)\n6.0(5.0)\u00d710\u221223\n1.1(1.1)\u00d710\u221225\n-3.1(-3.2)\n-4.9(-5.2)\nF-statistic 2.2(2.1)\u00d710\u221225\n0.96(0.95)\u00d710\u22123\n7.7(7.4)\u00d71034\n0.51(0.49)\n2.0(1.3)\u00d710\u221222\n1.1(1.1)\u00d710\u221225\n0.09(0.65)\n0.08(0.13)\n5n-vector\n2.8(4.0)\u00d710\u221225\n1.3(1.8)\u00d710\u22123\n1(1.4)\u00d71035\n0.66(0.93)\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n\u00b7 \u00b7 \u00b7\n1\nJ2022+3842\u03b2\n20.59 \u22123.65\u00d710\u221211\n10.00t\n1.07\u00d710\u221225\nBayesian\n1.9\u00d710\u221226\n1.0\u00d710\u22124\n8.1\u00d71033\n0.18\n1.4\u00d710\u221225\n8.6\u00d710\u221227\n-5.0\n-9.1\nF-statistic 1.7\u00d710\u221226\n8.9\u00d710\u22125\n7.2\u00d71033\n0.16\n8.0\u00d710\u221226\n9.0\u00d710\u221227\n0.90\n0.60\n5n-vector\n1.4\u00d710\u221226\n7.5\u00d710\u22125\n5.8\u00d71033\n0.13\n6.3\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n1\n0.77\nJ2043+2740\u03b3\n10.40 \u22121.37\u00d710\u221213\n1.48c\n6.26\u00d710\u221226\nBayesian\n1.1\u00d710\u221225\n3.7\u00d710\u22124\n2.8\u00d71034\n1.8\n1.2\u00d710\u221223\n5.2\u00d710\u221226\n-4.1\n-6.0\nF-statistic 1.0\u00d710\u221225\n3.4\u00d710\u22124\n2.5\u00d71034\n1.6\n1.3\u00d710\u221223\n4.4\u00d710\u221226\n0.42\n0.78\n5n-vector\n7.9\u00d710\u221226\n2.5\u00d710\u22124\n2.0\u00d71034\n1.2\n6.9\u00d710\u221224\n\u00b7 \u00b7 \u00b7\n0.26\n0.65\nJ2124\u22123358\u03b1\n202.79 \u22122.94\u00d710\u221216\n0.41e\n2.37\u00d710\u221227\nBayesian\n9.2\u00d710\u221227\n2.2\u00d710\u22128\n1.7\u00d71030\n3.9\n9.9\u00d710\u221227\n4.8\u00d710\u221227\n-5.0\n-10\nF-statistic 9.7\u00d710\u221227\n2.3\u00d710\u22128\n1.8\u00d71030\n4.1\n9.5\u00d710\u221227\n4.8\u00d710\u221227\n0.78\n0.23\n5n-vector\n5.4\u00d710\u221227\n1.3\u00d710\u22128\n9.8\u00d71029\n1.3\n5.1\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.73\n0.62\nJ2214+3000\u03b7\n320.59 \u22121.31\u00d710\u221215\n0.60u\n2.71\u00d710\u221227\nBayesian\n9.0\u00d710\u221227\n1.2\u00d710\u22128\n9.6\u00d71029\n3.3\n8.6\u00d710\u221227\n4.6\u00d710\u221227\n-5.3\n-10\nF-statistic 4.5\u00d710\u221227\n0.60\u00d710\u22128\n4.8\u00d71029\n1.7\n9.0\u00d710\u221227\n5.8\u00d710\u221227\n0.81\n0.87\n5n-vector\n5.4\u00d710\u221227\n7.4\u00d710\u22129\n5.7\u00d71029\n1.8\n7.5\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.11\n0.84\nJ2222\u22120137\u03b1\n30.47 \u22124.99\u00d710\u221216\n0.27v\n1.22\u00d710\u221226\nBayesian\n1.3\u00d710\u221226\n9.0\u00d710\u22127\n6.9\u00d71031\n1.1\n4.1\u00d710\u221226\n6.4\u00d710\u221227\n-5.1\n-9.7\nF-statistic 2.2\u00d710\u221226\n1.5\u00d710\u22126\n1.2\u00d71032\n1.9\n5.0\u00d710\u221226\n1.1\u00d710\u221226\n0.93\n0.06\n5n-vector\n1.3\u00d710\u221226\n9.1\u00d710\u22127\n7.0\u00d71031\n3.3\n4.9\u00d710\u221226\n\u00b7 \u00b7 \u00b7\n0.016\n0.15\nJ2229+6114\u03b3\n19.36 \u22122.9\u00d710\u221211\n3.00w\n3.29\u00d710\u221225\nBayesian\n1.5(0.9)\u00d710\u221226\n2.8(1.8)\u00d710\u22125\n2.2(1.4)\u00d71033\n0.045(0.028)\n1.8(1.6)\u00d710\u221225\n6.8(4.6)\u00d710\u221227\n-5.1(-5.3)\n-9.2(-9.4)\nF-statistic 1.5(0.63)\u00d710\u221226\n2.9(1.2)\u00d710\u22125\n2.2(0.98)\u00d71033\n0.046(0.032)\n2.9(2.5)\u00d710\u221225\n4.7(2.5)\u00d710\u221227\n0.24(0.41)\n0.99(0.99)\n5n-vector\n1.3(0.99)\u00d710\u221226\n2.4(1.9)\u00d710\u22125\n1.8(1.4)\u00d71033\n0.037(0.029)\n3.9(3.2)\u00d710\u221227\n\u00b7 \u00b7 \u00b7\n0.75\n0.88\nReferences\u2014 The last two columns refers to the significance of the data against the noise hypothesis (@ for the dual-harmonic emission model,\n# for the single-harmonic emission model). For the Bayesian method, the columns show the base-10 logarithm of the Bayesian odds, comparing\na coherent signal model modes to incoherent signal models. For the F-statistic and the 5n-vector method, the columns show the p-value (for the\n5n-vector method, considering a signal at just the l = 2 , m = 1 mode for the dual-harmonic emission model).\nReferences\u2014The following is a list of references for pulsar ephemeris data used in this analysis: Nancay: \u03b1, NICER: \u03b2, JBO: \u03b3, IAR: \u03b4, Hobart:\n\u03f5, FAST: \u03b6, CHIME: \u03b7, Chandra: \u03b8, Fermi-LAT: \u03ba.\nReferences\u2014The following is a list of references for pulsar distances and intrinsic period derivatives, and they should be consulted for information\non the associated uncertainties on these quantities: (a) Ding et al. (2023), (b) Storm et al. (2004), (c) Yao et al. (2017), (d) Roberts et al. (1993),\n(e) Reardon et al. (2016), (f) Trimble (1968), (g) Walker (2012), (h) Bassa et al. (2016), (i) Verbiest et al. (2012), (j) Mereghetti et al. (2021),\n(k) Ding et al. (2021), (l) Baumgardt & Vasiliev (2021), (m) Ferdman et al. (2014), (n) Green et al. (1988), (o) Torres et al. (2019), (p) Lin et al.\n(2009), (q) H. E. S. S. Collaboration et al. (2018), (r) Liu et al. (2024), (s) Kirichenko et al. (2015), (t) Arzoumanian et al. (2011), (u) Guillemot\net al. (2016), (v) Guo et al. (2021), (w) Halpern et al. (2001).\n\n29\nREFERENCES\nAasi, J., Abadie, J., Abbott, B. P., et al. 2014, ApJ, 785,\n119, doi: 10.1088/0004-637X/785/2/119\nAbac, A. G., Abbott, R., Abouelfettouh, I., et al. 2024a, A\nsearch using GEO600 for gravitational waves coincident\nwith fast radio bursts from SGR 1935+2154.\nhttps://arxiv.org/abs/2410.09151\n\u2014. 2024b, The Astrophysical Journal Letters, 970, L34,\ndoi: 10.3847/2041-8213/ad5beb\nAbadie, J., Abbott, B. P., Abbott, R., et al. 2011, ApJ,\n737, 93, doi: 10.1088/0004-637X/737/2/93\nAbbott, B. P., Abbott, R., Abbott, T. 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As a reference,\nwe list also the number of templates, Ntrials, in the f \u2212\u02d9f plane. We report as well the lowest p-value found in the analysis\nwith the corresponding threshold set after correcting a FAP of 10\u22122 for the trial factor. The nomenclature \u201dpg\u201d identifies the\npost-glitch analysis.\nPulsar Name\nNtrials\nh95%\n0\nh95%\n0\n/hsd\n0\nLowest p-value\nThreshold p-value\n(J2000)\n\u00d7106\n\u00d710\u221226\n\u00d710\u22125\n\u00d710\u221211\nJ0205+6449\n90\n9.60\n0.22\n1.54\n1.10\nJ0534+2200\n1383\n4.16\n0.03\n0.77\n0.07\nJ0537-6910\n298\n3.52\n1.21\n0.13\n0.33\nJ0537-6910 pg\n119\n3.75\n1.29\n4 \u00b7 10\u22124\n0.84\nJ0540-6919\n11\n14.23\n2.45\n0.44\n8.95\nJ0540-6919 pg\n248\n7.38\n1.27\n0.02\n0.40\nJ0835-4510\n23\n21.53\n0.06\n8.50\n4.18\nJ1811-1925\n23\n9.71\n0.72\n0.45\n4.29\nJ1813-1246\n24\n5.81\n0.31\n4.07\n4.03\nJ1813-1749\n182\n5.17\n0.23\n0.04\n0.55\nJ1838-0655\n21\n12.98\n1.27\n2.93\n4.68\nJ1913+1011\n15\n4.14\n0.77\n1.40\n6.45\nJ1935+2025\n16\n17.84\n1.17\n0.63\n5.94\nJ1952+3252\n18\n4.24\n0.41\n1.06\n5.55\nJ2016+3711\n73\n6.31\n0.40\n1.37\n1.37\nJ2021+3651\n12\n37.11\n0.86\n0.25\n7.73\nJ2022+3842\n99\n5.80\n0.54\n0.25\n1.01\nJ2229+6114\n77\n6.19\n0.19\n0.62\n1.28\nEspinoza, C. M., Lyne, A. G., Stappers, B. W., & Kramer,\nM. 2011, MNRAS, 414, 1679,\ndoi: 10.1111/j.1365-2966.2011.18503.x\nFerdman, R. D., Stairs, I. H., Kramer, M., et al. 2014,\nMNRAS, 443, 2183, doi: 10.1093/mnras/stu1223\nFesik, L., & Papa, M. A. 2020, ApJ, 895, 11,\ndoi: 10.3847/1538-4357/ab8193\nFriedman, J. L., & Morsink, S. M. 1998, ApJ, 502, 714,\ndoi: 10.1086/305920\nFujisawa, K., Kisaka, S., & Kojima, Y. 2022, MNRAS, 516,\n5196, doi: 10.1093/mnras/stac2585\nGancio, G., Lousto, C. O., Combi, L., et al. 2020, A&A,\n633, A84, doi: 10.1051/0004-6361/201936525\nGendreau, K. 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A., Laffon, H., et al. 2016, A&A,\n587, A109, doi: 10.1051/0004-6361/201527847\nGuillemot, L., Cognard, I., van Straten, W., Theureau, G.,\n& G\u00b4erard, E. 2023, A&A, 678, A79,\ndoi: 10.1051/0004-6361/202347018\nGuo, Y. J., Freire, P. C. C., Guillemot, L., et al. 2021,\nA&A, 654, A16, doi: 10.1051/0004-6361/202141450\n\n31\nTable 4. Limits on GW amplitude from dipole radiation in Brans-Dicke\ntheory.\nPulsar Name\nfrot\n\u02d9frot\nDistance\nh95%\n0d\nFAP\n(J2000)\n(Hz)\n(Hz s\u22121)\n(kpc)\nJ0030+0451\u03b1\n205.53\n\u22124.23\u00d710\u221216\n0.33a\n8.77\u00d710\u221227\n0.98\nJ0058\u22127218\u03b2\n45.94\n\u22126.1\u00d710\u221211\n59.70b\n3.02\u00d710\u221226\n0.73\nJ0117+5914\u03b3\n9.86\n\u22125.69\u00d710\u221213\n1.77c\n2.03\u00d710\u221223\n1\nJ0205+6449\u03b3\n15.22\n\u22124.49\u00d710\u221211\n3.20d\n3.78(2.57)\u00d710\u221225\n0.99(0.79)\nJ0437\u22124715\u03b4\n173.69\n\u22124.15\u00d710\u221216\n0.16e\n8.13\u00d710\u221227\n0.98\nJ0534+2200\u03b3\n29.95\n\u22123.78\u00d710\u221210\n2.00f\n1.37(0.86)\u00d710\u221225\n0.46(0.99)\nJ0537\u22126910\u03b2\n62.03\n\u22121.99\u00d710\u221210\n49.70g\n1.84(1.11)\u00d710\u221226\n0.98(0.60)\nJ0540\u22126919\u03b2\n19.77\n\u22121.87\u00d710\u221210\n49.70g\n2.41(1.44)\u00d710\u221225\n0.92(0.36)\nJ0614\u22123329\u03b1\n317.59\n\u22121.76\u00d710\u221215\n0.63h\n1.78\u00d710\u221226\n0.56\nJ0737\u22123039A\u03b1\n44.05\n\u22123.41\u00d710\u221215\n1.10i\n4.08\u00d710\u221226\n0.83\nJ0835\u22124510\u03f5\n11.19\n\u22121.57\u00d710\u221211\n0.28i\n4.12(2.73)\u00d710\u221224\n0.80(0.33)\nJ1231\u22121411\u03b1\n271.45\n\u22125.92\u00d710\u221216\n0.42c\n3.21\u00d710\u221226\n1\nJ1412+7922\u03b2\n17.18\n\u22129.72\u00d710\u221213\n3.30j\n5.56\u00d710\u221226\n0.93\nJ1537+1155\u03b1\n26.38\n\u22121.65\u00d710\u221215\n0.93k\n5.93\u00d710\u221226\n0.97\nJ1623\u22122631\u03b3\n90.29\n\u22125.26\u00d710\u221215\n1.85l\n3.10\u00d710\u221225\n0.77\nJ1719\u22121438\u03b1\n172.71\n\u22122.22\u00d710\u221216\n0.34c\n5.44\u00d710\u221227\n1\nJ1744\u22121134\u03b1\n245.43\n\u22124.34\u00d710\u221216\n0.40e\n1.60\u00d710\u221226\n0.92\nJ1745\u22120952\u03b1\n51.61\n\u22122.3\u00d710\u221216\n0.23c\n4.30\u00d710\u221226\n0.81\nJ1756\u22122251\u03b3\n35.14\n\u22121.26\u00d710\u221215\n0.73m\n5.29\u00d710\u221226\n0.64\nJ1809\u22121917\u03b3\n12.08\n\u22123.73\u00d710\u221212\n3.27c\n3.25\u00d710\u221224\n0.90\nJ1811\u22121925\u03b2\n15.46\n\u22121.05\u00d710\u221211\n5.00n\n6.20\u00d710\u221225\n0.98\nJ1813\u22121246\u03b2\n20.80\n\u22127.6\u00d710\u221212\n2.63o\n3.60\u00d710\u221225\n0.44\nJ1813\u22121749\u03b2\n22.35\n\u22126.34\u00d710\u221211\n6.15c\n1.09\u00d710\u221225\n0.97\nJ1823\u22123021A\u03b3\n183.82\n\u22121.14\u00d710\u221213\n8.02l\n1.84\u00d710\u221226\n0.58\nJ1824\u22122452A\u03b1\n327.41\n\u22121.73\u00d710\u221213\n5.37l\n2.08\u00d710\u221226\n0.49\nJ1826\u22121334\u03b3\n9.85\n\u22127.31\u00d710\u221212\n3.61c\n3.69\u00d710\u221225\n0.98\nJ1828\u22121101\u03b3\n13.88\n\u22122.85\u00d710\u221212\n4.77c\n3.68\u00d710\u221224\n1\nJ1831\u22120952\u03b3\n14.87\n\u22121.84\u00d710\u221212\n3.68c\n1.13\u00d710\u221224\n0.87\nJ1833\u22120827\u03b3\n11.72\n\u22121.26\u00d710\u221212\n4.50i\n3.79\u00d710\u221224\n0.82\nJ1837\u22120604\u03b3\n10.38\n\u22124.84\u00d710\u221212\n4.78c\n9.77\u00d710\u221224\n0.91\nJ1838\u22120655\u03b2\n14.18\n\u22129.9\u00d710\u221212\n6.60p\n2.91\u00d710\u221224\n0.51\nJ1849\u22120001\u03b2\n25.96\n\u22129.54\u00d710\u221212\n7.00q\n1.70\u00d710\u221225\n0.34\nJ1856+0245\u03b3\n12.36\n\u22129.49\u00d710\u221212\n6.32c\n7.32\u00d710\u221225\n1\nJ1913+1011\u03b3\n27.85\n\u22122.62\u00d710\u221212\n4.61c\n8.43\u00d710\u221226\n0.88\nJ1925+1720\u03b3\n13.22\n\u22121.83\u00d710\u221212\n5.05c\n4.00\u00d710\u221224\n0.70\nJ1935+2025\u03b3\n12.48\n\u22129.47\u00d710\u221212\n4.60c\n1.57\u00d710\u221224\n0.95\nJ1952+3252\u03b3\n25.30\n\u22123.74\u00d710\u221212\n3.00i\n1.01\u00d710\u221225\n0.78\nJ2016+3711\u03b6\n19.68\n\u22122.81\u00d710\u221211\n6.10r\n1.91\u00d710\u221225\n0.90\nJ2021+3651\u03b3\n9.64\n\u22128.89\u00d710\u221212\n1.80s\n1.32(0.61)\u00d710\u221222\n0.39(0.08)\nJ2022+3842\u03b2\n20.59\n\u22123.65\u00d710\u221211\n10.00t\n7.44\u00d710\u221224\n0.67\nJ2043+2740\u03b3\n10.40\n\u22121.37\u00d710\u221213\n1.48c\n3.93\u00d710\u221224\n0.97\nJ2214+3000\u03b7\n320.59\n\u22121.31\u00d710\u221215\n0.60u\n5.68\u00d710\u221227\n1\nJ2222\u22120137\u03b1\n30.47\n\u22124.99\u00d710\u221216\n0.27v\n5.21\u00d710\u221226\n0.96\nJ2229+6114\u03b3\n19.36\n\u22122.9\u00d710\u221211\n3.00w\n2.31(1.61)\u00d710\u221225\n0.86(0.25)\nNote\u2014For references and other notes see Table 2. 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Ansoldi,45, 46 J. M. Antelis,47 S. Antier,48 M. Aoumi,49 E. Z. Appavuravther,50, 51 S. Appert,11 S. K. Apple,52\nK. Arai,11 A. Araya,53 M. C. Araya,11 M. Arca Sedda,43 J. S. Areeda,54 L. Argianas,55 N. Aritomi,2\nF. Armato,56, 57 S. Armstrong,58 N. Arnaud,38, 59 M. Arogeti,60 S. M. Aronson,12 K. G. Arun,61 G. Ashton,62\nY. Aso,24, 63 M. Assiduo,64, 65 S. Assis de Souza Melo,59 S. M. Aston,66 P. Astone,67 F. Attadio,68, 67 F. Aubin,69\nK. AultONeal,70 G. Avallone,71 S. Babak,72 F. Badaracco,56 C. Badger,73 S. Bae,74 S. Bagnasco,27 E. Bagui,75\nL. Baiotti,76 R. Bajpai,24 T. Baka,77 T. Baker,78 M. Ball,79 G. Ballardin,59 S. W. Ballmer,80 S. Banagiri,81\nB. Banerjee,43 D. Bankar,15 T. M. Baptiste,12 P. Baral,10 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2\nN. Barman,15 P. Barneo,41, 82 F. Barone,83, 4 B. Barr,28 L. Barsotti,34 M. Barsuglia,72 D. Barta,84\nA. M. Bartoletti,85 M. A. Barton,28 I. Bartos,44 S. Basak,23 A. Basalaev,86 R. Bassiri,87 A. Basti,88, 89\nD. E. Bates,32 M. Bawaj,90, 50 P. Baxi,91 J. C. Bayley,28 A. C. Baylor,10 P. A. Baynard II,60 M. Bazzan,92, 93\nV. M. Bedakihale,94 F. Beirnaert,95 M. Bejger,96 D. Belardinelli,21 A. S. Bell,28 D. S. Bellie,81 L. Bellizzi,89, 88\nD. Beltran-Martinez,97 W. Benoit,98 I. Bentara,99 J. D. Bentley,86 M. Ben Yaala,58 S. Bera,100 F. Bergamin,8, 9\nB. K. Berger,87 S. Bernuzzi,26 M. Beroiz,11 C. P. L. Berry,28 D. Bersanetti,56 A. Bertolini,36 J. Betzwieser,66\nD. Beveridge,29 G. Bevilacqua,101 N. Bevins,55 R. Bhandare,102 R. Bhatt,11 D. Bhattacharjee,103, 104\nS. Bhaumik,44 S. Bhowmick,105 V. Biancalana,101 A. Bianchi,36, 106 I. A. Bilenko,107 G. Billingsley,11 A. Binetti,108\nS. Bini,109, 110 C. Binu,111 O. Birnholtz,112 S. Biscoveanu,81 A. Bisht,9 M. Bitossi,59, 89 M.-A. Bizouard,48\nS. Blaber,113 J. K. Blackburn,11 L. A. Blagg,79 C. D. Blair,29, 66 D. G. Blair,29 F. Bobba,71, 114 N. Bode,8, 9\nG. Boileau,48 M. Boldrini,67, 68 G. N. Bolingbroke,115 A. Bolliand,116, 37 L. D. Bonavena,44, 92 R. Bondarescu,41\nF. Bondu,117 E. Bonilla,87 M. S. Bonilla,54 A. Bonino,118 R. Bonnand,30, 116 P. Booker,8, 9 A. Borchers,8, 9\nS. Borhanian,7 V. Boschi,89 S. Bose,119 V. Bossilkov,66 A. Boudon,99 A. Bozzi,59 C. Bradaschia,89 P. R. Brady,10\nA. Branch,66 M. Branchesi,43, 120 I. Braun,103 T. Briant,121 A. Brillet,48 M. Brinkmann,8, 9 P. Brockill,10\nE. Brockmueller,8, 9 A. F. Brooks,11 B. C. Brown,44 D. D. Brown,115 M. L. Brozzetti,90, 50 S. Brunett,11\nG. Bruno,14 R. Bruntz,122 J. Bryant,118 Y. Bu,123 F. Bucci,65 J. Buchanan,122 O. Bulashenko,41, 82 T. Bulik,124\nH. J. Bulten,36 A. Buonanno,125, 1 K. Burtnyk,2 R. Buscicchio,126, 127 D. Buskulic,30 C. Buy,128 R. L. Byer,87\nG. S. Cabourn Davies,78 G. Cabras,45, 46 R. Cabrita,14 V. C\u00b4aceres-Barbosa,7 L. Cadonati,60 G. Cagnoli,129\nC. Cahillane,80 A. Calafat,100 J. Calder\u00b4on Bustillo,130 T. A. Callister,131 E. Calloni,31, 4 M. Canepa,57, 56\nG. Caneva Santoro,42 K. C. Cannon,40 H. Cao,34 L. A. Capistran,132 E. Capocasa,72 E. Capote,2 G. Capurri,89, 88\nG. Carapella,71, 114 F. Carbognani,59 M. Carlassara,8, 9 J. B. Carlin,123 T. K. Carlson,133 M. F. Carney,103\nM. Carpinelli,126, 134, 59 G. Carrillo,79 J. J. Carter,8, 9 G. Carullo,135 J. Casanueva Diaz,59 C. Casentini,136, 20, 21\nS. Y. Castro-Lucas,105 S. Caudill,133, 36, 77 M. Cavagli`a,104 R. Cavalieri,59 G. Cella,89 P. Cerd\u00b4a-Dur\u00b4an,137, 138\nE. Cesarini,21 W. Chaibi,48 P. Chakraborty,8, 9 S. Chakraborty,102 S. Chalathadka Subrahmanya,86\nJ. C. L. Chan,139 M. Chan,113 R.-J. Chang,140 S. Chao,141, 142 E. L. Charlton,122 P. Charlton,143\nE. Chassande-Mottin,72 C. Chatterjee,144 Debarati Chatterjee,15 Deep Chatterjee,34 D. Chattopadhyay,81\nM. Chaturvedi,102 S. Chaty,72 K. Chatziioannou,11 C. Checchia,101 A. Chen,16 A. H.-Y. Chen,145 D. Chen,146\nH. Chen,141 H. Y. Chen,147 S. Chen,144 Y. Chen,141 Yanbei Chen,148 Yitian Chen,149 H. P. Cheng,150 P. Chessa,90, 50\nH. T. Cheung,91 S. Y. Cheung,6 F. Chiadini,151, 114 G. Chiarini,93 R. Chierici,99 A. Chincarini,56\nM. L. Chiofalo,88, 89 A. Chiummo,4, 59 C. Chou,145 S. Choudhary,29 N. Christensen,48 S. S. Y. Chua,33 P. Chugh,6\nG. Ciani,109, 110 P. Ciecielag,96 M. Cie\u00b4slar,124 M. Cifaldi,21 R. Ciolfi,152, 93 F. Clara,2 J. A. Clark,11, 60 J. Clarke,32\nT. A. Clarke,6 P. Clearwater,153 S. Clesse,75 S. M. Clyne,154 E. Coccia,43, 120, 42 E. Codazzo,155 P.-F. Cohadon,121\nS. Colace,57 E. Colangeli,78 M. Colleoni,100 C. G. Collette,156 J. Collins,66 S. Colloms,28 A. Colombo,157, 127\nC. M. Compton,2 G. Connolly,79 L. Conti,93 T. R. Corbitt,12 I. Cordero-Carri\u00b4on,158 S. Corezzi,90, 50\nN. J. Cornish,159 A. Corsi,160 S. Cortese,59 R. Cottingham,66 M. W. Coughlin,98 A. Couineaux,67 J.-P. Coulon,48\nJ.-F. Coupechoux,99 P. Couvares,11, 60 D. M. Coward,29 R. Coyne,154 K. Craig,58 J. D. E. Creighton,10\nT. D. Creighton,161 P. Cremonese,100 A. W. Criswell,98 S. Crook,66 R. Crouch,2 J. Csizmazia,2 J. R. Cudell,162\nT. J. Cullen,11 A. Cumming,28 E. Cuoco,163, 164 M. Cusinato,137 P. Dabadie,129 L. V. Da Conceic\u00b8\u02dcao,165\nT. Dal Canton,38 S. Dall\u2019Osso,67 S. Dal Pra,166 G. D\u00b4alya,128 B. D\u2019Angelo,56 S. Danilishin,35, 36 S. D\u2019Antonio,21\nK. Danzmann,9, 8, 9 K. E. Darroch,122 L. P. Dartez,66 A. Dasgupta,94 S. Datta,61 V. Dattilo,59 A. Daumas,72\nN. Davari,167, 134 I. Dave,102 A. Davenport,105 M. Davier,38 T. F. Davies,29 D. Davis,11 L. Davis,29 M. C. Davis,98\nP. Davis,168, 169 M. Dax,1 J. De Bolle,95 M. Deenadayalan,15 J. Degallaix,170 M. De Laurentis,31, 4 S. Del\u00b4eglise,121\nF. De Lillo,22 D. Dell\u2019Aquila,167, 134 F. Della Valle,101 W. Del Pozzo,88, 89 F. De Marco,68, 67 G. Demasi,171, 65\narXiv:2508.18083v2 [astro-ph.HE] 17 Sep 2025\n\n2\nF. De Matteis,20, 21 V. D\u2019Emilio,11 N. Demos,34 T. Dent,130 A. Depasse,14 N. DePergola,55 R. De Pietri,172, 173\nR. De Rosa,31, 4 C. De Rossi,59 M. Desai,34 R. DeSalvo,174 A. DeSimone,175 R. De Simone,151 A. Dhani,1 R. Diab,44\nM. C. D\u00b4\u0131az,161 M. Di Cesare,31, 4 G. Dideron,176 N. A. Didio,80 T. Dietrich,1 L. Di Fiore,4 C. Di Fronzo,29\nM. Di Giovanni,68, 67 T. Di Girolamo,31, 4 D. Diksha,36, 35 A. Di Michele,90 J. Ding,34, 72, 177 S. Di Pace,68, 67\nI. Di Palma,68, 67 F. Di Renzo,99 Divyajyoti,178 A. Dmitriev,118 Z. Doctor,81 N. Doerksen,165 E. Dohmen,2\nD. Dominguez,179 L. D\u2019Onofrio,67 F. Donovan,34 K. L. Dooley,32 T. Dooney,77 S. Doravari,15 O. Dorosh,180\nM. Drago,68, 67 J. C. Driggers,2 J.-G. Ducoin,181, 72 L. Dunn,123 U. Dupletsa,43 D. D\u2019Urso,167, 155 H. Duval,182\nS. E. Dwyer,2 C. Eassa,2 M. Ebersold,30 T. Eckhardt,86 G. Eddolls,80 B. Edelman,79 T. B. Edo,11 O. Edy,78\nA. Effler,66 J. Eichholz,33 H. Einsle,48 M. Eisenmann,24 R. A. Eisenstein,34 A. Ejlli,32 M. Emma,62 K. Endo,183\nR. Enficiaud,1 A. J. Engl,87 L. Errico,31, 4 R. Espinosa,161 M. Esposito,4, 31 R. C. Essick,184 H. Estell\u00b4es,1\nT. Etzel,11 M. Evans,34 T. Evstafyeva,185 B. E. Ewing,7 J. M. Ezquiaga,139 F. Fabrizi,64, 65 F. Faedi,65, 64\nV. Fafone,20, 21 S. Fairhurst,32 A. M. Farah,131 B. Farr,79 W. M. Farr,186, 187 G. Favaro,92 M. Favata,188 M. Fays,162\nM. Fazio,58 J. Feicht,11 M. M. Fejer,87 R. Felicetti,189 E. Fenyvesi,84, 190 D. L. Ferguson,147 T. Fernandes,191, 137\nA. Fernando,111 D. Fernando,111 S. Ferraiuolo,192, 68, 67 I. Ferrante,88, 89 T. A. Ferreira,12 F. Fidecaro,88, 89\nP. Figura,96 A. Fiori,89, 88 I. Fiori,59 M. Fishbach,184 R. P. Fisher,122 R. Fittipaldi,193, 114 V. Fiumara,194, 114\nR. Flaminio,30 S. M. Fleischer,195 L. S. Fleming,19 E. Floden,98 H. Fong,113 J. A. Font,137, 138 C. Foo,1\nB. Fornal,196 P. W. F. Forsyth,33 K. Franceschetti,172 N. Franchini,197 S. Frasca,68, 67 F. Frasconi,89\nA. Frattale Mascioli,68, 67 Z. Frei,198 A. Freise,36, 106 O. Freitas,191, 137 R. Frey,79 W. Frischhertz,66\nP. Fritschel,34 V. V. Frolov,66 G. G. Fronz\u00b4e,27 M. Fuentes-Garcia,11 S. Fujii,199 T. Fujimori,200 P. Fulda,44\nM. Fyffe,66 B. Gadre,77 J. R. Gair,1 S. Galaudage,201 V. Galdi,174 H. Gallagher,111 B. Gallego,202 R. Gamba,7, 26\nA. Gamboa,1 D. Ganapathy,34 A. Ganguly,15 B. Garaventa,56, 57 J. Garc\u00b4\u0131a-Bellido,203 C. Garc\u00b4\u0131a N\u00b4u\u02dcnez,19\nC. Garc\u00b4\u0131a-Quir\u00b4os,204 J. W. Gardner,33 K. A. Gardner,113 J. Gargiulo,59 A. Garron,100 F. Garufi,31, 4\nP. A. Garver,87 C. Gasbarra,20, 21 B. Gateley,2 F. Gautier,205 V. Gayathri,10 T. Gayer,80 G. Gemme,56\nA. Gennai,89 V. Gennari,128 J. George,102 R. George,147 O. Gerberding,86 L. Gergely,206 Archisman Ghosh,95\nSayantan Ghosh,207 Shaon Ghosh,188 Shrobana Ghosh,8, 9 Suprovo Ghosh,15 Tathagata Ghosh,15 J. A. Giaime,12, 66\nK. D. Giardina,66 D. R. Gibson,19 D. T. Gibson,185 C. Gier,58 S. Gkaitatzis,88, 89 J. Glanzer,11 F. Glotin,38\nJ. Godfrey,79 P. Godwin,11 A. S. Goettel,32 E. Goetz,113 J. Golomb,11 S. Gomez Lopez,68, 67 B. Goncharov,43\nY. Gong,208 G. Gonz\u00b4alez,12 P. Goodarzi,209 S. Goode,6 A. W. Goodwin-Jones,11, 29 M. Gosselin,59 R. Gouaty,30\nD. W. Gould,33 K. Govorkova,34 S. Goyal,1 B. Grace,33 A. Grado,90, 50 V. Graham,28 A. E. Granados,98\nM. Granata,170 V. Granata,71 S. Gras,34 P. Grassia,11 A. Gray,98 C. Gray,2 R. Gray,28 G. Greco,50\nA. C. Green,36, 106 S. M. Green,78 S. R. Green,210 A. M. Gretarsson,70 E. M. Gretarsson,70 D. Griffith,11\nW. L. Griffiths,32 H. L. Griggs,60 G. Grignani,90, 50 C. Grimaud,30 H. Grote,32 S. Grunewald,1 D. Guerra,137\nD. Guetta,211 G. M. Guidi,64, 65 A. R. Guimaraes,12 H. K. Gulati,94 F. Gulminelli,168, 169 A. M. Gunny,34 H. Guo,212\nW. Guo,29 Y. Guo,36, 35 Anchal Gupta,11 Anuradha Gupta,213 I. Gupta,7 N. C. Gupta,94 P. Gupta,36, 77\nS. K. Gupta,44 T. Gupta,159 V. Gupta,98 N. Gupte,1 J. Gurs,86 N. Gutierrez,170 F. Guzman,132 D. Haba,179\nM. Haberland,1 S. Haino,214 E. D. Hall,34 E. Z. Hamilton,100 G. Hammond,28 W.-B. Han,215 M. Haney,36, 204\nJ. Hanks,2 C. Hanna,7 M. D. Hannam,32 O. A. Hannuksela,216 A. G. Hanselman,131 H. Hansen,2 J. Hanson,66\nR. Harada,40 A. R. Hardison,175 S. Harikumar,180 K. Haris,36, 77 T. Harmark,135 J. Harms,43, 120 G. M. Harry,217\nI. W. Harry,78 J. Hart,103 B. Haskell,96 C.-J. Haster,218 K. Haughian,28 H. Hayakawa,49 K. Hayama,219\nR. Hayes,32 A. Heffernan,220 M. C. Heintze,66 J. Heinze,118 J. Heinzel,34 H. Heitmann,48 F. Hellman,221\nA. F. Helmling-Cornell,79 G. Hemming,59 O. Henderson-Sapir,115 M. Hendry,28 I. S. Heng,28 M. H. Hennig,28\nC. Henshaw,60 M. Heurs,8, 9 A. L. Hewitt,185, 222 J. Heyns,34 S. Higginbotham,32 S. Hild,35, 36 S. Hill,28\nY. Himemoto,223 N. Hirata,24 C. Hirose,224 S. Hochheim,8, 9 D. Hofman,170 N. A. Holland,36, 106 D. E. Holz,131\nL. Honet,75 C. Hong,87 S. Hoshino,224 J. Hough,28 S. Hourihane,11 N. T. Howard,144 E. J. Howell,29 C. G. Hoy,78\nC. A. Hrishikesh,20 H.-F. Hsieh,141 H.-Y. Hsieh,141 C. Hsiung,225 W.-F. Hsu,108 Q. Hu,28 H. Y. Huang,142 Y. Huang,7\nY. T. Huang,80 A. D. Huddart,226 B. Hughey,70 D. C. Y. Hui,227 V. Hui,30 S. Husa,100 R. Huxford,7 L. Iampieri,68, 67\nG. A. Iandolo,35 M. Ianni,21, 20 A. Ierardi,43 A. Iess,228, 89 H. Imafuku,40 K. Inayoshi,229 Y. Inoue,142 G. Iorio,92\nP. Iosif,189, 46 M. H. Iqbal,33 J. Irwin,28 R. Ishikawa,230 M. Isi,186, 187 Y. Itoh,231, 200 H. Iwanaga,231 M. Iwaya,199\nB. R. Iyer,23 C. Jacquet,128 P.-E. Jacquet,121 S. J. Jadhav,232 S. P. Jadhav,153 T. Jain,185 A. L. James,11\nP. A. James,122 R. Jamshidi,156 K. Jani,144 J. Janquart,14 K. Janssens,22, 48 N. N. Janthalur,232 S. Jaraba,203\nP. Jaranowski,233 R. Jaume,100 W. Javed,32 A. Jennings,2 W. Jia,34 J. Jiang,150 C. Johanson,133 G. R. Johns,122\nN. A. Johnson,44 M. C. Johnston,218 R. Johnston,28 N. Johny,8, 9 D. H. Jones,33 D. I. Jones,234 E. J. Jones,12\nR. Jones,28 S. Jose,178 P. Joshi,7 S. K. Joshi,15 J. Ju,235 L. Ju,29 K. Jung,236 J. Junker,33 V. Juste,75\nH. B. Kabagoz,66 T. Kajita,237 I. Kaku,231 V. Kalogera,81 M. Kalomenopoulos,218 M. Kamiizumi,49 N. Kanda,200, 231\nS. Kandhasamy,15 G. Kang,238 N. C. Kannachel,6 J. B. Kanner,11 S. J. Kapadia,15 D. P. Kapasi,33 S. Karat,11\nR. Kashyap,7 M. Kasprzack,11 W. Kastaun,8, 9 T. Kato,199 E. Katsavounidis,34 W. Katzman,66 R. Kaushik,102\nK. Kawabe,2 R. Kawamoto,231 A. Kazemi,98 A. Kedia,111 D. Keitel,100 J. Kennington,7 R. Kesharwani,15\nJ. S. Key,239 R. Khadela,8, 9 S. Khadka,87 F. Y. Khalili,107 F. Khan,8, 9 I. Khan,240, 37 T. Khanam,160\nM. Khursheed,102 N. M. Khusid,186, 187 W. Kiendrebeogo,48, 241 N. Kijbunchoo,115 C. Kim,242 J. C. Kim,243 K. Kim,244\nM. H. Kim,235 S. Kim,227 Y.-M. Kim,244 C. Kimball,81 M. Kinley-Hanlon,28 M. Kinnear,32 J. S. Kissel,2\nS. Klimenko,44 A. M. Knee,113 N. Knust,8, 9 K. Kobayashi,199 P. Koch,8, 9 S. M. Koehlenbeck,87 G. Koekoek,36, 35\nK. Kohri,245, 246 K. Kokeyama,32 S. Koley,43 P. Kolitsidou,118 K. Komori,40, 39 A. K. H. Kong,141 A. Kontos,247\n\n3\nM. Korobko,86 R. V. Kossak,8, 9 X. Kou,98 A. Koushik,22 N. Kouvatsos,73 M. Kovalam,29 D. B. Kozak,11\nS. L. Kranzhoff,35, 36 V. Kringel,8, 9 N. V. Krishnendu,118 A. Kr\u00b4olak,248, 180 K. Kruska,8, 9 J. Kubisz,249\nG. Kuehn,8, 9 S. Kulkarni,213 A. Kulur Ramamohan,33 A. Kumar,232 Praveen Kumar,130 Prayush Kumar,23\nRahul Kumar,2 Rakesh Kumar,94 J. Kume,250, 251, 40 K. Kuns,34 N. Kuntimaddi,32 S. Kuroyanagi,203, 252\nS. Kuwahara,40 K. Kwak,236 K. Kwan,33 J. Kwok,185 G. Lacaille,28 P. Lagabbe,30, 109 D. Laghi,128 S. Lai,145\nE. Lalande,253 M. Lalleman,22 P. C. Lalremruati,254 M. Landry,2 P. Landry,184 B. B. Lane,34 R. N. Lang,34\nJ. Lange,147 R. Langgin,218 B. Lantz,87 A. La Rana,67 I. La Rosa,100 J. Larsen,195 A. Lartaux-Vollard,38\nP. D. Lasky,6 J. Lawrence,161, 255 M. N. Lawrence,12 M. Laxen,66 C. Lazarte,137 A. Lazzarini,11 C. Lazzaro,256, 155\nP. Leaci,68, 67 L. Leali,98 Y. K. Lecoeuche,113 H. M. Lee,243 H. W. Lee,257 J. Lee,80 K. Lee,235 R.-K. Lee,141\nR. Lee,34 Sungho Lee,258 Sunjae Lee,235 Y. Lee,142 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,176 M. Le Jean,170\nA. Lema\u02c6\u0131tre,259 M. Lenti,65, 171 M. Leonardi,109, 110, 24 M. Lequime,37 N. Leroy,38 M. Lesovsky,11 N. Letendre,30\nM. Lethuillier,99 Y. Levin,6 K. Leyde,72, 78 A. K. Y. Li,11 K. L. Li,140 T. G. F. Li,108 X. Li,148 Y. Li,81 Z. Li,28\nA. Lihos,122 C-Y. Lin,260 E. T. Lin,141 L. C.-C. Lin,140 Y.-C. Lin,141 C. Lindsay,19 S. D. Linker,202\nT. B. Littenberg,261 A. Liu,216 G. C. Liu,225 Jian Liu,29 F. Llamas Villarreal,161 J. Llobera-Querol,100\nR. K. L. Lo,139 J.-P. Locquet,108 M. R. Loizou,133 L. T. London,73, 34 A. Longo,64, 65 D. Lopez,162, 204\nM. Lopez Portilla,77 M. Lorenzini,20, 21 A. Lorenzo-Medina,130 V. Loriette,38 M. Lormand,66 G. Losurdo,228, 89\nE. Lotti,133 T. P. Lott IV,60 J. D. Lough,8, 9 H. A. Loughlin,34 C. O. Lousto,111 N. Low,123 M. J. Lowry,122\nN. Lu,33 L. Lucchesi,89 H. L\u00a8uck,9, 8, 9 D. Lumaca,21 A. P. Lundgren,78 A. W. Lussier,253 L.-T. Ma,141 S. Ma,176\nR. Macas,78 A. Macedo,54 M. MacInnis,34 R. R. Maciy,8, 9 D. M. Macleod,32 I. A. O. MacMillan,11 A. Macquet,38\nD. Macri,34 K. Maeda,183 S. Maenaut,108 S. S. Magare,15 R. M. Magee,11 E. Maggio,1 R. Maggiore,36, 106\nM. Magnozzi,56, 57 M. Mahesh,86 M. Maini,154 S. Majhi,15 E. Majorana,68, 67 C. N. Makarem,11 D. Malakar,104\nJ. A. Malaquias-Reis,18 U. Mali,184 S. Maliakal,11 A. Malik,102 L. Mallick,165, 184 A. Malz,62 N. Man,48\nV. Mandic,98 V. Mangano,67, 68 B. Mannix,79 G. L. Mansell,80 G. Mansingh,217 M. Manske,10 M. Mantovani,59\nM. Mapelli,92, 93, 262 F. Marchesoni,51, 50, 263 C. Marinelli,101 D. Mar\u00b4\u0131n Pina,41, 82, 264 F. Marion,30 S. M\u00b4arka,265\nZ. M\u00b4arka,265 A. S. Markosyan,87 A. Markowitz,11 E. Maros,11 S. Marsat,128 F. Martelli,64, 65 I. W. Martin,28\nR. M. Martin,188 B. B. Martinez,132 M. Martinez,42, 266 V. Martinez,129 A. Martini,109, 110 J. C. Martins,18\nD. V. Martynov,118 E. J. Marx,34 L. Massaro,35, 36 A. Masserot,30 M. Masso-Reid,28 M. Mastrodicasa,67, 68\nS. Mastrogiovanni,67 T. Matcovich,50 M. Matiushechkina,8, 9 M. Matsuyama,231 N. Mavalvala,34 N. Maxwell,2\nG. McCarrol,66 R. McCarthy,2 D. E. McClelland,33 S. McCormick,66 L. McCuller,11 S. McEachin,122\nC. McElhenny,122 G. I. McGhee,28 J. McGinn,28 K. B. M. McGowan,144 J. McIver,113 A. McLeod,29 T. McRae,33\nD. Meacher,10 Q. Meijer,77 A. Melatos,123 S. Mellaerts,108 C. S. Menoni,105 F. Mera,2 R. A. Mercer,10\nL. Mereni,170 K. Merfeld,160 E. L. Merilh,66 J. R. M\u00b4erou,100 J. D. Merritt,79 M. Merzougui,48 C. Messenger,28\nC. Messick,10 B. Mestichelli,43 M. Meyer-Conde,267 F. Meylahn,8, 9 A. Mhaske,15 A. Miani,109, 110 H. Miao,268\nI. Michaloliakos,44 C. Michel,170 Y. Michimura,11, 40 H. Middleton,118 S. J. Miller,11 M. Millhouse,60\nE. Milotti,189, 46 V. Milotti,92 Y. Minenkov,21 N. Mio,269 Ll. M. Mir,42 L. Mirasola,155, 256 M. Miravet-Ten\u00b4es,137\nC.-A. Miritescu,42 A. K. Mishra,23 A. Mishra,23 C. Mishra,178 T. Mishra,44 A. L. Mitchell,36, 106 J. G. Mitchell,70\nS. Mitra,15 V. P. Mitrofanov,107 R. Mittleman,34 O. Miyakawa,49 S. Miyamoto,199 S. Miyoki,49 G. Mo,34\nL. Mobilia,64, 65 S. R. P. Mohapatra,11 S. R. Mohite,7 M. Molina-Ruiz,221 C. Mondal,168 M. Mondin,202\nM. Montani,64, 65 C. J. Moore,185 D. Moraru,2 A. More,15 S. More,15 E. A. Moreno,34 G. Moreno,2\nS. Morisaki,40, 199 Y. Moriwaki,183 G. Morras,203 A. Moscatello,92 M. Mould,34 P. Mourier,220, 270 B. Mours,69\nC. M. Mow-Lowry,36, 106 F. Muciaccia,68, 67 D. Mukherjee,261 Samanwaya Mukherjee,15 Soma Mukherjee,161\nSubroto Mukherjee,94 Suvodip Mukherjee,13, 176, 271 N. Mukund,34 A. Mullavey,66 H. Mullock,113 J. Munch,115\nJ. Mundi,217 C. L. Mungioli,29 Y. Murakami,199 M. Murakoshi,230 P. G. Murray,28 S. Muusse,33 D. Nabari,109, 110\nS. L. Nadji,8, 9 A. Nagar,27, 272 N. Nagarajan,28 K. Nakagaki,49 K. Nakamura,24 H. Nakano,273 M. Nakano,11\nD. Nanadoumgar-Lacroze,42 D. Nandi,12 V. Napolano,59 P. Narayan,213 I. Nardecchia,21 T. Narikawa,199\nH. Narola,77 L. Naticchioni,67 R. K. Nayak,254 A. Nela,28 A. Nelson,132 T. J. N. Nelson,66 M. Nery,8, 9\nA. Neunzert,2 S. Ng,54 L. Nguyen Quynh,274, 275 S. A. Nichols,12 A. B. Nielsen,276 G. Nieradka,96 Y. Nishino,24, 277\nA. Nishizawa,278 S. Nissanke,271, 36 E. Nitoglia,99 W. Niu,7 F. Nocera,59 M. Norman,32 C. North,32\nJ. Novak,116, 279, 280 J. F. Nu\u02dcno Siles,203 L. K. Nuttall,78 K. Obayashi,230 J. Oberling,2 J. O\u2019Dell,226\nM. Oertel,279, 116, 281, 280 A. Offermans,108 G. Oganesyan,43, 120 J. J. Oh,282 K. Oh,227 T. O\u2019Hanlon,66 M. Ohashi,49\nM. Ohkawa,224 F. Ohme,8, 9 R. Oliveri,116, 281, 280 R. Omer,98 B. O\u2019Neal,122 K. Oohara,283, 284 B. O\u2019Reilly,66\nN. D. Ormsby,122 M. Orselli,50, 90 R. O\u2019Shaughnessy,111 S. O\u2019Shea,28 Y. Oshima,39 S. Oshino,49 C. Osthelder,11\nI. Ota,12 D. J. Ottaway,115 A. Ouzriat,99 H. Overmier,66 B. J. Owen,285 A. E. Pace,7 R. Pagano,12 M. A. Page,24\nA. Pai,207 L. Paiella,43 A. Pal,286 S. Pal,254 M. A. Palaia,89, 88 M. P\u00b4alfi,198 P. P. Palma,68, 20, 21 C. Palomba,67\nP. Palud,72 J. Pan,29 K. C. Pan,141 R. Panai,155, 92 P. K. Panda,232 Shiksha Pandey,7 Swadha Pandey,34\nP. T. H. Pang,36, 77 F. Pannarale,68, 67 K. A. Pannone,54 B. C. Pant,102 F. H. Panther,29 F. Paoletti,89\nA. Paolone,67, 287 A. Papadopoulos,28 E. E. Papalexakis,209 L. Papalini,89, 88 G. Papigkiotis,288 A. Paquis,38\nA. Parisi,90, 50 B.-J. Park,258 J. Park,289 W. Parker,66 G. Pascale,8, 9 D. Pascucci,95 A. Pasqualetti,59\nR. Passaquieti,88, 89 L. Passenger,6 D. Passuello,89 O. Patane,2 D. Pathak,15 L. Pathak,290 A. Patra,32\nB. Patricelli,88, 89 A. S. Patron,12 B. G. Patterson,32 K. Paul,178 S. Paul,79 E. Payne,11 T. Pearce,32\nM. Pedraza,11 A. Pele,11 F. E. Pe\u02dcna Arellano,291 S. Penn,292 M. D. Penuliar,54 A. Perego,109, 110 Z. Pereira,133\nJ. J. Perez,44 C. P\u00b4erigois,152, 93, 92 G. Perna,92 A. Perreca,109, 110 J. Perret,72 S. Perri`es,99 J. W. Perry,36, 106\n\n4\nD. Pesios,288 S. Petracca,174 C. Petrillo,90 H. P. Pfeiffer,1 H. Pham,66 K. A. Pham,98 K. S. Phukon,118\nH. Phurailatpam,216 M. Piarulli,128 L. Piccari,68, 67 O. J. Piccinni,33 M. Pichot,48 M. Piendibene,88, 89\nF. Piergiovanni,64, 65 L. Pierini,67 G. Pierra,99 V. Pierro,293, 114 M. Pietrzak,96 M. Pillas,162 F. Pilo,89\nL. Pinard,170 I. M. Pinto,293, 114, 294, 31 M. Pinto,59 B. J. Piotrzkowski,10 M. Pirello,2 M. D. Pitkin,185, 222\nA. Placidi,50 E. Placidi,68, 67 M. L. Planas,100 W. Plastino,295, 21 C. Plunkett,34 R. Poggiani,88, 89 E. Polini,34\nL. Pompili,1 J. Poon,216 E. Porcelli,36 E. K. Porter,72 C. Posnansky,7 R. Poulton,59 J. Powell,153\nM. Pracchia,162 B. K. Pradhan,15 T. Pradier,69 A. K. Prajapati,94 K. Prasai,87 R. Prasanna,232 P. Prasia,15\nG. Pratten,118 G. Principe,189, 46 M. Principe,174 G. A. Prodi,109, 110 L. Prokhorov,118 P. Prosperi,89\nP. Prosposito,20, 21 A. C. Providence,70 A. Puecher,36, 77 J. Pullin,12 M. Punturo,50 P. Puppo,67 M. P\u00a8urrer,154\nH. Qi,16 J. Qin,33 G. Qu\u00b4em\u00b4ener,169, 116 V. Quetschke,161 P. J. Quinonez,70 I. Rainho,137 S. Raja,102 C. Rajan,102\nB. Rajbhandari,111 K. E. Ramirez,66 F. A. Ramis Vidal,100 A. Ramos-Buades,36, 1 D. Rana,15 S. Ranjan,60\nK. Ransom,66 P. Rapagnani,68, 67 B. Ratto,70 A. Ray,10 V. Raymond,32 M. Razzano,88, 89 J. Read,54\nM. Recaman Payo,108 T. Regimbau,30 L. Rei,56 S. Reid,58 D. H. Reitze,11 P. Relton,32 A. I. Renzini,11, 126\nB. Revenu,296, 38 R. Reyes,202 A. S. Rezaei,67, 68 F. Ricci,68, 67 M. Ricci,67, 68 A. Ricciardone,88, 89\nJ. W. Richardson,209 M. Richardson,115 A. Rijal,70 K. Riles,91 H. K. Riley,32 S. Rinaldi,262, 92 J. Rittmeyer,86\nC. Robertson,226 F. Robinet,38 M. Robinson,2 A. Rocchi,21 L. Rolland,30 J. G. Rollins,11 A. E. Romano,297\nR. Romano,3, 4 A. Romero,30 I. M. Romero-Shaw,185 J. H. Romie,66 S. Ronchini,7, 43, 120 T. J. Roocke,115 L. Rosa,4, 31\nT. J. Rosauer,209 C. A. Rose,60 D. Rosi\u00b4nska,124 M. P. Ross,52 M. Rossello-Sastre,100 S. Rowan,28 S. Roy,14\nS. K. Roy,186, 187 D. Rozza,126, 127 P. Ruggi,59 N. Ruhama,236 E. Ruiz Morales,298, 203 K. Ruiz-Rocha,144 S. Sachdev,60\nT. Sadecki,2 J. Sadiq,130 P. Saffarieh,36, 106 S. Safi-Harb,165 M. R. Sah,13 S. Saha,141 T. Sainrat,69\nS. Sajith Menon,211, 68, 67 K. Sakai,299 M. Sakellariadou,73 S. Sakon,7 O. S. Salafia,157, 127, 126 F. Salces-Carcoba,11\nL. Salconi,59 M. Saleem,98 F. Salemi,68, 67 M. Sall\u00b4e,36 S. U. Salunkhe,15 S. Salvador,169, 168 A. Samajdar,77, 36\nA. Sanchez,2 E. J. Sanchez,11 J. H. Sanchez,81 L. E. Sanchez,11 N. Sanchis-Gual,137 J. R. Sanders,175\nE. M. S\u00a8anger,1 F. Santoliquido,43 F. Sarandrea,27 T. R. Saravanan,15 N. Sarin,6 P. Sarkar,8, 9 S. Sasaoka,179\nA. Sasli,288 P. Sassi,50, 90 B. Sassolas,170 B. S. Sathyaprakash,7, 32 R. Sato,224 Y. Sato,183 O. Sauter,44\nR. L. Savage,2 T. Sawada,49 H. L. Sawant,15 S. Sayah,30 V. Scacco,20, 21 D. Schaetzl,11 M. Scheel,148\nA. Schiebelbein,184 M. G. Schiworski,80 P. Schmidt,118 S. Schmidt,77 R. Schnabel,86 M. Schneewind,8, 9\nR. M. S. Schofield,79 K. Schouteden,108 B. W. Schulte,8, 9 B. F. Schutz,32, 8, 9 E. Schwartz,87 M. Scialpi,300\nJ. Scott,28 S. M. Scott,33 R. M. Sedas,66 T. C. Seetharamu,28 M. Seglar-Arroyo,42 Y. Sekiguchi,301 D. Sellers,66\nA. S. Sengupta,302 D. Sentenac,59 E. G. Seo,28 J. W. Seo,108 V. Sequino,31, 4 M. Serra,67 G. Servignat,72, 281\nA. Sevrin,182 T. Shaffer,2 U. S. Shah,60 M. S. Shahriar,81 M. A. Shaikh,243 L. Shao,229 A. K. Sharma,23\nP. Sharma,102 S. Sharma Chaudhary,104 M. R. Shaw,32 P. Shawhan,125 N. S. Shcheblanov,303, 259 Y. Shikano,304, 305\nM. Shikauchi,40 K. Shimode,49 H. Shinkai,306 J. Shiota,230 S. Shirke,15 D. H. Shoemaker,34 D. M. Shoemaker,147\nR. W. Short,2 S. ShyamSundar,102 A. Sider,156 H. Siegel,186, 187 D. Sigg,2 L. Silenzi,50, 51 M. Simmonds,115\nL. P. Singer,307 A. Singh,213 D. Singh,7 M. K. Singh,23 N. Singh,100 S. Singh,179, 63 A. Singha,35, 36 A. M. Sintes,100\nV. Sipala,167, 155 V. Skliris,32 B. J. J. Slagmolen,33 D. A. Slater,195 T. J. Slaven-Blair,29 J. Smetana,118\nJ. R. Smith,54 L. Smith,28, 189 R. J. E. Smith,6 W. J. Smith,144 K. Somiya,179 I. Song,141 K. Soni,15 S. Soni,34\nV. Sordini,99 F. Sorrentino,56 H. Sotani,308 A. Southgate,32 F. Spada,89 V. Spagnuolo,35, 36 A. P. Spencer,28\nM. Spera,46, 309 P. Spinicelli,59 C. A. Sprague,274 A. K. Srivastava,94 F. Stachurski,28 D. A. Steer,310\nN. Steinle,165 J. Steinlechner,35, 36 S. Steinlechner,35, 36 N. Stergioulas,288 P. Stevens,38 S. P. Stevenson,153\nF. Stolzi,101 M. StPierre,154 G. Stratta,311, 136, 67, 312 M. D. Strong,12 A. Strunk,2 R. Sturani,313 A. L. Stuver,55, \u2217\nM. Suchenek,96 S. Sudhagar,96 N. Sueltmann,86 L. Suleiman,54 K. D. Sullivan,12 J. Sun,238 L. Sun,33 S. Sunil,94\nJ. Suresh,48 B. J. Sutton,73 P. J. Sutton,32 T. Suzuki,224 Y. Suzuki,230 B. L. Swinkels,36 A. Syx,69\nM. J. Szczepa\u00b4nczyk,314, 44 P. Szewczyk,124 M. Tacca,36 H. Tagoshi,199 S. C. Tait,11 H. Takahashi,267\nR. Takahashi,24 A. Takamori,53 T. Takase,49 K. Takatani,231 H. Takeda,315 K. Takeshita,179 C. Talbot,131\nM. Tamaki,199 N. Tamanini,128 D. Tanabe,142 K. Tanaka,49 S. J. Tanaka,230 T. Tanaka,315 D. Tang,29 S. Tanioka,80\nD. B. Tanner,44 W. Tanner,8, 9 L. Tao,209 R. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n,36 R. Tarafder,11 C. Taranto,20, 21\nA. Taruya,316 J. D. Tasson,317 J. G. Tau,111 R. Tenorio,100 H. Themann,202 A. Theodoropoulos,137\nM. P. Thirugnanasambandam,15 L. M. Thomas,11 M. Thomas,66 P. Thomas,2 J. E. Thompson,234 S. R. Thondapu,102\nK. A. Thorne,66 E. Thrane,6 J. Tissino,43 A. Tiwari,15 P. Tiwari,43 S. Tiwari,204 V. Tiwari,118 M. R. Todd,80\nA. M. Toivonen,98 K. Toland,28 A. E. Tolley,78 T. Tomaru,24 K. Tomita,231 V. Tommasini,11 T. Tomura,49\nH. Tong,6 C. Tong-Yu,142 A. Toriyama,230 N. Toropov,118 A. Torres-Forn\u00b4e,137, 138 C. I. Torrie,11 M. Toscani,128\nI. Tosta e Melo,318 E. Tournefier,30 M. Trad Nery,48 A. Trapananti,51, 50 F. Travasso,51, 50 G. Traylor,66\nC. Trejo,11 M. Trevor,125 M. C. Tringali,59 A. Tripathee,91 G. Troian,189, 46 A. Trovato,189, 46 L. Trozzo,4\nR. J. Trudeau,11 T. T. L. Tsang,32 S. Tsuchida,319 L. Tsukada,218 K. Turbang,182, 22 M. Turconi,48 C. Turski,95\nH. Ubach,41, 82 N. Uchikata,199 T. Uchiyama,49 R. P. Udall,11 T. Uehara,320 M. Uematsu,231 S. Ueno,230\nV. Undheim,276 T. Ushiba,49 M. Vacatello,89, 88 H. Vahlbruch,8, 9 G. Vajente,11 A. Vajpeyi,6 G. Valdes,321\nJ. Valencia,100 A. F. Valentini,12 M. Valentini,106, 36 S. A. Vallejo-Pe\u02dcna,297 S. Vallero,27 V. Valsan,10\nN. van Bakel,36 M. van Beuzekom,36 M. van Dael,36, 322 J. F. J. van den Brand,35, 106, 36 C. Van Den Broeck,77, 36\nD. C. Vander-Hyde,80 M. van der Sluys,36, 77 A. Van de Walle,38 J. van Dongen,36, 106 K. Vandra,55\nH. van Haevermaet,22 J. V. van Heijningen,36, 106 P. Van Hove,69 J. Vanier,253 M. VanKeuren,103 J. Vanosky,2\nM. H. P. M. van Putten,17 Z. Van Ranst,35, 36 N. van Remortel,22 M. Vardaro,35, 36 A. F. Vargas,123\n\n5\nJ. J. Varghese,70 V. Varma,133 A. N. Vazquez,87 A. Vecchio,118 G. Vedovato,93 J. Veitch,28 P. J. Veitch,115\nS. Venikoudis,14 J. Venneberg,8, 9 P. Verdier,99 M. Vereecken,14 D. Verkindt,30 B. Verma,133 P. Verma,180\nY. Verma,102 S. M. Vermeulen,11 F. Vetrano,64 A. Veutro,67, 68 A. M. Vibhute,2 A. Vicer\u00b4e,64, 65 S. Vidyant,80\nA. D. Viets,85 A. Vijaykumar,184 A. Vilkha,111 V. Villa-Ortega,130 E. T. Vincent,60 J.-Y. Vinet,48 S. Viret,99\nA. Virtuoso,46 S. Vitale,34 A. Vives,79 H. Vocca,90, 50 D. Voigt,86 E. R. G. von Reis,2 J. S. A. von Wrangel,8, 9\nL. Vujeva,139 S. P. Vyatchanin,107 J. Wack,11 L. E. Wade,103 M. Wade,103 K. J. Wagner,111 A. Wajid,56, 57\nM. Walker,122 G. S. Wallace,58 L. Wallace,11 E. J. Wang,87 H. Wang,39 J. Z. Wang,91 W. H. Wang,161\nY. F. Wang,1 Z. Wang,142 G. Waratkar,207 J. Warner,2 M. Was,30 T. Washimi,24 N. Y. Washington,11\nD. Watarai,40 K. E. Wayt,103 B. R. Weaver,32 B. Weaver,2 C. R. Weaving,78 S. A. Webster,28\nN. L. Weickhardt,86 M. Weinert,8, 9 A. J. Weinstein,11 R. Weiss,34 F. Wellmann,8, 9 L. Wen,29 P. We\u00dfels,8, 9\nK. Wette,33 J. T. Whelan,111 B. F. Whiting,44 C. Whittle,11 E. G. Wickens,78 J. B. Wildberger,1 D. Wilken,8, 9, 9\nD. J. Willadsen,85 K. Willetts,32 D. Williams,28 M. J. Williams,78 N. S. Williams,118 J. L. Willis,11\nB. Willke,9, 8, 9 M. Wils,108 C. W. Winborn,104 J. Winterflood,29 C. C. Wipf,11 G. Woan,28 J. Woehler,35, 36\nN. E. Wolfe,34 H. T. Wong,142 I. C. F. Wong,216, 108 J. L. Wright,33 M. Wright,28 C. Wu,141 D. S. Wu,8, 9 H. Wu,141\nT. Y. Wu,323, 324 E. Wuchner,54 D. M. Wysocki,10 V. A. Xu,34 Y. Xu,204 N. Yadav,96 H. Yamamoto,11\nK. Yamamoto,183 T. S. Yamamoto,40 T. Yamamoto,49 S. Yamamura,199 R. Yamazaki,230 T. Yan,118 F. W. Yang,325\nF. Yang,265 K. Z. Yang,98 Y. Yang,145 Z. Yarbrough,12 H. Yasui,49 S.-W. Yeh,141 A. B. Yelikar,111 X. Yin,34\nJ. Yokoyama,326, 40, 39 T. Yokozawa,49 J. Yoo,149 H. Yu,148 S. Yuan,29 H. Yuzurihara,49 A. Zadro\u02d9zny,180\nM. Zanolin,70 M. Zeeshan,111 T. Zelenova,59 J.-P. Zendri,93 M. Zeoli,14 M. Zerrad,37 M. Zevin,81 A. C. Zhang,265\nL. Zhang,11 R. Zhang,150 T. Zhang,118 Y. Zhang,33 C. Zhao,29 Yue Zhao,325 Yuhang Zhao,72 Y. Zheng,104\nH. Zhong,98 R. Zhou,221 X.-J. Zhu,327 Z.-H. Zhu,327, 208 A. B. Zimmerman,147 M. E. Zucker,34, 11 J. Zweizig,11\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n15Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n18Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n19SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n20Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n21INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n22Universiteit Antwerpen, 2000 Antwerpen, Belgium\n23International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n24Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n25Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n27INFN Sezione di Torino, I-10125 Torino, Italy\n28SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n29OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n30Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n31Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n32Cardiff University, Cardiff CF24 3AA, United Kingdom\n33OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n34LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n\n6\n35Maastricht University, 6200 MD Maastricht, Netherlands\n36Nikhef, 1098 XG Amsterdam, Netherlands\n37Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n38Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n39Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n40University of Tokyo, Tokyo, 113-0033, Japan.\n41Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n42Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n43Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n44University of Florida, Gainesville, FL 32611, USA\n45Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n46INFN, Sezione di Trieste, I-34127 Trieste, Italy\n47Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, Monterrey 64849, Mexico\n48Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n49Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n50INFN, Sezione di Perugia, I-06123 Perugia, Italy\n51Universit`a di Camerino, I-62032 Camerino, Italy\n52University of Washington, Seattle, WA 98195, USA\n53Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n54California State University Fullerton, Fullerton, CA 92831, USA\n55Villanova University, Villanova, PA 19085, USA\n56INFN, Sezione di Genova, I-16146 Genova, Italy\n57Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n58SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n59European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n60Georgia Institute of Technology, Atlanta, GA 30332, USA\n61Chennai Mathematical Institute, Chennai 603103, India\n62Royal Holloway, University of London, London TW20 0EX, United Kingdom\n63Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n64Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n65INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n66LIGO Livingston Observatory, Livingston, LA 70754, USA\n67INFN, Sezione di Roma, I-00185 Roma, Italy\n68Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n69Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n70Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n71Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n72Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n73King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n74Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n75Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n76International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n77Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n78University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n79University of Oregon, Eugene, OR 97403, USA\n80Syracuse University, Syracuse, NY 13244, USA\n81Northwestern University, Evanston, IL 60208, USA\n82Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n83Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n84HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n85Concordia University Wisconsin, Mequon, WI 53097, USA\n86Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n87Stanford University, Stanford, CA 94305, USA\n88Universit`a di Pisa, I-56127 Pisa, Italy\n\n7\n89INFN, Sezione di Pisa, I-56127 Pisa, Italy\n90Universit`a di Perugia, I-06123 Perugia, Italy\n91University of Michigan, Ann Arbor, MI 48109, USA\n92Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n93INFN, Sezione di Padova, I-35131 Padova, Italy\n94Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n95Universiteit Gent, B-9000 Gent, Belgium\n96Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n97Centro de Investigaciones Energ\u00b4eticas Medioambientales y Tecnol\u00b4ogicas, Avda. Complutense 40, 28040, Madrid, Spain\n98University of Minnesota, Minneapolis, MN 55455, USA\n99Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n100IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n101Universit`a di Siena, I-53100 Siena, Italy\n102RRCAT, Indore, Madhya Pradesh 452013, India\n103Kenyon College, Gambier, OH 43022, USA\n104Missouri University of Science and Technology, Rolla, MO 65409, USA\n105Colorado State University, Fort Collins, CO 80523, USA\n106Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n107Lomonosov Moscow State University, Moscow 119991, Russia\n108Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n109Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n110INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n111Rochester Institute of Technology, Rochester, NY 14623, USA\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n114INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n128L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n129Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n130IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n131University of Chicago, Chicago, IL 60637, USA\n132University of Arizona, Tucson, AZ 85721, USA\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n135Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142National Central University, Taoyuan City 320317, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n\n8\n146Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Cornell University, Ithaca, NY 14850, USA\n150Northeastern University, Boston, MA 02115, USA\n151Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n153OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n154University of Rhode Island, Kingston, RI 02881, USA\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n157INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n158Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n159Montana State University, Bozeman, MT 59717, USA\n160Johns Hopkins University, Baltimore, MD 21218, USA\n161The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n162Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n163DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n164Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2, Bologna, Italy\n165University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n166INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n167Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n168Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n169Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n170Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n171Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n172Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n173INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n174University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n175Marquette University, Milwaukee, WI 53233, USA\n176Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n177Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n178Indian Institute of Technology Madras, Chennai 600036, India\n179Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n180National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n181Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n182Vrije Universiteit Brussel, 1050 Brussel, Belgium\n183Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n184Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n185University of Cambridge, Cambridge CB2 1TN, United Kingdom\n186Stony Brook University, Stony Brook, NY 11794, USA\n187Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n188Montclair State University, Montclair, NJ 07043, USA\n189Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n190HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n191Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n192Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n193CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n194Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n195Western Washington University, Bellingham, WA 98225, USA\n196Barry University, Miami Shores, FL 33168, USA\n197Centro de Astrof\u00b4\u0131sica e Gravita\u00b8c\u02dcao, Departamento de F\u00b4\u0131sica, Instituto Superior T\u00b4ecnico - IST, Universidade de Lisboa - UL, Av.\nRovisco Pais 1, 1049-001 Lisboa, Portugal\n198E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n199Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n\n9\n200Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n201Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n202California State University, Los Angeles, Los Angeles, CA 90032, USA\n203Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n204University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n205Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n206University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n207Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n208School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n209University of California, Riverside, Riverside, CA 92521, USA\n210University of Nottingham NG7 2RD, UK\n211Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n212University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n213The University of Mississippi, University, MS 38677, USA\n214Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n215Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n216The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n217American University, Washington, DC 20016, USA\n218University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n219Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n220IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n221University of California, Berkeley, CA 94720, USA\n222University of Lancaster, Lancaster LA1 4YW, United Kingdom\n223College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n224Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n225Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n226Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n227Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n228Scuola Normale Superiore, I-56126 Pisa, Italy\n229Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n230Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n234University of Southampton, Southampton SO17 1BJ, United Kingdom\n235Sungkyunkwan University, Seoul 03063, Republic of Korea\n236Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n237Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n238Chung-Ang University, Seoul 06974, Republic of Korea\n239University of Washington Bothell, Bothell, WA 98011, USA\n240Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n241Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n242Ewha Womans University, Seoul 03760, Republic of Korea\n243Seoul National University, Seoul 08826, Republic of Korea\n244Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n245Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n246Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n247Bard College, Annandale-On-Hudson, NY 12504, USA\n248Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n249Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n250Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n251Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n\n10\n252Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n253Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n254Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n255Texas Tech University, Lubbock, TX 79409, USA\n256Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n257Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n258Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,\nYuseong-gu, Daejeon 34055, Republic of Korea\n259NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n260National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n261NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n262Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n263School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n264Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n265Columbia University, New York, NY 10027, USA\n266Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n267Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n268Tsinghua University, Beijing 100084, China\n269Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n270School of Physical & Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand\n271GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n272Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n273Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n274Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n275Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, To Huu street Yen Nghia Ward, Ha Dong District, Hanoi,\nVietnam\n276University of Stavanger, 4021 Stavanger, Norway\n277Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n278Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 903-0213, Japan\n279Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n280Observatoire de Paris, 75014 Paris, France\n281Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n282National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n283Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n284Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n289Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n290Department of Astronomy & Astrophysics, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai 400005,\nMaharashtra, India.\n291Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n292Hobart and William Smith Colleges, Geneva, NY 14456, USA\n293Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n294Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n295Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n296Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n297Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n298Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n\n11\n299Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n300Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n301Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n302Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n303Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n304University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n305Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n306Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n307NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n308iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n309Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n310Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS, Universit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e),\nF-75005 Paris, France\n311Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n312INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n313Universidade Estadual Paulista, 01140-070 S\u02dcao Paulo, Brazil\n314Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n315Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n316Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n317Carleton College, Northfield, MN 55057, USA\n318University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n319National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n320Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n321Texas A&M University, College Station, TX 77843, USA\n322Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n323Department of Physics and Astronomy, University of North Carolina at Chapel Hill, 120 E. Cameron Ave, Chapel Hill, NC, 27599,\nUSA\n324David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto, 50 St George St, Toronto ON M5S 3H4, Canada\n325The University of Utah, Salt Lake City, UT 84112, USA\n326Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City,\nChiba 277-8583, Japan\n327Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n(Compiled: 19 September 2025)\nABSTRACT\nWe detail the population properties of merging compact objects using 158 mergers from the cumula-\ntive Gravitational-Wave Transient Catalog 4.0, which includes three types of binary mergers: binary\nneutron star, neutron star\u2013black hole binary, and binary black hole mergers. We resolve multiple\nover- and under-densities in the black hole mass distribution: features persist at primary masses of\n10 M\u2299and 35 M\u2299with a possible third feature at \u223c20 M\u2299. These are departures from an otherwise\npower-law-like continuum that steepens above 35 M\u2299. Binary black holes with primary masses near\n10 M\u2299are more likely to have less massive secondaries, with a mass ratio distribution peaking at\nq = 0.74+0.13\n\u22120.13, potentially a signature of stable mass transfer during binary evolution. Black hole spins\nare inferred to be non-extremal, with 90% of black holes having \u03c7 < 0.57, and preferentially aligned\nwith binary orbits, implying many merging binaries form in isolation. However, we find a significant\nfraction, 0.24\u20130.42, of binaries have negative effective inspiral spins, suggesting many could be formed\ndynamically in gas-free environments. We find evidence for correlation between effective inspiral spin\nand mass ratio, though it is unclear if this is driven by variation in the mode of the distribution or\nthe width. The binary black hole merger rate increases with redshift as (1 + z)\u03ba with \u03ba = 3.2+0.94\n\u22121.00,\nconsistent with the cosmic star formation density. While there is no evidence of the mass spectrum\nevolving with redshift, the distribution of effective inspiral spin is found to broaden as redshift increases\n\n12\nout to z \u22481. We infer the local merger rates (i.e., at redshift z = 0) to be 7.6\u2013250 Gpc\u22123 yr\u22121 for\nbinary neutron stars, 9.1\u201384 Gpc\u22123 yr\u22121 for neutron star\u2013black hole binaries, and 14\u201326 Gpc\u22123 yr\u22121\nfor binary black holes; all values reflect central 90% credible intervals.\n1. INTRODUCTION\nGravitational waves (GWs) have revolutionized the\nstudy of compact objects and their populations (Ab-\nbott et al. 2016, 2019a, 2021a, 2023a), with observa-\ntions now extending beyond redshift z = 1. Searches for\nGWs from compact binary mergers have robustly quan-\ntifiable selection effects, which enable detailed inference\nof population properties with few sources of potential\nbias (Mandel et al. 2019; Essick & Fishbach 2024). By\nstudying the growing catalog of compact binary merg-\ners, we aim to uncover both where these systems form,\nand how they evolve toward merger. For example, are\nthey formed from stars that are gravitationally bound\nat birth, possibly as the products of chemically homo-\ngeneous evolution (Mandel & de Mink 2016; Marchant\net al. 2016; de Mink & Mandel 2016), or brought close\nenough together for GW-driven inspiral through phases\nof common envelope evolution (Bethe & Brown 1998;\nPortegies Zwart & Yungelson 1998; Belczynski et al.\n2001; Dominik et al. 2015) or stable mass transfer (Hur-\nley et al. 2002; Neijssel et al. 2019; van Son et al. 2022b)?\nCould binaries be assisted in assembly and hardening in\nthe gaseous disks of active galactic nuclei (AGN) (McK-\nernan et al. 2012; Bartos et al. 2017; Stone et al. 2017;\nFragione et al. 2019) or through dynamical interactions\nin dense stellar environments (Kulkarni et al. 1993; Sig-\nurdsson & Hernquist 1993; Portegies Zwart & McMillan\n2000; Ziosi et al. 2014)?\nFrom the first three observing runs of the LIGO\u2013\nVirgo\u2013KAGRA Collaboration (LVK), we established\nthat stellar-mass black holes (BHs) in merging bina-\nries have a broad distribution of masses, with peaks\nat primary masses of \u223c10 M\u2299and \u223c35 M\u2299, that falls\noff steeply above \u223c45 M\u2299(Abbott et al. 2023a). De-\nspite the steep decline, the rate of mergers in the ex-\npected pair-instability supernova (PISN) gap, predicted\nto begin at \u223c45 \u2013 50 M\u2299(Woosley 2017; Farmer et al.\n2019), was found to be non-zero (Abbott et al. 2020c,d).\nLikewise, the rate of mergers in the purported lower\nmass gap between \u223c3 \u2013 5 M\u2299(Bailyn et al. 1998; Ozel\net al. 2010; Farr et al. 2011) was found to be small but\nnon-zero (Abbott et al. 2020e; Abac et al. 2024). The\nneutron star (NS) mass distribution does not require\na peak in the distribution at \u223c1.33 M\u2299, as is seen in\nthe galactic binary neutron star (BNS) population (\u00a8Ozel\n\u2217Deceased, September 2024.\n& Freire 2016; Farrow et al. 2019). The binary black\nhole (BBH) merger rate was found to definitively in-\ncrease with redshift. Spins were found to be small in\nmagnitude, with a non-zero fraction of systems with spin\ncomponents anti-aligned with the binary orbit.\nAdvanced\nLIGO\n(Aasi\net\nal.\n2015),\nAdvanced\nVirgo (Acernese et al. 2015), and KAGRA (Akutsu\net al. 2021) began their fourth observing run (O4)\non 2023 May 24 at 15:00 UTC. The first part of the\nfourth observing run (O4a) ended on 2024 January\n16 at 16:00 UTC. The accompanying Gravitational-\nWave Transient Catalog (GWTC) version 4.0 (here-\nafter, GWTC-4.0) (Abac et al. 2025a,b,c) contains those\nevents observed in previous observing runs, O1 (Abbott\net al. 2016), O2 (Abbott et al. 2019b), and O3 (Abbott\net al. 2021b, 2023b, 2024), together with the newest ob-\nservations from O4a.\nWe use the updated catalog to\ninfer the population properties of BNS, neutron star\u2013\nblack hole binary (NSBH), and BBH systems in the local\nUniverse.\nGWTC-3.0 included 76 candidates with false alarm\nrate (FAR) < 1 yr\u22121: 69 BBHs, 4 NSBHs, 2 BNSs, and\none event GW190814 211039 (henceforth, GW190814)\nthat is either a NSBH or BBH. Abac et al. (2025c) iden-\ntifies 128 candidate signals in O4a with a probability of\nastrophysical compact binary origin of pastro \u22650.5, of\nwhich 85 (84 BBHs and 1 NSBH) have FAR < 1 yr\u22121.\nSelecting BBHs from the catalog using this threshold\nyields a cumulative BBH count of 153.\nWith fewer\nsignal candidates from binaries containing at least one\nNS, maintaining a comparable contamination fraction\nto that of BBH mergers (\u223c5%) requires a more conser-\nvative threshold (see Section 3 for more details).\nWe\nadopt the same threshold used for similar analyses of\nGWTC-3.0, FAR < 0.25 yr\u22121, for analyses that include\nNS-containing populations (Abbott et al. 2023a). This\nyields two NSBH candidates from O3, and one new\ncandidate, GW230529 181500 (henceforth, GW230529),\ndetected above this threshold in designated observing\ntime during O4a (Abac et al. 2024). Section 3 provides\nfurther details and discussion of threshold choices and\ncandidate inclusion.\nAdopting the more conservative\nFAR < 0.25 yr\u22121 threshold reduces the O4a BBH count\nto 76, resulting in a catalog of 2 BNSs, 3 NSBHs, and\n138 BBHs for analyses that include BNS and NSBH pop-\nulations in this work.\nThe remainder of the paper is structured as follows.\nIn Section 2 we provide a brief description of our infer-\n\n13\nence techniques (with remaining details in Appendix A)\nand the classes of models used (with full descriptions\nof the models in Appendices B and C, and how they\nwere chosen in Appendix D). Section 3 describes our\ndataset and sample selection, including brief descrip-\ntions of search techniques, threshold choices, and wave-\nform models used.\nIn Section 4 we present measure-\nments of the complete compact-binary mass spectrum\n(NSs and BHs).\nIn Section 5, we study the proper-\nties of the NS-containing population in detail, and in\nSection 6 focus on the ensemble properties of BBHs,\nincluding their masses, spins, redshifts, and associated\ncorrelations. Section 7 concludes by summarizing the\nkey results of this work. Associated data releases pro-\nvide analysis results and figure generation scripts (LIGO\nScientific Collaboration et al. 2025) and data products\nfor estimating sensitivity (Essick 2025a,b).\n2. METHODS\nWe determine the population properties of merging\ncompact binaries using hierarchical Bayesian inference\nas has been done in previous studies (Abbott et al.\n2019a, 2021a, 2023a). Our aim here is to estimate the\nposterior distribution p(\u039b|d) on population-level model\nparameters \u039b (also referred to as hyperparameters) in\nlight of new data d representing the observed GW data\nfrom individual merger events. These model-dependent\nhyperparameters describe the population-level proper-\nties of GW source parameters \u03b8 (masses, spins, redshifts,\netc.). According to Bayes\u2019 theorem,\np(\u039b|d) = L(d|\u039b)\u03c0(\u039b)\np(d)\n,\n(1)\nwhere \u03c0(\u039b) is the prior probability distribution and\nL(d|\u039b) is the likelihood\u2014the probability of obtaining\nthe data d given some \u039b. The Bayesian evidence p(d)\nensures that p(\u039b|d) is properly normalized.\nIn order to use Bayes\u2019 theorem to infer the posterior\nprobability distribution of hyperparameters, we need the\nlikelihood of obtaining the observed catalog of events\ngiven a set of hyperparameters and a population model.\nBecause GW detectors are not equally sensitive to dif-\nferent astrophysical sources, the likelihood must account\nfor selection biases. Assuming (i) a Poisson process gen-\nerates realizations from the source population of which\na subset is detected, and (ii) the observed data associ-\nated are statistically independent (e.g., no overlapping\nsignals), the likelihood is given by (Loredo 2004; Farr\net al. 2015; Mandel et al. 2019; Thrane & Talbot 2019;\nVitale et al. 2020)\nL({di}, Ndet|\u039b) \u221d\nN(\u039b)Ndete\u2212Nexp(\u039b)\nNdet\nY\ni=1\nZ\nd\u03b8 L(di|\u03b8)\u03c0(\u03b8|\u039b) ,\n(2)\nwhere N(\u039b) is the total number of mergers (detected\nand undetected) incident on the detectors within the\nobserving period, Ndet is the number of detections, di\nare the strain data corresponding to the ith detection,\nand L(di|\u03b8) is the likelihood of the data di given the GW\nsource parameters \u03b8 (Abac et al. 2025b). The expected\nnumber of detections is Nexp(\u039b) = N \u03be(\u039b), with \u03be(\u039b)\nbeing the expected fraction of the population parame-\nterized by \u039b that is detectable. Formally, we impose a\ndetection criterion on the data, e.g., a FAR threshold,\nby the selection function x(d) acting on a data segment\nd. A GW event is detectable in d if x(d) > xthr, where\nxthr is the chosen detectability threshold. Then,\n\u03be(\u039b) =\nZ\nx(d)>xthr\ndd d\u03b8 p(d|\u03b8)\u03c0(\u03b8|\u039b).\n(3)\nIn Equation (3), the domain of integration is over all\ndata d which surpasses the detection threshold xthr (Es-\nsick et al. 2025). When a prior \u03c0(N) \u221d1/N is assumed,\nEquation (2) can be analytically marginalized over N\nleaving the rate-marginalized hierarchical likelihood\nL({d}, Ndet|\u039b) \u221d\nNdet\nY\ni=1\nR\nd\u03b8 L(di|\u03b8)\u03c0(\u03b8|\u039b)\n\u03be(\u039b)\n.\n(4)\nThis likelihood may also be obtained by marginaliz-\ning over a prior on the expected number of detections,\nNexp = N\u03be(\u039b), rather than on N (Essick & Fishbach\n2024).\nHaving described the hierarchical likelihood in Equa-\ntion (2) and Equation (4) we have one of the two in-\ngredients necessary for sampling the posterior in Equa-\ntion (1). We also must choose a prior over the space\nof hyperparameters.\nThis depends on the population\nmodel, which we describe in more detail below.\nWe\nspecify the priors for each model in Appendix B.\nEquation (2) is the exact form of the likelihood. How-\never, calculating \u03be(\u039b) and integrating over \u03b8 is analyt-\nically intractable. Therefore, we approximate the like-\nlihood via Monte Carlo reweighting using importance\nsampling. Our Monte Carlo approximation for the likeli-\nhood carries some uncertainty and may not be converged\nappropriately for some hyperparameter values. There-\nfore, we discard hyperparameters whose likelihood un-\ncertainty exceeds a chosen threshold a posteriori (Talbot\n& Golomb 2023). For more description of this problem\nand our approach for mitigating it, see Appendix A.\n\n14\nThe Bayesian inference problem is stated here in terms\nof the population probability density \u03c0(\u03b8|\u039b) and the\noverall number of merging binaries N. This can be con-\nverted to another astrophysical quantity of interest, the\ncomoving source-frame merger rate density\nR(z) =\ndN\ndVcdts\n(z) =\ndN\ndtddz\n\u0012dVc\ndz\n1\n1 + z\n\u0013\u22121\n,\n(5)\nwhere ts is the time measured in the comoving source\nframe, td is the time at the detector (redshift z = 0) and\ndVc/dz is the differential comoving volume with respect\nto redshift z (see e.g., Essick et al. 2025). The comov-\ning source frame merger rate represents the number of\nmergers in a unit of comoving volume and source-frame\ntime, conventionally measured in units Gpc\u22123 yr\u22121.\nTo construct models for the population distribution\nof astrophysical GW sources, we take one of two ap-\nproaches. The first approach\u2014which we call the strongly\nmodeled approach (sometimes called the parametric\napproach)\u2014assumes a specific functional form \u03c0(\u03b8|\u039b)\nfor the astrophysical distribution a priori, e.g., a Gaus-\nsian distribution or a power law. A second approach\u2014\nwhich we call the weakly modeled approach (elsewhere\ndata-driven, flexible, or nonparametric)\u2014attempts to\nmake minimal a priori assumptions about the under-\nlying astrophysical population, e.g., a spline model. We\nelaborate on each approach in the following two subsec-\ntions, and provide details for the models presented in\nthis work falling in each category.\n2.1. Strongly Modeled Approach\nThe strongly modeled approach assumes that the un-\nderlying astrophysical distribution of binary properties\ncan be described by a fixed functional form and associ-\nated hyperparameters. Consequently, this approach has\nfar fewer hyperparameters as compared to the weakly\nmodeled approach. The parameterization may be moti-\nvated by theoretical expectations about the astrophysi-\ncal population and/or could be selected because it seems\nto fit the observed data well. This has the benefit of be-\ning simple and interpretable, as hyperparameters can\nbe designed to correspond directly to physical features\nof interest. Examples of such features are a distribu-\ntion\u2019s minimum or maximum, the location parameter for\nan overdensity corresponding to e.g., pulsational pair-\ninstability supernovae, etc. On the other hand, these\napproaches can be overly restrictive: features present\nin the true astrophysical distribution that are not cap-\ntured by our parameterization cannot be easily discov-\nered. Additionally, the inferred parameters can be bi-\nased due to a mis-specified model (e.g., Romero-Shaw\net al. 2022).\nThe parameterized models selected for this work are\ngenerally simple extensions to those employed in the pre-\nvious LVK astrophysical population studies paper from\nGWTC-3.0 (Abbott et al. 2023a).\nUpdates to these\nmodels are motivated by features that have emerged due\nto new data in GWTC-4.0 and improved interpretations\nsince GWTC-3.0.\nTable 1 lists the strongly modeled approaches used in\nthis paper, with details in Appendix B. We also describe\nthe parameterizations and priors for these models in Ap-\npendix B, and our procedure for selecting the default\nstrongly modeled approach in Appendix D. For most\nmodels, we assume that masses, spins, and redshifts are\nall uncorrelated. We also study a selection of pairwise\ncorrelations between parameters in Section 6.5.\n2.2. Weakly Modeled Approach\nThe weakly modeled approach adopts models that de-\nliberately make few assumptions about the nature of\nthe underlying compact-binary population.\nSuch ap-\nproaches typically require a larger number of hyperpa-\nrameters in order to effectively approximate a wide va-\nriety of distributions. The philosophy of a weakly mod-\neled approach is to discover unexpected features in the\npopulation, which may be unforeseen or difficult to pa-\nrameterize. However, they could yield results that are\nmore difficult to interpret astrophysically. The differ-\nence between the strongly modeled and weakly mod-\neled approaches can be understood in terms of the bias\u2013\nvariance tradeoff; the former has low variance with a\nrisk of bias, whereas the latter has low bias but elevated\nvariance.\nWeakly modeled approaches must make some assump-\ntions, however, and must be designed with different\nfeatures in mind.\nFor example, different approaches\nhave sensitivity to astrophysical correlations, narrow\nstructures, or gaps in the population. While a unified\nBayesian approach to capture generic population fea-\ntures is still an open problem (Mandel et al. 2017; Tiwari\n2021; Rinaldi & Del Pozzo 2021; Edelman et al. 2023;\nGolomb & Talbot 2023; Payne & Thrane 2023; Toubiana\net al. 2023; Callister & Farr 2024; Ray et al. 2023a;\nFarah et al. 2025b; Heinzel et al. 2025a), we use two\ndifferent weakly modeled approaches\u2014B-Spline and\nBinned Gaussian Process (BGP)\u2014to verify results\nfrom our strongly modeled approaches (see Table 1). We\ndescribe two additional weakly modeled approaches\u2014\nAutoregressive Process (AR) and Flexible Mix-\ntures (FM)\u2014in Appendix C, and compare these ap-\nproaches in Appendix D.4.\n\n15\nTable 1. Summary of Models\nModel Type\nModel Name\nDescription\nStrongly Modeled:\nFullPop-4.0\nModels the mass spectrum of all CBCs simultaneously with\nMass\nappropriate power-law and peak components. Also allows for a\ngap between the most massive NS and the least massive BH.\nBroken Power Law + 2 Peaks \u22c6\nThe primary mass distribution has a broken power law\ncontinuum between a minimum and maximum mass, plus\ntwo Gaussian peaks around \u223c10 M\u2299and \u223c35 M\u2299. The\ndistribution of mass ratio q is a power law between\nsome minimum value and 1.\nExtended Broken Power\nThe mass-ratio power-law is allowed to differ between\nLaw + 2 Peaks\nprimary masses in the continuum and in the 35 M\u2299peak.\nStrongly Modeled:\nGaussian Component Spins \u22c6\nThe spin magnitude population is a Gaussian truncated over\nComponent Spin\nthe physical range \u03c7 \u2208[0, 1). The distribution of cosine spin tilts\nrelative to the orbital angular momentum includes an isotropic\n(i.e., uniform) component and a truncated Gaussian component.\nStrongly Modeled:\nGaussian Effective Spins\nThe joint \u03c7eff\u2013\u03c7p effective spin distribution is a bivariate\nEffective Spin\nGaussian allowing for correlations.\nSkew-normal Effective Spin\nThe \u03c7eff marginal effective spin distribution is skew normal,\ntruncated to [\u22121, 1].\nStrongly Modeled:\nPower Law Redshift \u22c6\nThe merger rate per unit comoving volume and source-frame\nRedshift\ntime evolves with redshift z as a power law i.e., \u221d(1 + z)\u03ba.\nStrongly Modeled:\nCopula\nTruncated Gaussian distributions are assumed for \u03c7eff and\nCorrelations\n\u03c7p. A Frank copula density function correlates two variables.\nSeparate copula models correlate (q, \u03c7eff), (z, \u03c7eff), (m1, \u03c7eff),\nand (m1, z).\nLinear\nA truncated Gaussian distribution is assumed for \u03c7eff with\nthe mean and width linearly dependent on either q or z.\nSpline\nA truncated Gaussian distribution is assumed for \u03c7eff with\nthe mean and width dependent on either q or z. This\ndependence is flexibly modeled with a cubic spline.\nWeakly Modeled:\nB-Spline\nFits the astrophysical distribution as a separable joint\nAll Parameters\ndistribution with one-dimensional basis splines. Large numbers\nof basis functions allow for flexibility, with difference-based\npriors imposing smooth evolution a priori.\nBinned Gaussian Process\nAssumes a fixed binning scheme and infers the event rate under\nthe assumption of a constant rate within each bin, and a\nGaussian process prior imposing smooth covariance across bins.\nStrongly modeled and weakly modeled approaches used to study the mass, spin, and redshift distributions of merging compact\nbinaries. We provide a brief description of each model here, with detailed descriptions in Appendix B and Appendix C. Models\nmarked with a \u22c6are treated as defaults and are used whenever no model is explicitly indicated for a certain parameter. All\nstrongly modeled approaches mentioned below target BBHs, with the exception of FullPop-4.0 that is used to model the entire\nCBC population.\n\n16\n3. DATASET\n3.1. Data Collection Duration\nAnalyses presented in this paper use selected data\nproducts from GWTC-4.0 (Abac et al. 2025a,b,c,d).\nThis section and Section\n3.2 provide details on the\nselection criteria for events analyzed for this paper.\nGWTC-4.0 includes GW candidates and data from O1\nthrough the end of O4a, as well as a GW candidate and\ndata collected during an engineering run (ER) (Abbott\net al. 2020a) directly preceding the start of O4a. ERs\nare periods dedicated to final commissioning and con-\nfiguration of the instruments prior to an observing run;\nthe instruments may be in locked and low-noise con-\nfigurations, but are not generally intended to perform\nastrophysical observations.\nThe ER data included in\nGWTC-4.0 is deliberately chosen to contain a few days\nof data around a GW event potentially originating from\na NSBH binary merger, GW230518 125908 (henceforth,\nGW230518).\nThe analyses and results quoted in this\npaper exclude data obtained during the ER; the inclu-\nsion of this data would introduce human selection effects\nthat cannot be easily incorporated into \u03be(\u039b), and hence\nmay bias our inferences.\n3.2. Event Selection Criteria\n3.2.1. Significance Thresholds\nTo ensure that the dataset we use in this paper has\nreduced contamination from noise events, we adopt a\nsignificance threshold of FAR < 1 yr\u22121 in at least one\nGW search pipeline, which is consistent with the cri-\nterion adopted in Abbott et al. (2023a). Based on the\nFAR threshold, a total of 161 CBC candidates have been\ndetected from O1 through O4a (Abbott et al. 2019b,\n2021b, 2024, 2023b) by the GW search pipelines (Abac\net al. 2025c), of which 85 were from O4a.\nThis is a\nnoteworthy increase in the number of observations re-\nported in Abbott et al. (2023b), which contained 76\nevents meeting the FAR < 1 yr\u22121 threshold. With this\nFAR threshold and assuming noise signals are produced\nindependently, we expect P\nk FAR \u00d7 Tk \u22436.7 contami-\nnant noise events in our results, where Tk is an estimate\nof the time examined by the kth search. The list of GW\nevents included in the analyses of this paper contains\nGW231123 135430 (henceforth, GW231123), which has\nhigh probability for being the most massive BBH with\nFAR < 1 yr\u22121 detected to date by the GWs with both\ncomponent masses possibly in the upper mass gap (Abac\net al. 2025e; Woosley 2017; Mapelli et al. 2020; Farmer\net al. 2019, 2020; Woosley & Heger 2021; Hendriks et al.\n2023).\nNot all events reported in the GWTCs pa-\npers (Abbott et al. 2019b, 2021b, 2024, 2023b; Abac\net al. 2025c) are included in our analyses, as previous\nGWTC papers thresholded event candidates using pastro\n\u22650.5 or FAR < 2 yr\u22121, whereas the analyses presented\nin our paper select events with a significance of FAR <\n1 yr\u22121. Here, pastro is the estimate of the probability of\nastrophysical origin of the event candidates (Abac et al.\n2025b,c).\nIn addition, GW230630 070659 is excluded\nfrom the analyses and the number of events reported in\nthis paper, due to concerns of the data quality around\nthe time of this event (Abac et al. 2025c).\n3.2.2. Mass and Significance Thresholds for Events with\nNSs\nTo distinguish NS-containing events from events con-\ntaining only BHs, we first threshold events by checking\nwhether the 1% lower limit on the component mass is\nsmaller or larger than 3 M\u2299. As far fewer GW candi-\ndates with NSs have been observed compared to BBHs,\nthis paper adopts a stricter FAR threshold of < 0.25\nyr\u22121 in at least one GW search pipeline for GW can-\ndidates with NSs to ensure a purer sample, as done\nin Abbott et al. (2023a).\nThis FAR threshold ex-\ncludes GW190917 114630 and GW190426 152155 (Ab-\nbott et al. 2024), which are consistent with originat-\ning from NSBHs but have FARs of > 0.25 yr\u22121.\nIn\naddition, we exclude certain events whose category is\nambiguous from dedicated BBH and NSBH analyses.\nSpecifically, we exclude GW190814 as its source\u2019s sec-\nondary mass is lower than the component masses of\nevents classified as BBHs but higher than the inferred\nNS mass range, leaving its classification ambiguous (Ab-\nbott et al. 2020e; Essick et al. 2022; Abbott et al.\n2023a).\nThis event is included in Section 4 which\nconsiders binary-merger populations across all masses.\nHence, the only NS-containing event detected in O4a\nconsidered in this paper is GW230529 (Abac et al.\n2024), in addition to the previously reported NSBHs,\nGW200105 162426 and GW200115 042309 (henceforth,\nGW200105 and GW200115, respectively). The results\nare presented in Section 5.\n3.2.3. Exclusion of Non-LVK Catalog Events\nIn addition to the catalog of event candidates and\nits analyses conducted by the LVK, independent teams\nhave analyzed the public GW data from O1 through\nsecond half of the third observing run (O3b) using\nalternative algorithms and have identified additional\nGW binary-merger event candidates (Venumadhav et al.\n2019, 2020; Olsen et al. 2022; Mehta et al. 2025; Wadekar\net al. 2023; Zackay et al. 2019; Nitz et al. 2019, 2020,\n2021, 2023; Kumar & Dent 2024; Mishra et al. 2025;\nKoloniari et al. 2025). We do not include these addi-\ntional events in our analyses here due to subtleties with\n\n17\nconsistently combining sensitivity estimates from these\nindependent catalogs.\n3.3. Sensitivity of GW Searches\nA key ingredient in the estimation of population level\nproperties is the sensitivity of our GW searches \u03be(\u039b).\nThe following four search pipelines analyzed detector\ndata for real GW signals as well as simulated GW sig-\nnals, called injections: GstLAL (Messick et al. 2017;\nSachdev et al. 2019; Hanna et al. 2020; Cannon et al.\n2020; Ewing et al. 2024; Tsukada et al. 2023; Sakon\net al. 2024; Ray et al. 2023b; Joshi et al. 2025a,b),\nMBTA (Adams et al. 2016; Aubin et al. 2021; Andres\net al. 2022; All\u00b4en\u00b4e et al. 2025), PyCBC (Usman et al.\n2016; Nitz et al. 2017, 2018; Dal Canton et al. 2021), and\nthe cWB analysis (Klimenko et al. 2005, 2008, 2016;\nTiwari et al. 2016; Drago et al. 2020; Klimenko 2022;\nMishra et al. 2021, 2022, 2025). Injections were added\nto data at an artificially higher rate than observed GW\nsignals, and were used to quantify the pipelines\u2019 sensi-\ntivities to GW signals (Essick et al. 2025; Abac et al.\n2025b). The distribution of injections was chosen to en-\nable efficient and accurate resampling to a wide range\nof astrophysically plausible populations (Essick et al.\n2025).\nFor all the analyses in this paper, the detec-\ntion efficiency \u03be(\u039b) is estimated using these injections\nthrough a Monte Carlo integral (Abac et al. 2025b; Ti-\nwari 2018; Farr 2019).\n3.4. Source Properties\nParameter estimation (PE) pipelines use Bayesian in-\nference to estimate the properties of GW events (Abac\net al. 2025b). The hierarchical Bayesian inference frame-\nwork described in Section 2 requires as input PE sam-\nples from individual events. For events detected in O4a,\nwe use samples drawn from the posterior distribution\nusing the NRSur7dq4 (Varma et al. 2019) waveform\napproximant if available. If these are not available e.g.,\nbecause the signal duration is too long to be analyzed\nby NRSur7dq4, we instead use a mixture of sam-\nples from the IMRPhenomXPHM SpinTaylor (Prat-\nten et al. 2021; Colleoni et al. 2025) and SEOB-\nNRv5PHM (Ramos-Buades et al. 2023; Pompili et al.\n2023) approximants. These are referred to as Mixed\nsamples in the PE data products. More details about\nvarious choices made in the PE procedure can be found\nin Section 5 of Abac et al. (2025b) and Section 3 of Abac\net al. (2025c).\nFor all events detected before O4a, we use the Mixed\nsamples reported in the GWTC-3.0 (Abbott et al.\n2023b) and GWTC-2.1 (Abbott et al. 2024) data re-\nleases. One exception is the BNS merger GW170817,\nfor which we use samples obtained with the IMR-\nPhenomPv2 NRTidal waveform approximant (Diet-\nrich et al. 2019) and a prior allowing for large spin mag-\nnitudes (Abbott et al. 2019c). We also reweight these\nsamples to a distance prior that is uniform in comoving\nvolume and source-frame time following the prescription\nin Appendix C of Abbott et al. (2021b).\nWhile this work was in its final stages, a normalization\nerror was discovered in the noise-weighted inner product\nused in the PE likelihood function (Abac et al. 2025b;\nTalbot et al. 2025b).\nWhile there is a version of the\nPE samples that account for the correct likelihood via\na reweighting prescription (Abac et al. 2025b; Talbot\net al. 2025b), we do not use these samples in this work.\nFurther, for candidates detected during the first three\nobserving runs, we discovered that incorrect priors were\nused when marginalizing over the uncertainty in the cal-\nibration of the LIGO detectors (Abac et al. 2025b). Pre-\nliminary re-analysis indicates that for each candidate the\nimpact of this error in marginalization is small, and we\nexpect the impact on our population analyses to be neg-\nligible compared to other sources of systematic error.\n4. BINARY MERGER POPULATION ACROSS ALL\nMASSES\nWe begin our analysis of the astrophysical distribu-\ntion of merging compact binaries with a joint analy-\nsis of all events discussed in Section 3\u2014BNSs, NSBHs,\nand BBHs\u2014without distinguishing between these dif-\nferent source classes. This allows for a broad look at\nthe complete population, self-consistent measurements\nof the merger rates in each binary source class, and an\nanalysis of the population at the transition between NSs\nand BHs. As mentioned in Section 3, we adopt a uni-\nform detection threshold of FAR < 0.25 yr\u22121 to ensure a\nhigh catalog purity of NS systems, where we have fewer\ndetections and so are more sensitive to non-astrophysical\nfalse-alarm contaminants.\n4.1. The Mass Spectrum of Compact Binaries\nIn Figure 1 we show the joint primary and secondary-\nmass distributions, inferred using a strongly modeled\nand a weakly modeled approach.\nOur FullPop-\n4.0 strongly modeled approach is modified from the\nPower law + Dip + Break analysis of the pre-\nvious GWTC-3.0 catalog (Fishbach et al. 2020; Farah\net al. 2022; Abbott et al. 2023a; Mali & Essick 2025);\nsee Appendix B.1 for a model description. Our weakly\nmodeled analysis approximates the m1\u2013m2 space with a\nBGP (Mandel et al. 2017; Abbott et al. 2023a; Ray et al.\n2023a, 2024); see Appendix C.2 for further discussion.\nThe FullPop-4.0 model uses the default models in Ta-\nble 1 for the redshift and component spins, and for NS\n\n18\nmasses (m < 2.5 M\u2299) the spin magnitude distribution is\ntruncated over the range \u03c7 \u2208[0, 0.4]. The BGP analysis\nfixes the Power Law Redshift evolution to \u03ba = 3 (see\nAppendix B.4), and the spin distribution to be uniform\nin magnitude (again truncated over \u03c7 \u2208[0, 0.4] for NS\nmasses) and isotropic in orientation.\nWe observe an enhanced merger rate around\nm1 \u223cm2 \u22722 M\u2299,\nrepresenting BNS systems,\nan additional subpopulation at unequal masses\nm1 \u223c9 M\u2299and m2 \u22722 M\u2299consistent with\nNSBHs,\nand a third BBH subpopulation at\nm1, m2 \u22739 M\u2299. In the upper triangle of Figure 1, we\nshow the fractional uncertainty as a function of mass, a\nunitless quantity \u2206R/R defined as the 95th - 5th per-\ncentile uncertainty divided by the median merger rate.\nThe rate is best constrained at equal masses, where the\nmajority of mergers are observed, and in the BBH range\n10\u201340 M\u2299. Due to fewer observations, the uncertainty\nis larger for BNS and NSBH systems.\nIn Figure 2,\nwe show the marginalized primary\nand secondary-mass distributions for our strongly and\nweakly modeled reconstructions of the merger rate, fo-\ncusing on the transition between NSs and BHs.\nThe\nmodels are consistent within uncertainties, indicat-\ning that systematic error from model assumptions are\nsmaller than the statistical uncertainties. The most no-\ntable difference between the FullPop-4.0 and BGP re-\nsults is the large uncertainty in the BGP primary-mass\ndistribution relative to the secondary mass. There are\nsignificantly more observed CBCs with light secondary\nmasses m2 \u227215 M\u2299than primary masses m1 \u227215 M\u2299\n(simply by the definition m2 < m1), and so the data-\ndriven BGP is more uncertain for small primary masses,\nwhile the FullPop-4.0 results are more model driven.\nAt m2 = 5 M\u2299, the FullPop-4.0 model adopts an al-\nternative pairing function to more naturally distinguish\nthe pairing behavior of BNS and NSBH systems from\nthat of BBH systems, introducing a discontinuity in the\nsecondary-mass distribution (Figure 2) at the transition\npoint.\nWe discuss the behavior of the population at\nthe transition from NSs to BHs and the astrophysical\ninsights below in Section 4.3.\n4.2. Merger Rates\nSince we self-consistently include all events in the cat-\nalog, our measurements of the binary merger rates are\nrobust to events which straddle different source classes.\nWe calculate the rates of BNS, NSBH, and BBH mergers\nby assuming any object with mass 1 M\u2299< m < 2.5 M\u2299\nis a NS, and any object with mass m > 2.5 M\u2299is a BH.\nIn all models, we assume the rate evolves with redshift\nin a manner that is uncorrelated with mass (Fishbach\net al. 2018; Abbott et al. 2023a). We quote merger rates\nin the local Universe, at redshift z = 0.\nOur\nstrongly-modeled\nFullPop-4.0\nand\nweakly-\nmodeled BGP approaches infer different rates over\nthe m1\u2013m2 space, and hence different rates in each\nbinary source class.\nTo marginalize over the sys-\ntematic modeling uncertainty, we take the union of\nboth 90% credible intervals.\nThe rates thus ob-\ntained are 7.6\u2013250 Gpc\u22123 yr\u22121 for BNS mergers,\n9.1\u201384 Gpc\u22123 yr\u22121 for NSBH mergers, and 14\u2013\n26 Gpc\u22123 yr\u22121 for BBH mergers. In Table 2, we\nshow rates in these classes using different models and\nwithin purported mass gaps.\nThe BNS merger rate measurements may be sensitive\nto assumptions about NS pairing, and so we also es-\ntimate the BNS merger rate assuming a simple, fixed\npopulation.\nWe assume a uniform mass distribution\nbetween 1 M\u2299and 2.5 M\u2299for the component masses,\nisotropically distributed spins with uniform spin magni-\ntudes below 0.4, and a merger rate uniform in comoving\nvolume up to z = 0.15. Under this fiducial model (de-\nnoted Simple Uniform BNS in Table 2), we infer a\nBNS merger rate of 13\u2013170 Gpc\u22123 yr\u22121.\nThe estimates in Table 2 are consistent with our previ-\nous analysis (Abbott et al. 2023a) and the uncertainties\non the rate in each source class have generally decreased\ndue to our larger catalog size.\nAlthough it is within\nuncertainties, our inferred merger rate for BNS systems\nhas notably decreased by a factor of \u223c2 (cf. PDB (pair)\nand BGP in Table 2 of Abbott et al. 2023a). This is a\nresult of the improved detector range and observing time\ntogether with the lack of new BNS detections.\n4.3. The Neutron Star\u2013Black Hole Transition\nElectromagnetic (EM) observations have previously\nsuggested the existence of a mass gap between NSs and\nBHs (Bailyn et al. 1998; Ozel et al. 2010; Farr et al.\n2011).\nOn the lower end of the gap, nonrotating NS\nmasses are bounded by a physical limit, the Tolman\u2013\nOppenheimer\u2013Volkoff (TOV) mass (e.g., Kalogera &\nBaym 1996). Astrophysical observations, heavy-ion col-\nlision experiments, and modeling of the dense mat-\nter equation of state (EoS) at nuclear densities bound\nMmax,TOV \u223c2.2\u20132.5 M\u2299(Landry et al. 2020; Dietrich\net al. 2020; Legred et al. 2021; Huth et al. 2022; Ai\net al. 2023; Dittmann et al. 2024; Rutherford et al. 2024;\nKoehn et al. 2025), and studies on the remnant in the\nBNS merger GW170817 (Abbott et al. 2017) place limits\nin the range \u22722.3 M\u2299(Margalit & Metzger 2017; Rez-\n\n19\n100\n101\nFractional uncertainty\n1\n3\n10\n30\n100\nm1 [M\u2299]\n1\n3\n10\n30\n100\nm2 [M\u2299]\nFullPop-4.0\n1\n3\n10\n30\n100\nm1 [M\u2299]\n1\n3\n10\n30\n100\nBGP\n10\u22123\n10\u22121\n101\n103\ndR\nd(ln m1)d(ln m2) [Gpc\u22123 yr\u22121]\nFigure 1.\nThe complete mass spectrum, inferred using the strongly modeled FullPop-4.0 and weakly modeled BGP analyses.\nIn the lower triangle of the m1\u2013m2 plane (where m1 > m2 by definition), we show median merger rate density across primary\nand secondary masses.\nAt m2 = 5 M\u2299, the FullPop-4.0 model transitions to an alternative pairing function to allow for\nNSBHs, hence the discontinuity at m2 = 5 M\u2299. In the upper triangle we show the fractional uncertainty in the merger rate\nreflected across the diagonal. The fractional uncertainty \u2206R/R is difference of the 95th and 5th percentile values divided by\nthe median merger rate. Both the FullPop-4.0 and BGP models show similar broad features: a population of BNSs at primary\nand secondary masses \u22722 M\u2299, a population of NSBHs at primary mass \u223c9 M\u2299and secondary mass \u22722 M\u2299, and finally the\npopulation of BBHs with primary and secondary masses \u22739 M\u2299. The uncertainties are the smallest in the \u223c9 M\u2299and \u223c30 M\u2299\nBBH peaks.\nTable 2. Merger rates in units Gpc\u22123 yr\u22121 in different mass ranges, according to the FullPop-4.0 and BGP models.\nBNS\nNSBH\nBBH\nNS\u2013Gap\nBH\u2013Gap\nFull\nm1 \u2208[1, 2.5] M\u2299\nm1 > 2.5 M\u2299\nm1 > 2.5 M\u2299\nm1 \u2208[2.5, 5] M\u2299\nm1 > 2.5 M\u2299\nm1 > 1 M\u2299\nm2 \u2208[1, 2.5] M\u2299\nm2 \u2208[1, 2.5] M\u2299\nm2 > 2.5 M\u2299\nm2 \u2208[1, 2.5] M\u2299\nm2 \u2208[2.5, 5] M\u2299\nm2 > 1 M\u2299\nFullPop-4.0\n89+159\n\u221267\n23+20\n\u221213\n19+7\n\u22125\n6.7+9.2\n\u22124.6\n2.5+3.4\n\u22121.6\n130+160\n\u221280\nBGP\n49+121\n\u221242\n30+54\n\u221221\n19+7\n\u22125\n15+46\n\u221214\n1.5+4.9\n\u22121.3\n110+130\n\u221260\nMerged\n7.6\u2013250\n9.1\u201384\n14\u201326\n1.2\u201361\n0.2\u20136.3\n49\u2013300\nSimple Uniform BNS\n13\u2013170\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nNote\u2014For BNS systems, we also estimate the rate assuming a Simple Uniform BNS model. We show rates of BNS, NSBH, and\nBBH assuming objects with mass m \u2208[1, 2.5] M\u2299are NSs and m > 2.5 M\u2299are BHs. We also show rates within the purported\nlower-mass gap between astrophysical NSs and BHs, according to these models. In the third row, we show the merged estimates,\ntaking the union of the 90% credible intervals for the FullPop-4.0 and BGP models, in order to account for model systematics.\nWe quote merger rates at redshift z = 0.\nzolla et al. 2018; Ruiz et al. 2018; Abbott et al. 2020b;\nNathanail et al. 2021).\nOn the upper end of the gap, EM observations histor-\nically identified a dearth of BHs in the range \u223c3\u20135 M\u2299\n(Bailyn et al. 1998; Ozel et al. 2010; Farr et al. 2011),\nhinting at an astrophysical mass gap between NSs and\nBHs, or perhaps a selection effect obscuring such ob-\njects. More recently, observations of noninteracting bi-\nnary systems (Thompson et al. 2018; Jayasinghe et al.\n2021) and radio pulsar surveys (Barr et al. 2024) suggest\nthe presence of a population of compact objects within\nthe gap.\nIndeed, the GW events GW190814 (Abbott\net al. 2020e) and GW230529 (Abac et al. 2024) are fur-\nther evidence that the transition between NSs and BHs\nis populated, albeit sparsely.\n\n20\n2\n4\n6\n8\n10\n12\n14\nm1 [M\u2299]\n10\u22122\n10\u22121\n100\n101\n102\n103\ndR/dm1 [Gpc\u22123 yr\u22121M\u22121\n\u2299]\nFullPop-4.0\nBGP\n2\n4\n6\n8\n10\n12\n14\nm2 [M\u2299]\n10\u22122\n10\u22121\n100\n101\n102\n103\ndR/dm2 [Gpc\u22123 yr\u22121M\u22121\n\u2299]\n0.0\n0.5\n1.0\nA (gap depth)\np(A)\nFigure 2.\nA comparison of the merger rate at redshift z = 0, as a function of component mass for the FullPop-4.0 and\nBGP models. In the upper panel, we show the merger rate as a function of primary mass, marginalized over secondary mass.\nIn the lower panel, we show the merger rate as a function of the secondary mass, marginalized over the primary mass. At\nm2 = 5 M\u2299, the FullPop-4.0 model transitions to an alternative pairing function to allow for NSBHs, hence the discontinuity\nin the secondary mass. The median of the inferred merger rate is shown with a solid line, and the 90% credible interval is shown\nin the shaded region. The BGP weakly modeled approach has larger uncertainties due to increased flexibility. Both the strongly\nmodeled and weakly modeled approaches find local maxima in the merger rate at m2 \u223c1 \u22122 M\u2299and m2 \u223c6.5 \u22129 M\u2299in the\nsecondary-mass distribution. However, the BGP model does not confidently recover the low mass peaks in the primary-mass\ndistribution. In the inset, we show the FullPop-4.0 inferred gap depth parameter A (see Appendix B.1), where A = 1 (a\ncompletely empty gap) is disfavored.\nWith the additional GWTC-4.0 data, the GW picture\nof the purported lower-mass gap is becoming clearer and\nstructures around the transition from NSs to BHs are\nemerging. In both our strongly modeled FullPop-4.0\nand weakly modeled BGP analyses, we find evidence for\na prominent pair of peaks at NS masses \u223c1.5M\u2299\nand at BH masses \u223c9 M\u2299on each side of the\nlower-mass gap.\nA completely empty gap be-\ntween NSs and BHs is disfavored. We cannot rule\nout the existence of extremely narrow gaps in the com-\npact object spectrum, though such a feature requires\nfine tuning of the supernova explosion mechanism, fall-\nback, binary interactions or other physical processes\n(e.g., Fryer et al. 2012; Belczynski et al. 2012).\nOur FullPop-4.0 model detects a peak in the BH\nmerger rate at 9.02+0.41\n\u22121.21 M\u2299. We find that merging NSs\nrepresent the global maximum of the compact object\nmass spectrum at 1.23+0.14\n\u22120.15 M\u2299. At the transition from\nNSs to BHs, FullPop-4.0 allows for an additional sup-\npression in the merger rate, parameterized by a gap\n\n21\ndepth parameter A where A = 1 corresponds to an ab-\nsolute gap with zero mergers and A = 0 corresponds to\nno additional suppression. We show the measurement\non A in the inset in Figure 2. A is consistent with zero,\nand the lower and upper bounds of the gap (e.g., the\nmaximum NS mass and the minimum BH mass) are not\nmeasured away from the prior.\nEarlier precursor analyses to FullPop-4.0 showed\nthat the merger rate between \u223c3\u20135 M\u2299is likely sup-\npressed relative to a power-law continuum (Fishbach\net al. 2020; Abbott et al. 2021a; Farah et al. 2022), us-\ning older datasets. In Abbott et al. (2023a), we used a\nstrongly modeled analysis on GWTC-3.0 (compare the\nPDB model to FullPop-4.0) to argue that the tran-\nsition from NSs to BHs is likely suppressed, but also\nmay be partially filled. FullPop-4.0 measures a simi-\nlar mass spectrum to these previous analyses, but rein-\ntreprets the data as evidence for a rise at \u223c9 M\u2299,\nand no additional suppression between the NS and BH\npeaks (Mali & Essick 2025 make similar conclusions on\nGWTC-3.0).\nWe corroborate our strongly modeled FullPop-4.0\nconclusions with a weakly modeled BGP approach, and\nour constraints are improved relative to a similar BGP-\nbased model in Abbott et al. (2023a).\nUnlike the\nFullPop-4.0 model, however, the BGP analysis does\nnot distinguish between peaks, gaps, or a continuum: as\na weakly modeled approach, the shape of the population\nis inferred directly without an associated interpretation.\nThe BGP model infers a nonzero merger rate between\nthe NS to BH peaks consistent with an underlying con-\ntinuum, and no evidence for a sharp gap.\nHowever,\nthe smoothing kernel in the BGP model makes it a\npriori less sensitive to deep gaps, so we cannot rule\nthem out either. The BGP model also observes NS and\nBH peaks.\nWe quantify the significance as the frac-\ntion of hyperparameter samples where the merger rate\ndensity is higher than the merger rate in the neigh-\nboring bins.\nThe merger rate maximizes for NSs in\nthe range 1 M\u2299\u2264m2 \u22642 M\u2299at 99% credibility and\nthe low-mass BH peak occurs in the secondary mass\n7.5 M\u2299\u2264m2 \u22649 M\u2299bin at 97% credibility.\nAs our knowledge improves about the compact object\npopulation at the boundary between NSs and BHs, we\nstand to learn about supernova physics (e.g., Burrows &\nVartanyan 2021) and the formation mechanisms of the\nheaviest NSs and lightest BHs (Abac et al. 2024, and\nreferences therein). If future catalogs continue to dis-\nfavor a completely empty gap, the standard picture of\nrapid core-collapse supernovae \u2014which features a sharp\ntransition in remnant masses; successful explosions leave\nNSs with m \u22722 M\u2299and failed explosions promptly col-\nlapse to BHs with m \u22735 M\u2299(e.g., Fryer & Kalogera\n2001; Fryer et al. 2012)\u2014 may require modifications to\ninclude fallback, slower instability growth, or stochas-\nticity (e.g., Fryer & Kalogera 2001; Fryer et al. 2012;\nBelczynski et al. 2012; Sukhbold et al. 2016; Ertl et al.\n2019; Mandel & M\u00a8uller 2020). Fallback of stellar mate-\nrial can produce black holes from the maximum neutron\nstar mass to the lightest BH mass (\u223c6 M\u2299) in the rapid\nimplosion scenario (e.g., Ertl et al. 2019), or a slower\ninstability growth timescale could allow the proto-NS\nto accrete enough mass before the explosion to popu-\nlate the mass gap (e.g., Belczynski et al. 2012; Olejak\net al. 2022; Fryer et al. 2022).\nAnother possibility is\nthat stochasticity in the stellar evolution and supernovae\nsmooths out the remnant mass distribution and occupy\nthe lower-mass gap (e.g., Mandel & M\u00a8uller 2020; Man-\ndel et al. 2020). Alternatively, the gap between NSs and\nBHs may be populated by a pollution mechanism, such\nas the remnants of BNS or white dwarf collisions which\nparticipate in further hierarchical mergers (e.g., Gupta\net al. 2020; Ye et al. 2020, 2024; Barr et al. 2024; Maha-\npatra et al. 2025a) or other exotic scenarios like primor-\ndial black holes (e.g., Clesse & Garcia-Bellido 2022) or\ngravitationally lensed events, which could be mistaken\nfor mass gap objects (e.g., Bianconi et al. 2023; Janquart\net al. 2024; Farah et al. 2025a).\n5. POPULATION PROPERTIES OF MERGERS\nCONTAINING NEUTRON STARS\nIn O4a, GW230529 (Abac et al. 2024) is the only NS-\ncontaining event identified with a FAR < 0.25 yr\u22121. We\ndo not include the NSBH candidate GW230518 iden-\ntified during the ER preceding O4a. Additionally, no\ncoincident EM counterparts were identified for triggers\n(i.e., preliminary candidate GW signals flagged by the\ndetection pipelines when their ranking statistic exceeded\nthe alert threshold) during O4a based on follow-up ef-\nforts conducted by EM telescopes.\nThus, conclusions\npresented in previous papers (Abbott et al. 2023a; Abac\net al. 2024) about the population properties of BNS and\nNSBH mergers remain largely unchanged.\nWe adopt models and methods consistent with those\nused in GWTC-3.0 (Abbott et al. 2023a). Specifically,\nwe adopt two different models for the NS mass distribu-\ntion, one in which masses are assumed to be Gaussian\ndistributed, and another in which they are assumed to\nfollow a power law (Abbott et al. 2023a). These are re-\nferred to as the Peak model and the Power model re-\nspectively. We assume that the redshift evolution of the\nmerger rate is fixed, and that the spins are distributed\nfollowing the PE prior (Abac et al. 2025b). A uniform\nprior is used for hyperparameters of the population, with\n\n22\nthe condition mmin \u2264\u00b5 \u2264mmax (where \u00b5 is the mean\nof the Gaussian bump in the Peak model), assuming\nmmax does not exceed Mmax,TOV (the maximum per-\nmissible NS mass as expected from the TOV limit), as\ndetailed in Appendix B.\nWhen assumed to follow the Power model, NS\nmasses favor a mass distribution with a power-law slope\nconstrained to \u03b1 = 7.7+5.1\n\u22125.5.\nThe inference from the\nPeak model is broad, with largely unconstrained peak\nwidth \u03c3 = 0.68+1.2\n\u22120.45 M\u2299and location \u00b5 = 1.4+0.48\n\u22120.25 M\u2299.\nWhile these results may hint at a peak emerging near\n1.4 M\u2299, it is much broader than the relatively sharp peak\nin the mass distribution of Galactic NS systems (Far-\nrow et al. 2019; El-Badry et al. 2024). Our inferred NS\nmass distribution remains broad, with greater support\nfor high-mass NSs.\nAs no new NSBHs beyond GW230529 were confi-\ndently observed in O4a, the population-level results\nin Abac et al. (2024) produced using the NSBHPop\nmodel (Biscoveanu et al. 2022b) remain unchanged.\nSpecifically, our inferred minimum BH mass in NSBH\nsystems remains 3.4+1.0\n\u22121.2 M\u2299(Abac et al. 2024).\n6. BINARY BLACK HOLE POPULATION\nIn this section, we analyze the astrophysical popula-\ntion of BBHs using data from GW events with a FAR\n< 1 yr\u22121. We only include events whose 1% lower limit\non both component mass posteriors (under the PE pri-\nors) is larger than 3 M\u2299. There are 84 events from O4a\nthat meet this criterion in addition to the 69 BBH events\nfrom GWTC-3.0, which brings the total number of BBH\nevents passing our FAR threshold to 153. Of the events\nconsidered in O4a, only GW230529 does not meet this\ncriterion and is not considered in the analyses below (see\nSection 3).\n6.1. Primary Mass\nIn this section, we illustrate the main findings of the\nstrongly and weakly modeled approaches using results\nfrom the Broken Power Law + 2 Peaks (see Ap-\npendix B.3) and B-Spline (see Appendix C.1) models,\nrespectively. We chose the Broken Power Law + 2\nPeaks model as our fiducial mass model because it per-\nformed the best in our model comparison study. It was\nfirst introduced by Callister & Farr (2024) to describe\nthe GWTC-3.0 mass distribution. Results from a selec-\ntion of other models considered in the model compari-\nson study can be found in Appendix D.1, while models\nthat employ a weakly modeled approach can be found\nin Appendix D.4, both of which include comparisons\nto the fiducial Broken Power Law + 2 Peaks and\nB-Spline models. The strongly modeled approach em-\nploys the default models listed in Table 1 for the other\nsource parameters, namely the Power Law Redshift\nand Gaussian Component Spins models.\nWe identify a global peak at \u223c10 M\u2299and find\nthat it is robust to model variations. A Gaussian-\nlike peak at \u223c10 M\u2299was first identified by Tiwari\n& Fairhurst (2021) and Edelman et al. (2022) using\nGWTC-2.0 and later by the weakly modeled approaches\nin Abbott et al. (2023a) using GWTC-3.0.\nFigure 3\nshows the rate dR/dm1 as a function of primary mass\nat z = 0.2 inferred by these models compared to the\nPower Law + Peak (see Appendix B of Abbott et al.\n2023a for a description of this model) inference with\nGWTC-3.0 from Abbott et al. (2023a).1 The low-mass\nGaussian component of the Broken Power Law + 2\nPeaks model infers a global peak in the primary mass\nspectrum at m1 = 9.8+0.3\n\u22120.6 M\u2299relative to the underly-\ning broken power law continuum. The B-Spline model\nalso recovers a global peak at m1 = 10.1+0.7\n\u22120.7 M\u2299. Both\nvalues are consistent with GWTC-3.0, which inferred a\nglobal peak at m1 = 10.2+0.3\n\u22120.6 M\u2299by modeling the mass\nspectrum as a power law modulated by a spline.\nA broken power law is necessary to describe the\ncontinuum structure above \u223c15 M\u2299(see Figure 3).\nBelow \u223c35 M\u2299, the continuum of BH masses is well de-\nscribed by a power law with spectral index \u03b11 = 1.7+1.2\n\u22121.8.\nAbove \u223c35 M\u2299, the continuum steepens, with a spectral\nindex of \u03b12 = 4.5+1.6\n\u22121.3 that is consistent with the Power\nLaw + Peak result from GWTC-3.0 (\u03b1 = 3.5+0.6\n\u22120.6 M\u2299).\nWe find that \u03b12 > \u03b11 at 97.7% credibility.\nThough\nthis continuum structure was identified by Callister &\nFarr (2024), it was not identified by the strongly mod-\neled approaches in Abbott et al. (2023a), in part due\nto the limited flexibility of models employed in Abbott\net al. (2023a). To illustrate this, in Figure 4 we present\na re-analysis of GWTC-3.0 using the Broken Power\nLaw + 2 Peaks model alongside the GWTC-4.0 result,\nwhich shows improved constraints across the full mass\nspectrum.\nWe identify a feature at \u223c35 M\u2299.\nUsing the\nstrongly modeled approach, we find that this feature is\nconsistent with either: (i) an over-density that peaks\nat m1 = 32.7+2.7\n\u22126.5 M\u2299relative to an underlying bro-\nken power law (i.e., the Broken Power Law + 2\nPeaks result), or (ii) a broken power law with break\nmass mbreak = 34.1+3.8\n\u22123.3 M\u2299(i.e., a broken power law\nwithout a second peak near the break). See Appendix\nD.1 for a more detailed discussion of this result. The\nformer conclusion is supported by the B-Spline model,\n1We quote BBH merger rates at z = 0.2 to be consistent with\nAbbott et al. (2023a) and because z \u223c0.2 is where we best\nconstrain the merger rate.\n\n23\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\nB-Spline, GWTC-4.0\nBroken Power Law + 2 Peaks, GWTC-4.0\nPower Law + Peak, GWTC-3.0\nFigure 3. Differential merger rate as a function of primary mass (evaluated at z = 0.2) of the Broken Power Law + 2\nPeaks model (orange) and B-Spline model (blue) compared to the Power Law + Peak model from GWTC-3.0 (Abbott et al.\n2023a). The solid lines indicate the posterior medians and the shaded regions show the 90% credible interval of each model.\nComparing these results, it is clear that a single power law is a poor description of the the low-mass end of the spectrum.\nwhich exhibits a local peak at m1 = 33.5+2.2\n\u22124.5 M\u2299, con-\nsistent with other models that employ a weakly modeled\napproach in Appendix D.4.\nAdditional structure may be present in the\nmass spectrum.\nA bump near \u223c20 M\u2299is present\nin some of the weakly modeled approaches (see Fig-\nure 20 in Appendix D.4).\nWe cannot conclude with\nthe strongly modeled approach whether adding a third\nGaussian component to the Broken Power Law + 2\nPeaks model in this region is required by the data or not\n(as quantified by the log Bayes factor log10 B = \u22120.34\nbetween the default model and one including a third\npeak). This feature was first reported in an analysis of\nGWTC-2.0 (Tiwari & Fairhurst 2021) and was present\nin several analyses of GWTC-3.0 (Abbott et al. 2023a;\nEdelman et al. 2023; Tiwari 2023; Godfrey et al. 2023).\nAdditionally, the B-Spline and other weakly modeled\napproaches show a rise in the merger rate relative to the\nBroken Power Law + 2 Peaks result in the \u223c60 M\u2299\nregion, which can be seen in Figure 3 and Figure 20. A\nprevious study of GWTC-3.0 found evidence for a simi-\nlar feature in this region (Maga\u02dcna Hernandez & Palmese\n2025).\nWe do not place informative constraints on the indi-\nvidual parameters that govern low-mass smoothing for\nthe Broken Power Law + 2 Peaks model. We cau-\ntion against astrophysically interpreting the BBH pri-\nmary mass distribution below \u223c8 M\u2299because of the bias\nthat may be introduced by removing the probable NS-\ncontaining events in the manner described in Section 3.\nRemoving such events is responsible for the discrepancy\nbelow \u223c8 M\u2299between Figure 2 and Figure 3.\nGWTC-4.0 includes an exceptional high-mass BBH,\nGW231123 (Abac et al. 2025e), whose inferred compo-\nnent masses lie at the extreme upper end of those in our\ndataset. To check if GW231123 is an outlier with respect\nto the mass distribution of BBHs, we construct mock\ncatalogs containing 153 detected events following the in-\nferred population without GW231123, and calculate the\ndistribution of maximum detectable BH masses.\nThe\ntotal mass of GW231123 lies at the 87+6\n\u221210th percentile\nof this distribution. This shows that while GW231123\nlies in the tail of the distribution, its total mass is con-\nsistent with the inferred mass spectrum; the degree of\nconsistency is more than was the case with GWTC-3.0\ndata alone (Abac et al. 2025e).\nThe main compact binary formation scenarios (Man-\ndel & Farmer 2022 and references therein)\u2014isolated bi-\nnary evolution and dynamical assembly in dense stellar\nenvironments\u2014have both been shown to produce popu-\nlations consistent with current observations (Mandel &\nBroekgaarden 2022). A peak near m1 \u223c10 M\u2299is often\npredicted by isolated binary evolution models (Dominik\net al. 2015; Belczynski et al. 2020; Giacobbo & Mapelli\n2018; Wiktorowicz et al. 2019; Neijssel et al. 2019), while\nmass distributions from dynamical formation, such as in\nyoung and globular clusters, typically peak above 10 M\u2299\n(Rodriguez et al. 2016a; Hong et al. 2018; Rodriguez\net al. 2019; Banerjee 2021; Antonini & Gieles 2020).\nHowever, predictions from isolated and dynamical for-\nmation often overlap and can vary significantly based\n\n24\n10\n20\n40\n60\n100\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\n\u22123\n0\n3\n6\n9\n\u03b11\n\u22123\n0\n3\n6\n9\n\u03b12\nGWTC-4.0\nGWTC-3.0\nFigure 4. Differential merger rate as a function of primary mass (evaluated at z = 0.2) of the Broken Power Law + 2\nPeaks model inferred with GWTC-4.0 compared to the same model applied to only GWTC-3.0 BBH events. The orange shaded\nregion shows the 90% credible interval for GWTC-4.0 and the solid orange curve shows the posterior median, while the black\ndashed curves bound the 90% credible region for GWTC-3.0 and the solid black curve shows the posterior median. The inferred\ndistribution is similar between catalogs, which highlights that the low-mass structure identified in GWTC-4.0 was present in\nGWTC-3.0. The inset figure shows the joint posterior of the broken power law index parameters \u03b11 and \u03b12 for GWTC-3.0\n(gray) and GWTC-4.0 (orange), with the contours showing the 5th, 50th, and 95th percentiles. The black dashed curve in the\ninset indicates where \u03b11 = \u03b12.\non the assumptions and methodologies used, making it\ndifficult to conclude the origin of the observed catalog\nor constrain formation physics based on features in the\nmarginal mass distributions.\nA feature that may provide distinguishing power be-\ntween the isolated and dynamical channels is the ex-\nistence of an upper mass gap, in the range 45 M\u2299\u2272\nm \u2272120 M\u2299. Such a dearth would be consistent with\nthe theorized pair-instability mass gap, arising from\nthe complete disruption of massive stars due to run-\naway electron\u2013positron pair production (Woosley 2017;\nMapelli et al. 2020; Farmer et al. 2019). While the pre-\ncise locations of the lower and upper edges of the pair-\ninstability mass gap are sensitive to physical assump-\ntions (Renzo et al. 2020; van Son et al. 2020; Woosley\n& Heger 2021; Shen et al. 2023; Winch et al. 2024),\nthe feature tends to be a robust prediction of most stel-\nlar evolution models (Marchant et al. 2018; Marchant &\nMoriya 2020; Renzo et al. 2020; Woosley & Heger 2021).\nThe gap may not be completely empty due to overmas-\nsive stellar envelope fallback or stellar mergers (Di Carlo\net al. 2019, 2020; Mapelli et al. 2020; Kremer et al. 2020),\nhierarchical BBH mergers in clusters or in AGN envi-\nronments (Mckernan et al. 2018; Rodriguez et al. 2019;\nMcKernan et al. 2020; Yang et al. 2019; Mapelli et al.\n2021; Antonini et al. 2019; Fragione & Silk 2020; Liu &\nLai 2021; Martinez et al. 2020; Arca Sedda 2020; Maha-\npatra et al. 2021, 2025b, 2024), or even due to primordial\nBHs (Postnov & Yungelson 2014; Bird et al. 2016; Clesse\n& Garcia-Bellido 2022). The decrease in the merger rate\nabove m1 \u223c35 M\u2299seen in all models and the tentative\nrise near m1 \u223c60 M\u2299seen in the weakly modeled ap-\nproaches may hint toward a polluted mass gap.\n6.2. Mass-Ratio\nFigure 5 shows the differential merger rate dR/dq\nevaluated at z = 0.2 inferred by the Broken Power\nLaw + 2 Peaks and B-Spline models compared to\nthe Power Law + Peak result from GWTC-3.0.2\nWe find that the mass-ratio distribution can\nbe described by a power-law with an index\n\u03b2q = 1.2+1.2\n\u22121.0 that is consistent with GWTC-3.0 (\u03b2q =\n1.1+1.7\n\u22121.3) with a reduction in uncertainty. The B-Spline\nmodel shows a reduced rate above q \u22730.8 relative to the\nBroken Power Law + 2 Peaks result. More flexible\nparametrizations in the strongly modeled approach were\nexplored (see also the other weakly modeled approaches\n2Models that utilize B-Splines infer the separable distribution p(q)\nbut the results of such models shown in this section are actually\nthe conditional marginal distribution p(q|m2>3M\u2299).\nSee Ap-\npendix C.1 for further details.\n\n25\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n10\u22121\n100\n101\n102\n103\ndR/dq\n\u0002\nGpc\u22123 yr\u22121\u0003\nB-Spline, GWTC-4.0\nBroken Power Law + 2 Peaks, GWTC-4.0\nPower Law + Peak, GWTC-3.0\nFigure 5. Differential merger rate as a function of mass-\nratio (evaluated at z = 0.2) of the Broken Power Law +\n2 Peaks model (orange) and B-Spline model (blue). The\nfiducial Power Law + Peak model from Abbott et al.\n(2023a) is included for comparison.\nSolid curves indicate\nposterior medians and the shaded (dashed) regions show 90%\ncredible intervals.\nin Figure 20, which do peak near unity), but model com-\nparisons were inconclusive.\nSimilarly, in GWTC-3.0,\nGodfrey et al. (2023) inferred a mass-ratio distribution\npeaked away from unity using a weakly modeled ap-\nproach, while Rinaldi et al. (2025) found equal evidence\nfor two strongly modeled approaches with very distinct\nbehavior above q \u22730.7.\nModels that incorporate correlations between source\nparameters have a greater potential to distinguish be-\ntween formation channels than uncorrelated ones. We\nnext present results from two different models that cor-\nrelate features of the primary mass spectrum with dif-\nferent mass-ratio distributions.\nBHs with masses \u223c35 M\u2299preferentially merge\nwith other BHs of more equal mass relative to\nthose in the underlying mass continuum.\nThe\nExtended Broken Power Law + 2 Peaks model\nmodifies the Broken Power Law + 2 Peaks model\nby allowing each primary mass mixture component (i.e.,\nthe broken power law and two Gaussian components) to\nbe associated with a different power-law-mass-ratio dis-\ntribution. Figure 6 shows the mass-ratio distribution for\neach mixture component. Specifically, each component\ninfers a different power-law index \u03b2q, with \u03b2BP\nq\n= 0.1+1.7\n\u22121.3\nfor the broken power law, \u03b2peak1\nq\n= 1.6+9.6\n\u22128.1 for the\nGaussian component that captures the \u223c10 M\u2299peak,\nand \u03b2peak2\nq\n= 7.4+4.8\n\u22125.1 for the second Gaussian com-\nponent that captures the \u223c35 M\u2299feature.\nCritically,\n\u03b2peak2\nq\n> \u03b2BP\nq\nat 97.3% credibility.\nOther studies of\nGWTC-3.0 have drawn similar conclusions about the\npairing preferences of high mass BHs (e.g.,\nLi et al.\n2022; Baibhav et al. 2023; Sadiq et al. 2024; Galaudage\n& Lamberts 2025; Roy et al. 2025).\nBHs with masses \u223c10 M\u2299may prefentially\nmerge with lighter BHs. The region bounded by the\nsolid blue curves in the bottom panel of Figure 6 shows\nthe mass-ratio distribution of the \u223c10 M\u2299peak inferred\nwith the Isolated Peak model. This model is a mix-\nture of a Gaussian peak and a B-Spline (continuum)\nin primary mass, and the mass ratio and spin distribu-\ntions are inferred separately for each mixture component\nwith B-Splines (see Appendix C for further details). The\nGaussain peak is inferred at \u223c10 M\u2299and its mass-ratio\ndistribution exhibits a peak at q = 0.74+0.13\n\u22120.13, a feature\nthat a single power law is unable to reproduce. This\ncould explain the large uncertainty in \u03b2peak1\nq\nfrom the\nExtended Broken Power Law + 2 Peaks model.\nThe solid blue curve in Figure 6 shows the mass-ratio\ndistribution of masses outside of the \u223c10 M\u2299peak in-\nferred by the B-Spline mixture component. Unlike the\nfull population mass-ratio distribution inferred by the\nB-Spline model in Figure 5, this result does not pos-\nsess a peak near q \u223c0.8, indicating that the peak seen\nin the full population is due largely to the events around\n\u223c10 M\u2299. This mass feature was identified in GWTC-3.0\nby Godfrey et al. (2023).\nMost formation channels generally favor equal mass\nsystems.\nFor example, dynamical formation can pro-\nduce systems with a wide range of mass ratios, but pre-\ndicted distributions typically peak at unity (Rodriguez\net al. 2016a; Torniamenti et al. 2024).\nCertain hier-\narchical mergers may not necessarily follow this trend,\nin particular mergers between first generation and sec-\nond generation BHs have been shown to produce a\nmass-ratio distribution peaked near q \u223c0.5 (Rodriguez\net al. 2019).\nMass transfer during the contact phase\nof binaries formed via chemically homogeneous evolu-\ntion (de Mink & Mandel 2016; Marchant et al. 2016)\nleads to a strong preference for equal mass-ratio systems,\nbut this mechanism is thought to be important for bi-\nnaries with m1 \u227310 M\u2299(du Buisson et al. 2020; Zevin\net al. 2021; Riley et al. 2021). Mass-ratio reversal within\nthe stable mass transfer channel can lead to a peak in\nthe mass-ratio distribution between q \u223c0.6-0.8 (Neijs-\nsel et al. 2019; van Son et al. 2022b), which is qualita-\ntively consistent with the mass-ratio distribution of the\n\u223c10 M\u2299inferred with the Isolated Peak model. Sta-\nble mass transfer also predicts a peak near \u223c10 M\u2299that\nis robust to uncertainties in the metallicity-dependent\nstar formation history (van Son et al. 2022a) and other\nphysical uncertainties of the channel (van Son et al.\n2022c).\n\n26\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n10\u22123\n10\u22122\n10\u22121\n100\n101\np(q)\nExtended BP2P\nPeak 1, \u223c10 M\u2299\nPeak 2, \u223c35 M\u2299\nBroken Power Law\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n10\u22123\n10\u22122\n10\u22121\n100\n101\np(q)\nIsolated Peak\nPeak, \u223c10 M\u2299\nContinuum\nFigure 6.\nTop Panel: The 90% credible regions for the\nmass-ratio distribution of the \u223c10 M\u2299peak (solid orange\ncurves), \u223c35 M\u2299peak (dashed curves), and continuum (or-\nange shaded region) components of the Extended Broken\nPower Law + 2 Peaks model. Bottom Panel: The 90%\ncredible regions for mass-ratio distribution of the \u223c10 M\u2299\npeak (solid blue curves) and the rest of the mass spec-\ntrum (blue shaded region) inferred with the Isolated Peak\nmodel. The \u223c10 M\u2299peak mass-ratio distribution from the\nExtended Broken Power Law + 2 Peaks is included for\ncomparison.\n6.3. Spin\nWe next present the spin distribution of the BBH pop-\nulation through O4a. We model spins using two different\nparameterizations: the magnitudes \u03c7i and tilt angles \u03b8i\n(Section 6.3.1), and the effective inspiral spin \u03c7eff and\neffective precessing spin \u03c7p (Section 6.3.2). The effec-\ntive inspiral spin \u03c7eff is the mass-weighted average of\nthe component spins aligned with the binary\u2019s orbital\nangular momentum (Racine 2008; Ajith et al. 2011).\nThe effective precessing spin \u03c7p characterizes the degree\nof relativistic precession caused by spin\u2013orbit misalign-\nment, capturing the effect of the in-plane spin compo-\nnents (Schmidt et al. 2011, 2012, 2015; Gerosa et al.\n2021); these are defined in Equations 15 and 16 of Abac\net al. (2025a). More details about spin parameterization\nare given in Appendix B.5.\nPrevious analyses of the BBHs observed through\nO3 found that BH spin vectors tend to be small\nin magnitude (\u03c7 \u22720.3) and preferentially\u2014but not\nexclusively\u2014lie above the orbital plane (cos \u03b8 > 0; Ab-\nbott et al. 2019a, 2021a, 2023a).\nThe new observa-\ntions in GWTC-4.0 further support these conclusions\nand additionally suggest more structure in the compo-\nnent and effective spin distributions, enabled by changes\nto the models used in previous population analyses: (i)\nthe spin magnitude distribution has support at\n\u03c7 \u22480, (ii) the spin tilt distribution may peak\naway from perfect alignment with the orbital an-\ngular momentum, and (iii) the \u03c7eff distribution\nis asymmetric about its peak. We elaborate upon\nthese new features in the following subsections.\n6.3.1. Spin Magnitudes and Tilts\nSpin magnitudes and tilt angles provide insight about\nBBH formation and evolution (e.g., Mandel & Farmer\n2022; Mapelli 2020); we begin with spin magnitudes. If\nangular momentum transport in stars is efficient, stellar\ncores rotate slowly, resulting in small spin magnitudes\nfor isolated BHs (Fuller & Ma 2019; Ma & Fuller 2019;\nFuller et al. 2019). However, binary interactions can sig-\nnificantly influence BH spins through mechanisms such\nas tides (Hut 1981; Packet 1981; Zaldarriaga et al. 2018;\nQin et al. 2018; Bavera et al. 2020; Mandel & Fragos\n2020) and accretion (Hut 1981; Packet 1981; van den\nHeuvel et al. 2017; Neijssel et al. 2019; Steinle & Kes-\nden 2021; Stegmann & Antonini 2021). If a BBH forms\nfrom a pre-existing isolated stellar binary, tidal inter-\nactions can spin up the progenitor of the second-born\nBH (Bavera et al. 2020; Qin et al. 2019), yielding spin\nmagnitudes of \u03c7 \u22480.2\u22120.4 (Ma & Fuller 2023), al-\nthough these can be reduced by stellar winds (Tout\n& Pringle 1992). Chemically homogeneous evolution\u2014\ninvolving tidally locked, high-mass, low-metallicity, close\nbinaries\u2014may produce even larger spins (Mandel &\nde Mink 2016; de Mink & Mandel 2016). Alternatively,\nlarge spin magnitudes may point toward a hierarchical\nmerger origin, where one or both BHs are remnants of\nprevious BBH mergers (Rodriguez et al. 2019; Zhang\net al. 2023; Doctor et al. 2019; Kimball et al. 2020; Payne\net al. 2024; Gerosa & Fishbach 2021; Fishbach et al.\n2017; Gerosa & Berti 2017; Mould et al. 2022b; Maha-\npatra et al. 2021, 2025b, 2024), which are predicted to\nhave \u03c7 \u223c0.7 (Lousto et al. 2010).\nWith this astrophysical context, we present our mea-\nsurement of the spin magnitude distribution through\nO4a. The left column of Figure 7 shows the marginal\n\n27\nDefault, GWTC-3.0\nGaussian Component\nSpins, GWTC-4.0\nB-Spline, GWTC-4.0\nFigure 7. Marginal spin magnitude \u03c7 (left) and cosine tilt angle cos \u03b8 (right) distributions under the Gaussian Component\nSpins (blue) and B-Spline (green) models. The results from the GWTC-3.0 Default are shown for comparison (black dashed);\nnote that this model is different from what is used for GWTC-4.0. The GWTC-3.0 analysis employed a Beta distribution for spin\nmagnitudes rather than a truncated normal, and fixed the location of the Gaussian component of the spin tilt angle distribution\nto cos \u03b8 = 1 rather than letting it vary freely in inference. The solid lines show the median of the inferred distributions from\nGWTC-4.0, and the shaded regions show their 90% credible regions. The thick dashed lines show the median from GWTC-3.0,\nwhile the thin dashed lines show its 90% credible region.\ndistributions of \u03c7 using the strongly modeled ap-\nproach (Gaussian\nComponent\nSpins;\nblue) and\nweakly modeled approach (B-Spline; green).\nThe\nGaussian Component Spins model (Equation B26)\ndescribes the \u03c7 population as a truncated Gaussian dis-\ntribution. This is a departure from the Default spin\nmodel of GWTC-3.0. There, a non-singular Beta dis-\ntribution was used (Abbott et al. 2023a), which forces\np(\u03c7) = 0 at \u03c7 = 0, 1 and thus cannot measure contribu-\ntions to the population at near-minimal or near-maximal\nspins. Allowing for more model flexibility at the \u03c7 dis-\ntribution\u2019s boundaries is crucial, as there exists an on-\ngoing discussion in the literature about whether or not\nthere is an over-density of BBHs with \u03c7 \u22720.01 (Kim-\nball et al. 2020; Galaudage et al. 2021; Callister et al.\n2022; Tong et al. 2022; Mould et al. 2022a; Hussain\net al. 2024). We find that the Gaussian Component\nSpins model is preferred over the Default spin model\nof GWTC-3.0 by log10 B = 0.66; additional parametric\nspin magnitude (and tilt) models are discussed in Ap-\npendix D.2. The widening of the 90% credible regions\nfor the \u03c7 and cos \u03b8 distributions at their boundaries un-\nder the B-Spline model seen in Figure 7 is a prior-\ndriven effect common in spline modeling (e.g., Golomb\n& Talbot 2023; Edelman et al. 2023).\nIn GWTC-4.0, we constrain p(\u03c7 \u22480) > 0 un-\nder both the strongly and weakly modeled ap-\nproaches. At 90% credibility, our recovered spin mag-\nnitude distribution peaks between \u03c7 = 0.01\u20130.23, as\nmeasured by the \u00b5\u03c7 location parameter. Broadly, BH\nspins are inferred to be predominantly non-extremal,\nwith the Gaussian Component Spins model finding\nthat 90% of BHs having \u03c7 < 0.57.\nThe comparative\ndearth of observed BBHs with large spins disfavors a\npopulation dominated by second-generation BHs. How-\never, the precise fraction of systems with large spin\nmagnitudes is model dependent: the Gaussian Com-\nponent Spins and B-Spline models only disagree at\n90% credibility for \u03c7 > 0.83.\nAt \u03c7 = 0.8, 0.9, and\n1.0, their p(\u03c7) distributions differ at the 85%, 96%, and\n98% levels, respectively.\nWhile the Gaussian Com-\nponent Spins model approaches p(\u03c7) \u223c0 at \u03c7 = 1,\nthe B-Spline model infers a larger, nearly flat distribu-\ntion from \u03c7 = 0.6 to 1. Similar behavior was found in\nGWTC-3.0 (Godfrey et al. 2023), and attributed to a\nsubpopulation with near-uniform spin magnitudes. The\ndiscrepancy between our two models may arise from lim-\nited flexibility in the strongly modeled approach; a sin-\ngle truncated Gaussian cannot increase the probability\nat \u03c7 \u22730.8 without also increasing it at \u03c7 \u223c0.2\u22120.5. In\nGWTC-4.0, a handful of events do have preferentially\nlarge spin magnitudes, including GW231123 which has\nprimary spin \u03c71 > 0.5 with high confidence (Abac et al.\n2025e).\nUnder both the Gaussian Component Spins and\nB-Spline models, the results presented in Figure 7 as-\nsume that the spin magnitudes are independently and\nidentically distributed (IID), meaning that the func-\ntion describing the population distribution is factoriz-\nable in terms of \u03c71 and \u03c72, and the two are described\nby the same set of hyperparameters. The data prefer\nidentically distributed spin magnitudes over those which\n\n28\n\u03c7A\n\u03c7B\nFigure 8. Larger (\u03c7A, darker blue) and smaller (\u03c7B, lighter\nblue) spin magnitude distributions, derived from imposing\norder statistics on the Gaussian Component Spins \u03c7 dis-\ntribution shown in Figure 7. The solid lines show the median\nof each inferred distribution, and the shaded regions show the\n90% credible intervals.\nare non-identically distributed, cf. Table 12. However,\nmathematically, the primary and secondary spins can-\nnot be IID if the purported correlation between q and\n\u03c7eff is true (Farr & Farr 2025). We probe this corre-\nlation in Section 6.5.2, and find support for its exis-\ntence, albeit with evidence that has diminished since\nGWTC-3.0. Thus, we interpret the Bayes factor in fa-\nvor of IID spins as a statement that, under the Gaus-\nsian Component Spins model, we cannot yet say with\nstatistical certainty that the spins are not identically dis-\ntributed. This statement is likely driven by the fact that\nindividual-event spin magnitude posterior distributions\nare typically wide, making \u03c71 and \u03c72 hard to distin-\nguish.\nIn general, \u03c71 and \u03c72 are not expected to be\nidentically distributed in nature; if q and \u03c7eff are in-\ndeed correlated, more informative \u03c7i measurements may\neventually reveal their non-identical nature. Figure 17\nin Appendix D.2 presents posteriors on the Gaussian\nComponent Spins hyperparameters under the assump-\ntion that spin magnitudes (and tilts) are identically ver-\nsus non-identically distributed.\nNext, Figure 8 shows the inferred spin magnitude\ndistributions if, rather than sorting by the more ver-\nsus less massive BH, we instead sort by the BH with\nthe larger (subscript A) and smaller (subscript B) spin\nmagnitude (Biscoveanu et al. 2021).\nThe magnitudes\n\u03c7A and \u03c7B are derived quantities and are not fit in-\ndependently: to generate their distributions, we take\nresults from the Gaussian Component Spins model\nand impose order statistics, assuming that \u03c7A is the\nlarger of two draws from the p(\u03c7) distribution in the\nleft panel of Figure 7 and \u03c7B is the smaller (Abbott\net al. 2023a; Biscoveanu et al. 2021). This analysis does\nnot assume any sort of pairing function between spins.\nSpin sorting offers an alternative way to visualize and\ninterpret the spin information from the IID model. The\nmore rapidly spinning component has a wide spin mag-\nnitude distribution, with a population predictive distri-\nbution (PPD) peaking at \u03c7A = 0.35, and support up\nto \u03c7A,99% = 0.92+0.04\n\u22120.08 (value of \u03c7A at which each p(\u03c7A)\ntrace reaches its 99th percentile, serving as a proxy for\nthe distribution\u2019s maximum). The vanishing probabil-\nity at \u03c7A = 0 is a Jacobian effect of the order statis-\ntics.\nHowever, if both BHs had \u03c7 \u22480, the \u03c7A dis-\ntribution would be much more strongly peaked at small\nvalues (Szemraj & Biscoveanu 2025), meaning that spin-\nsorting results on GWTC-4.0 indicate that at least one\nBH per binary has \u03c7 \u22730. The more slowly spin-\nning component, on the other hand, is consistent with\na narrower distribution peaking at \u03c7B = 0, and only\nhas support up to \u03c7B,99% = 0.6+0.09\n\u22120.07. The observation\nthat spin \u03c7B magnitudes are preferentially small could\nindicate small natal spins for at least one of the two\nBHs, while the fact that the population is consistent\nwith only one BH per binary having large spin supports\nthe existence of some variety of spin-up mechanism in\nBBH evolution.\nWe next turn to the spin tilt distribution. Many au-\nthors argue that if BBHs are formed primarily in the\nisolated binary scenario, large tilt angles are hard to ex-\nplain without invoking large supernovae kicks and ineffi-\ncient tides (Kalogera 2000; Gerosa et al. 2018; Steinle &\nKesden 2021; Wysocki et al. 2018; Stevenson 2022; Cal-\nlister et al. 2021a), although others claim that, depend-\ning on the specifics of poorly understood supernovae\nphysics, even small kicks can misalign a binary (Baib-\nhav & Kalogera 2024; Tauris 2022).\nComplete anti-\nalignment (cos \u03b8 = \u22121) is a possible result of mass trans-\nfer in the isolated channel (Stegmann & Antonini 2021).\nOn the other hand, BBHs formed dynamically in stel-\nlar clusters are predicted to have istropically distributed\nspin orientations, as there is no a priori preferential spin\ndirection in these environments (Rodriguez et al. 2015,\n2016a, 2018; Farr et al. 2017). However, recent stud-\nies indicate that mechanisms could possibly exist for\ndynamically formed BBHs to have slight preference for\ncos \u03b8 > 0 (Trani et al. 2021; Banerjee et al. 2023; K\u0131ro\u02d8glu\net al. 2025), especially for BBHs formed dynamically in\nthe disks of active galactic nuclei (Wang et al. 2021;\nMcKernan et al. 2022).\nThe right-hand column of Figure 7 shows the marginal\ndistribution of the cosine of the tilt angle,\ncos \u03b8.\nThe cos \u03b8 population under the Gaussian Compo-\n\n29\nnent Spins model is a mixture between isotropic and\ntruncated Gaussian sub-populations (Equation B27).\nFollowing GWTC-3.0 and earlier population analyses,\nwe assume that spin tilt angles are nonindependently\nbut identically distributed (NID) under the Gaussian\nComponent Spins model, meaning that while cos \u03b81\nand cos \u03b82 are described by the same hyperparameters,\nthe population distribution is not separable in terms of\nthe two: we require that both BHs in a binary are drawn\nfrom the same sub-population (either the isotropic or\nthe truncated Gaussian). NID tilts are favored by the\ndata over non-identical distribution, cf. Table 12. The\nB-Spline model naturally assumes spin tilt angles are\nIID, as it does not probe separate tilt sub-populations.\nThe Default model of GWTC-3.0 fixed the location of\nthe Gaussian sub-population at exact spin\u2013orbit align-\nment (Vitale et al. 2017; Talbot & Thrane 2017; Ab-\nbott et al. 2023a), making it a half-Gaussian peaking\nat cos \u03b8 = 1. In GWTC-4.0, the strongly and weakly\nmodeled approaches both find that the spin tilt dis-\ntribution may peak away from exact spin\u2013orbit\nalignment. The Gaussian Component Spins model\nfinds that the cos \u03b8 distribution reaches its maximum\nbetween \u22120.36 and 0.94 at 90% credibility; consistently,\nthe B-Spline model finds the peak to lie between \u22120.23\nand 0.96. The possibility that the tilt angle distribution\npeaks away from alignment is also found in GWTC-3.0\nunder various models which permit such a feature (Vi-\ntale et al. 2022; Edelman et al. 2023; Golomb & Talbot\n2023).\nIt is not impossible, however, for the peak of\na cos \u03b8 distribution to be inferred away from alignment\neven when the true underlying population does peak at\ncos \u03b8 = 1 (Vitale & Mould 2025).\nThe inferred peak\nof the GWTC-4.0 cos \u03b8 distribution is more strongly\nconstrained away from unity than nearly all of those\nspuriously found with simulated catalogs of the same\nsize (cf. Figure 17 with Figure 4 of Vitale & Mould 2025).\nUnder both the strongly and weakly modeled ap-\nproaches, the cos \u03b8 distribution shown in Figure 7 has\nsupport across a wide range of spin tilts, with a slightly\nlarger fraction of positive cos \u03b8 compared to negative.\nGiven this broad support, we next ask the question:\nwhat is the lowest spin tilt angle that is absolutely re-\nquired to fit GWTC-4.0 reasonably? To probe this, we\nuse a model which is similar to the Gaussian Compo-\nnent Spins model but with p(cos \u03b8 < tmin) = 0 for\nan inferred value tmin, where t \u2261cos \u03b8 (Tong et al.\n2022; Callister et al. 2022); see Equation (B28).\nWe\nfind tmin = \u22120.71+0.15\n\u22120.19 at 90% credibility.\nThat the\nposterior for the minimum required cos \u03b8 is inconsistent\nwith \u22121 but remains confidently negative is a somewhat\nunexpected astrophysical result. If most BBHs form in\nisolation, a minimum tilt cutoff is plausible but would\nbe expected to be closer to zero, potentially even posi-\ntive. Conversely, dynamically formed BBHs should ex-\nhibit isotropic tilts extending down to cos \u03b8 = \u22121. Our\nobserved tilt distribution therefore does not preclude ei-\nther broad scenario of isolated or dynamical formation\u2014\nor a mixture of both. However, the fact that the inferred\nminimum required tilt is significantly negative suggests\nthe contribution of a dynamical formation channel to the\nBBH population. We further discuss the astrophysical\ninterpretation of negative spin tilts and potential sub-\npopulations in Section 6.3.2 in the context of effective\nspins.\n6.3.2. Effective Spins\nWe next turn to the inferred distributions of the effec-\ntive spins \u03c7eff and \u03c7p. Figure 9 shows the marginal dis-\ntributions of \u03c7eff (left) and \u03c7p (right) under the Skew-\nnormal Effective Spin model (red solid; Equa-\ntion B37), compared to the Gaussian Effective\nSpins model result from GWTC-3.0 (purple dashed;\nEquation B36). The Skew-normal Effective Spin\nmodel (Banagiri et al. 2025) differs from the previously-\nused Gaussian Effective Spins in two ways. First,\nit allows for asymmetry in the \u03c7eff marginal distri-\nbution.\nSecond, the marginal \u03c7p distribution is a\ntruncated Gaussian which is not correlated with \u03c7eff.\nOn GWTC-4.0 data, the Gaussian Effective Spins\nmodel finds that \u03c7eff and \u03c7p are preferentially uncorre-\nlated, although this conclusion depends on analysis set-\ntings; see Figure 19 in Appendix D.3 and the discussion\ntherein.\nWe find that the \u03c7eff distribution is skewed and\nasymmetric about zero with more support for\npositive values. Asymmetry can be directly probed\nwith the \u03f5 skewness parameter of the Skew-normal\nEffective Spin model, defined in Equation (B37). We\nfind that the skewness \u03f5 is less than 0 (symmetry) with\n99.3% credibility, as can be seen in the inset of the\nleft panel of Figure 9.\nThis corresponds to a wider\n\u03c7eff distribution to the right of the peak, and a nar-\nrower distribution to the left, and is known as positive\nskew. As discussed in Section 6.5.2, asymmetry is also\nfound when allowing for a linear or spline correlation\nbetween \u03c7eff and mass ratio. Results for the GWTC-4.0\n\u03c7eff distribution measured with more models, including\nthe Gaussian Effective Spins model and with the\nweakly modeled approach are presented in Figures 19\nand 21 in Appendix D.\n\n30\n\u22121.0\n\u22120.5\n0.0\n\u03f5 (skew)\nSkewnormal E\ufb00ective Spin,\nGWTC-4.0\nGaussian E\ufb00ective Spins,\nGWTC-3.0\nFigure 9. Marginal \u03c7eff (left panel) and \u03c7p (right panel) distributions. The solid lines show the median of each inferred distri-\nbution, and the shaded regions show the 90% credible intervals. The GWTC-4.0 results under the Skew-normal Effective\nSpin model are shown in red; the GWTC-3.0 results under the Gaussian Effective Spins model are shown in purple dashed.\nThe histogram inset in the left panel shows the skew parameter \u03f5 for the Skew-normal Effective Spin model. There is\nsignificant preference for a skewed \u03c7eff distribution, indicated by \u03f5 < 0 with 99.3% credibility.\nTable 3.\nSummary of probes of spin misalignment, as measured by \u03c7eff.\nModel\n\u03c7eff,1%\nFraction \u03c7eff < 0\nHM Fraction\nGaussian Effective Spins (GWTC-3.0)\n\u22120.18+0.09\n\u22120.12\n0.28+0.12\n\u22120.13\n< 3.1 \u00d7 10\u22122\nGaussian Effective Spins (GWTC-4.0)\n\u22120.2+0.06\n\u22120.07\n0.34+0.09\n\u22120.1\n< 1.9 \u00d7 10\u22122\nSkew-normal Effective Spin (GWTC-4.0)\n\u22120.11+0.04\n\u22120.08\n0.34+0.08\n\u22120.09\n< 1.3 \u00d7 10\u22124\nNote\u2014 Summary of probes of spin misalignment, as measured by \u03c7eff. We give 90% credible\nintervals for the \u03c7eff value of the first percentile of the distribution (\u03c7eff,1%), serving as a proxy\nfor the minimum \u03c7eff, and the fraction of \u03c7eff < 0. The HM fraction provides an upper limit to\nthe fraction of BBHs of hierarchical merger origin, equal to 0.16 times the fraction of systems\nwith \u03c7eff < \u22120.3 (Fishbach et al. 2022; Baibhav et al. 2020); we provide its 90% upper limit.\nPosteriors for these quantities for these and other models are plotted in Figure 21.\nWe now discuss BBHs with spin tilts lying below\nthe orbital plane. These interesting probes of dynam-\nical BBH formation have cos \u03b8 < 0 and thus negative\n\u03c7eff. In Table 3, we present 90% bounds for three quan-\ntities which probe negative \u03c7eff in the population, using\nboth the Skew-normal Effective Spin and Gaus-\nsian Effective Spins models for a straightforward\ncomparison to GWTC-3.0.\nFirst, we report the first\npercentile of \u03c7eff distribution, which serves as a proxy\nfor the distribution\u2019s minimum without necessitating the\ninclusion of sharp features in the distribution itself (Cal-\nlister et al. 2022), constraining it to fall between \u22120.27\nand \u22120.08.\nThe Gaussian Effective Spins model\nfinds more extremal minimum spins than the Skew-\nnormal Effective Spin model, likely due to its re-\nquired symmetry about its peak; fitting the positive side\nof the distribution forces a longer tail into the negative\nregion. Second, we report the fraction of the population\nwith negative \u03c7eff to be 0.24\u20130.42, with the two models\nfinding nearly identical results. Assuming isotropy, an\nupper bound on the fraction of BBHs formed dynam-\nically in gas-free environments can be placed by dou-\nbling the fraction of negative \u03c7eff (Equation 7 of Abbott\net al. 2021a); we thus find that at most 84% of BBHs\nform dynamically. Third, we give the 90% upper limit\non the fraction of BBHs coming from the hierarchical\nmerger (HM) scenario. The HM fraction is bounded by\nthe consideration that \u223c16% of BBHs coming from the\nHM formation channel will have \u03c7eff < \u22120.3 (Baibhav\net al. 2020; Fishbach et al. 2022); we limit this fraction\nto \u22723%. Figure 21 in Appendix D.4 shows posterior\ndistributions on the quantities in Table 3 for the mod-\n\n31\nels presented here and those using the weakly modeled\napproach.\nIt is possible that the support for \u03c7eff < 0 may be a\nbyproduct of the models fitting for a peak at \u03c7eff \u223c0\nwithout having the flexibility for a sharp decline beyond\n\u03c7eff < 0. This type of sharp feature could occur if com-\nponent spin magnitudes cluster around \u03c7 \u223c0 but their\ntilts seldom reach below cos \u03b8 = 0. In Section 6.3.1, we\naddress this by directly fitting for the minimum required\ncos \u03b8 which is found to be confidently negative, and cor-\nresponds to a fraction 0.41+0.05\n\u22120.05 of systems with spins\nlaying below the orbital plane. These probes of negative\nspin indicate that between \u223c20\u201340% the BBH pop-\nulation has spins which are more than 90 degrees\nmisaligned with the orbital angular momentum.\nIt is unlikely that the entire observed BBH popula-\ntion originates from a single formation channel (Zevin\net al. 2021; Mandel & Broekgaarden 2022; Cheng et al.\n2023; Afroz & Mukherjee 2025; Colloms et al. 2025).\nFeatures in our spin distributions indeed suggest the\npresence of multiple sub-populations. A purely random\nspin channel would produce a symmetric distribution\naround \u03c7eff = 0 (Rodriguez et al. 2016a,b; Farr et al.\n2017). However, for all models, the observed \u03c7eff distri-\nbution is asymmetric about zero, c.f., Figure 21. This\nasymmetry suggests contribution from a preferentially\naligned subpopulation (Gerosa et al. 2018; Arca Sedda\net al. 2023; Banagiri et al. 2025). The skew observed\nin the Skew-normal Effective Spin, as well as the\n(q, \u03c7eff) Linear and (q, \u03c7eff) Spline models (see Sec-\ntion 6.5.2 and Figure 21) further supports the presence\nof an aligned component, either as a sub-dominant sub-\npopulation or a dominant sub-population with small\nspin magnitudes. We find a preference for small spin\nmagnitude (Figure 7), perhaps favoring the latter.\nFinally, we discuss the effective precessing spin \u03c7p,\nwhich can provide additional insight about spin pre-\ncession in the population. The right panel of Figure 9\nshows the marginal inferred \u03c7p distribution (red). We\nfind that precession exists on a population level, as our\nmodels do not support (\u00b5p, \u03c3p) = (0, 0) at high credi-\nbility. The GWTC-4.0 results support larger \u03c7p than\nGWTC-3.0, shown for comparison in Figure 9 (pur-\nple dashed). However, different likelihood convergence\ncriteria (Appendix A.1) were used between GWTC-4.0\nand GWTC-3.0, meaning these results are not directly\ncomparable. Under the less-stringent GWTC-3.0 con-\nvergence criterion, the \u03c7p distribution inferred from\nGWTC-4.0 data is more consistent with that found in\nGWTC-3.0, albeit still with less support for low \u00b5p\nand low \u03c3p. The inferred \u03c7p distribution is more de-\npendent on analysis settings than other parameters,\nlargely because the individual-event prior has no sup-\nport at \u03c7p = 0 making it technically difficult to reweight\nindividual-event posteriors to the population. We dis-\ncuss the sensitivity of the \u03c7p distribution to analysis\nsettings in detail in Appendix D.3; see Figures 18 and\n19.\n6.4. Merger Rate and Redshift Evolution\nImprovements in the sensitivity of current GW ob-\nservatories (Ganapathy et al. 2023; Capote et al. 2025;\nAbac et al. 2025a) not only provide more BBH detec-\ntions, but also observations of increasingly faint sources\nat higher redshifts. These observations allow us to im-\nprove our population-level constraints on the evolution\nof the merger rate across redshift.\nFollowing Abbott et al. (2023a), we repeat the Power\nLaw Redshift strongly modeled approach. We assume\nthat the merger rate evolves as R(z) \u221d(1 + z)\u03ba, and\nwe infer the proportionality constant and the power-law\nindex \u03ba. We find that the BBH merger rate at\nz = 0.2 is 29+8.5\n\u22126.5 Gpc\u22123 yr\u22121, and the power-law\nexponent is constrained to \u03ba = 3.2+0.94\n\u22121.00, which\nrepresent consistent and improved constraints over our\nGWTC-3.0 analysis. We infer that 99% of detectable\nBBHs fall below z = 1.5+0.2\n\u22120.2 (cf.\nthe maximum ob-\nservable redshift inferred as z = 1.1+0.2\n\u22120.2 in Fishbach\n& van Son 2023, from GWTC-3.0).\nWe also use the\nweakly modeled B-Spline approach to explore if the\ndata support behavior beyond a power-law evolution,\nand compare our results in Figure 10. While the results\nare consistent\u2014indicating that the Power Law Red-\nshift model is sufficient\u2014the B-Spline approach infers\na larger merger rate of 38+19\n\u221210 Gpc\u22123 yr\u22121 at z = 0.2.\nOur results are nominally consistent with the cosmic\nstar formation rate density, with \u03baSFR = 2.7 (Madau &\nDickinson 2014).\nOur constraints on the merger rate evolution informs\nour understanding of the BBH progenitor formation rate\nand the delay time distribution between formation and\nmerger (Vitale et al. 2019; Rodriguez & Loeb 2018; Fra-\ngione & Kocsis 2018; Fishbach et al. 2018; Baibhav et al.\n2019; Romero-Shaw et al. 2021; Broekgaarden et al.\n2022b; Mapelli et al. 2022; Fishbach & Kalogera 2021;\nChru\u00b4sli\u00b4nska 2024; Fishbach & Fragione 2023; Boesky\net al. 2024). For BBHs formed from isolated binary evo-\nlution, the merger rate evolution is typically well approx-\nimated as a power law at small redshift, though the value\nof the power-law index \u03ba is sensitive to the assumed\npopulation synthesis parameters (Neijssel et al. 2019;\nBroekgaarden et al. 2022b; Gallegos-Garcia et al. 2021;\nde S\u00b4a et al. 2024). Nevertheless, models typically prefer\nvalues around \u03ba \u223c1 (Dominik et al. 2013; Baibhav et al.\n\n32\n\u22122\n0\n2\n4\n6\n\u03ba\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\np(\u03ba)\nGWTC-3.0\nGWTC-4.0\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nz\n101\n102\n103\nR(z) [Gpc\u22123 yr\u22121]\nStar Formation (Arbitrary Norm)\nPower Law Redshift, GWTC-3.0\nPower Law Redshift, GWTC-4.0\nB-Spline, GWTC-4.0\nFigure 10.\nComparison of redshift models between\nGWTC-3.0 and GWTC-4.0.\nTop: Posterior on the \u03ba pa-\nrameter for the Power Law Redshift model. GWTC-4.0\nshows increased support for positive values. Bottom: Median\nand 90% credible regions for the comoving source frame rate\nin the Power Law Redshift model. We also show a com-\nparison of the Power Law Redshift model and the weakly\nmodeled B-Spline model and a scaled cosmic star formation\nrate density (Madau & Dickinson 2014), which are consistent\nwithin uncertainties (\u03baSFR = 2.7).\n2019). BBHs originating from dense star clusters predict\nlocal merger rates of R \u223c10 Gpc\u22123 yr\u22121 (Arca Sedda\net al. 2024) and steeper values of \u03ba \u223c2 (Antonini &\nGieles 2020), albeit with large theoretical uncertainties\nthat can account for a similar evolution to the isolated\nbinary evolution predictions. Our observations sug-\ngest a steeper evolution, with \u03ba \u223c2\u20134. While this\ndoes not rule out either class of BBH formation, it may\nbe suggestive of (i) progenitor formation rates that peak\nat an earlier redshift as compared to the cosmic star\nformation rate density, e.g., due to a preference for low-\nmetallicity progenitors, and/or (ii) shorter delay times,\nperhaps with a tail toward long delay times (Fishbach\n& Kalogera 2021; Karathanasis et al. 2023; Fishbach &\nvan Son 2023; Turbang et al. 2024; Vijaykumar et al.\n2024; Schiebelbein-Zwack & Fishbach 2024).\nModels of isolated binary evolution and dense star\nclusters often predict that the merger rate evolves dif-\nferently across the mass spectrum (van Son et al. 2022b;\nMapelli et al. 2022; Ye & Fishbach 2024); however,\nanalyses of the previous catalog have not found evi-\ndence for or against differential rate evolution (Fishbach\net al. 2021; Sadiq et al. 2022; van Son et al. 2022b; Ray\net al. 2023a; Heinzel et al. 2025b; Sadiq et al. 2025a).\nWe discuss potential mass-redshift correlations in Sec-\ntion 6.5.4.\n6.5. Population-level Correlations between Parameters\nWhile much can be learned by studying the distribu-\ntions of individual BBH parameters, we can glean ad-\nditional information on the population by considering\nhow parameters are correlated with one another across\nsystems. In this subsection, we provide an overview of\nhow parameters in the BBH population appear to be\nbroadly structured in various two-dimensional slices of\nparameter space, briefly discussing the astrophysical im-\nplications of our findings.\n6.5.1. Mass Ratio and Spin Correlations\nWe begin by following up on the purported anti-\ncorrelation between BBH mass ratio q and effective in-\nspiral spin \u03c7eff.\nAlthough we find less support\nfor the specific case of anti-correlation between\nq and \u03c7eff relative to GWTC-3.0, we find com-\npelling evidence for some correlated structure in\n(q, \u03c7eff). Namely, larger positive values of \u03c7eff appear\nto be favored as q decreases, but it is unclear if this\nis accompanied by a preference for larger negative val-\nues of \u03c7eff as well. The (q, \u03c7eff) Linear model imposes\na linear functional dependence between BBH mass ra-\ntio, and the mean and (natural log) width of the \u03c7eff\ndistribution (see Appendix B.7). Fitting this model to\nGWTC-3.0 data suggests that a linear correlation co-\nefficient of \u03b4\u00b5eff|q < 0 (i.e., the case of a negative q-\ndependence on the mean of the \u03c7eff distribution) with\n98% credibility (Abbott et al. 2023a).\nUpdating this\nanalysis to include data obtained over O4a softens the\nevidence for an anti-correlation between q and the mean\nof the \u03c7eff distribution, with a value of \u03b4\u00b5eff|q < 0 now\ninferred at 82% credibility. However, we now see notable\nevidence for a linear increase in the log width of the \u03c7eff\ndistribution as mass ratios become more unequal \u2013 with\n\u03b4 ln \u03c3eff|q < 0 at 95% credibility.\nWe plot the mass-ratio dependent mean and width of\nthe \u03c7eff distribution inferred using the Linear model\nin Figure 11.\nIn the bottom panel of Figure 11, we\ninclude the two-dimensional posterior distribution of\n\u03b4\u00b5eff|q and \u03b4 ln \u03c3eff|q.\nInspecting this plot, we see an\n\n33\nanti-correlation in the posterior of the two hyperparam-\neters, where larger negative values of \u03b4\u00b5eff|q imply values\nof \u03b4 ln \u03c3eff|q closer to zero, and larger negative values of\n\u03b4 ln \u03c3eff|q imply values of \u03b4\u00b5eff|q closer to zero. The case\nin which both parameters are zero (no correlation be-\ntween q and \u03c7eff of any kind) appears to be ruled out\nat > 99% credibility. In practice, this implies that the\nLinear model finds support for larger positive values of\n\u03c7eff at more unequal mass ratios, but cannot yet con-\nclude whether these are accompanied by larger negative\nvalues of \u03c7eff as well.\nNext, we probe for more intricate correlations be-\ntween q and \u03c7eff using the Spline model. Similar to\nthe Linear model, the Spline model allows for the\nmean and width of the \u03c7eff distribution to evolve with\nmass ratio.\nHowever, these mass ratio dependences,\nrather than being linear, are modeled flexibly with cu-\nbic splines (see Appendix B.7 and Heinzel et al. 2024).\nWe plot the q-dependent means and widths inferred\nfrom the Spline model alongside those from the Lin-\near model in Figure 11.\nDespite fluctuations emerg-\ning in the Spline model, the two models are, within\n90% credible bounds, consistent.\nThe preference for\nbroadening in the \u03c7eff distribution as q decreases found\nwith the Linear model, does not clearly appear in the\nSpline model. In the bottom panel of Figure 11, we also\nplot the inferred gradient of the \u03c7eff distribution\u2019s mean\nand (natural log) width relative to mass ratio at q = 0.6\n(roughly the value at which covariance appears most\npronounced). Here, we see a similar structure to that of\nthe Linear model\u2019s (\u03b4\u00b5eff|q, \u03b4 ln \u03c3eff|q) posterior, albeit\nwith much more uncertainty. As a final observation from\nthe Spline model in Figure 11, we see that the inferred\n\u03c7eff distribution at low mass ratios (q \u22720.2) grows in\nuncertainty, roughly recovering the prior. This implies\nthat any correlation inferred by the Linear model is\nlikely driven by observations with mass ratios q \u22730.2.\nAs such, the inferences from this model should be in-\nterpreted with caution as q \u21920, where the trend is\neffectively being extrapolated from the more populated\nq \u22730.2 region due to a lack of model flexibility.\nWe now move to the Copula model, which allows for\na correlation between q and \u03c7eff with a variable strength\n\u03baq,eff (see Appendix B.6). This framework has the added\nadvantage that the level of correlation is decoupled from\nthe shape of the marginal distribution (e.g., Adamcewicz\n& Thrane 2022), with less flexibility for covariant struc-\nture relative to other correlated population models. Fit-\nting the Copula model to GWTC-4.0 suggests that q\nand \u03c7eff are anti-correlated (\u03baq,eff < 0) with 92% cred-\nibility. Specifically, we infer \u03baq,eff = \u22122.1+2.4\n\u22122.9. Adam-\ncewicz et al. (2023) analyzed GWTC-3.0 data with a\n\u22120.5\n0.0\n0.5\n\u00b5e\ufb00(q)\nLinear\nSpline\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n10\u22122\n10\u22121\n100\n\u03c3e\ufb00(q)\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\n0.5\n1.0\n\u03b4\u00b5e\ufb00|q\n\u221210\n\u22125\n0\n5\n10\n\u03b4 ln \u03c3e\ufb00|q\nLinear\nSpline (q = 0.6)\nFigure 11.\nThe inferred peak (top) and width (middle)\nof the \u03c7eff distribution as a function of mass ratio for the\n(q, \u03c7eff) Linear model (blue) and Spline model (orange).\nThe shaded regions in these panels give the 90% credible\nintervals.\nThe bottom panel gives the posterior distribu-\ntion for the gradient of the \u03c7eff distribution\u2019s peak (\u03b4\u00b5eff|q)\nand natural log width (\u03b4 ln \u03c3eff|q) dependent on mass ratio.\nFrom dark to light, the shaded regions represent the 50%,\n90% and 99% credible intervals. Again, blue gives the result\nof the Linear model, while orange shows the result of the\nSpline model sliced through q = 0.6 (the approximate point\nat which the gradients are largest).\nIt appears that mass\nratio and \u03c7eff exhibit some kind of correlation, but the exact\nnature is unclear.\ncopula model to find that (q, \u03c7eff) are anti-correlated\nwith > 99% credibility, suggesting greater evidence for\nan anti-correlation than is measured here.\nHowever,\nthese results are not directly comparable to those pre-\nsented in this work, due to different modeling assump-\ntions and different convergence criteria in the population\nlikelihood. Qualitatively, we see that the Copula model\nand Linear model exhibit a subtle anti-correlation in\n(q, \u03c7eff), as seen in the respective two-dimensional PPDs\nin Figure 12.\n\n34\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n\u22120.75\n\u22120.50\n\u22120.25\n0.00\n0.25\n0.50\n0.75\n\u03c7e\ufb00\nCopula\nLinear\nFigure 12.\nMass ratio and \u03c7eff PPDs for the Cop-\nula model (blue) and Linear model (orange).\nThe con-\ntours, from dark to light, mark 50%, 90%, and 99% of the\nvolume. We see a subtle preference for an anti-correlation,\nalthough this feature is far less prevalent than it appeared\nin GWTC-3.0. We also see evidence for a broadening in the\ndistribution as mass ratios become more unequal in the Lin-\near model. The Copula model is not flexible in a way that\nit can capture a broadening.\nThere are a number of potential astrophysical implica-\ntions if the anti-correlation in (q, \u03c7eff) is real. If isolated\nbinaries make up a substantial fraction of the population\nand undergo tidal spin up, stable mass transfer and the\nresulting mass ratio reversal of systems (Broekgaarden\net al. 2022a; Zevin & Bavera 2022; Olejak et al. 2024)\nmay produce an such an anti-correlation in the popu-\nlation. This feature could also be explained by binaries\nundergoing a common-envelope phase provided common\nenvelope efficiencies are sufficiently high (Bavera et al.\n2021).\nCovariance in (q, \u03c7eff) could also be a result of hierar-\nchical mergers contributing to a considerable fraction of\nthe BBH merger rate (Antonini et al. 2025b,a). Hierar-\nchical mergers should exhibit mass ratios that are more\nunequal and spin magnitudes that are larger than iso-\nlated, or first-generation dynamical mergers. If hierar-\nchical mergers occur in typical dynamical environments,\nthe spins of the BHs will be isotropically distributed,\nthus producing a broadening in the \u03c7eff distribution as\nmass ratios become unequal. Meanwhile, BHs in AGN\nmay have spins preferentially aligned with one another,\nmeaning hierarchical mergers in these environments can\nproduce a correlation between mass ratios and spins that\nis asymmetrical about \u03c7eff = 0 (McKernan et al. 2022;\nSantini et al. 2023). Stronger evidence for unequal mass\nbinaries preferring positive values of \u03c7eff could then in-\ndicate that binaries merging in AGN are predominantly\ncoaligned with the rotation of the AGN disk (Santini\net al. 2023).\n6.5.2. Mass and Spin Correlations\nWe find model-dependent evidence for correla-\ntions between m1 and \u03c7eff. Motivated by the feature\nin the mass distribution around the \u223c30\u221240 M\u2299range,\nwe use a BGP analysis allowing for correlations in m1\nand \u03c7eff (see Appendix C.2) to see if this feature in the\ndistribution of masses is accompanied by a deviation\nin the BBH spin distribution. Using GWTC-4.0, these\nstudies find weak evidence that BBH systems with at\nleast one mass in the \u223c30\u221240 M\u2299peak tend to have\nspins that are symmetrically distributed about \u03c7eff = 0,\nwhile binaries outside of this mass range have spins\nthat are skewed toward positive (aligned) values of \u03c7eff.\nQuantitatively, this BGP analysis infers that for every\nmerger in the \u223c30\u221240 M\u2299peak with a negative value\nof \u03c7eff, there are 1.9+4.8\n\u22121.2 with a positive value of \u03c7eff.\nMeanwhile, for every event outside of this mass range\nwith a negative value of \u03c7eff, there are 6.6+14.1\n\u22124.2\nwith a\npositive value of \u03c7eff. We illustrate this result in the top\npanel of Figure 13. Furthermore, in the BGP analysis\nthe inferred distribution of masses for BBH systems with\neffective inspiral spins (|\u03c7eff| \u22720.1) exhibits a preference\nfor a larger proportion of mergers with m1 \u223c30\u221240 M\u2299,\ncompared to systems with \u03c7eff \u22730.1. These distribu-\ntions, however, remain consistent within 90% credible\nintervals. This is illustrated in the bottom two panels\nof Figure 13. These features were also recovered with\nsame analyses applied to GWTC-3.0 data, albeit with\nless certainty (Ray et al. 2024). However, more recent\nGWTC-3.0 analyses find conflicting evidence, suggest-\ning that the \u03c7eff distribution of \u224830 M\u2299BHs is posi-\ntively skewed (Sadiq et al. 2025b; Roy et al. 2025).\nThe Isolated Peak model (see also Godfrey et al.\n2023) fits the data to a model containing multiple\nmass subpopulations with independent spin distribu-\ntions. One subpopulation consists of a single peak in\nthe mass distribution (which is inferred to center on\n\u223c10 M\u2299), while other subpopulations are flexibly fit\nwith the B-Spline method. Applying these analyses to\nGWTC-4.0 suggests that BHs within the \u223c10 M\u2299peak\nhave a spin magnitude distribution consistent (within\n90% credibile intervals) with the rest of the BBH popu-\nlation. Meanwhile, although there is some overlap in the\n90% credibile regions of the cosine tilt distributions for\nboth subpopulations, the distribution of tilts for BHs\nin the \u223c10 M\u2299peak favors alignment and is inconsis-\ntent with isotropy. The distribution of cosine tilts for\nBHs outside this mass peak appears more symmetrical\nabout cos \u03b8 = 0 and does not rule out isotropy. Roughly\n\n35\n\u22120.3\n\u22120.2\n\u22120.1\n0.0\n0.1\n0.2\n0.3\n0.4\n\u03c7e\ufb00\n0.0\n2.5\n5.0\n7.5\n10.0\n12.5\n15.0\np(\u03c7e\ufb00|m1, m2)\nm \u2208(30M\u2299, 40M\u2299)\nm /\u2208(30M\u2299, 40M\u2299)\n20\n40\n60\n80\n100\nm1 [M\u2299]\n10\u22125\n10\u22123\n10\u22121\np(m1|\u03c7e\ufb00)\n\u03c7e\ufb00\u2208(\u22120.05, 0.05)\n\u03c7e\ufb00\u2208(0.1, 0.2)\n20\n40\n60\n80\n100\nm2 [M\u2299]\n10\u22125\n10\u22123\n10\u22121\np(m2|\u03c7e\ufb00)\n\u03c7e\ufb00\u2208(\u22120.05, 0.05)\n\u03c7e\ufb00\u2208(0.1, 0.2)\nFigure 13.\nTop: inferred distributions of effective inspiral\nspin \u03c7eff in the correlated mass\u2013spin BGP analysis. The solid\nlines give the median, while the shaded regions indicate the\n90% credible intervals. In blue, we have the \u03c7eff distribution\nof BBH systems with at least one mass inside the 30\u221240 M\u2299\npeak range. In orange, we have the \u03c7eff distribution of BBH\nsystems masses outside the 30\u221240 M\u2299peak range.\nWhile\nthe two distributions are consistent within 90% credible in-\ntervals, systems outside the peak range appear to favour\na distribution of \u03c7eff skewed toward more positive values.\nMeanwhile, systems inside the peak range appear to favour\na more symmetrical distribution about \u03c7eff = 0.\nMiddle:\ninferred distributions of primary mass from the correlated\nmass\u2013spin BGP analysis. Bottom: inferred distributions of\nsecondary mass from the correlated mass\u2013spin BGP analysis.\nIn both mass plots, blue shows the distribution for systems\nwith small spins, \u03c7eff in the range (\u22120.05, 0.05), while or-\nange shows the distribution for systems with larger spins,\n\u03c7eff in the range (0.1, 0.2). Note the preference for a higher\nproportion of mergers with masses \u224830\u221240 M\u2299for low spin\nsystems (blue).\nspeaking, this corresponds to a distribution of \u03c7eff that\nmay be symmetrical about zero for the BBH population\noutside of the \u223c10 M\u2299peak. Inside this mass peak, how-\never, the implied \u03c7eff distribution skews toward positive\nvalues.\nWe also model a correlation between primary mass\nand \u03c7eff using a copula model (see Appendix B.6). Fit-\nting this Copula model with GWTC-4.0 data, we in-\nfer a correlation of \u03bam1,eff = 0.4+1.6\n\u22121.4 between m1 and\n\u03c7eff. Hence, the Copula analysis finds no evidence for\na single, smooth, population-wide correlation between\nprimary mass and \u03c7eff.\nBroadly, our analyses of the joint mass and spin dis-\ntribution recover similar features to recent works that\nprobe for features in GWTC-3.0.\nFirst, analyses of\nGWTC-3.0 do not find evidence for a smoothly corre-\nlated distribution in primary mass and \u03c7eff (Safarzadeh\net al. 2020; Biscoveanu et al. 2022a; Fishbach et al. 2022;\nHeinzel et al. 2024, 2025b; Antonini et al. 2025b), as is\nthe case in this work.\nMeanwhile, a number of anal-\nyses find evidence for separate subpopulations in mass\nand spin consistent with predictions of dynamical and\nfield mergers. More specifically, these works tend to find\na subpopulation with lower masses and smaller, mostly\naligned spins, and a second subpopulation of heavier bi-\nnaries with larger, isotropically distributed spins, where\nthe subpopulations transition around \u223c40 M\u2299(Wang\net al. 2022; Mould et al. 2022b; Godfrey et al. 2023; Li\net al. 2024; Antonini et al. 2025b; Pierra et al. 2024; Guo\net al. 2024; Li et al. 2025; Sadiq et al. 2025b). While the\nanalyses presented in this work do not recover this exact\nfeature (nor do they probe directly for it), the Isolated\nPeak model\u2019s preference for aligned spins at \u223c10 M\u2299\nand isotropically distributed spins at higher masses may\nbe related.\n6.5.3. Redshift and Spin Correlations\nWe find evidence that the \u03c7eff\ndistribution\nbroadens as redshift increases up to z \u223c1. We\nagain look for correlations between redshift and \u03c7eff by\nmodeling the mean and width of the \u03c7eff distribution\nwith a linear dependence on redshift (see Appendix B.7).\nBiscoveanu et al. (2022a) employed a Linear model for\n(z, \u03c7eff) to analyze GWTC-3.0 data, finding no evidence\nfor redshift dependence in the mean of the \u03c7eff distribu-\ntion, but suggesting that the \u03c7eff distribution broadens\nwith increasing redshift (\u03b4 ln \u03c3eff|z > 0 at 99% credibil-\nity). Updating this analysis to include O4a data, we find\nmore evidence for a broadening in the \u03c7eff distribution\nwith redshift, with \u03b4 ln \u03c3eff|z > 0 now inferred at > 99%\ncredibility. The mean and width of the \u03c7eff distribution\nas functions of redshift are shown in Figure 14.\n\n36\nThe Spline model, which models the redshift depen-\ndence on the mean and width of the \u03c7eff distribution\nflexibly with cubic splines (see Appendix B.8), is broadly\nconsistent with the Linear model.\nThe exception is\nthat the Spline model tends to recover the prior be-\nyond a redshift of z \u22731. This likely indicates that the\nLinear model is fitting a trend at low redshifts, then\nextending this trend to redshifts z \u22731 due to a lack\nof flexibility. To further illustrate this point, the gray\ndashed line in Figure 14 indicates the redshift under\nwhich 90% of the catalog\u2019s cumulative posterior sup-\nport is contained. Roughly speaking, this means our in-\nferences above this redshift are informed by only \u223c10%\nof the data. Therefore, while we find evidence that the\n\u03c7eff distribution broadens as binaries approach z \u223c1,\nwe are unable to determine if this trend continues at\nhigher redshifts.\nWe also model a correlation between redshift and \u03c7eff\nusing a copula model, with variable correlation \u03baz,eff\n(see Appendix B.6). In contrast to the above analyses,\nthe Copula model finds evidence for a positive corre-\nlation in (z, \u03c7eff), inferring a value of \u03baz,eff = 4.6+3.0\n\u22123.1\n(or \u03baz,eff > 0 with 98% credibility). While the Cop-\nula model lacks the flexibility to fit a broadening di-\nrectly, the long (albeit shallow) posterior tails reach-\ning into both large-negative and large-positive values\nfor \u03baz,eff may relate to the broadening in the \u03c7eff dis-\ntribution recovered by the Linear and Spline mod-\nels (see the subtle mode at negative values of \u03baz,eff\nin Appendix D.6). If the z-dependent broadening and\nconstant mean of the \u03c7eff distribution from the Lin-\near and Spline models is to be believed, it is unclear\nwhy the posterior on \u03baz,eff skews toward positive values,\nrather than being symmetric about zero.\nIt is unclear what this broadening in the \u03c7eff distri-\nbution at greater redshifts might imply astrophysically.\nProvided BH progenitors experience significant spin up\ndue to tidal torques, smaller orbital separations and pe-\nriods will result in more efficient spin up of BBH com-\nponents (Zaldarriaga et al. 2018; Mapelli 2020; Bavera\net al. 2021, 2022; Fuller & Lu 2022). Of course, smaller\norbital separations correspond to shorter delay-times to\nmerger. This means that these systems may contribute\nmore to the merger rate in the earlier Universe (higher\nz), where systems with wider orbits have not had time\nto merge.\nFurthermore, given that higher metallicity\nsystems are expected to evolve to longer orbital peri-\nods due to experiencing more mass loss during core he-\nlium burning (Qin et al. 2018; Fuller & Lu 2022), one\nmight predict that larger spin magnitudes should be ob-\nserved in regions of lower metallicity and thus also at\nhigher redshifts. However, the correlation in the Lin-\n\u22120.75\n\u22120.50\n\u22120.25\n0.00\n0.25\n0.50\n\u00b5e\ufb00(z)\nLinear\nSpline\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nz\n10\u22122\n10\u22121\n\u03c3e\ufb00(z)\nFigure 14.\nThe inferred mean (top) and width (bot-\ntom) of the \u03c7eff distribution as a function of redshift for\nthe Linear model (blue) and the Spline model (orange).\nThe shaded regions give the 90% credible intervals.\nThe\ngray dashed line indicates the redshift under which 90% of\nthe cumulative posterior probability lies across all events in\nGWTC-4.0.\nTherefore, inferences above this redshift are\ndominated by the prior or population model. Note the loga-\nrithmic scale on the width (bottom panel). In either model,\nwe find evidence that the width of the effective inspiral spin\ndistribution increases with redshift up to z \u223c1.\near and Spline models is between redshift and the\nwidth of the \u03c7eff distribution rather than the mean.\nThis includes an increasing number of systems with both\nlarge-positive and large-negative values of \u03c7eff. An in-\ncrease in systems with large-negative \u03c7eff may be some-\nwhat difficult to square with the above hypothesis, given\nthat tidal spin up is only relevant in isolated systems,\nand that large supernovae kicks are required to misalign\nthe BH spins so significantly (Kalogera 2000; Wysocki\net al. 2018; Gerosa et al. 2018; Callister et al. 2021a;\nSteinle & Kesden 2021; Stevenson 2022; Tauris 2022;\nBaibhav & Kalogera 2024). On the other hand, if the\nCopula results are to be taken at face-value, the prefer-\nence for a positive correlation in (z, \u03c7eff) fits more neatly\nwith the aforementioned hypothesis.\nAnother possibility, following discussion from Sec-\ntion 6.3, is that multiple separate subpopulations of\nBBH mergers are being observed, where the more dom-\ninant (in terms of redshift-dependent merger rate) sub-\npopulation changes at some nearby redshift. Hierarchi-\ncal mergers becoming more dominant at higher redshifts\nfor example could potentially explain such a broadening\nin the effective spin distribution.\nThis interpretation\nwould also imply some level of correlation between mass\n\n37\nand redshift, which we do not find evidence for below in\nSection 6.5.4.\nAs a final caveat, using GWTC-3.0 data, Biscoveanu\net al. (2022a) fit the BBH population to a model in which\nthe \u03c7eff distribution is linearly dependent on both pri-\nmary mass and redshift. In doing so, the authors find\ndegeneracies between the (m1, \u03c7eff) and (z, \u03c7eff) corre-\nlations. While we do not explore correlations beyond\ntwo dimensions in this work, we acknowledge that the\nassumption of independence between other pairs of pa-\nrameters may have notable effects on our inferences.\n6.5.4. Redshift and Mass Correlations\nFinally, we consider potential correlations between\nBBH mass and redshift. We do not find evidence\nfor evolution in the mass distribution with red-\nshift.\nWe emphasize that these inferences are con-\nstrained to the nearby Universe, with relatively little\ndata beyond z \u223c1 (19 out of 153 BBH events hav-\ning posteriors consistent with z > 1 to 90% credibil-\nity). We model correlations between primary mass and\nredshift using a copula with correlation \u03bam1,z (see Ap-\npendix B.6). Using this Copula model, we infer a corre-\nlation of \u03bam1,z = 0.6+2.8\n\u22122.6. We also search for correlations\nbetween mass and redshift using a BGP analysis that\nallows for covariance in m1 and z (see Appendix C.2).\nSimilarly, this analysis finds that the mass distribution\ndoes not show a distinguishable evolution with redshift\n(see Appendix D.6). This conclusion is mostly in line\nwith studies using GWTC-3.0, which are also unable\nto infer any correlation between mass and redshift with\nconfidence (Fishbach et al. 2021; Sadiq et al. 2022; van\nSon et al. 2022b; Karathanasis et al. 2023; Ray et al.\n2023a; Heinzel et al. 2024, 2025b; Lalleman et al. 2025;\nSadiq et al. 2025a). This is with the exception of Rinaldi\net al. (2024) finding a positive correlation between BBH\nprimary mass and redshift, although a novel method is\nused to account for selection effects.\n7. CONCLUSION\nIn this paper, we present population-level analyses of\nevents included in the fourth Gravitational-Wave Tran-\nsient Catalog GWTC-4.0. This dataset more than dou-\nbles the number of events analyzed compared to the pre-\nvious catalog. Our main findings are:\n1. Features identified in the third catalog GWTC-3.0\npersist, including clear overabudances in the mass\ndistribution at 1\u20132 M\u2299and around 10 M\u2299, and a\nfeature near 35 M\u2299.\nThere is no conclusive evi-\ndence to either support or refute a suppression of\nthe merger rate between these features.\n2. We estimate the merger rates at redshift z = 0 to\nbe 7.6\u2013250 Gpc\u22123 yr\u22121 for binary neutron stars,\n9.1\u201384 Gpc\u22123 yr\u22121 for neutron star\u2013black hole bi-\nnaries, 14\u201326 Gpc\u22123 yr\u22121 for binary black holes.\n3. The binary black hole primary mass distribution\nis well described by a broken power law, shallow\nat low masses and steep at high masses, modu-\nlated by overdensities near 10 M\u2299and 35 M\u2299. A\nweakly modeled approach finds evidence of over-\ndensity around 20 M\u2299.\n4. Black holes in the 35 M\u2299feature tend to pair with\ncompanions of similar mass more frequently than\nlower-mass black holes do.\n5. The distribution of effective inspiral spins is asym-\nmetric about \u03c7eff = 0 and is skewed toward pos-\nitive \u03c7eff values. Spin magnitudes span a broad\nrange from 0 to 1, although \u223c90% of BHs have\n\u03c7 < 0.57.\n6. The redshift evolution of the binary black hole\nmerger rate R(z) remains consistent with the cos-\nmic star formation rate density. A merger rate uni-\nform in comoving volume and source-frame time is\nruled out.\n7. We find that black holes outside the 30\u201340 M\u2299\nrange prefer an asymmetric effective inspiral spin\ndistribution skewed toward higher values, while\nthose within this range show no such preference.\nCompared to GWTC-3.0, we observe stronger evi-\ndence that the width of the effective spin distribu-\ntion increases with redshift and weaker evidence\nfor an anti-correlation between mass ratio and ef-\nfective spin. No redshift evolution is observed in\nthe mass distribution.\n8. The neutron star mass distribution remain consis-\ntent with previous results, favoring a broad distri-\nbution of neutron star masses between 1 M\u2299and\n3 M\u2299.\nThe analysis of this expanded dataset refines the sta-\ntistical significance of previously reported trends and re-\nveals new features in the population of compact binary\nmergers. Several of these findings, such as the persis-\ntent \u223c10 M\u2299feature, pose challenges to current models\nof supernova physics, binary mass transfer, and dynami-\ncal formation in dense stellar environments. Future data\nfrom the remainder of the fourth observing run O4 will\nfurther enhance our understanding and may uncover ad-\nditional structure in the population.\n\n38\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies as well as by the Council of Scientific and Indus-\ntrial Research of India, the Department of Science and\nTechnology, India, the Science & Engineering Research\nBoard (SERB), India, the Ministry of Human Resource\nDevelopment, India, the Spanish Agencia Estatal de\nInvestigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comunitat\nAuton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Com-\nmission, the European Social Funds (ESF), the Euro-\npean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish Uni-\nversities Physics Alliance, the Hungarian Scientific Re-\nsearch Fund (OTKA), the French Lyon Institute of Ori-\ngins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering\nResearch Council of Canada (NSERC), the Canadian\nFoundation for Innovation (CFI), the Brazilian Min-\nistry of Science, Technology, and Innovations, the In-\nternational Center for Theoretical Physics South Ameri-\ncan Institute for Fundamental Research (ICTP-SAIFR),\nthe Research Grants Council of Hong Kong, the Na-\ntional Natural Science Foundation of China (NSFC),\nthe Israel Science Foundation (ISF), the US-Israel Bina-\ntional Science Fund (BSF), the Leverhulme Trust, the\nResearch Corporation, the National Science and Tech-\nnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, the JSPS\nLeading-edge\nResearch\nInfrastructure\nProgram,\nJSPS Grant-in-Aid for Specially Promoted Research\n26000005, JSPS Grant-in-Aid for Scientific Research\non Innovative Areas 2402:\n24103006, 24103005, and\n2905:\nJP17H06358,\nJP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grants-in-Aid for Scientific Research (S)\n17H06133 and 20H05639, JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cos-\nmic Ray Research, University of Tokyo, the National\nResearch Foundation (NRF), the Computing Infrastruc-\nture Project of the Global Science experimental Data\nhub Center (GSDC) at KISTI, the Korea Astronomy\nand Space Science Institute (KASI), the Ministry of\nScience and ICT (MSIT) in Korea, Academia Sinica\n(AS), the AS Grid Center (ASGC) and the National\nScience and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research\nProgram, the Advanced Technology Center (ATC) of\nNAOJ, and the Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individ-\nual authors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the\npurpose of open access, the authors have applied a Cre-\native Commons Attribution (CC BY) license to any\nAuthor Accepted Manuscript version arising.\nWe re-\nquest that citations to this article use \u2019A. G. Abac et\nal. (LIGO-Virgo-KAGRA Collaboration), ...\u2019 or similar\nphrasing, depending on journal convention.\nAPPENDIX\n\n39\nA. HIERARCHICAL INFERENCE DETAILS\nA.1. Likelihood Estimation\nThe analytic integrals in Equation (2) are not tractable, and so we estimate the integrals using Monte Carlo estimation\n(Tiwari 2018; Farr 2019; Essick & Farr 2022; Talbot & Golomb 2023). For example, the estimator for the likelihood\n\u02c6L(di|\u039b) is\n\u02c6L(di|\u039b) \u221d\n1\nNPE\nNPE\nX\nj=1\n\u03c0(\u03b8ij|\u039b)\np(\u03b8ij) ,\n(A1)\nwhere {\u03b8ij}NPE\nj=1 are a collection of NPE samples from the posterior on the GW parameters of the ith event di. We\ndivide out by the parameter estimation prior p(\u03b8), and so the Monte Carlo estimator in Equation (A1) converges to\nthe ith integral inside the product of Equation (2) in the limit of NPE \u2192\u221e.\nSimilarly, the estimator for the selection efficiency \u02c6\u03be is (Tiwari 2018; Farr 2019; Essick & Farr 2022)\n\u02c6\u03be(\u039b) \u221d\n1\nNdraw\nNfound\nX\nj=1\n\u03c0(\u03b8j|\u039b)\n\u03c0(\u03b8j|\u039bdraw),\n(A2)\nwhere Ndraw events with parameters \u03b8i are injected into representative noise from the detectors. The search pipelines\nthen search these synthetically generated data and recover some subset Nfound of the events with the detection statistic\nexceeding some threshold. In the limit of Ndraw \u2192\u221e, this approaches the true integral in Equation (3).\nBecause we only have a finite number of samples from each event and finite Ndraw, we must be careful to account for\nthe intrinsic variance in the estimation of the likelihood. To be sure our Monte Carlo estimators for the likelihood are\ntrustworthy, we study the impact of Monte Carlo uncertainty in every inference we perform. Specifically, we compute\nthe variance in the log-likelihood estimator, which varies across parameter space due to our resampling techniques in\nEquation (A1) and Equation (A2). Propagating the uncertainty in the log-likelihood along independent degrees of\nfreedom, the variance in the log-likelihood estimator \u03c32\nln \u02c6\nL in combining Equation (2), Equation (3), and Equation (A1)\ncan be estimated as (e.g., Essick & Farr 2022)\n\u03c32\nln \u02c6\nL(\u039b) =\nNdet\nX\ni=1\n\u03c32\n\u02c6\nLi(\u039b)\n\u02c6Li(\u039b)2 + N 2\ndet\u03c32\n\u03be(\u039b),\n(A3)\nwhere\n\u03c32\n\u02c6\nLi(\u039b) =\n1\nNPE\n\uf8ee\n\uf8f0\n1\nNPE \u22121\nNPE\nX\nj=1\n\u0012\u03c0(\u03b8ij|\u039b)\np(\u03b8ij)\n\u00132\n\u2212\u02c6Li(\u039b)2\n\uf8f9\n\uf8fb\n(A4)\nis the Monte Carlo variance in the single event Monte Carlo integrals of Equation (A1) and\n\u03c32\n\u03be(\u039b) =\n1\nNdraw\n\uf8ee\n\uf8f0\n1\nNdraw \u22121\nNfound\nX\nj=1\n\u0012\n\u03c0(\u03b8j|\u039b)\np(\u03b8j|\u039bdraw)\n\u00132\n\u2212\u02c6\u03be(\u039b)2\n\uf8f9\n\uf8fb\n(A5)\nis the variance in the detection efficiency Monte Carlo integral of Equation (A2). When the rate-marginalized likelihood\nof Equation (4) is used, \u03c32\nln \u02c6\nL takes a slightly different form\n\u03c32\nln \u02c6\nL(\u039b) =\nNdet\nX\ni=1\n\u03c32\n\u02c6\nLi(\u039b)\n\u02c6Li(\u039b)2 + N 2\ndet\n\u03c32\n\u03be(\u039b)\n\u02c6\u03be(\u039b)2 .\n(A6)\nIt has been shown that GW population inference can be biased when the variance in log-likelihood estimator exceeds\n1. Consequently, we adopt a threshold on \u03c32\nln \u02c6\nL of 1 to manage the bias of the posterior. Above this threshold the\nlikelihood estimate may not be converged, and thus we ignore posterior samples with variances above this chosen\nthreshold.\nEquation (A3) describes the pointwise variance in the estimation of the log-likelihood.\nHowever, for\naccurate sampling of the posterior we only require that the difference of log-likelihoods to be small. A small pointwise\nlog-likelihood variance is sufficient for the variance of the difference of log-likelihoods to be small but not necessary,\n\n40\nrendering our threshold conservative (Farr 2019; Essick & Farr 2022). Indeed, for some models, a large region of\nhyperparameter space is removed by this threshold, limiting the range of potential populations that can be explored; for\nan example, see Appendix D.3. Improvements to likelihood estimation are an active area of ongoing research (Wysocki\net al. 2019; Doctor et al. 2019; Delfavero et al. 2021; Golomb & Talbot 2022; Mould et al. 2024; Hussain et al. 2024;\nMancarella & Gerosa 2025).\nA.2. Sampling Techniques\nIn each model, we draw samples from the posterior to study the population distributions consistent with the data and\nthe population model. We draw samples using a variety of stochastic sampling algorithms, where the exact approach\ndepends on the model. For most strongly modeled approaches, we use the nested sampler Dynesty (Speagle 2020)\nwrapper in Bilby (Ashton et al. 2019), and the GWPopulation implementation of the hierarchical likelihood (Talbot\net al. 2025a).\nHowever, our weakly modeled approaches tend to have a large number of hyperparameters and so have a high\ndimensional posterior. Nested sampling struggles with high dimensional distributions, so we use the Hamiltonian\nMonte Carlo (HMC) adaptive No-U-Turn Sampler (NUTS) implementation in NumPyro (Phan et al. 2019; Bingham\net al. 2019). The NumPyro adaptive NUTS requires an autodifferentiable implementation of the likelihood, which\nwe write in Jax (Bradbury et al. 2018). This gradient information allows the NUTS algorithm to efficiently explore\nhigh dimensional posteriors.\nB. SUMMARY OF MODELS USED IN THE STRONGLY MODELED APPROACH\nB.1. Mass Model for the Full CBC Population\nOur strongly modeled FullPop-4.0 mass model is based on Power Law+Dip (Fishbach et al. 2020), Broken\nPower Law + Dip (Farah et al. 2022), and MultiPDB (Mali & Essick 2025). It is also similar to the Power\nLaw+Dip+Break model (Abbott et al. 2023a), but in our FullPop-4.0 model we now include additional structure.\nWe allow for the possibility of an upper mass gap, as well as separate pairing functions for NS-containing binaries\nand BBHs. Additionally, we include explicit peaks at low and mid-range BH masses to capture the \u223c9\u201310 M\u2299and\n\u223c30\u201340 M\u2299features found by the weakly modeled approaches. As discussed in Section 4, we find that the addition\nof a low-mass BH peak eliminates the need to explicitly model a gap between NSs and BHs masses.\nOur mass model is parameterized as\n\u03c0(m1, m2|\u039b) \u221d\u03c0m(m1|\u039b)\u03c0m(m2|\u039b)f(m1, m2)\u0398(m2 < m1)\n(B7)\nwhere the one-dimensional mass distribution \u03c0m(m|\u039b) is given by\n\u03c0m(m|\u039b) =\n[1 + c1N[mmin,mmax](m|\u00b51, \u03c31) + c2N[mmin,mmax](m|\u00b52, \u03c32)]n1(m | mNSmax, mBHmin, \u03b7NSmax, \u03b7BHmin, A)\n\u00d7n2(m | mUMGmin, mUMGmax, \u03b7UMGmin, \u03b7UMGmax, A2)h(m | mNSmin, \u03b7NSmin)l(m | mBHmax, \u03b7BHmax)\n\u00d7\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\nm\u03b11\nif m < mNSmax\nm\u03b1dipm\u03b11\u2212\u03b1dip\nNSmax\nif mNSmax \u2264m < mBHmin\nm\u03b12m\u03b11\u2212\u03b1dip\nNSmax m\u03b1dip\u2212\u03b12\nBHmin\nif m \u2265mBHmin.\n(B8)\nThis \u03c0m(m|\u039b) represents a universal mass function to describe the primary and secondary mass distributions. Note\nthat the marginal mass distribution is different from the universal mass distribution due to the pairing formalism.\nN[a,b](\u00b5, \u03c3) represents a truncated normal distribution over [a, b] with location and width parameters \u00b5 and \u03c3. The\nhigh-pass, low-pass and notch functions are defined as follows:\n\n41\nl(m|mBHmax, \u03b7BHmax) =\n\u0014\n1 +\n\u0012\nm\nmBHmax\n\u0013\u03b7BHmax\u0015\u22121\n,\n(B9)\nh(m|mNSmin, \u03b7NSmin) = 1 \u2212l(m|mNSmin, \u03b7NSmin),\n(B10)\nn1(m|mNSmax, mBHmin, \u03b7NSmax, \u03b7BHmin, A) = 1 \u2212Al(m|mNSmax, \u03b7NSmax)h(m|mBHmin, \u03b7BHmin),\n(B11)\nn2(m|mUMGmin, mUMGmax, \u03b7UMGmin, \u03b7UMGmax, A2) = 1 \u2212A2l(m|mUMGmin, \u03b7UMGmin)h(m|mUMGmax, \u03b7UMGmax).\n(B12)\n(B13)\nThe pairing function\nf(m1, m2|\u03b2BH, \u03b2NS) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n\u0012m2\nm1\n\u0013\u03b21\nif m2 < 5 M\u2299\n\u0012m2\nm1\n\u0013\u03b22\nif m2 > 5 M\u2299\n(B14)\ncontrols how much merging binaries favor/disfavor equal masses. We allow for alternative pairing for binaries with\nvery light secondary masses (NSBHs or BBH with the secondary component in the lower-mass gap, e.g., GW190814\nAbbott et al. 2020e). We show the priors and describe the parameters of the FullPop-4.0 model in Table 4.\nB.2. Neutron Star Mass Models\nFollowing previous work (Landry & Read 2021; Abbott et al. 2023a), the mass distribution of NS-containing events is\nmodeled as\n\u03c0(m1, m2|\u039b) \u221d\n\uf8f1\n\uf8f2\n\uf8f3\n\u03c0(m1|\u039b) \u03c0(m2|\u039b)\nif BNS,\nU(3 M\u2299, 60 M\u2299) \u03c0(m2|\u039b)\nif NSBH,\n(B15)\nTo model \u03c0(m|\u039b), we use either of the following models\n1. Power model:\n\u03c0(m|\u039b) \u221d\n\uf8f1\n\uf8f2\n\uf8f3\nm\u03b1\nif mmin \u2264m \u2264mmax,\n0\notherwise.\n(B16)\n2. Peak model:\n\u03c0(m|\u039b) \u221d\n\uf8f1\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f3\nexp\n\u0014\n\u2212(m \u2212\u00b5)2\n2\u03c32\n\u0015\nif mmin \u2264m \u2264mmax,\n0\notherwise.\n(B17)\nSee Table 5 for a description of the parameters used in the model and the corresponding prior ranges.\nB.3. Binary Black Hole Mass Models\nBroken Power Law + 2 Peaks: The fiducial BBH mass model is a mixture between a broken power law and\ntwo left-truncated Gaussian peaks, with low mass tapering applied to the full distribution. The broken power law is\ngiven by\npBP(m1|\u03b11, \u03b12, mbreak, m1,low, mhigh) = 1\nN\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n\u0012\nm1\nmbreak\n\u0013\u2212\u03b11\nm1,low \u2264m1 < mbreak\n\u0012\nm1\nmbreak\n\u0013\u2212\u03b12\nmbreak \u2264m1 < mhigh,\n(B18)\nwhere \u03b11 and \u03b12 are the power law indices, the transition between the low-mass and high-mass power law occurs at\nmbreak, and the normalization constant is\n\n42\nTable 4. Summary of FullPop-4.0 model parameters and priors.\nCategory\nParameter\nUnit\nDescription\nPrior\nPairing Function\n\u03b21\n\u2013\nSpectral index below 5 M\u2299\nU(\u22122, 3)\n\u03b22\n\u2013\nSpectral index above 5 M\u2299\nU(\u22122, 7)\nBroken Power-Law\n\u03b11\n\u2013\nPowerlaw below mNS max\nU(\u221210, 2)\n\u03b1dip\n\u2013\nPowerlaw between mNS max and mBH min\nU(\u22123, 2)\n\u03b12\n\u2013\nPowerlaw above mBH min\nU(\u22123, 2)\nmbrk\nM\u2299\nBreak point between \u03b11 and \u03b12\n5\nHighpass Filter\nmNS min\nM\u2299\nLow-mass roll-off\nU(1, 1.4)\n\u03b7min\n\u2013\nSharpness at mNS min\n50\nLowpass Filter\nmBHmax\nM\u2299\nHigh-mass roll-off\nU(60, 200)\n\u03b7max\n\u2013\nSharpness at mBHmax\nU(\u22124, 12)\nLow-Mass Notch\nmNS max\nM\u2299\nLower notch edge\nU(1.4, 5)\n\u03b7low\n1\n\u2013\nSharpness at mNS max\n50\nmBH min\nM\u2299\nUpper notch edge\nU(5, 9)\n\u03b7high\n1\n\u2013\nSharpness at mBH min\n50\nA1\n\u2013\nNotch depth\n0\nHigh-Mass Notch\nmUMGmin\nM\u2299\nLower notch edge\nU(30, 90)\n\u03b7low\n2\n\u2013\nSharpness at mUMGmin\n30\nmUMGmax\nM\u2299\nUpper notch edge\nU(60, 150)\n\u03b7high\n2\n\u2013\nSharpness at mUMGmax\n30\nA2\n\u2013\nDepth of high-mass notch\nU(0, 1)\nLow-Mass Peak\n\u00b5peak\n2\nM\u2299\nPeak location\nU(6, 12)\n\u03c3peak\n2\nM\u2299\nPeak width\nU(0, 5)\nc2\n\u2013\nPeak height\nU(0, 500)\nHigh-Mass Peak\n\u00b5peak\n1\nM\u2299\nPeak location\nU(17, 50)\n\u03c3peak\n1\nM\u2299\nPeak width\nU(4, 20)\nc1\n\u2013\nPeak height\nU(0, 1000)\nNote\u2014U(x, y) denotes a Uniform prior between x and y.\nTable 5. Summary of Power and Peak NS mass model parameters.\nParameter\nUnit\nDescription\nPrior\n\u03b1\n\u2013\nSpectral index for the power-law in the Power NS mass distribution.\nU(\u221215, 5)\nmmin\nM\u2299\nMinimum mass of the NS mass distribution.\nU(1.0, 1.5)\nmmax\nM\u2299\nMaximum mass of the NS mass distribution.\nU(1.5, 3.0)\n\u00b5\nM\u2299\nLocation of the Gaussian peak in the Peak NS mass distribution.\nU(1.0, 3.0)\n\u03c3\nM\u2299\nWidth of the Gaussian peak in the Peak NS mass distribution.\nU(0.01, 2.00)\nNote\u2014U(x, y) denotes a Uniform prior between x and y.\n\n43\nN = mbreak\n\uf8ee\n\uf8ef\uf8f0\n1 \u2212\n\u0010\nm1,low\nmbreak\n\u00111\u2212\u03b11\n1 \u2212\u03b11\n+\n\u0010\nm1,high\nmbreak\n\u00111\u2212\u03b12\n\u22121\n1 \u2212\u03b12\n\uf8f9\n\uf8fa\uf8fb.\n(B19)\nThe full mixture distribution \u03c0(m1|\u039b) is\n\u03c0(m1|\u039b) \u221d\n\"\n\u03bb0pBP(m1|\u03b11, \u03b12, mbreak, m1,low, mhigh) + \u03bb1Nlt(m1|\u00b51, \u03c31, low = m1,low)\n(B20)\n+ (1 \u2212\u03bb0 \u2212\u03bb1)Nlt(m1|\u00b52, \u03c32, low = m1,low)\n#\nS(m1|m1,low, \u03b4m,1),\nwhere Nlt is a left-truncated normal distribution. The Planck tapering function S ensures a smooth turn-on of the\ndistribution in the range (m1,low, m1,low + \u03b4m,1] and is given by\nS(m|mlow, \u03b4m) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n0\nm < mlow,\n[1 + f(m \u2212mlow, \u03b4m)]\u22121\nmlow \u2264m < mlow + \u03b4m,\n1\nmlow + \u03b4m \u2264m,\n(B21)\nwith\nf(m\u2032, \u03b4m) = exp\n \n\u03b4m\nm\u2032 +\n\u03b4m\nm\u2032 \u2212\u03b4m\n!\n.\nWe model the mass ratio as a power law with index \u03b2q and low-mass tapering applied to secondary mass m2,\nconditioned on primary mass m1,\npPL(q|m1, \u03b2q, m2,low, \u03b4m,2) \u221dq\u03b2qS(m1q|m2,low, \u03b4m,2),\n(B22)\nwith the same tapering function defined above. We numerically normalize the mass ratio distribution as a function of\nprimary mass, and interpolate the normalization to arbitrary primary masses with a log-uniform grid across primary\nmass. We define m2 \u2264m1, and therefore must enforce m2,low \u2264m1,low. We use a prior which is uniform in the two\ndimensional triangular space satisfying the inequality and between 3 and 10 M\u2299. Specifically, this defines the priors\n\u03c0(m1,low) =\n2\n(max \u2212min)2 (m1,low \u2212min),\n(B23)\n\u03c0(m2,low|m1,low) =\n1\nm1,low \u2212min,\nwhere min = 3 M\u2299, max = 10 M\u2299. The priors used in this model can be found in Table 6.\nExtended Broken Power Law + 2 Peaks: This model incorporates correlations between the primary mass\nand mass ratio, by allowing each primary mass mixture component in the Broken Power Law + 2 Peaks to be\nassociated with a separate power law mass ratio model. In terms of the functions defined above, the model is expressed\nas\n\u03c0(m1, q|\u039b) \u221d\n\"\n\u03bb0pBP(m1|\u03b11, \u03b12, mbreak, m1,low, mhigh)pPL(q|m1, \u03b2BP\nq\n, mBP\n2,low, \u03b4BP\nm,2)\n(B24)\n+ \u03bb1Nlt(m1|\u00b51, \u03c31, low = m1,low)pPL(q|m1, \u03b2peak1\nq\n, mpeak1\n2,low , \u03b4peak1\nm,2 )\n+ (1 \u2212\u03bb0 \u2212\u03bb1)Nlt(m1|\u00b52, \u03c32, low = m1,low)pPL(q|m1, \u03b2peak2\nq\n, mpeak2\n2,low , \u03b4peak2\nm,2 )\n#\nS(m1|m1,low, \u03b4m,1),\n\n44\nTable 6. Summary of Broken Power Law + 2 Peaks model parameters and priors.\nParameter\nDescription\nPrior\n\u03b11\nSpectral index of 1st primary mass power law\nU(\u22124, 12)\n\u03b12\nSpectral index of 2nd primary mass power law\nU(\u22124, 12)\nmbreak\nPower law break location\nU(20, 50)\n\u00b51\nLocation of the first peak\nU(5, 20)\n\u03c31\nWidth of the first peak\nU(0, 10)\n\u00b52\nLocation of the second peak\nU(25, 60)\n\u03c32\nWidth of the second peak\nU(0, 10)\nm1,low\nLower edge of taper function\nsee (B23)\n\u03b4m,1\nMass range of low mass tapering\nU(0, 10)\n\u03bb0, \u03bb1\nMixing fractions between power law and peaks\nDir(\u03b1 = (1, 1, 1))\nmhigh\nMaximum mass for distribution, which is pinned to mhigh = 300 M\u2299by default\n\u03b4(mhigh \u2212300)\n\u03b2q\nSpectral index of mass ratio power law\nU(\u22122, 7)\nm2,low\nLower edge of taper function in m2\nsee (B23)\n\u03b4m,2\nMass range of low mass tapering in m2\nU(0, 10)\nNote\u2014The priors for the Extended Broken Power Law + 2 Peaks model are the same except for the \u03b2q\nparameters, which assume a prior of U(\u221210, 13).\nTable 7. Summary of Power Law Redshift model parameter and prior.\nParameter\nDescription\nPrior\n\u03ba\nPower-law index on comoving merger rate evolution\nU(\u221210, 10)\nwhere the superscripts (BP, peak1, and peak2) denote the different mass ratio hyperparameters (\u03b2q, m2,low, \u03b4m,2) for\nthe broken power law, first Gaussian, and second Gaussian components. The priors on these hyperparameters are the\nsame as those used in the Broken Power Law + 2 Peaks model, listed in Table 6, except for the power law index\nparameters \u03b2q, which assume U(\u221210, 13).\nB.4. Power Law Redshift Model\nWe model redshift evolution by the comoving merger rate density (Equation 5). In particular, we use the model\n\u03c0(z|\u03ba) \u221d\n1\n1 + z\ndVc\ndz (1 + z)\u03ba\n(B25)\nwhere the prefactor converts from a rate density in comoving volume and source frame time to detector frame time\nand redshift. In other words, the comoving rate density scales as R \u221d(1 + z)\u03ba. We use a prior on \u03ba as specified in\nTable 7.\nB.5. Spin Models\nBBH spins can be parameterized in several ways which are useful for GW data analysis. Here, we use dimensionless\nspin magnitudes for the BHs \u03c71 and \u03c72, and cosine tilt angles cos \u03b81 and cos \u03b82, as well as the effective spin parameters\n\u03c7eff (Racine 2008; Ajith et al. 2011; Damour 2001) and \u03c7p (Schmidt et al. 2011, 2012, 2015). The effective inspiral spin\n\u03c7eff used because it is typically the most precisely measured BBH spin parameter, due to its lower-order appearance\n\n45\nTable 8. Summary of Gaussian Component Spins model parameters for spin magnitudes\n(Equation B26) and tilt angles (Equation B27, B28).\nParameter\nDescription\nPrior\n\u00b5\u03c7\nLocation of the \u03c7 distribution\nU(0, 1)\n\u03c3\u03c7\nWidth of the \u03c7 distribution\nU(0.005, 1)\n\u00b5t\nLocation of the Gaussian component of the cos \u03b8 distribution\nU(\u22121, 1)\n\u03c3t\nWidth of the Gaussian component of the cos \u03b8 distribution\nU(0.01, 4)\n\u03b6\nFraction in the Gaussian component of the cos \u03b8 distribution\nU(0, 1)\ntmin\nMinimum of the cos \u03b8 distribution\nU(\u22121, 1)\nNote\u2014U stands for a uniform prior.\npost-Newtonian expansions (Arun et al. 2009). Other parametrizations of spin precession exist (e.g., Fairhurst et al.\n2020; Gerosa et al. 2021; Thomas et al. 2021) but for reasons of convention, we only work with the typical parameter-\nization given in Equation 16 of Abac et al. (2025a). When modeling the effective spins, we use the analytic per-event\nparameter-estimation prior on \u03c7eff, \u03c7p, and q (Iwaya et al. 2025) in the calculation of the hierarchical likelihood\n(Equation 2). For all models presented in this work, we assume that azimuthal angles \u03d5i are distributed uniformly\nbetween 0 and 2\u03c0\u2014the same as their parameter estimation prior\u2014due to their typically uninformative individual-event\nposteriors. See Table 3 of Abac et al. (2025a) for more information about spin parameters.\nWe report results with spin vectors defined at the reference frequencies used for inference on each signal (Abac et al.\n2025b). The effective spin \u03c7eff is approximately conserved throughout the inspiral (Racine 2008; Gerosa et al. 2015),\nso its population distribution should be unaffected by the choice of reference frequency. While the effective precessing\nspin \u03c7p and the spin angles are dependent on reference frequency, they are comparatively weakly constrained by the\ndata. Additionally, their parameter estimation priors are invariant under time evolution, meaning measurements are\nrobust against different reference frequencies. At the current number of events and because of model dependence while\nmeasuring tilt distributions, we do not expect significant differences between the inferred tilt or \u03c7p distributions at\ndifferent reference frequencies (Mould & Gerosa 2022). Our approach is consistent with past LVK analyses, where\nevolved spins have not been used (Abbott et al. 2019a, 2021a, 2023a).\nB.5.1. Component Spin Models\nGaussian Component Spins: We model the spin magnitudes (\u03c7i) as a truncated Gaussian distribution between\n0 and 1, assuming they are identically and independently distributed:\n\u03c0(\u03c7i|\u00b5\u03c7, \u03c3\u03c7) = N[0,1](\u03c71|\u00b5\u03c7, \u03c3\u03c7)N[0,1](\u03c72|\u00b5\u03c7, \u03c3\u03c7) .\n(B26)\nThis choice attempts to rectify shortcomings of the non-singular Beta distribution used to model the spin magnitudes\nin previous work (Abbott et al. 2019a, 2021a, 2023a); see Equation (B29) below. The non-singular Beta distribution\nis forced to go to \u03c0(\u03c7) = 0 at \u03c7 = 0, 1, which crucially does not allow for measurements of contributions to the\npopulation at \u03c7 = 0 or \u03c7 = 1, even though non-trivial contributions may exist (Callister et al. 2022; Galaudage et al.\n2021; Hussain et al. 2024). Allowing the Beta distribution to be singular would add limited additional model flexibility,\nonly adding the option for \u03c0(\u03c7) = \u221eat the \u03c7 = 0, 1, but not anywhere in between 0 and \u221e. Thus, we opt for the\ntruncated Gaussian model, which can take on a continuous range of values at \u03c7\u2019s boundaries.\nWe model the distribution of the cosine spin tilt angle (cos \u03b8i) as a mixture between a Gaussian distribution truncated\non \u22121 to 1 and an isotropic distribution, assuming they are identically but not independently distributed:\n\u03c0(cos \u03b8i|\u00b5t, \u03c3t, \u03b6) = \u03b6 N[\u22121,1](cos \u03b81|\u00b5t, \u03c3t)N[\u22121,1](cos \u03b82|\u00b5t, \u03c3t) + 1 \u2212\u03b6\n4\n.\n(B27)\nWe here allow for the location of the Gaussian sub-population to vary, following Vitale et al. (2022), rather than fixing\nit at \u00b5t = 1 as was done in previous work (Abbott et al. 2019a, 2021a, 2023a). Priors on the Gaussian Component\nSpins hyperparameters are given in Table 8.\n\n46\nMinimum Tilt Model: For the spin tilts, we also use a model in which tmin (where t \u2261cos \u03b8), a hard lower\ntruncation of \u03c0(cos \u03b8), is informed by the data. In this case the population distribution becomes\n\u03c0(cos \u03b8i|\u00b5t, \u03c3t, \u03b6, tmin) =\n\uf8f1\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f3\n\u03b6 N[tmin,1](cos \u03b81|\u00b5t, \u03c3t)N[tmin,1](cos \u03b82|\u00b5t, \u03c3t) +\n1 \u2212\u03b6\n(1 \u2212tmin)2\ncos \u03b8i > tmin ,\n0\ncos \u03b8i \u2264tmin .\n(B28)\nEquation (B27) is the same as Equation (B28) with tmin = \u22121. The prior on tmin and other hyperparameters are given\nin Table 8.\nBeta Distribution Spin Magnitude: In Appendix D.2, we compare the Gaussian Component Spins model\nto alternatives. For the spin magnitudes, these are the Constrained and Unconstrained Beta Distributions, which both\nfollow the form:\n\u03c0(\u03c7i|\u03b1, \u03b2) \u221d\u03c7i\n\u03b1\u22121(1 \u2212\u03c7i)\u03b2\u22121 .\n(B29)\nThe Constrained Beta was the Default model for GWTC-3.0 (Abbott et al. 2023a) and requires the shape parameters\n\u03b1, \u03b2 > 1, which forces \u03c0(\u03c7i = 0, 1) = 0 (Wysocki et al. 2019; Abbott et al. 2021a). The Unconstrained Beta relaxes\nthis constraint on the the shape parameters.\nIf 0 < \u03b1, \u03b2 < 1, the Beta distribution becomes singular, meaning\n\u03c0(\u03c7i = 0, 1) = \u221e. Following Abbott et al. (2023a), we sample the mean and standard deviation of the Beta distribution,\nrather than \u03b1 and \u03b2, and use the same priors for \u00b5\u03c7 and \u03c3\u03c7 as given in Table 8 for the Gaussian Component Spins\nmodel. For the Constrained Beta case, we additionally impose the cut \u03b1, \u03b2 > 1. The relationship between {\u00b5\u03c7, \u03c3\u03c7}\nand {\u03b1, \u03b2} is given in Equation 5 of Abbott et al. (2019a).\nB.5.2. Identical versus Non-identically Distributed Spin Magnitudes and Tilts\nIn Appendix D.2, we investigate whether or not the primary and secondary spins are identically distributed, assuming\nthe Gaussian Component Spins model. Identical distribution means that the two distributions share the same set\nof hyperparameters, while non-identical means that each is described by different hyperparameters. Spin magnitudes\nare also independently distributed, meaning that \u03c0(\u03c71, \u03c72) is separable in terms of \u03c71 and \u03c72. The acronym IID means\nthey are independently and identically distributed, while IND means independently and non-identically distributed:\n\u03c7i IID =\u21d2\u03c0(\u03c71,2|\u00b5\u03c7, \u03c3\u03c7) = N[0,1](\u03c71|\u00b5\u03c7, \u03c3\u03c7) N[0,1](\u03c72|\u00b5\u03c7, \u03c3\u03c7) ,\n(B30)\n\u03c7i IND =\u21d2\u03c0(\u03c71,2|\u00b5\u03c7,1, \u03c3\u03c7,1, \u00b5\u03c7,2, \u03c3\u03c7,2) = N[0,1](\u03c71|\u00b5\u03c7,1, \u03c3\u03c7,1) N[0,1](\u03c72|\u00b5\u03c7,2, \u03c3\u03c7,2) .\n(B31)\nThe tilt angles, on the other hand, are non-independently distributed, meaning that \u03c0(cos \u03b81, cos \u03b82) is not separable.\nThe acronynm NID means they are non-independently but identically distributed, while NND means non-independently\nand non-identically distributed:\ncos \u03b8i NID =\u21d2\u03c0(cos \u03b81,2|\u03b6, \u00b5t, \u03c3t) = \u03b6 N[\u22121,1](cos \u03b81|\u00b5t, \u03c3t) N[\u22121,1](cos \u03b82|\u00b5t, \u03c3t) + 1 \u2212\u03b6\n4\n,\n(B32)\ncos \u03b8i NND =\u21d2\u03c0(cos \u03b81,2|\u03b6, \u00b5t,1, \u03c3t,1, \u00b5t,2, \u03c3t,2) = \u03b6 N[\u22121,1](cos \u03b81|\u00b5t,1, \u03c3t,1) N[\u22121,1](cos \u03b82|\u00b5t,2, \u03c3t,2) + 1 \u2212\u03b6\n4\n. (B33)\nFor the non-identically distributed cases, each component\u2019s hyperparameters have the same priors as those listed in\nTable 8 for the identically distributed case. Table 12 gives Bayes factors between different combinations of IID/IND\nspin magnitudes and NID/NND spin tilts; see associated dicsussion in Appendix D.2.\nB.5.3. Effective Spin Models\nGaussian Effective Spins: We here assume that the distribution of \u03c7eff and \u03c7p across the BBH population is a\nbivariate truncated Gaussian (Miller et al. 2020; Roulet & Zaldarriaga 2019) characterized by the location and width\nof the \u03c7eff and \u03c7p distributions, and the covariance between them:\n\u03c0(\u03c7eff, \u03c7p|\u00b5, \u03a3) \u221dN(\u03c7eff, \u03c7p|\u00b5, \u03a3) ,\n(B34)\nwhere \u00b5 = (\u00b5eff, \u00b5p) and\n\u03a3 =\n \n\u03c32\neff\n\u03c1 \u03c3eff \u03c3p\n\u03c1 \u03c3eff \u03c3p\n\u03c32\np\n!\n.\n(B35)\n\n47\nTable 9. Summary of Gaussian Effective Spins (Equation B36) and Skew-normal\nEffective Spin (Equation B37) spin parameters.\nParameter\nDescription\nPrior G\nPrior SN\n\u00b5eff\nLocation of the \u03c7eff distribution\nU(\u22121, 1)\nU(\u22121, 1)\n\u03c3eff\nWidth of the \u03c7eff distribution\nU(0.05, 1)\nLU(0.01, 4)\n\u00b5p\nLocation of the \u03c7p distribution\nU(0.05, 1)\nU(0.01, 1)\n\u03c3p\nWidth of the \u03c7p distribution\nU(0.07, 1)\nLU(0.01, 1)\n\u03c1\nDegree of correlation between \u03c7eff and \u03c7p\nU(\u22120.75, 0.75)\nN/A\n\u03f5\nSkew of the \u03c7eff distribution\nN/A\nU(\u22121, 1)\nNote\u2014The first column of priors (G) gives those used for the Gaussian Effective\nSpins results, the second column (SN) is Skew-normal Effective Spin. U stands for\na uniform prior; LU for log-uniform.\nThis expands to:\n\u03c0(\u03c7eff, \u03c7p|\u00b5, \u03a3) \u221dexp\n\u0014\n\u2212\n1\n2(1 \u2212\u03c12)\n\u0012(\u03c7eff \u2212\u00b5eff)2\n\u03c32\neff\n\u22122\u03c1(\u03c7eff \u2212\u00b5eff)(\u03c7p \u2212\u00b5p)\n\u03c3eff\u03c3p\n+ (\u03c7p \u2212\u00b5p)2\n\u03c32p\n\u0013\u0015\n.\n(B36)\nThe bivariate Gaussian is truncated over the range \u03c7eff \u2208[\u22121, 1], \u03c7p \u2208[0, 1] and is normalized numerically. Priors on\nthe hyperparameters are given in Table 9.\nSkew-normal Effective Spin: To account for observational evidence that the \u03c7eff distribution is not symmet-\nric (Callister et al. 2021b; Adamcewicz & Thrane 2022; Banagiri et al. 2025), we additionally model \u03c7eff as a skewed,\ntruncated Gaussian distribution:\n\u03c0(\u03c7eff|\u00b5eff, \u03c3eff, \u03f5) \u221d\n\uf8f1\n\uf8f2\n\uf8f3\n(1 + \u03f5) N[\u22121,1](\u03c7eff|\u00b5eff, \u03c3eff(1 + \u03f5))\n\u03c7eff \u22640 ,\n(1 \u2212\u03f5) N[\u22121,1](\u03c7eff|\u00b5eff, \u03c3eff(1 \u2212\u03f5))\n\u03c7eff \u22650 .\n(B37)\nThis model includes a parameter \u03f5 which describes the skew of the distribution, such that \u03f5 > 0 characterizes a\ndistribution with more support for \u03c7eff < \u00b5eff, while \u03f5 < 0 has more support when \u03c7eff > \u00b5eff. The Skew-normal\nEffective Spin distribution reduces to a standard, symmetric Gaussian in the case that \u03f5 = 0. We here model \u03c7p as\na truncated normal distribution and infer its location and width. Priors on the hyperparameters are given in Table 9.\nB.6. Copula Correlation Models\nCopulas allow for a variable correlation between two parameters x and y while keeping the marginal distributions\nfor the respective parameters fixed. This is done using the fact that the cumulative distribution function (CDF) of any\nrandomly distributed variable is itself a uniformly distributed variable between 0 and 1, in order to model the CDFs of\nx and y with a correlated two-dimensional uniform distribution. This correlated two-dimensional uniform distribution,\nknown as a copula density function, is dependent on a (hyper)parameter \u03bax,y, which determines the level (or strength)\nof the correlation.\nA coordinate transformation (which is determined by the chosen marginal distributions for x\nand y) can then be applied to provide a correlated two-dimensional model in the desired coordinates. Conveniently,\nthe Jacobian for this transformation turns out to be the product of the chosen marginal distributions, meaning the\ntwo-dimensional population model can be written as\n\u03c0xy(x, y|\u039b, \u03bax,y) = \u03c0c (u(x|\u039b), v(y|\u039b)|\u03bax,y) \u03c0x(x|\u039b)\u03c0y(y|\u039b).\n(B38)\nHere, \u039b are the set of hyperparameters governing the marginal distributions \u03c0x and \u03c0y, while \u03c0c denotes the chosen\ncopula density function. Finally,\nu(x|\u039b) =\nZ x\nxmin\ndx\u2032 \u03c0x(x\u2032|\u039b),\n(B39)\n\n48\nTable 10.\nSummary of parameters exclusive to the Copula, Linear, and Spline correlated models,\nalong with their priors.\nParameter\nDescription\nPrior\n\u03bax,y\nLevel of correlation between parameters x and y inferred with a copula\nU(\u221220, 20)\n\u00b5eff|q\nq = 1 intercept in linear \u00b5eff(q)\nU(\u22121, 1)\n\u03b4\u00b5eff|q\nGradient in linear \u00b5eff(q)\nU(\u22122, 2)\nln \u03c3eff|q\nq = 1 intercept in linear ln \u03c3eff(z)\nU(\u22125, 0)\n\u03b4 ln \u03c3eff|q\nGradient in linear ln \u03c3eff(q)\nU(\u221212, 4)\n\u00b5eff|z\nz = 0 intercept in linear \u00b5eff(z)\nU(\u22121, 1)\n\u03b4\u00b5eff|z\nGradient in linear \u00b5eff(z)\nU(\u22121, 1)\nln \u03c3eff|z\nz = 0 intercept in linear ln \u03c3eff(z)\nU(\u22125, 0)\n\u03b4 ln \u03c3eff|z\nGradient in linear ln \u03c3eff(z)\nU(\u22123, 5)\n\u00b5i\neff|q\nith node in spline \u00b5eff(q)\nU(\u22121, 1)\nln \u03c3i\neff|q\nith node in spline ln \u03c3eff(q)\nU(\u22125, 0)\n\u00b5i\neff|z\nith node in spline \u00b5eff(z)\nU(\u22121, 1)\nln \u03c3i\neff|z\nith node in spline ln \u03c3eff(z)\nU(\u22125, 0)\nNote\u2014 There are four variations of the Copula model in which (x, y) = (q, \u03c7eff), (m1, \u03c7eff), (z, \u03c7eff)\nand finally, (m1, z). Within the spline models, we use four nodes i.\nand\nv(y|\u039b) =\nZ y\nymin\ndy\u2032 \u03c0y(y\u2032|\u039b),\n(B40)\nwhich we refer to as u and v for the sake of brevity, are the CDFs of x and y respectively.\nThe Copula models all assume the same marginal distributions and copula density functions, but differ in which\npairs of parameters they correlate (i.e., which parameters u and v are functions of in the above notation). Namely,\nthe mass distribution is assumed to follow the default Broken Power Law + 2 Peaks model, redshift follows the\ndefault power-law redshift model, and \u03c7eff and \u03c7p are Gaussian distributed, but uncorrelated (i.e., they follow the\nGaussian Effective Spins model with \u03c1 = 0). We assume a Frank copula density function\n\u03c0c (u, v|\u03bax,y) =\n\u2212\u03bax,ye\u2212\u03bax,y(u+v)(e\u2212\u03bax,y \u22121)\n\u0000e\u2212\u03bax,y \u2212e\u2212\u03bax,yu \u2212e\u2212\u03bax,yv + e\u2212\u03bax,y(u+v)\u00012 ,\n(B41)\nwhere \u03bax,y \u2208(\u2212\u221e, \u221e).\nPositive values of \u03bax,y imply a correlation, while negative values of \u03bax,y imply an anti-\ncorrelation. The Frank copula density function is not defined at \u03bax,y = 0, but becomes uncorrelated as \u03bax,y \u21920\nfrom above and below, so we assume \u03c0c (u, v|\u03bax,y = 0) = 1 (technically, making this a piece-wise function). The Frank\ncopula density function is chosen as it allows for positive and negative correlations that are symmetric about \u03bax,y = 0,\nand gives rise to correlated distributions that we believe appear physically reasonable (Adamcewicz & Thrane 2022;\nAdamcewicz et al. 2023). The prior on \u03bax,y (which is the same for all copula model variations), is given in Table 10.\nCopulas are advantageous as they allow for a potential correlation to be quantified by a single variable \u03bax,y, that\notherwise has no influence on the distribution of the population. However, relative to the linear and spline models\nexplored below, they suffer from a lack of flexibility when it comes to covariance. There are a limited number of copula\ndensity functions available, all of which introduce a correlation in a unique, but rigid way (e.g, Adamcewicz & Thrane\n2022; Adamcewicz et al. 2023). Furthermore, known two-dimensional copulas depend on a single parameter \u03bax,y, and\ncannot infer, for example, a separable broadening and correlation with the mean of a distribution simultaneously. As\na result, using copulas to probe for more complex structure in two-dimensions (assuming fixed marginal distributions),\nrequires model comparison between a number of different copula density functions (e.g., Adamcewicz et al. 2023).\n\n49\nB.7. Linear Correlation Models\nThe (q, \u03c7eff) and (z, \u03c7eff) Linear models begin by assuming that \u03c7eff is Gaussian distributed for any given value of\nmass ratio q and redshift z respectively. As the two models are otherwise identical, for the remainder of this Section, we\nsubstitute x for q and z. This parameter-dependent Gaussian distribution for \u03c7eff, \u03c0(\u03c7eff|x), is truncated at unphysical\nvalues of |\u03c7eff| \u22651. From here, the mean and (natural log) width of the \u03c7eff distribution are allowed to evolve with\nthe chosen variable x linearly:\n\u00b5eff(x) = \u00b5eff|x + \u03b4\u00b5eff|xx,\n(B42)\nand\nln \u03c3eff(x) = ln \u03c3eff|x + \u03b4 ln \u03c3eff|x0x.\n(B43)\nHere, \u00b5eff|x, \u03b4\u00b5eff|x, ln \u03c3eff|x, and \u03b4 ln \u03c3eff|x0 are all hyperparameters fit to the data, where \u03b4\u00b5eff|x and \u03b4 ln \u03c3eff|x0 quantify\nthe strength of the correlation between x and the mean and width of the \u03c7eff distribution respectively. The priors for\nthese parameters are given in Table 10. Meanwhile, masses follow the default Broken Power Law + 2 Peaks model\nand redshift is distributed according to the default power-law redshift model.\nThese models (in the style of those presented in Safarzadeh et al. 2020; Callister et al. 2021b; Biscoveanu et al. 2022a),\ntherefore allow us to infer separable trends in the mean and width of the \u03c7eff distribution with another parameter.\nThe inferred correlations should be interpreted with care as, unlike the copula models defined in Section B.6, the\ncorrelation hyperparameters here will also affect the shape of the marginal \u03c7eff distribution. As such, it can be difficult\nto be certain whether an inferred correlation is entirely due to a trend between \u03c7eff and another parameter, or is in\npart due to a better fit to the marginal \u03c7eff distribution (Adamcewicz & Thrane 2022).\nB.8. Spline Correlation Models\nThe Spline models (Heinzel et al. 2024) are similar to the Linear models defined in Section B.7. The key difference\nis that the Spline models more flexibly model the parameter-dependent mean \u00b5eff(x) and (natural log) width ln \u03c3eff(x)\nof the \u03c7eff distribution as cubic splines dependent on x. Each spline has four nodes \u00b5i\neff and ln \u03c3i\neff|x that are placed\nuniformly in log10 x, and are inferred from the data. The priors for these nodes are given in Table 10.\nC. SUMMARY OF MODELS USED IN THE WEAKLY MODELED APPROACH\nWe describe weakly modeled approaches\u2014B-Spline, BGP, AR, FM\u2014used in this work. Results in the main text\nmake use of B-Spline and BGP models. BGP was chosen since it was the only model capable of modeling the full\nmass spectrum, while B-Spline was chosen for most BBH analyses for its ease of description and flexibility, as it\nsimultaneously models all parameters with B-Splines. See Appendix D.4 for comparison of these weakly modeled\napproaches.\nC.1. B-Spline models\nB-Spline: The B-Spline model (Edelman et al. 2023) simultaneously fits all population parameters with Basis-\nsplines (B-splines). A kth order B-spline of variable x consists of a linear combination of n basis functions {Bk,n(x)},\neach of which are degree k \u22121 piecewise polynomials joined at a set of m locations called knots {xm}. The number of\nbasis functions n defined across any range of x values is determined solely by the order of the spline k and the total\nnumber of knots m as n = k + m. This forms a basis that spans the space of possible interpolants between the knots\n{xm}. Given a vector of coefficients \u03b1, any function f can then be approximated as\n\u02dcf(x) =\nn\nX\ni=1\nBk,i(x)\u03b1i.\n(C44)\nIn the case of this work, f is a probability distribution p(\u03b8|\u03b1\u03b8) for a population-level parameter \u03b8, where the B-spline\ncoefficients \u03b1\u03b8 are the hyperparameters of the distribution that are inferred during parameter estimation.\nGiven an adequate number of knots, a B-spline is highly flexible and therefore capable of identifying sharp features\nthat could be present in the data. This does, however, naturally make the B-Spline model prone to overfitting. To\ncombat this, we include a smoothing prior \u03c0BS that penalizes large differences between neighboring coefficients. The\nprior is defined as\np(\u03b1|\u03c4) = exp\n\u0012\n\u22121\n2\u03c4\u03b1TDT\nr Dr\u03b1\n\u0013\n,\n(C45)\n\n50\nwhere Dr is the r-order difference matrix with shape (n \u2212r) \u00d7 n and \u03c4 is a scalar that controls the level of smoothing.\nIdeally, \u03c4 is also inferred during parameter estimation. We found that \u03c4 consistently railed against prior boundaries,\nwhich meant that the limits imposed on the likelihood uncertainty was the main driver of smoothness. We therefore\nfix \u03c4 to a reasonable value (roughly between 5\u221210) for each population distribution. With a sufficient number of bases,\ntypically n \u223c30\u221240, this penalty prior will prevent the B-spline from overfitting the data while the large number of\nbases will provide enough flexibility to fit sharp features.\nThe mass and spin distributions are modeled as B-splines, and the redshift distribution is modeled as a power law\nmodulated by a B-spline (Edelman et al. 2023), with all components inferred simultaneously.\nOne of the weakly\nmodeled approaches used in previous analyses (Abbott et al. 2023a) was the Powerlaw + Spline model. This\nmodel assumed that the primary BBH mass followed a power-law distribution with moderate deviations controlled by\na cubic spline. The B-Spline model does not assume an underlying shape for the primary mass distribution, instead\nallowing for full model flexibility.\nThe B-Spline model infers the separable components of the mass distributions, p(m1) and p(q), wherein the primary\nmass is defined over the range 3\u2212300 M\u2299and the mass ratio is defined over the range 0.03\u22121. Unlike the Broken\nPower Law + 2 Peaks model, a minimum secondary mass is not enforced during parameter estimation. To provide\na more direct comparison to the strongly modeled approach, the B-Spline mass distributions shown in Section 6.1 are\nnot the separable components p(m1) or p(q) but instead the marginal distributions conditioned on m2 > 3 M\u2299, that\nis, p(q|m2 > 3 M\u2299) =\nR\np(q)p(m1)\u0398(m1q \u22123)dm1. We include the separable distributions along with the conditional\nmarginal distributions in the mass ratio plot in Figure 20 to illustrate how this assumption affects the shape of the\nmass ratio distribution.\nIsolated Peak: This model is defined by two subpopulations (Godfrey et al. 2023). One assumes a primary mass\ndistribution described by a log-Gaussian peak while the other infers the mass distribution with a B-spline. Mass ratio,\nspin magnitude, and spin tilt distributions are inferred separately for each subpopulation, also using B-splines. The\nredshift distribution is the same for each subpopulation and is inferred with a power law modulated by a B-spline.\nC.2. Binned Gaussian Process (BGP) Model\nIn previous population analyses (Abbott et al. 2023a), we used the BGP model to study the joint distribution\nof primary and secondary masses. Here, we extend it to model the joint distributions of mass, spin, and redshift.\nThe BGP approach models the rate of BBH, BNS and NSBH mergers as a piecewise constant function over a set of\nfixed bins across the one-, two-, or three-dimensional joint space. The comoving merger rate density in each bin is a\nhyperparameter of the model. In addition, the BGP model couples the logarithm of the rate density in each bin with\na Gaussian process covariance, assuming an exponential quadratic kernel (also known as a radial basis function (RBF)\nkernel). The exponential quadratic kernel has a hyper-hyperparameter length scale \u03bb for each parameter in the joint\nspace.\nThe covariance between two bins is proportional to the exponential of the negative squared distance between the bin\ncenters, in units of the length scales along each parameter. In addition, there is one more hyper-hyperparameter \u03c3,\nwhich acts as an overall multiplicative scaling of the covariance matrix (Ray et al. 2023a). The BGP approach directly\ninfers the rate density in each bin, as well as the hyper-hyperparameters of the covariance kernel. The prior on the\nparameter \u03c3 is a half-normal with width 1, and the length scale priors were tuned to the mean and variation in the\nset of distances between the bin centers.\nWe used 22 bins spaced uniformly in log-mass for the mass BGP models, and 15 bins spaced uniformly between\n\u03c7eff \u2208[\u22120.7, 0.7] for the effective spin BGP models.\nThe BGP approach has the advantage of being able to model nontrivial correlations in the population of compact\nbinaries. However, it assumes an arbitrary binning scheme, which reduces the resolution of the constraints and leads to\nunphysical discontinuities at the boundary between bins. Furthermore, measurements of the rate density in some bins\nmay be driven by the a priori assumption of a Gaussian covariance, and not the data. This can also cause smoothing\nnear sharp features e.g., near the m1 = m2 boundary.\nC.3. Autoregressive Process (AR) Model\nThe AR model (Callister & Farr 2024) is a highly flexible model for one dimensional marginal merger rate densities.\nThe Monte Carlo integrals for estimating the likelihood in Equation (2) involve a large set of parameter estimation\nsamples [Equation (A1)] and found injections for the selection efficiency [Equation (A2)]. The merger rate density at\n\n51\nTable 11. Bayes factor comparison of selected models from the\nmass model comparison study.\nModel\nAbbreviation\nlog10 B\nBroken Power Law + 2 Peaks \u22c6\nBP2P\n0\nBroken Power Law + 1 Peak\nBP1P\n\u22120.06\nBroken Power Law + 3 Peaks\nBP3P\n\u22120.34\nPower Law + Peak\nPP\n\u22122.43\neach sample is its own hyperparameter, which is directly inferred from the data. Without any further assumptions,\nsuch a model is severely underconstrained and will converge on the maximum likelihood functional distribution (Payne\n& Thrane 2023). In order to a priori favor smoother distributions, this finite list of samples is ordered along the\ndimension of interest like, for example, their primary mass.\nThe marginal merger rate density is then assumed\nto be an autoregressive Gaussian random walk in log-space. There are two hyper-hyperparameters, \u03c3AR and \u03c4AR,\nwhich control the scale of variability and the autocorrelation length along the Gaussian random walk respectively.\nThese hyper-hyperparameters have half-normal and log-normal priors respectively, tuned to the scale of the data: see\nAppendix B in Callister & Farr (2024) for details. These hyper-hyperparameters are jointly inferred along with the\nlogarithmic merger rate density at each sample.\nThe AR model is particularly well-suited to distributions with sharp features and nontrivial evolution, complementing\nthe BGP approach. However, the AR model used here cannot model correlations in the population. Furthermore,\nas in the BGP approach, the inferred merger rate may extrapolate based off nearby constraints in regions of little\ninformation. When evaluating uncertainties in the AR model, one should consider the impact of the AR smoothing\nprior. In particular, lower bounds on the merger rate in some regions may not be an accurate lower bound on the true\ndistribution.\nLike the B-Spline model, the AR model does not enforce a minimum secondary mass through a mass-dependent\nmass ratio.\nC.4. Flexible Mixtures (FM) Model\nThe FM model (Tiwari 2021) is a flexible mixture model framework for modeling the BBH population. FM models\nthe population as a Gaussian mixture model in chirp mass and aligned spins, and a power law in mass ratio and\nredshift (Tiwari 2022). Furthermore, FM is able to model correlations between parameters in the population, and\nadditionally has a variable model dimension, sampling the trans-dimensional posterior using a reversible-jump MCMC\nmethod. For the analyses presented here, FM uses 11 mixture components.\nD. RESULT VALIDATION STUDIES\nIn the following sub-appendices, we describe various methods used to select and validate the data, models, and\napproaches presented in the main text.\nIn Appendix D.1 and Appendix D.2 we discuss the process for selecting\nthe fiducial mass and spin models, respectively, under the strongly modeled approach and present results from other\nmodels which were under consideration. Appendix D.3 describes how the specific convergence cut biases the inferred\neffective spin distribution. In Appendix D.4, we compare various types of methods for the weakly modeled approach,\nwhich were presented in Appendix C. Appendix D.5 gives compact object merger rates when sub-threshold triggers are\nconsidered, i.e., using a lower FAR threshold. Finally, Appendix D.6 provides supplementary results for population-\nlevel correlations between masses, spins, and redshifts.\nD.1. Model Comparison Study: Mass\nThe fiducial mass model is a strongly modeled approach that is intended to provide a minimal but accurate description\nof the data with a parametrization that is more readily interpretable than the weakly modeled approaches. Table 11\nshows the Bayes factors between the models that performed the best in our study and our fiducial model Broken\nPower Law + 2 Peaks. We also compare to our previous fiducial model from Abbott et al. (2023a), the Power\n\n52\n20\n40\n60\n80\n100\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\nBS\nBP2P\nPLP\n20\n40\n60\n80\n100\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\nBS\nBP2P\nBP1P\n20\n40\n60\n80\n100\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\nBS\nBP2P\nBP3P\nFigure 15. Inferred mass distributions of various strongly modeled approaches compared to the fiducial mass model Broken\nPower Law + 2 Peaks (gray shaded) and the B-Spline model (black dashed). The fiducial model from GWTC-3.0, Power\nLaw + Peak, is shown in orange, a broken power law with a single peak in blue, and a broken power law with three peaks in\npink.\n\n53\n20\n30\n40\n50\n60\n70\nm1 [M\u2299]\n10\u22122\n10\u22121\n100\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\n30\n40\n\u00b52\n0\n5\n10\n\u03c32\nMode 1\nMode 2\nBP1P\nFigure 16. Differential merger rate as a function of primary mass (evaluated at z = 0.2) of the two different modes recovered\nby the Broken Power Law + 2 Peaks model. The orange shaded region shows the 90% credible interval for the dominant\nmode (71% of posterior), reflecting a distinct peak at 35 M\u2299, and the purple shaded region shows the 90% credible interval for\nthe subdominant mode (29% of posterior), reflecting a broken power law morphology without a distinct 35 M\u2299peak. The black\ndashed lines show the 90% credible bounds of the Broken Power Law + 1 Peak model for comparison. The inset figure\nshows the joint posterior of the peak mean \u00b52 and width \u03c32 for each mode. The vertical grey shaded region indicates the 90%\ncredible interval of the sum \u00b52 + \u03c32, which is consistent between both modes.\nLaw + Peak model. In Figure 15, we see that Power Law + Peak infers the peak component at 35M\u2299, as in\nAbbott et al. (2023a), but a broken power law plus 1 peak (BP1P) model infers the peak component at 10M\u2299and\nthe power law break at 35M\u2299. In Table 11, we see that all models that include a broken power law are strongly\nfavored over the Power Law + Peak model. Among models with a broken power law, the Bayes factors do not\nshow strong support for one model over another. While Bayes factors are an important model comparison statistic to\nconsider, they can be influenced by prior assumptions. In the case of the models in Table 11 where Bayes factors are\nnot decisive, we ultimately chose as our fiducial model the model that was a minimal extension of the Power Law\n+ Peak model and probed features shared among all of the weakly modeled approaches shown in Figure 20. The\nBroken Power Law + 2 Peaks model best fit these criteria, though with some nuances that we discuss below.\nIn GWTC-3.0, the Power Law + Peak model identified an overdensity in the merger rate at m1 = 35+1.7\n\u22122.9 M\u2299\nrelative to a global power law. Evidence for this feature first appeared in Abbott et al. (2019a) and was strengthened\nin Abbott et al. (2021a) and Abbott et al. (2023a). As mentioned in Section 6.1, this feature at 35M\u2299may be an\noverdensity relative to an underlying mass continuum or could mark the onset of a decline in the merger rate. In\naddition to the Bayes factor comparison shown in Table 11, this ambiguity is also present in the Broken Power\nLaw + 2 Peaks posterior, which includes two modes that correspond to two different morphologies, shown in Figure\n16. The dominant mode is correlated with a narrower (\u03c32 = 3.1+2.7\n\u22122.0 M\u2299) peak at \u00b52 = 33+2.8\n\u22122.1 M\u2299and accounts for\n71% of the posterior volume, while the subdominant mode is correlated with a wider (\u03c32 = 7.3+2.3\n\u22122.5 M\u2299) peak at\n\u00b52 = 29+2.9\n\u22123.6 M\u2299and accounts for 29% of the posterior volume. This latter mode has a morphology nearly identical\nto the inferred BP1P distribution (see Figure 16). The inflection point of the Gaussian, \u00b52 + \u03c32 = 37+3.7\n\u22123.0 M\u2299, is\nconsistent between both modes, which indicates that the right half of the Gaussian must fall below the power law to\nmatch the declining rate in this region (the gray vertical shaded region in Figure 16).\nThe power law indices, \u03b11 and \u03b12 are not correlated with the two modes present in the BP2P posterior, though the\nmeasured slope of the mass distribution between 18\u221219 M\u2299is not equivalent to \u03b11 in the subdominant mode. In this\nmode, the slope (calculated by finite difference) is 0.72+1.4\n\u22121.7, which includes more support for negative values compared\nto the inferred power law index, \u03b11 = 1.7+1.4\n\u22121.9. We infer the power law break location at mbreak = 36+12\n\u221213 M\u2299. The\n\n54\nTable 12.\nComparison of different parametric models for spin magnitudes \u03c7i and\ntilt angles cos \u03b8i.\n\u03c7i model\ncos \u03b8i model\nlog10 B\nTruncated Gaussian \u22c6\nIID\nIsotropic + Truncated Gaussian\nNID\n0.0\nConstrained Beta\nIID\nIsotropic + Aligned Gaussian\nNID\n\u22120.66\nConstrained Beta\nIID\nIsotropic + Truncated Gaussian\nNID\n\u22120.64\nUnconstrained Beta\nIID\nIsotropic + Truncated Gaussian\nNID\n\u22120.98\nTruncated Gaussian\nIID\nIsotropic + Aligned Gaussian\nNID\n\u22120.08\nTruncated Gaussian\nIND\nIsotropic + Truncated Gaussian\nNID\n\u22121.09\nTruncated Gaussian\nIID\nIsotropic + Truncated Gaussian\nNND\n\u22120.17\nTruncated Gaussian\nIND\nIsotropic + Truncated Gaussian\nNND\n\u22120.91\nNote\u2014The first row is the Default model for GWTC-4.0 (Gaussian Component\nSpins), while the second is the Default that was used for GWTC-3.0 and earlier (Ab-\nbott et al. 2019a, 2021a, 2023a; Talbot & Thrane 2017). The third through final\nare other models explored. All log Bayes factors (log10 B) are with respect to the\nfirst row.\nBP1P model, which does not include a second Gaussian component, measures the break location much more precisely\nat mbreak = 34.1+3.8\n\u22123.3 M\u2299. The uncertainty in the BP2P power law break is due to the presence of the second Gaussian\ncomponent, which likely obscures the break most of the time. Because the peak is narrower in the dominant BP2P\nmode, one might expect the break location to be better constrained in this mode; however, this is not the case. The\nbreak location does not appear to be correlated with either mode.\nD.2. Model Comparison Study: Spin Magnitudes and Tilt Angles\nWe consider two additional spin magnitude models beyond the Gaussian Component Spins model from Sec-\ntion 6.3.1: the Constrained Beta and Unconstrained Beta models, both defined by Equation (B29). We also consider\none additional spin tilt model, the Isotropic + Aligned Gaussian, which fixes \u00b5t = 1 in the Gaussian Component\nSpins model and served as the Default in GWTC-3.0 (Talbot & Thrane 2017; Abbott et al. 2023a). The first five\nrows of Table 12 give the log Bayes factors between these models. Within the Gaussian Component Spins model, we\nalso test whether the primary and secondary spins are identically and independently distributed (see Appendix B.5.2),\nwith log Bayes factors given in the bottom three rows of Table 12. The Gaussian Component Spins model with\nIID spin magnitudes and NID spin tilts performs the best, and is adopted as the default component spin model in the\nmain text.\nFigure 17 shows posteriors for the magnitude and tilt hyperparameters assuming that \u03c7i and cos \u03b8i are both identi-\ncally distributed (gray) versus both non-identically distributed (blue and red). The primary and secondary spins have\nconsistent hyperparameter distributions. Assuming identical distribution makes the hyperparameters more-precisely\nconstrained\u2014yielding tighter 90% bands on the resultant population distributions\u2014but does not affect the overall\nshape of the distributions. The only difference of note is that \u03c72 has less support for a small \u00b5\u03c7 than \u03c71, potentially\nhinting at more highly spinning secondary BHs on a population level.\nD.3. Dependence of the Effective Spin Distribution on the Likelihood Variance Cut\nWe next investigate the effect of the likelihood variance threshold (see Appendix A.1) on our strongly modeled\neffective spin results. To ensure that posteriors generated using Monte Carlo estimation are trustworthy, i.e., the\nlikelihood estimate is converged, we enforce that all hyperparameter samples yield a log-likelihood variance \u03c32\nln \u02c6\nL < 1\nfor all analyses presented in the main text (Talbot & Golomb 2023). In GWTC-3.0, however, a different quantity\nwas used to assess the Monte Carlo uncertainty: the effective number of independent samples, Neff (Farr 2019). It\nwas there imposed that Neff be greater than 4Nevents for the sensitivity injections used in Equation (3) and greater\n\n55\nBH 1\nBH 2\nidentical\nmu chi\n0.25\n0.50\n0.75\n1.00\n\u03c3\u03c7\nmu chi\n\u22121\n0\n1\n\u00b5t\nsigma chi\n0.0\n0.2\n0.4\n\u00b5\u03c7\n0\n2\n4\n\u03c3t\n0.0\n0.5\n\u03c3\u03c7\n\u22121\n0\n1\n\u00b5t\n0\n2\n4\n\u03c3t\nFigure 17. Distribution of Gaussian Component Spins hyperparameters for the primary BH (blue) and secondary BH (red)\nwhen neither magnitudes nor tilts are assumed identical (last row of Table 12), compared to when they are both assumed\nidentical (gray, first row of Table 12). The contours of the two dimensional distributions mark the 50th and 90th percentiles.\nthan 10 for every event in the catalog of CBCs. This Neff cut is generally less stringent than the approach taken for\nGWTC-4.0. The \u03c7p distribution is sensitive to which method is used to cut out samples.\nFor the most direct comparison to GWTC-3.0, we here use the Gaussian Effective Spins model. Figure 18 shows\nthe posteriors for the Gaussian Effective Spins parameters where the \u03c32\nln \u02c6\nL (purple) versus Neff (green) cuts are\ndone on the GWTC-4.0 results. The LVK GWTC-3.0 results (with the Neff cut) are shown in comparison (black).\nFigure 19 shows the resultant marginal and joint \u03c7eff\u2013\u03c7p population distributions. There are three main differences\nbetween the results with the two cuts on GWTC-4.0 data:\n1. The \u03c32\nln \u02c6\nL cut yields a \u00b5p posterior which is constrained away from zero, while the the Neff cut does not.\n2. The Neff cut allows for wider \u03c7p distributions (larger \u03c3p) than the \u03c32\nln \u02c6\nL cut.\n3. Under the Neff cut, \u03c7eff and \u03c7p are preferentially positively correlated, while under the \u03c32\nln \u02c6\nL cut we remain\nagnostic, with preference for small-to-zero correlation.\nThus, the claims that the \u03c7p distribution does not peak at zero, and that the data prefer \u03c7eff and \u03c7p being uncorrelated\nat the population level, are not necessarily astrophysical in origin. Rather, they are driven by regions of the parameter-\nspace that our events and sensitivity injections allow us reliably probe with Monte Carlo likelihood estimators.\n\n56\nThe particular sensitivity of the \u03c7p distribution to these cuts can be at-least partly attributed to the use of a uniform\nand isotropic spin prior in GWTC-4.0 parameter estimation, which induces a \u03c7p prior that goes to 0 at \u03c7p = 0, 1.\nThus, Equation (2) is prone to yield a small Neff and/or large \u03c32\nln \u02c6\nL when \u03c7p is near-minimal or near-maximal. Using\nalternative spin priors in parameter estimation could aid in getting more effective samples at small \u03c7p, improving\nour ability to probe the presence or absence of negligibly precessing BHs at the population level. The Monte Carlo\nuncertainty from working with a finite number of samples to estimate the likelihood will only grow more problematic\nas the number of observed CBCs increases (Talbot & Golomb 2023); development of mitigation techniques is an area\nof active research (e.g., Gerosa et al. 2020; Rinaldi & Del Pozzo 2021; Talbot & Thrane 2022; Callister et al. 2022;\nTalbot & Golomb 2023; Leyde et al. 2024; Hussain et al. 2024; Callister et al. 2024; Lorenzo-Medina & Dent 2025;\nMancarella & Gerosa 2025).\nD.4. Comparison of Weakly Modeled Approach Results\nMass distributions: We supplement the strongly modeled approach with various weakly modeled approaches. Figure\n20 (top panel) shows the inferred primary mass distribution using the B-Spline, AR, Flexible Mixtures, and BGP\nmodels compared to the fiducial Broken Power Law + 2 Peaks model. All models agree within their 90% credible\nregions, though the Flexible Mixtures model is the only model that does not exhibit a prominent peak at \u223c10M\u2299. The\nFlexible Mixtures model does not directly infer the primary mass, but instead it models the chirp mass as a Gaussian\nmixture model and the mass ratio with a power law. The primary mass distribution shown in Figure 20 is then derived\nfrom these two distributions. The discrepancy between this model and the other weakly modeled approaches could be\ndue to model misspecification, i.e., assuming the mass ratio distribution follows a power law for all primary masses.\nThe fact that the discrepancy exists primarily in the \u223c10M\u2299region supports the Isolated Peak result in Section\n6.2, which suggests the \u223c10M\u2299peak disfavors equal mass mergers (i.e., is inconsistent with a power law in mass ratio)\ncompared to higher mass BBHs. The mass ratio distributions inferred by the B-Spline, AR, and Flexible Mixtures is\nshown Figure 20 (bottom panel). The 90% credible regions are consistent between each model. The B-Spline model\ninfers a peak away from q = 1, which is not present in the AR or Flexible Mixtures results. This may be due to the\nB-Spline model\u2019s greater flexibility compared to the AR and Flexible Mixtures models, as it infers all parameters\nsimultaneously with B-Splines. The AR model assumes an auto-regressive process only in primary mass and mass\nratio, while other parameters are inferred with the fiducial models listed in Table 1. As noted in Appendix C.1, the\nfigure includes the marginal distributions conditioned on m2 > 3M\u2299from the B-Spline and AR models in addition\nto the fully separable components (dashed lines). The two distributions are essentially identical above q \u223c0.4, below\nwhich the marginal distribution falls off sharply. This implies that the behavior of the strongly modeled approach\nbelow q \u223c0.4 is primarily due to the prior assumption of a minimum mass cutoff, and not due to information inferred\nabout the shape of the distribution in that regime.\nEffective spin distributions: In addition to the Skew-normal Effective Spin model and various correlation\nmodels presented for \u03c7eff in the main text (Figures 9 and 12), we use the weakly modeled approach for a consistency\ncheck and find the distributions shown in the top panel of Figure 21. We plot the \u03c7eff distribution directly inferred with\na binned Gaussian process (BGP; blue) as well as that reconstructed from the spin magnitude and tilt B-Spline model\nresults (green), and compare them to the Skew-normal Effective Spin (red-orange), Gaussian Effective Spins\n(purple), and (q, \u03c7eff) Spline (maroon) results from the main text. The two approaches paint the same qualitative\npicture: the \u03c7eff distribution peaks at small values. However, there is variation between the weakly modeled approach\nand strongly modeled approach; the weakly modeled distributions are wider than the strongly modeled distributions.\nIn Figure 21, we additionally plot posteriors distributions on statistics derived from each \u03c7eff distribution (c.f., Table 3),\nwith results summarized as follows:\n\u2022 First percentile of the \u03c7eff distribution (\u03c7eff,1%): The three strongly modeled distributions find consistent first-\npercentiles, around \u223c0.2, while the weakly modeled find that the \u03c7eff distribution extends to lower values. In\nthe case of the BGP, the first-percentile distribution rails against the minimum allowed value of \u22120.7.\n\u2022 Fraction of BBHs with negative \u03c7eff: All models yield consistent posteriors with one another and find that the\nfraction of BBHs with negative \u03c7eff is greater than zero and less than \u223c0.8. The BGP posterior on this fraction\nis the widest, and the B-Spline posterior peaks at a higher values than the near-identical strongly modeled\nposteriors.\n\n57\nGWTC-3, Ne\ufb00cut\nGWTC-4, Ne\ufb00cut\nGWTC-4, \u03c32\nln \u02c6\nL cut\n0.05\n0.10\n0.15\n0.20\n\u03c3e\ufb00\n0.0\n0.2\n0.4\n\u00b5p\n0.00\n0.25\n0.50\n0.75\n1.00\n\u03c3p\n0.0\n0.1\n\u00b5e\ufb00\n\u22121.0\n\u22120.5\n0.0\n0.5\n1.0\n\u03c1\n0.1\n0.2\n\u03c3e\ufb00\n0.2\n0.4\n\u00b5p\n0.2\n0.4\n\u03c3p\n\u22120.5\n0.0\n0.5\n\u03c1\nFigure 18.\nPosterior for the Gaussian Effective Spins model hyperparameters, as defined in Table 9, for GWTC-4.0\nunder two methods of cutting out samples that may lead to an unconverged likelihood. Posteriors excluding samples with a\nsubstantially large log-likelhood variance (\u03c32\nln \u02c6\nL cut) are shown in purple; those excluding samples with a substantially small\nnumber of effective samples (Neff cut) are in green. In black are the GWTC-3.0 results with the Neff cut for comparison. The\n\u03c7eff hyperparameters are not affected by the cuts, while the \u03c7p and joint-distribution hyperparameters are. The contours of the\ntwo dimensional distributions mark the 50th and 90th percentiles.\n\u2022 HM fraction: The HM fraction is a heuristic for the upper limit of the fraction of BBHs coming from hierarchical\nmergers; it is calculated as 0.16 times the fraction of \u03c7eff < \u22120.3 (Fishbach et al. 2022; Baibhav et al. 2020). We\nconsistently constrain the HM fraction to be small, with the three parametric models finding it \u2272O(10\u22121). The\ntwo non-parametric models, on the other hand, find it to be \u2273O(10\u22122).\n\n58\nGWTC-4, Ne\ufb00cut\nGWTC-4, \u03c32\nln \u02c6\nL cut\n\u22120.4\n\u22120.2\n0.0\n0.2\n0.4\n\u03c7e\ufb00\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03c7p\nFigure 19.\nMarginal and joint \u03c7eff and \u03c7p distributions under the Gaussian Effective Spins model using two methods of\ncutting out hyperparameter samples that may lead to an unconverged likelihood (see Figure 18). The marginal distributions\nshow the median (solid line) and 90% credible interval on the probability density for each population distribution (shaded). The\njoint distribution is the PPD with contours marking the 50th and 90th quantiles.\n\u2022 Skew of the \u03c7eff distribution about its peak: Each model finds fairly different values of the skew, which is here\ndefined as the difference between the fraction of \u03c7eff > \u03c70 and \u03c7eff < \u03c70, where \u03c70 is the value of \u03c7eff at which\nthe distribution peaks (Banagiri et al. 2025, Equation 5). By design, the Gaussian Effective Spins model\nwill always have a skew of \u223c0: truncated normal distributions are approximately symmetric about their peak\nif the truncation occurs substantially far from the distribution\u2019s bulk, which is here the case. All other models\nfind a preference for positive skew, meaning that the distribution has more support for \u03c7eff above its peak than\nbelow. This is the most pronounced for the Skew-normal Effective Spin, which is entirely inconsistent with\na skew of 0.\nD.5. Merger Rates Including Subthreshold Triggers\nSearch pipelines compute signal-to-noise ratios (SNRs) of detector data to identify portions of data with above-\nthreshold SNR, i.e., \u201ctriggers\u201d, which may contain GW events (Abac et al. 2025b). Based on pipeline-specific ranking\nstatistics, triggers are assigned significances quantified by FARs.\nIn the main text, merger rates were calculated\nfrom population analyses that only used triggers surpassing a fixed-significance FAR threshold, which was motivated\nto introduce minimal contamination from noise events. By design, the list of triggers included in those analyses is\nthreshold-dependent. Here, we explore the merger rates by including subthreshold triggers (Farr et al. 2015; Kapadia\net al. 2020), which ensures that the inferred rates are free of biases due to arbitrary significance thresholds and\nmitigates loss of information from excluding subthreshold GW candidates. Specifically, we consider the full set of\n\n59\n101\n102\nm1 [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\n101\ndR/dm1\n\u0002\nGpc\u22123 yr\u22121 M\u22121\n\u2299\n\u0003\nBGP\nAR\nB-Spline\nFlexible Mixtures\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nq\n10\u22121\n100\n101\n102\ndR/dq\n\u0002\nGpc\u22123 yr\u22121\u0003\nAR\nB-Spline\nFlexible Mixtures\nFigure 20. (Top) Primary mass distributions using the weakly modeled approaches outlined in Appendix C. The Broken\nPower Law + 2 Peaks result is shown in black for comparison. All distributions show rates evaluated at z = 0.2, except for\nBGP, which shows the rate evaluated on the z = 0.1\u22120.25 bin. Note that Flexible Mixtures does not infer primary mass directly,\nbut instead derives it from the chirp mass Gaussian mixture model and the mass ratio as a power law distribution. The lack\nof substructure in the Flexible Mixtures mass distribution relative to the other models is likely due to model misspecification\nfrom assuming a power law mass ratio model. (Bottom) Mass ratio distributions using the weakly modeled approaches outlined\nin Appendix C. The Broken Power Law + 2 Peaks result is shown in black for comparison. Flexible Mixtures models the\nchirp mass as a Gaussian mixture model and the mass ratio as a power law. For the B-Spline and AR models, the separable\ndistribution p(q) is shown by dashed lines and the conditional marginal distribution p(q|m2 > 3M\u2299) =\nR\np(q)p(m1)\u0398(m1q \u2212\n3)dm1 is shown by the shaded regions, highlighting that the low mass ratio truncation seen in the strongly modeled approach\nis largely a prior effect.\navailable triggers from a matched-filtering search, GstLAL (Messick et al. 2017; Sachdev et al. 2019; Hanna et al.\n2020; Cannon et al. 2020; Ewing et al. 2024; Tsukada et al. 2023; Sakon et al. 2024; Ray et al. 2023b; Joshi et al.\n2025a,b).\nThe method used by GstLAL to self-consistently classify triggers and compute pastro (Abbott et al. 2019b, 2024,\n2023b; Kapadia et al. 2020; Abac et al. 2025b,c; Ray et al. 2023b) values provides the rate densities described here for\n\n60\n\u22120.6\n\u22120.4\n\u22120.2\n0.0\n0.2\n0.4\n0.6\n\u03c7e\ufb00\n10\u22122\n10\u22121\n100\n101\np(\u03c7e\ufb00)\nBinned Gaussian Process\nB-Spline\nSkewnormal E\ufb00ective Spin\nGaussian E\ufb00ective Spins\n(q, \u03c7e\ufb00) Spline Correlation\n\u22120.6\n\u22120.4\n\u22120.2\n0.0\n\u03c7e\ufb00,1%\n0\n10\n20\nProbability density\n0.0\n0.2\n0.4\n0.6\nFraction \u03c7e\ufb00< 0\n0\n5\n10\n\u22125\n\u22124\n\u22123\n\u22122\n\u22121\n0\nlog10(HM Fraction)\n0\n1\n2\n3\nProbability density\n\u22120.2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nSkew about peak\n0.0\n2.5\n5.0\n7.5\nFigure 21.\nFirst row: Marginal \u03c7eff distributions with BGP (blue) and B-Spline (green) models, as compared to the Skew-\nnormal Effective Spin (red-orange), Gaussian Effective Spins (purple), and (q, \u03c7eff) Spline (maroon) models. The PPD\n(average) is shown with a dark line, and the 90% confidence intervals are shaded. Second and third rows: Posteriors on the\nfirst percentile of the \u03c7eff distribution (upper left), the fraction of \u03c7eff < 0 (upper right), HM fraction (lower left), and the\nskew (lower right). See Section 6.3.2 for a discussion of these quantities. Colors correspond to the top panel; purple dashed is\nGWTC-3.0 with the Gaussian Effective Spins model for comparison.\nBNSs, NSBHs, and BBHs (Abac et al. 2025b; Kapadia et al. 2020). The approach is a simplified version of the methods\ndescribed in Appendix C 3 of Abbott et al. (2023a), as well as the discovery of GW200105 and GW200115 (Abbott\net al. 2021c) and GW230529 (Abac et al. 2024). The simplification involves fixing the mass distribution to the Salpeter\nmodel (Salpeter 1955) as opposed to marginalizing over population uncertainties inferred by the above-threshold event\nanalyses explored in the main text. We do not expect the marginalization over population uncertainties to have a\nsignificant impact on the inferred merger rates, given the uncertainty ranges. When we apply the simpler model to\nGWTC-3.0 (Abbott et al. 2023a), the estimated rates are comparable to those derived when marginalizing over the\ninferred population. For effective inspiral spins of each trigger, we use a uniform distribution. Consistent with how\nsearches categorize triggers and compute \u27e8V T\u27e9(Abac et al. 2025b), we set the boundary between NSs and BHs to be\n\n61\n3 M\u2299. For triggers categorized as BNS or NSBH, we set the bounds of the spins corresponding to a NS to \u00b10.4. These\nbounds are consistent with what the analyses in the main text adopt (see Section 3.2 and Section 5).\nUsing the fixed population distribution and the Poisson mixture model of Kapadia et al. (2020), we infer the merger\nrate densities of the different source categories (BNS, NSBH, and BBH) from the full list of available GstLAL triggers\nwith FAR < 1 hour\u22121. This is done while self-consistently accounting for the possibility that some of these triggers are\nlikely noise artifacts. We construct the posterior of astrophysical counts of BNS, NSBH, and BBH events by utilizing\nmass-based binning template weights (Ray et al. 2023b). We estimate the time\u2013volume sensitivity (Tiwari 2018; Abac\net al. 2025b) \u27e8V T\u27e9for each event category \u03b1 (\u03b1 = BNS, NSBH, BBH), using injections (Essick et al. 2025), and their\ncontributions to the counts posterior (Kapadia et al. 2020). Finally, we compute the rates posterior from marginalized\ncounts posterior and the estimated \u27e8V T\u27e9(Abbott et al. 2019b, 2021a, 2023a; Abac et al. 2025c):\np (R\u03b1) = p (\u039b1\u03b1|x) \u27e8V T\u27e9O1-O4a,\u03b1.\n(D46)\nHere, p (\u039b1\u03b1|x) is the marginalized counts posterior where \u039b1\u03b1 is the astrophysical count for event category \u03b1 and\n\u039b1\u03b1 = R\u03b1\u27e8V T\u27e9O1-O4a,\u03b1. Here, O1-O4a indicates that data from O1 throughout O4a are used. The vector x represents\nthe set of triggers using in this analysis, where each xi consists of the ranking statistics information, SNR, and an\nidentifier for the template associated with the trigger.\nA Jeffreys prior, \u221dN \u22121/2, is imposed on the astrophysical counts for BBHs to construct their posterior from\nthe mixed Poisson likelihood and compute the merger rate. The merger rate of BBHs is computed to be 13.1\u201317.3\nGpc\u22123 yr\u22121. This is consistent with the BBH merger rate provided in the analyses presented in the main text, and\nthe rate has been further narrowed compared to the results of Abbott et al. (2023a) while still being consistent within\nuncertainties. A uniform prior is used for NSBHs and BNSs, as the number of detected events containing a NS is\nsmall. We compute the NSBH merger rates to be 22.2\u2013143 Gpc\u22123 yr\u22121, which is consistent with the NSBH merger\nrate presented in main text. Similarly to the rate for BBHs, the rate of NSBHs is consistent with the rate obtained\nfrom the analyses of GWTC-3.0 but has been further narrowed. The BNS merger rate is calculated to be 30.9\u2013361\nGpc\u22123 yr\u22121, which is consistent with the BNS merger rate presented in the main text and has been narrowed down\ncompared to the rate obtained from the analyses of GWTC-3.0.\nD.6. Supplementary Results: BBH Correlations\nHere, we supplement the correlated BBH population results presented in Section 6.5 with additional results and\nfigures. In the top panel of Figure 22, we plot the posterior distribution for the level of correlation \u03ba\u03c7eff,z inferred\nin the Copula model for (z, \u03c7eff). Note the peak at positive values, and long tail into negative values. The middle\npanels show the inferred mass distributions, using a mass-redshift correlated BGP analysis, binned by redshift. We\nsee that both the primary and secondary mass distribution appear to be broadly consistent across redshifts up to\nz = 1. Finally, we investigate mass and spin correlations with the data-driven FM analyses. In the bottom panels of\nFigure 22, we plot the inferred distribution of orbital aligned spin \u03c7z as a function of both chirp mass and mass ratio,\nobtained with the FM analysis. We see that the results have a large degree of uncertainty, and are broadly consistent\nwith findings explored here and in Section 6.5.\n\n62\n\u221215\n\u221210\n\u22125\n0\n5\n10\n\u03ba\u03c7e\ufb00,z\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n20\n40\n60\n80\n100\nm1 [M\u2299]\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\n102\np(m1|z)\n20\n40\n60\n80\n100\nm2 [M\u2299]\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\n102\np(m2|z)\nz \u2208(0.01, 0.1)\nz \u2208(0.1, 0.25)\nz \u2208(0.25, 0.5)\nz \u2208(0.5, 0.75)\nz \u2208(0.75, 1.0)\n0.2\n0.4\n0.6\n0.8\nq\n\u22120.6\n\u22120.4\n\u22120.2\n0.0\n0.2\n0.4\np(\u03c7z|q)\n20\n40\n60\n80\nM [M\u2299]\n0.0\n0.2\n0.4\n0.6\np(|\u03c7z||M)\nFigure 22.\nTop: Posterior distributions for the level of correlation between redshift and effective inspiral spin \u03ba\u03c7eff ,z inferred\nusing the Copula model. The vertical black dashed line in each plot indicates a value of \u03ba\u03c7eff ,z, at which no correlation is\nimplied. Middle: Inferred distributions of primary mass (left), and secondary mass (right) in the redshift and spin correlated\nBGP analysis. The solid lines bound the 90% credible intervals for each redshift bin. We can see that all redshift bins from\nz = 0.01 to z = 1 are consistent within 90% credibility. Bottom: Correlated mass and spin PPDs from the FM model. Solid lines\ngive the medians, while the shaded regions encompass 90% of the PPD volume. The left panel gives the inferred distribution\nof aligned spin \u03c7z given mass ratio. We do not see any evidence for or against a correlation. The right panel gives the inferred\ndistribution of the aligned spin magnitude |\u03c7z| as a function of chirp mass. We see that the uncertainty is very large, with a\nnotable drop in the \u223c20\u221230 M\u2299region. 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Soc., 441, 3703,\ndoi: 10.1093/mnras/stu824\n", "Draft version May 23, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nA search using GEO600 for gravitational waves coincident with fast radio bursts from SGR 1935+2154\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\nABSTRACT\nThe magnetar SGR 1935+2154 is the only known Galactic source of fast radio bursts (FRBs). FRBs\nfrom SGR 1935+2154 were first detected by the Canadian Hydrogen Intensity Mapping Experiment\n(CHIME)/FRB and the Survey for Transient Astronomical Radio Emission 2 in 2020 April, after the\nconclusion of the LIGO, Virgo, and KAGRA Collaborations\u2019 O3 observing run. Here, we analyze four\nperiods of gravitational wave (GW) data from the GEO600 detector coincident with four periods of\nFRB activity detected by CHIME/FRB, as well as X-ray glitches and X-ray bursts detected by NICER\nand NuSTAR close to the time of one of the FRBs. We do not detect any significant GW emission\nfrom any of the events. Instead, using a short-duration GW search (for bursts \u22641 s) we derive 50%\n(90%) upper limits of 1048 (1049) erg for GWs at 300 Hz and 1049 (1050) erg at 2 kHz, and constrain\nthe GW-to-radio energy ratio to \u22641014 \u22121016. We also derive upper limits from a long-duration search\nfor bursts with durations between 1 and 10 s. These represent the strictest upper limits on concurrent\nGW emission from FRBs.\nKeywords: gravitational waves\u2014fast radio bursts\u2014multi-messenger astronomy\u2014magnetars\u2014neutron\nstars\n1.\nINTRODUCTION\nFast radio bursts (FRBs) are a class of extremely ener-\ngetic radio transients that are theorized to be associated\nwith neutron stars (Thornton et al. 2013; Petroff et al.\n2019; Platts et al. 2019; Bailes 2022; Zhang 2023). To\ndate, thousands of FRBs have been detected. The ma-\njority of these have been discovered using the Canadian\nHydrogen Intensity Mapping Experiment (CHIME) tele-\nscope (Amiri et al. 2022) by the CHIME/FRB Collabora-\ntion (CHIME/FRB) (CHIME/FRB Collaboration et al.\n2018)1. Though the origins of FRBs remain unknown\n(Lorimer et al. 2024), their dispersion measure (DM)\nas observed by radio telescopes localizes them to extra-\ngalactic (and even cosmological) distances (Lorimer et al.\n2007; Chatterjee et al. 2017; Cordes & Chatterjee 2019).\nThe notable exceptions to this extragalactic consen-\nsus are the FRBs associated with FRB 20200428A.\nCorresponding author: LIGO Scientific Collaboration, Virgo Col-\nlaboration, and KAGRA Collaboration Spokespersons\nlsc-spokesperson@ligo.org,\nvirgo-spokesperson@ego-gw.it,\nkscboard-chair@icrr.u-tokyo.ac.jp\n1 https://www.chime-frb.ca/voevents\nFirst detected in 2020 April by CHIME/FRB and the\nSurvey for Transient Astronomical Radio Emission 2\n(STARE2) (Bochenek et al. 2020a), FRB 20200428A\nwas quickly found to be associated with the Galactic\nmagnetar SGR 1935+2154, which was undergoing an\nunusual period of flaring X-ray activity at that time\n(CHIME/FRB Collaboration et al. 2020; Bochenek et al.\n2020b; Barthelmy et al. 2020; Palmer & BAT Team\n2020). Simultaneous X-ray observations from Konus-\nWind (Frederiks et al. 2022), INTEGRAL (Mereghetti\net al. 2020), AGILE (Tavani et al. 2020), and Insight-\nHXMT (Li et al. 2022) led to the first coincident obser-\nvation of both radio emission and X-rays from an FRB\nsource. FRBs from SGR 1935+2154 were also observed\nduring three other epochs by CHIME/FRB and others,\non 2020 October 08, 2022 October 14, and 2022 Decem-\nber 01.2 Additionally, X-ray glitches and bursts from\n2 We note that the classification of these radio bursts as FRBs\nremains unclear: the SGR 1935+2154 radio bursts are a few orders\nof magnitude less luminous than typical extragalactic FRBs, but\nare still brighter than most giant radio pulses (Giri et al. 2023).\nBochenek et al. (2020a) name them as FRBs while Giri et al.\n(2023) call them FRB-like. Here, we describe them as FRBs.\narXiv:2410.09151v2 [astro-ph.HE] 21 May 2025\n\n2\nSGR 1935+2154 were observed by NICER and NuSTAR\nduring the nine hours surrounding the 2022 October 14\nFRB (Hu et al. 2024). The connection between these\nX-ray bursts and FRBs, even from the same magnetar, is\nnot well understood\u2014indeed, radio emission with no co-\nincident X-rays has been detected from SGR 1935+2154\n(Zhu et al. 2023) and vice versa (Younes et al. 2017).\nThe compact object nature of these powerful transients\nsuggests that gravitational waves (GWs) could also be\nemitted by the same mechanisms that produce FRBs.\nThe detection of GWs from an FRB source (or lack\nthereof) could help to elucidate the mechanisms behind\nFRBs (Zhang 2023), and potentially expand the realm\nof detected GWs beyond those with compact binary\ncoalescence (CBC) origins.\nPrevious works by the LIGO, Virgo, and KAGRA\nCollaborations (LVK) have searched for GW emission\ncoincident with FRBs (Abbott et al. 2016, 2023), as well\nas for GWs from magnetar bursts (Abbott et al. 2019a,b;\nMacquet et al. 2021; Abbott et al. 2024) and pulsar\nglitches (Abadie et al. 2011; Keitel et al. 2019; Abbott\net al. 2022) using the Advanced LIGO and Advanced\nVirgo GW observatories (Aasi et al. 2015; Acernese et al.\n2014). While no detections were found in these studies,\nthe searches have established upper limits on GW energy\nthat may have been emitted in association with these\nevents. In particular, Abbott et al. (2023) performed\na search for GW emission coincident with FRBs from\nCHIME/FRB during the O3a LIGO\u2013Virgo observing\nrun, with searches targeted at GWs from CBCs as well\nas generic GW transients, setting an upper limit of 1051\u2212\n1057 erg of GW energy within 70-3560 Hz. In addition,\nAbbott et al. (2024) placed upper limits on GW energy\n(\u223c1043 erg) coincident with 11 X-ray and soft gamma-ray\nmagnetar bursts from SGR 1935+2154.\nSGR 1935+2154, as the first (and at the time of writ-\ning, only) FRB source to be confidently associated with a\nspecific neutron-star progenitor, presents a unique oppor-\ntunity to search for GWs when the source is localized to\na particular compact object. Additionally, at \u223c6.6 kpc\n(Zhou et al. 2020), it is more than two orders of magni-\ntude nearer to Earth than the next closest FRB, which\nhas been localized to the nearby galaxy M81, 3.6 Mpc\naway (Bhardwaj et al. 2021; Kirsten et al. 2022).\nThe four periods of FRB activity from SGR 1935+2154\nfell between the O3 and O4 observing runs of the LVK,\nwhen the LIGO and Virgo detectors were offline3. For-\ntunately, GEO600 (Grote et al. 2004; Lueck et al. 2010;\nAffeldt et al. 2014; Dooley et al. 2016), a GW detector\n3 https://observing.docs.ligo.org/plan/\nin Hannover, Germany that is operated by members\nof the LIGO Scientific Collaboration, was observing in\nAstrowatch mode (Grote & the LIGO Scientific Collab-\noration 2010) and collecting GW data during all four\nperiods. The CHIME/FRB events for three of the four\nperiods occurred when GEO600 was in observing mode,\nwhile the fourth FRB occurred within minutes of when\nGEO600 was observing (see Sec. 3).\nIn this paper, we analyze GEO600 data to search for\nGW emission coincident with the four FRBs observed\nby CHIME/FRB from SGR 1935+2154. We conduct\ntwo searches for unmodeled GW transients: one targeted\nat short-duration bursts with O(second) durations, and\nanother aimed at long-duration bursts lasting from 1 to\n10 seconds. Due to SGR 1935+2154\u2019s proximity, the re-\nsults constitute the most sensitive searches for GWs from\nFRB sources to date, despite GEO600\u2019s lower sensitivity\ncompared to LIGO and Virgo (see Fig. 1). We also search\nfor GWs coincident with the two X-ray glitches and the\nX-ray burst peak observed by NICER and NuSTAR in\nthe hours around the FRB on 2022 October 14 (Hu et al.\n2024). This paper is organized as follows. In Sec. 2, we\ndescribe the electromagnetic (EM) observations of FRBs\nfrom SGR 1935+2154. Section 3 details our short- and\nlong-duration searches for GWs, with results presented\nin Sec. 4. We discuss the implications of these findings\nand conclude in Sec. 5.\n100\n1000\nFrequency [Hz]\n10\u221224\n10\u221223\n10\u221222\n10\u221221\n10\u221220\n10\u221219\nAmplitude spectral density [1/\n\u221a\nHz]\nH1 O3\nL1 O3\nVirgo O3\nGEO600\nFigure 1.\nAmplitude spectral density of GEO600 on 2020\nApril 28 compared to those of LIGO Hanford, LIGO Liv-\ningston, and Virgo during O3 (Abbott et al. 2020). While\nat low frequencies GEO600\u2019s sensitivity is substantially di-\nminished compared to that of the larger detectors, the gap\nnarrows at frequencies around 2 kHz, near the expected\nneutron-star f-mode frequency.\n\n3\n2.\nFAST RADIO BURSTS FROM SGR 1935+2154\nThe magnetar SGR 1935+2154 was discovered by Swift\nin 2014 (Stamatikos et al. 2014; Lien et al. 2014). Since\nthen, it has been highly active, with periods of intense\nemission in the X-ray and radio (Israel et al. 2016; Younes\net al. 2017).\nOn 2020 April 27, Swift observed multiple X-ray bursts\nfrom SGR 1935+2154, suggesting that the magnetar had\nentered a period of high activity (Barthelmy et al. 2020).\nLess than 24 hours later, CHIME/FRB and STARE2\ndetected an FRB from the location of SGR 1935+2154\n(CHIME/FRB Collaboration et al. 2020; Bochenek et al.\n2020b). Konus-Wind (Frederiks et al. 2022), INTEGRAL\n(Mereghetti et al. 2020), AGILE (Tavani et al. 2020),\nand Insight-HXMT (Li et al. 2022) observed hard X-\nrays arriving at the same time, serving as the first ever\nobservation of simultaneous radio and X-ray emission\nfrom an FRB source. Follow-up radio observations dur-\ning the same active period by the Five-hundred-meter\nAperture Spherical radio Telescope (FAST) (Zhang et al.\n2020) and radio telescopes from the European VLBI Net-\nwork (EVN) (Kirsten et al. 2021) identified additional\nradio bursts from SGR 1935+2154, though at lower en-\nergies. At higher energies, no gamma-ray emission has\nbeen observed from this source (Abdalla et al. 2021;\nPrincipe et al. 2023).\nSince 2020 April, SGR 1935+2154 has had multi-\nple periods of high activity leading to the emission of\nFRBs.\nOn 2020 October 08, CHIME/FRB observed\nthree FRBs from SGR 1935+2154 arriving within a few\nseconds (Good & CHIME/FRB Collaboration 2020; Pleu-\nnis & CHIME/FRB Collaboration 2020; Giri et al. 2023).\nCHIME/FRB and the Green Bank Telescope (GBT)\nobserved FRBs again two years later on 2022 October\n14, with a CHIME/FRB event surrounded by five GBT\nFRBs within 1.5 seconds (Dong & CHIME/FRB Col-\nlaboration 2022; Maan et al. 2022; Giri et al. 2023).\nDuring the days around the FRBs on 2022 October 14,\nSGR 1935+2154 was undergoing a period of intense X-\nray burst activity. This burst storm began on October\n10 (Mereghetti et al. 2022; Palmer 2022) and was moni-\ntored by various telescopes, such as NICER, NuSTAR,\nand XMM-Newton (see, e.g., Hu et al. 2024; Ibrahim\net al. 2024), which detected hundreds of milliseconds- to\nseconds-long bursts of high-energy photons. The X-ray\nburst rate peaked during a flare 2.5 hr (\u00b11 min) before\nthe FRB and then steadily decreased over the next hours\n(Hu et al. 2024). In addition, the high-cadence moni-\ntoring observations allowed accurate measurements of\nthe spin rate of SGR 1935+2154 (nominally 0.308 Hz;\nIsrael et al. 2016). The evolution of the spin rate showed\nthat SGR 1935+2154 underwent a spin-up glitch about\n4.4 hr (\u00b130 min) before the FRB and another spin-up\nglitch about 4.4 hr (\u00b130 min) after the FRB, while the\nmagnetar\u2019s spin-down rate between these two glitches\nwas about one hundred times higher than its normal\nrate (Hu et al. 2024). X-ray bursts were also detected by\nGECAM and HEBS (Wang et al. 2022) and Konus-Wind\n(Frederiks et al. 2022) arriving within the expected FRB\ndispersion time. In addition to the NICER and NuS-\nTAR observations mentioned above (Enoto et al. 2022),\nInsight-HXMT (Li et al. 2022) also observed X-rays from\nSGR 1935+2154 during this active period, though at the\ntime of the FRB all three were occulted by the Earth.\nFinally, a fourth FRB was detected by CHIME/FRB on\n2022 December 01 (Pearlman & CHIME/FRB Collab-\noration 2022; Giri et al. 2023), accompanied by a faint\nhard X-ray signal detected by Fermi-GBM (Younes et al.\n2022).\nMost estimates and methods place the distance to\nSGR 1935+2154 between 1.5 and 15 kpc (Park et al.\n2013; Pavlovic et al. 2014; Surnis et al. 2016; Kothes\net al. 2018; Ranasinghe et al. 2018; Zhong et al. 2020;\nZhou et al. 2020; Bailes et al. 2021).\nWe adopt the\ndetermination by Zhou et al. (2020) of 6.6 \u00b1 0.7 kpc,\nfalling near the mean of the measurements.\nThese SGR 1935+2154 FRBs are not quite like the\nrest of the population of FRBs, as mentioned in Sec. 1.\nAs shown in Nimmo et al. (2022), they exhibit char-\nacteristics very similar to the extragalactic FRBs, but\nare a few orders of magnitude less luminous. Whether\nthe SGR 1935+2154 FRBs are in the tail of the same\npopulation or truly occupy a different part of the phase\nspace remains an open question. For example, while\nthe 2020 April FRB from SGR 1935+2154 was several\norders of magnitude less energetic than most FRBs, it\nwas three orders of magnitude brighter than the next\nbrightest previously observed radio flare from a magnetar\n(CHIME/FRB Collaboration et al. 2020). Figure 2 shows\nthe radio energy as a function of distance for the FRBs\nfrom SGR 1935+2154, alongside a sample of 749 FRBs\nfrom CHIME/FRB4 (CHIME/FRB Collaboration et al.\n2021), the FRBCAT (Petroff et al. 2016), and the 76 m\nLovell telescope (Rajwade et al. 2020) as collected and\ndescribed in Principe et al. (2023). This could suggest\nthat the emission mechanism which produces FRBs from\nSGR 1935+2154 may be different from that which re-\nsults in FRBs from cosmological distances. Despite this\nreduced brightness compared to the typical FRB popu-\nlation, SGR 1935+2154\u2019s proximity as the only known\nGalactic FRB source means that it presents the most\n4 https://www.chime-frb.ca/repeaters\n\n4\n10\u22122\n10\u22121\n100\n101\n102\n103\n104\nDL [Mpc]\n1030\n1032\n1034\n1036\n1038\n1040\n1042\nEradio [erg]\nscaled FRB20200428D radio energy\nOther FRB events\nEvents from SGR 1935+2154\nFigure 2.\nRadio energy versus luminosity distance for\nthe SGR 1935+2154 FRBs investigated in this work (dark\norange, Giri et al. (2023)) and for 749 other public FRBs\npublished by CHIME/FRB and others (Petroff et al. 2016;\nRajwade et al. 2020; CHIME/FRB Collaboration et al. 2021)\n(blue). The FRB sample and the calculation of distances and\nradio energies is described in Principe et al. (2023) (with the\nexception of the FRBs studied in Abbott et al. (2023), for\nwhich we use the lower bound 90% distances from that analy-\nsis). Note that the radio energies from CHIME/FRB (derived\nfrom fluxes and fluences) should be interpreted as lower lim-\nits (CHIME/FRB Collaboration et al. 2021; Andersen et al.\n2023). We show the radio energy required to produce a flare\nas bright as that the brighest FRB from SGR 1935+2154,\nFRB20200428D, as a function of distance.\npromising opportunity to date for multiwavelength and\nmultimessenger studies of FRB emitters.\n2.1.\nModels for coincident GW-FRB emission\nMagnetars have long been theorized to be progeni-\ntors of FRBs (Platts et al. 2019).\nThe detection of\nFRBs from SGR 1935+2154, a well-studied magnetar,\nhas now confirmed this association for at least some\nFRBs, though the exact emission mechanism remains\nunclear (Lyubarsky 2021; Zhang 2023).\nMost models which predict GW emission from FRB\nprogenitors assume a CBC association, such as during\nor after the final stages of the CBC inspiral (Wang et al.\n2016; Yamasaki et al. 2018), long before the CBC merger\nthrough interactions of magnetospheres (Zhang 2020),\nor other interactions of compact binaries with their envi-\nronments (see Platts et al. (2019) for a review of FRB\ntheory). Prior studies such as Abbott et al. (2023) have\nsearched for GWs from these sources using targeted\nmatched-filter analyses, aimed at CBC sources. Since\nSGR 1935+2154 is not in a compact binary (Chrimes\net al. 2022) and has exhibited multiple periods of FRB\nactivity, we do not expect CBC-like GW emission from\nthis source. Instead, as a magnetar, we can focus on only\na few possible emission mechanisms for GWs coincident\nwith FRBs. In particular, because GWs are induced\nby time-varying quadrupole moments, we review models\nwhich predict EM magnetar activity associated with such\nmoments.\nSince at least some FRBs originate from magnetars,\ntheories have drawn connections between them and mag-\nnetar giant flares (Tendulkar et al. 2016; Margalit et al.\n2020; Cehula et al. 2024), which are are thought to be\npowered by magnetic activity near the surface of a neu-\ntron star (Thompson & Duncan 1996; Gaensler et al.\n2005). These giant flares are rare but so energetic that\nGW emission may be detectable due to hydromagnetic\ncoupling of the magnetic dipole to the mass quadrupole\n(Ioka 2001; Corsi & Owen 2011). Quasi-periodic oscil-\nlations in the X-ray tails of giant flares may also create\nGWs through torsional or Alfv\u00b4en modes which alter the\nstar\u2019s quadrupole moment (Levin & van Hoven 2011;\nGlampedakis & Jones 2014; Quitzow-James et al. 2017).\nWhile no giant flares from SGR 1935+2154 were detected\nduring its periods of FRB activity, the coincident X-ray\nactivity suggests a potential link in the provenance of\nthe high-energy EM emission.\nCrustal f-modes are a possible source of transient GWs\nfrom isolated neutron stars (Glampedakis & Gualtieri\n2018; Ho et al. 2020). These typically fall at around 2 kHz\n(Andersson & Kokkotas 1996), near the frequencies where\nGEO600 is most sensitive (see Fig. 1).\nMoreover, neutron-star glitches, such as those from\nSGR 1935+2154 in 2022 October investigated in this\nwork, may emit GWs potentially observable by current\nGW detectors (Prix et al. 2011; Warszawski & Melatos\n2012; Melatos et al. 2015). Previous limits were derived\nfor the Vela pulsar (located at 290 pc; Dodson et al.\n(2003)) glitch in 2006, providing limits on the emitted\nGW energy of the order of 1045 erg (Abadie et al. 2011).\n3. SEARCH FOR GRAVITATIONAL WAVES\nUsing data from GEO600, we search for generic GW\ntransients from SGR 1935+2154 around the times of\nfour FRBs detected by CHIME/FRB.\nGEO600 is a\ndual-recycled Michelson interferometer with folded arms\nand takes astrophysical observations in the 40 Hz - 6\nkHz frequency band when operating in Astrowatch mode\n(Grote & the LIGO Scientific Collaboration 2010). Over\nthe past two decades, it has pioneered several key tech-\nnologies for GW detectors (Affeldt et al. 2014; Lough\net al. 2021). GEO600 has lower sensitivity compared\nto the Advanced LIGO and Advanced Virgo detectors\n(\u223c10\u221222/\n\u221a\nHz at 1 kHz, see Fig. 1), but has strengths\nin uptime. It continued taking observations during the\n\n5\ninitial period of the COVID-19 pandemic and subse-\nquent LIGO and Virgo upgrades throughout 2020-2022,\nduring which CHIME/FRB observed these FRBs from\nSGR 1935+2154.\nGiven the unknown nature of the emission mechanism\nof the FRBs, we search for generic transient gravitational-\nwave signals present in the GEO600 data using two un-\nmodeled burst searches: PySTAMP (Macquet et al. 2021),\ntargeted at long-duration bursts with lengths from 1 to\n10 s, and X-Pipeline (Sutton et al. 2010; Was et al.\n2012), for short-duration bursts lasting less than 1 s.\nPrevious searches for GWs coincident with FRBs, such\nas the ones presented in Abbott et al. (2023), also con-\nsidered a possible CBC origin for the GW emission; the\nnon-compact binary nature of SGR 1935+2154 precludes\nthe use of CBC matched-filter searches.\nGiven that\nSGR 1935+2154 is a magnetar, we follow the previous\nGW magnetar study presented in Abbott et al. (2024)\nand employ PySTAMP to perform a long-duration search,\nwhich has not previously been used for GW FRB anal-\nyses. Additionally, prior searches have typically been\nrestricted to coincidences with FRBs where data from\nat least two GW detectors is available. For these FRBs\nfrom SGR 1935+2154, only GEO600 was observing, so\nwe employ a single-detector search. This limits our ability\nto veto candidates based on coherence between detec-\ntors and the amount of background that can be esti-\nmated, reducing the search sensitivity, but given the\nextraordinary nature of these FRBs, we determined that\na single-detector search in GEO600 data was warranted.\nFor the 2020 April 28, 2020 October 08, and 2022\nOctober 14 FRBs, we perform a search within an \u201con-\nsource\u201d time window starting at 1200 s before the infinite-\nfrequency arrival time (i.e., the time accounting for the\nfrequency-dependent delay introduced by the dispersion\nmeasure) of the FRB, t0, and ending 120 s after. This\nasymmetric window is motivated by the expectation that\nany potential GWs are likely generated from the inte-\nrior of the magnetar, preceding FRB emission from the\nmagnetosphere or beyond. On 2020 October 08, three\nbursts were detected by CHIME/FRB within 3 s; we\nuse the first time, corresponding to the FRB with the\nhighest fluence on that day, as our t0. The FRB on 2022\nDecember 01 occurred during a time when GEO600 was\nnot taking data, having exited observing mode approx-\nimately six minutes before the FRB, at 22:01:09 UTC.\nGEO600 returned to observing mode 23 minutes later, at\n22:23:59 UTC. To be consistent with the on-source win-\ndow for the other FRBs, we analyze the 800 s period of\ndata beginning 1200 s before the FRB and ending shortly\nbefore GEO600 exited observing mode. Due to the large\nuncertainties in FRB\u2013GW models (as described above\nin Sec. 2.1), we use a wide extended on-source window of\n[\u22121200, 120] s. This allows us to probe a broad parame-\nter space while keeping the detector behavior relatively\nstationary. We also employ a compact [\u22124, 4] s search\nwindow in the short-duration search to probe the time\nimmediately surrounding the FRB with higher sensitiv-\nity. In addition, we search for emission around the time\nof three X-ray events detected by NuSTAR and NICER\non 2022 October 14. These events consisted of a spin-up\nglitch, a peak in the X-ray burst emission, and another\nspin-up glitch. Since the uncertainty in their times is\ngreater than a minute, we only perform an extended-\nwindow search, targeting a symmetric [\u22121000, 1000] s\nwindow, subject to data availability. Table 1 summarizes\nthe times and windows for which we perform searches.\nWe restrict our search to frequencies from 300 Hz to\n4096 Hz, with the lower cutoff set by the low frequency\nsensitivity of GEO600 and the upper cutoff aiming to\ncapture neutron-star crustal f-modes, which are predicted\nto fall at approximately 2 kHz (Andersson & Kokkotas\n1996).\n3.1.\nSimulated waveforms to quantify sensitivity\nWe measure the sensitivity of our search by inserting\nsimulated waveforms (\u201cinjections\u201d) into the off-source\ndata and quantifying the pipeline\u2019s ability to recover\nthem. For the short-duration X-Pipeline search, these\ninjections are largely the same as those used in Abbott\net al. (2023). The waveforms include Sine-Gaussians and\ndamped sinusoids and are summarized in Table 2. We\nbriefly describe each waveform family below:\n\u2022 Sine-Gaussians: The majority of the simulated\nwaveforms we use are Sine-Gaussians, which can\nmodel starquakes and certain neutron-star f-modes.\nThey are described in Eq. 1 of Abbott et al. (2017).\nMost of these injections are performed with incli-\nnations chosen randomly, but we also employ some\noptimally inclined (circular polarization only, emit-\nted face-on to the observer) waveforms near the\nexpected f-modes at \u223c2000 Hz to better constrain\nour sensitivity to these models. In all the injected\nwaveforms, we use a quality factor Q = 9 (the\napproximate number of cycles in the waveform)\nfollowing Abbott et al. (2021, 2023), with central\nfrequencies f0 spanning from 300 Hz to 3560 Hz,\nas shown in Table 2.\n\u2022 Damped sinusoids: We also use damped sinu-\nsoids to characterize any ringdown behavior in the\nmagnetar. The waveform is described in Eq. C12\nof Abbott et al. (2024). These are placed at two\nfrequencies, 1590 Hz and 2020 Hz, to represent\n\n6\nTable 1.\nTable of FRB and X-ray events for which we perform GW searches. The long-duration PySTAMP search is performed\nwith one time window, while the short-duration X-Pipeline search is performed with both a compact window and an extended\nwindow, where data availability and timing uncertainties permit. A dash (-) indicates that no search was performed, while an\nasterisk (*) denotes search windows which were necessarily truncated due to data availability.\nWindow for\nCompact window for\nExtended window for\nFRB/X-ray event\nTime (UTC)\nlong-duration search (s)\nshort-duration search (s)\nshort-duration search (s)\n2020 April 28\n14:34:24\n[\u22121200, 120]\n[\u22124, 4]\n[\u22121200, 120]\n2020 October 08\n02:23:33\n[\u22121200, 120]\n[\u22124, 4]\n[\u22121200, 120]\n2022 October 14 X-ray glitch 1\n15:07:12\n-\n-\n[\u2212480, \u2212240]*\n2022 October 14 X-ray burst peak\n16:55:12\n-\n-\n[\u22121000, 1000]\n2022 October 14\n19:21:39\n[\u2212687, 120]*\n[\u22124, 4]\n[\u2212600, 120]*\n2022 October 14 X-ray glitch 2\n23:45:36\n-\n-\n[\u2212500, 500]*\n2022 December 01\n22:06:59\n-\n-\n[\u22121200, \u2212400]*\nplausible f-mode signals. For each frequency, we\nuse two damping timescales to probe a larger pa-\nrameter space.\nThe waveforms used by the long-duration PySTAMP anal-\nysis are also Sine-Gaussians, but with a duration param-\neter of 10 s. They are also described in Table 2.\n3.2.\nLong-duration search with PySTAMP\nWe use PySTAMP (Macquet et al. 2021) to target GW\nsignals with durations longer than 1 s around the three\nFRBs with coincident GEO600 data. The background\ndistribution and the detection efficiency of the search are\ncharacterized using an off-source window that consists of\n\u223c12 hr of data centered on the event time, excluding the\non-source window described above. The workflow of the\npipeline is as follows. The data are first down-sampled\nfrom 16384 Hz to 8192 Hz, and then high-pass filtered\nwith a frequency cutoff of 40 Hz to remove potential\nspectral leakage from lower frequencies.\nAfter these\npreprocessing steps, the resulting time series are split\ninto 1 s Hann-windowed segments with 50% overlap. The\nfast Fourier transform is computed over each segment to\nbuild a time-frequency map (tf-map) with a resolution\nof 1 s \u00d71 Hz. For each frequency bin, the power spectral\ndensity (PSD) is estimated by taking the median of the\nsquared modulus of the Fourier transform over 1320 s of\nadjacent data (similar to Welch\u2019s method but using the\nmedian instead of the mean), and a signal-to-noise ratio\n(S/N) tf-map is built by dividing the value of the Fourier\ntransform in each pixel by the square root of the PSD.\nTo identify candidate GW events, a pattern recognition\nalgorithm is run over the tf-map. We use the burstegard\nalgorithm (Prestegard 2016) which identifies clusters of\nneighboring pixels whose S/N is above a threshold of\n2.5. Clusters consisting of 5 or more pixels are saved as\ncandidate GW events. Each cluster is then assessed a\nranking statistic \u039b that is the sum of the S/N of each of\nits pixels divided by the square root of the total number\nof pixels.\nClusters found in the off-source window form the back-\nground of the search and are used to estimate the false-\nalarm rate (FAR) of clusters found in the on-source\nwindow as a function of the ranking statistic \u039b. PySTAMP\nis primarily intended to work on cross-correlated data\nfrom a pair of independent detectors, which allows for\nthe simulation of an extended amount of background by\nshifting the time series of one detector with respect to\nthe other. Such a method cannot be applied here in the\nsingle-detector GEO600 search. Hence, the background\nlifetime is limited to the duration of the off-source win-\ndow, so the FAR of each cluster can only be estimated\ndown to a minimum of \u223c1 per 12 hours (2.3 \u00d7 10\u22125 Hz).\nSee Sec. 5 for further discussion of the limited FAR.\nNoise from GW detectors typically features narrow-\nband spectral artifacts that appear as horizontal lines in\na time-frequency representation (or vertical lines in the\namplitude spectral density; see Fig. 1). Because the PSD\nis estimated for each frequency bin by taking the median\nover neighboring time segments, most of these lines are\ncorrectly factored into the PSD and do not generate high\nS/N pixels. However, we observe an excess of clusters in\nthe off-source window around some specific frequencies,\nlikely due to fluctuations of spectral lines around their\ncentral values. We therefore remove clusters for a narrow\nrange of frequencies corresponding to known GEO600\nspectral lines. In order to reject short, broadband noise\ntransients (known as glitches), we also remove clusters\nfor which more than 30% of the total energy is contained\nwithin a single 1 s time segment.\n3.3.\nShort-duration search with X-Pipeline\nWe perform a search for short-duration unmodeled GW\ntransients using X-Pipeline (Sutton et al. 2010; Was\n\n7\nTable 2.\nParameters for waveforms injected into off-source\ndata for recovery to quantify each search\u2019s sensitivity. For\nthe generic short-duration transient search X-Pipeline, we\nfollow the labeling convention in Abbott et al. (2023) for\neach waveform, where \u201cSG\u201d waveforms are sine-Gaussians\nand \u201cDS2P\u201d (damped sinusoid 2 polarizations) waveforms\nrepresent ringdowns. There are few enough long-duration\nwaveforms that we did not assign labels to them. The duration\nparameter scales the width of the Gaussian envelope for the\nsine-Gaussian chirplets, and describes the damping time of\nthe damped sinusoids used as ringdown waveforms. The c\nsuperscript denotes waveforms with circular polarizations.\nLabel\nFrequency f0\nDuration Parameter\n[Hz]\n[ms]\nShort-duration Sine\u2013Gaussian Chirplets\nSG-D\n300\n3.3\nSG-E\n500\n0.20\nSG-F\n1100\n0.91\nSG-G\n1600\n0.63\nSG-H\n1995\n0.50\nSG-I\n2600\n0.38\nSG-J\n3100\n0.32\nSG-K\n3560\n0.28\nSG-Lc\n1600\n0.63\nSG-Mc\n1995\n0.50\nShort-duration Ringdowns\nDS2P-A\n1590\n100\nDS2P-B\n1590\n200\nDS2P-C\n2020\n100\nDS2P-D\n2020\n200\nLong-duration Sine\u2013Gaussian Chirplets\n-\n520\n104\n-\n1020\n104\n-\n1520\n104\n-\n2020\n104\net al. 2012). While typically run as a coherent search\nacross multiple detectors (such as in previous searches\nfor GWs from FRBs (Abbott et al. 2023), gamma ray\nbursts (GRBs) (Abbott et al. 2021, 2022), and magnetars\n(Abbott et al. 2024)), we use X-Pipeline in a single-\ndetector mode because GEO600 was the only GW detec-\ntor collecting data at the time of the FRBs. X-Pipeline\nsplits the PSD-whitened data into 64 s segments, then\napplies a Fourier transform to produce time-frequency\nmaps. The time-frequency pixels with amplitudes in\nthe highest 1% that neighbor each other are clustered\ninto candidate detection events. Each event is then as-\nsigned a ranking statistic based on the summed energy\ncontained in the pixels. To determine the significance\nof these candidate events, we compare them against a\ndistribution of background energies empirically measured\nin an identical manner from an \u201coff-source\u201d period. This\nis chosen to fall around (but not including) the time\nof the on-source data and to be long enough to allow\nfor meaningful significances to be calculated but not so\nlong that the detector\u2019s behavior is nonstationary. We\nemploy a 24-hour off-source window, symmetric about\neach event\u2019s time.\nWhen X-Pipeline is run on data from multiple detec-\ntors as is typical, vetoes of problematic event candidates\ncan be applied by utilizing the presumed coherence of\nany real GW event across detectors. This is unfortu-\nnately not an option in a single-detector search such as\nthis, meaning that the search becomes more vulnerable\nto background noise. To improve the sensitivity of our\nsearch, we apply frequency-domain vetoes based on the\ndistribution of time-frequency candidate events in the\noff-source window for each FRB search. We veto narrow\nfrequency bands (\u223c10 Hz bandwidth) where there is con-\nsiderable excess noise; most of these vetoes corresponded\nto known spectral lines from the GEO600 detector.\n4.\nSEARCH RESULTS AND LIMITS ON\nCOINCIDENT EMISSION\nIn this section, we present the results of the long- and\nshort-duration searches described above (see Table 1 for\na summary).\nWe do not find any candidate GW events in either\nthe long-duration or short-duration compact-window\nsearches for any of the FRBs. For the long-duration\nPySTAMP search, no triggers survive the cuts described\nin Sec. 3.2 for the 2020 April and 2022 October FRBs.\nFive triggers survive for the 2020 October FRB, but\nthe loudest trigger has a FAR of \u223c1 per 1000 s with\na p-value of 0.76 and is thus not significant.\nIn the\nshort-duration X-Pipeline case, only the 2020 April,\n2020 October, and 2022 October FRBs compact-window\nsearches had enough background to be considered useful\nfor GW searches, as described above. The only surviv-\ning trigger from these three searches is from the 2022\nOctober FRB and has a p-value of 0.53, and thus is also\nnot significant.\nFor the short-duration extended-window searches, long\noff-source windows are required to estimate the back-\nground, and the single-detector nature of this search\nprevents the use of \u201ctime-slides\u201d between multiple de-\ntectors to artificially generate background. These limita-\ntions mean that for the extended-window short-duration\nsearches, there are sometimes as few as six off-source\nbackground trials, limiting any potential detection\u2019s max-\n\n8\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\nFrequency [Hz]\n1048\n1049\n1050\n1051\n1052\n1053\n1054\n1055\n1056\n1057\n1058\n1059\n90% upper limits on EGW [erg]\nRange of O3a limits\nShort-duration ringdown\nShort-duration SG\nLong-duration SG\nFigure 3.\nThe 90% upper limits on the emitted GW energy from SGR 1935+2154 coincident with FRBs, alongside GW\nenergy limits from FRBs during the O3a observing run as reported in Abbott et al. (2023). We plot the short-duration ringdown\n(orange) and Sine-Gaussian (SG; blue) waveforms from Table 5, and the long-duration SG waveforms (aquamarine) from Table 3.\nThe previous range of 90% limits from Abbott et al. (2023), based on the lower bounds of the 90% credible distance as reported\nin their Table A1, are plotted in vertical black lines. These are for a short-duration search; Abbott et al. (2023) did not perform\na long-duration analysis.\nTable 3.\nThe 50% and 90% upper limits on GW emission energy in ergs from the long-duration PySTAMP search. Each frequency\ncorresponds to the central frequency f0 of a Sine-Gaussian waveform with duration parameter equal to 10 s.\nEvent\n520 Hz\n1020 Hz\n1520 Hz\n2020 Hz\n50%\n90%\n50%\n90%\n50%\n90%\n50%\n90%\n2020 April 28\n2.0 \u00d7 1050\n5.7 \u00d7 1050\n7.4 \u00d7 1050\n2.7 \u00d7 1051\n3.3 \u00d7 1051\n1.1 \u00d7 1052\n2.3 \u00d7 1052\n7.3 \u00d7 1052\n2020 October 08\n1.6 \u00d7 1051\n1.0 \u00d7 1052\n4.4 \u00d7 1051\n2.9 \u00d7 1052\n1.7 \u00d7 1052\n1.1 \u00d7 1053\n1.1 \u00d7 1053\n6.8 \u00d7 1053\n2022 October 14\n8.6 \u00d7 1049\n3.0 \u00d7 1050\n4.3 \u00d7 1050\n1.4 \u00d7 1051\n2.4 \u00d7 1051\n8.1 \u00d7 1051\n1.5 \u00d7 1052\n4.6 \u00d7 1052\nimum significance to a p-value of 1/6 \u22480.17\u2014insufficient\nfor any meaningful statement about the astrophysical\nnature of any outlier in the data. Thus, instead of report-\ning potential GW candidates from the extended-window\nsearches with inconsequential statements about signifi-\ncance, we decided to use the searches only to determine\nthe loudest trigger within the on-source window for a\ngiven waveform model, thereby setting an upper limit\non the corresponding GW energy. This is the \u201cloudest\nevent statistic\u201d (Biswas et al. 2009, 2013).\nFor all searches and windows (listed in Table 1), we\nestimate the root-sum-square signal amplitude of the\nGW strain hrss (see Eqs. 3 and 4 of Sutton (2013)) at\n50% and 90% detection efficiency to set upper limits\non the GW energy emitted. To convert the hrss values\nfor each injection type that are output by the search\npipelines to energy, we use (following Sutton (2013))\nEGW = 2\n5\n\u03c02c3\nG D2\nLf 2\n0 h2\nrss,\n(1)\nwith f0 describing the central frequency of each injection\nand DL set to the 6.6 kpc distance of SGR 1935+2154\n\n9\nTable 4.\nThe 50% upper limits on GW emission energy in ergs from the short-duration X-Pipeline search. Each injection\nwaveform is defined as in Table 2. Dashes indicate that no limit was obtainable for this set of injections due to insufficient\nbackground or poor data quality.\nEvent\nSG-D\nSG-E\nSG-F\nSG-G\nSG-H\nSG-I\nSG-J\nDate\nWindow\n300 Hz\n500 Hz\n1100 Hz\n1600 Hz\n1995 Hz\n2600 Hz\n3100 Hz\n2020 April 28\nCompact\n7.1 \u00d7 1048\n3.4 \u00d7 1048\n1.1 \u00d7 1049\n2.9 \u00d7 1049\n8.3 \u00d7 1049\n1.6 \u00d7 1050\n3.2 \u00d7 1050\n2020 April 28\nExtended\n2.0 \u00d7 1049\n9.2 \u00d7 1048\n3.0 \u00d7 1049\n7.9 \u00d7 1049\n2.1 \u00d7 1050\n4.2 \u00d7 1050\n8.3 \u00d7 1050\n2020 October 08\nCompact\n5.8 \u00d7 1049\n1.7 \u00d7 1049\n3.6 \u00d7 1049\n9.1 \u00d7 1049\n2.3 \u00d7 1050\n5.4 \u00d7 1050\n1.1 \u00d7 1051\n2020 October 08\nExtended\n1.7 \u00d7 1051\n3.4 \u00d7 1050\n7.6 \u00d7 1050\n1.8 \u00d7 1051\n4.4 \u00d7 1051\n8.9 \u00d7 1051\n1.7 \u00d7 1052\n2022 October 14 glitch 1\nExtended\n-\n8.2 \u00d7 1049\n3.3 \u00d7 1050\n1.0 \u00d7 1051\n2.6 \u00d7 1051\n6.5 \u00d7 1051\n1.4 \u00d7 1052\n2022 October 14 X-ray peak\nExtended\n-\n3.8 \u00d7 1049\n1.6 \u00d7 1050\n5.1 \u00d7 1050\n1.2 \u00d7 1051\n3.0 \u00d7 1051\n6.6 \u00d7 1051\n2022 October 14\nCompact\n-\n1.3 \u00d7 1048\n6.4 \u00d7 1048\n2.0 \u00d7 1049\n4.4 \u00d7 1049\n1.2 \u00d7 1050\n2.6 \u00d7 1050\n2022 October 14\nExtended\n-\n7.1 \u00d7 1048\n3.3 \u00d7 1049\n1.0 \u00d7 1050\n2.3 \u00d7 1050\n5.7 \u00d7 1050\n1.2 \u00d7 1051\n2022 October 14 glitch 2\nExtended\n4.8 \u00d7 1050\n1.6 \u00d7 1050\n7.4 \u00d7 1050\n2.5 \u00d7 1051\n6.8 \u00d7 1051\n2.0 \u00d7 1052\n4.5 \u00d7 1052\n2022 December 1\nExtended\n9.4 \u00d7 1049\n3.4 \u00d7 1049\n9.3 \u00d7 1049\n2.7 \u00d7 1050\n7.4 \u00d7 1050\n1.7 \u00d7 1051\n3.1 \u00d7 1051\nEvent\nSG-K\nSG-L\nSG-M\nDS2P-A\nDS2P-B\nDS2P-C\nDS2P-D\nDate\nWindow\n3560 Hz\n1600 Hz\n1995 Hz\n1590 Hz\n1590 Hz\n2020 Hz\n2020 Hz\n2020 April 28\nCompact\n5.8 \u00d7 1050\n1.0 \u00d7 1049\n2.4 \u00d7 1049\n2.5 \u00d7 1049\n2.9 \u00d7 1049\n1.6 \u00d7 1050\n2.3 \u00d7 1050\n2020 April 28\nExtended\n1.5 \u00d7 1051\n2.5 \u00d7 1049\n6.0 \u00d7 1049\n7.8 \u00d7 1049\n7.5 \u00d7 1049\n3.6 \u00d7 1050\n6.6 \u00d7 1050\n2020 October 08\nCompact\n2.0 \u00d7 1051\n2.8 \u00d7 1049\n7.1 \u00d7 1049\n8.9 \u00d7 1049\n8.7 \u00d7 1049\n3.2 \u00d7 1050\n3.4 \u00d7 1050\n2020 October 08\nExtended\n3.5 \u00d7 1052\n4.7 \u00d7 1050\n1.0 \u00d7 1051\n1.8 \u00d7 1051\n2.0 \u00d7 1051\n6.7 \u00d7 1051\n6.7 \u00d7 1051\n2022 October 14 glitch 1\nExtended\n2.2 \u00d7 1052\n3.2 \u00d7 1050\n9.1 \u00d7 1050\n1.1 \u00d7 1051\n1.2 \u00d7 1051\n3.0 \u00d7 1051\n2.9 \u00d7 1051\n2022 October 14 X-ray peak\nExtended\n1.0 \u00d7 1052\n1.6 \u00d7 1050\n4.3 \u00d7 1050\n5.7 \u00d7 1050\n5.6 \u00d7 1050\n1.4 \u00d7 1051\n1.4 \u00d7 1051\n2022 October 14\nCompact\n4.3 \u00d7 1050\n6.3 \u00d7 1048\n1.6 \u00d7 1049\n1.7 \u00d7 1049\n1.7 \u00d7 1049\n4.1 \u00d7 1049\n4.7 \u00d7 1049\n2022 October 14\nExtended\n2.0 \u00d7 1051\n3.1 \u00d7 1049\n8.0 \u00d7 1049\n9.9 \u00d7 1049\n9.6 \u00d7 1049\n2.5 \u00d7 1050\n2.6 \u00d7 1050\n2022 October 14 glitch 2\nExtended\n1.0 \u00d7 1053\n8.8 \u00d7 1050\n2.2 \u00d7 1051\n2.8 \u00d7 1051\n2.7 \u00d7 1051\n8.8 \u00d7 1051\n8.9 \u00d7 1051\n2022 December 1\nExtended\n5.9 \u00d7 1051\n7.9 \u00d7 1049\n1.9 \u00d7 1050\n2.4 \u00d7 1050\n2.5 \u00d7 1050\n7.9 \u00d7 1050\n8.1 \u00d7 1050\n(Zhou et al. 2020).\nThe results of the long-duration\nsearch are shown in Tab. 3. The 50% and 90% limits\nfrom the short-duration analysis are shown in Tab. 4 and\nTab. 5 respectively. We show in Fig. 3 our 90% upper\nlimits from both the long- and short-duration analyses\nas a function of frequency, corresponding to the upper\nlimits at which 90% of the injected signals were recovered.\nTo be explicit, the X% hrss value for a given waveform\nmodel (and corresponding GW energy) is calculated by\nfinding the hrss at which X% of the injected waveforms\nare recovered (i.e., found with a significance higher than\nthe loudest non-injection event in the window).\nFor some injections in the short-duration search\n(mostly those at lower frequencies such as SG-D with\nf0 = 300 Hz), limits could not be established because\nnoise in the detector prevented sufficient recovery of the\ninjected signals. Limited data availability and poor data\nquality around the time of the 2020 October 08 event\nmeant that no injection reached 90% recovery, leading\nto the lack of 90% limits.\nThe nondetection of GW emission from our analyzed\nFRBs implies that the GW-to-radio energy ratio must\nbe less than EGW/Eradio \u223c8 \u00d7 1014 at the 90% level,\nfor a time window from [-4, 4] s at a GW frequency of\napproximately 300 Hz. At the \u223c2 kHz frequencies close\nto the neutron-star f-mode, EGW/Eradio \u22721.7 \u00d7 1016\nat the 90% level. The GW and radio energies for our\nanalyzed FRBs are shown in Fig. 4, alongside the same\nquantities for FRBs from O3a analyzed in Abbott et al.\n(2023).\n5.\nDISCUSSION AND CONCLUSION\nThe previous best limits on coincident GW emission\nwith FRBs were set by Abbott et al. (2023) using ex-\ntragalactic FRBs observed during the O3a LVK observ-\ning run, using SG waveforms and X-Pipeline. Fig. 3\nshows the 90% upper limits on the GW energy during\nour analyzed FRBs from SGR 1935+2154, compared\nprevious limits presented as a range spanning the best\nand worst 90% limits from Abbott et al. (2023).\nIn\nthe short-duration search at approximately 300 Hz, the\nbest previous 90% upper limit on GW energy was set at\n3.4\u00d71051 erg; at approximately 2 kHz, the best previous\n90% upper limit was 7.9 \u00d7 1054 erg. We improve on the\n300 Hz constraint by about two orders of magnitude, and\nthe 2 kHz constraint by over four orders of magnitude.\nNo previous long-duration searches around FRB events\nhave been performed, so the long-duration search results\n\n10\nTable 5.\nSame as Table 4 but with 90% upper limits. For some injections (marked by a dash), fewer than 90% of the injections\nare recovered, preventing the calculation of 90% limits.\nEvent\nSG-D\nSG-E\nSG-F\nSG-G\nSG-H\nSG-I\nSG-J\nDate\nWindow\n300 Hz\n500 Hz\n1100 Hz\n1600 Hz\n1995 Hz\n2600 Hz\n3100 Hz\n2020 April 28\nCompact\n4.2 \u00d7 1049\n2.0 \u00d7 1049\n5.6 \u00d7 1049\n1.5 \u00d7 1050\n9.3 \u00d7 1050\n1.1 \u00d7 1051\n2.2 \u00d7 1051\n2020 April 28\nExtended\n8.2 \u00d7 1049\n4.0 \u00d7 1049\n1.5 \u00d7 1050\n4.0 \u00d7 1050\n1.3 \u00d7 1051\n2.3 \u00d7 1051\n5.2 \u00d7 1051\n2020 October 08\nCompact\n-\n-\n-\n-\n-\n-\n-\n2020 October 08\nExtended\n-\n-\n-\n-\n-\n-\n-\n2022 October 14 glitch 1\nExtended\n-\n5.7 \u00d7 1050\n1.9 \u00d7 1051\n6.6 \u00d7 1051\n-\n4.1 \u00d7 1052\n-\n2022 October 14 X-ray peak\nExtended\n-\n1.6 \u00d7 1050\n6.8 \u00d7 1050\n2.2 \u00d7 1051\n4.6 \u00d7 1051\n1.1 \u00d7 1052\n2.9 \u00d7 1052\n2022 October 14\nCompact\n-\n6.4 \u00d7 1048\n3.9 \u00d7 1049\n1.3 \u00d7 1050\n2.3 \u00d7 1050\n6.3 \u00d7 1050\n1.3 \u00d7 1051\n2022 October 14\nExtended\n-\n3.0 \u00d7 1049\n1.3 \u00d7 1050\n3.9 \u00d7 1050\n1.0 \u00d7 1051\n2.2 \u00d7 1051\n5.1 \u00d7 1051\n2022 October 14 glitch 2\nExtended\n2.1 \u00d7 1051\n7.2 \u00d7 1050\n2.7 \u00d7 1051\n9.3 \u00d7 1051\n2.8 \u00d7 1052\n8.4 \u00d7 1052\n1.9 \u00d7 1053\n2022 December 1\nExtended\n-\n-\n-\n-\n-\n2.1 \u00d7 1054\n6.0 \u00d7 1052\nEvent\nSG-K\nSG-L\nSG-M\nDS2P-A\nDS2P-B\nDS2P-C\nDS2P-D\nDate\nWindow\n3560 Hz\n1600 Hz\n1995 Hz\n1590 Hz\n1590 Hz\n2020 Hz\n2020 Hz\n2020 April 28\nCompact\n3.3 \u00d7 1051\n2.7 \u00d7 1049\n1.1 \u00d7 1050\n2.0 \u00d7 1050\n1.9 \u00d7 1050\n1.0 \u00d7 1052\n-\n2020 April 28\nExtended\n9.3 \u00d7 1051\n7.4 \u00d7 1049\n2.5 \u00d7 1050\n4.5 \u00d7 1050\n4.3 \u00d7 1050\n-\n-\n2020 October 08\nCompact\n-\n-\n-\n-\n-\n-\n-\n2020 October 08\nExtended\n-\n-\n-\n-\n-\n-\n-\n2022 October 14 glitch 1\nExtended\n-\n7.0 \u00d7 1050\n1.3 \u00d7 1051\n6.1 \u00d7 1051\n8.1 \u00d7 1051\n1.6 \u00d7 1052\n1.6 \u00d7 1052\n2022 October 14 X-ray peak\nExtended\n4.3 \u00d7 1052\n3.3 \u00d7 1050\n6.1 \u00d7 1050\n-\n2.5 \u00d7 1051\n5.0 \u00d7 1051\n6.0 \u00d7 1051\n2022 October 14\nCompact\n2.1 \u00d7 1051\n1.6 \u00d7 1049\n3.8 \u00d7 1049\n9.5 \u00d7 1049\n9.6 \u00d7 1049\n2.0 \u00d7 1050\n2.6 \u00d7 1050\n2022 October 14\nExtended\n8.9 \u00d7 1051\n6.1 \u00d7 1049\n1.3 \u00d7 1050\n4.5 \u00d7 1050\n4.4 \u00d7 1050\n9.5 \u00d7 1050\n1.3 \u00d7 1051\n2022 October 14 glitch 2\nExtended\n3.9 \u00d7 1053\n1.5 \u00d7 1051\n4.5 \u00d7 1051\n1.3 \u00d7 1052\n1.1 \u00d7 1052\n3.2 \u00d7 1052\n4.1 \u00d7 1052\n2022 December 01\nExtended\n-\n-\n8.5 \u00d7 1050\n-\n6.6 \u00d7 1051\n6.2 \u00d7 1052\n2.0 \u00d7 1053\npresented here represent the first constraints on such\nemission. Studies have predicted that magnetar flares\ncan emit up to 1048 \u22121049 erg in GW energy near the\nf-mode for \u223c200 ms (Ioka 2001; Corsi & Owen 2011)\u2014a\nregime that is probed by our most stringent 50% short-\nduration constraints at approximately 2 kHz (see SG-H\nwaveform in Table 4). We also slightly improve the upper\nlimit on EGW/Eradio, as shown in Fig. 4.\nWe note that our results are not the most con-\nstraining limits on GW emission from the magnetar\nSGR 1935+2154, which are reported in Abbott et al.\n(2024) in a search for GW emission around times of\nmagnetar X-ray and gamma-ray flares. The relationship\nbetween these magnetar bursts and FRBs is poorly un-\nderstood, but are likely to be caused by different physical\nprocesses, even if the underlying magnetar behavior may\nbe related (Tsuzuki et al. 2024). Hence, both GW limits\nare complementary and can help to better understand\nthe emission mechanisms at play. Considering the X-ray\nspin-up glitches, our best limits on the emitted GW en-\nergy (\u223c1051 erg at 300 Hz) are still far from the X-ray\nmeasured changes in rotational energy (\u223c1042 erg from\nHu et al. (2024)).\nSince EGW \u221dD2\nL in Eq. 1, our constraints are heavily\ndependent on the distance to SGR 1935+2154. As men-\ntioned in Sec. 2, estimates for SGR 1935+2154\u2019s distance\nvary by almost an order of magnitude. If its true dis-\ntance is as close as the 1.5 kpc measured by Bailes et al.\n(2021), our energy constraints would improve by a factor\nof almost 20. On the other hand, if SGR 1935+2154 is\nat almost 15 kpc, as suggested by Surnis et al. (2016),\nour constraints would worsen by a factor of 5.\nAs a single-detector search, the number of possible\nbackground trials (and thus the assessment of GW can-\ndidates via p-value or FAR) is limited by the time in\nwhich the detector behavior remains similar to that of\nthe on-source window. For example, the minimum FAR\nfor the long-duration PySTAMP search was limited to \u223c\n1 per 12 hours. Since we do not recover any candidates\nin the on-source windows which appear to differentiate\nthemselves from the background, we did not have to as-\nsess any candidate\u2019s significance beyond 1 per 12 hours,\nmeaning that this limitation did not affect our results.\nHowever, future single-detector searches may encounter\nthe problem where a candidate in the on-source window\nis unlike anything found in the background trials, compli-\ncating an accurate assessment of its significance. Some\nGW CBC searches have implemented techniques to im-\nprove single-detector significance estimation (Sachdev\net al. 2019; Cabourn Davies & Harry 2022); unmodeled\n\n11\n1029\n1030\n1031\n1032\n1033\n1034\n1035\n1036\n1037\n1038\n1039\nEradio [erg]\n1048\n1049\n1050\n1051\n1052\n1053\n1054\n1055\n1056\n1057\n1058\n1059\n1060\n1061\n1062\n1063\n90% upper limit on EGW [erg]\n1013\u00d7Eradio\n1015\u00d7Eradio\n1017\u00d7Eradio\n1019\u00d7Eradio\n1021\u00d7Eradio\n1023\u00d7Eradio\nAbbott+2023 - 1995 Hz\nAbbott+2023 - 290 Hz\nShort-duration - 1995 Hz\nShort-duration - 300 Hz\nLong-duration - 2020 Hz\nLong-duration - 520 Hz\nFigure 4.\n90% upper limits on the emitted GW energy from FRBs as a function of the FRB\u2019s radio energy. In the pink,\norange, red, and purple, we show limits from FRBs emitted by SGR 1935+2154, for both our short- and long-duration searches.\nWe plot limits for the Sine-Gaussian model at 300 Hz (SG-D) and 1995 Hz (SG-H) for the short-duration search and at 520 Hz\nand 2020 Hz for the long-duration search. In the blue and green markers, we show the upper limits on GW energy and the\ncorresponding radio energy for FRBs analyzed in Abbott et al. (2023), at 290 Hz and 1995 Hz, for events with radio flux/fluence\ninformation from CHIME/FRB Collaboration et al. (2021) allowing for radio energy reconstruction. The estimated radio energies\nare calculated as described in Principe et al. (2023), scaled to the lower bound 90% distances as reported in Abbott et al. (2023).\nNote that the radio energies (derived from fluxes and fluences) should be interpreted as lower limits (CHIME/FRB Collaboration\net al. 2021; Andersen et al. 2023). We also plot dotted lines representing different ratios of EGW to Eradio, showing a slight\nimprovement in EGW/Eradio compared to the Abbott et al. (2023) results.\nsearches like PySTAMP and X-Pipeline may also benefit\nfrom such enhancements.\nAt the time of writing, no FRBs have been detected\nfrom SGR 1935+2154 since 2022. The O4 observing\nrun of the LVK, with participation from the LIGO,\nVirgo, and KAGRA detectors will continue until mid-\n2025. Given the increased sensitivity of these detectors\ncompared to GEO600, any SGR 1935+2154 FRB during\nthe remainder of O4 could provide another opportunity\nto probe the GW\u2013FRB connection.\nWe thank Teruaki Enoto, Chin-Ping Hu, and George\nYounes for assistance with their X-ray results. We also\nthank Vicky Kaspi, Kiyoshi Masui, and Kaitlyn Shin for\nhelpful discussions, and the anonymous referee for their\nuseful comments.\nThe gravitational-wave data analyzed in this paper\nis available on the Gravitational Wave Open Science\nCenter at LIGO Scientific Collaboration, Virgo Collabo-\nration and KAGRA Collaboration (2024a). The scripts\nand data used to produce the figures in this paper are\navailable at LIGO Scientific Collaboration, Virgo Collab-\noration and KAGRA Collaboration (2024b).\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United King-\ndom, the Max-Planck-Society (MPS), and the State of\nNiedersachsen/Germany for support of the construction\nof Advanced LIGO and construction and operation of\nthe GEO 600 detector. Additional support for Advanced\nLIGO was provided by the Australian Research Council.\nThe authors gratefully acknowledge the Italian Istituto\nNazionale di Fisica Nucleare (INFN), the French Centre\n\n12\nNational de la Recherche Scientifique (CNRS) and the\nNetherlands Organization for Scientific Research (NWO)\nfor the construction and operation of the Virgo detector\nand the creation and support of the EGO consortium.\nThe authors also gratefully acknowledge research support\nfrom these agencies as well as by the Council of Scientific\nand Industrial Research of India, the Department of Sci-\nence and Technology, India, the Science & Engineering\nResearch Board (SERB), India, the Ministry of Human\nResource Development, India, the Spanish Agencia Es-\ntatal de Investigaci\u00b4on (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comunitat\nAuton`oma de les Illes Balears through the Direcci\u00b4o Gen-\neral de Recerca, Innovaci\u00b4o i Transformaci\u00b4o Digital with\nfunds from the Tourist Stay Tax Law ITS 2017-006, the\nConselleria d\u2019Economia, Hisenda i Innovaci\u00b4o, the FEDER\nOperational Program 2021-2027 of the Balearic Islands,\nthe Conselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Soci-\netat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish\nNational Agency for Academic Exchange, the National\nScience Centre of Poland and the European Union \u2013 Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scottish\nUniversities Physics Alliance, the Hungarian Scientific\nResearch Fund (OTKA), the French Lyon Institute of\nOrigins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek \u2013 Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Science and Engineering\nResearch Council of Canada (NSERC), the Canadian\nFoundation for Innovation (CFI), the Brazilian Ministry\nof Science, Technology, and Innovations, the Interna-\ntional Center for Theoretical Physics South American\nInstitute for Fundamental Research (ICTP-SAIFR), the\nResearch Grants Council of Hong Kong, the National\nNatural Science Foundation of China (NSFC), the Israel\nScience Foundation (ISF), the US-Israel Binational Sci-\nence Fund (BSF), the Leverhulme Trust, the Research\nCorporation, the National Science and Technology Coun-\ncil (NSTC), Taiwan, the United States Department of\nEnergy, and the Kavli Foundation. The authors grate-\nfully acknowledge the support of the NSF, STFC, INFN\nand CNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-in-Aid for Scientific Research on Innovative Areas\n2905: JP17H06358, JP17H06361 and JP17H06364, JSPS\nCore-to-Core Program A, Advanced Research Networks,\nJSPS Grants-in-Aid for Scientific Research (S) 17H06133\nand 20H05639, JSPS Grant-in-Aid for Transformative\nResearch Areas (A) 20A203: JP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nthe University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Rising\nStar Program and Science Vanguard Research Program,\nthe Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising. 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Aiello\n16, 17, 18\nA. Ain\n19\nP. Ajith\n20\nT. Akutsu\n21, 22\nS. Albanesi\n23, 24, 25\nR. A. Alfaidi\n26\nA. Al-Jodah\n27\nC. All\u00b4en\u00b4e28\nA. Allocca\n29, 5\nS. Al-Shammari18\nP. A. Altin\n30\nS. Alvarez-Lopez\n31\nA. Amato\n32, 33\nL. Amez-Droz34\nA. Amorosi34\nC. Amra35\nA. Ananyeva2\nS. B. Anderson\n2\nW. G. Anderson\n2\nM. Andia\n36\nM. Ando37\nT. Andrade38\nN. Andres\n28\nM. Andr\u00b4es-Carcasona\n39\nT. Andri\u00b4c\n40, 41, 1, 42\nJ. Anglin43\nS. Ansoldi\n44, 45\nJ. M. Antelis\n46\nS. Antier\n47\nM. Aoumi48\nE. Z. Appavuravther49, 50\nS. Appert2\nS. K. Apple51\nK. Arai\n2\nA. Araya\n37\nM. C. Araya\n2\nJ. S. Areeda\n52\nL. Argianas53\nN. Aritomi3\nF. Armato\n54, 55\nN. Arnaud\n36, 56\nM. Arogeti\n57\nS. M. Aronson\n9\nG. Ashton\n58\nY. Aso\n21, 59\nM. Assiduo60, 61\nS. Assis de Souza Melo56\nS. M. Aston62\nP. Astone\n63\nF. Attadio\n64, 63\nF. Aubin\n65\nK. AultONeal\n66\nG. Avallone\n67\nD. Azrad68\nS. Babak\n69\nF. Badaracco\n54\nC. Badger70\nS. Bae\n71\nS. Bagnasco\n23\nE. Bagui72\nJ. G. Baier\n73\nL. Baiotti\n74\nR. Bajpai\n21\nT. Baka75\nM. Ball76\nG. Ballardin56\nS. W. Ballmer77\nS. Banagiri\n78\nB. Banerjee\n42\nD. Bankar\n11\nP. Baral\n8\nJ. C. Barayoga2\nB. C. Barish2\nD. Barker3\nP. Barneo\n38, 79\nF. Barone\n80, 5\nB. Barr\n26\nL. Barsotti\n31\nM. Barsuglia\n69\nD. Barta\n81\nA. M. Bartoletti82\nM. A. Barton\n26\nI. Bartos43\nS. Basak\n20\nA. Basalaev\n83\nR. Bassiri\n15\nA. Basti\n84, 85\nD. E. Bates18\nM. Bawaj\n86, 49\nP. Baxi87\nJ. C. Bayley\n26\nA. C. Baylor\n8\nP. A. Baynard II57\nM. Bazzan88, 89\nV. M. Bedakihale90\nF. Beirnaert\n91\nM. Bejger\n92\nD. Belardinelli\n17\nA. S. Bell\n26\nV. Benedetto93\nW. Benoit\n94\nJ. D. Bentley\n83\nM. Ben Yaala95\nS. Bera\n96\nM. Berbel\n97\nF. Bergamin\n40, 41\nB. K. Berger\n15\nS. Bernuzzi\n24\nM. Beroiz\n2\nD. Bersanetti\n54\nA. Bertolini33\nJ. Betzwieser\n62\nD. Beveridge\n27\nN. Bevins\n53\nR. Bhandare98\nU. Bhardwaj\n99, 33\nR. Bhatt2\nD. Bhattacharjee\n73, 100\nS. Bhaumik\n43\nS. Bhowmick101\nA. Bianchi33, 102\nI. A. Bilenko103\nG. Billingsley\n2\nA. Binetti\n104\nS. Bini\n105, 106\nO. Birnholtz\n68\nS. Biscoveanu\n78\nA. Bisht41\nM. Bitossi\n56, 85\nM.-A. Bizouard\n47\nJ. K. Blackburn\n2\nL. A. Blagg76\nC. D. Blair27, 62\nD. G. Blair27\nF. Bobba67, 107\nN. Bode\n40, 41\nG. Boileau\n19, 47\nM. Boldrini\n64, 63\nG. N. Bolingbroke\n108\nA. Bolliand109, 35\nL. D. Bonavena\n88\nR. Bondarescu\n38\nF. Bondu\n110\nE. Bonilla\n15\nM. S. Bonilla\n52\nA. Bonino111\nR. Bonnand\n28\nP. Booker40, 41\nA. Borchers40, 41\nV. Boschi\n85\nS. Bose112\nV. Bossilkov62\nV. Boudart\n113\nA. Boudon114\nA. Bozzi56\nC. Bradaschia85\nP. R. Brady\n8\nM. Braglia\n115\nA. Branch62\nM. Branchesi\n42, 116\nJ. Brandt57\nI. Braun73\nM. Breschi\n24\nT. Briant\n117\nA. Brillet47\nM. Brinkmann40, 41\nP. Brockill8\nE. Brockmueller\n40, 41\nA. F. Brooks\n2\nB. C. Brown43\nD. D. Brown108\nM. L. Brozzetti\n86, 49\nS. Brunett2\nG. Bruno10\nR. Bruntz\n118\nJ. Bryant111\nF. Bucci61\nJ. Buchanan118\nO. Bulashenko\n38, 79\nT. Bulik119\nH. J. Bulten33\nA. Buonanno\n120, 1\nK. Burtnyk3\nR. Buscicchio\n121, 122\nD. Buskulic28\nC. Buy\n123\nR. L. Byer15\nG. S. Cabourn Davies\n124\nG. Cabras\n44, 45\nR. Cabrita\n10\nV. C\u00b4aceres-Barbosa7\nL. Cadonati\n57\nG. Cagnoli\n125\nC. Cahillane\n77\nJ. Calder\u00b4on Bustillo126\nT. A. Callister127\nE. Calloni29, 5\nJ. B. Camp128\nM. Canepa55, 54\nG. Caneva Santoro\n39\nK. C. Cannon\n37\nH. Cao108\nL. A. Capistran129\nE. Capocasa\n69\nE. Capote\n77\nG. Carapella67, 107\nF. Carbognani56\nM. Carlassara40, 41\nJ. B. Carlin\n130\nM. Carpinelli\n121, 131, 56\nG. Carrillo76\nJ. J. Carter\n40, 41\nG. Carullo\n132\nJ. Casanueva Diaz56\nC. Casentini\n133, 16, 17\nS. Y. Castro-Lucas101\nS. Caudill134, 33, 75\nM. Cavagli`a\n100\nR. Cavalieri\n56\nG. Cella\n85\nP. Cerd\u00b4a-Dur\u00b4an\n135, 136\nE. Cesarini\n17\nW. Chaibi47\nP. Chakraborty\n40, 41\nS. Chalathadka Subrahmanya\n83\nJ. C. L. Chan\n137\nM. Chan138\nK. Chandra7\nR.-J. Chang139\nS. Chao\n140, 141\nE. L. Charlton118\nP. Charlton\n142\nE. Chassande-Mottin\n69\nC. Chatterjee\n143\nDebarati Chatterjee\n11\nDeep Chatterjee\n31\nM. Chaturvedi98\nS. Chaty\n69\nA. Chen12\nA. H.-Y. Chen144\nD. Chen\n145\nH. Chen140\nH. Y. Chen\n146\nJ. Chen\n31\nK. H. Chen141\nY. Chen140\nYanbei Chen147\nYitian Chen\n148\nH. P. Cheng149\nP. Chessa\n86, 49\nH. T. Cheung87\nS. Y. Cheung150\nF. Chiadini\n151, 107\nG. Chiarini89\nR. Chierici114\nA. Chincarini\n54\nM. L. Chiofalo\n84, 85\nA. Chiummo\n5, 56\nC. Chou144\nS. Choudhary\n27\nN. Christensen\n47\nS. S. Y. Chua\n30\nP. Chugh150\nG. Ciani\n88, 89\nP. Ciecielag\n92\nM. Cie\u00b4slar\n119\nM. Cifaldi\n17\nR. Ciolfi\n152, 89\nF. Clara3\nJ. A. Clark\n2, 57\nJ. Clarke18\nT. A. Clarke\n150\nP. Clearwater153\nS. Clesse72\nE. Coccia42, 116, 39\nE. Codazzo\n42\nP.-F. Cohadon\n117\nS. Colace\n55\nM. Colleoni\n96\nC. G. Collette34\nJ. Collins62\nS. Colloms26\nA. Colombo\n121, 122, 154\nM. Colpi\n121, 122\nC. M. Compton3\nG. Connolly76\nL. Conti\n89\nT. R. Corbitt\n9\nI. Cordero-Carri\u00b4on\n155\nS. Corezzi86, 49\nN. J. Cornish\n156\nA. Corsi\n157\nS. Cortese\n56\nC. A. Costa14\nR. Cottingham62\nM. W. Coughlin\n94\nA. Couineaux63\nJ.-P. Coulon47\nS. T. Countryman\n158\nJ.-F. Coupechoux114\nP. Couvares\n2, 57\nD. M. Coward27\nM. J. Cowart62\nR. Coyne\n159\nK. Craig95\nR. Creed18\nJ. D. E. Creighton\n8\nT. D. Creighton160\nP. Cremonese\n96\nA. W. Criswell\n94\nJ. C. G. Crockett-Gray9\nS. Crook62\nR. Crouch3\nJ. Csizmazia3\nJ. R. Cudell\n113\nT. J. Cullen\n2\nA. Cumming\n26\nE. Cuoco56, 85\nM. Cusinato\n135\nP. Dabadie125\nT. Dal Canton\n36\nS. Dall\u2019Osso\n63\nS. Dal Pra\n63\nG. D\u00b4alya\n123\nB. D\u2019Angelo\n54\nS. Danilishin\n32, 33\nS. D\u2019Antonio\n17\nK. Danzmann41, 40, 41\nK. E. Darroch118\nL. P. Dartez3\nA. Dasgupta90\nS. Datta\n161\nV. Dattilo56\nA. Daumas69\nN. Davari162, 131\nI. Dave98\nA. Davenport101\nM. Davier36\nT. F. Davies27\nD. Davis\n2\nL. Davis27\nM. C. Davis\n94\nP. J. Davis\n163, 164\nM. Dax\n1\nJ. De Bolle\n91\nM. Deenadayalan11\n\n17\nJ. Degallaix\n165\nM. De Laurentis\n29, 5\nS. Del\u00b4eglise\n117\nF. De Lillo\n10\nD. Dell\u2019Aquila\n162, 131\nW. Del Pozzo\n84, 85\nF. De Marco\n64, 63\nF. De Matteis\n16, 17\nV. D\u2019Emilio\n2\nN. Demos31\nT. Dent\n126\nA. Depasse\n10\nN. DePergola53\nR. De Pietri\n166, 167\nR. De Rosa\n29, 5\nC. De Rossi\n56\nR. DeSalvo\n168\nR. De Simone151\nA. Dhani1\nR. Diab43\nM. C. D\u00b4\u0131az\n160\nM. Di Cesare\n29\nG. Dideron169\nN. A. Didio77\nT. Dietrich\n1\nL. Di Fiore5\nC. Di Fronzo\n34\nM. Di Giovanni\n64, 63\nT. Di Girolamo\n29, 5\nD. Diksha33, 32\nA. Di Michele\n86\nJ. Ding\n69, 170\nS. Di Pace\n64, 63\nI. Di Palma\n64, 63\nF. Di Renzo\n114\nDivyajyoti\n171\nA. Dmitriev\n111\nZ. Doctor\n78\nE. Dohmen3\nP. P. Doleva118\nD. Dominguez172\nL. D\u2019Onofrio\n63\nF. Donovan31\nK. L. Dooley\n18\nT. Dooney75\nS. Doravari\n11\nO. Dorosh173\nM. Drago\n64, 63\nJ. C. Driggers\n3\nJ.-G. Ducoin174, 69\nL. Dunn\n130\nU. Dupletsa42\nD. D\u2019Urso\n162, 131\nH. Duval\n175\nP.-A. Duverne36\nS. E. Dwyer3\nC. Eassa3\nM. Ebersold\n28\nT. Eckhardt\n83\nG. Eddolls\n77\nB. Edelman\n76\nT. B. Edo2\nO. Edy\n124\nA. Effler\n62\nJ. Eichholz\n30\nH. Einsle47\nM. Eisenmann21\nR. A. Eisenstein31\nA. Ejlli\n18\nR. M. Eleveld176\nM. Emma\n58\nK. Endo177\nA. J. Engl15\nE. Enloe57\nL. Errico\n29, 5\nR. C. Essick\n178\nH. Estell\u00b4es\n1\nD. Estevez\n65\nT. Etzel2\nM. Evans\n31\nT. Evstafyeva179\nB. E. Ewing7\nJ. M. Ezquiaga\n137\nF. Fabrizi\n60, 61\nF. Faedi61, 60\nV. Fafone\n16, 17\nS. Fairhurst\n18\nA. M. Farah\n127\nB. Farr\n76\nW. M. Farr\n180, 181\nG. Favaro\n88\nM. Favata\n182\nM. Fays\n113\nM. Fazio95\nJ. Feicht2\nM. M. Fejer15\nR. . Felicetti\n183\nE. Fenyvesi\n81, 184\nD. L. Ferguson\n146\nS. Ferraiuolo\n185, 64, 63\nI. Ferrante\n84, 85\nT. A. Ferreira9\nF. Fidecaro\n84, 85\nP. Figura\n92\nA. Fiori\n85, 84\nI. Fiori\n56\nM. Fishbach\n178\nR. P. Fisher118\nR. Fittipaldi186, 107\nV. Fiumara\n187, 107\nR. Flaminio28\nS. M. Fleischer\n188\nL. S. Fleming189\nE. Floden94\nE. M. Foley94\nH. Fong138\nJ. A. Font\n135, 136\nB. Fornal\n190\nP. W. F. Forsyth30\nK. Franceschetti166\nN. Franchini69\nS. Frasca64, 63\nF. Frasconi\n85\nA. Frattale Mascioli\n64, 63\nZ. Frei\n191\nA. Freise\n33, 102\nO. Freitas\n192, 135\nR. Frey\n76\nW. Frischhertz62\nP. Fritschel31\nV. V. Frolov62\nG. G. Fronz\u00b4e\n23\nM. Fuentes-Garcia\n2\nS. Fujii193\nT. Fujimori194\nP. Fulda43\nM. Fyffe62\nB. Gadre\n75\nJ. R. Gair\n1\nS. Galaudage\n195\nV. Galdi168\nH. Gallagher196\nS. Gallardo197\nB. Gallego197\nR. Gamba\n24\nA. Gamboa\n1\nD. Ganapathy\n31\nA. Ganguly\n11\nB. Garaventa\n54, 55\nJ. Garc\u00b4\u0131a-Bellido\n115\nC. Garc\u00b4\u0131a N\u00b4u\u02dcnez189\nC. Garc\u00b4\u0131a-Quir\u00b4os\n198\nJ. W. Gardner\n30\nK. A. Gardner138\nJ. Gargiulo\n56\nA. Garron\n96\nF. Garufi\n29, 5\nC. Gasbarra\n16, 17\nB. Gateley3\nV. Gayathri\n8\nG. Gemme\n54\nA. Gennai\n85\nV. Gennari\n123\nJ. George98\nR. George\n146\nO. Gerberding\n83\nL. Gergely\n199\nS. Ghonge\n57\nArchisman Ghosh\n91\nSayantan Ghosh200\nShaon Ghosh\n182\nShrobana Ghosh40, 41\nSuprovo Ghosh\n11\nTathagata Ghosh\n11\nL. Giacoppo64, 63\nJ. A. Giaime\n9, 62\nK. D. Giardina62\nD. R. Gibson189\nD. T. Gibson179\nC. Gier\n95\nP. Giri\n85, 84\nF. Gissi93\nS. Gkaitatzis\n84, 85\nJ. Glanzer9\nF. Glotin36\nJ. Godfrey76\nP. Godwin2\nN. L. Goebbels\n83\nE. Goetz\n138\nJ. Golomb2\nS. Gomez Lopez\n64, 63\nB. Goncharov\n42\nY. Gong201\nG. Gonz\u00b4alez\n9\nP. Goodarzi202\nS. Goode150\nA. W. Goodwin-Jones\n27\nM. Gosselin56\nA. S. G\u00a8ottel\n18\nR. Gouaty\n28\nD. W. Gould30\nK. Govorkova31\nS. Goyal\n1\nB. Grace\n30\nA. Grado\n203, 5\nV. Graham\n26\nA. E. Granados\n94\nM. Granata\n165\nV. Granata\n67\nS. Gras31\nP. Grassia2\nA. Gray94\nC. Gray3\nR. Gray\n26\nG. Greco49\nA. C. Green\n33, 102\nS. M. Green124\nS. R. Green\n204\nA. M. Gretarsson66\nE. M. Gretarsson66\nD. Griffith2\nW. L. Griffiths\n18\nH. L. Griggs\n57\nG. Grignani86, 49\nA. Grimaldi\n105, 106\nC. Grimaud28\nH. Grote\n18\nD. Guerra\n135\nD. Guetta\n205, 63\nG. M. Guidi\n60, 61\nA. R. Guimaraes9\nH. K. Gulati90\nF. Gulminelli\n163, 164\nA. M. Gunny31\nH. Guo\n190\nW. Guo\n27\nY. Guo\n33, 32\nAnchal Gupta\n2\nAnuradha Gupta\n206\nIsh Gupta\n7\nN. C. Gupta90\nP. Gupta33, 75\nS. K. Gupta43\nT. Gupta\n156\nN. Gupte1\nJ. Gurs83\nN. Gutierrez165\nF. Guzman\n129\nH.-Y. H140\nD. Haba172\nM. Haberland\n1\nS. Haino207\nE. D. Hall\n31\nE. Z. Hamilton96\nG. Hammond\n26\nW.-B. Han\n208\nM. Haney\n33\nJ. Hanks3\nC. Hanna7\nM. D. Hannam18\nO. A. Hannuksela\n209\nA. G. Hanselman\n127\nH. Hansen3\nJ. Hanson62\nR. Harada37\nA. R. Hardison210\nK. Haris33, 75\nT. Harmark\n132\nJ. Harms\n42, 116\nG. M. Harry\n211\nI. W. Harry\n124\nJ. Hart73\nB. Haskell92\nC.-J. Haster\n212\nJ. S. Hathaway196\nK. Haughian\n26\nH. Hayakawa48\nK. Hayama213\nR. Hayes18\nA. Heffernan\n96\nA. Heidmann\n117\nM. C. Heintze62\nJ. Heinze\n111\nJ. Heinzel31\nH. Heitmann\n47\nF. Hellman\n214\nP. Hello36\nA. F. Helmling-Cornell\n76\nG. Hemming\n56\nO. Henderson-Sapir\n108\nM. Hendry\n26\nI. S. Heng26\nE. Hennes\n33\nC. Henshaw\n57\nT. Hertog104\nM. Heurs\n40, 41\nA. L. Hewitt\n179, 215\nJ. Heyns31\nS. Higginbotham18\nS. Hild32, 33\nS. Hill26\nY. Himemoto\n216\nN. Hirata21\nC. Hirose217\nW. C. G. Ho\n218\nS. Hoang36\nS. Hochheim40, 41\nD. Hofman165\nN. A. Holland33, 102\nK. Holley-Bockelmann143\nZ. J. Holmes\n108\nD. E. Holz\n127\nL. Honet72\nC. Hong15\nJ. Hornung76\nS. Hoshino217\nJ. Hough\n26\nS. Hourihane2\nE. J. Howell\n27\nC. G. Hoy\n124\nC. A. Hrishikesh16\nH.-F. Hsieh\n140\nC. Hsiung219\nH. C. Hsu141\nW.-F. Hsu\n104\nP. Hu143\nQ. Hu\n26\nH. Y. Huang\n141\nY.-J. Huang\n7\nA. D. Huddart220\nB. Hughey66\nD. C. Y. Hui\n221\nV. Hui\n28\nS. Husa\n96\nR. Huxford7\nT. Huynh-Dinh62\nL. Iampieri\n64, 63\nG. A. Iandolo\n32\nM. Ianni17, 16\nA. Iess\n222, 85\nH. Imafuku37\nK. Inayoshi\n223\nY. Inoue141\nG. Iorio\n88\nM. H. Iqbal30\nJ. Irwin\n26\nR. Ishikawa224\nM. Isi\n180, 181\nM. A. Ismail\n141\nY. Itoh\n194, 225\nH. Iwanaga194\nM. Iwaya193\nB. R. Iyer\n20\nV. JaberianHamedan\n27\nC. Jacquet123\nP.-E. Jacquet\n117\nS. J. Jadhav226\nS. P. Jadhav\n153\nT. Jain179\nA. L. James\n2\nP. A. James118\nR. Jamshidi34\nJ. Janquart75, 33\nK. Janssens\n19, 47\nN. N. Janthalur226\nS. Jaraba\n115\nP. Jaranowski\n227\nR. Jaume\n96\nW. Javed18\nA. Jennings3\nW. Jia31\nJ. Jiang\n43\nJ. Kubisz\n228\nC. Johanson134\nG. R. Johns118\nN. A. Johnson43\nM. C. Johnston\n212\nR. Johnston26\nN. Johny40, 41\nD. H. Jones\n30\nD. I. Jones229\nR. Jones26\nS. Jose171\nP. Joshi7\nL. Ju\n27\nK. Jung\n230\nJ. Junker\n30\nV. Juste72\nT. Kajita\n231\nI. Kaku194\nC. Kalaghatgi75, 33, 232\nV. Kalogera\n78\n\n18\nM. Kamiizumi\n48\nN. Kanda\n225, 194\nS. Kandhasamy\n11\nG. Kang\n233\nJ. B. Kanner2\nS. J. Kapadia\n11\nD. P. Kapasi\n30\nS. Karat2\nC. Karathanasis\n39\nR. Kashyap\n7\nM. Kasprzack\n2\nW. Kastaun40, 41\nT. Kato193\nE. Katsavounidis31\nW. Katzman62\nR. Kaushik\n98\nK. Kawabe3\nR. Kawamoto194\nA. Kazemi94\nD. Keitel\n96\nJ. Kelley-Derzon43\nJ. Kennington\n7\nR. Kesharwani11\nJ. S. Key\n234\nR. Khadela40, 41\nS. Khadka15\nF. Y. Khalili\n103\nF. Khan\n40, 41\nI. Khan235, 35\nT. Khanam157\nM. Khursheed98\nN. M. Khusid180, 181\nW. Kiendrebeogo\n47, 236\nN. Kijbunchoo\n108\nC. Kim237\nJ. C. Kim238\nK. Kim\n239\nM. H. Kim240\nS. Kim\n221\nY.-M. Kim\n239\nC. Kimball\n78\nM. Kinley-Hanlon\n26\nM. Kinnear18\nJ. S. Kissel\n3\nS. Klimenko43\nA. M. Knee\n138\nN. Knust\n40, 41\nK. Kobayashi193\nP. Koch40, 41\nS. M. Koehlenbeck\n15\nG. Koekoek33, 32\nK. Kohri\n241, 242\nK. Kokeyama\n18\nS. Koley\n42\nP. Kolitsidou\n111\nM. Kolstein\n39\nK. Komori\n37\nA. K. H. Kong\n140\nA. Kontos\n243\nM. Korobko\n83\nR. V. Kossak40, 41\nX. Kou94\nA. Koushik19\nN. Kouvatsos\n70\nM. Kovalam27\nD. B. Kozak2\nS. L. Kranzhoff32, 33\nV. Kringel40, 41\nN. V. Krishnendu\n20\nA. Kr\u00b4olak\n244, 173\nK. Kruska40, 41\nG. Kuehn40, 41\nP. Kuijer\n33\nS. Kulkarni\n206\nA. Kulur Ramamohan\n30\nA. Kumar226\nPraveen Kumar\n126\nPrayush Kumar\n20\nRahul Kumar3\nRakesh Kumar90\nJ. Kume\n88, 89, 37\nK. Kuns\n31\nN. Kuntimaddi18\nS. Kuroyanagi\n115, 245\nN. J. Kurth9\nS. Kuwahara\n37\nK. Kwak\n230\nK. Kwan30\nJ. Kwok179\nG. Lacaille26\nP. Lagabbe28\nD. Laghi\n123\nS. Lai144\nA. H. Laity159\nM. H. Lakkis34\nE. Lalande246\nM. Lalleman\n19\nP. C. Lalremruati247\nM. Landry3\nB. B. Lane31\nR. N. Lang\n31\nJ. Lange146\nB. Lantz\n15\nA. La Rana\n63\nI. La Rosa\n96\nA. Lartaux-Vollard\n36\nP. D. Lasky\n150\nJ. Lawrence157\nM. N. Lawrence9\nM. Laxen\n62\nA. Lazzarini\n2\nC. Lazzaro88, 89\nP. Leaci\n64, 63\nY. K. Lecoeuche\n138\nH. M. Lee\n238\nH. W. Lee\n248\nK. Lee\n240\nR.-K. Lee\n140\nR. Lee31\nS. Lee\n239\nY. Lee141\nI. N. Legred2\nJ. Lehmann40, 41\nL. Lehner169\nM. Le Jean\n165\nA. Lema\u02c6\u0131tre249\nM. Lenti\n61, 250\nM. Leonardi\n105, 106, 21\nM. Lequime35\nN. Leroy\n36\nM. Lesovsky2\nN. Letendre28\nM. Lethuillier\n114\nS. E. Levin202\nY. Levin150\nK. Leyde\n69\nA. K. Y. Li2\nK. L. Li\n139\nT. G. F. Li209, 104\nX. Li\n147\nZ. Li26\nA. Lihos118\nC-Y. Lin\n251\nC.-Y. Lin141\nE. T. Lin\n140\nF. Lin141\nH. Lin141\nL. C.-C. Lin\n139\nY.-C. Lin\n140\nF. Linde232, 33\nS. D. Linker197\nT. B. Littenberg252\nA. Liu\n209\nG. C. Liu\n219\nJian Liu\n27\nF. Llamas Villarreal160\nJ. Llobera-Querol\n96\nR. K. L. Lo\n137\nJ.-P. Locquet104\nL. T. London70, 31, 99\nA. Longo\n60, 61\nD. Lopez\n113\nM. Lopez Portilla75\nM. Lorenzini\n16, 17\nA. Lorenzo-Medina\n126\nV. Loriette36\nM. Lormand62\nG. Losurdo\n85\nT. P. Lott IV\n57\nJ. D. Lough\n40, 41\nH. A. Loughlin31\nC. O. Lousto\n196\nM. J. Lowry118\nN. Lu\n30\nH. L\u00a8uck41, 40, 41\nD. Lumaca\n17\nA. P. Lundgren124\nA. W. Lussier\n246\nL.-T. Ma\n140\nS. Ma169\nM. Ma\u2019arif\n141\nR. Macas\n124\nA. Macedo\n52\nM. MacInnis31\nR. R. Maciy40, 41\nD. M. Macleod\n18\nI. A. O. MacMillan\n2\nA. Macquet\n36\nD. Macri31\nK. Maeda177\nS. Maenaut\n104\nI. Maga\u02dcna Hernandez8\nS. S. Magare11\nC. Magazz`u\n85\nR. M. Magee\n2\nE. Maggio\n1\nR. Maggiore33, 102\nM. Magnozzi\n54, 55\nM. Mahesh83\nS. Mahesh253\nM. Maini159\nS. Majhi11\nE. Majorana64, 63\nC. N. Makarem2\nE. Makelele73\nJ. A. Malaquias-Reis14\nU. Mali\n178\nS. Maliakal2\nA. Malik98\nN. Man47\nV. Mandic\n94\nV. Mangano\n63, 64\nB. Mannix76\nG. L. Mansell\n77, 31\nG. Mansingh211\nM. Manske\n8\nM. Mantovani\n56\nM. Mapelli\n88, 89, 254\nF. Marchesoni50, 49, 255\nD. Mar\u00b4\u0131n Pina\n38, 79, 256\nF. Marion\n28\nS. M\u00b4arka\n158\nZ. M\u00b4arka\n158\nA. S. Markosyan15\nA. Markowitz2\nE. Maros2\nS. Marsat\n123\nF. Martelli\n60, 61\nI. W. Martin\n26\nR. M. Martin\n182\nB. B. Martinez129\nM. Martinez39, 257\nV. Martinez\n125\nA. Martini105, 106\nK. Martinovic70\nJ. C. Martins\n14\nD. V. Martynov111\nE. J. Marx31\nL. Massaro32, 33\nA. Masserot28\nM. Masso-Reid\n26\nM. Mastrodicasa63, 64\nS. Mastrogiovanni\n63\nT. Matcovich49\nM. Matiushechkina\n40, 41\nM. Matsuyama194\nN. Mavalvala\n31\nN. Maxwell3\nG. McCarrol62\nR. McCarthy3\nS. McCormick62\nL. McCuller\n2\nS. McEachin118\nC. McElhenny118\nG. I. McGhee26\nJ. McGinn26\nK. B. M. McGowan143\nJ. McIver\n138\nA. McLeod\n27\nT. McRae30\nD. Meacher\n8\nQ. Meijer75\nA. Melatos130\nS. Mellaerts\n104\nA. Menendez-Vazquez\n39\nC. S. Menoni\n101\nF. Mera3\nR. A. Mercer\n8\nL. Mereni165\nK. Merfeld157\nE. L. Merilh62\nJ. R. M\u00b4erou\n96\nJ. D. Merritt76\nM. Merzougui47\nC. Messenger\n26\nC. Messick8\nM. Meyer-Conde\n194\nF. Meylahn\n40, 41\nA. Mhaske11\nA. Miani\n105, 106\nH. Miao258\nI. Michaloliakos\n43\nC. Michel\n165\nY. Michimura\n2, 37\nH. Middleton\n111\nA. L. Miller\n33\nS. Miller2\nM. Millhouse\n57\nE. Milotti\n183, 45\nV. Milotti\n88\nY. Minenkov17\nN. Mio37\nLl. M. Mir\n39\nL. Mirasola\n259, 63\nM. Miravet-Ten\u00b4es\n135\nC.-A. Miritescu\n39\nA. K. Mishra20\nA. Mishra11\nC. Mishra\n171\nT. Mishra\n43\nA. L. Mitchell33, 102\nJ. G. Mitchell66\nS. Mitra\n11\nV. P. Mitrofanov\n103\nR. Mittleman31\nO. Miyakawa\n48\nS. Miyamoto193\nS. Miyoki\n48\nG. Mo\n31\nL. Mobilia60, 61\nS. R. P. Mohapatra2\nS. R. Mohite\n7\nM. Molina-Ruiz\n214\nC. Mondal163\nM. Mondin197\nM. Montani60, 61\nC. J. Moore179\nD. Moraru3\nA. More\n11\nS. More\n11\nG. Moreno3\nC. Morgan18\nS. Morisaki\n37, 193\nY. Moriwaki\n177\nG. Morras\n115\nA. Moscatello\n88\nP. Mourier\n96\nB. Mours\n65\nC. M. Mow-Lowry\n33, 102\nF. Muciaccia\n64, 63\nArunava Mukherjee260\nD. Mukherjee\n252\nSamanwaya Mukherjee11\nSoma Mukherjee160\nSubroto Mukherjee90\nSuvodip Mukherjee\n261, 169, 99\nN. Mukund\n31\nA. Mullavey62\nJ. Munch108\nJ. Mundi211\nC. L. Mungioli27\nW. R. Munn Oberg262\nY. Murakami193\nM. Murakoshi224\nP. G. Murray\n26\nS. Muusse30\nD. Nabari\n105, 106\nS. L. Nadji40, 41\nA. Nagar23, 263\nN. Nagarajan\n26\nK. N. Nagler66\nK. Nakagaki48\nK. Nakamura\n21\nH. Nakano\n264\nM. Nakano2\nD. Nandi9\nV. Napolano56\nP. Narayan206\nI. Nardecchia\n17\nH. Narola75\nL. Naticchioni\n63\nR. K. Nayak\n247\nJ. Neilson93, 107\nA. Nelson129\nT. J. N. Nelson62\nM. Nery40, 41\nA. Neunzert\n3\nS. Ng52\nL. Nguyen Quynh\n265\nS. A. Nichols9\nA. B. Nielsen\n266\nG. Nieradka92\nA. Niko\n141\nY. Nishino21, 37\nA. Nishizawa\n267\nS. Nissanke99, 33\nE. Nitoglia\n114\nW. Niu7\nF. Nocera56\nM. Norman18\nC. North18\nJ. Novak\n109, 268, 269, 270\nJ. F. Nu\u02dcno Siles\n115\nL. K. Nuttall\n124\nK. Obayashi224\n\n19\nJ. Oberling\n3\nJ. O\u2019Dell220\nM. Oertel\n109, 268, 269, 271, 270\nA. Offermans104\nG. Oganesyan42, 116\nJ. J. Oh272\nK. Oh\n221\nT. O\u2019Hanlon62\nM. Ohashi\n48\nM. Ohkawa\n217\nF. Ohme\n40, 41\nA. S. Oliveira\n158\nR. Oliveri\n109, 268, 269\nB. O\u2019Neal118\nK. Oohara\n273, 274\nB. O\u2019Reilly\n62\nN. D. Ormsby118\nM. Orselli\n49, 86\nR. O\u2019Shaughnessy\n196\nS. O\u2019Shea26\nY. Oshima\n37\nS. Oshino\n48\nS. Ossokine\n1\nC. Osthelder2\nI. Ota\n9\nD. J. Ottaway\n108\nA. Ouzriat114\nH. Overmier62\nB. J. Owen\n157\nA. E. Pace7\nR. Pagano\n9\nM. A. Page\n21\nA. Pai\n200\nA. Pal275\nS. Pal\n247\nM. A. Palaia\n85, 84\nM. P\u00b4alfi191\nP. P. Palma64, 16, 17\nC. Palomba\n63\nP. Palud\n69\nH. Pan140\nJ. Pan27\nK. C. Pan\n140\nR. Panai\n259, 88\nP. K. Panda226\nS. Pandey7\nL. Panebianco60, 61\nP. T. H. Pang33, 75\nF. Pannarale\n64, 63\nK. A. Pannone52\nB. C. Pant98\nF. H. Panther27\nF. Paoletti\n85\nA. Paolone63, 276\nE. E. Papalexakis202\nL. Papalini\n85, 84\nG. Papigkiotis277\nA. Paquis36\nA. Parisi\n86, 49\nB.-J. Park239\nJ. Park\n278\nW. Parker\n62\nG. Pascale40, 41\nD. Pascucci\n91\nA. Pasqualetti56\nR. Passaquieti\n84, 85\nL. Passenger150\nD. Passuello85\nO. Patane\n3\nD. Pathak11\nM. Pathak108\nA. Patra18\nB. Patricelli\n84, 85\nA. S. Patron9\nK. Paul\n171\nS. Paul\n76\nE. Payne\n2\nT. Pearce18\nM. Pedraza2\nR. Pegna\n85\nA. Pele\n2\nF. E. Pe\u02dcna Arellano\n46\nS. Penn\n262\nM. D. Penuliar52\nA. Perego\n105, 106\nZ. Pereira134\nJ. J. Perez43\nC. P\u00b4erigois\n152, 89, 88\nG. Perna\n88\nA. Perreca\n105, 106\nJ. Perret69\nS. Perri`es\n114\nJ. W. Perry33, 102\nD. Pesios277\nS. Petracca168\nC. Petrillo86\nH. P. Pfeiffer\n1\nH. Pham62\nK. A. Pham\n94\nK. S. Phukon\n111, 33, 232\nH. Phurailatpam209\nM. Piarulli123\nL. Piccari\n64, 63\nO. J. Piccinni\n39\nM. Pichot\n47\nM. Piendibene\n84, 85\nF. Piergiovanni\n60, 61\nL. Pierini\n63\nG. Pierra\n114\nV. Pierro\n93, 107\nM. Pietrzak92\nM. Pillas\n47\nF. Pilo\n85\nL. Pinard165\nI. M. Pinto\n93, 107, 279, 29\nM. Pinto56\nB. J. Piotrzkowski\n8\nM. Pirello3\nM. D. Pitkin\n179, 215\nA. Placidi\n61\nE. Placidi\n64, 63\nM. L. Planas\n96\nW. Plastino\n280, 17\nR. Poggiani\n84, 85\nE. Polini\n28\nL. Pompili\n1\nJ. Poon209\nE. Porcelli33\nE. K. Porter69\nC. Posnansky7\nR. Poulton\n56\nJ. Powell\n153\nM. Pracchia113\nB. K. Pradhan\n11\nT. Pradier65\nA. K. Prajapati90\nK. Prasai15\nR. Prasanna226\nP. Prasia11\nG. Pratten\n111\nG. Principe\n183, 45\nM. Principe168, 93, 279, 107\nG. A. Prodi\n105, 106\nL. Prokhorov\n111\nP. Prosposito16, 17\nA. Puecher33, 75\nJ. Pullin\n9\nM. Punturo\n49\nP. Puppo63\nM. P\u00a8urrer\n159\nH. Qi\n12\nJ. Qin\n30\nG. Qu\u00b4em\u00b4ener\n164, 109\nV. Quetschke160\nC. Quigley18\nP. J. Quinonez66\nR. Quitzow-James100\nF. J. Raab\n3\nS. S. Raabith9\nG. Raaijmakers99, 33\nS. Raja98\nC. Rajan98\nB. Rajbhandari\n196\nK. E. Ramirez\n62\nF. A. Ramis Vidal\n96\nA. Ramos-Buades\n33\nD. Rana11\nS. Ranjan\n57\nK. Ransom62\nP. Rapagnani\n64, 63\nB. Ratto66\nS. Rawat94\nA. Ray\n8\nV. Raymond\n18\nM. Razzano\n84, 85\nJ. Read52\nM. Recaman Payo104\nT. Regimbau28\nL. Rei\n54\nS. Reid95\nD. H. Reitze\n2\nP. Relton\n18\nA. I. Renzini2\nP. Rettegno\n23\nB. Revenu\n281, 69\nR. Reyes197\nA. S. Rezaei\n63, 64\nF. Ricci64, 63\nM. Ricci\n63, 64\nA. Ricciardone\n84, 85\nJ. W. Richardson\n202\nM. Richardson108\nA. Rijal66\nK. Riles\n87\nH. K. Riley18\nS. Rinaldi\n254, 88\nJ. Rittmeyer83\nC. Robertson220\nF. Robinet36\nM. Robinson3\nA. Rocchi\n17\nL. Rolland\n28\nJ. G. Rollins\n2\nA. E. Romano\n282\nR. Romano\n4, 5\nA. Romero\n175\nI. M. Romero-Shaw179\nJ. H. Romie62\nS. Ronchini\n42, 116\nT. J. Roocke\n108\nL. Rosa5, 29\nT. J. Rosauer202\nC. A. Rose8\nD. Rosi\u00b4nska\n119\nM. P. Ross\n51\nM. Rossello\n96\nS. Rowan\n26\nS. K. Roy\n180, 181\nS. Roy75\nD. Rozza\n121, 122\nP. Ruggi56\nN. Ruhama230\nE. Ruiz Morales\n283, 115\nK. Ruiz-Rocha143\nS. Sachdev\n57\nT. Sadecki3\nJ. Sadiq\n126\nP. Saffarieh33, 102\nM. R. Sah\n261\nS. S. Saha140\nS. Saha\n140\nT. Sainrat65\nS. Sajith Menon\n205, 64, 63\nK. Sakai284\nM. Sakellariadou\n70\nS. Sakon\n7\nO. S. Salafia\n154, 122, 121\nF. Salces-Carcoba\n2\nL. Salconi56\nM. Saleem\n94\nF. Salemi\n64, 63\nM. Sall\u00b4e\n33\nS. Salvador\n164, 163, 109\nA. Sanchez3\nE. J. Sanchez2\nJ. H. Sanchez\n78\nL. E. Sanchez2\nN. Sanchis-Gual\n135\nJ. R. Sanders210\nE. M. S\u00a8anger\n1\nF. Santoliquido42\nT. R. Saravanan11\nN. Sarin150\nS. Sasaoka\n172\nA. Sasli\n277\nP. Sassi\n49, 86\nB. Sassolas\n165\nH. Satari27, 18\nR. Sato217\nY. Sato177\nO. Sauter\n43\nR. L. Savage\n3\nT. Sawada\n48\nH. L. Sawant11\nS. Sayah28\nV. Scacco16, 17\nD. Schaetzl2\nM. Scheel147\nA. Schiebelbein178\nM. G. Schiworski\n108\nP. Schmidt\n111\nS. Schmidt\n75\nR. Schnabel\n83\nM. Schneewind40, 41\nR. M. S. Schofield76\nK. Schouteden104\nB. W. Schulte40, 41\nB. F. Schutz18, 40, 41\nE. Schwartz\n18\nM. Scialpi285\nJ. Scott\n26\nS. M. Scott\n30\nT. C. Seetharamu26\nM. Seglar-Arroyo\n39\nY. Sekiguchi\n286\nD. Sellers62\nA. S. Sengupta\n287\nD. Sentenac56\nE. G. Seo\n26\nJ. W. Seo\n104\nV. Sequino29, 5\nM. Serra\n63\nG. Servignat\n268\nA. Sevrin175\nT. Shaffer3\nU. S. Shah\n57\nM. A. Shaikh\n238\nL. Shao\n223\nA. K. Sharma20\nP. Sharma98\nS. Sharma-Chaudhary100\nM. R. Shaw18\nP. Shawhan\n120\nN. S. Shcheblanov\n288, 249\nE. Sheridan143\nY. Shikano\n289, 290\nM. Shikauchi37\nK. Shimode\n48\nH. Shinkai\n291\nJ. Shiota224\nD. H. Shoemaker\n31\nD. M. Shoemaker\n146\nR. W. Short3\nS. ShyamSundar98\nA. Sider34\nH. Siegel\n180, 181\nM. Sieniawska10\nD. Sigg\n3\nL. Silenzi\n49, 50\nM. Simmonds108\nL. P. Singer\n128\nA. Singh206\nD. Singh\n7\nM. K. Singh\n20\nS. Singh21, 59\nA. Singha\n32, 33\nA. M. Sintes\n96\nV. Sipala162, 131\nV. Skliris\n18\nB. J. J. Slagmolen\n30\nT. J. Slaven-Blair27\nJ. Smetana111\nJ. R. Smith\n52\nL. Smith\n26\nR. J. E. Smith\n150\nW. J. Smith\n143\nJ. Soldateschi\n250, 292, 61\nK. Somiya\n172\nI. Song\n140\nK. Soni\n11\nS. Soni\n31\nV. Sordini114\nF. Sorrentino54\nN. Sorrentino\n84, 85\nH. Sotani\n293\nR. Soulard47\nA. Southgate18\nV. Spagnuolo32, 33\nA. P. Spencer\n26\nM. Spera\n45, 294\nP. Spinicelli56\nJ. B. Spoon9\nC. A. Sprague265\nA. K. Srivastava90\nF. Stachurski\n26\nD. A. Steer\n69\nJ. Steinlechner32, 33\nS. Steinlechner\n32, 33\nN. Stergioulas\n277\nP. Stevens36\nM. StPierre159\nG. Stratta\n295, 133, 63, 296\nM. D. Strong9\nA. Strunk3\nR. Sturani297\nA. L. Stuver\n53\nM. Suchenek92\nS. Sudhagar\n92\nN. Sueltmann83\nL. Suleiman\n52\nK. D. Sullivan9\nL. Sun\n30\nS. Sunil90\nJ. Suresh10\nP. J. Sutton\n18\nT. Suzuki\n217\nY. Suzuki224\nB. L. Swinkels\n33\nA. Syx65\nM. J. Szczepa\u00b4nczyk\n298, 43\nP. Szewczyk\n119\nM. Tacca\n33\nH. Tagoshi\n193\nS. C. Tait\n2\nH. Takahashi\n299\nR. Takahashi\n21\n\n20\nA. Takamori\n37\nT. Takase48\nK. Takatani194\nH. Takeda\n300\nK. Takeshita172\nC. Talbot127\nM. Tamaki193\nN. Tamanini\n123\nD. Tanabe141\nK. Tanaka48\nS. J. Tanaka\n224\nT. Tanaka\n300\nD. Tang27\nS. Tanioka\n77\nD. B. Tanner43\nL. Tao\n43\nR. D. Tapia7\nE. N. Tapia San Mart\u00b4\u0131n\n33\nR. Tarafder2\nC. Taranto16, 17, 64\nA. Taruya\n301\nJ. D. Tasson\n176\nM. Teloi34\nR. Tenorio\n96\nH. Themann197\nA. Theodoropoulos135\nM. P. Thirugnanasambandam11\nL. M. Thomas\n2\nM. Thomas62\nP. Thomas3\nJ. E. Thompson\n147\nS. R. Thondapu98\nK. A. Thorne62\nE. Thrane150\nJ. Tissino\n42\nA. Tiwari11\nP. Tiwari42\nS. Tiwari\n198\nV. Tiwari\n111\nM. R. Todd77\nA. M. Toivonen\n94\nK. Toland\n26\nA. E. Tolley\n124\nT. Tomaru\n21\nK. Tomita194\nT. Tomura\n48\nC. Tong-Yu141\nA. Toriyama224\nN. Toropov\n111\nA. Torres-Forn\u00b4e\n135, 136\nC. I. Torrie2\nM. Toscani\n123\nI. Tosta e Melo\n302\nE. Tournefier\n28\nA. Trapananti\n50, 49\nF. Travasso\n50, 49\nG. Traylor62\nM. Trevor120\nM. C. Tringali\n56\nA. Tripathee\n87\nG. Troian183\nL. Troiano303, 107\nA. Trovato\n183, 45\nL. Trozzo5\nR. J. Trudeau2\nT. T. L. Tsang\n18\nR. Tso147, \u2217\nS. Tsuchida\n304\nL. Tsukada7\nT. Tsutsui\n37\nK. Turbang\n175, 19\nM. Turconi\n47\nC. Turski91\nH. Ubach\n38, 79\nT. Uchiyama\n48\nR. P. Udall\n2\nT. Uehara\n305\nM. Uematsu194\nK. Ueno\n37\nS. Ueno224\nV. Undheim\n266\nT. Ushiba\n48\nM. Vacatello\n85, 84\nH. Vahlbruch\n40, 41\nN. Vaidya\n2\nG. Vajente\n2\nA. Vajpeyi150\nG. Valdes\n129\nJ. Valencia\n96\nM. Valentini\n206, 102, 33\nS. A. Vallejo-Pe\u02dcna\n282\nS. Vallero23\nV. Valsan\n8\nN. van Bakel33\nM. van Beuzekom\n33\nM. van Dael\n33, 306\nJ. F. J. van den Brand\n32, 102, 33\nC. Van Den Broeck75, 33\nD. C. Vander-Hyde77\nM. van der Sluys\n33, 75\nA. Van de Walle36\nJ. van Dongen\n33, 102\nK. Vandra53\nH. van Haevermaet\n19\nJ. V. van Heijningen\n33, 102\nP. Van Hove\n65\nM. VanKeuren73\nJ. Vanosky2\nM. H. P. M. van Putten\n13\nZ. van Ranst\n32, 33\nN. van Remortel\n19\nM. Vardaro32, 33\nA. F. Vargas130\nJ. J. Varghese66\nV. Varma\n134\nM. Vas\u00b4uth81, \u2020\nA. Vecchio\n111\nG. Vedovato89\nJ. Veitch\n26\nP. J. Veitch\n108\nS. Venikoudis10\nJ. Venneberg\n40, 41\nP. Verdier\n114\nD. Verkindt\n28\nB. Verma134\nP. Verma173\nY. Verma\n98\nS. M. Vermeulen\n2\nF. Vetrano60\nA. Veutro\n63, 64\nA. M. Vibhute\n3\nA. Vicer\u00b4e\n60, 61\nS. Vidyant77\nA. D. Viets\n82\nA. Vijaykumar\n178\nA. Vilkha196\nV. Villa-Ortega\n126\nE. T. Vincent\n57\nJ.-Y. Vinet47\nS. Viret114\nA. Virtuoso\n183, 45\nS. Vitale\n31\nA. Vives76\nH. Vocca\n86, 49\nD. Voigt\n83\nE. R. G. von Reis3\nJ. S. A. von Wrangel40, 41\nS. P. Vyatchanin\n103\nL. E. Wade73\nM. Wade\n73\nK. J. Wagner\n196\nA. Wajid54, 55\nM. Walker118\nG. S. Wallace95\nL. Wallace2\nH. Wang\n37\nJ. Z. Wang87\nW. H. Wang160\nZ. Wang141\nG. Waratkar\n200\nJ. Warner3\nM. Was\n28\nT. Washimi\n21\nN. Y. Washington2\nD. Watarai37\nK. E. Wayt73\nB. R. Weaver18\nB. Weaver3\nC. R. Weaving124\nS. A. Webster26\nM. Weinert40, 41\nA. J. Weinstein\n2\nR. Weiss31\nF. Wellmann40, 41\nL. Wen27\nP. We\u00dfels40, 41\nK. Wette\n30\nJ. T. Whelan\n196\nB. F. Whiting\n43\nC. Whittle\n2\nJ. B. Wildberger1\nO. S. Wilk73\nD. Wilken\n40, 41, 41\nA. T. Wilkin202\nD. J. Willadsen82\nK. Willetts18\nD. Williams\n26\nM. J. Williams\n124\nN. S. Williams111\nJ. L. Willis\n2\nB. Willke\n41, 40, 41\nM. Wils\n104\nJ. Winterflood27\nC. C. Wipf2\nG. Woan\n26\nJ. Woehler32, 33\nJ. K. Wofford\n196\nN. E. Wolfe31\nH. T. Wong\n141\nH. W. Y. Wong\n209\nI. C. F. Wong\n209\nJ. L. Wright30\nM. Wright\n26\nC. Wu\n140\nD. S. Wu\n40, 41\nH. Wu\n140\nE. Wuchner52\nD. M. Wysocki\n8\nV. A. Xu\n31\nY. Xu\n198\nN. Yadav\n92\nH. Yamamoto\n2\nK. Yamamoto\n177\nT. S. Yamamoto\n245\nT. Yamamoto\n48\nS. Yamamura193\nR. Yamazaki\n224\nS. Yan15\nT. Yan111\nF. W. Yang\n190\nF. Yang158\nK. Z. Yang\n94\nY. Yang\n144\nZ. Yarbrough\n9\nH. Yasui48\nS.-W. Yeh140\nA. B. Yelikar\n196\nX. Yin31\nJ. Yokoyama\n307, 37\nT. Yokozawa48\nJ. Yoo\n148\nH. Yu\n147\nS. Yuan27\nH. Yuzurihara\n48\nA. Zadro\u02d9zny173\nM. Zanolin66\nM. Zeeshan\n196\nT. Zelenova56\nJ.-P. Zendri89\nM. Zeoli113, 10\nM. Zerrad35\nM. Zevin\n78\nA. C. Zhang158\nL. Zhang2\nR. Zhang\n43\nT. Zhang111\nY. Zhang\n30\nC. Zhao\n27\nYue Zhao190\nYuhang Zhao\n69\nY. Zheng\n100\nH. Zhong\n94\nR. Zhou214\nX.-J. Zhu\n308\nZ.-H. Zhu\n308, 201\nM. E. Zucker31, 2\nJ. Zweizig\n2\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3LIGO Hanford Observatory, Richland, WA 99352, USA\n4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n5INFN, Sezione di Napoli, I-80126 Napoli, Italy\n6University of Warwick, Coventry CV4 7AL, United Kingdom\n7The Pennsylvania State University, University Park, PA 16802, USA\n8University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n9Louisiana State University, Baton Rouge, LA 70803, USA\n10Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n11Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n12Queen Mary University of London, London E1 4NS, United Kingdom\n13Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n14Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n15Stanford University, Stanford, CA 94305, USA\n16Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n17INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n18Cardiff University, Cardiff CF24 3AA, United Kingdom\n19Universiteit Antwerpen, 2000 Antwerpen, Belgium\n\n21\n20International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n21Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n22Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n23INFN Sezione di Torino, I-10125 Torino, Italy\n24Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n25Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n26SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n27OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n28Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n29Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n30OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n31LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n32Maastricht University, 6200 MD Maastricht, Netherlands\n33Nikhef, 1098 XG Amsterdam, Netherlands\n34Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n35Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n36Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n37University of Tokyo, Tokyo, 113-0033, Japan.\n38Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n39Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n40Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n41Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n42Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n43University of Florida, Gainesville, FL 32611, USA\n44Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n45INFN, Sezione di Trieste, I-34127 Trieste, Italy\n46Tecnol\u00b4ogico de Monterrey Campus Guadalajara, 45201 Zapopan, Jalisco, Mexico\n47Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n48Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu\n506-1205, Japan\n49INFN, Sezione di Perugia, I-06123 Perugia, Italy\n50Universit`a di Camerino, I-62032 Camerino, Italy\n51University of Washington, Seattle, WA 98195, USA\n52California State University Fullerton, Fullerton, CA 92831, USA\n53Villanova University, Villanova, PA 19085, USA\n54INFN, Sezione di Genova, I-16146 Genova, Italy\n55Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n56European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62LIGO Livingston Observatory, Livingston, LA 70754, USA\n63INFN, Sezione di Roma, I-00185 Roma, Italy\n64Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n65Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n66Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n67Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n68Bar-Ilan University, Ramat Gan, 5290002, Israel\n69Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n70King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n71Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n72Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n73Kenyon College, Gambier, OH 43022, USA\n74International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n\n22\n75Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n76University of Oregon, Eugene, OR 97403, USA\n77Syracuse University, Syracuse, NY 13244, USA\n78Northwestern University, Evanston, IL 60208, USA\n79Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n80Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n81HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n82Concordia University Wisconsin, Mequon, WI 53097, USA\n83Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n84Universit`a di Pisa, I-56127 Pisa, Italy\n85INFN, Sezione di Pisa, I-56127 Pisa, Italy\n86Universit`a di Perugia, I-06123 Perugia, Italy\n87University of Michigan, Ann Arbor, MI 48109, USA\n88Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n89INFN, Sezione di Padova, I-35131 Padova, Italy\n90Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n91Universiteit Gent, B-9000 Gent, Belgium\n92Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n93Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n94University of Minnesota, Minneapolis, MN 55455, USA\n95SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n96IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n97Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n98RRCAT, Indore, Madhya Pradesh 452013, India\n99GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n100Missouri University of Science and Technology, Rolla, MO 65409, USA\n101Colorado State University, Fort Collins, CO 80523, USA\n102Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n103Lomonosov Moscow State University, Moscow 119991, Russia\n104Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n105Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n106INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n107INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n108OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n109Centre national de la recherche scientifique, 75016 Paris, France\n110Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n111University of Birmingham, Birmingham B15 2TT, United Kingdom\n112Washington State University, Pullman, WA 99164, USA\n113Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n114Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n115Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n116INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n117Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n118Christopher Newport University, Newport News, VA 23606, USA\n119Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n120University of Maryland, College Park, MD 20742, USA\n121Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n122INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n123L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n124University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n125Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n126IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n127University of Chicago, Chicago, IL 60637, USA\n128NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n129Texas A&M University, College Station, TX 77843, USA\n130OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n\n23\n131INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n132Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n133Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n136Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n137Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n138University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n139Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n140National Tsing Hua University, Hsinchu City 30013, Taiwan\n141National Central University, Taoyuan City 320317, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n145Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n146University of Texas, Austin, TX 78712, USA\n147CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n148Cornell University, Ithaca, NY 14850, USA\n149Northeastern University, Boston, MA 02115, USA\n150OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n151Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n153OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n154INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n155Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n156Montana State University, Bozeman, MT 59717, USA\n157Texas Tech University, Lubbock, TX 79409, USA\n158Columbia University, New York, NY 10027, USA\n159University of Rhode Island, Kingston, RI 02881, USA\n160The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n161Chennai Mathematical Institute, Chennai 603103, India\n162Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n163Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n164Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n165Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n166Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n167INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n168University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n169Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n170Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n171Indian Institute of Technology Madras, Chennai 600036, India\n172Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n173National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n174Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n175Vrije Universiteit Brussel, 1050 Brussel, Belgium\n176Carleton College, Northfield, MN 55057, USA\n177Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n178Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n179University of Cambridge, Cambridge CB2 1TN, United Kingdom\n180Stony Brook University, Stony Brook, NY 11794, USA\n181Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n182Montclair State University, Montclair, NJ 07043, USA\n183Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n184HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n185Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n186CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n\n24\n187Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n188Western Washington University, Bellingham, WA 98225, USA\n189SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n190The University of Utah, Salt Lake City, UT 84112, USA\n191E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n192Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n193Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n194Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n195Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n196Rochester Institute of Technology, Rochester, NY 14623, USA\n197California State University, Los Angeles, Los Angeles, CA 90032, USA\n198University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n199University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n200Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n201School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n202University of California, Riverside, Riverside, CA 92521, USA\n203INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n204University of Nottingham NG7 2RD, UK\n205Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n206The University of Mississippi, University, MS 38677, USA\n207Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n208Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n209The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n210Marquette University, Milwaukee, WI 53233, USA\n211American University, Washington, DC 20016, USA\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n214University of California, Berkeley, CA 94720, USA\n215University of Lancaster, Lancaster LA1 4YW, United Kingdom\n216College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n217Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n218Department of Physics and Astronomy, Haverford College, 370 Lancaster Avenue, Haverford, PA 19041, USA\n219Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n220Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n221Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n222Scuola Normale Superiore, I-56126 Pisa, Italy\n223Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n224Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n225Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n226Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n227University of Bia lystok, 15-424 Bia lystok, Poland\n228Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n229University of Southampton, Southampton SO17 1BJ, United Kingdom\n230Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of\nKorea\n231Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n232Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n233Chung-Ang University, Seoul 06974, Republic of Korea\n234University of Washington Bothell, Bothell, WA 98011, USA\n235Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n236Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n237Ewha Womans University, Seoul 03760, Republic of Korea\n238Seoul National University, Seoul 08826, Republic of Korea\n\n25\n239Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n240Sungkyunkwan University, Seoul 03063, Republic of Korea\n241Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n242Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n243Bard College, Annandale-On-Hudson, NY 12504, USA\n244Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n245Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n246Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n247Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n248Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n249NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n250Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n251National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science Park,\nHsinchu City 30076, Taiwan\n252NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n253West Virginia University, Morgantown, WV 26506, USA\n254Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n255School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n256Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n257Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n258Tsinghua University, Beijing 100084, China\n259INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n260Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n261Tata Institute of Fundamental Research, Mumbai 400005, India\n262Hobart and William Smith Colleges, Geneva, NY 14456, USA\n263Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n264Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n265Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n266University of Stavanger, 4021 Stavanger, Norway\n267Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 903-0213, Japan\n268Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n269Observatoire de Paris, 75014 Paris, France\n270Universit\u00b4e PSL, 75006 Paris, France\n271Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n272National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n273Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n274Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122, Japan\n275CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n276Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n277Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n278Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n279Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n280Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n281Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n282Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n283Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n284Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n285Universit`a Degli Studi Di Ferrara, Via Savonarola, 9, 44121 Ferrara FE, Italy\n286Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n287Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n288Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n289Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n290Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n\n26\n291Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n292INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n293iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n294Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n295Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n296INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n297Universidade Estadual Paulista, 01140-070 S\u02dcao Paulo, Brazil\n298Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n299Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n300Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n301Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n302University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n303Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n304National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n305Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n306Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n307Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City,\nChiba 277-8583, Japan\n308Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n", "Draft version July 30, 2024\nTypeset using LATEX twocolumn style in AASTeX631\nObservation of Gravitational Waves from the Coalescence\nof a 2.5\u20134.5 M\u2299Compact Object and a Neutron Star\nA. G. Abac,1 R. Abbott,2 I. Abouelfettouh,3 F. Acernese,4, 5 K. Ackley,6 S. Adhicary,7 N. Adhikari,8\nR. X. Adhikari,2 V. K. Adkins,9 D. Agarwal,10, 11 M. Agathos,12 M. Aghaei Abchouyeh,13 O. D. Aguiar,14\nI. Aguilar,15 L. Aiello,16, 17, 18 A. Ain,19 P. Ajith,20 S. Akc\u00b8ay,21 T. Akutsu,22, 23 S. Albanesi,24, 25, 26 R. A. Alfaidi,27\nA. Al-Jodah,28 C. All\u00b4en\u00b4e,29 A. Allocca,30, 5 S. Al-Shammari,18 P. A. Altin,31 S. Alvarez-Lopez,32 A. Amato,33, 34\nL. Amez-Droz,35 A. Amorosi,35 C. Amra,36 A. Ananyeva,2 S. B. Anderson,2 W. G. Anderson,2 M. Andia,37\nM. Ando,38 T. Andrade,39 N. Andres,29 M. Andr\u00b4es-Carcasona,40 T. Andri\u00b4c,41, 42, 1, 43 J. Anglin,44 S. Ansoldi,45, 46\nJ. M. Antelis,47 S. Antier,48 M. Aoumi,49 E. Z. Appavuravther,50, 51 S. Appert,2 S. K. Apple,52 K. Arai,2\nA. Araya,38 M. C. Araya,2 J. S. Areeda,53 L. Argianas,54 N. Aritomi,3 F. Armato,55, 56 N. Arnaud,37, 57\nM. Arogeti,58 S. M. Aronson,9 K. G. Arun,59 G. Ashton,60 Y. Aso,22, 61 M. Assiduo,62, 63 S. Assis de Souza Melo,57\nS. M. Aston,64 P. Astone,65 F. Attadio,66, 65 F. Aubin,67 K. AultONeal,68 G. Avallone,69 D. Azrad,70 S. Babak,71\nF. Badaracco,55 C. Badger,72 S. Bae,73 S. Bagnasco,24 E. Bagui,74 J. G. Baier,75 L. Baiotti,76 R. Bajpai,22\nT. Baka,77 M. Ball,78 G. Ballardin,57 S. W. Ballmer,79 S. Banagiri,80 B. Banerjee,43 D. Bankar,11 P. Baral,8\nJ. C. Barayoga,2 B. C. Barish,2 D. Barker,3 P. Barneo,39, 81 F. Barone,82, 5 B. Barr,27 L. Barsotti,32\nM. Barsuglia,71 D. Barta,83 A. M. Bartoletti,84 M. A. Barton,27 I. Bartos,44 S. Basak,20 A. Basalaev,85\nR. Bassiri,15 A. Basti,86, 87 D. E. Bates,18 M. Bawaj,88, 50 P. Baxi,89 J. C. Bayley,27 A. C. Baylor,8\nP. A. Baynard II,58 M. Bazzan,90, 91 V. M. Bedakihale,92 F. Beirnaert,93 M. Bejger,94 D. Belardinelli,17\nA. S. Bell,27 V. Benedetto,95 W. Benoit,96 I. Bentara,97 J. D. Bentley,85 M. Ben Yaala,98 S. Bera,99\nM. Berbel,100 F. Bergamin,41, 42 B. K. Berger,15 S. Bernuzzi,25 M. Beroiz,2 C. P. L. Berry,27 D. Bersanetti,55\nA. Bertolini,34 J. Betzwieser,64 D. Beveridge,28 N. Bevins,54 R. Bhandare,101 U. Bhardwaj,102, 34 R. Bhatt,2\nD. Bhattacharjee,75, 103 S. Bhaumik,44 S. Bhowmick,104 A. Bianchi,34, 105 I. A. Bilenko,106 G. Billingsley,2\nA. Binetti,107 S. Bini,108, 109 O. Birnholtz,70 S. Biscoveanu,80 A. Bisht,42 M. Bitossi,57, 87 M.-A. Bizouard,48\nJ. K. Blackburn,2 L. A. Blagg,78 C. D. Blair,28, 64 D. G. Blair,28 F. Bobba,69, 110 N. Bode,41, 42 G. Boileau,19, 48\nM. Boldrini,66, 65 G. N. Bolingbroke,111 A. Bolliand,112, 36 L. D. Bonavena,90 R. Bondarescu,39 F. Bondu,113\nE. Bonilla,15 M. S. Bonilla,53 A. Bonino,114 R. Bonnand,29 P. Booker,41, 42 A. Borchers,41, 42 V. Boschi,87\nS. Bose,115 V. Bossilkov,64 V. Boudart,116 A. Boudon,97 A. Bozzi,57 C. Bradaschia,87 P. R. Brady,8 M. Braglia,117\nA. Branch,64 M. Branchesi,43, 118 J. Brandt,58 I. Braun,75 M. Breschi,25 T. Briant,119 A. Brillet,48\nM. Brinkmann,41, 42 P. Brockill,8 E. Brockmueller,41, 42 A. F. Brooks,2 B. C. Brown,44 D. D. Brown,111\nM. L. Brozzetti,88, 50 S. Brunett,2 G. Bruno,10 R. Bruntz,120 J. Bryant,114 F. Bucci,63 J. Buchanan,120\nO. Bulashenko,39, 81 T. Bulik,121 H. J. Bulten,34 A. Buonanno,122, 1 K. Burtnyk,3 R. Buscicchio,123, 124\nD. Buskulic,29 C. Buy,125 R. L. Byer,15 G. S. Cabourn Davies,126 G. Cabras,45, 46 R. Cabrita,10\nV. C\u00b4aceres-Barbosa,7 L. Cadonati,58 G. Cagnoli,127 C. Cahillane,79 J. Calder\u00b4on Bustillo,128 T. A. Callister,129\nE. Calloni,30, 5 J. B. Camp,130 M. Canepa,56, 55 G. Caneva Santoro,40 K. C. Cannon,38 H. Cao,111\nL. A. Capistran,131 E. Capocasa,71 E. Capote,79 G. Carapella,69, 110 F. Carbognani,57 M. Carlassara,41, 42\nJ. B. Carlin,132 M. Carpinelli,123, 133, 57 G. Carrillo,78 J. J. Carter,41, 42 G. Carullo,134 J. Casanueva Diaz,57\nC. Casentini,135, 16, 17 S. Y. Castro-Lucas,104 S. Caudill,136, 34, 77 M. Cavagli`a,103 R. Cavalieri,57 G. Cella,87\nP. Cerd\u00b4a-Dur\u00b4an,137, 138 E. Cesarini,17 W. Chaibi,48 P. Chakraborty,41, 42 S. Chalathadka Subrahmanya,85\nJ. C. L. Chan,139 M. Chan,140 K. Chandra,7 R.-J. Chang,141 S. Chao,142, 143 P. Char,116 E. L. Charlton,120\nP. Charlton,144 E. Chassande-Mottin,71 C. Chatterjee,145 Debarati Chatterjee,11 Deep Chatterjee,32\nD. Chattopadhyay,18 M. Chaturvedi,101 S. Chaty,71 K. Chatziioannou,2 A. Chen,12 A. H.-Y. Chen,146 D. Chen,147\nH. Chen,142 H. Y. Chen,148 J. Chen,32 K. H. Chen,143 Y. Chen,142 Yanbei Chen,149 Yitian Chen,150 H. P. Cheng,151\nP. Chessa,88, 50 H. T. Cheung,89 S. Y. Cheung,152 F. Chiadini,153, 110 G. Chiarini,91 R. Chierici,97 A. Chincarini,55\nM. L. Chiofalo,86, 87 A. Chiummo,5, 57 C. Chou,146 S. Choudhary,28 N. Christensen,48 S. S. Y. Chua,31 P. Chugh,152\nG. Ciani,90, 91 P. Ciecielag,94 M. Cie\u00b4slar,121 M. Cifaldi,17 R. Ciolfi,154, 91 F. Clara,3 J. A. Clark,2, 58 J. Clarke,18\nT. A. Clarke,152 P. Clearwater,155 S. Clesse,74 E. Coccia,43, 118, 40 E. Codazzo,43 P.-F. Cohadon,119 S. Colace,56\nM. Colleoni,99 C. G. Collette,35 J. Collins,64 S. Colloms,27 A. Colombo,123, 124, 156 M. Colpi,123, 124\nC. M. Compton,3 G. Connolly,78 L. Conti,91 T. R. Corbitt,9 I. Cordero-Carri\u00b4on,157 S. Corezzi,88, 50\nN. J. Cornish,158 A. Corsi,159 S. Cortese,57 C. A. Costa,14 R. Cottingham,64 M. W. Coughlin,96 A. Couineaux,65\nJ.-P. Coulon,48 S. T. Countryman,160 J.-F. Coupechoux,97 P. Couvares,2, 58 D. M. Coward,28 M. J. Cowart,64\nR. Coyne,161 K. Craig,98 R. Creed,18 J. D. E. Creighton,8 T. D. Creighton,162 P. Cremonese,99 A. W. Criswell,96\nJ. C. G. Crockett-Gray,9 S. Crook,64 R. Crouch,3 J. Csizmazia,3 J. R. Cudell,116 T. J. Cullen,2 A. Cumming,27\nE. Cuoco,57, 87 M. Cusinato,137 P. Dabadie,127 T. Dal Canton,37 S. Dall\u2019Osso,65 S. Dal Pra,65 G. D\u00b4alya,125\nB. D\u2019Angelo,55 S. Danilishin,33, 34 S. D\u2019Antonio,17 K. Danzmann,42, 41, 42 K. E. Darroch,120 L. P. Dartez,3\nA. Dasgupta,92 S. Datta,59 V. Dattilo,57 A. Daumas,71 N. Davari,163, 133 I. Dave,101 A. Davenport,104 M. Davier,37\nT. F. Davies,28 D. Davis,2 L. Davis,28 M. C. Davis,96 P. J. Davis,164, 165 M. Dax,1 J. De Bolle,93 M. Deenadayalan,11\nJ. Degallaix,166 M. De Laurentis,30, 5 S. Del\u00b4eglise,119 F. De Lillo,10 D. Dell\u2019Aquila,163, 133 W. Del Pozzo,86, 87\narXiv:2404.04248v3 [astro-ph.HE] 26 Jul 2024\n\n2\nF. De Marco,66, 65 F. De Matteis,16, 17 V. D\u2019Emilio,2 N. Demos,32 T. Dent,128 A. Depasse,10 N. DePergola,54\nR. De Pietri,167, 168 R. De Rosa,30, 5 C. De Rossi,57 R. DeSalvo,169 R. De Simone,153 A. Dhani,1 R. Diab,44\nM. C. D\u00b4\u0131az,162 M. Di Cesare,30 G. Dideron,170 N. A. Didio,79 T. Dietrich,1 L. Di Fiore,5 C. Di Fronzo,35\nM. Di Giovanni,66, 65 T. Di Girolamo,30, 5 D. Diksha,34, 33 A. Di Michele,88 J. Ding,71, 171 S. Di Pace,66, 65\nI. Di Palma,66, 65 F. Di Renzo,97 Divyajyoti,172 A. Dmitriev,114 Z. Doctor,80 E. Dohmen,3 P. P. Doleva,120\nD. Dominguez,173 L. D\u2019Onofrio,65 F. Donovan,32 K. L. Dooley,18 T. Dooney,77 S. Doravari,11 O. Dorosh,174\nM. Drago,66, 65 J. C. Driggers,3 J.-G. Ducoin,175, 71 L. Dunn,132 U. Dupletsa,43 D. D\u2019Urso,163, 133 H. Duval,176\nP.-A. Duverne,37 S. E. Dwyer,3 C. Eassa,3 M. Ebersold,29 T. Eckhardt,85 G. Eddolls,79 B. Edelman,78\nT. B. Edo,2 O. Edy,126 A. Effler,64 J. Eichholz,31 H. Einsle,48 M. Eisenmann,22 R. A. Eisenstein,32 A. Ejlli,18\nR. M. Eleveld,177 M. Emma,60 K. Endo,178 A. J. Engl,15 E. Enloe,58 L. Errico,30, 5 R. C. Essick,179 H. Estell\u00b4es,1\nD. Estevez,67 T. Etzel,2 M. Evans,32 T. Evstafyeva,180 B. E. Ewing,7 J. M. Ezquiaga,139 F. Fabrizi,62, 63\nF. Faedi,63, 62 V. Fafone,16, 17 S. Fairhurst,18 A. M. Farah,129 B. Farr,78 W. M. Farr,181, 182 G. Favaro,90\nM. Favata,183 M. Fays,116 M. Fazio,98 J. Feicht,2 M. M. Fejer,15 R. . Felicetti,184 E. Fenyvesi,83, 185\nD. L. Ferguson,148 S. Ferraiuolo,186, 66, 65 I. Ferrante,86, 87 T. A. Ferreira,9 F. Fidecaro,86, 87 P. Figura,94\nA. Fiori,87, 86 I. Fiori,57 M. Fishbach,179 R. P. Fisher,120 R. Fittipaldi,187, 110 V. Fiumara,188, 110 R. Flaminio,29\nS. M. Fleischer,189 L. S. Fleming,190 E. Floden,96 E. M. Foley,96 H. Fong,140 J. A. Font,137, 138 B. Fornal,191\nP. W. F. Forsyth,31 K. Franceschetti,167 N. Franchini,71 S. Frasca,66, 65 F. Frasconi,87 A. Frattale Mascioli,66, 65\nZ. Frei,192 A. Freise,34, 105 O. Freitas,193, 137 R. Frey,78 W. Frischhertz,64 P. Fritschel,32 V. V. Frolov,64\nG. G. Fronz\u00b4e,24 M. Fuentes-Garcia,2 S. Fujii,194 T. Fujimori,195 P. Fulda,44 M. Fyffe,64 B. Gadre,77 J. R. Gair,1\nS. Galaudage,196 V. Galdi,169 H. Gallagher,197 S. Gallardo,198 B. Gallego,198 R. Gamba,25 A. Gamboa,1\nD. Ganapathy,32 A. Ganguly,11 B. Garaventa,55, 56 J. Garc\u00b4\u0131a-Bellido,117 C. Garc\u00b4\u0131a N\u00b4u\u02dcnez,190 C. Garc\u00b4\u0131a-Quir\u00b4os,199\nJ. W. Gardner,31 K. A. Gardner,140 J. Gargiulo,57 A. Garron,99 F. Garufi,30, 5 C. Gasbarra,16, 17 B. Gateley,3\nV. Gayathri,8 G. Gemme,55 A. Gennai,87 V. Gennari,125 J. George,101 R. George,148 O. Gerberding,85\nL. Gergely,200 S. Ghonge,58 Archisman Ghosh,93 Sayantan Ghosh,201 Shaon Ghosh,183 Shrobana Ghosh,41, 42\nSuprovo Ghosh,11 Tathagata Ghosh,11 L. Giacoppo,66, 65 J. A. Giaime,9, 64 K. D. Giardina,64 D. R. Gibson,190\nD. T. Gibson,180 C. Gier,98 P. Giri,87, 86 F. Gissi,95 S. Gkaitatzis,86, 87 J. Glanzer,9 F. Glotin,37 J. Godfrey,78\nP. Godwin,2 N. L. Goebbels,85 E. Goetz,140 J. Golomb,2 S. Gomez Lopez,66, 65 B. Goncharov,43 Y. Gong,202\nG. Gonz\u00b4alez,9 P. Goodarzi,203 S. Goode,152 A. W. Goodwin-Jones,28 M. Gosselin,57 A. S. G\u00a8ottel,18 R. Gouaty,29\nD. W. Gould,31 K. Govorkova,32 S. Goyal,1 B. Grace,31 A. Grado,204, 5 V. Graham,27 A. E. Granados,96\nM. Granata,166 V. Granata,69 S. Gras,32 P. Grassia,2 A. Gray,96 C. Gray,3 R. Gray,27 G. Greco,50\nA. C. Green,34, 105 S. M. Green,126 S. R. Green,205 A. M. Gretarsson,68 E. M. Gretarsson,68 D. Griffith,2\nW. L. Griffiths,18 H. L. Griggs,58 G. Grignani,88, 50 A. Grimaldi,108, 109 C. Grimaud,29 H. Grote,18 D. Guerra,137\nD. Guetta,206, 65 G. M. Guidi,62, 63 A. R. Guimaraes,9 H. K. Gulati,92 F. Gulminelli,164, 165 A. M. Gunny,32\nH. Guo,191 W. Guo,28 Y. Guo,34, 33 Anchal Gupta,2 Anuradha Gupta,207 Ish Gupta,7 N. C. Gupta,92 P. Gupta,34, 77\nS. K. Gupta,44 T. Gupta,158 N. Gupte,1 J. Gurs,85 N. Gutierrez,166 F. Guzman,131 H.-Y. H,142 D. Haba,173\nM. Haberland,1 S. Haino,208 E. D. Hall,32 E. Z. Hamilton,99 G. Hammond,27 W.-B. Han,209 M. Haney,34 J. Hanks,3\nC. Hanna,7 M. D. Hannam,18 O. A. Hannuksela,210 A. G. Hanselman,129 H. Hansen,3 J. Hanson,64 R. Harada,38\nA. R. Hardison,211 K. Haris,34, 77 T. Harmark,134 J. Harms,43, 118 G. M. Harry,212 I. W. Harry,126 J. Hart,75\nB. Haskell,94 C.-J. Haster,213 J. S. Hathaway,197 K. Haughian,27 H. Hayakawa,49 K. Hayama,214 R. Hayes,18\nA. Heffernan,99 A. Heidmann,119 M. C. Heintze,64 J. Heinze,114 J. Heinzel,32 H. Heitmann,48 F. Hellman,215\nP. Hello,37 A. F. Helmling-Cornell,78 G. Hemming,57 O. Henderson-Sapir,111 M. Hendry,27 I. S. Heng,27\nE. Hennes,34 C. Henshaw,58 T. Hertog,107 M. Heurs,41, 42 A. L. Hewitt,180, 216 J. Heyns,32 S. Higginbotham,18\nS. Hild,33, 34 S. Hill,27 Y. Himemoto,217 N. Hirata,22 C. Hirose,218 S. Hoang,37 S. Hochheim,41, 42 D. Hofman,166\nN. A. Holland,34, 105 K. Holley-Bockelmann,145 Z. J. Holmes,111 D. E. Holz,129 L. Honet,74 C. Hong,15\nJ. Hornung,78 S. Hoshino,218 J. Hough,27 S. Hourihane,2 E. J. Howell,28 C. G. Hoy,126 C. A. Hrishikesh,16\nH.-F. Hsieh,142 C. Hsiung,219 H. C. Hsu,143 W.-F. Hsu,107 P. Hu,145 Q. Hu,27 H. Y. Huang,143 Y.-J. Huang,7\nA. D. Huddart,220 B. Hughey,68 D. C. Y. Hui,221 V. Hui,29 S. Husa,99 R. Huxford,7 T. Huynh-Dinh,64\nL. Iampieri,66, 65 G. A. Iandolo,33 M. Ianni,17, 16 A. Iess,222, 87 H. Imafuku,38 K. Inayoshi,223 Y. Inoue,143 G. Iorio,90\nM. H. Iqbal,31 J. Irwin,27 R. Ishikawa,224 M. Isi,181, 182 M. A. Ismail,143 Y. Itoh,195, 225 H. Iwanaga,195 M. Iwaya,194\nB. R. Iyer,20 V. JaberianHamedan,28 C. Jacquet,125 P.-E. Jacquet,119 S. J. Jadhav,226 S. P. Jadhav,155 T. Jain,180\nA. L. James,2 P. A. James,120 R. Jamshidi,35 J. Janquart,77, 34 K. Janssens,19, 48 N. N. Janthalur,226 S. Jaraba,117\nP. Jaranowski,227 R. Jaume,99 W. Javed,18 A. Jennings,3 W. Jia,32 J. Jiang,44 J. Kubisz,228 C. Johanson,136\nG. R. Johns,120 N. A. Johnson,44 N. K. Johnson-McDaniel,207 M. C. Johnston,213 R. Johnston,27 N. Johny,41, 42\nD. H. Jones,31 D. I. Jones,229 R. Jones,27 S. Jose,172 P. Joshi,7 L. Ju,28 K. Jung,230 J. Junker,31 V. Juste,74\nT. Kajita,231 I. Kaku,195 C. Kalaghatgi,77, 34, 232 V. Kalogera,80 M. Kamiizumi,49 N. Kanda,225, 195 S. Kandhasamy,11\nG. Kang,233 J. B. Kanner,2 S. J. Kapadia,11 D. P. Kapasi,31 S. Karat,2 C. Karathanasis,40 R. Kashyap,7\nM. Kasprzack,2 W. Kastaun,41, 42 T. Kato,194 E. Katsavounidis,32 W. Katzman,64 R. Kaushik,101 K. Kawabe,3\nR. Kawamoto,195 A. Kazemi,96 A. Kedia,197 D. Keitel,99 J. Kelley-Derzon,44 J. Kennington,7 R. Kesharwani,11\nJ. S. Key,234 R. Khadela,41, 42 S. Khadka,15 F. Y. Khalili,106 F. Khan,41, 42 I. Khan,235, 36 T. Khanam,159\nM. Khursheed,101 N. M. Khusid,181, 182 W. Kiendrebeogo,48, 236 N. Kijbunchoo,111 C. Kim,237 J. C. Kim,238 K. Kim,239\nM. H. Kim,240 S. Kim,221 Y.-M. Kim,239 C. Kimball,80 M. Kinley-Hanlon,27 M. Kinnear,18 J. S. Kissel,3\nS. Klimenko,44 A. M. Knee,140 N. Knust,41, 42 K. Kobayashi,194 P. Koch,41, 42 S. M. Koehlenbeck,15 G. Koekoek,34, 33\n\n3\nK. Kohri,241, 242 K. Kokeyama,18 S. Koley,43 P. Kolitsidou,114 M. Kolstein,40 K. Komori,38 A. K. H. Kong,142\nA. Kontos,243 M. Korobko,85 R. V. Kossak,41, 42 X. Kou,96 A. Koushik,19 N. Kouvatsos,72 M. Kovalam,28\nD. B. Kozak,2 S. L. Kranzhoff,33, 34 V. Kringel,41, 42 N. V. Krishnendu,20 A. Kr\u00b4olak,244, 174 K. Kruska,41, 42\nG. Kuehn,41, 42 P. Kuijer,34 S. Kulkarni,207 A. Kulur Ramamohan,31 A. Kumar,226 Praveen Kumar,128\nPrayush Kumar,20 Rahul Kumar,3 Rakesh Kumar,92 J. Kume,90, 91, 38 K. Kuns,32 N. Kuntimaddi,18\nS. Kuroyanagi,117, 245 N. J. Kurth,9 S. Kuwahara,38 K. Kwak,230 K. Kwan,31 J. Kwok,180 G. Lacaille,27\nP. Lagabbe,29 D. Laghi,125 S. Lai,146 A. H. Laity,161 M. H. Lakkis,35 E. Lalande,246 M. Lalleman,19\nP. C. Lalremruati,247 M. Landry,3 P. Landry,179 B. B. Lane,32 R. N. Lang,32 J. Lange,148 B. Lantz,15\nA. La Rana,65 I. La Rosa,99 A. Lartaux-Vollard,37 P. D. Lasky,152 J. Lawrence,159 M. N. Lawrence,9 M. Laxen,64\nA. Lazzarini,2 C. Lazzaro,90, 91 P. Leaci,66, 65 Y. K. Lecoeuche,140 H. M. Lee,238 H. W. Lee,248 K. Lee,240\nR.-K. Lee,142 R. Lee,32 S. Lee,239 Y. Lee,143 I. N. Legred,2 J. Lehmann,41, 42 L. Lehner,170 M. Le Jean,166\nA. Lema\u02c6\u0131tre,249 M. Lenti,63, 250 M. Leonardi,108, 109, 22 M. Lequime,36 N. Leroy,37 M. Lesovsky,2 N. Letendre,29\nM. Lethuillier,97 S. E. Levin,203 Y. Levin,152 K. Leyde,71 A. K. Y. Li,2 K. L. Li,141 T. G. F. Li,210, 107 X. Li,149\nZ. Li,27 A. Lihos,120 C-Y. Lin,251 C.-Y. Lin,143 E. T. Lin,142 F. Lin,143 H. Lin,143 L. C.-C. Lin,141 Y.-C. Lin,142\nF. Linde,232, 34 S. D. Linker,198 T. B. Littenberg,252 A. Liu,210 G. C. Liu,219 Jian Liu,28 F. Llamas Villarreal,162\nJ. Llobera-Querol,99 R. K. L. Lo,139 J.-P. Locquet,107 L. T. London,72, 32, 102 A. Longo,62, 63 D. Lopez,116\nM. Lopez Portilla,77 M. Lorenzini,16, 17 A. Lorenzo-Medina,128 V. Loriette,37 M. Lormand,64 G. Losurdo,87\nT. P. Lott IV,58 J. D. Lough,41, 42 H. A. Loughlin,32 C. O. Lousto,197 M. J. Lowry,120 N. Lu,31 H. L\u00a8uck,42, 41, 42\nD. Lumaca,17 A. P. Lundgren,126 A. W. Lussier,246 L.-T. Ma,142 S. Ma,170 M. Ma\u2019arif,143 R. Macas,126\nA. Macedo,53 M. MacInnis,32 R. R. Maciy,41, 42 D. M. Macleod,18 I. A. O. MacMillan,2 A. Macquet,37 D. Macri,32\nK. Maeda,178 S. Maenaut,107 I. Maga\u02dcna Hernandez,8 S. S. Magare,11 C. Magazz`u,87 R. M. Magee,2 E. Maggio,1\nR. Maggiore,34, 105 M. Magnozzi,55, 56 M. Mahesh,85 S. Mahesh,253 M. Maini,161 S. Majhi,11 E. Majorana,66, 65\nC. N. Makarem,2 E. Makelele,75 J. A. Malaquias-Reis,14 U. Mali,179 S. Maliakal,2 A. Malik,101 N. Man,48\nV. Mandic,96 V. Mangano,65, 66 B. Mannix,78 G. L. Mansell,79, 32 G. Mansingh,212 M. Manske,8 M. Mantovani,57\nM. Mapelli,90, 91, 254 F. Marchesoni,51, 50, 255 D. Mar\u00b4\u0131n Pina,39, 81, 256 F. Marion,29 S. M\u00b4arka,160 Z. M\u00b4arka,160\nA. S. Markosyan,15 A. Markowitz,2 E. Maros,2 S. Marsat,125 F. Martelli,62, 63 I. W. Martin,27 R. M. Martin,183\nB. B. Martinez,131 M. Martinez,40, 257 V. Martinez,127 A. Martini,108, 109 K. Martinovic,72 J. C. Martins,14\nD. V. Martynov,114 E. J. Marx,32 L. Massaro,33, 34 A. Masserot,29 M. Masso-Reid,27 M. Mastrodicasa,65, 66\nS. Mastrogiovanni,65 T. Matcovich,50 M. Matiushechkina,41, 42 M. Matsuyama,195 N. Mavalvala,32 N. Maxwell,3\nG. McCarrol,64 R. McCarthy,3 D. E. McClelland,31 S. McCormick,64 L. McCuller,2 S. McEachin,120\nC. McElhenny,120 G. I. McGhee,27 J. McGinn,27 K. B. M. McGowan,145 J. McIver,140 A. McLeod,28 T. McRae,31\nD. Meacher,8 Q. Meijer,77 A. Melatos,132 S. Mellaerts,107 A. Menendez-Vazquez,40 C. S. Menoni,104 F. Mera,3\nR. A. Mercer,8 L. Mereni,166 K. Merfeld,159 E. L. Merilh,64 J. R. M\u00b4erou,99 J. D. Merritt,78 M. Merzougui,48\nC. Messenger,27 C. Messick,8 M. Meyer-Conde,195 F. Meylahn,41, 42 A. Mhaske,11 A. Miani,108, 109 H. Miao,258\nI. Michaloliakos,44 C. Michel,166 Y. Michimura,2, 38 H. Middleton,114 A. L. Miller,34 S. Miller,2 M. Millhouse,58\nE. Milotti,184, 46 V. Milotti,90 Y. Minenkov,17 N. Mio,38 Ll. M. Mir,40 L. Mirasola,259, 65 M. Miravet-Ten\u00b4es,137\nC.-A. Miritescu,40 A. K. Mishra,20 A. Mishra,11 C. Mishra,172 T. Mishra,44 A. L. Mitchell,34, 105 J. G. Mitchell,68\nS. Mitra,11 V. P. Mitrofanov,106 R. Mittleman,32 O. Miyakawa,49 S. Miyamoto,194 S. Miyoki,49 G. Mo,32\nL. Mobilia,62, 63 S. R. P. Mohapatra,2 S. R. Mohite,7 M. Molina-Ruiz,215 C. Mondal,164 M. Mondin,198\nM. Montani,62, 63 C. J. Moore,180 D. Moraru,3 A. More,11 S. More,11 G. Moreno,3 C. Morgan,18 S. Morisaki,38, 194\nY. Moriwaki,178 G. Morras,117 A. Moscatello,90 P. Mourier,99 B. Mours,67 C. M. Mow-Lowry,34, 105\nF. Muciaccia,66, 65 Arunava Mukherjee,260 D. Mukherjee,252 Samanwaya Mukherjee,11 Soma Mukherjee,162\nSubroto Mukherjee,92 Suvodip Mukherjee,261, 170, 102 N. Mukund,32 A. Mullavey,64 J. Munch,111 J. Mundi,212\nC. L. Mungioli,28 W. R. Munn Oberg,262 Y. Murakami,194 M. Murakoshi,224 P. G. Murray,27 S. Muusse,31\nD. Nabari,108, 109 S. L. Nadji,41, 42 A. Nagar,24, 263 N. Nagarajan,27 K. N. Nagler,68 K. Nakagaki,49 K. Nakamura,22\nH. Nakano,264 M. Nakano,2 D. Nandi,9 V. Napolano,57 P. Narayan,207 I. Nardecchia,17 T. Narikawa,194\nH. Narola,77 L. Naticchioni,65 R. K. Nayak,247 J. Neilson,95, 110 A. Nelson,131 T. J. N. Nelson,64 M. Nery,41, 42\nA. Neunzert,3 S. Ng,53 L. Nguyen Quynh,265 S. A. Nichols,9 A. B. Nielsen,266 G. Nieradka,94 A. Niko,143\nY. Nishino,22, 38 A. Nishizawa,267 S. Nissanke,102, 34 E. Nitoglia,97 W. Niu,7 F. Nocera,57 M. Norman,18 C. North,18\nJ. Novak,112, 268, 269, 270 J. F. Nu\u02dcno Siles,117 L. K. Nuttall,126 K. Obayashi,224 J. Oberling,3 J. O\u2019Dell,220\nM. Oertel,112, 268, 269, 271, 270 A. Offermans,107 G. Oganesyan,43, 118 J. J. Oh,272 K. Oh,221 T. O\u2019Hanlon,64 M. Ohashi,49\nM. Ohkawa,218 F. Ohme,41, 42 A. S. Oliveira,160 R. Oliveri,112, 268, 269 B. O\u2019Neal,120 K. Oohara,273, 274 B. O\u2019Reilly,64\nN. D. Ormsby,120 M. Orselli,50, 88 R. O\u2019Shaughnessy,197 S. O\u2019Shea,27 Y. Oshima,38 S. Oshino,49 S. Ossokine,1\nC. Osthelder,2 I. Ota,9 D. J. Ottaway,111 A. Ouzriat,97 H. Overmier,64 B. J. Owen,159 A. E. Pace,7 R. Pagano,9\nM. A. Page,22 A. Pai,201 A. Pal,275 S. Pal,247 M. A. Palaia,87, 86 M. P\u00b4alfi,192 P. P. Palma,66, 16, 17 C. Palomba,65\nP. Palud,71 H. Pan,142 J. Pan,28 K. C. Pan,142 R. Panai,259, 90 P. K. Panda,226 S. Pandey,7 L. Panebianco,62, 63\nP. T. H. Pang,34, 77 F. Pannarale,66, 65 K. A. Pannone,53 B. C. Pant,101 F. H. Panther,28 F. Paoletti,87\nA. Paolone,65, 276 E. E. Papalexakis,203 L. Papalini,87, 86 G. Papigkiotis,277 A. Paquis,37 A. Parisi,88, 50 B.-J. Park,239\nJ. Park,278 W. Parker,64 G. Pascale,41, 42 D. Pascucci,93 A. Pasqualetti,57 R. Passaquieti,86, 87 L. Passenger,152\nD. Passuello,87 O. Patane,3 D. Pathak,11 M. Pathak,111 A. Patra,18 B. Patricelli,86, 87 A. S. Patron,9 K. Paul,172\nS. Paul,78 E. Payne,2 T. Pearce,18 M. Pedraza,2 R. Pegna,87 A. Pele,2 F. E. Pe\u02dcna Arellano,47 S. Penn,262\nM. D. Penuliar,53 A. Perego,108, 109 Z. Pereira,136 J. J. Perez,44 C. P\u00b4erigois,154, 91, 90 G. Perna,90 A. Perreca,108, 109\n\n4\nJ. Perret,71 S. Perri`es,97 J. W. Perry,34, 105 D. Pesios,277 S. Petracca,169 C. Petrillo,88 H. P. Pfeiffer,1\nH. Pham,64 K. A. Pham,96 K. S. Phukon,114, 34, 232 H. Phurailatpam,210 M. Piarulli,125 L. Piccari,66, 65\nO. J. Piccinni,40 M. Pichot,48 M. Piendibene,86, 87 F. Piergiovanni,62, 63 L. Pierini,65 G. Pierra,97 V. Pierro,95, 110\nM. Pietrzak,94 M. Pillas,48 F. Pilo,87 L. Pinard,166 I. M. Pinto,95, 110, 279, 30 M. Pinto,57 B. J. Piotrzkowski,8\nM. Pirello,3 M. D. Pitkin,180, 216 A. Placidi,63 E. Placidi,66, 65 M. L. Planas,99 W. Plastino,280, 17 R. Poggiani,86, 87\nE. Polini,29 L. Pompili,1 J. Poon,210 E. Porcelli,34 E. K. Porter,71 C. Posnansky,7 R. Poulton,57 J. Powell,155\nM. Pracchia,116 B. K. Pradhan,11 T. Pradier,67 A. K. Prajapati,92 K. Prasai,15 R. Prasanna,226 P. Prasia,11\nG. Pratten,114 G. Principe,184, 46 M. Principe,169, 95, 279, 110 G. A. Prodi,108, 109 L. Prokhorov,114 P. Prosposito,16, 17\nA. Puecher,34, 77 J. Pullin,9 M. Punturo,50 P. Puppo,65 M. P\u00a8urrer,161 H. Qi,12 J. Qin,31 G. Qu\u00b4em\u00b4ener,165, 112\nV. Quetschke,162 C. Quigley,18 P. J. Quinonez,68 F. J. Raab,3 S. S. Raabith,9 G. Raaijmakers,102, 34 S. Raja,101\nC. Rajan,101 B. Rajbhandari,197 K. E. Ramirez,64 F. A. Ramis Vidal,99 A. Ramos-Buades,34 D. Rana,11\nS. Ranjan,58 K. Ransom,64 P. Rapagnani,66, 65 B. Ratto,68 S. Rawat,96 A. Ray,8 V. Raymond,18 M. Razzano,86, 87\nJ. Read,53 M. Recaman Payo,107 T. Regimbau,29 L. Rei,55 S. Reid,98 D. H. Reitze,2 P. Relton,18 A. I. Renzini,2\nP. Rettegno,24 B. Revenu,281, 71 R. Reyes,198 A. S. Rezaei,65, 66 F. Ricci,66, 65 M. Ricci,65, 66 A. Ricciardone,86, 87\nJ. W. Richardson,203 M. Richardson,111 A. Rijal,68 K. Riles,89 H. K. Riley,18 S. Rinaldi,254, 90 J. Rittmeyer,85\nC. Robertson,220 F. Robinet,37 M. Robinson,3 A. Rocchi,17 L. Rolland,29 J. G. Rollins,2 A. E. Romano,282\nR. Romano,4, 5 A. Romero,176 I. M. Romero-Shaw,180 J. H. Romie,64 S. Ronchini,43, 118 T. J. Roocke,111 L. Rosa,5, 30\nT. J. Rosauer,203 C. A. Rose,8 D. Rosi\u00b4nska,121 M. P. Ross,52 M. Rossello,99 S. Rowan,27 S. K. Roy,181, 182 S. Roy,77\nD. Rozza,123, 124 P. Ruggi,57 N. Ruhama,230 E. Ruiz Morales,283, 117 K. Ruiz-Rocha,145 S. Sachdev,58 T. Sadecki,3\nJ. Sadiq,128 P. Saffarieh,34, 105 M. R. Sah,261 S. S. Saha,142 S. Saha,142 T. Sainrat,67 S. Sajith Menon,206, 66, 65\nK. Sakai,284 M. Sakellariadou,72 S. Sakon,7 O. S. Salafia,156, 124, 123 F. Salces-Carcoba,2 L. Salconi,57\nM. Saleem,96 F. Salemi,66, 65 M. Sall\u00b4e,34 S. Salvador,165, 164, 112 A. Sanchez,3 E. J. Sanchez,2 J. H. Sanchez,80\nL. E. Sanchez,2 N. Sanchis-Gual,137 J. R. Sanders,211 E. M. S\u00a8anger,1 F. Santoliquido,43 T. R. Saravanan,11\nN. Sarin,152 S. Sasaoka,173 A. Sasli,277 P. Sassi,50, 88 B. Sassolas,166 H. Satari,28 B. S. Sathyaprakash,7, 18\nR. Sato,218 Y. Sato,178 O. Sauter,44 R. L. Savage,3 T. Sawada,49 H. L. Sawant,11 S. Sayah,29 V. Scacco,16, 17\nD. Schaetzl,2 M. Scheel,149 A. Schiebelbein,179 M. G. Schiworski,111 P. Schmidt,114 S. Schmidt,77 R. Schnabel,85\nM. Schneewind,41, 42 R. M. S. Schofield,78 K. Schouteden,107 B. W. Schulte,41, 42 B. F. Schutz,18, 41, 42\nE. Schwartz,18 M. Scialpi,285 J. Scott,27 S. M. Scott,31 T. C. Seetharamu,27 M. Seglar-Arroyo,40\nY. Sekiguchi,286 D. Sellers,64 A. S. Sengupta,287 D. Sentenac,57 E. G. Seo,27 J. W. Seo,107 V. Sequino,30, 5\nM. Serra,65 G. Servignat,268 A. Sevrin,176 T. Shaffer,3 U. S. Shah,58 M. A. Shaikh,238 L. Shao,223 A. K. Sharma,20\nP. Sharma,101 S. Sharma-Chaudhary,103 M. R. Shaw,18 P. Shawhan,122 N. S. Shcheblanov,288, 249 E. Sheridan,145\nY. Shikano,289, 290 M. Shikauchi,38 K. Shimode,49 H. Shinkai,291 J. Shiota,224 D. H. Shoemaker,32\nD. M. Shoemaker,148 R. W. Short,3 S. ShyamSundar,101 A. Sider,35 H. Siegel,181, 182 M. Sieniawska,10 D. Sigg,3\nL. Silenzi,50, 51 M. Simmonds,111 L. P. Singer,130 A. Singh,207 D. Singh,7 M. K. Singh,20 S. Singh,22, 61 A. Singha,33, 34\nA. M. Sintes,99 V. Sipala,163, 133 V. Skliris,18 B. J. J. Slagmolen,31 T. J. Slaven-Blair,28 J. Smetana,114\nJ. R. Smith,53 L. Smith,27 R. J. E. Smith,152 W. J. Smith,145 J. Soldateschi,250, 292, 63 K. Somiya,173 I. Song,142\nK. Soni,11 S. Soni,32 V. Sordini,97 F. Sorrentino,55 N. Sorrentino,86, 87 H. Sotani,293 R. Soulard,48\nA. Southgate,18 V. Spagnuolo,33, 34 A. P. Spencer,27 M. Spera,46, 294 P. Spinicelli,57 J. B. Spoon,9\nC. A. Sprague,265 A. K. Srivastava,92 F. Stachurski,27 D. A. Steer,71 J. Steinlechner,33, 34 S. Steinlechner,33, 34\nN. Stergioulas,277 P. Stevens,37 S. Stevenson,155 M. StPierre,161 G. Stratta,295, 135, 65, 296 M. D. Strong,9\nA. Strunk,3 R. Sturani,297 A. L. Stuver,54 M. Suchenek,94 S. Sudhagar,94 N. Sueltmann,85 L. Suleiman,53\nK. D. Sullivan,9 L. Sun,31 S. Sunil,92 J. Suresh,10 P. J. Sutton,18 T. Suzuki,218 Y. Suzuki,224 B. L. Swinkels,34\nA. Syx,67 M. J. Szczepa\u00b4nczyk,298, 44 P. Szewczyk,121 M. Tacca,34 H. Tagoshi,194 S. C. Tait,2 H. Takahashi,299\nR. Takahashi,22 A. Takamori,38 T. Takase,49 K. Takatani,195 H. Takeda,300 K. Takeshita,173 C. Talbot,129\nM. Tamaki,194 N. Tamanini,125 D. Tanabe,143 K. Tanaka,49 S. J. Tanaka,224 T. Tanaka,300 D. Tang,28 S. Tanioka,79\nD. B. Tanner,44 L. Tao,44 R. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n,34 R. Tarafder,2 C. Taranto,16, 17, 66 A. Taruya,301\nJ. D. Tasson,177 M. Teloi,35 R. Tenorio,99 H. Themann,198 A. Theodoropoulos,137 M. P. Thirugnanasambandam,11\nL. M. Thomas,2 M. Thomas,64 P. Thomas,3 J. E. Thompson,149 S. R. Thondapu,101 K. A. Thorne,64 E. Thrane,152\nJ. Tissino,43 A. Tiwari,11 P. Tiwari,43 S. Tiwari,199 V. Tiwari,114 M. R. Todd,79 A. M. Toivonen,96 K. Toland,27\nA. E. Tolley,126 T. Tomaru,22 K. Tomita,195 T. Tomura,49 H. Tong,152 C. Tong-Yu,143 A. Toriyama,224\nN. Toropov,114 A. Torres-Forn\u00b4e,137, 138 C. I. Torrie,2 M. Toscani,125 I. Tosta e Melo,302 E. Tournefier,29\nA. Trapananti,51, 50 F. Travasso,51, 50 G. Traylor,64 M. Trevor,122 M. C. Tringali,57 A. Tripathee,89 G. Troian,184\nL. Troiano,303, 110 A. Trovato,184, 46 L. Trozzo,5 R. J. Trudeau,2 T. T. L. Tsang,18 R. Tso,149, \u2217S. Tsuchida,304\nL. Tsukada,7 T. Tsutsui,38 K. Turbang,176, 19 M. Turconi,48 C. Turski,93 H. Ubach,39, 81 N. Uchikata,194\nT. Uchiyama,49 R. P. Udall,2 T. Uehara,305 M. Uematsu,195 K. Ueno,38 S. Ueno,224 V. Undheim,266 T. Ushiba,49\nM. Vacatello,87, 86 H. Vahlbruch,41, 42 N. Vaidya,2 G. Vajente,2 A. Vajpeyi,152 G. Valdes,131 J. Valencia,99\nM. Valentini,207, 105, 34 S. A. Vallejo-Pe\u02dcna,282 S. Vallero,24 V. Valsan,8 N. van Bakel,34 M. van Beuzekom,34\nM. van Dael,34, 306 J. F. J. van den Brand,33, 105, 34 C. Van Den Broeck,77, 34 D. C. Vander-Hyde,79\nM. van der Sluys,34, 77 A. Van de Walle,37 J. van Dongen,34, 105 K. Vandra,54 H. van Haevermaet,19\nJ. V. van Heijningen,34, 105 P. Van Hove,67 M. VanKeuren,75 J. Vanosky,2 M. H. P. M. van Putten,13\nZ. van Ranst,33, 34 N. van Remortel,19 M. Vardaro,33, 34 A. F. Vargas,132 J. J. Varghese,68 V. Varma,136\nM. Vas\u00b4uth,83, \u2020 A. Vecchio,114 G. Vedovato,91 J. Veitch,27 P. J. Veitch,111 S. Venikoudis,10 J. Venneberg,41, 42\n\n5\nP. Verdier,97 D. Verkindt,29 B. Verma,136 P. Verma,174 Y. Verma,101 S. M. Vermeulen,2 F. Vetrano,62\nA. Veutro,65, 66 A. M. Vibhute,3 A. Vicer\u00b4e,62, 63 S. Vidyant,79 A. D. Viets,84 A. Vijaykumar,179 A. Vilkha,197\nV. Villa-Ortega,128 E. T. Vincent,58 J.-Y. Vinet,48 S. Viret,97 A. Virtuoso,184, 46 S. Vitale,32 A. Vives,78\nH. Vocca,88, 50 D. Voigt,85 E. R. G. von Reis,3 J. S. A. von Wrangel,41, 42 S. P. Vyatchanin,106 L. E. Wade,75\nM. Wade,75 K. J. Wagner,197 A. Wajid,55, 56 M. Walker,120 G. S. Wallace,98 L. Wallace,2 H. Wang,38 J. Z. Wang,89\nW. H. Wang,162 Z. Wang,143 G. Waratkar,201 J. Warner,3 M. Was,29 T. Washimi,22 N. Y. Washington,2\nD. Watarai,38 K. E. Wayt,75 B. R. Weaver,18 B. Weaver,3 C. R. Weaving,126 S. A. Webster,27 M. Weinert,41, 42\nA. J. Weinstein,2 R. Weiss,32 F. Wellmann,41, 42 L. Wen,28 P. We\u00dfels,41, 42 K. Wette,31 J. T. Whelan,197\nB. F. Whiting,44 C. Whittle,2 J. B. Wildberger,1 O. S. Wilk,75 D. Wilken,41, 42, 42 A. T. Wilkin,203\nD. J. Willadsen,84 K. Willetts,18 D. Williams,27 M. J. Williams,126 N. S. Williams,114 J. L. Willis,2\nB. Willke,42, 41, 42 M. Wils,107 J. Winterflood,28 C. C. Wipf,2 G. Woan,27 J. Woehler,33, 34 J. K. Wofford,197\nN. E. Wolfe,32 H. T. Wong,143 H. W. Y. Wong,210 I. C. F. Wong,210 J. L. Wright,31 M. Wright,27 C. Wu,142\nD. S. Wu,41, 42 H. Wu,142 E. Wuchner,53 D. M. Wysocki,8 V. A. Xu,32 Y. Xu,199 N. Yadav,94 H. Yamamoto,2\nK. Yamamoto,178 T. S. Yamamoto,245 T. Yamamoto,49 S. Yamamura,194 R. Yamazaki,224 S. Yan,15 T. Yan,114\nF. W. Yang,191 F. Yang,160 K. Z. Yang,96 Y. Yang,146 Z. Yarbrough,9 H. Yasui,49 S.-W. Yeh,142 A. B. Yelikar,197\nX. Yin,32 J. Yokoyama,307, 38 T. Yokozawa,49 J. Yoo,150 H. Yu,149 S. Yuan,28 H. Yuzurihara,49 A. Zadro\u02d9zny,174\nM. Zanolin,68 M. Zeeshan,197 T. Zelenova,57 J.-P. Zendri,91 M. Zeoli,116, 10 M. Zerrad,36 M. Zevin,80\nA. C. Zhang,160 L. Zhang,2 R. Zhang,44 T. Zhang,114 Y. Zhang,31 C. Zhao,28 Yue Zhao,191 Yuhang Zhao,71\nY. Zheng,103 H. Zhong,96 R. Zhou,215 X.-J. Zhu,308 Z.-H. Zhu,308, 202 A. B. Zimmerman,148 M. E. Zucker,32, 2 and\nJ. Zweizig2\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3LIGO Hanford Observatory, Richland, WA 99352, USA\n4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n5INFN, Sezione di Napoli, I-80126 Napoli, Italy\n6University of Warwick, Coventry CV4 7AL, United Kingdom\n7The Pennsylvania State University, University Park, PA 16802, USA\n8University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n9Louisiana State University, Baton Rouge, LA 70803, USA\n10Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n11Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n12Queen Mary University of London, London E1 4NS, United Kingdom\n13Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n14Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n15Stanford University, Stanford, CA 94305, USA\n16Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n17INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n18Cardiff University, Cardiff CF24 3AA, United Kingdom\n19Universiteit Antwerpen, 2000 Antwerpen, Belgium\n20International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n21University College Dublin, Belfield, D4, Dublin, Ireland\n22Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n23Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n24INFN Sezione di Torino, I-10125 Torino, Italy\n25Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n26Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n27SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n28OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n29Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n30Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n31OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n32LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n33Maastricht University, 6200 MD Maastricht, Netherlands\n34Nikhef, 1098 XG Amsterdam, Netherlands\n35Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n36Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n37Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n38University of Tokyo, Tokyo, 113-0033, Japan.\n\n6\n39Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n40Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n41Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n42Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n43Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n44University of Florida, Gainesville, FL 32611, USA\n45Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n46INFN, Sezione di Trieste, I-34127 Trieste, Italy\n47Tecnol\u00b4ogico de Monterrey Campus Guadalajara, 45201 Zapopan, Jalisco, Mexico\n48Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n49Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n50INFN, Sezione di Perugia, I-06123 Perugia, Italy\n51Universit`a di Camerino, I-62032 Camerino, Italy\n52University of Washington, Seattle, WA 98195, USA\n53California State University Fullerton, Fullerton, CA 92831, USA\n54Villanova University, Villanova, PA 19085, USA\n55INFN, Sezione di Genova, I-16146 Genova, Italy\n56Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n57European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n58Georgia Institute of Technology, Atlanta, GA 30332, USA\n59Chennai Mathematical Institute, Chennai 603103, India\n60Royal Holloway, University of London, London TW20 0EX, United Kingdom\n61Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n62Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n63INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n64LIGO Livingston Observatory, Livingston, LA 70754, USA\n65INFN, Sezione di Roma, I-00185 Roma, Italy\n66Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n67Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n68Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n69Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n70Bar-Ilan University, Ramat Gan, 5290002, Israel\n71Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n72King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n73Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n74Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n75Kenyon College, Gambier, OH 43022, USA\n76International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n77Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Northwestern University, Evanston, IL 60208, USA\n81Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n82Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n83HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n84Concordia University Wisconsin, Mequon, WI 53097, USA\n85Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n86Universit`a di Pisa, I-56127 Pisa, Italy\n87INFN, Sezione di Pisa, I-56127 Pisa, Italy\n88Universit`a di Perugia, I-06123 Perugia, Italy\n89University of Michigan, Ann Arbor, MI 48109, USA\n90Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n91INFN, Sezione di Padova, I-35131 Padova, Italy\n92Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n\n7\n93Universiteit Gent, B-9000 Gent, Belgium\n94Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n95Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n96University of Minnesota, Minneapolis, MN 55455, USA\n97Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n98SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n99IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n100Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n101RRCAT, Indore, Madhya Pradesh 452013, India\n102GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n103Missouri University of Science and Technology, Rolla, MO 65409, USA\n104Colorado State University, Fort Collins, CO 80523, USA\n105Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n106Lomonosov Moscow State University, Moscow 119991, Russia\n107Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n108Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n109INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n110INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n111OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n112Centre national de la recherche scientifique, 75016 Paris, France\n113Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n114University of Birmingham, Birmingham B15 2TT, United Kingdom\n115Washington State University, Pullman, WA 99164, USA\n116Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n117Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n118INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n119Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n120Christopher Newport University, Newport News, VA 23606, USA\n121Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n122University of Maryland, College Park, MD 20742, USA\n123Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n124INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n125L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n126University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n127Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n128IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n129University of Chicago, Chicago, IL 60637, USA\n130NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n131Texas A&M University, College Station, TX 77843, USA\n132OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n133INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n136University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n141Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143National Central University, Taoyuan City 320317, Taiwan\n144OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n145Vanderbilt University, Nashville, TN 37235, USA\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148University of Texas, Austin, TX 78712, USA\n\n8\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Cornell University, Ithaca, NY 14850, USA\n151Northeastern University, Boston, MA 02115, USA\n152OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n153Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n154INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n157Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n158Montana State University, Bozeman, MT 59717, USA\n159Texas Tech University, Lubbock, TX 79409, USA\n160Columbia University, New York, NY 10027, USA\n161University of Rhode Island, Kingston, RI 02881, USA\n162The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n163Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n164Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n165Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n166Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n167Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n168INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n169University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n170Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n171Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n172Indian Institute of Technology Madras, Chennai 600036, India\n173Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n174National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n175Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n176Vrije Universiteit Brussel, 1050 Brussel, Belgium\n177Carleton College, Northfield, MN 55057, USA\n178Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n179Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n180University of Cambridge, Cambridge CB2 1TN, United Kingdom\n181Stony Brook University, Stony Brook, NY 11794, USA\n182Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n183Montclair State University, Montclair, NJ 07043, USA\n184Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n185HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n186Centre de Physique des Particules de Marseille, 163, avenue de Luminy, 13288 Marseille cedex 09, France\n187CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n188Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n189Western Washington University, Bellingham, WA 98225, USA\n190SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n191The University of Utah, Salt Lake City, UT 84112, USA\n192E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n193Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n194Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n195Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n196Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n197Rochester Institute of Technology, Rochester, NY 14623, USA\n198California State University, Los Angeles, Los Angeles, CA 90032, USA\n199University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n200University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n201Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n202School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n\n9\n203University of California, Riverside, Riverside, CA 92521, USA\n204INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n205University of Nottingham NG7 2RD, UK\n206Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n207The University of Mississippi, University, MS 38677, USA\n208Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n209Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n210The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n211Marquette University, Milwaukee, WI 53233, USA\n212American University, Washington, DC 20016, USA\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n215University of California, Berkeley, CA 94720, USA\n216University of Lancaster, Lancaster LA1 4YW, United Kingdom\n217College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n218Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n219Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n220Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n221Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n222Scuola Normale Superiore, I-56126 Pisa, Italy\n223Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n224Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n225Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n226Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n227University of Bia lystok, 15-424 Bia lystok, Poland\n228Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n229University of Southampton, Southampton SO17 1BJ, United Kingdom\n230Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n231Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n232Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n233Chung-Ang University, Seoul 06974, Republic of Korea\n234University of Washington Bothell, Bothell, WA 98011, USA\n235Aix Marseille Universit\u00b4e, Jardin du Pharo, 58 Boulevard Charles Livon, 13007 Marseille, France\n236Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n237Ewha Womans University, Seoul 03760, Republic of Korea\n238Seoul National University, Seoul 08826, Republic of Korea\n239Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n240Sungkyunkwan University, Seoul 03063, Republic of Korea\n241Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n242Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n243Bard College, Annandale-On-Hudson, NY 12504, USA\n244Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n245Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n246Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n247Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n248Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n249NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n250Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n251National Center for High-performance Computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n252NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n253West Virginia University, Morgantown, WV 26506, USA\n254Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n\n10\n255School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n256Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n257Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n258Tsinghua University, Beijing 100084, China\n259INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n260Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n261Tata Institute of Fundamental Research, Mumbai 400005, India\n262Hobart and William Smith Colleges, Geneva, NY 14456, USA\n263Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n264Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n265Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n266University of Stavanger, 4021 Stavanger, Norway\n267Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 903-0213, Japan\n268Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n269Observatoire de Paris, 75014 Paris, France\n270Universit\u00b4e PSL, 75006 Paris, France\n271Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n272National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n273Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n274Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n275CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n276Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n277Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n278Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n279Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n280Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n281Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n282Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n283Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n284Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n285Universit`a Degli Studi Di Ferrara, Via Savonarola, 9, 44121 Ferrara FE, Italy\n286Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n287Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n288Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n289Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan\n290Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n291Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n292INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n293iTHEMS (Interdisciplinary Theoretical and Mathematical Sciences Program), RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n294Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea, 265, I-34136, Trieste TS, Italy\n295Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n296INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n297Universidade Estadual Paulista, 01140-070 S\u02dcao Paulo, Brazil\n298Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n299Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n300Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n301Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n302University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n303Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n304National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n\n11\n305Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n306Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n307Kavli Institute for the Physics and Mathematics of the Universe, WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City,\nChiba 277-8583, Japan\n308Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\nABSTRACT\nWe report the observation of a coalescing compact binary with component masses 2.5\u20134.5 M\u2299\nand 1.2\u20132.0 M\u2299(all measurements quoted at the 90% credible level). The gravitational-wave sig-\nnal GW230529 181500 was observed during the fourth observing run of the LIGO\u2013Virgo\u2013KAGRA\ndetector network on 2023 May 29 by the LIGO Livingston observatory. The primary component of\nthe source has a mass less than 5 M\u2299at 99% credibility.\nWe cannot definitively determine from\ngravitational-wave data alone whether either component of the source is a neutron star or a black\nhole. However, given existing estimates of the maximum neutron star mass, we find the most probable\ninterpretation of the source to be the coalescence of a neutron star with a black hole that has a mass\nbetween the most massive neutron stars and the least massive black holes observed in the Galaxy.\nWe provisionally estimate a merger rate density of 55+127\n\u221247 Gpc\u22123 yr\u22121 for compact binary coalescences\nwith properties similar to the source of GW230529 181500; assuming that the source is a neutron star\u2013\nblack hole merger, GW230529 181500-like sources may make up the majority of neutron star\u2013black\nhole coalescences. The discovery of this system implies an increase in the expected rate of neutron\nstar\u2013black hole mergers with electromagnetic counterparts and provides further evidence for compact\nobjects existing within the purported lower mass gap.\nKeywords: Gravitational wave astronomy (675) \u2014 Gravitational wave detectors (676) \u2014 Gravitational\nwave sources (677) \u2014 Stellar mass black holes (1611) \u2014 Neutron stars (1108)\n1. INTRODUCTION\nIn 2023 May, the fourth observing run (O4) of the Ad-\nvanced LIGO (Aasi et al. 2015), Advanced Virgo (Acer-\nnese et al. 2015), and KAGRA (Somiya 2012; Aso et al.\n2013) observatory network commenced following a series\nof upgrades to increase the sensitivity of the network.\nThe prior three observing runs opened the field of ob-\nservational gravitational-wave (GW) astronomy, with 90\nprobable compact binary coalescence (CBC) candidates\nreported by the LIGO Scientific, Virgo, and KAGRA\nCollaboration (LVK) at the conclusion of the third ob-\nserving run (O3; Abbott et al. 2023a) and further candi-\ndates found by external analyses (e.g., Nitz et al. 2023;\nMehta et al. 2023b; Wadekar et al. 2023).\nThese in-\ncluded the first observation of merging stellar-mass black\nholes (Abbott et al. 2016a), the first observation of a\nstellar-mass black hole merging with a neutron star (Ab-\nbott et al. 2021a), and the first observation of two merg-\ning neutron stars (Abbott et al. 2017a). The first ob-\nservation of two merging neutron stars was also a mul-\ntimessenger event accompanied by emission across the\n\u2217Deceased, November 2022.\n\u2020 Deceased, February 2024.\nelectromagnetic (EM) spectrum (Abbott et al. 2017b;\nMargutti & Chornock 2021).\nThe continued discov-\nery of CBCs by the international GW detector network\nin O4 and beyond promises to reveal new information\nabout the formation pathways of compact binaries and\nthe physics of their evolution.\nWhile GW observations have enabled detailed char-\nacterization of the population of stellar-mass compact-\nobject binary mergers overall (e.g., Abbott et al. 2023b),\nthe small number of observed mergers at the low-mass\nend of the black hole mass spectrum leads to consider-\nable uncertainty in this region of the mass distribution.\nDynamical mass measurements of X-ray binary systems\nwithin the Milky Way suggest a paucity of compact ob-\njects with masses between \u223c3 and 5 M\u2299, and hence a\nlower mass gap that divides the population of neutron\nstars (with masses less than \u223c3 M\u2299; Rhoades & Ruffini\n1974; Kalogera & Baym 1996) and stellar-mass black\nholes (observed to have masses above 5 M\u2299; Bailyn et al.\n1998; Ozel et al. 2010; Farr et al. 2011b). Although a\nnumber of recent observations of noninteracting binary\nsystems (Thompson et al. 2019; Jayasinghe et al. 2021),\nradio pulsar surveys (Barr et al. 2024), and GW obser-\nvations (Abbott et al. 2020c, 2023b) have found hints\nof compact objects residing in the lower mass gap, GW\n\n12\nobservations have yet to quantify the extent and poten-\ntial occupation of this gap (Fishbach et al. 2020; Farah\net al. 2022; Abbott et al. 2023b).\nHere we report on the compact binary merger\nsignal GW230529 181500, henceforth abbreviated as\nGW230529, which was detected by the LIGO Livingston\nobservatory on 2023 May 29 at 18:15:00 UTC; all other\nobservatories either were offline or did not have the sen-\nsitivity required to observe this signal.\nWe find that\nthe compact binary source of GW230529 had component\nmasses of 3.6+0.8\n\u22121.2 M\u2299and 1.4+0.6\n\u22120.2 M\u2299(all measurements\nare reported as symmetric 90% credible intervals around\nthe median of the marginalized posterior distribution\nwith default uniform priors, unless otherwise specified).\nAlthough we cannot definitively determine the nature\nof the higher-mass (primary) compact object in the bi-\nnary system, if we assume that all compact objects with\nmasses below current constraints on the maximum neu-\ntron star mass are indeed neutron stars, the most prob-\nable interpretation for the source of GW230529 is the\ncoalescence between a 2.5\u20134.5 M\u2299black hole and a neu-\ntron star. GW230529 provides further evidence that a\npopulation of compact objects exists with masses be-\ntween the heaviest neutron stars and lightest black holes\nobserved in the Milky Way. Furthermore, if the source\nof GW230529 was a merger between a neutron star and\na black hole, its masses are significantly more symmetric\nthan the neutron star\u2013black holes (NSBHs) previously\nobserved via GWs (Abbott et al. 2023a), which increases\nthe expected rate of NSBHs that may be accompanied\nby an EM counterpart.\nWe report on the status of the detector network at the\ntime of GW230529 in Section 2 and provide details of the\ndetection in Section 3. In Section 4 we present estimates\nof the source properties, along with a discussion of the\ninferred masses, spins, tidal effects, and consistency of\nthe signal with general relativity. We provide updated\nconstraints on merger rates and the inferred properties\nof the compact binary and NSBH populations, as well as\npopulation-informed posteriors on source properties, in\nSection 5. Section 6 provides analysis and interpretation\nof the physical nature of the source components. Impli-\ncations for multimessenger astrophysics and the forma-\ntion of low-mass black holes are discussed in Sections\n7 and 8, respectively. Section 9 summarizes our find-\nings. Data from the analyses in this work are available\non Zenodo (LIGO Scientific, Virgo, and KAGRA Col-\nlaboration 2024).\n2. OBSERVATORY STATUS AND DATA QUALITY\nAt the time of GW230529 (2023 May 29 18:15:00.7\nUTC), LIGO Livingston was in observing mode; LIGO\nHanford was offline, having gone out of observing mode\n1.5 hr prior to the detection.\nThe Virgo observatory\nwas undergoing upgrades and was not operational at the\ntime of the detection. The KAGRA observatory was in\nobserving mode, but its sensitivity was insufficient to\nimpact the analysis of GW230529. Hence, only the data\nfrom the LIGO Livingston observatory are used in the\nanalysis of GW230529.\nLIGO Livingston was observing with stable sensitiv-\nity for \u224866 hr up to and including the time of the\nGW signal.\nAt the time of the detection, the sky-\naveraged binary neutron star (BNS) inspiral range was\n\u2248150 Mpc. From the start of O4 until this event, the\nLIGO Livingston BNS inspiral range (Chen et al. 2021a)\nvaried between 140\u2013160 Mpc, a 4.5\u201319.4% increase com-\npared to the median BNS range in O3 (Buikema et al.\n2020; Abbott et al. 2023a). Additional details on up-\ngrades to the LIGO observatories for O4 can be found\nin Appendix A.\nThe Advanced LIGO observatories are laser interfer-\nometers that measure strain (Aasi et al. 2015).\nThe\nobservatories are calibrated via photon radiation pres-\nsure actuation. An amplitude-modulated laser beam is\ndirected onto the end test masses, inducing a known\nchange in the arm length from the equilibrium posi-\ntion (Karki et al. 2016; Viets et al. 2018). For the strain\ndata used in the GW230529 analysis, the maximum 1\u03c3\nbounds on calibration uncertainties at LIGO Livingston\nwere 6% in amplitude and 6.5\u25e6in phase for the frequency\nrange 20\u20132048 Hz.\nDetection vetting procedures similar to those of past\nGW candidates (Davis et al. 2021; Abbott et al. 2016b),\nwhen applied to GW230529, find no evidence that in-\nstrumental or environmental artifacts (Helmling-Cornell\net al. 2024; Nguyen et al. 2021; Effler et al. 2015) could\nhave caused GW230529. We find no evidence of tran-\nsient noise that is likely to impact the recovery of the\nGW signal in the 256 s LIGO Livingston data segment\ncontaining the signal.\n3. DETECTION OF GW230529\nGW230529 was initially detected in low latency in\ndata from the LIGO Livingston observatory. The sig-\nnal was detected independently by three matched-filter\nsearch pipelines: GstLAL (Messick et al. 2017; Sachdev\net al. 2019; Hanna et al. 2020; Cannon et al. 2021; Ew-\ning et al. 2024; Tsukada et al. 2023), MBTA (Adams\net al. 2016; Aubin et al. 2021) and PyCBC (Allen et al.\n2012; Allen 2005; Dal Canton et al. 2021; Usman et al.\n2016; Nitz et al. 2017; Davies et al. 2020). Although\nGW230529 occurred when only a single detector was\nobserving, it was detected by all three pipelines with\n\n13\nhigh significance, and stands out from the background\ndistribution of noise triggers. More details are given in\nAppendix B.\nAll three pipelines have a similar matched-filter-based\napproach to identify GW candidates but differ in the\ndetails of implementation. Each pipeline begins by per-\nforming a matched-filtering analysis on the data from\nthe observatory with a bank of GW templates (Sakon\net al. 2024; Roy et al. 2019; Florian et al. 2024). Times\nof high signal-to-noise ratio (S/N) are identified, after\nwhich each pipeline performs its own set of signal con-\nsistency tests, combines them with the S/N to make a\nsingle ranking statistic for each candidate GW event,\nand calculates a false alarm rate (FAR) by comparing\nthe ranking statistic of the candidate with the back-\nground distribution. The FAR is the expected rate of\ntriggers caused by noise with a ranking statistic greater\nthan or equal to that of the candidate.\nFor each pipeline, this procedure can be done in two\nmodes: a low-latency or online mode, and an offline\nmode. In the online mode, the pipelines only use the\nbackground information available at the time of a candi-\ndate to estimate its significance, along with low-latency\ndata-quality information. In the offline mode, pipelines\nuse more background information gathered from sub-\nsequent observing times to estimate the significance of\ncandidates and use more refined data-quality informa-\ntion. The offline mode enables more robust and repro-\nducible results at the cost of greater latency.\nIn both cases, the background distribution is extrap-\nolated to higher significances. This enables the inverse\nFAR to be greater than the time for which the back-\nground was collected. Pipelines have differing extrapo-\nlation methods and differing methods for calculating the\nFAR of single-detector GW candidates, details of which\ncan be found in Appendix C. These differing meth-\nods can cause the FARs reported by different pipelines\nfor the same candidate to vary to a significant degree,\nas seen in the case of GW230529. However, all three\npipelines recover a nearly identical S/N for GW230529,\nas expected for an astrophysical signal with a high match\nto the search templates. This, in concert with the fact\nthat the inverse FARs from the offline analyses of all\npipelines are much greater than the duration of the first\nhalf of the fourth observing run (O4a), makes it highly\nlikely that GW230529 is of astrophysical origin. Table 1\nshows the online S/N, online inverse FAR, and offline\ninverse FAR for each search pipeline.\n4. SOURCE PROPERTIES\nThe source properties of GW230529 are inferred us-\ning a Bayesian analysis of the data from the LIGO Liv-\nTable 1.\nProperties of the detection of GW230529 from\neach search pipeline. Significance is measured by the inverse\nof the FAR.\nGstLAL\nMBTA\nPyCBC\nOnline S/N\n11.3\n11.4\n11.6\nOnline inverse FAR (yr)\n1.1\n1.1\n160.4\nOffline inverse FAR (yr)\n60.3\n>1000\n>1000\ningston observatory. We analyze 128 s of data including\nfrequencies in the range of 20\u20131792 Hz in the calculation\nof the likelihood. To describe the detector noise, we as-\nsume a noise power spectral density (PSD) given by the\nmedian estimate provided by BayesWave (Littenberg\n& Cornish 2015; Cornish & Littenberg 2015; Cornish\net al. 2021).\nWe use the Bilby (Ashton et al. 2019;\nRomero-Shaw et al. 2020) or Parallel Bilby (Smith\net al. 2020) inference libraries to generate samples from\nthe posterior distribution of the source parameters us-\ning a nested sampling (Skilling 2006) algorithm, as im-\nplemented in the Dynesty software package (Speagle\n2020).\nGiven the uncertain nature of the compact objects of\nthe source, we analyze GW230529 using a range of wave-\nform models that incorporate a number of key physi-\ncal effects. For our primary analysis, we employ binary\nblack hole (BBH) waveform models that include higher-\norder multipole moments, the effects of spin-induced or-\nbital precession, and allow for spin magnitudes on both\ncomponents up to the Kerr limit, but do not include\ntidal effects on either component.\nSystematic errors in inferred source properties due\nto waveform modeling may be significant for NSBH\nsystems (Huang et al. 2021).\nWe mitigate these ef-\nfects by combining the posteriors inferred using two dif-\nferent signal models: the phenomenological frequency-\ndomain\nmodel\nIMRPhenomXPHM\n(Pratten\net\nal.\n2020; Garc\u00b4\u0131a-Quir\u00b4os et al. 2020; Pratten et al. 2021),\nand a time-domain effective-one-body model SEOB-\nNRv5PHM (Khalil et al. 2023; Pompili et al. 2023;\nRamos-Buades et al. 2023; van de Meent et al. 2023).\nThe posterior samples obtained independently using the\ntwo signal models are broadly consistent. Unless other-\nwise noted, we present results throughout this work ob-\ntained by an equal-weight combination of the posterior\nsamples from both models under the default priors de-\nscribed in Appendix D. Our measurements of key source\nparameters for GW230529 are presented in Table 2.\n\n14\nTable 2.\nSource properties of GW230529 from the pri-\nmary combined analysis (BBH waveforms, high-spin, default\npriors).\nWe report the median values together with the\n90% symmetric credible intervals at a reference frequency\nof 20 Hz.\nParameter\nValue\nPrimary mass m1/M\u2299\n3.6+0.8\n\u22121.2\nSecondary mass m2/M\u2299\n1.4+0.6\n\u22120.2\nMass ratio q = m2/m1\n0.39+0.41\n\u22120.12\nTotal mass M/M\u2299\n5.1+0.6\n\u22120.6\nChirp mass M/M\u2299\n1.94+0.04\n\u22120.04\nDetector-frame chirp mass (1 + z)M/M\u2299\n2.026+0.002\n\u22120.002\nPrimary spin magnitude \u03c71\n0.44+0.40\n\u22120.37\nEffective inspiral-spin parameter \u03c7eff\n\u22120.10+0.12\n\u22120.17\nEffective precessing-spin parameter \u03c7p\n0.40+0.39\n\u22120.30\nLuminosity distance DL/Mpc\n201+102\n\u221296\nSource redshift z\n0.04+0.02\n\u22120.02\nAnalysis details and results from other waveform mod-\nels we consider are reported in Appendix D; we find\nthat the key conclusions of the analyses presented here\nare not sensitive to the choice of signal model. In par-\nticular, the use of BBH models is validated by com-\nparison to waveform models that include tidal effects,\nfinding no evidence that the BNS or NSBH models are\npreferred, consistent with previous observations (Abbott\net al. 2021a). This is expected given the moderate S/N\nwith which GW230529 was detected (Huang et al. 2021).\nThe analysis of GW230529 indicates that it is an\nasymmetric compact binary with a mass ratio q =\nm2/m1 = 0.39+0.41\n\u22120.12 and source component masses m1 =\n3.6+0.8\n\u22121.2 M\u2299and m2 = 1.4+0.6\n\u22120.2 M\u2299.\nThe primary is\nconsistent with a black hole that resides in the lower\nmass gap (3 M\u2299\u2272m1 \u22725 M\u2299; Ozel et al. 2010;\nFarr et al. 2011b), with a mass < 5 M\u2299at the 99%\ncredible level. The posterior distribution on the mass\nof the secondary is peaked around \u223c1.4 M\u2299with\nan extended tail beyond 2 M\u2299, such that P(m2 >\n2 M\u2299) = 5%.\nThe mass of the secondary is con-\nsistent with the distribution of known neutron star\nmasses, including Galactic pulsars (Antoniadis et al.\n2016; \u00a8Ozel & Freire 2016; Alsing et al. 2018; Farrow\net al. 2019) and extragalactic GW observations (Landry\n& Read 2021; Abbott et al. 2023b).\nFigure 1 shows\nthe component mass posteriors of GW230529 relative\nto other BNSs (GW170817 and GW190425) and NSBHs\nFigure 1.\nThe one- and two-dimensional posterior\nprobability distributions for the component masses of the\nsource binary of GW230529 (teal).\nThe contours in the\nmain panel denote the 90% credible regions, with vertical\nand horizontal lines in the side panels denoting the 90%\ncredible interval for the marginalized one-dimensional pos-\nterior distributions.\nAlso shown are the two O3 NSBH\nevents GW200105 162426 and GW200115 042309 (orange\nand blue, respectively; Abbott et al. 2021a) with FAR\n< 0.25 yr\u22121 (Abbott et al. 2023a), the two confident BNS\nevents GW170817 and GW190425 (pink and green, re-\nspectively; Abbott et al. 2017a, 2019a, 2020a, 2024), and\nGW190814 (red; Abbott et al. 2020c, 2024) where the sec-\nondary component may be a black hole or a neutron star.\nLines of constant mass ratio are indicated by dotted gray\nlines.\nThe gray shaded region marks the 3\u20135 M\u2299range\nof primary masses. The NSBH events and GW190814 use\ncombined posterior samples assuming a high-spin prior anal-\nogous to those presented in this work. The BNS events use\nhigh-spin IMRPhenomPv2 NRTidal (Dietrich et al. 2019a)\nsamples.\n(GW200105 162426 and GW200115 042309, henceforth\nabbreviated as GW200105 and GW200115) observed by\nthe LVK, as well as GW190814 (Abbott et al. 2017a,\n2020a,c, 2021a).\nTo capture dominant spin effects on the GW signal,\nwe present constraints on the effective inspiral spin \u03c7eff,\nwhich is defined as a mass-weighted projection of the\nspins along the unit Newtonian orbital angular momen-\ntum vector \u02c6LN (Damour 2001; Racine 2008; Ajith et al.\n2014),\n\u03c7eff =\n\u0010m1\nM \u03c71 + m2\nM \u03c72\n\u0011\n\u00b7 \u02c6LN,\n(1)\n\n15\nFigure 2.\nSelected source properties of GW230529.\nThe plot shows the one-dimensional (diagonal) and two-\ndimensional (off-diagonal) marginal posterior distributions\nfor the primary mass m1, the mass ratio q, and the spin\ncomponent parallel to the orbital angular momentum \u03c71,z \u2261\n\u03c71 \u00b7 \u02c6LN.\nThe shaded regions denote the posterior proba-\nbility, with the solid (dashed) curves marking the 50% and\n90% credible regions for the posteriors determined using a\nhigh-spin (low-spin) prior on the secondary of \u03c72 < 0.99\n(\u03c72 < 0.05).\nThe vertical lines in the one-dimensional\nmarginal posteriors mark the 90% credible intervals.\nwhere the dimensionless spin vector \u03c7i of each compo-\nnent is related to the spin angular momentum Si by\n\u03c7i = cSi/(Gm2\ni ). If \u03c7eff is negative, it indicates that\nat least one of the spin component projections must be\nantialigned with respect to the orbital angular momen-\ntum, i.e., \u03c7i,z \u2261\u03c7i \u00b7 \u02c6LN < 0. We measure an effective\ninspiral spin of \u03c7eff = \u22120.10+0.12\n\u22120.17, which is consistent\nwith a binary in which one of the spin components is\nantialigned or a binary with negligible spins. The mea-\nsurement is primarily driven by the spin component of\nthe primary compact object \u03c71,z = \u22120.11+0.19\n\u22120.35, with a\nprobability that \u03c71,z < 0 of 83%. However, there is a\ndegeneracy between the measured masses and spins of\nthe binary components such that more comparable mass\nratios correlate to more negative values of \u03c7eff (Cutler &\nFlanagan 1994) for this system. We show the correlation\nbetween \u03c71,z and the mass ratio and primary mass in\nFigure 2, with more negative values of \u03c71,z correspond-\ning to more symmetric mass ratios and smaller primary\nmasses. The secondary spin is only weakly constrained\nand broadly symmetric about 0, \u03c72,z = \u22120.03+0.43\n\u22120.52. We\nfind no evidence for precession, with the posteriors on\nthe effective precessing spin \u03c7p (Schmidt et al. 2015)\nbeing uninformative.\nThe presence of a neutron star in a compact binary im-\nprints tidal effects onto the emitted GW signal (Flana-\ngan & Hinderer 2008). The strength of this interaction is\ngoverned by the tidal deformability of the neutron star,\nwhich quantifies how easily the star will be deformed in\nthe presence of an external tidal field. In contrast, the\ntidal deformability of a black hole is zero (Binnington\n& Poisson 2009; Damour & Nagar 2009; Chia 2021), of-\nfering a potential avenue for distinguishing between a\nblack hole and a neutron star. We investigate the tidal\nconstraints for both the primary and secondary com-\nponents using waveform models that account for tidal\neffects (Dietrich et al. 2019a; Matas et al. 2020; Thomp-\nson et al. 2020a), which do not qualitatively change the\nmass and spin conclusions discussed above.\nIrrespec-\ntive of whether we analyze GW230529 with a NSBH\nmodel that assumes only the tidal deformability of the\nprimary compact object to be zero or a BNS model that\nincludes the tidal deformability of both objects, we find\nthe tidal deformability of the secondary object to be\nunconstrained. The dimensionless tidal deformability of\nthe primary peaks at zero, consistent with a black hole.\nThe constraints on this parameter are also consistent\nwith dense matter equation of state (EOS) predictions\nfor neutron stars in this mass range.\nWe also perform parameterized tests of the GW phase\nevolution to verify whether GW230529 is consistent with\ngeneral relativity and find no evidence of inconsisten-\ncies. More detailed information on tidal deformability\nanalyses and testing general relativity can be found in\nAppendices E.3 and F, respectively.\n5. IMPACT OF GW230529 ON MERGER RATES\nAND POPULATIONS\nWe provide a provisional update to the NSBH merger\nrate reported in our earlier studies (Abbott et al. 2021a,\n2023b) by incorporating data from the first 2 weeks of\nO4a using two different methods.\nIn the first, event-\nbased approach, we consider GW230529 to be represen-\ntative of a new class of CBCs and assume its contribu-\ntion to the total number of NSBH detections to be a sin-\ngle Poisson-distributed count (Kim et al. 2003; Abbott\net al. 2021a) over the span of time from the beginning\nof the first observing run (O1) through the first 2 weeks\nof O4a. We find the rate of GW230529-like mergers to\nbe R230529 = 55+127\n\u221247 Gpc\u22123 yr\u22121. When computing the\nrates of the significant NSBH events in O3 detected with\nFAR< 0.25 yr\u22121 (Abbott et al. 2021a, 2023a) using the\nsame method, we find a total event-based NSBH merger\n\n16\nFigure 3.\nPosterior on the merger rates of NSBH systems.\nThe solid and dashed lines represent the broad population-\nbased rate calculation and the event-based rate calculation,\nrespectively.\nrate of RNSBH = 85+116\n\u221257\nGpc\u22123 yr\u22121. Using this selec-\ntion criterion, the same as Abbott et al. (2023b), the\npopulation of NSBH mergers includes GW200105 and\nGW200115; we do not include GW190814, as its source\nbinary is most probably a BBH (Abbott et al. 2020c,\n2023b; Essick & Landry 2020).\nFor the second, broad population-based approach, we\nconsider GW200105, GW200115, and GW230529 to be\nmembers of a single CBC class, together with an ensem-\nble of less significant candidates. The definition of this\nclass is determined by a simple cut on masses and spins\nresulting in an NSBH-like region of parameter space. We\naggregate data from all the triggers found by GstLAL\nfrom the beginning of O1 through the first 2 weeks of\nO4a, assess their impact on the estimated merger rates\nof NSBHs while also accounting for the possibility that\nsome of them are of terrestrial origin (Farr et al. 2015;\nKapadia et al. 2020), and update the NSBH merger\nrate obtained at the end of O3 (Abbott et al. 2023a) to\nRNSBH = 94+109\n\u221264 Gpc\u22123 yr\u22121. Further details regarding\nthe classification of triggers in the population-based rate\nmethod can be found in Appendix G.\nWe show updates to both the event-based and\npopulation-based\nNSBH\nrate\nconstraints\nin\nFig-\nure 3.\nThe event-based rate estimates highlight that\nGW230529-like systems merge at a similar (or poten-\ntially higher) rate to the more asymmetric NSBHs iden-\ntified in GWTC-3. The population-based rate estimate\nis more representative of the full NSBH merger rate, as\nit includes less significant GW events in the data. Both\nof our updated estimates are consistent with the find-\nings of Abbott et al. (2021a) within the measurement\nuncertainties. Further details about rate estimates can\nbe found in Appendix G.\nIn addition to updates to the overall merger rate of\nNSBHs, we also study the impact of GW230529 on the\nmass and spin distributions of the compact binary pop-\nulation as inferred from GWTC-3 (Abbott et al. 2023b).\nWe employ hierarchical Bayesian inference to marginal-\nize over the properties of individual events and infer the\nparameters of a given population model (e.g., Thrane &\nTalbot 2019; Mandel et al. 2019; Vitale et al. 2020). The\nupdates to population model results in this work are pro-\nvisional because they only include one GW signal from\nO4a, although the biases resulting from this selection\nwill not be severe since GW230529 occurred near the\nstart of the observing run. We quantify this by compar-\ning the event-based rate estimate (which accounts for\nO4a sensitivity to compute its detectable time\u2013volume)\nwith the NSBH rates attained by the various population\nanalyses considered in this work, finding that they are\nconsistent with each other.\nWe use three different population models in our anal-\nysis. The first two models consider the population of\ncompact-object binaries as a whole without distinguish-\ning by source classification, using either the parame-\nterized Power law + Dip + Break model (Fish-\nbach et al. 2020; Farah et al. 2022; Abbott et al.\n2023b) or the nonparametric Binned Gaussian Pro-\ncess model (Mohite 2022; Ray et al. 2023b; Abbott et al.\n2023b). The Power law + Dip + Break model is\ndesigned to search for a separation in masses between\nneutron stars and black holes by explicitly allowing for,\nbut not enforcing, a dip in the component mass distri-\nbution. The Binned Gaussian Process model is de-\nsigned to capture the structure of the mass distribution\nwith minimal assumptions about the population. The\nbroad CBC population analyses include all candidates\nreported in GWTC-3 with FAR < 0.25 yr\u22121, the same\nselection criterion used in Abbott et al. (2023b, see Table\n1 therein). The third model we investigate (NSBH-pop;\nBiscoveanu et al. 2022) considers only the population of\nNSBH mergers with FAR < 0.25 yr\u22121. NSBH-pop is a\nparametric model designed to constrain the population\ndistributions of NSBH masses and black hole spin mag-\nnitudes. This model assumes all analyzed events have a\nblack hole primary and neutron star secondary; we do\nnot include GW190814 in this analysis. Further details\nregarding the population model parameterizations and\npriors can be found in Appendix H.\nThe inclusion of GW230529 in our population analyses\nhas several effects on the inferred properties of NSBH\nsystems and the CBC population as a whole.\n\n17\nFigure 4.\nThe differential merger rate of NSBH systems as a function of black hole masses (solid curves: mean; shaded\nregions: 90% credible interval) and minimum black hole mass (dashed lines: 90% credible interval) using the NSBH-pop model\nwith (teal) and without (gray) GW230529. The minimum black hole mass mBH,min is a parameter of the NSBH-pop population\nmodel; see Table 7. While the median rate is always inside the credible region, the mean can be outside the credible region.\nThe\ninferred\nminimum\nmass\nof\nblack\nholes\nin\nthe NSBH population decreases with the inclusion of\nGW230529. The mass spectrum of black holes in the\nNSBH population with and without GW230529 inferred\nusing the NSBH-pop model is shown in Figure 4. As\nthe source of GW230529 is the NSBH with the small-\nest black hole mass observed to date, the minimum\nmass of black holes in NSBH mergers shows a sig-\nnificant decrease with the inclusion of this candidate:\nmmin,BH = 3.4+1.0\n\u22121.2 M\u2299with GW230529 compared to\nmmin,BH = 6.0+1.8\n\u22123.2 M\u2299without. In contrast, the pa-\nrameter that governs the lower edge of the dip feature\nin the Power law + Dip + Break model, which rep-\nresents the minimum black hole mass in the CBC pop-\nulation, does not shift significantly with the inclusion\nof GW230529. This difference is because the Power\nlaw + Dip + Break model makes no assumptions\nabout the classification of the components and there-\nfore does not enforce sharp features at the edges of each\nsubpopulation, meaning that the source of GW230529\nis not necessarily an NSBH in this model. However, the\nBinned Gaussian Process and Power law + Dip\n+ Break models are designed to capture the structure\nof the full compact binary mass spectrum; because they\ndo not assign a source classification to either of the bi-\nnary components, features present in these population\nmodels can have differing astrophysical interpretations\nfrom the NSBH-pop model.\nGW230529 increases the inferred rate of compact bi-\nnary mergers with a component in the 3\u20135 M\u2299range. A\nregion of interest in the mass distribution is the border\nbetween the masses of neutron stars and black holes. We\nchoose 3\u20135 M\u2299to represent the nominal gap between\nthese populations. In Figure 5 we show the posterior on\nthe rate of mergers with one or both component masses\nin the 3\u20135 M\u2299range, with and without GW230529.\nFor the Power law + Dip + Break model there\nis a small increase in the merger rate within this mass\nrange, Rgap = 24+28\n\u221216 Gpc\u22123 yr\u22121 with GW230529 ver-\nsus Rgap = 17+25\n\u221214 Gpc\u22123 yr\u22121 without. For the Binned\nGaussian Process model there is a larger increase\nin the merger rate, Rgap = 33+89\n\u221229 Gpc\u22123 yr\u22121 with\nGW230529 versus Rgap = 7.5+46.4\n\u22126.5 Gpc\u22123 yr\u22121 without.\nThe differing degree of change between the two models\nis due to different assumptions for the mass ratio distri-\nbution of merging compact binaries, as well as the po-\ntential dip in the merger rate at low black hole masses\nbuilt into the Power law + Dip + Break model.\nBinned Gaussian Process does not fit for a specific\npairing function, while Power law + Dip + Break\nassumes the same mass ratio distribution throughout\nthe whole population of CBCs. As most observed BBHs\nfavor equal masses, any population model conditioned\non those observations should also favor equal masses in\nthe BBH mass range. The implicit assumptions within\nthe Power law + Dip + Break model require this\npreference to be imposed for all masses, including rel-\natively low mass systems like GW230529.\nHowever,\nthe assumptions in Binned Gaussian Process do not\nbroadcast this preference as strongly across different\nmass scales and therefore may support more asymmet-\nric mass ratios at lower masses. Regardless of the mass\nratio distribution assumptions made by each model, we\nfind that the inclusion of GW230529 provides further\n\n18\nFigure 5.\nPosterior on the merger rate of binaries with one\nor both components between 3 and 5 M\u2299. The solid curves\nshow the results from the Binned Gaussian Process analy-\nsis, and the dashed curves show the results from the Power\nlaw + Dip + Break analysis. Both models analyze the\nfull black hole and neutron star mass distribution. The teal\nand gray curves show the analysis results with and without\nGW230529, respectively.\nevidence that the \u223c3\u20135 M\u2299region is not completely\nempty.\nGW230529 is consistent with the population inferred\nfrom previously observed CBC candidates. In Figure 6,\nwe show the population distributions of the full black\nhole and neutron star mass spectrum for the primary\ncomponent of compact binary mergers using the Binned\nGaussian Process (top panel) and Power law +\nDip + Break (bottom panel) population models. We\nqualitatively see that GW230529 is not an outlier with\nrespect to the masses of previously observed compact-\nobject binaries because the inclusion of GW230529 in\nthe population does not significantly alter the full-\npopulation posterior constraints. This differs from the\ndetection of GW190814, which was an outlier with re-\nspect to the rest of the observed BBH population at the\ntime due to its small secondary mass (Essick et al. 2022).\nThe observation of GW190814 strongly suggested the re-\ngion between the masses of neutron stars and black holes\nwas populated (Abbott et al. 2023b), a conclusion that\nis strengthened with the detection of GW230529 (even\nthough it is not an outlier).\nThe component masses inferred for GW230529 differ\nacross differing population-informed priors. In Figure 7,\nwe show the mass and spin posteriors obtained using\npriors informed by each of the population models con-\nsidered in this work. The priors informed by the NSBH-\npop model prefer unequal mass ratios and small black\nFigure 6.\nThe differential binary merger rate as a function\nof the mass of the primary component using the Binned\nGaussian Process model (top panel) and the Power law\n+ Dip + Break model (bottom panel) for the full compact\nbinary population (solid curves: mean; shaded regions: 90%\ncredible interval) with (teal) and without (gray) GW230529.\nhole spins; they suppress the extended posterior tail out\nto equal masses and antialigned spins.\nThe Binned\nGaussian Process model also pulls the posteriors to\nmore asymmetric mass ratios and has less support for\nantialigned spins.\nAs shown in the top panel of Fig-\nure 6, the merger rate density inferred using the Binned\nGaussian Process model is nearly flat across the re-\ngion of parameter space covered by GW230529, mean-\ning that the priors informed by this population model\nhave less of an impact on the shape of the posterior\ncompared to the parameterized models considered. Un-\nlike the NSBH-pop model, the Power law + Dip +\nBreak model has a sharp drop in the merger rate above\n3 M\u2299.\nThis sharp feature results in the posterior on\nthe primary component being pulled below 3 M\u2299and\nthe posterior on the secondary being pulled to higher\nmasses. The Binned Gaussian Process model has a\n\n19\nFigure 7.\nPosterior distributions of GW230529 under vari-\nous prior assumptions. The solid teal curve shows the poste-\nrior distributions using the default high-spin priors described\nin Appendix D. The various dashed and dotted curves show\nposteriors obtained using population priors based on the\nNSBH-pop model (orange), Binned Gaussian Process\n(blue), and Power law + Dip + Break (red) models.\nsimilar feature, although it is closer to 2 M\u2299and there-\nfore too low to significantly affect the mass estimates for\nthis system. The Power law + Dip + Break model\nalso assumes the same preference for equal-mass systems\nacross the entire mass spectrum and thus, given that the\nmajority of the CBC population is consistent with sym-\nmetric mass ratios, infers that the GW230529 binary\ncomponents are more similar in mass. The combination\nof the drop in the differential merger rate and the pref-\nerence for symmetric mass ratios increases the support\nfor more extreme spins oriented in the hemisphere oppo-\nsite the orbital angular momentum. From these models\nwe find that the binary source of GW230529 either has\nasymmetric components with low values of \u03c7eff or has\ncomponents that are similar in mass with \u03c7eff \u223c\u22120.3.\nThese results highlight that the choice of prior has a\nsignificant impact on the inferred masses and spins of\nthe GW230529 source and hence the inferred nature of\nthe binary components.\nWe assess the nature of the\ncomponents further in Section 6. More details on the\npopulation prior reweighting are given in Appendix H.4.\nWe assess whether any of our population models are\nfavored as priors for GW230529 by calculating Bayes\nfactors. Given that the population models consider dif-\nferent sets of GW events, Bayesian evidences for each\npopulation model are not directly comparable.\nHow-\never, we may compare the evidence for the single event\nGW230529 under different models. In this calculation\nwe only consider the effect of the different shapes of the\npopulation models, not their overall normalization over\nthe broader mass parameter space considered by each\nmodel. Thus, we normalize each of the population mod-\nels over the same range of component masses as the orig-\ninal parameter estimation priors. We find no significant\npreference between the population models, with Bayes\nfactors between all three models of log10 B \u22721.0.\n6. NATURE OF THE COMPACT OBJECTS IN\nTHE GW230529 BINARY\nWithout clear evidence for or against tidal effects in\nthe signal, the physical nature of the compact objects in\nthe GW230529 source binary can be assessed by com-\nparing the measured masses and spins of each compo-\nnent with the maximum masses and spins of neutron\nstars allowed by previous observational data. However,\nstatistical uncertainties in component masses make it\nespecially difficult to determine whether compact ob-\njects with masses between \u223c2.5 and 5 M\u2299are consis-\ntent with being black holes or neutron stars (Hannam\net al. 2013; Littenberg et al. 2015). Nevertheless, we as-\nsess the nature of the source components by marginal-\nizing over our uncertainties in the masses and spins of\nGW230529, in the population of merging binaries, and\nin the supranuclear EOS, to compute the posterior prob-\nability that each component had a mass and spin less\nthan the maximum mass and spin supported by the\nEOS. We follow the procedure introduced in the con-\ntext of GW190814 (Abbott et al. 2020c; Essick & Landry\n2020), which relied on only the maximum neutron star\nmass, and has subsequently been extended to include\nthe effects of spin (Abbott et al. 2020c, 2021a, 2023b).\nOur analysis provides only an upper limit on the prob-\nability that an object is a neutron star, as it assumes\nthat all objects consistent with the maximum mass and\nspin of a neutron star are indeed neutron stars (Essick\n& Landry 2020).\nTo assess the nature of the component masses of the\nGW230529 source, we consider two versions of an as-\ntrophysically agnostic population model that is uniform\nin source-frame component masses and spin magnitudes\nand isotropic in spin orientations: one with component\nspin magnitudes \u03c7i \u2261|\u03c7i| that are allowed to be large\n(\u03c71, \u03c72 \u22640.99) and one where they are restricted a\npriori to be small (\u03c71, \u03c72 \u22640.05).\nWe also consider\nthe Power law + Dip + Break population model\n(Appendix H.2) fit to the GW candidates from GWTC-\n3 (Abbott et al. 2023a); including GW230529 in the\n\n20\nTable 3.\nProbabilistic source classification based on consistency of component masses with the maximum neutron star mass\nand spin. All estimates marginalize over uncertainty in the masses, spins, and redshift of the source as well as uncertainty in\nthe astrophysical population and the EOS. We consider three population models: two distributions that use astrophysically\nagnostic priors and consider either large spins (\u03c71, \u03c72 \u22640.99) or small spins (\u03c71, \u03c72 \u22640.05), and a population prior using the\nPower law + Dip + Break model fit with only the events from GWTC-3 (Abbott et al. 2023b). We use an EOS posterior\nconditioned on massive pulsars and GW observations (Landry et al. 2020). All errors approximate 90% uncertainty from the\nfinite number of Monte Carlo samples used with the exception of the low-spin results, for which we only place an upper or lower\nbound.\n\u03c71, \u03c72 \u22640.99\n\u03c71, \u03c72 \u22640.05\nPower law + Dip + Break\nP(m1 is NS)\n2.9 \u00b1 0.4%\n< 0.1%\n8.8 \u00b1 2.8%\nP(m2 is NS)\n96.1 \u00b1 0.4%\n> 99.9%\n98.4 \u00b1 1.3%\npopulation model does not significantly affect the re-\nsults. For each population, we marginalize over the un-\ncertainty in the maximum neutron star mass conditioned\non the existence of massive pulsars and previous GW ob-\nservations (Landry et al. 2020) using a flexible Gaussian\nprocess (GP) representation of the EOS (Landry & Es-\nsick 2019; Essick et al. 2020b). More information on the\nEOS choices can be found in Appendix I.\nTable 3 reports the probability that each component\nof the merger is consistent with a neutron star. In gen-\neral, we find that the secondary is almost certainly con-\nsistent with a neutron star, and the primary is most\nprobably a black hole.\nHowever, when incorporating\ninformation from the Power law + Dip + Break\npopulation model, we find that there is a \u223c1 in 10\nchance that the primary is consistent with a neutron\nstar. If we further relax the fixed spin assumptions im-\nplicit within the Power law + Dip + Break model\nfor objects with masses \u22642.5 M\u2299from \u03c7i \u22640.4 to\n\u03c7i \u22640.99 (see Appendix H.2), we can find probabilities\nas high as P(m1 is NS) = 27.3 \u00b1 3.8%. This ambigu-\nity is similar to the secondary component of GW190814\n(2.50 \u2264m2/M\u2299\u22642.67), which is consistent with a neu-\ntron star if it was rapidly spinning (e.g., Abbott et al.\n2020c; Essick & Landry 2020; Most et al. 2020a).\nThe differences observed between population models\nprimarily reflect the uncertainty in the mass ratio and\nspins of the GW230529 source. For example, incorporat-\ning the Power law + Dip + Break population model\nas a prior updates the posterior for m1 from 3.6+0.8\n\u22121.2 M\u2299\nto 2.7+0.9\n\u22120.4 M\u2299. Additional observations of compact ob-\njects in or near the lower mass gap may clarify the com-\nposition of GW230529 by further constraining the ex-\nact shape of the distribution of compact objects below\n\u223c5 M\u2299or the supranuclear EOS.\n7. IMPLICATIONS FOR MULTIMESSENGER\nASTROPHYSICS\nIn NSBH mergers, the neutron star can either plunge\ndirectly into the black hole or be tidally disrupted by its\ngravitational field. Tidal disruption would leave some\nremnant baryonic material outside the black hole that\ncould potentially power a range of EM counterparts, in-\ncluding a kilonova (Lattimer & Schramm 1974; Li &\nPaczynski 1998; Tanaka & Hotokezaka 2013; Tanaka\net al. 2014; Fern\u00b4andez et al. 2017; Kawaguchi et al. 2016)\nor a gamma-ray burst (Mochkovitch et al. 1993; Janka\net al. 1999; Paschalidis et al. 2015; Shapiro 2017; Ruiz\net al. 2018). The conditions for tidal disruption are de-\ntermined by the mass ratio of the binary, the compo-\nnent of the black hole spin aligned with the orbital an-\ngular momentum, and the compactness of the neutron\nstar (Pannarale et al. 2011; Foucart 2012; Foucart et al.\n2018; Kr\u00a8uger & Foucart 2020).\nWhile the disruption\nprobability of the neutron star in GW230529 can be in-\nferred based on the binary parameters, we are unlikely\nto directly observe the disruption in the GW signal with-\nout next-generation observatories (Clarke et al. 2023).\nWe use the ensemble of fitting formulae collected in\nBiscoveanu et al. (2022), including the spin-dependent\nproperties of neutron stars (Foucart et al. 2018; Cipol-\nletta et al. 2015; Breu & Rezzolla 2016; Most et al.\n2020b), to constrain the remnant baryon mass out-\nside the final black hole following GW230529, assum-\ning it was produced by an NSBH merger. We addition-\nally marginalize over the uncertainty in the GP-EOS\nresults obtained using the method introduced in Sec-\ntion 6 (Legred et al. 2021, 2022). Using the high-spin\ncombined posterior samples obtained with default pri-\nors, we find a probability of neutron star tidal disruption\nof 0.1, corresponding to an upper limit on the remnant\nbaryon mass produced in the merger of 0.052 M\u2299at 99%\n\n21\ncredibility. The low secondary spin priors (\u03c72 < 0.05)\nyield a tidal disruption probability and remnant baryon\nmass upper limit of 0.042 and 0.011 M\u2299, respectively.\nA rapidly spinning neutron star is less compact than a\nslowly spinning neutron star of the same gravitational\nmass under the same EOS. This decrease in compact-\nness leads to a larger disruption probability and a larger\nremnant baryon mass following the merger, explaining\nthe trend we see when comparing the results obtained\nunder the low secondary spin and high-spin priors. The\nsource binary of GW230529 is the most probable of the\nconfident NSBHs reported by the LVK to have under-\ngone tidal disruption because of the increased symmetry\nin its component masses. However, the exact value of\nthe tidal disruption probability and the remnant baryon\nmass for this system are prior dependent.\nWe can also gauge how the inclusion of GW230529\nimpacts estimates of the fraction of NSBH systems de-\ntected in GWs that may be accompanied by an EM\ncounterpart, fEM-bright. Using the mass and spin dis-\ntributions inferred under the NSBH-pop population\nmodel described in Section 5, we find a 90% credi-\nble upper limit on the fraction of NSBH mergers that\nmay be EM-bright of fEM-bright \u22640.18 when includ-\ning GW230529, an increase relative to fEM-bright \u22640.06\nobtained when excluding GW230529 from the analysis.\nWhen including GP-EOS constraints additionally con-\nditioned on NICER observations (Legred et al. 2021,\n2022), the posterior on the EM-bright fraction fur-\nther increases to peak away from zero, fEM-bright =\n0.13+0.19\n\u22120.11. Additional details on analyses with this alter-\nnative choice of EOS constraint are given in Appendix I.\nThese estimates assume that any remnant baryon mass\nM b\nrem,min \u22650 could power a counterpart, although the\nactual threshold value is astrophysically uncertain. Fig-\nure 8 shows the posterior for fEM\u2013bright with and with-\nout the inclusion of GW230529. While the exact value\nof fEM-bright depends on the assumed population model,\nthe increase in fEM-bright for NSBHs upon the inclusion\nof GW230529 in the population is robust against mod-\neling assumptions.\nUsing these updated multimessenger prospects, we\ncan infer the contribution of NSBH mergers to the pro-\nduction of heavy elements (Biscoveanu et al. 2022) and\nthe generation of gamma-ray bursts (Biscoveanu et al.\n2023).\nAssuming that all remnant baryon mass pro-\nduced in NSBH mergers is enriched in heavy elements\nvia r-process nucleosynthesis (Lattimer & Schramm\n1974, 1976), we infer that NSBH mergers contribute at\nmost 1.1 M\u2299Gpc\u22123 yr\u22121 to the production of heavy\nelements and that the rate of gamma-ray bursts with\nNSBH progenitors is at most 23 Gpc\u22123 yr\u22121 at 90%\nFigure 8.\nPosterior on the fraction of NSBH systems\ndetected with GWs that may be EM bright, fEM-bright, de-\npending on the threshold remnant mass required to power\na counterpart, f(M b\nrem > M b\nrem,min). The solid and dashed\ncurves represent different values of the minimum remnant\nmass M b\nrem,min. The teal and gray curves show the analysis\nresults with and without GW230529, respectively.\ncredibility.\nThis likely represents a small fraction\nof all short gamma-ray bursts, for which astrophysi-\ncal beaming-corrected rate estimates are in the range\nof O(10\u20131000) Gpc\u22123 yr\u22121 (Mandel & Broekgaarden\n2022), and of the total r-process material produced by\ncompact-object mergers (C\u02c6ot\u00b4e et al. 2018; Chen et al.\n2021b).\nNo significant counterpart candidates have been re-\nported for GW230529 (IceCube Collaboration 2023;\nKarambelkar et al. 2023; Lipunov et al. 2023; Longo\net al. 2023; Lesage et al. 2023; Savchenko et al. 2023;\nSugita et al. 2023a,b; Waratkar et al. 2023). This is un-\nsurprising given that it was only observed by a single\ndetector and hence was poorly localized on the sky.\n8. ASTROPHYSICAL IMPLICATIONS\nSince the late 1990s, there have been claims about the\nexistence of a mass gap between the maximum neutron\nstar mass and the minimum black hole mass (\u223c3\u20135 M\u2299)\nbased on dynamical mass measurements of Galactic X-\nray binaries (Bailyn et al. 1998; Ozel et al. 2010; Farr\net al. 2011b). The lower edge of this purported mass\ngap depends on the maximum possible mass with which\na neutron star can form in a supernova explosion, which\ncannot exceed the maximum allowed neutron star mass\ngiven by the EOS. Some EOSs support masses up to\n\u223c3 M\u2299for nonrotating neutron stars (Mueller & Serot\n1996; Godzieba et al. 2021) and even larger masses for\nrotating neutron stars (Friedman & Ipser 1987; Cook\net al. 1994), although such large values are disfavored by\n\n22\nthe tidal deformability inferred for GW170817 (Abbott\net al. 2019b) and Galactic observations (Alsing et al.\n2018; Farr & Chatziioannou 2020). The upper edge and\nextent of the mass gap depend on the minimum black\nhole mass that can form from stellar core collapse. How-\never, it remains an open question whether observational\nor evolutionary selection effects inherent to the detec-\ntion of Galactic X-ray binaries can lead to the observed\ngap in compact-object masses (Fryer & Kalogera 2001;\nKreidberg et al. 2012; Siegel et al. 2023).\nIn recent years, new EM observations have unveiled a\nfew candidates in the \u223c3 M\u2299region, mostly from nonin-\nteracting binary systems (Thompson et al. 2019; van den\nHeuvel & Tauris 2020; Thompson et al. 2020b) and ra-\ndio surveys for pulsar binary systems (Barr et al. 2024).\nMicrolensing surveys do not support the existence of a\nmass gap but cannot exclude it either (Wyrzykowski\net al. 2016; Wyrzykowski & Mandel 2020). The LVK\nhas already observed one component of a merger whose\nmass falls between the most massive neutron stars and\nleast massive black holes observed in the Galaxy: the\nsecondary component of GW190814 (2.5\u20132.7 M\u2299at the\n90% credible level; Abbott et al. 2020c, 2024).\nThe\nsecondary components of the GW200210 092254 and\nGW190917 114630 source binaries also have support in\nthe lower mass gap (Abbott et al. 2024, 2023a), although\ntheir mass estimates are also consistent with a high-mass\nneutron star. Unlike GW230529, the primary compo-\nnents of all three of these binaries can be confidently\nidentified as black holes. Overall, the existence of a mass\ngap between the most massive neutron stars and least\nmassive black holes still stands as an open question in\nastrophysics.\nGW230529 is the first compact binary with a primary\ncomponent that has a high probability of residing in the\nlower mass gap. Hence, GW230529 reinforces the con-\nclusion that the 3\u20135 M\u2299range is not completely empty\n(see Figure 5 in Section 5). However, the 3\u20135 M\u2299range\nmay still be less populated than the surrounding regions\nof the mass spectrum. This conclusion is consistent with\nprevious population analyses and rate estimates based\non GWTC-3 (Abbott et al. 2023b).\nThe formation of GW230529 raises a number of ques-\ntions. Given our current understanding of core collapse\nin massive stars (O\u2019Connor & Ott 2011; Janka 2012;\nErtl et al. 2020), it is unlikely that the primary compo-\nnent formed via direct collapse because of its low mass,\nalthough stochasticity in the physical mechanisms that\ndetermine remnant mass may populate the low-mass end\nof the black hole mass spectrum (Mandel & M\u00a8uller 2020;\nAntoniadis et al. 2022). Formation by fallback is a vi-\nable scenario: recent numerical models of core-collapse\nsupernovae suggest that the formation of 3\u20136 M\u2299black\nholes via substantial fallback is rare but still possible\n(e.g., Sukhbold et al. 2016; Ertl et al. 2020; Vigna-\nG\u00b4omez et al. 2021). One-dimensional hydrodynamical\nsimulations of core collapse adopting pure helium star\nmodels predict that there is no empty gap, only a less\npopulated region between 3 and 5 M\u2299, with the low-\nest mass of black holes produced by prompt implosions\nstarting at \u22486 M\u2299(Ertl et al. 2020). Another rele-\nvant parameter is the timescale for instability growth\nand launch of the core-collapse supernova; if this is long\nenough (\u2273200 ms), the proto-neutron star might ac-\ncrete enough mass before the explosion to become a\nmass-gap object (Fryer & Kalogera 2001; Fryer et al.\n2012).\nCompact binary population synthesis models\nthat allow for longer instability growth timescales natu-\nrally produce merging NSBH systems with the primary\ncomponent in the lower mass gap (Belczynski et al. 2012;\nChattopadhyay et al. 2021; Zevin et al. 2020; Broekgaar-\nden et al. 2021; Olejak et al. 2022). It may also be pos-\nsible to form mass-gap objects through accretion onto a\nneutron star. If the first-born neutron star in the binary\naccretes enough material prior to the formation of the\nsecond-born compact object, it can trigger an accretion-\ninduced collapse into a black hole, yielding a mass-gap\nobject (Siegel et al. 2023). This scenario may be aided\nby super-Eddington accretion onto the first-born neu-\ntron star, which has been proposed to explain NSBHs\nwith mass-gap black holes like the source of GW230529\n(Zhu et al. 2024). Considering the large number of un-\ncertainties about the outcome of core-collapse super-\nnovae (e.g., Burrows & Vartanyan 2021), the primary\nmass of GW230529 provides a piece of evidence to in-\nform and constrain future models. Overall, astrophysi-\ncal models in the past have preferentially adopted pre-\nscriptions that enforce the presence of a lower mass\ngap (e.g., Fryer et al. 2012), and the inferred rate of\nGW230529-like systems urges a change of paradigm in\nsuch model assumptions.\nAlternatively, the primary component of GW230529\nmight be the result of the merger of two neutron stars.\nFor instance, the 90% credible intervals for the remnant\nmass of GW190425 and the primary mass of GW230529\noverlap (Abbott et al. 2020a). This may hint at a sce-\nnario where the primary component could be either the\nmember of a former triple or quadruple system (Fra-\ngione et al. 2020; Lu et al. 2021; Vynatheya & Hamers\n2022; Gayathri et al. 2023), or the result of a dynami-\ncal capture in a star cluster (Clausen et al. 2013; Gupta\net al. 2020; Rastello et al. 2020; Arca Sedda 2020, 2021)\nor an active galactic nucleus disk (Tagawa et al. 2021;\nYang et al. 2020). This scenario was proposed for the\n\n23\nformation of a compact object discovered in a binary\nwith a pulsar in the globular cluster NGC 1851, which is\nmeasured to have a mass of 2.09\u20132.71 M\u2299at 95% confi-\ndence (Barr et al. 2024). However, dynamically induced\nBNS mergers are predicted to be rare in dense stellar en-\nvironments (O(10\u22122) Gpc\u22123 yr\u22121; e.g., Ye et al. 2020;\nSamsing & Hotokezaka 2021). Thus, the rate of mergers\nbetween a BNS merger remnant and a neutron star may\nbe at least several orders of magnitude lower than the\nrate we infer for GW230529-like mergers, making this\nscenario improbable.\nNon-stellar-origin black hole formation scenarios such\nas primordial black holes (e.g., Clesse & Garcia-Bellido\n2022) remain a possibility. However, there are signifi-\ncant uncertainties in the predicted mass spectrum and\nmerger rate of primordial black hole binaries, thus mak-\ning it difficult to attribute a primordial origin to com-\npact objects that have masses consistent with predic-\ntions from massive-star core collapse. Furthermore, re-\nsults from microlensing surveys indicate that primordial\nblack hole mergers cannot be a dominant source of GWs\nin the local universe (Mroz et al. 2024).\nIt has also been suggested that mergers apparently in-\nvolving mass-gap objects could instead be gravitation-\nally lensed BNSs (Bianconi et al. 2023; Magare et al.\n2023), with the lensing magnification making them ap-\npear heavier and closer (Wang et al. 1996; Dai et al.\n2017; Hannuksela et al. 2019).\nThis scenario is diffi-\ncult to explicitly test in the absence of tidal informa-\ntion (Pang et al. 2020) or EM counterparts (Bianconi\net al. 2023), but the expected relative rate of strong lens-\ning is low at current detector sensitivities (Smith et al.\n2023; Magare et al. 2023; Abbott et al. 2023c).\nFinally, we also find mild support for the possibility\nthat the primary component is a neutron star rather\nthan a black hole when considering the population-based\nPower law + Dip + Break prior that incorporates\nthe potential presence of a gap at low black hole masses.\nIn this case, GW230529 would be the most massive neu-\ntron star binary yet observed, with both components\n\u22732.0 M\u2299, and have non zero spins that are anti aligned\nwith the orbital angular momentum. The effective in-\nspiral spin of the BNSs in this scenario would differ\nsignificantly from BNS sources previously observed in\nGWs (Abbott et al. 2017a, 2020a) as well as those in-\nferred for Galactic BNSs if they were to merge (Zhu\net al. 2018). Spins oriented in the hemisphere opposite\nthe binary orbital angular momentum could be the re-\nsult of supernova natal kicks (Kalogera 2000; Farr et al.\n2011a; O\u2019Shaughnessy et al. 2017; Chan et al. 2020) or\nspin-axis tossing (Tauris 2022) at birth. For example,\none of the neutron stars in the binary pulsar system\nJ0737\u20133039 is significantly misaligned with respect to\nboth the spin of its companion and the orbital angu-\nlar momentum of the binary system, which may require\noff-axis kicks (Farr et al. 2011a). Alternatively, isotropi-\ncally oriented component spins that result from random\npairing in dynamical environments could lead to the sig-\nnificant spin misalignment (e.g., Rodriguez et al. 2016).\n9. SUMMARY\nGW230529 is a GW signal from the coalescence of a\n2.5\u20134.5 M\u2299compact object and a compact object con-\nsistent with neutron star masses.\nThe more massive\ncomponent in the merger provides evidence that com-\npact objects in the hypothesized lower mass gap ex-\nist in merging binaries.\nBased on mass estimates of\nthe two components in the merger and current con-\nstraints on the supranuclear EOS, we find the most prob-\nable interpretation of the GW230529 source to be an\nNSBH coalescence. In this scenario, the source binary\nof GW230529 is the most symmetric-mass NSBH merger\nyet observed, and the primary component of the merger\nis the lowest-mass primary black hole observed in GWs\nto date. Because NSBHs with more symmetric masses\nare more susceptible to tidal disruption, the observa-\ntion of GW230529 implies that more NSBHs than pre-\nviously inferred may produce EM counterparts. How-\never, we cannot rule out the contrasting scenario that\nthe source of GW230529 consisted of two neutron stars\nrather than a neutron star and a black hole. In this case,\nthe source of GW230529 would be the only BNS coales-\ncence observed to have strong support for nonzero and\nantialigned spins, as well as the highest-mass BNS sys-\ntem observed to date. Regardless of the true nature of\nthe GW230529 source, it is a novel addition to the grow-\ning population of CBCs observed via their GW emission\nand highlights the importance of continued exploration\nof the CBC parameter space in O4 and beyond.\nStrain data containing the signal from the LIGO Liv-\ningston observatory are available from the Gravitational\nWave Open Science Center.1\nSpecifically, we release\nthe L1:GDS-CALIB STRAIN CLEAN AR channel, where the\nAR designation means that the strain data are analy-\nsis ready; this strain channel was also released at the\nend of O3.\nSamples from the posterior distributions\nof the source parameters, hyperposterior distributions\nfrom population analyses, and notebooks for reproduc-\ning all results and figures in this paper are available on\nZenodo (LIGO Scientific, Virgo, and KAGRA Collabo-\n1 https://doi.org/10.7935/6k89-7q62\n\n24\nration 2024). The software packages used in our analyses\nare open-source.\nThis material is based on work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS), and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies, as well as by the Council of Scientific and In-\ndustrial Research of India, the Department of Science\nand Technology, India, the Science & Engineering Re-\nsearch Board (SERB), India, the Ministry of Human Re-\nsource Development, India, the Spanish Agencia Estatal\nde Investigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comuni-\ntat Auton`oma de les Illes Balears through the Direcci\u00b4o\nGeneral de Recerca, Innovaci\u00b4o i Transformaci\u00b4o Digi-\ntal with funds from the Tourist Stay Tax Law ITS\n2017-006, the Conselleria d\u2019Economia, Hisenda i Inno-\nvaci\u00b4o, the FEDER Operational Program 2021-2027 of\nthe Balearic Islands, the Conselleria d\u2019Innovaci\u00b4o, Uni-\nversitats, Ci`encia i Societat Digital de la Generalitat\nValenciana and the CERCA Programme Generalitat de\nCatalunya, Spain, the National Science Centre of Poland\nand the European Union \u2013 European Regional Develop-\nment Fund; Foundation for Polish Science (FNP), the\nPolish Ministry of Science and Higher Education, the\nSwiss National Science Foundation (SNSF), the Rus-\nsian Science Foundation, the European Commission,\nthe European Social Funds (ESF), the European Re-\ngional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the\nNational Research, Development and Innovation Office\nHungary (NKFIH), the National Research Foundation\nof Korea, the Natural Science and Engineering Research\nCouncil Canada, Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoreti-\ncal Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council\nof Hong Kong, the National Natural Science Founda-\ntion of China (NSFC), the Leverhulme Trust, the Re-\nsearch Corporation, the National Science and Technol-\nogy Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The au-\nthors gratefully acknowledge the support of the NSF,\nSTFC, INFN, and CNRS for provision of computa-\ntional resources. This work was supported by MEXT,\nJSPS Leading-edge Research Infrastructure Program,\nJSPS Grant-in-Aid for Specially Promoted Research\n26000005, JSPS Grant-in-Aid for Scientific Research on\nInnovative Areas 2905: JP17H06358, JP17H06361 and\nJP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grant-in-Aid for Scientific\nResearch (S) 17H06133 and 20H05639, JSPS Grant-\nin-Aid for Transformative Research Areas (A) 20A203:\nJP20H05854, the joint research program of the Insti-\ntute for Cosmic Ray Research, University of Tokyo, Na-\ntional Research Foundation (NRF), Computing Infras-\ntructure Project of Global Science experimental Data\nhub Center (GSDC) at KISTI, Korea Astronomy and\nSpace Science Institute (KASI), and Ministry of Sci-\nence and ICT (MSIT) in Korea, Academia Sinica (AS),\nAS Grid Center (ASGC) and the National Science and\nTechnology Council (NSTC) in Taiwan under grants in-\ncluding the Rising Star Program and Science Vanguard\nResearch Program, Advanced Technology Center (ATC)\nof NAOJ, and Mechanical Engineering Center of KEK.\nWe thank the anonymous journal referee for helpful com-\nments.\nSoftware:\nCalibration of the LIGO strain data\nwas performed with a GstLAL-based calibration soft-\nware pipeline (Viets et al. 2018). Data-quality prod-\nucts and event-validation results were computed us-\ning the DMT (Zweizig, J. 2006), DQR (LIGO Sci-\nentific Collaboration and Virgo Collaboration 2018),\nDQSEGDB (Fisher et al. 2021), gwdetchar (Urban et al.\n2021), hveto (Smith et al. 2011), iDQ (Essick et al.\n2020a), Omicron (Robinet et al. 2020), and Python-\nVirgoTools (Virgo Collaboration 2021) software pack-\nages and contributing software tools. Analyses in this\ncatalog relied on software from the LVK Algorithm Li-\n\n25\nbrary Suite (LIGO Scientific, Virgo, and KAGRA Col-\nlaboration 2018). The detection of the signals and subse-\nquent significance evaluations were performed with the\nGstLAL-based inspiral software pipeline (Messick et al.\n2017; Sachdev et al. 2019; Hanna et al. 2020; Cannon\net al. 2021), with the MBTA pipeline (Adams et al.\n2016; Aubin et al. 2021), and with the PyCBC (Us-\nman et al. 2016; Nitz et al. 2017; Davies et al. 2020)\npackages. Estimates of the noise spectra and glitch mod-\nels were obtained using BayesWave (Cornish & Litten-\nberg 2015; Littenberg et al. 2016; Cornish et al. 2021).\nLow-latency source localization was performed using\nBAYESTAR (Singer & Price 2016). Source-parameter\nestimation was primarily performed with the Bilby\nand Parallel Bilby libraries (Ashton et al. 2019;\nSmith et al. 2020; Romero-Shaw et al. 2020) using\nthe Dynesty nested sampling package (Speagle 2020).\nSEOBNRv5PHM waveforms used in parameter estima-\ntion were generated using pySEOBNR (Mihaylov et al.\n2023). FTI and TIGER waveforms used for testing gen-\neral relativity were generated using Bilby TGR (Ash-\nton et al. 2024). PESummary was used to post-process\nand collate parameter estimation results (Hoy & Ray-\nmond 2021). The various stages of the parameter es-\ntimation analysis were managed with the Asimov li-\nbrary (Williams et al. 2023). Plots were prepared with\nMatplotlib (Hunter 2007), seaborn (Waskom 2021)\nand GWpy (Macleod et al. 2021). NumPy (Harris et al.\n2020) and SciPy (Virtanen et al. 2020) were used for\nanalyses in the manuscript.\nAPPENDIX\nA. UPGRADES TO THE DETECTOR NETWORK FOR O4\nThe Advanced LIGO, Advanced Virgo, and KAGRA detectors have all undergone a series of upgrades to improve\nthe network sensitivity in preparation for O4. In this appendix we focus on upgrades made to the LIGO Livingston\nobservatory, as it was the only detector to observe GW230529; similar upgrades were made at LIGO Hanford. Some\nof these improvements are a part of the Advanced LIGO Plus (A+) detector upgrades (Abbott et al. 2020b).\nThe principal commissioning work done in preparation for O4 was to enhance the optics systems in the detector.\nThe pre-stabilized laser was redesigned for O4 with amplifiers allowing input power up to 125 W (Bode et al. 2020;\nCahillane & Mansell 2022). LIGO Livingston operated at 63 W in O4a. Both end test masses at LIGO Livingston\nwere replaced because their mirror coatings contained small, pointlike absorbers that limited detector sensitivity by\ndegrading the power-recycling gain (Brooks et al. 2021). For O4, frequency-dependent squeezing was implemented\nwith the addition of a 300 m filter cavity to rotate the squeezed vacuum quadrature across the bandwidth of the\ndetector (Dwyer et al. 2022; McCuller et al. 2020). With frequency-dependent squeezing, uncertainty is reduced in\nboth the amplitude and phase quadratures, allowing for a broadband reduction in quantum noise (Ganapathy et al.\n2023). Squeezing was implemented independently of frequency in O3, which only reduced the quantum noise at high\nfrequencies (Tse et al. 2019).\nOther commissioning work was done to improve data quality and reduce noise at low frequencies. For O4, scattered-\nlight noise was mitigated by removing some problematic scattering surfaces and improving the resonant damping of\nother scatterers (Soni et al. 2020; Davis et al. 2021). Low-frequency technical noise (i.e., noise that is not intrinsic to\nthe detector design but can limit the detector sensitivity and performance) was reduced with the commissioning of\nfeedback control loops, noise subtraction, and better electronics. Overall, the upgrades made during the commissioning\nperiod for O4 led to a broadband reduction in noise and improvement in detector sensitivity and performance.\nB. DETECTION TIME LINE AND CIRCULARS\nThe LVK issues low-latency alerts to facilitate prompt follow-up of GW candidates (Chaudhary et al. 2023).\nGW230529 was initially identified in a low-latency search using data from the LIGO Livingston observatory. The\ncandidate was given the name S230529ay in the Gravitational-Wave Candidate Event Database (GraceDB).2\nAfter the detection of GW230529, an initial notice was sent out to astronomers through NASA\u2019s General Coordinates\nNetwork (GCN; LIGO Scientific, Virgo, and KAGRA Collaboration 2023a). The sky localization computed in low\nlatency by BAYESTAR (Singer & Price 2016; Singer et al. 2016) had a 90% credible area of \u224824,200 deg2; the large\ncredible area was due to GW230529 only being observed by a single detector. The initial alert also included low-latency\n2 https://gracedb.ligo.org/\n\n26\nFigure 9.\nThe noise background for the LIGO Livingston observatory collected by the GstLAL pipeline in offline mode,\nwith the S/N\u2013\u03be2 values of GW230529 overlaid. The test statistic \u03be2 measures signal consistency. The background is collected\nfrom templates that are part of the same bin as the template that recovered GW230529 and is consequently the background\nused to rank GW230529 and calculate its significance. The background distribution has effectively no support at the position\nof GW230529. The color bar represents the probability of producing a certain S/N and \u03be2 from noise triggers.\nestimates of the mass-based source classification (BNS, BBH, and NSBH) produced by the PyCBC pipeline (Villa-\nOrtega et al. 2022). Additional estimates that the source binary of GW230529 contained at least one neutron star (>\n99.9%), contained at least one compact object in the lower mass gap 3\u20135 M\u2299(98.5%), and had neutron star matter\nejected outside the final compact object (12.1%) were produced by a machine-learning method trained to infer source\nproperties from the search pipeline results (Chatterjee et al. 2020).\nLow-latency parameter estimation was performed with Bilby (Ashton et al. 2019; Romero-Shaw et al. 2020) and used\nto produce an updated sky localization and estimates of source properties sent out in another alert (LIGO Scientific,\nVirgo, and KAGRA Collaboration 2023b). The updated sky localization had a 90% credible area of \u224825,600 deg2.\nThe updated estimate of source properties led to decreases in the probabilities that the source binary included at least\none neutron star (98.5%), one compact object in the mass gap (69.4%), and ejected matter outside the remnant object\n(1.1%).\nC. QUANTIFYING SIGNIFICANCE FOR A SINGLE-DETECTOR CANDIDATE EVENT\nEach search pipeline has its own method for calculating the FAR of a single-detector GW candidate. In this appendix\nwe will summarize these methods.\nC.1. GstLAL\nThe GstLAL pipeline assigns a likelihood ratio to all of its candidate signals as the ranking statistic to estimate\ntheir significance. The likelihood ratio is the ratio of the probability of obtaining the candidate under the signal\nhypothesis to the probability of obtaining the candidate under the noise hypothesis. The latter probability is largely\ncalculated by collecting S/N and \u03be2 statistics of noise triggers during the analysis, where \u03be2 is a signal consistency\ntest statistic (Messick et al. 2017). Similar templates in the template bank are grouped together on the basis of the\npost-Newtonian (PN) expansion of their waveforms (Morisaki & Raymond 2020; Sakon et al. 2024). Each template bin\ncollects its own S/N and \u03be2 statistics, which get used to rank candidates recovered by templates in that bin. Further\ndetails about the calculation of the probability of obtaining the candidate under the noise hypothesis, as well as the\nGstLAL likelihood ratio in general, can be found in Tsukada et al. (2023). The S/N\u2013\u03be2 statistics collected from noise\ntriggers from the same template bin as GW230529 with GW230529 superimposed are shown in Figure 9. GW230529\nclearly stands out from the background, and there are no noise triggers at its position in S/N\u2013\u03be2 space.\nSince nonstationary noise transients known as glitches (Nuttall 2018) are not expected to be correlated across\ndetectors, single-detector GW candidates, whether during times when a single or multiple detectors are observing, are\nmore likely to be glitches than coincident GW candidates. To account for this, the GstLAL pipeline downweights\n\n27\nFigure 10.\nRanking statistic distribution of MBTA single-detector triggers in the LIGO Livingston observatory during the\nfirst 2 weeks of O4, excluding significant public alerts aside from GW230529.\nthe logarithm of the likelihood ratio of single-detector candidates by subtracting an empirically tuned factor of 13,\nwhich is optimized to maximize the recovery of candidates with an astrophysical origin while minimizing the recovery\nof glitches (Abbott et al. 2020a). The FAR of the GstLAL pipeline for GW230529 quoted in Table 1 is calculated\nafter the application of this penalty.\nFinally, the FAR for a candidate in the search is computed by comparing its likelihood ratio with the likelihood ratios\nof noise triggers not found in coincidence, after accounting for the live time of the analysis. These noise triggers not\nfound in coincidence allow the pipeline to extrapolate the background distribution of likelihood ratios to large values,\nenabling the inverse FAR of a candidate to be greater than the duration of the analysis. While in the low-latency\nmode, the GstLAL FAR calculation uses the background from the start of the analysis period until the time of the\ncandidate. In contrast, for its offline analysis, the GstLAL pipeline uses background collected from the full analysis\nperiod, including the entirety of O4a, to rank candidates. This differs from the other search pipelines presented in\nthis work, which only use background from the first 2 weeks of O4a for their offline search results presented here.\nThe GstLAL offline analysis was performed using the same template bank as the online analysis (Sakon et al. 2024;\nEwing et al. 2024). Details are liable to change for future offline GstLAL analyses in O4a. However, for such a\nsignificant candidate as GW230529, we do not expect these changes to impact its interpretation as highly likely being\nof astrophysical origin.\nC.2. MBTA\nThe MBTA single-detector candidate search for O4a focuses on a subset of the full MBTA parameter space. The goal\nis to focus on BNS and NSBH signals, which are most interesting because of their rarity and possible EM counterparts.\nTheir long signal duration also makes them easier to identify and allows for a better sensitivity to be reached when\ncompared to a single-detector candidate search using the whole MBTA parameter space. The parameter space for the\nO4a online single-detector search was defined based on the detector-frame (redshifted) primary mass and chirp mass\nof the templates and motivated by the computation of the probability for whether a nonzero amount of neutron star\nmaterial remained outside the final remnant compact object (Chatterjee et al. 2020) introduced in Appendix B. The\nconsidered space is (1 + z) m1 < 50 M\u2299and (1 + z) M < 5 M\u2299(Juste 2023). For the offline analysis, this space was\nadapted and we consider only (1 + z) M < 7 M\u2299. MBTA online also applied selection criteria based on data-quality\ntests to its single-detector candidates (Juste 2023). This was changed to a reweighting of the ranking statistic for the\noffline analysis.\nThe ranking statistic for MBTA single-detector triggers is a reweighted S/N.\nThe reweighting is based on the\ncomputation of a quantity called auto \u03c72 (Aubin et al. 2021), which tests the consistency of the time evolution of the\nS/N time series. The additional reweighting used in the offline analysis relies on the computation of a quantity that\nidentifies an excess of S/N for single-detector triggers. The excess of S/N is larger for triggers that have a noise origin\ncompared to astrophysical signals or injections and therefore allows for discrimination between astrophysical signals\n\n28\nFigure 11.\nRanking statistic distribution of PyCBC offline single-detector triggers in the LIGO Livingston observatory\nduring the first 2 weeks of O4. The plotted distribution may include triggers from other less significant signals arriving during\nthe period analyzed.\nand noise. The ranking statistic distribution of the MBTA offline analysis for single-detector triggers during the first\n2 weeks of O4a is shown in Figure 10. Other triggers that produced significant public alerts have been removed from\nthe plotted distribution. GW230529 stands out from the background with a high ranking statistic that reflects the\nauto \u03c72 value being completely consistent with a signal origin.\nThe FAR in MBTA is a function of pastro (Andres et al. 2022), the probability of astrophysical origin of the\ncandidate. It is derived from the combined parameterizations of the FAR as a function of the ranking statistic and\nof pastro as a function of the ranking statistic. Inverting the latter gives the ranking statistic as a function of pastro\nand eventually the FAR as a function of pastro. The background estimation for MBTA single-detector triggers was\ncomputed differently during the online and offline analyses. The online analysis relies on the computation of simulated\nsingle-detector triggers obtained through random combinations of single frequency band data (Juste 2023). O4a online\nanalysis and the method of randomly combining single frequency band data showed that the background for MBTA\nsingle-detector triggers follows an exponential distribution and is stable in time beyond statistical fluctuations. This\nprompted us to update the model we use for the offline (and future) analyses to reach greater sensitivity. This new\nmodel involves extrapolating the observed distribution of single-detector triggers and removing the significant triggers.\nA safety margin is used in the extrapolation such that the FAR is overestimated relative to the best-fit extrapolated\ndistribution. This change in methods, in addition to the difference in handling of single-detector triggers online and\noffline, explains the difference in inverse FAR for the online (1.1 yr) and offline (>1000 yr) analyses.\nC.3. PyCBC\nIn PyCBC, each GW candidate is assigned a ranking statistic, and then a FAR is calculated by comparing the\nranking statistic of the candidate with the background distribution. The details of this procedure differ between the\nonline and offline versions of the PyCBC search.\nIn the online pipeline, we consider single-detector candidates only from templates with duration greater than 7 s\nabove a starting frequency of 17 Hz, corresponding to a range of masses and spins for which EM emission due to\nneutron star ejecta might be expected. Low-latency data-quality time series produced by iDQ, a machine-learning\nframework for autonomous detection of noise artifacts using only auxiliary data channels insensitive to GWs (Essick\net al. 2020a), are used to veto candidates at times when a glitch is likely to be present in the data. The remaining\nsingle-detector candidates are ranked by the reweighted S/N (Nitz 2018). Only candidates with a \u03c72 statistic (Allen\n2005) < 2.0 and reweighted S/N > 6.75 are kept. The rate density of single-detector triggers above the reweighted\nS/N threshold is fit with a decreasing exponential.\nIn offline PyCBC, we only consider single-detector candidates from templates with duration greater than 0.3 s\nabove a starting frequency of 15 Hz. We also require that candidates have a \u03c72 statistic < 10.0, a reweighted S/N\n> 5.5, and a PSD variation statistic (Mozzon et al. 2020) < 10.0, in order to exclude high-amplitude noise transients.\n\n29\nTable 4.\nSummary of parameter estimation analysis choices for GW230529, and the physical content of each waveform model\nused. Here tides refers to modeling of neutron star tidal deformability and disruption when tidal forces overcome the self-gravity\nof the neutron star. The spin prior denotes any restrictions on the spin magnitude of the binary components.\nWaveform Model\nPrecession\nHigher Multipoles\nTides\nDisruption\nSpin Prior\nIMRPhenomNSBH\n\u2212\n\u2212\n\u2713\n\u2713\n\u03c71 < 0.50, \u03c72 < 0.05\nIMRPhenomPv2 NRTidalv2\n\u2713\n\u2212\n\u2713\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.05\nIMRPhenomXPHM\n\u2713\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.99\nSEOBNRv5PHM\n\u2713\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.99\nSEOBNRv4 ROM NRTidalv2 NSBH\n\u2212\n\u2212\n\u2713\n\u2713\n\u03c71 < 0.90, \u03c72 < 0.05\nIMRPhenomXPHM\n\u2713\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.05\nIMRPhenomXP\n\u2713\n\u2212\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.99\nIMRPhenomXHM\n\u2212\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.99\nIMRPhenomXAS\n\u2212\n\u2212\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.99\nIMRPhenomXAS\n\u2212\n\u2212\n\u2212\n\u2212\n\u03c71 < 0.50, \u03c72 < 0.05\nIMRPhenomPv2 NRTidalv2\n\u2713\n\u2212\n\u2713\n\u2212\n\u03c71 < 0.05, \u03c72 < 0.05\nIMRPhenomXPHM\n\u2713\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.05, \u03c72 < 0.05\nSEOBNRv5PHM\n\u2713\n\u2713\n\u2212\n\u2212\n\u03c71 < 0.99, \u03c72 < 0.05\nEach candidate is assigned a ranking statistic equal to the logarithm of the ratio of astrophysical signal likelihood to\ndetector noise likelihood. The PyCBC O4 offline search introduced two changes to the ranking statistic relative to\nthe O3 calculation. First, an explicit model of the signal distribution covering the space of binary masses and spins is\nincluded (Kumar & Dent 2024). The model is designed to maximize the number of detected signals from the known\ncompact binary distribution, while also maintaining sensitivity to signals in previously unpopulated regions. Second,\nthe model of the rate density of events caused by detector noise now includes a term describing the variation in rate\nduring times of heightened detector noise (Davis et al. 2022). The rate density of single-detector candidates above a\nranking statistic threshold of 0 is fit with a decreasing exponential.\nIn both the online and offline versions of PyCBC, the exponential fit of trigger rate density above the relevant\nranking statistic threshold is used to extrapolate the FAR of single-detector candidates beyond the observing time of\nthe search (Cabourn Davies & Harry 2022). The FAR calculations for GW230529 used triggers from the first 2 weeks\nof O4 at the LIGO Livingston observatory. The distribution of ranking statistics for offline single-detector candidates\nat the LIGO Livingston observatory is shown in Figure 11. Similar to the other searches, GW230529 clearly stands\nout from the background distribution.\nD. PRIORS, WAVEFORM SYSTEMATICS, AND BAYES FACTORS\nGiven the uncertain nature of the compact objects, we analyze GW230529 with a suite of models that incorporate a\nnumber of key physical effects. The choices of data duration (128 s) and frequency bandwidth (20\u20131792 Hz) analyzed\nwere informed by comparing waveforms spanning the mass range recovered in preliminary analyses with the detector\nnoise PSD at the time of the event. The high-frequency cutoff is chosen to avoid loss of power at high frequencies\ndue to low-pass filtering of the data. For a subset of the signal models below, we employ a range of techniques to\nspeed up the evaluation of the likelihood, including heterodyning (also known as relative binning; Cornish 2010, 2021;\nZackay et al. 2018; Krishna et al. 2023), multibanding (Garc\u00b4\u0131a-Quir\u00b4os et al. 2021; Morisaki 2021), and reduced-order\nquadratures (Canizares et al. 2015; Smith et al. 2016; Morisaki et al. 2023).\n\n30\nThe physical effects included and the spin prior ranges for each waveform model considered in this work are shown\nin Table 4. All analyses use mass priors that are flat in the redshifted component masses with chirp masses M =\n(m1m2)3/5/(m1+m2)1/5 \u2208[2.0214, 2.0331] M\u2299and mass ratios q \u2208[0.125, 1]. The luminosity distance prior is uniform\nin comoving volume and source-frame time in the range DL \u2208[1, 500] Mpc. The priors on the tidal deformability\nparameters are chosen to be uniform in the component tidal deformabilities over \u039b \u2208[0, 5000]. Standard priors (e.g.,\nRomero-Shaw et al. 2020; Abbott et al. 2024) are used for all the other extrinsic binary parameters. Below we provide\nfurther motivation for considering this suite of waveform models.\nThe primary analysis in this work uses the IMRPhenomXPHM and SEOBNRv5PHM BBH waveform models (corre-\nsponding to the third and fourth rows in Table 4), which provide an accurate description of BBHs but do not incorporate\ntidal effects or the potential tidal disruption of a companion neutron star. We did not consider an extension of IMR-\nPhenomXPHM that incorporates additional physics beyond the two precessing higher-order multipole moment BBH\nmodels used here, as these effects only enter at high frequencies and are not relevant for this event (Thompson et al.\n2024). In order to quantify the impact of neglecting tidal physics, we analyze GW230529 with NSBH and BNS wave-\nform models that incorporate different tidal information. The NSBH models only incorporate tidal information from\nthe less massive compact object, are restricted to spins aligned with the orbital angular momentum, and only model\nthe dominant \u2113= m = 2 multipole moment. However, they do model the possible tidal disruption of the neutron star,\nwhich occurs when tidal forces of the black hole dominate over the self-gravity of the neutron star.\nWe use two NSBH models, a frequency-domain phenomenological model IMRPhenomNSBH (Thompson et al. 2020a)\nand a frequency-domain effective-one-body (EOB) surrogate model SEOBNRv4 ROM NRTidalv2 NSBH (Matas et al.\n2020). IMRPhenomNSBH uses the BBH models IMRPhenomC (Santamaria et al. 2010) and IMRPhenomD (Husa et al.\n2016; Khan et al. 2016) as baselines for the amplitude and phase, respectively, incorporating corrections to the phase\ndue to tidal effects following the NRTidal model (Dietrich et al. 2017, 2019b,a) and to the amplitude following Pannarale\net al. (2013, 2015). SEOBNRv4 ROM NRTidalv2 NSBH uses the SEOBNRv4 BBH model as a baseline (Boh\u00b4e et al.\n2017) and applies the same corrections to account for tidal deformability and disruption as IMRPhenomNSBH but\nis additionally calibrated against numerical relativity (NR) simulations of NSBH mergers (Foucart et al. 2013, 2014,\n2019; Kyutoku et al. 2010, 2011). As the NSBH waveform models do not capture spin-induced orbital precession,\nwe analyze GW230529 with the aligned-spin BBH waveform models IMRPhenomXAS (Pratten et al. 2020), which\nonly contains the dominant harmonic, and IMRPhenomXHM (Garc\u00b4\u0131a-Quir\u00b4os et al. 2020), which includes higher-order\nmultipole moments. Models for NSBH binaries that contain both higher-order multipole moments and precession are\nunder active development (Gonzalez et al. 2023) and could potentially allow for a more consistent model selection\nbetween the different source categories.\nGiven that the mass of the primary overlaps with current estimates of the maximum known neutron star mass (Landry\n& Read 2021; Romani et al. 2022), we also analyze GW230529 with a BNS waveform model that allows for tidal interac-\ntions on both the primary and the secondary components of the binary. We use IMRPhenomPv2 NRTidalv2 (Dietrich\net al. 2019a), which adds a model for the tidal phase that is calibrated against both EOB and NR simulations to\nthe underlying precessing-spin point-particle waveform model IMRPhenomPv2 (Hannam et al. 2014). A limitation is\nthat IMRPhenomPv2 NRTidalv2 is calibrated against a suite of equal-mass, nonspinning BNS NR simulations, where\nthe maximum neutron star mass is only 1.372 M\u2299. Nevertheless, the model has been validated against a catalog\nof EOB\u2013NR hybrid waveforms that includes asymmetric configurations and heavier neutron star masses (Dietrich\net al. 2019a; Abac et al. 2024).\nBecause of large uncertainties in BNS postmerger waveform modeling, IMRPhe-\nnomPv2 NRTidalv2 includes an amplitude taper from 1 to 1.2 times the estimated merger frequency (Dietrich et al.\n2019b). The resulting suppression of S/N at these frequencies may be responsible for the posterior differences between\nIMRPhenomPv2 NRTidalv2 and the BBH and NSBH waveform models we consider (Figure 12).\nFrom the mass estimates alone, the secondary object is consistent with being a neutron star. As such, we follow\nearlier analyses and analyze GW230529 with two spin priors (Abbott et al. 2021a): an agnostic high-spin prior and an\nastrophysically motivated low-spin prior. The high-spin prior assumes that the spins on both objects are isotropically\noriented and have dimensionless spin magnitudes that are uniformly distributed up to \u03c71, \u03c72 \u22640.99. The low-spin\nprior, on the other hand, is inspired by the extrapolated maximum spin observed in Galactic BNSs that will merge\nwithin a Hubble time (Burgay et al. 2003; Stovall et al. 2018) and restricts the spin magnitude of the secondary to\nbe \u03c72 \u22640.05 while keeping \u03c71 \u22640.99. As the nature of the primary as a black hole or neutron star is uncertain, we\nalso use a third choice of prior where both spins are restricted to \u03c71, \u03c72 \u22640.05 for the IMRPhenomPv2 NRTidalv2\nand IMRPhenomXPHM waveform models (rows 11 and 12 of Table 4, respectively). The purpose of using multiple\n\n31\nFigure 12.\nThe two-dimensional q\u2013\u03c7eff posterior probability distributions for GW230529 using various BBH, NSBH, and BNS\nsignal models. The vertical dotted lines indicate primary masses that have been mapped to the mass ratio given the median\nchirp mass estimated from the IMRPhenomXPHM high-spin analysis.\npriors is to help gauge whether astrophysical assumptions on the neutron star spin impact any of the statements on\nthe probability that the primary object lies in the lower mass gap. In Figure 12, we show the impact of waveform\nsystematics and prior assumptions on the strongly correlated mass ratio\u2013effective inspiral spin distribution.\nThe degree to which a given waveform model under certain assumptions matches the data can be gauged using\nthe Bayes factor. However, Bayes factors penalize extra degrees of freedom in models that do not improve the fit\nwhen those extra degrees of freedom are constrained by the data (Mackay 2003). We find no significant preference\n(log10 B \u22720.5) between the high-spin and low-spin prior on the secondary; we similarly do not find a statistical\npreference for or against the effects of precession, higher-order multipole moments, or tidal deformation or disruption\nof the secondary object.\nE. ADDITIONAL SOURCE PROPERTIES\nE.1. Component Spins and Precession\nAssuming a high-spin prior, the posteriors for the primary spin magnitude are only weakly informative, disfavoring\nzero and extremal spins with \u03c71 = 0.07\u20130.85. For the secondary, the posteriors are even less informative. Under\nthe low-spin prior, the primary spin magnitude posterior is peaked at slightly higher values, with zero and extremal\nspins being disfavored to a larger degree, \u03c71 = 0.10\u20130.84. The secondary spin is completely uninformative over the\nrestricted range of spin magnitudes. The joint two-dimensional posterior probability distribution of the dimensionless\nspin magnitude and the spin tilt are shown in Figure 13. Regions of high (low) probability are denoted by a darker\n(lighter) shade.\nWhen the spins are misaligned with the orbital angular momentum, relativistic spin\u2013orbit and spin\u2013spin couplings\ndrive the evolution of the orbital plane and the spins themselves (Apostolatos et al. 1994; Kidder 1995). The leading-\norder effect can be captured by an effective precession spin parameter, 0 \u2264\u03c7p \u22641, which approximately measures\nthe degree of in-plane spin and can be used to parameterize the rate of precession of the orbital plane (Schmidt et al.\n2015)\n\u03c7p = max\n\u0014\n\u03c71 sin \u03b81,\n\u00123 + 4q\n4 + 3q\n\u0013\nq \u03c72 sin \u03b82\n\u0015\n.\n(E1)\n\n32\nFigure 13.\nTwo-dimensional posterior probability distributions for the spin magnitude \u03c7i and the spin-tilt angle \u03b8i for the\nprimary (left) and secondary (right) compact objects at a reference frequency of 20 Hz. A spin-tilt angle of 0\u25e6(180\u25e6) indicates\na spin that is perfectly aligned (antialigned) with the orbital angular momentum \u02c6L. The pixels have equal prior probability,\nand shading denotes the posterior probability of each pixel of the high-spin prior analysis, after marginalizing over azimuthal\nangles. The solid (dashed) contours denote the 90% credible region for the high-spin (low-spin) prior analyses. The probability\ndistributions are marginalized over the azimuthal spin angles.\nWe find the constraints on \u03c7p to be uninformative, and we are not able to make any significant statements on precession.\nThe uninformative nature of these results is corroborated by the Bayes factor between the precessing and nonprecessing\nphenomenological waveform models, log10 BXP\nXAS = 0.22.\nE.2. Source Location and Distance\nAs GW230529 was a single-detector observation, the sky localization is poor and covers a sky area of \u224824,100 deg2\nat the 90% credible level. The luminosity distance is inferred to be DL = 201+102\n\u221296\nMpc, corresponding to a redshift\nof z = 0.04+0.02\n\u22120.02 computed using the Planck 2015 cosmological parameters (Ade et al. 2016). The luminosity distance\nhas a degeneracy with the inclination angle of the binary\u2019s total angular momentum with respect to the line of\nsight, \u03b8JN (e.g., Cutler & Flanagan 1994; Nissanke et al. 2010; Aasi et al. 2013; Vitale & Chen 2018). The posterior\ndistribution on \u03b8JN is broadly unconstrained, showing no preference for a total angular momentum vector that is\npointed toward or away from the line of sight.\nE.3. Tidal Deformability\nThe tidal deformability of a neutron star is defined by\n\u03bb = 2\n3k2R5,\n(E2)\nwhere k2 is the gravitational Love number of the object and R is its radius (Damour et al. 1992; Mora & Will 2004;\nFlanagan & Hinderer 2008; Damour & Nagar 2009). However, it is often convenient to introduce a dimensionless tidal\ndeformability\n\u039b = \u03bb\nm5 = 2\n3k2C\u22125,\n(E3)\nwhere C = m/R is the compactness of the neutron star in geometrized units.\n\n33\nFigure 14.\nConstraints on dimensionless tidal deformability \u039b for the primary (green dashed) and secondary (green solid)\ncomponents of GW230529. We also show tidal deformabilities predicted for the secondary object under the BSK24 neutron\nstar EOS (navy; Goriely et al. 2013; Pearson et al. 2018; Perot et al. 2019) and constraints obtained from BNS and pulsar\nobservations using the GP model (GP-EOS; red).\nUsing the IMRPhenomPv2 NRTidalv2 model, which allows for tidal deformability on both objects but does not\nmodel tidal disruption, we infer \u039b1 \u22641462 at 90% credibility with the \u03c71 < 0.99, \u03c72 < 0.05 spin prior; the posterior\npeaks at \u039b1 = 0. We do not constrain \u039b2 relative to the prior. Constraints on the tidal deformability \u039b of both\ncomponents of GW230529 are shown in Figure 14.\nWe also show the tidal deformability predicted by the \u039b(m)\nrelation of the specific neutron star EOS model BSK24 (Goriely et al. 2013; Pearson et al. 2018) weighted by the\nm2 posterior distribution. BSK24 is chosen as an illustrative EOS that is thermodynamically consistent and falls\nwithin the range of support of constraints from nuclear physics and astrophysics, including GW170817 (Perot et al.\n2019). Even under the assumption that the EOS is known (BSK24), \u039b2 is not well constrained, due to the relatively\nwide m2 posterior. The \u039b2 prediction of the set of GP-EOS constraints (red; Section 6) is consistent with both the\ninferred value of \u039b2 (green solid) and the BSK24 value of \u039b2 (navy). In addition to the tidal deformability posteriors,\nwe use two distinct likelihood interpolation schemes (Ray et al. 2023a; Landry & Essick 2019) to directly constrain\nthe neutron star EOS using both spectral (Lindblom 2010; Lindblom & Indik 2012, 2014) and GP (Landry & Essick\n2019; Essick et al. 2020b) representations. Both methods incorporate consistency with the observed heavy pulsars\nPSR J0740+6620 (Fonseca et al. 2021) and PSR J0348+0432 (Antoniadis et al. 2013) as priors on the EOS and\nenforce thermodynamic stability and causality. Unlike other analyses where the GP representations are conditioned\non both GW and pulsar data, here we only include the pulsar constraints in the prior, in order to distinguish the\nEOS information provided by GW230529 alone. These direct EOS inferences are also uninformative, returning their\nrespective priors.\nF. TESTING GENERAL RELATIVITY\nWe perform several analyses to verify whether GW230529 is consistent with general relativity (S\u00a8anger et al. 2024).\nSpecifically, we perform parameterized tests searching for deviations in the PN coefficients that determine the phase\nevolution of the GW signal (Blanchet & Sathyaprakash 1994, 1995; Arun et al. 2006a,b; Yunes & Pretorius 2009;\nMishra et al. 2010; Li et al. 2012a,b). We search for parametric deviations to the GW inspiral phasing applied to the\nfrequency-domain waveform models IMRPhenomXP NRTidalv2 (Colleoni et al. 2023) and IMRPhenomXPHM (Prat-\nten et al. 2020; Garc\u00b4\u0131a-Quir\u00b4os et al. 2020; Pratten et al. 2021) using the TIGER framework (Agathos et al. 2014;\nMeidam et al. 2018), and SEOBNRv4 ROM NRTidalv2 NSBH (Matas et al. 2020) and SEOBNRv4HM ROM (Boh\u00b4e\net al. 2017; Cotesta et al. 2018, 2020) using the FTI framework (Mehta et al. 2023a). These waveform models each\ncapture different physical effects (precession, higher-order multipole moments, and neutron star tidal deformability)\nto determine whether their absence in the model leads to inferred inconsistencies with general relativity.\nFor all waveform models and PN orders whose analyses have been completed, we find that GW230529 is consistent\nwith general relativity within the inferred uncertainties on the deviation parameters. We do not yet include results\n\n34\nabout 0PN deviations, which are being examined separately owing to technical issues related to the degeneracy between\nthe 0PN deviation parameter and the chirp mass (Payne et al. 2023). The constraints obtained at \u22121PN are an order\nof magnitude tighter than previously reported bounds for NSBH and BBH (Abbott et al. 2021b). The previously\nreported bounds using GW170817 remain the tightest constraints on \u22121PN deviations obtained with GWs (Abbott\net al. 2019c).\nG. COMPACT BINARY MERGER RATE METHODS\nA key component of the event-based rate estimation described in Section 5 is the sensitive time\u2013volume of our GW\nsearches. The sensitivities to GW200105-, GW200115-, and GW230529-like events are computed from O1 through the\nfirst 2 weeks of O4a according to the corresponding mass and spin posteriors from the IMRPhenomXPHM high-spin\nanalyses of these signals. The posterior samples chosen for this analysis are consistent with previous event-based rate\nestimates presented for NSBH mergers (Abbott et al. 2021a). Simulated signals, whose binary parameters are drawn\nfrom the mass and spin posteriors for each signal, are distributed uniformly in comoving volume and following the\nother extrinsic parameter distributions given in Appendix D, and are added to simulated detector noise characterized\nby representative PSDs for each observing run. The detectability of these injections is then calculated semianalytically\nto determine the sensitive time\u2013volume by calculating network responses to the simulated signals and applying a\nthreshold on the network optimal S/N of > 10.\nThis choice of threshold was previously tuned to the results of\nmatched-filter searches (LIGO Scientific, Virgo, and KAGRA Collaboration 2023c) and is comparable to threshold\nstatistics calculated for semianalytic sensitivity estimates (Essick 2023).\nFor the population-based approach, we estimate the merger rate of three astrophysical populations (BBH, BNS,\nand NSBH) by aggregating triggers found by GstLAL from O1 through the first 2 weeks of O4, while accounting for\nthe possibility that some of these triggers are of terrestrial origin. Our population analyses do not, however, include\ndata from the engineering run preceding the start of O4, during which another NSBH candidate was identified (LIGO\nScientific, Virgo, and KAGRA Collaboration 2023d). As outlined and implemented in previous LVK results (Abbott\net al. 2021a, 2023b), we construct the joint likelihood on the Poisson parameters of the astrophysical populations\n(\u039bBBH, \u039bBNS, \u039bNSBH) and of the terrestrial triggers (\u039bbackground; Farr et al. 2015; Kapadia et al. 2020). We then\nextrapolate the sensitive time\u2013volume to each astrophysical population (\u27e8V T\u27e9BBH, \u27e8V T\u27e9BNS, \u27e8V T\u27e9NSBH) obtained at\nthe end of O3 (Abbott et al. 2023b) to account for the additional 2 weeks of observation time during O4 during\nwhich GW230529 was detected. Using a uniform prior on the merger rates R\u03b1 = \u039b\u03b1/\u27e8V T\u27e9\u03b1, we infer their posterior\ndistributions. The three astrophysical populations are defined by dividing up the space of compact binary component\nmasses and spins into disjoint regions. We consider all components with masses between 1 and 3 M\u2299to be neutron\nstars and assume a maximum dimensionless spin of 0.05 for such components; all components that are more massive\nare assumed to be black holes with a maximum dimensionless spin of 0.99. The distribution of component masses\nwithin each region is assumed to be a power law in primary mass with index \u22122.35 and uniform in secondary mass.\nEven though we infer the posterior distributions of the merger rates of all three populations, we only present RNSBH\ngiven that GW230529 contributes negligibly to RBBH and RBNS.\nH. ADDITIONAL DETAILS OF POPULATION ANALYSES\nWe use three different models to analyze the population of compact-object binaries with and without GW230529.\nH.1. Binned Gaussian Process\nThe Binned Gaussian Process method models the merger rate density per log component masses as a piecewise\nconstant function. By inferring the merger rate density in each bin, we reconstruct the shape of the CBC mass spectrum\nup to the resolution limit imposed by our choice of binning. A GP prior with an exponential quadratic kernel is imposed\non the logarithmic rate densities to smooth out the inferred shapes over sparse regions of the parameter space. To\nassess the impact of GW230529 on the shape of the CBC mass spectrum, we use the same bin locations and priors on\nthe GP hyperparamters as the GWTC-3 analysis (Abbott et al. 2023b). The means (\u00b5), correlation length (l), and\ncovariance amplitude (\u03c3) of the GP are drawn from normal, lognormal, and half-normal priors, respectively. Further\ndetails of these priors are summarized in Table 5.\nUnlike more recent implementations of the Binned Gaussian Process model that also fit for the redshift distri-\nbution (Ray et al. 2023b), we assume a redshift distribution such that the overall merger rate of compact binaries\nis uniform in comoving volume and source-frame time. This facilitates a direct comparison with the findings of the\n\n35\nTable 5.\nSummary of Binned Gaussian Process model parameters (Ray et al. 2023b; Mandel et al. 2017; Mohite 2022).\nArguments in the priors specify the mean and standard deviation in a normal (N) or half-normal (HN) distribution.\nParameter\nDescription\nPrior\n\u00b5\nMean log\n\u0012\nRate\nGpc\u22123 yr\u22121 M \u22122\n\u2299\n\u0013\nin each bin\nN(0, 10)\n\u03c3\nAmplitude of the covariance kernel\nHN(0, 10)\nlog(l)\nlog\n\u0012\nLength scale\nlog(M/M\u2299)\n\u0013\nof the covariance kernel\nN(\u22120.085, 0.93)\nGWTC-3 analysis (Abbott et al. 2023b) and avoids any systematic biases in Binned Gaussian Process-based red-\nshift distribution models originating from the inclusion of low-mass events, which remains an active area of study. As\nin previous analyses (Abbott et al. 2023b; Ray et al. 2023b), we fix the spin distributions for each component to be\nisotropic in direction and uniform in spin magnitude.\nH.2. Power law + Dip + Break\nThe Power law + Dip + Break model is designed to search for a separation in masses between neutron stars and\nblack holes by employing a broken power law with a dip at the location of the power-law break. The dip is modeled\nby a notch filter with depth A, which is fit along with other model parameters in order to determine the existence and\ndepth of a potential mass gap (Farah et al. 2022). A value A = 0 corresponds to no gap, whereas A = 1 corresponds to\nzero merger rate over the interval of the gap, i.e., a maximally deep gap. Power law + Dip + Break also employs\na low-pass filter at high black hole masses to allow for a tapering of the mass spectrum, which has the effect of adding\na smooth second break to the power law.\nThe component mass distributions in this model are both fit by the same broken power law with exponents \u03b11\nbetween mmin and M gap\nlow and \u03b12 between M gap\nlow and mmax.\nThe model additionally includes a power-law pairing\nfunction in mass ratio (Fishbach & Holz 2020), assumed to be the same for all component masses. The parameters for\nthis mass model are summarized in Table 6. Like the Binned Gaussian Process model, the Power law + Dip +\nBreak model additionally assumes that CBCs are uniformly distributed in comoving volume and source-frame time\nand that component spins are isotropically oriented and uniformly distributed in magnitude. These assumptions are\nmade for simplicity and consistency with GWTC-3 analyses (Abbott et al. 2023b). Components with m < 2.5 M\u2299\nare limited to spin magnitudes < 0.4, while components with m > 2.5 M\u2299can have spin magnitudes up to 0.99.\nH.3. NSBH-pop\nThe NSBH-pop model (Biscoveanu et al. 2022) is designed to capture the mass and spin distributions of the NSBH\npopulation. The black hole mass distribution is fit by a truncated power law, and the conditional mass ratio distribution\np(q|m1) is fit by a truncated Gaussian between qmin = 1 M\u2299/m1 and qmax = min(mNS,max/m1, 1). The black hole spin\nmagnitude distribution is modeled as a Beta distribution (including singular distributions that peak at the edges of\nthe \u03c71 \u2208[0, 0.99] space), while the neutron star spin magnitude distribution is assumed to be uniform over \u03c72 \u2208[0, 0.7]\nto encapsulate the effect of the neutron star breakup spin at the mass-shedding limit (Shao et al. 2020; Most et al.\n2020a). We assume the redshift distribution is uniform in comoving volume and source-frame time and that spins are\nisotropically oriented. The parameters for this model are summarized in Table 7.\nH.4. Population reweighting\nWe use the population-level mass and spin distributions inferred using all three population models to reweight\n(e.g., Payne et al. 2019) the high-spin combined parameter estimation samples from the default priors described in\nAppendix D to three different astrophysically motivated priors given by the one-left-out posterior predictive distribu-\ntions (Galaudage et al. 2020; Callister 2021; Essick & Fishbach 2021) inferred for each model. A comparison of the\nposteriors under the default and astrophysically motivated priors is shown in Figure 7.\nBecause of the q\u2013\u03c7eff degeneracy, the spin distribution assumptions also impact the inferred component masses, and\nhence classification, for this source. However, the fact that the Binned Gaussian Process and NSBH-pop model\n\n36\nTable 6.\nSummary of Power law + Dip + Break model parameters (Farah et al. 2022). Arguments in the Prior column\nspecify the lower and upper bounds of a uniform (U) distribution.\nThe first several entries describe the mass distribution\nparameters, and the last two entries describe the spin distribution parameters.\nParameter\nDescription\nPrior\n\u03b11\nSpectral index for the power law of the mass distribution below M gap\nlow\nU(\u22128, 2)\n\u03b12\nSpectral index for the power law of the mass distribution above M gap\nlow\nU(\u22123, 2)\nA\nLower mass gap depth\nU(0, 1)\nM gap\nlow (M\u2299)\nLocation of the lower end of the mass gap\nU(1.4, 3)\nM gap\nhigh (M\u2299)\nLocation of the upper end of the mass gap\nU(3.4, 9)\n\u03b7low\nParameter controlling how the rate tapers at the low end of the mass gap\n50\n\u03b7high\nParameter controlling how the rate tapers at the high end of the mass gap\n50\n\u03b7\nParameter controlling tapering the power law at high black hole mass\nU(\u22124, 12)\n\u03b2\nSpectral index for the power law-in-mass-ratio pairing function\nU(\u22122, 7)\nmmin (M\u2299)\nMinimum mass of the mass distribution\nU(1 , 1.4)\nmmax (M\u2299)\nMaximum mass of the mass distribution\nU(35, 100)\n\u03c7max,NS\nMaximum allowed component spin for objects with mass < 2.5M\u2299\n0.4\n\u03c7max,BH\nMaximum allowed component spin for objects with mass \u22652.5M\u2299\n0.99\npriors recover similar mass posteriors indicates that the different spin distribution assumptions have a subdominant\neffect compared to the different mass distribution assumptions.\nH.5. Selection effects\nFor our population analyses, we account for search selection bias to measure the underlying astrophysical mass and\nspin distributions of the NSBH and CBC populations (Loredo 2004; Mandel et al. 2019; Farr 2019; Vitale et al. 2020).\nTo estimate the sensitivity of the searches over the data recorded by the detector network across the binary parameter\nspace, we use a large suite of injections and impose a significance threshold on the FAR. In contrast to the two\nmethods for calculating merger rates described in Appendix G, we use the same set of injections used for GWTC-3\npopulation studies recovered using matched-filter searches (Abbott et al. 2023b). By using the combined injection\nsets from the first three observing runs (LIGO Scientific, Virgo, and KAGRA Collaboration 2023c), we are effectively\nassuming that GW230529 occurred at the end of O3. Without accounting for the extra time\u2013volume provided by the\nfirst 2 weeks of O4, this introduces a bias in our inferred estimates of the merger rate in the mass gap (Figure 5),\nrate of gamma-ray bursts with NSBH progenitors, and total contribution of NSBH mergers to the production of heavy\nelements (Section 7). However, this effect is negligible given that GW230529 occurred in the first 2 weeks of O4a and\nthe detector sensitivity during this period was not drastically different from that during O3 (see Section 2), meaning\nthat the additional time\u2013volume unaccounted for in the injection sets is small.\nTo generate samples from the hierarchical likelihood for our population analyses, we use the Dynesty nested\nsampler (Speagle 2020) as implemented in GWPopulation (Talbot et al. 2019) for the Power law + Dip + Break\nand NSBH-pop analyses and the Hamiltonian Monte Carlo sampler implemented in the PyMC package (Salvatier\net al. 2016) for the Binned Gaussian Process analysis.\nI. EQUATION OF STATE\nTo assess the effect of the EOS constraint used for source classification (Section 6) and calculation of fEM-bright (Sec-\ntion 7), we repeat these analyses using GP-EOS constraints additionally conditioned on NICER observations (Legred\net al. 2021, 2022) of J0030+0451 (Miller et al. 2019; Riley et al. 2019; Vinciguerra et al. 2024) and J0740+6620 (Miller\net al. 2021; Riley et al. 2021; Salmi et al. 2022, 2023).\n\n37\nTable 7.\nSummary of NSBH-pop model parameters (Biscoveanu et al. 2022). Arguments in the Prior column specify the\nlower and upper bounds of a uniform (U) distribution.\nParameter\nDescription\nPrior\n\u03b1\nBlack hole mass power-law index\nU(\u22124, 12)\nmBH,min (M\u2299)\nMinimum black hole mass\nU(2, 10)\nmBH,max (M\u2299)\nMaximum black hole mass\nU(8, 20)\nmNS,max (M\u2299)\nMaximum neutron star mass\nU(1.97, 2.7)\n\u00b5\nMass ratio mean\nU(0.1, 0.6)\n\u03c3\nMass ratio standard deviation\nU(0.1, 1)\n\u03b1\u03c7\nBeta distribution shape parameter (\u03b1) for black hole spin distribution\nU(0.1, 10)\n\u03b2\u03c7\nBeta distribution shape parameter (\u03b2) for black hole spin distribution\nU(0.1, 10)\nWe find that including the NICER observations only changes the source classification results by at most a few\npercent. This is because the constraint on the maximum neutron star mass used in the source classification analysis is\nprimarily driven by the observation of massive pulsars. 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Andri\u00b4c,1, 40 S. Ansoldi,41, 42 J. M. Antelis,43\nS. Antier,44 M. Aoumi,45 T. Apostolatos,46 E. Z. Appavuravther,47, 48 S. Appert,2 S. K. Apple,49 K. Arai,2\nA. Araya,50 M. C. Araya,2 J. S. Areeda,51 N. Aritomi,52 F. Armato,53 N. Arnaud,35, 54 M. Arogeti,55\nS. M. Aronson,10 K. G. Arun,56 G. Ashton,57 Y. Aso,21, 58 M. Assiduo,59, 60 S. Assis de Souza Melo,54\nS. M. Aston,61 P. Astone,62 F. Aubin,60 K. AultONeal,43 S. Babak,63 A. Badalyan,64 F. Badaracco,53\nC. Badger,65 S. Bae,66 S. Bagnasco,24 Y. Bai,2 J. G. Baier,67 R. Bajpai,21 T. Baka,68 M. Ball,69 G. Ballardin,54\nS. W. Ballmer,70 G. Baltus,71 S. Banagiri,72 B. Banerjee,40 D. Bankar,14 P. Baral,9 J. C. Barayoga,2\nJ. Barber,18 B. C. Barish,2 D. Barker,52 P. Barneo,38, 73 F. Barone,74, 5 B. Barr,25 L. Barsotti,75 M. Barsuglia,63\nD. Barta,76 S. D. Barthelmy,77 M. A. Barton,25 I. Bartos,78 S. Basak,20 A. Basalaev,79 R. Bassiri,17 A. Basti,80, 19\nM. Bawaj,81, 47 P. Baxi,82 J. C. Bayley,25 A. C. Baylor,9 M. Bazzan,83, 84 B. B\u00b4ecsy,85 V. M. Bedakihale,86\nF. Beirnaert,87 M. Bejger,88 A. S. Bell,25 V. Benedetto,89 D. Beniwal,90 W. Benoit,29 J. D. Bentley,79\nM. Ben Yaala,91 S. Bera,92 M. Berbel,93 F. Bergamin,12, 13 B. K. Berger,17 S. Bernuzzi,94 M. Beroiz,2\nC. P. L. Berry,25 D. Bersanetti,53 A. Bertolini,32 J. Betzwieser,61 D. Beveridge,26 N. Bevins,95 R. Bhandare,96\nA. V. Bhandari,14 U. Bhardwaj,97, 32 R. Bhatt,2 D. Bhattacharjee,67 S. Bhaumik,78 A. Bianchi,32, 98\nI. A. Bilenko,99 M. Bilicki,100 G. Billingsley,2 A. Binetti,101 S. Bini,102, 103 O. Birnholtz,104 S. Biscans,2, 75\nM. Bischi,59, 60 S. Biscoveanu,75 A. Bisht,13 M. Bitossi,54, 19 M.-A. Bizouard,44 J. K. Blackburn,2 C. D. Blair,26, 61\nD. G. Blair,26 F. Bobba,105, 106 N. Bode,12, 13 M. Bo\u00a8er,44 G. Bogaert,44 G. Boileau,107, 44 M. Boldrini,108, 62\nG. N. Bolingbroke,90 L. D. Bonavena,83 R. Bondarescu,38 F. Bondu,109 E. Bonilla,17 G. S. Bonilla,51\nR. Bonnand,27 P. Booker,12, 13 V. Boschi,19 S. Bose,14 V. Bossilkov,61 V. Boudart,71 A. Bozzi,54 C. Bradaschia,19\nP. R. Brady,9 M. Braglia,110 A. Branch,61 M. Branchesi,40, 111 M. Breschi,94 T. Briant,112 A. Brillet,44\nM. Brinkmann,12, 13 P. Brockill,9 A. F. Brooks,2 D. D. Brown,90 M. L. Brozzetti,81, 47 S. Brunett,2 G. Bruno,113\nR. Bruntz,114 J. Bryant,115 F. Bucci,60 J. Buchanan,114 O. Bulashenko,38, 73 T. Bulik,116 H. J. Bulten,32\nA. Buonanno,117, 1 K. Burtnyk,52 R. Buscicchio,118, 119 D. Buskulic,27 C. Buy,120 G. S. Cabourn Davies,121\nG. Cabras,41, 42 R. Cabrita,113 L. Cadonati,55 G. Cagnoli,122 C. Cahillane,70 H. W. Cain III,10\nJ. Calder\u00b4on Bustillo,123 J. D. Callaghan,25 T. A. Callister,124 E. Calloni,28, 5 J. B. Camp,77 M. Canepa,125, 53\nG. Caneva Santoro,39 M. Cannavacciuolo,105 K. C. Cannon,126 H. Cao,34 Z. Cao,127 L. A. Capistran,128\nE. Capocasa,63 E. Capote,70 G. Carapella,105, 106 F. Carbognani,54 M. Carlassara,12, 13 J. B. Carlin,129\nM. Carpinelli,118, 130, 54 J. J. Carter,12, 13 G. Carullo,131 J. Casanueva Diaz,54 C. Casentini,132, 133 G. Castaldi,134\nS. Y. Castro-Lucas,135 S. Caudill,32, 68 M. Cavagli`a,136 R. Cavalieri,54 G. Cella,19 P. Cerd\u00b4a-Dur\u00b4an,137, 138\nE. Cesarini,133 W. Chaibi,44 S. Chalathadka-Subrahmanya,79 C. Chan,126 J. C. L. Chan,124 K. H. M. Chan,139\nM. Chan,30 W. L. Chan,139 K. Chandra,140 I. P. Chang,141 R.-J. Chang,142 W. Chang,141 P. Chanial,63\nS. Chao,141, 143 C. Chapman-Bird,25 E. L. Charlton,114 P. Charlton,144 E. Chassande-Mottin,63 L. Chastain,7\nC. Chatterjee,26 Debarati Chatterjee,14 Deep Chatterjee,75 M. Chaturvedi,96 S. Chaty,63 K. Chatziioannou,2\nA. Chen,145 A. H.-Y. Chen,146 D. Chen,147 H. Chen,141 H. Y. Chen,148 J. Chen,75 K. H. Chen,143 X. Chen,26\nY.-R. Chen,141 Y. Chen,149 H. Cheng,78 P. Chessa,80, 19 H. Y. Chia,78 F. Chiadini,150, 106 C. Chiang,143 G. Chiarini,84\nA. Chiba,151 R. Chiba,152 R. Chierici,153 A. Chincarini,53 M. L. Chiofalo,80, 19 A. Chiummo,54 C. Chou,146\nS. Choudhary,26 N. Christensen,44 S. S. Y. Chua,11 K. W. Chung,65 G. Ciani,83, 84 P. Ciecielag,88 M. Cie\u00b4slar,88\nM. Cifaldi,132, 133 A. A. Ciobanu,90 R. Ciolfi,154, 84 F. Clara,52 J. A. Clark,2, 55 T. A. Clarke,7 P. Clearwater,155\nS. Clesse,156 F. Cleva,44 E. Coccia,40, 111, 39 E. Codazzo,40 P.-F. Cohadon,112 M. Colleoni,92 C. G. Collette,33\nJ. Collins,61 A. Colombo,118, 119, 157 M. Colpi,118, 119 C. M. Compton,52 L. Conti,84 S. J. Cooper,115 T. R. Corbitt,10\nI. Cordero-Carri\u00b4on,158 S. Corezzi,81, 47 N. J. Cornish,85 A. Corsi,159 S. Cortese,54 C. A. Costa,16\nR. Cottingham,61 M. W. Coughlin,29 A. Couineaux,62 J.-P. Coulon,44 S. T. Countryman,160 J.-F. Coupechoux,153\nB. Cousins,8 P. Couvares,2, 55 D. M. Coward,26 M. J. Cowart,61 B. D. Cowburn,161 D. C. Coyne,2 R. Coyne,162\nK. Craig,91 J. D. E. Creighton,9 T. D. Creighton,163 A. W. Criswell,29 J. C. G. Crockett-Gray,10\nM. Croquette,112 R. Crouch,52 S. G. Crowder,164 J. R. Cudell,71 T. J. Cullen,2 A. Cumming,25 E. Cuoco,54, 165, 19\nM. Cury lo,116 M. Cusinato,137 P. Dabadie,122 T. Dal Canton,35 S. Dall\u2019Osso,62 G. D\u00b4alya,87 B. D\u2019Angelo,53\nS. Danilishin,31, 32 S. D\u2019Antonio,133 K. Danzmann,13, 12, 13 K. E. Darroch,114 C. Darsow-Fromm,79 L. P. Dartez,52\nA. Dasgupta,86 S. Datta,56 V. Dattilo,54 A. Daumas,63 I. Dave,96 A. Davenport,135 M. Davier,35 D. Davis,2\nM. C. Davis,95 E. J. Daw,166 M. Dax,1 M. Deenadayalan,14 J. Degallaix,167 M. De Laurentis,28, 5 S. Del\u00b4eglise,112\nV. Del Favero,77 F. De Lillo,113 D. Dell\u2019Aquila,168, 130 W. Del Pozzo,80, 19 F. De Marco,62, 108 F. De Matteis,132, 133\nV. D\u2019Emilio,18 N. Demos,75 T. Dent,123 A. Depasse,113 R. De Pietri,169, 170 R. De Rosa,28, 5 C. De Rossi,54\narXiv:2308.03822v1 [astro-ph.HE] 7 Aug 2023\n\n2\nR. De Simone,150 S. Dhurandhar,14 R. Diab,78 P. Z. Diamond,67 M. C. D\u00b4\u0131az,163 N. A. Didio,70 T. Dietrich,1\nL. Di Fiore,5 C. Di Fronzo,33 F. Di Giovanni,137 M. Di Giovanni,40 T. Di Girolamo,28, 5 D. Diksha,32, 31\nA. Di Lieto,80, 19 A. Di Michele,81 J. Ding,63, 171 S. Di Pace,108, 62 I. Di Palma,108, 62 F. Di Renzo,153 Divyajyoti,172\nA. Dmitriev,115 Z. Doctor,72 E. Dohmen,52 P. P. Doleva,114 L. Donahue,173 L. D\u2019Onofrio,28, 5 F. Donovan,75\nK. L. Dooley,18 T. Dooney,68 S. Doravari,14 O. Dorosh,174 M. Drago,108, 62 J. C. Driggers,52 Y. Drori,2 H. Du,30\nJ.-G. Ducoin,175, 63 L. Dunn,129 U. Dupletsa,40 D. D\u2019Urso,168, 130 H. Duval,176 P.-A. Duverne,35 S. E. Dwyer,52\nC. Eassa,52 M. Ebersold,177, 27 T. Eckhardt,79 G. Eddolls,25 B. Edelman,69 T. B. Edo,2 O. Edy,121 A. Effler,61\nJ. Eichholz,11 H. Einsle,44 M. Eisenmann,21 R. A. Eisenstein,75 A. Ejlli,18 E. Engelby,51 A. J. Engl,17\nL. Errico,28, 5 R. C. Essick,178 H. Estell\u00b4es,1 D. Estevez,179 T. Etzel,2 C. R. Evans,18 M. Evans,75 T. M. Evans,61\nT. Evstafyeva,15 B. E. Ewing,8 J. M. Ezquiaga,124 F. Fabrizi,59, 60 F. Faedi,60, 59 V. Fafone,132, 133, 40 H. Fair,70\nS. Fairhurst,18 P. C. Fan,173 A. M. Farah,124 B. Farr,69 W. M. Farr,180, 181 E. J. Fauchon-Jones,18 G. Favaro,83\nM. Favata,182 M. Fays,71 J. Feicht,2 M. M. Fejer,17 E. Fenyvesi,76, 183 D. L. Ferguson,148 I. Ferrante,80, 19\nT. A. Ferreira,16 F. Fidecaro,80, 19 A. Fiori,19, 80 I. Fiori,54 M. Fishbach,178 R. P. Fisher,114 R. Fittipaldi,184, 106\nV. Fiumara,185, 106 R. Flaminio,27 S. M. Fleischer,186 L. S. Fleming,187 E. Floden,29 H. Fong,30 J. A. Font,137, 138\nB. Fornal,188 P. W. F. Forsyth,11 K. Franceschetti,169 A. Franke,79 S. Frasca,108, 62 F. Frasconi,19\nA. Frattale Mascioli,108, 62 Z. Frei,189 A. Freise,32, 98 O. Freitas,190, 137 R. Frey,69 W. Frischhertz,61\nP. Fritschel,75 V. V. Frolov,61 G. G. Fronz\u00b4e,24 S. Fujii,152 I. Fukunaga,191 P. Fulda,78 M. Fyffe,61\nW. E. Gabella,192 B. Gadre,68 J. R. Gair,1 J. Gais,139 S. Galaudage,7 S. Gallardo,193 R. Gamba,94\nD. Ganapathy,75 A. Ganguly,14 S. G. Gaonkar,14 B. Garaventa,53, 125 J. Garcia-Bellido,110 C. Garc\u00b4\u0131a-N\u00b4u\u02dcnez,187\nC. Garc\u00b4\u0131a-Quir\u00b4os,92 J. W. Gardner,11 K. A. Gardner,30 J. Gargiulo,54 F. Garufi,28, 5 C. Gasbarra,132, 133\nB. Gateley,52 V. Gayathri,9 G. Gemme,53 A. Gennai,19 J. George,96 O. Gerberding,79 L. Gergely,194 N. Ghadiri,51\nAbhirup Ghosh,1 Archisman Ghosh,87 Shaon Ghosh,182 Shrobana Ghosh,12, 13 Suprovo Ghosh,14\nTathagata Ghosh,14 L. Giacoppo,108, 62 J. A. Giaime,10, 61 K. D. Giardina,61 D. R. Gibson,187 C. Gier,91 P. Giri,19, 80\nF. Gissi,89 S. Gkaitatzis,80 J. Glanzer,10 A. E. Gleckl,51 F. Glotin,35 J. Godfrey,69 P. Godwin,2 E. Goetz,30\nR. Goetz,78 J. Golomb,2 S. Gomez Lopez,108, 62 B. Goncharov,40 G. Gonz\u00b4alez,10 A. W. Goodwin-Jones,26\nM. Gosselin,54 R. Gouaty,27 D. W. Gould,11 S. Goyal,20 B. Grace,11 A. Grado,195, 5 V. Graham,25\nA. E. Granados,29 M. Granata,167 V. Granata,105 S. Gras,75 P. Grassia,2 C. Gray,52 R. Gray,25 G. Greco,47\nA. C. Green,98 S. M. Green,121 S. R. Green,1 A. M. Gretarsson,43 E. M. Gretarsson,43 D. Griffith,2\nW. L. Griffiths,18 H. L. Griggs,55 G. Grignani,81, 47 A. Grimaldi,102, 103 C. Grimaud,27 H. Grote,18 A. S. Gruson,51\nD. Guerra,137 D. Guetta,62 G. M. Guidi,59, 60 A. R. Guimaraes,10 H. K. Gulati,86 F. Gulminelli,196, 197\nA. M. Gunny,75 H. Guo,188 Y. Guo,32, 31 Anchal Gupta,2 Anuradha Gupta,198 Ish Gupta,8 N. C. Gupta,86\nP. Gupta,32, 68 S. K. Gupta,140 N. Gupte,1 R. Gurav,34 J. Gurs,79 E. K. Gustafson,2 N. Gutierrez,167 F. Guzman,128\nD. Haba,3 L. Haegel,63 G. Hain,114 S. Haino,199 O. Halim,42 E. D. Hall,75 E. Z. Hamilton,177 G. Hammond,25\nW.-B. Han,200 M. Haney,177, 32 J. Hanks,52 C. Hanna,8 M. D. Hannam,18 O. A. Hannuksela,139 A. G. Hanselman,124\nH. Hansen,52 J. Hanson,61 R. Harada,126 T. Harder,44 K. Haris,32, 68 T. Harmark,131 J. Harms,40, 111 G. M. Harry,49\nI. W. Harry,121 D. Hartwig,79 B. Haskell,88 C.-J. Haster,201 J. S. Hathaway,161 K. Haughian,25 H. Hayakawa,45\nK. Hayama,202 F. J. Hayes,25 J. Healy,161 A. Heffernan,92 A. Heidmann,112 M. C. Heintze,61 J. Heinze,115\nJ. Heinzel,75 H. Heitmann,44 F. Hellman,203 P. Hello,35 A. F. Helmling-Cornell,69 G. Hemming,54 M. Hendry,25\nI. S. Heng,25 E. Hennes,32 J.-S. Hennig,31, 32 M. Hennig,31, 32 C. Henshaw,55 A. Hernandez,182 T. Hertog,101\nM. Heurs,12, 13 A. L. Hewitt,15, 204 S. Higginbotham,18 S. Hild,31, 32 P. Hill,91 Y. Himemoto,205 A. S. Hines,128\nN. Hirata,21 C. Hirose,206 J. Ho,143 S. Hoang,35 S. Hochheim,12, 13 D. Hofman,167 J. N. Hohmann,79\nN. A. Holland,32, 98 K. Holley-Bockelmann,192 I. J. Hollows,166 Z. J. Holmes,90 D. E. Holz,124 C. Hong,17\nQ. Hong,141 J. Hornung,69 S. Hoshino,206 J. Hough,25 S. Hourihane,2 E. J. Howell,26 C. G. Hoy,121 D. Hoyland,115\nH.-F. Hsieh,141 C. Hsiung,207 H. C. Hsu,143 S.-C. Hsu,208, 141 W.-F. Hsu,101 P. Hu,192 Q. Hu,25 H. Y. Huang,143\nY.-J. Huang,8 Y. Huang,75 Y. T. Huang,208 M. T. H\u00a8ubner,129 A. D. Huddart,209 B. Hughey,43 D. C. Y. Hui,210\nV. Hui,27 R. Hur,69 S. Husa,92 R. Huxford,8 T. Huynh-Dinh,61 J. Hyland,25 A. Iakovlev,211 G. A. Iandolo,31\nA. Iess,165, 19 K. Inayoshi,212 Y. Inoue,143 G. Iorio,83 P. Iosif,213 J. Irwin,25 M. Isi,180, 181 M. A. Ismail,143\nY. Itoh,191, 214 M. Iwaya,152 B. R. Iyer,20 V. JaberianHamedan,26 T. Jacqmin,112 P.-E. Jacquet,112 S. J. Jadhav,215\nS. P. Jadhav,155 D. Jain,7 T. Jain,15 A. L. James,18 P. A. James,114 R. Jamshidi,33 A. Z. Jan,148 K. Jani,192\nL. Janiurek,25 J. Janquart,68, 32 K. Janssens,107, 44 N. N. Janthalur,215 S. Jaraba,110 P. Jaranowski,216 S. Jarov,30\nP. Jasal,38 R. Jaume,92 W. Javed,18 K. Jenner,90 A. Jennings,52 W. Jia,75 J. Jiang,78 H.-B. Jin,217, 218\nK. Johansmeyer,182 G. R. Johns,114 N. A. Johnson,78 R. Johnston,25 N. Johny,12, 13 D. H. Jones,11 D. I. Jones,219\nR. Jones,25 P. Joshi,8 L. Ju,26 K. Jung,220 J. Junker,12, 13 V. Juste,179 T. Kajita,152 C. Kalaghatgi,68, 32, 221\nV. Kalogera,72 M. Kamiizumi,45 N. Kanda,214, 191 S. Kandhasamy,14 G. Kang,222 J. B. Kanner,2 S. J. Kapadia,14\nD. P. Kapasi,11 S. Karat,2 C. Karathanasis,39 S. Karki,136 T. Karydas,27 Y. A. Kas-danouche,64 R. Kashyap,8\nM. Kasprzack,2 W. Kastaun,12, 13 J. Kato,151 T. Kato,152 S. Katsanevas,54, \u2217E. Katsavounidis,75 J. K. Katsuren,64\nW. Katzman,61 T. Kaur,26 K. Kawabe,52 F. K\u00b4ef\u00b4elian,44 D. Keitel,92 J. Kelley-Derzon,78 S. A. Kemper,43\nJ. Kennington,8 R. Kesharwani,14 J. S. Key,223 S. Khadka,17 F. Y. Khalili,99 T. Khanam,159 E. A. Khazanov,211\nM. Khursheed,96 N. Kijbunchoo,11 C. Kim,224 J. C. Kim,225 K. Kim,224 M. H. Kim,226 P. Kim,226 S. Kim,210\nW. S. Kim,227 Y.-M. Kim,228 C. Kimball,72 N. Kimura,45 M. Kinley-Hanlon,25 R. Kirchhoff,12, 13 J. S. Kissel,52\nT. Kiyota,191 S. Klimenko,78 T. Klinger,18 A. M. Knee,30 N. Knust,12, 13 P. Koch,12, 13 S. M. Koehlenbeck,17\nG. Koekoek,32, 31 K. Kohri,229 K. Kokeyama,18 S. Koley,40 N. D. Koliadko,64 P. Kolitsidou,18 M. Kolstein,39\n\n3\nK. Komori,126 V. Kondrashov,2 A. K. H. Kong,141 A. Kontos,230 M. Korobko,79 R. V. Kossak,12, 13 N. Kouvatsos,65\nM. Kovalam,26 N. Koyama,206 D. B. Kozak,2 S. L. Kranzhoff,31, 32, 12, 13 V. Kringel,12, 13 N. V. Krishnendu,20\nA. Kr\u00b4olak,231, 174 G. Kuehn,12, 13 P. Kuijer,32 S. Kulkarni,198 A. Kulur Ramamohan,11 A. Kumar,215\nPraveen Kumar,123 Prayush Kumar,20 Rahul Kumar,52 Rakesh Kumar,86 J. Kume,126 K. Kuns,75\nS. Kuroyanagi,110, 232 S. Kuwahara,126 K. Kwak,220 K. Kwan,11 G. Lacaille,25 P. Lagabbe,27 D. Laghi,120 S. Lai,146\nM. H. Lakkis,33 E. Lalande,233 M. Lalleman,107 A. Lamberts,44, 234 M. Landry,52 B. B. Lane,75 R. N. Lang,75\nJ. Lange,148 B. Lantz,17 A. La Rana,62 I. La Rosa,108, 27 A. Lartaux-Vollard,35 P. D. Lasky,7 J. Lawrence,159\nM. Laxen,61 A. Lazzarini,2 C. Lazzaro,83, 84 P. Leaci,108, 62 S. Leavey,12, 13 S. LeBohec,188 Y. K. Lecoeuche,30\nH. M. Lee,225 H. W. Lee,235 K. Lee,226 R.-K. Lee,141 R. Lee,75 S. Lee,236 Y. Lee,143 I. N. Legred,2 J. Lehmann,12, 13\nL. Lehner,237 A. Lema\u02c6\u0131tre,238 M. Lenti,60, 239 M. Leonardi,240, 21 E. Leonova,97 N. Leroy,35 M. Lesovsky,2\nN. Letendre,27 M. Lethuillier,153 C. Levesque,233 Y. Levin,7 K. Leyde,63 A. K. Y. Li,2 K. L. Li,142\nT. G. F. Li,139, 101 X. Li,149 Chien-Yu Lin,143, 141 Chun-Yu Lin,241 E. T. Lin,141 F. Lin,143 H. Lin,143 L. C.-C. Lin,142\nY. Lin,43 F. Linde,221, 32 S. D. Linker,134, 193 T. B. Littenberg,242 A. Liu,139 G. C. Liu,207 Jian Liu,26 F. Llamas,163\nR. K. L. Lo,2 T. Lo,141 J.-P. Locquet,101 L. London,97 A. Longo,59, 60 D. Lopez,177 M. Lopez Portilla,68\nM. Lorenzini,132, 133 V. Loriette,35 M. Lormand,61 G. Losurdo,19 T. P. Lott,55 J. D. Lough,12, 13 H. A. Loughlin,75\nC. O. Lousto,161 G. Lovelace,51 M. J. Lowry,114 H. L\u00a8uck,13, 12, 13 D. Lumaca,132, 133 A. P. Lundgren,121\nA. W. Lussier,233 J. E. Lynam,114 L.-T. Ma,141 S. Ma,149 M. Ma\u2019arif,143 R. Macas,121 M. MacInnis,75\nD. M. Macleod,18 I. A. O. MacMillan,2 A. Macquet,39 K. Maeda,151 S. Maenaut,101 I. Maga\u02dcna Hernandez,9\nC. Magazz`u,19 R. M. Magee,2 R. Maggiore,32, 98 M. Magnozzi,53, 125 M. Mahesh,79 S. Mahesh,243 M. Maini,162\nS. Majhi,14 E. Majorana,108, 62 C. N. Makarem,2 S. Maliakal,2 A. Malik,96 N. Man,44 V. Mandic,29\nV. Mangano,62, 108 B. Mannix,69 G. L. Mansell,70, 75 G. Mansingh,49 M. Manske,9 M. Mantovani,54 M. Mapelli,83, 84\nF. Marchesoni,48, 47, 244 D. Mar\u00b4\u0131n Pina,38, 73, 245 F. Marion,27 S. M\u00b4arka,160 Z. M\u00b4arka,160 C. Markakis,145\nA. S. Markosyan,17 A. Markowitz,2 E. Maros,2 A. Marquina,158 S. Marsat,120 F. Martelli,59, 60 I. W. Martin,25\nR. M. Martin,182 B. B. Martinez,128 M. Martinez,39, 246 V. A. Martinez,78 V. Martinez,122 K. Martinovic,65\nD. V. Martynov,115 E. J. Marx,75 H. Masalehdan,79 A. Masserot,27 M. Masso-Reid,25 M. Mastrodicasa,62\nS. Mastrogiovanni,62 M. Mateu-Lucena,92 M. Matiushechkina,12, 13 M. Matsuyama,191 N. Mavalvala,75\nN. Maxwell,52 G. McCarrol,61 R. McCarthy,52 D. E. McClelland,11 S. McCormick,61 L. McCuller,2\nG. I. McGhee,25 J. McGinn,25 M. Mchedlidze,182 C. McIsaac,121 J. McIver,30 K. McKinney,164 A. McLeod,26\nT. McRae,11 S. T. McWilliams,243 D. Meacher,9 M. Mehmet,12, 13 A. K. Mehta,1 Q. Meijer,68 A. Melatos,129\nS. Mellaerts,101 A. Menendez-Vazquez,39 C. S. Menoni,135 R. A. Mercer,9 L. Mereni,167 K. Merfeld,69\nE. L. Merilh,61 J. D. Merritt,69 M. Merzougui,44 C. Messenger,25 C. Messick,75 M. Meyer-Conde,191\nF. Meylahn,12, 13 A. Mhaske,14 A. Miani,102, 103 H. Miao,247 I. Michaloliakos,78 C. Michel,167 Y. Michimura,2, 126\nH. Middleton,115 D. P. Mihaylov,1 A. L. Miller,32 A. Miller,193 B. Miller,97, 32 S. Miller,2 M. Millhouse,55\nE. Milotti,248, 42 Y. Minenkov,133 N. Mio,249 Ll. M. Mir,39 L. Mirasola,250, 62 M. Miravet-Ten\u00b4es,137\nC. . Miritescu,39 A. Mishkin,78 A. Mishra,14 C. Mishra,172 T. Mishra,78 T. Mistry,166 A. L. Mitchell,32, 98\nS. Mitra,14 V. P. Mitrofanov,99 G. Mitselmakher,78 R. Mittleman,75 O. Miyakawa,45 S. Miyamoto,152\nS. Miyoki,45 G. Mo,75 L. Mobilia,59, 60 L. M. Modafferi,92 S. R. P. Mohapatra,2 S. R. Mohite,9 M. Molina-Ruiz,203\nC. Mondal,196 M. Mondin,193 M. Montani,59, 60 C. J. Moore,115 M. Morales,51 D. Moraru,52 F. Morawski,88\nA. More,14 S. More,14 C. Moreno,43 G. Moreno,52 S. Morisaki,126, 152 Y. Moriwaki,151 G. Morras,110\nA. Moscatello,83 B. Mours,179 C. M. Mow-Lowry,32, 98 S. Mozzon,121 F. Muciaccia,108, 62 Arunava Mukherjee,251\nD. Mukherjee,242 Soma Mukherjee,163 Subroto Mukherjee,86 Suvodip Mukherjee,252, 237, 97 N. Mukund,12, 13\nA. Mullavey,61 J. Munch,90 E. A. Mu\u02dcniz,70 M. Murakoshi,253 P. G. Murray,25 S. Muusse,90 S. L. Nadji,12, 13\nA. Nagar,24, 254 T. Nagar,7 N. Nagarajan,25 K. Nakamura,21 H. Nakano,255 M. Nakano,61 V. Napolano,54\nI. Nardecchia,132, 133 T. Narikawa,152 H. Narola,68 L. Naticchioni,62 R. K. Nayak,256 B. F. Neil,26 J. Neilson,89, 106\nA. Nelson,128 T. J. N. Nelson,61 M. Nery,12, 13 S. Nesseris,110 A. Neunzert,52 K. Y. Ng,75 S. W. S. Ng,90\nC. Nguyen,63 P. Nguyen,69 L. Nguyen Quynh,257 S. A. Nichols,10 G. Nieradka,88 A. Niko,143 Y. Nishino,21, 258\nA. Nishizawa,126 S. Nissanke,97, 32 E. Nitoglia,153 W. Niu,8 F. Nocera,54 M. Norman,18 C. North,18\nJ. Novak,259, 260, 261, 262 J. F. Nu\u02dcno Siles,110 G. Nurbek,163 L. K. Nuttall,121 K. Obayashi,253 J. Oberling,52\nJ. O\u2019Dell,209 E. Oelker,25 M. Oertel,259, 260, 261, 263, 262 A. Offermans,101 G. Oganesyan,40, 111 J. J. Oh,227 K. Oh,210\nS. H. Oh,227 T. O\u2019Hanlon,61 M. Ohashi,45 M. Ohkawa,206 F. Ohme,12, 13 H. Ohta,126 A. S. Oliveira,160\nR. Oliveri,259, 260, 261 V. Oloworaran,26 B. O\u2019Neal,114 K. Oohara,264, 265 B. O\u2019Reilly,61 R. G. Ormiston,29\nN. D. Ormsby,114 M. Orselli,47, 81 R. O\u2019Shaughnessy,161 Y. Oshima,266 S. Oshino,45 S. Ossokine,1 C. Osthelder,2\nD. J. Ottaway,90 A. Ouzriat,153 H. Overmier,61 A. E. Pace,8 R. Pagano,10 M. A. Page,21 A. Pai,140 S. A. Pai,96\nA. Pal,267 S. Pal,256 O. Palashov,211 M. P\u00b4alfi,189 C. Palomba,62 K.-C. Pan,141 P. K. Panda,215 L. Panebianco,59, 60\nP. T. H. Pang,32, 68 F. Pannarale,108, 62 B. C. Pant,96 F. H. Panther,26 C. D. Panzer,29 F. Paoletti,19 A. Paoli,54\nA. Paolone,62, 268 E. E. Papalexakis,34 L. Papalini,19, 80 G. Pappas,213 A. Parisi,32, 97 J. Park,236 W. Parker,61\nD. Pascucci,87 A. Pasqualetti,54 R. Passaquieti,80, 19 D. Passuello,19 M. Patel,114 D. Pathak,14 M. Pathak,90\nA. Patra,18 B. Patricelli,80, 19 A. S. Patron,10 S. Paul,69 E. Payne,2 T. Pearce,18 M. Pedraza,2 R. Pegna,19\nM. Pegoraro,84 A. Pele,2 F. E. Pe\u02dcna Arellano,45 S. Penn,269 A. Perego,102, 103 A. Pereira,122 C. J. Perez,52\nJ. J. Perez,78 L. H. Perez,43 C. P\u00b4erigois,154, 84, 83 C. C. Perkins,78 A. Perreca,102, 103 J. Perret,63 S. Perri`es,153\nJ. W. Perry,32, 98 D. Pesios,213 J. Petermann,79 C. Petrillo,81 H. P. Pfeiffer,1 H. Pham,61 K. A. Pham,29\nK. S. Phukon,32, 221 H. Phurailatpam,139 O. J. Piccinni,39 M. Pichot,44 M. Piendibene,80, 19 F. Piergiovanni,59, 60\n\n4\nL. Pierini,108, 62 G. Pierra,153 V. Pierro,89, 106 M. . Pietrzak,88 G. Pillant,54 M. Pillas,35 F. Pilo,19 L. Pinard,167\nC. Pineda-Bosque,193 I. M. Pinto,89, 106, 270, 28, 54 M. Pinto,54 B. J. Piotrzkowski,9 M. Pirello,52 M. D. Pitkin,15, 204, 25\nA. Placidi,47, 81 E. Placidi,108, 62 M. L. Planas,92 W. Plastino,271, 272 R. Poggiani,80, 19 E. Polini,27 L. Pompili,1\nS. Ponrathnam,14, \u2020 J. Poon,139 E. Porcelli,32 J. Portell,38, 73, 245 E. K. Porter,63 C. Posnansky,8 R. Poulton,54\nJ. Powell,155 M. Pracchia,27 B. K. Pradhan,14 T. Pradier,179 A. K. Prajapati,86 K. Prasai,17 R. Prasanna,215\nP. Prasia,14 G. Pratten,115 M. Principe,134, 89, 270, 106 G. A. Prodi,273, 103 L. Prokhorov,115 P. Prosposito,132, 133\nL. Prudenzi,1 A. Puecher,32, 68 J. Pullin,10 M. Punturo,47 F. Puosi,19, 80 P. Puppo,62 M. P\u00a8urrer,1 H. Qi,10 J. Qin,11\nV. Quetschke,163 P. J. Quinonez,43 R. Quitzow-James,136 F. J. Raab,52 G. Raaijmakers,97, 32 N. Radulesco,44\nP. Raffai,189 S. X. Rail,233 S. Raja,96 C. Rajan,96 K. E. Ramirez,61 A. Ramos-Buades,1 D. Rana,14 E. Randel,135\nP. R. Rangnekar,17 P. Rapagnani,108, 62 A. Ray,9 V. Raymond,18 N. Raza,30 M. Razzano,80, 19 J. Read,51\nM. Recaman Payo,101 T. Regimbau,27 L. Rei,53 S. Reid,91 S. W. Reid,114 D. H. Reitze,2 P. Relton,18 A. Renzini,2\nP. Rettegno,24 B. Revenu,63, 274 A. Reza,32 M. Rezac,51 A. S. Rezaei,62, 108 F. Ricci,108, 62 M. Ricci,62 D. Richards,209\nJ. W. Richardson,34 A. Rijal,43 K. Riles,82 H. K. Riley,18 S. Rinaldi,80, 19 C. Robertson,209 N. A. Robertson,2\nF. Robinet,35 M. Robinson,52 A. Rocchi,133 L. Rolland,27 J. G. Rollins,2 M. Romanelli,109 A. E. Romano,275\nR. Romano,4, 5 A. Romero,176 I. M. Romero-Shaw,15 J. H. Romie,61 S. Ronchini,40, 111 T. J. Roocke,90 L. Rosa,5, 28\nT. J. Rosauer,34 C. A. Rose,9 D. Rosi\u00b4nska,116 M. P. Ross,208 M. Rossello,92 S. Rowan,25 S. Roy,68 A. Royzman,188\nD. Rozza,168, 130 P. Ruggi,54 E. Ruiz Morales,110 K. Ruiz-Rocha,192 S. Sachdev,55 T. Sadecki,52 J. Sadiq,123\nP. Saffarieh,32, 98 S. S. Saha,141 T. Sainrat,179 S. Sajith Menon,62 K. Sakai,276 M. Sakellariadou,65 T. Sako,151\nS. Sakon,8 O. S. Salafia,118, 119, 157 F. Salces-Carcoba,2 L. Salconi,54 M. Saleem,29 F. Salemi,102, 103 M. Sall\u00b4e,32\nS. Salvador,197, 196, 259 A. Sanchez,52 E. J. Sanchez,2 J. H. Sanchez,72 L. E. Sanchez,2 N. Sanchis-Gual,277, 137\nJ. R. Sanders,278 E. M. S\u00a8anger,1 T. R. Saravanan,14 N. Sarin,7 A. Sasli,213 P. Sassi,47, 81 B. Sassolas,167\nH. Satari,26 R. Sato,206 S. Sato,151 Y. Sato,151 O. Sauter,78 R. L. Savage,52 V. Savant,14 T. Sawada,45\nH. L. Sawant,14 S. Sayah,167 D. Schaetzl,2 M. Scheel,149 S. J. Scherf,17 J. Scheuer,72 M. G. Schiworski,90\nP. Schmidt,115 S. Schmidt,68 S. J. Schmitz,67 R. Schnabel,79 M. Schneewind,12, 13 R. M. S. Schofield,69\nA. Sch\u00a8onbeck,79 K. Schouteden,101 H. Schuler,8 B. W. Schulte,12, 13 B. F. Schutz,18, 1 E. Schwartz,18 J. Scott,25\nS. M. Scott,11 T. C. Seetharamu,25 M. Seglar-Arroyo,39 Y. Sekiguchi,279 D. Sellers,61 A. S. Sengupta,280\nD. Sentenac,54 E. G. Seo,25 J. W. Seo,101 V. Sequino,28, 5 G. Servignat,260 Y. Setyawati,68 T. Shaffer,52\nM. S. Shahriar,72 M. A. Shaikh,225 B. Shams,188 L. Shao,212 P. Sharma,96 S. Sharma-Chaudhary,136 P. Shawhan,117\nN. S. Shcheblanov,281, 238 A. Sheela,172 B. Shen,117 K. G. Shepard,64 Y. Shikano,282, 283 M. Shikauchi,126\nK. Shimode,45 H. Shinkai,284 J. Shiota,253 D. H. Shoemaker,75 D. M. Shoemaker,148 R. W. Short,52\nS. ShyamSundar,96 A. Sider,33 H. Siegel,180, 181 M. Sieniawska,113 D. Sigg,52 L. Silenzi,47, 48 M. Simmonds,90\nL. P. Singer,77 A. Singh,198 D. Singh,8 M. K. Singh,20 A. Singha,31, 32 A. M. Sintes,92 V. Sipala,168, 130 V. Skliris,18\nB. J. J. Slagmolen,11 T. J. Slaven-Blair,26 J. Smetana,115 J. R. Smith,51 L. Smith,25 R. J. E. Smith,7\nJ. Soldateschi,239, 285, 60 S. N. Somala,286 K. Somiya,3 K. Soni,14 S. Soni,75 V. Sordini,153 F. Sorrentino,53\nN. Sorrentino,80, 19 R. Soulard,44 T. Souradeep,14, 287 E. Sowell,159 V. Spagnuolo,31, 32 A. P. Spencer,25\nM. Spera,83, 84 P. Spinicelli,54 A. K. Srivastava,86 V. Srivastava,70 C. Stachie,44 F. Stachurski,25 D. A. Steer,63\nJ. Steinlechner,31, 32 S. Steinlechner,31, 32 D. Stephens,72 N. Stergioulas,213 P. Stevens,35 M. StPierre,162\nL. C. Strang,129 G. Stratta,288, 289, 62, 290 M. D. Strong,10 A. Strunk,52 R. Sturani,291 A. L. Stuver,95\nM. Suchenek,88 S. Sudhagar,14, 88 N. Sueltmann,79 H. G. Suh,9 A. G. Sullivan,160 T. Z. Summerscales,64 L. Sun,11\nS. Sunil,86 A. Sur,88 J. Suresh,126, 113 P. J. Sutton,18 Takamasa Suzuki,206 Takanori Suzuki,3 B. L. Swinkels,32\nA. Syx,179 M. J. Szczepa\u00b4nczyk,78 P. Szewczyk,116 M. Tacca,32 H. Tagoshi,152 S. C. Tait,25 H. Takahashi,292\nR. Takahashi,21 A. Takamori,50 K. Takatani,191 H. Takeda,293 M. Takeda,191 C. J. Talbot,91 C. Talbot,75\nM. Tamaki,152 N. Tamanini,120 D. Tanabe,143 K. Tanaka,152 S. J. Tanaka,253 T. Tanaka,293 A. J. Tanasijczuk,113\nS. Tanioka,70 D. B. Tanner,78 D. Tao,2 L. Tao,78 R. D. Tapia,8 E. N. Tapia San Mart\u00b4\u0131n,32 R. Tarafder,2\nC. Taranto,132 A. Taruya,294 J. D. Tasson,173 M. Teloi,33 R. Tenorio,92 L. Terkowski,79 H. Themann,193\nM. P. Thirugnanasambandam,14 L. M. Thomas,115 M. Thomas,61 P. Thomas,52 J. E. Thompson,18 S. R. Thondapu,96\nK. A. Thorne,61 E. Thrane,7 J. Tissino,40 Shubhanshu Tiwari,177 Srishti Tiwari,14 V. Tiwari,18 A. M. Toivonen,29\nA. E. Tolley,121 T. Tomaru,21 K. Tomita,191 T. Tomura,45 M. Tonelli,80, 19 A. Toriyama,253\nA. Torres-Forn\u00b4e,137, 138 C. I. Torrie,2 M. Toscani,120 I. Tosta e Melo,130 E. Tournefier,27 A. A. Trani,126\nA. Trapananti,48, 47 F. Travasso,48, 47 G. Traylor,61 J. Trenado,38 M. Trevor,117 M. C. Tringali,54 A. Tripathee,82\nL. Troiano,295, 106 A. Trovato,42, 248 L. Trozzo,5 R. J. Trudeau,2 M. Tse,75 R. Tso,149 S. Tsuchida,296 L. Tsukada,8\nT. Tsutsui,126 K. Turbang,176, 107 M. Turconi,44 C. Turski,87 H. Ubach,38, 73 A. S. Ubhi,115 N. Uchikata,152\nT. Uchiyama,45 R. P. Udall,2 T. Uehara,297 K. Ueno,126 C. S. Unnikrishnan,252 T. Ushiba,45 A. Utina,31, 32\nH. Vahlbruch,12, 13 N. Vaidya,2 G. Vajente,2 A. Vajpeyi,7 G. Valdes,128 M. Valentini,98, 32 S. A. Vallejo-Pe\u02dcna,275\nS. Vallero,24 V. Valsan,9 N. van Bakel,32 M. van Beuzekom,32 M. van Dael,32, 298 J. F. J. van den Brand,31, 98, 32\nC. Van Den Broeck,68, 32 D. C. Vander-Hyde,70 M. van der Sluys,32, 68 A. Van de Walle,35 J. van Dongen,32, 98\nH. van Haevermaet,107 J. V. van Heijningen,113 J. Vanosky,2 M. H. P. M. van Putten,299 Z. van Ranst,31, 32\nN. van Remortel,107 M. Vardaro,31, 32 A. F. Vargas,129 V. Varma,1 M. Vas\u00b4uth,76 A. Vecchio,115 G. Vedovato,84\nJ. Veitch,25 P. J. Veitch,90 J. Venneberg,12, 13 P. Verdier,153 D. Verkindt,27 P. Verma,174 Y. Verma,96\nS. M. Vermeulen,18 D. Veske,160 F. Vetrano,59 A. Veutro,62 A. Vicer\u00b4e,59, 60 S. Vidyant,70 A. D. Viets,300\nA. Vijaykumar,20 V. Villa-Ortega,123 E. T. Vincent,55 J.-Y. Vinet,44 S. Viret,153 A. Virtuoso,248, 42 S. Vitale,75\nH. Vocca,81, 47 D. Voigt,79 E. R. G. von Reis,52 J. S. A. von Wrangel,12, 13 S. P. Vyatchanin,99 L. E. Wade,67\n\n5\nM. Wade,67 K. J. Wagner,161 R. C. Walet,32 M. Walker,114 G. S. Wallace,91 L. Wallace,2 H. Wang,266\nJ. Z. Wang,82 W. H. Wang,163 R. L. Ward,11 J. Warner,52 M. Was,27 T. Washimi,21 N. Y. Washington,2\nK. Watada,114 D. Watarai,126 K. E. Wayt,67 B. Weaver,52 C. R. Weaving,121 S. A. Webster,25 M. Weinert,12, 13\nA. J. Weinstein,2 R. Weiss,75 C. M. Weller,208 R. A. Weller,192 F. Wellmann,12, 13 L. Wen,26 P. We\u00dfels,12, 13\nK. Wette,11 J. T. Whelan,161 D. D. White,51 B. F. Whiting,78 C. Whittle,75 J. B. Wildberger,1 O. S. Wilk,67\nD. Wilken,12, 13, 13 K. Willetts,18 D. Williams,25 M. J. Williams,25 A. R. Williamson,121 J. L. Willis,2\nB. Willke,13, 12, 13 M. Wils,101 C. C. Wipf,2 G. Woan,25 J. Woehler,12, 13 J. K. Wofford,161 D. Wong,30\nH. T. Wong,143 I. C. F. Wong,139 M. Wright,25 C. Wu,141 D. S. Wu,12, 13 H. Wu,141 D. M. Wysocki,9 L. Xiao,2\nV. A. Xu,75 N. Yadav,88 H. Yamamoto,2 K. Yamamoto,151 M. Yamamoto,151 T. S. Yamamoto,232 T. Yamamoto,45\nS. Yamamura,152 R. Yamazaki,253 S. Yan,17 F. W. Yang,188 K. Z. Yang,29 L.-C. Yang,146 Y.-C. Yang,141\nYang Yang,78 Yi Yang,146 M. J. Yap,11 Z. Yarbrough,10 S.-W. Yeh,141 A. B. Yelikar,161 S. M. C. Yeung,9\nT. Y. Yeung,64 J. Yokoyama,36, 37 T. Yokozawa,45 J. Yoo,301 H. Yu,149 H. Yuzurihara,45 A. Zadro\u02d9zny,174\nA. J. Zannelli,114 M. Zanolin,43 M. Zeeshan,161 T. Zelenova,54 J.-P. Zendri,84 M. Zevin,124 J. Zhang,11 L. Zhang,2\nR. Zhang,78 T. Zhang,302 Yanqi Zhang,128 Ya Zhang,11 C. Zhao,26 Yue Zhao,188 Yuhang Zhao,152, 21, 63 Y. Zheng,136\nH. Zhong,29 R. Zhou,203 Z.-H. Zhu,127, 303 A. B. Zimmerman,148 M. E. Zucker,75, 2 and J. Zweizig2\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n3Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n5INFN, Sezione di Napoli, I-80126 Napoli, Italy\n6University of Warwick, Coventry CV4 7AL, United Kingdom\n7OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n8The Pennsylvania State University, University Park, PA 16802, USA\n9University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n10Louisiana State University, Baton Rouge, LA 70803, USA\n11OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n12Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n13Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n14Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n15University of Cambridge, Cambridge CB2 1TN, United Kingdom\n16Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n17Stanford University, Stanford, CA 94305, USA\n18Cardiff University, Cardiff CF24 3AA, United Kingdom\n19INFN, Sezione di Pisa, I-56127 Pisa, Italy\n20International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n21Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n22Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n23Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n24INFN Sezione di Torino, I-10125 Torino, Italy\n25SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n26OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n27Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n28Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n29University of Minnesota, Minneapolis, MN 55455, USA\n30University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n31Maastricht University, 6200 MD Maastricht, Netherlands\n32Nikhef, 1098 XG Amsterdam, Netherlands\n33Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n34University of California, Riverside, Riverside, CA 92521, USA\n35Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n36Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.\n37Research Center for the Early Universe (RESCEU), University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.\n38Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n39Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n40Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n\n6\n41Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n42INFN, Sezione di Trieste, I-34127 Trieste, Italy\n43Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n44Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n45Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n46Department of Physics, National and Kapodistrian University of Athens, 15771 Ilissia, Greece\n47INFN, Sezione di Perugia, I-06123 Perugia, Italy\n48Universit`a di Camerino, I-62032 Camerino, Italy\n49American University, Washington, DC 20016, USA\n50Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n51California State University Fullerton, Fullerton, CA 92831, USA\n52LIGO Hanford Observatory, Richland, WA 99352, USA\n53INFN, Sezione di Genova, I-16146 Genova, Italy\n54European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n55Georgia Institute of Technology, Atlanta, GA 30332, USA\n56Chennai Mathematical Institute, Chennai 603103, India\n57Royal Holloway, University of London, London TW20 0EX, United Kingdom\n58The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n59Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n60INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n61LIGO Livingston Observatory, Livingston, LA 70754, USA\n62INFN, Sezione di Roma, I-00185 Roma, Italy\n63Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n64Andrews University, Berrien Springs, MI 49104, USA\n65King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n66Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n67Kenyon College, Gambier, OH 43022, USA\n68Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n69University of Oregon, Eugene, OR 97403, USA\n70Syracuse University, Syracuse, NY 13244, USA\n71Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n72Northwestern University, Evanston, IL 60208, USA\n73Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n74Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n75LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n76Wigner RCP, RMKI, H-1121 Budapest, Hungary\n77NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n78University of Florida, Gainesville, FL 32611, USA\n79Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n80Universit`a di Pisa, I-56127 Pisa, Italy\n81Universit`a di Perugia, I-06123 Perugia, Italy\n82University of Michigan, Ann Arbor, MI 48109, USA\n83Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n84INFN, Sezione di Padova, I-35131 Padova, Italy\n85Montana State University, Bozeman, MT 59717, USA\n86Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n87Universiteit Gent, B-9000 Gent, Belgium\n88Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n89Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n90OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n91SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n92IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n93Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n94Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n95Villanova University, Villanova, PA 19085, USA\n\n7\n96RRCAT, Indore, Madhya Pradesh 452013, India\n97GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n98Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n99Lomonosov Moscow State University, Moscow 119991, Russia\n100Center for Theoretical Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland\n101Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n102Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n103INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n104Bar-Ilan University, Ramat Gan, 5290002, Israel\n105Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n106INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n107Universiteit Antwerpen, 2000 Antwerpen, Belgium\n108Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n109Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n110Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n111INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n112Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n113Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n114Christopher Newport University, Newport News, VA 23606, USA\n115University of Birmingham, Birmingham B15 2TT, United Kingdom\n116Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n117University of Maryland, College Park, MD 20742, USA\n118Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n119INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n120L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n121University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n122Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n123IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n124University of Chicago, Chicago, IL 60637, USA\n125Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n126University of Tokyo, Tokyo, 113-0033, Japan.\n127Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n128Texas A&M University, College Station, TX 77843, USA\n129OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n130INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n131Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n132Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n133INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n134University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n135Colorado State University, Fort Collins, CO 80523, USA\n136Missouri University of Science and Technology, Rolla, MO 65409, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n140Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n143National Central University, Taoyuan City 320317, Taiwan\n144OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n145Queen Mary University of London, London E1 4NS, United Kingdom\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148University of Texas, Austin, TX 78712, USA\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n\n8\n152Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n153Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n154INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n157INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n158Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n159Texas Tech University, Lubbock, TX 79409, USA\n160Columbia University, New York, NY 10027, USA\n161Rochester Institute of Technology, Rochester, NY 14623, USA\n162University of Rhode Island, Kingston, RI 02881, USA\n163The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n164Bellevue College, Bellevue, WA 98007, USA\n165Scuola Normale Superiore, I-56126 Pisa, Italy\n166The University of Sheffield, Sheffield S10 2TN, United Kingdom\n167Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n168Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n169Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n170INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n171Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n172Indian Institute of Technology Madras, Chennai 600036, India\n173Carleton College, Northfield, MN 55057, USA\n174National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n175Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n176Vrije Universiteit Brussel, 1050 Brussel, Belgium\n177University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n178Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n179Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n180Stony Brook University, Stony Brook, NY 11794, USA\n181Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n182Montclair State University, Montclair, NJ 07043, USA\n183Institute for Nuclear Research, H-4026 Debrecen, Hungary\n184CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n185Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n186Western Washington University, Bellingham, WA 98225, USA\n187SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n188The University of Utah, Salt Lake City, UT 84112, USA\n189E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n190Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n191Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n192Vanderbilt University, Nashville, TN 37235, USA\n193California State University, Los Angeles, Los Angeles, CA 90032, USA\n194University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n195INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n196Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n197Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n198The University of Mississippi, University, MS 38677, USA\n199Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n200Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n201University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n202Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n203University of California, Berkeley, CA 94720, USA\n204University of Lancaster, Lancaster LA1 4YW, United Kingdom\n205College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n\n9\n206Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n207Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n208University of Washington, Seattle, WA 98195, USA\n209Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n210Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n211Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n212Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n213Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n214Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n215Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n216University of Bia lystok, 15-424 Bia lystok, Poland\n217National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n218School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n219University of Southampton, Southampton SO17 1BJ, United Kingdom\n220Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n221Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n222Chung-Ang University, Seoul 06974, Republic of Korea\n223University of Washington Bothell, Bothell, WA 98011, USA\n224Ewha Womans University, Seoul 03760, Republic of Korea\n225Seoul National University, Seoul 08826, Republic of Korea\n226Sungkyunkwan University, Seoul 03063, Republic of Korea\n227National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n228Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n229Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n230Bard College, Annandale-On-Hudson, NY 12504, USA\n231Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n232Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n233Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n234Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n235Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n236Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute (KASI), 776 Daedeokdae-ro,\nYuseong-gu, Daejeon 34055, Republic of Korea\n237Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n238NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n239Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n240Department of Physics, University of Trento, via Sommarive 14, Povo, 38123 TN, Italy\n241National Center for High-performance computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n242NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n243West Virginia University, Morgantown, WV 26506, USA\n244School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n245Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n246Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n247Tsinghua University, Beijing 100084, China\n248Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n249Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n250INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n251Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n252Tata Institute of Fundamental Research, Mumbai 400005, India\n253Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n254Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n255Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n256Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n\n10\n257Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n258Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n259Centre national de la recherche scientifique, 75016 Paris, France\n260Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n261Observatoire de Paris, 75014 Paris, France\n262Universit\u00b4e PSL, 75006 Paris, France\n263Universit\u00b4e de Paris Cit\u00b4e, 75006 Paris, France\n264Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n265Niigata Study Center, The Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n266Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n267CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n268Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n269Hobart and William Smith Colleges, Geneva, NY 14456, USA\n270Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n271Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n272INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n273Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n274Subatech, CNRS/IN2P3 - Institut Mines-Telecom Atlantique - Universit\u00b4e de Nantes, 4 rue Alfred Kastler BP 20722 44307 Nantes\nC\u2019EDEX 03, France\n275Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n276Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n277Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\n3810-183 Aveiro, Portugal\n278Marquette University, Milwaukee, WI 53233, USA\n279Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n280Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n281Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n282Graduate School of Science and Technology, Gunma University, 4-2 Aramaki, Maebashi, Gunma 371-8510, Japan\n283Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n284Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n285INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n286Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n287Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n288Institut f\u00a8ur Theoretische Physik, Johann Wolfgang Goethe-Universit\u00a8at, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n289Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n290INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy\n291Universidade Estadual Paulista, 01140-070 Campinas, S\u02dcao Paulo, Brazil\n292Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya, Tokyo\n158-0082, Japan\n293Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n294Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n295Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n296National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n297Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n298Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n299Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n300Concordia University Wisconsin, Mequon, WI 53097, USA\n301Cornell University, Ithaca, NY 14850, USA\n302Maastricht University, 6200 MD, Maastricht, Netherlands\n303School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n\n11\nABSTRACT\nDespite the growing number of confident binary black hole coalescences observed through gravita-\ntional waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity\nis one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however,\nremains challenging due to the limited availability of gravitational waveforms that include effects of\neccentricity. Here, we present observational results for a waveform-independent search sensitive to\neccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detec-\ntors. We identified no new high-significance candidates beyond those that were already identified with\nsearches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass\n(total mass M > 70 M\u2299) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use\nthis to compare model predictions to search results. Assuming all detections are indeed quasi-circular,\nfor our fiducial population model, we place an upper limit for the merger rate density of high-mass\nbinaries with eccentricities 0 < e \u22640.3 at 0.33 Gpc\u22123 yr\u22121 at 90% confidence level.\nKeywords: Gravitational wave sources, eccentricity, black holes\n1. INTRODUCTION\nThe LIGO (Aasi et al. 2015) and Virgo (Acernese et al.\n2015) gravitational wave observatories have completed\nthree observing runs thus far.\nDuring these runs, 90\ncompact binary merger candidates were identified that\nhad probability of astrophysical origin pastro > 0.5 (Ab-\nbott et al. 2021b; Abbott et al. 2021a). These discover-\nies opened previously inaccessible avenues to study the\nUniverse, including the first direct information on binary\nblack holes (Abbott et al. 2016a,b), the multi-messenger\nobservation of a binary neutron star coalescence (Abbott\net al. 2017; Abbott et al. 2017a; Margutti & Chornock\n2021), a new type of constraint on cosmic expansion\n(Abbott et al. 2017b; Abbott et al. 2021b), and novel\ntests of general relativity (Abbott et al. 2016c, 2017c;\nAbbott et al. 2021c).\nDespite the growing number of candidates and the\ninsight they have provided, the astrophysical sites and\nprocesses that produce the observed merging binaries re-\nmain uncertain. Multiple viable scenarios exist. The bi-\nnary black holes could have formed in an isolated stellar\nbinary (e.g., Bethe & Brown 1998; Dominik et al. 2015;\nInayoshi et al. 2017; Marchant et al. 2016; de Mink &\nMandel 2016; Gallegos-Garcia et al. 2021), via dynami-\ncal interactions in dense stellar clusters (e.g., Portegies\nZwart & McMillan 2000; Banerjee et al. 2010; Ziosi et al.\n2014; Morscher et al. 2015; Mapelli 2016; Rodriguez\net al. 2016a; Askar et al. 2017) or triple systems (e.g.,\nAntonini et al. 2017; Martinez et al. 2020; Vigna-G\u00b4omez\net al. 2021), or via gas capture in the disks of active\ngalactic nuclei (AGN; e.g., McKernan et al. 2012; Bar-\ntos et al. 2017; Fragione et al. 2019; Tagawa et al. 2020).\n\u2217Deceased, November 2022.\n\u2020 Deceased, March 2022.\nGravitational waves carry information about the\nmasses and spins of the merging black holes, which\ncan be used to probe the binaries\u2019 origin (Abbott et al.\n2016b; Vitale et al. 2017; Zevin et al. 2021). Different\nformation channels have diverse predictions for the most\ncommon component masses, mass ratios, spin magni-\ntudes and spin orientations (Belczynski et al. 2002;\nDominik et al. 2013; Vitale et al. 2017).\nFor exam-\nple, isolated binaries are typically expected to produce\nblack holes with spins mostly aligned with the binary\u2019s\norbital axis with possible misalignments that could stem\nfrom recoil velocities imparted during supernova explo-\nsion (e.g., Rodriguez et al. 2016b; Gerosa et al. 2018;\nWysocki et al. 2019). Dynamically formed binaries, on\nthe other hand, generally have an isotropic spin dis-\ntribution (e.g., Rodriguez et al. 2016b; Fishbach et al.\n2017; Baibhav et al. 2020). However, while masses and\nspins provide crucial information about the binaries\u2019\norigin, there is often overlap between their distributions\nfor various formation channels. A catalogue of binary\nblack holes must therefore be considered to make statis-\ntical inferences about their origins using these properties\nalone.\nOrbital eccentricity, e is a unique signature that dis-\nfavors isolated binaries and favors triple systems, stellar\nclusters or AGN-assisted mergers as the possible for-\nmation scenario of the binary.\nWhile isolated black\nhole binaries can be born with an initial eccentricity,\ngravitational-wave emission will circularize their orbit\nby the time their orbital frequency reaches the sensitive\nband of ground-based gravitational-wave observatories\n(Peters 1964).\nDynamical encounters can form bina-\nries closer to merger, leaving insufficient time for or-\nbital circularization. In AGN disks, eccentricity can be\nenhanced for a significant fraction of mergers, e.g., via\nbinary\u2013single interactions (Samsing et al. 2022; Tagawa\n\n12\net al. 2021).\nEccentricity can also be enhanced for\nfield binaries by a nearby third object via the Kozai\u2013\nLidov mechanism (Kozai 1962; Lidov 1962; Naoz 2016;\nAntonini et al. 2017; Randall & Xianyu 2018; Bartos\net al. 2023). Identifying orbital eccentricity (or the lack\nthereof) in the population of binary black holes con-\nsequently places clear constraints on the proportion of\nbinaries originating from various formation channels.\nDespite the advantages that come with estimating the\nbinary\u2019s orbital eccentricity, it has been difficult to probe\nthis parameter through gravitational-wave observations\nfor several reasons. (i) Eccentric orbits have wider dy-\nnamical range than quasi-circular, or e = 0 orbits, mak-\ning them more challenging to model semi-analytically\n(Huerta et al. 2014; Tanay et al. 2016).\n(ii) Eccen-\ntricity increases the dimension of the binary parameter\nspace, requiring more gravitational waveform templates\nand substantially increasing the computational cost of\nboth waveform computation (Cornish & Shapiro Key\n2010) and running template-based searches (Lenon et al.\n2021). (iii) Given these challenges and the lack of ex-\npected eccentricity in field binaries, the development of\neccentric waveform models began with significant de-\nlay compared to circular waveform models (Junker &\nSchaefer 1992). Nonetheless, eccentric waveform devel-\nopment has been an active area recently, with several\npromising waveform models that can be useful in the\nfuture (e.g., Hinderer & Babak 2017; Cao & Han 2017;\nLiu et al. 2022; Nagar et al. 2021; Albanesi et al. 2021;\nKhalil et al. 2021; Ramos-Buades et al. 2022; Islam et al.\n2021; Setyawati & Ohme 2021; Wang et al. 2023).\nWhile no comprehensive eccentric gravitational-wave\ntemplate bank is currently available, indications of ec-\ncentricity already exist within the catalog of detected\ngravitational waves. The basis of such results is that\nstandard gravitational-wave search algorithms devel-\noped to target circular binaries also have some sensitiv-\nity to eccentric binaries. For low masses \u227210 M\u2299, circu-\nlar template-based searches show undiminished sensitiv-\nity for small residual eccentricities (e \u22720.05 at 40 Hz).\nTo detect signals with eccentricities beyond e \u22730.1, we\nwould however require template banks that include ec-\ncentric waveforms (Brown & Zimmerman 2010). In con-\ntrast, for higher masses and eccentricities, it has been\nshown that eccentricities can be found without signif-\nicant loss of signal-to-noise ratio (SNR) using model-\nagnostic searches (Abbott et al. 2019).\nTo identify detected binaries as eccentric, two ap-\nproaches have been carried out so far that circumvent\nthe need for comprehensive template banks:\n\u2022 One approach is to employ Bayesian analyses us-\ning existing eccentric waveform models.\nAn ec-\ncentric waveform model limited to eccentricities\ne < 0.2 was used to show that the binary merger\nthat produced the signal GW190521 as well as\ntwo others are consistent with originating from ec-\ncentric binary black holes (eBBH). (Romero-Shaw\net al. 2020, 2021).\nUsing a different waveform\nmodel that includes the full eccentricity range,\nGamba et al. (2023) found strong support for the\nbinary coalescence that produced GW190521 be-\ning highly eccentric.\nBoth models were limited\nto waveforms with black hole spins aligned with\nthe binary orbit.\nOrbital eccentricity and mis-\naligned spins that induce precession of the orbital\nplane produce similar imprints in the gravitational\nwave, and both of these effects should preferably\nbe accounted for in order to accurately analyze the\nevent (Calder\u00b4on Bustillo et al. 2021; Romero-Shaw\net al. 2023).\n\u2022 A different approach relies on numerical relativ-\nity simulations of eBBHs.\nDue to the compu-\ntational cost, only a limited number of simula-\ntions can be carried out, which can only sparsely\ncover the parameter space. Gayathri et al. (2022)\nused such numerical relativity waveforms that\ndiscretely cover the full eccentricity space and\nincludes waveforms with both aligned and mis-\naligned spin with the binary orbit. Interpolation\nmethods and consistency checks were applied to\nrecover the eccentricity and other parameters of\nthe binary. They found that the signal GW190521\nis most consistent with being produced by a highly\neccentric (e \u223c0.7) binary.\nThe GW190521 signal for which the above analyses were\napplied was already considered special even without\nthe indication of eccentricity, having had a high recon-\nstructed total black hole mass of 153.1+42.2\n\u221216.2 M\u2299, along\nwith high and probably misaligned spin (Abbott et al.\n2020).\nIn this paper, we carry out a search focusing on eccen-\ntric black hole coalescences over the third observing run\n(O3) of the LIGO\u2013Virgo network. We use a minimally\nmodeled search algorithm (Klimenko et al. 2005; Salemi\net al. 2019; Tiwari et al. 2016) that we optimize for sen-\nsitivity for a set of high-mass (total mass M \u226570 M\u2299),\neccentric gravitational waveforms (Hinder et al. 2018;\nBoyle et al. 2019). As methods to estimate the eccen-\ntricity of individual events are under development, we\ninstead focus on potential detections that have not al-\nready been discovered by other searches, and charac-\nterize the sensitivity of our search to eccentric binaries,\nrelying on methods with well understood performance.\n\n13\nThe paper is organized as follows. In Section 2 we in-\ntroduce our search algorithm and demonstrate its sen-\nsitivity to eccentric waveforms. In Section 3 we present\nour search results. In Section 4 we discuss constraints\non astrophysical populations based on our search results.\nWe conclude in Section 5.\nGravitational wave strain data (LIGO Scientific Col-\nlaboration, Virgo Collaboration and KAGRA Collabo-\nration 2021) and posterior samples (Abbott et al. 2021a)\nfor all events from GWTC-3 are available from the Zen-\nodo platform or the Gravitational Wave Open Science\nCenter (Abbott et al. 2021b).\n2. SEARCH ALGORITHM AND SENSITIVITY\n2.1. Characterization of eccentricity\nDue to the emission of gravitational waves, binary or-\nbits have a gradually decreasing orbital separation. Ec-\ncentric binary orbits also circularize over time due to\nthe emission of gravitational waves (Peters 1964). This\nmakes the definition of eccentricity challenging. Deter-\nmining eccentricity is particularly difficult at the late\nstages of the binary evolution when less than a full orbit\nseparates the black holes from merger.\nThere have been various efforts to define eccentric-\nity for binary compact object systems.\nThese eccen-\ntricity definitions involve Keplerian orbit assumptions\n(Peters & Mathews 1963; Loutrel et al. 2018), angular\nfrequencies at apocenter and pericenter (Mora & Will\n2004), calculations using instantaneous radial accelera-\ntion (Healy et al. 2018) and using coordinate separations\n(Buonanno et al. 2011). A detailed list of the different\neccentricity definitions that have been developed so far\ncan be found in Loutrel et al. (2018).\nFor our analysis, we adopt the eccentricity definition\nfollowing Ramos-Buades et al. (2022), based on calcu-\nlation first developed by Mora & Will (2004) and later\nused by Lewis et al. (2017), Ramos-Buades et al. (2020)\nand Shaikh et al. (2023). To compute eccentricity for\neach orbit, we used the gravitational-wave frequencies\nat apocenter (\u03c9a) and the consecutive pericenter (\u03c9p).\nWith these, eccentricity for the given orbit is\ne = cos(\u03c8/3) \u2212\n\u221a\n3 sin(\u03c8/3)\n(1)\nwith\n\u03c8 = arctan\n\u00121 \u2212e2\n22\n2e22\n\u0013\n,\n(2)\nwhere\ne22 =\n\u221a\u03c9p \u2212\u221a\u03c9a\n\u221a\u03c9p + \u221a\u03c9a\n.\n(3)\nWe used the orbital frequency of the \u2113= 2, m = 2\nmultipole moments of the gravitational-wave signal.\nIn order to characterize the eccentricity as a function\nof time, we associate this eccentricity with a frequency\nthat is an average of the pericenter and apocenter fre-\nquencies. This method of computing eccentricity using\nthe waveform itself is advantageous because (i) it en-\nables us to compute the evolution of eccentricity as a\nfunction of time (and frequency); (ii) it is gauge in-\ndependent; and (iii) this definition can be uniformly\napplied to all waveform models and can be computed\nduring post-processing. We quote eccentricity values at\n15 Hz gravitational-wave emission frequency unless spec-\nified otherwise. We choose this specific value as this is\napproximately the low-frequency limit of LIGO\u2013Virgo\nnetwork\u2019s sensitivity, and is therefore of the order of the\ninitial frequency of detected gravitational-wave signals.\nThis also compares well to the frequency at which ec-\ncentricity is typically quoted by different astrophysical\nmodels (usually defined at a gravitational-wave emission\nfrequency of \u223c10 \u221215 Hz ; e.g., Fragione & Bromberg\n2019; Zevin et al. 2021).\n2.2. Eccentric waveforms\nThere are multiple ongoing efforts to develop a com-\nprehensive set of eccentric binary coalescence wave-\nforms. Multiple waveform families have been generated\nusing the semi-analytical effective-one-body formalism,\nwhich are currently restricted to non-precessing spins\n(Nagar et al. 2021; Ramos-Buades et al. 2022). A suite\nof numerical relativity simulations have also been car-\nried out that cover virtually the full eccentric and spin\nparameter space (Gayathri et al. 2022; Healy & Lousto\n2022).\nFor our analysis, we adopted 12 state-of-the-art nu-\nmerical relativity waveforms from the Simulating eX-\ntreme Spacetimes (SXS) Collaboration (Hinder et al.\n2018; Boyle et al. 2019), which were the only high-\nfidelity waveforms available to us at the time of this\nstudy.\nThese waveforms cover the eccentricity space\nup to 0.3 defined at 15 Hz gravitational-wave frequency,\nand include a range of mass ratios:\nq \u2261m2/m1 =\n{1, 0.5, 0.33}, where m2 and m1 are the lighter and heav-\nier masses, respectively.\nAs the numerical relativity simulations were carried\nout for the late stage of the binary coalescence, they\ncover the gravitational waveform for the full frequency\nband of the ground-based detectors only for total bi-\nnary source masses \u227370 M\u2299.\nAbove this mass limit\nany binary mass can be obtained by a simple scaling\nof the simulated waveforms due to the scale invariance\nof general relativity (Tiglio & Villanueva 2021).\nThe\nselected waveforms are non-spinning, which has lim-\nited effect on the sensitivity estimates we compute be-\n\n14\nq\ne\nWaveform ID\n0.33\n0.08\nSXS:BBH:1371\n0.33\n0.12\nSXS:BBH:1372\n0.33\n0.27\nSXS:BBH:1374\n0.5\n0.09\nSXS:BBH:1365\n0.5\n0.14\nSXS:BBH:1366\n0.5\n0.29\nSXS:BBH:1369\n0.5\n0.30\nSXS:BBH:1370\n1.0\n0.06\nSXS:BBH:1355\n1.0\n0.14\nSXS:BBH:1357\n1.0\n0.22\nSXS:BBH:1361\n1.0\n0.29\nSXS:BBH:1362\n1.0\n0.30\nSXS:BBH:1363\nTable 1. Parameters of the 12 numerical relativity simu-\nlations adopted from the SXS binary black hole simulations\ncatalog (Boyle et al. 2019). Columns show the binary\u2019s mass\nratio q, and eccentricity e at a reference emission frequency\nof 15 Hz (Section 2.1) for a binary source total mass of 90M\u2299.\nSpin amplitudes \u03c71 and \u03c72 are zero for all considered mod-\nels.\nlow.\nWhen reconstructing the properties of detected\ngravitational-wave signals, it is important to include\nspins, as eccentricity and spin precession can mimic each\nother (Calder\u00b4on Bustillo et al. 2021; Romero-Shaw et al.\n2023). Since we do not use these waveforms to recon-\nstruct properties of signals in this analysis, this problem\nis not relevant here. We list the properties of the wave-\nforms in Table 1. Figure 1 shows the change in signal\nmorphology as the orbital eccentricity is changed while\nkeeping other source parameters fixed.\nWe used this set of 12 numerical relativity wave-\nforms to quantify the search sensitivity to high-mass\n(\u227370 M\u2299) eccentric black hole mergers. However, with\nthis limited set of waveforms we could not reconstruct\nthe eccentricity of events.\n2.3. Search optimization and sensitivity improvement\nCurrent template-based searches (Cannon et al. 2021;\nAubin et al. 2021; Nitz et al. 2017) do not include eccen-\ntric gravitational waveforms. As a consequence, their\nsensitivity is limited for such events, in particular at\nhigh eccentricities and low masses (Brown & Zimmer-\nman 2010). Our search was therefore based on the coher-\nent WaveBurst algorithm (cWB; Klimenko et al. 2005;\nTiwari et al. 2016; Salemi et al. 2019), which uses min-\nimal assumptions about the signal waveform and hence\nis expected to be sensitive to eccentric signals.\nThe cWB algorithm uses the Wilson\u2013Daubechies\u2013\nMeyer filter to transform time domain detector data\nto time\u2013frequency representations (Necula et al. 2012).\nExcess power regions in the time\u2013frequency represen-\ntation of strain data that are obtained from the net-\nwork of detectors are then identified by cWB using\nclustering algorithms. Selected clusters with excess en-\nergy above the expected detector noise are identified as\nevents. The signal waveform, sky coordinates and wave-\nform polarization of the source are then reconstructed\nfor these events using maximum-likelihood analysis (Kli-\nmenko et al. 2016).\nOnce the search pipeline is run, thresholds are placed\nby cWB on the coherent statistics that it derives for\neach candidate event. These are used to better differ-\nentiate between astrophysical signals and noise artifacts\n(Gayathri et al. 2019). We will refer to these thresh-\nolds on cWB statistics as vetoes. Vetoes define a part\nof the parameter space over the coherent statistics that\nshould be excluded from the analysis due to the high\nrate of non-Gaussian noise artifacts there. To maximize\nthe sensitivity of cWB to eccentric binaries, we carried\nout an optimization of these vetoes applied by cWB to\neach event. The first two sets of vetoes that are common\nto the standard cWB pipeline and the eccentric search\npipeline are summarized in Appendix A.\nTransient non-Gaussian noise artifacts, also known\nas glitches,\ncan limit the detector\u2019s sensitivity to\ngravitational-wave signals. Targeted vetoes are placed\nby the standard cWB pipeline to mitigate this problem.\nThese glitch-focused vetoes are derived using cWB sum-\nmary statistics Qa and TF. The waveform shape param-\neter derived by cWB is denoted by Qa, and is a function\nof another cWB parameter Qveto (Qa = \u221aQveto). This\nparameter quantifies how well the total energy of the sig-\nnal is distributed across time (Vedovato 2018; Gayathri\net al. 2019; Mishra et al. 2021). The threshold Qa > 0.3\nis placed to better distinguish between gravitational\nwaves and a class of low-frequency transient noise arti-\nfacts called Blip glitches (Cabero et al. 2019; Davis et al.\n2021). Signals due to Blip glitches, which have most of\ntheir energy localized to a small time segment have low\nQa values as opposed to signals from binary coalescence,\nwhich have higher Qa values as a consequence of signal\nenergy being distributed over a longer duration.\nThe\nTF parameter is a function of the signal bandwidth,\nduration, and power which are additional statistics that\ncWB estimates for candidate events.\nA threshold on\nthis parameter is placed to ensure that short-duration\nglitches that mimic gravitational-wave signals from in-\ntermediate mass binary black hole systems are removed.\nWe injected simulated gravitational-wave signals from\nequal mass, almost head-on systems (Healy & Lousto\n2022) into real detector data to find the set of vetoes that\ndo not remove highly eccentric signals while still reject-\n\n15\n\u22121.0\n\u22120.8\n\u22120.6\n\u22120.4\n\u22120.2\n0.0\nTime [s]\n\u22121.0\n\u22120.5\n0.0\n0.5\n1.0\nStrain\n\u00d710\u221220\ne = 0.06, SXS ID = SXS:BBH:1355\ne = 0.29, SXS ID = SXS:BBH:1362\nFigure 1. Examples of time-domain waveforms with two different eccentricities (indicated in the legend) for equal mass binary\nsystems with total source mass of 90 M\u2299at a distance of 100 Mpc. The simulations start at an orbital separation that translates\nto an orbital frequency flow = 15 Hz. The eccentricity values indicated in the legend are defined at the same flow.\ning most noise artifacts. To perform this optimization,\nthe cWB algorithm was used to detect these injected\nsignals and derive their properties. Vetoes were selected\nsuch that they maximized the number of detections at\nfixed false alarm rates.\nWe observed that Qa and TF vetoes were prone to\nremoving a significant fraction of highly eccentric sim-\nulated signals. We found that we could mitigate this\nproblem if we removed these two thresholds, and instead\nintroduced a new Qa\u2013Qp veto to better distinguish be-\ntween signals from highly eccentric binaries and short-\nduration glitches. This veto removes events identified by\ncWB that do not satisfy the condition Qa(Qp \u22120.8) >\n0.07. The summary statistic Qp quantifies the number\nof cycles in the reconstructed signal. The Qa\u2013Qp veto\nalong with the first two sets of vetoes from the standard\nsearch which are summarized in Appendix A were se-\nlected as the set of post-production vetoes for the eBBH\nsearch. We will refer to this version of cWB that is op-\ntimized to eccentric mergers as cWB-eBBH. While the\nvetoes were optimized using equal-mass waveforms, we\nconfirmed that the optimized search improved eccentric\nevent recovery for unequal mass injections as well.\nFigure 2 shows an example of the standard-cWB Qa\nveto and the new cWB-eBBH Qa\u2013Qp veto for quasi-\ncircular and highly eccentric systems. We also look at\nthis veto\u2019s performance with background events.\nTo\ngenerate background events, data from one detector is\ntime-shifted relative to the other detector\u2019s data by an\namount greater than the maximum time for a gravita-\ntional wave signal to travel between the detectors (Ab-\nbott et al. 2016d). The standard veto does well in re-\nmoving background events and recovering the majority\nof quasi-circular simulation events. However, the distri-\nbution of simulation signals in the Qa\u2212Qp space changes\nfor highly eccentric systems and as a consequence, the\nstandard cWB veto removes a significant fraction of sim-\nulation events.\nWe characterize the sensitivity improvement due to\nthe optimization procedure by computing the number of\ninjected gravitational waves detected by cWB-eBBH but\nnot by standard cWB, divided by the total number of\ndetections by standard cWB. Here we consider a signal\ndetected if it corresponds to an inverse false alarm rate\n(IFAR) of \u22651 yr. This IFAR threshold of \u22651 yr was\nonly used to assess the improvement in sensitivity from\nthe introduction of the cWB-eBBH veto, and not as a\ngeneral detection threshold.\nThe fraction of events recovered with IFAR \u22651 yr by\ncWB-eBBH that are removed by the standard pipeline\nwith respect to the total number of events recovered\nby the standard pipeline is \u223c28% for head-on collision\n(highly eccentric) equal mass systems with a source total\nmass of 150 M\u2299. Additionally, we see that this fraction\nis higher (\u223c34%) for systems with more unequal mass.\nTherefore, our optimization is the most significant for\nhighly eccentric binaries with unequal masses. The per-\nformance of cWB-eBBH for low eccentricity signals re-\nmains comparable (within 5%) to the standard pipeline.\nWe conclude that the cWB-eBBH veto does significantly\nbetter than the standard veto to improve sensitivity for\nhighly eccentric systems without degrading sensitivity\nto less eccentric systems.\n3. RESULTS\n3.1. Search sensitivity\nWe carried out a search for simulated gravitational-\nwave signals to quantify the sensitivity of the cWB-\neBBH search algorithm.\nWe performed injections in\noffline (high-latency) re-calibrated O3 strain data with\n\n16\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nQa\nQuasi-circular\neBBH veto\nStandard cWB veto\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\nQp\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nQa\nAlmost head-on\n0\n20\n50\n100\n150\nSimulated Signals\nFigure 2. Distribution of Qa and Qp for simulated signals\n(shown as two-dimensional histogram with colorbar denot-\ning number of events in each two-dimensional bin) and loud\nsimulated background events (shown as black dots).\nThe\ncWB statistics Qa and Qp describe the morphology of a sig-\nnal. The yellow line represents the standard cWB Qa veto\nand the red dashed line denotes the eBBH Qa\u2013Qp veto. The\nwhite dots correspond to loud background events that re-\nmain after all standard cWB vetoes (Lopez et al. 2022) are\napplied. Top: Simulated signals correspond to equal mass,\nsource total mass, M = 150 M\u2299, quasi-circular orbit sys-\ntems. Bottom: Simulated signals correspond to equal mass,\nM = 150M\u2299, almost head-on (highly eccentric) systems.\ncategory 0, 1, 2 and 4 data-quality vetoes (Davis et al.\n2021; Abbott et al. 2021a). Category 0 vetoes are ap-\nplied to ensure that the segments of data used in this\nanalysis were collected when the detectors were in ob-\nserving mode.\nCategory 1 vetoes are used to discard\ndata from periods in which the detectors were running\nin an improper configuration, data-dropout or on-site\nmaintenance occurred at either detector, or when there\nare major problems with the operation of an instrument\nat the detectors. Category 2 vetoes flag data segments\nthat likely contain non-Gaussian noise artifacts. Cate-\ngory 4 vetoes flag data segments that contain hardware\ninjections.\nThe injected waveforms have source total\nmass M \u2208[70 M\u2299, 200 M\u2299]. We used the possible 12\nconfigurations of e and q, with 6 choices of source to-\ntal mass for each of these configurations.\nWaveforms\nwith different masses were obtained by scaling each of\nthe 12 numerical relativity waveforms listed in Table 1.\nThe simulated signals for each fixed set of source pa-\nrameters of (M, e, q) were uniformly distributed in sky\nlocation (\u03b8, \u03d5) and inclination \u03b9.\nThey were also dis-\ntributed uniformly in co-moving volume up to a maxi-\nmum redshift zmax. For each waveform, we separately\ncalculated zmax up to which they must be injected so\nthat we do not make unnecessary injections that the\nsearch cannot detect. This was calculated with an opti-\nmal two-detector-network (Livingston\u2013Hanford) signal-\nto-noise-ratio threshold of 5.0. Since we observe signals\nwith redshifted mass (Krolak & Schutz 1987), it is in\nprinciple possible to inject simulations with total source\nmass < 70 M\u2299if we populate them at higher redshifts.\nThis was however not performed in the presented anal-\nysis. Injections spaced uniformly in time approximately\nevery 100 s in the O3 dataset.\nWe used the fraction of detected and injected wave-\nforms to compute the sensitive distance of the search for\nthe given waveform. Sensitive distance (Abbott et al.\n2019) is defined such that a detector that detects every\nevent within the sensitive distance and no event beyond,\nit would have the same detection rate as our detector\nnetwork.\nA similar analysis was carried out with data from the\nfirst two observing runs of LIGO\u2013Virgo using approxi-\nmate eccentric waveform models (Abbott et al. 2019).\nThis analysis spanned the binary mass parameter space\nfrom 10 M\u2299to 100 M\u2299while the analysis described in\nthis paper covers binary mass of 70 M\u2299to 200 M\u2299. The\nsensitivities reported in this paper are higher than that\nanalysis due to increased sensitivity of the detector dur-\ning the third observing run, and due to the higher masses\nconsidered here. There have also been studies to char-\nacterize the effect of eccentricity in the sensitivity of\nlong-duration signals with unmodeled search pipelines\nusing hybrid inspiral\u2013merger\u2013ringdown waveform mod-\nels (Abbott et al. 2021c). However, these studies were\ntargeted towards low mass binary black holes and bi-\nnary neutron stars as opposed to our search, which is\n\n17\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\n0.35\nEccentricity [flow = 15 Hz]\n1.0\n1.2\n1.4\n1.6\n1.8\nSensitive Distance [Gpc]\n200 M\u2299\n175 M\u2299\n150 M\u2299\n110 M\u2299\n90 M\u2299\n70 M\u2299\nq = 1.0\nq = 0.5\nq = 0.33\nFigure 3. Sensitive distance as a function of orbital eccen-\ntricity for different binary total masses and mass ratios. Dif-\nferent marker shapes represent systems with different mass\nratios and the different colors represent the various total\nmasses considered here.\nWe used an IFAR threshold of\n1.32 yr, which was the loudest new candidate\u2019s IFAR. The\nhorizontal axis denotes the eccentricity of the binary at an\norbital separation that corresponds to a frequency of 15 Hz.\nThe statistical error bars on the obtained sensitive distance\nare smaller than can be presented on this plot.\ntargeted towards high mass eccentric binaries. There-\nfore, the search sensitivities reported in Abbott et al.\n(2021c) are lower than what we obtain in this paper.\nThe obtained sensitive distance is shown in Figure 3,\nfor different source total masses and mass ratios, as\na function of binary eccentricity. The statistical error\nbars for the obtained sensitive distance range between\n0.21 Mpc and 5.63 Mpc. We see that the sensitivity at\nthe considered high masses is mostly independent of the\neccentricity up to our highest eccentricity of 0.3.\nWe\nalso see, as expected, that sensitivity is highest for equal\nmass binaries, and gradually drops as the difference be-\ntween the two black hole masses increases.\n3.2. Search and loudest event\nWe carried out the cWB-eBBH search over the third\nobserving run of the LIGO and Virgo detectors.\nFor\nmost of the observing run we used data from only the\ntwo LIGO detectors, as search sensitivity was not ap-\npreciably affected by the addition of Virgo data. For\nthe January 4, 2020 to January 22, 2020 period we also\nincorporated Virgo in the search to analyze the candi-\ndate 200114 020818, which was found by the intermedi-\nate mass black hole binary search (Abbott et al. 2022) in\nthe three detector network configuration comprising the\nLIGO and Virgo detectors. Follow-up studies for this\nevent (Abbott et al. 2022, Appendix B) showed incon-\nsistent results under a quasi-circular binary black hole\nhypothesis. We investigated if this candidate had higher\nsignificance under the eccentric hypothesis.\nHowever,\n10\u22122\n10\u22121\n100\n101\n102\n103\n104\nInverse False Alarm Rate [years]\n100\n101\nCumulative Number of Events\n190706 004633\nExpected background\nSearch Results (No BBH)\nSearch Results (Known BBH)\n50%\n90%\nFigure 4. Cumulative number of events as a function of\nIFAR recovered by the cWB-eBBH search. The solid line\nrepresents the expected background for the O3 search, and\nthe gray regions correspond to the 50% and 90% Poisson un-\ncertainty regions. Green squares denote previously reported\ngravitional-wave candidates (Abbott et al. 2021a; Abbott\net al. 2022) recovered by our search, and red triangles show\nevents that were not previously reported by other searches.\nthis candidate was removed by the cWB-eBBH vetoes.\nThe search and sensitivity results presented below were\nobtained using data from only the two LIGO detectors.\nOur search recovered 28 gravitational-wave candidates\nwith IFAR > 1 yr. By choosing this IFAR threshold, we\neliminate low significance candidates that could have\nbeen due to noise artifacts in the detector.\nAll but\none of these events have been identified previously by\nother searches as well (Abbott et al. 2021a; Abbott et al.\n2022). The results of our search are summarized in Fig-\nure 4.\nThe search results excluding previously found\ncandidates is consistent with background noise.\nWe identified one event candidate with an IFAR > 1 yr\nthat was not previously reported. This most significant\nnew candidate, hereafter referred to as 190706 004633,\nwas observed on July 6, 2019. It was recovered with an\nIFAR of 1.32 yr. It has an SNR of 12.2 and a central\nfrequency of 74 Hz. Figure 5 shows the time\u2013frequency\nmap of this event candidate.\nIn order to better understand whether 190706 004633\nis of astrophysical origin, we carried out a detailed study\nof the detector performance and characteristics at the\ntime of the event. This study was aimed to uncover signs\nof instrumental or environmental artifacts that could\nhave altered the gravitational wave data and hence pro-\nduced the candidate (Davis et al. 2021, Section 3.2.4).\nNo such artifacts were found. However, the Gravity Spy\nmachine learning classifier (Zevin et al. 2017; Soni et al.\n2021) classified the excess power in LIGO Livingston as\na Tomte glitch. Tomtes are a common glitch class that\nare similar in morphology to high-mass binary coales-\ncence signals (Ashton et al. 2022). No glitch or signal\n\n18\n\u22120.3\n\u22120.2\n\u22120.1\n0.0\n0.1\n0.2\n0.3\nTime [s]\n20\n100\n150\n30\n40\n60\n200\nFrequency [Hz]\n\u22120.3\n\u22120.2\n\u22120.1\n0.0\n0.1\n0.2\n0.3\nTime [s]\n0\n5\n10\n15\n20\n25\nLIGO-Hanford\nNormalized energy\n0\n20\n40\n60\n80\nLIGO-Livingston\nNormalized energy\nFigure 5. Time-frequency map (spectrogram) of the most significant new candidate identified by the cWB-eBBH search. We\nshow the spectrogram for the LIGO-Hanford (left) and LIGO-Livingston (right) detectors. The individual detector SNRs in the\nLIGO-Hanford and LIGO-Livingston are 5.6 and 10.9 respectively. Since the energies in the two detectors are very different,\nwe use different scales on the colorbar. The Virgo detector was in observing mode during the time of this event. We used data\nfrom all three detectors for follow-up studies and observed that the SNR in the Virgo detector for this event was low (\u223c2).\nwas identified in the LIGO Hanford data by the same\nclassifier. However, as the Gravity Spy machine learning\nmodel is not designed to search for astrophysical signals\n(Glanzer et al. 2023) or to differentiate eccentric binary\nblack hole merger signals from glitches, we cannot rule\nout an astrophysical origin.\nTo further investigate this event we carried out a stan-\ndard parameter estimation analysis of the data using\nLALInference (Veitch et al. 2015) with nested sampling\nassuming a quasi-circular waveform.\nWe investigated\nproperties of this event using data from the two LIGO\ndetectors as well as the Virgo detector. For this analysis,\nin lieu of an eccentric waveform that fully covers the nec-\nessary parameter space, we adopted the quasi-circular\nbinary approximant IMRPhenomXPHM (Pratten et al.\n2021). This estimation found that the estimated source\ntotal mass of 190706 004633 is M \u223c320 M\u2299, and its\nestimated redshift is z \u223c0.3. Studies have shown that\nthe chirp mass of a binary with low to moderate eccen-\ntricity can be reconstructed with a bias of up to 4 % us-\ning parameter estimation with quasi-circular waveforms\n(O\u2019Shea & Kumar 2021). However, the reconstructed\nparameters would be considerably more inaccurate if the\nsignal originated from a highly eccentric binary. There-\nfore, these results indicate that the signal, if astrophysi-\ncal, would correspond to a high-mass binary, but should\nnot be used to give precise indications of source proper-\nties.\nAlthough astrophysical origin could not be ruled out,\nwe conclude from the large difference measured in the\nLIGO Hanford and Livingston SNRs that this event is in\naccordance with an incoherent noise origin rather than\na binary black hole origin. In the following section we\ntherefore compute upper limits to merger rates assuming\nnon-detection of any eccentric event.\n4. ECCENTRIC BINARY POPULATION MODELS\nIn order to understand the astrophysical implications\nof our results, we computed the expected number of de-\ntections for a fiducial source model. For this we adopt\nthe joint total mass and mass ratio probability density\np(M, q) which was found to be the best fit for LIGO\u2013\nVirgo\u2019s observations listed in the GWTC-3 catalog (Ab-\nbott et al. 2021a; Abbott et al. 2023) assuming the\nPower Law + Peak model described in Abbott et al.\n(2021a). As we have waveforms and simulations that\nare sparsely sampled in mass and mass ratio, we linearly\ninterpolated the sensitivity of the existing waveforms to\npoints in between the available points in order to obtain\na sensitive distance for any source total mass and mass\nratio within 70 M\u2299\u2264M \u2264200 M\u2299and 0.33 < q < 1.0.\nFor a more general distribution, we considered a power-\nlaw black hole mass distribution of M \u22122.3 (assuming a\nSalpeter initial mass function; Perna et al. 2019) and a\nuniform distribution in mass ratio. We further adopted\nan eccentricity distribution in which the probability den-\nsity of the binaries\u2019 eccentricity is p(e) \u221d2(1 \u2212e). This\ndistribution is chosen to characterize a population which\nhas a larger fraction of low eccentric binaries.\nHaving defined the probability density of our fiducial\npopulation with respect to the binary parameters, using\nthe sensitive distance obtained over the considered pa-\nrameter space (see Section 3.1), we computed the total\nvolume\u2013time VT (Abbott et al. 2019, Appendix A) cov-\n\n19\nered by our search during O3, assuming an IFAR thresh-\nold of 1.32 yr, which is the IFAR of our search\u2019s loudest\nnew event. For our fiducial model, we obtained VT =\n6.88 Gpc3 yr for eccentric binaries with 0 < e < 0.3. As-\nsuming non-detection of any eccentric event, this would\ncorrespond to a constraint of < 0.33 Gpc\u22123 yr\u22121 on\nthe merger rate density at 90% confidence level in the\n70 M\u2299\u2264M \u2264200 M\u2299and 0.33 < q < 1.0 parameter\nspace.\nWith the small number of available eccentric wave-\nforms for this study, we cannot determine if discovered\nbinaries are eccentric.\nTherefore, we cannot discount\nthe possibility that previously identified gravitational-\nwave candidates originate from eccentric binaries.\nIn\nthis case, the number of observed eccentric binaries is\ngreater than zero, and so the merger rate could po-\ntentially be higher than our upper limits. Conversely,\nfor some parts of the parameter space, template-based\nsearches have better sensitivities, although we expect\nthem to lose sensitivity at higher eccentricities. Hence,\nincluding the VT from these searches (Abbott et al.\n2021b; Abbott et al. 2021a) would tighten our upper\nlimits. For simplicity, we limit our results to those from\nthe cWB-eBBH analysis assuming all previously identi-\nfied candidates are from quasicircular binaries.\nSince binary mergers from dynamical formation chan-\nnels can follow a mass distribution different from the\none obtained from GWTC-3, we additionally computed\nVT assuming other parameter distributions. We sum-\nmarize our results in Table 2. Our focus on high-mass,\neccentric events can be particularly interesting for as-\ntrophysical formation channels that favor the produc-\ntion of both high mass and high eccentricity, such as\ngas-driven capture in AGN disks.\nFor this scenario\nwe adopted the AGN model of Gayathri et al. (2021)\nas an illustrative example.\nOur search sensitivity for\nthis model is marginally higher than for the GWTC-\n3 distribution because this model favors higher masses\nthat are more likely to fall in the mass interval that we\nare most sensitive to in this analysis. Assuming non-\ndetection of any eccentric event, we place a constraint\nof < 0.29 Gpc\u22123 yr\u22121 on the merger rate density at 90%\nconfidence level for AGN-assisted mergers. Taking an\nestimated \u223c70% of mergers being eccentric (Samsing\net al. 2022) and \u223c4% of mergers having M > 70 M\u2299\n(Gayathri et al. 2021), we project the corresponding up-\nper limit on the merger rate density to obtain upper\nlimits on the overall AGN-assisted merger rate density\nas \u223c0.29 Gpc\u22123 yr\u22121 /(0.7 \u00d7 0.04) \u223c10.4 Gpc\u22123 yr\u22121.\nThis is consistent with rate estimates in the literature\n(e.g., Yang et al. 2019; Gayathri et al. 2021).\nAs a second illustrative model we used the distri-\nbution expected in dense star clusters (DSC), adopted\nfrom Zevin et al. (2021). For this population, we are\nable to place a constraint of < 0.34 Gpc\u22123 yr\u22121 on the\nmerger rate density at 90% confidence level assuming\nnon-detection of any eccentric event.\nTaking an esti-\nmated \u223c10% being eccentric and \u223c18% of mergers\nhaving M > 70 M\u2299, we project the corresponding up-\nper limit on the merger rate density to obtain upper\nlimits on the overall DSC-assisted merger rate density\nas \u223c0.34 Gpc \u22123 yr\u22121 /(0.1 \u00d7 0.18) \u223c18.9 Gpc\u22123 yr\u22121.\nThis is consistent with rate estimates in the literature\n(Kremer et al. 2020; Zevin et al. 2021).\np(M)\np(q)\np(e)\nVT\n[Gpc3yr]\nGWTC-3\nGWTC-3\n2(1 \u2212e)\n6.88\nGWTC-3\nGWTC-3\nuniform\n6.93\nM \u22122.3\nuniform\n2(1 \u2212e)\n8.22\nM \u22122.3\nuniform\nuniform\n8.27\nAGN\nAGN\n2(1 \u2212e)\n7.85\nAGN\nAGN\nuniform\n7.91\nDSC\nDSC\nDSC\n6.69\nTable 2. Total volume\u2013time covered by cWB-eBBH search\nassuming various source total mass, mass ratio, and eccen-\ntricity probability density functions for the different illustra-\ntive models described in Section 4.\n5. CONCLUSION\nWe carried out a search that does not rely on tem-\nplate banks, and optimized it to be sensitive to high-\nmass (M > 70 M\u2299) eccentric binary black hole coales-\ncences. We characterized the sensitivity for this search\nto understand our findings\u2019 implications for possible ec-\ncentric astrophysical populations. Our conclusions are\nas follows:\n1. We did not identify any high significance candidate\nthat was not already detected by other searches.\nOur loudest and most significant new event has an\nIFAR of 1.32 yr. We performed detailed follow-\nup for this event, and concluded that astrophysi-\ncal origin could not be ruled out. However, our\nsearch results are consistent with the expected\nbackground for O3.\n2. For our fiducial model, we adopted a mass dis-\ntribution that assumes a Power Law + Peak\nmodel and best fits the observations listed in the\nGWTC-3 catalog.\nWe also chose an eccentric-\nity distribution (defined in Section 4) that favors\n\n20\nquasi-circular binaries. For this assumed popula-\ntion, our search sensitivity is such that assuming\nnon-detection of eccentric events, we can place a\nconstraint of < 0.33 Gpc\u22123 yr\u22121 on the merger\nrate density at 90% confidence level.\nThis ob-\ntained overall sensitivity is similar to that of other\nsearches for circular black hole mergers in a similar\nmass range (cf. inferred rate of 0.08+0.19\n\u22120.07 Gpc\u22123\nyr\u22121 of mergers similar to GW190521; Abbott\net al. 2022).\n3. As an illustrative example, we found that non-\ndetection of any eccentric event corresponds a con-\nstraint of < 10.4 Gpc\u22123 yr\u22121 on the AGN-assisted\nmerger rate density, consistent with rate estimates\nin the literature (e.g., Yang et al. 2019; Gayathri\net al. 2021).\n4. As a second illustrative model, we computed our\nsearch sensitivity to mergers in dense star clusters,\nconsidering the model of Zevin et al. (2021). The\nresults are similar to the AGN channel and our\nexpected sensitivity for a generic eccentric model.\nFor this model, we found that non-detection of\neccentric events corresponds to a constraint of\n< 18.9 Gpc\u22123 yr\u22121 on the merger rate density,\nconsistent with rate estimates in literature (Kre-\nmer et al. 2020; Zevin et al. 2021).\nThe constraints we place on the rate of eccentric bi-\nnary coalescences in this work are significantly improved\nover those computed with data obtained from the first\nand second observing runs (Abbott et al. 2019). This\nimprovement can be attributed to increased sensitivity\nof the detectors, progress in the development of highly\naccurate eccentric waveforms in the high mass domain,\nand an optimized eccentric search. In view of the ex-\npected sensitivity of the fourth observing run by LIGO\u2013\nVirgo\u2013KAGRA (Abbott et al. 2018), we anticipate to\nsee a significant rise in the number of binary black hole\ndetections.\nThis increases our prospects of detecting\ngravitational-wave signals from eccentric binary coales-\ncences. Regardless, a non-detection would enable us to\nfurther constrain the binary black hole merger rates in\nastrophysical models favouring eccentric orbits.\nFuture works will need to expand the study to eccen-\ntricities greater than 0.3, and to include masses below\n70 M\u2299as well as black hole spins.\nData-quality products and event-validation results\nwere computed using the DQR Collaboration & Collabo-\nration (2018), DMT John Zweizig (2006), gwdetchar Ur-\nban et al. (2021), hveto Smith et al. (2011) and iDQ Es-\nsick et al. (2020) software packages and contributing\nsoftware tools. Analyses in this paper relied upon the\nLALSuite software library LIGO Scientific Collabora-\ntion (2018). The detection of the signals and subsequent\nsignificance evaluations in this paper were performed\nwith the coherent WaveBurst (cWB) Klimenko et al.\n(2005, 2016) package.\nEstimates of the noise spectra\nand glitch models were obtained using BayesWave Cor-\nnish & Littenberg (2015); Littenberg et al. (2016); Cor-\nnish et al. (2021).\nSource-parameter estimation was\nperformed with the LALInference Veitch et al. (2015)\nlibrary.\nPESummary was used to post-process and\ncollate parameter-estimation results Hoy & Raymond\n(2021).\nPlots were prepared with Matplotlib Hunter\n(2007) and GWpy Macleod et al. (2021). NumPy Har-\nris et al. (2020) and SciPy Virtanen et al. (2020) were\nused in the preparation of the manuscript.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO), for the construction and oper-\nation of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agencies\nas well as by the Council of Scientific and Industrial Re-\nsearch of India, the Department of Science and Technol-\nogy, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource De-\nvelopment, India, the Spanish Agencia Estatal de In-\nvestigaci\u00b4on (AEI), the Spanish Ministerio de Ciencia e\nInnovaci\u00b4on and Ministerio de Universidades, the Con-\nselleria de Fons Europeus, Universitat i Cultura and the\nDirecci\u00b4o General de Pol\u00b4\u0131tica Universitaria i Recerca del\nGovern de les Illes Balears, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the National Science Centre\nof Poland and the European Union \u2013 European Re-\ngional Development Fund; Foundation for Polish Science\n(FNP), the Swiss National Science Foundation (SNSF),\nthe Russian Foundation for Basic Research, the Rus-\nsian Science Foundation, the European Commission,\n\n21\nthe European Social Funds (ESF), the European Re-\ngional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the\nNational Research, Development and Innovation Office\nHungary (NKFIH), the National Research Foundation\nof Korea, the Natural Science and Engineering Research\nCouncil Canada, Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoreti-\ncal Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council\nof Hong Kong, the National Natural Science Founda-\ntion of China (NSFC), the Leverhulme Trust, the Re-\nsearch Corporation, the National Science and Technol-\nogy Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-inAid for Scientific Research on Innovative Ar-\neas 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grantin-Aid for Scientific Research (S)\n17H06133 and 20H05639 , JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cos-\nmic Ray Research, University of Tokyo, National Re-\nsearch Foundation (NRF), Computing Infrastructure\nProject of Global Science experimental Data hub Cen-\nter (GSDC) at KISTI, Korea Astronomy and Space\nScience Institute (KASI), and Ministry of Science and\nICT (MSIT) in Korea, Academia Sinica (AS), AS Grid\nCenter (ASGC) and the National Science and Technol-\nogy Council (NSTC) in Taiwan under grants includ-\ning the Rising Star Program and Science Vanguard Re-\nsearch Program, Advanced Technology Center (ATC) of\nNAOJ, and Mechanical Engineering Center of KEK.\nWe would like to thank all of the essential workers who\nput their health at risk during the COVID-19 pandemic,\nwithout whom we would not have been able to complete\nthis work.\nAPPENDIX\nA. POST-PRODUCTION VETOES\nIn this appendix, we will describe in detail the post-production vetoes that are applied by the standard cWB pipeline\n(Gayathri et al. 2019; Lopez et al. 2022) to distinguish between true gravitational-wave signals and non-Gaussian noise\nartifacts that can mimic gravitational-wave signals.\nThe first set of vetoes are based on the morphology of the reconstructed signals.\nThese vetoes are applied to\nthe following cWB summary statistics: the energy-weighted central frequency of the signal f0; M\u2217which is the\nreconstructed chirp mass parameter is obtained by fitting the signal with the characteristic time\u2013frequency evolution\nfor a quasi-circular binary (f \u221d(t \u2212tc)\u22123/8), and Qa, the waveform shape parameter introduced in Section 2.3. Qa\nis a function of the cWB parameter Qveto (Vedovato 2018; Gayathri et al. 2019; Mishra et al. 2021), which quantifies\nhow well the total energy of the signal is distributed across time. The first set of vetoes removes events that do not\nsatisfy 24 Hz < f0 < 100 Hz, |M\u2217/M\u2299| > 10, |(M\u2217/M\u2299)/Q2\na| > 15, M\u2217/M\u2299> \u2212100.\nThe next set of vetoes are based on cWB reconstruction, and the correlation of the event across the network of\ndetectors. The cWB summary statistics involved in this set are: norm, defined as the ratio between the total energy\nover all wavelet resolution levels used for the analysis and the reconstructed energy of the event; \u03c72, a parameter\nthat quantifies the quality of signal reconstruction by computing the residual noise energy that remains once the\nreconstructed signal is subtracted from data (Gayathri et al. 2019), and finally the cc[0] and cc[2] parameters that\ndescribe the correlation of the signal across the network of detectors in time domain and frequency domain, respectively\n(Tiwari et al. 2015). The second set of vetoes remove candidate events that do not satisfy norm > 4, log10(\u03c72) < 0.4,\ncc[0] > 0.8, cc[2] > 0.7.\nThe two sets of vetoes described above were optimized with gravitational waveforms for quasi-circular binary black\nhole coalescences for the standard cWB pipeline. We found that they performed optimally in recovering eBBH signals\nas well. Therefore, these vetoes along with the new eBBH veto introduced in Section 2.3 were chosen as the final set\nof vetoes for the cWB-eBBH search pipeline.\n\n22\nREFERENCES\nAasi, J., Abbott, B. P., Abbott, R., et al. 2015, Classical\nand Quantum Gravity, 32, 074001\nAbbott, B. P., Abbott, R., Abbott, T. D., et al. 2016a,\nPhRvL, 116, 061102\nAbbott, B. P., et al. 2016b, PhRvL, 116, 241102\n\u2014. 2016c, PhRvL, 116, 221101, [Erratum: PhRvL. 121,\n129902 (2018)]\n\u2014. 2016d, Class. Quant. Grav., 33, 134001\nAbbott, B. P., Abbott, R., Abbott, T. D., et al. 2017,\nApJL, 848, L12\nAbbott, B. P., et al. 2017a, Astrophys. J. 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M., Mapelli, M., Branchesi, M., & Tormen, G.\n2014, MNRAS, 441, 3703\n", "Cosmological and High Energy Physics implications from gravitational-wave\nbackground searches in LIGO-Virgo-KAGRA\u2019s O1-O4a runs\nThe LIGO Scientific Collaboration, The Virgo Collaboration, and The KAGRA Collaboration\u2217\n(Dated: November 10, 2025)\nWe search for gravitational-wave background signals produced by various early Universe processes\nin the Advanced LIGO O4a dataset, combined with the data from the earlier O1, O2, and O3 (LIGO-\nVirgo) runs. The absence of detectable signals enables powerful constraints on fundamental physics.\nWe derive gravitational-wave background energy density upper limits from the O1-O4a data to\nconstrain parameters associated with various possible processes in the early Universe: first-order\nphase transitions, cosmic strings, domain walls, stiff equation of state, axion inflation, second-order\nscalar perturbations, primordial black hole binaries, and parity violation.\nIn our analyses, the\npresence of an astrophysical background produced by compact (black hole and neutron star) binary\ncoalescences throughout the Universe is also considered. We address the implications for various\ncosmological and high energy physics models based on the obtained parameter constraints.\nWe\nconclude that LIGO-Virgo data already yield significant constraints on numerous early Universe\nscenarios.\nI.\nINTRODUCTION\nAdvanced LIGO [1], Advanced Virgo [2] and KA-\nGRA [3] have completed three observational runs. LIGO,\nVirgo and KAGRA are now in their fourth observational\nrun, O4, which began in May 2023.\nThe O4a part of\nthe run started on May 24, 2023, going until Jan. 16th,\n2024 [4]. Data acquired in these observation runs have\nresulted in a series of novel scientific pursuits. This in-\ncludes discovery of over 200 compact binary (black hole\nand neutron star) mergers [5], increasingly stringent tests\nof General Relativity [6], multi-messenger measurements\nof the Hubble constant [7], and measurements of the neu-\ntron star equation-of-state [8].\nOne of the primary targets of these observations is the\ngravitational-wave background produced by a superpo-\nsition of a large number of uncorrelated gravitational-\nwave signals [9]. Observations of stellar mass compact\nbinary mergers by Advanced LIGO and Advanced Virgo\nimply that a gravitational-wave background of astrophys-\nical origin [10\u201315] should exist and that it may be de-\ntectable by the LIGO-Virgo-KAGRA network in the near\nfuture [16\u201319]. Furthermore, a gravitational-wave back-\nground could be of cosmological origin, generated in a\nvariety of processes in early phases of the Universe. Con-\nsequently, gravitational-wave background searches can\nbe used to probe high energy physics models at energy\nscales beyond the ones reached at the Large Hadron Col-\nlider [20], and to explore early Universe cosmological sce-\nnarios [21\u201324].\nIn what follows, we present searches for a gravitational-\nwave background produced by various cosmological mod-\nels, using the LIGO O1 [25], O2, O3 [26] and O4a [27, 28]\ndata, plus Virgo O3 [29] data, and we report the re-\nsulting constraints on their parameters. Motivations for\nconsidering sources of a cosmological gravitational-wave\n\u2217Full author list given at the end of the article.\nbackground descend from open questions of fundamental\nphysics. Indeed, despite the extraordinary success of the\nStandard Model of Particle Physics and Cosmology, our\nunderstanding of basic aspects of fundamental physics is\nstill incomplete. The nature of dark matter, the origin\nof the matter/anti-matter asymmetry, the explanation of\nthe neutrino masses, and the realization of inflation re-\nmain as important open questions. In order to solve these\nissues, scenarios of physics beyond the Standard Model\nare investigated and are under scrutiny in astro-particle\nexperiments, from colliders to telescopes. Many of these\nbeyond the Standard Model scenarios also imply novel\nphenomena happening in the very early stages of the\nUniverse, potentially leaving footprints in the form of a\ngravitational-wave background. The models for which we\nconduct gravitational-wave background searches are first-\norder phase transitions, cosmic strings, domain walls,\nstiff equation of state, axion inflation, second-order scalar\nperturbations, primordial black holes, and parity viola-\ntion.\nThe first three models (first-order phase transitions,\ncosmic strings, domain walls) we consider are related to\ncosmological phase transitions, common in theories with\nspontaneously broken symmetries [30\u201332]. If the phase\ntransition is first-order, it can generate a gravitational-\nwave background [33].\nPhase transitions followed by\nspontaneously broken symmetries can lead to topologi-\ncal defects, such as cosmic strings [34, 35] and domain\nwalls [36\u201342], extended objects in the Universe that can\nproduce a gravitational-wave background.\nThe next three models (stiff equation of state, axion in-\nflation, second-order scalar perturbations) we study lead\nto a gravitational-wave background generated during in-\nflation. While single-field slow-roll inflation within the\n\u039bCDM cosmological model predicts a gravitational-wave\nbackground that is too weak to be observed with cur-\nrent detectors, other inflationary models may produce\na detectable gravitational-wave background. For an ex-\notic early Universe cosmological model with a stiff equa-\ntion of state [43\u201351], we explore the gravitational-wave\narXiv:2510.26848v2 [gr-qc] 7 Nov 2025\n\n2\nbackground generated during inflation [50\u201353]. For the\naxion inflation model, we consider a coupling between\nthe scalar field driving inflation and an SU(2) gauge\nfield, and calculate the produced gravitational-wave\nbackground [54\u201357]. For second-order scalar perturba-\ntions [58], we estimate the gravitational-wave background\ninduced by primordial curvature perturbations [59\u201363].\nNext we study a gravitational-wave background gener-\nated by mergers of primordial black holes [64] that could\nhave formed by a variety of mechanisms in the early Uni-\nverse. Finally, we study a gravitational-wave background\nthat exhibits chiral polarization. We consider a model-\nindependent parametrization of such a background, as\nwell as a particular case where parity violation originates\nfrom axion inflation [65].\nFor each of these cosmological models, the absence of\na gravitational-wave background constrains their param-\neters. The results of our analysis show that the LIGO-\nVirgo O1-O4a data can already be used to successfully\nderive new constraints on a wide range of theories beyond\nthe Standard Model.\nFormalism and methodology:\nThe gravitational-wave\nbackground is quantified in terms of its energy density\nper logarithmic frequency interval, and compared to the\ncritical energy density of the Universe. Specifically,\n\u2126GW(f) = f\n\u03c1c\nd\u03c1GW\ndf\n,\n(1)\nwhere\n\u03c1GW\nis\nthe\nenergy\ndensity\nof\ngravitational\nwaves, the critical energy density of the Universe is\n\u03c1c = 3c2H2\n0/(8\u03c0G) \u22487.7 \u00d7 10\u22129 erg cm\u22123, H0 =\n100 h km/s/Mpc is the Hubble constant with h = 0.68\nfrom the Planck measurements [66], c the speed of light,\nand G Newton\u2019s constant. The gravitational-wave back-\nground spectrum is often approximated by the power-law\n(PL) form with the spectral index \u03b1\n\u2126PL\nGW(f) = \u2126ref\n\u0012 f\nfref\n\u0013\u03b1\n,\n(2)\nwhere \u2126ref is the gravitational-wave energy density at\nthe reference frequency fref. A background produced by\ncompact binary mergers from population I or II stars\ncan be approximated as having \u03b1 = 2/3 [67]. Cosmolog-\nical backgrounds can also be typically approximated as\npower laws, or as broken power laws, as we show in the\nfollowing.\nFor the first three observing runs, the LIGO-Virgo-\nKAGRA collaboration reported an upper limit on the\nstrength of an isotropic gravitational-wave background\nof \u2126GW\n\u22645.8 \u00d7 10\u22129 for \u03b1 = 0 and 95% credi-\nble level [68] with 99% of the sensitivity coming from\nthe band (20\u201376.6) Hz.\nFor \u03b1 = 2/3, the limit was\n\u2126GW(25Hz) \u22643.4\u00d710\u22129 in the band (20\u201390.6) Hz. This\nupper bound was derived from the LIGO data acquired\nduring O1, O2, and O3 observing runs, as well as Virgo\ndata of O3.\nThere have also been searches for back-\ngrounds with non-standard polarizations, such as scalar\nand vector (in addition to tensor) [69, 70]. Anisotropic\nbackgrounds have been also explored [15, 71].\nThe O4a data, combined with the data from O1, O2\nand O3, do not provide evidence for the detection of a\ngravitational-wave background [19]. As such, an upper\nlimit of \u2126GW \u22642.8\u00d710\u22129 is set for \u03b1 = 0 and 95% confi-\ndence, with 99% of the sensitivity coming from the band\n(20 \u2013 58.2) Hz. For \u03b1 = 2/3 the limit is \u2126GW(25Hz) \u2264\n2.0 \u00d7 10\u22129 in the band (20 \u2013 86.8) Hz [19]. The LIGO-\nVirgo-KAGRA Collaboration has also searched for an\nanisotropic gravitational-wave background [71].\nTo derive constraints on the cosmological model pa-\nrameters, we perform a Bayesian analysis [72] using\nthe data from the LIGO-Virgo O1-O4a observing runs,\nfollowing the methods developed in [73].\nAssuming\nthe cross correlation estimator \u02c6CIJ(f) [68] is Gaussian-\ndistributed, we write the following likelihood function\np( \u02c6CIJ(f)|\u03b8, \u03bb)\n\u221dexp\n\uf8ee\n\uf8f0\u22121\n2\nX\nf\n[ \u02c6CIJ(f) \u2212\u03bb \u2126GW(f, \u03b8)]2\n\u03c32\nIJ(f)\n\uf8f9\n\uf8fb,\n(3)\nusing data from detectors I\nand J,\nwhile \u03c32\nIJ(f)\nis the variance.\nBoth\n\u02c6CIJ(f) and \u03c32\nIJ(f) are data\nproducts from the LIGO-Virgo-KAGRA collaboration\nisotropic gravitational-wave background search analy-\nsis [19], where they are calculated from the LIGO-Virgo\ndata. It is assumed that such an isotropic search does\nnot have correlated noise between detectors I and J,\nfor example, from correlated magnetic noise [74]. Hence\na standard Gaussian noise model is preferred [68], and\nthe potential contribution from correlated magnetic noise\n(Schumann resonances) [75] can be neglected [19]. The\nfunction \u2126GW(f, \u03b8) corresponds to the model considered,\ndescribed by the set of parameters \u03b8, while the parame-\nter \u03bb, which we marginalize over, accounts for the detec-\ntors\u2019 calibration uncertainties [19]. A minimum of two\ndetectors are needed in order to conduct this analysis.\nThe two LIGO detectors contribute the most to the cor-\nrelation due to the smallest distance separation in the\nnetwork, their optimal alignment [76, 77], and their sen-\nsitivities [68].\nIn our analyses, we take into account the contri-\nbution from an isotropic astrophysical background of\ncompact binary coalescences (CBC) \u2126CBC(f, \u03b8CBC) =\n\u2126CBC(f, \u2126ref, \u03b1), which we model by Eq. 2 where fref =\n25 Hz [68]. The cosmologically produced gravitational-\nwave background is \u2126Cosmo(f, \u03b8Cosmo).\nThe total\ngravitational-wave background is\n\u2126GW(f, \u03b8) = \u2126CBC(f, \u2126ref, \u03b1) + \u2126Cosmo(f, \u03b8Cosmo). (4)\nThis publication is organized as follows: we present\nlimits on various cosmological models in the following\nsections; first-order phase transitions in Sec. II; cosmic\nstrings in Sec. III; domain walls in Sec. IV; stiff equation\nof state in Sec. V; axion inflation in Sec. VI; second-order\n\n3\nscalar perturbations in Sec. VII; primordial black holes in\nSec. VIII; and parity violation in Sec. IX. For each of the\neight scenarios we discuss the motivation, we present the\nmodel considered, and give the constraints to the model\nparameters using O1-O4a LIGO-Virgo data. Conclusions\nare given in Sec. X.\nII.\nFIRST-ORDER PHASE TRANSITIONS\nA.\nMotivation\nCosmological phase transitions are among the most\nwell-motivated early Universe phenomena we anticipate\n(see e.g. [30\u201332]). They are a common feature of parti-\ncle physics models that exhibit symmetry breaking. The\nphase transition is first-order when the effective poten-\ntial of the theory develops a new minimum (true vac-\nuum) with a free energy density lower than that of the\nminimum at high temperature (false vacuum), and both\nare separated by a potential barrier. The Universe then\nviolently transitions from the symmetric higher energy\nfalse vacuum to the broken lower energy true vacuum.\nA first order phase transition is a powerful source of a\ngravitational-wave background.\nGiven our knowledge of the cosmological history and\nparticle physics, such transitions could have occurred\nwithin the first one-trillionth of a second after the Big\nBang, at energies higher than those accessible in present-\nday particle accelerators. Their gravitational wave im-\nprints would be an important key to determining the\ncorrect theory beyond the Standard Model realized in\nNature.\nThe Standard Model itself undergoes two phase tran-\nsitions:\nthe electroweak phase transition due to the\nbreaking of electroweak symmetry, and the confinement-\ndeconfinement phase transition due to chiral symmetry\nbreaking in quantum chromodynamics (QCD). Neither\nof these Standard Model phase transitions is first order\n(or generates stable topological defects), thus no corre-\nsponding gravitational wave signatures are expected.\nHowever, many extensions of the Standard Model with\nenlarged symmetry structures at high energies necessarily\nundergo spontaneous symmetry breaking (for sufficiently\nhigh reheating temperature).\nSuch a first order phase\ntransition corresponds to nucleation of bubbles of true\nvacuum in various points in the Universe. Those bubbles\nthen expand, collide with each other, and eventually fill\nout the entire space. During this process, gravitational\nwaves are generated from processes such as bubble colli-\nsions [78, 79], sound waves propagating in the early Uni-\nverse plasma [80, 81], and magnetohydrodynamic turbu-\nlence [82], with the first two contributions being typically\ndominant (see e.g. [33] and references therein).\nThe strong connection of the resulting primordial grav-\nitational wave background to particle physics provides\ngravitational wave astronomy with a unique opportu-\nnity to probe regions of parameter space of physics mod-\nels completely inaccessible in any other types of exper-\niments.\nThis includes various extensions of the Stan-\ndard Model, e.g., models with an extended electroweak\ngauge sector [83\u201385], theories with dark sectors [86\u201388],\naxion models [89\u201391], unification models [92, 93], super-\nsymmetric theories [94\u201396], or theories with extra dimen-\nsions [97]. In turn, the information about physics at en-\nergies beyond the electroweak scale may provide insight\ninto solutions to problems such as the nature of dark mat-\nter or the origin of the matter-antimatter asymmetry of\nthe Universe.\nAs it has recently been shown based on the LIGO-\nVirgo observing runs O1-O3, already current data can\nbe used to provide meaningful constraints on the parame-\nters of first order phase transitions [98]. This method was\nsuccessfully applied to particle physics models in the con-\ntext of supercooled transitions (see e.g. [99, 100]), lead-\ning to novel constraints on beyond-Standard Model the-\nories [101]. In the following, we utilize the LIGO-Virgo\nO1-O4a data to derive new and improved bounds on the\nparameters of early Universe first order phase transitions.\nB.\nModel\nIn this scenario the cosmological component \u2126Cosmo of\nthe gravitational wave background in Eq. (4) depends on\nthe parameters describing the phase transition, i.e. on\nthe details of the particle physics model. From an effec-\ntive theory point of view, a first order phase transition\ncan be fully described by just several parameters: vw\n\u2013 the bubble wall velocity (given in units of the speed\nof light), TPT \u2013 the temperature of the phase transition,\n\u03b1PT \u2013 the strength of the phase transition, which is equal\nto the density of the energy released divided by the en-\nergy density of radiation, \u03ba \u2013 the fraction of the energy\ncorresponding to a given source, \u03b2 \u2013 the inverse time\nduration of the transition, and g\u2217\u2013 the number of effec-\ntive degrees of freedom (equal to 106.75 in the Standard\nModel at high temperatures).\nIn our analysis we first discuss the sound wave con-\ntribution which is typically dominant in case of ther-\nmal phase transitions (where friction from the Standard\nModel plasma is relevant), and then focus on the bubble\ncollision contribution which is the leading source of grav-\nitational waves for vacuum phase transitions (where fric-\ntion is negligible). We disregard magnetohydrodynamic\nturbulence since its effects are typically subdominant and\ntheir characterization is subject of ongoing research. As\nfor the gravitational wave background spectral shape for\nthese two types of contributions, we select two repre-\nsentative forms, while acknowledging the fact that new\nresults and simulations are continuously proposed in the\nliterature (see discussion after Eq. (10)).\nSound wave contribution\nWe first address the leading source of gravitational\nwaves for a thermal first order phase transition which\n\n4\ncomes from sound waves in the primordial plasma, and\nis caused by the coupling between the scalar field under-\ngoing the phase transition and the thermal bath [80, 81,\n102]. A fruitful description of the physics of this process\nis provided by the sound shell model [103\u2013105], although\nits accuracy has been challenged [102, 106]. The result\nof numerical simulations yields [81, 107]\nh2\u2126SW(f) \u2248(1.86 \u00d7 10\u22125) vw\n\u0012HPT\n\u03b2\n\u0013\u0012\u03b1PT \u03basw\n\u03b1PT + 1\n\u00132\u0012100\ng\u2217\n\u00131\n3\n\u00d7\n(f/fsw)3\n\u0002\n1 + 0.75 (f/fsw)2\u0003 7\n2 \u03a5 ,\n(5)\nwhere the peak frequency fSW is\nfSW = (1.9\u00d710\u22125 Hz)\nvw\n\u0012\n\u03b2\nHPT\n\u0013 \u0012\nTPT\n100 GeV\n\u0013 \u0010 g\u2217\n100\n\u0011 1\n6, (6)\nHPT is the Hubble constant at the phase transition, \u03basw\nis the fraction of the latent heat transformed into the\nbulk motion of the plasma [108]\n\u03baSW =\n\u03b1PT\n0.73 + 0.083\u221a\u03b1PT + \u03b1PT\n,\n(7)\nand the suppression factor \u03a5 due to the finite lifetime of\nsound waves is [105, 109]\n\u03a5 = 1 \u2212\n1\n\u0010\n1 + 8\u03c01/3vw\n\u0000 HPT\n\u03b2\n\u0001\u0000\u03b1PT+1\n3\u03b1PT\u03baSW\n\u00011/2\u00111/2 , (8)\nderived assuming a lifetime on the order of the timescale\nfor the onset of turbulence.\nBubble collision contribution\nIn some cases, e.g., when the first order phase transi-\ntion occurs in the vacuum of a dark sector without sizable\ninteractions with the Standard Model, the sound wave\ncontribution is suppressed and the bubble collision part\nbecomes dominant. The corresponding spectrum is ob-\ntained within the envelope approximation by assuming a\nzero width for the bubble wall and neglecting contribu-\ntions from overlapping bubble segments [79, 110, 111]. It\nis given by [107, 112], using numerical simulations,\nh2\u2126BC(f) \u2248(1.66 \u00d7 10\u22125) v3\nw\n1 + 2.4v2w\n\u0012HPT\n\u03b2\n\u00132 \u0012\u03b1PT \u03baBC\n\u03b1PT + 1\n\u00132\n\u00d7\n\u0012100\ng\u2217\n\u00131\n3\n(f/fBC)2.8\n1 + 2.8(f/fBC)3.8 ,\n(9)\nwhere the peak frequency fBC is\nfBC =\n(10\u22125 Hz)\n1.8 \u22120.1vw + v2w\n\u0012 \u03b2\nHPT\n\u0013 \u0012\nTPT\n100 GeV\n\u0013 \u0010 g\u2217\n100\n\u0011 1\n6,\n(10)\nand \u03baBC is the fraction of the latent heat deposited into\nthe bubble front [82].\nWe will take \u03baBC = 1 for con-\ncreteness.\nThe shape of the spectrum at low frequen-\ncies \u223cf 2.8, close to the expected \u223cf 3 from causality,\n6\n8\nlog10[TPT/GeV]\n\u22122\n\u22121\n0\n1\n2\nlog10 \u03b1PT\n95%\n68%\n0.0\n0.5\n1.0\n1.5\n2.0\nlog10 \u03b2/HPT\n95%\n68%\n68%\n\u221212 \u221210 \u22128 \u22126\nlog10 \u2126ref\n6\n8\n10\nlog10[TPT/GeV]\n95%\n68%\n68%\n\u22122 \u22121\n0\n1\n2\nlog10 \u03b1PT\n68%\n68%\n0.0 0.5 1.0 1.5 2.0\nlog10 \u03b2/HPT\n68%\nFIG. 1. Constraints from the LIGO-Virgo observing runs O1-\nO4a data on the first order phase transition parameters \u03b1PT,\n\u03b2/HPT, and TPT, assuming a dominant sound wave contri-\nbution and taking into account the CBC background. The\npriors selected are shown in Table I. The 95% and 68% con-\nfidence level exclusion contours are shown in blue and red,\nrespectively. Clearly, less conservative choices of priors could\nlead to stronger constraints. The green lines correspond to\n\u03b2/HPT = (8\u03c0)1/3.\nwhereas at high frequencies \u223c1/f from the dominant\nsingle bubble contribution [112].\nWhile we will use Eq. (9) in our analysis, we note that\nthe precise shape of the gravitational-wave spectrum for\nbubble collisions is not fully settled.\nIt was reported\nin [113] that simulations beyond the envelope approxi-\nmation yield at high frequencies \u223c1/f1.5.\nIn [114] a\ndependence on wall thickness was found to change the\nhigh-frequency spectrum from \u223c1/f 1.4 to \u223c1/f 2.3 with\nincreasing thickness. Further variations of the spectrum\nwere discussed in [115\u2013118]. In the next section we will\ncomment on how our results change by considering vary-\ning power law indices.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nHere we determine the 95% confidence level (CL) up-\nper limits on the strength of the gravitational-wave signal\nfrom sound waves \u2126sw and bubble collisions \u2126bc, arising\nfrom the LIGO-Virgo observing runs O1-O4a data. The\nprevious analyses of this type in [98, 101] were based\nonly on the O1-O3 data set. To this end, we perform a\nBayesian analysis for the two cases (using pygwb [119])\nassuming the priors on the parameters of the model and\nthe CBC background specified in Table I. For the CBC\nbackground, we fix the power law index to \u03b1 = 2/3 and\nwe vary the amplitude \u2126ref.\nOur analysis yields the Bayes factor ln BCBC+SW\nnoise\n=\n\u22120.647 in the sound wave case, and ln BCBC+BC\nnoise\n=\n\n5\nParameter\nPrior\n\u03b1PT\nLogUniform[10\u22122, 102]\n\u03b2/HPT\nLogUniform[1, 102]\nTPT/GeV\nLogUniform[105, 1010]\n\u2126ref\nLogUniform[10\u221213, 10\u22126]\nvw\nfixed at 1\nTABLE I. Prior distributions assumed for the parameters\nof the model and the CBC background.\nFor \u03b1PT \u226a1\nthe gravitational-wave signal would be suppressed, while for\n\u03b1PT \u226b1 the signal shape becomes independent from \u03b1PT.\nThe parameter \u03b2/HPT cannot be less than 1 for consistency\n(see explanation in the text), while larger values suppress the\ngravitational-wave signal beyond detectability. The parame-\nter TPT is chosen such that the broken power law spectrum\npeak is at frequencies close to the ones accessible with LIGO-\nVirgo-KAGRA.\n6\n8\nlog10[TPT/GeV]\n\u22122\n\u22121\n0\n1\n2\nlog10 \u03b1PT\n95%\n68%\n0.0\n0.5\n1.0\n1.5\n2.0\nlog10 \u03b2/HPT\n95%\n68%\n95%\n68%\n\u221212 \u221210 \u22128 \u22126\nlog10 \u2126ref\n6\n8\n10\nlog10[TPT/GeV]\n5%\n68%\n68%\n\u22122 \u22121\n0\n1\n2\nlog10 \u03b1PT\n95%\n68%\n68%\n0.0 0.5 1.0 1.5 2.0\nlog10 \u03b2/HPT\n68%\nFIG. 2.\nSimilarly as in Fig. 1, the constraints from the\nLIGO-Virgo observing runs O1-O4a data on the first order\nphase transition parameters including the CBC background,\nbut for a dominant bubble collision contribution.\n\u22120.679 for bubble collisions, indicating no evidence for\na combined first order phase transition plus CBC back-\nground in the data.\nFig. 1 shows the posterior distributions for the com-\nbined CBC and first order phase transition search in the\ncase of a dominant sound wave contribution. The 95%\nand 68% CL exclusion contours are highlighted. In the\nposterior distributions, we also show with a gray dashed\nline the LogUniform priors.\nSimilarly, Fig. 2 presents the constraints from the com-\nbined CBC and first order phase transition search for a\ndominant bubble collision contribution. As Fig. 2 demon-\nstrates, with the priors listed in Table I, the data excludes\nat 95% CL part of the parameter space of the bubble col-\nlision dominated phase transitions, especially the region\nof TPT \u2273108 GeV and \u03b2/HPT \u22723. We conclude that\nparticle physics models predicting first order phase tran-\nsitions are testable with the LIGO-Virgo-KAGRA data.\nIt is important to remark that small values of \u03b2 are at\nthe edge of the consistency with the description of the\nphase transition. Note that the bubble size is related to\nthe \u03b2 parameter as R\u22123\n\u2217\n\u223c(1/8\u03c0)(\u03b2/vw)3 [120], so we in-\ndicated with a green dashed line in Figs 1 and 2 the limit\nin which the size of the bubbles becomes comparable to\nthe Hubble volume (see e.g. [121\u2013123] for recent studies\non this regime).\nOur\nstudy\nis\nrestricted\nto\nthe\ntwo\ntypes\nof\ngravitational-wave spectra described in the previous sub-\nsection. Given the continuous developments in the pre-\ndiction of the power law of the gravitational-wave back-\nground (particularly for bubble collisions) we have also\nrepeated our analysis but with varying power law index,\nin the range indicated at the end of the previous section.\nThe marginalization makes the constraining power of the\ndata weaker and results in even weaker constraints on the\nparameters of the phase transition.\nNote that our analysis sets a 95% CL upper limit on\nthe amplitude of the CBC background, \u2126ref, of 2.0\u00d710\u22129\nand 2.3 \u00d7 10\u22129 for the sound wave and bubble collision\ncases, respectively. These values are compatible with the\nones reported in [19].\nIII.\nCOSMIC STRINGS\nA.\nMotivation\nCosmic strings are topological defects in the Uni-\nverse, that can be generated from spontaneous symmetry\nbreaking of a global or gauge symmetry which has non-\ntrivial winding of the vacuum manifold during cosmolog-\nical phase transitions [34] via the Kibble-Zurek mecha-\nnism [35, 124\u2013126]. The width of the cosmic strings is\ninversely proportional to the energy scale of the sym-\nmetry breaking, and is thus generally tiny, making these\nstrings line-like. Formed mainly as super-horizon objects,\nthese long strings intercommute and intersect to form a\nnetwork of string loops. String loops oscillate due to their\ntension and shrink due to the emission of gravitational\nwaves, Nambu-Goldstone bosons, or gauge bosons, de-\npending on which coupling of the radiated particle to the\nstring world-sheet is dominant.\nOne of the simplest string models is the axion string\nmodel, resulting from a spontaneous symmetry breaking\nof U(1) global symmetry. The QCD axion string, as a\nglobal string, is one of the well-motivated axion string\nmodels since QCD axions [127\u2013135] could contribute to\nthe dark matter relic abundance. Axion strings predom-\ninantly radiate Nambu-Goldstone bosons (axions), and\nthus gravitational waves radiated by axion strings are\nsubdominant. A recent study [136] embeds the QCD ax-\nion string into the gauged global string model resulting\nfrom two subsequent spontaneous symmetry breakings of\n\n6\nglobal U(1) and gauge U(1) symmetries. The model con-\ntains both global strings and gauge strings, and the gauge\nstring as a bound state of two types of global strings can\neither radiate gravitational waves or axions depending on\nwhether the gauge coupling is significantly smaller than\nthe gravitational coupling. Thus, it enriches the radia-\ntion channels from gauge strings. Without further as-\nsumption on the string model, in what follows, we only\nconsider gauge strings for which gravitational-waves is\nthe dominant radiation channel.\nThe evolution of the string loops in an expanding Uni-\nverse eventually results in a scaling distribution, with\nloop sizes proportional to the cosmic time or the Hub-\nble radius. At high frequencies, the gravitational-wave\nproduction is dominated by cusps, kinks, and kink-kink\ncollisions. The dimensionless decay constant that char-\nacterizes the radiation power of gravitational waves from\ncusps, kinks, and kink-kink collisions can be estimated\nby\n\u0393d \u2261PGW\nG\u00b52 =\nX\ni\nPGW,i\nG\u00b52\n,\n(11)\nwhere G\u00b5 is the string tension, and i = {c, k, kk} de-\nnotes cusp, kink, and kink-kink collision cases.\nInco-\nherent superpositions of these gravitational waves lead\nto a gravitational-wave background, the detection of\nwhich can be used to infer the energy scale of the sym-\nmetry breaking, and is thus an important target for\ngravitational-wave detectors.\nThis target has been previously searched for with\nLIGO\u2019s O1 [137] and O2 [138] data, and more recently\nwith LIGO and Virgo\u2019s O3 data combined with previ-\nous O1 and O2 data [139].\nIt has also been searched\nfor by pulsar timing array experiments [140\u2013142], and\nremains an important source of gravitational-wave back-\nground for future space-based gravitational-wave detec-\ntors [143\u2013145], and atomic interferometers [146].\nB.\nModel\nThe gravitational-wave spectrum is\n\u2126CS(f) = 4\u03c02\n3H2\n0\nf 3 X\ni\nZ\ndz\nZ\ndlh2\ni\nd2Ri\ndzdl ,\n(12)\nwhere the index i runs over cusps, kinks and kink-\nkink collisions, l denotes the invariant loop length, z\nstands for the redshift, and hi = Ai(l, z)f \u2212qi, with\nAi = g1,iG\u00b5l2\u2212qi/[(1+z)qi\u22121r(z)], r(z) the comoving dis-\ntance of the loop, q = 4/3, 5/3, 2 respectively for cusps,\nkinks, and kink-kink collisions, and g1,i \u22480.85, 0.29, 0.10\ncorrespondingly. For each type i, the burst rate per red-\nshift and loop size is\nd2Ri\ndzdl =\n\u03c6V (z)\nH3\n0(1 + z)\n2Ni\nl n(l, t)\u2206i ,\n(13)\nwhere \u2206i = (\u03b8m/2)3(2\u2212qi), with \u03b8m \u2261[g2f(1 + z)l]\u22121/3\nand g2 =\n\u221a\n3/4, denotes the fraction of burst events that\ncan be detected, n(l, t) is the loop distribution function\n(the number of loops of size l at time t per loop size\nper volume), Ni is the number of burst events per loop\noscillation time, and \u03c6V (z) = H3\n0dV (z)/dz, with V (z)\nthe proper volume at redshift z.\nThe spectrum above includes only the contribution\nfrom sub-horizon string loops, though long strings can\nalso emit gravitational waves. As long strings intercom-\nmute, they are building a small-scale structure, resulting\nin the emission of radiation [147, 148]. This additional\ncontribution is generally sub-dominant as compared with\nthat from string loops, hence usually neglected.\nAs in O3 studies [139], we consider three typical mod-\nels of the string loop population n(\u03b3, z) in a scaling\nregime within a Friedmann-Lema\u02c6\u0131tre-Robertson-Walker\nmetric, where \u03b3 = \u2113/t is the dimensionless loop size,\nand derive constraints on each of them. Model A [149]\nand B [150] (called Model 2 and 3 respectively in O1\nstudy) are based on results from numerical simulations of\nNambu-Goto string networks (zero thickness strings with\nintercommutation probability equal to unity), wherein\nthe former infers the loop production function and the\nlatter obtains directly the loop distribution.\nThe an-\nalytical modeling [151] of Model B considers also the\neffect of gravitational-wave back-reaction on the loops.\nModel B leads to a higher number of small loops than\nmodel A, leading to important consequences in the rate\nof gravitational-wave events we can detect and on the\namplitude of the gravitational-wave background. Model\nC [152] is constructed to incorporate features of both\nmodel A and B. It assumes that the scaling loop distri-\nbution is a power-law, but leaves its slope unspecified.\nAs in O3 study, we consider two different examples of\nmodel C by choosing parameters to reproduce A and B\nin radiation and matter eras. Model C-1 (respectively C-\n2) reproduces qualitatively the loop production function\nof model A (respectively B) in the radiation-dominated\nera and the loop production of model B (respectively A)\nin the matter-dominated era.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nFollowing the O3 study [139], we carry out a Bayesian\nanalysis with the same posterior as previously\np(G\u00b5|Nk) \u221dL( \u02c6CIJ\na |G\u00b5, Nk)p(G\u00b5|I, Nk) ,\n(14)\nwhere L( \u02c6CIJ\na |G\u00b5, Nk) is the likelihood\nln L = \u22121\n2\nX\nIJ,a\n[ \u02c6CIJ\na\n\u2212\u2126CS(fa; G\u00b5, Nk)]2\n\u03c32\nIJ(fa)\n,\n(15)\n\u02c6CIJ\na\n\u2261\n\u02c6CIJ(fa) and \u03c3IJ are, respectively, the cross-\ncorrelation estimator and the variance for the detec-\ntor pair IJ, running over LIGO-Livingston & LIGO-\nHanford, LIGO-Hanford & Virgo and LIGO-Livingston\n\n7\nFIG. 3. Exclusion regions at the 95% CL on the cosmic string\nparamter space (G\u00b5, Nk).\n& Virgo [19].\nThe data used encompasses those used\nin O3 analysis, i.e., from O1, O2, and O3 runs, and in\naddition the data of LIGO-Livingston & LIGO-Hanford\nfrom the O4a period, while Virgo was not running dur-\ning this period. In addition, p(G\u00b5|I) is the prior on G\u00b5,\nand we impose a log-uniform prior for G\u00b5 in the range\n10\u221218 \u2264G\u00b5 \u226410\u22126, and do the analysis for each value\nof Nk, while fixing Nc = 1.\nSince there is no detection, we show in Fig. 3 the exclu-\nsion region at the 95% CL on the parameters G\u00b5 versus\nNk for the four loop distribution models, with O1, O2,\nO3 and O4a data.\nCompared with previous results, the limits generally\nbecome stringent. For model A, the region G\u00b5 \u2273(4.5 \u00d7\n10\u22129 \u223c5.1 \u00d7 10\u22127) is excluded for 1 \u2264Nk \u2264200, with\nthe strongest constraint achieved at Nk = 1. This result\nimproves over that of O1-O3 for a wide range of Nk.\nIt becomes worse only for unrealistically high values of\nNk \u2265120. More precisely, for Nk < 120, the constraint\non G\u00b5 is better at most by a factor of about 0.47 while\nfor Nk \u2265120 it is worse by at most 1.6.\nFor model B, the region G\u00b5 \u2273(2.7 \u223c4.2) \u00d7 10\u221215 is\nexcluded and this improves over that of O3 by a factor\nof 0.66 over the range of Nk considered here. For model\nC-1, the region G\u00b5 \u2273(1.5\u22123.2)\u00d710\u221215 is excluded, and\nthis improves on the previous result in all the range of Nk\nby a factor of (0.33 \u223c0.79). Due to the features of the\nspectrum for this model, there is a region that cannot be\nexcluded for higher values of G\u00b5. However, this region\nshrinks after the O4a data are included. For model C-2,\nthe region G\u00b5 \u2273(3.4 \u223c5.5) \u00d7 10\u221215 is excluded, which\nimproves by a factor of 0.77 compared to O3.\nIt should be noted that the results presented here treat\neach choice of Nk as a separate model (with Nc = 1) in\nthe Bayesian analysis.\nIncreasing Nc has a similar ef-\nfect as increasing Nk, as both lead to enhanced power of\ngravitational-wave emission, while the resulting changes\nto the constraints are different for the three models, with\nmodel A weakened, and model B and C less sensitive.\nIdeally, a joint distribution of Nk together with Nc should\nbe used and a marginalization over these two parameters\nshould be performed to obtain the constraint on G\u00b5. Due\nto a lack of simulations to get this information, we have\nadopted this approach. It should also be noted that the\nchoice \u0393d = 50 is commonly used, according to simula-\ntion results. Enforcing this power emission corresponds\nto setting (Nc, Nk) \u2248(1, 9) or (0, 18). The constraints for\n(Nc = 0, Nk = 18) are slightly more stringent for most\nmodels except for C-1. This is due to the smaller value\nof \u0393d, despite the absence of gravitational-wave emission\nfrom cusps. More specifically, the excluded regions are\nG\u00b5 \u22739.2\u00d710\u22129 for model A, G\u00b5 \u22733.0\u00d710\u221215 for model\nB, G\u00b5 \u22732.6\u00d710\u221215 for model C1, and G\u00b5 \u22733.5\u00d710\u221215\nfor model C2.\nIn this analysis, the average number of cusps per oscil-\nlation on a loop has been set to 1. As it has been already\nshown in the O3 analysis [139], a high number of cusps\ngives qualitatively the same result as increasing the num-\n\n8\nber of kinks. More precisely, numerical simulations have\nshown that the constraints are weakened for model A,\nwhereas the bounds are insensitive to Nc for models B\nand C.\nWe include in Fig. 3 the corresponding constraints from\npulsar timing arrays (PTA), Cosmic Microwave Back-\nground (CMB), and Big Bang Nucleosynthesis (BBN)\nobtained from the O3 analysis [139].\nNote that these\nlimits are obtained considering the nanohertz limit of the\nprimordial background obtained from the Parkes Pulsar\nTiming Array [22] \u2126CS < 2.3\u00d710\u221210 at a single frequency\nof 2.8\u00d710\u22129 Hz, which is comparable to the latest results\nof NANOGrav, EPTA and ParkesParkes [140\u2013142].\nWe briefly comment on the contribution from long\nstrings [147, 153]. While generally subdominant for the\ncase of Nambu-Goto strings [35, 143, 154, 155], they can\nprovide the main contribution for Abelian-Higgs strings\nwherein simulations suggest the absence of stable string\nloops [156\u2013159]. Moreover, recent works [160\u2013162] sug-\ngest enhanced gravitational-wave production from long\nstrings using a semi-analytic approach and a model-\ning of the kink structure with sharpness [163].\nThis\nmakes the long string scenario potentially detectable by\nthe LIGO-Virgo-KAGRA network. Adopting the spec-\ntrum from [162], we find that the excluded region is\nG\u00b5 \u22732.06 \u00d7 10\u22127, comparable to the results obtained\nfrom the loop distribution of model A.\nIV.\nDOMAIN WALLS\nA.\nMotivation\nIn a cosmological context, domain walls (DWs) are\ntwo\u2013dimensional defects that arise when a discrete sym-\nmetry is spontaneously broken during the thermal his-\ntory of the Universe [35, 36]. Around the temperature of\nthis symmetry\u2013breaking phase transition, uncorrelated\npatches in space will select one among the possible dis-\nconnected degenerate vacua of the theory. DWs are then\nformed at the boundaries of those regions where the\nscalar field interpolates between different vacua. These\nfield configurations are topologically stable owing to the\nunderlying discrete symmetry. At the center of the DW,\nthe field is trapped at the maximum of the scalar poten-\ntial leading to a high energy density localized within the\nwall width. This results in a large DW tension, which\nis effectively the wall mass per unit surface. The rela-\ntivistic motion of the DWs, driven by their own tension\nforce or by vacuum pressure, acts as a powerful source of\ngravitational waves that can be detected today.\nSimilarly to other topological defects such as cosmic\nstrings, DWs in the early Universe are known to reach a\nscaling regime with a constant O(1) number of walls per\nHubble volume [37\u201342]. Differently from the strings, this\nimplies that the relative importance of the DW network\nin the energy budget of the Universe grows with time, po-\ntentially leading to a phase of DW domination. As this is\ninconsistent with the standard evolution of the Universe,\nDWs have been often regarded as a cosmological prob-\nlem. Crucially, however, a DW network is not expected to\nbe absolutely stable, as the underlying discrete symmetry\nneeds not to be exact but only approximate. In this case,\nDWs can annihilate before dominating the expansion of\nthe Universe, leading to a strong gravitational-wave sig-\nnal and no contradiction with standard cosmology.\nNew physics scenarios involving the formation of DWs\nare characterized by the presence of (approximate) dis-\ncrete symmetries that are spontaneously broken in the\nearly Universe. Relevant examples include the QCD ax-\nion [127\u2013132, 164] and more generally axion\u2013like par-\nticles, where a residual ZN subgroup of the original\nU(1) Peccei\u2013Quinn symmetry (we generally refer to U(1)\nPeccei-Quinn also for the case of axion\u2013like particles that\nare not related to the strong CP problem) is left un-\ntouched by its chiral anomaly. This particular class of\nmodels implies the formation of cosmic strings at tem-\nperatures of the order of the axion decay constant, fa,\nwhen the Peccei-Quinn symmetry is spontaneously bro-\nken and the axion is effectively massless. If this occurs\nafter cosmic inflation, the strings and the corresponding\ninhomogeneous axion field will play an important role\nin the subsequent evolution of the system. In fact, as\nthe axion mass increases while the Universe cools down,\na network of axion DWs will ultimately form with each\nstring attached to N walls of tension \u03c3DW \u223cmaf 2\na, where\nma is the axion mass [165, 166]. The temperature of DW\nformation in this case can be estimated as the moment\nwhen the axion\u2013like particle mass overcomes the Hubble\nfriction, ma \u223cH.\nThe following dynamics depends on the value of N,\nwhich is referred to as the DW number.\nFor N = 1\nthe string\u2013wall network collapses very quickly after DW\nformation, as the theory actually possesses a unique vac-\nuum. On the other hand, for N > 1 axion DWs are topo-\nlogically stable and can be long\u2013lived depending on the\nquality of the underlying Peccei-Quinn symmetry. This\nlatter scenario is the one relevant for a gravitational-wave\nsignal from DWs, as the string\u2013wall dynamics is mostly\ncontrolled by the walls in this case.\nMinimal QCD axion models predict the formation of\nDWs at temperatures around the QCD scale, \u039bQCD \u223c\n150 MeV, so that the corresponding gravitational waves\nwould not overlap with the LIGO-Virgo-KAGRA obser-\nvation band.\nEarlier formation of DWs leading to a\ndetectable gravitational-wave signal is, however, possi-\nble for the so\u2013called heavy QCD-axion models [167\u2013169],\nwhich still solve the strong CP problem and ameliorate\nthe issue with the quality of the U(1) Peccei-Quinn sym-\nmetry [170\u2013175], or for general axion\u2013like particles de-\npending on the relevant scales [176].\nBeyond the case of axions and axion\u2013like particles,\nmany other scenarios of new physics involve new dis-\ncrete symmetries that can ultimately lead to the for-\nmation of a DW network.\nWell\u2013motivated models in-\nclude discrete flavor symmetries [177], left\u2013right symmet-\n\n9\nric models [178], supersymmetry [179\u2013183], grand unifica-\ntion [184\u2013186], and discrete spacetime symmetries [187].\nB.\nModel\nThe dynamics of the DW network is controlled on one\nhand by the tension force, which tends to stretch the\nwalls and reduce their surface to minimize the energy,\nand on the other hand by the Hubble expansion as well\nas the interaction of the walls with the primordial plasma.\nWhen particle friction can be neglected, DWs are known\nto approach a scaling regime in which the typical scale of\nthe network, such as the average curvature and distance\nbetween the walls, is given by the Hubble radius, H\u22121,\nindicating the presence of O(1) DWs per Hubble volume\nat any time [37\u201342]. In this regime, the energy density of\nthe network is given by\n\u03c1DW = 2A\u03c3DWH ,\n(16)\nwhere A = O(1) and \u03c3DW is the DW tension or mass\nper unit surface. Eq. (16) indicates that the energy den-\nsity of the network decreases more slowly than matter or\nradiation, eventually leading to a DW\u2013dominated epoch\nthat is inconsistent with cosmological observations [36].\nThe temperature at which this would occur can be\nestimated by equating the energy density of the DWs to\nthe critical density of the Universe, \u03c1c = 3H2c2/(8\u03c0G),\nyielding\nTdom =\n\u0012 80 G\n\u03c0c4g\u2217\n\u00131/4 \u221a\u03c3DW ,\n(17)\nwhere we have assumed radiation domination with g\u2217\nbeing the number of relativistic degrees of freedom.\nCrucially, DW domination can be avoided if the un-\nderlying discrete symmetry is only approximate and the\ndifferent vacua of the theory are actually biased by a\nsmall energy difference, \u2206V , such that there exists only\na unique true vacuum state [166, 188]. The microscopic\norigin of this bias will depend on the specific particle\nphysics under consideration. However, according to the\nno global symmetry conjecture in quantum gravity [189\u2013\n192], one expects the DW discrete symmetry to be ulti-\nmately broken at the Planck scale or earlier. In the case\nof axions and axion\u2013like particles, the bias term can then\ndescend from Planck\u2013suppressed higher\u2013dimensional op-\nerators that break the U(1) Peccei-Quinn symmetry as\nwell as its ZN subgroup relevant for DW formation.\nThe vacuum pressure resulting from the potential bias\n\u2206V competes with the tension force trying to annihilate\nthe DW network. The temperature at which the collapse\ninitiates, Tann, can be estimated by equating the bias to\nthe tension force or equivalently the DW energy density\nin the scaling regime, namely \u2206V \u223c\u03c1DW, leading to\nTann \u223c108 GeV\n \n1011 GeV\n\u03c31/3\nDW\n! 3\n2 \u0012 \u2206V 1/4\n108 GeV\n\u00132 \u0012100\ng\u2217\n\u0013 1\n4\n.\n(18)\nFor consistency, the annihilation temperature needs to be\nsmaller than the temperature at which DWs form, which\nis at most as large as the DW tension \u03c31/3\nDW and paramet-\nrically suppressed for axion DWs. In the following we\nwill hence restrict ourselves to Tann \u2272\u03c31/3\nDW.\nDuring the lifetime of the DW network, gravitational\nwaves are copiously produced by the relativistic motion\nof the walls [193\u2013196]. As the energy density of the net-\nwork actually increases with time compared to the criti-\ncal density according to Eq. (16), the gravitational-wave\nemission is the strongest around the final time of DW\nannihilation. While the dynamics of the DW collapse it-\nself can contribute to the emission of gravitational waves\n[197, 198], we will here consider only the gravitational-\nwave spectrum coming from the last period of scaling just\nbefore the collapse begins, namely at T = Tann. From nu-\nmerical simulations [196], the energy density spectrum is\nfound to be a broken power-law\n\u2126DW(f) = \u2126peak\nDW \u00d7\n(\n(f/fpeak)3\nf < fpeak\n(f/fpeak)\u22121\nf > fpeak\n, (19)\nwhere the peak amplitude associated to gravitational-\nwave emission at Tann and red-shifted until today is given\nby\n\u2126peak\nDW = 4.9 \u00d7 10\u22126 \u0010 g\u2217\n100\n\u0011 \u0010 g\u2217s\n100\n\u0011\u22124\n3 \u0012Tdom\nTann\n\u00134\n,\n(20)\nwith g\u2217s the effective number of entropy degrees of free-\ndom, and the red-shifted peak frequency is\nfpeak = 17 Hz\n\u0010 g\u2217\n100\n\u0011 1\n2 \u0010 g\u2217s\n100\n\u0011\u22121\n3 \u0012\nTann\n108 GeV\n\u0013\n.\n(21)\nIn Fig. 4, we show a benchmark spectrum to highlight\nthe effect of varying the DW tension, as well as the an-\nnihilation temperature.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nWe perform a Bayesian analysis following the approach\ndescribed in Section I, and using the pygwb package\n[119]. For the gravitational-wave spectrum, we consider\nthe contribution from a DW network, given by Eq.(19),\nin combination with the astrophysical gravitational-wave\nbackground from unresolved CBCs (defined as in Eq.(2)\nwith \u03b1 = 2/3 and fref = 25 Hz)\n\u2126GW(f|\u03b8) = \u2126DW(f) + \u2126CBC(f) .\n(22)\nThe parameters of interest are \u03b8 = (\u2126ref, \u03c3DW, Tann),\nwith \u2126ref the CBC background amplitude, and Tann\nand \u03c31/3\nDW the parameters determining the cosmological\ngravitational-wave signal from DWs. The prior distribu-\ntions for these parameters are summarized in Table II.\nThe resulting posterior distributions are shown in\nFig. 5, which displays contour regions corresponding to\n\n10\n0.1\n1\n10\n100\n1000\n10-11\n10-10\n10-9\n10-8\n10-7\nO4a\nA+\nO3\nFIG. 4.\nThe gravitational-wave spectrum of DW networks\nfor a benchmark for the wall tension \u03c3DW and annihilation\ntemperature Tann. The schematic in the top left box illus-\ntrates the impact of these parameters on the spectra: increas-\ning the wall tension \u03c3DW enhances the peak amplitude, while\na higher annihilation temperature Tann reduces the amplitude\nand shifts the spectrum to higher frequencies. In addition, the\nassumed shape for the overlapping astrophysical gravitational\nwave background is displayed in green, for a representative\nvalue of \u2126ref (and with \u03b1 = 2/3). Finally, sensitivity curves\nfor LIGO-Virgo O3 run [68], as well as the ones of the O4a\nrun [19] and LIGO A+ detector [199] are included.\nParameter\nPrior\n\u2126ref\nLogUniform[10\u221213, 10\u22126]\n\u03c31/3\nDW/GeV\nLogUniform[1010, 1013]\nTann/GeV\nLogUniform[106, 1010]\nTABLE II. Prior distributions assumed for the parameters of\nthe DW model and the CBC background. The prior on \u2126ref\ncomes from estimates of the CBC background [17], whereas\nthe range for the priors on the tension \u03c3DW and the annihi-\nlation temperature Tann are chosen large enough to include\nregion of parameter space that would lead to gravitational-\nwave signals within the LIGO-Virgo-KAGRA observational\nband. Values for Tann larger than \u03c31/3\nDW are not considered, as\npreviously discussed around Eq.(18).\n1 to 2\u03c3 CLs. From the posterior of the CBC background\namplitude \u2126ref, we set an upper limit at the 95% CL,\nwith a value 2.42 \u00d7 10\u22129.\nFor the parameters controlling the DW signal, the re-\ngion excluded by the gravitational-wave data is visual-\nized in white in the bottom-middle panel. In the same\npanel, we have shaded in gray the values of Tann and\n\u03c3DW for which the DW system would have dominated\nthe Universe, leading to inconsistent cosmology. The ex-\ncluded white region is close to DW domination, as the\ngravitational-wave signal is strongest when Tann \u223cTdom.\nOur analysis can rule out annihilation temperatures in\nthe range 107GeV < Tann < 109GeV for sufficiently large\nDW tension.\n10\n11\n12\n13\n6\n8\n10\nLog10(Tann/GeV)\n\u221213\u221212\u221211\u221210\u22129 \u22128 \u22127 \u22126 \u22125\n10.0\n10.5\n11.0\n11.5\n12.0\n12.5\n13.0\nLog10(\u03c31/3\nDW/GeV)\n95\n68\n\u221213\u221212\u221211\u221210\u22129 \u22128 \u22127 \u22126 \u22125\nLog10 \u2126ref\n6.0\n6.5\n7.0\n7.5\n8.0\n8.5\n9.0\n9.5\n10.0\nLog10(Tann/GeV)\n95\n95\n68\n10.0 10.5 11.0 11.5 12.0 12.5 13.0\nLog10(\u03c31/3\nDW/GeV)\n6.0\n6.5\n7.0\n7.5\n8.0\n8.5\n9.0\n9.5\n10.0\n95\n68\n68\n68\nDomain Wall Domination\nFIG. 5. Posteriors for the strength of the CBC background\namplitude \u2126ref, the tension \u03c3DW of the DW network and\nthe temperature Tann at which the network annihilates us-\ning LIGO-Virgo data from O1, O2, O3 and O4a. The gray\nregion in the bottom corresponds to a region where the DW\nnetwork dominates the Universe, i.e. Tann \u2264Tdom.\nConsidering\nthe\nhypothesis\nof\na\ncombined\ngravitational-wave\nbackground\nsignal\nfrom\na\nDW\nnetwork and CBCs versus noise, the analysis yields a\nBayes factor of ln BDW+CBC\nnoise\n= \u22121.15, indicating no\nevidence for such a background in the data. Similarly,\nfor a CBC-only background, we find ln BCBC\nnoise = \u22120.52,\nimplying a preference for the CBC-only scenario with\nln BDW+CBC\nCBC\n= \u22120.63.\nIn conclusion, we find no evidence for a gravitational-\nwave signal from a DW network. The constraints on \u03c3DW\nand Tann derived from gravitational-wave data exclude\nspecific regions of parameter space, which can be used in\nthe context of particle physics models.\nV.\nSTIFF EQUATION OF STATE\nA.\nMotivation\nStandard inflationary models in the slow roll regime\ntypically give rise to a gravitational-wave background\nthat is too weak to be detected by the current and fu-\nture gravitational-wave experiments.\nIndeed, the cur-\nrent constraints on the scale of inflation and on the\ntensor-to-scalar ratio implies that the typical primordial\ngravitational-wave flat spectrum lies below the sensitiv-\nity of current and future gravitational-wave experiments\nin the \u039bCDM model.\nHowever, the detailed form of the primordial spectrum\n\n11\nand hence its detectability depends on the assumptions\nabout the cosmological history in the period between\nreheating and the onset of BBN. In particular, adding\nan exotic era dominated by stiff energy (called the stiff\ndominated (SD) epoch, see e.g. [43\u201351]) leads to an infla-\ntionary gravitational-wave background growing at higher\nfrequencies (i.e. blue tilted), making it accessible to the\nLIGO-Virgo-KAGRA network [50\u201353], future third gen-\neration detectors and space-based laser interferometer ex-\nperiments [47, 200\u2013210]. There are several concrete mod-\nels in physics beyond the Standard Model that lead to\ncosmological periods with a stiff equation of state. We list\nhere for instance quintessence models [43, 44, 211], ax-\nion scenarios [212\u2013215], models with string theory mod-\nuli [216, 217], Peccei-Quinn inflation models [218], etc.\nIn the following, we will introduce a model independent\nparametrization for a stiff epoch and explore the con-\nstraints imposed on this scenario by the O1 to O4a runs\nof LIGO-Virgo-KAGRA. The same model was previously\nconstrained using the O1-O3 data in [53].\nB.\nModel\nThe Universe can be described as a cosmological fluid\nwith two key parameters:\ndensity \u03c1 and pressure P.\nThe equation of state parameter w = P/\u03c1 character-\nizes the Universe\u2019s behavior across different epochs. In\nthe \u039bCDM Model, inflation is immediately followed by\na period of Radiation Domination (RD), with w = 1/3,\nthen a period of Matter Domination (MD) with w = 0,\nand currently, a period of Dark Energy Domination with\nw = \u22121. Modifications to this sequence can be made by\ninserting other eras between the end of inflation and the\nonset of Big Bang Nucleosynthesis (BBN), provided the\nUniverse is RD during BBN [46].\nOur model introduces an unconventional sequence of\nepochs preceding the standard eras: an exotic RD era\n(denoted by RD1), an exotic MD era (denoted by MD1)\nand an exotic era driven by stiff energy, described by an\nequation of state parameter 1/3 \u2264ws \u22641 (denoted by\nSD). The most extreme case of such a SD era is called\nkination, in which ws is fixed to 1.\nThis cosmological model is motivated by high energy\nphysics and can have a variety of observational conse-\nquences. Indeed, this specific sequence of epochs (in the\ncase of kination) naturally arises in axion models [212\u2013\n215] (see also [219\u2013221]), providing a theoretical motiva-\ntion for this cosmological scenario. In addition, a stiff\nera leads to a blue tilt in the inflationary gravitational-\nwave spectrum, making it observationally interesting. Fi-\nnally, including a MD era suppresses the gravitational-\nwave spectrum at higher frequencies, allowing the model\nto evade indirect constraints from CMB and BBN obser-\nvations.\nThe unconventional cosmological history enhances the\ninflationary gravitational-wave background, which re-\nsults in a spectral shape with the following asymptotic\nbehavior [53]\n\u2126SD(f) = \u2126SD|(0)\nplateau\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f3\nA1\nif\nf \u226afRD\nA\u03b1s\n\u0010\nf\nfRD\n\u00112(1\u2212\u03b1s)\nif\nfRD \u226af \u226afSD\nA2\n\u0010\nfSD\nfRD\n\u00112(1\u2212\u03b1s) \u0010\nfSD\nf\n\u00112\nif\nfSD \u226af \u226afMD\nA1\n\u0010\nfSD\nfRD\n\u00112(1\u2212\u03b1s) \u0010\nfSD\nfMD\n\u00112\nif\nfMD \u226af\n(23)\nwith A\u03b1era a coefficient that depends on the equation of\nstate at the moment when the gravitational-wave mode\nre-enters the Hubble radius, given by [46]\nA\u03b1era \u2261\u03932(\u03b1era + 1/2)\n\u03c0\n\u0012 2\n\u03b1era\n\u00132\u03b1era\n, \u03b1era \u2261\n2\n1 + 3wera\n,\n(24)\nand where [50]\n\u2126(0)\nSD|plateau \u2261Gk\n\u2126(0)\nrad\n12\u03c02\n\u0012Hinf\nMPl\n\u00132\n,\n(25)\nwith \u2126(0)\nrad \u22489 \u00d7 10\u22125 and with MPl = 1/\n\u221a\n8\u03c0G \u2248\n2.44 \u00d7 1018 GeV the reduced Planck mass.\nMoreover,\nthe factor Gk = [g\u2217,k/g\u2217,0][gs,0/gs,k]\n4\n3 encodes the change\nin relativistic degrees of freedom between today and\nthe time when the mode k enters the Hubble radius at\nk = aH.\nThe detailed gravitational-wave background\nassuming instantaneous transitions between subsequent\nepochs can be found in [53], and it is the one used in the\nfollowing.\nThere are five different parameters that influence the\nspectrum, as can be seen in Fig. 6.\nThe Hubble scale of inflation Hinf influences the size\nof the spectrum. CMB polarization experiments Planck\n2018, BICEP2, Keck Array and BICEP3 [222] constrain\nthe tensor-to-scalar-ratio r and therefore also the infla-\ntionary power spectrum as Hinf < Hinf,max = 5.12 \u00d7\n1013 GeV. The next-generation CMB experiment Lite-\nBIRD [223] is expected to lead to an improvement in\n\n12\nthis bound as Hinf < 1.21 \u00d7 1013 GeV.\nThen, fRD is the frequency corresponding to the mo-\nment of transition between SD and RD2 and influences\nthe position of the elbow between plateau and increase in\nspectrum (here RD2 denotes the standard radiation era\noccurring after the SD phase). Note that BBN should\noccur during the RD2 era, implying that fRD \u2265fBBN \u2243\n1.41 \u00d7 10\u221211 Hz.\nMoreover, the equation of state parameter during the\nSD era, ws, determines the slope of the increasing part\nof the spectrum. The range for the related parameter\n\u03b1s \u22612/(1 + 3ws) is 0.5 \u2264\u03b1s \u22641, where the lower bound\ncorresponds to kination and the upper bound to radia-\ntion.\nThen, fSD, which corresponds to the transition mo-\nment between MD1 and SD influences the peak ampli-\ntude and the location of the peak.\nLastly, fMD, which is the transition moment between\nRD1 and MD1 influences the elbow between the decreas-\ning spectrum and the plateau on the right.\nA+\nO4a\nO3\nRD2\nSD\nMD1\nRD1\nFIG. 6. The gravitational-wave background spectrum result-\ning from the exotic cosmology, for different choices of ws. The\nsensitivity curves for LIGO-Virgo O3 run [68], as well as the\nones of the O4a run [19] and the LIGO A+ detector [199]\nare shown.\nThe parameters that control the gravitational-\nwave spectrum are chosen as Hinf = Hinf,max, fRD = 10\u22125\nHz, fSD = 75 Hz, and fMD is fixed, so that the right plateau\nand the left plateau have the same amplitude. The standard\ninflationary gravitational-wave background is denoted with\na purple dashed line. The parameter Hinf affects the over-\nall gravitational-wave background amplitude, as indicated by\nthe double arrow. The low-frequency part of the spectrum is\nshaped by fRD: lower values of fRD shift the low-frequency\nplateau to the left, resulting in a stronger gravitational-wave\nbackground, while higher values shift it to the right, resulting\nin a weaker gravitational-wave background.\nThe peak fre-\nquency of the spectrum depends on fSD: lower values shift\nthe peak to the left (weaker gravitational-wave background),\nand higher values shift it to the right (stronger gravitational-\nwave background).\nThe gravitational-wave energy density can be con-\nstrained because of its contribution to the relativistic\ndegrees of freedom in the Universe [23]. For the model\nconsidered here, we can estimate this bound as\n\u0012h2\u03c1GW\n\u03c1c\n\u0013 \f\f\f\n\u03c4=\u03c40 \u2248\n1\n2(1 \u2212\u03b1s)h2\u2126SD(fpeak) < 1.3\u00d710\u22126 ,\n(26)\nwhere the right hand side is evaluated at the peak fre-\nquency fpeak \u223cfSD, and where we used the 2\u03c3 limit on\n\u2206Neff from the CMB plus BBN analysis [224]. Further\nconstraints on a stiff epoch could possibly arise from the\nenhancement of scalar modes [221], depending on the in-\nflationary model.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nWe use the Bayesian analysis as described in Section I\nand employ the pygwb package [119]. The model for the\ngravitational-wave energy density spectrum \u2126GW(f|\u03b8)\ncombines the inflationary gravitational-wave background\nenhanced by a stiff era \u2126SD(f) and the astrophysical\ngravitational-wave background from unresolved CBCs\n\u2126CBC(f): \u2126GW(f|\u03b8) = \u2126SD(f) + \u2126CBC(f). Within the\nrelevant frequency range, the CBC background takes the\nform of Eq. 2 where fref = 25 Hz is the reference fre-\nquency and \u2126ref is the amplitude of the CBC background\nat this frequency, and we fix the power law to 2/3.\nThe\nparameter\nspace\nis\ndefined\nby\n\u03b8\n=\n(\u2126ref, Hinf, fMD, fSD, fRD, \u03b1s).\nFor\nthe\nBayesian\nanalysis, however, Hinf and fMD are fixed by using delta\nfunction priors centered around a constant value. First,\nwe fix Hinf to Hinf,max = 5.12 \u00d7 1013 GeV, which max-\nimizes the amplitude of the gravitational-wave signal.\nNote that, for the signal in the LIGO-Virgo-KAGRA\nobservational frequency band, there is a degeneracy\nbetween Hinf and fRD, which could be used to translate\nthe results presented here to another value of Hinf\n(for more details, see [53]).\nSecond, we assume that\nfMD is higher than the maximal frequency detectable\nwith LIGO-Virgo-KAGRA. Specifically, notice that as\nsoon as fMD \u2273100 Hz, the high-frequency portion\nof the gravitational-wave spectrum, which is set by\nfMD, lies beyond the LIGO-Virgo-KAGRA observa-\ntional band and therefore does not affect our analysis\n(see [53] for more details).\nFor definiteness we set\nfMD = fi = 1.8 \u00d7 108 Hz , where fi represents the\nfrequency associated with the end of inflation (assuming\na constant Hubble scale during inflation and no entropy\ninjection between RD1 and RD2).\nThe priors for the\nother parameters are reported in Table III.\nIn our analysis, we concretely consider two scenarios:\n\u2022 Kination Model:\nwe fix \u03b1s = 0.5, which corre-\nsponds to the maximum value for ws. This model\nis denoted as \u201ckination+CBC\u201d and its results are\ngiven in Fig. 7.\n\u2022 General SD epoch Model: in this case ws is allowed\n\n13\nParameters \u03b8\nPrior\n\u2126ref\nLogUniform[10\u221213, 10\u22126]\nfRD/Hz\nLogUniform[10\u221210, 10\u22125]\nfSD/Hz\nLogUniform[10\u22123, 106]\n\u03b1s\nUniform[0.5, 1]\nTABLE III.\nPriors assumed for the Bayesian analysis.\nThe prior for \u2126ref comes from estimates of the CBC back-\nground [17]. The prior for \u03b1s is determined by the allowed\nrange of ws: 1/3 \u2264ws \u22641. The prior ranges for fRD and fSD\nare set to satisfy fBBN \u2264fRD < fSD. They are selected over a\nsufficiently wide range to ensure that they include regions of\nparameter space leading to gravitational-wave signals within\nthe LIGO-Virgo-KAGRA frequency band. We have verified\nthat the posteriors are not significantly affected if we make\nthe priors larger.\n2.5 0.0\n2.5\n5.0\nLog10(fSD/Hz)\n10\n9\n8\n7\n6\n5\nLog10(fRD/Hz)\n95%\n68%\n12\n10\n8\n6\nLog10(\nref)\n2\n0\n2\n4\nLog10(fSD/Hz)\n68%\n95%\n10\n9\n8\n7\n6\n5\nLog10(fRD/Hz)\n2\n0\n2\n4\n68%\n95%\nExclusion by indirect limits\nFIG. 7.\nPosteriors of the Bayesian analysis for the kina-\ntion+CBC model.\nHere \u03b1s is fixed to \u03b1s = 0.5.\nFor the\ncontour regions the same colors as in Figure 8 are used. The\ngray region in the bottom panel is excluded by indirect limits\nfrom BBN and CMB as in (26).\nto vary, referred to as \u201cSD+CBC\u201d. Its results are\ngiven in Fig. 8.\nOur study finds no evidence for either of these\nbackgrounds,\nwith\nlog\nBayes\nfactors\nas\nfollows:\nln(Bkination+CBC\nNoise\n) = \u22121.16 for the kination model, and\nln(BSD+CBC\nNoise\n) = \u22120.62 for the model with varying \u03b1s.\nWe also compare a CBC-only background with a com-\nbined SD+CBC signal. For the kination model, we ob-\ntain ln(Bkination+CBC\nCBC\n) = \u22120.62, suggesting a preference\n0.0\n0.1\n0.2\n0.6\n0.8\n1.0\ns\n10\n9\n8\n7\n6\n5\nLog10(fRD/Hz)\n95%\n68%\n2\n0\n2\n4\nLog10(fSD/Hz)\n95%\n68%\n68%\n12 10\n8\n6\nLog10(\nref)\n0.5\n0.6\n0.7\n0.8\n0.9\ns\n68%\n95%\n10\n8\n6\nLog10(fRD/Hz)\n68%\n95%\n2.5 0.0 2.5 5.0\nLog10(fSD/Hz)\n95%\n68%\nFIG. 8. Posteriors of the Bayesian analysis for an SD+CBC\nmodel. Contour regions in purple correspond to 95% CL and\nthose in red to 68% CL.\nfor a CBC-only background. For the general SD model,\nwe find ln(BSD+CBC\nCBC\n) = \u22120.09, that indicates a small\npreference for a CBC background only.\nIn summary, we do not find evidence in the O1 to\nO4a LIGO-Virgo data for either a CBC background or\na gravitational-wave background coming from a stiff era.\nConsequently, we derive 95% CL upper limits on some of\nthe parameters characterizing this unconventional cos-\nmology.\nThese are identified by the white regions in\nFig. 7 and Fig. 8 (and slightly improve on the previ-\nous analysis performed only with O1-O3 data [53]). In\nFig. 7, in the case of kination, we show that the data\ncan exclude a portion of parameter space in the fRD vs\nfSD plane which would otherwise still be allowed by in-\ndirect limits.\nOur analysis, independently on the stiff\nepoch, also sets an upper limits on the amplitude of the\nastrophysical background, with value \u2126ref \u22642.9 \u00d7 10\u22129.\nVI.\nAXION INFLATION\nA.\nMotivation\nGravitational waves offer a novel tool to test inflation-\nary models and constrain their parameters. One infla-\ntionary model motivated by high energy physics is ax-\nion inflation, where a pseudo-scalar axion, coupled to a\ngauge field, leads to the early Universe accelerated ex-\npansion [54\u201357]. This model offers rich opportunities for\ncosmological observations [225, 226], including distinc-\ntive CMB features [227, 228], the formation of primordial\n\n14\nblack holes [229] arising from the effective multi-field dy-\nnamics induced by the gauge field background, and a chi-\nral gravitational-wave background [55, 230\u2013233], which\nmay be detectable by the LIGO-Virgo-KAGRA detec-\ntors.\nAlthough U(1) gauge fields have been studied exten-\nsively, non-Abelian gauge fields, such as SU(2), present\na compelling alternative. Their key difference is that the\nSU(2) gauge field can have an isotropic background value,\nwhereas the U(1) cannot. As a result, gravitational-wave\nproduction can be computed using linear analysis in the\ncase of SU(2), while it becomes a nonlinear process for\nU(1), generally requiring a more involved analysis to pre-\ndict gravitational-wave amplitude [230, 234]. In our anal-\nysis, we focus on the SU(2) gauge field.\nGravitational waves can be efficiently produced when\nbackground gauge fields induce linear couplings between\nmetric and tensor perturbations [235, 236].\nWhile the\noriginal cosine inflaton potential is excluded by CMB ob-\nservations [237, 238], other more complex models [232,\n239\u2013247] can evade CMB constraints and generate sig-\nnals at currently detectable interferometric scales.\nB.\nModel\nWe consider chromo-natural inflation [248, 249], for\nwhich the action reads [56, 248]\nS =\nZ\nd4x\u221a\u2212\u00afg\nhM 2\nPl\n2 R \u22121\n2(\u2202\u03d5)2\n\u2212V (\u03d5) \u22121\n4F a\n\u00b5\u03bdF a\u00b5\u03bd + \u03b1f\n4 \u03d5F a\n\u00b5\u03bd \u02dcF a\u00b5\u03bdi\n,\n(27)\nwhere MPl is the reduced Planck mass, \u00afg = det(g\u00b5\u03bd),\nR denotes the Ricci scalar, \u03d5 is the inflaton axion field\nwith a scalar potential V (\u03d5). The SU(2) gauge field Aa\n\u00b5\nhas field strength F a\n\u00b5\u03bd = \u2202\u00b5Aa\n\u03bd \u2212\u2202\u03bdAa\n\u00b5 \u2212g\u03b5abcAb\n\u00b5Ac\n\u03bd, and\nits dual is \u02dcF a\u00b5\u03bd = \u03b5\u00b5\u03bd\u03c1\u03c3F a\n\u03c1\u03c3/(2\u221a\u2212\u00afg). The axion\u2013gauge\ncoupling is denoted by \u03b1f, and the gauge coupling by g.\nWe consider an isotropic ansatz for the homogeneous\ncomponent of the gauge field,\nAa\n0 = 0,\nAa\ni = \u03b4a\ni a(t)Q(t),\n(28)\nwhere Q \u2243(\u2212\u2202\u03d5V/3\u03b1fgH)1/3 with H \u2261\u02d9a/a the Hubble\nparameter [250\u2013252].\nThe coupling between the inflaton and the SU(2)\ngauge field induces a tachyonic instability in one helic-\nity mode of the gauge field. This leads to exponential\namplification of that mode, which in turn sources a chi-\nral (parity-violating) gravitational wave background [56,\n238]. When the gauge coupling is small or the gauge field\nis weak, a non-Abelian SU(N) gauge theory behaves ap-\nproximately like N 2\u22121 independent copies of an Abelian\nU(1) gauge theory. In the non-Abelian regime, the back-\nground gauge field acquires a nonzero vacuum expecta-\ntion value (VEV), which enables a linear coupling be-\ntween gauge field tensor perturbations and the metric\ntensor perturbations. This linear coupling allows the en-\nhanced helicity +2 mode of the gauge field to efficiently\nsource gravitational waves during inflation. In contrast,\nin the Abelian case, such couplings only arise at the non-\nlinear level, making the gravitational wave production\nless efficient.\nTherefore, we focus on the non-Abelian\nregime.\nThe gravitational wave background sourced in the non-\nAbelian regime can be analytically approximated as [246]\n\u2126SU(2)(k) \u2243\n\u221a\n2\u2126(0)\nrad\n3\n\u0010 \u03be3H\n\u03c0MPl\n\u00112\n\u03be=\u03becr\n\u0010He(2\u2212\n\u221a\n2)\u03c0\u03be\ng\u221a\u03be\n\u00112\n\u03be=\u03beref\n,\n(29)\nwhere \u2126(0)\nrad = 9 \u00d7 10\u22125 and \u03be = \u03b1f \u02d9\u03d5/2H. In Eq. (29),\nthe first term is evaluated at \u03becr = \u03be(x = 1), while the\nsecond term is evaluated at \u03beref = \u03be(x = (2 +\n\u221a\n2)\u03becr),\nwith x = \u2212k\u03c4 for conformal time \u03c4. The non-Abelian\nregime is conservatively defined by the condition [246]\n0.008e2.8\u03be \u22731/g .\n(30)\nA straightforward way to evade the CMB constraints is\nto consider the piecewise linear potential originally pro-\nposed by Starobinsky [253, 254],\nV (\u03d5) =\n\u001a\nV0 + A+(\u03d5 \u2212\u03d50), for \u03d5 > \u03d50\nV0 + A\u2212(\u03d5 \u2212\u03d50), for \u03d5 < \u03d50 ,\n(31)\nwhere V0 sets the energy scale of the potential, and A+\nand A\u2212determine the slopes on either side of \u03d50. Within\nthe slow-roll approximation, the inflaton velocity remains\napproximately constant, leading to a constant velocity\nparameter \u03be. This property greatly simplifies analytical\ncalculations and facilitates the computation of the result-\ning gravitational-wave spectrum.\nIn Fig.9, we show the spectrum \u2126SU(2)(k) for different\nparameter sets.\nDue to the constant velocity parame-\nter \u03be, the gravitational-wave amplitude remains constant\nover the relevant scales. We assume that the transition\nfrom the Abelian to the non-Abelian regime occurs near\n\u03d50, positioned between CMB and interferometer scales,\nwhich determines where the enhanced gravitational-wave\nproduction begins.\nFor further discussion of the al-\nlowed parameter space and analyses of alternative mod-\nels, see [255].\nAlthough the SU(2) gauge field can enhance gravita-\ntional waves during inflation, observational constraints\nexist, which we summarize below.\nCosmic Microwave Background:\nThe Hubble ex-\npansion\nrate\nduring\ninflation\nat\nthe\nCMB\nscale,\nHCMB, sets the amplitude of the vacuum contribu-\ntion to the gravitational-wave background, \u2126vac(k) =\n\u2126(0)\nradH2/(12\u03c02M 2\nPl). The observable tensor-to-scalar ra-\ntio r is related to HCMB through\nHCMB = 2.7 \u00d7 1014r1/2GeV .\n(32)\nThe latest observational constraint, r < 0.036 at 95%\nCL [222], translates into HCMB < 2.1\u00d710\u22125MPl, thereby\nruling out certain classes of inflationary models.\n\n15\n10\n1\n10\n2\n10\n3\nf [Hz]\n10\n14\n10\n12\n10\n10\n10\n8\n10\n6\n10\n4\n10\n2\n10\n0\n\u2126SU(2)\nO4a\n\u03be0 = 5.36, g = 4.29 \u00d7 10\u22125\n\u03be0 = 5.36, g = 5.62 \u00d7 10\u22124\n\u03be0 = 5.90, g = 4.29 \u00d7 10\u22125\nFIG. 9. Examples of Non-Abelian gravitational-wave back-\nground spectra for varying \u03be0, g, plotted with the O4a power-\nlaw integrated curve.\nPrimordial\nBlack\nHole\noverproduction:\nGauge-\nfield\u2013induced tensor modes can amplify primordial cur-\nvature fluctuations through second-order effects in cos-\nmological perturbation theory.\nOnce these fluctua-\ntions re-enter the Hubble radius, they may collapse\ninto primordial black holes, whose abundance is tightly\nconstrained by cosmological and astrophysical observa-\ntions [256, 257]. If the curvature perturbations obey \u03c72\nstatistics, primordial black hole formation is more effi-\ncient than in the Gaussian case, excluding a substantial\nregion of parameter space [230]. This bound may how-\never be alleviated in certain case. Lattice simulations of\naxion inflation with a U(1) gauge field suggest that, in\nthe strong back-reaction regime, curvature perturbations\napproach a Gaussian distribution [258], reducing the ex-\npected primordial black hole abundance. While a similar\nanalysis has not yet been carried out for SU(2) gauge field\nmodels, it is plausible that back-reaction effects could\nlikewise relax primordial black hole constraints.\nThe strength of the back-reaction is controlled by the\nparameter \u03ba [255, 259]\n\u03ba \u2243g\n\u0012\n24\u03c02\n2.3e3.9mQ\nm2\nQ\n1 + m2\nQ\n\u0013\u22121/2\n,\n(33)\nwhere mQ \u2261gQ/H plays the role of an effective mass.\nWhen back-reaction is an efficient mechanism, \u03ba \u22431,\nthe curvature perturbations would approach a Gaussian\ndistribution and the primordial black hole constraint\nmay be relaxed. However, if the back-reaction becomes\ntoo strong (\u03ba > 1), the analytical expressions for the\ngravitational-wave spectrum are no longer reliable, and\na dedicated numerical analysis would be required. We\nthus do not consider this latter case.\n5\n4\n3\n2\n1\n0\nlog10 g\n2\n3\n4\n5\n6\n7\n\u03be0\n\u22651\nAbelian Regime\nSU(2) + CBC\nHCMB free\nHCMB = 10\u22127 MPl\nHCMB = 10\u22126 MPl\nHCMB = 10\u22125 MPl\nFIG. 10. Marginalized posterior in the \u03be0 \u2212log10 g plane ob-\ntained from a search for early Universe axion inflation with\nan overlaid astrophysical background, assuming fixed val-\nues of HCMB = 10\u22127 MPl, 10\u22126 MPl, 10\u22125 MPl (dotted,\ndot-dashed, and dashed green lines, respectively), and also\ntreating it as a free parameter (solid green line). The gray\nshaded region denotes the Abelian regime, where efficient\ngravitational-wave production is expected. The purple shaded\nregion corresponds to the parameter space where strong back-\nreaction is anticipated, namely \u03ba \u22651 , and the gravitational\nwave amplitude estimates may no longer be reliable.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nParameter\nPrior\n\u2126ref\nLogUniform[10\u221212, 10\u22127]\nNCMB\nUniform[50, 60]\nf0/Hz\nLogUniform[10\u22126, 10]\n\u03d5end/MPl\nUniform[0, 25]\nA+/M 3\nPl\nLogUniform[10\u221220, 10\u22126]\nA\u2212/M 3\nPl\nLogUniform[10\u221220, 10\u22126]\nV0/M 4\nPl\nLogUniform[10\u221220, 10\u22126]\n\u03b1f/M \u22121\nPl\nUniform[0, 250]\ng\nLogUniform[10\u22125, 1]\nTABLE IV. Prior distributions assumed for the parameters\nof the model and the CBC background.\nWe perform a Bayesian parameter estimation search\nfor a combined non-Abelian and CBC background using\npygwb [119]. The model has 8 free parameters and the\n\n16\nParameters\nHCMB free\nHCMB = 10\u22125 MPl HCMB = 10\u22126 MPl HCMB = 10\u22127 MPl\n\u2126ref\n2.48 \u00d7 10\u22129\n3.18 \u00d7 10\u22129\n3.37 \u00d7 10\u22129\n2.72 \u00d7 10\u22129\ng\n0.411\n0.421\n0.322\n0.325\nV0\n4.41 \u00d7 10\u22129\n2.36 \u00d7 10\u221210\n2.37 \u00d7 10\u221212\n2.50 \u00d7 10\u221214\nA+\n2.77 \u00d7 10\u221212\n3.73 \u00d7 10\u221211\n3.77 \u00d7 10\u221213\n3.69 \u00d7 10\u221215\nA\u2212\n2.01 \u00d7 10\u221210\n1.60 \u00d7 10\u221211\n2.23 \u00d7 10\u221213\n2.36 \u00d7 10\u221215\n\u03be0\n5.936\n4.104\n4.976\n5.884\nHCMB/MPl 4.18 \u00d7 10\u22125\n-\n-\n-\nTABLE V. 95% upper bounds on the SU(2)+CBC model and CBC background\u2019s parameters obtained under different Hubble\nconstant HCMB prior assumptions.\nHCMB\nlog BGWB\nnoise\nFree\n\u22120.515 \u00b1 0.028\n10\u22127 MPl \u22120.541 \u00b1 0.029\n10\u22126 MPl \u22120.555 \u00b1 0.029\n10\u22125 MPl \u22120.511 \u00b1 0.028\nTABLE VI. Parameter estimation log Bayes evidence factor\nfor the searched combined model and CBC background under\ndifferent Hubble constant HCMB prior assumptions.\nprior ranges are summarized in Table IV.\nFigure 10 shows the 95% constraints obtained from the\njoint SU(2) + CBC analysis. We show both cases where\nall the 8 parameters are searched and where HCMB is\nfixed at HCMB = 10\u22125MPl, 10\u22126MPl, 10\u22127MPl. The con-\nstraint is shown in the log10 g \u2013 \u03be0 plane and other param-\neters are marginalized over. As discussed in the previous\nsection, the viable region for \u03be and g is limited to a cer-\ntain area around the diagonal line in Fig. 10. The grav-\nitational wave amplitude is proportional to g\u22122 and an\nexponentially increasing function of \u03be0 (see Eq. (29)), and\nit becomes larger toward the upper-left region of Fig. 10.\nConsequently, the gravitational-wave observations con-\nstrain the parameter space above the green lines.\nThe constraint is most sensitive to the value of HCMB,\nas it affects the overall amplitude. As we can see from\nthe figure, we obtain tighter constraints on g and \u03be0 when\nHCMB is large, and vice versa.\nWe can also observe\nthat, when HCMB is left free and marginalized over, the\nconstraint is relatively weak.\nThis is because, due to\nour prior allowing very small HCMB values, small HCMB\nlikely dominate the results when HCMB is marginalized\nover. In other words, the constraints is endent on the\nprior of HCMB, and fixing HCMB eliminates this ambigu-\nity.\nThis result can be understood physically as follows.\nIn Fig. 10, if we fix g and gradually increase \u03be0 from a\nsmall value, the energy transfer from the inflaton to the\ngauge field is initially too weak, keeping the system in the\nAbelian regime, where gravitational wave production re-\nmains inefficient. However, beyond a certain threshold,\nthe non-Abelian nature of the gauge field becomes signif-\nicant, leading to enhanced gravitational wave generation.\nHowever, if \u03be0 becomes too large, backreaction effects be-\ncome dominant, violating the assumptions of our analy-\nsis, or the resulting gravitational-wave signal would con-\ntradict LIGO-Virgo observations, leading to exclusion.\nThe result presented here applies specifically to the\nform of the potential given in Eq. (31). Different infla-\ntionary potentials yield different gravitational-wave spec-\ntra, as the latter is determined by the evolution of the\nscalar field (namely, \u03be evolves differently). We chose the\ndouble linear potential model because a linear potential\nleads to a constant solution for the velocity parameter\n\u03be, and the two-stage inflation allows us to avoid concerns\nabout CMB constraints. This provides a relatively simple\npicture in which the gravitational-wave spectrum is de-\ntermined by the velocity parameter at the second stage,\n\u03be0. For discussions on cosine-type potentials and the R2\npotential, we refer the reader to [246, 255].\nVII.\nSECOND-ORDER SCALAR\nPERTURBATIONS\nA.\nMotivation\nThe scalar-induced gravitational-wave background,\narising from large-amplitude primordial curvature per-\nturbations, provides an observational test for probing di-\nrectly the epoch of inflation [58]. This topic has recently\ngained significant attention due to its connection with\nprimordial black holes [260, 261]. In scenarios where pri-\nmordial curvature fluctuations are amplified during in-\nflation, primordial black holes form through the collapse\nof extremely dense regions shortly after the correspond-\ning modes enter the Hubble radius [262, 263]. Associated\nwith this process, gravitational waves are sourced by the\nsecond-order terms of scalar perturbations, in the con-\ntext of cosmological perturbation theory [59\u201363]. Thus,\nan upper bound on the gravitational-wave background\ncan provide constraints on primordial curvature pertur-\nbations [264\u2013267].\nThe amplification of the primordial curvature spec-\ntrum can be achieved through various mechanisms.\n\n17\nWithin the framework of single-field inflation, this can\noccur via the Hilltop-type or running mass models [268,\n269].\nHowever, these models typically enhance curva-\nture perturbations toward the end of inflation, result-\ning in high-frequency signals that are not accessible with\nthe observational band of LIGO-Virgo-KAGRA detec-\ntors [270].\nAn ultra slow-roll phase, achieved through\na plateau region in the inflationary potential [271\u2013273],\nprovides a flexibility to adjust the scale of enhance-\nment. Another possibility is to consider multi-field in-\nflation, which can predict enhanced curvature perturba-\ntions through mechanisms such as hybrid inflation with\na tachyonic instability [274, 275] or turns in field space,\ncorresponding to a bending of the inflationary trajec-\ntory [276, 277].\nB.\nModel\nAlthough extensive phenomenological studies have\nbeen conducted on the scalar-induced gravitational-wave\nbackground, we provide constraints based on the simplest\nassumptions: a log-normal spectral shape and a Gaussian\ndistribution of the primordial curvature perturbations.\nThe peak in the primordial curvature power spectrum is\nassumed to take the form [278]\nP\u03b6(k) =\nA\n\u221a\n2\u03c0\u2206exp\n\u0014\n\u2212ln2(k/k\u2217)\n2\u22062\n\u0015\n.\n(34)\nIt is defined by its position k\u2217with its width controlled\nby the parameter \u2206and its amplitude characterized by\nA. In the \u2206\u21920 limit, Eq. 34 reduces to a Dirac delta\nfunction P\u03b6(k) = A\u03b4(ln(k/k\u2217)). The assumption for the\nprimordial curvature power, Eq. 34, provides constraints\nin a model-independent manner and serves as a good\napproximation for many inflationary models.\nFurther-\nmore, given the relatively narrow frequency band, our\nconstraints are not sensitive to the detailed shape of the\nspectrum. Inflationary models typically predict an en-\nhanced curvature perturbation spectrum over a wider\nrange of scales, which can be well-approximated by a log-\nnormal peak with a large width within the LIGO-Virgo\nfrequency coverage.\nIn our analysis we focus on a Gaussian distribu-\ntion for the primordial curvature perturbations.\nNon-\nGaussianity can significantly modify the spectrum of the\nscalar-induced gravitational-wave background [279\u2013285],\nhowever the precise form of non-Gaussianity depends on\nthe inflation model and a general parametrization is lack-\ning.\nHence, assuming a Gaussian distribution for the cur-\nvature perturbations, the energy-density spectrum of\nthe scalar-induced gravitational-wave background can\nbe computed using the approximate analytical expres-\nsion [286, 287]\n\u2126Scalar(k)h2\n\u22431.62 \u00d7 10\u22125\n \n\u2126(0)\nradh2\n4.18 \u00d7 10\u22125\n! \u0010\ng\u2217\n106.75\n\u0011 \u0010 g\u2217,s\n106.75\n\u0011\u22124/3\n\u00d7\n1\n12\nZ 1\n\u22121\ndx\nZ \u221e\n1\ndy P\u03b6\n\u0012\nk y \u2212x\n2\n\u0013\nP\u03b6\n\u0012\nk x + y\n2\n\u0013\nF(x, y) ,\n(35)\nwhere \u2126(0)\nrad is the present value of the energy density frac-\ntion of radiation, and g\u2217and g\u2217,s are the effective number\nof degrees of freedom for energy density and entropy den-\nsity, respectively. The function F(x, y) is given by\nF(x, y) = 288(x2 + y2 \u22126)2(x2 \u22121)2(y2 \u22121)2\n(x \u2212y)8(x + y)8\n\u00d7\nh\u0010\nx2 \u2212y2 + x2 + y2 \u22126\n2\nln\n\f\f\fy2 \u22123\nx2 \u22123\n\f\f\f\n\u00112\n+ \u03c02\n4 (x2 + y2 \u22126)2\u03b8(y \u2212\n\u221a\n3)\ni\n,\n(36)\nwhere \u03b8 denotes the Heaviside step function. The fre-\nquency range of our search corresponds to wavenum-\nbers between approximately 1016 and 1019 Mpc\u22121. These\nscales re-entered the Hubble horizon when the tempera-\nture exceeded 108 GeV, allowing us to set g\u2217= g\u2217,s =\n106.75 within the Standard Model framework.\nFigure 11 shows the spectrum assuming a log-normal\ncurvature power spectrum for different values of the\nwidth parameter, \u2206= 0, 0.1, 1, while keeping A and k\u2217\nfixed.\nAs \u2206increases, the peak becomes broader and\nthe spectral amplitude decreases. The integrated ampli-\ntude A sets the overall normalization, with the spectrum\nscaling as \u2126Scalar(f) \u221dA2, while the peak scale k\u2217de-\ntermines the frequency at which the spectrum reaches its\nmaximum.\nThe peak scale is set by the specific mechanism that\nenhances scalar perturbations during inflation, and the\ngravitational-wave spectrum peaks at approximately the\nsame wavenumber as the curvature power spectrum. If\nprimordial black holes form after the corresponding mode\nre-enters the Hubble radius, their mass can be related to\nthe peak frequency as\nf\u2217\u2261ck\u2217\n2\u03c0 = 25\n\u0012\nk\u2217\n1.6 \u00d7 1016 Mpc\u22121\n\u0013\nHz\n\u224325 \u03b31/2\nH\n\u0012\nMPBH\n5.3 \u00d7 10\u221220M\u2299\n\u0013\u22121/2\nHz ,\n(37)\nwhere M\u2299\u22432 \u00d7 1030 kg is the solar mass, and \u03b3H :=\nMPBH/MH, typically of order unity, accounts for the dif-\nference between the primordial black hole mass MPBH\nand the horizon mass MH.\n\n18\n10\n1\n10\n2\nf [Hz]\n10\n13\n10\n12\n10\n11\n10\n10\n10\n9\n10\n8\n10\n7\n10\n6\n\u2126Scalar\nO4a\n\u2206\u21920\n\u2206= 0.1\n\u2206= 1\nFIG. 11. Spectrum for different values of width \u2206= 0, 0.1, 1\nplotted with the O4a power-law integrated curve. We assume\nA = 0.01 and f\u2217= 50Hz.\nParameter\nPrior\n\u2126ref\nLogUniform[10\u221213, 10\u22125]\nA\nLogUniform[10\u22126, 100.5]\nf\u2217/Hz\nLogUniform[10\u22122, 106]\n\u2206\nfixed at 0 and 1\nTABLE VII. Prior distributions assumed for the parameters\nof the scalar-induced gravitational wave background and the\nCBC background.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nThe result of the Bayesian parameter estimation, ob-\ntained using pygwb [119], are shown in Fig.\n12.\nThe\nbounds set on A from the O4a data (shaded red re-\ngion) are compared with BBN/CMB constraints for \u2206\u2192\n0 and for \u2206= 1.\nThe bottom and top horizontal\naxis represent the peak scale of the curvature pertur-\nbation k\u2217and the primordial black hole masses related\nwith the scale calculated using Eq. (37), respectively.\nThe shaded blue region represents indirect bounds from\nBBN/CMB on the abundance of the stochastic gravi-\ntational wave background. We calculate the bound by\nusing the recent joint CMB+BBN analysis, which indi-\ncates that\nR\nd ln f h2\u2126GW(f) < 1.3 \u00d7 10\u22126 at 2\u03c3 for\nf > 2 \u00d7 10\u221211Hz [224]. Since marginalized constraints\ntend to be prior dependent, here we run the Bayesian\nsearch by fixing the value of \u2206and taking k\u2217and A as\nfree parameters.\nThe upper bound on A for different\ncombinations of \u2206and k\u2217are summarized in Table VIII.\n10\n3\n10\n5\n10\n7\n10\n9\n10\n11\n10\n13\n10\n15\nMk \u2217[kg]\n10\n14\n10\n15\n10\n16\n10\n17\n10\n18\n10\n19\n10\n20\n10\n21\nk \u2217/Mpc\u22121\n10\n2\n10\n1\n10\n0\nA\n\u2206\u21920\nBBN/CMB bounds\nO1-O4a stochastic\n10\n3\n10\n5\n10\n7\n10\n9\n10\n11\n10\n13\n10\n15\nMk \u2217[kg]\n10\n14\n10\n15\n10\n16\n10\n17\n10\n18\n10\n19\n10\n20\n10\n21\nk \u2217/Mpc\u22121\n10\n2\n10\n1\n10\n0\nA\n\u2206= 1\nBBN/CMB bounds\nO1-O4a stochastic\nFIG. 12. Constraints on the curvature perturbation ampli-\ntude for \u2206= 0 (delta function case) and \u2206= 1.\nk\u2217= 1015 Mpc\u22121 k\u2217= 1017 Mpc\u22121 k\u2217= 1019 Mpc\u22121\n\u2206\u21920\n1.44\n0.01\n0.15\n\u2206= 1\n0.96\n0.05\n2.12\nTABLE VIII. 95% CL Upper bounds on the power A of the\ncurvature spectrum for fixed values of the peak position k\u2217\nand width \u2206.\nVIII.\nPRIMORDIAL BLACK HOLES\nA.\nMotivation\nSeveral mechanisms have been proposed for the for-\nmation of primordial black holes. One of the most ex-\ntensively studied scenarios involves the amplification of\nsmall-scale perturbations during inflation.\nOther pro-\nposed mechanisms [64] include formation during phase\ntransitions, an early matter-dominated era, scalar field\ninstabilities, and the collapse of topological defects,\namong others. Their masses can span a wide range, from\nasteroid-like scales to supermassive sizes, depending on\n\n19\nthe formation scenario. Primordial black holes are com-\npelling candidates for dark matter [64, 288, 289] and may\ncontribute to the observed population of binary black\nholes [290\u2013298].\nJust like astrophysical black holes, primordial black\nholes can form binaries and emit gravitational waves.\nThe resulting gravitational-wave background, produced\nby a collection of unresolved events, provides a powerful\nprobe of source populations in the early Universe [299\u2013\n308].\nMoreover, it offers a unique opportunity to test\nthe existence of primordial black hole binaries, since the\nabundance of astrophysical black holes is expected to be\nlow at high redshifts during the cosmic dark ages, before\nstar formation. In contrast, primordial black holes could\nform binaries during this epoch, generating gravitational\nwaves from the early Universe.\nHere, two main formation channels are considered: one\noperating in the early Universe and another in the late\nUniverse, as discussed in the following subsection. A key\nfactor determining the merger rate is the number density\nof primordial black holes, typically quantified by fPBH,\nthe fraction of dark matter composed of primordial black\nholes today. While current observations rule out fPBH =\n1, primordial black holes could still make up a significant\nfraction of dark matter.\nB.\nModel\nThe mass function of primordial black holes is com-\nmonly parametrized using monochromatic or log-normal\ndistributions.\nThis provides a good approximation for\nprimordial black holes produced by a peak in the pri-\nmordial power spectrum [309]. We define the log-normal\nmass function p(m) as\np(m) =\n1\n\u03c1PBH\nd\u03c1PBH\nd ln m ,\n(38)\nwhere \u03c1PBH stands for the primordial black hole energy\ndensity. For a log-normal distribution, the mass function\ntakes the form\np(m) =\n1\n\u221a\n2\u03c0\u03c3 exp\n\"\n\u2212(ln m \u2212ln \u00b5)2\n2\u03c32\n#\n,\n(39)\nwhere \u00b5 is the median mass and \u03c3 controls the width of\nthe distribution in logarithmic space. The mass function\nis normalized such that\nR\np(m)d ln m = 1.\nWe calculate the gravitational-wave background gen-\nerated by an ensemble of binary events by summing the\nenergy spectra of individual binaries, considering the red-\nshift of gravitational waves since emission and using the\nmerger rate distribution [11]:\n\u2126PBH(f) =\nf\n\u03c1c,0\nZ zmax\n0\ndz\nZ\nd ln m1 d ln m2\np(m1)p(m2)\n(1 + z)H(z)\n\u00d7\nd2REB/LB\nd ln m1d ln m2\ndEGW\ndfr\n.\n(40)\nIn Eq. (40) the integration is over the masses m1\nand m2 of the binaries, and fr\n= (1 + z)f is the\ngravitational-wave frequency in the source frame. The\nquantity d2REB/LB/d ln m1/d ln m2 represents the differ-\nential merger rate per unit time, comoving volume, and\nmass interval.\nDifferent binary formation mechanisms\nare denoted by EB (Early Binary) and LB (Late Binary).\nEarly binaries form during the radiation-dominated era\nshortly after primordial black hole formation, while late\nbinaries form later via dynamical capture in primordial\nblack hole clusters during the matter-dominated era. We\nmodel the single-source energy spectrum dEGW/dfr by\nthe phenomenological fitting function of [310], which cap-\ntures the inspiral, merger, and ringdown phases.\nAl-\nthough binaries at high redshift emit gravitational waves\nearly, the nearest binaries typically dominate the back-\nground power unless the merger rate rises sharply with\nredshift. Since the merger rate in our model does not\nincrease steeply, we take zmax = 100, which is sufficient\nto include all relevant contributions to the gravitational-\nwave background.\nSeveral uncertainties may influence the shape of the\ngravitational-wave background, such as the binary for-\nmation mechanism and the potential disruption of bina-\nries by a third body. The formation scenario can also\naffect properties like eccentricity, spin, and precession,\nwhich in turn modify the waveform. In what follows, we\nonly consider non-spinning binaries.\nThe gravitational-wave background is composed of pri-\nmordial black hole merger events occurring across a range\nof redshifts. If nearby binaries are the dominant ones, the\nspectrum exhibits a peak at the characteristic merger fre-\nquency, determined mainly by the primordial black holes\nmasses.\nFor equal-mass binaries, the energy spectrum\nhas a peak at\nf \u22438.3 \u00d7 103\n\u0012MPBH\nM\u2299\n\u0013\u22121\nHz .\n(41)\nHence LIGO\u2013Virgo\u2013KAGRA detectors are sensitive to\nbinaries with masses ranging from sub-solar scales up to\nO(102)M\u2299. The possibility of probing such a background\nwith the LIGO\u2013Virgo\u2013KAGRA detectors has been inves-\ntigated in the literature [294, 301\u2013303, 308, 311\u2013313].\nThere are two major binary formation channels. In the\nEarly Binary formation scenario, a binary originates from\na pair of closely spaced primordial black holes, where\nthe tidal influence of a third nearby object imparts the\nangular momentum necessary for binary formation. The\nmerger rate for early binaries at cosmic time t is given\nby [291, 314\u2013318]\nd2REB\nd ln m1d ln m2\n= 1.6 \u00d7 106\nGpc3yr f 53/37\nPBH\nh t\nt0\ni\u221234/37\n\u00d7\n\u0012m1 + m2\nM\u2299\n\u0013\u221232/37 \u0014\nm1m2\n(m1 + m2)2\n\u0015\u221234/37\n\u00d7 S(m1, m2, fPBH),\n(42)\n\n20\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\nf [Hz]\n10\n13\n10\n12\n10\n11\n10\n10\n10\n9\n10\n8\n10\n7\n10\n6\n\u2126PBH\nO4a\nlate\nMPBH = 1M \u2299\nMPBH = 10M \u2299\nMPBH = 100M \u2299\nearly\nMPBH = 1M \u2299\nMPBH = 10M \u2299\nMPBH = 100M \u2299\nFIG. 13.\nGravitational-wave background spectrum for\nmonochromatic mass function, for both early (red solid) and\nlate (blue dashed) binary formation channels. Different curves\nshow different primordial black hole masses. We also plot the\nO4a power-law integrated curve. Here we assume fPBH = 1,\nfixed supression factor S = 0.002 and Rclust = 400.\nwhere t0 is the age of the Universe. A rate suppression\nfactor, S, has been introduced to take into account two\nmain mechanisms that can suppress binary formation.\nOne resulting from local matter inhomogeneities and\nnearby primordial black holes S1(m1, m2, fPBH), and the\nother from clustering due to their initial Poissonian fluc-\ntuations S2(fPBH) [293, 294, 318]. We employ suppres-\nsion factors modeled with analytical methods [294, 318].\nIn the Late Binary formation senario, binaries can\nform within dense environments if clusters of primor-\ndial black holes develop during the matter-dominated\nera [290]. Analytical expressions for the merger rate can\nbe derived by considering the two-body capture process\nwithin a cluster, under the assumption that the merger\ntimescale of the resulting binary is much shorter than the\nage of the Universe [319, 320],\nd2RLB\nd ln m1d ln m2\n= Rclust\nGpc3yrf 2\nPBH\n(m1 + m2)10/7\n(m1m2)5/7\n.\n(43)\nThe parameter Rclust captures the enhancement of the\nprimordial black hole merger rate due to local cluster-\ning [300, 321], which depends on their velocity dispersion\nand density contrast. We consider three representative\nvalues: Rclust = [1, 4 \u00d7 102, 103], corresponding to (i)\nmodest clustering consistent with \u039bCDM [290], (ii) the\nlevel needed to match observed binary merger rates, and\n(iii) an optimistic scenario with highly efficient cluster\nformation [321].\nWith O4a sensitivity, the merger rate of late binaries is\ntypically subdominant compared to early binaries, except\nfor mPBH \u2273100, M\u2299. This behavior is also illustrated in\nFig. 13, which shows example spectra for both formation\nchannels.\nParameter\nPrior\n\u2126ref\nLogUniform[10\u221212, 10\u22127]\n\u00b5 /M\u2299\nLogUniform[10\u22121, 103]\n\u03c3\nLogUniform[10\u22122, 1]\nfPBH\nLogUniform[10\u22125, 1]\nTABLE IX. Prior distributions for the model parameters in\nBayesian Analysis.\nRclust\n\u00b5 = 1 [M\u2299] \u00b5 = 30 [M\u2299] \u00b5 = 103 [M\u2299]\n1\n1.5 \u00d7 10\u22122\n3.7 \u00d7 10\u22123\n6.4 \u00d7 10\u22121\n4 \u00d7 102 1.6 \u00d7 10\u22122\n3.6 \u00d7 10\u22123\n4.5 \u00d7 10\u22121\n103\n1.4 \u00d7 10\u22122\n3.8 \u00d7 10\u22123\n4.1 \u00d7 10\u22121\nTABLE X. 95% CL on fPBH for various masses.\nC.\nConstraints using O1-O4a LIGO-Virgo data\n10\u22121\n100\n101\n102\n103\nMPBH [M\u2299]\n10\u22123\n10\u22122\n10\u22121\n100\nfPBH\nEROS\nSNe\nOGLE\nCMB-strict\nRclust = 4 \u00d7 102\nRclust = 103\nRclust = 1\n1030\n1031\n1032\n1033\nMPBH [kg]\nFIG. 14.\nThe 95% CL constraints on fPBH as a func-\ntion of MPBH (= \u00b5) from the Bayesian analysis, shown for\nRclust = 1, 4\u00d7102, 103 (dotted, solid, and dashed red curves).\nWe also show other observational constraints such as super-\nnova lensing constraints (SNe, black) [322] , Massive Compact\nHalo Object constraints (EROS, yellow) [323], the recent Op-\ntical Gravitational Lensing Experiment constraints (OGLE,\ngreen) [324], and Cosmic Microwave Background constraints\n(CMB, blue)[325].\nThe prior ranges for the parameters are summarized\nin Table IX. Note that we adopt relatively narrow prior\nfor the width of the mass function \u03c3, since the merger\nrate is known to be reliable only when the mass func-\ntion is sharply peaked, particularly in the early binary\nformation scenario. The Bayesian analysis implies that\nno substantial gravitational-wave background sourced by\nprimordial black holes or CBCs has been detected. We\nestablish upper limits on the CBC energy density pa-\nrameter \u2126ref \u223c3 \u00d7 10\u22129 at the 95% CL level, which are\n\n21\nconsistent with the constraints from the isotropic back-\nground search [19].\nEven in the absence of a detection, we can still con-\nstrain fPBH as a function of \u00b5. We show our constraint\nin Fig. 14, along with those from other analyses. Our\nconstraint is derived by marginalizing over the mass\nfunction width \u03c3 and \u2126ref.\nFor MPBH \u22732 \u00d7 102M\u2299,\nthe spectral amplitude of the gravitational-wave back-\nground is predominantly attributed to the late binary\nformation channel.\nHowever, the O4a sensitivity loses\nits constraining power sharply in this mass range due to\nthe limited frequency range. These findings underscore\nthe ongoing and future importance of gravitational-wave\nbackground searches as a tool for probing phenomena\nwithin the mass range of [1, 3 \u00d7 102] M\u2299. The resulting\nbounds are complementary to existing ones from indi-\nvidual binary events, microlensing surveys, and Cosmic\nMicrowave Background observations. The posterior dis-\ntributions of each parameter are shown in Fig. 15, and\nthe 95% upper bound on fPBH for various combinations\nof \u00b5 and Rclust are presented in Table X.\nFIG. 15. Corner plots of the posterior distributions for the\ngravitational-wave background from primordial black hole bi-\nnaries, assuming Rclust = 4\u00d7102. The results for other values\nof Rclust are very similar.\nLastly, we note that the parameters exhibit a de-\ngeneracy with the CBC contribution, \u2126ref, because\nboth primordial and astrophysical sources produce a\ngravitational-wave spectrum with the same frequency de-\npendence, \u221df 2/3, during the inspiral phase. This simi-\nlarity is particularly relevant when the average black hole\nmass is \u227210M\u2299. However, our results indicate the high-\nest sensitivity to primordial black hole masses around\n\u223c100M\u2299, where the dominant contribution comes from\nthe merger phase. In this regime, the spectrum has a\ncharacteristic frequency dependence, and its shape is sen-\nsitive to the assumed merger rate and mass distribution,\nallowing us to break the degeneracy between parame-\nters.\nIX.\nPARITY VIOLATION\nA.\nMotivation\nSeveral string-theory models and scalar-tensor mod-\nels of gravity can result in circularly polarized gravita-\ntional waves, most notably models inspired by Chern-\nSimons gravity [326\u2013329] and by inflationary scenarios\ncoupled to Abelian gauge fields [330\u2013335]. Chirality is\nalso expected in various models of early Universe phase\ntransitions [336\u2013342] and axion inflation sourced by non-\nAbelian gauge fields, commonly referred to as chromo-\nnatural inflation [56, 236, 246, 248, 343].\nWe describe a generic parity-violation search based\non a power-law energy density gravitational-wave spec-\ntrum [65], then detail more theoretically motivated polar-\nized gravitational-wave background models of early Uni-\nverse turbulence and chromo-natural inflation.\nB.\nModel\nIn searching for parity-violating models, we adopt the\nformalism [65] that uses modified cross-correlation esti-\nmator\n\u27e8\u02c6Cd1d2\u27e9=\nZ \u221e\n\u2212\u221e\ndf\nZ \u221e\n\u2212\u221e\ndf \u2032\u03b4T (f \u2212f \u2032)\u27e8s\u2217\nd1(f)sd2(f \u2032)\u27e9\u02dcQ(f \u2032)\n= 3H2\n0T\n10\u03c02\nZ \u221e\n0\ndf \u2126\u2032\nGW(f)\u03b3d1d2\nI\n(f) \u02dcQ(f)\nf 3\n,\n(44)\nwhere\n\u2126\u2032\nGW = \u2126GW\n\u0014\n1 + \u03a0(f)\u03b3d1d2\nV\n(f)\n\u03b3d1d2\nI\n(f)\n\u0015\n,\n(45)\nwith\n\u03b3d1d2\nI\n(f) =\n5\n8\u03c0\nZ\nd\u02c6\u2126(F +\nd1F +\u2217\nd2 + F \u00d7\nd1F \u00d7\u2217\nd2 )e2\u03c0if \u02c6\u2126\u00b7\u2206\u20d7x,\n\u03b3d1d2\nV\n(f) = \u22125\n8\u03c0\nZ\nd\u02c6\u2126(F +\nd1F \u00d7\u2217\nd2 \u2212F \u00d7\nd1F +\u2217\nd2 )e2\u03c0if \u02c6\u2126\u00b7\u2206\u20d7x .\nWe\ndenote\nT\nthe\nmeasurement\ntime,\n\u03b4T (f)\n=\nsin(\u03c0fT)/(\u03c0f), sd(f) the strain time series of the two\ngravitational-wave detectors (denoted by d1, d2).\n\u02dcQ(f)\nis a filter and F A\nn stands for the contraction of the ten-\nsor modes of polarization A = +, \u00d7 to the nth detec-\ntor\u2019s geometry.\nWe denote by \u03b3d1d2\nI\nthe usual (unpo-\nlarized isotropic gravitational-wave background) overlap\nreduction function of detectors d1, d2 [76], and \u03b3d1d2\nV\nas\nthe overlap function associated with the parity violation\nterm [344]. The polarization degree,\n\u03a0(f) = V (f)/I(f) = PR(f) \u2212PL(f)\nPR(f) + PL(f) ,\n(46)\nranges from -1 (fully left polarization) and 1 (fully right\npolarization), with \u03a0 = 0 corresponding to an unpolar-\nized isotropic gravitational-wave background. We indi-\ncate by I, V the Stokes parameters and PR/L denote\n\n22\nthe right- and left-hand gravitational-wave power spec-\ntra.\nNote that allowing \u03a0 = 0 in Eqs. (44), (46) re-\nturns the formalism to one utilized in standard, isotropic\nsearches [19].\n1.\nModel-independent\nWe conduct a generic search for a parity-violating\ngravitational-wave background exhibiting power-law be-\nhavior, Eq. (2), with fref = 25 Hz. We use a log-uniform\namplitude prior from 10\u221213 and 10\u22125, while the model\nspectral index prior is a Gaussian distribution centered\nat 0 with a standard deviation of 3.5.\nWe search for\nthis model using the O1-O4a gravitational-wave data and\nplace upper limits on its parameters.\nWe investigate both a simplified model with constant\n\u03a0 and a model in which the polarization varies with fre-\nquency.\nIn the constant polarization case, we search\nuniformly for \u03a0 between -1 and 1.\nAdditionally, two\nsearches that fix \u03a0 = \u22121 and 1 are conducted to compare\nconstraints under maximal chiral assumptions. For the\nfrequency-dependent model, we use \u03a0(f) = \u00b1(f/1 Hz)\u03b2\nwith a uniform prior \u03b2 between -2 and 0. This is moti-\nvated from theoretical models where \u03a0 decays with in-\ncreasing frequency [345, 346].\nIn our analysis we only\nconsider frequencies larger than 1 Hz \u2013 at lower frequen-\ncies terrestrial detectors are limited by seismic noise \u2013\nand hence the form of \u03a0(f) guarantees that the physi-\ncally allowed bound |\u03a0| \u22641 is valid.\nParameter\nPrior\n\u2126PV\nref\nLogUniform[10\u221213, 10\u22125]\n\u03b1\nGaussian[0, 3.5]\n\u03a0\nUniform[\u22121, 1]\n\u03b2\nUniform[\u22122, 0]\nTABLE XI. Prior distribution for the model-independent\nparity-violation searches.\n2.\nEarly Universe Turbulence\nA parity-violating turbulent source during a phase\ntransition will produce circularly polarized gravitational\nwaves. Depending on the helicity strength, there are two\ntypes of turbulent gravitational-wave spectra [347, 348].\nWhen energy dissipation at small scales dominates, it\nleads to a helical Kolmogorov spectrum, and we consider\nthis type of polarization.\nParity violation at the electroweak scale can be re-\nalized in extensions of the Standard Model of particle\nphysics, manifesting as helical (or chiral) turbulent mo-\ntion [349, 350]. Circularly polarised gravitational waves\nare generated by parity-violating turbulent sources [351].\nTheir spectrum has a broken power-law spectrum with\na peak at the characteristic frequency of the source. We\nsearch gravitational-wave data for models [352\u2013354]\n\u2126Turbulence(f) =\n(\n\u2126peak(f/fpeak)\n,\nf \u2264fpeak\n\u2126peak(f/fpeak)\u22128/3\n,\nf > fpeak .\n(47)\nThe peak frequency fpeak is related to the temperature T\u2217\nat which the first-order phase transition takes place. At\nan energy scale of T\u2217\u223c108 GeV, the predicted chiral tur-\nbulence spectrum would exhibit a peak within the current\nLIGO-Virgo-KAGRA observational band. We therefore\nsearch for fpeak over a broad range (10 \u22122000)Hz.\nPrevious numerical studies calculated the net circular\npolarization of gravitational waves under various initial\nturbulent conditions, determining the degree of polariza-\ntion as a function of the wave number k. They identified\nmodels where \u03a0 depends on the frequency [345, 351]. We\nmodel the polarization as the power-law functional form\ndescribed previously.\nParameter\nPrior\n\u2126peak\nLogUniform[10\u221213, 10\u22125]\nfpeak/Hz\nUniform[5, 2000]\n\u03b2\nUniform[\u22122, 0]\nTABLE XII. Prior distribution for the turbulence parity-\nviolation searches.\n3.\nNon-Abelian Axion Inflation\nThe Chern-Simons interaction term sources exponen-\ntial production of gravitational waves through the in-\nduced linear couplings between metric and gauge field\ntensor perturbations, and is given in Eq.(29).\nThe total gravitational-wave spectrum includes the\nvacuum contribution\n\u2126Vacuum(k) = \u2126R,0\n12\u03c02\nH2\nM 2\nPl\n.\n(48)\nWe consider a piecewise linear model potential, given pre-\nviously in Eq.(31). The inflaton velocity, in the slow-roll\napproximation, is approximately constant\n\u03be =\n\u001a\n\u03beCMB = A+\u03b1f/2V0, for \u03d5 > \u03d50\n\u03be0 = A\u2212\u03b1f/2V0, for \u03d5 < \u03d50 ,\n(49)\nwhere CMB constraints set un upper bound of \u03beCMB <\n2.5 at 95% CL [355]. More studies for this model can be\nfound in [254].\nThe Chern-Simons term not only sources significant\nproduction of gravitational waves, the spin-2 fluctuation\nof the gauge field leads to an asymmetry between its left-\nand right-handed polarization states. Thus, the gauge\nfield can produce a chiral gravitational-wave signal within\nthe ground detectors\u2019 frequency band.\nIn [235], it was shown that the enhanced helicity is\nmodel-dependent, and relies on the inflaton VEV sign;\n\n23\nright-handed tensor modes corresponding to positive\nVEV, left-handed modes for negative VEV. For the toy\nmodel studied, the polarization can be well approximated\nas\n\u03a0 \u2243\n[\u00af\u03c1YM/\u00af\u03c1]G2\n+(mQ)\n[\u00af\u03c1YM/\u00af\u03c1]G2\n+(mQ) + 1 = const. > 0 ,\n(50)\nwhere \u00af\u03c1YM/\u00af\u03c1 \u2272\u03f52 for slow-roll parameter \u03f5, effective\nmass mQ is approximated as \u03be \u2243mQ + m\u22121\nQ\nand the\nexplicit functional form of Gs(mQ) is detailed in [235]. It\nis easy to show that \u03a0(f) \u22431 for \u03be0 \u22734 and \u00af\u03c1YM/\u00af\u03c1 \u2273\n5 \u00d7 10\u22125 over the ground detectors\u2019 frequency band.\nWe perform a search for parity-violating axion infla-\ntion, a model investigated in Sec. VI by introducing an\nadditional parameter for the polarization amplitude \u03a0\nwith a uniform prior range of [0, 1]. For the other pa-\nrameters, we use the same prior range as in Table. IV.\nNote that we impose a non-negative prior on the polar-\nization amplitude, as we expect \u03a0 \u22650 for the studied\ntoy model.\nParameter\nPrior\n\u2126ref\nLogUniform[10\u221213, 10\u22125]\nNCMB [efolds]\nUniform[50, 60]\nf0/Hz\nLogUniform[10\u22126, 10]\n\u03d5end/MPl\nUniform[0, 25]\nA+/M 3\nPl\nLogUniform[10\u221220, 10\u22126]\nA\u2212/M 3\nPl\nLogUniform[10\u221220, 10\u22126]\nV0/M 4\nPl\nLogUniform[10\u221220, 10\u22126]\n\u03b1f/M \u22121\nPl\nUniform[0, 250]\ng\nLogUniform[10\u22125, 1]\n\u03a0\nUniform[0, 1]\nTABLE XIII. Prior distribution for the SU(2) axion inflation\nparity-violation searches. Note: the same as the previously\nlisted prior table in Sec. VI, just with added \u03a0 prior.\nC.\nConstraints using O1-O4a LIGO-Virgo data\nWe present the results for the models where a search\nwas conducted. We find no evidence for parity-violation;\nconstraints on such models are set.\n1.\nModel-independent\nWe plot the results and the 65%, 95% confidence con-\ntours for the searched general models with an assumed\nCBC background in Figs. 16 and 17. Although no con-\nstraints can be placed on the parity-violating associated\nparameter, we set upper bounds on the background\u2019s\nstrength parameter \u2126PV\nref . We list the 95% upper bound\non \u2126PV\nref and \u2126ref, plus the logarithmic Bayes factor for\neach general search in Table XIV.\nFigure 18 displays the 68%, 95% confidence contours\nof the resulting \u2126PV\nref \u2212\u03b1 posteriors from an assumed\n10\n5\nlog10\nref\n10\n5\n0\n5\n10\n95%\n68%\n1.0\n0.5\n0.0\n0.5\n1.0\n95%\n68%\n12\n10\n8\n6\nlog10\nPV\nref\n12\n10\n8\n6\nlog10\nref\n95%\n68%\n95%\n95%\n68%\n68%\n10\n5\n0\n5\n10\n95%\n68%\n1.0\n0.5 0.0\n0.5\n1.0\n95%\n68%\nFIG. 16. Posterior distributions for a power-law gravitational-\nwave background model with \u03a0(f) = const., assuming an\noverlaying CBC background.\n10\n5\nlog10\nref\n10\n5\n0\n5\n10\n95%\n95%\n2.0\n1.5\n1.0\n0.5\n0.0\n95%\n68%\n95%\n68%\n12\n10\n8\n6\nlog10\nPV\nref\n12\n10\n8\n6\nlog10\nref\n95%\n68%\n5%\n68%\n95%\n95%\n95%\n10\n5\n0\n5\n10\n95%\n95%\n2.0\n1.5\n1.0\n0.5 0.0\n95%\n8%\n95%\n68%\nFIG. 17. Posterior distributions for a power-law gravitational-\nwave background model with \u03a0(f) = \u00b1(f/Hz)\u03b2 (positive\npower-law in red, negative in purple) assuming an overlay-\ning CBC background.\n\n24\nPV model\n95% upper bound of \u2126PV\nref 95% upper bound of \u2126ref ln BPV Model+CBC\nnoise\n\u03a0 = const.\n2.54 \u00d7 10\u22129\n2.61 \u00d7 10\u22129\n\u22121.175 \u00b1 0.047\n\u03a0 = +(f/Hz)\u03b2\n2.41 \u00d7 10\u22129\n2.95 \u00d7 10\u22129\n\u22121.222 \u00b1 0.043\n\u03a0 = \u2212(f/Hz)\u03b2\n2.76 \u00d7 10\u22129\n2.46 \u00d7 10\u22129\n\u22121.203 \u00b1 0.044\nTABLE XIV. General parity-violating model search results with an assumed overlaying CBC background\n.\n3\n2\n1\n0\n1\n2\n3\n12\n11\n10\n9\n8\n7\nlog10\nPV\nref\n95%\n68%\n95%\n68%\nFIG. 18. \u2126PV\nref \u2212\u03b1 confidence curve at 95% (solid) and 68%\n(dashed) level for assumed \u03a0 = 1 (red) and \u03a0 = \u22121 (blue)\npolarization.\n\u03a0 = \u00b11 polarization. One can see that more stringent\nconstraints can be made for an assumed entirely right-\nhanded polarization (2.82 \u00d7 10\u22129 < \u2126PV,95%\nref\n, red) than\nfor a left-handed polarization (2.94 \u00d7 10\u22129 < \u2126PV,95%\nref\n,\nblue); this was also found using the O3 data [356]. This\npreference can be explained by the ratio between the\nstandard and parity-violating associated overlap reduc-\ntion functions \u03c2d1d2 \u2261\u03b3d1d2\nV\n/\u03b3d1d2\nI\n. While \u03c2HV and \u03c2LV\nare roughly periodic in the considered frequency range,\n\u03c2HL is preferentially positive. Preferentially positive \u03c2HL\ncombined with \u03a0 > 0 results in enhanced modified \u2126GW\n(Eq. (46)), hence leading to stricter constraints on right-\nhand polarized signals.\nA general power-law search assuming no parity-\nviolation (\u03a0 = 0) yields a logarithmic Bayes factor of\nln B\u03a0=0+CBC\nnoise\n= \u22121.194 \u00b1 0.042.\nIn combination with\nTable XIV, we find no statistical preference between po-\nlarized (\u03a0 \u0338= 0) and non-polarized (\u03a0 = 0) power-law\nmodels.\n2.\nEarly Universe Turbulence\nWe plot the resulting constraints from a parity-\nviolating turbulence with overlaying CBC model search\nin Fig. 19.\nWe calculate a log Bayes factor of\nlog BTurb+CBC\nnoise\n= \u22120.830 \u00b1 0.035, indicating no evidence\nfor a chiral turbulent background.\nNo constraints on\n10\n5\nlog10\nref\n800\n1600\nfbreak\n95%\n68%\n2.0\n1.5\n1.0\n0.5\n0.0\n5%\n68%\n12\n10\n8\n6\nlog10\nPV\nref\n12\n10\n8\n6\nlog10\nref\n95%\n68%\n68%\n800\n1600\nfbreak\n95%\n68%\n2.0\n1.5\n1.0\n0.5 0.0\n95%\n68%\nFIG. 19.\nPosterior distributions for early Universe turbu-\nlence with an overlaying CBC background model with \u03a0(f) =\n(f/Hz)\u03b2.\nparity-violating parameter \u03b2 could be made. We find the\n95% upper bound of the gravitational-wave background\nstrength to be \u2126peak < 5.39 \u00d7 10\u22128 - larger compared\nto power-law background model constraints due to the\nallowed broken power-law spectra being able to peak at\nfrequencies with poor sensitivity.\n3.\nNon-Abelian Axion Inflation\nWe find a log Bayes factor of log BPV SU(2)+CBC\nnoise\n=\n\u22120.545 \u00b1 0.029, and thus no evidence of such a model\nnor a preference for a polarized model over a non-chiral\nmodel.\nWe list the 95% confidence limits on both\nsearched models in Table XV, and there do not appear\nto be large discrepancies in the parameter estimation be-\ntween the searched models.\nIn Fig. 20, we show the\n2D posterior \u03be0 \u2212HCMB results.\nSimilarly, there are\nsmall differences between the searched models, highlight-\ning the lack of statistical preference between chiral and\n\n25\nParameter\n\u03a0 = 0\n\u03a0 \u0338= 0\ng\n0.411\n0.385\nV0/M 4\nPl\n4.41 \u00d7 10\u22129\n3.47 \u00d7 10\u22129\nA+/M 3\nPl\n2.77 \u00d7 10\u221212 1.62 \u00d7 10\u221212\nA\u2212/M 3\nPl\n2.01 \u00d7 10\u221210 2.55 \u00d7 10\u221210\n\u03be0\n5.936\n5.843\nHCMB/MPl 4.18 \u00d7 10\u22125\n3.94 \u00d7 10\u22125\n\u2126ref\n2.48 \u00d7 10\u22129\n2.80 \u00d7 10\u22129\nTABLE XV. Parameter estimation 95% confidence upper\nbound for the searched chiral and non-chiral models.\n5\n4\n3\n2\n1\n0\nlog10 g\n2\n3\n4\n5\n6\n7\n\u03be0\n\u22651\nAbelian Regime\n\u03a0 = 0\n\u03a0\n0\nFIG. 20. Parameter estimation 95% confidence limit contours\nfor the SU(2) gauge field model. The blue and orange curves\nshow the 95% confidence limit contours for chiral (\u03a0 \u0338= 0) and\nnon-chiral (\u03a0 = 0) searches.\nnon-chiral models. It is important to highlight that these\nresults do not exclude other parity-violating models of\naxion inflation based on other scalar potential models.\nX.\nCONCLUSIONS\nThe LIGO-Virgo-KAGRA collaboration uses the O4a\ndata from LIGO Hanford and LIGO Livingston to search\nfor a gravitational-wave background signal, in addition to\nthe data from LIGO-Virgo from O1, O2 and O3. In this\npublication we report the results of dedicated searches\nof various particle physics models and cosmological sce-\nnarios which could contribute to the gravitational-wave\nbackground. These are first-order phase transitions, cos-\nmic strings, domain walls, stiff equation of state, axion\ninflation, second-order scalar perturbations, primordial\nblack holes, and parity violation. They can all lead to a\ngravitational-wave background potentially detectable by\nthe LIGO-Virgo-KAGRA network.\nFirst-order phase transitions could have occurred\nwithin the first one-trillionth of a second after the Big\nBang, and their gravitational-wave imprints would be\nan important key to determining the correct theory be-\nyond the Standard Model. They could generate gravi-\ntational waves from processes such as bubble collisions,\nsound waves propagating in the early Universe plasma,\nand magnetohydrodynamic turbulence.\nWe place new\nconstraints on the strength, temperature and duration of\nthese transitions.\nCosmic strings are one-dimensional topological defects\nthat can be generated after phase transitions followed by\nspontaneously symmetry breaking. Cosmic string loops\noscillate because of their tension and shrink as a result\nof the emission of gravitational waves. We constrain the\nstring tension, a parameter related to the temperature of\nthe symmetry breaking. In particular, we exclude cosmic\nstrings with a tension greater than O(10\u221215).\nDomain walls are two-dimensional topological defects.\nOur analysis constrains the domain wall tension, and the\ntemperature at which they collapse, resulting in their an-\nnihilation, to avoid domain wall dominance in the Uni-\nverse. For sufficiently large domain wall tension, we rule\nout 107GeV < Tann < 109GeV.\nHigh energy physics can motivate a cosmological model\nwith a stiff equation of state (1/3 \u2264ws \u22641). We derive\n95% CL upper limits on some of the parameters charac-\nterizing this unconventional cosmology.\nGravitational waves offer a novel tool to test infla-\ntionary models and constrain their parameters. While\nsingle-field slow-roll inflation within the \u039bCDM cosmo-\nlogical model predicts a gravitational-wave background\nthat is too weak to be observed with current detec-\ntors, other inflationary models may produce a detectable\ngravitational-wave background. We consider an axion in-\nflation model, where a pseudo-scalar axion is coupled to\na gauge field and we impose constraints on the gauge\ncoupling and the inflaton velocity.\nThe scalar-induced gravitational-wave background,\narising from large-amplitude primordial curvature per-\nturbations, provides an observational test for probing\ndirectly the epoch of inflation. In scenarios where pri-\nmordial curvature fluctuations are amplified during in-\nflation, primordial black holes form through the collapse\nof extremely dense regions shortly after the correspond-\ning modes enter the Hubble radius. We impose an up-\nper bound on a gravitational-wave background, lead-\ning to constraints on primordial curvature perturbations,\nstronger than the one imposed by Big Bang Nucleosyn-\nthesis and Cosmic Microwave Background at a scale of\n\u223c1017Mpc.\nSeveral mechanisms have been proposed for the for-\nmation of primordial black holes. Just like astrophysi-\n\n26\ncal black holes, primordial black holes can form binaries\nand emit gravitational waves.\nA key factor determin-\ning the merger rate is the number density of primordial\nblack holes, typically quantified by fPBH, the fraction of\ndark matter composed of primordial black holes today.\nWe find 95% UL constraints on fPBH as a function of\nthe primordial black hole mass.\nIn particular, we set\nfPBH < 10\u22122 for primordial black holes with masses in\nthe range (1 \u2212100)M\u2299.\nSeveral string-theory models and scalar-tensor models\nof gravity can result in circularly polarized gravitational\nwaves. We study a generic parity-violation search based\non a power-law energy density gravitational-wave spec-\ntrum, then detail more theoretically motivated polarized\ngravitational-wave background models of early Universe\nturbulence and axion inflation.\nWe impose new con-\nstraints on parity violation parameters.\nIn\nsearching\nfor\na\ncosmologically\nproduced\ngravitational-wave background,\nwe also account for\nthe presence of an astrophysical CBC background,\ncomposed of black holes and neutron stars.\nThis is\na background that LIGO\u2013Virgo\u2013KAGRA will likely\ndetect before the cosmological background [15].\nFor\nthe current generation of ground-based detectors, it\nwill be challenging to separate astrophysical and cos-\nmological contributions [357, 358].\nVarious methods\nhave been proposed for signal separation with future\ndetectors [359\u2013363], such as the Einstein Telescope [364]\nand the Cosmic Explorer [365].\nNo gravitational-wave background signal has been de-\ntected for any of the cosmological and high energy physics\nmodels considered here, leading to constraints on their\nparameters. No CBC produced gravitational-wave back-\nground has been detected either. Nevertheless, our anal-\nyses demonstrate that the LIGO-Virgo data can already\nbe used to derive new constraints on a variety of beyond\nthe Standard Model theories, thereby enabling the test-\ning of early Universe scenarios and particle physics mod-\nels at energy scales otherwise inaccessible. We expect the\nconstraints presented in this publication to be useful for\nparticle physics and cosmological model building.\nThe LIGO\u2013Virgo\u2013KAGRA collaboration will continue\nto improve gravitational-wave background limits using\ndata from the remainder of O4, with updated results to\nfollow its completion. Although the sensitivity changes\nacross O4a, O4b, and O4c are modest, the extended ob-\nserving time will improve the sensitivity to the energy\ndensity of the gravitational-wave background. The sub-\nsequent O5 run will push these limits even further, deep-\nening their impact on cosmology and high-energy physics.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO con-\nsortium.\nThe authors also gratefully acknowledge re-\nsearch support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India,\nthe Department of Science and Technology, India, the\nScience & Engineering Research Board (SERB), India,\nthe Ministry of Human Resource Development, India,\nthe Spanish Agencia Estatal de Investigaci\u00b4on (AEI), the\nSpanish Ministerio de Ciencia, Innovaci\u00b4on y Universi-\ndades, the European Union NextGenerationEU/PRTR\n(PRTR-C17.I1), the ICSC - CentroNazionale di Ricerca\nin High Performance Computing, Big Data and Quantum\nComputing, funded by the European Union NextGener-\nationEU, the Comunitat Auton`oma de les Illes Balears\nthrough the Conselleria d\u2019Educaci\u00b4o i Universitats, the\nConselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat\nDigital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish\nNational Agency for Academic Exchange, the National\nScience Centre of Poland and the European Union - Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scot-\ntish Universities Physics Alliance, the Hungarian Scien-\ntific Research Fund (OTKA), the French Lyon Institute\nof Origins (LIO), the Belgian Fonds de la Recherche Sci-\nentifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of\nScience, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute\nfor Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Sci-\nence Foundation of China (NSFC), the Israel Science\nFoundation (ISF), the US-Israel Binational Science Fund\n(BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC),\nTaiwan, the United States Department of Energy, and\n\n27\nthe Kavli Foundation. The authors gratefully acknowl-\nedge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources.\nThis work was supported by MEXT, the JSPS\nLeading-edge Research Infrastructure Program, JSPS\nGrant-in-Aid for Specially Promoted Research 26000005,\nJSPS Grant-in-Aid for Scientific Research on Inno-\nvative Areas 2402:\n24103006, 24103005, and 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-\nto-Core Program A. Advanced Research Networks, JSPS\nGrants-in-Aid for Scientific Research (S) 17H06133 and\n20H05639, JSPS Grant-in-Aid for Transformative Re-\nsearch Areas (A) 20A203:\nJP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nUniversity of Tokyo, the National Research Foundation\n(NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineering\nCenter of KEK.\n[1] J. Aasi et al. (LIGO Scientific), Class. Quant. Grav. 32,\n074001 (2015), arXiv:1411.4547 [gr-qc].\n[2] F. Acernese et al. (VIRGO), Class. Quant. 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Al-Kershi,8, 9 C. All\u00b4en\u00b4e,31 A. Allocca\n,32, 4\nS. Al-Shammari,33 P. A. Altin\n,34 S. Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37\nF. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41\nM. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9 J. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49\nS. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11 S. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42\nM. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,55\nN. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 G. Ashton\n,58 Y. Aso\n,25, 59 L. Asprea,28 M. Assiduo,60, 61\nS. Assis de Souza Melo,62 S. M. Aston,63 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,64 K. AultONeal\n,65\nG. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51\nM. Ball,77 G. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12\nP. Baral\n,10 M. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11 D. Bersanetti\n,29\nT. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101 N. Bevins\n,102\nR. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46 V. Biancalana\n,101\nA. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75 C. Binu,110 S. Biot,111\nO. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113 S. Blaber,114\nJ. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 S. Blasi\n,115 N. Bode\n,8, 9 N. Boettner,97\nG. Boileau\n,113 M. Boldrini\n,38 G. N. Bolingbroke\n,116 A. Bolliand,117, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82\nF. Bondu\n,118 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,119 R. Bonnand\n,31, 117 A. Borchers,8, 9 S. Borhanian,7\nV. Boschi\n,80 S. Bose,120 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 T. D. Boybeyi\n,18\nM. Boyle,121 A. Bozzi,62 C. Bradaschia,80 P. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104\nT. Briant\n,122 A. Brillet,113 M. Brinkmann,8, 9 P. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46\nD. D. Brown,116 M. L. Brozzetti\n,76, 51 S. Brunett,11 G. Bruno,15 R. Bruntz\n,123 J. Bryant,119 Y. Bu,124\nF. Bucci\n,61 J. Buchanan,123 O. Bulashenko\n,82, 83 T. Bulik,125 H. J. Bulten,37 A. Buonanno\n,126, 1 K. Burtnyk,2\nR. Buscicchio\n,127, 128 D. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15\nV. C\u00b4aceres-Barbosa\n,7 L. Cadonati\n,57 G. Cagnoli\n,129 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,130\nE. Calloni,32, 4 S. R. Callos\n,77, 29 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,131\nE. Capocasa\n,20 E. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 132 F. Carbognani,62 M. Carlassara,8, 9\nJ. B. Carlin\n,124 T. K. Carlson,133 M. F. Carney,104 M. Carpinelli\n,127, 62 G. Carrillo,77 J. J. Carter\n,8, 9\nG. Carullo\n,119, 134 A. Casallas-Lagos,135 J. Casanueva Diaz\n,62 C. Casentini\n,136, 22 S. Y. Castro-Lucas,137\nS. Caudill,133 M. Cavagli`a\n,105 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,138, 139\nE. Cesarini\n,22 N. Chabbra,34 W. Chaibi,113 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103\nS. Chalathadka Subrahmanya\n,97 J. C. L. Chan\n,140 M. Chan,114 K. Chang,141 S. Chao\n,142, 141\nP. Charlton\n,143 E. Chassande-Mottin\n,20 C. Chatterjee\n,144 Debarati Chatterjee\n,79 Deep Chatterjee\n,35\nM. Chaturvedi,103 S. Chaty\n,20 A. Chen\n,145 A. H.-Y. Chen,146 D. Chen\n,147 H. Chen,142 H. Y. Chen\n,148\nS. Chen,144 Yanbei Chen,149 Yitian Chen\n,121 H. P. Cheng,150 P. Chessa\n,76, 51 H. T. Cheung\n,90\nS. Y. Cheung,6 F. Chiadini\n,151, 132 G. Chiarini,8, 9, 92 A. Chiba,152 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80\nA. Chiummo\n,4, 62 C. Chou,146 S. Choudhary\n,72 N. Christensen\n,113, 153 S. S. Y. Chua\n,34 G. Ciani\n,74, 75\nP. Ciecielag\n,95 M. Cie\u00b4slar\n,125 M. Cifaldi\n,22 B. Cirok,154 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6\nP. Clearwater,155 S. Clesse,111 F. Cleva,113, 117 E. Coccia,44, 45, 43 E. Codazzo\n,156, 157 P.-F. Cohadon\n,122\nS. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98 C. G. Collette,158 J. Collins,63 S. Colloms\n,86 A. Colombo\n,159, 128\nC. M. Compton,2 G. Connolly,77 L. Conti\n,92 T. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,160 S. Corezzi\n,76, 51\nN. J. Cornish\n,161 I. Coronado,162 A. Corsi\n,163 R. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38\nP. Couvares\n,11, 57 D. M. Coward,72 R. Coyne\n,164 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,165\n\n35\nP. Cremonese\n,98 S. Crook,63 R. Crouch,2 J. Csizmazia,2 J. R. Cudell\n,166 T. J. Cullen\n,11 A. Cumming\n,86\nE. Cuoco\n,167, 168 M. Cusinato\n,138 L. V. Da Concei\u00b8c\u02dcao\n,169 T. Dal Canton\n,41 S. Dal Pra\n,170\nG. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,123\nL. P. Dartez\n,63 R. Das,106 A. Dasgupta,93 V. Dattilo\n,62 A. Daumas,20 N. Davari,171, 172 I. Dave,103\nA. Davenport,137 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72 M. C. Davis\n,18 P. Davis\n,173, 174\nE. J. Daw\n,175 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,176 M. De Laurentis\n,32, 4\nF. De Lillo\n,23 S. Della Torre\n,128 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,177, 61\nF. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,178 A. Depasse\n,15 N. DePergola,102 R. De Pietri\n,179, 180\nR. De Rosa\n,32, 4 C. De Rossi\n,62 M. Desai\n,35 R. DeSalvo\n,181 A. DeSimone,182 R. De Simone,151, 132\nA. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,165 M. Di Cesare\n,32, 4 G. Dideron,183 T. Dietrich\n,1 L. Di Fiore,4\nC. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 184 S. Di Pace\n,39, 38\nI. Di Palma\n,39, 38 D. Di Piero,185, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,119 J. P. Docherty,86\nZ. Doctor\n,96 N. Doerksen\n,169 E. Dohmen,2 A. Doke,133 A. Domiciano De Souza,186 L. D\u2019Onofrio\n,38\nF. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,187 W. J. D. Doyle,123 M. Drago\n,39, 38\nJ. C. Driggers\n,2 L. Dunn\n,124 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,171, 156 P. Dutta Roy\n,46\nH. Duval\n,115 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,188, 31 T. Eckhardt\n,97 G. Eddolls\n,78 A. Effler\n,63\nJ. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25 M. Emma\n,58 K. Endo,152 R. Enficiaud\n,1 L. Errico\n,32, 4\nR. Espinosa,165 M. Esposito\n,4, 32 R. C. Essick\n,189 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,183\nB. E. Ewing,7 J. M. Ezquiaga\n,140 F. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,130\nB. Farr\n,77 W. M. Farr\n,190, 191 G. Favaro\n,91 M. Favata\n,192 M. Fays\n,166 M. Fazio\n,55 J. Feicht,11\nM. M. Fejer,89 R. Felicetti\n,185, 48 E. Fenyvesi\n,87, 193 J. Fernandes,194 T. Fernandes\n,195, 138 D. Fernando,110\nS. Ferraiuolo\n,196, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81 I. Fiori\n,62\nM. Fishbach\n,189 R. P. Fisher,123 R. Fittipaldi\n,197, 132 V. Fiumara\n,198, 132 R. Flaminio,31 S. M. Fleischer\n,199\nL. S. Fleming,200 E. Floden,18 H. Fong,114 J. A. Font\n,138, 139 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal\n,201\nK. Franceschetti,179 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,202 A. Freise\n,37, 107\nO. Freitas\n,195, 138 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,203 T. Fujimori,204 T. Fujita\n,205 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71\nJ. R. Gair\n,1 S. Galaudage\n,186 V. Galdi,206 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,181 D. Ganapathy\n,207\nA. Ganguly\n,79 B. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,208 C. Garc\u00b4\u0131a-Quir\u00b4os\n,188 J. W. Gardner\n,34\nK. A. Gardner,114 S. Garg,42 J. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89\nC. Gasbarra\n,21, 22 B. Gateley,2 F. Gautier\n,209 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29 A. Gennai\n,80\nV. Gennari\n,100 J. George,103 R. George\n,148 O. Gerberding\n,97 L. Gergely\n,154 Archisman Ghosh\n,94\nSayantan Ghosh,194 Shaon Ghosh\n,192 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,210 Tathagata Ghosh\n,79\nJ. A. Giaime\n,12, 63 K. D. Giardina,63 D. R. Gibson,200 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11\nF. Glotin\n,41 J. Godfrey,77 R. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11\nS. Gomez Lopez\n,39, 38 B. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,211 S. Goode,6 A. W. Goodwin-Jones\n,15\nM. Gosselin,62 R. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86\nA. E. Granados\n,18 M. Granata\n,176 V. Granata\n,212, 132 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2\nR. Gray\n,86 G. Greco,51 A. C. Green\n,37, 107 L. Green,213 S. M. Green,73 S. R. Green\n,214 C. Greenberg,133\nA. M. Gretarsson,65 H. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33\nS. Grunewald\n,1 D. Guerra\n,138 D. Guetta\n,215 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93\nF. Gulminelli\n,173, 174 H. Guo\n,145 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,216 I. Gupta\n,7 N. C. Gupta,93\nS. K. Gupta,46 V. Gupta\n,18 N. Gupte,1 J. Gurs,97 N. Gutierrez,176 N. Guttman,6 F. Guzman\n,131 D. Haba,217\nM. Haberland\n,1 S. Haino,218 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2\nC. Hanna\n,7 M. D. Hannam,33 O. A. Hannuksela\n,219 A. G. Hanselman\n,130 H. Hansen,2 J. Hanson,63\nS. Hanumasagar,57 R. Harada,42 A. R. Hardison,182 S. Harikumar\n,187 K. Haris,37, 71 I. Harley-Trochimczyk,131\nT. Harmark\n,134 J. Harms\n,44, 45 G. M. Harry\n,220 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 221, 222\nC. J. Haster\n,213 K. Haughian\n,86 H. Hayakawa,50 K. Hayama,223 M. C. Heintze,63 J. Heinze\n,119 J. Heinzel,35\nH. Heitmann\n,113 F. Hellman\n,207 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,116\nM. Hendry\n,86 I. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,224, 225 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,226 N. Hirata,25 C. Hirose,227\nD. Hofman,176 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,175 D. E. Holz\n,130 L. Honet,111\nD. J. Horton-Bailey,207 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,144 E. J. Howell\n,72 C. G. Hoy\n,73\n\n36\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,142 H.-Y. Hsieh,142 C. Hsiung,228 S.-H. Hsu,146 W.-F. Hsu\n,109\nQ. Hu\n,86 H. Y. Huang\n,141 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,229 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,132 J. Iascau,77\nK. Ide,230 R. Iden,217 A. Ierardi,44, 45 S. Ikeda,147 H. Imafuku,42 Y. Inoue,141 G. Iorio\n,91 P. Iosif\n,185, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,230 M. Isi\n,190, 191 K. S. Isleif\n,231 Y. Itoh\n,204, 232 M. Iwaya,203\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,122 T. Jacquot,41 S. J. Jadhav,233 S. P. Jadhav\n,155 M. Jain,133\nT. Jain,224 A. L. James\n,11 K. Jani\n,144 J. Janquart\n,15 N. N. Janthalur,233 S. Jaraba\n,234 P. Jaranowski\n,235\nR. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,150 H.-B. Jin\n,236, 237 G. R. Johns,123\nN. A. Johnson,46 M. C. Johnston\n,213 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,210 R. Jones,86\nH. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,238 L. Ju\n,72 K. Jung\n,239 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,240 I. Kaku,204 V. Kalogera\n,96 M. Kalomenopoulos\n,213\nM. Kamiizumi\n,50 N. Kanda\n,232, 204 S. Kandhasamy\n,79 G. Kang\n,241 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,133 M. Kasprzack\n,11 H. Kato,152\nT. Kato,203 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,204 D. Keitel\n,98\nL. J. Kemperman\n,116 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,242 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,163 M. Khursheed,103\nN. M. Khusid,190, 191 W. Kiendrebeogo\n,113, 243 N. Kijbunchoo\n,116 C. Kim,244 J. C. Kim,245 K. Kim\n,246\nM. H. Kim\n,238 S. Kim\n,247 Y.-M. Kim\n,246 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,203 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,248, 249 K. Kokeyama\n,33, 250 S. Koley\n,44, 166 P. Kolitsidou\n,119 A. E. Koloniari\n,251\nK. Komori\n,42 A. K. H. Kong\n,142 A. Kontos\n,252 L. M. Koponen,119 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,152 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,119 S. Kroker,253 A. Kr\u00b4olak\n,254, 187 K. Kruska,8, 9 J. Kubisz\n,255 G. Kuehn,8, 9\nS. Kulkarni\n,216 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,233 Praveen Kumar\n,178\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,256, 257, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,208, 258 S. Kuwahara\n,42 K. Kwak\n,239 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,188, 100\nA. H. Laity,164 E. Lalande,259 M. Lalleman\n,23 P. C. Lalremruati,260 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,148 R. Langgin\n,213 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,199 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,165 M. Laxen\n,63 C. Lazarte\n,138 A. Lazzarini\n,11 C. Lazzaro,157, 156 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,261 H. W. Lee\n,262 J. Lee,78 K. Lee\n,238 R.-K. Lee\n,142 R. Lee,35\nSungho Lee\n,246 Sunjae Lee,238 Y. Lee,141 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,183 M. Le Jean\n,176, 117\nA. Lema\u02c6\u0131tre\n,263 M. Lenti\n,61, 177 M. Leonardi\n,74, 75, 264 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,265 T. G. F. Li,109 X. Li\n,149\nY. Li,96 Z. Li,86 A. Lihos,123 E. T. Lin\n,142 F. Lin,141 L. C.-C. Lin\n,265 Y.-C. Lin\n,142 C. Lindsay,200\nS. D. Linker,181 A. Liu\n,219 G. C. Liu\n,228 Jian Liu\n,72 F. Llamas Villarreal,165 J. Llobera-Querol\n,98\nR. K. L. Lo\n,140 J.-P. Locquet,109 S. C. G. Loggins,266 M. R. Loizou,133 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,166 M. Lopez Portilla,71 A. Lorenzo-Medina\n,178 V. Loriette,41 M. Lormand,63 G. Losurdo\n,267, 80\nE. Lotti,133 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,124 N. Lu\n,34\nL. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,268, 269 A. W. Lussier\n,259 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,152 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,164\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,189\nS. Maliakal,11 A. Malik,103 L. Mallick\n,169, 189 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,171, 156 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 270\nC. Marinelli\n,101 F. Marion\n,31 A. Mariotti\n,115 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100\nF. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,192 B. B. Martinez,131 D. A. Martinez,54 M. Martinez,43, 271\nV. Martinez\n,129 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,119 E. J. Marx,35 L. Massaro,36, 37\nA. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,209\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,123 C. McElhenny,123 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,144\nJ. McIver\n,114 A. McLeod\n,72 I. McMahon\n,188 T. McRae,34 R. McTeague\n,86 D. Meacher\n,10 B. N. Meagher,78\nR. Mechum,110 Q. Meijer,71 A. Melatos,124 C. S. Menoni\n,137 F. Mera,2 R. A. Mercer\n,10 L. Mereni,176\nK. Merfeld,163 E. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10 B. Mestichelli,44\n\n37\nM. Meyer-Conde\n,272 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,273 C. Michel\n,176\nY. Michimura\n,42 H. Middleton\n,119 D. P. Mihaylov\n,104 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,185, 48\nV. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43 L. Mirasola\n,156, 157 M. Miravet-Ten\u00b4es\n,138\nC.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46 A. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79\nV. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35\nL. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,207 M. Mondin,181 M. Montani,60, 61\nC. J. Moore,224 D. Moraru,2 A. More\n,79 S. More\n,79 C. Moreno\n,135 E. A. Moreno\n,35 G. Moreno,2\nA. Moreso Serra,82 S. Morisaki\n,42, 203 Y. Moriwaki\n,152 G. Morras\n,208 A. Moscatello\n,91 M. Mould\n,35\nB. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,177, 61 F. Muciaccia\n,39, 38 D. Mukherjee\n,119\nSamanwaya Mukherjee,24 Soma Mukherjee,165 Subroto Mukherjee,93 Suvodip Mukherjee\n,13 N. Mukund\n,35\nA. Mullavey,63 H. Mullock,114 J. Mundi,220 C. L. Mungioli,72 M. Murakoshi,230 P. G. Murray\n,86 D. Nabari\n,74, 75\nS. L. Nadji,8, 9 A. Nagar,28, 274 N. Nagarajan\n,86 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,275 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,62 P. Narayan\n,216 I. Nardecchia\n,22 T. Narikawa,203\nH. Narola,71 L. Naticchioni\n,38 R. K. Nayak\n,260 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,131\nT. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen Quynh\n,276 S. A. Nichols,12 A. B. Nielsen\n,277\nY. Nishino,25, 42 A. Nishizawa\n,278 S. Nissanke,279, 37 W. Niu\n,7 F. Nocera,62 J. Noller,280 M. Norman,33\nC. North,33 J. Novak\n,117, 234, 281 R. Nowicki\n,144 J. F. Nu\u02dcno Siles\n,208 L. K. Nuttall\n,73 K. Obayashi,230\nJ. Oberling\n,2 J. O\u2019Dell,229 E. Oelker\n,35 M. Oertel\n,234, 117, 282, 281 G. Oganesyan,44, 45 T. O\u2019Hanlon,63\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,117, 282, 281 R. Omer,18 B. O\u2019Neal,123 M. Onishi,152 K. Oohara\n,283\nB. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110 S. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11\nI. Ota\n,12 D. J. Ottaway\n,116 A. Ouzriat,56 H. Overmier,63 B. J. Owen\n,284 R. Ozaki,230 A. E. Pace\n,7\nR. Pagano\n,12 M. A. Page\n,25 A. Pai\n,194 L. Paiella,44 A. Pal,285 S. Pal\n,260 M. A. Palaia\n,80, 81\nM. P\u00b4alfi,202 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,142 J. Pan,72 K. C. Pan\n,142\nP. K. Panda,233 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38 K. A. Pannone,54\nB. C. Pant,103 F. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 286 A. Papadopoulos\n,86\nE. E. Papalexakis,211 L. Papalini\n,80, 81 G. Papigkiotis\n,251 A. Paquis,41 A. Parisi\n,76, 51 B.-J. Park,246\nJ. Park\n,287 W. Parker\n,63 G. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80\nL. Passenger,6 D. Passuello,80 O. Patane\n,2 A. V. Patel\n,141 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80\nB. G. Patterson,33 K. Paul\n,106 S. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna\nArellano\n,288 X. Peng,119 Y. Peng,57 S. Penn\n,289 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,133\nC. P\u00b4erigois\n,290, 92, 91 G. Perna\n,91 A. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107\nD. Pesios,251 S. Peters,166 S. Petracca,206 C. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18\nK. S. Phukon\n,119 H. Phurailatpam,219 M. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113\nM. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,291, 132 M. Pietrzak,95\nM. Pillas\n,166 F. Pilo\n,80 L. Pinard\n,176 I. M. Pinto\n,291, 132, 292, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10\nM. Pirello,2 M. D. Pitkin\n,224, 86 A. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,212, 22\nC. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35 J. Pomper,80, 81 L. Pompili\n,1 J. Poon,219 E. Porcelli,37\nE. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62 J. Powell\n,155 G. S. Prabhu,79 M. Pracchia\n,166\nB. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93 K. Prasai\n,293 R. Prasanna,233 P. Prasia,79 G. Pratten\n,119\nG. Principe\n,185, 48 G. A. Prodi\n,74, 75 P. Prosperi,80 P. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1\nJ. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,164 H. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,174, 117 V. Quetschke,165\nP. J. Quinonez,65 N. Qutob,57 R. Rading,231 I. Rainho,138 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110\nK. E. Ramirez\n,63 F. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,165 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57\nK. Ransom,63 P. Rapagnani\n,39, 38 A. Rase\n,115 B. Ratto,65 A. Ravichandran,133 A. Ray\n,96 V. Raymond\n,33\nM. Razzano\n,81, 80 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini\n,127, 11\nB. Revenu\n,294, 41 A. Revilla Pe\u02dcna,82 R. Reyes,181 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,211 M. L. Richardson,116 A. Rijal,65 K. Riles\n,90 H. K. Riley,33\nS. Rinaldi\n,270 J. Rittmeyer,97 C. Robertson,229 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,295 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,224 J. H. Romie,63\nS. Ronchini\n,7 T. J. Roocke\n,116 L. Rosa,4, 32 T. J. Rosauer,211 C. A. Rose,57 D. Rosi\u00b4nska\n,125 M. P. Ross\n,53\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,190, 191 S. Roy\n,15 D. Rozza\n,127, 128 P. Ruggi,62 N. Ruhama,239\nE. Ruiz Morales\n,296, 208 K. Ruiz-Rocha,144 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,169\nM. R. Sah\n,13 S. Saha\n,142 T. Sainrat\n,64 S. Sajith Menon\n,215, 39, 38 K. Sakai,297 Y. Sakai\n,272\n\n38\nM. Sakellariadou\n,67 S. Sakon\n,7 O. S. Salafia\n,159, 128, 127 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,148\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,79 S. Salvador\n,174, 173 A. Salvarese,148 A. Samajdar\n,71, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,138 J. R. Sanders,182 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,251 P. Sassi\n,51, 76\nB. Sassolas\n,176 B. S. Sathyaprakash\n,7, 33 R. Sato,227 S. Sato,152 Yukino Sato,152 Yu Sato,152 O. Sauter\n,46\nR. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,79 S. Sayah,176 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,149\nA. Schiebelbein,189 M. G. Schiworski\n,78 P. Schmidt\n,119 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9\nR. M. S. Schofield,77 K. Schouteden\n,109 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,298 M. Scialpi\n,299\nJ. Scott\n,86 S. M. Scott\n,34 R. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,300\nD. Sellers,63 N. Sembo,204 A. S. Sengupta\n,301 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38\nA. Sevrin,115 T. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,261 L. Shao\n,302 A. K. Sharma\n,98 Preeti Sharma,12\nPrianka Sharma,103 Ritwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,126 N. S. Shcheblanov\n,303, 263\nE. Sheridan,144 Z.-H. Shi,142 M. Shikauchi,42 R. Shimomura,304 H. Shinkai\n,304 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,148 R. W. Short,2 S. ShyamSundar,103 A. Sider,158 H. Siegel\n,190, 191 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 170 M. Simmonds,116 L. P. Singer\n,305 Amitesh Singh,216 Anika Singh,11\nD. Singh\n,207 N. Singh\n,98 S. Singh,217, 59 A. M. Sintes\n,98 V. Sipala,171, 156 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,199 T. J. Slaven-Blair,72 J. Smetana,119 J. R. Smith\n,54 L. Smith\n,86, 185, 48 R. J. E. Smith\n,6\nW. J. Smith\n,144 S. Soares de Albuquerque Filho,60 M. Soares-Santos,188 K. Somiya\n,217 I. Song\n,142 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,306 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,123 D. A. Steer\n,307 N. Steinle\n,169 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,251 P. Stevens,41 M. StPierre,164 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,230 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,241 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,217 M. Suzuki,203\nB. L. Swinkels\n,37 A. Syx\n,117 M. J. Szczepa\u00b4nczyk\n,308 P. Szewczyk\n,125 M. Tacca\n,37 H. Tagoshi\n,203\nK. Takada,203 H. Takahashi\n,272 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,309 H. Takeda\n,310, 311\nK. Takeshita,217 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,130 M. Tamaki,203 N. Tamanini\n,100\nD. Tanabe,141 K. Tanaka,50 S. J. Tanaka\n,230 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,211\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,312 J. D. Tasson\n,153 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,181 A. Theodoropoulos\n,138 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,210 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,194 S. Tiwari\n,188 V. Tiwari\n,119\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,141 A. Torres-Forn\u00b4e\n,138, 139 C. I. Torrie,11 I. Tosta e Melo\n,313\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,123 A. Trapananti\n,52, 51 R. Travaglini\n,168 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,126 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,185, 48 A. Trovato\n,185, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,314 L. Tsukada\n,213 K. Turbang\n,115, 23 M. Turconi\n,113\nC. Turski,94 H. Ubach\n,82, 83 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,315 K. Ueno\n,42 V. Undheim\n,277\nL. E. Uronen,219 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,295 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 316\nE. Van den Bossche\n,115 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,120 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,259 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,124 V. Varma\n,133 A. N. Vazquez,89 A. Vecchio\n,119 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,116 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,133\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,189 A. Vilkha,110 N. Villanueva Espinosa,138 V. Villa-Ortega\n,178\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,231 L. Vujeva\n,140 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,217 J. Z. Wang,90 W. H. Wang,165\nY. F. Wang\n,1 G. Waratkar\n,194 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\nA. T. Wilkin,211 B. M. Williams,120 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\n\n39\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,141 I. C. F. Wong\n,219, 109 K. Wong,189 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,142 D. S. Wu\n,8, 9 H. Wu\n,142 K. Wu,120 Q. Wu,53 Y. Wu,96\nZ. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,207 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,152 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,230 T. Yan,119 K. Z. Yang\n,18\nY. Yang\n,146 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,142 A. B. Yelikar\n,144 X. Yin,35 J. Yokoyama\n,317, 42\nT. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110 T. Zelenova,62 J.-P. Zendri,92\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 H. Zhang\n,145 L. Zhang,11 N. Zhang,57 R. Zhang\n,150 T. Zhang,119\nC. Zhao\n,72 Yue Zhao,162 Yuhang Zhao,20 Z.-C. Zhao\n,318 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78 H. O. Zhu,72\nZ.-H. Zhu\n,318, 319 A. B. Zimmerman\n,148 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n\n40\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n\n41\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115Vrije Universiteit Brussel, 1050 Brussel, Belgium\n116OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n117Centre national de la recherche scientifique, 75016 Paris, France\n118Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n119University of Birmingham, Birmingham B15 2TT, United Kingdom\n120Washington State University, Pullman, WA 99164, USA\n121Cornell University, Ithaca, NY 14850, USA\n122Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n123Christopher Newport University, Newport News, VA 23606, USA\n124OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n125Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n126University of Maryland, College Park, MD 20742, USA\n127Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n128INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n129Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n130University of Chicago, Chicago, IL 60637, USA\n131University of Arizona, Tucson, AZ 85721, USA\n132INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Colorado State University, Fort Collins, CO 80523, USA\n138Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n139Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n140Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n141National Central University, Taoyuan City 320317, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148University of Texas, Austin, TX 78712, USA\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Northeastern University, Boston, MA 02115, USA\n151Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n153Carleton College, Northfield, MN 55057, USA\n154University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n157Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n158Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n159INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n160Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n161Montana State University, Bozeman, MT 59717, USA\n\n42\n162The University of Utah, Salt Lake City, UT 84112, USA\n163Johns Hopkins University, Baltimore, MD 21218, USA\n164University of Rhode Island, Kingston, RI 02881, USA\n165The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n166Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n167DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n168Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n169University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n170INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n171Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n172INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n173Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n174Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n175The University of Sheffield, Sheffield S10 2TN, United Kingdom\n176Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n177Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n178IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n179Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n180INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n181California State University, Los Angeles, Los Angeles, CA 90032, USA\n182Marquette University, Milwaukee, WI 53233, USA\n183Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n184Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n185Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n186Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n187National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n190Stony Brook University, Stony Brook, NY 11794, USA\n191Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n192Montclair State University, Montclair, NJ 07043, USA\n193HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n194Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n195Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n196Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n197CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n198Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n199Western Washington University, Bellingham, WA 98225, USA\n200SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n201Barry University, Miami Shores, FL 33168, USA\n202E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n203Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n204Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n205Department of Physics, Ochanomizu University, Bunkyo, Tokyo 112-8610, Japan\n206University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n207University of California, Berkeley, CA 94720, USA\n208Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n209Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211University of California, Riverside, Riverside, CA 92521, USA\n212Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214University of Nottingham NG7 2RD, UK\n215Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n\n43\n216The University of Mississippi, University, MS 38677, USA\n217Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n218Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n219The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Helmut Schmidt University, D-22043 Hamburg, Germany\n232Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n233Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n234Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n235Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n236National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n238Sungkyunkwan University, Seoul 03063, Republic of Korea\n239Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n240Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n241Chung-Ang University, Seoul 06974, Republic of Korea\n242University of Washington Bothell, Bothell, WA 98011, USA\n243Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n248Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n249Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n250Nagoya University, Nagoya, 464-8601, Japan\n251Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n252Bard College, Annandale-On-Hudson, NY 12504, USA\n253Technical University of Braunschweig, D-38106 Braunschweig, Germany\n254Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n255Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n256Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n257Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n258Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n259Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n260Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n261Seoul National University, Seoul 08826, Republic of Korea\n\n44\n262Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n263NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n264Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n265Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n266St. Thomas University, Miami Gardens, FL 33054, USA\n267Scuola Normale Superiore, I-56126 Pisa, Italy\n268Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n269Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n270Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n271Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n272Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n273Tsinghua University, Beijing 100084, China\n274Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n275Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n276Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n277University of Stavanger, 4021 Stavanger, Norway\n278Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n279GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n280University College London, London WC1E 6BT, United Kingdom\n281Observatoire de Paris, 75014 Paris, France\n282Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n283Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n285CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n286Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n287Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n288Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n289Hobart and William Smith Colleges, Geneva, NY 14456, USA\n290INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n291Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n292Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n293Kennesaw State University, Kennesaw, GA 30144, USA\n294Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n295Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n296Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n297Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n298Trinity College, Hartford, CT 06106, USA\n299Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n300Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n301Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n302Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n303Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n304Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n305NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n\n45\n306Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n307Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n308Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n309Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n310The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n311Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n314National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n315Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n316Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n317Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n318Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n319School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(Dated: November 10, 2025)\n\u2217Deceased, September 2024.\n", "Direct multi-model dark-matter search with gravitational-wave interferometers\nusing data from the first part of the fourth LIGO-Virgo-KAGRA observing run\nThe LIGO Scientific Collaboration, The Virgo Collaboration, and The KAGRA Collaboration\u2217\n(Dated: December 12, 2025)\nGravitational-wave detectors can probe the existence of dark matter with exquisite sensitivity.\nHere, we perform a search for three kinds of dark matter \u2013 dilatons (spin-0), dark photons (spin-\n1) and tensor bosons (spin-2) \u2013 using three independent methods using the first part of the most\nrecent data from the fourth observing run of LIGO\u2013Virgo\u2013KAGRA. Each form of dark matter\ncould have interacted with different standard-model particles in the instruments, causing unique\ndifferential strains on the interferometers. While we do not find any evidence for a signal, we place\nthe most stringent upper limits to-date on each of these models. For scalars with masses between\n[4 \u00d7 10\u221214, 1.5 \u00d7 10\u221213] eV that couple to photons or electrons, our constraints improve upon those\nfrom the third observing run by one order of magnitude, with the tightest limit of \u223c10\u221220 GeV\u22121\nat a mass of \u223c2 \u00d7 10\u221213 eV. For vectors with masses between [7 \u00d7 10\u221213, 8.47 \u00d7 10\u221212] eV that\ncouple to baryons, our constraints supersede those from MICROSCOPE and E\u00a8ot-Wash by one\nto two orders of magnitude, reaching a minimum of \u223c5 \u00d7 10\u221224 at a mass of \u223c10\u221212 eV. For\ntensors with masses of [4 \u00d7 10\u221214, 8.47 \u00d7 10\u221212] eV (the full mass range analyzed) that couple via a\nYukawa interaction, our constraints surpass those from fifth-force experiments by four to five orders\nof magnitude, achieving a limit as low as \u223c8 \u00d7 10\u22129 at \u223c2 \u00d7 10\u221213 eV. Our results show that\ngravitational-wave interferometers have become frontiers for new physics and laboratories for direct\nmulti-model dark-matter detection.\nI.\nINTRODUCTION\nThe existence of dark matter (DM) is well established,\nyet its fundamental nature remains one of the most press-\ning mysteries in modern physics [1]. Across a vast range\nof possible masses and interaction strengths, dark mat-\nter could take many forms \u2013 from particles with masses\nof O(10\u221222) eV, whose wave-like behavior spans galactic\nscales [2], to primordial black holes with masses com-\nparable to stars [3\u20135]. Among these possibilities, ultra-\nlight dark matter with masses mDM \u226a1 eV presents\na particularly compelling scenario.\nNot only do high-\nenergy theories, including string theory, naturally predict\nsuch particles, but their extraordinarily low mass also im-\nplies a quantum-mechanical coherence over macroscopic\ndistances, effectively turning them into oscillating back-\nground fields. If these fields interact weakly with stan-\ndard model particles, they could produce distinctive,\nnearly monochromatic signals detectable by precision ex-\nperiments [6, 7].\nGravitational-wave (GW) detectors, such as LIGO,\nVirgo and KAGRA [8\u201310], have already reshaped as-\ntrophysics by measuring the signals from merging black\nholes and neutron stars [11\u201313]. But their extraordinary\nsensitivity also makes them powerful tools for probing\nfundamental physics beyond GWs [14\u201317].\nThe same\nprecision that captures the faint signals from GWs could\nreveal subtle interactions between dark matter and ordi-\nnary matter, also placing these detectors at the frontier\nof searches for new physics. Along these lines, multiple\nsearches for dilatons and dark photons have been per-\n\u2217full author list given at the end of the article.\nformed on previous GW data [18\u201322], resulting in strin-\ngent constraints on dilatons and dark photons.\nIn contrast to previous works, we explore here how GW\ndetectors can be used to search for ultralight dark mat-\nter in various forms simultaneously: scalar fields (such\nas dilatons, which may induce oscillations in fundamental\nconstants) [7, 23\u201325], vector fields (like dark photons, ex-\nerting weak oscillating forces on matter) [6], and massive\ntensor fields (closely resembling GWs but with a nonzero\nmass) [26\u201329]. Each of these candidates leaves a unique\nimprint on GW detectors, offering a new way to con-\nstrain \u2013 or perhaps discover \u2013 some of the most elusive\ndark matter candidates predicted by theory.\nII.\nDARK MATTER INTERACTION MODELS\nCold, ultralight DM consists of an enormous number\nof extremely light particles, which motivates its treat-\nment as a classical oscillating field.\nThe angular fre-\nquency of this field is fixed by the ultralight DM mass:\n\u03c9 = mDMc2/\u210f; however, there is a small, stochastic fre-\nquency change caused by the Maxwell-Boltzmann veloc-\nity distribution of the DM particles: \u2206\u03c9/\u03c9 \u223cv2\n0/c2 \u223c\n10\u22126, where v0 is the virial velocity of DM around the\ncenter of the galaxy. This frequency spread implies that\nthe signal has a finite coherence time, of O(104) s at\nmDM \u223c10\u221212 eV, in which the signal can be treated as\npurely monochromatic, but spreads over \u2206\u03c9 if observ-\ning for longer than the coherence time.\nLikewise, the\nfinite coherence time implies a finite coherence length,\nwhich greatly exceeds the separation of earth-based inter-\nferometers. Taken together, the finite coherence time and\nlength indicate that the ultralight DM signal is narrow-\nband, stochastic and correlated, regardless of the ultra-\narXiv:2510.27022v4 [astro-ph.CO] 11 Dec 2025\n\n2\nlight DM model considered.\nThe following subsections consider the physics of each\ntype of DM, and how it interacts with GW interferome-\nters.\nA.\nScalar, dilaton dark matter\nModels of ultralight dark matter predict that it could\nhave originated through a vacuum misalignment mech-\nanism in the early universe, and would manifest today\nas a coherently oscillating scalar field [24]. The coupling\nof such DM would effectively induce an oscillation of the\nvalues of fundamental constants, namely the electron rest\nmass and the fine structure constant, thus leading to the\nexpansion and contraction of solids. When a field gradi-\nent exists, objects can also be accelerated. Many ideas\nhave been proposed to detect such effects [30\u201333], with\nthe current strongest direct constraints coming from ex-\nperiments looking for the oscillation of fundamental con-\nstants using atomic clocks or spectroscopy [34\u201345]. More\nrecently, several coupling paths were discovered to detect\nthose same oscillations using gravitational-wave interfer-\nometers [7, 23\u201325, 46, 47]. The potential for DM-induced\nacceleration of the arm mirrors was used to derive upper\nlimits in LIGO data [21], while oscillations in the size of\nthe beamsplitter was used with the GEO600 detector [20]\nand the Fermilab holometer [48]. An additional coupling\npath through arm mirror size oscillations was discovered\nand used in [22, 49], and is used in this study.\nConsidering a simple linear expansion to the Standard\nModel Lagrangian L, we can write the scalar field \u03d5\nas [20]:\nL \u2283\u03d5\n\u039b\u03b3\nF\u00b5\u03bdF \u00b5\u03bd\n4\n\u2212\u03d5\n\u039be\nme \u00af\u03c8e\u03c8e,\n(1)\nwhere, F\u00b5\u03bd is the electromagnetic field tensor, \u03c8e and\n\u00af\u03c8e are the standard-model electron field and its Dirac\nconjugate, respectively, me is the electron rest-mass, and\n\u039b\u03b3 and \u039be denote the scalar DM coupling constants to\nthe photon and electron, respectively. We can see that\nwhen the \u039b\u22121\ni\nis non-zero, the DM field induces changes\nin me and the fine structure constant \u03b1 through F\u00b5\u03bd. In\nturn, this modulates the sizes and refractive indices of\nsolids.\nIn LIGO, by considering only oscillations in the size of\nthe beamsplitter and test arm mirrors, we can relate the\nmeasured strain h(\u03c9) to the aforementioned DM coupling\nconstants as [22]:\nh(f0) \u2248\n\u0012 1\n\u039b\u03b3\n+ 1\n\u039be\n\u0013 c \u221a2 \u03c1DM\n2\u03c0f0\n1\nAcal(f0),\n(2)\nwhere \u03c1DM = 0.4 GeV cm\u22123 is the local DM energy den-\nsity according to the standard galactic DM halo model\n[50] and f0 = \u03c9/(2\u03c0) is the DM frequency. Acal, see Sec-\ntion A, is obtained through detailed optical simulations\nthat account for finite light travel time effects [47], and\nencodes the interferometer response to scalar DM [22].\nB.\nVector dark photon dark matter\nSpin-1 dark photons1 could completely explain the relic\nabundance of DM [52]. These particles could arise from\nthe misalignment mechanism [53\u201355], parametric reso-\nnance or the tachyonic instability of a scalar field [56\u201359],\nor from cosmic string network decays [60]. The observ-\nable effect would result from a coupling of dark photons\nto standard-model particles \u2013 either baryons or baryon\nminus leptons. In particular, this interaction would cause\n\u201cdark\u201d force on the mirrors, causing them to oscillate at\na frequency fixed by the mass of the dark photon [6, 61].\nThe Lagrangian L that characterizes the dark photon\ncoupling to a number current density J\u00b5 of baryons or\nbaryons minus leptons is:\nL = \u22121\n4\u00b50\nF \u00b5\u03bdF\u00b5\u03bd +\n1\n2\u00b50\n\u0010mDMc\n\u210f\n\u00112\nA\u00b5A\u00b5 \u2212\u03f5eJ\u00b5A\u00b5,\n(3)\nwhere \u00b50 is the magnetic permeability in vacuum, e is\nthe electron charge, A\u00b5 is the dark four-vector potential,\nand \u03f5 is the strength of the particle/dark photon coupling\nnormalized by the electromagnetic coupling constant.\nThe strain on the interferometers caused by a dark\nphoton DM signal is [6, 47]:\nq\n\u27e8h2\nD\u27e9=\n\u221a\n2\n3\nQ\nM\n\u210fe\nc4\u221a\u03f50\np\n2\u03c1DMv0\n\u03f5\nf0\n,\n\u22436.56 \u00d7 10\u221226 \u0010\n\u03f5\n10\u221222\n\u0011 \u0012100 Hz\nf0\n\u0013\n,\n(4)\nwhere \u03f50 is the permittivity of free space, Q/M is\nthe charge-to-mass ratio of the mirrors in LIGO and\n\u03c9 = 2\u03c0f0.\nWe take Q/M\n= m\u22121\np , where mp\n=\n0.93827 GeV/c2 is the proton rest mass [62].\nA second strain also appears because light takes a fi-\nnite amount of time to travel between the input and end\nmirrors in the interferometer, during which the mirrors\nhave moved in response to the ultralight DM field [47]:\nq\n\u27e8h2\nC\u27e9=\n\u221a\n3\n2\nq\n\u27e8h2\nD\u27e92\u03c0f0L\nv0\n,\n\u22436.58 \u00d7 10\u221225 \u0010\n\u03f5\n10\u221222\n\u0011\n,\n(5)\nwhere L = 4 km is the arm-length of the LIGO interfer-\nometers. The total strain is: \u27e8h2\ntotal\u27e9= \u27e8h2\nD\u27e9+\u27e8h2\nC\u27e9. The\naverages are taken over polarization direction, detector\ngeometry, and the Maxwell-Boltzmann velocity distribu-\ntion.\n1 These dark photons are different than those that kinetically mix\nwith the ordinary photon [51].\n\n3\nC.\nTensor dark matter\nA novel massive spin-2 particle, derived from a mas-\nsive gravity theory, could modify gravity and emerge as\na promising DM candidate.\nThe foundational frame-\nwork for linear massive gravity was established by Fierz\nand Pauli in 1939 [63].\nThis theory was extended to\nthe nonlinear level, enabling the incorporation of mas-\nsive gravitons. However, this generalization introduced\na non-stable degree of freedom known as the Boulware-\nDeser ghost [64]. To address this issue, a ghost-free mas-\nsive gravity theory was constructed [65, 66], which later\nevolved into the bimetric gravity [67] and multigravity\ntheories [68]. In particular, in bimetric gravity [67, 69],\ntwo spin-2 particles produced by the misalignment mech-\nanism [30] \u2013 one massless and one massive \u2013 could inter-\nact and explain DM [27].\nThe Fierz-Pauli Lagrangian density [70] describes this\ntensor field \u03c7\u00b5\u03bd:\nL = \u22121\n4\u03c7\u00b5\u03bdE\u00b5\u03bd,\u03b1\u03b2\u03c7\u03b1\u03b2 \u22121\n8\n\u0010mDMc\n\u210f\n\u00112 \u0000\u03c7\u00b5\u03bd\u03c7\u00b5\u03bd \u2212\u03c72\u0001\n,\n(6)\nwhere \u03c7 \u2261\u03c7\u00b5\n\u00b5 and E\u00b5\u03bd,\u03b1\u03b2 is a second-order derivative\noperator defined in Eq. 2.13 of [26].\nUsing\nthe\nFriedman-Lemaitre-Robertson-Walker\n(FLRW) background metric, one can derive the equa-\ntions of motion for this ultralight field at late times in\nthe universe [27, 71, 72].\nThe strain on interferometers arises analogously to\nthat from GWs: a stretching of space-time in the pres-\nence of the field, since the massive spin-2 metric and its\ncoupling constant can be absorbed into the definition of\nthe massless spin-2 metric in the linear regime of the cou-\npling constant \u03b1; thus, the strain can be derived [26, 29]2:\nh(f0) =\n2\u03b1\u2206\u03b5\n2\u03c0f0mPl\nr\n\u03c1DM\u210fc\n2\n\u22431.23 \u00d7 10\u221225\n\u0012\n\u03b1\n5 \u00d7 10\u22128\n\u0013 \u0012100 Hz\nf0\n\u0013\n(7)\nwhere \u2206\u03b5 := \u03b5ij(ninj \u2212mimj), n, m are unit vectors\npointing down each interferometer arm, \u03b5ij describes\neach of the five polarizations of the ultralight DM field\n[28], \u03b1 is the Yukawa coupling, and mPl is the reduced\nPlanck mass.\n2 Note that Refs. [26, 29] and Refs. [27, 28] differ by a factor of 2\nin the strain induced by tensor DM, which results from a factor\nof 8 difference in the Lagrangians. We use the prescriptions in\n[26, 29] throughout this paper, which leads to a factor of two\nstronger upper limits than would be obtained using the formalism\nof [27, 28]\nIII.\nDATA\nWe analyze data from the first part of the fourth ob-\nserving run (O4a) of the LIGO Livingston (L1) and Han-\nford (H1) detectors. The sensitivity of the detectors in\nthis observing run improved significantly across all fre-\nquencies, particularly above 400 Hz [73\u201375]. The strain\ndata were collected between May 24, 2023, at 15:00 UTC,\nand January 16, 2024, at 16:00 UTC, with L1 and H1 op-\nerating 69.0% and 67.5% of the time, respectively [76].\nVirgo was not operational during O4a, and KAGRA only\nobserved for one month. The data are calibrated by di-\nrecting a laser onto the test masses and comparing the\nmeasured response to the expected one [77, 78].\nAd-\nditionally, the data have been cleaned to remove short-\nduration disturbances (known as \u201cglitches\u201d) [79], and are\nonly analyzed if they are in \u201cscience mode\u201d [80].\nAt\nworst, amplitude and phase uncertainties at 1\u03c3 are 10%\nand 10 degrees, respectively, between the frequency range\nanalyzed by all methods: [10, 2000] Hz.\nIn this analysis, we use three independent pipelines,\ndescribed in detail in Section IV, to search for direct DM\ninteractions with GW interferometers. Each one employs\ndata in different formats.\nThe first, called the BSD-\nexcess-power method, uses Band Sampled Data (BSD)\nstructures [81] as the input to this search, which are de-\nrived from short fast Fourier transform databases [82].\nBSDs contain complex-valued time-series representations\nof the data every 10 Hz every month, and are derived\nfrom the strain channel GDS-CALIB_STRAIN_CLEAN_AR.\nThe other two methods, cross-correlation and Logarith-\nmic Power Spectral Density (LPSD), use gated3 data\nfrom the channel GDS-CALIB_STRAIN_CLEAN_GATED_G02,\nin which spurious glitches have been removed [83, 84].\nThe cross-correlation method employs 1800-s long short\nFourier transforms (SFTs) created from G02 gated data\nduring the O4a period for H1 and L1. In total, 5696 pairs\nof coincident SFTs for H1 and L1 were used, correspond-\ning to a total of 2848 hours. In contrast, the data used\nby LPSD were divided in continuous segments of at least\n1 \u00d7 105 s each, resulting in 30 segments totaling about\n1157 h, similarly to [22].\nIV.\nSEARCH METHODS\nWe present three different methods that searched for\nultralight DM coupling to the interferometers. All meth-\nods are sensitive to each kind of DM presented in Sec-\ntion II.\n3 Gating refers to removing the cumulative effect of many loud,\ntransient glitches that can collectively raise the noise floor and\ninhibit the recovery of CW signals.\n\n4\nA.\nCross-Correlation\nThe effect of a large population of ultralight dark pho-\ntons on the interferometers is similar to a stochastic GW\nbackground, and the long coherence length of the field,\ne.g. O(109) m at mDM = 10\u221212 eV [6, 61], is much larger\nthan the separation between H1 and L1, both of which\nmotivate a cross-correlation search. Additionally, the ve-\nlocity spread of the dark photon field leads to a very nar-\nrow relative frequency spread of the order \u223c10\u22126 for\nthe signal, leading naturally to a frequency-domain peak\nhunt in each frequency bin of size 1/1800 Hz (see [18, 19]\nfor previous searches with O1 and O3 data). The signal-\nto-noise ratio (SNR) for the frequency bin j is defined\nas\nSNRj = Sj\n\u03c3j\n.\n(8)\nHere the signal part Sj is the signal strength constructed\nby cross-correlating the FFT data z1,ij and z2,ij of de-\ntectors 1 and 2 for segment i, and averaging over the\nsegments:\nSj =\n1\nNFFT\nNFFT\nX\ni=1\nz1,ijz\u2217\n2,ij\nP1,ijP2,ij\n,\n(9)\nwhere P1(2),ij is the noise power estimated from the\nneighboring 50 frequency bins4 using a running median,\nand is related to the one-sided power spectral density\n(PSD) by PSD1(2),ij = 2P1(2),ij/TFFT. In the absence\nof a signal, the expectation value of Sj is zero, with a\nvariance for its real and imaginary parts being\n\u03c32\nj =\n1\nNFFT\n\u001c\n1\n2P1,ijP2,ij\n\u001d\nNFFT\n.\n(10)\nThe length TFFT of each time segment is 1800s, and an\nefficiency factor obtained from simulations is used to cor-\nrect for the power loss due to this binning choice and ran-\ndom bin boundary when the calculated SNR is converted\nto upper limits [18]. In the presence of the dark photons,\nthe SNR thus defined takes a negative and real value\ndue to the relative orientation of the two detectors which\nresults in a negative overlap reduction function, close to\n\u22120.9 for the entire frequency range we consider here, and\nis used in converting the SNR at each frequency bin to\nan upper limit. In the search for the candidate, bins that\nare contaminated by narrow spectral artifacts, defined\nto be within \u223c0.056 Hz, are excluded in the analysis.\nThe upper limits are derived with the Feldman-Cousins\nformalism [85] in the absence of a detection.\n4 Fifty bins ensures that the signal does not pollute the background\nestimation and the noise properties do not differ by too much\nacross the frequency range of the estimation.\nB.\nBSD excess power method\nIn each 1-Hz band, BSD-excess-power changes the fast\nFourier transform coherence time TFFT to match the DM\nsignal coherence time Tcoh ensuring that all power is con-\nfined to one frequency bin for the full observing run. We\nthen take Fourier transforms of the strain data with dura-\ntions TFFT to make time-frequency \u201cpeakmaps\u201d [82, 86].\n\u201cPeakmaps\u201d are collections of ones that represent when\nthe power in particular frequency bins has exceeded a\nthreshold in the equalized spectrum and is also a local\nmaxima. We then count the number of peaks at each\nfrequency to find bins with large numbers of peaks. By\nsumming the ones in the peakmap, and not the actual\npower in each frequency bin, we are more robust against\nnon-Gaussian noise artifacts that could contaminate par-\nticular frequency bins and bias our detection statistic.\nWe define the critical ratio CR to be our detection\nstatistic:\nCR = y \u2212\u00b5\n\u03c3\n,\n(11)\nwhere y is the number of peaks at a particular frequency,\nand \u00b5 and \u03c3 are the mean and standard deviations of\nthe number counts across all frequencies in the band. In\nGaussian noise, the CR is approximately normally dis-\ntributed with zero mean and unit variance, and approxi-\nmately a normalized non-central \u03c72 distribution with two\ndegrees of freedom in the presence of a signal.\nWe select enough candidates5 in each 1-Hz band such\nthat one coincident candidate between two detectors\nwould occur in Gaussian noise.\nThis ensures that we\nselect uniformly over the frequency range.\nC.\nLPSD\nThe crux of the LPSD approach is to exactly match\nthe integration time in Fourier transforms to the DM co-\nherence time in every bin. This allows it to maximize\nthe SNR to a theoretical maximum. The resulting neces-\nsary logarithmic frequency spacing in this method poses\na challenge as FFT-based algorithms are no longer ap-\nplicable.\nWith a computational complexity scaling as\nO(N 2), where N is the number of data points, this ap-\npears to lead to intractable costs. In [49], a method was\ndeveloped that leverages symmetries between the time\nand frequency domains. This allows us to perform the\nfull logarithmic calculation with a single FFT followed\nby a heavily zero-suppressed transformation without the\nneed for an expensive pre-computation.\nHaving efficiently calculated PSDs over large segments of\ndata with this method, we follow the approach in [22, 49]\n5 The number of candidates selected ranges from 20 and 285 at\n2000 Hz and 10 Hz, respectively and depends on TFFT.\n\n5\nwhere, similar to LIGO calibration, a background model\nis constructed by fitting cubic splines in log-log space to\nthe PSD as a function of frequency. Because the PSDs\nvary by several orders of magnitude, we conduct fits over\nintervals of 104 frequency bins. Within these intervals,\npotential DM signals are identified as positive deviations\nfrom the fits by using a profile likelihood test (see Eq.\n15 in [49]) assuming, as validated empirically, that the\nresiduals follow a skew-normal distribution.\nV.\nRESULTS\nA.\nCross-Correlation\nWith the definition of the SNR (Eq. (8), the desired\ncandidate needs to satisfy Re(SNR) < \u22125.8 to corre-\nspond to a detection with an overall \u223c1% false alarm\nprobability. No such candidate was found in this analy-\nsis. We have also checked the subthreshold outliers with\nabsolute values in the range [5.0, 5.8] for either the real\nor imaginary part of the SNR. Of ten such outliers, nine\nare due to loud instrumental artifacts, and the remaining\none is consistent with Gaussian noise.\nIn the absence of a detection, we then set 95%\nconfidence-level upper limits on each of the aforemen-\ntioned DM models in each frequency (or mass) bin, which\ninduces fluctuations in the limits that are broader than\nthose from the other methods, in which the limits are set\nroughly every one Hz.\nB.\nBSD Excess power method\nOur search returned 6847 candidates present in the\nsame frequency bin in both L1 and H1 and that did not\noverlap with known noise disturbances [79].\nHowever,\nafter requiring that the average CR be greater than five\n(corresponding to 5\u03c3 significance in Gaussian noise), only\nten candidates remained.\nTo determine whether these\ncandidates resulted from DM, we performed three follow-\nup procedures: (1) we varied the observation time Tobs\nat the chosen TFFT to see if there was a steady increase\nin the CR \u221dT 1/2\nobs , (2) we increased TFFT > Tcoh to see\nif there was a decrease in the CR [20, 61], and (3) we\ncorrelated the spectra from L1 and H1 with an expected\nDM waveform using the Wiener filter [87] and computed\nthe residual between them [88]. No candidate survived\nall three follow-ups.\nIn the absence of candidates, we set upper limits on\nthe minimum detectable strain amplitude at 95% confi-\ndence h95%\n0,min induced by a generic DM signal using Eq.\n75 of [17], which depends on the detector power spec-\ntral density, the maximum of the coincident candidates\u2019\nCRs, TFFT, and Tobs. Up to an O(1) factor that depends\non the DM polarization and the geometry of LIGO, these\nlimits can then be mapped to any kind of DM interaction\nthat would induce a differential strain on the detector.\nC.\nLPSD\nWe obtain candidates by performing a profile likeli-\nhood ratio test in each bin, as outlined in [49], and re-\nquire a 5\u03c3 significance corrected for the look-elsewhere ef-\nfect6 in rejecting the no-DM hypothesis. After clustering\nneighboring bins, requiring significance and compatibil-\nity in both detectors, we find only one candidate which\nwas found to originate from a non-optimal setting in the\nbackground fit.\nThe resulting 95% confidence-level upper limits on\n\u039b\u22121\ni , where \u039bi is either \u039be or \u039b\u03b3 (see Eq. (2)) when\nassuming the other is zero, can be seen in Fig. 1(a). As\none can see, we improve on the O3 results by up to an\norder of magnitude over the entire frequency range. We\nnote that the O3 curve in the plot is multiplied by a fac-\ntor 2.226 compared to the results in [22] after we found\na conversion error. The improvement at higher frequen-\ncies can be attributed to the better detector sensitivity in\nO4a. At lower frequencies, a larger arm mirror thickness\ndifference compared to O3 leads to a roughly factor of\nthree improvement, and the gating procedure \u2013 not used\nin the O3 search \u2013 leads to an improvement up to a factor\nof two. Injection tests were performed that confirmed the\nupper limits at the expected level, but found a system-\natic leading us to overestimate the limits by 13%. This\nis small compared to the 30% statistical uncertainty.\nD.\nUpper limits\nFor all three pipelines, the follow-up steps, predeter-\nmined before analyzing the data, yielded no surviving\ncandidates. Thus, we show in Fig. 1 upper limits for each\nof the three DM models using each pipeline, as argued in\n[17, 95]. For all three DM models, we see significant im-\nprovements in the constraints on the coupling constants\nwith respect to existing experiments. For dark photons,\ncross-correlation obtains less stringent constraints than\nthose from BSD-excess-power and LPSD because it is\nsignificantly less sensitive to the finite-light travel time\neffect [29, 47]. For dilatons, cross-correlation is consis-\ntent with or outperforms BSD-excess-power and LPSD\nbecause all three methods are equally sensitive to the fi-\nnite light-travel time effect. For tensor bosons, the upper\nlimits obtained by all three pipelines are consistent and\nsignificantly outperform fifth-force experiments by sev-\neral orders of magnitude, as expected from [28, 96].\nWe note that the indirect fifth-force upper limits are\nstronger than those obtained from our search for scalar\nDM. In this case, the sensitivity of GW interferometers\ndoes not benefit significantly from the arm length, as\n6 This effect arises because when searching over a large parameter\nspace, noise has an increased opportunity to cause a false alarm\nsomewhere in the space.\n\n6\n10\n13\n10\n12\n10\n11\nmass (eV)\n10\n23\n10\n22\n10\n21\n10\n20\n10\n19\n10\n18\n10\n17\n10\n16\ndilaton coupling \n1\ni, 95% (GeV\n1)\ncross-correlation\nBSD excess power\nLPSD\nO3 LPSD\nO3 acceleration effect\nE\u00f6t-Wash\nGEO600\nMICROSCOPE\n101\n102\n103\nfrequency (Hz)\n(a) Dilatons\n10\n13\n10\n12\n10\n11\nmass (eV)\n10\n23\n10\n22\n10\n21\n10\n20\ndark photon-baryon coupling 95%\ncross correlation\nBSD excess power\nLPSD\nE\u00f6t-Wash\nMICROSCOPE\n101\n102\n103\nfrequency (Hz)\n(b) Dark photons\n10\n13\n10\n12\n10\n11\nmass (eV)\n10\n8\n10\n7\n10\n6\n10\n5\n10\n4\n10\n3\n10\n2\nYukawa coupling \n95%\ncross-correlation\nBSD excess power\nLPSD\nfifth-force\n101\n102\n103\nfrequency (Hz)\n(c) Tensor bosons\nFIG. 1. Upper limits on the coupling strengths of ultralight scalar, vector and tensor bosons to standard-model\nparticles in LIGO. Solid lines denote the constraints from this work (\u201ccross-correlation,\u201d \u201cBSD excess power,\u201d and \u201cLPSD\u201d).\nThe dashed and dotted-dashed lines indicate constraints from other experiments (\u201cE\u00a8ot-Wash\u201d and \u201cMICROSCOPE\u201d) and\nfrom other searches on GW interferometer data (\u201cGEO600\u201d, \u201cO3 LPSD\u201d and \u201cO3 acceleration effect\u201d). (a) Our constraints\napply to the coupling of dilatons to both photons and to electrons. They improve upon those from previous searches with\nGW interferometers [20\u201322] and beat those from O3 by one order of magnitude. Constraints from E\u00a8ot-Wash [89, 90] and\nMICROSCOPE [91, 92] correspond to the coupling of the dilaton to the electron. (b) The constraints on vector dark photon\nDM improve upon existing limits by a couple of order of magnitudes in the dark-photon/baryon coupling constant. To produce\nlimits on dark photon/baryon minus lepton coupling, U(1)B\u2212L, these limits should be multiplied by two. (c) For the first time,\nwe derive constraints on tensor DM using GW interferometers, which are up to five orders of magnitude superior to those\nobtained indirectly from fifth-force experiments [93, 94]. Note that for tensor bosons, using the calculated strain amplitudes in\nRefs. [27, 28] would require multiplying the limits on the tensor boson coupling constant by two.\nshown in the recent GEO600 search [20], where the rel-\nevant effect was the differential strain induced by the\noscillating beam-splitter.\nImprovements by accounting\nfor the different thicknesses of the test masses [22], to-\ngether with the better low-frequency sensitivity of LIGO\ncompared to GEO600 [97, 98], lead to substantial gains\nbelow 200 Hz relative to the GEO600 results, but still\nremain weaker than fifth-force constraints.\nBy contrast, the sensitivity to dark photons and tensor\nbosons in LIGO, Virgo and KAGRA depends primarily\non the interferometer arm length, just as for GWs. In\nthese cases, the differential strain induced by DM cou-\npling to the test masses, or spacetime distortions from\ntensor fields, is amplified by the long arms, enhancing our\nsensitivity to these kinds of DM. In particular, for tensor\nbosons, a torsion balance responds as a single bulk ob-\nject, analogous to early resonant-bar detectors, which are\nfar less sensitive than interferometers [99]. Thus, the sen-\nsitivity of fifth-force experiments is strongest for scalars\nand weakens for vectors and tensors, while GW interfer-\nometers are more powerful probes of vectors and tensors\nthan scalars.\nVI.\nCONCLUSIONS\nWe have shown that it may be possible for GW in-\nterferometers to detect different kinds of DM\u2013 dilatons,\ndark photons and tensor bosons \u2013 using computation-\nally efficient search techniques. Each form of DM inter-\nacts uniquely with the components of the interferometers,\nleading to signals that may be distinguishable. Though\nwe have not found any evidence for DM in our searches,\nwe have placed stringent upper limits on three DM mod-\nels that improve over those of existing experiments by\norders of magnitude. Specifically, for dilatons and dark\nphotons, we continue to probe weaker and weaker cou-\nplings due to upgrades in GW interferometers and im-\nprovements in our analysis techniques; for tensor bosons,\nwe surpass by five orders of magnitude fifth-force con-\nstraints for the first time. We note that all upper limits\ndo not include an average of the Maxwell-Boltzmann dis-\ntributed velocities, which is a conservative choice \u2013 such\nan average would result in the strengthening of the dark\nphoton limits by a factor of \u223c\np\n3/2, though would not\nimpact the other limits. In future work, we will consider\nmore systematically the impact of the velocity distribu-\ntion on the upper limits, which will likely lead to im-\nprovements in the dark photon limits. Thus, our results\nmotivate treating LIGO, Virgo and KAGRA as highly\nprecise DM detectors, permitting an unexpected way to\nprobe new physics.\nAppendix A: Transfer functions\nIn the dilaton search, we use transfer functions to relate\nthe DM-induced fluctuations of the optics and the theo-\nrized coupling constants \u039b\u22121\ni\n(see Eq. (1)). Following the\napproach in [22], we use detailed optical simulations in\nFinesse to calculate the transfer functions between the\ninterferometer\u2019s photodiode output amplitude and DM-\n\n7\ninduced fluctuations in the beamsplitter and arm test\nmirrors. The results, see Fig. 2, clearly show that in O4a,\nLLO is the more sensitive detector, with roughly a factor\nthree gain in sensitivity (see Section V C) between O3\nand O4a from the transfer function difference alone. At\nthe same time, we also find that the performance of LHO\nhas diminished over the same time period, though only\nslightly. In both cases, the differences are due to small\nchanges in mirror thicknesses between the two runs.\n101\n102\n103\nFrequency (Hz)\n22\n20\n18\n16\n14\n12\nTransfer function (dB)\nO4a LHO\nO3 LHO\nO4a LLO\nO3 LLO\nFIG. 2. Scalar dark matter transfer functions in dB, consid-\nering beamsplitter as well as arm test mirror size oscillations.\nThe dotted lines show the LHO transfer functions, and the\nothers show LLO results.\nAs one can see, while the effect\nhas reduced sligthly in LHO between O3 and O4a, it has in-\ncreased considerably in LLO, making LLO the more sensitive\ndetector in O4a.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO con-\nsortium.\nThe authors also gratefully acknowledge re-\nsearch support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India,\nthe Department of Science and Technology, India, the\nScience & Engineering Research Board (SERB), India,\nthe Ministry of Human Resource Development, India,\nthe Spanish Agencia Estatal de Investigaci\u00b4on (AEI), the\nSpanish Ministerio de Ciencia, Innovaci\u00b4on y Universi-\ndades, the European Union NextGenerationEU/PRTR\n(PRTR-C17.I1), the ICSC - CentroNazionale di Ricerca\nin High Performance Computing, Big Data and Quantum\nComputing, funded by the European Union NextGener-\nationEU, the Comunitat Auton`oma de les Illes Balears\nthrough the Conselleria d\u2019Educaci\u00b4o i Universitats, the\nConselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat\nDigital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish\nNational Agency for Academic Exchange, the National\nScience Centre of Poland and the European Union - Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scot-\ntish Universities Physics Alliance, the Hungarian Scien-\ntific Research Fund (OTKA), the French Lyon Institute\nof Origins (LIO), the Belgian Fonds de la Recherche Sci-\nentifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of\nScience, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute\nfor Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Sci-\nence Foundation of China (NSFC), the Israel Science\nFoundation (ISF), the US-Israel Binational Science Fund\n(BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC),\nTaiwan, the United States Department of Energy, and\nthe Kavli Foundation. The authors gratefully acknowl-\nedge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources.\nThis work was supported by MEXT, the JSPS\nLeading-edge Research Infrastructure Program, JSPS\nGrant-in-Aid for Specially Promoted Research 26000005,\nJSPS Grant-in-Aid for Scientific Research on Inno-\nvative Areas 2402:\n24103006, 24103005, and 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-\nto-Core Program A. Advanced Research Networks, JSPS\nGrants-in-Aid for Scientific Research (S) 17H06133 and\n20H05639, JSPS Grant-in-Aid for Transformative Re-\nsearch Areas (A) 20A203:\nJP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nUniversity of Tokyo, the National Research Foundation\n(NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n\n8\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineering\nCenter of KEK.\nJ.S. is supported by the Peking University under\nstartup Grant No. 7101302974, the NSFC under Grants\nNo. 12025507, No. 12150015, No.12450006.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising.\nWe\nrequest that citations to this article use \u2019A. 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AultONeal\n,65\nG. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51\nM. Ball,77 G. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12\nP. Baral\n,10 M. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11\nD. Bersanetti\n,29 T. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101\nN. Bevins\n,102 R. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46\nV. Biancalana\n,101 A. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75\nC. Binu,110 S. Biot,111 O. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113\nS. Blaber,114 J. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 N. Bode\n,8, 9 N. Boettner,97\nG. Boileau\n,113 M. Boldrini\n,38 G. N. Bolingbroke\n,115 A. Bolliand,116, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82\nF. Bondu\n,117 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,118 R. Bonnand\n,31, 116 A. Borchers,8, 9 V. Boschi\n,80\nS. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 M. Boyle,120 A. Bozzi,62 C. Bradaschia,80\nP. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104 T. Briant\n,121 A. Brillet,113 M. Brinkmann,8, 9\nP. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,115 M. L. Brozzetti\n,76, 51\nS. Brunett,11 G. Bruno,15 R. Bruntz\n,122 J. Bryant,118 Y. Bu,123 F. Bucci\n,61 J. Buchanan,122\nO. Bulashenko\n,82, 83 T. Bulik,124 H. J. Bulten,37 A. Buonanno\n,125, 1 K. Burtnyk,2 R. Buscicchio\n,126, 127\nD. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7\nL. Cadonati\n,57 G. Cagnoli\n,128 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,129 E. Calloni,32, 4\nS. R. Callos\n,77 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,130 E. Capocasa\n,20\nE. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 131 F. Carbognani,62 M. Carlassara,8, 9 J. B. Carlin\n,123\nT. K. Carlson,132 M. F. Carney,104 M. Carpinelli\n,126, 62 G. Carrillo,77 J. J. Carter\n,8, 9 G. Carullo\n,118, 133\nA. Casallas-Lagos,134 J. Casanueva Diaz\n,62 C. Casentini\n,135, 22 S. Y. Castro-Lucas,136 S. Caudill,132\nM. Cavagli`a\n,105 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,137, 138 E. Cesarini\n,22 N. Chabbra,34\nW. Chaibi,113 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103 S. Chalathadka Subrahmanya\n,97\nJ. C. L. Chan\n,139 M. Chan,114 K. Chang,140 S. Chao\n,141, 140 P. Charlton\n,142 E. Chassande-Mottin\n,20\nC. Chatterjee\n,143 Debarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,103 S. Chaty\n,20 A. Chen\n,144\nA. H.-Y. Chen,145 D. Chen\n,146 H. Chen,141 H. Y. Chen\n,147 S. Chen,143 Yanbei Chen,148 Yitian Chen\n,120\nH. P. Cheng,149 P. Chessa\n,76, 51 H. T. Cheung\n,90 S. Y. Cheung,6 F. Chiadini\n,150, 131 G. Chiarini,8, 9, 92\nA. Chiba,151 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80 A. Chiummo\n,4, 62 C. Chou,145 S. Choudhary\n,72\nN. Christensen\n,113, 152 S. S. Y. Chua\n,34 G. Ciani\n,74, 75 P. Ciecielag\n,95 M. Cie\u00b4slar\n,124 M. Cifaldi\n,22\nB. Cirok,153 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6 P. Clearwater,154 S. Clesse,111 F. Cleva,113, 116\nE. Coccia,44, 45, 43 E. Codazzo\n,155, 156 P.-F. Cohadon\n,121 S. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98\nC. G. Collette,157 J. Collins,63 S. Colloms\n,86 A. Colombo\n,158, 127 C. M. Compton,2 G. Connolly,77 L. Conti\n,92\n\n11\nT. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,159 S. Corezzi\n,76, 51 N. J. Cornish\n,160 I. Coronado,161 A. Corsi\n,162\nR. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 57 D. M. Coward,72 R. Coyne\n,163\nA. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,164 P. Cremonese\n,98 S. Crook,63 R. Crouch,2\nJ. Csizmazia,2 J. R. Cudell\n,165 T. J. Cullen\n,11 A. Cumming\n,86 E. Cuoco\n,166, 167 M. Cusinato\n,137\nL. V. Da Concei\u00b8c\u02dcao\n,168 T. Dal Canton\n,41 S. Dal Pra\n,169 G. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37\nS. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,122 L. P. Dartez\n,63 R. Das,106 A. Dasgupta,93 V. Dattilo\n,62\nA. Daumas,20 N. Davari,170, 171 I. Dave,103 A. Davenport,136 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72\nM. C. Davis\n,18 P. Davis\n,172, 173 E. J. Daw\n,174 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,175\nM. De Laurentis\n,32, 4 F. De Lillo\n,23 S. Della Torre\n,127 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38\nG. Demasi,176, 61 F. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,177 A. Depasse\n,15 N. DePergola,102\nR. De Pietri\n,178, 179 R. De Rosa\n,32, 4 C. De Rossi\n,62 M. Desai\n,35 R. DeSalvo\n,180 A. DeSimone,181\nR. De Simone,150, 131 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,164 M. Di Cesare\n,32, 4 G. Dideron,182 T. Dietrich\n,1\nL. Di Fiore,4 C. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 183\nS. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,184, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,118\nJ. P. Docherty,86 Z. Doctor\n,96 N. Doerksen\n,168 E. Dohmen,2 A. Doke,132 A. Domiciano De Souza,185\nL. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,186 W. J. D. Doyle,122\nM. Drago\n,39, 38 J. C. Driggers\n,2 L. Dunn\n,123 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,170, 155\nP. Dutta Roy\n,46 H. Duval\n,187 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,188, 31 T. Eckhardt\n,97 G. Eddolls\n,78\nA. Effler\n,63 J. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25 M. Emma\n,58 K. Endo,151 R. Enficiaud\n,1\nL. Errico\n,32, 4 R. Espinosa,164 M. Esposito\n,4, 32 R. C. Essick\n,189 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35\nT. Evstafyeva,182 B. E. Ewing,7 J. M. Ezquiaga\n,139 F. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33\nA. M. Farah\n,129 B. Farr\n,77 W. M. Farr\n,190, 191 G. Favaro\n,91 M. Favata\n,192 M. Fays\n,165 M. Fazio\n,55\nJ. Feicht,11 M. M. Fejer,89 R. Felicetti\n,184, 48 E. Fenyvesi\n,87, 193 J. Fernandes,194 T. Fernandes\n,195, 137\nD. Fernando,110 S. Ferraiuolo\n,196, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81\nI. Fiori\n,62 M. Fishbach\n,189 R. P. Fisher,122 R. Fittipaldi\n,197, 131 V. Fiumara\n,198, 131 R. Flaminio,31\nS. M. Fleischer\n,199 L. S. Fleming,200 E. Floden,18 H. Fong,114 J. A. Font\n,137, 138 F. Fontinele-Nunes,18 C. Foo,1\nB. Fornal\n,201 K. Franceschetti,178 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,202\nA. Freise\n,37, 107 O. Freitas\n,195, 137 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,203 T. Fujimori,204 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1\nS. Galaudage\n,185 V. Galdi,205 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,180 D. Ganapathy\n,206 A. Ganguly\n,79\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,207 C. Garc\u00b4\u0131a-Quir\u00b4os\n,188 J. W. Gardner\n,34 K. A. Gardner,114 S. Garg,42\nJ. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,208 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29 A. Gennai\n,80 V. Gennari\n,100\nJ. George,103 R. George\n,147 O. Gerberding\n,97 L. Gergely\n,153 Archisman Ghosh\n,94 Sayantan Ghosh,194\nShaon Ghosh\n,192 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,209 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63\nK. D. Giardina,63 D. R. Gibson,200 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,210 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18\nM. Granata\n,175 V. Granata\n,211, 131 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,86 G. Greco,51\nA. C. Green\n,37, 107 L. Green,212 S. M. Green,73 S. R. Green\n,213 C. Greenberg,132 A. M. Gretarsson,65\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,137 D. Guetta\n,214 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,172, 173\nH. Guo\n,144 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,215 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,97 N. Gutierrez,175 N. Guttman,6 F. Guzman\n,130 D. Haba,216 M. Haberland\n,1\nS. Haino,217 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,218 A. G. Hanselman\n,129 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,181 S. Harikumar\n,186 K. Haris,37, 71 I. Harley-Trochimczyk,130 T. Harmark\n,133\nJ. Harms\n,44, 45 G. M. Harry\n,219 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 220, 221 C. J. Haster\n,212\nK. Haughian\n,86 H. Hayakawa,50 K. Hayama,222 M. C. Heintze,63 J. Heinze\n,118 J. Heinzel,35 H. Heitmann\n,113\nF. Hellman\n,206 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,115 M. Hendry\n,86\nI. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,223, 224 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,225 N. Hirata,25 C. Hirose,226\n\n12\nD. Hofman,175 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,174 D. E. Holz\n,129 L. Honet,111\nD. J. Horton-Bailey,206 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,143 E. J. Howell\n,72 C. G. Hoy\n,73\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,141 H.-Y. Hsieh,141 C. Hsiung,227 S.-H. Hsu,145 W.-F. Hsu\n,109\nQ. Hu\n,86 H. Y. Huang\n,140 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,228 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,131 J. Iascau,77\nK. Ide,229 R. Iden,216 A. Ierardi,44, 45 S. Ikeda,146 H. Imafuku,42 Y. Inoue,140 G. Iorio\n,91 P. Iosif\n,184, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,229 M. Isi\n,190, 191 K. S. Isleif\n,230 Y. Itoh\n,204, 231 M. Iwaya,203\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,121 T. Jacquot,41 S. J. Jadhav,232 S. P. Jadhav\n,154 M. Jain,132\nT. Jain,223 A. L. James\n,11 K. Jani\n,143 J. Janquart\n,15 N. N. Janthalur,232 S. Jaraba\n,233 P. Jaranowski\n,234\nR. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,149 H.-B. Jin\n,235, 236 G. R. Johns,122\nN. A. Johnson,46 M. C. Johnston\n,212 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,209 R. Jones,86\nH. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,237 L. Ju\n,72 K. Jung\n,238 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,239 I. Kaku,204 V. Kalogera\n,96 M. Kalomenopoulos\n,212\nM. Kamiizumi\n,50 N. Kanda\n,231, 204 S. Kandhasamy\n,79 G. Kang\n,240 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,132 M. Kasprzack\n,11 H. Kato,151\nT. Kato,203 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,204 D. Keitel\n,98\nL. J. Kemperman\n,115 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,241 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,162 M. Khursheed,103\nN. M. Khusid,190, 191 W. Kiendrebeogo\n,113, 242 N. Kijbunchoo\n,115 C. Kim,243 J. C. Kim,244 K. Kim\n,245\nM. H. Kim\n,237 S. Kim\n,246 Y.-M. Kim\n,245 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,203 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,247, 248 K. Kokeyama\n,33, 249 S. Koley\n,44, 165 P. Kolitsidou\n,118 A. E. Koloniari\n,250\nK. Komori\n,42 A. K. H. Kong\n,141 A. Kontos\n,251 L. M. Koponen,118 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,151 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,118 S. Kroker,252 A. Kr\u00b4olak\n,253, 186 K. Kruska,8, 9 J. Kubisz\n,254 G. Kuehn,8, 9\nS. Kulkarni\n,215 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,232 Praveen Kumar\n,177\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,255, 256, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,207, 257 S. Kuwahara\n,42 K. Kwak\n,238 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,188, 100\nA. H. Laity,163 E. Lalande,258 M. Lalleman\n,23 P. C. Lalremruati,259 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,147 R. Langgin\n,212 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,199 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,164 M. Laxen\n,63 C. Lazarte\n,137 A. Lazzarini\n,11 C. Lazzaro,156, 155 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,260 H. W. Lee\n,261 J. Lee,78 K. Lee\n,237 R.-K. Lee\n,141 R. Lee,35\nSungho Lee\n,245 Sunjae Lee,237 Y. Lee,140 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,182 M. Le Jean\n,175, 116\nA. Lema\u02c6\u0131tre\n,262 M. Lenti\n,61, 176 M. Leonardi\n,74, 75, 263 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,264 T. G. F. Li,109 X. Li\n,148\nY. Li,96 Z. Li,86 A. Lihos,122 E. T. Lin\n,141 F. Lin,140 L. C.-C. Lin\n,264 Y.-C. Lin\n,141 C. Lindsay,200\nS. D. Linker,180 A. Liu\n,218 G. C. Liu\n,227 Jian Liu\n,72 F. Llamas Villarreal,164 J. Llobera-Querol\n,98\nR. K. L. Lo\n,139 J.-P. Locquet,109 S. C. G. Loggins,265 M. R. Loizou,132 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,165 M. Lopez Portilla,71, 21, 22 A. Lorenzo-Medina\n,177 V. Loriette,41 M. Lormand,63 G. Losurdo\n,266, 80\nE. Lotti,132 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,123 N. Lu\n,34\nL. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,267, 268 A. W. Lussier\n,258 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,151 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,163\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,189\nS. Maliakal,11 A. Malik,103 L. Mallick\n,168, 189 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,170, 155 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 269\nC. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100\nF. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,192 B. B. Martinez,130 D. A. Martinez,54 M. Martinez,43, 270\nV. Martinez\n,128 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,118 E. J. Marx,35 L. Massaro,36, 37\nA. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,208\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,122 C. McElhenny,122 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,143\nJ. McIver\n,114 A. McLeod\n,72 I. McMahon\n,188 T. McRae,34 R. McTeague\n,86 D. Meacher\n,10 B. N. Meagher,78\n\n13\nR. Mechum,110 Q. Meijer,71 A. Melatos,123 C. S. Menoni\n,136 F. Mera,2 R. A. Mercer\n,10 L. Mereni,175\nK. Merfeld,162 E. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10 B. Mestichelli,44\nM. Meyer-Conde\n,271 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,272 C. Michel\n,175 Y. Michimura\n,42\nH. Middleton\n,118 D. P. Mihaylov\n,104 A. L. Miller\n,37, 71 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,184, 48\nV. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43 L. Mirasola\n,155, 156 M. Miravet-Ten\u00b4es\n,137\nC.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46 A. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79\nV. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35\nL. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,206 M. Mondin,180 M. Montani,60, 61\nC. J. Moore,223 D. Moraru,2 A. More\n,79 S. More\n,79 C. Moreno\n,134 E. A. Moreno\n,35 G. Moreno,2\nA. Moreso Serra,82 S. Morisaki\n,42, 203 Y. Moriwaki\n,151 G. Morras\n,207 A. Moscatello\n,91 M. Mould\n,35\nB. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,176, 61 F. Muciaccia\n,39, 38 D. Mukherjee\n,118\nSamanwaya Mukherjee,24 Soma Mukherjee,164 Subroto Mukherjee,93 Suvodip Mukherjee\n,13 N. Mukund\n,35\nA. Mullavey,63 H. Mullock,114 J. Mundi,219 C. L. Mungioli,72 M. Murakoshi,229 P. G. Murray\n,86 D. Nabari\n,74, 75\nS. L. Nadji,8, 9 A. Nagar,28, 273 N. Nagarajan\n,86 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,274 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,62 P. Narayan\n,215 I. Nardecchia\n,22 T. Narikawa,203\nH. Narola,71 L. Naticchioni\n,38 R. K. Nayak\n,259 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,130\nT. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen Quynh\n,275 S. A. Nichols,12 A. B. Nielsen\n,276\nY. Nishino,25, 42 A. Nishizawa\n,277 S. Nissanke,278, 37 W. Niu\n,7 F. Nocera,62 J. Noller,279 M. Norman,33\nC. North,33 J. Novak\n,116, 233, 280 R. Nowicki\n,143 J. F. Nu\u02dcno Siles\n,207 L. K. Nuttall\n,73 K. Obayashi,229\nJ. Oberling\n,2 J. O\u2019Dell,228 E. Oelker\n,35 M. Oertel\n,233, 116, 281, 280 G. Oganesyan,44, 45 T. O\u2019Hanlon,63\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,116, 281, 280 R. Omer,18 B. O\u2019Neal,122 M. Onishi,151 K. Oohara\n,282\nB. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110 S. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11\nI. Ota\n,12 D. J. Ottaway\n,115 A. Ouzriat,56 H. Overmier,63 B. J. Owen\n,283 R. Ozaki,229 A. E. Pace\n,7\nR. Pagano\n,12 M. A. Page\n,25 A. Pai\n,194 L. Paiella,44 A. Pal,284 S. Pal\n,259 M. A. Palaia\n,80, 81 M. P\u00b4alfi,202\nP. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,141 J. Pan,72 K. C. Pan\n,141 P. K. Panda,232\nShiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38 K. A. Pannone,54 B. C. Pant,103\nF. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 285 A. Papadopoulos\n,86 E. E. Papalexakis,210\nL. Papalini\n,80, 81 G. Papigkiotis\n,250 A. Paquis,41 A. Parisi\n,76, 51 B.-J. Park,245 J. Park\n,286 W. Parker\n,63\nG. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80 L. Passenger,6 D. Passuello,80\nO. Patane\n,2 A. V. Patel\n,140 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80 B. G. Patterson,33 K. Paul\n,106\nS. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna Arellano\n,287 X. Peng,118\nY. Peng,57 S. Penn\n,288 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,132 C. P\u00b4erigois\n,289, 92, 91 G. Perna\n,91\nA. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107 D. Pesios,250 S. Peters,165 S. Petracca,205\nC. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18 K. S. Phukon\n,118 H. Phurailatpam,218\nM. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113 M. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61\nL. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,290, 131 M. Pietrzak,95 M. Pillas\n,165 F. Pilo\n,80 L. Pinard\n,175\nI. M. Pinto\n,290, 131, 291, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,223, 86 A. Placidi\n,51\nE. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,211, 22 C. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35\nJ. Pomper,80, 81 L. Pompili\n,1 J. Poon,218 E. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62\nJ. Powell\n,154 G. S. Prabhu,79 M. Pracchia\n,165 B. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93\nK. Prasai\n,292 R. Prasanna,232 P. Prasia,79 G. Pratten\n,118 G. Principe\n,184, 48 G. A. Prodi\n,74, 75 P. Prosperi,80\nP. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,163 H. Qi\n,16\nM. Qiao\n,144 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,173, 116 V. Quetschke,164 P. J. Quinonez,65 N. Qutob,57 R. Rading,230\nI. Rainho,137 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110 K. E. Ramirez\n,63 F. A. Ramis Vidal\n,98\nM. Ramos Arevalo\n,164 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57 K. Ransom,63 P. Rapagnani\n,39, 38 B. Ratto,65\nA. Ravichandran,132 A. Ray\n,96 V. Raymond\n,33 M. Razzano\n,81, 80 J. Read,54 T. Regimbau,31 S. Reid,55\nC. Reissel,35 D. H. Reitze\n,11 V. Rella,39 A. I. Renzini\n,126, 11 B. Revenu\n,293, 41 A. Revilla Pe\u02dcna,82 R. Reyes,180\nL. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39 A. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,210\nM. L. Richardson,115 A. Rijal,65 K. Riles\n,90 H. K. Riley,33 S. Rinaldi\n,269 J. Rittmeyer,97 C. Robertson,228\nF. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31 J. G. Rollins\n,11 A. E. Romano\n,294 R. Romano\n,3, 4\nA. Romero\n,31 I. M. Romero-Shaw,223 J. H. Romie,63 S. Ronchini\n,7 T. J. Roocke\n,115 L. Rosa,4, 32\nT. J. Rosauer,210 C. A. Rose,57 D. Rosi\u00b4nska\n,124 M. P. Ross\n,53 M. Rossello-Sastre\n,98 S. Rowan\n,86\nS. K. Roy\n,190, 191 S. Roy\n,15 D. Rozza\n,126, 127 P. Ruggi,62 N. Ruhama,238 E. Ruiz Morales\n,295, 207\n\n14\nK. Ruiz-Rocha,143 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,168 M. R. Sah\n,13 S. Saha\n,141\nT. Sainrat\n,64 S. Sajith Menon\n,214, 39, 38 K. Sakai,296 Y. Sakai\n,271 M. Sakellariadou\n,67 S. Sakon\n,7\nO. S. Salafia\n,158, 127, 126 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,147 F. Salemi\n,39, 38 M. Sall\u00b4e\n,37\nS. U. Salunkhe,79 S. Salvador\n,173, 172 A. Salvarese,147 A. Samajdar\n,71, 37 A. Sanchez,2 E. J. Sanchez,11\nL. E. Sanchez,11 N. Sanchis-Gual\n,137 J. R. Sanders,181 E. M. S\u00a8anger\n,1 F. Santoliquido\n,44, 45 F. Sarandrea,28\nT. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,250 P. Sassi\n,51, 76 B. Sassolas\n,175 B. S. Sathyaprakash\n,7, 33\nR. Sato,226 S. Sato,151 Yukino Sato,151 Yu Sato,151 O. Sauter\n,46 R. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,79\nS. Sayah,175 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,148 A. Schiebelbein,189 M. G. Schiworski\n,78\nP. Schmidt\n,118 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9 R. M. S. Schofield,77 K. Schouteden\n,109\nB. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,297 M. Scialpi\n,298 J. Scott\n,86 S. M. Scott\n,34\nR. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,299 D. Sellers,63 N. Sembo,204\nA. S. Sengupta\n,300 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38 A. Sevrin,187 T. Shaffer,2\nU. S. Shah\n,57 M. A. Shaikh\n,260 L. Shao\n,301 A. K. Sharma\n,98 Preeti Sharma,12 Prianka Sharma,103\nRitwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,125 N. S. Shcheblanov\n,302, 262 E. Sheridan,143\nZ.-H. Shi,141 M. Shikauchi,42 R. Shimomura,303 H. Shinkai\n,303 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,147 R. W. Short,2 S. ShyamSundar,103 A. Sider,157 H. Siegel\n,190, 191 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 169 M. Simmonds,115 L. P. Singer\n,304 Amitesh Singh,215 Anika Singh,11\nD. Singh\n,206 N. Singh\n,98 S. Singh,216, 59 A. M. Sintes\n,98 V. Sipala,170, 155 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,199 T. J. Slaven-Blair,72 J. Smetana,118 J. R. Smith\n,54 L. Smith\n,86, 184, 48 R. J. E. Smith\n,6\nW. J. Smith\n,143 S. Soares de Albuquerque Filho,60 M. Soares-Santos,188 K. Somiya\n,216 I. Song\n,141 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,305 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,122 D. A. Steer\n,306 N. Steinle\n,168 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,250 P. Stevens,41 M. StPierre,163 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,229 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,240 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,216 M. Suzuki,203\nB. L. Swinkels\n,37 A. Syx\n,116 M. J. Szczepa\u00b4nczyk\n,307 P. Szewczyk\n,124 M. Tacca\n,37 H. Tagoshi\n,203\nK. Takada,203 H. Takahashi\n,271 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,308 H. Takeda\n,309, 310\nK. Takeshita,216 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,129 M. Tamaki,203 N. Tamanini\n,100\nD. Tanabe,140 K. Tanaka,50 S. J. Tanaka\n,229 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,210\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,311 J. D. Tasson\n,152 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,180 A. Theodoropoulos\n,137 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,209 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,194 S. Tiwari\n,188 V. Tiwari\n,118\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,140 A. Torres-Forn\u00b4e\n,137, 138 C. I. Torrie,11 I. Tosta e Melo\n,312\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,122 A. Trapananti\n,52, 51 R. Travaglini\n,167 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,125 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,184, 48 A. Trovato\n,184, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,313 L. Tsukada\n,212 K. Turbang\n,187, 23 M. Turconi\n,113\nC. Turski,94 H. Ubach\n,82, 83 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,314 K. Ueno\n,42 V. Undheim\n,276\nL. E. Uronen,218 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,294 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 315\nE. Van den Bossche\n,187 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,258 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,123 V. Varma\n,132 A. N. Vazquez,89 A. Vecchio\n,118 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,115 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,132\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,189 A. Vilkha,110 N. Villanueva Espinosa,137 V. Villa-Ortega\n,177\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,230 L. Vujeva\n,139 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,216 J. Z. Wang,90 W. H. Wang,164\nY. F. Wang\n,1 G. Waratkar\n,194 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\n\n15\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\nA. T. Wilkin,210 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,140 I. C. F. Wong\n,218, 109 K. Wong,189 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,141 D. S. Wu\n,8, 9 H. Wu\n,141 K. Wu,119 Q. Wu,53 Y. Wu,96\nZ. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,206 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,151 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,229 T. Yan,118 F. Yang\n,46, 316\nK. Z. Yang\n,18 Y. Yang\n,145 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,141 A. B. Yelikar\n,143 X. Yin,35\nJ. Yokoyama\n,317, 42 T. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110 T. Zelenova,62\nJ.-P. Zendri,92 M. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57 R. Zhang\n,149 T. Zhang,118\nC. Zhao\n,72 Yue Zhao,161 Yuhang Zhao,20 Z.-C. Zhao\n,318 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78 H. O. Zhu,72\nZ.-H. Zhu\n,318, 319 A. B. Zimmerman\n,147 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\nand\nJ. Shu\n320, 321, 322\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n\n16\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n\n17\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120Cornell University, Ithaca, NY 14850, USA\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n128Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n132University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n135Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n136Colorado State University, Fort Collins, CO 80523, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140National Central University, Taoyuan City 320317, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144University of Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Beijing 100190, China\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n146Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n\n18\n156Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n157Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n159Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n161The University of Utah, Salt Lake City, UT 84112, USA\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n165Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n166DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n171INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n172Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n173Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n174The University of Sheffield, Sheffield S10 2TN, United Kingdom\n175Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n176Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n177IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n178Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n179INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n180California State University, Los Angeles, Los Angeles, CA 90032, USA\n181Marquette University, Milwaukee, WI 53233, USA\n182Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n183Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n184Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n185Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n186National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n187Vrije Universiteit Brussel, 1050 Brussel, Belgium\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n190Stony Brook University, Stony Brook, NY 11794, USA\n191Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n192Montclair State University, Montclair, NJ 07043, USA\n193HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n194Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n195Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n196Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n197CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n198Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n199Western Washington University, Bellingham, WA 98225, USA\n200SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n201Barry University, Miami Shores, FL 33168, USA\n202E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n203Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n204Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n205University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n206University of California, Berkeley, CA 94720, USA\n207Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n208Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n209University of Southampton, Southampton SO17 1BJ, United Kingdom\n210University of California, Riverside, Riverside, CA 92521, USA\n\n19\n211Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213University of Nottingham NG7 2RD, UK\n214Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n215The University of Mississippi, University, MS 38677, USA\n216Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n217Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n218The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n219American University, Washington, DC 20016, USA\n220Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n221INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n222Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n223University of Cambridge, Cambridge CB2 1TN, United Kingdom\n224University of Lancaster, Lancaster LA1 4YW, United Kingdom\n225College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n226Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n227Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n228Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n229Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n230Helmut Schmidt University, D-22043 Hamburg, Germany\n231Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n234Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n235National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n236School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237Sungkyunkwan University, Seoul 03063, Republic of Korea\n238Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n239Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n240Chung-Ang University, Seoul 06974, Republic of Korea\n241University of Washington Bothell, Bothell, WA 98011, USA\n242Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n243Ewha Womans University, Seoul 03760, Republic of Korea\n244National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n245Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n246Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n247Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n248Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n249Nagoya University, Nagoya, 464-8601, Japan\n250Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n251Bard College, Annandale-On-Hudson, NY 12504, USA\n252Technical University of Braunschweig, D-38106 Braunschweig, Germany\n253Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n254Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n255Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n256Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n\n20\n257Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n258Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n259Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n260Seoul National University, Seoul 08826, Republic of Korea\n261Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n262NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n263Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n264Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n265St. Thomas University, Miami Gardens, FL 33054, USA\n266Scuola Normale Superiore, I-56126 Pisa, Italy\n267Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n268Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n269Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n270Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n271Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n272Tsinghua University, Beijing 100084, China\n273Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n274Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n275Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n276University of Stavanger, 4021 Stavanger, Norway\n277Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n278GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n279University College London, London WC1E 6BT, United Kingdom\n280Observatoire de Paris, 75014 Paris, France\n281Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n282Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n283University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n284CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n285Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n286Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n287Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n288Hobart and William Smith Colleges, Geneva, NY 14456, USA\n289INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n290Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n291Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n292Kennesaw State University, Kennesaw, GA 30144, USA\n293Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n294Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n295Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n296Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n297Trinity College, Hartford, CT 06106, USA\n298Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n299Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n300Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n301Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n\n21\n302Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n303Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n304NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n305Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n306Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n307Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n308Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n309The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n310Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n311Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n313National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n314Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n315Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n316Department of Physics and Astronomy, University of Notre Dame, South Bend, IN 46556, USA\n317Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n318Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n319School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n320School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China\n321Center for High Energy Physics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n322Beijing Laser Acceleration Innovation Center, Huairou, Beiing,101400, China\n(Dated: December 12, 2025)\n\u2217Deceased, September 2024.\n", "Draft version 3 November 2025\nTypeset using LATEX twocolumn style in AASTeX631\nGW241011 and GW241110: Exploring Binary Formation and Fundamental Physics with Asymmetric,\nHigh-Spin Black Hole Coalescences\nA. G. Abac\n,1 I. Abouelfettouh,2 F. Acernese,3, 4 K. Ackley\n,5 C. Adamcewicz\n,6 S. Adhicary\n,7\nD. Adhikari,8, 9 N. Adhikari\n,10 R. X. Adhikari\n,11 V. K. Adkins,12 S. Afroz\n,13 A. Agapito,14\nD. Agarwal\n,15 M. Agathos\n,16 N. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar\n,19 I.-L. Ahrend,20\nL. Aiello\n,21, 22 A. Ain\n,23 P. Ajith\n,24 T. Akutsu\n,25, 26 S. Albanesi\n,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9\nC. All\u00b4en\u00b4e,31 A. Allocca\n,32, 4 S. Al-Shammari,33 P. A. Altin\n,34 S. Alvarez-Lopez\n,35 W. Amar,31\nO. Amarasinghe,33 A. Amato\n,36, 37 F. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11\nW. G. Anderson\n,11 M. Andia\n,41 M. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9 J. Anglin,46\nS. Ansoldi\n,47, 48 J. M. Antelis\n,49 S. Antier\n,41 F. Antonini,33 M. Aoumi,50 E. Z. Appavuravther,51, 52\nS. Appert,11 S. K. Apple\n,53 K. Arai\n,11 C. Ara\u00b4ujo-\u00b4Alvarez,54 A. Araya\n,42 M. C. Araya\n,11\nM. Arca Sedda\n,44, 45 J. S. Areeda\n,55 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,56 N. Arnaud\n,57\nM. Arogeti\n,58 S. M. Aronson\n,12 K. G. Arun\n,59 G. Ashton\n,60 Y. Aso\n,25, 61 L. Asprea,28 M. Assiduo,62, 63\nS. Assis de Souza Melo,64 S. M. Aston,65 P. Astone\n,38 P. S. Aswathi,34 F. Attadio\n,39, 38 F. Aubin\n,66\nK. AultONeal\n,67 G. Avallone\n,68 E. A. Avila\n,49 S. Babak\n,20 C. Badger,69 S. Bae\n,70 S. Bagnasco\n,28\nL. Baiotti\n,71 R. Bajpai\n,72 T. Baka,73, 37 A. M. Baker,6 K. A. Baker,74 T. Baker\n,75 G. Baldi\n,76, 77\nN. Baldicchi\n,78, 51 M. Ball,79 G. Ballardin,64 S. W. Ballmer,80 S. Banagiri\n,6 B. Banerjee\n,44\nD. Bankar\n,81 T. M. Baptiste,12 P. Baral\n,10 M. Baratti\n,82, 83 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2\nN. Barman,81 P. Barneo\n,84, 85, 86 F. Barone\n,87, 4 B. Barr\n,88 L. Barsotti\n,35 M. Barsuglia\n,20\nD. Barta\n,89 A. M. Bartoletti,90 M. A. Barton\n,88 I. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,91\nA. Basti\n,83, 82 M. Bawaj\n,78, 51 P. Baxi,92 J. C. Bayley\n,88 A. C. Baylor\n,10 P. A. Baynard II,58\nM. Bazzan,93, 94 V. M. Bedakihale,95 F. Beirnaert\n,96 M. Bejger\n,97 D. Belardinelli\n,22 A. S. Bell\n,88\nD. S. Bellie,98 L. Bellizzi\n,82, 83 W. Benoit\n,18 I. Bentara\n,57 J. D. Bentley\n,99 M. Ben Yaala,56\nS. Bera\n,100, 101 F. Bergamin\n,33 B. K. Berger\n,91 S. Bernuzzi\n,27 M. Beroiz\n,11 C. P. L. Berry\n,88\nD. Bersanetti\n,29 T. Bertheas,102 A. Bertolini,37, 36 J. Betzwieser\n,65 D. Beveridge\n,74 G. Bevilacqua\n,103\nN. Bevins\n,104 R. Bhandare,105 R. Bhatt,11 D. Bhattacharjee\n,106, 107 S. Bhattacharyya,108 S. Bhaumik\n,46\nV. Biancalana\n,103 A. Bianchi,37, 109 I. A. Bilenko,110 G. Billingsley\n,11 A. Binetti\n,111 S. Bini\n,11, 76, 77\nC. Binu,112 S. Biot,113 O. Birnholtz\n,114 S. Biscoveanu\n,98 A. Bisht,9 M. Bitossi\n,64, 82 M.-A. Bizouard\n,115\nS. Blaber,116 J. K. Blackburn\n,11 L. A. Blagg,79 C. D. Blair,74, 65 D. G. Blair,74 N. Bode\n,8, 9 N. Boettner,99\nG. Boileau\n,115 M. Boldrini\n,38 G. N. Bolingbroke\n,117 A. Bolliand,118, 40 L. D. Bonavena\n,46\nR. Bondarescu\n,84 F. Bondu\n,119 E. Bonilla\n,91 M. S. Bonilla\n,55 A. Bonino,120 R. Bonnand\n,31, 118\nA. Borchers,8, 9 S. Borhanian,7 V. Boschi\n,82 S. Bose,121 V. Bossilkov,65 Y. Bothra\n,37, 109 A. Boudon,57\nL. Bourg,58 M. Boyle,122 A. Bozzi,64 C. Bradaschia,82 P. R. Brady\n,10 A. Branch,65 M. Branchesi\n,44, 45\nI. Braun,106 T. Briant\n,123 A. Brillet,115 M. Brinkmann,8, 9 P. Brockill,10 E. Brockmueller\n,8, 9\nA. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,117 M. L. Brozzetti\n,78, 51 S. Brunett,11 G. Bruno,15\nR. Bruntz\n,124 J. Bryant,120 Y. Bu,125 F. Bucci\n,63 J. Buchanan,124 O. Bulashenko\n,84, 85 T. Bulik,126\nH. J. Bulten,37 A. Buonanno\n,127, 1 K. Burtnyk,2 R. Buscicchio\n,128, 129 D. Buskulic,31 C. Buy\n,102\nR. L. Byer,91 G. S. Cabourn Davies\n,75 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7 L. Cadonati\n,58\nG. Cagnoli\n,130 C. Cahillane\n,80 A. Calafat,100 J. Calder\u00b4on Bustillo,54 T. A. Callister,131, 132 E. Calloni,32, 4\nS. R. Callos\n,79 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,133 E. Capocasa\n,20\nE. Capote\n,2, 11 G. Capurri\n,83, 82 G. Carapella,68, 134 F. Carbognani,64 M. Carlassara,8, 9 J. B. Carlin\n,125\nT. K. Carlson,135 M. F. Carney,106 M. Carpinelli\n,128, 64 G. Carrillo,79 J. J. Carter\n,8, 9 G. Carullo\n,120, 136\nA. Casallas-Lagos,137 J. Casanueva Diaz\n,64 C. Casentini\n,138, 22 S. Y. Castro-Lucas,139 S. Caudill,135\nM. Cavagli`a\n,107 R. Cavalieri\n,64 A. Ceja,55 G. Cella\n,82 P. Cerd\u00b4a-Dur\u00b4an\n,140, 141 E. Cesarini\n,22\nN. Chabbra,34 W. Chaibi,115 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,105\nS. Chalathadka Subrahmanya\n,99 J. C. L. Chan\n,142 M. Chan,116 K. Chang,143 S. Chao\n,144, 143\nP. Charlton\n,145 E. Chassande-Mottin\n,20 C. Chatterjee\n,146 Debarati Chatterjee\n,81\nDeep Chatterjee\n,35 M. Chaturvedi,105 S. Chaty\n,20 K. Chatziioannou\n,11 A. Chen\n,147 A. H.-Y. Chen,148\nD. Chen\n,149 H. Chen,144 H. Y. Chen\n,150 S. Chen,146 Yanbei Chen,151 Yitian Chen\n,122 H. P. Cheng,152\nP. Chessa\n,78, 51 H. T. Cheung\n,92 S. Y. Cheung,6 F. Chiadini\n,153, 134 D. Chiaramello,28 G. Chiarini,8, 9, 94\nA. Chiba,154 A. Chincarini\n,29 M. L. Chiofalo\n,83, 82 A. Chiummo\n,4, 64 C. Chou,148 S. Choudhary\n,74\narXiv:2510.26931v1 [astro-ph.HE] 30 Oct 2025\n\n2\nN. Christensen\n,115, 155 S. S. Y. Chua\n,34 G. Ciani\n,76, 77 P. Ciecielag\n,97 M. Cie\u00b4slar\n,126 M. Cifaldi\n,22\nB. Cirok,156 F. Clara,2 J. A. Clark\n,11, 58 T. A. Clarke\n,6 P. Clearwater,157 S. Clesse,113 F. Cleva,115, 118\nE. Coccia,44, 45, 43 E. Codazzo\n,158, 159 P.-F. Cohadon\n,123 S. Colace\n,30 E. Colangeli,75 M. Colleoni\n,100\nC. G. Collette,160 J. Collins,65 S. Colloms\n,88 A. Colombo\n,161, 129 C. M. Compton,2 G. Connolly,79\nL. Conti\n,94 T. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,162 S. Corezzi\n,78, 51 N. J. Cornish\n,163 I. Coronado,164\nA. Corsi\n,165 R. Cottingham,65 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 58 D. M. Coward,74\nR. Coyne\n,166 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,167 P. Cremonese\n,100 S. Crook,65\nR. Crouch,2 J. Csizmazia,2 J. R. Cudell\n,168 T. J. Cullen\n,11 A. Cumming\n,88 E. Cuoco\n,169, 170\nM. Cusinato\n,140 L. V. Da Conceic\u00b8\u02dcao\n,171 T. Dal Canton\n,41 S. Dal Pra\n,172 G. D\u00b4alya\n,102\nB. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,124 L. P. Dartez\n,65\nR. Das,108 A. Dasgupta,95 V. Dattilo\n,64 A. Daumas,20 N. Davari,173, 174 I. Dave,105 A. Davenport,139 M. Davier,41\nT. F. Davies,74 D. Davis\n,11 L. Davis,74 M. C. Davis\n,18 P. Davis\n,175, 176 E. J. Daw\n,177 M. Dax\n,1\nJ. De Bolle\n,96 M. Deenadayalan,81 J. Degallaix\n,178 M. De Laurentis\n,32, 4 F. De Lillo\n,23\nS. Della Torre\n,129 W. Del Pozzo\n,83, 82 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,179, 63\nF. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,54 A. Depasse\n,15 N. DePergola,104 R. De Pietri\n,180, 181\nR. De Rosa\n,32, 4 C. De Rossi\n,64 M. Desai\n,35 R. DeSalvo\n,182 A. DeSimone,183 R. De Simone,153, 134\nA. Dhani\n,1 R. Dhurkunde,8, 9, 75 R. Diab,46 M. C. D\u00b4\u0131az\n,167 M. Di Cesare\n,32, 4 G. Dideron,184 T. Dietrich\n,1\nL. Di Fiore,4 C. Di Fronzo\n,74 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 185\nS. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,186, 48 F. Di Renzo\n,57 Divyajyoti\n,33 A. Dmitriev\n,120\nJ. P. Docherty,88 Z. Doctor\n,98 N. Doerksen\n,171 E. Dohmen,2 A. Doke,135 A. Domiciano De Souza,187\nL. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33 T. Dooney,73 S. Doravari\n,81 O. Dorosh,188\nW. J. D. Doyle,124 M. Drago\n,39, 38 J. C. Driggers\n,2 L. Dunn\n,125 U. Dupletsa,44 P.-A. Duverne\n,20\nD. D\u2019Urso\n,173, 158 P. Dutta Roy\n,46 H. Duval\n,189 S. E. Dwyer,2 C. Eassa,2 W. E. East,184\nM. Ebersold\n,190, 31 T. Eckhardt\n,99 G. Eddolls\n,80 A. Effler\n,65 J. Eichholz\n,34 H. Einsle,115\nM. Eisenmann,25 M. Emma\n,60 K. Endo,154 R. Enficiaud\n,1 L. Errico\n,32, 4 R. Espinosa,167 M. Esposito\n,4, 32\nR. C. Essick\n,191 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,184 B. E. Ewing,7\nJ. M. Ezquiaga\n,142 F. Fabrizi\n,62, 63 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,131 B. Farr\n,79\nW. M. Farr\n,192, 193 G. Favaro\n,93 M. Favata\n,194 M. Fays\n,168 M. Fazio\n,56 J. Feicht,11 M. M. Fejer,91\nR. Felicetti\n,186, 48 E. Fenyvesi\n,89, 195 J. Fernandes,196 T. Fernandes\n,197, 140 D. Fernando,112\nS. Ferraiuolo\n,198, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,83, 82 P. Figura\n,97 A. Fiori\n,82, 83 I. Fiori\n,64\nM. Fishbach\n,191 R. P. Fisher,124 R. Fittipaldi\n,199, 134 V. Fiumara\n,200, 134 R. Flaminio,31 S. M. Fleischer\n,201\nL. S. Fleming,202 E. Floden,18 H. Fong,116 J. A. Font\n,140, 141 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal\n,203\nK. Franceschetti,180 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,82 J. P. Freed,67 Z. Frei\n,204 A. Freise\n,37, 109\nO. Freitas\n,197, 140 R. Frey\n,79 W. Frischhertz,65 P. Fritschel,35 V. V. Frolov,65 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,205 T. Fujimori,206 P. Fulda,46 M. Fyffe,65 B. Gadre\n,73 J. R. Gair\n,1\nS. Galaudage\n,187 V. Galdi,207 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,182 D. Ganapathy\n,208 A. Ganguly\n,81\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,209 C. Garc\u00b4\u0131a-Quir\u00b4os\n,190 J. W. Gardner\n,34 K. A. Gardner,116\nS. Garg,42 J. Gargiulo\n,64 X. Garrido\n,41 A. Garron\n,100 F. Garufi\n,32, 4 P. A. Garver,91\nC. Gasbarra\n,21, 22 B. Gateley,2 F. Gautier\n,210 V. Gayathri\n,10 T. Gayer,80 G. Gemme\n,29 A. Gennai\n,82\nV. Gennari\n,102 J. George,105 R. George\n,150 O. Gerberding\n,99 L. Gergely\n,156 Archisman Ghosh\n,96\nSayantan Ghosh,196 Shaon Ghosh\n,194 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,211 Tathagata Ghosh\n,81\nJ. A. Giaime\n,12, 65 K. D. Giardina,65 D. R. Gibson,202 C. Gier\n,56 S. Gkaitatzis\n,83, 82 J. Glanzer\n,11\nF. Glotin\n,41 J. Godfrey,79 R. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,116 J. Golomb,11\nS. Gomez Lopez\n,39, 38 B. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,212 S. Goode,6\nA. W. Goodwin-Jones\n,15 M. Gosselin,64 R. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,78, 51\nV. Graham\n,88 A. E. Granados\n,18 M. Granata\n,178 V. Granata\n,213, 134 S. Gras,35 P. Grassia,11 J. Graves,58\nC. Gray,2 R. Gray\n,88 G. Greco,51 A. C. Green\n,37, 109 L. Green,214 S. M. Green,75 S. R. Green\n,215\nC. Greenberg,135 A. M. Gretarsson,67 H. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,58 G. Grignani,78, 51\nC. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1 D. Guerra\n,140 D. Guetta\n,216 G. M. Guidi\n,62, 63\nA. R. Guimaraes,12 H. K. Gulati,95 F. Gulminelli\n,175, 176 H. Guo\n,147 W. Guo\n,74 Y. Guo\n,37, 36\nAnuradha Gupta\n,217 I. Gupta\n,7 N. C. Gupta,95 S. K. Gupta,46 V. Gupta\n,18 N. Gupte,1 J. Gurs,99\nN. Gutierrez,178 N. Guttman,6 F. Guzman\n,133 D. Haba,218 M. Haberland\n,1 S. Haino,219 E. D. Hall\n,35\nE. Z. Hamilton\n,100 G. Hammond\n,88 M. Haney,37 J. Hanks,2 C. Hanna\n,7 M. D. Hannam,33\nO. A. Hannuksela\n,220 A. G. Hanselman\n,131 H. Hansen,2 J. Hanson,65 S. Hanumasagar,58 R. Harada,42\nA. R. Hardison,183 S. Harikumar\n,188 K. Haris,37, 73 I. Harley-Trochimczyk,133 T. Harmark\n,136 J. Harms\n,44, 45\n\n3\nG. M. Harry\n,221 I. W. Harry\n,75 J. Hart,106 B. Haskell,97, 222, 223 C. J. Haster\n,214 K. Haughian\n,88\nH. Hayakawa,50 K. Hayama,224 A. Heffernan,100 M. C. Heintze,65 J. Heinze\n,120 J. Heinzel,35 H. Heitmann\n,115\nF. Hellman\n,208 A. F. Helmling-Cornell\n,79 G. Hemming\n,64 O. Henderson-Sapir\n,117 M. Hendry\n,88\nI. S. Heng,88 M. H. Hennig\n,88 C. Henshaw\n,58 M. Heurs\n,8, 9 A. L. Hewitt\n,225, 226 J. Heynen,15 J. Heyns,35\nS. Higginbotham,33 S. Hild,36, 37 S. Hill,88 Y. Himemoto\n,227 N. Hirata,25 C. Hirose,228 D. Hofman,178\nB. E. Hogan,67 N. A. Holland,37, 109 I. J. Hollows\n,177 D. E. Holz\n,131 L. Honet,113 D. J. Horton-Bailey,208\nJ. Hough\n,88 S. Hourihane\n,11 N. T. Howard,146 E. J. Howell\n,74 C. G. Hoy\n,75 C. A. Hrishikesh,21 P. Hsi,35\nH.-F. Hsieh\n,144 H.-Y. Hsieh,144 C. Hsiung,229 S.-H. Hsu,148 W.-F. Hsu\n,111 Q. Hu\n,88 H. Y. Huang\n,143\nY. Huang\n,7 Y. T. Huang,80 A. D. Huddart,230 B. Hughey,67 V. Hui\n,31 S. Husa\n,100 R. Huxford,7\nL. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,134 J. Iascau,79 K. Ide,231 R. Iden,218\nA. Ierardi,44, 45 S. Ikeda,149 H. Imafuku,42 Y. Inoue,143 G. Iorio\n,93 P. Iosif\n,186, 48 M. H. Iqbal,34 J. Irwin\n,88\nR. Ishikawa,231 M. Isi\n,192, 193 K. S. Isleif\n,232 Y. Itoh\n,206, 233 M. Iwaya,205 B. R. Iyer\n,24 C. Jacquet,102\nP.-E. Jacquet\n,123 T. Jacquot,41 S. J. Jadhav,234 S. P. Jadhav\n,157 M. Jain,135 T. Jain,225 A. L. James\n,11\nK. Jani\n,146 J. Janquart\n,15 N. N. Janthalur,234 S. Jaraba\n,235 P. Jaranowski\n,236 R. Jaume\n,100\nW. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,152 H.-B. Jin\n,237, 238 G. R. Johns,124 N. A. Johnson,46\nM. C. Johnston\n,214 R. Johnston,88 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,211 R. Jones,88 H. E. Jose,79\nP. Joshi\n,7 S. K. Joshi,81 G. Joubert,57 J. Ju,239 L. Ju\n,74 K. Jung\n,240 J. Junker\n,34 V. Juste,113\nH. B. Kabagoz\n,65, 35 T. Kajita\n,241 I. Kaku,206 V. Kalogera\n,98 M. Kalomenopoulos\n,214 M. Kamiizumi\n,50\nN. Kanda\n,233, 206 S. Kandhasamy\n,81 G. Kang\n,242 N. C. Kannachel,6 J. B. Kanner,11 S. A. KantiMahanty,18\nS. J. Kapadia\n,81 D. P. Kapasi\n,55 M. Karthikeyan,135 M. Kasprzack\n,11 H. Kato,154 T. Kato,205\nE. Katsavounidis,35 W. Katzman,65 R. Kaushik\n,105 K. Kawabe,2 R. Kawamoto,206 D. Keitel\n,100\nL. J. Kemperman\n,117 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,81 J. S. Key\n,243 R. Khadela,8, 9\nS. Khadka,91 S. S. Khadkikar,7 F. Y. Khalili\n,110 F. Khan\n,8, 9 T. Khanam,165 M. Khursheed,105\nN. M. Khusid,192, 193 W. Kiendrebeogo\n,115, 244 N. Kijbunchoo\n,117 C. Kim,245 J. C. Kim,246 K. Kim\n,247\nM. H. Kim\n,239 S. Kim\n,248 Y.-M. Kim\n,247 C. Kimball\n,98 K. Kimes,55 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,116 E. J. Knox,79 N. Knust\n,8, 9 K. Kobayashi,205 S. M. Koehlenbeck\n,91\nG. Koekoek,37, 36 K. Kohri\n,249, 250 K. Kokeyama\n,33, 251 S. Koley\n,44, 168 P. Kolitsidou\n,120\nA. E. Koloniari\n,252 K. Komori\n,42 A. K. H. Kong\n,144 A. Kontos\n,253 L. M. Koponen,120 M. Korobko\n,99\nX. Kou,18 A. Koushik\n,23 N. Kouvatsos\n,69 M. Kovalam,74 T. Koyama,154 D. B. Kozak,11 S. L. Kranzhoff,36, 37\nV. Kringel,8, 9 N. V. Krishnendu\n,120 S. Kroker,254 A. Kr\u00b4olak\n,255, 188 K. Kruska,8, 9 J. Kubisz\n,256\nG. Kuehn,8, 9 S. Kulkarni\n,217 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,234 Praveen Kumar\n,54\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,95 J. Kume\n,257, 258, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,209, 259 S. Kuwahara\n,42 K. Kwak\n,240 K. Kwan,34 S. Kwon\n,42 G. Lacaille,88\nD. Laghi\n,190, 102 A. H. Laity,166 E. Lalande,260 M. Lalleman\n,23 P. C. Lalremruati,261 M. Landry,2\nB. B. Lane,35 R. N. Lang\n,35 J. Lange,150 R. Langgin\n,214 B. Lantz\n,91 I. La Rosa\n,100 J. Larsen,201\nA. Lartaux-Vollard\n,41 P. D. Lasky\n,6 J. Lawrence\n,167 M. Laxen\n,65 C. Lazarte\n,140 A. Lazzarini\n,11\nC. Lazzaro,159, 158 P. Leaci\n,39, 38 L. Leali,18 Y. K. Lecoeuche\n,116 H. M. Lee\n,262 H. W. Lee\n,263 J. Lee,80\nK. Lee\n,239 R.-K. Lee\n,144 R. Lee,35 Sungho Lee\n,247 Sunjae Lee,239 Y. Lee,143 I. N. Legred,11 J. Lehmann,8, 9\nL. Lehner,184 M. Le Jean\n,178, 118 A. Lema\u02c6\u0131tre\n,264 M. Lenti\n,63, 179 M. Leonardi\n,76, 77, 265 M. Lequime,40\nN. Leroy\n,41 M. Lesovsky,11 N. Letendre,31 M. Lethuillier\n,57 Y. Levin,6 K. Leyde,75 A. K. Y. Li,11\nK. L. Li\n,266 T. G. F. Li,111 X. Li\n,151 Y. Li,98 Z. Li,88 A. Lihos,124 E. T. Lin\n,144 F. Lin,143 L. C.-C. Lin\n,266\nY.-C. Lin\n,144 C. Lindsay,202 S. D. Linker,182 A. Liu\n,220 G. C. Liu\n,229 Jian Liu\n,74 F. Llamas Villarreal,167\nJ. Llobera-Querol\n,100 R. K. L. Lo\n,142 J.-P. Locquet,111 S. C. G. Loggins,267 M. R. Loizou,135 L. T. London,69\nA. Longo\n,62, 63 D. Lopez\n,168 M. Lopez Portilla,73 A. Lorenzo-Medina\n,54 V. Loriette,41 M. Lormand,65\nG. Losurdo\n,268, 82 E. Lotti,135 T. P. Lott IV\n,58 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,112\nN. Low,125 N. Lu\n,34 L. Lucchesi\n,82 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,269, 270 A. W. Lussier\n,260\nR. Macas\n,75 M. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,154\nS. Maenaut\n,111 S. S. Magare,81 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 109 M. Magnozzi\n,29, 30\nP. Mahapatra,33, 59 M. Mahesh,99 M. Maini,166 S. Majhi,81 E. Majorana,39, 38 C. N. Makarem,11 N. Malagon,112\nD. Malakar\n,107 J. A. Malaquias-Reis,19 U. Mali\n,191 S. Maliakal,11 A. Malik,105 L. Mallick\n,171, 191\nA.-K. Malz\n,60 N. Man,115 M. Mancarella\n,101 V. Mandic\n,18 V. Mangano\n,173, 158 N. Manning,112\nB. Mannix,79 G. L. Mansell\n,80 M. Manske\n,10 M. Mantovani\n,64 M. Mapelli\n,93, 94, 271 C. Marinelli\n,103\nF. Marion\n,31 A. S. Markosyan,91 A. Markowitz,11 E. Maros,11 S. Marsat\n,102 F. Martelli\n,62, 63\nI. W. Martin\n,88 R. M. Martin\n,194 B. B. Martinez,133 D. A. Martinez,55 M. Martinez,43, 272 V. Martinez\n,130\nA. Martini,76, 77 J. C. Martins\n,19 D. V. Martynov,120 E. J. Marx,35 L. Massaro,36, 37 A. Masserot,31\n\n4\nM. Masso-Reid\n,88 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,210\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,65 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,65\nL. McCuller\n,11 S. McEachin,124 C. McElhenny,124 G. I. McGhee\n,88 J. McGinn,88 K. B. M. McGowan,146\nJ. McIver\n,116 A. McLeod\n,74 I. McMahon\n,190 T. McRae,34 R. McTeague\n,88 D. Meacher\n,10\nB. N. Meagher,80 R. Mechum,112 Q. Meijer,73 A. Melatos,125 C. S. Menoni\n,139 F. Mera,2 R. A. Mercer\n,10\nL. Mereni,178 K. Merfeld,165 E. L. Merilh,65 J. R. M\u00b4erou\n,100 J. D. Merritt,79 M. Merzougui,115 C. Messick\n,10\nB. Mestichelli,44 M. Meyer-Conde\n,273 F. Meylahn\n,8, 9 A. Mhaske,81 A. Miani\n,76, 77 H. Miao,274\nC. Michel\n,178 Y. Michimura\n,42 H. Middleton\n,120 D. P. Mihaylov\n,106 S. J. Miller\n,11 M. Millhouse\n,58\nE. Milotti\n,186, 48 V. Milotti\n,93 Y. Minenkov,22 E. M. Minihan,67 Ll. M. Mir\n,43 L. Mirasola\n,158, 159\nM. Miravet-Ten\u00b4es\n,140 C.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,108 T. Mishra\n,46 A. L. Mitchell,37, 109\nJ. G. Mitchell,67 S. Mitra\n,81 V. P. Mitrofanov\n,110 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50\nS. Miyoki\n,50 A. Miyoko,67 G. Mo\n,35 L. Mobilia\n,62, 63 S. R. P. Mohapatra,11 S. R. Mohite\n,7\nM. Molina-Ruiz\n,208 M. Mondin,182 M. Montani,62, 63 C. J. Moore,225 D. Moraru,2 A. More\n,81 S. More\n,81\nC. Moreno\n,137 E. A. Moreno\n,35 G. Moreno,2 A. Moreso Serra,84 S. Morisaki\n,42, 205 Y. Moriwaki\n,154\nG. Morras\n,209 A. Moscatello\n,93 M. Mould\n,35 B. Mours\n,66 C. M. Mow-Lowry\n,37, 109\nL. Muccillo\n,179, 63 F. Muciaccia\n,39, 38 D. Mukherjee\n,120 Samanwaya Mukherjee,24 Soma Mukherjee,167\nSubroto Mukherjee,95 Suvodip Mukherjee\n,13 N. Mukund\n,35 A. Mullavey,65 H. Mullock,116 J. Mundi,221\nC. L. Mungioli,74 M. Murakoshi,231 P. G. Murray\n,88 D. Nabari\n,76, 77 S. L. Nadji,8, 9 A. Nagar,28, 275\nN. Nagarajan\n,88 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,276 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,64 P. Narayan\n,217 I. Nardecchia\n,22 T. Narikawa,205\nH. Narola,73 L. Naticchioni\n,38 R. K. Nayak\n,261 L. Negri,73 A. Nela,88 C. Nelle,79 A. Nelson\n,133\nT. J. N. Nelson,65 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,55 L. Nguyen Quynh\n,277 S. A. Nichols,12\nA. B. Nielsen\n,278 Y. Nishino,25, 42 A. Nishizawa\n,279 S. Nissanke,280, 37 W. Niu\n,7 F. Nocera,64 J. Noller,281\nM. Norman,33 C. North,33 J. Novak\n,118, 235, 282 R. Nowicki\n,146 J. F. Nu\u02dcno Siles\n,209 L. K. Nuttall\n,75\nK. Obayashi,231 J. Oberling\n,2 J. O\u2019Dell,230 E. Oelker\n,35 M. Oertel\n,235, 118, 283, 282 G. Oganesyan,44, 45\nT. O\u2019Hanlon,65 M. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,118, 283, 282 R. Omer,18 B. O\u2019Neal,124 M. Onishi,154\nK. Oohara\n,284 B. O\u2019Reilly\n,65 M. Orselli\n,51, 78 R. O\u2019Shaughnessy\n,112 S. O\u2019Shea,88 S. Oshino\n,50\nC. Osthelder,11 I. Ota\n,12 D. J. Ottaway\n,117 A. Ouzriat,57 H. Overmier,65 B. J. Owen\n,285 R. Ozaki,231\nA. E. Pace\n,7 R. Pagano\n,12 M. A. Page\n,25 A. Pai\n,196 L. Paiella,44 A. Pal,286 S. Pal\n,261\nM. A. Palaia\n,82, 83 M. P\u00b4alfi,204 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,144 J. Pan,74\nK. C. Pan\n,144 P. K. Panda,234 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 73 F. Pannarale\n,39, 38\nK. A. Pannone,55 B. C. Pant,105 F. H. Panther,74 M. Panzeri,62, 63 F. Paoletti\n,82 A. Paolone\n,38, 287\nA. Papadopoulos\n,88 E. E. Papalexakis,212 L. Papalini\n,82, 83 G. Papigkiotis\n,252 A. Paquis,41 A. Parisi\n,78, 51\nB.-J. Park,247 J. Park\n,288 W. Parker\n,65 G. Pascale,8, 9 D. Pascucci\n,96 A. Pasqualetti\n,64\nR. Passaquieti\n,83, 82 L. Passenger,6 D. Passuello,82 O. Patane\n,2 A. V. Patel\n,143 D. Pathak,81 A. Patra,33\nB. Patricelli\n,83, 82 B. G. Patterson,33 K. Paul\n,108 S. Paul\n,79 E. Payne\n,11 T. Pearce,33 M. Pedraza,11\nA. Pele\n,11 F. E. Pe\u02dcna Arellano\n,289 X. Peng,120 Y. Peng,58 S. Penn\n,290 M. D. Penuliar,55 A. Perego\n,76, 77\nZ. Pereira,135 C. P\u00b4erigois\n,291, 94, 93 G. Perna\n,93 A. Perreca\n,76, 77, 44 J. Perret\n,20 S. Perri`es\n,57\nJ. W. Perry,37, 109 D. Pesios,252 S. Peters,168 S. Petracca,207 C. Petrillo,78 H. P. Pfeiffer\n,1 H. Pham,65\nK. A. Pham\n,18 K. S. Phukon\n,120 H. Phurailatpam,220 M. Piarulli,102 L. Piccari\n,39, 38 O. J. Piccinni\n,34\nM. Pichot\n,115 M. Piendibene\n,83, 82 F. Piergiovanni\n,62, 63 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,292, 134\nM. Pietrzak,97 M. Pillas\n,168 F. Pilo\n,82 L. Pinard\n,178 I. M. Pinto\n,292, 134, 293, 32 M. Pinto\n,64\nB. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,225, 88 A. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,100\nW. Plastino\n,213, 22 C. Plunkett\n,35 R. Poggiani\n,83, 82 E. Polini,35 J. Pomper,82, 83 L. Pompili\n,1 J. Poon,220\nE. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,64 J. Powell\n,157 G. S. Prabhu,81\nM. Pracchia\n,168 B. K. Pradhan\n,81 T. Pradier\n,66 A. K. Prajapati,95 K. Prasai\n,294 R. Prasanna,234\nP. Prasia,81 G. Pratten\n,120 G. Principe\n,186, 48 G. A. Prodi\n,76, 77 P. Prosperi,82 P. Prosposito,21, 22\nA. C. Providence,67 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,166 H. Qi\n,16 J. Qin\n,34\nG. Qu\u00b4em\u00b4ener\n,176, 118 V. Quetschke,167 P. J. Quinonez,67 N. Qutob,58 R. Rading,232 I. Rainho,140 S. Raja,105\nC. Rajan,105 B. Rajbhandari\n,112 K. E. Ramirez\n,65 F. A. Ramis Vidal\n,100 M. Ramos Arevalo\n,167\nA. Ramos-Buades\n,100, 37 S. Ranjan\n,58 K. Ransom,65 P. Rapagnani\n,39, 38 B. Ratto,67 A. Ravichandran,135\nA. Ray\n,98 V. Raymond\n,33 M. Razzano\n,83, 82 J. Read,55 T. Regimbau,31 S. Reid,56 C. Reissel,35\nD. H. Reitze\n,11 A. I. Renzini\n,11, 128 B. Revenu\n,295, 41 A. Revilla Pe\u02dcna,84 R. Reyes,182 L. Ricca\n,15\nF. Ricci\n,39, 38 M. Ricci\n,38, 39 A. Ricciardone\n,83, 82 J. Rice,80 J. W. Richardson\n,212 M. L. Richardson,117\nA. Rijal,67 K. Riles\n,92 H. K. Riley,33 S. Rinaldi\n,271 J. Rittmeyer,99 C. Robertson,230 F. Robinet,41\n\n5\nM. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31 J. G. Rollins\n,11 A. E. Romano\n,296 R. Romano\n,3, 4\nA. Romero\n,31 I. M. Romero-Shaw,225 J. H. Romie,65 S. Ronchini\n,7 T. J. Roocke\n,117 L. Rosa,4, 32\nT. J. Rosauer,212 C. A. Rose,58 D. Rosi\u00b4nska\n,126 M. P. Ross\n,53 M. Rossello-Sastre\n,100 S. Rowan\n,88\nS. K. Roy\n,192, 193 S. Roy\n,15 D. Rozza\n,128, 129 P. Ruggi,64 N. Ruhama,240 E. Ruiz Morales\n,297, 209\nK. Ruiz-Rocha,146 S. Sachdev\n,58 T. Sadecki,2 P. Saffarieh\n,37, 109 S. Safi-Harb\n,171 M. R. Sah\n,13\nS. Saha\n,144 T. Sainrat\n,66 S. Sajith Menon\n,216, 39, 38 K. Sakai,298 Y. Sakai\n,273 M. Sakellariadou\n,69\nS. Sakon\n,7 O. S. Salafia\n,161, 129, 128 F. Salces-Carcoba\n,11 L. Salconi,64 M. Saleem\n,150 F. Salemi\n,39, 38\nM. Sall\u00b4e\n,37 S. U. Salunkhe,81 S. Salvador\n,176, 175 A. Salvarese,150 A. Samajdar\n,73, 37 A. Sanchez,2\nE. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,140 J. R. Sanders,183 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,81 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,252 P. Sassi\n,51, 78\nB. Sassolas\n,178 B. S. Sathyaprakash\n,7, 33 R. Sato,228 S. Sato,154 Yukino Sato,154 Yu Sato,154 O. Sauter\n,46\nR. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,81 S. Sayah,178 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,151\nA. Schiebelbein,191 M. G. Schiworski\n,80 P. Schmidt\n,120 S. Schmidt\n,73 R. Schnabel\n,99 M. Schneewind,8, 9\nR. M. S. Schofield,79 K. Schouteden\n,111 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,299 M. Scialpi\n,300\nJ. Scott\n,88 S. M. Scott\n,34 R. M. Sedas\n,65 T. C. Seetharamu,88 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,301\nD. Sellers,65 N. Sembo,206 A. S. Sengupta\n,302 E. G. Seo\n,88 J. W. Seo\n,111 V. Sequino,32, 4 M. Serra\n,38\nA. Sevrin,189 T. Shaffer,2 U. S. Shah\n,58 M. A. Shaikh\n,262 L. Shao\n,303 A. K. Sharma\n,100 Preeti Sharma,12\nPrianka Sharma,105 Ritwik Sharma,18 S. Sharma Chaudhary,107 P. Shawhan\n,127 N. S. Shcheblanov\n,304, 264\nE. Sheridan,146 Z.-H. Shi,144 M. Shikauchi,42 R. Shimomura,305 H. Shinkai\n,305 S. Shirke,81 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,150 R. W. Short,2 S. ShyamSundar,105 A. Sider,160 H. Siegel\n,192, 193 N. Siemonsen,306\nD. Sigg\n,2 L. Silenzi\n,36, 37 L. Silvestri\n,39, 172 M. Simmonds,117 L. P. Singer\n,307 Amitesh Singh,217\nAnika Singh,11 D. Singh\n,208 M. K. Singh,24 N. Singh\n,100 S. Singh,218, 61 A. M. Sintes\n,100 V. Sipala,173, 158\nV. Skliris\n,33 B. J. J. Slagmolen\n,34 D. A. Slater,201 T. J. Slaven-Blair,74 J. Smetana,120 J. R. Smith\n,55\nL. Smith\n,88, 186, 48 R. J. E. Smith\n,6 W. J. Smith\n,146 S. Soares de Albuquerque Filho,62 M. Soares-Santos,190\nK. Somiya\n,218 I. Song\n,144 S. Soni\n,35 V. Sordini\n,57 F. Sorrentino,29 H. Sotani\n,308 F. Spada\n,82\nV. Spagnuolo\n,37 A. P. Spencer\n,88 P. Spinicelli\n,64 A. K. Srivastava,95 F. Stachurski\n,88 C. J. Stark,124\nD. A. Steer\n,309 N. Steinle\n,171 J. Steinlechner,36, 37 S. Steinlechner\n,36, 37 N. Stergioulas\n,252 P. Stevens,41\nS. P. Stevenson,157 M. StPierre,166 M. D. Strong,12 A. Strunk,2 A. L. Stuver,104, \u2217M. Suchenek,97\nS. Sudhagar\n,97 Y. Sudo,231 N. Sueltmann,99 L. Suleiman\n,55 K. D. Sullivan,12 J. Sun\n,242 L. Sun\n,34\nS. Sunil,95 J. Suresh\n,115 B. J. Sutton,69 P. J. Sutton\n,33 K. Suzuki,218 M. Suzuki,205 B. L. Swinkels\n,37\nA. Syx\n,118 M. J. Szczepa\u00b4nczyk\n,310 P. Szewczyk\n,126 M. Tacca\n,37 H. Tagoshi\n,205 K. Takada,205\nH. Takahashi\n,273 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,311 H. Takeda\n,312, 313 K. Takeshita,218\nI. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,80 C. Talbot,131 M. Tamaki,205 N. Tamanini\n,102 D. Tanabe,143\nK. Tanaka,50 S. J. Tanaka\n,231 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,212 R. D. Tapia,7\nE. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,314 J. D. Tasson\n,155 J. G. Tau\n,112 D. Tellez,55\nR. Tenorio\n,100 H. Themann,182 A. Theodoropoulos\n,140 M. P. Thirugnanasambandam,81 L. M. Thomas\n,11\nM. Thomas,65 P. Thomas,2 J. E. Thompson\n,211 S. R. Thondapu,105 K. A. Thorne,65 E. Thrane\n,6\nJ. Tissino\n,44, 45 A. Tiwari,81 Pawan Tiwari,44 Praveer Tiwari,196 S. Tiwari\n,190 V. Tiwari\n,120 M. R. Todd,80\nM. Toffano,93 A. M. Toivonen\n,18 K. Toland\n,88 A. E. Tolley\n,75 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,143 A. Torres-Forn\u00b4e\n,140, 141 C. I. Torrie,11 I. Tosta e Melo\n,315\nE. Tournefier\n,31 M. Trad Nery,115 K. Tran,124 A. Trapananti\n,52, 51 R. Travaglini\n,170 F. Travasso\n,52, 51\nG. Traylor,65 M. Trevor,127 M. C. Tringali\n,64 A. Tripathee\n,92 G. Troian\n,186, 48 A. Trovato\n,186, 48\nL. Trozzo,4 R. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,316 L. Tsukada\n,214 K. Turbang\n,189, 23\nM. Turconi\n,115 C. Turski,96 H. Ubach\n,84, 85 N. Uchikata\n,205 T. Uchiyama\n,50 R. P. Udall\n,11\nT. Uehara\n,317 K. Ueno\n,42 V. Undheim\n,278 L. E. Uronen,220 T. Ushiba\n,50 M. Vacatello\n,82, 83\nH. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6 J. Valencia\n,100 M. Valentini\n,109, 37\nS. A. Vallejo-Pe\u02dcna\n,296 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 318 E. Van den Bossche\n,189\nJ. F. J. van den Brand\n,36, 109, 37 C. Van Den Broeck,73, 37 M. van der Sluys\n,37, 73 A. Van de Walle,41\nJ. van Dongen\n,37, 109 K. Vandra,104 M. VanDyke,121 H. van Haevermaet\n,23 J. V. van Heijningen\n,37, 109\nP. Van Hove\n,66 J. Vanier,260 M. VanKeuren,106 J. Vanosky,2 N. van Remortel\n,23 M. Vardaro,36, 37\nA. F. Vargas\n,125 V. Varma\n,135 A. N. Vazquez,91 A. Vecchio\n,120 G. Vedovato,94 J. Veitch\n,88\nP. J. Veitch\n,117 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,57 M. Vereecken,15 D. Verkindt\n,31\nB. Verma,135 Y. Verma\n,105 S. M. Vermeulen\n,11 F. Vetrano,62 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,62, 63\nS. Vidyant,80 A. D. Viets\n,90 A. Vijaykumar\n,191 A. Vilkha,112 N. Villanueva Espinosa,140\nV. Villa-Ortega\n,54 E. T. Vincent\n,58 J.-Y. Vinet,115 S. Viret,57 S. Vitale\n,35 H. Vocca\n,78, 51 D. Voigt\n,99\n\n6\nE. R. G. von Reis,2 J. S. A. von Wrangel,8, 9 W. E. Vossius,232 L. Vujeva\n,142 S. P. Vyatchanin\n,110 J. Wack,11\nL. E. Wade,106 M. Wade\n,106 K. J. Wagner\n,112 L. Wallace,11 E. J. Wang,91 H. Wang\n,218 J. Z. Wang,92\nW. H. Wang,167 Y. F. Wang\n,1 G. Waratkar\n,196 J. Warner,2 M. Was\n,31 T. Washimi\n,25\nN. Y. Washington,11 D. Watarai,42 B. Weaver,2 S. A. Webster,88 N. L. Weickhardt\n,99 M. Weinert,8, 9\nA. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,74 K. Wette\n,34 J. T. Whelan\n,112 B. F. Whiting\n,46\nC. Whittle\n,11 E. G. Wickens,75 D. Wilken\n,8, 9, 9 A. T. Wilkin,212 B. M. Williams,121 D. Williams\n,88\nM. J. Williams\n,75 N. S. Williams\n,1 J. L. Willis\n,11 B. Willke\n,9, 8, 9 M. Wils\n,111 L. Wilson,106\nC. W. Winborn,107 J. Winterflood,74 C. C. Wipf,11 G. Woan\n,88 J. Woehler,36, 37 N. E. Wolfe,35\nH. T. Wong\n,143 H. W. Y. Wong,220 I. C. F. Wong\n,220, 111 K. Wong,191 T. Wouters,73, 37 J. L. Wright,2\nM. Wright\n,88, 73 B. Wu,80 C. Wu\n,144 D. S. Wu\n,8, 9 H. Wu\n,144 K. Wu,121 Q. Wu,53 Y. Wu,98 Z. Wu\n,102\nE. Wuchner,55 D. M. Wysocki\n,10 V. A. Xu\n,208 Y. Xu\n,100 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,154 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,231 T. Yan,120 K. Z. Yang\n,18\nY. Yang\n,148 Z. Yarbrough\n,12 J. Yebana,100 S.-W. Yeh,144 A. B. Yelikar\n,146 X. Yin,35 J. Yokoyama\n,319, 42\nT. Yokozawa,50 S. Yuan,74 H. Yuzurihara\n,50 M. Zanolin,67 M. Zeeshan\n,112 T. Zelenova,64 J.-P. Zendri,94\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,98 L. Zhang,11 N. Zhang,58 R. Zhang\n,152 T. Zhang,120 C. Zhao\n,74\nYue Zhao,164 Yuhang Zhao,20 Z.-C. Zhao\n,320 Y. Zheng\n,107 H. Zhong\n,18 H. Zhou,80 H. O. Zhu,74\nZ.-H. Zhu\n,320, 321 A. B. Zimmerman\n,150 L. Zimmermann,57 Y. Zlochower,112 M. E. Zucker\n,35, 11 J. Zweizig\n,11\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e, Campus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n\n7\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n55California State University Fullerton, Fullerton, CA 92831, USA\n56SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n57Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n58Georgia Institute of Technology, Atlanta, GA 30332, USA\n59Chennai Mathematical Institute, Chennai 603103, India\n60Royal Holloway, University of London, London TW20 0EX, United Kingdom\n61Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n62Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n63INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n64European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n65LIGO Livingston Observatory, Livingston, LA 70754, USA\n66Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n67Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n68Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n69King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n70Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n71International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n72Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n73Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n74OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n75University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n76Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n77INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n78Universit`a di Perugia, I-06123 Perugia, Italy\n79University of Oregon, Eugene, OR 97403, USA\n80Syracuse University, Syracuse, NY 13244, USA\n81Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n82INFN, Sezione di Pisa, I-56127 Pisa, Italy\n83Universit`a di Pisa, I-56127 Pisa, Italy\n84Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n85Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n86Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n87Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n88IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n89HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n90Concordia University Wisconsin, Mequon, WI 53097, USA\n\n8\n91Stanford University, Stanford, CA 94305, USA\n92University of Michigan, Ann Arbor, MI 48109, USA\n93Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n94INFN, Sezione di Padova, I-35131 Padova, Italy\n95Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n96Universiteit Gent, B-9000 Gent, Belgium\n97Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n98Northwestern University, Evanston, IL 60208, USA\n99Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n100IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n101Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n102Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n103Universit`a di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n104Villanova University, Villanova, PA 19085, USA\n105RRCAT, Indore, Madhya Pradesh 452013, India\n106Kenyon College, Gambier, OH 43022, USA\n107Missouri University of Science and Technology, Rolla, MO 65409, USA\n108Indian Institute of Technology Madras, Chennai 600036, India\n109Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n110Lomonosov Moscow State University, Moscow 119991, Russia\n111Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n112Rochester Institute of Technology, Rochester, NY 14623, USA\n113Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n114Bar-Ilan University, Ramat Gan, 5290002, Israel\n115Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n116University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n117OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n118Centre national de la recherche scientifique, 75016 Paris, France\n119Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n120University of Birmingham, Birmingham B15 2TT, United Kingdom\n121Washington State University, Pullman, WA 99164, USA\n122Cornell University, Ithaca, NY 14850, USA\n123Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n124Christopher Newport University, Newport News, VA 23606, USA\n125OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n126Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n127University of Maryland, College Park, MD 20742, USA\n128Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n129INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n130Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n131University of Chicago, Chicago, IL 60637, USA\n132Williams College, Williamstown, MA 01267, USA\n133University of Arizona, Tucson, AZ 85721, USA\n134INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n135University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n136Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n137Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n138Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n139Colorado State University, Fort Collins, CO 80523, USA\n140Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n141Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n142Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n143National Central University, Taoyuan City 320317, Taiwan\n144National Tsing Hua University, Hsinchu City 30013, Taiwan\n145OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n146Vanderbilt University, Nashville, TN 37235, USA\n147University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n\n9\n148Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n149Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n150University of Texas, Austin, TX 78712, USA\n151CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n152Northeastern University, Boston, MA 02115, USA\n153Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n154Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n155Carleton College, Northfield, MN 55057, USA\n156University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n157OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n158INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n159Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n160Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n161INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n162Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n163Montana State University, Bozeman, MT 59717, USA\n164The University of Utah, Salt Lake City, UT 84112, USA\n165Johns Hopkins University, Baltimore, MD 21218, USA\n166University of Rhode Island, Kingston, RI 02881, USA\n167The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n168Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n169DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n170Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n171University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n172INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n173Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n174INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n175Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n176Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n177The University of Sheffield, Sheffield S10 2TN, United Kingdom\n178Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n179Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n180Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n181INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n182California State University, Los Angeles, Los Angeles, CA 90032, USA\n183Marquette University, Milwaukee, WI 53233, USA\n184Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n185Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n186Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n187Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n188National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n189Vrije Universiteit Brussel, 1050 Brussel, Belgium\n190University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n191Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n192Stony Brook University, Stony Brook, NY 11794, USA\n193Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n194Montclair State University, Montclair, NJ 07043, USA\n195HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n196Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n197Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n198Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n199CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n200Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n201Western Washington University, Bellingham, WA 98225, USA\n202SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n203Barry University, Miami Shores, FL 33168, USA\n\n10\n204E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n205Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n206Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n207University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n208University of California, Berkeley, CA 94720, USA\n209Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n210Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212University of California, Riverside, Riverside, CA 92521, USA\n213Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n214University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n215University of Nottingham NG7 2RD, UK\n216Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n217The University of Mississippi, University, MS 38677, USA\n218Graduate School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n219Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n220The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n221American University, Washington, DC 20016, USA\n222Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n223INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n224Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n225University of Cambridge, Cambridge CB2 1TN, United Kingdom\n226University of Lancaster, Lancaster LA1 4YW, United Kingdom\n227College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n228Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n229Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n230Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n231Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n232Helmut Schmidt University, D-22043 Hamburg, Germany\n233Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n236Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n237National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n238School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n241Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n242Chung-Ang University, Seoul 06974, Republic of Korea\n243University of Washington Bothell, Bothell, WA 98011, USA\n244Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n245Ewha Womans University, Seoul 03760, Republic of Korea\n246National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n247Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n248Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n249Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n250Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n251Nagoya University, Nagoya, 464-8601, Japan\n252Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n253Bard College, Annandale-On-Hudson, NY 12504, USA\n254Technical University of Braunschweig, D-38106 Braunschweig, Germany\n\n11\n255Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n256Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n257Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n258Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n259Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n260Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n261Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n262Seoul National University, Seoul 08826, Republic of Korea\n263Department of Computer Simulation, Inje University, 197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n264NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n265Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n266Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n270Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n278University of Stavanger, 4021 Stavanger, Norway\n279Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 739-8526, Japan\n280GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n281University College London, London WC1E 6BT, United Kingdom\n282Observatoire de Paris, 75014 Paris, France\n283Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n284Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n289Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n290Hobart and William Smith Colleges, Geneva, NY 14456, USA\n291INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n292Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Kennesaw State University, Kennesaw, GA 30144, USA\n295Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n296Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n297Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n298Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n299Trinity College, Hartford, CT 06106, USA\n300Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n301Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n302Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n303Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n304Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n305Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n\n12\n306Department of Physics, Princeton University, Princeton, NJ 08544, USA\n307NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n308Faculty of Science and Technology, Kochi University, 2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n309Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS, Universit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e),\nF-75005 Paris, France\n310Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n311Laser Interferometry and Gravitational Wave Astronomy, Max Planck Institute for Gravitational Physics, Callinstrasse 38, 30167\nHannover, Germany\n312The Hakubi Center for Advanced Research, Kyoto University, Yoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n313Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n314Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n315University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n316National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n317Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n318Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n319Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha,\nKashiwa City, Chiba 277-8583, Japan\n320Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n321School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(Compiled: 3 November 2025)\nABSTRACT\nWe report the observation of gravitational waves from two binary black hole coalescences during\nthe fourth observing run of the LIGO\u2013Virgo\u2013KAGRA detector network, GW241011 and GW241110.\nThe sources of these two signals are characterized by rapid and precisely measured primary spins,\nnon-negligible spin\u2013orbit misalignment, and unequal mass ratios between their constituent black holes.\nThese properties are characteristic of binaries in which the more massive object was itself formed\nfrom a previous binary black hole merger, and suggest that the sources of GW241011 and GW241110\nmay have formed in dense stellar environments in which repeated mergers can take place. As the third\nloudest gravitational-wave event published to date, with a median network signal-to-noise ratio of 36.0,\nGW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar\nstructure of gravitational-wave generation, and the existence of ultralight bosons within the mass range\n10\u221213\u201310\u221212 eV.\n1. INTRODUCTION\nIt has been a decade since the inception of practi-\ncal gravitational-wave astronomy In the years following\nthe first direct observation of gravitational waves from\na binary black hole coalescence in 2015 (Abbott et al.\n2016a), the Advanced LIGO, Advanced Virgo, and KA-\nGRA experiments (Aasi et al. 2015; Acernese et al. 2015;\nAkutsu et al. 2021) have operated in tandem to regu-\nlarly identify an ever-increasing number of gravitational-\nwave signals (Abbott et al. 2024, 2023a). The recently-\nreleased fourth Gravitational-Wave Transient Catalog\n(GWTC-4.0), including signals discovered through Jan-\nuary 2024, contains hundreds of gravitational-wave sig-\nnals (Abac et al. 2025a), and the rate of discoveries\n\u2217Deceased, September 2024.\ncontinues to accelerate as further upgrades improve-\nment broadband instrumental sensitivity to gravita-\ntional waves (Ganapathy et al. 2023; Jia et al. 2024;\nCapote et al. 2025; Soni et al. 2025; Acernese et al.\n2023; Abac et al. 2025b). The growing collection of ob-\nserved gravitational-wave sources includes binary neu-\ntron stars (Abbott et al. 2017a, 2020a), one of which\nwas accompanied by transient multimessenger emission\nseen across the electromagnetic spectrum (e.g., Abbott\net al. 2017b,a; Goldstein et al. 2017; Coulter et al. 2017;\nHallinan et al. 2017; Margutti et al. 2017), as well as\nlikely neutron star\u2013black hole binaries (Abbott et al.\n2021a, 2023a; Abac et al. 2024, 2025a).\nAnd it in-\ncludes a growing number of black holes whose masses,\nwhether unexpectedly large, unexpectedly small, or un-\nexpectedly unequal, challenge present understanding of\n\n13\ncompact binary formation and evolution (Abbott et al.\n2016b, 2020b,c; Abac et al. 2024, 2025c).\nHere,\nwe\nreport\na\npair\nof\ngravitational-wave\nevents discovered in late 2024, GW241011 233834 and\nGW241110 124123, arising from binary black hole coa-\nlescences that each contain at least one rapidly rotating\nblack hole. As illustrated in Fig. 1, the primary (more\nmassive) source black hole of GW241011 233834 (here-\nafter abbreviated GW241011) exhibits one of the most\nrapid and precisely measured spins observed to date,\nwith \u03c71 = 0.78+0.09\n\u22120.09. This event provides a larger lower\nbound on both spin magnitude and \u20d7\u03c71 \u00b7 \u02c6LN, the spin\nprojected parallel to a binary\u2019s Newtonian orbital an-\ngular momentum \u20d7LN, than any other binary previously\npublished in GWTC-4.0 (Abac et al. 2025a). The pri-\nmary spin of GW241011\u2019s source is tilted by \u223c30 deg\nwith respect to \u02c6LN, and the gravitational-wave signal\nconfidently exhibits relativistic spin-orbit precession. In\ncontrast, the primary component of GW241110 124123\n(hereafter GW241110) is measured to be spinning in a\ndirection antiparallel to its orbital angular momentum\nvector, the most confidently antiparallel spin observed.\nDespite the opposite character of their spins, the sources\nof GW241011 and GW241110 possess similar masses.\nEach is inferred to contain a primary mass between ap-\nproximately 15\u201320 M\u2299and both favor unequal compo-\nnent black hole masses, with GW241011 in particular\nrequiring an approximately 3:1 mass ratio.\nThe rapid primary spins, significant spin\u2013orbit mis-\nalignment, and unequal mass ratios of GW241011 and\nGW241110 are in tension with expectations from iso-\nlated evolution of massive stellar binaries (Kalogera\n2000; Belczynski et al. 2016a; de Mink & Mandel 2016;\nMarchant et al. 2016; Rodriguez et al. 2016; Callis-\nter et al. 2021; Broekgaarden et al. 2022; Zevin &\nBavera 2022).\nThe source properties of GW241011\nand GW241110 are consistent, however, with those ex-\npected from hierarchical mergers in dense stellar clus-\nters.\nBinary black hole mergers yield remnant black\nholes that are rapidly rotating, with spin magnitudes of\n\u03c7 \u22480.7 (Pretorius 2005; Buonanno et al. 2008; Berti &\nVolonteri 2008). Asymmetric gravitational-wave emis-\nsion can cause these remnant black holes to receive large\nkicks, with velocities that can reach thousands of kilo-\nmeters per second (Fitchett 1983; Favata et al. 2004;\nSchnittman & Buonanno 2007; Campanelli et al. 2007;\nGonzalez et al. 2007). In environments with sufficiently\nhigh escape velocities, however, remnant black holes\nmay remain gravitationally bound, capture new part-\nners, and participate in subsequent binary mergers (Lee\n1995; O\u2019Leary et al. 2006; Giersz et al. 2015; Antonini &\nRasio 2016; Gerosa & Berti 2017; Fishbach et al. 2017;\nRodriguez et al. 2018b; Antonini et al. 2019; Rodriguez\net al. 2019; Baibhav et al. 2020; Fragione & Silk 2020;\nKimball et al. 2021; Baibhav et al. 2021; Doctor et al.\n2021; Fragione et al. 2022; Gerosa & Fishbach 2021; Ma-\nhapatra et al. 2021; Mapelli et al. 2021; Antonini et al.\n2023; Arca Sedda et al. 2023; Mahapatra et al. 2025b;\nChattopadhyay et al. 2023). Under this hypothesis, the\nprimary black holes of GW241011 and GW241110 may\nthemselves each be a product of a previous binary black\nhole merger.\nThe rapid spins and unequal mass ratios of GW241011\nand GW241110 furthermore make them prime laborato-\nries with which to test fundamental physics. GW241011,\nin particular, exhibits both significant relativistic spin\nprecession (Apostolatos et al. 1994; Kidder 1995) and\ngravitational radiation from higher-order multipole mo-\nments (Thorne 1980).\nBy virtue of these features,\nGW241011 offers one of the most precise confirmations\nto date of the Kerr nature of spinning black holes (Kerr\n1963; Carter 1971; Hansen 1974) and the multipolar\nemission pattern of gravitational waves.\nThe rest of this paper is organized as follows. In Sec-\ntion 2, we describe the low-latency identification and\nsubsequent validation of GW241011 and GW241110. In\nSection 3, we discuss the measured properties of these\ntwo events. In Section 4, we describe the possible astro-\nphysical interpretation and implications of GW241011\nand GW241110, and in Section 5 present tests of gen-\neral relativity (GR) using GW241011. We conclude in\nSection 6. Additional details and results are provided in\nthe Appendices.\n2. DETECTION AND SIGNIFICANCE\n2.1. GW241011\nGW241011 passed through the Earth\u2019s geocenter on\nOctober 11, 2024 at 23:38:34.9 UTC. It was detected\nin low latency in LIGO Hanford and Virgo data (Ligo\nScientific Collaboration et al. 2024a) by the GstLAL\nmatched-filter search pipeline (Messick et al. 2017;\nSachdev et al. 2019; Hanna et al. 2020; Cannon et al.\n2021; Sakon et al. 2024; Ewing et al. 2024; Tsukada\net al. 2023; Ray et al. 2023; Joshi et al. 2025a,b). The\nsignal was measured with optimized signal-to-noise ra-\ntios (SNRs) of 35.4 and 9.1 in LIGO Hanford and Virgo,\nrespectively, and a false alarm rate (FAR) of < 10\u22125 yr.\nLIGO Livingston was not operating at the time of the\nevent. Significant candidates were also identified by the\nMBTA (Adams et al. 2016; Aubin et al. 2021; All\u00b4en\u00b4e\net al. 2025) and PyCBC (Allen 2005; Allen et al. 2012;\nUsman et al. 2016; Nitz 2018; Nitz et al. 2017; Dal Can-\nton et al. 2021; Davies et al. 2020) pipelines at the time\nof GW241011, but fell outside the mass range for which\n\n14\nFigure 1.\nTop: Central 90% credible bounds on the dimensionless primary spins \u20d7\u03c71 of GW241011 (blue) and GW241110\n(green), projected parallel to the direction \u02c6LN of each binary\u2019s Newtonian orbital angular momentum.\nShown in grey for\ncomparison are 90% credible bounds on the projected primary spins of previously-published compact binary coalescences in\nthe fourth Gravitational-Wave Transient Catalog (GWTC-4.0; Abac et al. 2025a), sorted by their median posterior values of\n\u03c71,z \u2261\u20d7\u03c71 \u00b7 \u02c6LN. We specifically show events with false alarm rates (FARs) below 1 yr\u22121, consistent with the significance threshold\nadopted for compact binary population studies in GWTC-3.0 and GWTC-4.0 (Abbott et al. 2023b; Abac et al. 2025d). The\nsource of GW241011 contains one of the most rapidly spinning black holes observed by LIGO\u2013Virgo\u2013KAGRA to date, possessing\nthe largest lower limit on both its primary spin magnitude and projected spin \u20d7\u03c71,z. GW241110, conversely, yields the most\nconfident measurement to date of a black hole spinning retrograde with respect to its orbit, with \u03c71,z < 0 at 97.7% credibility.\nBottom: 90% credible posterior bounds on the primary masses and mass ratios of GW241011 and GW241110, together with all\nbinary mergers in GWTC-4.0 with FAR < 1 yr\u22121. Despite the opposite nature of their spins, GW241011 and GW241110 are\nlikely to have very similar masses, each favoring a primary of 15\u201320 M\u2299and unequal mass ratios.\nthese searches report candidates in low latency seen in\nonly one LIGO instrument (Abac et al. 2025e). LIGO\nHanford and Virgo were each operating normally at\nthe time of detection, with stable angle-averaged binary\nneutron star inspiral ranges of approximately 160 and\n50 Mpc, respectively (Finn & Chernoff 1993; Chen et al.\n2021). In subsequent high-latency searches, for which\nmore comprehensive data quality assessment and precise\nbackground estimates were available, GstLAL, MBTA,\nand PyCBC each detected GW241011 with false alarm\nrates below 3 \u00d7 10\u22125 yr\u22121. GW241011\u2019s high network\nSNR makes it the third-loudest gravitational-wave event\npublished to date, behind GW230814 230901 (Abac\net al. 2025a) and GW250114 082203 (Abac et al. 2025f).\n2.2. GW241110\nGW241110 arrived at Earth on November 10, 2024\nat 12:41:23.6 UTC. It was identified in low latency in\nLIGO Hanford, LIGO Livingston, and Virgo data (Ligo\nScientific Collaboration et al. 2024b), assigned FAR =\n0.15 yr\u22121 by the GstLAL search pipeline and lower\nsignificances by MBTA and PyCBC. At the time of\nGW241110, the LIGO instruments had angle-averaged\nbinary neutron star inspiral ranges of approximately\n160 Mpc, while Virgo\u2019s inspiral range was near 50 Mpc.\n\n15\nHigh-latency analyses with the PyCBC, GstLAL, and\nMBTA pipelines later re-identified GW241110 with\nfalse alarm rates of 6.3 \u00d7 10\u22124 yr\u22121, 0.099 yr\u22121, and\n0.85 yr\u22121 respectively.\nFor\nseveral\nhours\naround\nthe\narrival\ntime\nof\nGW241110, microseismic ground motion near LIGO\nLivingston was elevated. Elevated microseism is known\nto increase the rate of scattered light glitches in detec-\ntor strain data, particularly below 30 Hz (Soni et al.\n2020, 2024). Between 0.3 and 2 s after the coalescence\ntime, three noise transients are observed in the data, all\nbelow 30 Hz. Two are low-SNR transients, while the\nthird is a high-SNR scattered-light glitch occurring be-\nlow 15 Hz. Although these transients are not expected to\naffect the observation and analysis of GW241110 (Macas\net al. 2022; Hourihane & Chatziioannou 2025), all fur-\nther studies of GW241110\u2019s properties (see Section 3)\nuse LIGO Livingston data only above 30 Hz.\n3. SOURCE PROPERTIES\nBayesian\nparameter\nestimation\nis\nperformed\non\nGW241011 and GW241110 following the methodology\ndescribed in Abac et al. (2025e).\nNoise power spec-\ntral densities are obtained with the BayesWave algo-\nrithm (Cornish & Littenberg 2015; Littenberg & Cornish\n2015; Littenberg et al. 2016; Cornish et al. 2021; Gupta\n& Cornish 2024) and astrophysical parameter inference\nis performed using the RIFT (Pankow et al. 2015; Lange\net al. 2017; Wysocki et al. 2019) and Bilby (Ashton\net al. 2019; Romero-Shaw et al. 2020b) code packages,\nthe latter of which invokes the Dynesty (Speagle 2020)\nnested sampler.\nAnalysis of GW241011 includes 32 s\nof data between 20\u20131792 Hz from LIGO Hanford and\nVirgo. Analysis of GW241110 incorporates 16 s of data\nfrom all three LIGO and Virgo instruments; data be-\ntween 20\u20131792 Hz are used from LIGO Hanford and\nVirgo, whereas LIGO Livingston data are used only at\nfrequencies above 30 Hz due to the presence of nonsta-\ntionary low-frequency noise. We adopt priors that are\nuniform in detector-frame component masses, uniform\nand isotropic in component spin magnitudes and orien-\ntations, and uniform in comoving volume and source-\nframe time (Abac et al. 2025e).\nBlack hole spin ori-\nentations evolve over the course of an inspiral due to\nrelativistic spin-orbit precession; we present spin mea-\nsurements corresponding to the asymptotic values in\nthe limit of infinite binary separation (Mould & Gerosa\n2022; Johnson-McDaniel et al. 2022; Gerosa et al. 2023).\nThe inferred source properties of GW241011 and\nGW241110 are summarized in Table 1.\nPosteriors\non the primary black hole\u2019s spin vectors of each bi-\nnary are shown in Figure 2, while posteriors on a\nFigure 2.\nPosterior on the primary spin vector of\nGW241011 (left) and GW241110 (right). Within each sub-\nplot, radial coordinates span the range 0 to 1 and corre-\nspond to dimensionless spin magnitudes. The polar angles,\nspanning 0 to 180 deg, correspond to spin\u2013orbit misalign-\nment angles. Color saturation indicates posterior probabil-\nity as a function of spin magnitude and orientation. Pixels\nare spaced linearly in spin magnitude and cosine tilt an-\ngle such that they each contain equal prior probability; a\ncompletely uninformative spin measurement would therefore\nyield a uniformly colored disk. GW241011 has a precisely\nmeasured spin magnitude of \u03c71 = 0.78+0.09\n\u22120.09 that is mis-\naligned by 31+11\n\u221214 degrees with respect to its orbital angular\nmomentum. The primary spin of GW241110, in contrast, is\nconstrained to be misaligned by more than 110 deg from its\norbital angular momentum.\nsubset of other binary parameters appear in Fig-\nure 3.\nThese results comprise the union of pos-\nterior samples obtained using three different wave-\nform models, SEOBNRv5PHM (Ramos-Buades et al.\n2023a),\nIMRPhenomXPHM-SpinTaylor (Colleoni\net al. 2025) and IMRPhenomXO4a (Thompson et al.\n2024), that each include the effects of spin\u2013orbit pre-\ncession and higher-order spherical harmonic modes.\nFurther details about parameter inference, including\nsource properties inferred with each individual waveform\nmodel, are presented in Appendix A.\n3.1. Properties of GW241011\nThe source of GW241011 is inferred to possess a\n19.6+3.6\n\u22122.5 M\u2299primary mass and a confidently unequal\nmass ratio, q = 0.30+0.09\n\u22120.08. It has a large and precisely\nmeasured primary spin magnitude, \u03c71 = 0.78+0.09\n\u22120.09, and\n\n16\nTable 1.\nInferred source properties of GW241011 and GW241110. Shown are each source\u2019s primary mass (m1), secondary\nmass (m2), mass ratio (q), chirp mass (M), and luminosity distance DL, with mass parameters defined in the rest-frame of the\nsource binary. We additionally quote a variety of spin measurements: primary dimensionless spin magnitude (\u03c71) and spin\u2013orbit\nmisalignment angle (\u03b81), primary spin components projected parallel (\u03c71,z = \u03c71 cos \u03b81) and perpendicular (\u03c71,\u22a5= \u03c71 sin \u03b81) to\nthe binaries\u2019 Newtonian orbital angular momenta, the effective inspiral spin \u03c7eff (Racine 2008; Ajith et al. 2011; Santamaria\net al. 2010), and the effective precessing spin \u03c7p (Hannam et al. 2014; Schmidt et al. 2015). We do not obtain informative\nconstraints on the secondary spins of each source; see Appendix A for secondary spin measurements. We follow parameter\nconventions as defined in Table 3 of (Abac et al. 2025b). For all but one parameter, we quote posterior medians and central 90%\ncredible uncertainties. For \u03b81 alone, uncertainties instead correspond to values containing the 90% credible highest posterior\ndensity interval for cos \u03b81. This is done to minimize the influence of the uniform-in-cos \u03b8 priors, which exclude \u03b81 = 0. Spin\nparameters are quoted at infinite binary separation.\nEvent\nm1 [M\u2299]\nm2 [M\u2299]\nq\nM [M\u2299]\nDL [Mpc]\n\u03c71\n\u03b81 [deg]\n\u03c71,z\n\u03c71,\u22a5\n\u03c7eff\n\u03c7p\nGW241011\n19.6+3.6\n\u22122.5\n5.9+0.8\n\u22120.8\n0.30+0.09\n\u22120.08\n9.1+0.1\n\u22120.1\n214+44\n\u221248\n0.78+0.09\n\u22120.09\n31+11\n\u221214\n0.66+0.08\n\u22120.09\n0.39+0.19\n\u22120.14\n0.49+0.06\n\u22120.07\n0.39+0.19\n\u22120.14\nGW241110\n17.2+5.0\n\u22124.4\n7.7+2.2\n\u22121.5\n0.45+0.32\n\u22120.17\n9.8+0.5\n\u22120.4\n736+270\n\u2212267\n0.61+0.33\n\u22120.40\n133+47\n\u221225\n\u22120.39+0.34\n\u22120.37\n0.40+0.34\n\u22120.30\n\u22120.28+0.23\n\u22120.20\n0.42+0.33\n\u22120.27\nits primary spin is inferred to be misaligned with re-\nspect to its Newtonian orbital angular momentum by\n\u03b81 = 31+11\n\u221214 deg.\nThe spin of GW241011\u2019s secondary\nblack hole is unconstrained, as expected for an unequal-\nmass systems in which the primary\u2019s spin angular mo-\nmentum dominates. The inferred geometry of the spin\nvector of GW241011\u2019s primary black hole is depicted in\nthe left-hand side of Figure 2.\nWithin this plot, the\nradial distance depicts the magnitude of GW241011\u2019s\nprimary spin vector, while the polar coordinate denotes\nits spin\u2013orbit misalignment angle; color saturation indi-\ncates posterior probability. GW241011 is, furthermore,\nprobably the closest binary black hole merger observed\nto date, with a luminosity distance of DL < 248 Mpc at\n90% credibility.\nThe primary of GW241011 is among the most rapidly\nrotating black holes observed to date.\nAt 95% credi-\nbility, GW241011 has the largest lower limit obtained\nthus far on the spin of any merging black hole, with\n\u03c71\n> 0.69.\nFigure 4 compares this primary spin\nmeasurement to two signals with similar spin mag-\nnitude limits, GW190517 (Abbott et al. 2023a) and\nthe recently-announced GW231123 (Abac et al. 2025c),\nwhose sources have \u03c71 > 0.52 and \u03c71 > 0.63 at 95%\ncredibility, respectively. GW190403 051519 favors simi-\nlarly rapid spins, but this candidate does not meet the\nsignificance threshold adopted for population analyses.\nAdditionally, both the primary aligned spin \u03c71,z and the\neffective inspiral spin of GW241011 (Racine 2008; Ajith\net al. 2011; Santamaria et al. 2010), defined as\n\u03c7eff = (m1\u20d7\u03c71 + m2\u20d7\u03c72) \u00b7 \u02c6LN\nm1 + m2\n,\n(1)\nare bounded higher than any other gravitational-wave\nsource.\nAmong black holes that are confidently ro-\ntating, the primary spin magnitude of GW241011 is\nalso the most precisely measured, with a 90% cred-\nible region that is half as wide as the next-most-\nprecise measurement, made using GW190412 (Abbott\net al. 2020d).\nThe binary neutron star source of\nGW170817 (Abbott et al. 2017c), the lower mass gap\nbinary source of GW190814 (Abbott et al. 2020c),\nand the low-significance neutron star-black hole candi-\ndate GW191219 163120 each have more precisely mea-\nsured spins, but these spins are consistent with zero.\nGW241011 is therefore the gravitational-wave event\nthat, taken individually, provides the strongest evidence\nto date that at least some component black holes in\nmerging binaries spin rapidly, with dimensionless spins\nwith magnitudes \u223c0.7 or greater.\nGW241011 additionally exhibits strong signatures of\norbital plane precession and radiation in higher spher-\nical harmonic modes. Orbital plane precession occurs\ndue to relativistic spin\u2013orbit coupling, an effect that is\nmaximized by the large and misaligned primary spin of\nGW241011. The degree of spin-orbit precession may be\nparametrized using the effective precessing spin (Han-\nnam et al. 2014; Schmidt et al. 2015),\n\u03c7p = Max\n\u0014\n\u03c71 sin \u03b81, 3 + 4q\n4 + 3q q\u03c72 sin \u03b82\n\u0015\n,\n(2)\nrelated to the in-plane spin components \u03c7i,\u22a5= \u03c7i sin \u03b8i.\nThe source of GW241011 has confidently non-zero effec-\ntive precessing spin, with \u03c7p = 0.39+0.19\n\u22120.14, and we ob-\ntain a log-Bayes factor of log10 B = 5.4 in favor of a\nprecessing source over a model in which spins are re-\nstricted to be co-aligned with their orbit.\nAs Bayes\nfactors may, in general, be sensitive to one\u2019s choice of\nprior, we additionally quantify evidence for precession\nvia the precession SNR \u03c1p (Fairhurst et al. 2020a,b),\nthe posterior distribution of which is shown in Figure 5.\nWe find \u03c1p = 5.3+2.1\n\u22121.9. In the absence of precession, \u03c1p\nis expected to follow the null distribution indicated in\nFig. 5. Random draws from GW241011\u2019s \u03c1p posterior\n\n17\nFigure 3.\nPosterior probabilities on selected properties of GW241011 (blue) and GW241110 (green): their primary masses\nm1, mass ratios q, effective inspiral spins \u03c7eff, primary spin magnitudes \u03c71, and components of their primary spins projected\nparallel (\u03c71,z) and perpendicular (\u03c71,\u22a5) to each binary\u2019s Newtonian orbital angular momentum. Panels along the diagonal show\nmarginalized posteriors on each parameter; the dashed histograms correspond to the prior probability distributions adopted\nduring parameter estimation. Off-diagonal panels illustrate joint two-dimensional posteriors on each pair of parameters; thick\nand thin contours denote central 50% and 90% credible bounds. Shaded grey regions indicate to parts of parameter space that\nthe constraint that spin magnitudes be less than or equal to one. Despite their extreme and opposite spins, GW241011 and\nGW241110 have consistent component mass measurements, each favoring a 15\u201320 M\u2299primary and an unequal mass ratio.\nexceed random draws from this null distribution 99.5%\nof the time.\nThe significant mass asymmetry of GW241011 also\nyields significant radiation in higher-order spherical har-\nmonic modes. Whereas gravitational-wave radiation is\ntypically dominated by (\u2113, m) = (2, \u00b12) spherical har-\nmonics, subdominant modes, such as (\u2113, m) = (2, \u00b11)\nor (3, \u00b13), become increasingly important for systems\nwith considerable mass asymmetry (Thorne 1980; Berti\net al. 2007; Blanchet 2014; Mills & Fairhurst 2021).\nGW241011 exhibits significant radiation in the (\u2113, m) =\n(3, \u00b13) spherical harmonics, here assuming symmetric\ncontributions from m = 3 and \u22123 modes thus neglect-\ning small asymmetries arising from source precession.\nWe find a log-Bayes factor of log10 B = 5.2 in favor of a\nsignal model including higher-order spherical harmonics,\ncompared to a model including only contributions from\n(\u2113, m) = (2, \u00b12) modes. A posterior distribution on the\nSNR \u03c133 measured in higher-order modes is shown in\nFigure 5, with \u03c133 = 5.9+1.0\n\u22121.1. Random draws from the\nposterior on \u03c133 exceed draws from the null distribution\nover 99.9% of the time. No detection is made of other\nspherical harmonic modes.\n3.2. Properties of GW241110\nGW241110 is inferred to have component masses con-\nsistent with those of GW241011, albeit with larger un-\ncertainties due to its lower SNR: the primary mass and\n\n18\nFigure 4.\nPosterior on the primary spin magnitude of\nGW241011 (blue). The spin of GW241011\u2019s primary black\nhole has the largest lower bound than that of all other merg-\ning compact objects observed to date. We obtain \u03c71 > 0.69\nat 95% credibility. For comparison, also shown are the pri-\nmary spin measurements from GW231123 (black; Abac et al.\n2025c) and GW190517 (Abbott et al. 2023a, dashed grey),\nwhich provide the two next-largest lower limits of \u03c71 > 0.63\nand \u03c71 > 0.52, respectively.\nmass ratio of GW241110 are measured to be m1 =\n17.2+5.0\n\u22124.4 M\u2299and q = 0.45+0.32\n\u22120.17 (see Figure 3). Although\nGW241110 favors unequal component masses, mass ra-\ntios of q \u22481 cannot be fully excluded.\nIn contrast to GW241011, though, GW241110 is mea-\nsured to have a primary spin that is likely significantly\nmisaligned with respect to its orbital angular momen-\ntum.\nThe angle between the binary\u2019s orbital angular\nmomentum and the spin vector of its more massive black\nhole is \u03b81 = 133+47\n\u221225 degrees, with \u03b81 > 108 degrees at\n90% credibility and \u03b81 > 90 degrees at 97.7% credibility.\nThe spin of GW241110\u2019s secondary black hole is uncon-\nstrained. GW241110 favors negative effective spin, with\n\u03c7eff < 0 at 98.1% credibility. As illustrated in Figure 3,\nGW241110 inferred mass ratio is strongly anticorrelated\nwith its inferred \u03c7eff and \u03c71,z. This effect arises from a\ndegeneracy in the post-Newtonian expansion of a com-\npact binary\u2019s phase evolution (Cutler & Flanagan 1994;\nPoisson & Will 1995; Baird et al. 2013; P\u00a8urrer et al.\n2013; Ng et al. 2018). Thus, if one requires GW241110\nto have positive \u03c7eff (1.9% probability), it must also be\nthe case that its mass ratio is q \u22720.3. If GW241110\u2019s\nmass ratio is above q = 0.3, then the event must have\nnegative \u03c7eff at 99.9% credibility.\nGW241110 offers the most significant, although not\nnecessarily conclusive, direct evidence to date that at\nleast some merging black holes have spins antialigned\nFigure 5.\nPosterior distribution on GW241011\u2019s precession\nSNR ratio and its SNR in (\u2113, m) = (3, \u00b13) spherical harmonic\nmodes.\nThe precession SNR quantifies the observational\nstrength of spin\u2013orbit precession, while (\u2113, m) = (3, \u00b13)\nmode radiation arises from source multipoles beyond the\nleading-order mass quadrupole.\nThe unequal mass ratio\nand large, misaligned primary spin of GW241011 together\nyield \u03c1p = 5.3+2.1\n\u22121.9 and \u03c133 = 5.9+1.0\n\u22121.1. For comparison, the\ndashed histogram illustrates the expected null distribution (a\n\u03c7-distribution with four degrees of freedom, two per detec-\ntor active during GW241011) of \u03c1p and \u03c133 in the absence of\nspin\u2013orbit precession or higher-order radiation modes (Prix\n2007; Harry & Fairhurst 2011). This null distribution is con-\nservative; in some cases the null distribution may take al-\nternative forms (such as a \u03c7-distribution with fewer degrees\nof freedom) concentrated towards smaller SNRs (Fairhurst\net al. 2020b; Hoy et al. 2022, 2025).\nwith their orbital angular momentum. A growing num-\nber of binary black holes have been observed with\nlarge spin\u2013orbit misalignment angles (with, e.g., \u03b8 \u2273\n50 degrees at high credibility).\nSeveral detections, in-\ncluding, e.g., GW231230 170116, GW230723 101834,\nand GW230609 064958, furthermore favor misalignment\nangles greater than 90 degrees, but only at \u223c80% cred-\nibilities. (Abac et al. 2025a).\nAnalysis of the binary\nblack hole GW191109 010717 (GW191109; Abbott et al.\n2023a) with a numerical-relativity surrogate waveform\nmodel, meanwhile, found a negative effective inspiral\nspin at > 99% credibility (Islam et al. 2025). The ro-\nbustness of GW191109\u2019s spin measurement is uncertain,\nhowever, due to significant contamination by noise tran-\nsients (Abbott et al. 2023a); reanalyses that simulta-\nneously seek to model and subtract these glitches are\ninconclusive (Udall et al. 2025).\nThe spin measure-\nment with GW241110, in contrast, is not believed to\nbe subject to data-quality concerns.\nUnder uniform\nand isotropic spin priors and standard waveform mod-\n\n19\nels, there does remain a 1.9% probability that the source\npossesses zero or positive effective inspiral spin.\nThe\nconfidence in GW241110\u2019s spin anti-alignment is further\nbolstered when adopting an astrophysically-informed\nprior (see Appendix C.2), but we cannot completely ex-\nclude the possibility that the source has zero or positive\nprimary spin.\n3.3. Relationship with the binary black hole population\nAlthough GW241011 and GW241110 are remarkable\nfor their large and well-measured black hole spins, we do\nnot conclude that they are outliers with respect to the\nknown binary black hole population; see Appendix C\nfor details. These events do, however, individually rein-\nforce conclusions that have been previously drawn only\non statistical grounds. Past studies of the binary black\nhole spin distribution have concluded (i) that merging\nblack holes are usually, but not exclusively, slowly rotat-\ning, (ii) that black hole spins are unlikely to be isotropic,\nstatistically favoring spin\u2013orbit alignment and positive\neffective spins, but that (iii) black hole spins neverthe-\nless exhibit a wide range of spin\u2013orbit misalignment an-\ngles, with some component black holes misaligned by\nnearly or greater than 90 deg with respect to their or-\nbit (Farr et al. 2017, 2018; Abbott et al. 2019; Roulet &\nZaldarriaga 2019; Miller et al. 2020; Abbott et al. 2020d,\n2023b; Callister et al. 2022; Tong et al. 2022; Vitale et al.\n2022; Callister & Farr 2024; Banagiri et al. 2025; Abac\net al. 2025d).\nGW241110 offers the strongest confir-\nmation to date of this latter conclusion. The tension\nbetween population-level conclusions and the paucity of\nindividual binary black holes favoring anti-aligned spins\ncan be understood as a confluence of three factors: the\nlarge uncertainties typically inherent in spin measure-\nments (van der Sluys et al. 2008; Vitale et al. 2014;\nGhosh et al. 2016; Vitale et al. 2017; Chatziioannou\net al. 2018; Pratten et al. 2020; Biscoveanu et al. 2021),\na degeneracy between mass ratio and spins that asym-\nmetrically biases \u03c7eff measurements towards larger pos-\nitive values (Cutler & Flanagan 1994; Poisson & Will\n1995; Baird et al. 2013; P\u00a8urrer et al. 2013; Ng et al.\n2018), and selection effects that cause events with larger,\npositive \u03c7eff to be more readily detected and more pre-\ncisely characterized (Flanagan & Hughes 1998; Campan-\nelli et al. 2006; Ng et al. 2018). These effects together\nhave been shown to resolve the apparent inconsistency\nbetween individual binary black hole properties and sta-\ntistical population-level conclusions (Hoy et al. 2025;\nPayne et al. 2024).\nWhile we do not conclude that GW241011 and\nGW241110 are outliers, it is possible that they are\nmembers of an emerging subpopulation of binary black\nholes, characterized by low primary masses, unequal\nmass ratios, and a wide range of spin\u2013orbit misalign-\nment angles.\nIt remains unknown, however, whether\nsuch a subpopulation exists and can be formally char-\nacterized. This question will be further explored in fu-\nture work involving additional observations from LIGO\u2013\nVirgo\u2013KAGRA\u2019s fourth observing run.\n4. ASTROPHYSICAL INTERPRETATION AND\nIMPLICATIONS\n4.1. GW241011 and GW241110 through isolated\nbinary evolution\nThe primary spins of GW241011 and GW241110 are\ndifficult to explain via isolated binary evolution. Effi-\ncient angular momentum transport from stellar interiors\nis predicted to yield black holes that are born slowly ro-\ntating (Spruit 1999, 2002; Qin et al. 2018; Fuller & Ma\n2019), and torques exerted via mass transfer or tides are\nexpected to coalign residual spin with a binary\u2019s orbital\nangular momentum (Zaldarriaga et al. 2018; Gerosa\net al. 2018; Qin et al. 2018; Bavera et al. 2020, 2021;\nMa & Fuller 2023). The natal spins of black holes do\nremain highly uncertain, however, with the prediction of\nsmall spins due to the Spruit\u2013Tayler dynamo being only\none of many possibilities (Miller & Miller 2014). Mod-\nels predicting larger natal spins may better accommo-\ndate the observed source properties of GW241011 and\nGW241110.\nAlternative scenarios can also potentially explain the\nspin properties of GW241011 and GW241110 in the\ncontext of isolated binary evolution.\nStochastic spin-\nup of stellar cores immediately preceding core collapse\ncould impart large and misaligned birth spins to black\nholes (Fuller et al. 2014, 2015; Gilkis & Soker 2016; Ma &\nFuller 2019; McNeill & M\u00a8uller 2020; Antoni & Quataert\n2022, 2023; Baibhav & Kalogera 2024). Although black\nhole progenitors are generally predicted to experience\nsmall natal kicks due to near-complete fallback accre-\ntion (e.g., Fryer et al. 2012; Zevin et al. 2017; Mandel &\nM\u00a8uller 2020; Vigna-G\u00b4omez et al. 2024), stronger-than-\nexpected natal kicks and/or asymmetric fallback might\nmisalign spins either by tilting a binary\u2019s orbital plane\nor by torquing of a black hole\u2019s spin vector (Wongwatha-\nnarat et al. 2013; Chan et al. 2020; Janka et al. 2022;\nTauris 2022; Burrows et al. 2024); spin\u2013orbit misalign-\nment among some black hole X-ray binaries may provide\nevidence for such effects (Zdziarski et al. 2018; Salvesen\n& Pokawanvit 2020; Poutanen et al. 2022; Zdziarski\net al. 2023). Finally, the von Zeipel\u2013Lidov\u2013Kozai mech-\nanism (von Zeipel 1910; Lidov 1962; Kozai 1962) due\nto a tertiary companion can, when coupled to relativis-\ntic spin\u2013orbit precession and gravitational-wave emis-\n\n20\nsion, tilt the orbital plane as well as component spins to\nyield a large spin\u2013orbit misalignment (Liu & Lai 2017;\nAntonini et al. 2018; Liu & Lai 2018; Fragione & Kocsis\n2020; Liu et al. 2019; Yu et al. 2020; Stegmann & Klencki\n2025); however, this mechanism does not explain large\nspin magnitudes.\n4.2. GW241011 and GW241110 as hierarchical\nmergers\nA more natural interpretation for GW241011 and\nGW241110 is that they involve the mergers of second-\ngeneration black holes in dense stellar environments,\nsuch as globular, nuclear, and young massive star clus-\nters (Portegies Zwart et al. 2010; Neumayer et al. 2020).\nCompact binaries merging within clusters yield rem-\nnants that may be retained by the cluster, continue\nto interact dynamically, and themselves participate in\nsubsequent mergers driven by gravitational wave emis-\nsion (e.g., Lee 2001; O\u2019Leary et al. 2006; Miller &\nLauburg 2009; Giersz et al. 2015; Antonini & Rasio 2016;\nRodriguez et al. 2019; Doctor et al. 2021; Fragione et al.\n2022; Mahapatra et al. 2021; Rizzuto et al. 2022; Atallah\net al. 2023; Mahapatra et al. 2025b; Arca Sedda et al.\n2023). Such second-generation black holes are systemat-\nically more massive than their first-generation ancestors\nand are expected to be rapidly rotating; the spin distri-\nbution of remnant black holes is generically and robustly\nconcentrated about \u03c7 \u22480.7 (Pretorius 2005; Buonanno\net al. 2008; Berti & Volonteri 2008). A remnant black\nhole\u2019s spin arises from the total remaining angular mo-\nmentum of its ancestral binary at merger, which, for\napproximately equal-mass mergers, is dominated by the\norbital angular momentum. The spin angular momenta\nof the ancestral black holes do affect the remnant\u2019s spin,\nbut their contribution is, in part, countered by the re-\nlationship between spin and inspiral duration. Binaries\nwith larger aligned spins undergo longer inspirals and\nradiate away more orbital angular momentum, while\nbinaries with small or anti-aligned spins merge more\npromptly and thus retain more orbital angular momen-\ntum (Campanelli et al. 2006).\nObservationally, mergers involving second-generation\nobjects (often called hierarchical mergers) would distin-\nguish themselves via their large spin magnitudes, sta-\ntistically isotropic spin orientations, and mass ratios\nthat are typically less than unity.\nThe spin magni-\ntudes, spin\u2013orbit misalignments, and unequal mass ra-\ntios of GW241011 and GW241110 therefore make these\nsignals prime candidates for arising from a hierarchical\norigin. Figure 6, for example, illustrates predictions for\nthe possible primary spin magnitudes (upper row) and\nmass ratios (lower row) among binary black hole merg-\ners in dense star clusters. Dashed contours indicate pre-\ndicted properties of mergers in which both components\nare first generation black holes, while solid contours cor-\nrespond to systems in which at least one component\nis the product of a previous merger.\nWe show data\nfrom two models, the Cluster Monte Carlo cata-\nlog (CMC; Kremer et al. 2020; Rodriguez et al. 2022)\nand the clusterBHBdynamics model (cBHBd; An-\ntonini & Gieles 2020a; Antonini et al. 2023); further de-\ntails regarding both models are provided in Appendix D.\nThe spin magnitude and mass ratio of GW241011, in\nparticular, are inconsistent with the properties predicted\nof first-generation mergers, but lie within ranges pre-\ndicted by both models for higher-generation hierarchi-\ncal mergers.\nFigure 6 does not, however, convey rel-\native numbers of first-generation and higher-generation\nmergers; both models predict approximately one higher-\ngeneration merger per five first-generation mergers.\nHierarchical black hole mergers are often associ-\nated with massive black holes.\nAt sub-solar metal-\nlicities, black holes masses are thought to be lim-\nited by (pulsational)-pair-instability processes (Barkat\net al. 1967; Woosley et al. 2007), preventing the for-\nmation of first-generation black holes with masses be-\ntween \u223c50 and \u223c120 M\u2299(e.g., Spera & Mapelli 2017;\nWoosley & Heger 2021; Hendriks et al. 2023).\nHier-\narchical mergers may yield second-generation remnants\nwith masses situated in this range, and are therefore\na possible evolutionary origin for massive systems like\nthe sources of GW190521 (Abbott et al. 2020b) and\nGW231123 135430 (Abac et al. 2025c). The sources of\nGW241011 and GW241110 are, in contrast, relatively\nlight. These masses are not inconsistent with a hierar-\nchical origin, however. The three columns of Figure 6\ncorrespond to predictions for clusters of differing stellar\nmetallicities. At high metallicities, stellar winds increas-\ningly strip massive stars of their envelopes, preventing\nthe formation of massive carbon-oxygen cores and reduc-\ning the final masses of black holes (e.g., Belczynski et al.\n2001; Fryer et al. 2012; Belczynski et al. 2016b; Spera\net al. 2016). Therefore, although hierarchical mergers\nin low-metallicity environments predominantly involve\nhigh primary masses, clusters with stellar metallicities\nZ \u22480.1 Z\u2299and above are predicted to readily yield hi-\nerarchical mergers with \u223c20 M\u2299primaries, consistent\nwith the sources of GW241011 and GW241110 (Ye et al.\n2025).\n4.3. The ancestors of GW241011 and GW241110\nIf the primaries of GW241011 and GW241110 are\nsecond-generation remnants of previous mergers, we can\nindirectly constrain the masses, spins, and recoil kicks\n\n21\nFigure 6.\n90% credible bounds on the primary masses, mass ratios, spins of GW241011 (blue) and GW241110 (green),\ncompared to predicted properties of merging black holes in dense star clusters from the Cluster Monte Carlo catalog (Kremer\net al. 2020; Rodriguez et al. 2022), and clusterBHBddynamics models (Antonini et al. 2023). Dashed contours correspond\nto merging first-generation black holes, while solid contours correspond to higher-generation binaries containing remnants\nfrom previous mergers.\nBoth models assume black holes to be born non-rotating.\nThe three columns correspond to star\ncluster simulations with stellar populations at three different metallicities: Z = 0.01 Z\u2299, 0.1 Z\u2299, and Z\u2299. Under the modeling\nassumptions, the masses of GW241011 and GW241110 appear inconsistent with those predicted in low-metallicity stellar clusters\nwith Z = 0.01 Z\u2299. Their masses and spins may be consistent, though, with those predicted among hierarchical binary black\nhole mergers that are formed in clusters of moderate or near-solar metallicities.\nassociated with their first-generation ancestors (e.g.,\nBaibhav et al. 2021; Barrera & Bartos 2022; Payn-\nter & Thrane 2023; Mahapatra et al. 2024; Ara\u00b4ujo-\n\u00b4Alvarez et al. 2024; Mahapatra et al. 2025a). We ex-\nplore this question using two complementary methods.\nIn the first method (the Forward approach), we adopt\nastrophysically-informed priors on the ancestral masses\nand spins of GW241011 and GW241110\u2019s hypothesized\nfirst-generation ancestors. Priors are chosen to follow\nclosely the results from stellar cluster simulations pre-\nsented in Figure 6, strongly preferring equal masses and\nfirst-generation black hole spins near zero; these pri-\nors are described in more detail in Appendix E. We\nthen proceed via a hierarchical Bayesian approach, us-\ning observed strain data to obtain posteriors on ances-\ntral properties, marginalized over the source properties\nof GW241011 and GW241110 (Mahapatra et al. 2024).\nIn the second method (the Backward approach), we\nproceed more agnostically. Beginning with the source\nmasses and spins of GW241011 and GW241110\u2019s pri-\nmaries from Section 3, for each posterior sample we iden-\ntify an ancestral binary whose remnant mass and spin\nare consistent, within a small tolerance, with this poste-\nrior sample. This approach allows us to construct pos-\nteriors on required ancestral properties while preserv-\ning the astrophysically-agnostic priors and posteriors\non the source properties of GW241011 and GW241110\nthemselves (Ara\u00b4ujo-\u00b4Alvarez et al. 2024). In both cases,\nnumerical-relativity simulations are used to map be-\ntween ancestral binaries and remnant properties (Varma\net al. 2019).\nFigure\n7\nillustrates\nthe\nrequired\nproperties\nof\nGW241011 and GW241110\u2019s ancestors estimated in the\nmore agnostic Backward approach.\nWe infer a first-\ngeneration ancestor of GW241011 to have had masses\n13.3+4.8\n\u22123.2 M\u2299and 7.5+3.2\n\u22123.9 M\u2299.\nA first generation an-\ncestor to GW241110 likely possessed similar masses:\n12.3+5.6\n\u22124.2 M\u2299and 5.1+3.6\n\u22121.9 M\u2299.\nThe effective inspiral\nspin of GW241011\u2019s ancestor is constrained to \u03c7eff =\n0.23+0.29\n\u22120.28; larger or smaller values would over- or under-\npredict, respectively, the observed primary spin \u03c71. The\nprimary spin of GW241110 is measured less precisely\nand so allows for a broader range of ancestral effective\nspins: \u03c7eff = \u22120.04+0.65\n\u22120.57. For both binaries, the remnant\nrecoil kicks are inferred to lie between approximately\n100\u20132000 km s\u22121. Constraints on recoil kicks are, how-\n\n22\nm1 = 19.6+3.6\n\u22122.5 M\u2299\n\u03c71 = 0.78+0.09\n\u22120.09\nm2 = 5.9+0.8\n\u22120.8 M\u2299\nm1 = 13.3+4.8\n\u22123.2 M\u2299\nm2 = 7.5+3.2\n\u22123.9 M\u2299\nGW241011\n\u03c7eff = 0.23+0.29\n\u22120.28\nm1 = 17.2+5.0\n\u22124.4 M\u2299\n\u03c71 = 0.61+0.33\n\u22120.40\nm2 = 7.7+2.2\n\u22121.5 M\u2299\nm1 = 12.3+5.6\n\u22124.2 M\u2299\nm2 = 5.1+3.6\n\u22121.9 M\u2299\nGW241110\n\u03c7eff = \u22120.04+0.65\n\u22120.57\nvrecoil = 750+1400\n\u2212630 km s\u22121\nvrecoil = 480+1270\n\u2212330 km s\u22121\nFigure 7.\nInferred properties of the first-generation ancestors to the more massive black holes in GW241011 and GW241110,\nunder the hypothesis that these black holes were formed hierarchically from a previous merger. Shown are median and 90%\ncredible bounds inferred on ancestral component masses and effective inspiral spins, as well as the recoil kicks imparted to each\nremnant black hole due to asymmetric gravitational-wave-emission. We compute ancestral properties in two manners: one (the\nBackward approach) that agnostically retains the same priors and posteriors on GW241011 and GW241110\u2019s source properties\nas presented in Section 3, and one (the Forward approach) that adopts an astrophysically-informed prior on possible ancestral\nproperties. This figure includes results from the agnostic Backward approach; constraints obtained under the astrophysically-\ninformed Forward approach are described in the text.\never, almost entirely prior dominated, and it is therefore\nunclear if they yield meaningful constraints on environ-\nmental escape velocities required for successful remnant\nretention.\nIn\nthe\nForward\napproach,\nthe\nastrophysically-\ninformed yields posteriors favoring more equal-mass an-\ncestors.\nThe ancestor of GW241011 is inferred to\nhave component masses 11.0+1.9\n\u22121.6 M\u2299and 9.6+1.7\n\u22121.8 M\u2299,\nwhile GW241110\u2019s ancestor is inferred to have masses\n9.6+3.1\n\u22122.0 M\u2299and 8.0+2.1\n\u22122.3 M\u2299. The global maximum of the\nbinary black hole mass function is situated at approxi-\nmately 10 M\u2299(Tiwari & Fairhurst 2021; Abbott et al.\n2023b; Farah et al. 2023; Abac et al. 2025d); the ances-\ntral black holes of both GW241011 and GW241110 are\ninferred to lie near this peak. Because the astrophysical\nprior adopted in the Forward approach requires ances-\ntral spins to be near zero, inferred recoil kicks are sys-\ntematically lower, ranging between approximately 10\u2013\n300 km s\u22121. As in the Backward approach above, this\nrange is a consequence of our prior.\nA more detailed presentation of both sets of results\nand additional methodological detail is provided in Ap-\npendix E.\n4.4. No evidence for eccentricity\nBinary black hole coalescences arising dynamically\nin dense stellar environments may bear unique signa-\ntures of orbital eccentricity in their gravitational-wave\nemission. Gravitational-wave emission rapidly circular-\nizes initially eccentric orbits (Peters 1964), and bina-\nries evolving in isolation are expected to be nearly per-\nfectly quasi-circular by the time their gravitational-wave\nemission enters the sensitivity band of ground-based\ndetectors.\nFollowing many-body encounters in dense\nclusters, however, binaries can be placed on nearly-\nhyperbolic trajectories and merge promptly.\nSeveral\npercent of these binaries may retain observable eccen-\ntricity in the frequency band of ground-based detectors.\nIn old, metal-poor globular clusters, 5\u201310% of binary\nblack hole mergers in the local universe are predicted to\nhave eccentricities measurable by the LIGO, Virgo, and\nKAGRA experiments (Wen 2003; Gultekin et al. 2006;\nO\u2019Leary et al. 2006; Antonini & Perets 2012; Antonini\net al. 2014; Samsing et al. 2018; Samsing & Ramirez-\nRuiz 2017; Samsing 2018; Rodriguez et al. 2018a; Zevin\net al. 2019), although this may decrease by a factor\nof a couple when assuming higher initial cluster den-\nsities (Antonini & Gieles 2020b). The non-secular evo-\nlution of isolated triple systems may yield \u227310% of\nsystems with measurable eccentricities, and potentially\n\n23\nFigure 8.\nPosteriors on the orbital eccentricity of\nGW241011 and GW241110.\nResults are obtained us-\ning\nthe\nSEOBNRv5EHM\n(Gamboa\net\nal.\n2025)\nand\nTEOBRESUMS-DAL\u00b4I (Nagar et al. 2024) waveform mod-\nels, and eccentricities are quoted at a reference frequency of\n13.33 Hz, when higher-order spherical harmonic modes first\nenter the observable frequency band. Neither event exhibits\nevidence for residual eccentricity.\nWe bound e < 0.05 at\n90% credibility for GW241011 under both waveform mod-\nels. GW241110, meanwhile, yields 90% credible upper limits\nof e < 0.17 and e < 0.14 under the SEOBNRv5EHM and\nTEOBRESUMS-DAL\u00b4I models, respectively.\nhave a higher merger rate of eccentric sources in the lo-\ncal universe (Dorozsmai et al. 2025). The total merger\nrate in active galactic nuclei is uncertain with predic-\ntions that span multiple orders of magnitude (Gr\u00a8obner\net al. 2020), with predictions for measurably eccentric\nfraction ranging from \u227310% (Tagawa et al. 2021) up to\n\u223c70% (Samsing et al. 2022). There exists growing evi-\ndence that at least some observed compact binary merg-\ners may possess residual eccentricity (Gayathri et al.\n2022; Romero-Shaw et al. 2020a; Gamba et al. 2023;\nRomero-Shaw et al. 2022; Iglesias et al. 2024; Gupte\net al. 2024; Romero-Shaw et al. 2025; Planas et al. 2025;\nMorras et al. 2025), possibly indicating binary formation\nin one or more of these environments.\nIf GW241011 and GW241110 evolved dynamically in\ndense clusters, they may be prime candidates to ex-\nhibit measurable eccentricity. We reanalyze GW241011\nand GW241110 using a pair of alternative waveform\nmodels, SEOBNRv5EHM (Gamboa et al. 2025) and\nTEOBRESUMS-DAL\u00b4I (Nagar et al. 2024), that de-\nscribe gravitational-wave emission from eccentric com-\npact binaries through binary inspiral, merger, and ring-\ndown.\nThese waveform models are valid under re-\nstricted spin geometries, requiring component spins to\nbe purely parallel or antiparallel to a binary\u2019s orbital\nangular momentum. The gravitational-wave signatures\nof orbital eccentricity and spin\u2013orbit misalignment are\nknown to be degenerate (e.g., Calder\u00b4on Bustillo et al.\n2021; Romero-Shaw et al. 2020a, 2023; Divyajyoti et al.\n2024b; Planas et al. 2025). Degeneracies between spin\nmisalignment and eccentricity are weakest for binaries\nlike GW241011 and GW241110 (Romero-Shaw et al.\n2023; Divyajyoti et al. 2024b) with low chirp masses,\nwhich complete many observable cycles. Nevertheless,\neccentricity measurements that neglect effects of spin\u2013\norbit precession (or, conversely, spin measurements that\nneglect eccentricity, as in Section 3) may be biased.\nConstraints on the orbital eccentricity of GW241011\nand GW241110 are presented in Figure 8.\nOrbital\neccentricity is an evolving function of time; results\nare quoted at the instant when the binaries\u2019 orbit-\naveraged quadrupole emission is observed at 13.33 Hz,\ncorresponding to the time at which \u2113= 3 spherical\nharmonic modes enter the observable band at 20 Hz.\nNeither event possesses measurable eccentricity.\nUn-\nder both waveform models, GW241011 is bounded to\nhave e < 0.05 at 90% credibility, while GW241110 has\ne < 0.17 and e < 0.14 under the SEOBNRv5EHM and\nTEOBRESUMS-DAL\u00b4I models, respectively.\nThis is\nnot inconsistent with a dynamical origin; the vast ma-\njority of mergers in clusters are expected to have eccen-\ntricities e \u22720.1 at frequencies accessible to Advanced\nLIGO, Advanced Virgo, and KAGRA (Gultekin et al.\n2006; O\u2019Leary et al. 2006; Samsing et al. 2014; Samsing\n2018; Rodriguez et al. 2018b; Gond\u00b4an et al. 2018; Zevin\net al. 2019; Dall\u2019Amico et al. 2024). On the basis of ec-\ncentricity alone, though, we cannot rule out any individ-\nual formation scenarios for GW241011 and GW241110.\nFurther details are presented in Appendix B.\n5. TESTS OF FUNDAMENTAL PHYSICS\nGravitational waveforms from compact binary coales-\ncences encode detailed information about the nature and\ninternal structure of the merging objects, enabling rig-\norous tests of general relativity (GR) and fundamen-\ntal physics.\nThe large primary spin and significant\nmass asymmetry of GW241011, in particular, makes this\nevent a uniquely powerful probe of the Kerr nature of\nblack holes and the multipolar structure of gravitational-\nwave emission.\n5.1. Black hole spin-induced quadrupole moment\nWithin GR, rotating and charge-neutral black holes\nare uniquely described by the Kerr solution (Kerr 1963;\nCarter 1971). In Kerr spacetime, the black hole spin-\ninduced quadrupole moment, the leading contribution of\nspin to a black hole spacetime\u2019s multipolar expansion, is\n\n24\nFigure 9.\nDeviations from the Kerr prediction for the\nspin-induced quadrupole moment of GW241011\u2019s primary\nblack hole, \u03b4\u03ba1, as well as the deviation \u03b4\u03bas in the symmetric\ncombination \u03bas = (\u03ba1 +\u03ba2)/2 (Krishnendu et al. 2017, 2019;\nAbbott et al. 2021b). We bound \u03b4\u03ba1 = 0.10+0.82\n\u22120.82 and \u03b4\u03bas =\n0.10+0.09\n\u22120.11, consistent with expectations from GR. The next-\nmost informative event, GW190412 (Abbott et al. 2020d),\nyielded a constraint \u03b4\u03bas = 0+2\n\u221291 (Divyajyoti et al. 2024a).\ngiven by Q = \u2212\u03baS2/(mc2). Here, m is the black hole\u2019s\nmass, S is its spin angular momentum, c is the speed of\nlight, and \u03ba = 1 exactly (Hansen 1974). Non-black hole\nspacetimes, including neutron stars (Laarakkers & Pois-\nson 1999; Pappas & Apostolatos 2012a,b; Harry & Hin-\nderer 2018), boson stars (Ryan 1997; Herdeiro & Radu\n2014; Baumann et al. 2019; Chia & Edwards 2020), and\nother exotic compact objects, may in contrast exhibit\nsignificantly different values of \u03ba owing to differences in\ninternal structure and composition. Gravitational-wave\nsources containing rapidly-spinning black holes enable\ndirect measurements of the spin-induced quadrupole\nmoment and tests of the Kerr hypothesis (Arun et al.\n2009; Mishra et al. 2016); any measured deviation from\n\u03ba = 1 would strongly suggest the presence of non-black\nhole constituents or indicate new physics beyond the\npredictions of GR.\nWe define \u03ba1 = 1 + \u03b4\u03ba1 and \u03ba2 = 1 + \u03b4\u03ba2 as the spin-\ninduced quadrupole coefficients of each compact object\nin GW241011\u2019s source binary. We repeat parameter esti-\nmation with a modified IMRPhenomXPHM waveform\nmodel (Pratten et al. 2021), allowing for non-zero \u03b4\u03ba1\nand \u03b4\u03ba2 (Divyajyoti et al. 2024a). The resulting poste-\nrior is shown in Fig. 9. The spin-induced quadrupole\ncoefficient of GW241011\u2019s primary deviates from the\nKerr prediction by \u03b4\u03ba1 = 0.10+0.82\n\u22120.82, consistent with\nGR (constraints on \u03b4\u03ba2 are uninformative). This is the\nmost stringent constraint to date on the spin-induced\nquadrupole of a compact object. The constraints offered\nby GW241011 on \u03b4\u03ba1 are unusual, enabled by the event\u2019s\nhigh SNR, large primary spin, and unequal mass ratio.\nTypically, gravitational-wave signals primarily constrain\nonly the symmetric combination \u03bas = (\u03ba1 + \u03ba2)/2 (Kr-\nishnendu et al. 2017, 2019; Abbott et al. 2021b; Divya-\njyoti et al. 2024a). GW241011 constrains this symmet-\nric combination to be within \u03b4\u03bas = 0.10+0.09\n\u22120.11 of the\nKerr hypothesis, under the assumption that \u03ba1 = \u03ba2.\nThe previous best constraint on \u03bas was obtained from\nthe binary black hole GW190412 (Divyajyoti et al.\n2024a), which gave \u03b4\u03bas = 0+2\n\u221291. GW241011 improves on\nthis constraint by approximately three orders of mag-\nnitude. A different implementation for the estimation\nof the spin-induced quadrupole moment, utilizing the\nSEOBNRv5HM ROM (Pompili et al. 2023) waveform\nmodel, yields consistent results and is discussed in Ap-\npendix F.1.\nMeasurement\nof\nGW241011\u2019s\nspin-induced\nquadrupole moment may rule out a wide range of exotic\ncompact objects or black hole mimickers. Massive bo-\nson star models (Ryan 1997; Pacilio et al. 2020) predict\nspin-induced quadrupole moment parameters of order\n\u223c10\u2013150 for self-interacting spinning boson stars with\nquadratic coupling.\nThe measurement of \u03b4\u03bas \u22640.17\nat 90% credibility from GW241011 likely rules out all\nthe massive boson star models described in e.g. Pa-\ncilio et al. (2020). Other models, such as minimal boson\nstars (Kaup 1968; Ruffini & Bonazzola 1969; Vaglio et al.\n2022) and solitonic boson stars (Friedberg et al. 1987),\nremain poorly understood in terms of their spin-induced\nmultipole moments (Cardoso et al. 2017; Cardoso &\nPani 2019). Another class of exotic compact objects are\nthe gravastars (Mottola 2023), where the spin-induced\nmultipole moments can take negative values due to the\nprolate deformation induced by their spinning motion.\nAlthough spin-induced quadrupole moment values have\nbeen predicted for thin-shell gravastar models (Uchikata\n& Yoshida 2016), the GW241011 data is insufficient to\nmake definitive conclusions.\n5.2. Radiation beyond the quadrupole approximation\nGravitational-wave radiation may be generically de-\ncomposed into an expansion over spin-weight \u22122 spher-\nical harmonics, \u22122Ylm.\nThe gravitational waves from\nmerging compact binaries are dominated by the (\u2113, m) =\n(2, \u00b12) spherical harmonic, sourced by a binary\u2019s mass\nquadrupole moment. As discussed in Section 3, however,\nGW241011 exhibits significant radiation in the (\u2113, m) =\n(3, \u00b13) mode sourced by the current quadrupole and\nmass octupole moments.\nGeneral relativity fixes the\nrelative amplitudes of gravitational radiation received\n\n25\nFigure 10.\nPosterior constraints on the amplitude\nof GW241011\u2019s gravitational radiation in (\u2113, m) = (3, \u00b13)\nspherical harmonic modes, relative to the prediction from\nGR. GW241011 is consistent with expectation, with devia-\ntions from the GR limited to the interval \u22121.9 \u2264\u03b4A33 \u22640.5\nat 90% credibility. Degeneracy with orbital inclination yields\na strongly bimodal structure in the posterior for \u03b4A33. The\ndominant mode has \u03b4A33 = 0.0+0.5\n\u22120.3, consistent with GR,\nwhile the subdominant mode has \u03b4A33 = \u22122.1+0.4\n\u22120.5.\nFor\ncomparison, also shown are the posteriors obtained from the\nnext-most-informative gravitational-wave events, GW190814\nand GW190412 (Abbott et al. 2020d,c; Puecher et al. 2022;\nAbac et al. 2025g).\nin different spherical harmonic modes. The strong de-\ntection of multiple modes in a gravitational-wave signal,\nas in GW241011, offers an opportunity to test these pre-\ndictions (Capano & Nitz 2020; Puecher et al. 2022; Ma-\nhapatra 2024; Abac et al. 2025g).\nWe repeat inference on the properties of GW241011,\nbut now introduce a parameter \u03b4A33 that allows for de-\nviations in the signal\u2019s (\u2113, m) = (3, \u00b13) mode ampli-\ntudes, relative to the (2, \u00b12) mode content (Puecher\net al. 2022; Abac et al. 2025g).\nHigher-order modes,\nsuch as (4, \u00b14) spherical harmonics, are not detected in\nGW241011, and so are not tested here. The resulting\nposterior distribution on \u03b4A33 is shown in Figure 10.\nPosteriors on \u03b4A33 are characteristically bimodal, due\nto degeneracies between a binary\u2019s inclination, orbital\nphase, and expected (3, \u00b13) mode amplitude (Mills &\nFairhurst 2021; Puecher et al. 2022).\nThe dominant\nmode is consistent with GR, with \u03b4A33 = 0.0+0.5\n\u22120.3, while\nthe subdominant mode has \u03b4A33 = \u22122.1+0.4\n\u22120.5. Taking\nboth posterior modes together, we find \u22121.9 \u2264\u03b4A33 \u2264\n0.5 at 90% credibility.\nThis is the best measurement\nto date of \u03b4A33.\nAmong binaries in GWTC-4, the\nnext-best constraints are provided by GW190814 and\nGW190412 (Abbott et al. 2020d,c; Puecher et al. 2022),\nFigure 11.\nMasses of novel ultralight scalar (top) and\nvector (bottom) bosons that are excluded at 90% credibility\nby the non-zero spin measurements of GW241011. If bosons\nwith masses lying in the shaded regions existed, then the\nprimary black hole of GW241011 would have undergone the\nsuperradiance instability, spontaneously generating a cloud\nof bound boson particles and driving the black holes\u2019 spins\nbelow their observed values. The superradiance instability\ncan deplete a black hole\u2019s spin over an astrophysically-brief\ntimescale, but this timescale becomes significantly longer\noutside a narrow range of boson masses.\nThe exclusion\ncurves therefore depend on the presumed age of GW241011\u2019s\nprimary black hole.\nwhich give \u22123.6 \u2264\u03b4A33 \u22641.6 and \u22125.3 \u2264\u03b4A33 \u22644.0,\nrespectively (Abac et al. 2025g). GW241011 therefore\nconfirms that gravitational waves radiated in (3, \u00b13)\nspherical harmonic modes have amplitudes consistent\nwith expectations from GR. Further details are elabo-\nrated in Appendix F.2.\n5.3. Ultralight bosons\nSpinning black holes may prodigiously and sponta-\nneously source particle production through the super-\nradiant instability mechanism (Press & Teukolsky 1972;\nDamour et al. 1976; Brito et al. 2015a). Ingoing waves\n\n26\nmay acquire energy as they scatter off a rotating black\nhole. In the vicinity of a rotating black hole, an oscillat-\ning, gravitationally bound fluctuation in a bosonic field\nmay grow exponentially, spontaneously turning an ini-\ntially small perturbation into a macroscopic boson cloud\nsurrounding the black hole. Cloud growth is powered at\nthe expense of the black hole\u2019s rotational energy and\nmay occur on timescales as short as days or minutes.\nThis superradiance instability is specifically relevant for\nbosons with Compton wavelengths comparable to the\nblack hole\u2019s size.\nIf mb is the boson mass, G is the\ngravitational constant, and M the black hole\u2019s mass,\nthen superradiance requires mb \u223c\u210fc2/(GM). Thus, the\nobservation of a rapidly-rotating black hole of mass M\nimmediately excludes the existence of novel bosons with\nmasses near mb; if such a particle existed, it should have\nlong since depleted the black hole\u2019s spin. Constraints\ncan, in principle, be performed using both electromag-\nnetic and gravitational-wave observations, and for both\nsupermassive and stellar-mass black holes (e.g., Arvani-\ntaki et al. 2010; Arvanitaki & Dubovsky 2011; Pani et al.\n2012; Baryakhtar et al. 2017; Fernandez et al. 2019; Ng\net al. 2021a,b; Stott 2020).\nThe confidently rapid primary spin of GW241011 ex-\ncludes the existence of ultralight bosons with masses be-\ntween approximately 10\u221213 and 3\u00d710\u221212 eV. Figure 11\nshows the boson masses excluded by the primary spin\nmeasurement of GW241011, as a function of the pre-\nsumed age of each binary\u2019s primary black hole and com-\nputed using the SuperRad package (Siemonsen et al.\n2023; May et al. 2025); see Appendix F.3 for details.\nThe top and bottom panels correspond to scalar and\nvector bosons, respectively. The filled contours indicate\nregions in which the primaries of both binaries should\nhave undergone the superradiance instability, yielding\nfinal present-day spins that are inconsistent with obser-\nvation at 90% credibility. Since all relevant azimuthal\nmodes are included for the black hole ages considered,\nthe narrow exclusion region near 4 \u00d7 10\u221212 eV in the\nscalar case arises from cloud growth with a higher az-\nimuthal number m = 3. Conservatively assuming an age\nof 105 years for the primary black hole of GW241011,\nthis signal excludes the existence of scalar bosons with\nmasses in the interval [0.3, 2.6] \u00d7 10\u221212 eV. The signal\nexcludes vector bosons, meanwhile, with masses in the\n[0.1, 5.3] \u00d7 10\u221212 eV interval.\nDue to its more uncer-\ntain spin measurements, GW241110 does not apprecia-\nbly constrain the existence of ultralight bosons.\nGW241011 rules out the existence of bosons at higher\nmasses than those excluded by previous gravitational-\nwave observations.\nAn analysis considering the pop-\nulation of black holes comprising the LIGO\u2013Virgo\u2013\nKAGRA GWTC-2 catalog strongly disfavored scalar bo-\nson masses between [2.2, 2.7] \u00d7 10\u221213 eV when assuming\n105 year old black holes (Ng et al. 2021b). Under the\nsame age assumption, recent analysis using GW231123\nand GW190517 excluded scalar and vector boson masses\nin the intervals [0.6, 11]\u00d710\u221213 and [0.1, 18]\u00d710\u221213 eV,\nrespectively, at 90% credibility (Aswathi et al. 2025). A\ncomplementary analysis of GW231123 with a relativistic\nmodel for self-interacting scalars excludes axion masses\nin the interval [0.6, 5] \u00d7 10\u221213 eV with decay constants\n\u22731014 GeV (Caputo et al. 2025).\n6. CONCLUSIONS\nIn this paper, we have presented gravitational-wave\nsignals from two binary black hole coalescences \u2013\nGW241011 and GW241110 \u2013 discovered during the sec-\nond part of the fourth observing run of the LIGO, Virgo,\nand KAGRA observatories. The measured properties of\nthese events naturally suggest consideration as a pair.\nThe spins of the more massive black holes in GW241011\nand GW241110 are respectively situated at either ex-\ntreme of the binary black hole population. The primary\nblack hole of GW241011 possesses one of the largest\nand most precisely measured black hole spins observed\nvia gravitational waves, and is spinning in a direction\nprimarily (but not exactly) aligned with its orbital an-\ngular momentum. Conversely, the primary black hole\nof GW241110 is rapidly spinning in a direction confi-\ndently antiparallel to its orbit, the first confidently anti-\naligned black hole spin measured to date. At the same\ntime, these two binary black holes exhibit nearly identi-\ncal masses, with each event favoring a primary mass in\nthe range 15\u201320 M\u2299and an unequal mass ratio between\ntheir component black holes.\nTaken together,\nthe mass ratios,\nlarge primary\nspins, and significant spin-orbit misalignment angles of\nGW241011 and GW241110 are strongly suggestive of hi-\nerarchical binary black hole mergers in dense stellar en-\nvironments, such as globular, nuclear, or young stellar\nclusters. Under this interpretation, the primary black\nholes of both binaries are themselves the remnants of\npast black hole mergers. However, although the proper-\nties of GW241011 and GW241110 are in strong tension\nwith predictions from isolated binary evolution, from\ngravitational-wave data alone we cannot rule out for-\nmation by massive stellar binaries (or systems of higher\nmultiplicity). GW241011 and GW241110 nevertheless\nsuggest that at least some merging binary black holes\nmerge dynamically in dense environments, and that\nthese environments are sufficiently massive to retain\nremnant black holes and foster repeated mergers.\n\n27\nThe large and precisely measured primary spin of\nGW241011 furthermore enables myriad tests of funda-\nmental physics. In particular, we find that this event\nprovides the best measurements to date of a black hole\u2019s\nspin induced quadrupole moment, confirming the Kerr\nprediction to within a factor of two (or to within 10%,\ndepending on the parametrization used, an improve-\nment in precision by two orders of magnitude; see Sec-\ntion 5.1). The nature of this test is independent from\nand complementary to the ringdown spectroscopy per-\nformed on the extremely loud event GW250114; anal-\nysis of GW250114\u2019s ringdown identified overtones with\nfrequencies constrained to within 30% of their Kerr pre-\ndictions (Abac et al. 2025f,h). GW241011\u2019s strong radi-\nation in multiple spherical harmonic modes furthermore\nenables the best constraint to date on the relative am-\nplitudes of (\u2113, m) = (2, \u00b12) and (3, \u00b13) modes, confirm-\ning the expected structure of gravitational-wave emis-\nsion beyond the quadrupole approximation. Finally, the\nlarge spins of both GW241011 and GW241110 rule out\nthe existence of novel boson particles with masses in the\nrange 10\u221213 to 10\u221212 eV.\nGrowing\ngravitational-wave\ncatalogs,\nenabled\nby\nthe\nconcurrent\noperation\nof\nincreasingly\nsensitive\ngravitational-wave\nobservatories,\ncontinue\nto\nyield\nindividually-interesting sources that expand our knowl-\nedge of the compact binary landscape.\nGravitational\nwaves detected during the fourth observing run of the\nLIGO, Virgo, and KAGRA observatories have thus\nfar enabled novel tests of relativity and gravitational-\nwaveform models (Abac et al. 2025i,f,h) and provided\nsources in new and unexpected regions of parameter\nspace (Abac et al. 2024, 2025c). We expect discoveries\nto continue through the remainder of the fourth LIGO\u2013\nVirgo\u2013KAGRA observing run and beyond.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies as well as by the Council of Scientific and Indus-\ntrial Research of India, the Department of Science and\nTechnology, India, the Science & Engineering Research\nBoard (SERB), India, the Ministry of Human Resource\nDevelopment, India, the Spanish Agencia Estatal de\nInvestigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comunitat\nAuton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Com-\nmission, the European Social Funds (ESF), the Euro-\npean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish Uni-\nversities Physics Alliance, the Hungarian Scientific Re-\nsearch Fund (OTKA), the French Lyon Institute of Ori-\ngins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering\nResearch Council of Canada (NSERC), the Canadian\nFoundation for Innovation (CFI), the Brazilian Min-\nistry of Science, Technology, and Innovations, the In-\nternational Center for Theoretical Physics South Ameri-\ncan Institute for Fundamental Research (ICTP-SAIFR),\nthe Research Grants Council of Hong Kong, the Na-\ntional Natural Science Foundation of China (NSFC),\nthe Israel Science Foundation (ISF), the US-Israel Bina-\ntional Science Fund (BSF), the Leverhulme Trust, the\nResearch Corporation, the National Science and Tech-\nnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The au-\nthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computa-\ntional resources. This work was supported by MEXT,\n\n28\nthe JSPS Leading-edge Research Infrastructure Pro-\ngram, JSPS Grant-in-Aid for Specially Promoted Re-\nsearch 26000005, JSPS Grant-in-Aid for Scientific Re-\nsearch on Innovative Areas 2402: 24103006, 24103005,\nand 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grants-in-Aid for Scientific Research (S)\n17H06133 and 20H05639, JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cosmic\nRay Research, University of Tokyo, the National Re-\nsearch Foundation (NRF), the Computing Infrastruc-\nture Project of the Global Science experimental Data\nhub Center (GSDC) at KISTI, the Korea Astronomy\nand Space Science Institute (KASI), the Ministry of Sci-\nence and ICT (MSIT) in Korea, Academia Sinica (AS),\nthe AS Grid Center (ASGC) and the National Science\nand Technology Council (NSTC) in Taiwan under grants\nincluding the Science Vanguard Research Program, the\nAdvanced Technology Center (ATC) of NAOJ, and the\nMechanical Engineering Center of KEK.\nWe are grateful for the valuable feedback provided by\nanonymous reviewers. Additional acknowledgements for\nsupport of individual authors may be found in the fol-\nlowing document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising. We\nrequest that citations to this article use \u2018A. G. Abac et\nal. (LIGO-Virgo-KAGRA Collaboration), ...\u2019 or similar\nphrasing, depending on journal convention.\nSoftware:\nCalibration of the LIGO strain data\nwas performed with a GstLAL-based calibration soft-\nware pipeline (Viets et al. 2018). Data-quality prod-\nucts and event-validation results were computed us-\ning the DMT (Zweizig, J. 2006), DQR (LIGO Sci-\nentific Collaboration and Virgo Collaboration 2018),\nDQSEGDB (Fisher et al. 2021), gwdetchar (Macleod\net al. 2025), hveto (Smith et al. 2011), iDQ (Essick et al.\n2020), Omicron (Robinet et al. 2020), and PythonVir-\ngoTools (Virgo Collaboration 2021) software packages\nand contributing software tools. Analyses in this cata-\nlog relied on software from the LVK Algorithm Library\nSuite (LIGO Scientific, Virgo, and KAGRA Collabora-\ntion 2018; Wette 2020). The detection of the signals and\nsubsequent significance evaluations were performed with\nthe GstLAL-based inspiral software pipeline (Messick\net al. 2017; Sachdev et al. 2019; Hanna et al. 2020; Can-\nnon et al. 2021; Sakon et al. 2024; Ewing et al. 2024;\nTsukada et al. 2023; Ray et al. 2023; Joshi et al. 2025a,b),\nwith the MBTA pipeline (Adams et al. 2016; Aubin et al.\n2021; All\u00b4en\u00b4e et al. 2025), and with the PyCBC (Us-\nman et al. 2016; Nitz 2018; Nitz et al. 2017; Dal Canton\net al. 2021; Davies et al. 2020) packages. Estimates of\nthe noise spectra and glitch models were obtained us-\ning BayesWave (Cornish & Littenberg 2015; Litten-\nberg & Cornish 2015; Littenberg et al. 2016; Cornish\net al. 2021; Gupta & Cornish 2024). Low-latency source\nlocalization was performed using BAYESTAR (Singer &\nPrice 2016). Source-parameter estimation was performed\nwith the Bilby library (Ashton et al. 2019; Romero-\nShaw et al. 2020b), using the Dynesty nested sampling\npackage (Speagle 2020), and the RIFT (Pankow et al.\n2015; Lange et al. 2017; Wysocki et al. 2019) package.\nSEOBNRv5PHM waveforms used in parameter estima-\ntion were generated using pySEOBNR (Mihaylov et al.\n2023). PESummary was used to post-process and collate\nparameter estimation results (Hoy & Raymond 2021).\nThe various stages of the parameter estimation anal-\nysis were managed with the Asimov library (Williams\net al. 2023). Population inference was performed with\nthe GWPopulation package (Talbot et al. 2025). The\nSuperRad package (Siemonsen et al. 2023; May et al.\n2025) was used to characterize superradiance phenom-\nena. Plots were prepared with Matplotlib (Hunter\n2007). NumPy (Harris et al. 2020) and SciPy (Virtanen\net al. 2020) were used for analyses in the manuscript.\nData availability:\nStrain data from the LIGO and\nVirgo observatories associated with GW241011 and\nGW241110 are available from the Gravitational Wave\nOpen Science Center. Datasets generated as part of this\nstudy, including posterior samples on the source prop-\nerties of both events, are available on Zenodo, together\nwith notebooks reproducing figures in this paper (LIGO\nScientific, Virgo, and KAGRA Collaboration 2025).\nAPPENDIX\nA. SOURCE PARAMETER ESTIMATION: FURTHER RESULTS AND DETAILS\nResults quoted in the main text are given by the union of posterior samples under three different gravi-\ntational waveform models:\nSEOBNRv5PHM (SEOBNR; Ramos-Buades et al. 2023a), IMRPhenomXPHM-\nSpinTaylor (XPHM; Pratten et al. 2021; Colleoni et al. 2025) and IMRPhenomXO4a (XO4a; Thompson et al.\n\n29\nTable 2.\nInferred source properties of GW241011 under different waveform models.\nWaveform\nm1 [M\u2299]\nm2 [M\u2299]\nq\nM [M\u2299]\nDL [Mpc]\n\u03c71\n\u03b81 [deg]\n\u03c71,z\n\u03c71,\u22a5\n\u03c7eff\n\u03c7p\nSEOBNRv5PHM\n21.1+2.8\n\u22123.6\n5.5+0.9\n\u22120.5\n0.26+0.11\n\u22120.05\n9.0+0.1\n\u22120.1\n225+39\n\u221240\n0.79+0.09\n\u22120.08\n35+11\n\u221214\n0.64+0.06\n\u22120.08\n0.45+0.19\n\u22120.15\n0.50+0.05\n\u22120.06\n0.45+0.19\n\u22120.15\nIMRPhenomXPHM-ST\n19.8+2.4\n\u22122.4\n5.9+0.7\n\u22120.5\n0.30+0.08\n\u22120.06\n9.1+0.1\n\u22120.1\n214+41\n\u221243\n0.75+0.07\n\u22120.07\n31+10\n\u221212\n0.64+0.06\n\u22120.09\n0.38+0.15\n\u22120.13\n0.51+0.05\n\u22120.04\n0.38+0.15\n\u22120.13\nIMRPhenomXO4a\n18.6+2.1\n\u22122.1\n6.2+0.7\n\u22120.5\n0.33+0.08\n\u22120.06\n9.1+0.1\n\u22120.1\n201+44\n\u221246\n0.79+0.08\n\u22120.10\n27+9\n\u221212\n0.70+0.05\n\u22120.08\n0.35+0.17\n\u22120.13\n0.44+0.05\n\u22120.04\n0.35+0.17\n\u22120.13\nTable 3.\nInferred source properties of GW241110 under different waveform models.\nWaveform\nm1 [M\u2299]\nm2 [M\u2299]\nq\nM [M\u2299]\nDL [Mpc]\n\u03c71\n\u03b81 [deg]\n\u03c71,z\n\u03c71,\u22a5\n\u03c7eff\n\u03c7p\nSEOBNRv5PHM\n17.4+5.1\n\u22124.7\n7.7+2.3\n\u22121.5\n0.44+0.33\n\u22120.17\n9.8+0.5\n\u22120.4\n736+277\n\u2212280\n0.59+0.34\n\u22120.39\n133+47\n\u221226\n\u22120.37+0.34\n\u22120.38\n0.39+0.34\n\u22120.29\n\u22120.27+0.23\n\u22120.20\n0.40+0.33\n\u22120.26\nIMRPhenomXPHM\n17.2+5.0\n\u22124.5\n7.7+2.2\n\u22121.5\n0.45+0.33\n\u22120.17\n9.9+0.5\n\u22120.4\n738+263\n\u2212261\n0.58+0.35\n\u22120.39\n132+48\n\u221226\n\u22120.37+0.33\n\u22120.38\n0.39+0.34\n\u22120.29\n\u22120.27+0.22\n\u22120.20\n0.40+0.33\n\u22120.26\nIMRPhenomXO4a\n16.9+4.9\n\u22124.2\n7.8+2.1\n\u22121.6\n0.46+0.31\n\u22120.17\n9.8+0.5\n\u22120.4\n731+268\n\u2212260\n0.65+0.30\n\u22120.41\n133+47\n\u221222\n\u22120.43+0.35\n\u22120.35\n0.43+0.32\n\u22120.32\n\u22120.30+0.22\n\u22120.20\n0.45+0.31\n\u22120.29\nFigure 12.\nPosterior on the source properties of GW241011 under each individual waveform model considered. Different\nwaveform models yield qualitatively similar conclusions, although waveforms exhibit non-negligible systematic differences due\nto the strong precession and unequal masses of the source binary.\n2024). Although all of these models describe quasi-circular precessing binaries and include higher-order multipole\nmoments, they differ in the approach used to model the waveforms. The SEOBNR, XPHM, and XO4a models are\neach constructed from a combination of analytical and numerical information. They offer a complete description of\n\n30\nFigure 13.\nAs in Figure 12, but for GW241110.\nbinary inspiral, merger, and ringdown, and are therefore applicable to systems of any mass. The SEOBNR model\ncomputes the signal in the time domain. The XPHM and XO4a models each calculate signals in the frequency domain,\nbut differ in their treatment of spin precession. Whereas the XPHM model numerically solves the post-Newtonian\nspin-precession dynamics, the XO4a model adopts a phenomenological ansatz that is fit to numerical-relativity sim-\nulations, calibrating evolution of precession angles, the coprecessing frame, and modal asymmetries between positive\nand negative m modes.\nThe main text presented only primary spin measurements with GW241011 and GW241110. For completeness, in\nFigure 14 we present posteriors on both the primary and secondary dimensionless spin magnitude of each binary black\nhole. The magnitude and orientation of the events\u2019 secondary spin vectors are unconstrained; neither the secondary\nspin magnitudes, the secondary spin\u2013orbit misalignment angles, nor the azimuthal angles between component spins\nconstrained away from the boundaries of their respective priors.\nIn Table 2 and Figure 12, we present posteriors on the source properties of GW241011 obtained independently with\neach waveform. All models recover nearly identical binary chirp masses. At the same time, they each provide slightly\ndifferent (although statistically consistent) estimates of the binary\u2019s primary mass, mass ratio, and primary spin. Such\nsystematic differences between waveform models are not unexpected; the unequal mass ratio, high spin, significant\nspin precession, and high SNR of this source are likely to exacerbate differences between waveform models (Dhani\net al. 2025; Mac Uilliam et al. 2024; Ak\u00b8cay et al. 2025). Table 3 and Figure 13, in turn, shows properties of GW241110\ninferred under the previously listed waveform models. We recover good agreement between the different waveforms,\nwith only small differences in the width and mean of the posterior for parameters like the chirp mass and the spin\nparameters.\n\n31\nFigure 14.\nPosterior on both the primary and secondary spin vectors of GW241011 (left) and GW241110 (right). As in\nFig. 2, radial and polar coordinates correspond to dimensionless spin magnitude vectors and spin-orbit misalignment angles,\nrespectively. Pixels spaced uniformly in spin magnitude and in cosine-tilt angles, such that each pixel contains equal prior\nprobability. For both events, the properties of the secondary spin vectors are unconstrained.\nB. ECCENTRICITY MEASUREMENTS: FURTHER DETAILS\nGravitational-wave measurements of orbital eccentricity have long been challenging, as the dynamics of eccentric\norbits vary rapidly on short orbital timescales and give rise to complex waveform morphologies. Recently, however,\na number of mature models have been developed that describe gravitational-wave emission from eccentric compact\nbinaries through binary inspiral, merger, and ringdown. We study the eccentricity of GW241011 and GW241110 using\ntwo waveform models: the SEOBNRv5EHM (Gamboa et al. 2025) and TEOBRESUMS-DAL\u00b4I (Nagar et al. 2024)\nwaveforms. Both models define eccentricity based a Keplerian parametrization of the orbit (Darwin 1959), in which\nthe deformation of the orbit is measured by the Keplerian eccentricity e and the relative position of the binary along\nthe orbit at a specific reference frequency is determined by the relativistic anomaly (SEOBNRv5EHM) or mean\nanomaly (TEOBRESUMS-DAL\u00b4I). Each model restricts spin to lie parallel (or antiparallel) to a binary\u2019s orbital\nangular momentum, and therefore neglects precessional effects due to in-plane spin components. We adopt Bayesian\npriors that are uniform in detector-frame component masses, uniform in comoving volume and detector-frame time,\nand isotropic in source position and orientation. The prior on aligned spin components is taken to be the projection\nof uniform-in-magnitude and isotropic spin priors, consistent with the prior adopted in Sec. 3. We adopt uniform\npriors on the relativistic anomaly and on the eccentricity at a reference frequency of 13.33 Hz (Ramos-Buades et al.\n2023b). Sampling of the SEOBNRv5EHM waveform model is performed using both the Bilby (Ashton et al. 2019;\nRomero-Shaw et al. 2020b) and RIFT (Pankow et al. 2015; Lange et al. 2017; Wysocki et al. 2019) packages, the\nformer invoking the Dynesty (Speagle 2020) nested sampler; posterior samples from each software are combined in\nequal proportion. Sampling of the SEOBNRv5EHM waveform model is performed with RIFT.\nFigure 15 shows more complete posteriors on the source properties of GW241011 and GW241110 using both waveform\nmodels. The component masses, effective inspiral spin, and primary aligned spin of both sources are consistent with\nresults presented above using quasicircular and precessing waveform models, with little correlation between these\nparameters and orbital eccentricity. This suggests, although does not prove, that eccentricity limits for GW241011\nand GW241110 are minimally biased by the lack of precessional effects, and conversely that measurements of spin-orbit\nprecession are likely robust despite neglecting eccentricity.\nCare must be taken when comparing eccentricities among waveform families and to predictions from the literature.\nFirst, the orbital eccentricity for inspiraling compact binaries is not uniquely defined; different waveform families\n\n32\nFigure 15.\nPosteriors on the source properties of GW241011 and GW241110, obtained using the eccentric and spin-aligned\nSEOBNRv5EHM (Gamboa et al. 2025) and TEOBRESUMS-DAL\u00b4I (Nagar et al. 2024) waveform models. Orbital eccentric-\nities, quoted at a reference frequency of 13.33 Hz, are consistent with e = 0, while other source parameters are consistent with\nestimates obtained elsewhere using quasicircular and precessing waveform models.\nmay adopt distinct, gauge-dependent choices for e. Growing efforts exist to standardize the definition of compact\nbinary eccentricity using waveform-based descriptions to remove gauge-ambiguity (Shaikh et al. 2023; Islam & Venu-\nmadhav 2025; Shaikh et al. 2025), but in this paper we have not attempted to unify the SEOBNRv5EHM and\nTEOBRESUMS-DAL\u00b4I definitions in this fashion. We nevertheless find strong consistency between eccentricity lim-\nits placed by both waveform models. Second, orbital eccentricity rapidly evolves under gravitational-wave radiation,\nand thus must be quoted at a specific time. As in our case above, orbital eccentricity is typically quoted at a fixed\ngravitational-wave reference frequency, to be taken as a proxy for time. The instantaneous frequency of an eccen-\ntric binary inspiral is not monotonic in time, however, and so there exist different conventions with which to define\nreference frequencies. In this work, we define the reference frequency as the orbit-averaged detector-frame frequency\nof a binary\u2019s (\u2113, m) = (2, \u00b12) quadrupole radiation. Astrophysical predictions, in contrast, tend to adopt reference\nfrequencies defined by the frequency of the instantaneously loudest frequency harmonic (Wen 2003). Eccentricities\nquoted at numerically identical reference frequencies can, under both prescriptions, correspond to eccentricities at\nvery distinct times in a binary\u2019s evolution (Vijaykumar et al. 2024).\nC. BINARY BLACK HOLE POPULATION INFERENCE WITH GW241011 AND GW241110\nIn Section 3.3, we noted that GW241011 and GW241110 do not appear to be clear outliers with respect to the\npopulation of merging binary black holes. This appendix elaborates on this statement, presenting and discussing\nupdated measurements of the binary black hole population using GW241011 and GW241110.\n\n33\nFigure 16.\nInferred distribution of component spin magnitudes (left) and cosine spin\u2013orbit misalignment angles (right) of\nmerging binary black holes, with and without GW241011 and GW241110. We use the Gaussian Component Spin population\nmodel from Abac et al. (2025d), in which spin magnitudes are Gaussian-distributed, and cosine spin\u2013orbit angles follow a mixture\nbetween Gaussian and uniform components. Dashed lines indicate 90% credible bounds on p(\u03c7) and p(cos \u03b8) when using binary\nblack holes from GWTC-4.0 (Abac et al. 2025a), while the thick red lines indicate updated bounds when additionally including\nGW241011 and GW241110. The ensemble of thin red lines shows the probability distributions corresponding to individual\ndraws on our population posterior, when including GW241011 and GW241110. The inclusion of GW241011 and GW241110\nnegligibly affects the inferred spin magnitude and spin\u2013orbit tilt distributions.\nC.1. The binary black hole spin distribution\nWe hierarchically measure the population properties of binary black holes following the methodology described\nin Abac et al. (2025d). We select all binary black holes among GWTC-4.0 (Abac et al. 2025a), detected with a false-\nalarm rate below 1 yr\u22121 by at least one search algorithm, and exclude the events GW190814 (Abbott et al. 2020c),\nGW190917 114630 (Abbott et al. 2024), and GW230529 (Abac et al. 2024) that contain low-mass objects of unknown\nnature. This yields a total of 153 binary black hole coalescences, plus GW241011 and GW241110. Selection biases are\nestimated using a suite of simulated signals added to data from the first three observing runs (O1, O2, and O3) and the\nfirst part of the fourth LIGO\u2013Virgo\u2013KAGRA observing run (O4a; Essick et al. 2025; Abac et al. 2025d). We neglect\nthe additional time\u2013volume surveyed early in the second part of the fourth observing run (O4b), in which GW241011\nand GW241110 were detected. This slightly biases our measurements of the binary black hole population, but the\nshort duration and comparable sensitivity of early O4b render this bias negligible. We perform hierarchical inference\nusing the GWPopulation package (Talbot et al. 2019, 2025) and the Dynesty nested sampler (Speagle 2020).\nFigure 16 illustrates the inferred distributions of spin magnitudes (left) and spin\u2013orbit misalignment angles (right)\namong binary black holes, with and without GW241011 and GW241110. We use the Gaussian Component Spin\nmodel described in Abac et al. (2025d), in which component spin magnitudes are identically and independently drawn\nfrom a truncated normal distribution,\np(\u03c71, \u03c72) = N[0,1](\u03c71|\u00b5\u03c7, \u03c3\u03c7)N[0,1](\u03c72|\u00b5\u03c7, \u03c3\u03c7),\n(C1)\nand cosine spin\u2013orbit tilts are jointly distributed as a mixture between Gaussian and uniform components:\np(cos \u03b81, cos \u03b82) = \u03b6N[\u22121,1](cos \u03b81|\u00b5t, \u03c3t)N[\u22121,1](cos \u03b82|\u00b5t, \u03c3t) + (1 \u2212\u03b6)U[\u22121,1](cos \u03b81)U[\u22121,1](cos \u03b82).\n(C2)\nHere, N[a,b] and U[a,b] represent Gaussian and uniform distributions truncated and normalized on the interval [a, b],\nand the means \u00b5\u03c7 and \u00b5t, standard deviations \u03c3\u03c7 and \u03c3t, and mixing fraction \u03b6 are free parameters inferred from data.\nWe assume that black hole masses and redshifts follow the default distributions adopted in Abac et al. (2025d) and\nadopt the same Bayesian priors. We see that the inclusion of events GW241011 and/or GW241110 yields a spin-tilt\ndistribution marginally more consistent with isotropy, but that these events otherwise have negligible effects on the\ninferred spin distributions.\n\n34\nFigure 17.\nRight: Inferred distribution of cosine spin\u2013orbit misalignment angles, when additionally inferring the maximum\nmisalignment angle (minimum cos \u03b8 value) among the binary black hole population (the Max-Tilt model). As in Figure 16,\ndashed lines indicate 90% credible bounds using black holes from GWTC-4.0 (Abac et al. 2025a), thick red lines indicate updated\nbounds when additionally including GW241011 and GW241110, and thin red lines illustrate individual draws from our updated\npopulation posterior. Left: Posterior obtained on the minimum value cos(\u03b8max) below which the cos \u03b8 distribution is truncated.\nThe inclusion of GW241011 and GW241110 minimally affects inference of the maximum spin misalignment angle among the\nbinary black hole population. Inference using GWTC-4.0 binary black holes requires cos \u03b8max < \u22120.57 (\u03b8max > 125 degrees) at\n90% credibility. Adding GW241011 and GW241110 gives cos(\u03b8max) \u2264\u22120.55 and \u22120.59, respectively.\nIt is possible that the Gaussian Component Spin model, with unimodal spin magnitude and tilt distributions,\nmay provide a poor description of events like GW241011 and GW241110. We therefore explore two extensions of this\nmodel to further study the implications of GW241011 and GW241110.\n1. First, whereas the cos \u03b8 distribution in Eq. (C2) was truncated on the interval [\u22121, 1], we instead introduce a\nvariable lower truncation bound cos(\u03b8max) (Galaudage et al. 2021; Tong et al. 2022) (i.e. a maximum spin tilt\nangle \u03b8max) with a prior uniform on the interval [\u22121, 1], and ask how extreme spin\u2013orbit misalignment angles\nmust be to accommodate events like GW241110 (the Max-Tilt model),\np(cos \u03b81, cos \u03b82) = \u03b6N[cos(\u03b8max),1](cos \u03b81|\u00b5t, \u03c3t)N[cos(\u03b8max),1](cos \u03b82|\u00b5t, \u03c3t)\n+ (1 \u2212\u03b6)U[cos(\u03b8max),1](cos \u03b81)U[cos(\u03b8max),1](cos \u03b82).\n(C3)\n2. Second, we allow for the existence of a distinct subpopulation of rapidly spinning black holes with large \u03c7,\ndesigned to explore whether events like GW241011 require a multimodal spin distribution (High-Spin model).\nWe extend the C1 model by introducing a high spin Gaussian,\np(\u03c71, \u03c72) =\n\u0010\n\u03be\u03c7N[0,1](\u03c71|\u00b5\u03c7, \u03c3\u03c7) + (1 \u2212\u03be\u03c7)N[0,1](\u03c71|\u00b5\u03c7,high, \u03c3\u03c7,high)\n\u0011\n\u00d7\n\u0010\n\u03be\u03c7N[0,1](\u03c72|\u00b5\u03c7, \u03c3\u03c7) + (1 \u2212\u03be\u03c7)N[0,1](\u03c72|\u00b5\u03c7,high, \u03c3\u03c7,high)\n\u0011\n,\n(C4)\nwhere \u00b5\u03c7,high is the mean high spin Gaussian with a prior the uniform on the interval [0.5, 1], \u03c3\u03c7,high is the width\nof the high spin Gaussian with a prior the uniform on the interval [0.005, 1], and finally \u03be\u03c7 is the mixing fraction\nbetween the low spin and high spin Gaussians with a uniform prior on the interval [0, 1].\nFigure 17 shows the measured distribution of spin\u2013orbit misalignment angles \u03b8 when inferring the maximum misalign-\nment angle \u03b8max. The left-hand panel shows the posterior on cos(\u03b8max). Binary black holes among GWTC-4.0 require\n\n35\nFigure 18.\nRight: Inferred distribution of black hole component spin magnitudes when allowing for a distinct subpopulation of\nrapidly spinning black holes where one or both black hole components occupy this high spin region (the High-Spin model). As\nabove, the dashed lines and filled region span 90% credible bounds with and without GW241011 and GW241110, respectively.\nLeft: Inferred fraction of black holes comprising a possible highly-spinning subpopulation. As above, results are negligibly\naffected by the inclusion or exclusion of GW241011 and GW241110. In both cases, current data do not require the existence\nof a distinct population of events with rapidly-spinning components. When including GW241011 and GW241110, we bound\nf\u03c7,high \u22640.36 at 90% credibility, consistent with zero.\nmaximum spin\u2013orbit misalignment angles of \u03b8max \u2265125 degrees (cos \u03b8max \u2264\u22120.57) at 90% credibility. This result is\nonly marginally affected by the inclusion of GW241011 or GW241110, which yield \u03b8max \u2265124 degrees and 126 degrees,\nrespectively. Figure 18, meanwhile, shows the inferred black hole spin-magnitude distribution when allowing for a\ndistinct subpopulation of rapidly spinning black holes, together with the inferred fraction of events f\u03c7,high with one or\nboth components occupying a possible high-spin population. When compared to Figure 16, it is clear that different\nmodels yield slight, systematic differences in the measured spin magnitude distribution; the High-Spin model gives a\nspin distribution more concentrated at small \u03c7 with an extended tail to high spin magnitudes. However, the addition\nor exclusion of GW241011 and GW241110 again result in negligible differences. Binary black holes among GWTC-4.0\ndo not require the existence of a distinct, high-spinning subpopulation, with f\u03c7,high < 0.32 at 90% credibility. When\nincluding GW241011 and GW241110, the high-spin fraction remains consistent with zero, with f\u03c7,high < 0.36.\nTaken together, our results indicate that GW241011 and GW241110 are not evident population outliers, requiring\nneither greater spin\u2013orbit misalignments nor larger spin magnitudes than already afforded by binary black holes among\nGWTC-4.0.\nC.2. Population Reweighting\nWe reweight the parameter estimation samples using population-informed mass and spin distributions using the\nthree population models.\nReweighted posteriors are obtained with leave-one-out posterior predictive distribu-\ntions (Galaudage et al. 2020; Callister 2021; Essick & Fishbach 2021), providing astrophysically motivated priors\n(such reweighting excludes the contribution of the event in question to the population inference, thus avoiding double-\ncounting effects). The resulting posteriors for the Gaussian Component Spin population model, for example, are\nshown in Figure 19.\nFor the posterior on cos(\u03b81) of GW241110, reweighted by the population using the Gaussian Component Spin,\nMax-Tilt and High-Spin, the upper limit (or minimum misalignment) is given by \u22120.43, \u22120.26 and \u22120.37 respec-\ntively at 90% credibility. The Max-Tilt fit gives the least misaligned result as the model has the flexibility to cut off\nat values of cos(\u03b81) > \u22121 whereas the other two models require the fit to end at cos(\u03b81) = \u22121. For the posterior on\n\u03c71 of GW241011, reweighted by the population using the Gaussian Component Spin, Max-Tilt and High-Spin,\nthe lower limit (or minimum spin magnitude) is given by 0.68, 0.68 and 0.69 respectively. The lower limit on the spin\nmagnitude is consistent under all three models.\n\n36\nFigure 19.\nComparison of original and population-informed (using the Gaussian Component Spin population model)\nposterior distributions for GW241011 and GW241110.\nTable 4.\nNumber of binary black hole mergers included in datasets from the CMC and cBHBd catalogs. We include the\ntotal numbers of first-generation and higher-generation black hole mergers in each catalog, as well as the number of mergers at\neach stellar metallicity as highlighted in Figure 6.\nModel\nGeneration\nZ = 0.01 Z\u2299\nZ = 0.1 Z\u2299\nZ = Z\u2299\nTotal\nCluster Monte Carlo\nFirst-generation\n3681\n3566\n3758\n11005\nCluster Monte Carlo\nHigher-generation\n660\n625\n978\n2263\nclusterBHBdynamics\nFirst-generation\n1690\n1761\n1825\n5276\nclusterBHBdynamics\nHigher-generation\n316\n351\n638\n1305\nD. CLUSTER MODELS: FURTHER DETAILS\nIn this appendix, we provide further details regarding the astrophysical population models plotted alongside the\nproperties of GW241011 and GW241110 in Figure 6. For a complete description of the stellar (binary) evolution and\ncluster dynamics models underlying these results, we direct the reader to Kremer et al. (2020), Rodriguez et al. (2022),\nand Antonini et al. (2023).\nThe CMC catalog (Kremer et al. 2020; Rodriguez et al. 2022) contains a suite of 148 cluster simulations, pri-\nmarily comprising a grid of 144 models with varying particle number (N = {2, 4, 8, 16} \u00d7 105), virial radius\n(rv = {0.5, 1, 2, 4} pc), metallicity (Z/Z\u2299= {0.01, 0.1, 1}), and Galactocentric distance (Rgc = {2, 8, 20} kpc). In\naddition, the CMC catalog include four more massive clusters with N = 3.2 \u00d7 106 at Rgc = 20 kpc, spanning two\nmetallicities (0.01 and 1 Z\u2299). Compared to earlier CMC model suites (Chatterjee et al. 2010, 2013; Morscher et al.\n2015), this set extends the explored ranges of rv and Z, and decouples metallicity from Galactocentric distance. Cluster\nmodels are evolved dynamically over one Hubble time, and binary black hole mergers are identified as those binaries\nthat successfully coalesce over this timescale. The total numbers of available black hole mergers (both first-generation\nand hierarchical) are provided in Table 4. In Figure 6 we specifically show the direct union of binary black hole mergers\nobtained across all simulations at each given metallicity, in order to illustrate the range of binary black hole masses,\nmass ratios, and spins that can be achieved over a broad range of cluster conditions. A more detailed prediction for\nthe merger population expected from clusters, in contrast, would likely adopt a weighted combination corresponding\nto assumptions about the distribution of cluster masses, metallicities, and formation histories.\nThe cBHBd code is a semi-analytical model that applies cluster dynamics and energy-balance theory to follow the\ncoupled evolution of clusters and their black hole populations, yielding predictions for black hole binary merger rates\nand properties. We use the cBHBd catalog published in Antonini et al. (2023), containing 106 cluster models that are\nsampled uniformly in the mass range 102M\u2299to 2\u00d7107M\u2299. We select the subset of models with the same metallicities\nconsidered above (Z/Z\u2299= {0.01, 0.1, 1}) and with initial half-mass densities of 105M\u2299pc\u22123, yielding a sample of 129\n\n37\nFigure 20.\nThe impact of observational selection effects on the predicted properties of binary black hole mergers in dense\nstellar clusters. We specifically show the properties predicted in the CMC catalog for clusters of stellar metallicity Z = Z\u2299,\ncorresponding to the right-hand column of Figure 6. The upper row corresponds to mergers in which both components are\nfirst-generation black holes, and the bottom row to mergers in which one or both components are formed from a previous binary\nblack hole coalescence. Light red distributions correspond to predictions directly from CMC (and shown previously in Figure 6),\nwhile dark red distributions have been subjected to an observational selection cut calculated using a campaign of simulated\nsignals injected into LIGO and Virgo data (Essick et al. 2025; Abac et al. 2025j).\ncluster models with total masses up to 2\u00d7106 M\u2299. The cluster models are evolved over one Hubble time, and Figure 6\ncontains binary black holes that merge in this time. The total numbers of available mergers are given in Table 4. As\nwith the CMC results above, we take the direct union of binary mergers across all cluster masses, in order to illustrate\nthe range of possible binary properties.\nFigure 6 illustrates the range of binary black hole properties predicted under two models of globular cluster evolution.\nIt does not, however, account for observational selection effects, which may alter the range of binary properties that\nwe expect to successfully detect. We verify that the inclusion of selection effects does not significantly affect the\ncontent of Figure 6 by using a suite of simulated signals injected into LIGO and Virgo data (Essick et al. 2025; Abac\net al. 2025j). We reweight these simulated signals from their original proposal distribution to target distributions\ndefined by the CMC and cBHBd. Selecting only successfully recovered signals then yields the expected distribution\nof detectable binaries arising from stellar clusters. The target distributions are themselves obtained by fitting Gaussian\nmixture models to CMC and cBHBd predictions at each stellar metallicity; the number of mixture components is\ndetermined by minimizing the Akaike information criterion (Akaike 1974) on reserved testing data. In order to establish\ndetectability, it is necessary to assume a redshift distribution for binary black hole mergers. We choose a volumetric\nmerger rate that grows with redshift z as (1 + z)2.6, following the low-redshift star formation rate of Madau & Fragos\n(2017). Our results do not depend strongly on this particular choice, however.\nAs an example, Figure 20 shows the original range (light red) of properties among first-generation (top row) and\nhigher-generation (bottom row) black hole mergers, as predicted by CMC for a cluster of stellar metallicity Z = Z\u2299.\nImposing an observational selection cut shifts the distributions of binary masses and mass ratios to higher values, at\nwhich expected SNRs are largest. The effect is small, however. The black hole spin distributions predicted by both\nCMC and cBHBd are sufficiently narrow (nearly delta functions at spin magnitudes of zero or \u223c0.7) that they are\nunaffected by a selection cut. Despite the slight shift to larger mass ratios, mergers at the highest mass ratios are\nconversely suppressed by observational selection effects. This is due to the fact that binaries with the largest total\nmasses tend to be those with more unequal mass ratios. Thus, although measured SNR is maximized by increasing\n\n38\nTable 5.\nProperties of the ancestral binary black holes of GW241011 and GW241110, under the hypothesis that the primary\nmass of each observed merger is itself a remnant from a previous merger. Specifically, we include constraints on the primary and\nsecondary masses of the hypothesized ancestors, the ancestors\u2019 effective inspiral spins, and the recoil velocity experienced by\nthe remnants following each merger. For each event, we show ancestral properties inferred under two different approaches. In\nthe Forward approach, we place astrophysically-informed priors directly on the ancestral properties GW241011 and GW241110.\nIn the Backward approach, we agnostically maintain the source parameters of GW241011 and GW241110 inferred in standard\nparameter estimation and identify ancestral binaries compatible with these measured parameters.\nEvent\nMethod\nAncestral m1 [M\u2299]\nAncestral m2 [M\u2299]\nAncestral \u03c7eff\nvrecoil [km s\u22121]\nGW241011\nForward\n11.0+1.9\n\u22121.6\n9.6+1.7\n\u22121.8\n0.02+0.08\n\u22120.06\n100+190\n\u221270\nGW241011\nBackward\n13.3+4.8\n\u22123.2\n7.5+3.2\n\u22123.9\n0.23+0.29\n\u22120.28\n750+1400\n\u2212630\nGW241110\nForward\n9.6+3.1\n\u22122.0\n8.0+2.1\n\u22122.3\n\u22120.00+0.06\n\u22120.06\n100+160\n\u221280\nGW241110\nBackward\n12.3+5.6\n\u22124.2\n5.1+3.6\n\u22121.9\n\u22120.04+0.65\n\u22120.57\n480+1270\n\u2212330\nmass ratio at fixed total mass, in practice we see that large SNRs most commonly occur for massive sources with\nsomewhat unequal mass ratios.\nE. FURTHER DETAILS ON ESTIMATING PROGENITOR BINARY PARAMETERS\nThis appendix provides additional details regarding calculation of GW241011 and GW241110\u2019s ancestral binaries,\nunder the hypothesis that these events events contain second-generation black holes born from a previous binary black\nhole merger. As discussed in the main text, we approach this calculation in two ways. In the Forward approach,\nwe adopt a hierarchical Bayesian formalism, placing astrophysically-informed priors on the hypothesized ancestral\nbinaries and marginalizing over the source properties of GW241011 and GW241110 to directly obtain posteriors on\nancestral properties. In the Backward approach, we more agnostically adopt the same uninformative priors on the\nsource properties of GW241011 and GW241110 used in standard parameter estimation.\nMore details about each\napproach are described in Appendices E.1 and E.2 below.\nE.1. The Forward Approach\nGiven the gravitational-wave data d due to a binary black hole merger containing a second-generation remnant, we\nwish to obtain a probability distribution p(\u20d7\u03b81g|d) on the properties \u20d7\u03b81g of that black hole\u2019s first-generation ancestors.\nRather than repeat Bayesian parameter estimation, we proceed using the results of standard parameter estimation\nperformed directly on GW241011 and GW241110, constructing the posterior (Mahapatra et al. 2024)\np(\u20d7\u03b81g|d) = \u03c0(\u20d7\u03b81g)\nZ1g(d)\np(\u20d7\u03b82g|d)\n\u03c0(\u20d7\u03b82g)\n\f\f\f\f\u20d7\u03b82g= \u20d7F (\u20d7\u03b81g)\n.\n(E5)\nHere, \u03c0(\u20d7\u03b81g) is the prior distribution on \u20d7\u03b81g. The quantity \u20d7\u03b82g denotes parameters of the observed binary merger (i.e.\nGW241011 and GW241110 themselves); p(\u20d7\u03b82g|d) and \u03c0(\u20d7\u03b82g) are the posterior and prior probability distributions for\nthese events obtained through ordinary parameter estimation. The normalization constant\nZ1g(d) \u2261\nZ\n\u03c0(\u20d7\u03b81g) p(\u20d7\u03b82g|d)\n\u03c0(\u20d7\u03b82g)\n\f\f\f\f\u20d7\u03b82g=F (\u20d7\u03b81g)\nd\u20d7\u03b81g\n(E6)\nis the evidence for d under the hierarchical merger hypothesis, while F(\u20d7\u03b81g) = \u20d7\u03b82g is the function mapping the\nancestral binary\u2019s properties to the final mass and spin of its remnant black hole. We compute F(\u20d7\u03b81g) using the the\nnumerical-relativity remnant surrogate model NRSur7dq4Remnant (Varma et al. 2019), valid for binary black holes\nin quasi-circular orbits. In practice, we reconstruct p(\u20d7\u03b82g|d) and \u03c0(\u20d7\u03b82g) using a Gaussian kernel density estimator fit\nto samples from each distribution. To sample possible ancestral properties from p(\u20d7\u03b81g|d), we employ Bilby (Ashton\net al. 2019) using the Dynesty (Speagle 2020) nested sampler.\nWe choose a prior distribution \u03c0(\u20d7\u03b81g|d) that is a close match to the properties of first-generation binary mergers, as\npredicted in the CMC catalog and shown in Figure 6. Upon combining successful mergers across all simulated clusters,\nthe primary masses of first-generation mergers follow an approximately log-normal distribution, with best-fit mean\n\n39\nFigure 21.\nInferred parameters on the ancestral binary black holes that previously merged to form the primary components\nof GW241011 (top row) and GW241110 (bottom row), under the hypothesis that each system contains a second-generation\nprimary. We show results obtained under two sets of priors. Darker distributions correspond to an agnostic approach that\nleaves the priors on GW241011 and GW241110\u2019s source properties unchanged, relative to standard parameter estimation.\nLighter distributions correspond to an astrophysically-motivated approach, in which priors are placed on the ancestral binaries,\ninducing priors on GW241011 and GW241110\u2019s primary masses and spins consistent with their hypothesized hierarchical origin.\nFor comparison, the dashed histograms illustrate the distribution of cluster escape velocities predicted by CMC. In order for\nthe sources of GW241011 and GW241110 to remain consistent with a hierarchical origin in globular clusters, their ancestral\nrecoil velocities should not exceed these escape velocities.\n\u00b5ln m1 = 2.9 and standard deviation \u03c3ln m1 = 0.6, while mass ratios are well-described by a power law p(q) \u221dq\u03b2, with\n\u03b2 = 4.3. We adopt these distributions as our priors on ancestral primary masses and mass ratios. In the CMC catalog,\nfirst-generation black holes are assumed to have identically zero spins. We accordingly limit spins to be small but\nnon-zero, adopting a half-normal prior distribution with a standard deviation of 0.1 on both primary and secondary\nspin magnitudes.\nE.2. The Backward Approach\nThe above method sets priors on ancestral black hole parameters which, in turn, lead to posterior distributions on\nthe source properties of the observed gravitational waves that are modified with respect to those obtained in standard\nparameter estimation. As an alternative, the method presented in Ara\u00b4ujo-\u00b4Alvarez et al. (2024) preserves the agnostic\npriors on the source properties of GW241011 and GW241110 themselves, thereby preserving the original posteriors\non the observed \u201cchild\u201d binaries (provided that all child parameters can be realized with non-negligible probability\nfrom a chosen prior range of ancestral black holes). More precisely, this method yields a joint posterior p(\u20d7\u03b81g, \u20d7\u03b82g|d)\nthat, when marginalized over \u20d7\u03b81g, yields a posterior that is proportional to our original posterior p(\u20d7\u03b8|d), for all \u20d7\u03b82g\nsatisfying p(\u20d7\u03b82g|\u20d7\u03b81g) \u0338= 0. Equality is achieved when every child parameter is compatible with at least one ancestral\nconfiguration under the proposed prior. This method differs from that of Appendix E.1 simply by replacing the term\n\u03c0(\u20d7\u03b82g) in Eq. (E5), which denotes the prior probability on the child parameters set by our original Bayesian parameter\nestimation, with \u03c0(\u20d7\u03b81g), the prior probability on the child parameters induced by the priors on the ancestral ones.\n\n40\nIn practice, we proceed by drawing 2\u00d7106 random samples from a broad ancestral prior p(\u20d7\u03b81g). Ancestral component\nmasses are drawn uniformly from the range [3M\u2299, 300M\u2299], with the mass ratio constrained to lie between 1/6 and unity,\nand dimensionless spin magnitudes are sampled uniformly from the range [0, 0.99]. Remnant properties and a recoil\nkick are computed for each sample, yielding the induced prior distribution p(\u20d7\u03b82g) on possible remnant properties. For\neach primary mass and spin posterior sample {m1, \u03c71} obtained from p(\u20d7\u03b82g|d) via the original parameter estimation,\nwe draw random samples from p(\u20d7\u03b82g) satisfying {mf, \u03c7f} = {m1 \u00b1 \u03b4m1, \u03c71 \u00b1 \u03b4\u03c71}. We stress that, depending on\nthe choice of ancestral prior p(\u20d7\u03b81g), this will only be possible for a fraction of the posterior samples. The usage of\nnon-zero tolerances \u03b4m1 and \u03b4\u03c71 is motivated by the fact that the discrete nature of our samples for p(\u20d7\u03b81g) would\nnaturally prevent us from encountering samples exactly matching the remnant posterior samples. In our case, we\nchoose (\u03b4m1, \u03b4\u03c71) = (1, 0.05), identified in Ara\u00b4ujo-\u00b4Alvarez et al. (2024) to yield stable results.\nE.3. Progenitor Properties: Additional Results\nTable 5 and Figure 21 present the posterior distributions on ancestral properties, as obtained through both the\nastrophysically-motivated Forward approach and the agnostic Backward approach.\nBoth approaches yield similar\nestimates for the ancestral primary masses of GW241011 and GW241110. The Forward approach, with more stringent\npriors favoring equal mass ratios, yields more precise estimates of the ancestors\u2019 secondary masses. Under an agnostic\nprior, GW241011 is consistent with an ancestral binary with moderately large, positive effective spin, although both\nGW241011 and GW241110 are also consistent with non-spinning ancestors.\nRecoil velocities are almost entirely\ndominated by spin priors; the low ancestral spins required in the Forward approach limit recoil kicks to lower velocities,\nwhile the large spins allowed in the Backward approach yield more rapid recoils.\nDespite recoil velocity posteriors being prior dominated, for self-consistency it is valuable to check that these posteri-\nors are not inconsistent with expected cluster escape velocities. The dashed histograms in Fig. 21 show the distribution\nof cluster escape velocities predicted in the CMC catalog. If the sources of GW241011 and GW241110 are to be con-\nsistent with a hierarchical origin in dense clusters (or at least clusters with masses similar to those explored in the\nCMC catalog), their inferred ancestral recoil velocities must not be larger than these predicted escape velocities. The\nForward approach yields recoil velocity posteriors consistent with the distribution of expected escape velocities. The\nBackward approach yields a posterior with support in the range of expected escape velocities, although the posterior\nalso extends to much higher recoil velocities; this is expected, due to the deliberately agnostic prior allowing for rapidly\nspinning ancestors.\nF. TESTS OF FUNDAMENTAL PHYSICS: FURTHER DETAILS\nF.1. Spin-induced quadrupole moment\nIn this appendix we provide further detail regarding constraints on GW241011\u2019s spin-induced quadrupole moment,\ndiscussed in Sec. 5.1.\nWhen testing for the spin-induced quadrupole moment, corrections are added to the inspiral phase of the gravitational\nwaveform, with uniform priors adopted on the correction parameters. In addition to the results shown in Figure 9,\nbased on corrections to the IMRPhenomXPHM waveform model (Pratten et al. 2021; Divyajyoti et al. 2024a), we\nadditionally explored results using corrections to the SEOBNRv5HM ROM (Pompili et al. 2023) waveform model\nunder the Flexible Theory-Independent framework (Mehta et al. 2023). Besides relying on different base waveform\nmodels, these two approaches differ in the treatment of the binary\u2019s evolution from inspiral to merger and ringdown.\nAdditionally, the IMRPhenomXPHM includes spin precession while SEOBNRv5HM ROM assumes spin-aligned\nbinaries.\nGiven the significant spin precession effects in GW241011, the IMRPhenomXPHM-based results from\nFigure 9 should therefore be taken as the most physically-meaningful constraints on the spin-induced quadrupole,\nbut the SEOBNRv5HM ROM results are helpful in quantifying the degree of systematic uncertainties arising from\nmissing waveform physics.\nThe SEOBNRv5HM ROM-based test gives \u03b4\u03ba1 = \u22120.44+1.66\n\u22122.01 and \u03b4\u03bas = \u22120.45+0.39\n\u22121.01. While \u03b4\u03ba1 is consistent with\na Kerr black hole in GR, \u03b4\u03bas is shifted slightly towards negative values, with the Kerr value lying beyond the 95%\ncredible interval.\nThis bias, as well as the broadened posteriors relative to IMRPhenomXPHM results is due\nto the absence of relativistic spin-orbit precession noted above (Lyu et al. 2024; Divyajyoti et al. 2024a). To verify\nthis, we analyzed simulated signals with source parameters consistent with those of GW241011. We considered both\nsignals with misaligned precessing spins and with aligned spin configurations. When analyzing simulated aligned-spin\n\n41\nsignals with SEOBNRv5HM ROM, posteriors are unbiased and peak near zero. When instead analyzing simulated\nprecessing signals, posteriors are instead biased towards negative values, as in the case of GW241011.\nF.2. Subdominant mode amplitude consistency\nThe gravitational-wave strain emitted by compact binary mergers can be decomposed into spin-weighted spherical\nharmonics of weight \u22122 as:\nh(t, \u03b8JN, \u03bb) =\nX\n\u2113\u22652\n\u2113\nX\nm=\u2212\u2113\nh\u2113m(t, \u03bb) \u22122Y\u2113m(\u03b8JN, \u03d50),\n(F7)\nwhere (\u03b8JN, \u03d50) specify the observer\u2019s orientation in the source frame, and \u03bb encodes intrinsic parameters such as\nmasses and spins. Following common practice, we fix \u03d50 = 0 so that \u03b8JN denotes the angle between the binary\u2019s total\nangular momentum vector and the observer\u2019s line of sight (Pratten et al. 2021).\nTypically, gravitational-wave signals are dominated by the quadrupole (\u2113, m) = (2, \u00b12) multipole. However, higher-\norder multipoles such as (2, \u00b11) and (3, \u00b13) become increasingly relevant for systems with unequal masses or for\nviewing angles away from face-on (\u03b8JN \u0338= 0). To quantify potential deviations of these subdominant multipoles from\nGR, the subdominant multipole amplitude (SMA) test (Puecher et al. 2022) introduces amplitude deviations \u03b4A\u2113m\nexplicitly into the (2, \u00b11) and the (3, \u00b13) multipoles in the XPHM waveform model:\nh(t, \u03b8JN, \u03bb) =\nX\nm=\u00b12\nh2m(t, \u03bb) \u22122Y2m(\u03b8JN, 0) +\nX\nm=\u00b11\n(1 + \u03b4A21) h2m(t, \u03bb) \u22122Y2m(\u03b8JN, 0)\n+\nX\nm=\u00b13\n(1 + \u03b4A33) h3m(t, \u03bb) \u22122Y3m(\u03b8JN, 0) +\nX\nother HOM\nh\u2113m(t, \u03bb) \u22122Y\u2113m(\u03b8JN, 0).\n(F8)\nThe application of the SMA test requires sufficient SNR in the multipole of interest. For each (\u2113, \u00b1m) mode, the\nmode-specific SNR, \u03c1\u2113m, is computed by projecting h\u2113\u00b1m onto the subspace orthogonal to the dominant (2, \u00b12) mode\nand evaluating the optimal SNR of the residual (Mills & Fairhurst 2021). In the absence of the (\u2113, \u00b1m) multipole in\nsignal, \u03c1\u2113m follows a \u03c7 distribution with two degrees of freedom in Gaussian noise, portrayed as the null distribution in\nFigure 5. To ensure sufficient mode content, we adopt a conservative selection threshold: a given mode for an event is\nincluded in the SMA analysis only if the lower bound of the 68% credible interval of its \u03c1\u2113m distribution exceeds 2.145,\ncorresponding to the 90th percentile of the null distribution. Among the two considered events, only the (3, \u00b13) mode\nin GW241011 satisfies this criterion. Accordingly, we perform parameter estimation for this mode with a uniform prior\non \u03b4A33 in the range [\u221210, 10].\nF.3. Constraining ultralight bosons through superradiance\nIn the presence of an ultralight scalar or vector field, a spinning black hole is unstable to the superradiant insta-\nbility (Brito et al. 2015a). Oscillating bosonic modes that satisfy the superradiant condition, \u03c9R < m\u2126BH, grow\nexponentially with time at the expense of the black hole\u2019s rotational energy. Here \u03c9R \u223cmbc2/\u210fis the angular fre-\nquency, m is the azimuthal number, and \u2126BH is the horizon frequency of the black hole. The growth of a mode and\nspindown of the black hole persist until the superradiant condition is saturated (Arvanitaki et al. 2010; Brito et al.\n2015b; East & Pretorius 2017; East 2018). Typically, the lowest m mode that is superradiant grows the fastest, but\nwith sufficient time multiple modes can grow and saturate, reducing the black hole\u2019s spin to ever smaller values. The\nvector boson instability rate is parametrically faster than the scalar rate, such that vector bosons spin down a black\nhole to lower values in a fixed time. For example, adopting the median mass and spin values for the primary black\nhole in GW241011 (Table 1), the shortest e-folding time for mass growth of a boson cloud is \u223c8 s for a vector boson\nand 9 hr for a scalar. This assumes a boson mass optimally matched to the black hole; for smaller boson masses the\ninstability timescales lengthen\u2014roughly as \u221dm\u22127\nb\nand \u221dm\u22129\nb\nfor vector and scalar modes, respectively (Baryakhtar\net al. 2017).\nGiven a boson mass and a time since black hole formation (or the time since the black hole gained angular momen-\ntum), there will be excluded regions of the black hole\u2019s mass\u2013spin parameter space where the superradiant instability\nshould have reduced the black hole\u2019s spin to lower values. We calculate this excluded region using the SuperRad\npackage (Siemonsen et al. 2023; May et al. 2025), based on the linear superradiantly unstable modes and including\nall relevant azimuthal number modes, for both vectors and scalars. For the dominant modes, with m \u22642, we use\n\n42\nthe relativistic frequencies and instability rates. For higher azimuthal modes, we use a non-relativistic approximation,\nwhich in general underestimates the instability rate and is thus conservative.\nUsing the posteriors for the source primary masses and spins of GW241011 and GW241110, we determine the fraction\nP of each event\u2019s posterior samples lying in the region permitted by the given boson mass and black hole age (Aswathi\net al. 2025). Sufficiently small P would disfavor this mass\u2013age combination. It is important, however, to guard against\nprior effects; it is possible for uninformative data, with spin magnitude samples drawn randomly from a uniform prior,\nto yield small P for specific ultralight boson masses. Following Aswathi et al. (2025), we therefore also calculate a\nprior fraction P \u2032, obtained by replacing the black hole spin posterior with samples drawn from a uniform distribution\n[0, 1). The exclusion regions shown in Figure 11 correspond to the requirement that P < 0.1 P \u2032; this corresponds to a\n90% or better credible bound while also ensuring that constraints are strongly likelihood-driven.\nThis analysis assumes only a minimally coupled boson with gravitational interactions, but will also apply to scalar\nor vector bosons with sufficiently weak interactions so as to not disrupt the black hole spindown. 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Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11\nD. Bersanetti\n,29 T. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101\nN. Bevins\n,102 R. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46\nV. Biancalana\n,101 A. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75\nC. Binu,110 S. Biot,111 O. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113\nS. Blaber,114 J. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 N. Bode\n,8, 9 N. Boettner,97\nG. Boileau\n,113 M. Boldrini\n,38 G. N. Bolingbroke\n,115 A. Bolliand,116, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82\nF. Bondu\n,117 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,118 R. Bonnand\n,31, 116 A. Borchers,8, 9 S. Borhanian,7\nV. Boschi\n,80 S. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 G. Bouyer,120 M. Boyle,121\nA. Bozzi,62 C. Bradaschia,80 P. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104 T. Briant\n,122\nA. Brillet,113 M. Brinkmann,8, 9 P. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46\nD. D. Brown,115 M. L. Brozzetti\n,76, 51 S. Brunett,11 G. Bruno,15 R. Bruntz\n,123 J. Bryant,118 Y. Bu,124\nF. Bucci\n,61 J. Buchanan,123 O. Bulashenko\n,82, 83 T. Bulik,125 H. J. Bulten,37 A. Buonanno\n,126, 1 K. Burtnyk,2\nR. Buscicchio\n,127, 128 D. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15\nV. C\u00b4aceres-Barbosa\n,7 L. Cadonati\n,57 G. Cagnoli\n,129 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,130\nE. Calloni,32, 4 S. R. Callos\n,77 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,131\nE. Capocasa\n,20 E. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 132 F. Carbognani,62 M. Carlassara,8, 9\nJ. B. Carlin\n,124 T. K. Carlson,133 M. F. Carney,104 M. Carpinelli\n,127, 62 G. Carrillo,77 J. J. Carter\n,8, 9\nG. Carullo\n,118, 134 A. Casallas-Lagos,135 J. Casanueva Diaz\n,62 C. Casentini\n,136, 22 S. Y. Castro-Lucas,137\nS. Caudill,133 M. Cavagli`a\n,105 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,138, 139\nE. Cesarini\n,22 N. Chabbra,34 W. Chaibi,113 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103\nS. Chalathadka Subrahmanya\n,97 J. C. L. Chan\n,140 M. Chan,114 K. Chang,141 S. Chao\n,142, 141 P. Charlton\n,143\nE. Chassande-Mottin\n,20 C. Chatterjee\n,144 Debarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,103\nS. Chaty\n,20 K. Chatziioannou\n,11 A. Chen\n,145 A. H.-Y. Chen,146 D. Chen\n,147 H. Chen,142 H. Y. Chen\n,120\nS. Chen,144 Yanbei Chen,148 Yitian Chen\n,121 H. P. Cheng,149 P. Chessa\n,76, 51 H. T. Cheung\n,90\nS. Y. Cheung,6 F. Chiadini\n,150, 132 G. Chiarini,8, 9, 92 A. Chiba,151 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80\nA. Chiummo\n,4, 62 C. Chou,146 S. Choudhary\n,72 N. Christensen\n,113, 152 S. S. Y. Chua\n,34 G. Ciani\n,74, 75\nP. Ciecielag\n,95 M. Cie\u00b4slar\n,125 M. Cifaldi\n,22 B. Cirok,153 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6\nP. Clearwater,154 S. Clesse,111 F. Cleva,113, 116 E. Coccia,44, 45, 43 E. Codazzo\n,155, 156 P.-F. Cohadon\n,122\nS. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98 C. G. Collette,157 J. Collins,63 S. Colloms\n,86 A. Colombo\n,158, 128\narXiv:2508.20721v1 [gr-qc] 28 Aug 2025\n\n2\nC. M. Compton,2 G. Connolly,77 L. Conti\n,92 T. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,159 S. Corezzi\n,76, 51\nN. J. Cornish\n,160 I. Coronado,161 A. Corsi\n,162 R. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38\nP. Couvares\n,11, 57 D. M. Coward,72 R. Coyne\n,163 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,164\nP. Cremonese\n,98 S. Crook,63 R. Crouch,2 J. Csizmazia,2 J. R. Cudell\n,165 T. J. Cullen\n,11 A. Cumming\n,86\nE. Cuoco\n,166, 167 M. Cusinato\n,138 L. V. Da Concei\u00b8c\u02dcao,168 T. Dal Canton\n,41 S. Dal Pra\n,169 G. D\u00b4alya\n,100\nB. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,123 L. P. Dartez\n,63\nR. Das,106 A. Dasgupta,93 V. Dattilo\n,62 A. Daumas,20 N. Davari,170, 171 I. Dave,103 A. Davenport,137 M. Davier,41\nT. F. Davies,72 D. Davis\n,11 L. Davis,72 M. C. Davis\n,18 P. Davis\n,172, 173 E. J. Daw\n,174 M. Dax\n,1\nJ. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,175 M. De Laurentis\n,32, 4 F. De Lillo\n,23 S. Della Torre\n,128\nW. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,176, 61 F. De Matteis\n,21, 22 N. Demos,35\nT. Dent\n,177 A. Depasse\n,15 N. DePergola,102 R. De Pietri\n,178, 179 R. De Rosa\n,32, 4 C. De Rossi\n,62\nM. Desai\n,35 R. DeSalvo\n,180 A. DeSimone,181 R. De Simone,150, 132 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,164\nM. Di Cesare\n,32, 4 G. Dideron,182 T. Dietrich\n,1 L. Di Fiore,4 C. Di Fronzo\n,72 M. Di Giovanni\n,39, 38\nT. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 183 S. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,184, 48\nF. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,118 J. P. Docherty,86 Z. Doctor\n,96 N. Doerksen,168\nE. Dohmen,2 A. Doke,133 A. Domiciano De Souza,185 L. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33\nT. Dooney,71 S. Doravari\n,79 O. Dorosh,186 W. J. D. Doyle,123 M. Drago\n,39, 38 J. C. Driggers\n,2\nL. Dunn\n,124 U. Dupletsa,44 D. D\u2019Urso\n,170, 155 P. Dutta Roy,46 H. Duval\n,187 S. E. Dwyer,2 C. Eassa,2\nM. Ebersold\n,188, 31 T. Eckhardt\n,97 G. Eddolls\n,78 A. Effler\n,63 J. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25\nM. Emma\n,58 K. Endo,151 R. Enficiaud\n,1 L. Errico\n,32, 4 R. Espinosa,164 M. C. Espitia,189 M. Esposito\n,4, 32\nR. C. Essick\n,190 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,182 B. E. Ewing,7 J. M. Ezquiaga\n,140\nF. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,130 B. Farr\n,77 W. M. Farr\n,191, 192\nG. Favaro\n,91 M. Favata\n,193 M. Fays\n,165 M. Fazio\n,55 J. Feicht,11 M. M. Fejer,89 R. Felicetti\n,184, 48\nE. Fenyvesi\n,87, 194 J. Fernandes,195 T. Fernandes\n,196, 138 D. Fernando,110 S. Ferraiuolo\n,197, 39, 38\nT. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81 I. Fiori\n,62 M. Fishbach\n,190 R. P. Fisher,123\nR. Fittipaldi\n,198, 132 V. Fiumara\n,199, 132 R. Flaminio,31 S. M. Fleischer\n,200 L. S. Fleming,201 E. Floden,18\nH. Fong,114 J. A. Font\n,138, 139 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal\n,202 K. Franceschetti,178 F. Frappez,31\nS. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,203 A. Freise\n,37, 107 O. Freitas\n,196, 138 R. Frey\n,77\nW. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28 M. Fuentes-Garcia\n,11 S. Fujii,204\nT. Fujimori,205 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1 S. Galaudage\n,185 V. Galdi,206 R. Gamba,7\nA. Gamboa\n,1 S. Gamoji,180 D. Ganapathy\n,207 A. Ganguly\n,79 B. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,208\nC. Garc\u00b4\u0131a-Quir\u00b4os\n,188 J. W. Gardner\n,34 K. A. Gardner,114 S. Garg,42 J. Gargiulo\n,62 X. Garrido\n,41\nA. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22 B. Gateley,2 F. Gautier\n,209 V. Gayathri\n,10\nT. Gayer,78 G. Gemme\n,29 A. Gennai\n,80 V. Gennari\n,100 J. George,103 R. George\n,120 O. Gerberding\n,97\nL. Gergely\n,153 Archisman Ghosh\n,94 Sayantan Ghosh,195 Shaon Ghosh\n,193 Shrobana Ghosh,8, 9\nSuprovo Ghosh\n,210 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63 K. D. Giardina,63 D. R. Gibson,201\nC. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77 R. V. Godley,8, 9 P. Godwin\n,11\nA. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11 S. Gomez Lopez\n,39, 38 B. Goncharov\n,44 G. Gonz\u00b4alez\n,12\nP. Goodarzi\n,211 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62 R. Gouaty\n,31 D. W. Gould,34\nK. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18 M. Granata\n,175 V. Granata\n,212, 132\nS. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,86 G. Greco,51 A. C. Green\n,37, 107 L. Green,213\nS. M. Green,73 S. R. Green\n,214 C. Greenberg,133 A. M. Gretarsson,65 H. K. Griffin,18 D. Griffith,11\nH. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1 D. Guerra\n,138\nD. Guetta\n,215 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,172, 173 H. Guo\n,145\nW. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,216 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46 V. Gupta\n,18\nN. Gupte,1 J. Gurs,97 N. Gutierrez,175 N. Guttman,6 F. Guzman\n,131 D. Haba,217 M. Haberland\n,1\nS. Haino,218 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,219 A. G. Hanselman\n,130 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,181 S. Harikumar\n,186 K. Haris,37, 71 I. Harley-Trochimczyk,131 T. Harmark\n,134\nJ. Harms\n,44, 45 G. M. Harry\n,220 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 221, 222 C. J. Haster\n,213\nK. Haughian\n,86 H. Hayakawa,50 K. Hayama,223 M. C. Heintze,63 J. Heinze\n,118 J. Heinzel,35 H. Heitmann\n,113\nF. Hellman\n,207 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,115 M. Hendry\n,86\nI. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,224, 225 J. Heynen,15\n\n3\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,226 N. Hirata,25 C. Hirose,227\nD. Hofman,175 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,174 D. E. Holz\n,130 L. Honet,111\nD. J. Horton-Bailey,207 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,144 E. J. Howell\n,72 C. G. Hoy\n,73\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,142 H.-Y. Hsieh,142 C. Hsiung,228 S.-H. Hsu,146 W.-F. Hsu\n,109\nQ. Hu\n,86 H. Y. Huang\n,141 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,229 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,132 J. Iascau,77\nK. Ide,230 R. Iden,217 A. Ierardi,44, 45 S. Ikeda,147 H. Imafuku,42 Y. Inoue,141 G. Iorio\n,91 P. Iosif\n,184, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,230 M. Isi\n,191, 192 K. S. Isleif\n,231 Y. Itoh\n,205, 232 M. Iwaya,204\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,122 T. Jacquot,41 S. J. Jadhav,233 S. P. Jadhav\n,154 M. Jain,133\nT. Jain,224 A. L. James\n,11 K. Jani\n,144 J. Janquart\n,15 K. Janssens\n,23 N. N. Janthalur,233 S. Jaraba\n,234\nP. Jaranowski\n,235 R. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,149 H.-B. Jin\n,236, 237\nG. R. Johns,123 N. A. Johnson,46 M. C. Johnston\n,213 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,210\nR. Jones,86 H. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,238 L. Ju\n,72 K. Jung\n,239 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,240 I. Kaku,205 V. Kalogera\n,96 M. Kalomenopoulos\n,213\nM. Kamiizumi\n,50 N. Kanda\n,232, 205 S. Kandhasamy\n,79 G. Kang\n,241 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,133 M. Kasprzack\n,11 H. Kato,151\nT. Kato,204 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,205 D. Keitel\n,98\nL. J. Kemperman\n,115 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,242 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,162 M. Khursheed,103\nN. M. Khusid,191, 192 W. Kiendrebeogo\n,113, 243 N. Kijbunchoo\n,115 C. Kim,244 J. C. Kim,245 K. Kim\n,246\nM. H. Kim\n,238 S. Kim\n,247 Y.-M. Kim\n,246 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,204 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,248, 249 K. Kokeyama\n,33, 250 S. Koley\n,44, 165 P. Kolitsidou\n,118 A. E. Koloniari\n,251\nK. Komori\n,42 A. K. H. Kong\n,142 A. Kontos\n,252 L. M. Koponen,118 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,151 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,118 S. Kroker,253 A. Kr\u00b4olak\n,254, 186 K. Kruska,8, 9 J. Kubisz\n,255 G. Kuehn,8, 9\nS. Kulkarni\n,216 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,233 Praveen Kumar\n,177\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,256, 257, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,208, 258 S. Kuwahara\n,42 K. Kwak\n,239 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,188, 100\nA. H. Laity,163 E. Lalande,259 M. Lalleman\n,23 P. C. Lalremruati,260 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,120 R. Langgin\n,213 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,200 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,164 M. Laxen\n,63 C. Lazarte\n,138 A. Lazzarini\n,11 C. Lazzaro,156, 155 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,261 H. W. Lee\n,262 J. Lee,78 K. Lee\n,238 R.-K. Lee\n,142 R. Lee,35\nSungho Lee\n,246 Sunjae Lee,238 Y. Lee,141 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,182 M. Le Jean\n,175, 116\nA. Lema\u02c6\u0131tre\n,263 M. Lenti\n,61, 176 M. Leonardi\n,74, 75, 264 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,265 T. G. F. Li,109 X. Li\n,148\nY. Li,96 Z. Li,86 A. Lihos,123 E. T. Lin\n,142 F. Lin,141 L. C.-C. Lin\n,265 Y.-C. Lin\n,142 C. Lindsay,201\nS. D. Linker,180 A. Liu\n,219 G. C. Liu\n,228 Jian Liu\n,72 F. Llamas Villarreal,164 J. Llobera-Querol\n,98\nR. K. L. Lo\n,140 J.-P. Locquet,109 S. C. G. Loggins,266 M. R. Loizou,133 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,165 M. Lopez Portilla,71 M. Lorenzini\n,21, 22 A. Lorenzo-Medina\n,177 V. Loriette,41 M. Lormand,63\nG. Losurdo\n,267, 80 E. Lotti,133 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,124\nN. Lu\n,34 L. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,268, 269 A. W. Lussier\n,259 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,151 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,163\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,190\nS. Maliakal,11 A. Malik,103 L. Mallick\n,168, 190 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,170, 155 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 270\nC. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100 F. Martelli\n,60, 61\nI. W. Martin\n,86 R. M. Martin\n,193 B. B. Martinez,131 D. A. Martinez,54 M. Martinez,43, 271 V. Martinez\n,129\nA. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,118 E. J. Marx,35 L. Massaro,36, 37 A. Masserot,31\nM. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 N. Mavalvala\n,35\nN. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63 L. McCuller\n,11\nS. McEachin,123 C. McElhenny,123 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,144 J. McIver\n,114\n\n4\nA. McLeod\n,72 I. McMahon\n,188 T. McRae,34 R. McTeague,86 D. Meacher\n,10 B. N. Meagher,78 R. Mechum,110\nQ. Meijer,71 A. Melatos,124 C. S. Menoni\n,137 F. Mera,2 R. A. Mercer\n,10 L. Mereni,175 K. Merfeld,162\nE. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10 B. Mestichelli,44\nM. Meyer-Conde\n,272 P. M. Meyers\n,11 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,273 C. Michel\n,175\nY. Michimura\n,42 H. Middleton\n,118 D. P. Mihaylov\n,104 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,184, 48\nV. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43 L. Mirasola\n,155, 156 M. Miravet-Ten\u00b4es\n,138\nC.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46 A. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79\nV. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35\nL. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,207 M. Mondin,180 J. K. Monsalve,189\nM. Montani,60, 61 C. J. Moore,224 D. Moraru,2 A. More\n,79 S. More\n,79 C. Moreno\n,135 E. A. Moreno\n,35\nG. Moreno,2 A. Moreso Serra,82 S. Morisaki\n,42, 204 Y. Moriwaki\n,151 G. Morras\n,208 A. Moscatello\n,91\nM. Mould\n,35 B. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,176, 61 F. Muciaccia\n,39, 38 D. Mukherjee\n,118\nSamanwaya Mukherjee,24 Soma Mukherjee,164 Subroto Mukherjee,93 Suvodip Mukherjee\n,13 N. Mukund\n,35\nA. Mullavey,63 H. Mullock,114 J. Mundi,220 C. L. Mungioli,72 M. Murakoshi,230 P. G. Murray\n,86 D. Nabari\n,74, 75\nS. L. Nadji,8, 9 A. Nagar,28, 274 N. Nagarajan\n,86 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,275 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,62 P. Narayan\n,216 I. Nardecchia\n,22 T. Narikawa,204\nH. Narola,71 L. Naticchioni\n,38 R. K. Nayak\n,260 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,131\nT. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen Quynh\n,276 S. A. Nichols,12 A. B. Nielsen\n,277\nY. Nishino,25, 42 A. Nishizawa\n,278 S. Nissanke,279, 37 W. Niu\n,7 F. Nocera,62 J. Noller,280 M. Norman,33\nC. North,33 J. Novak\n,116, 234, 281 R. Nowicki\n,144 J. F. Nu\u02dcno Siles\n,208 L. K. Nuttall\n,73 K. Obayashi,230\nJ. Oberling\n,2 J. O\u2019Dell,229 E. Oelker\n,35 M. Oertel\n,234, 116, 282, 281 G. Oganesyan,44, 45 T. O\u2019Hanlon,63\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,116, 282, 281 R. Omer,18 B. O\u2019Neal,123 M. Onishi,151 K. Oohara\n,283\nB. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110 S. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11\nI. Ota\n,12 D. J. Ottaway\n,115 A. Ouzriat,56 H. Overmier,63 B. J. Owen\n,284 R. Ozaki,230 A. E. Pace\n,7\nR. Pagano\n,12 M. A. Page\n,25 A. Pai\n,195 L. Paiella,44 A. Pal,285 S. Pal\n,260 M. A. Palaia\n,80, 81 M. P\u00b4alfi,203\nP. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,142 J. Pan,72 K. C. Pan\n,142 P. K. Panda,233\nShiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38 K. A. Pannone,54 B. C. Pant,103\nF. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 286 A. Papadopoulos\n,86 E. E. Papalexakis,211\nL. Papalini\n,80, 81 G. Papigkiotis\n,251 A. Paquis,41 A. Parisi\n,76, 51 B.-J. Park,246 J. Park\n,287 W. Parker\n,63\nG. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80 L. Passenger,6 D. Passuello,80\nO. Patane\n,2 A. V. Patel\n,141 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80 B. G. Patterson,33 K. Paul\n,106\nS. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna Arellano\n,288 X. Peng,118\nY. Peng,57 S. Penn\n,289 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,133 C. P\u00b4erigois\n,290, 92, 91 G. Perna\n,91\nA. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107 D. Pesios,251 S. Peters,165 S. Petracca,206\nC. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18 K. S. Phukon\n,118 H. Phurailatpam,219\nM. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113 M. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61\nL. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,291, 132 M. Pietrzak,95 M. Pillas\n,165 F. Pilo\n,80 L. Pinard\n,175\nI. M. Pinto\n,291, 132, 292, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,224, 86 A. Placidi\n,51\nE. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,212, 22 C. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35\nJ. Pomper,80, 81 L. Pompili\n,1 J. Poon,219 E. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62\nJ. Powell\n,154 G. S. Prabhu,79 M. Pracchia\n,165 B. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93\nK. Prasai\n,293 R. Prasanna,233 P. Prasia,79 G. Pratten\n,118 G. Principe\n,184, 48 G. A. Prodi\n,74, 75\nP. Prosperi,80 P. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,163\nH. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,173, 116 V. Quetschke,164 L. H. Quiceno,189 P. J. Quinonez,65\nN. Qutob,57 R. Rading,231 I. Rainho,138 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110 K. E. Ramirez\n,63\nF. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,164 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57 K. Ransom,63\nP. Rapagnani\n,39, 38 B. Ratto,65 A. Ravichandran,133 A. Ray\n,96 V. Raymond\n,33 M. Razzano\n,81, 80 J. Read,54\nT. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini,11 A. Renzini\n,127 B. Revenu\n,294, 41\nA. Revilla Pe\u02dcna,82 R. Reyes,180 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39 A. Ricciardone\n,81, 80 J. Rice,78\nJ. W. Richardson\n,211 M. L. Richardson,115 A. Rijal,65 K. Riles\n,90 H. K. Riley,33 S. Rinaldi\n,270\nJ. Rittmeyer,97 C. Robertson,229 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31 J. G. Rollins\n,11\nA. E. Romano\n,189 J. D. Romano\n,164 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,224 J. H. Romie,63\nS. Ronchini\n,7 T. J. Roocke\n,115 L. Rosa,4, 32 T. J. Rosauer,211 C. A. Rose,57 D. Rosi\u00b4nska\n,125 M. P. Ross\n,53\n\n5\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,191, 192 S. Roy\n,15 D. Rozza\n,127, 128 P. Ruggi,62 N. Ruhama,239\nE. Ruiz Morales\n,295, 208 K. Ruiz-Rocha,144 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,168\nM. R. Sah\n,13 S. Saha\n,142 T. Sainrat\n,64 S. Sajith Menon\n,215, 39, 38 K. Sakai,296 Y. Sakai\n,272\nM. Sakellariadou\n,67 S. Sakon\n,7 O. S. Salafia\n,158, 128, 127 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,120\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,79 S. Salvador\n,173, 172 A. Salvarese,120 A. Samajdar\n,71, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,138 J. R. Sanders,181 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,251 P. Sassi\n,51, 76\nB. Sassolas\n,175 B. S. Sathyaprakash\n,7, 33 R. Sato,227 S. Sato,151 Yukino Sato,151 Yu Sato,151 O. Sauter\n,46\nR. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,79 S. Sayah,175 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,148\nA. Schiebelbein,190 M. G. Schiworski\n,78 P. Schmidt\n,118 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9\nR. M. S. Schofield,77 K. Schouteden\n,109 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,297 M. Scialpi\n,298\nJ. Scott\n,86 S. M. Scott\n,34 R. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,299\nD. Sellers,63 N. Sembo,205 A. S. Sengupta\n,300 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38\nA. Sevrin,187 T. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,261 L. Shao\n,301 A. K. Sharma\n,98 Preeti Sharma,12\nPrianka Sharma,103 Ritwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,126 N. S. Shcheblanov\n,302, 263\nE. Sheridan,144 Z.-H. Shi,142 M. Shikauchi,42 R. Shimomura,303 H. Shinkai\n,303 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,120 R. W. Short,2 S. ShyamSundar,103 A. Sider,157 H. Siegel\n,191, 192 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 169 M. Simmonds,115 L. P. Singer\n,304 Amitesh Singh,216 Anika Singh,11\nD. Singh\n,207 N. Singh\n,98 S. Singh,217, 59 A. M. Sintes\n,98 V. Sipala,170, 155 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,200 T. J. Slaven-Blair,72 J. Smetana,118 J. R. Smith\n,54 L. Smith\n,86, 184, 48 R. J. E. Smith\n,6\nW. J. Smith\n,144 S. Soares de Albuquerque Filho,60 M. Soares-Santos,188 K. Somiya\n,217 I. Song\n,142 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,305 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,123 D. A. Steer\n,306 N. Steinle\n,168 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,251 P. Stevens,41 M. StPierre,163 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,230 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,241 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,217 M. Suzuki,204\nB. L. Swinkels\n,37 A. Syx\n,116 M. J. Szczepa\u00b4nczyk\n,307 P. Szewczyk\n,125 M. Tacca\n,37 H. Tagoshi\n,204\nK. Takada,204 H. Takahashi\n,272 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,308 H. Takeda\n,309, 310\nK. Takeshita,217 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,130 M. Tamaki,204 N. Tamanini\n,100\nD. Tanabe,141 K. Tanaka,50 S. J. Tanaka\n,230 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,211\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,311 J. D. Tasson\n,152 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,180 A. Theodoropoulos\n,138 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,210 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,195 S. Tiwari\n,188 V. Tiwari\n,118\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,141 A. Torres-Forn\u00b4e\n,138, 139 C. I. Torrie,11 I. Tosta e Melo\n,312\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,123 A. Trapananti\n,52, 51 R. Travaglini\n,167 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,126 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,184, 48 A. Trovato\n,184, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,313 L. Tsukada\n,213 K. Turbang\n,187, 23 M. Turconi\n,113 C. Turski,94\nH. Ubach\n,82, 83 N. Uchikata\n,204 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,314 K. Ueno\n,42 V. Undheim\n,277\nL. E. Uronen,219 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,189 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 315\nE. Van den Bossche\n,187 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,259 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,124 V. Varma\n,133 A. N. Vazquez,89 A. Vecchio\n,118 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,115 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,133\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,190 A. Vilkha,110 N. Villanueva Espinosa,138 V. Villa-Ortega\n,177\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,231 L. Vujeva\n,140 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,217 J. Z. Wang,90 W. H. Wang,164\nY. F. Wang\n,1 G. Waratkar\n,195 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\n\n6\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\nA. T. Wilkin,211 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,141 I. C. F. Wong\n,219, 109 K. Wong,190 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,142 D. S. Wu\n,8, 9 H. Wu\n,142 K. Wu,119 Q. Wu,53\nT. Y. Wu\n,316, 317 Y. Wu,96 Z. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,207 Y. Xu\n,98\nN. Yadav\n,28 H. Yamamoto\n,11 K. Yamamoto\n,151 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,230\nT. Yan,118 K. Z. Yang\n,18 Y. Yang\n,146 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,142 A. B. Yelikar\n,144\nX. Yin,35 J. Yokoyama\n,318, 42 T. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110\nT. Zelenova,62 J.-P. Zendri,92 M. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57 R. Zhang\n,149\nT. Zhang,118 C. Zhao\n,72 Yue Zhao,161 Yuhang Zhao,20 Z.-C. Zhao\n,319 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78\nH. O. Zhu,72 Z.-H. Zhu\n,319, 320 A. B. Zimmerman\n,120 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n\n7\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n\n8\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120University of Texas, Austin, TX 78712, USA\n121Cornell University, Ithaca, NY 14850, USA\n122Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n123Christopher Newport University, Newport News, VA 23606, USA\n124OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n125Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n126University of Maryland, College Park, MD 20742, USA\n127Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n128INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n129Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n130University of Chicago, Chicago, IL 60637, USA\n131University of Arizona, Tucson, AZ 85721, USA\n132INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Colorado State University, Fort Collins, CO 80523, USA\n138Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n139Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n140Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n141National Central University, Taoyuan City 320317, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n157Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n\n9\n159Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n161The University of Utah, Salt Lake City, UT 84112, USA\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n165Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n166DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n171INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n172Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n173Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n174The University of Sheffield, Sheffield S10 2TN, United Kingdom\n175Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n176Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n177IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n178Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n179INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n180California State University, Los Angeles, Los Angeles, CA 90032, USA\n181Marquette University, Milwaukee, WI 53233, USA\n182Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n183Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n184Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n185Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n186National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n187Vrije Universiteit Brussel, 1050 Brussel, Belgium\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n190Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n191Stony Brook University, Stony Brook, NY 11794, USA\n192Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n193Montclair State University, Montclair, NJ 07043, USA\n194HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n195Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n196Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n197Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n198CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n199Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n200Western Washington University, Bellingham, WA 98225, USA\n201SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n202Barry University, Miami Shores, FL 33168, USA\n203E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n204Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n205Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n206University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n207University of California, Berkeley, CA 94720, USA\n208Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n209Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211University of California, Riverside, Riverside, CA 92521, USA\n212Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n\n10\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214University of Nottingham NG7 2RD, UK\n215Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n216The University of Mississippi, University, MS 38677, USA\n217Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n218Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n219The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Helmut Schmidt University, D-22043 Hamburg, Germany\n232Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n233Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n234Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n235Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n236National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n238Sungkyunkwan University, Seoul 03063, Republic of Korea\n239Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n240Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n241Chung-Ang University, Seoul 06974, Republic of Korea\n242University of Washington Bothell, Bothell, WA 98011, USA\n243Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n248Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n249Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n250Nagoya University, Nagoya, 464-8601, Japan\n251Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n252Bard College, Annandale-On-Hudson, NY 12504, USA\n253Technical University of Braunschweig, D-38106 Braunschweig, Germany\n254Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n255Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n256Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n257Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n258Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n259Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n\n11\n260Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n261Seoul National University, Seoul 08826, Republic of Korea\n262Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n263NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n264Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n265Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n266St. Thomas University, Miami Gardens, FL 33054, USA\n267Scuola Normale Superiore, I-56126 Pisa, Italy\n268Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n269Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n270Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n271Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n272Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n273Tsinghua University, Beijing 100084, China\n274Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n275Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n276Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n277University of Stavanger, 4021 Stavanger, Norway\n278Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n279GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n280University College London, London WC1E 6BT, United Kingdom\n281Observatoire de Paris, 75014 Paris, France\n282Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n283Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n285CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n286Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n287Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n288Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n289Hobart and William Smith Colleges, Geneva, NY 14456, USA\n290INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n291Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n292Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n293Kennesaw State University, Kennesaw, GA 30144, USA\n294Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n295Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n296Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n297Trinity College, Hartford, CT 06106, USA\n298Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n299Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n300Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n301Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n302Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n303Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n\n12\n304NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n305Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n306Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n307Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n308Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n309The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n310Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n311Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n313National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n314Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n315Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n316Department of Physics and Astronomy, University of North Carolina at Chapel Hill,\n120 E. Cameron Ave, Chapel Hill, NC, 27599, USA\n317David A. Dunlap Department of Astronomy and Astrophysics,\nUniversity of Toronto, 50 St George St, Toronto ON M5S 3H4, Canada\n318Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n319Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n320School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nWe present results from the search for an isotropic gravitational-wave background using Advanced\nLIGO and Advanced Virgo data from O1 through O4a, the first part of the fourth observing run.\nThis background is the accumulated signal from unresolved sources throughout cosmic history and\nencodes information about the merger history of compact binaries throughout the Universe, as well\nas exotic physics and potentially primordial processes from the early cosmos. Our cross-correlation\nanalysis reveals no statistically significant background signal, enabling us to constrain several the-\noretical scenarios. For compact binary coalescences which approximately follow a 2/3 power-law\nspectrum, we constrain the fractional energy density to \u2126GW(25 Hz) \u22642.0 \u00d7 10\u22129 (95% credibility),\na factor of 1.7 improvement over previous results. Scale-invariant backgrounds are constrained to\n\u2126GW(25 Hz) \u22642.8 \u00d7 10\u22129, representing a 2.1\u00d7 sensitivity gain. We also place new limits on al-\nternative gravity theories predicting non-standard polarization modes and confirm that terrestrial\nmagnetic noise sources remain below our detection threshold. Combining these spectral limits with\npopulation models for GWTC-4, the latest gravitational-wave event catalog, we find our constraints\nremain above predicted merger backgrounds but are approaching detectability. The joint analysis\ncombining the background limits shown here with the GWTC-4 catalog enables improved inference\nof the binary black hole merger rate evolution across cosmic time. Furthermore, employing GWTC-4\ninference results and standard modeling choices, we estimate that the total background arising from\ncompact binary coalescences is \u2126CBC(25Hz) = 0.9+1.1\n\u22120.5 \u00d7 10\u22129 at 90% confidence, where the largest\ncontribution is due to binary black holes only, \u2126BBH(25 Hz) = 0.8+1.1\n\u22120.5 \u00d7 10\u22129.\nI.\nINTRODUCTION\nThe\nsuperposition\nof\nindividually\nunresolved\ngravitational-wave (GW) signals accumulated through-\nout cosmic history gives rise to a gravitational-wave\nbackground (GWB) [1, 2] which produces a persis-\ntent incoherent signal in GW detectors.\nThe GWB\nis commonly referred to as \u201cstochastic\u201d as it can be\ncharacterized statistically as a mean zero stochastic\n\u2217Deceased, September 2024.\nfield [1].\nGWB sources can be categorized as cosmological or as-\ntrophysical based on their origin. The former provides a\nunique probe of the early Universe, as GWs propagate di-\nrectly from the inflationary epoch, while the latter results\nfrom an ensemble of unresolved astrophysical events, of-\nfering insights into source populations at high redshift.\nPotential contributors to the GWB include distant un-\nresolved compact binary mergers [3\u20137], core-collapse su-\npernovae [3, 7\u20139], rotating neutron stars [8\u201314], stellar\ncore collapse [15, 16] and superradiance of axion clouds\naround black holes [17\u201321].\nSome of the cosmological\nsources are cosmic strings [22\u201335], first-order phase tran-\n\n13\nsitions in the early Universe [36\u201344], primordial black\nholes [45\u201352], a stiff equation of state in the early Uni-\nverse [53\u201358], and gravitational waves generated during\ninflation [59\u201369].\nThe Laser Interferometer Gravitational-wave Observa-\ntory (LIGO) [70], Virgo [71], and KAGRA [72] collabo-\nrations (LVK collaborations [73]) have previously placed\nupper limits on both isotropic [74] and anisotropic [75]\nGWBs using data from the first three observing runs\ncollected by the LIGO Hanford, LIGO Livingston, and\nVirgo interferometers.\nThese searches relied on cross-\ncorrelating data between detector pairs [1].\nThe im-\nplications of the upper limits placed on the GWB en-\nergy density spectrum with LVK data have been far-\nreaching, setting competitive bounds on early Universe\nphysics [26, 27, 43, 44, 50, 51, 58, 65], and expanding our\nknowledge of the astrophysical binary population proper-\nties complementary to what is obtained from individual\nGW sources [74, 76\u201378].\nThe most compelling astrophysical sources of a GWB\nin our detector range are compact binary coalescences\n(CBCs).\nThe CBC background is expected to be an\napproximately isotropic [79\u201381] spectral power-law sig-\nnal, peaking around a few hundred Hz (depending on\nthe features of the CBC population [81\u201384]). The sig-\nnal is not expected to be Gaussian due to the intermit-\ntent nature of the background, in the frequency range\nprobed [85].\nIn this work, we update our models to\nestimate the expected contributions from binary black\nholes (BBHs), binary neutron stars (BNSs) and neutron\nstar-black hole (NSBH) coalescences, incorporating the\nmost recent observational data from O4a [86\u201389].\nFor\nthe BBH population in particular, we adopt the method-\nology of [76] to constrain the redshift-dependent merger\nrate by combining individually resolved events with up-\nper limits from the cross-correlation analysis presented\nin this paper.\nThis approach allows us to construct a\nfull posterior distribution for the resulting energy den-\nsity spectrum, accounting for current uncertainties in the\nmass, spin and redshift distributions of the BBH popula-\ntion. Additionally, by combining the contributions from\nall classes of CBCs and comparing the resulting GWB\nspectrum with the projected sensitivity curves of the up-\ngraded Advanced LIGO detectors (A+) [90] and Virgo\ndetector (V+) [91], we demonstrate that one year of time-\ncoincident data between detectors in the network at de-\nsign sensitivity would enable us to substantially probe\nand potentially detect the expected signal arising from\nthe CBC population.\nIn this work we follow the same methodology as pre-\nvious observing runs, cross-correlating data from LIGO\nHanford and Livingston detectors during the first por-\ntion of the fourth observing run, hereinafter referred to\nas O4a.\nDuring this first part of the run, Virgo was\nnot in science mode, hence why it is not included in\nour analysis.\nIn this paper, we focus exclusively on\nthe isotropic GWB, while complementary results from\nan anisotropic search are presented in a companion pa-\nper [92]. The cross-correlation search method employed\nis optimal for a continuous Gaussian signal, given ap-\npropriate caveats [1, 93], while it is sub-optimal but still\nsensitive to an intermittent signal [94]. Several alterna-\ntive search methods are currently being explored tailored\nto intermittent signals [94\u201397].\nAs we do not detect a GWB, we set upper limits on\nits amplitude. We include inference on a set of possible\nGWB models, including an astrophysical signal sourced\nby CBCs and alternative GWB polarization modes [98]\narising in theories of gravity beyond General Relativity\n(GR). As in O3, loud glitches are excluded from the anal-\nysis [99, 100]. Additionally, as correlated magnetic noise\nis a potential limiting factor in stochastic background\nsearches especially as detector sensitivity improves, we\nconstruct a magnetic noise budget, and find it lies well\nbelow the current GWB sensitivity. Alongside this pa-\nper, the LVK collaboration is also releasing a companion\npaper exploring the cosmological implications of our re-\nsults [101], focusing on the constraints these place on\npotential early-Universe sources of the GWB.\nThis paper is organized as follows. In Section II, we\noutline the analysis methods employed throughout. Sec-\ntion III details the procedures implemented to remove\nidentifiable sources of detector artifacts that can bias\nthe results and implications of the search.\nSection IV\npresents the results of our analysis. Finally, in Section V,\nwe discuss the astrophysical implications of our findings\nand provide constraints on the BBH merger rate.\nII.\nMETHODS\nThe isotropic stochastic analysis presented here tar-\ngets the spectral properties of the GWB, modeling the\nsignal as isotropic, unpolarized, stationary, and Gaussian\nin the limit of long observing time [1, 102]. The signal\nis also assumed to be weak with respect to the detector\nsensitivity [93].\nThe GWB spectrum may be expressed in terms of the\nfractional GW energy density spectrum \u2126GW(f), defined\nas\n\u2126GW(f) = 1\n\u03c1c\nd\u03c1GW(f)\nd ln f\n,\n(1)\nwhere d\u03c1GW is the GW energy density in the frequency\nband [f, f + df], and \u03c1c = 3H2\n0c2/(8\u03c0G) is the crit-\nical energy density in the Universe, with c the speed\nof light and G Newton\u2019s constant. Integrating \u2126GW(f)\nover d ln f returns the total dimensionless GW energy\ndensity.\nIn what follows, we adopt the Planck 2015\ncosmological parameters, fixing the Hubble constant to\nH0 = 67.9 km s\u22121 Mpc\u22121 and the present-day matter\ndensity parameter to \u2126m,0 = 0.3065 [103].\nThe analysis presented is carried out with the pygwb\nanalysis package [104, 105].\nIn the following we sum-\nmarize the methodological approach and specific choices\n\n14\nmade in the analysis of the O4a dataset. Methods em-\nployed here do not vary significantly from those of pre-\nvious observing runs O1 [106], O2 [107], and O3 [74], so\nthat the resulting spectra may be ultimately combined\ninto a single result.\nChanges with respect to previous\nanalyses are highlighted in the text.\nA.\nCross-correlation spectra\nFollowing [108], we employ cross-correlation spectra\ncalculated from pairs of independent, time-coincident de-\ntector strain datastreams to construct an estimator for\n\u2126GW(f):\n\u02c6\u21260(f) = Re[CIJ(f)]\n\u03b3IJ(f)S0(f) ,\n(2)\nwhere CIJ is the cross-spectral density (CSD) calculated\nfrom the Fourier-transformed strain data \u02dcs(f) of duration\nT from two non-coincident detectors I and J:\nCIJ(f) = 2\nT \u02dcs\u2217\nI(f)\u02dcsJ(f).\n(3)\nThe geometric quantity \u03b3IJ(f) is referred to as the\noverlap reduction function (ORF) [1, 109], which quanti-\nfies the frequency-dependent decoherence that affects the\ncross-correlation of data from two geographically sepa-\nrated interferometers.\nThis reduction depends on the\nindividual detector responses as well as their relative sep-\naration and orientation [1]. The function S0(f) converts\nunits of GW strain power into fractional energy density,\nwhilst encoding also a frequency weighting specific to a\nchosen spectral model F0(f):\nS0(f) = 3H2\n0F 2\n0 (f)\n10\u03c02\n1\nf 3 .\n(4)\nAs discussed in [93], in the case of noise-dominated data\nstreams the cross-correlation statistic described above is\na quasi-optimal 1 estimator for the background spectrum.\nIn line with previous analyses [74, 106, 107], here we\nassume a power-law spectral model expressed as an am-\nplitude \u2126\u03b1 with respect to the fixed reference frequency\nfref = 25 Hz scaling with a power-law index \u03b1,\n\u2126GW(f) = \u2126\u03b1F\u03b1(f) ,\nF\u03b1(f) =\n\u0012\nf\n25 Hz\n\u0013\u03b1\n.\n(5)\nIn Eq. (2) specifically, the chosen spectral model is fixed\nto a power law with spectral index \u03b1 = 0, as indicated by\nthe subscript of S0 and that of the estimator in Eq. (2).\n1 Sub-optimality is due to corrections to the variance Eq. (6) of the\nsame order of magnitude of the signal, which become negligible\nwhen the signal is weak compared to the detector noise.\nThe corresponding variance estimate is [1]\n\u03c32\n0(f) =\n1\n2T\u2206f\nPI(f)PJ(f)\n\u03b32\nIJ(f)S2\n0(f) ,\n(6)\nwhere PI(f) is the one-sided power spectral density for\ndetector I, and \u2206f is the frequency resolution employed\nin the analysis.\nIn practice, due to noise non-stationarities and compu-\ntational efficiency the \u02c6\u21260(f) spectrum is estimated from\na weighted average over a large number of data segments,\nwhere for each time segment i there is a corresponding\nCSD estimate CIJ, i and PSD estimates PI, i, PJ, i. Fur-\nther details about this cross-correlation computation may\nbe found in the pygwb publication [104].\nB.\nFrequency estimator\nWe construct a narrow-band estimator \u02c6\u21260(f) with as-\nsociated variance \u03c32\n0(f):\n\u02c6\u21260(f) =\nP\ni\nh\n\u02c6\u21260(f; ti)\u03c3\u22122\n0 (f; ti)\ni\nP\ni \u03c3\u22122\n0 (f; ti)\n,\n(7)\n\u03c30(f) =\n\"X\ni\n\u03c3\u22122\n0 (f; ti)\n#\u22121/2\n,\n(8)\nwhere i labels data from ti to ti + \u2206t.\nIn practice,\nthe cross-spectral densities are calculated from the data\nwith a 50% overlap to make up for the impact of Hann-\nwindowing each segment, hence each independent time\nestimate is achieved by handling even and odd segments\nseparately as described in [104].\nThis calculation is performed employing the S0(f)\nweighting function. However, note that it can be per-\nformed by choosing any other power-law weighting \u03b1,\nand it is possible to re-weight from one index, \u03b11, to\nanother, \u03b12, as\n\u02c6\u2126\u03b11(f) = \u02c6\u2126\u03b12(f)F\u03b11(f)\nF\u03b12(f) .\n(9)\nBroadband estimates for a spectral index \u03b1 and at ref-\nerence frequency 25 Hz are obtained by optimally weight-\ning the narrowband estimator, as described in [74, 104]:\n\u02c6\u2126\u03b1|25 Hz =\nP\nf \u02c6\u21260(f)F\u03b1(f)\u03c3\u22122\n0 (f)\nP\nf F 2\u03b1(f)\u03c3\u22122\n0 (f)\n,\n(10)\n\u03c3\u03b1|25 Hz =\n\uf8ee\n\uf8f0X\nf\nF\u03b1(f)\u03c3\u22122\n0 (f)\n\uf8f9\n\uf8fb\n\u22121/2\n.\n(11)\n\n15\nC.\nParameter estimation\nParameter estimation is performed here using a hy-\nbrid approach that combines frequentist and Bayesian\nanalysis techniques [110]. Specifically, the frequentist es-\ntimators from the previous sections, \u02c6\u21260(f) and \u03c30(f),\ncombined over the entire observing period, are used as\ninput data to calculate posterior probability distribu-\ntions of GWB model parameters. These in turn are used\nto compute upper bounds on the spectral amplitude of\nthe GWB. In [93] the authors show that in the weak-\nsignal approximation this hybrid approach does not lose\ninformation compared to a fully Bayesian search, which\nproduces posterior distributions from the full time series\ndata rather than from the time-averaged frequency esti-\nmators.\nWe assume that, in each frequency bin, the un-\nweighted spectral estimate \u02c6\u21260 is Gaussian-distributed\nwith variance \u03c32\n0 [74]:\np(\u02c6\u21260|\u0398) \u221dexp\n\uf8ee\n\uf8f0\u22121\n2\nX\nf\n(\u02c6\u21260(f) \u2212\u2126GW(f; \u0398))2\n\u03c32\n0(f)\n\uf8f9\n\uf8fb, (12)\nwhere \u2126GW(f; \u0398) is an assumed model for the GWB\nsignal, parametrized via a set of model parameters \u0398.\nPosteriors for the model parameters \u0398 are obtained by\nemploying the pygwb library [104] and the Bilby li-\nbrary [111] for detector modeling and likelihood evalu-\nation. As in previous work, e.g. [74], this analysis is per-\nformed using data from multiple detector pairs, I, J (i.e.,\nbaselines).\nData from different baselines are assumed\nto be independent, such that the combined inference as-\nsumes likelihood (12) holds for data from each individual\nbaseline, \u02c6\u2126IJ\n0 (f), \u03c3IJ\n0 (f), and the total likelihood is the\nresult of the product of the likelihood calculated for each\nbaseline.\nWe consider different models for the GWB:\n\u2022 Noise: \u2126GW(f; \u0398) = 0. We implicitly include un-\ncorrelated Gaussian noise as part of every model\nthat follows in the prior choices for the model pa-\nrameters. This noise model is not strictly correct as\nthere are potential sources of correlated noise, such\nas Schumann resonances [112]. However, these ef-\nfects may be neglected in the present search due to\ndetector sensitivity, as shown in Sec. III F.\n\u2022 Power law: \u2126GW(f; \u0398) = \u2126refF\u03b1(f), as per Eq. (5).\nIn this analysis, the two parameters \u0398 = {\u2126ref, \u03b1}\nare inferred independently, and hence we choose\nthis notation to avoid confusion with the cross-\ncorrelation estimators described above.\nThe ref-\nerence frequency is set to fref = 25 Hz as in past\nanalyses [74] due to the location of peak stochas-\ntic sensitivity, for lower values of \u03b1. Note that the\nprecise sensitivity depends on the spectral index \u03b1.\n\u2022 Scalar-vector-tensor (SVT) power law: this model\nassumes that the signal may include vector and\nscalar polarizations as well as the standard tensor\npolarization predicted by General Relativity. This\nbackground is modeled as a superposition of indi-\nvidual contributions, labeled (p) = {T, V, S} where\neach component is individually modeled by a power\nlaw [113]:\n\u2126GW(f; \u0398) =\nX\n(p)\n\u03b2(p)(f)\u2126(p)\nref F\u03b1p(f) ,\n(13)\nwhere \u03b2(p)(f) \u2261\u03b3(p)\nIJ (f)/\u03b3IJ(f) is the ratio be-\ntween the ORF for polarization (p) and the stan-\ndard (tensor) polarization [98].\n\u2022 Magnetic: describes correlations between pairs of\ndetectors induced by large-scale coherent magnetic\nfields that can mimic a GWB signal.\nThese are\nmodeled in terms of magnetometer correlations and\na transfer function between the local magnetic field\nand the strain channel of the detectors.\nFurther\ndiscussion on this model is given in section IV D.\n\u2022 Compact binary coalescences (CBC): the predom-\ninant contribution to the GWB is expected to be\nthe superposition of all merging compact binaries\nin the observable Universe [82]. The total GW frac-\ntional energy density due to compact binary merg-\ners, \u2126CBC, can be parametrized as a function of\nthe mass distribution of compact binaries and their\nmerger rate as a function of redshift. This model\nwill be discussed in Section V. Assuming \u2126CBC is\nthe only contributor to the stochastic signal in the\nanalyzed frequency band, we can infer mass and\nmerger rate population parameters.\nTo test these different models against the data, we cal-\nculate Bayes factors for each model.\nUnless otherwise\nspecified, we compute the Bayes factor between the hy-\npothesis of a specific signal model with respect to the\nnoise model, \u2126GW(f; \u0398) \u22610.\nIII.\nDATA QUALITY\nThis section describes the data quality and handling\nspecifics for the strain data collected during the first por-\ntion of the fourth observing run (O4a) by the LIGO\nHanford and Livingston detectors.\nNote that results\npresented in the following sections include the combi-\nnation of this data with previous datasets O1, O2, O3,\nwhose relevant instrument performances and data quality\nfeatures are described in [114\u2013117], [118\u2013120], [121\u2013124]\nrespectively.\nThe O3 analysis also includes data from\nVirgo [125\u2013130]. For further details on the performance\nof the LIGO detectors and the quality of their data dur-\ning O4a [131, 132], see also [133].\n\n16\nA.\nData\nThe O4a observing period ran from 15:00 UTC on May\n24, 2023 to 16:00 UTC on January 16, 2024. The total\ncoincident time for the Hanford-Livingston (HL) baseline\nin this period was 126.57 days, before applying data qual-\nity cuts. The strain data used in this analysis were cali-\nbrated strain data with narrow-band features from pho-\nton calibrator and actuation injections and power mains\nnoise, subtracted [134], followed by the application of\nnon-stationary noise subtraction [135].\nThe correlated\nmagnetic noise was monitored using low-noise LEMI120\nmagnetometers located at each site [136]. The same data\nprocessing was carried out for both strain and magne-\ntometer data to allow a comparison between the mag-\nnetic and GW analyses.\nBoth strain and magnetic datastreams are initially\ndownsampled from the original sample rate of 16384 Hz\nto 4096 Hz. This downsampling is used because the GW\nsources targeted in this search populate frequencies below\n2 kHz. The data are high-pass filtered using a 16th-order\nButterworth filter with a knee frequency of 11 Hz, which\nis constructed using second-order sections. As in anal-\nyses described in [74, 104], each data stream is divided\ninto 50% overlapping, Hann-windowed 192-second seg-\nments, coarse-grained to a frequency resolution of 1/32\nHz. The analyzed frequency range spans 20 \u22121726 Hz;\nthe minimum frequency is chosen based on the detec-\ntor sensitivities [133], while the maximum frequency is\nchosen to be sufficiently below the Nyquist frequency to\navoid aliasing effects.\nIn the following text, tables, and figures, we label\nthe LIGO Hanford detector as LHO and the LIGO Liv-\ningston as LLO.\nB.\nTime domain cuts: vetoed times\nData quality for analysis purposes was assessed jointly\nwith the Detector Characterization groups of LIGO,\nVirgo, and KAGRA. Data quality flags are employed to\ndefine observing time periods to be vetoed from analy-\nsis. Most significant to this search are the \u201cCategory 1\u201d\nvetoes. These vetoes correspond to times when the de-\ntector was known to be operating outside of its nominal\ncondition. For more details on the O4a data quality and\nthe specific time-domain cuts made for stochastic data\nquality purposes, please refer to [133], Sec. 4.3. After ap-\nplying vetoes, the remaining viable time-coincident data\nis 126.47 days. The relevant segment information used to\nexclude vetoed data from this analysis will be available\non GWOSC [137].\nC.\nTime domain cuts: gating\nIn the third LVK observing run (O3), a large popula-\ntion of loud glitches [74] led to very frequent flagging of\ndata segments by non-stationarity checks (see Sec. III D).\nTo mitigate this effect, time-domain gating of the data\nwas introduced [138, 139]: loud glitches are removed from\nthe data stream by multiplying the data with an in-\nverse Planck-taper window with parameters tailored to\nthe specific non-stationary feature (e.g., duration) [140].\nIn O4a, data are preprocessed with an auto-gating pro-\ncedure as described in [105]. The parameters chosen for\nthe auto-gating were optimized for this specific search,\nminimizing the amount of data lost whilst retaining sta-\ntionarity. A total of 0.093% of analyzed Hanford data\nand 0.068% of Livingston data were gated; more details\ncan be found in Sec. 4.3.2. of [133].\nD.\nTime domain cuts: stationarity checks\nAs in previous runs, we apply a non-stationarity cut\n(often referred to as the \u2206\u03c3 cut [104]) by removing times\nwhere the square root of the variance in Eq. (6) is found\nto vary by more than 20% between neighbouring seg-\nments. We cut the union of segments that do not satisfy\nthe stationarity test assuming a set of different spectral\nweights: \u03b1 = {\u22125, 0, 3, 5}, implemented as in Eq. (2). As\neach power law accumulates SNR in a different frequency\nband, these may flag different segments depending on\ntheir specific spectral narrowband/broadband features.\nThis cut additionally removes 8.1% of the analysed seg-\nments, leaving 108.41 days of viable data.\nE.\nFrequency domain cuts: narrowband features\nIn addition to broadband features that determine the\nexclusion of entire data segments from the analysis,\nalso narrowband deviations from Gaussianity are inves-\ntigated, and data cuts are applied to exclude problem-\natic frequency bins. These frequencies are determined by\nmonitoring the coherence between the GW channels at\ndifferent sites, and between the GW channel and auxil-\niary channels at the same site. Bins that show evidence of\ninstrumental noise or that manifest strong non-Gaussian\nbehavior are excluded from the analysis: for more details,\nsee [133], Sec. 2.1. The list of problematic frequencies,\ni.e., the notch list, is determined at the end of the ob-\nserving run and then applied identically throughout the\nentire data analysis process (with a small exception in\nparameter estimation, as discussed in Sec. IV B). This\nlist is included in the appended data release.\nThe notches include the following components:\n\u2022 Calibration lines: these are stationary lines injected\ninto each detector\u2019s differential arm feedback loop\nso as to continually monitor the detector response\nand the corresponding calibration amplitude fac-\ntor. These include the stationary calibration lines\ninjected throughout O4a [141], and one calibration\nline at 24.5 Hz that was turned on between July\n25, 2023, and August 9, 2023.\n\n17\n\u2022 Pulsar injections:\neach injection corresponds to\na simulation of a quasi-monochromatic, persistent\nGW signal as expected from a rapidly rotating, iso-\nlated neutron star. These were injected throughout\nthe entire O4a run at both LIGO sites and emulate\nhow canonical continuous-wave (CW) signals would\nappear in the detectors [142].\n\u2022 Quadruple suspension violin modes: resonances of\nthe detector mirror suspension fibers [70].\n\u2022 Powerline harmonics: integer harmonics of the 60\nHz power mains present at both detectors.\n\u2022 Other artifacts: DuoTone signals (960Hz, 961Hz)\nand their 1 Hz side band present in both LIGO\ndetectors in O4a from the timing system, used to\nsynchronize data collection across the global detec-\ntor network and in each interferometer [143].\nOverall, the notch list cuts 8.4% of the spectrum; how-\never, note that in the frequency range [20, 300] Hz where\nthe detectors are most sensitive, only 2.7% of the spec-\ntrum is cut.\nF.\nMagnetic noise budget\nCorrelated magnetic noise present across multiple de-\ntectors is a probable hindrance for stochastic analy-\nses [144\u2013146].\nExamples of such correlated magnetic\nnoise are Schumann resonances [147, 148], standing waves\nin the cavity between the Earth\u2019s surface and the iono-\nsphere that may be excited by lightning strikes; and at\nhigher frequencies, f > 100 Hz, correlated fields from\nlightning strikes.\nMagnetic fields of any source couple\nto the detector via electric cables in the detector build-\nings or couple to the actuation magnets controlling the\ndetector test mass mirrors [125].\nMagnetic fields are monitored with sensitive probes\nplaced outside the detector buildings to produce a mag-\nnetic \u201cnoise budget\u201d, quantifying the strength of corre-\nlated magnetic noise present across detectors, which is\nthen compared to the sensitivity of the detector network\nto a stochastic signal [149]. If this budget becomes large\nenough, correlated magnetic fields can contribute to cor-\nrelated noise which may mimic a signal in the stochastic\nanalysis presented here.\nWe compute the magnetic correlated noise budget via\n\u02c6\u2126mag, IJ(f) = 2\nT\n|TI(f)| |TJ(f)|\nqP\nab | \u02dcm\u22c6\nI,a(f) \u02dcmJ,b(f)|2\n\u03b3IJ(f)S0(f)\n,\n(14)\nwhere TI(f) and TJ(f) are the magnetic coupling func-\ntions of detectors I and J, and \u02dcmI,a(f) is the Fourier-\ntransformed magnetic data from the outside probes of\ndetector I pointing in the direction a, which can be ei-\nther along the X or Y arms of a detector, and its sum runs\nover the four possible combinations of a and b. Magnetic\ncoupling functions consist of the product of two terms: an\noutside-to-inside coupling, TOTI, and an inside-to-strain\ncoupling, TITS. The TOTI term is given by the ratio of\nthe strength of a magnetic source measured outside the\ndetector buildings to the strength of the same source\nmeasured inside the buildings, and reduces to an over-\nall constant averaged over several independent measure-\nments, while TITS is estimated via hardware injections as\nexplained below. Uncertainties on these measurements\ninclude the uncertainty on the outside-to-inside coupling\nas measured in O3 at LLO, and, to be conservative, an\nintrinsic uncertainty factor of 2 as the magnetometers in\nthe building (used for the measurements) are not located\nat the exact location where the magnetic field couples to\nthe strain.\nThe TITS functions are estimated by each detector site\nteam by injecting far-field magnetic fields within the de-\ntector building and measuring the response in the strain\nchannel [112, 123, 125]. A value is recorded as a mea-\nsurement when both the magnetometer sensor and strain\nchannel amplitude spectral densities (ASDs) exceed their\nrespective set thresholds; otherwise, if only the magne-\ntometer ASD exceeds the threshold, the value is treated\nas an upper limit.\nThe coupling function is interpo-\nlated to the frequencies of the computed magnetic CSD,\nRe [ \u02dcm\u22c6\nI(f) \u02dcmJ(f)]. This does not create any artifacts in\nthe coupling functions as these have a finer frequency\nresolution than the CSD. We include a calibration fac-\ntor in the magnetic CSDs2 and take the quadrature sum\nof the magnetic CSDs of four baselines, one for every\ncombination of the two outside magnetometers at each\ndetector used for computing the budget, as a most con-\nservative estimate. These quantities are then combined\nin Eq. (14) to produce the magnetic budget shown in\nFig. 1. Here the red bands show the uncertainties on the\nbudget, compared to the 2\u03c3 power-law integrated sen-\nsitivity (PI) curve [150], showing the sensitivity of our\nsearch to power-law backgrounds.\nThe final budget indicates that no correlated (mag-\nnetic) noise observation is expected. Some narrowband\nfeatures are expected, such as the harmonics of the US\npower lines at 60 Hz, and the ORF zero-crossings (re-\nlated to the fact that a single baseline was considered for\nthis analysis).\nWhile the magnetic budget computation in O3 was\nperformed differently3, we can compare the two budgets\nat an order-of-magnitude level. At lower frequencies f <\n60 Hz, the O4a budget is consistently within the band of\nthe O3 budget, but in a narrow frequency band 60 Hz <\nf < 65 Hz, the O4a budget becomes slightly larger than\n2 The calibration factor is an intrinsic conversion factor between\nthe measured current in the magnetometers and the actual mag-\nnetic field.\n3 In O3, weekly magnetic couplings were used and, due to fluctu-\nations, computing a budget every single week produces a wide\nuncertainty band instead of a single line [123].\n\n18\n102\n103\nFrequency [Hz]\n10\u221212\n10\u221210\n10\u22128\n10\u22126\n10\u22124\n\u2126GW(f)\n1\u03c3\n2\u03c3\n3\u03c3\nO4a budget\nO1-O4a (2\u03c3)\nFIG. 1. The computed magnetic budget is shown in blue, in-\ncluding \u02c6\u2126mag + 1\u03c3, \u02c6\u2126mag + 2\u03c3, and \u02c6\u2126mag + 3\u03c3 uncertainties\n(in progressively lighter shades of red). The magnetic bud-\nget remains consistently below the 2\u03c3 power-law integrated\nsensitivity curve (black), except for narrowband features nu-\nmerically induced by the overlap reduction function (ORF)\nand harmonics of the 60 Hz power lines.\nthe maximum value in O3.\nThis is related to a zero-\ncrossing of the ORF virtually enhancing the magnetic\nbudget due to its presence in the denominator of Eq. (14),\nand does not accurately represent a magnetic response\nof the detector and thus the actual magnetic budget in\nO4a. At higher frequencies f > 65 Hz, the O4a budget\nis broadly consistent with the O3 magnetic budget.\nG.\nCalibration uncertainties\nCalibration uncertainties account for both statistical\nuncertainties and systematic errors arising from the cali-\nbration process of LVK data4 [151, 152]. These are incor-\nporated in parameter estimation [104, 153] by introduc-\ning a Gaussian-distributed, positive-definite calibration\nfactor \u039b. As a result, the likelihood presented in Eq. (12)\nis modified as (see also App. B of [104])\np(\u02c6\u21260|\u0398, \u039b) \u221dexp\n\uf8ee\n\uf8f0\u22121\n2\nX\nf\n(\u02c6\u21260(f) \u2212\u039b\u2126GW(f; \u0398))2\n\u03c32\n0(f)\n\uf8f9\n\uf8fb,\n(15)\nwhere \u039b is marginalized over, assuming the prior\np(\u039b) =\n1\np\n2\u03c0\u03c32\n\u039b\nexp\n\u0014\n\u2212(\u039b \u22121)2\n2\u03c32\n\u039b\n\u0015\n.\n(16)\n4 Calibration is the procedure used to convert the digital output\nof a gravitational-wave detector into the relative displacement of\nthe test masses within the detector.\nThe calibration variance \u03c3\u039b is estimated in collabora-\ntion with the LIGO Calibration Group. Hourly calibra-\ntion uncertainties provided by the Calibration Group are\ncombined to obtain uncertainties in both the magnitude\nand phase of the strain at the 68% confidence level (CL).\nThese uncertainties are frequency-dependent; however,\nwe adopt a conservative approach and select the largest\nuncertainty across the entire frequency range for both\nmagnitude and phase. The corresponding maximum un-\ncertainties are summarized in Table I.\nInterferometer\nLHO\nLLO\nMagnitude\n6.9%\n4.1%\nPhase\n4.3\u25e6\n5.1\u25e6\nTABLE I. Maximum calibration uncertainties on the mag-\nnitude and phase of detector strain at 68% confidence level\n(CL), for the LIGO Hanford (LHO) and LIGO Livingston\n(LLO) detectors.\nProvided it remains approximately below 5 degrees,\nthe phase uncertainty does not introduce a significant\nbias in stochastic background estimates [154]. Hence we\nrestrict the calculation of calibration uncertainty to the\nmagnitude term only, taking the quadrature sum of the\nmagnitude uncertainties for each detector strain. This\nyields a final value of \u03c3\u039b = 8.1%.\nIV.\nRESULTS\nWe present results obtained with the analysis methods\ndescribed above using data from the O4a observing run\ncombined with data from the O1\u2212O3 observing runs.\nWe do not find evidence of a background signal in our\nanalyses, as outlined below, hence we set upper limits on\nseveral models. We perform three different analyses: (i)\nwe calculate the point estimate spectrum and variance of\nthe GWB signal using cross-correlation optimal filtering\n(Sec. IV A) and set upper limits (Sec. IV B) considering\na power-law spectral model for the overall background,\nboth in the case of a fixed known spectral index \u03b1, and\nmarginalizing over \u03b1; (ii) we set upper limits on SVT\nmodel parameters (Sec. IV C); and (iii) we perform joint\ninference in the case where a correlated magnetic signal\nis present in the data together with a GWB (Sec. IV D).\nA.\nCross-correlation estimates\nWe produce broadband estimates\n\u02c6\u2126\u03b1 and associ-\nated variance using an optimal filter for three different\npower-law models motivated by different potential GWB\nsources:\n\u2022 \u03b1 = 0 corresponds to a scale-invariant signal, which\napproximately describes a GWB arising from a cos-\nmic string network [26, 155\u2013158] or slow-roll infla-\ntion [64, 159, 160] in the LVK frequency band.\n\n19\n20\n40\n60\n80\n100\n120\n140\n160\nf (Hz)\n\u22121.0\n\u22120.5\n0.0\n0.5\n1.0\n\u02c6\u21260(f)\n\u00d710\u22125\nO1 \u2212O4a\n1\u03c3 CL O1 \u2212O4a\n1\u03c3 CL O4a\n20\n30\n40\n50\n60\nf (Hz)\n\u22122.0\n\u22121.5\n\u22121.0\n\u22120.5\n0.0\n0.5\n1.0\n1.5\n2.0 \u00d710\u22126\nFIG. 2. Cross-correlation spectrum obtained from O1 to O4a data. The black lines denote the boundaries of the 1\u03c3 region: the\ndotted line shows results calculated from O4a data, while the solid line corresponds to the full O1\u2212O4a dataset. The spectrum\nremains consistent with 0 across all frequency bins, indicating no evidence of a signal. The left panel shows the spectrum over\nthe 20\u2212160 Hz range, while the right panel zooms in on frequencies below 60 Hz to highlight the contribution from O4a data\nat these frequencies.\nPower law\nfO4a\n99%[Hz]\n\u02c6\u2126O4a/10\u22129\nfO1\u2212O4a\n99%\n[Hz]\n\u02c6\u2126O1\u2212O4a/10\u22129\n0\n54.8\n\u22122.2 \u00b1 5.8\n58.2\n\u22121.3 \u00b1 4.7\n2/3\n83.6\n\u22121.6 \u00b1 4.5\n86.8\n\u22121.2 \u00b1 3.5\n3\n376.7\n\u22120.1 \u00b1 0.8\n336.6\n\u22120.3 \u00b1 0.6\nTABLE II. Search results for an isotropic GWB using cross-correlation optimal filtering for power-law GWBs with \u03b1 = 0, 2/3, 3.\nFor each case, we report the point estimate and associated 1\u03c3 uncertainty of the amplitude \u02c6\u2126\u03b1 at 25 Hz, along with the frequency\nrange from 20 Hz to f99%, which contains 99% of the total sensitivity. These estimates are derived by combining the individual\nvalues from independent frequency bins following Eq. (11). The final two columns show results obtained by combining data\nfrom all observing runs (O1\u2212O4a) following the prescription shown in [74] ( Eq. (7)). Note that Virgo data contributed to the\nO3 measurements, implying three separate baseline contributions to the O3 results.\n\u2022 \u03b1 = 2/3 characterizes the CBC GWB when the\ninspiral phase dominates, which is a good approxi-\nmation in the LVK frequency band [161]. However,\nthis approximation may break down for mergers of\nbinaries originating from Population III stars [162]\nor for heavy BBH mergers with masses exceeding\nthe pair-instability mass gap [163].\n\u2022 \u03b1 = 3 is a fiducial choice which provides an ap-\nproximate description of a subset of astrophysical\nsources, such as supernovae [8, 164]. It also corre-\nsponds to a GWB with a flat strain power spectral\ndensity, following Sh(f) \u221df \u22123\u2126GW(f) [108]. This\nis the spectral shape detectors are most sensitive to\nby construction, as the optimal filter depends solely\non the noise PSD, hence frequencies are weighted\naccording to the detector sensitivity thereby maxi-\nmizing the cross-correlation search sensitivity.\nThe point estimate spectrum \u02c6\u21260(f) computed as de-\nfined in Eq. (7) is shown in Fig. 2.\nThe 1\u03c3 contours\ncalculated from O4a data as well as the entire O1\u2212O4a\ndataset are compatible with 0, as expected in the pres-\nence of uncorrelated noise and in the absence of a corre-\nlated gravitational-wave signal. This behavior is consis-\ntent with the expectation that, after applying the data\nquality cuts described in Section III, the data remain\ndominated by Gaussian noise.\nThis is further demon-\nstrated by the Kolmogorov-Smirnov (KS) test, which re-\nturns a p-value of p = 0.99 in favour of Gaussianity.\nPoint estimates \u02c6\u2126\u03b1 and 1\u03c3 uncertainty using the O4a\ndata only as well as combined results from all the ad-\nvanced observing runs are presented in Table II. Point\nestimates for all spectral models are consistent with 0\nwithin 1\u03c3, which implies no detection of a GWB. We also\nreport the upper edge of the frequency band that con-\ntributes 99% of the sensitivity to each spectral-weighted\nsearch, f99%.\nWe observe a decrease in variance with increasing spec-\ntral index, which is expected since, as mentioned above,\nour search is most sensitive to a flat strain spectrum\n(\u03b1 = 3). Notably, the sensitivity improvement compared\nto O1\u2212O3 results is a factor of 1.6 for \u03b1 = 0, 1.6 for\n\u03b1 = 2/3, and 1.4 for \u03b1 = 3. This is driven by the fact\nthat the most significant sensitivity enhancement in our\ndetectors occurred at lower frequencies [131], below 40\nHz, as discussed below.\n\n20\n10\n100\n1000\nFrequency [Hz]\n10\u22123\n10\u22122\n10\u22121\n100\n101\n102\n103\nASD Ratio ( O3/O4a )\nLHO\nLLO\nFIG. 3. Ratio of the detector strain sensitivity curves between\nO3 and O4a for LHO (blue) and LLO (red). A ratio above\nunity indicates an improvement in sensitivity compared to\nO3.\nAltogether, these observations indicate that there is no\nevidence for a detectable GWB in the analyzed data. We\nalso note that O4a contributes primarily at frequencies\nbelow 60 Hz, as highlighted in the right-hand-side panel\nof Fig. 2 which shows the portion of the spectrum in the\n20 \u221260 Hz band, where the 1\u03c3 contours from O4a and\nO1\u2212O4a data are almost overlapping.\nThe frequency\ndependence of the sensitivity change between O4a and\nO3 is described in Fig. 3, which shows the ratio of the\nPSDs calculated in the two runs. We observe that this\nratio lies consistently above 1 in the range 10 \u221260 Hz,\nwhich matches the range highlighted in Fig. 3 where\nthe O4a data contributes the most to the measurement\nof a stochastic spectrum. The effect of this frequency-\ndependent improvement in sensitivity to the GWB be-\ntween O4a and past runs is further quantified below.\nB.\nUpper Limits on the GWB\nGiven the absence of evidence for a signal (see Ta-\nble II), we set upper limits on the amplitude of the GWB,\nassuming a power-law model as in Eq. (5). The narrow-\nband estimators \u02c6\u21260(f) and \u03c30(f) are employed in infer-\nence as described in Sec. II B, where the frequency lines\ndescribed in Sec. III E are notched from the spectra. We\nexplore different priors for both the amplitude and the\nspectral index. Specifically, we consider uniform and log-\nuniform priors for the amplitude, and uniform and Gaus-\nsian priors on the spectral index. A log-uniform prior\nis more sensitive to signals of small amplitude, yield-\ning tighter constraints, while a uniform prior provides\nmore conservative limits. In both cases, we set the prior\nrange for the \u2126ref parameter between \u2126ref,min = 10\u221213\nand \u2126ref,max = 10\u22126.\nWe perform a fixed model analysis, fixing the spectral\nindex to {0, 2/3, 3}, where each value corresponds to a\nspecific source as indicated above. We also perform joint\ninference on the amplitude and spectral index, where we\ntest both a Gaussian prior and uniform prior on the lat-\nter. The uniform prior range is set to \u03b1 \u2208[\u22127, 7] 5. In\nthe case of a Gaussian prior on \u03b1, we impose zero mean\nand a standard deviation of\nlog10 \u2126ref,max \u2212log10 \u2126ref,min\n2\n= 3.5.\n(17)\nThe choice of the prior over \u03b1 can be understood as\nfollows.\nThe log-uniform prior over \u2126ref induces some\nimplicit prior over \u03b1 that can be shown [113] to be a\ntriangular prior centered on \u03b1 = 0 and non-zero for\n|\u03b1| \u2264(log10 \u2126ref,max \u2212log10 \u2126ref,min). To avoid a van-\nishing prior outside of this range, we choose a Gaussian\nprior for \u03b1 with a standard deviation comparable with\nthe triangular prior [113].\nWe set spectral-independent constraints on the signal\namplitude by marginalizing over the spectral index pos-\nteriors obtained with the Gaussian prior. We take the\nresults obtained with the log-uniform prior on the ampli-\ntude as our main result.\nTable III summarizes results for the fixed spectral in-\ndex and marginalized analyses. We set 95% confidence\nlevel upper limits on \u2126ref at fref = 25 Hz at individual\nvalues of \u03b1, \u2126(\u03b1)\nref , fixing the \u03b1 prior to a delta function\nat the chosen values; we also set upper limits marginal-\nized over the Gaussian \u03b1 posterior. For comparison, we\nreport the corresponding upper limits from O1\u2212O3 anal-\nyses. As expected, log-uniform priors on the background\namplitude yield tighter constraints compared to uniform\npriors. Broadband constraints at 25 Hz are tightest for\n\u03b1 = 3 as this corresponds to a flat strain power spectrum,\nyielding the most broadband detectable signal, while con-\nstraints are weakest for a scale-invariant spectrum as this\nsignal corresponds to a strain power spectrum with the\nmost negative spectral index out of the set. Furthermore,\nmarginalized results over the spectral index yield overall\nweaker constraints as these admit higher uncertainty on\nthe signal model. Overall, we observe improvements in\nthe upper limits ranging from a factor of 1.2 to 2.3.\nPosterior distributions for \u2126ref and \u03b1 obtained in these\nanalyses are shown in Fig. 4 assuming a log-uniform prior\non \u2126ref and either a Gaussian or uniform prior on \u03b1. As\nmay be observed in Fig. 4, \u03b1 is not constrained, and the\nprior on \u03b1 has little impact on the \u2126ref posteriors. The\nBayes factor comparing the signal-versus-noise hypothe-\nsis to the noise-only hypothesis is log10 B = \u22120.19 \u00b1 0.03\n(log10 B = \u22120.11 \u00b1 0.03) at 68% confidence level assum-\ning a Gaussian (uniform) prior on \u03b1, further confirming\nno evidence of a signal in the data.\n5 This prior has been widened with respect to past analyses [74],\nwhich employed \u03b1 \u2208[\u22125, 5], to investigate a small mode in the\nposterior in \u03b1 which appeared at the edge of the prior range, as\ndiscussed below.\n\n21\nUniform prior\nLog-uniform prior\n\u03b1\nO1-O4a\nO1-O3\nImprovement\nO1-O4a\nO1-O3\nImprovement\n0\n8.6 \u00d7 10\u22129 1.7 \u00d7 10\u22128\n2.0\n2.8 \u00d7 10\u22129\n5.8 \u00d7 10\u22129\n2.1\n2/3\n6.3 \u00d7 10\u22129 1.2 \u00d7 10\u22128\n1.9\n2.0 \u00d7 10\u22129\n3.4 \u00d7 10\u22129\n1.7\n3\n1.0 \u00d7 10\u22129 1.3 \u00d7 10\u22129\n1.3\n3.2 \u00d7 10\u221210 3.9 \u00d7 10\u221210\n1.2\nMarginalized 1.5 \u00d7 10\u22128 2.7 \u00d7 10\u22128\n1.8\n2.9 \u00d7 10\u22129\n6.6 \u00d7 10\u22129\n2.3\nTABLE III. Upper limits at 95% CL on the amplitude \u2126ref of the GWB assuming uniform (left) and log-uniform (right) prior.\nWe quote the upper limits obtained employing data up to the O4a data run (O1\u2212O4a), comparing these with those obtained\npreviously [74] (O1\u2212O3), at individual values of \u03b1 (which corresponds to imposing a delta function prior on \u03b1 at the quoted\nvalue), and marginalized over the \u03b1 posterior (assuming a Gaussian prior on \u03b1). We observe an overall improvement between\na factor 1.2 to 2.3. The improvement in upper limits compared to O3 is more significant for smaller spectral indices. This is\nbecause the greatest enhancement in detector sensitivity occurred at low frequencies. Furthermore, the difference between the\nupper limit for \u03b1 = 0 and the marginalized case is minimal, due to statistical fluctuations from the MCMC.\nFIG. 4. Posterior distributions on the power-law model pa-\nrameters {\u2126ref, \u03b1} obtained assuming a log-uniform prior on\n\u2126ref and either a Gaussian (blue) or a uniform (red) prior on\n\u03b1. Prior functions for the \u03b1 parameter are included in the\ncorresponding one-dimensional panel (gray dashed lines).\nWe point out a small narrow mode that appears in\nthe posterior plot at \u03b1 = 5, present for both prior as-\nsumptions and more evident in the case of a uniform\nprior on \u03b1.\nNote that \u03b1 = 5 is not associated with\nany known physical GW signals and usually coincides\nwith the edge of the broad prior range assumed for this\nanalysis, however in this case the prior was broadened\nto confirm no railing was occurring. This mode has been\ntraced back to weak, broad-band residual noise coherence\nbetween the LHO and LLO detectors during O4a in the\n650 \u2212850 Hz band, which corresponds to the frequency\nrange most sensitive to an \u03b1 = 5 power-law signal. The\nORF introduced in Eq. (2) for the LHO\u2013LLO baseline is\nhighly suppressed at these frequencies (to \u223c0.2 \u22120.1%\nrelative to its magnitude at 1 Hz), strongly suggesting\nthis weak coherence is detector noise and not GW sig-\nnal.\nExcluding this frequency range from the analysis\n\u22121\n0\n1\n2\n3\n4\n\u03b1\n10\u22129\n10\u22128\n\u2126(\u03b1)\nref\nO1-O3 UL\nO1-O4a UL\n\u22121\n0\n1\n2\n3\n4\n\u03b1\n1.0\n1.5\n2.0\nO3/O4a\nFIG. 5. Upper limits (UL) on \u2126(\u03b1)\nref at 95% CL as a function\nof \u03b1, obtained assuming the GWB is described by a power-\nlaw model using a log-uniform prior on the amplitude \u2126(\u03b1)\nref .\nThe blue curve shows the results using data from O1 to O3,\nwhile the red curve includes O4a data as well. The inset plot\nshows the ratio between the two sets of limits, highlighting\nimprovement in O4a as a function of spectral weighting.\nremoves this feature completely. The four 60 Hz power-\nline harmonics in this range, [660, 720, 780, 840] Hz,\nappear significantly wider and noisier than in past ob-\nserving runs, hence notches around these lines have been\nwidened accordingly for this analysis. Numerous other\nweak unidentified noise features such as broadened lines\nand bumps have been found in both detectors. While\nthese are not loud enough to significantly impact the\nanalysis presented here, as demonstrated by broad-band\nsignal point estimates (Table II) as well as the Bayes\u2019\nfactors above, the significance of this feature will be re-\nvisited in the next portion of the O4 data.\nFinally, Fig. 5 shows upper limits on \u2126ref at 95% CL\nas a function of \u03b1. Note that \u03b1 values in this plot are\nnot directly motivated by specific sources, but rather\nare chosen to highlight the overall trend: upper limits\ndecrease as the spectral index increases, which is ex-\n\n22\npected due to the extrapolation of the low-frequency sen-\nsitivity at higher frequencies, and as a consequence of\n\u2126GW \u221df 3Sh(f). Fig. 5 also includes upper limits ob-\ntained up to and including the O3 data run. The relative\nimprovement between these and the limits obtained in-\ncluding O4a decreases as \u03b1 increases, indicating that the\nsensitivity enhancement between runs is more significant\nat lower frequencies, as discussed above.\nC.\nNon-GR polarizations\nWe employ the approach first presented in [113] to\nconstrain potential deviations from GR. The detection\nof scalar or vector polarization modes would provide di-\nrect evidence of a violation of GR, whereas their absence\nallows us to place stringent constraints on extended the-\nories of gravity.\nMultiple runs with differently polarized backgrounds\nwere conducted.\nFirst, we consider a mixed-polarized\nbackground, as introduced in Sec. II C. In this scenario,\nthe parameters of our model are\n\u0398 = {\u2126ref,T, \u2126ref,V, \u2126ref,S, \u03b1T, \u03b1V, \u03b1S} .\n(18)\nWe set a log-uniform prior on the amplitudes \u2126ref,(p),\nfor (p) = {T, V, S}, over the range 10\u221213 to 10\u22126 and a\nGaussian prior on the spectral indices, centered at 0 with\na standard deviation of 3.5. We set 95% CL upper limits\non \u2126ref,(p), presented in the third column of Table IV.\nWe find an improvement in the upper limits of over a\nfactor of 2 with respect to O3 results [74]. It is worth\nnoting that the upper limit for the scalar-polarized case\nis less stringent as the ORF for scalar polarization is ap-\nproximately three times smaller in amplitude than those\nfor other polarizations [113]. As a result, our detector\nnetwork is inherently less sensitive to a scalar-polarized\nbackground.\nPolarization O1\u2212O3 O1\u2212O4a Improvement\nTensor\n6.4 \u00b7 10\u22129 2.6 \u00b7 10\u22129\n\u223c2.5\nVector\n7.9 \u00b7 10\u22129 2.9 \u00b7 10\u22129\n\u223c2.7\nScalar\n2.1 \u00b7 10\u22128 7.4 \u00b7 10\u22129\n\u223c2.8\nTABLE IV. Upper limits (ULs) at 95% confidence level (CL)\non the amplitude of each individual polarization assuming a\nmixed-polarized background. The are improved by over a fac-\ntor of 2 compared to ULs obtained from O1\u2212O3 data [74]. We\nobserve the UL for the scalar-polarized case is less stringent as\nthe ORF for scalar polarization is smaller in amplitude than\nthose for other polarizations [113].\nAdditionally, we set upper limits on the amplitudes\n\u2126ref,T(25Hz) \u22642.9 \u00b7 10\u22129, \u2126ref,V(25Hz) \u22642.7 \u00b7 10\u22129 and\n\u2126ref,S(25Hz) \u22642.9\u00b710\u22129, assuming single-polarized back-\ngrounds. The upper limits are similar across polariza-\ntions due to the reduced detector network in O4a, since\nonly LHO and LLO were operational, unlike O3 which\nincluded all three detectors. This limits our ability to\ndistinguish polarization modes.\nThe signal versus noise hypothesis Bayes factor yields\nlog10 B = \u22120.87 \u00b1 0.01 at 68% confidence level, indicat-\ning no evidence for the presence of a signal in our data.\nIn this case, the signal is defined as the equal-weighted\ncombination of the individual polarization components,\n{T, V, S}, as well as their combinations: tensor\u2013vector\n(TV), tensor\u2013scalar (TS), vector\u2013scalar (VS), and ten-\nsor\u2013vector\u2013scalar (TVS). This approach treats all signal\nconfigurations equally.\nAdditionally, the Bayes factor for non-GR versus\nGR-supported polarized backgrounds yields log10 B =\n\u22120.44\u00b10.03 at 68% confidence level. This result suggests\nthat a tensor-polarized background (in accordance with\nGR) is favoured over vector, scalar, and mixed-polarized\nalternatives. However, in the absence of a detection we\nexpect this result to be driven by the Occam penalty fac-\ntor introduced by overfitting un-informed parameters in\nthe search.\nD.\nJoint fit for GWB and magnetic noise\nCorrelated magnetic noise can provide a significant\nlimitation to the search for an isotropic stochastic sig-\nnal [112, 144\u2013146]. To mitigate this, the likelihood pre-\nsented in Eq. (12) may be extended to jointly model cor-\nrelated magnetic noise appearing in the GW detectors\nand a GWB power-law signal, as described in [165]:\n\u2126GW(f|\u0398) = \u2126refF\u03b1(f) + \u2126MAG(f|\u0398MAG) .\n(19)\nIn Section III F, we showed that correlated magnetic\nnoise is not expected to contaminate O4a data.\nNev-\nertheless, this analysis provides a complementary check\nby simultaneously fitting both the GWB and the corre-\nlated magnetic noise. Instead of utilizing the measured\ncoupling functions at the detectors from Section III F, we\nnow model the magnetic term \u2126MAG with the parameters\n\u0398MAG = {\u03baI, \u03baJ, \u03b2I, \u03b2J}, approximating the inside-to-\nstrain magnetic coupling functions TI,ITS(f) as a simple\npower law,\n|TI,ITS(f)| = \u03baI\n\u0012\nf\n10Hz\n\u0013\u2212\u03b2I\n,\n(20)\nwhere \u03baI is the magnitude of the amplitude at 10 Hz and\n\u03b2I is the spectral index of the power law.\nThe prior\ndistribution for \u03baI is log-uniform in the range 10\u221225 to\n10\u221222 pT\u22121 for both detectors and the prior on the spec-\ntral index \u03b2I is uniform in the range 0 \u221212 and 1 \u221210\nfor HLO and LLO respectively, related to measured min-\nimum and maximum values of the spectral index during\nmagnetic injections. As before, the GWB model param-\neters are \u2126ref and \u03b1. This allows us to estimate either\nthe evidence for a simultaneous measurement of a back-\nground and correlated magnetic noise, or estimate the\n\n23\nevidence for correlated magnetic noise only.\nWe set joint constraints on the power-law GWB and\nthe magnetic correlated noise, employing the same priors\nfor the magnetic parameters as in the O3 analysis [74].\nWe find the log Bayes factor comparing a magnetic noise\nmodel to a (Gaussian) noise-only model is log10 BMAG\nN\n=\n\u22120.048, indicating no evidence in favour of the presence\nof magnetic noise. We also find that for a joint model\nwith a power-law background and magnetic noise mod-\neled as described above that log10 BPL+MAG\nN\n= \u22120.306,\nshowing no preference for such a model compared to a\nnoise-only model.\nV.\nASTROPHYSICAL IMPLICATIONS\nLeveraging the upper limits on the GWB presented in\nSection IV B, we examine the implications of these results\nfor the GWB of astrophysical origin, namely from the co-\nalescing population of compact binaries including BBHs,\nBNSs, and NSBHs. We compare our upper limits to the\nmost recent predictions for the energy density spectrum\nassociated with different classes of CBC sources. In par-\nticular for BBHs, following Ref. [76], we combine BBH\nobservations in the local Universe with stochastic upper\nlimits to constrain their merger rate at high redshifts, and\npredict the uncertainty in the BBH background using a\nfully GW data-driven approach.\nA.\nCBC Model\nTo model the GWB from binary systems we follow in\npart the approach of LVK isotropic search papers from\nthe O1 to O3 observing runs [74, 106, 107, 166], and ad-\nditionally we introduce advances in our knowledge of the\nCBC population [89, 167, 168]. We categorize the pop-\nulation into classes, each labeled by k, to differentiate\nbetween BBHs, BNSs and NSBHs. Each class is charac-\nterized by distinct values of source parameters, such as\nmasses and spins, which we denote as \u03b8k. The total as-\ntrophysical background is then the sum of contributions\nfrom all classes. The contribution of class k to the back-\nground can be expressed as an integral over the redshift\nz, given by [82, 169\u2013171]\n\u2126GW(f; \u03b8k) =\nf\n\u03c1cH0\nZ zmax\n0\ndz\nRm(z; \u03b8k)\u27e8dEGW\ndfs (fs; \u03b8k)\u27e9\n(1 + z)E(\u2126m,0, \u2126\u039b,0, z) ,\n(21)\nwhere\nRm(z; \u03b8k)\ndenotes\nthe\nbinary\nmerger\nrate\nin\nthe\nsource\nframe\nper\nunit\ncomoving\nvolume,\n\u27e8dEGW/dfs(fs, \u03b8k)\u27e9is the energy spectrum emitted by\na single binary evaluated in terms of the source fre-\nquency fs = (1 + z)f and averaged over the ensem-\nble properties of source class k, and E(\u2126m,0, \u2126\u039b,0, z) =\np\n\u2126m,0(1 + z)3 + \u2126\u039b,0 accounts for the dependence of co-\nmoving volume on cosmology, assuming \u2126\u039b,0 = 1\u2212\u2126m,0.\nWe impose an upper redshift cutoff at zmax = 10, beyond\nwhich the compact binary merger rate in conventional\nformation scenarios is expected to be negligible [172]. We\ndo not consider potential contributions to the GWB from\nformation channels involving Population III stars [173] or\nprimordial black holes [174, 175].\nThe energy spectrum \u27e8dEGW/dfs\u27e9is determined from\nthe\nstrain\nwaveform\nof\nthe\nbinary\nsystem.\nFor\ncomputing the backgrounds of BBH and NSBH we\nuse IMRPhenomXP, a phenomenological inspiral-merger-\nringdown frequency-domain model for gravitational-wave\nsignals emitted by quasi-circular precessing BBHs [176,\n177]. For BNS background computation, we employ the\nIMRPhenomXP NRTidalv3 waveform model, which tapers\nthe merger-ringdown part from the baseline IMRPhenomXP\nmodel and has the option to include tidal effects [178\u2013\n180].\nTo compute the GWB from CBCs throughout\nthe Universe according to Eq. (21), we use methods de-\nveloped for the GWB calculation in [74, 84], as well\nas popstock, a Python-based module that predicts the\nbackground spectrum and its uncertainty given a CBC\npopulation and merger rate evolution [83].\nB.\nBinary black holes\nTo model the BBH background we generally follow the\napproach in [74] with some adjustments in the presumed\nmass, redshift, and spin distributions of BBHs.\nIn [74] it was assumed that the BBH primary mass dis-\ntribution is approximated by a mixture between a Gaus-\nsian peak near 35 M\u2299and a power-law continuum, that\nmass ratios are power-law distributed, and, for simplicity,\nthat spins are negligible. We update these assumptions\nto match the latest understanding of the black hole pop-\nulation in GWTC-4 [88]. Following [89], we assume that\nblack hole primary masses follow a mixture between two\nGaussians, centered near 10 M\u2299and 35 M\u2299, and a broken\npower-law continuum extending up to 200 M\u2299. Whereas\nwe previously neglected spins, we now include a realistic\nmodel for the black hole spin distribution; we follow [89]\nand assume spin magnitudes are described by a truncated\nnormal distribution and spin orientations by a mixture\nbetween isotropic and preferentially-oriented subpopula-\ntions. Black hole mass ratios are again assumed to be\npower-law distributed. As in [74], we do not fix the pa-\nrameters of these models, but instead show a projection\nfor \u2126BBH(f) that self-consistently includes observational\nuncertainties in the BBH mass, spin, and mass ratio dis-\ntributions.\nPrevious forecasts of the BBH background included\nuncertainties in the ensemble of intrinsic black hole prop-\nerties and the local BBH merger rate, while imposing a\nfixed fiducial model describing how this rate evolved with\nredshift. In [74], for example, we assumed a BBH birth\nrate proportional to low-metallicity star formation, with\na power-law time delay distribution between binary for-\nmation and merger. Here, we revise our projections to\n\n24\nadditionally reflect systematic uncertainties in the BBH\nmerger rate. We assume the BBH merger rate density\nfollows the broken power law [181]\nRBBH(z) = C(\u03b1z, \u03b2z, zp)\nR0(1 + z)\u03b1z\n1 +\n\u0010\n1+z\n1+zp\n\u0011\u03b1z+\u03b2z ,\n(22)\nwhere parameters \u03b1z and \u03b2z represent the low and high\nredshift power laws to which the merger rate history\nasymptotes, respectively, while zp is the redshift at which\nthe merger rate history peaks. Specifically, Eq. (22) im-\nplies that RBBH(z) \u221d(1 + z)\u03b1z for redshifts z \u226azp and\nRBBH(z) \u221d(1 + z)\u2212\u03b2z for z \u226bzp, and the normalization\nconstant C(\u03b1z, \u03b2z, zp) is defined such that RBBH(z) = R0\nat z = 0. This parametrization allows us to cover a broad\nrange of theoretical predictions for the redshift evolution\nof the BBH merger rate. It accommodates scenarios in-\nvolving isolated binary evolution, where the merger rate\nclosely follows the metallicity-dependent cosmic star for-\nmation rate with a distribution of time delays between\nformation and merger [182\u2013184]. At the same time, it\ncan represent dynamically assembled mergers in dense\nstar clusters, which are less directly tied to star forma-\ntion and often exhibit a merger rate that peaks at higher\nredshifts [185, 186].\nWe combine all direct detections of BBHs in GWTC-4\nwith our updated constraints on the astrophysical GWB\nto measure the underlying distributions of BBH primary\nmasses, mass ratios, spins, and redshifts.\nWe assume\nthese distributions are well-described by the models listed\nabove, and we follow the methods presented in [76\u201378,\n89]. In order to self-consistently combine data from direct\nBBH detections with constraints on the GWB, we adopt\na factorized likelihood given by\np(\u02c6\u21260, {di}|\u039bBBH) = pBBH({di}|\u039bBBH)\u00d7pstoch(\u02c6\u21260|\u039bBBH) .\n(23)\nHere, pstoch(\u02c6\u21260|\u039bBBH) is the likelihood of our cross-\ncorrelation\nmeasurements\n[see\nEq.\n(12)],\ngiven\na\nBBH population model denoted \u039bBBH.\nMeanwhile,\npBBH({di}|\u039bBBH) is the likelihood of the direct compact\nbinary detections comprising GWTC-4 [89].\nIn prac-\ntice, rather than evaluating Eq. (23) directly, we sam-\nple the likelihood in a two step process, first sampling\nfrom the posterior p\u039bBBH|BBH({di}) and then rejection\nsampling these draws using pstoch(\u02c6\u21260|\u039bBBH).\nThe re-\nsulting \u2126BBH(f) spectra calculated from each posterior\nsample \u039b after rejection sampling are shown in the left-\nhand side of Fig. 6. At a reference frequency of 25 Hz,\nwe predict \u2126BBH(25 Hz) = 0.8+1.3\n\u22120.5 \u00d7 10\u22129 before reject-\ning according to the GWB upper limits.\nAfter rejec-\ntion sampling, the predicted BBH GWB amplitude is\n\u2126BBH(25 Hz) = 0.8+1.1\n\u22120.5 \u00d7 10\u22129. Here and henceforth, all\nuncertainties are quoted as 90% credible intervals.\nThe inferred BBH merger rate RBBH(z) is shown in the\nright side of Fig. 6. Black and red curves again show 90%\ncredible bounds and individual posterior samples, respec-\ntively.\nThe present-day merger rate is inferred to be\nR0 = 15.4+6.0\n\u22124.5 Gpc\u22123 yr\u22121. For comparison, dotted black\ncurves indicate 90% credible bounds obtained previously\nwhen analyzing BBH mergers in GWTC-3 [168, 188].\nNew results are consistent with previous estimates, al-\nthough it is now found that the rate with which RBBH(z)\nincreases (\u03b1z = 3.2+1.1\n\u22121.0) is near the upper end of previ-\nous bounds (\u03b1z = 2.7+2.2\n\u22121.9). The high redshift parame-\nters \u03b2z and zp remain poorly constrained (\u03b2z = 5.1+4.5\n\u22124.6,\nzp = 2.6+1.2\n\u22121.3).\nThe forecasted \u2126BBH(25 Hz) reported above is approx-\nimately a factor of two larger than previously estimated\nin [74] and [168]. This increase is due primarily to two\neffects. The increased sample of direct compact binary\ndetections indicates that the BBH merger rate likely in-\ncreases more quickly with redshift than previously mea-\nsured. Secondly, whereas past forecasts used simple para-\nmetric estimates for the energy spectrum of a given bi-\nnary [189], our updated forecasts adopt the significantly\nmore mature IMRPhenomXP waveform model to compute\nradiated energy.\nThe non-detection of a stochastic background provides\nan additional constraint on the population history of\nBBHs, effectively ruling out scenarios with high merger\nrates at large redshifts that would otherwise yield a de-\ntectable background signal [76]. While the background\nupper limits effectively do not impact the inferred merger\nrate, these imply a modest tightening of the upper uncer-\ntainty bound on the BBH background amplitude as de-\nscribed above. This result implies that, when modeling\nthe BBH merger history via Eq. (22), the direct detec-\ntions already require \u03b1z to be sufficiently small that most\npossible astrophysical backgrounds lie below the current\ndetection threshold. In future observing runs, the exact\ndegree to which stochastic search results are or are not\ninformative will depend on the achieved sensitivity and\nrun duration, as well as updated inference of \u03b1z.\nC.\nBinary neutron stars\nSince neither the local merger rate nor the mass and\nspin distribution of BNS mergers are well constrained\nfrom current GW catalogs, we cannot adopt detailed\ndata-driven models of the BNS population. Instead, we\nforecast the astrophysical background from BNSs using\nthe methodology of [74], which adopts a fixed star for-\nmation history convoluted with a time delay distribution\nand simplified assumptions for mass and spin. We as-\nsume that BNS progenitor formation follows the star for-\nmation rate described in [190] (Eq.(22) with \u03b1z = 2.6,\n\u03b2z = 3.6 and zp = 2.2), with a distribution p(td) \u223ct\u22121\nd\nof time delays td between binary formation and merger,\nwhere 20 Myr < td < 13.5 Gyr. Following [89], we as-\nsume a simple fixed population model, with a uniform\nmass distribution between 1 \u22122.5 M\u2299and isotropic spin\norientations with uniformly distributed spin magnitudes\nbelow 0.4.\nUnder these assumptions, the local merger\n\n25\n101\n102\n103\nf [Hz]\n10\u221211\n10\u221210\n10\u22129\n10\u22128\n10\u22127\n10\u22126\n\u2126BBH(f)\nO1-O4a (2\u03c3)\n0\n1\n2\n3\n4\n5\nRedshift\n10\u22121\n100\n101\n102\n103\n104\nRBBH(z) [Gpc\u22123 yr\u22121]\nO3\nO4a\nFIG. 6.\nLeft: Forecast for the stochastic energy-density spectrum of the BBH population, given the population of direct BBH\ndetections within the LVK GWTC-4 catalog [89] and the GWB upper limit presented here. The black curves indicate 90%\ncredible bounds on \u2126BBH(f), while red traces show individual posterior samples on the energy-density spectrum, obtained by\nsampling over the possible mass, spin, and redshift distributions of BBH mergers. For comparison, the blue curve indicates\nthe 2\u03c3 PI curve calculated using O1\u2212O4a HLV data [150], integrated over all observing runs to date. Right: Inferred redshift\nevolution of the BBH merger rate density, measured hierarchically using the direct BBH detections in GWTC-4 and the GWB\nupper limit. Solid black and red lines again mark 90% credible bounds and individual posterior samples, respectively, while\ndotted black lines denote the 90% credible bounds obtained previously with GWTC-3 [168].\n101\n102\n103\nf [Hz]\n10\u221211\n10\u221210\n10\u22129\n10\u22128\n\u2126GW(f)\nBBH\nBNS\nNSBH\n101\n102\nf [Hz]\n10\u221211\n10\u221210\n10\u22129\n10\u22128\n\u2126GW(f)\nTotal GWB\nMedian GWB\nO1-O4a (2\u03c3)\nO5 target (2\u03c3)\nFIG. 7.\nLeft: Projected astrophysical GWB contributions from BBH, BNS and NSBH coalescences. Shaded bands represent\nthe 90% credible bounds for each CBC class. Right: The solid purple line shows the median estimate of \u2126BBH+BNS+NSBH(f) as\na function of frequency, while the shaded purple band illustrates 90% credible uncertainties. We also show the 2\u03c3 PI sensitivity\ncurve calculated using data from stochastic isotropic searches O1 through O4a, considering the three HLV baselines. We include\nthe target 2\u03c3 PI curve for O5, assuming the target sensitivity curves for the HLV baselines as detailed in [187] and [91] .\nrate is estimated to be 61+113\n\u221248\nGpc\u22123yr\u22121. When mod-\neling \u2126BNS(f), we do not consider any tidal effects nor\ncontributions from a potential post-merger signal [191].\nThese modeling choices lead to an estimated BNS GWB\nshown in Fig. 7, specifically at the reference frequency of\n25 Hz, we predict \u2126BNS(25Hz) = 3.6+6.7\n\u22122.8 \u00d7 10\u221211.\nD.\nNeutron star-black hole binaries\nSimilar to BNSs, few compact binaries with masses\nconsistent with NSBH systems have been observed [192\u2013\n194], and so the details of the NSBH population remain\nlargely unknown. As in the BNS case above, we again\nfollow the simplified modeling approach undertaken pre-\nviously in [168]. The black hole masses are drawn from a\nlog-uniform distribution between 3 and 50 M\u2299, and neu-\n\n26\ntron star masses from a uniform distribution between\n1 \u22122.5 M\u2299. Black hole spins are assumed to be isotrop-\nically distributed with uniform spin magnitude below\n0.99, while the neutron star spin follows the same dis-\ntribution as for BNS. The energy emission from NSBH\nbinaries is calculated using the BBH waveform model\nIMRPhenomXP, which provides a reliable approximation,\nespecially for systems with large mass ratios [195]. How-\never, the model does not include tidal deformability or\nthe possibility of tidal disruption of the neutron star, ef-\nfects that can affect the emitted GW signal from binaries\nwith more comparable component masses [196]. For the\ngiven population model, the local merger rate of NSBH\nbinaries is estimated to be 30+34\n\u221219 Gpc\u22123yr\u22121 [89]. More-\nover, we assume that the rate evolves in redshift in a\nmanner identical to BNS systems as described above.\nWith these assumptions we find \u2126NSBH(25Hz)\n=\n5.0+5.6\n\u22123.1 \u00d7 10\u221211. The 90% credible band over the whole\nfrequency range is displayed in Fig. 7.\nWe note that\n\u2126NSBH(f) is predicted to be significantly flatter than\nin past estimates, deviating noticeably from a canonical\nf 2/3 power law above \u223c30 Hz. This change is primarily\ndue to our adoption of an updated waveform model, in\nwhich the energy spectra of highly unequal-mass binaries\nare suppressed at high frequencies.\nE.\nTotal compact binary background\nIn Fig. 7 (right hand side), we present an updated\nestimate of the combined CBC GWB. Our model pre-\ndicts this background at \u2126BBH+BNS+NSBH(25Hz)\n=\n0.9+1.1\n\u22120.5 \u00d7 10\u22129. Additionally, we show the estimated sen-\nsitivity of the search described in this paper by presenting\nthe 2\u03c3 power-law integrated sensitivity curve including\ndata from O1\u2212O4a. Although our estimate for the back-\nground amplitude is below current limits, it may become\naccessible with the A+ configuration of the LIGO de-\ntectors. This may be seen from the comparison shown in\nFig. 7 with the target 2\u03c3 power-law integrated sensitivity\ncurve for the O5 data run (dashed curve), which includes\nsubstantial planned updates for the LIGO sites [131, 187]\nand the Virgo detector [91], and assumes one year of un-\ninterrupted data. It is important to note that these are\ntarget sensitivities that are expected to be reached by the\nend of the observing run, hence the O5 target sensitiv-\nity curve in Fig. 7 should be interpreted as an optimistic\nlimit for the observing scenario.\nVI.\nCONCLUSIONS\nIn this paper, we presented an isotropic search con-\nducted on data spanning from the first LVK observ-\ning run (O1) to the first part of the fourth observing\nrun (O4a), incorporating 115.51 days of new coincident\nLIGO-Hanford and LIGO-Livingston observation.\nNo\nevidence for a GWB is found, and we limit the net energy\ndensity of the GWB to \u2126ref(25 Hz) \u22642.9 \u00d7 10\u22129 under a\nlog-uniform prior (\u22641.5 \u00d7 10\u22128 under a uniform prior),\nan improvement of approximately a factor of 2 relative\nto previous bounds [74].\nWe additionally constrain alternative theories of grav-\nity by searching for non-standard gravitational-wave po-\nlarizations, including scalar and vector modes beyond\ngeneral relativity\u2019s tensor predictions. Our analysis im-\nproves existing bounds on these exotic polarization states\nby factors of two compared to previous datasets. How-\never, the absence of any detectable background prevents\nus from distinguishing between standard tensor-only sce-\nnarios and models incorporating additional polarization\nmodes.\nAs GWB searches improve in sensitivity, previously\nnegligible terrestrial noise sources, including magnetic\ncoupling from Schumann resonances and lightning activ-\nity, might contaminate our results and require characteri-\nzation and possible mitigation. To quantify the potential\nimpact of magnetic couplings on our result, we combine\nmeasurements of the magnetic environments surrounding\nLHO and LLO with measured transfer functions between\nexternal magnetic fields and measured strain, estimating\na net magnetic noise budget. We find that, given cur-\nrent search sensitivities, contamination due to correlated\nmagnetic environments does not significantly impact our\nresults.\nWe conclude by examining how close our sensitivity\nhas come to detecting the expected astrophysical back-\nground from the population of merging compact binaries\nacross the Universe.\nWe present updated estimates of\nenergy-density spectra arising from distant binary black\nholes, binary neutron stars, and neutron-star black hole\nbinaries, incorporating updated measurements of these\nsources\u2019 merger rates and demographics.\nCombining\nthese three source classes, we estimate a total astrophys-\nical background amplitude \u2126BBH+BNS+NSBH(25Hz) =\n0.9+1.1\n\u22120.5 \u00d7 10\u22129, consistent with but marginally smaller\nthan previous estimates [168]. This decrease is primar-\nily driven by lower inferred BNS and NSBH merger rates,\ngiven the lack of such systems detected during O4a. This\nestimate lies at least a factor of three below the sensitiv-\nity of our search, and is thus consistent with a current\nnon-detection of a GWB.\nSeveral companion papers further extend the method-\nology presented here and elaborate on additional impli-\ncations of a GWB non-detection. In this work, we have\nlimited ourselves to exploring a purely isotropic stochas-\ntic background. Alternate analyses targeting anisotropic\nbackgrounds are presented in [92].\nAdditionally, al-\nthough we have commented on the astrophysical back-\nground expected from merging compact binaries, there\nexist a host of predicted mechanisms that may yield\nGWBs of cosmological origin.\nImplications of our up-\ndated constraints on the GWB on such cosmological\nbackgrounds are discussed in [101].\n\n27\nVII.\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO consor-\ntium. The authors also gratefully acknowledge research\nsupport from these agencies as well as by the Council of\nScientific and Industrial Research of India, the Depart-\nment of Science and Technology, India, the Science & En-\ngineering Research Board (SERB), India, the Ministry of\nHuman Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00b4on (AEI), the Spanish Ministe-\nrio de Ciencia, Innovaci\u00b4on y Universidades, the European\nUnion NextGenerationEU/PRTR (PRTR-C17.I1), the\nICSC - CentroNazionale di Ricerca in High Performance\nComputing, Big Data and Quantum Computing, funded\nby the European Union NextGenerationEU, the Comuni-\ntat Auton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Commis-\nsion, the European Social Funds (ESF), the European\nRegional Development Funds (ERDF), the Royal Soci-\nety, the Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek - Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the Na-\ntional Research, Development and Innovation Office of\nHungary (NKFIH), the National Research Foundation of\nKorea, the Natural Sciences and Engineering Research\nCouncil of Canada (NSERC), the Canadian Foundation\nfor Innovation (CFI), the Brazilian Ministry of Science,\nTechnology, and Innovations, the International Center for\nTheoretical Physics South American Institute for Fun-\ndamental Research (ICTP-SAIFR), the Research Grants\nCouncil of Hong Kong, the National Natural Science\nFoundation of China (NSFC), the Israel Science Founda-\ntion (ISF), the US-Israel Binational Science Fund (BSF),\nthe Leverhulme Trust, the Research Corporation, the Na-\ntional Science and Technology Council (NSTC), Taiwan,\nthe United States Department of Energy, and the Kavli\nFoundation. The authors gratefully acknowledge the sup-\nport of the NSF, STFC, INFN and CNRS for provision\nof computational resources.\nThis work was supported\nby MEXT, the JSPS Leading-edge Research Infrastruc-\nture Program, JSPS Grant-in-Aid for Specially Promoted\nResearch 26000005, JSPS Grant-in-Aid for Scientific Re-\nsearch on Innovative Areas 2402: 24103006, 24103005,\nand 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. 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X. Adhikari\n,11 V. K. Adkins,12 S. Afroz\n,13 A. Agapito,14 D. Agarwal\n,15\nM. Agathos\n,16 N. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar\n,19 I.-L. Ahrend,20 L. Aiello\n,21, 22 A. Ain\n,23\nP. Ajith\n,24 T. Akutsu\n,25, 26 S. Albanesi\n,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9 C. All\u00b4en\u00b4e,31 A. Allocca\n,32, 4\nS. Al-Shammari,33 P. A. Altin\n,34 S. Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37\nF. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41\nM. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9 J. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49\nS. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11 S. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42\nM. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,55\nN. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 G. Ashton\n,58 Y. Aso\n,25, 59 L. Asprea,28 M. Assiduo,60, 61\nS. Assis de Souza Melo,62 S. M. Aston,63 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,64 K. AultONeal\n,65\nG. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51\nM. Ball,77 G. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12\nP. Baral\n,10 M. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11 D. Bersanetti\n,29\nT. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101 N. Bevins\n,102\nR. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46 V. Biancalana\n,101\nA. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75 C. Binu,110 S. Biot,111\nO. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113 S. Blaber,114\nJ. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 N. Bode\n,8, 9 N. Boettner,97 G. Boileau\n,113\nM. Boldrini\n,38 G. N. Bolingbroke\n,115 A. Bolliand,116, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82 F. Bondu\n,117\nE. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,118 R. Bonnand\n,31, 116 A. Borchers,8, 9 S. Borhanian,7 V. Boschi\n,80\nS. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 M. Boyle,120 A. Bozzi,62 C. Bradaschia,80\nP. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104 T. Briant\n,121 A. Brillet,113 M. Brinkmann,8, 9\nP. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,115 M. L. Brozzetti\n,76, 51\nS. Brunett,11 G. Bruno,15 R. Bruntz\n,122 J. Bryant,118 Y. Bu,123 F. Bucci\n,61 J. Buchanan,122\nO. Bulashenko\n,82, 83 T. Bulik,124 H. J. Bulten,37 A. Buonanno\n,125, 1 K. Burtnyk,2 R. Buscicchio\n,126, 127\nD. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7\nL. Cadonati\n,57 G. Cagnoli\n,128 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,129 E. Calloni,32, 4 S. R. Callos\n,77\nG. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,130 E. Capocasa\n,20 E. Capote\n,2, 11\nG. Capurri\n,81, 80 G. Carapella,66, 131 F. Carbognani,62 M. Carlassara,8, 9 J. B. Carlin\n,123 T. K. Carlson,132\nM. F. Carney,104 M. Carpinelli\n,126, 62 G. Carrillo,77 J. J. Carter\n,8, 9 G. Carullo\n,118, 133 A. Casallas-Lagos,134\nJ. Casanueva Diaz\n,62 C. Casentini\n,135, 22 S. Y. Castro-Lucas,136 S. Caudill,132 M. Cavagli`a\n,105\nR. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,137, 138 E. Cesarini\n,22 N. Chabbra,34 W. Chaibi,113\nA. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103 S. Chalathadka Subrahmanya\n,97 J. C. L. Chan\n,139\nM. Chan,114 K. Chang,140 S. Chao\n,141, 140 P. Charlton\n,142 E. Chassande-Mottin\n,20 C. Chatterjee\n,143\nDebarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,103 S. Chaty\n,20 K. Chatziioannou\n,11 A. Chen\n,144\nA. H.-Y. Chen,145 D. Chen\n,146 H. Chen,141 H. Y. Chen\n,147 S. Chen,143 Yanbei Chen,148 Yitian Chen\n,120\nH. P. Cheng,149 P. Chessa\n,76, 51 H. T. Cheung\n,90 S. Y. Cheung,6 F. Chiadini\n,150, 131 G. Chiarini,8, 9, 92\nA. Chiba,151 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80 A. Chiummo\n,4, 62 C. Chou,145 S. Choudhary\n,72\nN. Christensen\n,113, 152 S. S. Y. Chua\n,34 G. Ciani\n,74, 75 P. Ciecielag\n,95 M. Cie\u00b4slar\n,124 M. Cifaldi\n,22\nB. Cirok,153 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6 P. Clearwater,154 S. Clesse,111 F. Cleva,113, 116\nE. Coccia,44, 45, 43 E. Codazzo\n,155, 156 P.-F. Cohadon\n,121 S. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98\nC. G. Collette,157 J. Collins,63 S. Colloms\n,86 A. Colombo\n,158, 127 C. M. Compton,2 G. Connolly,77 L. Conti\n,92\nT. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,159 S. Corezzi\n,76, 51 N. J. Cornish\n,160 I. Coronado,161 A. Corsi\n,162\narXiv:2510.17487v1 [gr-qc] 20 Oct 2025\n\n2\nR. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 57 D. M. Coward,72 R. Coyne\n,163\nA. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,164 P. Cremonese\n,98 S. Crook,63 R. Crouch,2\nJ. Csizmazia,2 J. R. Cudell\n,165 T. J. Cullen\n,11 A. Cumming\n,86 E. Cuoco\n,166, 167 M. Cusinato\n,137\nL. V. Da Concei\u00b8c\u02dcao\n,168 T. Dal Canton\n,41 S. Dal Pra\n,169 G. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37\nS. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,122 L. P. Dartez\n,63 R. Das,106 A. Dasgupta,93 V. Dattilo\n,62\nA. Daumas,20 N. Davari,170, 171 I. Dave,103 A. Davenport,136 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72\nM. C. Davis\n,18 P. Davis\n,172, 173 E. J. Daw\n,174 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,175\nM. De Laurentis\n,32, 4 F. De Lillo\n,23 S. Della Torre\n,127 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38\nG. Demasi,176, 61 F. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,177 A. Depasse\n,15 N. DePergola,102\nR. De Pietri\n,178, 179 R. De Rosa\n,32, 4 C. De Rossi\n,62 M. Desai\n,35 R. DeSalvo\n,180 A. DeSimone,181\nR. De Simone,150, 131 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,164 M. Di Cesare\n,32, 4 G. Dideron,182 T. Dietrich\n,1\nL. Di Fiore,4 C. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 183\nS. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,184, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,118\nJ. P. Docherty,86 Z. Doctor\n,96 N. Doerksen\n,168 E. Dohmen,2 A. Doke,132 A. Domiciano De Souza,185\nL. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,186 W. J. D. Doyle,122\nM. Drago\n,39, 38 J. C. Driggers\n,2 L. Dunn\n,123 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,170, 155\nP. Dutta Roy\n,46 H. Duval\n,187 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,188, 31 T. Eckhardt\n,97 G. Eddolls\n,78\nA. Effler\n,63 J. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25 M. Emma\n,58 K. Endo,151 R. Enficiaud\n,1\nL. Errico\n,32, 4 R. Espinosa,164 M. Esposito\n,4, 32 R. C. Essick\n,189 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35\nT. Evstafyeva,182 B. E. Ewing,7 J. M. Ezquiaga\n,139 F. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33\nA. M. Farah\n,129 B. Farr\n,77 W. M. Farr\n,190, 191 G. Favaro\n,91 M. Favata\n,192 M. Fays\n,165 M. Fazio\n,55\nJ. Feicht,11 M. M. Fejer,89 R. Felicetti\n,184, 48 E. Fenyvesi\n,87, 193 J. Fernandes,194 T. Fernandes\n,195, 137\nD. Fernando,110 S. Ferraiuolo\n,196, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81\nI. Fiori\n,62 M. Fishbach\n,189 R. P. Fisher,122 R. Fittipaldi\n,197, 131 V. Fiumara\n,198, 131 R. Flaminio,31\nS. M. Fleischer\n,199 L. S. Fleming,200 E. Floden,18 H. Fong,114 J. A. Font\n,137, 138 F. Fontinele-Nunes,18 C. Foo,1\nB. Fornal\n,201 K. Franceschetti,178 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,202\nA. Freise\n,37, 107 O. Freitas\n,195, 137 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,203 T. Fujimori,204 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1\nS. Galaudage\n,185 V. Galdi,205 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,180 D. Ganapathy\n,206 A. Ganguly\n,79\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,207 C. Garc\u00b4\u0131a-Quir\u00b4os\n,188 J. W. Gardner\n,34 K. A. Gardner,114 S. Garg,42\nJ. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,208 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29 A. Gennai\n,80 V. Gennari\n,100\nJ. George,103 R. George\n,147 O. Gerberding\n,97 L. Gergely\n,153 Archisman Ghosh\n,94 Sayantan Ghosh,194\nShaon Ghosh\n,192 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,209 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63\nK. D. Giardina,63 D. R. Gibson,200 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,210 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18\nM. Granata\n,175 V. Granata\n,211, 131 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,86 G. Greco,51\nA. C. Green\n,37, 107 L. Green,212 S. M. Green,73 S. R. Green\n,213 C. Greenberg,132 A. M. Gretarsson,65\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,137 D. Guetta\n,214 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,172, 173\nH. Guo\n,144 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,215 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,97 N. Gutierrez,175 N. Guttman,6 F. Guzman\n,130 D. Haba,216 M. Haberland\n,1\nS. Haino,217 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,218 A. G. Hanselman\n,129 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,181 S. Harikumar\n,186 K. Haris,37, 71 I. Harley-Trochimczyk,130 T. Harmark\n,133\nJ. Harms\n,44, 45 G. M. Harry\n,219 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 220, 221 C. J. Haster\n,212\nK. Haughian\n,86 H. Hayakawa,50 K. Hayama,222 M. C. Heintze,63 J. Heinze\n,118 J. Heinzel,35 H. Heitmann\n,113\nF. Hellman\n,206 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,115 M. Hendry\n,86\nI. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,223, 224 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,225 N. Hirata,25 C. Hirose,226\nD. Hofman,175 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,174 D. E. Holz\n,129 L. Honet,111\n\n3\nD. J. Horton-Bailey,206 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,143 E. J. Howell\n,72 C. G. Hoy\n,73\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,141 H.-Y. Hsieh,141 C. Hsiung,227 S.-H. Hsu,145 W.-F. Hsu\n,109\nQ. Hu\n,86 H. Y. Huang\n,140 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,228 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,131 J. Iascau,77\nK. Ide,229 R. Iden,216 A. Ierardi,44, 45 S. Ikeda,146 H. Imafuku,42 Y. Inoue,140 G. Iorio\n,91 P. Iosif\n,184, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,229 M. Isi\n,190, 191 K. S. Isleif\n,230 Y. Itoh\n,204, 231 M. Iwaya,203\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,121 T. Jacquot,41 S. J. Jadhav,232 S. P. Jadhav\n,154 M. Jain,132\nT. Jain,223 A. L. James\n,11 K. Jani\n,143 J. Janquart\n,15 N. N. Janthalur,232 S. Jaraba\n,233 P. Jaranowski\n,234\nR. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,149 H.-B. Jin\n,235, 236 G. R. Johns,122\nN. A. Johnson,46 M. C. Johnston\n,212 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,209 R. Jones,86\nH. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,237 L. Ju\n,72 K. Jung\n,238 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,239 I. Kaku,204 V. Kalogera\n,96 M. Kalomenopoulos\n,212\nM. Kamiizumi\n,50 N. Kanda\n,231, 204 S. Kandhasamy\n,79 G. Kang\n,240 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,132 M. Kasprzack\n,11 H. Kato,151\nT. Kato,203 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,204 D. Keitel\n,98\nL. J. Kemperman\n,115 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,241 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,162 M. Khursheed,103\nN. M. Khusid,190, 191 W. Kiendrebeogo\n,113, 242 N. Kijbunchoo\n,115 C. Kim,243 J. C. Kim,244 K. Kim\n,245\nM. H. Kim\n,237 S. Kim\n,246 Y.-M. Kim\n,245 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,203 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,247, 248 K. Kokeyama\n,33, 249 S. Koley\n,44, 165 P. Kolitsidou\n,118 A. E. Koloniari\n,250\nK. Komori\n,42 A. K. H. Kong\n,141 A. Kontos\n,251 L. M. Koponen,118 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,151 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,118 S. Kroker,252 A. Kr\u00b4olak\n,253, 186 K. Kruska,8, 9 J. Kubisz\n,254 G. Kuehn,8, 9\nS. Kulkarni\n,215 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,232 Praveen Kumar\n,177\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,255, 256, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,207, 257 S. Kuwahara\n,42 K. Kwak\n,238 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,188, 100\nA. H. Laity,163 E. Lalande,258 M. Lalleman\n,23 P. C. Lalremruati,259 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,147 R. Langgin\n,212 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,199 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,164 M. Laxen\n,63 C. Lazarte\n,137 A. Lazzarini\n,11 C. Lazzaro,156, 155 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,260 H. W. Lee\n,261 J. Lee,78 K. Lee\n,237 R.-K. Lee\n,141 R. Lee,35\nSungho Lee\n,245 Sunjae Lee,237 Y. Lee,140 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,182 M. Le Jean\n,175, 116\nA. Lema\u02c6\u0131tre\n,262 M. Lenti\n,61, 176 M. Leonardi\n,74, 75, 263 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,264 T. G. F. Li,109 X. Li\n,148\nY. Li,96 Z. Li,86 A. Lihos,122 E. T. Lin\n,141 F. Lin,140 L. C.-C. Lin\n,264 Y.-C. Lin\n,141 C. Lindsay,200\nS. D. Linker,180 A. Liu\n,218 G. C. Liu\n,227 Jian Liu\n,72 F. Llamas Villarreal,164 J. Llobera-Querol\n,98\nR. K. L. Lo\n,139 J.-P. Locquet,109 S. C. G. Loggins,265 M. R. Loizou,132 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,165 M. Lopez Portilla,71 A. Lorenzo-Medina\n,177 V. Loriette,41 M. Lormand,63 G. Losurdo\n,266, 80\nE. Lotti,132 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,123 N. Lu\n,34\nL. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,267, 268 A. W. Lussier\n,258 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,151 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,163\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,189\nS. Maliakal,11 A. Malik,103 L. Mallick\n,168, 189 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,170, 155 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 269\nC. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100\nF. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,192 B. B. Martinez,130 D. A. Martinez,54 M. Martinez,43, 270\nV. Martinez\n,128 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,118 E. J. Marx,35 L. Massaro,36, 37\nA. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,208\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,122 C. McElhenny,122 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,143\nJ. McIver\n,114 A. McLeod\n,72 I. McMahon\n,188 T. McRae,34 R. McTeague\n,86 D. Meacher\n,10 B. N. Meagher,78\nR. Mechum,110 Q. Meijer,71 A. Melatos,123 C. S. Menoni\n,136 F. Mera,2 R. A. Mercer\n,10 L. Mereni,175\n\n4\nK. Merfeld,162 E. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10 B. Mestichelli,44\nM. Meyer-Conde\n,271 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,272 C. Michel\n,175\nY. Michimura\n,42 H. Middleton\n,118 D. P. Mihaylov\n,104 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,184, 48\nV. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43 L. Mirasola\n,155, 156 M. Miravet-Ten\u00b4es\n,137\nC.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46 A. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79\nV. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35\nL. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,206 M. Mondin,180 M. Montani,60, 61\nC. J. Moore,223 D. Moraru,2 A. More\n,79 S. More\n,79 C. Moreno\n,134 E. A. Moreno\n,35 G. Moreno,2\nA. Moreso Serra,82 S. Morisaki\n,42, 203 Y. Moriwaki\n,151 G. Morras\n,207 A. Moscatello\n,91 M. Mould\n,35\nB. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,176, 61 F. Muciaccia\n,39, 38 D. Mukherjee\n,118\nSamanwaya Mukherjee,24 Soma Mukherjee,164 Subroto Mukherjee,93 Suvodip Mukherjee\n,13 N. Mukund\n,35\nA. Mullavey,63 H. Mullock,114 J. Mundi,219 C. L. Mungioli,72 M. Murakoshi,229 P. G. Murray\n,86 D. Nabari\n,74, 75\nS. L. Nadji,8, 9 A. Nagar,28, 273 N. Nagarajan\n,86 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,274 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,62 P. Narayan\n,215 I. Nardecchia\n,22 T. Narikawa,203\nH. Narola,71 L. Naticchioni\n,38 R. K. Nayak\n,259 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,130\nT. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen Quynh\n,275 S. A. Nichols,12 A. B. Nielsen\n,276\nY. Nishino,25, 42 A. Nishizawa\n,277 S. Nissanke,278, 37 W. Niu\n,7 F. Nocera,62 J. Noller,279 M. Norman,33\nC. North,33 J. Novak\n,116, 233, 280 R. Nowicki\n,143 J. F. Nu\u02dcno Siles\n,207 L. K. Nuttall\n,73 K. Obayashi,229\nJ. Oberling\n,2 J. O\u2019Dell,228 E. Oelker\n,35 M. Oertel\n,233, 116, 281, 280 G. Oganesyan,44, 45 T. O\u2019Hanlon,63\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,116, 281, 280 R. Omer,18 B. O\u2019Neal,122 M. Onishi,151 K. Oohara\n,282\nB. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110 S. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11\nI. Ota\n,12 D. J. Ottaway\n,115 A. Ouzriat,56 H. Overmier,63 B. J. Owen\n,283 R. Ozaki,229 A. E. Pace\n,7\nR. Pagano\n,12 M. A. Page\n,25 A. Pai\n,194 L. Paiella,44 A. Pal,284 S. Pal\n,259 M. A. Palaia\n,80, 81\nM. P\u00b4alfi,202 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,141 J. Pan,72 K. C. Pan\n,141\nP. K. Panda,232 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38 K. A. Pannone,54\nB. C. Pant,103 F. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 285 A. Papadopoulos\n,86\nE. E. Papalexakis,210 L. Papalini\n,80, 81 G. Papigkiotis\n,250 A. Paquis,41 A. Parisi\n,76, 51 B.-J. Park,245\nJ. Park\n,286 W. Parker\n,63 G. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80\nL. Passenger,6 D. Passuello,80 O. Patane\n,2 A. V. Patel\n,140 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80\nB. G. Patterson,33 K. Paul\n,106 S. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna\nArellano\n,287 X. Peng,118 Y. Peng,57 S. Penn\n,288 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,132\nC. P\u00b4erigois\n,289, 92, 91 G. Perna\n,91 A. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107\nD. Pesios,250 S. Peters,165 S. Petracca,205 C. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18\nK. S. Phukon\n,118 H. Phurailatpam,218 M. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113\nM. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,290, 131 M. Pietrzak,95\nM. Pillas\n,165 F. Pilo\n,80 L. Pinard\n,175 I. M. Pinto\n,290, 131, 291, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10\nM. Pirello,2 M. D. Pitkin\n,223, 86 A. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,211, 22\nC. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35 J. Pomper,80, 81 L. Pompili\n,1 J. Poon,218 E. Porcelli,37\nE. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62 J. Powell\n,154 G. S. Prabhu,79 M. Pracchia\n,165\nB. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93 K. Prasai\n,292 R. Prasanna,232 P. Prasia,79 G. Pratten\n,118\nG. Principe\n,184, 48 G. A. Prodi\n,74, 75 P. Prosperi,80 P. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1\nJ. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,163 H. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,173, 116 V. Quetschke,164\nP. J. Quinonez,65 N. Qutob,57 R. Rading,230 I. Rainho,137 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110\nK. E. Ramirez\n,63 F. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,164 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57\nK. Ransom,63 P. Rapagnani\n,39, 38 B. Ratto,65 A. Ravichandran,132 A. Ray\n,96 V. Raymond\n,33\nM. Razzano\n,81, 80 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini\n,126, 11\nB. Revenu\n,293, 41 A. Revilla Pe\u02dcna,82 R. Reyes,180 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,210 M. L. Richardson,115 A. Rijal,65 K. Riles\n,90 H. K. Riley,33\nS. Rinaldi\n,269 J. Rittmeyer,97 C. Robertson,228 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,294 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,223 J. H. Romie,63\nS. Ronchini\n,7 T. J. Roocke\n,115 L. Rosa,4, 32 T. J. Rosauer,210 C. A. Rose,57 D. Rosi\u00b4nska\n,124 M. P. Ross\n,53\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,190, 191 S. Roy\n,15 D. Rozza\n,126, 127 P. Ruggi,62 N. Ruhama,238\nE. Ruiz Morales\n,295, 207 K. Ruiz-Rocha,143 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,168\n\n5\nM. R. Sah\n,13 S. Saha\n,141 T. Sainrat\n,64 S. Sajith Menon\n,214, 39, 38 K. Sakai,296 Y. Sakai\n,271\nM. Sakellariadou\n,67 S. Sakon\n,7 O. S. Salafia\n,158, 127, 126 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,147\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,79 S. Salvador\n,173, 172 A. Salvarese,147 A. Samajdar\n,71, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,137 J. R. Sanders,181 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,250 P. Sassi\n,51, 76\nB. Sassolas\n,175 B. S. Sathyaprakash\n,7, 33 R. Sato,226 S. Sato,151 Yukino Sato,151 Yu Sato,151 O. Sauter\n,46\nR. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,79 S. Sayah,175 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,148\nA. Schiebelbein,189 M. G. Schiworski\n,78 P. Schmidt\n,118 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9\nR. M. S. Schofield,77 K. Schouteden\n,109 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,297 M. Scialpi\n,298\nJ. Scott\n,86 S. M. Scott\n,34 R. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,299\nD. Sellers,63 N. Sembo,204 A. S. Sengupta\n,300 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38\nA. Sevrin,187 T. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,260 L. Shao\n,301 A. K. Sharma\n,98 Preeti Sharma,12\nPrianka Sharma,103 Ritwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,125 N. S. Shcheblanov\n,302, 262\nE. Sheridan,143 Z.-H. Shi,141 M. Shikauchi,42 R. Shimomura,303 H. Shinkai\n,303 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,147 R. W. Short,2 S. ShyamSundar,103 A. Sider,157 H. Siegel\n,190, 191 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 169 M. Simmonds,115 L. P. Singer\n,304 Amitesh Singh,215 Anika Singh,11\nD. Singh\n,206 N. Singh\n,98 S. Singh,216, 59 A. M. Sintes\n,98 V. Sipala,170, 155 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,199 T. J. Slaven-Blair,72 J. Smetana,118 J. R. Smith\n,54 L. Smith\n,86, 184, 48 R. J. E. Smith\n,6\nW. J. Smith\n,143 S. Soares de Albuquerque Filho,60 M. Soares-Santos,188 K. Somiya\n,216 I. Song\n,141 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,305 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,122 D. A. Steer\n,306 N. Steinle\n,168 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,250 P. Stevens,41 M. StPierre,163 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,229 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,240 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,216 M. Suzuki,203\nB. L. Swinkels\n,37 A. Syx\n,116 M. J. Szczepa\u00b4nczyk\n,307 P. Szewczyk\n,124 M. Tacca\n,37 H. Tagoshi\n,203\nK. Takada,203 H. Takahashi\n,271 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,308 H. Takeda\n,309, 310\nK. Takeshita,216 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,129 M. Tamaki,203 N. Tamanini\n,100\nD. Tanabe,140 K. Tanaka,50 S. J. Tanaka\n,229 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,210\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,311 J. D. Tasson\n,152 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,180 A. Theodoropoulos\n,137 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,209 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,194 S. Tiwari\n,188 V. Tiwari\n,118\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,140 A. Torres-Forn\u00b4e\n,137, 138 C. I. Torrie,11 I. Tosta e Melo\n,312\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,122 A. Trapananti\n,52, 51 R. Travaglini\n,167 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,125 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,184, 48 A. Trovato\n,184, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,313 L. Tsukada\n,212 K. Turbang\n,187, 23 M. Turconi\n,113 C. Turski,94\nH. Ubach\n,82, 83 N. Uchikata\n,203 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,314 K. Ueno\n,42 V. Undheim\n,276\nL. E. Uronen,218 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,294 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 315\nE. Van den Bossche\n,187 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,258 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,123 V. Varma\n,132 A. N. Vazquez,89 A. Vecchio\n,118 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,115 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,132\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,189 A. Vilkha,110 N. Villanueva Espinosa,137 V. Villa-Ortega\n,177\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,230 L. Vujeva\n,139 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,216 J. Z. Wang,90 W. H. Wang,164\nY. F. Wang\n,1 G. Waratkar\n,194 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\n\n6\nA. T. Wilkin,210 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,140 I. C. F. Wong\n,218, 109 K. Wong,189 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,141 D. S. Wu\n,8, 9 H. Wu\n,141 K. Wu,119 Q. Wu,53 Y. Wu,96\nZ. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,206 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,151 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,229 T. Yan,118 K. Z. Yang\n,18\nY. Yang\n,145 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,141 A. B. Yelikar\n,143 X. Yin,35 J. Yokoyama\n,316, 42\nT. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110 T. Zelenova,62 J.-P. Zendri,92\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57 R. Zhang\n,149 T. Zhang,118 C. Zhao\n,72\nYue Zhao,161 Yuhang Zhao,20 Z.-C. Zhao\n,317 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78 H. O. Zhu,72\nZ.-H. Zhu\n,317, 318 A. B. Zimmerman\n,147 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n\n7\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n\n8\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120Cornell University, Ithaca, NY 14850, USA\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n128Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n132University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n135Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n136Colorado State University, Fort Collins, CO 80523, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140National Central University, Taoyuan City 320317, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n146Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n157Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n159Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n161The University of Utah, Salt Lake City, UT 84112, USA\n\n9\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n165Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n166DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n171INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n172Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n173Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n174The University of Sheffield, Sheffield S10 2TN, United Kingdom\n175Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n176Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n177IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n178Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n179INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n180California State University, Los Angeles, Los Angeles, CA 90032, USA\n181Marquette University, Milwaukee, WI 53233, USA\n182Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n183Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n184Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n185Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n186National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n187Vrije Universiteit Brussel, 1050 Brussel, Belgium\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n190Stony Brook University, Stony Brook, NY 11794, USA\n191Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n192Montclair State University, Montclair, NJ 07043, USA\n193HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n194Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n195Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n196Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n197CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n198Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n199Western Washington University, Bellingham, WA 98225, USA\n200SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n201Barry University, Miami Shores, FL 33168, USA\n202E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n203Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n204Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n205University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n206University of California, Berkeley, CA 94720, USA\n207Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n208Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n209University of Southampton, Southampton SO17 1BJ, United Kingdom\n210University of California, Riverside, Riverside, CA 92521, USA\n211Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213University of Nottingham NG7 2RD, UK\n214Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n215The University of Mississippi, University, MS 38677, USA\n\n10\n216Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n217Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n218The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n219American University, Washington, DC 20016, USA\n220Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n221INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n222Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n223University of Cambridge, Cambridge CB2 1TN, United Kingdom\n224University of Lancaster, Lancaster LA1 4YW, United Kingdom\n225College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n226Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n227Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n228Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n229Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n230Helmut Schmidt University, D-22043 Hamburg, Germany\n231Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n234Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n235National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n236School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237Sungkyunkwan University, Seoul 03063, Republic of Korea\n238Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n239Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n240Chung-Ang University, Seoul 06974, Republic of Korea\n241University of Washington Bothell, Bothell, WA 98011, USA\n242Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n243Ewha Womans University, Seoul 03760, Republic of Korea\n244National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n245Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n246Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n247Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n248Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n249Nagoya University, Nagoya, 464-8601, Japan\n250Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n251Bard College, Annandale-On-Hudson, NY 12504, USA\n252Technical University of Braunschweig, D-38106 Braunschweig, Germany\n253Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n254Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n255Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n256Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n257Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n258Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n259Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n260Seoul National University, Seoul 08826, Republic of Korea\n261Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n\n11\n262NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n263Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n264Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n265St. Thomas University, Miami Gardens, FL 33054, USA\n266Scuola Normale Superiore, I-56126 Pisa, Italy\n267Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n268Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n269Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n270Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n271Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n272Tsinghua University, Beijing 100084, China\n273Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n274Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n275Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n276University of Stavanger, 4021 Stavanger, Norway\n277Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n278GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n279University College London, London WC1E 6BT, United Kingdom\n280Observatoire de Paris, 75014 Paris, France\n281Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n282Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n283University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n284CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n285Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n286Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n287Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n288Hobart and William Smith Colleges, Geneva, NY 14456, USA\n289INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n290Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n291Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n292Kennesaw State University, Kennesaw, GA 30144, USA\n293Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n294Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n295Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n296Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n297Trinity College, Hartford, CT 06106, USA\n298Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n299Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n300Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n301Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n302Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n303Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n304NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n305Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n\n12\n306Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n307Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n308Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n309The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n310Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n311Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n313National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n314Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n315Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n316Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n317Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n318School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nThe angular distribution of gravitational-wave power from persistent sources may exhibit\nanisotropies arising from the large-scale structure of the Universe.\nThis motivates directional\nsearches for astrophysical and cosmological gravitational-wave backgrounds, as well as continuous-\nwave emitters. We present results of such a search using data from the first observing run through\nthe first portion of the fourth observing run of the LIGO-Virgo-KAGRA Collaborations. We apply\ngravitational-wave radiometer techniques to generate skymaps and search for both narrowband and\nbroadband persistent gravitational-wave sources. Additionally, we use spherical harmonic decom-\nposition to probe spatially extended sources. No evidence of persistent gravitational-wave signals is\nfound, and we set the most stringent constraints to date on such emissions. For narrowband point\nsources, our sensitivity estimate to effective strain amplitude lies in the range (0.03 \u22128.4) \u00d7 10\u221224\nacross all sky and frequency range (20 \u2212160) Hz. For targeted sources\u2014Scorpius X-1, SN 1987A,\nthe Galactic Center, Terzan 5, and NGC 6397\u2014we constrain the strain amplitude with best limits\nranging from \u223c1.1 \u00d7 10\u221225 to 6.5 \u00d7 10\u221224. For persistent broadband sources, we constrain the\ngravitational-wave flux F 95%,UL\n\u03b1,\u02c6n\n(25 Hz) < (0.008 \u22125.5) \u00d7 10\u22128 erg cm\u22122 s\u22121 Hz\u22121, depending on the\nsky direction \u02c6n and spectral index \u03b1 = 0, 2/3, 3. Finally, for extended sources, we place upper\nlimits on the strain angular power spectrum C1/2\n\u2113\n< (0.63 \u221217) \u00d7 10\u221210 sr\u22121.\nI.\nINTRODUCTION\nA gravitational-wave background (GWB) is a diffuse\nsignal resulting from the incoherent superposition of nu-\nmerous unresolved gravitational wave (GW) sources. Its\nstochastic nature may stem from either the formation\nmechanisms of the sources or the limited sensitivity of\ncurrent detectors. A wide range of sources is expected\nto contribute to the GWB, each with distinct character-\nistics and frequency signatures. The GWB is typically\ncategorized into two main types: the astrophysical GWB\n[1], arising from unresolved sources such as compact bi-\nnary coalescences [2\u20136] and rotating neutron stars [7\u201315],\nand the cosmological GWB [16], potentially generated by\nearly-universe phenomena such as inflation [17\u201319], cos-\nmic strings [20\u201323], or phase transitions [24, 25].\nWhile to first order the GWB is expected to be ho-\nmogeneous and isotropic across the sky, it may exhibit\n\u2217Deceased, September 2024.\ntwo kinds of anisotropy: large-scale and local.\nLarge-\nscale anisotropies may arise from the uneven distribu-\ntion of sources on cosmological scales [26\u201334], propaga-\ntion effects due to large-scale structures along the line of\nsight [35], and kinematic anisotropies caused by the mo-\ntion of the observer relative to the GWB rest frame [36\u2013\n40].\nIn contrast, local anisotropies can be caused by\nnearby, spatially clustered sources, for example a con-\ncentration of millisecond pulsars in regions such as the\nGalactic plane and Virgo cluster, leading to prominent\nhotspots in the sky [36, 41\u201345].\nThe LIGO-Virgo-KAGRA Collaboration (LVK) has\nset progressively improved upper limits (ULs) on the\nGWB energy density of both isotropic and anisotropic\ncomponents [46\u201354].\nTo look for GWB anisotropies,\nthe LVK performs directional searches using a GW-\nradiometer\nalgorithm\nto\ngenerate\nskymaps\nand\na\nspherical harmonics (SPH) decomposition to compute\nangular power spectra [55\u201357]. These tools can be used to\nidentify cosmological, astrophysical, or local anisotropies.\nIn addition, the GW radiometer algorithm designed to\nsearch for GWB is also well suited to look for other types\n\n13\nof persistent GW sources, including continuous gravita-\ntional wave (CGW) sources.\nUntil the third observing run (O3), the pixel-based\nanisotropic searches [51\u201353] performed by LVK, targeting\npoint-like persistent sources, typically followed two ap-\nproaches: narrowband radiometer (NBR) searches, which\nfocused on specific directions (Scorpius X-1, the Galac-\ntic Center, SN 1987A, etc.) across multiple narrow fre-\nquency bins, and broadband radiometer (BBR) searches,\nwhich scanned the entire sky but averaged over a wide\nfrequency range.\nAs a result, the prospects of detect-\ning unknown anisotropies were limited, since neither ap-\nproach could simultaneously explore the full angular and\nspectral properties of the signal. In addition, matched-\nfiltering-based searches for persistent signals from galac-\ntic or extragalactic sources, such as neutron stars [58\u2013\n60] or boson clouds around black holes [61\u201363], are com-\nputationally expensive and inherently limited by signal\nmodeling assumptions. To address this limitation, we in-\ntroduced a new strategy in O3: performing directional\nsearches in narrow frequency bins across the whole sky.\nThis approach, formalized as the all-sky-all-frequency ra-\ndiometer (ASAF) search [54], enables a more comprehen-\nsive exploration of potential anisotropic signals without\nprior assumptions on their location or frequency content.\nAll of the above searches are performed in pixel basis,\nwhich is well-suited for probing localized sources. How-\never, as mentioned above, GWB anisotropies can also be\nexpanded in the SPH basis, which is more appropriate\nfor studying extended or diffuse sources. The LVK has\nalso conducted searches using the SPH basis and reported\nULs on the angular power spectra using data up to O3\n[51\u201353].\nIn this paper, we present results from all four analy-\nses: ASAF, targeted NBR, BBR, and SPH, performed\non the LVK observational data from the first observing\nrun (O1), second observing run (O2), O3, and the first\nportion of the fourth observing run (O4a). These anal-\nyses benefit from data collected by an increasingly sen-\nsitive global network of GW detectors, whose improved\nsensitivity over the years has significantly enhanced our\nability to probe anisotropic sources of persistent GWs.\nDespite this progress, we do not find evidence for such\nsources in any of the four analyses and therefore set ULs\non the GW emission depending on specific sky directions\nor angular scales.\nWe note that this paper has two companions, one fo-\ncusing on new results of the isotropic GWB search [64]\nand the other discussing cosmological implications of the\nnew isotropic search results [65].\nThe paper is organized as follows. In Sec. II, we intro-\nduce the GW radiometer algorithm and search method-\nologies. In Sec. III, we present results from ASAF ra-\ndiometer search, targeted NBR search, BBR search, and\nSPH search for extended sources. Finally, in Sec. IV, we\nsummarize our findings and outline prospects for future\nsearches. Comprehensive descriptions of the individual\nanalyses can be found in the Appendices.\nII.\nMOTIVATION AND METHODS\nA.\nGravitational Wave Radiometer\nThe dimensionless GW energy density parameter,\n\u2126GW(f, \u02c6n), characterizes the energy content of the GWB\nper unit logarithmic frequency f and unit solid angle in\nthe direction \u02c6n. It is given by\n\u2126GW(f, \u02c6n) = 2\u03c02\n3H2\n0\nf 3 P(f, \u02c6n) ,\n(1)\nwhere P(f, \u02c6n) denotes the one-sided power spectral den-\nsity (PSD) of the GW strain field. This quantity cor-\nresponds to the second moment of a stationary, Gaus-\nsian, and unpolarized stochastic GW signal [66]. H0 =\n67.9 km s\u22121Mpc\u22121 in the above equation denotes the\nHubble constant [67].\nWe aim to measure the angular distribution of the\nGWB, i.e., P(f, \u02c6n), by performing a cross-correlation1\nbetween data from a pair of detectors (usually referred\nto as baseline, denoted by I, with the subscripts i = 1, 2\nlabeling the two detectors) that are geographically sep-\narated. We construct the cross spectral density (CSD)\nestimator:\nCI(t; f) \u2261\n2\nT w1w2\n\u02dcs\u2217\n1(t; f) \u02dcs2(t; f) ,\n(2)\nwhere \u02dcsi(t; f) represents the short Fourier transform\n(SFT) computed from a time segment centered around\ntime t, using a 50% overlapping Hann window with a seg-\nment duration of T = 192 s. The factor w1w2 accounts\nfor the effect of windowing on the estimator [68, 69].\nIn the presence of Gaussian, additive, and stationary\nnoise\u2014assumed to be uncorrelated between detectors at\ndifferent sites\u2014the noise- and source-averaged correla-\ntion, denoted by \u27e8\u00b7\u27e9\u02dch,N, is given by\n\u27e8CI(t; f)\u27e9\u02dch,N =\nZ\nd2\u02c6n \u03b3I(t; f, \u02c6n) P(f, \u02c6n) ,\n(3)\nwhich encodes information about the source anisotropy.\nThe\noverlap\nreduction\nfunction\n(ORF)\n[70\u201372],\n\u03b3I(t; f, \u02c6n),\nacts as a transfer function by mapping\nthe spatial distribution of GW power onto the measured\ncross-correlation. It depends on the signal frequency, the\nobservation time, the source sky location, the individual\ndetector response functions, and the distance between\nthe detectors.\n1 We note that the estimator constructed via cross-correlation is\nnearly optimal, given that the auto-correlation is not utilized to\ndetect the GWB signal [50].\n\n14\nTo probe specific types of angular distributions, we discretize the sky P(f, \u02c6n) using an appropriate basis e\u00b5(\u02c6n), i.e.,\nP(f, \u02c6n) \u2261\nX\n\u00b5\nP\u00b5(f) e\u00b5(\u02c6n) .\n(4)\nThe explicit expression for the ORF in an appropriate basis is given by\n\u03b3I\n\u00b5(t; f) \u2261\nX\nA=+,\u00d7\nZ\nd2\u02c6n F A\n1 (t, \u02c6n)F A\n2 (t, \u02c6n) e\u00b5(\u02c6n) e\u22122\u03c0if \u2206\u20d7xI (t)\u00b7\u02c6n\nc\n,\n(5)\nwhere F A\ni denotes the individual detector response functions, and \u2206\u20d7xI is the separation vector between the detectors.\nIn this article, we utilize two types of bases: (i) the pixel\nbasis e\u00b5(\u02c6n) = \u03b42(\u02c6n\u2212\u02c6n\u00b5) under the assumption the source\nis localized in the direction \u02c6n\u00b5; and (ii) the SPH basis\ne\u00b5(\u02c6n) = Y\u2113m(\u02c6n), with \u00b5 = (\u2113, m), under the assumption\nthe source is spatially extended. We note that the esti-\nmators can be transformed between pixel and SPH basis\nvia forward and inverse SPH transforms [73]. Addition-\nally, it is important to note that e\u00b5(\u02c6n) = Y00(\u02c6n) corre-\nsponds to the isotropic component of the GWB angular\ndistribution.\nAssuming that the CSD for each time segment is a Gaussian random variable, the maximum likelihood estimator\nfor GWB anisotropy, P\u00b5(f), (for positive frequency) is obtained by maximizing the joint likelihood across different\ntimes and baselines as in Ref. [54], and it reads\n\u02c6Pf = \u0393\u22121\nf\n\u00b7 Xf ,\n\u02c6P\u00b5(f) =\nX\n\u00b5\u2032\n(\u0393\u22121)\u00b5\u00b5\u2032(f) X\u00b5\u2032(f) .\n(6)\nHere, Xf is the narrowband dirty map and \u0393f is the narrowband Fisher information matrix, defined as follows\n[54, 74]:\nXf \u2261\u03b3\u2020\nf \u00b7 N \u22121\nf\n\u00b7 Cf,\nX\u00b5(f) \u221d\nX\nIt; 1,2\u2208I\n\u03b3I\u2217\n\u00b5 (t; f) CI(t; f)\nP1(t; f) P2(t; f) ,\n\u0393f \u2261\u03b3\u2020\nf \u00b7 N \u22121\nf\n\u00b7 \u03b3f,\n\u0393\u00b5\u00b5\u2032(f) \u221d\nX\nIt; 1,2\u2208I\n\u03b3I\u2217\n\u00b5 (t; f) \u03b3I\n\u00b5\u2032(t; f)\nP1(t; f) P2(t; f) ,\n(7)\nwhere Nf denotes the covariance matrix for the CSD and P1,2(t; f) are the noise one-sided PSDs. The narrowband\nskymaps in the above equations are the foundation of all the anisotropic analyses in this paper.\nB.\nAll-sky All-frequency radiometer search\nThe ASAF radiometer search targets point-like, persis-\ntent, narrowband GW sources by scanning the frequency\nband and the sky using a HEALPix grid (Nside = 16)2 [75]\nand a frequency bin of 1/32 Hz. Such sources can exhibit\ntwo types of waveforms in the time domain: (i) CGW\nsignal from a single GW source, and (ii) a narrowband\nGWB arising from multiple unresolved sources along a\ngiven line of sight, resulting in an incoherent signal. Be-\ning an unmodeled search, the radiometer search is ro-\nbust against the signal model and serves as an alternative\nfor detecting GW signatures from poorly known sources,\n2 This results in a sky grid with 12 N2\nside = 3072 pixels, each cov-\nering 13.4 deg2.\ne.g., neutron stars having frequent glitches and/or ac-\ncretion from a binary companion [76] or unknown CGW\nsources [60].\nWe compute the point estimate, which serves as an\nestimator for the signal power and its associated uncer-\ntainty due to random noise. This is achieved by utilizing\nnarrowband dirty maps and the Fisher information ma-\ntrix shown in Eq. (7), both constructed in the pixel basis,\nas described by the equations below\n\u02c6P\u02c6n(f) = [\u0393\u02c6n\u02c6n(f)]\u22121 X\u02c6n(f) ,\n\u03c32\n\u02c6n(f) = [\u0393\u02c6n\u02c6n(f)]\u22121 ,\n(8)\nwhere there is no summation over \u02c6n.\nOwing to the\nbaseline\u2019s blind spots, the Fisher information matrix in\nthe pixel basis is highly ill-conditioned [56, 77\u201381]. To\navoid introducing numerical noise due to inversion of in-\nsensitive modes and their dependence on regularization,\n\n15\nwe proceed without incorporating pixel correlations. As\nshown in Ref. [80], this approximation is justified given\nthe current detector sensitivity when constructing clean\nmap estimators.\nC.\nTargeted-narrowband radiometer search\nThe radiometer algorithm can be used in a pixel-based\napproach to target specific sky locations. For this anal-\nysis, five astrophysically motivated locations have been\nselected: three of them\u2014Scorpius X-1, the Galactic Cen-\nter, and the supernova remnant SN 1987A\u2014were also an-\nalyzed in previous directional stochastic searches [51\u201353],\nwhile two globular clusters, Terzan 5 and NGC 6397, are\nintroduced as new targets. These sources span a range\nof astrophysical scenarios, including accreting neutron\nstars, dense stellar environments, and young supernova\nremnants, and are all plausible hosts of CGW emission\n[60]. A brief overview of each source and its relevance to\nGW searches is provided in Appendix C 1.\nUnlike the ASAF search, targeting specific locations\nallows us to account for the specific signal spread caused\nby Earth\u2019s Doppler modulation or the intrinsic character-\nistics of the source. To do so, we combine the information\nfrom nearby frequency bins by performing a running av-\nerage throughout the entire search frequency range. The\ncharacteristic window of the average is defined as the N\nneighboring bins around a fixed frequency bin required\nto recover all the power spread by the phase evolution of\nthe source. The output of the bin combination is a new\npower spectrum with the same original frequency resolu-\ntion \u03b4f, but now accounting for the frequency variations\nof the signal throughout the observation time. The de-\ntails regarding how the values of N can be determined\nare given in Appendix C 2.\nD.\nBroadband radiometer search\nThe BBR search is designed to measure the GWB en-\nergy density from point-like sources across the sky and\nserves as a crucial tool for identifying persistent sources\nwhen there is stochasticity in the phase evolution of the\nsignal due to a large number of sources.\nThis search\nstill relies on the same methods as in the ASAF analy-\nsis, while further assuming the point-like GWB sources\nare broadband in frequency with an angular power spec-\ntral density P(f, \u02c6n). Throughout this work, we search for\nGWBs whose P(f, \u02c6n) can be factorized in one frequency-\ndependent and one angular-dependent factor [36, 53, 66],\nnamely:\nP(f, \u02c6n) = P\u02c6n0(f) \u03b42(\u02c6n \u2212\u02c6n0) = \u00afH(f) P(\u02c6n) ,\n(9)\nwhere \u00afH(f) is the spectral shape of the GWB, normal-\nized such that \u00afH(fref) = 1, with fref = 25 Hz [50, 53].\nWe model \u00afH(f) as a simple power law, characterized by\na spectral index \u03b1 that is fixed throughout the search,\nsuch that [66]\n\u00afH(f) \u2261\u00afH(f; \u03b1, fref) =\n\u0012 f\nfref\n\u0013\u03b1\u22123\n,\n(10)\nP(\u02c6n) \u2261P(\u02c6n; \u03b1, fref) = P\u03b1, \u02c6n0(fref) \u03b42(\u02c6n \u2212\u02c6n0) .\n(11)\nWe consider three different GWB power-law models: \u03b1 =\n0, consistent with a cosmological GWB from slow-roll\ninflation or cosmic strings [16]; \u03b1 = 2/3, compatible with\nan astrophysical GWB from compact binary coalescence\n(CBC)s [1]; and \u03b1 = 3, corresponding to a flat strain\npower spectrum [82].\nBy following the same maximum-likelihood approach\npresented in Sec. II A, one can derive the expressions for\nthe broadband dirty maps and Fisher matrix:\nX\u02c6n =\nX\nf\n\u00afH(f) X\u02c6n(f) ,\n(12)\n\u0393\u02c6n\u02c6n\u2032 =\nX\nf\n\u00afH2(f) \u0393\u02c6n\u02c6n\u2032(f) ,\n(13)\nwith X\u02c6n(f) and \u0393\u02c6n\u02c6n\u2032(f) from Eq. (7), and the maximum-\nlikelihood estimator for P(\u02c6n)\n\u02c6P\u02c6n =\nP\nf \u00afH(f)\u03c3\u22122\n\u02c6n (f) \u02c6P\u02c6n(f)\nP\nf \u2032 \u00afH2(f \u2032)\u03c3\u22122\n\u02c6n (f \u2032)\n.\n(14)\nWe rescale this estimator to express it in units of the\nGW energy flux spectrum at the reference frequency fref,\nwhere P(fref, \u02c6n) = P\u03b1,\u02c6n given \u00afH(fref) = 1, as\n\u02c6F\u03b1,\u02c6n(fref) = \u03c0c3\n4G f 2\nref \u02c6P\u03b1,\u02c6n .\n(15)\nE.\nSpherical harmonics search\nThis analysis is intended to search for an anisotropic\ndistribution of spatially extended sources with a broad-\nband spectrum, as opposed to the point sources targeted\nby the radiometer analyses discussed above. While we\nfollow the same factorization as given by Eq. (9) of the\nBBR search, we adopt the SPH functions as a basis to\ncharacterize the anisotropies of extended sources [57]\nP(f, \u02c6n) = \u00afH(f)\n\u2113max\nX\n\u2113=0\n\u2113\nX\nm=\u2212\u2113\nP\u2113m Y\u2113m(\u02c6n) ,\n(16)\nwhere Ylm(\u02c6n) is an SPH function of the mode (\u2113, m) eval-\nuated at the sky position \u02c6n . Since now we search for\na GWB signal with a broadband spectrum, we construct\na broadband version of the \u02c6P estimator from its narrow-\nband counterpart, following the derivation in Eq. (14) but\nadapted to the SPH basis. The \u02c6P estimator is referred to\nas the clean map, and the inversion of the Fisher matrix\nphysically represents the deconvolution of the antenna\npattern and detector noise.\n\n16\nTo interpret the anisotropies of GWBs under the as-\nsumption of statistical isotropy, we are more interested\nin the angular power of estimated \u02c6P\u2113m, rather than their\nspecific realization on the sky. Therefore, we introduce\nthe estimator of the angular power spectrum in the unit\nof sr\u22122\n\u02c6C\u2113=\n\u00122\u03c02f 3\nref\n3H2\n0\n\u00132\n1\n2\u2113+ 1\nX\nm\nh\n| \u02c6P\u2113m|2 \u2212(\u03a3R)\u2113m,\u2113m\ni\n,\n(17)\nwith its variance (under the weak-signal limit) given by:\nVar[ \u02c6C\u2113] \u2248\n\u00122\u03c02f 3\nref\n3H2\n0\n\u00134\n2\n(2\u2113+ 1)2\nX\nm,m\u2032\n|(\u03a3R)\u2113m,\u2113m\u2032|2 ,\n(18)\n\u03a3R is the covariance matrix of the regularized clean-map\nestimator, defined as:\n\u03a3R = \u0393\u22121\nR \u00b7 \u0393 \u00b7 \u0393\u22121\nR ,\n(19)\nwhere \u0393 is the Fisher matrix of the dirty map on the SPH\nbasis and \u0393R is its regularized version, whose details can\nbe found in Appendix E 2.\nAlso, due to the angular resolution limit, we perform\nthe analysis for SPH modes only up to the angular scale\ngiven by \u2113max = 3, 4, 16 for \u03b1 = 0, 2/3, 3, respectively [51\u2013\n53]. Technical details concerning the Fisher-matrix regu-\nlarization as well as the angular resolution are discussed\nin Appendices E 1 and E 2. We eventually compare this\n\u02c6C\u2113estimator to its theoretical predictions to character-\nize a potential signal or to place constraints on relevant\ntheoretical models.\nThe estimator described above, which we refer to as\nthe auto- \u02c6C\u2113estimator, has been used in previous LVK\nanalyses [51\u201353]. However, Ref. [83] showed that in the\npresence of an astrophysical GWB, it is significantly bi-\nased by the shot-noise-dominated nature of the signal,\nwhich arises from the discrete spatial or temporal real-\nization of individual events. This consideration motivates\nus to also adopt the cross- \u02c6C\u2113estimator, defined as\n\u02c6C(cross)\n\u2113\n=\n\u00122\u03c02f 3\nref\n3H2\n0\n\u00132\n1\n2\u2113+ 1\n1\nn(n \u22121)\nX\nm\nX\ni\u0338=j\n\u02c6P(i)\n\u2113m \u02c6P(j)\u2217\n\u2113m ,\n(20)\nwith its variance (under the weak-signal limit3 )\nVar[ \u02c6C\u2113] \u2248\n\u00122\u03c02f 3\nref\n3H2\n0\n\u00134\n2\n(2\u2113+ 1)2\n1\nn2(n \u22121)2\n\u00d7\nX\nm,m\u2032\nX\ni\u0338=j\n(\u03a3(i)\nR )\u2113m,\u2113m\u2032(\u03a3(j)\nR )\u2113m\u2032,\u2113m ,\n(21)\n3 While the weak-signal limit mentioned in Sec. II A assumes the\ndetector noise to dominate over the GWB signal and astro-\nphysical shot noise in the individual time-frequency components,\nEqs. (18) and (21) involve the whole dataset and subsets, respec-\ntively, after marginalizing across times and frequencies.\nwhere n distinct clean maps are involved and \u03a3(i)\nR repre-\nsents a covariance matrix of regularized clean maps de-\nrived from i-th dataset. See Appendix E 3 for how we\ndivide the whole dataset into subsets in the optimal way.\nTo either claim a detection of an anisotropic GWB\nor place ULs on the angular power spectrum, given the\nobserved \u02c6P\u2113m estimator, we evaluate its statistical sig-\nnificance. Specifically, we compute p-values for the real\nand imaginary parts of the \u02c6P estimator, respectively, in\neach SPH mode using its expected probability density\nfunction (PDF) based on Monte Carlo samples with the\ndetailed procedure discussed in Appendix E 4. We gener-\nate 50,000 such \u02c6P\nsim samples for the whole dataset and\ncompute a p-value for each real and imaginary part of\neach SPH mode. As a significance indicator, we adopt a\n5% p-value threshold, which we refer to as a local thresh-\nold.\nAdditionally, due to the presence of multiple ob-\nservations across all the SPH modes, we account for the\ntrials factor in a conservative way by dividing each local\nthreshold by the number of SPH modes, (\u2113max + 1)2, to\nobtain the global p-value threshold.\nIII.\nRESULTS\nTo perform all the four analyses described above, we\nanalyze data from O1 and O2 of the LIGO detectors [84\u2013\n90] located in Hanford (H) and Livingston (L); from O3\nof LIGO [91\u201394] and Virgo [95\u201398] (V); and from O4a of\nLIGO [99\u2013102].\nThese datasets are preprocessed following the proce-\ndure described in [64].\nTime-domain cuts are applied\nby removing segments affected by non-Gaussian features,\nhardware injections, and known instrumental artifacts;\napplying non-stationarity cuts; and gating loud glitches.\nThese cuts are identical to those used in [64]. In addi-\ntion, frequency-domain cuts are applied to remove bins\nidentified through coherence studies as contaminated by\ninstrumental artifacts. Details of the observing run, in-\ncluding the time- and frequency-domain cuts and the ef-\nfective dataset, are provided in Tab. IV of Appendix A.\nWe compute the CSD by combining the SFTs of 192-\nsecond segments from all detector pairs, using a coarse-\ngrained frequency resolution of \u2206f = 1/32 Hz and in-\ncluding the corresponding variances.\nTo reduce computational and storage costs in GWB\nsearches, we fold the 192-second segments across a side-\nreal day (23h 56m 4s), leveraging the temporal symmetry\nof the ORF due to Earth\u2019s rotation [69, 103]. This pre-\nserves all necessary information while enabling efficient\nmaximum-likelihood analysis over the full run.\nWe generate folded datasets for all observing runs [104]\nup to and including O4a, and perform all analyses using\nthe PyStoch package [73, 74], which now provides a uni-\nfied framework supporting both pixel- and SPH-based\nanalyses from O4a onward.\n\n17\nA.\nAll-sky All-frequency radiometer search\nTo identify a potential GW signature in the data and\nset constraints on source parameters in the absence of a\ndetection, we use the estimators constructed in Sec. II B\nfollowing the method outlined in Ref. [54] and detailed\nin Appendix B.\nWe use a detection statistic, the signal-to-noise ratio\n(SNR), defined as\n\u02c6\u03c1\u02c6n(f) \u2261\n\u02c6P\u02c6n(f)\n\u03c3\u02c6n(f) ,\n(22)\nto evaluate the significance of the data. The distribution\nof this statistic, obtained from O4a data using both the\nrandom (unphysical) timeshift method [54] and the zero-\nlag data (i.e., data without timeshift), is shown in Ap-\npendix B 1. The zero-lag data is mostly consistent with\nthe random-timeshifted data within 2-sigma Poisson er-\nrors. With a global p-value threshold of 5%, no evidence\nis found for a persistent narrowband GW source. A total\nof 505 sub-threshold candidates identified for follow-up,\nand details are provided in Appendix B 1.\nNext, assuming that the GW signal remains in the\nsame frequency bin and sky direction, we combine data\nfrom the O1\u2013O4a observing runs (including multiple\nbaselines for O3). This assumption sets an upper bound\non the frequency drift of a CGW signal:\n0.03125 Hz\n8.3 years\n= 1.2 \u00d7 10\u221210 Hz s\u22121 .\n(23)\nWe note that incorporating data from multiple datasets\nreduced the notch fraction from 11.4% in O4a to 7.9%\nin O1\u2013O4a. The zero-lag data remains consistent with\nthe null hypothesis. Additionally, we investigate the top\nthree SNR candidates in zero-lag with SNR>5.5.\nWe\nfind that these candidates are associated with data qual-\nity issues at these frequencies, including hardware injec-\ntions and calibration lines [99]. Finally, a total of 562\nsub-threshold follow-up candidates have been identified\nfor the follow-up with methods tuned for searching for a\nCGW (see Appendix B 1 for the details).\nHaving found the data to be consistent with Gaussian\nnoise, we set Bayesian ULs on the effective strain ampli-\ntude, defined as\nheff,\u02c6n(f) \u2261[P\u02c6n(f) \u2206f]1/2 ,\n(24)\nwith 95% confidence. We note that the effective strain\namplitude defined above is equal to the intrinsic strain\namplitude h0 for a circularly polarized CGW, provided\nthe signal remains confined within a single frequency\nbin [105, 106]]. In practice, this assumption is violated\ndue to factors such as arbitrary polarization, Doppler\nshifts from the Earth\u2019s orbital motion, and intrinsic\nsource motion (e.g., proper motion or binary orbital\nmotion), which introduce biases in the estimator. The\nDoppler shift from the Earth\u2019s motion around the Sun\ncan be approximated as f0 \u00d7 2 \u00d7 10\u22124 cos \u03b4, where f0\nis GW frequency in the Solar System Barycentre frame\nand \u03b4 is the source declination.\nConsequently, above\n\u223c160 Hz, the signal drifts beyond a single frequency bin.\nWe therefore restrict our UL estimates to the 20\u2013160 Hz\nrange, which we refer to as sensitivity estimates in further\ndiscussion.\nAs shown in Tab. I, the sensitivity estimate with O4a\nand O1-O3 data across sky and frequencies lie in the\nranges (3.46 \u2212223.12) \u00d7 10\u221226 and (3.39 \u2212963.23) \u00d7\n10\u221226 [54], respectively.\nAfter combining all available\ndata (i.e., O1-O4a), the sensitivity lies in range (2.94 \u2212\n845.68) \u00d7 10\u221226.\nTo assess the improvement in the sensitivity estimate\nwith the addition of the latest data, comparing only the\nminimum or maximum sensitivity across datasets is not\na robust approach.\nThis is primarily due to two rea-\nsons. First, specific frequency bins may be notched in\none dataset but present in another, preventing a uniform\ncomparison. For example, the notch fraction decreases\nfrom 7.6% in O4a to 0.4% in the combined O1\u2013O4a\ndataset (below 160 Hz). Second, the reported sensitiv-\nity incorporates both a point estimate and its associated\nuncertainty, both of which can fluctuate across the sky,\nintroducing intrinsic statistical variability. We therefore\ncompute the sensitivity improvement using the ratio of\nmedian sensitivity across these shared frequency bins. As\nshown in Tab. I, the median sensitivity ratios for O4a to\nO1\u2013O3 and O1\u2013O4a to O1\u2013O3 are 0.89 and 0.79 respec-\ntively, indicating an overall improvement by a factor of\n1.12 (1.26).\nTo understand the variation of sensitivity across sky di-\nrections and frequencies, we consider a simplified model\nin which the sensitivity for each frequency-pixel pair is\napproximated as a combination of the point estimate\nand its associated uncertainty. Given that the observed\nSNR for frequency-pixel pairs is consistent with Gaus-\nsian noise with zero mean, the point-estimate \u02c6P\u02c6n(f) can\nbe assumed to be centered near zero. Consequently, the\nsky-averaged sensitivity can be approximated as (using\nEqs. 7 and 8)\nSensitivity(f) \u2261\u27e8\u03c3\u02c6n(f)\u27e91/2\n\u02c6n\n\u221d(P1(f)P2(f))1/4 ,\n(25)\nwhere P1(f) and P2(f) are noise PSD for detector 1 and\n2 in baseline I. The sky-averaged sensitivity as a func-\ntion of frequency is shown in the left panel of Fig. 1 for\nO1\u2013O4a (blue) and O1\u2013O3 (yellow). The trend follows\nthe shape of the typical noise curve, i.e., (P1(f)P2(f))1/4,\nwith the shaded region indicating 1-sigma sky fluctua-\ntions. Similarly, the frequency-averaged sensitivity for a\ngiven sky direction \u02c6n is given by (using Eqs. 7 and 8)\nSensitivity\u02c6n \u2261\u27e8\u03c3\u02c6n(f)\u27e91/2\nf\n\u221d\n X\nt\n\u0393\u02c6n(t)\n!1/4\n,\n(26)\nwhere \u0393\u02c6n(t) = P\nA F A\n1 (t, \u02c6n) F A\n2 (t, \u02c6n) is the combined an-\ntenna response [56], and the summation is over observing\n\n18\nRun\nVetoed-Frequency\nRange\nMedian\nMedian\nMedian (Mean) Ratio\nFraction (%)\n(\u00d710\u221226)\n(\u00d710\u221226)\nCommon f (\u00d710\u221226)\nRun\nO1\u2212O3\nO4a\n7.6\n3.46 - 223.12\n9.00\n9.29\n0.89 (0.72)\nO1-O3\n1.2\n3.39 - 963.23\n10.04\n10.39\n1 (1)\nO1-O4a\n0.4\n2.94 - 845.68\n8.41\n8.24\n0.79 (0.67)\nTABLE I. We present Bayesian sensitivity estimate on the effective strain amplitude heff for three datasets: O4a, O1\u2013O3, and\nthe combined O1\u2013O4a. When comparing the median sensitivity of O4a to O1-O4a, an improvement is observed. To account for\ndifferences in the vetoed frequency bins across observing runs, we also compare median sensitivity over the common frequency\nrange.\n20\n40\n60\n80\n100\n120\n140\n160\nFrequency (Hz)\n10\u221225\n10\u221224\nh95%\ne\ufb00\nSky-Averaged Sensitivity (O1-O4a)\nSky-Averaged Sensitivity (O1-O3)\n1 \u2212\u03c3 Sky-Variation of Sensitivity (O1-O4a)\n1 \u2212\u03c3 Sky-Variation of Sensitivity (O1-O3)\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\nFrequency Averaged Sensitivity O1-O4a\nCommon Frequencies\n1.2E-25\n1.4E-25\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\nRatio of Frequency Averaged Sensitivity O1-O4a/O1-O3\nCommon Frequencies\n6.3E-01\n7.1E-01\nFIG. 1. Bayesian sensitivity estimate to Effective Strain Amplitude heff: Left panel: Sky-averaged sensitivity from the O1-O3\nand O1-O4a datasets are shown as blue and yellow solid lines, respectively. The shaded regions represent 1-sigma variations in\nthe estimates across the sky. The overall shape of the curves reflects the detectors\u2019 sensitivity profiles. Gaps indicate vetoed\nfrequency bins, while narrow vertical peaks correspond to instrumental spectral lines that were not vetoed, as their impact\non the analysis was minimal. Top Right Panel: Skymap of frequency-averaged sensitivity using O1\u2013O4a data. The observed\npattern reflects the typical sky sensitivity of an HL-dominated network. As expected, the sensitivity is worse near the poles\nand equator, with improved sensitivity in the mid-declination regions. Bottom Right Panel: Skymap showing the ratio of\nfrequency-averaged sensitivity from O1-O4a to that from O1-O3.\ntime. This captures the directional variation in detector\nresponse over the full observing run.\nThe correspond-\ning skymap of frequency-averaged sensitivity for O1\u2013O4a\nis shown in the top right panel of Fig. 1. For the HL\nbaseline-dominated data, the most sensitive sky regions\nlie between declinations of approximately 20\u25e6\u201360\u25e6, with\nreduced sensitivity near the celestial poles and equator.\nThe bottom right panel of Fig. 1 presents the ratio\nof frequency-averaged sensitivity between O1\u2013O4a and\nO1\u2013O3 across the sky, which varies between 0.63 and\n0.71.\n1.\nMarginal Outlier at 92.8125 Hz\nSigns of non-Gaussianity are observed in the negative\nSNR tails of the zero-lag data, with the samples originat-\ning from the same frequency bin at 92.8125 Hz. While\nan actual astrophysical source is not expected to produce\nnegative SNR in our analysis, this candidate lies close to\nthe SNR threshold for a two-sided p-value. Therefore, a\nfollow-up analysis was conducted, with details provided\nbelow.\nIn the O4a data, we identified a frequency bin at\n92.8125 Hz with extreme SNR values: a minimum of\n\u22126.12 and a maximum of 5.2 in the zero-lag dataset. The\nminimum SNR lies in the negative tail and is just above\nthe two-sided threshold of \u22126.18 corresponding to a 5%\np-value (see O4a SNR histogram in Appendix B). While\nthe positive SNR is not significant enough to be classi-\nfied as an outlier, the frequency-pixel pair was selected\nas a sub-threshold follow-up candidate. The associated\nSNR skymap is given in Appendix B. In the random-\ntimeshifted dataset, the SNR range narrows to \u22122 to 2,\nand the skymap structure disappears\u2014consistent with\nbehaviour expected in the case of a persistent signal. We\ninvestigate both tails to determine whether the excess\npower arises from detector noise or a GW signal.\n\n19\nWe note that, while most hardware injections were\ntoo weak to be confidently detected with our search\nmethod, the injection near 52.8 Hz was identified as\na sub-threshold follow-up candidate, with an SNR of\n4.25\u2014lower than that of the observed \u201coutlier\u201d.\nAs\nshown in Appendix B, the SNR in the outlier frequency\nbin steadily builds up in the zero-lag run and stands out\ncompared to both neighbouring frequency bins and the\nrandom time-shifted dataset.\nWe also performed a simulation by injecting a GW sig-\nnal with SNR\u223c4.9 at the sky location corresponding to\nthe observed maximum SNR, convolved with the detector\nresponse, and added to numerous noise realizations. We\nfind that, in approximately 4 out of 104 trials, the neg-\native SNR exceeds the positive by a magnitude of 0.9,\nwith the maximum SNR exceeding 5.1, and the observed\nskymap is found to be a good match with the simulated\nmap (see Appendix B).\nWhen combining O4a data with previous observing\nruns (O1\u2013O4a), the SNR decreases from \u22126.12 to \u22124.3\nand from 5.2 to 3.6. For a persistent astrophysical source\nlasting \u223c8 years, we would expect the SNR\u2014particularly\nin the positive direction\u2014to increase if earlier data were\nsensitive and the signal remained in the same frequency\nbin. Otherwise, a decrease in SNR upon combining runs\nmay instead indicate a detector noise artifact that was\nabsent in previous runs.\nWe note that O3 HL data\nhave sensitivity comparable to O4a HL data, while other\ndatasets were insufficiently sensitive.\nWe do not see any excess auto-power localized in these\nfrequency bins in the individual detectors; the nearest\nunknown excess power is observed in the L detector at\naround 92.7 Hz (3 bins away). We have not identified any\ncoherent instrumental witness channel that could account\nfor the elevated SNR. While some periods of elevated de-\ntector noise are present, there is no evidence of persistent\nor long-term non-stationary noise. Removing these pe-\nriods from the analysed data does reduce the SNR, but\nthe pattern in the sky persists. The results remain in-\nconclusive, and this frequency bin will be monitored in\nfuture observing runs to gather additional data.\nB.\nTargeted-narrowband radiometer search\nFor all five directions, we computed the SNR by com-\nbining the appropriately sized frequency bins across the\ndetectors.\nThe best SNRs after bin combination are\nshown in Tab. II, together with their p-values. The p-\nvalues are calculated from the maximum SNR distribu-\ntion obtained by simulating many realizations of strain\npower (details are shown in Appendix C 3).\nSince we do not find any evidence for narrowband\nGWs, we place 95% confidence ULs on the GW strain\nspectrum from the five selected targets, shown in Fig. 2\ntogether with the 1\u03c3 sensitivity. The results indicate a\nmedian improvement by a factor of 1.6\u20131.7 compared to\nprevious results from O1 to O3, with strain amplitudes\nranging from \u223c1.1 \u00d7 10\u221225 to 6.5 \u00d7 10\u221224 depending on\nthe target.\nSince the O4a data have the best sensitivity so far, it is\nworth comparing the contribution that the O4a dataset\nis giving to improve the reach of our searches. At higher\nfrequencies, O4a alone can provide better sensitivity than\nthe combined O1 to O3 data. It also helps to improve\nthe previous ULs in all the frequency ranges for all se-\nlected targets.\nThe combination with future stages of\nthe run promises to significantly increase the reach of\nour searches.\nIt is also useful to compare the results obtained with\nCGW searches. CGW searches use techniques that, for\nsources with at least a partial knowledge of the parame-\nters, grant a much longer coherence time and hence bet-\nter sensitivity than the targeted radiometer (for example,\nRef. [107] for the previous run and [108] for O4a).\nTaking into account the several semi-coherent methods\nused for the O3 all-sky search for isolated pulsars [109],\nthe sensitivity estimation over the whole sky is compa-\nrable to the ULs shown in this section. However, more\nprecise UL estimation, like the one shown in the first half\nof the third observing run (O3a) all-sky isolated CGW\nsearch [110], can lead to significantly lower limits than\nthe best ones obtained with SN 1987A of h0 \u224310\u221225.\nAs a reference for the most recent SN 1987A dedicated\nsearch, see also the 90% confidence UL on O3 data in\n[111].\nA directed search to the Galactic Center in O3, using a\nCW semi-coherent method, generally showed better sen-\nsitivity estimations than the targeted NBR search [112].\nRegarding Sco X-1, to assess the astrophysical signif-\nicance of the signal strength probed in this search, a\ncommonly used benchmark is the torque-balance level.\nIn most CGW searches of this target (see, for example,\n[113, 114], and the studies with updated ephemeris in\n[115, 116]), an order-of-magnitude estimate of the torque-\nbalance level is adopted as a reference point to evaluate\nwhether the explored parameter space is astrophysically\nrelevant. Given the absence of a detection in our search,\nwe compare our ULs with this benchmark and find that\nthey remain above the torque-balance level.\nThese upper limits assume a generic polarization and\nmarginalize over inclination and polarization angle (see\nAppendix C 4). However, if we instead consider the cir-\ncular polarization case\u2014typically not quoted in our fully\nunmodeled analyses\u2014our results indicate that the search\nhas surpassed the torque-balance threshold under the hy-\npothesis of circular polarization (more details are shown\nin Appendix C 5).\nC.\nBroadband radiometer search\nWe present the results of the BBR analysis for the O4a\ndataset only and after combining them with the previ-\nously existing results from O1 to O3, which we also sum-\nmarize in Tab. III. We have performed such an analysis\n\n20\nFIG. 2. Plots showing the ULs for the five targets of the O1-O4a NBR search. In each plot, the black solid line shows the\nBayesian ULs set at 95% confidence level, while the gray line is the 1\u03c3 sensitivity estimation in the hypothesis of no signal.\nThe shaded blue area shows the 1\u03c3 sensitivity estimation with data up to the O3 run, highlighting the sensitivity improvement\ngranted by adding the O4a run to the analyses.\nfor three spectral indices, namely \u03b1 = {0, 2/3, 3}, whose\nfinal results are the skymaps shown in Fig. 3.\nAs in\nRef. [53] we pixelate the sky by employing the HEALPix\nscheme [75], but instead of using Nside = 32 as in [53],\nhere we use Nside = 16. We have opted for this choice as\na compromise among the different angular resolutions of\nthe baselines at the lower and upper ends of their most\nsensitive frequency bands, for different spectral indices \u03b1\n[56, 117]. We recall that we apply the same data quality\nprescriptions as detailed in Sec. III and Appendix A.\nFollowing the methods from Appendix D, we have first\nevaluated the SNR maps for \u03b1 = 0, 2/3, and 3, and then\n\n21\nDirection\nMax SNR\nFrequency band (Hz)\np-value (%)\nBest UL (\u00d710\u221225)\nFrequency band (Hz)\nScorpius X-1\n4.2\n1706.09375 \u22121707.21875\n53.7\n1.5\n192.9375 \u2212193.0625\nSN 1987A\n4.1\n1672.6875 \u22121672.75\n59.0\n1.1\n246.75 \u2212246.8125\nGalactic Center\n4.4\n372.28125 \u2212372.90625\n22.5\n1.9\n227.4062 \u2212228.03125\nTerzan5\n4.5\n821.46875 \u2212822.09375\n16.3\n1.9\n260.71875 \u2212261.34375\nNGC6397\n4.5\n264.84375 \u2212265.40625\n18.2\n1.7\n251.40625 \u2212251.96875\nTABLE II. Results of the targeted-narrowband radiometer search on the O1-O4a combined datasets. We show the maximum\nSNR with its estimated p-value and frequency bin for each search direction. We also give the best 95% confidence-level GW\nstrain ULs, with the corresponding frequency band, taken as the median of the most sensitive 1-Hz band.\nMax SNR (% p-value)\nUL ranges (10\u22128)\n[erg cm\u22122 s\u22121 Hz\u22121]\n\u03b1\n\u2126gw(f)\n\u00afH(f)\nHL(O4a)\nO1+O2+O3+O4a\nO1+O2+O3+O4a\nO1+O2+O3 (HLV)\n0\nconstant\n\u221df \u22123\n1.7 (93)\n2.2 (72)\n1.2 \u2013 5.5\n1.7 \u2013 7.6\n2/3\n\u221df 2/3\n\u221df \u22127/3\n1.8 (97)\n2.4 (76)\n0.6 \u2013 3.0\n0.85 \u2013 4.1\n3\n\u221df 3\nconstant\n3.8 (20)\n3.8 (19)\n0.008 \u2013 0.092\n0.013 \u2013 0.11\nTABLE III. The maximum SNR across all sky positions, its estimated p-value, and the range of the 95% ULs on GW energy\nflux F 95%, UL\n\u03b1,\u02c6n\n(25 Hz) [erg cm\u22122 s\u22121 Hz\u22121] set by the BBR search by combining the LIGO data from O1 to O4a and the Virgo\nO3 data. The median improvement across the sky compared to limits from the O3 analysis is a factor of 1.4-1.7, depending on\n\u03b1. O1+O2+O3 (HLV) ULs reported in the last column differ from the ULs in [53] due to the different Nside parameter we are\nemploying here.\nwe have assessed the statistical significance of the max-\nimum SNR for each spectral index. We find that these\nSNR values are consistent with the noise-only hypothe-\nsis, and we therefore proceed with the UL calculation.\nThere is no evidence of outliers in the BBR results, in\ncontrast to the ASAF outlier in the 92.8125 Hz skymap.\nThis is not inconsistent with the ASAF outlier, which is a\nnarrowband feature and does not contribute significantly\nwhen integrating over the whole frequency band in the\nBBR analysis [118].\nFig. 3 illustrates the skymaps showing the 95%\nBayesian ULs on the GW energy flux F\u03b1,\u02c6n(25 Hz) in CGS\nunits for \u03b1 = 0, 2/3 and 3, obtained by combining the\ndata from O1 to O4a. When comparing Fig. 3 to the\nresults from the first three observing runs, we find that\nthe median improvement in ULs across the sky is a fac-\ntor of 1.4 for \u03b1 = 0, 1.4 for \u03b1 = 2/3, and 1.7 for \u03b1 = 3,\nrespectively.\nD.\nSpherical harmonics search\nFollowing the procedure for significance assessment de-\nscribed in Sec. II E, we compute the p-value for each real\nand imaginary part of the clean map estimator for the\ncombined dataset across O1-O4a, and compare them to\nthe local and global p-value thresholds, respectively. We\nfind that all SPH modes lie within the global p-value\nthreshold across the three power-law spectrum models,\nindicating consistency with a Gaussian distribution. See\nAppendix E 4 for more details. Given the absence of a\ndetected GWB signal, we compute ULs on C1/2\n\u2113\nat each\nangular scale characterized by the \u2113value, for different\npower-law frequency spectrum models. Fig. 4 shows the\nC\u2113ULs derived from the two estimators for each power-\nlaw spectrum model. Also, the uncertainties of \u02c6C\u2113mea-\nsurement are improved by factors of 1.4-2.2 compared\nto the previous search, as discussed with more details in\nAppendix E 4.\nNote that the variance of the \u02c6C\u2113estimator and its ULs\ndepend on the definition of the \u02c6C\u2113estimator or even\nthe specific regularization we apply to the Fisher ma-\ntrix. Therefore, one should not quantitatively compare\nthe ULs reported here to those in Ref. [53], where the\nregularization was performed differently as compared to\nwhat is presented in this paper. The improvement fac-\ntors mentioned above are based on the ULs recomputed\nfor O1+O2+O3 data using the consistent regularization\nmethod, described in Appendix E 2 for either definition\nof the C\u2113estimators. For the same reason, these ULs\ncannot be compared between the two different estima-\ntors. Even though we apply the same regularization to\nboth cases, the variance of the cross- \u02c6C\u2113estimator also de-\npends on how the entire dataset is split into subsets since\nthe inversion of a Fisher matrix is not a linear operation.\nTherefore, we treat these estimators as two different ways\nto present our search results.\nBelow, we consider the implications of our results for\ndifferent astrophysical models.\nFor \u03b1 = 2/3, the UL\nfound here for the corresponding \u2113modes is C1/2\n\u2113\n<\n1.2 \u00d7 10\u22129 sr\u22121, whereas several theoretical studies in\nthe literature [119\u2013121] predict a range of C1/2\n\u2113\n\u223c(0.2 \u2212\n5) \u00d7 10\u221211 sr\u22121 for 1 \u2264\u2113\u22644, assuming the normal-\nized GW energy density due to an isotropic GWB of\ncompact binaries is \u2126GW <\u223c(2.2 \u22126.7) \u00d7 10\u22129 [64].\nAlso, note that the shot noise term is expected to be\n\n22\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\n1.2\n2.6\n4.1\n5.5\n[erg cm\u22122 Hz\u22121 s\u22121]\n\u00d710\u22128\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\n0.6\n1.4\n2.2\n3.0\n[erg cm\u22122 Hz\u22121 s\u22121]\n\u00d710\u22128\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\n0.8\n3.6\n6.4\n9.2\n[erg cm\u22122 Hz\u22121 s\u22121]\n\u00d710\u221210\nFIG. 3.\n95% confidence Bayesian UL skymaps from a BBR search for point-like sources.\nThe maps are presented in the\nequatorial coordinate system and show UL skymaps of the GW energy flux from the combination of all the data from O1 to\nO4a LIGO observing runs and the Virgo O3 data. \u03b1 = 0, 2/3, and 3 are represented from left to right.\n(Cshot\n\u2113\n)1/2 \u223c10\u221210 sr\u22121, dominating the anticipated true\nastrophysical power spectrum [122], and is still below the\nobtained ULs by an order of magnitude. This is consis-\ntent with the fact that the point estimates for the two\ntypes of the \u02c6C\u2113estimators are not significantly different.\nFor \u03b1 = 0, we find the UL to be C1/2\n\u2113\n\u2264(0.7 \u22121.7) \u00d7\n10\u22129 sr\u22121 for 1 \u2264\u2113\u22643, whereas the theoretical study on\nNambu-Goto strings based on the model 3 in Ref. [123],\ncombined with the most up-to-date constraints on G\u00b5\nusing the isotropic component of the GWB [65], G\u00b5 <\u223c\n(2.7 \u223c4.2) \u00d7 10\u221215, sets C1/2\n1\n<\u223c10\u221212 sr\u22121. For both\nchoices of the power spectra (\u03b1 = 0 and \u03b1 = 2/3), we\nconclude that the predictions of the theoretical models\nare consistent with the search results presented here.\nIV.\nCONCLUSIONS\nWe do not find evidence for GW signals in any of the\nfour analyses using data from the first three observing\nruns of LIGO, Virgo, and O4a.\nHence, each analysis\nyielded the most stringent constraints to date from the\ndirectional search for persistent GWs. For the all-sky all-\nfrequency analysis, we observe a median (mean) improve-\nment factor of 1.12 (1.38) in Bayesian sensitivity estimate\nto the effective strain amplitude when comparing O4a to\nO1\u2013O3 in Tab. I. Combining data from O1\u2013O4a enhances\nthis improvement by a factor of 1.13 relative to O4a\nalone, and the fraction of notched frequency bins is re-\nduced from 11.4% to 7.9%. For the targeted-narrowband\nradiometer analysis, O4a contributes significantly to im-\nprove the upper limits of the entire frequency range (see\nFig. 2), in particular at higher frequencies. In the broad-\nband radiometer analysis, when comparing with the first\nthree observing runs in Tab. III, the median improvement\nacross the sky in the upper limits on the GW energy flux\nis 1.4, 1.4, and 1.7 for \u03b1 = 0, 2/3, 3, respectively. Lastly,\nthe spherical harmonic analysis has introduced a cross-C\u2113\nestimator to remove the potential shot noise and GWB\nbias as opposed to the conventional auto-C\u2113estimator.\nThe uncertainty on the angular power spectrum, C\u2113, de-\nrived from each estimator has improved by a factor of\n1.4-2.2 compared to the first three observing runs. Also,\nthe upper limits for each estimator shown in Fig. 4 are\nconsistent with the predictions of the theoretical models,\nsuch as cosmic strings and kinematic dipole.\nDuring O4a, the Virgo detector was not in science\nmode and is therefore not included in our analysis. How-\never, as noted in previous studies [53], incorporating the\nVirgo detector into the network (even with its higher\nnoise levels compared to the LIGO detectors) serves as\na natural regularizer in extended source searches. This,\nin turn, enables us to resolve finer structures in the GW\nskymaps. As shown in [124], current directional analyses\nare not affected by correlated noise, such as magnetic cor-\nrelations between detectors. While these contributions\nare currently negligible, they are expected to become in-\ncreasingly important as detector sensitivities improve.\nImprovements in detector sensitivity, longer observing\nruns, and larger network configuration will get us closer\nto the detection of potential local anisotropies or previ-\nously unknown point-like sources. It is also worth noting\nthat the potential of all-sky all-frequency sources to un-\ncover unknown narrowband signals represents an exciting\ndirection for future investigations. A thorough investiga-\ntion of the potential follow-up candidates from the all-sky\nall-frequency analyses, as presented in Ref. [125], could\nprovide valuable insights into the nature and significance\nof the identified candidates.\nLooking ahead, as the fourth observing run progresses,\nwe will continue to incorporate additional data and up-\ndate the findings reported in this paper.\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\n\n23\nFIG. 4. 95% ULs on the two C\u2113estimators for different \u03b1 using combined O1+O2+O3+O4a data.\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO consor-\ntium. The authors also gratefully acknowledge research\nsupport from these agencies as well as by the Council of\nScientific and Industrial Research of India, the Depart-\nment of Science and Technology, India, the Science & En-\ngineering Research Board (SERB), India, the Ministry of\nHuman Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00b4on (AEI), the Spanish Ministe-\nrio de Ciencia, Innovaci\u00b4on y Universidades, the European\nUnion NextGenerationEU/PRTR (PRTR-C17.I1), the\nICSC - CentroNazionale di Ricerca in High Performance\nComputing, Big Data and Quantum Computing, funded\nby the European Union NextGenerationEU, the Comuni-\ntat Auton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Commis-\nsion, the European Social Funds (ESF), the European\nRegional Development Funds (ERDF), the Royal Soci-\nety, the Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek - Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the Na-\ntional Research, Development and Innovation Office of\nHungary (NKFIH), the National Research Foundation of\nKorea, the Natural Sciences and Engineering Research\nCouncil of Canada (NSERC), the Canadian Foundation\nfor Innovation (CFI), the Brazilian Ministry of Science,\nTechnology, and Innovations, the International Center for\nTheoretical Physics South American Institute for Fun-\ndamental Research (ICTP-SAIFR), the Research Grants\nCouncil of Hong Kong, the National Natural Science\nFoundation of China (NSFC), the Israel Science Founda-\ntion (ISF), the US-Israel Binational Science Fund (BSF),\nthe Leverhulme Trust, the Research Corporation, the Na-\ntional Science and Technology Council (NSTC), Taiwan,\nthe United States Department of Energy, and the Kavli\nFoundation. The authors gratefully acknowledge the sup-\nport of the NSF, STFC, INFN and CNRS for provision\nof computational resources.\nThis work was supported\nby MEXT, the JSPS Leading-edge Research Infrastruc-\nture Program, JSPS Grant-in-Aid for Specially Promoted\nResearch 26000005, JSPS Grant-in-Aid for Scientific Re-\nsearch on Innovative Areas 2402: 24103006, 24103005,\nand 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grants-in-Aid for Scientific Research (S)\n17H06133 and 20H05639, JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cosmic\nRay Research, University of Tokyo, the National Re-\nsearch Foundation (NRF), the Computing Infrastructure\nProject of the Global Science experimental Data hub\n\n24\nCenter (GSDC) at KISTI, the Korea Astronomy and\nSpace Science Institute (KASI), the Ministry of Science\nand ICT (MSIT) in Korea, Academia Sinica (AS), the AS\nGrid Center (ASGC) and the National Science and Tech-\nnology Council (NSTC) in Taiwan under grants including\nthe Science Vanguard Research Program, the Advanced\nTechnology Center (ATC) of NAOJ, and the Mechanical\nEngineering Center of KEK.\nAppendix A: Observing runs and dataset\nTab. IV details each individual observing run of the\ndetectors from O1 to O4a, including their start and end\ntimes, the amount of data lost through time-domain cuts,\nand the effective data available for the GWB directional\nsearches. As part of the time-domain cuts, we exclude\ndata contaminated by instrumental artifacts, hardware\ninjections used for signal validation, and segments con-\ntaining known GW signals. We also apply a standard\nnon-stationarity cut [64] to eliminate segments that do\nnot behave as Gaussian noise. The table also shows the\nfraction of frequency bins removed from the analysis.\nThese removals follow the same frequency-domain cuts\ndescribed earlier, based on coherence studies identifying\ncontamination from instrumental artifacts. The specific\nbins removed may vary across analyses depending on sen-\nsitivity to narrow spectral features.\nAppendix B: ASAF radiometer search\n1.\nSignificance\nWe summarize the statistical framework used here to\nidentify the GW signal in the ASAF search.\nThe null hypothesis assumes that the data contain only\nGaussian noise, while the alternative hypothesis is that\na GW source is present in at least one frequency-pixel\npair. The detection statistic is the SNR (Eq. (22)), which\nunder the null ideally follows a zero-mean Gaussian dis-\ntribution.\nBecause real detector data include non-Gaussian fea-\ntures such as narrowband artifacts and glitches, the null\nSNR distribution is obtained using the random time-shift\n(TS) method [54]. The procedure involves dividing the\ndata from the entire observing run into multiple jobs\n(2493 in the case of O4a), each typically having a max-\nimum duration of 5000 seconds. For each job, the data\nfrom one detector is held fixed while the data from the\nother detector is shifted by a random time delay, uni-\nformly sampled between 1 and 2 seconds. This random\ntime-shifting process effectively eliminates any coherent\nand persistent signals, ensuring that only the noise back-\nground remains in the data [54].\nAfter ensuring the Gaussianity of the null distribution,\nwe proceed to test the zero-lag (ZL) data (without an\nunphysical time-shift) against the null hypothesis. We\ndetermine the observed highest SNR across frequency-\npixel pairs and compute the local p-value, pL, assuming a\nGaussian distribution for noise. Since many simultaneous\ntests increase the chances of false positives (the look-\nelsewhere effect). we adjust to global p-value, pG, using\nSidak\u2019s correction [126, 127]:\npG = 1 \u2212(1 \u2212pL)Ntrials \u2248Ntrials pL\nfor pL \u226a1. (B1)\nwhere Ntrials is the number of frequency-pixel pairs. We\nreject the null hypothesis if pG < 5%.\n2.\nFollow-up Candidates Identification\nAfter assessing the significance of our data,\nwe\nidentify sub-threshold candidates for follow-up using\nmore sensitive methods, such as matched-filtering-based\nsearches [125]. We first determine the sky pixel with the\nmaximum SNR,\n\u02c6\u03c1max(f) \u2261max\u02c6n \u02c6\u03c1\u02c6n(f) ,\n(B2)\nfor each frequency bin in both zero-lag and time-shifted\ndata.\nThe full frequency range is divided into 10 Hz\nsub-bands for the time-shifted data. For each sub-band,\nwe compute the histogram of \u02c6\u03c1max(f) and determine\nthe threshold below which 99% of the histogram area\nlies. This results in an array of sub-band-wise thresh-\nolds, which are then smoothed using a running average.\nCandidates in the zero-lag data with SNR exceeding this\nthreshold are selected for further investigation.\nIf the\nzero-lag data is consistent with random-timeshifted data\n(and Gaussian noise), this procedure is expected to yield\nat least \u2248513 candidates.\nThe following calculation\nshows why this number of candidates is expected:\nSub-bands = (1726 \u221220) Hz\n10 Hz\n\u2248171,\nBins per sub-band = 10 Hz\n\u2206f\n= 320 ,\nTop-1% candidates per sub-band = 320 \u00d7 0.01 \u22483 ,\nTotal Top-1% candidates = 171 \u00d7 3 = 513 .\n(B3)\n3.\nUpper Limit Calculation\nWe adopt a hybrid frequentist-Bayesian approach for\nsetting constraints [128]. Assuming the point estimate\nis a sufficient statistic for measuring GW source proper-\nties, we apply Bayes\u2019 theorem to construct the posterior\ndistribution.\nFor\nclarity,\nthe\ndependence\nof\nestimators\nh\n\u02c6P \u02c6n(f), \u03c3\u02c6n(f)\ni\nand\nstrain\nparameter\nheff,\u02c6n(f)\non\ndirection and frequency is assumed to be implicit in\n\n25\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\nSNR\n10\u22121\n100\n101\n102\n103\n104\n105\n106\n107\nCount\nO4a\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\nSNR\nCount\nO1-O4a\nZL\nTS\nN\n\u221a\nN Errors\n2\n\u221a\nN Errors\n1-sided 5% global p-value\n2-sided 5% global p-value\nFIG. 5. ASAF search results \u2014 Significance: Left Panel: Distribution of SNR for the zero-lag (blue) and time-shifted (magenta)\ndatasets with O4a observing run. The time-shifted (unphysical) distribution is consistent with a Gaussian (gray line) with\nmean \u22125 \u00d7 10\u22124 and standard deviation 0.98. Poisson 1- and 2-sigma uncertainties for the time-shifted histogram are shown\nas a yellow-shaded region. The zero-lag histogram is largely consistent with the time-shifted data, except for non-Gaussian\nexcess at negative SNR. Vertical brown lines (solid and dashed) indicate the 1- and 2-sided 5% global p-value SNR thresholds.\nAlthough an astrophysical signal is expected to yield a positive SNR, we investigate the origin of the observed negative SNR\nfeature. Right Panel: Same as the figure in the right panel but with O1-O4a data.\nFIG. 6. Follow-up sub-threshold candidates: Left Panel: Distribution of the maximum SNR statistic (y-axis) as a function\nof frequency (x-axis) obtained with O4a observing run, where Max (SNR) denotes the maximum SNR across the sky within\neach frequency bin. Scatter points for the zero-lag and time-shifted datasets are shown in blue and magenta, respectively.\nGray vertical lines indicate vetoed frequency bins excluded due to known instrumental artifacts. The brown horizontal line\nindicates the SNR threshold corresponding to a 5% 1-sided global p-value. The yellow curve shows the maxSNR threshold\ncorresponding to a 99% local p-value in each 10-Hz band, smoothed over three neighboring bands. While the zero-lag data\nis consistent with Gaussian noise, we identify 505 sub-threshold follow-up candidates marked with teal circles, which may be\nfurther analysed using matched-filtering-based CGW search pipelines. Right Panel: Same as the left panel, but using data\nfrom O1-O4a observing runs.\n\n26\nRun\n[51\u201354]\nStart time\n(UTC)\nEnd time\n(UTC)\nDetectors\nTime\ndomain cut\n(%)\nEffective data\n(days)\nFrequency notch fraction (%)\nASAF analysis Other analyses\nO1\n2015-09-18 15:00\n2016-01-12 16:00\nH, L\n35\n29.85\n25.5\n21.1\nO2\n2016-11-30 16:00\n2017-08-25 22:00\nH, L\n16\n99\n19.6\n15.3\nO3\n2019-04-01 15:00\n2020-03-27 17:00 H, L, V\n10.7 (HL)\n14.3 (HV)\n14.7 (LV)\n169 (HL)\n146 (HV)\n153 (LV)\n21 (HL)\n34.8 (HV)\n28.15 (LV)\n14.8 (HL)\n25.2 (HV)\n21.9 (LV)\nO4a\n2023-05-24 15:00\n2024-01-16 16:00\nH, L\n8.3\n108.65\n11.4\n11.4\nTABLE IV. This table shows the individual observing runs, their start and end times, the detectors involved, the data quality\ncuts (both time and frequency domain) applied, and the effective data used in this analysis.\n0\n20\n40\n60\n80\n100\n(Observation Days)\n\u22124\n\u22122\n0\n2\n4\n6\nCumulative SNR\nf0 = 92.8125 Hz, \u2206f = 0.03125 Hz\nZL; (f0 \u2212\u2206f)\nZL; f0\nZL; (f0 + \u2206f)\nRT; (f0 \u2212\u2206f)\nRT; f0\nRT; (f0 + \u2206f)\n\u221aTobs \u22124.9\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\nmax (SNR) pixel\nmin (SNR) pixel\n\u22126.13\n\u22122.34\n1.44\n5.22\n12h\n6h\n18h\n45\u00b0\n0\u00b0\n-45\u00b0\n\u22126.13\n\u22122.36\n1.41\n5.18\nFIG. 7. Details of O4a marginal outlier towards negative SNR tail: The SNR skymap for 92.8125 Hz marginal outlier in O4a\nis shown in the top right panel. The positive and negative SNR blobs may be correlated through the point spread function:\na GW source at the location of maximum SNR could produce a corresponding negative SNR feature next to it. To test this,\nwe simulate skymap by injecting a source in the positive SNR direction and recover a map similar to the observed map, as\nshown in the bottom right panel. This motivates further investigation of both blobs. In the left panel, we show the evolution of\ncumulative SNR in the direction of maximum SNR (marked by an up triangle in the top right panel) as a function of observing\ndays during O4a. The thick blue indicates the outlier frequency bin, while the two other thin blue curves represent the adjacent\nfrequency bins immediately before and after the outlier. The magenta lines represent SNR evolution for random timeshifted\ndata.\n\n27\nthe following discussion.\nEach element in the matri-\nces\nh\n\u02c6P, \u03c3\ni\nhere represents an observation from the\nindividual dataset (e.g., baseline or observing run).\n0.95 =\nZ (heff)95%\n0\ndheff\nL( \u02c6P \u2206f|E, heff) p(heff)\nR\ndheff L( \u02c6P \u2206f|E, heff) p(heff)\n.\n(B4)\nThe integrand in the above equation represents the\nposterior distribution for heff, where L( \u02c6P \u2206f|E, heff) is\nthe likelihood and p(heff) is the prior for heff.\nThe\nlikelihood L( \u02c6P \u2206f|E, heff) is modelled as a multivari-\nate Gaussian distribution for the random vector \u02c6P \u2206f \u223c\nN[(heff)2 I, E] where I is a column matrix with unit ele-\nments. The prior is assumed to follow a uniform distribu-\ntion, heff \u223cU[0, 10 \u221a\u03c3 \u2206f ] [54] where \u03c32 is squared sum\nof variance from individual dataset, i.e., \u03c32 = P\ni \u03a3ii.\nWe note that the integration in the denominator spans\nthe prior-defined range of heff.\nGiven that the strain data is obtained by calibrating\nthe detector response to GW strain, our estimator is sub-\nject to calibration uncertainties (see [48\u201354, 129] for de-\ntails). Marginalization over calibration uncertainty intro-\nduces an additional covariance term to the noise variance\nmatrix of \u02c6P [130]. The modified covariance matrix E is\ngiven by\nE = \u03a3 + (heff)4 D ,\n(B5)\nwhere \u03a3 is the noise covariance matrix, defined as \u03a3ij =\n\u03c32\ni \u03b4ij \u2206f, and D accounts for calibration errors.\nThe\nindices i, j run over the number of analyzed datasets. As\nan example, for the baselines HL and LV, the D matrix\nis\nD =\n\u0012\n\u03f52\nH + \u03f52\nL + \u03f52\nH\u03f52\nL\n\u03f52\nL\n\u03f52\nL\n\u03f52\nL + \u03f52\nV + \u03f52\nL\u03f52\nV\n\u0013\n,\n(B6)\nwhere \u03f5H, \u03f5L, and \u03f5V are the amplitude calibration un-\ncertainties of the individual detectors [131].4\nThe off-\ndiagonal elements in the matrix are present only when\nthe datasets analyzed from a given observing run share\ncommon detectors.\nAppendix C: Targeted narrowband radiometer\n1.\nSource direction and its relevance\nIn this section, we list the sources chosen for the tar-\ngeted search, explaining their relevance and selection cri-\nteria.\n4 The uncertainties adopted for different detectors and observing\nruns in this study are as follows: \u03f5O1\nH\n= 0.048, \u03f5O1\nL\n= 0.054,\n\u03f5O2\nH\n= 0.026, \u03f5O2\nL\n= 0.0385, \u03f5O3\nH\n= 0.0696, \u03f5O3\nL\n= 0.0637, \u03f5O3\nV\n=\n0.05, \u03f5O4a\nH\n= 0.0693, and \u03f5O4a\nL\n= 0.041.\nScorpius X-1: It is a neutron star in a low mass X-\nray binary (LMXB) system, considered one of the most\npromising targets for CGW searches [58, 59].\nIn sev-\neral searches [114, 116, 132], a torque balance is as-\nsumed between accretion spin-up from the companion\nstar and angular momentum loss by gravitational emis-\nsion (see also [133, 134]), and it has a known position\nand ephemeris.\nHowever, its rotational frequency re-\nmains unknown [135], and a spin wandering effect is ex-\npected, caused by stochastic fluctuations of the accretion\nrate [136]. The difficulty in characterizing its rotation\nmakes it an optimal target for an unmodeled narrowband\nsearch, like the targeted NBR, across a large frequency\nrange.\nGalactic Center: Identified as the location of the super-\nmassive black hole Sagittarius A*, it has been addressed\nas the host of multiple potential GWs sources, making\nit a target for dedicated searches for persistent signals\n[54, 137, 138]. Being a potential host of many unresolved\nsources with unknown parameters, it is another natural\ntarget for our search.\nSN 1987A: A young supernova (SN) remnant, SN\n1987A has been identified as a promising target for GW\nsearches due to its recent origin [139, 140]. However, until\nrecently, it was not possible to confirm the existence of a\nneutron star at its center. This has now been established\nthrough electromagnetic emission detected by the James\nWebb Space Telescope [141]. Although the source param-\neters remain unknown, this confirmation underscores the\nrelevance of SN 1987A as a target for GW searches.\nTerzan 5 and NGC 6397: Globular clusters are known\nto contain many neutron stars and can be promising tar-\ngets for GW searches. Among the possible selection cri-\nteria, we follow [142] and [143] that point to Terzan 5\nand NGC 6397 as a possible host of a large number of\nunresolved sources, together with the fact that Terzan 5\nalone hosts approximately 18% of the known millisecond\npulsars [144]. However, other criteria exist (for example,\nsee [145]).\n2.\nBin Combination\nThe value of the number N of bins to be combined, for\nthe individual sources analyzed, is determined as follows:\nfor Scorpius X-1, assuming torque balance and hence ne-\nglecting steady spin variation during the observing time,\nit is computed using the evolution predicted by its orbital\nparameters (see [146]). For the Galactic Center, Terzan\n5, and NGC 6397 \u2013 which may host a large number of un-\nknown sources \u2013 we compensate only the Earth\u2019s Doppler\nmodulation, fixing N = 10 for all of them.\nThe high latitude of SN 1987A causes a negligible\nDoppler spread due to Earth\u2019s motion with the default\nfrequency resolution used (\u2206f = 1/32 Hz); hence, in this\ncase, N = 1.\nHowever, SN 1987A is a young supernova remnant, and\nit is expected to have a strong spin-down effect due to\n\n28\nrotational energy loss. We did not consider the cumula-\ntive effect of different observing runs when establishing\nthe bin combination, as this would require specific tech-\nniques to account for the several-month gaps between\nruns, under various assumptions about the source\u2019s spin\nderivatives (see, for example, the study carried out in\n[147]).\nThis leads to ULs that are less conservative than those\nobtained by combining additional bins, under the as-\nsumption that the entire signal is confined to a single\nfrequency bin rather than distributed across several.\n3.\nSignificance\nFor a given target \u02c6n, to assess the significance of the\nSNR-frequency data results after the bin combination, a\np-value is estimated with the following process: 1) a large\nnumber (n \u223c256) noise-only distributions of P\u02c6n(f) are\ngenerated, drawing for each frequency bin a value from\nGaussian distributions with mean 0 and the correspond-\ning \u03c3f obtained from the data; 2) for each realization, the\ngenerated P\u02c6nsim(f) and the measured \u03c3(f) are combined\naccording to the data from the given target, yielding a\nsimulated SNR distribution with the same bin combina-\ntion; 3) the maximum SNR from each of the simulated\ndistributions is stored; 4) a range of p-values running\nfrom [0, 1] in n steps are generated and associated with\nthe maximum SNRs obtained; 5) via a linear interpo-\nlation the data SNRs are matched to the SNR\u2013p-value\ndistribution obtained by the simulations.\nA frequency\nbin whose SNR corresponds to a p-value of less than 5%\nis considered an outlier that needs to be analyzed more\nthoroughly.\n4.\nBayesian posterior and UL plots\nIn the following, the calculation of the upper limits\nvia the integration of Bayesian posteriors will be broken\ndown. The starting point is the definition of expectation\nvalue and variance of the cross-correlation statistics for\npersistent GW signals. They can be written respectively\n[105]:\n\u00b5P =\nP\nj(A+2F +\n1jF +\n2j + A\u00d72F \u00d7\n1jF \u00d7\n2j)(F +\n1jF +\n2j + F \u00d7\n1jF \u00d7\n2j)\nP\nj(F +\n1jF +\n2j + F \u00d7\n1jF \u00d7\n2j)2\n.\n(C1)\nand\n\u03c32\nP =\n2P1P2\nT 2\ncoh\nP\nj(F +\n1jF +\n2j + F \u00d7\n1jF \u00d7\n2j)2 ,\n(C2)\nwhere the sum is over the M segments of the semicoher-\nent search with coherence time Tcoh; the GW amplitudes\nfor the two polarizations A+, A\u2212depend on the source\ninclination angle \u03b9 and the GW strain tensor amplitude\nh0 5; the antenna patterns for the two polarizations and\nthe two detectors at the time segment j, F {+,\u00d7}\n{1,2}j , de-\npend explicitly on the polarization angle \u03c8; the single-\nsided power spectral density estimations for the two de-\ntectors are P1,2. In the case of circularly polarised signal\nA+ = A\u00d7 = h0 and \u00b5P = h2\n0.\nThe ULs are computed by integrating the Bayesian\nposterior function up to the value hUL\n0\nthat returns the\nchosen 95% confidence:\n0.95 =\nZ hUL\n0\n0\np(h0|P, \u03c3P).\n(C3)\nFor a given frequency bin, the posterior comes from\nthe marginalization integral\np(h0|P) \u221d\nZ 1\n\u22121\nd(cos \u03b9)p(\u03b9)\nZ \u03c0/4\n\u2212\u03c0/4\nd\u03c8 p(\u03c8)\nZ 3\n\u22121\nd\u03bb p(P|h0, \u03b9, \u03c8, \u03bb)p(\u03bb)\n(C4)\nover the inclination angle \u03b9, the polarization angle \u03c8[105]\nand the calibration factor \u03bb [130].\nThe priors for the first two integrals\u2014respectively p(\u03b9)\nand p(\u03c8)\u2014will be uniform distributions within the in-\ntegral range, and their values will be absorbed in the \u221d\nsymbol. The latter integral is over an unknown correction\nfactor representing the uncertainty in the calibration. We\nassume for it a Gaussian prior distribution p(\u03bb), with \u03c3\u03bb\nas standard deviation, a known parameter called calibra-\ntion error.\nThe likelihood distribution is\nL(P|h0, \u03b9, \u03c8, \u03bb) = exp\n\"\n\u22121\n2\n\u0012\u03bbP \u2212\u00b5P\n\u03bb\u03c3P\n\u00132#\n,\n(C5)\nwhere the dependence on h0,\u03b9,\u03c8 lies within \u00b5P.\nThe marginalized posterior for a generic polarization\nwill be:\np(h0|P) \u221d\nZ 1\n\u22121\nd(cos \u03b9)\nZ \u03c0/4\n\u2212\u03c0/4\nd\u03c8\nZ 3\n\u22121\nd\u03bb exp\n\"\n\u22121\n2\n\u0012\u03bbP \u2212\u00b5P\n\u03bb\u03c3P\n\u00132\n\u22121\n2\n\u0012 \u03bb\n\u03c3\u03bb\n\u00132#\n.\n(C6)\nIn the case of a circularly polarized signal, the likeli-\nhood becomes independent of \u03b9 and \u03c8, and the posterior\nintegral will simply reduce to\nL(h0|P) \u221d\nZ 3\n\u22121\nd\u03bb exp\n\"\n\u22121\n2\n\u0012\u03bbP \u2212h0\n\u03bb\u03c3P\n\u00132\n\u22121\n2\n\u0012 \u03bb\n\u03c3\u03bb\n\u00132#\n.\n(C7)\n5 A+ = 1\n2 h0(1 + cos2 \u03b9) and A\u00d7 = h0 cos \u03b9, where \u03b9 is the source\ninclination angle.\n\n29\nIt has been shown that there is a scale factor of \u223c2.5\nbetween ULs computed with a marginalization for a\ngeneric polarization with respect to the circular polariza-\ntion ones, which depends only on the SNR of the search\nresults [105]. Calculating the integrals in Eq. (C6) for\neach frequency bin can consume a large amount of com-\nputing resources, hence ULs for the two cases are simu-\nlated only for a small number of SNR values between -8\nand 8. The ratio between the two simulated distributions\nwill be called \u201cupper limit ratios\u201d.\nThe final UL values are computed under the computa-\ntionally much simpler hypothesis of circular polarization.\nAssuming a Gaussian prior for the calibration factor, an\nanalytical solution for the marginalized posterior exists\n[148, 149] in the form of:\np(h0|P) \u221d\n1\n\u221a\n2\u03c0E2 exp\n\"\n\u22121\n2\n\u0000P \u2212h2\n0\n\u00012\nE2\n#\n,\n(C8)\nwhere E \u2261\u03c3P + h4\n0\u03c3\u03bb. By interpolation on the real SNR\ndata, the UL ratios are applied to reproduce the ULs for\na generic polarization.\nFor the combination of datasets, we have to treat the\ncombined effect of the calibration error of the different\nruns, changing how the ULs are produced.\nIt can be\nshown that the combined likelihood is the product of the\nsingle dataset likelihood [130]:\nL(P|h0, \u03bb) =\nY\ni\nL(Pi|h0, \u03bbi).\n(C9)\nWith P = {P1, ..., Pn} we indicate the vector of the\ndetection statistics for a fixed frequency bin and with\n\u03bb = {\u03bb1, ..., \u03bbn} the vector of the unknown calibration\nfactor we want to marginalize, across the n datasets. The\nmarginalized posterior will, in turn, be\np(h0|P) \u221d\nZ\nd\u03bb L(P|h0, \u03bb)p(\u03bb).\n(C10)\nIt is important to underline that the detector base-\nline calibration uncertainty affecting our results is the\ncombination of the single detector calibration uncertain-\nties. This, in general, will produce covariance matrices\nwith off-diagonal elements like in the example in Eq. (B6)\nthat have to be considered in the integration. If, in turn,\nwe consider the same baseline across different runs, we\ncan consider the single-run calibration uncertainties in-\ndependently of each other and separate the integrals. In\nthis case as well, the marginalized posterior will be the\nproduct of the single dataset posteriors:\np(h0|P) =\nY\ni\np(h0|Pi).\n(C11)\n5.\nComparison between UL and torque balance for\nScorpius X-1\nAn order-of-magnitude estimate of the torque-balance\nlevel, often used in Sco X-1 CGW searches [113, 114] to\nFIG. 8. Comparison of the UL for generic polarization (solid\nblack line) and a circularly polarized signal (solid gray line)\nwith the torque-balance level from Eq. (C12) (dashed black\nline).\nWhile the former does not reach the torque-balance\nthreshold, the latter lies well below it.\ngauge the astrophysical relevance of the explored param-\neter space, is given by\nh0 \u22483.4 \u00d7 10\u221226\n\u0012\nf0\n600 Hz\n\u0013\u22121/2\n.\n(C12)\nThis curve is shown in Fig. 8 as a dashed black line.\nIf we compare the 95% confidence level UL obtained by\nthe NBR search to the torque-balance curve, it is evident\nthat for a generic polarization, the search does not reach\namplitudes below the torque balance hypothesis.\nOn the other hand, if we consider a circularly polar-\nized signal, then the ULs are not marginalized over in-\nclination and polarization angle, reaching lower effective\nstrain amplitudes.\nIn this scenario, and in agreement\nwith the aforementioned searches, our results surpass the\ntorque-balance limit.\nAppendix D: Broadband radiometer search -\nStatistical significance\nTo assess whether a signal is present or not in the BBR\nsearch data in Sec. III C, we consider the SNR map for\neach spectral index and evaluate the statistical signifi-\ncance of the maximum SNR under the hypothesis that\nonly noise is present in the data. This is accomplished\nby simulating Ntrials realizations of the SNR sky-maps\nand selecting the maximum SNR for each of them, hence\nconstructing the probability distribution function of the\nmaximum SNR. In practice, for each trial: 1) we simu-\nlate a skymap where each pixel contains Gaussian noise;\n2) we color the noise in each pixel by using the singular\nvalues decomposition of the Fisher matrix to generate\n\n30\nthe simulated dirty map in the absence of any signal;\n3) we use the diagonal of the Fisher matrix to obtain\n\u03c3\u02c6n = (diag {\u0393\u02c6n\u02c6n\u2032})\u22121/2 and the simulated estimator map\n\u02c6P\u02c6n, noise in the absence of a signal; 4) we obtain the SNR\nmap as \u02c6P\u02c6n, noise/\u03c3\u02c6n; 5) we select the maximum SNR and\nadd it to the histogram of the maximum-SNR distribu-\ntion. After Ntrials, we evaluate the maximum-SNR sta-\ntistical significance (p-value) as the ratio of the number\nof histogram entries that exceed the maximum value of\nthe observed SNRs to the total number of the histogram\nentries (i.e., Ntrial).\nIf the statistical significance of the maximum SNR is\nconsistent with the noise-only hypothesis, we proceed\nwith the evaluation of the ULs on the GWB angular\npower spectrum. The evaluation of the ULs follows the\nsame Bayesian approach as that described in Appendix B\nby replacing heff\n0\nwith P and \u02c6P \u2206f with \u02c6P in Eq. (B4),\nwhich we then rescale to GW energy flux units.\nAppendix E: Spherical harmonics analysis\n1.\nAngular resolution\nThe number of SPH modes to evaluate scales as\n(\u2113max + 1)2, and hence, in practice, one cannot search\nfor arbitrary high-order modes due to substantial com-\nputational costs.\nMore importantly, the interferome-\ntry in general imposes a minimum angular scale below\nwhich a given baseline becomes insensitive to real sig-\nnals. For a monochromatic signal at the frequency f\u2217,\nthe interferometry-limited angular scale is given by\n\u03b8 =\nc\n2 d f \u2217,\n(E1)\nwhere d is the separation of two GW detectors, e.g.,\nd = 3000 km for the LIGO detectors.\nSince SPH\nsearches target broadband signals, f \u2217cannot be uniquely\ndetermined, but is approximated by the dominant fre-\nquency component of the signals.\nThis dominant fre-\nquency can be estimated by the tangent point between a\ngiven power-law spectrum and the baseline\u2019s sensitivity\ncurve, i.e., power-law integrated curve [150]. Therefore,\nthe larger power-law index \u03b1 leads to a higher value of\nf \u2217, e.g., f \u2217= 52.5, 256.5 Hz for \u03b1 = 0, 3, respectively.\nOnce \u03b8 is known, the highest SPH mode \u2113max, which\ncorresponds to the minimum angular scale, can be ex-\npressed as \u2113max = \u03c0/\u03b8.\nFollowing this argument, we\nhave adopted \u2113max = 3, 4, 16 for \u03b1 = 0, 2/3, 3, respec-\ntively [51\u201353].\n2.\nRegularization of the Fisher matrix\nApart from the angular resolution mentioned above,\nanother numerical issue arises from the fact that the\nFisher matrix is often ill-conditioned\u2014that is, some of\nits eigenvalues are extremely small, which makes the in-\nversion of the Fisher matrix numerically unstable and\nintroduces additional numerical noise.\nThis issue can\nbe mitigated by regularizing the Fisher matrix; in pre-\nvious analyses, we addressed this by discarding negligi-\nble eigenmodes.\nIn O4a, we revisited the criterion for\nidentifying such negligible eigenmodes, taking into ac-\ncount their residual sum of squares (RSS) to strike a\nbalance between noise variance and signal recovery bias.\nRegularizing the Fisher matrix is a common mathemat-\nical problem, and hence, there are several regularization\nmethods developed in the field of astronomy [77, 81, 151\u2013\n153]. Our approach is to replace the singular values for\na subset of the SPH modes (e.g., M out of the total N\nmodes) that have smaller eigenvalues than a given thresh-\nold (\u03bbM) with infinities, i.e.,\nU \u0393 V = diag(\u03bb1, \u00b7 \u00b7 \u00b7 , \u03bbM, \u00b7 \u00b7 \u00b7 , \u03bbN)\n(E2)\n\u2192diag(\u221e, \u00b7 \u00b7 \u00b7 , \u221e, \u03bbM+1, \u00b7 \u00b7 \u00b7 , \u03bbN),\n(E3)\nwhere U, V are each a unitary matrix, which diagonal-\nizes \u0393, and \u03bbi are the i-th singular values of \u0393 sorted as\n\u03bb1 < \u03bb2 < \u00b7 \u00b7 \u00b7 < \u03bbN. This would effectively remove the\ncontribution from the regularized SPH modes after in-\nverting the Fisher matrix [57]. Note that the clean map\nestimator would be affected by a potential bias in the\npresence of astrophysical anisotropies\n\u27e8\u02c6P\u00b5\u27e9= \u0393\u22121\nR \u00b7 \u0393 \u00b7 P \u0338= P,\n(E4)\nwhere \u0393R is a regularized Fisher matrix. Although, tech-\nnically speaking, the fractional number of singular modes\nto keep, fkeep, is still arbitrary, optimizing the regular-\nization involves a trade-off relation between a lower vari-\nance, i.e., larger SNR, and the accuracy of the clean map\nestimator [117].\nSince O1, LVK has adopted an empirical approach that\nkeeps 2/3 of the total modes, i.e., fkeep = (N \u2212M)/N =\n2/3 across different \u03b1 values [51\u201353]. In O4a, we revisit\nthis approach and introduce an alternative justification\nby computing RSS of the clean map estimator for a given\nsimulated signal [77, 81]. This is defined as\nRSS = | \u02c6P(k) \u2212Pinj|2,\n(E5)\nwhere Pinj is an injected GWB signal and \u02c6P(k) is a clean\nmap estimator with the noise realization using the Fisher\nmatrix derived from the time-shifted O4a dataset, and\nthe regularization keeping k singular modes.\nFor each\nk, we repeat this computation with 10 different noise\nrealizations and take their mean value. Since the mean\nof RSS follows\n\u27e8RSS\u27e9= \u27e8| \u02c6P(k)|2\u27e9\u22122 Re\nh\n\u27e8\u02c6P(k)\u27e9\u00b7 Pinji\n+ |Pinj|2 (E6)\n=\n\u03c32\nP\n|{z}\nvariance\n+\n\f\f\f\u27e8\u02c6P(k)\u27e9\u2212Pinj\f\f\f\n2\n|\n{z\n}\nbias\n,\n(E7)\n\n31\nFIG. 9.\nNormalized RSS as a function of fkeep for each \u03b1\nvalue.\nthe first and second terms in Eq. (E7) represent the vari-\nance and bias of the clean map, respectively. Therefore,\nminimizing \u27e8RSS\u27e9in terms of k identifies the optimal\npoint that compromises the variance and bias. In prin-\nciple, RSS values depend on the anisotropy model of the\ninjected GWB, and here we consider only the monopole\ncomponent, i.e., P\u2113m = 0 (\u2113\u0338= 0 or m \u0338= 0), as a plausible\ndetection scenario.\nFig. 9 shows a normalized RSS as a function of fkeep\nfor each \u03b1 value, which demonstrates the optimal fkeep\nof 0.3, 0.35 and 0.72 for \u03b1 = 0, 2/3, 3, respectively. We\nwill adopt these values for the regularization applied to\nthe main results of the SPH analysis.\nAlso, Fig. 10 shows the distribution of eigenvalues for\nthe Fisher matrix with different \u03b1 values combining O1\nto O4a data. The two dashed lines with each color com-\npare the number of modes to keep between the conven-\ntional (fkeep = 2/3) and the RSS regularization meth-\nods. Compared to the conventional fkeep = 2/3, the new\nregularization keeps fewer modes for \u03b1 = 0, 2/3, while\nkeeping more modes for \u03b1 = 3. Although this change in\nfkeep alters the variance of the clean map estimator, we\nnote that it does not indicate a physical change in the\nsensitivity, but rather a different way of presenting the\nresults.\n3.\nCross \u02c6C\u2113estimator\nIn the limiting case where the detector data con-\ntain only detector noise, the auto- \u02c6C\u2113estimator given by\nEq. (17) is unbiased.\nHowever, Ref. [83] showed that\nin the presence of an astrophysical GWB, it is signifi-\ncantly biased by the shot-noise-dominated nature of the\nsignal, which arises from the discrete spatial or tem-\nporal realization of individual events.\nAlso, this shot\nnoise effect scales as \u221d1/Tobs in terms of C\u2113, where\nFIG. 10.\nDistribution of eigenvalues for the Fisher matrix\nwith different \u03b1 values combining O1 to O4a data. The two\ndashed lines with each color compare the number of modes to\nkeep between the conventional (fkeep = 2/3) and new (RSS)\nregularization methods.\nTobs is the observation time, which is the same scaling\nexpected for the ULs set by the search.\nAs a result,\nshot noise may become a limiting factor in future SPH\nsearches\u2014particularly if sensitivity improves faster than\nthe 1/Tobs scaling, whether due to enhanced detector sen-\nsitivity or the inclusion of additional detectors. In such\na regime, the analysis could begin to detect GWB sig-\nnals from plausible astrophysical populations, e.g., from\nCBCs. In addition, Ref. [83] found that the auto- \u02c6C\u2113es-\ntimator is biased even in the absence of shot noise in the\nGWB signal.\nTherefore, we introduced the cross- \u02c6C\u2113estimator shown\nin Eq. (20), which involves multiple clean maps derived\nfrom subsets of the whole dataset. For each subset, we\ncompute the corresponding dirty map X(i) and Fisher\nmatrix \u0393(i), and follow the same deconvolution procedure\nas described earlier to obtain the individual clean maps.\nThis cross- \u02c6C\u2113estimator, obtained by summing over all\npairs of distinct maps, is by construction unbiased, ac-\ncounting for the fact that the bias arises from autocorre-\nlation of each data segment. This concerns contributions\nto the bias not only due to the GWB signal and shot\nnoise but also the detector noise, which is why \u03a3R is no\nlonger subtracted from the clean map product, unlike in\nEq. (17). In practice, there are many ways to divide the\ntotal dataset into subsets, with no trivial choice. How-\never, following Ref. [83], we aim for constructing subsets\nof the data with approximately equal sensitivity, leading\nto the best UL on the C\u2113measurement. Therefore, in our\ncase, we combine data across different observing runs and\nbaselines to yield data subsets with approximately equal\nsensitivity as follows: The data from the O1 and O2, as\nwell as the HV and LV baselines of the O3, are combined\ninto one subset. The total dirty map and Fisher matrix\n\n32\nof this subset are then given by\nX(1) = XO1 + XO2 + XO3(HV) + XO3(LV) ,\n\u0393(1) = \u0393O1 + \u0393O2 + \u0393O3(HV) + \u0393O3(LV) ,\n(E8)\nrespectively, similar to Ref. [52]. We construct the first\nsubset in this manner and divide the HL baseline dataset\nfrom O3 and O4a according to the sensitivity of this\ndataset, since O1, O2, and the HV and LV baselines of\nO3 are significantly less sensitive than the HL baselines\nof O3 and O4a. Specifically, the data from the HL base-\nline of O3 and O4a are divided equally into 6 and 11\nsubsets, respectively. For each subset, we compute the\ncorresponding dirty map, X(i), and Fisher matrix, \u0393(i),\nwhere the index i ranges from 2 to 7 for O3 and from 8\nto 18 for O4a.\n4.\nUL and significance computation\nFollowing the procedure for significance assessment de-\nscribed in Sec. II E, we compute the p-value for each\nreal and imaginary part of the clean map estimator for\nthe combined dataset across O1-O4a, and compare all\nthese p-values to the local and global p-value thresh-\nolds, respectively. For better visualization, we convert\neach p-value to a z-score, which ranges between [\u2212\u221e, \u221e],\nthrough the inverse error function. Including the \u03b1 = 3\ncase shown in Fig. 11, all SPH modes lie within the\nglobal p-value threshold (the dashed lines) across the\nthree power-law spectrum models, indicating the consis-\ntency with a Gaussian distribution. Similarly, we inves-\ntigate p-values for the 18 subsets of data used to com-\npute the cross- \u02c6C\u2113estimator and confirm that they remain\nwithin the global p-value threshold with very few excep-\ntions6. Therefore, we confirm that no confident detec-\ntion is made at a p-value below < 5%. We then compute\nthe C\u2113point estimates and their 1\u03c3 uncertainty using\nEqs. (18) and (21) for either of the two estimators, re-\nspectively. Although the auto- \u02c6C\u2113estimator is potentially\nbiased due to shot noise in an astrophysical GWB signal,\nFig. 12 shows that the differences between the two es-\ntimators remain consistently within their 1\u03c3 error bars\nacross all \u2113values. This suggests that such a bias is not\nnoticeable, as expected in the absence of a detected sig-\nnal, given the current search sensitivity.\nGiven the absence of a detected GWB signal, we com-\npute ULs on C1/2\n\u2113\nat each angular scale characterized\nby the \u2113value, for different power-law frequency spec-\ntrum models, by constructing Bayesian posteriors from\n6 Considering all individual data subsets and for \u03b1 \u2208{2/3, 3}, the\nglobal p-value threshold was exceeded for a negligible number\nof SPH modes. For \u03b1 = 0, however, this occurred for approx-\nimately 4% of all SPH modes.\nDue to this notable deviation\nfrom Gaussianity in the latter case, the results of the cross- \u02c6C\u2113\nestimator for \u03b1 = 0 should be interpreted with caution.\nthe Monte Carlo samples using the same procedure de-\nscribed for computing p-values in Sec. II E. The \u02c6P\nsim\nsamples generated for the whole dataset and each of the\n18 subsets are converted into the auto- \u02c6C\u2113and cross- \u02c6C\u2113es-\ntimators based on Eq. (17) and Eq. (20), respectively. We\nadd the observed C\u2113point estimates to each sample and\nconstruct the simulated PDF, p(C\u2113| \u02c6C\u2113). Furthermore, we\naccount for the calibration uncertainty by marginalizing\nthis simulated PDF over the calibration factor \u03bb such\nthat\np(C\u2113| \u02c6C\u2113) =\nZ\nd\u03bb p(C\u2113| \u02c6C\u2113, \u03bb) p(\u03bb) ,\n(E9)\nwhere\np(C\u2113| \u02c6C\u2113, \u03bb) = p(C\u2113/\u03bb2| \u02c6C\u2113, \u03bb0 = 1) ,\n(E10)\np(\u03bb) \u221dexp\n\u001a\u0012\n\u2212(\u03bb \u22121)2\n2\u03c32\n\u03bb\n\u0013\u001b\n.\n(E11)\nThe variance of the calibration factor, \u03c32\n\u03bb, is given by the\nsum of the individual calibration uncertainties measured\nin each baseline and observing run7, i.e., \u03c32\n\u03bb = P\ni \u03f52\ni .\nEventually, we identify 95th percentiles of p(C\u2113| \u02c6C\u2113) and\ndefine it as the UL at the 95% confidence level.\nWhen we generate the \u02c6P\nsim samples, we need to ac-\ncount for a complication due to the requirement that the\nclean maps be real quantities on the pixel basis; each\nsample needs to conserve the following symmetry\n\u0393\u2113\u2212m,\u2113\u2032\u2212m\u2032 = (\u22121)m+m\u2032\u0393\u2217\n\u2113m,\u2113\u2032m\u2032 .\n(E12)\nThe clean map estimator \u02c6P\u2113m follows a multi-variate\ncomplex Gaussian distribution with zero mean and the\ncovariance matrix \u03a3 given by Eq. (19). To satisfy this\ncondition, we draw each real and imaginary part of a\nsample separately by constructing a real covariance ma-\ntrix\n\u0012Re \u02c6P\nsim\nIm \u02c6P\nsim\n\u0013\n\u223cN\n\u0012\u0014\n0\n0\n\u0015\n,\n\u0014\n\u03a3RR \u03a3RI\n\u03a3IR\n\u03a3II\n\u0015\u0013\n,\n(E13)\nwhere each block matrix in the real covariance matrix is\n7 Technically, for the cross- \u02c6C\u2113estimator, the propagation of the\ncalibration error differs from the auto- \u02c6C\u2113estimator because it\ncomputes the cross-power of the clean map across the subsets\nrather than its auto-power, and hence this calibration factor\nshould be derived differently. We leave this modification as fu-\nture work.\n\n33\nFIG. 11. z-score distribution of \u03b1 = 3 case for the combined O1-O4a data.\nFIG. 12. C\u2113point estimates using either type of the estimators mentioned above for each power-law spectrum model with the\ncombined O1+O2+O3+O4a data.\ndefined as\n\u03a3RR = 1\n4{\u03a3lml\u2032m\u2032 + (\u22121)m\u03a3l\u2212ml\u2032m\u2032\n+ (\u22121)m\u2032\u03a3lml\u2032\u2212m\u2032 + (\u22121)m+m\u2032\u03a3l\u2212ml\u2032\u2212m\u2032} ,\n(E14)\n\u03a3II = 1\n4{\u03a3lml\u2032m\u2032 \u2212(\u22121)m\u03a3l\u2212ml\u2032m\u2032\n\u2212(\u22121)m\u2032\u03a3lml\u2032\u2212m\u2032 + (\u22121)m+m\u2032\u03a3l\u2212ml\u2032\u2212m\u2032} ,\n(E15)\n\u03a3RI = \u03a3\u22a4\nIR\n= \u2212i\n4 {\u03a3lml\u2032m\u2032 + (\u22121)m\u03a3l\u2212ml\u2032m\u2032\n\u2212(\u22121)m\u2032\u03a3lml\u2032\u2212m\u2032 \u2212(\u22121)m+m\u2032\u03a3l\u2212ml\u2032\u2212m\u2032} .\n(E16)\n\n34\n[1] T. Regimbau, The astrophysical gravitational wave\nstochastic background, Res. Astron. Astrophys. 11, 369\n(2011), arXiv:1101.2762 [astro-ph.CO].\n[2] C. Wu, V. Mandic, and T. 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ASTON,63 P. ASTONE,38 F. ATTADIO,39, 38 F. AUBIN,64 K. AULTONEAL,65 G. AVALLONE,66 E. A. AVILA,49 S. BABAK,20\nC. BADGER,67 S. BAE,68 S. BAGNASCO,28 L. BAIOTTI,69 R. BAJPAI,70 T. BAKA,71, 37 A. M. BAKER,6 K. A. BAKER,72 T. BAKER,73\nG. BALDI,74, 75 N. BALDICCHI,76, 51 M. BALL,77 G. BALLARDIN,62 S. W. BALLMER,78 S. BANAGIRI,6 B. BANERJEE,44 D. BANKAR,79\nT. M. BAPTISTE,12 P. BARAL,10 M. BARATTI,80, 81 J. C. BARAYOGA,11 B. C. BARISH,11 D. BARKER,2 N. BARMAN,79\nP. BARNEO,82, 83, 84 F. BARONE,85, 4 B. BARR,86 L. BARSOTTI,35 M. BARSUGLIA,20 D. BARTA,87 A. M. BARTOLETTI,88\nM. A. BARTON,86 I. BARTOS,46 A. BASALAEV,8, 9 R. BASSIRI,89 A. BASTI,81, 80 M. BAWAJ,76, 51 P. BAXI,90 J. C. BAYLEY,86\nA. C. BAYLOR,10 P. A. BAYNARD II,57 M. BAZZAN,91, 92 V. M. BEDAKIHALE,93 F. BEIRNAERT,94 M. BEJGER,95 D. BELARDINELLI,22\nA. S. BELL,86 D. S. BELLIE,96 L. BELLIZZI,80, 81 W. BENOIT,18 I. BENTARA,56 J. D. BENTLEY,97 M. BEN YAALA,55 S. BERA,98, 99\nF. BERGAMIN,33 B. K. BERGER,89 S. BERNUZZI,27 M. BEROIZ,11 C. P. L. BERRY,86 D. BERSANETTI,29 T. BERTHEAS,100\nA. BERTOLINI,37, 36 J. BETZWIESER,63 D. BEVERIDGE,72 G. BEVILACQUA,101 N. BEVINS,102 R. BHANDARE,103 R. BHATT,11\nD. BHATTACHARJEE,104, 105 S. BHATTACHARYYA,106 S. BHAUMIK,46 V. BIANCALANA,101 A. BIANCHI,37, 107 I. A. BILENKO,108\nG. BILLINGSLEY,11 A. BINETTI,109 S. BINI,11, 74, 75 C. BINU,110 S. BIOT,111 O. BIRNHOLTZ,112 S. BISCOVEANU,96 A. BISHT,9\nM. BITOSSI,62, 80 M.-A. BIZOUARD,113 S. BLABER,114 J. K. BLACKBURN,11 L. A. BLAGG,77 C. D. BLAIR,72, 63 D. G. BLAIR,72\nN. BODE,8, 9 N. BOETTNER,97 G. BOILEAU,113 M. BOLDRINI,38 G. N. BOLINGBROKE,115 A. BOLLIAND,116, 40 L. D. BONAVENA,46\nR. BONDARESCU,82 F. BONDU,117 E. BONILLA,89 M. S. BONILLA,54 A. BONINO,118 R. BONNAND,31, 116 A. BORCHERS,8, 9\nS. BORHANIAN,7 V. BOSCHI,80 S. BOSE,119 V. BOSSILKOV,63 Y. BOTHRA,37, 107 A. BOUDON,56 L. BOURG,57 G. BOUYER,120\nM. BOYLE,121 A. BOZZI,62 C. BRADASCHIA,80 P. R. BRADY,10 A. BRANCH,63 M. BRANCHESI,44, 45 I. BRAUN,104 T. BRIANT,122\nA. BRILLET,113 M. BRINKMANN,8, 9 P. BROCKILL,10 E. BROCKMUELLER,8, 9 A. F. BROOKS,11 B. C. BROWN,46 D. D. BROWN,115\nM. L. BROZZETTI,76, 51 S. BRUNETT,11 G. BRUNO,15 R. BRUNTZ,123 J. BRYANT,118 Y. BU,124 F. BUCCI,61 J. BUCHANAN,123\nO. BULASHENKO,82, 83 T. BULIK,125 H. J. BULTEN,37 A. BUONANNO,126, 1 K. BURTNYK,2 R. BUSCICCHIO,127, 128 D. BUSKULIC,31\nC. BUY,100 R. L. BYER,89 G. S. CABOURN DAVIES,73 R. CABRITA,15 V. C\u00c1CERES-BARBOSA,7 L. CADONATI,57 G. CAGNOLI,129\nC. CAHILLANE,78 A. CALAFAT,98 T. A. CALLISTER,130 E. CALLONI,32, 4 S. R. CALLOS,77 M. CANEPA,30, 29 G. CANEVA SANTORO,43\nK. C. CANNON,42 H. CAO,35 L. A. CAPISTRAN,131 E. CAPOCASA,20 E. CAPOTE,2, 11 G. CAPURRI,81, 80 G. CARAPELLA,66, 132\nF. CARBOGNANI,62 M. CARLASSARA,8, 9 J. B. CARLIN,124 T. K. CARLSON,133 M. F. CARNEY,104 M. CARPINELLI,127, 62\nG. CARRILLO,77 J. J. CARTER,8, 9 G. CARULLO,118, 134 A. CASALLAS-LAGOS,135 J. CASANUEVA DIAZ,62 C. CASENTINI,136, 22\nS. Y. CASTRO-LUCAS,137 S. CAUDILL,133 M. CAVAGLI\u00c0,105 R. CAVALIERI,62 A. CEJA,54 G. CELLA,80 P. CERD\u00c1-DUR\u00c1N,138, 139\nE. CESARINI,22 N. CHABBRA,34 W. CHAIBI,113 A. CHAKRABORTY,13 P. CHAKRABORTY,8, 9 S. CHAKRABORTY,103\nS. CHALATHADKA SUBRAHMANYA,97 J. C. L. CHAN,140 M. CHAN,114 K. CHANG,141 S. CHAO,142, 141 P. CHARLTON,143\nE. CHASSANDE-MOTTIN,20 C. CHATTERJEE,144 DEBARATI CHATTERJEE,79 DEEP CHATTERJEE,35 M. CHATURVEDI,103 S. CHATY,20\nK. CHATZIIOANNOU,11 A. CHEN,145 A. H.-Y. CHEN,146 D. CHEN,147 H. CHEN,142 H. Y. CHEN,120 S. CHEN,144 YANBEI CHEN,148\nYITIAN CHEN,121 H. P. CHENG,149 P. CHESSA,76, 51 H. T. CHEUNG,90 S. Y. CHEUNG,6 F. CHIADINI,150, 132 G. CHIARINI,8, 9, 92\nA. CHIBA,151 A. CHINCARINI,29 M. L. CHIOFALO,81, 80 A. CHIUMMO,4, 62 C. CHOU,146 S. CHOUDHARY,72 N. CHRISTENSEN,113, 152\nS. S. Y. CHUA,34 G. CIANI,74, 75 P. CIECIELAG,95 M. CIE \u00b4SLAR,125 M. CIFALDI,22 B. CIROK,153 F. CLARA,2 J. A. CLARK,11, 57\nT. A. CLARKE,6 P. CLEARWATER,154 S. CLESSE,111 F. CLEVA,113, 116 E. COCCIA,44, 45, 43 E. 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DAW,174 M. DAX,1\nJ. DE BOLLE,94 M. DEENADAYALAN,79 J. DEGALLAIX,175 M. DE LAURENTIS,32, 4 F. DE LILLO,23 S. DELLA TORRE,128\nW. DEL POZZO,81, 80 A. DEMAGNY,31 F. DE MARCO,39, 38 G. DEMASI,176, 61 F. DE MATTEIS,21, 22 N. DEMOS,35 T. DENT,177\nA. DEPASSE,15 N. DEPERGOLA,102 R. DE PIETRI,178, 179 R. DE ROSA,32, 4 C. DE ROSSI,62 M. DESAI,35 R. DESALVO,180\nA. DESIMONE,181 R. DE SIMONE,150, 132 A. DHANI,1 R. DIAB,46 M. C. D\u00cdAZ,164 M. DI CESARE,32, 4 G. DIDERON,182 T. DIETRICH,1\nL. DI FIORE,4 C. DI FRONZO,72 M. DI GIOVANNI,39, 38 T. DI GIROLAMO,32, 4 D. DIKSHA,37, 36 J. DING,20, 183 S. DI PACE,39, 38\nI. DI PALMA,39, 38 D. DI PIERO,184, 48 F. DI RENZO,56 DIVYAJYOTI,33 A. DMITRIEV,118 J. P. DOCHERTY,86 Z. DOCTOR,96\nN. DOERKSEN,168 E. DOHMEN,2 A. DOKE,133 A. DOMICIANO DE SOUZA,185 L. D\u2019ONOFRIO,38 F. DONOVAN,35 K. L. DOOLEY,33\nT. DOONEY,71 S. DORAVARI,79 O. DOROSH,186 W. J. D. DOYLE,123 M. DRAGO,39, 38 J. C. DRIGGERS,2 M. DUBOIS,100 L. DUNN,124\narXiv:2508.18079v3 [gr-qc] 4 Nov 2025\n\n2\nU. DUPLETSA,44 P.-A. DUVERNE,20 D. D\u2019URSO,170, 155 P. DUTTA ROY,46 H. DUVAL,187 S. E. DWYER,2 C. EASSA,2\nM. EBERSOLD,188, 31 T. ECKHARDT,97 G. EDDOLLS,78 A. EFFLER,63 J. EICHHOLZ,34 H. EINSLE,113 M. EISENMANN,25 M. EMMA,58\nK. ENDO,151 R. ENFICIAUD,1 L. ERRICO,32, 4 R. ESPINOSA,164 M. C. ESPITIA,189 M. ESPOSITO,4, 32 R. C. ESSICK,190 H. ESTELL\u00c9S,1\nT. ETZEL,11 M. EVANS,35 T. EVSTAFYEVA,182 B. E. EWING,7 J. M. EZQUIAGA,140 F. FABRIZI,60, 61 V. FAFONE,21, 22 S. FAIRHURST,33\nA. M. FARAH,130 B. FARR,77 W. M. FARR,191, 192 G. FAVARO,91 M. FAVATA,193 M. FAYS,165 M. FAZIO,55 J. FEICHT,11 M. M. FEJER,89\nR. FELICETTI,184, 48 E. FENYVESI,87, 194 J. FERNANDES,195 T. FERNANDES,196, 138 D. FERNANDO,110 S. FERRAIUOLO,197, 39, 38\nT. A. FERREIRA,12 F. FIDECARO,81, 80 P. FIGURA,95 A. FIORI,80, 81 I. FIORI,62 M. FISHBACH,190 R. P. FISHER,123 R. FITTIPALDI,198, 132\nV. FIUMARA,199, 132 R. FLAMINIO,31 S. M. FLEISCHER,200 L. S. FLEMING,201 E. FLODEN,18 H. FONG,114 J. A. FONT,138, 139\nF. FONTINELE-NUNES,18 C. FOO,1 B. FORNAL,202 K. FRANCESCHETTI,178 F. FRAPPEZ,31 S. FRASCA,39, 38 F. FRASCONI,80\nJ. P. FREED,65 Z. FREI,203 A. FREISE,37, 107 O. FREITAS,196, 138 R. FREY,77 W. FRISCHHERTZ,63 P. FRITSCHEL,35 V. V. FROLOV,63\nG. G. FRONZ\u00c9,28 M. FUENTES-GARCIA,11 S. FUJII,204 T. FUJIMORI,205 P. FULDA,46 M. FYFFE,63 B. GADRE,71 J. R. GAIR,1\nS. GALAUDAGE,185 V. GALDI,206 R. GAMBA,7 A. GAMBOA,1 S. GAMOJI,180 D. GANAPATHY,207 A. GANGULY,79 B. GARAVENTA,29\nJ. GARC\u00cdA-BELLIDO,208 C. GARC\u00cdA-QUIR\u00d3S,188 J. W. GARDNER,34 K. A. GARDNER,114 S. GARG,42 J. GARGIULO,62 X. GARRIDO,41\nA. GARRON,98 F. GARUFI,32, 4 P. A. GARVER,89 C. GASBARRA,21, 22 B. GATELEY,2 F. GAUTIER,209 V. GAYATHRI,10 T. GAYER,78\nG. GEMME,29 A. GENNAI,80 V. GENNARI,100 J. GEORGE,103 R. GEORGE,120 O. GERBERDING,97 L. GERGELY,153\nARCHISMAN GHOSH,94 SAYANTAN GHOSH,195 SHAON GHOSH,193 SHROBANA GHOSH,8, 9 SUPROVO GHOSH,210 TATHAGATA GHOSH,79\nJ. A. GIAIME,12, 63 K. D. GIARDINA,63 D. R. GIBSON,201 C. GIER,55 S. GKAITATZIS,81, 80 J. GLANZER,11 F. GLOTIN,41 J. GODFREY,77\nR. V. GODLEY,8, 9 P. GODWIN,11 A. S. GOETTEL,33 E. GOETZ,114 J. GOLOMB,11 S. GOMEZ LOPEZ,39, 38 B. GONCHAROV,44\nG. GONZ\u00c1LEZ,12 P. GOODARZI,211 S. GOODE,6 A. W. GOODWIN-JONES,15 M. GOSSELIN,62 R. GOUATY,31 D. W. GOULD,34\nK. GOVORKOVA,35 A. GRADO,76, 51 V. GRAHAM,86 A. E. GRANADOS,18 M. GRANATA,175 V. GRANATA,212, 132 S. GRAS,35\nP. GRASSIA,11 J. GRAVES,57 C. GRAY,2 R. GRAY,86 G. GRECO,51 A. C. GREEN,37, 107 L. GREEN,213 S. M. GREEN,73 S. R. GREEN,214\nC. GREENBERG,133 A. M. GRETARSSON,65 H. K. GRIFFIN,18 D. GRIFFITH,11 H. L. GRIGGS,57 G. GRIGNANI,76, 51 C. GRIMAUD,31\nH. GROTE,33 S. GRUNEWALD,1 D. GUERRA,138 D. GUETTA,215 G. M. GUIDI,60, 61 A. R. GUIMARAES,12 H. K. GULATI,93\nF. GULMINELLI,172, 173 H. GUO,145 W. GUO,72 Y. GUO,37, 36 ANURADHA GUPTA,216 I. GUPTA,7 N. C. GUPTA,93 S. K. GUPTA,46\nV. GUPTA,18 N. GUPTE,1 J. GURS,97 N. GUTIERREZ,175 N. GUTTMAN,6 F. GUZMAN,131 D. HABA,217 M. HABERLAND,1 S. HAINO,218\nE. D. HALL,35 E. Z. HAMILTON,98 G. HAMMOND,86 M. HANEY,37 J. HANKS,2 C. HANNA,7 M. D. HANNAM,33\nO. A. HANNUKSELA,219 A. G. HANSELMAN,130 H. HANSEN,2 J. HANSON,63 S. HANUMASAGAR,57 R. HARADA,42\nA. R. HARDISON,181 S. HARIKUMAR,186 K. HARIS,37, 71 I. HARLEY-TROCHIMCZYK,131 T. HARMARK,134 J. HARMS,44, 45\nG. M. HARRY,220 I. W. HARRY,73 J. HART,104 B. HASKELL,95, 221, 222 C. J. HASTER,213 K. HAUGHIAN,86 H. HAYAKAWA,50\nK. HAYAMA,223 M. C. HEINTZE,63 J. HEINZE,118 J. HEINZEL,35 H. HEITMANN,113 F. HELLMAN,207 A. F. HELMLING-CORNELL,77\nG. HEMMING,62 O. HENDERSON-SAPIR,115 M. HENDRY,86 I. S. HENG,86 M. H. HENNIG,86 C. HENSHAW,57 M. HEURS,8, 9\nA. L. HEWITT,224, 225 J. HEYNEN,15 J. HEYNS,35 S. HIGGINBOTHAM,33 S. HILD,36, 37 S. HILL,86 Y. HIMEMOTO,226 N. HIRATA,25\nC. HIROSE,227 D. HOFMAN,175 B. E. HOGAN,65 N. A. HOLLAND,37, 107 I. J. HOLLOWS,174 D. E. HOLZ,130 L. HONET,111\nD. J. HORTON-BAILEY,207 J. HOUGH,86 S. HOURIHANE,11 N. T. HOWARD,144 E. J. HOWELL,72 C. G. HOY,73 C. A. HRISHIKESH,21\nP. HSI,35 H.-F. HSIEH,142 H.-Y. HSIEH,142 C. HSIUNG,228 S.-H. HSU,146 W.-F. HSU,109 Q. HU,86 H. Y. HUANG,141 Y. HUANG,7\nY. T. HUANG,78 A. D. HUDDART,229 B. HUGHEY,65 V. HUI,31 S. HUSA,98 R. HUXFORD,7 L. IAMPIERI,39, 38 G. A. IANDOLO,36\nM. IANNI,22, 21 G. IANNONE,132 J. IASCAU,77 K. IDE,230 R. IDEN,217 A. IERARDI,44, 45 S. IKEDA,147 H. IMAFUKU,42 Y. INOUE,141\nG. IORIO,91 P. IOSIF,184, 48 M. H. IQBAL,34 J. IRWIN,86 R. ISHIKAWA,230 M. ISI,191, 192 K. S. ISLEIF,231 Y. ITOH,205, 232 M. IWAYA,204\nB. R. IYER,24 C. JACQUET,100 P.-E. JACQUET,122 T. JACQUOT,41 S. J. JADHAV,233 S. P. JADHAV,154 M. JAIN,133 T. JAIN,224\nA. L. JAMES,11 K. JANI,144 J. JANQUART,15 N. N. JANTHALUR,233 S. JARABA,234 P. JARANOWSKI,235 R. JAUME,98 W. JAVED,33\nA. JENNINGS,2 M. JENSEN,2 W. JIA,35 J. JIANG,149 H.-B. JIN,236, 237 G. R. JOHNS,123 N. A. JOHNSON,46 M. C. JOHNSTON,213\nR. JOHNSTON,86 N. JOHNY,8, 9 D. H. JONES,34 D. I. JONES,210 R. JONES,86 H. E. JOSE,77 P. JOSHI,7 S. K. JOSHI,79 G. JOUBERT,56\nJ. JU,238 L. JU,72 K. JUNG,239 J. JUNKER,34 V. JUSTE,111 H. B. KABAGOZ,63, 35 T. KAJITA,240 I. KAKU,205 V. KALOGERA,96\nM. KALOMENOPOULOS,213 M. KAMIIZUMI,50 N. KANDA,232, 205 S. KANDHASAMY,79 G. KANG,241 N. C. KANNACHEL,6\nJ. B. KANNER,11 S. A. KANTIMAHANTY,18 S. J. KAPADIA,79 D. P. KAPASI,54 M. KARTHIKEYAN,133 M. KASPRZACK,11 H. KATO,151\nT. KATO,204 E. KATSAVOUNIDIS,35 W. KATZMAN,63 R. KAUSHIK,103 K. KAWABE,2 R. KAWAMOTO,205 D. KEITEL,98\nL. J. KEMPERMAN,115 J. KENNINGTON,7 F. A. KERKOW,18 R. KESHARWANI,79 J. S. KEY,242 R. KHADELA,8, 9 S. KHADKA,89\nS. S. KHADKIKAR,7 F. Y. KHALILI,108 F. KHAN,8, 9 T. KHANAM,162 M. KHURSHEED,103 N. M. KHUSID,191, 192\nW. KIENDREBEOGO,113, 243 N. KIJBUNCHOO,115 C. KIM,244 J. C. KIM,245 K. KIM,246 M. H. KIM,238 S. KIM,247 Y.-M. KIM,246\nC. KIMBALL,96 K. KIMES,54 M. KINNEAR,33 J. S. KISSEL,2 S. KLIMENKO,46 A. M. KNEE,114 E. J. KNOX,77 N. KNUST,8, 9\nK. KOBAYASHI,204 S. M. KOEHLENBECK,89 G. KOEKOEK,37, 36 K. KOHRI,248, 249 K. KOKEYAMA,33, 250 S. KOLEY,44, 165\nP. KOLITSIDOU,118 A. E. KOLONIARI,251 K. KOMORI,42 A. K. H. KONG,142 A. KONTOS,252 L. M. KOPONEN,118 M. KOROBKO,97\nX. KOU,18 A. KOUSHIK,23 N. KOUVATSOS,67 M. KOVALAM,72 T. KOYAMA,151 D. B. KOZAK,11 S. L. KRANZHOFF,36, 37 V. KRINGEL,8, 9\nN. V. KRISHNENDU,118 S. KROKER,253 A. KR\u00d3LAK,254, 186 K. KRUSKA,8, 9 J. KUBISZ,255 G. KUEHN,8, 9 S. KULKARNI,216\nA. KULUR RAMAMOHAN,34 ACHAL KUMAR,46 ANIL KUMAR,233 PRAVEEN KUMAR,177 PRAYUSH KUMAR,24 RAHUL KUMAR,2\nRAKESH KUMAR,93 J. KUME,256, 257, 42 K. KUNS,35 N. KUNTIMADDI,33 S. KUROYANAGI,208, 258 S. KUWAHARA,42 K. KWAK,239\nK. KWAN,34 S. KWON,42 G. LACAILLE,86 D. LAGHI,188, 100 A. H. LAITY,163 E. LALANDE,259 M. LALLEMAN,23 P. C. LALREMRUATI,260\nM. LANDRY,2 B. B. LANE,35 R. N. LANG,35 J. LANGE,120 R. LANGGIN,213 B. LANTZ,89 I. LA ROSA,98 J. LARSEN,200\nA. LARTAUX-VOLLARD,41 P. D. LASKY,6 J. LAWRENCE,164 M. LAXEN,63 C. LAZARTE,138 A. LAZZARINI,11 C. LAZZARO,156, 155\nP. LEACI,39, 38 L. LEALI,18 Y. K. LECOEUCHE,114 H. M. LEE,261 H. W. LEE,262 J. LEE,78 K. LEE,238 R.-K. LEE,142 R. LEE,35\nSUNGHO LEE,246 SUNJAE LEE,238 Y. LEE,141 I. N. LEGRED,11 J. LEHMANN,8, 9 L. LEHNER,182 M. LE JEAN,175, 116 A. LEMA\u00ceTRE,263\nM. LENTI,61, 176 M. LEONARDI,74, 75, 264 M. LEQUIME,40 N. LEROY,41 M. LESOVSKY,11 N. LETENDRE,31 M. LETHUILLIER,56\nY. LEVIN,6 K. LEYDE,73 A. K. Y. LI,11 K. L. LI,265 T. G. F. LI,109 X. LI,148 Y. LI,96 Z. LI,86 A. LIHOS,123 E. T. LIN,142 F. LIN,141\nL. C.-C. LIN,265 Y.-C. LIN,142 C. LINDSAY,201 S. D. LINKER,180 A. LIU,219 G. C. LIU,228 JIAN LIU,72 F. LLAMAS VILLARREAL,164\nJ. LLOBERA-QUEROL,98 R. K. L. LO,140 J.-P. LOCQUET,109 S. C. G. LOGGINS,266 M. R. LOIZOU,133 L. T. LONDON,67 A. LONGO,60, 61\n\n3\nD. LOPEZ,165 M. LOPEZ PORTILLA,71 A. LORENZO-MEDINA,177 V. LORIETTE,41 M. LORMAND,63 G. LOSURDO,267, 80 E. LOTTI,133\nT. P. LOTT IV,57 J. D. LOUGH,8, 9 H. A. LOUGHLIN,35 C. O. LOUSTO,110 N. LOW,124 N. LU,34 L. LUCCHESI,80 H. L\u00dcCK,9, 8, 9\nD. LUMACA,22 A. P. LUNDGREN,268, 269 A. W. LUSSIER,259 R. MACAS,73 M. MACINNIS,35 D. M. MACLEOD,33\nI. A. O. MACMILLAN,11 A. MACQUET,41 K. MAEDA,151 S. MAENAUT,109 S. S. MAGARE,79 R. M. MAGEE,11 E. MAGGIO,1\nR. MAGGIORE,37, 107 M. MAGNOZZI,29, 30 M. MAHESH,97 M. MAINI,163 S. MAJHI,79 E. MAJORANA,39, 38 C. N. MAKAREM,11\nD. MALAKAR,105 J. A. MALAQUIAS-REIS,19 U. MALI,190 S. MALIAKAL,11 A. MALIK,103 L. MALLICK,168, 190 A.-K. MALZ,58\nN. MAN,113 M. MANCARELLA,99 V. MANDIC,18 V. MANGANO,170, 155 B. MANNIX,77 G. L. MANSELL,78 M. MANSKE,10\nM. MANTOVANI,62 M. MAPELLI,91, 92, 270 C. MARINELLI,101 F. MARION,31 A. S. MARKOSYAN,89 A. MARKOWITZ,11 E. MAROS,11\nS. MARSAT,100 F. MARTELLI,60, 61 I. W. MARTIN,86 R. M. MARTIN,193 B. B. MARTINEZ,131 D. A. MARTINEZ,54 M. MARTINEZ,43, 271\nV. MARTINEZ,129 A. MARTINI,74, 75 J. C. MARTINS,19 D. V. MARTYNOV,118 E. J. MARX,35 L. MASSARO,36, 37 A. MASSEROT,31\nM. MASSO-REID,86 S. MASTROGIOVANNI,38 T. MATCOVICH,51 M. MATIUSHECHKINA,8, 9 L. MAURIN,209 N. MAVALVALA,35\nN. MAXWELL,2 G. MCCARROL,63 R. MCCARTHY,2 D. E. MCCLELLAND,34 S. MCCORMICK,63 L. MCCULLER,11 S. MCEACHIN,123\nC. MCELHENNY,123 G. I. MCGHEE,86 J. MCGINN,86 K. B. M. MCGOWAN,144 J. MCIVER,114 A. MCLEOD,72 I. MCMAHON,188\nT. MCRAE,34 R. MCTEAGUE,86 D. MEACHER,10 B. N. MEAGHER,78 R. MECHUM,110 Q. MEIJER,71 A. MELATOS,124 C. S. MENONI,137\nF. MERA,2 R. A. MERCER,10 L. MERENI,175 K. MERFELD,162 E. L. MERILH,63 J. R. M\u00c9ROU,98 J. D. MERRITT,77 M. MERZOUGUI,113\nC. MESSICK,10 B. MESTICHELLI,44 M. MEYER-CONDE,272 F. MEYLAHN,8, 9 A. MHASKE,79 A. MIANI,74, 75 H. MIAO,273 C. MICHEL,175\nY. MICHIMURA,42 H. MIDDLETON,118 D. P. MIHAYLOV,104 S. J. MILLER,11 M. MILLHOUSE,57 E. MILOTTI,184, 48 V. MILOTTI,91\nY. MINENKOV,22 E. M. MINIHAN,65 LL. M. MIR,43 L. MIRASOLA,155, 156 M. MIRAVET-TEN\u00c9S,138 C.-A. MIRITESCU,43 A. MISHRA,24\nC. MISHRA,106 T. MISHRA,46 A. L. MITCHELL,37, 107 J. G. MITCHELL,65 S. MITRA,79 V. P. MITROFANOV,108 K. MITSUHASHI,25\nR. MITTLEMAN,35 O. MIYAKAWA,50 S. MIYOKI,50 A. MIYOKO,65 G. MO,35 L. MOBILIA,60, 61 S. R. P. MOHAPATRA,11 S. R. MOHITE,7\nM. MOLINA-RUIZ,207 M. MONDIN,180 J. K. MONSALVE,189 M. MONTANI,60, 61 C. J. MOORE,224 D. MORARU,2 A. MORE,79\nS. MORE,79 C. MORENO,135 E. A. MORENO,35 G. MORENO,2 A. MORESO SERRA,82 S. MORISAKI,42, 204 Y. MORIWAKI,151\nG. MORRAS,208 A. MOSCATELLO,91 M. MOULD,35 B. MOURS,64 C. M. MOW-LOWRY,37, 107 L. MUCCILLO,176, 61 F. MUCIACCIA,39, 38\nD. MUKHERJEE,118 SAMANWAYA MUKHERJEE,24 SOMA MUKHERJEE,164 SUBROTO MUKHERJEE,93 SUVODIP MUKHERJEE,13\nN. MUKUND,35 A. MULLAVEY,63 H. MULLOCK,114 J. MUNDI,220 C. L. MUNGIOLI,72 M. MURAKOSHI,230 P. G. MURRAY,86\nD. NABARI,74, 75 S. L. NADJI,8, 9 A. NAGAR,28, 274 N. NAGARAJAN,86 K. NAKAGAKI,50 K. NAKAMURA,25 H. NAKANO,275\nM. NAKANO,11 D. NANADOUMGAR-LACROZE,43 D. NANDI,12 V. NAPOLANO,62 P. NARAYAN,216 I. NARDECCHIA,22 T. NARIKAWA,204\nH. NAROLA,71 L. NATICCHIONI,38 R. K. NAYAK,260 L. NEGRI,71 A. NELA,86 C. NELLE,77 A. NELSON,131 T. J. N. NELSON,63\nM. NERY,8, 9 A. NEUNZERT,2 S. NG,54 L. NGUYEN QUYNH,276 S. A. NICHOLS,12 A. B. NIELSEN,277 Y. NISHINO,25, 42\nA. NISHIZAWA,278 S. NISSANKE,279, 37 W. NIU,7 F. NOCERA,62 J. NOLLER,280 M. NORMAN,33 C. NORTH,33 J. NOVAK,116, 234, 281\nR. NOWICKI,144 J. F. NU\u00d1O SILES,208 L. K. NUTTALL,73 K. OBAYASHI,230 J. OBERLING,2 J. O\u2019DELL,229 E. OELKER,35\nM. OERTEL,234, 116, 282, 281 G. OGANESYAN,44, 45 T. O\u2019HANLON,63 M. OHASHI,50 F. OHME,8, 9 R. OLIVERI,116, 282, 281 R. OMER,18\nB. O\u2019NEAL,123 M. ONISHI,151 K. OOHARA,283 B. O\u2019REILLY,63 M. ORSELLI,51, 76 R. O\u2019SHAUGHNESSY,110 S. O\u2019SHEA,86 S. OSHINO,50\nC. OSTHELDER,11 I. OTA,12 D. J. OTTAWAY,115 A. OUZRIAT,56 H. OVERMIER,63 B. J. OWEN,284 R. OZAKI,230 A. E. PACE,7\nR. PAGANO,12 M. A. PAGE,25 A. PAI,195 L. PAIELLA,44 A. PAL,285 S. PAL,260 M. A. PALAIA,80, 81 M. P\u00c1LFI,203 P. P. PALMA,39, 21, 22\nC. PALOMBA,38 P. PALUD,20 H. PAN,142 J. PAN,72 K. C. PAN,142 P. K. PANDA,233 SHIKSHA PANDEY,7 SWADHA PANDEY,35\nP. T. H. PANG,37, 71 F. PANNARALE,39, 38 K. A. PANNONE,54 B. C. PANT,103 F. H. PANTHER,72 M. PANZERI,60, 61 F. PAOLETTI,80\nA. PAOLONE,38, 286 A. PAPADOPOULOS,86 E. E. PAPALEXAKIS,211 L. PAPALINI,80, 81 G. PAPIGKIOTIS,251 A. PAQUIS,41 A. PARISI,76, 51\nB.-J. PARK,246 J. PARK,287 W. PARKER,63 G. PASCALE,8, 9 D. PASCUCCI,94 A. PASQUALETTI,62 R. PASSAQUIETI,81, 80 L. PASSENGER,6\nD. PASSUELLO,80 O. PATANE,2 A. V. PATEL,141 D. PATHAK,79 A. PATRA,33 B. PATRICELLI,81, 80 B. G. PATTERSON,33 K. PAUL,106\nS. PAUL,77 E. PAYNE,11 T. PEARCE,33 M. PEDRAZA,11 A. PELE,11 F. E. PE\u00d1A ARELLANO,288 X. PENG,118 Y. PENG,57 S. PENN,289\nM. D. PENULIAR,54 A. PEREGO,74, 75 Z. PEREIRA,133 C. P\u00c9RIGOIS,290, 92, 91 G. PERNA,91 A. PERRECA,74, 75, 44 J. PERRET,20\nS. PERRI\u00c8S,56 J. W. PERRY,37, 107 D. PESIOS,251 S. PETERS,165 S. PETRACCA,206 C. PETRILLO,76 H. P. PFEIFFER,1 H. PHAM,63\nK. A. PHAM,18 K. S. PHUKON,118 H. PHURAILATPAM,219 M. PIARULLI,100 L. PICCARI,39, 38 O. J. PICCINNI,34 M. PICHOT,113\nM. PIENDIBENE,81, 80 F. PIERGIOVANNI,60, 61 L. PIERINI,38 G. PIERRA,38 V. PIERRO,291, 132 M. PIETRZAK,95 M. PILLAS,165 F. PILO,80\nL. PINARD,175 I. M. PINTO,291, 132, 292, 32 M. PINTO,62 B. J. PIOTRZKOWSKI,10 M. PIRELLO,2 M. D. PITKIN,224, 86 A. PLACIDI,51\nE. PLACIDI,39, 38 M. L. PLANAS,98 W. PLASTINO,212, 22 C. PLUNKETT,35 R. POGGIANI,81, 80 E. POLINI,35 J. POMPER,80, 81 L. POMPILI,1\nJ. POON,219 E. PORCELLI,37 E. K. PORTER,20 C. POSNANSKY,7 R. POULTON,62 J. POWELL,154 G. S. PRABHU,79 M. PRACCHIA,165\nB. K. PRADHAN,79 T. PRADIER,64 A. K. PRAJAPATI,93 K. PRASAI,293 R. PRASANNA,233 P. PRASIA,79 G. PRATTEN,118\nG. PRINCIPE,184, 48 G. A. PRODI,74, 75 P. PROSPERI,80 P. PROSPOSITO,21, 22 A. C. PROVIDENCE,65 A. PUECHER,1 J. PULLIN,12\nP. PUPPO,38 M. P\u00dcRRER,163 H. QI,16 J. QIN,34 G. QU\u00c9M\u00c9NER,173, 116 V. QUETSCHKE,164 L. H. QUICENO,189 P. J. QUINONEZ,65\nN. QUTOB,57 R. RADING,231 I. RAINHO,138 S. RAJA,103 C. RAJAN,103 B. RAJBHANDARI,110 K. E. RAMIREZ,63 F. A. RAMIS VIDAL,98\nM. RAMOS AREVALO,164 A. RAMOS-BUADES,98, 37 S. RANJAN,57 K. RANSOM,63 P. RAPAGNANI,39, 38 B. RATTO,65\nA. RAVICHANDRAN,133 A. RAY,96 V. RAYMOND,33 M. RAZZANO,81, 80 J. READ,54 T. REGIMBAU,31 S. REID,55 C. REISSEL,35\nD. H. REITZE,11 A. I. RENZINI,11, 127 B. REVENU,294, 41 A. REVILLA PE\u00d1A,82 R. REYES,180 L. RICCA,15 F. RICCI,39, 38 M. RICCI,38, 39\nA. RICCIARDONE,81, 80 J. RICE,78 J. W. RICHARDSON,211 M. L. RICHARDSON,115 A. RIJAL,65 K. RILES,90 H. K. RILEY,33\nS. RINALDI,270 J. RITTMEYER,97 C. ROBERTSON,229 F. ROBINET,41 M. ROBINSON,2 A. ROCCHI,22 L. ROLLAND,31 J. G. ROLLINS,11\nA. E. ROMANO,189 R. ROMANO,3, 4 A. ROMERO,31 I. M. ROMERO-SHAW,224 J. H. ROMIE,63 S. RONCHINI,7 T. J. ROOCKE,115\nL. ROSA,4, 32 T. J. ROSAUER,211 C. A. ROSE,57 D. ROSI \u00b4NSKA,125 M. P. ROSS,53 M. ROSSELLO-SASTRE,98 S. ROWAN,86\nS. K. ROY,191, 192 S. ROY,15 D. ROZZA,127, 128 P. RUGGI,62 N. RUHAMA,239 E. RUIZ MORALES,295, 208 K. RUIZ-ROCHA,144\nS. SACHDEV,57 T. SADECKI,2 P. SAFFARIEH,37, 107 S. SAFI-HARB,168 M. R. SAH,13 S. SAHA,142 T. SAINRAT,64\nS. SAJITH MENON,215, 39, 38 K. SAKAI,296 Y. SAKAI,272 M. SAKELLARIADOU,67 S. SAKON,7 O. S. SALAFIA,158, 128, 127\nF. SALCES-CARCOBA,11 L. SALCONI,62 M. SALEEM,120 F. SALEMI,39, 38 M. SALL\u00c9,37 S. U. SALUNKHE,79 S. SALVADOR,173, 172\nA. SALVARESE,120 A. SAMAJDAR,71, 37 A. SANCHEZ,2 E. J. SANCHEZ,11 L. E. SANCHEZ,11 N. SANCHIS-GUAL,138 J. R. SANDERS,181\nE. M. S\u00c4NGER,1 F. SANTOLIQUIDO,44, 45 F. SARANDREA,28 T. R. SARAVANAN,79 N. SARIN,6 P. SARKAR,8, 9 A. SASLI,251 P. SASSI,51, 76\n\n4\nB. SASSOLAS,175 B. S. SATHYAPRAKASH,7, 33 R. SATO,227 S. SATO,151 YUKINO SATO,151 YU SATO,151 O. SAUTER,46 R. L. SAVAGE,2\nT. SAWADA,50 H. L. SAWANT,79 S. SAYAH,175 V. SCACCO,21, 22 D. SCHAETZL,11 M. SCHEEL,148 A. SCHIEBELBEIN,190\nM. G. SCHIWORSKI,78 P. SCHMIDT,118 S. SCHMIDT,71 R. SCHNABEL,97 M. SCHNEEWIND,8, 9 R. M. S. SCHOFIELD,77\nK. SCHOUTEDEN,109 B. W. SCHULTE,8, 9 B. F. SCHUTZ,33, 8, 9 E. SCHWARTZ,297 M. SCIALPI,298 J. SCOTT,86 S. M. SCOTT,34\nR. M. SEDAS,63 T. C. SEETHARAMU,86 M. SEGLAR-ARROYO,43 Y. SEKIGUCHI,299 D. SELLERS,63 N. SEMBO,205 A. S. SENGUPTA,300\nE. G. SEO,86 J. W. SEO,109 V. SEQUINO,32, 4 M. SERRA,38 A. SEVRIN,187 T. SHAFFER,2 U. S. SHAH,57 M. A. SHAIKH,261 L. SHAO,301\nA. K. SHARMA,98 PREETI SHARMA,12 PRIANKA SHARMA,103 RITWIK SHARMA,18 S. SHARMA CHAUDHARY,105 P. SHAWHAN,126\nN. S. SHCHEBLANOV,302, 263 E. SHERIDAN,144 Z.-H. SHI,142 M. SHIKAUCHI,42 R. SHIMOMURA,303 H. SHINKAI,303 S. SHIRKE,79\nD. H. SHOEMAKER,35 D. M. SHOEMAKER,120 R. W. SHORT,2 S. SHYAMSUNDAR,103 A. SIDER,157 H. SIEGEL,191, 192 D. SIGG,2\nL. SILENZI,36, 37 L. SILVESTRI,39, 169 M. SIMMONDS,115 L. P. SINGER,304 AMITESH SINGH,216 ANIKA SINGH,11 D. SINGH,207\nN. SINGH,98 S. SINGH,217, 59 A. M. SINTES,98 V. SIPALA,170, 155 V. SKLIRIS,33 B. J. J. SLAGMOLEN,34 D. A. SLATER,200\nT. J. SLAVEN-BLAIR,72 J. SMETANA,118 J. R. SMITH,54 L. SMITH,86, 184, 48 R. J. E. SMITH,6 W. J. SMITH,144\nS. SOARES DE ALBUQUERQUE FILHO,60 M. SOARES-SANTOS,188 K. SOMIYA,217 I. SONG,142 S. SONI,35 V. SORDINI,56\nF. SORRENTINO,29 H. SOTANI,305 F. SPADA,80 V. SPAGNUOLO,37 A. P. SPENCER,86 P. SPINICELLI,62 A. K. SRIVASTAVA,93\nF. STACHURSKI,86 C. J. STARK,123 D. A. STEER,306 N. STEINLE,168 J. STEINLECHNER,36, 37 S. STEINLECHNER,36, 37\nN. STERGIOULAS,251 P. STEVENS,41 M. STPIERRE,163 M. D. STRONG,12 A. STRUNK,2 A. L. STUVER,102, * M. SUCHENEK,95\nS. SUDHAGAR,95 Y. SUDO,230 N. SUELTMANN,97 L. SULEIMAN,54 K. D. SULLIVAN,12 J. SUN,241 L. SUN,34 S. SUNIL,93 J. SURESH,113\nB. J. SUTTON,67 P. J. SUTTON,33 K. SUZUKI,217 M. SUZUKI,204 B. L. SWINKELS,37 A. SYX,116 M. J. SZCZEPA \u00b4NCZYK,307\nP. SZEWCZYK,125 M. TACCA,37 H. TAGOSHI,204 K. TAKADA,204 H. TAKAHASHI,272 R. TAKAHASHI,25 A. TAKAMORI,42 S. TAKANO,308\nH. TAKEDA,309, 310 K. TAKESHITA,217 I. TAKIMOTO SCHMIEGELOW,44, 45 M. TAKOU-AYAOH,78 C. TALBOT,130 M. TAMAKI,204\nN. TAMANINI,100 D. TANABE,141 K. TANAKA,50 S. J. TANAKA,230 S. TANIOKA,33 D. B. TANNER,46 W. TANNER,8, 9 L. TAO,211\nR. D. TAPIA,7 E. N. TAPIA SAN MART\u00cdN,37 C. TARANTO,21, 22 A. TARUYA,311 J. D. TASSON,152 J. G. TAU,110 D. TELLEZ,54\nR. TENORIO,98 H. THEMANN,180 A. THEODOROPOULOS,138 M. P. THIRUGNANASAMBANDAM,79 L. M. THOMAS,11 M. THOMAS,63\nP. THOMAS,2 J. E. THOMPSON,210 S. R. THONDAPU,103 K. A. THORNE,63 E. THRANE,6 J. TISSINO,44, 45 A. TIWARI,79\nPAWAN TIWARI,44 PRAVEER TIWARI,195 S. TIWARI,188 V. TIWARI,118 M. R. TODD,78 M. TOFFANO,91 A. M. TOIVONEN,18\nK. TOLAND,86 A. E. TOLLEY,73 T. TOMARU,25 V. TOMMASINI,11 T. TOMURA,50 H. TONG,6 C. TONG-YU,141\nA. TORRES-FORN\u00c9,138, 139 C. I. TORRIE,11 I. TOSTA E MELO,312 E. TOURNEFIER,31 M. TRAD NERY,113 K. TRAN,123\nA. TRAPANANTI,52, 51 R. TRAVAGLINI,167 F. TRAVASSO,52, 51 G. TRAYLOR,63 M. TREVOR,126 M. C. TRINGALI,62 A. TRIPATHEE,90\nG. TROIAN,184, 48 A. TROVATO,184, 48 L. TROZZO,4 R. J. TRUDEAU,11 T. TSANG,33 S. TSUCHIDA,313 L. TSUKADA,213\nK. TURBANG,187, 23 M. TURCONI,113 C. TURSKI,94 H. UBACH,82, 83 N. UCHIKATA,204 T. UCHIYAMA,50 R. P. UDALL,11 T. UEHARA,314\nK. UENO,42 V. UNDHEIM,277 L. E. URONEN,219 T. USHIBA,50 M. VACATELLO,80, 81 H. VAHLBRUCH,8, 9 N. VAIDYA,11 G. VAJENTE,11\nA. VAJPEYI,6 J. VALENCIA,98 M. VALENTINI,107, 37 S. A. VALLEJO-PE\u00d1A,189 S. VALLERO,28 V. VALSAN,10 M. VAN DAEL,37, 315\nE. VAN DEN BOSSCHE,187 J. F. J. VAN DEN BRAND,36, 107, 37 C. VAN DEN BROECK,71, 37 M. VAN DER SLUYS,37, 71 A. VAN DE WALLE,41\nJ. VAN DONGEN,37, 107 K. VANDRA,102 M. VANDYKE,119 H. VAN HAEVERMAET,23 J. V. VAN HEIJNINGEN,37, 107 P. VAN HOVE,64\nJ. VANIER,259 M. VANKEUREN,104 J. VANOSKY,2 N. VAN REMORTEL,23 M. VARDARO,36, 37 A. F. VARGAS,124 V. VARMA,133\nA. N. VAZQUEZ,89 A. VECCHIO,118 G. VEDOVATO,92 J. VEITCH,86 P. J. VEITCH,115 S. VENIKOUDIS,15 R. C. VENTEREA,18\nP. VERDIER,56 M. VEREECKEN,15 D. VERKINDT,31 B. VERMA,133 Y. VERMA,103 S. M. VERMEULEN,11 F. VETRANO,60\nA. VEUTRO,38, 39 A. VICER\u00c9,60, 61 S. VIDYANT,78 A. D. VIETS,88 A. VIJAYKUMAR,190 A. VILKHA,110 N. VILLANUEVA ESPINOSA,138\nV. VILLA-ORTEGA,177 E. T. VINCENT,57 J.-Y. VINET,113 S. VIRET,56 S. VITALE,35 H. VOCCA,76, 51 D. VOIGT,97 E. R. G. VON REIS,2\nJ. S. A. VON WRANGEL,8, 9 W. E. VOSSIUS,231 L. VUJEVA,140 S. P. VYATCHANIN,108 J. WACK,11 L. E. WADE,104 M. WADE,104\nK. J. WAGNER,110 L. WALLACE,11 E. J. WANG,89 H. WANG,217 J. Z. WANG,90 W. H. WANG,164 Y. F. WANG,1 G. WARATKAR,195\nJ. WARNER,2 M. WAS,31 T. WASHIMI,25 N. Y. WASHINGTON,11 D. WATARAI,42 B. WEAVER,2 S. A. WEBSTER,86\nN. L. WEICKHARDT,97 M. WEINERT,8, 9 A. J. WEINSTEIN,11 R. WEISS,35 L. WEN,72 K. WETTE,34 J. T. WHELAN,110 B. F. WHITING,46\nC. WHITTLE,11 E. G. WICKENS,73 D. WILKEN,8, 9, 9 A. T. WILKIN,211 B. M. WILLIAMS,119 D. WILLIAMS,86 M. J. WILLIAMS,73\nN. S. WILLIAMS,1 J. L. WILLIS,11 B. WILLKE,9, 8, 9 M. WILS,109 L. WILSON,104 C. W. WINBORN,105 J. WINTERFLOOD,72\nC. C. WIPF,11 G. WOAN,86 J. WOEHLER,36, 37 N. E. WOLFE,35 H. T. WONG,141 I. C. F. WONG,219, 109 K. WONG,190 T. WOUTERS,71, 37\nJ. L. WRIGHT,2 M. WRIGHT,86, 71 B. WU,78 C. WU,142 D. S. WU,8, 9 H. WU,142 K. WU,119 Q. WU,53 Y. WU,96 Z. WU,100\nE. WUCHNER,54 D. M. WYSOCKI,10 V. A. XU,207 Y. XU,98 N. YADAV,28 H. YAMAMOTO,11 K. YAMAMOTO,151 T. S. YAMAMOTO,42\nT. YAMAMOTO,50 R. YAMAZAKI,230 T. YAN,118 K. Z. YANG,18 Y. YANG,146 Z. YARBROUGH,12 J. YEBANA,98 S.-W. YEH,142\nA. B. YELIKAR,144 X. YIN,35 J. YOKOYAMA,316, 42 T. YOKOZAWA,50 S. YUAN,72 H. YUZURIHARA,50 M. ZANOLIN,65 M. ZEESHAN,110\nT. ZELENOVA,62 J.-P. ZENDRI,92 M. ZEOLI,15 M. ZERRAD,40 M. ZEVIN,96 L. ZHANG,11 N. ZHANG,57 R. ZHANG,149 T. ZHANG,118\nC. ZHAO,72 YUE ZHAO,161 YUHANG ZHAO,20 Z.-C. ZHAO,317 Y. ZHENG,105 H. ZHONG,18 H. ZHOU,78 H. O. ZHU,72 Z.-H. ZHU,317, 318\nA. B. ZIMMERMAN,120 L. ZIMMERMANN,56 M. E. ZUCKER,35, 11 J. ZWEIZIG,11\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n\n5\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00e9orique, Aix-Marseille Universit\u00e9, Campus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n20Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, 64849 Monterrey, Nuevo Le\u00f3n, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n\n6\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n82Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n83Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00e9, Universit\u00e9 de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit\u00e0 di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120University of Texas, Austin, TX 78712, USA\n121Cornell University, Ithaca, NY 14850, USA\n\n7\n122Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n123Christopher Newport University, Newport News, VA 23606, USA\n124OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n125Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n126University of Maryland, College Park, MD 20742, USA\n127Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n128INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n129Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n130University of Chicago, Chicago, IL 60637, USA\n131University of Arizona, Tucson, AZ 85721, USA\n132INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Colorado State University, Fort Collins, CO 80523, USA\n138Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n139Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n140Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n141National Central University, Taoyuan City 320317, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n157Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n159Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n161The University of Utah, Salt Lake City, UT 84112, USA\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n165Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n166DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n171INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n172Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n173Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n174The University of Sheffield, Sheffield S10 2TN, United Kingdom\n175Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n176Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n177IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n178Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n\n8\n179INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n180California State University, Los Angeles, Los Angeles, CA 90032, USA\n181Marquette University, Milwaukee, WI 53233, USA\n182Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n183Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n184Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n185Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n186National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n187Vrije Universiteit Brussel, 1050 Brussel, Belgium\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Universidad de Antioquia, Medell\u00edn, Colombia\n190Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n191Stony Brook University, Stony Brook, NY 11794, USA\n192Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n193Montclair State University, Montclair, NJ 07043, USA\n194HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n195Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n196Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n197Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n198CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n199Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n200Western Washington University, Bellingham, WA 98225, USA\n201SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n202Barry University, Miami Shores, FL 33168, USA\n203E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n204Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n205Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,\nJapan\n206University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n207University of California, Berkeley, CA 94720, USA\n208Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n209Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211University of California, Riverside, Riverside, CA 92521, USA\n212Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214University of Nottingham NG7 2RD, UK\n215Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n216The University of Mississippi, University, MS 38677, USA\n217Graduate School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n218Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n219The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit\u00e0 degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Helmut Schmidt University, D-22043 Hamburg, Germany\n232Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n233Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n\n9\n234Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n235Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n236National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n237School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n238Sungkyunkwan University, Seoul 03063, Republic of Korea\n239Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n240Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n241Chung-Ang University, Seoul 06974, Republic of Korea\n242University of Washington Bothell, Bothell, WA 98011, USA\n243Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n248Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n249Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n250Nagoya University, Nagoya, 464-8601, Japan\n251Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n252Bard College, Annandale-On-Hudson, NY 12504, USA\n253Technical University of Braunschweig, D-38106 Braunschweig, Germany\n254Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n255Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n256Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n257Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n258Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n259Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n260Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n261Seoul National University, Seoul 08826, Republic of Korea\n262Department of Computer Simulation, Inje University, 197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n263NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n264Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n265Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n266St. Thomas University, Miami Gardens, FL 33054, USA\n267Scuola Normale Superiore, I-56126 Pisa, Italy\n268Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, E-08010 Barcelona, Spain\n269Institut de F\u00edsica d\u2019Altes Energies, E-08193 Barcelona, Spain\n270Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n271Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n272Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa\n224-8551, Japan\n273Tsinghua University, Beijing 100084, China\n274Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n275Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n276Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n277University of Stavanger, 4021 Stavanger, Norway\n278Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima\n739-8526, Japan\n279GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n280University College London, London WC1E 6BT, United Kingdom\n281Observatoire de Paris, 75014 Paris, France\n282Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n283Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n285CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n286Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n287Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n288Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n\n10\n289Hobart and William Smith Colleges, Geneva, NY 14456, USA\n290INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n291Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n292Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n293Kennesaw State University, Kennesaw, GA 30144, USA\n294Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n295Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n296Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n297Trinity College, Hartford, CT 06106, USA\n298Dipartimento di Fisica e Scienze della Terra, Universit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n299Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n300Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n301Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n302Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n303Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n304NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n305Faculty of Science and Technology, Kochi University, 2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n306Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS, Universit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n307Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n308Laser Interferometry and Gravitational Wave Astronomy, Max Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n309The Hakubi Center for Advanced Research, Kyoto University, Yoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n310Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n311Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n313National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n314Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n315Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n316Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8583, Japan\n317Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n318School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nABSTRACT\nLIGO, Virgo, and KAGRA form a network of gravitational-wave observatories. Data and analysis results\nfrom this network are made publicly available through the Gravitational Wave Open Science Center. This paper\ndescribes open data from this network, including the addition of data from the first part of the fourth observing\nrun (O4a) and selected periods from the preceding engineering run, collected from May 2023 to January 2024.\nThe public data set includes calibrated strain time series for each instrument, data from additional channels\nused for noise subtraction and detector characterization, and analysis data products from version 4.0 of the\nGravitational-Wave Transient Catalog.\n1. INTRODUCTION\nThe Laser Interferometer Gravitational-Wave Observatory\n(LIGO; Aasi et al. 2015), Virgo (Acernese et al. 2015),\nKAGRA (Akutsu et al. 2021a) and GEO 600 (Luck\net al. 2010; Affeldt et al. 2014; Dooley et al. 2016)\nare observing the gravitational-wave (GW) Universe with\nunprecedented sensitivity (Abac et al. 2025a).\nData from\nthese observatories are shared and jointly analyzed as\ndescribed in a Memorandum of Agreement (LIGO, Virgo,\nand KAGRA 2019), so that the insruments form a global\nnetwork. The instruments operate in a series of observing\nruns, with breaks between observing periods for instrument\n* Deceased, September 2024.\nupgrades and detector commissioning (Abbott et al. 2020a;\nCapote et al. 2025).\nFollowing a proprietary period for\nwork by the LIGO\u2013Virgo\u2013KAGRA Collaboration (LVK),\ndata from each observing run are publicly released via the\nGravitational Wave Open Science Center (GWOSC) for\nuse by the entire scientific community.1\nThe schedule of\ndata releases for LIGO is maintained in the LIGO Data\nManagement Plan (LIGO Laboratory 2025).\nData from previous observing runs have been released with\na history going back more than a decade, starting with data\nfrom initial LIGO released in 2014 (Vallisneri et al. 2015).\nData from the advanced-detector era are organized into an\n1\nGWOSC Home Page, https://gwosc.org\n\n11\nongoing series of observing runs, beginning with data from\nthe first observing run (O1) and second observing run (O2;\nAbbott et al. 2021a), and continuing with data released from\nthe third observing run (O3; Abbott et al. 2023a).\nThe fourth observing run is divided into several segments,\nwith the first segment (O4a) spanning time from May 24,\n2023 to January 16, 2024. This paper describes the publicly\navailable data from the LVK with an emphasis on the new\nO4a public data release.\nAt the time of this writing, as\ndescribed in Subsection 2.1, this data release includes data\nfrom LIGO only.\nPublic data include time series strain data from the\ninstruments, additional time series channels describing the\ninstrument state, and segment information describing data\nquality of each instrument.\nIn addition, the full set of\nevents known as the Gravitational-Wave Transient Catalog\n(GWTC) identified by the LVK is publicly available. The\nO4a data release also includes a number of analysis results\nfrom the fourth version of the Gravitational-Wave Transient\nCatalog (GWTC-4.0, Abac et al. 2025b), including an\nelectronic version of the catalog that can be browsed\nonline and queried through a Representational State Transfer\nApplication Programming Interface (REST API). This paper\nis included in a suite of papers describing GWTC-4.0 (Abac\net al. 2025a), and is best understood in the context of the\nrelated papers.\nIn Section 2 we discuss the primary data products from\nGW observatories and the epochs of data taking known\nas observing runs.\nIn Section 3 we explain the basics\nof calibration of interferometer strain data.\nSection 4\noutlines some non-astrophysical noise sources that impact\nGW data analysis and noise mitigations. In Section 5 we\ndescribe the details for the strain data available on GWOSC\nand alternative services.\nSection 6 discusses additional\ninstrumental monitoring channels used for noise subtraction\nand production of data-quality flags that are now also\ndistributed by GWOSC. Finally, the GWOSC Event Portal\nthat provides electronic catalogs of detected GW transients\nis described in Section 7.\n2. DATA SET OVERVIEW\n2.1. Observing Time\nThe instruments operated in a series of observing runs\ndescribed in Abac et al. (2025a), with the following dates:\n\u2022 O1: 12 September 2015 0:00 UTC (GPS 1126051217)\nto 19 January 2016 16:00 UTC (GPS 1137254417)\n\u2022 O2: 30 November 2016 16:00 UTC (GPS 1164556817)\nto 25 August 2017 22:00 UTC (GPS 1187733618)\n\u2022 O3: 1 April 2019 15:00 UTC (GPS 1238166018)\nto 27 March 2020 17:00 UTC (GPS 1269363618)\n\u2022 O4a: 24 May 2023 15:00 UTC (GPS 1368975618)\nto 16 January 2024 16:00 UTC (GPS 1389456018)\nThe O4a data release also includes some additional\ndata from the preceding engineering run (see Section 5.3).\nSome observational data are also available from other\ntimes studied in targeted LVK publications, including data\nfrom the GEO 600 (Dooley et al. 2016) and KAGRA\n(Akutsu et al. 2021a) detectors, as described in LIGO\nScientific Collaboration, Virgo Collaboration and KAGRA\nCollaboration (2017, 2022, 2024).\nThe observatories do not record astrophysical data at\nall times.\nMany types of phenomena can interrupt data\ntaking,\nincluding instrument maintenance and detector\nimprovements,\nseismic\nactivity,\npower\noutages,\nand\ninstrument lock-loss for other reasons. A comparison of the\ntotal amount of observing time for each run is shown in Table\n1. The amount of calendar time for each observing run is\nshown at the top of each table section (e.g., O4a spanned 237\ncalendar days). The O3 runs includes observing time from\nboth O3a and O3b, as well as a commissioning break with\nno observing time.\nDuring\nO4a,\nVirgo\nwas\nnot\nobserving\ndue\nto\ncommissioning activities. KAGRA and GEO 600 data were\nless sensitive than the other observatories, and so were not\nused for most analyses. Therefore, only data from LIGO\nare included in this data release. The total coincident time\nwith both LIGO Hanford Observatory (LHO) and LIGO\nLivingston Observatory (LLO) observing simultaneously\nduring O4a was 126.5 days. The table shows similar statistics\nfor each of O1, O2, and O3, with additional information on\npast data releases available in Abbott et al. (2021a) and\nAbbott et al. (2023a).\n2.2. Time-series Data\nThe primary data product from a GW observatory is the\ncalibrated strain data, often called h(t). The strain data are\nrecorded as a time series, so that each time sample records\none measurement of the fractional difference in lengths in the\ninterferometer arms, \u2206L/L. The LIGO, Virgo, and KAGRA\nobservatories typically use a sampling rate of 16384 samples\nper second, corresponding to a data rate of \u223c4 TB per year\nper instrument for the strain data. This is a small fraction\nof the total data rate of serveral PB per year, which includes\nhundreds of thousands of diagnostic channels to monitor the\nstate of the instrument and the local environment.\nFor current instruments, the strain time series consists\nprimarily of instrumental noise at most times (Abbott et al.\n2020b). The noise levels in the instruments fluctuate over\ntime, so that the sensitivities of the instruments vary from\nmoment to moment.\nOne long-used figure of merit for\nthe instrument sensitivity is the binary neutron star (BNS)\ninspiral range (Finn & Chernoff 1993; Chen et al. 2021),\nwhich is briefly summarized in Abac et al. (2025a), and gives\nan estimate of the distance to which a detector could detect\na BNS merger with a signal-to-noise ratio (SNR) of 8 after\naveraging over sky location and orientation. The variability\nin the BNS inspiral range over the course of O4a is shown\nin Figure 1. The plot shows that the observatories frequently\noperated near their peak sensitivity of around 160 Mpc in\nO4a.\nHowever, there are also times when elevated noise\n\n12\nTable 1. The amount of observing time in days and\nthe corresponding fraction of the total run time for\neach detector (IFO) combination.\nThe amount of\ncalendar time for each observing run is shown at the\ntop of each table section.\nIFO Combination\nObserving Time\nFraction\nO1: 129.7 d\nLHO\n27.7 d\n21.4 %\nLLO\n16.8 d\n13.0 %\nLHO, LLO\n49.0 d\n37.8 %\nO2: 268.3 d\nLHO\n37.8 d\n14.1 %\nLLO\n33.5 d\n12.5 %\nVirgo\n1.7 d\n0.6 %\nLHO, LLO\n103.0 d\n38.4 %\nLHO, Virgo\n1.7 d\n0.6 %\nLLO, Virgo\n2.2 d\n0.8 %\nLHO, LLO, Virgo\n15.3 d\n5.7 %\nO3a: 183.0 d\nLHO\n5.6 d\n3.1 %\nLLO\n6.3 d\n3.4 %\nVirgo\n15.7 d\n8.6 %\nLHO, LLO\n25.9 d\n14.2 %\nLHO, Virgo\n17.5 d\n9.5 %\nLLO, Virgo\n25.3 d\n13.8 %\nLHO, LLO, Virgo\n80.8 d\n44.2 %\nO3b: 147.1 d\nLHO\n4.5 d\n3.1 %\nLLO\n3.4 d\n2.3 %\nVirgo\n9.3 d\n6.3 %\nLHO, LLO\n22.9 d\n15.6 %\nLHO, Virgo\n14.5 d\n9.8 %\nLLO, Virgo\n13.8 d\n9.4 %\nLHO, LLO, Virgo\n73.4 d\n49.9 %\nO3: 361.1 d\nLHO\n10.1 d\n2.8 %\nLLO\n9.7 d\n2.7 %\nVirgo\n25.0 d\n6.9 %\nLHO, LLO\n48.9 d\n13.5 %\nLHO, Virgo\n31.9 d\n8.8 %\nLLO, Virgo\n39.1 d\n10.8 %\nLHO, LLO, Virgo\n154.3 d\n42.7 %\nO3GK: 13.7 d\nGEO 600\n4.5 d\n32.9 %\nKAGRA\n0.9 d\n6.5 %\nGEO 600, KAGRA\n6.4 d\n46.7 %\nO4a: 237.0 d\nLHO\n33.3 d\n14.1 %\nLLO\n37.0 d\n15.6 %\nLHO, LLO\n126.5 d\n53.4 %\nlevels cause the sensitivity to drop, as well as times when\nthe detectors are not operating at all or operating for periods\ntoo short to make a reliable inspiral range estimate, and in\nthis case the inspiral range is set to zero. This variability\nin instrument sensitivity is an important feature of the strain\ndata, and needs to be properly accounted for in any analysis.\nOver the course of O1 through O4, the typical BNS inspiral\nrange of the instruments generally improved for each run due\nto occasional hardware upgrades and commissioning work at\nthe observatories (Brooks et al. 2021; Driggers et al. 2019;\nBuikema et al. 2020; Soni et al. 2021; Capote et al. 2025; Jia\net al. 2024; Tse et al. 2019; Soni et al. 2024). The evolution\nof this range is described in Abac et al. (2025a) and Abbott\net al. (2020a).\nIn addition to the strain time series, the observatories also\nrecord a large number of auxiliary channels to measure the\nstate of each instrument and the local environment (Nguyen\net al. 2021; Huxford et al. 2024).\nThese channels record\nquantities like laser-power levels, temperatures, seismic\nmotion, angular alignments of mirrors, and many other\ntypes of information that can be used to assess instrument\nperformance (Rollins 2016; Soni et al. 2025). A subset of\nthese auxiliary channels is included in the O3 and O4a data\nreleases, and is described in Section 6.\n3. CALIBRATION\nGround-based interferometers make use of a feedback\ncontrol loop in order to hold the differential arm degree\nof freedom, \u2206L(t) = \u2206Lx(t) \u2212\u2206Ly(t), in resonance.\nCalibration refers to the process of reconstructing the\nexternal differential arm motion \u2206L(t) through a model for\nthe interferometer response function R and the measured\nerror signal from the differential arm feedback loop, derr\n(Abbott et al. 2017; Viets et al. 2018). In the time domain,\nthe strain can be reconstructed through a convolution of the\ndifferential arm error signal and the interferometer response\nfunction\n\u2206L(t) = R(t) \u229bderr(t),\n(1)\nwhere \u229brepresents a convolution, implemented using digital\nfinite impulse response filters for the response function (Viets\net al. 2018). The strain h(t) is the ratio of the differential arm\nmotion to the unperturbed interferometer arm length L,\nh(t) = \u2206L(t)\nL\n,\n(2)\nwhere L is the length of an interferometer arm and L \u2243\n3995 m for LIGO.\nImperfect calibration results in small errors in the\nmeasured strain values. For LIGO in O4a, the broadband\nuncertainty on the calibrated strain data is determined on\nan hourly cadence using a modified version of the methods\ndescribed in Sun et al. (2020) that incorporates additional\ncontinuous measurements of the calibrated strain systematic\nerror at discrete frequencies (Wade et al. 2025). Calibration\nuncertainty values for all runs are available in the LIGO\nDocument Control Center (LIGO, Virgo, and KAGRA 2021,\n2025a).\n\n13\nFigure 1. BNS inspiral range over time for O4a. Each point corresponds to a time interval of 4096 seconds, corresponding to the time range\nof one strain data file. The fast Fourier transform window length used is 8 seconds with a 4 seconds overlap. These inspiral range values are\nstored as metadata for each file in the GWOSC database and are accessible via the GWOSC website.\nFigure 2. LIGO Hanford (left) and Livingston (right) frequency-dependent calibration error for a one-hour time period in O4a starting at\nJanuary 15, 2024 08:00:00 UTC. The magnitude of the calibration error is shown in the top plots and the phase of the calibration error (in\nunits of degrees) is shown in the bottom plots. The median systematic error of the calibration is given by the solid line. The 1\u03c3 uncertainty on\nthis systematic error is given by the dotted lines. The black dots overlaid on the figure at specific frequencies are direct measurements of the\ncalibration error at a specific frequency during this one-hour time period. These measurements are made using sinusoidal injections with the\nphoton-calibrator system. These uncertainties are representative of typical LIGO calibration uncertainties throughout O4a.\n\n14\nCalibration methods for past observing runs are described\nin Abbott et al. (2017); Cahillane et al. (2017); Sun et al.\n(2020, 2021); Chen et al. (2025) and Acernese et al.\n(2018, 2022).\nDuring O4a, the final calibrated-strain\ndata for both LIGO observatories were computed in near-\nrealtime. The photon-calibrator system was used in O4a to\ninject continuous, sinusoidal excitations at eight frequencies\nthroughout the run (Karki et al. 2016; Bhattacharjee et al.\n2024).\nThe systematic error in the calibration at these\nfrequencies was then inferred through the transfer function of\nthe photon-calibrator excitation strain and the reconstructed\nstrain (Wade et al. 2025). The measured systematic error\nat each of these frequencies was included in the modeled\nsystematic error.\nThe O4a run marked the first time\ncalibration uncertainty estimates were provided for the near-\nrealtime calibrated strain data in LIGO, making this data\nusable as the final calibrated strain data product. Example\nuncertainty envelopes for the LHO and LLO calibrated strain\ndata are shown in Figure 2.\nThese envelopes represent\nthe median systematic calibration error as well as the 1\u03c3\nuncertainty on the systematic error for a one-hour time period\nduring O4a. The black dots overlayed on the envelopes are\ndirect measurements of the calibration systematic error over\nthe one-hour time period using sinusoidal photon-calibrator\ninjections at specific frequencies. The calibrated strain data\nfor LIGO in O4a should be considered valid for analyses\nwithin the provided hourly uncertainty envelopes in the range\n10\u20135000 Hz.\n4. DATA QUALITY\nNoise in the strain data is sometimes approximated as\nstationary and Gaussian.\nHowever, real strain data are\nalso affected by disturbances originating from instrumental\nand environmental sources (Abbott et al. 2020b; Soni et al.\n2025).\nThese artifacts can manifest as broadband, non-\nGaussian, short-duration features known as glitches (Nuttall\n2018; Glanzer et al. 2023), or as narrowband spectral features\nreferred to as spectral lines (Covas et al. 2018). In addition,\nGW observatories can experience periods of degraded\nperformance due to issues in control systems, calibration\nprocedures, or environmental disturbances. These episodes\ncan compromise data quality over extended durations,\nreducing the sensitivity of the detectors and potentially\nbiasing astrophysical parameter estimation (Pankow et al.\n2018; Macas et al. 2022; Kwok et al. 2022; Ghonge et al.\n2024).\nTo support robust analyses, the LVK employs a\nsuite of data-quality metrics designed to identify and allow\nmitigation of the impact of instrumental and environmental\nnoise. An overview of LIGO detector characterization efforts\nis available in Soni et al. (2025). Detector characterization\nmethods for past observing runs are described in Davis et al.\n(2021); Acernese et al. (2023a); Nuttall et al. (2015); Abbott\net al. (2016, 2018); Covas et al. (2018); Nguyen et al. (2021);\nAcernese et al. (2023b); and Akutsu et al. (2021b).\nSearches for different types of signals exhibit distinct\nsusceptibility to different noise sources,\nbut detector\ncharacterization is needed in all cases to remove signals of\nterrestrial origin and strengthen the confidence of detections.\nData-quality products are employed across four broad\ncategories of searches, each with customized detector-\ncharacterization methods (Caudill et al. 2021).\nCompact\nbinary coalescence (CBC) searches (Abac et al. 2025c) target\nGW signals from the coalescence of neutron stars and/or\nblack holes by applying matched-filtering techniques with\nmodeled waveform templates. GW burst (BURST) analyses\n(Abac et al. 2025d) aim to identify short-duration transients\nwithout strong assumptions on the signal morphology, by\ndetecting excess power in the time\u2013frequency representation\nof the strain data. Continuous wave (CW) searches (Abbott\net al. 2022a) focus on long-duration, nearly monochromatic\nsignals such as GWs emitted by non-axisymmetric rotating\nneutron stars. Stochastic (STOCH) searches (Abbott et al.\n2021b) aim to detect a diffuse GW background resulting\nfrom the superposition of numerous unresolved sources.\n4.1. Hardware Injections\nSimulated GW signals, known as hardware injections\n(Biwer et al. 2017), are introduced by physically displacing\nthe interferometer test masses to mimic true astrophysical\nevents and characterize the performance of the detectors\nand analyses.\nHardware injections with signals that\nmimic expected astrophysical sources are labeled by the\nsimulation type, corresponding to the different classes of\npotential sources (CBC, BURST, STOCH, or CW). Detector\ncharacterization safety injections are labeled as DETCHAR\ninjections.\nThese are used to test couplings between\nchannels used to monitor instrumental and environmental\nnoise sources.\nWe identify auxiliary channels that can be used to indicate\na detector problem, for example, when they display excess\nnoise levels.\nHowever, some channels are unsafe for\nidentifying noise because they respond to astrophysical\nsignals and therefore a response in the auxiliary channel\ncould indicate a real signal. An auxiliary channel is said\nto be safe to use for identifying noise transients only if it\ndoes not respond to astrophysical signals. Safety injections\nare used to identify unsafe channels. They are performed by\nactuating the end test-mass mirror using a photon calibrator,\nthereby generating a response in the primary strain channel\n(Karki et al. 2016). Channels that exhibit a response to these\ninjections are considered unsafe to use for vetoes, and are\nidentified following the method in Essick et al. (2021).\nHardware injection times are available on the GWOSC\nwebsite via a tool called Timelines2. Additional notes about\nhardware injections are also provided in the documentation\nfor each data release. In O4a there were no injections labeled\nCBC, BURST, DETCHAR, or STOCH during observing\nmode. The only hardware injections present in the released\ndata are of the CW type and consist of simulations of 18\nspinning neutron stars whose parameters are given on the\n2\nTimelines App, https://gwosc.org/timeline/\n\n15\nGWOSC website,3 with GW frequencies spanning 12\u20133000\nHz.\nInjecting simulated CW signals allows, within the\nuncertainties of the hardware injection system, a direct end-\nto-end assessment of degradation in CW signal detection due\nto imperfect calibration or due to noise subtraction. These\ninjections are almost always present (in O4a, only 1.7%\nof the released LHO data and 2.6% of LLO data do not\nhave CW injections) but because they are faint and nearly\nmonochromatic they have minimal impact on transient-signal\nsearches.\n4.2. Data-quality Flags\nData-quality flags are used to identify periods during\nwhich the strain data are affected by data-quality issues.\nThese flags are used by analysis pipelines to exclude\nor down-weight compromised data segments.\nFlags are\nclassified in order of descending severity, such that the most\nsevere problems are labeled Category 1 (CAT1).\nThese\nflags mark intervals of time affected by well-understood and\nsevere data-quality issues (hardware faults, control-system\nfailures, or known periods of malfunction) during which\nthe strain data are not considered suitable for astrophysical\nanalyses; these times are systematically excluded from\nall GW searches and parameter-estimation studies.\nSome\nsearches also apply the less severe Category 2 (CAT2), which\nare typically shorter in duration than CAT1 (Abac et al.\n2025c). Category 3 (CAT3) flags are used to identify possible\nissues of unknown origin which are found through statistical\nstudies.\nDuring O4a, some searches used only the CAT1 flag set.\nCAT2 flags were applied only to BURST searches.\nThe\nmethodology for identifying and applying these flags during\nO4a is described in detail in Soni et al. (2025).\nFor CBC analyses, an additional data quality product used\nduring O4a is the set of statistical flags derived from the\niDQ supervised-learning framework (Essick et al. 2020).\nThis pipeline evaluates the likelihood that transient noise\nis present in the strain data based on activity in auxiliary\nchannels that are not expected to be sensitive to astrophysical\nsources.\nThe iDQ pipeline produces several statistical\noutputs sampled at 128 Hz.\nThe low-latency versions of\nthe iDQ outputs are available in the alternate strain release\ndescribed in Section 5.5; the corresponding channel names\nare listed in Table 2. The offline iDQ outputs are available\nin Zenodo as LIGO, Virgo, and KAGRA (2025b). The OK\nflag indicates whether the iDQ outputs are reliable at a given\ntime, taking the value 1 when valid and 0 otherwise. Other\noutputs include a normalized RANK score that reflects the raw\nclassifier output, an estimated detection efficiency (EFF), the\nfalse alarm probability (FAP) of misclassifying clean times\nas glitchy, and the log likelihood-ratio (LOGLIKE), where\npositive values suggest the presence of a glitch and negative\nvalues suggest clean data. For CBC searches, the iDQ flags\ntypically used are derived by thresholding the LOGLIKE\n3\nO4a Injections, https://gwosc.org/O4/o4_inj\nchannel; segments with LOGLIKE > 5 are flagged as likely\nto be glitch-contaminated. Unlike CAT1 and CAT2 flags,\niDQ flags are not applied universally. Searches algorithms\nmay choose to use them either as vetoes or to re-rank the\nsignificance of candidate events.\nTable 2. The iDQ channel names in the alternate strain release\ndescribed in Section 5.5, sampled at 128 Hz. Ifo corresponds to H1\nfor Hanford or L1 for Livingston and AR stands for Analysis Ready.\nChannel name\nOK Flag\nIfo:IDQ-OK_OVL_10_2048_AR\nRank\nIfo:IDQ-RANK_OVL_10_2048_AR\nFalse Alarm Prob.\nIfo:IDQ-FAP_OVL_10_2048_AR\nEfficiency\nIfo:IDQ-EFF_OVL_10_2048_AR\nLog likelihood-ratio\nIfo:IDQ-LOGLIKE_OVL_10_2048_AR\n4.3. Spectral Line Catalog\nSpectral lines are narrowband, often persistent features\nthat appear in the amplitude spectral density of GW strain\ndata.\nThese features arise from a variety of instrumental\nand environmental sources, including mechanical resonances\n(e.g., violin-mode resonances from the suspension system),\ninjected lines used for calibration, digital dither signals, and\nharmonics of the electrical mains. Although their impact on\nCBC and BURST searches is minimal, spectral lines are a\nsignificant concern for persistent searches. Spectral artifacts\nthat overlap with the target signal frequency can severly\nimpact CW searches, which rely on coherence over long\ntimescales. Similarly, STOCH searches are sensitive to lines,\nespecially those of common origin or at harmonics of shared\nnoise sources.\nTo support the identification and mitigation of these\nfeatures, the LVK maintains a curated catalog of instrumental\nspectral lines (Covas et al. 2018). The catalog includes both\npreviously known artifacts and newly identified lines, and\nprovides relevant metadata such as frequency, amplitude,\ndetector, and, where possible, a suspected source.\nThis\ninformation is used by various search pipelines to identify\ncontaminated frequency bins, apply vetoes, or model noise\ncontamination. Spectral line catalogs are publicly available\non the GWOSC website as part of the documentation of each\nrun\u2019s data release.4\n4.4. Glitch Subtraction\nGlitches represent a significant source of contamination\nin strain data, particularly affecting transient searches while\nhaving limited impact on persistent searches.\nIn a small\nnumber of cases, a glitch occurs in close temporal and\n4\nGWOSC data releases, https://gwosc.org/data\n\n16\nspectral proximity to a candidate GW signal, requiring\ntargeted mitigation to reliably recover the astrophysical\nsignal.\nSubtraction techniques are employed to remove\nlocalized excess power in the time\u2013frequency domain\n(Pankow et al. 2018).\nOne such method is BayesWave\n(Cornish et al. 2021; Hourihane et al. 2022), which models\nand subtracts transient noise features from the data without\nrequiring a specific model for the astrophysical signal. A\ncomplementary method is linear noise subtraction (Davis\net al. 2019), which removes known, repeatable noise\ncontributions using information from auxiliary sensors that\nmonitor the detector environment and instrumental systems.\nDuring O4a, 16 candidate events with a false alarm rate\n(FAR) below 1 per year required such glitch mitigation in at\nleast one interferometer (Abac et al. 2025b). These events\nare listed in Table 3, along with their GPS time, affected\ninterferometer(s), and the time\u2013frequency region used to\nconstrain the subtraction and assess residuals.\nAll glitch\nmitigated data listed in Table 3 were produced with the\nBayesWave pipeline.\n5. STRAIN DATA\nSections 5.1 to 5.4 describe the default strain-data release,\nwhich can be downloaded directly from the GWOSC\nwebsite or accessed via the fetch_open_data method\nof the gwpy package (Macleod et al. 2021). Alternatively,\nespecially for downloading large data sets, such as an\nentire observation run, users can download data from the\nnetwork data server NDS2 (Zweizig et al. 2021) or the\nOpen Science Data Federation (OSDF) service that acts as\na storage resource broker and optimizes data access through\na worldwide network of data centers.5\nWhile much of\nthe content in this section is similar across observing runs,\nSection 5.4 describes differences between runs.\nData in the LVK archives are stored as gravitational-wave\nframe files (gwf; LIGO Scientific Collaboration and Virgo\nCollaboration 2022), a custom binary format developed\nwithin the GW community in which data are uniquely\nidentified by a channel name and a frame type. Files for\nthe default strain-data release are created by repackaging the\noriginal LVK data, whose identifiers are listed in Table 4 for\nall observing runs. The best calibration version available is\nused in the default strain release. In addition to the default\nstrain-data release, several alternate strain channels have\nalso been released starting from O3 (see Section 5.5).\nThe released calibrated strain data of the observing runs\nare divided into files containing 4096 seconds of data each.\nWhen data are missing or do not meet the necessary quality\nstandards for analysis, strain values are recorded as NaNs.\nThe strain data are available at both the original sampling\nrate of 16384 Hz and a reduced rate of 4096 Hz, referred\nas 16 kHz and 4 kHz in the remainder of this paper. The\ndownsampling process is carried out using the standard\ndecimation method scipy.signal.decimate, from\n5\nLarge Scale Data and Computing Resources, https://gwosc.org/osdf\nthe Python library SciPy (Virtanen et al. 2020).\nBefore\ndownsampling, an order 8 Chebyshev type I filter (Smith\n1999) is used as anti-aliasing filter.\nThe maximum resolvable frequency in a given dataset\nis constrained by the Nyquist\u2013Shannon sampling theorem\n(Nyquist 1924) and corresponds to half of the sampling rate.\nDue to the roll-off effect of the anti-aliasing filters applied\nduring resampling, the valid frequency range is slightly lower\nthan the Nyquist frequency. Consequently, for data sampled\nat 4 kHz, frequencies above approximately 1700 Hz are\nincreasingly attenuated by the anti-aliasing filter, which can\nsuppress but not entirely eliminate usable signal content. For\ndata sampled at 16 kHz, however, the limiting factor is given\nby the calibration which restricts the valid data to 5 kHz, as\ndescribed in Section 3.\nThese considerations on the maximum frequency are\na crucial factor to consider when selecting a dataset to\ndownload. On the other hand, data sampled at higher rates\nrequire increased storage space and longer download times.\nUsers should, therefore, select the dataset that best aligns\nwith their specific requirements.\n5.1. Structure of the Default Strain-Data Files\nThe default strain files include not only the strain data but\nalso information on data quality and injections. The main file\nformats used for the GWOSC open data are the Hierarchical\nData Format (hdf; Koziol & Robinson 2018), a data format\ndesigned for storing and organizing large datasets that is\neasily readable by many programming languages, and the\ngwf format, which is the file format used in the LVK archives\nas already mentioned.\nFor all available file formats, file names in the default strain\nrelease contain the following information:\n\u2022 Obs: the observatory, i.e. the site, that is indicated by\none letter and can have values L for LIGO Livingston,\nH for LIGO Hanford, V for Virgo, G for GEO 600 or\nK for KAGRA.\n\u2022 Ifo:\nthe interferometer label, created by adding a\nnumber to the letter that indicates the observatory. This\nchoice allows the identification of multiple detectors\ninstalled in the same site, as was the case for Initial\nLIGO (Abbott et al. 2009). For the LVK observation\nruns it can have values H1, L1, V1, G1 or K1.\n\u2022 Run: the observing run name, i.e., O4a.\n\u2022 sKHZ or s: the sampling rate in kHz, s can have values\n4 or 16 (4096 Hz or 16384 Hz).\n\u2022 Rn or Vn: release number or version number of the\nfile. The letter V was used only for O1, then it was\navoided because it could be confused with the Virgo\ninterferometer name.\n\u2022 GPSstart: the starting time of the data contained in the\nfile, as a 10-digit GPS value (in seconds).\n\n17\nTable 3. List of O4a events from Abac et al. (2025b) with FAR < 1 per year, for which glitch subtraction was performed using BayesWave\n(Cornish et al. 2021). For each event, we provide the GPS time, the interferometer (IFO) where subtraction was applied, and the time and\nfrequency windows used for subtraction. The time window indicates the aproximate time of the glitch and is referenced from the indicated GPS\ntime, with negative values before the merger and positive values after the merger. A similar table is included in Abac et al. (2025b).\nEvent\nGPS Time\nIFO\nTime (s)\nFrequency (Hz)\nGW230606_004305\n1370047403.79\nLHO\n[1.11, 1.31]\n[8.0, 512]\nGW230707_124047\n1372768865.35\nLHO\n[\u22120.15, 0.1]\n[15.0, 30.0]\nGW230708_053705\n1372829843.12\nLHO\n[\u22122.02, 0.98]\n[10.0, 50.0]\nGW230806_204041\n1375389659.94\nLHO\n[1.8, 2.0]\n[25.0, 65.0]\nGW230819_171910\n1376500768.45\nLLO\n[\u22123.2, \u22122.8]\n[8.0, 512]\nGW231113_122623\n1383913601.88\nLLO\n[0.01, 0.22]\n[70.0, 120.0]\nGW231114_043211\n1383971549.25\nLHO\n[\u22120.95, \u22120.6]\n[10.0, 30.0]\nGW231118_090602\n1384333580.01\nLHO\n[\u22124.81, \u22124.51]\n[15.0, 50.0]\nGW231123_135430\n1384782888.63\nLHO\n[\u22121.7, \u22121.1]\n[15.0, 30.0]\nGW231129_081745\n1385281083.64\nLLO\n[1.4, 1.8]\n[10.0, 170.0]\nGW231221_135041\n1387201859.32\nLHO\n[0.3, 0.4]\n[200.0, 450.0]\nGW231223_032836\n1387337334.05\nLHO\n[\u22120.55, \u22120.25]\n[10.0, 25.0]\nTable 4. Channel names and frame types that allow tracing the provenance of strain data released on GWOSC. H1, L1, V1, G1 and K1 are\nshort versions of the interferometer names. The attribute CLEAN in H1 and L1 indicates that noise subtraction (Vajente et al. 2020; Davis et al.\n2019; Viets & Wade 2021) was used. AR stands for Analysis Ready and indicates that these channels contain only data for times ready to be\nanalysed. The other parts of the names refer in general to the calibration version.\nRun\nIFO\nChannel name\nFrame type\nO1\nLHO\nH1:DCS-CALIB_STRAIN_C02\nH1_HOFT_C02\nO1\nLLO\nL1:DCS-CALIB_STRAIN_C02\nL1_HOFT_C02\nO2\nLHO\nH1:DCH-CLEAN_STRAIN_C02\nH1_CLEANED_HOFT_C02\nO2\nLLO\nL1:DCH-CLEAN_STRAIN_C02\nL1_CLEANED_HOFT_C02\nO2\nVirgo\nV1:Hrec_hoft_V1O2Repro2A_16384Hz\nV1O2Repro2A\nO3a\nLHO\nH1:DCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01\nH1_HOFT_CLEAN_SUB60HZ_C01\nO3a\nLLO\nL1:DCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01\nL1_HOFT_CLEAN_SUB60HZ_C01\nO3a\nVirgo\nV1:Hrec_hoft_16384Hz\nV1Online\nO3a(last two weeks)\nVirgo\nV1:Hrec_hoft_V1O3ARepro1A_16384Hz\nV1O3Repro1A\nO3b\nLHO\nH1:DCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01\nH1_HOFT_CLEAN_SUB60HZ_C01\nO3b\nLLO\nL1:DCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01\nL1_HOFT_CLEAN_SUB60HZ_C01\nO3b\nVirgo\nV1:Hrec_hoft_16384Hz\nV1Online\nO3GK\nGEO 600\nG1:DER_DATA_HD_CLEAN\nG1_RDS_C02_L3\nO3GK\nKAGRA\nK1:DAC-STRAIN_C20\nK1_HOFT_C20\nO4a\nLHO\nH1:GDS-CALIB_STRAIN_CLEAN_AR\nH1_HOFT_C00_AR\nO4a\nLLO\nL1:GDS-CALIB_STRAIN_CLEAN_AR\nL1_HOFT_C00_AR\n\u2022 Dur: the duration in seconds of the file, typically\n4096 seconds.\n\u2022 Ext: the extension corresponding to the file format\n(gwf, hdf or txt).\nThe structure of the file names is:\nObs\u2014FrameType\u2014GPSstart\u2014Dur.Ext\nwhere the FrameType is Ifo_GWOSC_Run_sKHZ_Rn.\nThe hdf files contain three folders (or groups).\n\u2022 The folder meta hosts the metadata of the file:\nDescription, DescriptionURL, Detector (e.g., L1),\nObservatory (e.g., L), Duration, GPSstart, UTCstart\n(duration and starting time, using GPS and UTC\nstandards,\nrespectively,\nof the segment of data\n\n18\ncontained in a file), StrainChannel and FrameType\nused in the LVK archives as listed in Table 4.\n\u2022 The folder strain contains the array Strain of h(t)\nvalues with useful attributes such as Xstart and\nXspacing that define the GPS start time of the data\ncontained in the array and the temporal distance\nbetween points in the array.\n\u2022 The folder quality contains two subfolders: one for\ndata quality and another for injections. Each subfolder\nincludes a bitmask that indicates, for each second,\nthe status of data quality or injections, along with a\ndescription of each bit in the mask (see Section 5.2 for\ndetails).\nThe GWOSC gwf files include three channels (for strain\ndata, data quality, and injections), whose names are listed in\nTable 5.\nTable 5.\nChannel names in the GWOSC gwf files.\nThe\nnomenclature is similar to that described for the file name\nconventions: Ifo is the interferometer, s is the sampling rate, n is\nthe version or release (until now only 1 has been used).\nChannel name\nStrain\nIfo:GWOSC-sKHZ_Rn_STRAIN\nData-quality mask\nIfo:GWOSC-sKHZ_Rn_DQMASK\nInjections mask\nIfo:GWOSC-sKHZ_Rn_INJMASK\n5.2. Data Quality and Injections in GWOSC Files\nThe data-quality information is encoded in the default\nstrain release as a bitmask following the structure described\nin Table 6, with a 1 Hz sampling rate.6\nThe meaning\nof the data-quality flags is explained in Section 4.\nFor\ntemplate-based binary coalescence searches and minimally\nmodeled searches, labeled respectively as CBC and BURST\nin Table 6, the bitmask allows 3 categories of data quality\n(labeled with CAT1, CAT2 and CAT3).\nWe keep this\nstructure even for runs in which not all the categories have\nbeen used.\nThis choice avoids confusion that could arise\nif the same bit would have different meaning in different\nruns. A bit value of 1 indicates the data has passed both the\nindicated level and lower-level checks; for example, a 1 in\nthe CBC_CAT2 bit indicates the data pass both CBC_CAT1\nand CBC_CAT2.\nThe data-quality bit labeled as DATA is obtained requiring\nthat both CBC_CAT1 and BURST_CAT1 are satisfied. This\nis the criterion that defines what data are released in the\ndefault strain-data release.\n6\nSee tutorial 3 of https://github.com/gwosc-tutorial/introduction_gwosc_\ndata to learn how to get data-quality information from GWOSC files.\nIn\nO4a,\ntwo\nadditional\nbits\nhave\nbeen\nadded\nto\naccommodate Category 1 data quality for STOCH searches\n(STOCH_CAT1)\nand\nfor\nCW\nsearches\n(CW_CAT1).\nMoreover, the Categories 2 and 3 have not been used for\nthe CBC data-quality flag so the corresponding segments\ncoincide with those marked as CBC_CAT1 (and also DATA\nin this case). BURST searches in O4a did not apply any\nCategory 3 flags. The CW data-quality flag CW_CAT1 is\nidentical to CBC_CAT1.\nTable 6. Meaning of the bits in the data-quality bitmask of the\nGWOSC files. Each bit has value 1 if the data quality passes the\ncorresponding data quality requirement, otherwise the value is zero.\nBits 7 and 8 were introduced in O4 and are not present in previous\nruns (Abbott et al. 2021a, 2023a).\nBit\nShort name\nDescription\n0\nDATA\nData present\n1\nCBC_CAT1\nPass CAT1 test for CBC search\n2\nCBC_CAT2\nPass CAT1 and CAT2 test\nfor CBC search\n3\nCBC_CAT3\nPass CAT1 and CAT2 and CAT3 test\nfor CBC search\n4\nBURST_CAT1\nPass CAT1 test for BURST search\n5\nBURST_CAT2\nPass CAT1 and CAT2 test\nfor BURST search\n6\nBURST_CAT3\nPass CAT1 and CAT2 and CAT3 test\nfor BURST search\n7\nSTOCH_CAT1\nPass CAT1 test for STOCH search\n8\nCW_CAT1\nPass CAT1 test for CW search\nAs discussed in Section 4, a crucial way to test the response\nof the detector is the use of hardware injections. In GWOSC\nfiles the information about injections is provided as 1 Hz time\nseries containing a bitmask detailed in Table 7.7 Five bits\nare used to distinguish injections relevant for astrophysical\nsearches or detector-characterization studies.\n5.3. Additional Segments in the O4a Strain-Data Release\nThe O4a run started on 24 May 2023 at 15:00 UTC.\nHowever, a few segments of data from the engineering\nrun just prior to the start of the run were used in the\nsearch for GW emitted from SN 2023ixf (Abac et al.\n2025e) and for the neutron star\u2013black hole binary candidate\nGW230518_125908 (Abac et al. 2025b), and they have\nbeen added to this release. These additional data segments\nspan between times 15 May 2023 14:13:22 UTC (GPS\n1368195220) and 19 May 2023 17:31:33 UTC (GPS\n7\nSee tutorials in https://gwosc.org/tutorials/ to learn how to get hardware\ninjections information from GWOSC files.\n\n19\nTable 7.\nMeaning of the bits in the injections bitmask of the\nGWOSC files. The mask indicates when injections are not present,\nso the bit value is set to 1 to indicate no injection and 0 when there\nis an injection. HW_INJ stands for hardware injection.\nBit\nShort name\nDescription\n0\nNO_CBC_HW_INJ\nNo CBC injections\n1\nNO_BURST_HW_INJ\nNo BURST injections\n2\nNO_DETCHAR_HW_INJ\nNo DETCHAR injections\n3\nNO_CW_HW_INJ\nNo CW injections\n4\nNO_STOCH_HW_INJ\nNo STOCH injections\n1368552711) when both LHO and LLO were in observing\nmode. These segments have a total duration of 0.8 days.\nIncluding this addition, the total amount of observing time\nin O4a is 160.8 days for LHO and 164.3 days for LLO\n(to compare with Table 1, 0.8 days have to be added to\nthe coincident times). Using this total amount of time as\nreference, the percentage of the observing time for which the\ndata quality pass each category described in Table 6 in O4a\ncan be calculated. Since these percentages are close to 100%,\nTable 8 summarizes the percentages of failing times.\nTable 8. Percentage of the observing time in O4a, including the\nextra 0.8 days of engineering run data, for which data quality fail\nthe categories described in Table 6.\nShort name\nPercentage in LHO\nPercentage in LLO\nDATA\n0.0971%\n0.0059%\nCBC_CAT1\n0.0971%\n0.0059%\nCBC_CAT2\n0.0971%\n0.0059%\nCBC_CAT3\n0.0971%\n0.0059%\nBURST_CAT1\n0.0971%\n0.0059%\nBURST_CAT2\n0.2242%\n0.1188%\nBURST_CAT3\n0.2242%\n0.1188%\nSTOCH_CAT1\n0.0979%\n0.0065%\nCW_CAT1\n0.0971%\n0.0059%\n5.4. Previous Runs Data Releases\nThe structure described here for the default strain data is\nlargely valid for all data released to date (Abbott et al. 2021a,\n2023a), with few differences. These concern details in the\nnaming conventions of the files and the channels within them.\nFor example, the FrameType mentioned in Section 5.1 is\nIfo_LOSC_s_Vn in O1, the StrainChannel and FrameType\nhave been present in files since O2, while the channel names\nin the gwf files used only in O1 are shown in Table 9.\nThe main difference that the user will notice is that up to\nO3, for each published GW detection, data snippets centered\non the event detection time are also released via the GWOSC\nEvent Portal, described in Section 7. These data snippets are\nprovided as plain-text files in addition to the hdf and gwf\nfiles described above. The text files contain strain values in\na single column. As of O4, data snippets for most events\nare no longer published, but instead the associated files from\nthe default strain-data release are linked for each event in the\nEvent Portal, if available at the time of posting the event.\nTable 9. Channel names in the GWOSC gwf files, used only in O1\nfor the 4 kHz release (Ifo is the interferometer name).\nChannel name\nStrain\nIfo:LOSC-STRAIN\nData-quality mask\nIfo:LOSC-DQMASK\nInjections mask\nIfo:LOSC-INJMASK\n5.5. Alternate Strain Release\nThe default strain files described in Sections 5.1\u20135.4 are\nprepared after each observing run in order to provide a\nuser-friendly file format that includes the preferred strain\nchannel and the final data quality and injection segments.\nFor O3 and O4a, in addition to these user-friendly files, each\ndata release also includes an alternate strain release, which\nincludes several versions of the strain channel and more\nclosely matches the data available to LVK members before\nthe data release.\nDetailed documentation is available on\nthe GWOSC website (LIGO Scientific Collaboration, Virgo\nCollaboration and KAGRA Collaboration 2021a,b, 2025).\nAlternate strain releases from O3 and O4a are available\nfor all times the detectors passed the conditions for\nANALYSIS_READY, meaning that the detectors were\nnominally in a good working state. This set of times includes\na small amount of time that fails CAT1 data quality, and\nso there are some times in the alternate strain releases that\nare not available in the default strain files. Files and strain\nchannels are marked with the tag AR, to indicate that only\nANALYSIS_READY times are included. For O3, this release\nwas prepared after the run had ended, with three channels of\nvarying noise subtraction levels for LIGO, and two channels\nfor Virgo: a main and a short-duration one covering a period\nwhen additional noise subtraction was needed (Abbott et al.\n2023a).\nStarting in O4a, the AR frames are produced during\nthe run.\nA calibration pipeline runs at all times and\nwrites out strain data in one second long frame files in\norder to produce low-latency strain data, including the\npreferred channel GDS-CALIB_STRAIN_CLEAN. Low-\nlatency analyses, include pipelines that produce public\ntransient alerts, use these low-latency frame files.\nTo\nproduce the AR frames, a frame aggregator collects the one\nsecond files into ANALYSIS_READY frame files of up to\n\n20\n4096 seconds long, excludes any times that are not marked\nas ready for analysis, and adds the tag AR to the channel\nnames. The AR frame files are then used for most offline\nLVK analyses, so that the released product exactly matches\ndata used inside the collaboration.\nThe alternate strain releases are not currently available for\ndirect download from the GWOSC website; instead, they\nare available via OSDF and NDS2, as discussed earlier in\nSection 5.\nThe O4a alternate strain release includes four versions\nof the strain channel for each LIGO instrument, which are\nsummarized in Table 10 and described below. In addition\nto the strain channels, the O4a ANALYSIS_READY frames\nalso include a number of auxiliary channels that record data-\nquality information and calibration parameters.\nThe O4a\nstrain channels are (Ifo corresponds to H1 for Hanford or L1\nfor Livingston):\n\u2022 Ifo:GDS-CALIB_STRAIN_AR\nThis\nis\nthe\ncalibrated strain data with no noise subtraction\napplied\nand\ncorresponds\nto\nthe\nchannel\nname\nDCS-CALIB_STRAIN_C01_AR in O3 (Abbott et al.\n2023a).\n\u2022 Ifo:GDS-CALIB_STRAIN_NOLINES_AR This is\nthe calibrated strain data after removing narrowband\nnoise.\nThis\nchannel\nremoves\nthe\ncalibration\nlines,\n60 Hz power-mains line,\nand harmonics\nof the power-mains line as described in Viets\n& Wade (2021).\nIt corresponds to the channel\nname DCS-CALIB_STRAIN_CLEAN_C01_AR in\nO3 (Abbott et al. 2023a).\n\u2022 Ifo:GDS-CALIB_STRAIN_CLEAN_AR\nThis\nis\nthe calibrated strain data,\nafter subtracting both\nnarrowband and broadband noise.\nThis applies\nadditional broadband noise subtraction on to the\nIfo:GDS-CALIB_STRAIN_NOLINES_AR channel,\nusing the method described in Vajente et al. (2020).\nThis is the recommended channel for transient\nsearches, and it corresponds to the channel name\nDCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01_AR\nin O3 (Abbott et al. 2023a).\n\u2022 Ifo:GDS-GATED_STRAIN_AR\nThis\nis\nthe\nIfo:GDS-CALIB_STRAIN_NOLINES_AR channel\nwhere times with loud glitches are replaced with zeros\nby applying a window function around short segments\nof elevated noise (Zweizig & Riles 2020; Usman et al.\n2016). This channel was not used for analyses by the\nLVK.\nDuring\nsome\nintervals\nof\nO4a,\nthe\nbroadband-\nnoise\nsubtraction\nwas\nturned\noff,\nso\nthat\nthe\nchannels\nIfo:GDS-CALIB_STRAIN_NOLINES_AR\nand\nIfo:GDS-CALIB_STRAIN_CLEAN_AR\ncontained\nidentical data. At LHO, broadband noise subtraction was\nturned off from 21 June 2023 16:00 UTC until 11 November\n2023 01:00:00 UTC. At LLO, this period was from 24 May\n2023 15:00:00 UTC until 10 November 2023 23:00:00 UTC.\n6. AUXILIARY CHANNELS\nIn addition to the strain time series, LIGO records\naround 200,000 auxiliary channels for each instrument.\nAuxiliary channels are stored as time series data and record\nthe state of the instrument, the local environment, and a\nnumber of digital-filter settings. Auxiliary channels include\nreadings from seismometers, accelerometers, photodiodes,\nmagnetometers, wind monitors, and microphones (Nguyen\net al. 2021; Huxford et al. 2024).\nThe O3 and O4a data releases include the set of LIGO\nauxiliary channels used for noise subtraction and to produce\ndata-quality flags. These are the ways that auxiliary channels\ndirectly contribute to the GWTC-4.0 analysis. The auxiliary\ndata release consists of about 40 channels for each LIGO\ndetector for each run. The online documentation includes\nthe name of each available channel along with the associated\nsampling rate and a short description of the channel content.8\nAuxiliary channels should be used with caution, as the data\nare not necessarily calibrated and may include times when\nthe data values are missing or corrupt. For example, sensors\nsometimes break or become disconnected leading to periods\nof corrupted data. Auxiliary data are available at all times\nwhen the detector is in ANALYSIS_READY with the exact\ntimes marked in segment lists that are available with the data\nrelease documentation.\nIn addition to channels used for noise subtraction and\ndata-quality flags, some auxiliary data has been released\non request and are now available on the GWOSC website.\nFor O3, these releases include a data set to support a study\nof machine learning applied to detector characterization\n(Gurav et al. 2024), and a study of noise-subtraction methods\n(Zackay et al. 2023).\nAuxiliary-channel data cannot currently be downloaded\ndirectly through the GWOSC website or the API. Instead,\nauxiliary-channel data are available through the NDS2 and\nOSDF interfaces described in Section 5.\n7. EVENT PORTAL\nThe GWOSC Event Portal provides an online interface\nto a database of published GW transient events.9\nThese\nevents are short-duration GW signals identified in the strain\ndata by search analyses. They are typically attributed to a\nsignal consistent with a CBC source. Not all events in the\nEvent Portal will be from CBCs, some may be noise with an\ninstrumental origin.\nUsers of the Event Portal can discover an array of data\nproducts associated with each event, including strain data,\nsegment lists, detection confidence, astrophysical source\nparameters, and documentation. In most cases, the database\n8\nSee https://gwosc.org/O3/auxiliary/ for O3 and https://gwosc.org/O4/\no4a_auxiliary/ for O4a.\n9\nGWOSC Event Portal, https://gwosc.org/eventapi\n\n21\nTable 10. Alternate strain channels in the O4a release and the layers of noise subtraction applied to them. NOLINES means that narrowband\nnoise features have been subtracted, while CLEAN means that broadband noise features have also been subtracted and GATED means the\nremoval of loud glitches.\nChannel name\nNarrowband\nBroadband\nGlitch\nnoise subtraction\nnoise subtraction\nremoval\nIfo:GDS-CALIB_STRAIN_AR\nIfo:GDS-CALIB_STRAIN_NOLINES_AR\n\u2713\nIfo:GDS-CALIB_STRAIN_CLEAN_AR\n\u2713\n\u2713\nIfo:GDS-GATED_STRAIN_AR\n\u2713\n\u2713\nalso includes links to additional analysis products, such as\nposterior samples describing source properties and source\nlocalizations.\nThe Event Portal may be accessed as browsable HTML\nwebpages or via a REST API. A Python client, named\ngwosc, can be used to query the API and download\ncontent.10 Documentation of the Event Portal and REST API\nare available on the GWOSC website.\n7.1. User Interfaces to the Data\nA collection of GW transients in the Event Portal is labeled\na release. A release might be a set of events published in\na single paper, such as the new CBC candidates added for\nGWTC-4.0 (Abac et al. 2025a), or a collection of events that\nare related in some other way, such as all the GW transients\npublished in stand-alone discovery papers such as the O3\nobserving run. As a result there are a number of ways to\ninteract with the data through the Event Portal.\nThe Release List View in the Event Portal displays\na\nlist\nof\nall\navailable\nreleases,\nsummarized\nin\nTable\n11.\nSeveral\nreleases\nare\nlabeled\nmarginal,\ni.e.,\nGWTC-1-marginal,\nGWTC-2.1-marginal,\nGWTC-3-marginal,\nO3_IMBH_marginal,\nwhich\ninclude candidate triggers that have a plausible instrumental\norigin, falling short of the criteria required for the event to be\nlabeled as confident.\nIn addition, there is one release, GWTC-2.1-auxilary,\nin which revised analyses in GWTC-2.1 (Abbott et al. 2024)\nresulted in the demotion of events that were previously\nidentified in GWTC-2 (Abbott et al. 2021c) as statistically\nsignificant. They are included separately for completeness.\nWith the exception of GWTC-4.0, events available in the\nindividual releases are documented in the tables found in\nthe publications that first reported the events. In the case of\nGWTC-4.0 the events found in the Event Portal satisfy\npastro > 0.5 or FAR < 1 yr\u22121\n(3)\nwhere pastro is the probability that a GW candidate is of\nastrophysical origin and FAR is the false alarm rate (the rate\nof noise triggers with a detection statistic at least as high as\nthe candidate).\n10\nGWOSC Client API, https://pypi.org/project/gwosc/\nDetailed documentation and references to publications are\navailable for each release on the GWOSC website.\nBy selecting one of the releases, an Event List table is\ngenerated showing all events in the release, along with\nsource parameters and credible intervals where available.\nThe Event List view includes estimates of a number of\nphysical parameters, such as mass, distance, and spin, as well\nas search-pipeline outputs such as SNR and FAR. If more\nthan one parameter-estimation analysis is available for any\nevent, then values from the analysis marked as Default\nPE for the specific event are displayed in the Event List to\nindicate which of the muliple results are captured in the table.\nAdditionally, the lowest FAR and highest probability of\nastrophysical origin pastro from all available search-analysis\nresults are included in the Event List table.\nA special case of the Event List view is the electronic\nversion of the GWTC, a collection of GW candidates\nidentified by the LVK (Abac et al. 2025a).\nSelecting the\nGWTC option returns this set of events as an Event List.\nIt includes confidently detected events from multiple data\nreleases.\nEvent Lists are also available to browse specific events\nusing customized queries.\nEvent Lists may include more\nthan one version of an event, as some events have appeared\nin multiple publications, or have been re-analysed with\nnewer code or models.\nThe Query Page presents the\nuser with a form that allows selection of events based on\nname, membership in particular releases, various ranges\nof masses, distance, redshift, effective inspiral spin (\u03c7eff),\npastro, SNR, FAR, UTC and GPS times.\nThe query also\nallows specification of the output format to return, with\nsupport for HTML, JSON, CSV and ASCII.\nThe Single Event View shows key parameters for an\nindividual event in the Event Portal. The view can include\nsets of parameters from different pipelines, including search-\npipeline outputs such as SNR and FAR, and inferred source\nproperties such as masses and spins.\nThe Single Event\nView also includes images showing a spectrogram (Chatterji\n2005) of the strain data for each detector at the time of\nthe event, and links to download the associated strain time\nseries in multiple file formats, as described in Section 5.\nThe Single Event View also provides links to documentation,\nlow-latency information in Gravitational-Wave Candidate\n\n22\nTable 11. List of releases currently available under the GWOSC Event Portal.a\nRelease Name\nNotes\nGWTC\nCumulative set of GW transients maintained by the LVK (Abac et al. 2025a)\nInitial_LIGO_Virgo\nEvent release from initial LIGO and Virgo, 2005\u20132010 (Abadie et al. 2012)\nO1_O2-Preliminary\nNotable events in O1 and O2 published prior to GWTC-1 release (Abbott et al. 2019)\nGWTC-1-confident\nConfident detections from the O1 and O2 runs (Abbott et al. 2019)\nGWTC-1-marginal\nMarginal candidates from O1 and O2 runs (Abbott et al. 2019)\nGWTC-2\nConfident detections from the O3a run (Abbott et al. 2021c)\nGWTC-2.1-confident\nConfident detections from O3a run based on a revised analysis (Abbott et al. 2024)\nGWTC-2.1-marginal\nMarginal candidates from O3a run based on a revised analysis (Abbott et al. 2024)\nGWTC-2.1-auxiliary\nCandidates from GWTC-2 that were demoted in GWTC-2.1 (Abbott et al. 2021c)\nGWTC-3-confident\nConfident detection from O3b run (Abbott et al. 2023b)\nGWTC-3-marginal\nMarginal candidates from O3b run (Abbott et al. 2023b)\nIAS-O3a\nEvents from O3a as described in a community catalog (Olsen et al. 2022)\nO3_Discovery_Papers\nNotable events in O3 run published independently (Abbott et al. 2020c,d,e,f, 2021d)\nO3_IMBH_marginal\nMarginal intermediate-mass black hole candidates from O3 run (Abbott et al. 2022b)\nO4_Discovery_Papers\nNotable events in O4 run published independently (Abac et al. 2024; Collaboration et al. 2025)\nGWTC-4.0\nAll events from O4a data product release (Abac et al. 2025b)\na\nGWOSC Event Portal, https://gwosc.org/eventapi/html\nEvent Database (GraceDB),11 General Coordinates Network\n(GCN) Circulars and Notices, and links to segment lists for\ntimes around the event (see Section 5.2 for details). A new\nfeature found on these pages is the Event Viewer which\nleads to a web app that generates plots of waveforms, source\nparameters and sky localization for each GW event.12\n7.2. Parameter-Estimation Results\nMost events in the Event Portal include one or more sets of\ncredible intervals drawn from the publication associated with\nthe event. The naming of parameters is based on the LVK\nstandard names convention.13 Many entries include multiple\nsets of values attributed to different priors, waveforms, or\nanalysis changes (Abac et al. 2025c).\nIn some cases, a\npublication will present credible intervals describing samples\ncombined from several analyses using different waveform\nmodels.\nThe results for any individual parameter are\nexpressed as the median value with its 90% symmetric\ncredible interval.\nDetails regarding how the posterior\nsamples were constructed can be found in the publication\nfrom which the event is released or in the supplemental\nreleases linked from the Single Event View.\n7.3. Supplemental Data Releases\nFor most events, the Single Event View includes links\nto supplemental data.\nThese data vary between releases,\n11\nGraceDB website, https://gracedb.ligo.org/\n12\nGW Event Viewer, https://peviewer.igwn.org\n13\nParameter Estimation Name Standard,\nhttps://lscsoft.docs.ligo.org/\npesummary/stable/gw/parameters.html\nbut in general will include links to the parameter-estimation\nposterior samples,\nsource localization,\nand additional\nresources. Supplemental data releases are published either\nin the LIGO Document Control Center14 or under the LVK\nZenodo Community.15\nIn addition, GWOSC maintains a\nsnapshot of the Event Portal\u2019s version history as a dataset\navailable on Zenodo.16 Each snapshot consists of JSON files\ndownloaded from the Event Portal with data for each event.\n7.4. Community Catalogs\nThe Event Portal has recently been extended to provide\nGW events from catalog authors outside of the LVK, which\nare collectively organized as Community Catalogs.\nThe\npresentation of results for Community Catalogs is identical to\nthat available with any LVK release of events, adhering to the\nwebsite layout and search capabilities discussed previously.\nThis is achieved by standardizing on a JSON schema\nfile format for GWOSC staff to use to ingest search and\nparameter-estimation values. The details for this standard\nJSON are publicly available in GitHub,17 along with useful\ntest scripts, notebooks, and documentation. The criteria for\nauthors outside the LVK to have their catalogs included in\n14\nPublic LIGO Document Control Center, https://dcc.ligo.org/cgi-bin/\nDocDB/DocumentDatabase\n15\nLVK\nZenodo\nData\nReleases,\nhttps://zenodo.org/communities/\nligo-virgo-kagra/\n16\nGWOSC Zenodo Event Portal Snapshots, https://zenodo.org/records/\n10071492\n17\nGWOSC Github Community Catalog Schema,\nhttps://github.com/\ngwosc-tutorial/gwosc-catalog\n\n23\nGWOSC is documented in the GWOSC Community Catalogs\nGuidelines.18\n8. SUMMARY\nData from LIGO recorded during O4a are now publicly\navailable through the GWOSC website at gwosc.org. This\npaper can serve as a practical guide for users interested in\nanalyzing this set of open data. It provides important details\nabout calibration and data quality, explains the structure\nof the datasets available online, and offers instructions for\nusing the Event Portal, which gives access to the list of\nastrophysical sources identified by the LVK.\nMaking these resources available maximizes the scientific\npotential of the dataset. The O4a data contain a wealth of\ncompact object mergers, many of which are listed in version\n4.0 of the Gravitational-Wave Transient Catalog (Abac et al.\n2025b). By releasing the data publicly, the community is\nempowered to further explore and discover new insights.\nThe present release covers only the first part of the O4\nobserving run. The second and third parts are planned for\nrelease in May and December of 2026, respectively (LIGO\nLaboratory 2025).\nWith these forthcoming datasets, we\nanticipate even more opportunities for discovery.\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation.\nThe authors also\ngratefully acknowledge the support of the Science and\nTechnology\nFacilities\nCouncil\n(STFC)\nof\nthe\nUnited\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construction\nof Advanced LIGO and construction and operation of\nthe GEO 600 detector.\nAdditional support for Advanced\nLIGO was provided by the Australian Research Council.\nThe authors gratefully acknowledge the Italian Istituto\nNazionale di Fisica Nucleare (INFN), the French Centre\nNational de la Recherche Scientifique (CNRS) and the\nNetherlands Organization for Scientific Research (NWO)\nfor the construction and operation of the Virgo detector\nand the creation and support of the EGO consortium.\nThe authors also gratefully acknowledge research support\nfrom these agencies as well as by the Council of\nScientific and Industrial Research of India, the Department\nof\nScience\nand\nTechnology,\nIndia,\nthe\nScience\n&\nEngineering Research Board (SERB), India, the Ministry\nof Human Resource Development,\nIndia,\nthe Spanish\nAgencia\nEstatal\nde\nInvestigaci\u00f3n\n(AEI),\nthe\nSpanish\nMinisterio de Ciencia, Innovaci\u00f3n y Universidades, the\nEuropean Union NextGenerationEU/PRTR (PRTR-C17.I1),\nthe ICSC - CentroNazionale di Ricerca in High Performance\nComputing, Big Data and Quantum Computing, funded\nby the European Union NextGenerationEU, the Comunitat\n18\nGWOSC\nCommunity\nCatalogs\nGuidelines,\nhttps://dcc.ligo.org/\nLIGO-M2500012/public\nAuton\u00f2ma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00f3 i Universitats, the Conselleria d\u2019Innovaci\u00f3,\nUniversitats, Ci\u00e8ncia i Societat Digital de la Generalitat\nValenciana and the CERCA Programme Generalitat de\nCatalunya, Spain, the Polish National Agency for Academic\nExchange, the National Science Centre of Poland and the\nEuropean Union - European Regional Development Fund;\nthe Foundation for Polish Science (FNP), the Polish Ministry\nof Science and Higher Education, the Swiss National Science\nFoundation (SNSF), the Russian Science Foundation, the\nEuropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scottish\nUniversities Physics Alliance, the Hungarian Scientific\nResearch Fund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00e9es (ARC) and\nFonds Wetenschappelijk Onderzoek - Vlaanderen (FWO),\nBelgium, the Paris \u00cele-de-France Region, the National\nResearch, Development and Innovation Office of Hungary\n(NKFIH), the National Research Foundation of Korea, the\nNatural Sciences and Engineering Research Council of\nCanada (NSERC), the Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science,\nTechnology,\nand Innovations, the International Center for Theoretical\nPhysics South American Institute for Fundamental Research\n(ICTP-SAIFR), the Research Grants Council of Hong\nKong, the National Natural Science Foundation of China\n(NSFC), the Israel Science Foundation (ISF), the US-Israel\nBinational Science Fund (BSF), the Leverhulme Trust, the\nResearch Corporation, the National Science and Technology\nCouncil (NSTC), Taiwan, the United States Department of\nEnergy, and the Kavli Foundation. The authors gratefully\nacknowledge the support of the NSF, STFC, INFN and\nCNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks,\nJSPS Grants-in-Aid for Scientific\nResearch (S) 17H06133 and 20H05639,\nJSPS Grant-\nin-Aid for Transformative Research Areas (A) 20A203:\nJP20H05854, the joint research program of the Institute for\nCosmic Ray Research, University of Tokyo, the National\nResearch Foundation (NRF), the Computing Infrastructure\nProject of the Global Science experimental Data hub Center\n(GSDC) at KISTI, the Korea Astronomy and Space Science\nInstitute (KASI), the Ministry of Science and ICT (MSIT) in\nKorea, Academia Sinica (AS), the AS Grid Center (ASGC)\nand the National Science and Technology Council (NSTC)\nin Taiwan under grants including the Science Vanguard\nResearch Program, the Advanced Technology Center (ATC)\nof NAOJ, and the Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\n\n24\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to any\nAuthor Accepted Manuscript version arising. We request that\ncitations to this article use \u2019A. G. Abac et al. (LIGO-Virgo-\nKAGRA Collaboration), ...\u2019 or similar phrasing, depending\non journal convention.\nSoftware:\nThis software infrastructure used to publish\ndata products onto the GWOSC website made significant\nuse of the IGWN Software Environment (IGWN Computing\nand Software Working Group 2025) curated by the LVK to\nprovide a reproducible computing environment built around\ntools needed for GW data analysis. Plots were prepared with\nMatplotlib (Hunter 2007).\nDATA AVAILABILITY\nAll data products described in this work are publicly\navailable on the Gravitational Wave Open Science Center,19\nthe Zenodo LVK community page,20 and through the OSDF\nand NDS2 data repositories, as described in the previous\nsections of this paper. Data products are provided under a\nCreative Commons Attribution 4.0 International license.21\nREFERENCES\nAasi, J., et al. 2015, Class. Quant. 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Rep.\nT2000384. https://dcc.ligo.org/LIGO-T2000384/public\nZweizig, Z., Maros, E., Hanks, J., & Areeda, J. 2021.\nhttps://wiki.ligo.org/Computing/NDSClient/\n", "DRAFT VERSION SEPTEMBER 7, 2025\nTypeset using LATEX twocolumn style in AASTeX631\nGWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth\nLIGO-Virgo-KAGRA Observing Run\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n(SEE THE END MATTER FOR THE FULL LIST OF AUTHORS)\n(Compiled: September 7, 2025)\nABSTRACT\nVersion 4.0 of the Gravitational-Wave Transient Catalog (GWTC-4.0) adds new candidates detected by the\nLIGO, Virgo, and KAGRA observatories through the \ufb01rst part of the fourth observing run (O4a: 2023 May 24\n15:00:00 to 2024 January 16 16:00:00 UTC) and a preceding engineering run. In these new data, we \ufb01nd 128\ncompact binary coalescence candidates that are identi\ufb01ed by at least one of our search algorithms with a proba-\nbility of astrophysical origin pastro \u22650.5 and that are not vetoed during event validation. We also provide de-\ntailed source property measurements for 86 of these that have a false alarm rate < 1 yr\u22121. Based on the inferred\ncomponent masses, these candidates are consistent with signals from binary black holes and neutron star\u2013black\nhole binaries (GW230518_125908 and GW230529_181500). Median inferred component masses of binary\nblack holes in the catalog now range from 5.79M\u2299(GW230627_015337) to 137M\u2299(GW231123_135430),\nwhile GW231123_135430 was probably produced by the most massive binary observed in the catalog. For\nthe \ufb01rst time we have discovered binary black hole signals with network signal-to-noise ratio exceeding 30,\nGW230814_230901 and GW231226_101520, enabling high-\ufb01delity studies of the waveforms and astrophys-\nical properties of these systems. Combined with the 90 candidates included in GWTC-3.0, the catalog now\ncontains 218 candidates with pastro \u22650.5 and not otherwise vetoed, more than doubling the size of the catalog\nand further opening our view of the gravitational-wave Universe.\nKeywords: Gravitational wave astronomy (675); Gravitational wave detectors (676); Gravitational wave sources\n(677); Stellar mass black holes (1611); Neutron stars (1108)\n1. INTRODUCTION\nAn increasingly diverse population of gravitational-wave\n(GW) sources in our Universe is now being uncovered\nby the Laser Interferometer Gravitational-Wave Observa-\ntory (LIGO; Aasi et al. 2015) and the Virgo (Acernese et al.\n2015) and KAGRA (Abbott et al. 2020a) observatories. In\nthe past decade, these detectors have seen transient GWs\nfrom binary black holes (BBHs; Abbott et al. 2016a), bi-\nnary neutron stars (BNSs; Abbott et al. 2017a), and neutron\nstar\u2013black hole binaries (NSBHs; Abbott et al. 2021a) with\na signi\ufb01cant impact on physics, astrophysics, and cosmol-\nogy. This work presents the observations and results of ver-\nsion 4.0 of the LIGO\u2013Virgo\u2013KAGRA Collaboration (LVK)\nGravitational-Wave Transient Catalog (GWTC-4.0) and is\npart of a collection of articles which also includes an intro-\nduction (Abac et al. 2025a) and a description of the data-\nCorresponding author: LSC P&P Committee, via LVK Publications as\nproxy\nlvc.publications@ligo.org\nanalysis methods (Abac et al. 2025b); we refer readers to\nthese articles for contextual information on the results pre-\nsented here.\nGWTC-4.0 updates the previous GWTC-3.0 (Abbott et al.\n2023a) by including the results of searches for compact bi-\nnary coalescences (CBCs) in data collected through to the\nend of the \ufb01rst part of the fourth observing run (O4a). This\nperiod consists of data collected by the two-detector net-\nwork of LIGO Hanford Observatory (LHO) and LIGO Liv-\ningston Observatory (LLO) between 2023 May 24 15:00:00\nand 2024 January 16 16:00:00 UTC. In the analysis, we also\ninclude \ufb01ve days\u2019 of data (between 2023 May 15 and 2023\nMay 19) from a pre-O4a engineering run which was con-\nducted between 2023 April 26 and 2023 May 24 UTC (Abac\net al. 2025c). The KAGRA detector joined the beginning of\nO4a, collecting data until 2023 June 20, however we do not\ninclude this data in the analyses presented in this article as\nit is substantially less sensitive than the data from LHO and\nLLO.\nWe identify 1382 candidates with false alarm rate (FAR)\n< 2 d\u22121 in at least one of our four search pipelines. Of\n\n2\nthese candidates, 128 have a probability of astrophysical\nCBC origin of pastro \u22650.5 in at least one of our four search\npipelines and are not vetoed during event validation (Abac\net al. 2025b), bringing the total number of transients in the\ncumulative GWTC ful\ufb01lling these criteria to 218.\nWe analyze in detail the properties of a smaller, higher-\npurity subset of 86 candidates with FAR < 1 yr\u22121 and which\npass our event-validation criteria. The bulk of new candi-\ndates reported here have properties that span a similar range\nof values as those reported in previous GWTC versions (Ab-\nbott et al. 2019a, 2021b, 2024, 2023a); however, a number of\ncandidates exhibit new extremes.\nThe source of GW231123_135430 (Abac et al. 2025d) is\nprobably more massive than that of any of our previously\ndetected BBH candidates, with an inferred total mass M =\n236+29\n\u221248 M\u2299. GWTC-4.0 also includes the highest signal-to-\nnoise ratio (SNR; throughout, we de\ufb01ne the SNR to be the\nmatched-\ufb01lter network SNR) signal detected through to the\nend of O4a, GW230814_230901 (Abac et al. 2025e). With\nan SNR of 42.1, it is signi\ufb01cantly louder than the previous\nrecord-holder, GW170817, which had an SNR of 32.4 (Ab-\nbott et al. 2017a).\nIn addition, the catalog update includes two NSBH\ncandidates: GW230529_181500 (Abac et al. 2024a) and\nGW230518_125908, observed during the pre-O4a engineer-\ning run. All other O4a candidates have inferred component\nmasses above the theoretical upper limit of the neutron star\n(NS) maximum mass (Rhoades & Ruf\ufb01ni 1974; Kalogera &\nBaym 1996), and are thus consistent with BBH systems.\nAs our catalog grows in tandem with the increasing sensi-\ntivity of the GW detector network, we detect a larger number\nof remarkable candidates as well as a larger number of can-\ndidates whose source properties we measure well. Several\nBBH sources reported here have total masses above 100 M\u2299,\nincluding the source of GW231028_153006, which has a\ntotal mass 152+29\n\u221214 M\u2299(here, and throughout this work, we\npresent the median value and uncertainties based on the 90%\ncredible interval).\nThis BBH probably has a large, posi-\ntive effective inspiral spin \u03c7e\ufb00= 0.4+0.2\n\u22120.2, a measure of the\ntotal spin angular momentum aligned with the orbital an-\ngular momentum (see Abac et al. 2025a, for a de\ufb01nition).\nOther BBH sources are notable for having measured masses\nthat rule out equal component masses, for example that of\nGW231114_043211 which has mass ratio q < 0.55 with\n90% probability. We also add a number of candidates with\nsupport for non-negligible spins to GWTC-4.0. One such ex-\nample is GW231118_005626, whose source has asymmetric\nmasses, with a mass-ratio q = 0.55+0.37\n\u22120.22 and a large \u03c7e\ufb00,\nwith a primary spin magnitude \u03c71 = 0.65+0.28\n\u22120.38.\nAs in past observing runs (Abbott et al. 2019b, 2021b,\n2023a), GW candidates identi\ufb01ed by initial analysis of the\ndata were publicly announced to enable searches for mul-\ntimessenger counterparts.\nIn O4a these announcements\nwere in the form of Notices distributed via General Coor-\ndinates Network (GCN; NASA 2025) and SCiMMA Hop-\nskotch (SCiMMA 2025), and through GCN Circulars. There\nwere 1697 candidates assigned a FAR < 2 d\u22121 by at least\none analysis in low latency. Of these candidates, 93 had a\nFAR < 1 per 30 d after applying a trials factor to account for\nthe number of simultaneously observing analyses and were\nreported as signi\ufb01cant detection candidates. No con\ufb01dent\nmultimessenger counterparts have been reported for any O4a\ncandidates. Our of\ufb02ine analyses recover 77 of the candidates\nidenti\ufb01ed as signi\ufb01cant in low-latency searches in our higher-\npurity subset with both pastro \u22650.5 and FAR < 1 yr\u22121. We\nidentify 8 new candidates with pastro \u22650.5 and which were\nnot part of the 1697 candidates identi\ufb01ed in low-latency as\neither signi\ufb01cant or of low signi\ufb01cance; of these only one\nhas FAR < 1 yr\u22121. GWTC-4.0 is the most comprehensive\nset of GW observations to date.\nThe remainder of this article is structured as follows. In\nSection 2, we present the new candidates identi\ufb01ed by search\npipelines and discuss similarities and differences with the set\nidenti\ufb01ed by low-latency analyses. For a high-purity sub-\nset of these candidates, we present measurements of the in-\nferred astrophysical source properties and discuss the impact\nof systematic differences between waveform models in Sec-\ntion 3. Finally, we summarize the results and discuss future\nprospects for GW astronomy in Section 4.\n2. CANDIDATE LIST\nSearch algorithms operate in two different modes: online\n(low latency) and of\ufb02ine. Online searches analyze data in\nnear-real time as they are collected. The rapid identi\ufb01ca-\ntion of candidate astrophysical transients in low latency en-\nables public alerts and facilitates searches for multimessen-\nger counterparts. Of\ufb02ine analyses can be run at a higher la-\ntency using data that have undergone \ufb01nal calibration, and\nbene\ufb01t from noise subtraction (Vajente et al. 2020; Soni\net al. 2025) and the identi\ufb01cation of transient noise artifacts,\nknown as glitches (Nuttall 2018; Glanzer et al. 2023; Soni\net al. 2025), based on detector-monitor channel informa-\ntion (Essick et al. 2020; Huxford et al. 2024). Additionally,\nonline analyses may be subject to occasional data dropout\ndue to network instability or computing outages, while of-\n\ufb02ine analyses have access to the complete dataset. For these\nreasons, of\ufb02ine analyses are more sensitive than their online\ncounterparts, which leads to differences between the \ufb01nal\ncandidate list and the initial online results. The majority of\nlow-FAR online candidates (e.g., with FAR < 1 yr\u22121) are\nexpected to remain signi\ufb01cant in of\ufb02ine analyses, but can-\ndidates that were initially identi\ufb01ed with a higher FAR can\nchange in signi\ufb01cance when later re-evaluated.\nIn this paper, we describe the of\ufb02ine search results in\nO4a data from four search pipelines:\nCWB-BBH (Kli-\nmenko et al. 2005, 2008, 2016; Mishra et al. 2025), GST-\nLAL (Messick et al. 2017; Sachdev et al. 2019; Tsukada\net al. 2023; Sakon et al. 2024; Joshi et al. 2025), MBTA (Al-\nl\u00e9n\u00e9 et al. 2025), and PYCBC (Allen et al. 2012; Dal Canton\net al. 2014; Usman et al. 2016; Nitz et al. 2017). Each of\nthese analyses also searched for GW transients in low la-\ntency (Cannon et al. 2012; Adams et al. 2016; Nitz et al.\n2018), as did the SPIIR analysis (Chu et al. 2022); the on-\nline candidates are discussed more in Section 2.1.1.\nThe\n\n3\nCWB-BBH analysis is a minimally modeled search that co-\nherently analyzes the data from the network to identify tran-\nsient signals, while GSTLAL, MBTA, PYCBC, and SPIIR\nuse matched \ufb01ltering to correlate the data with CBC wave-\nform templates. Additional differences are detailed in Abac\net al. (2025b).\n2.1. Search results\nWhile there are many potential sources of transient GWs,\nonly CBCs have been con\ufb01dently identi\ufb01ed (Abbott et al.\n2017b, 2019c, 2021c; Abac et al. 2025f) to-date. We there-\nfore limit the GWTC-4.0 candidate list to potential BBHs,\nNSBHs, and BNSs. In GWTC-3.0 (Abbott et al. 2023a),\ncandidates found by at least one pipeline with a probabil-\nity of astrophysical origin pastro \u22650.5 were selected for\ndetailed analysis. Here, we additionally impose a threshold\non the FAR of a given candidate, which is a measure of its\ndetection signi\ufb01cance de\ufb01ned by the estimated rate of non-\nastrophysical (noise) events found by a pipeline with a rank\nat least as high as the candidate. Both pastro and FAR depend\non the speci\ufb01c noise background seen by each pipeline, and\nalso incorporate assumptions on the (absolute or relative) as-\ntrophysical rates of signals for different binary sources. The\npastro calculation also depends on the sensitivity of the analy-\nses to CBC signals, which varies across the source parameter\nspace as seen in Figure 1. This, coupled with methodologi-\ncal differences in estimating the noise background, can lead\nto signi\ufb01cant differences in estimated FAR and pastro across\npipelines. Such differences are more pronounced for candi-\ndates of marginal signi\ufb01cance, as well as those with inferred\nproperties (under the assumption of astrophysical origin) ly-\ning outside the range of previously observed sources.\nGiven such systematic variability over pipelines, we sort\ncandidates into three disjoint sets.\nFirst, candidates with\nboth FAR < 1 yr\u22121 and pastro \u22650.5 in one or more\npipelines. Second, candidates with pastro \u22650.5 in one or\nmore pipelines but FAR \u22651 yr\u22121 in all pipelines. Third,\nsubthreshold candidates with pastro < 0.5 in all pipelines.\nThere are no candidates with FAR < 1 yr\u22121 for which pastro\n< 0.5 in all pipelines.\nAll candidates identi\ufb01ed in GW data by the search\npipelines are named with a GW pre\ufb01x (see also Abac et al.\n2025a). Those GW candidates found in O4a with a FAR\n< 1 yr\u22121 in at least one analysis, and for which pastro > 0.5,\ncan be found in Table 1 alongside their FAR, SNR, and pastro.\nTheir individual detector SNRs are reported in Table 6 of Ap-\npendix A. We carry out event validation for this high-purity\nsubset of candidates (Abac et al. 2025b), and for those that\npass validation we estimate their source properties, which we\nreport in Section 3. In addition, we list all other candidates\nassigned pastro \u22650.5 by at least one pipeline in Table 2,\nand discuss the remaining subthreshold candidates in Sec-\ntion 2.1.4 below.\n2.1.1. Online candidates\nIn O4a, \ufb01ve pipelines conducted online searches for CBCs:\nCWB-BBH (Mishra et al. 2022), GSTLAL (Ewing et al.\n2024), MBTA (All\u00e9n\u00e9 et al. 2025), PYCBC (Dal Canton\net al. 2021), and SPIIR (Chu et al. 2022). These searches\ndistributed Notices via GCN (NASA 2025) and SCiMMA\nHopskotch (SCiMMA 2025) for 1697 GW candidates with\nFAR < 2 d\u22121. Of these, 93 passed a stricter threshold of\nFAR < 1 per 30 d after applying a trials factor to account\nfor the number of simultaneous searches (LIGO Scienti\ufb01c\nCollaboration et al. 2025); these candidates were reported\nas high-signi\ufb01cance candidates. The high-signi\ufb01cance can-\ndidates underwent human vetting (LIGO Scienti\ufb01c Collab-\noration et al. 2025), and additional information was dis-\nseminated via GCN Circulars. These alerts facilitated rapid\nsearches for potential electromagnetic counterparts to tran-\nsient GWs.\nThe online searches run in near-real time and are only able\nto use data collected up to the current time. Data quality\ncan vary suddenly and noise transients in the detectors can\nbe mistakenly identi\ufb01ed as astrophysical in origin. Of the\n93 high-signi\ufb01cance candidates identi\ufb01ed in low latency, 11\nwere later retracted. Of these 11 retractions, 4 were due to\ntriggers from early-warning search pipelines (Sachdev et al.\n2020; All\u00e9n\u00e9 et al. 2025; Nitz et al. 2020a; Kovalam et al.\n2022) which did not have corresponding triggers in the full-\nbandwidth analyses. The other 7 retracted candidates were\nall found to be signi\ufb01cant by only one analysis. None of the\n11 retracted online candidates were recovered with a FAR\n< 2 d\u22121 in the of\ufb02ine analyses.\nTable 1. Candidate GW signals from O4a with a FAR \u22641 yr\u22121 in at least one analysis and for which pastro > 0.5.\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW230518_125908\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n13.7\n> 0.99\n< 1.0 \u00d7 10\u22125\n14.1\n> 0.99\n7.1 \u00d7 10\u22124\n13.6\n> 0.99\nTable 1 continued\n\n4\nTable 1 (continued)\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW230529_181500\nL\n\u2013\n\u2013\n\u2013\n0.0058\n11.8\n0.85\n2.2 \u00d7 10\u22124\n11.4\n> 0.99\n1.0 \u00d7 10\u22123\n11.7\n> 0.99\nGW230601_224134\nHL\n0.0013\n13.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.8\n> 0.99\n0.0082\n12.4\n> 0.99\n0.0010\n12.2\n> 0.99\nGW230605_065343\nHL\n560\n7.5\n< 0.01\n2.4 \u00d7 10\u22125\n10.7\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.1\n> 0.99\n1.3 \u00d7 10\u22125\n11.4\n> 0.99\nGW230606_004305\nHL\n0.0067\n11.1\n> 0.99\n0.0013\n10.9\n> 0.99\n1.9\n10.9\n0.83\n4.1 \u00d7 10\u22124\n10.7\n> 0.99\nGW230608_205047\nHL\n0.032\n9.9\n> 0.99\n0.0012\n10.2\n> 0.99\n0.27\n10.2\n0.96\n\u2013\n\u2013\n\u2013\nGW230609_064958\nHL\n0.0013\n10.6\n> 0.99\n1.4 \u00d7 10\u22124\n10.0\n> 0.99\n3.6\n10.5\n0.73\n0.0011\n9.6\n> 0.99\nGW230624_113103\nHL\n0.0022\n11.4\n> 0.99\n1.8 \u00d7 10\u22124\n10.0\n> 0.99\n0.018\n10.3\n> 0.99\n0.017\n10.2\n> 0.99\nGW230627_015337\nHL\n0.0011\n27.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n28.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n28.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n28.7\n> 0.99\nGW230628_231200\nHL\n0.0011\n16.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n15.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n15.9\n> 0.99\n< 1.0 \u00d7 10\u22125\n15.9\n> 0.99\nGW230630_070659\u2217HL\n\u2013\n\u2013\n\u2013\n0.47\n9.8\n0.88\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW230630_125806\nHL\n0.16\n9.0\n0.97\n0.25\n8.1\n0.93\n1.3\n8.2\n0.87\n0.48\n8.1\n> 0.99\nGW230630_234532\nHL\n\u2013\n\u2013\n\u2013\n0.028\n9.8\n0.99\n4.2 \u00d7 10\u22124\n9.9\n> 0.99\n0.25\n9.8\n> 0.99\nGW230702_185453\nHL\n0.0089\n10.1\n> 0.99\n< 1.0 \u00d7 10\u22125\n9.8\n> 0.99\n0.21\n9.9\n0.97\n0.031\n9.2\n> 0.99\nGW230704_021211\nHL\n\u2013\n\u2013\n\u2013\n0.21\n9.4\n0.94\n2.7\n9.2\n0.78\n0.38\n9.2\n> 0.99\nGW230704_212616\nHL\n43\n8.3\n0.14\n11\n8.3\n0.30\n0.51\n8.7\n0.93\n\u2013\n\u2013\n\u2013\nGW230706_104333\nHL\n\u2013\n\u2013\n\u2013\n0.23\n9.2\n0.94\n\u2013\n\u2013\n\u2013\n1.5\n8.8\n0.98\nGW230707_124047\nHL\n0.0011\n11.9\n> 0.99\n0.0026\n10.1\n> 0.99\n0.072\n10.3\n0.99\n0.0055\n10.5\n> 0.99\nGW230708_053705\nHL\n\u2013\n\u2013\n\u2013\n2.5\n8.6\n0.63\n54\n8.9\n0.15\n0.22\n8.9\n> 0.99\nGW230708_230935\nHL\n1.2\n10.0\n0.80\n0.0037\n9.6\n> 0.99\n0.26\n9.7\n0.96\n0.012\n9.4\n> 0.99\nGW230709_122727\nHL\n0.071\n10.2\n> 0.99\n0.16\n9.9\n0.95\n12\n10.1\n0.48\n0.011\n10.0\n> 0.99\nGW230712_090405\nHL\n0.018\n9.5\n> 0.99\n99\n8.2\n0.05\n\u2013\n\u2013\n\u2013\n260\n8.2\n0.19\nGW230723_101834\nHL\n\u2013\n\u2013\n\u2013\n0.0053\n9.9\n> 0.99\n0.0034\n10.0\n> 0.99\n0.0038\n10.1\n> 0.99\nGW230726_002940\nL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n10.5\n> 0.99\n\u2013\n\u2013\n\u2013\n4.5\n10.0\n0.58\nGW230729_082317\nHL\n\u2013\n\u2013\n\u2013\n0.18\n9.5\n0.95\n\u2013\n\u2013\n\u2013\n31\n9.4\n0.77\nGW230731_215307\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n12.2\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.9\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.9\n> 0.99\nGW230803_033412\nHL\n3.0\n9.4\n0.68\n3.0\n8.0\n0.59\n19\n8.6\n0.35\n0.31\n8.2\n> 0.99\nGW230805_034249\nHL\n7.5\n9.5\n0.49\n0.0065\n9.3\n> 0.99\n6.4\n9.4\n0.62\n0.0037\n9.4\n> 0.99\nGW230806_204041\nHL\n0.0065\n9.4\n> 0.99\n0.0037\n9.1\n> 0.99\n0.20\n9.4\n0.97\n0.035\n9.1\n> 0.99\nGW230811_032116\nHL\n0.0013\n13.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.9\n> 0.99\n8.6 \u00d7 10\u22125\n13.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.4\n> 0.99\nGW230814_061920\nHL\n0.0039\n11.2\n> 0.99\n6.3 \u00d7 10\u22124\n10.2\n> 0.99\n0.041\n10.0\n> 0.99\n0.0081\n9.6\n> 0.99\nGW230814_230901\nL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n42.3\n> 0.99\n\u2013\n\u2013\n\u2013\n1.0 \u00d7 10\u22123\n43.0\n> 0.99\nGW230819_171910\nHL\n0.011\n9.9\n> 0.99\n0.013\n9.0\n> 0.99\n\u2013\n\u2013\n\u2013\n11\n8.9\n0.81\nGW230820_212515\nHL\n68\n7.9\n0.10\n0.24\n9.1\n0.93\n0.30\n9.3\n0.96\n0.96\n9.0\n0.97\nGW230824_033047\nHL\n0.0035\n11.1\n> 0.99\n< 1.0 \u00d7 10\u22125\n10.5\n> 0.99\n0.017\n10.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n10.7\n> 0.99\nGW230825_041334\nHL\n1.3\n8.8\n0.83\n0.10\n8.7\n0.97\n1.8\n8.5\n0.84\n0.83\n8.7\n0.98\nTable 1 continued\n\n5\nTable 1 (continued)\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW230831_015414\nHL\n27\n7.8\n0.20\n0.63\n8.6\n0.86\n1.4\n8.6\n0.87\n0.29\n8.5\n> 0.99\nGW230904_051013\nHL\n\u2013\n\u2013\n\u2013\n3.9 \u00d7 10\u22125\n10.5\n> 0.99\n4.3 \u00d7 10\u22125\n10.4\n> 0.99\n0.0042\n10.2\n> 0.99\nGW230911_195324\nH\n\u2013\n\u2013\n\u2013\n0.014\n10.7\n> 0.99\n\u2013\n\u2013\n\u2013\n1.0 \u00d7 10\u22123\n11.1\n> 0.99\nGW230914_111401\nHL\n0.0012\n17.2\n> 0.99\n< 1.0 \u00d7 10\u22125\n15.9\n> 0.99\n< 1.0 \u00d7 10\u22125\n16.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n16.0\n> 0.99\nGW230919_215712\nHL\n0.0012\n16.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n16.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n16.1\n> 0.99\n< 1.0 \u00d7 10\u22125\n16.5\n> 0.99\nGW230920_071124\nHL\n0.0012\n11.1\n> 0.99\n< 1.0 \u00d7 10\u22125\n10.1\n> 0.99\n0.11\n10.2\n0.98\n3.4 \u00d7 10\u22124\n9.6\n> 0.99\nGW230922_020344\nHL\n0.013\n13.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.3\n> 0.99\n4.1 \u00d7 10\u22125\n12.2\n> 0.99\n3.6 \u00d7 10\u22124\n11.9\n> 0.99\nGW230922_040658\nHL\n0.0012\n12.5\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.6\n> 0.99\n3.0 \u00d7 10\u22124\n11.6\n> 0.99\n6.3 \u00d7 10\u22124\n11.6\n> 0.99\nGW230924_124453\nHL\n0.0012\n13.5\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.0\n> 0.99\nGW230927_043729\nHL\n0.0012\n12.1\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.3\n> 0.99\n8.6 \u00d7 10\u22124\n11.1\n> 0.99\n1.1 \u00d7 10\u22124\n11.1\n> 0.99\nGW230927_153832\nHL\n0.0012\n20.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n19.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n20.2\n> 0.99\n< 1.0 \u00d7 10\u22125\n19.6\n> 0.99\nGW230928_215827\nHL\n0.0035\n10.5\n> 0.99\n1.5 \u00d7 10\u22125\n9.5\n> 0.99\n1.3\n9.3\n0.88\n0.0092\n9.5\n> 0.99\nGW230930_110730\nHL\n5.4\n9.0\n0.58\n0.17\n8.5\n0.95\n1.1\n8.6\n0.89\n0.73\n8.3\n> 0.99\nGW231001_140220\nHL\n0.0012\n11.5\n> 0.99\n1.6 \u00d7 10\u22125\n10.3\n> 0.99\n1.8 \u00d7 10\u22124\n10.6\n> 0.99\n0.0031\n9.9\n> 0.99\nGW231004_232346\nHL\n0.16\n8.9\n0.97\n6.5\n7.9\n0.41\n\u2013\n\u2013\n\u2013\n420\n7.0\n0.01\nGW231005_021030\nHL\n0.010\n10.4\n> 0.99\n0.17\n9.3\n0.95\n0.019\n9.7\n> 0.99\n0.21\n9.8\n> 0.99\nGW231005_091549\nHL\n54\n11.0\n0.13\n0.040\n8.9\n0.99\n2.6\n8.6\n0.79\n3.6\n8.5\n0.97\nGW231008_142521\nHL\n\u2013\n\u2013\n\u2013\n0.0016\n9.3\n> 0.99\n1.6\n9.1\n0.86\n0.17\n8.7\n> 0.99\nGW231014_040532\nHL\n29\n8.6\n0.23\n0.21\n9.0\n0.94\n1.2\n8.8\n0.88\n3.2\n8.7\n0.96\nGW231018_233037\nHL\n\u2013\n\u2013\n\u2013\n130\n8.7\n0.04\n0.68\n9.1\n0.93\n170\n8.6\n0.29\nGW231020_142947\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n11.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.0\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.8\n> 0.99\nGW231028_153006\nHL\n0.0012\n22.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n21.0\n> 0.99\n< 1.0 \u00d7 10\u22125\n21.9\n> 0.99\n< 1.0 \u00d7 10\u22125\n21.9\n> 0.99\nGW231029_111508\nL\n\u2013\n\u2013\n\u2013\n5.2 \u00d7 10\u22125\n10.8\n> 0.99\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW231102_071736\nHL\n0.0012\n15.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n14.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.4\n> 0.99\nGW231104_133418\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n11.3\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.8\n> 0.99\nGW231108_125142\nHL\n2.1 \u00d7 10\u22124\n12.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.6\n> 0.99\n7.5 \u00d7 10\u22125\n12.5\n> 0.99\n< 1.0 \u00d7 10\u22125\n12.3\n> 0.99\nGW231110_040320\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n11.4\n> 0.99\n8.7 \u00d7 10\u22124\n11.5\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.1\n> 0.99\nGW231113_122623\nHL\n\u2013\n\u2013\n\u2013\n0.75\n8.3\n0.83\n38\n8.6\n0.16\n0.28\n8.6\n> 0.99\nGW231113_200417\nHL\n\u2013\n\u2013\n\u2013\n8.0 \u00d7 10\u22124\n10.3\n> 0.99\n3.8 \u00d7 10\u22125\n10.1\n> 0.99\n3.7 \u00d7 10\u22124\n10.5\n> 0.99\nGW231114_043211\nHL\n\u2013\n\u2013\n\u2013\n1.3 \u00d7 10\u22124\n10.0\n> 0.99\n2.0 \u00d7 10\u22124\n9.9\n> 0.99\n0.0059\n9.6\n> 0.99\nGW231118_005626\nHL\n\u2013\n\u2013\n\u2013\n1.2 \u00d7 10\u22125\n10.4\n> 0.99\n< 1.0 \u00d7 10\u22125\n10.7\n> 0.99\n8.4 \u00d7 10\u22125\n10.5\n> 0.99\nGW231118_071402\nHL\n0.078\n9.2\n> 0.99\n0.0047\n9.2\n> 0.99\n0.50\n9.2\n0.93\n0.0028\n9.2\n> 0.99\nGW231118_090602\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n10.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.0\n> 0.99\n7.1 \u00d7 10\u22125\n10.8\n> 0.99\nGW231119_075248\nHL\n22\n7.9\n0.30\n0.51\n8.1\n0.88\n1.9\n8.0\n0.83\n0.019\n8.3\n> 0.99\nGW231123_135430\nHL\n1.0 \u00d7 10\u22124\n21.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n20.1\n> 0.99\n0.016\n19.0\n> 0.99\n0.0063\n19.9\n> 0.99\nTable 1 continued\n\n6\nTable 1 (continued)\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW231127_165300\nHL\n0.010\n9.9\n> 0.99\n0.032\n9.8\n0.99\n0.24\n9.5\n0.96\n0.73\n9.6\n0.98\nGW231129_081745\nHL\n0.056\n9.4\n> 0.99\n0.23\n8.5\n0.93\n2.3\n8.4\n0.80\n1.1\n8.5\n0.97\nGW231206_233134\nHL\n0.0012\n12.8\n> 0.99\n< 1.0 \u00d7 10\u22125\n11.9\n> 0.99\n0.074\n11.7\n0.98\n1.6 \u00d7 10\u22125\n11.5\n> 0.99\nGW231206_233901\nHL\n0.0012\n21.9\n> 0.99\n< 1.0 \u00d7 10\u22125\n20.7\n> 0.99\n< 1.0 \u00d7 10\u22125\n21.4\n> 0.99\n1.6 \u00d7 10\u22125\n21.0\n> 0.99\nGW231213_111417\nHL\n0.0046\n10.0\n> 0.99\n< 1.0 \u00d7 10\u22125\n10.2\n> 0.99\n0.029\n10.4\n> 0.99\n7.7 \u00d7 10\u22125\n10.1\n> 0.99\nGW231221_135041\nHL\n0.54\n10.0\n0.96\n8.7\n8.4\n0.34\n520\n8.1\n< 0.01\n240\n8.3\n0.11\nGW231223_032836\nHL\n0.0046\n10.2\n> 0.99\n3.8 \u00d7 10\u22124\n9.4\n> 0.99\n13\n9.1\n0.42\n0.0015\n9.0\n> 0.99\nGW231223_075055\nHL\n\u2013\n\u2013\n\u2013\n9.7\n9.3\n0.32\n1.6\n9.4\n0.85\n0.55\n9.4\n0.98\nGW231223_202619\nH\n\u2013\n\u2013\n\u2013\n7.1\n10.0\n0.39\n\u2013\n\u2013\n\u2013\n0.0020\n10.0\n> 0.99\nGW231224_024321\nHL\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n13.0\n> 0.99\n< 1.0 \u00d7 10\u22125\n14.0\n> 0.99\n< 1.0 \u00d7 10\u22125\n13.3\n> 0.99\nGW231226_101520\nHL\n0.0012\n34.7\n> 0.99\n< 1.0 \u00d7 10\u22125\n34.2\n> 0.99\n< 1.0 \u00d7 10\u22125\n33.6\n> 0.99\n< 1.0 \u00d7 10\u22125\n33.2\n> 0.99\nGW231230_170116\nHL\n0.42\n8.2\n0.96\n70\n8.0\n0.07\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW231231_154016\nH\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n13.4\n> 0.99\n\u2013\n\u2013\n\u2013\n1.0 \u00d7 10\u22123\n13.4\n> 0.99\nGW240104_164932\nH\n\u2013\n\u2013\n\u2013\n< 1.0 \u00d7 10\u22125\n14.8\n> 0.99\n\u2013\n\u2013\n\u2013\n0.042\n12.2\n0.99\nGW240107_013215\nHL\n0.37\n9.4\n0.95\n0.24\n9.1\n0.93\n0.24\n9.6\n0.96\n0.028\n9.1\n> 0.99\nGW240109_050431\nH\n\u2013\n\u2013\n\u2013\n2.3 \u00d7 10\u22124\n10.4\n> 0.99\n\u2013\n\u2013\n\u2013\n1.0 \u00d7 10\u22123\n10.0\n> 0.99\nNOTE\u2014 The date and time of each candidate is encoded in the name as GWYYMMDD_hhmmss. The names of candidates not previously\nreported are given in bold. The detectors that were observing at the time of each transient are denoted by a single-letter (e.g., H for LIGO\nHanford). This does not necessarily indicate that the same detectors contributed triggers for a given candidate. We include results from\nanalyses that observe a candidate with FAR > 1 yr\u22121 in italics. A dash (\u2013) indicates that a candidate was not found by an analysis. There\nis evidence that the candidate labeled with an asterisk (*) is of instrumental origin. FARs have been capped at 1 \u00d7 10\u22125 yr\u22121 to maintain a\nconsistent limiting FAR across pipelines.\nThere were 5 candidates identi\ufb01ed as signi\ufb01cant low-\nlatency candidates that were not retracted but are also not\nrecovered with a FAR < 1 yr\u22121 in the of\ufb02ine analyses:\n\u2022 S230708z, S230807f, and S230822bm were all found\nin low latency by GSTLAL in both LHO and LLO.\nAll of these candidates were found with a SNR <\n10.\nThese BBH candidates were all identi\ufb01ed of-\n\ufb02ine by multiple pipelines with a FAR > 1 yr\u22121.\nThey each have pastro \u22650.5 and are reported in\nTable 2 as GW230708_071859, GW230807_205045,\nand GW230822_230337.\n\u2022 S230802aq was a single-detector BBH candidate in\nLHO found by GSTLAL with SNR <\n10.\nNo\npipelines recover an of\ufb02ine trigger at this time with a\nFAR < 2 d\u22121.\n\u2022 S231020bw was identi\ufb01ed by GSTLAL while both\nLHO and LLO were observing, but with disparate SNR\nin each detector. No pipelines recover an of\ufb02ine trigger\nat this time with a FAR < 2 d\u22121.\n2.1.2. New O4a candidates\nThere are 8 candidates identi\ufb01ed with pastro \u22650.5 by at\nleast one of\ufb02ine analysis that were not identi\ufb01ed in low la-\ntency and not previously shared via GCN or SCiMMA Hop-\nskotch Notices or GCN Circulars. These new candidates are\nindicated in bold in Tables 1 and 2.\nThe 8 new candidates were all identi\ufb01ed by a single\npipeline.\nThe majority are of low signi\ufb01cance (FAR >\n1 yr\u22121) and are listed in Table 2. All of the new candidates\nhave moderate network SNRs (\u227210), with the exception\nof GW240105_151143 which has an SNR > 25. However,\nthere are multiple regions of signi\ufb01cant excess power incon-\nsistent with a CBC signal in the time\u2013frequency spectrogram\nof GW240105_151143, as shown in Appendix C, which may\n\n7\ncontribute to its identi\ufb01cation by only one pipeline despite its\nlarge SNR. Of the 8 new candidates, 6 are coincident triggers\ninvolving both LHO and LLO. Only GW230531_141100\nand GW240105_151143 are observed using data from a sin-\ngle detector.\nGW230630_070659 is the only new candidate found with\nFAR < 1 yr\u22121. However, of\ufb02ine followup (Soni et al. 2025)\nof the data quality for this event indicated evidence of in-\nstrumental origin. Speci\ufb01cally, excess power in strain data\nin both detectors was found to be inconsistent with a CBC\nsignal. This conclusion was based on both calculating the\nresidual power in the strain data (Vazsonyi & Davis 2023)\nand machine-learning-based image classi\ufb01cation (Alvarez-\nLopez et al. 2024). A spectrogram for this event is shown in\nAppendix C. In contrast to GWTC-3.0 Abbott et al. (2023a),\nhere we do not remove the GW pre\ufb01x for candidates where\nthere is evidence of terrestrial or instrumental noise origin,\nwe instead assign the pre\ufb01x to all candidates identi\ufb01ed by a\nsearch pipeline. We thus report GW230630_070659 with the\nother candidates with FAR < 1 yr\u22121, and pastro \u22650.5 (Ta-\nble 1) according to the search pipelines. We do not estimate\nsource properties for GW230630_070659.\nTable 2. Candidate GW signals from O4a with pastro \u22650.5 in at least one analysis and a FAR > 1 yr\u22121.\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR pastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW230531_141100\nL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n3.5\n8.0\n0.69\nGW230603_174756\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n210\n8.0\n0.03\n8.4\n7.9\n0.73\nGW230606_024545\nHL\n\u2013\n\u2013\n\u2013\n450\n7.4\n< 0.01\n\u2013\n\u2013\n\u2013\n3.2\n7.5\n0.88\nGW230609_010824\nHL\n46\n8.0\n0.16\n2.8\n7.9\n0.60\n16\n7.9\n0.40\n14\n7.7\n0.81\nGW230615_160825\nHL\n320\n8.9\n0.02\n4.3\n8.3\n0.50\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW230618_102550\nHL\n\u2013\n\u2013\n\u2013\n190\n7.8\n0.03\n\u2013\n\u2013\n\u2013\n49\n7.6\n0.59\nGW230624_214944\nH\n\u2013\n\u2013\n\u2013\n570\n10.1\n< 0.01\n\u2013\n\u2013\n\u2013\n2.2\n10.6\n0.69\nGW230625_211655\nHL\n\u2013\n\u2013\n\u2013\n42\n7.9\n0.11\n280\n8.1\n0.02\n50\n7.9\n0.61\nGW230702_162025\nHL\n\u2013\n\u2013\n\u2013\n640\n8.5\n< 0.01\n6.5\n9.2\n0.60\n\u2013\n\u2013\n\u2013\nGW230708_071859\nHL\n5.3\n9.1\n0.54\n1.5\n8.1\n0.73\n74\n7.8\n0.10\n470\n7.0\n0.11\nGW230709_063445\nHL\n310\n7.9\n0.02\n40\n7.3\n0.11\n91\n7.3\n0.08\n15\n7.5\n0.83\nGW230717_102139\nHL\n\u2013\n\u2013\n\u2013\n130\n7.8\n0.04\n67\n8.2\n0.12\n29\n8.3\n0.70\nGW230721_222634\nHL\n290\n7.9\n0.02\n\u2013\n\u2013\n\u2013\n4.1\n7.6\n0.73\n\u2013\n\u2013\n\u2013\nGW230723_084820\nHL\n3.9\n8.4\n0.65\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n210\n6.9\n0.01\nGW230728_083628\nHL\n\u2013\n\u2013\n\u2013\n1.5\n13.1\n0.73\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW230807_205045\nHL\n30\n7.9\n0.20\n2.9\n8.1\n0.59\n\u2013\n\u2013\n\u2013\n1.8 \u00d7 10 3\n8.7\n< 0.01\nGW230817_212349\nHL\n\u2013\n\u2013\n\u2013\n130\n7.6\n0.04\n590\n7.4\n< 0.01\n6.2\n7.8\n0.86\nGW230822_230337\nHL\n95\n8.3\n0.07\n1.5\n8.2\n0.72\n85\n7.5\n0.08\n6.1\n8.0\n0.86\nGW230823_142524\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n1.6\n8.8\n0.86\n400\n8.6\n0.10\nGW230824_135331\nHL\n6.2\n9.7\n0.58\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW230830_064744\nHL\n\u2013\n\u2013\n\u2013\n3.5\n8.5\n0.55\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW230831_134621\nHL\n\u2013\n\u2013\n\u2013\n42\n8.8\n0.11\n20\n8.8\n0.34\n12\n8.5\n0.80\nGW230902_122814\nHL\n220\n8.1\n0.03\n\u2013\n\u2013\n\u2013\n2.0\n8.1\n0.84\n\u2013\n\u2013\n\u2013\nGW230902_172430\nHL\n\u2013\n\u2013\n\u2013\n280\n8.4\n0.02\n98\n8.4\n0.07\n39\n8.5\n0.59\nGW230902_224555\nHL\n\u2013\n\u2013\n\u2013\n82\n7.4\n0.06\n\u2013\n\u2013\n\u2013\n51\n7.5\n0.52\nGW230904_152545\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n37\n9.2\n0.19\n18\n9.0\n0.74\nTable 2 continued\n\n8\nTable 2 (continued)\nCandidate\nInst.\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\nFAR\nSNR pastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\nFAR\nSNR\npastro\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\n(yr\u22121)\nGW230920_064709\nHL\n\u2013\n\u2013\n\u2013\n490\n9.5\n< 0.01\n200\n9.2\n0.03\n4.8\n9.2\n0.81\nGW230925_143957\nHL\n35\n8.0\n0.20\n\u2013\n\u2013\n\u2013\n8.2\n7.4\n0.55\n\u2013\n\u2013\n\u2013\nGW231002_143916\nHL\n\u2013\n\u2013\n\u2013\n78\n8.8\n0.06\n1.0\n9.4\n0.90\n\u2013\n\u2013\n\u2013\nGW231005_144455\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n60\n7.3\n0.55\nGW231013_135504\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n64\n8.4\n0.54\nGW231026_130704\nHL\n\u2013\n\u2013\n\u2013\n1.7\n8.1\n0.70\n340\n8.3\n0.02\n1.8\n8.1\n0.93\nGW231102_052214\nHL\n75\n7.7\n0.11\n\u2013\n\u2013\n\u2013\n4.0\n7.9\n0.72\n\u2013\n\u2013\n\u2013\nGW231102_232433\nHL\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n2.5\n7.6\n0.80\n\u2013\n\u2013\n\u2013\nGW231113_150041\nHL\n2.4\n8.7\n0.81\n4.7\n7.9\n0.48\n130\n8.0\n0.04\n1.8\n7.9\n0.96\nGW231120_022103\nHL\n\u2013\n\u2013\n\u2013\n3.8\n9.6\n0.53\n12\n10.0\n0.45\n5.4\n9.6\n0.90\nGW231126_010928\nHL\n4.6\n9.1\n0.67\n8.7\n8.5\n0.34\n4.2\n8.4\n0.71\n6.2\n8.6\n0.86\nGW231204_090648\nHL\n\u2013\n\u2013\n\u2013\n3.6\n8.4\n0.54\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\nGW231206_010629\nHL\n17\n9.7\n0.46\n59\n7.9\n0.08\n6.9\n8.2\n0.58\n65\n7.6\n0.30\nGW231220_173406\nHL\n68\n7.9\n0.16\n35\n7.6\n0.13\n\u2013\n\u2013\n\u2013\n6.2\n7.4\n0.77\nGW231231_120147\nHL\n7.5\n11.3\n0.61\n61\n9.0\n0.08\n150\n8.6\n0.03\n4.5\n9.2\n0.86\nGW240105_151143\nH\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n3.3\n25.9\n0.70\nNOTE\u2014 These candidates do not meet our criterion for source- property estimation, but are likely astrophysical in origin. The names of\ncandidates not previously reported are given in bold. The date and time of each candidate is encoded in the name as GWYYMMDD_hhmmss.\nThe detectors that were observing at the time of each transient are denoted by a single-letter (e.g., H for LIGO Hanford). This does not\nnecessarily indicate that the same detectors contributed triggers for a given candidate. We include results from analyses that observe a\ncandidate with pastro < 0.5. Italics denote that the candidate was found with FAR > 1 yr\u22121. A dash (\u2013) indicates that a candidate was not\nfound by an analysis.\n2.1.3. Pipeline consistency\nThe search algorithms, methods, and con\ufb01gurations used\ndiffer between our analyses (Abac et al. 2025b), which\ncauses them to have different responses to both noise and\nastrophysical transients. As a result, we expect candidate\nlists to differ between pipelines. There is less disagreement\nbetween pipelines for high-SNR candidates.\nLower-SNR\ncandidates, however, may be identi\ufb01ed by only a subset of\npipelines. Some candidates are observed in only one detec-\ntor, which increases the uncertainty in signi\ufb01cance estima-\ntion and can lead to additional disagreement across pipelines\nin both the estimated FAR and pastro.\nNot all of the 129 candidates with pastro \u22650.5 were ob-\nserved with pastro \u22650.5 by all pipelines.\nOf these can-\ndidates, 54 were found by CWB-BBH, 89 were found by\nGSTLAL, 76 were found by MBTA, and 103 were found\nby PYCBC. Only 39 of these candidates were found by all\npipelines, while 62 were found by all matched-\ufb01lter-based\npipelines, 68 by three or more pipelines, and 86 by two or\nmore pipelines. Of the 129 candidates for which pastro \u22650.5\nin any pipeline, several meet this criterion uniquely in only a\nsingle pipeline:\n\u2022 The\nCWB-BBH\nanalysis found 6 unique can-\ndidates,\n4 of which were assigned a FAR <\n1 yr\u22121:\nGW230712_090405, GW231004_232346,\nGW231221_135041, and GW231230_170116.\nIn\neach case, the coherent SNR reported by CWB-BBH\nis higher than the matched-\ufb01lter SNR obtained by the\nother analyses. If these candidates are astrophysical\nin origin, this disagreement in SNRs could result from\nphysics not captured by the matched-\ufb01lter templates,\nsuch as spin effects or orbital eccentricity (Mishra\net al. 2025), or the difference in SNR de\ufb01nition (Abac\net al. 2025b). GW230824_135331 has no triggers from\nany other pipeline. Here, we do not require indepen-\ndent support from a matched-\ufb01lter based pipeline for\na CWB-BBH-only candidate to remain in the can-\n\n9\ndidate list. Further discussion and a spectrogram of\nGW230824_135331 can be found in Appendix C.\n\u2022 The GSTLAL analysis found 7 unique candidates, all\nof which are classi\ufb01ed by the GSTLAL pastro esti-\nmate as BBH candidates.\nGW230807_205045 and\nGW231029_111508 were both identi\ufb01ed with FAR\n< 1 per 30 d in low latency; the former was demoted in\nsigni\ufb01cance after of\ufb02ine analysis and can be found in\nTable 2. GW231029_111508 is a single-detector can-\ndidate found by a high-mass template. MBTA and PY-\nCBC do not produce single-detector triggers for can-\ndidates with detector-frame chirp masses (1 + z)M >\n7M\u2299or durations \u22720.3 s, respectively (Abac et al.\n2025b).\n\u2022 The MBTA analysis found 11 unique candidates.\nThese\ncandidates\nare\nall\ninferred\nto\nbe\nfrom\nBBHs via the multicomponent pastro measurement.\nGW230704_212616 and GW231018_233037 were\nfound with a lower signi\ufb01cance in low latency by mul-\ntiple pipelines. These are found of\ufb02ine by MBTA with\nFAR < 1 yr\u22121 and are listed in Table 1. The remaining\nunique MBTA candidates can be found in Table 2.\n\u2022 The\nPYCBC\nanalysis\nfound\n19\nunique\ncandi-\ndates.\nGW230904_152545,\nGW230920_064709,\nGW231013_135504, and GW240105_151143 have\ngreater support from PYCBC for being NSBH can-\ndidates, more than that of GSTLAL or MBTA; their\nmulticomponent pastro can be found in Table 7. The\nremaining candidates are inferred to be from BBHs.\nGW231223_202619 was identi\ufb01ed in low latency with\na lower signi\ufb01cance. This candidate is found of\ufb02ine by\nPYCBC with FAR < 1 yr\u22121 and is listed in Table 1.\nThe other unique PYCBC candidates are all listed in\nTable 2.\n2.1.4. Subthreshold candidates\nWe have highlighted 129 GW candidates in O4a with\npastro \u22650.5. Of those, 42 with FAR > 1 yr\u22121 are listed\nin Table 2. The 87 candidates assigned a FAR < 1 yr\u22121,\nlisted in Table 1, underwent additional analysis (excluding\nGW230630_070659) and are discussed in more detail in Sec-\ntion 3.\nThese candidates are a subset of the O4a candi-\ndates in GWTC-4.0, which is comprised of 1382 triggers.\nThe remaining 1253 subthreshold candidates in O4a have a\nFAR < 2 d\u22121 and pastro < 0.5. These candidates are made\npublicly available at Gravitational Wave Open Science Cen-\nter (GWOSC; Abac et al. 2025c) for completeness, but they\nhave not been examined for possibly being instrumental in\norigin. The purity of this sample is expected to be low: 0.013\nwhen considering all of the subthreshold candidates as esti-\nmated in Section 2.2.\n2.2. Search sensitivity\nHere we describe the estimated sensitivity of each analy-\nsis, calculated by simulating astrophysical signals in the data\nand running search pipelines to recover them. These simu-\nlated signals are referred to as injections. We parameterize\nthe sensitivity of the search analyses via the estimated time\u2013\nvolume product or hypervolume \u27e8V T\u27e9(Abac et al. 2025a).\nAs discussed further in Abac et al. (2025b), the number of\nastrophysical signals, \u02c6N, that a pipeline is expected to detect\ncan be estimated as\n\u02c6N = \u27e8V T\u27e9R ,\n(1)\nwhere R is the volumetric rate of mergers per unit (source-\nframe) time. To estimate \u27e8V T\u27e9for each pipeline, we simu-\nlate a distribution of signals that approximates the detected\npopulation of BBHs, NSBHs, and BNSs (Essick et al. 2025).\nTo estimate the overall catalog sensitivity, each pipeline an-\nalyzes the same set of simulated signals: the injections are\nadded into the collected data, and we record how many are\nrecovered signi\ufb01cantly.\nAs in Abbott et al. (2023a), several combinations of masses\nare used to assess our sensitivity to BBH, NSBH, and BNS\nsystems. We thus estimate \u27e8V T\u27e9at a set of \ufb01ducial points in\nthe component mass space:\n\u2022 Black holes (BHs) at 35M\u2299.\nThese correspond to\nGW150914-like systems (Abbott et al. 2016b, 2024).\nThis is also approximately where we see a peak in the\nBH mass spectrum (Abac et al. 2025g).\n\u2022 BHs at 100M\u2299, 60M\u2299, 20M\u2299, 10M\u2299, and 5M\u2299.\nThese lie within the range of previously detected BH\nmasses (Abbott et al. 2023a).\n\u2022 NSs at 1.5M\u2299, which is consistent with the distribution\nof known NS masses (Antoniadis et al. 2016; Alsing\net al. 2018; \u00d6zel & Freire 2016; Farrow et al. 2019;\nLandry & Read 2021; Abbott et al. 2023b).\nFor each given point, injections are weighted so that they fol-\nlow a log-normal distribution about the central mass with a\nwidth of 0.1 (Essick et al. 2025). Figure 1 shows the result-\ning variation in the O4a \u27e8V T\u27e9with a detection threshold of\nFAR < 1 yr\u22121 across the component mass parameter space\nfor each search.\nThe results presented as from the Any pipeline in Figure 1\ncome from taking the minimum FAR for an injection from\nall of the analyses, and represent our overall sensitivity to\nCBCs in the speci\ufb01ed region. The sensitivity is greatest for\nthe Any pipeline for 100M\u2299+ 100M\u2299binaries, though dif-\nferent pipelines are more or less sensitive to different regions\nof the binary parameter space. Only sensitivity estimates that\nhave an uncertainty smaller than 50% are shown in Figure 1.\nWe also estimate the number of astrophysical signals\namong the set of 1253 subthreshold candidates. If the source\npopulation distribution assumed for pastro calculations is\nclose to the true astrophysical distribution, then for each in-\ndividual pipeline the sum of pastro values provides the ex-\npected number of true signals. The expected signal count for\na given pipeline is also proportional to that pipeline\u2019s \u27e8V T\u27e9\nfor the true signal population, thus if we knew the true \u27e8V T\u27e9\n\n10\nFigure 1. The sensitive hypervolume \u27e8V T\u27e9for searches of O4a data applying a signi\ufb01cance threshold FAR < 1 yr\u22121, evaluated at points in\ncomponent mass space. The Any results come from calculating the \u27e8V T\u27e9for injections found by at least one search analysis. The color of each\ncircle corresponds to the \u27e8V T\u27e9value. The plotted points correspond to the central points of log-normal distributions with widths 0.1 used to\nestimate \u27e8V T\u27e9.\n\n11\nwe could scale the sum of pastro values accordingly to obtain\nan estimate of the signal count for the Any pipeline (Abbott\net al. 2023a). Due to the larger differences in \u27e8V T\u27e9across\npipelines in GWTC-4.0 relative to GWTC-3.0, we compute\nthe sum of pastro of subthreshold candidates and take the av-\nerage over the number of pipelines as a conservative lower\nbound on the expected signal count. From this bound we es-\ntimate \u227316 signals among the subthreshold candidates.\n3. SOURCE PROPERTIES\nAfter identifying GW candidates, we coherently analyze\nthe data from the network of GW detectors to infer the prop-\nerties of the source of each signal (Abac et al. 2025b). These\ninferences are in turn used in companion papers to under-\nstand the population of compact objects (Abac et al. 2025g),\nmeasure cosmic expansion history (Abac et al. 2025h), and\nas a baseline for analyses that extend beyond our standard as-\nsumptions, such as for tests of general relativity carried out\non new candidates from O4a (Abac et al. 2025i,j,k). These\ndownstream analyses set stricter thresholds than used in Sec-\ntion 2 in order to mitigate the impact of differing methods of\ncomputing pastro across search pipelines and attain a higher\npurity subset of candidates. We restrict our estimation of the\nsource properties to those that have both pastro \u22650.5 and\nFARs < 1 yr\u22121. Additionally, we exclude from considera-\ntion GW230630_070659, which we \ufb01nd likely to be of in-\nstrumental origin (Section 2.1.2 and Appendix C).\nWe use Bayesian parameter estimation in order to infer the\nposterior probability distributions over the source parameters\ngiven a segment of data around each candidate. The posteri-\nors are derived assuming models of GW emission and under\nthe assumption of stationary, Gaussian noise which is uncor-\nrelated across detectors (e.g., Veitch et al. 2015; Abbott et al.\n2016b; Thrane & Talbot 2019; Abbott et al. 2020b; Chris-\ntensen & Meyer 2022; Abac et al. 2025b). When we iden-\ntify the presence of transient, non-Gaussian noise around the\ntime of a candidate, we exclude the affected frequency band\nor model and coherently remove the noise transient using the\nBAYESWAVE algorithm (Cornish & Littenberg 2015; Litten-\nberg & Cornish 2015; Cornish et al. 2021; Hourihane et al.\n2022). We discuss these cases further in Appendix B. Our\ndefault priors are chosen to be agnostic and suf\ufb01ciently wide\nto cover the region of the parameter space where the poste-\nriors have support (Abac et al. 2025b). Speci\ufb01cally, they are\nuniform in (redshifted) component masses, uniform in spin\nmagnitudes, isotropic in spin orientations, isotropic in binary\norientation, uniform in merger time and coalescence phase,\nisotropic in sky location, and our distance prior corresponds\nto a uniform merger rate in comoving volume and time. Our\ninferences are given in terms of samples from the posteriors,\nfrom which we derive point estimates and uncertainties for\nthe binary parameters (in the form of median values and 90%\ncredible intervals) after marginalizing over the remaining pa-\nrameters.\nFor all candidates, we assume quasi-circular orbits, and\nwe carry out inference using multiple waveform models.\nFuller details of these models and their development are\ngiven in Abac et al. (2025b). For each BBH candidate, we\nuse the IMRPHENOMXPHM_SPINTAYLOR (Pratten et al.\n2021; Colleoni et al. 2025) and SEOBNRV5PHM (Pompili\net al. 2023; Ramos-Buades et al. 2023) waveform models,\neach of which incorporates the effects of higher-order mul-\ntipolar emission and spin precession. Depending on the in-\nferred intrinsic parameters of these candidates, we use one\nto three additional waveform models.\nMany BBH candi-\ndates lie within the parameter-space coverage of the surro-\ngate model NRSUR7DQ4 (Varma et al. 2019) which is built\ndirectly on numerical simulations of BBH coalescences, and\nin these cases we use NRSUR7DQ4 for parameter estima-\ntion. For candidates with asymmetric masses or evidence\nof precession, we also use IMRPHENOMXO4A (Hamilton\net al. 2021; Thompson et al. 2024) because this waveform\nmodel includes a more complete physical description of pre-\ncession effects (Abac et al. 2025b).\nFor our BBH candi-\ndates we report our posteriors by combining equal numbers\nof samples from each waveform model, in order to mitigate\nuncertainties associated with our theoretical models (Abbott\net al. 2016b). For the NSBH candidate GW230518_125908,\nwe use IMRPHENOMXPHM_SPINTAYLOR to produce our\n\ufb01ducial posteriors, while for GW230529_181500 (Abac\net al. 2024a) we combine equal numbers of samples\nproduced using IMRPHENOMXPHM_SPINTAYLOR and\nSEOBNRV5PHM. Although these models incorporate key\nphysical effects, they do not include the imprint of mat-\nter. Therefore for both NSBH candidates we use the IM-\nRPHENOMPV2_NRTIDALV2 (Dietrich et al. 2019), IM-\nRPHENOMNSBH (Thompson et al. 2020), and SEOB-\nNRV4_ROM_NRTIDALV2_NSBH (Matas et al. 2020)\nmodels to constrain the tidal deformability of the NSs. The\nthree tidal models do not include the effect of higher multi-\npolar emission, and the latter two neglect the effects of spin\nprecession on the waveform.\nOur key results for O4a candidates with FAR < 1 yr\u22121\nare summarized in Table 3 and shown in Figures 2, 3, and 4.\nOur default agnostic priors (Abac et al. 2025b) do not make\nstrong assumptions about the nature of the underlying as-\ntrophysical population. In addition to the default prior, we\nalso reweight the inferred posterior distribution of our BBH\ncandidates using a population-informed prior (default model,\nTable 1 of Abac et al. 2025g), and show these population-\ninformed measurements in Figure 2.\n\n12\nTable 3. The inferred properties of GW event candidates from O4a with FAR \u22641yr\u22121 and pastro > 0.5. For one-dimensional distributions, we\nprovide the median and 90% symmetric credible intervals, while for the localization area \u2206\u2126we provide the 90% credible area.\nCandidate\nM\n[M\u2299]\nM\n[M\u2299]\nm1\n[M\u2299]\nm2\n[M\u2299]\n\u03c7eff\nDL\n[Gpc]\nz\nMf\n[M\u2299]\n\u03c7f\n\u2206\u2126\n[deg2]\nSNR\nGW230518_125908\n9.61+0.76\n\u22120.79\n2.80+0.06\n\u22120.06\n8.17+0.84\n\u22120.92\n1.45+0.13\n\u22120.10\n\u22120.01+0.09\n\u22120.11\n0.24+0.11\n\u22120.10\n0.05+0.02\n\u22120.02\n9.46+0.76\n\u22120.80\n0.38+0.03\n\u22120.03\n490\n14.2+0.2\n\u22120.4\nGW230529_181500\n5.08+0.61\n\u22120.60\n1.94+0.04\n\u22120.04\n3.66+0.82\n\u22121.21\n1.42+0.60\n\u22120.22\n\u22120.10+0.12\n\u22120.18\n0.2+0.1\n\u22120.1\n0.04+0.02\n\u22120.02\n4.92+0.62\n\u22120.63\n0.58+0.08\n\u22120.06\n24000\n11.6+0.3\n\u22120.4\nGW230601_224134\n107+22\n\u221215\n45.0+10.0\n\u22127.3\n64+17\n\u221213\n44+14\n\u221215\n\u22120.03+0.27\n\u22120.32\n3.7+2.1\n\u22121.8\n0.60+0.28\n\u22120.26\n102+21\n\u221214\n0.67+0.12\n\u22120.13\n3300\n12.3+0.2\n\u22120.3\nGW230605_065343\n28.6+4.0\n\u22122.8\n11.9+1.0\n\u22120.9\n17.2+6.5\n\u22123.5\n11.1+2.5\n\u22122.7\n0.06+0.16\n\u22120.10\n1.1+0.6\n\u22120.5\n0.21+0.10\n\u22120.09\n27.3+4.1\n\u22122.7\n0.69+0.05\n\u22120.05\n1000\n10.5+0.3\n\u22120.4\nGW230606_004305\n63.4+13.4\n\u22128.3\n26.5+5.7\n\u22123.6\n37.6+13.4\n\u22127.6\n25.8+8.1\n\u22128.3\n\u22120.1+0.3\n\u22120.3\n2.7+1.5\n\u22121.4\n0.48+0.20\n\u22120.22\n60.7+12.8\n\u22127.9\n0.64+0.11\n\u22120.14\n1400\n10.3+0.3\n\u22120.4\nGW230608_205047\n79+16\n\u221211\n32.8+7.3\n\u22125.4\n48+13\n\u221211\n31.0+11.0\n\u221210.0\n0.04+0.25\n\u22120.26\n3.5+2.2\n\u22121.7\n0.58+0.29\n\u22120.26\n75+15\n\u221211\n0.69+0.11\n\u22120.14\n2200\n9.8+0.3\n\u22120.5\nGW230609_064958\n60.3+12.9\n\u22128.0\n25.5+5.8\n\u22123.6\n35.3+10.7\n\u22126.9\n25.2+7.5\n\u22127.5\n\u22120.1+0.2\n\u22120.3\n3.4+1.9\n\u22121.7\n0.56+0.25\n\u22120.25\n57.8+12.2\n\u22127.7\n0.64+0.09\n\u22120.13\n1700\n9.8+0.3\n\u22120.5\nGW230624_113103\n43.8+11.1\n\u22126.6\n18.0+3.2\n\u22122.4\n27.2+13.4\n\u22126.9\n16.1+4.8\n\u22124.5\n0.2+0.3\n\u22120.3\n1.9+1.3\n\u22121.0\n0.35+0.19\n\u22120.16\n41.8+10.7\n\u22126.3\n0.72+0.12\n\u22120.11\n1300\n9.7+0.4\n\u22120.5\nGW230627_015337\n14.2+0.8\n\u22120.4\n6.02+0.16\n\u22120.07\n8.37+1.67\n\u22121.26\n5.79+0.95\n\u22120.92\n0.02+0.08\n\u22120.03\n0.31+0.06\n\u22120.13\n0.07+0.01\n\u22120.03\n13.5+0.8\n\u22120.5\n0.68+0.02\n\u22120.03\n110\n28.5+0.1\n\u22120.1\nGW230628_231200\n59.3+8.6\n\u22124.9\n25.5+3.8\n\u22122.2\n32.5+5.9\n\u22123.9\n27.1+4.9\n\u22125.2\n\u22120.01+0.16\n\u22120.16\n2.3+0.8\n\u22121.1\n0.40+0.12\n\u22120.17\n56.5+8.1\n\u22124.6\n0.69+0.08\n\u22120.06\n660\n15.5+0.2\n\u22120.3\nGW230630_125806\n84+26\n\u221219\n35.0+11.4\n\u22128.5\n51+20\n\u221214\n33+15\n\u221213\n0.2+0.3\n\u22120.3\n5.4+5.1\n\u22123.0\n0.83+0.59\n\u22120.41\n80+25\n\u221218\n0.75+0.11\n\u22120.16\n4300\n8.1+0.4\n\u22120.5\nGW230630_234532\n16.8+2.1\n\u22121.4\n7.06+0.57\n\u22120.48\n10.0+3.5\n\u22121.8\n6.64+1.46\n\u22121.59\n\u22120.04+0.16\n\u22120.08\n1.1+0.5\n\u22120.5\n0.21+0.09\n\u22120.09\n16.1+2.1\n\u22121.4\n0.66+0.04\n\u22120.05\n1500\n9.4+0.3\n\u22120.5\nGW230702_185453\n60+15\n\u221211\n22.9+4.0\n\u22123.5\n40+20\n\u221213\n18.0+8.5\n\u22126.5\n0.05+0.29\n\u22120.26\n2.4+1.9\n\u22121.1\n0.43+0.27\n\u22120.17\n57+15\n\u221211\n0.64+0.13\n\u22120.15\n2500\n9.5+0.3\n\u22120.5\nGW230704_021211\n52.7+10.8\n\u22128.2\n21.8+4.4\n\u22123.2\n32.4+11.9\n\u22127.9\n19.9+6.5\n\u22126.0\n\u22120.01+0.21\n\u22120.24\n2.7+1.8\n\u22121.5\n0.48+0.25\n\u22120.23\n50.5+10.6\n\u22127.9\n0.66+0.10\n\u22120.13\n1500\n9.0+0.3\n\u22120.5\nGW230704_212616\n139+49\n\u221231\n55+23\n\u221214\n89+42\n\u221227\n49+30\n\u221225\n0.3+0.3\n\u22120.4\n7.2+6.1\n\u22124.2\n1.1+0.7\n\u22120.5\n132+47\n\u221230\n0.77+0.12\n\u22120.19\n7400\n8.0+1.0\n\u22121.0\nGW230706_104333\n27.9+4.4\n\u22123.0\n11.8+1.7\n\u22121.1\n16.3+5.4\n\u22123.0\n11.5+2.6\n\u22122.7\n0.2+0.1\n\u22120.1\n1.9+0.9\n\u22121.0\n0.35+0.14\n\u22120.16\n26.5+4.3\n\u22122.8\n0.75+0.07\n\u22120.06\n1500\n9.0+0.3\n\u22120.5\nGW230707_124047\n82+19\n\u221212\n35.1+8.6\n\u22125.3\n46.1+12.2\n\u22128.2\n36.4+10.6\n\u22129.8\n\u22120.05+0.25\n\u22120.29\n4.5+2.3\n\u22122.3\n0.71+0.29\n\u22120.32\n78+18\n\u221211\n0.68+0.09\n\u22120.10\n3200\n10.6+0.2\n\u22120.4\nGW230708_053705\n51.9+10.2\n\u22127.6\n22.2+4.4\n\u22123.3\n29.1+8.2\n\u22125.4\n22.8+5.5\n\u22125.4\n0.07+0.23\n\u22120.24\n3.3+2.0\n\u22121.7\n0.55+0.27\n\u22120.25\n49.4+9.7\n\u22127.2\n0.72+0.09\n\u22120.09\n1900\n8.3+0.4\n\u22120.6\nGW230708_230935\n103+21\n\u221216\n42.5+9.7\n\u22127.8\n64+20\n\u221215\n39+14\n\u221215\n0.01+0.27\n\u22120.30\n3.5+2.3\n\u22121.6\n0.58+0.29\n\u22120.24\n98+20\n\u221215\n0.67+0.12\n\u22120.16\n2600\n9.2+0.3\n\u22120.5\nGW230709_122727\n74+20\n\u221214\n31.0+9.4\n\u22126.6\n45+16\n\u221211\n30+13\n\u221213\n0.08+0.30\n\u22120.31\n4.6+3.5\n\u22122.4\n0.73+0.43\n\u22120.34\n71+19\n\u221213\n0.71+0.12\n\u22120.15\n3600\n8.5+0.3\n\u22120.5\nGW230712_090405\n46+22\n\u221211\n16.5+11.1\n\u22123.2\n32.0+17.0\n\u221210.0\n13.1+14.6\n\u22125.9\n\u22120.03+0.35\n\u22120.31\n2.0+2.6\n\u22121.0\n0.37+0.36\n\u22120.17\n45+20\n\u221211\n0.66+0.17\n\u22120.22\n1400\n8.0+1.0\n\u22121.0\nGW230723_101834\n27.5+4.3\n\u22122.6\n11.4+1.6\n\u22120.9\n16.7+5.9\n\u22123.4\n10.6+2.8\n\u22122.8\n\u22120.2+0.2\n\u22120.2\n1.6+0.7\n\u22120.9\n0.30+0.11\n\u22120.16\n26.4+4.2\n\u22122.6\n0.61+0.09\n\u22120.08\n1100\n9.7+0.3\n\u22120.5\nGW230726_002940\n63.6+10.3\n\u22127.9\n27.3+4.4\n\u22123.4\n35.6+9.0\n\u22125.9\n27.9+6.0\n\u22126.0\n\u22120.02+0.21\n\u22120.23\n2.0+1.2\n\u22121.0\n0.37+0.18\n\u22120.17\n60.6+9.7\n\u22127.4\n0.69+0.08\n\u22120.08\n28000\n10.2+0.2\n\u22120.4\nGW230729_082317\n20.3+5.0\n\u22122.4\n8.33+0.94\n\u22120.75\n12.3+7.6\n\u22122.7\n7.62+2.12\n\u22122.63\n0.1+0.2\n\u22120.1\n1.6+0.8\n\u22120.8\n0.31+0.13\n\u22120.13\n19.4+5.1\n\u22122.4\n0.71+0.06\n\u22120.06\n2200\n8.2+0.3\n\u22120.6\nGW230731_215307\n18.3+1.6\n\u22121.0\n7.77+0.58\n\u22120.36\n10.4+2.9\n\u22121.4\n7.80+1.24\n\u22121.64\n\u22120.05+0.11\n\u22120.06\n1.1+0.3\n\u22120.5\n0.22+0.06\n\u22120.08\n17.4+1.6\n\u22121.0\n0.67+0.04\n\u22120.03\n710\n11.9+0.2\n\u22120.3\nGW230803_033412\n74+22\n\u221216\n30.5+9.3\n\u22126.7\n45+19\n\u221212\n28.0+12.0\n\u221210.0\n0.06+0.29\n\u22120.31\n4.9+4.0\n\u22122.6\n0.77+0.47\n\u22120.35\n70+21\n\u221215\n0.71+0.12\n\u22120.14\n4100\n7.7+0.4\n\u22120.6\nGW230805_034249\n54.9+13.8\n\u22129.7\n23.1+5.9\n\u22124.2\n32.1+12.5\n\u22127.3\n22.6+7.8\n\u22127.5\n0.06+0.27\n\u22120.28\n3.5+2.6\n\u22121.7\n0.58+0.33\n\u22120.25\n52.4+13.0\n\u22129.2\n0.71+0.11\n\u22120.12\n2400\n9.0+0.3\n\u22120.5\nGW230806_204041\n85+24\n\u221215\n35.8+10.7\n\u22126.9\n51+18\n\u221212\n35+14\n\u221213\n0.08+0.28\n\u22120.27\n5.5+3.7\n\u22122.9\n0.84+0.44\n\u22120.39\n81+23\n\u221215\n0.71+0.11\n\u22120.13\n4600\n8.5+0.3\n\u22120.5\nGW230811_032116\n57.9+8.7\n\u22126.6\n24.0+4.1\n\u22122.4\n35.6+8.7\n\u22127.5\n22.1+6.7\n\u22125.1\n0.02+0.18\n\u22120.18\n2.1+1.2\n\u22121.1\n0.38+0.17\n\u22120.18\n55.3+8.3\n\u22126.4\n0.69+0.09\n\u22120.09\n940\n12.8+0.3\n\u22120.4\nGW230814_061920\n110+26\n\u221220\n45.5+11.9\n\u22129.9\n69+19\n\u221217\n42+17\n\u221216\n0.05+0.29\n\u22120.28\n4.0+3.4\n\u22122.0\n0.65+0.42\n\u22120.28\n105+24\n\u221219\n0.69+0.12\n\u22120.14\n5200\n9.4+0.3\n\u22120.5\nGW230814_230901\n61.8+2.0\n\u22122.1\n26.7+0.9\n\u22121.0\n33.6+2.8\n\u22122.2\n28.3+2.1\n\u22123.0\n\u22120.01+0.06\n\u22120.08\n0.28+0.17\n\u22120.13\n0.06+0.04\n\u22120.03\n58.9+1.9\n\u22121.9\n0.68+0.02\n\u22120.03\n26000\n42.1+0.1\n\u22120.1\nGW230819_171910\n106+41\n\u221222\n42+14\n\u221211\n70+47\n\u221221\n35+20\n\u221219\n\u22120.04+0.36\n\u22120.43\n4.0+3.9\n\u22122.2\n0.65+0.49\n\u22120.31\n102+41\n\u221222\n0.64+0.19\n\u22120.25\n4800\n8.9+0.4\n\u22120.5\nGW230820_212515\n96+22\n\u221216\n38.6+11.2\n\u22129.8\n62+23\n\u221215\n34+18\n\u221218\n0.2+0.3\n\u22120.3\n4.0+3.0\n\u22122.1\n0.65+0.38\n\u22120.30\n92+21\n\u221216\n0.74+0.12\n\u22120.25\n2100\n8.4+0.4\n\u22120.5\nGW230824_033047\n88+20\n\u221214\n37.0+9.1\n\u22126.3\n52+16\n\u221212\n36+12\n\u221213\n\u22120.004+0.232\n\u22120.267\n4.7+2.9\n\u22122.3\n0.74+0.36\n\u22120.32\n84+19\n\u221213\n0.68+0.10\n\u22120.13\n3700\n10.0+0.2\n\u22120.4\nGW230825_041334\n71+22\n\u221215\n29.4+9.4\n\u22126.3\n43+17\n\u221212\n27.3+11.9\n\u22128.9\n0.3+0.2\n\u22120.3\n4.9+4.2\n\u22122.9\n0.77+0.50\n\u22120.40\n67+20\n\u221215\n0.79+0.08\n\u22120.15\n3400\n8.1+0.5\n\u22120.6\nGW230831_015414\n73+26\n\u221215\n30.7+10.6\n\u22126.5\n42.0+18.0\n\u221210.0\n30.0+12.0\n\u221210.0\n0.03+0.30\n\u22120.30\n4.9+4.2\n\u22122.9\n0.77+0.50\n\u22120.40\n69+24\n\u221214\n0.71+0.12\n\u22120.12\n4000\n8.1+0.3\n\u22120.7\nGW230904_051013\n17.9+2.4\n\u22121.6\n7.54+0.53\n\u22120.60\n10.6+4.1\n\u22121.9\n7.12+1.52\n\u22121.88\n0.05+0.15\n\u22120.07\n1.0+0.6\n\u22120.4\n0.20+0.10\n\u22120.08\n17.1+2.5\n\u22121.6\n0.69+0.04\n\u22120.04\n1800\n10.2+0.3\n\u22120.5\nGW230911_195324\n55.3+7.8\n\u22127.0\n23.1+3.4\n\u22123.0\n33.6+8.1\n\u22127.3\n21.7+5.6\n\u22125.7\n\u22120.03+0.19\n\u22120.23\n1.4+1.2\n\u22120.7\n0.26+0.18\n\u22120.13\n53.0+7.4\n\u22126.7\n0.67+0.09\n\u22120.11\n27000\n10.6+0.3\n\u22120.4\nGW230914_111401\n95.0+15.0\n\u221210.0\n39.6+7.5\n\u22126.2\n59+12\n\u221211\n36+13\n\u221212\n0.1+0.2\n\u22120.2\n2.7+1.6\n\u22121.2\n0.47+0.23\n\u22120.19\n90.9+14.0\n\u22129.7\n0.71+0.09\n\u22120.14\n1900\n16.2+0.2\n\u22120.3\nGW230919_215712\n49.0+4.2\n\u22124.5\n21.0+1.8\n\u22121.9\n27.3+5.5\n\u22123.7\n21.4+3.5\n\u22124.3\n0.2+0.1\n\u22120.1\n1.3+0.8\n\u22120.5\n0.26+0.13\n\u22120.09\n46.5+3.9\n\u22124.3\n0.75+0.06\n\u22120.05\n730\n15.7+0.2\n\u22120.3\nGW230920_071124\n56.4+10.2\n\u22128.0\n23.9+4.6\n\u22123.4\n32.4+9.1\n\u22126.2\n23.8+6.6\n\u22126.9\n0.002+0.223\n\u22120.227\n2.9+1.8\n\u22121.4\n0.50+0.24\n\u22120.21\n53.9+9.6\n\u22127.6\n0.69+0.10\n\u22120.10\n2100\n10.1+0.3\n\u22120.4\nGW230922_020344\n68.6+8.9\n\u22126.5\n29.2+3.6\n\u22122.6\n39.3+10.0\n\u22126.3\n29.2+5.6\n\u22126.2\n0.03+0.20\n\u22120.21\n1.6+0.7\n\u22120.7\n0.31+0.11\n\u22120.12\n65.4+8.4\n\u22126.1\n0.70+0.08\n\u22120.08\n330\n11.8+0.3\n\u22120.4\nGW230922_040658\n125+36\n\u221221\n52+17\n\u221212\n76+28\n\u221218\n51+23\n\u221224\n0.3+0.3\n\u22120.3\n6.4+4.1\n\u22123.5\n0.96+0.47\n\u22120.45\n119+34\n\u221221\n0.79+0.08\n\u22120.14\n5100\n11.4+0.2\n\u22120.4\nGW230924_124453\n51.8+7.0\n\u22124.9\n22.3+3.1\n\u22122.1\n28.8+5.9\n\u22124.0\n23.1+4.4\n\u22124.4\n0.02+0.18\n\u22120.18\n2.4+1.0\n\u22121.0\n0.42+0.15\n\u22120.16\n49.3+6.6\n\u22124.6\n0.70+0.07\n\u22120.06\n1300\n12.9+0.2\n\u22120.3\nGW230927_043729\n61.8+12.6\n\u22128.0\n26.5+5.5\n\u22123.5\n34.9+8.7\n\u22126.1\n27.1+7.2\n\u22126.5\n0.005+0.204\n\u22120.215\n3.3+1.7\n\u22121.7\n0.55+0.23\n\u22120.26\n58.9+11.9\n\u22127.6\n0.69+0.08\n\u22120.08\n1500\n10.5+0.2\n\u22120.4\nGW230927_153832\n38.3+3.3\n\u22122.2\n16.4+1.4\n\u22120.8\n21.9+3.7\n\u22122.9\n16.5+2.6\n\u22122.5\n0.03+0.08\n\u22120.08\n1.2+0.4\n\u22120.5\n0.23+0.06\n\u22120.10\n36.5+3.1\n\u22122.1\n0.69+0.04\n\u22120.03\n330\n19.7+0.2\n\u22120.2\nGW230928_215827\n83+22\n\u221218\n33.6+9.9\n\u22127.5\n54+19\n\u221215\n29+14\n\u221211\n0.4+0.2\n\u22120.3\n5.0+3.9\n\u22122.5\n0.78+0.47\n\u22120.34\n79+21\n\u221217\n0.83+0.07\n\u22120.15\n3700\n8.9+0.4\n\u22120.6\nGW230930_110730\n59.0+15.0\n\u221210.0\n24.9+6.3\n\u22124.2\n34.4+12.9\n\u22127.8\n24.4+8.3\n\u22127.4\n0.03+0.26\n\u22120.27\n4.9+3.2\n\u22122.5\n0.77+0.38\n\u22120.34\n56.3+14.2\n\u22129.7\n0.69+0.10\n\u22120.12\n3300\n8.0+0.3\n\u22120.5\nGW231001_140220\n115+32\n\u221222\n46.4+14.3\n\u22129.9\n75+26\n\u221222\n40+18\n\u221216\n\u22120.04+0.32\n\u22120.35\n4.4+3.8\n\u22122.4\n0.71+0.47\n\u22120.34\n111+31\n\u221221\n0.64+0.15\n\u22120.20\n4300\n9.6+0.3\n\u22120.5\nTable 3 continued\n\n13\nTable 3 (continued)\nCandidate\nM\n[M\u2299]\nM\n[M\u2299]\nm1\n[M\u2299]\nm2\n[M\u2299]\n\u03c7eff\nDL\n[Gpc]\nz\nMf\n[M\u2299]\n\u03c7f\n\u2206\u2126\n[deg2]\nSNR\nGW231004_232346\n100+28\n\u221219\n40.1+11.7\n\u22128.5\n65+24\n\u221219\n35+16\n\u221214\n\u22120.05+0.30\n\u22120.37\n4.3+3.6\n\u22122.2\n0.69+0.44\n\u22120.31\n96+26\n\u221219\n0.64+0.14\n\u22120.19\n3500\n8.2+0.3\n\u22120.6\nGW231005_021030\n132+37\n\u221225\n54+17\n\u221212\n83+31\n\u221222\n49+22\n\u221220\n0.10+0.35\n\u22120.37\n6.4+4.7\n\u22123.3\n0.95+0.54\n\u22120.43\n126+35\n\u221224\n0.72+0.14\n\u22120.17\n5600\n9.4+0.3\n\u22120.4\nGW231005_091549\n50.2+11.3\n\u22128.3\n21.3+4.8\n\u22123.5\n28.8+10.1\n\u22126.1\n21.2+6.4\n\u22126.1\n\u22120.03+0.23\n\u22120.26\n3.8+2.6\n\u22121.9\n0.62+0.33\n\u22120.27\n48.0+10.8\n\u22127.9\n0.68+0.10\n\u22120.11\n2900\n8.0+0.3\n\u22120.6\nGW231008_142521\n71+16\n\u221213\n28.9+6.8\n\u22125.6\n45+17\n\u221212\n25.5+10.7\n\u22129.7\n\u22120.009+0.256\n\u22120.282\n3.0+2.5\n\u22121.3\n0.51+0.33\n\u22120.20\n68+15\n\u221213\n0.66+0.13\n\u22120.19\n3000\n8.9+0.4\n\u22120.5\nGW231014_040532\n35.5+7.0\n\u22124.6\n15.0+2.7\n\u22121.9\n20.6+7.8\n\u22124.0\n14.7+3.9\n\u22124.3\n0.2+0.3\n\u22120.3\n2.3+1.4\n\u22121.2\n0.42+0.20\n\u22120.20\n33.8+6.6\n\u22124.3\n0.75+0.10\n\u22120.11\n1800\n8.7+0.4\n\u22120.5\nGW231018_233037\n19.1+3.3\n\u22122.0\n7.90+0.88\n\u22120.68\n11.6+4.9\n\u22122.5\n7.23+1.87\n\u22122.00\n0.01+0.17\n\u22120.13\n1.5+0.8\n\u22120.7\n0.29+0.12\n\u22120.13\n18.2+3.3\n\u22122.0\n0.67+0.05\n\u22120.07\n1600\n8.2+0.3\n\u22120.6\nGW231020_142947\n19.8+6.0\n\u22122.1\n8.06+0.81\n\u22120.53\n12.1+9.1\n\u22122.7\n7.30+2.06\n\u22122.85\n0.1+0.3\n\u22120.1\n1.2+0.5\n\u22120.6\n0.24+0.09\n\u22120.11\n18.9+6.3\n\u22122.0\n0.72+0.06\n\u22120.04\n1500\n10.5+0.3\n\u22120.4\nGW231028_153006\n152+29\n\u221214\n63.0+13.0\n\u221210.0\n95+33\n\u221220\n58+21\n\u221225\n0.4+0.2\n\u22120.2\n4.1+1.4\n\u22121.9\n0.67+0.18\n\u22120.27\n144+27\n\u221214\n0.84+0.05\n\u22120.10\n1300\n21.0+0.2\n\u22120.2\nGW231029_111508\n106+22\n\u221216\n44.2+10.5\n\u22128.0\n65+17\n\u221214\n42+15\n\u221216\n0.1+0.2\n\u22120.2\n3.1+2.4\n\u22121.7\n0.53+0.32\n\u22120.25\n101+21\n\u221215\n0.72+0.10\n\u22120.15\n29000\n11.2+0.2\n\u22120.3\nGW231102_071736\n102+21\n\u221213\n43.4+9.3\n\u22126.3\n61+14\n\u221212\n43+13\n\u221213\n0.06+0.23\n\u22120.22\n3.8+2.1\n\u22121.8\n0.63+0.26\n\u22120.26\n98+19\n\u221212\n0.70+0.09\n\u22120.10\n3000\n13.3+0.2\n\u22120.3\nGW231104_133418\n21.0+2.8\n\u22121.7\n8.84+0.87\n\u22120.56\n12.3+4.5\n\u22122.1\n8.56+1.79\n\u22122.16\n0.1+0.1\n\u22120.1\n1.5+0.5\n\u22120.7\n0.28+0.09\n\u22120.11\n20.0+2.8\n\u22121.7\n0.72+0.05\n\u22120.04\n1100\n11.0+0.2\n\u22120.4\nGW231108_125142\n40.6+5.1\n\u22123.3\n17.3+2.1\n\u22121.3\n23.2+5.5\n\u22123.6\n17.4+3.2\n\u22123.1\n\u22120.08+0.13\n\u22120.15\n2.1+0.7\n\u22120.9\n0.37+0.11\n\u22120.15\n38.8+4.9\n\u22123.2\n0.66+0.06\n\u22120.05\n1000\n12.4+0.2\n\u22120.3\nGW231110_040320\n32.2+4.3\n\u22123.4\n13.4+1.7\n\u22121.2\n19.5+5.8\n\u22124.1\n12.5+3.1\n\u22122.9\n0.2+0.1\n\u22120.1\n1.9+0.9\n\u22120.9\n0.35+0.13\n\u22120.15\n30.6+4.2\n\u22123.3\n0.74+0.06\n\u22120.05\n800\n11.0+0.3\n\u22120.4\nGW231113_122623\n67+16\n\u221213\n27.9+6.3\n\u22125.5\n39.7+17.3\n\u22129.6\n26.4+9.0\n\u22129.4\n0.3+0.2\n\u22120.3\n3.4+2.4\n\u22121.7\n0.57+0.31\n\u22120.25\n63+15\n\u221212\n0.81+0.08\n\u22120.16\n2800\n7.8+0.4\n\u22120.7\nGW231113_200417\n19.2+3.1\n\u22121.9\n8.01+0.68\n\u22120.64\n11.5+5.1\n\u22122.3\n7.41+1.76\n\u22122.00\n0.1+0.1\n\u22120.1\n1.2+0.6\n\u22120.5\n0.23+0.11\n\u22120.10\n18.3+3.2\n\u22121.9\n0.72+0.06\n\u22120.04\n1600\n10.1+0.3\n\u22120.5\nGW231114_043211\n31.0+7.6\n\u22124.8\n11.6+1.1\n\u22121.1\n22.7+9.6\n\u22126.4\n8.20+2.56\n\u22122.18\n0.08+0.22\n\u22120.16\n1.4+0.9\n\u22120.6\n0.26+0.14\n\u22120.11\n30.0+7.8\n\u22124.8\n0.61+0.06\n\u22120.06\n1700\n9.8+0.3\n\u22120.5\nGW231118_005626\n30.9+5.3\n\u22123.6\n12.6+1.6\n\u22121.1\n19.8+6.6\n\u22124.9\n10.9+3.3\n\u22122.4\n0.4+0.1\n\u22120.1\n2.2+0.9\n\u22121.0\n0.39+0.14\n\u22120.16\n29.3+5.3\n\u22123.6\n0.80+0.06\n\u22120.05\n1100\n10.5+0.3\n\u22120.5\nGW231118_071402\n72+18\n\u221214\n30.4+7.9\n\u22126.1\n43.0+15.0\n\u221210.0\n30.0+10.0\n\u221210.0\n0.1+0.3\n\u22120.3\n4.3+3.5\n\u22122.2\n0.69+0.43\n\u22120.32\n69+17\n\u221213\n0.72+0.11\n\u22120.14\n3600\n8.5+0.3\n\u22120.5\nGW231118_090602\n20.7+10.2\n\u22122.3\n8.37+0.76\n\u22120.56\n13.1+13.7\n\u22123.3\n7.29+2.13\n\u22123.27\n0.08+0.36\n\u22120.09\n1.4+0.5\n\u22120.6\n0.26+0.09\n\u22120.11\n19.7+10.6\n\u22122.3\n0.70+0.08\n\u22120.04\n1100\n10.9+0.4\n\u22120.4\nGW231119_075248\n82+29\n\u221218\n34.4+12.4\n\u22127.8\n49+23\n\u221213\n34+15\n\u221213\n\u22120.002+0.279\n\u22120.302\n6.7+5.5\n\u22123.7\n0.99+0.62\n\u22120.48\n79+27\n\u221218\n0.68+0.11\n\u22120.16\n5900\n7.7+0.3\n\u22120.5\nGW231123_135430\n236+29\n\u221248\n101+13\n\u221230\n137+23\n\u221218\n101+22\n\u221251\n0.3+0.2\n\u22120.4\n2.2+2.0\n\u22121.5\n0.39+0.28\n\u22120.25\n222+27\n\u221242\n0.84+0.07\n\u22120.19\n1700\n20.7+0.2\n\u22120.3\nGW231127_165300\n74+22\n\u221215\n30.5+9.5\n\u22126.7\n45+18\n\u221212\n29+12\n\u221212\n0.05+0.30\n\u22120.32\n4.5+3.6\n\u22122.5\n0.71+0.44\n\u22120.35\n71+21\n\u221214\n0.69+0.12\n\u22120.17\n4400\n8.3+0.3\n\u22120.5\nGW231129_081745\n69+18\n\u221214\n27.7+7.7\n\u22125.7\n45+15\n\u221213\n23.8+10.0\n\u22128.2\n0.02+0.27\n\u22120.26\n3.8+3.6\n\u22122.1\n0.63+0.45\n\u22120.31\n66+17\n\u221214\n0.67+0.13\n\u22120.16\n3700\n7.5+0.4\n\u22120.7\nGW231206_233134\n63.5+13.4\n\u22128.8\n27.2+5.9\n\u22123.9\n35.6+9.1\n\u22126.3\n28.1+7.5\n\u22127.1\n\u22120.09+0.22\n\u22120.24\n3.2+1.8\n\u22121.8\n0.54+0.25\n\u22120.27\n60.6+12.7\n\u22128.4\n0.67+0.09\n\u22120.10\n2400\n11.0+0.3\n\u22120.4\nGW231206_233901\n66.0+5.3\n\u22123.7\n28.1+2.7\n\u22121.7\n37.6+6.6\n\u22124.6\n28.4+5.4\n\u22126.0\n\u22120.05+0.14\n\u22120.15\n1.5+0.3\n\u22120.5\n0.28+0.05\n\u22120.08\n63.1+5.0\n\u22123.4\n0.67+0.06\n\u22120.07\n350\n21.0+0.1\n\u22120.2\nGW231213_111417\n62.5+14.3\n\u22129.3\n26.7+6.3\n\u22124.2\n35.5+10.3\n\u22126.7\n27.2+8.1\n\u22127.5\n0.06+0.24\n\u22120.23\n4.0+2.3\n\u22122.0\n0.65+0.30\n\u22120.29\n59.5+13.4\n\u22128.8\n0.71+0.09\n\u22120.09\n2600\n9.7+0.2\n\u22120.4\nGW231221_135041\n76+21\n\u221215\n30.7+9.5\n\u22126.8\n47+21\n\u221213\n28+13\n\u221213\n0.01+0.36\n\u22120.38\n4.6+3.7\n\u22122.5\n0.73+0.45\n\u22120.36\n72+20\n\u221215\n0.69+0.15\n\u22120.17\n3700\n7.8+0.4\n\u22120.6\nGW231223_032836\n76+18\n\u221213\n31.8+8.6\n\u22127.0\n46+16\n\u221211\n31+12\n\u221214\n\u22120.2+0.3\n\u22120.4\n4.2+3.1\n\u22122.1\n0.67+0.39\n\u22120.30\n73+17\n\u221213\n0.63+0.13\n\u22120.17\n4200\n8.8+0.3\n\u22120.5\nGW231223_075055\n19.0+4.6\n\u22122.0\n7.79+0.58\n\u22120.59\n11.9+6.8\n\u22122.8\n6.80+2.00\n\u22122.13\n0.06+0.22\n\u22120.12\n0.97+0.58\n\u22120.43\n0.19+0.10\n\u22120.08\n18.1+4.8\n\u22121.9\n0.69+0.06\n\u22120.05\n1500\n8.8+0.4\n\u22120.6\nGW231223_202619\n19.6+2.2\n\u22121.5\n8.36+0.66\n\u22120.57\n11.1+3.8\n\u22121.6\n8.33+1.36\n\u22121.93\n0.10+0.13\n\u22120.11\n0.89+0.49\n\u22120.44\n0.18+0.08\n\u22120.08\n18.7+2.2\n\u22121.5\n0.71+0.05\n\u22120.05\n27000\n9.8+0.2\n\u22120.4\nGW231224_024321\n16.7+1.3\n\u22120.8\n7.13+0.48\n\u22120.29\n9.31+2.20\n\u22121.09\n7.30+1.01\n\u22121.33\n\u22120.007+0.076\n\u22120.058\n0.95+0.29\n\u22120.40\n0.19+0.05\n\u22120.07\n15.9+1.3\n\u22120.8\n0.68+0.04\n\u22120.03\n390\n12.9+0.2\n\u22120.3\nGW231226_101520\n74.8+4.1\n\u22123.0\n32.4+1.8\n\u22121.4\n40.1+4.4\n\u22122.9\n35.0+3.2\n\u22124.9\n\u22120.09+0.09\n\u22120.10\n1.2+0.2\n\u22120.4\n0.23+0.04\n\u22120.06\n71.4+3.8\n\u22122.8\n0.67+0.04\n\u22120.04\n190\n33.7+0.1\n\u22120.1\nGW231230_170116\n89+49\n\u221220\n36.9+14.3\n\u22128.4\n54+50\n\u221215\n35+15\n\u221214\n\u22120.2+0.3\n\u22120.4\n5.7+4.8\n\u22123.2\n0.87+0.56\n\u22120.43\n86+47\n\u221219\n0.62+0.13\n\u22120.20\n6700\n7.4+0.4\n\u22120.7\nGW231231_154016\n39.9+4.1\n\u22123.4\n17.1+1.6\n\u22121.4\n22.5+5.7\n\u22123.3\n17.2+2.9\n\u22123.2\n\u22120.03+0.12\n\u22120.12\n1.1+0.6\n\u22120.5\n0.21+0.10\n\u22120.10\n38.1+4.0\n\u22123.2\n0.67+0.06\n\u22120.05\n27000\n13.1+0.2\n\u22120.3\nGW240104_164932\n74.3+11.4\n\u22128.5\n31.8+5.1\n\u22123.9\n42.3+9.4\n\u22126.7\n32.1+7.5\n\u22128.0\n0.09+0.19\n\u22120.19\n1.9+1.1\n\u22121.0\n0.35+0.16\n\u22120.16\n70.6+10.7\n\u22127.9\n0.73+0.08\n\u22120.08\n28000\n14.1+0.2\n\u22120.3\nGW240107_013215\n92+29\n\u221220\n36.2+14.0\n\u22129.5\n59+27\n\u221218\n32+20\n\u221216\n0.3+0.3\n\u22120.4\n5.8+4.8\n\u22123.2\n0.87+0.56\n\u22120.43\n87+28\n\u221219\n0.79+0.10\n\u22120.19\n4800\n8.5+0.4\n\u22120.5\nGW240109_050431\n47.1+6.7\n\u22125.7\n19.6+2.7\n\u22122.2\n28.8+7.5\n\u22126.2\n18.1+4.8\n\u22124.1\n\u22120.07+0.20\n\u22120.23\n1.5+1.0\n\u22120.8\n0.29+0.16\n\u22120.13\n45.1+6.5\n\u22125.5\n0.64+0.09\n\u22120.09\n27000\n10.4+0.2\n\u22120.4\nNOTE\u2014The columns show the source-frame total mass M, source-frame chirp mass M, source-frame component masses mi, effective inspiral spin \u03c7eff, luminosity distance DL,\nredshift z, source-frame remnant mass Mf, remnant spin \u03c7f, localisation area \u2206\u2126, and SNR.\nHighlights from the new candidates in GWTC-4.0 include:\n\u2022 GW230518_125908 is one of two high-signi\ufb01cance\ncandidates added to GWTC-4.0 whose sources have\nmasses consistent with an NSBH binary. This can-\ndidate was previously reported as a probable online\nNSBH candidate, although no unambiguous multimes-\nsenger counterpart was identi\ufb01ed in follow-up elec-\ntromagnetic searches.1\nIts source properties are re-\nported here for the \ufb01rst time. In addition to having\nmore asymmetric masses than GW230529_181500,\nwith mass ratio q = 0.18+0.04\n\u22120.03 and larger total mass\nM = 9.61+0.76\n\u22120.79 M\u2299, the spin of its primary is con-\nstrained to be relatively small \u03c71 < 0.16 (90% credi-\nble level), and we infer \u03c7e\ufb00= \u22120.01+0.09\n\u22120.11.\n1 As reported in General Coordinates Network circulars related to this event;\nsee also Paek et al. (2025); Pillas et al. (2025) and the references therein.\n\n14\n\u2022 GW230529_181500 (Abac et al. 2024a) is the sec-\nond high-signi\ufb01cance candidate whose sources have\nmasses consistent with an NSBH binary. Its compo-\nnent masses mean that the primary probably lies in the\nputative lower mass gap between 3 and 5 M\u2299(Bailyn\net al. 1998; Ozel et al. 2010; Farr et al. 2011; Krei-\ndberg et al. 2012). Relative to our previous results,\nwe have corrected the implementation of calibration\nmarginalization for this event (Abac et al. 2025b), cor-\nrected the normalization of the noise-weighted inner\nproduct used in the likelihood (Abac et al. 2025b; Tal-\nbot et al. 2025), and reweighted our priors to the ref-\nerence cosmology used throughout GWTC-4.0. Our\ninferences of this candidate\u2019s source properties remain\nnearly identical to those previously presented (Abac\net al. 2024a).\n\u2022 While GW230814_230901 (Abac et al. 2025e) is\nthe highest-SNR candidate, with an SNR 42.1, its\nsource properties are relatively common, with m1 =\n33.6+2.8\n\u22122.2 M\u2299, m2 = 28.3+2.1\n\u22123.0 M\u2299, and spins con-\nsistent with zero, with effective inspiral spin \u03c7e\ufb00=\n\u22120.01+0.06\n\u22120.08. Due to its high SNR, it is a promising\nsignal for tests of relativity (Abac et al. 2025e).\n\u2022 The source of GW231028_153006 is a massive BBH,\nwith total mass M = 152+29\n\u221214 M\u2299. It has a large effec-\ntive inspiral spin \u03c7e\ufb00= 0.4+0.2\n\u22120.2 and unequal masses,\nwith mass ratio q = m2/m1 = 0.63+0.33\n\u22120.35. Similar\nto GW231123_135430 (Abac et al. 2025d), this event\ndisplays signi\ufb01cant systematic modeling uncertainties\nand multimodal posteriors.\n\u2022 GW231118_005626\nis\nanother\ncandidate\nwhose\nsource has unequal masses and signatures of large\nspins. The binary has total mass M = 30.9+5.3\n\u22123.6 M\u2299,\nq = 0.55+0.37\n\u22120.22, and large spins, with \u03c7e\ufb00= 0.4+0.1\n\u22120.1\nand \u03c71 = 0.65+0.28\n\u22120.38.\n\u2022 The source of GW231123_135430 (Abac et al. 2025d)\nis, with high probability, the most massive BBH in our\ncatalog of those with FAR < 1 yr\u22121. We infer it to\nhave total mass M = 236+29\n\u221248 M\u2299and large spins.\nIt also displays signi\ufb01cant systematic differences be-\ntween inferences made with different waveform mod-\nels.\nIn what follows we give further detail about our inferences\nof masses, spins, matter effects, and locations of the sources\nof our high-purity candidates from O4a, highlighting addi-\ntional sources that lie at the extremes of the parameter space\n(Sections 3.1\u20133.4). Some of our candidates display multi-\nple modes in their inferred source parameters. This multi-\nmodality complicates the interpretation of sources where it is\npresent (Abbott et al. 2023a), and it is not usually possible\nto isolate the probable reason for multiple modes. In Sec-\ntion 3.5 we discuss candidates which display multiple modes.\nSystematic uncertainties in our modeling affect our parame-\nter inference for some candidates. In Section 3.6 we dis-\ncuss these cases in greater detail, and present an analysis of\nthe consistency between model-based and minimally mod-\neled waveform reconstructions for a number of candidates.\n3.1. Masses\nThe masses of a compact binary source of GWs are often\nthe most well-constrained parameters as they are the primary\ndeterminant of the phase evolution of the signal (Abac et al.\n2025a,b). The component masses are of particular interest\nsince they indicate whether the compact objects are likely to\nbe BHs or NSs; however, combinations of the two masses\nsuch as the chirp mass M or total mass M are often more\nprecisely measured than the individual masses (e.g., Abac\net al. 2025a). For example, the chirp mass is the dominant\nparameter controlling the rate of binary inspiral, and so it\nis measured well in lower-mass systems where many cycles\nof inspiral can be observed (Kafka 1988; Finn & Chernoff\n1993; Cutler et al. 1993; Cutler & Flanagan 1994). Mean-\nwhile, the mass ratio q \u2261m2/m1 \u22641 is generally less well\nmeasured (Cutler et al. 1993; Cutler & Flanagan 1994; Pois-\nson & Will 1995).\nThe detectors measure the redshifted masses (1 + z)mi,\nwhere z is the source redshift (Krolak & Schutz 1987). To\nrecover the source-frame masses, we combine the measured\nredshifted masses with the inferred luminosity distance using\nan assumed cosmology (Ade et al. 2016). Due to the uncer-\ntainties in our estimation of the luminosity distance, source-\nframe mass parameters are generally less well constrained\nthan their redshifted values. By default we report source-\nframe mass values, using default agnostic priors as described\nabove.\nFigure 2 shows the marginalized one-dimensional\nposteriors for the chirp mass M and mass ratio q of each\nof the O4a candidates analyzed here. Figure 3 shows the\nmarginalized two-dimensional posteriors for the individual\ncomponent masses, m1 and m2, as well as for the total mass\nM and mass ratio q. Similarly, Figure 4 shows the marginal-\nized two-dimensional posteriors in M and effective inspiral\nspin \u03c7e\ufb00, described in Section 3.2. These representations\nof the inferred source masses of our newly added candidates\ndisplay a large range, with total masses spanning nearly two\norders of magnitude.\nWe use the inferred component masses to classify the prob-\nable nature of the binary components. For example, if one\ncomponent has a mass above the maximum possible mass of\na NS, we infer it to be a BH, even in the absence of other\nconstraints on the presence of matter in the binary (see Sec-\ntion 3.3). The maximum possible non-spinning NS mass is\nunknown, although data from terrestrial experiments, elec-\ntromagnetic observations of NSs, and GW detections have\nbeen used to bound this mass to \u223c2.2\u20132.5 M\u2299(e.g., Riley\net al. 2019; Miller et al. 2019; Lim et al. 2021; Landry et al.\n2020; Dietrich et al. 2020; Riley et al. 2021; Miller et al.\n2021; Legred et al. 2021; Raaijmakers et al. 2021; Huth et al.\n2022; Fan et al. 2024; Biswas & Rosswog 2025; Rutherford\net al. 2024; Golomb et al. 2025; Brandes & Weise 2025).\n\n15\nThe electromagnetic counterpart to GW170817 (Abbott et al.\n2017a,c) has been used together with models of the emis-\nsion to place more stringent limits on the maximum mass of\nnon-spinning NSs (e.g., Margalit & Metzger 2017; Rezzolla\net al. 2018; Ruiz et al. 2018; Abbott et al. 2020c; Nathanail\net al. 2021). On the other hand, spin increases the upper\nlimit of possible NS masses. To account for the remaining\nuncertainty, we very conservatively select 3 M\u2299as a robust\nupper limit on the maximum NS mass (Rhoades & Ruf\ufb01ni\n1974; Kalogera & Baym 1996).\nAs in GWTC-3.0 (Ab-\nbott et al. 2023a), we divide our candidates into two cate-\ngories: unambiguous BBHs, where both components are BHs\n(mi > 3 M\u2299at 99% probability), and potential-NS binaries\nwhere at least one component mass could have been a NS.\nGWTC-4.0 also contains candidates with FAR \u22651 yr\u22121\nfor which at least one detection pipeline assigns a probability\nof astrophysical origin pastro \u22650.5. Since we do not infer the\nsource properties of these candidates, the classi\ufb01cation of the\nsources of these candidates is provided through their multi-\ncomponent pastro values. All such candidates with nonzero\nprobability for containing a NS, as determined by pBNS +\npNSBH > 0.001, are given in Table 7.\n3.1.1. Candidates with m2 \u22653M\u2299: Unambiguous BBHs\nOur unambiguous BBH candidates span more than an or-\nder of magnitude in their inferred masses. Since the chirp\nmass is lower for asymmetric binaries at a \ufb01xed total mass,\nthe systems with the largest and smallest chirp masses do\nnot necessarily correspond to the most and least massive bi-\nnaries. Nevertheless, we \ufb01nd that the same two transients,\nGW231123_135430 and GW230627_015337, lie at the ex-\ntremes for both mass parameters. GW231123_135430 (Abac\net al. 2025d) probably has the largest chirp mass of the\ncandidates we analyze, with M = 101+13\n\u221230 M\u2299, as well\nas the largest total mass with M\n= 236+29\n\u221248 M\u2299.\nIt is\nthe most massive source in our catalog of those with FAR\n< 1 yr\u22121.\nGW230627_015337 is the unambiguous BBH\nwith the smallest chirp mass, M = 6.02+0.16\n\u22120.07 M\u2299, as well\nas the smallest total mass with M = 14.2+0.8\n\u22120.4 M\u2299.\nThe individual components of our BBHs span masses\nbetween 5.79+0.95\n\u22120.92 M\u2299\nand 137+23\n\u221218 M\u2299,\nwith primary\nmasses ranging from 8.37+1.67\n\u22121.26 M\u2299for GW230627_015337\nto 137+23\n\u221218 M\u2299for GW231123_135430,\nand secondary\nmasses ranging from 5.79+0.95\n\u22120.92 M\u2299to 101+22\n\u221251 M\u2299for\nGW230627_015337 and GW231123_135430, respectively.\nThe BBH mass distribution inferred using all the candidates\nin GWTC-4.0 is discussed in depth in Abac et al. (2025g).\nGW231123_135430 is probably more massive than the\nsource of the less signi\ufb01cant candidate GW190426_190642,\nwhich is inferred to have M = 182.3+40.2\n\u221235.7 M\u2299and a FAR\n> 1 yr\u22121, although with pastro \u22650.5 (Abbott et al. 2024).\nWith a 94% probability of m1 being greater than 120 M\u2299,\nGW231123_135430 has a component mass above the ap-\nproximate upper boundary of the pair-instability supernova\nmass gap (Woosley & Heger 2021; Mehta et al. 2022; Fowler\n& Hoyle 1964; Barkat et al. 1967; Fryer et al. 2001; Bel-\nczynski et al. 2016; Spera & Mapelli 2017; Stevenson et al.\n2019). In addition to GW231123_135430, several transients\nhave remnant mass Mf \u2265100 M\u2299, satisfying a conven-\ntional threshold to be considered intermediate-mass BHs.\nThe remnants of GW230704_212616, GW230922_040658,\nGW231005_021030, and GW231028_153006 all have >\n90% probability of Mf \u2265100 M\u2299.\nAt masses below 5 M\u2299there is a putative lower mass gap,\nhypothesized based on X-ray binary observations (Bailyn\net al. 1998; Ozel et al. 2010; Farr et al. 2011; Kreidberg\net al. 2012). We identify several unambiguous-BBH tran-\nsients whose secondary components could possibly fall into\nthis mass gap: GW230627_015337, GW231020_142947,\nGW231118_090602, and GW231223_075055. The sources\nof GW231020_142947 and GW231118_090602 are inferred\nto have m2 \u22645 M\u2299with 12% and 14% probability, respec-\ntively. Both of GW230627_015337 and GW231223_075055\nhave similar and slightly smaller probabilities of having sec-\nondary source mass m2 \u22645 M\u2299, 8% and 9% respectively.\nNo unambiguous-BBH candidate had signi\ufb01cant posterior\nsupport for a primary mass value in the lower mass gap.\nThe sources of several candidates have notable pos-\nterior support for unequal masses.\nGW231114_043211\nhas\nthe\nmost\nsupport\nof\nthe\nunambiguous\nBBHs,\nwith\na\nmass\nratio\nof\nq\n=\n0.36+0.27\n\u22120.17.\nIn\nad-\ndition,\nGW230702_185453,\nGW230712_090405,\nGW230928_215827, GW231001_140220, GW231004_232346,\nGW231118_005626, and GW231129_081745 all have mass\nratios \u22640.85 at the 90% credible level.\n3.1.2. Candidates with m2 < 3 M\u2299\nTwo candidates are consistent with sources containing a\nsecondary mass m2\n< 3 M\u2299, GW230518_125908 and\nGW230529_181500 (Abac et al. 2024a). We infer that these\ntwo candidates have negligible posterior support for m2 \u2265\n3 M\u2299. No con\ufb01dent multimessenger counterparts were re-\nported for either of these candidates, or any other O4a can-\ndidate. Without an electromagnetic counterpart, we can only\ninfer the presence of matter in a CBC via its impact on the\nGW signal. Matter can leave an imprint on the waveform\nduring inspiral through tidal effects, or modify the merger\nand postmerger dynamics, as discussed in Section 3.3.\nThe secondary of each system is consistent with the ob-\nserved Galactic NS population (Antoniadis et al. 2016; Als-\ning et al. 2018; Farrow et al. 2019; El-Badry et al. 2024).\nFurther, the mass of the primary of GW230518_125908 is\nwell above 3 M\u2299, with m1 = 8.17+0.84\n\u22120.92 M\u2299, leading us\nto conclude that this system is likely a NSBH.\nFurther,\nthe source of GW230518_125908 has clearly asymmetric\nmasses, with a mass ratio of q = 0.18+0.04\n\u22120.03. The source of\nGW230529_181500 is most probably another NSBH, since\nits primary mass m1 = 3.66+0.82\n\u22121.21 M\u2299is consistent with a\nlow-mass BH (Abac et al. 2024a).\n3.2. Spins\nCompared to the masses, spins have a weaker impact on\nthe GW emission and are more dif\ufb01cult to measure from ob-\n\n16\n\n17\nFigure 2.\nThe marginal probability distributions for the source frame chirp mass M, mass ratio q, effective inspiral spin \u03c7e\ufb00, effective\nprecession spin \u03c7p, and luminosity distance DL for O4a candidates with FAR < 1 yr\u22121. The colored upper half of the plot shows the marginal\nposterior distributions using our default agnostic priors (Abac et al. 2025b), while the white lower halves show these marginal distributions\nafter reweighting according to the inferred population model (Abac et al. 2025g) for each BBH. The two NSBH candidates have only the\nnon-reweighted posterior distributions. The vertical thickness of each region is proportional to the marginal posterior probability at that value\nfor each candidate.\n\n18\nFigure 3.\nCredible-region contours for O4a candidates with FAR < 1 yr\u22121. Top: Credible-region contours for the inferred primary and\nsecondary component masses m1 and m2. The upper shaded region denotes the area excluded by the convention m1 \u2265m2. The lower shaded\nregion denotes the most-extreme mass-ratio prior used by parameter-estimation analyses. Bottom:\nCredible-region contours for the inferred\ntotal mass M and mass ratio q. The dotted lines separate regions where the primary and secondary component masses are below 3 M\u2299. Each\ncontour indicates the 90% credible region for a given candidate. We use colors to highlight candidates: GW230518_125908 which is an NSBH\ncandidate; GW230529_181500 which is also an NSBH candidate with an inferred \u03c7e\ufb00< 0 at 92% credibility; GW231114_043211 which\nhas the largest support for the most unequal inferred mass ratio of the unambiguous BBHs; GW231118_005626 which has inferred \u03c7e\ufb00> 0;\nGW230814_230901 which is the highest SNR candidate observed in O4a; and GW231123_135430 which we infer to have the most-massive\nsource observed in O4a.\n\n19\nFigure 4.\nCredible-region contours in the chirp mass M and effective inspiral spin \u03c7e\ufb00plane for O4a candidates with FAR < 1 yr\u22121.\nEach contour indicates the 90% credible region for a given candidate.\nWe use colors to highlight candidates GW230518_125908;\nGW230529_181500 which has an inferred \u03c7e\ufb00< 0 at 92% credibility; GW231028_153006 and GW231118_005626 which have inferred\n\u03c7e\ufb00> 0; GW230814_230901 which was the highest-SNR candidate observed in O4a; and GW231123_135430 which we infer to have the\nmost-massive source observed in O4a.\n\n20\nservations (Poisson & Will 1995; Baird et al. 2013; Pratten\net al. 2020; Chatziioannou et al. 2015; Vitale et al. 2014;\nFarr et al. 2016; Vitale et al. 2017a; Abbott et al. 2016c;\nGarc\u00eda-Bellido et al. 2021). The component spins of com-\npact binaries, \u03c71 and \u03c72, are typically poorly constrained\nsince the leading-order spin contribution to the GW signal\nis determined by mass-weighted combinations of the com-\nponents (Damour 2001; Blanchet 2014; P\u00fcrrer et al. 2016;\nNg et al. 2018; Zevin et al. 2020). Here, we focus on two\nspeci\ufb01c mass-weighted spin parameters: the effective inspi-\nral spin \u03c7e\ufb00and the effective precession spin \u03c7p (Abac et al.\n2025a).\nThe effective inspiral spin \u03c7e\ufb00(Ajith et al. 2011; Santa-\nmaria et al. 2010) is a mass-weighted combination of the\ncomponents of the spin aligned with the Newtonian orbital\nangular momentum. It appears in the leading-order spin term\ndue to spin-orbit coupling at 1.5 post-Newtonian order, and\nis approximately conserved throughout the inspiral (Racine\n2008). Positive and negative \u03c7e\ufb00indicate that there is net\nspin aligned and anti-aligned, respectively, with the orbital\nangular momentum.\nThe effective precession spin \u03c7p (Schmidt et al. 2015)\nmeasures the mass-weighted in-plane spin component that\ncontributes to spin precession (Apostolatos et al. 1994; Kid-\nder 1995). It is bounded between 0 and 1, with \u03c7p = 0 in-\ndicating no spin precession and \u03c7p = 1 indicating maximal\nprecession. This parameter is typically weakly constrained,\nand posterior measurements of \u03c7p are often dominated by the\nprior.\nThe spin orientations \u03b8i of a binary are of particular inter-\nest for the insight they provide to its evolutionary history (Vi-\ntale et al. 2017b; Fishbach et al. 2017; Stevenson et al. 2017;\nTalbot & Thrane 2017; Wysocki et al. 2019; Zevin et al.\n2021).\nCompact binaries form via a myriad of channels,\nbut can be broadly classi\ufb01ed as either dynamically assembled\nor formed via isolated binary evolution. Roughly speaking,\nin dynamically formed binaries the spins are expected to be\nisotropically oriented, while binaries formed in isolation are\nexpected to have spins more nearly aligned with the orbital\naxis. Nonzero \u03c7p or negative \u03c7e\ufb00are therefore more consis-\ntent with dynamically formed binaries than those formed in\nisolation. Further discussion of the connection between spin\norientations and compact binary formation channels is given\nin Abac et al. (2025g).\nMost of the candidates analyzed from O4a are consis-\ntent with having sources with \u03c7e\ufb00= 0, as seen in Fig-\nures 2 and 4.\nHowever, 16 candidates have sources with\n\u03c7e\ufb00\u22650 with greater than 90% probability. Two sources\nwith notably large \u03c7e\ufb00values are that of GW231028_153006\nwith \u03c7e\ufb00= 0.4+0.2\n\u22120.2, and that of GW231118_005626 with\n\u03c7e\ufb00= 0.4+0.1\n\u22120.1. GW231123_135430 is inferred to have large\ncomponent spins (Abac et al. 2025d) and has a 88% prob-\nability of \u03c7e\ufb00> 0. Fewer candidates are probable to have\nnegative effective inspiral spins, with only 3 sources having\n\u03c7e\ufb00< 0 with greater than 90% probability. Of these, is\nremarkable. This candidate has the second largest SNR of\nthose in GWTC-4.0, with an SNR of 33.7+0.1\n\u22120.1. Its source\nFigure 5.\nPosterior (upper,\ncoloured);\nand the ef-\nfective prior (lower,\nwhite) probability distributions for the\ndimensionless\neffective\nprecession\nspin\n\u03c7p\nfor\ncandidates\nGW230518_125908,\nGW230627_015337,\nGW230712_090405,\nGW230814_230901,\nGW231028_153006,\nGW231114_043211,\nand GW231123_135430. Vertical lines mark the median and sym-\nmetric 90% interval for the distributions. These candidates are the\nones which show the greatest deviation between the posterior distri-\nbution and the effective prior over the \u03c7p parameter from the set of\nnew candidates presented in this work.\nhas \u03c7e\ufb00= \u22120.09+0.09\n\u22120.10, and \u03c7e\ufb00< 0 with 93% probability.\nAnother is the NSBH candidate GW230529_181500 (Abac\net al. 2024a), whose source has \u03c7e\ufb00< 0 with 92% probabil-\nity when analyzed with our \ufb01ducial set of waveforms (Abac\net al. 2025b).\nFigure 5 shows the \u03c7p posterior probability distribution\ncompared to the prior distribution after conditioning on the\n\u03c7e\ufb00measurement (Abbott et al. 2019a), for a selection of\ncandidates. These distributions would be the same if no in-\nformation about the in-plane spin components had been ex-\ntracted from the signal, and the selected candidates have the\ngreatest difference between the two distributions. For most\nof the candidates, the \u03c7p posteriors are broad and uninfor-\nmative.\nFigure 6 shows the posterior distribution of the source\ncomponent spin magnitudes \u03c7i and tilt angles \u03b8i inferred\nfor a subset of the analyzed candidates.\nThese candi-\ndates are highlighted due to their relatively strong spin con-\nstraints, exceptional nature, or presence of systematic differ-\nences in the inferences made with different waveform mod-\nels (Section 3.6). We exclude exceptional candidates whose\nspin magnitudes and tilt angles have been reported else-\nwhere (Abac et al. 2024a, 2025e,d). In many other cases the\ncomponent spins of the sources are poorly measured and our\nposteriors are similar to our priors. For those binaries where\n\u03c7e\ufb00is constrained to be relatively small, the posteriors of the\ncomponent spins may be concentrated in the equatorial plane\neven without positive evidence for precession, due to ruling\n\n21\nFigure 6.\nPosterior probability distributions for the dimensionless component spins \u03c71 = cS1/(Gm2\n1) and \u03c72 = cS2/(Gm2\n2)\n(with S1 and S2 the spin vectors of the components) relative to the orbital plane, marginalized over azimuthal angles, for can-\ndidates GW230518_125908, GW230624_113103, GW230627_015337, GW230712_090405, GW231028_153006, GW231114_043211,\nGW231118_005626, GW231118_090602, and GW231226_101520. In these plots, the histogram bins are constructed linearly in spin magni-\ntude and the cosine of the tilt angles such that they contain equal prior probability.\nout spins either relatively aligned or anti-aligned with the or-\nbital angular momentum (Abbott et al. 2017d).\nOf the sources analyzed from O4a, GW231123_135430\nis inferred to have the highest primary spin magnitude,\n\u03c71 = 0.90+0.08\n\u22120.27 (Abac et al. 2025d). Two other systems\nwhich are inferred to have high primary spins are the sources\nof GW230928_215827 and GW231028_153006, for which\n\u03c71 > 0.8 with 44% and 47% probabilities, respectively.\nThe \ufb01nal spin \u03c7f of the remnant BH following coales-\ncence has contributions from the orbital angular momentum\nat merger and the spin angular momenta of the binary com-\nponents. It is determined for our BBH candidates from the\ninferred component masses and spins, using \ufb01ts to numeri-\ncal relativity simulations (Abac et al. 2025b). The candidates\nwith \u03c7f > 0.75 at 90% probability are GW231028_153006,\nand GW231118_005626.\n3.3. Tidal effects\nBinary systems with at least one NS component display\nmodi\ufb01cations to their gravitational waveform due to the pres-\n\n22\nence of matter in the system. During the inspiral, tidal defor-\nmations of the NS constituents are imprinted on the wave-\nform (Flanagan & Hinderer 2008; Vines et al. 2011; Pan-\nnarale et al. 2011). Tidal effects are quanti\ufb01ed by the tidal\ndeformability parameter of each component \u039bi, which are\nlarger for stiffer NS equations of state and smaller for softer\nones. Matter effects also modify the \ufb01nal merger and post-\nmerger phases of the GW signal at relatively high frequen-\ncies (e.g., Abbott et al. 2017e, 2019d). For example, the GW\nemission from these phases may be truncated in NSBH sys-\ntems if the NS is tidally disrupted before merger (Kyutoku\net al. 2021). At the sensitive frequencies of current detectors,\ntidal effects are the dominant source of information about\nmatter effects in GW signals.\nFor the new candidates detected in O4a, only two\nsources have component masses consistent with one of\nthe two components being a NS, GW230518_125908 and\nGW230529_181500 (see Section 3.1.2). We have analyzed\nthe GW signal from GW230518_125908 with three wave-\nform models which include tidal effects, and in all cases\nthe data do not constrain \u039b2, as expected given the signal\u2019s\nSNR and our mass inferences. Similarly, when analyzing\nGW230529_181500 with NSBH waveform models, the data\ndo not constrain the tidal deformability \u039b2 of the NS (Abac\net al. 2024a).\n3.4. Localization\nAs GW detectors continue to improve their sensitivity, we\nare able to observe GW sources from a greater range of cos-\nmic distances. The closest source observed in O4a is prob-\nably that of the NSBH candidate GW230529_181500, in-\nferred to be at a luminosity distance DL = 0.20+0.10\n\u22120.10 Gpc.\nThe more massive NSBH source of GW230518_125908 was\nalso inferred to be nearby, and probably closer than any BBH\ncandidate (DL = 0.24+0.11\n\u22120.10 Gpc).\nDuring O4a a number of relatively nearby BBH signals\nwere also observed.\nThe source which is probably the\nclosest of these is also the source of the highest-SNR GW\ncandidate detected through O4a, GW230814_230901 (Abac\net al. 2025e), with DL\n=\n0.28+0.17\n\u22120.13 Gpc .\nHowever\nGW230627_015337 (DL = 0.31+0.06\n\u22120.13 Gpc), which has a\nlarge network SNR of 28.5 and is also the lightest BBH with\nM = 14.2+0.8\n\u22120.4 M\u2299may be closer; both events have consider-\nable overlap between the credible ranges of their luminosity\ndistances.\nThe farthest source of the candidates analyzed is proba-\nbly for GW230704_212616, which is inferred to lie at DL =\n7.2+6.1\n\u22124.2 Gpc. As there are several candidates with sources at\nsimilar distances, GW230704_212616 has only a 22% proba-\nbility of having the most-distant source. The next most prob-\nable to have the most-distant source is GW231119_075248\nat DL = 6.7+5.5\n\u22123.7 Gpc, with a 15% probability of being\nthe most distant candidate. These distant candidates are at\ncomparable, but probably larger, luminosity distances than\nthe farthest sources detected in third observing run (O3)\nwith FAR < 1 yr\u22121, for example GW190805_211137 with\nDL = 6.1+3.7\n\u22123.1 Gpc (Abbott et al. 2024).\nThe inferred sky location of each candidate depends\nlargely on the number of observing GW detectors at the time\nof the detection (Schutz 1986; Fairhurst 2009, 2011; Nis-\nsanke et al. 2011; Veitch et al. 2012; Nissanke et al. 2013;\nKasliwal & Nissanke 2014; Grover et al. 2014; Singer et al.\n2014; Berry et al. 2015; Abbott et al. 2020a). During O4a\nonly the two LIGO detectors were operating with signi\ufb01cant\nsensitivity to CBC signals. As as result, even the best local-\nized new candidates in GWTC-4.0 have greater uncertainties\nin their sky location than many candidates detected previ-\nously with a network that included the Virgo detector (Abbott\net al. 2019a,d, 2021b, 2024, 2023a). While the NSBH can-\ndidate GW230529_181500 is inferred to be nearby, it was\nonly detected in the Livingston detector and as such it is\npoorly localized in the sky (Abac et al. 2024a). Meanwhile\nGW230518_125908 was observed with both LIGO detec-\ntors, and it is constrained to a sky area of 490 deg2 (90%\ncredible level). The best localized candidate in terms of sky\narea is the lowest-mass BBH candidate GW230627_015337,\nwhich is inferred to lie in a region of sky of 110 deg2 (90%\ncredible level).\nThe highest-SNR candidate GW230814_230901 was de-\ntected in only the Livingston detector. In common with other\ncandidates identi\ufb01ed in only a single observatory, it is only\nweakly localised by the antenna pattern of the detector. This\nis true also of the NSBH candidate GW230529_181500 de-\nspite being inferred to be nearby.\nThe three-dimensional volume localization of each candi-\ndate depends on both its inferred distance and sky localiza-\ntion (Singer et al. 2016; Del Pozzo et al. 2018). Broadly\nspeaking, nearby candidates have the best volume local-\nization, provided they are observed in multiple detectors.\nThe NSBH candidate GW230518_125908 is well-localized\nas compared to the other candidates in O4a, to a vol-\nume 0.0019 Gpc3 (90% credible level).\nThe candidate\nwith the best three-dimensional localization from O4a is\nGW230627_015337, which has a 90% credible volume of\n0.00062 Gpc3. The next best localized BBH is probably the\nsecond-highest SNR candidate GW231226_101520, which\nhas a SNR of 33.7 and is constrained to a comparatively\nmuch larger 90% credible volume of 0.056 Gpc3.\n3.5. Multimodality\nAs\nwith\nsome\nof\nthe\ncandidates\nreported\nin\nGWTC-3.0 (Abbott et al. 2023a), a few of our candidates\ndisplay multimodal posteriors. Multimodality can be an in-\ndication that the inferred parameters of a candidate lie in a\nregion where our waveform models have a complex structure\nand where subtle changes in modeling may be important.\nThis is especially true when models incorporate higher-order\nmultipole moments (Nitz et al. 2021; Estell\u00e9s et al. 2022b;\nMehta et al. 2022; Chia et al. 2022) or precession (Abbott\net al. 2019d, 2020d). Multiple modes can also arise from\nnoise \ufb02uctuations in low-SNR signals (Huang et al. 2018)\ndue to the presence of glitches (Powell 2018; Chatziioannou\net al. 2021; Ashton et al. 2022; Soni et al. 2025), or through\nthe overlap of multiple signals (Relton & Raymond 2021),\n\n23\nalthough this \ufb01nal possibility is unlikely at current detection\nrates. As a result, multimodality is expected in at least some\ncases.\nIn addition if the inferences drawn using different\nwaveform models display signi\ufb01cant systematic differences\nfor a given candidate, multimodality can be produced upon\ncombining samples across each model for our \ufb01nal infer-\nences.\nMost mass posterior distributions are unimodal,\nas\nshown in Figure 2.\nCandidates which display multi-\nple modes in the distribution of their inferred source\nmasses are GW230712_090405, GW230723_101834, and\nGW231118_090602.\nThe sources of GW230712_090405\nand GW230723_101834 are inferred to have bimodal chirp\nmasses. Since the uncertainty in redshift tends to broaden\nour mass inferences in the source frame, the bimodalities\nfor these two candidates are more easily seen in the red-\nshifted chirp mass (1 + z)M posteriors.\nAdditionally,\nGW231118_090602, a system with M = 8.37+0.76\n\u22120.56 M\u2299,\nshows multimodality in m2.\nMultimodality in posterior distributions for mass pa-\nrameters often correlates with multiple modes in other\nparameters, especially spin quantities.\nThis is true of\nGW230723_101834, whose multiple modes are prominently\nseen in the two-dimensional marginalized distribution of the\ndetector frame chirp mass (1 + z)M and effective inspiral\nspin \u03c7e\ufb00.\nSimilarly, for GW231118_090602 the mode at\nsmaller m2 values correlates with a mode of higher \u03c7e\ufb00val-\nues.\nThe degree of multimodality can depend on the wave-\nform model.\nFor example, the bimodality in (1 + z)M\nfor GW230712_090405 is present for all models, but for\nIMRPHENOMXO4A the multimodality in this parameter\nis more prominent, with additional modes present.\nFor\nGW231118_090602, m2 is unimodal when analyzed us-\ning SEOBNRV5PHM and bimodal when using IMRPHE-\nNOMXPHM_SPINTAYLOR. The two high-mass candidates\nGW231028_153006 and GW231123_135430 display both\nmultimodal mass inferences for some waveform models, and\nsystematic differences between models that generate further\nmultimodality upon combining samples. More detailed dis-\ncussion of this multimodality for GW231123_135430 may\nbe found in Abac et al. (2025d).\nThe candidate GW231001_140220 displayed bimodal\nposteriors for M in our preliminary analysis using the de-\nfault lower-frequency cutoff (20 Hz) for our likelihood inte-\ngration and the IMRPHENOMXPHM_SPINTAYLOR wave-\nform model. While our initial data-quality checks did not\nindicate a glitch coincident with this candidate, i.e., a glitch\nwith support in time and frequency overlapping the candidate\nsignal, further parameter-estimation analysis using data from\nindividual detectors indicated possible non-Gaussian noise in\nthe Livingston detector at the time of the detection. When\nanalyzed with a lower-frequency cutoff of flow = 40 Hz in\nthe likelihood integral for the Livingston data, we obtain uni-\nmodal posteriors while losing only a small amount of the to-\ntal SNR for this candidate. We present our parameter infer-\nences for this candidate using this narrower frequency range.\n3.6. Waveform systematics and consistency\nThe results presented in this paper are the combined sam-\nples from a number of parameter-estimation analyses that\nuse different waveform models (Abac et al. 2025b).\nThe\ncombined samples include results obtained with IMRPHE-\nNOMXPHM_SPINTAYLOR and SEOBNRV5PHM for all\ncandidates. Additionally, for candidates with source prop-\nerties within the model\u2019s calibration region, we also in-\nclude results obtained with NRSUR7DQ4, and where anal-\nyses were conducted using the IMRPHENOMXO4A model\nfor an event these are also shown. For the high-mass can-\ndidate GW231123_135430 we additionally use the time-\ndomain phenomenological model IMRPHENOMTPHM (Es-\ntell\u00e9s et al. 2022a), and samples are combined across the \ufb01ve\nmodels (Abac et al. 2025d). Here we focus on systematic\ndifferences among the two to four \ufb01ducial models used to\nanalyze the bulk of our BBH candidates.\nWe \ufb01nd that for almost all the signals analyzed here, the\ndifferences between results obtained with the different mod-\nels are subdominant compared to the statistical uncertainty.\nAs for previous observations, differences are typically small,\nand most noticeable for parameters like the spins (Abbott\net al. 2016d, 2019a,d, 2021b). For candidates that show sig-\nni\ufb01cant differences between waveform models, potentially\ndue to systematic uncertainties from waveform modeling, we\nplot a selection of the posteriors for all models in Figure 7.\nAdditionally, in Table 4 we show the median and 90% cred-\nible intervals for these source parameters as inferred by each\nwaveform model used in our analysis, along with our \ufb01ducial\ninferences from combining the samples across models (Abac\net al. 2025b). The candidates we identi\ufb01ed with signi\ufb01cant\nsystematics between waveform models are:\n\u2022 GW230624_113103, a BBH candidate, whose source\nhas a total mass M\n=\n43.8+11.1\n\u22126.6 M\u2299.\nThe\ninferred values of its mass ratio q show visible\ndifferences between IMRPHENOMXPHM_SPINTAY-\nLOR and SEOBNRV5PHM results, with SEOB-\nNRV5PHM favoring more asymmetric masses. This\nresults in systematic differences in the inferred compo-\nnent masses. These differences are correlated with our\nknowledge of the spin parameters of the source, and we\nfavor larger values of both \u03c7e\ufb00and \u03c7p when analyzing\nthis candidate with SEOBNRV5PHM as compared to\nIMRPHENOMXPHM_SPINTAYLOR.\n\u2022 GW231028_153006, which displays signi\ufb01cant sys-\ntematic variations in its source mass and spin infer-\nences across waveform models.\nFor this candidate,\nno data-quality issues requiring mitigation were iden-\nti\ufb01ed. We apply all four of our BBH waveform mod-\nels in our inferences for GW231028_153006, and none\nof the models show close agreement with each other\nacross component masses. Systematic differences in\nour inferences of \u03c7e\ufb00are also visible, and a subdom-\ninant, second mode at high \u03c7p values is visible in the\nsamples drawn with IMRPHENOMXO4A. These sys-\n\n24\nFigure 7. The marginal probability distributions for the (source-frame) total mass M, mass ratio q, effective inspiral spin \u03c7e\ufb00, and effective\nprecession spin \u03c7p for \ufb01ve O4a candidates which show signi\ufb01cant waveform systematics.\ntematic differences broaden our uncertainties in our\noverall combined results for this candidate, but it is\nclear that its source is massive, with M = 152+29\n\u221214 M\u2299\nand m1 = 95+33\n\u221220 M\u2299. The source of this candidate\nprobably has a large \u03c7e\ufb00and has support for a large\nprimary spin \u03c71.\n\u2022 GW231118_005626, a BBH candidate, whose source\nhas M = 30.9+5.3\n\u22123.6 M\u2299and credibly unequal masses\nq\n= 0.55+0.37\n\u22120.22.\nThe source has large and well-\nmeasured effective inspiral spin, \u03c7e\ufb00\n=\n0.4+0.1\n\u22120.1.\nFor this candidate the inferences drawn with SEOB-\nNRV5PHM and IMRPHENOMXO4A are in good\nagreement, but display some differences with those\ndrawn using the IMRPHENOMXPHM_SPINTAYLOR\nmodel. The total mass and chirp mass posteriors dis-\nplay a heavier tail towards larger values for IMR-\nPHENOMXPHM_SPINTAYLOR.\nMore apparent are\nthe differences in the \u03c71 and \u03c7p posteriors, which for\nIMRPHENOMXPHM_SPINTAYLOR extend towards\nhigher values than those obtained with the other two\nmodels.\n\u2022 GW231118_090602, whose source is a relatively low-\nmass BBH with M = 20.7+10.2\n\u22122.3 M\u2299and mass ra-\ntio q = 0.56+0.38\n\u22120.41.\nThis candidate displays multi-\nmodal source mass and spin posteriors, as discussed\nin Section 3.5.\nThis multimodality is present only\nin the posterior samples drawn using the IMRPHE-\nNOMXPHM_SPINTAYLOR model, which includes a\ndistinct high-likelihood mode at q \u223c0.15, which cor-\nrelates with larger values of \u03c7e\ufb00\u223c0.4. This mode\nat asymmetric masses also correlates with systemati-\ncally larger \u03c7p values than the broader mode at more\nequal masses, which has 0.3 \u2272q \u22721. Meanwhile\nthe samples drawn using SEOBNRV5PHM are uni-\nmodal in masses and spins, and largely agree with the\nhigher-q mode from IMRPHENOMXPHM_SPINTAY-\nLOR, although they favor a larger median \u03c7p than the\nIMRPHENOMXPHM_SPINTAYLOR results.\n\u2022 GW231123_135430 displays signi\ufb01cant systematic\ndifferences in its inferred source mass and spins, de-\npending on the waveform model (Abac et al. 2025d).\n\n25\nTable 4. Median and 90% symmetric CIs for selected source properties as inferred by different waveform models.\nCandidate\nModel\nM\n[M\u2299]\nq\n\u03c7e\ufb00\n\u03c7p\nDL\n[Gpc]\nGW230624_113103\nMIXED\n18.0+3.2\n\u22122.4\n0.59+0.35\n\u22120.29\n0.2+0.3\n\u22120.3\n0.39+0.42\n\u22120.28\n1.9+1.3\n\u22121.0\nIMRPHENOMXPHM_SPINTAYLOR\n17.7+2.9\n\u22122.2\n0.63+0.32\n\u22120.32\n0.1+0.3\n\u22120.2\n0.34+0.43\n\u22120.25\n2.0+1.2\n\u22121.0\nSEOBNRV5PHM\n18.4+3.3\n\u22122.5\n0.55+0.37\n\u22120.26\n0.2+0.3\n\u22120.3\n0.44+0.40\n\u22120.31\n1.9+1.3\n\u22120.9\nGW231028_153006\nMIXED\n63+13\n\u221210\n0.63+0.33\n\u22120.35\n0.4+0.2\n\u22120.2\n0.52+0.30\n\u22120.29\n4.1+1.4\n\u22121.9\nIMRPHENOMXPHM_SPINTAYLOR 64.3+13.4\n\u22127.8\n0.71+0.25\n\u22120.36\n0.5+0.1\n\u22120.2\n0.49+0.29\n\u22120.30\n4.5+1.2\n\u22122.0\nSEOBNRV5PHM\n63.5+13.4\n\u22127.9\n0.57+0.39\n\u22120.29\n0.5+0.1\n\u22120.2\n0.53+0.28\n\u22120.29\n4.0+1.3\n\u22121.8\nNRSUR7DQ4\n59.8+14.0\n\u22129.6\n0.53+0.43\n\u22120.26\n0.4+0.2\n\u22120.2\n0.50+0.29\n\u22120.26\n4.1+1.4\n\u22121.9\nIMRPHENOMXO4A\n62+12\n\u221211\n0.61+0.35\n\u22120.35\n0.4+0.2\n\u22120.2\n0.54+0.32\n\u22120.29\n4.0+1.6\n\u22121.8\nGW231118_005626\nMIXED\n12.6+1.6\n\u22121.1\n0.55+0.37\n\u22120.22\n0.4+0.1\n\u22120.1\n0.44+0.34\n\u22120.27\n2.2+0.9\n\u22121.0\nIMRPHENOMXPHM_SPINTAYLOR\n12.7+1.6\n\u22121.1\n0.50+0.39\n\u22120.21\n0.4+0.1\n\u22120.1\n0.48+0.31\n\u22120.31\n2.1+1.0\n\u22121.0\nSEOBNRV5PHM\n12.5+1.6\n\u22121.1\n0.58+0.35\n\u22120.21\n0.4+0.1\n\u22120.1\n0.40+0.36\n\u22120.25\n2.3+0.9\n\u22121.0\nIMRPHENOMXO4A\n12.6+1.6\n\u22121.1\n0.56+0.35\n\u22120.20\n0.4+0.1\n\u22120.1\n0.45+0.31\n\u22120.27\n2.2+0.9\n\u22120.9\nGW231118_090602\nMIXED\n8.37+0.76\n\u22120.56\n0.56+0.38\n\u22120.41\n0.08+0.36\n\u22120.09\n0.36+0.43\n\u22120.27\n1.4+0.5\n\u22120.6\nIMRPHENOMXPHM_SPINTAYLOR 8.37+0.76\n\u22120.56\n0.51+0.42\n\u22120.38\n0.1+0.4\n\u22120.1\n0.35+0.40\n\u22120.25\n1.4+0.5\n\u22120.6\nSEOBNRV5PHM\n8.38+0.77\n\u22120.57\n0.60+0.34\n\u22120.33\n0.07+0.21\n\u22120.08\n0.38+0.45\n\u22120.28\n1.3+0.6\n\u22120.6\nGW231123_135430\nMIXED\n101+13\n\u221230\n0.74+0.22\n\u22120.38\n0.3+0.2\n\u22120.4\n0.72+0.19\n\u22120.28\n2.2+2.0\n\u22121.5\nIMRPHENOMXPHM_SPINTAYLOR\n100+13\n\u221215\n0.61+0.13\n\u22120.14\n0.01+0.17\n\u22120.24\n0.75+0.18\n\u22120.23\n0.89+0.39\n\u22120.34\nSEOBNRV5PHM\n105+13\n\u221211\n0.82+0.15\n\u22120.20\n0.4+0.2\n\u22120.2\n0.64+0.22\n\u22120.27\n2.2+1.4\n\u22121.0\nNRSUR7DQ4\n103+10\n\u221214\n0.85+0.13\n\u22120.16\n0.3+0.2\n\u22120.4\n0.72+0.20\n\u22120.29\n1.8+1.6\n\u22121.0\nIMRPHENOMXO4A\n75+13\n\u221210\n0.39+0.07\n\u22120.16\n0.3+0.2\n\u22120.2\n0.82+0.11\n\u22120.14\n3.5+1.3\n\u22121.4\nNOTE\u2014 Values are given for a subset of the GW event candidates from O4a with FAR < 1 yr\u22121 which show signi\ufb01cant waveform\nsystematics. The columns show chirp mass M, mass ratio q, effective inspiral spin \u03c7e\ufb00, effective precession spin \u03c7p, and luminosity\ndistance DL. The MIXED row gives our \ufb01ducial estimates, derived from combining samples from all available models equally (Abac et al.\n2025b). For the exceptional event GW231123_135430, we include samples from an additional model IMRPHENOMTPHM (Estell\u00e9s\net al. 2022a) in the MIXED samples (Abac et al. 2025d). We also evolve the spin quantities for all waveform in GW231123_135430 to a\nlarge binary separation (Abac et al. 2025b).\nOne possible source of systematic differences in our infer-\nences is signal content that may be absent from our default\nCBC models. A method for testing for any missing signal\ncontent, or even to discover unexpected phenomena, is to es-\ntimate the overlap between the modeled reconstructions of\nour GW signals and the minimally modeled waveform re-\nconstructions (Abac et al. 2025b). We test for missing signal\ncontent by selecting a subset of our O4a GW candidates and\ncomparing their source inferences generated with the NR-\nSUR7DQ4 waveform (Varma et al. 2019) to reconstructions\nmade with minimal assumptions about the waveform mor-\nphology. We select 23 candidates using criteria to optimize\nperformance of the minimally modeled reconstruction meth-\nods (Abac et al. 2025b).\nTo assess the statistical signi\ufb01cance of the overlap between\nthese reconstructions, we perform systematic injection stud-\nies (Abbott et al. 2019a; Salemi et al. 2019; Ghonge et al.\n2020; Abbott et al. 2021b; Johnson-McDaniel et al. 2022).\nWe inject simulated signals with parameters drawn from the\nposterior distributions into nearby detector data not overlap-\nping the candidate time. These off-source waveforms are\nthen reconstructed using minimally modeled methods. By\ncomparing the overlaps between the on-source reconstruc-\ntion of the actual candidate and the distribution of off-source\noverlaps, we compute a p-value indicating the fraction of off-\nsource overlaps greater than or equal to the on-source over-\nlap.\nWe\nuse\nthree\nmethods\nfor\nreconstructing\nthe\nsig-\nnals with minimal assumptions about their morphology:\nBAYESWAVE (Cornish & Littenberg 2015; Littenberg &\nCornish 2015; Cornish et al. 2021) and CWB-2G (Klimenko\net al. 2016; Drago et al. 2020), which are designed for generic\nGW transients, and CWB-BBH (Klimenko 2022), which is\noptimized speci\ufb01cally for CBC signals. The results, summa-\nrized in Table 5 and shown in Figure 8, show no signi\ufb01cant\ndeviations between the on-source and off-source reconstruc-\ntions across all three methods. However, as noted in Abac\net al. (2025b), all three pipelines show some level of bias in\ntheir respective tests to assess the p-values.\n\n26\nTable 5. The on-source and the median off-source overlap (with 90% con\ufb01dence intervals) values, and p-values for three\nminimally-modeled waveform reconstruction methods on a selection of candidates.\nCandidate\nBAYESWAVE\nCWB-2G\nCWB-BBH\nOn-source Off-source p-value On-source Off-source p-value On-source Off-source p-value\nGW230601_224134\n0.85\n0.89+0.06\n\u22120.17\n0.34\n0.91\n0.91+0.04\n\u22120.07\n0.43\n0.93\n0.91+0.04\n\u22120.07\n0.83\nGW230606_004305\n0.91\n0.78+0.11\n\u22120.40\n0.97\n0.92\n0.85+0.06\n\u22120.11\n0.99\n0.94\n0.86+0.06\n\u22120.11\n0.99\nGW230608_205047\n0.80\n0.83+0.09\n\u22120.18\n0.39\n0.89\n0.86+0.06\n\u22120.12\n0.73\n0.91\n0.86+0.06\n\u22120.10\n0.91\nGW230609_064958\n0.75\n0.71+0.16\n\u22120.39\n0.60\n0.79\n0.82+0.07\n\u22120.14\n0.28\n0.92\n0.84+0.07\n\u22120.13\n0.99\nGW230628_231200\n0.93\n0.89+0.05\n\u22120.14\n0.84\n0.92\n0.90+0.03\n\u22120.05\n0.79\n0.92\n0.91+0.03\n\u22120.06\n0.64\nGW230702_185453\n0.60\n0.64+0.22\n\u22120.60\n0.40\n0.82\n0.78+0.08\n\u22120.14\n0.73\n0.88\n0.81+0.08\n\u22120.13\n0.90\nGW230707_124047\n0.88\n0.85+0.08\n\u22120.19\n0.67\n0.90\n0.88+0.05\n\u22120.09\n0.69\n0.91\n0.89+0.05\n\u22120.10\n0.72\nGW230708_230935\n0.80\n0.78+0.14\n\u22120.70\n0.56\n0.89\n0.86+0.06\n\u22120.12\n0.80\n0.93\n0.87+0.06\n\u22120.13\n0.95\nGW230814_061920\n0.77\n0.82+0.11\n\u22120.43\n0.26\n0.85\n0.88+0.06\n\u22120.10\n0.31\n0.87\n0.89+0.05\n\u22120.09\n0.30\nGW230824_033047\n0.89\n0.84+0.08\n\u22120.24\n0.74\n0.91\n0.88+0.06\n\u22120.09\n0.71\n0.96\n0.89+0.05\n\u22120.09\n1.00\nGW230914_111401\n0.95\n0.93+0.03\n\u22120.07\n0.85\n0.92\n0.93+0.02\n\u22120.04\n0.29\n0.95\n0.94+0.03\n\u22120.04\n0.76\nGW230920_071124\n0.83\n0.76+0.14\n\u22120.65\n0.65\n0.80\n0.80+0.08\n\u22120.14\n0.48\n0.84\n0.83+0.07\n\u22120.15\n0.58\nGW230922_020344\n0.79\n0.86+0.08\n\u22120.24\n0.22\n0.73\n0.80+0.07\n\u22120.19\n0.16\n0.84\n0.84+0.05\n\u22120.12\n0.52\nGW230922_040658\n0.87\n0.89+0.06\n\u22120.13\n0.41\n0.92\n0.91+0.04\n\u22120.08\n0.75\n0.94\n0.92+0.03\n\u22120.08\n0.74\nGW230924_124453\n0.84\n0.81+0.09\n\u22120.31\n0.67\n0.86\n0.84+0.06\n\u22120.10\n0.71\n0.87\n0.86+0.05\n\u22120.10\n0.55\nGW230927_043729\n0.83\n0.79+0.11\n\u22120.32\n0.72\n0.88\n0.83+0.07\n\u22120.12\n0.89\n0.90\n0.85+0.06\n\u22120.13\n0.88\nGW231028_153006\n0.99\n0.97+0.02\n\u22120.04\n0.99\n0.97\n0.96+0.01\n\u22120.02\n0.74\n0.97\n0.97+0.01\n\u22120.02\n0.42\nGW231102_071736\n0.91\n0.92+0.04\n\u22120.10\n0.43\n0.95\n0.93+0.03\n\u22120.05\n0.88\n0.96\n0.94+0.03\n\u22120.05\n0.97\nGW231123_135430\n0.97\n0.96+0.02\n\u22120.06\n0.74\n0.96\n0.96+0.01\n\u22120.03\n0.57\n0.98\n0.96+0.01\n\u22120.03\n0.92\nGW231206_233134\n0.89\n0.87+0.07\n\u22120.24\n0.69\n0.84\n0.86+0.06\n\u22120.10\n0.36\n0.88\n0.88+0.05\n\u22120.11\n0.48\nGW231206_233901\n0.96\n0.95+0.02\n\u22120.03\n0.63\n0.94\n0.93+0.02\n\u22120.03\n0.76\n0.96\n0.95+0.02\n\u22120.04\n0.78\nGW231213_111417\n0.84\n0.74+0.15\n\u22120.53\n0.82\n0.85\n0.83+0.07\n\u22120.12\n0.66\n0.90\n0.85+0.06\n\u22120.14\n0.89\nGW231226_101520\n0.99\n0.98+0.01\n\u22120.01\n0.88\n0.96\n0.97+0.01\n\u22120.01\n0.19\n0.97\n0.97+0.01\n\u22120.01\n0.34\nNOTE\u2014The three minimally-modeled waveform reconstruction methods used were BAYESWAVE, CWB-2G (both designed for generic\ngravitational-wave bursts), and CWB-BBH (speci\ufb01cally optimized for CBC signals with tailored frequency bands and time-frequency\nresolutions). The p-values are calculated by comparing the on-source value with the off-source distribution of overlaps.\nTaken together, these studies show that while a few of the\nnew candidates added to GWTC-4.0 show noticeable system-\natic uncertainties in our inferences of their source properties,\nthere is as yet no strong evidence for missing signal content\nin our models.\n4. CONCLUSION\nWe present GWTC-4.0 which contains 218 CBC events\nwith pastro \u22650.5 and which are not determined to be likely\nof instrumental origin during further event validation. Ana-\nlyzing data from O4a, this version of the catalog adds 128\nGW candidates consistent with BBHs and NSBHs to the cu-\nmulative catalog of events, more than doubling the census\nof CBCs passing these criteria from the \ufb01rst three observing\nruns (Abbott et al. 2023a). For high-signi\ufb01cance candidates\nwith FARs < 1 yr\u22121, we also estimate their source prop-\nerties. These include: GW230518_125908, a new NSBH\nsignal observed during the engineering run preceding O4a\nwith detailed analysis presented for the \ufb01rst time in this\ncatalog; GW230529_181500, which most likely originates\nfrom an NSBH binary with a primary mass \u22645M\u2299(Abac\net al. 2024a); GW230814_061920, the highest-SNR event\nobserved so far (Abac et al. 2025e); and GW231123_135430,\nthe most-massive BBH in the catalog (Abac et al. 2025d)\nwith a FAR < 1 yr\u22121.\nAdditional results related to candidates in the catalog\nare interpreted in other papers of the GWTC-4.0 focus is-\nsue (Abac et al. 2025l). This includes inferring the mass\nand spin distributions of the CBCs we have observed (Abac\net al. 2025g), testing general relativity in the strong-\ufb01eld\nregime (Abac et al. 2025i,j,k), providing independent mea-\nsures of local cosmology (Abac et al. 2025h), and search-\ning for gravitationally lensed counterparts to our candi-\ndates (Abac et al. 2025m).\nThe data products associated with the results described\nhere, as well as a complete list of all candidates with FARs\n\u22642 d\u22121 and the underlying strain data are publicly available\nthrough GWOSC and are described in detail in Abac et al.\n\n27\nFigure 8.\nA comparison of the the overlap between the on-source and off-source (with 90% con\ufb01dence intervals) reconstructions for three\ndifferent minimally modeled pipelines, BAYESWAVE, CWB-2G, and CWB-BBH for candidates which had data from both interferometers and\nwhere the NRSUR7DQ4 waveform was used in parameter estimation, the network SNR was greater than 10, and the redshifted chirp mass\n(1 + z)M > 15M\u2299. The gray line denotes equal overlap between the on- and off-source reconstructions, indicating that there is no signi\ufb01cant\ndifference between the two.\n(2025c). Past releases of the public strain data have led to ad-\nditional GW candidates (Nitz et al. 2019; Venumadhav et al.\n2020, 2019; Zackay et al. 2021, 2019; Magee et al. 2019;\nNitz et al. 2020b, 2021, 2023; Olsen et al. 2022; Kumar &\nDent 2024; Mishra et al. 2025; Koloniari et al. 2025), and the\ndata products have enabled myriad studies probing the nature\nof individual detections, population properties, and other as-\ntrophysical inferences.\nOn 2024 January 16, the LIGO interferometers paused op-\nerations to begin a commissioning break to further improve\nsensitivity. The second part of the fourth observing run (O4b)\nbegan on 2024 April 10 during which the LIGO detectors\nwhere joined by the Virgo detector (Acernese et al. 2015).\nThen on 2025 January 28 the third part of the fourth observ-\ning run (O4c) started. On 2025 June 11, during this observing\nrun, the KAGRA detector (Akutsu et al. 2019) also rejoined\nthe network. Increasing the number of detectors will greatly\nimprove the ability of the network to infer source localiza-\ntions and also provide a higher rate of detections; analysis of\nthis data will be presented in a future version of the GWTC\nreleases.\nIn the coming years, the LVK network will undergo ad-\nditional upgrades to further improve its sensitivity and un-\ncover hitherto hidden parts of the gravitational universe (Ab-\nbott et al. 2020a). Future GW transients could include novel\nCBC sources, such as subsolar-mass compact binaries (Ab-\nbott et al. 2018, 2019e, 2022a, 2023c; Nitz & Wang 2021a,b)\nor other exotica, but also new classes of GW transients such\nas supernovae (Abbott et al. 2021d), cosmic strings (Ab-\nbott et al. 2021e), and bursts of unknown origin (Abac\n\n28\net al. 2025f,f; Abbott et al. 2021c). We additionally antici-\npate long-lived GW signals from rapidly rotating NSs (Abac\net al. 2025f; Abbott et al. 2022b) and the stochastic back-\nground (Abbott et al. 2021f,g) of the Universe. As the detec-\ntors improve in sensitivity, we therefore expect to deepen our\nunderstanding of the Universe.\nDATA AVAILABILITY\nAll strain data analysed as part of GWTC-4.0 are pub-\nlicly availably through GWOSC.\nThe details of this data\nrelease and information about the digital version of the\nGWTC are described in detail in Abac et al. (2025c).\nWe also provide data releases of the search pipeline re-\nsults and initial source localization (LIGO Scienti\ufb01c Col-\nlaboration, Virgo Collaboration, and KAGRA Collaboration\n2025a), parameter-estimation samples (LIGO Scienti\ufb01c Col-\nlaboration, Virgo Collaboration, and KAGRA Collaboration\n2025b), glitch modelling (LIGO Scienti\ufb01c Collaboration,\nVirgo Collaboration, and KAGRA Collaboration 2025c), and\ndata-quality products (LIGO Scienti\ufb01c Collaboration, Virgo\nCollaboration, and KAGRA Collaboration 2025d) Finally,\nwe also note that the search sensitivity estimates are also pub-\nlicly available (LIGO Scienti\ufb01c Collaboration, Virgo Collab-\noration, and KAGRA Collaboration 2025e,f)\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded by\nthe National Science Foundation. The authors also grate-\nfully acknowledge the support of the Science and Technol-\nogy Facilities Council (STFC) of the United Kingdom, the\nMax-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO 600 de-\ntector. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucle-\nare (INFN), the French Centre National de la Recherche\nScienti\ufb01que (CNRS) and the Netherlands Organization for\nScienti\ufb01c Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and support of\nthe EGO consortium. The authors also gratefully acknowl-\nedge research support from these agencies as well as by the\nCouncil of Scienti\ufb01c and Industrial Research of India, the\nDepartment of Science and Technology, India, the Science\n& Engineering Research Board (SERB), India, the Ministry\nof Human Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00f3n (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00f3n y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC - Cen-\ntroNazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the European\nUnion NextGenerationEU, the Comunitat Auton\u00f2ma de les\nIlles Balears through the Conselleria d\u2019Educaci\u00f3 i Universi-\ntats, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia i So-\ncietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Science\nCentre of Poland and the European Union - European Re-\ngional Development Fund; the Foundation for Polish Sci-\nence (FNP), the Polish Ministry of Science and Higher Ed-\nucation, the Swiss National Science Foundation (SNSF), the\nRussian Science Foundation, the European Commission, the\nEuropean Social Funds (ESF), the European Regional De-\nvelopment Funds (ERDF), the Royal Society, the Scottish\nFunding Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scienti\ufb01c Research Fund (OTKA), the French\nLyon Institute of Origins (LIO), the Belgian Fonds de la\nRecherche Scienti\ufb01que (FRS-FNRS), Actions de Recherche\nConcert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek\n- Vlaanderen (FWO), Belgium, the Paris \u00cele-de-France Re-\ngion, the National Research, Development and Innovation\nOf\ufb01ce of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of Sci-\nence, Technology, and Innovations, the International Center\nfor Theoretical Physics South American Institute for Funda-\nmental Research (ICTP-SAIFR), the Research Grants Coun-\ncil of Hong Kong, the National Natural Science Foundation\nof China (NSFC), the Israel Science Foundation (ISF), the\nUS-Israel Binational Science Fund (BSF), the Leverhulme\nTrust, the Research Corporation, the National Science and\nTechnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The authors\ngratefully acknowledge the support of the NSF, STFC, INFN\nand CNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scienti\ufb01c Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grants-in-Aid for Scienti\ufb01c Re-\nsearch (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for\nTransformative Research Areas (A) 20A203: JP20H05854,\nthe joint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and the\nNational Science and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research Pro-\ngram, the Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the pur-\npose of open access, the authors have applied a Creative\nCommons Attribution (CC BY) license to any Author Ac-\ncepted Manuscript version arising. We request that citations\nto this article use \u2019A. G. Abac et al. (LIGO-Virgo-KAGRA\n\n29\nCollaboration), ...\u2019 or similar phrasing, depending on journal\nconvention.\nFacility: LIGO\nSoftware:\nCalibration of the LIGO strain data was\nperformed with a GSTLAL-based calibration software\npipeline (Viets et al. 2018). Data-quality products and event-\nvalidation results were computed using the DMT (Zweizig\n2006), DQR (LIGO Scienti\ufb01c Collaboration and Virgo\nCollaboration 2018), DQSEGDB (Fisher et al. 2020),\nGWDETCHAR (Urban et al. 2021), HVETO (Smith et al.\n2011),\nIDQ (Essick et al. 2020), OMICRON (Robinet\net al. 2020) and PYTHONVIRGOTOOLS (Virgo Collaboration\n2021) software packages and contributing software tools.\nAnalyses in this catalog relied upon the LALSUITE software\nlibrary (LIGO Scienti\ufb01c Collaboration et al. 2018; Wette\n2020). The detection of the signals and subsequent signif-\nicance evaluations in this catalog were performed with the\nGSTLAL-based inspiral software pipeline (Messick et al.\n2017; Sachdev et al. 2019; Hanna et al. 2020; Cannon et al.\n2020), with the MBTA pipeline (Adams et al. 2016; Aubin\net al. 2021), and with the PYCBC (Usman et al. 2016; Nitz\net al. 2017; Davies et al. 2020) and the CWB (Klimenko &\nMitselmakher 2004; Klimenko et al. 2011, 2016) packages.\nEstimates of the noise spectra and glitch models were ob-\ntained using BAYESWAVE (Cornish & Littenberg 2015; Lit-\ntenberg et al. 2016; Cornish et al. 2021). Source-parameter\nestimation was performed with the BILBY library (Ashton\net al. 2019; Romero-Shaw et al. 2020) using the DYNESTY\nnested sampling package (Speagle 2020). PESUMMARY was\nused to postprocess and collate parameter-estimation re-\nsults (Hoy & Raymond 2021). The various stages of the\nparameter-estimation analysis were managed with the ASI-\nMOV library (Williams et al. 2023). Plots were prepared with\nMATPLOTLIB (Hunter 2007), SEABORN (Waskom 2021) and\nGWPY (Macleod et al. 2021). NUMPY (Harris et al. 2020)\nand SCIPY (Virtanen et al. 2020) were used in the prepara-\ntion of the manuscript.\nAPPENDIX\nA. ADDITIONAL SEARCH RESULTS\nWe present the individual-detector SNRs for all candidates with FAR \u22641 yr\u22121 in Table 6, extending the information provided\nin Table 1 and offering additional context on the search pipeline responses to the signals observed in data from individual\ndetectors.\nTable 6. Individual-detector SNRs for all candidates with FAR \u22641 yr\u22121.\nCandidate\nCWB-BBH\nGSTLAL\nMBTA\nPyCBC\nH\nL\nH\nL\nH\nL\nH\nL\nGW230518_125908\n\u2013\n\u2013\n10.0\n9.3\n10.6\n9.4\n10.2\n9.0\nGW230529_181500\n\u2013\n\u2013\n\u2013\n11.8\n\u2013\n11.4\n\u2013\n11.7\nGW230601_224134\n9.3\n9.6\n8.6\n8.2\n8.4\n9.1\n8.7\n8.5\nGW230605_065343\n4.4\n6.1\n6.8\n8.3\n6.7\n8.8\n7.2\n8.8\nGW230606_004305\n9.1\n6.3\n9.4\n5.4\n9.3\n5.7\n9.4\n5.2\nGW230608_205047\n8.1\n5.8\n8.2\n6.2\n8.3\n5.9\n\u2013\n\u2013\nGW230609_064958\n6.9\n8.1\n5.6\n8.2\n5.7\n8.7\n5.7\n7.7\nGW230624_113103\n8.5\n7.6\n7.8\n6.3\n8.1\n6.4\n8.1\n6.1\nGW230627_015337\n21.4\n17.7\n22.1\n17.8\n21.7\n18.3\n22.0\n18.4\nGW230628_231200\n12.3\n10.8\n12.2\n9.3\n12.5\n9.8\n12.8\n9.4\nGW230630_070659\n\u2013\n\u2013\n4.4\n8.7\n\u2013\n\u2013\n\u2013\n\u2013\nGW230630_125806\n6.1\n6.7\n5.4\n6.0\n5.0\n6.5\n5.2\n6.2\nGW230630_234532\n\u2013\n\u2013\n7.3\n6.4\n7.4\n6.7\n7.2\n6.6\nGW230702_185453\n7.1\n7.3\n6.2\n7.6\n5.9\n7.9\n5.6\n7.3\nGW230704_021211\n\u2013\n\u2013\n5.0\n7.9\n5.0\n7.8\n5.1\n7.6\nGW230704_212616\n5.6\n6.2\n4.5\n7.0\n4.6\n7.3\n\u2013\n\u2013\nGW230706_104333\n\u2013\n\u2013\n5.7\n7.3\n\u2013\n\u2013\n5.9\n6.6\nGW230707_124047\n8.4\n8.4\n5.7\n8.4\n5.7\n8.6\n6.2\n8.4\nGW230708_053705\n\u2013\n\u2013\n6.7\n5.4\n7.1\n5.3\n7.1\n5.4\nGW230708_230935\n8.1\n5.9\n7.6\n5.9\n7.6\n6.0\n7.4\n5.8\nTable 6 continued\n\n30\nTable 6 (continued)\nCandidate\nCWB-BBH\nGSTLAL\nMBTA\nPyCBC\nH\nL\nH\nL\nH\nL\nH\nL\nGW230709_122727\n7.2\n7.2\n6.9\n7.1\n7.3\n7.0\n6.8\n7.3\nGW230712_090405\n5.8\n7.5\n4.0\n7.2\n\u2013\n\u2013\n4.5\n6.9\nGW230723_101834\n\u2013\n\u2013\n7.4\n6.6\n7.4\n6.7\n7.6\n6.6\nGW230726_002940\n\u2013\n\u2013\n\u2013\n10.5\n\u2013\n\u2013\n\u2013\n10.0\nGW230729_082317\n\u2013\n\u2013\n7.0\n6.4\n\u2013\n\u2013\n7.0\n6.3\nGW230731_215307\n\u2013\n\u2013\n8.5\n8.8\n8.0\n8.9\n8.0\n8.8\nGW230803_033412\n7.1\n6.0\n5.8\n5.5\n6.6\n5.6\n6.1\n5.5\nGW230805_034249\n6.3\n7.2\n6.1\n7.0\n6.3\n7.0\n6.1\n7.1\nGW230806_204041\n7.0\n6.3\n7.3\n5.4\n7.2\n6.0\n6.9\n5.9\nGW230811_032116\n9.0\n10.2\n6.7\n11.0\n6.8\n11.4\n6.4\n10.6\nGW230814_061920\n8.8\n7.0\n8.1\n6.2\n7.9\n6.2\n7.1\n6.4\nGW230814_230901\n\u2013\n\u2013\n\u2013\n42.3\n\u2013\n\u2013\n\u2013\n43.0\nGW230819_171910\n7.3\n6.7\n7.1\n5.6\n\u2013\n\u2013\n6.9\n5.7\nGW230820_212515\n5.9\n5.2\n7.5\n5.1\n7.6\n5.3\n7.4\n5.1\nGW230824_033047\n7.8\n7.8\n6.8\n8.0\n6.9\n8.1\n6.6\n8.4\nGW230825_041334\n6.3\n6.2\n7.0\n5.1\n6.8\n5.1\n6.9\n5.2\nGW230831_015414\n5.6\n5.4\n6.9\n5.2\n6.7\n5.4\n6.5\n5.4\nGW230904_051013\n\u2013\n\u2013\n6.8\n8.0\n6.1\n8.5\n6.2\n8.1\nGW230911_195324\n\u2013\n\u2013\n10.7\n\u2013\n\u2013\n\u2013\n11.1\n\u2013\nGW230914_111401\n10.7\n13.4\n10.2\n12.2\n10.5\n12.9\n10.3\n12.2\nGW230919_215712\n12.6\n11.2\n11.9\n11.1\n11.4\n11.4\n11.5\n11.8\nGW230920_071124\n8.0\n7.7\n7.1\n7.2\n7.2\n7.2\n6.9\n6.6\nGW230922_020344\n8.9\n9.9\n6.6\n10.4\n6.6\n10.3\n6.5\n10.0\nGW230922_040658\n8.8\n8.8\n7.6\n8.7\n7.6\n8.7\n8.1\n8.3\nGW230924_124453\n8.6\n10.3\n9.9\n8.8\n9.7\n9.1\n9.7\n8.8\nGW230927_043729\n9.1\n7.9\n8.9\n7.0\n8.8\n6.8\n8.7\n6.9\nGW230927_153832\n13.5\n15.1\n11.8\n16.0\n12.1\n16.2\n11.6\n15.8\nGW230928_215827\n7.8\n7.1\n6.7\n6.7\n6.9\n6.3\n6.7\n6.8\nGW230930_110730\n6.4\n6.2\n5.9\n6.1\n6.0\n6.1\n6.1\n5.7\nGW231001_140220\n8.6\n7.6\n7.2\n7.4\n7.6\n7.4\n7.2\n6.7\nGW231004_232346\n5.2\n7.3\n4.0\n6.8\n\u2013\n\u2013\n\u2013\n7.0\nGW231005_021030\n7.1\n7.6\n6.2\n6.9\n6.6\n7.2\n6.6\n7.3\nGW231005_091549\n8.2\n7.4\n6.3\n6.2\n6.1\n6.1\n6.2\n5.9\nGW231008_142521\n\u2013\n\u2013\n6.7\n6.5\n6.2\n6.6\n6.1\n6.2\nGW231014_040532\n5.5\n6.6\n5.9\n6.8\n6.1\n6.2\n6.2\n6.1\nGW231018_233037\n\u2013\n\u2013\n5.4\n6.8\n5.3\n7.4\n5.0\n7.0\nGW231020_142947\n\u2013\n\u2013\n9.9\n6.5\n10.2\n6.3\n9.9\n6.5\nGW231028_153006\n14.1\n17.4\n12.0\n17.2\n12.5\n18.0\n11.8\n18.4\nGW231029_111508\n\u2013\n\u2013\n\u2013\n10.8\n\u2013\n\u2013\n\u2013\n\u2013\nGW231102_071736\n11.0\n11.1\n9.8\n9.7\n10.3\n10.6\n8.8\n10.1\nGW231104_133418\n\u2013\n\u2013\n7.7\n8.3\n7.8\n8.4\n8.0\n8.7\nGW231108_125142\n8.1\n9.7\n8.1\n9.7\n8.4\n9.3\n8.0\n9.3\nGW231110_040320\n\u2013\n\u2013\n6.7\n9.2\n6.8\n9.3\n6.7\n8.9\nGW231113_122623\n\u2013\n\u2013\n5.6\n6.2\n5.4\n6.6\n5.6\n6.5\nGW231113_200417\n\u2013\n\u2013\n8.1\n6.3\n8.0\n6.2\n8.3\n6.5\nGW231114_043211\n\u2013\n\u2013\n7.4\n6.7\n7.4\n6.5\n7.6\n6.0\nGW231118_005626\n\u2013\n\u2013\n7.5\n7.2\n7.7\n7.4\n7.4\n7.4\nGW231118_071402\n6.0\n7.0\n7.1\n5.9\n6.8\n6.2\n6.9\n6.1\nTable 6 continued\n\n31\nTable 6 (continued)\nCandidate\nCWB-BBH\nGSTLAL\nMBTA\nPyCBC\nH\nL\nH\nL\nH\nL\nH\nL\nGW231118_090602\n\u2013\n\u2013\n7.8\n7.4\n7.8\n7.8\n7.7\n7.6\nGW231119_075248\n5.4\n5.7\n5.4\n6.0\n5.3\n6.0\n5.2\n6.5\nGW231123_135430\n13.3\n17.2\n13.1\n15.2\n10.9\n15.5\n12.2\n15.8\nGW231127_165300\n7.2\n6.9\n8.0\n5.6\n7.9\n5.4\n7.9\n5.4\nGW231129_081745\n7.0\n6.3\n6.7\n5.1\n6.6\n5.2\n6.8\n5.2\nGW231206_233134\n9.1\n9.0\n7.0\n9.6\n6.6\n9.7\n6.9\n9.2\nGW231206_233901\n12.2\n18.2\n12.1\n16.9\n11.8\n17.8\n11.7\n17.5\nGW231213_111417\n6.6\n7.5\n6.3\n8.0\n6.5\n8.1\n6.3\n7.9\nGW231221_135041\n7.8\n6.2\n7.1\n4.5\n6.4\n4.9\n7.1\n4.4\nGW231223_032836\n7.2\n7.3\n6.5\n6.8\n6.5\n6.4\n6.5\n6.2\nGW231223_075055\n\u2013\n\u2013\n7.0\n6.2\n7.0\n6.2\n7.2\n6.1\nGW231223_202619\n\u2013\n\u2013\n10.0\n\u2013\n\u2013\n\u2013\n10.0\n\u2013\nGW231224_024321\n\u2013\n\u2013\n8.1\n10.2\n8.6\n11.0\n8.4\n10.3\nGW231226_101520\n26.9\n21.9\n26.2\n22.0\n26.4\n20.8\n26.3\n20.3\nGW231230_170116\n6.3\n5.3\n6.4\n4.7\n\u2013\n\u2013\n\u2013\n\u2013\nGW231231_154016\n\u2013\n\u2013\n13.4\n\u2013\n\u2013\n\u2013\n13.4\n\u2013\nGW240104_164932\n\u2013\n\u2013\n14.8\n\u2013\n\u2013\n\u2013\n12.2\n\u2013\nGW240107_013215\n7.8\n5.3\n7.1\n5.6\n8.0\n5.3\n7.4\n5.3\nGW240109_050431\n\u2013\n\u2013\n10.4\n\u2013\n\u2013\n\u2013\n10.0\n\u2013\nNOTE\u2014LIGO Hanford and LIGO Livingston are denoted by H and L, respectively. Entries\nin italics indicate candidates that were recovered with a FAR \u22651 yr\u22121 by a given analysis.\nDashes (\u2013) indicate that a candidate was not found by an analysis.\nIn Table 7 we provide the calculated probabilities that a candidate comes from a BBH (pBBH), a NSBH (pNSBH), or a BNS\n(pBNS) for all new candidates in GWTC-4.0 with the maximum pastro > 0.5 and minimum FARs > 1 yr\u22121 across pipelines.\nWe only show systems where pNSBH + pBNS > 0.001; the remaining marginal candidates are consistent with BBHs. GSTLAL\nestimates the relative probabilities of different astrophysical source types using the component masses of the matching template,\nand SNR of the signal (Ray et al. 2023); MBTA uses the chirp mass and mass ratio of the identifying template (Andres et al.\n2022), and PYCBC only uses the chirp mass, along with an estimate of the source luminosity distance (Dal Canton et al. 2021;\nVilla-Ortega et al. 2022). Neglecting mass ratio information can systematically impact the source categorization (Villa-Ortega\net al. 2022). The full details of the pastro calculations are described in Abac et al. (2025b).\nTable 7. Multicomponent pastro for all candidates with FAR > 1 yr\u22121, pastro > 0.5 and pBNS + pNSBH > 0.001.\nCandidate\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\npastro\npBBH\npNSBH\npBNS\npastro\npBBH\npNSBH\npBNS\npastro\npBBH\npNSBH\npBNS\npastro\nGW230729_082317\n\u2013\n0.95\n< 0.01\n< 0.01\n0.95\n\u2013\n\u2013\n\u2013\n\u2013\n0.73\n0.04\n< 0.01\n0.77\nGW230831_134621\n\u2013\n0.11\n< 0.01\n< 0.01\n0.11\n0.34\n< 0.01\n< 0.01\n0.34\n0.69\n0.12\n< 0.01\n0.80\nGW230902_172430\n\u2013\n0.02\n< 0.01\n< 0.01\n0.02\n0.07\n< 0.01\n< 0.01\n0.07\n0.51\n0.08\n< 0.01\n0.59\nGW230904_152545\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n0.03\n0.15\n0.02\n0.19\n< 0.01\n0.72\n0.02\n0.74\nGW230920_064709\n\u2013\n< 0.01\n< 0.01\n< 0.01\n< 0.01\n0.03\n< 0.01\n< 0.01\n0.03\n0.16\n0.65\n< 0.01\n0.81\nGW231013_135504\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n0.10\n0.44\n< 0.01\n0.54\nGW231120_022103\n\u2013\n0.53\n< 0.01\n< 0.01\n0.53\n0.45\n< 0.01\n< 0.01\n0.45\n0.63\n0.27\n< 0.01\n0.90\nGW240105_151143\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n\u2013\n0.34\n0.37\n< 0.01\n0.70\nTable 7 continued\n\n32\nTable 7 (continued)\nCandidate\nCWB-BBH\nGstLAL\nMBTA\nPyCBC\npastro\npBBH\npNSBH\npBNS\npastro\npBBH\npNSBH\npBNS\npastro\npBBH\npNSBH\npBNS\npastro\nNOTE\u2014These candidates do not meet the criterion for source property estimation. Entries in italics indicate candidates that were recovered with a FAR > 1 yr\u22121\nby a given analysis. Dashes (\u2013) indicate that a candidate was not found by an analysis. The BBH, BNS, and NSBH categories are de\ufb01ned by the masses of the\nsearch template that recovered the candidate and are not necessarily indicative of true astrophysical population.\nB. GLITCH MITIGATION\nWhen a glitch is identi\ufb01ed around the time of a candidate, we carry out further procedures to mitigate its impact on our\ninferences described in Section 4 of Abac et al. (2025b). For the candidates identi\ufb01ed in O4a, we either model and coherently\nsubtract the glitch with the BAYESWAVE algorithm (Cornish & Littenberg 2015; Littenberg & Cornish 2015; Cornish et al. 2021;\nHourihane et al. 2022; Abac et al. 2025b) or we integrate the parameter-estimation likelihood in a narrower frequency band to\nexclude the effect of the glitch by increasing the low-frequency cutoff flow. For cases where we applied BAYESWAVE, Table 8\nshows input parameters into the algorithm: the reference trigger time of the CBC candidate as determined by GW searches,\nand the bands in time and frequency space where the glitch is a-priori identi\ufb01ed to have power. For cases where we narrow the\nfrequency band, we give the flow value used to set the lower bound; the upper bound fhigh is the Nyquist frequency multiplied\nby a roll-off factor as described in Abac et al. (2025b).\nTable 8. List of O4a candidates with FAR < 1 yr\u22121, for which glitch mitigation was performed.\nCandidate\nGPS time [s]\nDetector\nTime window [s]\nFrequency range [Hz]\nflow [Hz]\nGW230601_224134\n\u2013\nH\n\u2013\n\u2013\n20.93\nGW230601_224134\n\u2013\nL\n\u2013\n\u2013\n20.93\nGW230606_004305\n1370047403.79\nH\n[1.11, 1.31]\n[8.0, 512]\n\u2013\nGW230702_185453\n\u2013\nH\n\u2013\n\u2013\n20\nGW230707_124047\n1372768865.35\nH\n[\u22120.15, 0.1]\n[15.0, 30.0]\n\u2013\nGW230708_053705\n1372829843.12\nH\n[\u22122.02, 0.98]\n[10.0, 50.0]\n\u2013\nGW230709_122727\n\u2013\nH\n\u2013\n\u2013\n50\nGW230729_082317\n\u2013\nH\n\u2013\n\u2013\n50\nGW230731_215307\n\u2013\nH\n\u2013\n\u2013\n40\nGW230803_033412\n\u2013\nH\n\u2013\n\u2013\n30\nGW230806_204041\n1375389659.94\nH\n[1.8, 2.0]\n[25.0, 65.0]\n\u2013\nGW230819_171910\n1376500768.45\nL\n[\u22123.2, \u22122.8]\n[8.0, 512]\n\u2013\nGW230814_061920\n\u2013\nH\n\u2013\n\u2013\n21.48\nGW230814_061920\n\u2013\nL\n\u2013\n\u2013\n21.48\nGW230814_230901\n\u2013\nL\n\u2013\n\u2013\n24\nGW230824_033047\n\u2013\nH\n\u2013\n\u2013\n22.18\nGW230824_033047\n\u2013\nL\n\u2013\n\u2013\n22.18\nGW230831_015414\n\u2013\nL\n\u2013\n\u2013\n22\nGW230911_195324\n\u2013\nH\n\u2013\n\u2013\n28.38\nGW230920_071124\n\u2013\nH\n\u2013\n\u2013\n40\nGW231001_140220\n\u2013\nL\n\u2013\n\u2013\n40\nGW231014_040532\n\u2013\nH\n\u2013\n\u2013\n50\nGW231018_233037\n\u2013\nH\n\u2013\n\u2013\n30\nGW231020_142947\n\u2013\nH\n\u2013\n\u2013\n45\nGW231102_071736\n\u2013\nH\n\u2013\n\u2013\n20.13\nGW231102_071736\n\u2013\nL\n\u2013\n\u2013\n20.13\nGW231113_122623\n1383913601.88\nL\n[0.01, 0.22]\n[70.0, 120.0]\n\u2013\nGW231114_043211\n1383971549.25\nH\n[\u22120.95, \u22120.6]\n[10.0, 30.0]\n\u2013\nTable 8 continued\n\n33\nTable 8 (continued)\nCandidate\nGPS time [s]\nDetector\nTime window [s]\nFrequency range [Hz]\nflow [Hz]\nGW231118_005626\n\u2013\nH\n\u2013\n\u2013\n30\nGW231118_071402\n\u2013\nH\n\u2013\n\u2013\n50\nGW231118_090602\n1384333580.01\nH\n[\u22124.81, \u22124.51]\n[15.0, 50.0]\n\u2013\nGW231123_135430\n1384782888.63\nH\n[\u22121.7, \u22121.1]\n[15.0, 30.0]\n\u2013\nGW231127_165300\n\u2013\nH\n\u2013\n\u2013\n50\nGW231129_081745\n1385281083.64\nL\n[1.4, 1.8]\n[10.0, 170.0]\n\u2013\nGW231129_081745\n\u2013\nH\n\u2013\n\u2013\n60\nGW231206_233134\n\u2013\nH\n\u2013\n\u2013\n40\nGW231206_233134\n\u2013\nL\n\u2013\n\u2013\n30\nGW231221_135041\n1387201859.32\nH\n[0.3, 0.4]\n[200.0, 450.0]\n\u2013\nGW231223_032836\n1387337334.05\nH\n[\u22120.55, \u22120.25]\n[10.0, 25.0]\n\u2013\nGW231223_075055\n\u2013\nH\n\u2013\n\u2013\n40\nGW231223_075055\n\u2013\nL\n\u2013\n\u2013\n30\nGW231223_202619\n\u2013\nH\n\u2013\n\u2013\n40\nGW231224_024321\n\u2013\nH\n\u2013\n\u2013\n40\nGW240107_013215\n\u2013\nH\n\u2013\n\u2013\n40\nNOTE\u2014 For each candidate, we show the GPS time, and the interferometer(s) where glitch subtraction was applied\n(H and L indicate LIGO Hanford and LIGO Livingston respectively). For candidates where glitch subtraction was\nperformed using BAYESWAVE, we provide the time and frequency windows used for subtraction. For candidates\nwhere the low-frequency cut-off, flow, was changed (from the standard 20 Hz) to excise contaminate data, we\nquote the cut-off used.\nC. SPECTROGRAMS OF SELECTED EVENTS\nHere we provide time\u2013frequency spectrograms (Brown 1991; Chatterji et al. 2004) for several candidates of particular interest.\nGW230630_070659 is discussed in Section 2.1.2 and is presented in Table 1 with other candidates identi\ufb01ed by our searches with\nboth pastro \u22650.5 and FAR < 1 yr\u22121. GW230824_135331 and GW240105_151143 are discussed in Sections 2.1.3 and 2.1.2,\nrespectively, and further information on them is in Table 2, together with other candidates with pastro \u22650.5 but which do not\nmeet the threshold for detailed investigation of their source properties or event validation.\nThe top panels of Figure 9 show the time\u2013frequency spectrograms for GW230630_070659, which has been determined to be\nlikely of instrumental origin. This candidate was found only by the GSTLAL matched-\ufb01lter search pipeline. The event-validation\nprocedures discussed in Section 2.1.2 identi\ufb01ed excess power from scattered light (Ottaway et al. 2012; Soni et al. 2025) in both\ndetectors at the time of the candidate.\nThe middle panels of Figure 9 show the time\u2013frequency spectrograms of GW230824_135331. This candidate was recovered\nonly by the minimally modeled CWB-BBH search pipeline, with pastro = 0.58. It was not recovered, even as a subthreshold\ncandidate with FAR < 2 d\u22121 and pastro < 0.5, by any matched-\ufb01lter pipelines; it is the only candidate with pastro \u22650.5 in this\ncatalog with that distinction. The CWB-BBH search pipeline has the potential to detect BBH candidates impacted by physical\neffects neglected in the matched-\ufb01lter searches, such as precession and eccentricity (e.g., Abac et al. 2024b; Mishra et al. 2025),\nin addition to non-CBC transients. However, the computation of pastro assumes a prior CBC source population (Abac et al.\n2025b). These assumptions may not be valid if a source arises from a population which our matched-\ufb01lter CBC searches are not\nsensitive to (Abbott et al. 2023a). Our event-validation procedures were not applied to GW230824_135331, since it has FAR\n> 1 yr\u22121. However the appearance of this candidate in the time\u2013frequency spectrograms is not clearly a genuine CBC signal.\nThe spectrograms also show the presence of excess power in LHO at the time of the event.\nThe bottom panels of Figure 9 present the time\u2013frequency spectrograms of GW240105_151143, a high-SNR (> 25) candidate\ndetected by only the PYCBC matched-\ufb01lter search pipeline. There are several regions with signi\ufb01cant excess power in LHO that\nare not consistent with a CBC signal, and could contribute to its identi\ufb01cation by only one search pipeline with a large SNR. Our\nevent-validation procedures were not applied to GW230824_135331, since it has FAR > 1 yr\u22121.\n\n34\nFigure 9.\nSpectrograms for three candidates of interest. Top panels: Spectrograms for GW230630_070659, a candidate identi\ufb01ed by\nGSTLAL with FAR < 1 yr\u22121 but which event validation indicates is likely of instrumental origin. We do not carry out parameter estimation\non this candidate. Middle panels: Spectrograms for GW230824_135331, a CWB-BBH candidate which is not identi\ufb01ed as a candidate or\nsubthreshold candidate by any matched \ufb01lter search. Excess power is visible in LHO around the time of the candidate. Bottom panels:\nSpectrograms for GW240105_151143, a candidate identi\ufb01ed by only PYCBC. Signi\ufb01cant excess power is present in LHO at the time of the\ncandidate.\n\n35\nREFERENCES\nAasi, J., et al. 2015, Class. Quant. Grav., 32, 074001,\ndoi: 10.1088/0264-9381/32/7/074001\nAbac, A. G., et al. 2024a, Astrophys. J. Lett., 970, L34,\ndoi: 10.3847/2041-8213/ad5beb\n\u2014. 2024b, Astrophys. 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ADHIKARI,8, 9\nN. ADHIKARI\n,10\nR. X. ADHIKARI\n,11\nV. K. ADKINS,12\nS. AFROZ\n,13\nA. AGAPITO,14\nD. AGARWAL\n,15\nM. AGATHOS\n,16\nN. AGGARWAL,17\nS. AGGARWAL,18\nO. D. AGUIAR\n,19\nI.-L. AHREND,20\nL. AIELLO\n,21, 22\nA. AIN\n,23\nP. AJITH\n,24\nS. AKCAY\n,25\nT. AKUTSU\n,26, 27\nS. ALBANESI\n,28, 29\nW. ALI,30, 31\nS. AL-KERSHI,8, 9\nC. ALL\u00c9N\u00c9,32\nA. ALLOCCA\n,33, 4\nS. AL-SHAMMARI,34\nP. A. ALTIN\n,35\nS. ALVAREZ-LOPEZ\n,36\nW. AMAR,32\nO. AMARASINGHE,34\nA. AMATO\n,37, 38\nF. AMICUCCI\n,39, 40\nC. AMRA,41\nA. ANANYEVA,11\nS. B. ANDERSON\n,11\nW. G. ANDERSON\n,11\nM. ANDIA\n,42\nM. ANDO,43\nM. ANDR\u00c9S-CARCASONA\n,44\nT. ANDRI \u00b4C\n,45, 46, 8, 9\nJ. ANGLIN,47\nS. ANSOLDI\n,48, 49\nJ. M. ANTELIS\n,50\nS. ANTIER\n,42\nM. AOUMI,51\nE. Z. APPAVURAVTHER,52, 53\nS. APPERT,11\nS. K. APPLE\n,54\nK. ARAI\n,11\nA. ARAYA\n,43\nM. C. ARAYA\n,11\nM. ARCA SEDDA\n,45, 46\nJ. S. AREEDA\n,55\nN. ARITOMI,2\nF. ARMATO\n,30, 31\nS. ARMSTRONG\n,56\nN. ARNAUD\n,57\nM. AROGETI\n,58\nS. M. ARONSON\n,12\nK. G. ARUN\n,59\nG. ASHTON\n,60\nY. ASO\n,26, 61\nL. ASPREA,29\nM. ASSIDUO,62, 63\nS. ASSIS DE SOUZA MELO,64\nS. M. ASTON,65\nP. ASTONE\n,39\nF. ATTADIO\n,40, 39\nF. AUBIN\n,66\nK. AULTONEAL\n,67\nG. AVALLONE\n,68\nE. A. AVILA\n,50\nS. BABAK\n,20\nC. BADGER,69\nS. BAE\n,70\nS. BAGNASCO\n,29\nL. BAIOTTI\n,71\nR. BAJPAI\n,72\nT. BAKA,73, 38\nA. M. BAKER,6\nK. A. BAKER,74\nT. BAKER\n,75\nG. BALDI\n,76, 77\nN. BALDICCHI\n,78, 52\nM. BALL,79\nG. BALLARDIN,64\nS. W. BALLMER,80\nS. BANAGIRI\n,6\nB. BANERJEE\n,45\nD. BANKAR\n,81\nT. M. BAPTISTE,12\nP. BARAL\n,10\nM. BARATTI\n,82, 83\nJ. C. BARAYOGA,11\nB. C. BARISH,11\nD. BARKER,2\nN. BARMAN,81\nP. BARNEO\n,84, 85, 86\nF. BARONE\n,87, 4\nB. BARR\n,88\nL. BARSOTTI\n,36\nM. BARSUGLIA\n,20\nD. BARTA\n,89\nA. M. BARTOLETTI,90\nM. A. BARTON\n,88\nI. BARTOS,47\nA. BASALAEV\n,8, 9\nR. BASSIRI\n,91\nA. BASTI\n,83, 82\nM. BAWAJ\n,78, 52\nP. BAXI,92\nJ. C. BAYLEY\n,88\nA. C. BAYLOR\n,10\nP. A. BAYNARD II,58\nM. BAZZAN,93, 94\nV. M. BEDAKIHALE,95\nF. BEIRNAERT\n,96\nM. BEJGER\n,97\nD. BELARDINELLI\n,22\nA. S. BELL\n,88\nD. S. BELLIE,98\nL. BELLIZZI\n,82, 83\nW. BENOIT\n,18\nI. BENTARA\n,57\nJ. D. BENTLEY\n,99\nM. BEN YAALA,56\nS. BERA\n,100, 101\nF. BERGAMIN\n,34\nB. K. BERGER\n,91\nS. BERNUZZI\n,28\nM. BEROIZ\n,11\nC. P. L. BERRY\n,88\nD. BERSANETTI\n,30\nT. BERTHEAS,102\nA. BERTOLINI,38, 37\nJ. BETZWIESER\n,65\nD. BEVERIDGE\n,74\nG. BEVILACQUA\n,103\nN. BEVINS\n,104\nR. BHANDARE,105\nS. A. BHAT\n,106\nR. BHATT,11\nD. BHATTACHARJEE\n,107, 108\nS. BHATTACHARYYA,109\nS. BHAUMIK\n,47\nV. BIANCALANA\n,103\nA. BIANCHI,38, 110\nI. A. BILENKO,111\nG. BILLINGSLEY\n,11\nA. BINETTI\n,112\nS. BINI\n,11, 76, 77\nC. BINU,113\nS. BIOT,114\nO. BIRNHOLTZ\n,115\nS. BISCOVEANU\n,98\nA. BISHT,9\nM. BITOSSI\n,64, 82\nM.-A. BIZOUARD\n,116\nS. BLABER,117\nJ. K. BLACKBURN\n,11\nL. A. BLAGG,79\nC. D. BLAIR,74, 65\nD. G. BLAIR,74\nN. BODE\n,8, 9\nN. BOETTNER,99\nG. BOILEAU\n,116\nM. BOLDRINI\n,39\nG. N. BOLINGBROKE\n,118\nA. BOLLIAND,119, 41\nL. D. BONAVENA\n,47\nR. BONDARESCU\n,84\nF. BONDU\n,120\nE. BONILLA\n,91\nM. S. BONILLA\n,55\nA. BONINO,121\nR. BONNAND\n,32, 119\nA. BORCHERS,8, 9\nS. BORHANIAN,7\nV. BOSCHI\n,82\nS. BOSE,122\nV. BOSSILKOV,65\nY. BOTHRA\n,38, 110\nA. BOUDON,57\nL. BOURG,58\nM. BOYLE,123\nA. BOZZI,64\nC. BRADASCHIA,82\nP. R. BRADY\n,10\nA. BRANCH,65\nM. BRANCHESI\n,45, 46\nI. BRAUN,107\nT. BRIANT\n,124\nA. BRILLET,116\nM. BRINKMANN,8, 9\nP. BROCKILL,10\nE. BROCKMUELLER\n,8, 9\nA. F. BROOKS\n,11\nB. C. BROWN,47\nD. D. BROWN,118\nM. L. BROZZETTI\n,78, 52\nS. BRUNETT,11\nG. BRUNO,15\nR. BRUNTZ\n,125\nJ. BRYANT,121\nY. BU,126\nF. BUCCI\n,63\nJ. BUCHANAN,125\nO. BULASHENKO\n,84, 85\nT. BULIK,127\nH. J. BULTEN,38\nA. BUONANNO\n,128, 1\nK. BURTNYK,2\nR. BUSCICCHIO\n,129, 130\nD. BUSKULIC,32\nC. BUY\n,102\nR. L. BYER,91\nG. S. CABOURN DAVIES\n,75\nR. CABRITA\n,15\nV. C\u00c1CERES-BARBOSA\n,7\nL. CADONATI\n,58\nG. CAGNOLI\n,131\nC. CAHILLANE\n,80\nA. CALAFAT,100\nJ. CALDER\u00d3N BUSTILLO\n,132\nT. A. CALLISTER,133\nE. CALLONI,33, 4\nS. R. CALLOS\n,79\nM. CANEPA,31, 30\nG. CANEVA SANTORO\n,44\nK. C. CANNON\n,43\nH. CAO,36\nL. A. CAPISTRAN,134\nE. CAPOCASA\n,20\nE. CAPOTE\n,2, 11\nG. CAPURRI\n,83, 82\nG. CARAPELLA,68, 135\nF. CARBOGNANI,64\nM. CARLASSARA,8, 9\nJ. B. CARLIN\n,126\nT. K. CARLSON,136\nM. F. CARNEY,107\nM. CARPINELLI\n,129, 64\nG. CARRILLO,79\nJ. J. CARTER\n,8, 9\nG. CARULLO\n,121, 137\nA. CASALLAS-LAGOS,138\nJ. CASANUEVA DIAZ\n,64\nC. CASENTINI\n,139, 22\nS. Y. CASTRO-LUCAS,140\nS. CAUDILL,136\nM. CAVAGLI\u00c0\n,108\nR. CAVALIERI\n,64\nA. CEJA,55\nG. CELLA\n,82\nP. CERD\u00c1-DUR\u00c1N\n,141, 142\nE. CESARINI\n,22\nN. CHABBRA,35\nW. CHAIBI,116\nA. CHAKRABORTY\n,13\nP. CHAKRABORTY\n,8, 9\nS. CHAKRABORTY,105\nS. CHALATHADKA SUBRAHMANYA\n,99\nJ. C. L. CHAN\n,143\nM. CHAN,117\nK. CHANG,144\nS. CHAO\n,145, 144\nP. CHARLTON\n,146\nE. CHASSANDE-MOTTIN\n,20\nC. CHATTERJEE\n,147\nDEBARATI CHATTERJEE\n,81\nDEEP CHATTERJEE\n,36\nM. CHATURVEDI,105\nS. CHATY\n,20\nK. CHATZIIOANNOU\n,11\nA. CHEN\n,148\nA. H.-Y. CHEN,149\nD. CHEN\n,150\nH. CHEN,145\nH. Y. CHEN\n,151\nS. CHEN,147\nYANBEI CHEN,152\nYITIAN CHEN\n,123\nH. P. CHENG,153\nP. CHESSA\n,78, 52\nH. T. CHEUNG\n,92\nS. Y. CHEUNG,6\nF. CHIADINI\n,154, 135\nG. CHIARINI,8, 9, 94\nA. CHIBA,155\nA. CHINCARINI\n,30\nM. L. CHIOFALO\n,83, 82\nA. CHIUMMO\n,4, 64\nC. CHOU,149\nS. CHOUDHARY\n,74\nN. CHRISTENSEN\n,116, 156\nS. S. Y. CHUA\n,35\nG. CIANI\n,76, 77\nP. CIECIELAG\n,97\nM. CIE \u00b4SLAR\n,127\nM. CIFALDI\n,22\nB. CIROK,157\nF. CLARA,2\nJ. A. CLARK\n,11, 58\nT. A. CLARKE\n,6\nP. CLEARWATER,158\nS. CLESSE,114\nF. CLEVA,116, 119\nS. M. CLYNE,159\nE. COCCIA,45, 46, 44\nE. CODAZZO\n,160, 161\nP.-F. COHADON\n,124\nS. COLACE\n,31\nE. COLANGELI,75\nM. COLLEONI\n,100\nC. G. COLLETTE,162\nJ. COLLINS,65\nS. COLLOMS\n,88\nA. COLOMBO\n,163, 130\nC. M. COMPTON,2\nG. CONNOLLY,79\nL. CONTI\n,94\nT. R. CORBITT\n,12\nI. CORDERO-CARRI\u00d3N\n,164\nS. COREZZI\n,78, 52\nN. J. CORNISH\n,165\nI. CORONADO,166\nA. CORSI\n,167\nR. COTTINGHAM,65\nM. W. COUGHLIN\n,18\nA. COUINEAUX,39\nP. COUVARES\n,11, 58\nD. M. COWARD,74\nR. COYNE\n,159\nA. COZZUMBO,45\nJ. D. E. CREIGHTON\n,10\nT. D. CREIGHTON,168\nP. CREMONESE\n,100\nS. CROOK,65\n\n42\nR. CROUCH,2\nJ. CSIZMAZIA,2\nJ. R. CUDELL\n,169\nT. J. CULLEN\n,11\nA. CUMMING\n,88\nE. CUOCO\n,170, 171\nM. CUSINATO\n,141\nL. V. DA CONCEI\u00c7\u00c3O\n,172\nT. DAL CANTON\n,42\nS. DAL PRA\n,173\nG. D\u00c1LYA\n,102\nB. D\u2019ANGELO\n,30\nS. DANILISHIN\n,37, 38\nS. D\u2019ANTONIO\n,39\nK. DANZMANN,9, 8, 9\nK. E. DARROCH,125\nL. P. DARTEZ\n,65\nR. DAS,109\nA. DASGUPTA,95\nV. DATTILO\n,64\nA. DAUMAS,20\nN. DAVARI,174, 175\nI. DAVE,105\nA. DAVENPORT,140\nM. DAVIER,42\nT. F. DAVIES,74\nD. DAVIS\n,11\nL. DAVIS,74\nM. C. DAVIS\n,18\nP. DAVIS\n,176, 177\nE. J. DAW\n,178\nM. DAX\n,1\nJ. DE BOLLE\n,96\nM. DEENADAYALAN,81\nJ. DEGALLAIX\n,179\nU. DEKA\n,180\nM. DE LAURENTIS\n,33, 4\nF. DE LILLO\n,23\nS. DELLA TORRE\n,130\nW. DEL POZZO\n,83, 82\nA. DEMAGNY,32\nF. DE MARCO\n,40, 39\nG. DEMASI,181, 63\nF. DE MATTEIS\n,21, 22\nN. DEMOS,36\nT. DENT\n,182\nA. DEPASSE\n,15\nN. DEPERGOLA,104\nR. DE PIETRI\n,183, 184\nR. DE ROSA\n,33, 4\nC. DE ROSSI\n,64\nM. DESAI\n,36\nR. DESALVO\n,185\nA. DESIMONE,186\nR. DE SIMONE,154, 135\nA. DHANI\n,1\nR. DIAB,47\nM. C. D\u00cdAZ\n,168\nM. DI CESARE\n,33, 4\nG. DIDERON,187\nT. DIETRICH\n,1\nL. DI FIORE,4\nC. DI FRONZO\n,74\nM. DI GIOVANNI\n,40, 39\nT. DI GIROLAMO\n,33, 4\nD. DIKSHA,38, 37\nJ. DING\n,20, 188\nS. DI PACE\n,40, 39\nI. DI PALMA\n,40, 39\nD. DI PIERO,189, 49\nF. DI RENZO\n,57\nDIVYAJYOTI\n,34\nA. DMITRIEV\n,121\nJ. P. DOCHERTY,88\nZ. DOCTOR\n,98\nN. DOERKSEN\n,172\nE. DOHMEN,2\nA. DOKE,136\nA. DOMICIANO DE SOUZA,190\nL. D\u2019ONOFRIO\n,39\nF. DONOVAN,36\nK. L. DOOLEY\n,34\nT. DOONEY,73\nS. DORAVARI\n,81\nO. DOROSH,191\nW. J. D. DOYLE,125\nM. DRAGO\n,40, 39\nJ. C. DRIGGERS\n,2\nL. DUNN\n,126\nU. DUPLETSA,45\nP.-A. DUVERNE\n,20\nD. D\u2019URSO\n,174, 160\nP. DUTTA ROY\n,47\nH. DUVAL\n,192\nS. E. DWYER,2\nC. EASSA,2\nM. EBERSOLD\n,193, 32\nT. ECKHARDT\n,99\nG. EDDOLLS\n,80\nA. EFFLER\n,65\nJ. EICHHOLZ\n,35\nH. EINSLE,116\nM. EISENMANN,26\nM. EMMA\n,60\nK. ENDO,155\nR. ENFICIAUD\n,1\nL. ERRICO\n,33, 4\nR. ESPINOSA,168\nM. ESPOSITO\n,4, 33\nR. C. ESSICK\n,194\nH. ESTELL\u00c9S\n,1\nT. ETZEL,11\nM. EVANS\n,36\nT. EVSTAFYEVA,187\nB. E. EWING,7\nJ. M. EZQUIAGA\n,143\nF. FABRIZI\n,62, 63\nV. FAFONE\n,21, 22\nS. FAIRHURST\n,34\nA. M. FARAH\n,133\nB. FARR\n,79\nW. M. FARR\n,195, 196\nG. FAVARO\n,93\nM. FAVATA\n,197\nM. FAYS\n,169\nM. FAZIO\n,56\nJ. FEICHT,11\nM. M. FEJER,91\nR. FELICETTI\n,189, 49\nE. FENYVESI\n,89, 198\nJ. FERNANDES,199\nT. FERNANDES\n,200, 141\nD. FERNANDO,113\nS. FERRAIUOLO\n,201, 40, 39\nT. A. FERREIRA,12\nF. FIDECARO\n,83, 82\nP. FIGURA\n,97\nA. FIORI\n,82, 83\nI. FIORI\n,64\nM. FISHBACH\n,194\nR. P. FISHER,125\nR. FITTIPALDI\n,202, 135\nV. FIUMARA\n,203, 135\nR. FLAMINIO,32\nS. M. FLEISCHER\n,204\nL. S. FLEMING,205\nE. FLODEN,18\nH. FONG,117\nJ. A. FONT\n,141, 142\nF. FONTINELE-NUNES,18\nC. FOO,1\nB. FORNAL\n,206\nK. FRANCESCHETTI,183\nF. FRAPPEZ,32\nS. FRASCA,40, 39\nF. FRASCONI\n,82\nJ. P. FREED,67\nZ. FREI\n,207\nA. FREISE\n,38, 110\nO. FREITAS\n,200, 141\nR. FREY\n,79\nW. FRISCHHERTZ,65\nP. FRITSCHEL,36\nV. V. FROLOV,65\nG. G. FRONZ\u00c9\n,29\nM. FUENTES-GARCIA\n,11\nS. FUJII,208\nT. FUJIMORI,209\nP. FULDA,47\nM. FYFFE,65\nB. GADRE\n,73\nJ. R. GAIR\n,1\nS. GALAUDAGE\n,190\nV. GALDI,210\nR. GAMBA,7\nA. GAMBOA\n,1\nS. GAMOJI,185\nD. GANAPATHY\n,211\nA. GANGULY\n,81\nB. GARAVENTA\n,30\nJ. GARC\u00cdA-BELLIDO\n,212\nC. GARC\u00cdA-QUIR\u00d3S\n,193\nJ. W. GARDNER\n,35\nK. A. GARDNER,117\nS. GARG,43\nJ. GARGIULO\n,64\nX. GARRIDO\n,42\nA. GARRON\n,100\nF. GARUFI\n,33, 4\nP. A. GARVER,91\nC. GASBARRA\n,21, 22\nB. GATELEY,2\nF. GAUTIER\n,213\nV. GAYATHRI\n,10\nT. GAYER,80\nG. GEMME\n,30\nA. GENNAI\n,82\nV. GENNARI\n,102\nJ. GEORGE,105\nR. GEORGE\n,151\nO. GERBERDING\n,99\nL. GERGELY\n,157\nARCHISMAN GHOSH\n,96\nSAYANTAN GHOSH,199\nSHAON GHOSH\n,197\nSHROBANA GHOSH,8, 9\nSUPROVO GHOSH\n,214\nTATHAGATA GHOSH\n,81\nJ. A. GIAIME\n,12, 65\nK. D. GIARDINA,65\nD. R. GIBSON,205\nC. GIER\n,56\nS. GKAITATZIS\n,83, 82\nJ. GLANZER\n,11\nF. GLOTIN\n,42\nJ. GODFREY,79\nR. V. GODLEY,8, 9\nP. GODWIN\n,11\nA. S. GOETTEL\n,34\nE. GOETZ\n,117\nJ. GOLOMB,11\nS. GOMEZ LOPEZ\n,40, 39\nB. GONCHAROV\n,45\nG. GONZ\u00c1LEZ\n,12\nP. GOODARZI\n,215\nS. GOODE,6\nA. W. GOODWIN-JONES\n,15\nM. GOSSELIN,64\nR. GOUATY\n,32\nD. W. GOULD,35\nK. GOVORKOVA,36\nA. GRADO\n,78, 52\nV. GRAHAM\n,88\nA. E. GRANADOS\n,18\nM. GRANATA\n,179\nV. GRANATA\n,216, 135\nS. GRAS,36\nP. GRASSIA,11\nJ. GRAVES,58\nC. GRAY,2\nR. GRAY\n,88\nG. GRECO,52\nA. C. GREEN\n,38, 110\nL. GREEN,217\nS. M. GREEN,75\nS. R. GREEN\n,218\nC. GREENBERG,136\nA. M. GRETARSSON,67\nH. K. GRIFFIN,18\nD. GRIFFITH,11\nH. L. GRIGGS\n,58\nG. GRIGNANI,78, 52\nC. GRIMAUD\n,32\nH. GROTE\n,34\nS. GRUNEWALD\n,1\nD. GUERRA\n,141\nD. GUETTA\n,219\nG. M. GUIDI\n,62, 63\nA. R. GUIMARAES,12\nH. K. GULATI,95\nF. GULMINELLI\n,176, 177\nH. GUO\n,148\nW. GUO\n,74\nY. GUO\n,38, 37\nANURADHA GUPTA\n,220\nI. GUPTA\n,7\nN. C. GUPTA,95\nS. K. GUPTA,47\nV. GUPTA\n,18\nN. GUPTE,1\nJ. GURS,99\nN. GUTIERREZ,179\nN. GUTTMAN,6\nF. GUZMAN\n,134\nD. HABA,221\nM. HABERLAND\n,1\nS. HAINO,222\nE. D. HALL\n,36\nR. HAMBURG\n,223\nE. Z. HAMILTON\n,100\nG. HAMMOND\n,88\nM. HANEY,38\nJ. HANKS,2\nC. HANNA\n,7\nM. D. HANNAM,34\nO. A. HANNUKSELA\n,224\nA. G. HANSELMAN\n,133\nH. HANSEN,2\nJ. HANSON,65\nS. HANUMASAGAR,58\nR. HARADA,43\nA. R. HARDISON,186\nS. HARIKUMAR\n,191\nK. HARIS,38, 73\nI. HARLEY-TROCHIMCZYK,134\nT. HARMARK\n,137\nJ. HARMS\n,45, 46\nG. M. HARRY\n,225\nI. W. HARRY\n,75\nJ. HART,107\nB. HASKELL,97, 226, 227\nC. J. HASTER\n,217\nK. HAUGHIAN\n,88\nH. HAYAKAWA,51\nK. HAYAMA,228\nA. HEFFERNAN\n,229\nM. C. HEINTZE,65\nJ. HEINZE\n,121\nJ. HEINZEL,36\nH. HEITMANN\n,116\nF. HELLMAN\n,211\nA. F. HELMLING-CORNELL\n,79\nG. HEMMING\n,64\nO. HENDERSON-SAPIR\n,118\nM. HENDRY\n,88\nI. S. HENG,88\nM. H. HENNIG\n,88\nC. HENSHAW\n,58\nM. HEURS\n,8, 9\nA. L. HEWITT\n,230, 231\nJ. HEYNEN,15\nJ. HEYNS,36\nS. HIGGINBOTHAM,34\nS. HILD,37, 38\nS. HILL,88\nY. HIMEMOTO\n,232\nN. HIRATA,26\nC. HIROSE,233\nD. HOFMAN,179\nB. E. HOGAN,67\nN. A. HOLLAND,38, 110\nI. J. HOLLOWS\n,178\nD. E. HOLZ\n,133\nL. HONET,114\nD. J. HORTON-BAILEY,211\nJ. HOUGH\n,88\nS. HOURIHANE\n,11\nN. T. HOWARD,147\nE. J. HOWELL\n,74\nC. G. HOY\n,75\nC. A. HRISHIKESH,21\nP. HSI,36\nH.-F. HSIEH\n,145\nH.-Y. HSIEH,145\nC. HSIUNG,234\nS.-H. HSU,149\nW.-F. HSU\n,112\nQ. HU\n,88\nH. Y. HUANG\n,144\nY. HUANG\n,7\nY. T. HUANG,80\nA. D. HUDDART,235\nB. HUGHEY,67\nV. HUI\n,32\nS. HUSA\n,100\nR. HUXFORD,7\nL. IAMPIERI\n,40, 39\nG. A. IANDOLO\n,37\nM. IANNI,22, 21\nG. IANNONE\n,135\nJ. IASCAU,79\nK. IDE,236\nR. IDEN,221\nA. IERARDI,45, 46\nS. IKEDA,150\nH. IMAFUKU,43\nY. INOUE,144\nG. IORIO\n,93\nP. IOSIF\n,189, 49\nM. H. IQBAL,35\nJ. IRWIN\n,88\n\n43\nR. ISHIKAWA,236\nM. ISI\n,195, 196\nK. S. ISLEIF\n,237\nY. ITOH\n,209, 238\nM. IWAYA,208\nB. R. IYER\n,24\nC. JACQUET,102\nP.-E. JACQUET\n,124\nT. JACQUOT,42\nS. J. JADHAV,239\nS. P. JADHAV\n,158\nM. JAIN,136\nT. JAIN,230\nA. L. JAMES\n,11\nA. JAN\n,151\nK. JANI\n,147\nJ. JANQUART\n,15\nN. N. JANTHALUR,239\nS. JARABA\n,240\nP. JARANOWSKI\n,241\nR. JAUME\n,100\nW. JAVED,34\nA. JENNINGS,2\nM. JENSEN,2\nW. JIA,36\nJ. JIANG\n,153\nH.-B. JIN\n,242, 243\nS. J. JIN\n,74\nG. R. JOHNS,125\nN. A. JOHNSON,47\nN. K. JOHNSON-MCDANIEL\n,220\nM. C. JOHNSTON\n,217\nR. JOHNSTON,88\nN. JOHNY,8, 9\nD. H. JONES\n,35\nD. I. JONES,214\nR. JONES,88\nH. E. JOSE,79\nP. JOSHI\n,7\nS. K. JOSHI,81\nG. JOUBERT,57\nJ. JU,244\nL. JU\n,74\nK. JUNG\n,245\nJ. JUNKER\n,35\nV. JUSTE,114\nH. B. KABAGOZ\n,65, 36\nT. KAJITA\n,246\nI. KAKU,209\nV. KALOGERA\n,98\nM. KALOMENOPOULOS\n,217\nM. KAMIIZUMI\n,51\nN. KANDA\n,238, 209\nS. KANDHASAMY\n,81\nG. KANG\n,247\nN. C. KANNACHEL,6\nJ. B. KANNER,11\nS. A. KANTIMAHANTY,18\nS. J. KAPADIA\n,81\nD. P. KAPASI\n,55\nM. KARTHIKEYAN,136\nM. KASPRZACK\n,11\nH. KATO,155\nT. KATO,208\nE. KATSAVOUNIDIS,36\nW. KATZMAN,65\nR. KAUSHIK\n,105\nK. KAWABE,2\nR. KAWAMOTO,209\nD. KEITEL\n,100\nL. J. KEMPERMAN\n,118\nJ. KENNINGTON\n,7\nF. A. KERKOW,18\nR. KESHARWANI\n,81\nJ. S. KEY\n,248\nR. KHADELA,8, 9\nS. KHADKA,91\nS. S. KHADKIKAR,7\nF. Y. KHALILI\n,111\nF. KHAN\n,8, 9\nT. KHANAM,167\nM. KHURSHEED,105\nN. M. KHUSID,195, 196\nW. KIENDREBEOGO\n,116, 249\nN. KIJBUNCHOO\n,118\nC. KIM,250\nJ. C. KIM,251\nK. KIM\n,252\nM. H. KIM\n,244\nS. KIM\n,253\nY.-M. KIM\n,252\nC. KIMBALL\n,98\nK. KIMES,55\nM. KINNEAR,34\nJ. S. KISSEL\n,2\nS. KLIMENKO,47\nA. M. KNEE\n,117\nE. J. KNOX,79\nN. KNUST\n,8, 9\nK. KOBAYASHI,208\nS. M. KOEHLENBECK\n,91\nG. KOEKOEK,38, 37\nK. KOHRI\n,254, 255\nK. KOKEYAMA\n,34, 256\nS. KOLEY\n,45, 169\nP. KOLITSIDOU\n,121\nA. E. KOLONIARI\n,257\nK. KOMORI\n,43\nA. K. H. KONG\n,145\nA. KONTOS\n,258\nL. M. KOPONEN,121\nM. KOROBKO\n,99\nX. KOU,18\nA. KOUSHIK\n,23\nN. KOUVATSOS\n,69\nM. KOVALAM,74\nT. KOYAMA,155\nD. B. KOZAK,11\nS. L. KRANZHOFF,37, 38\nV. KRINGEL,8, 9\nN. V. KRISHNENDU\n,121\nS. KROKER,259\nA. KR\u00d3LAK\n,260, 191\nK. KRUSKA,8, 9\nJ. KUBISZ\n,261\nG. KUEHN,8, 9\nS. KULKARNI\n,220\nA. KULUR RAMAMOHAN\n,35\nACHAL KUMAR,47\nANIL KUMAR,239\nPRAVEEN KUMAR\n,182\nPRAYUSH KUMAR\n,24\nRAHUL KUMAR,2\nRAKESH KUMAR,95\nJ. KUME\n,262, 263, 43\nK. KUNS\n,36\nN. KUNTIMADDI,34\nS. KUROYANAGI\n,212, 264\nS. KUWAHARA\n,43\nK. KWAK\n,245\nK. KWAN,35\nS. KWON\n,43\nG. LACAILLE,88\nD. LAGHI\n,193, 102\nA. H. LAITY,159\nE. LALANDE,265\nM. LALLEMAN\n,23\nP. C. LALREMRUATI,266\nM. LANDRY,2\nB. B. LANE,36\nR. N. LANG\n,36\nJ. LANGE,151\nR. LANGGIN\n,217\nB. LANTZ\n,91\nI. LA ROSA\n,100\nJ. LARSEN,204\nA. LARTAUX-VOLLARD\n,42\nP. D. LASKY\n,6\nJ. LAWRENCE\n,168\nM. LAXEN\n,65\nC. LAZARTE\n,141\nA. LAZZARINI\n,11\nC. LAZZARO,161, 160\nP. LEACI\n,40, 39\nL. LEALI,18\nY. K. LECOEUCHE\n,117\nH. M. LEE\n,267\nH. W. LEE\n,268\nJ. LEE,80\nK. LEE\n,244\nR.-K. LEE\n,145\nR. LEE,36\nSUNGHO LEE\n,252\nSUNJAE LEE,244\nY. LEE,144\nI. N. LEGRED,11\nJ. LEHMANN,8, 9\nL. LEHNER,187\nM. LE JEAN\n,179, 119\nA. LEMA\u00ceTRE\n,269\nM. LENTI\n,63, 181\nM. LEONARDI\n,76, 77, 270\nM. LEQUIME,41\nN. LEROY\n,42\nM. LESOVSKY,11\nN. LETENDRE,32\nM. LETHUILLIER\n,57\nY. LEVIN,6\nK. LEYDE,75\nA. K. Y. LI,11\nK. L. LI\n,271\nT. G. F. LI,112\nX. LI\n,152\nY. LI,98\nZ. LI,88\nA. LIHOS,125\nE. T. LIN\n,145\nF. LIN,144\nL. C.-C. LIN\n,271\nY.-C. LIN\n,145\nC. LINDSAY,205\nS. D. LINKER,185\nA. LIU\n,224\nG. C. LIU\n,234\nJIAN LIU\n,74\nF. LLAMAS VILLARREAL,168\nJ. LLOBERA-QUEROL\n,100\nR. K. L. LO\n,143\nJ.-P. LOCQUET,112\nS. C. G. LOGGINS,272\nM. R. LOIZOU,136\nL. T. LONDON,69\nA. LONGO\n,62, 63\nD. LOPEZ\n,169\nM. LOPEZ PORTILLA,73\nA. LORENZO-MEDINA\n,182\nV. LORIETTE,42\nM. LORMAND,65\nG. LOSURDO\n,273, 82\nE. LOTTI,136\nT. P. LOTT IV\n,58\nJ. D. LOUGH\n,8, 9\nH. A. LOUGHLIN,36\nC. O. LOUSTO\n,113\nN. LOW,126\nN. LU\n,35\nL. LUCCHESI\n,82\nH. L\u00dcCK,9, 8, 9\nD. LUMACA\n,22\nA. P. LUNDGREN\n,274, 275\nA. W. LUSSIER\n,265\nR. MACAS\n,75\nM. MACINNIS,36\nD. M. MACLEOD\n,34\nI. A. O. MACMILLAN\n,11\nA. MACQUET\n,42\nK. MAEDA,155\nS. MAENAUT\n,112\nS. S. MAGARE,81\nR. M. MAGEE\n,11\nE. MAGGIO\n,1\nR. MAGGIORE,38, 110\nM. MAGNOZZI\n,30, 31\nM. MAHESH,99\nM. MAINI,159\nS. MAJHI,81\nE. MAJORANA,40, 39\nC. N. MAKAREM,11\nD. MALAKAR\n,108\nJ. A. MALAQUIAS-REIS,19\nU. MALI\n,194\nS. MALIAKAL,11\nA. MALIK,105\nL. MALLICK\n,172, 194\nA.-K. MALZ\n,60\nN. MAN,116\nM. MANCARELLA\n,101\nV. MANDIC\n,18\nV. MANGANO\n,174, 160\nB. MANNIX,79\nG. L. MANSELL\n,80\nM. MANSKE\n,10\nM. MANTOVANI\n,64\nM. MAPELLI\n,93, 94, 276\nC. MARINELLI\n,103\nF. MARION\n,32\nA. S. MARKOSYAN,91\nA. MARKOWITZ,11\nE. MAROS,11\nS. MARSAT\n,102\nF. MARTELLI\n,62, 63\nI. W. MARTIN\n,88\nR. M. MARTIN\n,197\nB. B. MARTINEZ,134\nD. A. MARTINEZ,55\nM. MARTINEZ,44, 277\nV. MARTINEZ\n,131\nA. MARTINI,76, 77\nJ. C. MARTINS\n,19\nD. V. MARTYNOV,121\nE. J. MARX,36\nL. MASSARO,37, 38\nA. MASSEROT,32\nM. MASSO-REID\n,88\nS. MASTROGIOVANNI\n,39\nT. MATCOVICH\n,52\nM. MATIUSHECHKINA\n,8, 9\nL. MAURIN,213\nN. MAVALVALA\n,36\nN. MAXWELL,2\nG. MCCARROL,65\nR. MCCARTHY,2\nD. E. MCCLELLAND\n,35\nS. MCCORMICK,65\nL. MCCULLER\n,11\nS. MCEACHIN,125\nC. MCELHENNY,125\nG. I. MCGHEE\n,88\nJ. MCGINN,88\nK. B. M. MCGOWAN,147\nJ. MCIVER\n,117\nA. MCLEOD\n,74\nI. MCMAHON\n,193\nT. MCRAE,35\nR. MCTEAGUE\n,88\nD. MEACHER\n,10\nB. N. MEAGHER,80\nR. MECHUM,113\nQ. MEIJER,73\nA. MELATOS,126\nM. MELCHING\n,8, 278\nC. S. MENONI\n,140\nF. MERA,2\nR. A. MERCER\n,10\nL. MERENI,179\nK. MERFELD,167\nE. L. MERILH,65\nJ. R. M\u00c9ROU\n,100\nJ. D. MERRITT,79\nM. MERZOUGUI,116\nC. MESSICK\n,10\nB. MESTICHELLI,45\nM. MEYER-CONDE\n,279\nF. MEYLAHN\n,8, 9\nA. MHASKE,81\nA. MIANI\n,76, 77\nH. MIAO,280\nC. MICHEL\n,179\nY. MICHIMURA\n,43\nH. MIDDLETON\n,121\nD. P. MIHAYLOV\n,107\nS. J. MILLER\n,11\nM. MILLHOUSE\n,58\nE. MILOTTI\n,189, 49\nV. MILOTTI\n,93\nY. MINENKOV,22\nE. M. MINIHAN,67\nLL. M. MIR\n,44\nL. MIRASOLA\n,160, 161\nM. MIRAVET-TEN\u00c9S\n,141\nC.-A. MIRITESCU\n,44\nA. MISHRA,24\nC. MISHRA\n,109\nT. MISHRA\n,47\nA. L. MITCHELL,38, 110\nJ. G. MITCHELL,67\nS. MITRA\n,81\nV. P. MITROFANOV\n,111\nK. MITSUHASHI,26\nR. MITTLEMAN,36\nO. MIYAKAWA\n,51\nS. MIYOKI\n,51\nA. MIYOKO,67\nG. MO\n,36\nL. MOBILIA\n,62, 63\nS. R. P. MOHAPATRA,11\nS. R. MOHITE\n,7\nM. MOLINA-RUIZ\n,211\nM. MONDIN,185\nM. MONTANI,62, 63\nC. J. MOORE,230\nD. MORARU,2\nA. MORE\n,81\nS. MORE\n,81\nC. MORENO\n,138\nE. A. MORENO\n,36\nG. MORENO,2\nA. MORESO SERRA,84\n\n44\nS. MORISAKI\n,43, 208\nY. MORIWAKI\n,155\nG. MORRAS\n,212\nA. MOSCATELLO\n,93\nM. MOULD\n,36\nP. MOURIER\n,229, 281\nB. MOURS\n,66\nC. M. MOW-LOWRY\n,38, 110\nL. MUCCILLO\n,181, 63\nF. MUCIACCIA\n,40, 39\nD. MUKHERJEE\n,121\nSAMANWAYA MUKHERJEE,24\nSOMA MUKHERJEE,168\nSUBROTO MUKHERJEE,95\nSUVODIP MUKHERJEE\n,13\nN. MUKUND\n,36\nA. MULLAVEY,65\nH. MULLOCK,117\nJ. MUNDI,225\nC. L. MUNGIOLI,74\nM. MURAKOSHI,236\nP. G. MURRAY\n,88\nD. NABARI\n,76, 77\nS. L. NADJI,8, 9\nA. NAGAR,29, 282\nN. NAGARAJAN\n,88\nK. NAKAGAKI,51\nK. NAKAMURA\n,26\nH. NAKANO\n,283\nM. NAKANO,11\nD. NANADOUMGAR-LACROZE\n,44\nD. NANDI,12\nV. NAPOLANO,64\nP. NARAYAN\n,220\nI. NARDECCHIA\n,22\nT. NARIKAWA,208\nH. NAROLA,73\nL. NATICCHIONI\n,39\nR. K. NAYAK\n,266\nL. NEGRI,73\nA. NELA,88\nC. NELLE,79\nA. NELSON\n,134\nT. J. N. NELSON,65\nM. NERY,8, 9\nA. NEUNZERT\n,2\nS. NG,55\nL. NGUYEN QUYNH\n,284\nS. A. NICHOLS,12\nA. B. NIELSEN\n,285\nY. NISHINO,26, 43\nA. NISHIZAWA\n,286\nS. NISSANKE,287, 38\nW. NIU\n,7\nF. NOCERA,64\nJ. NOLLER,288\nM. NORMAN,34\nC. NORTH,34\nJ. NOVAK\n,119, 240, 289\nR. NOWICKI\n,147\nJ. F. NU\u00d1O SILES\n,212\nL. K. NUTTALL\n,75\nK. OBAYASHI,236\nJ. OBERLING\n,2\nJ. O\u2019DELL,235\nE. OELKER\n,36\nM. OERTEL\n,240, 119, 290, 289\nG. OGANESYAN,45, 46\nT. O\u2019HANLON,65\nM. OHASHI\n,51\nF. OHME\n,8, 9\nR. OLIVERI\n,119, 290, 289\nR. OMER,18\nB. O\u2019NEAL,125\nM. ONISHI,155\nK. OOHARA\n,291\nB. O\u2019REILLY\n,65\nR. ORAM,65\nM. ORSELLI\n,52, 78\nR. O\u2019SHAUGHNESSY\n,113\nS. O\u2019SHEA,88\nS. OSHINO\n,51\nC. OSTHELDER,11\nI. OTA\n,12\nD. J. OTTAWAY\n,118\nA. OUZRIAT,57\nH. OVERMIER,65\nB. J. OWEN\n,292\nR. OZAKI,236\nA. E. PACE\n,7\nR. PAGANO\n,12\nM. A. PAGE\n,26\nA. PAI\n,199\nL. PAIELLA,45\nA. PAL,293\nS. PAL\n,266\nM. A. PALAIA\n,82, 83\nM. P\u00c1LFI,207\nP. P. PALMA,40, 21, 22\nC. PALOMBA\n,39\nP. PALUD\n,20\nH. PAN,145\nJ. PAN,74\nK. C. PAN\n,145\nP. K. PANDA,239\nSHIKSHA PANDEY,7\nSWADHA PANDEY,36\nP. T. H. PANG,38, 73\nF. PANNARALE\n,40, 39\nK. A. PANNONE,55\nB. C. PANT,105\nF. H. PANTHER,74\nM. PANZERI,62, 63\nF. PAOLETTI\n,82\nA. PAOLONE\n,39, 294\nA. PAPADOPOULOS\n,88\nE. E. PAPALEXAKIS,215\nL. PAPALINI\n,82, 83\nG. PAPIGKIOTIS\n,257\nA. PAQUIS,42\nA. PARISI\n,78, 52\nB.-J. PARK,252\nJ. PARK\n,295\nW. PARKER\n,65\nG. PASCALE,8, 9\nD. PASCUCCI\n,96\nA. PASQUALETTI\n,64\nR. PASSAQUIETI\n,83, 82\nL. PASSENGER,6\nD. PASSUELLO,82\nO. PATANE\n,2\nA. V. PATEL\n,144\nD. PATHAK,81\nL. PATHAK\n,81\nA. PATRA,34\nB. PATRICELLI\n,83, 82\nB. G. PATTERSON,34\nK. PAUL\n,109\nS. PAUL\n,79\nE. PAYNE\n,11\nT. PEARCE,34\nM. PEDRAZA,11\nA. PELE\n,11\nF. E. PE\u00d1A ARELLANO\n,296\nX. PENG,121\nY. PENG,58\nS. PENN\n,297\nM. D. PENULIAR,55\nA. PEREGO\n,76, 77\nZ. PEREIRA,136\nC. P\u00c9RIGOIS\n,298, 94, 93\nG. PERNA\n,93\nA. PERRECA\n,76, 77, 45\nJ. PERRET\n,20\nS. PERRI\u00c8S\n,57\nJ. W. PERRY,38, 110\nD. PESIOS,257\nS. PETERS,169\nS. PETRACCA,210\nC. PETRILLO,78\nH. P. PFEIFFER\n,1\nH. PHAM,65\nK. A. PHAM\n,18\nK. S. PHUKON\n,121\nH. PHURAILATPAM,224\nM. PIARULLI,102\nL. PICCARI\n,40, 39\nO. J. PICCINNI\n,35\nM. PICHOT\n,116\nM. PIENDIBENE\n,83, 82\nF. PIERGIOVANNI\n,62, 63\nL. PIERINI\n,39\nG. PIERRA\n,39\nV. PIERRO\n,299, 135\nM. PIETRZAK,97\nM. PILLAS\n,169\nF. PILO\n,82\nL. PINARD\n,179\nI. M. PINTO\n,299, 135, 300, 33\nM. PINTO\n,64\nB. J. PIOTRZKOWSKI\n,10\nM. PIRELLO,2\nM. D. PITKIN\n,230, 88\nA. PLACIDI\n,52\nE. PLACIDI\n,40, 39\nM. L. PLANAS\n,100\nW. PLASTINO\n,216, 22\nC. PLUNKETT\n,36\nR. POGGIANI\n,83, 82\nE. POLINI,36\nJ. POMPER,82, 83\nL. POMPILI\n,1\nJ. POON,224\nE. PORCELLI,38\nE. K. PORTER,20\nC. POSNANSKY\n,7\nR. POULTON\n,64\nJ. POWELL\n,158\nG. S. PRABHU,81\nM. PRACCHIA\n,169\nB. K. PRADHAN\n,81\nT. PRADIER\n,66\nA. K. PRAJAPATI,95\nK. PRASAI\n,301\nR. PRASANNA,239\nP. PRASIA,81\nG. PRATTEN\n,121\nG. PRINCIPE\n,189, 49\nG. A. PRODI\n,76, 77\nP. PROSPERI,82\nP. PROSPOSITO,21, 22\nA. C. PROVIDENCE,67\nA. PUECHER\n,1\nJ. PULLIN\n,12\nP. PUPPO,39\nM. P\u00dcRRER\n,159\nH. QI\n,16\nJ. QIN\n,35\nG. QU\u00c9M\u00c9NER\n,177, 119\nV. QUETSCHKE,168\nP. J. QUINONEZ,67\nN. QUTOB,58\nR. RADING,237\nI. RAINHO,141\nS. RAJA,105\nC. RAJAN,105\nB. RAJBHANDARI\n,113\nK. E. RAMIREZ\n,65\nF. A. RAMIS VIDAL\n,100\nM. RAMOS AREVALO\n,168\nA. RAMOS-BUADES\n,100, 38\nS. RANJAN\n,58\nK. RANSOM,65\nP. RAPAGNANI\n,40, 39\nB. RATTO,67\nA. RAVICHANDRAN,136\nA. RAY\n,98\nV. RAYMOND\n,34\nM. RAZZANO\n,83, 82\nJ. READ,55\nT. REGIMBAU,32\nS. REID,56\nC. REISSEL,36\nD. H. REITZE\n,11\nA. I. RENZINI,11\nA. RENZINI\n,129\nB. REVENU\n,302, 42\nA. REVILLA PE\u00d1A,84\nR. REYES,185\nL. RICCA\n,15\nF. RICCI\n,40, 39\nM. RICCI\n,39, 40\nA. RICCIARDONE\n,83, 82\nJ. RICE,80\nJ. W. RICHARDSON\n,215\nM. L. RICHARDSON,118\nA. RIJAL,67\nK. RILES\n,92\nH. K. RILEY,34\nS. RINALDI\n,276\nJ. RITTMEYER,99\nC. ROBERTSON,235\nF. ROBINET,42\nM. ROBINSON,2\nA. ROCCHI\n,22\nL. ROLLAND\n,32\nJ. G. ROLLINS\n,11\nA. E. ROMANO\n,303\nR. ROMANO\n,3, 4\nA. ROMERO\n,32\nI. M. ROMERO-SHAW,230\nJ. H. ROMIE,65\nS. RONCHINI\n,7\nT. J. ROOCKE\n,118\nL. ROSA,4, 33\nT. J. ROSAUER,215\nC. A. ROSE,58\nD. ROSI \u00b4NSKA\n,127\nM. P. ROSS\n,54\nM. ROSSELLO-SASTRE\n,100\nS. ROWAN\n,88\nS. K. ROY\n,195, 196\nS. ROY\n,15\nD. ROZZA\n,129, 130\nP. RUGGI,64\nN. RUHAMA,245\nE. RUIZ MORALES\n,304, 212\nK. RUIZ-ROCHA,147\nS. SACHDEV\n,58\nT. SADECKI,2\nP. SAFFARIEH\n,38, 110\nS. SAFI-HARB\n,172\nM. R. SAH\n,13\nS. SAHA\n,145\nT. SAINRAT\n,66\nS. SAJITH MENON\n,219, 40, 39\nK. SAKAI,305\nY. SAKAI\n,279\nM. SAKELLARIADOU\n,69\nS. SAKON\n,7\nO. S. SALAFIA\n,163, 130, 129\nF. SALCES-CARCOBA\n,11\nL. SALCONI,64\nM. SALEEM\n,151\nF. SALEMI\n,40, 39\nM. SALL\u00c9\n,38\nS. U. SALUNKHE,81\nS. SALVADOR\n,177, 176\nA. SALVARESE,151\nA. SAMAJDAR\n,73, 38\nA. SANCHEZ,2\nE. J. SANCHEZ,11\nL. E. SANCHEZ,11\nN. SANCHIS-GUAL\n,141\nJ. R. SANDERS,186\nE. M. S\u00c4NGER\n,1\nF. SANTOLIQUIDO\n,45, 46\nF. SARANDREA,29\nT. R. SARAVANAN,81\nN. SARIN,6\nP. SARKAR,8, 9\nA. SASLI\n,257\nP. SASSI\n,52, 78\nB. SASSOLAS\n,179\nB. S. SATHYAPRAKASH\n,7, 34\nR. SATO,233\nS. SATO,155\nYUKINO SATO,155\nYU SATO,155\nO. SAUTER\n,47\nR. L. SAVAGE\n,2\nT. SAWADA\n,51\nH. L. SAWANT,81\nS. SAYAH,179\nV. SCACCO,21, 22\nD. SCHAETZL,11\nM. SCHEEL,152\nA. SCHIEBELBEIN,194\nM. G. SCHIWORSKI\n,80\nP. SCHMIDT\n,121\nS. SCHMIDT\n,73\nR. SCHNABEL\n,99\nM. SCHNEEWIND,8, 9\nR. M. S. SCHOFIELD,79\nK. SCHOUTEDEN\n,112\nB. W. SCHULTE,8, 9\nB. F. SCHUTZ,34, 8, 9\nE. SCHWARTZ\n,306\nM. SCIALPI\n,307\nJ. SCOTT\n,88\nS. M. SCOTT\n,35\nR. M. SEDAS\n,65\nT. C. SEETHARAMU,88\nM. SEGLAR-ARROYO\n,44\nY. SEKIGUCHI\n,308\nD. SELLERS,65\nN. SEMBO,209\nA. S. SENGUPTA\n,309\nE. G. SEO\n,88\nJ. W. SEO\n,112\nV. SEQUINO,33, 4\nM. SERRA\n,39\nA. SEVRIN,192\nT. SHAFFER,2\nU. S. SHAH\n,58\n\n45\nM. A. SHAIKH\n,267\nL. SHAO\n,310\nA. K. SHARMA\n,100\nA. SHARMA\n,311\nPREETI SHARMA,12\nPRIANKA SHARMA,105\nRITWIK SHARMA,18\nS. SHARMA CHAUDHARY,108\nP. SHAWHAN\n,128\nN. S. SHCHEBLANOV\n,312, 269\nE. SHERIDAN,147\nZ.-H. SHI,145\nM. SHIKAUCHI,43\nR. SHIMOMURA,313\nH. SHINKAI\n,313\nS. SHIRKE,81\nD. H. SHOEMAKER\n,36\nD. M. SHOEMAKER\n,151\nR. W. SHORT,2\nS. SHYAMSUNDAR,105\nA. SIDER,162\nH. SIEGEL\n,195, 196\nD. SIGG\n,2\nL. SILENZI\n,37, 38\nL. SILVESTRI\n,40, 173\nM. SIMMONDS,118\nL. P. SINGER\n,314\nAMITESH SINGH,220\nANIKA SINGH,11\nD. SINGH\n,211\nM. K. SINGH\n,315\nN. SINGH\n,100\nS. SINGH,221, 61\nA. M. SINTES\n,100\nV. SIPALA,174, 160\nV. SKLIRIS\n,34\nB. J. J. SLAGMOLEN\n,35\nD. A. SLATER,204\nT. J. SLAVEN-BLAIR,74\nJ. SMETANA,121\nJ. R. SMITH\n,55\nL. SMITH\n,88, 189, 49\nR. J. E. SMITH\n,6\nW. J. SMITH\n,147\nS. SOARES DE ALBUQUERQUE FILHO,62\nM. SOARES-SANTOS,193\nK. SOMIYA\n,221\nI. SONG\n,145\nS. SONI\n,36\nV. SORDINI\n,57\nF. SORRENTINO,30\nH. SOTANI\n,316\nF. SPADA\n,82\nV. SPAGNUOLO\n,38\nA. P. SPENCER\n,88\nP. SPINICELLI\n,64\nA. K. SRIVASTAVA,95\nF. STACHURSKI\n,88\nC. J. STARK,125\nD. A. STEER\n,317\nN. STEINLE\n,172\nJ. STEINLECHNER,37, 38\nS. STEINLECHNER\n,37, 38\nN. STERGIOULAS\n,257\nP. STEVENS,42\nS. P. STEVENSON,158\nM. STPIERRE,159\nM. D. STRONG,12\nA. STRUNK,2\nA. L. STUVER,104, \u2217\nM. SUCHENEK,97\nS. SUDHAGAR\n,97\nY. SUDO,236\nN. SUELTMANN,99\nL. SULEIMAN\n,55\nJ. M. SULLIVAN\n,318\nK. D. SULLIVAN,12\nJ. SUN\n,247\nL. SUN\n,35\nS. SUNIL,95\nJ. SURESH\n,116\nB. J. SUTTON,69\nP. J. SUTTON\n,34\nK. SUZUKI,221\nM. SUZUKI,208\nB. L. SWINKELS\n,38\nA. SYX\n,119\nM. J. SZCZEPA \u00b4NCZYK\n,319\nP. SZEWCZYK\n,127\nM. TACCA\n,38\nH. TAGOSHI\n,208\nK. TAKADA,208\nH. TAKAHASHI\n,279\nR. TAKAHASHI\n,26\nA. TAKAMORI\n,43\nS. TAKANO\n,320\nH. TAKEDA\n,321, 322\nK. TAKESHITA,221\nI. TAKIMOTO SCHMIEGELOW,45, 46\nM. TAKOU-AYAOH,80\nC. TALBOT,133\nM. TAMAKI,208\nN. TAMANINI\n,102\nD. TANABE,144\nK. TANAKA,51\nS. J. TANAKA\n,236\nS. TANIOKA\n,34\nD. B. TANNER,47\nW. TANNER,8, 9\nL. TAO\n,215\nR. D. TAPIA,7\nE. N. TAPIA SAN MART\u00cdN\n,38\nC. TARANTO,21, 22\nA. TARUYA\n,323\nJ. D. TASSON\n,156\nJ. G. TAU\n,113\nD. TELLEZ,55\nR. TENORIO\n,100\nH. THEMANN,185\nA. THEODOROPOULOS\n,141\nM. P. THIRUGNANASAMBANDAM,81\nL. M. THOMAS\n,11\nM. THOMAS,65\nP. THOMAS,2\nJ. E. THOMPSON\n,214\nS. R. THONDAPU,105\nK. A. THORNE,65\nE. THRANE\n,6\nS. TIBREWAL\n,151\nJ. TISSINO\n,45, 46\nA. TIWARI,81\nPAWAN TIWARI,45\nPRAVEER TIWARI,199\nS. TIWARI\n,193\nV. TIWARI\n,121\nM. R. TODD,80\nM. TOFFANO,93\nA. M. TOIVONEN\n,18\nK. TOLAND\n,88\nA. E. TOLLEY\n,75\nT. TOMARU\n,26\nV. TOMMASINI,11\nT. TOMURA\n,51\nH. TONG\n,6\nC. TONG-YU,144\nA. TORRES-FORN\u00c9\n,141, 142\nC. I. TORRIE,11\nI. TOSTA E MELO\n,324\nE. TOURNEFIER\n,32\nM. TRAD NERY,116\nK. TRAN,125\nA. TRAPANANTI\n,53, 52\nR. TRAVAGLINI\n,171\nF. TRAVASSO\n,53, 52\nG. TRAYLOR,65\nM. TREVOR,128\nM. C. TRINGALI\n,64\nA. TRIPATHEE\n,92\nG. TROIAN\n,189, 49\nA. TROVATO\n,189, 49\nL. TROZZO,4\nR. J. TRUDEAU,11\nT. TSANG\n,34\nS. TSUCHIDA\n,325\nL. TSUKADA\n,217\nK. TURBANG\n,192, 23\nM. TURCONI\n,116\nC. TURSKI,96\nH. UBACH\n,84, 85\nN. UCHIKATA\n,208\nT. UCHIYAMA\n,51\nR. P. UDALL\n,11\nT. UEHARA\n,326\nK. UENO\n,43\nV. UNDHEIM\n,285\nL. E. URONEN,224\nT. USHIBA\n,51\nM. VACATELLO\n,82, 83\nH. VAHLBRUCH\n,8, 9\nN. VAIDYA\n,11\nG. VAJENTE\n,11\nA. VAJPEYI,6\nJ. VALENCIA\n,100\nM. VALENTINI\n,110, 38\nS. A. VALLEJO-PE\u00d1A\n,303\nS. VALLERO,29\nV. VALSAN\n,10\nM. VAN DAEL\n,38, 327\nE. VAN DEN BOSSCHE\n,192\nJ. F. J. VAN DEN BRAND\n,37, 110, 38\nC. VAN DEN BROECK,73, 38\nM. VAN DER SLUYS\n,38, 73\nA. VAN DE WALLE,42\nJ. VAN DONGEN\n,38, 110\nK. VANDRA,104\nM. VANDYKE,122\nH. VAN HAEVERMAET\n,23\nJ. V. VAN HEIJNINGEN\n,38, 110\nP. VAN HOVE\n,66\nJ. VANIER,265\nM. VANKEUREN,107\nJ. VANOSKY,2\nN. VAN REMORTEL\n,23\nM. VARDARO,37, 38\nA. F. VARGAS\n,126\nV. VARMA\n,136\nA. N. VAZQUEZ,91\nA. VECCHIO\n,121\nG. VEDOVATO,94\nJ. VEITCH\n,88\nP. J. VEITCH\n,118\nS. VENIKOUDIS,15\nR. C. VENTEREA\n,18\nP. VERDIER\n,57\nM. VEREECKEN,15\nD. VERKINDT\n,32\nB. VERMA,136\nY. VERMA\n,105\nS. M. VERMEULEN\n,11\nF. VETRANO,62\nA. VEUTRO\n,39, 40\nA. VICER\u00c9\n,62, 63\nS. VIDYANT,80\nA. D. VIETS\n,90\nA. VIJAYKUMAR\n,194\nA. VILKHA,113\nN. VILLANUEVA ESPINOSA,141\nV. VILLA-ORTEGA\n,182\nE. T. VINCENT\n,58\nJ.-Y. VINET,116\nS. VIRET,57\nS. VITALE\n,36\nH. VOCCA\n,78, 52\nD. VOIGT\n,99\nE. R. G. VON REIS,2\nJ. S. A. VON WRANGEL,8, 9\nW. E. VOSSIUS,237\nL. VUJEVA\n,143\nS. P. VYATCHANIN\n,111\nJ. WACK,11\nL. E. WADE,107\nM. WADE\n,107\nK. J. WAGNER\n,113\nL. WALLACE,11\nE. J. WANG,91\nH. WANG\n,221\nJ. Z. WANG,92\nW. H. WANG,168\nY. F. WANG\n,1\nG. WARATKAR\n,199\nJ. WARNER,2\nM. WAS\n,32\nT. WASHIMI\n,26\nN. Y. WASHINGTON,11\nD. WATARAI,43\nB. WEAVER,2\nS. A. WEBSTER,88\nN. L. WEICKHARDT\n,99\nM. WEINERT,8, 9\nA. J. WEINSTEIN\n,11\nR. WEISS,36\nL. WEN\n,74\nK. WETTE\n,35\nJ. T. WHELAN\n,113\nB. F. WHITING\n,47\nC. WHITTLE\n,11\nE. G. WICKENS,75\nD. WILKEN\n,8, 9, 9\nA. T. WILKIN,215\nB. M. WILLIAMS,122\nD. WILLIAMS\n,88\nM. J. WILLIAMS\n,75\nN. S. WILLIAMS\n,1\nJ. L. WILLIS\n,11\nB. WILLKE\n,9, 8, 9\nM. WILS\n,112\nL. WILSON,107\nC. W. WINBORN,108\nJ. WINTERFLOOD,74\nC. C. WIPF,11\nG. WOAN\n,88\nJ. WOEHLER,37, 38\nN. E. WOLFE,36\nH. T. WONG\n,144\nI. C. F. WONG\n,224, 112\nK. WONG,194\nT. WOUTERS,73, 38\nJ. L. WRIGHT,2\nM. WRIGHT\n,88, 73\nB. WU,80\nC. WU\n,145\nD. S. WU\n,8, 9\nH. WU\n,145\nK. WU,122\nQ. WU,54\nY. WU,98\nZ. WU\n,102\nE. WUCHNER,55\nD. M. WYSOCKI\n,10\nV. A. XU\n,211\nY. XU\n,100\nN. YADAV\n,29\nH. YAMAMOTO\n,11\nK. YAMAMOTO\n,155\nT. S. YAMAMOTO\n,43\nT. YAMAMOTO\n,51\nR. YAMAZAKI\n,236\nT. YAN,121\nK. Z. YANG\n,18\nY. YANG\n,149\nZ. YARBROUGH\n,12\nJ. YEBANA,100\nS.-W. YEH,145\nA. B. YELIKAR\n,147\nX. YIN,36\nJ. YOKOYAMA\n,328, 43\nT. YOKOZAWA,51\nS. YUAN,74\nH. YUZURIHARA\n,51\nM. ZANOLIN,67\nM. ZEESHAN\n,113\nT. ZELENOVA,64\nJ.-P. ZENDRI,94\nM. ZEOLI\n,15\nM. ZERRAD,41\nM. ZEVIN\n,98\nL. ZHANG,11\nN. ZHANG,58\nR. ZHANG\n,153\nT. ZHANG,121\nC. ZHAO\n,74\nYUE ZHAO,166\nYUHANG ZHAO,20\nZ.-C. ZHAO\n,329\nY. ZHENG\n,108\nH. ZHONG\n,18\nH. ZHOU,80\nH. O. ZHU,74\nZ.-H. ZHU\n,329, 330\nA. B. ZIMMERMAN\n,151\nL. ZIMMERMANN,57\nM. E. ZUCKER\n36, 11 AND J. ZWEIZIG\n11\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n\n46\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00e9orique, Aix-Marseille Universit\u00e9, Campus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n20Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25University College Dublin, Bel\ufb01eld, Dublin 4, Ireland\n26Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n28Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n29INFN Sezione di Torino, I-10125 Torino, Italy\n30INFN, Sezione di Genova, I-16146 Genova, Italy\n31Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n32Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n33Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n34Cardiff University, Cardiff CF24 3AA, United Kingdom\n35OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n36LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n37Maastricht University, 6200 MD Maastricht, Netherlands\n38Nikhef, 1098 XG Amsterdam, Netherlands\n39INFN, Sezione di Roma, I-00185 Roma, Italy\n40Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n41Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n42Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n43University of Tokyo, Tokyo, 113-0033, Japan\n44Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n45Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n46INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n47University of Florida, Gainesville, FL 32611, USA\n48Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n49INFN, Sezione di Trieste, I-34127 Trieste, Italy\n50Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, 64849 Monterrey, Nuevo Le\u00f3n, Mexico\n51Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n52INFN, Sezione di Perugia, I-06123 Perugia, Italy\n53Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n54University of Washington, Seattle, WA 98195, USA\n55California State University Fullerton, Fullerton, CA 92831, USA\n56SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n57Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n\n47\n58Georgia Institute of Technology, Atlanta, GA 30332, USA\n59Chennai Mathematical Institute, Chennai 603103, India\n60Royal Holloway, University of London, London TW20 0EX, United Kingdom\n61Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n62Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n63INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n64European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n65LIGO Livingston Observatory, Livingston, LA 70754, USA\n66Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n67Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n68Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n69King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n70Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n71International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n72Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n73Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n74OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n75University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n76Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n77INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n78Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n79University of Oregon, Eugene, OR 97403, USA\n80Syracuse University, Syracuse, NY 13244, USA\n81Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n82INFN, Sezione di Pisa, I-56127 Pisa, Italy\n83Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n84Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n85Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n86Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n87Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n88IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n89HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n90Concordia University Wisconsin, Mequon, WI 53097, USA\n91Stanford University, Stanford, CA 94305, USA\n92University of Michigan, Ann Arbor, MI 48109, USA\n93Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n94INFN, Sezione di Padova, I-35131 Padova, Italy\n95Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n96Universiteit Gent, B-9000 Gent, Belgium\n97Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n98Northwestern University, Evanston, IL 60208, USA\n99Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n100IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n101Aix-Marseille Universit\u00e9, Universit\u00e9 de Toulon, CNRS, CPT, Marseille, France\n102Laboratoire des 2 In\ufb01nis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n103Universit\u00e0 di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n104Villanova University, Villanova, PA 19085, USA\n105RRCAT, Indore, Madhya Pradesh 452013, India\n106Inter-university Center for Astronomy and Astrophysics, Pune 411007, India\n107Kenyon College, Gambier, OH 43022, USA\n108Missouri University of Science and Technology, Rolla, MO 65409, USA\n109Indian Institute of Technology Madras, Chennai 600036, India\n110Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n111Lomonosov Moscow State University, Moscow 119991, Russia\n112Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n113Rochester Institute of Technology, Rochester, NY 14623, USA\n114Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n\n48\n115Bar-Ilan University, Ramat Gan, 5290002, Israel\n116Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n117University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n118OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n119Centre national de la recherche scienti\ufb01que, 75016 Paris, France\n120Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n121University of Birmingham, Birmingham B15 2TT, United Kingdom\n122Washington State University, Pullman, WA 99164, USA\n123Cornell University, Ithaca, NY 14850, USA\n124Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n125Christopher Newport University, Newport News, VA 23606, USA\n126OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n127Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n128University of Maryland, College Park, MD 20742, USA\n129Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n130INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n131Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n132IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain\n133University of Chicago, Chicago, IL 60637, USA\n134University of Arizona, Tucson, AZ 85721, USA\n135INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n136University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n137Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n138Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n139Istituto di Astro\ufb01sica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n140Colorado State University, Fort Collins, CO 80523, USA\n141Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n142Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n143Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n144National Central University, Taoyuan City 320317, Taiwan\n145National Tsing Hua University, Hsinchu City 30013, Taiwan\n146OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n147Vanderbilt University, Nashville, TN 37235, USA\n148University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Paci\ufb01c, Bejing 100049, China\n149Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n150Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n151University of Texas, Austin, TX 78712, USA\n152CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n153Northeastern University, Boston, MA 02115, USA\n154Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n155Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n156Carleton College, North\ufb01eld, MN 55057, USA\n157University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n158OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n159University of Rhode Island, Kingston, RI 02881, USA\n160INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n161Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n162Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n163INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n164Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n165Montana State University, Bozeman, MT 59717, USA\n166The University of Utah, Salt Lake City, UT 84112, USA\n167Johns Hopkins University, Baltimore, MD 21218, USA\n168The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n169Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n170DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n171Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n\n49\n172University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n173INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n174Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n175INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n176Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n177Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n178The University of Shef\ufb01eld, Shef\ufb01eld S10 2TN, United Kingdom\n179Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n180International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India\n181Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n182IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n183Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n184INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n185California State University, Los Angeles, Los Angeles, CA 90032, USA\n186Marquette University, Milwaukee, WI 53233, USA\n187Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n188Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n189Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n190Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n191National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n192Vrije Universiteit Brussel, 1050 Brussel, Belgium\n193University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n194Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n195Stony Brook University, Stony Brook, NY 11794, USA\n196Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n197Montclair State University, Montclair, NJ 07043, USA\n198HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n199Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n200Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n201Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n202CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n203Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n204Western Washington University, Bellingham, WA 98225, USA\n205SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n206Barry University, Miami Shores, FL 33168, USA\n207E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n208Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n209Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,\nJapan\n210University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n211University of California, Berkeley, CA 94720, USA\n212Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n213Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n214University of Southampton, Southampton SO17 1BJ, United Kingdom\n215University of California, Riverside, Riverside, CA 92521, USA\n216Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n217University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n218University of Nottingham NG7 2RD, UK\n219Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n220The University of Mississippi, University, MS 38677, USA\n221Graduate School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n222Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n223Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA\n224The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n225American University, Washington, DC 20016, USA\n226Dipartimento di Fisica, Universit\u00e0 degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n227INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n\n50\n228Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n229IAC3IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n230University of Cambridge, Cambridge CB2 1TN, United Kingdom\n231University of Lancaster, Lancaster LA1 4YW, United Kingdom\n232College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n233Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n234Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n235Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n236Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n237Helmut Schmidt University, D-22043 Hamburg, Germany\n238Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n239Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n240Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n241Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n242National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n243School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n244Sungkyunkwan University, Seoul 03063, Republic of Korea\n245Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n246Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n247Chung-Ang University, Seoul 06974, Republic of Korea\n248University of Washington Bothell, Bothell, WA 98011, USA\n249Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n250Ewha Womans University, Seoul 03760, Republic of Korea\n251National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n252Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n253Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n254Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n255Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n256Nagoya University, Nagoya, 464-8601, Japan\n257Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n258Bard College, Annandale-On-Hudson, NY 12504, USA\n259Technical University of Braunschweig, D-38106 Braunschweig, Germany\n260Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n261Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n262Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n263Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n264Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n265Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n266Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n267Seoul National University, Seoul 08826, Republic of Korea\n268Department of Computer Simulation, Inje University, 197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n269NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n270Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n271Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n272St. Thomas University, Miami Gardens, FL 33054, USA\n273Scuola Normale Superiore, I-56126 Pisa, Italy\n274Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, E-08010 Barcelona, Spain\n275Institut de F\u00edsica d\u2019Altes Energies, E-08193 Barcelona, Spain\n276Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n277Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n278Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n279Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa\n224-8551, Japan\n280Tsinghua University, Beijing 100084, China\n281School of Physical & Chemical Sciences, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand\n282Institut des Hautes Etudes Scienti\ufb01ques, F-91440 Bures-sur-Yvette, France\n\n51\n283Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n284Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n285University of Stavanger, 4021 Stavanger, Norway\n286Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima\n739-8526, Japan\n287GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n288University College London, London WC1E 6BT, United Kingdom\n289Observatoire de Paris, 75014 Paris, France\n290Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n291Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n292University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n293CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n294Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n295Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n296Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n297Hobart and William Smith Colleges, Geneva, NY 14456, USA\n298INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n299Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n300Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n301Kennesaw State University, Kennesaw, GA 30144, USA\n302Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n303Universidad de Antioquia, Medell\u00edn, Colombia\n304Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n305Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n306Trinity College, Hartford, CT 06106, USA\n307Dipartimento di Fisica e Scienze della Terra, Universit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n308Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n309Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n310Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n311Department of Physics, Indian Institute of Technology Gandhinagar, Gujarat 382055, India\n312Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n313Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n314NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n315Gravity Exploration Institute, Cardiff School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, United Kingdom\n316Faculty of Science and Technology, Kochi University, 2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n317Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS, Universit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n318School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA\n319Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n320Laser Interferometry and Gravitational Wave Astronomy, Max Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n321The Hakubi Center for Advanced Research, Kyoto University, Yoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n322Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n323Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n324University of Catania, Department of Physics and Astronomy, Via S. So\ufb01a, 64, 95123 Catania CT, Italy\n325National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n326Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n327Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n328Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8583, Japan\n329Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n330School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n", "Draft version 11 November 2025\nTypeset using LATEX twocolumn style in AASTeX631\nGW231123: a Binary Black Hole Merger with Total Mass 190-265 M\u2299\nA. G. Abac,1 I. Abouelfettouh,2 F. Acernese,3, 4 K. Ackley,5 C. Adamcewicz,6 S. Adhicary,7 D. Adhikari,8, 9\nN. Adhikari,10 R. X. Adhikari,11 V. K. Adkins,12 S. Afroz,13 A. Agapito,14 D. Agarwal,15 M. Agathos,16\nN. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar,19 I.-L. Ahrend,20 L. Aiello,21, 22 A. Ain,23 P. Ajith,24 T. Akutsu,25, 26\nS. Albanesi,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9 C. All\u00b4en\u00b4e,31 A. Allocca,32, 4 S. Al-Shammari,33 P. A. Altin,34\nS. Alvarez-Lopez,35 W. Amar,31 O. Amarasinghe,33 A. Amato,36, 37 F. Amicucci,38, 39 C. Amra,40 A. Ananyeva,11\nS. B. Anderson,11 W. G. Anderson,11 M. Andia,41 M. Ando,42 M. Andr\u00b4es-Carcasona,43 T. Andri\u00b4c,44, 45, 8, 9\nJ. Anglin,46 S. Ansoldi,47, 48 J. M. Antelis,49 S. Antier,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11\nS. K. Apple,53 K. Arai,11 C. Araujo Alvarez,54 A. Araya,42 M. C. Araya,11 M. Arca Sedda,44, 45 J. S. Areeda,55\nN. Aritomi,2 F. Armato,29, 30 S. Armstrong,56 N. Arnaud,57 M. Arogeti,58 S. M. Aronson,12 K. G. Arun,59\nG. Ashton,60 Y. Aso,25, 61 L. Asprea,28 M. Assiduo,62, 63 S. Assis de Souza Melo,64 S. M. Aston,65 P. Astone,38\nF. Attadio,39, 38 F. Aubin,66 K. AultONeal,67 G. Avallone,68 E. A. Avila,49 S. Babak,20 C. Badger,69 S. Bae,70\nS. Bagnasco,28 L. Baiotti,71 R. Bajpai,72 T. Baka,73, 37 A. M. Baker,6 K. A. Baker,74 T. Baker,75 G. Baldi,76, 77\nN. Baldicchi,78, 51 M. Ball,79 G. Ballardin,64 S. W. Ballmer,80 S. Banagiri,6 B. Banerjee,44 D. Bankar,81\nT. M. Baptiste,12 P. Baral,10 M. Baratti,82, 83 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,81\nP. Barneo,84, 85, 86 F. Barone,87, 4 B. Barr,88 L. Barsotti,35 M. Barsuglia,20 D. Barta,89 A. M. Bartoletti,90\nM. A. Barton,88 I. Bartos,46 A. Basalaev,8, 9 R. Bassiri,91 A. Basti,83, 82 M. Bawaj,78, 51 P. Baxi,92 J. C. Bayley,88\nA. C. Baylor,10 P. A. Baynard II,58 M. Bazzan,93, 94 V. M. Bedakihale,95 F. Beirnaert,96 M. Bejger,97\nD. Belardinelli,22 A. S. Bell,88 D. S. Bellie,98 L. Bellizzi,82, 83 W. Benoit,18 I. Bentara,57 J. D. Bentley,99\nM. Ben Yaala,56 S. Bera,100, 101 F. Bergamin,33 B. K. Berger,91 S. Bernuzzi,27 M. Beroiz,11 C. P. L. Berry,88\nD. Bersanetti,29 T. Bertheas,102 A. Bertolini,37, 36 J. Betzwieser,65 D. Beveridge,74 G. Bevilacqua,103\nN. Bevins,104 R. Bhandare,105 R. Bhatt,11 D. Bhattacharjee,106, 107 S. Bhattacharyya,108 S. Bhaumik,46\nS. Bhagwat,109 V. Biancalana,103 A. Bianchi,37, 110 I. A. Bilenko,111 G. Billingsley,11 A. Binetti,112 S. Bini,11, 76, 77\nC. Binu,113 S. Biot,114 O. Birnholtz,115 S. Biscoveanu,98 A. Bisht,9 M. Bitossi,64, 82 M.-A. Bizouard,116\nS. Blaber,117 J. K. Blackburn,11 L. A. Blagg,79 C. D. Blair,74, 65 D. G. Blair,74 N. Bode,8, 9 N. Boettner,99\nG. Boileau,116 M. Boldrini,38 G. N. Bolingbroke,118 A. Bolliand,119, 40 L. D. Bonavena,46 R. Bondarescu,84\nF. Bondu,120 E. Bonilla,91 M. S. Bonilla,55 A. Bonino,109 R. Bonnand,31, 119 A. Borchers,8, 9 S. Borhanian,7\nV. Boschi,82 S. Bose,121 V. Bossilkov,65 Y. Bothra,37, 110 A. Boudon,57 L. Bourg,58 M. Boyle,122 A. Bozzi,64\nC. Bradaschia,82 P. R. Brady,10 A. Branch,65 M. Branchesi,44, 45 I. Braun,106 T. Briant,123 A. Brillet,116\nM. Brinkmann,8, 9 P. Brockill,10 E. Brockmueller,8, 9 A. F. Brooks,11 B. C. Brown,46 D. D. Brown,118\nM. L. Brozzetti,78, 51 S. Brunett,11 G. Bruno,15 R. Bruntz,124 J. Bryant,109 Y. Bu,125 F. Bucci,63 J. Buchanan,124\nO. Bulashenko,84, 85 T. Bulik,126 H. J. Bulten,37 A. Buonanno,127, 1 K. Burtnyk,2 R. Buscicchio,128, 129\nD. Buskulic,31 C. Buy,102 R. L. Byer,91 G. S. Cabourn Davies,75 R. Cabrita,15 V. C\u00b4aceres-Barbosa,7\nL. Cadonati,58 G. Cagnoli,130 C. Cahillane,80 A. Calafat,100 J. Calder\u00b4on Bustillo,54 T. A. Callister,131\nE. Calloni,32, 4 S. R. Callos,79 M. Canepa,30, 29 G. Caneva Santoro,43 K. C. Cannon,42 H. Cao,35\nL. A. Capistran,132 E. Capocasa,20 E. Capote,2, 11 G. Capurri,83, 82 G. Carapella,68, 133 F. Carbognani,64\nM. Carlassara,8, 9 J. B. Carlin,125 T. K. Carlson,134 M. F. Carney,106 M. Carpinelli,128, 64 G. Carrillo,79\nJ. J. Carter,8, 9 G. Carullo,109, 135 A. Casallas-Lagos,136 J. Casanueva Diaz,64 C. Casentini,137, 22\nS. Y. Castro-Lucas,138 S. Caudill,134 M. Cavagli`a,107 R. Cavalieri,64 A. Ceja,55 G. Cella,82 P. Cerd\u00b4a-Dur\u00b4an,139, 140\nE. Cesarini,22 N. Chabbra,34 W. Chaibi,116 A. Chakraborty,13 P. Chakraborty,8, 9 S. Chakraborty,105\nS. Chalathadka Subrahmanya,99 J. C. L. Chan,141 M. Chan,117 K. Chandra,7 K. Chang,142 S. Chao,143, 142\nP. Charlton,144 E. Chassande-Mottin,20 C. Chatterjee,145 Debarati Chatterjee,81 Deep Chatterjee,35\nM. Chaturvedi,105 S. Chaty,20 K. Chatziioannou,11 A. Chen,146 A. H.-Y. Chen,147 D. Chen,148 H. Chen,143\nH. Y. Chen,149 S. Chen,145 Yanbei Chen,150 Yitian Chen,122 H. P. Cheng,151 P. Chessa,78, 51 H. T. Cheung,92\nS. Y. Cheung,6 F. Chiadini,152, 133 G. Chiarini,8, 9, 94 A. Chiba,153 A. Chincarini,29 M. L. Chiofalo,83, 82\nA. Chiummo,4, 64 C. Chou,147 S. Choudhary,74 N. Christensen,116, 154 S. S. Y. Chua,34 G. Ciani,76, 77 P. Ciecielag,97\nM. Cie\u00b4slar,126 M. Cifaldi,22 B. Cirok,155 F. Clara,2 J. A. Clark,11, 58 T. A. Clarke,6 P. Clearwater,156\nS. Clesse,114 F. Cleva,116, 119 E. Coccia,44, 45, 43 E. Codazzo,157, 158 P.-F. Cohadon,123 S. Colace,30 E. Colangeli,75\nM. Colleoni,100 C. G. Collette,159 J. Collins,65 S. Colloms,88 A. Colombo,160, 129 C. M. Compton,2 G. Connolly,79\nL. Conti,94 T. R. Corbitt,12 I. Cordero-Carri\u00b4on,161 S. Corezzi,78, 51 N. J. Cornish,162 I. Coronado,163 A. Corsi,164\nR. Cottingham,65 M. W. Coughlin,18 A. Couineaux,38 P. Couvares,11, 58 D. M. Coward,74 R. Coyne,165\nA. Cozzumbo,44 J. D. E. Creighton,10 T. D. Creighton,166 P. Cremonese,100 S. Crook,65 R. Crouch,2\nJ. Csizmazia,2 J. R. Cudell,167 T. J. Cullen,11 A. Cumming,88 E. Cuoco,168, 169 M. Cusinato,139\nL. V. Da Conceic\u00b8\u02dcao,170 T. Dal Canton,41 S. Dal Pra,171 G. D\u00b4alya,102 B. D\u2019Angelo,29 S. Danilishin,36, 37\nS. D\u2019Antonio,38 K. Danzmann,9, 8, 9 K. E. Darroch,124 L. P. Dartez,65 R. Das,108 A. Dasgupta,95 V. Dattilo,64\nA. Daumas,20 N. Davari,172, 173 I. Dave,105 A. Davenport,138 M. Davier,41 T. F. Davies,74 D. Davis,11 L. Davis,74\nM. C. Davis,18 P. Davis,174, 175 E. J. Daw,176 M. Dax,1 J. De Bolle,96 M. Deenadayalan,81 J. Degallaix,177\narXiv:2507.08219v3 [astro-ph.HE] 10 Nov 2025\n\n2\nM. De Laurentis,32, 4 F. De Lillo,23 S. Della Torre,129 W. Del Pozzo,83, 82 A. Demagny,31 F. De Marco,39, 38\nG. Demasi,178, 63 F. De Matteis,21, 22 N. Demos,35 T. Dent,54 A. Depasse,15 N. DePergola,104 R. De Pietri,179, 180\nR. De Rosa,32, 4 C. De Rossi,64 M. Desai,35 R. DeSalvo,181 A. DeSimone,182 R. De Simone,152, 133 A. Dhani,1\nR. Diab,46 M. C. D\u00b4\u0131az,166 M. Di Cesare,32, 4 G. Dideron,183 T. Dietrich,1 L. Di Fiore,4 C. Di Fronzo,74\nM. Di Giovanni,39, 38 T. Di Girolamo,32, 4 D. Diksha,37, 36 J. Ding,20, 184 S. Di Pace,39, 38 I. Di Palma,39, 38\nD. Di Piero,185, 48 F. Di Renzo,57 Divyajyoti,33 A. Dmitriev,109 J. P. Docherty,88 Z. Doctor,98 N. Doerksen,170\nE. Dohmen,2 A. Doke,134 A. Domiciano De Souza,186 L. D\u2019Onofrio,38 F. Donovan,35 K. L. Dooley,33 T. Dooney,73\nS. Doravari,81 O. Dorosh,187 W. J. D. Doyle,124 M. Drago,39, 38 J. C. Driggers,2 L. Dunn,125 U. Dupletsa,44\nP.-A. Duverne,20 D. D\u2019Urso,172, 157 P. Dutta Roy,46 H. Duval,188 S. E. Dwyer,2 C. Eassa,2 M. Ebersold,189, 31\nT. Eckhardt,99 G. Eddolls,80 A. Effler,65 J. Eichholz,34 H. Einsle,116 M. Eisenmann,25 M. Emma,60 K. Endo,153\nR. Enficiaud,1 L. Errico,32, 4 R. Espinosa,166 M. Esposito,4, 32 R. C. Essick,190 H. Estell\u00b4es,1 T. Etzel,11\nM. Evans,35 T. Evstafyeva,183 B. E. Ewing,7 J. M. Ezquiaga,141 F. Fabrizi,62, 63 V. Fafone,21, 22 S. Fairhurst,33\nA. M. Farah,131 B. Farr,79 W. M. Farr,191, 192 G. Favaro,93 M. Favata,193 M. Fays,167 M. Fazio,56 J. Feicht,11\nM. M. Fejer,91 R. Felicetti,185, 48 E. Fenyvesi,89, 194 J. Fernandes,195 T. Fernandes,196, 139 D. Fernando,113\nS. Ferraiuolo,197, 39, 38 T. A. Ferreira,12 F. Fidecaro,83, 82 P. Figura,97 A. Fiori,82, 83 I. Fiori,64 R. P. Fisher,124\nR. Fittipaldi,198, 133 V. Fiumara,199, 133 R. Flaminio,31 S. M. Fleischer,200 L. S. Fleming,201 E. Floden,18 H. Fong,117\nJ. A. Font,139, 140 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal,202 K. Franceschetti,179 N. Franchini,203\nF. Frappez,31 S. Frasca,39, 38 F. Frasconi,82 J. P. Freed,67 Z. Frei,204 A. Freise,37, 110 O. Freitas,196, 139 R. Frey,79\nW. Frischhertz,65 P. Fritschel,35 V. V. Frolov,65 G. G. Fronz\u00b4e,28 M. Fuentes-Garcia,11 S. Fujii,205\nT. Fujimori,206 P. Fulda,46 M. Fyffe,65 B. Gadre,73 J. R. Gair,1 S. Galaudage,186 V. Galdi,207 R. Gamba,7\nA. Gamboa,1 S. Gamoji,181 D. Ganapathy,208 A. Ganguly,81 B. Garaventa,29 J. Garc\u00b4\u0131a-Bellido,209\nC. Garc\u00b4\u0131a-Quir\u00b4os,189 J. W. Gardner,34 K. A. Gardner,117 S. Garg,42 J. Gargiulo,64 X. Garrido,41 A. Garron,100\nF. Garufi,32, 4 P. A. Garver,91 C. Gasbarra,21, 22 B. Gateley,2 F. Gautier,210 V. Gayathri,10 T. Gayer,80\nG. Gemme,29 A. Gennai,82 V. Gennari,102 J. George,105 R. George,149 O. Gerberding,99 L. Gergely,155\nSayantan Ghosh,195 Shaon Ghosh,193 Shrobana Ghosh,8, 9 Suprovo Ghosh,211 Tathagata Ghosh,81\nJ. A. Giaime,12, 65 K. D. Giardina,65 D. R. Gibson,201 C. Gier,56 S. Gkaitatzis,83, 82 J. Glanzer,11 F. Glotin,41\nJ. Godfrey,79 R. V. Godley,8, 9 P. Godwin,11 A. S. Goettel,33 E. Goetz,117 J. Golomb,11 S. Gomez Lopez,39, 38\nB. Goncharov,44 G. Gonz\u00b4alez,12 P. Goodarzi,212 S. Goode,6 M. Gosselin,64 R. Gouaty,31 D. W. Gould,34\nK. Govorkova,35 A. Grado,78, 51 V. Graham,88 A. E. Granados,18 M. Granata,177 V. Granata,213, 133 S. Gras,35\nP. Grassia,11 J. Graves,58 C. Gray,2 R. Gray,88 G. Greco,51 A. C. Green,37, 110 L. Green,214 S. M. Green,75\nS. R. Green,215 C. Greenberg,134 A. M. Gretarsson,67 H. K. Griffin,18 D. Griffith,11 H. L. Griggs,58\nG. Grignani,78, 51 C. Grimaud,31 H. Grote,33 S. Grunewald,1 D. Guerra,139 D. Guetta,216 G. M. Guidi,62, 63\nA. R. Guimaraes,12 H. K. Gulati,95 F. Gulminelli,174, 175 H. Guo,146 W. Guo,74 Y. Guo,37, 36 Anuradha Gupta,217\nI. Gupta,7 N. C. Gupta,95 S. K. Gupta,46 V. Gupta,18 N. Gupte,1 J. Gurs,99 N. Gutierrez,177 N. Guttman,6\nF. Guzman,132 D. Haba,218 M. Haberland,1 S. Haino,219 E. D. Hall,35 E. Z. Hamilton,100 G. Hammond,88\nM. Haney,37 J. Hanks,2 C. Hanna,7 M. D. Hannam,33 A. G. Hanselman,131 H. Hansen,2 J. Hanson,65\nS. Hanumasagar,58 R. Harada,42 A. R. Hardison,182 S. Harikumar,187 K. Haris,37, 73 I. Harley-Trochimczyk,132\nT. Harmark,135 J. Harms,44, 45 G. M. Harry,220 I. W. Harry,75 J. Hart,106 B. Haskell,97, 221, 222 C. J. Haster,214\nK. Haughian,88 H. Hayakawa,50 K. Hayama,223 M. C. Heintze,65 J. Heinze,109 J. Heinzel,35 H. Heitmann,116\nF. Hellman,208 A. F. Helmling-Cornell,79 G. Hemming,64 O. Henderson-Sapir,118 M. Hendry,88 I. S. Heng,88\nM. H. Hennig,88 C. Henshaw,58 M. Heurs,8, 9 A. L. Hewitt,224, 225 J. Heynen,15 J. Heyns,35 S. Higginbotham,33\nS. Hild,36, 37 S. Hill,88 Y. Himemoto,226 N. Hirata,25 C. Hirose,227 D. Hofman,177 B. E. Hogan,67\nN. A. Holland,37, 110 I. J. Hollows,176 D. E. Holz,131 L. Honet,114 D. J. Horton-Bailey,208 J. Hough,88\nS. Hourihane,11 N. T. Howard,145 E. J. Howell,74 C. G. Hoy,75 C. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh,143\nH.-Y. Hsieh,143 C. Hsiung,228 S.-H. Hsu,147 W.-F. Hsu,112 Q. Hu,88 H. Y. Huang,142 Y. Huang,7 Y. T. Huang,80\nA. D. Huddart,229 B. Hughey,67 V. Hui,31 S. Husa,100 R. Huxford,7 L. Iampieri,39, 38 G. A. Iandolo,36 M. Ianni,22, 21\nG. Iannone,133 J. Iascau,79 K. Ide,230 R. Iden,218 A. Ierardi,44, 45 S. Ikeda,148 H. Imafuku,42 Y. Inoue,142 G. Iorio,93\nP. Iosif,185, 48 M. H. Iqbal,34 J. Irwin,88 R. Ishikawa,230 M. Isi,191, 192 K. S. Isleif,231 Y. Itoh,206, 232 M. Iwaya,205\nB. R. Iyer,24 C. Jacquet,102 P.-E. Jacquet,123 T. Jacquot,41 S. J. Jadhav,233 S. P. Jadhav,156 M. Jain,134 T. Jain,224\nA. L. James,11 K. Jani,145 N. N. Janthalur,233 S. Jaraba,234 P. Jaranowski,235 R. Jaume,100 W. Javed,33\nA. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang,151 H.-B. Jin,236, 237 G. R. Johns,124 N. A. Johnson,46\nN. K. Johnson-McDaniel,217 M. C. Johnston,214 R. Johnston,88 N. Johny,8, 9 D. H. Jones,34 D. I. Jones,211\nR. Jones,88 H. E. Jose,79 P. Joshi,7 S. K. Joshi,81 G. Joubert,57 J. Ju,238 L. Ju,74 K. Jung,239 J. Junker,34\nV. Juste,114 H. B. Kabagoz,65, 35 T. Kajita,240 I. Kaku,206 V. Kalogera,98 M. Kalomenopoulos,214 M. Kamiizumi,50\nN. Kanda,232, 206 S. Kandhasamy,81 G. Kang,241 N. C. Kannachel,6 J. B. Kanner,11 S. A. KantiMahanty,18\nS. J. Kapadia,81 D. P. Kapasi,55 M. Karthikeyan,134 M. Kasprzack,11 H. Kato,153 T. Kato,205 E. Katsavounidis,35\nW. Katzman,65 R. Kaushik,105 K. Kawabe,2 R. Kawamoto,206 D. Keitel,100 L. J. Kemperman,118 J. Kennington,7\nF. A. Kerkow,18 R. Kesharwani,81 J. S. Key,242 R. Khadela,8, 9 S. Khadka,91 S. S. Khadkikar,7 F. Y. Khalili,111\nF. Khan,8, 9 T. Khanam,164 M. Khursheed,105 N. M. Khusid,191, 192 W. Kiendrebeogo,116, 243 N. Kijbunchoo,118\nC. Kim,244 J. C. Kim,245 K. Kim,246 M. H. Kim,238 S. Kim,247 Y.-M. Kim,246 C. Kimball,98 K. Kimes,55 M. Kinnear,33\nJ. S. Kissel,2 S. Klimenko,46 A. M. Knee,117 E. J. Knox,79 N. Knust,8, 9 K. Kobayashi,205 S. M. Koehlenbeck,91\nG. Koekoek,37, 36 K. Kohri,248, 249 K. Kokeyama,33, 250 S. Koley,44, 167 P. Kolitsidou,109 A. E. Koloniari,251\n\n3\nK. Komori,42 A. K. H. Kong,143 A. Kontos,252 L. M. Koponen,109 M. Korobko,99 X. Kou,18 A. Koushik,23\nN. Kouvatsos,69 M. Kovalam,74 T. Koyama,153 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu,109 S. Kroker,253 A. Kr\u00b4olak,254, 187 K. Kruska,8, 9 J. Kubisz,255 G. Kuehn,8, 9 S. Kulkarni,217\nA. Kulur Ramamohan,34 Achal Kumar,46 Anil Kumar,233 Praveen Kumar,54 Prayush Kumar,24 Rahul Kumar,2\nRakesh Kumar,95 J. Kume,256, 257, 42 K. Kuns,35 N. Kuntimaddi,33 S. Kuroyanagi,209, 258 S. Kuwahara,42 K. Kwak,239\nK. Kwan,34 S. Kwon,42 G. Lacaille,88 D. Laghi,189, 102 A. H. Laity,165 E. Lalande,259 M. Lalleman,23\nP. C. Lalremruati,260 M. Landry,2 B. B. Lane,35 R. N. Lang,35 J. Lange,149 R. Langgin,214 B. Lantz,91\nI. La Rosa,100 J. Larsen,200 A. Lartaux-Vollard,41 P. D. Lasky,6 J. Lawrence,166 M. Laxen,65 C. Lazarte,139\nA. Lazzarini,11 C. Lazzaro,158, 157 P. Leaci,39, 38 L. Leali,18 Y. K. Lecoeuche,117 H. M. Lee,261 H. W. Lee,262\nJ. Lee,80 K. Lee,238 R.-K. Lee,143 R. Lee,35 Sungho Lee,246 Sunjae Lee,238 Y. Lee,142 I. N. Legred,11 J. Lehmann,8, 9\nL. Lehner,183 M. Le Jean,177, 119 A. Lema\u02c6\u0131tre,263 M. Lenti,63, 178 M. Leonardi,76, 77, 264 M. Lequime,40 N. Leroy,41\nM. Lesovsky,11 N. Letendre,31 M. Lethuillier,57 Y. Levin,6 K. Leyde,75 A. K. Y. Li,11 K. L. Li,265 X. Li,150 Y. Li,98\nZ. Li,88 A. Lihos,124 E. T. Lin,143 F. Lin,142 L. C.-C. Lin,265 Y.-C. Lin,143 C. Lindsay,201 S. D. Linker,181 A. Liu,266\nG. C. Liu,228 Jian Liu,74 F. Llamas Villarreal,166 J. Llobera-Querol,100 R. K. L. Lo,141 J.-P. Locquet,112\nS. C. G. Loggins,267 M. R. Loizou,134 L. T. London,69 A. Longo,62, 63 D. Lopez,167 M. Lopez Portilla,73\nM. Lorenzini,21, 22 A. Lorenzo-Medina,54 V. Loriette,41 M. Lormand,65 G. Losurdo,268, 82 E. Lotti,134\nT. P. Lott IV,58 J. D. Lough,8, 9 H. A. Loughlin,35 C. O. Lousto,113 N. Low,125 N. Lu,34 L. Lucchesi,82\nH. L\u00a8uck,9, 8, 9 D. Lumaca,22 A. P. Lundgren,269, 270 A. W. Lussier,259 R. Macas,75 M. MacInnis,35 D. M. Macleod,33\nI. A. O. MacMillan,11 A. Macquet,41 K. Maeda,153 S. Maenaut,112 S. S. Magare,81 R. M. Magee,11 E. Maggio,1\nR. Maggiore,37, 110 M. Magnozzi,29, 30 M. Mahesh,99 M. Maini,165 S. Majhi,81 E. Majorana,39, 38 C. N. Makarem,11\nD. Malakar,107 J. A. Malaquias-Reis,19 U. Mali,190 S. Maliakal,11 A. Malik,105 L. Mallick,170, 190 A.-K. Malz,60\nN. Man,116 M. Mancarella,101 V. Mandic,18 V. Mangano,172, 157 B. Mannix,79 G. L. Mansell,80 M. Manske,10\nM. Mantovani,64 M. Mapelli,93, 94, 271 C. Marinelli,103 F. Marion,31 A. S. Markosyan,91 A. Markowitz,11\nE. Maros,11 S. Marsat,102 F. Martelli,62, 63 I. W. Martin,88 R. M. Martin,193 B. B. Martinez,132 D. A. Martinez,55\nM. Martinez,43, 272 V. Martinez,130 A. Martini,76, 77 J. C. Martins,19 D. V. Martynov,109 E. J. Marx,35\nL. Massaro,36, 37 A. Masserot,31 M. Masso-Reid,88 S. Mastrogiovanni,38 T. Matcovich,51 M. Matiushechkina,8, 9\nL. Maurin,210 N. Mavalvala,35 N. Maxwell,2 G. McCarrol,65 R. McCarthy,2 D. E. McClelland,34\nS. McCormick,65 L. McCuller,11 S. McEachin,124 C. McElhenny,124 G. I. McGhee,88 J. McGinn,88\nK. B. M. McGowan,145 J. McIver,117 A. McLeod,74 I. McMahon,189 T. McRae,34 R. McTeague,88 D. Meacher,10\nB. N. Meagher,80 R. Mechum,113 Q. Meijer,73 A. Melatos,125 C. S. Menoni,138 F. Mera,2 R. A. Mercer,10\nL. Mereni,177 K. Merfeld,164 E. L. Merilh,65 J. R. M\u00b4erou,100 J. D. Merritt,79 M. Merzougui,116 C. Messick,10\nB. Mestichelli,44 M. Meyer-Conde,273 F. Meylahn,8, 9 A. Mhaske,81 A. Miani,76, 77 H. Miao,274 C. Michel,177\nY. Michimura,42 H. Middleton,109 D. P. Mihaylov,106 S. J. Miller,11 M. Millhouse,58 E. Milotti,185, 48\nV. Milotti,93 Y. Minenkov,22 E. M. Minihan,67 Ll. M. Mir,43 L. Mirasola,157, 158 M. Miravet-Ten\u00b4es,139\nC.-A. Miritescu,43 A. Mishra,24 C. Mishra,108 T. Mishra,46 A. L. Mitchell,37, 110 J. G. Mitchell,67 S. Mitra,81\nV. P. Mitrofanov,111 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa,50 S. Miyoki,50 A. Miyoko,67 G. Mo,35\nL. Mobilia,62, 63 S. R. P. Mohapatra,11 S. R. Mohite,7 M. Molina-Ruiz,208 M. Mondin,181 M. Montani,62, 63\nC. J. Moore,224 D. Moraru,2 A. More,81 S. More,81 C. Moreno,136 E. A. Moreno,35 G. Moreno,2\nA. Moreso Serra,84 S. Morisaki,42, 205 Y. Moriwaki,153 G. Morras,209 A. Moscatello,93 M. Mould,35 B. Mours,66\nC. M. Mow-Lowry,37, 110 L. Muccillo,178, 63 F. Muciaccia,39, 38 D. Mukherjee,109 Samanwaya Mukherjee,24\nSoma Mukherjee,166 Subroto Mukherjee,95 Suvodip Mukherjee,13 N. Mukund,35 A. Mullavey,65 H. Mullock,117\nJ. Mundi,220 C. L. Mungioli,74 M. Murakoshi,230 P. G. Murray,88 D. Nabari,76, 77 S. L. Nadji,8, 9 A. Nagar,28, 275\nN. Nagarajan,88 K. Nakagaki,50 K. Nakamura,25 H. Nakano,276 M. Nakano,11 D. Nanadoumgar-Lacroze,43\nD. Nandi,12 V. Napolano,64 P. Narayan,217 I. Nardecchia,22 T. Narikawa,205 H. Narola,73 L. Naticchioni,38\nR. K. Nayak,260 L. Negri,73 A. Nela,88 C. Nelle,79 A. Nelson,132 T. J. N. Nelson,65 M. Nery,8, 9 A. Neunzert,2\nS. Ng,55 L. Nguyen Quynh,277 S. A. Nichols,12 A. B. Nielsen,278 Y. Nishino,25, 42 A. Nishizawa,279 S. Nissanke,280, 37\nW. Niu,7 F. Nocera,64 J. Noller,281 M. Norman,33 C. North,33 J. Novak,119, 234, 282 R. Nowicki,145\nJ. F. Nu\u02dcno Siles,209 L. K. Nuttall,75 K. Obayashi,230 J. Oberling,2 J. O\u2019Dell,229 E. Oelker,35\nM. Oertel,234, 119, 283, 282 G. Oganesyan,44, 45 T. O\u2019Hanlon,65 M. Ohashi,50 F. Ohme,8, 9 R. Oliveri,119, 283, 282 R. Omer,18\nB. O\u2019Neal,124 M. Onishi,153 K. Oohara,284 B. O\u2019Reilly,65 M. Orselli,51, 78 R. O\u2019Shaughnessy,113 S. O\u2019Shea,88\nS. Oshino,50 C. Osthelder,11 I. Ota,12 D. J. Ottaway,118 A. Ouzriat,57 H. Overmier,65 B. J. Owen,285 R. Ozaki,230\nA. E. Pace,7 R. Pagano,12 M. A. Page,25 A. Pai,195 L. Paiella,44 A. Pal,286 S. Pal,260 M. A. Palaia,82, 83 M. P\u00b4alfi,204\nP. P. Palma,39, 21, 22 C. Palomba,38 P. Palud,20 H. Pan,143 J. Pan,74 K. C. Pan,143 P. K. Panda,233 Shiksha Pandey,7\nSwadha Pandey,35 P. T. H. Pang,37, 73 F. Pannarale,39, 38 K. A. Pannone,55 B. C. Pant,105 F. H. Panther,74\nM. Panzeri,62, 63 F. Paoletti,82 A. Paolone,38, 287 A. Papadopoulos,88 E. E. Papalexakis,212 L. Papalini,82, 83\nG. Papigkiotis,251 A. Paquis,41 A. Parisi,78, 51 B.-J. Park,246 J. Park,288 W. Parker,65 G. Pascale,8, 9 D. Pascucci,96\nA. Pasqualetti,64 R. Passaquieti,83, 82 L. Passenger,6 D. Passuello,82 O. Patane,2 A. V. Patel,142 D. Pathak,81\nA. Patra,33 B. Patricelli,83, 82 B. G. Patterson,33 K. Paul,108 S. Paul,79 E. Payne,11 T. Pearce,33 M. Pedraza,11\nA. Pele,11 F. E. Pe\u02dcna Arellano,289 X. Peng,109 Y. Peng,58 S. Penn,290 M. D. Penuliar,55 A. Perego,76, 77\nZ. Pereira,134 C. P\u00b4erigois,291, 94, 93 G. Perna,93 A. Perreca,76, 77, 44 J. Perret,20 S. Perri`es,57 J. W. Perry,37, 110\nD. Pesios,251 S. Peters,167 S. Petracca,207 C. Petrillo,78 H. P. Pfeiffer,1 H. Pham,65 K. A. Pham,18\nK. S. Phukon,109 H. Phurailatpam,266 M. Piarulli,102 L. Piccari,39, 38 O. J. Piccinni,34 M. Pichot,116\n\n4\nM. Piendibene,83, 82 F. Piergiovanni,62, 63 L. Pierini,38 G. Pierra,38 V. Pierro,292, 133 M. Pietrzak,97 M. Pillas,167\nF. Pilo,82 L. Pinard,177 I. M. Pinto,292, 133, 293, 32 M. Pinto,64 B. J. Piotrzkowski,10 M. Pirello,2 M. D. Pitkin,224, 88\nA. Placidi,51 E. Placidi,39, 38 M. L. Planas,100 W. Plastino,213, 22 C. Plunkett,35 R. Poggiani,83, 82 E. Polini,35\nJ. Pomper,82, 83 L. Pompili,1 J. Poon,266 E. Porcelli,37 E. K. Porter,20 C. Posnansky,7 R. Poulton,64 J. Powell,156\nG. S. Prabhu,81 M. Pracchia,167 B. K. Pradhan,81 T. Pradier,66 A. K. Prajapati,95 K. Prasai,294 R. Prasanna,233\nP. Prasia,81 G. Pratten,109 G. Principe,185, 48 G. A. Prodi,76, 77 P. Prosperi,82 P. Prosposito,21, 22\nA. C. Providence,67 A. Puecher,1 J. Pullin,12 P. Puppo,38 M. P\u00a8urrer,165 H. Qi,16 J. Qin,34 G. Qu\u00b4em\u00b4ener,175, 119\nV. Quetschke,166 P. J. Quinonez,67 N. Qutob,58 R. Rading,231 I. Rainho,139 S. Raja,105 C. Rajan,105\nB. Rajbhandari,113 K. E. Ramirez,65 F. A. Ramis Vidal,100 M. Ramos Arevalo,166 A. Ramos-Buades,100, 37\nS. Ranjan,58 K. Ransom,65 P. Rapagnani,39, 38 B. Ratto,67 A. Ravichandran,134 A. Ray,98 V. Raymond,33\nM. Razzano,83, 82 J. Read,55 T. Regimbau,31 S. Reid,56 C. Reissel,35 D. H. Reitze,11 A. I. Renzini,11, 128\nB. Revenu,295, 41 A. Revilla Pe\u02dcna,84 R. Reyes,181 L. Ricca,15 F. Ricci,39, 38 M. Ricci,38, 39 A. Ricciardone,83, 82\nJ. Rice,80 J. W. Richardson,212 M. L. Richardson,118 A. Rijal,67 K. Riles,92 H. K. Riley,33 S. Rinaldi,271\nJ. Rittmeyer,99 C. Robertson,229 F. Robinet,41 M. Robinson,2 A. Rocchi,22 L. Rolland,31 J. G. Rollins,11\nA. E. Romano,296 R. Romano,3, 4 A. Romero,31 I. M. Romero-Shaw,224 J. H. Romie,65 S. Ronchini,7 T. J. Roocke,118\nL. Rosa,4, 32 T. J. Rosauer,212 C. A. Rose,58 D. Rosi\u00b4nska,126 M. P. Ross,53 M. Rossello-Sastre,100 S. Rowan,88\nS. K. Roy,191, 192 S. Roy,15 D. Rozza,128, 129 P. Ruggi,64 N. Ruhama,239 E. Ruiz Morales,297, 209 K. Ruiz-Rocha,145\nS. Sachdev,58 T. Sadecki,2 P. Saffarieh,37, 110 S. Safi-Harb,170 M. R. Sah,13 S. Saha,143 T. Sainrat,66\nS. Sajith Menon,216, 39, 38 K. Sakai,298 Y. Sakai,273 M. Sakellariadou,69 S. Sakon,7 O. S. Salafia,160, 129, 128\nF. Salces-Carcoba,11 L. Salconi,64 M. Saleem,149 F. Salemi,39, 38 M. Sall\u00b4e,37 S. U. Salunkhe,81 S. Salvador,175, 174\nA. Salvarese,149 A. Samajdar,73, 37 A. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual,139\nJ. R. Sanders,182 E. M. S\u00a8anger,1 F. Santoliquido,44, 45 F. Sarandrea,28 T. R. Saravanan,81 N. Sarin,6\nP. Sarkar,8, 9 A. Sasli,251 P. Sassi,51, 78 B. Sassolas,177 B. S. Sathyaprakash,7, 33 R. Sato,227 S. Sato,153\nYukino Sato,153 Yu Sato,153 O. Sauter,46 R. L. Savage,2 T. Sawada,50 H. L. Sawant,81 S. Sayah,177 V. Scacco,21, 22\nD. Schaetzl,11 M. Scheel,150 A. Schiebelbein,190 M. G. Schiworski,80 P. Schmidt,109 S. Schmidt,73 R. Schnabel,99\nM. Schneewind,8, 9 R. M. S. Schofield,79 K. Schouteden,112 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz,299\nM. Scialpi,300 J. Scott,88 S. M. Scott,34 R. M. Sedas,65 T. C. Seetharamu,88 M. Seglar-Arroyo,43\nY. Sekiguchi,301 D. Sellers,65 N. Sembo,206 A. S. Sengupta,302 E. G. Seo,88 J. W. Seo,112 V. Sequino,32, 4\nM. Serra,38 A. Sevrin,188 T. Shaffer,2 U. S. Shah,58 M. A. Shaikh,261 L. Shao,303 A. K. Sharma,100\nPreeti Sharma,12 Prianka Sharma,105 Ritwik Sharma,18 S. Sharma Chaudhary,107 P. Shawhan,127\nN. S. Shcheblanov,304, 263 E. Sheridan,145 Z.-H. Shi,143 M. Shikauchi,42 R. Shimomura,305 H. Shinkai,305 S. Shirke,81\nD. H. Shoemaker,35 D. M. Shoemaker,149 R. W. Short,2 S. ShyamSundar,105 A. Sider,159 H. Siegel,191, 192 D. Sigg,2\nL. Silenzi,36, 37 L. Silvestri,39, 171 M. Simmonds,118 L. P. Singer,306 Amitesh Singh,217 Anika Singh,11 D. Singh,208\nN. Singh,100 S. Singh,218, 61 A. M. Sintes,100 V. Sipala,172, 157 V. Skliris,33 B. J. J. Slagmolen,34 D. A. Slater,200\nT. J. Slaven-Blair,74 J. Smetana,109 J. R. Smith,55 L. Smith,88, 185, 48 R. J. E. Smith,6 W. J. Smith,145\nS. Soares de Albuquerque Filho,62 M. Soares-Santos,189 K. Somiya,218 I. Song,143 S. Soni,35 V. Sordini,57\nF. Sorrentino,29 H. Sotani,307 F. Spada,82 V. Spagnuolo,37 A. P. Spencer,88 P. Spinicelli,64 A. K. Srivastava,95\nF. Stachurski,88 C. J. Stark,124 D. A. Steer,308 N. Steinle,170 J. Steinlechner,36, 37 S. Steinlechner,36, 37\nN. Stergioulas,251 P. Stevens,41 S. P. Stevenson,156 M. StPierre,165 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,104, \u2217M. Suchenek,97 S. Sudhagar,97 Y. Sudo,230 N. Sueltmann,99 L. Suleiman,55 K. D. Sullivan,12\nJ. Sun,241 L. Sun,34 S. Sunil,95 J. Suresh,116 B. J. Sutton,69 P. J. Sutton,33 K. Suzuki,218 M. Suzuki,205 S. Swain,109\nB. L. Swinkels,37 A. Syx,119 M. J. Szczepa\u00b4nczyk,309 P. Szewczyk,126 M. Tacca,37 H. Tagoshi,205 K. Takada,205\nH. Takahashi,273 R. Takahashi,25 A. Takamori,42 S. Takano,310 H. Takeda,311, 312 K. Takeshita,218\nI. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,80 C. Talbot,131 M. Tamaki,205 N. Tamanini,102 D. Tanabe,142\nK. Tanaka,50 S. J. Tanaka,230 S. Tanioka,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao,212 R. D. Tapia,7\nE. N. Tapia San Mart\u00b4\u0131n,37 C. Taranto,21, 22 A. Taruya,313 J. D. Tasson,154 J. G. Tau,113 D. Tellez,55\nR. Tenorio,100 H. Themann,181 A. Theodoropoulos,139 M. P. Thirugnanasambandam,81 L. M. Thomas,11\nM. Thomas,65 P. Thomas,2 J. E. Thompson,211 S. R. Thondapu,105 K. A. Thorne,65 E. Thrane,6 J. Tissino,44, 45\nA. Tiwari,81 Pawan Tiwari,44 Praveer Tiwari,195 S. Tiwari,189 V. Tiwari,109 M. R. Todd,80 M. Toffano,93\nA. M. Toivonen,18 K. Toland,88 A. E. Tolley,75 T. Tomaru,25 V. Tommasini,11 T. Tomura,50 H. Tong,6\nC. Tong-Yu,142 A. Torres-Forn\u00b4e,139, 140 C. I. Torrie,11 I. Tosta e Melo,314 E. Tournefier,31 M. Trad Nery,116\nK. Tran,124 A. Trapananti,52, 51 R. Travaglini,169 F. Travasso,52, 51 G. Traylor,65 M. Trevor,127 M. C. Tringali,64\nA. Tripathee,92 G. Troian,185, 48 A. Trovato,185, 48 L. Trozzo,4 R. J. Trudeau,11 T. Tsang,33 S. Tsuchida,315\nL. Tsukada,214 K. Turbang,188, 23 M. Turconi,116 C. Turski,96 H. Ubach,84, 85 N. Uchikata,205 T. Uchiyama,50\nR. P. Udall,11 T. Uehara,316 K. Ueno,42 V. Undheim,278 L. E. Uronen,266 T. Ushiba,50 M. Vacatello,82, 83\nH. Vahlbruch,8, 9 N. Vaidya,11 G. Vajente,11 A. Vajpeyi,6 J. Valencia,100 M. Valentini,110, 37 S. A. Vallejo-Pe\u02dcna,296\nS. Vallero,28 V. Valsan,10 M. van Dael,37, 317 E. Van den Bossche,188 J. F. J. van den Brand,36, 110, 37\nC. Van Den Broeck,73, 37 M. van der Sluys,37, 73 A. Van de Walle,41 J. van Dongen,37, 110 K. Vandra,104\nM. VanDyke,121 H. van Haevermaet,23 J. V. van Heijningen,37, 110 P. Van Hove,66 J. Vanier,259 M. VanKeuren,106\nJ. Vanosky,2 N. van Remortel,23 M. Vardaro,36, 37 A. F. Vargas,125 V. Varma,134 A. N. Vazquez,91 A. Vecchio,109\nG. Vedovato,94 J. Veitch,88 P. J. Veitch,118 S. Venikoudis,15 R. C. Venterea,18 P. Verdier,57 M. Vereecken,15\nD. Verkindt,31 B. Verma,134 Y. Verma,105 S. M. Vermeulen,11 F. Vetrano,62 A. Veutro,38, 39 A. Vicer\u00b4e,62, 63\n\n5\nS. Vidyant,80 A. D. Viets,90 A. Vijaykumar,190 A. Vilkha,113 N. Villanueva Espinosa,139 V. Villa-Ortega,54\nE. T. Vincent,58 J.-Y. Vinet,116 S. Viret,57 S. Vitale,35 H. Vocca,78, 51 D. Voigt,99 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,231 L. Vujeva,141 S. P. Vyatchanin,111 J. Wack,11 L. E. Wade,106\nM. Wade,106 K. J. Wagner,113 L. Wallace,11 E. J. Wang,91 H. Wang,218 J. Z. Wang,92 W. H. Wang,166 Y. F. Wang,1\nG. Waratkar,195 J. Warner,2 M. Was,31 T. Washimi,25 N. Y. Washington,11 D. Watarai,42 B. Weaver,2\nS. A. Webster,88 N. L. Weickhardt,99 M. Weinert,8, 9 A. J. Weinstein,11 R. Weiss,35 L. Wen,74 K. Wette,34\nJ. T. Whelan,113 B. F. Whiting,46 C. Whittle,11 E. G. Wickens,75 D. Wilken,8, 9, 9 A. T. Wilkin,212\nB. M. Williams,121 D. Williams,88 M. J. Williams,75 N. S. Williams,1 J. L. Willis,11 B. Willke,9, 8, 9 M. Wils,112\nL. Wilson,106 C. W. Winborn,107 J. Winterflood,74 C. C. Wipf,11 G. Woan,88 J. Woehler,36, 37 N. E. Wolfe,35\nH. T. Wong,142 H. W. Y. Wong,266 I. C. F. Wong,266, 112 K. Wong,190 T. Wouters,73, 37 J. L. Wright,2 B. Wu,80\nC. Wu,143 D. S. Wu,8, 9 H. Wu,143 K. Wu,121 Q. Wu,53 Y. Wu,98 Z. Wu,102 E. Wuchner,55 D. M. Wysocki,10\nV. A. Xu,208 Y. Xu,100 N. Yadav,28 H. Yamamoto,11 K. Yamamoto,153 T. S. Yamamoto,42 T. Yamamoto,50\nR. Yamazaki,230 T. Yan,109 K. Z. Yang,18 Y. Yang,147 Z. Yarbrough,12 J. Yebana,100 S.-W. Yeh,143 A. B. Yelikar,145\nX. Yin,35 J. Yokoyama,318, 42 T. Yokozawa,50 S. Yuan,74 H. Yuzurihara,50 M. Zanolin,67 M. Zeeshan,113\nT. Zelenova,64 J.-P. Zendri,94 M. Zeoli,15 M. Zerrad,40 M. Zevin,98 L. Zhang,11 N. Zhang,58 R. Zhang,151\nT. Zhang,109 C. Zhao,74 Yue Zhao,163 Yuhang Zhao,20 Z.-C. Zhao,319 Y. Zheng,107 H. Zhong,18 H. Zhou,80\nH. O. Zhu,74 Z.-H. Zhu,319, 320 A. B. Zimmerman,149 L. Zimmermann,57 M. E. Zucker,35, 11 and J. Zweizig11\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e, Campus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n\n6\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra\n(Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n55California State University Fullerton, Fullerton, CA 92831, USA\n56SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n57Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n58Georgia Institute of Technology, Atlanta, GA 30332, USA\n59Chennai Mathematical Institute, Chennai 603103, India\n60Royal Holloway, University of London, London TW20 0EX, United Kingdom\n61Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n62Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n63INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n64European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n65LIGO Livingston Observatory, Livingston, LA 70754, USA\n66Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n67Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n68Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n69King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n70Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n71International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n72Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n73Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n74OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n75University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n76Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n77INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n78Universit`a di Perugia, I-06123 Perugia, Italy\n79University of Oregon, Eugene, OR 97403, USA\n80Syracuse University, Syracuse, NY 13244, USA\n81Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n82INFN, Sezione di Pisa, I-56127 Pisa, Italy\n83Universit`a di Pisa, I-56127 Pisa, Italy\n84Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n85Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n86Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n87Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n88IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n89HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n90Concordia University Wisconsin, Mequon, WI 53097, USA\n91Stanford University, Stanford, CA 94305, USA\n92University of Michigan, Ann Arbor, MI 48109, USA\n93Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n94INFN, Sezione di Padova, I-35131 Padova, Italy\n95Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n\n7\n96Universiteit Gent, B-9000 Gent, Belgium\n97Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n98Northwestern University, Evanston, IL 60208, USA\n99Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n100IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n101Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n102Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n103Universit`a di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n104Villanova University, Villanova, PA 19085, USA\n105RRCAT, Indore, Madhya Pradesh 452013, India\n106Kenyon College, Gambier, OH 43022, USA\n107Missouri University of Science and Technology, Rolla, MO 65409, USA\n108Indian Institute of Technology Madras, Chennai 600036, India\n109University of Birmingham, Birmingham B15 2TT, United Kingdom\n110Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n111Lomonosov Moscow State University, Moscow 119991, Russia\n112Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n113Rochester Institute of Technology, Rochester, NY 14623, USA\n114Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n115Bar-Ilan University, Ramat Gan, 5290002, Israel\n116Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n117University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n118OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n119Centre national de la recherche scientifique, 75016 Paris, France\n120Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n121Washington State University, Pullman, WA 99164, USA\n122Cornell University, Ithaca, NY 14850, USA\n123Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n124Christopher Newport University, Newport News, VA 23606, USA\n125OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n126Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n127University of Maryland, College Park, MD 20742, USA\n128Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n129INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n130Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n131University of Chicago, Chicago, IL 60637, USA\n132University of Arizona, Tucson, AZ 85721, USA\n133INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n136Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n137Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n138Colorado State University, Fort Collins, CO 80523, USA\n139Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n140Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n141Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n142National Central University, Taoyuan City 320317, Taiwan\n143National Tsing Hua University, Hsinchu City 30013, Taiwan\n144OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n145Vanderbilt University, Nashville, TN 37235, USA\n146University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n147Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n148Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n149University of Texas, Austin, TX 78712, USA\n150CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n151Northeastern University, Boston, MA 02115, USA\n152Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n\n8\n153Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n154Carleton College, Northfield, MN 55057, USA\n155University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n156OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n157INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n158Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n159Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n160INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n161Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n162Montana State University, Bozeman, MT 59717, USA\n163The University of Utah, Salt Lake City, UT 84112, USA\n164Johns Hopkins University, Baltimore, MD 21218, USA\n165University of Rhode Island, Kingston, RI 02881, USA\n166The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n167Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n168DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n169Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n170University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n171INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n172Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n173INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n174Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n175Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n176The University of Sheffield, Sheffield S10 2TN, United Kingdom\n177Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622\nVilleurbanne, France\n178Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n179Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n180INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n181California State University, Los Angeles, Los Angeles, CA 90032, USA\n182Marquette University, Milwaukee, WI 53233, USA\n183Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n184Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n185Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n186Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n187National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n188Vrije Universiteit Brussel, 1050 Brussel, Belgium\n189University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n190Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n191Stony Brook University, Stony Brook, NY 11794, USA\n192Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n193Montclair State University, Montclair, NJ 07043, USA\n194HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n195Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n196Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n197Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n198CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n199Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n200Western Washington University, Bellingham, WA 98225, USA\n201SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n202Barry University, Miami Shores, FL 33168, USA\n203CENTRA, Departamento de F\u00b4\u0131sica, Instituto Superior T\u00b4ecnico \u2013 IST, Universidade de Lisboa \u2013 UL, Avenida Rovisco Pais 1,\n1049-001 Lisboa, Portugal\n204E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n205Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n\n9\n206Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n207University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n208University of California, Berkeley, CA 94720, USA\n209Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n210Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212University of California, Riverside, Riverside, CA 92521, USA\n213Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n214University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n215University of Nottingham NG7 2RD, UK\n216Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n217The University of Mississippi, University, MS 38677, USA\n218Graduate School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n219Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Helmut Schmidt University, D-22043 Hamburg, Germany\n232Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n233Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n234Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n235Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n236National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n237School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n238Sungkyunkwan University, Seoul 03063, Republic of Korea\n239Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic\nof Korea\n240Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n241Chung-Ang University, Seoul 06974, Republic of Korea\n242University of Washington Bothell, Bothell, WA 98011, USA\n243Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n248Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n249Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n250Nagoya University, Nagoya, 464-8601, Japan\n251Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n252Bard College, Annandale-On-Hudson, NY 12504, USA\n253Technical University of Braunschweig, D-38106 Braunschweig, Germany\n254Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n255Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n256Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n257Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n\n10\n258Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n259Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n260Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n261Seoul National University, Seoul 08826, Republic of Korea\n262Department of Computer Simulation, Inje University, 197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n263NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n264Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n265Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n266The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n270Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120\nHeidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA), Passeig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku,\nYokohama, Kanagawa 224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n278University of Stavanger, 4021 Stavanger, Norway\n279Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima\nCity, Hiroshima 739-8526, Japan\n280GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n281University College London, London WC1E 6BT, United Kingdom\n282Observatoire de Paris, 75014 Paris, France\n283Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n284Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n289Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n290Hobart and William Smith Colleges, Geneva, NY 14456, USA\n291INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n292Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Kennesaw State University, Kennesaw, GA 30144, USA\n295Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n296Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n297Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n298Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n299Trinity College, Hartford, CT 06106, USA\n300Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n301Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n302Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n303Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n304Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n305Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n306NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n307Faculty of Science and Technology, Kochi University, 2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n\n11\n308Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS, Universit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e),\nF-75005 Paris, France\n309Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n310Laser Interferometry and Gravitational Wave Astronomy, Max Planck Institute for Gravitational Physics, Callinstrasse 38, 30167\nHannover, Germany\n311The Hakubi Center for Advanced Research, Kyoto University, Yoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n312Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto\n606-8502, Japan\n314University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n315National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n316Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n317Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n318Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha,\nKashiwa City, Chiba 277-8583, Japan\n319Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n320School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(Compiled: 11 November 2025)\nABSTRACT\nOn 2023 November 23 the two LIGO observatories both detected GW231123, a gravitational-wave\nsignal consistent with the merger of two black holes with masses 137+23\n\u221218 M\u2299and 101+22\n\u221250 M\u2299(90%\ncredible intervals), at luminosity distance 0.7\u20134.1 Gpc and redshift of 0.40+0.27\n\u22120.25, and a network signal-\nto-noise ratio of \u223c20.7.\nBoth black holes exhibit high spins, 0.90+0.10\n\u22120.19 and 0.80+0.20\n\u22120.52 respectively.\nA massive black hole remnant is supported by an independent ringdown analysis. Some properties\nof GW231123 are subject to large systematic uncertainties, as indicated by differences in inferred\nparameters between signal models. The primary black hole lies within or above the theorized mass\ngap where black holes between 60\u2013130 M\u2299should be rare due to pair instability mechanisms, while\nthe secondary spans the gap. The observation of GW231123 therefore suggests the formation of black\nholes from channels beyond standard stellar collapse, and that intermediate-mass black holes of mass\n\u223c200 M\u2299form through gravitational-wave driven mergers.\n1. INTRODUCTION\nFrom 2015 to 2020 the LIGO-Virgo-KAGRA Collab-\noration identified 69 gravitational-wave signals from bi-\nnary black hole mergers with false alarm rates below\none per year (Aasi et al. 2015; Acernese et al. 2015;\nAbbott et al. 2020c; Akutsu et al. 2020; Abbott et al.\n2023a). Of these, the most massive was the source of\nGW190521, with a merger remnant of \u223c140 M\u2299(Ab-\nbott et al. 2020d,e). The small number of observable\ncycles of GW190521 limits our ability to accurately in-\nfer the source\u2019s properties, and subsequent studies have\nproposed a wide range of alternative interpretations, in-\ncluding highly eccentric orbits, dynamical capture sce-\nnarios, exotic object mergers, and cosmic string col-\nlapse (Gayathri et al. 2022; Romero-Shaw et al. 2020a;\nGamba et al. 2023; Calder\u00b4on Bustillo et al. 2021b; Aur-\nrekoetxea et al. 2024). Here we present a yet more chal-\n\u2217Deceased, September 2024.\nlenging signal: GW231123 135430 (hereafter referred to\nas GW231123), confidently observed through a coin-\ncident detection in both the LIGO Hanford and Liv-\ningston detectors during the first part of their fourth\nobserving run, O4a (2023 May 24 to 2024 January 16).\nThe combination of data from the two observatories was\nessential in making a confident detection.\nGW231123 consists of \u223c5 cycles over a frequency\nrange of 30\u201380 Hz, similar to GW190521.\nWe inter-\npret GW231123 as a binary-black-hole merger and in-\nfer a total mass between 190 M\u2299and 265 M\u2299and high\ncomponent black-hole spins (\u223c0.9 and \u223c0.8). While a\nfew gravitational-wave candidates have been observed\nwith similarly high total masses (Abbott et al. 2023a;\nWadekar et al. 2023), none have false alarm rates less\nthan 1 per year; in addition, GW231123 has both a\nlarge signal-to-noise ratio and high statistical signifi-\ncance. Such high masses and spins pose a challenge to\nour most accurate waveform models, leading to larger\nuncertainties in the black-hole masses, and the binary\n\n12\norientation and distance, than any previous signal of\ncomparable strength.\nPair-instability supernova (PISN) and pulsational\nPISNe are expected to preclude stellar collapse to black\nholes with masses \u224860\u2013130M\u2299(Farmer et al. 2019;\nFarmer et al. 2020; Woosley & Heger 2021; Hendriks\net al. 2023), and the majority of the astrophysical\npopulation of black holes inferred from gravitational-\nwave catalogs lies below this gap (Abbott et al. 2023b).\nThe large measurement uncertainties in the source of\nGW231123 mean that the primary black hole may be\nwithin or beyond the mass gap, while the secondary mass\nspans the entire gap within the 90% credible intervals\nof our analysis. It is also possible that the two black-\nhole masses lie on either side of the gap. The scenarios\nwith the highest probability require a formation chan-\nnel that populates the mass gap, such as prior stellar\nmergers (e.g., Di Carlo et al. 2020; Renzo et al. 2020a;\nKremer et al. 2020), black-hole mergers (for a review, see\nGerosa & Fishbach 2021 and references therein), or ac-\ncretion in a gaseous environment (e.g., McKernan et al.\n2012). Though these channels can produce highly spin-\nning black holes (e.g., a characteristic value of \u223c0.7 for\nblack-hole mergers), the inferred spins may be higher\nthan typical of remnant black holes and those of rem-\nnants from mergers previously observed with gravita-\ntional waves.\nIn this paper we present the LIGO-Virgo-KAGRA\nanalysis of GW231123.\nIn Section 2, we establish\nGW231123 as a confident gravitational wave (GW) de-\ntection. In Section 3, we discuss the data quality at the\ntime of the observation. In Section 4, we first discuss our\ntreatment of waveform uncertainties, then present the\nsource properties and additional waveform consistency\nchecks. In Section 5, we analyse the ringdown portion\nto test the consistency of a black hole (BH) remnant\ninterpretation. In Section 6 we present a range of po-\ntential astrophysical implications. Although the binary\nblack hole (BBH) merger scenario presented throughout\nthis paper is the most plausible astrophysical explana-\ntion for the source of GW231123, alternative scenarios\ncannot be ruled out and we discuss a selection of these\nin Section 7. We conclude in Section 8, and provide ad-\nditional material in support of our results in a series of\nappendices.\n2. DETECTION SIGNIFICANCE\nOn 2023 November 23, at 13:54:30 UTC, the Ad-\nvanced LIGO Hanford and Livingston detectors ob-\nserved the GW transient GW231123.\nThe Advanced\nVirgo and KAGRA detectors were not online at this\ntime.\nDespite its short duration (\u223c0.1 s) and limited\nbandwidth (Figure 1), coherent detection in both de-\ntectors allowed the signal to be identified in our analy-\nses with high statistical significance, reported in terms\nof inverse false-alarm rate (IFAR); see Table 1. With-\nout coincidence in two or more detectors, a high-mass\nBBH signal like GW231123 would likely have been dis-\nmissed as a noise artefact (glitch). It was first detected\nby PyCBC Live, a matched-filter search for compact\nbinaries (Allen 2005; Usman et al. 2016; Nitz et al.\n2017; Dal Canton et al. 2021). It was also reported by\ncoherent WaveBurst (cWB)-BBH, a minimally modelled\ncoherent excess power search (Mishra et al. 2025). The\ncWB-BBH search uses the WaveScan time\u2013frequency\n(TF) transformation (Klimenko 2022) and ranks identi-\nfied triggers using a machine-learning classifier trained\nspecifically on BBH signals (Mishra et al. 2021, 2022,\n2025).\nIn addition, the event was also detected by\ntwo model-independent low-latency cWB searches, or\nburst searches, designed to identify generic GW tran-\nsients: cWB-2G and cWB-XP. The former is based on\nthe Wilson\u2013Debauchies\u2013Meyer TF transformation (Kli-\nmenko et al. 2008, 2016a; Drago et al. 2020), while\nthe latter uses the WaveScan TF transformation. Both\napply a machine-learning classifier (XGBoost), trained\non generic white-noise-bursts to rank identified trig-\ngers (Szczepa\u00b4nczyk et al. 2023). For further details on\nmodel-independent searches, see Abac et al. (2025a).\nSubsequent offline or archival reanalyses using im-\nproved background estimation and data quality informa-\ntion further increased the event\u2019s statistical significance\nin both the PyCBC and cWB pipelines (Table 1). Fur-\nthermore, two additional matched-filter searches, Gst-\nLAL (Messick et al. 2017; Sachdev et al. 2019; Hanna\net al. 2020; Cannon et al. 2021; Sakon et al. 2024; Ewing\net al. 2024; Tsukada et al. 2023; Joshi et al. 2025) and\nMBTA (Adams et al. 2016; Aubin et al. 2021; All\u00b4en\u00b4e\net al. 2025), which did not detect this event with sig-\nnificant confidence in low-latency (IFAR higher than\n1 year), recovered it in their offline analyses.\nThese\nsearches differ from PyCBC (Davies et al. 2020; Chan-\ndra et al. 2021b; Davis et al. 2022; Kumar & Dent\n2024) in their implementation and use of signal\u2013noise\ndiscriminators.\nGstLAL\u2019s enhanced significance (the\nhigher IFAR in Table. 1) is primarily driven by a higher\nmass extension of the search with specific settings to\ncompute the background for such higher mass mergers\naccurately.\nMore details of the settings are provided\nin (?Joshi et al. 2025).\nThese changes improved the\nsignal and noise models in this part of the parameter\nspace in general, leading to a better recovery of this high\nmass signal. Additionally, cWB-GMM, an entirely of-\nfline model-independent search, uses Gaussian Mixture\n\n13\n2\n0\n2\nnoise\nHanford\n0.10\n0.05\n0.00\n0.05\n0.10\nTime [s]\n20\n40\n60\n80\n100\n120\n140\nFrequency [Hz]\nLivingston\n0.10\n0.05\n0.00\n0.05\n0.10\nTime [s]\n2.5\n5.0\n7.5\n10.0\nAmplitude\nWhitened data\nBBH Template Reconstruction (Bilby)\nWavelet Reconstruction (BayesWave)\ncWB Reconstruction\nFigure 1.\nThe GW event GW231123 as observed by the LIGO Hanford (left panels) and LIGO Livingston (right panels)\ndetectors. Time is measured relative to 2023 November 23 at 13:54:30.619 UTC. The top panels show the time-domain strain\ndata (black), sampled at 1024 Hz, whitened and then bandpass-filtered with a passband from 20 Hz to 256 Hz (Abbott et al.\n2020a). Also shown are the point-estimate whitened waveform from the cWB-BBH search (red), the 90% credible interval of\nwhitened waveforms inferred from a coherent Bayesian analysis using the combined samples from five BBH waveform models\n(blue bands), and the 90% credible interval inferred from BayesWave using a generic wavelet-based model (shaded purple).\nThe vertical axis is in units of the noise standard deviation, \u03c3noise. The bottom panels display the corresponding whitened\ntime-frequency representations of the strain data, obtained using a continuous wavelet transform (CWT) with a Morlet\u2013Gabor\nwavelet. The color scale is in units of the amplitude of the CWT coefficients.\nTable 1. Properties of the detection of GW231123 by vari-\nous search pipelines.\nCBC pipelines\nOffline\nOnline\nOffline\nSNR\nIFAR (yr)\nIFAR (yr)\nPyCBC\n19.9\n> 100\n160\nGstLAL\n20.1\n2 \u00d7 10\u22124\n> 10000\nMBTA\n19.0\n\u2013\n60\ncWB-BBH\n21.8\n> 490\n9700\nBurst pipelines\ncWB-2G\n21.4\n> 250\n> 490\ncWB-XP\n21.1\n> 240\n> 480\ncWB-GMM\n21.4\n\u2013\n100\nNote\u2014The significance is reported in terms of the inverse\nfalse-alarm rate (FAR) (IFAR) = 1/FAR as measured by\neach search.\nModels (Gayathri et al. 2020; Lopez et al. 2022; Smith\net al. 2024) to rerank the triggers identified by cWB-2G.\nThe differences in the IFARs reported by the of-\nfline search pipelines\u2014despite broadly consistent signal-\nto-noise ratios (SNRs)\u2014primarily reflect differences\nin their ability to separate GW231123-like signals\nfrom background noise in a comparable parameter\nrange.\nSimilar discrepancies have been observed\npreviously,\nparticularly between matched-filter and\nminimally-modelled searches, when searching for non-\neccentric intermediate-mass black hole (IMBH) bina-\nries (Calder\u00b4on Bustillo et al. 2018; Chandra et al. 2020;\nAbbott et al. 2020d; Chandra et al. 2021a; Szczepa\u00b4nczyk\net al. 2021). These differences arise not only from how\neffectively each search separates signals from glitches,\nbut also from the differing approaches used to estimate\nthe noise background.\nTo assess whether the observed variation in statistical\nsignificance across pipelines is consistent with expecta-\ntions, we conducted a dedicated injection campaign. Us-\ning the NRSur7dq4 (NRSur) waveform model (Varma\net al. 2019), we simulated \u223c8000 non-eccentric BBH\nsignals with intrinsic parameters consistent with those\ninferred for GW231123 (Section 4).\nWe sampled the\nsky positions and binary orientations isotropically and\ndrew redshifts uniformly in comoving volume up to\nzmax = 1.5, assuming a flat \u039bCDM cosmology (Ade\net al. 2016). We added these simulated signals uniformly\nover several days around the event and re-ran our offline\nsearch pipelines using the same configuration as applied\nto the real data.\nWe found that for simulated signals observed in both\nAdvanced LIGO detectors, the CBC searches recovered\n\n14\nthe following fractions with a IFAR above 100 years,\ncWB-BBH 32%, PyCBC 27%, GstLAL 41%, and MBTA\n16%.\nFor the Burst searches, cWB-2G and cWB-XP\neach recovered 22%, while cWB-GMM recovered 10%.\nSince Burst searches identify coherent power across the\ndetector network without relying on BBH waveform\nmodels, their efficiencies are not directly comparable\nto CBC searches.\nHowever, within each search cate-\ngory, detection pipelines reporting a higher IFAR for\nGW231123 consistently demonstrated higher recovery\nfractions for simulated signals with masses and spins\nrepresentative of those inferred for GW231123.\nGiven that all pipelines detected GW231123 with an\nIFAR above the typical threshold of 1 year used for pop-\nulation analyses, and a detailed background study for\none pipeline (cWB-BBH) identified GW231123 with an\nIFAR of 9700 years, we consider GW231123 to be a con-\nfident detection.\n3. DATA QUALITY\nThe event GW231123 was detected during the first\npart of the fourth observing run (O4a), a time when the\nLIGO Hanford and LIGO Livingston detectors were ob-\nserving with a typical binary neutron star inspiral range\nof 152 Mpc and 160 Mpc (Capote et al. 2025).\nThe\ndetectors\u2019 data were calibrated in near real-time to pro-\nduce the online dataset used for low-latency searches\n(Abbott et al. 2020b; Klimenko et al. 2016b; Tsukada\net al. 2023; Ewing et al. 2024; Dal Canton et al. 2021;\nChu et al. 2022; Aubin et al. 2021) and parameter esti-\nmation (Singer & Price 2016; Ashton et al. 2019; Pankow\net al. 2015).\nThe calibration process subtracts linear\nspectral features from known instrumental sources, iden-\ntified through auxiliary witness sensors, and intention-\nally injected calibration lines used to measure the in-\nstruments\u2019 response at various frequencies (Viets et al.\n2018a; Sun et al. 2020, 2021).\nFollowing the data-quality procedures established for\nO4a (Soni et al. 2025), including broadband noise sub-\ntraction (Vajente et al. 2020) and data-quality report\nanalysis routines (Davis et al. 2021), detector data sur-\nrounding the event were evaluated for signs of non-\nGaussian excess power (glitches) within the target time-\nfrequency analysis window using a spectrogram-based\nglitch-identification tool (Vazsonyi & Davis 2023).\nIt\nwas determined that glitches were present in each de-\ntector around, but not coincident with the event.\nFrom spectrograms, we determined that a glitch was\npresent in the LIGO Hanford data 1.7\u20131.1 s before the\nevent, in a frequency range between 15\u201330 Hz.\nThe\nglitch is possibly related to the LIGO Hanford differ-\nential arm control loop (Aasi et al. 2015). This control\nloop leads to nonstationary noise from the high root-\nmean-square drive applied to the electrostatic drive ac-\ntuator. This issue has been fixed in the second part of\nthe fourth observing run (Vajente 2024). This glitch was\nclose to the event and within the time\u2013frequency window\nused to infer the source properties, so BayesWave (Cor-\nnish & Littenberg 2015; Cornish et al. 2021; Chatziioan-\nnou et al. 2021) was used to model simultaneously the\ncompact binary signal and the glitch (Soni et al. 2025).\nWe removed this non-Gaussianity from the data by sub-\ntracting a phenomenological, wavelet-based model of\nthe excess power noise (Hourihane et al. 2022; Ghonge\net al. 2024).\nThe glitch-subtracted data successfully\npassed the validation process, which compares the resid-\nual noise to Gaussian noise (Soni et al. 2025; Vazsonyi\n& Davis 2023).\nAdditional broadband non-stationary\nnoise was present in the Hanford detector in the hours\nof data surrounding GW231123, but we found no evi-\ndence that this impacted the analysis of GW231123.\nIn LIGO Livingston data, a glitch was identified 3.0\u2013\n2.0 s before the event, in a frequency range between\n10\u201320 Hz. Given that LIGO Livingston had recurring\nlow-frequency scattered light glitches (Soni et al. 2025),\nthis glitch was likely caused by scattered light. We de-\ntermined the time\u2013frequency profile of the glitch to have\nno measurable effect on the GW231123 analysis, so the\nanalyses from here on use the LIGO Livingston original\ndata and the LIGO Hanford glitch-subtracted data.\n4. SOURCE PROPERTIES\nIn the following, we describe the methods used to es-\ntimate the source properties (Section 4.1), and how we\ndeal with the systematic differences in results from mul-\ntiple signal models (Section 4.2). Having discussed our\nmethods and sources of error, we present and discuss our\nestimates of the source properties in Section 4.3, and fi-\nnally our waveform consistency checks (Section 4.4).\n4.1. Methods\nWe report the properties of GW231123 using signal\nmodels for non-eccentric BBH mergers in a coherent\nBayesian analysis (Abbott et al. 2016a) of the LIGO\nHanford and LIGO Livingston data around the time of\nGW231123. (We discuss potential eccentricity further\nin Section 6.) We calculate the likelihood using 8 s of\ndata (6 s before and 2 s after the reported merger time of\nGW231123), and consider frequencies within the range\n20\u2013448 Hz. This range was chosen to contain the signal\nbased on preliminary analyses at the time of the event,\nand to avoid loss of power at high frequencies due to\nlow-pass filtering of the data (Abac et al. 2025b). All\nanalyses employ standard priors used in previous anal-\nyses (Abbott et al. 2021a, 2024a, 2023a), and we use a\n\n15\nPlanck 2015 \u039bCDM cosmology (Ade et al. 2016). The\nNRSur analysis employs a reduced prior mass range\ndue to model constraints, mass ratios below 6:1. The\nother models employ a wider mass prior, mass ratios\nbelow \u223c10:1, and no posterior support is found beyond\nthe NRSur analysis. We characterise the detector noise\nvia the median estimate of different power spectral den-\nsity (PSD) realizations calculated with BayesWave (Cor-\nnish & Littenberg 2015; Littenberg & Cornish 2015).\nAs done previously (Chatziioannou et al. 2019; Abbott\net al. 2023a), we calculate the median PSD for data\ncontaining the trigger. To sample the posterior distri-\nbution, we interface with the dynesty nested sampling\npackage (Speagle 2020) via the bilby library (Ashton\net al. 2019; Romero-Shaw et al. 2020b). We present re-\nsults with 1000 live points, and verify that the results\nremain consistent when the number of live points is in-\ncreased to 3000, as well as when we lower the frequency\nrange to include data between 16\u201320 Hz.\n4.2. Waveform Systematics\nThe source properties of GW231123 lie in a challeng-\ning region of parameter space for current waveform mod-\nels, to such an extent that measurements using differ-\nent models show significant disagreement, with multiple\nparameters failing to agree within 90% credible inter-\nvals. (See Appendix A for examples.) For typical sig-\nnals, our models are well within our observations\u2019 ac-\ncuracy requirements, and the level of model disagree-\nment for GW231123 has not been seen in any previous\nLVK GW observation with moderate SNRs (>12). All\nmodels show strong support for spins >0.8, and since\nno theoretical signal model is calibrated to numerical-\nrelativity (NR) waveforms from precessing binaries with\nspins above 0.8, waveform uncertainties are one possible\ncause of the measurement differences. Hence, before pre-\nsenting the source properties, we describe how we quan-\ntify waveform-model uncertainties. We do not study in\ndetail the impact of Gaussian noise fluctuations or low-\nSNR glitches that are difficult to identify and mitigate\nusing the methods presented in Section 3.\nWe consider five state-of-the-art inspiral\u2013merger\u2013\nringdown (IMR) signal models, NRSur7dq4 (NRSur;\nVarma\net\nal.\n2019),\nSEOBNRv5PHM\n(v5PHM;\nRamos-Buades\net\nal.\n2023a),\nIMRPhenomT-\nPHM (TPHM; Estell\u00b4es et al. 2022a), IMRPhenomX-\nPHM (XPHM; Colleoni et al. 2025) and IMRPhe-\nnomXO4a (XO4a; Thompson et al. 2024). The first\nthree model the signal in the time domain while the\nlatter two natively employ the frequency domain. All\nmodels use information from numerical relativity to in-\nform the merger-ringdown in the aligned-spin sector.\nHowever only NRSur; fully interpolates two-spin pre-\ncessing systems in the precessing sector, while XO4a\nis calibrated to single-spin precessing systems; all other\nmodels employ results from post-Newtonian and per-\nturbation theory through merger and ringdown. (More\ndetails are given in Appendix A.) The model papers\nreferenced here include studies to assess the accuracy of\nthese models across the BBH parameter space, but here\nwe focus on the likely region of parameter space for this\nobservation; high total mass, q = m2/m1 \u22651/3, and\nmoderate to high spins.\nWe quantify the models\u2019 accuracy against NR results,\nincluding a set of simulations that extend up to spins\nof 0.95 (Boyle et al. 2019; Hamilton et al. 2024; Scheel\net al. 2025). A standard waveform accuracy measure is\nthe mismatch between two waveforms (Cutler & Flana-\ngan 1994), where waveform uncertainties will not bias\na parameter measurement if the model\u2019s mismatch un-\ncertainty is less than \u03c72\nk(1\u2212p)/(2\u03c12) (McWilliams et al.\n2010; Baird et al. 2013), where \u03c1 is the SNR and \u03c72\nk(1\u2212p)\nis the chi-square value for k degrees of freedom at proba-\nbility p. For single-parameter measurements k = 1 pro-\nvides a lower bound (Thompson et al. 2025), so the mis-\nmatch criterion for the 90% credible interval at \u03c1 = 22\nis 1.35/\u03c12 = 0.0028. Figure 2 reports the distribution of\nmismatches of each model against 1123 NR waveforms\nwith q \u22651/3, all scaled to the redshifted (detector-\nframe) total mass (1 + z)M = 300 M\u2299, at six equally\nspaced inclinations in cos \u03b9 from \u03b9 = 0 to \u03c0/2 inclu-\nsive. The mismatches are calculated for precessing sys-\ntems (Schmidt et al. 2015; Harry et al. 2016) follow-\ning the procedure described in Hamilton et al. (2021),\nmaximising over time shifts, a global phase and tem-\nplate polarisation and optimising over in-plane spin ro-\ntations. A subset of the simulations come from the third\nrelease of the SXS catalog (Scheel et al. 2025) and con-\ntain GW memory, which introduces a constant late-time\noffset that we handle for the mismatch calculations with\na highpass filtering technique (Xu et al. 2024; Valencia\net al. 2024; Chen et al. 2024) to mitigate possible arte-\nfacts in the Fourier domain. We employ the same PSD\nfor the LIGO Livingston detector as utilised in the co-\nherent Bayesian analysis. NRSur performs better than\nthe other models (by roughly an order of magnitude for\nlow-spin cases), and all other models have comparable\naccuracy. However, NRSur does not meet the conserva-\ntive accuracy criterion for all cases, and for spins greater\nthan 0.8 the mismatches are higher in 10% of 98 cases.\nEven if we apply a less conservative mismatch criterion\nfrom the literature (e.g., with k = 7 for non-eccentric\nbinaries and p = 0.67 (Chatziioannou et al. 2017; Scheel\net al. 2025) we have 0.0072) there are configurations\n\n16\n0\n50\n100\nCount\n\u03c71 and \u03c72 > 0.8\nXPHM\nXO4a\nTPHM\nNRSur\nv5PHM\n10\u22125\n10\u22124\n10\u22123\n10\u22122\n10\u22121\nMismatch\n0\n500\n1000\nCount\n\u03c71 or \u03c72 \u22640.8\nFigure 2. Mismatch accuracy of the waveform models con-\nsidered in this paper against 1123 NR simulations at a total\nmass of 300M\u2299and a range of inclinations between \u03b9 = 0\nand \u03c0/2. The vertical dashed line at a mismatch of 0.0028\nshows the conservative criterion discussed in the text.\nwhere NRSur exceeds the criterion (2%). The relative\naccuracy of models is also not uniform across all cases,\ne.g., we find cases in which other models show compa-\nrable or improved performance relative to NRSur.\nTo test whether these waveform uncertainties will re-\nsult in biases, we performed our standard Bayesian pa-\nrameter estimation analysis on a series of NR injections,\nas detailed in Appendix A. We observe that, while the\nfive models considered here perform well for most sig-\nnals, there are configurations where all models may incur\nbiases for massive high-spin signals. We also find that\nthe relative performance of each model can change in\nthe presence of Gaussian noise, although this requires\nmore detailed study in future work. To properly cor-\nrect for this, we would ideally marginalise over wave-\nform uncertainties or incorporate model accuracy into\nBayesian analyses (Read 2023; Khan 2024; Hoy et al.\n2024; Pompili et al. 2024; Kumar et al. 2025; Mezzasoma\net al. 2025). Without access to a model of the waveform-\nmodel uncertainties, we follow what has been done pre-\nviously (Abbott et al. 2016a) and combine the results\nfrom multiple models to marginalise over the model un-\ncertainties. In choosing models in addition to NRSur,\nwe note that all other models exhibit a comparable range\nof mismatches, and no model is clearly preferred in our\ninjection studies, and so we include all five state-of-the-\nart models. We combine posterior results inferred from\nNRSur, v5PHM, TPHM, XPHM, XO4a with equal\nweight and report the combined samples throughout this\npaper. To illustrate the variation between the combined\nTable 2. Source properties of GW231123.\nPrimary mass m1/M\u2299\n137+23\n\u221218\nSecondary mass m2/M\u2299\n101+22\n\u221250\nMass ratio q = m2/m1\n0.74+0.23\n\u22120.37\nTotal mass M/M\u2299\n236+30\n\u221247\nFinal mass Mf/M\u2299\n222+28\n\u221242\nPrimary spin magnitude \u03c71\n0.90+0.10\n\u22120.19\nSecondary spin magnitude \u03c72\n0.80+0.20\n\u22120.52\nEffective inspiral spin \u03c7eff\n0.32+0.25\n\u22120.41\nEffective precessing spin \u03c7p\n0.77+0.18\n\u22120.19\nFinal spin \u03c7f\n0.84+0.08\n\u22120.16\nLuminosity distance DL/Gpc\n2.2+1.9\n\u22121.5\nInclination angle \u03b8JN/rad\n1.3+0.9\n\u22120.9\nSource redshift z\n0.40+0.27\n\u22120.25\nNetwork matched filter SNR \u03c1\n20.7+0.2\n\u22120.3\nNote\u2014We report combined results from five models that\nhave been mixed with equal weight. In most cases we present\nthe median value of the 1D marginalized posterior distribu-\ntion and the 90% symmetric credible intervals. For proper-\nties that have physical bounds, including the primary spin\nmagnitude, secondary spin magnitude, mass ratio, effective\nprecessing-spin, inclination angle and the final spin of the\nremnant, we report the median value as well as the 90%\nhighest posterior density (HPD) credible interval. The incli-\nnation of the binary is defined as the angle between the total\nangular momentum and the line of sight, \u03b8JN. All mass mea-\nsurements are reported in the source frame. Our results are\nreported at a reference frequency of 10 Hz. Results obtained\nwith individual models can be found in Appendix B.\nresults and single models, in some figures we also show\nthe NRSur results.\nIn some analyses we expect the\nchoice of model to have little impact, e.g., the detection\nsignificance study in Section 2, and in these cases, we\nuse only the NRSur samples.\n4.3. Inference\nOur Bayesian analysis indicates that GW231123 was\nproduced from a high-mass compact binary merger\nwith highly spinning components. We infer individual\nsource component masses m1 = 137+23\n\u221218 M\u2299and m2 =\n101+22\n\u221250 M\u2299with spin magnitudes \u03c71 = 0.90+0.10\n\u22120.19 and\n\u03c72 = 0.80+0.20\n\u22120.52. We present a summary of the key source\nproperties of GW231123 in Table 2. Unless otherwise\nstated, we report all mass measurements in the source\nframe, and all measurements correspond to the median\nand 90% symmetric credible level.\n\n17\nFigure 3.\nThe posterior distribution of the primary and\nsecondary source masses. We show the posterior distribution\nresulting from equally combining samples from five waveform\nmodels that include precession and higher-order multipoles\n(purple). We separately show the posterior distribution ob-\ntained with NRSur (green dash dot). We compare against\nestimates for the source frame masses of GW190521 (red\nsolid, Abbott et al. 2020d,e, 2023a). Each contour, as well\nas the colored horizontal and vertical lines, shows the 90%\ncredible intervals. In blue dashed we show the posterior pre-\ndictive distribution for the largest BH mass mobs\nmax in mock\ncatalogs similar to GWTC-3 (Abbott et al. 2023a,b); see Sec-\ntion 6. The solid orange bands show the putative mass gap\nfrom (pulsational) pair instability from 60\u2013130 M\u2299.\nAlthough we observe differences depending on the\nmodel, the primary and secondary component masses\nnevertheless have a significant probability of lying within\nthe mass gap from (pulsational) PISN processes, as\nshown in Figure 3, where we assume a nominal gap\nranging from \u223c60\u2013130 M\u2299(see Section 6 for a de-\ntailed discussion).\nThe binary\u2019s total mass is con-\nstrained to be within 189\u2013266 M\u2299. This measurement\nexceeds the 95th percentile of the inferred total mass\nfrom GW190521 (Abbott et al. 2023a).\nAssuming a\nFAR threshold of one per year, similar to Abbott et al.\n(2023b), the source of GW231123 is the highest mass\nBBH observed by the LVK to date; other lower sig-\nnificance high-mass observations have been discussed\nin Abbott et al. (2024a); Wadekar et al. (2023); Williams\n(2025); Ruiz-Rocha et al. (2025).\nWe consistently infer that both BHs are highly spin-\nning independent of the model we use. As shown in Fig-\nure 4, we infer that the primary spin magnitude \u03c71 \u22650.7\nFigure 4.\nThe posterior distribution of the primary and\nsecondary spin magnitudes. We show the posterior distribu-\ntion based on the combined samples (purple) and from the\nNRSur7dq4 waveform model (NRSur, green dash dot). Each\ncontour, as well as the colored horizontal and vertical lines,\nshows the 90% credible intervals.\nat 91% probability and the secondary spin magnitude\n\u03c72 \u22650.7 at 63% probability, see Sec. 6.5 for details.\nThe primary component of GW231123 has one of the\nhighest confidently measured BH spins observed through\nGWs (evidence for highly spinning BHs has also been\npresented in Hannam et al. 2022; Nitz et al. 2020; Ab-\nbott et al. 2024a, 2023a; Wadekar et al. 2023; Williams\n2025).\nWe are unable to reliably infer the spin orientation\nof the binary; we infer polar angles between each spin\nvector and the orbital angular momentum that vary\nnot only between models, but also when independently\nanalysing data obtained by LIGO Livingston compared\nto LIGO Hanford, see Appendix B. In an attempt to\nunderstand these differences we carried out a series of\nanalyses with different frequency ranges. We found that\nall models consistently infer greater support for spin\ncomponents aligned with the orbital angular momen-\ntum, and no sign of systematics, when independently\nanalysing LIGO Hanford data, and when excluding data\nfrom LIGO Livingston below 50 Hz. However, as with\nthe systematics issues discussed in Section 4.2 and Ap-\npendix A, we were not able to conclusively reproduce\nthis behaviour with injections of mock signals, and did\nnot find any significant noise features below 50 Hz that\ncould be the cause, although we did not perform a de-\n\n18\ntailed study of Gaussian noise fluctuations or low-SNR\nglitches. When spin misalignment is inferred, we are un-\nable to conclusively constrain the spin orientation away\nfrom aligned.\nThe uncertainty in the spin misalignment affects the\ninferred effective inspiral spin \u03c7eff, which parameter-\nizes the spin aligned with the orbital angular momen-\ntum (Santamaria et al. 2010; Ajith et al. 2011). Neg-\native \u03c7eff would imply that at least one spin is mis-\naligned with the orbital angular momentum by more\nthan ninety degrees. We cannot rule out \u03c7eff < 0, but\nthere is an 89% probability that \u03c7eff is positive. The\ninferred effective precessing spin (Schmidt et al. 2015)\nis consistently measured between models and deviates\nfrom the prior, \u03c7p = 0.77+0.18\n\u22120.19.\nAlthough we infer\nvariation between models, we consistently obtain large\nBayes factors (103 : 1 \u2212108 : 1) in favor of the precess-\ning hypothesis compared to the spin-aligned hypothe-\nsis (spins aligned with the orbital angular momentum).\nSince the distribution of Bayes factors from noise alone\nis unknown, we additionally quantify the evidence for\nprecession in GW231123 by computing the precession\nSNR, \u03c1p (Fairhurst et al. 2020a,b). In the absence of\nany precession in the signal, we expect \u03c1p < 2.1 in 90%\nof cases. We infer an SNR of \u03c1p = 2.0+5.2\n\u22121.2. Although\nthe high SNR tail is consistent with the large Bayes fac-\ntors (Green et al. 2021; Pratten et al. 2020b), we infer\nnon-negligible support below \u03c1p = 2.1. We are therefore\nunable to confidently claim precession in GW231123.\nGW190521 was also found to exhibit mild evidence for\nspin-precession (Abbott et al. 2020d,e).\nWe observe significant differences in the inferred lu-\nminosity distance and inclination angle of GW231123\u2019s\nsource, depending on the model, although we repeat-\nedly infer nearly symmetric distributions for the inclina-\ntion angle around \u03c0/2 rad for all models except XO4a.\nWe also infer substantial variation in the detector-frame\nquantities, despite seeing agreement between several\nmodels in the source-frame parameters. See Appendix A\nfor a detailed discussion. Owing to disagreements in the\ninferred inclination angle of the binary, we similarly ob-\nserve differences in the inferred SNRs in each higher-\norder multipole obtained by each model. Following the\nmethodology in Abbott et al. (2020f,g), where for each\nmultipole the IMRPhenomXHM signal model (Garc\u00b4\u0131a-\nQuir\u00b4os et al. 2020) is used to remove any contribution\nparallel to the dominant multipole and to calculate the\northogonal optimal SNR (Mills & Fairhurst 2021), we\nnevertheless find that all models provide support for the\n(\u2113, m) = (3, 3) multipole in GW231123. We infer an av-\nerage orthogonal optimal SNR of 3.3 when combining\nthe results from all models with equal weight.\nThe properties of the remnant BH are estimated in\ndifferent ways depending on the model. We apply the\nNRSur7dq4Remnant model (Varma et al. 2019) to\nthe samples obtained by NRSur, and we average several\nfits calibrated to numerical relativity simulations (Hof-\nmann et al. 2016; Healy & Lousto 2017; Jim\u00b4enez-Forteza\net al. 2017) for samples obtained by v5PHM, TPHM,\nXPHM, XO4a. When combining the results with equal\nweight, we infer the final mass and spin of the remnant\nBH to be Mf = 222+28\n\u221242 M\u2299and \u03c7f = 0.84+0.08\n\u22120.16 respec-\ntively. For certain binary configurations, the remnant\nBH may receive a recoil velocity that is enough to eject\nthe remnant from its host galaxy (Merritt et al. 2004).\nWe infer a measurement of the remnant BH\u2019s recoil ve-\nlocity that differs from the effective prior distribution:\nvf = 884+973\n\u2212814 km s\u22121. This measurement is based on the\nNRSur analysis and the NRSur7dq4Remnant rem-\nnant model, the only fit providing recoil velocities esti-\nmates (Varma et al. 2019, 2020).\n4.4. Waveform Consistency Checks\nTo further assess whether a CBC signal with the in-\nferred parameters in Section 4.3 adequately represents\nthe data, we perform several consistency checks using\na signal-agnostic approach that reconstructs coherent\ntransient power, and through a model incorporating a\nmodified wave dispersion relationship. First, we com-\npare the waveform of the maximum-likelihood sample\nfrom parameter estimation in Section 4.1 to one ob-\ntained through minimally modelled analyses that make\nno assumptions about the source or morphology of the\nsignal (Szczepa\u00b4nczyk et al. 2021; Salemi et al. 2019;\nGhonge et al. 2020).\nSecond, we conduct a resid-\nuals analysis, subtracting the best-fit waveform from\nthe detector data and searching for coherent residual\npower (Abbott et al. 2021b).\nDiscrepancies between\nthe modelled and minimally modelled waveforms, or the\npresence of significant excess residual power, could indi-\ncate physical effects in addition to or alternative to those\nin our BBH signal models or unaccounted-for noise fea-\ntures (Johnson-McDaniel et al. 2022).\nFor the waveform reconstruction comparisons, we use\nBayesWave (Cornish & Littenberg 2015; Cornish et al.\n2021; Chatziioannou et al. 2021), cWB-2G (Klimenko\net al. 2008, 2016a; Drago et al. 2020), and cWB-\nBBH (Mishra et al. 2025) for the minimally modelled\nanalysis.\nTo evaluate the agreement between the sig-\nnal as found by the modelled analysis and minimally\nmodelled approach, we calculate the overlap between the\nmaximum-likelihood sample from parameter estimation\nusing the NRSur model and the median BayesWave\nor cWB maximum-likelihood waveform. An overlap of\n\n19\n1 indicates perfect agreement, while an overlap of 0\nindicates no similarity between waveforms.\nTo assess\nwhether the overlaps are consistent with signals of com-\nparable parameters and noise realizations, we perform\na dedicated set of injections wherein we inject wave-\nforms generated by draws from the posterior distribu-\ntion of the source parameters into detector data sur-\nrounding the event. The BayesWave analysis performed\n400 injections into approximately 8 hours of data sur-\nrounding the event, and the cWB analysis injected about\n2800 draws from the posterior distribution in an inter-\nval of two weeks around the event. We find good agree-\nment between the minimally modelled and CBC wave-\nform reconstructions. The overlaps between the CBC\nmaximum-likelihood waveform and BayesWave, cWB-\n2G, and cWB-BBH are 0.97, 0.96, and 0.98, respec-\ntively. Compared to the distributions of overlaps from\nthe injections, the p-values (defined as the fraction of\ninjections with overlaps below that of the real event)\nare 0.74, 0.57, and 0.92 for BayesWave, cWB-2G, and\ncWB-BBH, respectively. Under the hypothesis that the\noverlaps between the BayesWave and cWB reconstruc-\ntions with the maximum-likelihood waveform are drawn\nfrom the same distribution as the injection overlaps, the\np-values should be distributed uniformly from 0 to 1,\nso these results indicate that the overlaps are consistent\nwith expectations from systems similar to GW231123.\nFor the residuals test, we produce residual data\nby subtracting from the original data the maximum-\nlikelihood waveform from the NRSur parameter estima-\ntion samples. If the signal has been modelled sufficiently,\nthe residual data should be consistent with Gaussian\nnoise. We analyze the residual data with BayesWave,\nand calculate the 90% credible upper limit on the recov-\nered network SNR (SNR90). To compare to expected\nvalues of SNR90, we also analyze segments of data (with\nno injected signal) selected randomly from 16384 s of\ndata surrounding the event, and calculate the probabil-\nity of obtaining an SNR90 higher than that of residual\ndata. Details of this procedure can be found in (Abbott\net al. 2021b). We find no significant excess SNR in the\nresidual data beyond what is expected from only Gaus-\nsian noise. Compared to the distribution of SNR90 from\nthe noise-only runs, the p-value is 0.35.\nThis further\nconfirms that minimally modelled tests do not flag any\nfeatures in the data missed by the analyses described in\nSection 4.1.\nWe additionally search for post-ringdown echo sig-\nnals (Tsang et al. 2018, 2020) with a BayesWave-based\nsearch, finding negative evidence for their presence (as\nquantified by the Bayes factor log10 Bsignal\nnoise\n< 0), con-\nsistent with the above findings. As a final consistency\ncheck, an analysis incorporating a modified wave dis-\npersion relation due to non-zero graviton mass (Abbott\net al. 2021b) yields agreement with massless wave prop-\nagation when based on the NRSur or TPHM mod-\nels. Instead, when assuming the XPHM or XO4a tem-\nplates, a statistically significant violation is found, sug-\ngesting missing signal components not captured by these\nmodels, which is consistent with the discussion of sys-\ntematics in Section 4.2.\n5. BLACK-HOLE RINGDOWN\nMassive systems dominated by merger-ringdown, such\nas GW231123, are ideal to test the BH signal inter-\npretation by applying BH spectroscopy techniques (De-\ntweiler 1980; Dreyer et al. 2004; Berti et al. 2006, 2009,\n2025), yielding remnant properties under minimal as-\nsumptions on the remnant formation process.\nWe fit\nsuperpositions of damped sinusoids, aiming to associate\nthem with characteristic quasi-normal modes (QNMs) of\na BH, which drive its relaxation to equilibrium. In prin-\nciple, the resulting parameter estimates make it possible\nto robustly validate IMR measurements, since a QNM\ndescription is generic to any BH remnant (e.g., a BH\nformed from an eccentric binary).\nWe\ntruncate\nportions\nof\ndata\nin\nthe\ntime\ndomain\nat\ndifferent\nanalysis\nstart\ntimes\ntstart,\nand\nfit\ntwo\nsets\nof\nmodels.\nThe\nfirst\n(DS-N)\nis\na\nsuperposition\nof\nN\ndamped-sinusoids\nPN\nj=1 Ajei[2\u03c0fj(t\u2212tstart)+\u03d5j]e\u2212(t\u2212tstart)/\u03c4j, with constants\nAj, \u03d5j, fj, \u03c4j as free parameters, assuming fj > 0 (cir-\ncularly polarized wave). In the second (Kerr), complex\nfrequencies are identified with QNMs of a Kerr BH,\nfi = f\u2113mn(M det\nf\n, \u03c7f) and \u03c4i = \u03c4\u2113mn(M det\nf\n, \u03c7f), with de-\ntector frame (redshifted) mass M det\nf\n, spin \u03c7f, and \u2113mn\nthe QNM angular (\u2113, m) and overtone (n) indices. In\naddition to the longest-lived \u2113mn = 220, we consider\n\u2113mn = {221, 210, 200, 330, 320, 440}, the linear QNMs\nwith the largest predicted amplitudes for binary merg-\ners (Kamaretsos et al. 2012; London et al. 2014; Cheung\net al. 2024; Zhu et al. 2025; Nobili et al. 2025; Carullo\n2024).\nHere, we include both \u00b1f\u2113mn contributions,\naccommodating generic signal polarizations, and M det\nf\nenters the expression as mode amplitudes A\u2113mn are\ndegenerate with the source distance.\nWe use the pyRing pipeline (Carullo et al. 2019) with\nstandard analysis settings (Isi & Farr 2021; Abbott et al.\n2021b; Gennari et al. 2024). We pre-condition the data\nby subtracting the 60 Hz power line, which reduces the\nrequired analysis duration to T = 0.2 s (Siegel et al.\n2025). We sample the posterior distribution using the\nCPNest nested sampling algorithm (Veitch et al. 2020).\nTimes are relative to tpol\npeak := maxt[h2\n+(t) + h2\n\u00d7(t)] =\n\n20\n38.14 [ms]\n41.08 [ms]\n44.01 [ms]\nIMR combined\n0\n20\n40\n\u03c41 [ms]\nFigure 5.\nTwo-dimensional frequency and damping time\nposterior distribution (90% credible levels), when starting\nthe analysis at late times and assuming a single damped si-\nnusoid with positive frequency; the combined IMR estimates\nfor the longest-lived \u2113mn = 220 QNM are shown for compar-\nison. For visualisation purposes, we display up to \u03c41 = 45ms,\nwhile the posterior tail extends up to \u03c41 = 80ms.\n1384782888.5998s in the LIGO Hanford data, compati-\nble with the median of the polarizations peak time from\nthe NRSur reconstructed waveform, subject to an un-\ncertainty O(0.01)s. The sky location is fixed to a value\ncompatible with the NRSur maximum likelihood value,\nfixing the analysis start time in LIGO Livingston, as re-\nquired by the truncated time-domain formulation of the\nanalysis (Isi & Farr 2021). We have verified that repeat-\ning the analysis at different sky location values drawn\nfrom the NRSur posterior does not affect our conclu-\nsions.\nDamped\nsinusoids\nare\nexpected\nto\nbe\nvalid\nin\nthe stationary regime of BH relaxation,\ntypically\n[10, 20]GM det\nf\n/c3\n(namely\n[14.7, 29.4] ms\nassuming\nM det\nf\n\u2243298M\u2299) past the signal peak; fitting earlier may\nprovide spurious support for additional modes (Berti\net al. 2025).\nHowever, a time-domain waveform re-\nconstruction of GW231123 indicates a highly complex\nmorphology, displaying a monotonic decay only after\ntstrain\npeak \u2243tpol\npeak + 19 ms. This is significantly later than\nthe nominal tpol\npeak, after which monotonic decay is ex-\npected for vanilla signal morphologies; see Appendix C.\nGiven this uncertainty, we explore a wide range of times\ntstart = tpol\npeak + [\u22127.4, 58.7] ms in steps of \u22483 ms.\nFits that start at late times tstart \u2243tpol\npeak + 41 ms,\nwhen we are confident on the validity of an exponen-\ntial decay description, find preference for a single mode\nwith both models (as quantified by Bayes factors B). A\nsingle damped sinusoid (DS-1) fit yields a multi-modal\nf1 \u2212\u03c41 distribution, shown in Figure 5, unlike what is\nobserved in previous events at such late times. One peak\nwith f1 \u224868 Hz and A1 \u22482 \u00d7 10\u221222 overlaps with the\ndominant Kerr \u2113mn = 220 frequency f220 as predicted\nby IMR models, supporting the BH hypothesis.\nThe\ndamping time spans a broad range, overlapping with\n\u03c4220. A second peak is centred around f1 \u224845 Hz, cor-\nrelating with a larger amplitude value A1 \u22486 \u00d7 10\u221222.\nAmong linear Kerr QNMs predicted by the IMR mod-\nels, this frequency peak shows the largest overlap with\nf200. The damping time is also bimodal: the peak as-\nsociated to f1 \u224845 Hz is centred around \u03c41 \u224810 ms, a\nsmaller value compared to \u03c4200 \u224818 ms, but overlapping\nthe latter distribution. Under a Kerr 220 fit, the two-\ndimensional M det\nf\n\u2013 \u03c7f distribution is also multi-modal:\none peak overlaps with the IMR predictions, while a\nsecond prefers lower remnant spins.\nFitting at earlier times, Bayes factors indicate over-\nwhelming preference (log10 B > 6) for two modes over\none until tstart \u2243tpol\npeak + 32.3 ms in both the DS-N\nand Kerr models, but in this range we may be fit-\nting a complex merger signal, and a QNM superposi-\ntion may not be valid. At these early times, a DS-2 fit\nyields two frequencies consistent with the two peaks ob-\nserved at later times. Amplitudes and damping times\nare comparable in magnitude between the two damped\nsinusoids, and both damping times are larger than the\n\u224810 ms peak observed at later times. In addition to\nthe 220 mode, in the time range explored we find the\nKerr 320, 210, 200 modes to be on average the most\nfavoured by Bayes factors, while 330 is preferred around\ntstart \u2243tpol\npeak + 23.5 ms. The Kerr two-modes combina-\ntions robustly yield a massive remnant, M det\nf\n\u2273200M\u2299,\nalso at these earlier times.\nThese multi-mode combinations are in tension with\nIMR analyses.\nThe most favoured Kerr mode in ad-\ndition to the 220 according to Bayes factors, the 320,\nimplies a M det\nf\n\u2013 \u03c7f distribution that does not overlap\nwith IMR estimates. Adding 210 only results in par-\ntial overlap, while the 221 overlaps to a larger degree.\nHowever, the short-lived 221 mode alone is not expected\nto give rise to the features observed in the signal un-\ntil late times.\nThe 200 mode addition results in the\nmost significant overlap, with a 200 amplitude compa-\nrable to the 220, consistently with later times results.\n\n21\nWhile \u2113mn = 210, 200 QNMs can be strongly excited\nin highly precessing systems with large mass asymme-\ntry (O\u2019Shaughnessy et al. 2013; Zhu et al. 2025; No-\nbili et al. 2025), the IMR analyses of GW231123 pre-\ndict minimal power in the 200 mode, as discussed in\nAppendix D. Highly eccentric configurations can excite\nm = 0 modes (Sperhake et al. 2008), but we lack suffi-\nciently complete merger\u2013ringdown models for eccentric-\nbinary signals to reliably assess this possibility; see Sec-\ntion 7 for further discussion. DS-N analyses with N > 3\ndid not prefer more than two modes, but future inves-\ntigations will be required to determine whether the ob-\nserved features can be induced by a superposition of\nmany overlapping modes.\nIn summary,\nthe Kerr fits recover the remnant\nspin with large uncertainty, and they robustly predict\nM det\nf\n\u2273200M\u2299at all times, supporting the interpre-\ntation of a massive BH remnant.\nFurther investiga-\ntions will be required to characterize the nature of the\nbi-modal features persistently observed in the signal\nand consistently interpret the multi-mode fits at ear-\nlier times. Given these large uncertainties, we do not\nconsider tests of the no-hair properties of BHs in gen-\neral relativity that would be enabled by a confident two-\nmode identification (Detweiler 1980; Dreyer et al. 2004;\nBerti et al. 2006, 2009; Gossan et al. 2012; Brito et al.\n2018; Carullo et al. 2018; Bhagwat et al. 2020; Isi & Farr\n2021; Berti et al. 2025).\n6. ASTROPHYSICAL IMPLICATIONS\nHere, we discuss the astrophysical implications of the\nlarge masses and spins of GW231123\u2019s source and its\npossible origin given current understanding of (pulsa-\ntional) PISNe and formation channels of merging BBHs.\n6.1. Single-event rate estimate\nFirst, we quantify the merger rate of GW231123-like\nevents following (Kim et al. 2003; Abbott et al. 2016b).\nThe sensitive volume\u2013time of the detectors to signals\nwhose source properties are consistent with the posterior\ndistribution of GW231123 is estimated using the cWB-\nBBH results for the injection campaign in Section 2.\nAssuming a constant merger rate R over comoving vol-\nume and source-frame time with prior \u221d1/\n\u221a\nR and a\nPoisson likelihood for the number of triggers, we find\nR = 0.08+0.19\n\u22120.07 Gpc\u22123 yr\u22121. This is consistent with the\nrate of mergers like GW190521 (0.13+0.30\n\u22120.11 Gpc\u22123 yr\u22121;\nAbbott et al. 2020d,e) and upper limits of IMBH merg-\ners (e.g., even the most stringent 90% upper limit <\n0.06 Gpc\u22123 yr\u22121 from Abbott et al. 2022 and see Ta-\nble 3 therein for constraints across source properties),\nbut lower than the overall rate of BBHs with compo-\nnent masses < 100 M\u2299inferred through GWTC-3 (16\u2013\n61 Gpc\u22123 yr\u22121; Abbott et al. 2023b).\n6.2. Relation to the previous inferred population\nTo further assess GW231123 in the context of the 69\nBBH mergers with FARs < 1 yr\u22121 through GWTC-3\n(Abbott et al. 2023a) and test if its masses and spins are\nsurprising, we perform posterior predictive checks based\non the fiducial BBH population fit from (Abbott et al.\n2023b, Section III C; we extend the prior on the maxi-\nmum BH mass up to 200 M\u2299as there is support from\nGW190521 above the limit of 100 M\u2299imposed in the\noriginal GWTC-3 analysis). From the inferred popula-\ntion, we construct mock catalogs containing 69 detected\nevents and plot the distribution of their largest BH mass\n\u224883+43\n\u221226 M\u2299in Figure 3. Using the combined parameter\nestimates in Section 4.3, the primary mass of GW231123\nfalls at the 98+2\n\u22125 % level of this distribution, indeed indi-\ncating that this event is an unlikely draw. However, due\nto large uncertainties in its masses, it is not conclusively\nan outlier as it may be less massive than the most mas-\nsive mock events (equivalent comparisons for secondary\nand total mass are less significant). Similarly, the largest\nBH spin in these catalogs is 0.78+0.14\n\u22120.14, against which the\nprimary and secondary spins of GW231123 can fall at\nany percentile and thus are not outliers. Compared to its\nmasses, the spins of GW231123\u2019s source are more con-\nsistent with the known population as it does not rule\nout large values.\n6.3. Possible formation channels\nFrom theoretical predictions for the late-stage evolu-\ntion of massive stars (Fowler & Hoyle 1964; Barkat et al.\n1967; Rakavy & Shaviv 1967; Fraley 1968; Bond et al.\n1984; Woosley et al. 2002; Woosley 2017), contraction\nof the core leads to electron\u2013positron pair production\nthat reduces internal pressure support, causing further\ncontraction that powers explosive nuclear burning and a\nrebounding shock. For helium-core masses \u224832\u201364 M\u2299,\nmultiple pulsational episodes can eject sufficient mate-\nrial to reduce the mass below the pair-instability regime,\nending with a BH remnant. A single pulse can entirely\ndisrupt stars with larger helium cores, leaving behind no\nremnant in a PISN. At even larger helium-core masses\n\u2273135 M\u2299, this is avoided as the high core temperature\nresults in photodisintegration that accelerates gravita-\ntional collapse to a massive BH. This leads to the robust\nprediction from single-star evolution of the existence of\na gap in the BH mass distribution. Though this gap is\nbroadly consistent with the range \u224860\u2013130 M\u2299, there\nare several theoretical uncertainties that affect both the\nlower edge and total extent of the gap (Belczynski et al.\n\n22\n2016; Stevenson et al. 2019; Farmer et al. 2019; Mapelli\net al. 2020; Renzo et al. 2020b; Marchant & Moriya 2020;\nWoosley & Heger 2021; Hendriks et al. 2023). Uncer-\ntainties in nuclear reaction rates alone can shift the lower\nedge of the pair-instability mass gap from \u224850 M\u2299to\n\u2248100 M\u2299(Farmer et al. 2020).\nSome stellar and binary evolution processes are pre-\ndicted to be able to populate the pair-instability mass\ngap. Weaker stellar winds (Mapelli et al. 2020) or core\ndredge-up episodes (Costa et al. 2021) may allow a star\nto retain a hydrogen envelope and collapse to a BH\nwith mass inside the gap (Spera et al. 2019).\nShort-\nperiod stellar binaries might avoid merging and produce\nbinary BHs with large, equal masses \u223c100 M\u2299from\nrapidly rotating metal-poor stars due to chemically ho-\nmogeneous evolution (de Mink & Mandel 2016; Mandel\n& de Mink 2016; Marchant et al. 2016). However, most\nmodels of isolated-binary formation predict small natal\nspins and at most one of the BHs spinning, due to tidal\nsynchronization or accretion-induced spin up, and so bi-\nnaries with masses and spins like those inferred from\nGW231123 are difficult to form (Belczynski et al. 2020;\nQin et al. 2018; Fuller & Ma 2019; Bavera et al. 2020;\nBelczynski et al. 2020; van Son et al. 2020). In fact, the\ncomponents BHs and especially the primary are so mas-\nsive that they may have formed through core collapse\nabove the pair-instability mass gap (Ezquiaga & Holz\n2021; Franciolini et al. 2024).\nAlternatively, in hierarchical mergers, one or both of\nthe binary components is the product of a previous BBH\nmerger, with characteristically large masses and spins\n(Gerosa & Fishbach 2021). As seen in Figure 4, the spins\ninferred from GW231123 may be even larger than typ-\nically predicted from hierarchical BH mergers (Gerosa\n& Berti 2017; Fishbach et al. 2017), although the ex-\npected distribution for sources retained in their host en-\nvironments may accommodate a wider range of spins\n(Borchers et al. 2025). Previous analyses have suggested\nevidence for hierarchical mergers in GW catalogs (Kim-\nball et al. 2021; Mould et al. 2022; Wang et al. 2022; Li\net al. 2024; Pierra et al. 2024; Hussain et al. 2024; An-\ntonini et al. 2025), but the population of BH remnants\nreceive gravitational recoils as high as 102\u2013104 km s\u22121\n(Doctor et al. 2021; Mahapatra et al. 2021), requiring\nenvironments with high escape speeds (Antonini & Ra-\nsio 2016) such as dense stellar clusters (Miller & Hamil-\nton 2002; Antonini et al. 2019; Rodriguez et al. 2019;\nFragione & Silk 2020; Mapelli et al. 2021; Arca Sedda\net al. 2021; Kritos et al. 2023; Mahapatra et al. 2025) or\nactive galactic nucleus (AGN) disks (Bartos et al. 2017;\nStone et al. 2017; Mckernan et al. 2018; Yang et al. 2019;\nTagawa et al. 2020; McKernan et al. 2020; Vaccaro et al.\n2024; Arca Sedda et al. 2023b) to be retained.\nThis is in contrast to stellar mergers, which receive\nsmaller recoils from asymmetric mass loss (Gaburov\net al. 2010; Glebbeek et al. 2013) and therefore may be\nmore efficient at producing BHs with large masses in dy-\nnamical environments. The large masses inferred from\nGW231123 may be explained by multiple such merg-\ners in dense clusters or multiple systems (Mapelli 2016;\nDi Carlo et al. 2020; Renzo et al. 2020a; Kremer et al.\n2020; Gonz\u00b4alez et al. 2021; Rizzuto et al. 2022; Costa\net al. 2022; Arca Sedda et al. 2023a), a scenario that\ncould also describe the formation of massive central BHs\n(Portegies Zwart et al. 2004; Greene et al. 2020).\nBesides mass transfer between the components of a\nstellar binary, BH mass growth may also occur via ac-\ncretion in other gaseous environments. BHs embedded\nin the disk of an AGN may accrete material directly\nfrom the disk or from collisions with disk stars (McK-\nernan et al. 2012).\nSimilarly, in dense clusters, BHs\nmay accrete from stars after undoing dynamical interac-\ntions (Giersz et al. 2015; Lopez et al. 2019; K\u0131ro\u02d8glu et al.\n2025). Furthermore, these accretion processes may also\nincrease BH spins.\nA different possibility is that of primordial BHs being\nthe binary components, which may exist across a range\nof mass scales, including within the pair-instability mass\ngap (Bird et al. 2016, 2023; Clesse & Garc\u00b4\u0131a-Bellido\n2017, 2022). However, there are remaining theoretical\nuncertainties, e.g., on whether primordial BHs could ac-\ncrete sufficiently to spin up as rapidly as the BHs in-\nferred from GW231123 (Green & Kavanagh 2021).\nAltogether, these theoretical predictions and their un-\ncertainties make it difficult to determine whether or not\nthe BHs in the source of GW231123 have an astrophys-\nical origin directly from stellar collapse.\nWe quantify\nthis in more detail below.\n6.4. Stellar collapse\nTo account for a range of possible locations for the\npair-instability mass gap, in Figure 6 we compute the\nprobability that one or both component masses fall\nwithin the gap as a function of its lower edge from 40\u2013\n100 M\u2299and upper edge from 120\u2013180 M\u2299, using the\ncombined parameter estimates.\nIn the following, we\nquote these probabilities specifically for the putative gap\n60\u2013130 M\u2299. The probabilities that the secondary (pri-\nmary) BH lies in, above, and below this gap are 83 %\n(28 %), 1 % (72 %), and 16 % (0 %), respectively. Con-\nsidering scenarios in which at least one of the compo-\nnents falls in this gap, the joint probability that: both\nBHs are in the gap (upper left panel of Figure 6) is 26 %;\n\n23\n120\n130\n140\n150\n160\n170\n180\nUpper edge [M\u2299]\n40M\u2299\n60M\u2299\n80M\u2299\n100M\u2299\nm1 in, m2 in\n40M\u2299\n60M\u2299\n80M\u2299\n100M\u2299\nm1 above, m2 in\n40\n50\n60\n70\n80\n90 100\nLower edge [M\u2299]\n120\n130\n140\n150\n160\n170\n180\nUpper edge [M\u2299]\n40M\u2299\n60M\u2299\n80M\u2299\n100M\u2299\nm1 in, m2 below\n40\n50\n60\n70\n80\n90 100\nLower edge [M\u2299]\n40M\u2299\n60M\u2299\n80M\u2299\n100M\u2299\nm1 above, m2 below\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\nProbability\nFigure 6.\nProbability using the combined parameter es-\ntimates for GW231123 that:\nboth BHs are in the pair-\ninstability mass gap (top left); the primary is above the gap\nand the secondary is within (top right); the primary is within\nand the secondary is below (bottom left); the primary is\nabove and the secondary is below (bottom right). Probabil-\nities are computed varying the lower and upper edges of the\ngap, while dashed lines mark constant gap widths.\nthe primary is above while the secondary is within (up-\nper right) is 57 %; and that the primary is within while\nthe secondary is below (lower left) is 2 %. Alternatively,\na scenario with neither BH in the gap is possible in the\ncase of a straddling binary (Fishbach & Holz 2020), with\na primary BH above the upper edge and secondary be-\nlow the lower edge (lower right) having a probability of\n14 %.\nOverall, this implies that within the uncertainties on\nthe combined parameter estimates (assuming our de-\nfault prior) and the location of the pair-instability mass\ngap, scenarios with both BHs outside the gap have lower\nprobability than those with at least one BH in the gap.\n6.5. Hierarchical mergers\nGiven the high probability of at least one of the\nBHs lying inside the pair-instability mass gap, we con-\nsider the possibility that this is due to repeated BBH\nmergers. Assuming hierarchical origins, several works\nhave inferred the source properties of potential BBHs\nwhose merger products are observed with GWs in a\nsubsequent merger (Baibhav et al. 2021; Barrera &\nBartos 2022; \u00b4Alvarez et al. 2024; Mahapatra et al.\n2024).\nWe follow (\u00b4Alvarez et al. 2024) and use the\nNRSur7dq4Remnant surrogate model (Varma et al.\n2019) to find the distribution of BBH source proper-\nties such that the corresponding distribution of BH rem-\nnant properties reproduces the combined parameter esti-\nmates over mass and spin for the primary and secondary\nBH inferred from GW231123. As the primary-spin pos-\nterior favors large values \u22730.7, this constrains the par-\nent binary of the primary BH to have unequal masses\n105+24\n\u221229 M\u2299and 38+33\n\u221217 M\u2299; for more equal masses, both\nBH spins can reduce the total angular momentum if\nmisaligned, whereas unequal-mass binaries are domi-\nnated by the single heavier BH. The parent binary of\nthe primary BH may have had a large effective inspi-\nral spin, with \u03c7eff = 0.55+0.25\n\u22120.60, but \u03c7eff \u22720 is not\nruled out.\nA similar picture holds for the secondary\nBH, with parent masses 73+26\n\u221237 M\u2299and 25+28\n\u221215 M\u2299, but\nmore uncertain effective inspiral spin \u03c7eff = 0.29+0.47\n\u22120.88\ndue to the larger uncertainty on the secondary spin in\nthe source of GW231123. These mergers would have im-\nparted kicks of 749+1320\n\u2212630 km s\u22121 and 494+1410\n\u2212363 km s\u22121 in\nthe case of the primary and secondary, respectively, re-\nsulting in ejection from environments with escape speeds\n\u2272100 km s\u22121, such as young star clusters or globular\nclusters (Antonini & Rasio 2016).\nThe heavier of the two BHs in both parent binaries\nmay also lie within the pair-instability mass gap, with\nprobabilities 96 % and 71 % for the heavier parent of the\nprimary and secondary, respectively, when taking a gap\nfrom 60\u2013130 M\u2299, as above. Therefore, if either of the\ncomponent BHs of GW231123\u2019s source is interpreted as\nthe product of a previous BH merger, it may be the\nresult of multiple previous mergers or require the com-\nponents of the parent binary to have formed with larger\nmasses via other astrophysical processes, such as stellar\nmergers or BH accretion, as discussed in Section 6.3.\n7. ALTERNATIVE INTERPRETATIONS\nAll GW observations to date have been inferred to be\nfrom compact binaries consisting of BHs and/or neutron\nstars (Abbott et al. 2016c, 2021a, 2024a, 2023a; Venu-\nmadhav et al. 2020; Olsen et al. 2022; Mehta et al. 2025;\nNitz et al. 2023; Wadekar et al. 2023), and we consider\na BBH the most astrophysically plausible interpretation\nof GW231123, finding that a non-eccentric BBH model\nfits the signal with no significant residual. Nonetheless,\nthe low number of observable GW cycles invites alter-\nnative interpretations. We discuss several here.\n7.1. Eccentricity\nBinaries formed in dense environments may retain\nresidual eccentricity in the sensitive band of current GW\ndetectors (Antonini et al. 2014; Samsing 2018; Rodriguez\net al. 2018; Zevin et al. 2019; Chattopadhyay et al. 2023;\nDall\u2019Amico et al. 2024) or form with large eccentrici-\nties and merge promptly after due to a dynamical cap-\nture (Gold & Br\u00a8ugmann 2013; East et al. 2013; Gamba\n\n24\net al. 2023; Andrade et al. 2024; Albanesi et al. 2025b),\nbut for high masses their GW signals can be confused\nwith those of non-eccentric mergers (Romero-Shaw et al.\n2020a; Calder\u00b4on Bustillo et al. 2021a; Romero-Shaw\net al. 2023). Our signal models assume a non-eccentric\ninspiral, while state-of-the-art IMR models that include\neccentricity (Liu et al. 2022; Gamboa et al. 2024; Paul\net al. 2025; Albanesi et al. 2025a; Planas et al. 2025a)\nassume circularization in the merger\u2013ringdown stages\nand would thus be unsuitable to infer the parameters\nof GW231123\u2019s source if it was eccentric when observed\n(Ramos-Buades et al. 2023b; Iglesias et al. 2024; Gupte\net al. 2024; Planas et al. 2025b). Extensions of QNM\namplitude models beyond eccentric non-spinning con-\nfigurations (Carullo 2024) will be required to investigate\nthe possible m = 0 ringdown mode excitation hinted at\nin Section 5. Many studies have found that the merger-\nringdown signal is robust with respect to moderate inspi-\nral eccentricity (Hinder et al. 2008; Huerta et al. 2019;\nHealy & Lousto 2022; Carullo et al. 2024; Nee et al.\n2025). Relaxing the non-eccentric assumption is not ex-\npected to significantly change our results unless the ec-\ncentricity is larger than \u223c0.6 close to merger (Healy &\nLousto 2022; Carullo et al. 2024), which would be rare\nin the dynamical-capture scenarios above. For example,\nChattopadhyay et al. (2023) find an overall merger rate\n< 1 Gpc\u22123 yr\u22121 in dense stellar clusters, \u223c10% with ec-\ncentricity > 0.1 at a GW frequency of 10 Hz and \u223c10%\ninvolving BHs with masses > 100 M\u2299, implying a rate\nof massive eccentric mergers < 0.01 Gpc\u22123 yr\u22121, already\nat the lower limit of our constraint for GW231123 with-\nout considering the decline in the number of sources at\nincreasing mass and eccentricity. Although we do not\nexplicitly rule out large eccentricity for the source of\nGW231123, we therefore consider it astrophysically un-\nlikely.\n7.2. Gravitational lensing\nGW signals may be strongly lensed by galaxies or\ngalaxy clusters, producing multiple copies of the orig-\ninal signal (Hannuksela et al. 2019; Abbott et al. 2021c,\n2024b). However, no closely matching super-threshold\ncounterpart candidates for GW231123 have been found\nfrom standard CBC searches. GWs can also undergo\nwave-optics lensing (Takahashi & Nakamura 2003) when\nthey encounter smaller objects (\u223c102\u2013106 M\u2299for sig-\nnals in the LVK band). GW231123 shows the strongest\nsupport for distorted lensed signals seen so far for\nboth a point-mass model (Wright & Hendry 2022)\nand phenomenological analyses (Liu et al. 2023), al-\nthough preliminary background analyses suggest that\nsome GW231123-like signals may be mis-identified as\nlensed. More in-depth investigations are needed to as-\nsess the significance of the lensing hypothesis, and these\nwill be presented in future work.\n7.3. Other scenarios\nSeveral possible burst-like sources (Powell & Lasky\n2025) of astrophysical and cosmological origin may pro-\nduce signals of similar duration to GW231123, such\nas core-collapse supernovae, cosmic strings, and ex-\notic compact objects.\nFor most supernova wave-\nforms,\nthe peak signal is expected at frequencies\nhigher than observed in GW231123 (Abdikamalov et al.\n2020; Mezzacappa & Zanolin 2024).\nThe ringdown-\ndominated signals of high-mass BBH mergers can be\nmimicked by waveforms from the collapse of cosmic\nstrings (Abbott et al. 2020e; Aurrekoetxea et al. 2024)\nand collisions of exotic compact objects (e.g.\nboson\nstars) (Calder\u00b4on Bustillo et al. 2021b; Siemonsen & East\n2023; Evstafyeva et al. 2024). Though we do not explic-\nitly rule out these scenarios, the detection of GW231123\nis consistent with the rates and properties of the cur-\nrently understood population under the interpretation\nof a high-mass BBH merger, which has higher astro-\nphysical probability.\n8. SUMMARY\nGW231123 is a short-duration GW signal consisting of\n\u223c5 observable cycles, most likely produced by a binary-\nblack-hole merger. On that basis, we infer a total mass\nbetween 190 M\u2299and 265 M\u2299, which is larger than any\npreviously observed with high confidence in GWs, and\nstrong support for large spins on both black holes. We\nreport source property measurements with larger uncer-\ntainties than we would expect for a binary of this mass\nand a signal with SNR \u223c21, most likely due to uncertain-\nties in current signal models at high spins. A ringdown\nanalysis also supports a massive remnant under minimal\nassumptions, consistent with full-signal estimates. The\nmeasured masses of GW231123\u2019s source lie at the edge\nof the currently understood population of binary black\nholes. The scenario with the highest probability is that\nat least one of the black hole sits in the pair-instability\nmass gap. If either is interpreted as the product of a pre-\nvious black-hole merger, at least one of the black holes\nin its parent binary probably also lies in the mass gap.\nSuch a sequence of black-hole mergers would require an\nenvironment with high escape speed, unless the black-\nhole masses are grown by other astrophysical processes,\nsuch as stellar mergers.\nGiven the small number of observable GW cycles, the\nlarge uncertainties in our measurements, and the limi-\ntations of current signal models, we expect that there\n\n25\nis much still to learn about GW231123 and its source.\nThe feasibility of a wide range of other alternatives to\nblack-hole mergers remains to be investigated.\nEven\nwithin the binary-black-hole merger interpretation, we\nexpect to learn more from detailed studies of high-spin\nbinaries, high-eccentricity mergers, hyperbolic encoun-\nters, and lensed signals.\nForthcoming analyses of the\ncombined catalog of GW events, alongside continued\nstudies of pair-instability processes and the formation\nof intermediate-mass black holes, may help to reveal the\norigins of GW231123. All studies will have to contend\nwith the limited information that can be extracted from\nshort signals, but a clearer picture may emerge if a pop-\nulation of such signals is observed in future observing\nruns.\nStrain data from the LIGO detectors associated with\nGW231123 are available from the Gravitational Wave\nOpen Science Center 1. Samples from posterior distri-\nbutions of the source parameters, additional materials,\nand notebooks for reproducing the figures are available\non Zenodo (LIGO Scientific, Virgo, and KAGRA Col-\nlaboration 2025).\nThe software packages used in our\nanalyses are open-source.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agen-\ncies as well as by the Council of Scientific and Indus-\ntrial Research of India, the Department of Science and\nTechnology, India, the Science & Engineering Research\nBoard (SERB), India, the Ministry of Human Resource\nDevelopment, India, the Spanish Agencia Estatal de\nInvestigaci\u00b4on (AEI), the Spanish Ministerio de Cien-\ncia, Innovaci\u00b4on y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\n1 https://doi.org/10.7935/anj7-6q40\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comunitat\nAuton`oma de les Illes Balears through the Conselleria\nd\u2019Educaci\u00b4o i Universitats, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the Polish National Agency\nfor Academic Exchange, the National Science Centre of\nPoland and the European Union - European Regional\nDevelopment Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Edu-\ncation, the Swiss National Science Foundation (SNSF),\nthe Russian Science Foundation, the European Com-\nmission, the European Social Funds (ESF), the Euro-\npean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish Uni-\nversities Physics Alliance, the Hungarian Scientific Re-\nsearch Fund (OTKA), the French Lyon Institute of Ori-\ngins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering\nResearch Council of Canada (NSERC), the Canadian\nFoundation for Innovation (CFI), the Brazilian Min-\nistry of Science, Technology, and Innovations, the In-\nternational Center for Theoretical Physics South Ameri-\ncan Institute for Fundamental Research (ICTP-SAIFR),\nthe Research Grants Council of Hong Kong, the Na-\ntional Natural Science Foundation of China (NSFC),\nthe Israel Science Foundation (ISF), the US-Israel Bina-\ntional Science Fund (BSF), the Leverhulme Trust, the\nResearch Corporation, the National Science and Tech-\nnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, the JSPS\nLeading-edge\nResearch\nInfrastructure\nProgram,\nJSPS Grant-in-Aid for Specially Promoted Research\n26000005, JSPS Grant-in-Aid for Scientific Research\non Innovative Areas 2402:\n24103006, 24103005, and\n2905:\nJP17H06358,\nJP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grants-in-Aid for Scientific Research (S)\n17H06133 and 20H05639, JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cos-\n\n26\nmic Ray Research, University of Tokyo, the National\nResearch Foundation (NRF), the Computing Infrastruc-\nture Project of the Global Science experimental Data\nhub Center (GSDC) at KISTI, the Korea Astronomy\nand Space Science Institute (KASI), the Ministry of\nScience and ICT (MSIT) in Korea, Academia Sinica\n(AS), the AS Grid Center (ASGC) and the National\nScience and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research\nProgram, the Advanced Technology Center (ATC) of\nNAOJ, and the Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individ-\nual authors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising. We\nrequest that citations to this article use \u2019A. G. Abac et\nal. (LIGO-Virgo-KAGRA Collaboration), ...\u2019 or similar\nphrasing, depending on journal convention.\nSoftware:\nCalibration of the LIGO strain data\nwas performed with a GstLAL-based calibration soft-\nware pipeline (Viets et al. 2018b). Data-quality prod-\nucts and event-validation results were computed us-\ning the DMT (Zweizig, J. 2006), DQR (LIGO Sci-\nentific Collaboration and Virgo Collaboration 2018),\nDQSEGDB (Fisher et al. 2021), gwdetchar (Urban et al.\n2021), hveto (Smith et al. 2011), iDQ (Essick et al.\n2020), Omicron (Robinet et al. 2020), and PythonVir-\ngoTools (Virgo Collaboration 2021) software packages\nand contributing software tools. Analyses in this cata-\nlog relied on software from the LVK Algorithm Library\nSuite (LIGO Scientific, Virgo, and KAGRA Collabo-\nration 2018; Wette 2020). The detection of the signals\nand subsequent significance evaluations were performed\nwith the GstLAL-based inspiral software pipeline (Mes-\nsick et al. 2017; Sachdev et al. 2019; Hanna et al. 2020;\nCannon et al. 2021), with the MBTA pipeline (Adams\net al. 2016; Aubin et al. 2021), with the PyCBC (Usman\net al. 2016; Nitz et al. 2017; Davies et al. 2020) packages,\nwith cWB-BBH pipeline (Mishra et al. 2025), cWB-2G\n(Klimenko et al. 2008, 2016a; Drago et al. 2020) cWB-\nXP (Klimenko 2022), cWB-GMM (Gayathri et al. 2020;\nLopez et al. 2022; Smith et al. 2024). Low-latency source\nlocalization was performed using BAYESTAR (Singer &\nPrice 2016). Estimates of the noise spectra and glitch\nmodels were obtained using BayesWave (Cornish & Lit-\ntenberg 2015; Littenberg & Cornish 2015; Cornish et al.\n2021). Source-parameter estimation was primarily per-\nformed with the Bilby and BilbyPipe libraries (Ashton\net al. 2019; Smith et al. 2020; Romero-Shaw et al. 2020b)\nusing the Dynesty nested sampling package (Spea-\ngle 2020). SEOBNRv5PHM waveforms used in param-\neter estimation were generated using pySEOBNR (Mi-\nhaylov et al. 2025). PESummary was used to postpro-\ncess and collate parameter-estimation results (Hoy &\nRaymond 2021). Some of the parameter-estimation anal-\nyses were managed with the Asimov library (Williams\net al. 2023). Ringdown analyses were performed us-\ning the pyRing (Carullo et al. 2025) library, relying on\nthe CPNest nested sampling algorithm (Veitch et al.\n2020). The manuscript content has been derived mak-\ning use of additional publicly available software: mat-\nplotlib (Hunter 2007), numpy (Harris et al. 2020),\nscipy (Virtanen & others 2020), seaborn (Waskom\net al. 2021), sxs (Scheel et al. 2025).\nAPPENDIX\nA. SYSTEMATICS STUDIES\nFor this analysis we consider the models NRSur, v5PHM, TPHM, XPHM and XO4a. These models all describe\nprecessing quasi-circular binaries and include higher multipole content. The three model families NRSur, SEOBNR\nand Phenom use different approaches to model the waveforms (Chatziioannou et al. 2024). In short, NRSur interpo-\nlates between NR data (Field et al. 2014; Blackman et al. 2015), making it typically the most accurate of the models for\nhigh-mass signals, such as GW231123. The SEOBNR and Phenom families instead use a combination of analytical\nand numerical information to create a complete inspiral-merger-ringdown model applicable to systems at any total\nmass (Buonanno & Damour 1999, 2000; Buonanno et al. 2007; Ajith et al. 2011). The models NRSur, v5PHM, and\nTPHM calculate the signal in the time domain, while XPHM and XO4a model directly in the frequency domain.\nThese models comprise the five state-of-the-art models currently available for LVK analyses of observations in O4a.\nNRSur is fully calibrated to numerical waveforms over the binary parameter space up to dimensionless spin mag-\nnitudes \u03c71 = \u03c72 = 0.8 and mass ratios q = 1/4, and can be extrapolated up to dimensionless spin magnitudes\n\u03c71 = \u03c72 = 1.0 and mass ratios q = 1/6.\nBy construction, NRSur automatically includes all multipoles up to\n\u2113= 4 and characteristics of precession such as mode asymmetry (Varma et al. 2019). By contrast, v5PHM, TPHM,\n\n27\nFigure 7. Marginalized posterior probability for the Left: redshifted (detector-frame) total binary mass and the mass ratio,\nand Right: primary and secondary source-frame masses inferred from GW231123 for each of the five models considered. Each\ncontour, as well as the colored horizontal and vertical lines, shows the 90% credible intervals.\nand XPHM are calibrated to NR only in the aligned-spin sector (Pompili et al. 2023; Estell\u00b4es et al. 2022b; Prat-\nten et al. 2020a; Garc\u00b4\u0131a-Quir\u00b4os et al. 2020) and instead model precession either by extending post-Newtonian and\neffective-one-body results or by employing BH perturbation theory results through merger and ringdown. During\nthe inspiral, v5PHM, TPHM, and XPHM implement precession dynamics by numerically evolving the spins (Khalil\net al. 2023; Estell\u00b4es et al. 2021; Colleoni et al. 2025). XO4a uses closed-form, orbit-averaged expressions during the\ninspiral (Chatziioannou et al. 2017; Pratten et al. 2021) and phenomenological expressions calibrated to single-spin\nprecessing simulations with \u03c71 < 0.8 through merger and ringdown (Hamilton et al. 2021). Further, XO4a includes\nmode asymmetry of the dominant multipole (Ghosh et al. 2024).\nThe different modeling approaches and treatments of the precession dynamics make these models relatively indepen-\ndent. In the presence of features in the data beyond the physical effects incorporated in the models (e.g., mismodelling\nin the high-spin regime, eccentricity, GW memory, or noise artefacts) one might therefore expect the models to in-\nteract with these features differently and display model systematics, as are seen in the posteriors for this event. The\naccuracy of these models for typical signals has been comprehensively assessed through comparison to NR, both in the\nmodelling papers themselves and elsewhere (Mac Uilliam et al. 2024, e.g., [).For GW231123 we have performed the\naccuracy analysis in Section 4.2, and a series of targeted NR injections, which we now describe. We hope that more\ncan be learned in the future from improved models in the high-spin regime, and a detailed study of the behaviour of\nour models in Gaussian noise.\nIn order to investigate the likelihood of the presence of waveform systematics in the high total mass, comparable-\nmass (q > 1/3), highly precessing region of parameter space, we perform a simulation study where we simulate a set\nof signals consisting of highly precessing NR waveforms from the SXS catalog (Boyle et al. 2019; Scheel et al. 2025)\nand recover with the five waveform models under consideration. From several tens of simulations, we discuss here the\nresults from two that span the range of observed results, from unbiased parameter estimation displaying no systematics\nto large systematic differences between models and clear biases in parameter recovery.\nFor both configurations, we show the total mass and mass ratio as measured in the data (the detector frame). For\nhigh-mass binaries, we expect the total mass to be one of the most reliably measured quantities. The detector-frame\nmasses are not the true source masses, but the redshifted masses, and to calculate the true masses, we must also measure\nthe redshift. The relative accuracy of the detector-frame and source-frame masses may therefore differ, depending on\n\n28\nFigure 8. Marginalized posterior probability for (left column) redshifted (detector-frame) total binary mass and the mass ratio\nand (right column) primary and secondary source-frame masses inferred from two highly spinning precessing NR simulations\nwith (detector-frame) total binary mass of 300 M\u2299observed approximately edge on. The Top row shows the results for the\nSXS:BBH:0483 (Boyle et al. 2019) with masses m1 \u223c135 M\u2299, m2 \u223c110 M\u2299and mass ratio q = 0.8. The Bottom row shows the\nresults for the SXS:BBH:4030 (Scheel et al. 2025) with masses m1 = m2 \u223c130 M\u2299. The 5 models used to analyse GW231123\nwere also used to analyse these simulations. Each contour, as well as the colored horizontal and vertical lines, shows the 90%\ncredible intervals. The black vertical and horizontal lines indicate the true source properties. In some panels, the true value is\nbeyond the axis range of the figure.\nthe accuracy of the redshift. For this reason, we also show the individual masses m1 and m2 after correcting for the\nredshift.\n\n29\nThe results for GW231123 are shown in Figure 7. In the left panel, we see clear evidence of systematics in the\nmeasurement of both the total mass and the mass ratio, with no overlap of the 90% credible intervals for some models\nin both parameters. When we correct for the redshift, some of the differences appear to \u201ccancel out\u201d, and we see\nagreement between several models in the source masses. This is likely coincidental; we expect any model biases in the\ndetector-frame masses and redshift to be independent. This expectation is borne out in the examples below.\nIn the majority of cases simulated, we were unable to reproduce this degree of systematics.\nIn both examples\ndiscussed here, we choose a large inclination angle as the mismatch performance is worst, and thus the associated\nexpectations of evidence of systematics are greater, for systems with the greatest contribution from higher multipoles.\nIt should be noted, however, that since the orbital plane precesses, the inclination is not constant over the binary\u2019s\nevolution. An example of a typical recovery is shown in the top row of Figure 8, where we consider the SXS:BBH:0483\nprecessing NR simulation with total mass M = 300 M\u2299, mass ratio q = 0.8, and spin magnitudes \u03c71 = \u03c72 = 0.80 on\nboth BHs. The simulation is added to zero-noise using the fiducial inclination angle \u03b9 = \u03c0/2 rad at 10 Hz. For this\nconfiguration, the mismatch for NRSur was unambiguously below the conservative distinguishability criterion, with a\nvalue of 3.92 \u00d7 10\u22124, while for the other models we see values O\n\u000010\u22123\u0001\n. In this case, the large differences in mismatch\ndo not translate into noticeable differences in the accuracy of parameter recovery. The posteriors from all models\noverlap and we can be confident in our recovered source properties. Note, however, that the source-frame m2 is too\nlow. This is a known bias for edge-on configurations: signals from face-on and face-off binaries are louder, meaning\nthat larger distances (redshifts) are consistent with a fixed GW amplitude. This leads to a significantly larger prior\nvolume, and thus a prior preference for smaller inclination angles (Usman et al. 2019), larger distances, and thus lower\n(redshifted) source masses.\nClear evidence of systematics was nevertheless seen in a limited number of simulations, as is demonstrated in the\nbottom row of Figure 8. We consider the SXS:BBH:4030 precessing NR simulation with total mass M = 300 M\u2299,\nequal mass components (q = 1), and spin magnitudes \u03c71 = \u03c72 = 0.95 on both BHs. The simulation is added to\nzero-noise using the fiducial inclination angle \u03b9 = \u03c0/2 rad at 15 Hz. This injection was chosen from the set of cases\nwith very high spins, with a mismatch between 2.36 \u00d7 10\u22123 (NRSur) and 9.45 \u00d7 10\u22123 (TPHM), mostly above the\nconservative indistinguishability criterion. This numerical relativity (NR) waveform also includes GW memory, which\ncan require additional data processing for injection (Xu et al. 2024; Valencia et al. 2024; Chen et al. 2024), but we\nfind that our results are unchanged if we first subtract the memory features before injection. We see unequivocal\nevidence of waveform systematics and biases in all models. Only the posterior of TPHM includes the true value of\nthe detector-frame total mass, and all models exclude it at 90% credibility. No model recovers the true mass ratio\n(q = 1). In the source-frame, the true value of m1 lies in the 90% credible region for all models, but m2 is significantly\nbiased from its true value of 100 M\u2299.\nB. SOURCE PROPERTIES\nIn Table 3, we present the individual source properties of GW231123 for each of the five models considered in the\nanalysis of this event for those interested in a more detailed picture of the systematics. As demonstrated in Appendix A,\nthe source properties of this event lie in a challenging region of parameter space for all waveform models employed.\nFrom the analysis performed here, we cannot guarantee that the results from any given model will be free from bias in\nthis region of parameter space. We also find that different models fit the data better than others. All models except\nXPHM obtain a larger Bayesian evidence than the NRSur analysis, as reflected in the differing SNRs in Table 3. For\nexample, for some parameters XO4a yields significantly different results to many of the other models, yet it obtains\na Bayes factor of at least 140:1 over NRSur. However, such differences are not necessarily indicative of one model\nbeing more accurate than another (Hoy 2022; Hoy et al. 2024). Consequently, we combine the posteriors from multiple\nmodels to achieve a conservative error estimate, which is reported throughout the main body of the paper.\nWe also illustrate in Figure 9 the differences in inferred spin orientation when considering the data from LIGO\nHanford (left), LIGO Livingston (middle), and the full detector network (right). LIGO Hanford shows support for\naligned-spin binaries, while LIGO Livingston has a clear preference for misalignment. The stronger signal in LIGO\nLivingston dominates the network results. The differences between the results in the two detectors could potentially be\nexplained by lower signal power in LIGO Hanford (such that precession is not measurable), but we have not been able\nto reproduce this discrepancy between detectors with injections in zero-noise, for example, of the NRSur waveform\nat its maximum-likelihood parameters.\n\n30\nTable 3. Individual source properties of GW231123 from each of the five models considered.\nXPHM\nXO4a\nTPHM\nNRSur\nv5PHM\nPrimary mass m1/M\u2299\n149+14\n\u221213\n143+26\n\u221216\n133+19\n\u221213\n128+16\n\u221216\n133+19\n\u221215\nSecondary mass m2/M\u2299\n92+21\n\u221222\n55+12\n\u221218\n110+16\n\u221217\n108+16\n\u221220\n109+17\n\u221222\nMass ratio q = m2/m1\n0.61+0.13\n\u22120.14\n0.39+0.07\n\u22120.16\n0.82+0.16\n\u22120.14\n0.85+0.15\n\u22120.12\n0.82+0.18\n\u22120.15\nTotal mass M/M\u2299\n241+30\n\u221228\n198+30\n\u221218\n242+28\n\u221219\n237+23\n\u221232\n241+28\n\u221223\nFinal mass Mf/M\u2299\n231+27\n\u221225\n190+29\n\u221217\n227+26\n\u221217\n222+22\n\u221232\n226+25\n\u221222\nPrimary spin magnitude \u03c71\n0.79+0.21\n\u22120.20\n0.92+0.07\n\u22120.06\n0.92+0.08\n\u22120.14\n0.90+0.10\n\u22120.19\n0.91+0.09\n\u22120.16\nSecondary spin magnitude \u03c72\n0.67+0.33\n\u22120.47\n0.47+0.41\n\u22120.47\n0.87+0.13\n\u22120.25\n0.91+0.09\n\u22120.22\n0.81+0.19\n\u22120.35\nEffective inspiral spin \u03c7eff\n0.03+0.17\n\u22120.25\n0.31+0.19\n\u22120.19\n0.43+0.16\n\u22120.19\n0.27+0.24\n\u22120.35\n0.43+0.20\n\u22120.25\nEffective precessing spin \u03c7p\n0.74+0.21\n\u22120.21\n0.82+0.10\n\u22120.12\n0.76+0.17\n\u22120.17\n0.76+0.19\n\u22120.17\n0.74+0.20\n\u22120.19\nFinal spin \u03c7f\n0.70+0.08\n\u22120.11\n0.85+0.06\n\u22120.07\n0.88+0.04\n\u22120.04\n0.82+0.06\n\u22120.11\n0.88+0.05\n\u22120.06\nLuminosity distance DL/Gpc\n0.9+0.4\n\u22120.3\n3.5+1.2\n\u22121.4\n2.7+1.2\n\u22121.1\n1.9+1.7\n\u22121.0\n2.3+1.4\n\u22121.0\nInclination angle \u03b8JN/rad\n1.6+0.4\n\u22120.4\n0.5+2.1\n\u22120.3\n1.9+0.3\n\u22121.0\n1.3+0.8\n\u22120.4\n1.2+1.0\n\u22120.4\nSource redshift z\n0.18+0.07\n\u22120.06\n0.58+0.17\n\u22120.20\n0.46+0.16\n\u22120.16\n0.34+0.24\n\u22120.18\n0.40+0.20\n\u22120.16\nNetwork matched filter SNR \u03c1\n20.5+0.2\n\u22120.3\n20.8+0.2\n\u22120.2\n20.8+0.2\n\u22120.3\n20.6+0.2\n\u22120.3\n20.7+0.2\n\u22120.3\nNote\u2014As in Table 2 in most cases we present the median value of the 1D marginalized posterior distribution and the symmetric\n90% credible interval. For properties that have physical bounds we report the median value as well as the 90% highest posterior\ndensity (HPD) credible interval. Our results are reported at a reference frequency of 10 Hz.\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\n0.0\n0.2\n0.4\n0.6\n0.8\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\ncS1/(Gm2\n1)\ncS2/(Gm2\n2)\ntilt\n\u00d710\u22123\n0\n2\n4\n6\n8\nposterior probability per pixel\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\n0.0\n0.2\n0.4\n0.6\n0.8\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\ncS1/(Gm2\n1)\ncS2/(Gm2\n2)\ntilt\n\u00d710\u22123\n0\n2\n4\n6\n8\nposterior probability per pixel\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\n0.0\n0.2\n0.4\n0.6\n0.8\n0\u25e6\n30\u25e6\n60\u25e6\n90\u25e6\n120\u25e6\n150\u25e6\n180\u25e6\ncS1/(Gm2\n1)\ncS2/(Gm2\n2)\ntilt\n\u00d710\u22123\n0\n2\n4\n6\n8\nposterior probability per pixel\nFigure 9. Posterior probabilities for the dimensionless component spins, cS1/(Gm2\n1) and cS2/(Gm2\n1), relative to the orbital\nangular momentum axis \u02c6L. From left to right, we compare the posterior probabilities obtained when analysing LIGO Hanford\ndata only (blue), LIGO Livingston data only (green), and a coherent analysis of LIGO Hanford and LIGO Livingston data\n(purple). In all cases, we show the posterior distribution resulting from equally combining samples from five waveform models.\nThe tilt angles are 0\u25e6for spins aligned with the orbital angular momentum and 180\u25e6for spins anti-aligned. Probabilities are\nmarginalized over the azimuthal angles. The pixels have equal prior probability, being equally spaced in the spin magnitudes\nand the cosines of tilt angles. The spin orientations are defined at a fiducial GW frequency of 10 Hz.\n\n31\n5.0\n2.5\n0.0\n2.5\n5.0\nh(t) \u00d7 10 22\nMean posterior\n90% interval\ntstrain\npeak\ntpol\npeak\n5.0\n2.5\n0.0\n2.5\n5.0\nhmodes(t) \u00d7 10 22\n0.15\n0.10\n0.05\n0.00\n0.05\n0.10\n0.15\n0.20\nTime [s]\n2\n0\n2\nnoise\n0.1\n0.0\n0.1\n0.5\n0.0\n0.5\n0.1\n0.0\n0.1\n0.5\n0.0\n0.5\n[(2, 0)]\n[(2, 1), (2, -1)]\n[(2, 2), (2, -2)]\n[(3, 3), (3, -3)]\n[(4, 4), (4, -4)]\nFigure 10.\nTop panel: Posterior probability density functions of the NRSur waveform timeseries, obtained via Bilby using\nthe NRSur waveform model in the LIGO Hanford detector. The red band shows the uncertainty in the measurement of tpol\npeak,\nand the grey band shows the uncertainty in tstrain\npeak . Middle and bottom panel: Posterior probability density functions of the\nmode strain, F+h+ + F\u00d7h\u00d7, with h+ \u2212ih\u00d7 = \u22122Y\u2113,mh\u2113,m + \u22122Y\u2113,\u2212mh\u2113,\u2212m, shown for the LIGO Hanford detector. The top part\nreports the unwhitened waveform and the bottom part the whitened one, showcasing the impact of whitening in visualising the\nsignal morphology. The inset focuses on the (\u2113, \u00b1m) = (2, 0), (3, 3), (4, 4) modes. The red line indicates the median of tpol\npeak, and\nthe dashed-dotted black lines show the median of tmodes\npeak .\nC. SIGNAL PEAK TIME\nWe require the time of peak GW emission to determine a valid starting time for ringdown analyses. The peak\nGW power is emitted at time tmodes\npeak\n= maxt\nr\nP\n\u2113,m\n\f\f\f\u02d9h\u2113m(t)\n\f\f\f\n2\n, where h\u2113m(t) are the multipoles in a spin-weighted\nspherical-harmonic decomposition of the signal. Alternatively, we can estimate the peak time using the peak of the\npolarisation tpol\npeak = max\nt\n|h+ \u2212ih\u00d7|2. This quantity depends on the binary\u2019s relative orientation to the detector and\nwill be uncertain to within roughly one GW period, but it can be compared to an estimate computed through an\nunmodelled waveform reconstruction, allowing for a more agnostic analysis. One can also conservatively estimate the\nonset of ringdown directly from the maximum value of the strain tstrain\npeak , after which the signal displays a clear decay.\nFigure 10 shows these times for GW231123, on top of the unwhitened NRSur strain reconstruction from which they\nwere computed. From this reconstruction, we find tstrain\npeak is 1384782888.6191+0.0098\n\u22120.0322 s and 1384782888.6142+0.0107\n\u22120.0195 s in\nthe LIGO Hanford and Livingston detectors respectively. Instead, in the LIGO Hanford detector (chosen as reference\nfor the ringdown analysis), we find tmodes\npeak\n\u2212tpol\npeak \u22486 ms.\n\n32\nThe differences among these estimates, together with the time-domain reconstruction shown in Figure 10, attest to\nthe highly complex signal morphology and invite care when selecting a peak time definition to be used as reference\nin a ringdown analysis. Hence, in the main text we repeat the analysis over a wide range of times, and plot results\naround a conservative tstart \u2248tstrain\npeak + 15GM det\nf\n/c3 (assuming M det\nf\n\u2243298M\u2299), when we are confident on the validity\nof a QNM description.\nD. HIGHER-ORDER RADIATION MULTIPOLES\nGiven the support for large binary inclination from most IMR models, subdominant multipole moments (referred\nto as \u201cmodes\u201d below) beyond the dominant (\u2113, m) = (2, \u00b12) spherical-harmonic multipole moment are expected\nto contribute appreciably to the observed signal (Blanchet 2014). Here, we investigate in detail their contribution\nthroughout the signal. Using NRSur posterior samples, we estimate optimal SNR values of 2.27+1.45\n\u22121.05 for the (3, \u00b13)\nmode, 2.92+0.70\n\u22120.89 for the (4, \u00b14) mode, 0.68+3.29\n\u22120.48 for the (2, \u00b11) mode and 0.25+0.65\n\u22120.16 for the (2, 0) mode. Unlike the (3, 3)\nand (4, 4) modes, the inferred distribution for the (2, 1), (2, 0) modes are consistent with expectations from random\nGaussian noise fluctuations, implying a lack of statistically significant support for their presence in the data. Relevant\nto the ringdown analysis, the strain contribution from the (2, 0) mode remains significantly subdominant compared\nto the more prominent (3, \u00b13) and (4, \u00b14) modes throughout the signal duration, as illustrated in Figure 10 (showing\nLIGO Hanford, with similar conclusions obtained for LIGO Livingston). As seen in the bottom panel, the whitening\nprocess suppresses the lower-frequency content of the signal, causing the peak amplitude to appear quieter relative to\nthe higher-frequency ringdown. This filtering effect also reduces the visibility of subdominant modes such as (2, \u00b11)\nand (2, 0), which fall largely outside the detector\u2019s sensitive band. In contrast, the (3, \u00b13) and (4, \u00b14) modes remain\nvisible post-merger due to their higher frequency content, making them detectable. This result is consistent with\nthe SNR estimates above. The IMR modes are defined with respect to the binary\u2019s total angular momentum at a\ngiven reference time during the inspiral, while the ringdown modes are defined with respect to the remnant spin at\nasymptotically late times. The direction between these two vectors may be offset by a few degrees (Hamilton et al.\n2021), but we do not expect that would be sufficient to increase the power in (2, 1) or (2, 0) to a level measurable in\nGaussian noise, i.e., above an SNR of \u223c2.1.\nIn summary, we conclude that a significant excitation of the (2, 0, 0) or (2, 1, 0) ringdown modes, suggested by the\noverlap of damped sinusoids fitting parameters with the remnant properties inferred by NRSur, is in tension with\nNRSur multipole moments content.\n\n33\nREFERENCES\nAasi, J., et al. 2015, Class. Quant. Grav., 32, 074001\nAbac, A. G., et al. 2025a, in preparation\n\u2014. 2025b, arXiv:2508.18081\nAbbott, B. P., et al. 2016a, Phys. Rev. Lett., 116, 241102\n\u2014. 2016b, Astrophys. J. 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Dasgupta,94 V. Dattilo\n,63 A. Daumas,20 N. Davari,171, 172 I. Dave,104 A. Davenport,138 M. Davier,41\nT. F. Davies,73 D. Davis\n,11 L. Davis,73 M. C. Davis\n,18 P. Davis\n,173, 174 E. J. Daw\n,175 M. Dax\n,1\nJ. De Bolle\n,95 M. Deenadayalan,80 J. Degallaix\n,176 M. De Laurentis\n,32, 4 F. De Lillo\n,23 S. Della Torre\n,129\nW. Del Pozzo\n,82, 81 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,177, 62 F. De Matteis\n,21, 22 N. Demos,35\nT. Dent\n,178 A. Depasse\n,15 N. DePergola,103 R. De Pietri\n,179, 180 R. De Rosa\n,32, 4 C. De Rossi\n,63\nM. Desai\n,35 R. DeSalvo\n,181 A. DeSimone,182 R. De Simone,151, 133 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,165\nM. Di Cesare\n,32, 4 G. Dideron,183 T. Dietrich\n,1 L. Di Fiore,4 C. Di Fronzo\n,73 M. Di Giovanni\n,39, 38\nT. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 184 S. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,185, 48\nF. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,119 J. P. Docherty,87 Z. Doctor\n,97 N. Doerksen,169\nE. Dohmen,2 A. Doke,134 A. Domiciano De Souza,186 L. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33\nT. Dooney,72 S. Doravari\n,80 O. Dorosh,187 W. J. D. Doyle,124 M. Drago\n,39, 38 J. C. Driggers\n,2\nL. Dunn\n,125 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,171, 156 P. Dutta Roy,46 H. Duval\n,188\nS. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,189, 31 T. Eckhardt\n,98 G. Eddolls\n,79 A. Effler\n,64 J. Eichholz\n,34\nH. Einsle,114 M. Eisenmann,25 M. Emma\n,59 K. Endo,152 R. Enficiaud\n,1 L. Errico\n,32, 4 R. Espinosa,165\nM. C. Espitia,190 M. Esposito\n,4, 32 R. C. Essick\n,191 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,183\nB. E. Ewing,7 J. M. Ezquiaga\n,141 F. Fabrizi\n,61, 62 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,131\nB. Farr\n,78 W. M. Farr\n,192, 193 G. Favaro\n,92 M. Favata\n,194 M. Fays\n,166 M. Fazio\n,55 J. Feicht,11\nM. M. Fejer,90 R. Felicetti\n,185, 48 E. Fenyvesi\n,88, 195 J. Fernandes,196 T. Fernandes\n,197, 139 D. Fernando,111\nS. Ferraiuolo\n,198, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,82, 81 P. Figura\n,96 A. Fiori\n,81, 82 I. Fiori\n,63\nM. Fishbach\n,191 R. P. Fisher,124 R. Fittipaldi\n,199, 133 V. Fiumara\n,200, 133 R. Flaminio,31 S. M. Fleischer\n,201\nL. S. Fleming,202 E. Floden,18 H. Fong,115 J. A. Font\n,139, 140 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal\n,203\nK. Franceschetti,179 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,81 J. P. Freed,66 Z. Frei\n,204 A. Freise\n,37, 108\nO. Freitas\n,197, 139 R. Frey\n,78 W. Frischhertz,64 P. Fritschel,35 V. V. Frolov,64 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,205 T. Fujimori,206 P. Fulda,46 M. Fyffe,64 B. Gadre\n,72 J. R. Gair\n,1\nS. Galaudage\n,186 V. Galdi,207 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,181 D. Ganapathy\n,208 A. Ganguly\n,80\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,209 C. Garc\u00b4\u0131a-Quir\u00b4os\n,189 J. W. Gardner\n,34 K. A. Gardner,115 S. Garg,42\nJ. Gargiulo\n,63 X. Garrido\n,41 A. Garron\n,99 F. Garufi\n,32, 4 P. A. Garver,90 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,210 V. Gayathri\n,10 T. Gayer,79 G. Gemme\n,29 A. Gennai\n,81 V. Gennari\n,101\nJ. George,104 R. George\n,121 O. Gerberding\n,98 L. Gergely\n,154 Archisman Ghosh\n,95 Sayantan Ghosh,196\nShaon Ghosh\n,194 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,211 Tathagata Ghosh\n,80 J. A. Giaime\n,12, 64\nK. D. Giardina,64 D. R. Gibson,202 C. Gier\n,55 S. Gkaitatzis\n,82, 81 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,78\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,115 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,212 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,63\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,77, 51 V. Graham\n,87 A. E. Granados\n,18\nM. Granata\n,176 V. Granata\n,213, 133 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,87 G. Greco,51\nA. C. Green\n,37, 108 L. Green,214 S. M. Green,74 S. R. Green\n,215 C. Greenberg,134 A. M. Gretarsson,66\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,77, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,139 D. Guetta\n,216 G. M. Guidi\n,61, 62 A. R. Guimaraes,12 H. K. Gulati,94 F. Gulminelli\n,173, 174\nH. Guo\n,146 W. Guo\n,73 Y. Guo\n,37, 36 Anuradha Gupta\n,217 I. Gupta\n,7 N. C. Gupta,94 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,98 N. Gutierrez,176 N. Guttman,6 F. Guzman\n,132 D. Haba,218 M. Haberland\n,1\nS. Haino,219 E. D. Hall\n,35 E. Z. Hamilton\n,99 G. Hammond\n,87 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,220 A. G. Hanselman\n,131 H. Hansen,2 J. Hanson,64 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,182 S. Harikumar\n,187 K. Haris,37, 72 I. Harley-Trochimczyk,132 T. Harmark\n,135\nJ. Harms\n,44, 45 G. M. Harry\n,221 I. W. Harry\n,74 J. Hart,105 B. Haskell,96, 222, 223 C. J. Haster\n,214\nK. Haughian\n,87 H. Hayakawa,50 K. Hayama,224 M. C. Heintze,64 J. Heinze\n,119 J. Heinzel,35 H. Heitmann\n,114\nF. Hellman\n,208 A. F. Helmling-Cornell\n,78 G. Hemming\n,63 O. Henderson-Sapir\n,116 M. Hendry\n,87\nI. S. Heng,87 M. H. Hennig\n,87 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,225, 226 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,87 Y. Himemoto\n,227 N. Hirata,25 C. Hirose,228\n\n3\nD. Hofman,176 B. E. Hogan,66 N. A. Holland,37, 108 I. J. Hollows\n,175 D. E. Holz\n,131 L. Honet,112\nD. J. Horton-Bailey,208 J. Hough\n,87 S. Hourihane\n,11 N. T. Howard,145 E. J. Howell\n,73 C. G. Hoy\n,74\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,143 H.-Y. Hsieh,143 C. Hsiung,229 S.-H. Hsu,147 W.-F. Hsu\n,110\nQ. Hu\n,87 H. Y. Huang\n,142 Y. Huang\n,7 Y. T. Huang,79 A. D. Huddart,230 B. Hughey,66 V. Hui\n,31\nS. Husa\n,99 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,133 J. Iascau,78\nK. Ide,231 R. Iden,218 A. Ierardi,44, 45 S. Ikeda,148 H. Imafuku,42 Y. Inoue,142 G. Iorio\n,92 P. Iosif\n,185, 48\nM. H. Iqbal,34 J. Irwin\n,87 R. Ishikawa,231 M. Isi\n,192, 193 T. Islam,134 K. S. Isleif\n,232 Y. Itoh\n,206, 233\nM. Iwaya,205 B. R. Iyer\n,24 C. Jacquet,101 P.-E. Jacquet\n,123 T. Jacquot,41 S. J. Jadhav,234 S. P. Jadhav\n,155\nM. Jain,134 T. Jain,225 A. L. James\n,11 K. Jani\n,145 J. Janquart\n,15 N. N. Janthalur,234 S. Jaraba\n,235\nP. Jaranowski\n,236 R. Jaume\n,99 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,150 H.-B. Jin\n,237, 238\nG. R. Johns,124 N. A. Johnson,46 M. C. Johnston\n,214 R. Johnston,87 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,211\nR. Jones,87 H. E. Jose,78 P. Joshi\n,7 S. K. Joshi,80 G. Joubert,56 J. Ju,239 L. Ju\n,73 K. Jung\n,240 J. Junker\n,34\nV. Juste,112 H. B. Kabagoz\n,64, 35 T. Kajita\n,241 I. Kaku,206 V. Kalogera\n,97 M. Kalomenopoulos\n,214\nM. Kamiizumi\n,50 N. Kanda\n,233, 206 S. Kandhasamy\n,80 G. Kang\n,242 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,80 D. P. Kapasi\n,54 M. Karthikeyan,134 M. Kasprzack\n,11 H. Kato,152\nT. Kato,205 E. Katsavounidis,35 W. Katzman,64 R. Kaushik\n,104 K. Kawabe,2 R. Kawamoto,206 D. Keitel\n,99\nL. J. Kemperman\n,116 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,80 J. S. Key\n,243 R. Khadela,8, 9\nS. Khadka,90 S. S. Khadkikar,7 F. Y. Khalili\n,109 F. Khan\n,8, 9 T. Khanam,163 M. Khursheed,104\nN. M. Khusid,192, 193 W. Kiendrebeogo\n,114, 244 N. Kijbunchoo\n,116 C. Kim,245 J. C. Kim,246 K. Kim\n,247\nM. H. Kim\n,239 S. Kim\n,248 Y.-M. Kim\n,247 C. Kimball\n,97 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,115 E. J. Knox,78 N. Knust\n,8, 9 K. Kobayashi,205 S. M. Koehlenbeck\n,90\nG. Koekoek,37, 36 K. Kohri\n,249, 250 K. Kokeyama\n,33, 251 S. Koley\n,44, 166 P. Kolitsidou\n,119 A. E. Koloniari\n,252\nK. Komori\n,42 A. K. H. Kong\n,143 A. Kontos\n,253 L. M. Koponen,119 M. Korobko\n,98 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,68 M. Kovalam,73 T. Koyama,152 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,119 S. Kroker,254 A. Kr\u00b4olak\n,255, 187 K. Kruska,8, 9 J. Kubisz\n,256 G. Kuehn,8, 9\nS. Kulkarni\n,217 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,234 Praveen Kumar\n,178\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,94 J. Kume\n,257, 258, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,209, 259 S. Kuwahara\n,42 K. Kwak\n,240 K. Kwan,34 S. Kwon\n,42 G. Lacaille,87 D. Laghi\n,189, 101\nA. H. Laity,164 E. Lalande,260 M. Lalleman\n,23 P. C. Lalremruati,261 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,121 R. Langgin\n,214 B. Lantz\n,90 I. La Rosa\n,99 J. Larsen,201 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,165 M. Laxen\n,64 C. Lazarte\n,139 A. Lazzarini\n,11 C. Lazzaro,157, 156 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,115 H. M. Lee\n,262 H. W. Lee\n,263 J. Lee,79 K. Lee\n,239 R.-K. Lee\n,143 R. Lee,35\nSungho Lee\n,247 Sunjae Lee,239 Y. Lee,142 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,183 M. Le Jean\n,176, 117\nA. Lema\u02c6\u0131tre\n,264 M. Lenti\n,62, 177 M. Leonardi\n,75, 76, 265 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,74 A. K. Y. Li,11 K. L. Li\n,266 T. G. F. Li,110 X. Li\n,149\nY. Li,97 Z. Li,87 A. Lihos,124 E. T. Lin\n,143 F. Lin,142 L. C.-C. Lin\n,266 Y.-C. Lin\n,143 C. Lindsay,202\nS. D. Linker,181 A. Liu\n,220 G. C. Liu\n,229 Jian Liu\n,73 F. Llamas Villarreal,165 J. Llobera-Querol\n,99\nR. K. L. Lo\n,141 J.-P. Locquet,110 S. C. G. Loggins,267 M. R. Loizou,134 L. T. London,68 A. Longo\n,61, 62\nD. Lopez\n,166 M. Lopez Portilla,72 M. Lorenzini\n,21, 22 A. Lorenzo-Medina\n,178 V. Loriette,41 M. Lormand,64\nG. Losurdo\n,268, 81 E. Lotti,134 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,111 N. Low,125\nN. Lu\n,34 L. Lucchesi\n,81 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,269, 270 A. W. Lussier\n,260 R. Macas\n,74\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,152 S. Maenaut\n,110\nS. S. Magare,80 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 108 M. Magnozzi\n,29, 30 M. Mahesh,98 M. Maini,164\nS. Majhi,80 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,106 J. A. Malaquias-Reis,19 U. Mali\n,191\nS. Maliakal,11 A. Malik,104 L. Mallick\n,169, 191 A.-K. Malz\n,59 N. Man,114 M. Mancarella\n,100 V. Mandic\n,18\nV. Mangano\n,171, 156 B. Mannix,78 G. L. Mansell\n,79 M. Manske\n,10 M. Mantovani\n,63 M. Mapelli\n,92, 93, 271\nC. Marinelli\n,102 F. Marion\n,31 A. S. Markosyan,90 A. Markowitz,11 E. Maros,11 S. Marsat\n,101 F. Martelli\n,61, 62\nI. W. Martin\n,87 R. M. Martin\n,194 B. B. Martinez,132 D. A. Martinez,54 M. Martinez,43, 272 V. Martinez\n,130\nA. Martini,75, 76 J. C. Martins\n,19 D. V. Martynov,119 E. J. Marx,35 L. Massaro,36, 37 A. Masserot,31\nM. Masso-Reid\n,87 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,210\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,64 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,64\nL. McCuller\n,11 S. McEachin,124 C. McElhenny,124 G. I. McGhee\n,87 J. McGinn,87 K. B. M. McGowan,145\nJ. McIver\n,115 A. McLeod\n,73 I. McMahon\n,189 T. McRae,34 R. McTeague,87 D. Meacher\n,10 B. N. Meagher,79\n\n4\nR. Mechum,111 Q. Meijer,72 A. Melatos,125 C. S. Menoni\n,138 F. Mera,2 R. A. Mercer\n,10 L. Mereni,176\nK. Merfeld,163 E. L. Merilh,64 J. R. M\u00b4erou\n,99 J. D. Merritt,78 M. Merzougui,114 C. Messick\n,10 B. Mestichelli,44\nM. Meyer-Conde\n,273 F. Meylahn\n,8, 9 A. Mhaske,80 A. Miani\n,75, 76 H. Miao,274 C. Michel\n,176\nY. Michimura\n,42 H. Middleton\n,119 D. P. Mihaylov\n,105, 72 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,185, 48\nV. Milotti\n,92 Y. Minenkov,22 E. M. Minihan,66 Ll. M. Mir\n,43 L. Mirasola\n,156, 157 M. Miravet-Ten\u00b4es\n,139\nC.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,107 T. Mishra\n,46 A. L. Mitchell,37, 108 J. G. Mitchell,66 S. Mitra\n,80\nV. P. Mitrofanov\n,109 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,66 G. Mo\n,35\nL. Mobilia\n,61, 62 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,208 M. Mondin,181 J. K. Monsalve,190\nM. Montani,61, 62 C. J. Moore,225 D. Moraru,2 A. More\n,80 S. More\n,80 C. Moreno\n,136 E. A. Moreno\n,35\nG. Moreno,2 A. Moreso Serra,83 S. Morisaki\n,42, 205 Y. Moriwaki\n,152 G. Morras\n,209 A. Moscatello\n,92\nM. Mould\n,35 B. Mours\n,65 C. M. Mow-Lowry\n,37, 108 L. Muccillo\n,177, 62 F. Muciaccia\n,39, 38 D. Mukherjee\n,119\nSamanwaya Mukherjee,24 Soma Mukherjee,165 Subroto Mukherjee,94 Suvodip Mukherjee\n,13 N. Mukund\n,35\nA. Mullavey,64 H. Mullock,115 J. Mundi,221 C. L. Mungioli,73 M. Murakoshi,231 P. G. Murray\n,87 D. Nabari\n,75, 76\nS. L. Nadji,8, 9 A. Nagar,28, 275 N. Nagarajan\n,87 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,276 M. Nakano,11\nD. Nanadoumgar-Lacroze\n,43 D. Nandi,12 V. Napolano,63 P. Narayan\n,217 I. Nardecchia\n,22 T. Narikawa,205\nH. Narola,72 L. Naticchioni\n,38 R. K. Nayak\n,261 L. Negri,72 A. Nela,87 C. Nelle,78 A. Nelson\n,132\nT. J. N. Nelson,64 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen Quynh\n,277 S. A. Nichols,12 A. B. Nielsen\n,278\nY. Nishino,25, 42 A. Nishizawa\n,279 S. Nissanke,280, 37 W. Niu\n,7 F. Nocera,63 J. Noller,281 M. Norman,33\nC. North,33 J. Novak\n,117, 235, 282 R. Nowicki\n,145 J. F. Nu\u02dcno Siles\n,209 L. K. Nuttall\n,74 K. Obayashi,231\nJ. Oberling\n,2 J. O\u2019Dell,230 E. Oelker\n,35 M. Oertel\n,235, 117, 283, 282 G. Oganesyan,44, 45 T. O\u2019Hanlon,64\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,117, 283, 282 R. Omer,18 B. O\u2019Neal,124 M. Onishi,152 K. Oohara\n,284\nB. O\u2019Reilly\n,64 M. Orselli\n,51, 77 R. O\u2019Shaughnessy\n,111 S. O\u2019Shea,87 S. Oshino\n,50 C. Osthelder,11\nI. Ota\n,12 D. J. Ottaway\n,116 A. Ouzriat,56 H. Overmier,64 B. J. Owen\n,285 R. Ozaki,231 A. E. Pace\n,7\nR. Pagano\n,12 M. A. Page\n,25 A. Pai\n,196 L. Paiella,44 A. Pal,286 S. Pal\n,261 M. A. Palaia\n,81, 82 M. P\u00b4alfi,204\nP. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,143 J. Pan,73 K. C. Pan\n,143 P. K. Panda,234\nShiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 72 F. Pannarale\n,39, 38 K. A. Pannone,54 B. C. Pant,104\nF. H. Panther,73 M. Panzeri,61, 62 F. Paoletti\n,81 A. Paolone\n,38, 287 A. Papadopoulos\n,87 E. E. Papalexakis,212\nL. Papalini\n,81, 82 G. Papigkiotis\n,252 A. Paquis,41 A. Parisi\n,77, 51 B.-J. Park,247 J. Park\n,288 W. Parker\n,64\nG. Pascale,8, 9 D. Pascucci\n,95 A. Pasqualetti\n,63 R. Passaquieti\n,82, 81 L. Passenger,6 D. Passuello,81\nO. Patane\n,2 A. V. Patel\n,142 D. Pathak,80 A. Patra,33 B. Patricelli\n,82, 81 B. G. Patterson,33 K. Paul\n,107\nS. Paul\n,78 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna Arellano\n,289 X. Peng,119\nY. Peng,57 S. Penn\n,290 M. D. Penuliar,54 A. Perego\n,75, 76 Z. Pereira,134 C. P\u00b4erigois\n,291, 93, 92 G. Perna\n,92\nA. Perreca\n,75, 76, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 108 D. Pesios,252 S. Peters,166 S. Petracca,207\nC. Petrillo,77 H. P. Pfeiffer\n,1 H. Pham,64 K. A. Pham\n,18 K. S. Phukon\n,119 H. Phurailatpam,220\nM. Piarulli,101 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,114 M. Piendibene\n,82, 81 F. Piergiovanni\n,61, 62\nL. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,292, 133 M. Pietrzak,96 M. Pillas\n,166 F. Pilo\n,81 L. Pinard\n,176\nI. M. Pinto\n,292, 133, 293, 32 M. Pinto\n,63 B. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,225, 87 A. Placidi\n,51\nE. Placidi\n,39, 38 M. L. Planas\n,99 W. Plastino\n,213, 22 C. Plunkett\n,35 R. Poggiani\n,82, 81 E. Polini,35\nJ. Pomper,81, 82 L. Pompili\n,1 J. Poon,220 E. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,63\nJ. Powell\n,155 G. S. Prabhu,80 M. Pracchia\n,166 B. K. Pradhan\n,80 T. Pradier\n,65 A. K. Prajapati,94\nK. Prasai\n,294 R. Prasanna,234 P. Prasia,80 G. Pratten\n,119 G. Principe\n,185, 48 G. A. Prodi\n,75, 76\nP. Prosperi,81 P. Prosposito,21, 22 A. C. Providence,66 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,164\nH. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,174, 117 V. Quetschke,165 L. H. Quiceno,190 P. J. Quinonez,66\nN. Qutob,57 F. J. Raab\n,2 R. Rading,232 I. Rainho,139 S. Raja,104 C. Rajan,104 B. Rajbhandari\n,111\nK. E. Ramirez\n,64 F. A. Ramis Vidal\n,99 M. Ramos Arevalo\n,165 A. Ramos-Buades\n,99, 37 S. Ranjan\n,57\nK. Ransom,64 P. Rapagnani\n,39, 38 B. Ratto,66 A. Ravichandran,134 A. Ray\n,97 V. Raymond\n,33\nM. Razzano\n,82, 81 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini,11\nA. Renzini\n,128 B. Revenu\n,295, 41 A. Revilla Pe\u02dcna,83 R. Reyes,181 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,82, 81 J. Rice,79 J. W. Richardson\n,212 M. L. Richardson,116 A. Rijal,66 K. Riles\n,91 H. K. Riley,33\nS. Rinaldi\n,271 J. Rittmeyer,98 C. Robertson,230 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,190 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,225 J. H. Romie,64\nS. Ronchini\n,7 T. J. Roocke\n,116 L. Rosa,4, 32 T. J. Rosauer,212 C. A. Rose,57 D. Rosi\u00b4nska\n,126 M. P. Ross\n,53\nM. Rossello-Sastre\n,99 S. Rowan\n,87 S. K. Roy\n,192, 193 S. Roy\n,15 D. Rozza\n,128, 129 P. Ruggi,63 N. Ruhama,240\n\n5\nE. Ruiz Morales\n,296, 209 K. Ruiz-Rocha,145 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 108 S. Safi-Harb\n,169\nM. R. Sah\n,13 S. Saha\n,143 T. Sainrat\n,65 S. Sajith Menon\n,216, 39, 38 K. Sakai,297 Y. Sakai\n,273\nM. Sakellariadou\n,68 S. Sakon\n,7 O. S. Salafia\n,159, 129, 128 F. Salces-Carcoba\n,11 L. Salconi,63 M. Saleem\n,121\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,80 S. Salvador\n,174, 173 A. Salvarese,121 A. Samajdar\n,72, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,139 J. R. Sanders,182 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,80 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,252 P. Sassi\n,51, 77\nB. Sassolas\n,176 B. S. Sathyaprakash\n,7, 33 R. Sato,228 S. Sato,152 Yukino Sato,152 Yu Sato,152 O. Sauter\n,46\nR. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,80 S. Sayah,176 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,149\nA. Schiebelbein,191 M. G. Schiworski\n,79 P. Schmidt\n,119 S. Schmidt\n,72 R. Schnabel\n,98 M. Schneewind,8, 9\nR. M. S. Schofield,78 K. Schouteden\n,110 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,298 M. Scialpi\n,299\nJ. Scott\n,87 S. M. Scott\n,34 R. M. Sedas\n,64 T. C. Seetharamu,87 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,300\nD. Sellers,64 N. Sembo,206 A. S. Sengupta\n,301 E. G. Seo\n,87 J. W. Seo\n,110 V. Sequino,32, 4 M. Serra\n,38\nA. Sevrin,188 T. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,262 L. Shao\n,302 A. K. Sharma\n,99 Preeti Sharma,12\nPrianka Sharma,104 Ritwik Sharma,18 S. Sharma Chaudhary,106 P. Shawhan\n,127 N. S. Shcheblanov\n,303, 264\nE. Sheridan,145 Z.-H. Shi,143 M. Shikauchi,42 R. Shimomura,304 H. Shinkai\n,304 S. Shirke,80 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,121 R. W. Short,2 S. ShyamSundar,104 A. Sider,158 H. Siegel\n,192, 193 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 170 M. Simmonds,116 L. P. Singer\n,305 Amitesh Singh,217 Anika Singh,11\nD. Singh\n,208 N. Singh\n,99 S. Singh,218, 60 A. M. Sintes\n,99 V. Sipala,171, 156 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,201 T. J. Slaven-Blair,73 J. Smetana,119 J. R. Smith\n,54 L. Smith\n,87, 185, 48 R. J. E. Smith\n,6\nW. J. Smith\n,145 S. Soares de Albuquerque Filho,61 M. Soares-Santos,189 K. Somiya\n,218 I. Song\n,143 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,306 F. Spada\n,81 V. Spagnuolo\n,37 A. P. Spencer\n,87 P. Spinicelli\n,63\nA. K. Srivastava,94 F. Stachurski\n,87 C. J. Stark,124 D. A. Steer\n,307 N. Steinle\n,169 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,252 P. Stevens,41 M. StPierre,164 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,103, \u2217M. Suchenek,96 S. Sudhagar\n,96 Y. Sudo,231 N. Sueltmann,98 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,242 L. Sun\n,34 S. Sunil,94 J. Suresh\n,114 B. J. Sutton,68 P. J. Sutton\n,33 K. Suzuki,218 M. Suzuki,205\nB. L. Swinkels\n,37 A. Syx\n,117 M. J. Szczepa\u00b4nczyk\n,308 P. Szewczyk\n,126 M. Tacca\n,37 H. Tagoshi\n,205\nK. Takada,205 H. Takahashi\n,273 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,309 H. Takeda\n,310, 311\nK. Takeshita,218 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,79 C. Talbot,131 M. Tamaki,205 N. Tamanini\n,101\nD. Tanabe,142 K. Tanaka,50 S. J. Tanaka\n,231 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,212\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,312 J. D. Tasson\n,153 J. G. Tau\n,111\nD. Tellez,54 R. Tenorio\n,99 H. Themann,181 A. Theodoropoulos\n,139 M. P. Thirugnanasambandam,80\nL. M. Thomas\n,11 M. Thomas,64 P. Thomas,2 J. E. Thompson\n,211 S. R. Thondapu,104 K. A. Thorne,64\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,80 Pawan Tiwari,44 Praveer Tiwari,196 S. Tiwari\n,189 V. Tiwari\n,119\nM. R. Todd,79 M. Toffano,92 A. M. Toivonen\n,18 K. Toland\n,87 A. E. Tolley\n,74 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,142 A. Torres-Forn\u00b4e\n,139, 140 C. I. Torrie,11 I. Tosta e Melo\n,313\nE. Tournefier\n,31 M. Trad Nery,114 K. Tran,124 A. Trapananti\n,52, 51 R. Travaglini\n,168 F. Travasso\n,52, 51\nG. Traylor,64 M. Trevor,127 M. C. Tringali\n,63 A. Tripathee\n,91 G. Troian\n,185, 48 A. Trovato\n,185, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,314 L. Tsukada\n,214 K. Turbang\n,188, 23 M. Turconi\n,114 C. Turski,95\nH. Ubach\n,83, 84 N. Uchikata\n,205 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,315 K. Ueno\n,42 V. Undheim\n,278\nL. E. Uronen,220 T. Ushiba\n,50 M. Vacatello\n,81, 82 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,99 M. Valentini\n,108, 37 S. A. Vallejo-Pe\u02dcna\n,190 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 316\nE. Van den Bossche\n,188 J. F. J. van den Brand\n,36, 108, 37 C. Van Den Broeck,72, 37 M. van der Sluys\n,37, 72\nA. Van de Walle,41 J. van Dongen\n,37, 108 K. Vandra,103 M. VanDyke,120 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 108 P. Van Hove\n,65 J. Vanier,260 M. VanKeuren,105 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,125 V. Varma\n,134 A. N. Vazquez,90 A. Vecchio\n,119 G. Vedovato,93 J. Veitch\n,87\nP. J. Veitch\n,116 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,134\nY. Verma\n,104 S. M. Vermeulen\n,11 F. Vetrano,61 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,61, 62 S. Vidyant,79 A. D. Viets\n,89\nA. Vijaykumar\n,191 A. Vilkha,111 N. Villanueva Espinosa,139 V. Villa-Ortega\n,178 E. T. Vincent\n,57\nJ.-Y. Vinet,114 S. Viret,56 S. Vitale\n,35 H. Vocca\n,77, 51 D. Voigt\n,98 E. R. G. von Reis,2 J. S. A. von Wrangel,8, 9\nW. E. Vossius,232 L. Vujeva\n,141 S. P. Vyatchanin\n,109 J. Wack,11 L. E. Wade,105 M. Wade\n,105 K. J. Wagner\n,111\nL. Wallace,11 E. J. Wang,90 H. Wang\n,218 J. Z. Wang,91 W. H. Wang,165 Y. F. Wang\n,1 G. Waratkar\n,196\nJ. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42 B. Weaver,2 S. A. Webster,87\nN. L. Weickhardt\n,98 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,73 K. Wette\n,34 J. T. Whelan\n,111\n\n6\nB. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,74 D. Wilken\n,8, 9, 9 A. T. Wilkin,212 B. M. Williams,120\nD. Williams\n,87 M. J. Williams\n,74 N. S. Williams\n,1 J. L. Willis\n,11 B. Willke\n,9, 8, 9 M. Wils\n,110 L. Wilson,105\nC. W. Winborn,106 J. Winterflood,73 C. C. Wipf,11 G. Woan\n,87 J. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,142\nI. C. F. Wong\n,220, 110 K. Wong,191 T. Wouters,72, 37 J. L. Wright,2 M. Wright\n,87, 72 B. Wu,79 C. Wu\n,143\nD. S. Wu\n,8, 9 H. Wu\n,143 K. Wu,120 Q. Wu,53 Y. Wu,97 Z. Wu\n,101 E. Wuchner,54 D. M. Wysocki\n,10\nV. A. Xu\n,208 Y. Xu\n,99 N. Yadav\n,28 H. Yamamoto\n,11 K. Yamamoto\n,152 T. S. Yamamoto\n,42\nT. Yamamoto\n,50 R. Yamazaki\n,231 T. Yan,119 K. Z. Yang\n,18 Y. Yang\n,147 Z. Yarbrough\n,12 J. Yebana,99\nS.-W. Yeh,143 A. B. Yelikar\n,145 X. Yin,35 J. Yokoyama\n,317, 42 T. Yokozawa,50 S. Yuan,73 H. Yuzurihara\n,50\nM. Zanolin,66 M. Zeeshan\n,111 T. Zelenova,63 J.-P. Zendri,93 M. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,97 L. Zhang,11\nN. Zhang,57 R. Zhang\n,150 T. Zhang,119 C. Zhao\n,73 Yue Zhao,162 Yuhang Zhao,20 Z.-C. Zhao\n,318 Y. Zheng\n,106\nH. Zhong\n,18 H. Zhou,79 H. O. Zhu,73 Z.-H. Zhu\n,318, 319 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n\n7\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Chennai Mathematical Institute, Chennai 603103, India\n59Royal Holloway, University of London, London TW20 0EX, United Kingdom\n60Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n61Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n62INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n63European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n64LIGO Livingston Observatory, Livingston, LA 70754, USA\n65Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n66Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n67Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n68King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n69Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n70International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n71Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n72Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n73OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n74University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n75Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n76INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n77Universit`a di Perugia, I-06123 Perugia, Italy\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n81INFN, Sezione di Pisa, I-56127 Pisa, Italy\n82Universit`a di Pisa, I-56127 Pisa, Italy\n83Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n84Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n85Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n86Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n87IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n88HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n89Concordia University Wisconsin, Mequon, WI 53097, USA\n90Stanford University, Stanford, CA 94305, USA\n91University of Michigan, Ann Arbor, MI 48109, USA\n92Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n93INFN, Sezione di Padova, I-35131 Padova, Italy\n94Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n95Universiteit Gent, B-9000 Gent, Belgium\n96Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n97Northwestern University, Evanston, IL 60208, USA\n98Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n99IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n100Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n101Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n\n8\n102Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n103Villanova University, Villanova, PA 19085, USA\n104RRCAT, Indore, Madhya Pradesh 452013, India\n105Kenyon College, Gambier, OH 43022, USA\n106Missouri University of Science and Technology, Rolla, MO 65409, USA\n107Indian Institute of Technology Madras, Chennai 600036, India\n108Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n109Lomonosov Moscow State University, Moscow 119991, Russia\n110Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n111Rochester Institute of Technology, Rochester, NY 14623, USA\n112Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n113Bar-Ilan University, Ramat Gan, 5290002, Israel\n114Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n115University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n116OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n117Centre national de la recherche scientifique, 75016 Paris, France\n118Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n119University of Birmingham, Birmingham B15 2TT, United Kingdom\n120Washington State University, Pullman, WA 99164, USA\n121University of Texas, Austin, TX 78712, USA\n122Cornell University, Ithaca, NY 14850, USA\n123Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n124Christopher Newport University, Newport News, VA 23606, USA\n125OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n126Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n127University of Maryland, College Park, MD 20742, USA\n128Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n129INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n130Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n131University of Chicago, Chicago, IL 60637, USA\n132University of Arizona, Tucson, AZ 85721, USA\n133INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n136Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n137Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n138Colorado State University, Fort Collins, CO 80523, USA\n139Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n140Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n141Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n142National Central University, Taoyuan City 320317, Taiwan\n143National Tsing Hua University, Hsinchu City 30013, Taiwan\n144OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n145Vanderbilt University, Nashville, TN 37235, USA\n146University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n147Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n148Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Northeastern University, Boston, MA 02115, USA\n151Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n153Carleton College, Northfield, MN 55057, USA\n154University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n157Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n158Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n159INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n\n9\n160Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n161Montana State University, Bozeman, MT 59717, USA\n162The University of Utah, Salt Lake City, UT 84112, USA\n163Johns Hopkins University, Baltimore, MD 21218, USA\n164University of Rhode Island, Kingston, RI 02881, USA\n165The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n166Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n167DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n168Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n169University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n170INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n171Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n172INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n173Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n174Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n175The University of Sheffield, Sheffield S10 2TN, United Kingdom\n176Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n177Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n178IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n179Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n180INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n181California State University, Los Angeles, Los Angeles, CA 90032, USA\n182Marquette University, Milwaukee, WI 53233, USA\n183Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n184Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n185Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n186Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n187National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n188Vrije Universiteit Brussel, 1050 Brussel, Belgium\n189University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n190Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n191Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n192Stony Brook University, Stony Brook, NY 11794, USA\n193Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n194Montclair State University, Montclair, NJ 07043, USA\n195HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n196Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n197Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n198Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n199CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n200Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n201Western Washington University, Bellingham, WA 98225, USA\n202SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n203Barry University, Miami Shores, FL 33168, USA\n204E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n205Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n206Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n207University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n208University of California, Berkeley, CA 94720, USA\n209Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n210Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212University of California, Riverside, Riverside, CA 92521, USA\n213Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n\n10\n214University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n215University of Nottingham NG7 2RD, UK\n216Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n217The University of Mississippi, University, MS 38677, USA\n218Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n219Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n220The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n221American University, Washington, DC 20016, USA\n222Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n223INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n224Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n225University of Cambridge, Cambridge CB2 1TN, United Kingdom\n226University of Lancaster, Lancaster LA1 4YW, United Kingdom\n227College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n228Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n229Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n230Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n231Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n232Helmut Schmidt University, D-22043 Hamburg, Germany\n233Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n236Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n237National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n238School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n241Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n242Chung-Ang University, Seoul 06974, Republic of Korea\n243University of Washington Bothell, Bothell, WA 98011, USA\n244Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n245Ewha Womans University, Seoul 03760, Republic of Korea\n246National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n247Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n248Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n249Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n250Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n251Nagoya University, Nagoya, 464-8601, Japan\n252Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n253Bard College, Annandale-On-Hudson, NY 12504, USA\n254Technical University of Braunschweig, D-38106 Braunschweig, Germany\n255Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n256Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n257Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n258Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n259Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n260Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n\n11\n261Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n262Seoul National University, Seoul 08826, Republic of Korea\n263Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n264NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n265Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n266Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n270Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n278University of Stavanger, 4021 Stavanger, Norway\n279Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n280GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n281University College London, London WC1E 6BT, United Kingdom\n282Observatoire de Paris, 75014 Paris, France\n283Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n284Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n289Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n290Hobart and William Smith Colleges, Geneva, NY 14456, USA\n291INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n292Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Kennesaw State University, Kennesaw, GA 30144, USA\n295Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n296Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n297Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n298Trinity College, Hartford, CT 06106, USA\n299Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n300Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n301Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n302Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n303Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n304Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n305NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n\n12\n306Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n307Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n308Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n309Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n310The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n311Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n314National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n315Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n316Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n317Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n318Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n319School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(compiled July 24, 2025)\nWe present an all-sky search for long-duration gravitational waves (GWs) from the first part\nof the LIGO-Virgo-KAGRA fourth observing run (O4), called O4a and comprising data taken\nbetween 24 May 2023 and 16 January 2024. The GW signals targeted by this search are the so-\ncalled \u201clong-duration\u201d (\u22731 s) transients expected from a variety of astrophysical processes, including\nnon-axisymmetric deformations in magnetars or eccentric binary coalescences. We make minimal\nassumptions on the emitted GW waveforms in terms of morphologies and durations. Overall, our\nsearch targets signals with durations \u223c1\u20131000 s and frequency content in the range 16\u20132048 Hz. In\nthe absence of significant detections, we report the sensitivity limits of our search in terms of root-\nsum-square signal amplitude (hrss) of reference waveforms. These limits improve upon the results\nfrom the third LIGO-Virgo-KAGRA observing run (O3) by about 30% on average.\nMoreover,\nthis analysis demonstrates substantial progress in our ability to search for long-duration GW signals\nowing to enhancements in pipeline detection efficiencies. As detector sensitivities continue to advance\nand observational runs grow longer, unmodeled long-duration searches will increasingly be able to\nexplore a range of compelling astrophysical scenarios involving neutron stars and black holes.\nI.\nINTRODUCTION\nThe direct detection of gravitational waves (GWs)\nfrom a pair of black holes (BHs) during the first observing\nrun (O1) [1] of the Laser Interferometer Gravitational-\nwave Observatory (LIGO) [2] marked a major milestone\nin GW astrophysics. The detection of GWs from the bi-\nnary neutron star (NS) merger GW170817 during the sec-\nond LIGO and Virgo [3] observing run (O2) [4] initiated\nthe era of multi-messenger astrophysics, via the identi-\nfication of an electromagnetic counterpart in practically\nall bands of the spectrum by a suite of electromagnetic\nobservatories from the ground and space [5, 6].\nDuring the third observing run (O3) of Advanced\nLIGO, Virgo, and KAGRA [7, 8], several other interest-\ning compact binary systems were detected. These include\na likely NS-NS merger with total mass significantly larger\n\u2217Deceased, September 2024.\nthan that of known galactic binary NS systems [9]; BH-\nNS candidates [10]; pairs of compact objects with one of\nthe two belonging to the so-called lower mass gap (the\ndividing line between the heaviest NSs and the lightest\nBHs) [11] and a BH-BH coalescence whose compact rem-\nnant falls in the intermediate BH mass range [12]. In to-\ntal, about 90 transient GW signals have been confidently\ndetected in the O1-O3 runs, all of them confidently asso-\nciated with compact binary coalescences (CBC) [13\u201315].\nThe O4 run is the longest LIGO-Virgo-KAGRA observ-\ning run to date. Similarly to the O1-O3 runs, the first\neight months of O4 (called O4a) have brought new CBC\ndetections, including the notable GW230529\u2014a merger\nof a NS with a lower mass-gap BH [16].\nWhile all of the above mentioned O1\u2013O4 detections are\nexciting, we are yet to probe the large variety of astro-\nphysical scenarios that predict GWs from systems other\nthan CBCs. This motivates continued searches for other\nclasses of GW signals (e.g., [17\u201323]). Here, we present a\nsearch for unmodeled, long-lived (\u223c1\u20141000 s) GW tran-\nsients in O4a data, updating results from the first three\n\n13\nruns [17\u201319].\nThis analysis includes the first application of the XG-\nBoost [24] post-processing classifier of coherent Wave-\nBurst (cWB) to long-duration GW searches (Section\nIII), and results from the first PySTAMPAS [25] all-\nsky search for long-duration GWs (Section III). The use\nof diverse methods in the search for long-duration GW\nsignals is motivated by the wide range of potential sig-\nnal morphologies\u2014including variations in duration, tem-\nporal evolution, and frequency content\u2014expected from\ndifferent astrophysical scenarios. Many of these scenar-\nios remain unexplored and constraining them via GW\nobservations holds the promise of significantly advanc-\ning our understanding of the physics and astrophysics\nof compact objects.\nHence, this analysis targets a va-\nriety of GW signals including those produced by non-\naxisymmetric deformations in newly-born NSs or magne-\ntars formed in massive star core collapses or binary NS\nmergers [26\u201329], fallback accretion onto newly-born NSs\nor BHs [30\u201333], or instabilities and fragmentation in the\naccretion disks around BHs [34]. Low-mass CBCs can\nalso generate GW signals that are relatively long-lived\n(\u22731 s) in the frequency band of ground-based GW de-\ntectors. Generally, these CBC signals are well-modeled,\nand therefore better searched for with matched filter-\ning techniques [35]. However, here we also target low-\nmass (total mass \u22645 M\u2299) CBCs with high eccentric-\nity (0.2 \u2264e \u22640.6), as these do not fall within the pa-\nrameter space covered by matched filter-based searches.\nHereafter, we refer to these systems as eccentric compact\nbinary coalescences (ECBCs). Our results complement\nother dedicated waveform-independent searches for high\nmass (source total mass M \u226570 M\u2299) eccentric CBC sig-\nnals with eccentricity e \u22640.3 (e.g., [36]).\nThis paper is organized as follows. In Section II we\ndescribe our dataset.\nSections III and IV present our\ndata analysis methods and the reference waveforms used\nto quantify our sensitivity, respectively. In Section V and\nVI we report our results and conclude.\nII.\nDATA\nThe LIGO-Virgo-KAGRA fourth observing run (O4)\nstarted on 24 May 2023 at 15:00 UTC. The first part of\nthe O4 observing run, O4a, ended on 16 January 2024\nat 16:00 UTC. During O4a, the LIGO Hanford (LHO)\nand Livingston (LLO) detectors operated at improved\nsensitivity compared to their O3 run.\nA conventional\nmeasure of sensitivity is the binary neutron star (BNS)\ninspiral range, which quantifies the average distance at\nwhich a fiducial 1.4-1.4 M\u2299BNS could be detected with\na signal-to-noise ratio (SNR) of 8 (see e.g., [37] and refer-\nences therein). During O4a, the LHO and LLO detectors\nreached a BNS range of about 160 Mpc, corresponding to\napproximately 30% and 15% improvements, respectively,\ncompared to O3 [38]. The Virgo detector did not join\nO4a.\nThe search algorithms employed in this work require\ncoincident data from at least two detectors.\nBecause\nthe BNS range for the KAGRA detector was substan-\ntially smaller than that of the LIGO detectors in O4a,\nwe do not include KAGRA data in our search and we\nconsider only data where both LIGO detectors are si-\nmultaneously available. A total of 126.6 days of coinci-\ndent LHO-LLO data were collected during O4a.\nThis\ncorresponds to a duty cycle of about 53% for joint obser-\nvations collecting so-called \u201cANALYSIS READY\u201d data.\nThe last are data collected with the interferometers op-\nerating under observing conditions that are considered\nsuitable for searching for GW signals. Removal of coinci-\ndent data with significant data quality issues (by apply-\ning so-called \u201ccategory 1\u201d vetoes, as defined in [39]), left\nus with about 125 days of coincident LHO-LLO data [40].\nNext, a small fraction (about 1 \u22122%) of this coincident\ndata is discarded because their duration is shorter than\nthe time window used by each pipeline (see Section III\nfor details). Finally, as we describe in the next Section,\nstrategies to reduce the impact of glitches (transient noise\nevents that have a variety of origins), resulted in small\n(\u22721%) amount of data being removed from the analysis.\nDuring O4a, the calibration uncertainty in amplitude\nbelow 2 kHz was less than 10%, and it improved in the\nsecond half of O4a to be less than 2% below 2 kHz. Cal-\nibration uncertainty is not taken into account in the re-\nsults presented in this paper as these calibration errors\nare much smaller than the astrophysical uncertainties\nthat affect the class of signals we target here.\nIII.\nSEARCH METHODS\nGiven the large uncertainties in potential post-merger\nGW signal characteristics (Fig. 1; [26\u201334]), hereafter we\nuse two independent unmodeled search methods (and\ncorresponding background estimations) that are based on\ndifferent data-processing and clustering techniques: cWB\n[24, 41] and PySTAMPAS [25]. In this Section, we discuss\nbriefly their basic workings. More details are provided in\nSections III A-III B.\nUnmodeled searches for long-duration GW transients\ntypically look for patterns of excess power in some time-\nfrequency representation of the data, and rely on the\ncross-correlation between the data streams of non co-\nlocated detectors to distinguish actual astrophysical GWs\nfrom background events generated by instrumental or en-\nvironmental noise in the detectors [42\u201351].\nTo estimate the distribution of background events, the\ndata from one detector are time-shifted with respect to\nthe other by an amount of time large enough to remove\nany coherent GW signal from the cross-correlated data.\nThe process of time sliding the data is repeated multiple\ntimes for different values of the time shift to estimate\nthe inverse false-alarm rate (iFAR) of potential candidate\nevents accurately.\n\n14\nA.\nCoherent Wave Burst\ncWB is an unmodeled transient search pipeline [41].\nIt is based on a multi-resolution time-frequency wavelet\ntransform known as Wilson-Daubechies-Meyer (WDM)\n[52]. Time-frequency pixels that contain excess energy\n(as estimated from the wavelet coefficients) across the\ndetector network are selected and nearby pixels are clus-\ntered.\nIn the pixel selection process, periods where a\nknown physical factor is affecting the detector\u2019s data\nquality are removed (so-called \u201ccategory 2\u201d vetoes, de-\nfined as in [39, 40]).\nAfter the clustering step, cWB performs an all-sky\nsearch for each cluster of pixels by utilizing a likelihood\nalgorithm computed over an equal area pixelated grid of\nsky positions obtained using the Hierarchical Equal Area\nisoLatitude Pixelization (HEALPix1) scheme [53, 54].\nTriggers are reconstructed from the sky position where\nthe likelihood reaches a maximum.\nIn the post-processing, cWB (version 6.4.5.0) uses a\nsupervised boosted decision tree classifier, XGBoost [24],\nto re-weight the network coherent signal-to-noise ratio\n(SNR) of triggers. The re-weighted values are used as\nranking statistics [55]. We note that this XGBoost re-\nweighting procedure entirely replaces the waveform du-\nration cut (and all other thresholds in post-processing)\nused for cWB long-duration searches in O2 [17] and O3\n[19]. Eliminating the duration cut enables long-duration\nsearches on a larger parameter space, while enhancing\nsensitivity. Consequently, some CBC triggers with high\nSNR identified by cWB during the search retain high\nranking statistics after the re-weighting process. Hence,\nsimilar to the approach employed for short-duration sig-\nnals [56], CBC signals are excised a posteriori from the\nanalysis (see Section V and Figure 2 for more details).\nIn the O4a long-duration analysis, the data are di-\nvided into four chunks of approximately equal duration\nacross the approximately 122 days of observing time ana-\nlyzed. The chunks are further split into 1200 s-long data\nsegments, which are then transformed with the WDM\nwavelet into seven time-frequency resolutions (frequency\nbins ranging from 0.5 Hz to 16 Hz; time bins ranging from\n1/64 s to 1 s) covering the frequency range 16\u20132048 Hz.\nTo estimate the background distribution of noise triggers,\ntime slides are performed by sliding the data between de-\ntectors 600 times in 2-second steps within each 1200s-long\ndata segment. A 2-second time step is longer than the\nlongest time bin utilized for the cWB search, and suffi-\ncient to break any coherence in the time-frequency pix-\nels. This process is further extended by performing shifts\nacross different data segments of each chunk, resulting in\na total of 2400 independent time shifts per chunk. This\nyields a background of about 772 years in total for the\nfour chunks (half of which is used for training, as de-\nscribed below).\n1 http://healpix.sf.net\nThe XGBoost models for each chunk are trained inde-\npendently, with dedicated training sets. These training\nsets are created by randomly selecting 50% of the back-\nground data from the corresponding chunk, and injecting\na series of white noise burst signals to cover the analysis\nfrequency range. The produced XGBoost model is then\napplied to the remaining 50% background to produce the\nbackground statistical distribution. To evaluate the effi-\nciency of the XGBoost model, a set of simulations with\na selection of waveform models, as described in Section\nIV, is analyzed with the XGBoost models.\nWe note that in O4a, excessive noise fluctuations\naround the known 60 Hz and 180 Hz power lines and har-\nmonics are observed in the background.\nThus, in the\npost-production, noise fluctuations at these frequencies\nare excised (from both the background and the fore-\nground).\nB.\nPySTAMPAS\nPySTAMPAS [25] is an enhanced version of the\nStochastic Transient Analysis Multi-detector Pipeline\n(STAMP) [57] that was used in previous analyses [18, 19].\nIt is designed to perform unmodeled all-sky searches for\nlong-duration GW transients at a reduced computational\ncost compared to STAMP [25]. The data are split into\n512 s-long windows which overlap by 50%. For each win-\ndow and each detector, spectrograms of the auto-power\nSNR are built using the Short-Time Fourier Transform\n(STFT) over short segments with duration 0.5 s, 1 s, 2 s,\nand 4 s, that are Hann-windowed and overlap by 50%.\nThe four spectrograms are then combined into a single\nmulti-resolution spectrogram that covers the frequency\nband 22\u20132000 Hz.\nFor each frequency bin, the power\nspectral density (PSD) is estimated by taking the median\nof the squared modulus of the STFT over the window du-\nration. A seed-based clustering algorithm is applied on\neach multi-resolution spectrogram to extract clusters of\npixels that form candidate GW triggers. Pixels forming\neach cluster are then cross-correlated with the spectro-\ngram from the other detector and a coherent detection\nstatistic is computed for the whole trigger [19].\nTo estimate the background distribution of noise trig-\ngers, the spectrogram from the other detector is time-\nshifted by an amount of time greater than 1000 s. This is\na conservative choice that allows us to break any coher-\nence in time over the duration of the longest signals tar-\ngeted by this search, regardless of signal frequency con-\ntent. This operation is repeated 320 times with different\nvalues of the time shift, allowing to simulate 108 years\nof background.\nTo deal with non-Gaussian noise arti-\nfacts, frequency bins that correspond to known spectral\nlines in the detectors and that generate an excess of noise\ntriggers, are masked. In total, 9% of the total frequency\nband is masked in this analysis. As was done in previous\nsearches with STAMP [19], triggers for which the maxi-\nmal fraction of SNR in a single time bin exceeds 0.3, or\n\n15\nDuration\n0\n250\n500\n750\n1000\n1250\n1500\n1750\n2000\nFrequency [Hz]\nMagnetar\nD\nE\nF\nG\nISCOChirp\nA\nB\nC\nECBC\nA\nB\nCDE F G H I\nGRBPlateauA\nadiB\nPTA\nB\nsgC\nwnbA\nmsmagnetarA\ninspiralB\n500s\nFIG. 1. Time-frequency representation of the waveforms used\nto test the sensitivity of this search. The x-axis represents\na linear time axis with the various signal types off-set hori-\nzontally for clarity. Waveforms that are new in this analysis\n(compared to O2 [18, 58] and O3 [19] long-duration burst\nsearches) are marked in red.\nfor which the ratio of auto-power SNR between the two\ndetectors exceeds 5, or that have a duration lower than\n10 s, are vetoed in post-processing. Because of the high\nrate of noise fluctuations at low frequency, triggers whose\ncentral frequency is below 50 Hz are also dismissed. Fi-\nnally, spectrograms for which the fraction of pixels above\nthe threshold considered for clustering is above 0.5% are\nremoved from the analysis. These correspond to unusu-\nally noisy stretches of data that the clustering algorithm\nis unable to handle. About 0.03% of the O4 data consid-\nered for this search (see Section II) are removed by this\ncut.\nIV.\nWAVEFORM MODELS\nThe analysis presented here is an unmodeled search\nfor GW signals, and as such it does not rely on the use\nof template waveforms to make detection statements. In\nthe absence of a detection, to put our results in context,\nwe quantify the sensitivity of our search by setting upper\nlimits on the GW strain amplitude of a set of simulated\nwaveforms added coherently into detector data. We note\nthat because of the limited distance reach of our anal-\nysis, we do not consider redshift effects on the model\nwaveforms.\nThe waveform models used in this analysis include\nthose from a similar search performed on O3 data [19].\nThese waveforms are representative of some compelling\nastrophysical scenarios, such as post-merger magnetars\n(Magnetar) with ellipticity in the range 0.005\u22120.08,[29],\naccretion disk instabilities (ADI) [34], newly formed\nmagnetars powering gamma-ray burst plateaus (GRB-\nplateau) [26, 30, 59], inspiral-merger-ringdown ECBC\nwaveforms [60] with eccentricity between 0.2 and 0.6 and\ntotal mass between 2.8 and 10 M\u2299, and broadband chirps\nfrom innermost stable circular orbit waves around rotat-\ning BHs with mass between 5 and 20 M\u2299(ISCOchirp)\n[33].\nIn addition to the above, we include in our analysis\nGW signals modeled for binary NS mergers (inspiralB),\nmillisecond magnetars (msmagnetar-A), and fallback ac-\ncretion onto NSs (PT-A; PT-B) with their time frequency\nrepresentation shown in Figure 1.\nThe inspiral model\nemploys the IMRPhenomPv2NRTidalv2 approximant for\nequal-mass binaries (1.4 M\u2299) [61]. The millisecond mag-\nnetar model is an analytical model derived from the dy-\nnamics of spinning down nascent NSs proposed by Sarin\net al. [28] and Lasky et al. [27] with frequency evolu-\ntion modeled with an arbitrary but fixed braking index.\nThe PT models (A and B) were proposed by Piro and\nThrane [32] for stars of intermediate mass that end their\nlives forming NSs which eventually collapse to BHs via\nfallback accretion. When the incoming material has suf-\nficient angular momentum to form a disk, the accretion\nspins up the NS sufficiently to produce non-axisymmetric\ninstabilities and gravitational radiation with frequencies\nin the range 700\u20132400 Hz for about 30\u20133000 s until col-\nlapse to a BH occurs.\nFinally, to fill out the parameter space, we perform\nsensitivity estimates also for \u201cad-hoc\u201d waveforms: band-\nlimited white noise burst (WNB) and sine-Gaussian\nbursts (SG).\nV.\nRESULTS\nSimilarly to what was done in the O2 and O3 long-\nduration GW searches [18, 19], for both the PySTAM-\nPAS and cWB analyses we set a detection threshold cor-\nresponding to an iFAR higher than 50 years.\nIn the cWB analysis, we find 25 CBC triggers (11 of\nwhich with iFAR above the 50 years detection threshold)\nthat were confidently detected by low-latency searches,\nand subsequently reported as public alerts [62\u201386]. After\nexcluding triggers associated with these known, quasi-\ncircular CBC events, the cWB search remains sensitive\nto ECBC signals. As shown in Figure 2, the resulting\ndistribution of cWB triggers is consistent with the back-\nground within 2\u03c3.\nThe most significant trigger has a\nSNR of 11, centered at 54 Hz, with an iFAR of 0.70 years\nand a false alarm probability (FAP) of 0.38. This trigger\nhappened during a period of elevated glitch rate. This,\ncombined with the estimated FAP of 0.38, suggests that\nthe trigger is likely due to noise.\nThe distribution of triggers found by PySTAMPAS is\nalso consistent with the background within 2\u03c3, as shown\nin the bottom panel of Figure 2. The most significant\ntrigger has an iFAR of 0.49 years (FAP \u22480.52), and\nis consistent with a noise fluctuation in LLO between\n242 Hz and 250 Hz. PySTAMPAS did not recover any of\nthe CBC triggers identified by cWB because these had\ndurations shorter than 10 s and are therefore removed in\n\n16\n10\n2\n10\n1\n100\n101\n102\niFAR [years]\n100\n101\n102\nCumulative number of events\ncWB\nPredicted\nSearch results\nSearch results excluding known BBH\n10\n2\n10\n1\n100\n101\n102\niFAR [years]\n100\n101\n102\nCumulative number of events\nPySTAMPAS\nPredicted\nSearch results\nFIG. 2. Cumulative number of events as a function of the\niFAR found by cWB (top) and PySTAMPAS (bottom). Cross\nmarkers represent all events found in the search, while triangle\nones exclude known BBH events found in low latency. Assum-\ning a Poisson distribution for noise events, the expected value\nfor the background (i.e., T/iFAR, where T is the observing\ntime) is shown by the solid line, while the shaded regions rep-\nresents the 1 \u22122 \u22123 \u03c3 uncertainties. We note that the \u22482\u03c3\nexcess in the PySTAMPAS distribution over several iFAR bins\nis dominated by the contribution of the three loudest back-\nground events with FAP approximately 0.52, 0.62, and 0.65,\nrespectively.\npost-processing.\nIn the absence of a significant GW candidate in either\nanalysis, we derive sensitivity estimates on the GW am-\nplitude of the various waveform models described in Sec-\ntion IV. To this end, simulated waveforms are injected co-\nherently into the detectors\u2019 data at different amplitudes,\nand the detection efficiency (fraction of the total num-\nber of injections that are recovered) is measured as a\nfunction of waveform amplitude. The spanned range of\namplitudes is chosen so that the detection efficiency is\nsampled across the whole range of its possible values\u2014\nfrom 0% to 100%. For each injected signal of a given\nTABLE I. Rate upper limits per unit volume at 90% confi-\ndence level on eccentric CBC with various component masses\nmasses and eccentricity e, computed with Eq. 2. In the last\ncolumn, we show updated results from the O3 run, which we\nhave recomputed as discussed in Section VI. We find that un-\ncertainties on these values are dominated by systematic errors\nassociated to the method used to fit the efficiency curves, es-\ntimated to be of order 15% (see text for discussion).\nWaveform M1[M\u2299] M2[M\u2299] e\nR90% [Gpc\u22123yr\u22121]\nO4a\nO3\nECBC A\n1.4\n1.4\n0.2 9.1 \u00d7 103 2.0 \u00d7 104\nECBC B\n1.4\n1.4\n0.4 1.1 \u00d7 104 2.4 \u00d7 104\nECBC C\n1.4\n1.4\n0.6 1.8 \u00d7 104 4.4 \u00d7 104\nECBC D\n3.0\n3.0\n0.2 1.3 \u00d7 103 4.6 \u00d7 103\nECBC E\n3.0\n3.0\n0.4 1.4 \u00d7 103 5.5 \u00d7 103\nECBC F\n3.0\n3.0\n0.6 3.7 \u00d7 103 8.9 \u00d7 103\nECBC G\n5.0\n5.0\n0.2 4.2 \u00d7 102 3.0 \u00d7 103\nECBC H\n5.0\n5.0\n0.4 5.2 \u00d7 102 4.0 \u00d7 103\nECBC I\n5.0\n5.0\n0.6 8.0 \u00d7 102 4.7 \u00d7 103\namplitude, the starting time, sky position (right ascen-\nsion and cosine of the declination), polarization angle,\nand cosine of the inclination angle are randomly drawn\nfollowing a uniform distribution. We note that for esti-\nmating the detection efficiency, a signal is considered to\nbe recovered by a given pipeline if it produces a trigger\nwithin the time and frequency boundaries of the injected\nwaveform, with an iFAR higher than 50 years.\nThe results are presented in Fig. 3 as root-sum-square\namplitudes (hrss) at 50% detection efficiency, where:\nhrss =\nsZ \u221e\n\u2212\u221e\n(h2\n+(t) + h2\n\u00d7(t))dt.\n(1)\nIn the above equation, h+ and h\u00d7 are the GW amplitudes\nfor the + and \u00d7 polarizations. For each waveform, the\nlowest value from either of the two pipelines is reported.\nWe discuss these results in Section VI.\nWe also derive upper limits on the rate of eccentric\nCBC events (ECBCs), updating previous results from O2\n[18] and O3 [19]. In the absence of a detection, assum-\ning that these events are uniformly distributed in the\nobserved volume and follow a Poisson distribution, the\n90% confidence upper limit on their rates is given by [87]\nR90% =\n2.3\n4\u03c0T\nR rmax\n0\ndr r2 \u03f5(r),\n(2)\nwhere \u03f5(r) is the detection efficiency as a function of dis-\ntance r, rmax is the maximal detectable distance, and T\nis the observing time [88]. In Table I we report our best\nresults, derived using the cWB pipeline (which has the\nbest sensitivity for this family of waveforms). We discuss\nthese results in Section VI.\n\n17\n102\n103\nFrequency [Hz]\n10\n23\n10\n22\n10\n21\nStrain/ Hz\nH1 ASD\nL1 ASD\ninspiral\nISCOchirp\nECBC\nmagnetar\nPT\nmsmagnetar\nADI\nGRBplateau\nSG\nWNB\nO3 hrss\nFIG. 3. Root-sum-square amplitude at 50% detection efficiency as a function of the central frequency of each tested wave-\nform with iFAR > 50 years (black markers). The O3 results [19] are represented by light-gray square markers, showing the\nimprovement in sensitivity (vertical arrows). For each waveform, the most constraining result from either of the two pipelines\nis shown. For reference, the mean amplitude spectral densities of the Livingston (blue) and Hanford (red) detectors during O4a\nare plotted, along with those from the O3b (faded dashed curves).\nVI.\nDISCUSSION\nThe hrss at 50% efficiency of this O4a search has de-\ncreased by 30% (on average across the detector band-\nwidth) compared to O3 (Figure 3). This improvement is\nprimarily driven by the sensitivity increase of the LIGO\ndetectors between O3 and O4a. However, the pipelines\nused for this search are also different from the ones used\nin O3. This improves the O4a sensitivity (compared to\nO3) for most waveforms.\nSpecifically, the ECBCs are\nbetter recovered than in O3 (up to a factor about 2\nlower in hrss at 50% efficiency), because the new version\nof cWB, enhanced with XGBoost, better discriminates\nthese signals from noise transients [24]. The sensitivity\nto monochromatic SGs has also improved by a factor of\nabout 10 thanks to a more robust PSD estimation in\nPySTAMPAS (which is now based on the median PSD\nover a time window longer than twice the duration of\nthe signal). The sensitivity to magnetar waveforms has\nnot improved compared to O3, as these signals are best\nrecovered using the seedless clustering strategy used in\nO3 [44]. The seedless clustering strategy is being devel-\noped in the PySTAMPAS package at the time of writing.\nHence, this strategy has not been used for the O4a results\npresented here.\nTo put the above results in the context of previ-\nous analyses, we note that the O3 long-duration search\nbroadly constrained GW signals with energies of order\n10\u22122 M\u2299(comparable to the maximum rotational energy\nof a 1.4 M\u2299NS [89]), and morphologies similar to the\n\n18\n101\n102\nDistance [Mpc]\n0.0\n0.2\n0.4\n0.6\n0.8\nDetection efficiency\nSigmoid fit\nQuadratic interpolation\nFIG. 4.\nDetection efficiency as a function of the distance\nrecovered by cWB for the ECBC-A waveform model on O4a\ndata. The black dots represent data points, and the dashed\nand dashed dotted curves represent a fit by a sigmoid function\nand a quadratic interpolation respectively.\nThis illustrates\nhow a sigmoid fit overestimates the detection efficiency at\nlarge distances, leading to a detection volume overestimated\nby a factor \u223c2 in that case.\nones considered here, to distances \u22731\u221210 Mpc (see Fig-\nure 2 in [19]). For a GW signal with an energy EGW\nand central frequency f0, the horizon distance d corre-\nsponding to a given hrss is d \u2243\nq\n5GEGW\n2\u03c02c3f 2\n0 h2rss [90]. The\noverall improvement of \u224830% in hrss at 50% efficiency\nachieved via this analysis pushes the above lower limits\non the distances to values about 30% larger.\nWe also derive rates upper limits on ECBC events\n(Table I). The upper limits range from 420 Gpc\u22123yr\u22121\nto 18, 000 Gpc\u22123yr\u22121 depending on the mass and ec-\ncentricity of the system. These ECBC rate constraints\nare compatible with expectations that, overall, only a\nsmall fraction of CBC systems have a significant eccen-\ntricity [91], given current estimates of CBC rates (10 \u2212\n1, 700Gpc\u22123yr\u22121 for NS-NS systems, 7.8\u2212140Gpc\u22123yr\u22121\nfor NS-BH, and 17.9 \u221244 Gpc\u22123yr\u22121 for BH-BH [92]).\nThe above rate upper limits ECBCs require a careful\nsampling and modeling of the tail of the detection effi-\nciency curve at large distances. For this analysis (O4a\ncolumn in Table I), we revisit and improve the efficiency\nestimation procedure that was employed in O3. First,\nwe use a quadratic interpolation of the sampled efficiency\nvalues instead of the sigmoid fit used in O3 [19]. To assess\nthe robustness of the quadratic interpolation, we compare\nour results with a log-normal distribution fit and a linear\ninterpolation.\nBoth these methods give results consis-\ntent with the quadratic interpolation within about 15%\nof the estimated rate upper limit. On the other hand,\na sigmoid fit systematically overestimates the detection\nvolume (the integral in the denominator of Eq. 2), result-\ning in an underestimate of the 90% rate upper limits by a\nfactor of about 2\u20133 across different waveforms and detec-\ntion pipelines. An example of this is presented in Figure\n4. As a second improvement to our detection efficiency\nestimates, we limit the rmax in Eq. 2 to the highest sam-\npled distance so as to ensure that the 90% rate upper-\nlimits are not affected by errors that may be introduced\nwhen extrapolating fits or interpolations to the efficiency\ncurves at distances beyond the range that was actually\nsampled. In the O3 long duration search [19], the lack\nof the above constraint resulted in an underestimation of\nthe rate upper limits by factor of about 5 (on average\nacross ECBC waveforms) for the cWB pipeline. This is-\nsue did not affect the O3 STAMP-AS Zebragard results\n[19].\nGiven the above noted improvements in the detection\nvolume estimates, in the rightmost column of Table I we\ncompare our O4a results with the rate upper limits that\nwe derive applying the same efficiency curve estimation\nof our O4a analysis to the (previously unpublished) O3\nSTAMP-AS Zebragard results for ECBCs. The O4a up-\nper limits improve on O3 results by factors of about 2\u22127,\nconsistently with the improvement in sensitivity shown\nin Fig. 3 and the fact that the observing time of O4a is\nabout half of O3. Indeed, for this waveform family, the\nimproved O4a sensitivity implies a distance reach about\n1.4 \u22122.4 times larger than in O3, hence a detection vol-\nume about 2.7\u221214 times larger, and therefore rate upper\nlimits 1.4 \u22127 times smaller.\nIn conclusion, with this O4a analysis we have made\nsubstantial progress in our ability to search for long-\nduration GW signals, thanks to the combination of the\nimproved O4a sensitivity and enhancements in pipeline\ndetection efficiencies. With further progress in GW de-\ntectors\u2019 sensitivity [93] and longer data taking runs, long-\nduration unmodeled searches have the potential to probe\nseveral interesting astrophysical scenarios involving NSs\nand BHs [26\u201334].\nWe note that the pipeline improve-\nments described in this search can also benefit triggered\nsearches for long-duration post-merger signals [58, 94],\naddressing a key open question left open by the multi-\nmessenger detection of GW170817, namely, what is the\nnature of the post-merger remnant.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\n\n19\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO con-\nsortium.\nThe authors also gratefully acknowledge re-\nsearch support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India,\nthe Department of Science and Technology, India, the\nScience & Engineering Research Board (SERB), India,\nthe Ministry of Human Resource Development, India,\nthe Spanish Agencia Estatal de Investigaci\u00b4on (AEI), the\nSpanish Ministerio de Ciencia, Innovaci\u00b4on y Universi-\ndades, the European Union NextGenerationEU/PRTR\n(PRTR-C17.I1), the ICSC - CentroNazionale di Ricerca\nin High Performance Computing, Big Data and Quantum\nComputing, funded by the European Union NextGener-\nationEU, the Comunitat Auton`oma de les Illes Balears\nthrough the Conselleria d\u2019Educaci\u00b4o i Universitats, the\nConselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat\nDigital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish\nNational Agency for Academic Exchange, the National\nScience Centre of Poland and the European Union - Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scot-\ntish Universities Physics Alliance, the Hungarian Scien-\ntific Research Fund (OTKA), the French Lyon Institute\nof Origins (LIO), the Belgian Fonds de la Recherche Sci-\nentifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of\nScience, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute\nfor Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Sci-\nence Foundation of China (NSFC), the Israel Science\nFoundation (ISF), the US-Israel Binational Science Fund\n(BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC),\nTaiwan, the United States Department of Energy, and\nthe Kavli Foundation. The authors gratefully acknowl-\nedge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources.\nThis work was supported by MEXT, the JSPS\nLeading-edge Research Infrastructure Program, JSPS\nGrant-in-Aid for Specially Promoted Research 26000005,\nJSPS Grant-in-Aid for Scientific Research on Inno-\nvative Areas 2402:\n24103006, 24103005, and 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-\nto-Core Program A. Advanced Research Networks, JSPS\nGrants-in-Aid for Scientific Research (S) 17H06133 and\n20H05639, JSPS Grant-in-Aid for Transformative Re-\nsearch Areas (A) 20A203:\nJP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nUniversity of Tokyo, the National Research Foundation\n(NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineering\nCenter of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied a\nCreative Commons Attribution (CC BY) license to any\nAuthor Accepted Manuscript version arising. 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ANTIER,41 M. AOUMI,50 E. Z. APPAVURAVTHER,51, 52 S. APPERT,11 S. K. APPLE,53 K. ARAI,11 A. ARAYA,42\nM. C. ARAYA,11 M. ARCA SEDDA,44, 45 J. S. AREEDA,54 N. ARITOMI,2 F. ARMATO,29, 30 S. ARMSTRONG,55 N. ARNAUD,56\nM. AROGETI,57 S. M. ARONSON,12 K. G. ARUN,58 G. ASHTON,59 Y. ASO,25, 60 L. ASPREA,28 M. ASSIDUO,61, 62\nS. ASSIS DE SOUZA MELO,63 S. M. ASTON,64 P. ASTONE,38 F. ATTADIO,39, 38 F. AUBIN,65 K. AULTONEAL,66 G. AVALLONE,67\nE. A. AVILA,49 S. BABAK,20 C. BADGER,68 S. BAE,69 S. BAGNASCO,28 L. BAIOTTI,70 R. BAJPAI,71 T. BAKA,72, 37 A. M. BAKER,6\nK. A. BAKER,73 T. BAKER,74 G. BALDI,75, 76 N. BALDICCHI,77, 51 M. BALL,78 G. BALLARDIN,63 S. W. BALLMER,79 S. BANAGIRI,6\nB. BANERJEE,44 D. BANKAR,80 T. M. BAPTISTE,12 P. BARAL,10 M. BARATTI,81, 82 J. C. BARAYOGA,11 B. C. BARISH,11 D. BARKER,2\nN. BARMAN,80 P. BARNEO,83, 84, 85 F. BARONE,86, 4 B. BARR,87 L. BARSOTTI,35 M. BARSUGLIA,20 D. BARTA,88 A. M. BARTOLETTI,89\nM. A. BARTON,87 I. BARTOS,46 A. BASALAEV,8, 9 R. BASSIRI,90 A. BASTI,82, 81 M. BAWAJ,77, 51 P. BAXI,91 J. C. BAYLEY,87\nA. C. BAYLOR,10 P. A. BAYNARD II,57 M. BAZZAN,92, 93 V. M. BEDAKIHALE,94 F. BEIRNAERT,95 M. BEJGER,96 D. BELARDINELLI,22\nA. S. BELL,87 D. S. BELLIE,97 L. BELLIZZI,81, 82 W. BENOIT,18 I. BENTARA,56 J. D. BENTLEY,98 M. BEN YAALA,55 S. BERA,99, 100\nF. BERGAMIN,33 B. K. BERGER,90 S. BERNUZZI,27 M. BEROIZ,11 C. P. L. BERRY,87 D. BERSANETTI,29 T. BERTHEAS,101\nA. BERTOLINI,37, 36 J. BETZWIESER,64 D. BEVERIDGE,73 G. BEVILACQUA,102 N. BEVINS,103 R. BHANDARE,104 R. BHATT,11\nD. BHATTACHARJEE,105, 106 S. BHATTACHARYYA,107 S. BHAUMIK,46 V. BIANCALANA,102 A. BIANCHI,37, 108 I. A. BILENKO,109\nM. BILICKI,110 G. BILLINGSLEY,11 A. BINETTI,111 S. BINI,11, 75, 76 C. BINU,112 S. BIOT,113 O. BIRNHOLTZ,114 S. BISCOVEANU,97\nA. BISHT,9 M. BITOSSI,63, 81 M.-A. BIZOUARD,115 S. BLABER,116 J. K. BLACKBURN,11 L. A. BLAGG,78 C. D. BLAIR,73, 64\nD. G. BLAIR,73 N. BODE,8, 9 N. BOETTNER,98 G. BOILEAU,115 M. BOLDRINI,38 G. N. BOLINGBROKE,117 A. BOLLIAND,118, 40\nL. D. BONAVENA,46 R. BONDARESCU,83 F. BONDU,119 E. BONILLA,90 M. S. BONILLA,54 A. BONINO,120 R. BONNAND,31, 118\nA. BORCHERS,8, 9 S. BORHANIAN,7 V. BOSCHI,81 S. BOSE,121 V. BOSSILKOV,64 Y. BOTHRA,37, 108 A. BOUDON,56 L. BOURG,57\nM. BOYLE,122 A. BOZZI,63 C. BRADASCHIA,81 P. R. BRADY,10 A. BRANCH,64 M. BRANCHESI,44, 45 I. BRAUN,105 T. BRIANT,123\nA. BRILLET,115 M. BRINKMANN,8, 9 P. BROCKILL,10 E. BROCKMUELLER,8, 9 A. F. BROOKS,11 B. C. BROWN,46 D. D. BROWN,117\nM. L. BROZZETTI,77, 51 S. BRUNETT,11 G. BRUNO,15 R. BRUNTZ,124 J. BRYANT,120 Y. BU,125 F. BUCCI,62 J. BUCHANAN,124\nO. BULASHENKO,83, 84 T. BULIK,126 H. J. BULTEN,37 A. BUONANNO,127, 1 K. BURTNYK,2 R. BUSCICCHIO,128, 129 D. BUSKULIC,31\nC. BUY,101 R. L. BYER,90 G. S. CABOURN DAVIES,74 R. CABRITA,15 V. C\u00c1CERES-BARBOSA,7 L. CADONATI,57 G. CAGNOLI,130\nC. CAHILLANE,79 A. CALAFAT,99 T. A. CALLISTER,131 E. CALLONI,32, 4 S. R. CALLOS,78 M. CANEPA,30, 29 G. CANEVA SANTORO,43\nK. C. CANNON,42 H. CAO,35 L. A. CAPISTRAN,132 E. CAPOCASA,20 E. CAPOTE,2, 11 G. CAPURRI,82, 81 G. CARAPELLA,67, 133\nF. CARBOGNANI,63 M. CARLASSARA,8, 9 J. B. CARLIN,125 T. K. CARLSON,134 M. F. CARNEY,105 M. CARPINELLI,128, 63\nG. CARRILLO,78 J. J. CARTER,8, 9 G. CARULLO,120, 135 A. CASALLAS-LAGOS,136 J. CASANUEVA DIAZ,63 C. CASENTINI,137, 22\nS. Y. CASTRO-LUCAS,138 S. CAUDILL,134 M. CAVAGLI\u00c0,106 R. CAVALIERI,63 A. CEJA,54 G. CELLA,81 P. CERD\u00c1-DUR\u00c1N,139, 140\nE. CESARINI,22 N. CHABBRA,34 W. CHAIBI,115 A. CHAKRABORTY,13 P. CHAKRABORTY,8, 9 S. CHAKRABORTY,104\nS. CHALATHADKA SUBRAHMANYA,98 J. C. L. CHAN,141 M. CHAN,116 K. CHANG,142 S. CHAO,143, 142 P. CHARLTON,144\nE. CHASSANDE-MOTTIN,20 C. CHATTERJEE,145 DEBARATI CHATTERJEE,80 DEEP CHATTERJEE,35 M. CHATURVEDI,104 S. CHATY,20\nK. CHATZIIOANNOU,11 A. CHEN,146 A. H.-Y. CHEN,147 D. CHEN,148 H. CHEN,143 H. Y. CHEN,149 S. CHEN,145 YANBEI CHEN,150\nYITIAN CHEN,122 H. P. CHENG,151 P. CHESSA,77, 51 H. T. CHEUNG,91 S. Y. CHEUNG,6 F. CHIADINI,152, 133 G. CHIARINI,8, 9, 93\nA. CHIBA,153 A. CHINCARINI,29 M. L. CHIOFALO,82, 81 A. CHIUMMO,4, 63 C. CHOU,147 S. CHOUDHARY,73 N. CHRISTENSEN,115, 154\nS. S. Y. CHUA,34 G. CIANI,75, 76 P. CIECIELAG,96 M. CIE \u00b4SLAR,126 M. CIFALDI,22 B. CIROK,155 F. CLARA,2 J. A. CLARK,11, 57\nT. A. CLARKE,6 P. CLEARWATER,156 S. CLESSE,113 F. CLEVA,115, 118 E. COCCIA,44, 45, 43 E. CODAZZO,157, 158 P.-F. COHADON,123\nS. COLACE,30 E. COLANGELI,74 M. COLLEONI,99 C. G. COLLETTE,159 J. COLLINS,64 S. COLLOMS,87 A. COLOMBO,160, 129\nC. M. COMPTON,2 G. CONNOLLY,78 L. CONTI,93 T. R. CORBITT,12 I. CORDERO-CARRI\u00d3N,161 S. COREZZI,77, 51 N. J. CORNISH,162\nI. CORONADO,163 A. CORSI,164 R. COTTINGHAM,64 M. W. COUGHLIN,18 A. COUINEAUX,38 P. COUVARES,11, 57 D. M. COWARD,73\nR. COYNE,165 A. COZZUMBO,44 J. D. E. CREIGHTON,10 T. D. CREIGHTON,166 P. CREMONESE,99 S. CROOK,64 R. CROUCH,2\nJ. CSIZMAZIA,2 J. R. CUDELL,167 T. J. CULLEN,11 A. CUMMING,87 E. CUOCO,168, 169 M. CUSINATO,139 L. V. DA CONCEI\u00c7\u00c3O,170\nT. DAL CANTON,41 S. DAL PRA,171 G. D\u00c1LYA,101 B. D\u2019ANGELO,29 S. DANILISHIN,36, 37 S. D\u2019ANTONIO,38 K. DANZMANN,9, 8, 9\nK. E. DARROCH,124 L. P. DARTEZ,64 R. DAS,107 A. DASGUPTA,94 V. DATTILO,63 A. DAUMAS,20 N. DAVARI,172, 173 I. DAVE,104\nA. DAVENPORT,138 M. DAVIER,41 T. F. DAVIES,73 D. DAVIS,11 L. DAVIS,73 M. C. DAVIS,18 P. DAVIS,174, 175 E. J. DAW,176 M. DAX,1\nJ. DE BOLLE,95 M. DEENADAYALAN,80 J. DEGALLAIX,177 M. DE LAURENTIS,32, 4 F. DE LILLO,23 S. DELLA TORRE,129\nW. DEL POZZO,82, 81 A. DEMAGNY,31 F. DE MARCO,39, 38 G. DEMASI,178, 62 F. DE MATTEIS,21, 22 N. DEMOS,35 T. DENT,179\nCorresponding author: LSC P&P Committee, via LVK Publications as\nproxy\nlvc.publications@ligo.org\narXiv:2509.04348v2 [astro-ph.CO] 7 Oct 2025\n\n2\nA. DEPASSE,15 N. DEPERGOLA,103 R. DE PIETRI,180, 181 R. DE ROSA,32, 4 C. DE ROSSI,63 M. DESAI,35 R. DESALVO,182\nA. DESIMONE,183 R. DE SIMONE,152, 133 A. DHANI,1 R. DIAB,46 M. C. D\u00cdAZ,166 M. DI CESARE,32, 4 G. DIDERON,184 T. DIETRICH,1\nL. DI FIORE,4 C. DI FRONZO,73 M. DI GIOVANNI,39, 38 T. DI GIROLAMO,32, 4 D. DIKSHA,37, 36 J. DING,20, 185 S. DI PACE,39, 38\nI. DI PALMA,39, 38 D. DI PIERO,186, 48 F. DI RENZO,56 DIVYAJYOTI,33 A. DMITRIEV,120 J. P. DOCHERTY,87 Z. DOCTOR,97\nN. DOERKSEN,170 E. DOHMEN,2 A. DOKE,134 A. DOMICIANO DE SOUZA,187 L. D\u2019ONOFRIO,38 F. DONOVAN,35 K. L. DOOLEY,33\nT. DOONEY,72 S. DORAVARI,80 O. DOROSH,188 W. J. D. DOYLE,124 M. DRAGO,39, 38 J. C. DRIGGERS,2 L. DUNN,125 U. DUPLETSA,44\nP.-A. DUVERNE,20 D. D\u2019URSO,172, 157 P. DUTTA ROY,46 H. DUVAL,189 S. E. DWYER,2 C. EASSA,2 M. EBERSOLD,190, 31\nT. ECKHARDT,98 G. EDDOLLS,79 A. EFFLER,64 J. EICHHOLZ,34 H. EINSLE,115 M. EISENMANN,25 M. EMMA,59 K. ENDO,153\nR. ENFICIAUD,1 L. ERRICO,32, 4 R. ESPINOSA,166 M. ESPOSITO,4, 32 R. C. ESSICK,191 H. ESTELL\u00c9S,1 T. ETZEL,11 M. EVANS,35\nT. EVSTAFYEVA,184 B. E. EWING,7 J. M. EZQUIAGA,141 F. FABRIZI,61, 62 V. FAFONE,21, 22 S. FAIRHURST,33 A. M. FARAH,131\nB. FARR,78 W. M. FARR,192, 193 G. FAVARO,92 M. FAVATA,194 M. FAYS,167 M. FAZIO,55 J. FEICHT,11 M. M. FEJER,90\nR. FELICETTI,186, 48 E. FENYVESI,88, 195 J. FERNANDES,196 T. FERNANDES,197, 139 D. FERNANDO,112 S. FERRAIUOLO,198, 39, 38\nT. A. FERREIRA,12 F. FIDECARO,82, 81 P. FIGURA,96 A. FIORI,81, 82 I. FIORI,63 M. FISHBACH,191 R. P. FISHER,124 R. FITTIPALDI,199, 133\nV. FIUMARA,200, 133 R. FLAMINIO,31 S. M. FLEISCHER,201 L. S. FLEMING,202 E. FLODEN,18 H. FONG,116 J. A. FONT,139, 140\nF. FONTINELE-NUNES,18 C. FOO,1 B. FORNAL,203 K. FRANCESCHETTI,180 F. FRAPPEZ,31 S. FRASCA,39, 38 F. FRASCONI,81\nJ. P. FREED,66 Z. FREI,204 A. FREISE,37, 108 O. FREITAS,197, 139 R. FREY,78 W. FRISCHHERTZ,64 P. FRITSCHEL,35 V. V. FROLOV,64\nG. G. FRONZ\u00c9,28 M. FUENTES-GARCIA,11 S. FUJII,205 T. FUJIMORI,206 P. FULDA,46 M. FYFFE,64 B. GADRE,72 J. R. GAIR,1\nS. GALAUDAGE,187 V. GALDI,207 R. GAMBA,7 A. GAMBOA,1 S. GAMOJI,182 D. GANAPATHY,208 A. GANGULY,80 B. GARAVENTA,29\nJ. GARC\u00cdA-BELLIDO,209 C. GARC\u00cdA-QUIR\u00d3S,190 J. W. GARDNER,34 K. A. GARDNER,116 S. GARG,42 J. GARGIULO,63 X. GARRIDO,41\nA. GARRON,99 F. GARUFI,32, 4 P. A. GARVER,90 C. GASBARRA,21, 22 B. GATELEY,2 F. GAUTIER,210 V. GAYATHRI,10 T. GAYER,79\nG. GEMME,29 A. GENNAI,81 V. GENNARI,101 J. GEORGE,104 R. GEORGE,149 O. GERBERDING,98 L. GERGELY,155\nARCHISMAN GHOSH,95 SAYANTAN GHOSH,196 SHAON GHOSH,194 SHROBANA GHOSH,8, 9 SUPROVO GHOSH,211 TATHAGATA GHOSH,80\nJ. A. GIAIME,12, 64 K. D. GIARDINA,64 D. R. GIBSON,202 C. GIER,55 S. GKAITATZIS,82, 81 J. GLANZER,11 F. GLOTIN,41 J. GODFREY,78\nR. V. GODLEY,8, 9 P. GODWIN,11 A. S. GOETTEL,33 E. GOETZ,116 J. GOLOMB,11 S. GOMEZ LOPEZ,39, 38 B. GONCHAROV,44\nG. GONZ\u00c1LEZ,12 P. GOODARZI,212 S. GOODE,6 A. W. GOODWIN-JONES,15 M. GOSSELIN,63 R. GOUATY,31 D. W. GOULD,34\nK. GOVORKOVA,35 A. GRADO,77, 51 V. GRAHAM,87 A. E. GRANADOS,18 M. GRANATA,177 V. GRANATA,213, 133 S. GRAS,35\nP. GRASSIA,11 J. GRAVES,57 C. GRAY,2 R. GRAY,87 G. GRECO,51 A. C. GREEN,37, 108 L. GREEN,214 S. M. GREEN,74 S. R. GREEN,215\nC. GREENBERG,134 A. M. GRETARSSON,66 H. K. GRIFFIN,18 D. GRIFFITH,11 H. L. GRIGGS,57 G. GRIGNANI,77, 51 C. GRIMAUD,31\nH. GROTE,33 S. GRUNEWALD,1 D. GUERRA,139 D. GUETTA,216 G. M. GUIDI,61, 62 A. R. GUIMARAES,12 H. K. GULATI,94\nF. GULMINELLI,174, 175 H. GUO,146 W. GUO,73 Y. GUO,37, 36 ANURADHA GUPTA,217 I. GUPTA,7 N. C. GUPTA,94 S. K. GUPTA,46\nV. GUPTA,18 N. GUPTE,1 J. GURS,98 N. GUTIERREZ,177 N. GUTTMAN,6 F. GUZMAN,132 D. HABA,218 M. HABERLAND,1 S. HAINO,219\nE. D. HALL,35 E. Z. HAMILTON,99 G. HAMMOND,87 M. HANEY,37 J. HANKS,2 C. HANNA,7 M. D. HANNAM,33\nO. A. HANNUKSELA,220 A. G. HANSELMAN,131 H. HANSEN,2 J. HANSON,64 S. HANUMASAGAR,57 R. HARADA,42\nA. R. HARDISON,183 S. HARIKUMAR,188 K. HARIS,37, 72 I. HARLEY-TROCHIMCZYK,132 T. HARMARK,135 J. HARMS,44, 45\nG. M. HARRY,221 I. W. HARRY,74 J. HART,105 B. HASKELL,96, 222, 223 C. J. HASTER,214 K. HAUGHIAN,87 H. HAYAKAWA,50\nK. HAYAMA,224 M. C. HEINTZE,64 J. HEINZE,120 J. HEINZEL,35 H. HEITMANN,115 F. HELLMAN,208 A. F. HELMLING-CORNELL,78\nG. HEMMING,63 O. HENDERSON-SAPIR,117 M. HENDRY,87 I. S. HENG,87 M. H. HENNIG,87 C. HENSHAW,57 M. HEURS,8, 9\nA. L. HEWITT,225, 226 J. HEYNEN,15 J. HEYNS,35 S. HIGGINBOTHAM,33 S. HILD,36, 37 S. HILL,87 Y. HIMEMOTO,227 N. HIRATA,25\nC. HIROSE,228 D. HOFMAN,177 B. E. HOGAN,66 N. A. HOLLAND,37, 108 I. J. HOLLOWS,176 D. E. HOLZ,131 L. HONET,113\nD. J. HORTON-BAILEY,208 J. HOUGH,87 S. HOURIHANE,11 N. T. HOWARD,145 E. J. HOWELL,73 C. G. HOY,74 C. A. HRISHIKESH,21\nP. HSI,35 H.-F. HSIEH,143 H.-Y. HSIEH,143 C. HSIUNG,229 S.-H. HSU,147 W.-F. HSU,111 Q. HU,87 H. Y. HUANG,142 Y. HUANG,7\nY. T. HUANG,79 A. D. HUDDART,230 B. HUGHEY,66 V. HUI,31 S. HUSA,99 R. HUXFORD,7 L. IAMPIERI,39, 38 G. A. IANDOLO,36\nM. IANNI,22, 21 G. IANNONE,133 J. IASCAU,78 K. IDE,231 R. IDEN,218 A. IERARDI,44, 45 S. IKEDA,148 H. IMAFUKU,42 Y. INOUE,142\nG. IORIO,92 P. IOSIF,186, 48 M. H. IQBAL,34 J. IRWIN,87 R. ISHIKAWA,231 M. ISI,192, 193 K. S. ISLEIF,232 Y. ITOH,206, 233 M. IWAYA,205\nB. R. IYER,24 C. JACQUET,101 P.-E. JACQUET,123 T. JACQUOT,41 S. J. JADHAV,234 S. P. JADHAV,156 M. JAIN,134 T. JAIN,225\nA. L. JAMES,11 K. JANI,145 J. JANQUART,15 N. N. JANTHALUR,234 S. JARABA,235 P. JARANOWSKI,236 R. JAUME,99 W. JAVED,33\nA. JENNINGS,2 M. JENSEN,2 W. JIA,35 J. JIANG,151 H.-B. JIN,237, 238 G. R. JOHNS,124 N. A. JOHNSON,46 M. C. JOHNSTON,214\nR. JOHNSTON,87 N. JOHNY,8, 9 D. H. JONES,34 D. I. JONES,211 R. JONES,87 H. E. JOSE,78 P. JOSHI,7 S. K. JOSHI,80 G. JOUBERT,56\nJ. JU,239 L. JU,73 K. JUNG,240 J. JUNKER,34 V. JUSTE,113 H. B. KABAGOZ,64, 35 T. KAJITA,241 I. KAKU,206 V. KALOGERA,97\nM. KALOMENOPOULOS,214 M. KAMIIZUMI,50 N. KANDA,233, 206 S. KANDHASAMY,80 G. KANG,242 N. C. KANNACHEL,6\nJ. B. KANNER,11 S. A. KANTIMAHANTY,18 S. J. KAPADIA,80 D. P. KAPASI,54 M. KARTHIKEYAN,134 M. KASPRZACK,11 H. KATO,153\nT. KATO,205 E. KATSAVOUNIDIS,35 W. KATZMAN,64 R. KAUSHIK,104 K. KAWABE,2 R. KAWAMOTO,206 D. KEITEL,99\nL. J. KEMPERMAN,117 J. KENNINGTON,7 F. A. KERKOW,18 R. KESHARWANI,80 J. S. KEY,243 R. KHADELA,8, 9 S. KHADKA,90\nS. S. KHADKIKAR,7 F. Y. KHALILI,109 F. KHAN,8, 9 T. KHANAM,164 M. KHURSHEED,104 N. M. KHUSID,192, 193\nW. KIENDREBEOGO,115, 244 N. KIJBUNCHOO,117 C. KIM,245 J. C. KIM,246 K. KIM,247 M. H. KIM,239 S. KIM,248 Y.-M. KIM,247\nC. KIMBALL,97 K. KIMES,54 M. KINNEAR,33 J. S. KISSEL,2 S. KLIMENKO,46 A. M. KNEE,116 E. J. KNOX,78 N. KNUST,8, 9\nK. KOBAYASHI,205 S. M. KOEHLENBECK,90 G. KOEKOEK,37, 36 K. KOHRI,249, 250 K. KOKEYAMA,33, 251 S. KOLEY,44, 167\nP. KOLITSIDOU,120 A. E. KOLONIARI,252 K. KOMORI,42 A. K. H. KONG,143 A. KONTOS,253 L. M. KOPONEN,120 M. KOROBKO,98\nX. KOU,18 A. KOUSHIK,23 N. KOUVATSOS,68 M. KOVALAM,73 T. KOYAMA,153 D. B. KOZAK,11 S. L. KRANZHOFF,36, 37 V. KRINGEL,8, 9\nN. V. KRISHNENDU,120 S. KROKER,254 A. KR\u00d3LAK,255, 188 K. KRUSKA,8, 9 J. KUBISZ,256 G. KUEHN,8, 9 S. KULKARNI,217\nA. KULUR RAMAMOHAN,34 ACHAL KUMAR,46 ANIL KUMAR,234 PRAVEEN KUMAR,179 PRAYUSH KUMAR,24 RAHUL KUMAR,2\nRAKESH KUMAR,94 J. KUME,257, 258, 42 K. KUNS,35 N. KUNTIMADDI,33 S. KUROYANAGI,209, 259 S. KUWAHARA,42 K. KWAK,240\nK. KWAN,34 S. KWON,42 G. LACAILLE,87 D. LAGHI,190, 101 A. H. LAITY,165 E. LALANDE,260 M. LALLEMAN,23 P. C. LALREMRUATI,261\nM. LANDRY,2 B. B. LANE,35 R. N. LANG,35 J. LANGE,149 R. LANGGIN,214 B. LANTZ,90 I. LA ROSA,99 J. LARSEN,201\nA. LARTAUX-VOLLARD,41 P. D. LASKY,6 J. LAWRENCE,166 M. LAXEN,64 C. LAZARTE,139 A. LAZZARINI,11 C. LAZZARO,158, 157\n\n3\nP. LEACI,39, 38 L. LEALI,18 Y. K. LECOEUCHE,116 H. M. LEE,262 H. W. LEE,263 J. LEE,79 K. LEE,239 R.-K. LEE,143 R. LEE,35\nSUNGHO LEE,247 SUNJAE LEE,239 Y. LEE,142 I. N. LEGRED,11 J. LEHMANN,8, 9 L. LEHNER,184 M. LE JEAN,177, 118 A. LEMA\u00ceTRE,264\nM. LENTI,62, 178 M. LEONARDI,75, 76, 265 M. LEQUIME,40 N. LEROY,41 M. LESOVSKY,11 N. LETENDRE,31 M. LETHUILLIER,56\nY. LEVIN,6 K. LEYDE,74 A. K. Y. LI,11 K. L. LI,266 T. G. F. LI,111 X. LI,150 Y. LI,97 Z. LI,87 A. LIHOS,124 E. T. LIN,143 F. LIN,142\nL. C.-C. LIN,266 Y.-C. LIN,143 C. LINDSAY,202 S. D. LINKER,182 A. LIU,220 G. C. LIU,229 JIAN LIU,73 F. LLAMAS VILLARREAL,166\nJ. LLOBERA-QUEROL,99 R. K. L. LO,141 J.-P. LOCQUET,111 S. C. G. LOGGINS,267 M. R. LOIZOU,134 L. T. LONDON,68 A. LONGO,61, 62\nD. LOPEZ,167 M. LOPEZ PORTILLA,72 M. LORENZINI,21, 22 A. LORENZO-MEDINA,179 V. LORIETTE,41 M. LORMAND,64\nG. LOSURDO,268, 81 E. LOTTI,134 T. P. LOTT IV,57 J. D. LOUGH,8, 9 H. A. LOUGHLIN,35 C. O. LOUSTO,112 N. LOW,125 N. LU,34\nL. LUCCHESI,81 H. L\u00dcCK,9, 8, 9 D. LUMACA,22 A. P. LUNDGREN,269, 270 A. W. LUSSIER,260 R. MACAS,74 M. MACINNIS,35\nD. M. MACLEOD,33 I. A. O. MACMILLAN,11 A. MACQUET,41 K. MAEDA,153 S. MAENAUT,111 S. S. MAGARE,80 R. M. MAGEE,11\nE. MAGGIO,1 R. MAGGIORE,37, 108 M. MAGNOZZI,29, 30 M. MAHESH,98 M. MAINI,165 S. MAJHI,80 E. MAJORANA,39, 38\nC. N. MAKAREM,11 D. MALAKAR,106 J. A. MALAQUIAS-REIS,19 U. MALI,191 S. MALIAKAL,11 A. MALIK,104 L. MALLICK,170, 191\nA.-K. MALZ,59 N. MAN,115 M. MANCARELLA,100 V. MANDIC,18 V. MANGANO,172, 157 B. MANNIX,78 G. L. MANSELL,79\nM. MANSKE,10 M. MANTOVANI,63 M. MAPELLI,92, 93, 271 C. MARINELLI,102 F. MARION,31 A. S. MARKOSYAN,90 A. MARKOWITZ,11\nE. MAROS,11 S. MARSAT,101 F. MARTELLI,61, 62 I. W. MARTIN,87 R. M. MARTIN,194 B. B. MARTINEZ,132 D. A. MARTINEZ,54\nM. MARTINEZ,43, 272 V. MARTINEZ,130 A. MARTINI,75, 76 J. C. MARTINS,19 D. V. MARTYNOV,120 E. J. MARX,35 L. MASSARO,36, 37\nA. MASSEROT,31 M. MASSO-REID,87 S. MASTROGIOVANNI,38 T. MATCOVICH,51 M. MATIUSHECHKINA,8, 9 L. MAURIN,210\nN. MAVALVALA,35 N. MAXWELL,2 G. MCCARROL,64 R. MCCARTHY,2 D. E. MCCLELLAND,34 S. MCCORMICK,64 L. MCCULLER,11\nS. MCEACHIN,124 C. MCELHENNY,124 G. I. MCGHEE,87 J. MCGINN,87 K. B. M. MCGOWAN,145 J. MCIVER,116 A. MCLEOD,73\nI. MCMAHON,190 T. MCRAE,34 R. MCTEAGUE,87 D. MEACHER,10 B. N. MEAGHER,79 R. MECHUM,112 Q. MEIJER,72 A. MELATOS,125\nC. S. MENONI,138 F. MERA,2 R. A. MERCER,10 L. MERENI,177 K. MERFELD,164 E. L. MERILH,64 J. R. M\u00c9ROU,99 J. D. MERRITT,78\nM. MERZOUGUI,115 C. MESSICK,10 B. MESTICHELLI,44 M. MEYER-CONDE,273 F. MEYLAHN,8, 9 A. MHASKE,80 A. MIANI,75, 76\nH. MIAO,274 C. MICHEL,177 Y. MICHIMURA,42 H. MIDDLETON,120 D. P. MIHAYLOV,105 A. L. MILLER,37, 72 S. J. MILLER,11\nM. MILLHOUSE,57 E. MILOTTI,186, 48 V. MILOTTI,92 Y. MINENKOV,22 E. M. MINIHAN,66 LL. M. MIR,43 L. MIRASOLA,157, 158\nM. MIRAVET-TEN\u00c9S,139 C.-A. MIRITESCU,43 A. MISHRA,24 C. MISHRA,107 T. MISHRA,46 A. L. MITCHELL,37, 108 J. G. MITCHELL,66\nS. MITRA,80 V. P. MITROFANOV,109 K. MITSUHASHI,25 R. MITTLEMAN,35 O. MIYAKAWA,50 S. MIYOKI,50 A. MIYOKO,66 G. MO,35\nL. MOBILIA,61, 62 S. R. P. MOHAPATRA,11 S. R. MOHITE,7 M. MOLINA-RUIZ,208 M. MONDIN,182 M. MONTANI,61, 62 C. J. MOORE,225\nD. MORARU,2 A. MORE,80 S. MORE,80 C. MORENO,136 E. A. MORENO,35 G. MORENO,2 A. MORESO SERRA,83 S. MORISAKI,42, 205\nY. MORIWAKI,153 G. MORRAS,209 A. MOSCATELLO,92 M. MOULD,35 B. MOURS,65 C. M. MOW-LOWRY,37, 108 L. MUCCILLO,178, 62\nF. MUCIACCIA,39, 38 D. MUKHERJEE,120 SAMANWAYA MUKHERJEE,24 SOMA MUKHERJEE,166 SUBROTO MUKHERJEE,94\nSUVODIP MUKHERJEE,13 N. MUKUND,35 A. MULLAVEY,64 H. MULLOCK,116 J. MUNDI,221 C. L. MUNGIOLI,73 M. MURAKOSHI,231\nP. G. MURRAY,87 D. NABARI,75, 76 S. L. NADJI,8, 9 A. NAGAR,28, 275 N. NAGARAJAN,87 K. NAKAGAKI,50 K. NAKAMURA,25\nH. NAKANO,276 M. NAKANO,11 D. NANADOUMGAR-LACROZE,43 D. NANDI,12 V. NAPOLANO,63 P. NARAYAN,217 I. NARDECCHIA,22\nT. NARIKAWA,205 H. NAROLA,72 L. NATICCHIONI,38 R. K. NAYAK,261 L. NEGRI,72 A. NELA,87 C. NELLE,78 A. NELSON,132\nT. J. N. NELSON,64 M. NERY,8, 9 A. NEUNZERT,2 S. NG,54 L. NGUYEN QUYNH,277 S. A. NICHOLS,12 A. B. NIELSEN,278\nY. NISHINO,25, 42 A. NISHIZAWA,279 S. NISSANKE,280, 37 W. NIU,7 F. NOCERA,63 J. NOLLER,281 M. NORMAN,33 C. NORTH,33\nJ. NOVAK,118, 235, 282 R. NOWICKI,145 J. F. NU\u00d1O SILES,209 L. K. NUTTALL,74 K. OBAYASHI,231 J. OBERLING,2 J. O\u2019DELL,230\nE. OELKER,35 M. OERTEL,235, 118, 283, 282 G. OGANESYAN,44, 45 T. O\u2019HANLON,64 M. OHASHI,50 F. OHME,8, 9 R. OLIVERI,118, 283, 282\nR. OMER,18 B. O\u2019NEAL,124 M. ONISHI,153 K. OOHARA,284 B. O\u2019REILLY,64 M. ORSELLI,51, 77 R. O\u2019SHAUGHNESSY,112 S. O\u2019SHEA,87\nS. OSHINO,50 C. OSTHELDER,11 I. OTA,12 D. J. OTTAWAY,117 A. OUZRIAT,56 H. OVERMIER,64 B. J. OWEN,285 R. OZAKI,231\nA. E. PACE,7 R. PAGANO,12 M. A. PAGE,25 A. PAI,196 L. PAIELLA,44 A. PAL,286 S. PAL,261 M. A. PALAIA,81, 82 M. P\u00c1LFI,204\nP. P. PALMA,39, 21, 22 C. PALOMBA,38 P. PALUD,20 H. PAN,143 J. PAN,73 K. C. PAN,143 P. K. PANDA,234 SHIKSHA PANDEY,7\nSWADHA PANDEY,35 P. T. H. PANG,37, 72 F. PANNARALE,39, 38 K. A. PANNONE,54 B. C. PANT,104 F. H. PANTHER,73 M. PANZERI,61, 62\nF. PAOLETTI,81 A. PAOLONE,38, 287 A. PAPADOPOULOS,87 E. E. PAPALEXAKIS,212 L. PAPALINI,81, 82 G. PAPIGKIOTIS,252 A. PAQUIS,41\nA. PARISI,77, 51 B.-J. PARK,247 J. PARK,288 W. PARKER,64 G. PASCALE,8, 9 D. PASCUCCI,95 A. PASQUALETTI,63 R. PASSAQUIETI,82, 81\nL. PASSENGER,6 D. PASSUELLO,81 O. PATANE,2 A. V. PATEL,142 D. PATHAK,80 A. PATRA,33 B. PATRICELLI,82, 81 B. G. PATTERSON,33\nK. PAUL,107 S. PAUL,78 E. PAYNE,11 T. PEARCE,33 M. PEDRAZA,11 A. PELE,11 F. E. PE\u00d1A ARELLANO,289 X. PENG,120 Y. PENG,57\nS. PENN,290 M. D. PENULIAR,54 A. PEREGO,75, 76 Z. PEREIRA,134 C. P\u00c9RIGOIS,291, 93, 92 G. PERNA,92 A. PERRECA,75, 76, 44 J. PERRET,20\nS. PERRI\u00c8S,56 J. W. PERRY,37, 108 D. PESIOS,252 S. PETERS,167 S. PETRACCA,207 C. PETRILLO,77 H. P. PFEIFFER,1 H. PHAM,64\nK. A. PHAM,18 K. S. PHUKON,120 H. PHURAILATPAM,220 M. PIARULLI,101 L. PICCARI,39, 38 O. J. PICCINNI,34 M. PICHOT,115\nM. PIENDIBENE,82, 81 F. PIERGIOVANNI,61, 62 L. PIERINI,38 G. PIERRA,38 V. PIERRO,292, 133 M. PIETRZAK,96 M. PILLAS,167 F. PILO,81\nL. PINARD,177 I. M. PINTO,292, 133, 293, 32 M. PINTO,63 B. J. PIOTRZKOWSKI,10 M. PIRELLO,2 M. D. PITKIN,225, 87 A. PLACIDI,51\nE. PLACIDI,39, 38 M. L. PLANAS,99 W. PLASTINO,213, 22 C. PLUNKETT,35 R. POGGIANI,82, 81 E. POLINI,35 J. POMPER,81, 82 L. POMPILI,1\nJ. POON,220 E. PORCELLI,37 E. K. PORTER,20 C. POSNANSKY,7 R. POULTON,63 J. POWELL,156 G. S. PRABHU,80 M. PRACCHIA,167\nB. K. PRADHAN,80 T. PRADIER,65 A. K. PRAJAPATI,94 K. PRASAI,294 R. PRASANNA,234 P. PRASIA,80 G. PRATTEN,120\nG. PRINCIPE,186, 48 G. A. PRODI,75, 76 P. PROSPERI,81 P. PROSPOSITO,21, 22 A. C. PROVIDENCE,66 A. PUECHER,1 J. PULLIN,12\nP. PUPPO,38 M. P\u00dcRRER,165 H. QI,16 J. QIN,34 G. QU\u00c9M\u00c9NER,175, 118 V. QUETSCHKE,166 P. J. QUINONEZ,66 N. QUTOB,57\nR. RADING,232 P. RAFFAI,295 I. RAINHO,139 S. RAJA,104 C. RAJAN,104 B. RAJBHANDARI,112 K. E. RAMIREZ,64 F. A. RAMIS VIDAL,99\nM. RAMOS AREVALO,166 A. RAMOS-BUADES,99, 37 S. RANJAN,57 K. RANSOM,64 P. RAPAGNANI,39, 38 B. RATTO,66\nA. RAVICHANDRAN,134 A. RAY,97 V. RAYMOND,33 M. RAZZANO,82, 81 J. READ,54 T. REGIMBAU,31 S. REID,55 C. REISSEL,35\nD. H. REITZE,11 A. I. RENZINI,11, 128 B. REVENU,296, 41 A. REVILLA PE\u00d1A,83 R. REYES,182 L. RICCA,15 F. RICCI,39, 38 M. RICCI,38, 39\nA. RICCIARDONE,82, 81 J. RICE,79 J. W. RICHARDSON,212 M. L. RICHARDSON,117 A. RIJAL,66 K. RILES,91 H. K. RILEY,33\nS. RINALDI,271 J. RITTMEYER,98 C. ROBERTSON,230 F. ROBINET,41 M. ROBINSON,2 A. ROCCHI,22 L. ROLLAND,31 J. G. ROLLINS,297\nR. ROMANO,3, 4 A. ROMERO,31 I. M. ROMERO-SHAW,225 J. H. ROMIE,64 S. RONCHINI,7 T. J. ROOCKE,117 L. ROSA,4, 32\n\n4\nT. J. ROSAUER,212 C. A. ROSE,57 D. ROSI \u00b4NSKA,126 M. P. ROSS,53 M. ROSSELLO-SASTRE,99 S. ROWAN,87 S. K. ROY,192, 193 S. ROY,15\nD. ROZZA,128, 129 P. RUGGI,63 N. RUHAMA,240 E. RUIZ MORALES,298, 209 K. RUIZ-ROCHA,145 S. SACHDEV,57 T. SADECKI,2\nP. SAFFARIEH,37, 108 S. SAFI-HARB,170 M. R. SAH,13 S. SAHA,143 T. SAINRAT,65 S. SAJITH MENON,216, 39, 38 K. SAKAI,299 Y. SAKAI,273\nM. SAKELLARIADOU,68 S. SAKON,7 O. S. SALAFIA,160, 129, 128 F. SALCES-CARCOBA,11 L. SALCONI,63 M. SALEEM,149 F. SALEMI,39, 38\nM. SALL\u00c9,37 S. U. SALUNKHE,80 S. SALVADOR,175, 174 A. SALVARESE,149 A. SAMAJDAR,72, 37 A. SANCHEZ,2 E. J. SANCHEZ,11\nL. E. SANCHEZ,11 N. SANCHIS-GUAL,139 J. R. SANDERS,183 E. M. S\u00c4NGER,1 F. SANTOLIQUIDO,44, 45 F. SARANDREA,28\nT. R. SARAVANAN,80 N. SARIN,6 P. SARKAR,8, 9 A. SASLI,252 P. SASSI,51, 77 B. SASSOLAS,177 B. S. SATHYAPRAKASH,7, 33 R. SATO,228\nS. SATO,153 YUKINO SATO,153 YU SATO,153 O. SAUTER,46 R. L. SAVAGE,2 T. SAWADA,50 H. L. SAWANT,80 S. SAYAH,177\nV. SCACCO,21, 22 D. SCHAETZL,11 M. SCHEEL,150 A. SCHIEBELBEIN,191 M. G. SCHIWORSKI,79 P. SCHMIDT,120 S. SCHMIDT,72\nR. SCHNABEL,98 M. SCHNEEWIND,8, 9 R. M. S. SCHOFIELD,78 K. SCHOUTEDEN,111 B. W. SCHULTE,8, 9 B. F. SCHUTZ,33, 8, 9\nE. SCHWARTZ,300 M. SCIALPI,301 J. SCOTT,87 S. M. SCOTT,34 R. M. SEDAS,64 T. C. SEETHARAMU,87 M. SEGLAR-ARROYO,43\nY. SEKIGUCHI,302 D. SELLERS,64 N. SEMBO,206 A. S. SENGUPTA,303 E. G. SEO,87 J. W. SEO,111 V. SEQUINO,32, 4 M. SERRA,38\nA. SEVRIN,189 T. SHAFFER,2 U. S. SHAH,57 M. A. SHAIKH,262 L. SHAO,304 A. K. SHARMA,99 PREETI SHARMA,12\nPRIANKA SHARMA,104 RITWIK SHARMA,18 S. SHARMA CHAUDHARY,106 P. SHAWHAN,127 N. S. SHCHEBLANOV,305, 264\nE. SHERIDAN,145 Z.-H. SHI,143 M. SHIKAUCHI,42 R. SHIMOMURA,306 H. SHINKAI,306 S. SHIRKE,80 D. H. SHOEMAKER,35\nD. M. SHOEMAKER,149 R. W. SHORT,2 S. SHYAMSUNDAR,104 A. SIDER,159 H. SIEGEL,192, 193 D. SIGG,2 L. SILENZI,36, 37\nL. SILVESTRI,39, 171 M. SIMMONDS,117 L. P. SINGER,307 AMITESH SINGH,217 ANIKA SINGH,11 D. SINGH,208 N. SINGH,99\nS. SINGH,218, 60 A. M. SINTES,99 V. SIPALA,172, 157 V. SKLIRIS,33 B. J. J. SLAGMOLEN,34 D. A. SLATER,201 T. J. SLAVEN-BLAIR,73\nJ. SMETANA,120 J. R. SMITH,54 L. SMITH,87, 186, 48 R. J. E. SMITH,6 W. J. SMITH,145 S. SOARES DE ALBUQUERQUE FILHO,61\nM. SOARES-SANTOS,190 K. SOMIYA,218 I. SONG,143 S. SONI,35 V. SORDINI,56 F. SORRENTINO,29 H. SOTANI,308 F. SPADA,81\nV. SPAGNUOLO,37 A. P. SPENCER,87 P. SPINICELLI,63 A. K. SRIVASTAVA,94 F. STACHURSKI,87 C. J. STARK,124 D. A. STEER,309\nN. STEINLE,170 J. STEINLECHNER,36, 37 S. STEINLECHNER,36, 37 N. STERGIOULAS,252 P. STEVENS,41 S. P. STEVENSON,156\nM. STPIERRE,165 M. D. STRONG,12 A. STRUNK,2 A. L. STUVER,103, \u2217M. SUCHENEK,96 S. SUDHAGAR,96 Y. SUDO,231\nN. SUELTMANN,98 L. SULEIMAN,54 K. D. SULLIVAN,12 J. SUN,242 L. SUN,34 S. SUNIL,94 J. SURESH,115 B. J. SUTTON,68\nP. J. SUTTON,33 K. SUZUKI,218 M. SUZUKI,205 B. L. SWINKELS,37 A. SYX,118 M. J. SZCZEPA \u00b4NCZYK,310 P. SZEWCZYK,126\nM. TACCA,37 H. TAGOSHI,205 K. TAKADA,205 H. TAKAHASHI,273 R. TAKAHASHI,25 A. TAKAMORI,42 S. TAKANO,311\nH. TAKEDA,312, 313 K. TAKESHITA,218 I. TAKIMOTO SCHMIEGELOW,44, 45 M. TAKOU-AYAOH,79 C. TALBOT,131 M. TAMAKI,205\nN. TAMANINI,101 D. TANABE,142 K. TANAKA,50 S. J. TANAKA,231 S. TANIOKA,33 D. B. TANNER,46 W. TANNER,8, 9 L. TAO,212\nR. D. TAPIA,7 E. N. TAPIA SAN MART\u00cdN,37 C. TARANTO,21, 22 A. TARUYA,314 J. D. TASSON,154 J. G. TAU,112 D. TELLEZ,54\nR. TENORIO,99 H. THEMANN,182 A. THEODOROPOULOS,139 M. P. THIRUGNANASAMBANDAM,80 L. M. THOMAS,11 M. THOMAS,64\nP. THOMAS,2 J. E. THOMPSON,211 S. R. THONDAPU,104 K. A. THORNE,64 E. THRANE,6 J. TISSINO,44, 45 A. TIWARI,80\nPAWAN TIWARI,44 PRAVEER TIWARI,196 S. TIWARI,190 V. TIWARI,120 M. R. TODD,79 M. TOFFANO,92 A. M. TOIVONEN,18\nK. TOLAND,87 A. E. TOLLEY,74 T. TOMARU,25 V. TOMMASINI,11 T. TOMURA,50 H. TONG,6 C. TONG-YU,142\nA. TORRES-FORN\u00c9,139, 140 C. I. TORRIE,11 I. TOSTA E MELO,315 E. TOURNEFIER,31 M. TRAD NERY,115 K. TRAN,124\nA. TRAPANANTI,52, 51 R. TRAVAGLINI,169 F. TRAVASSO,52, 51 G. TRAYLOR,64 M. TREVOR,127 M. C. TRINGALI,63 A. TRIPATHEE,91\nG. TROIAN,186, 48 A. TROVATO,186, 48 L. TROZZO,4 R. J. TRUDEAU,11 T. TSANG,33 S. TSUCHIDA,316 L. TSUKADA,214\nK. TURBANG,189, 23 M. TURCONI,115 C. TURSKI,95 H. UBACH,83, 84 N. UCHIKATA,205 T. UCHIYAMA,50 R. P. UDALL,11 T. UEHARA,317\nK. UENO,42 V. UNDHEIM,278 L. E. URONEN,220 T. USHIBA,50 M. VACATELLO,81, 82 H. VAHLBRUCH,8, 9 N. VAIDYA,11 G. VAJENTE,11\nA. VAJPEYI,6 J. VALENCIA,99 M. VALENTINI,108, 37 S. A. VALLEJO-PE\u00d1A,318 S. VALLERO,28 V. VALSAN,10 M. VAN DAEL,37, 319\nE. VAN DEN BOSSCHE,189 J. F. J. VAN DEN BRAND,36, 108, 37 C. VAN DEN BROECK,72, 37 M. VAN DER SLUYS,37, 72 A. VAN DE WALLE,41\nJ. VAN DONGEN,37, 108 K. VANDRA,103 M. VANDYKE,121 H. VAN HAEVERMAET,23 J. V. VAN HEIJNINGEN,37, 108 P. VAN HOVE,65\nJ. VANIER,260 M. VANKEUREN,105 J. VANOSKY,2 N. VAN REMORTEL,23 M. VARDARO,36, 37 A. F. VARGAS,125 V. VARMA,134\nA. N. VAZQUEZ,90 A. VECCHIO,120 G. VEDOVATO,93 J. VEITCH,87 P. J. VEITCH,117 S. VENIKOUDIS,15 R. C. VENTEREA,18\nP. VERDIER,56 M. VEREECKEN,15 D. VERKINDT,31 B. VERMA,134 Y. VERMA,104 S. M. VERMEULEN,11 F. VETRANO,61\nA. VEUTRO,38, 39 A. VICER\u00c9,61, 62 S. VIDYANT,79 A. D. VIETS,89 A. VIJAYKUMAR,191 A. VILKHA,112 N. VILLANUEVA ESPINOSA,139\nV. VILLA-ORTEGA,179 E. T. VINCENT,57 J.-Y. VINET,115 S. VIRET,56 S. VITALE,35 H. VOCCA,77, 51 D. VOIGT,98 E. R. G. VON REIS,2\nJ. S. A. VON WRANGEL,8, 9 W. E. VOSSIUS,232 L. VUJEVA,141 S. P. VYATCHANIN,109 J. WACK,11 L. E. WADE,105 M. WADE,105\nK. J. WAGNER,112 L. WALLACE,11 E. J. WANG,90 H. WANG,218 J. Z. WANG,91 W. H. WANG,166 Y. F. WANG,1 G. WARATKAR,196\nJ. WARNER,2 M. WAS,31 T. WASHIMI,25 N. Y. WASHINGTON,11 D. WATARAI,42 B. WEAVER,2 S. A. WEBSTER,87\nN. L. WEICKHARDT,98 M. WEINERT,8, 9 A. J. WEINSTEIN,11 R. WEISS,35 L. WEN,73 K. WETTE,34 J. T. WHELAN,112 B. F. WHITING,46\nC. WHITTLE,11 E. G. WICKENS,74 D. WILKEN,8, 9, 9 A. T. WILKIN,212 B. M. WILLIAMS,121 D. WILLIAMS,87 M. J. WILLIAMS,74\nN. S. WILLIAMS,1 J. L. WILLIS,11 B. WILLKE,9, 8, 9 M. WILS,111 L. WILSON,105 C. W. WINBORN,106 J. WINTERFLOOD,73\nC. C. WIPF,11 G. WOAN,87 J. WOEHLER,36, 37 N. E. WOLFE,35 H. T. WONG,142 I. C. F. WONG,220, 111 K. WONG,191 T. WOUTERS,72, 37\nJ. L. WRIGHT,2 M. WRIGHT,87, 72 B. WU,79 C. WU,143 D. S. WU,8, 9 H. WU,143 K. WU,121 Q. WU,53 Y. WU,97 Z. WU,101\nE. WUCHNER,54 D. M. WYSOCKI,10 V. A. XU,208 Y. XU,99 N. YADAV,28 H. YAMAMOTO,11 K. YAMAMOTO,153 T. S. YAMAMOTO,42\nT. YAMAMOTO,50 R. YAMAZAKI,231 T. YAN,120 K. Z. YANG,18 Y. YANG,147 Z. YARBROUGH,12 J. YEBANA,99 S.-W. YEH,143\nA. B. YELIKAR,145 X. YIN,35 J. YOKOYAMA,320, 42 T. YOKOZAWA,50 S. YUAN,73 H. YUZURIHARA,50 M. ZANOLIN,66 M. ZEESHAN,112\nT. ZELENOVA,63 J.-P. ZENDRI,93 M. ZEOLI,15 M. ZERRAD,40 M. ZEVIN,97 L. ZHANG,11 N. ZHANG,57 R. ZHANG,151 T. ZHANG,120\nC. ZHAO,73 YUE ZHAO,163 YUHANG ZHAO,20 Z.-C. ZHAO,321 Y. ZHENG,106 H. ZHONG,18 H. ZHOU,79 H. O. ZHU,73 Z.-H. ZHU,321, 322\nA. B. ZIMMERMAN,149 L. ZIMMERMANN,56 M. E. ZUCKER,35, 11 J. ZWEIZIG,11\nTHE LIGO SCIENTIFIC COLLABORATION, THE VIRGO COLLABORATION, AND THE KAGRA COLLABORATION\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n\n5\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00e9orique, Aix-Marseille Universit\u00e9, Campus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n20Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, 64849 Monterrey, Nuevo Le\u00f3n, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Chennai Mathematical Institute, Chennai 603103, India\n\n6\n59Royal Holloway, University of London, London TW20 0EX, United Kingdom\n60Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n61Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n62INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n63European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n64LIGO Livingston Observatory, Livingston, LA 70754, USA\n65Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n66Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n67Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n68King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n69Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n70International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n71Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n72Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n73OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n74University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n75Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n76INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n77Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n81INFN, Sezione di Pisa, I-56127 Pisa, Italy\n82Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n83Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n84Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n85Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n86Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n87IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n88HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n89Concordia University Wisconsin, Mequon, WI 53097, USA\n90Stanford University, Stanford, CA 94305, USA\n91University of Michigan, Ann Arbor, MI 48109, USA\n92Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n93INFN, Sezione di Padova, I-35131 Padova, Italy\n94Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n95Universiteit Gent, B-9000 Gent, Belgium\n96Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n97Northwestern University, Evanston, IL 60208, USA\n98Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n99IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n100Aix-Marseille Universit\u00e9, Universit\u00e9 de Toulon, CNRS, CPT, Marseille, France\n101Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n102Universit\u00e0 di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n103Villanova University, Villanova, PA 19085, USA\n104RRCAT, Indore, Madhya Pradesh 452013, India\n105Kenyon College, Gambier, OH 43022, USA\n106Missouri University of Science and Technology, Rolla, MO 65409, USA\n107Indian Institute of Technology Madras, Chennai 600036, India\n108Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n109Lomonosov Moscow State University, Moscow 119991, Russia\n110Center for Theoretical Physics of the Polish Academy of Sciences, al. Lotnik\u2019ow 32/46, 02-668, Warsaw, Poland\n111Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n112Rochester Institute of Technology, Rochester, NY 14623, USA\n113Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n114Bar-Ilan University, Ramat Gan, 5290002, Israel\n115Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n\n7\n116University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n117OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n118Centre national de la recherche scientifique, 75016 Paris, France\n119Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n120University of Birmingham, Birmingham B15 2TT, United Kingdom\n121Washington State University, Pullman, WA 99164, USA\n122Cornell University, Ithaca, NY 14850, USA\n123Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n124Christopher Newport University, Newport News, VA 23606, USA\n125OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n126Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n127University of Maryland, College Park, MD 20742, USA\n128Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n129INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n130Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n131University of Chicago, Chicago, IL 60637, USA\n132University of Arizona, Tucson, AZ 85721, USA\n133INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n134University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n135Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n136Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n137Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n138Colorado State University, Fort Collins, CO 80523, USA\n139Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n140Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n141Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n142National Central University, Taoyuan City 320317, Taiwan\n143National Tsing Hua University, Hsinchu City 30013, Taiwan\n144OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n145Vanderbilt University, Nashville, TN 37235, USA\n146University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n147Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n148Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n149University of Texas, Austin, TX 78712, USA\n150CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n151Northeastern University, Boston, MA 02115, USA\n152Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n153Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n154Carleton College, Northfield, MN 55057, USA\n155University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n156OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n157INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n158Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n159Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n160INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n161Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n162Montana State University, Bozeman, MT 59717, USA\n163The University of Utah, Salt Lake City, UT 84112, USA\n164Johns Hopkins University, Baltimore, MD 21218, USA\n165University of Rhode Island, Kingston, RI 02881, USA\n166The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n167Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n168DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n169Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n170University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n171INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n172Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n\n8\n173INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n174Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n175Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n176The University of Sheffield, Sheffield S10 2TN, United Kingdom\n177Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n178Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n179IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n180Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n181INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n182California State University, Los Angeles, Los Angeles, CA 90032, USA\n183Marquette University, Milwaukee, WI 53233, USA\n184Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n185Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n186Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n187Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n188National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n189Vrije Universiteit Brussel, 1050 Brussel, Belgium\n190University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n191Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n192Stony Brook University, Stony Brook, NY 11794, USA\n193Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n194Montclair State University, Montclair, NJ 07043, USA\n195HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n196Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n197Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n198Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n199CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n200Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n201Western Washington University, Bellingham, WA 98225, USA\n202SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n203Barry University, Miami Shores, FL 33168, USA\n204E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n205Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n206Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585,\nJapan\n207University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n208University of California, Berkeley, CA 94720, USA\n209Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n210Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212University of California, Riverside, Riverside, CA 92521, USA\n213Dipartimento di Ingegneria Industriale, Elettronica e Meccanica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n214University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n215University of Nottingham NG7 2RD, UK\n216Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n217The University of Mississippi, University, MS 38677, USA\n218Graduate School of Science, Institute of Science Tokyo, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n219Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n220The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n221American University, Washington, DC 20016, USA\n222Dipartimento di Fisica, Universit\u00e0 degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n223INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n224Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n225University of Cambridge, Cambridge CB2 1TN, United Kingdom\n226University of Lancaster, Lancaster LA1 4YW, United Kingdom\n227College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n228Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n\n9\n229Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n230Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n231Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n232Helmut Schmidt University, D-22043 Hamburg, Germany\n233Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n236Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n237National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n238School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Department of Physics, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n241Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n242Chung-Ang University, Seoul 06974, Republic of Korea\n243University of Washington Bothell, Bothell, WA 98011, USA\n244Laboratoire de Physique et de Chimie de l\u2019Environnement, Universit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n245Ewha Womans University, Seoul 03760, Republic of Korea\n246National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n247Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n248Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n249Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n250Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n251Nagoya University, Nagoya, 464-8601, Japan\n252Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n253Bard College, Annandale-On-Hudson, NY 12504, USA\n254Technical University of Braunschweig, D-38106 Braunschweig, Germany\n255Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n256Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n257Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n258Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n259Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n260Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n261Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n262Seoul National University, Seoul 08826, Republic of Korea\n263Department of Computer Simulation, Inje University, 197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n264NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n265Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n266Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, E-08010 Barcelona, Spain\n270Institut de F\u00edsica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg, Universitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA), Passeig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa\n224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n278University of Stavanger, 4021 Stavanger, Norway\n279Physics Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima\n739-8526, Japan\n280GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n281University College London, London WC1E 6BT, United Kingdom\n282Observatoire de Paris, 75014 Paris, France\n\n10\n283Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n284Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n289Department of Physics, University of Guadalajara, Av. Revolucion 1500, Colonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n290Hobart and William Smith Colleges, Geneva, NY 14456, USA\n291INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n292Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Kennesaw State University, Kennesaw, GA 30144, USA\n295Eotvos University, Budapest 1117, Hungary\n296Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9, 4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n297LIGO Laboratory, California Institrenziniute of Technology, Pasadena, CA 91125, USA\n298Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n299Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n300Trinity College, Hartford, CT 06106, USA\n301Dipartimento di Fisica e Scienze della Terra, Universit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n302Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n303Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n304Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n305Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n306Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n307NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n308Faculty of Science and Technology, Kochi University, 2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n309Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS, Universit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n310Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n311Laser Interferometry and Gravitational Wave Astronomy, Max Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n312The Hakubi Center for Advanced Research, Kyoto University, Yoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n313Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n314Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n315University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n316National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n317Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n318Universidad de Antioquia, Medell\u00edn, Colombia\n319Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n320Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8583, Japan\n321Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n322School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nABSTRACT\nWe analyze data from 142 of the 218 gravitational-wave (GW) sources in the fourth LIGO\u2013Virgo\u2013KAGRA\nCollaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-4.0) to estimate the Hubble constant H0\njointly with the population properties of merging compact binaries. We measure the luminosity distance and\nredshifted masses of GW sources directly; in contrast, we infer GW source redshifts statistically through i)\nlocation of features in the compact object mass spectrum and merger rate evolution, and ii) identifying potential\nhost galaxies in the GW localization volume. Probing the relationship between source luminosity distances and\nredshifts obtained in this way yields constraints on cosmological parameters. We also constrain parameterized\ndeviations from general relativity which affect GW propagation, specifically those modifying the dependence\nof a GW signal on the source luminosity distance. Assuming our fiducial model for the source-frame mass\ndistribution and using GW candidates detected up to the end of the fourth observing run (O4a), together with\nthe GLADE+ all-sky galaxy catalog, we estimate H0 = 76.6+13.0\n\u22129.5 (76.6+25.2\n\u221214.0) km s\u22121 Mpc\u22121. This value is\nreported as a median with 68.3% (90%) symmetric credible interval, and includes combination with the H0\nmeasurement from GW170817 and its electromagnetic counterpart. Using a parametrization of modified GW\n\n11\npropagation in terms of the magnitude parameter \u039e0, we estimate \u039e0 = 1.2+0.8\n\u22120.4 (1.2+2.4\n\u22120.5), where \u039e0 = 1\nrecovers the behavior of general relativity.\nKeywords: Gravitational wave astronomy (675) \u2013 Gravitational wave sources (677) \u2013 Hubble constant (758) \u2013\nObservational cosmology (1146)\n1. INTRODUCTION\nObtaining independent measurements of the Hubble constant\n(H0) is a major focus of gravitational-wave (GW) cosmol-\nogy, driven by the existing discrepancy between early Uni-\nverse measurements from the cosmic microwave background\n(CMB) radiation and local measurements from standardiz-\nable sources such as Type Ia supernovae (SNe Ia).\nMea-\nsurements of H0 made by the Planck Collaboration in the\nPlanck 2018 Data Release (Aghanim et al. 2020) and the Su-\npernovae H0 for the Equation of State (SH0ES) project with\nthe recalibration of supernovae by Large Magellanic Cloud\nCepheids (Riess et al. 2022) have now reached an \u223c8% dis-\ncrepancy with \u22735\u03c3 credibility, although other local mea-\nsurements, including alternative methods of calibrating the\ndistance ladder, suggest a smaller tension (e.g., Di Valentino\n& Brout 2024).\nThe possibility of using GW detections to infer cosmolog-\nical parameters, such as H0, was first proposed by Schutz\n(1986).\nGWs from compact binary coalescences (CBCs)\nserve as standard sirens (Holz & Hughes 2005), providing\na self-calibrated measure of luminosity distance that is in-\ndependent of traditional methods such as the cosmic dis-\ntance ladder. If combined with redshift information, GWs\ncan be used as probes of the luminosity distance-redshift\nrelation, which depends on the cosmological model and\nits parameters.\nIn this way GW sources may help to re-\nsolve the H0 discrepancy, and can also provide insights\ninto possible new physics beyond the standard Lambda\ncold dark matter (\u039bCDM) cosmological model (Bull et al.\n2016; Perivolaropoulos & Skara 2022; Abdalla et al. 2022;\nDi Valentino et al. 2025).\nHowever, the redshift of a CBC source cannot be deter-\nmined from the GW signal itself due to its degeneracy with\nthe binary source masses (Krolak & Schutz 1987).\nSev-\neral methods have been proposed to break this degeneracy.\nIf a counterpart in the electromagnetic (EM) spectrum can\nbe uniquely associated to the GW event, the redshift of the\ngalaxy host can be determined via astronomical photome-\ntry or spectroscopy (Holz & Hughes 2005; Dalal et al. 2006;\nNissanke et al. 2010, 2013a; Abbott et al. 2017a; Chen et al.\n2018; Feeney et al. 2019): we will refer to such an event\nas a bright siren. The only bright siren observed to date is\nthe binary neutron star (BNS) merger GW170817 (Abbott\net al. 2017b), which, combined with coincident EM tran-\nsients associated with the host galaxy NGC 4993 (Abbott\net al. 2017c), provided the first bright standard siren mea-\n\u2217Deceased, September 2024.\nsurement of H0 (Abbott et al. 2017a). While we are waiting\nfor the next bright siren event, the steady increase of detec-\ntions from binary black hole (BBH), neutron star\u2013black hole\nbinary (NSBH) and other BNS candidates without confident\nEM counterparts has driven forward other methods to mea-\nsure H0.\nOne approach relies on the presence of features in the\nmass spectrum of binary compact objects to break the mass-\nredshift degeneracy (Chernoff & Finn 1993; Markovic 1993;\nTaylor et al. 2012; Farr et al. 2019; You et al. 2021; Mastro-\ngiovanni et al. 2021; Ezquiaga & Holz 2021, 2022), a method\nwe will refer to as the spectral siren method (also sometimes\ncalled the population method). By making some assumptions\nabout the source-frame mass distribution of CBCs, the cos-\nmological parameters are sampled together with a set of pop-\nulation parameters describing the source-frame mass distri-\nbution and the CBC merger rate (distributions of other CBC\nparameters, such as spins, may be included). This method\nhas been applied in Abbott et al. (2023a) to the BBH can-\ndidates reported in the Gravitational-Wave Transient Cata-\nlog (GWTC) 3.0 (Abbott et al. 2021b).\nA second approach consists of supplementing the spec-\ntral siren method with additional redshift information from\ngalaxy surveys (Schutz 1986; MacLeod & Hogan 2008;\nDel Pozzo 2012; Nishizawa 2017; Fishbach et al. 2019;\nSoares-Santos et al. 2019; Gray et al. 2020; Palmese et al.\n2020; Abbott et al. 2021a; Finke et al. 2021a; Abbott et al.\n2023a; Gair et al. 2023; Borghi et al. 2024; Bom et al. 2024).\nWe will refer to this as the dark siren method (also called\ngalaxy catalog method, or galaxy host identification method)\nAlternative approaches to infer the source redshift, which\nwe will not consider in this work, take advantage of the\ncross-correlation between the spatial distribution of GWs and\ngalaxies (Camera & Nishizawa 2013; Oguri 2016; Mukher-\njee et al. 2020, 2021b, 2024; Afroz & Mukherjee 2024; Fon-\nseca et al. 2023; Zazzera et al. 2025; Ferri et al. 2024; Pedrotti\net al. 2025), the adoption of theoretical priors on the merger-\nredshift distributions (Ding et al. 2019; Ye & Fishbach 2021),\nand the use of tidal distortions of neutron stars (NSs) (Mes-\nsenger & Read 2012; Del Pozzo et al. 2017; Chatterjee et al.\n2021).\nIn previous LIGO\u2013Virgo\u2013KAGRA Collaboration (LVK)\nanalyses, it was possible to apply the dark siren method\nto GWs only by fixing the population parameters to some\nfiducial values, due to the computational challenges of sam-\npling the cosmological and population parameter space to-\ngether with highly structured redshift information coming\nfrom a galaxy catalog. However, as shown in Abbott et al.\n(2023a), this made the results strongly dependent on the\n\n12\nassumed BBH source mass distribution parameters. These\nchallenges have recently been overcome in the latest version\nof the codes used by the LVK, gwcosmo 3.0 (Gray et al.\n2020, 2022, 2023) and icarogw 2.0 (Mastrogiovanni et al.\n2023, 2024), from hereon simply referred to as gwcosmo\nand icarogw. Both codes now implement the dark siren\nmethod allowing marginalization over the GW population\nparameters, while incorporating galaxy catalog information.\nBy applying this new method to the full set of publicly avail-\nable LVK GW observations, we are able to obtain cosmolog-\nical constraints that are more robust to the systematic uncer-\ntainties introduced by the population assumptions (Mastro-\ngiovanni et al. 2021; Abbott et al. 2023a).\nThe fourth observing run (O4) of the LVK network of de-\ntectors began on 2023 May 24 at 15:00:00 UTC, and included\nthe two Laser Interferometer Gravitational-Wave Observa-\ntory (LIGO; Aasi et al. 2015) detectors in observing mode\nafter several upgrades that improved their sensitivity (Gana-\npathy et al. 2023; Jia et al. 2024; Capote et al. 2025), while\nthe Virgo (Acernese et al. 2015) and KAGRA (Akutsu et al.\n2021) detectors did not join the observing run in order to con-\ntinue commissioning (Abac et al. 2025b). The first part of\nthe fourth observing run (O4a) ended on 2024 January 16 at\n16:00:00 UTC, and the accompanying version of the Gravi-\ntational Wave Transient Catalog 4.0, hereafter referred to as\nGWTC-4.0 (Abac et al. 2025b,c,d), contains all the candi-\ndates reported in previous observing runs, which include the\nfirst observing run (O1; Abbott et al. 2016), the second ob-\nserving run (O2; Abbott et al. 2019a), and the third observ-\ning run (O3; Abbott et al. 2021b, 2023b, 2024), in addition\nto the latest observations from O4a, for a total of 218 can-\ndidates. See Abac et al. (2025b) for a general introduction\nto GWTC-4.0, and the articles presented in the GWTC-4.0\nFocus Issue (Abac et al. 2025e) for other aspects of this data\nset.\nIn this paper we present an updated estimate of H0 using\nthe full population of BNS, NSBH, and BBH candidates re-\nported in GWTC-4.0. We select candidates for inclusion in\nthe analysis based on a false alarm rate (FAR) of less than\n0.25 per year to reduce contamination from noise events.\nThis allows us to combine the bright siren event GW170817\nwith an additional 141 GW detections used as dark sirens to\nobtain our final estimate of H0.\nIn addition, we present constraints on deviations from\ngeneral relativity (GR) that affect the propagation of GWs\nand which can be parametrized in terms of a modified\nGW\u2013EM luminosity-distance ratio (Belgacem et al. 2018a;\nEzquiaga 2021; Mancarella et al. 2022; Leyde et al. 2022;\nMastrogiovanni et al. 2023; Chen et al. 2024a). These con-\nstraints test the hypothesis that gravity behaves differently\nfrom GR on cosmological scales, leading to a mistaken in-\nference of a dark energy component (see Clifton et al. 2012\nfor a comprehensive review of modified gravity models).\nThe remainder of this paper is organized as follows. In\nSection 2 we present the spectral and dark siren statistical\nmethods adopted in this study to infer the cosmological and\npopulation parameters. In Section 3 we detail the proper-\nties of the GW candidates and the galaxy catalog used. In\nSection 4 we present the results of our analysis and the tests\nmade to check its robustness against systematic errors, while\nin Section 5 we discuss how our results compare with the lit-\nerature and the limitations of our analysis. In Section 6 we\npresent our conclusions.\nThroughout this paper, unless otherwise stated, we assume\na flat-\u039bCDM cosmology and the best-fit Planck-2015 value\nof \u2126m = 0.3065 for the fractional matter density in the cur-\nrent epoch (Ade et al. 2016).\n2. METHODS\n2.1. Dark Sirens Statistical Framework\nTo infer cosmology and population\u2013level properties of GW\nsources from the observed event catalog, we employ a hi-\nerarchical Bayesian framework (Mandel et al. 2019; Vitale\net al. 2020). The observed sample is modeled as resulting\nfrom an inhomogeneous Poisson process in the presence of\nselection effects, assuming statistically independent and non-\noverlapping events. Each event in the catalog is described\nby detector\u2013frame parameters \u03b8det, which include the de-\ntector\u2013frame masses and GW luminosity distance, \u03b8det \u220b\n{mdet\n1 , mdet\n2 , DGW\nL\n} (where mdet\n1\n\u2265mdet\n2 ). For each event,\nlabeled by the index i, individual parameter constraints are\ngiven in the form of samples from the posterior probabil-\nity p\n\u0000\u03b8det\ni\n|di\n\u0001\nfor the parameters \u03b8det\ni\ngiven the observed\ndata di. These are assumed to be obtained with a param-\neter estimation prior that we denote \u03c0PE(\u03b8det). The event\nparameters are drawn from a distribution which is modeled\nas a function of source\u2013frame quantities \u03b8, which include\nthe source\u2013frame masses and redshift, \u03b8 \u220b{m1, m2, z}.\nThe population distribution ppop(\u03b8|\u039b) is described paramet-\nrically by a set of hyperparameters \u039b (sometimes simply re-\nferred as parameters). We infer the cosmological hyperpa-\nrameters, denoted here as \u039bc, in addition to the population\nhyperparameters. As population properties are modeled in\nsource\u2013frame, while GW observations provide information\non detector\u2013frame quantities, evaluating the population func-\ntion implies assuming a cosmology. We therefore write the\nsource\u2013frame variables as functions of the detector\u2013frame\nones and of the parameters \u039bc, \u03b8i = \u03b8i(\u03b8det\ni\n, \u039bc).\nThe posterior probability on the parameters {\u039b, \u039bc} given\nthe ensemble of GW strain data {d} from Ndet detections can\nbe written as (Loredo 2004; Mandel et al. 2019; Vitale et al.\n2020):\np (\u039b, \u039bc|{d}, Ndet) \u221d\u03c0(\u039b) \u03c0(\u039bc)\n\u00d7 \u03be(\u039b, \u039bc)\u2212Ndet\nNdet\nY\ni=1\nZ\nd\u03b8det\ni\np\n\u0000\u03b8det\ni\n|di\n\u0001\n\u03c0PE(\u03b8det\ni\n)\n\u00d7\n\"\f\f\fd\u03b8det\ni\n(\u03b8i, \u039bc)\nd\u03b8i\n\f\f\f\n\u22121\nppop(\u03b8i|\u039b)\n#\n\u03b8i=\u03b8i(\u03b8det\ni\n,\u039bc)\n,\n(1)\n\n13\nwhere \u03c0(\u00b7) denotes a prior,\n\f\f\fd\u03b8det\ni\n(\u03b8i, \u039bc)/d\u03b8i\n\f\f\f is the Jaco-\nbian of the transformation from source to detector frame, and\n\u03be(\u039b, \u039bc) =\nZ\nd\u03b8det P(det|\u03b8det)\n\u00d7\n\"\f\f\fd\u03b8det(\u03b8, \u039bc)\nd\u03b8\n\f\f\f\n\u22121\nppop(\u03b8|\u039b)\n#\n\u03b8=\u03b8(\u03b8det,\u039bc)\n(2)\nis the expected fraction of detected events in the population.\nThis term corrects for selection effects, namely the fact that\nthe detectors observe a fraction of the real underlying popu-\nlation described by ppop(\u03b8|\u039b). Here, P(det|\u03b8det) \u2208[0, 1]\nis the probability of detecting an event with parameters \u03b8det.\nThis function must be evaluated by matching the detection\ncriterion used to obtain the observed catalog (Essick & Fish-\nbach 2024). Finally, Equation (1) assumes marginalization\nover the overall total number of mergers in the observing\ntime, N, with a scale\u2013invariant prior \u221d1/N (Mandel et al.\n2019).\nThe population distribution in Equations (1) and (2) inher-\nits an explicit dependence on the cosmological parameters\nstemming from the conversion from detector to source frame.\nThis property allows constraints on cosmological parameters.\nSpecifically, we can relate detector\u2013and source\u2013frame quan-\ntities using\nz = z(DGW\nL\n; \u039bc) ,\n(3)\nm1,2 =\nmdet\n1,2\n1 + z(DGW\nL\n; \u039bc) .\n(4)\nThe redshift is obtained from the luminosity distance for\ngiven cosmological parameters via the inversion of the dis-\ntance\u2013redshift relation (see Section 2.4.1 for details).\nIn\nthe presence of features in the source\u2013frame mass distri-\nbution as modeled in ppop, the above relation between the\nsource\u2013frame mass and the redshifted mass can be used to\nprobe cosmology even in the absence of an explicit EM coun-\nterpart, which corresponds to the spectral method (Chernoff\n& Finn 1993; Taylor et al. 2012; Taylor & Gair 2012; Farr\net al. 2019). The Jacobian transformation from source to de-\ntector frame also introduces a dependence on the cosmologi-\ncal parameters. Explicitly,\n\f\f\fd\u03b8det(\u03b8, \u039bc)\nd\u03b8i\n\f\f\f = (1 + z)2 dDGW\nL\n(z, \u039bc)\ndz\n.\n(5)\nThe explicit expression for the luminosity distance needed to\ncompute the Jacobian is given in Equations (19), (22), and\n(23) below for the scenarios considered in this paper.\nIn addition to the mass distribution, an informative popula-\ntion prior on the redshift of an event can be constructed by us-\ning a galaxy catalog, corresponding to the dark siren method.\nWe describe the construction of the redshift prior in detail in\nSection 2.2. Any consistent inference must account for selec-\ntion effects via Equation (2), where the detection probability\nis a function of any variable \u03b8det determining the GW wave-\nform. As a consequence, any analysis based on the construc-\ntion of a redshift prior from a galaxy catalog also requires as-\nsumptions on the mass distribution to compute the selection\neffects. This implies one has to marginalize over the parame-\nters of the mass distribution to obtain consistent and unbiased\nresults. Also note that both the individual\u2013event likelihood\nand detection probability P(det|\u03b8det) depend on more pa-\nrameters than just mass and redshift, e.g., inclination angles\n(namely, the angle between the orbital angular momentum\nof the binary and the observer\u2019s line-of-sight) and spins of\nthe compact objects. Neglecting those additional parameters\ncorresponds to implicitly assuming that their astrophysical\ndistribution ppop coincides with the prior used in the individ-\nual\u2013event parameter estimation. In particular, in absence of a\nspecific model, spins are assumed to have a distribution uni-\nform in magnitude and isotropic in orientation (Abac et al.\n2025d).\nThe two pipelines used in our analysis, icarogw and\ngwcosmo (Mastrogiovanni et al. 2024; Gray et al. 2023),\nadopt different strategies to evaluate the posterior in Equa-\ntion (1). Detailed technical descriptions are provided in Ap-\npendix A.\n2.2. Construction of Redshift Priors\nIn this Section, we detail the construction of population pri-\nors on redshift.\nWe give here a general overview of the\nmethod, and we refer the reader to Mastrogiovanni et al.\n(2023) and Gray et al. (2023) for more specifics.\nWe split the source\u2013frame parameters \u03b8 as \u03b8 \u2261{z, \u2126, \u00af\u03b8}\nwhere \u00af\u03b8 denotes all source\u2013frame waveform parameters\nother than redshift and sky position \u2126. We write the popu-\nlation distribution appearing in Equation (1) in terms of the\nsource\u2013frame merger rate as (Mastrogiovanni et al. 2023;\nGray et al. 2023; Mastrogiovanni et al. 2024)\nppop(\u03b8i|\u039b) \u221dppop(\u00af\u03b8i|\u039b)\u03c8(z|\u039b)\n1 + z\n\u00d7\n\"\ndN eff\ngal,cat\ndzd\u2126\n+\ndN eff\ngal,out\ndzd\u2126\n#\n.\n(6)\nIn the above Equation, \u03c8(z|\u039b) parametrizes the redshift de-\npendence of the CBC merger rate and the factor of (1 + z)\u22121\naccounts for the conversion of time intervals from source\nto observer frame. The terms in square brackets represent\nthe contributions to the redshift prior from galaxies within\nthe catalog (first term), and a model for unobserved \u2018out-of-\ncatalog\u2019 galaxies (second term). We will discuss the details\nof these two terms next.\nIn\u2013catalog part, dN eff\ngal,cat/(dzd\u2126) \u2014This term is built start-\ning from the galaxies in the catalog. The sky is divided in\nequal\u2013size pixels, labeled with their central coordinates \u2126, of\narea \u2206\u2126, with the healpix pixelization algorithm (G\u00f3rski\net al. 2005; Zonca et al. 2019). Inside each pixel, we select\nall galaxies with apparent magnitude brighter than the me-\ndian inside the pixel, denoted as mthr(\u2126). To compute this\n\n14\nmedian threshold, we adopt nside = 32 in the healpix\nscheme. However, as described in Section 3.2, a higher res-\nolution is used to pixelize the galaxy catalog used in the\nanalysis.\nThe choice of a coarser resolution to compute\nthe skymap of median thresholds ensures robustness against\nsmall-number statistics with the numbers of galaxies (Gray\net al. 2022, 2023). This median threshold can depend on the\nsky position if the galaxy catalog is compiled from multiple\nsurveys and does not have uniform coverage. For each pixel,\na redshift prior is constructed as a weighted sum of the pos-\nterior distributions for the true redshift z given observed red-\nshifts zj\nobs for the selected galaxies j = 1, . . . , Ngal(\u2126) in the\npixel, each denoted by p(z|zj\nobs, \u03c3j\nz,obs, \u039bc). The in\u2013catalog\nterm is then obtained as\ndN eff\ngal,cat\ndzd\u2126\n=\n1\n\u2206\u2126\nNgal(\u2126)\nX\nj\nwj(\u03f5, Mj)\n\u00d7 p(z|zj\nobs, \u03c3j\nz,obs, \u039bc) \u03b4(\u2126\u2212\u2126j) ,\n(7)\nwhere Mj is the absolute magnitude of a galaxy in a specific\nband. We assume negligible uncertainties on the sky posi-\ntion, and define the weights (Gray et al. 2020)\nwj(\u03f5, Mj) =\n\f\f\f\f\nLj\nL\u2217\n\f\f\f\f\n\u03f5\n= 10\u22120.4\u03f5(Mj\u2212M\u2217) ,\n(8)\nwhere L\u2217and M\u2217are the reference luminosity and corre-\nsponding magnitude at the knee of the luminosity function,\nrespectively. We assume the luminosity function to be given\nby the Schechter function (Schechter 1976), described in\nmore detail in Appendix B.\nIn Equation (7), we weight each galaxy by Equation (8),\nnamely by the absolute luminosity in a specific band, Lj,\nraised to a power \u03f5 which we treat as a fixed parameter. In\nparticular, we consider the cases \u03f5 = 0, corresponding to\nequal probability for all galaxies to host CBCs, which we\nwill refer to as no\u2013weighting case, and \u03f5 = 1 correspond-\ning to a linear weight of galaxies by their luminosity, which\nwe will refer to as luminosity\u2013weighting case. It is known\nthat luminosity in specific magnitude bands correlates with\ngalaxy properties such as stellar mass or star formation rate,\nfor example. Luminosity\u2013weighting reflects an assumption\nthat such galaxy properties may also correlate with likeli-\nhood to host CBC mergers, see Gray et al. (2020); P\u00e1lfi et al.\n(2025) for more extended discussions.\nThe absolute magnitude Mj is obtained for each galaxy\nfrom the measured apparent magnitude mj via Mj = mj +\n5\u22125 log DL(z, \u039bc)\u2212Kcorr (with DL expressed in pc), where\nthe K-correction term Kcorr accounts for the shifting of the\nobserved spectrum for galaxy at redshift z.1,2 K\u2013corrections\n1 We use the symbol m for both source-frame masses and galaxy apparent\nmagnitudes, clarifying its meaning when necessary.\n2 We have assumed that the apparent magnitude is known with a negligible\nuncertainty, as we have used galaxies in the K\u2013band that are significantly\nbright compared to the flux limits. This assumption may have to be revis-\nited when using fainter galaxies closer to the flux limits.\nare computed following Kochanek et al. (2001). The conver-\nsion from apparent to absolute magnitude depends in princi-\nple on the computation of a distance, hence on cosmology.\nHowever, the overall dependence on H0 in such conversion\ncancels out in the ratio L/L\u2217, as L\u2217shares the same scaling\nwith H0. This leaves in principle a residual dependence on\nother parameters of the distance\u2013redshift relation such as \u2126m\nin our dark siren analyses, which we consider fixed. Under\nthis assumption, the difference Mj \u2212M\u2217in Equation (8) can\nbe considered only a function of mj and z.\nEach redshift measurement is assumed to be described by a\nGaussian distribution with mean zj\nobs and standard deviation\n\u03c3j\nz,obs (see Palmese et al. 2020; Turski et al. 2023, for the\nimpact of using more generalized distributions). Specifically,\nwe test both the assumption that the Gaussian distribution\nmodels directly the redshift posterior probability, in which\ncase p(z|zj\nobs, \u03c3j\nz,obs, \u039bc) = N(z|zj\nobs, \u03c3j\nz,obs), and that it\nmodels the likelihood instead. In the second case, we obtain\nthe posterior as\np(z|zj\nobs, \u03c3j\nz,obs, \u039bc) =\nN(zj\nobs|z, \u03c3j\nz,obs) \u03c0V (z, \u039bc)\nR\ndz N(zj\nobs|z, \u03c3j\nz,obs) \u03c0V (z, \u039bc)\n,\n(9)\nwhere the likelihood N(zj\nobs|z, \u03c3j\nz,obs) is multiplied by a vol-\numetric prior \u03c0V (z, \u039bc) (representing our prior knowledge\nfor the true galaxies\u2019 redshift in absence of measurements)\nto obtain the posterior. We choose the prior as uniform in\ncomoving volume, that is\n\u03c0V (z, \u039bc) \u221ddVc(z, \u039bc)\ndzd\u2126\n,\n(10)\nwith dVc(z, \u039bc)/(dzd\u2126) being the differential comoving\nvolume element:\ndVc\ndzd\u2126(z, \u039bc) =\nc D2\nL\nH0 (1 + z)2 E(z) ,\n(11)\nwhere E(z) is the expansion rate defined below in Sec-\ntion 2.4.1. We verified that both assumptions lead to neg-\nligible differences.\nOut\u2013of\u2013catalog part, dN eff\ngal,out/(dzd\u2126) \u2014This term models\nthe contributions from galaxies that are missed by the sur-\nvey due to magnitude limits.\nIt requires some prior as-\nsumption on the number and distribution of missing galax-\nies in luminosity, redshift, and sky position.\nWe assume\nthat galaxies are uniformly distributed in comoving volume\nand solid angle, and that their absolute magnitude M fol-\nlows a redshift\u2013independent Schechter function Sch(M; \u03bb)\nwith parameters \u03bb = {\u03b1, \u03d5\u2217, M\u2217} between lower and up-\nper ends Mmin and Mmax. Here \u03b1 is the faint-end slope of\nthe Schecter function, \u03d5\u2217is the overall amplitude, and M \u2217\nwas introduced in Equation 8. We note that these parameters\ntake different values in different luminosity bands. See Ap-\npendix B for details. The number of missing galaxies per unit\n\n15\nredshift, solid angle, and absolute magnitude is estimated as\ndNgal,out\ndzd\u2126dM = dVc\ndzd\u2126(z, \u2126) Sch(M; \u03bb) pmiss(z, \u2126, M) ,\n(12)\nwhere dVc/(dzd\u2126) is the comoving volume element, and\npmiss(z, \u2126, M) = \u0398 (M \u2212Mthr [z, mthr(\u2126)]) is the prob-\nability of missing a galaxy. The latter is modeled as a Heav-\niside step function following the assumption that a galaxy is\nincluded in the in\u2013catalog part if its apparent magnitude m is\nsmaller (i.e., it is brighter) than the threshold mthr(\u2126).\nAn effective out\u2013of\u2013catalog term can be obtained in-\ntegrating Equation (12) with a luminosity weight \u221d\n10\u22120.4\u03f5(M\u2212M\u2217) (analog to Equation (8)) over the absolute\nmagnitude M between the faint end of the Schechter func-\ntion Mmax and the threshold Mthr(z, mthr(\u2126)). We provide\ndetails in Appendix B. One obtains\ndN eff\ngal,out\ndzd\u2126\n(z, \u2126) = dVc\ndzd\u2126(z, \u2126) \u03d5\u2217\nZ xmax\nxthr\ndx x\u03b1+\u03f5e\u2212x ,\n(13)\nwhere\nxthr = 100.4[M\u2217\u2212Mthr(z,mthr(\u2126))],\n(14)\nxmax = 100.4(M\u2217\u2212Mmax).\n(15)\nWe note that the out\u2013of\u2013catalog part is independent of H0.\nIn the luminosity\u2013weighting case (\u03f5 = 1), the probability of\ngalaxies to host a GW candidate reaches its maximum at the\nknee M\u2217of the luminosity function. As long as Mmax is\nsufficiently fainter than M\u2217, there is little sensitivity of our\nresults to Mmax. For the no\u2013weighting case (\u03f5 = 0), choice\nof arbitrarily faint Mmax would lead to a large increase in the\nnumber of galaxies that could potentially host GW events.\nSuch faint galaxies cannot be seen out to large redshifts due\nto the flux limit of the survey, which can drive up the in-\ncompleteness and subsequently result in the redshift prior to\nbe completely dominated by the out\u2013of\u2013catalog term (Bera\net al. 2020).\n2.3. Population Models\nWe construct CBC rate models from independent redshift\nand source mass distributions, while we assume the CBC\nspins to be isotropically distributed with uniform distribu-\ntion in the spin magnitudes. Specifically, the term \u03c8(z|\u039b)\nin Equation (6), describing the merger rate evolution as a\nfunction of the redshift, is modeled with a Madau\u2013Dickinson\nparametrization (Madau & Dickinson 2014), which is char-\nacterized by parameters {\u03b3, \u03ba, zp} \u2208\u039b, where \u03b3 and \u03ba are\nthe power\u2013law slopes respectively before and after the red-\nshift turning point, zp, between the two power\u2013law regimes.\nExplicitly,\n\u03c8 (z|\u03b3, \u03ba, zp) =\nh\n1 + (1 + zp)\u2212\u03b3\u2212\u03bai\n\u00d7\n(1 + z)\u03b3\n1 + [(1 + z)/ (1 + zp)]\u03b3+\u03ba .\n(16)\nThis parametrization is more complex than the one adopted\nin studies that focus solely on GW population properties,\nwhere usually it takes the form of simple power\u2013laws,\n\u03c8(z) \u221d(1 + z)\u03b3 (Abbott et al. 2023c; Abac et al. 2025f).\nThis choice is motivated by the fact that, when varying the\ncosmology, a GW event at given distance can be associated\nwith a redshift which is significantly higher than the one cor-\nresponding to the fiducial cosmology. The model in Equa-\ntion (16) ensures that the merger rate decays after a peak at\nz = zp, consistently with astrophysical expectations. The\nMadau\u2013Dickinson distribution is typically used to describe\nthe cosmic star formation rate, while the CBC merger rate is\nthen obtained by convolving with a time-delay distribution.\nIn practice, this is equivalent to using the same functional\nform with different values of \u03b3 and \u03ba, and by adopting wide\npriors on these parameters we effectively account for a broad\nrange of possible delay times.\nIn this study we consider three different models for the\ndistribution of primary mass, p (m1|\u039b), which enters the\nterm ppop in Equation (6).\nThese models are denoted\nas: POWER LAW + PEAK (PLP), MULTI PEAK (MLTP),\nand FULLPOP-4.0. These are phenomenological paramet-\nric models defined in terms of relatively simple functional\nforms that contain features motivated by either astrophysi-\ncal expectations or previous GW observations. These models\nare constructed as superpositions of truncated Gaussian and\npower\u2013law distributions with different parameters (described\nin Appendix C), and they are suited for the BBH spectrum de-\nscription only with the exception of the FULLPOP-4.0 model\n(see below). In this work we consider these mass models\nas redshift-independent; see Mukherjee (2022); Karathana-\nsis et al. (2023); Rinaldi et al. (2024) for investigations into\ntheir possible evolution. We will comment upon this further\nin Section 5.2. Figure 1 shows a sketch of the typical form of\nthese models, with the different mass features that character-\nize them highlighted. We now briefly describe these models\n(see Appendix C and Abac et al. 2025f for more details).\nThe PLP mass model (Talbot & Thrane 2018) has been\nused for the analysis of previous GW catalogs (Abbott et al.\n2023c,a).\nIt is based on a power\u2013law distribution with a\nsmooth low\u2013mass cutoff. In addition to this power\u2013law com-\nponent, the model includes a Gaussian peak to capture an ex-\ncess of events at intermediate masses, and a high\u2013mass cut-\noff. This model is described by eight population parameters.\nThe MLTP mass model is an extension of the PLP model,\noriginally introduced in Abbott et al. (2021c). Like the PLP\nmodel, it features a power\u2013law distribution for the primary\nmass spectrum with a smooth low\u2013mass cutoff and includes\na Gaussian peak to capture an excess at intermediate masses.\nThe distinguishing feature of the MLTP model is the inclu-\nsion of a second Gaussian peak, making it a combination of\na power\u2013law and two Gaussian components. This model is\nsimilar to the \u201cBROKEN POWER LAW + 2 PEAKS\u201d model\nadopted in Abac et al. (2025f), except our model has one\npower law instead of two. This model is characterized by\neleven population parameters.\n\n16\nm1 [M\u2299]\np(m1|\u039b) [M\u22121\n\u2299]\nPower Law + Peak\nPower\nLaw\nPeak\nm1 [M\u2299]\nMulti Peak\nPower\nLaw\nPeak 1\nPeak 2\nm1 [M\u2299]\nFullPop-4.0\nPower\nLaw\nDip\nPeak 1\nPeak 2\nNSs\nBHs\nFigure 1. Qualitative graphical representation of the three source-frame mass models considered in this paper and described in Section 2.3 and\nAppendix C. The mass distribution models displayed in the first two panels represent the mass ranges of BHs, while the third panel includes\nboth BHs NSs. The mass ranges shown are not to scale.\nIn the PLP and MLTP models the full mass distributions\nare factorized as\np(m1, m2|\u039b) = p(m1|\u039b) Sh(m1|\u039b)\n\u00d7 p(m2|m1, \u039b) Sh(m2|\u039b),\n(17)\nwhere p (m2|m1, \u039b) is the distribution of the secondary mass\ncomponent conditioned on the primary mass and Sh(m|\u039b) is\na smoothing function defined in Appendix C. This is mod-\neled assuming that the mass ratio q = m2/m1 follows a\npower\u2013law distribution.\nThe FULLPOP-4.0 model is a generalization of the previ-\nous mass models, extending the distribution to encompass\nthe full mass spectrum of CBCs, including BNS, NSBH, and\nBBH mergers. It is designed to cover a wide mass range,\nfrom a few to several hundred solar masses (Fishbach et al.\n2020; Farah et al. 2022; Mali & Essick 2025). The model\ncombines a first power\u2013law component for the low\u2013mass\nregion (representing NS-containing events) with a smooth\nlow\u2013mass cut\u2013off, and a second power\u2013law component for\nthe BBH mass distribution, which includes two Gaussian\npeaks. A dip function is introduced at the junction between\nthe two power\u2013law regimes, aiming to model the apparent\nmass gap between NSs and BHs. The parameters governing\nthis dip are treated as population parameters. This model is\ncharacterized by nineteen parameters.\nBy modeling the full population of compact objects in a\nunified framework, the FULLPOP-4.0 model allows us to in-\nclude a broader set of GW events in our analysis, offering\ngreater sensitivity to features in the mass spectrum and en-\nabling tighter constraints on cosmological parameters. An-\nother major distinction from the PLP and MLTP mass models\nlies in the parametrization of the secondary mass. Instead of\nmodeling m2 as a power\u2013law conditioned on m1, as in Equa-\ntion (17), the FULLPOP-4.0 model assumes that the distribu-\ntion of m2 is given by p(m2|\u039b) and employs a pairing func-\ntion f(m1, m2|\u039b) enforcing the condition m1 \u2265m2 and\nallowing for further flexibility for the secondary mass (Fish-\nbach & Holz 2020). Therefore, in this case, we have\np(m1, m2|\u039b) \u221dpS(m1|\u039b) pS(m2|\u039b)f(m1, m2|\u039b) ,\n(18)\nwhere pS(m|\u039b) is defined in terms of p(m|\u039b) and the\nsmoothing functions defined in Appendix C.\nThe equations which describe our three population models\ncan be found in Appendix C. For more details, see also Abac\net al. (2025f). In Section 4 we compare our analysis obtained\nusing single\u2013population models (the PLP and MLTP models\nwhich are valid for BBH candidates only) to that obtained\nusing a multi-population model (BNS + NSBH + BBH can-\ndidates), i.e., the FULLPOP-4.0 model.\n2.4. Cosmological Models\n2.4.1. Background Evolution\nUnder the assumptions of homogeneity and isotropy,\nthe luminosity distance can be computed based on the\nFriedmann\u2013Lema\u00eetre-Robertson\u2013Walker (FLRW) metric as\nDL = c(1 + z)\nH0\nZ z\n0\ndz\u2032\nE(z\u2032) ,\n(19)\nwhere E(z) = H(z)/H0 is the dimensionless expansion rate\nof the Universe. This depends on the cosmological model as-\nsumed and can be computed using the Friedmann equations.\nIn this paper, we restrict our focus to a flat\u2013\u039bCDM model.\nUnder this assumption, E(z) is given by\nE(z) =\n\u0002\n\u2126m(1 + z)3 + \u2126\u039b\n\u00031/2 .\n(20)\nHere, \u2126m is the fractional energy density in matter compo-\nnents today (cold dark matter + baryonic matter), and we\nhave ignored the radiation energy density which is negligi-\nble at the redshifts of our interest. Under this approximation,\nthe dark energy density fraction today is \u2126\u039b = 1 \u2212\u2126m.\nMore generally, the cosmic expansion history can be\nextended to include dark energy with a constant equa-\ntion\u2013of\u2013state parameter w0 \u0338= \u22121. If w0 is a constant, the\n\n17\ndark energy density evolves with redshift as \u223c(1+z)3(1+w0),\nand the expansion rate becomes\nE(z) =\nh\n\u2126m(1 + z)3 + \u2126\u039b(1 + z)3(1+w0)i1/2\n.\n(21)\nAs our data currently have no constraining power on w0, in\nthis work we will only consider such a generalization as a\nrobustness test (see Section 4.3). Our main results will be\nbased on the flat\u2013\u039bCDM model with w0 = \u22121.\n2.4.2. Parametrizations of Modified GW Propagation\nWe also analyze our data in the context of cosmological mod-\nified\u2013gravity models, which alter the behavior of cosmolog-\nical perturbations. There is a large landscape of such mod-\nels, introduced to explain dark energy (see Tsujikawa 2010;\nClifton et al. 2012; Joyce et al. 2016; Ezquiaga & Zumalac\u00e1r-\nregui 2018; Ishak 2019, for reviews). Whilst this model space\ncontains a wide variety of phenomenology, we focus here on\na common (but not universal) feature, sometimes referred to\nas GW friction (Saltas et al. 2014; Pettorino & Amendola\n2015; Nishizawa 2018; Amendola et al. 2018; Lagos et al.\n2019). Under this effect, new terms in the GW propaga-\ntion equation result in modifications to the GW amplitude\nreceived at the observer. This effect is indistinguishable from\na change in the luminosity distance to the GW source. The\nresult is that the luminosity distance DGW\nL\ninferred for a GW\nsource differs from the EM luminosity distance DL given\nby Equation (19). Any measurement of the GW source lu-\nminosity distance obtained using EM observables would be\nunaffected, i.e., DEM\nL\n= DL. In models where the theory\nof gravity on cosmological scales is GR, the luminosity dis-\ntance derived from GW events, DGW\nL\n, and that based on EM\nobservations, DEM\nL\n, are instead identical and given by Equa-\ntion (19).\nBased on this, multiple studies (Belgacem et al. 2018b,a,\n2019b,a; Mukherjee et al. 2021c; Finke et al. 2021a,b, 2022;\nEzquiaga 2021; Finke et al. 2021a; Mancarella et al. 2022;\nKalogera et al. 2021; Leyde et al. 2022; Liu et al. 2024;\nBranchesi et al. 2023; Chen et al. 2024a; Abac et al. 2025a)\nhave considered the ratio DGW\nL\n/DEM\nL\nas a convenient probe\nof departures from GR on cosmological scales.\nThe ra-\ntio is always equal to one in GR, and in cosmological\nmodified\u2013gravity models can become a function of redshift.\nRather than focusing on specific modified\u2013gravity models,\nhere we consider two commonly used parametrized forms\nfor the GW\u2013EM luminosity\u2013distance ratio.\nTwo assumptions are relevant to both parametrizations.\nFirst, we assume the GW propagation speed, cT , is lumi-\nnal. Such a choice relies on the tight GW constraint on cT\nfrom GW170817 (Abbott et al. 2017d), which is made at\nredshift \u223c0.01. Our data span up to redshift \u223c0.9, so break-\ning this assumption would require a theory where the rela-\ntive difference between cT and c (the speed of light) grows\nfrom \u223c10\u221215 by orders of magnitude in a redshift range be-\ntween 0.01 to < 1. Furthermore, Ray et al. (2024) provide\npercent\u2013level constraints on the GW propagation speed us-\ning dark BBHs candidates from GWTC-3.0. Given these re-\nsults, significant deviations from luminal speed do not ap-\npear to be favored by current data; hence we do not consider\nnon-luminal propagation in the present work. Non-luminal\npropagation at higher redshift could be incorporated in future\nanalyses to explore potential deviations in the speed of GWs\nover a broader redshift range. Additionally, we do not con-\nsider frequency\u2013dependent deviations in the speed of GWs.\nThis remains the standard assumption in most cosmological\ntests of GR, and currently used waveforms based on GR sug-\ngest that any such deviations should be small (Abbott et al.\n2019b, 2021d,e).\nSecond, we treat departures from GR impacting only the\npropagation phase of GW signals.\nIn cosmological mod-\nified\u2013gravity theories, changes to the strong\u2013field gravita-\ntional regime are usually suppressed by screening mecha-\nnisms, in order to obey stringent tests of GR within the Solar\nSystem (see Joyce et al. 2015 for a review). As such, we\ndo not consider here modifications to the generation of GWs,\nwhich would affect the waveform at source. Constraints on\nstrong\u2013field departures from GR are considered in Abac et al.\n(2025g,h,i); Abac et al. (2025h) also provides constraints on\ndispersive propagation effects.\n\u039e0\u2013n Parametrization \u2014In this parametrization, DGW\nL\nis de-\nscribed by (Belgacem et al. 2018a)\nDGW\nL\n= DEM\nL\n\u0012\n\u039e0 + 1 \u2212\u039e0\n(1 + z)n\n\u0013\n,\n(22)\nwhere both parameters \u039e0 and n are positive.\nThe pri-\nmary parameter of interest is \u039e0, which controls the over-\nall amplitude of departures from GR.\nAt low redshifts,\nDGW\nL\n/DEM\nL\n\u2192\n1 (irrespective of \u039e0), which models\nchanges to DGW\nL\nas an effect which accumulates with prop-\nagation distance. At high redshifts, DGW\nL\n/DEM\nL\n\u2192\u039e0 as\nchanges to DGW\nL\nshould saturate at redshifts where the frac-\ntional energy density of dark energy, \u2126\u039b(z), is negligible.\nThis holds under the assumption that deviations from GR are\nassociated to the late\u2013time emergence of dark energy. The\npower\u2013law index n controls the rate of transition between\nthese two regimes.\nThe \u039e0\u2013n parametrization is a direct phenomenological\nparametrization of the gravitational luminosity distance. The\nspecific form of the parametrization is an assumption, and\nEquation (22) was calibrated to cover a large spectrum\nof known luminal modified\u2013gravity theories (see Belgacem\net al. 2019b, for a thorough discussion). These include f(R)\ngravity (Hu & Sawicki 2007; Song et al. 2007; Starobinsky\n2007), Jordan\u2013Brans\u2013Dicke (Brans & Dicke 1961), Galileon\ntheories (Chow & Khoury 2009), nonlocal gravity (Maggiore\n2014; Maggiore & Mancarella 2014). Notable exceptions,\nfor which more complex parametrizations are needed to bet-\nter capture the evolution of the distance ratio, are degenerate\nhigher\u2013order scalar\u2013tensor theories (Langlois & Noui 2016),\nbigravity (Hassan & Rosen 2012), and extra\u2013dimensional\nparadigms (Dvali et al. 2000); see Abbott et al. (2019c) and\nCorman et al. (2022) for constraints on the number of space-\ntime dimensions. The GR limit of the theory is \u039e0 \u21921\n\n18\n(for any value of n). However, the parametrization is imper-\nfectly behaved, since n \u21920 also recovers the GR behavior\nDGW\nL\n= DEM\nL\n.\n\u03b1M Parametrization \u2014This parametrization is inspired by\nHorndeski gravity (Horndeski 1974; Deffayet et al. 2011;\nKobayashi et al. 2011), which is the most general family of\nscalar\u2013tensor gravity models with second\u2013order equations of\nmotion. In the widespread basis of Bellini & Sawicki (2014),\nadopted for describing linear cosmological perturbations of\nHorndeski theories around a FLRW solution, \u03b1M(z) is the\nrate of change of the effective Planck mass, and hence the\neffective gravitational coupling strength (Bellini & Sawicki\n2014; Gleyzes et al. 2015b). This results in the following\nexpression for DGW\nL\n(Lagos et al. 2019):\nDGW\nL\n= DEM\nL\nexp\n\u001a1\n2\nZ z\n0\ndz\u2032\n1 + z\u2032 \u03b1M (z\u2032)\n\u001b\n,\n(23)\nwhere in this work we will use the following ansatz for\n\u03b1M(z)\n\u03b1M(z) = cM\n\u2126\u039b(z)\n\u2126\u039b\n= cM\n1\nE2(z) ,\n(24)\nwhere \u2126\u039b = \u2126\u039b(z = 0) and cM is a constant of propor-\ntionality. For the dimensionless expansion rate, E(z), we\nuse Equation (20) which assumes a flat\u2013\u039bCDM model with\nconstant dark energy density, as in this work we are not con-\nsidering changes to the cosmological expansion history. In\nprinciple, \u03b1M(z) also enters the background evolution equa-\ntions; however, any resulting change can be absorbed into\nother functions such as the effective dark energy equation of\nstate (Bellini & Sawicki 2014). In addition, these background\neffects are highly subdominant compared to the impact on\nthe distance ratio (Belgacem et al. 2018b). Therefore, it is\nlegitimate to treat the background expansion as fixed, and we\nexplicitly verify that even when allowing the background to\nvary (through the dark energy equation-of-state parameter,\nsee section 4), this has no impact on our constraints. The GR\nlimit of the model is obtained for cM = 0.\nThe redshift\u2013dependent form of \u03b1M(z) is a choice, which\nwould be fixed in a fully specified theory of gravity.\nIn\nparticular, Equation (24) is motivated by the association of\nthe onset of \u03b1M(z) to the late\u2013time emergence of dark en-\nergy (Bellini & Sawicki 2014). The form of Equation (24)\nhas been widely adopted for large scale structure (LSS) con-\nstraints (Bellini et al. 2016; Noller & Nicola 2019; Baker &\nHarrison 2021; Seraille et al. 2024; Ishak et al. 2024), but\nalso criticized for not accurately representing a large num-\nber of modified\u2013gravity models (Linder et al. 2016; Linder\n2017; Denissenya & Linder 2018, see however Gleyzes 2017\nfor counter-arguments).\nIn a full treatment of Horndeski gravity, there are addi-\ntional effects to the cosmological expansion rate and growth\nof LSS that impact EM observables; we do not consider\nthese here, as our focus is on GW data analysis. Also, gen-\neral Horndeski gravity can allow non-luminal GW propaga-\ntion, but as noted above we do not consider this possibility.\nSee Kobayashi (2019) and references therein for a review of\nHorndeski gravity and its phenomena. Finally, we conduct\nour analysis in the Jordan frame, where the effect of possible\nnon-standard couplings between matter fields and the metric,\nthat could impact the background expansion as well as scalar\nperturbations (Gleyzes et al. 2015a, 2016), are not present.\nComparison among Parametrizations \u2014The \u039e0\u2013n parametriza-\ntion directly describes the redshift evolution of the distance\nratio. In contrast, in the \u03b1M parametrization the observable\ndistance ratio is related to the integral of the function \u03b1M(z),\nwhich encodes deviations from GR. As long as the dark\nenergy density \u2126\u039b(z) causes the integral in Equation (23)\nto saturate at large redshift, the resulting distance ratio ex-\nhibits the same qualitative behavior as described by Equa-\ntion (22). The two parametrizations can be matched analyt-\nically at z \u2192\u221eand z \u223c0. Under the assumption of a\nflat\u2013\u039bCDM cosmology, and under our ansatz in Equation 24,\nthe following relations hold:\nln \u039e0 = cM\n6\u2126\u039b\nln 1\n\u2126m\n,\nn = \u2212\n3\nln \u2126m\n,\n(25)\nas discussed in detail in Belgacem et al. (2019b); Baker\n& Harrison (2021); Mancarella et al. (2022).\nThe \u03b1M\nparametrization features only a single free parameter, with\nits time evolution fully specified by the dark energy density,\nwhereas the \u039e0\u2013n parametrization allows additional flex-\nibility via the redshift evolution index n, over which we\nmarginalize. This effectively makes the \u03b1M parametrization\na special case of the \u039e0\u2013n parametrization for a fixed n, al-\nbeit one with a direct link to theoretical models within the\nHorndeski class.\n3. DATA\n3.1. GW Events\nThe analyses presented are based on GWTC-4.0 (Abac et al.\n2025b,c,d) and based on the detection of GW candidates pro-\nduced by merging compact binaries between O1 and the end\nof O4a. To reduce the noise contamination of the datasets\nused in cosmological studies, we select a subset of GW\nevents with the lowest FAR among all search pipelines, en-\nsuring all events have FAR < 0.25 yr\u22121. The GW candidates\ncollected during the engineering run directly preceding the\nstart of O4a are not included in the analysis, to remain con-\nsistent with the principles deployed in previous LVK cosmol-\nogy analyses.\nA total of 142 CBC GW candidates with FARs below this\nthreshold have been detected by our search pipelines from O1\nto O4a. Following the GWTC-4.0 classification of candidates\ninto unambiguous BBHs and potential NS-binaries (Abac\net al. 2025d), 137 out of 142 events are believed to originate\nfrom the coalescence of BBH candidates and 5 from binaries\nwhere at least one component mass could have been a NS.\nFrom the list of events that pass the sensitivity cut in O4a,\nwe exclude GW231123_135430 (Abac et al. 2025j), as some\nof its inferred properties, such as the binary masses or its lu-\nminosity distance, appear to be more sensitive to the choice\n\n19\nof waveform model than those of other events in our dataset,\nand in this work we prefer to use results from a single wave-\nform model for each event, as discussed below.\nThis analysis shares 45 dark sirens with our previous cos-\nmological analysis (Abbott et al. 2023a), which used 46\ndark sirens.\nThe event not used in the present work is\nGW200105_162426, which is excluded here due to its low\nprobability of being of astrophysical origin (Abbott et al.\n2023b).\nThus, our analysis contains 96 additional dark\nsirens; 76 of these come from O4a, whilst 20 are additional\nevents from O3 which were not used previously. This is due\nto the fact that Abbott et al. (2023a) selected candidates based\non both a FAR and signal-to-noise ratio (SNR) threshold, re-\nsulting in fewer events analyzed. In this work we apply only\nthe FAR threshold stated above. Added to the 141 dark sirens\nis the special case of the multi-messenger event GW170817.\nThis is treated differently from the others, and will be used in\nthe rest of the paper as a bright siren.\nCompared to previous GW candidates (O1\u2013O3), the O4a\ndetections cover a similar parameter space in terms of lumi-\nnosity distance and masses. Figure 2 shows the distribution\nof the 90% credible region (CR) of the sky-localization of\nCBC events observed in the same LVK observing runs, as\nwell as that of the O4a events only. The sky localization of\nthe GW events detected during the O4a observing run is, on\naverage, relatively broad (see Figures 2 and 3). This is due\nto the fact that, during O4a, Virgo was not online resulting\nin two detector localizations. A full list of luminosity dis-\ntances, binary component masses, and sky uncertainties of\nthe GW candidates considered in our study can be found in\nAppendix E.\nDifferent waveform models have been used to perform the\nparameter estimation (PE) for each GW candidate across\nthe observing runs (Abac et al. 2025c).\nFor our anal-\nysis, we use posterior samples produced with a single\nwaveform approximant rather than a mixture of samples\nfrom different waveforms (Abac et al. 2025c,d).\nThis\nchoice mitigates potential difficulties in reweighting the PE\nsamples if different waveforms use slightly different prior\nbounds, such as those on the luminosity distance, for a\ngiven candidate. In particular, for candidates from the O1,\nO2, and O3 runs, we use the posterior samples based on\nthe IMRPHENOMXPHM waveform model (Pratten et al.\n2021), where for GW200115_042309 (Abbott et al. 2021f)\nwe use the large-spin magnitude prior posterior samples,\nwhile for GW190425_081805 (Abbott et al. 2020a) and\nGW170817 (Abbott et al. 2021a) we use the large-spin\nmagnitude prior posterior samples obtained with the IMR-\nPHENOMPV2_NRTIDAL (Dietrich et al. 2017, 2019) and a\nprior allowing for high-spin and low-spin magnitudes, re-\nspectively. For events from the O4a observing run, we use\nthe posterior samples produced with the IMRPHENOMX-\nPHM_SPINTAYLOR model (Colleoni et al. 2025), except\nfor GW230529_181500, for which we use posterior samples\nproduced using the IMRPHENOMXPHM waveform model\nand released in Abac et al. (2024). In this study we do not\nconsider the impact of waveform systematics, as they are\n101\n102\n103\n104\n\u2206\u212690% [deg2]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nCumulative Distribution\nO1+O2+O3+O4a (142)\nO4a (76)\nFigure 2.\nCumulative distribution of the size of the 90%\nCR of the sky localization of CBC candidates observed during\nO1+O2+O3+O4a in orange (142 total events including GW170817)\nand O4a-only in blue (76 events). It can be seen that the typical sky\nlocalization of O4a events was larger than that of O1\u2013O3 events.\nexpected to be relevant only in population analyses of GW\nevents with SNR above 100 (Kapil et al. 2024).\nDuring the final stages of this project, a normalization er-\nror was discovered in the noise-weighted inner product em-\nployed in the GW PE likelihood function (Abac et al. 2025c;\nTalbot et al. 2025). Although there is a version of the PE sam-\nples that accounts for the correct likelihood via a reweighting\nprescription (Abac et al. 2025c; Talbot et al. 2025), in this\nwork we do not use these samples, but those released in the\nfirst digital version of the GWTC-4.0 catalog (LIGO Scien-\ntific Collaboration, Virgo Collaboration, and KAGRA Col-\nlaboration 2025). Furthermore, we discovered that incorrect\npriors were used when marginalizing over the uncertainty in\nthe LIGO detector calibration for candidates detected during\nthe first three observing runs (Abac et al. 2025c). As dis-\ncussed in Abac et al. (2025c), we have checked that the im-\npact on the most affected events is individually negligible, so\nthat our previous results on the full population are also unaf-\nfected. We have checked that this error\u2019s impact on our cos-\nmological analyses is negligible compared to other sources\nof systematic error.\nFinally, we estimate the GW detection probability in Equa-\ntion (2) by using a set of simulated GW signals (called injec-\ntions) described in Essick et al. (2025); Abac et al. (2025c).\nMore details on how the injections are used to compute Equa-\ntion (2) can be found in Appendix A.\n3.2. Galaxy Catalog\nWe use the GLADE+ galaxy catalog (D\u00e1lya et al. 2018,\n2022) for our galaxy catalog method analysis. GLADE+ is\nan all-sky galaxy catalog containing around 22 million galax-\nies, which has been created from six different astronomical\ndatasets: the Gravitational Wave Galaxy Catalog (GWGC,\nWhite et al. 2011), HyperLEDA (Makarov et al. 2014), the\n\n20\n2 Micron All-Sky Survey Extended Source Catalog (2MASS\nXSC, Skrutskie et al. 2006), the 2MASS Photometric Red-\nshift Catalog (2MPZ, Bilicki et al. 2014), the WISExSCOS\nPhotometric Redshift Catalog (WISExSCOSPZ, Bilicki et al.\n2016) and the Sloan Digital Sky Survey quasar catalog from\nthe 16th data release (SDSS-DR16Q, Lyke et al. 2020). The\ncatalog provides nearly isotropic coverage of the whole sky,\napart from the band of the Milky Way, towards which dust\nand stars reduce the visibility of galaxies. The redshifts in the\ncatalog are corrected for the peculiar motions of the galaxies\nusing a method proposed in Mukherjee et al. (2021a) which\nrelies on the Bayesian Origin Reconstruction from Galaxies\n(BORG) formalism (Jasche & Wandelt 2013) up to a redshift\nof z = 0.05. The importance of peculiar velocity correc-\ntions diminishes above this range. GLADE+ also provides\nuncertainties on peculiar velocities. The median relative un-\ncertainty of these estimates, compared to the galaxy redshifts,\nis 1.1%. Therefore, we do not expect peculiar velocity uncer-\ntainties to significantly affect our analysis.\nGLADE+ reports galaxy magnitudes in 7 different bands,\nfrom which we chose to use the Ks band (reported in the\nVega system) for our main results, referred to as the K-\nband in this paper.\nThis choice is motivated by our ear-\nlier studies (Abbott et al. 2023a) on how well the number\ndensity of galaxies in different bands follow the theoretical\nluminosity Schechter function (Schechter 1976). We found\nthat the K-band absolute magnitude distribution of GLADE+\ngalaxies is well described by a Schechter function with pa-\nrameters M\u2217,K = \u221223.39 and \u03b1K = \u22121.09 taken from\nKochanek et al. (2001). GLADE+ contains K-band mag-\nnitudes for a subset of its entries, approximately 1.16 mil-\nlion sources. This subset that we used in our analysis mostly\nhas photometric redshifts available with an absolute error of\n\u03c3z,obs\u223c0.015 (Bilicki et al. 2014). Spectroscopic redshifts\nare available for \u223c23% of this subsample. The top panel of\nFigure 3 shows the catalog\u2019s completeness fraction (see Ap-\npendix B) in the K-band as a function of redshift. The dif-\nferent curves are calculated for a given percentage of the sky\ncoverage of the catalog, i.e., by excluding the \u223c5% of the sky\nwhere the catalog does not contain any galaxies with K\u2013band\nmagnitudes. For example, 20% of the coverage of GLADE+\nhas a completeness fraction lower than the blue curve and\n80% of the coverage has a higher completeness fraction. The\nlabel also shows the apparent magnitude thresholds corre-\nsponding to these curves. The apparent magnitude thresh-\nold was obtained as the median magnitude of the galaxies\nin the pixel. This conservative approach excludes all galax-\nies fainter than the calculated threshold in the pixel from the\nanalysis.\nThe bottom panel of Figure 3 presents the sky localizations\nof the ten best-localized GW events from O4a included in our\nanalysis, in superposition with a sky map showing the direc-\ntional dependence of the K-band apparent magnitude thresh-\nold for the GLADE+ galaxies. Outside of the Galactic plane,\nthe apparent magnitude threshold is typically mthr \u223c13.5\nfor the K\u2013band, while closer to the Galactic plane region\nthe apparent magnitude threshold is significantly lower (i.e.,\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nz\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nCompleteness fraction\n20% coverage with mthr \u226413.3\n40% coverage with mthr \u226413.5\n60% coverage with mthr \u226413.6\n80% coverage with mthr \u226413.7\n100% coverage with mthr \u226414.5\n0h\n21h\n18h\n15h\n12h\n9h\n6h\n3h\n0h\n0\u25e6\n30\u25e6\n60\u25e6\n30\u25e6\n\u221230\u25e6\n\u221260\u25e6\n\u221230\u25e6\nGW230627 015337\nGW230628 231200\nGW230731 215307\nGW230919 215712\nGW230922 020344\nGW230927 153832\nGW231110 040320\nGW231206 233901\nGW231224 024321\nGW231226 101520\nGW230927 153832\nGW231110 040320\nGW231206 233901\nGW231224 024321\nGW231226 101520\n13.00\n13.50\n14.00\nmthr\nFigure 3.\nTop panel: Completeness fraction of GLADE+ in\nthe K\u2013band, indicating the probability that the catalog contains the\nhost galaxy of a GW event, as a function of redshift for H0 =\n67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065. The different curves are\ncalculated for a given percentage of sky coverage computed by di-\nviding the sky in equal sized pixels of 3.35 deg2, for which the ap-\nparent magnitude threshold is brighter than the corresponding mthr\nvalue reported in the legend. The fraction of pixels with no galaxies\nis \u223c5%. Bottom panel: sky map showing the GLADE+ K\u2013band\napparent magnitude threshold, mthr, generated by dividing the sky\ninto 3.35 deg2 pixels. A mask is applied that removes all pixels\n(white region) with mthr < 12.5 in order to improve the figure\nreadability. Also shown are the 90% CR sky localizations for the 10\nbest-localized O4a GW events included in our analysis.\nbrighter). Since Virgo did not observe during O4a, the local-\nizations of events from this run are not as well constrained as\nthey could be. Consequently, we can only expect a modest\nimprovement in constraining power from the galaxy catalog\nrelative to GWTC-3.0.\nFor this analysis, we set bright and dim cutoffs at Mmin =\n\u221227.0 and Mmax = \u221219.0, respectively. These choices cor-\nrespond to the limits we used in our previous analysis (Abbott\net al. 2023a).\nThe dark siren analysis requires a pixelization of the\ngalaxy catalog; we adopt the healpix pixelization algo-\nrithm (G\u00f3rski et al. 2005; Zonca et al. 2019) with nside =\n64 and verify that the pixel size remains below the localiza-\ntion scale of the best-constrained GW events, rendering finer\nresolution unnecessary.\n4. RESULTS\n\n21\nIn this Section, we present our cosmological results based on\ndark siren, which are derived from the joint inference of cos-\nmological and population hyperparameters. These include\nparameters that describe the assumed mass distribution and\nmerger rate models. For the H0 results, we will also combine\nour dark siren constraints with those from the bright siren\nGW170817.\nWe sample the posterior in Equation (1) with the\nnormalizing-flows-enhanced\nnested-sampling\npackage\nnessai (Williams et al. 2021; Williams 2021).\nUnless otherwise stated, we present combined results from\nicarogw and gwcosmo as posterior distributions built\nfrom an equal-weighted mixture of samples (50% from each\npipeline). This approach ensures that our final constraints\nincorporate any residual (small) systematic uncertainty asso-\nciated with differences in the numerical implementation of\nthe likelihood.\nSection 4.1 focuses on the measurement of H0 in a flat-\n\u039bCDM model, obtained by combining population informa-\ntion with galaxy catalog data from GLADE+ (D\u00e1lya et al.\n2018, 2022). Section 4.2 presents constraints on modified\nGW propagation, and finally, Section 4.3 presents robustness\nchecks for our results. When quoting results, we report the\nmedian value plus its 68.3% (90%) symmetric credible inter-\nval (CI). We use the relative decrease in average uncertainty,\ncomputed from the CI, as a metric to measure the improve-\nment of our results.\n4.1. \u039bCDM Cosmology\nFigure 4 presents the marginalized posterior distributions\nof the Hubble constant for different cases.\nIn particular,\nthe best estimate of H0 comes from the combined pos-\nterior between the dark siren, luminosity-weighting anal-\nysis result with our fiducial mass model, FULLPOP-4.0,\nand the bright siren result of GW170817.\nThis yields\nH0 = 76.6+13.0\n\u22129.5 (76.6+25.2\n\u221214.0) km s\u22121 Mpc\u22121 (Figure 4, black\ncurve).\nFrom\nthe\ndark\nsiren\nmeasurement\nalone\n(Figure\n4,\nblue\ncurve),\nwe\nobtain\nH0\n=\n81.6+21.5\n\u221215.9 (81.6+42.0\n\u221226.8) km s\u22121 Mpc\u22121. This estimate of H0,\nbased solely on dark sirens, gives a posterior distribution of\nthe Hubble constant which is still slightly broader than that\nobtained from the bright siren GW170817 (Figure 4, yellow\ncurve), namely H0 = 78.4+25.7\n\u221212.0 (78.4+51.2\n\u221216.6) km s\u22121 Mpc\u22121.\nWe obtained our GW170817 H0 posterior by using the same\nlow-spin prior PE samples as in Abbott et al. (2021a), but\nwith an enlarged H0 prior and a different injection set to\nestimate the GW detection probability, in order to match\nthose used with the \u039bCDM spectral and dark siren analyses\npresented in this study. Our GW170817 H0 estimate is con-\nsistent with those reported in Abbott et al. (2017a, 2021a,\n2023a).\nWith the current set of dark sirens, most of the in-\nformation on the Hubble constant still comes from the\npresence of mass features in the population.\nWe assess\nthis by comparing to the case where galaxy-catalog infor-\nmation is not included and constraints on H0 are solely\ndriven by our population assumption, which corresponds to\nthe spectral siren result (Figure 4, orange curve), H0 =\n76.4+23.0\n\u221218.1 (76.4+41.2\n\u221228.6) km s\u22121 Mpc\u22121.\nThe spectral siren\nanalysis is further discussed in Appendix D.\nFrom GLADE+, we find that the inclusion of K-band in-\nformation improves the spectral siren constraints on the Hub-\nble constant by approximately 8.6% (3.1%). The most in-\nformative dark sirens can be identified by computing the\nposterior probability on H0 while fixing the population hy-\nperparameters to reference values, and identifying events\nfor which the information from the in-catalog term pro-\nvides the largest improvement in constraints with respect to\nnot using the catalog.\nThe additional constraining power\nprimarily arises from a few GW events that are nearby\nand well-localized, and for which the galaxy catalog is\nsufficiently complete, notably GW190814 (Abbott et al.\n2020c), GW230627_015337, GW230814_230901 (Abac\net al. 2025k) and GW230529_181500 (Abac et al. 2024).\nThe overall limited gain of information from the galaxy cat-\nalog can be attributed to the low completeness fraction of\nthe GLADE+ K-band data at the distances of most of the\nGWTC-4.0 events, see Figure 3 and Appendix E.\nIn Figure 5 we illustrate the impact of mass models and\ngalaxy weighting on the marginalized posteriors of H0. All\ncurves use K-band information from the GLADE+ galaxy\ncatalog, while the event GW170817 is excluded from the\ndark siren inferences, as it is treated solely as a bright siren\nin this paper (this choice is validated and discussed in de-\ntail in Section 5.2). The left panel presents results based on\nthree different source mass models in the galaxy luminosity-\nweighting case: the PLP, the MLTP, and the FULLPOP-4.0\nmodels. The right panel, in contrast, explores the difference\nbetween the no-weighting and luminosity-weighting cases,\nwhile keeping the source mass model fixed to our fiducial\nmass model (FULLPOP-4.0).\nBased on the left panel of Figure 5, we find some dif-\nferences in the measurements of H0 due to assumptions\nabout the shape of the mass spectrum. Though systematic\ndifferences are visible when comparing the PLP with the\nMLTP and FULLPOP-4.0 results, these are well within the\nstatistical uncertainty. The posterior distributions are wide\nand overlap with each other. In particular, assuming a uni-\nform prior H0 \u2208U(10, 200) km s\u22121 Mpc\u22121 and considering\nthe single-population BBH models, with the MLTP model\nwe obtain H0\n=\n87.3+48.0\n\u221228.2 (87.3+85.6\n\u221242.7) km s\u22121 Mpc\u22121,\nwhile\nwith\nthe\nPLP\nmodel\nwe\nfind\nH0\n=\n124.8+45.2\n\u221239.4 (124.8+63.2\n\u221260.1) km s\u22121 Mpc\u22121.\nThe MLTP distribution shows better agreement with the\nFULLPOP-4.0 distribution. Its higher-mass peak occurs in a\ndifferent location than that of the PLP model, and it is nar-\nrower. We find that the PLP distribution tends to drive the\nH0 estimate toward higher values compared to the MLTP\nmodel. This is due to the fact that a single peak is unable to\nfit the complex low-mass structure of the BBH primary mass\nspectrum, as will be explained in more detail below when\ndiscussing the reconstructed mass spectrum. Moreover, the\nPLP results are constrained by the assumed upper H0-prior\n\n22\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nH0 [km s\u22121 Mpc\u22121]\n0.000\n0.005\n0.010\n0.015\n0.020\n0.025\n0.030\n0.035\n0.040\np(H0|{d}) [km\u22121 s Mpc]\nPlanck\nSH0ES\nBright siren\nSpectral sirens\nDark sirens\nDark + bright sirens\nFigure 4. Hubble constant posterior for different cases. Yellow curve: posterior obtained from the bright siren GW170817 and its EM\ncounterpart. Orange curve: posterior obtained with the spectral siren method and the FULLPOP-4.0 mass model. Blue curve: posterior obtained\nusing all dark sirens with GLADE+ K-band in the luminosity-weighting case (\u03f5 = 1) and the FULLPOP-4.0 mass model. Black curve: posterior\nafter combining the dark and bright siren results. The pink and green shaded areas identify the 68% CI constraints on H0 inferred from CMB\nanisotropies (Ade et al. 2016) and in the local Universe from SH0ES (Riess et al. 2022), respectively.\nbound, which brings the PLP and MLTP distributions into\ncloser agreement.\nWithin\nthe\nsingle-population\n(BBH-candidates-only)\nframework, we find that the MLTP model is mildly preferred\nover the PLP model, which was favored in the previous\nGWTC-3.0 analysis (Abbott et al. 2023a,c). The Bayes fac-\ntor between these two models is log10 B = 0.30, which does\nnot directly allow us to discriminate between the two mass\nmodels. However, this conclusion strongly depends on the\nprior choice for the position of the two peaks in the MLTP\nmodel. Specifically, in the MLTP model, we let both peaks\nspan the mass range U(5, 100) M\u2299, differently from the PLP\nmodel where, following results from previous GWTC-3.0\nanalysis (Abbott et al. 2023a,c), the prior range for its single\npeak is restricted to U(20, 50) M\u2299.\nWe verified that adopting narrower priors for the peaks of\nthe MLTP model, which are compatible with those adopted\nin Abac et al. (2025f) for the BROKEN POWER LAW + 2\nPEAKS model, namely U(7, 12) M\u2299and U(20, 50) M\u2299, the\nPLP model is now strongly disfavored with a Bayes factor\nof log10 B = 2.3, while the posteriors are not constrained\nby the narrower priors. Finally, we are unable to perform a\nmodel-selection comparison between the single- and multi-\npopulation models, as they rely on different datasets.\nAnother key finding illustrated in the left panel of Fig-\nure 5 is the impact of incorporating the full population of\nCBCs, rather than restricting the analysis to BBHs candidates\nalone. Beside making the overall analysis more agnostic (by\nmaking no assumption about the nature of each GW candi-\ndate), the adoption of a multi-population mass model such\nas FULLPOP-4.0 significantly improves the dark siren con-\nstraints on H0, despite the inclusion of just 5 additional can-\ndidates with at least a potential NS. We respectively find an\nimprovement of \u223c56% (\u223c44%) and \u223c51% (\u223c46%) by\nusing the multi-population mass model with respect to the\nPLP and MLTP models, although the latter two models pro-\nvide substantially different medians from each other, with a\nrelative difference of \u223c47%. This is explained by the in-\nclusion of further characteristic scales in the mass spectrum,\nrelated to the mass gap between BHs and NSs (Abac et al.\n2025f). Importantly, the FULLPOP-4.0 model assumes iden-\ntical redshift evolution for both BH and NS merger rates; we\nverified that allowing different evolutionary tracks does not\nlead to statistically significant changes in our results.\n\n23\n20\n40\n60\n80\n100\n120\n140\n160\n180\nH0 [km s\u22121 Mpc\u22121]\n0.000\n0.005\n0.010\n0.015\n0.020\n0.025\np(H0|{d}) [km\u22121 s Mpc]\nImpact of mass modelling\nPlanck\nSH0ES\nPLP\nMLTP\nFullPop-4.0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nH0 [km s\u22121 Mpc\u22121]\nImpact of luminosity weighting\nPlanck\nSH0ES\nNo weighting\nLuminosity weighting\nFigure 5. Left panel: Hubble constant posteriors with the dark siren method using GLADE+ K-band, assuming three different mass models in\nthe luminosity-weighting case: PLP (magenta curve), MLTP (gold curve), and FULLPOP-4.0 (blue curve). See Section 2.3 and Appendix C for\ndefinitions of these models. Right panel: Hubble constant posteriors with the dark siren analysis in the no-weighting and luminosity-weighted\nschemes for host galaxies (blue dashed and solid curves, respectively). All analyses assume the FULLPOP-4.0 mass model. See Section 2.2\nfor details of the galaxy weighting scheme. In both panels the pink and green shaded areas identify the 68% CI constraints on H0 inferred,\nrespectively, from CMB anisotropies (Ade et al. 2016) and in the local Universe from SH0ES (Riess et al. 2022).\nThe right panel of Figure 5 shows the effect of the choice\nof different luminosity weights\u2014either \u03f5 = 0 or \u03f5 = 1,\nsee Equation (8). These choices balance computational cost\nand avoid likelihood inaccuracies that may arise with more\nextreme weightings.\nAlthough fixing these weights intro-\nduces a potential systematic uncertainty (Perna et al. 2024;\nHanselman et al. 2025), the results for the no-weighting and\nluminosity-weighting cases are in good agreement. The abil-\nity to constrain luminosity weights would have astrophysi-\ncal value, but we find no strong evidence, based on Bayes\nfactors, to favor uniform weighting over luminosity-based\nweighting.\nWe find log10 B = \u22120.02 in the luminosity-\nweighting case vs no-weighting case, indicating no signif-\nicant evidence for CBCs to occur in more luminous galax-\nies in the present data.\nThis outcome reflects the rela-\ntively limited impact of the galaxy catalog on the infer-\nence with the datasets used here. We expect that these dif-\nferences will become significant with larger datasets and\nbetter-localized events, in which case marginalizing over the\nweighting power-law index may offer a more robust ap-\nproach.\nThe left panel of Figure 6 shows the reconstructed pri-\nmary mass spectrum using the PLP, MLTP, and FULLPOP-\n4.0 mass models in the dark siren scenario.\nThe\nMLTP and FULLPOP-4.0 models identify two peaks around\n8.7+0.4\n\u22120.6 (8.7+0.7\n\u22121.3)M\u2299and 26.2+2.6\n\u22122.7 (26.2+4.2\n\u22124.6)M\u2299, where\nthe error budgets are given by the uncertainties on each Gaus-\nsian peak (values from the FULLPOP-4.0 mass model). The\nPLP model, in contrast, can only identify a single peak at\n27.5+4.2\n\u22124.3 (27.5+6.1\n\u22126.2) M\u2299, which is compatible with the value\nfound in (Abbott et al. 2023a), although a bit lower. As a con-\nsequence, the PLP model prefers lower masses to account for\nthe missing first peak, which puts GW sources at higher red-\nshifts, therefore leading to higher H0 values, as shown in Fig-\nure 5. The overly simplistic structure of the PLP model is not\nable to capture the full complexity of the observed mass spec-\ntrum (Abac et al. 2025f), and provides fewer mass scales to\ninform the H0 measurement. With the use of the FULLPOP-\n4.0 model, we also gain access to the NS mass range. In\nparticular, we find support for a minimum mass value around\n1.0+0.2\n\u22120.3 (1.0+0.3\n\u22120.5)M\u2299, as well as the presence of two local\nmaxima in the CBC mass spectrum at 2.4+0.4\n\u22120.6 (2.4+0.5\n\u22120.8)M\u2299\nand 7.2+1.1\n\u22121.6 (7.2+1.5\n\u22122.1)M\u2299(see Abac et al. 2025f for further\ndiscussions). Overall, the multi-population mass model re-\nconstructs features in agreement with our favored single-\npopulation model, namely the MLTP.\nThe right panel of Figure 6 presents the reconstruc-\ntion of the CBC merger rate, defined as p(z|{d})\n\u221d\n(dVc/dz)\u03c8(z|\u039b)/(1 + z), (see Section 2 for definitions of\nthese quantities) as derived in the same dark siren scenar-\nios. While the uncertainties remain large at redshifts beyond\nz = 0.5, we find that the reconstructed redshift distribu-\ntions are consistent across the three mass models, with the\nFULLPOP-4.0 and MLTP models predicting higher merger\nrate values than the PLP model. In absence of observations\nfalling in the region around or above the expected peak, any\nconclusion about the shape of the redshift distribution at the\ncorresponding redshifts is driven by the assumed parametric\nform of the merger rate and by the prior range of the associ-\nated parameters.\nThe above results for the merger rate evolution and\nmass spectrum reconstruction are based on the luminosity-\nweighted analysis. We verified that all key conclusions hold\nunchanged also in the no-weighing case, as well as in the\nspectral siren case\u2014see Appendix D for details on the spec-\ntral siren results.\nFinally, Figure 7 shows a reduced corner plot highlighting\na subset of the population and cosmological hyperparame-\n\n24\n100\n101\n102\nm1 [M\u2299]\n10\u22126\n10\u22125\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\np(m1|{d}) [M\u22121\n\u2299]\nPLP\nMLTP\nFullPop-4.0\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nz\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\np(z|{d})\nPLP\nMLTP\nFullPop-4.0\nFigure 6. Left panel: Reconstructed source-frame primary-mass distribution (solid curve: median; shaded region: 90% CI). Right panel:\nreconstructed CBC merger rate as defined in the main text. Results in both panels are obtained from dark siren analyses using the PLP, MLTP,\nand the FULLPOP-4.0 mass models and the GLADE+ K-band in the luminosity-weighting case.\nters inferred using our fiducial mass model in the dark siren\nanalysis and luminosity-weighting case. We observe a strong\ncorrelation between H0 and the locations of the two BH mass\npeaks, \u00b5low\ng\nand \u00b5high\ng\n(see Table 5), consistent with trends\nseen in our previous analysis (Abbott et al. 2023a). Changing\nH0 shifts the inferred redshift of the sources, which in turn\nrescales their intrinsic masses, so the mass spectrum shifts\nalongside H0 to match the observed signals. In contrast, the\nmaximum mass parameter mmax does not seem to correlate\nsignificantly with H0, although its posterior shows a long tail\nup to the upper prior boundary. The NS region of the mass\nspectrum exhibits very weak correlations with H0, likely due\nto the lack of significant structure and the smaller number of\nevents in that mass range. Overall, the Hubble constant ap-\npears to correlate only with certain mass scales, showing no\nsignificant correlation with merger-rate parameters such as\nthe power-law index \u03b3.\nAll constraints obtained in this section assume a fixed\nvalue of \u2126m = 0.3065 as well as a fixed dark energy\nequation-of-state parameter w0 = \u22121. Inferring the values\nof these parameters independently with dark sirens is not\npossible at present using our methods, due to the computa-\ntional cost of constructing redshift priors with varying \u2126m\nand w0. However, we can examine the impact of varying \u2126m\nand w0 with dedicated spectral siren analyses. We find that\nthe posterior distributions of these parameters are consistent\nwith the priors, due to the limited constraining power of our\ndata at high redshift, while the uncertainties on other param-\neters of interest are only marginally affected (as discussed in\nSection 4.3). This confirms that allowing these parameters to\nvary does not influence our main results.\n4.2. Modified Gravity\nIn this Section we present the results obtained by introducing\nparameterized deviations from GR that affect the luminos-\nity distance ratio, DGW\nL\n/DEM\nL\n, as described in Section 2.4.2.\nThe analysis is carried out using our fiducial mass model\nFULLPOP-4.0.\nFor each parametrization, we consider two different (flat)\npriors for the Hubble constant:\na wide prior, H0\n\u2208\nU(10, 120) km s\u22121 Mpc\u22121, and a narrow prior, H0\n\u2208\n6\n8\n10\n\u00b5low\ng\n20\n30\n\u00b5high\ng\n50\n100\n150\nH0\n50\n100\n150\n200\nmmax\n7.5\n10.0\n\u00b5low\ng\n20\n30\n\u00b5high\ng\n100\n200\nmmax\nFigure 7.\nCorner plot showing H0 and a subset of population\nparameters, obtained using a dark sirens analysis assuming the\nFULLPOP-4.0 mass model and with the GLADE+ K-band in the\nluminosity-weighing case. \u00b5low\ng\nand \u00b5high\ng\nare the central locations\nof the two peaks in the mass model, whilst mmax is the maximum\nallowed mass for either binary component. The solid contours indi-\ncate the 68.3% and 90% CR.\nU(65, 77) km s\u22121 Mpc\u22121 (for the narrow prior analysis, we\npresent results obtained with a single pipeline rather than a\nmixture of posterior samples). This choice is motivated by\nthe following considerations. In general, H0 and any param-\neter governing modified GW propagation are correlated to\nsome extent, as both affect the luminosity distance\u2013redshift\nrelation. Consequently, the most agnostic approach to con-\nstraining deviations from GR involves marginalizing over H0\nusing a broad enough prior\u2014hence the adoption of the wider\nrange. The broad prior adopted for H0 in this Section is nar-\nrower than the one used for the \u039bCDM case. This is because,\n\n25\nfor certain extreme combinations of H0 and \u039e0, a wider\nprior on H0 would lead to assigning very high redshifts\u2014\nbeyond z \u227310\u2014to the GW sources in the sample. Our red-\nshift priors, by construction, do not cover these redshifts as\nwe assume they are highly improbable. Furthermore, this\nwould cause instability in our treatment of selection effects\nbecause at these very high redshifts the stability criterion for\nMonte Carlo (MC) integration could fail (see Appendix A).\nTo avoid these issues, we restrict the H0 prior accordingly.\nConversely, it is also valuable to explore constraints on GR\nunder the assumption of prior knowledge of other cosmo-\nlogical parameters, which motivates our second choice of a\nnarrower prior which encompasses the region of the current\nHubble tension at approximately 4\u03c3 (Aghanim et al. 2020;\nRiess et al. 2022; Di Valentino & Brout 2024).\nHere we present the dark siren results with luminosity\nweighting, and focus on the comparison between broad and\nnarrow H0 priors in the figures. We also performed a spectral\nsiren analysis and find consistent results with the dark sirens\nmethod. We find that modified gravity results are not sig-\nnificantly improved by the inclusion of galaxy-catalog infor-\nmation, as the non-GR effects primarily emerge at redshifts\nwhere the catalog is significantly incomplete (see discussion\nin Section 2.4.2).\nFirst, we discuss results for the \u039e0\u2013n parametrization, see\nEquation (22). The uniform priors used in this analysis are\n\u039e0 \u2208U(0.435, 10) and n \u2208U(0.1, 10). The left panel of\nFigure 8 shows the 2D corner plot for \u039e0 and the low-redshift\npower-law slope of the merger rate, \u03b3. We find that \u03b3 shows a\nstrong correlation with the parameters describing deviations\nfrom GR (in this case \u039e0), in agreement with previous find-\nings (Mancarella et al. 2022; Leyde et al. 2022; Chen et al.\n2024a). This correlation occurs because \u039e0 and n modify\nthe relationship between DGW\nL\nand z, therefore affecting the\nobservability of GW sources as a function of redshift. A sim-\nilar change could be reproduced by adjusting the merger rate\nof CBCs as a function of redshift, which is what \u03b3 controls,\nleading to degeneracy.\nAdopting\na\nwide\nH0-prior,\nwe\nfind\n\u039e0\n=\n1.2+0.8\n\u22120.4 (1.2+2.4\n\u22120.5) , while with the narrow H0-prior we ob-\ntain \u039e0 = 1.0+0.4\n\u22120.2 (1.0+1.1\n\u22120.4) . This result is consistent with\nGR, recovered in the limit \u039e0 = 1. The parameter n is poorly\nconstrained, and we do not show it in Figure 8.\nThe right panel of Figure 8 shows the results for the\n\u03b1M parametrization (see Equations 23 and 24), now dis-\nplaying the parameters cM and \u03b3. The uniform prior used\nfor this analysis is cM\n\u2208U(\u221210, 50).\nWe find cM\n=\n0.3+1.6\n\u22121.4 (0.3+2.9\n\u22122.2) for the dark siren analysis with a wide H0-\nprior, and cM = \u22120.3+1.4\n\u22121.0 (\u22120.3+2.5\n\u22121.5) with a narrow H0-\nprior. This is also consistent with GR, recovered in the limit\ncM = 0. The degeneracy with the merger rate parameter \u03b3 is\nvisibly pronounced, for the same reasons discussed for \u039e0.\nIn full Horndeski gravity, the function \u03b1M can also be con-\nstrained through its effects on the CMB. However, in this\nwork we have fixed \u2126m to a value inferred in a flat-\u039bCDM\nanalysis of Planck data (Ade et al. 2016). This may introduce\na small bias in constraints on cM, which we do not expect to\nbe significant given the order-of-magnitude of the constraints\nobtained here. A fully correct approach would be to jointly\nanalyze the Planck data alongside our GW events, which is\nbeyond the scope of the present work; a related discussion is\nfound in Lagos et al. (2019).\nAs expected, we find a correlation between modified grav-\nity parameters and the Hubble constant. In particular, both \u039e0\nand cM are positively correlated with H0, with Pearson cor-\nrelation coefficients 0.31 and 0.58 respectively. This explains\nthe narrower error-bars when restricting H0 with a narrower\nprior.\nFinally, Figure 9 presents the reconstructed relation be-\ntween redshift and GW luminosity distance DGW\nL\nfor both\nthe \u039e0\u2013n and \u03b1M parametrizations, obtained with the dark\nsiren analysis. Figure 9 shows no deviation from the GR\nprediction (in which the distance ratio is always one), con-\nsidering both large and narrow priors on the local expansion\nrate of the Universe. The slight asymmetry of the contours\naround DGW\nL\n/DEM\nL\n= 1, particularly visible in the wide H0-\nprior case, is inherited from the asymmetry of the marginal-\nized posteriors on \u039e0 and cM visible in Figure 8.\nIn order to check consistency among the parametrizations,\nwe can map the constraint on cM (under our fiducial value\nof \u2126m) into a corresponding constraint on \u039e0 using Equa-\ntion (25).\nThis map implies that a flat prior on cM re-\nsults in a prior which is not flat in \u039e0.\nTherefore, for a\nfair comparison, we reweight the samples by the Jacobian\nimplied by Equation (25). Averaging one hundred realiza-\ntions to reduce the effect of random fluctuations, we ob-\ntain \u039e0 = 1.3+1.0\n\u22120.5 (1.3+2.1\n\u22120.7) with a wide H0-prior, and\n\u039e0 = 1.0+0.6\n\u22120.3 (1.0+1.5\n\u22120.4) with a narrow H0-prior. These val-\nues are consistent with the bounds obtained directly from the\n\u039e0 analysis, although with slightly larger uncertainties, in\nparticular at the high tail of the posterior. This can be at-\ntributed to the fact that, as explained in Section 2.4.2, the\ntime evolution of the distance ratio in the two parametriza-\ntions is not fully equivalent: the \u03b1M parametrization adopts\na fixed time evolution for the distance ratio, while in the \u039e0\u2013\nn parametrization the time evolution is encoded in the pa-\nrameter n, over which we marginalize. The fixed time evo-\nlution results in a more marked correlation between cM and\nthe parameter \u03b3 describing the low-redshift evolution of the\nmerger rate, which leads to a broader marginal posterior on\n\u039e0. We verify that this is the case with an analysis where\nwe vary \u039e0 while keeping n fixed to the value predicted\nby Equation (25), which is n \u22482.54. In this case, we re-\ncover a consistent correlation between \u03b3 and \u039e0 across the\ntwo parametrizations. The reconstructed distance ratio (Fig-\nure 9) also shows consistency among the two parametriza-\ntions, while also displaying explicitly the slight difference of\nthe contours as functions of redshift due to the different time\nevolution.\n4.3. Systematics Tests\nFinally, we summarize checks conducted to ensure robust-\nness of our results.\nFigure 10 shows a summary of the\n\n26\n2\n4\n\u039e0\n0\n2\n4\n6\n8\n\u03b3\n0.0\n2.5\n5.0\n7.5\n\u03b3\nWide H0-prior\nNarrow H0-prior\n0\n5\ncM\n0\n2\n4\n6\n8\n10\n\u03b3\n0\n5\n10\n\u03b3\nWide H0-prior\nNarrow H0-prior\nFigure 8. Corner plots of the modified gravity parameters \u039e0 (left) and cM (right), and the merger rate parameter \u03b3, obtained with the dark\nsiren method and assuming the FULLPOP-4.0 mass model. Vertical dashed lines in the abscissa indicate the GR limit of the respective modified\ngravity parameters. The contours indicate the 68.3% and 90% CR.\nconstraints on H0 varying several assumptions discussed\nin Sections 4.1 and 4.2, with additional numerical stabil-\nity checks that we discuss below. In particular, we display\nthe effects of luminosity weighting, varying mass models,\nvarying other parameters of the cosmic expansion history,\nand varying choices related to the accuracy of the likeli-\nhood evaluation. For these tests, we used the dark siren ap-\nproach with the FULLPOP-4.0 mass model and a luminosity-\nweighting scheme. The posteriors shown in this plot do not\ninclude constraints from GW170817, and are obtained with\nthe icarogw pipeline only.\nMost of these cases have already been discussed in previ-\nous sections, so here we focus on the numerical stability tests.\nAccurate likelihood evaluation relies on line-of-sight redshift\nintegrals. In particular, one of our two pipelines employs\nMC integration with a threshold on the effective number\nof PE samples neff,PE in the MC integral (see Appendix A\nfor details). We check the effect of changing this threshold\nfrom 10 (which is our baseline choice) to 50, or eliminat-\ning the threshold altogether (Figure 10, \u201cneff,PE > 50\u201d and\n\u201cNo threshold on neff,PE\u201d labels, respectively). Raising the\nthreshold corresponds to a more stringent condition on the\nprecision of the MC integration. However, adopting a cut\nthat is too high may lead to an artificial shift of the posterior\ntowards a low variance region. This motivates the need for\na check of the stability under this choice. We also consider\nthe possibility of thresholding on the total likelihood vari-\nance instead (Figure 10, \"Log-likelihood variance < 1\", see\nAppendix A for details).\nAlthough these thresholds effectively modify the likeli-\nhood by introducing a data-dependent condition, we find\ntheir effect negligible for the models considered in this work.\nNonetheless, this conclusion holds specifically for the set of\nmodels considered here, and should not be taken as a general\nstatement. In particular, this strategy could become prob-\nlematic when dealing with highly-peaked integrands, such as\nthose resulting from extreme luminosity-weighting schemes,\nwhere redshift priors are dominated by spikes from bright\ngalaxies.\nMC integration is also employed to compute the selection\neffect term (see Appendix A). We follow the criterion (Farr\net al. 2019) requiring the number of effective MC samples\nneff,inj to exceed four times the number of observed events\n(e.g., at least 564 for a sample of 141 events). We also test\nmore stringent thresholds, including increasing the require-\nment to 2000 or removing it entirely (Figure 10, \u201cneff,inj >\n2000\u201d and \u201cNo threshold on neff,inj\u201d labels, respectively),\nfinding no evidence of systematic bias resulting from these\nchanges.\nAs mentioned in Section 2.1, our population models im-\nplicitly assume that the CBC spin distribution is isotropic\nwith uniform distribution in the spin magnitudes (Abac et al.\n2025d). However, we verified that including spin distribu-\ntions for the BBH population using the DEFAULT model (Ab-\nbott et al. 2023c; Abac et al. 2025f) has no significant impact\non the current cosmological constraints (see Section 5). For\nthe spin-informed tests, we adopted the MLTP mass model,\nas this model better fits the BBH mass spectrum of the GW\ncandidates used in our analysis (Abac et al. 2025f).\n5. DISCUSSION AND PERSPECTIVES\n\n27\n0.6\n1\n2\nDGW\nL\n/DEM\nL\n\u039e0\u2013n parametrization\nGR\nWide H0-prior\nNarrow H0-prior\n10\u22121\n100\nz\n0.6\n1\n2\nDGW\nL\n/DEM\nL\n\u03b1M parametrization\nGR\nWide H0-prior\nNarrow H0-prior\nFigure 9. Reconstructed ratio DGW\nL\n/DEM\nL\nas a function of cosmological redshift z, for the two modified gravity parametrizations considered,\n\u039e0\u2013n and \u03b1M. In both cases the contours show the 90% CI with median (dotted curve) reconstructed from the wide-H0 prior (orange)\nand narrow-H0 prior (blue) analyses with the FULLPOP-4.0 mass model. The black dashed curve represents the GR limit. Note that the\nreconstructed distance ratio is asymmetric at higher redshifts.\nIn this Section, we compare our results to the literature,\nand discuss possible improvements and future developments\nwhich constitute negligible systematics at present.\n5.1. Comparison with Existing Results\nWe begin by discussing our constraints on the Hubble con-\nstant. Figure 11 summarizes our findings alongside previous\nmeasurements from the LVK.\nOur baseline result is obtained through a dark siren analy-\nsis that improves upon previous LVK measurements (Abbott\net al. 2023a) by implementing a more advanced methodol-\nogy, as detailed in Section 2. In particular, we perform a full\nmarginalization over the CBC mass distribution and merger\nrate parameters, even with the inclusion of redshift informa-\ntion coming from a galaxy catalog. In contrast, prior LVK\nanalyses with galaxy catalogs relied on fixed population pa-\nrameters. This makes a direct comparison unfair, as fixing\npopulation parameters leads to overly optimistic constraints\non H0. In contrast, our approach achieves comparable preci-\nsion while providing a more statistically robust treatment by\nfully accounting for population uncertainties. This explains\nthe narrower error bar associated to the measurement of Ab-\nbott et al. (2023a) in Figure 11 as compared to the result of\nthis work, despite the former being obtained with a smaller\nsample of GW data.\nThe spectral siren analysis, on the other hand, is directly\ncomparable to the GWTC-3.0 results obtained with the same\nmethod. In this case, without the use of GW170817 as a\nbright siren, our new measurement yields a \u223c60% improve-\nment with respect to Abbott et al. (2023a), driven by the in-\ncreased number of events and by the adoption of the more\ncomprehensive FULLPOP-4.0 population mass model.\nFinally, all our results remain statistically consistent with\nthe values reported by the Planck (Ade et al. 2016; Aghanim\net al. 2020) and SH0ES (Riess et al. 2021) collaborations at\nthe 90% CI.\nWe now turn to results on modified GW propagation.\nPrevious constraints on modified gravity parameters with\nthe GWTC-3.0 catalog were obtained by Mancarella et al.\n(2022); Leyde et al. (2022); Mastrogiovanni et al. (2023);\nChen et al. (2024a), while Ezquiaga (2021) previously had\nbound cM with GWTC-2.0. In particular, assuming a value\nof H0 compatible with Ade et al. (2016), Mancarella et al.\n(2022) and Mastrogiovanni et al. (2023) found \u039e0 = 1.3+0.9\n\u22120.5\nand \u039e0 = 1.44+1.17\n\u22120.93 (68% CI), respectively, while Mastro-\ngiovanni et al. (2023) also measured cM = 1.0+2.6\n\u22123.4 (68%\nCI) and Ezquiaga (2021) found cM = \u22123.2+3.4\n\u22122.0 (68% CI).\nIn Leyde et al. (2022), different constraints are reported de-\npending on the mass model and selection cut applied to the\ndata. Here, we refer to the result with a PLP model and 35\nBBH with SNR > 12. Adopting a prior on H0 restricted to\nthe tension region, Leyde et al. (2022) found \u039e0 = 1.4+1.8\n\u22120.8\nand cM = 0.4+3.2\n\u22123.0 (90% CI). Finally, including also three\n\n28\n40\n60\n80\n100\n120\n140\n160\n180\nH0 [km s\u22121 Mpc\u22121]\nFiducial\nNo-weighting\nPLP\nMLTP\nVarying \u2126m\nVarying w0\nNo threshold on ne\ufb00,inj\nne\ufb00,inj > 2000\nNo threshold on ne\ufb00,PE\nne\ufb00,PE > 50\nLog-likelihood variance < 1\nDark sirens\nSpectral sirens\nFigure 10. Robustness checks against various systematics discussed in Section 4, compared to the fiducial results (\u039bCDM, FULLPOP-4.0, and\nluminosity-weighting case for the dark sirens case). The box-plots show the median value as a vertical segment. The colored boxes stretches\nto the 68.3% CI, while the whiskers extend to encompass the 90% CI. The labels indicate variations with respect to the fiducial results. The\nposteriors shown in this plot do not include bounds from GW170817. In the analyses with varying \u2126m and w0 the priors used are U(0, 1) and\nU(\u22123, 0), respectively. All displayed checks were generated exclusively using icarogw, and not by merging posterior samples from both\npipelines, as done for the main results.\nNSBH mergers from GWTC-3.0, Chen et al. (2024a) found\ncM = 1.5+2.2\n\u22122.1 and \u039e0 = 1.29+0.93,\n\u22120.94 (68% CI) with a wide\nH0 prior. With respect to the best among those results, our\nresult with a wide H0-prior gives a \u223c36% improvement for\n\u039e0, and a \u223c30% improvement for cM.\nOur bound with a narrow H0-prior gives instead a \u223c42%\nimprovement for \u039e0 and a \u223c35% improvement for cM.\nThese improvements are due to the additional events from\nO4a and to the use of the FULLPOP-4.0 population model.\nAssuming \u03b1M is sourced by a scalar degree of freedom\nwithin the effective field theory (EFT) framework, and in the\nclass of Horndeski-type theories, our constraints from GW\nobservations can be compared to those from LSS and the\nCMB. When analyzing LSS and CMB data, it is essential\nto ensure that the scalar sector remains free from ghost and\ngradient instabilities. These theoretical consistency require-\nments further restrict the allowed parameter space. Recent\nLSS analyses that assume luminal tensor propagation (Noller\n& Nicola 2019; Baker & Harrison 2021; Seraille et al. 2024;\nIshak et al. 2024) impose such constraints. In a GW-only\nanalysis, we assume that stability can be enforced by appro-\npriate choices of additional EFT operators\u2014particularly the\nbraiding parameter \u03b1B\u2014which influence only the scalar sec-\ntor. For theories with \u03b1B = 0, regions with \u03b1M < 0 are\ntypically ruled out by stability arguments.\nThe latest available LSS bounds correspond to the clus-\ntering measurements from DESI 2024 (Ishak et al. 2024).\nThis work finds the bound cM < 1.14 (95% CI), assuming\nvanishing braiding and a \u039bCDM background. Relaxing the\nbraiding assumption and marginalizing over it yields a con-\nstraint of cM = 1.05 \u00b1 0.96 at 68% CI. More stringent con-\nstraints can be obtained by combining different LSS observ-\nables. In particular, the integrated Sachs\u2013Wolfe (ISW) ef-\nfect from galaxy\u2013CMB cross-correlations has been shown to\nprovide significant improvements (Renk et al. 2017; Seraille\net al. 2024).\nCombining LSS and CMB observables to\nISW, Seraille et al. (2024) find cM = 0.54+0.90\n\u22120.60 at 95% CI\nafter marginalization over the braiding parameter. Although\nconsistent with these bounds, our best result is weaker by ap-\nproximately \u223c25% and \u223c60% relative to the latter two, re-\nspectively. Despite this, our results are based on an entirely\nindependent dataset with different systematics.\n5.2. Perspectives\nConsiderations on the Spectral Siren Analysis \u2014Spectral siren\ninformation is driven by the shape of the mass spectrum of\ncompact objects.\nOur mass models are based on specific\nparametric forms. We choose a set of hyperparametric prior\nbounds from previous studies Abbott et al. (2023a,c). Ex-\ntending the prior range of the population parameters to sig-\nnificantly wider priors may significantly change the recon-\nstructed mass spectra and therefore effectively represent dif-\n\n29\n60\n70\n80\n90\n100\n110\n120\n130\nH0 [km s\u22121 Mpc\u22121]\nGW170817+O1+O2+O3+O4a [142 CBCs]\nThis work\nGW170817+O1+O2+O3+O4a [142 CBCs]\nGW170817+O1+O2+O3 [47 CBCs]\nGray et al. 2023\nJCAP, Vol. 12\nGW170817+O1+O2+O3 [43 CBCs]\nMastrogiovanni et al. 2023\nPRD, Vol. 108\nGW170817+O1+O2+O3 [47 CBCs]\nAbbott et al. 2023\nApJ, Vol. 949, No2\nGW170817+O1+O2+O3 [43 CBCs]\nGW170817+O1+O2 [7 CBCs]\nAbbott et al. 2021\nApJ, Vol. 909, No2\nGW170817\nThis work\nPlanck\nAde et al. 2016\nA&A, Vol. 594\nSH0ES\nRiess et al. 2022\nApJL, Vol. 934\nBright siren\nDark + bright sirens\nSpectral + bright sirens\nFigure 11. Summary of H0 measurements from GW detections, combining bright with dark or spectral siren analyses conducted by LVK\npipelines from O1 up to O4a. Non-LVK works are shown are labeled in light gray. In yellow, we report the bright siren result that has been\nrecalculated for this work. Note that previous papers combined results use the bright siren samples from Abbott et al. (2021a). We report\nthe dark siren results in blue and spectral siren results in orange, including the bright siren in both cases. The darker-shaded line covers the\nsymmetric 68.3% CI, and extends till 90% CI. Studies that assumed a fixed population model are marked with a dashed line style, and a star as\na marker for the median value. The study from Gray et al. (2023) is marked with a star and a solid line, as it assumed a fixed BNS population\nmodel, but not-fixed models for the BBH and NSBH populations. The total number of CBC events used in the analysis is indicated in square\nbrackets on top of each result. For details on the analysis settings, see the respective publications. The pink and green vertical bands indicate\nthe Planck (Ade et al. 2016) and SH0ES (Riess et al. 2022) median and 1\u03c3 values, respectively. The error bars obtained in this work are based\non our fiducial mass model FULLPOP-4.0.\nferent mass models, even though the analytical formulation\nof the mass model is the same Gennari et al. (2025). We\ndo not consider this possibility here. As discussed in Sec-\ntion 4.1, we observe some variation in the results obtained\nwith our simplest mass model, the PLP model, compared\nto those obtained with the MLTP and FULLPOP-4.0 mod-\nels, which are able to better describe the observed primary\nmass distribution (Abac et al. 2025f), as shown in Figure 5,\nFigure 6, and Figure 10.\nCompared to different galaxy-\nweighting schemes, this represents the dominant systematic\nin our analysis.\nRelated to this, we did not consider extra correlations be-\ntween population features, such as mass\u2013redshift and mass\u2013\nspin interplay. However, their possible existence is being in-\ncreasingly investigated. For example, Li et al. (2024b); Pierra\net al. (2024a) report correlations between spin magnitude and\nmass, which could influence cosmological inferences as cur-\nrent constraints are closely linked to the mass distribution,\nwhile Abac et al. (2025f) finds support for the evolution of\nthe spin distribution with redshift (Biscoveanu et al. 2022).\nTong et al. (2025) studies the impact of spin information in\nspectral siren cosmology, showing that its inclusion can mit-\nigate systematics related to mismodeling of the mass spec-\ntrum. Additionally Li et al. (2024a) find that modelling two\npopulations with different spin and mass distributions yields\nan improvement in Hubble constant bounds from GWTC-3.0\ndata.\nSimilarly, while current data do not robustly support evo-\nlution of the mass distribution with redshift (Heinzel et al.\n2025; Lalleman et al. 2025; Gennari et al. 2025; Abac et al.\n2025f), considering this effect may become important as GW\ndetector sensitivity improves. Such evolution could introduce\nbiases if not properly modeled (Pierra et al. 2024b; Agar-\nwal et al. 2025). Nevertheless, because cosmological effects\nimprint a coherent and predictable modulation on the mass\nspectrum observed across different redshifts, it is expected\nthat appropriate modeling should allow disentanglement of\nthese from astrophysical evolution (Ezquiaga & Holz 2022;\nChen et al. 2024b). In future studies, it would be valuable\nto incorporate comprehensive correlation modeling or adopt\ndata-driven approaches (Farah et al. 2025), which offer in-\ncreased flexibility and robustness by reconstructing features\ndirectly from the observations, without strong parametric as-\nsumptions.\nCombination with Bright Sirens \u2014When combining dark siren\nevents with bright sirens such as GW170817, particularly\nwithin a sample that includes both BNS mergers with and\nwithout EM counterparts, the correct approach would be to\n\n30\nmodel the joint GW and EM detection probabilities and per-\nform a unified hierarchical inference. At present, while our\npipelines fully account for GW selection effects, they do not\nyet model the EM detection probability (potential system-\natics related to EM selection effects, and related mitigation\nstrategies, can be found in Chen 2020; Chen et al. 2024c;\nMancarella et al. 2024; M\u00fcller et al. 2024; Salvarese & Chen\n2024). Consequently, we exclude GW170817 from the dark\nsiren inference and instead combine its posterior with that\nof the dark sirens a posteriori. We verify that this choice\ndoes not introduce any bias by checking that the exclusion of\nGW170817 does not affect the inferred BNS mass spectrum.\nWe therefore conclude that the a posteriori combination used\nhere is robust and does not impact the final cosmological con-\nstraints. Nevertheless, this effect will need to be included\nwhen more bright siren events occur.\nConsiderations on the Analysis with Galaxy catalog \u2014Given the\ncatalog\u2019s incompleteness, assumptions must be made about\nthe distribution of missing galaxies.\nWe model the ex-\npected number density with a redshift-independent Schechter\nfunction (see Section 3.2) and assume that missing galaxies\nare uniformly distributed in comoving volume and isotrop-\nically in sky position. While the latter is the most conser-\nvative choice, viable alternative assumptions include hav-\ning them trace the distribution of cataloged galaxies (Finke\net al. 2021a) or follow prior knowledge of large-scale struc-\nture (Dalang & Baker 2024; Leyde et al. 2024; Dalang et al.\n2024; Leyde et al. 2025). Future work could examine the\nsensitivity of results to these choices and their potential to\nimprove constraints. Possible systematics related to neglect-\ning a putative evolution of the Schechter function might be\nalso considered when using deeper catalogs. Furthermore, in\nthis work, we model the uncertainty on galaxy redshift us-\ning a Gaussian distribution. However, this assumption likely\nrepresents an oversimplification, as photometric redshift er-\nror distributions can be more complex and even vary on a\ngalaxy-by-galaxy basis.\nMore comprehensive approaches,\nsuch as the use of full photo-z PDFs, have been explored\nin the literature (e.g., Palmese et al. 2020). Redshift uncer-\ntainties can propagate into derived quantities that depend on\nredshift, such as K-corrections and absolute magnitudes (or\nluminosities). Turski et al. (2023) investigated two common\nerror models (Gaussian and modified Lorentzian) and found\nthat, under current levels of uncertainty, the choice of red-\nshift error model does not significantly affect constraints on\nthe Hubble constant. Nonetheless, this conclusion may not\nhold as future catalogs become more complete and system-\natic uncertainties are reduced, potentially making the choice\nof redshift uncertainty model more consequential.\nConsiderations on Modified Gravity \u2014The considerations in the\nprevious paragraphs apply also to modified-gravity analyses.\nThe possible evolution of mass features with redshift could\nbe potentially more impactful in this case, due to the redshift\ndependence of modified GW propagation.\nA specific point to address in this case is the parametriza-\ntion choice.\nWhile the parametrizations adopted here are\nwidespread and cover most known theories, they are not\nfully universal.\nTo avoid limitations imposed by specific\nparametrization choices, it would be valuable to consider\nmodel-independent approaches to constrain the GW-to-EM\ndistance ratio directly from data.\n6. CONCLUSIONS\nWe have presented cosmological constraints obtained from\nthe GWTC-4.0 catalog of GW events detected by the LVK\ndetectors. Our headline results are updated bounds on the\nHubble constant: when 141 events with FAR < 0.25 yr\u22121\nare analyzed as dark sirens with the GLADE+ galaxy cata-\nlog, and combined with the bright siren GW170817, we ob-\ntain a bound of H0 = 76.6+13.0\n\u22129.5 (76.6+25.2\n\u221214.0) km s\u22121 Mpc\u22121\n(using the FULLPOP-4.0 mass model and applying luminos-\nity weighting to the galaxy catalog). A summary of the dif-\nferent H0 values obtained using different data sets and model\nassumptions can be seen in Table 1.\nThe H0 bounds obtained from applying a spectral sirens\nanalysis to GWTC-4.0 are improved relative to those with\nGWTC-3.0 by \u223c60%. When spectral siren posteriors are\ncombined with those from the bright siren GW170817 the\nchange between GWTC-4.0 and GWTC-3.0 is somewhat re-\nduced, as can be seen by comparing the two orange bounds\nin Figure 11. This is consistent with GW170817 still being\nan important component of our constraints.\nThe comparison of some dark sirens bounds between\nGWTC-3.0 and GWTC-4.0 is not straightforward given the\nmajor upgrades in methodology that we have presented in\nthis work, such as marginalization over mass distribution and\nmerger rate parameters. The bounds shown in Figure 11 that\nuse a fixed or partially-fixed CBC mass distribution (indi-\ncated by a star) should be considered as artificially tight for\nthis reason. Comparing the results of this work to that of\nMastrogiovanni et al. (2023), which did vary merger rate and\nBBH mass distribution parameters, one can see that the im-\nprovement in the dark sirens results is essentially driven by\nthe improvement in the spectral sirens component (compar-\ning this work to the orange line from Abbott et al. 2023a.)\nWe have considered here a range of parameterized models\nfor the mass distribution of compact objects. The PLP model\nis now mildly disfavored relative to the MLTP model. How-\never, the tightest constraints on H0 are obtained using the\nFULLPOP-4.0 model which enables the NS and BH distribu-\ntions to be jointly analyzed. In comparison, the choice of lu-\nminosity weight applied to the host-galaxy probabilities has\nnegligible importance. Increasing our certainty about types\nand locations of features in the CBC mass distribution is a\nmajor route to tightening GW bounds on the Hubble con-\nstant, via the spectral siren method.\nIn addition, we have presented bounds on parameterized\ndeviations from GR affecting the GW luminosity distance.\nA summary of these constraints can be seen in Table 2.\nUsing two commonly-used parametrizations, we obtain the\ndark siren bounds of \u039e0 = 1.2+0.8\n\u22120.4 (1.2+2.4\n\u22120.5) and cM =\n0.3+1.6\n\u22121.4 (0.3+2.9\n\u22122.2) , where the GR limit is recovered in the\ncases \u039e0 = 1 and cM = 0, respectively. Hence, our re-\n\n31\n\u039bCDM \u2013 Dark sirens\nPopulation model\nGW candidates\nH0 (Dark sirens)\nH0 (Dark + bright sirens)\n[km s\u22121 Mpc\u22121]\n[km s\u22121 Mpc\u22121]\nPOWER LAW + PEAK\n137 (138)\n124.8+45.2\n\u221239.4 (124.8+63.2\n\u221260.1)\n85.9+24.4\n\u221215.9 (85.9+48.8\n\u221222.1)\nMULTI PEAK\n137 (138)\n87.3+48.0\n\u221228.2 (87.3+85.6\n\u221242.7)\n77.0+17.6\n\u221210.9 (77.0+35.3\n\u221215.7)\nFULLPOP-4.0\n141 (142)\n81.6+21.5\n\u221215.9 (81.6+42.0\n\u221226.8)\n76.6+13.0\n\u22129.5 (76.6+25.2\n\u221214.0)\nTable 1.\nValues of the Hubble constant measured in this study using different data sets and analysis methods, adopting a uniform prior\nH0 \u2208U(10, 200) km s\u22121 Mpc\u22121. Columns are: population mass model assumed in the analysis (first column), number of GW candidates\nanalyzed, including GW170817 in parentheses (second column), H0 dark siren measurement reported as a median with 68.3% and 90%\nsymmetric CI, before (third column) and after (fourth column) combination with the bright siren (GW170817) measurement.\nsults show good consistency with GR on cosmological dis-\ntance scales. The improvement in constraints on these pa-\nrameters is quite substantial (\u223c35\u201342% when using a nar-\nrow H0 prior) relative to previous GW analyses.\nThis is\nbecause these constraints in particular utilize higher-redshift\nGW events and are scarcely impacted by galaxy catalog lim-\nitations; so they benefit strongly from the \u223c3-fold increase\nin GW events in GWTC-4.0. Whilst not on an equal footing\nwith EM constraints (for parameters where these are avail-\nable), this work demonstrates the potential of LVK events to\nact as an independent probe of cosmological modified grav-\nity. In future, these tests could be honed on selected modified\ngravity parameters that are inaccessible through galaxy sur-\nveys.\nThe advances in methodology presented have been pos-\nsible due to upgrades in computational efficiency of our\nsoftware pipelines. We anticipate that continuing improve-\nments will open up more flexible parameterized models (e.g.,\nevolving mass-distribution models) in near-future analyses,\nand will ultimately allow non-parametric analyses (such as\nbinned approaches, splines or Gaussian processes).\nThis\nwill allow us to lift the assumptions of parameterized forms\nfor the mass distribution and luminosity distance ratio in\nmodified-gravity tests.\nA limiting factor affecting our present results is the com-\npleteness and redshift depth of the galaxy catalog used in\nour analysis.\nFor most events analyzed here, the bulk of\nthe luminosity-distance posterior distribution lies beyond the\nredshift range of the K-band GLADE+ catalog for the pre-\nferred values of H0. This means that for many events our\nresults are largely uninformed by the distribution of poten-\ntial galaxy hosts; instead, features in the mass distribution\nof CBCs dominate the constraints. However, the absence of\nVirgo during O4a means that O4a candidates have luminos-\nity distance errors that are, on average, larger than those of\nGWTC-3.0. Hence they are somewhat less informative than\nO3 events, even when used as spectral sirens.\nFortunately, both of these limiting factors have near-term\nsolutions. The additional contribution of the Virgo detector\nin the remainder of O4, when combined with the two LIGO\ndetectors, is expected to result in better-localized events, on\naverage. Source localization depends upon the number of\nGW observatories that can detect a source (Schutz 2011; Ab-\nbott et al. 2020b; Abac et al. 2025b). Good sky localiza-\ntion requires data from at least three observatories (Wen &\nChen 2010; Singer et al. 2014; Pankow et al. 2020), while\nvolume localization also depends upon the signal-to-noise ra-\ntio (Cutler & Flanagan 1994; Del Pozzo et al. 2018), which\nalso improves with more observatories. Precise localization\naids both follow-up to search for EM counterparts and cross-\nreferencing with galaxy catalogs (Nissanke et al. 2013b;\nGehrels et al. 2016; Singer et al. 2016; Chen & Holz 2016;\nPankow et al. 2020). Consequently, prospects for GW mea-\nsurements of H0 are significantly enhanced when there is a\nnetwork of at least three comparable-sensitivity GW obser-\nvatories online (Chen et al. 2018; Kiendrebeogo et al. 2023;\nEmma et al. 2024; Soni et al. 2024).\nMeanwhile, a deeper successor to the GLADE+ galaxy\ncatalog, UpGLADE, is in preparation for future release. The\nnext few years will also see further data releases from Stage\nIV galaxy surveys such as the Dark Energy Spectroscopic\nInstrument (Aghamousa et al. 2016), Euclid (Laureijs et al.\n2011; Mellier et al. 2025), and the start of observations by the\nVera Rubin Observatory (Ivezi\u00b4c et al. 2019). Using data from\nthese surveys is expected to strengthen the informativeness\nof the galaxy catalog component of the dark sirens method.\nForecasts using simulations of the 100 highest signal-to-\nnoise ratio events in O4 and O5 with a complete galaxy cata-\nlog are presented in Borghi et al. (2024); these yield bounds\non H0 better than 10% in O5 for both photometric and spec-\ntroscopic galaxy catalogs. Having this kind of galaxy data\nin hand will accelerate the progress towards competitive GW\nbounds on the Hubble constant presented in Figure 11.\nIt remains possible that future runs of the LVK detectors\nwill yield a further bright siren detection(s), although these\nare rare. Such an event would likely give GW measurements\nof H0 a rapid boost in constraining power. However, with or\nwithout such events, the methods and analyses of this paper\ndemonstrate that dark and spectral sirens can provide steady\nprogress towards the goals of GW cosmology.\nData Availability:\nAll strain data analyzed as part of\nGWTC-4.0 are publicly available through Gravitational\nWave Open Science Center (GWOSC). The details of this\ndata release and information about the digital version of the\nGWTC are described in detail in Abac et al. (2025l). The\ndata products generated by the methods described within this\n\n32\nModified gravity \u2013 Dark sirens\nParametrization \u039e0\u2013n\n\u039e0\nWide H0-prior\n1.2+0.8\n\u22120.4 (1.2+2.4\n\u22120.5)\nNarrow H0-prior\n1.0+0.4\n\u22120.2 (1.0+1.1\n\u22120.4)\nParametrization \u03b1M\ncM\nWide H0-prior\n0.3+1.6\n\u22121.4 (0.3+2.9\n\u22122.2)\nNarrow H0-prior\n\u22120.3+1.4\n\u22121.0 (\u22120.3+2.5\n\u22121.5)\nTable 2. Values of the modified-gravity parameters \u039e0 and cM constrained assuming two different parametrizations of modified GW propaga-\ntion. Both analyses are carried out assuming our fiducial population model FULLPOP-4.0 (141 GW candidates) with the dark siren method. We\nexplore wide and narrow priors for H0, i.e., H0 \u2208U(10, 120) km s\u22121 Mpc\u22121 and H0 \u2208U(65, 77) km s\u22121 Mpc\u22121, respectively (see the main\ntext for more details). We adopt uniform priors for \u039e0 \u2208U(0.435, 10) and n \u2208U(0.1, 10) (not reported in this table), and a uniform prior\nfor cM \u2208U(\u221210, 50). Columns are: H0 prior chosen for the analysis (first column), modified gravity parameter (\u039e0 or cM) measurement\nreported as a median with 68.3% (second column, first value) and 90% (second column, second value) symmetric CI. Note that, in contrast to\nTable 1, the bright siren GW170817 is not used as it is uninformative in this analysis.\nwork are available from Zenodo (LIGO Scientific Collabora-\ntion et al. 2025).\nACKNOWLEDGEMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded by\nthe National Science Foundation. The authors also grate-\nfully acknowledge the support of the Science and Technol-\nogy Facilities Council (STFC) of the United Kingdom, the\nMax-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO 600 de-\ntector. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucle-\nare (INFN), the French Centre National de la Recherche\nScientifique (CNRS) and the Netherlands Organization for\nScientific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and support of\nthe EGO consortium. The authors also gratefully acknowl-\nedge research support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India, the\nDepartment of Science and Technology, India, the Science\n& Engineering Research Board (SERB), India, the Ministry\nof Human Resource Development, India, the Spanish Agen-\ncia Estatal de Investigaci\u00f3n (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00f3n y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC - Cen-\ntroNazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the European\nUnion NextGenerationEU, the Comunitat Auton\u00f2ma de les\nIlles Balears through the Conselleria d\u2019Educaci\u00f3 i Universi-\ntats, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia i So-\ncietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Science\nCentre of Poland and the European Union - European Re-\ngional Development Fund; the Foundation for Polish Sci-\nence (FNP), the Polish Ministry of Science and Higher Ed-\nucation, the Swiss National Science Foundation (SNSF), the\nRussian Science Foundation, the European Commission, the\nEuropean Social Funds (ESF), the European Regional De-\nvelopment Funds (ERDF), the Royal Society, the Scottish\nFunding Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scientific Research Fund (OTKA), the French\nLyon Institute of Origins (LIO), the Belgian Fonds de la\nRecherche Scientifique (FRS-FNRS), Actions de Recherche\nConcert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek\n- Vlaanderen (FWO), Belgium, the Paris \u00cele-de-France Re-\ngion, the National Research, Development and Innovation\nOffice of Hungary (NKFIH), the National Research Foun-\ndation of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of Sci-\nence, Technology, and Innovations, the International Center\nfor Theoretical Physics South American Institute for Funda-\nmental Research (ICTP-SAIFR), the Research Grants Coun-\ncil of Hong Kong, the National Natural Science Foundation\nof China (NSFC), the Israel Science Foundation (ISF), the\nUS-Israel Binational Science Fund (BSF), the Leverhulme\nTrust, the Research Corporation, the National Science and\nTechnology Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation. The authors\ngratefully acknowledge the support of the NSF, STFC, INFN\nand CNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific Re-\nsearch (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for\nTransformative Research Areas (A) 20A203: JP20H05854,\n\n33\nthe joint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and the\nNational Science and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research Pro-\ngram, the Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor the purpose of open access, the authors have applied a\nCreative Commons Attribution (CC BY) license to any Au-\nthor Accepted Manuscript version arising. We request that\ncitations to this article use \u2019A. G. Abac et al. (LIGO-Virgo-\nKAGRA Collaboration), ...\u2019 or similar phrasing, depending\non journal convention.\nSoftware:\nCalibration of the LIGO strain data was\nperformed\nwith\nGSTLAL-based\ncalibration\nsoftware\npipeline (Viets et al. 2018). Data-quality products and event-\nvalidation results were computed using the DMT (John\nZweizig 2006), DQR (LIGO Scientific Collaboration and\nVirgo Collaboration 2018), DQSEGDB (Fisher et al. 2020),\nGWDETCHAR (Urban et al. 2021), HVETO (Smith et al.\n2011), IDQ (Essick et al. 2020), OMICRON (Robinet et al.\n2020) and PYTHONVIRGOTOOLS (Virgo Collaboration\n2021) software packages and contributing software tools.\nAnalyses in this catalog relied upon the LALSUITE software\nlibrary (LIGO Scientific Collaboration et al. 2018; Wette\n2020). The detection of the signals and subsequent sig-\nnificance evaluations in this catalog were performed with\nthe GSTLAL-based inspiral software pipeline (Messick\net al. 2017; Sachdev et al. 2019; Hanna et al. 2020; Can-\nnon et al. 2020), with the MBTA pipeline (Adams et al.\n2016; Aubin et al. 2021), and with the PYCBC (Usman\net al. 2016; Nitz et al. 2017; Davies et al. 2020) and the\nCWB (Klimenko & Mitselmakher 2004; Klimenko et al.\n2011, 2016) packages. Estimates of the noise spectra and\nglitch models were obtained using BAYESWAVE (Cornish\n& Littenberg 2015; Littenberg et al. 2016; Cornish et al.\n2021). Source-parameter estimation was performed with\nthe BILBY library (Ashton et al. 2019; Romero-Shaw et al.\n2020) using the DYNESTY nested sampling package (Spea-\ngle 2020). PESUMMARY was used to postprocess and collate\nparameter-estimation results (Hoy & Raymond 2021). The\nvarious stages of the parameter-estimation analysis were\nmanaged with the ASIMOV library (Williams et al. 2023).\nPlots were prepared with MATPLOTLIB (Hunter 2007),\nSEABORN (Waskom 2021) and GWPY (Macleod et al.\n2021). NUMPY (Harris et al. 2020) and SCIPY (Virtanen\net al. 2020) were used in the preparation of the manuscript.\nWe\nmade\nuse\nof\nthe\nsoftware\npackages\ngwcosmo,\nsee\nhttps://git.ligo.org/lscsoft/gwcosmo/-/releases/v3.0.0\nand\nicarogw,\nsee\nhttps://github.com/simone-\nmastrogiovanni/icarogw/releases/tag/v2.0.3.\nAPPENDIX\nA. DETAILS ON THE LIKELIHOOD EVALUATION\nIn this appendix, we provide more details on the likelihood evaluation. Assuming spins are neglected, the integrals in Equation (1)\nspan five dimensions, encompassing the component masses, sky position, and luminosity distance. A common strategy in GW\npopulation studies is to evaluate these integrals via MC integration. The posterior distributions for individual events p\n\u0000\u03b8det\ni\n|di\n\u0001\nare provided as discrete sets of samples, which can be repurposed to compute MC sums.\nIn icarogw the evaluation of the integrals at the numerator of the posterior in Equation (1) uses MC integration. Consider a\nnormalized probability distribution p(x) with\nR\ndx p(x) = 1, and the expectation value of a function f(x), i.e.,\n\u27e8f\u27e9=\nZ\ndx f(x) p(x) .\n(A1)\nThis can be approximated with the following MC estimator:\n\u02c6\n\u27e8f\u27e9=\n1\nNdraw\nNdraw\nX\nk=1\nf(xk) ,\n(A2)\nwhere the points xk are drawn from p(x), for a total of Ndraw draws. In the case of the posterior distribution in Equation (1), for\neach observed event labeled by i, we are given Ns,i samples \u03b8k,i \u223cp(\u03b8det\ni\n|di) from the corresponding posterior. The estimator\nof each integral in the product sign (denoted here as \u02c6Li) is therefore:\n\u02c6Li =\n1\nNs,i\nNs,i\nX\nk=1\n1\n\u03c0PE(\u03b8det\ni,k )\n\"\f\f\fd\u03b8det\ni\n(\u03b8i,k, \u039bc)\nd\u03b8i\n\f\f\f\n\u22121\nppop(\u03b8i,k|\u039b)\n#\n\u03b8i,k=\u03b8i(\u03b8det\ni,k ,\u039bc)\n.\n(A3)\n\n34\nThe advantage of MC integration lies in its ability to handle high-dimensional integrals efficiently, provided sufficient conver-\ngence is achieved. Specifically, MC integration introduces sampling variance that must be carefully managed (Farr 2019; Essick\n& Farr 2022; Talbot & Golomb 2023). The variance associated to the estimator in Equation (A2) can be written as\nvar(\u27e8f\u27e9) =\n1\nNdraw\n\u0002\n\u27e8f 2\u27e9\u2212\u27e8f\u27e92\u0003\n.\n(A4)\nTo ensure accuracy, one typically requires the variance to be small enough. A common diagnostic is the effective sample size (Farr\n2019),\nneff \u2261Ndraw\n\u27e8f\u27e92\n\u27e8f 2\u27e9.\n(A5)\nWe adopt the default choice neff,PE > 10 for the icarogw analyses presented in this work. Here, the suffix PE denotes the\nthreshold for the estimator in Equation (A3).\nIn contrast, gwcosmo employs a one-dimensional kernel density estimation (KDE) method. This approach first re-weights the\nposterior samples \u03b8i,k based on a given population model. For each sample the reweighting is calculated as\nwi,k = ppop(\u03b8i,k|\u039b)\n\u03c0PE(\u03b8i,k|\u039b) .\n(A6)\nThis is followed by the construction of a redshift kernel within each sky pixel \u2126. For each re-weighted sample a redshift zi,k is\ncalculated from its luminosity distance DGW\nL,i,k given \u039bc. The KDE is then used to construct the redshift probability distribution\nof the event i in the pixel \u2126,\np(z|di, \u2126, \u039b) \u2248\nX\nk\u2208\u2126j\nw\u2032\ni,kK(z \u2212zi,k, h),\n(A7)\nwith K(\u00b7, h) being a kernel with bandwidth h and w\u2032\ni,k the normalized weights. Including the catalog information explicitly, the\nlikelihood for a single event becomes\nLi(\u039b) \u221d\nX\nj\np(\u2126j|di, \u039b)\nZ\ndz p(z|\u2126j, \u039b) \u03c8(z|\u039b)\n1 + z p(z|di, \u2126j, \u039b) .\n(A8)\nIn this equation p(z|di, \u2126j, \u039b) is the population-weighted KDE in the pixel \u2126j, p(\u2126j|di, \u039b) is the per-pixel probability given\nevent di, and p(z|\u2126j, \u039b) is the prior from the catalog information. Here, the sum over pixels j effectively discretizes the integral\nover solid angle, so that each pixel \u2126j covers a finite \u2206\u2126j.\nWhile this approach effectively incorporates galaxy catalog information while avoiding the issues of numerical stability found\nwith the MC integration method, it is susceptible to systematic uncertainties if re-weighted sample sizes are too small.\nThe selection function \u03be(\u03bb) is estimated by both icarogw and gwcosmo through MC reweighting of simulated GW injections\ncampaigns (Tiwari 2018; Farr 2019). A number of Ndraw injections are generated with parameters \u03b8det\nk\ndrawn from a reference\ndistribution pdraw(\u03b8det\nk ). Then, the same detection threshold used for building the observed GW catalog is applied. As a result,\nthe detection probability is set to P(det|\u03b8det\nk ) = 1 for the Ndet injections that pass the threshold, and P(det|\u03b8det\nk ) = 0 for the\nrest. The MC estimator of the integral in Equation (2) is then\n\u02c6\u03be(\u03bb) =\n1\nNdraw\nNdet\nX\nk=1\n1\npdraw(\u03b8det\nk )\n\"\f\f\fd\u03b8det\ni\n(\u03b8k, \u039bc)\nd\u03b8i\n\f\f\f\n\u22121\nppop(\u03b8k|\u039b)\n#\n\u03b8k=\u03b8k(\u03b8det\nk\n,\u039bc)\n.\n(A9)\nMore details about the set of injections used in this study can be found in Essick et al. (2025); Abac et al. (2025c).\nFor the selection function \u03be(\u03bb), we follow the condition neff,inj > 4Nobs to ensure sufficient coverage of the parameter space\nby the injections (Farr 2019).\nWhen computing the per-event likelihoods entering the posterior in Equation (1), icarogw additionally imposes neff,PE > 10\nfor each term; as an alternative diagnostic, Talbot & Golomb (2023) suggests using the total variance of the population log-\nlikelihood:\nvar(ln L) =\nNobs\nX\ni=1\nvar(Li)\n\u02c6L2\ni\n+ N 2\nobs\nvar(\u03be)\n\u02c6\u03be2\n.\n(A10)\nA threshold var(ln L) < 1 is found to be sufficient for reliable inference. We also assess the impact of this condition when using\nicarogw.\nIn practice, these criteria act as regularization tools: they restrict the sampler from exploring regions where MC estimates are\nunreliable. These conditions are inherently data-dependent and effectively modify the likelihood surface. Nevertheless, they stem\nfrom numerical limitations, not the likelihood\u2019s theoretical form.\n\n35\nB. LUMINOSITY FUNCTION AND COMPLETENESS ESTIMATES\nB.1. Schechter Luminosity Function\nThe out-of-catalog term in the redshift prior term requires us to estimate the incompleteness of our galaxy catalog due to the\nflux limits of imaging or spectroscopic surveys they are obtained from. The luminosity function of galaxies which quantifies the\nnumber density of galaxies in the Universe is used to quantify this incompleteness. We use a parameterized Schechter function\nto describe the luminosity function such that\n\u03a6(L, \u03bb)dL = \u03d5\u2217\n\u0014 L\nL\u2217\n\u0015\u03b1\nexp\n\u0014\n\u2212L\nL\u2217\n\u0015 dL\nL\u2217\n,\n(B11)\nwhere the parameters \u03bb consist of: the normalization \u03d5\u2217, representing the galaxy number density at the characteristic luminosity,\nthe characteristic luminosity L\u2217, where the function transitions from a power-law to an exponential cutoff, and the faint-end slope\n\u03b1 that determines the abundance of low-luminosity galaxies.\nThe luminosity function can be further expressed in terms of magnitudes by using\nSch(M, \u03bb)dM = \u03a6(L, \u03bb)dL ,\n(B12)\nand the relation between absolute magnitude and luminosity. To express the luminosity function in terms of absolute magnitude\nM, we use the standard relation between luminosity and magnitude:\nL\nL\u2217\n= 100.4(M\u2217\u2212M) ,\n(B13)\nwhere M\u2217is the characteristic magnitude corresponding to L\u2217. Substituting this into Equation (B11), we obtain the Schechter\nfunction in terms of magnitude:\nSch(M; \u03bb) dM = 0.4 ln(10) \u03d5\u2217100.4(\u03b1+1)(M\u2217\u2212M) exp\nh\n\u2212100.4(M\u2217\u2212M)i\ndM ,\n(B14)\nwhere M\u2217is the characteristic magnitude corresponding to L\u2217. In summary, \u03bb = {\u03b1, \u03d5\u2217, M\u2217}. Finally, we assume the Schechter\nfunction to be defined in the interval Mmin \u2264M \u2264Mmax, and being zero outside.\nIn practice, the Schechter parameters are often provided assuming H0 = 100 km s\u22121 Mpc\u22121. To convert them to a cosmology\nwith arbitrary H0, the following scaling relations apply:\nM\u2217(h) = M\u2217(h = 1) + 5 log10 h ,\n(B15)\n\u03d5\u2217(h) = \u03d5\u2217(h = 1) h3 ,\n(B16)\nwhere we have defined h = H0/100 km\u22121 s Mpc. We also assume the luminosity function of galaxies to be non-evolving, i.e.,\nindependent of the redshift.\nFor the K-band luminosity function, we use M K\n\u2217\u22125 log h = \u221223.55, \u03b1 = \u22121.09 and \u03d5\u2217= 1.16 \u00d7 10\u22122h3 Mpc\u22123 based\non the results from the 2MASS galaxy survey (Kochanek et al. 2001). The parameter \u03d5\u2217can be reabsorbed in a normalization\nfactor, therefore its value does not impact our results (Mastrogiovanni et al. 2023; Gray et al. 2023).\nFinally, we discuss the calculation of the out-of-catalog contribution in Equation (12). One has\ndN eff\ngal,out(z, \u2126)\ndzd\u2126\n= dVc(z, \u2126)\ndzd\u2126\nZ Mmax\nMthr(z,mthr(\u2126))\ndM 10\u22120.4\u03f5(M\u2212M\u2217)Sch(M, \u03bb) =\n= dVc(z, \u2126)\ndzd\u2126\n\u03d5\u2217\nZ Lmax/L\u2217\nLthr(z,mthr(\u2126))/L\u2217\ndx x\u03b1+\u03f5e\u2212x ,\n(B17)\nwhere from the first to the second line we changed variables to x \u2261L/L\u2217and used Equation (B11).\nFor \u03b1 > \u22121, one can compute the integral in the second line of Equation (B17) as the difference of incomplete gamma\nfunctions, obtaining:\ndN eff\ngal,out(z, \u2126)\ndzd\u2126\n= dVc(z, \u2126)\ndzd\u2126\n\u03d5\u2217\nh\n\u0393inc(\u03b1 + \u03f5 + 1, xthr) \u2212\u0393inc(\u03b1 + \u03f5 + 1, xmax)\ni\n\u0012\n\u03b1 + \u03f5 > \u22121\n\u0013\n,\n(B18)\nwhere xthr = 100.4[M\u2217\u2212Mthr(z,mthr(\u2126))], xmax = 100.4(M\u2217\u2212Mmax).\nHowever, for values \u03b1 + \u03f5 < \u22121 (as is the case here), the incomplete Gamma functions in square brackets on the right-hand\nside of Equation (B18) are divergent, while their difference and the integral in the second line of Equation (B17) remain finite. In\nthis case, we compute the integral directly via numerical integration.\n\n36\nB.2. Over-density of Galaxies and Incompleteness of the Galaxy Catalog\nFor any given GW event, the over-density of galaxies towards the line-of-sight to an event can be defined as\nO(z, \u2126; \u03bb) =\n\"\ndNgal(z, \u2126)\ndzd\u2126\n+ dVc(z, \u2126)\ndzd\u2126\nZ Mmax(z,\u2126)\nMthr\ndM Sch(M; \u03bb)\n# \"\ndVc(z, \u2126)\ndzd\u2126\nZ Mmax(z,\u2126)\n\u2212\u221e\ndM Sch(M; \u03bb)\n#\u22121\n. (B19)\nThe first term in the numerator is evaluated based on the galaxies present in the galaxy catalog, while the integrals are performed\nbased on the assumed luminosity function parameters. If this ratio is greater (less) than unity, it indicates an over(under)-density\nof galaxies along the line of sight toward the GW source. We compute the mean of this quantity for all pixels at a given redshift,\nand then list the minimum and maximum of these values over the range of redshifts encompassing the 90% credible localization\nintervals in Table 8.\nIn Table 8, we list the minimum and maximum values of this quantity within the redshift range that covers the 90% credible\nlocalization for each event.\nThe incompleteness of the galaxy catalog in a given direction for the case of luminosity weighting is defined as:\nI(z, \u2126; \u03bb) =\n\"\ndVc(z, \u2126)\ndzd\u2126\nZ Mthr(z,\u2126)\n\u2212\u221e\ndM 10\u22120.4(M\u2212M\u2217)Sch(M; \u03bb)\n# \"\ndVc(z, \u2126)\ndzd\u2126\nZ Mmax(z,\u2126)\n\u2212\u221e\ndM 10\u22120.4(M\u2212M\u2217)Sch(M; \u03bb)\n#\u22121\n.\n(B20)\nAt every redshift, we compute the median of this quantity over all pixels corresponding to the 90% localization. We report values\ncorresponding to the minimum and maximum redshift that encompasses the 90% credible intervals as a range in Table 8.\nC. MASS AND MERGER RATE MODELS\nIn this appendix, we describe the population models that we have considered in this paper, both in terms of mass and merger rate\nof CBCs. All the adopted population models are composed of various simple mathematical functions which we describe below.\nThe truncated power law P (x|xmin, xmax, \u03b1) is described by slope \u03b1, and lower and upper bounds xmin, xmax where the\ndistribution shows hard cutoffs,\nP (x|xmin, xmax, \u03b1) \u221d\n(\nx\u03b1\n(xmin \u2264x \u2264xmax)\n0\notherwise\n.\n(C21)\nThe truncated Gaussian distribution with mean \u00b5 and standard deviation \u03c3 with support at [a, b] is defined as\nG(x|\u00b5, \u03c3, a, b) = G(a, b)\n\u03c3\n\u221a\n2\u03c0 exp\n\u0014\n\u2212(x \u2212\u00b5)2\n2\u03c32\n\u0015\n,\n(C22)\nwith the normalization G(a, b) implicitly determined through\nZ b\na\nG(x|\u00b5, \u03c3, a, b)dx = 1 .\n(C23)\nIn the PLP and MLTP population models, we apply a smoothing function at low masses (m = mmin), also called high-pass filter,\nso that\np(m1, m2|\u039b) \u221dp(m1|\u039b)Sh(m1|mmin, \u03b4m)p(m2|m1, \u039b)Sh(m2|mmin, \u03b4m) .\n(C24)\nHere, Sh(m|mmin, \u03b4m) is a sigmoid-like smoothing function that rises from 0 to 1 over the interval (mmin , mmin + \u03b4m) given by\nSh (m|mmin, \u03b4m) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n0\n(m < mmin)\n[f (m \u2212mmin, \u03b4m) + 1]\u22121\n(mmin \u2264m < mmin + \u03b4m) ,\n1\n(m \u2a7emmin + \u03b4m)\n(C25)\nwhere \u03b4m is a smoothing scale parameter and\nf (m\u2032, \u03b4m) = exp\n\u0012\u03b4m\nm\u2032 +\n\u03b4m\nm\u2032 \u2212\u03b4m\n\u0013\n.\n(C26)\nThe notation in Equation (C24) has been slightly misused because, due to the smoothing functions, the marginal distribution\np(m1,2|\u039b) is no longer obtained by marginalization of Equation (C24) over m2,1.\n\n37\nPOWER LAW + PEAK\nParameter\nDescription\nPrior\n\u03b1\nSpectral index of primary mass power law\nU(1.5, 12)\n\u03b2\nSpectral index of secondary mass power law\nU(\u22124, 12)\nmmin\nMinimum primary mass [M\u2299]\nU(2, 10)\nmmax\nMaximum primary mass [M\u2299]\nU(50, 200)\n\u03b4m\nSmoothing parameter [M\u2299]\nU(10\u22123, 10)\n\u00b5g\nLocation of the peak [M\u2299]\nU(20, 50)\n\u03c3g\nWidth of the peak [M\u2299]\nU(0.4, 10)\n\u03bbg\nFraction of events in the peak\nU(0, 1)\nTable 3. Summary of the hyperparameters priors used for the PLP model. U stands for uniform prior.\nThe PLP model (Talbot & Thrane 2018) describes the primary mass distribution as a combination of two components: a\ntruncated power law with slope \u2212\u03b1, defined between a minimum mass mmin and a maximum mass mmax, and a truncated\nGaussian distribution with mean \u00b5g and standard deviation \u03c3g defined in the range [mmin, mmax], with the parameter \u03bbg denoting\nthe fraction of events belonging to the Gaussian component; the secondary mass is modeled with a separate power law, defined\nbetween mmin and m1 and characterized by the slope \u03b2,\np(m1|\u039b) = (1 \u2212\u03bbg) P\n\u0000m1 | mmin, mmax, \u2212\u03b1\n\u0001\n+ \u03bbg G\n\u0000m1 | \u00b5g, \u03c3g, mmin, mmax\n\u0001\n,\n(C27)\np(m2|m1, \u039b) = P(m2|mmin, m1, \u03b2) .\n(C28)\nWe report the parameter priors of the PLP model in Table 3.\nThe MLTP model (Abbott et al. 2021c) is the direct extension of the PLP model. The primary mass distribution is based on\nEquation (C24) and consists of one power law combined with two Gaussian peaks,\np(m1|\u039b) = (1 \u2212\u03bbg)P(m1|mmin, mmax, \u2212\u03b1)\n+ \u03bbg\u03bblow\ng\nG(m1|\u00b5low\ng\n, \u03c3low\ng\n, mmin, mmax)\n+ \u03bbg(1 \u2212\u03bblow\ng\n)G(m1|\u00b5high\ng\n, \u03c3high\ng\n, mmin, mmax) ,\n(C29)\nwhere the two means of the Gaussian components are given by \u00b5low\ng\nand \u00b5high\ng\n, and their respective standard deviations by \u03c3low\ng\nand \u03c3high\ng\n. Once again, the respective fraction of events in the first and second Gaussian peak are given by \u03bbg and \u03bblow\ng\n. The\nsecondary mass distribution is still modeled as in Equation (C28). We report the parameter priors of the MLTP model in Table 4.\nThe FULLPOP-4.0 model (Abac et al. 2025f) spans the full mass distribution of CBCs and therefore includes BNSs, NSBHs,\nand BBHs. It consists of a broken power-law continuum, Gaussian peaks, and smoothing at the edges of the distribution. It\nadditionally includes notch filters to allow for both lower and upper mass gaps (Ozel et al. 2010; Farr et al. 2011; Fryer et al.\n2012; Belczynski et al. 2012). The depth of these mass gaps is a free parameter: the data can determine whether the rate goes\nto zero within the gap or if the gap is partially or totally filled. This model is an extension of the POWERLAW\u2013DIP\u2013BREAK\nmodel described in Fishbach et al. (2020); Farah et al. (2022), and is the same as the FULLPOP-4.0 model described in Abac et al.\n(2025f). The primary and secondary mass distributions of FULLPOP-4.0 are described by the following equation,\np(m|\u039b) =\nh\n(1 \u2212\u03bbg)B(m|mmin, mmax, \u03b11, \u03b12, b) + \u03bbg\u03bblow\ng\nG(m|\u00b5low\ng\n, \u03c3low\ng\n, mmin, mmax)\n+ \u03bbg(1 \u2212\u03bblow\ng\n)G(m|\u00b5high\ng\n, \u03c3high\ng\n, mmin, mmax)\ni\n.\n(C30)\nIn Equation (C30), the distributions G are the same Gaussian components as for the MLTP mass model, hence the hyperparameters\ngoverning the fractions of events in the peaks or the position of the mass features are named similarly. The function B is a broken\npower law constructed from two truncated power-law distributions that are joined at the point b such that:\nb = mbreak \u2212mmin\nmmax \u2212mmin\n,\n(C31)\n\n38\nwith\nmbreak = 0.5(mlow\nd\n+ mhigh\nd\n+ \u03b4min\nd\n\u2212\u03b4max\nd\n),\n(C32)\nnamely, the center of the mass gap between the NS and BH regions. The probability density distribution of the broken power law\nB for the primary and secondary masses is hence written as\nB(m|mmin, mmax, \u03b11, \u03b12, b) =\n1\nNB\n\u0014\nP(m|mmin, b, \u2212\u03b11) + P(b|mmin, b, \u2212\u03b11)\nP(b|b, mmax, \u2212\u03b12)P(m|b, mmax, \u2212\u03b12)\n\u0015\n,\n(C33)\nwhere NB is the normalization factor. Finally, the primary and secondary mass distributions are combined using low-, high-, and\nnotch filters to construct the FULLPOP-4.0 mass model. The total distribution is then given by the product of p(m|\u039b) with a\nhigh-pass filter Sh at mmin governed by \u03b4min\nm , a low-pass filter Sl at mmax governed by \u03b4max\nm\n, and a notch filter Sn between mlow\nd\nand mhigh\nd\n, governed by \u03b4min\nd\nand \u03b4max\nd\n. The low-pass filter is constructed similarly to the high-pass filter,\nSl (m|mmax, \u03b4m) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n0\n(m > mmax)\n[f (mmax \u2212m, \u03b4m) + 1]\u22121\n(mmax \u2212\u03b4m \u2264m < mmax) ,\n1\n(m \u2264mmax \u2212\u03b4m)\n(C34)\nwhere the function f(.) is the same as the one defined above in Equation (C26). The notch filter is defined as a combination of\nthe low- and high-pass filters,\nSn(m|mmin, \u03b4min\nm , mmax, \u03b4max\nm\n) = 1 \u2212A Sl(m|mmax, \u03b4max\nm\n)Sh(m|mmin, \u03b4min\nm ) ,\n(C35)\nwhere A \u2208[0, 1] is a parameter governing the deepness of the dip. Following the above definitions and using Equation (C30), we\ncan define\npS(m1|\u039b) \u221dp(m1|\u039b)Sh(m1|mmin, \u03b4min\nm )Sl(m1|mmax, \u03b4max\nm\n)Sn(m1|mlow\nd , \u03b4min\nd\n, mhigh\nd\n, \u03b4max\nd\n) ,\n(C36)\nand similarly for the secondary mass. The normalized joint probability density is then given by the product of both pS(m1|\u039b)\nand pS(m2|\u039b) with the pairing function f(m1, m2|\u039b) defined by\nf(m1, m2|\u03b21, \u03b22, mbreak) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f3\n\u0012m2\nm1\n\u0013\u03b21\n(m2 < mbreak)\n\u0012m2\nm1\n\u0013\u03b22\n(m2 \u2265mbreak) ,\n(C37)\nso that\np(m1, m2|\u039b) =\n1\nNS\npS(m1|\u039b)pS(m2|\u039b)f(m1, m2|\u039b) ,\n(C38)\nwhere NS is a normalization constant to be computed numerically. Note that due to the pairing formalism the marginal mass\ndistributions are different from the marginalized joint distribution (Abac et al. 2025f). The full set of parameter priors, descriptions\nand notations, are shown in Table 5.\nFinally, we describe the merger rate evolution as a function of the redshift, modeled with a Madau\u2013Dickinson parametriza-\ntion (Madau & Dickinson 2014), which is characterized by parameters {\u03b3, \u03ba, zp} \u2208\u039b, where \u03b3 and \u03ba are the power-law slopes\nrespectively before and after the redshift turning point between the two power-law regimes, zp. Explicitly,\n\u03c8 (z|\u03b3, \u03ba, zp) =\nh\n1 + (1 + zp)\u2212\u03b3\u2212\u03bai\n(1 + z)\u03b3\n1 + [(1 + z)/ (1 + zp)]\u03b3+\u03ba .\n(C39)\nThe parameter priors are shown in Table 6.\nD. SPECTRAL SIREN RESULTS\nIn this Appendix we report details on results using the spectral sirens method. Figure 12 displays the marginalized posteriors for\nthe Hubble constant estimated with each of the three mass models considered. As for the galaxy catalog results (see Figure 4),\nwe show the marginalized posterior for H0 from the spectral siren analysis, with different mass models, as well as the posterior\nfor the FULLPOP-4.0 model combined with the bright siren GW170817 (blue curve). The analyses using the PLP, MLTP, and\nFULLPOP-4.0 mass models yield H0 = 112.7+51.0\n\u221235.9(112.7+74.0\n\u221255.1) km s\u22121 Mpc\u22121, H0 = 77.1+40.8\n\u221226.3(77.1+83.5\n\u221239.1) km s\u22121 Mpc\u22121,\nand H0 = 76.4+23.0\n\u221218.1(76.4+41.2\n\u221228.6) km s\u22121 Mpc\u22121, respectively. We observe that, as for the dark siren analysis, the best precision\n\n39\nMULTI PEAK\nParameter\nDescription\nPrior\n\u03b1\nSpectral index of primary-mass power law\nU(1.5, 12)\n\u03b2\nSpectral index of secondary-mass power law\nU(\u22124, 12)\nmmin\nMinimum primary mass [M\u2299]\nU(2, 10)\nmmax\nMaximum primary mass [M\u2299]\nU(50, 200)\n\u03b4m\nSmoothing parameter [M\u2299]\nU(10\u22123, 10)\n\u00b5low\ng\nLocation of the first peak [M\u2299]\nU(5, 100)\n\u03c3low\ng\nWidth of the first peak [M\u2299]\nU(0.4, 5)\n\u00b5high\ng\nLocation of the second peak [M\u2299]\nU(5, 100)\n\u03c3high\ng\nWidth of the second peak [M\u2299]\nU(0.4, 10)\n\u03bbg\nFraction of sources in the peaks\nU(0, 1)\n\u03bblow\ng\nFraction of sources in the first peak\nU(0, 1)\nTable 4. Summary of the hyperparameters priors used for the MLTP model. U stands for uniform prior.\nFULLPOP-4.0\nParameter\nDescription\nPrior\n\u03b11\nSpectral index of the power law before b\nU(\u22124, 12)\n\u03b12\nSpectral index of the power law after b\nU(\u22124, 12)\n\u03b21\nSpectral index of the pairing function before mbreak\nU(\u22124, 12)\n\u03b22\nSpectral index of the pairing function after mbreak\nU(\u22124, 12)\nmmin\nMinimum primary and secondary mass [M\u2299]\nU(0.4, 1.4)\nmmax\nMaximum primary and secondary mass [M\u2299]\nU(50, 200)\n\u03b4min\nm\n1st smoothing parameter of the low mass [M\u2299]\nLU(10\u22122, 1)\n\u03b4max\nm\n2nd smoothing parameter of the low mass [M\u2299]\nLU(10\u22123, 1)\n\u00b5low\ng\nLocation of the first peak [M\u2299]\nU(5, 150)\n\u03c3low\ng\nWidth of the first peak [M\u2299]\nU(0.4, 5)\n\u00b5high\ng\nLocation of the second peak [M\u2299]\nU(5, 150)\n\u03c3high\ng\nWidth of the second peak [M\u2299]\nU(0.4, 10)\n\u03bbg\nFraction of sources in peaks\nU(0, 1)\n\u03bblow\ng\nFraction of sources in the first peak\nU(0, 1)\nmlow\nd\nLeft side of the dip [M\u2299]\nU(1.5, 3)\nmhigh\nd\nRight side of the dip [M\u2299]\nU(5, 9)\n\u03b4min\nd\nSmoothing of the left side of the dip [M\u2299]\nLU(0.01, 2)\n\u03b4max\nd\nSmoothing of the right side of the dip [M\u2299]\nLU(0.01, 2)\nA\nAmplitude of the dip\nU(0, 1)\nTable 5. Summary of the hyperparameters priors used for the FULLPOP-4.0 mass model. U (LU) stands for uniform (log-uniform) prior.\nis also achieved using the FULLPOP-4.0 population mass model, which benefits from a larger number of GW events and more\nmass features. Our most precise estimate is obtained by combining the FULLPOP-4.0 model with GW170817, which leads to a\nvalue of H0 = 74.6+13.4\n\u22129.1 (74.6+26.1\n\u221213.5) km s\u22121 Mpc\u22121, similar to the dark sirens results.\nFigure 13 shows the reconstructed primary mass spectrum from the spectral analysis using the PLP, MLTP, and FULLPOP-4.0\nmass models. As for the dark siren analysis, the MLTP and FULLPOP-4.0 models identify two peaks at 8.9+0.4\n\u22120.6(8.9+0.7\n\u22121.1)M\u2299and\n26.8+2.6\n\u22122.7(26.8+4.4\n\u22124.4)M\u2299, while the PLP model only identifies the latter at 28.6+3.9\n\u22124.9(28.6+6.0\n\u22127.0)M\u2299. For the NS region, the results\n\n40\nMerger rate model\nParameter\nDescription\nPrior\n\u03b3\nSlope of the power law before the point zp\nU(0, 12)\n\u03ba\nSlope of the power law after the point zp\nU(0, 6)\nzp\nRedshift turning point between the power laws\nU(0, 4)\nTable 6. Summary of the hyperpriors used in the merger rate evolution model. U stands for uniform prior.\n50\n100\n150\n200\nH0 [km s\u22121 Mpc\u22121]\n0.00\n0.01\n0.02\n0.03\n0.04\np(H0|{d}) [km\u22121 s Mpc]\nPlanck\nSH0ES\nPLP\nMLTP\nFullPop-4.0\nFullPop-4.0 + GW170817\n100\n101\n102\nm1 [M\u2299]\n10\u22126\n10\u22125\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\np(m1|{d}) [M\u22121\n\u2299]\nPLP\nMLTP\nFullPop-4.0\nFigure 12. Left panel: Hubble constant posteriors with the spectral sirens method assuming different population mass models, namely the\nPLP (magenta curve), MLTP (gold curve) and FULLPOP-4.0 (blue curve). The black curve corresponds to the combined posterior between the\nFULLPOP-4.0 result and the bright siren posterior measured with GW170817. The pink and green shaded areas identify the 68% CI constraints\non H0 inferred from CMB anisotropies (Ade et al. 2016) and in the local Universe from SH0ES (Riess et al. 2022) respectively. Right panel:\nreconstructed source-frame primary mass distribution with the spectral siren method assuming the PLP, MLTP, and the FULLPOP-4.0 mass\nmodels (solid curve: median; shaded region: 90% CI).\nare again consistent with the galaxy catalog analysis, supporting the presence of a shallow dip between 2.3+0.4\n\u22120.5(2.3+0.6\n\u22120.7)M\u2299and\n7.2+1.1\n\u22121.6(7.2+1.5\n\u22122.0)M\u2299.\nFigure 13 presents the reduced corner plot showing the most interesting population and cosmological parameters derived from\nthe spectral siren analysis with the FULLPOP-4.0 mass model, as in Figure 7. In addition, in Figure 13 we display results obtained\nwith our two pipelines separately, to show explicitly their consistency. These results are consistent with those obtained from the\ndark siren analysis.\nFinally, in addition to constraints on the Hubble constant, with the spectral siren approach in principle we are able to infer the\npresent-day matter density of the Universe, \u2126m and the dark energy equation-of-state parameter w0. To facilitate comparison\nwith the results of Section 4.1, the main results of this section keep \u2126m fixed. See Section 4.1 and Figure 10 for a discussion of\nthe impact of varying \u2126m and w0.\nA summary of the different H0 values obtained using different data sets and model assumptions can be seen in Table 7.\nE. EVENT LIST\nIn this Appendix we provide a list of the events used in our analyses with their main properties relevant for our analysis. For the\ndetails on the PE and waveform models used, see Sec. 3.1. For each of the 142 events used in our analyses, Table 8 reports the\nfollowing properties:\n\u2022 SNR: we give the value of the search pipeline which has reported the lowest FAR.\n\u2022 FAR: in units of inverse years, we report the lowest FAR among the pipelines.\n\u2022 mdet\n1 , mdet\n2 , DL, and z: detector-frame masses of the primary and secondary components, the luminosity distance to\nthe source and the corresponding redshift, calculated from the distance samples assuming Planck-15 (Ade et al. 2016)\ncosmology. We give the median of the samples and the 90% CI, cutting away 5% of samples at the edges of the posterior\ndistribution\n\n41\n6\n8\n10\n\u00b5low\ng\n20\n30\n\u00b5high\ng\n50\n100\n150\nH0\n2.5\n5.0\n\u03b3\n7.5\n10.0\n\u00b5low\ng\n20\n30\n\u00b5high\ng\n2.5\n5.0\n\u03b3\ngwcosmo\nicarogw\nFigure 13. Spectral siren reduced corner plot of the Hubble constant and a subset of the FULLPOP-4.0 model mass parameters obtained with\ngwcosmo and icarogw. The contours indicate the 68.3% and 90% CR.\n\u039bCDM \u2013 Spectral sirens\nPopulation model\nGW sources\nH0 (Spectral sirens)\nH0 (Spectral + bright sirens)\n[km s\u22121 Mpc\u22121]\n[km s\u22121 Mpc\u22121]\nPOWER LAW + PEAK\n137 (138)\n112.7+51.0\n\u221235.9 (112.7+74.0\n\u221255.1)\n74.8+15.5\n\u22129.9 (74.8+31.6\n\u221214.4)\nMULTI PEAK\n137 (138)\n77.1+40.8\n\u221226.3 (77.1+83.5\n\u221239.1)\n74.8+15.5\n\u22129.9 (74.8+31.6\n\u221214.4)\nFULLPOP-4.0\n141 (142)\n76.4+23.0\n\u221218.1 (76.4+41.2\n\u221228.6)\n74.6+13.4\n\u22129.1 (74.6+26.1\n\u221213.5)\nTable 7.\nValues of the Hubble constant measured using different data sets and analysis methods, adopting a uniform prior H0 \u2208\nU(10, 200) km s\u22121 Mpc\u22121. Columns are: population mass model assumed in the analysis (first column), number of GW sources analyzed\n(second column), H0 measurement reported as a median with 68.3% (third column) and 90% (fourth column) symmetric CI. The values in\nparentheses are those obtained after combining the dark and bright (GW170817) measurements.\n\u2022 Sky localization \u2206\u2126: the localization area of the event calculated from the skymap as a fraction of pixels containing the\n90% of the probability\n\u2022 Localization volume \u2206V : localization volume of the event at 90% CI, calculated as the fraction corresponding to the 90%\nof the sky area (see above) of the spherical shell, at the 90% CI of the event\u2019s redshift distribution\n\u2022 Ngal, over(under)-density and incompleteness: the number of galaxies inside the 90% localization volume, the over(under)-\ndensity fraction (see Equation (B19)), and the catalog (K-band of the GLADE+ catalog) incompleteness percentage (see\nEquation (B20)).\n\n42\nTable 8.\nList of the 142 CBC events selected with FAR < 0.25 yr\u22121. Columns with a \u2018*\u2019 have been computed assuming the reference cosmology in Ade et al. (2016), i.e.\nH0 = 67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065. This table reports all of the GW events considered in this work and summarizes some of their properties reported with their median\nvalues and 90% symmetric CI (Abbott et al. 2019a, 2021b, 2024, 2023b; Abac et al. 2025d). First, second and third columns: GW event label, detected SNR (the one corresponding\nto the lowest FAR among the different pipelines, see Abac et al. 2025d) and FAR. Fourth, fifth, sixth columns: estimated primary and secondary detector-frame masses, luminosity\ndistance. Seventh, eighth and ninth columns: redshift, sky localization area, and 3D localization comoving volume. The tenth column lists the number of galaxies in GLADE+ inside\nthe localization volume for each event with K-band observations, while the eleventh and twelfth columns report the under(over)-density of galaxies and the incompleteness fraction\nof the catalog for each event. The under(over)-density is computed as the fraction between the number of galaxies (in the K-band) corrected for incompleteness, and the effective\nnumber expected from the Schechter function. We report the minimum and maximum values, respectively. The lower and upper bounds on the incompleteness probabilities, instead,\nare derived from the incompleteness fractions at the boundaries of the 90% localization volume. The last three columns, number of galaxies, under(over)-density, and incompleteness\nfraction, do not apply to the GW170817 event. We report these values using a distance prior proportional to D2\nL and a uniform in detector-frame masses prior. For events released\nwith GWTC-3.0, we use the first data release associated with Abbott et al. (2023b).\nName\nSNR\nFAR\nmdet\n1\nmdet\n2\nDL\nz\u2217\n\u2206\u2126\n\u2206V \u2217\nN\u2217\ngal\nUnder(over)-density\u2217\nIncompleteness\u2217(%)\n\u2013\n\u2013\n[yr\u22121]\n[M\u2299]\n[M\u2299]\n[Mpc]\n\u2013\n[deg2]\n[Gpc3]\n\u2013\n\u2013\n\u2013\nGW150914\n24.4\n1.1 \u00d7 10\u221239\n38+5\n\u22123\n32+3\n\u22125\n463+132\n\u2212142\n0.10+0.03\n\u22120.03\n159\n2.0 \u00d7 10\u22123\n1.4 \u00d7 103\n0.98\u20131.15\n55\u201390\nGW151012\n10.0\n7.9 \u00d7 10\u22123\n30+19\n\u22127\n16+6\n\u22126\n1056+621\n\u2212493\n0.21+0.10\n\u22120.09\n1.5 \u00d7 103\n0.29\n6.7 \u00d7 103\n0.98\u20131.02\n88\u2013100\nGW151226\n13.1\n2.0 \u00d7 10\u221215\n16+12\n\u22124\n8+2.6\n\u22123.0\n471+158\n\u2212196\n0.10+0.03\n\u22120.04\n1.0 \u00d7 103\n0.02\n1.2 \u00d7 104\n\u223c1\u20131.19\n46\u201393\nGW170104\n13.0\n2.5 \u00d7 10\u22129\n35+8\n\u22125\n25+5\n\u22126\n1126+385\n\u2212466\n0.22+0.07\n\u22120.09\n938\n0.14\n3.1 \u00d7 103\n0.98\u20131.01\n93\u2013100\nGW170608\n14.9\n4.9 \u00d7 10\u221216\n12+5\n\u22121.7\n8+1.3\n\u22122.3\n334+123\n\u2212117\n0.07+0.03\n\u22120.02\n392\n2.5 \u00d7 10\u22123\n1.8 \u00d7 103\n0.54\u20132.12\n29\u201374\nGW170729\n10.8\n0.18\n77+16\n\u221214\n46+17\n\u221218\n2874+1630\n\u22121474\n0.49+0.22\n\u22120.23\n1.1 \u00d7 103\n1.9\n41\n\u223c1\u2013\u223c1\n100\u2013100\nGW170809\n12.4\n4.6 \u00d7 10\u221214\n41+10\n\u22126\n29+6\n\u22127\n1117+298\n\u2212352\n0.22+0.05\n\u22120.06\n269\n0.03\n487\n0.98\u2013\u223c1\n96\u2013100\nGW170814\n15.9\n1.2 \u00d7 10\u221219\n34+6\n\u22123\n28+3\n\u22125\n600+165\n\u2212226\n0.12+0.03\n\u22120.04\n85\n2.2 \u00d7 10\u22123\n744\n0.95\u20131.05\n63\u201397\nGW170817\n33.0\n7.9 \u00d7 10\u221251\n1.6+0.3\n\u22120.2\n1.2+0.2\n\u22120.2\n42+6\n\u221213\n0.01+0.00\n\u22120.00\n-\n-\n-\u2014\n-\u2014\n-\u2014\nGW170818\n11.3\n4.2 \u00d7 10\u22125\n43+8\n\u22125\n34+5\n\u22127\n1178+408\n\u2212422\n0.23+0.07\n\u22120.08\n29\n4.5 \u00d7 10\u22123\n1\n0.97\u2013\u223c1\n97\u2013100\nGW170823\n11.5\n4.6 \u00d7 10\u221212\n52+12\n\u22128\n39+8\n\u221211\n2115+836\n\u2212910\n0.38+0.12\n\u22120.15\n1.6 \u00d7 103\n1.1\n260\n\u223c1\u2013\u223c1\n100\u2013100\nGW190408_181802\n14.7\n2.1 \u00d7 10\u221215\n32+7\n\u22124\n24+4\n\u22125\n1575+439\n\u2212595\n0.30+0.07\n\u22120.10\n277\n0.07\n234\n\u223c1\u20131.01\n100\u2013100\nGW190412\n19.0\n1.9 \u00d7 10\u221227\n34+6\n\u22125\n10+1.3\n\u22121.1\n700+167\n\u2212187\n0.14+0.03\n\u22120.04\n31\n9.5 \u00d7 10\u22124\n91\n0.89\u20130.98\n78\u201397\nGW190413_134308\n8.9\n0.18\n83+19\n\u221215\n54+17\n\u221223\n4607+2384\n\u22122202\n0.73+0.29\n\u22120.30\n579\n2.1\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190421_213856\n10.5\n2.8 \u00d7 10\u22123\n61+13\n\u22129\n47+9\n\u221214\n2958+1450\n\u22121359\n0.51+0.20\n\u22120.21\n1.1 \u00d7 103\n1.7\n133\n\u223c1\u2013\u223c1\n100\u2013100\nGW190425\n12.9\n0.03\n2.2+0.5\n\u22120.4\n1.4+0.3\n\u22120.2\n143+75\n\u221261\n0.03+0.02\n\u22120.01\n9.1 \u00d7 103\n7.9 \u00d7 10\u22123\n8.6 \u00d7 103\n0.62\u20132.77\n4\u201331\nGW190503_185404\n12.0\n2.3 \u00d7 10\u22126\n54+12\n\u221210\n36+10\n\u221213\n1596+658\n\u2212640\n0.30+0.10\n\u22120.11\n108\n0.04\n89\n\u223c1\u2013\u223c1\n100\u2013100\nGW190512_180714\n12.2\n7.7 \u00d7 10\u221212\n30+8\n\u22127\n16+5\n\u22123\n1534+470\n\u2212621\n0.29+0.07\n\u22120.11\n264\n0.07\n322\n\u223c1\u20131.02\n99\u2013100\nGW190513_205428\n12.3\n1.3 \u00d7 10\u22125\n51+14\n\u221214\n25+11\n\u22127\n2283+934\n\u2212772\n0.41+0.14\n\u22120.12\n433\n0.33\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW190517_055101\n10.3\n3.5 \u00d7 10\u22124\n53+14\n\u221210\n32+10\n\u221212\n1920+1846\n\u2212976\n0.35+0.27\n\u22120.16\n434\n0.53\n393\n\u223c1\u20131.02\n100\u2013100\nGW190519_153544\n12.4\n2.2 \u00d7 10\u22126\n94+16\n\u221212\n59+18\n\u221219\n3057+2027\n\u22121343\n0.52+0.27\n\u22120.20\n579\n1.2\n17\n\u223c1\u2013\u223c1\n100\u2013100\nGW190521\n13.6\n1.3 \u00d7 10\u22123\n154+29\n\u221219\n102+38\n\u221242\n4527+2265\n\u22122635\n0.72+0.28\n\u22120.37\n899\n3.3\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190521_074359\n24.4\n5.0 \u00d7 10\u221233\n52+6\n\u22125\n39+6\n\u22127\n961+498\n\u2212420\n0.19+0.09\n\u22120.08\n457\n0.06\n2.5 \u00d7 103\n\u223c1\u20131.07\n87\u2013100\nGW190527_092055\n8.7\n0.23\n56+59\n\u221214\n35+35\n\u221217\n3221+4197\n\u22121686\n0.54+0.53\n\u22120.25\n3.7 \u00d7 103\n17\n169\n\u223c1\u2013\u223c1\n100\u2013100\nGW190602_175927\n12.3\n1.1 \u00d7 10\u22127\n107+25\n\u221218\n71+22\n\u221231\n3274+2026\n\u22121438\n0.55+0.27\n\u22120.21\n790\n1.8\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190620_030421\n10.9\n0.01\n88+25\n\u221218\n52+19\n\u221223\n3418+1670\n\u22121556\n0.57+0.22\n\u22120.23\n5.8 \u00d7 103\n12\n13\n\u223c1\u2013\u223c1\n100\u2013100\nGW190630_185205\n15.2\n1.4 \u00d7 10\u221210\n41+9\n\u22126\n29+5\n\u22127\n908+550\n\u2212380\n0.18+0.10\n\u22120.07\n1.1 \u00d7 103\n0.15\n9.3 \u00d7 103\n0.99\u20131.03\n83\u2013100\nGW190701_203306\n11.7\n5.7 \u00d7 10\u22123\n75+15\n\u221211\n56+12\n\u221218\n2217+807\n\u2212762\n0.40+0.12\n\u22120.12\n43\n0.03\n6\n\u223c1\u2013\u223c1\n100\u2013100\nTable 8 continued\n\n43\nTable 8 (continued)\nName\nSNR\nFAR\nmdet\n1\nmdet\n2\nDL\nz\u2217\n\u2206\u2126\n\u2206V \u2217\nN\u2217\ngal\nUnder(over)-density\u2217\nIncompleteness\u2217(%)\n\u2013\n\u2013\n[yr\u22121]\n[M\u2299]\n[M\u2299]\n[Mpc]\n\u2013\n[deg2]\n[Gpc3]\n\u2013\n\u2013\n\u2013\nGW190706_222641\n12.5\n5.0 \u00d7 10\u22125\n119+23\n\u221220\n65+26\n\u221227\n4420+2678\n\u22122328\n0.70+0.33\n\u22120.33\n2.4 \u00d7 103\n9.5\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190707_093326\n13.2\n2.7 \u00d7 10\u221215\n13+3\n\u22121.8\n10+1.5\n\u22121.8\n842+320\n\u2212366\n0.17+0.06\n\u22120.07\n926\n0.07\n4.6 \u00d7 103\n\u223c1\u20131.08\n83\u2013100\nGW190708_232457\n13.1\n3.1 \u00d7 10\u22124\n21+7\n\u22122.9\n15+2.3\n\u22124\n963+304\n\u2212386\n0.19+0.05\n\u22120.07\n1.2 \u00d7 104\n1.1\n3.9 \u00d7 104\n0.97\u2013\u223c1\n87\u2013100\nGW190720_000836\n11.5\n4.4 \u00d7 10\u22128\n16+8\n\u22124\n9+2.6\n\u22122.5\n775+571\n\u2212243\n0.16+0.10\n\u22120.05\n109\n0.01\n348\n0.95\u20131.01\n84\u2013100\nGW190727_060333\n12.1\n2.7 \u00d7 10\u221210\n59+13\n\u22128\n46+8\n\u221213\n3235+1210\n\u22121184\n0.55+0.16\n\u22120.17\n130\n0.19\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190728_064510\n13.4\n5.4 \u00d7 10\u221216\n15+11\n\u22123\n9+2.2\n\u22123\n907+247\n\u2212399\n0.18+0.04\n\u22120.07\n340\n0.03\n1.4 \u00d7 103\n0.98\u2013\u223c1\n84\u2013100\nGW190803_022701\n9.1\n0.07\n58+13\n\u22129\n44+9\n\u221213\n3573+1676\n\u22121520\n0.59+0.22\n\u22120.22\n1.0 \u00d7 103\n2.2\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190814\n22.2\n5.4 \u00d7 10\u221212\n24+1.6\n\u22121.4\n2.7+0.1\n\u22120.1\n233+43\n\u221246\n0.05+0.01\n\u22120.01\n22\n2.6 \u00d7 10\u22125\n30\n0.58\u20130.69\n23\u201342\nGW190828_063405\n16.3\n5.0 \u00d7 10\u221227\n43+7\n\u22125\n35+5\n\u22127\n2191+599\n\u2212925\n0.39+0.09\n\u22120.15\n315\n0.18\n37\n\u223c1\u20131.02\n100\u2013100\nGW190828_065509\n11.1\n3.5 \u00d7 10\u22125\n30+8\n\u22128\n13+5\n\u22122.7\n1646+674\n\u2212660\n0.31+0.10\n\u22120.11\n593\n0.23\n227\n\u223c1\u20131.01\n100\u2013100\nGW190910_112807\n13.4\n2.9 \u00d7 10\u22123\n57+9\n\u22127\n45+7\n\u221210\n1878+986\n\u2212873\n0.34+0.15\n\u22120.15\n8.0 \u00d7 103\n5.2\n3.8 \u00d7 103\n\u223c1\u2013\u223c1\n100\u2013100\nGW190915_235702\n13.0\n7.8 \u00d7 10\u22126\n43+9\n\u22126\n33+5\n\u22128\n1886+705\n\u2212681\n0.35+0.11\n\u22120.11\n452\n0.22\n128\n\u223c1\u2013\u223c1\n100\u2013100\nGW190924_021846\n13.0\n5.0 \u00d7 10\u221210\n10+7\n\u22122.7\n5+1.6\n\u22121.8\n556+205\n\u2212225\n0.12+0.04\n\u22120.04\n358\n9.3 \u00d7 10\u22123\n2.3 \u00d7 103\n0.67\u20130.97\n51\u201395\nGW190925_232845\n9.9\n7.2 \u00d7 10\u22123\n25+9\n\u22123\n18+2.8\n\u22125\n937+377\n\u2212337\n0.19+0.07\n\u22120.06\n1.1 \u00d7 103\n0.12\n5.9 \u00d7 103\n\u223c1\u20131.02\n89\u2013100\nGW190929_012149\n10.1\n0.16\n101+25\n\u221219\n45+26\n\u221219\n3769+3147\n\u22121692\n0.62+0.40\n\u22120.24\n1.7 \u00d7 103\n6.3\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW190930_133541\n10.0\n0.01\n14+13\n\u22122.8\n9+2.1\n\u22124\n790+318\n\u2212325\n0.16+0.06\n\u22120.06\n1.6 \u00d7 103\n0.11\n5.8 \u00d7 103\n0.99\u20131.03\n79\u2013100\nGW191105_143521\n9.8\n0.01\n13+5\n\u22122.1\n9+1.6\n\u22122.3\n1203+404\n\u2212474\n0.23+0.07\n\u22120.09\n683\n0.11\n1.0 \u00d7 103\n0.97\u2013\u223c1\n95\u2013100\nGW191109_010717\n15.2\n1.8 \u00d7 10\u22124\n80+10\n\u22128\n59+17\n\u221217\n1318+1378\n\u2212666\n0.25+0.21\n\u22120.12\n1.5 \u00d7 103\n0.90\n4.8 \u00d7 103\n0.99\u20131.01\n94\u2013100\nGW191127_050227\n10.3\n0.25\n96+58\n\u221235\n44+30\n\u221228\n4595+3459\n\u22122627\n0.73+0.42\n\u22120.37\n982\n4.9\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW191129_134029\n13.3\n1.3 \u00d7 10\u221223\n13+5\n\u22122.6\n8+1.9\n\u22121.7\n803+237\n\u2212320\n0.16+0.04\n\u22120.06\n843\n0.05\n8.1 \u00d7 103\n0.98\u20131.01\n79\u2013100\nGW191204_171526\n15.6\n3.5 \u00d7 10\u221225\n14+4\n\u22122.3\n9+1.7\n\u22121.8\n644+180\n\u2212219\n0.13+0.03\n\u22120.04\n260\n7.8 \u00d7 10\u22123\n1.6 \u00d7 103\n0.92\u2013\u223c1\n73\u201398\nGW191215_223052\n10.9\n1.3 \u00d7 10\u22126\n33+9\n\u22125\n25+4\n\u22125\n2102+866\n\u2212935\n0.38+0.13\n\u22120.15\n571\n0.39\n173\n\u223c1\u20131.01\n100\u2013100\nGW191216_213338\n18.6\n3.1 \u00d7 10\u221211\n14+7\n\u22123.0\n8+2.0\n\u22122.2\n343+109\n\u2212129\n0.07+0.02\n\u22120.03\n224\n1.4 \u00d7 10\u22123\n1.3 \u00d7 103\n0.65\u20131.44\n31\u201376\nGW191222_033537\n12.0\n2.8 \u00d7 10\u221213\n68+15\n\u221210\n52+11\n\u221215\n3382+1623\n\u22121768\n0.57+0.21\n\u22120.26\n1.9 \u00d7 103\n3.9\n92\n\u223c1\u2013\u223c1\n100\u2013100\nGW191230_180458\n10.4\n0.05\n83+18\n\u221212\n63+13\n\u221220\n4841+2194\n\u22122099\n0.76+0.27\n\u22120.28\n1.1 \u00d7 103\n3.9\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW200112_155838\n17.6\n8.0 \u00d7 10\u22126\n45+8\n\u22126\n34+6\n\u22127\n1299+427\n\u2212458\n0.25+0.07\n\u22120.08\n3.3 \u00d7 103\n0.62\n3.4 \u00d7 103\n\u223c1\u2013\u223c1\n98\u2013100\nGW200115_042309\n11.5\n3.0 \u00d7 10\u221210\n6+2.6\n\u22122.5\n1.6+0.8\n\u22120.4\n292+133\n\u221292\n0.06+0.03\n\u22120.02\n432\n2.3 \u00d7 10\u22123\n2.2 \u00d7 103\n0.82\u20131.30\n28\u201373\nGW200128_022011\n9.9\n4.3 \u00d7 10\u22123\n65+14\n\u22129\n50+10\n\u221213\n3871+2131\n\u22121972\n0.63+0.27\n\u22120.28\n2.2 \u00d7 103\n6.2\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW200129_065458\n26.5\n2.9 \u00d7 10\u221233\n44+10\n\u22126\n31+6\n\u22129\n973+219\n\u2212341\n0.19+0.04\n\u22120.06\n29\n2.2 \u00d7 10\u22123\n11\n0.96\u2013\u223c1\n94\u2013100\nGW200202_154313\n11.3\n5.2 \u00d7 10\u22128\n11+4\n\u22121.6\n8+1.3\n\u22122.0\n422+146\n\u2212160\n0.09+0.03\n\u22120.03\n156\n1.8 \u00d7 10\u22123\n321\n0.36\u20130.88\n34\u201381\nGW200208_130117\n10.8\n3.1 \u00d7 10\u22124\n53+12\n\u22128\n39+9\n\u221211\n2371+1029\n\u2212912\n0.42+0.15\n\u22120.14\n29\n0.03\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW200209_085452\n10.0\n0.05\n56+14\n\u221210\n43+11\n\u221213\n3935+1972\n\u22121875\n0.64+0.25\n\u22120.27\n834\n2.3\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW200219_094415\n10.7\n9.9 \u00d7 10\u22124\n59+13\n\u22129\n44+9\n\u221213\n3830+1677\n\u22121735\n0.63+0.22\n\u22120.25\n667\n1.6\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW200224_222234\n18.9\n2.4 \u00d7 10\u221232\n53+9\n\u22126\n42+6\n\u221210\n1772+473\n\u2212658\n0.33+0.07\n\u22120.11\n43\n0.01\n29\n\u223c1\u2013\u223c1\n100\u2013100\nGW200225_060421\n12.3\n1.1 \u00d7 10\u22125\n24+5\n\u22123\n17+3\n\u22125\n1157+505\n\u2212492\n0.23+0.08\n\u22120.09\n494\n0.09\n1.6 \u00d7 103\n\u223c1\u20131.01\n94\u2013100\nGW200302_015811\n10.6\n0.11\n49+9\n\u221210\n25+12\n\u22127\n1582+1028\n\u2212733\n0.30+0.16\n\u22120.13\n5.7 \u00d7 103\n3.1\n5.2 \u00d7 103\n\u223c1\u20131.01\n99\u2013100\nGW200311_115853\n17.7\n4.2 \u00d7 10\u221234\n42+9\n\u22125\n33+5\n\u22128\n1203+277\n\u2212388\n0.23+0.05\n\u22120.07\n35\n4.2 \u00d7 10\u22123\n1\n0.97\u2013\u223c1\n97\u2013100\nTable 8 continued\n\n44\nTable 8 (continued)\nName\nSNR\nFAR\nmdet\n1\nmdet\n2\nDL\nz\u2217\n\u2206\u2126\n\u2206V \u2217\nN\u2217\ngal\nUnder(over)-density\u2217\nIncompleteness\u2217(%)\n\u2013\n\u2013\n[yr\u22121]\n[M\u2299]\n[M\u2299]\n[Mpc]\n\u2013\n[deg2]\n[Gpc3]\n\u2013\n\u2013\n\u2013\nGW200316_215756\n10.1\n8.9 \u00d7 10\u22126\n17+14\n\u22124\n9+2.8\n\u22123\n1134+434\n\u2212429\n0.22+0.07\n\u22120.08\n203\n0.03\n297\n\u223c1\u20131.05\n97\u2013100\nGW230529_181500\n11.4\n2.2 \u00d7 10\u22124\n4+0.8\n\u22121.0\n1.6+0.6\n\u22120.2\n197+105\n\u221297\n0.04+0.02\n\u22120.02\n2.4 \u00d7 104\n0.05\n2.4 \u00d7 104\n0.67\u20131.46\n7\u201351\nGW230601_224134\n11.8\n1.8 \u00d7 10\u221210\n103+17\n\u221215\n70+16\n\u221224\n3423+1953\n\u22121665\n0.57+0.26\n\u22120.25\n2.3 \u00d7 103\n5.5\n154\n\u223c1\u2013\u223c1\n100\u2013100\nGW230605_065343\n11.1\n1.8 \u00d7 10\u22127\n21+7\n\u22124\n13+2.8\n\u22123\n1037+604\n\u2212469\n0.20+0.10\n\u22120.09\n967\n0.18\n2.2 \u00d7 103\n\u223c1\u20131.02\n91\u2013100\nGW230606_004305\n10.7\n4.1 \u00d7 10\u22124\n54+15\n\u221210\n38+9\n\u221212\n2689+1434\n\u22121370\n0.47+0.20\n\u22120.21\n1.2 \u00d7 103\n1.7\n186\n\u223c1\u2013\u223c1\n100\u2013100\nGW230608_205047\n10.2\n1.2 \u00d7 10\u22123\n76+14\n\u221213\n49+17\n\u221219\n3389+2172\n\u22121666\n0.57+0.28\n\u22120.25\n1.8 \u00d7 103\n4.5\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230609_064958\n10.0\n1.4 \u00d7 10\u22124\n54+11\n\u22128\n40+9\n\u221212\n3302+1776\n\u22121701\n0.56+0.23\n\u22120.25\n1.3 \u00d7 103\n2.7\n41\n\u223c1\u2013\u223c1\n100\u2013100\nGW230624_113103\n10.0\n1.8 \u00d7 10\u22124\n35+16\n\u22127\n22+6\n\u22126\n1897+1226\n\u2212935\n0.35+0.18\n\u22120.16\n989\n0.80\n841\n\u223c1\u20131.01\n100\u2013100\nGW230627_015337\n28.3\n6.8 \u00d7 10\u221239\n9+1.9\n\u22121.3\n6+1.0\n\u22120.9\n307+62\n\u2212131\n0.07+0.01\n\u22120.03\n92\n3.3 \u00d7 10\u22124\n213\n0.30\u20130.77\n18\u201356\nGW230628_231200\n15.3\n8.0 \u00d7 10\u221224\n45+7\n\u22124\n38+5\n\u22127\n2286+759\n\u22121062\n0.41+0.11\n\u22120.17\n519\n0.37\n14\n\u223c1\u2013\u223c1\n100\u2013100\nGW230630_125806\n9.0\n0.16\n95+32\n\u221219\n62+21\n\u221227\n5260+5031\n\u22122921\n0.81+0.59\n\u22120.40\n3.6 \u00d7 103\n27\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230630_234532\n9.9\n4.2 \u00d7 10\u22124\n12+4\n\u22122.0\n8+1.5\n\u22121.8\n1074+507\n\u2212473\n0.21+0.09\n\u22120.09\n1.1 \u00d7 103\n0.19\n4.9 \u00d7 103\n0.98\u2013\u223c1\n89\u2013100\nGW230702_185453\n9.8\n5.3 \u00d7 10\u22126\n60+30\n\u221219\n25+12\n\u22129\n2330+1689\n\u22121034\n0.41+0.24\n\u22120.17\n2.1 \u00d7 103\n2.9\n298\n\u223c1\u2013\u223c1\n100\u2013100\nGW230704_021211\n9.4\n0.21\n48+12\n\u22129\n29+8\n\u22128\n2574+1805\n\u22121408\n0.45+0.25\n\u22120.22\n1.4 \u00d7 103\n2.3\n411\n\u223c1\u2013\u223c1\n100\u2013100\nGW230706_104333\n9.2\n0.23\n22+6\n\u22123\n16+2.6\n\u22123\n1921+901\n\u2212968\n0.35+0.14\n\u22120.16\n1.3 \u00d7 103\n0.82\n685\n\u223c1\u2013\u223c1\n99\u2013100\nGW230707_124047\n11.9\n1.1 \u00d7 10\u22123\n78+14\n\u22129\n63+10\n\u221216\n4523+2180\n\u22122299\n0.72+0.27\n\u22120.32\n2.6 \u00d7 103\n9.2\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230708_053705\n8.9\n0.22\n45+10\n\u22126\n36+6\n\u22127\n3252+1953\n\u22121657\n0.55+0.26\n\u22120.25\n1.4 \u00d7 103\n3.1\n21\n\u223c1\u2013\u223c1\n100\u2013100\nGW230708_230935\n9.6\n3.7 \u00d7 10\u22123\n102+26\n\u221218\n61+23\n\u221226\n3364+2152\n\u22121524\n0.56+0.28\n\u22120.23\n2.1 \u00d7 103\n5.2\n10\n\u223c1\u2013\u223c1\n100\u2013100\nGW230709_122727\n10.0\n0.01\n78+19\n\u221214\n54+16\n\u221226\n4590+3399\n\u22122402\n0.73+0.41\n\u22120.34\n2.9 \u00d7 103\n14\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW230712_090405\n9.5\n0.02\n43+22\n\u221214\n16+27\n\u22127\n1984+2244\n\u2212981\n0.36+0.32\n\u22120.16\n1.3 \u00d7 103\n2.0\n285\n\u223c1\u2013\u223c1\n100\u2013100\nGW230723_101834\n10.0\n3.4 \u00d7 10\u22123\n22+7\n\u22124\n14+2.9\n\u22123\n1545+704\n\u2212992\n0.29+0.11\n\u22120.18\n862\n0.35\n4.7 \u00d7 103\n0.98\u20131.01\n83\u2013100\nGW230726_002940\n10.5\n7.8 \u00d7 10\u22126\n49+10\n\u22126\n39+6\n\u22128\n2076+1177\n\u22121048\n0.38+0.17\n\u22120.17\n2.8 \u00d7 104\n25\n5.8 \u00d7 103\n\u223c1\u2013\u223c1\n100\u2013100\nGW230729_082317\n9.5\n0.18\n16+11\n\u22123\n10+2.4\n\u22123\n1629+793\n\u2212760\n0.30+0.12\n\u22120.13\n2.0 \u00d7 103\n0.90\n1.9 \u00d7 103\n\u223c1\u20131.01\n99\u2013100\nGW230731_215307\n12.2\n3.0 \u00d7 10\u221214\n12+3\n\u22121.4\n10+1.2\n\u22121.9\n1113+335\n\u2212453\n0.22+0.06\n\u22120.08\n629\n0.08\n2.8 \u00d7 103\n0.99\u20131.01\n92\u2013100\nGW230805_034249\n9.4\n3.7 \u00d7 10\u22123\n53+17\n\u221212\n34+12\n\u221212\n3145+2318\n\u22121490\n0.53+0.31\n\u22120.22\n2.0 \u00d7 103\n4.9\n35\n\u223c1\u2013\u223c1\n100\u2013100\nGW230806_204041\n9.1\n3.7 \u00d7 10\u22123\n93+21\n\u221216\n66+18\n\u221225\n5515+3515\n\u22122897\n0.84+0.41\n\u22120.39\n3.8 \u00d7 103\n22\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230811_032116\n12.9\n4.4 \u00d7 10\u221219\n49+9\n\u22128\n30+8\n\u22127\n2029+1092\n\u22121047\n0.37+0.16\n\u22120.17\n817\n0.66\n766\n\u223c1\u20131.01\n100\u2013100\nGW230814_061920\n10.2\n6.3 \u00d7 10\u22124\n113+16\n\u221215\n70+23\n\u221226\n3774+2871\n\u22121813\n0.62+0.36\n\u22120.26\n3.6 \u00d7 103\n13\n54\n\u223c1\u2013\u223c1\n100\u2013100\nGW230814_230901\n42.3\n5.6 \u00d7 10\u221215\n36+2.7\n\u22122.0\n30+1.9\n\u22122.2\n274+131\n\u2212121\n0.06+0.03\n\u22120.03\n2.5 \u00d7 104\n0.13\n5.2 \u00d7 104\n0.64\u20130.95\n17\u201368\nGW230819_171910\n9.9\n0.01\n122+85\n\u221230\n58+31\n\u221231\n3865+3382\n\u22122110\n0.63+0.42\n\u22120.31\n4.1 \u00d7 103\n17\n19\n\u223c1\u2013\u223c1\n100\u2013100\nGW230820_212515\n9.1\n0.24\n105+29\n\u221223\n53+35\n\u221231\n3773+3000\n\u22121905\n0.62+0.38\n\u22120.28\n1.7 \u00d7 103\n6.3\n15\n\u223c1\u2013\u223c1\n100\u2013100\nGW230824_033047\n10.7\n4.8 \u00d7 10\u22126\n92+17\n\u221213\n64+16\n\u221226\n4621+2678\n\u22122167\n0.73+0.33\n\u22120.30\n3.2 \u00d7 103\n13\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230825_041334\n8.7\n0.10\n76+18\n\u221214\n51+14\n\u221217\n5039+4172\n\u22123043\n0.79+0.50\n\u22120.42\n3.0 \u00d7 103\n19\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW230904_051013\n10.5\n3.9 \u00d7 10\u22125\n13+5\n\u22122.2\n9+1.6\n\u22122.1\n1008+597\n\u2212412\n0.20+0.10\n\u22120.08\n1.7 \u00d7 103\n0.29\n5.7 \u00d7 103\n0.99\u20131.00\n90\u2013100\nGW230911_195324\n11.1\n1.0 \u00d7 10\u22123\n44+7\n\u22127\n25+8\n\u22127\n1129+971\n\u2212562\n0.22+0.16\n\u22120.10\n2.7 \u00d7 104\n9.4\n6.5 \u00d7 104\n0.98\u2013\u223c1\n87\u2013100\nGW230914_111401\n15.9\n5.8 \u00d7 10\u221224\n87+11\n\u221211\n53+19\n\u221219\n2588+1523\n\u22121160\n0.45+0.21\n\u22120.18\n1.6 \u00d7 103\n2.2\n72\n\u223c1\u2013\u223c1\n100\u2013100\nGW230919_215712\n16.3\n7.2 \u00d7 10\u221235\n34+7\n\u22124\n27+3\n\u22125\n1275+734\n\u2212483\n0.25+0.12\n\u22120.09\n570\n0.17\n716\n0.99\u2013\u223c1\n98\u2013100\nTable 8 continued\n\n45\nTable 8 (continued)\nName\nSNR\nFAR\nmdet\n1\nmdet\n2\nDL\nz\u2217\n\u2206\u2126\n\u2206V \u2217\nN\u2217\ngal\nUnder(over)-density\u2217\nIncompleteness\u2217(%)\n\u2013\n\u2013\n[yr\u22121]\n[M\u2299]\n[M\u2299]\n[Mpc]\n\u2013\n[deg2]\n[Gpc3]\n\u2013\n\u2013\n\u2013\nGW230920_071124\n10.1\n6.4 \u00d7 10\u22126\n48+12\n\u22127\n36+7\n\u221210\n2818+1691\n\u22121330\n0.49+0.23\n\u22120.20\n1.8 \u00d7 103\n3.0\n154\n\u223c1\u2013\u223c1\n100\u2013100\nGW230922_020344\n12.3\n8.4 \u00d7 10\u221216\n53+12\n\u22129\n37+7\n\u22128\n1453+763\n\u2212609\n0.28+0.12\n\u22120.11\n270\n0.10\n679\n\u223c1\u20131.01\n98\u2013100\nGW230922_040658\n11.6\n1.2 \u00d7 10\u22127\n151+37\n\u221225\n98+31\n\u221257\n6366+4090\n\u22123431\n0.95+0.47\n\u22120.45\n4.4 \u00d7 103\n32\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230924_124453\n13.3\n2.6 \u00d7 10\u221220\n41+7\n\u22124\n33+4\n\u22126\n2362+982\n\u2212981\n0.42+0.14\n\u22120.15\n1.0 \u00d7 103\n0.88\n9\n\u223c1\u2013\u223c1\n100\u2013100\nGW230927_043729\n11.3\n4.7 \u00d7 10\u22128\n53+11\n\u22127\n42+7\n\u22129\n3116+1732\n\u22121631\n0.53+0.23\n\u22120.25\n1.1 \u00d7 103\n2.2\n188\n\u223c1\u20131.01\n100\u2013100\nGW230927_153832\n19.8\n2.7 \u00d7 10\u221236\n27+4\n\u22123\n20+2.8\n\u22122.7\n1168+385\n\u2212516\n0.23+0.07\n\u22120.09\n273\n0.04\n1.4 \u00d7 103\n\u223c1\u20131.04\n94\u2013100\nGW230928_215827\n9.5\n1.5 \u00d7 10\u22125\n97+19\n\u221219\n53+16\n\u221219\n4359+3558\n\u22122032\n0.70+0.44\n\u22120.28\n3.0 \u00d7 103\n14\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW230930_110730\n8.5\n0.17\n60+17\n\u221210\n44+10\n\u221213\n4857+2994\n\u22122463\n0.76+0.36\n\u22120.34\n2.9 \u00d7 103\n13\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW231001_140220\n10.3\n1.6 \u00d7 10\u22125\n129+23\n\u221222\n68+31\n\u221227\n4173+3659\n\u22122278\n0.67+0.45\n\u22120.33\n3.3 \u00d7 103\n16\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW231004_232346\n8.9\n0.16\n111+29\n\u221222\n58+25\n\u221224\n4050+3308\n\u22122009\n0.66+0.41\n\u22120.29\n2.8 \u00d7 103\n12\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW231005_021030\n10.4\n0.01\n163+39\n\u221229\n95+34\n\u221242\n6279+4448\n\u22123139\n0.94+0.51\n\u22120.41\n4.9 \u00d7 103\n38\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW231005_091549\n8.9\n0.04\n46+13\n\u22126\n35+6\n\u221210\n3585+2433\n\u22121785\n0.59+0.31\n\u22120.26\n2.4 \u00d7 103\n7.1\n69\n\u223c1\u2013\u223c1\n100\u2013100\nGW231008_142521\n9.3\n1.6 \u00d7 10\u22123\n68+17\n\u221214\n38+15\n\u221215\n2787+2233\n\u22121207\n0.48+0.30\n\u22120.18\n2.6 \u00d7 103\n5.5\n87\n\u223c1\u2013\u223c1\n100\u2013100\nGW231014_040532\n9.0\n0.21\n29+11\n\u22125\n21+4\n\u22127\n2231+1388\n\u22121150\n0.40+0.20\n\u22120.19\n1.6 \u00d7 103\n1.8\n484\n\u223c1\u2013\u223c1\n100\u2013100\nGW231020_142947\n12.0\n6.6 \u00d7 10\u221210\n15+11\n\u22123\n9+2.2\n\u22123\n1229+507\n\u2212643\n0.24+0.08\n\u22120.12\n1.4 \u00d7 103\n0.30\n5.9 \u00d7 103\n0.98\u2013\u223c1\n88\u2013100\nGW231028_153006\n21.0\n2.8 \u00d7 10\u221224\n157+32\n\u221224\n110+19\n\u221247\n4514+1178\n\u22122032\n0.72+0.15\n\u22120.28\n1.2 \u00d7 103\n2.7\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW231029_111508\n10.8\n5.2 \u00d7 10\u22125\n100+17\n\u221215\n63+22\n\u221226\n3015+2348\n\u22121623\n0.51+0.31\n\u22120.25\n2.9 \u00d7 104\n71\n753\n\u223c1\u2013\u223c1\n100\u2013100\nGW231102_071736\n13.8\n8.8 \u00d7 10\u221213\n99+13\n\u221211\n70+16\n\u221220\n3619+1956\n\u22121648\n0.60+0.25\n\u22120.24\n2.2 \u00d7 103\n5.4\n18\n\u223c1\u2013\u223c1\n100\u2013100\nGW231104_133418\n11.3\n9.2 \u00d7 10\u221210\n16+5\n\u22122.3\n11+1.8\n\u22122.5\n1465+525\n\u2212646\n0.28+0.08\n\u22120.11\n909\n0.26\n1.4 \u00d7 103\n0.99\u2013\u223c1\n98\u2013100\nGW231108_125142\n12.6\n4.7 \u00d7 10\u221217\n32+6\n\u22124\n24+3\n\u22124\n2051+702\n\u2212892\n0.37+0.10\n\u22120.14\n897\n0.51\n302\n\u223c1\u2013\u223c1\n100\u2013100\nGW231110_040320\n11.4\n2.9 \u00d7 10\u221211\n26+7\n\u22125\n16+4\n\u22123\n1844+854\n\u2212892\n0.34+0.13\n\u22120.15\n656\n0.38\n211\n\u223c1\u20131.01\n100\u2013100\nGW231113_200417\n10.1\n3.8 \u00d7 10\u22125\n14+5\n\u22122.4\n9+1.9\n\u22122.2\n1146+645\n\u2212524\n0.22+0.11\n\u22120.10\n1.6 \u00d7 103\n0.36\n6.5 \u00d7 103\n0.99\u2013\u223c1\n91\u2013100\nGW231114_043211\n10.0\n1.3 \u00d7 10\u22124\n29+12\n\u22127\n10+2.8\n\u22122.4\n1328+830\n\u2212580\n0.26+0.13\n\u22120.10\n1.4 \u00d7 103\n0.51\n2.8 \u00d7 103\n\u223c1\u20131.01\n97\u2013100\nGW231118_005626\n10.7\n1.1 \u00d7 10\u22126\n29+10\n\u22127\n14+5\n\u22123\n2083+957\n\u2212917\n0.38+0.14\n\u22120.15\n1.0 \u00d7 103\n0.74\n342\n\u223c1\u20131.02\n100\u2013100\nGW231118_071402\n9.2\n2.8 \u00d7 10\u22123\n72+20\n\u221212\n51+14\n\u221218\n4074+3396\n\u22122139\n0.66+0.42\n\u22120.31\n3.0 \u00d7 103\n13\n1\n\u223c1\u2013\u223c1\n100\u2013100\nGW231118_090602\n11.0\n9.8 \u00d7 10\u22129\n17+20\n\u22125\n9+3\n\u22124\n1369+510\n\u2212620\n0.26+0.08\n\u22120.11\n1.1 \u00d7 103\n0.27\n2.1 \u00d7 103\n\u223c1\u20131.01\n97\u2013100\nGW231119_075248\n8.3\n0.02\n95+33\n\u221219\n68+22\n\u221228\n6538+5180\n\u22123575\n0.97+0.59\n\u22120.46\n5.1 \u00d7 103\n46\n0\n\u223c1\u2013\u223c1\n100\u2013100\nGW231127_165300\n9.9\n0.01\n79+21\n\u221217\n49+18\n\u221222\n4312+3484\n\u22122413\n0.69+0.43\n\u22120.34\n3.8 \u00d7 103\n18\n6\n\u223c1\u2013\u223c1\n100\u2013100\nGW231129_081745\n9.4\n0.06\n73+13\n\u221213\n39+15\n\u221214\n3598+3306\n\u22121945\n0.60+0.42\n\u22120.29\n3.2 \u00d7 103\n12\n3\n\u223c1\u2013\u223c1\n100\u2013100\nGW231206_233134\n11.9\n1.4 \u00d7 10\u221214\n54+9\n\u22127\n43+7\n\u221210\n3233+1739\n\u22121815\n0.55+0.23\n\u22120.28\n2.0 \u00d7 103\n4.3\n183\n\u223c1\u2013\u223c1\n100\u2013100\nGW231206_233901\n20.7\n1.1 \u00d7 10\u221237\n48+9\n\u22125\n37+6\n\u22128\n1483+333\n\u2212492\n0.28+0.05\n\u22120.08\n292\n0.06\n45\n\u223c1\u2013\u223c1\n99\u2013100\nGW231213_111417\n10.2\n2.3 \u00d7 10\u22126\n58+14\n\u22129\n46+9\n\u221213\n4035+2225\n\u22122012\n0.66+0.28\n\u22120.29\n1.9 \u00d7 103\n5.8\n9\n\u223c1\u2013\u223c1\n100\u2013100\nGW231223_032836\n9.4\n3.8 \u00d7 10\u22124\n77+18\n\u221212\n54+15\n\u221228\n3937+2960\n\u22121945\n0.64+0.37\n\u22120.28\n3.4 \u00d7 103\n13\n2\n\u223c1\u2013\u223c1\n100\u2013100\nGW231223_202619\n10.0\n2.0 \u00d7 10\u22123\n13+4\n\u22121.7\n10+1.4\n\u22122.3\n884+489\n\u2212434\n0.18+0.09\n\u22120.08\n2.6 \u00d7 104\n3.3\n7.6 \u00d7 104\n0.98\u20131.01\n76\u2013100\nGW231224_024321\n13.0\n2.0 \u00d7 10\u221216\n11+2.5\n\u22121.2\n9+1.0\n\u22121.5\n944+283\n\u2212389\n0.19+0.05\n\u22120.07\n351\n0.03\n1.5 \u00d7 103\n0.98\u20131.10\n88\u2013100\nGW231226_101520\n34.2\n3.8 \u00d7 10\u221244\n49+7\n\u22123\n43+3\n\u22126\n1168+222\n\u2212301\n0.23+0.04\n\u22120.05\n136\n0.01\n141\n\u223c1\u2013\u223c1\n99\u2013100\nGW231231_154016\n13.4\n2.3 \u00d7 10\u22128\n27+5\n\u22123\n21+2.7\n\u22123\n1058+588\n\u2212527\n0.21+0.10\n\u22120.10\n2.7 \u00d7 104\n5.2\n5.6 \u00d7 104\n0.97\u2013\u223c1\n84\u2013100\nTable 8 continued\n\n46\nTable 8 (continued)\nName\nSNR\nFAR\nmdet\n1\nmdet\n2\nDL\nz\u2217\n\u2206\u2126\n\u2206V \u2217\nN\u2217\ngal\nUnder(over)-density\u2217\nIncompleteness\u2217(%)\n\u2013\n\u2013\n[yr\u22121]\n[M\u2299]\n[M\u2299]\n[Mpc]\n\u2013\n[deg2]\n[Gpc3]\n\u2013\n\u2013\n\u2013\nGW240104_164932\n14.8\n2.1 \u00d7 10\u221210\n57+11\n\u22127\n44+8\n\u221211\n1915+1073\n\u2212951\n0.35+0.16\n\u22120.16\n2.9 \u00d7 104\n21\n7.7 \u00d7 103\n\u223c1\u2013\u223c1\n99\u2013100\nGW240107_013215\n9.1\n0.03\n112+37\n\u221229\n56+36\n\u221232\n5753+4833\n\u22123244\n0.88+0.56\n\u22120.43\n4.0 \u00d7 103\n31\n7\n\u223c1\u2013\u223c1\n100\u2013100\nGW240109_050431\n10.4\n2.3 \u00d7 10\u22124\n37+8\n\u22127\n23+6\n\u22124\n1452+967\n\u2212740\n0.28+0.15\n\u22120.13\n2.8 \u00d7 104\n13\n2.8 \u00d7 104\n\u223c1\u20131.01\n96\u2013100\n\n47\nREFERENCES\nAasi, J., et al. 2015, Class. 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Then, we identify\nclasses of primordial black-hole mass distributions for which these rate limits can be translated into\nrelevant constraints on the mass distribution of primordial black holes, assuming that they compose\nall of dark matter, in the mass range [10\u22126, 10\u22123]M\u2299. Our constraints are consistent with existing\nmicrolensing results in the planetary-mass range, and provide a complementary probe to sub-solar\nmass objects.\nI.\nINTRODUCTION\nBlack holes can form in the Universe from the core col-\nlapse of stars, or the merging of neutron stars or black\nholes.\nSince 2015, numerous gravitational-wave (GW)\nobservations has allowed us to probe these formation\nchannels and has revealed unexpected features\n[1\u201312],\nsuch as low effective spins, black holes in the low-mass\ngap ([3,5] M\u2299) [13], in the pair-instability mass gap [14]\nor with very unequal mass ratios [15, 16].\nThough a\nfraction of these could come from primordial black holes\n(PBHs), formed through the gravitational collapse of in-\nhomogeneities in the early Universe [17\u201321], uncertainties\nin the astrophysical and primordial formation scenarios\nand rates are too large to be able to disentangle the two\npopulations.\nA relatively unambiguous way to discover a PBH would\nbe to detect a sub-solar mass black hole. Matched filter-\ning has been used to search for PBHs between [0.1, 1] M\u2299,\nwhich has resulted in upper limits on the abundance of\nPBHs in the Universe [22\u201328]. Probing below 0.1 M\u2299,\nhowever, has been challenging for matched filtering be-\ncause longer signal durations \u2013 O(hours \u2212days) versus\nO(100 s)\u2013 lead to an insurmountable number of tem-\nplates to analyze.\nThese difficulties have motivated\nthe development of time-frequency domain methods to\nprobe PBHs with masses between [10\u22127, 10\u22122] M\u2299[29\u2013\n34], which have been used [35] to obtain the GW con-\nstraints on planetary-mass PBHs using data from the\nthird observing run of LIGO, Virgo and KAGRA [36\u2013\n38]. Another possibility is to search for the continu ous,\nalmost monochromatic GW signal from the early inspiral\nof planetary-mass PBH binaries within our galaxy [39\u2013\n41].\nIn this letter, we use data of the first part of the fourth\nobserving run of LIGO, Virgo and KAGRA to search for\nGWs from inspiraling PBH binaries. This work advances\nbeyond previous studies not only through the use of new\ndata, but also by identifying some relevant classes of PBH\n\u2217Full author list given at the end of the article.\nmass functions for which we obtain a significant con-\nstraint on the fraction of dark matter (DM) these PBHs\ncould compose. Additionally, we consider the impact of\nbinary eccentricity on our constraints.\nII.\nTHE SIGNAL\nInspiraling compact objects will lose orbital energy via\nGW emission, causing their orbit to shrink over time.\nWhen the objects are far from merger, we can write how\nquickly the GW frequency changes over time, i.e.\nthe\nspin-up \u02d9f, as [42]:\n\u02d9fGW = 96\n5 \u03c08/3\n\u0012GM\nc3\n\u00135/3\nf 11/3\nGW \u2261kf 11/3\nGW\n\u22431.25 \u00d7 10\u22124 Hz/s\n\u0012\nM\n10\u22123 M\u2299\n\u00135/3 \u0012 fGW\n100 Hz\n\u001311/3\n,\n(1)\nwhere M \u2261\n(m1m2)3/5\n(m1+m2)1/5 is the chirp mass of the sys-\ntem composed of objects with component masses m1, m2,\nk \u221dM5/3 is a proportionality constant, fGW is the GW\nfrequency, c is the speed of light, and G is Newton\u2019s grav-\nitational constant. We can then integrate Eq. (1) over\ntime to obtain how the GW frequency changes with time\nt:\nfGW(t) = f0\n\u0014\n1 \u22128\n3kf 8/3\n0\n(t \u2212t0)\n\u0015\u22123\n8\n,\n(2)\nwhere t0 is a reference time for the GW frequency\nf0.\nEq. (1) contains only the leading-order term in\nthe post-Newtonian (PN) expansion.\nHowever, the\nimpact of higher-order PN corrections on the sig-\nnal\u2019s time\u2013frequency evolution is negligible for the non-\nspinning, widely separated binaries considered here. We\ndiscuss how this approximation affects our upper limits\nin Section IV.\narXiv:2511.19911v2 [gr-qc] 5 Dec 2025\n\n2\nThe amplitude h0(t) of the GW signal also evolves with\ntime [42]:\nh0(t) = 4\nd\n\u0012GM\nc2\n\u00135/3 \u0012\u03c0fGW(t)\nc\n\u00132/3\n\u22432.56 \u00d7 10\u221223\n\u00121 kpc\nd\n\u0013 \u0012\nM\n10\u22123 M\u2299\n\u00135/3 \u0012fGW(t)\n100 Hz\n\u00132/3\n,\n(3)\nwhere d is the luminosity distance to the source.\nTo determine how long the inspiraling systems consid-\nered in this paper will emit GWs, we can invert Eq. (2) to\nobtain the time to coalescence tcoal and let fGW(t) \u2192\u221e:\ntcoal \u2243\n5\n256\n\u0012 1\n\u03c0f0\n\u00138/3 \u0012 c3\nGM\n\u00135/3\n\u22433.4 days\n\u0012100 Hz\nf0\n\u00138/3 \u001210\u22123 M\u2299\nM\n\u00135/3\n.\n(4)\nWe term these intermediate-duration signals lasting\nhours-days \u201ctransient continuous waves\u201d1, whose chirp\nmasses would range from O(10\u22125 \u221210\u22122) M\u2299. Systems\nwhose chirp masses are less than 10\u22125 M\u2299could spend\nyears in the LIGO\u2013Virgo\u2013KAGRA frequency band, and\nare termed \u201ccontinuous waves\u201d \u2013 analogous to canoni-\ncal GW emission from nonaxisymmetric rotating neutron\nstars [44] \u2013 and were also searched for in this dataset [45].\nIII.\nTHE SEARCH\nA.\nData\nWe consider data from the first part of the fourth ob-\nserving run of the LIGO Livingston (L1) and Hanford\n(H1) detectors, called O4a2. This observing run is more\nsensitive than previous ones across the full frequency\nband, but particularly at high frequencies [47\u201349]. Data\nwere collected between 24 May 2023 15:00:00 UTC and\n16 January 2024 16:00:00 UTC, with L1 and H1 online\nfor 69% and 67.5% of that time, respectively. The data\nare calibrated [50\u201352] such that, at worst, amplitude and\nphase uncertainties at 1\u03c3 are 10% and 10 degrees, respec-\ntively. We used data from times at which the interferom-\neters were in \u201cscience mode\u201d [53]. Virgo did not operate\nduring O4a, while KAGRA observed for one month.\nThe data structures that we used as the input to this\nsearch are called short fast Fourier transform databases\n[54], which contain frequency-domain representations of\n1 This term was coined originally in the context of signals arising\nafter pulsar glitches [43].\n2 We used the channel GDS\u2013CALIB STRAIN CLEAN AR with\nCAT1 vetoes [46].\nthe data every \u223c17 minutes that are cleaned of short\ntime-domain disturbances (\u201cglitches\u201d) [54]. Because we\nrequire the fast Fourier transform length TFFT \u226a17 min-\nutes, we inverse Fourier transform the data to the time\ndomain and create new time-frequency representations of\nthe data with the desired TFFT.\nB.\nMethod\nStandard searches for compact binary coalescences use\nmatched filtering to coherently match signal waveforms\nto GW data. Such analyses work well for short-duration\nsignals, but for the long-duration signals present here,\nmatched filtering would be computationally infeasible;\nthus, we employ a semi-coherent approach.\nWe break\nthe data into coherent chunks of length TFFT, and sum\nthe power across different FFTs incoherently. Such semi-\ncoherent searches require a choice of TFFT that ensures\nthat the GW frequency is monochromatic during each\nFFT. Practically, TFFT is a function of M, fGW and the\nsignal duration TPM, as described in Section III C.\nHere, we use the Generalized frequency-Hough to\nsearch for GWs from inspiraling compact objects [29,\n33, 55, 56]. For a given power-law model of the time-\nfrequency evolution of the signal (Eq. (2)), the General-\nized frequency-Hough operates on a time-frequency rep-\nresentation of the data called the peakmap (PM), a col-\nlection of ones and zeros that indicates the particular\nfrequencies whose power is a local maximum and greater\nthan a chosen threshold. This method performs a trans-\nformation from the t \u2212fGW plane of each detector sepa-\nrately to the f0 \u2212M plane of the source. In doing this\ntransformation, we sum over different possible tracks in\nthe time-frequency plane to accumulate the \u201cpeaks\u201d (the\nones) corresponding to specific chirp masses and coales-\ncence times. The number of unique tracks to search over\ndepends on our analyses parameters \u2013 TFFT, TPM \u2013 and\nfGW.\nIn contrast to previous searches, we use an implemen-\ntation of the Generalized frequency-Hough that is approx-\nimately an order of magnitude faster than previous ver-\nsions, permitting us to perform an extensive follow-up\ncampaign of significant time-frequency tracks.\nC.\nParameter space construction\nWe perform the search in a number of \u201cconfigurations\u201d,\nwhere each configuration corresponds to a particular fre-\nquency band [fmin, fmax], TFFT, a peakmap duration TPM\nand a chirp mass range [Mmin, Mmax]. These parameters\nare chosen to maximize the sensitivity, i.e. the distance\nreach Eq. (B1), towards systems with chirp masses be-\ntween [Mmin, Mmax] by considering the changing noise\npower spectral density of the interferometers, the varying\namplitude of the signal over time, and the steep increase\nin \u02d9f over time, which results in a decrease of the analy-\n\n3\nsis coherence time if we wish to confine the signal power\nto one frequency bin during TFFT. By looping over all\npossible chirp masses and GW frequencies, we can em-\npirically determine these parameters by calculating the\ndistance reach, and grouping nearby points in the param-\neter space to be searched for in a single peakmap with\nthe criterion that no more than 10% sensitivity is lost\nwith respect to creating separate peakmaps for each of\nthose nearby points. To limit the computational cost of\nthe search, we require that the chosen parameters would\nlead to detectable signals at least 0.1 kpc from us, and\nthe Doppler shift induced by the relative motion of the\nEarth and source is confined to one frequency bin for the\nsignal duration.\nAt the end of this process, we obtain 685 unique config-\nurations with TFFT \u2208[2, 13] s and TPM \u2208[2.3 h, 6.75 d]\ncovering systems with M \u2208[10\u22125, 10\u22122] M\u2299.\nD.\nResults\nWe perform the Generalized frequency-Hough on each\npeakmap in each configuration per detector separately,\nacross the whole observing run Tobs \u22438 months. Can-\ndidates returned from each detector with similar chirp\nmasses and coalescence times are considered \u201csignificant\u201d\nand \u201cin coincidence\u201d if (1) their parameters do not differ\nby more than three bins in the two-dimensional f0 \u2212M\nparameter space, (2) their detection statistics, called the\n\u201ccritical ratio\u201d (CR), are comparable (within 20% of each\nother), (3) their average CR exceeds a threshold of \u223c7\ndetermined by the trials factor and assuming Gaussian\nnoise, and (4) their time-frequency tracks do not overlap\nby more than 30% with a known noise line [46, 57].\nApproximately 5 \u00d7 105 candidates passed these four\ntests and were subject to a follow-up procedure in which\nthe original time-series data were demodulated based on\nthe expected phase evolution of the signal, obtained by\nintegrating Eq. (2).\nSuch a demodulation will ideally\nensure the signal remains monochromatic during its du-\nration, thus permitting us to use a longer coherence time.\nWe then compute a new time-frequency peakmap af-\nter doubling TFFT, and apply the frequency-Hough [58],\nwhich searches over residual\n\u02d9fGW that may occur for\nimperfect corrections.\nSimilarly to the Generalized\nfrequency-Hough, the frequency-Hough maps points in\nthe t\u2212fGW plane of the detector to lines in the f0 \u2212\u02d9fGW\nplane of the source. We require that the new CR exceeds\nthe previously found CR, which would occur for a real\nGW signal because the coherence time increased.\nThe parameters returned by the frequency-Hough are\nthen used to correct the peakmap for any residual mod-\nulations, which would lead to a monochromatic signal;\nthen, the peakmap is projected onto the frequency axis.\nNineteen candidates survived one doubling of TFFT until\nthe peakmap projection, after which all were vetoed. See\nSection A for more details regarding the final stages of\nthe search and the threshold selection.\nIV.\nUPPER LIMITS\nA.\nComputing expected distance reach\nThe procedure for semi-analytically computing upper\nlimits on the search\u2019s distance reach is described else-\nwhere [33] and was used in [35], so we highlight only\nthe important aspects here and provide more details in\nSection B. Although all coincident candidates have been\nvetoed, we can still use their CR values as thresholds\nto estimate the distance from which a real signal could\nhave originated in order to not produce a CR larger than\nthat observed in H1 and L1.\nIf a GW arising from a\nsource a certain distance away can pass these thresholds\nat least 95% of the time, we can set an upper limit on\nthe distance reach for sources similar to that particular\ncandidate dmax,95% at which 95% of injections would be\ndetected, i.e. at a particular time, frequency range, and\nchirp mass. We can compute dmax,95% in two ways: (1)\nby requiring that an injected GW signal in the data be\nrecovered with a CR larger than that returned in both\nH1 and L1 95% of the time, or (2) by analytically calcu-\nlating the distance reach as a function of the coincident\ncandidates returned in the search. We choose to do the\nlatter, but verify that both approaches produce consis-\ntent dmax,95% upper limits \u2013 see Section B.\nFor each of the coincident candidates in each configura-\ntion before thresholding the detection statistic, we com-\npute dmax,95%. To be conservative, we use the maximum\ndetection statistic of coincident candidates returned in\nH1 and L1, and apply the Feldman-Cousins procedure to\nit [59], effectively increasing the CR, thus reducing the\ndistance reach.\nIn each configuration, we compute the mean and stan-\ndard deviation of the distance reaches over different de-\ntector times and frequencies, which accounts for the vary-\ning power spectral density. Among all configurations, we\ntake the maximum distance reach at each chirp mass. We\nalso require that the time-frequency track of each candi-\ndate within TPM differs by no more than one frequency\nbin from the time-frequency track that the signal would\nfollow at 3.5PN:\n|fGW(t) \u2212f3.5PN(t)| \u2264\n1\nTFFT\n,\n(5)\nwhere f3.5PN(t) is given by Eq. 5.258 in [42]. This cri-\nterion has a bigger impact on the allowed candidates to\ncontribute to the upper limits for asymmetric mass-ratio\nsystems, since the mass ratio enters at 1PN.\nOur search is sensitive to ultra-compact objects inspi-\nraling for which M \u2208[10\u22125, 10\u22122] M\u2299, and whose time-\nfrequency evolution follow Eq. (2).\nThus, we provide\nin Fig. 1 constraints on the distance reach dmax,95% for\nequal-mass systems that are independent of the nature of\nthe compact objects and of the binary formation model.\nFrom Eq. (B1), a power-law behavior of dmax,95% \u221dM5/4\n\n4\nis expected. Fitting the curve, we find a power-law index\nof 1.24, within 1% from the theoretical value.\nThe procedure used to calculate dmax,95% has been val-\nidated through injection studies in both O3 [33] and O4a\n(see Section B), in which we have tested performance\nacross different times and frequency bands at fixed chirp\nmass.\nIts robustness to variations in curvature within\nthe time\u2013frequency plane is further supported by previ-\nous injection campaigns targeting rapidly spinning down\nisolated neutron stars in O2 [55, 60]. In those studies,\nthe algorithm tracked signals following distinct power-\nlaw time\u2013frequency evolutions with sensitivities consis-\ntent with Eq. (B1). Together, these results demonstrate\nthat the Generalized frequency-Hough performs reliably\nacross a broad range of chirping signals.\n10\n4\n10\n3\n10\n2\n (M\n)\n10\n1\n100\n101\n102\ndmax, 95% (kpc)\nFIG. 1. Model-independent distance reach constraints\nfor equal-mass inspiraling compact objects. We show\nthe distance reach at which 95% of signals would be re-\ncovered for equal-mass systems.\nThe green shaded region\ndenotes one standard deviation uncertainty on the distance\nreach, while the gray-shaded region indicates excluded dis-\ntances. These constraints follow the expected power-law of\ndmax,95% \u221dM5/4.\nB.\nComputing upper limits on merger rate density\nWe set upper limits on the merger rate density in a\ndifferent way than what is done to obtain dmax,95%. This\nis because dmax,95% is calculated based on the returned\ncoincident candidates in the search. We set upper limits\non rate density not via dmax,95% to account for the dif-\nferences between our analysis and those in matched-filter\nsub-solar mass searches [22\u201328].\nWe note that, in standard sub-solar mass searches [22\u2013\n28], the loudest event across the whole parameter space\nis used to set upper limits on rate density, which follows\nthe formalism in [61\u201363]. These are globally conservative\nupper limits.\nHowever, our search differs because the detection\nstatistic (the CR) is updated throughout the follow-up\nprocedure. Additionally, the coincident candidates have\nall been shown to be due to noise disturbances in the\nfollow-up (see Section A and Fig. 6 for details on these\nCRs.) In essence, the threshold that we set on our statis-\ntic, CRthr = 7, sets the sensitivity floor of the search: sig-\nnals with CR > CRthr enter the follow-up stage and can\nbe detected; signals with CR < CRthr are lost. Thus, we\ncan compute the upper limits on rate density by noting\nthat the probability density function of a certain value\nof the CR, given that it originates from a signal at a\ndistance r away, is\np(CR | r) =\n1\n\u221a\n2\u03c0 e\u2212(CR\u2212(D/r)2)2/2,\n(6)\nwhere D is the collection of prefactors that denote the\ndistance away we could detect a signal as a function of\nthe chirp mass, the frequencies covered by the signal and\nour analysis parameters TFFT, Tobs:\nD = 1.41\n\u0012GM\nc2\n\u00135/3 \u0010\u03c0\nc\n\u00112/3 TFFT\nTPM\n1/2\n\u00d7\n N\nX\nx\nf 4/3\nGW,x\nSn(fGW,x)\n!1/2 \u0012p0(1 \u2212p0)\nNp2\n1\n\u0013\u22121/4\n(7)\nSee Section B for the full equation and its validation\nagainst injections. Sn is the noise power spectral den-\nsity of the H1 or L1, N = Tobs/TFFT, and p0 and p1 are\ngiven in Eqs. (B2) and (B4). The integral of Eq. (6) gives\nthe efficiency \u03f5(r):\n\u03f5(r) = P(CR > CRthr | r) = 1\n2 erfc\n \nCRthr \u2212\n\u0000 D\nr\n\u00012\n\u221a\n2\n!\n(8)\nThen, the co-moving spacetime volume \u27e8V T\u27e9can be ap-\nproximated using Laplace\u2019s method (see Section C for\nmore details) :\n\u27e8V T\u27e9= Tobs\nZ \u221e\n0\n4\u03c0r2 \u03f5(r) dr\n\u2243Tobs\n4\n3\u03c0\n\u0012\nD\n\u221aCRthr\n\u00133\n(9)\nAssuming that the event rate for inspiraling ultra-\ncompact objects is Poissonian, consistent with other\nsearches [23, 24, 27], we can then calculate the upper\nlimits on the rate density at a chosen confidence level\n\u03b1 = 0.9:\nR90% = 2.303\n\u27e8V T\u27e9.\n(10)\n\n5\nWe show our upper limits on R90% in Fig. 2 for equal-\nmass and asymmetric mass-ratio systems. The rate den-\nsity follows a power law of approximately R \u221dD\u22123 \u221d\nM\u221215/4. From fitting the curve, we find the power-law\nindex to be \u20133.66, a 2% difference.\nC.\nModel-dependent constraints on PBHs\nTranslating these constraints into limits on the PBH\nabundance is subtle and highly model-dependent.\nIn-\ndeed, several binary formation channels have been pro-\nposed and each of them depend on the PBH mass distri-\nbution and subject to multiple astrophysical uncertain-\nties.\nFollowing state-of-the art rate prescriptions [64],\nearly-universe two-body binaries are typically the dom-\ninant binary formation channel for the masses and DM\nfraction relevant for this work. Their merger rate densi-\nties Rcos\nprim are given by\nRcos\nprim \u22481.6 \u00d7 10\u221212 kpc\u22123yr\u22121 \u02dcf 53/37\n\u00d7\n\u0012m1 + m2\nM\u2299\n\u0013\u221232/37 \u0014\nm1m2\n(m1 + m2)2\n\u0015\u221234/37\n, (11)\nwhere we define an effective parameter \u02dcf as:\n\u02dcf \u2261fPBH [fsupf(ln m1)\u2206ln m1f(ln m2)\u2206ln m2]37/53 ,\n(12)\nwhere f(ln m) is the PBH mass probability density func-\ntion, normalized such that\nR\nf(ln m)d ln m = 1.\nfPBH\nis the total fraction of DM made of PBHs and fsup is a\nmerger rate suppression factor (= 1 if no suppression)\nthat accounts for the various mechanisms affecting the\nbinary orbital properties throughout the history of the\nUniverse [65], changing their merger time or destroying\nthem3. Constraining \u02dcf eliminates the dominant sources\nof uncertainty, namely those arising from the suppres-\nsion factor and the mass distribution. In the following,\nwe will identify conditions on the mass distributions for\nwhich the suppression is minimal, which is required to\nlead to relevant constraints.\nCompared to standard compact binary coalescence\nsearches, the distance is limited to our galactic environ-\nment. One therefore has to translate cosmological merger\nrates into galactic rates, taking into account the galac-\ntic DM density profile.\nIf the galactic DM density was\nthe one at the Sun\u2019s location, \u03c1DM \u22431016 M\u2299Mpc\u22123\n[66], the merger rates would be enhanced to R = 3.3 \u00d7\n105Rcos\nprim [29]. However, with O4a data, we can probe\nsource distances comparable to the distance to the Galac-\ntic Center from Earth. We therefore have modified the\nrates by a factor F(d) that accounts for the integrated\n3 The fraction of PBHs that originally form in binaries versus as\nisolated systems is accounted for in the derivation of Eq. (11).\nDM density profile centered on the sun location at 8.2\nkpc from the galactic center, as described in Section D.\nThus, we rewrite Eq. (11) in both the equal-mass case\nR =1.04 \u00d7 10\u22126 kpc\u22123yr\u22121F(d)\n\u0012MPBH\nM\u2299\n\u0013\u221232/37\n\u02dcf 53/37 ,\n(13)\nwhere MPBH = 21/5M, and the asymmetric mass-ratio\ncase\nR = 5.28 \u00d7 10\u22127 kpc\u22123yr\u22121\n\u00d7 F(d)\n\u0012 m1\nM\u2299\n\u0013\u221232/37 \u0012m2\nm1\n\u0013\u221234/37\n\u02dcf 53/37 ,\n(14)\ndefining m2 < m1.\nIn Fig. 3, we show the constraints on \u02dcf in the asym-\nmetric mass-ratio case inferred from Fig. 2(b) (we do not\nfind relevant constraints in the equal-mass case).\nD.\nConstraining fPBH from \u02dcf\nThough we constrain the effective parameter \u02dcf down to\nabout 0.2 in a portion of the parameter space for asym-\nmetric mass-ratio binaries, in order to derive a mean-\ningful limit on fPBH, given Eq. (11), we need to find\nregimes in which fsup \u22730.04 or even close to unity. We\nidentify below some general conditions on the mass dis-\ntribution for which this is satisfied for asymmetric mass-\nratio binaries, and provide further details in Section D\nfor equal-mass systems, which remain unconstrained in\nthis analysis.\nFor asymmetric mass-ratio binaries, we can constrain\nf 53/37\nPBH f(ln m2), under some sufficient conditions: (i) if\nthere is a peak in the distribution at the mass m1, such\nthat f(ln m1)\u2206ln m1 \u22481 and the mean PBH mass is\n\u27e8m\u27e9\u2248m1, and (ii) if there is at least a small DM frac-\ntion in heavy black holes, enough to seed PBH clusters,\nsuch that the binary is unlikely to be perturbed by other\nPBHs. In this case, we obtain fsup \u22480.5 and can con-\nstrain f(ln m2) in the range 10\u22126 < m2/M\u2299< 10\u22124, if\nm1 is at the solar mass scale, as expected in the mo-\ntivated class of mass functions imprinted by the QCD\nepoch [67]. The most stringent limit on f(ln m2) is when\none assumes fPBH = 1, but one should note that this\nwould be in conflict with existing limits. We show these\nlimits on f(ln m2) assuming fPBH = 1 in Fig. 4, which\ncan be compared to existing experiments.\nV.\nCONCLUSIONS\nWe have performed a search for planetary-mass, ultra-\ncompact objects using data from the first part of the\nLIGO, Virgo and KAGRA fourth observing run. Though\nwe did not find any significant events, we placed up-\nper limits on both the distance reach and merger rate\n\n6\n10\n4\n10\n3\n10\n2\n (M\n)\n10\n7\n10\n6\n10\n5\n10\n4\n10\n3\n10\n2\n10\n1\n100\n101\n102\nR, 90% (kpc\n3 yr\n1)\n(a)\n(b)\nFIG. 2. Model-independent constraints on rate density at the 90% confidence-level for equal-mass (left) and\nasymmetric mass-ratio inspiraling compact objects (right).\nThese constraints are derived following the procedure\noutlined in Section IV B, and obey the expected power law of R \u221dM\u221215/4.\nFIG. 3. Model-dependent constraints on asymmetric\nmass-ratio inspiraling PBHs. We interpret the rate den-\nsities in Fig. 2(b) as arising from PBHs, and constrain the\neffective parameter \u02dcf as a function of asymmetric mass-ratio\nPBHs using Eq. (14). We restrict the plot only to masses for\nwhich \u02dcf < 1, and note that we were unable to constrain \u02dcf < 1\nfor equal-mass systems.\ndensity of equal-mass and asymmetric mass-ratio ultra-\ncompact binaries. Moreover, for certain classes of for-\nmation models, we constrain the fraction of DM that\nPBHs could compose for asymmetric mass-ratio sys-\ntems. Our work complements matched filtering searches\nfor sub-solar mass PBH binaries by considering lower-\nmass regimes that would require too much computational\npower to analyze with matched filtering.\nOur results\nprovide a complementary way to probe planetary-mass\nPBH binaries that could form in clusters. In Fig. 4, we\nshow how our bounds on f(ln m2) compare to other ob-\nservations, assuming fPBH = 1. We also find that our\nconstraints are valid for systems with eccentricities as\nhigh as 0.84 (see Section E for more details). Note that\neach method has its own systematics and assumptions,\nand it may happen that microlensing constraints weaken\ndue to a better understanding of the galactic rotation\ncurves [79], which strengthens the argument that we need\nmultiple probes of PBHs in this mass regime. Moreover,\nwe note that PBH physics is an evolving field: while\nwe consider particular mass functions and conditions to\narrive at Fig. 4, we emphasize that these limits could\nchange with time, and that different assumptions could\nlead to different constraints. Hence, we release the rate\ndensity constraints directly to allow readers to choose\ntheir own ways of interpreting our results, along with\ncodes to generate these plots [56, 80\u201382].\nAs we look forward to future ground- and space-based\nGW interferometers that will probe even lower frequen-\ncies than accessible now, the impact of eccentricity on\nthe inspiral signal will become even more significant.\nWaveforms to handle eccentricity [83\u201392] and DM effects\n[93\u201399] in matched filtering analyses are currently un-\nder development, but these effects will not impact semi-\ncoherent analyses, such as the Generalized frequency-\nHough, as much. Our analysis thus allows us to be sen-\nsitive to a range of rich physics while maintaining com-\nputational efficacy.\n\n7\nFIG. 4. Constraints on PBHs from this search, in red, and other GW and electromagnetic analyses. Our limits\non the mass function f(m2) (shorthand for f(ln m2)) are valid for mass distributions respecting the conditions mentioned in\nthe text for asymmetric mass ratio binaries, assuming fPBH = 1. No curve is shown for equal-mass systems, as \u02dcf < 1 is\nnot constrained. We assume f(ln m1)\u2206ln m1 \u223c1 and use the corresponding values of \u02dcf in Fig. 3 at m1 = 2.5 M\u2299to obtain\nthe red line on this plot. We emphasize that these constraints are valid only for the classes of mass functions discussed in\nSection IV D. If one wishes to produce our constraints for different choices of fPBH, the red curve will be scaled upwards by\nf \u221253/37\nPBH\n.\nConstraints from other probes (microlensing and GWs) are also presented for comparison on fPBH, and are implicitly\nvalid for monochromatic mass functions and subject to astrophysical uncertainties. Purple curves correspond to constraints\nfrom previous GW searches [22, 23, 28, 68\u201372], while dashed blue curves indicate microlensing constraints [73\u201376] that could\nweaken significantly due to PBH clustering [77, 78]. Our constraints on the mass function in red should be referenced to the\nred left y\u2212axis, while all other constraints are directly on fPBH and should be referenced to the right y\u2212axis.\nAppendix A: Details on final steps of the search\nWe select the top 1% of candidates in every Hough map\nthat is created. Each candidate is defined to have the fol-\nlowing parameters (1) the signal frequency at a reference\ntime, (2) the chirp mass, and (3) the detection statis-\ntic.\nThe analysis of each detector\u2019s data is performed\nseparately, meaning that we can look for coincident can-\ndidates, i.e. candidates with similar enough parameters\npresent at the same times in both detectors. We define\n\u201cclose enough\u201d to be three bins away:\ndist =\ns\u0012kLHO \u2212kLLO\n\u03b4k\n\u00132\n+\n\u0012z0,LHO \u2212z0,LLO\n\u03b4z0\n\u00132\n(A1)\nwhere \u03b4k and \u03b4z0 are the bin sizes in each of the coordi-\nnates in the Hough map. Note that we create the Hough\nmaps in the transformed coordinates z = 1/f 8/3 and k,\nnot f0 and M \u2013 see [55] for details on this transforma-\ntion.\n\u03b4k varies as a function of TFFT, k (M) and f0,\nwhile \u03b4z0 depends solely on f0 and TFFT [55].\nAt this stage, we apply a threshold on the critical ra-\ntio, CRthr \u22737, that ensures that we only consider can-\ndidates with a false alarm probability of 1% (accounting\nfor the trials factor) in Gaussian noise.\nThe data are\nnot Gaussian, which means that we tend to keep large\nnoise disturbances as well as potential signals. If we were\nto have estimated a background for the CR using time-\nslides or another method traditionally used in compact\nbinary searches, we would have obtained a higher thresh-\nold than CRthr \u223c7 due to the presence of non-Gaussian\nnoise disturbances. Thus, our threshold is conservative.\nThe number of coincident candidates that surpass\nthese tests is \u223c5 \u00d7 105.\nEach of these candidates is\nsubject to a follow-up procedure: the data are demod-\n\n8\nulated based on the candidate parameters, which would\nlead to a perfectly monochromatic signal if the demod-\nulation was done correctly. The search is then re-run,\nwhich a new TFFT equal to twice the original one. All\ncandidates are vetoed in this procedure, since they do\nnot produce CRs that exceed those from the first stage\nof the search, as would be expected for a monochromatic\nsignal with increased TFFT length.\nAppendix B: Obtaining distance reach upper limits\nWe describe how we set upper limits on the model-\nindependent distance reached as a function of chirp mass.\nTo do so, we employ a semi-analytic/ data-driven proce-\ndure outlined in [33], which uses as input results from\nour search (detection statistics and detector power spec-\ntral density), and an equation for theoretical sensitivity\nestimate of our method, as a way to obtain upper limits\non the maximum distance away that we could have seen\na source as a function of chirp mass, i.e. Fig. 1. Such a\nprocedure was designed to avoid extensive injection cam-\npaigns to set upper limits and instead use that computing\npower to follow-up interesting candidates.\nEven though each configuration is labeled by a par-\nticular chirp mass and starting frequency (M \u2032\ni,f \u2032\n0,i), the\npeakmaps and Hough maps generated can actually probe\nmany different chirp masses and starting frequencies. Let\nus label the space of chirp masses as Mk. Within a given\nHough map (say j) for a particular configuration (say\ni), all instances of Mk (with any starting frequency fl)\nare assigned a critical ratio (CRIF O\ni,j,k,l) per interferometer\nIFO. We then compute the distance reach using Eq. (B1)\nfor each detector separately with the following:\nd\u0393\nmax = 1.41\n\u0012GM\nc2\n\u00135/3 \u0010\u03c0\nc\n\u00112/3 TFFT\nTPM\n1/2\n\u0012p0(1 \u2212p0)\nNp2\n1\n\u0013\u22121/4\n\u00d7\n N\nX\nx\nf 4/3\nGW,x\nSn(fGW,x)\n!1/2 \u0010\nCR \u2212\n\u221a\n2erfc\u22121(2\u0393)\n\u0011\u22121/2\n.\n(B1)\nwhere \u0393 = 0.95 is the fraction of detectable signals in\nrepeated experiments, N = Tobs/TFFT is the number of\nFFTs used to make the peakmap, and p0 is the probability\nof selecting a peak above \u03b8thr = 2.5, the threshold on\nequalized power in the peakmap, and:\np0 = e\u2212\u03b8thr \u2212e\u22122\u03b8thr + 1\n3e\u22123\u03b8thr\n(B2)\nand\np1 = \u03b8thr\n\u00121\n2e\u2212\u03b8thr \u22121\n2e\u22122\u03b8thr + 1\n6e\u22123\u03b8thr\n\u0013\n(B3)\n+ 1\n4e\u22122\u03b8thr \u22121\n9e\u22123\u03b8thr.\n(B4)\nboth relate to the probability of selecting a peak above\nthe threshold \u03b8thr in the presence of a weak monochro-\nmatic signal [100]. We note that this equation is strictly\nvalid for signals lasting at least one sidereal day. How-\never, since it is evaluated millions of times for coincident\ncandidates occurring at random times in the run, the\nensemble of evaluations effectively samples all sidereal\nphases.\nIn Eq. (B1), we must input a value for the CR\nthat accounts for the fact that this equation was de-\nrived in the case of Gaussian noise, but our analy-\nsis was done in real noise.\nWe first take the maxi-\nmum of the two CRs returned from each interferome-\nter: CRi,j,k,l=maxIFO(CRIF O\ni,j,k,l). This is a conservative\nchoice, since it reduces d\u0393\nmax with respect to using the\naverage or minimum CR.\nThen, we employ the Feldman-Cousins (FC) [59] ap-\nproach, in which we assume that the CR follows a Gaus-\nsian distribution, and map the measured CRi,j,k,l to\na positive-definite value using the upper value of Tab.\n10 in [59] at 95% confidence. Here, we input CRi,j,k,l\ninto the Feldman-Cousins procedure.\nIn other words,\nCRFC,i,j,k,l = FC(CRi,j,k,l) in Eq. (B1), which serves\nto reduce the distance reach with respect to if we had\nused just the maximum CR of the coincident candidates.\nThus, the meaning of the upper limit is as follows: a\nreal signal would need to have a critical ratio larger than\nthat used in Eq. (B1) in order to be detectable in 95%\nof repeatable experiments, at a particular reference time,\nchirp mass and frequency.\nLet us call the result of inputting CRFC,i,j,k,l into\nEq. (B1) d\u0393\ni,j,k,l. For each combination of i, j, k, l \u2013 which\ncorresponds to each coincident candidate we have in the\nsearch, before applying any threshold or follow-ups \u2013,\nwe compute a distance reach at which 95% of signals in\na repeated number of experiments would be recovered,\nd95%\ni,j,k,l, which represents, in repeated experiments, the\ndistance at which 95% of signals with a given chirp mass\nat a given time during the run would have been detected.\nWe then take the median of all the distances over the\nduration of the observing run, i.e. d95%\ni,k\n= median(d95%\ni,j,k)\nover each set of Tobs/TPM values, leading to one distance\nreach per configuration per probed chirp mass.\nThese\ndenote the different sensitivities of each configuration to\nthat particular chirp mass, some of which will be more\nsensitive than others. Therefore, we take the maximum of\nthese distances for each chirp mass as the distance upper\nlimit, i.e. dmax,95%,k = max(d95%\ni,k ), which are shown in\nFig. 1.\nThe upper limits in Fig. 1 are independent of any\npopulation or formation model for planetary-mass ultra-\ncompact objects.\nThey indicate that a system with a\ngiven chirp mass could have been detected in 95% of re-\npeatable experiments at a particular distance away from\nus.\nAs shown in [29, 33, 40, 55], the use of Eq. (B1) pro-\nduces consistent upper limits compared to those that\nwould be obtained by injecting simulated signals.\nWe\n\n9\nalso provide an injection study done in this dataset for\na range of chirp masses in Fig. 5. For each chirp mass,\nwe perform fifty injections over a range of distances away\nfrom us, and determine the distance reach at which we\nrecovered at least 95% of injections above CRthr = 7 in\nboth detectors. We compare our results to the theoret-\nical distance reach at 95% efficiency given by Eq. (B1).\nNote that Eq. (B1) represents population-averaged upper\nlimits; therefore, we must specialize this equation to the\nspecific sources we simulate in order to compare them\nto the sensitivity obtained through injections.\nIn par-\nticular, we account for the fact that we have simulated\nfifty sources with (1) specific choices of inclination and\npolarization angles, and sky position, and (2) durations\nthat are much less than a sidereal day, both of which\naffect Eq. (B1). This per-source factor Cs, where s de-\nnotes the source number, must be divided out of Eq. (B1)\nto specialize it to a particular source [100], as discussed\npreviously in the appendices of [40, 101]:\nCs =\ns\nS2\n\u03b1,\u03b4,\u03c8,cos \u03b9\nS2\nt\n,\n(B5)\nwhere\nS2\n\u03b1,\u03b4,\u03c8,cos \u03b9 = \u27e8(F+A+ + F\u00d7A\u00d7)2\u27e9\u03b1,\u03b4,\u03c8,cos \u03b9 \u22484\n25\n(B6)\nis the factor obtained normally in the derivation of\nEq. (B1) by averaging the induced strain over one side-\nreal day, sky position \u03b1, \u03b4, cosine of the inclination angle\ncos \u03b9, and the polarization angle \u03c8. Additionally, A+ and\nA\u00d7 are the plus and cross polarizations of the GW, given\nby:\nA+ = 1 + cos2 \u03b9\n2\n,\n(B7)\nA\u00d7 = cos \u03b9.\n(B8)\nThe factor S2\nt is obtained at the specific parameters of\nthe source:\nS2\nt = \u27e8F 2\n+\u27e9tA2\n+ +\n\nF 2\n\u00d7\n\u000b\nt A2\n\u00d7,\n(B9)\nwhere \u03c8 has been averaged out, and the average over\ntime t is taken only over the duration of the source, and\nF+(t) = a(t) cos 2\u03c8 + b(t) sin 2\u03c8,\n(B10)\nF\u00d7(t) = b(t) cos 2\u03c8 \u2212a(t) sin 2\u03c8,\n(B11)\nare the time-varying beam pattern functions. The func-\ntions a(t) and b(t) are given in [102].\nWe calculate C = mean(Cs) as an average over the 50\nsource-specific factors Cs, and then divide Eq. (B1) by\nC to plot the dark blue curve in Fig. 5. Furthermore,\nwe shade the \u00b11\u03c3 around the dark blue curve, which\nencapsulates the range of possible C, i.e. \u03c3 = std(Cs).\nFinally, the upper limits that we quote in Fig. 1 rely on\nthe application of the Feldman-Cousins procedure, so we\nreevaluate the theoretical curve at CRFC = FC(CRthr =\n7) = 8.96 for comparison. We see that the injections lie\ncomfortably within the shaded area and are consistent\nwith both the source-specific theoretical curve and the\nFeldman-Cousins curve.\n10\n4\n10\n3\nchirp mass \n(M\n)\n100\n101\n102\ndistance reach d95% (kpc)\nSource duration: 7000 s\nTFFT = 2 s\n\u00b11 region\nsource-specific\nFeldman-Cousins upper limit\nInjection results\nFIG. 5. Comparison of upper limits on distance reach\ncalculated through injections and with the formula\ngiven in Eq. (B1).\nThe blue line indicates the theoreti-\ncal expectation for the distance reach at 95% confidence, ad-\njusted by the source-specific factor C (see text for details).\nThe shaded region denotes the \u00b11\u03c3 uncertainty on the dis-\ntance reach based on the range of source-specific Cs values.\nThe magenta points indicate the derived distance reach at\nwhich 95% of injections are recovered in our simulations. The\ngreen line indicates the upper limit that we would actually\nquote based on the Feldman-Cousins procedure. Our results\nshow that the injection studies agree well with the theoretical\nblue and green curves and fall well within the shaded region.\nFor each set of fifty injections, at each chirp mass, performed\nat different distance reaches to derive these results, we ana-\nlyze different frequency bands and different times across the\nO4a dataset.\nAppendix C: Obtaining rate density upper limits\nFor a fixed chirp mass and frequency range, the only\nparameter that affects the efficiency of the search is the\nGW amplitude \u2013 or, equivalently, the source distance \u2013\nfrom the interferometers, so the space-time volume \u27e8V T\u27e9\nto which we are sensitive can be written as\n\u27e8V T\u27e9= Tobs\nZ \u221e\n0\n4\u03c0r2 \u03f5(r) dr,\n(C1)\nr is an arbitrary distance and \u03f5(r) is the efficiency curve,\ngiven by Eq. (8). To compute \u27e8V T\u27e9, we can use Laplace\u2019s\nmethod, which allows us to solve this integral analytically\nby considering its asymptotic behavior. We define\n\n10\nFIG. 6. The critical ratios of coincident candidates re-\nturned in our search whose CR > CRthr = 7. Candidates\nwith CR < CRthr are not shown. CR is averaged from can-\ndidates returned in both H1 and L1, and corresponds to the\ncandidates that we followed up, all of which were vetoed. In\norder to compute upper limits on distance reach, we use these\nCRs in Eq. (B1) and apply the Feldman-Cousins procedure\n[59] that effectively increases CR to ensure 95% confidence-\nlevel coverage. In other words, real GW signals would have\nhad to generate CRs above the ones in this figure at a given\nchirp mass, time and frequency to have been detected by our\nsearch 95% of the time.\nx \u2261CRthr \u2212\n\u0000 D\nr\n\u00012\n\u221a\n2\n,\n(C2)\nwhere D is given by Eq. (7) and CRthr = 7 is the thresh-\nold on the critical ratio that we use to determine which\ncandidates to follow up, and expand linearly around\nr\u22c6= D/\u221aCRthr, which is the point at which x = 0:\nx(r) \u2243x(r = r\u22c6) + dx\ndr\n\f\f\f\f\nr=r\u22c6\n(r \u2212r\u22c6),\n\u2243\n\u221a\n2CR3/2\nthr\nD\n(r \u2212r\u22c6),\n(C3)\nand thus\n\u03f5(r) \u22431\n2erfc\n \u221a\n2CRthr\nD\n(r \u2212r\u22c6)\n!\n.\n(C4)\nTo leading order, we can replace \u03f5(r) by a step function at\nthe transition point r\u22c6, where the inverse error function\nerfc starts to rapidly decrease for values r > r\u22c6.\n\u27e8V T\u27e9\u2243Tobs\nZ r\u22c6\n0\n4\u03c0r2 dr,\n(C5)\n\u2243Tobs\n4\n3\u03c0\n\u0012\nD\n\u221aCRthr\n\u00133\n.\n(C6)\nSuppose that we would like to check what the next-to-\nleading correction would be, to ensure that it is small\nwith respect to what we quote in Eq. (9). To do this,\nwe can change variables such that u = a(r \u2212r\u22c6), where\na =\n\u221a\n2CR3/2\nthr\nD\nand write the integral as\n\u27e8V T\u27e9= Tobs4\u03c0\nZ \u221e\n0\n\u03f5(r) r2 dr\n\u2248Tobs4\u03c0 1\na\nZ \u221e\n\u2212ar\u22c6\n1\n2 erfc(u)\n\u0010\nr\u22c6+ u\na\n\u00112\ndu.\n(C7)\nSplitting erfc(u) into a step-function piece and a correc-\ntion piece:\n1\n2 erfc(u) = H(\u2212u) + s(u),\n(C8)\nwhere\ns(u) \u22611\n2 (erfc(u) \u22122H(\u2212u)) =\n(\n1\n2(erfc(u) \u22122),\nu < 0,\n1\n2erfc(u),\nu > 0,\n(C9)\nand noting that s(u) has the following properties:\nZ \u221e\n\u2212\u221e\ns(u) du = 0,\nZ \u221e\n\u2212\u221e\nu s(u) du = 1\n4,\n(C10)\nwe can calculate the next-to-leading-order piece of \u27e8V T\u27e9:\n\u2206\u27e8V T\u27e9= 4\u03c0Tobs\n1\na\nZ \u221e\n\u2212\u221e\n1\n2 s(u)\n\u0010\nr\u22c6+ u\na\n\u00112\ndu.\n(C11)\nHere, we have extended the lower bound from \u2212ar\u22c6to\n\u2212\u221ebecause the integral takes on the largest values\naround r = r\u22c6Using Eq. (C10) and dropping the u2\nterm, we arrive at:\n\u2206\u27e8V T\u27e9= 4\u03c0Tobs\nr\u22c6\n2a2 ,\n= 4\u03c0Tobs\nD3\n4CR7/2\nthr\n.\n(C12)\nFinally, we can express the leading- and next-to-leading-\norder contributions as:\n\u27e8V T\u27e9tot \u2243\u27e8V T\u27e9+ \u2206\u27e8V T\u27e9\n\u2243Tobs\n4\n3\u03c0\n\u0012\nD\n\u221aCRthr\n\u00133 \u0014\n1 +\n3\n4CR2\nthr\n+ . . .\n\u0015\n(C13)\nGiven that we use CRthr = 7 in this paper, the next-\nto-leading-order term is of O(10\u22122) and can thus be ne-\nglected, allowing us to safely set \u27e8V T\u27e9tot = \u27e8V T\u27e9.\n\n11\nFrom \u27e8V T\u27e9, we can compute the rate density con-\nstraint by assuming that the event rate for inspiraling\nplanetary-mass ultra-compact objects follows a Poisso-\nnian distribution, which is consistent with our expecta-\ntions of how binary black hole objects inspiral and merge.\nThe rate density equation can be derived independently\nof GW data analysis: we only need to consider inspirals\nas a Poisson process with a mean number of expected\nevents of \u03bb = R \u27e8V T\u27e9. In a Poisson process, the proba-\nbility that we observe zero events N is:\nP(N = 0|\u03bb) = e\u2212\u03bb\n(C14)\nTo obtain an upper limit at a given confidence level \u03b1,\nwe simply need to set:\nP(N = 0|\u03bb) = 1 \u2212\u03b1 = e\u2212\u03bb\n(C15)\nBy setting \u03b1 = 0.9 and solving for R, we obtain Eq. (10).\nAppendix D: From cosmological to galactic rates\nIn this section, we describe the methodology to obtain\ngalactic merger rates as a function of the distance reach D\noutputted by the search. The expected rate is obtained\nfrom the cosmological merger rate densities, multiplied\nby the probe volume 4\n3\u03c0D3 and by the ratio between the\naveraged DM density in this volume and the cosmological\ndensity. We use a standard Navarro-Frenk-White profile,\n\u03c1(r) =\n\u03c10\nr\nRs\n\u0010\n1 +\nr\nRs\n\u00112 ,\n(D1)\nwith Rs = 21.5 kpc and \u03c10 = 8 \u00d7 106 M\u2299kpc\u22123. Using\nanother type of profile, such as a Einasto profile, only\nchanges our results marginally. The enclosed DM mass\nMDM(D) is obtained by integrating the profile centered\non the Sun\u2019s location, at R\u2299= 8.2 kpc from the galactic\ncenter, to get\nMDM(D) = 2\u03c0\nZ \u03c0\n0\nZ D\n0\nr2\n\u00d7 \u03c1\n\u0012q\nr2 + R2\n\u2299\u22122rR\u2299cos(\u03d5)\n\u0013\nsin(\u03d5)drd\u03d5 .\n(D2)\nWe then compute the factor F(d) as the ratio between\nthe averaged density at distance d and the density at the\nsun location.\nThe obtained value of F(d) is shown in\nFig. 7. As expected, it is close to one for short distances\ncompared to the galaxy scale.\nIt shows a slight peak\nat d \u223c8 kpc that corresponds to the distance of the\ngalactic center where DM density is strongly enhanced.\nBut we note that the rate enhancement is small because\nthe search is sensitive to all directions of the sky and\nnot only the galactic center. At larger distances, F(d)\ndecreases and above 50 kpc, it decreases like 1/d3 as ex-\npected given that the DM density decays and the to-\ntal mass probed does not vary much. We then obtain a\nconstant rate value compatible with the one calculated\nin [29], Rgal \u22482 \u00d7 10\u22128 \u00d7 Rprim\ncos Gpc3.\n0\n50\n100\n150\n200\n250\n300\ndistance d (kpc)\n10\n3\n10\n2\n10\n1\n100\nF(d)\nFIG. 7. How the factor F(d) falls off as as a function\nof distance from Earth.\nF(d) encodes the ratio of the\naveraged DM density at a distance d compared to that at the\nSun\u2019s position.\nAppendix E: Evaluating robustness of constraints\n1.\nEccentricity\nOur constraints have implicitly assumed that GWs\nfrom\ninspiraling\ncompact\nobjects\nfollow\nthe\ntime-\nfrequency evolution f3.5P N(t). It is, however, worth dis-\ncussing whether additional physics could affect our abil-\nity to set upper limits on PBHs. We consider to what\nextent binary eccentricity would alter our conclusions.\nTo do this, we require that the frequency shift induced\nby eccentricity would be confined to one frequency bin\nfor the total signal duration.\nIn other words, we can-\nnot distinguish between f3.5P N(t) and the signal time-\nfrequency evolution with eccentricity.\nThe key quan-\ntity here is the time-frequency track: eccentricity does\nnot cause frequency fluctuations throughout the signal\u2019s\ntime-frequency track by more than one frequency bin. In\nother words, if [41, 42]\n\u02d9fGWg(e)TFFT \u2264\n1\nTFFT\n(E1)\nwe would not miss eccentric systems. The function that\ncharacterizes the eccentricity e is given by [42]:\ng(e) =\n\u00001 \u2212e2\u0001\u22127/2 \u0012\n1 + 73\n24e2 + 37\n96e4\n\u0013\n.\n(E2)\nPlugging Eq. (1) into Eq. (E1) and solving for g(e), we\nobtain:\n\n12\ng(e) \u22728000\n\u0012 1 s\nTFFT\n\u00132 \u001210\u22123 M\u2299\nM\n\u00135/3 \u0012100 Hz\nfGW\n\u001311/3\n.\n(E3)\nSolving for the eccentricity is analytically unfeasible, so\nwe numerically compute the maximum eccentricity emax\nto which each configuration is sensitive. Given that each\nconfiguration covers a wide range of fGW and M, we\ncalculate the median emax by sampling over the range of\nfGW, M each configuration could detect. We plot these\nmedian emax in Fig. 8.\nFor comparison, a pessimistic\nevaluation of Eq. (E3) using the maximum frequency and\nchirp mass in each configuration results in a sensitivity\nto binaries with maximum eccentricities of [0.33, 0.72],\nwith a median of 0.46. On the other hand, an optimistic\nevaluation using the minimum frequency and chirp mass\nprobed in each configuration would permit us to detect\nbinaries with eccentricities between [0.86, 0.97], with a\nmedian of 0.91.\nFIG. 8. The median maximum eccentricity that each\nconfiguration in our search could probe. We show that,\nfor asymmetric mass-ratio systems, we can be sensitive to\neccentricities as high as 0.84, depending on the GW frequency\nand chirp mass of the system.\n2.\nConditions on the PBH mass distribution\nCalculating\nPBH\nmerger\nrates\nis\nhighly\nmodel-\ndependent. In particular, the choice of the PBH mass\ndistribution can significantly affect the predicted sup-\npression of merger rates. This suppression mainly arises\nfrom the disruption of binaries, either through early in-\nteractions with intruding PBHs or via late encounters\nwith other PBHs within clusters formed by Poisson fluc-\ntuations. Some sufficient conditions to avoid such a sup-\npression have been identified, and in this appendix we\nprovide a more detailed explanation for these conditions,\nbased on the current prescriptions for the merger rates.\na.\nEarly perturbers\nThe first two conditions ensure that most binaries are\nnot gravitationally bound to their neighbors when form-\ning. Assuming fPBH \u226b\u03c3M (where \u03c32\nM is the variance\nof matter density perturbations at the time the binary\nforms), the suppression factor associated with the early\ndisruption of binaries by a nearby intruder can be ex-\npressed as [64, 65, 103]:\nf (dist)\nsup\n\u22481.42\n\u0012\u27e8m2\u27e9/\u27e8m\u27e92\n\u00afN(y) + 0.4\n\u0013\u221221/74\nexp(\u2212\u00afN),\n(E4)\nwhere \u00afN is the expected number of PBHs within the\nbinary\u2019s sphere of influence at scale factor a, given by\n\u00afN = M\n\u27e8m\u27e9\nfPBH\nfPBH + aeq/a,\n(E5)\nwith M denoting the total mass of the binary, \u27e8m\u27e9=\n\u03c1PBH/nPBH the average PBH mass, and aeq the scale fac-\ntor at matter-radiation equality. Since the number den-\nsity of PBHs, nPBH, scales inversely with mass, lighter\nPBHs can significantly outnumber the PBHs from the\npeak, even with a subdominant contribution to the total\nPBH energy density, increasing \u00afN and driving the sup-\npression factor towards zero. Consequently, only mass\nfunctions with a suppressed low-mass tail can survive\nsuch heavy disruption. In these cases, for symmetric bi-\nnaries, one typically finds \u00afN \u22482 yielding a suppression\nfactor of fsup \u22480.2. For asymmetric binaries, M \u2248m1\nsuch that \u00afN \u22481, which yield a suppression factor of\nfsup \u22480.5. These are the two cases we consider to pro-\nduce Fig. 4.\nb.\nLate perturbers\nOne additional condition that must be fulfilled in all\nscenarios is to avoid the rate suppression due to the inter-\nactions of the binaries with PBHs inside clusters seeded\nby Poisson fluctuations. The standard prescription, vali-\ndated by numerical simulations for peaked distributions,\nleads to a rate suppression factor today approximately\ngiven by\nf (cl)\nsup \u22480.01f \u22120.65\nPBH\n(E6)\nwhen a significant DM fraction is made of PBHs, i.e. an\nadditional suppression by up to two orders of magnitude.\nHowever, we can show that such a suppression can be\navoided for low-mass PBHs. From Ref. [64], binaries are\nperturbed by encounters with PBHs of mass m3 inside\nclusters when the impact parameter is\nb \u2272[m3(m1 + m2 + m3)]1/3 r1/2\na\nj1/3\n\u03c4\n(m1 + m2)1/6vrel\n(E7)\n\n13\nwhere ra is the separation and j\u03c4 the angular momen-\ntum of the binary, expected to merge today, for which\nestimations are provided in Ref. [64],\nj\u03c4 = 1.7 \u00d7 10\u22122\n\u0012m1 + m2\nM\u2299\n\u00135/37 (4m1m2)3/37\n(m1 + m2)6/37 f 16/37\nPBH\n(E8)\nand\nra = 2.13 \u00d7 109m \u00d7\n\u0014m1m2(m1 + m2)\nM 3\n\u2299\n\u00151/4\n,\n(E9)\nand where vrel is the relative velocity, of same order than\nthe virial velocity of the cluster. The corresponding inter-\naction cross-section is then given by \u03c3 = \u03c0b2 and one can\nthen estimate, for each PBH mass m3 with an abundance\ncharacterized by f(ln m3), the typical time it takes to\nperturb the binary, tpert = 1/[n(m3)\u03c3vrel], where n(m3)\nis the number density of perturbers of mass m3 in the\ncluster. For a wide mass distribution, one has to inte-\ngrate n(m3)\u03c3vrel over the full distribution to get the total\nperturbation rate. For simplicity, we only show here that\nany value of m3 gives rise to tpert \u226bt0, the age of the\nUniverse, with some conditions on the PBH clusters. But\nin general, tpert depend on the typical clustering scale.\nFrom Ref [64], this time was found to be typically much\nsmaller than the age of the Universe, leading to auto-\nmatic binary perturbations in clusters. Nevertheless, the\nclustering process is complex and is also impacted by the\ndynamical heating of small clusters and their dilution\nin larger clusters. As explained in [104], if there exist\na mass range m in the distribution for which one has\nf(m)m/M\u2299\u223cO(1), then the smallest clusters will have\na radius of order 20 parsecs and a mass around 106 M\u2299\nthat could be associated to ultra-faint dwarf galaxies, a\nlarger value of that combination being excluded by the\nobservations of these ultra-faint dwarfs. These clusters\nwould have virial velocities of order of a few km/s. We\nhave calculated the interaction time needed to perturb\nbinaries with component masses m1 and m2 as\ntpert \u22482.7 \u00d7 1010yr \u00d7 f \u221279/111\nPBH\nf(ln m3)\u22121\n\u00d7\n\u0012m1m2\nM 2\n\u2299\n\u0013\u221229\n148 \u0012 m3\nM\u2299\n\u0013 1\n3 \u0012m1 + m2\nM\u2299\n\u0013 29\n144\n\u00d7\n\u0012m1 + m2 + m3\nM\u2299\n\u0013\u22122\n3 \u0012Mcl\nM\u2299\n\u0013\u22121\n2 \u0012rcl\npc\n\u00135/2\n,\n(E10)\nwhere Mcl and rcl are the cluster mass and radius, re-\nspectively. Taking f(ln m3) = 1, for the typical above-\nmentioned clusters and the relevant masses and values of\nfPBH for this work, this time is found to exceed the age\nof the universe, lower abundances leading obviously to\neven larger interaction times. But let us note again the\nimportance of the large cluster mass compared to what\nwas considered in [64, 103]. A heavy-mass tail in the dis-\ntribution, or of a high peak at the solar-mass scale with a\nsignificant fPBH, are therefore required to prevent merger\nrates to be suppressed due to PBH clusters.\nFinally, let us notice that we have checked that the\nother PBH binary formation channels, reviewed in [64],\nnamely the 3-body early binary formation channel and\nthe late 2-body and 3-body channels in PBH clusters,\ngenerically lead to lower merger rates than for early bi-\nnaries, for significant values of fPBH, both for equal-mass\nsubsolar mergers and for asymmetric binaries.\nThese\nhave therefore not been considered in our analysis.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and operation\nof the GEO 600 detector.\nAdditional support for Ad-\nvanced LIGO was provided by the Australian Research\nCouncil. The authors gratefully acknowledge the Italian\nIstituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS)\nand the Netherlands Organization for Scientific Research\n(NWO) for the construction and operation of the Virgo\ndetector and the creation and support of the EGO con-\nsortium.\nThe authors also gratefully acknowledge re-\nsearch support from these agencies as well as by the\nCouncil of Scientific and Industrial Research of India,\nthe Department of Science and Technology, India, the\nScience & Engineering Research Board (SERB), India,\nthe Ministry of Human Resource Development, India,\nthe Spanish Agencia Estatal de Investigaci\u00b4on (AEI), the\nSpanish Ministerio de Ciencia, Innovaci\u00b4on y Universi-\ndades, the European Union NextGenerationEU/PRTR\n(PRTR-C17.I1), the ICSC - CentroNazionale di Ricerca\nin High Performance Computing, Big Data and Quantum\nComputing, funded by the European Union NextGener-\nationEU, the Comunitat Auton`oma de les Illes Balears\nthrough the Conselleria d\u2019Educaci\u00b4o i Universitats, the\nConselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat\nDigital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish\nNational Agency for Academic Exchange, the National\nScience Centre of Poland and the European Union - Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scot-\ntish Universities Physics Alliance, the Hungarian Scien-\ntific Research Fund (OTKA), the French Lyon Institute\n\n14\nof Origins (LIO), the Belgian Fonds de la Recherche Sci-\nentifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of\nScience, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute\nfor Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Sci-\nence Foundation of China (NSFC), the Israel Science\nFoundation (ISF), the US-Israel Binational Science Fund\n(BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC),\nTaiwan, the United States Department of Energy, and\nthe Kavli Foundation. The authors gratefully acknowl-\nedge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources.\nThis work was supported by MEXT, the JSPS\nLeading-edge Research Infrastructure Program, JSPS\nGrant-in-Aid for Specially Promoted Research 26000005,\nJSPS Grant-in-Aid for Scientific Research on Inno-\nvative Areas 2402:\n24103006, 24103005, and 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-\nto-Core Program A. Advanced Research Networks, JSPS\nGrants-in-Aid for Scientific Research (S) 17H06133 and\n20H05639, JSPS Grant-in-Aid for Transformative Re-\nsearch Areas (A) 20A203:\nJP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nUniversity of Tokyo, the National Research Foundation\n(NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineering\nCenter of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising.\nWe\nrequest that citations to this article use \u2019A. 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Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37\nF. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41\nM. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9 J. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49\nS. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11 S. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42\nM. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,55\nN. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 G. Ashton\n,58 Y. Aso\n,25, 59 L. Asprea,28 M. Assiduo,60, 61\nS. Assis de Souza Melo,62 S. M. Aston,63 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,64 K. AultONeal\n,65\nG. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51\nM. Ball,77 G. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12\nP. Baral\n,10 M. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11\nD. Bersanetti\n,29 T. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101\nN. Bevins\n,102 R. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46\nV. Biancalana\n,101 A. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75\nC. Binu,110 S. Biot,111 O. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113\nS. Blaber,114 J. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 N. Bode\n,8, 9 N. Boettner,97\nG. Boileau\n,113 M. Boldrini\n,38 G. N. Bolingbroke\n,115 A. Bolliand,116, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82\nF. Bondu\n,117 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,118 R. Bonnand\n,31, 116 A. Borchers,8, 9 V. Boschi\n,80\nS. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 M. Boyle,120 A. Bozzi,62 C. Bradaschia,80\nP. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104 T. Briant\n,121 A. Brillet,113 M. Brinkmann,8, 9\nP. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,115 M. L. Brozzetti\n,76, 51\nS. Brunett,11 G. Bruno,15 R. Bruntz\n,122 J. Bryant,118 Y. Bu,123 F. Bucci\n,61 J. Buchanan,122\nO. Bulashenko\n,82, 83 T. Bulik,124 H. J. Bulten,37 A. Buonanno\n,125, 1 K. Burtnyk,2 R. Buscicchio\n,126, 127\nD. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7\nL. Cadonati\n,57 G. Cagnoli\n,128 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,129 E. Calloni,32, 4\nS. R. Callos\n,77 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,130 E. Capocasa\n,20\nE. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 131 F. Carbognani,62 M. Carlassara,8, 9 J. B. Carlin\n,123\nT. K. Carlson,132 M. F. Carney,104 M. Carpinelli\n,126, 62 G. Carrillo,77 J. J. Carter\n,8, 9 G. Carullo\n,118, 133\nA. Casallas-Lagos,134 J. Casanueva Diaz\n,62 C. Casentini\n,135, 22 S. Y. Castro-Lucas,136 S. Caudill,132\nM. Cavagli`a\n,105 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,137, 138 E. Cesarini\n,22 N. Chabbra,34\nW. Chaibi,113 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103 S. Chalathadka Subrahmanya\n,97\nJ. C. L. Chan\n,139 M. Chan,114 K. Chang,140 S. Chao\n,141, 140 P. Charlton\n,142 E. Chassande-Mottin\n,20\nC. Chatterjee\n,143 Debarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,103 S. Chaty\n,20 A. Chen\n,144\nA. H.-Y. Chen,145 D. Chen\n,146 H. Chen,141 H. Y. Chen\n,147 S. Chen,143 Yanbei Chen,148 Yitian Chen\n,120\nH. P. Cheng,149 P. Chessa\n,76, 51 H. T. Cheung\n,90 S. Y. Cheung,6 F. Chiadini\n,150, 131 G. Chiarini,8, 9, 92\nA. Chiba,151 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80 A. Chiummo\n,4, 62 C. Chou,145 S. Choudhary\n,72\nN. Christensen\n,113, 152 S. S. Y. Chua\n,34 G. Ciani\n,74, 75 P. Ciecielag\n,95 M. Cie\u00b4slar\n,124 M. Cifaldi\n,22\nB. Cirok,153 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6 P. Clearwater,154 S. Clesse,111 F. Cleva,113, 116\nE. Coccia,44, 45, 43 E. Codazzo\n,155, 156 P.-F. Cohadon\n,121 S. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98\nC. G. Collette,157 J. Collins,63 S. Colloms\n,86 A. Colombo\n,158, 127 C. M. Compton,2 G. Connolly,77 L. Conti\n,92\nT. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,159 S. Corezzi\n,76, 51 N. J. Cornish\n,160 I. Coronado,161 A. Corsi\n,162\nR. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 57 D. M. Coward,72 R. Coyne\n,163\nA. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,164 P. Cremonese\n,98 S. Crook,63 R. Crouch,2\n\n18\nJ. Csizmazia,2 J. R. Cudell\n,165 T. J. Cullen\n,11 A. Cumming\n,86 E. Cuoco\n,166, 167 M. Cusinato\n,137\nL. V. Da Concei\u00b8c\u02dcao\n,168 T. Dal Canton\n,41 S. Dal Pra\n,169 G. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37\nS. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,122 L. P. Dartez\n,63 R. Das,106 A. Dasgupta,93 V. Dattilo\n,62\nA. Daumas,20 N. Davari,170, 171 I. Dave,103 A. Davenport,136 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72\nM. C. Davis\n,18 P. Davis\n,172, 173 E. J. Daw\n,174 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,175\nM. De Laurentis\n,32, 4 F. De Lillo\n,23 S. Della Torre\n,127 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38\nG. Demasi,176, 61 F. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,177 A. Depasse\n,15 N. DePergola,102\nR. De Pietri\n,178, 179 R. De Rosa\n,32, 4 C. De Rossi\n,62 M. Desai\n,35 R. DeSalvo\n,180 A. DeSimone,181\nR. De Simone,150, 131 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,164 M. Di Cesare\n,32, 4 G. Dideron,182 T. Dietrich\n,1\nL. Di Fiore,4 C. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 183\nS. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,184, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,118\nJ. P. Docherty,86 Z. Doctor\n,96 N. Doerksen\n,168 E. Dohmen,2 A. Doke,132 A. Domiciano De Souza,185\nL. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,186 W. J. D. Doyle,122\nM. Drago\n,39, 38 J. C. Driggers\n,2 L. Dunn\n,123 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,170, 155\nP. Dutta Roy\n,46 H. Duval\n,187 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,188, 31 T. Eckhardt\n,97 G. Eddolls\n,78\nA. Effler\n,63 J. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25 M. Emma\n,58 K. Endo,151 R. Enficiaud\n,1\nL. Errico\n,32, 4 R. Espinosa,164 M. Esposito\n,4, 32 R. C. Essick\n,189 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35\nT. Evstafyeva,182 B. E. Ewing,7 J. M. Ezquiaga\n,139 F. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33\nA. M. Farah\n,129 B. Farr\n,77 W. M. Farr\n,190, 191 G. Favaro\n,91 M. Favata\n,192 M. Fays\n,165 M. Fazio\n,55\nJ. Feicht,11 M. M. Fejer,89 R. Felicetti\n,184, 48 E. Fenyvesi\n,87, 193 J. Fernandes,194 T. Fernandes\n,195, 137\nD. Fernando,110 S. Ferraiuolo\n,196, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81\nI. Fiori\n,62 M. Fishbach\n,189 R. P. Fisher,122 R. Fittipaldi\n,197, 131 V. Fiumara\n,198, 131 R. Flaminio,31\nS. M. Fleischer\n,199 L. S. Fleming,200 E. Floden,18 H. Fong,114 J. A. Font\n,137, 138 F. Fontinele-Nunes,18 C. Foo,1\nB. Fornal\n,201 K. Franceschetti,178 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,202\nA. Freise\n,37, 107 O. Freitas\n,195, 137 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,203 T. Fujimori,204 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1\nS. Galaudage\n,185 V. Galdi,205 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,180 D. Ganapathy\n,206 A. Ganguly\n,79\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,207 C. Garc\u00b4\u0131a-Quir\u00b4os\n,188 J. W. Gardner\n,34 K. A. Gardner,114 S. Garg,42\nJ. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,208 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29 A. Gennai\n,80 V. Gennari\n,100\nJ. George,103 R. George\n,147 O. Gerberding\n,97 L. Gergely\n,153 Archisman Ghosh\n,94 Sayantan Ghosh,194\nShaon Ghosh\n,192 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,209 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63\nK. D. Giardina,63 D. R. Gibson,200 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,210 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18\nM. Granata\n,175 V. Granata\n,211, 131 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,86 G. Greco,51\nA. C. Green\n,37, 107 L. Green,212 S. M. Green,73 S. R. Green\n,213 C. Greenberg,132 A. M. Gretarsson,65\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,137 D. Guetta\n,214 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,172, 173\nH. Guo\n,144 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,215 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,97 N. Gutierrez,175 N. Guttman,6 F. Guzman\n,130 D. Haba,216 M. Haberland\n,1\nS. Haino,217 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,218 A. G. Hanselman\n,129 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,181 S. Harikumar\n,186 K. Haris,37, 71 I. Harley-Trochimczyk,130 T. Harmark\n,133\nJ. Harms\n,44, 45 G. M. Harry\n,219 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 220, 221 C. J. Haster\n,212\nK. Haughian\n,86 H. Hayakawa,50 K. Hayama,222 M. C. Heintze,63 J. Heinze\n,118 J. Heinzel,35 H. Heitmann\n,113\nF. Hellman\n,206 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,115 M. Hendry\n,86\nI. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,223, 224 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,225 N. Hirata,25 C. Hirose,226\nD. Hofman,175 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,174 D. E. Holz\n,129 L. Honet,111\nD. J. Horton-Bailey,206 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,143 E. J. Howell\n,72 C. G. Hoy\n,73\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,141 H.-Y. Hsieh,141 C. Hsiung,227 S.-H. Hsu,145 W.-F. Hsu\n,109\n\n19\nQ. Hu\n,86 H. Y. Huang\n,140 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,228 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,131 J. Iascau,77\nK. Ide,229 R. Iden,216 A. Ierardi,44, 45 S. Ikeda,146 H. Imafuku,42 Y. Inoue,140 G. Iorio\n,91 P. Iosif\n,184, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,229 M. Isi\n,190, 191 K. S. Isleif\n,230 Y. Itoh\n,204, 231 M. Iwaya,203\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,121 T. Jacquot,41 S. J. Jadhav,232 S. P. Jadhav\n,154 M. Jain,132\nT. Jain,223 A. L. James\n,11 K. Jani\n,143 J. Janquart\n,15 N. N. Janthalur,232 S. Jaraba\n,233 P. Jaranowski\n,234\nR. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,149 H.-B. Jin\n,235, 236 G. R. Johns,122\nN. A. Johnson,46 M. C. Johnston\n,212 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,209 R. Jones,86\nH. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,237 L. Ju\n,72 K. Jung\n,238 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,239 I. Kaku,204 V. Kalogera\n,96 M. Kalomenopoulos\n,212\nM. Kamiizumi\n,50 N. Kanda\n,231, 204 S. Kandhasamy\n,79 G. Kang\n,240 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,132 M. Kasprzack\n,11 H. Kato,151\nT. Kato,203 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,204 D. Keitel\n,98\nL. J. Kemperman\n,115 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,241 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,162 M. Khursheed,103\nN. M. Khusid,190, 191 W. Kiendrebeogo\n,113, 242 N. Kijbunchoo\n,115 C. Kim,243 J. C. Kim,244 K. Kim\n,245\nM. H. Kim\n,237 S. Kim\n,246 Y.-M. Kim\n,245 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,203 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,247, 248 K. Kokeyama\n,33, 249 S. Koley\n,44, 165 P. Kolitsidou\n,118 A. E. Koloniari\n,250\nK. Komori\n,42 A. K. H. Kong\n,141 A. Kontos\n,251 L. M. Koponen,118 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,151 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,118 S. Kroker,252 A. Kr\u00b4olak\n,253, 186 K. Kruska,8, 9 J. Kubisz\n,254 G. Kuehn,8, 9\nS. Kulkarni\n,215 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,232 Praveen Kumar\n,177\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,255, 256, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,207, 257 S. Kuwahara\n,42 K. Kwak\n,238 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,188, 100\nA. H. Laity,163 E. Lalande,258 M. Lalleman\n,23 P. C. Lalremruati,259 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,147 R. Langgin\n,212 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,199 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,164 M. Laxen\n,63 C. Lazarte\n,137 A. Lazzarini\n,11 C. Lazzaro,156, 155 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,260 H. W. Lee\n,261 J. Lee,78 K. Lee\n,237 R.-K. Lee\n,141 R. Lee,35\nSungho Lee\n,245 Sunjae Lee,237 Y. Lee,140 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,182 M. Le Jean\n,175, 116\nA. Lema\u02c6\u0131tre\n,262 M. Lenti\n,61, 176 M. Leonardi\n,74, 75, 263 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,264 T. G. F. Li,109 X. Li\n,148\nY. Li,96 Z. Li,86 A. Lihos,122 E. T. Lin\n,141 F. Lin,140 L. C.-C. Lin\n,264 Y.-C. Lin\n,141 C. Lindsay,200\nS. D. Linker,180 A. Liu\n,218 G. C. Liu\n,227 Jian Liu\n,72 F. Llamas Villarreal,164 J. Llobera-Querol\n,98\nR. K. L. Lo\n,139 J.-P. Locquet,109 S. C. G. Loggins,265 M. R. Loizou,132 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,165 M. Lopez Portilla,71 M. Lorenzini\n,21, 22 A. Lorenzo-Medina\n,177 V. Loriette,41 M. Lormand,63\nG. Losurdo\n,266, 80 E. Lotti,132 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,123\nN. Lu\n,34 L. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,267, 268 A. W. Lussier\n,258 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,151 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,163\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,189\nS. Maliakal,11 A. Malik,103 L. Mallick\n,168, 189 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,170, 155 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 269\nC. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100\nF. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,192 B. B. Martinez,130 D. A. Martinez,54 M. Martinez,43, 270\nV. Martinez\n,128 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,118 E. J. Marx,35 L. Massaro,36, 37\nA. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,208\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,122 C. McElhenny,122 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,143\nJ. McIver\n,114 A. McLeod\n,72 I. McMahon\n,188 T. McRae,34 R. McTeague\n,86 D. Meacher\n,10 B. N. Meagher,78\nR. Mechum,110 Q. Meijer,71 A. Melatos,123 C. S. Menoni\n,136 F. Mera,2 R. A. Mercer\n,10 L. Mereni,175\nK. Merfeld,162 E. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10\nB. Mestichelli,44 M. Meyer-Conde\n,271 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,272\n\n20\nC. Michel\n,175 Y. Michimura\n,42 H. Middleton\n,118 D. P. Mihaylov\n,104 A. L. Miller\n,37, 71 S. J. Miller\n,11\nM. Millhouse\n,57 E. Milotti\n,184, 48 V. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43\nL. Mirasola\n,155, 156 M. Miravet-Ten\u00b4es\n,137 C.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46\nA. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79 V. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35\nO. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35 L. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7\nM. Molina-Ruiz\n,206 M. Mondin,180 M. Montani,60, 61 C. J. Moore,223 D. Moraru,2 A. More\n,79 S. More\n,79\nC. Moreno\n,134 E. A. Moreno\n,35 G. Moreno,2 A. Moreso Serra,82 S. Morisaki\n,42, 203 Y. Moriwaki\n,151\nG. Morras\n,207 A. Moscatello\n,91 M. Mould\n,35 B. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,176, 61\nF. Muciaccia\n,39, 38 D. Mukherjee\n,118 Samanwaya Mukherjee,24 Soma Mukherjee,164 Subroto Mukherjee,93\nSuvodip Mukherjee\n,13 N. Mukund\n,35 A. Mullavey,63 H. Mullock,114 J. Mundi,219 C. L. Mungioli,72\nM. Murakoshi,229 P. G. Murray\n,86 D. Nabari\n,74, 75 S. L. Nadji,8, 9 A. Nagar,28, 273 N. Nagarajan\n,86\nK. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,274 M. Nakano,11 D. Nanadoumgar-Lacroze\n,43 D. Nandi,12\nV. Napolano,62 P. Narayan\n,215 I. Nardecchia\n,22 T. Narikawa,203 H. Narola,71 L. Naticchioni\n,38\nR. K. Nayak\n,259 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,130 T. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2\nS. Ng,54 L. Nguyen Quynh\n,275 S. A. Nichols,12 A. B. Nielsen\n,276 Y. Nishino,25, 42 A. Nishizawa\n,277\nS. Nissanke,278, 37 W. Niu\n,7 F. Nocera,62 J. Noller,279 M. Norman,33 C. North,33 J. Novak\n,116, 233, 280\nR. Nowicki\n,143 J. F. Nu\u02dcno Siles\n,207 L. K. Nuttall\n,73 K. Obayashi,229 J. Oberling\n,2 J. O\u2019Dell,228 E. Oelker\n,35\nM. Oertel\n,233, 116, 281, 280 G. Oganesyan,44, 45 T. O\u2019Hanlon,63 M. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,116, 281, 280\nR. Omer,18 B. O\u2019Neal,122 M. Onishi,151 K. Oohara\n,282 B. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110\nS. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11 I. Ota\n,12 D. J. Ottaway\n,115 A. Ouzriat,56 H. Overmier,63\nB. J. Owen\n,283 R. Ozaki,229 A. E. Pace\n,7 R. Pagano\n,12 M. A. Page\n,25 A. Pai\n,194 L. Paiella,44 A. Pal,284\nS. Pal\n,259 M. A. Palaia\n,80, 81 M. P\u00b4alfi,202 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,141 J. Pan,72\nK. C. Pan\n,141 P. K. Panda,232 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38\nK. A. Pannone,54 B. C. Pant,103 F. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 285\nA. Papadopoulos\n,86 E. E. Papalexakis,210 L. Papalini\n,80, 81 G. Papigkiotis\n,250 A. Paquis,41 A. Parisi\n,76, 51\nB.-J. Park,245 J. Park\n,286 W. Parker\n,63 G. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80\nL. Passenger,6 D. Passuello,80 O. Patane\n,2 A. V. Patel\n,140 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80\nB. G. Patterson,33 K. Paul\n,106 S. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna\nArellano\n,287 X. Peng,118 Y. Peng,57 S. Penn\n,288 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,132\nC. P\u00b4erigois\n,289, 92, 91 G. Perna\n,91 A. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107\nD. Pesios,250 S. Peters,165 S. Petracca,205 C. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18\nK. S. Phukon\n,118 H. Phurailatpam,218 M. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113\nM. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,290, 131 M. Pietrzak,95\nM. Pillas\n,165 F. Pilo\n,80 L. Pinard\n,175 I. M. Pinto\n,290, 131, 291, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10\nM. Pirello,2 M. D. Pitkin\n,223, 86 A. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,211, 22\nC. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35 J. Pomper,80, 81 L. Pompili\n,1 J. Poon,218 E. Porcelli,37\nE. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62 J. Powell\n,154 G. S. Prabhu,79 M. Pracchia\n,165\nB. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93 K. Prasai\n,292 R. Prasanna,232 P. Prasia,79 G. Pratten\n,118\nG. Principe\n,184, 48 G. A. Prodi\n,74, 75 P. Prosperi,80 P. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1\nJ. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,163 H. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,173, 116 V. Quetschke,164\nP. J. Quinonez,65 N. Qutob,57 R. Rading,230 I. Rainho,137 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110\nK. E. Ramirez\n,63 F. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,164 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57\nK. Ransom,63 P. Rapagnani\n,39, 38 B. Ratto,65 A. Ravichandran,132 A. Ray\n,96 V. Raymond\n,33\nM. Razzano\n,81, 80 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini\n,126, 11\nB. Revenu\n,293, 41 A. Revilla Pe\u02dcna,82 R. Reyes,180 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,210 M. L. Richardson,115 A. Rijal,65 K. Riles\n,90 H. K. Riley,33\nS. Rinaldi\n,269 J. Rittmeyer,97 C. Robertson,228 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,294 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,223 J. H. Romie,63\nS. Ronchini\n,7 T. J. Roocke\n,115 L. Rosa,4, 32 T. J. Rosauer,210 C. A. Rose,57 D. Rosi\u00b4nska\n,124 M. P. Ross\n,53\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,190, 191 S. Roy\n,15 D. Rozza\n,126, 127 P. Ruggi,62 N. Ruhama,238\nE. Ruiz Morales\n,295, 207 K. Ruiz-Rocha,143 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,168\nM. R. Sah\n,13 S. Saha\n,141 T. Sainrat\n,64 S. Sajith Menon\n,214, 39, 38 K. Sakai,296 Y. Sakai\n,271\nM. Sakellariadou\n,67 S. Sakon\n,7 O. S. Salafia\n,158, 127, 126 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,147\n\n21\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,79 S. Salvador\n,173, 172 A. Salvarese,147 A. Samajdar\n,71, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,137 J. R. Sanders,181 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,250 P. Sassi\n,51, 76\nB. Sassolas\n,175 R. Sato,226 S. Sato,151 Yukino Sato,151 Yu Sato,151 O. Sauter\n,46 R. L. Savage\n,2\nT. Sawada\n,50 H. L. Sawant,79 S. Sayah,175 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,148 A. Schiebelbein,189\nM. G. Schiworski\n,78 P. Schmidt\n,118 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9 R. M. S. Schofield,77\nK. Schouteden\n,109 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,297 M. Scialpi\n,298 J. Scott\n,86\nS. M. Scott\n,34 R. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,299 D. Sellers,63\nN. Sembo,204 A. S. Sengupta\n,300 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38 C. K. Sethi\n,301\nA. Sevrin,187 T. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,260 L. Shao\n,302 A. K. Sharma\n,98 Preeti Sharma,12\nPrianka Sharma,103 Ritwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,125 N. S. Shcheblanov\n,303, 262\nE. Sheridan,143 Z.-H. Shi,141 M. Shikauchi,42 R. Shimomura,304 H. Shinkai\n,304 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,147 R. W. Short,2 S. ShyamSundar,103 A. Sider,157 H. Siegel\n,190, 191 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 169 M. Simmonds,115 L. P. Singer\n,305 Amitesh Singh,215 Anika Singh,11\nD. Singh\n,206 N. Singh\n,98 S. Singh,216, 59 A. M. Sintes\n,98 V. Sipala,170, 155 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,199 T. J. Slaven-Blair,72 J. Smetana,118 J. R. Smith\n,54 L. Smith\n,86, 184, 48 R. J. E. Smith\n,6\nW. J. Smith\n,143 S. Soares de Albuquerque Filho,60 M. Soares-Santos,188 K. Somiya\n,216 I. Song\n,141 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,306 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,122 D. A. Steer\n,307 N. Steinle\n,168 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,250 P. Stevens,41 M. StPierre,163 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,229 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,240 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,216 M. Suzuki,203\nB. L. Swinkels\n,37 A. Syx\n,116 M. J. Szczepa\u00b4nczyk\n,308 P. Szewczyk\n,124 M. Tacca\n,37 H. Tagoshi\n,203\nK. Takada,203 H. Takahashi\n,271 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,309 H. Takeda\n,310, 311\nK. Takeshita,216 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,129 M. Tamaki,203 N. Tamanini\n,100\nD. Tanabe,140 K. Tanaka,50 S. J. Tanaka\n,229 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,210\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,312 J. D. Tasson\n,152 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,180 A. Theodoropoulos\n,137 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,209 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,194 S. Tiwari\n,188 V. Tiwari\n,118\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,140 A. Torres-Forn\u00b4e\n,137, 138 C. I. Torrie,11 I. Tosta e Melo\n,313\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,122 A. Trapananti\n,52, 51 R. Travaglini\n,167 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,125 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,184, 48 A. Trovato\n,184, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,314 L. Tsukada\n,212 K. Turbang\n,187, 23 M. Turconi\n,113\nC. Turski,94 H. Ubach\n,82, 83 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,315 K. Ueno\n,42 V. Undheim\n,276\nL. E. Uronen,218 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,294 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 316\nE. Van den Bossche\n,187 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,258 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,123 V. Varma\n,132 A. N. Vazquez,89 A. Vecchio\n,118 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,115 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,132\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,189 A. Vilkha,110 N. Villanueva Espinosa,137 V. Villa-Ortega\n,177\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,230 L. Vujeva\n,139 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,216 J. Z. Wang,90 W. H. Wang,164\nY. F. Wang\n,1 G. Waratkar\n,194 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\nA. T. Wilkin,210 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\n\n22\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,140 I. C. F. Wong\n,218, 109 K. Wong,189 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,141 D. S. Wu\n,8, 9 H. Wu\n,141 K. Wu,119 Q. Wu,53 Y. Wu,96\nZ. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,206 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,151 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,229 T. Yan,118 K. Z. Yang\n,18\nY. Yang\n,145 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,141 A. B. Yelikar\n,143 X. Yin,35 J. Yokoyama\n,317, 42\nT. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110 T. Zelenova,62 J.-P. Zendri,92\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57 R. Zhang\n,149 T. Zhang,118 C. Zhao\n,72\nYue Zhao,161 Yuhang Zhao,20 Z.-C. Zhao\n,318 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78 H. O. Zhu,72\nZ.-H. Zhu\n,318, 319 A. B. Zimmerman\n,147 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n\n23\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n\n24\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120Cornell University, Ithaca, NY 14850, USA\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n128Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n132University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n135Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n136Colorado State University, Fort Collins, CO 80523, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140National Central University, Taoyuan City 320317, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n146Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n157Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n159Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n161The University of Utah, Salt Lake City, UT 84112, USA\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n\n25\n165Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n166DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n171INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n172Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n173Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n174The University of Sheffield, Sheffield S10 2TN, United Kingdom\n175Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n176Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n177IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n178Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n179INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n180California State University, Los Angeles, Los Angeles, CA 90032, USA\n181Marquette University, Milwaukee, WI 53233, USA\n182Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n183Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n184Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n185Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n186National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n187Vrije Universiteit Brussel, 1050 Brussel, Belgium\n188University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n189Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n190Stony Brook University, Stony Brook, NY 11794, USA\n191Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n192Montclair State University, Montclair, NJ 07043, USA\n193HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n194Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n195Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n196Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n197CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n198Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n199Western Washington University, Bellingham, WA 98225, USA\n200SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n201Barry University, Miami Shores, FL 33168, USA\n202E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n203Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n204Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n205University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n206University of California, Berkeley, CA 94720, USA\n207Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n208Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n209University of Southampton, Southampton SO17 1BJ, United Kingdom\n210University of California, Riverside, Riverside, CA 92521, USA\n211Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n212University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n213University of Nottingham NG7 2RD, UK\n214Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n215The University of Mississippi, University, MS 38677, USA\n216Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n217Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n\n26\n218The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n219American University, Washington, DC 20016, USA\n220Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n221INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n222Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n223University of Cambridge, Cambridge CB2 1TN, United Kingdom\n224University of Lancaster, Lancaster LA1 4YW, United Kingdom\n225College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n226Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n227Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n228Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n229Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n230Helmut Schmidt University, D-22043 Hamburg, Germany\n231Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n232Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n233Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n234Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n235National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n236School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237Sungkyunkwan University, Seoul 03063, Republic of Korea\n238Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n239Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n240Chung-Ang University, Seoul 06974, Republic of Korea\n241University of Washington Bothell, Bothell, WA 98011, USA\n242Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n243Ewha Womans University, Seoul 03760, Republic of Korea\n244National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n245Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n246Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n247Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n248Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n249Nagoya University, Nagoya, 464-8601, Japan\n250Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n251Bard College, Annandale-On-Hudson, NY 12504, USA\n252Technical University of Braunschweig, D-38106 Braunschweig, Germany\n253Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n254Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n255Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n256Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n257Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n258Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n259Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n260Seoul National University, Seoul 08826, Republic of Korea\n261Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n262NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n263Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n\n27\n264Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n265St. Thomas University, Miami Gardens, FL 33054, USA\n266Scuola Normale Superiore, I-56126 Pisa, Italy\n267Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n268Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n269Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n270Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n271Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n272Tsinghua University, Beijing 100084, China\n273Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n274Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n275Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n276University of Stavanger, 4021 Stavanger, Norway\n277Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n278GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n279University College London, London WC1E 6BT, United Kingdom\n280Observatoire de Paris, 75014 Paris, France\n281Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n282Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n283University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n284CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n285Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n286Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n287Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n288Hobart and William Smith Colleges, Geneva, NY 14456, USA\n289INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n290Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n291Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n292Kennesaw State University, Kennesaw, GA 30144, USA\n293Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n294Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n295Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n296Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n297Trinity College, Hartford, CT 06106, USA\n298Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n299Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n300Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n301University of Cologne (Universit\u00a8at zu K\u00a8oln), Cologne, North Rhine-Westphalia, Germany\n302Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n303Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n304Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n305NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n306Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n307Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n\n28\n308Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n309Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n310The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n311Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n314National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n315Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n316Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n317Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n318Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n319School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(Dated: December 8, 2025)\n\u2217Deceased, September 2024.\n", "All-sky search for continuous gravitational-wave signals from unknown neutron stars\nin binary systems in the first part of the fourth LIGO-Virgo-KAGRA observing run\nThe LIGO Scientific Collaboration, the Virgo Collaboration and the KAGRA Collaboration\n(Dated: December 5, 2025)\nWe present the results of a blind all-sky search for continuous gravitational-wave signals from\nneutron stars in binary systems using data from the first part of the fourth observing run (O4a)\nusing LIGO detectors data. Rapidly rotating, non-axisymmetric neutron stars are expected to emit\ncontinuous gravitational waves, whose detection would significantly improve our understanding of\nthe galactic neutron star population and matter under extreme conditions, while also providing\nvaluable tests of general relativity. Neutron stars in binary systems likely constitute a substantial\nfraction of the unobserved galactic population and, due to potential mass accretion, may emit\nstronger gravitational-wave signals than their isolated counterparts.\nThis search targets signals\nfrom neutron stars with frequencies in the 100 \u2212350 Hz range, with orbital periods between 7 and\n15 days and projected semi-major axes between 5 and 15 light-seconds. The analysis employs the\nGPU-accelerated fasttracks pipeline. No credible astrophysical signals were identified, and, in the\nabsence of a detection, we report search sensitivity estimates on the population of neutron stars in\nbinary systems in the Milky Way.\nI.\nINTRODUCTION\nContinuous\ngravitational\nwaves\n(CWs)\nare\nlong-\nlasting, nearly monochromatic signals. One of the most\npromising sources of CWs are rapidly rotating neu-\ntron stars (NSs) with non-axisymmetric mass distribu-\ntions [1, 2]. These gravitational waves (GWs) arise from\nthe star\u2019s time-varying quadrupole moment and can be\ngenerated through several mechanisms, which in turn\nprovide a unique probe of the elastic, magnetic, ther-\nmal, and superfluid properties of NSs, both in isolated\nand binary systems [2, 3].\nNon-axisymmetric\ndistortions\n(\u201cmountains\u201d)\nsus-\ntained either by elastic stresses in the crust or by strong\nmagnetic fields can lead to the emission of CWs. Accret-\ning systems in particular may generate sizable deforma-\ntions [4\u20136]. Furthermore, non-axisymmetric instabilities\ncan drive oscillation modes, such as r-modes, that may\nemit GWs, although their strength is strongly depen-\ndent on damping mechanisms and uncertain saturation\namplitudes [7, 8].\nFinally, free precession caused by a\nmisalignment between the rotation and symmetry axes\ncan lead to quasi-periodic emission [9].\nThe maximum possible ellipticity of a NS depends\nstrongly on its interior composition and the poorly con-\nstrained equation of state, with estimates ranging from \u223c\n10\u22126 for hadronic matter to \u223c10\u22124 in scenarios allowing\nfor more exotic physics such as crystalline phases [4, 10].\nAdditional factors such as general relativistic effects and\nstrong magnetic fields can further influence the maximum\nsustainable deformation [11, 12]. By comparing the ob-\nservational spindown limits on the ellipticity with these\ntheoretical expectations, current CW searches probe as-\ntrophysically relevant regions of parameter space, and\ncan provide constraints on the physics of dense mat-\nter [13].\nNSs are among the densest known objects in the uni-\nverse, with core densities of the order of nuclear val-\nues [14]. This makes them unique laboratories for prob-\ning the composition and behavior of matter under condi-\ntions not achievable in terrestrial laboratories, as well as\nstudying potential deviations from general relativity, e.g.\nby looking for wave polarizations different from general\nrelativity [3].\nHighly magnetized rotating NSs can emit beams of\nelectromagnetic radiation that are detected as pulses, in\nwhich case they are known as pulsars. A significant por-\ntion of the known pulsar population resides in binary\nsystems [15], where mass accretion from a binary com-\npanion may increase the quadrupolar deformation of the\nNS, causing it to emit stronger CW signals than their\nisolated counterparts [6, 16\u201320]. Moreover, a large frac-\ntion of the known millisecond pulsars are in binary sys-\ntems, spinning at frequencies that are in the sensitive\nband of ground-based GW detectors. Therefore, NS in\nbinary systems are promising targets for CW detection\nin all-sky searches with data from current ground-based\ninterferometers (IFOs).\nAlthough numerous CW searches have been conducted\nto date, no detection has yet been achieved (see [1, 21\u201323]\nfor recent reviews, and [24\u201340] for results from the O3\nand O4 LIGO-Virgo-KAGRA observing runs [41\u201343]).\nIn comparison with signals from compact binary merg-\ners, from which all GW detections to date have origi-\nnated [44\u201349], CW amplitudes are expected to be several\norders of magnitude smaller, making them challenging to\ndetect. Moreover, CW signals are subject to significant\nfrequency modulation caused by the Earth\u2019s rotation and\norbital motion [50\u201352]. As a result, all-sky searches must\ncover wide ranges of frequencies, sky positions, and in\nthe case of binaries, orbital parameters [23]. These fac-\ntors enlarge the search parameter space and require vast\nnumbers of signal templates, up to more than 1016 tem-\nplates for all-sky searches such as the one presented here.\nTo make CW searches computationally feasible, semi-\ncoherent methods are commonly employed [53\u201356].\nThese approaches divide the data into shorter coherent\nsegments, combine them incoherently, and follow up the\narXiv:2511.16863v2 [gr-qc] 4 Dec 2025\n\n2\nmost significant candidates with longer coherence times.\nThis strategy reduces the computational load by allowing\nus to cover the parameter space less densely with tem-\nplates and by improving robustness to small mismatches\nwith the signal model, such as unmodeled astrophysical\neffects [57].\nAll-sky searches aim to detect CW emission from un-\nknown NSs within our galaxy, that is, those that have not\nbeen observed using electromagnetic telescopes neither as\npulsars nor as non-pulsating sources. Since only a small\nfraction of the estimated NS population has been ob-\nserved as pulsars [58, 59], conducting this type of searches\noffers a valuable opportunity to find these undetected\nNSs.\nTo date, several pipelines have been developed and im-\nplemented for all-sky CW searches targeting unknown\nNSs in binary systems.\nThese include the TwoSpect\npipeline [60], and the BinarySkyHough pipeline [61],\nwhich has been employed in searches using data from\nthe second [62] and third observing runs [63]. More re-\ncently, the BinarySkyHouF pipeline [64\u201366] has been in-\ntroduced and the Falcon pipeline is being extended to in-\nclude binary systems [67]. BinarySkyHough is based on\nthe SkyHough [54] method, which uses the Hough trans-\nform [68] to search for CWs semi-coherently with the\nHough number count detection statistic (see [54, 61, 69\u2013\n71] for other works that use the Hough transform for\nsearches of long-duration GW signals).\nEach of these\npipelines makes different trade-offs between sensitivity\nand parameter space coverage, sacrificing some sensitiv-\nity in order to scan wider or more complex parameter\nspaces.\nWe present an all-sky search for CWs from unknown\nNSs in binary systems, carried out with the newly de-\nveloped fasttracks pipeline [72]. fasttracks is a mas-\nsively parallel Python engine built on JAX [73], designed\nto evaluate detection statistics for generic CW signals\non Short Fourier Transform (SFT)-like data [74]. This\nincludes the detection statistics used in the first stage\nof this search, which are summed weighted normalized\npower from the SFTs and summed weighted Hough num-\nber count. fasttracks can exploit Graphics Processing\nUnits (GPUs) to accelerate the calculation of detection\nstatistics across large amount templates needed for all-\nsky searches. Since this template evaluation is by far the\nmost computationally expensive step, GPU acceleration\nmakes large-scale searches feasible.\nIn addition, we employ a novel parameter-space par-\ntitioning strategy originally introduced in [72], which\ndivides the high-dimensional search space into smaller\nregions, or \u201cboxes\u201d.\nEach box is searched indepen-\ndently, producing its own output.\nThis approach has\ntwo main advantages: different boxes can be computed\nin parallel in different GPUs and it avoids the need\nfor clustering procedures in post-processing. Thanks to\nthese improvements, fasttracks achieves higher compu-\ntational efficiency compared to previous searches such as\nBinarySkyHough [63] and streamlines analysis with the\nnew parameter-space partitioning strategy.\nThe remainder of this paper is organized as follows.\nin Sec. II, we outline the CW signal model.\nSec. III\ndescribes the usage of data from the early fourth ob-\nserving run (O4a). Sec. IV presents the details of the\nsearch pipeline. In Sec. V, we describe the line veto pro-\ncedure. Sec. VI contains the sensitivity depth estimates\nof the search.\nSec. VII discusses the most significant\noutliers identified, and explains how they were ruled out\nas non-astrophysical.\nThe search results are discussed\nin Sec. VIII. Finally, our conclusions are summarized in\nSec. IX.\nII.\nSIGNAL MODEL\nA NS exhibiting a deviation from perfect axial symme-\ntry with respect to its rotation axis is expected to emit\nCWs at twice its rotational frequency.\nThis emission\narises from the time-varying mass quadrupole moment\nassociated with the star\u2019s asymmetry. The resulting GW\nstrain amplitude h0, which can be measured by interfer-\nometric detectors, depends on the physical properties of\nthe source and can be expressed as [1]\nh0 = 4\u03c02G\nc4\nIzz\u03f5\nd f 2\n0 ,\n(1)\nwhere G is the gravitational constant, c is the speed of\nlight, Izz is the principal moment of inertia around the\nrotation axis (assumed to be the z-axis), d is the distance\nfrom the source to the detector, and f0 is the intrinsic\nGW frequency. The equatorial ellipticity of the star, \u03f5,\ncan be related to the mass quadrupole moment Q22 via [4]\n\u03f5 =\nr\n8\u03c0\n15\n|Q22|\nIzz\n.\n(2)\nDue to the motion of Earth-based detectors relative\nto the Solar System Barycenter (SSB) and the motion\nof the NS around the binary system barycenter, the ob-\nserved CW signal is subject to Doppler modulation from\nboth effects. As a result, for the circular, non-relativistic\nbinary orbit of the unknown searched NSs, the GW fre-\nquency measured at the detector is time-dependent and\ncan be expressed as [61, 72]\nf(t; \u03bb) = f0\n\u0014\n1 + \u20d7v(t)\nc\n\u00b7 \u02c6n \u2212ap\u2126cos(\u2126t \u2212\u03d5b)\n\u0015\n,\n(3)\nwhere \u20d7v (t) is the detector\u2019s velocity vector relative to the\nSSB, \u02c6n is a vector that points from the SSB to the sky\nlocation of the source, parametrized by \u03b1, the right as-\ncension and \u03b4, the declination. f0 is the GW frequency\nemitted by the source NS, ap is the projected semi-major\naxis of the binary orbit in light-seconds, \u2126is the angu-\nlar orbital frequency of the source, and \u03d5b is the initial\norbital phase.\nThe last three parameters describe the\norbital motion of the NS in the binary system.\n\n3\nThe resulting frequency evolution, or track, traced\nby the signal in time-frequency space is the target of\nthe search. It is parameterized by six quantities: \u03bb =\n{f0, \u02c6n, ap, \u2126, \u03d5b}, where \u02c6n is composed of \u03b1 and \u03b4.\nThe model described above assumes a circular, non-\nrelativistic binary orbit.\nHowever, the search remains\nsensitive to signals from NSs in slightly eccentric systems,\nwith an upper limit on the allowed eccentricity given by\n[61]\ne \u2265\n1\n2TSFTf0ap\u2126,\n(4)\nwhere TSFT is the duration of each of the SFTs used in\nthe analysis.\nWe assume that the NS does not undergo any glitches\nduring the observing time and that spin wandering\n(stochastic fluctuations in the star\u2019s rotation frequency)\ncan be neglected [75]. The typical glitch rate for known\npulsars is of order one per year or less [76]. Estimates of\nspin wandering for accreting NSs suggest much smaller\ndrifts than the frequency resolution of the semi-coherent\nmethods used here. [77]. Accordingly, searches with ob-\nserving duration of months to less than a few years may\nsafely neglect these effects\nFurthermore, as argued in [61], for observing durations\nof not more than a few years, CW searches targeting NS\nin binary systems do not require explicit searches of spin-\ndown parameters. Consequently, we do not search over\nspin frequency derivatives in this analysis. Nonetheless,\nthe search retains sensitivity to sources exhibiting spin-\ndown or spinup values up to\n\f\f\f \u02d9f0\n\f\f\f \u2264\n1\nTSFTTobs\n,\n(5)\nthe value above which the frequency track would deviate\nby more than one frequency bin in the data during the\ntotal observing run, Tobs.\nIII.\nDATA USED\nFor this search we use data from the first part of the\nfourth observing run of the LIGO-Virgo-KAGRA detec-\ntor network. This segment of the run covers the period\nfrom 24 May 2023 15:00 UTC (GPS time 1368975618 s)\nto 16 January 2024 16:00 UTC (GPS time 1389456018\ns). Correspondingly, this gives a total observing time of\nTobs = 20477806 s or 237 days.\nThis analysis makes use of data from the LIGO detec-\ntors at Hanford (H1) and Livingston (L1) [41]. We do\nnot use data from Virgo [42], which was not observing\nin O4a; nor from KAGRA [43], which was not online for\nmost of the run.\nDuring O4a, H1 and L1 were in observing mode 67.5%\nand 69.0% of the time, respectively [48]. This represents\na lower duty factor than in the O3a BinarySkyHough\nsearch [47, 63]. However, the observation time was signifi-\ncantly longer in O4a than in O3a (237 days vs 183 days).\nMultiplying the observing time by the duty factor, the\nrelative amount of observing data is increased by 20.26%\nin O4a compared to O3a.\nThe data exhibit several different artifacts that can\ninterfere with CW searches, including lines, combs, and\nhardware injections, any one of which may mimic the be-\nhavior of CW signals [78]. Instrumental lines are narrow-\nband features that appear as persistent monochromatic\npeaks in the detector\u2019s power spectral density.\nThese\nfeatures can originate from various sources such as in-\njected calibration lines, digital clocks, power supplies,\nor environmental couplings [79].\nThese lines can have\ntime dependent, non-stationary behavior in frequency\nand amplitude, and while some lines are isolated, others\nform part of broader spectral structures known as combs,\nwhich consist of multiple harmonics equally spaced in fre-\nquency and often arise from a common non-astrophysical\norigin [78].\nThe search is conducted using SFTs with a baseline du-\nration of TSFT = 1024 s [74]. We start from the calibrated\ndetector strain data channel GDS-CALIB STRAIN CLEAN\n(C00 calibration, [80]), restricted to science-mode seg-\nments with CAT1 vetoes [81]. These data are first pro-\ncessed by the self-gating algorithm [82], which removes\nlarge transient disturbances in the time domain.\nThe\ngated strain data (G02) are then processed into Short\nFourier Transform Data Base (SFDB) files [83]; this step\nincludes another time-domain cleaning stage to suppress\nsmaller glitches and transient artifacts.\nFor C00 low-latency data, the O4a uncertainty en-\nvelopes (v1) show amplitude and phase systematic\nerrors of approximately 2% and 2\u25e6across the 20-\n2000 Hz band [80].\nFinally, the cleaned and cali-\nbrated SFDBs are converted into SFTs with LALSuite\u2019s\nWriteSFTsfromSFDBs tool, following the same procedure\nemployed in the O3a all-sky binary CW search [63, 84].\nEach SFT is produced with a 50% overlap between\nconsecutive segments and a Tukey window with tapering\nparameter \u03b2Tukey = 0.5. Tukey-windowed SFTs contain\na flat central region and tapered edges overlapped with\nconsecutive SFTs, retaining high sensitivity to CW-type\nsignals [69]. This procedure results in 25,426 1024-s SFTs\nfrom the H1 data and 26,552 1024-s SFTs from the L1\ndata.\nIV.\nSEARCH PIPELINE\nThe search is built using the fasttracks pipeline to\nenable rapid evaluation of CW detection statistics with\nGPU acceleration, introduced in [72].\nIn this search,\nwe use a parameter-space partitioning strategy for the\nsix-dimensional search space \u03bb = {f0, \u02c6n, ap, \u2126, \u03d5b} (unit\nvector \u02c6n composed of \u03b1 and \u03b4) associated with binary\nCW signals, also introduced in [72]. The pipeline eval-\nuates detection statistics over several search templates,\nrandomly sampled and in separate parameter-space re-\ngions known as boxes. This novel parameter-space par-\n\n4\ntitioning naturally leads to a follow-up strategy: in each\nbox of parameter space, only the most significant out-\nliers are followed-up in a more sensitive search, while\nboxes dominated by instrumental artifacts can be vetoed\nand excluded from further analysis.\nMoreover, rather\nthan covering the parameter space with a regular grid\nof templates, we employ random sampling with resolu-\ntion chosen to control template mismatch. Details of the\nresolution criteria will be discussed in Sec. IV C, specif-\nically Eq. (13).\nThis approach does not degrade sen-\nsitivity compared with grid-based methods, as it keeps\nthe average mismatch between templates and potential\nsignals controlled and reduces correlations between tem-\nplates [85, 86].\nThe output from each box is then passed to a post-\nprocessing stage (Sec. V), where high-significance candi-\ndates are subsequently followed up using more sensitive\nmethods, as detailed in Sec. VII.\nA.\nParameter space\nWe perform a blind, all-sky search for CWs in the fre-\nquency range from 100 Hz to 350 Hz. The computational\ncost of the search grows steeply with frequency, scaling\nas f 6\n0 due to the six-dimensional parameter space as de-\nrived in [72].\nAs a result, higher-frequency bands are\nsignificantly more expensive to analyze than lower ones.\nThe total frequency range is divided into 0.125 Hz sub-\nbands, for a total of 2000. Each sub-band is processed\nindependently and partitioned into boxes (Sec. IV C).\n50\n100\n150\n200\n250\n300\n350\n400\nFrequency [Hz]\n10\u221247\n10\u221246\n10\u221245\n10\u221244\nPSD [1/Hz]\nSearch frequency range\nO3a\nO4a\nFIG. 1. Comparison of the O3a and O4a multi IFO power\nspectral density using the data from the H1 and L1 LIGO\ndetectors. The grey area indicates the search frequency range.\nThe IFO\u2019s sensitivity in each frequency band can be\nseen in Fig. 1, which illustrates the inverse square root\naveraged multi-IFO (H1 + L1) power spectral densities\n(PSDs). We compute the PSD from the single-sided IFO\nPSD, Sn(f), using an average of inverse-squared PSDs\nfrom individual SFTs, as in [87],\nSn(f) =\ns\nN\nP\n\u03b1 (S\u03b1(f))\u22122 ,\n(6)\nwhere N is the number of SFTs individually indexed\nby \u03b1 contributing to the estimate at frequency f and\nSn(f) is the estimated multi-IFO PSD in the frequency\nband, computed as the power-2 sum of the individual IFO\nPSDs.\nNote that different analyses differ in the mean\nused to compute the respective PSDs. In the case of CW\nsearches, the power-2 gives the most representative PSD\nfor our searches and for the search sensitivity estimation\nin Sec. VI.\nIn O4a, the detectors show improved sensitivity com-\npared to O3a. Whereas in O3a the most sensitive fre-\nquencies were in the 150-300 Hz range, in O4a, the op-\ntimal performance is in the 200-400 Hz range. The O4a\nsearch range overlaps with this most sensitive band of\nthe detectors during the run.\nFor the binary orbital parameters, we target signals\nfrom systems with projected semi-major axis amplitude\nap along the line of sight between 5 and 15 light-seconds\nand orbital periods P ranging from 7 to 15 days.\nAs\nillustrated in Fig. 2, this parameter space is chosen to\nmatch measured characteristics of observed galactic NSs,\nfocusing on a parameter region which circumscribes a\nhigh-density area of known pulsars in binary systems [15].\nThis choice also corresponds to Region B from the O3a\nBinarySkyHough search [63], and overlaps in the upper\n50 Hz with the range in [65] and for ap in the 10 to\n15 l-s range, but not in P. The O3a BinarySkyHough\nsearch [63] also included other parameter space regions\nbelow 100 Hz; we did not repeat the search in those areas\nin order to maximize the search sensitivity where the O4a\nsensitivity had improved the most compared to O3a.\n100\n101\n102\nP (days)\n100\n101\n102\nap (l-s)\nFIG. 2. Binary parameter space covered in the search. Large\nblack dots indicate known pulsars with possible CW emission\nfrequencies in the search range, while grey points correspond\nto sources outside this range. The boxed rectangular region\ndenotes the portion of the binary parameter space explored\nin this search. Source: ATNF Pulsar Catalogue [15].\n\n5\nParameter\nf0 [Hz]\n\u03b1 [rad]\n\u03b4 [rad]\nP [days] ap [l-s] \u03d5b [rad]\nRange\n[100,350) [0, 2\u03c0) (\u2212\u03c0\n2 , \u03c0\n2 )\n[7, 15)\n[5, 15]\n[0, 2\u03c0)\nTABLE I. Search parameter ranges.\nThe full search parameter space is summarized in Ta-\nble I. In addition to the intrinsic frequency and binary\norbital parameters discussed above, the search covers the\nwhole sky in \u03b1 and \u03b4. The binary orbital phase \u03d5b is also\nsearched over its entire physical range.\nB.\nDetection statistics\nTo identify potential CW signals in the data, we rely\non detection statistics that measure the accumulation of\nexcess power along the time\u2013frequency tracks predicted\nby a given signal model. In practice, a CW signal from a\nNS in a binary system will produce a characteristic fre-\nquency evolution determined by the source parameters.\nFor each template, we define a frequency track across\nthe sequence of SFTs, which represents how a CW sig-\nnal would evolve in time given the template parameters.\nAlong this track, we add together the corresponding val-\nues of the detection statistic from each SFT. If a real\nsignal is present, the detection statistic will accumulate\nalong the track and stand out above the random fluctua-\ntions of detector noise, whereas in the absence of a signal\nthe summed statistic will remain consistent with noise.\nAs in [72], we employ two complementary statistics:\nthe weighted normalized power, which directly measures\nexcess power in the data, and the Hough weighted num-\nber count, which is more useful to evaluate the persis-\ntence of such excess power across the observing time.\nThe derivation below introduces the normalized power\nstatistic and shows how it is summed along signal tracks\nto construct the detection statistic used in the search.\nFollowing the notation convention in [72], let \u02dcx [t; f]\ndenote the value of the SFT at time t (the start time\nof the SFT) and frequency f, each SFT is identified by\nan i index and the detector index X. Normalizing by\nthe single-sided noise PSD in the band under analysis\nSnXi [f] (The PSD is estimated with a 101-bin running-\nmedian estimate for each SFT and frequency f) and the\nSFT time baseline TSFT, we define the normalized power\nstatistic as\ns [t; f] =\n4 |\u02dcx [t; f]|2\nTSFTSnXi [f].\n(7)\nA search template \u03bb = {f0, \u02c6n, ap, \u2126, \u03d5b} defines a sig-\nnal frequency evolution f (t; \u03bb) across the observing time.\nThe summed weighted normalized power detection statis-\ntic is computed by summing the normalized power along\nthe signal track defined by the template,\ns(\u03bb) =\nX\nX,i\nwXi(\u02c6n)s[tXi; f(tXi; \u03bb)] ,\n(8)\nwhere wXi(\u02c6n) are time-dependent weights that incorpo-\nrate both detector sensitivity and antenna response, tXi\nrefers to time at index i and detector X. The appropri-\nate weights for all-sky searches from isotropically oriented\nsources are [87, 88]\nwXi(\u02c6n) \u221da2(tXi; \u02c6n) + b2(tXi; \u02c6n)\nSnXi\n,\n(9)\nwhere SnXi is the averaged single-sided PSD of the noise\nin the frequency band under analysis1, and where a and\nb are the detector\u2019s response functions to the two polar-\nizations of the GW for a source located in direction \u02c6n\non the sky. Their definition can be found at [50]. These\nweights are normalized such that\nX\nX,i\nwXi (\u02c6n) = 1.\n(10)\nIn order to evaluate the detection statistics across large\ntemplate banks, we use the vectorization of the com-\nputation over batches of templates as implemented in\nfasttracks [72, 89].\nThis vectorization is done using\nthe jax.vmap function [73].\nIn addition to the normalized power statistic, we also\nuse the weighted Hough number count [54] to filter out\ntransient noise artifacts.\nThis statistic was previously\nalso used in the O3a BinarySkyHough search [63] and has\nbeen used in a multitude of CW searches [27, 62, 69, 90].\nIt is defined as\nnc (\u03bb) =\nX\nX,i\nwXi(\u02c6n)nc [tXi; f (tXi; \u03bb)] ,\n(11)\nwhere the number count of an SFT is defined as the dig-\nitized normalized power per SFT given by\nnc [t, f] =\n(\n1\nif s [t; f] > 3.2\n0\notherwise\n.\n(12)\nAs in [72], the threshold s [t; f] > 3.2 is equivalent to\nthe \u03c1th > 1.6 optimal threshold to minimize the false\ndismissal rate derived in [54], given our definition of nor-\nmalized power in Eq. (7).\nThe Hough number count acts as a persistence filter.\nWhile transient noise may produce large spikes in the\nnormalized power statistic s [t; f], it may affect only a\nsmall subset of the time series. In contrast, a CW signal\nwill maintain consistent power increases over many seg-\nments. Hence, the Hough number count is more robust\nto brief transients and provides a discriminator against\nthem.\n1 Note the difference between Sn(f) in Eq. (6) (multi-IFO PSD\ncomputed as using average of inverse-squared PSD), the SnXi [f]\nin Eq. (7) (estimated with a 101-bin running-median estimate for\neach SFT and frequency f) and the SnXi in Eq. (9) (averaged\nsingle-sided PSD of the noise in the frequency band under anal-\nysis).\n\n6\nC.\nParameter space partitioning into boxes\nTo explore the six-dimensional parameter space \u03bb =\n{f0, \u02c6n, ap, \u2126, \u03d5b} of CW signals from NSs in binary sys-\ntems, we adopt a box-based partitioning strategy, first\nintroduced in [72].\nPartitioning the parameter space\nmakes post-processing more straightforward, since con-\ntaminated boxes can be vetoed and promising candidates\nfollowed up independently.\nUnlike previous searches,\nwhich required clustering strategies to sieve through the\nvast number of initial candidates and group together\nthose likely originating from the same source, our ap-\nproach reduces the results to a smaller set without this\nneed for clustering.\nThe idea is to divide the parameter space into a large\nnumber of non-overlapping regions (or \u201cboxes\u201d), each\ncovering a small portion of the total search volume. Each\nbox is searched independently using a random template\nbank that densely samples its region.\nTo determine the size and number of templates in each\nbox, we use characteristic resolution equations. For a box\ncentered at parameters (f0, \u02c6n, ap, \u2126, \u03d5b), the correspond-\ning step sizes in each parameter direction are\n\u03b4f0 =\n1\nTSFT\n,\n\u03b4sky =\n\u0012\n1\nTSFTf0v/c\n\u00132\n,\n\u03b4ap =\n1\nTSFTf0\u2126,\n\u03b4\u2126=\n1\nTSFTf0ap\u2126Tobs\n,\n\u03b4\u03d5b =\n1\nTSFTf0ap\u2126.\n(13)\nTo adjust the number of templates per box, we apply\nan oversampling factor, increasing or decreasing the step\nsizes defined in Eq. (13) times the oversampling factor.\nIncreasing this factor makes the template bank denser\n(and search potentially more sensitive), however, also\nmore computationally expensive. The oversampling val-\nues are tuned based on frequency band, as described in\nSec. IV D.\nThe box-based search proceeds as follows:\n1. Divide the search frequency range into 0.125 Hz\nsub-bands.\n2. The boundaries of each search box in the physical\nparameter space \u2206\u03bb are mapped to a properly de-\nfined auxiliary parameter space, in which the grid\nsteps defined above become uniform (see App. A\nfor the definition of the auxiliary parameter space\nand the construction of the uniform grid there).\n3. In this uniform space, divide the search volume into\nequally sized, non-overlapping boxes.\n4. Randomly sample the templates from a uniform\ndistribution inside each box. The number of tem-\nplates inside a box is the oversampling factor times\nthe amount of templates we would get with a grid\nif the step sizes were those in Eq. (13).\n5. Map each sampled template back to physical pa-\nrameter space, evaluate its detection statistics, and\nretain the template with the highest value accord-\ning to the criteria in Sec. IV D.\nThe number of boxes used per frequency band is shown\nin Fig. 3, and further details of the partitioning algorithm\ncan be found in App. A.\n100\n150\n200\n250\n300\nFrequency [Hz]\n20000\n40000\n60000\n80000\n100000\nBtotal\nA\nB\nC\nD\nE\nFIG. 3.\nTotal number of boxes per 0.125 Hz frequency band\nacross the full search range. The lettered regions (A-E) cor-\nrespond to the frequency intervals defined in Table II. The\ndashed horizontal line marks the minimum enforced number\nof boxes (104). Sudden changes in the number of boxes cor-\nrespond to transitions between regions where either the min-\nimum box constraint or the 108 templates-per-box criterion\ndominates the partitioning as explained in App. A.\nD.\nTwo step setup\nOur search adopts a two-step strategy inspired by\nthe methodology used in the O3a BinarySkyHough\nsearch [63].\nFor each box in the parameter space, we begin by eval-\nuating the weighted Hough number count statistic nc(\u03bb)\nfor all templates using only half of the available SFTs,\nskipping every other SFT in the time series. This first\nstep acts as a filter to identify templates associated with\nCW signal behavior, showing persistent power accumu-\nlation over time. We use half the SFTs in order to reduce\nthe computational cost of this first step.\nFrom this first-stage evaluation, we retain the top 0.2%\ntemplates per box ranked by nc(\u03bb). This fraction cor-\nresponds approximately to those templates whose nc(\u03bb)\nexceeds the mean by more than three standard devia-\ntions, assuming Gaussian noise. The mean and standard\ndeviation are calculated from all the nc(\u03bb) computed per\nbox.\nIn the second step of the search, we compute the\nweighted normalized power statistic s(\u03bb) for the subset\nof templates retained from the first step using the full set\nof SFTs. For each box, we identify the template with the\n\n7\nRegion Frequency [Hz] Oversampling Follow-up CR threshold\nA\n[100, 150)\n4.0\n7.0\nB\n[150, 170)\n2.0\n7.0\nC\n[170, 200)\n1.0\n7.0\nD\n[200, 275)\n0.25\n7.0\nE\n[275, 350)\n0.25\n7.2\nTABLE II. Oversampling factor and follow-up CR threshold\nused in each frequency region.\nhighest s(\u03bb) as the most significant candidate from that\nregion of parameter space.\nDifferent boxes contain different weight distributions\nwXi(\u03bb) because they can be located at different sky po-\nsitions. Therefore, to allow for sky-independent statis-\ntical significance comparisons across boxes, we use the\nweighted normalized power critical ratio (CR), defined\nas\n\u03a8s = s \u2212\u27e8s\u27e9\n\u03c3s\n,\n(14)\nwhere \u27e8s\u27e9and \u03c3s are the expected mean and standard\ndeviation of the weighted normalized power statistic in\nGaussian noise. These are computed analytically for each\nbox from the weights following the derivation in [72],\n\u27e8s\u27e9= 2\nX\nX,i\nwXi ,\n(15)\n\u03c32\ns = 4\nX\nX,i\nw2\nXi ,\n(16)\nwhere, given the weights normalization in Eq. (10), \u27e8s\u27e9=\n2.\nWe use different oversampling factors across the fre-\nquency range. At lower frequencies, where the number\nof required templates is relatively small, we use higher\noversampling values, resulting in denser template banks.\nConversely, at higher frequencies, where the parameter\nspace volume increases due to frequency-dependent res-\nolution scaling, we reduce the oversampling factor.\nWe define five frequency regions, each with a corre-\nsponding oversampling factor and follow-up threshold.\nCandidates with CR values above the specified threshold\nare further analyzed in the follow-up stage (see Sec. VII).\nThe different frequency regions together with their over-\nsampling factors and follow-up thresholds are described\nin Table II. The oversampling factors and follow-up\nthresholds are chosen based on the available computa-\ntional resources in order to maximize the search sensitiv-\nity to continuous gravitational waves.\nFig. 4 illustrates the highest CR values obtained per\neach frequency band in each region. In some frequency\nbands, the highest CR values are orders of magnitude\nlarger than those in neighboring bands, a sign of possible\ncontamination from instrumental artifacts.\nThis moti-\nvates the introduction of a band-vetoing stage to identify\nand veto such bands.\nV.\nKNOWN LINES VETO\nIn this step, we identify and discard candidates affected\nby known instrumental artifacts. This is used to mitigate\nthe contamination from spectral lines that can mimic the\nexpected behavior of CW signals [92].\nWe use the official list of known instrumental lines from\nthe O4a observing run [91] to identify such contamina-\ntions.\nEach known artifact in the list is examined to\ndetermine which frequency ranges affected by its har-\nmonics, based on the tracks searched for each frequency\nband. The contamination reach of each line is described\nin App. C.\nBased on the contamination, bands are classified as\neither non-vetoed, partially contaminated, or fully con-\ntaminated:\n\u2022 Non-vetoed bands: Bands with fewer than 2000\ncandidates above the CR threshold are not vetoed.\nOne candidate per box per band is retained for\nfollow-up. Candidates from these bands may still\nbe vetoed due to instrumental artifact contamina-\ntion after the first stage follow-up, as explained in\nSec. VII.\n\u2022 Fully vetoed bands:\nBands that are entirely\nwithin the contaminated region of one or more\nknown lines and that exceed 2000 candidates above\nthreshold are removed from the follow-up. These\nbands are presumed to be dominated by instrumen-\ntal artifacts.\n\u2022 Partially vetoed bands: Bands that are only\npartially affected by contamination and that also\ncontain more than 2000 candidate are cleaned by\nremoving candidates whose boxes fall within the\ncontaminated region. Candidates from the rest of\nthe band are followed-up.\nThe 2000 candidates threshold is an informed choice\nbased on the candidates per band resulting from the\nsearch and the distribution observed in Fig. 5, where\nmost bands have under 1000 candidates above the corre-\nsponding follow-up threshold.\nTo minimize the false dismissal probability of true as-\ntrophysical signals [92], only frequency regions with well-\ndocumented instrumental disturbances are vetoed out-\nright, and partially contaminated bands are partially ve-\ntoed (That is, vetoing only the part of the band that may\nbe contaminated by a known line as defined in in App. C)\nrather than excluded entirely.\nFrequency bands not vetoed by this procedure may still\nbe contaminated by unidentified instrumental artifacts.\nFor example, since the search targets signals whose am-\nplitude is much lower than the detector noise floor, it can\nbe affected by lines that were not seen by the O4a lines\nanalysis.\nAcross the 2000 search frequency bands, each of width\n0.125 Hz, the initial number of candidates above their\n\n8\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n7.5\n10.0\n12.5\n15.0\n17.5\n20.0\n\u03a8s per band\nA\nB\nC\nD\nE\nFIG. 4. Highest CR values per frequency band. Arrows indicate frequency bands where the highest value is above 20.\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n100\n101\n102\n103\n104\n105\nNcandidates > \u03a8threshold\ns\nA\nB\nC\nD\nE\nFIG. 5. Number of candidates per 0.125 Hz band with CR above the threshold, as a function of frequency. Frequency regions\nA through E correspond to those defined in Table II. Each black dot represents the number of candidates above threshold\nin a single band. Red dots indicate bands that were fully or partially vetoed due to contamination from known instrumental\nartifacts listed in the O4a lines list [91].\ncorresponding CR threshold (Table II) was 3,253,671.\nAfter the known lines veto, the number of surviving can-\ndidates is reduced to 927,443, corresponding to 28.5%\nof the original sample. Table III summarizes the clas-\nsification of the bands. Fig. 5 illustrates the number of\ncandidates above threshold in each band.\nThe vetoed\nfrequency ranges can be found in App. C.\nBand type\nCount\n% Bands\nBandwidth [Hz]\nNon-vetoed\n1818\n90.9%\n227.25\nVetoed\n182\n9.1%\n16.995\nTotally\n65\n3.25%\n8.125\nPartially\n117\n5.85%\n8.87\nTABLE III. Summary of frequency band classification af-\nter the application of line and comb vetoes. Partial vetoes\nrefers to bands where only a fraction of the templates are dis-\ncarded due to contamination. The partially vetoed bands sum\n14.625 Hz, of which 60.65% have been vetoed, corresponding\nto the 8.87 Hz on the table.\nVI.\nSENSITIVITY DEPTH ESTIMATION\nSimilar to previous all-sky searches, we assess the sen-\nsitivity of this search to putative sources in the search\nspace using software simulated signals added to detec-\ntor data in selected frequency bands [62, 63, 90, 93, 94].\nThrough these simulations, we establish a population-\nbased h0 that is detectable 95% of the time.\nWe measure this h0 using the sensitivity depth [95, 96],\ndefined as\nD =\np\nSn(f)\nh0\n,\n(17)\nwhere Sn is the single-sided IFO PSD of the detector\nnoise defined in Eq. (6), and h0 is the intrinsic signal\nstrain amplitude. The sensitivity depth provides a figure\nof merit that normalizes h0 by the detector noise, facili-\ntating comparisons across different frequency bands and\nsearch methods. Nonetheless, for these comparisons it\nis important to note that the sensitivity depth remains\n\n9\nhighly dependent on the searched parameter ranges in\naddition to frequency. These sensitivity depth estimates\nare used to set thresholds in the follow-up procedure\n(Sec. VII) and to study the astrophysical reach of the\nsearch (Sec. VIII).\nFor each 0.125 Hz frequency band in which injections\nare performed, we select the highest Sn(f) within the\nband to evaluate sensitivity depths and search for the\nD95% value at which we determine the amplitude h0 at\nwhich 95% of injections are recovered above threshold.\nFor each injected signal, we construct a small region\ncentered on the injection parameters. The region spans\n\u00b13 resolution units in all search dimensions according to\nEq. (13), except for the binary phase \u03d5b, where a \u00b15\nresolution range is used. This choice has been made be-\ncause it is more challenging to constrain the binary phase\nof simulated signals compared to the other parameters.\nThese regions are designed to be compatible with the\nfirst-stage follow-up prior ranges in Sec. VII, making sure\nthat any detectable signal in this setup is recovered and\nfollowed up by the pipeline.\nBesides the resolution intervals shown in Eq. (13), the\nspecific ones for \u03b1 and \u03b4 are set using\n\u03b4\u03b1 =\n1\nTSFT(v/c)f0\n1\ncos \u03b4 , \u03b4\u03b4\n=\n1\nTSFT(v/c)f0\n,\n(18)\nwhich take into account the cos \u03b4 dependence arising from\nspherical coordinates to make resolution intervals cor-\nrectly centered and spaced around injected signals.\nAll signals are injected into the same O4a SFT data\nused in the search using the PyFstat software pack-\nage [97\u2013100]. PyFstat is built on top of LALSuite [84]\nand contains multiple utilities for CW searches, such as\ninjection generation or candidate follow-ups. After in-\njecting the signals, we rerun the whole analysis on the\nsmall intervals, computing the detection statistics over\nthe corresponding box with the same oversampling factor\nas used in the main search. We then check whether the\ncandidate template CR value exceeds the corresponding\nCR follow-up threshold from Table II, which allows us\nto determine if the injection would have been one of the\noutliers passing to the follow-up stage. Afterwards, we\nuse this information to estimate the detection efficiency\nand corresponding sensitivity depths.\nTo classify an injected signal as detected, we require\nthat at least one candidate template within the injection\nsearch region satisfies the following three conditions:\n1. The number count statistic nc(\u03bb), computed using\nhalf of the SFTs, must be greater than the lowest\nnc(\u03bb) value from the first stage of the search for the\nbox in which the signal was injected. This ensures\nthat the candidate template would have passed the\npersistence filter used in the first search step.\n2. The CR must exceed the maximum found in the\nsecond stage of the search for that same box. This\nconfirms that the candidate template would have\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n17\n18\n19\n20\n21\n22\n23\n24\n25\nD95% [Hz\u22121/2]\nA\nB\nC\nD\nE\nO4a sensitivity\nO3a sensitivity\nO4a injection results\nFIG. 6.\n95% sensitivity depths D95% as a function of fre-\nquency. Each point represents a 0.125 Hz band with injection\nresults, with error bars showing \u00b1\u03c3 from the sigmoidal fit.\nShaded regions show the average sensitivity depth per fre-\nquency region with its 3\u03c3 uncertainty (see Table IV). Com-\nparison between the results of this search (in black) and the\nresults of the O3a BinarySkyHough search [63] (in red).\nbeen selected as the most significant outlier in that\nbox.\n3. The CR value must also surpass the follow-up CR\nthreshold for the corresponding frequency band.\nWe inject signals into at least one 0.125 Hz band every\n5 Hz across the search frequency range in non-vetoed\nbands in Sec. V. Therefore, the sensitivity estimates do\nnot apply to the vetoed frequencies from Sec V, listed in\nTable VI.\nIn each selected band, we inject 500 signals at different\ndepths centered around the expected D95%, with param-\neters drawn from uniform distributions over the phase\nand amplitude parameters.\nEach signal is injected at\na random frequency inside the band and with random\nbinary orbital parameters within the ranges defined in\nTable I. In order to estimate the sensitivity depth at\neach frequency, we compute the detection efficiency as\nthe proportion of detectable injections in each depth, and\nestimate the sensitivity using sigmoidal fits and interpo-\nlating at which sensitivity depth 95% of the injections are\ntagged as detected. The procedure is detailed in App. B.\nFig. 6 shows the results for sensitivity depth estimates\nas a function of frequency for the different selected fre-\nquency bands.\nThe mean value across each frequency\nregion (as defined in Table II) is computed from these\nvalues and is summarized in Table IV.\nVII.\nSEARCH OUTLIERS FOLLOW-UP\nCandidates with CRs above the follow-up thresh-\nolds (Table II) in the main stage of the search (see\n\n10\nRegion Frequency [Hz] \u27e8D95%\u27e9\u00b1 3\u03c3 [Hz\u22121/2]\nA\n[100, 150)\n23.3 \u00b1 0.6\nB\n[150, 170)\n22.7 \u00b1 0.5\nC\n[170, 200)\n22.2 \u00b1 0.4\nD\n[200, 275)\n20.4 \u00b1 0.6\nE\n[275, 350)\n19.6 \u00b1 0.7\nTABLE IV. Average 95% sensitivity depths across the fre-\nquency regions defined in Table II. The uncertainties corre-\nspond to \u00b13\u03c3 from the sigmoidal fit.\nFig. 5) are subjected to a more sensitive follow-up anal-\nysis.\nThe follow-up analysis is performed using the\nPyFstat software package [97\u2013100], as was done in the\nO3a BinarySkyHough search [63]. PyFstat utilizes the\nparallel-tempered Markov Chain Monte Carlo (PTM-\nCMC) sampler provided by the ptemcee package for the\ncandidate follow-up [101, 102].\nThis stage uses longer coherence times and includes ad-\nditional frequency-evolution parameters. Increasing co-\nherence times may also reject potential signals that do\nnot conform to the phase model enforced by the longer\ncoherence lengths [75]. Signals whose spindown is larger\nthan Eq. (5) or whose eccentricity is larger than Eq. (4)\nare expected to already be lost during the search stage\nand their high spindowns or eccentricities are not consid-\nered inside the parameter ranges of this follow-up stage.\nChanges to the frequency evolution model due to spin-\nwandering are not considered in the follow-up.\nIncreasing Tcoh strengthens real CWs relative to Gaus-\nsian noise because correctly demodulated signals accumu-\nlate coherent power with time, while instrumental arti-\nfacts, which lack the astrophysical Doppler modulations,\nare typically diminished by the demodulation and are\nfurther rejected by our prominence-crossing and line-list\nvetoes.\nCandidates are analyzed using F-statistic searches\n[50, 103]. The F-statistic compares data to signal tem-\nplates in the frequency domain using coherent integra-\ntion. The semi-coherent version, the segment-wise 2 \u02c6F, is\nconstructed by summing the coherent 2 \u02dcF statistic over\nNseg data segments, each with duration Tcoh,\n2 \u02c6F (\u03bb) =\nNseg\u22121\nX\ni=0\n2 \u02dcFi (\u03bb) .\n(19)\nIn the follow-up process, the MCMC algorithm takes\nsamples using 300 walkers each one with 300 steps to\nidentify and characterize potential maxima, which are\nthen used to determine whether a candidate passes a de-\ntection threshold. The MCMC-based follow-up and its\napplication to CW searches is detailed in [104].\nIn the first stage of the MCMC follow-up, candi-\ndates from the initial search are analyzed using a sig-\nnificantly increased coherence time to improve sensitiv-\nity. Specifically, we increase the coherence time from the\nTSFT = 1024 s used in the main search to Tcoh = 12\nhours for the follow-up. This configuration yields a to-\ntal of Nseg = 474 segments over the full observing time.\nThe follow-up priors and MCMC sampler configuration\nis developed in App. D.\nFig. 7 summarizes the results of the first-stage MCMC\nfollow-up across all frequency bands, showing the max-\nimum recovered 2 \u02c6F values as a function of frequency.\nAs seen, most frequency bands show minimums around\n2 \u02c6F = 3600 and maximums around 2 \u02c6F = 3900. However,\nthere are bands where the maximum sampled 2 \u02c6F is much\nhigher above 3900. A large number of them appear near\nthe instrumental disturbances around 270 Hz, which in-\ndicates that instrumental lines can highly increase the\nsampled 2 \u02c6F.\nTo determine which candidates should advance to a\nmore sensitive second follow-up stage, we calibrated a\nthreshold on the cumulative 2 \u02c6F using simulated signal\ninjections.\nThese injections were generated with the\nsame setup and randomized amplitudes described in the\nSec VI. The simulated signals were injected at the sen-\nsitivity depths values obtained per each region shown in\nTable IV. For each injected signal, we recorded the max-\nimum cumulative 2 \u02c6F value across all walkers within the\ncorresponding frequency band.\nBy repeating this pro-\ncess for many injections across different frequency bands,\nsampling at least one band every 5 Hz and covering all\nregions listed in Table II at the depths given in Ta-\nble IV, we built up the distribution of recovered 2 \u02c6F val-\nues, which was then used to set the threshold. After run-\nning 14750 injections, the detection threshold was then\nset at 2 \u02c6F = 3850, chosen such that fewer than 0.013% of\nthe injected signals (2 of the 14750) would fall below it.\nOnly injections that were tagged as detected by the\nsearch pipeline were followed-up to determine this thresh-\nold. Furthermore, the injection follow-up was performed\nwith the same MCMC sampler configuration and priors\nfor the search candidates.\nThe injection results are shown in Fig. 8. Candidates\npassing this initial 2 \u02c6F cut are then subjected to a second\nfollow-up stage with a longer coherence time, following\nthe methodology outlined in [97, 105, 106].\nAfter running the first-stage MCMC follow-up and ap-\nplying the cumulative 2 \u02c6F threshold, several outliers re-\nmained, as summarized in Table V. These surviving out-\nliers were further analyzed to determine whether they are\nconsistent with astrophysical signals or can be attributed\nto instrumental origins.\nCW signals are expected to accumulate 2 \u02c6F linearly\nover time, adding to the segment-wise 2 \u02dcF in a relatively\nuniform way across the observation period. However, if\na candidate\u2019s frequency evolution briefly overlaps with a\nstrong instrumental disturbance or narrow-band spectral\nline, it may produce a spike in 2 \u02dcF during that specific\ntime window, while remaining at background levels oth-\nerwise.\nTo identify such cases, we examine the segment-wise\n2 \u02dcF distributions of surviving candidates.\nFollowing\nthe same approach used in the O3a search, we flag\n\n11\n100\n150\n200\n250\n300\n350\nFrequency (Hz)\n3600\n3800\n4000\n4200\n4400\nMax sampled 2 \u02c6F\nFIG. 7. Results of the first-stage MCMC follow-up. The figure shows the maximum 2 \u02c6F values recovered for each candidate,\nplotted as a function of frequency.\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n10000\n20000\n30000\n40000\nMax sampled 2 \u02c6F\nFIG. 8.\nFirst-stage MCMC follow-up results on injection\nstudies with Tcoh = 12 h.\nEach point corresponds to the\nmaximum 2 \u02c6F value sampled for each injected signal. 14750\nInjections were run, with 2 obtaining a final 2 \u02c6F below 3850.\nSignals were injected at the sensitivity depths values obtained\nper each region shown in Table IV.\nany candidates in bands with at least one segment-wise\n2 \u02dcF value exceeding 100.\nThese outliers are classified\nas \u201cprominence-crossing\u201d cases and are likely caused\nby transient overlaps with lines or short-lived artifacts\nrather than persistent astrophysical signals.\nAll can-\ndidates within-bands that are tagged as prominence-\ncrossing are discarded in this stage and not followed-up.\nNotice that this prominence-crossing veto is necessary\neven if the number-count statistic has previously been\nused in the candidate selection. Using the number-count\nduring the search provides more importance to candi-\ndates consistent with high power across the observing\nrun.\nNonetheless, it is not a filter that eliminates all\ncandidates whose high power is a consequence of cross-\ning paths with an instrumental artifact.\nAn example is shown in Fig. 9, where the candidate\nband exhibits a sharp and isolated 2 \u02dcF spike near day\n150 of the run. While the total 2 \u02c6F surpasses the thresh-\nold, the strong deviation in a single segment suggests a\ntransient artifact rather than a genuine signal, and the\ncandidate is therefore discarded.\n0\n50\n100\n150\n200\nDays since start of O4a\n0\n1000\n2000\n3000\n4000\nCumulative 2 \u02c6F\nOutlier at 103.250 Hz, candidate 215\n0\n50\n100\n150\n200\nDays since start of O4a\n0\n50\n100\n150\n200\nSegment-wise 2 \u02c6F\nFIG. 9. Example of a prominence-crossing outlier. The can-\ndidate shows a large spike in 2 \u02dcF near day 150 of the observing\nrun. This spike allows it to exceed the follow-up threshold of\n2 \u02c6F = 3850, but the narrow change suggests a superposition\nwith an instrumental disturbance. This candidate is therefore\ndiscarded from second-stage follow-up.\n\n12\nThe broader distribution of such outliers is summa-\nrized in Fig. 10. The top panel shows those candidates\nthat have been tagged as prominence-crossing and re-\njected; they tend to be clustered within a few narrow\nfrequency ranges and exhibit significantly elevated 2 \u02c6F\nvalues.\nThe bottom panel shows the remaining 1,997\noutliers, which passed all veto criteria and are retained\nfor further second-stage follow-up analysis. The results\nfrom this prominence crossing veto are summarized in\nTable V.\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n3850\n3900\n3950\nMax sampled 2 \u02c6F\nNot prominence-crossing tagged outliers\nFIG. 10. Distribution of maximum 2 \u02c6F values for surviving\noutliers. The top panel shows outliers tagged as prominence-\ncrossing and discarded due to transient spectral contamina-\ntion.\nThese candidates tend to cluster in a few frequency\nbands and exhibit extremely high 2 \u02c6F values.\nThe bottom\npanel shows the remaining outliers, which were not flagged as\nline-crossing and are retained for further analysis.\nOf the 251,717 surviving candidates in Table V, 84%\ncome from the frequency range between 260 Hz and\n280 Hz, a range with a high amount of high-CR results\nas seen in Fig. 4 where there is also a high amount of\nvetoed bands as seen in Fig. 5. It appears that there is\na high amount of broad artifacts in the range, not all of\nthem vetoed in Sec. V.\nThe second-stage follows the multi-stage procedure es-\ntablished in previous works [97, 105, 106]. In this sec-\nond follow-up stage, we use a longer coherence time of\nTcoh = 26 h, which increases the sensitivity of the search\nFollow-up Summary\nCount\nTotal candidates followed up\n927,443\nCandidates surviving 2 \u02c6F > 3850\n251,717\n- Prominence crossings (discarded) 249,720\n- Surviving to 2nd stage\n1,997\nTABLE V. Summary of candidate outcomes from the first-\nstage MCMC follow-up. Of the 927,443 candidates analyzed,\n251,717 exceeded the threshold 2 \u02c6F > 3850, yielding a sur-\nvival rate of 27.14%.\nAmong these, 249,720 were tagged\nas prominence or prominence crossings and discarded, while\n1,997 (8%) were retained for second-stage follow-up.\nand improves the accuracy of parameter estimation. The\nrationale for this choice, together with the details of the\npriors and analysis setup, which runs again 300 walkers\nwith 300 steps each, is provided in App. D.\nThe second stage threshold for further follow-ups was\ncalibrated using software injections as in the first stage.\nFig. 11 shows the maximum 2 \u02c6F values sampled by the\nMCMC for each injected signal.\nThe lowest sampled\nvalue for detectable signals was close to 2200, indicat-\ning that a threshold of 2100 would give a false dismissal\nrate below 1/14000, given the 14000 injections run.\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n0\n10000\n20000\n30000\n40000\n50000\nMax sampled 2 \u02c6F\nFIG. 11. Second-stage MCMC follow-up results on injection\nstudies Tcoh = 26 h. Each dot represents the maximum sam-\npled 2 \u02c6F value for a detected injection across multiple fre-\nquency bands. A total of 14000 injections are shown. Signals\nwere injected at the sensitivity depths values obtained per\neach region shown in Table IV.\nThe second-stage pipeline was applied to the 1,997 can-\ndidates that survived the first stage.\nThe results are\nshown in Fig. 12. None of the recovered maximum 2 \u02c6F\nvalues exceeded the calibrated threshold of 2100. As seen\nagain in Fig. 5, there is a high amount of instrumental\ndisturbances around 270 Hz which have been vetoed in\nthis stage. All recovered values were well below the in-\njection minimum of 2200, and thus none of these outliers\nare consistent with a detectable CW signal.\nSince no candidate survives the second-stage threshold,\nno further follow-up stages have been carried out. The\n\n13\n100\n150\n200\n250\n300\n350\nFrequency [Hz]\n1800\n1850\n1900\n1950\n2000\n2050\nMax sampled 2 \u02c6F value\nFIG. 12.\nMaximum 2 \u02c6F values recovered from the second-\nstage MCMC follow-up for each of the 1,997 candidates. No\noutlier exceeds the detection threshold.\nfollow-up phase of the search concludes with no candidate\nconsistent with an astrophysical CW source.\nVIII.\nDISCUSSION\nThis analysis is the first large-scale application of the\nfasttracks pipeline [72, 89], designed to compute de-\ntection statistics with GPU acceleration using SFT-type\ndata. To address the large parameter space of the search,\nwe used a novel box-based partitioning strategy also in-\ntroduced in [72], in which each parameter-space par-\ntition, or box, is analyzed independently.\nThis novel\npartitioning makes post-processing more straightforward,\nsince contaminated boxes can be vetoed and candidates\nfrom each box followed up independently. Whereas pre-\nvious searches required clustering strategies to filter large\nnumbers of candidates and group those likely originating\nfrom the same source, our approach achieves comparable\nreduction in a simpler manner.\nA two-step search approach has been used, with a\nHough number count filter in the first step to prioritize\ncandidates showing persistent power accumulation. Us-\ning the O4a lines list, frequency bands were checked for\nline contamination and those with more than 2000 can-\ndidates and known line contamination were vetoed.\nThe surviving 27.14% of candidates after the known\nlines veto were analyzed using an MCMC follow-up\nmethod using the PyFstat package [97\u2013100] and Tcoh =\n12 h. These candidates were checked to determine if their\nhigh statistical values were due to prominence-crossing\nbehavior.\nThose deemed as not prominence-crossing\n(8%) were re-analyzed with a second stage follow-up,\nwhich concluded the search with no candidates consis-\ntent with astrophysical CW sources.\nTo evaluate the sensitivity of our search, we conducted\ninjection campaigns across all frequency regions, as de-\nscribed in Sec. VI. From these studies, we derived the\n95% confidence strain amplitude sensitivity h95%\n0\n, com-\nputed from the estimated sensitivity depths and the noise\npower spectral density shown in Fig. 1.\nThe result-\ning sensitivity curve is presented in Fig. 13. The best\nperformance was achieved at 199.9 Hz, with h95%\n0\n=\n(1.62 \u00b1 0.3) \u00d7 10\u221225, corresponding to an improvement\nby a factor 1.5 compared to the lowest amplitude ob-\ntained by the previous BinarySkyHough search on O3a\ndata [63]. This improvement over the O3a results is con-\nsistent with the expectations given the improvement in\nsearch sensitivity shown in Fig. 1 and longer observing\ntimes plus the improvement in sensitivity depth shown in\nFig. 6. These estimates are not applicable to the vetoed\nfrequency ranges listed in Table VI. As in [61], the re-\nported sensitivities are valid for eccentricities below the\nmaximum value defined in Eq. (4), above which the signal\ntrack would deviate by more than one frequency bin.\nFig. 14 illustrates the astrophysical reach of this search\n(in black) derived from the estimated h95%\n0\nsensitivities\nand its comparison with the O3a BinarySkyHough search\nresults [63] (in red). The figure shows the distance range\n(in kiloparsecs) at which NSs with various ellipticities\n\u03f5 could be detected, assuming the canonical moment of\ninertia Izz = 1038 kg\u00b7m2. The shaded regions indicate\nvalues excluded by being larger than the maximum spin-\ndown used in this search (see Eq. (5)).\nFig. 15 translates these sensitivity results into con-\nstraints on the NS ellipticity \u03f5, assuming sources are lo-\ncated at fixed distances. For sources within 1 kpc, the\nellipticity can be constrained to below 10\u22125 across the\nmajority of the analyzed band (above 130 Hz). These\nlimits begin to probe astrophysically interesting regimes:\ntheoretical expectations for the maximum ellipticity of\nrealistic NSs range from \u223c10\u22126 to 10\u22127 for conventional\nnuclear equations of state, up to \u223c10\u22125 for more extreme\nor exotic configurations [4, 107].\nUsing the ATNF pulsar catalogue [15], we find that of\nthe 3,473 known pulsars, 715 lie within 2 kpc of Earth,\n282 within 1 kpc, and 117 within 0.5 kpc.\nOf these,\n151, 66, and 16, respectively, are in binary systems. This\nconfirms that the sensitivity region of our search over-\nlaps with a non-negligible fraction of the known pulsar\npopulation, including binaries. Moreover, restricting the\nnearby binaries to orbital periods between 7 and 15 days\nand projected semi-major axes between 5 and 15 light-\nseconds, we identify 17, 8, and 1 such systems within\n2 kpc, 1 kpc, and 0.5 kpc, respectively.\nThese are a\nrelative small number of known pulsars probed by the\nsearch. Nonetheless, only a small fraction of the Galactic\nNS population is observable as radio or gamma-ray pul-\nsars [58, 59], with population synthesis models predicting\norders of magnitude more NSs than those currently de-\ntected. Consequently, our sensitivity may overlap with\na much larger, presently unseen NS population, includ-\ning systems with properties favorable for the emission\nof CW. Thus, this search directly probes the parameter\nspace occupied by several known binary pulsars, as well\nas potentially a much larger population of undetected\nNSs.\n\n14\n100\n150\n200\n250\n300\n350\nFrequency (Hz)\n10\u221224\nh95%\n0\nA\nB\nC\nD\nE\nO3a estimate\nO4a estimate\nFIG. 13. Estimated 95% strain amplitude sensitivity h95%\n0\nderived from the sensitivity depths in Table IV, using the inverse\nsquare root of the averaged PSD. Comparison between the O3a BinarySkyHough search results [63] (in red), and the results of\nthis present search (in black).\n100\n150\n200\n250\n300\n350\nFrequency (Hz)\n10\u22122\n10\u22121\n100\n101\nRange (kpc)\nA\nB\nC\nD\nE\n\u03f5 = 10\u22125\n\u03f5 = 10\u22126\nFIG. 14.\nEstimated distance reach for sources emitting at\nh95%\n0\n, based on the sensitivity of the search. Shaded regions\nindicate distances excluded by the limit imposed by the max-\nimum spindown used in the analysis. Comparison between\nthe O3a BinarySkyHough search results [63] (in red), and the\nresults of this present search (in black).\nIX.\nCONCLUSION\nWe have conducted an all-sky search for continuous\ngravitational waves from neutron stars in binary sys-\ntems using data from the first part of the fourth LIGO-\nVirgo-KAGRA observing run.\nThe search covered the\nfrequency range from 100 to 350 Hz, targeting systems\nwith projected semi-major axes between 5 and 15 light-\nseconds and orbital periods between 7 and 15 days.\nThis work represents the first large-scale application\nof the fasttracks pipeline. We analyzed O4a data with\na two-step procedure: a first Hough number count filter\nto identify persistent candidates, a second step comput-\n100\n150\n200\n250\n300\n350\nFrequency (Hz)\n10\u22126\n10\u22125\n10\u22124\nEllipticity\nA\nB\nC\nD\nE\nd = 2.0 kpc\nd = 1 kpc\nd = 0.5 kpc\nFIG. 15.\nCorresponding equatorial ellipticities estimated\nfrom the h95%\n0\nsensitivity, assuming a canonical NS moment\nof inertia Izz = 1038 kg\u00b7m2. The shaded regions are excluded\nby the maximum spindown constraint. Comparison between\nthe O3a BinarySkyHough search results [63] (in red), and the\nresults of this present search (in black).\ning weighted normalized power, followed by an MCMC\nanalysis with extended coherence time follow-ups with\nPyFstat.\nVetoes of line-contaminated bands reduced\nthe candidate set, however, no signals consistent with\nastrophysical continuous waves were found.\nSensitiv-\nity estimates from extensive injection campaigns show\na minimum detectable amplitude of h95%\n0\n= (1.62 \u00b1\n0.3)\u00d710\u221225 at 199.9 Hz, representing a 1.5-fold improve-\nment over the lowest amplitude achieved by the previous\nBinarySkyHough search on O3a data [63].\nThe achieved sensitivity covers binary parameters and\nspin frequencies consistent with those of many known bi-\nnary pulsars within a few kiloparsecs, as well as with a\n\n15\npotentially much larger unseen neutron star population.\nConstraints on the ellipticity of nearby sources reach be-\nlow 10\u22125, entering the regime predicted by some nuclear\nequations of state and more exotic neutron star mod-\nels. The non-detection of continuous gravitational waves\nat O4 sensitivity imposes strong constraints on neutron\nstars with exotic compositions within the distance reach\nof the sources.\nLooking ahead, upgrades to the global network of\nterrestrial gravitational-wave detectors are expected to\ndeliver enhanced strain sensitivity, extended frequency\ncoverage, and longer observing baselines in upcoming\nobserving runs, more so with third-generation detec-\ntors such as the Einstein Telescope [108] and Cosmic\nExplorer [109].\nThese advancements will increase the\nchances of detecting CW signals and improve constraints\non the galactic neutron star population. Complementary\nprogress will come from next-generation pulsar timing fa-\ncilities, such as the Square Kilometre Array [110], which\nwill expand the known pulsar population and improve the\nmeasurement of their evolution, thereby providing valu-\nable priors and targets for gravitational-wave searches.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector.\nAdditional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO) for the construction and opera-\ntion of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agencies\nas well as by the Council of Scientific and Industrial Re-\nsearch of India, the Department of Science and Technol-\nogy, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource Devel-\nopment, India, the Spanish Agencia Estatal de Investi-\ngaci\u00b4on (AEI), the Spanish Ministerio de Ciencia, Inno-\nvaci\u00b4on y Universidades, the Red Espa\u02dcnola de Supercom-\nputaci\u00b4on - Barcelona Supercomputing Center - Centro\nNacional de Supercomputaci\u00b4on (BSC-CNS). the Euro-\npean Union NextGenerationEU/PRTR (PRTR-C17.I1),\nthe ICSC - CentroNazionale di Ricerca in High Perfor-\nmance Computing, Big Data and Quantum Comput-\ning, funded by the European Union NextGenerationEU,\nthe Comunitat Auton`oma de les Illes Balears through\nthe Conselleria d\u2019Educaci\u00b4o i Universitats, the Consel-\nleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat Digi-\ntal de la Generalitat Valenciana and the CERCA Pro-\ngramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Sci-\nence Centre of Poland and the European Union - Eu-\nropean Regional Development Fund; the Foundation for\nPolish Science (FNP), the Polish Ministry of Science and\nHigher Education, the Swiss National Science Founda-\ntion (SNSF), the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scot-\ntish Universities Physics Alliance, the Hungarian Scien-\ntific Research Fund (OTKA), the French Lyon Institute\nof Origins (LIO), the Belgian Fonds de la Recherche Sci-\nentifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaan-\nderen (FWO), Belgium, the Paris \u02c6Ile-de-France Region,\nthe National Research, Development and Innovation Of-\nfice of Hungary (NKFIH), the National Research Founda-\ntion of Korea, the Natural Sciences and Engineering Re-\nsearch Council of Canada (NSERC), the Canadian Foun-\ndation for Innovation (CFI), the Brazilian Ministry of\nScience, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute\nfor Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Sci-\nence Foundation of China (NSFC), the Israel Science\nFoundation (ISF), the US-Israel Binational Science Fund\n(BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC),\nTaiwan, the United States Department of Energy, and\nthe Kavli Foundation. The authors gratefully acknowl-\nedge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources.\nThis work was supported by MEXT, the JSPS\nLeading-edge Research Infrastructure Program, JSPS\nGrant-in-Aid for Specially Promoted Research 26000005,\nJSPS Grant-in-Aid for Scientific Research on Inno-\nvative Areas 2402:\n24103006, 24103005, and 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-\nto-Core Program A. Advanced Research Networks, JSPS\nGrants-in-Aid for Scientific Research (S) 17H06133 and\n20H05639, JSPS Grant-in-Aid for Transformative Re-\nsearch Areas (A) 20A203:\nJP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nUniversity of Tokyo, the National Research Foundation\n(NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC)\nat KISTI, the Korea Astronomy and Space Science In-\nstitute (KASI), the Ministry of Science and ICT (MSIT)\nin Korea, Academia Sinica (AS), the AS Grid Center\n(ASGC) and the National Science and Technology Coun-\ncil (NSTC) in Taiwan under grants including the Science\nVanguard Research Program, the Advanced Technology\nCenter (ATC) of NAOJ, and the Mechanical Engineering\nCenter of KEK.\n\n16\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to\nany Author Accepted Manuscript version arising.\nWe\nrequest that citations to this article use \u2019A. G. Abac et\nal. (LIGO-Virgo-KAGRA Collaboration), ...\u2019 or similar\nphrasing, depending on journal convention.\nThis paper has been assigned document number LIGO-\nP2500437.\nAppendix A: Parameter-space Partitioning\nTo estimate the number of templates required to cover\na given region of parameter space, we begin with the\nresolution steps \u03b4\u03bb[k] given by Eq. (13) along each of the\nparameters in \u03bb = {f0, \u02c6n, ap, \u2126, \u03d5b}. The total number\nof templates within a volume \u2206\u03bb is given by\nN (\u2206\u03bb) =\nZ\n\u2206\u03bb\nd\u03bb\u03c1 (\u03bb) ,\n(A1)\nwhere the local template density, \u03c1 (\u03bb), is defined as [72]\n\u03c1 (\u03bb) =\nD\nY\nk=1\n1\n\u03b4\u03bb[k],\n(A2)\nwhere k is the running index over the search parameters,\nup to D = 6 in this case.\nIn order to sample the templates, we perform a coor-\ndinate transformation from the physical parameter space\n\u03bb to a uniform template space \u03be, in which the template\ndensity is constant.\nThis is achieved by applying the\ntransformation\nd\u03bb\u03c1(\u03bb) = d\u03be\n\u21d4\n\u03c1(\u03be) = 1.\n(A3)\nwhich we use to derivate the following relations between\nthe coordinates in the physical and uniform parameter\nspace\n\u03be[0] =C1/6\n6\nf 6\n0\n\u03be[1] =C1/6\u03b1\n\u03be[2] =C1/6 sin \u03b4\n\u03be[3] =C1/6\n3\na3\np\n\u03be[4] =C1/6\n4\n\u21264\n\u03be[5] =C1/6\u03d5b\n.\n(A4)\nwith C = T 6\nSFTTobs(v/c)2 (more details can be found\nin [72]).\nIn this transformed space, templates are generated by\nuniform random sampling over the search region. These\nsamples are then mapped back to the physical parame-\nter space \u03bb using the inverse transformation as described\nin [72]. As a result, the sampling in \u03bb automatically fol-\nlows the required non-uniform density \u03c1(\u03bb).\nThe number of templates in a volume region \u2206\u03be in the\nuniform space is simply\nN(\u2206\u03bb) =\nZ\n\u2206\u03be\nd\u03be =\nD\nY\nk=1\n\u2206\u03be[k].\n(A5)\nTo construct the boxes, the algorithm used is as fol-\nlows:\nWe begin by estimating the number of sky templates\nrequired due to the Doppler modulation induced by\nEarth\u2019s motion. This number depends on the frequency\nand the resolution of the sky grid, and is given by\nNsky =\nZ\nsky\n1\n\u03b4sky = 4\u03c0\n\u0010\nf0TSFT\nv\nc\n\u00112\n.\n(A6)\nWe then divide the sky into smaller patches so that each\nsky patch contains a fixed number of templates. We chose\nfor each sky patch a small number of templates, \u22489,\nin order to ensure that all templates in one box were\nspatially close to each other. Hence, the total number of\nsky boxes is\nBsky = Nsky\n9\n.\n(A7)\nWe split both sky coordinate parameters into the same\nnumber of subdivisions,\nB\u03b1,sin \u03b4 = round\n\u0010p\nBsky\n\u0011\n,\n(A8)\nand then calculate the number of templates assigned to\neach sky box\nNper sky box = NtotalO\nB2\n\u03b1,sin \u03b4\n.\n(A9)\nwhere O is the oversampling factor for a given frequency\nband and Ntotal the total amount of templates in the\nfrequency band, computed using Eq. (A5). The amount\nB\u03b1,sin \u03b4 per band is increased in discrete steps according\nto the increasing frequency (see Eq. A8). We start at\n100 Hz with 122 sky boxes ending with 422 at 350 Hz.\nWe also tune the number of subdivisions in the fre-\nquency and binary parameters so that each box contains\napproximately 108 templates. This limit was enforced by\nthe maximum number of templates that we were able to\nprocess at the same time in parallel in a modern NVIDIA\nA100 Tensor Core GPU as described in [72]. Maximizing\nthe number of templates to be processed for the efficient\nuse of GPU resources.\nHence, we partition the following three parameters:\nfrequency f0, projected semi-major axis ap, and or-\nbital frequency \u2126, into an equal number of subdivisions\n(Bf0 = Bap = B\u2126\u2261Bf0,ap,\u2126). The quantity Bf0,ap,\u2126\n\n17\nper frequency band is illustrated in Fig. 16. Addition-\nally, orbital phase parameter \u03d5b is not subdivided, it is\nsampled over its full physical range within each box. The\ntotal number of boxes is\nBtotal = B2\n\u03b1,sin \u03b4B3\nf0,ap,\u2126,\n(A10)\nand number of templates per box is\nNbox = NtotalO\nBtotal\n=\nNtotalO\nB2\n\u03b1,sin \u03b4B3\nf0,ap,\u2126\n.\n(A11)\nAs a consequence, the division of these three parameters\nis done according to\nBf0,ap,\u2126= round\n \n3\ns\nNtotalO\nNboxB2\n\u03b1,sin \u03b4\n!\n,\n(A12)\nper each 0.125 Hz band, where Nbox = 108.\nWe ensured that boxes were sufficiently small, in or-\nder to avoid that possible contaminations in one of them\naffected a large region in parameter space, by defining\na minimum of 104 boxes per frequency band: if the re-\nsulting Nbox from Eq. (A11) is less than 104, we further\nsubdivided the frequency and binary parameter space by\nincrementing Bf0,ap,\u2126according to\nBf0,ap,\u2126=\n&\n3\ns\nBmin\nB2\n\u03b1,sin \u03b4\n'\n.\n(A13)\nThe total amount of boxes per frequency band is illus-\ntrated in Fig. 3, and the number of templates per box in\nFig. 17.\nAppendix B: Fitting Sensitivity Estimation\nIn this appendix, we describe the procedure used to\nestimate the search sensitivity shown in Sec. VI. Our\ngoal is to quantify the amplitude of CW signals that\nthe search could detect with 95% efficiency across dif-\nferent frequency bands.\nThis is done by performing a\nlarge number of signal injection studies and analyzing\ntheir recovery.\nAfter separating detected and non-detected injections,\nwe construct efficiency-versus-depth curves by using six\ndifferent sensitivity depths. For each depth D, the detec-\ntion efficiency E is defined as the fraction of successfully\ndetected injections out of the total N performed (500\nfor each sensitivity depth). Its statistical uncertainty is\nassigned as\n\u03b4E =\nr\nE(1 \u2212E)\nN\n,\n(B1)\nthe standard error of a proportion when counting suc-\ncesses in a set of independent trials.\nTo extract the sensitivity depth corresponding to 95%\ndetection efficiency (D95%), we fit a sigmoid function to\n100\n150\n200\n250\n300\nFrequency [Hz]\n3.0\n3.5\n4.0\n4.5\n5.0\nBf0,ap,\u2126\nA\nB\nC\nD\nE\nFIG. 16.\nNumber of subdivisions in the intrinsic frequency\nf0, projected semi-major axis ap, and orbital frequency \u2126di-\nmensions per 0.125 Hz frequency band. The lettered regions\n(A-E) correspond to the frequency intervals defined in Ta-\nble II. Four major transitions can be observed, with different\noversampling factors. The first two drops in the number of\nsubdivisions (near 100 Hz and between 170-200 Hz) are due\nto the enforcement of a minimum total number of 104 boxes.\nThe drop at 170 Hz is due to a change in oversampling. At\n174 Hz there is another increase because the amount of tem-\nplates per box is above 1.5\u00d7108, hence, another subdivision is\nadded to round the number closer to 108. The sharp increase\nbeyond 300 Hz is instead driven by the\n108 templates-per-\nbox criterion.\n100\n150\n200\n250\n300\nFrequency [Hz]\n0.5\n1.0\n1.5\nNbox\n\u00d7108\nA\nB\nC\nD\nE\nFIG. 17.\nNumber of templates per box\n\u00af\nNbox as a func-\ntion of frequency.\nThe white dashed line marks the target\nthreshold of 108 templates per box. The five lettered regions\n(A-E) match the frequency intervals defined in Table II. The\nsawtooth pattern arises due to rounding of box counts and\nthe adaptive balancing of box size to the minimum amount\nof boxes and templates per box criteria as shown in Fig. 16.\nthe efficiency-versus-depth data.\nThe fit is performed\nusing the curve fit function from SciPy [111], with the\nform\nS(D; a, b) =\n1\n1 + exp\n\u0000 D\u2212b\na\n\u0001,\n(B2)\nwhere a and b are shape parameters. The 95% sensitivity\n\n18\n21\n22\n23\n24\n25\n26\nDepth [Hz\u22121/2]\n0.85\n0.90\n0.95\n1.00\nE\nSigmoidal \ufb01t\nFit error\nD95%\n\u03c3\n: 23.4\u00b10.3\nFIG. 18. Example of 95% sensitivity depth interpolation at\n105.75 Hz (Region A, oversampling = 4.0, threshold \u03a8s >\n7.0). Circles indicate injection results, the black line shows\nthe sigmoidal fit, and shaded bands represent 1, 2, and 3\u03c3\nconfidence intervals.\nThe star denotes the estimated D95%\nwith its \u00b1\u03c3 uncertainty.\ndepth is given by the value of D for which S(D; a, b) =\n0.95.\nThe uncertainty in the sigmoidal fit is propagated from\nthe covariance matrix C as\n\u03c3S(D) =\ns\u0012\u2202S\n\u2202a\n\u00132\nCaa +\n\u0012\u2202S\n\u2202b\n\u00132\nCbb + 2\u2202S\n\u2202a\n\u2202S\n\u2202b Cab,\n(B3)\nand the error in the D95% is done by bisecting the curves\ndefined by S(D; a, b) \u00b1 \u03c3S(D) with E = 0.95.\nIn Fig. 18, we show a representative example of the\nefficiency curve fit used to estimate the 95% sensitivity\ndepth, D95%, and its error. The 95% depth and its \u00b1\u03c3\nuncertainty are extracted from the fit and indicated with\na star.\nAppendix C: Vetoed frequency ranges\nThe total contaminated frequency range surrounding\na line is given by\nfcontaminated = fline \u00b1 (\u2206fline + fwings) ,\n(C1)\nwhere \u2206fline is the width towards each side of the line\n(left width towards lower frequencies and right width to-\nwards higher ones), and fwings accounts for the maximum\nDoppler excursion, computed as\nfwings = fline\n\u0010v\nc + ap\u2126\n\u0011\n.\n(C2)\nWe provide in this appendix Table VI, which contains\na list of the frequency ranges which have been vetoed\nas described in Sec. V. The contamination range caused\nby each line has been calculated using Eq. (C1). Out-\nliers from the search in these ranges have been vetoed\nand have not been followed up in the stage discussed in\nSec. VII.\nAppendix D: Outlier follow-up setup\n1.\nFirst-step follow-up setup\nFor the follow-up first stage, we employ 300 walkers\nwith 300 steps per walker. This setup is not expected to\nachieve full convergence of the MCMC chains. Nonethe-\nless, it is sufficient for our purpose of identifying promis-\ning candidates. Better convergence of the MCMC chains\nis expected to take place if further stages in case a CW\nsignal is detected.\nWe also add two additional frequency-evolution param-\neters to be searched over. The first one is the orbital ec-\ncentricity e. Due to considering non-zero eccentricities,\nthe full frequency-evolution equation for the CW signal\nis [61]\nf (t; \u03bb) = f0\n\u001a\n1 + \u20d7v (t)\nc\n\u00b7 \u02c6n \u2212ap\u2126\n\u0012\ncos [\u2126(t \u2212tasc)]\n+ e cos [\u03c9 + 2\u2126(t \u2212tasc)]\n\u0013\u001b\n.\n(D1)\nThe addition of eccentricity necessitates also the inclu-\nsion of the argument of periapsis \u03c9. Furthermore, the\nfirst stage is done with the time of periastron passage tp\ninstead of the time of ascending node tasc, since this is\nthe search parameter implemented in the MCMC using\nPyFstat package [97\u2013100]. These two are related through\ntasc = tp \u2212\u03c9\n\u2126,\n(D2)\nwhere the orbital phase \u03d5b can be calculated as\n\u03d5b = \u2126tasc.\n(D3)\nThe priors used for this stage are uniform over intervals\ncentered on the candidate parameters. The size of these\nprior regions is determined by the resolution Eq. (13),\n(18). Specifically, the frequency f0 is taken within \u00b11.5\nresolution intervals, the sky position (\u03b1, \u03b4) and the or-\nbital period P within \u00b13 resolution intervals, where the\norbital period resolution is given by\n\u03b4P = P 2\u03b4\u2126\n2\u03c0\n(D4)\nThe projected semi-major axis ap prior is within \u00b11 res-\nolution interval, the orbital phase reference time tp is\nallowed to vary over the full orbital period, while the ar-\ngument of periapsis \u03c9 spans the full range [0, 2\u03c0]. The ec-\ncentricity e is drawn from the range [0, emax], where emax\nis the maximum value to which the search is sensitive,\ngiven by Eq. (4). When the resulting prior boundaries\nextend beyond the physical limits of a parameter, such\nas \u03b4 exceeding \u03c0/2, they are truncated to ensure that no\nsamples fall outside.\n\n19\n2.\nSecond-stage follow-up setup\nIn the second stage, both the coherence time and the\npriors are modified. The higher coherence time makes\nthe parameter-space \u201cpeak\u201d of the signal higher and nar-\nrower. For that reason, the priors are also modified with\nsmaller intervals. One additional parameter, the possible\nspindown or spin-up of the signal, | \u02d9f0|, is also added to\nthis stage.\nAs shown in [106], the coherence time for stage j is\ngiven by\nT (j)\ncoh = N j/D\n\u2217\nT (0)\ncoh,\n(D5)\nwhere we take N\u2217= 103 as in [106], D is the number\nof resolvable parameters, and T (0)\ncoh is the coherence time\nused in the first stage (12 hours). For the second stage,\nthe additional parameter of the frequency spindown \u02d9f0\nis introduced, increasing the number of dimensions to\nD = 9. This gives a second-stage coherence time of ap-\nproximately 26 hours, corresponding to Nseg = 219 seg-\nments (down from Nseg = 474 in the first stage).\nIn the second stage, the priors are Gaussian distribu-\ntions centered on the candidate values recovered from the\nfirst stage, with narrower widths than those used previ-\nously. These gaussian priors allow for the exploration be-\nyond the expected location if the true signal lies slightly\nfurther away. Specifically, the frequency f0 has a Gaus-\nsian width of \u03b4f0/6, right ascension \u03b1 a width of \u03b4\u03b1/3,\nand declination \u03b4 a width of \u03b4\u03b4/3. The projected semi-\nmajor axis ap is assigned a width of \u03b4ap/9, the orbital\nperiod P a width of \u03b4P/3, the time of ascending node tp\na width of 5\u03b4tp/3, the eccentricity e a width of \u03b4e/9, and\nthe argument of periapsis \u03c9 a width of \u03b4\u03c9/9. The spin-\ndown | \u02d9f0| is instead given a uniform prior between mi-\nnus the maximum and the maximum spindown for which\nthe search remains sensitive, given in Eq. (5), allowing\nboth positive (spin-up) and negative (spindown) values.\nWhen the Gaussian support extends beyond physical lim-\nits, such as when the center \u00b1 ten times the width falls\noutside the allowed physical or search ranges, the prior\nis replaced with a uniform distribution covering only the\nphysically valid region.\nThese prior widths ensure that roughly 99.7% (3\u03c3) of\nthe initial walker distribution lies within one-third of the\nprior volume used in the first stage. 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Virtanen et al., Scipy 1.0: fundamental algorithms\nfor scientific computing in python, Nature Methods 17,\n261 (2020).\n\n24\nVetoed Frequency Ranges (Start, End) [Hz]\n(100.000, 100.026)\n(100.649, 100.702)\n(100.860, 100.913)\n(101.302, 101.355)\n(101.574, 101.699)\n(101.969, 102.178)\n(102.643, 102.696)\n(102.963, 103.131)\n(103.639, 103.693)\n(104.186, 104.313)\n(104.624, 104.697)\n(105.294, 105.348)\n(105.632, 105.687)\n(106.284, 106.339)\n(106.402, 106.457)\n(106.629, 106.684)\n(107.114, 107.170)\n(107.511, 107.566)\n(107.625, 107.681)\n(107.945, 108.001)\n(108.619, 108.678)\n(109.606, 109.784)\n(109.972, 110.028)\n(110.615, 110.672)\n(110.836, 110.893)\n(111.081, 111.138)\n(111.267, 111.324)\n(111.611, 111.677)\n(111.944, 112.002)\n(112.608, 112.666)\n(112.927, 112.986)\n(113.052, 113.111)\n(113.604, 113.796)\n(114.161, 114.220)\n(114.588, 114.667)\n(115.269, 115.329)\n(115.597, 115.657)\n(116.249, 116.309)\n(116.378, 116.438)\n(116.594, 116.654)\n(116.969, 123.091)\n(123.134, 123.279)\n(123.570, 123.634)\n(124.136, 124.200)\n(124.552, 124.638)\n(125.244, 125.309)\n(125.563, 125.636)\n(126.213, 126.418)\n(126.559, 126.625)\n(127.461, 127.622)\n(127.874, 127.940)\n(128.552, 128.636)\n(129.534, 129.624)\n(129.678, 129.745)\n(129.934, 130.001)\n(130.545, 130.613)\n(130.786, 130.854)\n(130.918, 130.985)\n(131.195, 131.263)\n(131.542, 131.610)\n(131.895, 131.963)\n(132.538, 132.924)\n(133.003, 133.072)\n(133.297, 133.366)\n(133.535, 133.604)\n(134.111, 134.181)\n(134.516, 134.610)\n(135.220, 135.289)\n(135.528, 135.598)\n(136.177, 136.247)\n(136.328, 136.398)\n(136.525, 136.595)\n(137.436, 137.592)\n(137.838, 137.909)\n(138.518, 138.616)\n(139.498, 139.596)\n(139.653, 139.725)\n(140.511, 140.583)\n(140.761, 140.834)\n(141.159, 141.232)\n(141.507, 141.580)\n(141.870, 141.943)\n(142.078, 142.245)\n(142.504, 142.577)\n(142.820, 143.052)\n(143.500, 143.574)\n(144.087, 144.161)\n(144.405, 144.581)\n(145.195, 145.270)\n(146.141, 146.217)\n(146.303, 146.575)\n(147.412, 147.488)\n(147.802, 147.878)\n(148.520, 148.597)\n(149.463, 149.566)\n(149.628, 149.706)\n(149.809, 149.886)\n(150.737, 150.814)\n(151.123, 151.201)\n(151.550, 151.728)\n(151.845, 151.923)\n(152.784, 152.863)\n(152.953, 153.032)\n(153.475, 153.555)\n(154.062, 154.141)\n(154.445, 154.552)\n(155.170, 155.250)\n(155.513, 155.594)\n(156.105, 156.186)\n(156.279, 156.359)\n(157.387, 157.468)\n(157.766, 157.847)\n(158.495, 158.577)\n(159.427, 159.686)\n(160.451, 160.535)\n(160.712, 160.795)\n(161.021, 161.211)\n(161.820, 161.904)\n(162.748, 162.832)\n(162.929, 163.013)\n(164.037, 164.122)\n(164.409, 164.523)\n(165.145, 165.231)\n(165.757, 165.954)\n(166.070, 166.155)\n(166.254, 166.339)\n(166.621, 166.707)\n(167.362, 167.515)\n(167.730, 167.817)\n(168.470, 168.557)\n(169.391, 169.666)\n(169.984, 170.071)\n(170.493, 170.775)\n(171.052, 171.140)\n(171.796, 171.884)\n(172.712, 172.801)\n(172.904, 172.993)\n(174.012, 174.102)\n(174.373, 174.494)\n(175.121, 175.211)\n(176.034, 176.125)\n(176.229, 176.320)\n(176.954, 183.046)\n(183.988, 184.082)\n(184.337, 184.465)\n(185.096, 185.191)\n(185.998, 186.094)\n(186.204, 186.300)\n(187.313, 187.409)\n(187.659, 187.755)\n(188.356, 188.518)\n(188.838, 188.935)\n(189.319, 189.660)\n(190.638, 190.736)\n(190.980, 191.078)\n(191.746, 191.845)\n(192.641, 192.740)\n(192.854, 192.954)\n(193.963, 194.063)\n(194.302, 194.436)\n(195.071, 195.172)\n(195.332, 195.434)\n(195.962, 196.063)\n(196.179, 196.280)\n(197.288, 197.389)\n(197.623, 197.725)\n(198.396, 198.498)\n(198.909, 199.143)\n(199.284, 199.421)\n(199.505, 199.607)\n(199.945, 200.049)\n(200.613, 200.716)\n(200.944, 201.048)\n(201.721, 201.825)\n(202.605, 202.709)\n(202.830, 202.934)\n(203.938, 204.043)\n(204.266, 204.407)\n(205.046, 205.152)\n(205.926, 206.032)\n(206.155, 206.261)\n(207.263, 207.370)\n(207.587, 207.694)\n(208.371, 208.626)\n(209.248, 209.588)\n(209.733, 209.841)\n(210.588, 210.697)\n(210.909, 211.017)\n(211.697, 211.805)\n(212.569, 212.679)\n(212.805, 212.914)\n(213.913, 214.023)\n(214.230, 214.378)\n(215.022, 215.132)\n(215.891, 216.002)\n(216.130, 216.241)\n(217.238, 217.350)\n(217.551, 217.663)\n(217.853, 218.109)\n(218.347, 218.459)\n(219.212, 219.363)\n(219.455, 219.568)\n(220.563, 220.677)\n(220.873, 220.986)\n(221.672, 221.786)\n(222.533, 222.648)\n(222.780, 222.895)\n(223.889, 224.004)\n(224.194, 224.349)\n(224.997, 225.113)\n(225.855, 225.971)\n(226.105, 226.222)\n(227.214, 227.633)\n(228.322, 228.439)\n(229.176, 229.335)\n(229.430, 229.548)\n(229.907, 230.025)\n(230.539, 230.657)\n(230.837, 230.956)\n(231.647, 231.766)\n(232.498, 232.617)\n(232.755, 232.875)\n(233.864, 233.984)\n(234.158, 234.320)\n(234.972, 235.093)\n(235.819, 235.940)\n(236.080, 236.202)\n(236.796, 243.061)\n(243.839, 243.964)\n(244.123, 244.291)\n(244.947, 245.073)\n(245.783, 245.910)\n(246.056, 246.182)\n(246.268, 246.559)\n(247.164, 247.291)\n(247.444, 247.571)\n(248.272, 248.400)\n(249.105, 249.277)\n(249.381, 249.509)\n(250.489, 250.618)\n(250.765, 250.894)\n(251.598, 251.727)\n(252.426, 252.556)\n(252.706, 252.836)\n(253.814, 253.945)\n(254.087, 254.262)\n(254.923, 255.054)\n(255.740, 256.163)\n(257.139, 257.272)\n(257.408, 257.540)\n(258.248, 258.380)\n(259.069, 259.248)\n(259.356, 259.489)\n(260.464, 260.598)\n(260.729, 260.864)\n(261.573, 261.707)\n(262.390, 262.525)\n(262.681, 262.816)\n(263.789, 263.925)\n(264.051, 264.233)\n(264.898, 265.034)\n(265.212, 265.525)\n(265.712, 265.848)\n(266.006, 266.143)\n(267.115, 267.510)\n(268.223, 268.361)\n(269.033, 269.219)\n(269.331, 269.470)\n(269.656, 269.795)\n(269.956, 270.095)\n(270.440, 270.579)\n(270.694, 270.833)\n(271.548, 271.688)\n(272.354, 272.494)\n(272.656, 272.797)\n(273.765, 273.905)\n(274.015, 274.204)\n(274.684, 275.014)\n(275.676, 275.817)\n(275.981, 276.123)\n(277.090, 277.232)\n(277.336, 277.479)\n(278.198, 278.341)\n(278.997, 279.190)\n(279.307, 279.450)\n(280.415, 280.559)\n(280.658, 280.802)\n(281.523, 281.668)\n(282.319, 282.464)\n(282.632, 282.777)\n(283.208, 283.513)\n(283.740, 284.491)\n(284.848, 284.995)\n(285.640, 285.787)\n(285.957, 286.104)\n(287.065, 287.213)\n(287.301, 287.448)\n(288.173, 288.321)\n(288.961, 289.161)\n(289.282, 289.430)\n(290.390, 290.771)\n(291.498, 291.648)\n(292.283, 292.433)\n(292.607, 292.757)\n(293.627, 294.146)\n(294.824, 294.975)\n(295.604, 295.756)\n(295.932, 296.084)\n(296.923, 303.522)\n(303.690, 303.846)\n(303.908, 304.117)\n(304.799, 304.955)\n(305.568, 305.725)\n(305.852, 306.568)\n(307.016, 307.690)\n(308.124, 308.282)\n(308.890, 309.103)\n(309.232, 309.391)\n(310.341, 310.710)\n(311.449, 311.609)\n(312.211, 312.372)\n(312.557, 312.940)\n(313.666, 314.088)\n(314.637, 315.474)\n(315.533, 315.695)\n(315.882, 316.045)\n(316.991, 317.356)\n(318.099, 318.263)\n(318.854, 319.074)\n(319.207, 319.371)\n(320.316, 320.480)\n(320.515, 320.679)\n(321.424, 321.589)\n(322.043, 322.423)\n(322.533, 322.698)\n(323.641, 324.060)\n(324.749, 324.916)\n(325.497, 325.664)\n(325.858, 326.025)\n(326.966, 327.326)\n(328.074, 328.243)\n(328.818, 329.045)\n(329.183, 329.352)\n(329.580, 329.750)\n(329.880, 330.049)\n(330.291, 330.649)\n(331.399, 331.907)\n(332.140, 332.310)\n(332.508, 332.679)\n(333.616, 334.031)\n(334.725, 334.896)\n(335.461, 335.633)\n(335.833, 336.005)\n(336.941, 337.295)\n(338.050, 338.223)\n(338.782, 339.016)\n(339.158, 339.332)\nTABLE VI. Vetoed frequency ranges due to known instrumental artifacts.\n\nAll-sky search for continuous gravitational-wave signals from unknown neutron stars\nin binary systems in the first part of the fourth LIGO-Virgo-KAGRA observing run\nA. G. Abac\n,1 I. Abouelfettouh,2 F. Acernese,3, 4 K. Ackley\n,5 C. Adamcewicz\n,6 S. Adhicary\n,7\nD. Adhikari,8, 9 N. Adhikari\n,10 R. X. Adhikari\n,11 V. K. Adkins,12 S. Afroz\n,13 A. Agapito,14 D. Agarwal\n,15\nM. Agathos\n,16 N. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar\n,19 I.-L. Ahrend,20 L. Aiello\n,21, 22 A. Ain\n,23\nP. Ajith\n,24 T. Akutsu\n,25, 26 S. Albanesi\n,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9 C. All\u00b4en\u00b4e,31 A. Allocca\n,32, 4\nS. Al-Shammari,33 P. A. Altin\n,34 S. Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37\nF. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41\nM. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9 J. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49\nS. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11 S. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42\nM. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,55\nN. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 G. Ashton\n,58 Y. Aso\n,25, 59 L. Asprea,28 M. Assiduo,60, 61\nS. Assis de Souza Melo,62 S. M. Aston,63 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,64 K. AultONeal\n,65\nG. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51\nM. Ball,77 G. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12\nP. Baral\n,10 M. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84\nF. Barone\n,85, 4 B. Barr\n,86 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86\nI. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86\nA. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95\nD. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96 L. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97\nM. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33 B. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11\nD. Bersanetti\n,29 T. Bertheas,100 A. Bertolini,37, 36 J. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101\nN. Bevins\n,102 R. Bhandare,103 R. Bhatt,11 D. Bhattacharjee\n,104, 105 S. Bhattacharyya,106 S. Bhaumik\n,46\nV. Biancalana\n,101 A. Bianchi,37, 107 I. A. Bilenko,108 G. Billingsley\n,11 A. Binetti\n,109 S. Bini\n,11, 74, 75\nC. Binu,110 S. Biot,111 O. Birnholtz\n,112 S. Biscoveanu\n,96 A. Bisht,9 M. Bitossi\n,62, 80 M.-A. Bizouard\n,113\nS. Blaber,114 J. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72 N. Bode\n,8, 9 N. Boettner,97\nG. Boileau\n,113 M. Boldrini\n,38 G. N. Bolingbroke\n,115 A. Bolliand,116, 40 L. D. Bonavena\n,46 R. Bondarescu\n,82\nF. Bondu\n,117 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,118 R. Bonnand\n,31, 116 A. Borchers,8, 9 V. Boschi\n,80\nS. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 107 A. Boudon,56 L. Bourg,57 M. Boyle,120 A. Bozzi,62 C. Bradaschia,80\nP. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,104 T. Briant\n,121 A. Brillet,113 M. Brinkmann,8, 9\nP. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,115 M. L. Brozzetti\n,76, 51\nS. Brunett,11 G. Bruno,15 R. Bruntz\n,122 J. Bryant,118 Y. Bu,123 F. Bucci\n,61 J. Buchanan,122\nO. Bulashenko\n,82, 83 T. Bulik,124 H. J. Bulten,37 A. Buonanno\n,125, 1 K. Burtnyk,2 R. Buscicchio\n,126, 127\nD. Buskulic,31 C. Buy\n,100 R. L. Byer,89 G. S. Cabourn Davies\n,73 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7\nL. Cadonati\n,57 G. Cagnoli\n,128 C. Cahillane\n,78 A. Calafat,98 T. A. Callister,129 E. Calloni,32, 4 S. R. Callos\n,77\nM. Canepa,30, 29 G. Caneva Santoro\n,43 K. C. Cannon\n,42 H. Cao,35 L. A. Capistran,130 E. Capocasa\n,20\nE. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 131 F. Carbognani,62 M. Carlassara,8, 9 J. B. Carlin\n,123\nT. K. Carlson,132 M. F. Carney,104 M. Carpinelli\n,126, 62 G. Carrillo,77 J. J. Carter\n,8, 9 G. Carullo\n,118, 133\nA. Casallas-Lagos,134 J. Casanueva Diaz\n,62 C. Casentini\n,135, 22 S. Y. Castro-Lucas,136 S. Caudill,132\nM. Cavagli`a\n,105 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,137, 138 E. Cesarini\n,22 N. Chabbra,34\nW. Chaibi,113 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,103 S. Chalathadka Subrahmanya\n,97\nJ. C. L. Chan\n,139 M. Chan,114 K. Chang,140 S. Chao\n,141, 140 P. Charlton\n,142 E. Chassande-Mottin\n,20\nC. Chatterjee\n,143 Debarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,103 S. Chaty\n,20 A. Chen\n,144\nA. H.-Y. Chen,145 D. Chen\n,146 H. Chen,141 H. Y. Chen\n,147 S. Chen,143 Yanbei Chen,148 Yitian Chen\n,120\nH. P. Cheng,149 P. Chessa\n,76, 51 H. T. Cheung\n,90 S. Y. Cheung,6 F. Chiadini\n,150, 131 G. Chiarini,8, 9, 92\nA. Chiba,151 A. Chincarini\n,29 M. L. Chiofalo\n,81, 80 A. Chiummo\n,4, 62 C. Chou,145 S. Choudhary\n,72\nN. Christensen\n,113, 152 S. S. Y. Chua\n,34 G. Ciani\n,74, 75 P. Ciecielag\n,95 M. Cie\u00b4slar\n,124 M. Cifaldi\n,22\nB. Cirok,153 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6 P. Clearwater,154 S. Clesse,111 F. Cleva,113, 116\nE. Coccia,44, 45, 43 E. Codazzo\n,155, 156 P.-F. Cohadon\n,121 S. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98\nC. G. Collette,157 J. Collins,63 S. Colloms\n,86 A. Colombo\n,158, 127 C. M. Compton,2 G. Connolly,77\nL. Conti\n,92 T. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,159 S. Corezzi\n,76, 51 N. J. Cornish\n,160 I. Coronado,161\n\n26\nA. Corsi\n,162 R. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 57 D. M. Coward,72\nR. Coyne\n,163 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,164 P. Cremonese\n,98 S. Crook,63\nR. Crouch,2 J. Csizmazia,2 J. R. Cudell\n,165 T. J. Cullen\n,11 A. Cumming\n,86 E. Cuoco\n,166, 167\nM. Cusinato\n,137 L. V. Da Concei\u00b8c\u02dcao\n,168 T. Dal Canton\n,41 S. Dal Pra\n,169 S. Dall\u2019Osso\n,170, 171\nG. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,122\nL. P. Dartez\n,63 R. Das,106 A. Dasgupta,93 V. Dattilo\n,62 A. Daumas,20 N. Davari,172, 173 I. Dave,103\nA. Davenport,136 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72 M. C. Davis\n,18 P. Davis\n,174, 175\nE. J. Daw\n,176 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,177 M. De Laurentis\n,32, 4\nF. De Lillo\n,23 S. Della Torre\n,127 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,178, 61\nF. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,179 A. Depasse\n,15 N. DePergola,102 R. De Pietri\n,180, 181\nR. De Rosa\n,32, 4 C. De Rossi\n,62 M. Desai\n,35 R. DeSalvo\n,182 A. DeSimone,183 R. De Simone,150, 131\nA. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,164 M. Di Cesare\n,32, 4 G. Dideron,184 T. Dietrich\n,1 L. Di Fiore,4\nC. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 185 S. Di Pace\n,39, 38\nI. Di Palma\n,39, 38 D. Di Piero,186, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,118 J. P. Docherty,86\nZ. Doctor\n,96 N. Doerksen\n,168 E. Dohmen,2 A. Doke,132 A. Domiciano De Souza,187 L. D\u2019Onofrio\n,38\nF. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,188 W. J. D. Doyle,122 M. Drago\n,39, 38\nJ. C. Driggers\n,2 L. Dunn\n,123 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,172, 155 P. Dutta Roy\n,46\nH. Duval\n,189 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,190, 31 T. Eckhardt\n,97 G. Eddolls\n,78 A. Effler\n,63\nJ. Eichholz\n,34 H. Einsle,113 M. Eisenmann,25 M. Emma\n,58 K. Endo,151 R. Enficiaud\n,1 L. Errico\n,32, 4\nR. Espinosa,164 M. Esposito\n,4, 32 R. C. Essick\n,191 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,184\nB. E. Ewing,7 J. M. Ezquiaga\n,139 F. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,129\nB. Farr\n,77 W. M. Farr\n,192, 193 G. Favaro\n,91 M. Favata\n,194 M. Fays\n,165 M. Fazio\n,55 J. Feicht,11\nM. M. Fejer,89 R. Felicetti\n,186, 48 E. Fenyvesi\n,87, 195 J. Fernandes,196 T. Fernandes\n,197, 137 D. Fernando,110\nS. Ferraiuolo\n,198, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 A. Fiori\n,80, 81 I. Fiori\n,62\nM. Fishbach\n,191 R. P. Fisher,122 R. Fittipaldi\n,199, 131 V. Fiumara\n,200, 131 R. Flaminio,31 S. M. Fleischer\n,201\nL. S. Fleming,202 E. Floden,18 H. Fong,114 J. A. Font\n,137, 138 F. Fontinele-Nunes,18 C. Foo,1 B. Fornal\n,203\nK. Franceschetti,180 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,204 A. Freise\n,37, 107\nO. Freitas\n,197, 137 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,205 T. Fujimori,206 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1\nS. Galaudage\n,187 V. Galdi,207 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,182 D. Ganapathy\n,208 A. Ganguly\n,79\nB. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,209 C. Garc\u00b4\u0131a-Quir\u00b4os\n,190 J. W. Gardner\n,34 K. A. Gardner,114 S. Garg,42\nJ. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98 F. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,210 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29 A. Gennai\n,80 V. Gennari\n,100\nJ. George,103 R. George\n,147 O. Gerberding\n,97 L. Gergely\n,153 Archisman Ghosh\n,94 Sayantan Ghosh,196\nShaon Ghosh\n,194 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,211 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63\nK. D. Giardina,63 D. R. Gibson,202 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,114 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00b4alez\n,12 P. Goodarzi\n,212 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18\nM. Granata\n,177 V. Granata\n,213, 131 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,86 G. Greco,51\nA. C. Green\n,37, 107 L. Green,214 S. M. Green,73 S. R. Green\n,215 C. Greenberg,132 A. M. Gretarsson,65\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,137 D. Guetta\n,216 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,174, 175\nH. Guo\n,144 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,217 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,97 N. Gutierrez,177 N. Guttman,6 F. Guzman\n,130 D. Haba,218 M. Haberland\n,1\nS. Haino,219 E. D. Hall\n,35 E. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,220 A. G. Hanselman\n,129 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,183 S. Harikumar\n,188 K. Haris,37, 71 I. Harley-Trochimczyk,130 T. Harmark\n,133\nJ. Harms\n,44, 45 G. M. Harry\n,221 I. W. Harry\n,73 J. Hart,104 B. Haskell,95, 222, 223 C. J. Haster\n,214\nK. Haughian\n,86 H. Hayakawa,50 K. Hayama,224 M. C. Heintze,63 J. Heinze\n,118 J. Heinzel,35 H. Heitmann\n,113\nF. Hellman\n,208 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,115 M. Hendry\n,86\nI. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,225, 226 J. Heynen,15\nJ. Heyns,35 S. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,227 N. Hirata,25 C. Hirose,228\n\n27\nD. Hofman,177 B. E. Hogan,65 N. A. Holland,37, 107 I. J. Hollows\n,176 D. E. Holz\n,129 L. Honet,111\nD. J. Horton-Bailey,208 J. Hough\n,86 S. Hourihane\n,11 N. T. Howard,143 E. J. Howell\n,72 C. G. Hoy\n,73\nC. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,141 H.-Y. Hsieh,141 C. Hsiung,229 S.-H. Hsu,145 W.-F. Hsu\n,109\nQ. Hu\n,86 H. Y. Huang\n,140 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,230 B. Hughey,65 V. Hui\n,31\nS. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,131 J. Iascau,77\nK. Ide,231 R. Iden,218 A. Ierardi,44, 45 S. Ikeda,146 H. Imafuku,42 Y. Inoue,140 G. Iorio\n,91 P. Iosif\n,186, 48\nM. H. Iqbal,34 J. Irwin\n,86 R. Ishikawa,231 M. Isi\n,192, 193 K. S. Isleif\n,232 Y. Itoh\n,206, 233 M. Iwaya,205\nB. R. Iyer\n,24 C. Jacquet,100 P.-E. Jacquet\n,121 T. Jacquot,41 S. J. Jadhav,234 S. P. Jadhav\n,154 M. Jain,132\nT. Jain,225 A. L. James\n,11 K. Jani\n,143 J. Janquart\n,15 N. N. Janthalur,234 S. Jaraba\n,235 P. Jaranowski\n,236\nR. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2 W. Jia,35 J. Jiang\n,149 H.-B. Jin\n,237, 238 G. R. Johns,122\nN. A. Johnson,46 M. C. Johnston\n,214 R. Johnston,86 N. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,211 R. Jones,86\nH. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,239 L. Ju\n,72 K. Jung\n,240 J. Junker\n,34\nV. Juste,111 H. B. Kabagoz\n,63, 35 T. Kajita\n,241 I. Kaku,206 V. Kalogera\n,96 M. Kalomenopoulos\n,214\nM. Kamiizumi\n,50 N. Kanda\n,233, 206 S. Kandhasamy\n,79 G. Kang\n,242 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,132 M. Kasprzack\n,11 H. Kato,151\nT. Kato,205 E. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,103 K. Kawabe,2 R. Kawamoto,206 D. Keitel\n,98\nL. J. Kemperman\n,115 J. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,243 R. Khadela,8, 9\nS. Khadka,89 S. S. Khadkikar,7 F. Y. Khalili\n,108 F. Khan\n,8, 9 T. Khanam,162 M. Khursheed,103\nN. M. Khusid,192, 193 W. Kiendrebeogo\n,113, 244 N. Kijbunchoo\n,115 C. Kim,245 J. C. Kim,246 K. Kim\n,247\nM. H. Kim\n,239 S. Kim\n,248 Y.-M. Kim\n,247 C. Kimball\n,96 K. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2\nS. Klimenko,46 A. M. Knee\n,114 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,205 S. M. Koehlenbeck\n,89\nG. Koekoek,37, 36 K. Kohri\n,249, 250 K. Kokeyama\n,33, 251 S. Koley\n,44, 165 P. Kolitsidou\n,118 A. E. Koloniari\n,252\nK. Komori\n,42 A. K. H. Kong\n,141 A. Kontos\n,253 L. M. Koponen,118 M. Korobko\n,97 X. Kou,18 A. Koushik\n,23\nN. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,151 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,118 S. Kroker,254 A. Kr\u00b4olak\n,255, 188 K. Kruska,8, 9 J. Kubisz\n,256 G. Kuehn,8, 9\nS. Kulkarni\n,217 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,234 Praveen Kumar\n,179\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,93 J. Kume\n,257, 258, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,209, 259 S. Kuwahara\n,42 K. Kwak\n,240 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,190, 100\nA. H. Laity,163 E. Lalande,260 M. Lalleman\n,23 P. C. Lalremruati,261 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,147 R. Langgin\n,214 B. Lantz\n,89 I. La Rosa\n,98 J. Larsen,201 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,164 M. Laxen\n,63 C. Lazarte\n,137 A. Lazzarini\n,11 C. Lazzaro,156, 155 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,114 H. M. Lee\n,262 H. W. Lee\n,263 J. Lee,78 K. Lee\n,239 R.-K. Lee\n,141 R. Lee,35\nSungho Lee\n,247 Sunjae Lee,239 Y. Lee,140 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,184 M. Le Jean\n,177, 116\nA. Lema\u02c6\u0131tre\n,264 M. Lenti\n,61, 178 M. Leonardi\n,74, 75, 265 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11\nN. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,266 T. G. F. Li,109 X. Li\n,148\nY. Li,96 Z. Li,86 A. Lihos,122 E. T. Lin\n,141 F. Lin,140 L. C.-C. Lin\n,266 Y.-C. Lin\n,141 C. Lindsay,202\nS. D. Linker,182 A. Liu\n,220 G. C. Liu\n,229 Jian Liu\n,72 F. Llamas Villarreal,164 J. Llobera-Querol\n,98\nR. K. L. Lo\n,139 J.-P. Locquet,109 S. C. G. Loggins,267 M. R. Loizou,132 L. T. London,67 A. Longo\n,60, 61\nD. Lopez\n,165 M. Lopez Portilla,71 M. Lorenzini\n,21, 22 A. Lorenzo-Medina\n,179 V. Loriette,41 M. Lormand,63\nG. Losurdo\n,268, 80 E. Lotti,132 T. P. Lott IV\n,57 J. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,110 N. Low,123\nN. Lu\n,34 L. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22 A. P. Lundgren\n,269, 270 A. W. Lussier\n,260 R. Macas\n,73\nM. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,151 S. Maenaut\n,109\nS. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 107 M. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,163\nS. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 D. Malakar\n,105 J. A. Malaquias-Reis,19 U. Mali\n,191\nS. Maliakal,11 A. Malik,103 L. Mallick\n,168, 191 A.-K. Malz\n,58 N. Man,113 M. Mancarella\n,99 V. Mandic\n,18\nV. Mangano\n,172, 155 B. Mannix,77 G. L. Mansell\n,78 M. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 271\nC. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89 A. Markowitz,11 E. Maros,11 S. Marsat\n,100\nF. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,194 B. B. Martinez,130 D. A. Martinez,54 M. Martinez,43, 272\nV. Martinez\n,128 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,118 E. J. Marx,35 L. Massaro,36, 37\nA. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,210\nN. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,122 C. McElhenny,122 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,143\nJ. McIver\n,114 A. McLeod\n,72 I. McMahon\n,190 T. McRae,34 R. McTeague\n,86 D. Meacher\n,10 B. N. Meagher,78\n\n28\nR. Mechum,110 Q. Meijer,71 A. Melatos,123 C. S. Menoni\n,136 F. Mera,2 R. A. Mercer\n,10 L. Mereni,177\nK. Merfeld,162 E. L. Merilh,63 J. R. M\u00b4erou\n,98 J. D. Merritt,77 M. Merzougui,113 C. Messick\n,10\nB. Mestichelli,44 M. Meyer-Conde\n,273 F. Meylahn\n,8, 9 A. Mhaske,79 A. Miani\n,74, 75 H. Miao,274\nC. Michel\n,177 Y. Michimura\n,42 H. Middleton\n,118 D. P. Mihaylov\n,104 A. L. Miller\n,37, 71 S. J. Miller\n,11\nM. Millhouse\n,57 E. Milotti\n,186, 48 V. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43\nL. Mirasola\n,155, 156 M. Miravet-Ten\u00b4es\n,137 C.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,106 T. Mishra\n,46\nA. L. Mitchell,37, 107 J. G. Mitchell,65 S. Mitra\n,79 V. P. Mitrofanov\n,108 K. Mitsuhashi,25 R. Mittleman,35\nO. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,65 G. Mo\n,35 L. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7\nM. Molina-Ruiz\n,208 M. Mondin,182 M. Montani,60, 61 C. J. Moore,225 D. Moraru,2 A. More\n,79 S. More\n,79\nC. Moreno\n,134 E. A. Moreno\n,35 G. Moreno,2 A. Moreso Serra,82 S. Morisaki\n,42, 205 Y. Moriwaki\n,151\nG. Morras\n,209 A. Moscatello\n,91 M. Mould\n,35 B. Mours\n,64 C. M. Mow-Lowry\n,37, 107 L. Muccillo\n,178, 61\nF. Muciaccia\n,39, 38 D. Mukherjee\n,118 Samanwaya Mukherjee,24 Soma Mukherjee,164 Subroto Mukherjee,93\nSuvodip Mukherjee\n,13 N. Mukund\n,35 A. Mullavey,63 H. Mullock,114 J. Mundi,221 C. L. Mungioli,72\nM. Murakoshi,231 P. G. Murray\n,86 D. Nabari\n,74, 75 S. L. Nadji,8, 9 A. Nagar,28, 275 N. Nagarajan\n,86\nK. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,276 M. Nakano,11 D. Nanadoumgar-Lacroze\n,43 D. Nandi,12\nV. Napolano,62 P. Narayan\n,217 I. Nardecchia\n,22 T. Narikawa,205 H. Narola,71 L. Naticchioni\n,38\nR. K. Nayak\n,261 L. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,130 T. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2\nS. Ng,54 L. Nguyen Quynh\n,277 S. A. Nichols,12 A. B. Nielsen\n,278 Y. Nishino,25, 42 A. Nishizawa\n,279\nS. Nissanke,280, 37 W. Niu\n,7 F. Nocera,62 J. Noller,281 M. Norman,33 C. North,33 J. Novak\n,116, 235, 282\nR. Nowicki\n,143 J. F. Nu\u02dcno Siles\n,209 L. K. Nuttall\n,73 K. Obayashi,231 J. Oberling\n,2 J. O\u2019Dell,230 E. Oelker\n,35\nM. Oertel\n,235, 116, 283, 282 G. Oganesyan,44, 45 T. O\u2019Hanlon,63 M. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,116, 283, 282\nR. Omer,18 B. O\u2019Neal,122 M. Onishi,151 K. Oohara\n,284 B. O\u2019Reilly\n,63 M. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,110\nS. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11 I. Ota\n,12 D. J. Ottaway\n,115 A. Ouzriat,56 H. Overmier,63\nB. J. Owen\n,285 R. Ozaki,231 A. E. Pace\n,7 R. Pagano\n,12 M. A. Page\n,25 A. Pai\n,196 L. Paiella,44 A. Pal,286\nS. Pal\n,261 M. A. Palaia\n,80, 81 M. P\u00b4alfi,204 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,141 J. Pan,72\nK. C. Pan\n,141 P. K. Panda,234 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38\nK. A. Pannone,54 B. C. Pant,103 F. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 287\nA. Papadopoulos\n,86 E. E. Papalexakis,212 L. Papalini\n,80, 81 G. Papigkiotis\n,252 A. Paquis,41 A. Parisi\n,76, 51\nB.-J. Park,247 J. Park\n,288 W. Parker\n,63 G. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80\nL. Passenger,6 D. Passuello,80 O. Patane\n,2 A. V. Patel\n,140 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80\nB. G. Patterson,33 K. Paul\n,106 S. Paul\n,77 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna\nArellano\n,289 X. Peng,118 Y. Peng,57 S. Penn\n,290 M. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,132\nC. P\u00b4erigois\n,291, 92, 91 G. Perna\n,91 A. Perreca\n,74, 75, 44 J. Perret\n,20 S. Perri`es\n,56 J. W. Perry,37, 107\nD. Pesios,252 S. Peters,165 S. Petracca,207 C. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63 K. A. Pham\n,18\nK. S. Phukon\n,118 H. Phurailatpam,220 M. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,113\nM. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,292, 131 M. Pietrzak,95\nM. Pillas\n,165 F. Pilo\n,80 L. Pinard\n,177 I. M. Pinto\n,292, 131, 293, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10\nM. Pirello,2 M. D. Pitkin\n,225, 86 A. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,213, 22\nC. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35 J. Pomper,80, 81 L. Pompili\n,1 J. Poon,220 E. Porcelli,37\nE. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62 J. Powell\n,154 G. S. Prabhu,79 M. Pracchia\n,165\nB. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93 K. Prasai\n,294 R. Prasanna,234 P. Prasia,79 G. Pratten\n,118\nG. Principe\n,186, 48 G. A. Prodi\n,74, 75 P. Prosperi,80 P. Prosposito,21, 22 A. C. Providence,65 A. Puecher\n,1\nJ. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,163 H. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,175, 116 V. Quetschke,164\nP. J. Quinonez,65 N. Qutob,57 R. Rading,232 I. Rainho,137 S. Raja,103 C. Rajan,103 B. Rajbhandari\n,110\nK. E. Ramirez\n,63 F. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,164 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57\nK. Ransom,63 P. Rapagnani\n,39, 38 B. Ratto,65 A. Ravichandran,132 A. Ray\n,96 V. Raymond\n,33\nM. Razzano\n,81, 80 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. I. Renzini\n,126, 11\nB. Revenu\n,295, 41 A. Revilla Pe\u02dcna,82 R. Reyes,182 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,212 M. L. Richardson,115 A. Rijal,65 K. Riles\n,90 H. K. Riley,33\nS. Rinaldi\n,271 J. Rittmeyer,97 C. Robertson,230 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,296 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,225 J. H. Romie,63\nS. Ronchini\n,7 T. J. Roocke\n,115 L. Rosa,4, 32 T. J. Rosauer,212 C. A. Rose,57 D. Rosi\u00b4nska\n,124 M. P. Ross\n,53\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,192, 193 S. Roy\n,15 D. Rozza\n,126, 127 P. Ruggi,62 N. Ruhama,240\n\n29\nE. Ruiz Morales\n,297, 209 K. Ruiz-Rocha,143 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 107 S. Safi-Harb\n,168\nM. R. Sah\n,13 S. Saha\n,141 T. Sainrat\n,64 S. Sajith Menon\n,216, 39, 38 K. Sakai,298 Y. Sakai\n,273\nM. Sakellariadou\n,67 S. Sakon\n,7 O. S. Salafia\n,158, 127, 126 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,147\nF. Salemi\n,39, 38 M. Sall\u00b4e\n,37 S. U. Salunkhe,79 S. Salvador\n,175, 174 A. Salvarese,147 A. Samajdar\n,71, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,137 J. R. Sanders,183 E. M. S\u00a8anger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,252 P. Sassi\n,51, 76\nB. Sassolas\n,177 R. Sato,228 S. Sato,151 Yukino Sato,151 Yu Sato,151 O. Sauter\n,46 R. L. Savage\n,2 T. Sawada\n,50\nH. L. Sawant,79 S. Sayah,177 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,148 A. Schiebelbein,191 M. G. Schiworski\n,78\nP. Schmidt\n,118 S. Schmidt\n,71 R. Schnabel\n,97 M. Schneewind,8, 9 R. M. S. Schofield,77 K. Schouteden\n,109\nB. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,299 M. Scialpi\n,300 J. Scott\n,86 S. M. Scott\n,34\nR. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,301 D. Sellers,63 N. Sembo,206\nA. S. Sengupta\n,302 E. G. Seo\n,86 J. W. Seo\n,109 V. Sequino,32, 4 M. Serra\n,38 A. Sevrin,189 T. Shaffer,2\nU. S. Shah\n,57 M. A. Shaikh\n,262 L. Shao\n,303 A. K. Sharma\n,98 Preeti Sharma,12 Prianka Sharma,103\nRitwik Sharma,18 S. Sharma Chaudhary,105 P. Shawhan\n,125 N. S. Shcheblanov\n,304, 264 E. Sheridan,143\nZ.-H. Shi,141 M. Shikauchi,42 R. Shimomura,305 H. Shinkai\n,305 S. Shirke,79 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,147 R. W. Short,2 S. ShyamSundar,103 A. Sider,157 H. Siegel\n,192, 193 D. Sigg\n,2\nL. Silenzi\n,36, 37 L. Silvestri\n,39, 169 M. Simmonds,115 L. P. Singer\n,306 Amitesh Singh,217 Anika Singh,11\nD. Singh\n,208 N. Singh\n,98 S. Singh,218, 59 A. M. Sintes\n,98 V. Sipala,172, 155 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,201 T. J. Slaven-Blair,72 J. Smetana,118 J. R. Smith\n,54 L. Smith\n,86, 186, 48 R. J. E. Smith\n,6\nW. J. Smith\n,143 S. Soares de Albuquerque Filho,60 M. Soares-Santos,190 K. Somiya\n,218 I. Song\n,141 S. Soni\n,35\nV. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,307 F. Spada\n,80 V. Spagnuolo\n,37 A. P. Spencer\n,86 P. Spinicelli\n,62\nA. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,122 D. A. Steer\n,308 N. Steinle\n,168 J. Steinlechner,36, 37\nS. Steinlechner\n,36, 37 N. Stergioulas\n,252 P. Stevens,41 M. StPierre,163 M. D. Strong,12 A. Strunk,2\nA. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,231 N. Sueltmann,97 L. Suleiman\n,54 K. D. Sullivan,12\nJ. Sun\n,242 L. Sun\n,34 S. Sunil,93 J. Suresh\n,113 B. J. Sutton,67 P. J. Sutton\n,33 K. Suzuki,218 M. Suzuki,205\nB. L. Swinkels\n,37 A. Syx\n,116 M. J. Szczepa\u00b4nczyk\n,309 P. Szewczyk\n,124 M. Tacca\n,37 H. Tagoshi\n,205\nK. Takada,205 H. Takahashi\n,273 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,310 H. Takeda\n,311, 312\nK. Takeshita,218 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,129 M. Tamaki,205 N. Tamanini\n,100\nD. Tanabe,140 K. Tanaka,50 S. J. Tanaka\n,231 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,212\nR. D. Tapia,7 E. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,313 J. D. Tasson\n,152 J. G. Tau\n,110\nD. Tellez,54 R. Tenorio\n,98 H. Themann,182 A. Theodoropoulos\n,137 M. P. Thirugnanasambandam,79\nL. M. Thomas\n,11 M. Thomas,63 P. Thomas,2 J. E. Thompson\n,211 S. R. Thondapu,103 K. A. Thorne,63\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,196 S. Tiwari\n,190 V. Tiwari\n,118\nM. R. Todd,78 M. Toffano,91 A. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,140 A. Torres-Forn\u00b4e\n,137, 138 C. I. Torrie,11 I. Tosta e Melo\n,314\nE. Tournefier\n,31 M. Trad Nery,113 K. Tran,122 A. Trapananti\n,52, 51 R. Travaglini\n,167 F. Travasso\n,52, 51\nG. Traylor,63 M. Trevor,125 M. C. Tringali\n,62 A. Tripathee\n,90 G. Troian\n,186, 48 A. Trovato\n,186, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,315 L. Tsukada\n,214 K. Turbang\n,189, 23 M. Turconi\n,113\nC. Turski,94 H. Ubach\n,82, 83 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,316 K. Ueno\n,42 V. Undheim\n,278\nL. E. Uronen,220 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9 N. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6\nJ. Valencia\n,98 M. Valentini\n,107, 37 S. A. Vallejo-Pe\u02dcna\n,296 S. Vallero,28 V. Valsan\n,10 M. van Dael\n,37, 317\nE. Van den Bossche\n,189 J. F. J. van den Brand\n,36, 107, 37 C. Van Den Broeck,71, 37 M. van der Sluys\n,37, 71\nA. Van de Walle,41 J. van Dongen\n,37, 107 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 107 P. Van Hove\n,64 J. Vanier,260 M. VanKeuren,104 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,123 V. Varma\n,132 A. N. Vazquez,89 A. Vecchio\n,118 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,115 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,132\nY. Verma\n,103 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78\nA. D. Viets\n,88 A. Vijaykumar\n,191 A. Vilkha,110 N. Villanueva Espinosa,137 V. Villa-Ortega\n,179\nE. T. Vincent\n,57 J.-Y. Vinet,113 S. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,232 L. Vujeva\n,139 S. P. Vyatchanin\n,108 J. Wack,11 L. E. Wade,104\nM. Wade\n,104 K. J. Wagner\n,110 L. Wallace,11 E. J. Wang,89 H. Wang\n,218 J. Z. Wang,90 W. H. Wang,164\nY. F. Wang\n,1 G. Waratkar\n,196 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,72\n\n30\nK. Wette\n,34 J. T. Whelan\n,110 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,73 D. Wilken\n,8, 9, 9\nA. T. Wilkin,212 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1 J. L. Willis\n,11\nB. Willke\n,9, 8, 9 M. Wils\n,109 L. Wilson,104 C. W. Winborn,105 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,140 I. C. F. Wong\n,220, 109 K. Wong,191 T. Wouters,71, 37\nJ. L. Wright,2 M. Wright\n,86, 71 B. Wu,78 C. Wu\n,141 D. S. Wu\n,8, 9 H. Wu\n,141 K. Wu,119 Q. Wu,53 Y. Wu,96\nZ. Wu\n,100 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,208 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,151 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,231 T. Yan,118 K. Z. Yang\n,18\nY. Yang\n,145 Z. Yarbrough\n,12 J. Yebana,98 S.-W. Yeh,141 A. B. Yelikar\n,143 X. Yin,35 J. Yokoyama\n,318, 42\nT. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50 M. Zanolin,65 M. Zeeshan\n,110 T. Zelenova,62 J.-P. Zendri,92\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57 R. Zhang\n,149 T. Zhang,118 C. Zhao\n,72\nYue Zhao,161 Yuhang Zhao,20 Z.-C. Zhao\n,319 Y. Zheng\n,105 H. Zhong\n,18 H. Zhou,78 H. O. Zhu,72\nZ.-H. Zhu\n,319, 320 A. B. Zimmerman\n,147 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n\n31\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n\n32\n102Villanova University, Villanova, PA 19085, USA\n103RRCAT, Indore, Madhya Pradesh 452013, India\n104Kenyon College, Gambier, OH 43022, USA\n105Missouri University of Science and Technology, Rolla, MO 65409, USA\n106Indian Institute of Technology Madras, Chennai 600036, India\n107Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n108Lomonosov Moscow State University, Moscow 119991, Russia\n109Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n110Rochester Institute of Technology, Rochester, NY 14623, USA\n111Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n112Bar-Ilan University, Ramat Gan, 5290002, Israel\n113Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n114University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n115OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n116Centre national de la recherche scientifique, 75016 Paris, France\n117Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n118University of Birmingham, Birmingham B15 2TT, United Kingdom\n119Washington State University, Pullman, WA 99164, USA\n120Cornell University, Ithaca, NY 14850, USA\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n128Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n129University of Chicago, Chicago, IL 60637, USA\n130University of Arizona, Tucson, AZ 85721, USA\n131INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n132University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n133Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n134Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n135Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n136Colorado State University, Fort Collins, CO 80523, USA\n137Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n138Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n139Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n140National Central University, Taoyuan City 320317, Taiwan\n141National Tsing Hua University, Hsinchu City 30013, Taiwan\n142OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n143Vanderbilt University, Nashville, TN 37235, USA\n144University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n145Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n146Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n147University of Texas, Austin, TX 78712, USA\n148CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n149Northeastern University, Boston, MA 02115, USA\n150Dipartimento di Ingegneria Industriale (DIIN),\nUniversit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n151Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n152Carleton College, Northfield, MN 55057, USA\n153University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n154OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n155INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n156Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n157Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n158INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n159Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n160Montana State University, Bozeman, MT 59717, USA\n\n33\n161The University of Utah, Salt Lake City, UT 84112, USA\n162Johns Hopkins University, Baltimore, MD 21218, USA\n163University of Rhode Island, Kingston, RI 02881, USA\n164The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n165Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n166DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n167Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n168University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n169INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n170Dipartimento di Fisica e Astronomia, Alma Mater Studiorum -\nUniversit`a di Bologna, Via Piero Gobetti 93/2 - 40129 Bologna, Italy\n171Istituto Nazionale di Fisica Nucleare, sede di Bologna,\nviale C. Berti-Pichat 6/2 - 40127 Bologna, Italy\n172Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n173INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n174Universit\u00b4e de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n175Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n176The University of Sheffield, Sheffield S10 2TN, United Kingdom\n177Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n178Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n179IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n180Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n181INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n182California State University, Los Angeles, Los Angeles, CA 90032, USA\n183Marquette University, Milwaukee, WI 53233, USA\n184Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n185Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n186Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n187Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n188National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n189Vrije Universiteit Brussel, 1050 Brussel, Belgium\n190University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n191Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n192Stony Brook University, Stony Brook, NY 11794, USA\n193Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n194Montclair State University, Montclair, NJ 07043, USA\n195HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n196Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n197Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n198Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n199CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n200Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n201Western Washington University, Bellingham, WA 98225, USA\n202SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n203Barry University, Miami Shores, FL 33168, USA\n204E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n205Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n206Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n207University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n208University of California, Berkeley, CA 94720, USA\n209Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n210Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212University of California, Riverside, Riverside, CA 92521, USA\n\n34\n213Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n214University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n215University of Nottingham NG7 2RD, UK\n216Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n217The University of Mississippi, University, MS 38677, USA\n218Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n219Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n220The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n221American University, Washington, DC 20016, USA\n222Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n223INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n224Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n225University of Cambridge, Cambridge CB2 1TN, United Kingdom\n226University of Lancaster, Lancaster LA1 4YW, United Kingdom\n227College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n228Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n229Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n230Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n231Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n232Helmut Schmidt University, D-22043 Hamburg, Germany\n233Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n236Faculty of Physics, University of Bia lystok, 15-245 Bia lystok, Poland\n237National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n238School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n241Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n242Chung-Ang University, Seoul 06974, Republic of Korea\n243University of Washington Bothell, Bothell, WA 98011, USA\n244Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n245Ewha Womans University, Seoul 03760, Republic of Korea\n246National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n247Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n248Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n249Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n250Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n251Nagoya University, Nagoya, 464-8601, Japan\n252Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n253Bard College, Annandale-On-Hudson, NY 12504, USA\n254Technical University of Braunschweig, D-38106 Braunschweig, Germany\n255Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n256Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n257Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n258Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n\n35\n259Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n260Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n261Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n262Seoul National University, Seoul 08826, Republic of Korea\n263Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n264NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n265Gravitational Wave Science Project, National Astronomical\nObservatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n266Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n270Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n276Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n277Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n278University of Stavanger, 4021 Stavanger, Norway\n279Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n280GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n281University College London, London WC1E 6BT, United Kingdom\n282Observatoire de Paris, 75014 Paris, France\n283Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n284Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n285University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n286CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n287Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n288Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n289Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n290Hobart and William Smith Colleges, Geneva, NY 14456, USA\n291INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n292Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n293Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n294Kennesaw State University, Kennesaw, GA 30144, USA\n295Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00b4EDEX 03, France\n296Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n297Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n298Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n299Trinity College, Hartford, CT 06106, USA\n300Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n301Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n302Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n303Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n\n36\n304Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n305Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n306NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n307Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n308Laboratoire de Physique de l\u2019\u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n309Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n310Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n311The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n312Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n314University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n315National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n316Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n317Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n318Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n319Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n320School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n(Dated: December 5, 2025)\n\u2217Deceased, September 2024.\n", "GW250114: Testing Hawking\u2019s Area Law and the Kerr Nature of Black Holes\nA. G. Abac\n,1 I. Abouelfettouh,2 F. Acernese,3, 4 K. Ackley\n,5 C. Adamcewicz\n,6 S. Adhicary\n,7 D. Adhikari,8, 9\nN. Adhikari\n,10 R. X. Adhikari\n,11 V. K. Adkins,12 S. Afroz\n,13 A. Agapito,14 D. Agarwal\n,15 M. Agathos\n,16\nN. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar\n,19 I.-L. Ahrend,20 L. Aiello\n,21, 22 A. Ain\n,23 P. Ajith\n,24 T. Akutsu\n,25, 26\nS. Albanesi\n,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9 C. All\u00b4en\u00b4e,31 A. Allocca\n,32, 4 S. Al-Shammari,33 P. A. Altin\n,34\nS. Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37 F. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11\nS. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41 M. Ando,42 M. Andr\u00b4es-Carcasona\n,43 T. Andri\u00b4c\n,44, 45, 8, 9\nJ. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49 S. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11\nS. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42 M. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2\nF. Armato\n,29, 30 S. Armstrong\n,55 N. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 G. Ashton\n,58 Y. Aso\n,25, 59\nL. Asprea,28 M. Assiduo,60, 61 S. Assis de Souza Melo,62 S. M. Aston,63 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,64\nK. AultONeal\n,65 G. Avallone\n,66 E. A. Avila\n,49 S. Babak\n,20 C. Badger,67 S. Bae\n,68 S. Bagnasco\n,28 L. Baiotti\n,69\nR. Bajpai\n,70 T. Baka,71, 37 A. M. Baker,6 K. A. Baker,72 T. Baker\n,73 G. Baldi\n,74, 75 N. Baldicchi\n,76, 51 M. Ball,77\nG. Ballardin,62 S. W. Ballmer,78 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,79 T. M. Baptiste,12 P. Baral\n,10\nM. Baratti\n,80, 81 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,79 P. Barneo\n,82, 83, 84 F. Barone\n,85, 4 B. Barr\n,86\nL. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,87 A. M. Bartoletti,88 M. A. Barton\n,86 I. Bartos,46 A. Basalaev\n,8, 9\nR. Bassiri\n,89 A. Basti\n,81, 80 M. Bawaj\n,76, 51 P. Baxi,90 J. C. Bayley\n,86 A. C. Baylor\n,10 P. A. Baynard II,57\nM. Bazzan,91, 92 V. M. Bedakihale,93 F. Beirnaert\n,94 M. Bejger\n,95 D. Belardinelli\n,22 A. S. Bell\n,86 D. S. Bellie,96\nL. Bellizzi\n,80, 81 W. Benoit\n,18 I. Bentara\n,56 J. D. Bentley\n,97 M. Ben Yaala,55 S. Bera\n,98, 99 F. Bergamin\n,33\nB. K. Berger\n,89 S. Bernuzzi\n,27 M. Beroiz\n,11 C. P. L. Berry\n,86 D. Bersanetti\n,29 T. Bertheas,100 A. Bertolini,37, 36\nJ. Betzwieser\n,63 D. Beveridge\n,72 G. Bevilacqua\n,101 N. Bevins\n,102 S. Bhagwat,103 R. Bhandare,104 R. Bhatt,11\nD. Bhattacharjee\n,105, 106 S. Bhattacharyya,107 S. Bhaumik\n,46 V. Biancalana\n,101 A. Bianchi,37, 108 I. A. Bilenko,109\nG. Billingsley\n,11 A. Binetti\n,110 S. Bini\n,11, 74, 75 C. Binu,111 S. Biot,112 O. Birnholtz\n,113 S. Biscoveanu\n,96 A. Bisht,9\nM. Bitossi\n,62, 80 M.-A. Bizouard\n,114 S. Blaber,115 J. K. Blackburn\n,11 L. A. Blagg,77 C. D. Blair,72, 63 D. G. Blair,72\nN. Bode\n,8, 9 N. Boettner,97 G. Boileau\n,114 M. Boldrini\n,38 G. N. Bolingbroke\n,116 A. Bolliand,117, 40 L. D. Bonavena\n,46\nR. Bondarescu\n,82 F. Bondu\n,118 E. Bonilla\n,89 M. S. Bonilla\n,54 A. Bonino,103 R. Bonnand\n,31, 117 A. Borchers,8, 9\nS. Borhanian,7 V. Boschi\n,80 S. Bose,119 V. Bossilkov,63 Y. Bothra\n,37, 108 A. Boudon,56 L. Bourg,57 M. Boyle,120 A. Bozzi,62\nC. Bradaschia,80 P. R. Brady\n,10 A. Branch,63 M. Branchesi\n,44, 45 I. Braun,105 T. Briant\n,121 A. Brillet,114 M. Brinkmann,8, 9\nP. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11 B. C. Brown,46 D. D. Brown,116 M. L. Brozzetti\n,76, 51 S. Brunett,11\nG. Bruno,15 R. Bruntz\n,122 J. Bryant,103 Y. Bu,123 F. Bucci\n,61 J. Buchanan,122 O. Bulashenko\n,82, 83 T. Bulik,124\nH. J. Bulten,37 A. Buonanno\n,125, 1 K. Burtnyk,2 R. Buscicchio\n,126, 127 D. Buskulic,31 C. Buy\n,100 R. L. Byer,89\nG. S. Cabourn Davies\n,73 R. Cabrita\n,15 V. C\u00b4aceres-Barbosa\n,7 L. Cadonati\n,57 G. Cagnoli\n,128 C. Cahillane\n,78\nA. Calafat,98 J. Calder\u00b4on Bustillo,129 T. A. Callister,130 E. Calloni,32, 4 S. R. Callos\n,77 M. Canepa,30, 29 G. Caneva Santoro\n,43\nK. C. Cannon\n,42 H. Cao,35 L. A. Capistran,131 E. Capocasa\n,20 E. Capote\n,2, 11 G. Capurri\n,81, 80 G. Carapella,66, 132\nF. Carbognani,62 M. Carlassara,8, 9 J. B. Carlin\n,123 T. K. Carlson,133 M. F. Carney,105 M. Carpinelli\n,126, 62 G. Carrillo,77\nJ. J. Carter\n,8, 9 G. Carullo\n,103, 134 A. Casallas-Lagos,135 J. Casanueva Diaz\n,62 C. Casentini\n,136, 22 S. Y. Castro-Lucas,137\nS. Caudill,133 M. Cavagli`a\n,106 R. Cavalieri\n,62 A. Ceja,54 G. Cella\n,80 P. Cerd\u00b4a-Dur\u00b4an\n,138, 139 E. Cesarini\n,22\nN. Chabbra,34 W. Chaibi,114 A. Chakraborty\n,13 P. Chakraborty\n,8, 9 S. Chakraborty,104 S. Chalathadka Subrahmanya\n,97\nJ. C. L. Chan\n,140 M. Chan,115 K. Chang,141 S. Chao\n,142, 141 P. Charlton\n,143 E. Chassande-Mottin\n,20 C. Chatterjee\n,144\nDebarati Chatterjee\n,79 Deep Chatterjee\n,35 M. Chaturvedi,104 S. Chaty\n,20 K. Chatziioannou\n,11 A. Chen\n,145\nA. H.-Y. Chen,146 D. Chen\n,147 H. Chen,142 H. Y. Chen\n,148 S. Chen,144 Yanbei Chen,149 Yitian Chen\n,120 H. P. Cheng,150\nP. Chessa\n,76, 51 H. T. Cheung\n,90 S. Y. Cheung,6 F. Chiadini\n,151, 132 D. Chiaramello,28 G. Chiarini,8, 9, 92 A. Chiba,152\nA. Chincarini\n,29 M. L. Chiofalo\n,81, 80 A. Chiummo\n,4, 62 C. Chou,146 S. Choudhary\n,72 N. Christensen\n,114, 153\nS. S. Y. Chua\n,34 G. Ciani\n,74, 75 P. Ciecielag\n,95 M. Cie\u00b4slar\n,124 M. Cifaldi\n,22 B. Cirok,154 F. Clara,2 J. A. Clark\n,11, 57\nT. A. Clarke\n,6 P. Clearwater,155 S. Clesse,112 F. Cleva,114, 117 E. Coccia,44, 45, 43 E. Codazzo\n,156, 157 P.-F. Cohadon\n,121\nS. Colace\n,30 E. Colangeli,73 M. Colleoni\n,98 C. G. Collette,158 J. Collins,63 S. Colloms\n,86 A. Colombo\n,159, 127\nC. M. Compton,2 G. Connolly,77 L. Conti\n,92 T. R. Corbitt\n,12 I. Cordero-Carri\u00b4on\n,160 S. Corezzi\n,76, 51 N. J. Cornish\n,161\nI. Coronado,162 A. Corsi\n,163 R. Cottingham,63 M. W. Coughlin\n,18 A. Couineaux,38 P. Couvares\n,11, 57 D. M. Coward,72\nR. Coyne\n,164 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,165 P. Cremonese\n,98 S. Crook,63 R. Crouch,2\nJ. Csizmazia,2 J. R. Cudell\n,166 T. J. Cullen\n,11 A. Cumming\n,86 E. Cuoco\n,167, 168 M. Cusinato\n,138 L. V. Da Conceic\u00b8\u02dcao,169\nT. Dal Canton\n,41 S. Dal Pra\n,170 T. Damour,171 G. D\u00b4alya\n,100 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38\narXiv:2509.08054v1 [gr-qc] 9 Sep 2025\n\n2\nK. Danzmann,9, 8, 9 K. E. Darroch,122 L. P. Dartez\n,63 R. Das,107 A. Dasgupta,93 V. Dattilo\n,62 A. Daumas,20 N. Davari,172, 173\nI. Dave,104 A. Davenport,137 M. Davier,41 T. F. Davies,72 D. Davis\n,11 L. Davis,72 M. C. Davis\n,18 P. Davis\n,174, 175\nE. J. Daw\n,176 M. Dax\n,1 J. De Bolle\n,94 M. Deenadayalan,79 J. Degallaix\n,177 M. De Laurentis\n,32, 4 F. De Lillo\n,23\nS. Della Torre\n,127 W. Del Pozzo\n,81, 80 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,178, 61 F. De Matteis\n,21, 22\nN. Demos,35 T. Dent\n,129 A. Depasse\n,15 N. DePergola,102 R. De Pietri\n,179, 180 R. De Rosa\n,32, 4 C. De Rossi\n,62\nM. Desai\n,35 R. DeSalvo\n,181 A. DeSimone,182 R. De Simone,151, 132 A. Dhani\n,1 R. Diab,46 M. C. D\u00b4\u0131az\n,165\nM. Di Cesare\n,32, 4 G. Dideron,183 T. Dietrich\n,1 L. Di Fiore,4 C. Di Fronzo\n,72 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4\nD. Diksha,37, 36 J. Ding\n,20, 184 S. Di Pace\n,39, 38 I. Di Palma\n,39, 38 D. Di Piero,185, 48 F. Di Renzo\n,56 Divyajyoti\n,33\nA. Dmitriev\n,103 J. P. Docherty,86 Z. Doctor\n,96 N. Doerksen,169 E. Dohmen,2 A. Doke,133 A. Domiciano De Souza,186\nL. D\u2019Onofrio\n,38 F. Donovan,35 K. L. Dooley\n,33 T. Dooney,71 S. Doravari\n,79 O. Dorosh,187 W. J. D. Doyle,122\nM. Drago\n,39, 38 J. C. Driggers\n,2 L. Dunn\n,123 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,172, 156 P. Dutta Roy,46\nH. Duval\n,188 S. E. Dwyer,2 C. Eassa,2 M. Ebersold\n,189, 31 T. Eckhardt\n,97 G. Eddolls\n,78 A. Effler\n,63 J. Eichholz\n,34\nH. Einsle,114 M. Eisenmann,25 M. Emma\n,58 K. Endo,152 R. Enficiaud\n,1 L. Errico\n,32, 4 R. Espinosa,165 M. Esposito\n,4, 32\nR. C. Essick\n,190 H. Estell\u00b4es\n,1 T. Etzel,11 M. Evans\n,35 T. Evstafyeva,183 B. E. Ewing,7 J. M. Ezquiaga\n,140\nF. Fabrizi\n,60, 61 V. Fafone\n,21, 22 S. Fairhurst\n,33 A. M. Farah\n,130 B. Farr\n,77 W. M. Farr\n,191, 192 G. Favaro\n,91\nM. Favata\n,193 M. Fays\n,166 M. Fazio\n,55 J. Feicht,11 M. M. Fejer,89 R. Felicetti\n,185, 48 E. Fenyvesi\n,87, 194 J. Fernandes,195\nT. Fernandes\n,196, 138 D. Fernando,111 S. Ferraiuolo\n,197, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,81, 80 P. Figura\n,95 E. Finch\n,11\nA. Fiori\n,80, 81 I. Fiori\n,62 M. Fishbach\n,190 R. P. Fisher,122 R. Fittipaldi\n,198, 132 V. Fiumara\n,199, 132 R. Flaminio,31\nS. M. Fleischer\n,200 L. S. Fleming,201 E. Floden,18 H. Fong,115 J. A. Font\n,138, 139 F. Fontinele-Nunes,18 C. Foo,1\nB. Fornal\n,202 K. Franceschetti,179 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,80 J. P. Freed,65 Z. Frei\n,203 A. Freise\n,37, 108\nO. Freitas\n,196, 138 R. Frey\n,77 W. Frischhertz,63 P. Fritschel,35 V. V. Frolov,63 G. G. Fronz\u00b4e\n,28 M. Fuentes-Garcia\n,11\nS. Fujii,204 T. Fujimori,205 P. Fulda,46 M. Fyffe,63 B. Gadre\n,71 J. R. Gair\n,1 S. Galaudage\n,186 V. Galdi,206 R. Gamba,7\nA. Gamboa\n,1 S. Gamoji,181 D. Ganapathy\n,207 A. Ganguly\n,79 B. Garaventa\n,29 J. Garc\u00b4\u0131a-Bellido\n,208\nC. Garc\u00b4\u0131a-Quir\u00b4os\n,189 J. W. Gardner\n,34 K. A. Gardner,115 S. Garg,42 J. Gargiulo\n,62 X. Garrido\n,41 A. Garron\n,98\nF. Garufi\n,32, 4 P. A. Garver,89 C. Gasbarra\n,21, 22 B. Gateley,2 F. Gautier\n,209 V. Gayathri\n,10 T. Gayer,78 G. Gemme\n,29\nA. Gennai\n,80 V. Gennari\n,100 J. George,104 R. George\n,148 O. Gerberding\n,97 L. Gergely\n,154 Archisman Ghosh\n,94\nSayantan Ghosh,195 Shaon Ghosh\n,193 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,210 Tathagata Ghosh\n,79 J. A. Giaime\n,12, 63\nK. D. Giardina,63 D. R. Gibson,201 C. Gier\n,55 S. Gkaitatzis\n,81, 80 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,77 R. V. Godley,8, 9\nP. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,115 J. Golomb,11 S. Gomez Lopez\n,39, 38 B. Goncharov\n,44 G. Gonz\u00b4alez\n,12\nP. Goodarzi\n,211 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,62 R. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35\nA. Grado\n,76, 51 V. Graham\n,86 A. E. Granados\n,18 M. Granata\n,177 V. Granata\n,212, 132 S. Gras,35 P. Grassia,11 J. Graves,57\nC. Gray,2 R. Gray\n,86 G. Greco,51 A. C. Green\n,37, 108 L. Green,213 S. M. Green,73 S. R. Green\n,214 C. Greenberg,133\nA. M. Gretarsson,65 H. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,76, 51 C. Grimaud\n,31 H. Grote\n,33\nS. Grunewald\n,1 D. Guerra\n,138 D. Guetta\n,215 G. M. Guidi\n,60, 61 A. R. Guimaraes,12 H. K. Gulati,93 F. Gulminelli\n,174, 175\nH. Guo\n,145 W. Guo\n,72 Y. Guo\n,37, 36 Anuradha Gupta\n,216 I. Gupta\n,7 N. C. Gupta,93 S. K. Gupta,46 V. Gupta\n,18\nN. Gupte,1 J. Gurs,97 N. Gutierrez,177 N. Guttman,6 F. Guzman\n,131 D. Haba,217 M. Haberland\n,1 S. Haino,218 E. D. Hall\n,35\nE. Z. Hamilton\n,98 G. Hammond\n,86 M. Haney,37 J. Hanks,2 C. Hanna\n,7 M. D. Hannam,33 O. A. Hannuksela\n,219\nA. G. Hanselman\n,130 H. Hansen,2 J. Hanson,63 S. Hanumasagar,57 R. Harada,42 A. R. Hardison,182 S. Harikumar\n,187\nK. Haris,37, 71 I. Harley-Trochimczyk,131 T. Harmark\n,134 J. Harms\n,44, 45 G. M. Harry\n,220 I. W. Harry\n,73 J. Hart,105\nB. Haskell,95, 221, 222 C. J. Haster\n,213 K. Haughian\n,86 H. Hayakawa,50 K. Hayama,223 M. C. Heintze,63 J. Heinze\n,103\nJ. Heinzel,35 H. Heitmann\n,114 F. Hellman\n,207 A. F. Helmling-Cornell\n,77 G. Hemming\n,62 O. Henderson-Sapir\n,116\nM. Hendry\n,86 I. S. Heng,86 M. H. Hennig\n,86 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,224, 225 J. Heynen,15 J. Heyns,35\nS. Higginbotham,33 S. Hild,36, 37 S. Hill,86 Y. Himemoto\n,226 N. Hirata,25 C. Hirose,227 D. Hofman,177 B. E. Hogan,65\nN. A. Holland,37, 108 I. J. Hollows\n,176 D. E. Holz\n,130 L. Honet,112 D. J. Horton-Bailey,207 J. Hough\n,86 S. Hourihane\n,11\nN. T. Howard,144 E. J. Howell\n,72 C. G. Hoy\n,73 C. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,142 H.-Y. Hsieh,142 C. Hsiung,228\nS.-H. Hsu,146 W.-F. Hsu\n,110 Q. Hu\n,86 H. Y. Huang\n,141 Y. Huang\n,7 Y. T. Huang,78 A. D. Huddart,229 B. Hughey,65\nV. Hui\n,31 S. Husa\n,98 R. Huxford,7 L. Iampieri\n,39, 38 G. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,132 J. Iascau,77\nK. Ide,230 R. Iden,217 A. Ierardi,44, 45 S. Ikeda,147 H. Imafuku,42 Y. Inoue,141 G. Iorio\n,91 P. Iosif\n,185, 48 M. H. Iqbal,34\nJ. Irwin\n,86 R. Ishikawa,230 M. Isi\n,231, 192 K. S. Isleif\n,232 Y. Itoh\n,205, 233 M. Iwaya,204 B. R. Iyer\n,24 C. Jacquet,100\nP.-E. Jacquet\n,121 T. Jacquot,41 S. J. Jadhav,234 S. P. Jadhav\n,155 M. Jain,133 T. Jain,224 A. L. James\n,11 K. Jani\n,144\nJ. Janquart\n,15 N. N. Janthalur,234 S. Jaraba\n,235 P. Jaranowski\n,236 R. Jaume\n,98 W. Javed,33 A. Jennings,2 M. Jensen,2\n\n3\nW. Jia,35 J. Jiang\n,150 H.-B. Jin\n,237, 238 G. R. Johns,122 N. A. Johnson,46 M. C. Johnston\n,213 R. Johnston,86 N. Johny,8, 9\nD. H. Jones\n,34 D. I. Jones,210 R. Jones,86 H. E. Jose,77 P. Joshi\n,7 S. K. Joshi,79 G. Joubert,56 J. Ju,239 L. Ju\n,72 K. Jung\n,240\nJ. Junker\n,34 V. Juste,112 H. B. Kabagoz\n,63, 35 T. Kajita\n,241 I. Kaku,205 V. Kalogera\n,96 M. Kalomenopoulos\n,213\nM. Kamiizumi\n,50 N. Kanda\n,233, 205 S. Kandhasamy\n,79 G. Kang\n,242 N. C. Kannachel,6 J. B. Kanner,11\nS. A. KantiMahanty,18 S. J. Kapadia\n,79 D. P. Kapasi\n,54 M. Karthikeyan,133 M. Kasprzack\n,11 H. Kato,152 T. Kato,204\nE. Katsavounidis,35 W. Katzman,63 R. Kaushik\n,104 K. Kawabe,2 R. Kawamoto,205 D. Keitel\n,98 L. J. Kemperman\n,116\nJ. Kennington\n,7 F. A. Kerkow,18 R. Kesharwani\n,79 J. S. Key\n,243 R. Khadela,8, 9 S. Khadka,89 S. S. Khadkikar,7\nF. Y. Khalili\n,109 F. Khan\n,8, 9 T. Khanam,163 M. Khursheed,104 N. M. Khusid,191, 192 W. Kiendrebeogo\n,114, 244\nN. Kijbunchoo\n,116 C. Kim,245 J. C. Kim,246 K. Kim\n,247 M. H. Kim\n,239 S. Kim\n,248 Y.-M. Kim\n,247 C. Kimball\n,96\nK. Kimes,54 M. Kinnear,33 J. S. Kissel\n,2 S. Klimenko,46 A. M. Knee\n,115 E. J. Knox,77 N. Knust\n,8, 9 K. Kobayashi,204\nS. M. Koehlenbeck\n,89 G. Koekoek,37, 36 K. Kohri\n,249, 250 K. Kokeyama\n,33, 251 S. Koley\n,44, 166 P. Kolitsidou\n,103\nA. E. Koloniari\n,252 K. Komori\n,42 A. K. H. Kong\n,142 A. Kontos\n,253 L. M. Koponen,103 M. Korobko\n,97 X. Kou,18\nA. Koushik\n,23 N. Kouvatsos\n,67 M. Kovalam,72 T. Koyama,152 D. B. Kozak,11 S. L. Kranzhoff,36, 37 V. Kringel,8, 9\nN. V. Krishnendu\n,103 S. Kroker,254 A. Kr\u00b4olak\n,255, 187 K. Kruska,8, 9 J. Kubisz\n,256 G. Kuehn,8, 9 S. Kulkarni\n,216\nA. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,234 Praveen Kumar\n,129 Prayush Kumar\n,24 Rahul Kumar,2\nRakesh Kumar,93 J. Kume\n,257, 258, 42 K. Kuns\n,35 N. Kuntimaddi,33 S. Kuroyanagi\n,208, 259 S. Kuwahara\n,42\nK. Kwak\n,240 K. Kwan,34 S. Kwon\n,42 G. Lacaille,86 D. Laghi\n,189, 100 A. H. Laity,164 E. Lalande,260 M. Lalleman\n,23\nP. C. Lalremruati,261 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35 J. Lange,148 R. Langgin\n,213 B. Lantz\n,89 I. La Rosa\n,98\nJ. Larsen,200 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6 J. Lawrence\n,165 M. Laxen\n,63 C. Lazarte\n,138 A. Lazzarini\n,11\nC. Lazzaro,157, 156 P. Leaci\n,39, 38 L. Leali,18 Y. K. Lecoeuche\n,115 H. M. Lee\n,262 H. W. Lee\n,263 J. Lee,78 K. Lee\n,239\nR.-K. Lee\n,142 R. Lee,35 Sungho Lee\n,247 Sunjae Lee,239 Y. Lee,141 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,183\nM. Le Jean\n,177, 117 A. Lema\u02c6\u0131tre\n,264 M. Lenti\n,61, 178 M. Leonardi\n,74, 75, 265 M. Lequime,40 N. Leroy\n,41\nM. Lesovsky,11 N. Letendre,31 M. Lethuillier\n,56 Y. Levin,6 K. Leyde,73 A. K. Y. Li,11 K. L. Li\n,266 T. G. F. Li,110\nX. Li\n,149 Y. Li,96 Z. Li,86 A. Lihos,122 E. T. Lin\n,142 F. Lin,141 L. C.-C. Lin\n,266 Y.-C. Lin\n,142 C. Lindsay,201\nS. D. Linker,181 A. Liu\n,219 G. C. Liu\n,228 Jian Liu\n,72 F. Llamas Villarreal,165 J. Llobera-Querol\n,98 R. K. L. Lo\n,140\nJ.-P. Locquet,110 S. C. G. Loggins,267 M. R. Loizou,133 L. T. London,67 A. Longo\n,60, 61 D. Lopez\n,166 M. Lopez Portilla,71\nM. Lorenzini\n,21, 22 A. Lorenzo-Medina\n,129 V. Loriette,41 M. Lormand,63 G. Losurdo\n,268, 80 E. Lotti,133 T. P. Lott IV\n,57\nJ. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,111 N. Low,123 N. Lu\n,34 L. Lucchesi\n,80 H. L\u00a8uck,9, 8, 9 D. Lumaca\n,22\nA. P. Lundgren\n,269, 270 A. W. Lussier\n,260 R. Macas\n,73 M. MacInnis,35 D. M. Macleod\n,33 I. A. O. MacMillan\n,11\nA. Macquet\n,41 K. Maeda,152 S. Maenaut\n,110 S. S. Magare,79 R. M. Magee\n,11 E. Maggio\n,1 R. Maggiore,37, 108\nM. Magnozzi\n,29, 30 M. Mahesh,97 M. Maini,164 S. Majhi,79 E. Majorana,39, 38 C. N. Makarem,11 N. Malagon,111\nD. Malakar\n,106 J. A. Malaquias-Reis,19 U. Mali\n,190 S. Maliakal,11 A. Malik,104 L. Mallick\n,169, 190 A.-K. Malz\n,58\nN. Man,114 M. Mancarella\n,99 V. Mandic\n,18 V. Mangano\n,172, 156 N. Manning,111 B. Mannix,77 G. L. Mansell\n,78\nM. Manske\n,10 M. Mantovani\n,62 M. Mapelli\n,91, 92, 271 C. Marinelli\n,101 F. Marion\n,31 A. S. Markosyan,89\nA. Markowitz,11 E. Maros,11 S. Marsat\n,100 F. Martelli\n,60, 61 I. W. Martin\n,86 R. M. Martin\n,193 B. B. Martinez,131\nD. A. Martinez,54 M. Martinez,43, 272 V. Martinez\n,128 A. Martini,74, 75 J. C. Martins\n,19 D. V. Martynov,103 E. J. Marx,35\nL. Massaro,36, 37 A. Masserot,31 M. Masso-Reid\n,86 S. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9\nL. Maurin,209 N. Mavalvala\n,35 N. Maxwell,2 G. McCarrol,63 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,63\nL. McCuller\n,11 S. McEachin,122 C. McElhenny,122 G. I. McGhee\n,86 J. McGinn,86 K. B. M. McGowan,144 J. McIver\n,115\nA. McLeod\n,72 I. McMahon\n,189 T. McRae,34 R. McTeague,86 D. Meacher\n,10 B. N. Meagher,78 R. Mechum,111 Q. Meijer,71\nA. Melatos,123 C. S. Menoni\n,137 F. Mera,2 R. A. Mercer\n,10 L. Mereni,177 K. Merfeld,163 E. L. Merilh,63 J. R. M\u00b4erou\n,98\nJ. D. Merritt,77 M. Merzougui,114 C. Messick\n,10 B. Mestichelli,44 M. Meyer-Conde\n,273 F. Meylahn\n,8, 9 A. Mhaske,79\nA. Miani\n,74, 75 H. Miao,274 C. Michel\n,177 Y. Michimura\n,42 H. Middleton\n,103 D. P. Mihaylov\n,105 S. J. Miller\n,11\nM. Millhouse\n,57 E. Milotti\n,185, 48 V. Milotti\n,91 Y. Minenkov,22 E. M. Minihan,65 Ll. M. Mir\n,43 L. Mirasola\n,156, 157\nM. Miravet-Ten\u00b4es\n,138 C.-A. Miritescu\n,43 A. Mishra,24 C. Mishra\n,107 T. Mishra\n,46 A. L. Mitchell,37, 108 J. G. Mitchell,65\nK. Mitman,120 S. Mitra\n,79 V. P. Mitrofanov\n,109 K. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50\nA. Miyoko,65 G. Mo\n,35 L. Mobilia\n,60, 61 S. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,207 M. Mondin,181\nM. Montani,60, 61 C. J. Moore,224 D. Moraru,2 A. More\n,79 S. More\n,79 C. Moreno\n,135 E. A. Moreno\n,35 G. Moreno,2\nA. Moreso Serra,82 S. Morisaki\n,42, 204 Y. Moriwaki\n,152 G. Morras\n,208 A. Moscatello\n,91 M. Mould\n,35 B. Mours\n,64\nC. M. Mow-Lowry\n,37, 108 L. Muccillo\n,178, 61 F. Muciaccia\n,39, 38 D. Mukherjee\n,103 Samanwaya Mukherjee,24\nSoma Mukherjee,165 Subroto Mukherjee,93 Suvodip Mukherjee\n,13 N. Mukund\n,35 A. Mullavey,63 H. Mullock,115\n\n4\nJ. Mundi,220 C. L. Mungioli,72 M. Murakoshi,230 P. G. Murray\n,86 D. Nabari\n,74, 75 S. L. Nadji,8, 9 A. Nagar,28, 171\nN. Nagarajan\n,86 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,275 M. Nakano,11 D. Nanadoumgar-Lacroze\n,43 D. Nandi,12\nV. Napolano,62 P. Narayan\n,216 I. Nardecchia\n,22 T. Narikawa,204 H. Narola,71 L. Naticchioni\n,38 R. K. Nayak\n,261\nL. Negri,71 A. Nela,86 C. Nelle,77 A. Nelson\n,131 T. J. N. Nelson,63 M. Nery,8, 9 A. Neunzert\n,2 S. Ng,54 L. Nguyen\nQuynh\n,276 S. A. Nichols,12 A. B. Nielsen\n,277 Y. Nishino,25, 42 A. Nishizawa\n,278 S. Nissanke,279, 37 W. Niu\n,7 F. Nocera,62\nJ. Noller,280 M. Norman,33 C. North,33 J. Novak\n,117, 235, 281 R. Nowicki\n,144 J. F. Nu\u02dcno Siles\n,208 L. K. Nuttall\n,73\nK. Obayashi,230 J. Oberling\n,2 J. O\u2019Dell,229 E. Oelker\n,35 M. Oertel\n,235, 117, 282, 281 G. Oganesyan,44, 45 T. O\u2019Hanlon,63\nM. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,117, 282, 281 R. Omer,18 B. O\u2019Neal,122 M. Onishi,152 K. Oohara\n,283 B. O\u2019Reilly\n,63\nM. Orselli\n,51, 76 R. O\u2019Shaughnessy\n,111 S. O\u2019Shea,86 S. Oshino\n,50 C. Osthelder,11 I. Ota\n,12 D. J. Ottaway\n,116\nA. Ouzriat,56 H. Overmier,63 B. J. Owen\n,284 R. Ozaki,230 A. E. Pace\n,7 R. Pagano\n,12 M. A. Page\n,25 A. Pai\n,195\nL. Paiella,44 A. Pal,285 S. Pal\n,261 M. A. Palaia\n,80, 81 M. P\u00b4alfi,203 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,142\nJ. Pan,72 K. C. Pan\n,142 P. K. Panda,234 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 71 F. Pannarale\n,39, 38\nK. A. Pannone,54 B. C. Pant,104 F. H. Panther,72 M. Panzeri,60, 61 F. Paoletti\n,80 A. Paolone\n,38, 286 A. Papadopoulos\n,86\nE. E. Papalexakis,211 L. Papalini\n,80, 81 G. Papigkiotis\n,252 A. Paquis,41 A. Parisi\n,76, 51 B.-J. Park,247 J. Park\n,287\nW. Parker\n,63 G. Pascale,8, 9 D. Pascucci\n,94 A. Pasqualetti\n,62 R. Passaquieti\n,81, 80 L. Passenger,6 D. Passuello,80\nO. Patane\n,2 A. V. Patel\n,141 D. Pathak,79 A. Patra,33 B. Patricelli\n,81, 80 B. G. Patterson,33 K. Paul\n,107 S. Paul\n,77\nE. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u02dcna Arellano\n,288 X. Peng,103 Y. Peng,57 S. Penn\n,289\nM. D. Penuliar,54 A. Perego\n,74, 75 Z. Pereira,133 C. P\u00b4erigois\n,290, 92, 91 G. Perna\n,91 A. Perreca\n,74, 75, 44 J. Perret\n,20\nS. Perri`es\n,56 J. W. Perry,37, 108 D. Pesios,252 S. Peters,166 S. Petracca,206 C. Petrillo,76 H. P. Pfeiffer\n,1 H. Pham,63\nK. A. Pham\n,18 K. S. Phukon\n,103 H. Phurailatpam,219 M. Piarulli,100 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,114\nM. Piendibene\n,81, 80 F. Piergiovanni\n,60, 61 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,291, 132 M. Pietrzak,95 M. Pillas\n,166\nF. Pilo\n,80 L. Pinard\n,177 I. M. Pinto\n,291, 132, 292, 32 M. Pinto\n,62 B. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,224, 86\nA. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,98 W. Plastino\n,212, 22 C. Plunkett\n,35 R. Poggiani\n,81, 80 E. Polini,35\nJ. Pomper,80, 81 L. Pompili\n,1 J. Poon,219 E. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,62 J. Powell\n,155\nG. S. Prabhu,79 M. Pracchia\n,166 B. K. Pradhan\n,79 T. Pradier\n,64 A. K. Prajapati,93 V. Prasad,7 K. Prasai\n,293\nR. Prasanna,234 P. Prasia,79 G. Pratten\n,103 G. Principe\n,185, 48 G. A. Prodi\n,74, 75 P. Prosperi,80 P. Prosposito,21, 22\nA. C. Providence,65 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00a8urrer\n,164 H. Qi\n,16 J. Qin\n,34 G. Qu\u00b4em\u00b4ener\n,175, 117\nV. Quetschke,165 P. J. Quinonez,65 N. Qutob,57 R. Rading,232 I. Rainho,138 S. Raja,104 C. Rajan,104 B. Rajbhandari\n,111\nK. E. Ramirez\n,63 F. A. Ramis Vidal\n,98 M. Ramos Arevalo\n,165 A. Ramos-Buades\n,98, 37 S. Ranjan\n,57 K. Ransom,63\nP. Rapagnani\n,39, 38 B. Ratto,65 A. Ravichandran,133 A. Ray\n,96 V. Raymond\n,33 M. Razzano\n,81, 80 J. Read,54\nT. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11 A. Renzini\n,126 B. Revenu\n,294, 41 A. Revilla Pe\u02dcna,82 R. Reyes,181\nL. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39 A. Ricciardone\n,81, 80 J. Rice,78 J. W. Richardson\n,211 M. L. Richardson,116\nA. Rijal,65 K. Riles\n,90 H. K. Riley,33 S. Rinaldi\n,271 J. Rittmeyer,97 C. Robertson,229 F. Robinet,41 M. Robinson,2\nA. Rocchi\n,22 L. Rolland\n,31 J. G. Rollins\n,11 A. E. Romano\n,295 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,224\nJ. H. Romie,63 S. Ronchini\n,7 T. J. Roocke\n,116 L. Rosa,4, 32 T. J. Rosauer,211 C. A. Rose,57 D. Rosi\u00b4nska\n,124 M. P. Ross\n,53\nM. Rossello-Sastre\n,98 S. Rowan\n,86 S. K. Roy\n,191, 192 S. Roy\n,15 D. Rozza\n,126, 127 P. Ruggi,62 N. Ruhama,240\nE. Ruiz Morales\n,296, 208 K. Ruiz-Rocha,144 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 108 S. Safi-Harb\n,169 M. R. Sah\n,13\nS. Saha\n,142 T. Sainrat\n,64 S. Sajith Menon\n,215, 39, 38 K. Sakai,297 Y. Sakai\n,273 M. Sakellariadou\n,67 S. Sakon\n,7\nO. S. Salafia\n,159, 127, 126 F. Salces-Carcoba\n,11 L. Salconi,62 M. Saleem\n,148 F. Salemi\n,39, 38 M. Sall\u00b4e\n,37\nS. U. Salunkhe,79 S. Salvador\n,175, 174 A. Salvarese,148 A. Samajdar\n,71, 37 A. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11\nN. Sanchis-Gual\n,138 J. R. Sanders,182 E. M. S\u00a8anger\n,1 F. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,79\nN. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,252 P. Sassi\n,51, 76 B. Sassolas\n,177 B. S. Sathyaprakash\n,7, 33 R. Sato,227 S. Sato,152\nYukino Sato,152 Yu Sato,152 O. Sauter\n,46 R. L. Savage\n,2 T. Sawada\n,50 H. L. Sawant,79 S. Sayah,177 V. Scacco,21, 22\nD. Schaetzl,11 M. Scheel,149 A. Schiebelbein,190 M. G. Schiworski\n,78 P. Schmidt\n,103 S. Schmidt\n,71 R. Schnabel\n,97\nM. Schneewind,8, 9 R. M. S. Schofield,77 K. Schouteden\n,110 B. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,298\nM. Scialpi\n,299 J. Scott\n,86 S. M. Scott\n,34 R. M. Sedas\n,63 T. C. Seetharamu,86 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,300\nD. Sellers,63 N. Sembo,205 A. S. Sengupta\n,301 E. G. Seo\n,86 J. W. Seo\n,110 V. Sequino,32, 4 M. Serra\n,38 A. Sevrin,188\nT. Shaffer,2 U. S. Shah\n,57 M. A. Shaikh\n,262 L. Shao\n,302 A. K. Sharma\n,98 Preeti Sharma,12 Prianka Sharma,104\nRitwik Sharma,18 S. Sharma Chaudhary,106 P. Shawhan\n,125 N. S. Shcheblanov\n,303, 264 E. Sheridan,144 Z.-H. Shi,142\nM. Shikauchi,42 R. Shimomura,304 H. Shinkai\n,304 S. Shirke,79 D. H. Shoemaker\n,35 D. M. Shoemaker\n,148 R. W. Short,2\nS. ShyamSundar,104 A. Sider,158 H. Siegel\n,191, 192 D. Sigg\n,2 L. Silenzi\n,36, 37 L. Silvestri\n,39, 170 M. Simmonds,116\n\n5\nL. P. Singer\n,305 Amitesh Singh,216 Anika Singh,11 D. Singh\n,207 N. Singh\n,98 S. Singh,217, 59 A. M. Sintes\n,98\nV. Sipala,172, 156 V. Skliris\n,33 B. J. J. Slagmolen\n,34 D. A. Slater,200 T. J. Slaven-Blair,72 J. Smetana,103 J. R. Smith\n,54\nL. Smith\n,86, 185, 48 R. J. E. Smith\n,6 W. J. Smith\n,144 S. Soares de Albuquerque Filho,60 M. Soares-Santos,189\nK. Somiya\n,217 I. Song\n,142 S. Soni\n,35 V. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,306 F. Spada\n,80 V. Spagnuolo\n,37\nA. P. Spencer\n,86 P. Spinicelli\n,62 A. K. Srivastava,93 F. Stachurski\n,86 C. J. Stark,122 D. A. Steer\n,307 N. Steinle\n,169\nJ. Steinlechner,36, 37 S. Steinlechner\n,36, 37 N. Stergioulas\n,252 P. Stevens,41 S. Stevenson,155 M. StPierre,164\nM. D. Strong,12 A. Strunk,2 A. L. Stuver,102, \u2217M. Suchenek,95 S. Sudhagar\n,95 Y. Sudo,230 N. Sueltmann,97\nL. Suleiman\n,54 K. D. Sullivan,12 J. Sun\n,242 L. Sun\n,34 S. Sunil,93 J. Suresh\n,114 B. J. Sutton,67 P. J. Sutton\n,33\nK. Suzuki,217 M. Suzuki,204 B. L. Swinkels\n,37 A. Syx\n,117 M. J. Szczepa\u00b4nczyk\n,308 P. Szewczyk\n,124 M. Tacca\n,37\nH. Tagoshi\n,204 K. Takada,204 H. Takahashi\n,273 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,309 H. Takeda\n,310, 311\nK. Takeshita,217 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,78 C. Talbot,130 M. Tamaki,204 N. Tamanini\n,100\nD. Tanabe,141 K. Tanaka,50 S. J. Tanaka\n,230 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9 L. Tao\n,211 R. D. Tapia,7\nE. N. Tapia San Mart\u00b4\u0131n\n,37 C. Taranto,21, 22 A. Taruya\n,312 J. D. Tasson\n,153 J. G. Tau\n,111 D. Tellez,54 R. Tenorio\n,98\nS. A. Teukolsky,120 H. Themann,181 A. Theodoropoulos\n,138 M. P. Thirugnanasambandam,79 L. M. Thomas\n,11\nM. Thomas,63 P. Thomas,2 J. E. Thompson\n,210 S. R. Thondapu,104 K. A. Thorne,63 K. S. Thorne,149 E. Thrane\n,6\nJ. Tissino\n,44, 45 A. Tiwari,79 Pawan Tiwari,44 Praveer Tiwari,195 S. Tiwari\n,189 V. Tiwari\n,103 M. R. Todd,78 M. Toffano,91\nA. M. Toivonen\n,18 K. Toland\n,86 A. E. Tolley\n,73 T. Tomaru\n,25 V. Tommasini,11 T. Tomura\n,50 H. Tong\n,6\nC. Tong-Yu,141 A. Torres-Forn\u00b4e\n,138, 139 C. I. Torrie,11 I. Tosta e Melo\n,313 E. Tournefier\n,31 M. Trad Nery,114 K. Tran,122\nA. Trapananti\n,52, 51 R. Travaglini\n,168 F. Travasso\n,52, 51 G. Traylor,63 M. Trevor,125 M. C. Tringali\n,62 A. Tripathee\n,90\nG. Troian\n,185, 48 A. Trovato\n,185, 48 L. Trozzo,4 R. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,314 L. Tsukada\n,213\nK. Turbang\n,188, 23 M. Turconi\n,114 C. Turski,94 H. Ubach\n,82, 83 N. Uchikata\n,204 T. Uchiyama\n,50 R. P. Udall\n,11\nT. Uehara\n,315 K. Ueno\n,42 V. Undheim\n,277 L. E. Uronen,219 T. Ushiba\n,50 M. Vacatello\n,80, 81 H. Vahlbruch\n,8, 9\nN. Vaidya\n,11 G. Vajente\n,11 A. Vajpeyi,6 J. Valencia\n,98 M. Valentini\n,108, 37 S. A. Vallejo-Pe\u02dcna\n,295 S. Vallero,28\nV. Valsan\n,10 M. van Dael\n,37, 316 E. Van den Bossche\n,188 J. F. J. van den Brand\n,36, 108, 37 C. Van Den Broeck,71, 37\nM. van der Sluys\n,37, 71 A. Van de Walle,41 J. van Dongen\n,37, 108 K. Vandra,102 M. VanDyke,119 H. van Haevermaet\n,23\nJ. V. van Heijningen\n,37, 108 P. Van Hove\n,64 J. Vanier,260 M. VanKeuren,105 J. Vanosky,2 N. van Remortel\n,23\nM. Vardaro,36, 37 A. F. Vargas\n,123 V. Varma\n,133 A. N. Vazquez,89 A. Vecchio\n,103 G. Vedovato,92 J. Veitch\n,86\nP. J. Veitch\n,116 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15 D. Verkindt\n,31 B. Verma,133\nY. Verma\n,104 S. M. Vermeulen\n,11 F. Vetrano,60 A. Veutro\n,38, 39 A. Vicer\u00b4e\n,60, 61 S. Vidyant,78 A. D. Viets\n,88\nA. Vijaykumar\n,190 A. Vilkha,111 N. Villanueva Espinosa,138 V. Villa-Ortega\n,129 E. T. Vincent\n,57 J.-Y. Vinet,114\nS. Viret,56 S. Vitale\n,35 H. Vocca\n,76, 51 D. Voigt\n,97 E. R. G. von Reis,2 J. S. A. von Wrangel,8, 9 W. E. Vossius,232\nL. Vujeva\n,140 S. P. Vyatchanin\n,109 J. Wack,11 L. E. Wade,105 M. Wade\n,105 K. J. Wagner\n,111 R. M. Wald,130 L. Wallace,11\nE. J. Wang,89 H. Wang\n,217 J. Z. Wang,90 W. H. Wang,165 Y. F. Wang\n,1 G. Waratkar\n,195 J. Warner,2 M. Was\n,31\nT. Washimi\n,25 N. Y. Washington,11 D. Watarai,42 B. Weaver,2 S. A. Webster,86 N. L. Weickhardt\n,97 M. Weinert,8, 9\nA. J. Weinstein\n,11 R. Weiss,35, \u2020 L. Wen\n,72 K. Wette\n,34 J. T. Whelan\n,111 B. F. Whiting\n,46 C. Whittle\n,11\nE. G. Wickens,73 D. Wilken\n,8, 9, 9 A. T. Wilkin,211 B. M. Williams,119 D. Williams\n,86 M. J. Williams\n,73 N. S. Williams\n,1\nJ. L. Willis\n,11 B. Willke\n,9, 8, 9 M. Wils\n,110 L. Wilson,105 C. W. Winborn,106 J. Winterflood,72 C. C. Wipf,11 G. Woan\n,86\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,141 I. C. F. Wong\n,219, 110 K. Wong,190 T. Wouters,71, 37 J. L. Wright,2\nM. Wright\n,86, 71 B. Wu,78 C. Wu\n,142 D. S. Wu\n,8, 9 H. Wu\n,142 K. Wu,119 Q. Wu,53 Y. Wu,96 Z. Wu\n,100\nE. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,207 Y. Xu\n,98 N. Yadav\n,28 H. Yamamoto\n,11 K. Yamamoto\n,152\nT. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,230 T. Yan,103 K. Z. Yang\n,18 Y. Yang\n,146 Z. Yarbrough\n,12\nJ. Yebana,98 S.-W. Yeh,142 A. B. Yelikar\n,144 X. Yin,35 J. Yokoyama\n,317, 42 T. Yokozawa,50 S. Yuan,72 H. Yuzurihara\n,50\nM. Zanolin,65 M. Zeeshan\n,111 T. Zelenova,62 J.-P. Zendri,92 M. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,96 L. Zhang,11 N. Zhang,57\nR. Zhang\n,150 T. Zhang,103 C. Zhao\n,72 Yue Zhao,162 Yuhang Zhao,20 Z.-C. Zhao\n,318 Y. Zheng\n,106 H. Zhong\n,18\nH. Zhou,78 H. O. Zhu,72 Z.-H. Zhu\n,318, 319 A. B. Zimmerman\n,148 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\u2021\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n\n6\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00b4eorique, Aix-Marseille Universit\u00b4e,\nCampus de Luminy, 163 Av. de Luminy, 13009 Marseille, France\n15Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n20Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), The Barcelona Institute of\nScience and Technology, Campus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00b4\u0131a y Ciencias, 64849 Monterrey, Nuevo Le\u00b4on, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit`a di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Royal Holloway, University of London, London TW20 0EX, United Kingdom\n59Astronomical course, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n60Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n61INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n62European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n63LIGO Livingston Observatory, Livingston, LA 70754, USA\n64Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n65Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n66Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n67King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n\n7\n68Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n69International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n70Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n71Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n72OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n73University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n74Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n75INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n76Universit`a di Perugia, I-06123 Perugia, Italy\n77University of Oregon, Eugene, OR 97403, USA\n78Syracuse University, Syracuse, NY 13244, USA\n79Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n80INFN, Sezione di Pisa, I-56127 Pisa, Italy\n81Universit`a di Pisa, I-56127 Pisa, Italy\n82Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu`es, 1, 08028 Barcelona, Spain\n83Departament de F\u00b4\u0131sica Qu`antica i Astrof\u00b4\u0131sica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00b4\u0131 i Franqu\u00b4es, 1, 08028 Barcelona, Spain\n84Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit`a, 2-4, 08034 Barcelona, Spain\n85Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n86IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n87HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n88Concordia University Wisconsin, Mequon, WI 53097, USA\n89Stanford University, Stanford, CA 94305, USA\n90University of Michigan, Ann Arbor, MI 48109, USA\n91Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n92INFN, Sezione di Padova, I-35131 Padova, Italy\n93Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n94Universiteit Gent, B-9000 Gent, Belgium\n95Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n96Northwestern University, Evanston, IL 60208, USA\n97Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n98IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n99Aix-Marseille Universit\u00b4e, Universit\u00b4e de Toulon, CNRS, CPT, Marseille, France\n100Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n101Universit`a di Siena, Dipartimento di Scienze Fisiche, della Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n102Villanova University, Villanova, PA 19085, USA\n103University of Birmingham, Birmingham B15 2TT, United Kingdom\n104RRCAT, Indore, Madhya Pradesh 452013, India\n105Kenyon College, Gambier, OH 43022, USA\n106Missouri University of Science and Technology, Rolla, MO 65409, USA\n107Indian Institute of Technology Madras, Chennai 600036, India\n108Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n109Lomonosov Moscow State University, Moscow 119991, Russia\n110Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n111Rochester Institute of Technology, Rochester, NY 14623, USA\n112Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n113Bar-Ilan University, Ramat Gan, 5290002, Israel\n114Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n115University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n116OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n117Centre national de la recherche scientifique, 75016 Paris, France\n118Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n119Washington State University, Pullman, WA 99164, USA\n120Cornell University, Ithaca, NY 14850, USA\n121Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS,\nENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n122Christopher Newport University, Newport News, VA 23606, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n125University of Maryland, College Park, MD 20742, USA\n126Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n127INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n\n8\n128Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1,\nCNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n129IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n130University of Chicago, Chicago, IL 60637, USA\n131University of Arizona, Tucson, AZ 85721, USA\n132INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Colorado State University, Fort Collins, CO 80523, USA\n138Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n139Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n140Niels Bohr Institute, University of Copenhagen, 2100 K\u00b4obenhavn, Denmark\n141National Central University, Taoyuan City 320317, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145University of the Chinese Academy of Sciences / International Centre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148University of Texas, Austin, TX 78712, USA\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Northeastern University, Boston, MA 02115, USA\n151Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n152Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n153Carleton College, Northfield, MN 55057, USA\n154University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INFN Cagliari, Physics Department, Universit`a degli Studi di Cagliari, Cagliari 09042, Italy\n157Universit`a degli Studi di Cagliari, Via Universit`a 40, 09124 Cagliari, Italy\n158Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n159INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n160Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n161Montana State University, Bozeman, MT 59717, USA\n162The University of Utah, Salt Lake City, UT 84112, USA\n163Johns Hopkins University, Baltimore, MD 21218, USA\n164University of Rhode Island, Kingston, RI 02881, USA\n165The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n166Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n167DIFA- Alma Mater Studiorum Universit`a di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n168Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna, viale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n169University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n170INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n171Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n172Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n173INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n174Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n175Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00b4echal Juin, F-14050 Caen, France\n176The University of Sheffield, Sheffield S10 2TN, United Kingdom\n177Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n178Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n179Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n180INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n181California State University, Los Angeles, Los Angeles, CA 90032, USA\n182Marquette University, Milwaukee, WI 53233, USA\n183Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n184Corps des Mines, Mines Paris, Universit\u00b4e PSL, 60 Bd Saint-Michel, 75272 Paris, France\n185Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n186Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n187National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n188Vrije Universiteit Brussel, 1050 Brussel, Belgium\n\n9\n189University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n190Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada\n191Stony Brook University, Stony Brook, NY 11794, USA\n192Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n193Montclair State University, Montclair, NJ 07043, USA\n194HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n195Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n196Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n197Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n198CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n199Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n200Western Washington University, Bellingham, WA 98225, USA\n201SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n202Barry University, Miami Shores, FL 33168, USA\n203E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n204Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n205Department of Physics, Graduate School of Science, Osaka Metropolitan University,\n3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n206University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n207University of California, Berkeley, CA 94720, USA\n208Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n209Laboratoire d\u2019Acoustique de l\u2019Universit\u00b4e du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211University of California, Riverside, Riverside, CA 92521, USA\n212Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit`a degli Studi Roma Tre, I-00146 Roma, Italy\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214University of Nottingham NG7 2RD, UK\n215Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n216The University of Mississippi, University, MS 38677, USA\n217Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n218Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n219The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit`a degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No. 151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Department of Astronomy, Columbia University, New York, NY 10027, USA\n232Helmut Schmidt University, D-22043 Hamburg, Germany\n233Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n234Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n235Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00b4e, 67000 Strasbourg, France\n236Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n237National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n238School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n239Sungkyunkwan University, Seoul 03063, Republic of Korea\n240Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n\n10\n241Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n242Chung-Ang University, Seoul 06974, Republic of Korea\n243University of Washington Bothell, Bothell, WA 98011, USA\n244Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00b4e Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n245Ewha Womans University, Seoul 03760, Republic of Korea\n246National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n247Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n248Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n249Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator\nResearch Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n250Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n251Nagoya University, Nagoya, 464-8601, Japan\n252Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n253Bard College, Annandale-On-Hudson, NY 12504, USA\n254Technical University of Braunschweig, D-38106 Braunschweig, Germany\n255Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n256Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n257Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n258Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n259Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n260Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n261Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n262Seoul National University, Seoul 08826, Republic of Korea\n263Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n264NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n265Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n266Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n267St. Thomas University, Miami Gardens, FL 33054, USA\n268Scuola Normale Superiore, I-56126 Pisa, Italy\n269Instituci\u00b4o Catalana de Recerca i Estudis Avan\u00b8cats, E-08010 Barcelona, Spain\n270Institut de F\u00b4\u0131sica d\u2019Altes Energies, E-08193 Barcelona, Spain\n271Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n272Institucio Catalana de Recerca i Estudis Avan\u00b8cats (ICREA),\nPasseig de Llu\u00b4\u0131s Companys, 23, 08010 Barcelona, Spain\n273Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n274Tsinghua University, Beijing 100084, China\n275Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n276Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n277University of Stavanger, 4021 Stavanger, Norway\n278Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n279GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n280University College London, London WC1E 6BT, United Kingdom\n281Observatoire de Paris, 75014 Paris, France\n282Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n283Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n285CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n286Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n287Department of Astronomy, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n288Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n289Hobart and William Smith Colleges, Geneva, NY 14456, USA\n290INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n291Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n292Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n\n11\n293Kennesaw State University, Kennesaw, GA 30144, USA\n294Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00b4e,\n4 rue Alfred Kastler BP 20722 44307 Nantes C \u00b4EDEX 03, France\n295Universidad de Antioquia, Medell\u00b4\u0131n, Colombia\n296Departamento de F\u00b4\u0131sica - ETSIDI, Universidad Polit\u00b4ecnica de Madrid, 28012 Madrid, Spain\n297Department of Electronic Control Engineering, National Institute of Technology,\nNagaoka College, 888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n298Trinity College, Hartford, CT 06106, USA\n299Dipartimento di Fisica e Scienze della Terra, Universit`a Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n300Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n301Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n302Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n303Laboratoire MSME, Cit\u00b4e Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00b4ee Cedex 2, France\n304Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n305NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n306Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n307Laboratoire de Physique de l\u2019 \u00b4Ecole Normale Sup\u00b4erieure, ENS, (CNRS,\nUniversit\u00b4e PSL, Sorbonne Universit\u00b4e, Universit\u00b4e Paris Cit\u00b4e), F-75005 Paris, France\n308Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n309Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n310The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n311Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n312Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n314National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n315Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n316Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n317Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n318Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n319School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nThe gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-\nfilter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal\nmasses m1 = 33.6+1.2\n\u22120.8 M\u2299and m2 = 32.2+0.8\n\u22121.3 M\u2299, and small spins \u03c71,2 \u22640.26 (90% credibility) and negligible\neccentricity e \u22640.03. Post-merger data excluding the peak region are consistent with the dominant quadrupolar\n(\u2113= |m| = 2) mode of a Kerr black hole and its first overtone. We constrain the modes\u2019 frequencies to \u00b130%\nof the Kerr spectrum, providing a test of the remnant\u2019s Kerr nature. We also examine Hawking\u2019s area law,\nalso known as the second law of black hole mechanics, which states that the total area of the black hole event\nhorizons cannot decrease with time. A range of analyses that exclude up to five of the strongest merger cycles\nconfirm that the remnant area is larger than the sum of the initial areas to high credibility.\nINTRODUCTION\nTen years after the detection of GW150914 [1] by the LIGO\ndetectors [2], gravitational-wave astronomy is thriving. Ad-\nvances in detector performance [3], including breakthroughs\nin quantum precision measurement [4\u20136], have led the field\nfrom the first glimpse of merging black holes [7, 8] to an\nexpanding catalog of hundreds of detections [9\u201318].\nHere\nwe report the observation of GW250114 082203, henceforth\nGW250114, shown in Fig. 1.\nWith similar parameters to\nGW150914, GW250114 reaches a similar strain amplitude\nof \u223c10\u221221. Yet, thanks to the LIGO detectors now operat-\ning near their design sensitivity [3], it registers at a signal-to-\nnoise ratio of 80, as opposed to 26 for GW150914 a decade\nago. This makes GW250114 the most clearly recorded signal\nto date, broadening the scope of fundamental tests of strong-\nfield gravity and black holes.\nFrom a theoretical standpoint, black holes are expected to\nbe remarkably simple objects [22\u201330].\nAccording to Ein-\nstein\u2019s theory of general relativity and under suitable regular-\n\n12\n10\n0\n10\nWhitened strain [ ]\nHanford, Washington (LHO)\nLHO data\nWaveform model reconstruction\nWavelet reconstruction\nLivingston, Louisiana (LLO)\nLLO data\nWaveform model reconstruction\nWavelet reconstruction\n0.10\n0.15\n0.20\nTime [s]\n32\n64\n128\n256\nFrequency [Hz]\n0.10\n0.15\n0.20\nTime [s]\n0\n8\n16\n24\n32\nNormalized amplitude\nFIG. 1.\nData from LIGO Hanford (left) and LIGO Livingston (right) and GW250114 signal reconstruction. Times are relative to January\n14th, 2025, 08:22:03 UTC. The top panels show whitened data versus time and signal reconstructions (90% credible regions), either with a\nwaveform model for black hole binaries in general relativity [19] or via a model-agnostic wavelet-based approach [20, 21]. Data and models\nhave been downsampled to 2048 Hz, whitened (effectively, divided) by the detector noise amplitude spectral density, and finally bandpassed to\n[20, 896] Hz. The bottom panels show a time\u2013frequency spectrogram of the data. The signal reaches >10\u03c3 above the noise.\nity assumptions, isolated stationary black holes can be fully\ncharacterized by just three parameters: mass, spin, and elec-\ntromagnetic charge. For neutral black holes, this implies that\nmass and spin determine the system through the Kerr metric\n[31], the unique axisymmetric, neutral solution to Einstein\u2019s\nequations [26]. This uniqueness is closely tied to key con-\njectures in classical gravitation, including weak cosmic cen-\nsorship [32] and the stability of rotating black holes [33\u201339],\nboth of which remain unproven.\nThe uniqueness and implied featurelessness of black holes\ngives rise to paradoxes in the context of quantum mechanics\nand thermodynamics [40]. The laws of black hole mechanics,\noriginally suspected to be only coincidentally reminiscent of\nstatistical mechanics [41], establish black holes as true ther-\nmodynamic systems [40, 42, 43]: the role of the entropy is\nassigned to the area of the event horizon [44, 45], while black\nholes radiate due to quantum effects as a black body with a\ntemperature related to their surface gravity [46]. Black hole\nthermodynamics plays a key role in the quest to reconcile\ngravity with the rest of physics [47], through concepts such\nas information loss [48], holographic gravity [49, 50], or the\nmicroscopic interpretation of black hole entropy [44, 51, 52].\nBlack holes are not just mathematical idealizations. They\nplay a central role in the phenomenology and evolution of the\nUniverse, displaying rich and complex behaviors from stel-\nlar to galactic scales [53\u201363]. Astrophysical black holes are\nexpected to not be significantly charged [64\u201366], thus con-\nforming to the Kerr metric\u2014yet, the extent to which they do\nso is an open question. Gravitational waves can inform this by\nobservationally probing the Kerr nature of black holes.\nAlthough black hole coalescences feature some of the\nstrongest and most dynamical gravitational fields, their ini-\ntial and final states are simple. A coalescence begins with a\nlong inspiral, during which two black holes orbit and approach\neach other as the system loses energy and angular momentum\nto gravitational radiation [67\u201369]. After the merger, the rem-\nnant black hole \u201crings\u201d [70] as it settles into a quiescent Kerr\nstate [71\u201373]. In this context, assuming a Kerr remnant im-\nplies a specific ringdown spectrum (frequencies and damping\nrates) which is a known function of the black hole mass and\nspin [74]. In parallel, the second law of black hole mechanics,\nalso known as Hawking\u2019s area law, requires a net increase in\nthe total event horizon area throughout the coalescence [75].\nGW250114 enables precise tests of both Hawking\u2019s area\nlaw and the Kerr nature of black holes. Excluding the neigh-\nborhood of the signal peak, we establish that the post-merger\ndata contain at least two distinct ringing modes of the rem-\nnant at the 4.1\u03c3 credible level. These modes are consistent\nwith the fundamental and first overtone of the quadrupolar\n(\u2113= |m| = 2) spectrum of a Kerr black hole; deviations in the\nmode frequencies are constrained to \u00b130%. To test the area\nlaw, we infer the initial black hole areas using pre-merger data\nthat exclude up to five merger signal cycles and the final black\nhole area using post-merger data with one-mode or two-mode\n\n13\n30\n35\n40\nm1 [M ]\n25\n30\n35\nm2 [M ]\nGW250114\nGW150914\nGW250114\nGW150914\nFIG. 2.\nPosterior distribution for the source-frame component\nmasses of GW250114, under the definition m1 \u2265m2 (marginals and\n90%-credible contours). For comparison we also show results for\nGW150914 [11, 76].\nmodels at their earliest time of applicability. In all cases, the\nremnant\u2019s event horizon area exceeds the total initial area at\nhigh credibility, in agreement with Hawking\u2019s law. Thanks to\nthe strength of GW250114, this test is possible even when ex-\ncising the loudest portion of the signal where gravity is at its\nstrongest and most dynamical.\nOBSERVATION OF GW250114\nGW250114 arrived at 08:22:03 UTC on January 14th,\n2025, while the LIGO Hanford and LIGO Livingston de-\ntectors [2] were operating nominally, Virgo [77] was under-\ngoing routine maintenance, and KAGRA [78] was not tak-\ning data. No significant data-quality issues were identified\nat the time [79].\nGW250114 was detected with high sig-\nnificance by all search pipelines operating at the time; Gst-\nLAL [80\u201391], MLy [92], SPIIR [93], MBTA [94, 95], Py-\nCBC [96], and cWB [97, 98], with a network matched-filter\nsignal-to-noise ratio, henceforth SNR, [99, 100] ranging be-\ntween 77 and 80. This is the highest reported SNR to date,\nsurpassing GW230814 230901 which had SNR 42 [18, 101].\nGW250114\u2019s record extends to the individual detectors, with\nSNRs of 53 and 60 at LIGO Hanford and LIGO Livingston\nrespectively. The combination of the two LIGO detectors at\ncomparable sensitivity enables the measurement precision re-\nported here.\nWe infer the source properties following standard proce-\ndures [102]. Here we quote selected results obtained with\nthe NRSur7dq4 waveform model [19], a surrogate of vacuum\nnumerical-relativity simulations of spin-precessing, quasicir-\ncular systems. We obtain consistent results with other mod-\nels [103\u2013112], presented with further technical details in the\nSupplement.\nThe source of GW250114 has a binary total\nmass M = 65.8+1.1\n\u22121.2 M\u2299and mass ratio q \u22650.91. Above and\nthroughout, all quantities are quoted at the 90% credible level\nunless stated otherwise. We constrain the component masses\nto within \u223c2 M\u2299, a factor of 3\u22124 improvement compared to\nGW150914 [1], at m1 = 33.6+1.2\n\u22120.8 M\u2299, m2 = 32.2+0.8\n\u22121.3 M\u2299; see\nFig. 2. The black hole dimensionless spins, \u03c7 \u2261S c/(Gm2)\nwhere S is the spin angular momentum, are both small,\n\u03c71 \u22640.24, \u03c72 \u22640.26, with no evidence for precession. The\nremnant black hole has a mass of Mf = 62.7+1.0\n\u22121.1 M\u2299and a\nspin of \u03c7f = 0.68+0.01\n\u22120.01. Furthermore, there is support for the\n\u2113= |m| = 4 radiation multipole with a network SNR of 3.6+1.4\n\u22121.5.\nThe source parameters are consistent with GW150914 and\nthe wider population of binary black hole mergers [14, 113],\nwhich contains an overdensity of observed black holes in\nthe 30\u221240 M\u2299mass range and small spins [113, 114]. The\nmodel-based signal reconstruction is consistent with a model-\nagnostic, wavelet-based approach [20], to within their sta-\ntistical uncertainties, see Fig. 1. Their noise-weighted over-\nlap [115, 116] is 0.995.\nA complementary analysis with models that allow for ec-\ncentric orbits but non-precessing spins [111, 112] finds that\nthe eccentricity is constrained to e \u22640.03 at a gravitational-\nwave frequency of 13.33 Hz.\nTHE RINGING OF THE REMNANT BLACK HOLE\nBackground. The merger process gives rise to a distorted\nblack hole that rings down into quiescence [31, 70\u201373, 117].\nModeling this ringdown signal is a key ingredient of probes\nof the Kerr nature of the remnant and the area law. Within the\nframework of perturbation theory, the remnant signal is dom-\ninated by a superposition of quasinormal modes of the form\nh \u223cexp(\u22122\u03c0ift \u2212\u03b3t) [33, 118\u2013121]. Each mode\u2019s frequency\nf and damping rate \u03b3 are determined by the asymptotic Kerr\nmass Mf and spin \u03c7f, while its amplitude and phase depend on\nthe details of the coalescence. Since the only relevant scale is\nthe black hole mass, heavier black holes ring at lower frequen-\ncies and for a longer time; for a given mass, spin generally in-\ncreases the damping time. While the spectrum depends on the\nassumptions of general relativity and a Kerr metric (with ingo-\ning and outgoing boundary conditions at the black hole and in-\nfinity, respectively), quasinormal modes arise generically also\nin alternative frameworks [122\u2013133]. Detected frequencies\nand times are scaled by a cosmological redshift factor, and the\ncorresponding redshifted timescale is tMf = (1 + z)GMf/c3.\nIndividual modes are indexed by angular numbers (\u2113, m)\nand an overtone number n. For a fixed (\u2113, m), modes with\na higher n typically have higher damping rates [134]. The\nquadrupolar geometry of the binary and the fact that gravita-\ntional radiation is leading-order quadrupolar [135\u2013137] mean\n\n14\nthat in equal-mass, nonprecessing, quasicircular binaries simi-\nlar to GW250114, prograde modes with \u2113= |m| = 2 dominate\nthe signal. The longest-lived, fundamental, n = 0 mode is\nthe main contributor at late times. Fits to numerical-relativity\nsimulations of similar systems additionally suggest that the\nnext strongest mode is n = 1, and that it decays below the\nfundamental around 10 tMf after the merger [138\u2013145].\nMethod. We model the post-merger signal from GW250114\nusing black hole perturbation theory, representing it as a su-\nperposition of generically polarized damped sinusoids [146,\n147].\nThis analysis is distinct from the full inspi-\nral\u2013merger\u2013ringdown treatment described earlier, which in-\ncorporates numerical relativity to capture the complex merger\ndynamics. Our objective here is to directly test the predictions\nof first-order perturbation theory against the data.\nWe choose a reference timescale and merger time consistent\nwith the full-signal analysis. We adopt a reference timescale\nof tMf = 0.337 ms. The reference time tpeak is defined via the\npeak of the inferred strain amplitude [19] and is measured to\nwithin \u00b10.4 tMf at each detector. Both tMf and tpeak are only\nreference points and not a true dependence of the analysis.\nUsing the time-domain ringdown [146] and pyRing [148] in-\nference packages, we model the data after some start time t>\nwith different mode combinations and obtain posteriors for\ntheir parameters. The start time t> is reported relative to tpeak.\nSee the Supplement for details.\nModes in GW250114. Since perturbation theory refers to\nthe asymptotic spacetime, we start by analyzing the data from\nlate times and seek the earliest time after which the signal can\nbe described by a single mode; see Fig. 3, blue. The mode\nfrequency and damping rate are parametrized in terms of a\nKerr black hole mass and spin; this is equivalent to directly\nparametrizing in terms of frequency and damping rate as in\nRef. [7] up to the choice of priors [146]. We find that data at\nlate times are consistent with a single damped sinusoid, whose\namplitude is confidently constrained away from zero at >7\u03c3\ncredibility for start times as late as t> = 20 tMf. The mode de-\ncays away, falling below 3\u03c3 credibility at t> = 27.0 tMf. The\ninferred mode amplitude evolves consistently with a damped\nsinusoid in noise (gray shading). As discussed above, sym-\nmetry and late-time arguments suggest that this mode is the\nfundamental (\u2113= |m| = 2, n = 0) mode of the remnant black\nhole, without any quantitative comparison to the full-signal\nanalysis [e.g., 7]\u2014we label the mode as such in the top panel\nof Fig. 3. Starting at t> = 10.5 tMf, this model recovers a\nSNR of 21 (Fig. 7 in Supplement) and infers the mode\u2019s (red-\nshifted) frequency and damping rate to be f220 = 247+6\n\u22126 Hz\nand \u03b3220 = 221+39\n\u221232 Hz, respectively.\nPushing t> earlier in time and toward the merger increases\nthe SNR, but risks contamination from other modes, linear ef-\nfects beyond exponentially damped sinusoids, or nonlinear ef-\nfects [139, 149\u2013153]. The nonorthogonality of damped sinu-\nsoids further means that a model with additional modes does\nnot necessarily lead to more faithful inference.\nWe there-\nfore again start from late times and seek (i) the time a sec-\nond mode is required and (ii) the earliest time after which\nthe data agree with two modes whose amplitudes decay self-\nconsistently. Given the identification of a single damped si-\nnusoid at late times, we expect any additional modes to be\nshort-lived. Following Refs. [137, 154\u2013163] and expectations\nfor GW250114-like systems [142, 145, 164], we enhance the\nmodel with the first overtone (\u2113= |m| = 2, n = 1), and\nparametrize the frequencies and damping rates of both modes\nas a function of a single mass and spin.\nFigure 3 shows two-mode results in pink. In the bottom\npanel, we confidently extract the overtone for a range of\nstart times. Its amplitude is nonzero at 4.1\u03c3 credibility for\nt> = 6 tMf and remains above 3\u03c3 until t> = 9.0 tMf. The sig-\nnificance drops below 1\u03c3 past t> = 10.5 tMf, when the data\nbecome consistent with a single damped sinusoid. Addition-\nally, t> = 6 tMf emerges as an inflection point in the amplitude\ntrend (gray shading): for later start times, the recovered ampli-\ntudes decay consistently with the expected exponential decay.\nThe divergence between the inferred overtone amplitude and\nthe expected decay for t> < 6 tMf hints at unmodeled features\nin the data, further explored in a forthcoming paper with ex-\ntended models [165]. At t> = 6 tMf, the two-mode SNR is 26,\nand the (redshifted) frequency and damping rate of the over-\ntone are f221 = 249+8\n\u22129 Hz and \u03b3221 = 708+116\n\u2212107 Hz, respectively.\nThe GW250114 post-merger signal after t> = 6 tMf has the\nsame SNR as GW150914 in its entirety.\nTHE KERR NATURE OF THE REMNANT\nIdentification of two modes in the data can be used to test\nthe Kerr nature of the merger remnant. Consistency with Kerr\namounts to the four observables (the frequency and damp-\ning rate of each mode) agreeing with the Kerr spectrum for\nsome mass and spin.\nBlack hole spectroscopy [166\u2013168]\nstarted in earnest with searches for \u2113= |m| = 2 modes in\nGW150914 [7, 148, 154, 156\u2013162, 169] and has since been\nextended to further events and modes [101, 137, 163, 170\u2013\n175]. To constrain deviations away from the Kerr spectrum,\nwe enhance our model with two additional parameters that al-\nlow for deviations in the frequency and damping rate of the\novertone respectively: f221 = f (Kerr)\n221\n(Mf, \u03c7f) exp(\u03b4f221) and\n\u03b3221 = \u03b3(Kerr)\n221 (Mf, \u03c7f) exp(\u03b4\u03b3221). The frequencies and damp-\ning rates of both modes are now parametrized via the remnant\nmass and spin, Mf and \u03c7f, and the deviations, \u03b4f221 and \u03b4\u03b3221.\nThe Kerr spectrum is recovered for \u03b4f221 = \u03b4\u03b3221 = 0.\nWith this setup, we constrain deviations from the Kerr spec-\ntrum at t> = 6 tM to be \u03b4f221 = 0.1+0.3\n\u22120.3, as seen in Fig. 4, while\n\u03b4\u03b3221 remains uninformative within its prior. This bolsters\nconfidence in the identification of this mode as the overtone,\nand establishes consistency with Kerr frequencies to \u00b130%.\nResults for a variety of start times are presented in a forth-\ncoming paper [165]. This is the first constraint of this kind\nderived from data confidently removed from the signal peak\n[137, 154, 163].\n\n15\n2\n3\n4\n5\n6\n7\n8\n9\n10\nt> =t\ntpeak [ms]\n0\n1\n2\n3\n4\nA220 [10 21]\n5\n10\n15\n20\n25\n30\nt> =t\ntpeak [tMf]\n0\n4\n8\nA221 [10 21]\n50%\n90%\n220 model\n220+221 model\nFIG. 3. Strain amplitudes of the fundamental mode A220 (top) and first overtone A221 (bottom) reported at the start of each analysis, t> = t\u2212tpeak,\nin units of tMf (bottom x-axis) and milliseconds (top x-axis). Bars mark 90% (thin) and 50% (thick) credible intervals around the median\n(circle), when modeling the data with one (blue) or two (pink) modes. Gray shading shows the expected amplitude decay as inferred from\nt> = 10.5 tMf for the single-mode analysis (top; 220 ref), and t> = 6 tMf for the two-mode analysis (bottom; 221 ref). Single-mode results are\nshown only after 10.5 tMf (top), where support for a second mode is < 1\u03c3. Overtone results are shown up to 15 tMf, by which time support\nfor a second mode has completely vanished. Results pre-6 tMf are given lower opacity as the overtone decay does not follow the expected\ntrend. Hatched regions are excluded to at least 3\u03c3; higher significance regions are contained within it. We plot ringdown results but obtain\nqualitatively consistent results with pyRing. Mode frequencies, damping rates and SNRs are plotted in the Supplement.\n200\n300\n400\n(1+z) f221 [Hz]\n220\n230\n240\n250\n260\n270\n280\n(1+z) f220 [Hz]\nf =0.68, (1+z)Mf =68.4M\n0.5\n0.0\n0.5\nf221\nPYRING\nRINGDOWN\nprior\nFIG. 4. Spectroscopic test of the Kerr nature of the remnant black\nhole for t> = 6 tMf. Left: 90% posterior for the observed fundamen-\ntal and overtone frequencies, compared to the range allowed by the\nKerr spectrum (black shaded region) for any black hole mass (vertical\nspan) and spin (horizontal span). The cross marks reference values\nfrom the full-signal analysis. Right: posterior on the deviation \u03b4 f221\nof the frequency of the first overtone from the Kerr spectrum, with\nshading and a line showing the 90% credible region and the median\nrespectively, a vertical line showing the Kerr prediction of \u03b4 f221 = 0,\nand a horizontal line showing the prior. The pyRing analysis (orange)\nstarts \u223c0.5 tMf after ringdown (green), which is why the posteriors\nare not identical, see the Supplement. The observed spectrum is con-\nsistent with Kerr to \u00b130%.\nHAWKING\u2019S AREA LAW\nBackground.\nThe second law of black hole mechanics,\noriginally proven by Hawking [75] (but previously explored as\nirreducible mass by Christodoulou [176], Christodoulou and\nRuffini [177] and stated by Penrose and Floyd [178]), states\nthat the black hole horizon area cannot decrease in time. A\ndirect consequence is an upper limit of 50% on the efficiency\nof gravitationally radiating processes in systems with initially\nvanishing binding energy; this is further limited to \u223c29% for\nnon spinning black holes [75].\nThe area law relies on three conditions. The first is the\nnull-energy condition, a restriction on the properties of mat-\nter. It is violated, for example, by Hawking radiation which\nextracts energy from a black hole and causes its horizon to\nshrink [46]\u2014in this case, the area law is superseded by a\ngeneralized law that considers both the entropy of the black\nhole and that of the radiation [45, 179]. The second is the\npremise that the observed objects are black holes and weak\ncosmic censorship holds, i.e., no naked singularities. Alter-\nnative compact objects [180\u2013183] have modified entropy and\nviolate the null-energy condition; their interactions could vio-\nlate the area law. The third is general relativity; the area law\ncan be violated in alternative theories [126, 129, 184\u2013186].\n\n16\nTesting the area law thus amounts to testing for physical be-\nhavior that violates at least one of these conditions.\nIn the context of a binary merger, the area law imposes an\nincrease in the horizon area of the remnant with respect to the\ntotal area of the initial black holes [75], providing a testable\nprediction [187\u2013191]. However, since black hole areas are not\ndirect observables, extracting them hinges on certain assump-\ntions: (i) GW250114 originated from a quasicircular merging\nbinary, (ii) general relativity is a good approximation away\nfrom highly dynamical regions, and (iii) the black holes are\nwell described by the Kerr metric. The latter guides the black\nhole states we probe: the initial black holes are considered at\nwide separations, while the final black hole is considered in its\nasymptotic state. We thus adopt the Kerr area formula [41],\nA(m, \u03c7) = 8\u03c0\n\u0012Gm\nc2\n\u00132 \n1 +\nq\n1 \u2212\u03c72\n!\n,\n(1)\nfor a black hole of mass m and spin \u03c7. This need not hold\nbeyond vacuum general relativity [126, 129, 192, 193].\nMethod. We extract the properties of the initial and final\nblack holes independently from the pre- and post-merger sig-\nnal respectively, discarding data in between. Our test, there-\nfore, probes for violations during the most nonlinear and dy-\nnamical portion of the signal, which it excludes. It is sen-\nsitive to any nonstandard process that may alter the radiated\nenergy or momentum, or any physics that modifies the ring-\ndown spectrum sufficiently to bias the inferred remnant mass\nand spin, e.g., electromagnetic charge or other deviations from\nKerr. Most generally, it is sensitive to physics that breaks any\nof the premises above and leads the inspiral and ringdown\nregimes to be better described independently than coherently\n[189]. Comparing the inspiral to the ringdown in this fash-\nion can provide complementary constraints to those derived\nfrom the ringdown alone [194\u2013200]. We truncate the data in\nthe time domain [146, 188, 189, 201, 202] rather than the fre-\nquency domain [203, 204], as there is no exact one-to-one\ncorrespondence between signal time and Fourier frequency\nbeyond the adiabatic inspiral [99, 205].\nThe initial horizon area. The initial black holes are consid-\nered at wide separations, where they obey the Kerr metric and\nthe total area is the sum of the individual areas. The quanti-\nties reported in data analysis differ by the amount of energy\nand angular momentum absorbed by the black holes through-\nout the binary evolution, which is negligible for comparable-\nmass systems [206, 207]. We therefore infer the black hole\nproperties from the inspiral signal and interpret them directly\nas the infinite-separation quantities. Assuming that general\nrelativity describes the inspiral [7, 137, 163, 208\u2013210] and\nthe binary orbit is quasicircular [211], we model the sig-\nnal with NRSur7dq4, up to a preselected time, t<, that is\nquoted in units of the total mass from the full-signal analy-\nsis, tM \u2261(1 + z)GM/c3= 0.354 ms. We then infer (among\nother parameters) the masses and spins of the initial black\nholes, informed only by data before t< using the TDInf infer-\nence package [189, 201, 202], and from them the initial area\nAi = A1 + A2. See the Supplement for details.\nTo interpret the pre-merger truncation times, we use the\ngravitational-wave luminosity to proxy how relativistic the\nsystem is [68]. Based on the full-signal analysis, in the Sup-\nplement we show that the luminosity is sharply peaked at\nmerger and drops to 10% of its maximum at \u221236 tM before\ntpeak. We present results for an array of t< in Fig. 5 and further\nhighlight t< = \u221240 tM, a choice that excludes the two loud-\nest signal cycles. For reference, the total signal SNR before\nt< = \u221240 tM is 55; even truncated, GW250114 has a higher\nSNR than any other signal to date [18].\nThe final horizon area. The mass and spin of the remnant\nare inferred through the post-merger signal. Picking an anal-\nysis start time requires balancing: (i) independence from the\nfull-signal analysis that assumes the area law, (ii) maximizing\nthe amount of data and thus the SNR, and (iii) using a model\nwithin its regime of validity. Since modes are not orthogonal,\nthe more complex two-mode model is not universally prefer-\nable, as the overtone may degrade the inference especially if\nit is not detectable. Therefore we adopt the most parsimo-\nnious model (single \u2113= |m| = 2, n = 0 mode) at its earliest\ntime of applicability (conservatively, t> = 10.5 tMf when the\novertone significance is <1\u03c3) thus minimizing potential con-\ntamination [212]. We then use the mode\u2019s inferred frequency\nand damping rate to calculate the mass and spin of the final\nKerr black hole and hence its area, A f .\nResults. Figure 5 shows the fractional difference between\nthe final and initial areas, (A f \u2212Ai)/Ai, where cosmological\nredshift factors cancel out because the area is proportional to\nthe mass squared. For t< = \u221240 tM, A f > Ai at the 4.4\u03c3 level,\ncomputed as described in the Supplement. We find consis-\ntency with an increase in the area to at least 3.4\u03c3 for all times\nt< > \u2212250 tM, exceeding 5\u03c3 for t< \u2265\u221210 tM. In the Supple-\nment we present results for more times and models; the two-\nmode model at its earliest time of applicability, t> = 6 tMf, also\nagrees with the area law at 3.6\u03c3. All results are further consis-\ntent with the general relativity expectation for GW250114, ob-\ntained from the full-signal analysis with NRSur7dq4 used in\nFig. 2, which considers the entire signal coherently and obeys\nthe area law a priori. The strength of GW250114 enables such\ntests even while excluding the loudest portions of the signal\nand without any modeling of the nonlinear merger dynamics\nthrough numerical relativity, cf. inset of Fig. 5. Similar analy-\nses of GW150914 [189, 190] yielded \u223c2\u03c3 results, albeit with\nless conservative assumptions: a pre-merger analysis that ex-\ntended to the waveform peak and a quasinormal mode model\nthat presumed circular polarization.\nCONCLUSION\nThe gravitational-wave signal GW250114 is a milestone in\nthe decade-long history of gravitational-wave science. With\nits high SNR, GW250114 offers an exquisitely clear view of\nthe highly dynamical process by which two black holes merge\nto give rise to a remnant black hole. Data from LIGO Hanford\nand LIGO Livingston are consistent with multiple quasinor-\n\n17\n80\n60\n40\n20\n0\nt< =t\ntpeak [ms]\n250\n200\n150\n100\n50\n0\nt< =t\ntpeak [tM]\n0\n1\n(\nf\ni)/\ni\n0\n1\n2\n3\nFractional Area Difference, (\nf\ni)/\ni\n0\n1\n2\nProbability Density\n100\n50\n0\n50\nt - tpeak [tM]\n1\n0\n1\nStrain [10 21]\nFIG. 5. Fractional difference between the area of the final black hole,\nAf , and the initial black holes, Ai. Top: Posterior as a function of\nthe pre-merger truncation time, t< = t \u2212tpeak. Bars represent 90%\n(thin line) and 50% (thick line) credible intervals around the median\n(circle). The vertical orange band denotes t< = \u221240 tM, when the\ngravitational-wave luminosity is at 10% of its maximum. Bottom:\nPosterior (histogram) and prior (dotted line) for t< = \u221240 tM. The his-\ntogram is produced from all pairwise combinations of ringdown and\npyRing post-merger samples with TDInf pre-merger samples. The\nshading on the right highlights configurations that would violate en-\nergy conservation M f \u2264m1 + m2, a bound saturated for maximally-\nspinning initial black holes that merge into a nonspinning remnant\n[75, 213, 214]. The shading on the left highlights configurations that\nwould violate the area law, (A f \u2212Ai)/Ai < 0. The vertical gray\nband is the 90% credible interval from the full-signal analysis used\nin Fig. 2, i.e., the general relativity expectation for GW250114. The\ninset illustrates the analysis via the signal reconstruction in LIGO\nLivingston from the full-signal (gray), and when split into the pre-\nmerger (orange) and post-merger (blue) stages; the merger phase is\nincluded in neither analysis. We find that Af > Ai to high credibil-\nity, indicating that GW250114 obeys Hawking\u2019s area law.\nmal modes of a remnant Kerr black hole and with Hawking\u2019s\narea law. Further precision tests of general relativity and the\nringdown are presented in a forthcoming publication [165].\nOur results suggest that astrophysical black holes are indeed\nextremely simple objects that follow general relativity and the\nKerr description. The strongly perturbed merger remnant set-\ntles into a higher-entropy, quiescent state within a few dynam-\nical timescales. The next decade of gravitational-wave science\nis bound to enhance our view of these highly dynamical, rela-\ntivistic systems.\nStrain data from the LIGO detectors for GW250114 are\navailable from the Gravitational Wave Open Science Center\n[215]. All the material required for reproducing the figures,\nincluding scripts and posterior distributions from the analy-\nses, is available in the data release [216].\nACKNOWLEDGMENTS\nThis work made use of the following software, listed in al-\nphabetical order: arviz [217], Asimov [218], astropy [219\u2013\n221], BayesWave [20], bilby [222, 223], cmasher [224], cp-\nnest [225], cWB [97, 98], dynesty [226], emcee [227], Gst-\nLAL [80\u201391], gwpy [228, 229], h5py [230], PhenomXPHM\n[103, 104], PhenomXO4a [109, 110], jax [231], jupyter\nand ipython [232\u2013234], lalsuite [235], swiglal [236], mat-\nplotlib [237, 238], MBTA [94, 95], MLy [92], NRSur7dq4\n[19], numpy [239], numpyro [240, 241], pandas [242, 243],\npesummary [244], PyCBC [96], pyRing [148, 245], py-\nSEOBNR [246], python [247], qnm [248, 249], RIFT [250\u2013\n252], ringdown [146, 253], scipy [254, 255], seaborn\n[256], SEOBNRv5PHM [105\u2013108], SEOBNRv5EHM [111],\nTEOBResumS-DALI [112], SPIIR [93], TDInf [201, 202,\n257], tqdm [258], Software citation information was aggre-\ngated using The Software Citation Station [259, 260].\nThis material is based upon work supported by NSF\u2019s LIGO\nLaboratory, which is a major facility fully funded by the Na-\ntional Science Foundation. The authors also gratefully ac-\nknowledge the support of the Science and Technology Facili-\nties Council (STFC) of the United Kingdom, the Max-Planck-\nSociety (MPS), and the State of Niedersachsen/Germany for\nsupport of the construction of Advanced LIGO and construc-\ntion and operation of the GEO 600 detector. Additional sup-\nport for Advanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the Ital-\nian Istituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scientifique (CNRS) and the\nNetherlands Organization for Scientific Research (NWO) for\nthe construction and operation of the Virgo detector and the\ncreation and support of the EGO consortium. The authors also\ngratefully acknowledge research support from these agencies\nas well as by the Council of Scientific and Industrial Research\nof India, the Department of Science and Technology, India,\nthe Science & Engineering Research Board (SERB), India, the\nMinistry of Human Resource Development, India, the Span-\nish Agencia Estatal de Investigaci\u00b4on (AEI), the Spanish Min-\nisterio de Ciencia, Innovaci\u00b4on y Universidades, the European\nUnion NextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Computing,\nBig Data and Quantum Computing, funded by the European\nUnion NextGenerationEU, the Comunitat Auton`oma de les\nIlles Balears through the Conselleria d\u2019Educaci\u00b4o i Universi-\ntats, the Conselleria d\u2019Innovaci\u00b4o, Universitats, Ci`encia i So-\ncietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the Polish Na-\ntional Agency for Academic Exchange, the National Science\nCentre of Poland and the European Union - European Re-\ngional Development Fund; the Foundation for Polish Science\n(FNP), the Polish Ministry of Science and Higher Education,\n\n18\nthe Swiss National Science Foundation (SNSF), the Russian\nScience Foundation, the European Commission, the Euro-\npean Social Funds (ESF), the European Regional Develop-\nment Funds (ERDF), the Royal Society, the Scottish Funding\nCouncil, the Scottish Universities Physics Alliance, the Hun-\ngarian Scientific Research Fund (OTKA), the French Lyon In-\nstitute of Origins (LIO), the Belgian Fonds de la Recherche\nScientifique (FRS-FNRS), Actions de Recherche Concert\u00b4ees\n(ARC) and Fonds Wetenschappelijk Onderzoek - Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the Na-\ntional Research, Development and Innovation Office of Hun-\ngary (NKFIH), the National Research Foundation of Korea,\nthe Natural Sciences and Engineering Research Council of\nCanada (NSERC), the Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology, and\nInnovations, the International Center for Theoretical Physics\nSouth American Institute for Fundamental Research (ICTP-\nSAIFR), the Research Grants Council of Hong Kong, the Na-\ntional Natural Science Foundation of China (NSFC), the Israel\nScience Foundation (ISF), the US-Israel Binational Science\nFund (BSF), the Leverhulme Trust, the Research Corporation,\nthe National Science and Technology Council (NSTC), Tai-\nwan, the United States Department of Energy, and the Kavli\nFoundation. The authors gratefully acknowledge the support\nof the NSF, STFC, INFN and CNRS for provision of compu-\ntational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2402:\n24103006, 24103005, and 2905: JP17H06358, JP17H06361\nand JP17H06364, JSPS Core-to-Core Program A. Advanced\nResearch Networks, JSPS Grants-in-Aid for Scientific Re-\nsearch (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for\nTransformative Research Areas (A) 20A203: JP20H05854,\nthe joint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of the\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and the\nNational Science and Technology Council (NSTC) in Taiwan\nunder grants including the Science Vanguard Research Pro-\ngram, the Advanced Technology Center (ATC) of NAOJ, and\nthe Mechanical Engineering Center of KEK.\nAdditional acknowledgements for support of individual au-\nthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied a Cre-\native Commons Attribution (CC BY) license to any Author\nAccepted Manuscript version arising. 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Riess, Tensions between the\nEarly and the Late Universe, Nature Astron. 3, 891 (2019),\narXiv:1907.10625 [astro-ph.CO].\n\n27\nSupplement to \u201cGW250114: Testing Hawking\u2019s Area Law and the Kerr Nature of Black Holes\u201d\nI. Observation and inference details\nHere we describe additional details relevant to the detection and parameter inference of GW250114. See also Ref. [102] for\nmore details on the methods for identifying and characterizing gravitational-wave transients.\nThe GstLAL [80\u201391] search pipeline was the first to report that it had identified GW250114 with high confidence 15 seconds\nafter the signal arrived. Within 75 s of the signal crossing the Earth, all operating low-latency search pipelines reported detections,\nincluding those targeting unmodelled transient events: MLy [92], SPIIR [93], MBTA [94, 95], PyCBC [96], and cWB [97, 98].\nAll pipelines assigned a false alarm rate of 1 per 100 years or lower. The modeled pipelines reported network matched-filter\nSNRs [100] ranging from 77 to 80. The variation is due to the discreteness in the sets of filter waveforms used [102] as well\nas differences in the estimation of the detector noise power spectral density at that time. This signal has by far the highest\nSNR yet recorded, with the previous highest being the single-detector signal GW230814 230901 with a matched-filter SNR\nof 42 [18, 101]. The two-detector sky localization was released publicly at 08:22:35 UTC, 32 s after the signal reached the\ndetectors. Based on the classification reported by the search pipelines [261], GW250114 was determined to have a greater than\n99% probability of having a binary black hole origin. The data-quality report noted no issues in LIGO Hanford. Some excess\npower was reported in LIGO Livingston, although glitch subtraction [20, 262, 263] was not needed due to the power being\nconfined to low frequencies.\nWe infer the source properties following standard procedures [102] using the Asimov workflow package [218]. We analyze 8 s\nof data in the 20\u2212896 Hz frequency range. The detector noise power spectral density is obtained with BayesWave [20, 21]. We\nuse the inference library bilby [222, 223] and the dynesty nested sampler [226] to sample from the posterior distribution of the\nsource parameters for the main analyses that assume quasicircular orbits. We further use bilby and RIFT [250\u2013252] for analyses\nthat allow for eccentric orbits, but are restricted to aligned spins. We marginalize over the luminosity distance with a prior that\ncorresponds to a uniform merger rate in co-moving volume using the Planck 2015 \u039bCDM cosmology model [264]. We further\nmarginalize over uncertainties in the detector calibration; the 1\u03c3 bounds on the calibration uncertainty remain within 4% in the\namplitude and 2 degrees in phase for both detectors within the analysis band.\nWe model the signal with four waveform models that include the effects of spin-precession and higher-order radiation modes\nbut are restricted to quasi-circular orbits: NRSur7dq4 [19], PhenomXPHM [103, 104], SEOBNRv5PHM [105\u2013108], and Phe-\nnomXO4a [109, 110]. Analysis settings for PhenomXPHM, SEOBNRv5PHM, and PhenomXO4a ensure that modes up to \u2113= 4\nare fully accounted for. Due to the finite length of NRSur7dq4, the \u2113= 3 and \u2113= 4 modes enter above 22.5 Hz and 30 Hz re-\nspectively. Priors are uniform in detector-frame component masses and spin magnitudes, isotropic in spin orientations, isotropic\nin the binary\u2019s orientation, uniform in merger time and coalescence phase, uniform in comoving volume, and isotropic in sky\nlocation. Figure 6 shows the two-dimensional posterior for the component masses and effective inspiral and precessing spin\nparameters obtained from each model. Even though the posteriors are not identical, they all lead to a similar interpretation of\nGW250114 as an equal-mass system with small spins. We list the 90% credible intervals for further parameters in Table I.\nWe additionally consider two models that allow for eccentric orbits but are restricted to aligned spins: SEOBNRv5EHM [111]\nand TEOBResumS-DALI [112]. We use identical settings to the main runs, and adopt uniform priors for the orbital eccentricity\nand relativistic (mean) anomaly for SEOBNRv5EHM (TEOBResumS-DALI). Both analyses yield no evidence for eccentricity,\nwith 90% upper limits of e\u22640.03 at an orbit-averaged gravitational-wave frequency [265] of 13.33 Hz.\nII. Technical details and further results for the post-merger analysis\nIIA. Reference parameters\nThe ringdown analyses in the main text are set up based on a number of reference parameters derived from a preliminary\nfull-signal NRSur7dq4 analysis, which are also consistent with the final production analysis. The first input needed is some\nguidance on the inferred merger time. As a proxy for this, we adopt the inferred peak of the gravitational-wave strain, integrated\nover the celestial sphere around the source; this quantity is independent of the observer\u2019s orientation and is commonly adopted\nas a reference in numerical-relativity studies [e.g., 145, 164]. This is also the quantity adopted by the NRSur7dq4 approximant\nas the definition of the coalescence time [19]. For a waveform decomposed in terms of spin-weighted spherical harmonics\n\u22122Y\u2113m(\u03b8, \u03d5) such that\nh+ \u2212ih\u00d7 =\nX\n\u2113m\nh\u2113m(t) \u22122Y\u2113m(\u03b8, \u03d5) ,\n(2)\n\n28\nTABLE I. Source properties of GW250114 for various parameters and four waveform models for spin-precessing, quasicircular systems. We\nreport the median values together with the 90% symmetric credible intervals at a reference frequency of 20 Hz. For parameters that rail against\nthe minimum (maximum) possible values we display upper (lower) limits at the 90% credible level.\nParameter\nNRSur7dq4\nSEOBNRv5PHM\nPhenomXPHM\nPhenomXO4a\nPrimary mass m1/M\u2299\n33.6+1.2\n\u22120.8\n33.5+1.2\n\u22120.8\n33.7+1.2\n\u22120.9\n33.5+1.3\n\u22120.9\nSecondary mass m2/M\u2299\n32.2+0.8\n\u22121.3\n32.2+0.9\n\u22121.3\n32.3+0.9\n\u22121.4\n32.1+0.9\n\u22121.5\nMass ratio q = m2/m1\n\u22650.91\n\u22650.91\n\u22650.91\n\u22650.91\nTotal mass M/M\u2299\n65.8+1.1\n\u22121.2\n65.7+1.1\n\u22121.1\n66.0+1.2\n\u22121.1\n65.5+1.3\n\u22121.3\nDetector-frame total mass (1 + z) M/M\u2299\n71.5+0.9\n\u22121.0\n71.1+1.1\n\u22121.1\n71.6+1.0\n\u22121.1\n70.9+1.3\n\u22121.2\nChirp mass M/M\u2299\n28.6+0.5\n\u22120.5\n28.6+0.5\n\u22120.5\n28.7+0.5\n\u22120.5\n28.5+0.6\n\u22120.6\nDetector-frame chirp mass (1 + z) M/M\u2299\n31.1+0.4\n\u22120.4\n30.9+0.5\n\u22120.5\n31.2+0.4\n\u22120.5\n30.8+0.6\n\u22120.5\nFinal mass Mf/M\u2299\n62.7+1.0\n\u22121.1\n62.6+1.0\n\u22121.0\n62.9+1.1\n\u22121.0\n62.5+1.2\n\u22121.1\nDetector-frame final mass (1 + z) M f /M\u2299\n68.1+0.8\n\u22120.9\n67.8+1.0\n\u22121.0\n68.2+0.9\n\u22121.0\n67.6+1.1\n\u22121.1\nPrimary spin magnitude \u03c71\n\u22640.24\n\u22640.32\n\u22640.32\n\u22640.30\nSecondary spin magnitude \u03c72\n\u22640.26\n\u22640.34\n\u22640.36\n\u22640.35\nEffective inspiral-spin \u03c7eff\n\u22120.03+0.03\n\u22120.04\n\u22120.05+0.04\n\u22120.05\n\u22120.03+0.04\n\u22120.05\n\u22120.07+0.06\n\u22120.05\nEffective precessing-spin \u03c7p\n0.11+0.15\n\u22120.11\n0.15+0.19\n\u22120.15\n0.15+0.21\n\u22120.15\n0.16+0.16\n\u22120.13\nFinal spin \u03c7f\n0.68+0.01\n\u22120.01\n0.67+0.01\n\u22120.01\n0.68+0.01\n\u22120.01\n0.67+0.02\n\u22120.01\nLuminosity distance DL/Mpc\n403+74\n\u221270\n385+75\n\u221269\n399+79\n\u221272\n381+77\n\u221272\nViewing angle \u0398/rad\n0.78+0.19\n\u22120.23\n0.82+0.19\n\u22120.22\n0.78+0.20\n\u22120.23\n0.82+0.21\n\u22120.23\nSource redshift z\n0.09+0.01\n\u22120.01\n0.08+0.01\n\u22120.01\n0.09+0.02\n\u22120.01\n0.08+0.02\n\u22120.01\nNetwork (\u2113= 4, |m| = 4) mode SNR \u03c144\n3.6+1.4\n\u22121.5\n3.9+1.4\n\u22121.5\n3.6+1.5\n\u22121.6\n4.0+1.5\n\u22121.6\n32\n33\n34\n35\nm1 [M ]\n32\n34\nm2 [M ]\nNRSur7dq4\nPhenomXPHM\nSEOBNRv5PHM\nPhenomXO4a\nNRSur7dq4\nPhenomXPHM\nSEOBNRv5PHM\nPhenomXO4a\n0.0\n0.1\n0.2\n0.3\n0.4\np\n0.15\n0.10\n0.05\n0.00\n0.05\neff\nNRSur7dq4\nPhenomXPHM\nSEOBNRv5PHM\nPhenomXO4a\nNRSur7dq4\nPhenomXPHM\nSEOBNRv5PHM\nPhenomXO4a\nFIG. 6. Marginal posterior distributions for the source-frame component masses (left) and effective inspiral and precessing spin parameters\n(right) of GW250114 using four waveform models for spin-precessing, quasicircular systems. All models favor an equal-mass system with\nsmall spins.\nthe peak of the strain over the celestial sphere is given by\ntpeak = argmaxt\n\uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0\nX\n\u2113m\n|h\u2113m(t)|2\n\uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb,\n(3)\n\n29\nTABLE II. Reference parameters for the ringdown analysis.\nParameter\nValue\nDescription\ntpeak (geocenter)\n1420878141.235932 s\nReference time at geocenter\n\u03b1\n2.333 rad\nRight ascension of source\n\u03b4\n0.190 rad\nDeclination of source\n\u03c8\n1.329 rad\nPolarization angle\ntLHO\npeak\n1420878141.2190118 s\nReference time at LIGO Hanford\ntLLO\npeak\n1420878141.2165165 s\nReference time at LIGO Livingston\n(1 + z) Mf\n68.409 M\u2299\nReference final black hole mass\ntMf\n0.337 ms\nReference (1 + z)Mf in units of time\n(1 + z) M\n71.849 M\u2299\nReference total mass\ntM\n0.354 ms\nReference (1 + z)M in units of time\nwhich is manifestly invariant under rotations. This is equivalent to the peak of the strain norm integrated over the celestial sphere\nbecause the angular harmonics are orthonormal.\nFor each sample in the NRSur7dq4 reference posterior, we use Eq. (3) to infer the arrival time of the peak strain at geocenter,\nor any given detector. This results in a posterior on the merger time at each detector. For the NRSur7dq4 run in the main text,\nthe measured GPS peak times are tLHO\npeak = 1420878141.2190+0.0001\n\u22120.0001 s at LIGO Hanford and tLLO\npeak = 1420878141.2165+0.0001\n\u22120.0001 s at\nLIGO Livingston. We select the maximum-likelihood sample from the preliminary reference posterior as a representative value\nfor the ringdown analysis. This is the reference time tpeak = 1420878141.235932 s at geocenter, with the corresponding sky\nlocation (\u03b1 = 2.333, \u03b4 = 0.190) implicitly encoding the individual detector times. We list all reference values in Table II.\nTo guide the analysis and report results, it is useful to define a reference timescale in units of the final black hole mass. We\nderive a posterior on the redshifted final black hole mass (1 + z)Mf and spin \u03c7f by applying the NRSur7dq4Remnant model\n[19] to NRSur7dq4 posterior samples. As reference to quote timescales in the ringdown analysis, we adopt the same maximum-\nlikelihood sample mentioned above, which is quoted in Table II together with the corresponding timescale tMf. Relative to\nthe chosen reference times, the peak distributions inferred by the NRSur7dq4 analysis in the main text are tLHO\npeak \u2212tLHO\nref\n=\n\u22120.07+0.37\n\u22120.37 tMf at LIGO Hanford and tLLO\npeak\u2212tLLO\nref\n= 0.07+0.38\n\u22120.38 tMf at LIGO Livingston. The standard deviations of those distributions\nare 0.22 tMf and 0.23 tMf respectively.\nIIB. Ringdown analyses\nIIB1. Parameterization and priors\nEach quasinormal mode is described by four parameters besides its frequency and damping rate: an overall amplitude A\u2113mn,\na polarization ellipticity \u03f5\u2113mn, a polarization angle \u03b8\u2113mn, and a fiducial phase \u03d5\u2113mn [146, 147]. These parameters control the\namplitude and phase of the two gravitational-wave polarizations (+ and \u00d7) for each mode:\nh+ = A \u0002cos \u03b8 cos(2\u03c0ft \u2212\u03d5) \u2212\u03f5 sin \u03b8 sin(2\u03c0ft \u2212\u03d5)\u0003 exp(\u2212\u03b3t) ,\n(4a)\nh\u00d7 = A \u0002sin \u03b8 cos(2\u03c0ft \u2212\u03d5) + \u03f5 cos \u03b8 sin(2\u03c0ft \u2212\u03d5)\u0003 exp(\u2212\u03b3t) ,\n(4b)\nsuppressing mode indices (\u2113, |m|, n) for brevity. This is the most generic expression for a quasinormal-mode signal and subsumes\nboth positive and negative frequency contributions, which jointly encode the polarization content of each mode [146, 147].\nAssuming prograde modes with nonvanishing m, the sign of the frequency is related to the sign of the azimuthal number by\nsgn(m) = sgn( f), so that the positive and negative frequencies encode the right- and left-handed polarized components of the\nmode. The same would be true for retrograde modes, except that sgn(m) = \u2212sgn(f). This paper only considers prograde modes.\nWithout information about the expected intrinsic amplitudes of the quasinormal modes, ringdown analyses cannot infer a\nluminosity distance and the only mass scale to which they are sensitive is the product (1 + z)Mf. In the case of a Kerr fit, all\nfrequencies and damping rates are derived from a given (1 + z)Mf and \u03c7f, such that f\u2113|m|n = f\u2113|m|n[(1 + z)Mf, \u03c7f] and \u03b3\u2113|m|n =\n\u03b3\u2113|m|n[(1 + z)Mf, \u03c7f]. For beyond-Kerr fits, we introduce additional parameters \u03b4f\u2113|m|n and \u03b4\u03b3\u2113|m|n such that f\u2113|m|n = f\u2113|m|n[(1 +\nz)Mf, \u03c7f] exp(\u03b4 f\u2113|m|n) and \u03b3\u2113|m|n = \u03b3\u2113|m|n[(1 + z)Mf, \u03c7f] exp(\u03b4\u03b3\u2113|m|n). The exponential parameterization avoids a singularity as the\ndeviation parameter approaches \u22121 [146].\nThe ringdown code places priors that are flat in (1 + z)Mf, \u03c7f, A, \u03b8, and \u03d5 as well as, when applicable, \u03b4f221 and \u03b4\u03b3221; the\nellipticity prior peaks at \u03f5 = 0 but has broad support over the entire domain (Fig. 16 in [147]). The amplitude prior is flat in\n\n30\nA over the interval [0, 5 \u00d7 10\u221220] and is broad enough to always offer full support to the posterior without truncating it. The\npriors in \u03b4 f221 and \u03b4\u03b3221 are flat over the intervals [\u22120.8, 0.8] and [\u22120.5, 0.5] respectively. The quasinormal-mode polarization\nangle \u03b8 is fully degenerate with the source polarization angle \u03c8 [146, 147], which defines the orientation of the source\u2019s angular\nmomentum relative to the celestial North pole and is used to compute the antenna pattern response functions for each detector\n[266, 267]. Given this exact degeneracy, the ringdown analysis chooses a fiducial angle \u03c8 = 1.329 to compute antenna patterns,\nbased on the same maximum-likelihood reference sample used to derive tpeak as explained above, although any arbitrary choice\nof \u03c8 would be valid. The prior in the ringdown code is independent for each mode in all parameters.\nThe pyRing code natively parameterizes the modes slightly differently. For a given (\u2113, |m|, n) mode, it uses\nh+ \u2212ih\u00d7 = C\u2113,+m,n \u22122Y\u2113+m(\u03b9, \u03c6 = 0) exp \u0002i \u00002\u03c0f\u2113|m|nt + \u03d5\u2113,+m,n\n\u0001\u0003 exp \u0002\u2212\u03b3\u2113|m|nt\u0003 +\nC\u2113,\u2212m,n \u22122Y\u2113\u2212m(\u03b9, \u03c6 = 0) exp \u0002i \u0000\u22122\u03c0f\u2113|m|nt + \u03d5\u2113,\u2212m,n\n\u0001\u0003 exp \u0002\u2212\u03b3\u2113|m|nt\u0003 ,\n(5)\nwhere \u03b9 is an inclination parameter that is sampled from a prior uniform in cos \u03b9, at the same time as the free amplitudes C\u2113,+m,n and\nC\u2113,\u2212m,n, which can be interpreted as the amplitude of the right and left-handed polarized contributions to the mode respectively;\nthe corresponding phases, \u03d5\u2113,+m,n and \u03d5\u2113,\u2212m,n, combine in difference and sum to produce \u03b8 and \u03d5 in Eq. (4) [147], and are fully\ndegenerate with the polarization angle \u03c8, which pyRing also samples over a flat prior. The pyRing prior is also flat on (1 + z)Mf\nand \u03c7f.\nThe pyRing prior on the mode amplitude A is implicitly defined by the priors on C\u2113,\u00b1m,n, which are uniform over the interval\n[0, 5 \u00d7 10\u221220], and the prior on \u03b9; because of prior volume effects, it amounts to a density that has no support at the origin and\ndisfavors A \u21920 (cf. Fig. 16 in [147]). Additionally, since all modes share cos \u03b9, the prior correlates the different modes. For a\ntwo-mode model with \u2113= |m| = 2 and n = 0, 1, the Jacobian to a flat prior in {A, \u03f5} can be computed analytically and is given by\nJ =\n(1 \u2212cos2 \u03b9)4\n4\nh\nC2,\u22122,0 (1 \u2212cos \u03b9)2 + C2,+2,0 (1 + cos \u03b9)2i h\nC2,\u22122,1 (1 \u2212cos \u03b9)2 + C2,+2,1 (1 + cos \u03b9)2i .\n(6)\nIn the main text, we reweight the pyRing posterior to a flat prior in {A, \u03f5} by applying this Jacobian and truncating to the\nappropriate bounds.\nThe pyRing code implements deviations from the Kerr spectrum by writing\n\u03c9221 = \u03c9221[(1 + z)Mf, \u03c7f] (1 + \u03b4\u03c9221) ,\n(7a)\n\u03c4221 = \u03c4221[(1 + z)Mf, \u03c7f] (1 + \u03b4\u03c4221) ,\n(7b)\nwhere \u03c9221 \u22612\u03c0 f221 and \u03c4221 \u22611/\u03b3221. For small deviation parameters, this parameterization is equivalent to the ringdown\none, except with a singularity at \u03b4\u03c9 = \u22121 and \u03b4\u03c4 = \u22121. The above implies the following relationship between the ringdown\nparameters (\u03b4 f221, \u03b4\u03b3221) and the pyRing parameters (\u03b4\u03c9221, \u03b4\u03c4221):\n\u03b4f221 = log(1 + \u03b4\u03c9221) , \u03b4\u03b3221 = \u2212log(1 + \u03b4\u03c4221) .\n(8)\nTo go from a uniform prior in (\u03b4\u03c9221, \u03b4\u03c4221) to a uniform prior in (\u03b4f221, \u03b4\u03b3221) we must apply a Jacobian given by\nJ = |1 + \u03b4\u03c9221|\u22121 |1 + \u03b4\u03c4221|\u22121 .\n(9)\nIn the main text, we reweight the pyRing posterior to a flat prior in \u03b4f221 and \u03b4\u03b3221 by applying this Jacobian and truncating to\nthe appropriate bounds.\nIIB2. Data conditioning\nBoth the pyRing and ringdown analyses are based on data sampled at 4096 Hz with a covariance matrix derived from the\nsame estimate of the power spectral density used in the main analysis described in Sec. I of this Supplement. Before obtaining\nthe covariance matrix, the power spectral density is treated to censor frequencies below 20 Hz and above 1830 Hz to match the\nintegration band for the likelihood in the full-signal analysis [174].\nAdditionally, pyRing applies a Butterworth bandpass filter to the data, suppressing frequencies below 20 Hz and above\n2043 Hz; the filtering is applied to 64 s of data around the event. ringdown only applies a high-pass Butterworth filter at\n10 Hz to remove zero-frequency offsets; there is no low-pass filtering other than truncation of the frequency series at Nyquist\n(the digital filter described in Ref. [174]); the conditioning is applied to 634 s of data around the event time. Neither code ap-\nplies any filtering to the signal templates in the likelihood calculation [174]. The difference in conditioning at high frequencies\n\n31\nbetween ringdown and pyRing is understood to cause a subdominant (but measurable) systematic difference in the two posterior\ndistributions.\nEstimates of the SNR accumulated after the signal peak indicate that an integration time of T = 0.6 s is sufficient to capture\nthe entirety of the post-merger signal; therefore, this is the analysis duration used in all runs by the ringdown code. For reasons\nof computational efficiency, the pyRing analysis is run with a shorter integration time of T = 0.2 s, leading to slightly broader\nposterior distributions. Also to reduce computational cost, the pyRing analysis was run on a sparser grid of start times.\nThe main root of the systematic differences between the two codes is understood to be in the selection of the analysis data.\nFor each choice of analysis start time t>, the ringdown code selects the first sample of the data to be analyzed at each detector\nbased on the native sampling rate of 16384 Hz provided by the LIGO detectors; once the sample closest to the requested start\ntime is identified in the 16384 Hz data, the ringdown code downsamples to 4096 Hz while preserving the selected sample. The\neffective timing precision of ringdown is thus \u03b4t \u22481/(16384 Hz) = 0.06 ms \u22480.18 tMf. The pyRing code, on the other hand, first\ndownsamples the data to 4096 Hz and then selects the first sample of the data to be analyzed at each detector, meaning that the\neffective timing precision is \u03b4t \u22481/(4096 Hz) = 0.24 ms \u22480.72 tMf. The effect of this coarse graining varies for each requested\nstart time and for each detector: if the start time happens to fall on a sample at a given detector, it is unlikely to also fall on a\nsample at the other.\nThe above means that the ringdown and pyRing results cannot be made to match by a uniform relabeling of the start times. For\nexample, for runs requesting t> = 10.5 tMf in the main text, the ringdown code starts the analysis at tLHO = 1420878141.222534 s\n(GPS) and tLLO = 1420878141.220032 s (GPS) for Hanford and Livingston respectively, which is \u22120.046 tMf and \u22120.067 tMf\nrelative to the requested t> in each detector respectively. The closest available pyRing run is the one that requested t> = 10 tMf; this\nstarts the analysis at tLHO = 1420878141.222412 s (GPS) and tLLO = 1420878141.219971 s (GPS) for Hanford and Livingston\nrespectively, which is \u22120.41 tMf and \u22120.25 tMf relative to the target time of t> = 10.5 tMf in each detector respectively. In other\nwords, the start time of the pyRing 10 tMf run differs from that in the ringdown 10.5 tMf run by \u22120.36 tMf for Hanford and\n\u22120.18 tMf in Livingston. A similar calculation shows that the pyRing 6 tMf start time is 0.54 tMf after the ringdown 6 tMf run in\nboth detectors. The fact that pyRing uses less data than ringdown explains the systematic differences in the posteriors presented\nin the main text, as was verified by running ringdown with the exact same data as pyRing and reproducing that code\u2019s results.\nJust as the inspiral time-domain analysis, the two sets of post-merger analyses also ignore the uncertainty over the detector\ncalibration, which is expected to have a negligible impact on ringdown analyses at this SNR [268].\nIIB3. Computation of amplitude significance\nIn the main text, we provide estimates for the significance with which we can establish that the amplitude A of a given\nquasinormal mode is greater than zero. This entails estimating the posterior probability density at A = 0, which represents\nthe boundary of the amplitude parameter space (A \u22650) and therefore will never be directly represented in the set of posterior\nsamples. Our significance estimates are based on the smallest probability p such that the highest posterior density (HPD)\ninterval enclosing probability mass p includes the origin. HPD intervals can produce counter-intuitive significance results when\nthe posterior has a sharp truncation at large amplitude, either because the prior cuts off the posterior or due to the structure of the\nlikelihood function, but our amplitude posteriors are not of this shape.\nWe choose to estimate the significance of the amplitude A > 0 by direct integration over an HPD interval of a KDE-based\nrepresentation of the posterior density, p(A). This method has an advantage over sample-based methods in that it can estimate\narbitrarily small values of p(0) (i.e. arbitrarily high significance), while direct sample-based methods bottom out at p(0) \u223c\n1/Nsamples. Compared to other, simpler estimates of the significance such as calculating the z-score z = \u00b5A/\u03c3A where \u00b5A and\n\u03c3A are the mean and standard deviation of the posterior samples, this method has the advantage that it can account for non-\nGaussian shapes of the posterior density. We first form a standard KDE estimate of the posterior density from the samples of\nthe amplitude A, using automatic bandwidth estimation from the scipy.stats.gaussian kde function. This density estimate,\nkraw(A) is normalized such that it integrates to unity over \u2212\u221e< A < \u221e. To account for the boundary at A = 0, we reflect the\ndensity estimate about the origin, defining\nk(A) = kraw(A) + kraw(\u2212A);\n(10)\nthis ensures that k(A) integrates to unity over 0 \u2264A < \u221e, and so is a suitable density estimate over our domain.\nWe then evaluate k(0), the (estimated) posterior density at A = 0. We evaluate the significance of the amplitude A > 0 by\nintegrating the posterior density estimate, k, over A values such that k(A) > k(0), i.e., computing the smallest p such that the\nhighest-posterior-density interval containing probability mass p includes A = 0. Thus,\np =\nZ\n{A|k(A)>k(0)}\ndA k(A).\n(11)\n\n32\nBy construction, 0 \u2264p \u22641.\nOnce we have an estimate for p, we communicate this as a number of \u03c3 by expressing this value in terms of tail probabilities\nfor the Gaussian distribution, i.e., we establish that A > 0 at x \u03c3 significance, where x is defined by\nZ x\n\u2212x\ndx\u2032 \u03d5 \u0000x\u2032\u0001 = p ,\n(12)\nwhere \u03d5 is the probability density function for the standard normal distribution. Equivalently (but more stably numerically), we\ncan define x by\nZ \u2212x\n\u2212\u221e\ndx\u2032 \u03d5 \u0000x\u2032\u0001 = 1 \u2212p\n2\n.\n(13)\nThis is the quantity that we estimate and report in the main text. The quantity 1 \u2212p can be computed by\n1 \u2212p =\nZ\n{A|k(A)\u2264k(0)}\ndA k(A),\n(14)\nwhich is more numerically stable to evaluate when p \u22431.\nIIC. Further parameter posteriors\nFigure 5 in the main text shows posteriors for the amplitude of the fundamental and overtone modes as a function of the\nanalysis start time. Amplitudes are referenced to the start time of each analysis and are presented for both the single-mode and\ntwo-mode models. For completeness, Fig. 7 shows the posteriors for the frequency and damping rate of each mode in similar\nstyle. In the bottom panel, we further show the network matched-filtered SNR as a function of time for both models. For the\ntwo-mode analysis, we present the SNR of the full model, as the mode nonorthogonality makes defining the SNR of each mode\nambiguous. The inferred frequencies and damping rates are consistent across all times of applicability of their respective model,\ni.e., after 6 tMf for the two-mode model. Uncertainties increase and the SNR decreases as the analysis start time is moved later, as\nexpected. Moreover, the SNR recovered by the two-mode and the one-mode models in their overlapping time region are highly\nconsistent.\nIII. Technical details and further tests for the pre-merger analysis\nTo enable the sharp truncation of the data and gravitational-wave model at a time before the binary merger [188\u2013190], we\ncarry out the analysis in the time-domain using TDinf [201, 202], guided by the reference parameters from Table II. The TDinf\ninference package samples the 15-dimensional parameter space of a quasicircular black-hole binary using the emcee sampler\n[227]. We adopt the same settings as the full-signal frequency-domain analyses with bilby (in terms of the data, trigger time,\npower spectral density, and bandwidth), other than the amount of data considered, certain priors, and the treatment of calibration.\nTime-domain analysis of the full signal is based on 1.4 s of data, which are appropriately truncated. The priors are the same as\nthe bilby analysis other than the masses (uniform in total mass and mass ratio), distance (uniform in luminosity distance), and\ntime (Gaussian centered around the geocenter trigger time with a standard deviation of 0.01 s). The distance prior has a minimal\neffect on the inferred area, which is based on redshifted masses that are minimally correlated with the distance. The composite\narea law prior is broad and relatively flat, as seen in Fig. 5 in the main text. We use the autocorrelation length (ACL) from\nthe full ensemble of walkers to determine the burn-in period and thinning of the chains. Depending on the truncation time, the\nlengths of these chains range between 100,000\u2013500,000 steps, each with 512 walkers. We use a burn-in of at least five times the\nmaximum ACL across sampled parameters, corresponding to > 40% the chain length, and thin by half of the minimum ACL. For\nsome of the truncation times, a handful of chains are not converged to the bulk of the posterior at the end of the burn-in, instead\nrepresenting a secondary mode in likelihood and sky location. For these chains, we manually extend the burn-in period until\nthey converge to the bulk of the posterior. We have verified that the posterior is not restricted by any of the prior edges. We have\nalso verified that the time-domain and bilby analyses of the full signal yield statistically identical posteriors when reweighted to\nthe same prior for both NRSur7dq4 and PhenomXPHM.\nAn additional difference is that the time-domain analysis neglects the uncertainty over the detector calibration, which bilby\nmarginalizes over. We have verified that this has a minimal impact by repeating the bilby analysis while neglecting calibration\nuncertainty. The posteriors for the detector-frame total mass with and without marginalizing over the calibration uncertainty\ndiffer by a Jensen\u2013Shannon divergence [269] of 0.002 nat. For reference, changing the waveform model from NRSur7dq4 to\n\n33\n2\n3\n4\n5\nt> =t\ntpeak [ms]\n220\n240\n260\nf220 [Hz]\n4\n6\n8\n10\n12\n14\n16\nt> =t\ntpeak [tMf]\n500\n1000\n220 [Hz]\n2\n3\n4\n5\nt> =t\ntpeak [ms]\n220\n240\n260\nf221 [Hz]\n220 model\n220+221 model\n4\n6\n8\n10\n12\n14\n16\nt> =t\ntpeak [tMf]\n500\n1000\n221 [Hz]\n4\n6\n8\n10\n12\n14\n16\nt> =t\ntpeak [tMf]\n15\n20\n25\nSNR\n220 model\n220+221 model\nFIG. 7. Similar to Fig. 3 in the main text, but showing the frequency (left) and damping rate (right) of the fundamental (top) and overtone\n(middle) modes as a function of the analysis start time. The bottom panel shows the network matched-filtered SNR as a function of time for\nboth the single-mode and two-mode models, which are highly consistent. In the two-mode model, both frequencies and damping rates are\ninferred jointly from a common mass and spin assuming a Kerr spectrum. We show the 90% credible intervals for the frequencies and damping\ntimes inferred from the full signal analysis as grey horizontal shaded areas. As in Fig. 3 in the main text, we show results with ringdown as\nthere is not exact timing correspondence between the ringdown and pyRing posteriors; we nonetheless obtain similar results with pyRing.\nPhenomXPHM yields a Jensen\u2013Shannon divergence of 0.018 nat, to SEOBNRv5PHM of 0.041 nat, and to PhenomXO4a of\n0.097 nat. The impact of calibration uncertainty is therefore subdominant compared to other potential sources of systematic\nerrors.\nThe main text presents results for a number of truncation times in Fig. 5. We use the gravitational-wave luminosity inferred\nfrom the full-signal analysis (a measure of how dynamical and relativistic the system is [68]) to determine that most of the\nemission occurs during the late coalescence stages. While the averaged gravitational-wave strain, defined as\n\u0010P\n\u2113,m |h\u2113m(t)|2\u00111/2,\npeaks at tpeak by definition, the flux, proportional to\n\u0010P\n\u2113,m |\u02d9h\u2113m(t)|2\u00111/2 (where a dot denotes differentiation with respect to time),\npeaks at 6 tM after tpeak. Specifically, the flux is 10% of its maximum \u221236 tM before tpeak and 1% of its maximum \u2212232 tM\nbefore tpeak. The former is also comparable to common estimates for the transition to merger [270\u2013272]. Based on these time\nestimates, Fig. 5 in the main text presents results for an array of truncation times after t< = \u2212250 tM and more detailed results\nfor t< = \u221240 tM.\nIV. Technical details and further results for the area law analysis\nThe area law test relies on the independent analyses of the pre-merger data described in Sec. III and the post-merger data\ndescribed in Sec. II of this Supplement. Both tests are carried out in the time-domain and avoid quantitative reference to the full-\nsignal results, which are based on waveform models within general relativity that obey the area law by construction. Since the\npre- and post-merger analyses are also independent of each other, there is no information shared between the two sets of results\n\n34\nand no assumption about the initial and final black holes sharing the same location in the sky. The only slight exception to this\nis that, by comparing initial and final quantities in the detector frame, we implicitly assume that the pre- and post-merger signals\nwere redshifted by the same factor. The recoil kick of the remnant can break this assumption by inducing a redshift; however,\nthis is at most 10% and only in the most extreme cases with large spins inconsistent with GW250114 [273]. An analysis in\nwhich the extrinsic parameters are sampled jointly for both the pre- and post-merger data, such as [190], could gain by imposing\nthe same location in the sky for the initial and final black holes.\nOur test yields independent measurements of the initial and final areas. If the posterior distributions on the final and initial\narea are denoted as pf (Af) and pi(Ai) respectively, the significance \u03c3 of a non-detection of a violation of Hawking\u2019s area law\nis given by the separation between pf (Af) and pi(Ai). Following the cosmology literature estimating the significance of the\nHubble tension [274, 275], we estimate the significance as X\u03c3 with\nX =\n\u00b5f \u2212\u00b5i\nq\n\u03c32\nf + \u03c32\ni\n,\n(15)\nwhere \u00b5i/\u00b5f and \u03c3i/\u03c3f are the means and standard deviations respectively of the initial and final area distributions. Since this\nestimate relies only on the first two cumulants, it is less sensitive to sampling error at the tails of the distribution. Empirically,\nsampling the posterior tails beyond the \u223c4\u03c3 level is unreliable and highly sensitive to sampler settings and minor analysis\nchoices, so we avoid using tail samples.\nIn the main text, Fig. 5 shows results where the final area has been measured via a single (\u2113= 2, |m| = 2, n = 0) mode\nstarting at 10.5 tMf, which is the earliest time that the overtone significance falls below 1\u03c3. Identification of this time is based on\nthe post-merger data alone, without requesting consistency with the full-signal analysis. Here we show similar results obtained\nfor different pre- and post-merger start times, for both the single-mode and two-mode ringdown models. Figure 8 displays the\ninferred initial and final areas as a function of inspiral end time t< and ringdown start time t>, respectively. Similarly to Fig. 5,\nwe show the 90% credible intervals for the initial and final areas as inferred from the full-signal analysis for reference. These\nare consistent with both the initial and final areas within statistical uncertainties, although this comparison does not guide any\nof the analysis choices in testing the area law. The significance, as defined in Eq. (15), can be assessed via the separation of the\ndistributions relative to their widths.\nAs expected, the uncertainty in the remnant area grows as the start time is pushed to later parts of the data where the signal\nis weaker; for the initial area, the opposite is true and the uncertainty grows as the analysis end time is pushed earlier. The\nsingle-mode ringdown result used in the main text corresponds to a start time of t> = 10.5 tMf and is highlighted by a vertical\nblue band. Including the overtone in the model at this and later times necessarily broadens the uncertainty in the final area. This\nis both because the overtone is not required to explain the data and because the overtone and the fundamental are not orthogonal:\nintroducing additional, unconstrained degrees of freedom broadens the posterior distribution.\nThe reference start time showcased in the main text was chosen independently of the full-signal analysis purely as the earliest\ntime at which the data are consistent with a single mode, according to our 1\u03c3 criterion. Had the SNR of this event been higher,\nwe would likely not have found the data to be sufficiently well-described by a single mode at t> = 10.5 tMf. This would have\nled us to use a later start time for the reference ringdown analysis with a single mode. Carrying out the area law test with the\ntwo-mode analysis instead selects 6 tMf as the earliest time at which this model explains the observed data. The area law is again\nconfidently satisfied at 3.6\u03c3 significance.\n\n35\n80\n60\n40\n20\n0\n250\n200\n150\n100\n50\n0\nt< =t\ntpeak [tM]\n2\n4\n6\n(1+z)2 \n [105 km2]\n2\n3\n4\n5\n6\n7\n6\n9\n12\n15\n18\nt> =t\ntpeak [tMf]\nt \u2212tpeak [ms]\nFIG. 8. Measurements for the initial and final black hole areas as a function of fit time. (Left panel) Initial black hole area inferred by analyzing\nthe pre-merger signal with TDinf, truncated at the time indicated on the x-axis. (Right panel) Final black hole areas inferred by analyzing the\npost-merger signal with ringdown, with the analysis start time indicated on the x-axis. We show results for the two-mode analysis from 6 tMf\nafter the peak strain and the single-mode only from 10.5 tMf after the peak strain. We highlight with vertical bands the reference areas quoted\nin this paper, at \u221240 tM before the peak strain for the inspiral analysis and 10.5 tMf after the peak strain for the single-mode ringdown analysis.\nHorizontal grey bands indicate the 90% credible intervals for the initial and final areas as inferred from the full inspiral-merger-ringdown\nanalysis.\n", "Directed searches for gravitational waves from ultralight vector boson clouds around\nmerger remnant and galactic black holes during the first part of the fourth\nLIGO\u2013Virgo\u2013KAGRA observing run\nA. G. Abac\n,1 I. Abouelfettouh,2 F. Acernese,3, 4 K. Ackley\n,5 C. Adamcewicz\n,6 S. Adhicary\n,7 D. Adhikari,8, 9\nN. Adhikari\n,10 R. X. Adhikari\n,11 V. K. Adkins,12 S. Afroz\n,13 A. Agapito,14 D. Agarwal\n,15\nM. Agathos\n,16 N. Aggarwal,17 S. Aggarwal,18 O. D. Aguiar\n,19 I.-L. Ahrend,20 L. Aiello\n,21, 22 A. Ain\n,23\nP. Ajith\n,24 T. Akutsu\n,25, 26 S. Albanesi\n,27, 28 W. Ali,29, 30 S. Al-Kershi,8, 9 C. All\u00e9n\u00e9,31 A. Allocca\n,32, 4\nS. Al-Shammari,33 P. A. Altin\n,34 S. Alvarez-Lopez\n,35 W. Amar,31 O. Amarasinghe,33 A. Amato\n,36, 37\nF. Amicucci\n,38, 39 C. Amra,40 A. Ananyeva,11 S. B. Anderson\n,11 W. G. Anderson\n,11 M. Andia\n,41\nM. Ando,42 M. Andr\u00e9s-Carcasona\n,43 T. Andri\u0107\n,44, 45, 8, 9 J. Anglin,46 S. Ansoldi\n,47, 48 J. M. Antelis\n,49\nS. Antier\n,41 M. Aoumi,50 E. Z. Appavuravther,51, 52 S. Appert,11 S. K. Apple\n,53 K. Arai\n,11 A. Araya\n,42\nM. C. Araya\n,11 M. Arca Sedda\n,44, 45 J. S. Areeda\n,54 N. Aritomi,2 F. Armato\n,29, 30 S. Armstrong\n,55\nN. Arnaud\n,56 M. Arogeti\n,57 S. M. Aronson\n,12 K. G. Arun\n,58 G. Ashton\n,59 Y. Aso\n,25, 60 L. Asprea,28\nM. Assiduo,61, 62 S. Assis de Souza Melo,63 S. M. Aston,64 P. Astone\n,38 F. Attadio\n,39, 38 F. Aubin\n,65\nK. AultONeal\n,66 G. Avallone\n,67 E. A. Avila\n,49 S. Babak\n,20 C. Badger,68 S. Bae\n,69 S. Bagnasco\n,28\nL. Baiotti\n,70 R. Bajpai\n,71 T. Baka,72, 37 A. M. Baker,6 K. A. Baker,73 T. Baker\n,74 G. Baldi\n,75, 76\nN. Baldicchi\n,77, 51 M. Ball,78 G. Ballardin,63 S. W. Ballmer,79 S. Banagiri\n,6 B. Banerjee\n,44 D. Bankar\n,80\nT. M. Baptiste,12 P. Baral\n,10 M. Baratti\n,81, 82 J. C. Barayoga,11 B. C. Barish,11 D. Barker,2 N. Barman,80\nP. Barneo\n,83, 84, 85 F. Barone\n,86, 4 B. Barr\n,87 L. Barsotti\n,35 M. Barsuglia\n,20 D. Barta\n,88 A. M. Bartoletti,89\nM. A. Barton\n,87 I. Bartos,46 A. Basalaev\n,8, 9 R. Bassiri\n,90 A. Basti\n,82, 81 M. Bawaj\n,77, 51 P. Baxi,91\nJ. C. Bayley\n,87 A. C. Baylor\n,10 P. A. Baynard II,57 M. Bazzan,92, 93 V. M. Bedakihale,94 F. Beirnaert\n,95\nM. Bejger\n,96 D. Belardinelli\n,22 A. S. Bell\n,87 D. S. Bellie,97 L. Bellizzi\n,81, 82 W. Benoit\n,18 I. Bentara\n,56\nJ. D. Bentley\n,98 M. Ben Yaala,55 S. Bera\n,99, 100 F. Bergamin\n,33 B. K. Berger\n,90 S. Bernuzzi\n,27\nM. Beroiz\n,11 D. Bersanetti\n,29 T. Bertheas,101 A. Bertolini,37, 36 J. Betzwieser\n,64 D. Beveridge\n,73\nG. Bevilacqua\n,102 N. Bevins\n,103 R. Bhandare,104 R. Bhatt,11 D. Bhattacharjee\n,105, 106 S. Bhattacharyya,107\nS. Bhaumik\n,46 V. Biancalana\n,102 A. Bianchi,37, 108 I. A. Bilenko,109 G. Billingsley\n,11 A. Binetti\n,110\nS. Bini\n,11, 75, 76 C. Binu,111 S. Biot,112 O. Birnholtz\n,113 S. Biscoveanu\n,97 A. Bisht,9 M. Bitossi\n,63, 81\nM.-A. Bizouard\n,114 S. Blaber,115 J. K. Blackburn\n,11 L. A. Blagg,78 C. D. Blair,73, 64 D. G. Blair,73 N. Bode\n,8, 9\nN. Boettner,98 G. Boileau\n,114 M. Boldrini\n,38 G. N. Bolingbroke\n,116 A. Bolliand,117, 40 L. D. Bonavena\n,46\nR. Bondarescu\n,83 F. Bondu\n,118 E. Bonilla\n,90 M. S. Bonilla\n,54 A. Bonino,119 R. Bonnand\n,31, 117\nA. Borchers,8, 9 S. Borhanian,7 V. Boschi\n,81 S. Bose,120 V. Bossilkov,64 Y. Bothra\n,37, 108 A. Boudon,56\nL. Bourg,57 M. Boyle,121 A. Bozzi,63 C. Bradaschia,81 P. R. Brady\n,10 A. Branch,64 M. Branchesi\n,44, 45\nI. Braun,105 T. Briant\n,122 A. Brillet,114 M. Brinkmann,8, 9 P. Brockill,10 E. Brockmueller\n,8, 9 A. F. Brooks\n,11\nB. C. Brown,46 D. D. Brown,116 M. L. Brozzetti\n,77, 51 S. Brunett,11 G. Bruno,15 R. Bruntz\n,123 J. Bryant,119\nY. Bu,124 F. Bucci\n,62 J. Buchanan,123 O. Bulashenko\n,83, 84 T. Bulik,125 H. J. Bulten,37 A. Buonanno\n,126, 1\nK. Burtnyk,2 R. Buscicchio\n,127, 128 D. Buskulic,31 C. Buy\n,101 R. L. Byer,90 G. S. Cabourn Davies\n,74\nR. Cabrita\n,15 V. C\u00e1ceres-Barbosa\n,7 L. Cadonati\n,57 G. Cagnoli\n,129 C. Cahillane\n,79 A. Calafat,99\nT. A. Callister,130 E. Calloni,32, 4 S. R. Callos\n,78 M. Canepa,30, 29 G. Caneva Santoro\n,43 K. C. Cannon\n,42\nH. Cao,35 L. A. Capistran,131 E. Capocasa\n,20 E. Capote\n,2, 11 G. Capurri\n,82, 81 G. Carapella,67, 132\nF. Carbognani,63 M. Carlassara,8, 9 J. B. Carlin\n,124 T. K. Carlson,133 M. F. Carney,105 M. Carpinelli\n,127, 63\nG. Carrillo,78 J. J. Carter\n,8, 9 G. Carullo\n,119, 134 A. Casallas-Lagos,135 J. Casanueva Diaz\n,63\nC. Casentini\n,136, 22 S. Y. Castro-Lucas,137 S. Caudill,133 M. Cavagli\u00e0\n,106 R. Cavalieri\n,63 A. Ceja,54 G. Cella\n,81\nP. Cerd\u00e1-Dur\u00e1n\n,138, 139 E. Cesarini\n,22 N. Chabbra,34 W. Chaibi,114 A. Chakraborty\n,13 P. Chakraborty\n,8, 9\nS. Chakraborty,104 S. Chalathadka Subrahmanya\n,98 J. C. L. Chan\n,140 M. Chan,115 K. Chang,141 S. Chao\n,142, 141\nP. Charlton\n,143 E. Chassande-Mottin\n,20 C. Chatterjee\n,144 Debarati Chatterjee\n,80 Deep Chatterjee\n,35\nM. Chaturvedi,104 S. Chaty\n,20 A. Chen\n,145 A. H.-Y. Chen,146 D. Chen\n,147 H. Chen,142 H. Y. Chen\n,148\nS. Chen,144 Yanbei Chen,149 Yitian Chen\n,121 H. P. Cheng,150 P. Chessa\n,77, 51 H. T. Cheung\n,91 S. Y. Cheung,6\nF. Chiadini\n,151, 132 G. Chiarini,8, 9, 93 A. Chiba,152 A. Chincarini\n,29 M. L. Chiofalo\n,82, 81 A. Chiummo\n,4, 63\nC. Chou,146 S. Choudhary\n,73 N. Christensen\n,114, 153 S. S. Y. Chua\n,34 G. Ciani\n,75, 76 P. Ciecielag\n,96\nM. Cie\u015blar\n,125 M. Cifaldi\n,22 B. Cirok,154 F. Clara,2 J. A. Clark\n,11, 57 T. A. Clarke\n,6 P. Clearwater,155\nS. Clesse,112 F. Cleva,114, 117 E. Coccia,44, 45, 43 E. Codazzo\n,156, 157 P.-F. Cohadon\n,122 S. Colace\n,30\nE. Colangeli,74 M. Colleoni\n,99 C. G. Collette,158 J. Collins,64 S. Colloms\n,87 A. Colombo\n,159, 128\narXiv:2509.07352v2 [gr-qc] 15 Sep 2025\n\n2\nC. M. Compton,2 G. Connolly,78 L. Conti\n,93 T. R. Corbitt\n,12 I. Cordero-Carri\u00f3n\n,160 S. Corezzi\n,77, 51\nN. J. Cornish\n,161 I. Coronado,162 A. Corsi\n,163 R. Cottingham,64 M. W. Coughlin\n,18 A. Couineaux,38\nP. Couvares\n,11, 57 D. M. Coward,73 R. Coyne\n,164 A. Cozzumbo,44 J. D. E. Creighton\n,10 T. D. Creighton,165\nP. Cremonese\n,99 S. Crook,64 R. Crouch,2 J. Csizmazia,2 J. R. Cudell\n,166 T. J. Cullen\n,11 A. Cumming\n,87\nE. Cuoco\n,167, 168 M. Cusinato\n,138 L. V. Da Concei\u00e7\u00e3o\n,169 T. Dal Canton\n,41 S. Dal Pra\n,170\nG. D\u00e1lya\n,101 B. D\u2019Angelo\n,29 S. Danilishin\n,36, 37 S. D\u2019Antonio\n,38 K. Danzmann,9, 8, 9 K. E. Darroch,123\nL. P. Dartez\n,64 R. Das,107 A. Dasgupta,94 V. Dattilo\n,63 A. Daumas,20 N. Davari,171, 172 I. Dave,104\nA. Davenport,137 M. Davier,41 T. F. Davies,73 D. Davis\n,11 L. Davis,73 M. C. Davis\n,18 P. Davis\n,173, 174\nE. J. Daw\n,175 M. Dax\n,1 J. De Bolle\n,95 M. Deenadayalan,80 J. Degallaix\n,176 M. De Laurentis\n,32, 4\nF. De Lillo\n,23 S. Della Torre\n,128 W. Del Pozzo\n,82, 81 A. Demagny,31 F. De Marco\n,39, 38 G. Demasi,177, 62\nF. De Matteis\n,21, 22 N. Demos,35 T. Dent\n,178 A. Depasse\n,15 N. DePergola,103 R. De Pietri\n,179, 180\nR. De Rosa\n,32, 4 C. De Rossi\n,63 M. Desai\n,35 R. DeSalvo\n,181 A. DeSimone,182 R. De Simone,151, 132\nA. Dhani\n,1 R. Diab,46 M. C. D\u00edaz\n,165 M. Di Cesare\n,32, 4 G. Dideron,183 T. Dietrich\n,1 L. Di Fiore,4\nC. Di Fronzo\n,73 M. Di Giovanni\n,39, 38 T. Di Girolamo\n,32, 4 D. Diksha,37, 36 J. Ding\n,20, 184 S. Di Pace\n,39, 38\nI. Di Palma\n,39, 38 D. Di Piero,185, 48 F. Di Renzo\n,56 Divyajyoti\n,33 A. Dmitriev\n,119 J. P. Docherty,87\nZ. Doctor\n,97 N. Doerksen\n,169 E. Dohmen,2 A. Doke,133 A. Domiciano De Souza,186 L. D\u2019Onofrio\n,38\nF. Donovan,35 K. L. Dooley\n,33 T. Dooney,72 S. Doravari\n,80 O. Dorosh,187 W. J. D. Doyle,123 M. Drago\n,39, 38\nJ. C. Driggers\n,2 L. Dunn\n,124 U. Dupletsa,44 P.-A. Duverne\n,20 D. D\u2019Urso\n,171, 156 P. Dutta Roy\n,46\nH. Duval\n,188 S. E. Dwyer,2 C. Eassa,2 W. E. East\n,183 M. Ebersold\n,189, 31 T. Eckhardt\n,98 G. Eddolls\n,79\nA. Effler\n,64 J. Eichholz\n,34 H. Einsle,114 M. Eisenmann,25 M. Emma\n,59 K. Endo,152 R. Enficiaud\n,1\nL. Errico\n,32, 4 R. Espinosa,165 M. Esposito\n,4, 32 R. C. Essick\n,190 H. Estell\u00e9s\n,1 T. Etzel,11 M. Evans\n,35\nT. Evstafyeva,183 B. E. Ewing,7 J. M. Ezquiaga\n,140 F. Fabrizi\n,61, 62 V. Fafone\n,21, 22 S. Fairhurst\n,33\nA. M. Farah\n,130 B. Farr\n,78 W. M. Farr\n,191, 192 G. Favaro\n,92 M. Favata\n,193 M. Fays\n,166 M. Fazio\n,55\nJ. Feicht,11 M. M. Fejer,90 R. Felicetti\n,185, 48 E. Fenyvesi\n,88, 194 J. Fernandes,195 T. Fernandes\n,196, 138\nD. Fernando,111 S. Ferraiuolo\n,197, 39, 38 T. A. Ferreira,12 F. Fidecaro\n,82, 81 P. Figura\n,96 A. Fiori\n,81, 82\nI. Fiori\n,63 M. Fishbach\n,190 R. P. Fisher,123 R. Fittipaldi\n,198, 132 V. Fiumara\n,199, 132 R. Flaminio,31\nS. M. Fleischer\n,200 L. S. Fleming,201 E. Floden,18 H. Fong,115 J. A. Font\n,138, 139 F. Fontinele-Nunes,18 C. Foo,1\nB. Fornal\n,202 K. Franceschetti,179 F. Frappez,31 S. Frasca,39, 38 F. Frasconi\n,81 J. P. Freed,66 Z. Frei\n,203\nA. Freise\n,37, 108 O. Freitas\n,196, 138 R. Frey\n,78 W. Frischhertz,64 P. Fritschel,35 V. V. Frolov,64 G. G. Fronz\u00e9\n,28\nM. Fuentes-Garcia\n,11 S. Fujii,204 T. Fujimori,205 P. Fulda,46 M. Fyffe,64 B. Gadre\n,72 J. R. Gair\n,1\nS. Galaudage\n,186 V. Galdi,206 R. Gamba,7 A. Gamboa\n,1 S. Gamoji,181 D. Ganapathy\n,207 A. Ganguly\n,80\nB. Garaventa\n,29 J. Garc\u00eda-Bellido\n,208 C. Garc\u00eda-Quir\u00f3s\n,189 J. W. Gardner\n,34 K. A. Gardner,115\nS. Garg,42 J. Gargiulo\n,63 X. Garrido\n,41 A. Garron\n,99 F. Garufi\n,32, 4 P. A. Garver,90 C. Gasbarra\n,21, 22\nB. Gateley,2 F. Gautier\n,209 V. Gayathri\n,10 T. Gayer,79 G. Gemme\n,29 A. Gennai\n,81 V. Gennari\n,101\nJ. George,104 R. George\n,148 O. Gerberding\n,98 L. Gergely\n,154 Archisman Ghosh\n,95 Sayantan Ghosh,195\nShaon Ghosh\n,193 Shrobana Ghosh,8, 9 Suprovo Ghosh\n,210 Tathagata Ghosh\n,80 J. A. Giaime\n,12, 64\nK. D. Giardina,64 D. R. Gibson,201 C. Gier\n,55 S. Gkaitatzis\n,82, 81 J. Glanzer\n,11 F. Glotin\n,41 J. Godfrey,78\nR. V. Godley,8, 9 P. Godwin\n,11 A. S. Goettel\n,33 E. Goetz\n,115 J. Golomb,11 S. Gomez Lopez\n,39, 38\nB. Goncharov\n,44 G. Gonz\u00e1lez\n,12 P. Goodarzi\n,211 S. Goode,6 A. W. Goodwin-Jones\n,15 M. Gosselin,63\nR. Gouaty\n,31 D. W. Gould,34 K. Govorkova,35 A. Grado\n,77, 51 V. Graham\n,87 A. E. Granados\n,18\nM. Granata\n,176 V. Granata\n,212, 132 S. Gras,35 P. Grassia,11 J. Graves,57 C. Gray,2 R. Gray\n,87 G. Greco,51\nA. C. Green\n,37, 108 L. Green,213 S. M. Green,74 S. R. Green\n,214 C. Greenberg,133 A. M. Gretarsson,66\nH. K. Griffin,18 D. Griffith,11 H. L. Griggs\n,57 G. Grignani,77, 51 C. Grimaud\n,31 H. Grote\n,33 S. Grunewald\n,1\nD. Guerra\n,138 D. Guetta\n,215 G. M. Guidi\n,61, 62 A. R. Guimaraes,12 H. K. Gulati,94 F. Gulminelli\n,173, 174\nH. Guo\n,145 W. Guo\n,73 Y. Guo\n,37, 36 Anuradha Gupta\n,216 I. Gupta\n,7 N. C. Gupta,94 S. K. Gupta,46\nV. Gupta\n,18 N. Gupte,1 J. Gurs,98 N. Gutierrez,176 N. Guttman,6 F. Guzman\n,131 D. Haba,217 M. Haberland\n,1\nS. Haino,218 E. D. Hall\n,35 E. Z. Hamilton\n,99 G. Hammond\n,87 M. Haney,37 J. Hanks,2 C. Hanna\n,7\nM. D. Hannam,33 O. A. Hannuksela\n,219 A. G. Hanselman\n,130 H. Hansen,2 J. Hanson,64 S. Hanumasagar,57\nR. Harada,42 A. R. Hardison,182 S. Harikumar\n,187 K. Haris,37, 72 I. Harley-Trochimczyk,131 T. Harmark\n,134\nJ. Harms\n,44, 45 G. M. Harry\n,220 I. W. Harry\n,74 J. Hart,105 B. Haskell,96, 221, 222 C. J. Haster\n,213\nK. Haughian\n,87 H. Hayakawa,50 K. Hayama,223 M. C. Heintze,64 J. Heinze\n,119 J. Heinzel,35 H. Heitmann\n,114\nF. Hellman\n,207 A. F. Helmling-Cornell\n,78 G. Hemming\n,63 O. Henderson-Sapir\n,116 M. Hendry\n,87 I. S. Heng,87\nM. H. Hennig\n,87 C. Henshaw\n,57 M. Heurs\n,8, 9 A. L. Hewitt\n,224, 225 J. Heynen,15 J. Heyns,35 S. Higginbotham,33\n\n3\nS. Hild,36, 37 S. Hill,87 Y. Himemoto\n,226 N. Hirata,25 C. Hirose,227 D. Hofman,176 B. E. Hogan,66\nN. A. Holland,37, 108 I. J. Hollows\n,175 D. E. Holz\n,130 L. Honet,112 D. J. Horton-Bailey,207 J. Hough\n,87\nS. Hourihane\n,11 N. T. Howard,144 E. J. Howell\n,73 C. G. Hoy\n,74 C. A. Hrishikesh,21 P. Hsi,35 H.-F. Hsieh\n,142\nH.-Y. Hsieh,142 C. Hsiung,228 S.-H. Hsu,146 W.-F. Hsu\n,110 Q. Hu\n,87 H. Y. Huang\n,141 Y. Huang\n,7\nY. T. Huang,79 A. D. Huddart,229 B. Hughey,66 V. Hui\n,31 S. Husa\n,99 R. Huxford,7 L. Iampieri\n,39, 38\nG. A. Iandolo\n,36 M. Ianni,22, 21 G. Iannone\n,132 J. Iascau,78 K. Ide,230 R. Iden,217 A. Ierardi,44, 45 S. Ikeda,147\nH. Imafuku,42 Y. Inoue,141 G. Iorio\n,92 P. Iosif\n,185, 48 M. H. Iqbal,34 J. Irwin\n,87 R. Ishikawa,230 M. Isi\n,191, 192\nK. S. Isleif\n,231 Y. Itoh\n,205, 232 M. Iwaya,204 B. R. Iyer\n,24 C. Jacquet,101 P.-E. Jacquet\n,122 T. Jacquot,41\nS. J. Jadhav,233 S. P. Jadhav\n,155 M. Jain,133 T. Jain,224 A. L. James\n,11 K. Jani\n,144 J. Janquart\n,15\nN. N. Janthalur,233 S. Jaraba\n,234 P. Jaranowski\n,235 R. Jaume\n,99 W. Javed,33 A. Jennings,2 M. Jensen,2\nW. Jia,35 J. Jiang\n,150 H.-B. Jin\n,236, 237 G. R. Johns,123 N. A. Johnson,46 M. C. Johnston\n,213 R. Johnston,87\nN. Johny,8, 9 D. H. Jones\n,34 D. I. Jones,210 R. Jones,87 H. E. Jose,78 P. Joshi\n,7 S. K. Joshi,80 G. Joubert,56\nJ. Ju,238 L. Ju\n,73 K. Jung\n,239 J. Junker\n,34 V. Juste,112 H. B. Kabagoz\n,64, 35 T. Kajita\n,240 I. Kaku,205\nV. Kalogera\n,97 M. Kalomenopoulos\n,213 M. Kamiizumi\n,50 N. Kanda\n,232, 205 S. Kandhasamy\n,80\nG. Kang\n,241 N. C. Kannachel,6 J. B. Kanner,11 S. A. KantiMahanty,18 S. J. Kapadia\n,80 D. P. Kapasi\n,54\nM. Karthikeyan,133 M. Kasprzack\n,11 H. Kato,152 T. Kato,204 E. Katsavounidis,35 W. Katzman,64 R. Kaushik\n,104\nK. Kawabe,2 R. Kawamoto,205 D. Keitel\n,99 L. J. Kemperman\n,116 J. Kennington\n,7 F. A. Kerkow,18\nR. Kesharwani\n,80 J. S. Key\n,242 R. Khadela,8, 9 S. Khadka,90 S. S. Khadkikar,7 F. Y. Khalili\n,109 F. Khan\n,8, 9\nT. Khanam,163 M. Khursheed,104 N. M. Khusid,191, 192 W. Kiendrebeogo\n,114, 243 N. Kijbunchoo\n,116 C. Kim,244\nJ. C. Kim,245 K. Kim\n,246 M. H. Kim\n,238 S. Kim\n,247 Y.-M. Kim\n,246 C. Kimball\n,97 K. Kimes,54\nM. Kinnear,33 J. S. Kissel\n,2 S. Klimenko,46 A. M. Knee\n,115 E. J. Knox,78 N. Knust\n,8, 9 K. Kobayashi,204\nS. M. Koehlenbeck\n,90 G. Koekoek,37, 36 K. Kohri\n,248, 249 K. Kokeyama\n,33, 250 S. Koley\n,44, 166 P. Kolitsidou\n,119\nA. E. Koloniari\n,251 K. Komori\n,42 A. K. H. Kong\n,142 A. Kontos\n,252 L. M. Koponen,119 M. Korobko\n,98\nX. Kou,18 A. Koushik\n,23 N. Kouvatsos\n,68 M. Kovalam,73 T. Koyama,152 D. B. Kozak,11 S. L. Kranzhoff,36, 37\nV. Kringel,8, 9 N. V. Krishnendu\n,119 S. Kroker,253 A. Kr\u00f3lak\n,254, 187 K. Kruska,8, 9 J. Kubisz\n,255 G. Kuehn,8, 9\nS. Kulkarni\n,216 A. Kulur Ramamohan\n,34 Achal Kumar,46 Anil Kumar,233 Praveen Kumar\n,178\nPrayush Kumar\n,24 Rahul Kumar,2 Rakesh Kumar,94 J. Kume\n,256, 257, 42 K. Kuns\n,35 N. Kuntimaddi,33\nS. Kuroyanagi\n,208, 258 S. Kuwahara\n,42 K. Kwak\n,239 K. Kwan,34 S. Kwon\n,42 G. Lacaille,87 D. Laghi\n,189, 101\nA. H. Laity,164 E. Lalande,259 M. Lalleman\n,23 P. C. Lalremruati,260 M. Landry,2 B. B. Lane,35 R. N. Lang\n,35\nJ. Lange,148 R. Langgin\n,213 B. Lantz\n,90 I. La Rosa\n,99 J. Larsen,200 A. Lartaux-Vollard\n,41 P. D. Lasky\n,6\nJ. Lawrence\n,165 M. Laxen\n,64 C. Lazarte\n,138 A. Lazzarini\n,11 C. Lazzaro,157, 156 P. Leaci\n,39, 38 L. Leali,18\nY. K. Lecoeuche\n,115 H. M. Lee\n,261 H. W. Lee\n,262 J. Lee,79 K. Lee\n,238 R.-K. Lee\n,142 R. Lee,35\nSungho Lee\n,246 Sunjae Lee,238 Y. Lee,141 I. N. Legred,11 J. Lehmann,8, 9 L. Lehner,183 M. Le Jean\n,176, 117\nA. Lema\u00eetre\n,263 M. Lenti\n,62, 177 M. Leonardi\n,75, 76, 264 M. Lequime,40 N. Leroy\n,41 M. Lesovsky,11 N. Letendre,31\nM. Lethuillier\n,56 Y. Levin,6 K. Leyde,74 A. K. Y. Li,11 K. L. Li\n,265 T. G. F. Li,110 X. Li\n,149 Y. Li,97 Z. Li,87\nA. Lihos,123 E. T. Lin\n,142 F. Lin,141 L. C.-C. Lin\n,265 Y.-C. Lin\n,142 C. Lindsay,201 S. D. Linker,181 A. Liu\n,219\nG. C. Liu\n,228 Jian Liu\n,73 F. Llamas Villarreal,165 J. Llobera-Querol\n,99 R. K. L. Lo\n,140 J.-P. Locquet,110\nS. C. G. Loggins,266 M. R. Loizou,133 L. T. London,68 A. Longo\n,61, 62 D. Lopez\n,166 M. Lopez Portilla,72\nA. Lorenzo-Medina\n,178 V. Loriette,41 M. Lormand,64 G. Losurdo\n,267, 81 E. Lotti,133 T. P. Lott IV\n,57\nJ. D. Lough\n,8, 9 H. A. Loughlin,35 C. O. Lousto\n,111 N. Low,124 N. Lu\n,34 L. Lucchesi\n,81 H. L\u00fcck,9, 8, 9\nD. Lumaca\n,22 A. P. Lundgren\n,268, 269 A. W. Lussier\n,259 R. Macas\n,74 M. MacInnis,35 D. M. Macleod\n,33\nI. A. O. MacMillan\n,11 A. Macquet\n,41 K. Maeda,152 S. Maenaut\n,110 S. S. Magare,80 R. M. Magee\n,11\nE. Maggio\n,1 R. Maggiore,37, 108 M. Magnozzi\n,29, 30 M. Mahesh,98 M. Maini,164 S. Majhi,80 E. Majorana,39, 38\nC. N. Makarem,11 D. Malakar\n,106 J. A. Malaquias-Reis,19 U. Mali\n,190 S. Maliakal,11 A. Malik,104\nL. Mallick\n,169, 190 A.-K. Malz\n,59 N. Man,114 M. Mancarella\n,100 V. Mandic\n,18 V. Mangano\n,171, 156\nB. Mannix,78 G. L. Mansell\n,79 M. Manske\n,10 M. Mantovani\n,63 M. Mapelli\n,92, 93, 270 C. Marinelli\n,102\nF. Marion\n,31 A. S. Markosyan,90 A. Markowitz,11 E. Maros,11 S. Marsat\n,101 F. Martelli\n,61, 62 I. W. Martin\n,87\nR. M. Martin\n,193 B. B. Martinez,131 D. A. Martinez,54 M. Martinez,43, 271 V. Martinez\n,129 A. Martini,75, 76\nJ. C. Martins\n,19 D. V. Martynov,119 E. J. Marx,35 L. Massaro,36, 37 A. Masserot,31 M. Masso-Reid\n,87\nS. Mastrogiovanni\n,38 T. Matcovich\n,51 M. Matiushechkina\n,8, 9 L. Maurin,209 N. Mavalvala\n,35 N. Maxwell,2\nT. May\n,183 G. McCarrol,64 R. McCarthy,2 D. E. McClelland\n,34 S. McCormick,64 L. McCuller\n,11 S. McEachin,123\nC. McElhenny,123 G. I. McGhee\n,87 J. McGinn,87 K. B. M. McGowan,144 J. McIver\n,115 A. McLeod\n,73\nI. McMahon\n,189 T. McRae,34 R. McTeague\n,87 D. Meacher\n,10 B. N. Meagher,79 R. Mechum,111 Q. Meijer,72\n\n4\nA. Melatos,124 C. S. Menoni\n,137 F. Mera,2 R. A. Mercer\n,10 L. Mereni,176 K. Merfeld,163 E. L. Merilh,64\nJ. R. M\u00e9rou\n,99 J. D. Merritt,78 M. Merzougui,114 C. Messick\n,10 B. Mestichelli,44 M. Meyer-Conde\n,272\nF. Meylahn\n,8, 9 A. Mhaske,80 A. Miani\n,75, 76 H. Miao,273 C. Michel\n,176 Y. Michimura\n,42 H. Middleton\n,119\nD. P. Mihaylov\n,105 A. L. Miller\n,37, 72 S. J. Miller\n,11 M. Millhouse\n,57 E. Milotti\n,185, 48 V. Milotti\n,92\nY. Minenkov,22 E. M. Minihan,66 Ll. M. Mir\n,43 L. Mirasola\n,156, 157 M. Miravet-Ten\u00e9s\n,138 C.-A. Miritescu\n,43\nA. Mishra,24 C. Mishra\n,107 T. Mishra\n,46 A. L. Mitchell,37, 108 J. G. Mitchell,66 S. Mitra\n,80 V. P. Mitrofanov\n,109\nK. Mitsuhashi,25 R. Mittleman,35 O. Miyakawa\n,50 S. Miyoki\n,50 A. Miyoko,66 G. Mo\n,35 L. Mobilia\n,61, 62\nS. R. P. Mohapatra,11 S. R. Mohite\n,7 M. Molina-Ruiz\n,207 M. Mondin,181 M. Montani,61, 62 C. J. Moore,224\nD. Moraru,2 A. More\n,80 S. More\n,80 C. Moreno\n,135 E. A. Moreno\n,35 G. Moreno,2 A. Moreso Serra,83\nS. Morisaki\n,42, 204 Y. Moriwaki\n,152 G. Morras\n,208 A. Moscatello\n,92 M. Mould\n,35 B. Mours\n,65\nC. M. Mow-Lowry\n,37, 108 L. Muccillo\n,177, 62 F. Muciaccia\n,39, 38 D. Mukherjee\n,119 Samanwaya Mukherjee,24\nSoma Mukherjee,165 Subroto Mukherjee,94 Suvodip Mukherjee\n,13 N. Mukund\n,35 A. Mullavey,64 H. Mullock,115\nJ. Mundi,220 C. L. Mungioli,73 M. Murakoshi,230 P. G. Murray\n,87 D. Nabari\n,75, 76 S. L. Nadji,8, 9 A. Nagar,28, 274\nN. Nagarajan\n,87 K. Nakagaki,50 K. Nakamura\n,25 H. Nakano\n,275 M. Nakano,11 D. Nanadoumgar-Lacroze\n,43\nD. Nandi,12 V. Napolano,63 P. Narayan\n,216 I. Nardecchia\n,22 T. Narikawa,204 H. Narola,72 L. Naticchioni\n,38\nR. K. Nayak\n,260 L. Negri,72 A. Nela,87 C. Nelle,78 A. Nelson\n,131 T. J. N. Nelson,64 M. Nery,8, 9 A. Neunzert\n,2\nS. Ng,54 L. Nguyen Quynh\n,276 S. A. Nichols,12 A. B. Nielsen\n,277 Y. Nishino,25, 42 A. Nishizawa\n,278\nS. Nissanke,279, 37 W. Niu\n,7 F. Nocera,63 J. Noller,280 M. Norman,33 C. North,33 J. Novak\n,117, 234, 281\nR. Nowicki\n,144 J. F. Nu\u00f1o Siles\n,208 L. K. Nuttall\n,74 K. Obayashi,230 J. Oberling\n,2 J. O\u2019Dell,229 E. Oelker\n,35\nM. Oertel\n,234, 117, 282, 281 G. Oganesyan,44, 45 T. O\u2019Hanlon,64 M. Ohashi\n,50 F. Ohme\n,8, 9 R. Oliveri\n,117, 282, 281\nR. Omer,18 B. O\u2019Neal,123 M. Onishi,152 K. Oohara\n,283 B. O\u2019Reilly\n,64 M. Orselli\n,51, 77 R. O\u2019Shaughnessy\n,111\nS. O\u2019Shea,87 S. Oshino\n,50 C. Osthelder,11 I. Ota\n,12 D. J. Ottaway\n,116 A. Ouzriat,56 H. Overmier,64\nB. J. Owen\n,284 R. Ozaki,230 A. E. Pace\n,7 R. Pagano\n,12 M. A. Page\n,25 A. Pai\n,195 L. Paiella,44 A. Pal,285\nS. Pal\n,260 M. A. Palaia\n,81, 82 M. P\u00e1lfi,203 P. P. Palma,39, 21, 22 C. Palomba\n,38 P. Palud\n,20 H. Pan,142 J. Pan,73\nK. C. Pan\n,142 P. K. Panda,233 Shiksha Pandey,7 Swadha Pandey,35 P. T. H. Pang,37, 72 F. Pannarale\n,39, 38\nK. A. Pannone,54 B. C. Pant,104 F. H. Panther,73 M. Panzeri,61, 62 F. Paoletti\n,81 A. Paolone\n,38, 286\nA. Papadopoulos\n,87 E. E. Papalexakis,211 L. Papalini\n,81, 82 G. Papigkiotis\n,251 A. Paquis,41 A. Parisi\n,77, 51\nB.-J. Park,246 J. Park\n,287 W. Parker\n,64 G. Pascale,8, 9 D. Pascucci\n,95 A. Pasqualetti\n,63 R. Passaquieti\n,82, 81\nL. Passenger,6 D. Passuello,81 O. Patane\n,2 A. V. Patel\n,141 D. Pathak,80 A. Patra,33 B. Patricelli\n,82, 81\nB. G. Patterson,33 K. Paul\n,107 S. Paul\n,78 E. Payne\n,11 T. Pearce,33 M. Pedraza,11 A. Pele\n,11 F. E. Pe\u00f1a\nArellano\n,288 X. Peng,119 Y. Peng,57 S. Penn\n,289 M. D. Penuliar,54 A. Perego\n,75, 76 Z. Pereira,133\nC. P\u00e9rigois\n,290, 93, 92 G. Perna\n,92 A. Perreca\n,75, 76, 44 J. Perret\n,20 S. Perri\u00e8s\n,56 J. W. Perry,37, 108 D. Pesios,251\nS. Peters,166 S. Petracca,206 C. Petrillo,77 H. P. Pfeiffer\n,1 H. Pham,64 K. A. Pham\n,18 K. S. Phukon\n,119\nH. Phurailatpam,219 M. Piarulli,101 L. Piccari\n,39, 38 O. J. Piccinni\n,34 M. Pichot\n,114 M. Piendibene\n,82, 81\nF. Piergiovanni\n,61, 62 L. Pierini\n,38 G. Pierra\n,38 V. Pierro\n,291, 132 M. Pietrzak,96 M. Pillas\n,166 F. Pilo\n,81\nL. Pinard\n,176 I. M. Pinto\n,291, 132, 292, 32 M. Pinto\n,63 B. J. Piotrzkowski\n,10 M. Pirello,2 M. D. Pitkin\n,224, 87\nA. Placidi\n,51 E. Placidi\n,39, 38 M. L. Planas\n,99 W. Plastino\n,212, 22 C. Plunkett\n,35 R. Poggiani\n,82, 81\nE. Polini,35 J. Pomper,81, 82 L. Pompili\n,1 J. Poon,219 E. Porcelli,37 E. K. Porter,20 C. Posnansky\n,7 R. Poulton\n,63\nJ. Powell\n,155 G. S. Prabhu,80 M. Pracchia\n,166 B. K. Pradhan\n,80 T. Pradier\n,65 A. K. Prajapati,94\nK. Prasai\n,293 R. Prasanna,233 P. Prasia,80 G. Pratten\n,119 G. Principe\n,185, 48 G. A. Prodi\n,75, 76 P. Prosperi,81\nP. Prosposito,21, 22 A. C. Providence,66 A. Puecher\n,1 J. Pullin\n,12 P. Puppo,38 M. P\u00fcrrer\n,164 H. Qi\n,16\nJ. Qin\n,34 G. Qu\u00e9m\u00e9ner\n,174, 117 V. Quetschke,165 P. J. Quinonez,66 N. Qutob,57 R. Rading,231 I. Rainho,138\nS. Raja,104 C. Rajan,104 B. Rajbhandari\n,111 K. E. Ramirez\n,64 F. A. Ramis Vidal\n,99 M. Ramos Arevalo\n,165\nA. Ramos-Buades\n,99, 37 S. Ranjan\n,57 K. Ransom,64 P. Rapagnani\n,39, 38 B. Ratto,66 A. Ravichandran,133\nA. Ray\n,97 V. Raymond\n,33 M. Razzano\n,82, 81 J. Read,54 T. Regimbau,31 S. Reid,55 C. Reissel,35 D. H. Reitze\n,11\nA. I. Renzini\n,11, 127 B. Revenu\n,294, 41 A. Revilla Pe\u00f1a,83 R. Reyes,181 L. Ricca\n,15 F. Ricci\n,39, 38 M. Ricci\n,38, 39\nA. Ricciardone\n,82, 81 J. Rice,79 J. W. Richardson\n,211 M. L. Richardson,116 A. Rijal,66 K. Riles\n,91 H. K. Riley,33\nS. Rinaldi\n,270 J. Rittmeyer,98 C. Robertson,229 F. Robinet,41 M. Robinson,2 A. Rocchi\n,22 L. Rolland\n,31\nJ. G. Rollins\n,11 A. E. Romano\n,295 R. Romano\n,3, 4 A. Romero\n,31 I. M. Romero-Shaw,224 J. H. Romie,64\nS. Ronchini\n,7 T. J. Roocke\n,116 L. Rosa,4, 32 T. J. Rosauer,211 C. A. Rose,57 D. Rosi\u0144ska\n,125 M. P. Ross\n,53\nM. Rossello-Sastre\n,99 S. Rowan\n,87 S. K. Roy\n,191, 192 S. Roy\n,15 D. Rozza\n,127, 128 P. Ruggi,63 N. Ruhama,239\nE. Ruiz Morales\n,296, 208 K. Ruiz-Rocha,144 S. Sachdev\n,57 T. Sadecki,2 P. Saffarieh\n,37, 108 S. Safi-Harb\n,169\nM. R. Sah\n,13 S. Saha\n,142 T. Sainrat\n,65 S. Sajith Menon\n,215, 39, 38 K. Sakai,297 Y. Sakai\n,272\n\n5\nM. Sakellariadou\n,68 S. Sakon\n,7 O. S. Salafia\n,159, 128, 127 F. Salces-Carcoba\n,11 L. Salconi,63 M. Saleem\n,148\nF. Salemi\n,39, 38 M. Sall\u00e9\n,37 S. U. Salunkhe,80 S. Salvador\n,174, 173 A. Salvarese,148 A. Samajdar\n,72, 37\nA. Sanchez,2 E. J. Sanchez,11 L. E. Sanchez,11 N. Sanchis-Gual\n,138 J. R. Sanders,182 E. M. S\u00e4nger\n,1\nF. Santoliquido\n,44, 45 F. Sarandrea,28 T. R. Saravanan,80 N. Sarin,6 P. Sarkar,8, 9 A. Sasli\n,251 P. Sassi\n,51, 77\nB. Sassolas\n,176 R. Sato,227 S. Sato,152 Yukino Sato,152 Yu Sato,152 O. Sauter\n,46 R. L. Savage\n,2 T. Sawada\n,50\nH. L. Sawant,80 S. Sayah,176 V. Scacco,21, 22 D. Schaetzl,11 M. Scheel,149 A. Schiebelbein,190 M. G. Schiworski\n,79\nP. Schmidt\n,119 S. Schmidt\n,72 R. Schnabel\n,98 M. Schneewind,8, 9 R. M. S. Schofield,78 K. Schouteden\n,110\nB. W. Schulte,8, 9 B. F. Schutz,33, 8, 9 E. Schwartz\n,298 M. Scialpi\n,299 J. Scott\n,87 S. M. Scott\n,34\nR. M. Sedas\n,64 T. C. Seetharamu,87 M. Seglar-Arroyo\n,43 Y. Sekiguchi\n,300 D. Sellers,64 N. Sembo,205\nA. S. Sengupta\n,301 E. G. Seo\n,87 J. W. Seo\n,110 V. Sequino,32, 4 M. Serra\n,38 A. Sevrin,188 T. Shaffer,2\nU. S. Shah\n,57 M. A. Shaikh\n,261 L. Shao\n,302 A. K. Sharma\n,99 Preeti Sharma,12 Prianka Sharma,104\nRitwik Sharma,18 S. Sharma Chaudhary,106 P. Shawhan\n,126 N. S. Shcheblanov\n,303, 263 E. Sheridan,144\nZ.-H. Shi,142 M. Shikauchi,42 R. Shimomura,304 H. Shinkai\n,304 S. Shirke,80 D. H. Shoemaker\n,35\nD. M. Shoemaker\n,148 R. W. Short,2 S. ShyamSundar,104 A. Sider,158 H. Siegel\n,191, 192 N. Siemonsen\n,305\nD. Sigg\n,2 L. Silenzi\n,36, 37 L. Silvestri\n,39, 170 M. Simmonds,116 L. P. Singer\n,306 Amitesh Singh,216 Anika Singh,11\nD. Singh\n,207 N. Singh\n,99 S. Singh,217, 60 A. M. Sintes\n,99 V. Sipala,171, 156 V. Skliris\n,33 B. J. J. Slagmolen\n,34\nD. A. Slater,200 T. J. Slaven-Blair,73 J. Smetana,119 J. R. Smith\n,54 L. Smith\n,87, 185, 48 R. J. E. Smith\n,6\nW. J. Smith\n,144 S. Soares de Albuquerque Filho,61 M. Soares-Santos,189 K. Somiya\n,217 I. Song\n,142\nS. Soni\n,35 V. Sordini\n,56 F. Sorrentino,29 H. Sotani\n,307 F. Spada\n,81 V. Spagnuolo\n,37 A. P. Spencer\n,87\nP. Spinicelli\n,63 A. K. Srivastava,94 F. Stachurski\n,87 C. J. Stark,123 D. A. Steer\n,308 N. Steinle\n,169\nJ. Steinlechner,36, 37 S. Steinlechner\n,36, 37 N. Stergioulas\n,251 P. Stevens,41 M. StPierre,164 M. D. Strong,12\nA. Strunk,2 A. L. Stuver,103, \u2217M. Suchenek,96 S. Sudhagar\n,96 Y. Sudo,230 N. Sueltmann,98 L. Suleiman\n,54\nK. D. Sullivan,12 J. Sun\n,241 L. Sun\n,34 S. Sunil,94 J. Suresh\n,114 B. J. Sutton,68 P. J. Sutton\n,33 K. Suzuki,217\nM. Suzuki,204 B. L. Swinkels\n,37 A. Syx\n,117 M. J. Szczepa\u0144czyk\n,309 P. Szewczyk\n,125 M. Tacca\n,37\nH. Tagoshi\n,204 K. Takada,204 H. Takahashi\n,272 R. Takahashi\n,25 A. Takamori\n,42 S. Takano\n,310\nH. Takeda\n,311, 312 K. Takeshita,217 I. Takimoto Schmiegelow,44, 45 M. Takou-Ayaoh,79 C. Talbot,130 M. Tamaki,204\nN. Tamanini\n,101 D. Tanabe,141 K. Tanaka,50 S. J. Tanaka\n,230 S. Tanioka\n,33 D. B. Tanner,46 W. Tanner,8, 9\nL. Tao\n,211 R. D. Tapia,7 E. N. Tapia San Mart\u00edn\n,37 C. Taranto,21, 22 A. Taruya\n,313 J. D. Tasson\n,153\nJ. G. Tau\n,111 D. Tellez,54 R. Tenorio\n,99 H. Themann,181 A. Theodoropoulos\n,138 M. P. Thirugnanasambandam,80\nL. M. Thomas\n,11 M. Thomas,64 P. Thomas,2 J. E. Thompson\n,210 S. R. Thondapu,104 K. A. Thorne,64\nE. Thrane\n,6 J. Tissino\n,44, 45 A. Tiwari,80 Pawan Tiwari,44 Praveer Tiwari,195 S. Tiwari\n,189 V. Tiwari\n,119\nM. R. Todd,79 M. Toffano,92 A. M. Toivonen\n,18 K. Toland\n,87 A. E. Tolley\n,74 T. Tomaru\n,25 V. Tommasini,11\nT. Tomura\n,50 H. Tong\n,6 C. Tong-Yu,141 A. Torres-Forn\u00e9\n,138, 139 C. I. Torrie,11 I. Tosta e Melo\n,314\nE. Tournefier\n,31 M. Trad Nery,114 K. Tran,123 A. Trapananti\n,52, 51 R. Travaglini\n,168 F. Travasso\n,52, 51\nG. Traylor,64 M. Trevor,126 M. C. Tringali\n,63 A. Tripathee\n,91 G. Troian\n,185, 48 A. Trovato\n,185, 48 L. Trozzo,4\nR. J. Trudeau,11 T. Tsang\n,33 S. Tsuchida\n,315 L. Tsukada\n,213 K. Turbang\n,188, 23 M. Turconi\n,114\nC. Turski,95 H. Ubach\n,83, 84 N. Uchikata\n,204 T. Uchiyama\n,50 R. P. Udall\n,11 T. Uehara\n,316 K. Ueno\n,42\nV. Undheim\n,277 L. E. Uronen,219 T. Ushiba\n,50 M. Vacatello\n,81, 82 H. Vahlbruch\n,8, 9 N. Vaidya\n,11\nG. Vajente\n,11 A. Vajpeyi,6 J. Valencia\n,99 M. Valentini\n,108, 37 S. A. Vallejo-Pe\u00f1a\n,295 S. Vallero,28 V. Valsan\n,10\nM. van Dael\n,37, 317 E. Van den Bossche\n,188 J. F. J. van den Brand\n,36, 108, 37 C. Van Den Broeck,72, 37\nM. van der Sluys\n,37, 72 A. Van de Walle,41 J. van Dongen\n,37, 108 K. Vandra,103 M. VanDyke,120\nH. van Haevermaet\n,23 J. V. van Heijningen\n,37, 108 P. Van Hove\n,65 J. Vanier,259 M. VanKeuren,105 J. Vanosky,2\nN. van Remortel\n,23 M. Vardaro,36, 37 A. F. Vargas\n,124 V. Varma\n,133 A. N. Vazquez,90 A. Vecchio\n,119\nG. Vedovato,93 J. Veitch\n,87 P. J. Veitch\n,116 S. Venikoudis,15 R. C. Venterea\n,18 P. Verdier\n,56 M. Vereecken,15\nD. Verkindt\n,31 B. Verma,133 Y. Verma\n,104 S. M. Vermeulen\n,11 F. Vetrano,61 A. Veutro\n,38, 39 A. Vicer\u00e9\n,61, 62\nS. Vidyant,79 A. D. Viets\n,89 A. Vijaykumar\n,190 A. Vilkha,111 N. Villanueva Espinosa,138 V. Villa-Ortega\n,178\nE. T. Vincent\n,57 J.-Y. Vinet,114 S. Viret,56 S. Vitale\n,35 H. Vocca\n,77, 51 D. Voigt\n,98 E. R. G. von Reis,2\nJ. S. A. von Wrangel,8, 9 W. E. Vossius,231 L. Vujeva\n,140 S. P. Vyatchanin\n,109 J. Wack,11 L. E. Wade,105\nM. Wade\n,105 K. J. Wagner\n,111 L. Wallace,11 E. J. Wang,90 H. Wang\n,217 J. Z. Wang,91 W. H. Wang,165\nY. F. Wang\n,1 G. Waratkar\n,195 J. Warner,2 M. Was\n,31 T. Washimi\n,25 N. Y. Washington,11 D. Watarai,42\nB. Weaver,2 S. A. Webster,87 N. L. Weickhardt\n,98 M. Weinert,8, 9 A. J. Weinstein\n,11 R. Weiss,35 L. Wen\n,73\nK. Wette\n,34 J. T. Whelan\n,111 B. F. Whiting\n,46 C. Whittle\n,11 E. G. Wickens,74 D. Wilken\n,8, 9, 9\nA. T. Wilkin,211 B. M. Williams,120 D. Williams\n,87 M. J. Williams\n,74 N. S. Williams\n,1 J. L. Willis\n,11\n\n6\nB. Willke\n,9, 8, 9 M. Wils\n,110 L. Wilson,105 C. W. Winborn,106 J. Winterflood,73 C. C. Wipf,11 G. Woan\n,87\nJ. Woehler,36, 37 N. E. Wolfe,35 H. T. Wong\n,141 I. C. F. Wong\n,219, 110 K. Wong,190 T. Wouters,72, 37\nJ. L. Wright,2 M. Wright\n,87, 72 B. Wu,79 C. Wu\n,142 D. S. Wu\n,8, 9 H. Wu\n,142 K. Wu,120 Q. Wu,53 Y. Wu,97\nZ. Wu\n,101 E. Wuchner,54 D. M. Wysocki\n,10 V. A. Xu\n,207 Y. Xu\n,99 N. Yadav\n,28 H. Yamamoto\n,11\nK. Yamamoto\n,152 T. S. Yamamoto\n,42 T. Yamamoto\n,50 R. Yamazaki\n,230 T. Yan,119 K. Z. Yang\n,18\nY. Yang\n,146 Z. Yarbrough\n,12 J. Yebana,99 S.-W. Yeh,142 A. B. Yelikar\n,144 X. Yin,35 J. Yokoyama\n,318, 42\nT. Yokozawa,50 S. Yuan,73 H. Yuzurihara\n,50 M. Zanolin,66 M. Zeeshan\n,111 T. Zelenova,63 J.-P. Zendri,93\nM. Zeoli\n,15 M. Zerrad,40 M. Zevin\n,97 L. Zhang,11 N. Zhang,57 R. Zhang\n,150 T. Zhang,119 C. Zhao\n,73\nYue Zhao,162 Yuhang Zhao,20 Z.-C. Zhao\n,319 Y. Zheng\n,106 H. Zhong\n,18 H. Zhou,79 H. O. Zhu,73\nZ.-H. Zhu\n,319, 320 A. B. Zimmerman\n,148 L. Zimmermann,56 M. E. Zucker\n,35, 11 and J. Zweizig\n11\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\n1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n2LIGO Hanford Observatory, Richland, WA 99352, USA\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5University of Warwick, Coventry CV4 7AL, United Kingdom\n6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n7The Pennsylvania State University, University Park, PA 16802, USA\n8Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n9Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n10University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n11LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n12Louisiana State University, Baton Rouge, LA 70803, USA\n13Tata Institute of Fundamental Research, Mumbai 400005, India\n14Centre de Physique Th\u00e9orique, Aix-Marseille Universit\u00e9,\nCampus de Luminy, 163 Av.\nde Luminy, 13009 Marseille, France\n15Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n16Queen Mary University of London, London E1 4NS, United Kingdom\n17University of California, Davis, Davis, CA 95616, USA\n18University of Minnesota, Minneapolis, MN 55455, USA\n19Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n20Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n21Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n22INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n23Universiteit Antwerpen, 2000 Antwerpen, Belgium\n24International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n25Gravitational Wave Science Project, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n26Advanced Technology Center, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n27Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n28INFN Sezione di Torino, I-10125 Torino, Italy\n29INFN, Sezione di Genova, I-16146 Genova, Italy\n30Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n31Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n32Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n33Cardiff University, Cardiff CF24 3AA, United Kingdom\n34OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n35LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n36Maastricht University, 6200 MD Maastricht, Netherlands\n37Nikhef, 1098 XG Amsterdam, Netherlands\n38INFN, Sezione di Roma, I-00185 Roma, Italy\n39Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n40Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, F-13013 Marseille, France\n41Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n42University of Tokyo, Tokyo, 113-0033, Japan\n43Institut de F\u00edsica d\u2019Altes Energies (IFAE), The Barcelona Institute of Science and Technology,\nCampus UAB, E-08193 Bellaterra (Barcelona), Spain\n44Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n45INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n46University of Florida, Gainesville, FL 32611, USA\n\n7\n47Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n48INFN, Sezione di Trieste, I-34127 Trieste, Italy\n49Tecnologico de Monterrey, Escuela de Ingenier\u00eda y Ciencias, 64849 Monterrey, Nuevo Le\u00f3n, Mexico\n50Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51INFN, Sezione di Perugia, I-06123 Perugia, Italy\n52Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n53University of Washington, Seattle, WA 98195, USA\n54California State University Fullerton, Fullerton, CA 92831, USA\n55SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n56Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n57Georgia Institute of Technology, Atlanta, GA 30332, USA\n58Chennai Mathematical Institute, Chennai 603103, India\n59Royal Holloway, University of London, London TW20 0EX, United Kingdom\n60Astronomical course, The Graduate University for Advanced Studies (SOKENDAI),\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n61Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n62INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n63European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n64LIGO Livingston Observatory, Livingston, LA 70754, USA\n65Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n66Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n67Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n68King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n69Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n70International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n71Accelerator Laboratory, High Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n72Institute for Gravitational and Subatomic Physics (GRASP),\nUtrecht University, 3584 CC Utrecht, Netherlands\n73OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n74University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n75Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n76INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n77Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n78University of Oregon, Eugene, OR 97403, USA\n79Syracuse University, Syracuse, NY 13244, USA\n80Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n81INFN, Sezione di Pisa, I-56127 Pisa, Italy\n82Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n83Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB),\nc.\nMart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n84Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA),\nUniversitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n85Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n86Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d,\nUniversit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n87IGR, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n88HUN-REN Wigner Research Centre for Physics, H-1121 Budapest, Hungary\n89Concordia University Wisconsin, Mequon, WI 53097, USA\n90Stanford University, Stanford, CA 94305, USA\n91University of Michigan, Ann Arbor, MI 48109, USA\n92Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n93INFN, Sezione di Padova, I-35131 Padova, Italy\n94Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n95Universiteit Gent, B-9000 Gent, Belgium\n96Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n97Northwestern University, Evanston, IL 60208, USA\n98Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n99IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n100Aix-Marseille Universit\u00e9, Universit\u00e9 de Toulon, CNRS, CPT, Marseille, France\n101Laboratoire des 2 Infinis - Toulouse (L2IT-IN2P3), F-31062 Toulouse Cedex 9, France\n102Universit\u00e0 di Siena, Dipartimento di Scienze Fisiche,\ndella Terra e dell\u2019Ambiente, I-53100 Siena, Italy\n\n8\n103Villanova University, Villanova, PA 19085, USA\n104RRCAT, Indore, Madhya Pradesh 452013, India\n105Kenyon College, Gambier, OH 43022, USA\n106Missouri University of Science and Technology, Rolla, MO 65409, USA\n107Indian Institute of Technology Madras, Chennai 600036, India\n108Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n109Lomonosov Moscow State University, Moscow 119991, Russia\n110Katholieke Universiteit Leuven, Oude Markt 13, 3000 Leuven, Belgium\n111Rochester Institute of Technology, Rochester, NY 14623, USA\n112Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n113Bar-Ilan University, Ramat Gan, 5290002, Israel\n114Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n115University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n116OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n117Centre national de la recherche scientifique, 75016 Paris, France\n118Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n119University of Birmingham, Birmingham B15 2TT, United Kingdom\n120Washington State University, Pullman, WA 99164, USA\n121Cornell University, Ithaca, NY 14850, USA\n122Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS,\nENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n123Christopher Newport University, Newport News, VA 23606, USA\n124OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n125Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n126University of Maryland, College Park, MD 20742, USA\n127Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n128INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n129Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1,\nCNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n130University of Chicago, Chicago, IL 60637, USA\n131University of Arizona, Tucson, AZ 85721, USA\n132INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n133University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA\n134Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n135Universidad de Guadalajara, 44430 Guadalajara, Jalisco, Mexico\n136Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n137Colorado State University, Fort Collins, CO 80523, USA\n138Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n139Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n140Niels Bohr Institute, University of Copenhagen, 2100 K\u00f3benhavn, Denmark\n141National Central University, Taoyuan City 320317, Taiwan\n142National Tsing Hua University, Hsinchu City 30013, Taiwan\n143OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n144Vanderbilt University, Nashville, TN 37235, USA\n145University of the Chinese Academy of Sciences / International\nCentre for Theoretical Physics Asia-Pacific, Bejing 100049, China\n146Department of Electrophysics, National Yang Ming Chiao Tung University, 101 Univ. Street, Hsinchu, Taiwan\n147Kamioka Branch, National Astronomical Observatory of Japan,\n238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n148University of Texas, Austin, TX 78712, USA\n149CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n150Northeastern University, Boston, MA 02115, USA\n151Dipartimento di Ingegneria Industriale (DIIN),\nUniversit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n152Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n153Carleton College, Northfield, MN 55057, USA\n154University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n155OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n156INFN Cagliari, Physics Department, Universit\u00e0 degli Studi di Cagliari, Cagliari 09042, Italy\n157Universit\u00e0 degli Studi di Cagliari, Via Universit\u00e0 40, 09124 Cagliari, Italy\n158Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n159INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n160Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n161Montana State University, Bozeman, MT 59717, USA\n\n9\n162The University of Utah, Salt Lake City, UT 84112, USA\n163Johns Hopkins University, Baltimore, MD 21218, USA\n164University of Rhode Island, Kingston, RI 02881, USA\n165The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n166Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n167DIFA- Alma Mater Studiorum Universit\u00e0 di Bologna, Via Zamboni, 33 - 40126 Bologna, Italy\n168Istituto Nazionale Di Fisica Nucleare - Sezione di Bologna,\nviale Carlo Berti Pichat 6/2 - 40127 Bologna, Italy\n169University of Manitoba, Winnipeg, MB R3T 2N2, Canada\n170INFN-CNAF - Bologna, Viale Carlo Berti Pichat, 6/2, 40127 Bologna BO, Italy\n171Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n172INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n173Universit\u00e9 de Normandie, ENSICAEN, UNICAEN,\nCNRS/IN2P3, LPC Caen, F-14000 Caen, France\n174Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n175The University of Sheffield, Sheffield S10 2TN, United Kingdom\n176Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA),\nIP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n177Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n178IGFAE, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain\n179Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n180INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n181California State University, Los Angeles, Los Angeles, CA 90032, USA\n182Marquette University, Milwaukee, WI 53233, USA\n183Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n184Corps des Mines, Mines Paris, Universit\u00e9 PSL, 60 Bd Saint-Michel, 75272 Paris, France\n185Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n186Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n187National Center for Nuclear Research, 05-400 \u015awierk-Otwock, Poland\n188Vrije Universiteit Brussel, 1050 Brussel, Belgium\n189University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n190Canadian Institute for Theoretical Astrophysics,\nUniversity of Toronto, Toronto, ON M5S 3H8, Canada\n191Stony Brook University, Stony Brook, NY 11794, USA\n192Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n193Montclair State University, Montclair, NJ 07043, USA\n194HUN-REN Institute for Nuclear Research, H-4026 Debrecen, Hungary\n195Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n196Centro de F\u00edsica das Universidades do Minho e do Porto,\nUniversidade do Minho, PT-4710-057 Braga, Portugal\n197Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France\n198CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n199Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n200Western Washington University, Bellingham, WA 98225, USA\n201SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n202Barry University, Miami Shores, FL 33168, USA\n203E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n204Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n205Department of Physics, Graduate School of Science,\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n206University of Sannio at Benevento, I-82100 Benevento,\nItaly and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n207University of California, Berkeley, CA 94720, USA\n208Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n209Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans, UMR CNRS 6613, F-72085 Le Mans, France\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211University of California, Riverside, Riverside, CA 92521, USA\n212Dipartimento di Ingegneria Industriale, Elettronica e Meccanica,\nUniversit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n213University of Nevada, Las Vegas, Las Vegas, NV 89154, USA\n214University of Nottingham NG7 2RD, UK\n215Ariel University, Ramat HaGolan St 65, Ari\u2019el, Israel\n\n10\n216The University of Mississippi, University, MS 38677, USA\n217Graduate School of Science, Institute of Science Tokyo,\n2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n218Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n219The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n220American University, Washington, DC 20016, USA\n221Dipartimento di Fisica, Universit\u00e0 degli studi di Milano, Via Celoria 16, I-20133, Milano, Italy\n222INFN, sezione di Milano, Via Celoria 16, I-20133, Milano, Italy\n223Department of Applied Physics, Fukuoka University,\n8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n224University of Cambridge, Cambridge CB2 1TN, United Kingdom\n225University of Lancaster, Lancaster LA1 4YW, United Kingdom\n226College of Industrial Technology, Nihon University,\n1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n227Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho,\nNishi-ku, Niigata City, Niigata 950-2181, Japan\n228Department of Physics, Tamkang University, No.\n151,\nYingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n229Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n230Department of Physical Sciences, Aoyama Gakuin University,\n5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n231Helmut Schmidt University, D-22043 Hamburg, Germany\n232Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP),\nOsaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n233Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n234Observatoire Astronomique de Strasbourg, 11 Rue de l\u2019Universit\u00e9, 67000 Strasbourg, France\n235Faculty of Physics, University of Bia\u0142ystok, 15-245 Bia\u0142ystok, Poland\n236National Astronomical Observatories, Chinese Academic of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n237School of Astronomy and Space Science, University of Chinese Academy of Sciences,\n20A Datun Road, Chaoyang District, Beijing, China\n238Sungkyunkwan University, Seoul 03063, Republic of Korea\n239Department of Physics, Ulsan National Institute of Science and Technology (UNIST),\n50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n240Institute for Cosmic Ray Research, The University of Tokyo,\n5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n241Chung-Ang University, Seoul 06974, Republic of Korea\n242University of Washington Bothell, Bothell, WA 98011, USA\n243Laboratoire de Physique et de Chimie de l\u2019Environnement,\nUniversit\u00e9 Joseph KI-ZERBO, 9GH2+3V5, Ouagadougou, Burkina Faso\n244Ewha Womans University, Seoul 03760, Republic of Korea\n245National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n246Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea\n247Department of Astronomy and Space Science, Chungnam National University,\n9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea\n248Institute of Particle and Nuclear Studies (IPNS),\nHigh Energy Accelerator Research Organization (KEK),\n1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n249Division of Science, National Astronomical Observatory of Japan,\n2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n250Nagoya University, Nagoya, 464-8601, Japan\n251Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n252Bard College, Annandale-On-Hudson, NY 12504, USA\n253Technical University of Braunschweig, D-38106 Braunschweig, Germany\n254Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n255Astronomical Observatory, Jagiellonian University, 31-007 Cracow, Poland\n256Department of Physics and Astronomy, University of Padova, Via Marzolo, 8-35151 Padova, Italy\n257Sezione di Padova, Istituto Nazionale di Fisica Nucleare (INFN), Via Marzolo, 8-35131 Padova, Italy\n258Department of Physics, Nagoya University, ES building,\nFurocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n259Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n260Indian Institute of Science Education and Research,\nKolkata, Mohanpur, West Bengal 741252, India\n\n11\n261Seoul National University, Seoul 08826, Republic of Korea\n262Department of Computer Simulation, Inje University,\n197 Inje-ro, Gimhae, Gyeongsangnam-do 50834, Republic of Korea\n263NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n264Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n265Department of Physics, National Cheng Kung University,\nNo.1, University Road, Tainan City 701, Taiwan\n266St. Thomas University, Miami Gardens, FL 33054, USA\n267Scuola Normale Superiore, I-56126 Pisa, Italy\n268Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats, E-08010 Barcelona, Spain\n269Institut de F\u00edsica d\u2019Altes Energies, E-08193 Barcelona, Spain\n270Institut fuer Theoretische Astrophysik, Zentrum fuer Astronomie Heidelberg,\nUniversitaet Heidelberg, Albert Ueberle Str. 2, 69120 Heidelberg, Germany\n271Institucio Catalana de Recerca i Estudis Avan\u00e7ats (ICREA),\nPasseig de Llu\u00eds Companys, 23, 08010 Barcelona, Spain\n272Research Center for Space Science, Advanced Research Laboratories, Tokyo City University,\n3-3-1 Ushikubo-Nishi, Tsuzuki-Ku, Yokohama, Kanagawa 224-8551, Japan\n273Tsinghua University, Beijing 100084, China\n274Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n275Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho,\nFushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n276Phenikaa Institute for Advanced Study (PIAS),\nPhenikaa University, Yen Nghia, Ha Dong, Hanoi, Vietnam\n277University of Stavanger, 4021 Stavanger, Norway\n278Physics Program, Graduate School of Advanced Science and Engineering,\nHiroshima University, 1-3-1 Kagamiyama, Higashihiroshima City, Hiroshima 739-8526, Japan\n279GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,\nUniversity of Amsterdam, 1098 XH Amsterdam, Netherlands\n280University College London, London WC1E 6BT, United Kingdom\n281Observatoire de Paris, 75014 Paris, France\n282Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n283Graduate School of Science and Technology, Niigata University,\n8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n284University of Maryland, Baltimore County, Baltimore, MD 21250, USA\n285CSIR-Central Glass and Ceramic Research Institute, Kolkata, West Bengal 700032, India\n286Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n287Department of Astronomy, Yonsei University,\n50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea\n288Department of Physics, University of Guadalajara, Av. Revolucion 1500,\nColonia Olimpica C.P. 44430, Guadalajara, Jalisco, Mexico\n289Hobart and William Smith Colleges, Geneva, NY 14456, USA\n290INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n291Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n292Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n293Kennesaw State University, Kennesaw, GA 30144, USA\n294Subatech, CNRS/IN2P3 - IMT Atlantique - Nantes Universit\u00e9,\n4 rue Alfred Kastler BP 20722 44307 Nantes C\u00c9DEX 03, France\n295Universidad de Antioquia, Medell\u00edn, Colombia\n296Departamento de F\u00edsica - ETSIDI, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain\n297Department of Electronic Control Engineering,\nNational Institute of Technology, Nagaoka College,\n888 Nishikatakai, Nagaoka City, Niigata 940-8532, Japan\n298Trinity College, Hartford, CT 06106, USA\n299Dipartimento di Fisica e Scienze della Terra,\nUniversit\u00e0 Degli Studi di Ferrara, Via Saragat, 1, 44121 Ferrara FE, Italy\n300Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n301Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n302Kavli Institute for Astronomy and Astrophysics, Peking University,\nYiheyuan Road 5, Haidian District, Beijing 100871, China\n303Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes,\nChamps-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n304Faculty of Information Science and Technology, Osaka Institute of Technology,\n1-79-1 Kitayama, Hirakata City, Osaka 573-0196, Japan\n305Princeton University, Princeton, NJ 08544, USA\n\n12\n306NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n307Faculty of Science and Technology, Kochi University,\n2-5-1 Akebono-cho, Kochi-shi, Kochi 780-8520, Japan\n308Laboratoire de Physique de l\u2019\u00c9cole Normale Sup\u00e9rieure, ENS, (CNRS,\nUniversit\u00e9 PSL, Sorbonne Universit\u00e9, Universit\u00e9 Paris Cit\u00e9), F-75005 Paris, France\n309Faculty of Physics, University of Warsaw, Ludwika Pasteura 5, 02-093 Warszawa, Poland\n310Laser Interferometry and Gravitational Wave Astronomy,\nMax Planck Institute for Gravitational Physics, Callinstrasse 38, 30167 Hannover, Germany\n311The Hakubi Center for Advanced Research, Kyoto University,\nYoshida-honmachi, Sakyou-ku, Kyoto City, Kyoto 606-8501, Japan\n312Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n313Yukawa Institute for Theoretical Physics (YITP), Kyoto University,\nKita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n314University of Catania, Department of Physics and Astronomy, Via S. Sofia, 64, 95123 Catania CT, Italy\n315National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n316Department of Communications Engineering, National Defense Academy of Japan,\n1-10-20 Hashirimizu, Yokosuka City, Kanagawa 239-8686, Japan\n317Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n318Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), WPI,\nThe University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8583, Japan\n319Department of Astronomy, Beijing Normal University,\nXinjiekouwai Street 19, Haidian District, Beijing 100875, China\n320School of Physics and Technology, Wuhan University,\nBayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\nWe present the first directed searches for long-transient and continuous gravitational waves from\nultralight vector boson clouds around known black holes (BHs). We use LIGO data from the first\npart of the fourth LIGO\u2013Virgo\u2013KAGRA observing run. The searches target two distinct types\nof BHs and use two new semicoherent methods: hidden Markov model (HMM) tracking for the\nremnant BHs of the mergers GW230814_230901 and GW231123_135430 (referred to as GW230814\nand GW231123 in this study), and a dedicated method using the Band Sampled Data (BSD)\nframework for the galactic BH in the Cygnus X-1 binary system. Without finding evidence of a\nsignal from vector bosons in the data, we estimate the mass range that can be constrained. For\nthe HMM searches targeting the remnants from GW231123 and GW230814, we disfavor vector\nboson masses in the ranges [0.94, 1.08] and [2.75, 3.28] \u00d7 10\u221213 eV, respectively, at 30% confidence,\nassuming a 1% false alarm probability. Although these searches are only marginally sensitive to\nsignals from merger remnants at relatively large distances, future observations are expected to\nyield more stringent constraints with high confidence. For the BSD search targeting the BH in\nCygnus X-1, we exclude vector boson masses in the range [0.85, 1.59] \u00d7 10\u221213 eV at 95% confidence,\nassuming an initial BH spin larger than 0.5.\nI.\nINTRODUCTION\nUltralight bosons are a class of theoretical particles\nproposed in certain extensions of the Standard Model,\nand their discovery could address numerous unresolved\nquestions in particle physics and cosmology (e.g., the\nnature of dark matter [1\u20134] or the strong charge-parity-\nproblem [5\u20137]). Theories predict different subclasses of ul-\ntralight bosons based on spin, including scalar (spin-0) [5\u2013\n9], vector (spin-1) [10\u201316], and tensor (spin-2) [17\u201322]\nfields. Assuming only gravitational coupling, the superra-\ndiance mechanism provides a means by which ultralight\nbosons may form bound states around rotating black\nholes (BHs) and grow into macroscopic clouds, producing\nquasi-monochromatic, long-duration gravitational wave\n(GW) signals that may be observable by ground-based\n\u2217Deceased, September 2024.\ndetectors [23\u201340].\nUltralight vector bosons with mass mV can extract\nrotational energy from a BH through the superradiance\nmechanism if the following condition is satisfied:\n0 < \u03c9 < m\u2126H,\n(1)\nwhere \u03c9 \u2248mV c2/\u210fis the angular frequency of the boson\nfield, m is the azimuthal quantum number, and \u2126H is\nthe angular frequency of the BH\u2019s outer horizon. Bound\nstates can therefore grow exponentially in time with an\ninstability growth rate that is maximized when the bo-\nson\u2019s Compton wavelength \u03bb is comparable to the BH\u2019s\nhorizon radius rg. For a superradiantly unstable state,\nthe instability extracts energy and angular momentum\nfluxes from the BH at the horizon into the bosonic field,\nwith the change in mass directly related to the change in\nangular momentum. If we assume the primary interaction\nof the ultralight bosons is gravitational, this results in\ncompound field amplification and the growth of a macro-\n\n13\nscopic cloud that may extract as much as \u223c10% of the\nBH\u2019s initial mass [23, 37, 41\u201348].\nThis exchange of energy and angular momentum con-\ntinues until Eq. (1) is saturated (\u03c9 = m\u2126H), or in other\nwords, until the BH has been spun down so much that su-\nperradiance can no longer occur. At this point, the cloud\nbegins to deplete through GW emission, which occurs at\nroughly twice the boson cloud oscillation frequency, with\na small positive frequency drift as the magnitude of the\nbosons\u2019 binding energy to the BH decreases [30, 37\u201339, 49\u2013\n52]. For stellar and intermediate-mass BHs and bosons\nwith masses within the range \u223c10\u221214\u201310\u221211 eV [26, 29],\nthis emission frequency falls in the sensitive band of\nground-based GW detectors. Thus, current and future\nground-based GW detector networks [53\u201359] offer a unique\nway to search for these ultralight bosons. If no detection\nis made, we are able to place constraints on the existence\nof ultralight bosons within the above mass range.\nMany observational studies have already been designed\nand implemented to search for ultralight scalar bosons,\nand, in the absence of a detection, constrain their exis-\ntence. Although a handful of studies have derived con-\nstraints on vector bosons as well, the vector signal mor-\nphology has only recently been accurately modeled via\nnumerical calculations in both the relativistic and non-\nrelativistic regimes,1 enabling more accurate predictions\nof the signal morphology and more robust constraints\non the boson mass [39]. Constraints are placed on the\nexistence of ultralight scalar [26, 29, 32, 60] and vec-\ntor [30, 32, 61] particles using BH spin measurements. In\nsome cases, however, there are systematic uncertainties\nrelated to the BH parameters that limit these studies.\nSearches for continuous gravitational waves (CWs) that\ntarget either the galactic center or the entire sky are used\nto constrain scalars and, based on certain astrophysical as-\nsumptions, they disfavor the mass range of approximately\n\u223c10\u221213\u201310\u221212 eV [62\u201366]. Using the null results from\nsearches for a stochastic GW background generated by\na population of BHs with scalar [67, 68] and vector [69]\nclouds, boson masses \u223c10\u221213 eV have been disfavored\nfor both scalars and vectors, based on certain assump-\ntions regarding the BH population and spin distributions.\nA directed search targeting the black hole in the X-ray\nbinary Cygnus X-1 excludes scalars in the mass range of\n\u223c[0.6, 1] \u00d7 10\u221212 eV, depending on the BH\u2019s estimated\nage [70, 71]. In addition to indirect searches, ground-\nbased interferometers are used as particle detectors for\nthe direct detection of ultralight scalars in Refs. [72\u201374]\nand vectors in Refs. [75, 76]. Looking to the future, the\nexistence of a scalar cloud could impact the inspiral of\nbinary BHs, and this may soon be detectable for certain\nboson masses and field strengths [33, 77, 78].\n1 In the relativistic regime, the BH and the superradiant cloud\nare approximately the same size, whereas in the non-relativistic\nregime, the cloud is much larger than the BH.\nIn this study, we present the results from the first di-\nrected searches for GW signals from ultralight vector\nboson clouds (VBCs) around selected known BHs, per-\nformed using data from the first part of the fourth observ-\ning run (O4a) of the LIGO Scientific Collaboration, Virgo\nCollaboration, and KAGRA Collaboration (LVK). We\nuse two semicoherent methods to target vector boson sig-\nnals produced by two different categories of astrophysical\nsources: i) using methods outlined in Refs. [79, 80] based\non a hidden Markov model (HMM), we undertake the\nfirst ever directed searches for GWs from VBCs around\ncompact binary merger remnant BHs [81\u201383], and ii) us-\ning a new method based on the so-called Band Sampled\nData (BSD) framework [84], we search for GWs from a\nVBC around the BH in the known binary system Cygnus\nX-1. Each method is tailored to track signals from a dif-\nferent type of source; while merger remnants are isolated\nand are expected to emit signals with rapidly evolving\nfrequencies, Cygnus X-1 is a binary system with a BH\nthat would emit a nearly monochromatic signal and has\nuncertain orbital parameters that must be accounted for.\nFor a more in-depth discussion of these sources and their\ndifferences, see Sec. II C.\nOne benefit of targeting known BHs\u2014whether they are\nremnants from previous GW observations or identified\nvia X-ray emissions\u2014is that more robust constraints can\nbe derived. In contrast to the broader searches mentioned\nabove, which rely on assumptions about the underlying\nBH population, directed searches benefit from more com-\nplete information about the target BHs. In particular,\nuncertainties in the BH age and spin\u2014which can strongly\ninfluence the resulting constraints\u2014are reduced or elimi-\nnated when the source is well-characterized. For young\nmerger remnants, very few hypotheses are needed on the\nhistory and evolution of the BHs since their formation.\nOn the other hand, targeting a galactic BH like Cygnus\nX-1 is beneficial due to its proximity [85]. In addition, be-\ncause the system is much older [86], any signal observable\nduring O4a must correspond to an emission process that\noccurs over much longer timescales and produces a more\nslowly evolving signal (i.e., like a traditional CW), and\nhence the search can be run across the full O4a dataset.2\nThe organization of the paper is as follows. In Sec. II,\nwe identify the target BHs and give an overview of the\nGW signal parameters relevant to the searches. In Sec. III,\nwe outline the two search methods used in this study. We\ndescribe the search configurations and general setup for\neach method in Sec. IV. In Sec. V, we discuss the results\nfrom the searches and explain the candidate follow-up\nprocess. Then, in Sec. VI, we estimate the range of vector\nboson masses that can be disfavored given that no signal\nis detected. We summarize our findings and conclude in\n2 While merger remnants could produce similarly long-lived GW\nemission if the bosons with appropriate masses exist, the growth\ntime of the corresponding clouds would far exceed the O4a time\nframe.\n\n14\nSec. VII.\nII.\nTARGET SOURCES\nIn this section, we give an overview of the BHs targeted\nby the two search pipelines, as well as their expected\nGW signal parameters, which can be predicted using a\ncombination of analytic [30, 87\u201390] and numerical [32, 36\u2013\n39, 91] methods. We generate the signal parameters using\nthe waveform model SuperRad, which models the dynam-\nics, oscillation frequency, and GW emission of ultralight\nboson clouds with high accuracy [52, 92].\nA.\nMerger remnant black holes\nFor the HMM search, we target two binary merger\nremnant BHs from O4a [83]:\nthe remnants of the\nGW230814_230901 [83] and GW231123_135430 [93]\nmergers (henceforth referred to as GW230814 and\nGW231123, respectively). The estimated median parame-\nters for each remnant are shown in Table I, where Mi and\n\u03c7i are the mass and dimensionless spin of the BH before\nsuperradiance has occurred, DL is the luminosity distance,\n\u03b9 is the inclination angle, and RA and Dec are the right\nascension and declination of the BH. The remnants from\nthese two events are chosen in particular because, for\neach BH, we find that the median estimated luminosity\ndistance is less than the furthest reachable distance (see\nFig. 9 in Ref. [79]) for a BH with the same median mass\nand spin. Note, because we use an earlier version of the\nparameter estimates (which were the most recent and\naccurate estimates available at the time of this study),\nthe values shown in Table I vary slightly from those re-\nported in Refs. [83] and [93]. However, these differences\nare minor and have no noticeable impact on the analyses\nor conclusions, as the searches are relatively insensitive\nto small deviations in the parameter estimates.3\nThe parameter estimates used in this study have been\ngenerated with the NRSur7dq4 waveform model [94]. This\nmodel has been chosen because it interpolates between\nnumerical relativity data without making additional wave-\nform modeling assumptions, and it typically performs well\nfor signals from higher-mass sources like GW231123 [93].\nIn standard astrophysical formation scenarios of binary\nsystems, the high spin for the primary BH favored by the\n3 For GW230814, the posterior distributions of the BH properties\nfrom the preliminary version of the parameter estimation are\nconsistent with those reported in Ref. [83]. For GW231123, the\nposterior distributions show minor differences compared to those\npresented in Ref. [93]. In particular, the distribution of DL in\nRef. [93] is more tightly constrained than the preliminary version\nused in this study; nonetheless, the two distributions remain\nconsistent at the 90% confidence level. Since we adopt the broader\nDL distribution, our results can be considered conservative.\nanalysis of GW231123 [93] is in tension with the existence\nof a vector boson with mass that would give the loudest\nsignal for the remnant BH [61]. Nonetheless, there is value\nin targeting the remnant for a direct and independent\nsearch.\nB.\nCygnus X-1\nIn the BSD-based search, we target the BH in the\nCygnus X-1 system, with parameters listed in Table I\ntaken from a recent study [85]. Cygnus X-1 is a binary\nsystem with an orbital period P = 5.599829 \u00b1 0.000016\ndays [95]. Several of its orbital parameters are constrained\nthrough X-ray observations and are summarized in Ta-\nble II. The age of the BH is estimated to be 6.2\u00b11.8\u00d7106\nyrs [86].\nGiven the system\u2019s age, any detectable signal is ex-\npected to exhibit high stability, with only small variations\nin the emission frequency over time. This expectation is\nsupported by simulations using the SuperRad waveform\nmodel, showing that the signal frequency drift remains\nwithin O(10\u221212) Hz s\u22121 across the entire parameter space,\nwhich is well below the frequency resolution of the analy-\nsis. Consequently, we assume a monochromatic emission\nfor the whole duration of O4a, and we neglect frequency\nderivatives typically included in standard Taylor expan-\nsions (e.g., [96, 97]).\nIn the literature, several studies report an extreme spin\n(\u22650.95) for the BH in Cygnus X-1 [98\u2013102]. These results\ndisfavor the existence of a VBC since a significant part of\nthe rotational energy of the BH would have been extracted\nthrough superradiance, so such a high spin could not be\nmeasured after superradiance took place. However, these\nmeasurements are impacted by systematic uncertainties\nand may depend on the accretion model. This is reflected\nby a disagreement in the literature with other studies\nallowing spin values between 0.5 and 0.9 [103\u2013108], some\neven compatible with a spin below 0.2 [109, 110]. In the\nCygnus X-1 search, we ignore this tension by treating the\nmeasurable final spin of the BH after superradiance as\na free parameter. To estimate the VBC properties, we\nadopt an initial spin value \u03c7i = 0.95, as shown in Table I.\nIn Sec. VI, we derive constraints on the possible boson\nmass for different assumed values of \u03c7i.\nC.\nGW signal parameters\nUsing the SuperRad waveform model [52, 92] and the\nvalues for Mi and \u03c7i shown in Table I, we find the opti-\nmal vector mass\u2014that is, the mass mopt\nV\nthat optimizes\nsuperradiant instability for a given BH, producing the\nmaximum GW strain amplitude attainable by the sys-\ntem at a reference epoch tref. For the remnants from\nGW230814 and GW231123, tref is fixed at the time when\nthe VBC reaches its full size [79], corresponding to the\ntime tsat when Eq. (1) is saturated. In the case of Cygnus\n\n15\nTable I. Estimated median parameters for the remnant BHs from the GW230814 and GW231123 mergers and for the galactic\nBH Cygnus X-1.\nSource\nMi [M\u2299]\n\u03c7i\nDL [Mpc]\ncos \u03b9\nRA [rad]\nDec [rad]\nRemnant from GW230814\n58.9+1.8\n\u22121.8\na\n0.68+0.01\n\u22120.02\n301+171\n\u2212138\n0.03+0.74\n\u22120.67\n3.21+2.62\n\u22122.95\nb\n0.04+1.02\n\u22121.08\nb\nRemnant from GW231123\n219.8+22.6\n\u221246.2\na\n0.85+0.05\n\u22120.18\n2054+2960\n\u22121280\n0.45+0.45\n\u22121.23\n3.37+1.67\n\u22120.59\nb\n0.38+0.40\n\u22120.63\nb\nBH in Cygnus X-1\n21.2+2.2\n\u22122.3\n0.95d\n0.00222+0.00018\n\u22120.00017\n0.887+0.005\n\u22120.006\n5.22883712c\n0.61438355c\na We use Mi and \u03c7i to represent the mass and dimensionless spin of the BH before superradiance occurs, i.e., the final BH mass (Mf) and\nspin (\u03c7f) used in the compact binary coalescence parameter estimation. The reason we do not use Mf and \u03c7f here is to avoid confusion\nwith the final BH mass and spin after superradiance occurs.\nb See Fig. 1.\nc At reference epoch MJD 56198.\nd The spin of Cygnus X-1 is debated in the literature. In our analysis, we treat the final spin of the BH as a free parameter and assume a\nnominal initial spin of \u03c7i = 0.95. The impact of the initial spin on the derived constraints is discussed in Sec. VI.\nTable II. Orbital parameters for Cygnus X-1.\nParameter\nSymbol\nValue\nRef.\nOrbital Period [days]\nP\n5.599829(16)\n[95]\nProj. Semi-major Axis [s]\nap\n36.88+4.02\n\u22123.65\n[85]\nEccentricity [-]\ne\n0.0188+0.0028\n\u22120.0026\n[85]\nArg. of periastron [deg]\n\u03c9\n306.6+6.6\n\u22126.3\n[85]\nX-1, we consider the start of the O4a period as the refer-\nence time. The values of mopt\nV\nare shown for each source\nin the second column of Table III. Then, based on these\nvalues and the median BH parameters, we use SuperRad\n(for the fastest growing, initially dominant mode m = 1)\nto estimate the GW signal parameters for each BH. The\nparameters, also listed in Table III, are defined as fol-\nlows. \u03c4growth and \u03c4GW are the VBC growth and depletion\ntimescales. The parameters heff\n0 , f0, and \u02d9f0 are, respec-\ntively, the peak GW strain amplitude in the detector\nframe,4 the GW emission frequency, and the frequency\ndrift, each evaluated at the reference time (t = tref).\nHere, we provide a depiction of how the signal frequency\nevolves once the VBC is saturated, independent of the\nspecific target being searched. At tsat, the VBC is oscillat-\ning around the BH with angular frequency \u03c9 = m\u2126H [38].\nThen, the initial frequency of the GW emission in the\nsource frame depends on this angular frequency at tsat:\nf0 = \u03c9/\u03c0. The evolution of the GW frequency can be\napproximated as [52]\nfGW(t) = f\u221e\u2212\n|fshift|\n1 + (t \u2212tsat)/\u03c4GW\n,\n(2)\nwhere f\u221eis the asymptotic frequency at late times\n(t \u2212tsat \u226b\u03c4GW), and fshift is the negative shift of fGW\naway from f\u221eas a result of the self-gravity of the VBC\n4 h0 in the detector frame is scaled by the orientation angle\nof the BH \u03b9 as follows:\nheff\n0\n= h0 2\u22121/2{[(1 + cos2 \u03b9)/2]2 +\ncos2 \u03b9}1/2 [111].\nat tsat [52, 79, 92], i.e., we have f0 = f\u221e\u2212|fshift|. While\nEq. (2) provides a useful illustration of how the emis-\nsion frequency evolves over time, the frequencies and\ntheir time derivatives shown in Table III are computed\nwith greater accuracy using Superrad, which incorporates\nhigher-order relativistic corrections [92]. Note that the\nsignal characteristics differ between merger remnants and\nCygnus X-1, as the depletion timescales \u03c4GW considered\nare different by orders of magnitude.\nAs is clear from Tables I and III, the characteristics of\nthese target BHs are quite different. While the merger\nremnants are young, isolated BHs that are expected\nto emit short-duration, more rapidly evolving signals,\nCygnus X-1 is a binary system with a much older BH\nthat is expected to emit a long-duration, approximately\nmonochromatic signal. Hence, we use two different search\nmethods, each designed to exploit a different aspect of\nVBC signals: HMM is a flexible, less model-dependent\nmethod that is well-suited for signals with larger frequency\ndrifts and greater uncertainties (see Sec. III A), whereas\nthe Binary BSD-VBC search technique is designed for\nsignals with negligible frequency drifts from sources whose\norbital motion must be taken into account (see Sec. III B).\nIn the case of BHs from merger remnants with\nDL \u223cO(Gpc), we must take into consideration the\nnon-negligible impact of redshift on the GW emission\nfrequency and timescale. The frequency in the detector\nframe scales as fdet = fsrc(1 + z)\u22121, and correspondingly,\nthe frequency derivative scales as \u02d9fdet = \u02d9fsrc(1 + z)\u22122,\nwhere fsrc ( \u02d9fsrc) is the frequency (derivative) in the source\nframe, and fdet ( \u02d9fdet) is the frequency (derivative) in\nthe detector frame. In a similar vein, the GW emission\ntimescale is modified as \u03c4 det\nGW = \u03c4 src\nGW(1 + z). For an in-\ndepth discussion of how these redshift corrections affect\nthe searches, see Sec. IV in Ref. [79].\nIII.\nMETHODS\nIn this paper, we use two semicoherent search meth-\nods: the HMM tracking method (Sec. III A) and the\nBinary BSD-VBC method (Sec. III B). Although both\n\n16\nTable III. Estimated GW signal parameters for the remnant BHs from the GW230814 and GW231123 mergers and the BH in\nCygnus X-1 using the median BH parameters and their respective mopt\nV\nvalues.\nSource\nmopt\nV\n[10\u221213 eV]\n\u03c4growth\n\u03c4GW\nheff\n0\n[10\u221224]\nf0 [Hz]\n\u02d9f0 [Hz s\u22121]\nRemnant from GW230814\n3.805\n7.8 h\n28 h\n0.341\n170.4\n6.2 \u00d7 10\u22127\nRemnant from GW231123\n1.652\n2.3 h\n2.5 h\n1.69\n51.2\n9.4 \u00d7 10\u22126\nBH in Cygnus X-1\n1.040\n560 y\n7.5 \u00d7 106 y\n1.75\n50.3\n1.6 \u00d7 10\u221219\nmethods are based on previous work on traditional CW\nsearches targeting individual spinning neutron stars with\nnonaxisymmetries [65, 84, 111, 112], this section describes\nhow they have been tailored to searches for vector boson\nsignals.\nA.\nHMM method: Merger remnants\nThe HMM tracking technique is useful for detecting\nsignals with wandering frequencies. It models the fre-\nquency evolution probabilistically as a Markov chain of\ntransitions between discrete, unobservable (\u201chidden\u201d) fre-\nquency states over a number of discrete time steps, and it\nconnects these hidden states with observable data through\nan emission probability. HMM tracking has been used\nin various searches for continuous or long-transient GW\nsignals [49, 70, 111\u2013121]. This method is beneficial for\ntwo main reasons: i) it is computationally efficient, which\nis important for this study because vector boson signals\nlive in a large, multi-dimensional parameter space, and\nii) it is more capable of accounting for both the detec-\ntor noise fluctuations and any uncertainties that may be\npresent in the predicted signal waveform than other, more\nmodel-dependent CW semicoherent search techniques (see\nRef. [122]).\nReference [49] was the first to propose using an HMM-\nbased method for follow-up searches targeting slowly-\nevolving scalar boson clouds around BH merger remnants.\nSince vector bound states carry spin angular momentum,\nthey can still grow via superradiance even with zero orbital\nangular momentum number (\u2113= 0). As a result, vector\nbound states can be concentrated closer to the BH, leading\nto clouds that grow and deplete more rapidly and radiate\nat much higher power than scalar clouds [30, 36, 38\u201340].\nThis results in GW signals that are short-lived by CW\nstandards [\u223cO(days-months)] with frequency drift pa-\nrameters that are too large for the capabilities of the\nstandard HMM method. Thus, building upon the work\nof Isi et al. [49], Ref. [79] implemented a modified HMM\nsearch pipeline capable of tracking signals from VBCs\nthat occur over shorter timescales. The pipeline is an\nefficient semicoherent search method combining the HMM\ntracking scheme with a frequency-domain matched filter\n(F-statistic), which quantifies the likelihood that a sig-\nnal, parameterized by its frequency and associated time\nderivatives, is present in the data [123]. Previous stud-\nies have shown that this pipeline is sensitive enough to\npotentially detect signals from VBCs using data from\ncurrent-generation detectors [79].\nIn the following two subsections, we summarize the\nHMM search pipeline described in Ref. [79], as well as\nthe process of choosing search configurations for a given\nsystem, explained in Ref. [80]. Section III A 1 is meant to\ngive a high-level overview of the HMM algorithm; for a\nmore detailed explanation, see Refs. [111, 112].\n1.\nSearch pipeline\nThe search pipeline combines the HMM tracking tech-\nnique with an F-statistic, computed over discrete time\nsegments. The F-statistic takes as its input short Fourier\ntransforms (SFTs) of the relevant time series data col-\nlected by each GW detector [124].\nNote that for the\nsimulated data used in various places throughout the\nstudy, we create these SFTs by injecting synthetic signal\nwaveforms generated by the waveform model SuperRad\ninto Gaussian noise using the simulateCW Python module\nin the LALPulsar library of LALSuite [125, 126].\nFor this pipeline, we compute the F-statistic coherently\nover time segments of length Tcoh. These coherent seg-\nments are then incoherently combined using an HMM,\nwhich is solved via the Viterbi algorithm [127].\nThe\nViterbi algorithm efficiently finds the most probable path\nof the signal evolution (also known as the Viterbi path) in\nthe frequency-time plane with NQ frequency bins of width\n\u03b4f and NT time segments of length Tcoh (see detailed for-\nmulation and descriptions in, e.g., Refs. [111, 112]). The\nvalue Tcoh (and correspondingly \u03b4f) are bounded by the\npredicted signal\u2019s maximum frequency derivative \u02d9fmax\nsuch that i) the signal may be thought of as monochro-\nmatic across a single time segment and ii) the signal\ncan increase at most one frequency bin between each\ntime segment. The frequency bin width \u03b4f is fixed to\n1/(2Tcoh). Given that the maximum spin-up of the signal\nacross the full search duration Tobs = TcohNT must satisfy\n\u02d9fmaxTcoh \u2264\u03b4f, we have the following upper bound on\nTcoh:\nTcoh \u2264(2 \u02d9fmax)\u22121/2.\n(3)\nBecause increasing Tcoh generally improves the search\nsensitivity [111], in these searches we fix Tcoh to its largest\npossible value to maximize sensitivity for a given source\nmodel configuration (see Section III A 2). The frequency\ndrift is at its maximum when the VBC reaches saturation\n\n17\nat a time tsat. Thus, for a given system, we compute \u02d9fmax\nusing SuperRad and then set Tcoh = (2 \u02d9fmax)\u22121/2. This\nensures that the signal will not evolve outside HMM\u2019s\ntracking capabilities.\nThe Viterbi path returned by the search pipeline has\nan associated detection statistic that quantifies its sig-\nnificance. There are different ways to define the detec-\ntion statistic (see, for example, the Viterbi score in, e.g.,\nRef. [111], or the log likelihood of the optimal path, L, in,\ne.g., Ref. [128]). For the searches in this paper, we use\nL divided by the number of coherent segments NT [79],\nwritten as\n\u00afL \u2261L/NT .\n(4)\nThe main reason for this choice is because \u00afL is more\nreliable for shorter duration CW searches, as compared\nto, e.g., the Viterbi score, which only remains reliable for\nvery long duration searches where NQ \u226bNT .\n2.\nConfigurations\nGiven a target BH, we start by finding mopt\nV .\nWe\nthen define a range of vector masses the pipeline may\nbe sensitive to, mV \u2208[0.6, 1.1]mopt\nV ,5 given the BH we\nconsider, and we choose some number of evenly spaced mV\nvalues from within this range [80]. We must then choose\na set of search configurations to sufficiently cover this\nparameter space. As demonstrated in Ref. [80], because\nwe use the flexible HMM search technique, even a single\nset of search configuration parameters can recover signals\ngenerated by systems with a range of parameters. Still, we\nrequire more than one configuration to provide adequate\ncoverage of the full parameter space.\nThe process of\nchoosing these configurations is explained in detail in\nAppendix A of Ref. [80] and summarized here.\nWe first impose several limits on the allowed search con-\nfigurations to ensure computational feasibility: We require\nthe SFT length to lie within 15 sec \u2264TSFT \u226430 min\n(they need not be fixed to the standard TSFT = 30 min\nused in most CW searches) and the coherent length within\n1 min \u2264Tcoh \u226410 day. The ratio Tcoh/TSFT must be an\ninteger value of at least four; that is, each detector must\ncontribute a minimum of four SFTs per Tcoh segment.\nFinally, we set Tobs = \u03c4GW but require that it must not\nexceed 180 days to minimize the computational cost of\nthe search [79]. The search computing cost for a given\nsystem scales with the duration of the signal, ranging\nfrom approximately 10 min to 1 hr on a single-core com-\nputer. For each remnant BH for the full parameter space,\nthe search takes roughly O(102) core-hours. If no signal\n5 As shown in Ref. [79], these searches are in fact more sensitive to\nsome sub-optimal vector masses than the optimal mass because,\nfor a given BH, sub-optimal masses produce longer-lived GW\nemission, allowing us to extend the Tcoh used in the search.\nis detected, deriving the final sensitivity across the full\nparameter space via simulations (using the same configu-\nrations) typically takes O(104) core-hours per target.\nFollowing the guidelines outlined in Ref. [80], we ran-\ndomly draw 200 posterior samples from the remnant BH\u2019s\nmultidimensional posterior distribution. For each sample\nBH and each value of mV we consider in the search, we\nfind the optimal search configuration {tstart, Tcoh, Tobs},\nwhere tstart is the GPS start time of the search (corre-\nsponding to when the VBC has reached saturation). We\nthen independently draw 11 values from each of these\nthree distributions at the following percentiles: 2, 10, 20,\n30, 40, 50, 60, 70, 80, 90, and 98. This forms 11 search\nconfigurations with which we will run the search (see\nTables IV and V for the sets of configurations used in this\nwork). For most systems drawn from the remnant\u2019s pos-\nterior distribution, more than one of these configurations\nshould be able to recover the signal, making this spacing\na conservative choice.\nB.\nBinary BSD-VBC method: Cygnus X-1\nThe Binary BSD-VBC pipeline developed in this work\nbuilds on the BSD framework [84], which provides a\ncompact and flexible format to manipulate and ana-\nlyze calibrated strain data. Thanks to its modularity,\nthe BSD framework has been applied to various CW\nsearches\u2014both fully coherent [129, 130] and semicoher-\nent [62, 65, 75, 96, 114, 131, 132]\u2014including the all-sky\nsearch for scalar boson clouds using data from the LVK\u2019s\nthird observing run [62].\nThe Binary BSD-VBC method adapts and extends\nthese pipelines to target CW signals emitted by VBCs\naround BHs in known binary systems. The main case\nstudy is Cygnus X-1, whose orbital parameters are well\nconstrained by X-ray observations [85, 86, 95]. Details of\nthe specific implementation for this source are given in\nSec. IV B.\n1.\nSearch pipeline\nIn this search, data are analyzed in sub-bands of 1 Hz\noverlapped by 0.5 Hz using the BSD format. The files\ncontain a complex time series downsampled to 1 Hz and\ncovering the full O4a.\nThe search pipeline follows a two-step approach based\non standard BSD tools. The first step aims to increase\nthe signal coherence by coherently removing the Doppler\nmodulation caused by the combined motion of the source\nand the detector. This correction is performed, for a given\nset of parameters \u039b, using a heterodyne method [84].\nThe second step consists of a standard semicoherent\nsearch for the demodulated signal. A collection of sig-\nnificant peaks in the time-frequency plane, known as\nthe peakmap, is generated using the method detailed in\n\n18\nRef. [133]. Under proper demodulation, the signal ap-\npears in the peakmap as a line of constant frequency, with\nall its power contained in the same frequency bin of width\n\u03b4f0 = 1/Tcoh. To identify the signal, the peakmap is\nprojected onto the frequency axis to produce a histogram\nof peak counts per frequency bin.\nThe significance of the number of peaks in each fre-\nquency bin is evaluated by the robust Critical Ratio (CR)\nstatistic [97], defined in Appendix A 3. Outliers are then\nselected by uniformly dividing the 1 Hz band into 50\nsub-bands of 0.02 Hz and choosing the frequency bin with\nthe highest CR statistic within each sub-band.\n2.\nConfigurations\nWe adopt a signal model, described in Appendix\nA 1, where the frequency modulation is entirely de-\nfined\nby\na\nset\nof\nmodulation\nparameters\n\u039b\n=\n{f0, RA, Dec, ap, tasc, \u2126, e, \u03c9} where f0 is the emission\nfrequency, ap = a sin(\u03b9)/c with a the semi-major axis, \u03b9\nthe inclination angle, and c the speed of light, tasc is the\ntime of ascending node, \u2126is the orbital angular frequency\nrelated to the orbital period P as \u2126= 2\u03c0/P, e is the\norbital eccentricity, and \u03c9 is the argument of periapse.\nThe sampling of parameters \u039b must ensure adequate cov-\nerage of the parameter space to avoid significant loss in\nthe detection sensitivity. At the same time, the compu-\ntational cost of the analysis scales with the number of\ntemplates, which must therefore be kept to a minimum.\nThe number of templates needed to cover a parameter\nspace is discussed in Sec. A 4.\nThe dimensionality of the parameter space to be cov-\nered can be reduced based on the following considerations.\nWe substitute the unknown emission frequency with the\ncentral frequency of the 1 Hz analysis band. The search\ntargets a system whose sky position is known with high\nprecision; we therefore fix RA and Dec to their elec-\ntromagnetic estimates. For the orbital parameters, we\nfurther assume that the angular frequency \u2126, eccentricity\ne, and argument of periastron \u03c9 are well-constrained from\nelectromagnetic observations, allowing the use of single\ncentral values of \u2126, e, and \u03c9 for the heterodyne correction.\nWith these assumptions, the parameter space for a\ngiven target BH is reduced to a two-dimensional plane\n(ap, tasc). The time of ascending node tasc is bounded by\nthe orbital period as tasc \u2208[\u2212P/2, P/2], and we further\nimpose constraints on ap consistent with electromagnetic\nobservations of the source. The validity of these assump-\ntions must be checked for each potential target of the\nmethod. The case of Cygnus X-1 is discussed in Sec. IV B\nand has been verified through simulated signal injections\ninto simulated data that mimics the detectors\u2019 noise levels.\nTo cover the remaining parameter space, we use a\nrestricted version of the binary search metric described in\nRef. [134]. From this metric, and allowing for a maximal\nloss in signal-to-noise ratio of 10%, the resolutions in the\norbital parameters are given by\n\u03b4ap =\n\u221a\n0.6\n\u03c0\u2126Tcohf0\n\u03b4tasc =\n\u221a\n0.6\n\u03c0\u21262apTcohf0\n.\n(5)\nThese resolutions are used to construct a square lattice\nZ2, as described in Refs. [134, 135]. Details on the grid\nconstruction can be found in Appendix A 4.\nTypically, an analysis satisfying these limitations would\ntake < O(105) core-hours to cover the reduced parameter\nspace, such as the one of Cygnus X-1. In the absence\nof detection, constraints can be derived very efficiently\nusing the method outlined in Sec. VI B 1, and the compu-\ntation time needed to derive these constraints is negligible\ncompared to the analysis time.\n3.\nCandidate selection and coincidences\nFor every 1 Hz band, the search is repeated for all\ntemplates \u039b, each of them producing 50 triggers. On these\ntriggers, we select a subset of the most significant outliers.\nSpecifically, for each frequency bin of width \u03b4f0 = 1/Tcoh,\nwe select the two outliers with the highest CR values.\nIn this way, and for the coherence time Tcoh = 1000 s\nconsidered in this search, a maximum of 2000 outliers are\nselected for each 1 Hz band. This step reduces the number\nof outliers to a manageable level. Since the upper limits\npresented in Sec. VI B 1 are evaluated every 1 Hz based\non the loudest outlier, this selection does not impact the\nconstraints placed by this search.\nCandidates are then filtered, keeping only those with a\nCR above a threshold. Similar to Ref. [114], the threshold\nis chosen for each 1 Hz band as the mean CR plus two\nstandard deviations of the CR distribution of the out-\nliers. This distribution is built by excluding candidates\nassociated with known instrumental lines (see Sec. V B).\nWe then identify pairs of outliers coincident between the\nHanford and Livingston detectors. Outliers are consid-\nered coincidental if they are on the same or adjacent\nfrequency bins. Furthermore, coincident outliers must\nhave compatible orbital parameters, i.e.,\ndmetric =\ns\u0012\u2206ap\n\u03b4ap\n\u00132\n+\n\u0012\u2206tasc\n\u03b4tasc\n\u00132\n< 3,\n(6)\nwhere \u2206ap and \u2206tasc denote the differences between the\nparameters of the candidates in each detector.\nCoincident pairs of candidates, referenced hereafter as\nstage-2 candidates, are further analyzed in the follow-up\nprocedure presented in Sec. V B.\nIV.\nSEARCH SETUP\nIn this section, we provide details on the parameters and\nconfigurations used to run the HMM and BSD searches.\nWe use data taken by the two Advanced LIGO detec-\ntors, Hanford and Livingston [53], during O4a, which\n\n19\nran from 15:00 UTC on May 24, 2023 to 16:00 UTC\non January 16, 2024 [56, 136\u2013138]. The HMM searches\nanalyze data spanning two different time segments (cor-\nresponding to the weeks following both the GW230814\nand GW231123 binary merger events), whereas the BSD\nsearch uses the full O4a data, for which the duty factors\nare 67% and 69% for Hanford and Livingston, respec-\ntively. All the data used in this paper, acquired when the\ndetectors were in science observing mode, are online cali-\nbrated (i.e., low-latency C00 frames), and analysis-ready\n(channel names: H1:GDS-CALIB_STRAIN_CLEAN_AR and\nL1:GDS-CALIB_STRAIN_CLEAN_AR) [137, 139\u2013145]. Cali-\nbration uncertainties in the strain data can affect boson\nparameter estimates (if a signal is detected) and influ-\nence constraints or sensitivity estimates (if not). In O4a,\nthe 1-\u03c3 frequency- and time-dependent uncertainties are\n\u227210% in magnitude and \u227210 deg in phase and differ\nbetween LIGO sites [139]. However, their overall impact\nis subdominant to noise fluctuations. We therefore do not\nexplicitly include calibration uncertainties in our analysis.\nThe HMM searches take as input SFTs generated after\napplying a glitch gating procedure [146]. The BSD are\ngenerated from the Short FFT Database (SFDB) [133],\nand cleaned using the double-gating procedure described\nin Refs. [84, 147].\nA.\nHMM searches: Merger remnants\n1.\nGW230814\nRecalling Sec. II C and Table III, for the remnant\nBH from GW230814, we find mopt\nV\n= 3.805 \u00d7 10\u221213 eV.\nThus, the interesting vector mass range [0.6, 1.1] mopt\nV\n(see\nSec. III A 2) becomes [2.283, 4.185] \u00d7 10\u221213 eV for this\nsearch. Each boson mass within this range, if it exists,\nwould emit GWs at a different frequency, so we have\na corresponding frequency range of [97, 196] Hz across\nwhich we run the search, divided into 1 Hz sub-bands.\nWhen choosing which sky position(s) to target, it may\nseem reasonable to simply target the median RA and\nDec listed in the table. However, because the estimated\nposterior distribution of the RA for this system is bimodal,\nthe median is not representative of the data (see top panel\nof Fig. 1).6 Instead, we choose the optimal sky positions\nempirically by drawing a joint random sample of 100\nRA and Dec values from the BH posterior distribution,\ninjecting them into Gaussian noise, and attempting to\nrecover them using a grid of sky positions. The spacing\nof this grid reflects the size of the effective point spread\nfunction (EPSF) shown in Fig. 2, in which a signal has\nbeen injected at RA, Dec = [3.854, 0.370] rad and then\n6 GW230814 was observed only by the Livingston detector, so\nthe remnant\u2019s poorly constrained sky location aligns with the\ndetector\u2019s antenna pattern.\nFigure 1. Joint RA and Dec posterior distribution for the\nmerger remnants from GW230814 (top) and GW231123 (bot-\ntom).\nThe black contours show the 90%, 50%, and 10%\nconfidence intervals. The red crosses indicate the sky positions\ntargeted in the search for each remnant.\nrecovered using a grid of sky positions offset from this\nsky position. Overall, the sky positions that recover the\nlargest number of randomly sampled injections are RA,\nDec = [1.088, -0.387], [1.388, -0.387], [3.254, 0.370], and\n[3.554, 0.370] rad. We target all four sky positions in\nthe search to obtain better coverage over the whole sky.7\nThey are marked with red crosses in the top panel of\nFig. 1. The search is not particularly sensitive to sky\nlocalization for short-duration signals with \u03c4GW \u22721 day,\n7 It is particularly valuable to target multiple sky positions (when\nthe true sky position is not well constrained) for the configurations\nthat use longer Tcoh values. This is because searches with longer\ncoherent segments are more sensitive to Doppler modulation\neffects and thus the assumed sky position, so there is a larger\nchance of missing a GW signal if an incorrect sky position is used.\n\n20\nalthough the low sky resolution does lead to degraded\nsensitivity [79]. For longer signals with \u03c4GW \u22731 day,\nhowever, a mismatch in sky position can still cause a\nmarginal signal to be missed. This uncertainty due to\npoorly-constrained sky localization is incorporated into\nthe sensitivity estimates we present in Sec. VI A.\n\u03c0\n7\u03c0/6\n4\u03c0/3\n3\u03c0/2\nRA [rad]\n\u2212\u03c0/6\n0\n\u03c0/6\n\u03c0/3\nDec [rad]\n1.0\n0.96\n0.98\n1.00\n1.02\n1.04\n\u00afL/ \u00afLth\nFigure 2. Colored contour of \u00afL/ \u00afLth as a function of RA and\nDec for a synthetic signal injected at [3.854, 0.370] rad, shown\nwith a white cross marker. The signal was generated using the\nmedian BH remnant parameters from the GW230814 merger\nshown in Table I and using mV = 2.283\u00d710\u221213 eV. The bright\nEPSF enclosed within the white contour signifies the region\nof the sky with \u00afL > \u00afLth where the signal has been recovered.\nUsing the method outlined in Appendix A of Ref. [80]\nfor choosing search configurations, we use 11 different\nconfigurations in the search, shown in Table IV. In partic-\nular, we choose a set of Tcoh values to cover the full\nrange of\n\u02d9fmax values that may occur for the system:\n\u223cO[10\u22129, 10\u22126] Hz s\u22121.\nAcross all 11 configurations,\nwe run the search on detector data spanning the GPS\ntimes [1376111180, 1385937626] s. Gaps are present in the\navailable data from Hanford and Livingston during this\ntime period, resulting from both scheduled maintenance\nand unexpected lock loss due to various environmental\ndisturbances.\nIn particular, although the duty factor\nis \u223c70% for each detector during the analysis time of\nGW230814, many of the data gaps lie within roughly\ntwo days post-merger, when the signal is expected to be\nstrongest. While the HMM search pipeline is designed to\naccommodate data gaps, the less data that is available,\nthe less sensitive the search becomes. This decreased\nsensitivity is reflected in the eventual estimated vector\nmass range that is disfavored by targeting this remnant\n(see Sec. VI A).\n2.\nGW231123\nAs in the previous section, we refer to Table III for the\noptimal boson mass corresponding to the remnant BH\nTable IV. Search configuration parameters and the percentiles\nat which they are drawn for the BH remnant from the\nGW230814 merger. These percentiles are chosen so that the\nconfigurations used in the search adequately cover the rem-\nnant\u2019s full posterior distribution.\nPercentile TSFT [m] Tcoh [m] Tobs [m] GPS start time [s]\n2\n2.85\n11.4\n991.8\n1376111180\n10\n3.4\n13.6\n1278.4\n1376115080\n20\n3.9\n15.6\n1653.6\n1376119160\n30\n4.55\n18.2\n2311.4\n1376124380\n40\n5.75\n23.0\n3519.0\n1376134280\n50\n7.45\n29.8\n5632.2\n1376148320\n60\n10.45\n41.8\n9823.0\n1376172680\n70\n15.05\n60.2\n17759.0\n1376211140\n80\n24.4\n97.6\n36990.4\n1376285360\n90\n26.85\n161.1\n79583.4\n1376412320\n98\n27.65\n248.85\n155780.1\n1376590820\nfrom GW231123: mopt\nV\n= 1.652 \u00d7 10\u221213 eV. Thus, for\nthe search we consider the range mV = [0.901, 1.502] \u00d7\n10\u221213 eV and the corresponding frequency band [21,\n73] Hz, split into 1 Hz sub-bands.\nOnce again, the RA posterior distribution shows some\nbimodality, but because the sky position is significantly\nmore well-constrained than GW230814 [i.e., the 90% con-\nfidence interval is constrained to O(103) deg2], for the\nsearch we simply target the two local maxima marked by\nred crosses in the bottom panel of Fig. 1, located at RA,\nDec = [3.329, 0.372] and [5.153, 0.318] rad. These two\nlocal maxima are tested using the same method described\nabove for GW230814, and we find that they provide suffi-\ncient coverage across the 90% credible region of the sky\nposition.\nWe start by identifying 11 potential search configura-\ntions at the same percentiles used for GW230814. How-\never, two configurations cannot be used in the search,\nas their GPS start times (1602835969 and 2785340449\nfor the 90th and 98th percentiles, respectively) do not\nfall within the fourth observing run (O4).8\nThus, we\nlimit the number of configurations used in the search\nto only the first 9, shown in Table V. Again, we choose\nthe set of Tcoh values to cover the potential \u02d9fmax range\n\u223cO[10\u221215, 10\u22125] Hz s\u22121 for this system. Gaps are again\npresent in the data available from both detectors, limiting\nthe search sensitivity; while the duty factor for Hanford\nis 68% across the relevant time frame, for Livingston it is\nonly 51%.\n8 These times correspond to a non-optimal region of the parameter\nspace where the VBC grows and dissipates very slowly and thus\nit will be O(years) before the GW emission reaches its peak.\n\n21\nTable V. Search configuration parameters and the percentiles at\nwhich they are drawn for the BH remnant from the GW231123\nmerger. These percentiles are chosen so that the configurations\nused in the search adequately cover the remnant\u2019s full posterior\ndistribution.\nPercentile TSFT [m] Tcoh [m] Tobs [m] GPS start time [s]\n2\n0.6\n2.4\n84.0\n1384788409\n10\n1.0\n4.0\n172.0\n1384792009\n20\n1.45\n5.8\n301.6\n1384796449\n30\n2.25\n9.0\n630.0\n1384804309\n40\n3.55\n14.2\n1235.4\n1384816729\n50\n6.0\n24.0\n2424.0\n1384837489\n60\n9.4\n37.6\n4587.2\n1384866949\n70\n14.35\n57.4\n9011.8\n1384911769\n80\n26.2\n157.2\n42601.2\n1385145169\nB.\nBSD search: Cygnus X-1\nUsing the median values for the parameters of Cygnus\nX-1 reported in Table I, we find the boson mass mopt\nV\n=\n1.040 \u00d7 10\u221213 eV produces the signal with the maximum\nstrain amplitude at the start of O4a. Taking into ac-\ncount the uncertainties in the BH parameters, we esti-\nmate the signal amplitudes corresponding to boson masses\naround mopt\nV\nusing the SuperRad model. Then, compar-\ning these values to the minimum detectable strain given\nin Eq. (67) of Ref. [97], we select the frequency band\nf0 \u2208[24.5, 125.5] Hz as the range of frequencies where a\nsignal could be detected. Therefore, the search spans 202\ndistinct 1 Hz bands, overlapped by 50%.\nWe fix the coherence time to Tcoh = 1000 s for all fre-\nquency bands investigated. This value is motivated by\nmultiple factors. Demodulating the data using the central\nfrequency of the band rather than the real\u2014unknown\u2014\nfrequency of the signal leads to a residual modulation of\nthe signal. Our choice of Tcoh ensures that, for any signal\npresent in the band, the residual modulation \u2206f is smaller\nthan the size of a frequency bin, i.e. 2\u2206f < 1/Tcoh. Sim-\nilarly, this coherence time ensures that the uncertainties\nin the eccentricity parameters of Cygnus X-1\u2019s orbit, re-\nported in Table II, are fully covered by a template using\nthe central values of the parameters. At the same time, a\ncoherence time Tcoh = 1000 s keeps the analysis time to\na realistic level with O(60 000) core-hours being needed\nto analyze the parameter space of Cygnus X-1 in both\nLIGO detectors.\nFollowing the grid construction method presented in\nSec. III B 2, for each band we define a set of parameter\npoints {\u039bi}N\ni=1 covering the uncertainties in the orbital\nparameters of Cygnus X-1 reported in Table II. The time\nof superior conjunction T0 of Cygnus X-1 has been esti-\nmated in Ref. [95], but the extrapolation of this value\nto estimate the time of ascending node tasc at the O4a\nperiod leads to significant uncertainties compared to our\nsearch resolution. We choose an agnostic approach where\nthe range of all possible values tasc \u2208[\u2212P/2, P/2] has\nbeen covered by the search. The number of templates per\nband ranges from N = 1 960 at 24.5 Hz to N = 43 416\nat 125.5 Hz, in agreement with Eq. (A12). Combining\nthe number of templates used in all the bands, the search\nuses 3 687 225 templates.\nThe search is performed with bands overlapped by\n0.5 Hz to avoid cropping signals close to the band edges\nduring BSD creation. Each band is searched indepen-\ndently, and each produces its own set of outliers, among\nwhich outliers and stage-2 candidates are selected follow-\ning the discussion in Sec. III B 3.\nV.\nCANDIDATE FOLLOW-UP\nIn this section, we outline the follow-up procedures\nused to eliminate any search candidates whose origins\nare not astrophysical. See Tables VI and VII for the\nnumbers of candidates that remain from the HMM and\nBSD searches after each veto procedure described in the\nfollowing sections.\nA.\nHMM searches: Merger remnants\nFor GW230814, we run the search over 99 individual 1\nHz bands, 11 search configurations, and 4 sky positions.\nThis is 4356 iterations in total. Similarly, for GW231123,\nwe have 52 1 Hz bands, 9 search configurations, and 2\nsky positions, yielding 936 search iterations. For each 1\nHz band, we require the detection statistic \u00afL to exceed a\nthreshold \u00afLth corresponding to a 1% false alarm proba-\nbility (Pfa).9 The value of \u00afLth, which varies for each Tcoh\nused in the searches, is obtained empirically as follows:\nFor a given value of Tcoh, we run 300 searches in pure\nGaussian noise (with Amplitude Spectral Density (ASD)\n= 4\u00d710\u221224 Hz\u22121/2) at a randomly chosen 1 Hz frequency\nband, and we define \u00afLth as the value of \u00afL that lies at the\n99th percentile of these results.\nAfter implementing this initial threshold cut, we have\n421 and 285 signal candidates across all configurations for\nGW230814 and GW231123, respectively. However, many\ncandidates actually appear to be the same candidates\npicked up by different configurations (e.g., for GW230814,\na candidate at \u223c102.1 Hz is identified for nearly every\nvalue of Tcoh and at every sky position). We expect a large\nfraction of these first-pass candidates to be simply the\nresult of noise artifacts (e.g., power line harmonics, ther-\nmally excited mirror suspension violin modes [137, 148])\nand non-Gaussianities in the interferometric data. We use\nthe known-line [149] and single-interferometer veto tech-\nniques described in Appendix B 1 (which are commonly\n9 The 1% false alarm probability corresponds to each configuration\nin each 1 Hz band.\n\n22\nused in CW searches) to help distinguish candidates of\nthis nature from a true astrophysical signal [128]. We\nmanually inspect any candidates that survive these initial\nvetoes by assessing their consistency with the signal model,\nscrutinizing the spectrograms, identifying clear character-\nistics of noise (such as a candidate occurring in only one\ndetector due to short-period artifacts and failing to meet\nthe stringent criteria of the single-interferometer veto),\netc. For a detailed description, see Appendix B 1. Ta-\nble VI shows the candidates that remain for each merger\nremnant after each veto. After manual inspection, no\nsignal candidates remain.\nTable VI. Number of candidates remaining from the search\ntargeting the remnants from the GW230814 and GW231123\nmergers after each veto has been applied.\nRemaining candidates\nStage\nGW230814\nGW231123\nInitial candidates\n421\n285\nKnown-line veto\n44\n209\nSingle-interferometer veto\n19\n101\nManual inspection\n0\n0\nB.\nBSD search: Cygnus X-1\nFrom the BSD-based search, we identify 27 stage-2\ncandidates that pass the selection process described in\nSec. III B 3. We follow up these candidates using the\nvetoing procedure described in Appendix B 2. The list of\ncandidates is first filtered by removing outliers associated\nwith known instrumental lines [149], reducing the list to\neight candidates. During the creation of outlier pairs (see\nSec. III B 3), the same outlier could be matched to multiple\ncoincident outliers in the other detector. To remove this\nredundancy, we cluster all pairs sharing a common outlier,\nwhich reduces the number of independent candidates to\nsix. We then apply standard vetoes adapted from previous\nBSD-based searches (e.g., [65, 114]), which are based on\nthe consistency of the candidates with the parameters\nof Cygnus X-1 and with the expected behavior of the\ndetection statistic. Three candidates pass these vetoes\nand are further inspected. All three are consistent with\nartifacts produced by non-Gaussianities in the detector.\nMore details on the follow-up procedure are given in\nAppendix B 2.\nTable VII summarizes the number of\ncandidates remaining after each veto.\nVI.\nCONSTRAINTS\nIn this section, we estimate the vector boson mass range\nthat can be constrained given the absence of a confident\ndetection in the searches described above.\nTable VII. Number of candidates remaining from the Cygnus\nX-1 search after each veto has been applied.\nRemaining candidates\nStage\nCygnus X-1\nInitial candidates\n27\nKnown-line veto\n8\nClustering\n6\nAstrophysical consistency veto\n5\nStatistical consistency check\n3\nManual inspection\n0\nA.\nHMM searches: Merger remnants\nAfter applying the veto procedures described in\nSec. V A, all candidates from the HMM searches are\neliminated. In this section, we investigate the confidence\nwith which we disfavor the existence of a given vector\nboson mass range. We adopt an empirical approach in\nwhich synthetic signals are injected into simulated Gaus-\nsian noise configured to match the real data, with ASDs\nderived from detector data at the corresponding times\nand frequencies, and with data gaps reproduced to reflect\nthose present during the analysis period. We marginalize\nthe detection probabilities over the BH parameter un-\ncertainties to reduce potential biases in the sensitivity\nestimates. We make a common assumption when inter-\npreting the search results: the vector field interacts only\ngravitationally, with no additional interactions or cou-\nplings to the Standard Model. See Sec. IV of Ref. [80] for\ndetails on how this assumption can be partially lifted.\nIn Ref. [80], a framework is developed for constraining\nthe boson mass that marginalizes over the parameter\nuncertainties typical to a binary merger remnant detected\ngravitationally. We start by drawing a number NBH of\nrandom samples from the BH posterior distribution with\nparameters \u03b8i. Then, for a given boson mass, we generate\na synthetic GW signal for each sample BH and inject the\nsignal into a number Nnoise of random Gaussian noise\nsimulations.\nWe evaluate the recovery rate across all\nsampled systems and noise realizations as shown:\nPdet(mV ) =\n1\nNBHNnoise\nNBH\nX\ni=1\nNdet(\u03b8i; mV ),\n(7)\nwhere Ndet(\u03b8i; mV ) is the number of recovered ( \u00afL >\n\u00afLth) signals out of Nnoise noise realizations for a given\nvector mass mV and set of BH parameters \u03b8i. This value\nPdet(mV ) can be interpreted as the confidence to which\nthe existence of the vector boson with mass mV can be\nexcluded given that no signal is detected in the searches.\nIn Fig. 3 we show the confidence with which we disfavor\nthe vector mass using this procedure for GW230814 (left\npanel) and GW231123 (right panel), where, following the\nguidelines in Ref. [80], we have used NBH = 200 and\n\n23\nNnoise = 10. We run the simulations across all config-\nurations used in the real searches (i.e., {RA, Dec} and\n{TSFT, Tcoh, Tobs, and search start time}). The synthetic\nsignal is considered recovered if at least one configuration\nreturns an above-threshold detection statistic. The or-\nange, blue, and purple lines in the figure indicate a 1%,\n5%, and 10% Pfa threshold, respectively. Pdet indicates\nthe confidence with which one can disfavor a vector mass\nrange given the null search results (i.e., if some range of\ndata points lie above a given Pdet value, that mass range is\ndisfavored with Pdet confidence). While the searches tar-\ngeting the remnant from GW230814 and GW231123 are\nnot sensitive enough to constrain the vector mass at high\nconfidence, the following is an example of how we would\nestimate the boson mass range that can be constrained:\nWe disfavor the vector mass ranges [2.75, 3.28] \u00d7 10\u221213\nand [0.94, 1.08]\u00d710\u221213 eV for GW230814 and GW231123,\nrespectively, with 30% confidence for Pfa = 1%.\nThese results show that we are approaching the sensi-\ntivity required to place robust constraints on the vector\nboson mass. As the detectors continue to undergo im-\nprovements in subsequent observing runs, we anticipate a\ngrowing number of high-SNR events, which will enable\nincreasingly sensitive searches and stronger constraints\nacross a wide range of the mass parameter space. In\naddition, once the vector mass can be constrained with\nhigher confidence, the results can be mapped to other\ninteraction models [80].\nB.\nBSD search: Cygnus X-1\nAmong the 27 stage-2 candidates obtained from the\nBSD search, none pass the follow-up procedure. In the\nabsence of a plausible signal candidate, we set upper\nlimits on the strain amplitude of CWs emitted by a VBC\nsurrounding Cygnus X-1. In the following subsections,\nwe outline the procedure used to estimate these upper\nlimits and describe how they are subsequently translated\ninto constraints on the mass of a hypothetical ultralight\nvector boson.\n1.\nUpper limits and Sensitivity\nIn this section, we estimate upper limits on the strain\namplitude h0, defined as the maximum amplitude above\nwhich the presence of a CW signal can be excluded at a\ngiven confidence level. The limits are computed using a\nconservative semi-analytical method previously applied in\nRefs. [62, 65, 96]. The method evaluates the upper limits\nin each 1 Hz frequency band using the analytical relation\n[62, 65, 96]\nh95%\nUL \u2248\nB\nN 1/4\ns\nSn(f)\nTcoh\np\nCRmax + 1.645,\n(8)\nwhere N \u223cTobs/Tcoh is the number of segments used\nto construct the peakmap, the value 1.645 is computed\nfrom Eq.(67) in Ref. [97] fixing the confidence level to\n95%, S1/2\nn\n(f) is the detector average ASD, and CRmax\nis the maximum CR value observed in the band. The\ncoefficient B accounts for the average detector response\nto the source sky position and signal polarization and\ndepends on the peak selection threshold. For this search\nand the sky position of Cygnus X-1, we evaluate B \u22483.37\nin Livingston and B \u22483.30 in Hanford. The computation\nof these factors is detailed in Appendix A 5 following the\ndiscussions in Refs. [65, 97] . The final upper limit placed\nin each band is taken as the less constraining limits of the\ntwo detectors.\nWe have verified that this semi-analytical approach\nyields conservative upper limits compared to those ob-\ntained with a classical frequentist approach based on\nsimulated signal injections, while requiring fewer compu-\ntational resources. This verification was performed on ten\n1 Hz frequency bands, randomly selected within the search\nfrequency range, using simulated data that reproduces\nthe detectors\u2019 noise levels. The validation complements\nprevious checks carried out for other observing runs of\nthe LIGO and Virgo detectors and for similar BSD-based\nmethods [65, 151].\nIn Fig. 4, we show the joint upper limits at a 95%\nconfidence level, reporting in each frequency band the\nworst-case estimate between the two detectors. We also\nreport the boson masses corresponding to the frequency\naxis, assuming the central astrophysical parameters of\nCygnus X-1 reported in Table I.\nWe quantify the performance of the search using the\nsensitivity depth [152], defined as\nD95% =\np\nSn(f)\nh95%\nUL\n.\n(9)\nThis quantity has become a key figure for assessing the\nperformance of a CW search configuration, independent\nof the noise level [96, 153\u2013155]. For the BSD search, we\nreport a sensitivity depth of 37.22 Hz\u22121/2 in the band\ncentered on 50.5 Hz corresponding to the optimal boson\nmass for Cygnus X-1 (see Table III). The average depth\nover all the analyzed bands is 35.15 Hz\u22121/2 and is more\nor less constant in all the bands, excluding the one with\nsignificant noise disturbances.\n2.\nConstraints\nThe upper limits obtained in the previous section can be\nused to constrain the existence of ultralight vector bosons\nby comparing them to the expected strain amplitude of a\nsignal emitted by a VBC in Cygnus X-1. The amplitude\nis estimated assuming the central value, the 5th, and the\n95th percentiles of the BH mass posterior distribution\nreported in Ref. [85]. We also consider the uncertainties\nin the BH age and distance and assume the BH spin\n\n24\n2.5\n3.0\n3.5\n4.0\nmV [eV]\n\u00d710\u221213\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nPdet\n1.0\n1.2\n1.4\n1.6\nmV [eV]\n\u00d710\u221213\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n100\n125\n150\n175\nf0 [Hz]\n30\n38\n46\n54\nf0 [Hz]\nmopt\nV\n1% Pfa\n5% Pfa\n10% Pfa\nFigure 3. The detection probability Pdet as a function of mV (bottom axis) and the corresponding GW frequency f0 in the\ndetector frame (top axis) with a 1% (orange), 5% (blue), and 10% (purple) false alarm probability for the remnant BHs from\nthe GW230814 (left) and GW231123 (right) mergers. A redshift correction has been applied to obtain f0 in the detector frame\nusing the median DL value for each remnant (as reported in Table I). The vertical dashed lines mark the optimal boson masses\nmopt\nV\nfor the remnants with median parameters also shown in Table I. The error bars represent the 1\u03c3 beta-binomial uncertainty\nin Pdet [150].\n40\n60\n80\n100\n120\nf0 [Hz]\n10\u221225\n10\u221224\nStrain [-]\n1.0\n1.5\n2.0\n2.5\nmV [eV]\n\u00d710\u221213\n95% CL UL\nmopt\nV\nBH mass [M\u2299]\n18.9\n21.2\n23.4\nFigure 4. Upper limit estimates at a 95% confidence level\n(black curve) as a function of frequency (top axis) and the\ncorresponding boson mass assuming the central values for\nthe mass and age of Cygnus X-1 (bottom axis). The hashed\nregions correspond to the predicted strain amplitude from\na VBC around Cygnus X-1, assuming the central value (or-\nange, circles), 5th percentile (blue, horizontal lines), and 95th\npercentile (purple, vertical lines) of the BH mass posterior\ndistribution from [85]. We assume the BH initial spin to be\n\u03c7i = 0.95 and the hashed regions account for uncertainties in\nthe BH age and distance.\nbefore the superradiant instability to be \u03c7i = 0.95. The\namplitude is then evaluated at different boson masses (i.e.,\nat different frequencies) using the SuperRad model [52, 92].\nThe simulated strain amplitudes are shown in Fig. 4, along\nwith the upper limits derived in the previous section.\nBy comparing the upper limits with the expected strain\namplitude, we can exclude the presence of a signal emitted\nby a VBC in Cygnus X-1 in every frequency band in the\nrange 41.25\u201380 Hz, with the exception of the narrow band\n69.75\u201370.25 Hz. The absence of a signal in these bands\nexcludes the existence of an ultralight vector boson with\na mass in the range [0.85, 1.65] \u00d7 10\u221213 eV (excluding the\nband [1.44, 1.45] \u00d7 10\u221213 eV).\nThese exclusion regions are obtained under the assump-\ntion that the initial spin of the BH was \u03c7i = 0.95. This\nassumption can be relaxed by computing the exclusion re-\ngion for different initial spin values. As the assumed initial\nspin decreases, the expected amplitude decreases accord-\ningly. Nevertheless, based on SuperRad simulations, for\nany value \u03c7i > 0.5, our upper limits can constrain the exis-\ntence of a signal between 41.25 and 77.25 Hz, correspond-\ning to boson masses within the range [0.85, 1.59]\u00d710\u221213 eV\n(with the same excluded band as before). For spin values\n\u03c7i < 0.5, the lower expected amplitude narrows down the\nconstrained frequency range. At \u03c7i = 0.2, we are still able\nto constrain frequencies in the range 50.25\u201377.25 Hz and\nboson masses [1.03, 1.59]\u00d710\u221213 eV. For lower initial spin\nvalues, the expected amplitude decreases rapidly, quickly\nleaving the existence of an ultralight vector boson uncon-\nstrained by our search. All of these exclusion intervals\nare computed at a 95% confidence and using the least\nconstraining values for the BH age, distance, and mass.\n\n25\nVII.\nCONCLUSION\nIn this paper, we carry out the first directed searches\nfor long-duration, quasi-monochromatic GWs from VBCs\naround known BHs. We analyze data from the first part\nof the LVK\u2019s fourth observing run, and we use two semi-\ncoherent CW search methods, HMM tracking and the\nBinary BSD-VBC pipeline. Having found no evidence of\na GW signal, we estimate the range of ultralight vector\nboson masses that can be constrained. From the HMM\nsearch, we disfavor the vector mass ranges [0.94, 1.08]\nand [2.75, 3.28] \u00d7 10\u221213 eV at 30% confidence (Pfa = 1%).\nWhile the present search sensitivity is limited because we\ntarget remnant BHs with SNR values \u227240\u2014and thus the\nconfidence level remains statistically insignificant\u2014future\nsearches targeting higher SNR events are expected to yield\nhigh-confidence constraints. Meanwhile, the BSD-based\nsearch excludes the mass range [0.85, 1.59] \u00d7 10\u221213 eV at\n95% confidence, assuming an initial spin value \u03c7i > 0.5\nfor Cygnus X-1.\nAs the BSD search demonstrates, we are now able to set\nconstraints on the existence of ultralight vector bosons by\ntargeting known galactic BHs. Although the constraints\nobtained from Cygnus X-1 cover only a narrow range\nof masses, future improvements in detector sensitivity\nwill enhance these constraints. The boson mass ranges\nthat can be constrained also highly depend upon the BH\nparameters. Therefore, running similar searches targeting\nother known galactic BHs could extend the exclusion\nregion.\nThe first HMM search targeting binary merger rem-\nnants demonstrates that we are approaching the required\nsensitivity to place high-confidence constraints on a range\nof vector masses. Targeting young merger remnants allows\nus to set independent constraints with minimal assump-\ntions about the BH\u2019s history and evolution since formation.\nSeveral contributing factors will improve the sensitivity of\nthis type of search: in particular, both increased detector\nsensitivity and improved search methodologies. Future ob-\nserving runs and next-generation GW detectors will offer\nenhanced sensitivity, enabling the detection of numerous\nbinary mergers in the high-SNR regime [57\u201359, 83]. These\nhigh-SNR events will yield remnant BHs with masses and\nspins that are more accurately and precisely measured.\nFor HMM-based searches, improved posteriors on these\nparameters will directly translate into tighter constraints\non the vector boson mass. In addition, future searches\ncan incorporate modifications to the analysis pipelines\nto further improve search sensitivity (e.g., extending the\nHMM-based analysis in suitable cases to track time deriva-\ntives of the signal frequency within the F-statistic, as\ndemonstrated in Ref. [121]).\nObservational studies have indirectly constrained the\nexistence of ultralight vector bosons either from BH spin\nmeasurements [30, 32], by reinterpreting the results of GW\nsearches [64], or from searches for a stochastic GW back-\nground [69]. A recent analysis using the GW231123 and\nGW190517 constituent BHs disfavors a vector mass range\nof [0.11, 18] \u00d7 10\u221213 eV assuming a BH age of 105 yrs [61].\nIn other searches, the interaction of ultralight vectors\nwith ground-based GW detectors has been directly con-\nstrained [75, 76]. While each approach involves its own\nassumptions and limitations, the results presented in this\npaper provide independent constraints obtained from di-\nrected searches that, consistent with previous studies,\ndisfavor the existence of vector bosons with masses of\n\u223c1 \u00d7 10\u221213 eV.\nVIII.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory, which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United King-\ndom, the Max-Planck-Society (MPS), and the State of\nNiedersachsen/Germany for support of the construction\nof Advanced LIGO and construction and operation of\nthe GEO 600 detector. Additional support for Advanced\nLIGO was provided by the Australian Research Council.\nThe authors gratefully acknowledge the Italian Istituto\nNazionale di Fisica Nucleare (INFN), the French Centre\nNational de la Recherche Scientifique (CNRS) and the\nNetherlands Organization for Scientific Research (NWO)\nfor the construction and operation of the Virgo detector\nand the creation and support of the EGO consortium.\nThe authors also gratefully acknowledge research support\nfrom these agencies as well as by the Council of Scientific\nand Industrial Research of India, the Department of Sci-\nence and Technology, India, the Science & Engineering\nResearch Board (SERB), India, the Ministry of Human\nResource Development, India, the Spanish Agencia Es-\ntatal de Investigaci\u00f3n (AEI), the Spanish Ministerio de\nCiencia, Innovaci\u00f3n y Universidades, the European Union\nNextGenerationEU/PRTR (PRTR-C17.I1), the ICSC -\nCentroNazionale di Ricerca in High Performance Com-\nputing, Big Data and Quantum Computing, funded by\nthe European Union NextGenerationEU, the Comuni-\ntat Auton\u00f2ma de les Illes Balears through the Direcci\u00f3\nGeneral de Recerca, Innovaci\u00f3 i Transformaci\u00f3 Digital\nwith funds from the Tourist Stay Tax Law ITS 2017-\n006, the Conselleria d\u2019Economia, Hisenda i Innovaci\u00f3, the\nFEDER Operational Program 2021-2027 of the Balearic\nIslands, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia\ni Societat Digital de la Generalitat Valenciana and the\nCERCA Programme Generalitat de Catalunya, Spain,\nthe Polish National Agency for Academic Exchange, the\nNational Science Centre of Poland and the European\nUnion \u201c European Regional Development Fund; the Foun-\ndation for Polish Science (FNP), the Polish Ministry of\nScience and Higher Education, the Swiss National Science\nFoundation (SNSF), the Russian Science Foundation, the\nEuropean Commission, the European Social Funds (ESF),\nthe European Regional Development Funds (ERDF), the\nRoyal Society, the Scottish Funding Council, the Scottish\n\n26\nUniversities Physics Alliance, the Hungarian Scientific\nResearch Fund (OTKA), the French Lyon Institute of\nOrigins (LIO), the Belgian Fonds de la Recherche Scien-\ntifique (FRS-FNRS), Actions de Recherche Concert\u00e9es\n(ARC) and Fonds Wetenschappelijk Onderzoek Vlaan-\nderen (FWO), the supercomputing facilities of the Uni-\nversit\u00e9 catholique de Louvain (CISM/UCL) and the Con-\nsortium des \u00c9quipements de Calcul Intensif en F\u00e9d\u00e9ration\nWallonie Bruxelles (C\u00c9CI), Belgium, the Paris \u00cele-de-\nFrance Region, the National Research, Development and\nInnovation Office of Hungary (NKFIH), the National Re-\nsearch Foundation of Korea, the Natural Science and\nEngineering Research Council of Canada (NSERC), the\nCanadian Foundation for Innovation (CFI), the Brazilian\nMinistry of Science, Technology, and Innovations, the\nInternational Center for Theoretical Physics South Amer-\nican Institute for Fundamental Research (ICTP-SAIFR),\nthe Research Grants Council of Hong Kong, the National\nNatural Science Foundation of China (NSFC), the Israel\nScience Foundation (ISF), the US-Israel Binational Sci-\nence Fund (BSF), the Leverhulme Trust, the Research\nCorporation, the National Science and Technology Coun-\ncil (NSTC), Taiwan, the United States Department of\nEnergy, and the Kavli Foundation. The authors gratefully\nacknowledge the support of the NSF, STFC, INFN and\nCNRS for provision of computational resources.\nThis work was supported by MEXT, the JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-in-Aid for Scientific Research on Innovative Areas\n2905: JP17H06358, JP17H06361 and JP17H06364, JSPS\nCore-to-Core Program A, Advanced Research Networks,\nJSPS Grants-in-Aid for Scientific Research (S) 17H06133\nand 20H05639, JSPS Grant-in-Aid for Transformative\nResearch Areas (A) 20A203: JP20H05854, the joint re-\nsearch program of the Institute for Cosmic Ray Research,\nthe University of Tokyo, the National Research Foun-\ndation (NRF), the Computing Infrastructure Project of\nGlobal Science experimental Data hub Center (GSDC) at\nKISTI, the Korea Astronomy and Space Science Institute\n(KASI), the Ministry of Science and ICT (MSIT) in Korea,\nAcademia Sinica (AS), the AS Grid Center (ASGC) and\nthe National Science and Technology Council (NSTC) in\nTaiwan under grants including the Rising Star Program\nand Science Vanguard Research Program, the Advanced\nTechnology Center (ATC) of NAOJ, and the Mechanical\nEngineering Center of KEK.\nAdditional acknowledgements for support of individual\nauthors may be found in the following document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nFor\nthe purpose of open access, the authors have applied\na Creative Commons Attribution (CC BY) license to any\nAuthor Accepted Manuscript version arising. We request\nthat citations to this article use \u2018A. G. Abac et al. (LIGO-\nVirgo-KAGRA Collaboration), ...\u2019 or similar phrasing,\ndepending on journal convention.\nAppendix A: Details on BSD search pipeline\n1.\nSignal phase\nThe phase evolution of a monochromatic signal emitted\nby a source in a binary system is, in the detector frame,\ngiven by\n\u03a6(t) = 2\u03c0f0t + \u2206\u03d5(t),\n(A1)\nwhere f0 is the signal frequency. The phase modulation\ndue to the combined motion of the source and the detector\nis given by\n\u2206\u03d5(t) = 2\u03c0f0\n\"\nr \u00b7 \u02c6n\nc\n\u2212R\n\u0000t + r\u00b7\u02c6n\nc\n\u0001\nc\n#\n,\n(A2)\nwith r the position vector of the detector relative to the\nSolar-System Barycenter (SSB), and \u02c6n the unit vector\npointing from the SSB to the source. The R\u00f8mer delay, R,\ncan be expressed in a low-eccentricity orbit approximation\n(consistent with the nearly circular orbit of Cygnus X-1),\nneglecting an irrelevant constant term [134]:\nR(t)\nc\n= ap\n\u0014\nsin(\u03c8(t)) + e cos(\u03c9)\n2\nsin(2\u03c8(t))\n\u2212e sin(\u03c9)\n2\ncos(2\u03c8(t))\n\u0015\n,\n(A3)\nwhere ap is the projected semi-major axis, e is the orbital\neccentricity, and \u03c9 is the argument of periapse.\nThe\nfunction \u03c8 is the mean orbital phase measured from the\ntime of ascending node tasc, defined as\n\u03c8(t) = \u2126(t \u2212tasc),\n(A4)\nwith \u2126the orbital angular frequency.\n2.\nHeterodyne correction\nThe procedure of the heterodyne correction of BSD\nis presented in Ref. [84]. It consists of multiplying the\ndata by a complex phase factor exp(\u2212i \u2206\u03d5(t)) to correct\nDoppler-induced variations.\nThe phase \u2206\u03d5(t) is com-\nputed from Eq. (A2) assuming a set of parameters \u039b to\ncompensate for the delays in the signal arrival time from\nthe motion of the source and the detector. The mod-\nulation also depends on the unknown signal frequency.\nTaking advantage of the BSD framework and the down-\nsampling of the data into 1 Hz bands, we substitute for f0\na reference value fixed at the central frequency. By doing\nso, we ensure that the error in frequency is bounded by\n|f0 \u2212f0,ref| \u22640.5 Hz.\n3.\nDetection statistic\nThe CR statistic is estimated on a peakmap by project-\ning the peakmap on the frequency axis and producing the\n\n27\ndistribution of number of peaks per frequency bin n(f).\nWe then use a robust estimator defined as [97]\nCR(f) = n(f) \u2212\u00afn\n\u03c3\n,\n(A5)\nwhere \u00afn is the median of the number of peaks per fre-\nquency bin, and the dispersion parameter \u03c3 is defined\nby\n\u03c3 = median(|n(f) \u2212\u00afn|)\n0.6745\n.\n(A6)\nThe normalization factor \u03c3 ensures that if n follows a\nnormal distribution, then \u03c3 is the standard deviation.\n4.\nTemplate placement\nFor the placement of templates to cover the ap, tasc\nparameter space, we use a restricted version of the binary\nsearch metric described in Ref. [134]. We use the metric in\nthe semicoherent short-segment regime, where Tcoh \u226aP,\ngapap = 1\n6(\u03c0\u2126Tcohf0)2,\n(A7)\ngtasctasc = 1\n6\n\u0000\u03c0\u21262Tcohf0ap\n\u00012.\n(A8)\nThe resolution in an orbital parameter i is then given\nby [134]10\n\u03b4i =\np\n0.1[g\u22121]ii,\n(A9)\nwhere g\u22121 is the inverse metric, and the factor 0.1 corre-\nsponds to a maximal loss of signal-to-noise ratio of 10%.\nExplicitly, we get for the two remaining orbital parameters\nap and tasc:\n\u03b4ap =\n\u221a\n0.6\n\u03c0\u2126Tcohf0\n,\n(A10)\n\u03b4tasc =\n\u221a\n0.6\n\u03c0\u21262apTcohf0\n.\n(A11)\nConstructing a template grid with varying resolution\nacross the parameter space can be challenging. To sim-\nplify this, we adopt a conservative strategy by fixing all\nthe variable parameters to values that maximize grid\ndensity.\nSpecifically, we use the maximum frequency\nf0, max within the 1 Hz band, and the maximum value\nof the projected semi-major axis ap,max within the range\nto be covered. Fixing the resolutions as \u03b4ap(f0, max) and\n\u03b4tasc(f0, max, ap,max) over the entire parameter space en-\nsures an overcoverage of the search parameter space. With\n10 Note that a factor 2 is missing compared to Ref. [134]. In the\npresent work, these resolutions are used to compute the distance\nfrom a template placed on the parameter space rather than the\ntotal extent of this template.\nthis simplification, the template grid is constructed using a\nstandard square lattice Z2, as described in Refs. [134, 135].\nWith this placement strategy, the number of templates\nneeded to cover the parameter space is given by [134]\nN \u2248\n\u0018 Rap\n\u221a\n2\u03b4ap\n\u0019 \u0018 Rtasc\n\u221a\n2\u03b4tasc\n\u0019\n,\n(A12)\nwhere Rap and Rtasc are the sizes of the dimensions to\nbe covered.\n5.\nUpper limits formula\nThe average prefactor B in Eq. 8 is computed by repro-\nducing the derivation of Eq.(67) in Ref. [97] and according\nto the correction detailed in Ref. [156]. The general ex-\npression of B is a function of time, the signal polarization\nangle \u03c8, the source sky-position (RA, Dec), and the source\ninclination angle \u03b9. It can be expressed as\nB =\nv\nu\nu\nt\n\u03c0\n2.4308\nD\n(F+A+ + F\u00d7A\u00d7)2E\nt\n\u0012p0(1 \u2212p0)\np2\n1\n\u00131/4\n(A13)\nwhere the factor\n\u03c0\n2.4308 is taken from Eq. B18 in Ref. [97],\nand p0 and p1 are functions of the peak selection threshold\n\u03b8thr [97, 156]. For \u03b8thr = 2.5, we have p0 = 0.075 and\np1 = 0.096, using the updated definition of p1 shown in\nRef. [156]. The two beam pattern functions F+ and F\u00d7\nare defined in Ref. [123], and the polarization amplitudes\nare given by A+ = 1+cos2 \u03b9\n2\nand A\u00d7 = cos \u03b9 [97].\nFor the BSD search, we evaluate the expression of B\nfor the sky-position of Cygnus X-1, and by averaging over\nthe inclination angle error range [85] and the polarization\nangle \u03c8 \u2208[\u2212\u03c0/4, \u03c0/4]. Using properties of the beam\npattern function [65], we can write\n\n(F+A+ + F\u00d7A\u00d7)2\u000b\nt,\u03c8,cos \u03b9\n\f\f\nDec\n=\n\nF 2\n\u00d7\n\u000b\nt,\u03c8\n\f\f\f\nDec\n\nA2\n+ + A2\n\u00d7\n\u000b\ncos \u03b9 .\n(A14)\nWe compute\n\nA2\n+ + A2\n\u00d7\n\u000b\ncos \u03b9 = 1.582, and, following the\ndevelopment in Ref. [65],\n\nF 2\n\u00d7\n\u000b\nt,\u03c8\n\f\f\f\nDec = 0.197 in Liv-\ningston and 0.206 in Hanford. Injecting these values in\nEq. A13 gives B \u22483.37 in Livingston and B \u22483.30 in\nHanford.\nAppendix B: Follow-up vetoes\nAs detailed in this section, we only veto candidates that\nwe are confident are caused by noise artifacts. The safety\nof the vetoes used prior to the final manual inspection has\nbeen verified in previous analyses employing HMM- and\nBSD-based techniques, using Monte Carlo simulations\n\n28\nin clean frequency bands (see, e.g., Refs. [65, 114, 115]).\nHowever, if a GW signal is present in the data but over-\nlaps with a noise artifact, it is deemed \u201ccontaminated\u201d\nand will be vetoed. In other words, we do not yet have\na sufficiently reliable method to separate signals from\noverlapping, unidentified noise artifacts. Consequently,\nthe false dismissal probability cannot be easily quantified\nfor the vetoes discussed here with the presence of noise\nartifacts.\n1.\nHMM searches: Merger remnants\na.\nKnown-line veto\nThe first veto we use in the HMM search involves\ncomparing the frequency path of each signal candidate\nagainst all known instrumental lines present in either\nthe Hanford or Livingston detector to see if there is any\noverlap [149]. We increase the width of the Viterbi path\n\u03b4f \u224810\u22126fi + 8 \u03b4fSFT, where fi is a given frequency\nanywhere along the path and \u03b4fSFT is the SFT frequency\nbin width. The first part accounts for the Doppler modu-\nlation due to Earth\u2019s sidereal motion, and the second part\naccounts for the additional data used in the F-statistic\ncalculation. We consider candidates with a wide range\nof sky positions, start times, and total durations. Be-\ncause most search timescales are much shorter than a\nyear, we conservatively choose not to factor in Earth\u2019s\norbital Doppler modulation in this initial veto. The few\nlonger-duration candidates (with Tobs > a few months)\nthat could have been vetoed if Earth\u2019s orbital Doppler\nmodulation had been included are addressed in later steps.\nb.\nSingle-interferometer veto\nNext we use a technique that vetoes candidates caused\nby noise artifacts in a single detector that are not yet\nwell understood or identified in the official release of\nO4a known instrumental lines. The detailed criteria are\nas follows: We run the search with each interferometer\nindividually. Then, a signal candidate can be vetoed as\nan unknown instrumental line if the detection statistic in\none detector is below threshold while the other is greater\nthan the detection statistic from the combined detector\nsearch, and if the Viterbi paths of the latter two searches\noverlap.\nc.\nManual inspection\nBecause the previous two veto procedures are designed\nfor following up long-duration CW search candidates, they\nare not always able to effectively identify candidates from\na short-duration search. Thus, there are many candidates\nthat still remain at this stage. We visually inspect each\ncandidate using a variety of approaches designed to dis-\ntinguish signals from noise artifacts, typically applying\nmultiple checks to each candidate for confirmation. These\napproaches are listed here.\n1. We relax certain criteria of the single interferometer\nveto based on close inspection; for example, we veto\nany candidate whose detection statistic is below\nthreshold in one detector and anomalously high in\nthe other (e.g., \u00afL \u2273100), regardless of the detection\nstatistic from the original combined search.\n2. We compare the frequency drift of the candidate\nacross Tobs against the expected frequency drift of\na real signal. If the candidate frequency remains\nwithin a single bin for at least three quarters of\nthe total duration, and if it is not identified by at\nleast one other configuration with a larger value of\nTcoh (which is by design more sensitive to signals\nwith smaller frequency drifts), then it is unlikely to\nbe a real signal. For example, one candidate from\nGW231123 has an apparent \u02d9f0 < 10\u22128 Hz s\u22121, but\nthe expected frequency drift optimized for Tcoh =\n14.2 m is \u02d9f0 \u223c7 \u00d7 10\u22127 Hz s\u22121. This veto criterion\nis typically applied in conjunction with at least one\nother veto as a cross-check.\n3. We assess whether the detection statistic of a given\ncandidate is consistent with expectations for a signal\nfrom the remnant BH given its distance estimate.\nIf the statistic is significantly larger than expected\n(e.g., \u00afL \u2273100), we can veto the candidate as a loud\nbut unidentified noise artifact. This veto is applied\nonly in conjunction with at least one other veto.\nFor example, if the detection statistic combining\ntwo detectors is significantly larger than expected\nfor the target\u2019s distance, it is usually accompanied\nby the candidate being much louder in one detector\nthan in the other, in which case the candidate is\nalso vetoed according to the first manual inspection\ncriterion described above.\n4. We examine the signal candidate in the spectrogram\nfrom each interferometer in the relevant frequency\nband and time segment to determine whether it\noverlaps with any visible noise artifacts.\n5. Finally, if two candidates with the same fre-\nquency path are found using two different search\nconfigurations\u2014in other words, if the same candi-\ndate is identified in two different searches\u2014and if\none of them has been vetoed by any of the above\ncriteria, we consider the other likely to have arisen\nfrom the same artifacts. This veto criterion is typ-\nically applied in conjunction with other manual\ninspections as a cross-check.\n\n29\n2.\nBSD search: Cygnus X-1\nFor the BSD search, the 27 stage-2 candidates have\nbeen filtered by removing outliers associated with known\ninstrumental lines [149] and clustering candidates that\nshared a common outlier. Six candidates remained after\nthis filtering and are listed in Table VIII. The values\nreported in the table correspond to the averages of the\ntemplate parameters between the two detectors, and the\nquoted uncertainties are obtained by propagating the tem-\nplate resolutions given in Eqs. A10 and A11. As discussed\nin Sec. III B 2, the other parameters, {RA, Dec, P, e, \u03c9},\nare fixed to the central values listed in Tables I and II,\nand are therefore identical for all the candidates.\nGiven the small number of surviving candidates, we\nconducted the following tests and visually inspected the\nresults for each. Although we did not formally estimate\nthe false dismissal probability, the validity and safety of\neach veto have been confirmed by applying the follow-up\nprocedure to simulated signals with parameters similar\nto those of the six candidates. The tests, adapted from\nprevious BSD-based searches (e.g., [65, 114]), are grouped\ninto three categories: (i) consistency of the candidate\nwith its astrophysical parameters, (ii) consistency of the\ndetection statistic with different search configurations,\nand (iii) a manual inspection where we associated some\ncandidates to artifacts caused by non-Gaussianities in the\ndetector. These tests are described in detail below.\nTable VIII. Parameters of the candidates from the BSD search,\naveraged between the two detectors. For each candidate, we\nindicate the test by which it was vetoed.\nf0 [Hz]\nap [s]\ntasc [s]\nVeto\n32.751\n38.84 \u00b1 0.82\n5 600 \u00b1 1 700\nStat.\n37.131\n36.09 \u00b1 0.73\n188 100 \u00b1 1 600\nManual\n41.176\n36.79 \u00b1 0.66\n\u22124 383 \u00b1 1 400\nAstro.\n41.627\n38.60 \u00b1 0.65\n\u221211 800 \u00b1 1 300\nStat.\n53.890\n40.62 \u00b1 0.50\n204 700 \u00b1 950\nManual\n96.114\n38.10 \u00b1 0.28\n223 790 \u00b1 570\nManual\na.\nKnown-line veto\nSimilar to the HMM method, we veto any candidate\nwhose frequency evolution crosses a known instrumental\nline in either the Hanford or Livingston detector [149].\nFor a candidate observed at a frequency f0, we estimate\nthe modulation range as f0 \u00b1 \u03b4f, where \u03b4f is the modula-\ntion size computed with the parameters of the candidate,\n\u03b4f = maxt\n\u0010\nd\u2206\u03d5(t)\ndt\n\u0011\n, where \u2206\u03d5(t) is the phase modula-\ntion defined in Eq. A2.\nb.\nClustering\nDuring the candidate selection process, we consider\nall possible pairs between the outliers of the two detec-\ntors. Some redundancy is therefore possible in the list\nof candidates. Indeed, from the eight candidates passing\nthe known-line veto, two outliers are repeated twice, in\nassociation with two different (but similar) outliers in the\nsecond detectors. We therefore cluster these two sets of\ncandidates and follow them up conjointly. The number\nof unique candidates is reduced to six.\nc.\nAstrophysical consistency veto\nThe second step of the follow-up procedure involves\nassessing the consistency of each candidate with an astro-\nphysical signal through two key checks. Any candidate\nfailing at least one of these tests is discarded from further\nanalysis.\n1. Frequency refinement. Since the search demod-\nulates the data using the central frequency of each\n1 Hz band, a real signal may not be perfectly cor-\nrected if its true frequency differs from this reference.\nTo refine the analysis, we re-run a localized search\nusing the candidate recovered frequency as the refer-\nence frequency for demodulation. A genuine signal\nmust persist with similar or improved significance\nunder this correction.\n2. Unmodulated test.\nAs the search is directed\ntoward a signal emitted from Cygnus X-1, the sig-\nnificance of an astrophysical signal should decrease\nwhen using parameters incompatible with the tar-\nget. In particular, we try to recover the candidate\nwithout performing the heterodyne correction. A\ncandidate persisting with comparable significance in\nthis configuration cannot be of astrophysical origin\nand is therefore vetoed.\nd.\nStatistical consistency check\n1. Sensitivity vetoes. For a true signal, the detection\nstatistic should scale with the sensitivity of each\ndetector. We check this by normalizing the CR with\nthe median ASD of the 1 Hz band, \u221aSn. We then\nrequire\nCR1\np\nSn1\n< 3 CR2\np\nSn2\n,\n(B1)\nwhere detector 1 is less sensitive and detector 2 is\nmore sensitive. The factor 3 is a conservative choice\nand indeed none of the candidate was vetoed by\nthis check.\n\n30\n2. Cumulative and Uniformity veto. A genuine\nastrophysical CW signal should persist throughout\nthe observation run, and we expect: (i) steadily\nincreasing significance as more data are included,\nand (ii) the candidate to be present in any subset\nof the data.\nWe first examined cumulative behavior by comput-\ning the CR and signal-to-noise ratio (SNR) over data\nsegments whose durations increased in 30-day steps,\nfor both detectors and for data with and without\nheterodyne correction. We compared the corrected\nand uncorrected results, looking for behavior incon-\nsistent with the presence of a signal. One candidate\nwas vetoed because the uncorrected data yielded\nhigher significance for most of the run. A second\ncandidate showed a sharp increase during the first\nmonth, indicating the presence of non-stationary\nnoise.\nTo verify the persistence across subsets, we ana-\nlyzed one-month segments with various start times,\nagain for both detectors and both data types. Some\nvariation is expected due to varying duty cycles or\nnoise levels, so results were interpreted with toler-\nance. For the second suspect candidate identified in\nthe cumulative test, corrected and uncorrected data\ngave similar CR values except in the first month,\nwhere the corrected data produced a much higher\nCR. This confirmed the non-persistent nature of the\ncandidate, and it was vetoed.\ne.\nManual inspection\nFinally, we manually inspect the three remaining candi-\ndates. For each, we investigate the spectra of the corrected\nand uncorrected data using two different frequency reso-\nlutions: 5.5 \u00d7 10\u22124 and 1.1 \u00d7 10\u22125 Hz, corresponding to\ncoherence times of 30 min and 1 day, respectively. In all\nthree candidates\u2019 bands, we observe strong non-Gaussian\nnoise profiles. Such non-Gaussianities are known to pro-\nduce artifacts in specific frequency bins during peakmap\npeak selection [133], and, coincidentally, all the remain-\ning candidates are present in one of these frequency bins.\nBy slightly modifying the resolution of the background\nestimation used to compute the equalized spectra [133],\nwe force the artifact-affected bins to be moved away from\nthe candidate bins. This modified setup ensures that\nthe candidates\u2019 frequency bins were not contaminated\nby the peakmap creation artifacts. We tested several\nsuch configurations, and in all cases the CR of each can-\ndidate dropped well below the selection threshold. 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Palomba, \u201cOn the sensitivity of peakmap-based meth-\nods for the search of continuous gravitational wave sig-\nnals,\u201d (2025).\n", "Future Circular Collider\nFeasibility Study Report\nVolume 2\nAccelerators, Technical Infrastructure\nand Safety\nMarch 31, 2025\nSubmitted to the European Physics Journal ST, a joint publication of EDP Sciences,\nSpringer Science+Business Media, and the Societ\u00e0 Italiana di Fisica.\n\nNote from the Editors\nOne of the recommendations of the 2020 update of the European Strategy for Particle Physics was that\n\u201cEurope, together with its international partners, should investigate the technical and financial feasibility\nof a future hadron collider at CERN with a centre-of-mass energy of at least 100 TeV and with an\nelectron-positron Higgs and electroweak factory as a possible first stage.\nIn June 2021, the CERN Council launched the FCC Feasibility Study to be completed by 2025, in\ntime for the next update of the European Strategy for Particle Physics. The study results are made\npublicly available through this FCC Feasibility Study Report, as input to the European Particle Physics\nStrategy update process, initiated by the CERN Council in March 2024. The studies presented in this\nFCC Feasibility Study Report do not imply any commitment by the CERN Member or Associate Member\nStates to build the Future Circular Collider.\nThis report and the assumptions contained in it do not prejudge further territorial feasibility analysis by\nthe Host States, France and Switzerland, as well as the outcome of their respective public debate and\nconcertation processes, and future decisions of their relevant authorities.\nii\n\nAcknowledgements\nWe would like to thank the International Steering Committee members:\nF. Gianotti (Chair), CERN\nR. Bello, CERN\nP. Chomaz, CEA, France\nM. Cobal, INFN and University of Udine, Italy\nB. Heinemann, DESY, Germany\nT. Koseki, KEK, Japan\nM. Lamont, CERN\nL. Merminga, FNAL, United States\nJ. Mnich, CERN\nM. Seidel, PSI and EPFL, Switzerland\nC. Warakaulle, CERN\nand the Scientific Advisory Committee members:\nA. Parker (Chair), Cambridge University, UK\nR. Bartolini, DESY, Germany\nA. Chabert, SFTRF, France\nH. Ehrbar, Heinz Ehrbar Partners LLC, Switzerland\nB. Gavela Legazpi, UAM Madrid, Spain\nG. Hiller, TU Dortmund, Germany\nS. Krishnagopal, FNAL, U.S.\nP. Kri\u017ean, University of Ljubljana, Slovenia\nP. Lebrun, ESI, France\nP. McIntosh, STFC, ASTeC, UKRI, UK\nM. Minty, BNL, U.S.\nR. Tenchini, INFN Sezione di Pisa, Italy\nfor their continued guidance and careful reviewing that helped to complete this report successfully.\niii\n\nThe research carried out by the international FCC collaboration hosted by CERN, which\nled to this publication, has received funding from the European Union\u2019s Horizon 2020\nresearch and innovation programme under the grant numbers 951754 (FCCIS), 654305\n(EuroCirCol), 764879 (EASITrain), 730871 (ARIES), 777563 (RI-Paths), 101086276\n(EAJADE), 101004730 (iFAST), 101131435 (iSAS), 101131850 (RF2.0) and from FP7 under grant\nnumber 312453 (EuCARD-2).\nThis work has also benefited from the support of CHART (Swiss Accelerator Research\nand Technology, founded in 2016 as an umbrella collaboration for accelerator research\nand technology activities. Present partners in CHART are CERN, PSI, EPFL, ETH-\nZurich and the University of Geneva.\nTrademark notice: All trademarks appearing in this report are acknowledged as such.\niv\n\nThis report was edited with the Overleaf.com collaborative writing and publishing system. Typesetting\nand final print preparation was performed using pdfTEX3.14159265-2.6-1.40.17\nCopyright CERN for the benefit of the FCC collaboration 2025\nCreative Commons Attribution 4.0\nKnowledge transfer is an integral part of CERN\u2019s mission.\nCERN publishes this volume Open Access under the Creative Commons Attribution 4.0 licence.\n(http://creativecommons.org/licenses/by/4.0/) in order to permit its wide dissemination and\nuse. The submission of a contribution to the CERN document server shall be deemed to constitute the\ncontributor\u2019s agreement to this copyright and license statement. Contributors are requested to obtain any\nclearances that may be necessary for this purpose.\nThis volume is indexed in: CERN Document Server (CDS):\nCERN-FCC-ACC-2025-0004\nDOI 10.17181/CERN.EBAY.7W4X\nhttp://cds.cern.ch/record/2928793\nThis report edition should be cited as:\nFuture Circular Collider Feasibility Study Report Volume 2: Accelerators, technical infrastructure and\nsafety, preprint edition edited by M. Benedikt et al., CERN accelerator reports,\nCERN-FCC-ACC-2025-0004,DOI 10.17181/CERN.EBAY.7W4X, Geneva, 2025.\nAvailable online: http://cds.cern.ch/record/2928793\nv\n\nList of Editors at 31 March 2025\nM. Benedikt1 (Study Leader), F. Zimmermann1 (Deputy Study Leader), B. Auchmann1,2,\nW. Bartmann1, J.P. Burnet1, C. Carli1, A. Chanc\u00e93, P. Craievich2, M. Giovannozzi1, C. Grojean4,5,\nJ. Gutleber1, K. Hanke1, A. Henriques1, P. Janot1, C. Louren\u00e7o1, M. Mangano1, T. Otto1, J. Poole1,\nS. Rajagopalan6, T. Raubenheimer7, E. Todesco1, L. Ulrici1, T. Watson1, G. Wilkinson1,8.\nList of Contributors at 31 March 2025\nA. Abada9,10,11, M. Abbrescia12,13, H. Abdolmaleki14,15, S.H. Abidi6, A. Abramov1, C. Adam9,16,17,\nM. Ady1, P.R. Ad\u02d8zi\u00b4c18, I. Agapov4, D. Aguglia1, I. Ahmed19, M. Aiba2, G. Aielli20,21, T. Akan22,\nN. Akchurin23, D. Akturk24, M. Al-Thakeel1,25,26, G.L. Alberghi25, J. Alcaraz Maestre27, M. Aleksa1,\nR. Aleksan3, F. Alharthi9,10,28, J. Alimena4, A. Alimenti29, S. Alioli30,31, L. Alix1,9,16,\nB.C. Allanach32, L. Allwicher4, A.A. Altintas33, M. Alt\u0131nl\u013133,34, M. Alviggi35,36, G. Ambrosio37,\nY. Amhis9,10,11, A. Amiri38,39, G. Ammirabile40, T. Andeen41, K.D.J. Andr\u00e91, J. Andrea9,42,43,\nA. Andreazza44,45, M. Andreini1, T. Andriollo46, L. Angel47, M. Angelucci48, S. Antusch49,\nM.N. Anwar12,50, L. Apolin\u00e1rio51, G. Apollinari37, R.B. Appleby52,53, A. Apresyan37, Aram Apyan54,\nArmen Apyan55, A. Arbey9,56,57, B. Argiento35,36, V. Ari58, S. Arias59, B. Arias Alonso1,\nO. Arnaez9,16,17, R. Arnaldi60, F. Arneodo61, H. Arnold62, P. Arrutia Sota1, M.E. Ascioti63,64,\nK.A. Assamagan6, S. Aumiller65, G. Ayd\u0131n66, K. Azizi38,67, P. Azzi68, N. Bacchetta68, A. Bacci44,\nB. Bai69, Y. Bai70, L. Balconi44,45, G. Baldinelli63,64, B. Balhan1, A.H. Ball1,71, A. Ballarino1,\nS. Banerjee72, S. Banik2,73, D.P. Barber4,74, M.B. Barbero9,75,76, D. Barducci40,77, D. Barna78,\nG.G. Barnaf\u00f6ldi78, M.J. Barnes1, A.J. Barr8, R. Bartek79, H. Bartosik1, S.A. Bass80, U. Bassler9,81,82,\nM.J. Basso83,84, A. Bastianin45,85, P. Bataillard86, M. Battistin1, J. Bauche1, L. Baudin1,\nJ. Baudot9,42,43, B. Baudouy3, L. Bauerdick37, C. Bay\u0131nd\u0131r87,88, H.P. Beck89, F. Bedeschi40, C. Bee62,\nM. Begel6, M. Behtouei48, L. Bellagamba25, N. Bellegarde1, E. Belli1,90, E. Bellingeri91,\nS. Belomestnykh37, A.D. Benaglia30, G. Bencivenni48, J. Bendavid1, M. Benmergui92, M. Benoit93,\nD. Benvenuti1,40, T. Bergauer94, N. Bernachot95, G. Bernardi9,96,97, J. Bernardi98, Q. Berthet99,100,101,\nS. Bertoni102, C. Bertulani103, M.I. Besana2, A. Besson9,42,43, M. Bettelini104, S. Bettoni2,\nS. Beuvier\u2020105, P.C. Bhat37, S. Bhattacharya106, J. Bhom107, M.E. Biagini48, A. Bibet-Chevalier108,\nM. Bicrel109, M. Biglietti110, G.M. Bilei63, B. Bilki111,112, K. Bisgaard Christensen1, T. Biswas113,\nF. Blanc114, F. Blekman4,115,116, A. Blondel9,101,117, J. Bl\u00fcmlein4, D. Boccanfuso35,118,\nA. Bogomyagkov119, P. Boillon108, P. Boivin100, M.J. Boland120, S. Bologna121, O. Bolukbasi33,\nR. Bonnet102, J. Borburgh1, F. Bordry1, P. Borges de Sousa1, G. Borghello1, L. Borriello35,\nD. Bortoletto8, M. Boscolo48, L. Bottura1, V. Boudry9,81,82, R. Boughezal122, D. Bourilkov123,\nM. Boyd83,124, D. Boye6, G. Bozzi125,126, V. Braccini91, C. Bracco1, B. Bradu1, A. Braghieri127,\nS. Braibant25,26, J. Bramante128, G.C. Branco129, R. Brenner130, N. Brisa102, D. Britzger131,\nG. Broggi1,90, L. Bromiley1, E. Brost6, Q. Bruant3, R. Bruce1, E. Br\u00fcndermann132, L. Brunetti9,16,17,\nO. Br\u00fcning1, O. Brunner1, X. Buffat1, E. Bulyak133, A. Burdyko44,134, H. Burkhardt1,135,\nP.N. Burrows136, S. Busatto44,90, S. Buschaert86, D. Buttazzo40, A. Butterworth1, D. Butti1,\nG. Cacciapaglia137,138,139, Y. Cai7, B. Caiffi140, V. Cairo1, O. Cakir58, P. Calafiura141, R. Calaga1,\nS. Calatroni1, D.G. Caldwell142, A. \u00c7al\u0131\u00b8skan143, C. Calpini144, M. Calviani1, E. Camacho-P\u00e9rez145,\nP. Camarri20,21, L. Caminada2,73, M. Campajola35,36, A.C. Canbay58, K. Canderan1, S. Candido1,\nF. Canelli73, A. Canepa37, S. Cantarella48, K.B. Cant\u00fan-Avila145, L. Capriotti146,147, A. Caram148,\nA. Carbone44, J.M. Carceller1, G. Carini6, F. Carlier1, C.M. Carloni Calame127, F. Carra1,\nC. Cartannaz86, S. Casenove1, G. Catalano149, V. Cavaliere6, C. Cazzaniga150, C. Cecchi63,64,\nF.G. Celiberto151, M. Cepeda27, F. Cerutti1, F. Cetorelli30,31, G. Chachamis51, Y. Chae4, F. Chagnet152,\nI. Chaikovska9,10,11, M. Chalhoub86, M. Chamizo-Llatas6, M. Champagne153, H. Chanal9,154,155,\nG. Chapelier108, P. Charitos1, C. Charles105, T.K. Charles156, C. Charlot9,81,82, S. Chatterjee4,\nA. Chaudhuri157, R. Chehab9,10,11, S.V. Chekanov158, H. Chen6, T. Chesne105, F. Chiapponi25,26,\nG. Chiarello159,160, M. Chiesa127, P. Chiggiato1, Ph. Chomaz3, M. Chorowski161, J.P. Chou162,\nvi\n\nM. Chrzaszcz107, W. Chung163, S. Ciarlantini68,164, A. Ciarma48, D. Cieri131, A.K. Ciftci165,\nR. Ciftci166, R. Cimino48, F. Cirotto35,36, M. Ciuchini110, M. Cobal167,168, A. Coccaro140,\nR. Coelho Lopes De Sa169, J.A. Coleman-Smith1, F. Collamati170, C. Colldelram171, P. Collier1,\nP. Collins1, J. Collot9,172,173, M. Colmenero1, L. Colnot149, G. Coloretti73, E. Conte9,42,43,\nF.A. Conventi35,174, A. Cook1, L. Cooley175,176, A.S. Cornell177, C. Cornella1, G. Cornette105,\nI. Corredoira178, P. Costa Pinto1, F. Couderc3, J. Coupard1, S. Coussy86, R. Crescenzi179,\nI. Crespo Garrido1,180, T. Critchley1,101, A. Crivellin73, T. Croci63, C. Cudr\u00e9105, G. Cummings37,\nF. Cuna12, R. Cunningham1, B. Cur\u00e91, E. Curtis181, M. D\u2019Alfonso182, L. D\u2019Aloia Schwartzentruber183,\nG. D\u2019Amen6, B. D\u2019Anzi12,13, A. D\u2019Avanzo35,36, D. d\u2019Enterria1, A. D\u2019Onofrio35, M. D\u2019Onofrio184,\nM. Da Col149, M. Da Rocha Rolo60, C. Dachauer185, B. Da\u02d8gli24, A. Dainese68, B. Dalena3,\nW. Dallapiazza186, M. Dam187, H. Damerau1, V. Dao62, A. Das188, M.S. Daugaard1, S. Dauphin108,\nA. David1, T. Dav\u00eddek189, G.J. Davies181, S. Dawson6, J. de Blas190, A. de Cosa150, S. De Curtis191,\nN. De Filippis12,50, E. De Lucia48, R. De Maria1, E. De Matteis44, A. De Roeck1, A. De Santis48,\nA. De Vita1,68,164, A. Deandrea9,56,57, C.J. Debono192, M. Deeb100, M.M. Defranchis1, J. Degens184,\nS. Deghaye1, V. Del Duca48, C.L. Del Pio6, A. Del Vecchio90, D. Delikaris1, A. Dell\u2019Acqua1,\nM. Della Pietra35,36, M. Delmastro9,16,17, L. Delprat1, E. Delugas149, Z. Demiragli193, L. Deniau1,\nD. Denisov6, H. Denizli194, A. Denner195, A. Denot108, G. Deptuch6, A. Desai196, H. Deveci1,\nA. Di Canto6, A. Di Ciaccio20,21, L. Di Ciaccio9,16,17, D. Di Croce1,114, C. Di Fraia35,36,\nB. Di Micco29,110, R. Di Nardo29,110, T.B. Dingley8, F. Djama9,75,76, F. Djurabekova197, D. Dockery37,\nS. Doebert1, D. Domange1,198, M. Doneg\u00e0150, U. Dosselli68, H.A. Dostmann1,199, J.A. Dragovich37,\nI. Drebot44, M. Drewes200, T.A. du Pree201, Z. Duan202, C. Duarte-Galvan203, O. Duboc204, M. Duda2,\nP. Duda161, H. Duran Yildiz58, H. Durand105, P. Durand105, G. Durieux200, Y. Dutheil1, I. Dutta37,\nJ.S. Dutta205, S. Dutta206, F. Duval1, F. Eder1, M. Eisterer98, Z. El Bitar9,42,43, A. El Saied207,\nM. Elisei44, J. Ellis1,208, W. Elmetenawee12, J. Elmsheuser6, V. Daniel Elvira37, S.C. Eno209,\nY. Enomoto210, B.A. Erdelyi68,164, O.E. Eruteya101,211, M. Escobar212, O. Etisken213, I. Eymard144,\nJ. Eysermans182, D. Falchieri25, C. Falkenberg204, F. Fallavollita1,131, A. Afalou1,9,10, J. Faltova189,\nJ. Fanini1, L. Fan\u00f263,64, K. Fanti105, R. Farinelli25, M. Farino163, S. Farinon140, H. Fatehi38,\nJ. Fatterbert105, A. Faure214, A. Faus-Golfe9,10,11, G. Favia1, L. Favilla35,118, W.J. Fawcett32,\nA. Federowicz37, L. Feligioni9,75,76, L. Felsberger1, Y. Feng23, A. Fern\u00e1ndez T\u00e9llez215, R. Ferrari127,\nL. Ferreira1, F. Ferro140, M. Fiascaris1, C. Fiorio45, S.A. Fleury1, L. Florez186, M. Florio45,149,\nA. Fondacci63, B. Fontimpe212, K. Foraz1, R. Fortunati2, M. Fouaidy9,10,11, A. Foussat1, A. Fowler1,\nJ.D. Fox216, M. Francesconi35, B. Francois1, R. Franqueira Ximenes1, F. Fransesini48, A. Frasca1,184,\nA. Freitas217, J.A. Frost8, K. Furukawa210, A. Gabrielli25,26, A. Gaddi1, F. Gaede4, A. Gall\u00e9n130,\nR. Galler218,219, E. Gallice105, E. Gallo4,115, H. Gamper1, G. Ganis1, S. Ganjour3, S. Gao6,\nA. Garand148, C. Garaus204, D. Garcia1, R. Garc\u00eda Al\u00eda1, R. Garc\u00eda Gil220, C.M. Garcia Jaimes1,114,\nH. Garcia Rodrigues2,221, C. Garion1, M. Garlasch\u00e81, D. Garnier152, M.V. Garzelli115,\nS. Gascon-Shotkin9,56,57, M. Gasior1, G. Gaudino35,118, G. Gaudio127, V. Gaur222, K. Gautam73,116,\nV. Gawas1, T. Gehrmann73, A. Gehrmann-De Ridder73,150, K. Geiger1, M. Genco149, F. Gerigk1,\nH. Gerwig1, A. Ghribi1,9,223, P. Giacomelli25, S. Giagu90,170, E. Gianfelice37, S. Giappichini132,\nD. Gibellieri1,224, F. Giffoni149, G. Gil da Silveira225, S.S. Gilardoni1, M. Giovannetti48, T. Girardet105,\nS. Girod1,105, P. Giubellino60, P. Giubilato68,164, F. Giuli20,21, M. Giuliani102, E.L. Gkougkousis1,73,\nS. Glukhov226, J. Gluza227, B. Goddard1, C. Goffing1,132, D. Goldsworthy1, T. Golling101,\nR. Gon\u00e7alo51,228, V.P. Gon\u00e7alves47,229, T. Gon\u00e7alves Da Silva212, J. Gonski7, R. Gonzalez Suarez130,\nS. Gorgi Zadeh1, S. Gori230, E. Gorini159,231, L. Gouskos232, M. Gouzevitch9,56,57, E. Granados1,\nF. Grancagnolo159, S. Grancagnolo159,231, A. Grassellino37, A. Grau132, E. Graverini40,77,114,\nF.G. Gravili159,231, H.M. Gray141,233, M. Grazzini73, Mario Greco29,110, Michela Greco60,234,\nA. Greljo49, J-L. Grenard1, A.V. Gritsan235, R. Gr\u00f6ber68,164, A. Grudiev1, E. Gschwendtner1, J. Gu236,\nD. Guadagnoli17,137,237, G. Guerrieri1, A. Guiavarch207, G. Guillermo Canton1,238, M. Guinchard1,\nY.O. G\u00fcnaydin239, K. Gurcel92, L.X. Gutierrez Guerrero240,241, D. Guti\u00e9rrez Rueda1,\nA. Guti\u00e9rrez-Rodr\u00edguez242, V. Guzey197,243, C. Haber141, T. Hacheney244, B. Hac\u0131\u00b8sahino\u02d8glu33,\nvii\n\nK. Hahn122, J. Hajer129, T. Hakulinen1, J.C. Hammersley245, M. Hance230, J.B. Hansen187,\nB. H\u00e4rer132, E. Hauzinger218, M. Haviernik189, B. Hegner1, C. Helsens114, Ana Henriques1,\nC. Hernalsteens1, H. Hern\u00e1ndez-Arellano215, R.J. Hern\u00e1ndez-Pinto203, M.A. Hern\u00e1ndez-Ru\u00edz242,\nJ. Hern\u00e1ndez-S\u00e1nchez215, J.W. Heron1, L.M. Herrmann1, R. Hirosky246, J.F. Hirschauer37,\nJ.D. Hobbs62, K. Hock6, S. H\u00f6che37, M. Hofer1, G. Hoffstaetter6,247, W. H\u00f6fle1, M. Hohlmann248,\nF. Holdener249, B. Holzer1, C.G. Honorato215, H. Hoorani250, A. Houver105, E. Howling1,8,136,\nX. Huang7, F. Hug251, B. Humann1, P. Hunchak120, Y. Husein1, A. Hussain1,252, G. Iadarola1,\nG. Iakovidis6, G. Iaselli12,50, P. Iengo35, A. Ilg73, M. Iodice110, A.O.M. Iorio35,36, V. Ippolito170,\nU. Iriso171, J. Isaacson37, G. Isidori73, R. Islam253, A. Istepanyan105, S. Izquierdo Bermudez1,\nV. Izzo35, P.D. Jackson196, R. Jafari1,38, S.S. Jagabathuni1,101, S. Jana254,255, C. J\u00e4rmyr Eriksson1,\nP. Jausserand152, M. Jensen256, J.M. Jimenez1, F.R. Joaquim129, O.R. Jones1, J. Joos108,\nE. Jourd\u2019huy9,257, E. Jourdan212, J.M. Jowett1,258, A. Jueid259, A.W. Jung205, M. Kagan7,\nI. Kahraman58, V. Kain1, J. Kalinowski260, J.F. Kamenik261,262, A. Kanso263, T. Kar264, S.O. Kara265,\nH. Karadeniz266, S.R. Karmarkar205, V. Karpati267, I. Karpov1, M. Karppinen1, P. Karst9,75,76,\nS. Kartal33, V.V. Kashikhin37, U. Kaya58, A. Kehagias1,268, J. Keintzel1, M. Kennouche1, M. Kenzie32,\nM. Kerr\u00e9veur-Lavaud46, R. Kersevan1,269, V. Keus197,270, H. Khanpour14,271,272, V.V. Khoze273,\nV.A. Khoze273, P. Kicsiny1, R. Kieffer1, C. Kiel114, J. Kieseler132, A. Kilic274, B. Kilminster73,\nS. Kim275, Z. K\u0131rca274, M. Klein\u2020184, A. Klimentov6, M. Klute132, V. Klyukhin119,276,\nM. Knecht137,277,278, B. Kniehl115, P. Ko279, S. Ko1, F. Kocak274, T. Koffas280, C. Kokkinos281,282,\nK. Ko\u0142odziej227, K. Kong283, P. Kontaxakis101, I.A. Koop119, P. Kopciewicz1, P. Koppenburg201,\nM. Koratzinos1,2, K. Kordas284, A Korsun9,10,11, O. Kortner131, S. Kortner131, B. Korzh101,\nT. Koseki210, J. Kosse2, P. Kostka1,184, S. Kostoglou1, A.V. Kotwal80, G. Kozlov1,276, I. Kozsar1,\nT. Kramer1, P. Krkoti\u00b4c1, H. Kroha131, K. Kr\u00f6ninger244, S. Kuday1,58, G. Kuhlmann285,\nO. Kuhlmann1,286, M. Kuhn287, A. Kulesza288, M. Kumar289, F. Kurian6, A. Kurtulus1,150,\nT.H. Kwok73, S. La Mendola1, M. Lackner98,290, T. \u0141adzi\u00b4nski1, D. Lafarge1, P. La\u00efdouni1,\nG. Lamanna9,16,17, N. Lamas19, G. Landsberg232, C. Lange2, D.J. Lange163, A. Langner1,\nA.J. Lankford291, L. Lari6, M.S. Larson292, K. Lasocha1, A. Latina1, S. Lauciani48, M. Laufenberg105,\nG. Lavezzari1, L. Lavezzi60, L. Lavezzo1, M. Le Garrec1,9,16, A. Le Jeune102, Ph. Lebrun1,293,\nY. L\u00e9chevin1, A. Lechner1, E. Lecointe105, J.S.H. Lee294, S.W. Lee295, S.J. Lee279,296, T. Lefevre1,\nC. Leggett141, T. Lehtinen297, S. Leone40, C. Leonidopoulos298, S. Leontsinis73,\nG. Leprince-Maill\u00e8re299, G. Lerner1, O. Leroy9,75,76, T. Lesiak107, P. Levai78, A. Leveratto91,\nR. Levi152, A. Li6, S. Li300,301, D. Liberati302, G.L. Lichtenstein47, M. Liepe247, Z. Ligeti141,\nH. Lin303, S. Linda144, E. Lipeles304, Z. Liu305, S.M. Liuzzo306, T. Loeliger287,\nA. Loeschcke Centeno307, A. Lorenzetti73, C. Lorin3, R. Losito1, M. Louka12,308,\nM.L. Loureiro Garc\u00eda180, I. Low122,158, K. Lubonis152, M.T. Lucchini30,31, V. Lukashenko73,\nG. Luminati48, A.J.G. Lunt1,309, A. Lusiani40,310, M. Luzum311, H. Ma6, A. Maas312,\nE. Macchia1,90,170, A. Macchiolo73, G.E. Machinet263, R. Madar9,154,155, T. Madlener4, C. Madrid23,\nA. Magalotti29, M. Maggiora60,234, A.-M. Magnan181, M.A. Mahmoud313, Y. Mahmoud314,315,\nF. Mahmoudi1,9,56, H. Mainaud Durand1, J. Maitre108, Y. Makhloufi101, B. Malaescu9,117,316,\nA. Malagoli91, C.H. Malan108, M. Malekhosseini38, A. Maloizel1,96,97, S. Malvezzi30, A. Malzac148,\nG. Manco127, L.S. Mandacar\u00fa Guerra163, P. Manfrinetti91,317, E. Manoni63, J. Mans305, L. Mantani318,\nS. Manzoni1, L. Marafatto167, C. Marcel1, T. Marcel109, R. Marchevski114, G. Marchiori9,96,97,\nF. Mariani44,90, V. Mariani63,64, S. Marin1, C. Marinas318, V. Marinozzi37, S. Mariotto44,45,\nC. Marquis105, J. Martelain319, G. Martelli63,64, A. Martens9,10,11, I. Martin-Melero1,\nV.I. Martinez Outschoorn169, F. Martinez215, C.M. Jardim27, L. Marzola320,321, S. Masciocchi258,264,\nA. Mashal14, A. Masi1, I. Masina146,147, P. Mastrapasqua200, V. Mateu322, S. Mattiazzo68,164,\nM. Maugis102, D. Mauree144, G.H.I. Maury-Cuna323, A. Mayoux1, E. Mazzeo1, S. Mazzoni1,\nM. McCullough1, M. Meena9,42,43, E. Meftah101, Andrew Mehta184, Ankita Mehta1, B. Mele170,\nR. Mena-Andrade1, M. Mentink1, D. Mergelkuhl1, V. Mertinger267, L. Mether1, S. Meylan105,\nT. Michel102, T. Michlmayr2, M. Migliorati90,170, A. Milanese1, C. Milardi48, G. Milhano51,\nviii\n\nM. Minty6, C. Mirabelli324, T. Miralles9,154,155, L. Miralles Verge1, D. Mirarchi1, K. Mirbaghestan73,\nN. Mirian4,325, V.A. Mitsou318, D.S. Mitzel244, M. Mlynarikova1, S. M\u00f6bius89,\nM. Mohammadi Najafabadi1,14, G.B. Mohanty326, R. N. Mohapatra209, S. Moneta63, P.F. Monni1,\nE. Monnier9,75,76, S. Monteil9,154,155, I. Le\u00f3n Monz\u00f3n203, F. Moortgat1,327, N. Morange9,10,11,\nM. Moretti146,147, S. Moretti71, T. Mori1,210, I. Morozov119, A. Morozzi63, M. Morrone1,\nA. Moscariello101, F. Moscatelli63,328, I. Moulin214, N. Mounet1, A. Mueller329, A.-S. M\u00fcller132,\nB.O. M\u00fcller285, J. Mundet220, E. Musa1,4, V. Musat1,8, R. Musenich140, E. Musumeci318, M. Mylona1,\nV.V. Mytrochenko9,10,133, B. Nachman141, S. Nagaitsev6, T. Nakamoto210, M. Napsuciale323,\nM. Nardecchia90,170, G. Nardini330, G. Narv\u00e1ez-Arango331, S. Naseem61, A. Natochii6,\nA. Navascues Cornago1, B. Naydenov1, G. Nergiz1, A.V. Nesterenko276, C. Neub\u00fcser332,\nH.B. Newman333, F. Niccoli1,334, O. Nicrosini127, U. Niedermayer226, G. Niehues132, J. Nielsen1,\nG. Nigrelli1,90,170, S. Nikitin119, I.B. Nikolaev119, A. Nisati170, N. Nitika167,168, J.M. No335,\nM. Nonis1, Y. Nosochkov7, A. Novokhatski1,7, J.M. O\u2019Callaghan336, S.A. Ochoa-Oregon203,\nK. Ohmi202,210, K. Oide1,101,210, V.A. Okorokov119, C. Oleari30,31, D. Oliveira Damazio1,6, Y. Onel112,\nA. Onofre337,338,339, P. Osland340, Y.M. Oviedo-Torres341,342,343, A. Ozansoy58, F. Ozaydin87,344,\nK. Ozdemir345, A. Ozturk1, M.A. P\u00e9rez de Le\u00f3n203, S. Pacetti63,64, H. Pacey8, J. Paciello108,\nC.E. Pagliarone346,347, A. Paillex105, H.F. Pais da Silva1, F. Palla40, A. Pampaloni140, C. Pancotti149,\nM. Pandurovi\u00b4c348, O. Panella63, G. Panizzo167,168, C. Pantouvakis68,164, L. Panwar9,117,316,\nP. Paolucci35, Y. Papa105, A. Papaefstathiou349, Y. Papaphilippou1, A. Paramonov158, A. Pareti127,350,\nB. Parker6, V. Parma1, F. Parodi140,317, M. Parodi1, B. Paroli44,45, J.A. Parsons351, D. Passarelli37,\nD. Passeri63,64, B. Pattnaik318, A. Patwa352, C. Paus182, F. Pauss150, F. Peauger1, I. Pedraza215,\nR. Pedro51, J. Pekkanen1, G. Peon1, A. Perez109, E. Perez1, F. P\u00e9rez171, J.C. Perez1, J.M. P\u00e9rez27,\nR. Perez-Ramos137,138,353, G. P\u00e9rez Segurana1, A. Perillo Marcone1, S. Perna35,36, K. Peters4,\nS. Petracca35,354, A.R. Petri44, F. Petriello122, A. Petrovic1, L. Pezzotti25, G. Piacquadio62,\nG. Piazza179, A. Piccini1, F. Piccinini127, A. Pich318, T. Pieloni114, J. Pierlot1, A.D. Pilkington52,\nM. Pillet324, M. Pinamonti167,168, N. Pinto235, L. Pintucci167,168, F. Pinzauti1, K. Piotrzkowski271,\nC. Pira48, M. Pitt1, R. Pittau190, S. Pittet1, P. Placidi63,64, W. P\u0142aczek355, S. Pl\u00e4tzer312,356,\nM.-A. Pleier6, E. Ploerer73,116, H. Podlech357,358, F. Poirier9,16,17, G. Polesello127, M. Poli Lener48,\nJ. Polinski161, Z. Polonsky73, N. Pompeo29, M. Pont171, G. Alexandru-Popeneciu359, W. Porod195,\nL. Porta1, L. Portales3, T. Portaluri307, M.A.C. Potenza45, C. Prasse285, E. Premat183, M. Presilla132,\nS. Prestemon141, A. Price355, M. Primavera159, R. Principe1, M. Prioli44, F.M. Procacci12,\nE. Proserpio44,134, A. Provino91,317, C. Pueyo1, T. Puig19, N. Pukhaeva276, S. Pulawski227,\nG. Punzi40,77, A. Pyarelal360, J. Qian303, H. Quack361, F. S. Queiroz47, G. Quintas-Neves299,\nH. Rafique71, J.-Y. Raguin2, J. Raidal320, M. Raidal320, P. Raimondi37, A. Rajabi4,\nS. Ram\u00edrez-Uribe203, S. Randles184, T. Rao6, C.\u00d8. Rasmussen6, A. Ratkus362, P.N. Ratoff53,363,\nP. Razis364,365, P. Rebello Teles1,366, M.N. Rebelo129, M. Reboud9,10,11, S. Redaelli1, C. Regazzoni105,\nL. Reichenbach1,367, M. Reissig132, E. Renou105, A. Renter\u00eda-Olivo318, J. Reuter4, S. Rey105,\nA. Ribon1, D. Ricci1, W. Riegler1, M. Rignanese68,164, S. Rimjaem368, R.A. Rimmer369, R. Rinaldesi1,\nL. Rinolfi1,293, O. Rios1, G. Ripellino130, B. Rivas370, A. Rivetti60, T. Robens371, F. Robert183,\nE. Robutti140, C. Roderick1, G. Rodrigo318, M. Rodr\u00edguez-Cahuantzi215, L. R\u00f6hrig154,155,244,\nM. Roig372, F. Rojat108, J. Rojo201,373, J. Roloff232, P. Roloff1, A. Romanenko37, A. Romero Francia1,\nH. Romeyer374, N. Rompotis184, N. Rongieras102, G. Rosaz1, K. Roslon375, M. Rossetti Conti44,\nA. Rossi63,64, E. Rossi35,36, L. Rossi44,45, A.N. Rossia68,164, S. Rostami38, G. Roy1, B. Rubik37,\nI. Ruehl1, A. Ruiz-Jimeno376, R. Ruprecht132, J.P. Rutherfoord360, L. Rygaard4, M.S. Ryu295,\nL. Sabato1,114, G. Sadowski9,42,43, D. Saez de Jauregui132,377, M. Sahin378, A. Sailer1, M. Saito379,\nP. Saiz1, G.P. Salam380,381, R. Salerno9,81,82, T. Salmi297, B. Salvachua1, J.P.T. Salvesen1,8,136,\nB. Salvi299, D. Sampsonidis284, Y. Villamizar137,138,139, C. Sandoval331, S. Sanfilippo2,\nE. Santopinto140, R. Santoro44,134, X. Sarasola114, L. Sarperi287, I.H. Sarp\u00fcn382, S. Sasikumar1,\nM. Sauvain383, A. Savoy-Navarro3,9, R. Sawada379, G. Sborlini384, J. Scamardella35,36, M. Schaer2,\nM. Schaumann1,4, M. Schenk1, C. Scheuerlein1, C. Schiavi140,317, A. Schloegelhofer1, D. Schoerling1,\nix\n\nA. Sch\u00f6ning264, S. Schramm101, D. Schulte1, P. Schwaller251,385, A. Schwartzman7, Ph. Schwemling3,\nR. Schwienhorst386, A. Sciandra6, L. Scibile1, I. Scimemi387, E. Scomparin60, C. Sebastiani1,\nB. Seeber388, J.T. Seeman7, F. Sefkow4, M. Seidel2,114, S. Seidel74, J. Seixas339,389,390, N. Selimovi\u00b4c68,\nM. Selvaggi1, C. Senatore101, A. Senol194, N. Serra73, A. Seryi369, A. Sfyrla101, Pramond Sharma391,\nPunit Sharma6, C.J. Sharp1, L. Shchutska114, V. Shiltsev392, M. Siano44,45, R. Sierra1, E. Silva29,\nR.C. Silva47,343, L. Silvestrini170, F. Simon132, G. Simonetti1, R. Simoniello1, B.K. Singh393,\nS. Singh6, B. Singhal79, A. Siodmok1,355, Y. Sirois9,81,82, E. Sirtori149, B. Sitar394, D. Sittard1,\nE. Sitti150, T. Sj\u00f6strand59, P. Skands395, L. Skinnari292, K. Skoufaris1, K. Skovpen327, M. Skrzypek107,\nP. Slavich137,138,139, V. Slokenbergs23, V. Smaluk6, J. Smiesko1,396, S.S. Snyder6, E. Solano171,\nP. Sollander1, O.V. Solovyanov1,9,154, M. Son397, F. Sonnemann1, R. Soos1,9,10, F. Sopkova189,\nT. Sorais398, M. Sorbi44,45, S. Sorti44,45, R. Soualah399, M. Souayah1, L. Spallino48, S. Spanier400,\nP. Spiller258, M. Spira2, D. Stagnara102, M. Stallmann186, D. Standen1, J.L. Stanyard1, B. Stapf1,\nG.H. Stark230, M. Statera44, C. Staudinger1,204, G. Streicher401, N.P. Strohmaier2, R. Stroynowski106,\nS. Stucci6, G. Stupakov7, S. Su360, A. Sublet1, K. Sugita258, M.K. Sullivan7, S. Sultansoy24,\nI. Syratchev1, R. Szafron6, A. Sznajder402, W. Tachon403, N.D. Tagdulang37,171,336, N.A. Tahir258,\nY. Takahashi123, J. Tamazirt9,10,11, S. Tang6, Y. Tanimoto210, I. Tapan274, G.F. Tassielli12,404,\nA.M. Teixeira9,154,155, V.I. Telnov119, H.H.J. Ten Kate1,405, V. Teotia6, J. ter Hoeve298, A. Thabuis1,\nG.T. Telles19, A. Tishelman-Charny6, S. Tissandier108, S. Tizchang14,406, J.-P. Tock1, B. Todd1,\nL. Toffolin1,167,407, A. Tolosa-Delgado1, R. Tom\u00e1s Garc\u00eda1, T. Tomasini408, G. Tonelli40,77, T. Tong409,\nF. Toral27, T. Torims1,362, L. Torino171, K. Torokhtii29, R. Torre140, E. Torrence410, R. Torres53,184,\nT. Mitsuhashi210, A. Tracogna149, O. Traver171, D. Treille1, A. Tricoli6, P. Trubacova1, E. Tsesmelis1,\nG. Tsipolitis268, V. Tsulaia141, B. Tuchming3, C.G. Tully163, I. Turk Cakir58, C. Turrioni63,\nJ. Tynan105, F.P. Ucci127,350, S. Udongwo411, C.S. \u00dcn274, A. Unnervik1, A. Upegui99,100,\nJ.P. Uribe-Ram\u00edrez203, J. Uythoven1, R. Vaglio36,91, F. Valchkova-Georgieva412, P. Valente170,\nR.U. Valente170, A.-M. Valente-Feliciano369, G. Valentino1,192, C.A. Valerio-Lizarraga203,323,\nS. Valette1, J.W.F. Valle318, L. Valle1, N. Valle127, N. Vallis1,2,114, G. Vallone141, P. van Gemmeren158,\nW. Van Goethem1, P. van Hees59, U. van Rienen411, L. van Riesen-Haupt1,114, P. Van Trappen1,\nM. Vande Voorde413,414, A.L. Vanel1, E.W. Varnes360, J.-L. Vay141, F. Veit285, I. Veliscek6, R. Veness1,\nA. Ventura159,231, M. Verducci40,77, C.B. Verhaaren415, C. Vernieri7, A.P. Verweij1, J.-F. Vian416,\nA. Vicini44,45, N. Vignaroli159,231, S. Vignetti149, M.C. Villeneuve218, I. Vivarelli25,26,\nE. Voevodina1,131, D.M. Vogt417, B. Voirin418, S. Voiriot105, J. Voiron144, P. Vojtyla1, V. V\u00f6lkl1,\nL. von Freeden1, Z. Vostrel1,419, N. Voumard1, E. Vryonidou52, V. Vysotsky119, R. Wallny150,\nL.-T. Wang420, Y. Wang9,10,11, R. Wanzenberg4, B.F.L. Ward421, N. Wardle181, Z. Wa\u00b8s107,\nL. Watrelot1, A.T. Watson422, M.F. Watson422, M.S. Weber89, C.P. Welsch53,184, M. Wendt1,6,\nJ. Wenninger1, B. Weyer1, G. White423, S. White306, B. Wicki1, M. Widorski1, U.A. Wiedemann1,\nA.R. Wiederhold52, A . Wiedl132, H.-U. Wienands158, A. Wieser150, C. Wiesner1, H. Wilkens1,\nD. Willi424, P.H. Williams53,425, S.L. Williams32, A. Winter422, R.B. Wittwer73, D. Wollmann1,\nY. Wu114, Z. Wu9,16,17, J. Xiao9,56,57, K. Xie386, S. Xie37,333, M. Yalvac22, F. Yaman425,426,\nW.-M. Yao141, M. Yeresko9,154,155, A. Yilmaz194, H.D. Yoo275, T. You208, F. Yu251,385, S.S. Yu79,\nT.-T. Yu410, S. Yue1, A. Zaborowska1, M. Zahnd105, C. Zamantzas1, G. Zanderighi65,131, C. Zannini1,\nR. Zanzottera44,45, P. Zaro102, R. Zennaro2, M. Zerlauth1, H. Zhang202, J. Zhang158, Y. Zhang202,\nZ. Zhang9,10,202, Y. Zhao1, Y.-M. Zhong427, B. Zhou303, D. Zhou210, J. Zhu303, G. Zick372,\nM.A. Zielinski1, E. Zimmermann105, A. Zingaretti68,164, J. Zinn-Justin3, A.V. Zlobin37, M. Zobov48,\nF. Zomer9,10,11, S. Zorzetti37, X. Zuo132, J. Zurita318, V.V. Zutshi392, M. Zykova2.\n\u2020 deceased\n1 Switzerland - CERN, European Organization for Nuclear Research\n2 Switzerland - PSI, Paul Scherrer Institute\n3 France - CEA/Irfu, Commissariat \u00e0 l\u2019Energie Atomique et aux Energies Alternatives, Institut de\nrecherche sur les lois fondamentales de l\u2019Univers\nx\n\n4 Germany - DESY, Deutsches Elektronen-Synchrotron\n5 Germany - Humboldt-Universit\u00e4t zu Berlin\n6 United States - BNL, Brookhaven National Laboratory\n7 United States - SLAC National Accelerator Laboratory\n8 United Kingdom - University of Oxford\n9 France - CNRS/IN2P3, Centre National de la Recherche Scientifique, Institut National de\nPhysique Nucl\u00e9aire et de Physique des Particules\n10 France - IJCLab, Laboratoire de Physique des 2 Infinis Ir\u00e8ne Joliot Curie\n11 France - Universit\u00e9 Paris-Saclay et Universit\u00e9 Paris-Cit\u00e9\n12 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bari\n13 Italy - Universit\u00e0 di Bari\n14 Iran - IPM, Institute for Research in Fundamental Science\n15 Iran - Malayer University\n16 France - LAPP, Laboratoire d\u2019Annecy de Physique des Particules\n17 France - Universit\u00e9 Savoie Mont Blanc\n18 Serbia - University of Belgrade\n19 Spain - ICMAB/CISC, Institut de Ci\u00e8ncia de Materials de Barcelona, Consejo Superior de\nInvestigaciones Cient\u00edificas\n20 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata\n21 Italy - Universit\u00e0 Roma Tor Vergata\n22 T\u00fcrkiye - Yozgat Bozok \u00dcniversitesi\n23 United States - Texas Tech University\n24 T\u00fcrkiye - TOBB ETU, TOBB Ekonomi ve Teknoloji \u00dcniversitesi\n25 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna\n26 Italy - Universit\u00e0 di Bologna\n27 Spain - CIEMAT, Centro de Investigaciones Energ\u00e9ticas, Medioambientales y Tecnol\u00f3gicas\n28 Saudi Arabia - KACST, King Abdulaziz City for Science and Technology\n29 Italy - Universit\u00e0 Roma Tre\n30 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano-Bicocca\n31 Italy - Universit\u00e0 di Milano-Bicocca\n32 United Kingdom - University of Cambridge\n33 T\u00fcrkiye - \u02d9Istanbul \u00dcniversitesi\n34 T\u00fcrkiye - Eski\u00b8sehir Teknik \u00dcniversitesi\n35 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli\n36 Italy - Universit\u00e0 di Napoli Federico II\n37 United States - FNAL, Fermi National Accelerator Laboratory\n38 Iran - University of Tehran\n39 Iran- FUM, Ferdowsi University of Mashhad\n40 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa\n41 United States - University of Texas Austin\n42 France - IPHC, Institut Pluridisciplinaire Hubert Curien\n43 France - Universit\u00e9 de Strasbourg\n44 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano\n45 Italy - Universit\u00e0 di Milano\nxi\n\n46 Switzerland - PIBG, P\u00f4le Invert\u00e9br\u00e9s du Basin Genevois\n47 Brazil - UFRN, Universidade Federal do Rio Grande do Norte\n48 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati\n49 Switzerland - UNIBAS, University of Basel\n50 Italy - Politecnico di Bari\n51 Portugal - LIP, Laborat\u00f3rio de Instrumenta\u00e7\u00e3o e F\u00edsica Experimental de Part\u00edculas\n52 United Kingdom - University of Manchester\n53 United Kingdom - CI, Cockcroft Institute\n54 United States - Brandeis University\n55 Armenia - A. Alikhanyan National Laboratory\n56 France - IP2I, Institut de Physique des 2 Infinis de Lyon\n57 France - Universit\u00e9 Claude Bernard Lyon 1\n58 T\u00fcrkiye - Ankara \u00dcniversitesi\n59 Sweden - Lund University\n60 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Torino\n61 United Arab Emirates - New York University Abu Dhabi\n62 United States - Stony Brook University\n63 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia\n64 Italy - Universit\u00e0 di Perugia\n65 Germany - Technische Universit\u00e4t M\u00fcnchen\n66 T\u00fcrkiye - Hatay Mustafa Kemal \u00dcniversitesi\n67 T\u00fcrkiye - Do\u02d8gu\u00b8s \u00dcniversitesi\n68 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Padova\n69 People\u2019s Republic of China - Harbin Institute of Technology\n70 United States - University of Wisconsin-Madison\n71 United Kingdom - RAL, Rutherford Appleton Laboratory, Science and Technology Facilities\nCouncil\n72 India - IMSc, Institute of Mathematical Sciences, Chennai\n73 Switzerland - Universit\u00e4t Z\u00fcrich\n74 United States - University of New Mexico\n75 France - CPPM, Centre de Physique des Particules de Marseille\n76 France - Aix-Marseille Universit\u00e9\n77 Italy - Universit\u00e0 di Pisa\n78 Hungary - HUN-REN Wigner Research Centre for Physics\n79 United States - Catholic University of America\n80 United States - Duke University\n81 France - LLR, Laboratoire Leprince-Ringuet\n82 France - \u00c9cole Polytechnique, Institut Polytechnique de Paris\n83 Canada - TRIUMF, Canada\u2019s National Laboratory for Particle and Nuclear Physics\n84 Canada - Simon Fraser University\n85 Italy - FEEM, Fondazione Ente Nazionale Idrocarburi (ENI) Enrico Mattei\n86 France - BRGM, Bureau de Recherches G\u00e9ologiques et Mini\u00e8res\n87 T\u00fcrkiye - I\u00b8s\u0131k \u00dcniversitesi\n88 T\u00fcrkiye - \u02d9Istanbul Teknik \u00dcniversitesi\nxii\n\n89 Switzerland - UNIBE, University of Bern\n90 Italy - Universit\u00e0 di Roma la Sapienza\n91 Italy - CNR-SPIN, Consiglio Nazionale delle Ricerche\n92 France - Expert naturaliste et entomologiste\n93 United States - ORNL, Oak Ridge National Laboratory\n94 Austria - HEPHY, Institut f\u00fcr Hochenergiephysik\n95 Switzerland - Geos, Bureau d\u2019ing\u00e9nieurs conseils en g\u00e9otechnique, g\u00e9nie civil, hydraulique et\nenvironnement\n96 France - APC, Laboratoire AstroParticule et Cosmologie\n97 France - Universit\u00e9 Paris Cit\u00e9\n98 Austria - TUWIEN, Technische Universit\u00e4t Wien\n99 Switzerland - HEPIA, Haute \u00c9cole du Paysage, d\u2019Ing\u00e9nierie et d\u2019Architecture de Gen\u00e8ve\n100 Switzerland - HES-SO University of Applied Sciences and Arts Western Switzerland\n101 Switzerland - UNIGE, Universit\u00e9 de Gen\u00e8ve\n102 France - SETEC ALS, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en infrastructures de transport, g\u00e9nie civil et\nenvironnement\n103 United States - East Texas A&M University\n104 Switzerland - Amberg Engineering Ltd\n105 Switzerland - ECOTEC Environnement SA, Bureau d\u2019\u00e9tudes et de conseil en environnement\n106 United States - Southern Methodist University\n107 Poland - IFJ PAN, Institute of Nuclear Physics, Polish Academy of Sciences\n108 France - Cerema, \u00e9tablissement public pour l\u2019\u00e9laboration, le d\u00e9ploiement et l\u2019\u00e9valuation de\npolitiques publiques d\u2019am\u00e9nagement et de transport\n109 United Kingdom - Rendel Ltd, Engineering design consultancy firm\n110 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre\n111 T\u00fcrkiye - \u02d9Istanbul Beykent \u00dcniversitesi\n112 United States - University of Iowa\n113 India - Indian Institute of Technology Kanpur\n114 Switzerland - EPFL, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne\n115 Germany - Universit\u00e4t Hamburg, Fakult\u00e4t f\u00fcr Mathematik, Informatik und Naturwissenschaften\n116 Belgium - VUB, Vrije Universiteit Brussel\n117 France - LPNHE, Laboratoire de Physique Nucl\u00e9aire et de Hautes \u00c9nergies\n118 Italy - Scuola Superiore Meridionale\n119 Affiliated with an institute formerly covered by a cooperation agreement with CERN\n120 Canada - University of Saskatchewan and the Canadian Light Source\n121 United Kingdom - University of Bristol\n122 United States - Northwestern University\n123 United States - University of Florida\n124 Canada - York University\n125 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari\n126 Italy - Universit\u00e0 di Cagliari\n127 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pavia\n128 Canada - Queen\u2019s University\n129 Portugal - CFTP-IST, Centro de F\u00edsica T\u00e9orica de Part\u00edculas, Instituto Superior Tecnico,\nxiii\n\nUniversidade de Lisboa\n130 Sweden - Uppsala University\n131 Germany - MPP, Max-Planck-Institut f\u00fcr Physik Garching\n132 Germany - KIT, Karlsruher Institut f\u00fcr Technologie\n133 Ukraine - NSC KIPT, National Science Center Kharkiv Institute of Physics and Technology\n134 Italy - Universit\u00e0 degli Studi dell\u2019Insubria\n135 Germany - Albert-Ludwigs-Universit\u00e4t Freiburg\n136 United Kingdom - JAI, John Adams Institute for Accelerator Science, University of Oxford\n137 France - CNRS/INP, Centre National de la Recherche Scientifique, Institut de Physique\n138 France - LPTHE, Laboratoire de Physique Th\u00e9orique et Hautes Energies\n139 France - Sorbonne Universit\u00e9\n140 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Genova\n141 United States - LBNL, Lawrence Berkeley National Laboratory\n142 Italy - IIT, Instituto Italiano di Tecnologia\n143 T\u00fcrkiye - G\u00fcm\u00fc\u00b8shane \u00dcniversitesi\n144 Switzerland - WSP Ing\u00e9nieurs Conseils SA\n145 Mexico - UADY, Autonomous University of Yucatan\n146 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara\n147 Italy - Universit\u00e0 di Ferrara\n148 France - MARCELEON, Cabinet d\u2019ing\u00e9nierie juridique et fonci\u00e8re\n149 Italy - CSIL (Economic Research Institute)\n150 Switzerland - ETHZ, Swiss Federal Institute of Technology Zurich\n151 Spain - UAH, Universidad de Alcal\u00e1 Madrid\n152 France - CIA, Conseil Ing\u00e9nierie Acoustique\n153 France - Evinerude, Bureau d\u2019\u00e9tudes environnementales\n154 France - LPCA, Laboratoire de Physique de Clermont Auvergne\n155 France - Universit\u00e9 Clermont Auvergne\n156 Australia - ANSTO, Australian Synchrotron\n157 India - Brahmananda Keshab Chandra College\n158 United States - ANL, Argonne National Laboratory\n159 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Lecce\n160 Italy - Universit\u00e0 di Palermo\n161 Poland - Wroc\u0142aw University of Science and Technology\n162 United States - Rutgers University\n163 United States - Princeton University\n164 Italy - Universit\u00e0 di Padova\n165 T\u00fcrkiye - IUE, \u02d9Izmir Ekonomi \u00dcniversitesi\n166 T\u00fcrkiye - Ege \u00dcniversitesi\n167 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Udine\n168 Italy - Universit\u00e0 di Udine\n169 United States - University of Massachusetts Amherst\n170 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma\n171 Spain - CELLS/ALBA, Consortium for the Construction, Equipment and Exploitation of the\nSynchrotron Light Laboratory\nxiv\n\n172 France - LPSC, Laboratoire de Physique Subatomique et de Cosmologie\n173 France - Universit\u00e9 Grenoble Alpes\n174 Italy - Universit\u00e0 degli Studi di Napoli Parthenope\n175 United States - National High Magnetic Field Laboratory\n176 United States - Florida State University\n177 South Africa - University of Johannesburg\n178 Spain - IGFAE, Instituto Galego de Fisica de Altas Enerx\u00edas, Universidade de Santiago de\nCompostela\n179 United Kingdom - LSE, London School of Economics\n180 Spain - Universidade de Santiago de Compostela\n181 United Kingdom - Imperial College London\n182 United States - MIT, Massachusetts Institute of Technology\n183 France - CETU, Centre d\u2019Etude des Tunnels\n184 United Kingdom - University of Liverpool\n185 Switzerland - Linde Kryotechnik AG\n186 Switzerland - ILF Consulting Engineers\n187 Denmark - NBI, Niels Bohr Institute\n188 Japan - Hokkaido University\n189 Czech Republic - CUNI, Charles University\n190 Spain - Universidad de Granada\n191 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Firenze\n192 Malta - University of Malta\n193 United States - BU, Boston University\n194 T\u00fcrkiye - IBU, Bolu Abant \u02d9Izzet Baysal \u00dcniversitesi\n195 Germany - Julius-Maximilians-Universit\u00e4t W\u00fcrzburg\n196 Australia - University of Adelaide\n197 Finland - HIP, Helsinki Institute of Physics, University of Helsinki\n198 Belgium - ULB, Universit\u00e9 Libre de Bruxelles\n199 Germany - IMA, Institut f\u00fcr Maschinenelemente, Universit\u00e4t Stuttgart\n200 Belgium - CP3, Centre de Cosmologie, de Physique des Particules et de Ph\u00e9nom\u00e9nologie,\nUniversit\u00e9 Catholique de Louvain\n201 Netherlands - NIKHEF, Nationaal instituut voor subatomaire fysica\n202 People\u2019s Republic of China - IHEP, Chinese Academy of Sciences\n203 Mexico - UAS, Universidad Aut\u00f3noma de Sinaloa\n204 Austria - BOKU, Universit\u00e4t f\u00fcr Bodenkultur Wien\n205 United States - Purdue University\n206 India - University of Delhi\n207 France - Ginger BURGEAP, bureau d\u2019\u00e9tudes en environnement\n208 United Kingdom - King\u2019s College London\n209 United States - University of Maryland\n210 Japan - KEK, High Energy Accelerator Research Organization\n211 Switzerland - Geoenergy, Reservoir Geology and Basin Analysis Group\n212 France - SETEC International, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie en charge des transports et des infrastructures\n213 T\u00fcrkiye - KKU, K\u0131r\u0131kkale \u00dcniversitesi\nxv\n\n214 France - SETEC LERM, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en mat\u00e9riaux de construction\n215 Mexico - BUAP, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla\n216 United States - Stanford University\n217 United States - University of Pittsburgh\n218 Austria - MUL, Montanuniversit\u00e4t Leoben, Lehrstuhl f\u00fcr Subsurface Engineering, Geotechnik\nund unterirdisches Bauen\n219 Austria - MUL-ZaB, Underground Research Center, Zentrum am Berg\n220 Spain - IFAE, Institut de F\u00edsica d\u2019Altes Energies\n221 Switzerland - FHNW, University of Applied Sciences Northwestern Switzerland\n222 India - UPES, University of Petroleum and Energy Studies\n223 France - GANIL, Grand Acc\u00e9l\u00e9rateur National d\u2019Ions Lourds\n224 France - Universit\u00e9 Caen Normandie\n225 Brazil - UFRGS, Universidade Federal do Rio Grande do Sul\n226 Germany - Technische Universit\u00e4t Darmstadt\n227 Poland - University of Silesia in Katowice\n228 Portugal - Universidade de Coimbra\n229 Brazil - UFPel, Universidade Federal de Pelotas\n230 United States - University of California Santa Cruz\n231 Italy - Universit\u00e0 del Salento\n232 United States - Brown University\n233 United States - University of California Berkeley\n234 Italy - Universit\u00e0 di Torino\n235 United States - Johns Hopkins University\n236 People\u2019s Republic of China - Fudan University\n237 France - LAPTh, Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique\n238 People\u2019s Republic of China - Dongguan University of Technology\n239 T\u00fcrkiye - Kahramanmara\u00b8s S\u00fct\u00e7\u00fc \u02d9Imam \u00dcniversitesi\n240 Mexico - UNACH, Universidad Aut\u00f3noma de Chiapas\n241 Mexico - MCTP, Mesoamerican Centre for Theoretical Physics\n242 Mexico - UAZ, Universidad Aut\u00f3noma de Zacatecas\n243 Finland - University of Jyv\u00e4skyl\u00e4\n244 Germany - Technische Universit\u00e4t Dortmund\n245 United Kingdom - Overleaf\n246 United States - University of Virginia\n247 United States - Cornell University\n248 United States - FIT, Florida Institute of Technology\n249 Switzerland - Shirokuma GmbH\n250 Pakistan - National Centre for Physics\n251 Germany - Johannes Gutenberg Universit\u00e4t Mainz\n252 Pakistan - PAEC, Pakistan Atomic Energy Commission\n253 India - Mathabhanga College\n254 India - Harish-Chandra Research Institute\n255 Germany - MPIK, Max-Planck-Institut f\u00fcr Kernphysik Heidelberg\n256 Sweden - European Spallation Source ERIC\nxvi\n\n257 France - Centre de calcul de l\u2019IN2P3\n258 Germany - GSI, Helmholtzzentrum f\u00fcr Schwerionenforschung GmbH\n259 Republic of Korea - IBS, Institute for Basic Science, Center for Theoretical Physics of the\nUniverse\n260 Poland - University of Warsaw\n261 Slovenia - University of Ljubljana\n262 Slovenia - Jozef Stefan Institute\n263 France - Microhumus, Bureau d\u2019\u00e9tude et d\u2019ing\u00e9nierie sp\u00e9cialis\u00e9 dans la gestion des sols d\u00e9grad\u00e9s\n264 Germany - Fakult\u00e4t f\u00fcr Physik und Astronomie, Universit\u00e4t Heidelberg\n265 T\u00fcrkiye - Ni\u02d8gde \u00d6mer Halisdemir \u00dcniversitesi\n266 T\u00fcrkiye - Giresun \u00dcniversitesi\n267 Hungary - University of Miskolc\n268 Greece - NTUA, National Technical University of Athens\n269 Switzerland - Transmutex SA\n270 Ireland - DIAS, Dublin Institute for Advanced Studies, School of Theoretical Physics\n271 Poland - AGH, University of Science and Technology\n272 Iran - University of Science and Technology of Mazandaran\n273 United Kingdom - IPPP, Institute for Particle Physics Phenomenology, Durham University\n274 T\u00fcrkiye - Bursa Uluda\u02d8g \u00dcniversitesi\n275 Republic of Korea - YU, Yonsei University\n276 Affiliated with an international laboratory covered by a cooperation agreement with CERN\n277 France - CPT, Centre de Physique Th\u00e9orique\n278 France - Aix-Marseille Universit\u00e9 et Universit\u00e9 du Sud Toulon Var\n279 Republic of Korea - KIAS, Korea Institute for Advanced Study\n280 Canada - Carleton University\n281 Greece - FEAC Engineering P.C.\n282 Greece - UPATRAS, University of Patras\n283 United States - University of Kansas\n284 Greece - AUTH, Aristotle University of Thessaloniki\n285 Germany - IML, Fraunhofer-Institut f\u00fcr Materialfluss und Logistik\n286 Germany - RWTH Aachen, Rheinisch-Westf\u00e4lische Technische Hochschule Aachen\n287 Switzerland - ZHAW, Zurich University of Applied Sciences\n288 Gernany - Universit\u00e4t M\u00fcnster\n289 South Africa - University of the Witwatersrand\n290 Austria - Fachhochschule Technikum Wien\n291 United States - University of California Irvine\n292 United States - Northeastern University\n293 France - ESI, European Scientific Institute\n294 Republic of Korea - UOS, University of Seoul\n295 Republic of Korea - KNU Kyungpook National University\n296 Republic of Korea - KU, Korea University\n297 Finland - Tampere University\n298 United Kingdom - University of Edinburgh\n299 Switzerland - BG Ing\u00e9nieurs Conseils\nxvii\n\n300 People\u2019s Republic of China - T.-D. Lee Institute\n301 People\u2019s Republic of China - Shanghai Jiao Tong University\n302 Italy - CNR, Consiglio Nazionale delle Ricerche\n303 United States - University of Michigan\n304 United States - University of Pennsylvania\n305 United States - University of Minnesota\n306 France - ESRF, European Synchrotron Radiation Facility\n307 United Kingdom - SUSSEX, University of Sussex\n308 Italy - Universit\u00e0 di Bari Aldo Moro\n309 United Kingdom - University of Bath\n310 Italy - Scuola Normale Superiore di Pisa\n311 Brazil - Universidade de S\u00e3o Paulo\n312 Austria - Universit\u00e4t Graz\n313 Egypt - Center for High Energy Physics, Fayoum University\n314 Egypt - Center of theoretical physics, British University in Egypt\n315 Egypt - Cairo University\n316 France - Sorbonne Universit\u00e9 et Universit\u00e9 Paris Cit\u00e9\n317 Italy - Universit\u00e0 di Genova\n318 Spain - IFIC-CSIC/UV, Instituto de F\u00edsica Corpuscular, Consejo Superior de Investigaciones\nCient\u00edficas/Universidad de Valencia\n319 Switzerland - Service de g\u00e9ologie, sols et d\u00e9chets du canton de Gen\u00e8ve\n320 Estonia - NICPB, National Institute for Chemical Physics and Biophysics\n321 Estonia - UT, University of Tartu\n322 Spain - Universidad de Salamanca\n323 Mexico - UGTO, Universidad de Guanajuato\n324 Switzerland - Edaphos engineering\n325 Germany - Helmholtz-Zentrum Dresden-Rossendorf\n326 India - Tata Institute of Fundamental Research Mumbai\n327 Belgium - Universiteit Gent\n328 Italy - CNR-IOM, Consiglio Nazionale delle Ricerche\n329 Austria - JKU, Johannes Kepler Universit\u00e4t Linz\n330 Norway - University of Stavanger\n331 Colombia - Universidad Nacional de Colombia\n332 Italy - Trento Institute for Fundamental Physics and Applications\n333 United States - Caltech, California Institute of Technology\n334 Italy - Universit\u00e0 dalla Calabria\n335 Spain - IFT, Instituto de F\u00edsica Te\u00f3rica, Universidad Aut\u00f3noma de Madrid\n336 Spain - UPC, Universitat Polit\u00e8cnica de Catalunya\n337 Portugal - Departamento de F\u00edsica, Universidade do Minho\n338 Portugal - Centro de F\u00edsica das Universidades do Minho e do Porto\n339 Portugal - LaPMET, Laboratory of Physics for Materials and Emergent Technologies\n340 Norway - University of Bergen\n341 Chile - SAPHIR, Instituto Milenio de F\u00edsica Subat\u00f3mica en la Frontera de Altas Energ\u00edas\n342 Chile - Universidad Andres Bello\nxviii\n\n343 Brazil - IIP, International Institute of Physics\n344 Japan - Tokyo International University\n345 T\u00fcrkiye - \u02d9Izmir Bak\u0131r\u00e7ay \u00dcniversitesi\n346 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso\n347 Italy - Universit\u00e1 degli Studi di Cassino e del Lazio Meridionale\n348 Serbia - Vin\u02d8ca Institute of Nuclear Sciences\n349 United States - Kennesaw State University\n350 Italy - Universit\u00e0 di Pavia\n351 United States - Columbia University\n352 United States - DOE, Department of Energy of the United States of America\n353 France - IPSA, Institut Polytechnique des Sciences Avanc\u00e9es\n354 Italy - Universit\u00e0 degli Studi del Sannio\n355 Poland - UJ, Jagiellonian University\n356 Austria - Universit\u00e4t Wien\n357 Germany - Goethe-Universit\u00e4t Frankfurt, Institut f\u00fcr Angewandte Physik\n358 Germany - HFFH, Helmholtz Forschungsakademie Hessen f\u00fcr FAIR\n359 Romania - INCDTIM, National Institute for Research and Development of Isotopic and\nMolecular Technologies\n360 United States - University of Arizona\n361 Germany - Technische Universit\u00e4t Dresden\n362 Latvia - RTU, Riga Technical University\n363 United Kingdom - Lancaster University\n364 Cyprus - University of Cyprus\n365 Cyprus - Cosmos Open University\n366 Brazil - CBPF, Centro Brasileiro de Pesquisas F\u00edsicas\n367 Germany - Universit\u00e4t Bonn\n368 Thailand - CMU, Chiang Mai University\n369 United States - JLAB, Thomas Jefferson National Accelerator Facility\n370 Ecuador - ESPOL, Escuela Superior Polit\u00e9cnica del Litoral\n371 Croatia - IRB, Rudjer Boskovic Institute\n372 France - Air Liquide Advanced Technologies\n373 Netherlands - VU Amsterdam\n374 France - ING\u00c9ROP ,Groupe d\u2019ing\u00e9nierie et de conseil en mobilit\u00e9 durable, transition \u00e9nerg\u00e9tique\net cadre de vie\n375 Poland - Warsaw University of Technology\n376 Spain - IFCA, Instituto de F\u00edsica de Cantabria\n377 Germany - Institut f\u00fcr Beschleunigerphysik und Technologie\n378 T\u00fcrkiye - U\u00b8sak \u00dcniversitesi\n379 Japan - ICEPP, International Center for Elementary Particle Physics, University of Tokyo\n380 United Kingdom - Rudolf Peierls Centre for Theoretical Physics, University of Oxford\n381 United Kingdom - All Souls College, University of Oxford\n382 T\u00fcrkiye - Akdeniz \u00dcniversitesi\n383 Switzerland - Latitude Durable SARL\n384 Spain - USAL, Universidad de Salamanca\nxix\n\n385 Germany - PRISMA+ Cluster of Excellence\n386 United States - Michigan State University\n387 Spain - Universidad Complutense Madrid\n388 Switzerland - scMetrology SARL\n389 Portugal - IST, Instituto Superior Tecnico, Universidade de Lisboa\n390 Portugal - CeFEMA, Center of Physics and Engineering of Advanced Materials\n391 India - Indian Institute of Science Education and Research Mohali\n392 United States - NIU, Northern Illinois University\n393 India - Banaras Hindu University\n394 Slovakia - Comenius University\n395 Australia - Monash University\n396 Slovakia - Slovak Academy of Sciences\n397 Republic of Korea - KAIST, Korea Advanced Institute of Science and Technology\n398 France - Amberg Engineering Chamb\u00e9ry\n399 United Arab Emirates - Khalifa University of Science and Technology\n400 United States - University of Tennessee\n401 Austria - WIFO, \u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\n402 Brazil - Universidade do Estado do Rio de Janeiro\n403 France - M\u00e9lica, NATURA SCOP, \u00c9tudes et expertises environnementales\n404 Italy - Universit\u00e0 LUM, Casamassima\n405 Netherlands - University of Twente\n406 Iran - Arak University\n407 Italy - Universit\u00e0 di Trieste\n408 France - ForestAllia, Cabinet de gestion et d\u2019expertise foresti\u00e8res\n409 Germany - Universit\u00e4t Siegen\n410 United States - University of Oregon\n411 Germany - Universit\u00e4t Rostock\n412 Switzerland - CEGELEC SA\n413 Sweden - KTH, Royal Institute of Technology, Stockholm\n414 Sweden - OKC, Oskar Klein Centre for Cosmoparticle Physics\n415 United States - Brigham Young University\n416 France - Expert foncier et agricole\n417 Germany - ITSM, Institut f\u00fcr Thermische Str\u00f6mungsmaschinen und Maschinenlaboratorium,\nUniversit\u00e4t Stuttgart\n418 France - \u00c9cole Normale Sup\u00e9rieure de Lyon\n419 Czech Republic - CTU, Czech Technical University\n420 United States - University of Chicago\n421 United States - Baylor University\n422 United Kingdom - University of Birmingham\n423 United Kingdom - University of Southampton\n424 Switzerland - Swisstopo, Federal Office of Topography\n425 United Kingdom - Daresbury Laboratory, Science and Technology Facilities Council\n426 T\u00fcrkiye - IZTECH, \u02d9Izmir Y\u00fcksek Teknoloji Enstit\u00fcs\u00fc\n427 Hong Kong - City University of Hong Kong\nxx\n\nAbstract\nIn response to the 2020 Update of the European Strategy for Particle Physics, the Future Circular Collider\n(FCC) Feasibility Study was launched as an international collaboration hosted by CERN. This report\ndescribes the FCC integrated programme, which consists of two stages: an electron-positron collider\n(FCC-ee) in the first phase, serving as a high-luminosity Higgs, top, and electroweak factory; followed\nby a proton-proton collider (FCC-hh) at the energy frontier in the second phase.\nThe FCC-ee is designed to operate at four key centre-of-mass energies: the Z pole, the WW\npair production threshold, the ZH production peak, and the top/anti-top production threshold\u2014each\ndelivering the highest possible luminosities to four experiments. Over 15 years of operation, FCC-ee\nwill produce more than 6 trillion Z bosons, 200 million WW pairs, nearly 3 million Higgs bosons, and\n2 million top anti-top pairs. Precise energy calibration at the Z pole and WW threshold will be achieved\nthrough frequent resonant depolarisation of pilot bunches. The sequence of operation modes between\nthe Z, WW, and ZH substages remains flexible.\nThe FCC-hh will operate at a centre-of-mass energy of approximately 85 TeV\u2014nearly an order\nof magnitude higher than the LHC\u2014and is designed to deliver 5 to 10 times the integrated luminosity\nof the upcoming High-Luminosity LHC. Its mass reach for direct discovery extends to several tens of\nTeV. In addition to proton-proton collisions, the FCC-hh is capable of supporting ion-ion, ion-proton,\nand lepton-hadron collision modes.\nThis second volume of the Feasibility Study Report presents the complete design of the FCC-\nee collider, its operation and staging strategy, the full-energy booster and injector complex, required\naccelerator technologies, safety concepts, and technical infrastructure. It also includes the design of the\nFCC-hh hadron collider, development of high-field magnets, hadron injector options, and key technical\nsystems for FCC-hh.\nxxi\n\nPreface from CERN\u2019s Director-General\nIn 2021, in response to the 2020 update of the European Strategy for Particle Physics, the CERN Council\ninitiated the Future Circular Collider (FCC) Feasibility Study.\nThis report summarises an immense amount of work carried out by the international FCC collabo-\nration over several years. It covers, inter alia, physics objectives and potential, geology, civil engineering,\ntechnical infrastructure, territorial implementation, environmental aspects, R&D needs for the acceler-\nators and detectors, socio-economic benefits and cost. It constitutes important input for the ongoing\nupdate of the European Strategy for Particle Physics.\nThe Feasibility Study required engagement with a broad range of stakeholders. In particular,\nthroughout the Study, CERN has been accompanied by its two Host States, France and Switzerland,\nand has been working with entities at local, regional and national level. I am very grateful to the Host\nState authorities and teams for their invaluable help. Furthermore, significant sections of the Study were\nsupported by the European Union under the Horizon 2020 and Horizon Europe framework programmes.\nThe Study also greatly benefited from contributions from accelerator laboratories and universities from\nacross Europe, such as the Swiss Accelerator Research and Technology (CHART) initiative, and from\nthe Americas, Asia, Africa and Australia.\nThe proposed FCC integrated programme consists of two possible stages: an electron\u2013positron\ncollider serving as a Higgs-boson, electroweak and top-quark factory running at different centre-of-mass\nenergies, followed at a later stage by a proton\u2013proton collider operating at an unprecedented collision\nenergy of around 100 TeV. The complementary physics programmes of each stage match the physics\npriorities expressed in the 2020 update of the European Strategy for Particle Physics.\nA major achievement of the Feasibility Study is the choice of placement of the collider ring and\nthe entire infrastructure, including the surface sites and the access shafts, which was developed and\noptimised over several years following the principle \u2018avoid, reduce, compensate\u2019. Sustainability studies\nhave assessed energy efficiency, land use, water and resource management, and socio-economic impact,\nensuring that the FCC is designed in accordance with the latest environmental and societal standards.\nI would like to thank all contributors to this report for their hard work and commitment, which\nallowed the outstanding results presented here to be achieved.\nFabiola Gianotti\nCERN, Director-General\nxxii\n\nPreface from the FCC Collaboration Board Chair\nBuilding on the earlier Future Circular Collider (FCC) Conceptual Design Study conducted between\n2014 and 2018, the FCC Feasibility Study (2021\u20132025) has been undertaken by a robust international\ncollaboration, now comprising over 160 institutes worldwide. The FCC \u2018integrated programme\u2019, de-\nveloped in the framework of the Feasibility Study, consists of an initial electron-positron collider, the\nFCC-ee, which could be followed by a proton-proton collider, the FCC-hh. This staging takes into ac-\ncount the physics priorities as formulated in the updates of the European Strategy for Particle Physics of\n2012 and 2020, as well as the relative technology readiness and costs of the FCC-ee and FCC-hh.\nOver the years, I have closely followed the steady progress of the study, representing the FCC\ncollaboration at the international steering committee and participating in annual FCC Week meetings,\nwhich include sessions of the International Collaboration Board. The commitment and enthusiasm of\nthe members of the collaboration has always been impressive. The collective effort is clearly visible.\nParticipation by students and early-career researchers is increasing. There is a shared determination and\nmomentum to move forward.\nThe strong international collaboration around the FCC and its global network provide a solid foun-\ndation for the future of this project. The FCC community continues to grow, with increasing engagement\nfrom new institutes and partners worldwide. This broad support will be essential as the project enters its\nnext phase.\nThe FCC Feasibility Study demonstrates not only the technical viability of the project, but also\nthe strength of the international community that supports it. As we move towards the next step in\nthe decision-making phase, this collective effort is key to showing a possible path forward. The FCC\npromises far-reaching scientific opportunities and long-term benefits for innovation, training, and global\ncollaboration in science and technology.\nPhilippe Chomaz\nCEA, Chair of the FCC International Collaboration Board\nxxiii\n\nContents\nIntroduction to the FCC integrated project\n1\nFCC design and layout considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n1\nFCC-ee goals and and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n3\nFCC-hh goals and and parameters\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n4\nSustainability goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n4\n1\nFCC-ee collider design and performance\n7\n1.1\nBeam-beam effects, parameter choices, and luminosity\n. . . . . . . . . . . . . . . . . . .\n7\n1.2\nOptics design\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n11\n1.3\nImpact of misalignments and field errors . . . . . . . . . . . . . . . . . . . . . . . . . . .\n21\n1.4\nCollective effects\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n26\n1.5\nCollimation\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n39\n1.6\nMachine-detector interface (MDI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n44\n1.7\nEnergy calibration and polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n52\n1.8\nInjection and extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n58\n1.9\nRadiation environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n64\n1.10\nOngoing studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n69\n2\nFCC-ee collider operation concept\n79\n2.1\nOperation requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n79\n2.2\nChanging operation modes\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n80\n2.3\nOperation and performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n83\n2.4\nAvailability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101\n2.5\nOperational model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106\n2.6\nMachine Protection\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109\n3\nFCC-ee collider technical systems\n115\n3.1\nMain magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115\n3.2\nVacuum system and electron cloud mitigation\n. . . . . . . . . . . . . . . . . . . . . . . . 121\n3.3\nRadiation shielding\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133\n3.4\nRadio frequency system layout, configurations and parameters\n. . . . . . . . . . . . . . . 135\n3.5\nSurvey and alignment systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161\n3.6\nBeam intercepting devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169\n3.7\nBeam transfer systems and separators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173\n3.8\nPowering systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175\n3.9\nBeam diagnostics\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182\n3.10\nArc region: integration and supporting systems . . . . . . . . . . . . . . . . . . . . . . . . 190\n3.11\nMachine protection hard- and software systems\n. . . . . . . . . . . . . . . . . . . . . . . 202\n3.12\nAn alternative arc magnet design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206\n3.13\nDismantling FCC-ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209\nxxiv\n\n4\nFCC-ee booster design and performance\n221\n4.1\nOptics design and Beam dynamics\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221\n4.2\nCollective effects\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228\n4.3\nRadiation environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233\n4.4\nInjection and extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235\n4.5\nOngoing studies and possible upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241\n5\nFCC-ee booster operation concept\n245\n5.1\nOperation and performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245\n5.2\nRequirements\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252\n5.3\nAvailability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260\n5.4\nConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263\n6\nFCC-ee booster technical systems\n265\n6.1\nMain magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265\n6.2\nBooster vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271\n6.3\nRadio frequency system layout, configurations, and parameters . . . . . . . . . . . . . . . 277\n6.4\nBeam intercepting devices (halo collimators, beam dump) . . . . . . . . . . . . . . . . . . 280\n6.5\nBeam transfer systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281\n6.6\nBeam Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284\n6.7\nPowering system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284\n6.8\nArc region: integration and supporting systems . . . . . . . . . . . . . . . . . . . . . . . . 285\n6.9\nMachine protection\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289\n7\nFCC-ee injector complex\n291\n7.1\nInjector overview\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291\n7.2\nElectron source\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294\n7.3\nElectron linac\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295\n7.4\nPositron source and linac\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297\n7.5\nDamping ring and bunch compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308\n7.6\nHigh energy linac and Energy Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . 311\n7.7\nTransfer lines from HE-linac to Booster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316\n7.8\nRF system for linacs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319\n7.9\nAvailability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324\n7.10\nCivil engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327\n7.11\nTechnical infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329\n7.12\nOngoing studies and possible upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331\n8\nTechnical infrastructure for FCCs\n333\n8.1\nRequirements and design considerations\n. . . . . . . . . . . . . . . . . . . . . . . . . . . 333\n8.2\n3D Integration Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335\n8.3\nCooling and ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360\nxxv\n\n8.4\nPower consumption and electricity distribution . . . . . . . . . . . . . . . . . . . . . . . . 371\n8.5\nCryogenic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395\n8.6\nTransport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409\n8.7\nCommunications, computing and data services . . . . . . . . . . . . . . . . . . . . . . . . 423\n8.8\nRobotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426\n8.9\nGeodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429\n8.10\nAvailability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433\n9\nFCC safety concepts\n437\n9.1\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437\n9.2\nSafety goals & objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437\n9.3\nPlanning for safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438\n9.4\nSafety concept for the operation phase\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . 441\n9.5\nSafety during the construction and installation phases\n. . . . . . . . . . . . . . . . . . . . 493\n9.6\nConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497\n10\nFCC-hh collider design and performance\n499\n10.1\nDesign and performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499\n10.2\nFCC-hh layout and optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500\n10.3\nFCC-hh injection\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518\n10.4\nHigh-field magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532\n10.5\nFCC-hh accelerator systems and technical infrastructures\n. . . . . . . . . . . . . . . . . . 546\nReferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556\nAppendices\n588\nA\nCosts\n589\nA.1\nFCC-ee construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589\nA.2\nFCC-ee operation costs\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589\nA.3\nFCC-hh Construction and Operational Costs . . . . . . . . . . . . . . . . . . . . . . . . . 590\nB\nInstallation\n591\nB.1\nInstallation planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591\nxxvi\n\nIntroduction to the FCC integrated project\nFCC design and layout considerations\nThe Future Circular Collider (FCC) \u2018integrated programme\u2019 consists of an initial electron-positron col-\nlider FCC-ee, which is later followed by a proton-proton collider, FCC-hh. This comprehensive pro-\ngramme is well matched to the current scientific landscape after 15 years of LHC operation. The pro-\nposed staging takes into account: (1) the physics priorities as developed and stated by the Updates of the\nEuropean Strategy for Particle Physics in 2013 and 2020; and (2) the relative technology readiness and\ncosts of FCC-ee and FCC-hh.\nBoth FCC-ee and FCC-hh are installed in the same 91 km circumference tunnel close to CERN,\nwhich allows reusing all of the FCC-ee civil engineering and much of the technical infrastructure for\nthe subsequent FCC-hh, thereby maximising the return on investment and ensuring guaranteed physics\ndeliverables along with the broadest and most versatile exploration potential of the intensity and energy\nfrontiers. Taking advantage of m a perfect four-fold superperiodicity, FCC-ee and FCC-hh each accom-\nmodate four detectors. The two FCC stages, FCC-ee and FCC-hh, are optimised so as to enable the\nwidest possible physics programme, with ample complementarity and synergies between stage 1 and\nstage 2.\nThe FCC-ee does not only serve as a Higgs and top factory, but it also produces several 1012 Z\nbosons, opening another access to new physics. The hadron collider, FCC-hh, operates at a centre-\nof-mass energy of about 85 TeV, extending the energy frontier by almost an order of magnitude com-\npared with the LHC, and providing a 5\u201310 times higher integrated luminosity than the upcoming High-\nLuminosity LHC. The mass reach for direct discovery at FCC-hh amounts to several tens of TeV, and it\nallows, for example, the direct production of new particles, whose existence could already be indirectly\nexposed by precision measurements at FCC-ee. The FCC-hh hadron collider can also accommodate ion\nand lepton-hadron collision options, allowing for complementary physics explorations.\nThe layouts of the FCC-ee electron-positron collider and its injector design are fully compatible\nwith the demands of, and do not compromise the performance of, the future hadron collider FCC-hh.\nThe main ring optics and RF configurations for both colliders were refined both to simplify operation\nacross the energy range of FCC-ee and to enable a smooth transition to FCC-hh after the completion of\nthe FCC-ee research programme.\nThe FCC-hh baseline assumes 14 Tesla Nb3Sn magnets which provide for a collision centre-of-\nmass energy of 85 TeV, with an R&D path towards HTS magnets, that would enable higher collision\nenergies and/or reduced energy consumption. Designing a detector for a \u223c100 TeV hadron collider is a\nchallenging enterprise. Recent detailed studies prove that it should be possible to build a detector that\ncan fully exploit the physics potential of such a machine, provided there is investment in the necessary\ndetector R&D. The experience gained from the Phase-II upgrades of the LHC detectors for the HL-LHC,\ndevelopments for further exploitation of the LHC, and ongoing detector R&D for future Higgs factories\nwill be important stepping stones in this endeavour.\nAs noted, the FCC layout is designed to accommodate, first, an e+/e\u2212and, then, a hadron-hadron\ncollider in the same tunnel. The arc tunnel diameter of 5.5 metres is larger than the LEP/LHC tunnel and\nsatisfies the integration requirements of both colliders while also being fully compatible with the safety\nconcept. Tunnel length and location are chosen to be consistent with the placement constraints described\nin Volume 3 and to allow hadron injection from either the SPS tunnel or the LHC tunnel at CERN, and\nlepton injection from an injector situated on the CERN Pr\u00e9vessin site. The FCC tunnel has also been\ndeveloped so that the lepton and hadron colliders can house four experiments each.\nA four-fold super-periodicity, with a particle physics experiment located at each quarter of the\n1\n\ncircumference, makes the ring appear like a four times smaller machine with a single interaction point.\nThe super-periodicity, therefore, reduces the density of strong resonances in the betatron tune diagram,\nallowing a maximum beam-beam tune shift and optimum performance, for both lepton and hadron ma-\nchines. Technical straight sections are located half-way between experiment insertion and these are used\nto accommodate important accelerator equipment and systems. The FCC layout accommodates 8 arcs\nof equal length, 4 technical straights (around the points PB, PF, PH and PL) and 4 experimental straights\n(around points PA, PD, PG and PJ), with lengths listed in Table 1. The final layout is illustrated in Figs. 1\nand 2 for FCC-ee and FCC-hh, respectively. The collision points of FCC-hh lie on top of the FCC-\nee interaction points, facilitating the sharing of some experimental infrastructure between FCC-ee and\nFCC-hh.\nTable 1: Parameters of the tunnel layout for the two FCC colliders.\ncircumference\narc (\u00d78)\ntechnical straight (\u00d74)\nexperimental straight (\u00d74)\n[m]\n[m]\n[m]\n[m]\n90 657.400\n9616.175\n2032.000\n1400.000\nFig. 1: The layout of the FCC-ee illustrating the four collision points and the four technical insertions.\nThe FCC-ee is conceived as a double-ring collider with separate beam pipes for electrons and\npositrons. Its luminosity is maximised by regular top-up injection from a full-energy booster synchrotron,\nwhich must also be located in the collider tunnel (sketched schematically by the green circle in Fig. 1).\nTransfer lines connecting from the FCC-ee injector on the CERN Pr\u00e9vessin site to the booster are indi-\ncated schematically around PA. For the FCC-ee, the straight around PL houses the booster radiofrequency\n(RF) system, and the one at PH accommodates the main-ring RF systems, as indicated in Fig. 1. Injection\n2\n\ninto the collider and extraction are integrated in a single technical straight section at PB. Both betatron\ncleaning and momentum collimation systems are located in the remaining straight section around PF, as\nshown in Fig. 1.\nFor the FCC-hh, two high-luminosity experiments can be installed in the diametrically opposed\nlocations PA and PG, and two special-purpose experiments in PD and PJ. The betatron collimation is\naccommodated in the technical straight at PH, while the momentum collimation is housed in the technical\nstraight around PB. In case of an abort, the beam is extracted in the straight around PF. The FCC-hh RF\nsystem is installed at PL, which for FCC-ee houses the booster RF. Note that the FCC-hh injection\nsystems are installed in PB and PL, which are, therefore, shared between two accelerator systems. The\nhadron transfer line tunnels also connect to the main tunnel in the vicinity of PA. The transfer lines\nthemselves continue inside the ring tunnel, on top of the arcs connecting PA with PL and PB where the\ncounter-clockwise and clockwise beams are injected into the collider rings, respectively.\nFig. 2: The layout of the FCC-hh illustrating the four collision points and the four technical insertions.\nFCC-ee goals and parameters\nThe FCC-ee achieves maximum peak and integrated luminosities at four main working points, corre-\nsponding to the Z pole, the WW threshold, the (Z)H production peak and the t\u00aft threshold. Integrated\nluminosity targets amount to the production of 6 \u00d7 1012 Z bosons (as required by the search for sterile\nright-handed neutrinos), more than 2 \u00d7 108 WW pairs, in excess of 2 \u00d7 106 Higgs bosons, and 2 \u00d7 106\nt\u00aft pairs. All these objectives can be achieved during a 15-year period, which includes a one-year shut-\ndown necessary to reconfigure the machine and install additional RF systems for the highest-energy t\u00aft\nrunning. With these integrated luminosities, the FCC-ee physics programme improves the precision of\nall electro-weak observables bytwo orders of magnitude, allows measurements of Higgs couplings (in a\nmodel-independent way) by up to an order of magnitude more precise than the HL-LHC, provides ten\n3\n\ntimes the Belle-2 design statistics for bottom quarks, charm quarks and tau leptons, boosts the indirect\ndiscovery potential up to approximately 100 TeV, and unlocks direct discovery potential for feebly-\ninteracting particles (e.g., heavy sterile right-handed neutrinos) over the 5 \u2013 100 GeV mass range.\nThe lepton-collider beam parameters are limited by various constraints and effects [1], such as\nbeamstrahlung [2], a coherent beam-beam instability in collision with a large crossing angle [3], synchro-\nbetatron resonances, polarisation requirements, and finally impedance effects, as discussed in Section 1.1.\nThe parameters were optimised under these constraints [1]. Further refined simulations combining the\neffect of the full nonlinear lattice and either weak-strong or quasi-strong-strong beam-beam simulations,\nand the reverse-phase operation scheme for the RF cavities (with the implied transient beam loading\neffects) have led to parameter adjustments. The latest set of parameters is presented in Table 2. The\nparameters have been largely stable since 2021.\nThe bunch population is held approximately constant for all modes of operation, while the number\nof bunches is varied to adjust the beam current. The beam current is limited by the synchrotron radiation\npower, and strongly decreases at higher beam energies. For the Z operating point, a large number of\n11 200 bunches are stored in each of the two collider rings. In this case, the bunches can be separated\ninto 40 bunch trains of 280 bunches, with a bunch-to-bunch separation of 25 ns and a train-to-train\nseparation of roughly 0.6 \u00b5s. Similarly, at the WW threshold with 1780 bunches, bunches might be\nseparated into 20 trains of 89 bunches having a bunch-to-bunch separation of roughly 150 ns and a\ntrain-to-train separation of roughly 2 \u00b5s. At the ZH and t\u00aft it is likely that the bunches are uniformly\ndistributed around the ring. Two contributions to the beam lifetime are indicated separately: (1) the\neffect of lattice dynamic aperture and beamstrahlung plus quantum fluctuation, and (2) the unavoidable\nluminosity-related radiative Bhabha scattering. The total beam lifetime is the inverse of the sum of the\nindividual inverse lifetimes. Finally, the luminosity and integrated luminosity at each operating point are\ndiscussed further in Section 1.1.\nFCC-hh goals and parameters\nThe hadron collider FCC-hh should provide proton\u2013proton collisions with a centre-of-mass energy of\nthe order of 85 TeV and an integrated proton-proton luminosity of about 20 ab\u22121 in each of the two\nmulti-purpose experiments during 25 years of operation. Two specialised detectors are located in the\nremaining two experiment straights. In addition to colliding protons with protons, also proton-ion and\nion-ion collisions, as with the LHC [5\u20137] but at much higher energy, are envisaged. Furthermore, an\ninteraction point could be upgraded to electron\u2013proton and electron\u2013ion collisions, in which case an\nadditional recirculating energy-recovery linac would provide the electron beam. The FCC\u2013hh would use\n(modified) parts of the existing CERN accelerator complex for its injector chain.\nThe design of the FCC-hh hadron collider is based on LHC experience. The key challenges are\nthe magnet technology and power consumption in the presence of strong synchrotron radiation. To limit\nthe latter and also because the radiation damping during the store is significant, the beam current and the\nbunch population are relaxed compared to those of the HL-LHC [8,9].\nThe key parameters for FCC-hh are compiled in Table 3. The bunch population (close to 1 \u00d7 1011\nprotons per bunch) and the beam current (0.5 A) are kept the same as in the 2018 CDR [10]. Table 3\npresents a baseline design with 14 T dipole magnets, which could be based on Nb3Sn technology. The\ntable illustrates how the synchrotron radiation strongly increases with higher magnetic field.\nThe synchrotron-radiation heat, which must be extracted from inside the cold magnets, is a major\ncontribution to cryogenic power. For the CDR, with 16 T Nb3Sn magnets, the FCC-hh cryogenics re-\nquired around 250 MW of electrical power. With the lower field of 14 T, this power can be significantly\nreduced. However, the cryogenic power might also be lowered for the higher-field magnets based on\nHTS technology, as these could conceivably be operated at higher temperature, together with an elevated\ntemperature of the beamscreen intercepting the synchrotron radiation.\n4\n\nTable 2: Parameters of FCC-ee. Peak luminosity values are given per interaction point (IP), for a total\nof 4 IPs, integrated luminosities refer to the sum over four IPs. Both natural bunch lengths due to\nsynchrotron radiation (SR) and collision values including beamstrahlung (BS) are shown. The FCC-ee\ncollider rings feature a combination of 400 MHz RF systems (at the first three energies) and 800 MHz\n(additional cavities for t\u00aft operation), with voltage strengths respectively indicated. For the integrated\nluminosity, 185 days of operation per year, and luminosity production at 75% efficiency with respect to\nthe ideal top-up running is assumed, as in the report [4].\nRunning mode\nZ\nWW\nZH\nt\u00aft\nNumber of IPs\n4\n4\n4\n4\nBeam energy (GeV)\n45.6\n80\n120\n182.5\nBunches/beam\n11200\n1856\n300\n60\nBeam current [mA]\n1292\n135\n26.8\n5.1\nLuminosity/IP [1034 cm\u22122 s\u22121]\n144\n20\n7.5\n1.45\nEnergy loss / turn [GeV]\n0.039\n0.369\n1.86\n9.94\nSynchrotron Radiation Power [MW]\n100\n100\n100\n100\nRF Voltage 400/800 MHz [GV]\n0.09/0\n1.0/0\n2.1/0\n2.1/9.2\nRms bunch length (SR) [mm]\n5.15\n3.46\n3.26\n1.91\nRms bunch length (+BS) [mm]\n15.2\n5.28\n5.59\n2.33\nRms relative momentum spread (SR) [%]\n0.039\n0.069\n0.102\n0.152\nRms relative momentum spread (+BS) [%]\n0.115\n0.105\n0.176\n0.186\nRms horizontal emittance \u03b5x [nm]\n0.71\n2.16\n0.66\n1.65\nRms vertical emittance \u03b5y [pm]\n2.1\n2.0\n1.0\n1.32\nLongitudinal damping time [turns]\n1171\n218\n65.4\n19.6\nHorizontal IP beta \u03b2\u2217\nx [mm]\n110\n220\n240\n900\nVertical IP beta \u03b2\u2217\ny [mm]\n0.7\n1.0\n1.0\n1.4\nHor. IP beam size \u03c3\u2217\nx [\u00b5m]\n9\n22\n13\n37\nVert. IP beam size \u03c3\u2217\ny [nm]\n40\n45\n32\n44\nBeam lifetime (q+BS+lattice) [min.]\n87\n75\n100\n105\nBeam lifetime (lum.) [min.]\n22\n16\n10\n11\nTotal beam lifetime [min.]\n18\n13\n9\n10\nTotal int. annual luminosity [ab\u22121/yr]\n68\u2020\n9.6\n3.6\n0.67\u2021\n\u2020 The integrated luminosity in the first two years of Z running is assumed to be half this value to account\nfor the machine commissioning and beam tuning; for WW and ZH running no additional commissioning\ntime is allocated since the machine configuration and hardware are unchanged from the Z operation.\n\u2021 The integrated luminosity in the first year of t\u00aft running, at the slightly lower beam energy of 170 \u2013\n175 GeV, is assumed to be about 65% of this value to account for the machine commissioning and\nbeam tuning. The shorter time for commissioning compared with the lower energy running reflects the\nLEP/LEP-2 experience.\n5\n\nTable 3: Parameters of FCC-hh compared with the HL-LHC and LHC. For the integrated luminosity,\n160 days of operation per year, and luminosity production at 75% efficiency with respect to the ideal\nrunning is assumed, as in the report [4]. The regular bunch spacing is 25 ns for all three colliders.\nFCC-hh\nHL-LHC\nLHC\nCentre-of-mass energy [TeV]\n85\n14\nCircumference [km]\n90.7\n26.7\nDipole field [T]\n14\n8.33\nBeam current [A]\n0.5\n1.1\n0.58\nBunch Intensity [1011]\n1.0\n2.2\n1.15\nNumber of bunches per beam\n9500\n2760\n2808\nTotal synchrotron radiation power [kW]\n2400\n15\n7\nSynchrotron radiation power power per unit length [W/m/aperture]\n6.5\n0.33\n0.17\nLongitudinal emittance damping time [h]\n0.75\n12.9\nInteraction Point (IP) beta function \u03b2\u2217\nx,y [m]\n0.3\n0.15 (min.)\n0.55\nNormalised rms emittance [\u00b5m]\n2.2\n2.5\n3.75\nPeak luminosity [1034 cm\u22122s\u22121]\n30\n5 (lev.)\n1\nPeak number of events per bunch crossing\n1000\n132\n27\nStored energy per beam [GJ]\n6.5\n0.7\n0.36\nIntegrated annual luminosity per IP [ab\u22121/yr]\n0.9\n0.25\n0.05\nSustainability goals\nThe general FCC implementation is driven by the principles of cost optimisation and sustainability, as\ndescribed in Volume 3 of this Feasibility Study Report. Examples include the minimisation of the number\nof surface sites and the length of access roads by the placement optimisation, the planned processing of\nthe excavated spoil for multiple purposes of reuse, and the local use of waste heat and cooling water.\nThe existence of a single such tunnel serving the global particle physics community until the end\nof the century exemplifies the discipline\u2019s commitment to sustainability. Moreover, the choice to propose\nthe project in France and Switzerland \u2013 where electricity is already largely decarbonised \u2013 demonstrates\na serious and proactive approach to environmental considerations. Finally, the fact that the FCC-ee is\nabout hundred thousand times more efficient than its predecessor LEP, in terms of luminosity per unit\nelectrical power, underscores the significant efforts of the community to advance responsibly.\nAs for the accelerators, storage rings are intrinsically sustainable machines, as they collide the\nsame beams again and again, at multiple interaction points and over millions of turns. Their efficiency is\nlimited only by the energy loss from synchrotron radiation, which, in the case of the FCC, is minimised\nby its large circumference.\nConcerning the technical systems of the FCC-ee accelerators, their energy consumption is re-\nstricted by a variety of measures and design choices, such as novel ultra-high efficient continuous-wave\n(cw) RF power sources like tristrons, with a projected efficiency exceeding 90%, or twin dipole and\nquadrupole magnets for the FCC-ee arcs, and an increased Q0 value of the superconducting RF cavities,\nby deploying exactly the same RF system for the first three modes of operation, and choosing a moderate\naccelerating gradient around 20 \u2013 22 MV/m for the injector linacs. With regard to materials, by fabri-\ncating the main 400 MHz RF cavities using thin-film (niobium on copper) coating technology, the total\namount of niobium is greatly reduced and the cavities also become more robust.\nFor the FCC-hh, the R&D aims at developing magnets with a cold-bore temperature higher than\n1.9 K, along with an elevated beamscreen temperature, which will relax the cryogenic power required,\nwhile the optimisation of the FCC-hh injector will further reduce the overall energy consumption.\n6\n\nChapter 1\nFCC-ee collider design and performance\n1.1\nBeam-beam effects, parameter choices, and luminosity\nThe FCC-ee will run at different beam energies, spanning the range from 45.6 to 182.5 GeV, so as to\ncover the Z pole, the WW threshold, the ZH production peak, and the t\u00aft threshold. The latest parameter\nsets for the various operating energies are listed in Table 1.2. The parameter optimisation process for the\nFCC-ee was discussed in Ref. [1].\nThe FCC-ee design for all energies is based on the \u2018crab-waist\u2019 collision scheme, following its\nsuccessful implementation at both DA\u03a6NE and SuperKEKB [11,12]. This scheme features flat beams\n(\u03c3\u2217\nx \u226b\u03c3\u2217\ny), a large crossing angle between the two colliding beams, and (either \u2018virtual\u2019 or real) crab\nsextupoles at suitable betatron phase advance on either side of each of the interaction points (IPs). The\ncrab waist scheme not only allows a small vertical beta function, but it also avoids coupling the vertical\nand horizontal betatron motion through the crossing-angle collision. It, thereby, ensures good stability\nof particle trajectories even when the beam-beam interaction is strong, thus enabling a high luminosity.\nThe luminosity at one IP may be expressed as\nL =\n\u03b3\n2ere\nItot\u03bey\n\u03b2\u2217\ny\nRG ,\n(1.1)\nwith the relativistic factor \u03b3, the elementary charge e, the classical electron radius re, the total beam\ncurrent Itot, the vertical beam-beam parameter per IP \u03bey, the vertical optical \u03b2 function at the IP \u03b2\u2217\ny\nand the geometric reduction factor RG, which represents both the \u2018hourglass\u2019 effect and the reduced\noverlap due to the crossing angle. The total current is constrained by the design limit for the synchrotron\nradiation power of 50 MW per beam. Therefore, the highest vertical beam-beam parameter is desired for\nmaximum luminosity. However, in order to keep the tune footprint away from low-order resonances, all\nFCC-ee configurations feature \u03bey \u22480.1 (Fig. 1.1).\nThe smallest \u03b2\u2217\ny is also desired, yet it is limited by the reduction of the luminosity due to the\nhourglass effect. The hourglass reduction factor is historically determined by the bunch length. However,\nin the crab waist collision scheme, the length of the overlap of the colliding beams is minimised through\nthe crossing angle, leading to the condition \u03b2\u2217\ny \u2248Li with the interaction length defined by\nLi =\n\u03c3z\nq\n1 + \u03d52 , with\n\u03d5 = \u03c3z\n\u03c3\u2217\nx\ntan\n\u0012\u03b8c\n2\n\u0013\n(1.2)\nthe so-called Piwinski angle, related to the rms bunch length \u03c3z the horizontal rms beam size at the\ncollision point \u03c3\u2217\nx, and the full crossing angle between the beams at the IP \u03b8c. In the small angle ap-\nproximation (\u03b8c \u226a1) for the large Piwinski angle regime (\u03d5 \u226b1), the interaction length reduces to\nLi \u22482\u03c3\u2217\nx/\u03b8c. The crossing angle \u03b8c is imposed by choice of the layout, in particular, due to the short\ncommon chamber around the IP specifically designed to avoid parasitic beam-beam encounters, and\nto allow a small \u03b2\u2217\ny with the lowest vertical chromaticity possible. Maximum luminosity, therefore, is\nachieved by minimising the horizontal beam size at the collision point, to allow for a reduction of \u03b2\u2217\ny.\nThe beam-beam tune shifts are given by\n\u03bex = Nbre\n2\u03c0\u03b3\n\u03b2\u2217\nx\n\u03c32\nx(1 + \u03d52)\n, \u03bey = Nbre\n2\u03c0\u03b3\n\u03b2\u2217\ny\n\u03c3x\u03c3y\nq\n1 + \u03d52\n(1.3)\n7\n\nFig. 1.1: Luminosity at the Z energy as a function of betatron tunes for the CDR configuration [13],\nrepresented by a single arc and a single IP. The colour scale extends from zero (blue) to 2.3\u00b71036 cm\u22122s\u22121\n(red) [14]. The white narrow rectangle above (0.57, 0.61) indicates the footprint due to the beam-beam\ninteraction\n.\nwith Nb the number of electron or positron per bunch, given by\nNb =\nItot\nefrevnb\n(1.4)\nwith the revolution frequency frev and the maximum number of bunches nb. The number of bunches\ncannot be arbitrarily large due to the need for a minimal spacing between bunches (about 25 ns) in order\nto avoid adverse effects such as electron clouds (Section 1.4) as well as the need for gaps for injection\nand extraction (Section 1.8). This constraint is mostly relevant for the Z, yielding a minimum bunch\ncharge of about 2 \u00b7 1011 e\u00b1.\nIn the small crossing angle and large Piwinski angle approximation, the beam-beam parameters\nreduce to\n\u03bex \u2248Nbre\n\u03c0\u03b3\n2\u03b2\u2217\nx\n(\u03c3z\u03b8c)2 , \u03bey \u2248Nbre\n\u03c0\u03b3\n1\n\u03c3z\u03b8c\ns\n\u03b2\u2217\ny\n\u03f5y\n.\n(1.5)\nThe bunch length, therefore, is another key parameter. It is determined by the effect of beamstrahlung,\nthe synchrotron radiation in the arcs, the RF voltage and RF frequency, and by the choice of lattice\nmainly through the momentum compaction factor \u03b1C. It can be expressed as:\n\u03c3z = \u03c3\u03b4\n\u03b1CC\n2\u03c0Qs\n, with Qs = 1\n2\u03c0\n\u0012eVRF \u03c9RF C0\np0c2\n\u03b1C cos \u03d5s\n\u00131/2\nand sin \u03d5s =\nU0\neVRF\n(1.6)\n8\n\nwhere VRF and \u03c9RF designate the RF voltage and frequency, C the ring circumference, p0 the reference\nmomentum, and U0 the total energy loss per turn. The synchrotron tune and synchronous phase are Qs\nand \u03d5s, respectively. The momentum spread is obtained from\n\u03c32\n\u03b4 = \u03c32\n\u03b4,SR + \u03c32\n\u03b4,BS, with \u03c32\n\u03b4,BS = nIP \u03c4E,SR c\n4C0\n55\n24\n\u221a\n3\nr2\ne\u03b35\n\u03b1e\nZ\nds\n\u001c 1\n\u03c13\n\u001d\nx,y,z\n(1.7)\nwhere \u03c3\u03b4,SR denotes the rms relative momentum spread caused by synchrotron radiation in the arcs\nand \u03c4E,SR the corresponding longitudinal radiation damping time, nIP the number of IPs, \u03b1e the fine\nstructure constant and \u03c1 the local bending radius of the particles\u2019 trajectories caused by the beam-beam\ninteraction. Under certain assumptions, the integral over the bending radius can be approximated as\nfollows [2]\nZ\nds\n\u001c 1\n\u03c13\n\u001d\n\u22480.77562\n\u221a\n2\u03c0\n3\u03c32\nz\u03d5\n \n2Nbre\n\u03b3\u03c3x\nr\n2\n\u03c0\n!3\n.\n(1.8)\nUsing the equations above, and introducing the parameter \u03b1BS \u22650 to represent the effect of beam-\nstrahlung 1, the equation for the momentum spread can be written as\n\u03c35\n\u03b4 \u2212\u03c32\n\u03b4,SR\u03c33\n\u03b4 \u2212\u03b1BS = 0, with \u03b1BS \u221dnIP \u03c4E,SR\u03b3\n1\n2 N3\nb\n\u03c32\nx\u03b8c\n\u0012VRF \u03c9RF\n\u03b1C\n\u0013 3\n2\n.\n(1.10)\nThe corresponding bunch length follows from Eq. (1.6). Due to its approximate nature, the equation\nis hardly used in the design process, and the impact of beamstrahlung is often obtained via tracking\nsimulations. Yet this equation reveals that, in the regime of strong beamstrahlung (\u03c3\u03b4 \u226b\u03c3\u03b4,SR), the\nsensitivity to RF parameters and momentum compaction factor is reduced from the usual square root\ndependence due to fact that the beam-beam force, and consequently the strength of the beamstrahlung,\ndepends on the bunch length. In the regime of strong beamstrahlung, the main drivers for the bunch\nlength and momentum spread are the bunch intensity and the horizontal beam size (\u03c3\u03b4 \u221dN3/5\nb\n\u03c3\u2217\nx\n\u22122/5).\nThese quantities must be adjusted to minimise the magnitude of the beamstrahlung.\nAs discussed above, the bunch intensity is constrained on the low-energy side, namely at the Z,\nby the electron-cloud instability. At higher energies, it needs to be kept large enough to maintain the\nbeam-beam parameter (and consequently the luminosity) at the specified level. Also, a low horizontal\nemittance is required to achieve a low vertical emittance. Indeed, the two quantities are bound by the\nquality of the optics correction: currently, it is assumed that \u03f5y \u2248\u03f5x/103 can be achieved (Section 1.4).\nThe low vertical emittance enters directly into the luminosity, but it is also important for maintaining a\ngood beam lifetime in the presence of a limited vertical dynamic aperture that comes along with the low\n\u03b2\u2217\ny. Thus, maintaining a high \u03b2\u2217\nx is key to reducing beamstrahlung. Nevertheless, the horizontal \u03b2\u2217is\nlimited on the high side by the corresponding increase of the horizontal beam-beam parameter as well\nas of the strength of horizontal synchrobetatron resonances. These aspects are critical as the transverse\ntunes are set just above the half-integer in the horizontal plane and above the coupling resonance but\nbelow the third-order resonance in the vertical plane (Fig. 1.1), thus minimising the impact of low-order\nresonances on the beam quality. In this area, synchro betatron sidebands of the half-integer resonance in\nthe horizontal plane are strongly excited due to the beam-beam interaction with a large Piwinski angle,\nleading to coherent instabilities, so-called x-z instabilities [3], as well as by incoherent blow up [15].\nConsequently, the horizontal \u03b2\u2217must be chosen to maintain the strength of synchrobetatron resonances\nand the horizontal beam-beam parameter (\u03bex \u226aQs) at an acceptable level. This optimisation, coupled\nto the relevant longitudinal aspects treated in the next paragraph, is done based on tracking simulation\n1\n\u03b1BS \u223c= 0.77562 \u00b7 220\n3\n\u221a\n3\nr5\ne\u03b32\n\u03b1e\nnIP \u03c4E,SR\nTrev\n\u0012 Qs\n\u03b1CC0\n\u00133 N 3\nb\n\u03c32\nx\u03b8c\nwith Qs from Eq. (1.6)\n(1.9)\n9\n\n(Section 1.4). Thanks to the increase in radiation damping and the shorter bunch length at higher energies,\nthese effects become less severe, and higher \u03b2\u2217\nx are allowed.\nThe tune space depicted in Fig. 1.1 corresponds to the CDR configuration, yet the main features\nhave not fundamentally changed. The main difference is the lowering of the tune per quarter of the\nmachine towards the half-integer (layout with 4 IPs), with respect to the half of the machine in the CDR\n(layout with 2 IPS) in order to maintain the total tune in the same area, thereby avoiding important\nresonances when considering the impact of the real lattice (Fig. 1.3). The total tune spread is large and a\ntight control of the resonances driven by the lattice including imperfections is important.\nThe longitudinal parameters are set to ensure a sufficiently large RF bucket height. At the same\ntime, the spin tune spread needs to remain smaller than the synchrotron tune to allow for energy calibra-\ntion via resonant depolarisation (Section 1.7). These two conditions are\n\u0012\u2206p\np\n\u0013\nmax\n=\n\u0012eVRF \u03c9RF C0\n2\u03c02c\u03b1CE0\n(2 cos(\u03d5) + (2\u03d5s \u2212\u03c0) sin(\u03d5s))\n\u00131/2\n> 0.01, and Qs > a\u03b3\u03c3\u03b4,SR\n(1.11)\nwith a the anomalous magnetic moment of the electron. Aiming at a high voltage and a low momentum\ncompaction factor, a high synchrotron tune is favoured. The RF voltage available is an important cost\ndriver, it is kept at a level required to compensate for the energy lost by synchrotron radiation, and to\nmaintain a sufficiently large RF momentum acceptance.\nAt the Z, an additional constraint on the RF voltage arises from the choice of operating 2-cell\ncavities in reverse polarity mode in order to keep the same RF system for the Z, WW and ZH energies\n(Section 3.4). The voltage may need to be kept higher than otherwise necessary to minimise the impact\nof transient beam loading.\nTwo different lattices are considered, with the one for the two highest energies (ZH and t\u00aft) featur-\ning a lower momentum compaction factor than the optics for the two lower energies (Z and WW). The\noptics change is required to maintain a low transverse emittance at the higher energies.\nWhile at the Z energy the maximum number of bunches is constrained by the electron cloud\ninstability, at other energies it can be fully optimised to obtain the highest luminosity. This is achieved\nby choosing the highest bunch charge that does not lead to a significant lifetime degradation or emittance\ngrowth (corresponding to a vertical beam-beam tune shift of about \u03bey \u22480.1) [16].\nA key difference from existing colliders is the fact that beam parameters are defined by an equi-\nlibrium condition that is mostly driven by the beam-beam interaction itself, and in particular by the\nbeamstrahlung. Transverse and longitudinal beam sizes are, thus, strongly coupled, introducing addi-\ntional constraints on the design and operation of the collider.\nAn important aspect is the need for a reasonably adiabatic ramp up of the beam-beam force such\nthat the energy spread and the bunch length may increase from the lattice equilibrium to the new equilib-\nrium with beamstrahlung avoiding uncontrolled losses in the process. Indeed, considering, for example,\nthe situation where one nominal beam would be circulating, with the lattice equilibrium emittances, and\na second lower intensity beam would be injected from the booster, a 3D flip-flop mechanism could occur\nwhere the injected beam blows up significantly, while the other one remains smaller than nominal. As a\nmitigation measure, the so-called bootstrap injection scheme was devised, where the intensity difference\nbetween colliding bunches does not exceed a few percent [16] (Section 1.8).\nThe 3D flip-flop mechanism is a direct consequence of the strong coupling between the equilibria\nin the different planes. In the case of an asymmetry in the strength of beamstrahlung between the two\ncolliding bunches, the bunch experiencing lesser beamstrahlung sees its length decrease, thus increasing\nthe strength of beamstrahlung for the other beam. As a result, beamstrahlung decreases further on the\nshorter bunch, thus again enhancing the effect. These dynamics may reach a stable equilibrium where\none beam is large and the other small in the longitudinal direction, a so-called \u2018flip-flop\u2019 effect. Similar\n\u2018flip-flop\u2019 phenomena, albeit without beamstrahlung and in the transverse direction, have been seen in\n10\n\ne+e\u2212colliders for the past half a century, e.g., Ref. [17]. At FCC-ee, due to the finite momentum\nacceptance, as well as the strong beam-beam force generated by the short bunch, the long, \u2018weak\u2019 bunch\nmay also experience transverse blow-up and possibly significant beam losses, making the mechanism\nthree dimensional. The \u20183D flip-flop\u2019 situation is considered irreversible so the affected bunches would\nneed to be dumped. Avoiding this mechanism imposes tight tolerances on the symmetry of the two\nbeams, regarding bunch intensity and optics control [16,18].\n1.2\nOptics design\nThis section describes the main electron and positron collider rings. Subsections describe the arc op-\ntics, the experimental insertions, and the design of the various technical straight sections. The baseline\noptics is called the Global Hybrid Correction (GHC) scheme, since the vertical chromaticity for the low-\nbeta insertion is corrected locally, with two sextupole magnets in the final focus, while the horizontal\nchromaticity is globally corrected globally using the arc sextupoles.\nThe baseline collider optics corresponds to a layout that can accommodate four interaction points\n(IPs), with a super-periodicity of four and fourfold symmetry, comprising eight arcs, and eigt long\nstraight sections (LSS), which are further divided into four technical \u201clong long straight sections\u201d (LLSS,\nat points PB, PF, PH, and PL), and four experiment \u201cshort long straight sections\u201d (SLSS, at points PA,\nPD, PG, and PJ), as are defined in Table 1.1 and illustrated in Fig. 1.2.\nTable 1.1: Parameters of the layout in metres.\ncircumference\narc\ntechnical LSS (LLSS)\nexperiment LSS (SLSS)\n90 657.400\n9616.175\n2032.000\n1400.000\nThe experiment long straight sections accommodate the optics leading to the interaction points\n(IPs) and the detectors. The beam crossing angle and the distance between the IP and the face of the first\nquadrupole (\u2113\u2217) are maintained at 30 mrad and 2.2 m, respectively. Each beam must arrive towards the IP\nfrom the inside to minimise the synchrotron radiation going into the detector; therefore the beams must\ncross in each technical long straight section. The technical LSSs are used for RF, injection, extraction,\nand collimation as illustrated in Fig. 1.2. The technical LSS at PH is used for the RF for the collider at\nall energies, while the LSS at PL is used for the booster RF. The beam optics of the collider RF section\nwill change at the transition from WW to ZH, so as to accommodate RF cryomodules common to both\ne+ and e\u2212for ZH, and separate for WW.\nThe PL long straight section is used for the booster RF. The RF section for the collider is concen-\ntrated in the PH long straight section for all energies. This seems to induce an additional non-structural\nsynchro-betatron resonance, limiting the choice of the transverse tune space at some energies.\nThe design goal of the LLSS is to use identical optics for the RF, injection/extraction, and colli-\nmation at Z and WW, in order to maintain the superperiodicity of the ring in terms of path length, phase\nadvance and chromaticity. Thus, no special tuning of the optics and sextupoles is required. At higher en-\nergies, for the ZH and tt modes of operation, the optics in the RF section changes, so as to accommodate\nthe RF cavities common to both e+ and e\u2212beams.\nThe optics in the other technical LSSs remain the same for all energies. At the experiment LSSs,\nthe IP localisation and beamline layouts deviate from the reference layout line defined by Table 1.1 to\ngenerate the crossing angle for the collision with reduced synchrotron radiation (SR) toward the IP.\nThe ring vertical chromaticities are set to +5 and +2 at Z and WW, respectively, and to 0 at other\nenergies. This is necessary to suppress the transverse mode coupling beam instability. The dynamic\naperture (DA) and beam lifetime are optimised under these chromaticities.\nThe choice of the betatron tunes and parameters related to beam-beam such as bunch intensity,\n11\n\nFig. 1.2: The layout of the FCC-ee illustrating the 4 collision points in the SLSS and the four technical\ninsertions at the LLSS.\n\u03b2\u2217, bunch length, chromaticities, etc., assumes the reverse-phase operation of the RF cavities. There are\nlimitations on the combination of parameters as discussed in Section 1.1.\nTable 1.2 lists machine parameters associated with the baseline design for four beam energies. The\neffect of the full non-linear lattice and the beam-beam collisions with beamstrahlung is now simulated\nsimultaneously. These simulations include the full lattice, synchrotron radiation from all components\nwith realistic photon spectra, tapering, beam-beam collisions, and beamstrahlung, using the simulation\ncodes SAD and BBWS. As a result, the beam lifetime is considered realistic, and the blow-up of the\nvertical emittance due to beam-beam effects and beamstrahlung is quantitatively estimated, as reported\nin the table.\nIt is important to distinguish the vertical emittance as \u2018emittance after collision\u2019 and \u2018emittance\nby lattice\u2019, as shown in Table 1.2. Roughly a factor of 2 blowup of the vertical emittance is expected at\neach energy according to the simulations above. The required lattice emittance will be the smallest at\nZ, 0.75 pm, including the vertical emittance generated by the interaction point (IP) solenoid, \u223c0.43 pm.\nTherefore, if such a small lattice vertical emittance must be achieved at Z, the lattice emittance at higher\nenergies should be reduced to a comparable level. Note that the solenoid emittance scales as Bz/E5, so\nit will be easier to achieve the same level of lattice emittance at higher energies. The vertical emittances\nin Table 1.2 are smaller than those in the CDR, which they had been chosen as 2% of the horizontal\nemittance in collision at each energy. At ZH, the lattice vertical emittance is required to be smaller than\n0.65 pm, which is even smaller than at the Z. However, at the Z there is the large, inevitable vertical\nemittance due to the solenoid, \u223c0.43 pm, which is reduced by \u223c1/E5, so that the emittance from the\nrest of the ring can still be larger at ZH than at Z.\n12\n\nTable 1.2: FCC-ee collider parameters for the GHC lattice. SR: synchrotron radiation, BS: +beam-\nstrahlung.\nBeam energy\n[GeV]\n45.6\n80\n120\n182.5\nLayout\nPA31-3.0\n# of IPs\n4\nCircumference\n[km]\n90.658509\nBend. radius of arc dipole\n[km]\n10.021\nEnergy loss / turn\n[GeV]\n0.0387\n0.369\n1.86\n9.93\nSR power / beam\n[MW]\n50\nBeam current\n[mA]\n1292\n135\n26.8\n5.0\nColliding bunches / beam\n11200\n1856\n300\n60\nColliding bunch population\n[1011]\n2.18\n1.38\n1.69\n1.58\nHor. emittance at collision \u03b5x\n[nm]\n0.71\n2.16\n0.66\n1.65\nVer. emittance at collision \u03b5y\n[pm]\n2.1\n2.0\n1.0\n1.32\nLattice v. emittance \u03b5y,lattice\n[pm]\n0.87\n1.20\n0.57\n0.82\nArc cell\nLong 90/90\n90/90\nMomentum compaction \u03b1p\n[10\u22126]\n28.52\n28.67\n7.52\n7.57\nArc sext families\n73\n144\n\u03b2\u2217\nx/y\n[mm]\n110 / 0.7\n220 / 1\n240 / 1\n900 / 1.4\nTransverse tunes Qx/y\n218.168 / 222.200\n218.185 / 222.220\n398.150 / 398.220\n394.148 / 390.218\nChromaticities Q\u2032\nx/y\n+5 / +5\n0 / +5\n0 / 0\n0 / 0\nEnergy spread (SR/BS) \u03c3\u03b4\n[%]\n0.039 / 0.115\n0.069 / 0.105\n0.102 / 0.176\n0.152 / 0.186\nBunch length (SR/BS) \u03c3z\n[mm]\n5.15 / 15.2\n3.46 / 5.28\n3.26 / 5.59\n1.91 / 2.34\nRF voltage 400/800 MHz\n[GV]\n0.0885 / 0\n1.00 / 0\n2.09 / 0\n2.10 / 9.20\nHarm. number for 400 MHz\n121200\nRF frequency (400 MHz)\nMHz\n400.788026\nSynchrotron tune Qs\n0.0310\n0.0809\n0.0334\n0.0892\nLong. damping time\n[turns]\n1179\n218\n65.4\n19.4\nRF acceptance\n[%]\n1.21\n3.32\n2.06\n3.07\nEnergy acceptance (DA)\n[%]\n\u00b11.0\n\u00b11.0\n\u00b11.9\n-2.8/+2.5\nBeam crossing angle at IP \u03b8x\n[mrad]\n\u00b115\nCrab waist ratio\n[%]\n60\n55\n50\n40\nBeam-beam \u03bex/\u03bey\n2\n0.0023 / 0.098\n0.013 / 0.129\n0.0108 / 0.130\n0.066 / 0.144\nPiwinski ang. (\u03b8x\u03c3z,BS)/\u03c3\u2217\nx\n25.8\n3.6\n6.6\n0.91\nLifetime (q + BS + lattice)\n[sec]\n5200\n4500\n6000\n6300\nLifetime (lum)3\n[sec]\n1330\n960\n600\n640\nLuminosity / IP /1034\n[/cm2s]\n144\n20\n7.5\n1.45\nTune scans for the lattices at the different working points are plotted in Fig. 1.3. It is interesting to\nnote that the resonance Qx + 2Qy \u2212Qs = int. disappears at ZH and t\u00aft. One may speculate that it is due\nto the faster damping rate at higher energies, but it is not. It has been found that even if the energy of the\nZH lattice is reduced to the WW energy, this resonance does not appear at all. So, this resonance seems\nto be related to the lattice itself.\nFigure 1.4 shows the vertical emittance in the collision and the beam lifetime as functions of the\nlattice emittance at each energy. The parameters in Table 1.2 are optimised within the range over which\nthe lifetime due to nonlinear lattice and beamstrahlung is much longer than the luminosity lifetime. How-\never, it is important to note that neither machine errors nor corrections are included in this calculation.\nThe resulting lifetime for the lattice and beamstrahlung may seem long at some energies, such as Z.\nMore luminosity may be obtained by increasing the bunch current, but it was decided not to push the pa-\nrameters and leave some room for future improvements. Considering that the luminosity simulations do\nnot yet include machine errors and corrections, leaving some margin appears reasonable for this design\nstudy phase.\n13\n\nFig. 1.3: The tune scan of the beam-beam effect with the full lattice, upper-left: Z, upper-right: WW,\nlower-left: ZH, lower-right: t\u00aft. At each energy, the left/right plots show the beam loss/vertical emittance\nblowup, respectively. The whiter areas correspond to longer lifetimes and higher luminosity. At the Z\nand WW, a strong resonance line Qx + 2Qy \u2212Qs = int. is seen. Also, at WW, strong vertical lines\nappear at Qx + nQs = int., (n = 1, 2). The red circles show the design tunes. Each orange arrow on\nthe colour scale of the blowup indicates the level at the design working point.\n14\n\nFig. 1.4: Results of beam-beam tracking with lattice and beamstrahlung for each energy of FCC-ee. Each\nplot shows the vertical emittance after collision (red) and the lifetime (green) against the lattice vertical\nemittance at each collision energy. The purple horizontal dashed line shows the target vertical emittance\nat collision, where the vertical emittance of the strong beam is set at.These results with SAD as well as\nthe DA have been reproduced by independent simulations with XSUITE.\n15\n\n1.2.1\nArc optics\nThe arc FODO cell phase advance at lower energies (Z, WW) is 90\u00b0/90\u00b0 with twice the cell length (long\n90/90) of the ZH and t\u00aft machine, as shown in Fig. 1.5. Twin aperture dipoles and quadrupoles are\nused in the arcs. The separation between the two beams is 35 cm. Multi-family \u2212I-paired sextupoles\nare deployed in the arc for global chromatic correction, respecting the fourfold superperiodicity. This\nmultifamily scheme provides great flexibility for controlling additional parameters such as the chromatic\nbehaviour at the IP or RF, and the dynamic aperture.\nFig. 1.5: Optics for the arc cell: Z/W operation modes (left) and Zh/tt operation modes (right). Labels\nshow the \u2212I paired sextupoles.\n1.2.2\nExperiment insertion optics\nThe critical photon energy of incoming synchrotron radiation from the dipoles in the interaction region\nis kept below 100 keV at t\u00aft up to \u223c450 m upstream of the IP, as in Ref. [19]. There are 32 sextupoles in\nthe interaction regions: 2 per side and per IP \u00d7 2 sides \u00d7 4 IPs \u00d7 2 beams. The optics uses the \u2018virtual\u2019\ncrab sextupoles scheme, using the vertical local chromaticity correction sextupoles as described in [20].\nThe lattice assumes a perfect solenoid compensation with counter-solenoids between the face of\nthe last quadrupole (QC1L1/R1) and the IP (\u2018local scheme\u2019). This scheme guarantees a perfect achro-\nmatic coupling correction with no leak of vertical orbit and dispersion to the outside. It is known that\nthis scheme also guarantees the perfect removal of harmful beam-beam effects coupled to the chromatic\ncoupling, from which SuperKEKB has been suffering so far. This compensation scheme, due to disper-\nsion and synchrotron radiation in the solenoid fields with crossing angle, generates a vertical emittance\nof 0.5 pm at the Z.\nThe optics of the experiment LSS incorporates the polarisation wigglers and a space for a Compton\npolarimeter. The latter is essential to detect the spin precession angle at each IP to provide additional\nconstraints for the beam energy calibration.\nThe optics for the experimental straight sections (short long straight section \u2014 SLSS) is shown in\nFig. 1.6.\n1.2.3\nCollimation insertion optics\nA global beam halo collimation system will be required in the FCC-ee to protect the machine hardware\nfrom unavoidable beam losses and for detector background control. Two global collimation systems\nare foreseen: one betatron collimation system to remove large amplitude particles and one momentum\ncleaning section to intercept particles with a significant momentum deviation. Both systems are foreseen\n16\n\nFig. 1.6: Layout and optics for the experiment straight section: Z/W operation modes (left) and ZH/tt\noperation modes (right). This section includes sections for an inverse-Compton polarimeter and polar-\nisation wigglers. The vertical lines show the location of the sextupoles for vertical local chromaticity\ncorrection and crab waist.\nto be located in the LSS at PF, as shown in Fig. 1.2. Additional collimation will be located in each\ninteraction region (IR) and is described in Section 1.6.4.\nThe layout and optics for a betatron and momentum collimation section are presented in Fig. 1.7\nfor both the Z and t\u00aft operation mode. A beam crossing section with a length of 200 m is located at the\ncentre of the insertion, where the incoming beam will cross from the outside to the inside of the ring.\nThe betatron collimation is installed upstream of the crossing, whereas the momentum collimation is\nlocated downstream. The optics is matched to obtain collimator half-gaps of more than 2 mm for the\nrequired betatron cuts in units of beam sigma. Moreover, the horizontal dispersion is kept low in the\nbetatron collimation section to avoid the collimators there becoming the momentum bottleneck. In the\nmomentum collimation section, the ratio of the horizontal dispersion and \u03b2-function is matched such\nthat the collimators there can provide a sufficiently small momentum cut without becoming the aperture\nbottleneck.\nThe collimation settings and performance of the collimation system is presented in Section 1.5\nand R&D challenges for the collimators are described in Section 3.6.3.\n1.2.4\nRF insertion optics\nTwo long-long straight sections (LLSS) of roughly 2000 metres in length will be used for SRF systems.\nIn particular, the LLSS at PL will house the booster RF systems and LLSS PH will house the main ring\nSRF systems as indicated in Fig. 1.2. The layouts of these insertions are based on initial models for the\n400 and 800 MHz cryomodules, which are based on existing cryomodules at CERN. These cryomodule\nmodels have not yet been optimised for the FCC-ee.\nThe requirements on the SRF insertions include:\n\u2013 accommodate the required number of SRF cavities into the 2032 metre long straight section; the\ndetails of the SRF systems can be found in Section 3.4.\n\u2013 provide a beam crossing, e.g., the beam entering on the outside of the tunnel leaves the LLSS on\nthe inside of the tunnel.\n\u2013 minimise synchrotron radiation reaching the SRF cavities.\n\u2013 provide the appropriate focusing and diagnostics to control the beam through the SRF cavities.\nIn addition, effort was made to ensure that the SRF systems along with the accelerators, the booster and\n17\n\nQuadrupole\nDipole\n0\n500\n1000\n1500\n2000\n\u03b2\n[m]\n\u03b2\nx\n\u03b2\ny\n33000\n33500\n34000\n34500\n35000\ns\n[m]\n0\n1\nD\nx\n[m]\nQuadrupole\nDipole\n0\n500\n1000\n\u03b2\n[m]\n\u03b2\nx\n\u03b2\ny\n33000\n33500\n34000\n34500\n35000\ns\n[m]\n\u22120.5\n0.0\n0.5\nD\nx\n[m]\nFig. 1.7: Layout and optics for a collimation insertion: Z operation mode (top) and tt operation mode\n(bottom).\ne+/e- main rings, and the technical infrastructure required could be accommodated into the 5.5 metre\ndiameter tunnel that is used elsewhere in the collider arcs and other LLSS.\nExample 400 MHz and 800 MHz cryomodule designs are shown in Section 3.4.11. Figures 1.9\nand 1.10 present tunnel cross sections including SRF cryomodules at PH and PL, respectively.\n18\n\nFig. 1.8: Layout and optics for LLSS: Z/W operation modes for RF, injection/extraction, collimation\n(left) and ZH/tt operation modes for RF (right). The left optics is identical for all four LLSSs at Z/W.\nThe left RF section is replaced by the right optics at ZH/tt for the common-RF scheme with an electro-\nmagnetic separator. The space for the RF components is 1890 m except the quadrupoles.\n(a) 400 MHz SRF cryomodules\n(b) 800 MHz SRF cryomodules\nFig. 1.9: Tunnel cross sections with 400 MHz (left) and 800 MHz SRF cryomodules (right) for the col-\nlider rings at point PH. The cryomodule on the right side of the tunnel indicatest he transport path.\n19\n\nFig. 1.10: Tunnel cross section with 800 MHz SRF cryomodule for the booster ring at PL. The cryomod-\nule on the right side of the tunnel indicatest he transport path.\n20\n\n1.3\nImpact of misalignments and field errors\nLattice imperfections may restrict the performance of the FCC-ee collider by affecting momentum accep-\ntance (MA), dynamic aperture (DA), beam lifetime, luminosity at the interaction points (IPs), emittance\nblow-up, injection efficiency, polarisation, energy calibration, and machine protection. The feasibility of\nthe FCC-ee operation in the presence of realistic imperfections is studied via computer simulations.\nEarly studies [21, 22] already indicated that linear optics corrections alone, as are applied, e.g.,\nin the LHC [23], do not ensure a good DA. The tuning simulations need to be extended by beam-based\nalignment (BBA) techniques and dispersion-free steering (DFS), as was the case for LEP [24,25] and at\nthe SLC [26, 27]. In addition, starting with a relaxed, or even ballistic, optics in the interaction regions\n(IRs), allows establishing a circulating beam in the uncorrected machine, as an intermediate step towards\nthe collision optics [28]. A ballistic optics was also used for the triplet alignment at the SLC [29,30].\nThe currently considered alignment and magnetic tolerances for the FCC-ee magnets and relevant\nbeam instrumentation are discussed in Section 1.3.1. The preliminary tolerances on the magnetic field\nquality are described in Section 1.3.4. The field quality tolerances likely require dedicated correction\ncircuits, and further studies are needed to finalise these. A first look at alignment tolerances for the\nInteraction Regions (IRs) is reported below and in Section 2.3.4.\nSimulations should, as much as possible, replicate the actual steps to be followed during FCC-\nee commissioning, as described in Section 2.3.4. Detailed descriptions of the different commissioning\nsteps are presented in Sections 2.3.4 and 1.3.3. The simulations are mostly carried out for the baseline\nGlobal Hybrid Correction (GHC) lattice [31] of Section 1.2. In general, the alternative Local Chromatic\nCorrection (LCC) lattice [32], described in Section 1.10.1, is less sensitive to lattice imperfections in the\narcs.\n1.3.1\nMain tolerances for magnets and beam instrumentation\nThe target alignment and magnetic strength tolerances for the arc elements are compiled in Table 1.3.\nIt is assumed that the group of quadrupole and sextupole magnets located between main arc dipoles\nare supported by a common girder. Therefore, the total misalignment of these elements needs to take\ninto account the independent alignment errors of the girder and of the elements on the girder.\nThe tolerance quoted for the BPM-to-quadrupole alignment refers to the offset between the electric\nand magnetic centres of the BPM and the quadrupole, respectively. Simulations have shown that by\napplying Beam Based Alignment (BBA), the initial BPM-to-quadrupole alignment tolerance could be\nrelaxed to 150 \u00b5m, if required.\nThe final-doublet quadrupoles, most of the other IR quadrupoles and the IR sextupoles will require\ntighter alignment tolerances than the arc components. Table 1.4 presents a preliminary set of tolerances\nfor the IR magnets. Details are discussed in Section 2.3.4.\nSpin dynamics studies demonstrate that, for most error seeds and after orbit correction only, with\nrms alignment errors of 100 \u00b5m in the arcs and 25 \u00b5m in the IR, the stringent energy calibration demands\ncan be met. Section 1.7.1 provides further information.\nTable 1.5 summarizes the arc BPM performance requirements. DA studies indicate that the phase\nadvance should be measured with a resolution better than 10\u22123 2\u03c0 [33]. Simulated optics measurements\nbased on a turn-by-turn technique demonstrate that this goal is achieved in the arcs uusing 50 000 turns\nand a BPM resolution of 1 um [34]. To sustain betatron oscillations for 50 000 turns it is mandatory to\nuse an AC dipole as in RHIC and at the LHC [35\u201341]. Location and design specifications of the AC\ndipoles still need to be defined.\nIn the IR, the sextupoles used for the local chromatic correction represent one of the most critical\nplaces where the phase advance must be determined to within 10\u22124 2\u03c0. By using only BPMs next\nto the defocusing quadrupoles in the region of interest and under the same measurement assumptions,\n21\n\nTable 1.3: Arc alignment and strength tolerances. These values correspond to the 1\u03c3 standard deviation\nfor a Gaussian distribution truncated at 2.5\u03c3. Quadrupoles and sextupoles are placed on top of common\ngirders.\nElement\n\u03c3x/y [\u00b5m]\n\u03c3\u03b8/\u03c8/\u03d5 [\u00b5rad] \u2206k/k [10\u22124]\nArc quads & sext.\n50\n50\n2\nDipoles\n1000\n1000\n2\nGirders\n150\n150\n-\nBPMs-to-quad\n100\n-\n-\nTable 1.4: Preliminary IR alignment tolerances, determined with reduced arc misalignments of 100 \u00b5m\nand neglecting BPM misalignments.\nElement\n\u03c3x/y [\u00b5m]\n\u03c3\u03b8 [\u00b5rad]\nFinal Doublet (FD) quads\n10\n10\nIR quads (excluding FD)\n100\n100\nSextupoles\n30\n30\nthis target is achieved, too. The BPM performance requirements so far still need to be validated given\ntransverse coupling and non-linear measurements.\nThe need for orbit stability determines the closed orbit measurement resolution. For BBA perfor-\nmance, a closed-orbit BPM resolution of 1 \u00b5m suffices for optimal results as is described in Section 2.3.4.\nTable 1.5: Arc BPM performance specifications.\nClosed orbit resolution\n0.1 \u00b5m\nTurn-by-turn (TbT) position resolution\n1 \u00b5m\nNumber of turns in TbT mode\n50 000\n1.3.2\nLocation of arc corrector magnets and BPMs\nTable 1.6 reports the baseline locations of arc magnets and BPMs. The skew quadrupole embedded in the\nsextupole magnet generates 65\u00d710\u22124 units of skew octupole at 10 mm when powered at its maximum\nstrength. This presents a concern for the DA and requires further studies with realistic distributions of\nthe skew quadrupole strengths.\nTuning studies performed using the GHC lattice have demonstrated that placing the BPMs attached\nto quadrupoles yields better results than when attached to sextupoles.\nTable 1.6: Location of arc magnet correctors and BPMs.\nDevice\nLocation\nHorizontal orbit corrector\nEmbedded at the edge of the main dipole next to main quadrupole\nVertical orbit corrector\nEmbedded at the sextupole or stand-alone\nQuadrupolar corrector\nTrim coil in all main quadrupoles\nSkew quadrupole\nEmbedded at the sextupole\nBPM (H & V)\nAttached to the main quadrupole\nTable 1.7 summarises the closed-orbit deviations, beta beating, and spurious dispersion errors\n22\n\nbefore and after the linear optics correction. The simulated dynamic aperture and momentum acceptance\nare presented in Section 1.3.3.\n1.3.3\nPerformance after global optics tuning\nFigure 2.5 shows the general sequence of the commissioning steps to be followed in FCC-ee. First orbit\nthreading steps require the sextupole magnets to be switched off. However, a reduced dynamic aperture\nfor this configuration [42,43] renders this approach impractical for the baseline optics. A new optics has\nbeen designed with both quadrupoles and sextupoles switched off near the IP [44]. This optics features\na lower natural chromaticity, lower beta functions in the IR, no synchrotron radiation in the final doublet\n(FD), and it allows establishing a straight reference trajectory across the IP in the absence of focusing\nelements. This is why this optics is named ballistic. Refined optics measurements are not possible\nimmediately after threading but dispersion-free steering (DFS) is effective at allowing the commissioning\nto then proceed with beam-based alignment (BBA). Global optics corrections are applied iteratively as\nthe optics transitions to the collision optics, following a \u03b2\u2217squeeze. Various relaxed optics have been\ndeveloped, e.g., Ref. [45]. The optics commissioning is further detailed in Section 2.3.4 and in Ref. [28].\nFor the optics at Z energy (GHC v22), the simulated dynamic aperture and momentum acceptance\nafter global corrections, including only arc errors, are presented in Fig. 1.11. While alignment errors do\nnot significantly affect the vertical DA, some seeds experience a clear degradation in the horizontal DA\nand all seeds suffer from a reduced momentum acceptance (MA). These degradations could significantly\naffect lifetime and injection efficiency. Dedicated nonlinear corrections will be required at this stage,\ndespite the fact that non-linear aberrations have not yet been introduced in the simulations. Tables 1.7\nand 1.8 summarise the residual orbit and optics errors after global corrections.\nIn the absence of IR errors, the IP optics parameters are under control thanks to the global correc-\ntions, yet they are at the edge of the imposed tolerances. For example, a vertical IP dispersion D\u2217\ny of 1 \u00b5m\nwas determined as the tolerance for a 5% increase of the vertical beam size [46], and a 3% \u03b2-beating\ncauses a measurable luminosity loss.\nTransverse coupling is characterised via the sum and difference resonance driving terms, f1010 and\nf1001, see e.g., Ref. [47]. Early tolerance estimates on the average values of f1010 and f1001 pointed at a\nfew 10\u22123 [48]. However, a specific tolerance for errors in the IP itself is still to be quantified.\nThese observations point to the need for robust IP tuning and luminosity optimisation techniques.\nPertinent studies are described in Section 2.3.4.\n1.3.4\nTolerances on magnet field quality\nThe field quality tolerances for the collision optics and also during top-up injection are studied using\n6D tracking simulations with XSUITE. These studies incorporate various random and systematic relative\nfield errors in dipole, quadrupole, and sextupole magnets within the arcs and in the interaction regions\n(IRs), along with beam-beam kicks and synchrotron radiation. This ongoing work complements previous\nstudies [43, 49, 50]. Field error tolerances are defined as the value at which a noticeable change is\nobserved in dynamic aperture (DA) or momentum acceptance (MA). Results for \u2018nominal\u2019 colliding\nbeams with the GHC lattice are summarised in Table 1.9. The deterioration of the simulated injection\nefficiency by 10% or more is used as an additional criterion to define field quality tolerances. Findings\nfor top-up injected beams are presented in Table 1.10. The top-up injection studies consider both the\nbaseline on-axis injection (\u03b4p/p offset: 0.95%) and also a hybrid injection mode (\u03b4p/p offset: 0.85%, x\noffset: 1.5 mm). The injection efficiency and DA/MA criteria yield similar tolerances for the systematic\ndipolar multipoles (b3, b4 and b5) on the order of 10\u22125, without any specific corrections.\nThese tolerances concerning magnetic design and manufacturing [51,52] are considered challeng-\ning. Future work will explore mitigation strategies, such as utilising dedicated corrector coils in the arcs\nand the IRs as implemented for the LHC [53, 54]. The additional nonlinear correctors, which might\n23\n\nFig. 1.11: DA (left) and MA (right) after linear optics corrections having used the errors described in\nTable 1.3, which neglect IR errors and magnetic multipolar errors, for betatron tunes of 217.77 and\n220.369.\nTable 1.7: Median rms values of several optics parameters before (after sextupole ramping) and after\nlinear optics correction (nominal lattice). \u2206\u03c8 stands for phase advance deviations between nearby BPMs.\nParameter\nBefore correction\n(rms)\nAfter correction\n(rms)\nhorizontal orbit (\u00b5m)\n120.2\n120.5\nvertical orbit (\u00b5m)\n217.5\n217.6\n\u2206\u03b2x/\u03b2x (%)\n7.41\n0.29\n\u2206\u03b2y/\u03b2y (%)\n15.79\n2.81\n\u2206Dx (mm)\n57.79\n0.28\n\u2206Dy (mm)\n62.24\n2.80\n\u03b5h (nm)\n0.72\n0.71\n\u03b5v (pm)\n26.01\n0.57\nhoriz. \u2206\u03c8 [2\u03c0]\n1.1 \u00d7 10\u22122\n2.9 \u00d7 10\u22124\nvert. \u2206\u03c8 [2\u03c0]\n1.9 \u00d7 10\u22122\n2.3 \u00d7 10\u22123\nRe f1001\n4.9 \u00d7 10\u22122\n1.7 \u00d7 10\u22124\nIm f1001\n4.4 \u00d7 10\u22122\n5.2 \u00d7 10\u22125\nRe f1010\n3.7 \u00d7 10\u22122\n1.3 \u00d7 10\u22124\nIm f1010\n3.7 \u00d7 10\u22122\n1.3 \u00d7 10\u22124\nrequire dedicated space in the lattice, would significantly relax the field quality tolerances.\n1.3.5\nImpact of errors on spin dynamics and polarisation\nThe precise beam energy measurement in FCC-ee relies on depolarising previously polarised low-intensity\npilot bunches using resonant depolarisation (RDP). This method is suitable for beam energies up to\nabout 80 GeV beam energy, above which the beam energy spread becomes too large and polarisation\nis expected to be lost. Section 1.7 presents more information related to the energy-calibration studies.\n24\n\nTable 1.8: Values of IP optics parameters after a global correction for the nominal lattice from simulations\nthat did not include any IR errors, nor dedicated IP corrections.\nParameter at the IP\nAfter correction (rms)\n\u2206\u03b2x/\u03b2x (%)\n0.34\n\u2206\u03b2y/\u03b2y (%)\n3.08\n\u2206Dx (mm)\n0.003\n\u2206Dy (mm)\n0.001\nRe f1001\n6.5 \u00d7 10\u22126\nIm f1001\n1.7 \u00d7 10\u22125\nRe f1010\n1.6 \u00d7 10\u22125\nIm f1010\n2.2 \u00d7 10\u22125\nTable 1.9: Preliminary bare field quality tolerances, without correction, in units of 10\u22124 at a reference\nradius of 1 cm, inferred from 6D tracking studies for the GHC Z lattice.\nError\nArc Dipoles\nArc Quadrupoles\nArc Sextupoles\nRandom\nSystematic\nRandom\nSystematic\nRandom\nSystematic\nb3\n0.25\n0.1\n1.5\n1.5\n\u2014\n\u2014\na3\n\u2014\n\u2014\n1\n2\n\u2014\n\u2014\nb4\n0.5\n0.25\n\u2014\n\u2014\n\u2014\n\u2014\na4\n\u2014\n\u2014\n\u2014\n\u2014\n30\n25\nb5\n0.3\n0.1\n\u2014\n\u2014\n36\n25\na5\n\u2014\n\u2014\n\u2014\n\u2014\n30\n25\nb6\n\u2014\n\u2014\n1\n0.5\n\u2014\n\u2014\nIR Dipoles\nIR Quadrupoles\nRandom\nSystematic\nRandom\nSystematic\nb3\n1\n1\n\u2014\n\u2014\nb4\n\u2014\n\u2014\n0.1\n0.4\na4\n\u2014\n\u2014\n\u2014\n\u2014\nb5\n1.5\n0.6\n\u2014\n\u2014\na5\n\u2014\n\u2014\n\u2014\n\u2014\nResonant depolarisation (RDP) requires a minimum polarisation level of approximately 10%. While\nthe theoretical equilibrium polarisation exceeds 90%, machine errors significantly reduce the achievable\npolarisation. Additionally, these errors can induce a spin-tune shift that does not correspond to a gen-\nuine beam energy shift, but instead leads to an error in the beam energy inferred from the spin-tune\nmeasurement.\nOn the Z pole, the expected uncertainty in the measured collision energy is 100 keV. To assess\nthe impact of misalignments on the spin dynamics, simulation studies [55] are performed using the code\nBMAD for an IR optics with a local solenoid compensation scheme. Arc and IR misalignments are\nincluded with varying magnitude of misalignment errors. Sextupole strengths are ramped up in a step-\nwise manner with orbit and tune corrections applied on each step. In simulation studies, up to 100 \u00b5m\nand 25 \u00b5m rms misalignments are applied to arc and IR magnets, respectively, along with other errors.\nFor the vast majority of seeds at various beam energies around the Z-pole, the resulting bias in the beam\nenergy extracted from the spin tune stays well below 100 keV, and an equilibrium polarisation above\n10% is reached. Further details are reported in Section 1.7.1.\n25\n\nTable 1.10: Preliminary bare field quality tolerances for arc dipoles, considering top-up injection without\ncorrection, in 10\u22124 units at a reference radius of 1 cm, deduced from 6D tracking studies, for the GHC\nZ lattice.\nError\nOn-axis Injection\nHybrid Injection\nArc Dipoles\nArc Dipoles\nRandom\nSystematic\nRandom\nSystematic\nb3\n\u2014\n0.12\n\u2014\n0.14\nb4\n\u2014\n0.07\n\u2014\n0.15\nb5\n\u2014\n0.07\n\u2014\n0.1\nFuture spin dynamics studies should include even larger misalignment errors along with magnetic\nfield imperfections, as in Table 1.3. The polarisation simulations do not yet include specific correction\ntechniques, which could reduce the spurious spin tune shifts or increase equilibrium polarisation, such\nas harmonic spin matching. Furthermore, alternative optics featuring a non-local solenoid compensation\nscheme and the latter\u2019s impact on polarisation remain to be investigated in greater detail.\n1.4\nCollective effects\nThis section describes the impact of collective effects on the main electron and positron rings. The first\nsubsection describes the impedance, while the second and third subsections show its impact on the beam\ndynamics for both non-colliding and colliding beams, respectively.\nThe fourth subsection discusses electron-cloud effects, which limit the bunch spacing in the col-\nlider. The last two subsections review the minor impact of intra-beam scattering and the increase in\nemittance due to interaction with residual gas.\n1.4.1\nImpedance and wakefield model\nThe low-energy machine, operating at 45.6 GeV, is the most affected by collective effects because of\nthe lowest beam energy combined with the highest beam current, the lowest emittances and the longest\ndamping times. The design of this machine is still in progress and also the coupling impedance budget is\ncontinuously evolving in parallel with the updates of the vacuum chamber components. Correspondingly,\nthe collective effects and instability thresholds need constant revision. The latest impedance model\nincludes vacuum chambers, collimators, bellows, taper transitions and initial models of BPMs and RF\ncavities.\nThe resistive wall (RW) beam coupling impedance of the arc vacuum chamber is one of the key\ncontributions to be assessed. The beam pipe, shown in Fig. 1.12, with a radius b of 30 mm, is made of\ncopper coated with a 150 nm thin layer of NEG (recently, it has been proposed to increase the thickness\nto 200 nm) used for pumping purposes and electron cloud suppression. There are two lateral winglets\nfor placing synchrotron radiation absorbers. The impedance model was initially obtained with the elec-\ntromagnetic code IW2D [56] in the circular vacuum chamber approximation. As a following step, the\ncalculation has been extended to include the effect of the winglets by using appropriate form factors,\nwhich have been numerically estimated with CST PARTICLE STUDIO. The results were also compared\nwith those of the 2D electromagnetic solver VACI [57] that can simulate the geometry, including the\nwinglets.\nThe collimation system is another important impedance source. The impedance model that is\nbeing evaluated accounts for the geometric dimensions, materials, and beta functions at collimator lo-\ncations. Since a mechanical design of a collimator still does not exist at the moment, the geometric\nimpedance has been evaluated assuming a linear taper with an angle of 15\u00b0 to go from the collimator\n26\n\nFig. 1.12: Beam pipe shape.\naperture to the chamber aperture of 30 mm.\nThe overall impedance of collimators, including material losses and tapers, has been obtained\nusing CST simulations. Additionally, the resistive part of the collimators\u2019 impedance has been evaluated\nwith IW2D using a flat chamber model. Therefore, by combining CST and IW2D results, resistive and\ngeometric contributions can be disentangled. The resistive wall impedance of the collimators is between\n5% and 10% of the vacuum chamber contribution, depending on the choice of material. The primary\nvertical collimator (tcp.v.b1) makes the highest contribution to this impedance source due to the very\nsmall gap.\nThe preliminary collimator model with linear tapers gives the largest impedance contribution in\nthe transverse plane. An optimised design of the collimator tapers, for example, by minimising the taper\nangle (increasing the taper length) and considering optimised nonlinear taper modelling, is crucial.\nBellows are another important source of impedance. A crucial component of the device is the RF\nshielding with comb-type fingers and small electric fingers to ensure electric contact between the two\nsides of the shielding. These fingers are shown on the left-hand side of Fig. 1.13 for a model similar to\nthat of SuperKEKB, designed by the vacuum group and shown on the right-hand side of the same figure.\nThe contribution of the shielding is fundamental to suppress the low-frequency resonances due to the\nbellows, which otherwise would lead to a high impedance contribution.\nAn important aspect of the bellows\u2019 contribution to the impedance model is related to their number.\nFor dipole arcs, quadrupoles/sextupoles sections, and including additional bellows for the RF system,\ninjection system, collimation, etc., a total number of 10 000 devices is assumed. Other geometries are\nunder study by the vacuum group.\nAdditionally, the impedance contribution due to the 400 MHz RF system has been evaluated. This\ncomprises 132 two-cell cavities per beam, arranged in groups of 4 for each cryomodule, with 50 cm long\ntapers on both ends, guaranteeing a transition from 50 mm to 150 mm circular pipe inside the cryomod-\nule. Finally, 4000 BPMs have also been taken into account.\nThe total impedance is shown in Fig. 1.14 for the longitudinal and transverse cases. The contribu-\ntion of each device to the longitudinal and vertical dipolar impedance is displayed in Fig. 1.15.\n27\n\nFig. 1.13: Simulated models of FCC-ee beam vacuum chamber including bellows.\nFig. 1.14: Total longitudinal (on the right) and transverse (on the left) impedance model.\n1.4.2\nImpedance induced collective effects\nLongitudinal effect\nBelow the microwave instability threshold, longitudinal wakefields result in bunch lengthening and bunch\nshape distortion. Above the instability threshold, the energy spread also starts growing, and the internal\nbunch motion becomes more turbulent. The internal bunch oscillations can be harmful to the process of\nreaching the nominal luminosity. However, in the FCC-ee the longitudinal dynamics is strongly affected\nby the beam-beam interaction with a large Piwinski angle and beamstrahlung. Both the bunch length\nand the energy spread increase in collision due to beamstrahlung help mitigate the longitudinal collective\neffects.\nLongitudinal beam dynamics simulations have been performed with the PYHEADTAIL code [58]\nwhich was compared with other tracking codes [59,60], for the FCC-ee case, giving excellent agreement.\nTwo regimes are being considered for beam dynamics studies: the single-beam mode and the\ncolliding beams mode. Both regimes are important for collider operations. While the single beam mode\nis important for the machine commissioning and tuning, the collision mode must be considered for\nthe luminosity production runs. In the first case, the bunch length at the nominal intensity is strongly\naffected by the potential well distortion, but the energy spread is essentially constant. In the second\ncase, thanks to the beamstrahlung, the potential well distortion due to the wakefield is small and the\ncollision predominantly defines the bunch lengthening and the energy spread growth. In this condition,\nhowever, a self-consistent study considering the beam-beam effects is necessary. This aspect is discussed\n28\n\nFig. 1.15: Contribution of each device included in the model. Longitudinal impedance on the right,\nvertical dipolar impedance on the left.\nin Section 1.4.3.\nTransverse effects\nThe main effect of the short-range transverse wakefield on the single bunch dynamics is the excitation of\nthe so-called transverse mode coupling instability (TMCI). Under certain conditions, the frequencies of\nsome coherent transverse oscillation modes of a bunch can shift and couple together. In particular, for\nFCC-ee, the \u20180\u2019 mode shifts towards the \u2018-1\u2019 mode. When they couple together, the instability occurs\nwith a consequent loss of the beam (or a part thereof).\nThe coherent frequencies of the lowest order coherent oscillation modes can be obtained from\nthe results of XSUITE/PYHEADTAIL with a proper Fourier analysis [61]. Additionally, it has been\nfound that for FCC-ee the TMCI threshold depends on the longitudinal wakefield. In Fig. 1.16, left-\nhand side, the real part of the tune shift of the first azimuthal transverse oscillation modes normalised\nby the synchrotron tune Qs0 is shown as a function of bunch population. As can be seen, the instability\nthreshold is about 3 \u00d7 1011, which is well above the nominal bunch intensity. This instability is not of\nthe \u2018mode coupling\u2019 type, but it is due to the single \u2018-1\u2019 oscillation mode. These results were obtained\nwithout accounting for the beamstrahlung due to collisions, but a transverse damper for stabilising the\ncoupled bunch instabilities and a value of the chromaticity equal to 5 were introduced.\nThe geometrical impedance of the collimators is not included since their design is still in progress.\nHowever, to take into account all the devices not evaluated so far, and to check for a possible upper limit\non the machine stability, simulations under the same conditions as for the left-hand side of Fig. 1.16 were\nperformed, but assuming an overall two times larger impedance. The results are shown in the right-hand\npicture.\nIn addition to the single bunch dynamics studies, a coupled bunch instability can be excited, driven\nessentially by the real part of the resistive wall impedance at low frequency. Its study can be performed\nby considering the motion of the entire beam (not of the single bunch) as a sum of coherently coupled\nbunch oscillation modes. Under some conditions, the growth rate of the \u00b5th mode (\u00b5 = 0, 1, ..., Nb \u22121)\nis\n\u03b1\u00b5,\u22a5= \u2212\ncI\n4\u03c0(E0/e)Q\u03b2\n\u221e\nX\nq=\u2212\u221e\nRe\n\u0002\nZ\u22a5\n\u0000\u03c9q\n\u0001\u0003\n(1.12)\nwhere I is the total beam current, Q\u03b2 the betatron tune, \u03c3\u03c4 the rms bunch length in time, and \u03c9q are\nfrequencies spaced by the revolution period and depending on the coupled bunch mode excited and on\n29\n\nFig. 1.16: Real part of the tune shift of the first azimuthal transverse coherent oscillation modes nor-\nmalised by the synchrotron tune Qs0 as a function of bunch population with a bunch-by-bunch feedback\nsystem and chromaticity = 5. On the right-hand side, the impedance is multiplied by a factor of 2 to\nexplore the margins with the current impedance model.\nchromaticity. When \u03b1\u00b5 is positive, the corresponding mode is unstable. This occurs when the transverse\nimpedance is evaluated at negative frequencies. The most unstable mode has a rise time of about 1.3 ms,\ncorresponding to a few turns. This instability depends on the fractional part of the betatron tune and\non chromaticity, and it can be mitigated by a bunch-by-bunch feedback system, like that used in other\ncircular accelerators (DA\u03a6NE, SuperKEKB, ...). Such feedback, in combination with the longitudinal\nwakefield, also has a mitigating effect on the TMCI. Without feedback, the TMCI threshold is expected\nto be below a bunch population of 1.0 \u00d7 1011.\nFinally, it must be noted that the results related to the transverse wakefield are valid in the single-\nbeam regime, without the beamstrahlung effect. For self-consistent results in a collision, the beam-beam\neffects must also be included.\n1.4.3\nInterplay between beam-beam and beam coupling impedance effects\nThe x-z instability\nAmong the new effects caused by beam-beam collisions, the large Piwinski angle causes the coherent\nhorizontal-longitudinal (x-z) beam-beam instability to become a critical limiting phenomenon for the\ncollider design performance [3]. Unlike impedance-induced collective instabilities, the x-z instability\nis driven by the beam\u2013beam force itself. This new coherent instability also differs from the classic\nincoherent synchro-betatron resonances excited by the beam\u2013beam interaction. The instability manifests\nitself as a horizontal beam position variation along the bunch length, similar to a head-tail instability. It\nlimits the ranges of horizontal tunes where the design luminosity can be achieved.\nThe interplay between the beam\u2013beam interaction, beamstrahlung and the longitudinal and trans-\nverse beam coupling impedance may affect both the x-z instability and the beam parameters in the stable\nbetatron tune areas. It has been observed in numerical simulations that the stable areas get narrower and\nthe stable regions on the betatron tune diagram are shifted because of the impedance-related synchrotron\ntune reduction. On the other hand, the horizontal beam blow-up becomes somewhat weaker due to the\nsynchrotron frequency spread and bunch lengthening induced by the longitudinal impedance [62].\nFigure 1.17 shows the results of strong-strong beam-beam simulations, featuring the effect of\nboth the longitudinal and transverse impedance for different horizontal tunes. The luminosity loss at\neach synchrotron sidebands of the horizontal half integer is clearly visible in the configuration without\nchromaticity. A chromaticity of 5 units is sufficient to stabilise the instability over a wide range of\nhorizontal tune. Here, it is important to consider the impact of transient beam loading, which is stronger\nwith the new reversed polarity operation of the double cell RF cavities at the Z energy. Different bunches\n30\n\nwill experience difference RF voltages ranging from 79 to 93 MV (Chap. 3.4). The stability has to\nbe ensured for all bunches with a given horizontal tune. A slightly higher chromaticity (6 units) is\nrequired to stabilise the x-z instability with higher voltages (Fig. 1.17, right). When considering the\nexisting impedance model, the horizontal tune range is constrained above \u223c0.55 by bunches featuring\nhigh RF voltage. However, when considering a stronger impedance, the constraint on the horizontal tune\nis relaxed, thanks to the bunch lengthening by the impedance. This shows that bunch lengthening is an\nefficient way to mitigate this instability. An alternative mitigation consists in reducing the horizontal \u03b2\u2217.\nFig. 1.17: Luminosity dependence on the horizontal tune due to the x-z instability. The left plot corre-\nsponds to the nominal configuration at the Z energy without active damper simulated by IBB [63] taking\ninto account the effect of the strong-strong beam-beam interaction as well as transverse and longitudinal\nwakefields [64]. The right plot corresponds to the same configuration but with a chromaticity of 6 units,\nincluding a transverse damper featuring a damping time of 10 turns and is obtained with XSUITE [65].\nThe results are shown for different RF voltages. Blue curves, marked (2x) feature an impedance twice as\nstrong as the existing impedance model.\nThe mode coupling instability of colliding beams\nWith a vertical beam-beam tune shift larger than the synchrotron tune, it is expected that the mode\ncoupling instability of colliding beams [66] may occur at the FCC-ee. This was confirmed with two\nsemi-analytical models as well as with tracking simulations [67, 68]. The mechanism is illustrated in\nFig. 1.18. The lower synchrotron sideband (head-tail mode -1) couples with the beam-beam \u03c0-mode\nleading to a strong instability. This instability can be partially mitigated by active feedback, yet a sizeable\nvertical chromaticity is required, as shown in Fig. 1.19. Based on these tracking simulations, it appears\nthat a rather low vertical chromaticity (2 units) is sufficient to maintain the beam stability considering the\npresent impedance model. Higher chromaticities are required if an impedance larger by a factor two is\nconsidered. It is clear that this instability constrains the vertical impedance budget.\n1.4.4\nElectron Cloud\nAs observed in several accelerators [69\u201372], electron clouds may cause several unwanted effects, in\nparticular beam instabilities, emittance growth, tune shifts, additional heat load on the vacuum chambers\nand vacuum degradation. Since electron cloud formation depends strongly on the bunch spacing, it is\na concern primarily at the Z operating point, where the high beam current requires a large number of\nclosely spaced bunches.\nElectron clouds can be created by secondary electron emission through a beam-induced multipact-\ning process, through an accumulation of photoelectrons, or a combination thereof. For their mitigation,\nit is important to identify the required constraints on the corresponding material properties to avoid elec-\n31\n\nFig. 1.18: Tune (left) and growth rate (right) for all coherent modes obtained with the circulant matrix\nmodel for the nominal configuration with varying bunch intensity without active damper or chromaticity.\nThe impact of the longitudinal impedance is also neglected. The most unstable low order mode of oscil-\nlation resulting from the interplay of the head-tail mode -1 with the beam-beam \u03c0-mode is highlighted\nin light blue.\nFig. 1.19: Luminosity dependence on the vertical chromaticity used to mitigate the mode coupling insta-\nbility of colliding beams for different RF voltages. The blue curves marked (2x) feature and impedance\ntwice as strong as the existing impedance model.\ntron cloud formation. This has been achieved by simulating the process of electron cloud formation in\nthe beam chamber, using the PYECLOUD code [73].\nSecondary electron emission\nElectron cloud formation strongly depends on the secondary electron yield (SEY) of the beam chamber\nsurface, defined as the ratio between the emitted and the impinging electron currents. The tendency for\nelectron cloud build-up for different values of the SEY has been determined in drift spaces, as well as in\nthe presence of the main arc dipolar, quadrupolar and sextupolar fields [74].\nThe build-up is found to depend strongly on the bunch intensity in addition to the SEY and the\nbunch spacing. The bunch intensity dependence is non-monotonic, so that electron cloud formation\noccurs more easily with bunch intensities that are lower than the nominal intensity. In particular, the\nmost critical intensities fall within the range of 1.0 to 1.5 \u00d7 1011 e+ per bunch, as shown in Fig 1.20.\nSince the machine relies on a top-up injection scheme, with individual injections of one-tenth of the\nnominal bunch population, the most critical intensities will be encountered when filling the machine. The\nmultipacting thresholds, i.e., the highest maximum SEY guaranteed to suppress build-up, with nominal\nintensity as well as any intensity between 0.2 \u00d7 1011 e+ per bunch and the nominal value of 2.14 \u00d7 1011\ne+ per bunch are summarised in Table 1.11. These results are obtained using the so-called ECLOUD\n32\n\nFig. 1.20: Average electron density in the vacuum chamber versus SEY for different bunch intensities\n(the nominal value is shown as a solid line) in dipole (left) and quadrupole (right) magnets. The SEY\nmultipacting threshold, considering all bunch intensities during the charge accumulation phase, is shown\nby the vertical dashed grey line.\nsecondary emission model [75], parametrising measurements of LHC Cu co-laminated beam screen\nsamples [76\u201378]. Simulations using the alternative Furman-Pivi model [79] reveal even tighter material\nconstraints [80]. The SEY requirements, especially for intensities below the nominal value, are not\nguaranteed to be achieved with the planned copper surface with a thin NEG coating [81, 82]. Several\nmitigation measures have been considered to alleviate these constraints, as discussed below.\nTable 1.11: SEY multipacting thresholds for the main arc elements.\nElement\nField\nBunch population\nThresholds\nDrift\n-\nnominal\n1.4\nbelow nominal\n1.2\nDipole\n15.2 mT\nnominal\n1.4\nbelow nominal\n1.0\nQuadrupole\n1.45 T/m\nnominal\n1.1\nbelow nominal\n1.0\nSextupole\n72.5 T/m2\nnominal\n1.1\nbelow nominal\n1.0\nPhotoelectron emission\nThe previous results do not take into account the photoelectrons. These are primary electrons produced\nthrough the photoemission from the chamber walls due to the synchrotron radiation emitted by the cir-\nculating beam. Photoelectrons enhance the electron cloud build-up process and, in large quantities, can\ninduce electron cloud effects even in the absence of beam-induced multipacting. The quantity of pho-\ntoelectrons emitted is determined by the photoelectron yield (PY) of the beam chamber, defined as the\nratio between the emitted photoelectrons and the number of impinging photons, along with the quantity\nof photons scattered into the main beam chamber.\nResults from electron cloud build-up simulations (see Fig. 1.21) indicate that an acceptable number\n33\n\nof photoelectrons is around npe = 1.0 \u00d7 10\u22124 (e+m)\u22121. The PY and the number of photoelectrons\ngenerated inside the central chamber are related through the following equation:\nPY =\nInpe\n\u03d5Lpipee ,\n(1.13)\nwhere I is the beam current, \u03d5 is the photon flux and Lpipe is the perimeter of the vacuum chamber.\nAlternatively,\nnpe = 5\u03c0\u03b1\u03b3 R PY\n\u221a\n3 Larc\n\u22480.08 R PY [e+m]\u22121\n(1.14)\nwith \u03b1e the fine-structure constant, Larc \u224877 km the total length of the FCC-ee arcs, \u03b3 the Lorentz factor\n(\u03b3 \u224890 000 for Z running) and R the fraction of primary photons absorbed (possibly after multiple re-\nflections) on the main circular part of the vacuum chamber. Preliminary ray-tracing simulations indicate\nthat the photon flux on the central part of the chamber is in the order of \u03d5 = 1013 - 1014 photons/(cm2\u00b7s),\nexcept immediately around the photon absorbers where an even higher flux is expected [83]. Combining\nthis information with the results from electron cloud build-up simulations using Eq. (1.13), a limit on\nPY in the range 3% - 3\u2030 is obtained. Photoelectron yields of order 2% have been measured for NEG\ncoated chambers [84]. For FCC-ee, many primary and reflected photons are absorbed at the photon stops\nor inside the winglets of the vacuum chamber, where they do not contribute to electron-cloud buildup. A\nnew design of the photon absorbers is predicted to reduce further the photon flux inside the main circular\npart of the vacuum chamber [85]; see Section 3.2.7).\nFig. 1.21: Central electron density versus SEY in the arc dipoles for different bunch intensities (left) and\nfor different photoelectron numbers npe (right), with the most critical bunch intensity of 1 \u00d7 1011 e+.\nThe theoretical stability threshold (Eq. 1.15) is indicated by the horizontal dashed black line.\nElectron cloud effects\nElectron cloud effects can be fully avoided only by ensuring the suppression of primary and secondary\nelectron emission according to the constraints above. In case the properties of the vacuum chamber\ncannot meet these constraints, the effects of the electron cloud on the beam and the machine environment\nmust be assessed.\nThe electron cloud can trigger beam instabilities as the beams pass through the dense cloud [86].\nThe electron cloud density corresponding to the single-bunch instability threshold can be estimated as\n34\n\n[87\u201389]\n\u03c1thr = 2\u03b3Qs\u03c9e\u03c3z/c\n\u221a\n3KQre\u03b2yL\n(1.15)\nwhere\n\u03c9e =\n \nNbrec2\n\u221a\n2\u03c0\u03c3z\u03c3y(\u03c3x + \u03c3y)\n!1/2\n(1.16)\nis the electron angular oscillation frequency, K = \u03c9e\u03c3z/c characterises how many electrons contribute\nto the instability, Q = min(K, 7) is the quality factor of the effective wake field and L is the length of the\nparticle accelerator, or the considered element. The stability threshold has also been evaluated through\nsimulations, using the PYECLOUD-PYHEADTAIL suite [90], for drift spaces and dipole fields. The\nresults between the theoretical estimate and the simulation studies are consistent to the level of the order\nof magnitude. This stability threshold must be compared with the electron cloud density close to the\nvacuum chamber centre before a bunch passage, as shown for the dipole magnets in Fig 1.21. The build-\nup studies show that the electron density exceeds the stability threshold whenever the SEY is above the\nmultipacting threshold in all the elements considered, except the sextupole magnets. In other words, if\nthe material constraints are not met, beam instabilities are expected to occur. In addition, other effects\ncaused by the interaction of the beam with a dense electron cloud, such as emittance growth, tune shift\nand tune spread, can also be expected.\nThe electron cloud impinging on the chamber surface can also cause environmental effects, such\nas outgassing and heat load. Build-up simulations estimate the total additional heat load in the arcs due\nto electron cloud to be in the order of a percentage of the synchrotron radiation power (50 MW per beam)\nwhen multipacting occurs.\nFurther mitigation measures\nIf the beam chamber material cannot be made to satisfy the multipacting thresholds, further mitigation\nmeasures are needed. Since the electron cloud build-up depends strongly on the bunch spacing, vari-\nous modifications to the beam train pattern can raise the multipacting thresholds and ease the material\nconstraints.\nOne approach to obtain larger SEY multipacting thresholds is choosing filling schemes with larger\nbunch spacing. A bunch spacing of 50 ns results in SEY multipacting thresholds that are larger than or\nequal to 1.3 for all the arc elements considered, see Fig. 1.22. However, increasing the bunch spacing\nwould require increasing the bunch intensity to maintain a constant beam current. Larger bunch inten-\nsities, in turn, could lead to problems due to other collective effects, such as exceeding the beam-beam\ntune shift limit and instabilities driven by the beam-coupling impedance [91].\nBecause the strictest constraints on the SEY arise during the charge accumulation phase, a filling\nscheme with non-uniform bunch intensities during this stage only, as discussed in Chapter 2, is sufficient\nto significantly relax the constraints. This approach leads to SEY multipacting thresholds over the full\ncharge accumulation phase that are equal or close to those for the nominal bunch intensity, as seen in\nFig. 1.22, since the effective spacing between bunches of intermediate intensity is significantly increased.\nAs with the nominal bunch intensity, the lowest SEY multipacting threshold is found in the quadrupoles\nat 1.1. A potential concern with this approach is having bunches of significantly different intensities in\nthe collider at the same time, which may make it difficult to find a working point that ensures stability\nfor all bunches due to the x-z instability discussed in Section 1.4.3.\nAnother possibility is to use filling schemes with permanently non-uniform bunch spacing, as\nalready successfully used for electron cloud mitigation in the LHC [92] and at the former PEP-II B fac-\ntory [93]. Such filling schemes have an internal structure, with a few closely spaced bunches followed\nby a larger gap, which repeats itself over the duration of the train. A simulation study has been done to\nidentify effective structures, keeping the duration and total number of bunches in the train equal to the\n35\n\nFig. 1.22: Average electron density versus SEY in the arc dipole magnets at different stages of the charge\naccumulation phase with 50 ns uniform bunch spacing (left) and a filling scheme with non-uniform bunch\nintensity during charge accumulation (right). The SEY multipacting threshold, considering all the bunch\nintensities during the charge accumulation phase, is shown by the vertical dashed grey line.\nFig. 1.23: Schematics of a non-uniform filling pattern (4e+16e) with a 5 ns bunch spacing and an internal\nstructure consisting of 4 consecutive bunches followed by 16 empty bunch slots (top) and the nominal\nfilling scheme with 25 ns uniform bunch spacing (bottom).\nfilling pattern with uniform bunch spacing. The study shows that the largest electron cloud suppression\ncan be achieved by reducing the bunch spacing of the closely spaced bunches as much as possible in\norder to maximise the length of the following gap. For example, the filling pattern shown in Fig. 1.23,\nusing an internal structure with 5 ns bunch spacing, consisting of 4 consecutive bunches followed by 16\nempty 5 ns bunch slots repeated over the full bunch train, gives good electron cloud suppression with\nSEY multipacting thresholds that are larger than or equal to 1.2, see Fig. 1.24. Such bunch train patterns\ncould even allow decreasing the nominal bunch population, with a corresponding increase in the total\nnumber of bunches, while keeping the surface requirements achievable. This approach could also have\nthe benefit of reducing the severity of other collective effects, such as beam-coupling impedance and\nbeam-beam effects.\n36\n\nFig. 1.24:\nAverage electron density versus SEY at different stages of the charge accumulation phase\nwith a non-uniform filling pattern (4b+16e) in the arc dipoles (left) and quadrupoles (right). The SEY\nmultipacting threshold, considering all the bunch intensities during the charge accumulation phase, is\nshown by the vertical dashed grey line.\n1.4.5\nSpace Charge\nGiven the large size of the FCC-ee ring and the small emittance, the space-charge tune shift is noticeable\nfor the Z running. The vertical space-charge tune shift is [94]\n\u2206QSC,y \u2248\nNbreC\n(2\u03c0)3/2\u03b33\u03c3z\n\u001c \u03b2y\n\u03c3y\u03c3x\n\u001d\n\u2248\nNbreC\n(2\u03c0)3/2\u03b33\u03c3z\u03b5x\u03ba1/2 \u0010\n1 + \u03ba1/2\u0011 ,\n(1.17)\nwhere \u03ba = \u03b5y/\u03b5x. Table 1.12 shows that the space charge tune shift approaches 0.01.\nPETRA IV\nSOLEIL II\nFCC-ee collider\nBeam energy [GeV]\n6.0\n2.75\n45.6\nCircumference [km]\n2.305\n0.354\n90.7\nMax. bunch charge [nC]\n8\n7.4\n35\nRms bunch length rms [mm]\n20\n15\n15.2\nRms vert. emittance \u03b5x [pm]\n20\n83\n710\nRms vert. emittance \u03b5y [pm]\n2\n8\n2.1\nEmittance ratio \u03ba\n0.1\n0.1\n0.1003\n\u2206QSC,y\n0.057\n0.036\n0.008\nTable 1.12: Estimated SC tune shifts in PETRA IV, SOLEIL II, and the FCC-ee collider rings on the Z\npole.\n1.4.6\nIntrabeam scattering\nIntrabeam scattering (IBS) is a possible issue for the Z running, since, here, the beam energy is the\nlowest and the radiation damping the weakest. The largest effect is in the horizontal plane. For the\nnominal beam parameters the horizontal amplitude growth time due to IBS, \u03c4IBS,x, amounts to 142 000\n37\n\nturns, compared with a horizontal radiation damping time, \u03c4SR,x of about 2400 turns. Consequently, at\nthe Z, IBS increases the rms horizontal equilibrium emittance by \u03c4SR,x/\u03c4IBS,x \u22481.5%. IBS will also\ngenerate a horizontal non-Gaussian beam halo. The IBS effect is negligible in the other two planes or at\nother beam energies.\n1.4.7\nVacuum and ion effects\nThe vacuum chamber of the two collider rings features winglets with regular photon stops to intercept\nand efficiently absorb synchrotron radiation. The chamber itself has a continuous coating of ultra-thin\nNEG material, in order to ensure an adequate vacuum pressure without long conditioning.\nBaseline parameters for the collider rings relevant for vacuum and ion effects in the arcs are com-\npiled in Table 1.13. As discussed in Section 2.3.7, at the FCC-ee in Z running mode, the beam consists\nof 40 trains, each containing 280 bunches spaced by tsep = 25 ns. After 1 hour of operation at nominal\nbeam current the average vacuum pressure in the collider arcs is expected to be below 10\u22127 mbar (see\nFig. 3.8).\nTable 1.13: Collider ring parameters for Z running (45.6 GeV).\nParameter\nSymbol\nValue\nUnit\nBunch population\nNb\n2.18\n1011\nBunch spacing\ntsep\n25\nns\nNo. bunches/train\nnb\n280\n\u2014\nBeam energy\nEb\n45.6\nGeV\nHor. emittance\n\u03b5x\n0.70\nnm\nVert. emittance\n\u03b5y\n1.05\npm\nRMS rel. momentum spread with BS\n0.121\n%\nAv. hor. \u03b2 function\n\u27e8\u03b2x\u27e9\n\u223c100\nm\nAv. hor. dispersion function\n\u27e8Dx\u27e9\n\u223c0.45\nm\nAv. vert. \u03b2 function\n\n\u03b2y\n\u000b\n\u223c100\nm\nAv. hor. beam size\n\u27e8\u03c3x\u27e9\n\u223c600\n\u00b5m\nAv. vert. beam size\n\n\u03c3y\n\u000b\n\u223c10\n\u00b5m\nTransv. ampl. damping time\n\u03c4x,y\n0.7\ns\nAverage vacuum pressure\n< P >\n< 10\u22129\nmbar\nEmittance damping rate\n\u2212d\u03b5x/dt\n2.5\nnm/s\nIBS emittance growth rate\nd\u03b5x/dt\n0.1\nnm/s\nA representative residual gas component for the NEG-coated vacuum system of the FCC-ee is\nH2. However, here we pessimistically consider CO, which has a shorter radiation length than H2. In a\nGaussian approximation [95], the emittance growth due to multiple gas scattering is\n\u001cd\u03b5x,y\ndt\n\u001d\n\u22481\n2\n\n\u03b2x,y\n\u000b \u001214.1MeV/c\np\n\u00132 mCOpCOc\nkbTX0,CO\n.\n(1.18)\nAssuming mCO = 14 g/mol, T = 300 K, X0,CO \u224840 g cm\u22122 (similar for N2 and CO2) gives\n\nd\u03b5x,y/dt\n\u000b\n\u22482 \u00d7 10\u22125 (m/s) pCO [Pa] .\n(1.19)\nAt a pressure of 10\u22127 mbar, or 10\u22125 Pa, as reached after 1 hour of nominal operation, this emittance\ngrowth of \u223c2 nm/s, due to multiple gas scattering, is a few percent of the horizontal emittance damping\n38\n\nor quantum excitation. However, in the vertical plane the growth is significant, and leads to a new rms\nequilibrium emittance of\n\u03f5y,eq \u2248\n\u001cd\u03b5x,y\ndt\n\u001d \u03c4y\n2 .\n(1.20)\nConsequently, to achieve the target equilibrium emittance of 1 pm, the average vacuum pressure must\nnot exceed 10\u22127 Pa or 10\u22129 mbar.\nAnother limit on the vacuum pressure is set by the beam lifetime due to bremsstrahlung [96]:\n1\n\u03c4brems\n= \u03c3brems c n ,\n(1.21)\nwhere the integrated Bethe-Heitler cross section for particle loss is [97]\n\u03c3brems \u22484\n3\n\u03c1\nnX0\n\u0012\nln 1\n\u03f5m\n\u22125\n8\n\u0013\n,\n(1.22)\nwith n = p/(kbT) the molecular density, \u03c1 the mass density, so that \u03c1/n = 28 g/NA for CO (with NA\nAvogadro\u2019s constant), and \u03f5m the fractional momentum acceptance, e.g. about 1% at the Z. For CO we\nobtain \u03c3brems \u22486 barn; for H2 the cross section is \u03c3brems \u22480.3 barn. At a residual gas pressure of 10\u22129\nmbar (10\u22127 Pa), the beam lifetime would be 60 hours in case of CO and 1300 hours for H2.\nThe ionisation cross section of carbon monoxide (CO) molecules impacted by high-energy charged\nparticles is \u03c3iion \u22482 Mbarn [98], which translates to an ion generation rate of \u03bb\u2032\nion \u22486 m\u22121 per electron\nat 1 Torr and 300 K. For hydrogen molecules (H2) the ionization cross section is about 0.4 Mbarn [98],\nso that in this case \u03bb\u2032\nion \u22481 m\u22121 per electron at 1 Torr and 300 K.\nIons are trapped between bunches if their atomic (or molecular) mass A (in units of proton mass)\nexceeds a critical mass Ac defined as [99]\nAc \u2261Nbrpc \u2206tsep\n2\u03c3y(\u03c3x + \u03c3y) .\n(1.23)\nFor the FCC-ee parameters of Table 1.13, Ac \u2248200, which is significantly larger than the mass of any\ntypical molecule of the residual gas. The Carli-Bartosik filling scheme described in Section 2.3.7 will\nalso help prevent the trapping of ions between bunches when filling from zero after a beam abort.\n1.5\nCollimation\nThe FCC-ee has a target highest stored beam energy of 17.5 MJ for the most critical Z mode, and 0.3 MJ\nfor the t\u00aft mode, leading to a risk of experiment backgrounds, superconducting magnet quenches, equip-\nment damage, radiation damage, and material activation, as a result of unavoidable beam losses. A\nrobust collimation system is therefore needed in FCC-ee, not only for controlling the backgrounds of the\nphysics experiments as in previous e+e\u2212colliders, but also to protect the machine. As a comparison,\nin SuperKEKB [100, 101], with a design stored beam energy of only 0.18 MJ, collimator damage and\nquenching of superconducting magnets have occurred as a result of sudden, unexpected beam losses, as\nwell as high backgrounds during injections [102,103].\nBoth beam losses and synchrotron radiation (SR) can cause detector backgrounds, with the latter\nexpected to be the dominating source of machine-induced background. A distinction is hence made\nbetween the beam halo collimation system, designed to protect the machine against beam losses, and the\nSR collimation system, designed to protect the detectors against SR photons. The SR system consists of\ndedicated collimators and masks upstream of the interaction points (IPs), studied for the CDR [13] and\nfurther optimised for the present collider layout, as discussed in Section 1.6.\nThe halo collimation must be designed to protect the aperture bottlenecks from regular and anoma-\nlous beam losses and safely dissipate the loss power away from the superconducting final focus quadrupoles\n39\n\nand other sensitive equipment. The beam halo collimation system must also protect the SR collimators.\nExcessive beam losses on these SR collimators might induce detector backgrounds or even damage them,\nas they are made of Inermet180 (a tungsten heavy alloy with high-Z chosen to optimise absorption) and\nhence less robust to beam losses than the beam-halo collimators (see below).\nThe beam halo collimation system was not studied for the CDR, and the following describes the\nfirst baseline design. It includes two-stage betatron and off-momentum collimation systems with spe-\ncialised optics in PF [104, 105]. The betatron collimation system is located upstream of the auxiliary\n(non-collision) beam crossing in the middle of PF and consists of 1 primary collimator (TCP) to inter-\ncept the primary beam halo and 2 secondary collimators (TCS) to intercept particles out-scattered by\nthe TCP, in each of the transverse planes, while the off-momentum collimation system is located down-\nstream of the crossing and consists of 1 TCP and 2 TCSs in the horizontal plane. Secondary particle\nshower absorbers are placed in between the TCP and the TCS, as will be described more in detail in Sec-\ntion 1.5.3. The studies shown in the following are carried out for the Z mode, as this is the most critical\nfor collimation. It should be noted that in this optics version, a vertical emittance blow-up resulting from\nthe combination of the beam-beam interactions and the super-periodicity breaking due to the specialised\ncollimation optics in PF has been discovered [106], as well as a reduction of the momentum acceptance.\nWork is ongoing to update the optics and hence also the layout, using a common LSS optics as discussed\nin Section 1.2. It is expected that a solution can be found, but it will imply some modifications to the\npresented layout.\nThe settings for the betatron TCPs, shown in Table 1.14, are selected to protect the aperture bot-\ntlenecks in the final focus doublets. Including alignment and beam tolerances [107] they are estimated\nto be 14.6 \u03c3 in the horizontal plane (\u03c3 is the rms betatron beam size) and 84.2 \u03c3 in the vertical plane\ndue to the asymmetric emittances (\u03f5x = 0.71 nm, \u03f5y = 1.9 pm). The minimum gap of the TCP is also\nconstrained by requirements of the top-up injection scheme [108], as well as by impedance and beam\nlifetime considerations. Therefore, the betatron TCP cuts were chosen as 11 \u03c3 in the horizontal plane\nand 65 \u03c3 in the vertical plane, protecting the aperture bottleneck while ensuring a half-gap of at least\n2 mm for impedance reasons. The physical opening is most challenging for the vertical TCP due to the\noptics and the flat beams. The horizontal TCP has an opening of 6.7 mm. The off-momentum TCP is set\nto a momentum cut \u03b4c=1.3%, slightly outside of the RF bucket and momentum acceptance of about 1%\n(target value obtained without collimation optics). The betatron secondary collimators are set to provide\na minimum retraction of 1\u03c3 or 0.6 mm in the horizontal and of 10\u03c3 or 0.3 mm in the vertical plane from\nthe corresponding TCP setting as preliminary values to ensure the collimation hierarchy is maintained\neven in the case of orbit drifts, \u03b2-beating or other dynamic effects [109, 110]. The hierarchy margins\nare tight with the presently assumed settings, especially in the vertical plane. However, the vertical TCP\nis currently placed relatively far from the vertical DA of about 30 \u03c3. Tightening their gaps is an option\nthat is being considered, and that will relax the hierarchy margin constraints, although it is not sure that\nthis still gives an acceptable impedance. The phase advance \u00b5 between the TCP and TCS is set by the\noptimal phase advance condition [111],\n\u00b5 = arctan\n q\nn2\nTCS \u2212n2\nTCP\nnTCP\n!\n,\n(1.24)\nwhere nTCP and nTCS are the gaps in units of \u03c3 for the TCP and TCS. Two tertiary collimators (TCT),\none for each transverse plane, are placed upstream of each IP to provide local protection of the SR\ncollimators and the aperture bottlenecks. The settings of the TCTs have been selected to be 13\u03c3 in the\nhorizontal plane and 80 \u03c3 in the vertical plane. The SR collimators have mechanical gaps in the range of\n8\u201317 mm, corresponding to a minimum aperture of 14 \u03c3 in the horizontal and 84.2\u03c3 in the vertical plane,\nabove the TCT apertures.\n40\n\n1.5.1\nCollimator design parameters\nThe beam halo collimators must be robust enough to handle the loss of a significant fraction of the beam\nenergy. Carbon-based materials like CFC, graphite, or molybdenum carbide-graphite (MoGr) [112] are\nhence considered for the TCPs and TCTs due to their potential exposure to direct large beam impacts.\nMoGr has about a factor 10 times better conductivity than graphite, while graphite is more robust to\nbeam impacts. Higher-density, higher-Z materials, like Mo, or TZM (Ti-Mo-Zr), are considered for\nthe TCSs, which intercept out-scattered particles from the TCPs. The design hence consists of 25 cm\nlong carbon-based TCPs and 30 cm long Mo TCS. The lengths were selected based on the first studies,\naiming to achieve a good balance between impedance and collimation efficiency [113\u2013115] (impedance\ncalculations are discussed in Section 1.4.1). In the tracking studies presented below, MoGr is assumed\nas TCP and TCT material, Mo as TCS material and Inermet180 as SR collimator material.\nAs for the mechanical design, described in detail in Section 3.6, is it assumed that the collimators\nhave two movable jaws as in the LHC [116], with built-in BPMs and separate motors for the upstream\nand downstream edges to allow control of the jaw tilt angle. An LHC-like minimum step of 5 \u00b5m at\neach motor is tentatively assumed, although it will be refined in future studies. SR collimators are also\nmovable but currently have no requirement for tilt angle adjustment, while the SR masks are fixed. The\ndesign of these devices is part of the MDI studies discussed in Section 1.6.\nThe collimator parameters and settings for all collimators, also including the SR collimators, are\nshown in Table 1.14. These parameters should be considered preliminary and might evolve in the future\nwhen detailed constraints from robustness and impedance are quantified.\nTable 1.14: Summary table of collimator parameters and settings for the FCC-ee Z operation mode.\nThe momentum cut \u03b4cut is not reported for collimators in nearly dispersion-free regions. All collimators\nare assumed to have two movable jaws and built-in BPMs.\nType\nCount\nPlane\nMaterial\nLength\n[m]\nGap\n[\u03c3]\nGap\n[mm]\n\u03b4cut\n[%]\nAngular\nadjustment\n\u03b2 TCP\n1\nH\nC-based\n0.25\n11.0\n6.7\n8.9\nyes\n\u03b2 TCS\n2\nH\nMo-based\n0.3\n12.0\n5.0, 7.0\n6.0, 22.8\nyes\n\u03b2 TCP\n1\nV\nC-based\n0.25\n65.0\n2.4\n\u2013\nyes\n\u03b2 TCS\n2\nV\nMo-based\n0.3\n75.0\n2.5, 2.9\n\u2013\nyes\n\u03b4 TCP\n1\nH\nC-based\n0.25\n18.5\n4.2\n1.3\nyes\n\u03b4 TCS\n2\nH\nMo-based\n0.3\n21.5\n4.6, 16.7\n2.1, 1.6\nyes\nTCSA\n1\nH\nMo-based\n0.3\n15\n8.2\n\u2013\nyes\nTCSA\n1\nV\nMo-based\n0.3\n91\n3.2\n\u2013\nyes\nTCT\n4\nV\nC-based\n0.25\n80.0\n3.4\n\u2013\nyes\nTCT\n4\nH\nC-based\n0.25\n13.0\n6.1\n\u2013\nyes\nSR BWL\n4\nH\nW-based\n0.1\n14.0\n16.9\n\u2013\nno\nSR QC3\n4\nH\nW-based\n0.1\n14.0\n17.1\n\u2013\nno\nSR QC0\n4\nV\nW-based\n0.1\n84.2\n8.2\n\u2013\nno\nSR QC0\n4\nH\nW-based\n0.1\n14.0\n17.4\n\u2013\nno\nSR QC2\n4\nV\nW-based\n0.1\n84.2\n8.0\n\u2013\nno\nSR QC2\n4\nH\nW-based\n0.1\n14.0\n17.0\n\u2013\nno\n1.5.2\nCollimation performance studies\nTo judge if the cleaning performance of the collimation system is sufficient, a number of beam loss\nscenarios have been simulated, and further beam loss scenarios will be studied in the future to ensure\nthat the machine is never at risk. For a full quantitative assessment of the adequacy of the collimation\n41\n\nperformance, tolerances to beam losses for different impacted elements are also needed, which are under\nstudy.\nThe collimation performance is evaluated using the XSUITE-BDSIM coupling simulation frame-\nwork [117\u2013122], integrating particle tracking in the magnetic lattice with particle-matter interactions in\nthe collimators. The scenarios studied so far include betatron and off-momentum generic beam halo\nlosses, losses from beam-residual-gas interactions, spent beam losses, and losses caused by fast insta-\nbilities for the most critical Z operation mode. The simulation outputs for these scenarios, presented in\nthe following, provide the loss distribution along the longitudinal coordinate s. With the present state of\nknowledge, the performance is fully adequate in all scenarios studied, with the possible exception of the\nfast instability. In this case, interlocks or redundant damper design should be considered, as explained\nbelow. Further details on the machine-protection aspects are found in Section 2.6. A first iteration of\nstudies has been done on the spent beam losses. However, further iterations need to be coupled to the\ncollimation optics due to the issues discovered with vertical emittance blow-up and reduced MA.\nGeneric beam halo losses\nThe scenario considered is that of a generic loss, impacting on the collimation system. The initial mecha-\nnism causing the loss is not simulated\u2014as in LHC studies [123], instead, the beam distribution is sampled\ndirectly at the impacted TCP. The maximum impact parameter assumed is 1 \u00b5m, which may be further\nrefined in the future. This allows to model the effect of collimator edge scattering and provides a suffi-\nciently pessimistic estimate of the collimation performance [105]. 5 \u00d7 106 primary particles are tracked\nfor 500 turns with SR, RF cavities and tapering of the magnets included. The loss maps in Fig. 1.25 show\nthe power load distribution from generic horizontal betatron losses around the collider ring, normalised\nto a beam lifetime drop to 5 min, corresponding to 58.3 kW of loss power. This is assumed as a design\nspecification that the system should be able to handle.\n\u03b2-collimation\n\u03b4-collimation\nFig. 1.25: Power load distribution loss map for generic beam halo losses of the FCC-ee positron beam,\nshown for horizontal betatron losses. The power loads are evaluated assuming a lifetime drop to 5 min.\nThe beam circulates from left to right. On the right, a magnification of the collimation insertion PF is\npresented.\nFigure 1.25 demonstrates an excellent cleaning performance, with the vast majority of losses\n(>99.5%) confined within the collimation insertion PF. The losses leaking out are safely intercepted\nby the TCTs upstream of the IPs. The collimation performance can be further enhanced by angularly\naligning the collimator jaws to the beam divergence at the collimator locations [114, 115]. The more\nsignificant the beam divergence, the higher is the performance gain obtained.\nBeam-gas losses\nThe scenario considered is that of beam losses caused by bremsstrahlung interactions with the residual\ngas in the vacuum chamber. The assumed gas composition (85% H2, 10% CO and 5% CO2) and\npressure distribution along the ring comes from dedicated vacuum studies see Section 3.2. To simulate\nthe interaction with the residual gas, 10 000 beam-gas scattering centres are included in the tracking [124]\n42\n\nand 10\u00d7106 primary particles are tracked for 17\u00d7106 equivalent turns with SR, RF cavities and magnet\ntapering enabled.\nFig. 1.26: Power load distribution loss map for beam-gas beam losses of the FCC-ee positron beam. The\nbeam circulates from left to right. The power loads are evaluated considering a 5 h lifetime resulting\nfrom the expected pressure after 1 h of beam conditioning at full nominal current of 1.27 A.\nThe loss map in Fig. 1.26 shows the power load distribution from beam-gas losses, normalised to\na beam-gas lifetime of 5 h that results from the expected pressure after 1 h of beam conditioning at full\nnominal current of 1.27 A. This pessimistic scenario represents the start of FCC-ee operation, and the\npressure is expected to condition down by a factor of up to 100 over time (Section 3.2). Consequently,\nbeam-gas interactions are unlikely to significantly affect the lifetime of the FCC-ee, which is primarily\ndetermined by Bhabha scattering at the IPs. Even in this pessimistic scenario, low power loads (<0.1 W)\nare expected on most components, with the highest loads recorded on the halo collimators (10-100 W)\nand SR collimators (1 W). Such power load levels are not a concern.\nFast instability\nThe fast instability scenario assumes the failure of the feedback system designed to mitigate the coupled\nbunch instability described in Section 1.4.2. This instability is not modelled using the beam interactions\nwith the impedance but through eight synchronised dipole kickers instead, one per arc, to reproduce\na smooth exponential growth of the betatron oscillation amplitude, either in the vertical or horizontal\nplane. The kicker strengths are defined as k = (A0/\u03c3x,y) cos\n\u00002\u03c0Qx,yt\n\u0001\nexp(t/\u03c4), where A0 denotes\nan arbitrary amplitude, \u03c3x,y the local beam size, Qx,y the betaron tunes, and \u03c4 the instability rise time.\nTwo scenarios are studied: a rise time of either three turns (representing the worst case) or six turns. The\ndependence on the phase advance is also analysed. In each case, 5 \u00d7 105, 45.6 GeV primary electrons\nare simulated with SR and magnet tapering enabled. Several phase advances between the initial kick and\nthe TCP have also been studied (0\u00b0, 30\u00b0, 60\u00b0, 90\u00b0).\nThe simulated beam oscillates coherently until the collimator apertures are reached, after which it\nis entirely lost within a few turns. At the Z mode, this results in the release of 17.5 MJ on collimators\nover a few turns. Due to the short rise time, losses of the order of MJ can be expected in the collimators\nas shown in Fig. 1.27. It is under study whether the collimators can sustain this impact, but the FCC-\nee should be designed in such a way that the instability does not occur in this way, for example by\ninterlocking the damper or the orbit, or through a redundant damper system that would increase the time\nconstants in case of failure.\n1.5.3\nStudies of energy deposition and shower absorbers\nIn addition to the studies of the global cleaning performance, FLUKA [125\u2013127] radiation transport\nsimulations for the PF insertion were carried out in order to quantify the beam-induced power deposition\nin the machine and the environment. A specific geometry model of the betatron collimation system,\nincluding collimators, beam pipes, magnets and the machine tunnel, was implemented. The collimator\njaws and tanks were represented by simplified models since no technical design existed at this early stage.\nThe absorber blocks of the primary and secondary collimators were assumed to be made of graphite and\n43\n\nFig. 1.27: Integrated loss map over all turns for a fast instability in the horizontal plane with a rise time\nof 3 turns.\nTZM, respectively, with a similar cross section to the LHC collimators. The blocks were embedded in a\nmetallic frame made of TZM. A generic beam loss scenario was simulated assuming that beam particles\nimpact on the front face of the primary collimators (vertical and horizontal), at a distance of 1 \u00b5m from\nthe collimator edge. The simulations were carried out for operation at the Z pole, since the stored beam\nenergy and hence the expected power loss in the betatron collimation system is much higher than for the\nother beam modes. The interaction of the 45.6 GeV electrons and positrons in the blocks results in the\nproduction of electromagnetic showers, which are not contained in the primary collimator jaws because\nof the significant shower length and the small impact parameter; the simulations show that primary\ncollimators absorb less than 0.5% of the impacting energy, while most of the energy is carried away by\nsecondary photons, electrons and positrons. Most of these shower particles are lost on the downstream\nvacuum chambers in PF, or they are intercepted by the secondary collimators. The simulations show\nthat the first secondary collimator absorbs about 40% of the power, while almost half of the power is\ndeposited in the chamber walls or leaks into the tunnel environment.\nConsidering the significant particle leakage from the collimators, it is necessary to install addi-\ntional shower absorbers in PF, which reduce the distributed production of radionuclides in the surround-\nings and mitigate radiation effects in other equipment. In addition, the shower absorbers dissipate the\nheat created in a more controlled way. The effects of placing two shower absorbers (one vertical and\none horizontal) between the primary and secondary collimators have been investigated. Their position\nwas optimised in such a way as to minimise the energy escaping to the vacuum chambers and the envi-\nronment. Using the same design as the TCS but with a wider gap (15\u03c3 and 91\u03c3 in the x- and y-plane,\nrespectively), the shower absorbers proved to be an effective strategy for mitigating the energy leakage;\njust two shower absorbers can reduce the power deposition in the vacuum chambers and tunnel to 15%.\nThe optimal position and number of shower absorbers in PF are expected to evolve in the future, depend-\ning on the final collimation layout and distances between the collimators. In addition, shower absorbers\nor masks are also likely to be needed for the momentum collimation system and possibly also near the\ntertiary collimators in the experiment insertions.\n1.6\nMachine-detector interface (MDI)\nThe MDI of the FCC-ee has a compact and complex design [128\u2013131] that fulfils constraints given both\nby the machine and the detector requirements.\nA common IR layout is requested for all FCC-ee energies and is shown in Fig. 1.28. The flexibility\nof the IR optics is obtained by splitting the final focus quadrupoles (FFQs) QC1 and QC2 into three and\ntwo segments, respectively, and by modulating their sign and strength according to the beam energy.\nTens of nanometres in the vertical beam size and a few micrometres horizontally require small\n\u03b2-functions at the IP, as reported in Table 1.2. The distance of the face of QC1 from the IP (\u2113\u2217) is 2.2 m,\nwell inside the detector volume. The crab-waist collision scheme requires a small horizontal beam size\nand a relatively large crossing angle at the IP, set to 30 mrad, which results with the beams entering/ex-\niting with separate beam pipes at about 1.32 m from the IP. In addition to the optical constraints on the\n44\n\ninteraction region (IR) layout, physics reconstruction benefits from a stay-clear cone of 100 mrad from\nthe interaction point (IP) along the z-axis. 4\nFig. 1.28: Section view of the accelerator components from the IP to the end of the first final focus\nquadrupole (QC1), at about 5.6 m.\nTwo schemes are considered to compensate for the coupling induced by the detector solenoidal\nmagnetic field and the crossing angle. The baseline one, called local scheme, uses a couple of strong\ncompensating solenoids with opposite sign with respect to the one of the detector and placed either\nside of the IP, within \u00b1\u2113\u2217(shown in Fig. 1.28); this scheme requires a maximum detector field of 2 T,\nand 5 T for the compensating one, in order to limit the vertical emittance growth to about 30%. An\nalternative scheme, named non-local , envisages an equal and opposite strength magnetic field to that of\nthe detector, positioned at either side of the IP several metres outside of the detector, possibly tolerating\nhigher detector magnetic fields to about 2.5 T, inducing however, a high spin-depolarisation effect whose\nmitigation is currently under study. In the local scheme the field integral\nR \u20d7Bds is cancelled before the\nFFQs, while in the non-local one the compensating solenoids need additional very weak local dipole\ncorrectors and skew quadrupoles around the FFQs, to correct orbit and dispersion. In both schemes a\nscreening solenoid is requested, around the QC1 portion inside the detector, to cancel the effects of the\ndetector magnetic field on both beams. In the non-local scheme the emission of synchrotron radiation\ndue to the compensating solenoid is much reduced with respect to the local scheme. These studies will\nbe completed in the next design phase.\nTwo calorimeters, known as LumiCal, are positioned in front of the compensating solenoids, as\nillustrated in Fig. 1.29. They are designed to measure the integrated luminosity with an accuracy of 10\u22124.\nAchieving this level of precision requires the relative positioning of the two calorimeters to be\nknown within \u00b1110 \u00b5m, necessitating long-term mechanical stability. Additionally, to avoid compro-\nmising the luminosity measurement, the material budget within their angular acceptance range (50 to\n110 mrad) must be minimised. To further reduce uncertainties in energy reconstruction, the LumiCal\nmust be assembled and installed as a single, mechanically rigid unit.\nThe vertex detector, also shown in Fig. 1.29, is placed as close as possible to the interaction\nregion (IR) beampipe, which has an internal radius of 1 cm. It covers an angular range of approximately\n| cos \u03b8| < 0.99. The above topics are discussed in more detail in Volume 1 of this report.\nThe sections below describe the main features of the MDI. A more detailed discussion can be\n4The detector\u2019s coordinate system is defined with its origin at the nominal collision point. The z-axis is aligned along\nthe bisector of the incoming and outgoing beam directions, with its positive direction corresponding to that of the outgoing\npositrons. The y-axis points vertically upward, while the x-axis extends radially outward from the centre of the FCC. The\nazimuthal angle \u03c6 is measured from the x-axis in the x-y plane, with the radial coordinate in this plane denoted as r. The polar\nangle \u03d1 is measured from the z-axis.\n45\n\nSupport tube\nLumiCal\nInner Vertex\nCompensating \nsolenoid\nQC1\nOuter Vertex\nScreening solenoid\nFig. 1.29: Layout of the interaction region. The support tube allows the integration of the luminosity\ncalorimeter (LumiCal) and the vertex detector. The three segments of the final focus quadrupoles (QC1)\nare shown with the screening and compensating solenoids.\nfound in Ref. [132].\n1.6.1\nInteraction Region layout\nThe central beam pipe is 18 cm long with 10 mm inner radius, followed by a pair of ellipto-conical beam\npipes 1064 mm long on either side, as shown in Fig. 1.30. All of these are made in AlBeMet162, an\nalloy of 62% of beryllium and 38% aluminium, chosen for its high modulus and low-density charac-\nteristics. The mechanical model of the IR vacuum chamber is designed to provide low impedance, low\nmaterial budget, and mechanical resistance while guaranteeing thermal stability by removing heat load\nwith a suitable cooling system. The impedance was minimised by carefully designing the transverse\nsection of the beam pipe, with a smooth transition from a circular to an elliptical transverse shape, as\ndiscussed in Ref. [133]. An internal coating layer of 5 \u00b5m gold, inside the central beam pipe, ensures\na good thermal and electrical conductivity to minimise the beam heat load, with a maximum value of\nnearly 60 W expected at the Z pole [133], and shields the vertex detector from residual high energy syn-\nchrotron radiation photons. The central vacuum chamber envisages a double layer structure made of two\nconcentric cylinders, each with a thickness of 0.35 mm and assembled with a 1 mm gap for the liquid\nparaffin cooling system, thus bringing its effective diameter to 23.4 mm.\nThe ellipto-conical vacuum chamber extends between 90 mm and 1154.5 mm from the IP, and\nits thickness is tapered from the central value until it reaches 2 mm. Water flowing into the AlbeMet\ncooling channels on top of the ellipto-conical beam pipe refrigerates it, extracting an expected heat load\nof about 130 W at the Z pole; an asymmetric design is needed to comply with the angular acceptance of\nthe luminosity calorimeter, which is centred around the outgoing beam pipe axis.\nThe beam pipes will be supported by an external lightweight carbon-fibre structure (support tube)\nby means of two bellows [129], inspired by the DA\u03a6NE and ESRF designs [134]. The support tube\nconsists of an empty cylindrical multilayered wall rigid structure, that eases the integration of the MDI\ncomponents, including the vertex and the LumiCal detector, providing a cantilevered support for the\ncentral beam pipe, as shown in Fig. 1.29.\nA thermo-structural analysis has been performed to calculate the temperature distribution, stress,\nstrain and displacement of the beam pipes. The temperature distribution for the two chambers is shown\nin Fig. 1.31 for operation at the Z pole which has the highest thermal load. The maximum temperature\n46\n\nFig. 1.30: Top Left: Central chamber including cooling inlets and outlets for the paraffin cooling circuit\nhoused in a double layer and its internal gold coating layer; Top Right: ellipto-conical vacuum chamber\nwith asymmetric cooling channels; Bottom: assembly of the IR chambers.\nof the central chamber reaches 29 \u25e6C, cooled with paraffin entering at 18 \u25e6C, and reaches 50 \u25e6C in the\nconical chamber which is cooled with water entering at 16 \u25e6C. The maximum stress has been calculated\nconsidering the constraint from the configuration of a cantilevered support, which results in a maximum\ndisplacement of 0.5 mm, and a maximum stress ten times lower than the AlBeMet162 yield strength\n(193 MPa).\nFig. 1.31: ANSYS simulation of the temperature distribution along the ellipto-conical chamber for a\ndeposited power of 54 W over the central chamber and 130 W over the conical chamber.\nThe integration of the vertex detector has been studied for the IDEA detector concept. The detector\nis placed on top of the vacuum chamber: two thin peek-based rings, anchored on either side at about\n170 mm from the IP on the ellipto-conical chamber, hold a carbon fibre structure supporting three layers\nof silicon vertex detectors located at about 13.7, 23.7, and 35 mm radii, as shown in Fig. 1.32. Additional\ncylindrical layers and disks of silicon detectors complement the vertex detector in the reconstruction of\ncharged particles. For a more comprehensive description, see Ref. [131].\n47\n\nA comprehensive calculation of beam induced HOM power deposition on the IR chambers includ-\ning the effects on the bellows, and BPMs has to be finalised.\nA remote vacuum connection device, located inside the niche of the front side of the QC1 cryostat\n(see Section 1.6.2), needs to be studied to provide a vacuum to the IR chambers once assembled inside\nthe detector. The tight space and accessibility in that area pose considerable challenges and a solution is\nbeing studied.\nParaffin cooling \ninlet-outlet \nLayer 1 and 2 cooling cone\nLayer 3 cooling cone\nSupport cone\nInner Vertex layers\nFig. 1.32: Longitudinal section of the beam pipe and the inner vertex. The dark grey object is the conical\nsupport of the vertex detector, which is supported by the conical beam pipe. At the right edge of the\nsupport cone, the inlet/outlet paraffin cooling manifolds are visible.\n1.6.2\nIR magnet system\nThe IR magnet system consists of the superconducting (SC) FFQs, the solenoids, and the correctors,\nall housed in a cryostat. The optimal solution is to house QC1 and QC2 in separate cryostats, since\nthe QC1 is entirely inside the detector, thus allowing it to be accessed separately from QC2, which is\noutside. A critical issue concerns the limited space available inside the QC1 cryostat, in which the two\nbeam pipes come very close to each other due to the crossing angle. At one end, the challenge is to\nallow sufficient thermal shield between the warm beam pipes and the cold quadrupole coils. At the other\nend, the challenge is to allow sufficient space for the winding of the corrector coils, especially around\nthe QC1 segment closest to the IP. As shown in Fig. 1.28, the shape of the QC1 cryostat closest to the\nIP features a niche to house warm elements, such as bellows, remote vacuum connection, and a beam\nposition monitor (BPM). Other BPMs should be placed at the entrances of QC1 and QC2 for each beam.\nWidening the angular size of the cryostat, as seen from the IP, currently set to 100 mrad, could alleviate\nthe problems mentioned above, but the impact on the detector calorimeter acceptance placed behind it\nneeds to be evaluated.\nThe FFQs are based on the canted cosine theta design (CCT), with Nb-Ti conductors. Three dif-\nferent options to operate the FFQ cryostat at different temperatures are envisaged: pressurised He II at\n1.9-2.1 K, supercritical He at 4.5 K, or He gas forced flow at 10-20 K. The first option allows a super-\nfluid regime, minimising any possible induced vibrations. The third one minimises the power budget,\nwhile the second is intermediate. Yet another solution under study considers using high-temperature\nsuperconducting (HTS) magnets, which would allow even further power reduction.\nThe anti-solenoid and screening solenoid needed to compensate for the coupling induced by the\ndetector field and the crossing angle, bring additional constraints to the IR magnet system. As said at the\nbeginning of this chapter, two coupling compensation schemes are under study.\n1.6.3\nAlignment, detector integration and maintenance\nAn alignment strategy and monitoring system is under study, and envisages three main components [135].\nThe first one monitors the shape deformation of the screening solenoid\u2019s support [136], and uses in-line\n48\n\nFig. 1.33: SR collimators and masks upstream the IR (left); SR masks shapes and locations at the FFQs\n(right).\nmultiplexed and distributed frequency scanning interferometry (IMD-FSI) [137] to monitor sections of\noptical fibres firmly installed on the inner surface of the screening solenoid support.\nThe second system utilises a mirror, installed at the end of each fibre, to redirect the laser beam\ntowards the centre of the assembly, targeting the FFQs, the BPMs, LumiCal. This is very similar to\nthe FSI heads installed on the low-\u03b2 quadrupoles in the HL-LHC MDI, as described in [138]. These\ndistance measurements will monitor the position of the inner components relative to the cryostat. Finally,\nto ensure the alignment of both sides of the MDI, a long-range alignment system will be installed, also\nbased on FSI but using a different optical setup to enable longer-distance measurements. A set-up at\nCERN is currently studying the experimental validation of the alignment system of the FFQs with the\nFSI system, using a 1:2 mock-up of the beam pipes and cryostat.\nThe accessibility in the FCC-ee MDI region may be limited by accelerator components, such as\nthe FFQ cryostats and the booster ring (Section 4.1). Three opening scenarios for the detectors installed\nin either the large or small experiment caverns are described in Section 5.3 of Volume 1.\n1.6.4\nBeam induced backgrounds\nBackgrounds in the IR arise either from processes where particles from one beam lose energy or deviate\nfrom their trajectory or interact with those of the opposite beam at the IP. Collimators and absorbers,\nas described in Section 1.5, remove the bulk of the particles (electrons/positrons and photons) which\neventually would hit the detectors, but some effects may remain due to the scattering of the particles of\nthese devices.\nThe effect of synchrotron radiation (SR) in the MDI region has been simulated with the latest\nversion of BDSIM [139, 140], utilising the GEANT4 toolkit, which includes the X-ray reflection. The\nbulk of the SR is almost collinear with the beam, and thanks to the final focus optics design, does not enter\nthe detector, however a fraction of it can still reach it as a result of magnet misalignments, imperfections,\nand beam tails [141]. SR masks are designed to stop such radiation close to the detector, located before\nand after the FFQs, as shown in the right plot of Fig. 1.33. The mask apertures are 15 mm for the\ncircular ones between QC1 and QC2, and 7 mm horizontal aperture for the mask after QC1, closest to\nthe IP. In realistic conditions, some scattering at their edges can still enter the detector region. Studies\nare ongoing to evaluate the effects in the various sub-detectors, and eventually optimise the masks and\ntertiary collimators; as an example Fig. 1.34 shows the power deposited in the IR, assuming 5 minutes\nbeam lifetime, non-zero closed orbits with a transverse deviation of 100 \u00b5m, transverse divergence of\n6 \u00b5rad, and beam tails.\n49\n\nFig. 1.34: SR power deposition in realistic conditions. The blue line represents the beam core with a\nhalo corresponding to 5 minutes lifetime, the yellow line represents a beam core with a non zero closed\norbit (NZCO) and halo.\nFig. 1.35: Power load distribution loss map for generic beam halo losses of the FCC-ee positron beam,\nillustrating horizontal betatron losses in the region spanning 700 m upstream of IPD. Power loads are\nevaluated assuming a beam lifetime drop to 5 min. The beam circulates from left to right.\nElectrons and positrons may lose energy or deviate from the central trajectory, thus populating\nthe tails of the phase space, and are commonly known as halo beam losses [142]. These particles are\nmostly intercepted by the collimators. This effect has been simulated with XSUITE-BDSIM simulation\ntool [143]. Some of these particles may scatter off the edges of the collimators and reach the interaction\nregion. The vast majority of the beam halo losses are intercepted by the tertiary collimators (TCTs)\nwhich have been added upstream of the SR collimators, and minimal losses (O(10mW) beyond the last\nSR collimators before the IPs are observed in all cases, as shown in Fig. 1.35. In this way, the background\ncontribution from beam halo particles that leak from the beam halo collimation system (located in PF)\nis not expected to be an issue. Nevertheless, the background contribution from particle showers arising\nfrom the interaction of beam halo particles with the SR collimators might not be negligible and should\nbe studied in the future.\nBackground and energy deposition due to beam-gas interactions, incoherent pair production, and\nradiative Bhabha scattering are discussed in Section 5.4 of Volume 1.\nThe bulk of the radiation emitted in the IR is collinear with the incoming and outgoing beams,\nand is dumped at the end of a 500 m long tunnel. This radiation is composed of two main contributions,\nbeamstrahlung and synchrotron radiation [144]. In addition, radiative Bhabha events produced at the\nIP generate off-energy electrons that are lost in the magnetic elements within 150 m of the IP. All these\nsources have been studied at the Z pole and above the t\u00aft threshold. Radiative Bhabha are the main source\nof radiation in the first 200 m at the Z, while beamstrahlung dominates at around 500 m at the dump. Due\nto the harder spectrum of synchrotron radiation at t\u00aft energies, which has a critical energy of the order\nof 1 MeV, this source overwhelms the others. For more technical discussions, see Section 1.9. Studies\n50\n\nare ongoing to evaluate the possibility of using the spatial profile of the beamstrahlung radiation for\nbeam-beam fine tuning, as proposed for other colliders.\nThe effects of the thermal photons and injection backgrounds will be studied in the next phase of\nthe project.\n1.6.5\nExperimental implementation of the interaction region\nThe finalisation of the system engineering of the IR is of paramount importance for both the machine\nand the detector layouts.\nThe construction of a full-scale mock-up of the IR beam pipes, including the results of the study\nof the integration with the vertex and LumiCal detectors and using the concept of the support tube, is\nongoing at INFN-Frascati in collaboration with INFN-Pisa and CERN.\nFig. 1.36: Measurement setup for central beam pipe cooling system.\nThe first prototype of the central beam pipe was manufactured in aluminium and equipped with\nflanges to validate the cooling performance. The assembly of its components (see Fig. 1.30) has been per-\nformed using laser beam-welding in the ENEA-Casaccia laboratory. The test system comprises a cooling\ncircuit with an operating range between 0.08 and 0.033 kg/s of liquid paraffin, temperature sensors, pre-\ncision pressure gauges, and flow-meters. An ohmic internal heater provides the heat load expected from\nthe wakefields, up to a total power of nearly 100 W allowing a factor of two safety margin. The setup\nis shown in Fig. 1.36. Initial measurements performed using water as a coolant confirm the expected\nbehaviour, showing that for a nominal power of 54 W, flowing water at 0.017 kg/s with an inlet temper-\nature of 18\u00b0C and 19\u00b0C at the exit, the beam pipe external surface temperature remains at 19\u00b0C, with a\npressure drop of 0.13 kPa. Raising the power to 100 W and reducing the flow to 0.08 kg/s the beam pipe\ntemperature increases to 24\u00b0C, still within the margins of the system.\nThe elliptic-conical beam pipe prototypes are being fabricated in aluminium and will eventually be\nwelded to the central beam pipe, also made in aluminium. The cooling manifolds of the elliptic-conical\nbeam pipes will be soldered using an electro-beam welding technique, and their performance will be\nvalidated using a similar system to that for the central beam pipe.\n51\n\nThe bellows prototype will be fabricated in aluminium, and will allow the study of the assembly\nprocedure, the welding of an elliptical geometry, and the effectiveness of the thermal/electrical contact.\nAt the same time, a mock-up of the inner vertex detector, along with the air-cooling cones, is being\nfabricated using carbon fibre. This aims to validate both the mechanical assembly procedure and the\ncooling performance in a dedicated experimental setup. The outer tracker and disks will be constructed\nfrom aluminium and integrated into the support tube, which will also house a LumiCal mock-up made\nfrom 3D-printed material.\nThe full-scale IR mock-up will ultimately be used to study the integration sequence of various\ncomponents, helping to identify potential critical issues. Additionally, it may serve as a platform for\ninvestigating the alignment system.\n1.7\nEnergy calibration and polarisation\nA principal task of FCC-ee is to probe for physics beyond the Standard Model by making ultra-precise\nmeasurements of a wide range of electroweak observables, whose overall consistency can then be as-\nsessed. Knowledge of the collision energy \u221as is a key input to many of these measurements, and this is\nobtained through measurements of the mean beam energy Eb. Corrections must then be applied to the\nnaive relation \u221as = 2Eb to obtain the centre-of-mass energy at each interaction point.\nIn electron or positron storage rings, transverse polarisation naturally builds up through the Sokolov-\nTernov effect. The spin tune, defined as the ratio of the spin precession frequency to the revolution\nfrequency, is proportional to the average beam energy Eb. The spin tune can be directly measured by\nthe procedure of resonant depolarisation (RDP), in which the frequency of a depolariser kicker mag-\nnet is varied until the polarisation is found to vanish, when the depolariser frequency corresponds to\nthe spin precession frequency. This technique has been exploited at many facilities, such as VEPP-\n2M [145], VEPP-4M [146], CESR [147], DORIS [148], and, most notably, at LEP in scans of the Z\nresonance [149]. Alternatively, in a free spin precession (FSP) measurement the depolariser may be used\nto rotate the spin vector into the horizontal plane, and the precession frequency can then be measured\ndirectly.\nThese polarisation-based precision measurements, however, will only be possible for Z-pole op-\neration and at energies up to and including the W+W\u2212threshold. At higher energies, the polarisation\nlevel will be too small for RDP and FSP measurements to be practical, and, here, the energy scale will\nhave to be determined from physics processes at the experiments, such as e+e\u2212\u2192f \u00aff\u03b3 production, as\nit was done by the LEP experiments, e.g. Ref. [150].\nFor the ZW and t\u00aft modes of operation, these energy-calibration data from the detectors could be\ncomplemented by dipole-magnet spectrometer techniques, as carried out at LEP [151] or based on the\ndistribution of laser-Compton back-scattered electrons, utilising the polarimeter set up [152] (Subsection\n1.7.5). Yet another possibility will be to regularly inject pilot bunches pre-polarised in the injector\ncomplex, and to measure their FSP after injection. Simulations predict that, up to the ZH energy, a\npolarisation level of \u223c10% can be preserved during the FCC-ee booster energy ramp [153].\nWhen calculating \u221as it is necessary to have good knowledge of the crossing angle of the two\nbeams, to account for local energy variations from synchrotron radiation, the RF system and impedance,\nand to consider the effects of opposite sign vertical dispersion at the interaction points.\nThe knowledge of Eb at LEP was dominated by the sampling rate of RDP measurements, which\nwere performed outside physics operation with a periodicity of around a week. The energy was found to\nvary significantly between measurements due to several effects, for example, earth tides [149]. In order\nto enable the much greater degree of systematic control that the vastly larger sample sizes at FCC-ee\nwarrants, the operational strategy will be very different to LEP. Measurements of Eb will be performed\nseveral times an hour on non-colliding pilot bunches. Around 160 pilot bunches per beam will be injected\nat the start of the fill, and wiggler magnets will be activated to speed up the polarisation time. One to\n52\n\ntwo hours will be required for the polarisation to build, after which the wigglers will be turned off and\nphysics (colliding) bunches will be injected. The RF frequency will be continually adjusted to keep the\nbeams centred in the quadrupoles, thus suppressing tide-driven energy changes, which would otherwise\nbe O(100 MeV). A model will be developed to track residual energy variations between measurements.\nIn Ref. [154], it was demonstrated that the systematic uncertainty from the knowledge of the col-\nlision energy on the key electroweak observables can be greatly reduced compared to what was possible\nat LEP. More recent studies have confirmed this conclusion and showed that further improvements are\npossible. For example, energy-related uncertainties of around 100 keV and 12 keV are envisaged for the\nZ mass and width, respectively, to be compared to the equivalent numbers of 1.7 MeV and 1.2 MeV at\nLEP [149]. These estimates should, however, be regarded as provisional, and efforts are underway to re-\nduce them further. The uncertainty expected on the W mass from the knowledge of \u221as is around 160 keV,\nwhich is sufficient for the statistical precision. Steps towards improvements and greater robustness in the\nenergy calibration were explored at a workshop at CERN in autumn 2022 [155].\nThe following provides a brief status report of the key components required for the \u221as calibration.\nThe discussion is focused on the accelerator, but remarks are also included on important inputs that will\ncome from the experiments, in particular, the measurement of the spread in the centre-of-mass energy\n\u03b4\u221as, which must also be known to a high degree of precision. More details are given in Volume 1 of this\nReport. A fuller discussion on all these topics may be found in Ref. [156].\n1.7.1\nBeam polarisation and optimisation\nThe polarisation of electron and positron beams naturally builds up over time. The maximum theoretical\npolarisation is 92.4% and it is oriented anti-parallel and parallel to the magnetic field, for electrons and\npositrons, respectively. In an error-free flat machine, i.e. in the absence of vertical bending magnets, or\nsolenoids, this means that the polarisation is fully vertical [157], and, hence, \u20d7n0 \u2225\u02c6y. The design-orbit\nspin tune is equal to \u03bd0 = a\u03b3rel, where a is the gyro-magnetic anomaly and \u03b3rel the relativistic Lorentz-\nfactor. The spin precesses around \u20d7n0. Due to strong synchrotron radiation, the local beam energy varies\nsignificantly along the circumference. \u03bd0 corresponds, therefore, to the average beam energy over one\nrevolution with an error below 0.3 keV.\nIn practice, the level of polarization is lowered by several mechanisms, including magnetic and\nalignment errors, which can lead to resonance excitation between the spin-orbit and the betatron- and syn-\nchrotron motion. Since depolarising effects are stronger for larger vertical, closed orbits, well-optimised\norbit correction and optics tuning techniques are required to achieve sufficient polarisation. In addi-\ntion to optics and emittance tuning techniques (see Section 1.3), dedicated spin-matching bumps have\nbeen studied, and these show an improvement in polarisation [158]. Furthermore, errors not only reduce\nthe achievable polarisation, but can also lead to a shift between a\u03b3 and the measured spin tune \u03bd0. To\nstudy the Z-line shape measurements at beam energies in the range of 43.85 to 47.37 GeV are foreseen.\nIn recent studies, no systematic offset between a\u03b3 and \u03bd0 is found between the studied beam energies\naround the Z-pole. Additionally, simulation studies which assume up to 100 \u00b5m arc and 25 \u00b5m IR rms\nmisalignments (plus 5% randomly missing BPMs, 1% BPM random scaling errors, and 1 \u00b5m random\nBPM resolution error) [159, 160], respectively, yield an absolute offset between a\u03b3 and \u03bd0 well below\n100 keV for the vast majority of seeds [159]. These studies only included orbit corrections. Additional\noptics tuning techniques are likely to reduce the remaining offset further.\nThe alternative IR layout with a non-local solenoid compensation scheme leads to interleaved spin\ndeflections around the longitudinal and the horizontal axis, resulting in a deviation of \u20d7n0 estimated to\nroughly 10 \u00b5rad. Nevertheless, this deflection reduces the asymptotic polarisation, simulated in SAD, to\nabout 1 %. Current studies aim at increasing the level of polarisation by introducing vertical pi-bumps, as\nwas performed in LEP [161]. Although these bumps could increase the vertical emittance, this effect is\npresumed to be minor since they only need to correct \u20d7n0 of 10 \u00b5rad, and thus, the required bump strength\nis expected to be rather small.\n53\n\n1.7.2\nWigglers\nAt 45.6 GeV, the natural polarisation time is 250 h. Thus, achieving a polarisation level in an error-free\nmachine of 5-10% requires 15 to 30 hours, which is an unacceptably long period without calibration at\nthe start of the fill. Reducing the polarisation rise time to about 12 h is feasible using wigglers, which also\nincrease the rms energy spread to 64 MeV. In the currently planned operational scenario, low-intensity (\u2248\n1010 particles) pilot bunches are injected at the start-of-fill and polarised using asymmetric polarisation\nwigglers [162, 163], similar to those at LEP [164]. When roughly 10% polarisation is achieved, after\napproximately 100 minutes at the Z-mode, the wigglers are switched off, and all the nominal-intensity\ncolliding bunches are then injected and brought into collision. Around 160 pilot bunches are injected\nat the start of each fill, with an estimated lifetime of roughly 20 h. This corresponds to roughly one\npilot bunch being available for an RDP scan every 7.5 min. By the time the last pilot bunch has been\ndepolarised for the first time, the pilot bunches that were depolarised first will have naturally reacquired\nsufficient polarisation to be measured again.\nThe wiggler design for FCC-ee follows the three-pole design of the LEP damping wigglers. Wig-\nglers will be grouped in packages of three units, and two packages will be installed in consecutive 16 m\nlong drift spaces. Their current placement in the FCC lattice is in the straight section downstream of\neach IP. The required number of polarisation wigglers and their specifications are given in Table 1.15.\nTable 1.15: Specification for the polarisation wigglers.\nNumber of units per beam\n24\nCentral field B+ [T]\n0.7\nCentral pole length L+ [mm]\n430\nAsymmetry ration r = B+/B\u2212= L\u2212/L+\n6\nCritical energy of SR photons Ec [keV]\n968\n1.7.3\nPre-polarised pilot bunches\nIn the current baseline approximately 100 min are required to polarise the pilot bunches in the main rings\nbefore commencing with injecting nominal physics bunches after every beam dump. Availability studies\npresented in Section 2.1.2 suggest that injecting pre-polarised pilot bunches could significantly enhance\nthe time available for physics, especially when considering failure scenarios. Furthermore, this scheme\nwould ease constraints on the maximum achievable polarisation and, hence, would limit the necessity\nof additional spin bumps, which could introduce additional vertical emittance. Nevertheless, injecting\npre-polarised pilot bunches into the main rings demands a careful evaluation of the injector design,\nwhich must be suitable for generating polarised electrons and positrons and allow sufficient polarisation\ntransport through the full injector chain and energy ramp. These studies have begun and will continue in\nthe next phase of the project.\n1.7.4\nDepolariser\nThe pilot bunches are depolarised with an electromagnetic kicker using transverse fields (RF-kicker),\nwith a TEM-wave travelling towards the beams and a varying excitation frequency. Once the driving\nfrequency is equal to the spin-tune, the polarisation vector is rotated away from the vertical direction,\nleading to depolarisation or spin flip. The proposed tune-changing rate corresponds to 1 keV/s.\nRadiative diffusion gives the spin resonance a natural width of about 200 keV at the Z-pole and\n1.4 MeV at the W-pair-threshold. These values are significantly larger than the desired precision. Recent\nstudies suggest that by alternating the scanning direction an uncertainty of a few keV at the Z-pole is\nachievable. Furthermore, RDP has recently been successfully simulated for the W-energy for the first\ntime. RDP only yields a sufficiently large change in polarisation if the spin-modulation index B =\n54\n\n\u03bd0\u03c3E/Qs < 1.5, with the energy spread \u03c3E and the synchrotron tune Qs, which ensures a low number\nof synchrotron-tune sidebands inside the distribution of the spin tune [165,166].\nTo achieve a sufficient spin rotation, a vertical kick of 10 \u00b5rad is required. A single kick would\nlead to a propagating orbit through the machine and thus this bump must be closed. In order to achieve a\nspin rotation, dipoles must be located within the closed orbit bump. It is found that the regular arc optics\nwould allow sufficient rotation over four FODO cells [167]. Since one closed orbit bump of 10 \u00b5rad\nwould lead to a vertical peak orbit above 1 mm, it is proposed to distribute it over four closed-orbit\nbumps per beam, each providing 2.5 \u00b5rad. At least two kickers per orbit bump are required, constraining\nthe phase advance to 180\u00b0. A weaker third kicker would ease this constraint. Hence, a total of 16 to 24\nkickers are required. The third correction kicker could be designed as a slightly shorter strip-line with\nless RF power installed, as it only has to provide corrections to the bump.\nEach kicker providing 2.5 \u00b5rad features a strip-line design of 1 m length with four electrodes,\noperating around 40 MHz. Keeping the nominal vacuum chamber diameter of 70 mm requires an RF\npower per kicker port (electrode) of 35 kW, and it is therefore suggested to reduce the vacuum chamber\nat the kicker to 26 mm with electrodes at a distance of 9 mm from the beam. This reduces the RF\npower per kicker port to 2.26 kW (9.04 kW per kicker). Studies are underway to ensure that the overall\nimpedance remains at an acceptable level [168]. The following Table 1.16 shows the configuration in\nTable 1.16: Possible configuration of depolariser kickers in point PA generating a local 2.5 \u00b5rad bump,\nassuming that the depolariser kicker system will be distributed over all four experiment points in a similar\nway to provide the total effect required for RDP. A shorter kicker is used for bump correction between\nthe two main depolariser kickers.\nLocation\nBeam\nFunction\nKicker\nlength\nPower per\nkicker\nPoint PA left\nelectron\nopen bump\n1.0 m\n9.04 kW\nPoint PA left\nelectron\ncorrection\n0.75 m\n4.5 kW\nPoint PA left\nelectron\nclose bump\n1.0 m\n9.04 kW\nPoint PA right\npositron\nopen bump\n1.0 m\n9.04 kW\nPoint PA right\npositron\ncorrection\n0.75 m\n4.5 kW\nPoint PA right\npositron\nclose bump\n1.0 m\n9.04 kW\npoint PA, where one-quarter of the necessary depolariser kickers are proposed to be installed. Similar\nconfigurations are proposed in the other three experiment points. All or part of the depolariser kickers\ncan also be used as kickers for transverse feedback systems for instability mitigation.\nThe technique of FSP is being investigated as a complementary approach to RDP. Here, the verti-\ncally orientated spin is flipped into the horizontal plane, and the coherent (free-spin) precession is then\nobserved. The spin tune is then retrieved by a Fourier transform, which also yields the full spin spec-\ntrum of the spin motion. This technique would require a kicker pulse about ten times stronger than that\nplanned for the RDP measurement [169].\nSince residual longitudinal polarisation in colliding bunches would modify the cross-section and\nforward-backward asymmetries, it must be controlled to a level below 10\u22125. Hence, it is envisaged to\nregularly depolarise colliding bunches, requiring a selective RF-kicker.\n1.7.5\nInverse Compton scattering polarimeter\nMeasurements of the polarisation of the FCC-ee beams will be performed through the process of inverse\nCompton scattering. The physics goals of FCC-ee set various requirements that the polarimeter system\nmust fulfil.\n55\n\n\u2013 The requirement to calibrate and study the electron and positron beams separately means that\neach ring requires at least one polarimeter. In order to provide redundancy and meet the target\navailability for the polarimeter measurements, which is set at 95%, it is foreseen to have two\ninstruments in each ring.\n\u2013 The polarimeters will be deployed on the pilot bunches for both RDP and FSP measurements.\nDuring Z-pole operation they will also perform measurements on physics bunches in order to\nensure that any longitudinal polarisation is kept sufficiently low.\n\u2013 The statistical precision on the measurements of the transverse polarisation of the pilot bunches\nshould be around 1% per second. A single bunch will be probed in each measurement.\n\u2013 Many more (\u223c100) physics bunches will be probed in a single measurement period, the laser tem-\nporal pattern being only indicative here and will be further optimised in the future. The physics-\nbunch studies place the most stringent demands on the systematic control of the absolute polarisa-\ntion measurement: it is desirable to measure a polarisation level consistent with zero to a precision\nof \u223c10\u22124.\n\u2013 FSP and longitudinal-polarisation studies require that the complete spin vector be characterised.\nThis can be achieved through measuring the spatial distribution of the scattered electrons (positrons),\nas well as the backscattered photons [170].\n\u2013 Knowledge of the relative positions of the scattered electrons (positrons), back-scattered photons\nand electrons (positrons) allows real-time measurement of the beam energy, which can attain a\nstatistical precision of 10\u22123 per second [170]. This capability will be valuable for many physics\nstudies and will be optimised in the ongoing design of the polarimeter system.\nA schematic drawing of the FCC-ee polarimeter is shown in Fig. 1.37.\nFig. 1.37: Schematic drawing of the FCC-ee polarimeter. More details can be found in Ref. [170].\nThe most suitable location for the polarimeter using the most recent machine optics design is in the\nstraight section 830 m upstream of the experiment IPs. The dispersion suppression dipole can then also\nbe used as the system spectrometer magnet. This location is followed by 100 m of field-free propagation,\nallowing sufficient separation of the Compton products from the main beam. The room that houses the\nlaser would be installed in a shielded region as close as possible to the laser interaction point (< 50 m). To\nmeet the targeted availability for the energy-calibration measurements in the next phase of the project, it\nwill be necessary to thoroughly investigate and validate the reliability of a system based on fully remote\nlaser control. Studies of the homogeneity requirements on the dispersion suppression magnet are also\nplanned.\nThe laser will operate at a green wavelength of around 515 nm, a choice which provides the opti-\nmum compromise between the field-free distance required and the reliability and versatility of operation.\nBoth Q-switched Nd:YAG and Yb mode-lock technologies are under consideration. Currently the latter\nis favoured, as it seems best adapted to providing suitable pulses to both the pilot and physics bunches.\nTable 1.17 shows the key parameters for such a choice. The crossing angle is implemented in both the\nhorizontal and vertical planes, with the vertical crossing angle necessary to take the scattered photons\n56\n\nout of the plane of the synchrotron radiation.\nTable 1.17: Preliminary laser parameters for pilot and colliding bunches. Note that single-bunch charges\nare different for pilot and colliding bunches.\nTechnology\nQ-switch\nModelock Yb\nModelock Yb\nBunch type\nPilot\nPilot\nColliding\nRepetition frequency\n3 kHz\n3 kHz\n3 kHz\nNumber of targeted bunches\n1\n1\n10\nPulse energy\n3 mJ\n3 mJ\n50 \u00b5J\nAverage power\n9 W\n9 W\n1.5 W\nPulse duration\n3 ns\n30 ps\n30 ps\nBeam width (\u03c3x/y,l)\n1 mm\n1 mm\n1 mm\nCrossing angle\n2 mrad\n8 deg\n8 deg\nScatters per bunch crossing\n260\n290\n94\nScatters per second\n8 105/s\n9 105/s\n28 105/s\nThe polarimeter will contain two detector systems. The first will record the transverse ellipse of\nthe Compton scattered electrons over a surface of about 5\u00d7300 mm2 (for Z-pole operation). The second\nwill record the peak-shaped distribution from the Compton gammas on a detector of about 10 \u00d7 10 mm2\ntransverse area. The baseline design for the detectors are pixelated sensors of 18-50 \u00b5m pitch in the\ntransverse direction.\nMonte Carlo simulation models are under development to evaluate and optimise the expected\npolarimeter capabilities. These models include a description of the laser/beam interaction chamber, the\nseparation chamber of almost 100 m, and the detector systems foreseen to record the Compton products.\nA preliminary study has been performed using the Toy Monte Carlo model described in Ref. [171].\nFurther investigations and optimisation of the system are now being pursued based on a complementary\nmodel developed using BDSIM [120], a GEANT4-based package that includes a description of particle-\nmatter interactions.\n1.7.6\nIP-specific corrections to the collision energy\nThe resonant-depolarisation measurements determine the mean beam energy around the ring. A variety\nof mechanisms either induce local variations in the beam energy or lead to other corrections that need to\nbe applied when calculating \u221as, the collision energy.\nThe beams experience continuous energy losses around the lattice from synchrotron radiation (SR)\nand resistive-wall impedance, which are compensated by the RF-cavities. It has been demonstrated in\nRef. [154] that to minimise the \u221as shifts at the IPs, both beams must have all RF-cavities located in\none straight section, identical for the electron and positron beam. This is planned for both Z pole and\nW+W\u2212operation. While SR radiation losses are identical for pilot and colliding bunches, being, for\nexample, 39 MeV at 45.6 GeV, impedance losses increase with increasing bunch intensity. Recent studies\nestimate a loss per revolution of about 0.8 MeV and 1.6 MeV at the Z pole, respectively, for 3 \u00d7 1010\nand 2.6 \u00d7 1010 particles per bunch [172]. Furthermore, beamstrahlung energy losses, which range from\n0.31 MeV per IP at \u221as = 91.2 GeV up to 14 MeV for \u221as = 365 GeV, must be monitored, for example\nby using a beamstrahlung monitor. Beamstrahlung losses increase with the beam energy and the bunch\npopulation, and lead to bunch lengthening, together with an increased energy spread. This beam-beam\ninteraction accelerates the particles before the collision, decelerates them afterwards, and also modifies\nthe crossing angle, but in a manner that leads to no net change in the collision energy.\nThe collision energy is also modified by opposite-sign vertical dispersion (OSVD) and collision\n57\n\noffsets at the IP. At each IP, the shift in collision energy is [154]\n\u2206\u221as = \u22122u0\n\u03c3E(Du,B1 \u2212Du,B2)\nE0(\u03c32\nB1 + \u03c32\nB2)\n,\n(1.25)\nwhere Du,B1,B2 is the dispersion at the IP for each beam, \u03c3E is the beam-energy spread, which is\nassumed to be identical between electrons and positrons, \u03c3B1,B2 are the beam sizes, E0 is the nominal\nbeam energy and u0 is the offset. Assuming 1 \u00b5m of spurious OSVD at the IP, as may occur according\nto optics tuning studies, the \u221as is shifted by roughly 100 keV per nm of offset. The vertical offset can\nbe determined and controlled via luminosity scans, where the beam positions at the IPs are scanned\nagainst each other until the optimum luminosity is achieved. At LEP such scans yielded a precision\nbetter than 0.1 \u00b5m at the Z-pole. However, at the FCC-ee an improvement by a factor 100 will be\nnecessary. Complementarily to observing the luminosity increase with vertical beam positions, beam-\nbeam deflection scans are envisaged; these rely on observing the change of crossing-angle from beam-\nbeam with varying vertical beam position. In principle, the dispersion of the colliding bunches at the IP\ncan be obtained by changing the momentum by applying a small RF-frequency shift and measuring the\nresulting orbit shift in the BPMs closest to the collision point. However, the maximum allowed RF-trim\nwhich does not alter the optics, as well as the interplay of orbit shifts due to beam-beam and dispersion,\nespecially at these BPMs, remains to be studied.\nAn alternative approach to determining the dispersion at the interaction point (IP) involves using a\ntransverse kicker to modify the path length of the pilot bunches and measuring the resulting orbit change.\nThis measurement enables the inference of the dispersion for the colliding bunches, assuming they share\nthe same OSVD as the pilot bunches. Since this method does not require altering the RF frequency, it\nprevents the potential induction of the flip-flop effect in the colliding bunches.\nA crucial final input for the \u221as calculation is the precise determination of the crossing angle at\neach interaction point (IP), which is provided by the experiments themselves.\n1.7.7\nInput from the experiments\nMeasurements conducted using collision data from the experiments provide essential input for determin-\ning key parameters related to the energy calibration.\nThe principal data set for these studies are e+e\u2212\u2192\u00b5+\u00b5\u2212(\u03b3) events. Reconstruction of the decay\ntopology allows the crossing angle to be determined, as well as providing insight as to how the crossing\nangle varies with bunch intensity. In addition, it is possible to determine the longitudinal boost and \u03b4\u221as,\nthe spread in collision energy. Good knowledge of \u03b4\u221as is vital for many key objectives of the FCC-ee\nprogramme, such as the measurement of \u0393Z. Current studies indicate that all these quantities can be\ndetermined from collision data with the required precision. Finally, reconstruction of e+e\u2212\u2192f \u00aff(\u03b3)\nevents and other processes provide a relative measurement of \u221as that can be of great interest at high\nenergies where RDP is not feasible. More details are given in Volume 1 of this report.\n1.8\nInjection and extraction\nThe technical straight section in point B (PB) of the FCC is dedicated to the beam transfer from the\nbooster to the collider and the dump systems. In total, eight systems are installed in this area, and this\nsection focuses on the collider system and the top-up injection and dump concepts.\n1.8.1\nTop-up injection\nThe integrated and peak luminosity targets of the collider necessitate a continuous injection scheme from\na full-energy booster, as the beam lifetime during collisions is well below 1 h. Due to the high bunch\ncharge in the collider and the limitations of the injector complex, a swap-out scheme is not feasible; thus,\na top-up injection scheme is required.\n58\n\nAmong the four operation modes, the Z mode is particularly challenging, with approximately\n18 MJ of stored beam energy per collider ring at an energy of 45.6 GeV. As such, the Z mode is the\ncurrent focus of the injection scheme design. In this mode, at each injection occurring every 3 s, up to\n10 % of the collider\u2019s maximum bunch intensity and up to 1120 bunches are injected totalling up to 1 %\nof the collider nominal intensity.\nThis intensity is deemed reasonably safe for transfer from the booster to the collider, provided\nthat a series of collimators is installed in the booster extraction region and along the transfer line to the\ncollider to intercept any mis-kicked bunches.\nSeveral potential schemes for implementing top-up injection at FCC-ee have been investigated\n[108]. Longitudinal injection schemes, which require an individual kick for each injected bunch trailing\ncirculating bunches, have been ruled out due to the complexity of the necessary kicker system. For the\nconventional off-axis injection scheme, modelling of the synchrotron radiation (SR) cone produced by\nthe beamlet, along with its impact on the SR mask and the aperture limitations around the experimental\ninsertion, indicated an unacceptable level of interference [173].\nOn axis injection\nFor on-axis injection, the beam is placed onto the chromatic closed orbit, where the energy offset together\nwith the ring\u2019s optics dispersion provides the horizontal separation between the injected and circulating\nbeams. The beamlet undergoes synchrotron oscillations, and around IPs it overlaps with the circulating\nbeam due to the zero dispersion, thus preventing any increase in the SR cones or of the experiment\nbackground.\nThe beamlet benefits from faster damping compared to off-axis injection since synchrotron oscil-\nlations damp twice as fast as betatron oscillations. Another advantage of on-axis injection was observed\nat the LEP collider, where this scheme provided higher efficiency and lower sensitivity to errors at the\ninjection point [174]. Therefore, the conventional on-axis injection has been selected for the present\nbaseline concept.\nThe distance between injected and circulating beams establishes the requirements on the energy\noffset and dispersion at the injection septum:\n|Dx\u2206| = 5\u03c3cir + S + 5\u03c3inj\n(1.26)\nwhere Dx is the dispersion at the injection point, \u2206is the relative energy offset of the injected beam, S is\nthe blade thickness of the septum, \u03c3cir and \u03c3inj are the beam sizes of the circulating and injected beams\nat the injection point.\nAs shown Eq. 1.26, the required energy offset increases with the septum blade thickness. Hence,\nan initial concept aimed at using an electrostatic septum to minimise its thickness but there are significant\nuncertainties on the reliability of such a system in the presence of synchrotron radiation. Therefore, the\npresent concept focuses on thin magnetic septa with S = 2.8 mm.\nDuring injection, the circulating beam closed orbit is placed at 5\u03c3cir from the septum blade (see\nEq. 1.26). This condition must be fulfilled for the shortest possible duration because the septum, or a\nprotection absorber placed immediately upstream, becomes the primary aperture of the ring. Therefore,\nthe baseline concept features a fast bump to bring the circulating beam close to the injection septum for\none single turn. Two sets of fast bumper magnets placed at a relative phase advance of \u03c0 are used to\nproduce the orbit bump with a height of 10\u03c3inj + S at the injection point. The nominal position of the\ncirculating beam is 15\u03c3cir from the edge of the injection septum. The failure of one of the bumpers\nwould cause an open oscillation of all circulating bunches, potentially resulting in significant losses at\ndownstream machine aperture bottlenecks (i.e., ideally at the collimators). The number of bumpers has to\nbe defined in order to keep the oscillation amplitude small enough to avoid major damage to the machine\nin case of failure. Moreover, an absorber must be installed upstream of the septum blade to shield it from\n59\n\naccidental and continuous losses. The absorber and the septum should never be the primary aperture\nbottleneck; this role should always remain with the collimators. The amplitude of the bump might need\nto be reviewed if this condition is not fulfilled.\nThe collider ring baseline optics for technical straight sections have been optimised so as to include\nthe on-axis injection requirements. This optimsied collider optics in the PB straight section is shown in\nFig. 1.38 with the injection region on the right side of the IP and the crossing dipoles in the centre. The\ninjection point is located at s = 800 m where it achieves a dispersion of Dx = \u22121.5 m and \u03b2x = 1000 m.\nThis allows on-axis injection with an energy offset of \u223c1%, providing sufficient space for the magnetic\nseptum blade of approximately 3 mm.\nFig. 1.38: The collider optics in the PB straight section with the longitudinal position relative to the IP.\nThe hardware requirements for the baseline injection scheme are summarised in Table 1.18.\nTable 1.18: Collider injection hardware requirements.\nSystem\nValue\nunit\nBeam energy\n45.6 \u2013 182.5\nGeV\nThick septum apparent thickness\n10\nmm\nThick septum deflection\n0.1\nmrad\nThin septum apparent thickness\n2.8\nmm\nThin septum deflection\n100\n\u00b5rad\nFast bump kicker angles\n40 and 60\n\u00b5rad\nFast bump kicker max. rise/fall time\n600\nns\nFast bump kicker flattop\n304\n\u00b5s\nFast bump kicker maximum ripple\n1.5\n%\nWhile the zero-dispersion condition was introduced to simplify the solution of Eq. 1.26 and to\nreduce the size of the injected beam at the injection septum, it also causes a mismatch between injected\nand circulating beams. The energy offset constrains the distance of the injected beam from the septum.\nIn the Z and WW modes, in particular, the lattice momentum acceptance limits the energy offset of\nthe injected beam to approximately 1%. On the other hand, the dispersion mismatch causes betatron\noscillations in the injected particles away from the chromatic closed orbit. This effect remains moderate,\nas the momentum spread of the injected beam \u03b4inj is small. Additional studies will be needed to quantify\n60\n\nthis effect and investigate different matching for each operation mode.\nA complete line design will need to be developed for the transfer from the booster to the collider.\nPresently, this line is approximately 500 m long from the booster extraction at the centre of the straight\nsection to the collider injection point (see Fig. 1.38). Since the booster ring is positioned 1030 mm above\nthe collider plane, special care must be taken to maintain the small vertical emittance and ensure precise\nmatching of the vertical optics to the collider ring. In the horizontal plane, just upstream of the thin\ncollider injection septum, a thicker magnetic septum is being considered for the beam trajectory, with\nspecifications detailed in Table 1.18.\nBoth booster and collider beam parameters depend on the operation mode (see Tables 1.2 and 4.1).\nIn the present concept, the lattice configuration of the injection straight section, as well as the injection\ndevices\u2019 specifications, remain the same for all operation modes. With fixed optics and septum thickness,\nthe energy offset is optimised for each energy mode to accommodate varying beam characteristics and\nthe ring\u2019s momentum acceptance. The baseline injection settings for the four operation modes are shown\nin Fig. 1.39.\n(a) Z mode, \u2206= 0.95 %.\n(b) WW mode, \u2206= 1 %.\n(c) H mode, \u2206= 1.4 %.\n(d) t\u00aft mode, \u2206= 1.6 %.\nFig. 1.39: Normalised horizontal phase space at the collider injection point for each operation mode.\nBeam distributions and associated 5 \u03c3 envelopes around the injection septum are shown for each mode.\nIn order to maintain a clearance of 5 \u03c3 for both the injected and circulating beam a larger energy\noffset is required for modes with higher beam emittance (see Eq. 1.26), and the energy offset in H and t\u00aft\nmode is increased to 1.4 % and 1.6 %, respectively. This remains compatible with the large momentum\nacceptance in Higgs and t\u00aft modes, which are \u00b11.6% and -2.8/+2.5%, respectively [31]. For Z mode, the\nRF acceptance is 1.06% and the momentum acceptance is approximately 1%, so the baseline injected\nbeam energy offset is set to 0.95% to ensure the entire injected beam fits within the ring acceptance.\nThe collider\u2019s and booster\u2019s equilibrium emittances in the WW mode are significantly larger, but\n61\n\nthe energy acceptance of the ring is still limited to 1 %. This prevents increasing the energy offset for the\nhigher energy modes and makes the on-axis scheme unable to provide sufficient clearance for the 2.8 mm\nseptum blade. The present concept introduces a small betatron offset to the scheme and moves towards\na hybrid injection for the WW mode. The purple dashed line in Fig. 1.39b represents the chromatic orbit\nfor the energy offset considered, and the injected beam is offset by 1 mm further away from the septum,\nwhich corresponds to 0.5 \u03c3cir.\nThe hybrid injection scheme increases the separation between injected and circulating beams with-\nout increasing the energy offset, making it partially on-axis and off-axis. While the off-axis injection is\nnot possible for the FCC collider, a small betatron oscillation is not incompatible with the SR absorp-\ntion around the experiment IPs [173]. Other effects discussed earlier, such as experiment background\nsensitivity and errors, may still play a significant role and will need to be quantified.\nFig. 1.40: Injection efficiency versus injected beam energy offset for the Z mode.\nPresently, the injection efficiency is modelled with particle tracking of the injected beam in the\ncollider ring lattice. The tracking consists of a Gaussian 6D distribution of 2500 injected particles,\nwhich are tracked for 3000 turns using the XSUITE code [175]. The synchrotron radiation model used\naccounts for quantum excitation to accurately predict the behaviour of particles injected near the edge\nof stability. Additional studies including strong-strong beam-beam effects are discussed Section 2.3.9.\nFurther comprehensive studies will need to include beam-beam interaction, collective effects and lattice\nerrors.\nThe evolution of the simulated injection efficiency for on-axis and hybrid injection schemes is\nshown in Fig. 1.40. The energy offset of the baseline on-axis injection is 0.95 %, with an injection\nefficiency of 99 %. This confirms that the baseline injection scheme is achievable with the present lattice,\nand the injected beam is within the acceptance of the ring.\nAt other injection offsets, only the energy of the injected beam is adjusted, but the optics is not\noptimised, and the physical beam position is unchanged. Below the baseline on-axis scheme energy\noffset, the injection efficiency remains high, which indicates that the DA and MA are sufficient to capture\nan injected beam with some betatron offset. At an energy offset below about 0.7 % the injection efficiency\ndecreases, which shows that a maximum betatron offset is reached and part of the injected beam is outside\nthe lattice DA. Due to the energy acceptance of the lattice, of \u00b11 %, the injection efficiency drops quickly\nfor energy offset above the baseline scheme.\nCollider dump\nThe stored beam energy can reach 18 MJ per beam during Z mode operation, which is the highest stored\nenergy among the lepton machines worldwide. Due to the synchrotron radiation damping, the beam\n62\n\nsizes in FCC-ee will be much smaller than in typical hadron machines, leading to a much higher energy\ndensity. The vertical beam size, in particular, is in the order of tens of micrometres, corresponding to\nenergy densities around 5 GJ/mm2, which cannot be absorbed safely [176]. The design and operation\nof the beam abort system must accommodate this destructive potential, requiring multiple safety mea-\nsures to prevent damage to accelerator components in the event of hardware failure. Protection elements\nstrategically positioned at a precise phase advance from the extraction kickers must be installed to inter-\ncept any mis-kicked beam in case of an unintended kicker firing that is not synchronised with the abort\ngap. Additionally, the voltage of the kickers, as well as the current of the septa and ring dipoles, must\nbe continuously monitored to ensure they remain within strict limits relative to the reference value for a\ngiven energy.\nA retriggering system, which fires all the remaining kickers in case of the spurious firing of one\nkicker, has to be envisaged, and the reaction time must be defined based on the consequences of such an\nevent. Redundancy in the powering scheme, the controls, and interlock logic have to be implemented to\nensure that the required level of reliability and availability of the system is achieved.\nThe number of magnets has to be defined with the aim of reducing the maximum operational\nvoltage and thus minimising the risk of spurious firing and the sensitivity to failures. Out-of-vacuum\ndesigns should be preferred to eliminate the risk of flashovers. The position of the beam at extraction has\nto be constantly monitored, and the beam dumped before orbit drifts translate into losses at extraction\nabove the level that can be considered safe (to be defined). Similar measures to the present LHC beam\ndump system will need to be considered, and adapted to the specificities of the FCC but presently no\nmajor fundamental obstacles have been identified.\nThe collider dump design is implemented at the entrance of the PB straight section and extracted\noutwards with the dump placed on the other side of the IP. The beam dump is located 5 m away from\nthe ring to allow sufficient space for shielding and to limit radiation to the ring equipment [177]. The\npresent geometry uses a small deflection angle to achieve the required separation and a long transport\nline of 700 m from the ring extraction point to the beam absorber.\nIn order to reduce the energy density on the dump, the present design aims for a large beta function\nand dispersion in both horizontal and vertical planes to maximise the beam size. Despite the significant\nlength of the line, the natural divergence of the beam at the extraction point is insufficient to produce a\nbeam spot that is large enough on the dump. Therefore, a set of four dedicated quadrupole magnets is\ninstalled in the transfer line to increase the beam divergence further. In the horizontal plane, the dump\nkicker and septa provide the deflection to reach the dump but also a significant dispersion that is further\namplified by the dump line quadrupoles to reach 20 m at the dump. Along with the beta function of\n121 km and the beam parameters in the collision, the present design achieves a horizontal beam size on\nthe dump of 10 mm for the Z mode [178].\nFor the vertical plane, a 1 mrad vertical dipole is placed at the start of the dump line to create\na vertical dispersion that is further amplified by the dump line quadrupoles to reach 23 m at the dump.\nBetween the betatron and dispersive contribution, this scheme also provides a large beam size in the\nvertical plane of 10 mm for the Z mode using the beam characteristics expected in a collision. The\nvertical deflection also places the dumped beam at the height of the booster.\nThe extraction design follows a traditional fast extraction scheme in the horizontal plane. The\ncirculating beam is extracted in one turn so that the kicker flattop must be 304 \u00b5s and its rise time should\nbe smaller than the filling scheme abort gap of 0.6 \u00b5s. The dump design hardware requirements are\nsummarised in Table 1.19.\n1.9\nRadiation environment\nThe emission of synchrotron radiation and the generation of secondary particles by other processes\n(beam-beam effects etc.) creates an intense radiation environment, which can have a significant impact\n63\n\nTable 1.19: Summary of the collider dump scheme hardware requirements.\nKicker\nSeptum\nBeam energy (GeV)\n45.6 \u2013 182.5\nDeflection angle per system (mrad)\n0.3\n5\nMaximum repetition frequency (Hz)\n0.3\n0.3\nKicker pulse flatness (%)\n\u00b120\nN/A\nRise/fall time (\u00b5s)\n0.6\nN/A\nflattop time (\u00b5s)\n304\nN/A\nBlade thickness (mm)\nN/A\n25\nAperture (H\u00d7V mm)\nN/A\n30\u00d710\nLongitudinal available space (m)\n20\n20\non machine components and other equipment in the tunnel. A thorough study of the expected radiation\nload and its associated effects is essential for designing the FCC-ee machine. Radiation can lead to sub-\nstantial heat deposition and, consequently, to thermal stress on the accelerator components. The power\ndeposited, in particular from synchrotron radiation, needs to be extracted in a controlled way otherwise\nequipment can be damaged. Excessive heat deposition in the tunnel environment would also pose a\nsignificant challenge to the ventilation system. Another important aspect is the lifetime of equipment,\nwhich can be affected by cumulative radiation damage. One of the main concerns for FCC-ee is the\ntotal ionising dose in cables, cable connectors, optical fibres, insulation materials, seals, etc. As already\nobserved in LEP, the ionising dose can severely compromise the organic insulation of magnet coils and\ncables and can rapidly degrade the functionality of optical fibres [179]; even covers of electrical junction\nboxes and hoses of fire extinguishers were found to be damaged [179], which demonstrates the challenge\nexpected for FCC-ee. Other long-term radiation effects include radiation-induced corrosion due to the\ndissociation of molecules in the tunnel atmosphere. Another concern for FCC-ee are stochastic and cu-\nmulative effects in electronics, which can impede the machine performance (e.g., premature beam aborts\ndue to single event effects) and can limit the lifetime of equipment electronics.\nIn order to mitigate radiation effects and manage their release, it is essential to sufficiently shield\nthe power FCC-ee machine equipment and infrastructure from the radiation load. This requires dedi-\ncated synchrotron radiation absorbers (see Section 3.2), as well as additional shielding on the magnets\nand in the tunnel. Due to the sheer size of the FCC-ee machine, continuous shielding of the vacuum\nchamber, as it was implemented in LEP, may be challenging to implement. In order to develop an\nadequate shielding configuration, it is necessary to create a detailed inventory of radiation-sensitive com-\nponents (e.g., cables, electronics, insulation) for all accelerator systems like magnets, power converters,\nbeam instrumentation, and the beam interlock system. Different components can exhibit different lev-\nels of sensitivity to radiation, which needs to be accounted for in the shielding design. For example,\norganic insulation of busbars can typically sustain several tens of MGy, whereas general-purpose cables\ncan only be used up to a few 100 kGy. Electronics systems based on commercial-off-the-shelf compo-\nnents can typically not withstand levels exceeding 1 kGy, even when designed to be radiation tolerant\nthrough commercial component selection and architectural mitigation solutions; for doses above 1 kGy\nit is necessary to rely on dedicated radiation-hard component designs that require investment in time and\nresources. Similar considerations apply to optical fibre cables. Finding a trade-off between shielding\nsolutions and a radiation-hard component design is an important objective for the FCC-ee design phase\nto avoid radiation-induced equipment failures or degradation of the collider performance.\nThis section provides a first overview of the expected power deposition and the radiation environ-\nment in the arcs and experiment insertion regions, based on FLUKA Monte Carlo simulations [125\u2013\n127]. A preliminary shielding design for the arc dipoles is presented, together with a possible electronics\n64\n\nFig. 1.41: Preliminary conceptual radiation shielding design for the collider dipoles in the FCC-ee arcs.\nThe left figure shows a model of a representative FODO cell for ZH and t\u00aft operation, whereas the right\nfigure presents a more detailed view of the shielding elements on the dipoles. The shielding encloses\ntightly the synchrotron radiation absorbers. The shielding is assumed to be made of antimonial lead and\nweighs about 400 kg per synchrotron radiation absorber.\nbunker near the arc quadrupoles. The present shielding and bunker design is only a first concept, with the\npurpose to quantify the achievable reduction of the radiation levels. A further evolution of the shielding\nand bunker design is expected in the engineering design phase (see also Section 3.3). No studies have\nbeen carried out so far for the technical insertion regions; the radiation levels will depend on different\nbeam loss mechanisms (e.g., beam losses during top-up injection or beam collimation), which have to be\nassessed in detail. It is expected that some shielding installations will also be needed in these insertion\nregions.\n1.9.1\nRadiation levels in the arcs and first shielding design\nThe main source of radiation in the FCC-ee arcs is the synchrotron radiation produced in the bending\ndipoles of the collider ring. Synchrotron radiation is emitted tangentially from the stored beams and the\nresulting energy loss increases steeply with the beam energy (\u221dE4/(m4\u03c1)). The bending radius \u03c1 of\nthe FCC-ee arc dipoles is about 10 km, which is about three times larger than for LEP. Considering the\nimportant impact of synchrotron radiation, the synchrotron power emitted in FCC-ee is limited by design\nto 100 MW (50 MW/beam) for all operation modes (see Table 1.2). The resulting radiation levels in\nthe tunnel are nevertheless more pronounced at higher beam energies since the emitted photons become\nmore penetrating. A key figure is the critical energy, Ec \u221dE3/\u03c1, which divides the photon spectrum into\ntwo parts of equal power emission. For a bending radius of 10 km, the critical energy is 0.02 MeV at the\nZ-pole (45.6 GeV), but it increases to 0.1 MeV in WW operation (80 GeV), to 0.4 MeV in ZH operation\n(120 GeV), and further to 1.3 MeV in t\u00aft operation (182.5 GeV). The resulting radiation environment\nin the tunnel is composed of secondary photons and electrons. In addition, photo-neutron production\nbecomes possible when the photon energies exceed the (\u03b3,n)-threshold, which is around 10 MeV for\ncopper. Neutron production by synchrotron photons is mostly relevant for t\u00aft operation, where the high-\nenergy tail of the synchrotron spectrum extends beyond the giant dipole resonance of the photo-nuclear\ncross section.\nThe vacuum system of the collider incorporates localised photon absorbers made of a copper\nalloy (CuCrZr), which intercept the synchrotron radiation fan (see Section 3.2). The absorbers have a\nlength of about 35 cm; they are placed every four to five metres in the winglets of the dipole chambers\nand shadow, as well as the short straight sections. At higher energies, the radiation leakage from these\nabsorbers becomes significant, which requires the integration of additional shielding elements in the\ndipoles. A first conceptual design of the collider shielding configuration is shown in Fig. 1.41. The\npresently considered baseline material is antimonial lead with a density of about 10.88 g/cm3. The\nshielding tightly encloses the radiation absorbers and consists of horizontal inserts, as well as shielding\n65\n\n 0\n 5\n 10\n 15\n 20\n 25\n 30\n 35\n 40\nx (cm)\n\u221215\n\u221210\n\u22125\n 0\n 5\n 10\n 15\ny (cm)\n 1\u00d7107\n 1\u00d7108\n 1\u00d7109\n 1\u00d71010\n 1\u00d71011\n 1\u00d71012\n 1\u00d71013\n 1\u00d71014\n 1\u00d71015\nPhoton flux (cm\u22122s\u22121)\nDipole yoke\nBusbar\nSR absorber\nPhoton flux without shielding (182.5 GeV)\n 0\n 5\n 10\n 15\n 20\n 25\n 30\n 35\n 40\nx (cm)\n\u221215\n\u221210\n\u22125\n 0\n 5\n 10\n 15\ny (cm)\n 1\u00d7107\n 1\u00d7108\n 1\u00d7109\n 1\u00d71010\n 1\u00d71011\n 1\u00d71012\n 1\u00d71013\n 1\u00d71014\n 1\u00d71015\nPhoton flux (cm\u22122s\u22121)\nDipole yoke\nBusbar\nShielding\nSR absorber\nShielding\nPhoton flux with shielding (182.5 GeV)\nFig. 1.42: Synchrotron radiation-induced photon flux around the dipole yoke in t\u00aft operation. The two\nplots compare the photon leakage without radiation shielding (left) and with the conceptual shielding\nillustrated in Fig. 1.41 (right). The flux was calculated with the FLUKA code, assuming a photon\ntransport cut of 10 keV. In this picture the x-axis exceptionally points towards the centre of the collider\nring, which is opposite to the convention adopted elsewhere in this document.\nplates above and below the dipole yoke. The integration of the shielding is a complex task and requires\ndesign iterations with the vacuum system and magnets. A description of technical aspects of the material\ndesign, including material selection and engineering considerations, is presented in Section 3.3.\nA first optimisation of the shielding topology has been carried out, to maximise the power absorp-\ntion and to reduce the total ionising dose in the tunnel sufficiently. Given the complexity of the shielding\nintegration and assembly, it is preferable to install the shielding before the start of FCC-ee operation. In\nthis case, the shielding design must account for all beam modes, including t\u00aft. A suitable figure of merit\nfor optimising the shielding geometry is the flux of secondary photons escaping vertically and horizon-\ntally from the dipoles. The attenuation length for 1 MeV photons in lead is about 1.3 cm, but it decreases\nto less than 1 mm for photon energies below 100 keV. With several centimetres of antimonial lead, the\nphoton flux in the tunnel can be reduced by multiple orders of magnitude, even at the highest beam en-\nergy (182.5 GeV). Figure 1.42 shows the simulated secondary photon flux around the dipole yoke for t\u00aft\noperation. The left plot is without shielding, whereas the right plot demonstrates the reduction achievable\nin the photon leakage with the preliminary shielding design shown in Fig. 1.41. The shielding must be\nsufficiently long (130 cm in the present design) to reduce the backscattering of photons into the tunnel.\nThe resulting shielding weight is about 400 kg per synchrotron radiation absorber.\nTable 1.20 summarises the resulting power deposition in the machine and the tunnel for all beam\nmodes, assuming the same shielding design for all beam energies. For comparison, the table also shows\nthe power deposition without shielding. The shielding has only a limited function at the Z mode since\nmost of the synchrotron radiation power (>98%) is dissipated by the synchrotron radiation absorbers\nthemselves. With increasing energy, the power absorption by the absorbers decreases to about 83% in\nWW operation and to less than 70% in ZH and t\u00aft operation. In these cases, the surrounding shielding\nis very efficient in reducing the power leakage to the dipoles and the environment by absorbing between\n10% (WW) and 20% (ZH and t\u00aft) of the power. Since only the dipole busbars are actively cooled but not\nthe yoke, a fraction of the heat deposited in the dipoles would also be dissipated in the air. Equipped with\na dedicated cooling circuit, the shielding substantially reduces the heat to be evacuated by the ventilation\nsystem.\nFigure 1.43 presents the corresponding annual dose in the arc tunnel. The plots illustrate the effect\nof the shielding for ZH and t\u00aft operation, which yield the highest contribution to the annual dose. The\nshielding reduces the dose levels in tunnel by more than two orders of magnitude. At the location of the\nupper cable trays on the walls (>2 m above floor level), the dose is <1 kGy/year for the ZH operation\nand <10 kGy/year for t\u00aft operation, down from several hundreds of kGy/year without shielding. With\n66\n\nthe present shielding design, it seems feasible that most cables in the cable trays receive <100 kGy/year\nin the full FCC-ee era, including t\u00aft. This is compatible with the criteria for general-purpose cables\npresently adopted for HL-LHC and other projects at CERN. The radiation level specifications and re-\nquired safety factors for FCC-ee cables and other equipment need to be scrutinised during the technical\ndesign phase and will depend on the chosen technologies. The results nevertheless demonstrate that\nradiation shielding can significantly reduce the need for expensive radiation-hard equipment in the tun-\nnel. Near the machine, radiation-hard cables and cable connectors qualified for MGy dose levels can\nlikely not be avoided. Depending on the evolution of equipment technology in the next years, the ra-\ndiation resistance criteria are still expected to evolve. The shielding requirements need to be adapted\naccordingly.\nEven with the dipole shielding, the annual dose in tunnel remains significant for electronics, i.e.,\nthe levels are too high for a radiation-tolerant system design based on commercial-off-the-shelf com-\nponents. In addition, the expected neutron flux in t\u00aft operation increases the likelihood of single event\neffects and enhances the expected displacement damage. A conceptual design of a possible electronics\nbunker has been devised (see Section 3.3), in order to reduce the radiation levels for electronics. In\nthis very first design, the bunker is assumed to be made of 10\u201320 cm-thick concrete walls, which are\nlined with borated polyethylene sheets. The latter is needed for moderating and capturing neutrons. The\nbunkers are assumed to be located below or near the arc quadrupoles. Table 1.21 compares the radiation\nlevels inside and outside the bunker for one year of t\u00aft operation. The results demonstrate that similar\nlevels as in the HL-LHC arcs can be achieved (see last column), with the exception of the total ionis-\ning dose which remains somewhat higher. With the bunker, using custom radiation tolerant electronics\nsystems based on commercial-off-the-shelf semiconductor devices could be feasible for FCC-ee.\n1.9.2\nRadiation levels in the experiment insertion regions\nThe primary radiation sources in the tunnel of FCC-ee experimental insertions are beamstrahlung ra-\ndiation, radiative Bhabha and synchrotron radiation, and their impact has been studied with FLUKA\nsimulations. Other sources of radiation, such as beam-gas interactions or others, may cause additional\nradiation showers, but they are not considered in the present study. Concerning beamstrahlung, a ded-\nicated absorber is needed to safely dispose of the photons because of the high power carried by the\noutgoing photon beam (several hundreds of kW at Z pole). The absorber will be placed about 500 m\ndownstream of the IP and needs to be shielded to limit the radiation leakage to the tunnel. A second\nTable 1.20: Relative power deposition by synchrotron radiation in the machine and the tunnel. The re-\nsults were obtained with FLUKA simulations for a representative arc cell, assuming 10 photon stoppers\nbetween successive quadrupole magnets, or roughly one photon stop every 5 metre for each beam. The\ntable compares two configurations for each beam mode, with and without radiation shielding around the\nsynchrotron radiation absorbers. The power deposition in the environment includes the power dissipated\nin the air, the tunnel walls and the surrounding earth or rock.\nZ\nWW\nZH\nt\u00aft\nw/o\nwith\nw/o\nwith\nw/o\nwith\nw/o\nwith\nSR absorbers\n98.1%\n98.1%\n82.8%\n82.8%\n69.9%\n69.7%\n68.3%\n68.1%\nRadiation shielding\n-\n-\n-\n19.1%\n-\n20.4%\nVacuum chambers\n1.8%\n8.2%\n9.0%\n8.9%\n8.1%\n8.0%\nDipoles\n0.1%\n7.8%\n16.7%\n2.3%\n17.4%\n3.5%\nQuadrupoles\n<0.001%\n<0.01%\n<0.02%\n<0.01%\n<0.1%\n<0.02%\nSextupoles\n<0.001%\n<0.01%\n<0.02%\n<0.01%\n<0.1%\n<0.02%\nEnvironment\n0.01%\n1.2%\n4.3%\n<0.01%\n6.1%\n<0.03%\n67\n\n\u22122\n\u22121\n 0\n 1\n 2\n 3\nx (m)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\ny (m)\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\nDose (MGy)\nWithout shielding (ZH, 120 GeV)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\nx (m)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\ny (m)\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\nDose (MGy)\nWith shielding (ZH, 120 GeV)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\nx (m)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\ny (m)\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\nDose (MGy)\nWithout shielding (tt\u2212, 182.5 GeV)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\nx (m)\n\u22122\n\u22121\n 0\n 1\n 2\n 3\ny (m)\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\n101\nDose (MGy)\nWith shielding (tt\u2212, 182.5 GeV)\nFig. 1.43: Annual dose in the arc tunnel due to synchrotron radiation emission by the stored beams in the\ncollider (top: ZH, bottom: t\u00aft). The left figures are without radiation shielding, whereas the right figures\nwere derived with the conceptual shielding illustrated in Fig. 1.41. The dose maps correspond to the\nposition of a synchrotron radiation absorber, where the dose reaches its maximum value. The maps were\ncalculated with FLUKA, assuming 185 days of operation with 75% operational efficiency. The collider\nis located in the origin. The x-axis points towards the centre of the collider ring.\nTable 1.21: Radiation levels inside and outside a possible electronics bunker near lattice quadrupoles\nin the arcs. The first two quantities describe cumulative effects, whereas the two last quantities are\nrelevant for single-event effects. The values correspond to one year of t\u00aft operation (185 days with 75%\noperational efficiency). The last column shows the radiation level specifications for the HL-LHC arcs\n(one year) [180].\nFCC-ee t\u00aft\nFCC-ee t\u00aft\nHL-LHC arcs\n(outside bunker)\n(inside bunker)\n(below magnets)\nTotal ionising dose\nfew kGy\n<10 Gy\n1.4 Gy\nSi 1 MeV neutron-equiv. fluence\n6 \u00d7 1011 cm\u22122\n\u223c1 \u00d7 1010 cm\u22122\n1.6 \u00d7 1010 cm\u22122\nHigh-energy hadron-equiv. fluence\n8 \u00d7 108 cm\u22122\n\u223c1 \u00d7 107 cm\u22122\n2.4 \u00d7 109 cm\u22122\nThermal neutron-equiv. fluence\n5 \u00d7 1011 cm\u22122\nfew 1 \u00d7 109 cm\u22122 1.2 \u00d7 1010 cm\u22122\nsource of radiation is the off-momentum electrons from radiative Bhabha interactions; a fraction of these\nelectrons is lost on the vacuum chamber when entering the first dipoles of the outgoing beam. Addi-\ntionally, the stored beams emit a non-negligible amount of synchrotron radiation in the bending dipoles\n68\n\nFig. 1.44: Top view of the annual ionising dose at the beamline level (average for y in [\u221220, 20] cm)\ncaused by beamstrahlung radiation, radiative Bhabha electrons and synchrotron radiation from the out-\ngoing beam. The top figure corresponds to Z mode operation, whereas the bottom figure is for t\u00aft. The\nmaps were simulated with FLUKA.\ndownstream of the IP, with more than 160 kW of power produced over the first 500 m. On the other\nhand, the synchrotron radiation power emitted by the incoming beams is only 1 kW, yielding a much\nsmaller contribution to the radiation levels in the tunnel.\nThe secondary radiation fields by these three radiation sources have been simulated using FLUKA.\nThe studies included similar CuCrZr synchrotron radiation absorbers as in the arcs but no additional\nshielding around the absorbers. The annual ionising dose from the IP (z=0) up to \u223c520 m downstream\nis displayed in Fig. 1.44, comparing Z and t\u00aft operation. The dose maps show that the radiation environ-\nments for the two operation modes are very different since different source terms dominate. At the Z\npole, losses from radiative Bhabha give high dose levels up to 200 m downstream of the IP; another hot\nspot occurs around 500 m due to leakage of radiation from the beamstrahlung absorber. The conceptual\nshielding for the absorber assumed in these preliminary simulations (20 cm of concrete) yields dose lev-\nels of several hundreds of kGy/y in the vicinity of the absorber and several tens of kGy/y at the beamline\nof the outgoing beam. Further optimisation of the shielding will be performed based on radiation protec-\ntion studies. It is expected that with thicker shielding, the dose can be reduced by orders of magnitude.\nThe synchrotron radiation emitted in the dipoles is less relevant for the radiation levels at the Z pole due\nto its soft spectrum; with critical energies ranging from 2 keV to 23 keV, 95% of its power is absorbed\nin the synchrotron radiation absorbers.\nThe situation is the opposite at t\u00aft, where the dose from synchrotron radiation is dominant while\nthe contributions from beamstrahlung and radiative Bhabha are smaller than for Z pole operation. The\nharder synchrotron spectra feature critical energies of the order of 1 MeV, reducing the power fraction\nabsorbed by the photon stoppers down to 68% (similar to the arcs). Dose hot spots of the order of 0.1\u2013\n1 MGy/y are observed around each synchrotron radiation absorber. This underlines that, like in the arcs,\nsynchrotron radiation absorbers alone are not enough to suppress the radiation leakage into the tunnel;\nit is expected that additional shielding similar to the arc shielding is needed to reduce the dose. In the\nclose proximity of the IP the dose levels are determined by radiative Bhabha, but they are two orders of\n69\n\nmagnitude lower than at Z pole because of the lower intensity.\nFor both operational modes, other sources of radiation (e.g., beam-gas interactions) are expected\nto give a negligible contribution to the radiation hotspots displayed in Fig. 1.44, but dedicated studies\nwould be needed to assess a possible impact in the portions of the tunnel where the sources studied so\nfar are yielding lower radiation levels.\n1.10\nOngoing studies\nThis section will summarise five of the ongoing studies for the FCC-ee optics design. These include\nthe local chromatic correction (LCC) optics which has the potential to improve the dynamic aperture\nand reduce the optics sensitivity to errors; a combined function optics design which improves the dipole\npacking fraction and reduces the amount of synchrotron radiation; a non-local detector solenoid compen-\nsation scheme which reduces the vertical emittance growth; a monochromatic optics configuration which\nwould reduce the energy width of the collisions and could enable direct measurement of the Higgs width\nthrough s-channel production; polarised e+e\u2212sources which could eliminate the downtime needed to\npolarise the pilot bunches and improve the integrated luminosity.\n1.10.1\nLCC optics\nLocal Chromatic Correction (LCC) optics have been proposed for the FCC-ee collider and are detailed\nin [32]. The structure of the accelerator is the same as the baseline optics, including four final focus\nsystems (FF) and four long straight sections (LSS) separated by eight arcs.\nThe LCC optics are designed to obtain anharmonic and achromatic beam dynamics for each of\nthese components independently. The layout of the optics in the arcs, FF and LSS are shown in Figs. 1.45,\n1.46 and 1.47 respectively.\nFig. 1.45: LCC HFD arc cell optics at t\u00aft. The same layout is used at Z.\nFig. 1.46: LCC FF optics at t\u00aft. The same layout is used at Z.\nThe arcs optics are based on novel hybrid focusing de-focussing optics (HFD). Five standard\nFODO cells are matched as a single one (10 quadrupoles and 10 dipoles) in order to obtain the desired\nfirst and second order amplitude and momentum detuning coefficients by setting optics values at specific\nlocations. Only two sextupoles families are needed. The HFD optics are extremely versatile and allow\nfor large dynamic aperture and momentum acceptance. The same magnetic layout is used to operate at\n(\u00b5h, \u00b5v) = (100, 74) deg for t\u00aft and (\u00b5h, \u00b5v) =(50,44) deg for Z.\n70\n\nFig. 1.47: LCC LSS optics at t\u00aft. The same layout is used at Z.\nThe four LSS and the FF systems are designed following the transparency conditions detailed in\n[181]. These conditions mean that the beam dynamics on- and off-energy, and with or without sextupoles,\nare periodic and matched to the arcs. The lattice beam dynamics properties are then as close as possible\nto a fully periodic lattice (arcs only).\nThe FF optics meet all the baseline specifications in terms of crossing angle, synchrotron radiation\nhandling and other geometrical constraints. Following the LCC principles, the chromaticity generated\nby the low-\u03b2 interaction points is fully corrected within the FF. Sextupoles at locations in phase with the\nIP are used to cancel first and second-order amplitude detuning coefficients. Decapoles placed in these\nexact locations minimise the detrimental effect of synchrotron radiation in the high gradient final doublet\nquadrupoles.\nThe same magnet specifications used for the baseline optics may be used. No reverse bends are\nneeded for the LCC optics. No superconducting magnets are required except for the final doublets. The\nnumber of magnets, length and integrated strengths for the LCC optics are remarkably lower compared\nto the baseline optics.\nThe HFD cell dipoles are about 29 m long. QD and QF quadrupoles are 1.8 m and 2.4 m long\nrespectively. 2240 quadrupoles per ring are needed for the arcs. SD and SF sextupoles are 50 cm and\n35 cm long respectively, making use of the sextupole design already available for the baseline optics.\nDipoles all have the same length, so the e+e\u2212arcs can be shifted longitudinally to align opposite polarity\nquadrupoles for the two rings. Twin quadrupoles and an additional short QF (60 cm long) can be used to\nreplace the QF/QDs of the two arcs. If high-temperature superconducting magnets are used, quadrupoles\ndo not need to be paired, and the sextupole coils can be wrapped around the quadrupole ones, thus\nimproving the dipole filling ratio and reducing the horizontal natural equilibrium emittance. Trim coils\nare foreseen on the sextupoles for orbit (horizontal and vertical correctors) and optics correction (normal\nand skew quadrupole). No additional correctors are needed.\nThe LCC lattice optics at Z and t\u00aft energies have been analysed in terms of sensitivity to alignment\nerrors in the arcs and in the final focus. As detailed in [32] the LCC lattice is for most parameters more\ntolerant or equivalent to the baseline optics and to other similar lattice designs such as CEPC [182].\nThe sensitivity to errors in the FF is dominant, and more studies on correction schemes and tuning\ntechniques will be addressed in the future to fully evaluate the tolerated alignment errors.\nSome relevant parameters for the Z and t\u00aft lattice options are reported in Table 1.22.\nAll non-linear magnets have been optimised using multi-objective minimisation tools in order to\nmaximise the final lattice performance. The transverse dynamic aperture computed in the centre of the\nstraight sections is well above 15\u03c3 in the horizontal plane and 70\u03c3 in the vertical plane for Z and t\u00aft\nenergies. The 6D tracking for 2350 turns at Z and 40 turns at t\u00aft includes quantum diffusion, synchrotron\nradiation, tapering, and crab sextupoles at the optimal value for maximum luminosity. For the same\ntracking conditions, the momentum acceptance is close to 2% for Z and 4% for t\u00aft.\nThe LCC optics are ready to be used for FCC-ee. Further work will be needed for the specification\nof optics at other energies. This work will benefit from the precise and deterministic strategies defined\n71\n\nTable 1.22: Full ring general parameters, for the two energies considered.\nZ\nt\u00aft\nC [km]\n90.659\n90.659\nEnergy [GeV]\n45.6\n182.5\nNum. IP per ring\n4\n4\nCrossing angle [mrad]\n30\n30\n\u03b2-tron tunes\n(198.26,174.38)\n(350.224,266.36)\nChromaticity\n(0.20,0.21)\n(0.23,1.66)\n\u03f5h [pm rad]\n684.72\n2100.9\nJ\n(1,1,2)\n(1,1,2)\n\u03b1c\n2.894e-05\n0.946e-05\nU0 [MeV/turn]\n34.3\n8808.2\n\u03c3E\n3.715e-4\n14.9e-4\n\u03b2\u2217\nh [mm]\n0.7\n1.6\n\u03b2\u2217\nv [mm]\n100\n1000\nbunch length [mm]\n3.4\n2.7\nRF Voltage [GV]\n0.17\n10.4\nRF frequency [MHz]\n400\n400\nLong. damp. time [ms]\n401.6\n6.3\nSynchrotron tune\n0.045\n0.074\nduring the LCC optics design as well as the matching and optimisation scripts available.\n1.10.2\nOptics with nested magnets\nAn alternative design considers nesting dipoles with the arc FODO quadrupoles and sextupoles to in-\ncrease the dipole fill factor and reduce the overall synchrotron radiation [183]. This could be achieved by\nusing dedicated superconducting arc magnets that nest dipoles with quadrupoles and sextupoles that are\ndesigned in close collaboration with the optics development [184]. These nested magnets would replace\nthe regular quadrupoles and sextupoles in the GHC lattice, while otherwise keeping the average cell\nlength and phase advance unchanged. The magnet design allows for individually tuning the overlapping\nfields, so that it can directly be used for energy tapering along with orbit and optics corrections.\nThe overlapping dipole and quadrupole fields directly impact the damping partitions, leading to\nsignificant changes in the horizontal equilibrium emittance and under certain conditions unstable beam\nsizes, for example when the dipole fields in the nested magnets match the arc dipole strength. The\nstability and the equilibrium emittance can be adjusted by carefully adjusting the dipole field nested\nwith the focusing arc quadrupoles and compensating for this by redistributing the integrated strength\namong the arc dipoles and the dipoles overlapping with the defocusing quadrupoles. This was done to\noptimise the equilibrium emittance of the nested t\u00aft lattice design to be 1.39 nm, roughly equal to that of\nthe baseline GHC design. This was achieved by having a dipole field in the focusing quadrupoles about\n46% lower than in the rest of the arc. The design lends itself to easily further optimising the horizontal\nequilibrium emittance by tuning the dipole strength in the focusing quadrupoles [183].\nThe phase advance of the FODO cell can be preserved by performing a small adjustment on the\nquadrupole strengths, leading to a change in the \u03b2-function of about 1 % compared to that of the baseline\nGHC design. This small change in the optics can be easily absorbed by a slight re-matching of the\nfirst few magnets in the straight sections to allow a largely unchanged design of the experiment and RF\ninsertions. The overall decrease in dipole field, due to the redistribution to the nested magnets results in\na significant reduction of the synchrotron radiation by 16.5% from about 10.0 GeV/turn to 8.4 GeV/turn\n72\n\nFig. 1.48: Illustration of arc cell layouts for GHC lattices in Z and t\u00aft operation.\nat the t\u00aft energy.\nWhen basing the design entirely on the GHC design, a complication arises due to the unequal\ndipole field distribution when taking into account the second beam. The baseline design assumes a twin\naperture design sharing the same yoke for the magnets of both beams, with a focusing quadrupole in one\nbeam paired with a defocusing quadrupole in the other beam and vice-versa. The unequal dipole fields\nand bending angle between focusing and defocusing quadrupole would result in the design trajectories\nof the two beams diverging in the arcs. In the case of the z-lattice, this would result in a maximum\ndeviation of about 1.5 mm, which would most likely be tolerable. However, an alternative arrangement\nwith matching polarities between the beams is also feasible and could be implemented with very few\nchanges to the design.\nA second complication is due to the changing arc cell length difference between the Z and t\u00aft\noperation. As is illustrated by Fig. 1.48, the shortening of the FODO cell by factor two between Z and\nt\u00aft operation results in the change in the polarity of the focusing arc quadrupoles. This, along with the\nnested dipole field that depends on the polarity of the quadrupole for stability reasons, results in a change\nin geometry between Z and t\u00aft operation. This effect can be compensated by a physical geometry that\ndeviates from the magnetic geometry when operating at Z energy. This can be modelled by assigning a\ndifferent magnetic k0 than the geometric bending angle. The effect can be largely mitigated by utilising\nthe dipoles in the gaps initially reserved for focusing quadrupoles, as orbit kickers in t\u00aft operation. Such\nan approach would result in a maximum orbit deviation of approximately 2 mm while also reducing the\nhorizontal equilibrium emittance.\nAn alternative, though more labour-intensive, solution would be to realign the magnets when tran-\nsitioning between the two operational modes, which might preclude the use of dual-aperture magnets.\nWhile the first approach is more practical and cost-effective, realigning the magnets would be less chal-\nlenging from a beam dynamics perspective, as it eliminates the need to manage sextupole feed-down\neffects. Both solutions should be explored to determine the optimal strategy.\nFor the sextupole placement, two options are considered, as shown in Fig. 1.49b. The first option\nenvisions nesting the sextupoles together with the quadrupole and dipole coils, whilst the second option\nwould nest the sextupoles with only dipoles and in series with the nested quadrupoles. Both options result\nin a similar dynamic aperture to the GHC lattice by linearly scaling the sextupole strength to recover the\ncorrect chromaticity. However, the momentum acceptance requires further sextupole optimisation [185].\nApart from requiring fewer superconducting magnets, a key advantage of Option 1 is that it could facili-\ntate the alignment of the quadrupole and sextupole coils with each other, potentially reducing sources of\ncoupling.\nOverall, the nested magnet design based on the GHC offers a performance comparable to that of\nthe GHC and is fully compatible with the insertion regions. A summary of the design parameters of\n73\n\n(a) Magnetic nested circuits proposed for Z and t\u00aft\noperation in nested magnet configuration.\n(b) Two options for nested sextupoles.\nFig. 1.49: Options for nested circuits.\nthe GHC and the nested magnet arc cell design is shown in Table 1.23. This was achieved by having\na non-uniform dipole field in the arc cells, which brings additional challenges that have been identi-\nfied and solved. Compared to the nominal GHC design, this solution offers reduced power loss due to\nohmic heating by having superconducting magnets in place of the quadrupoles and reduced synchrotron\nradiation, leading to an estimated decrease in power consumption of up to 20%, even when taking into\naccount the cooling for the cryogenic systems. Moreover, this solution reduces the number of dipole\nfamilies required, and the individual circuits that are necessary by default could be utilised to taper the\nlattice efficiently using only the superconducting magnets. Similar methods should apply to the LCC\ndesign; however, the more compact quadrupoles would diminish the advantage of reduced synchrotron\nradiation.\nTable 1.23: Overview of the different design parameters for the Z and t\u00aft lattices with nested magnets,\nincluding optical and synchrotron radiation properties.\nZ GHC\nZ NMs Realigned\nZ NMs K0\nt\u00aft GHC\nt\u00aft NMs\nDxmax [m]\n0.634\n0.638\n0.722\n0.559\n0.559\nI2 [10\u22124]\n6.417\n5.372\n5.367\n6.40\n5.35\nI5 [10\u221210]\n1.484\n1.027\n1.101\n0.194\n0.138\nU0 [MeV/turn]\n39.06\n32.70\n32.69\n9994.85\n8353.07\n\u03f5x [nm]\n0.705\n0.605\n0.500\n1.478\n1.388\nDamping\ntimes[s]\n0.709\n0.709\n0.354\n0.880\n0.848\n0.416\n0.675\n0.847\n0.486\n0.0110\n0.0110\n0.0055\n0.0146\n0.0132\n0.0063\nJx\n1.000\n0.963\n1.255\n0.999\n0.903\nJy\n1.000\n1.000\n1.001\n1.000\n1.000\nJz\n1.999\n2.036\n1.745\n2.000\n2.096\n1.10.3\nNon-local detector solenoid compensation\nFor cancelling the effect of the detector solenoid field, as an alternative to the baseline scheme, which\nconcentrates the compensation solenoid within \u00b1\u2113\u2217around the IP (local scheme), the compensation\n74\n\nsolenoid can also be placed behind the final quadrupole unit (non-local scheme). Both local and non-\nlocal schemes can compensate for the x-y coupling and the vertical dispersions without degrading the\nperformance (including the beam-beam effects). In the non-local scheme, the required compensation\nsolenoid field is weaker. While the non-local scheme, thereby, provides a better residual vertical emit-\ntance, it also seems to induce stronger spin depolarisation. Studies are needed to determine whether, for\nthe non-local scheme, introducing targeted spin-orbit bumps can recover the desired level of equilibrium\npolarisation.\nIt is noted that the former LEP collider, without a large crossing angle, used a non-local scheme\nconsisting of four pairs of anti-symmetrically powered tilted quadrupoles over one side of each insertion\nto compensate the betatron coupling induced by the detector solenoid [186,187].\n1.10.4\nMonochromatic operation mode\nOne of the most fundamental outstanding measurements, since the Higgs boson discovery [188,189], is\ndetermining its Yukawa couplings [13,190]. Measuring the coupling of first-generation fermions presents\nsignificant experimental challenges due to their low masses and, consequently, small Yukawa couplings\nto Higgs fields. The measurement of this coupling is virtually impossible at hadron colliders because the\nH \u2192e+e\u2212decay has a tiny branching ratio, completely swamped by the Drell-Yan dielectron continuum\nwith many orders of magnitude larger cross section. The FCC-ee, with unrivalled integrated luminosities\nof 10 ab\u22121 per year at 125 GeV could enable observing the resonant s-channel production of the scalar\nHiggs boson, namely the reaction e+e\u2212\u2192H on the Higgs pole [191, 192]. This possibility motivated\nphysics [193] and accelerator studies [194\u2013202] towards implementing this new operation mode.\nSuch a measurement is more easily feasible if the centre-of-mass (CM) energy spread of e+e\u2212\ncollisions, which is approximately 50 MeV due to energy spread from synchrotron radiation (SR) alone,\nand further enhanced by beamstrahlung, in a conventional collision scheme, can be reduced to a level\ncomparable to the natural width of the Standard Model Higgs boson \u0393H = 4.1 MeV. To reduce the\ncollision-energy spread and enhance the CM energy resolution in colliding-beam experiments, the con-\ncept of monochromatisation has long been proposed [203]. The basic idea consists of creating opposite\ncorrelations between spatial position and energy deviation within the colliding beams, which can be ac-\ncomplished in beam-optics terms by introducing a non-zero dispersion function with opposite signs for\nthe two beams at the interaction point (IP), as sketched in Fig. 1.50 for a crossing-angle configuration.\nFig. 1.50: Schematic of crossing-angle collision with monochromatisation based on nonzero horizontal\nIP dispersion, showing trajectories at the nominal energy E0 and with an energy offset of \u00b1\u2206E.\n75\n\nTaking as a starting point the GHC optics [204\u2013207], for the t\u00aft mode, different monochromati-\nsation schemes implying non-zero horizontal or vertical or both types of dispersion function at the IP\n(D\u2217\nx,y) have been studied. All newly proposed IR optics has been designed to remain compatible with a\nstandard operation mode without dispersion at the IP and also with the present tunnel configuration.\nGiven the presence of horizontal bending magnets in the vertical local chromaticity correction of\nthe FCC-ee GHC Interaction Region (IR), the most natural way to implement monochromatisation in this\nFCC-ee lattice type is reconfiguring these IR dipoles so as to generate a non-zero D\u2217\nx while maintaining\nthe same crossing angle \u03b8c. Indeed, a wide \u03c3\u2217\nx helps mitigate the impact of the beamstrahlung (BS) on\nthe energy spread \u03c3\u03b4, while preserving a small \u03c3\u2217\ny is crucial for attaining high L. Taking into account the\nbaseline parameters for the FCC-ee GHC lattice with horizontal betatron sizes (\u03c3\u2217\nx,\u03b2 =\np\n\u03b5x\u03b2\u2217\nx) at the IP\nof the order of 10 \u00b5m and a \u03c3\u03b4,SR of \u223c0.05 % at s-channel Higgs production energy (\u223c125 GeV), a D\u2217\nx\nof around 10 cm is required to achieve a monochromatisation factor (\u03bb) of \u223c5-8.\nBecause \u03c3\u2217\ny,\u03b2 (\u223cnm) \u226a\u03c3\u2217\nx (\u223c\u00b5m) for getting high luminosities, about 100 times smaller D\u2217\ny (\u223c\nmm) is needed to get a similar \u03bb. A nonzero D\u2217\ny of this magnitude could be generated by simply using\nskew quadrupole correctors around the IP [208\u2013210]. These quadrupoles could be located close to the\nsextupole pairs in the IR.\nAs an illustration, a monochromatisation IR optics with combined 0.105 m of horizontal and 1 mm\nvertical IP dispersion) based on the FCC-ee GHC t\u00aft optics as starting point has been developed using\nMAD-X [211]. It is shown in Fig. 1.51. Different monochromatised beam-optics designs, including\nones based on the lower-energy Z lattice, are detailed in Ref. [212].\nAfter global implementation, the results of the analytical global performance evaluation for the\nmonochromatisation IR optics based on the \u2018FCC-ee GHC t\u00aft\u2019 are summarised in Table 1.24, for the\ncrossing-angle configuration. Parameters due only to synchrotron radiation are marked with \u2018SR\u2019, while\nthose including the impact of beamstrahlung are marked with \u2018BS\u2019. For comparison, the first column\nlabelled Standard ZES, presents an energy-scaled (ES) optics configuration. Its performance parame-\nters were calculated after increasing the FCC-ee V22 t\u00aft optics from 45.6 GeV to 62.5 GeV, followed\nby completing all corrections and synchrotron radiation power loss compensation. The optics labelled\nMonochroM ZH4IP integrate the IP horizontal dispersion generation monochromatisation optics at all\nfour IPs, while MonochroM ZH2IP does so at only two of the four IPs. The designation MonochroM\nZHS refers to the re-matched standard optics design that is orbit-compatible with the MonochroM ZH4IP\noptics. The number of bunches per beam nb is constrained by the maximum beam-beam tune shift, taken\nto be 0.14, and by a minimum bunch spacing of 25 ns at FCC-ee. To select an appropriate nb, studies\noptimising the luminosity per IP L and the CM energy spread \u03c3W of the MonochroM ZH4IP optics, as\na function of nb were conducted, including the beamstrahlung impact under the crossing-angle collision\nconfiguration.\nTo accurately assess the performance of the FCC-ee monochromatisation IR optics, which features\nnon-zero dispersion at the IP, the \u03c3W and luminosity per IP L were calculated for the different configura-\ntions using the simulation tool GUINEA-PIG [213] and taking into account the impact of beamstrahlung.\nIn these calculations, the particle distribution at the IP was modelled as an ideal Gaussian distribution,\ncharacterised by the global optical parameters of each optics configuration.\nIt is noted that while the physics performance of a nonzero-D\u2217\ny scheme is less favourable, it would\nbe easier to implement without altering the IR orbit, rendering it an attractive option for existing low-\nenergy e+e\u2212colliders. Without the \u03f5y blow-up due to BS, this scheme could potentially achieve better\nperformance in such settings.\nLooking ahead, the optical parameters for the monochromatisation mode will be further opti-\nmised for enhanced performance. Second, the dynamic aperture optimisation for these new types of\nmonochromatisation optics will be carried out step-by-step by adjusting arc sextupole families according\nto particle tracking results. This will allow beam-beam simulations with non-zero IP dispersion in the\n76\n\nFig. 1.51: Monochromatisation IR lattices and optics with combined 0.105 m horizontal and 1 mm ver-\ntical IP dispersion, based on the FCC-ee GHC t\u00aft optics, developed using MAD-X. The beam direction\nis from left to right and the dashed line s = 0 marks the location of IP. In the lattice, dipoles, quadrupoles\nand sextupoles are shown in blue, red and green respectively, while focusing and defocusing elements\nare positioned above and below the orbit. In the optics, horizontal and vertical betatron functions are\ndisplayed in blue and red respectively, while horizontal and vertical dispersion functions are shown in\ngreen and purple, respectively.\ncode XSUITE, incorporating the hourglass and BS effects rather than relying solely on analytical eval-\nuations. Implementations of monochromatisation in more symmetric IRs, such as those in the FCC-ee\nLCC optics, will also be explored. Finally, studies are underway to validate the monochromatisation\nconcept experimentally in existing low-energy circular e+e\u2212colliders, such as BEPC II, DA\u03a6NE, and\nSuperKEKB [100,214,215]. These efforts will be essential for achieving the full potential of monochro-\nmatisation in future collider projects.\n1.10.5\nAlternate polarisation studies\nAs discussed in Sections 1.7.3 and 2.1.2, injecting pre-polarised pilot bunches could significantly en-\nhance the available time for physics, especially in case of frequent beam aborts, and in addition, ease\nconstraints on the maximum achievable polarisation. The injector would then need to generate polarised\npilot bunches of electrons and positrons, with sufficient transport of polarisation through the full injector\nchain and booster energy ramp. Polarised electron guns providing the required bunch intensity exist, e.g.,\nthe dc polarised electron gun developed for the Electron Ion Collider [216]. For the positrons, a small\npolarising ring located in, or inside, the damping ring [217] could pre-polarise and store a set of pilot\nbunches until they are needed for energy calibration in the collider.\n77\n\nTable 1.24: Global performance parameters of monochromatisation IR optics with nonzero horizontal IP\ndispersion based on the \u2018FCC-ee GHC t\u00aft\u2019 optics under the crossing-angle configuration.\nParameter\n[Unit]\nStandard ZES\nMonochroM\nMonochroM\nMonochroM\nZH4IP\nZH2IP\nZHS\n# of IPs nIP\n4\nFull crossing angle \u03b8c\n[mrad]\n30\nSR power / beam PSR\n[MW]\n50\n50\n49\n50\nBeam Energy E0\n[GeV]\n62.5\nEnergy loss / turn U0\n[GeV]\n0.138\n0.143\n0.141\n0.143\nBeam Current I\n[mA]\n360\n350\n350\n350\nBunches / beam nb\n12000\nBunch population Nb\n[1011]\n0.57\n0.55\n0.55\n0.55\nHor. emittance (SR/BS) \u03b5x\n[nm]\n0.17 / 0.17\n1.48 / 7.27\n0.84 / 4.23\n0.35 / 0.35\nVert. emittance (SR/BS) \u03b5y\n[pm]\n0.35 / 0.35\n2.96 / 2.96\n1.68 / 1.68\n0.71 / 0.71\nMomentum compaction factor \u03b1C\n[10\u22126]\n7.31\n6.92\n7.12\n7.06\n\u03b2\u2217\nx/y\n[mm]\n1000 / 1.6\n90 / 1\n90 / 1\n1000 / 1.6\nD\u2217\nx/y\n[m]\n0 / 0\n0.105 / 0\n0.105 / 0\n0 / 0\nRel. energy spread (SR/BS) \u03c3\u03b4\n[%]\n0.054 / 0.076\n0.055 / 0.057\n0.054 / 0.057\n0.055 / 0.068\nBunch length (SR/BS) \u03c3z\n[mm]\n3.86 / 5.49\n4.05 / 4.20\n3.95 / 4.12\n4.09 / 5.07\nRF voltage 400/800 MHz VRF\n[GV]\n0.170 / 0\nRF frequency (400MHz) fRF\n[MHz]\n399.994581\nSynchrotron tune Qs\n0.015\n0.014\n0.014\n0.014\nLong. damping time \u03c4E/Trev\n[turns]\n454\n436\n445\n436\nHoriz. beam-beam (SR/BS) \u03bex\n0.059 / 0.030 0.0025 / 0.0022 0.0027 / 0.0024 0.049 / 0.033\nVert. beam-beam (SR/BS) \u03bey\n0.24 / 0.17\n0.044 / 0.041\n0.060 / 0.056\n0.15 / 0.12\nCM energy spread (SR/BS) \u03c3W\n[MeV]\n47.45 / 67.58\n13.41 / 25.75\n10.25 / 20.95\n48.80 / 60.47\nLuminosity / IP (SR/BS) L\n[1034 cm\u22122s\u22121]\n72.8 / 51.9\n20.9 / 19.5\n28.3 / 26.6\n44.6 / 36.6\n78\n\nChapter 2\nFCC-ee collider operation concept\n2.1\nOperation requirements\n2.1.1\nPhysics requirements\nTable 2.1 shows the target integrated luminosities with four interaction points, allocated running times,\nand the total number of events, for the four baseline centre-of-mass energy stages at the Z pole, the WW\nproduction threshold, the ZH production cross-section maximum, and the top-pair production, in this\nchronological order.\nThe nominal integrated luminosity is computed by assuming 185 days of physics run time per\nyear, a hardware availability of at least 80%, and a corresponding \u2018physics efficiency\u2019 E of 75% (also\nsee Section 2.1.2). In addition, for determining the total integrated luminosity and the number of events\nexpected to be produced (in the last two rows of the table), the luminosity is assumed to be half the\ndesign value during the first two years at the Z pole and for the first year at the t\u00aft threshold. At the Z\npole, the integrated luminosity is distributed as follows: 40 ab\u22121 at 87.9 GeV, 125 ab\u22121 at 91.2 GeV, and\n40 ab\u22121 at 94.3 GeV. The number of Z decays results from this setup. At the WW threshold, the run\ntime is evenly distributed between 157.5 GeV and 162.5 GeV. The number of WW events include all \u221as\nvalues from 157.5 GeV up.\nFigure 2.1 displays the corresponding baseline sequence of events [218]. However, other mode\nsequences would be possible (see Section 2.2.1) and might be preferred. For example, scheduling a Z\npole run after the ZH run or the WW threshold run can be considered, ideally with an initial Z pole\nrun during the early phase of FCC-ee operation. Indeed, while the Z pole run offers an exceptionally\nrich set of physics opportunities, it is also the most ambitious and demanding part of the programme\nfrom all perspectives, including accelerator performance, energy calibration, detector systematic biases,\nand theoretical calculations. It will be extremely challenging to achieve all the goals of the Z pole run\nduring the first four years of the collider operation. The new versatile RF system designed accordingly,\nenables a quasi-total flexibility to choose the running sequence. For example, it would allow short initial\nZ pole and WW threshold runs, to commission the collider and the detectors, to establish the resonant\ndepolarisation procedures, etc. The ZH run could then proceed, before going back to the Z pole and the\nWW threshold, both now at full luminosity, with fully functional resonant depolarisation, and complete\nunderstanding of the collider.\n2.1.2\nTarget availability and efficiency\nAnnual integrated luminosity estimates for FCC-ee at each mode of operation are derived from three or\nfour parameters:\n\u2013 Nominal Instantaneous Luminosity L: The first two years of Z and the first year of t\u00aft are assumed\nto achieve, on average, 50% and 65% of this value, respectively, to account for machine commis-\nsioning and beam tuning. These reductions reflect LEP/LEP-2 experience. Nominal luminosity is\nthen assumed from the third year onward in Z pole operation and from the second year onward at\nthe t\u00aft threshold.\n\u2013 Annual Scheduled Physics Time T: It is assumed that 185 days per year are scheduled for physics.\nThis is obtained by subtracting from one year (365 days): 17 weeks of extended shutdowns (120 days),\n30 days of annual commissioning, 20 days for machine development and 10 days for technical\nstops.\n79\n\nTable 2.1: The baseline FCC-ee operation model with four interaction points, showing the centre-of-\nmass energies, design instantaneous luminosities for each IP, integrated luminosity per year summed\nover 4 IPs [218]. The integrated luminosity values correspond to 185 days of physics per year and\n75% operational efficiency (i.e., 1.2 107 seconds per year) [4], in the Z, WW, ZH, t\u00aft baseline sequence.\nThe last two rows indicate the total integrated luminosity and the total number of events expected to be\nproduced in the four detectors.\nWorking point\nZ pole\nWW thresh.\nZH\nt\u00aft\n\u221as (GeV)\n88, 91, 94\n157, 163\n240\n340\u2013350\n365\nLumi/IP (1034 cm\u22122s\u22121)\n140\n20\n7.5\n1.8\n1.4\nLumi/year (ab\u22121)\n68\n9.6\n3.6\n0.83\n0.67\nRun time (year)\n4\n2\n3\n1\n4\nIntegrated Lumi (ab\u22121)\n205\n19.2\n10.8\n0.42\n2.70\n2.2 106 HZ\n2 106 t\u00aft\nNumber of events\n6 1012 Z\n2.4 108 WW\n+\n+370k HZ\n65k WW \u2192H\n+92k WW \u2192H\n\u2013 Availability A: Represents the percentage of scheduled physics time when the collider and injec-\ntors are able to deliver beam, as opposed to a hardware failure leading to downtime and need to\nrepair. An overall machine availability of 80% is assumed.\n\u2013 Efficiency E: The efficiency factor E is an empirical factor, whose value can be extrapolated\nfrom other similar machines, or by simulations with average failure rate and average downtime.\nThanks to the top-up mode of operation, it is expected that E will be, within five percent, equal\nto the availability A of the collider complex. The target availability is at least 80% and, thereby,\na corresponding efficiency E > 75% is expected [4]. In the case of FCC-ee, no time is lost\nfor acceleration and the efficiency only reflects the relative downtime due to technical problems\nand associated re-filling and recovery time. Therefore, the efficiency will be roughly equal to the\nhardware availability, taken to be at least 80%, minus 5% reduction for beam recovery after a\nfailure. The assumed efficiency value of 75% with respect to the daily peak luminosity is lower\nthan achieved with top-up injection at KEKB and PEP-II [4]. However, at FCC-ee the need for\npilot bunches to be pre-polarised in the collider after each beam abort may pose a challenge for\nreaching the target collider efficiency in the Z and W modes of operation, which could be largely\nmitigated by generating polarised pilot bunches already in the injector (Fig. 2.24).\nFrom the above factors, the annual achieved integrated luminosity at each interaction point (IP) is calcu-\nlated, assuming top-up operation during stable beams, as\nLint = E T L .\n(2.1)\nUsing the above parameters, the integrated luminosity target in each energy mode is reached or exceeded.\nA detailed study to explore the implied challenges is summarised in Section 2.4, which also presents\nexample simulations for the collider-ring systems. Similar studies for the booster, injector complex and\ntechnical infrastructure are presented in Sections 5.3, 7.9 and 8.10, respectively.\n2.2\nChanging operation modes\n2.2.1\nSwitching between Z, WW, and ZH modes\nThe ability to easily switch between Z, WW and ZH modes of operation depends upon the following\nconditions and requirements.\n80\n\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\nYears\n0\n100\n200\n]\n-1\nIntegrated luminosity [ab\nZ\nWW\n 10\n\u00d7\nZH\n 10\n\u00d7\nTop\n 10\n\u00d7\nQuasi-total order flexibility\nFig. 2.1: Operation sequence for FCC-ee with four interaction points, showing the integrated luminosity\nat the Z pole (pink), the WW threshold (blue), the Higgs factory (red), and the top-pair threshold (green)\nas a function of time. In this baseline model, the sequence of events goes with increasing centre-of-\nmass energy, but there is quasi-total flexibility in the sequence all the way to 240 GeV. The integrated\nluminosity delivered during the first two years at the Z pole and the first year at the t\u00aft threshold is half\nthe annual design value. The hatched area indicates the shutdown time needed to prepare the collider for\nthe higher energy runs at the top-pair production threshold and above.\nThe 400 MHz cavities and cryomodules must all be installed in their final location from the start\nof operation; this represents 33 cryomodules on either side of point PH. This approach poses constraints\nfor the early procurement and installation of all cryomodules, but it has the great merit of avoiding a\nstaged installation of the cryogenics systems and later interventions in the tunnel for installing additional\ncryomodules.\nAt the Z and WW operating points, the incoming beam from the arc is arriving from the outer\naperture and first passes through the 33 cryomodules on the incoming side of the insertion; it is then\ndeviated towards a bypass line that goes around the other 33 cryomodules on the outgoing side of the\ninsertion, before being brought back towards the inside aperture of the outgoing arc. Hence, the two\ncounter-rotating beams are crossing at the middle of the RF insertion.\nWith the scheme of reverse phase operation for the 400 MHz RF, the switch between the Z and\nWW modes of operation involves only a reconfiguration of the RF system without any hardware inter-\nvention; the beamlines and beam paths stay the same.\nThe crossing of the beams in the middle of the insertion is done over a long length to avoid\nstring dipole bends that could generate synchrotron radiation towards the cavities. The adverse effect\nof this shallow horizontal crossing is that the electron and positron beams share a common vacuum\nchamber over a certain length, which, in turn, generates long-range beam-beam interactions that would\nbe very detrimental at the Z and WW modes of operation. For this reason, the horizontal crossing is\nsupplemented by a vertical bump in opposite directions for both beams, such that they can be in separate\nvacuum chambers over the horizontal crossing, avoiding all long-range beam-beam interactions.\nThe separation scheme and recombination at the Z and WW operating points involve only mag-\nnetic dipoles (see Fig. 2.2, top picture), the only point of attention being that the dipoles should not\ngenerate synchrotron radiation towards the RF cavities and ancillary equipment and that any synchrotron\nradiation generated should be minimal, both in terms of power radiated and critical energy of the photons.\nThe switch to the ZH operating point requires that both beams go through the entire set of two\n81\n\ntimes 33 cryomodules (Fig. 2.2, centre picture). The incoming beam from the arc coming from the outer\naperture first goes through the 33 cryomodules on the incoming side of the insertion. The deviation\ndipoles towards the bypass line are now switched off, and the beam goes straight in a different beampipe\ntowards the other side of the insertion, where it goes through the other 33 cryomodules on the outgoing\nside of the insertion. At the exit of the second set of cryomodules, the beam is deviated towards the\ninside aperture of the outgoing arc.\nBecause of the symmetry between the two beams, it is obvious that they share the same beam path\nacross the whole insertion in opposite directions. The first consequence is that the timing of the bunches\nin the beams must ensure that no collision occurs in the RF insertion. This can be done by having only\ntwo trains of bunches for each beam, colliding in experimental insertions only.\nThe second consequence is that the deviation of the beam on the outgoing side of the insertion must\nbe completely transparent for the incoming beam coming straight from the outer arc into the cryomod-\nules. With opposite particle charges and opposite directions of the two beams, this cannot be achieved\nwith simple magnetic elements. A single element can combine electrostatic and magnetic forces that add\nup for one charge and direction and cancel exactly for the opposite charge and opposite direction. The\nincoming beam from the outer aperture of the arc is not deviated and the outgoing beam is deviated to\nthe inner aperture of the arc.\nFinally, the ability to switch between Z, WW, and ZH operating points implies that both layouts\ncoexist in a single insertion, as is sketched in Fig. 2.2 (bottom picture). Equal path lengths for each layout\nare required to maintain the same distance between interaction points. Further, the phase advances for\neach layout also need to be equal, unless the phase advances in the other technical insertions at points\nPB, PF, and PL can be re-tuned.\nFig. 2.2: Schematics of the beam path configurations in the RF section at FCC Point PH for the Z and\nWW operating points (top), the ZH operating point (centre) and the proposed combined layout for Z,\nWW and ZH operating points with seamless transition (bottom). The yellow rectangles represent the set\nof cryomodules on each side of the insertion. The smaller rectangles on the outside of cryomodules on\nthe ZH and the combined schematics represent the combined electrostatic and magnetic separators.\n82\n\n2.2.2\nOptimizing RF performance for t\u00aft collisions\nTo complete the 2.1 GV delivered by the 400 MHz RF systems used at the ZH operating mode, additional\ncavities and RF sources are added during the year of shutdown to reach a total RF voltage of 11.3 GV\nrequired at the t\u00aft mode.\nFor the collider, an additional 102 cryomodules and 204 microwave vacuum tube amplifiers at\n800 MHz are installed in point PH. Each cryomodule hosting four 6-cell elliptical cavities will run at\ntheir maximum performances of 22.5 MV in order to produce 9.18 GV RF voltage. Each RF source will\npower two cavities at a level of 200 kW RF power each.\nFor the booster RF system in point PL, the same RF frequency of 800 MHz is used for all oper-\national modes from Z to t\u00aft. The 28 cryomodules used at the Z-W-H modes will be completed by 84\nadditional cryomodules of the same type to reach a total RF voltage of 10.18 GV. The 112 cryomod-\nules corresponding to 448 cavities will be powered individually by 10 kW solid state RF amplifiers after\nremoving the 28 RF sources used at the previous modes.\nFigure 2.3 shows the installation sequence of the RF cryomodules and high-power sources for the\ncollider and booster.\nIt is important to note that once the full SRF system for t\u00aft is installed, it will be impossible to run\nat the Z, W and H energy with the nominal beam current.\nFig. 2.3: RF system installation sequence for collider and high energy booster.\n2.3\nOperation and performance\n2.3.1\nEnergy calibration\nA principal goal of the FCC-ee is the ultra-precise measurement of electroweak (Z and W) observables,\nfor which an accurately determined collision energy is key. This involves beam energy calibration every\n10-15 minutes using non-colliding polarised pilot bunches, which circulate simultaneously with the main\ncolliding bunches. The energy of these pilot bunches is measured by resonant depolarisation (RDP),\nwhere the frequency of a kicker magnet is adjusted until the pilot bunch\u2019s polarisation vanishes.\nPilot bunches are polarised in the main ring at the start of every fill using wiggler magnets, a\nprocess that takes roughly 90 minutes. The wigglers are then turned off before the injection of the\nmain colliding bunches. During physics operation, the pilot bunches have a combined Touschek and\ngas scattering lifetime of less than 20 h [163]. Due to the long natural polarisation time (150 h in Z\nmode), it is presently unclear whether these pilot bunches will naturally achieve sufficient polarisation\n83\n\n(a) Z and WW modes.\n(b) ZH and t\u00aft modes\nFig. 2.4: Baseline operation cycles in the FCC-ee.\nfor RDP before expiring. The baseline simulation pessimistically expects that after 20 h the beam must\nbe dumped to refill again.\nIn ZH and t\u00aft modes, the energy spread makes RDP impossible but the required accuracy of the\nbeam energy is also significantly less demanding. Energy measurement is instead achieved by observing\ncollisions at the interaction point (IP). This removes the need for polarisation at the start of every fill.\nFurther, with a top-up injection, physics can continue uninterrupted until a beam dump occurs due to a\nmachine fault or schedule end. In these modes, pilot bunches are used only to verify optics before the\ninjection of bunches with nominal intensities.\n2.3.2\nOperation cycle\nEnergy calibration imposes distinct operation cycles for the electroweak (Z, WW) and high energy (ZH,\nt\u00aft) modes, shown inFig. 2.4. Phases in this cycle are as follows:\n1. Set Up: Main magnets are cycled, RF system is set and other equipment is prepared for injection.\n2. Pilot Bunch Injection: Pilot bunches are injected and equipment/optics are adjusted.\n3. Polarisation: Z and WW modes only. Wigglers are turned on to begin polarising the pilot bunches,\na process taking approximately 90 minutes.\n4. Fill: Wigglers are turned off and the main colliding bunches are injected. Fill time tf in each\nenergy mode is shown in Table 2.2. These times are indicative, and must be studied in detail\naccording to constraints in the injector complex.\n5. Adjust: Time to bring the beams into collision and make final adjustments to equipment before the\ndetectors can begin to observe useful collisions.\n6. Physics: Collisions begin at nominal luminosity. With top-up injection, flat luminosity can be\nmaintained. In Z and W modes, an upper limit on the duration of physics tph = 20 h is applied\ncorresponding to the Touschek and gas scattering lifetime of the pilot bunches.\n7. Burn Off: If the injector complex fails, the beam can be preserved in the main colliding rings with\ndecaying luminosity corresponding to lifetime \u03c4 (see Table 2.2). If the injector complex cannot be\nrestored, after the time \u03c4 the beam is taken to be dumped.\n8. Down for Repair: On equipment failure, the accelerator is stopped for repair.\n84\n\nTable 2.2: Operation cycle times.\nZ\nWW\nZH\nt\u00aft\nFill time\u2217, tf / minutes\n7.7\n2.5\n1.52\n1.45\nBurn off lifetime, \u03c4 / minutes\n15\n12\n12\n11\nMax. physics duration, tph / hours\n20\n20\n\u221e\n\u221e\n\u2217To be updated according to filling bunch intensity.\n2.3.3\nLuminosity\nLuminosity is produced only in Physics or Burn Off phases in the operation cycle. By tracking the time\nt spent in these operation phases, achieved integrated luminosity is calculated.\nLint =\n\uf8f1\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f3\nNIPLt,\nt \u2208physics\nNIPL\u03c4(1 \u2212e\u2212t\n\u03c4 ),\nt \u2208burn off\n0,\notherwise\n(2.2)\nwhere NIP = 4 is the number of interaction points and L is the nominal instantaneous luminosity as per\nTable 2. In the first two years of Z operation, and first year at t\u00aft, reduced luminosity is expected at 50 %\nand 65 %, respectively to account for machine commissioning and beam tuning.\n2.3.4\nOptics commissioning strategy\nThe optics commissioning strategy [21, 28, 50, 219] takes into account arc misalignment and strength\nerrors. The various available optics and the associated tolerances are described in Section 1.3. IR optics\nimperfections and non-linear errors are being assessed separately and both require further developments.\nCommissioning sequence\nFigure 2.5 presents the general sequence of beam optics commissioning steps for the FCC-ee. Initial\nbeam steering around the ring requires the sextupole magnets to be switched off. In this condition,\nstoring the beam with a reasonable lifetime is not possible for the nominal optics, due to a big reduction\nin dynamic aperture without the sextupoles [42,43]. Therefore, a commissioning optics was developed,\nin which both thequadrupole and sextupole magnets near the IP are switched off [44]. This optics features\na lower natural chromaticity and lower peak beta functions across the IR. It also implies no synchrotron\nradiation from the final doublet (FD). Since this optics allows establishing a straight reference trajectory\nacross the IP in the absence of focusing elements, it is called \u201cballistic\u201d optics.\nRight after threading the beam for the first time in the FCC-ee with the ballistic optics, and sex-\ntupoles switched off, large dispersion errors and too large a vertical emittance are observed (Table 2.3).\nAt this point, refined optics measurements are not possible, but dispersion free steering (DFS), or sim-\nply dispersion correction using orbit correctors, is very effective at mitigating these imperfections and\nallowing the commissioning to continue. The resulting DA for the ballistic optics is shown in Fig. 2.6.\nTurning to the nominal optics, Table 2.4 summarises the closed orbit deviations, beta beating, and\nspurious dispersion errors before and after the linear optics correction. The simulated dynamic aperture\nand momentum acceptance are presented in Section 1.3.3.\n85\n\nOrbit threading\n(Sexts Off)\nDisp. free\nsteering\nSexts\nOn\nLOCO\ncorrections\nArc\nBBA\nOptics\ncorrections\nBallistic optics\nOrbit correction\nIR +\nArc BBA\nOptics\ncorrections\nNon-linear\noptics corr.\nIP\ntuning\nRelaxed optics (various iterations decreasing \u03b2\u2217)\nOrbit correction\nOptics\ncorrections\nNon-linear\noptics corr.\nIP\ntuning\nBaseline optics\nFig. 2.5: Steps during the FCC-ee optics commissioning starting from the ballistic optics, followed by a\nsequence of relaxed optics [45] and, finally, the nominal collision optics.\nTable 2.3: Median RMS values of several optics parameters right after the first beam threading with\nand without being followed by dispersion free steering (DFS) using the orbit correctors for the ballistic\noptics.\nParameter\nWithout DFS\n(rms)\nWith DFS\n(rms)\nver. orbit (\u00b5m)\n222\n255\n\u2206Dx (mm)\n446\n70\n\u2206Dy (mm)\n416\n39\n\u03b5v (pm)\n659\n4\nBeam based alignment\nIn the commissioning sequence Beam Based Alignment (BBA) can be performed after sextupoles have\nbeen switched on.\nDue to the sheer size of the FCC performing BBA to individual magnets would be a very time-\nconsuming procedure and, hence, various promising parallel approaches are explored, aiming to achieve\napproximately 10 to 20 \u00b5m effective alignment after BBA.\nUsing Parallel Quadrupole Modulation System (PQMS), a technique which has already success-\nfully been tested at SPEAR, is applied to the FCC-ee. Modulating 10 quadrupoles in parallel with a\n\u2206K/K of 2 %, distributed equally over one arc, and using a calibrated lattice with 1 \u00b5m BPM resolu-\ntion, an accuracy below 20 um for vertical and horizontal arc quadrupole BBA is achieved [220].\nA different BBA technique is also studied for a relaxed \u03b2\u2217-optics with \u03b2\u2217of 7 mm based on\nmodulating 8 arc quadrupoles in parallel with a \u2206K/K of 1 %, again with a BPM resolution of 1 \u00b5m,\ninducing orbit shifts with vertical orbit correctors nested to the quadrupoles. This yields a BBA rms\naccuracy achieving the target value. Other BBA studies assuming individual horizontal and vertical orbit\ncorrectors, located next to, respectively, focusing and defocusing quadruples, are also performed for\nthe same optics modulating 20 quadrupoles in parallel. All studied seeds achieve an accuracy below\n20 \u00b5m [221]. In addition, parameter scans confirm this performance even when processing a larger\n86\n\nFig. 2.6: DA after optics correction with the ballistic optics and having included IR alignment errors of\n50 \u00b5m in addition to the arc errors in Section 1.3.1.\nTable 2.4: Median RMS values of several optics parameters before (after sextupole ramping) and after\nlinear optics correction (nominal lattice). \u2206\u03c8 stands for phase advance deviations between nearby BPMs.\nParameter\nBefore correction\n(rms)\nAfter correction\n(rms)\nhor. orbit (\u00b5m)\n120.25\n120.46\nver. orbit (\u00b5m)\n217.53\n217.56\n\u2206\u03b2x/\u03b2x (%)\n7.41\n0.29\n\u2206\u03b2y/\u03b2y (%)\n15.79\n2.81\n\u2206Dx (mm)\n57.79\n0.28\n\u2206Dy (mm)\n62.24\n2.80\n\u03b5h (nm)\n0.72\n0.71\n\u03b5v (pm)\n26.01\n0.57\nhor. \u2206\u03c8 [2\u03c0]\n1.13 \u00d7 10\u22122\n2.91 \u00d7 10\u22124\nver. \u2206\u03c8 [2\u03c0]\n1.93 \u00d7 10\u22122\n2.29 \u00d7 10\u22123\nRe F1001\n4.93 \u00d7 10\u22122\n1.66 \u00d7 10\u22124\nIm F1001\n4.43 \u00d7 10\u22122\n5.18 \u00d7 10\u22125\nRe F1010\n3.72 \u00d7 10\u22122\n1.35 \u00d7 10\u22124\nIm F1010\n3.68 \u00d7 10\u22122\n1.31 \u00d7 10\u22124\nnumber of magnets in parallel.\nIn addition to the quadrupoles, beam-based alignment (BBA) can also be performed for the sex-\ntupoles. In simulation studies, the center of the sextupole magnets is estimated using a response matrix\nmethod. Modulating six arc sextupoles in parallel yields a precision on the order of 20 to 50 \u00b5m [222].\nEach arc sextupole shares a common girder with the adjacent quadrupole magnet, so that BBA for both\nmay possibly yield redundant information.\n87\n\nIP tuning\nSimulations are also performed including IR alignment errors for the FCC-ee GHC lattice using pyAT. In\nthis IR study, the arc alignment tolerances are taken to be 100 \u00b5m and 100 \u00b5rad, which is slightly better\nthan the numbers presented in Section 1.3.1. Final-focus doublet (FD) quadrupoles must meet strict\nalignment tolerances. The simulations in this section consider transverse shifts and rotation errors to\n10 \u00b5m and 10 \u00b5rad, respectively. IR sextupoles, including crab-sextupoles required to correct the vertical\nchromaticity at the IP (SY \u2217), exhibit intermediate sensitivity. Their errors are set to 30 \u00b5m and 30 \u00b5rad.\nThe few strong non-linear magnets, combined with the alignment errors, make proper tuning difficult\nfor most seeds, resulting in a 75% success rate out of 100 seeds. The median vertical emittance for the\nsuccessful seeds is 1.8 pm.\nThe tuning and correction of optics in the IP region of FCC-ee are essential for reaching the desired\nluminosity levels. Dedicated IP tuning knobs such as \u03b2\u2217\nx,y, W \u2217\nx,y and D\u2217\ny are employed to correct lattice\nerrors across multiple IPs, ensuring the restoration of the intended optics design and facilitating DA\nanalysis on the fully corrected lattice. The tuning knobs have no effect on the dynamic aperture as shown\nin Fig. 2.7. The resulting dynamic aperture (DA) is comparable to that obtained in the previous study,\nwhich considered only arc errors (see Section 1.3). Relaxing alignment tolerances leads to a reduction\nin the DA and a decrease in the number of successful seeds in the simulations. To enhance both DA\nand momentum acceptance (MA), additional correction algorithms beyond linear corrections will be\nrequired.\nFig. 2.7: Dynamic aperture after 512 turns for 75% of successful seeds with (right) and without (left) IP\ntuning knobs.\n2.3.5\nLuminosity optimisation and interaction-point tuning\nFCC-ee luminosity optimisation relies on measuring realistic signals from Bhabha scattering, beam-\nstrahlung and vertex detector hits. Initial assessments of these signals examine the variations in lumi-\nnosity, beamstrahlung power and vertex detector hits in response to waist shifts, vertical dispersion and\ntransverse coupling at the collision point. Waist shifts (y\u2217\u2192y\u2217+ly\u2032\u2217, with l referring to the waist-shift)\nand vertical-dispersion (y\u2217\u2192y\u2217+D\u03b4i, where D is the dispersion and \u03b4i is the relative energy deviation)\nare IP sport size aberrations, and should be corrected over the time of few minutes.\nFigures 2.8 and 2.9 show the scans of the mentioned signals varying with waist-shifts produced in\nGUINEA-PIG for the Z and t\u00aft working points. At the t\u00aft working point, the luminosity drops to about\n85% for the maximum waist shift of \u00b1 1 mm and to 40% for a vertical dispersion of \u00b1 0.1 mm. At the Z\nworking point luminosity is slightly more sensitive to waist shifts and vertical dispersion. These studies\ndo not take into account the degradation of the emittances due to the beam-beam interactions in presence\n88\n\nof the IP aberrations which could be the dominant effect, as few micrometres of Dy can increase the\nvertical beam size by 5% [46].\nFig. 2.8: The variation of luminosity with a residual waist shift (top) and residual dispersion (bottom) in\nthe electron (horizontal axis) and positron beams (vertical axis) for the Z pole (left) and t\u00aft running, from\nsimulations with the code GUINEA-PIG.\nThe beamstrahlung power emissions increase with the residual waist shift and vertical dispersion.\nThe impact on total power due to both aberrations is within a similar range. However, residual dispersion\nin the e\u2212(e+) beam has a stronger effect, increasing the beamstrahlung from the e\u2212(e+) beam while\ndecreasing emissions from the e+(e\u2212) beam, compared to waist shifts.\nFurthermore, these studies aim to extract IP-aberration-related signals and integrate them into a\nmachine-learning-based approach for luminosity tuning and optimisation. A Gaussian process-based\nmodel could be trained to predict the residual waist-shift, dispersion and coupling at the IP, based on the\nsimulated or observed luminosity, beamstrahlung power and hits of secondaries in the vertex detector.\n2.3.6\nOperational feedbacks\nGlobal orbit feedback\nThe beam orbit around the ring must be stabilised by a global orbit feedback system, based on averaged\nbeam-position monitor (BPM) readings and orbit corrector magnets. The orbit feedback systems at the\nLHC and at the Swiss Light Source (SLC) serve as examples.\nThe LHC global orbit and energy feedback is of similar size and complexity as the future orbit\nfeedback for FCC-ee. The LHC system bandwidth of only about 1 Hz is limited by the maximum\nexcitation change permitted in the superconducting orbit-corrector magnets [223]. The rms orbit stability\nin the LHC arcs during long physics fills is of order 10 \u00b5m [224].\nAt the Swiss Light Source (SLS), a global fast orbit feedback (FOFB) system based on the digital\nbeam position monitor (DBPM) system has been in use during user operation since 2003. The singular\n89\n\nFig. 2.9: The variation of beamstrahlung power with a residual waist shift (left) and residual dispersion\n(right) in the electron (horizontal axis) and positron beams (vertical axis) for t\u00aft running, from simulations\nwith the code GUINEA-PIG.\nvalue decomposition (SVD)-based correction scheme operates at a sampling rate of 4 kHz, utilizing\nposition data from all 72 DBPM stations and applying corrections through 72 horizontal and 72 vertical\ncorrector magnets [225].\nThis fast orbit feedback effectively mitigates orbit distortions, which are primarily induced by\nground and girder vibrations, as well as a 3 Hz crosstalk from booster cycles. Additionally, it enables\nrapid and independent gap adjustments for the insertion devices, ensuring complete transparency for SLS\nusers. With top-up as the standard operation mode, the system has achieved global beam stability at the\n\u00b5m level over timescales ranging from milliseconds to days.\nFor the FCC-ee, it is assumed that an orbit feedback efficiently suppresses all beam oscillations\nbelow a critical frequency of about 1 Hz [226]. This assumption appears fairly conservative, if compared\nwith the orbit feedback performance at modern light sources like the SLS.\nInteraction point feedback\nInteraction point (IP) feedback systems are essential for maintaining luminosity in the presence of ma-\nchine perturbations, such as magnet vibrations, ground motion, and fluctuations or drifts in magnet\nstrengths. At each IP, beam position monitors detect offsets between the two colliding beams, and cor-\nrections are computed and applied by correctors in the interaction region. These corrections create a\nclosed orbit bump, forming a dedicated local correction system.\nFor small IP offsets, the deflection is well described by the linear centre-of-mass beam-beam kick\nformula\nD\n\u2206x\u2032\u2217E\n= \u00b12\u03c0\n\u03b2\u2217\nx\n\u03bex\n\n\u2206x\u2217\u000b\nand\nD\n\u2206y\u2032\u2217E\n= \u00b12\u03c0\n\u03b2\u2217\ny\n\u03bey\n\n\u2206y\u2217\u000b\n(2.3)\nwhere \u03bex,y is the beam beam parameter in the horizontal or vertical plane, respectively, \u2206x\u2217(or \u2206y\u2217)\ndenotes the horizontal (vertical) offset from the centre of the opposing beam, and the angular brackets\n< ... > represent an average over the bunch distribution. The nano-beam scheme and large horizontal\ncrossing angle of FCC-ee results in sensitivity to errors far greater in the vertical than in the horizontal\nplane, due to the much larger vertical beam-beam parameter (see Table 1.2). The deflections can be\n90\n\nmeasured by comparing orbits for colliding and non-colliding (pilot) bunches, taking into account any\npossible systematic errors due to different bunch intensity and bunch length.\nPerformance requirements\nBeam-beam collisions with IP offsets reduce luminosity and lifetime. Previous studies have determined\nthe resulting IP offset limit as 0.05\u03c3y [227]. Even tighter limits may be imposed by energy calibration\nand polarisation requirements (Section 1.7). The alignment of the IP to the detector is limited by the reso-\nlution of the luminosity calorimeter. Frequency response requirements are dependent on the performance\nof the global orbit feedback.\nObservables\nIP offset can be indirectly measured from a variety of signals:\nFrom the interaction region beam position monitors and a knowledge of the transfer matrices to\nand from the IP, the IP offset can be calculated. The proposed IR BPMs are elliptical button BPMs\nsituated on the common elliptical IR beampipe, described further in Section 3.9.1.\nLuminosity is detected at the luminosity calorimeter and additional fast luminosity monitors 3.9.5.\nAs a scalar signal, only the magnitude of the offset is identified.\nBeamstrahlung radiation power and centroid position both depend upon IP offset, in a scalar and\nvector way respectively. Monitoring beamstrahlung is challenging due to the high radiation power. The\nproposed beamstrahlung monitors discussed in 3.9.5.\nInitial studies are set out in [228] and Fig. 2.10 shows studies results at the Z working point for\nthe GHC lattice.\nFig. 2.10: The variation of relative luminosity, outgoing deflection angle and beamstrahlung radiation\npower with offset in the vertical plane. Simulations were performed with the Particle in cell solver\nGUINEA-PIG. Results for the Z working point of the \u2018GHC 24.3\u2019 lattice. The impact of the detector\nsolenoid and its compensation is not currently taken into account.\n91\n\nBeam-beam deflection feedback\nDue to the high vertical beam-beam parameter, vertical IP offsets result in strong beam deflections,\nchanging the outgoing angle. This change to the outgoing angle results in detectable differences at the\nBPMs. Such a beam-beam deflection feedback system is most promising to address offsets in the vertical\nplane and has been successfully operated at SuperKEKB [229], KEKB [230], and other machines.\nDither feedback\nThe low horizontal beam-beam parameter implies that beam-beam inducted deflections will not be de-\ntectable at the IR BPMs. An alternative approach is \u2018dithering\u2019: driving one beam at a known frequency\nand minimising the IP offset by finding the phase of optimal luminosity. This approach relies solely on\nmaximisation, and therefore, the absolute offset values are never required to be calculated. This type of\ndither feedback has been successfully operated at SuperKEKB (and others) [231].\n2.3.7\nFilling patterns\nThe number of bunch slots in FCC-ee for 25 ns bunch spacing is h25ns = 12120 = 23 \u00b73\u00b75\u00b7101. In these\nsections, so-called filling patterns indicating which slots are filled with bunches are described. As the\nrequired number of bunches depends on the operational mode, a filling pattern for each of the energies\nhas been devised. Note that the harmonic number corresponding to the RF frequency is higher such\nthat,many more filling patterns and shorter minimum spacing of, e.g., 5 ns (slightly reducing electron\ncloud threshold) are in principle possible. Such schemes are not proposed.\nThe main requirements and assumptions to design filling patterns are:\n\u2013 The periodicity of the filling pattern for high-intensity bunches must contain a factor of two (filling\nthe machine in half) to ensure that all physics bunches collide in all four IPs with bunches from\nthe counter-rotating beam.\n\u2013 Presence of gaps for the injection kicker rise and fall times and beam dump kicker rise time. This\nrequirement is satisfied with a regular pattern consisting of bunch trains and gaps between them.\nThe minimum length of the gaps has been reduced to 600 ns in order to mitigate beam loading\ntransients being a potential limitation for the Z mode.\n\u2013 Batches coming from the injectors and injected into the Booster contain four bunches spaced by\n25 ns for the Z and WW mode and two bunches with the same spacing for the higher energies.\nFor the Z mode, operation of the injectors with the maximum number of four bunches with the\nmaximum repetition rate of 100/s is mandatory.\n\u2013 Filling patterns for the H and t\u00aft modes must contain appropriate long gaps such that no encounters\nbetween counter-rotating bunches occur in the common RF section.\n\u2013 The filling patterns for operation at Z and WW energies must contain positions for low intensity\nbunches required for energy calibration. They are placed inside the gaps between trains of high in-\ntensity bunches. The minimum spacing between a polarised low intensity bunch and other bunches\nis 100 ns, as required, for the rise and fall time of the fast deflector used to excite a depolarising\nresonance for energy calibration. Calibration bunches of the two counter-rotating beams must not\ncollide.\nFilling pattern for Z mode\nFor Z mode operation, each of the two counter-rotating beams must contain NB = 11200 = 26 \u00b7 52 \u00b7 7\ncolliding high-intensity bunches. The number of bunch trains must be a product of common prime factors\nof NB and the number of bunch slots h25ns. Factor four of the former is taken to allow the booster to be\nfilled with injector trains consisting of four bunches. The number of trains chosen is NT = 23 \u00b7 5 = 40,\n92\n\neach containing 23 \u00b7 5 \u00b7 7 = 280 high intensity bunches, as sketched in Fig. 2.11. There are no gaps\nbetween trains from the injectors in order to maximise the total number of injected bunches. There\nare h25ns/NT \u2212280 = 23 empty positions between trains corresponding to the minimum spacing of\n24 \u00b7 25 ns = 600 ns between trains required for kicker gaps.\nFig. 2.11: Filling pattern for Z-mode (top) and a zoom into the first few trains (bottom), for the e+ beam\nshown in blue and the e\u2212beam in orange.\nA scheme to fill the gaps between high-intensity physics bunches with low-intensity energy cali-\nbration bunches is sketched in Fig. 2.12 and refers to one of the four IPs. A maximum of five bunches\n(in the example for the e+ beam) and four bunches (in the example for the e\u2212beam) can be placed for\nthe two beams such that the requirements are fulfilled. In case all gaps can be filled with calibration\nbunches and exchanging positions of e+ and e\u2212bunches for half of the gaps, 180 calibration bunches\ncan be injected per beam. Note that strict gap-to-gap alternation of calibration bunch patterns leads to\nfillings avoiding collisions between calibration bunches in all four IPs. In case one gap has to be kept free\nof low-intensity calibration bunches for the rise and fall times of injection and beam dump kickers, 175\ncalibration bunches of one type and 174 of the other types can be injected. However, the additional beam\nloading transients may necessitate keeping additional gaps without beam (e.g. four equidistant gaps).\nFig. 2.12: Gap between high-intensity physics bunch trains filled with low-intensity energy calibration\nbunches for the Z-mode.\nFilling pattern for WW mode\nThe filling pattern described and sketched in Fig. 2.13 is one out of many possible ones. The number of\nbunch trains is a product of common prime factors of the NB and the number of bunch slots h25ns.\n93\n\nChoosing 8 trains with 232 high-intensity bunches each, with 16 empty positions between injector\nbatches with a tain, leaves 371 empty positions between trains as sketched in Fig. 2.13.\nFig. 2.13: Filling pattern for W-mode (top) and a zoom into the first few trains (bottom), for the e+ beam\nshown in blue and the e\u2212beam in orange.\nA scheme to fill the gaps containing 371 available positions between high intensity physics bunches\nwith low intensity energy calibration bunches is presented in Fig. 2.14, referring to one of the IPs. A\nmaximum of 92 bunches (in the example for the e+ beam) and 91 bunches (in the example for the e\u2212\nbeam) can be placed for the two counter-rotating beams. Filling two opposite gaps between trains allows\nplacing of 182 and 184 bunches for the two beams. If needed, additional gaps can be filled.\nFig. 2.14: Gap between intensity physics bunch trains filled with low intensity energy calibration bunches\nfor Z-mode.\nFilling pattern for ZH mode\nFor ZH mode, an additional requirement with respect to the lower energy modes to be taken into account\nis that the RF section is common to the two counter-rotating beams and that bunch crossings in this\nsection must be avoided. The number of bunches per beam in the collider NB = 300 = 22 \u00b7 3 \u00b7 52 is low\nand allows many different filling schemes. For the one proposed here, the number of bunches per injector\ncycle is reduced to two, and the injector repetition rate is reduced to 50 Hz. Filling the collider with two\nidentical bunch trains opposite to each other ensures that all bunches collide at all four IPs. If the gaps\nbetween trains are sufficiently long, no bunch crossings take place in the RF section. The number of\nbunches per train is 150 and corresponds to 75 bunch pairs from the injector complex. Along a bunch\n94\n\ntrain, injector bunch pairs are separated by 19 empty positions. This leaves long gaps with 3764 empty\npositions between trains and corresponding to a distance of 3765\u00b725 ns = 91.125 \u00b5s between trains. The\nresulting filling pattern is sketched in Fig. 2.15.\nFig. 2.15: Filling pattern for ZH mode (top) and a close-up view of the first train (bottom), with the e+\nbeam shown in blue and the e\u2212beam in orange.\nFilling pattern for t\u00aft mode\nSince the definition of the t\u00aft mode filling pattern described here, optimisations led to slight change of\nthe number of bunches from 64 to 60 given in Table 2. The filling pattern will be adjusted accordingly\nin a future iteration. Many possible filling pattern exist for the t\u00aft mode with a low number of bunches\nNB = 64 = 28. The pattern proposed and sketched in Fig. 2.16 requires bunch pairs from the injectors\nassumed to be accumulated in the Booster with a repetition rate of 50 Hz. Two identical trains, consisting\neach of 32 bunches or 16 injector bunch pairs are foreseen per beam to ensure that no bunch crossings\noccur in the common RF section. Assuming 151 empty positions between bunch pairs from the injector\nin the same train gives the pattern shown in Fig. 2.16. The gaps between the trains comprise 3763 empty\npositions and have a length of (3763 + 1) \u00b7 25 ns = 94.1 \u00b5s.\nFig. 2.16: Filling pattern for the t\u00aft mode.\n2.3.8\nBootstrapping injection scheme\nThis section describes the procedures to ramp up the intensity of colliding high intensity bunches from an\nempty machine to a steady state situation with periodic top-up injections in order to keep the intensities\n95\n\nstable. For the two lower energy modes Z and WW, it is assumed that the low intensity bunches are\nalready injected and have been circulated over a sufficiently long period to generate polarisation levels\nsuitable for energy calibration. The asymmetric wigglers used to speed up the polarisation build-up for\nlow intensity calibration bunches are switched off before starting the intensity build-up of bunches.\nConstraints to be fulfilled by the intensity ramp-up procedure are\n\u2013 The intensity of bunches from the counter-rotating beams interacting via beam-beam encounters\nhave to be ramped up together. Large intensity imbalances between bunches interacting via the\nbeam-beam effect result in the flip-flop phenomenon with imbalances of other parameters: small\nemittances and bunch length for the higher intensity bunches lead to large emittances and bunch\nlength of the lower intensity bunch. The resulting lower life-time of the lower intensity bunch\nfurther enhances the intensity imbalance.\n\u2013 Limitations of the intensity of injected bunches: to avoid excessive requirements to the injec-\ntor complex, the maximum intensity increase of bunches circulating in the collider is limited to\n\u2206ni,max = 2.14 \u00b7 1010 per injection per bunch, which is one tenth of the nominal bunch intensity\nin the collider ring for the Z mode (all other modes have lower bunch intensities). Maximum bunch\nintensities in the booster must be somewhat higher to accommodate for losses in the booster and\nat collider injection.\n\u2013 Limitation of the total beam intensity circulating in the booster and being transferred to the collider\nto mitigate machine protection issues and effects related to the total intensity in the booster.\n\u2013 For operation at the lower energy modes and, in particular, for the Z mode, electron cloud build-up\nhas to be limited. Electron cloud build-up is more severe at intermediate intensities than at low\nand close to nominal intensities. Thus, situations with many or even all bunches at intermediate\nintensity during the ramp-up procedure must be avoided. A few bunches, say 10% of the total for\nZ operation, with intermediate intensity and not concentrated at a particular position of the ring is\nexpected to mitigate electron cloud build-up.\nIntensity ramp up for the Z mode\nThe total number of colliding bunches is divided into a sufficient number of groups, say 10 for the\nproposal described below.\nThe intensity of the 10 groups is not ramped up simultaneously to avoid having multiple bunches\nwith intermediate intensities in the collider ring during the ramp-up process. The proposed procedure is\none of several possible schemes and is best illustrated using Fig. 2.17, which displays the bunch pattern\nfor two out of 40 identical trains, and Fig. 2.18, which depicts the evolution of beam intensities for each\nfamily along with the luminosity.\nThe topmost image in Fig. 2.17 shows the intensity of circulating bunches in the collider ring after\nthe first injection, corresponding to the filling pattern of the booster for all high-intensity physics bunches.\nThe evolution of bunch intensities is plotted in the upper image of Fig. 2.18. At the start of the process,\nthe intensity of bunch family 1 is ramped up for both beams. Once its intensity exceeds a predefined\nthreshold, the ramp-up for family 4 begins. Figure 2.17b illustrates the state after six injections for\nfamily 1 and three injections for family 4.\nEach time all circulating bunches surpass the threshold intensity, the ramp-up of an additional fam-\nily begins. The booster cycles are then distributed between injections for families with intensities above\nthe threshold and injections for the most recently added family with intensity still below the threshold.\nAs a result, the ramp-up duration is longer for families added later in the process. Once the transition to\nregular top-up injection occurs, the intensity of the injected bunches is reduced and adjusted such that\nthe collider target bunch intensity is met after beam transfer.\nA drawback of the described scheme is that, at the same time, low and high intensity bunches\n96\n\na)\nb)\nc)\nd)\ne)\nf)\nFig. 2.17: Bunch intensity patterns in one ring at various stages during the intensity ramp procedure for\nZ mode operation. Patterns for only two out 40 identical trains are shown.\ncirculate while undergoing beam-beam interactions. Due to the potential well distortion, the low (high)\nintensity bunches have a higher (lower) synchrotron tune. This makes the choice of a suitable work-\ning point (mainly horizontal tune) more difficult, with the phenomena described in Section 1.4.3 [62].\nStudies are ongoing to devise solutions; the first results using a small positive chromaticity are promising.\nIntensity ramp up for the W mode\nNo issues are expected related to electron cloud in the collider for WW operation due to the larger gaps\nwith the trains of the proposed filling pattern. In order to limit the maximum total intensity in the booster,\nseparation of the collider bunches into two families is proposed for both intensity ramp-up and top-up\ninjections. The principle is documented in Fig. 2.19 showing bunch patterns for one out of the eight\n(identical) trains in one of the collider rings and Fig. 2.20 showing the evolution of the beam intensities\nfor the two families and the luminosity. Figure 2.19a shows the bunch pattern in the collider after one\ntransfer and for one out of 8 identical trains. Every second injector batch of the complete filling pattern\nshown in Fig. 2.13 is filled. The next booster cycle injects into the positions belonging to the family\ntwo of the same ring leading to the pattern shown in Fig. 2.19b. The next two booster cycles inject into\n97\n\nFig. 2.18: Bunch intensity evolution for the various families (upper plot) and evolution of the luminosity\nfor Z mode operation. Bunch intensities are plotted using solid and dashed lines for the two counter-\nrotating beams.\nthe counter-rotating beam. The same sequence is repeated periodically for intensity ramp-up and top-up\ninjection.\nIntensity ramp up for the ZH and t\u00aft modes\nDue to the low number of bunches in the collider, no limitations related to electron cloud build-up or total\nintensity circulating in the booster exist for FCC-ee operation at the higher energies. Thus, the intensity\nof all collider bunches is ramped up simultaneously. The resulting filling procedure is obvious and leads\nto a booster filling pattern identical to that in the collider.\n2.3.9\nTop-up injection\nThe top-up injection scheme (described in Section 1.8.1) was simulated with a perfect lattice, without\nconsideration of collective effects or machine imperfections. In practice, however, lower-than-expected\ninjection efficiencies and significant penalties on injection performance at higher circulating currents\nhave been major challenges at other lepton colliders [232,233].\nWhile the baseline injection scheme has a unique setting for on-axis injection, it is possible to\nuse a hybrid injection scheme in the range of injected beam energy offset between 0.7 % and 0.95 %\n(Fig. 1.40). In later revisions of the collider lattice, different injected beam energy offsets may become\nfeasible with the on-axis injection scheme by modifying the optics. In contrast, due to the septum thick-\nness, the hybrid injection scheme must maintain a constant physical separation between the injected and\ncirculating beams at the injection point. Since the optics remains unchanged, this constraint results in a\ngeometric condition in the DA-MA plane, represented by red dots in Fig. 2.21b. Injection is physically\npossible but constrained by the dynamic aperture (DA) and momentum acceptance (MA) in the region\nabove and to the right of this line. Conversely, injection is geometrically impossible in the region below\nand to the left of this line.\nThe injection efficiency for different hybrid schemes, different betatron offsets, is simulated and\nthe most promising results, showing improved efficiency over the baseline (on-axis injection), are plot-\nted in Fig. 2.21a. In these simulations, the weak-strong model of the beam-beam interactions is used.\nFigure 2.21b shows that a range of injection settings are possible between the geometrical constraints\n98\n\na)\nb)\nc)\nd)\nFig. 2.19: Bunch intensity patterns in one ring at various stages during the intensity ramp procedure for\nWW mode operation. Patterns for only two out 8 identical trains are shown.\nrepresented as the red dots and the DA and MA limits of the lattice shown as the blue lines [234].\nAt SuperKEKB, the injection efficiency reaches approximately 80 % with the aid of bunch-by-\nbunch (BbB) feedback. Without BbB feedback, the efficiency drops to around 50 %. The primary causes\nof this degradation are the larger-than-design emittance of the injected beam and the use of off-axis\ninjection. In contrast, FCC-ee\u2019s baseline design features on-axis injection and large curvature radii in\nthe beam transport from the booster to the collider ring, making the degradation of injection efficiency\nobserved at SuperKEKB unlikely. SuperKEKB has also experienced beam chamber deformation due to\nheat, which may contribute to injection efficiency degradation. Therefore, effective temperature man-\nagement is crucial.\nThis validates the feasibility of the present injection concept, but in the absence of comprehensive\ntracking that includes both errors and collective effects, it is not possible to be sure at this stage that\nhigh injection efficiency can be reached and maintained up to nominal intensity. Therefore, the present\nfeasibility study establishes an injection efficiency goal of 80% based on the status of the concept and\nexperience from other facilities [232,233]. This injection efficiency target is used in the feasibility study\nfor the sizing of the injector chain (Table 7.1).\n2.3.10\nInjection requirements\nThe top-up injection scheme strongly relies on the injected beam being considerably smaller horizon-\ntally than the circulating one (Fig. 1.39). By contrast, in the vertical plane, the injected beam could be\nseveral times larger than the stored beam. The horizontal beam parameters provided by the booster (see\nTable 4.1) must be maintained up to the nominal intensity, but also along all the bunches of the injected\ntrains, and stably over time. The beam transfer systems for both the booster extraction and collider in-\njection have to ensure a high level of stability and reproducibility to prevent any beam jitter that would\nincrease emittances and reduce the injection efficiency.\n99\n\nFig. 2.20: Bunch intensity evolution for the various families (upper plot) and evolution of the luminosity.\nBunch intensities are plotted using solid and dashed lines for the two counter-rotating beams.\n(a) Evolution of the injected beam intensity for three dif-\nferent injection betatron offset with beam-beam.\n(b) Quarter quadrant representation of the DA/MA\nwithout beam-beam with crosses denoting the three\ninjection settings simulated with beam-beam.\nFig. 2.21: Collider injection efficiency at various betatron offsets and their corresponding location in the\nDA/MA for the Z mode.\n2.3.11\nRefilling and pre-polarising pilot bunches after a beam abort\nAt the ZH and t\u00aft energies, the FCc-ee can be filled with the booststrapping injection scheme detailed in\nsubsection 2.3.8. At the Z and WW energies, prior to this, first pre-polarised must be produced, which\nare required for precise energy calibration from the start of each fill.\nAt 45.6 GeV the natural polarisation time is 250 h. Thus, achieving a polarisation level in an\nerror-free machine of 5-10% requires 15 to 30 hours, which is an unacceptably long period without\ncalibration at the start of fill. Reducing the polarisation rise time to about 12 h is feasible using special\npolarisation wigglers [162], which also increase the energy spread to 64 MeV. In the currently planned\noperational scenario, low-intensity (\u22481010 particles) pilot bunches are injected at the start-of-fill and\npolarised using wigglers. When roughly 5-10% polarisation is achieved, after 45 to 90 minutes, these\nwigglers are switched off, and all the nominal-intensity colliding bunches are then injected, according to\n100\n\nthe bootstrapping scheme, and brought into collision. Around 250 pilot bunches per beam are required\nin total, a number that follows from the assumption that five energy calibration measurements with two\npilot bunches are performed every hour. By the time the last pilot bunch has been depolarised for the first\ntime, the pilot bunches that were depolarised first will have naturally reacquired sufficient polarisation to\nbe measured again.\nAt 80 GeV, the polarisation time is approximately 15 hours, and polarisation wigglers are not\nrequired [162]. In this case, the pilot bunches take about 1.5 hours to reach 5% polarisation. Significantly\nfewer pilot bunches - of the order of 25 - are needed compared to operation at the Z pole, as they re-\npolarise ten times faster.\n2.4\nAvailability\nAvailability is defined as the percentage of scheduled physics time during which the machine success-\nfully delivers beam, as opposed to being in downtime or undergoing repairs. The availability of FCC-ee is\nclosely tied to its operational efficiency (Section 2.1.2) and the achieved integrated luminosity. Addition-\nally, it is influenced by various performance factors, including operational costs, safety considerations,\nand system design constraints.\nAn enhanced Monte Carlo simulation framework is used to model availability by deconstructing\nthe accelerator\u2019s main constituent systems. The simulation model is detailed in Sections 2.3.1-2.4.2, with\nthe results presented in Section 2.4.3.\n2.4.1\nContributing systems\nIn collaboration with relevant system experts, each main constituent system in FCC-ee was approximated\nfor availability. If fault data from a comparable representative system could be found, this was scaled to\nan equivalent system in FCC-ee using a generalised framework. For some systems, no such fault data\ncould be identified and a placeholder was used. The methodology in each case is as follows.\nSystems with representative fault data\nA generalised framework was designed for consistent and comparable representation of systems in the\nFCC-ee. Specific details relating to relevant peculiarities were then applied.\nGeneralised framework for system availability estimation\n1. A similar or comparable state-of-the-art representative system is identified that exists currently in\na working accelerator.\n2. Where possible, representative system is deconstructed into subcomponents and fault mechanisms\nto achieve better granularity of reliability estimation.\n3. Fault mechanisms are categorised by:\n\u2013 Repair type:\n\u2013 Remote Repairs: can be completed from the control room, e.g., by re-setting or by-\npassing the failed component.\n\u2013 Human Repairs: require on-site intervention by personnel. In addition to the time it\ntakes to complete the repair, the approach time to get a person to the site of the fault\nmust be considered. This is taken as the time to get from PA to the relevant access point\nby car, summarised in Table 2.5.\n\u2013 Equipment location:\n\u2013 Surface: Equipment located on the surface can be accessed for repair immediately when\nthe technician arrives.\n101\n\n\u2013 Tunnel: Equipment located inside the accelerator tunnel cannot be accessed until a suit-\nable cool-down time has passed at the relevant access point, corresponding to the time\nrequired to fully ventilate the tunnel. This is summarised Table 2.5 (Section 9.4.2).\n4. Fault data is extracted from the representative system to gain Mean Time Between Failures (MTBF)\nand Mean Time to Repair (MTTR) information for the system and, where possible, subsystems for\nfiner granularity.\n5. MTBF and MTTR are scaled from the representative system to the study system in the FCC-ee:\n\u2013 MTBF scales inversely proportionate to the relative number of components. The more com-\nponents in the FCC-ee system relative to the representative system, the lower the MTBF. If\nthe number of components in FCC-ee is not yet precisely known, an approximation is made,\nassuming a design specification similar to that of the representative system.\n\u2013 MTTR for remote repair faults is left unchanged. An approach time and/or cool downtime is\nadded to human repair times corresponding to the equipment location, Table 2.5.\n6. If applicable, a formulation for redundancy in the FCC-ee is defined.\nSystem specifics for availability approximation\nSpecifics used to approximate availability for each constituent system are also considered, in addition\nto the above generalised framework. Only faults leading to down time in the representative system\nare included, thereby assuming a similar degree of redundancy for each basic component family as\ncurrently exists in the working accelerator. Details of subsystems, scaling numbers, and any additionally\nimplemented system-level redundancy are provided in Table 2.6. Fault data was taken from CERN\u2019s\nAccelerator Fault Tracking (AFT) database [235] and is specific to LHC physics operation 2015-2024,\nunless otherwise stated.\nIf no representative fault data could be found, but the system is still deemed a high risk for machine\navailability, it was given an availability placeholder pending a more rigorous reliability assessment. This\napplied to two systems, the beamstrahlung dump absorbers, and the polarimeter.\nThe remaining accelerator systems specific to the booster, injector complex and technical infras-\ntructure are covered in Sections 5.3, 7.9 and 8.10, respectively.\n2.4.2\nRepair schedule\nWhen redundant and non-redundant systems are combined, the schedule with which repairs are imple-\nmented has significant impact on availability. A schedule similar to the LHC was simulated: Following\na dump, operators attempt for one hour to restore operation remotely from the control room. If operation\ncannot be restored during this time, only then people are called to begin human repairs. Once humans\nare in the tunnel they will finish all repairs, including all redundant components.\nTable 2.5: Approach time (the drive time from PA) and cool down time (see Section 9.4.2) relevant to\nhuman repair faults at each access point.\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\narc\nApproach Time (h)\n0.00\n0.75\n0.55\n0.8\n0.63\n0.600\n0.416\n0.283\nCool Down Time (h)\n1.54\n1.70\n1.54\n24*\n1.54\n0.717\u2020\n1.540\n0.717\u2020\n1.7\n*Collimation straight section without bypass tunnel.\n\u2020Klystron gallery only. A longer cool down time is required to access the beam tunnel.\n102\n\nTable 2.6: Parameters used to simulate availability of systems and subsystems in the FCC-ee Collider.\nSystem\nSubsystem\nRepresentative\nFCCee\nRedundancy\u2217\nLocation\nUnit\nGroup\nSystem\nMTBF\nMTBF\nMachine\n#\n#\n# (%)\nAP\ndays\ndays\nAccelerator\nControls\nSoftware\nLHC\n1\n1\n0 (0)\nall\n7.1\nHardware\n607\n2400\n0 (0)\nall\n15 840\n6.6\nAccess System\nAccess Points\nLHC\n8\n8\n0 (0)\nall\n178\n22.4\nBeam\nInstrumentation\nBPM\nLHC\n1000\n5906\n0 (0)\nall\n20 671\n3.5\nBLM\n3600\n1205\n0 (0)\nall\n36 632\n30.4\nOther\n1\n1\n0 (0)\nall\n24.5\nBeam Losses\nUFOs\nLHC\n54\n182\n0 (0)\nall\n1.2\nBeam Instability\n1\n1\n0 (0)\nall\n2.1\nBeamstrahlung\nDump\nSPS\n1\n8\n0 (0)\nPA, PD,\nPG, PJ\n68\n8.5\nTIDVG\nCollimation\nMoveable Collimator\nLHC\n108\n32\n0 (0)\nPF\n1549\n48.4\nElevators &\nHandling Equip.\nElevator Shafts per AP\nLHC\n1\n2\n1 (50)\nall\n74\n332.8\nExperiments\nIPs\nLHC\n4\n4\n0 (0)\nPA, PD,\nPG, PJ\n17\n4.3\nExtraction &\nBeam Dump\nDump Block\nLHC\n2\n2\n0 (0)\nPB\n224\n112\nControls\n2\n2\n0 (0)\nPB\n36\n18.2\nHardware\n2\n2\n0 (0)\nPB\n65\n32.7\nOther\n2\n2\n0 (0)\nPB\n71\n35.6\nInjection Systems\nMKI\nLHC\n2\n2\n0 (0)\nPB\n20\n10.1\nTDI\n2\n2\n0 (0)\nPB\n71\n35.6\nMachine\nProtection\nFMCM\nLHC\n1\n10\n0 (0)\nall\n39.2\nBIS\n1\n2\n0 (0)\nall\n32.7\nSMP\n1\n1\n0 (0)\nall\n87.1\nPIC\n1\n0.2\n0 (0)\nall\n261.4\nWIC\n1\n6\n0 (0)\nall\n21.8\nMagnets\nNormal-conducting\nCERN\n3532\n12 500\n0 (0)\nall\n71\u00d7106\n5681\nOperation\nLHC\n1\n1\n0 (0)\nall\n5.8\nPolarimeter\nN/A\n-\n1\n0 (0)\nPA, PG\n3.2\nPower\nConverters\nDipole\nLHC\n194\n16\nLHC\nall\n3672\n229.5\nQuadrupole\n194\n32\nLHC\nall\n3672\n114.8\nSextupole\n194\n1152\nLHC\nall\n3672\n3.2\nDipole Tapering\n1032\n710\nLHC\nall\n15 485\n21.8\nQuadrupole Tapering\n1032\n709\nLHC\nall\n15 485\n21.8\nHorizontal Corrector\n1032\n2824\nLHC\nall\n15 485\n5.5\nVertical Corrector\n1032\n2824\nLHC\nall\n15 485\n5.5\nSkew Quadrupole\n1032\n2824\nLHC\nall\n15 485\n5.5\nRadio\nFrequency\nCavity Circuit Z\nLHC\n16\n1322\n1 (0.75)\nPH\n61\n0.9\nCavity Circuit W\n16\n1322\n6 (4.5)\nPH\n61\n169.1\nCavity Circuit ZH\n16\n2643\n26 (10)\nPH\n61\n314.6\nCavity Circuit t\u00aft\n16\n7523\n75 (10)\nPH\n61\n465.2\nSmoke Detection\nSmoke Alarms\nSPS\n7\n91\n0 (0)\nall\n4.3\nTransverse\nDamper\nLHC\n2\n2\n0 (0)\nPH\n65.4\n32.7\nVacuum\nPumps\nLHC\n891\n3344\n0 (0)\nall\n349 448\n104.5\nGauges\n1052\n1808\n0 (0)\nall\n274 997\n152.1\nValves\n323\n452\n0 (0)\nall\n84 434\n186.8\nControllers\n789\n1584\n0 (0)\nall\n55 915\n35.3\n\u2217System-level redundancy in addition to that already implemented in the component family of the representative system.\n\u2020 Per beam.\n\u2021 Shared by both beams.\n103\n\nFig. 2.22: Unavailability and lost luminosity contribution from each main constituent system in the FCC-\nee. Systems are ordered according to Z mode lost luminosity contribution. contribution.\n2.4.3\nAvailability simulations\nFCC-ee availability is simulated using AVAILSIM4 [236], a discrete-event Monte Carlo tool developed\nin-house at CERN for analysing availability and reliability in complex systems. Each energy mode was\nsimulated for its full operation term (four years in Z, two years in WW, etc.), with performance averaged\nover 100 iterations.\nThe breakdown for unavailability and lost luminosity in each system under certain assumptions\nand based on data from LHC sytems is shown in Fig. 2.22. The booster, injector complex and technical\ninfrastructure are included for illustration; but treated in detail in Sections 5.3, 7.9 and 8.10, respectively.\nFor the collider, the main contributors to lost luminosity are the RF, power converters, beam losses and\nthe alarm system.\nThe RF system experiences the highest unavailability in Z mode due to the strict limit of single-\ncavity redundancy assumed. In WW mode, the ability to sustain beam operation despite the loss of\nup to six cavities eliminates the collider\u2019s unavailability contribution from the RF system. The booster\nsignificantly contributes to unavailability in both energy modes, as it lacks any redundancy. In ZH and\nt\u00aft modes, a 10% redundancy ensures zero downtime from the RF system, providing sufficient reserve to\naccommodate failed cavities until they can be repaired in the shadow of downtime scheduled for other\nsystems.\nPower converters show high contributions in all energy modes. This is predominantly due to the\nlow MTBF seen from sextupole and corrector converters and the high number of different magnet circuits\nused in the assumed optics configuration.\nBeam losses have lower contribution to unavailability as the recovery time to restore operation\nis short. But their contribution to lost luminosity is high as they cause frequent dumps, each of which\nincurs a turnaround penalty related to the time required to restore stable beams. Turnaround penalty is\ntwo hours in Z, W modes, and 30 minutes in ZH, t\u00aft.\nThe alarm system features relatively high due to the scaling factor from SPS (7 km) to the FCC-ee\ntunnel (91 km). The number of alarms combined with mandatory on-site safety evaluation in the event\nof fire detection leads to large amounts of down time.\n104\n\n2.4.4\nR&D opportunities\nSignificant improvement in reliability is required in order to meet luminosity targets, especially in the\nlower energy modes. Several R&D opportunities have been identified:\nRadiofrequency\nIncreasing redundancy in the RF system for the Z, W modes presents challenges due to high beam\nloading effects but should be further investigated given the potential performance gains. Additionally,\nRF redundancy in the booster system should be explored further, as it remains a significant contributor\nto unavailability in both energy modes.\nIt is important to note that zero RF downtime is currently assumed in the simulation due to the\nidealised assumption of perfect redundancy between cavity circuits. In reality, common-mode failures\nwould still occur, requiring reconditioning or replacement, which cannot always be immediately com-\npensated by a redundant cavity. Further modelling is necessary to better understand these fault types. In\nthe coming years, close collaboration with the RF design team will be essential to deconstruct the RF\ncircuit into subsystems, identify problematic fault types, and analyse high-failure component families.\nAnalysis of the auxiliary systems around the superconducting cavities would unearth further relia-\nbility opportunities. For example, the klystron gallery is accessible to personnel while the main colliding\nrings are in operation. If more high-failing auxiliary systems can be located there and designed to be\nredundant, modular and hot-swappable, significant gains could be achieved.\nPower converters\nThe current optics configuration powers sextupoles in groups of four. One failed converter would there-\nfore lead to four magnets failing simultaneously. Collaboration with the optics working group is required\nto consider how to preserve the beam if combinations of converters and magnets fail. A system-level re-\ndundancy approach could significantly improve reliability in this case.\nIt is important to note that the current simulation assumes the same level of redundancy in power\nconverters as is presently implemented in the LHC. Therefore, for an effective solution, the FCC-ee\nsextupole and corrector converters must be designed to be more robust than those used in the LHC. A\ndetailed study on power converter reliability will be essential in the coming years.\nReducing the number of corrector families, especially for the sextupole magnets, can drastically\nreduce the number of power converters required and in turn reduce their overall fault rate.\nOperation cycle\nOpportunities also exist within the operation cycle:\n1. Indefinite physics: If the lifetime of pilot bunches in the main ring can be made longer than\nthe natural polarisation time, pilot bunches could be topped up immediately after being used for\nmeasurement and allowed to naturally re-polarise. This avoids the need to dump after 20 h in order\nto re-fill with polarised pilot bunches. Physics can then continue uninterrupted in Z, W modes,\nuntil equipment failure dumps the beam.\nThe utility of this proposal is best illustrated by the distribution of stable beams durations at each\nenergy mode, shown in Fig. 2.23. This shows that, under the assumptions made here, stable beams\ncan rarely be sustained longer than 20 h without beam abort due to system failure.\n2. Polarised bunch injection: If pilot bunches can be polarised prior to injection, and their polari-\nsation preserved through the injector complex and booster, the 90-minute polarisation phase could\nbe eliminated from the Z, W operation cycle entirely. This would effectively result in the same\noperation cycle as the higher energy modes ZH, t\u00aft while maintaining the capability for precise\nenergy calibration.\n105\n\nFig. 2.23: Distributions for duration of stable beams in each energy mode.\nFig. 2.24: Effect of polarised injections on achieved integrated luminosity and fault rate, under certain\nassumptions.\nThe potential of this scheme is illustrated in Fig. 2.24. In both Z, WW modes, this approach\nmore than doubles the achieved integrated luminosity. This is because, by removing the 90-minute\npolarisation phase at the start of each fill, an equivalent duration of stable beams is effectively\ngained. This presents a potentially game-changing R&D opportunity to support physics objectives\nin this challenging reliability environment.\n2.5\nOperational model\nCERN has a long-standing tradition of designing, building, and operating accelerators, with well-defined\ngroups structured according to a clear division of responsibilities and tasks. The expectations regarding\ninterfaces between equipment, controls, and human operators - whether in control rooms or via remote\naccess - have been long established and are now considered immutable, ensuring maximum efficiency\nwithin the current CERN accelerator complex, which relies on a high degree of specialisation across\nvarious groups.\nHowever, with the unprecedented scale of the FCC accelerator, new constraints such as energy\nprovision from intermittent sources, and the assumption that CERN\u2019s human resources during the FCC\n106\n\nera will remain at levels similar to today, necessitate a new approach to designing, building, and operating\nparticle accelerators at CERN.\nThe necessary equipment paradigm can be summarised as:\n\u2013 Full digitalisation: Equipment needs to be fully digital and remotely controllable as well as analysable\nwith common interfaces and protocols.\n\u2013 Automation towards fully autonomous systems: All equipment needs to be designed with au-\ntomation in mind (across systems and within systems) to e.g., auto-configure, auto-stabilise, auto-\nanalyse, auto-recover etc. An example would be designing cars without steering wheels and asking\nwhich control algorithms, additional instrumentation and software layers would have to be in place\nto safely and efficiently drive and maintain the car while maximising the mobility of the car user.\nThe next design iteration will then address the new possibilities with the re-imagined system (with\nthe car analogy this could be things like \u201cAre close-by car parks still a necessity?\u201d, \u201cAre personal\ncars still required or can they all be shared?\u201d). A key additional aspect in this discussion are digital\ntwins for training and constraining control algorithms and differentiable simulations.\n\u2013 Full virtualisation: Space telescopes have the additional constraint that one cannot simply go there\nto fix them if things break. With the size of the FCC and the number of components, maintainabil-\nity is similarly constrained as for space telescopes. Humans should not be considered for on-site\nrepair at all or at least not during the run. This can be addressed with built-in margin, low failure\nrate, modularity, redundancy (possibility of degraded mode or auto-reconfiguration), robotics and\nother new technologies.\nThe next generation accelerator control system will have to foresee easy plug&play solutions and frame-\nworks to implement the above and provide integration of artificial intelligence (AI). This concept is\noften referred to as AI-ready accelerators or control systems. Examples of the required capabilities in-\nclude frameworks for sharing and storing ML/AI models (including continual learning functionalities),\nintegrated digital twins, platforms for IoT, optimisation frameworks, time-aligned data across the accel-\nerator, PYTHON (or equivalent) code infrastructure, and easily configurable virtual device services for\ncontinuous analysis and anomaly detection.\nClearly, the three elements of the proposed equipment paradigm outlined above are interlinked\nand mutually dependent. Many of today\u2019s systems in the LHC and other CERN accelerators already\nimplement item 1 and, in some cases, partial implementations of items 2 and 3. For the FCC, however,\nthe complete paradigm must become the standard for equipment integration, meaning it must be imposed\nat the design stage. This approach will significantly reduce the resources required for commissioning,\noperation, and maintenance, though it may increase construction costs due to factors such as redundancy,\nadditional connectivity, and additional sensors.\nWhile space telescopes have no choice but to adhere to such stringent design principles, for the\nearth-based FCC, trade-offs may be considered. These will depend on whether the increased construction\ncosts are deemed unacceptable and/or whether the potential increase in operations and maintenance costs,\nalong with documentation, training, long-term sustainability, and impact on availability, remains within\nacceptable limits. Forecast availability of the main constituent systems in the baseline FCC-ee design is\nprovided in Section 2.4, based on similar equipment operating today.\nThe new equipment paradigm should allow:\n\u2013 Preparing the FCC-ee injector complex and collider with a single person on shift; and\n\u2013 keeping the global maintenance and exploitation effort level (in total FTE) for equipment teams\nfor FCC-ee and injector complex at or below today\u2019s level (for LHC and the existing injector\ncomplex).\nEven today, the most sophisticated and relatively recent particle accelerator at CERN, the LHC, is\noperated with a single person on shift. This supports the vision of automating the FCC to such an extent\n107\n\nthat the entire electron complex could be run single-handedly. In the current setup, this would correspond\nto 7\u20139 full-time shift personnel. However, further automation and the integration of AI assistants in the\ncontrol room should enable an even more advanced approach, raising the question of whether full-time\nshift personnel will still be necessary in the 2040s.\nAlready today, LHC experiments operate with part-time, non-expert shifters drawn from a large\npool of short-term shift workers. A similar approach could be explored for the FCC. Nevertheless,\napproximately five daytime experts dedicated to particle accelerator operation will still be required, en-\nsuring sufficient expertise to support the rest of the accelerator complex as well.\n2.5.1\nReducing the operation effort for equipment teams\nOperating the FCC electron complex will require relatively few resources. The baseline availability\nmodel for FCC-ee, discussed in Section 2.4, provides an estimate of the number of on-site repairs needed\nper week, assuming the FCC-ee is built and operated following the same paradigm as the LHC today.\nTable 2.7 indicates that this number ranges between 12 and 20 interventions per week.\nTable 2.7: Estimated number of on-site interventions for the FCC-ee complex, if it were built and oper-\nated as a large-scale LHC [237].\nMode\nNumber of weekly\non-site interventions\nZ\n14.8\nWW\n15.0\nZH\n15.5\nt\u00aft\n20.3\nEquipment groups will greatly benefit from automating fault detection, analysis, repair and re-\ncovery. The goal should be to automate equipment to the extent that all \u2018typical\u2019 faults for equipment\ngroups during the run do not require human intervention and hence will not require standby services.\nOnly equipment which is designed, built and tested to this extent can be be considered suitable for op-\neration. This requires acceptance testing in realistic mock-ups, well-planned and sufficiently long first\ncommissioning phases and the requirement to be fully automated from the start of physics production. A\ncomprehensive analysis on what availability is needed per system to reach the physics goals and how this\ncan be reached in a robust and affordable manner is a key pre-requisite for equipment design. The right\ncompromise between adequate operational margins through machine parameter choice and passive mit-\nigation of e.g., radiation, automating fault detection and repair, and reliable design through redundancy,\ncomponent margins, etc. has to be established on a system by system basis.\nThe target of a constant workforce will require a significant reduction in the maintenance effort per\nequipment compared with today. The suggested target number of at least a 50% reduction in maintenance\neffort comes from the analysis of the evolution of fault numbers for some key accelerator systems and\nfrom the assumption that remote interventions could be fully automated already today, given recent\nadvances in technology. For example for the SY-ABT kicker systems, currently more than 50% of their\ninterventions can be done remotely. Similarly, for the LHC QPS system the ratio of remote interventions\nremained roughly 50% in recent years, Fig. 2.25.\nSetting-up/commissioning procedures (accTesting [238], re-conditioning procedures etc.) that\nneed to be done regularly (even if only annually) should also all be automated. This has the addi-\ntional benefit of increasing the flexibility for planning (as it allows for parallelisation without concern for\nsharing experts) and operational schedules.\nThe operation costs of the FCC-ee were assessed to amount to about 600 MCHF per annum. The\n108\n\nFig. 2.25: Graph showing the number of remote and total standby interventions on the LHC QPS systems.\nData extracted from the QPS standby logbook.\napproach consisted in assigning the nature of equipment with back-tested operation and maintenance\npercentages and related costs resulting in a bulk number of 200 MCHF, including a typical spending\nratio of staff per materials budget giving about 300 MCHF. As a result the operation cost estimate for the\nFCC-ee consists of about 200 MCHF materials, 300 MCHF personnel and 100 MCHF on average for the\nelectricity costs, an average total of 600 MCHF per annum.\n2.6\nMachine Protection\n2.6.1\nMachine protection requirements\nThe machine protection aspects of FCC-ee are challenging in several ways.\nThe transverse beam sizes are small because of the small equilibrium emittance in a ring that is so\nlarge. The typical vertical beam size can be smaller than 10 \u00b5m. The horizontal beam size varies between\n260 \u00b5m and 400 \u00b5m (assuming \u03b2x,y = 100 m). Because of the small emittances, the energy density of\nFCC-ee beams at the Z mode reaches up to 17 % of the value for the HL-LHC beams (7 TeV), although\nthe stored energy of the FCC-ee beams at Z is only 2.5 % of the HL-LHC\u2019s.\nThe risk of damage strongly depends on the actual loss scenario, where the shower development\nfor a beam hitting any material needs to be taken into account. Compared to the HL-LHC proton beams,\nthe energy is deposited over a much shorter distance, as illustrated in Fig. 2.26. The maximum energy\ndeposition density induced by a single FCC-ee bunch in copper is about 4 to 10 times lower than for a HL-\nLHC bunch, but it is still sufficient to reach the melting point. This highlights the need for a sophisticated\nmachine protection architecture that relies on a combination of active and passive protection systems.\nMachine protection aspects also have to be considered when designing accelerator hardware, in order to\nreduce the likelihood of beam losses and to mitigate the severity of any beam loss events.\nThe beams are stabilised by various means. Among them, the transverse feedback is particularly\ncritical as in case of its failure, multi-bunch instabilities leading to significant beam losses can develop\nwithin a few turns only. The bunch lengthening generated by beamstrahlung is also key for maintaining\nbeam stability and could be lost if the beams are not kept in collision. Due to the large circumference,\nwith a single beam dump system, the signal transmission time of the beam abort request is significant.\nThe synchrotron radiation itself will be challenging as 100 MW of synchrotron radiation power\nwill need to be absorbed and efficiently dissipated. At the higher beam energy modes, the effect of\nradiation on electronics will need to be taken into account in the design of the many electronic systems\nor of appropriate shielding.\n109\n\nMachine protection system inputs\nThe machine protection system interfaces with many hardware systems. Failure of these systems risks\naffecting the beams in such a way that damage can occur. There are also processes which can lead to\ndamage of the machine without being related to a specific hardware item. Such processes are also listed\nbelow. The machine can generally be protected against these events by surveying the beam properties\nvia beam diagnostics. Therefore, the beam diagnostics is part of the machine protection system and is\nlisted in the next section.\n\u2013 Beam instabilities are induced by the impedance seen by the beam. Both the transverse coupled\nbunch instability (TCBI) and collective effects in the transverse plane (TMCI) have been assessed.\nThe most dangerous mode has a rise time of about 1.3 ms and a bunch-by-bunch feedback system\nis used to suppress the TCBI. The estimated required damping time of 1 ms corresponds to about\nthree turns, which will be a challenge for the feedback system. The rise times for the TMCI are\nabout 8 ms (i.e. without beamstrahlung). At the Z pole, such short bunch length could be reached\nwithin about ten thousand turns if the collisions between the beams is lost. This needs to be taken\ninto account for example when dumping the two high intensity beams.\nMore detailed simulations of the instabilities and the interplay with the feedback systems are out-\nstanding. The values quoted here correspond to the Z-mode which is most critical since the beam\ncurrents here are the highest\n\u2013 The Transverse feedback system is vital for stabilising the high intensity beams. In case of\nfailure of the transverse feedback system the beam will need to be aborted within about 3 turns,\nwhich is challenging. Considering the criticality of the system, a redundant and distributed system\n100\n101\n102\n103\n104\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nPeak energy density (J/g)\nz (cm)\nHL\u2212LHC (7 TeV, 2.2x1011 p)\nFCC\u2212ee Z (45.6 GeV, 2.18x1011 e\u2212)\nFCC\u2212ee W+/\u2212 (80 GeV, 1.38x1011 e\u2212)\nFCC\u2212ee ZH (120 GeV, 1.69x1011 e\u2212)\nFCC\u2212ee tt\u2212 (182.5 GeV, 1.50x1011 e\u2212)\nPeak energy density in copper (one bunch) \u2212 HL\u2212LHC vs FCC\u2212ee\nFig. 2.26: Energy deposited in copper by a single FCC-ee (Z) electron bunch (top left) and HL-LHC\nproton bunch (top right). The maps show the energy density in the horizontal plane. The bottom figure\ncompares the corresponding peak energy density profiles, for all FCC-ee beam modes, assuming a \u03b2-\nfunction of 100 m in both planes. The melting point of copper is reached if the energy density exceeds\nabout 0.45 kJ/g.\n110\n\nwould be preferred. However, multiple feedback systems risk to counteract each other, leading to\nan unstable situation.\nThe same transverse feedback system is also foreseen to be used for depolarisation of the beam.\nThe cohabitation of systems for excitation and feedback needs further study. Strong transverse\nmomentum kicks of 10 \u00b5rad at 45 GeV are required for depolarisation and for this reason are\ncritical for safe operation of the machine, especially in case of failures like non-synchronised\nexcitations.\nProtection against damper failures will require monitoring both the damper hardware and the beam\nitself. This will be achieved using beam loss monitors and beam position monitors, strategically\nplaced at the appropriate phase advance relative to the kicker elements.\n\u2013 The RF system\nThe collider hardware is dominated by the RF system. To avoid hardware modification between\nthe Z, WW and ZH modes, it is foreseen to run in Reverse Phase Operation. First simulation results\nshow no risk of too high induced voltages in case of a cavity trip, which means that operation can\ncontinue with a small number of cavities that have tripped.\nIf a cavity voltage or power is missing, the beam will need to be dumped. The time constant to\nbe taken into account here is about 1/4 of a synchrotron motion, which is about 10 turns. The RF\ninterlock \u2014 most likely based on phase detection \u2014 is backed up by the Beam Loss Monitors.\nThe RF system must be able to control the RF parameters during the duration of the abort gap.\nPreliminary studies indicate that a 600 ns abort gap duration is feasible.\n\u2013 The injection and extraction systems\nInjection and extraction of high intensity beams are machine-protection critical as the failures\nof the hardware involved is by definition extremely fast, and there is no time for the machine\nprotection system to react to these failures. The injection and extraction systems are described in\ndetail in Section 1.8.\nFor injection in the collider, two kicker magnets create a closed bump to bring the stored beam\ntrajectory close to the injection septum. The bump is created by two kicker magnets, 180\u25e6phase\nadvance apart and originally planned to be constant over a single turn and having a rise and fall\ntime of 1100 ns. In case of a kicker failure, all circulating bunches can be affected, leading\nto unacceptable losses. From a machine protection point of view, a system with rise and fall\ntimes over several turns is preferred, as it will allow the machine protection system to react in\ncase of failures. The option that the injection bump is present over many turns will need to be\ncounterbalanced against arguments related to machine and dynamic aperture and also the beam\nimpedance.\nThe extraction to the dump must be highly reliable, as it must function without failure in the event\nof any issue arising in the machine. Fast extraction kickers are planned, with a rise time of 0.6 \u00b5s.\nThe rise time of the kicker magnets must be precisely synchronised with the passage of the particle-\nfree beam abort gap. The reaction time between a beam abort request and the full extraction of the\nbeam is critical due to the rapid nature of potential failure scenarios. Therefore, it is anticipated\nthat multiple beam abort gaps will be necessary.\nThe impact of failures in many injection and extraction related systems can be mitigated by seg-\nmenting them, for example, by dividing the injection kicker systems into multiple smaller, inde-\npendent units. Additionally, the likelihood of failure can be minimised through redundancy and\nhighly reliable designs.\nTo provide an additional layer of protection, multiple absorbers or passive diluters will be required\nas a final safety measure to shield septa and other machine components from fast failures of the\ninjection and extraction pulsed magnets. These elements will need to be studied in further detail.\nA preliminary list of typical fast system failures has been compiled, along with possible protection\nmeasures. However, a more comprehensive study is still required, incorporating the detailed design\nof the hardware systems involved.\n111\n\n\u2013 Collider electromagnetic separators\nElectromagnetic separators are required upstream and downstream of the RF section to separate\nthe beam in t\u00aft mode, as both beams will pass through the centre of the same cavities. Possible\nfailures include spontaneous discharges of the electrodes, a mismatch between the magnetic and\nelectric field in the longitudinal plane and synchrotron light shining on the HV electrodes, inducing\ndischarges and resulting in very fast and large kicks to the beams. These failures can possibly\nbe detected by using very fast interlocked beam position monitors and dedicated masks for the\nsynchrotron light.\n\u2013 Powering failures\nFirst analysis of a powering failure of one of the main dipole chains, shows that the beam can reach\nthe horizontal limiting aperture in only a few turns. This will be very challenging for the machine\nprotection system, even if the failure can be rapidly detected by the use of a fast magnet current\nchange monitor (FMCM), described below.\n\u2013 Beam-dust interaction\nBeam loss events due to the interaction of dust grains with high-energy particle beams have been\nobserved in hadron and lepton accelerators over many decades. In the LHC, beam-dust interac-\ntions have an important detrimental impact on machine availability. They caused more than 70\npremature beam dumps and more than ten quenches of superconducting magnets during Run 2\nand 3. At the electron-positron collider SuperKEKB, a significant amount of beam aborts related\nto beam-dust interactions were observed and reproduced using a mechanical knocker. In recent\nyears, very fast beam losses occurred at SuperKEKB, causing damage to machine components.\nPresently, the root cause of this phenomenon remains unknown. However, beam-dust interactions\nhave been hypothesised as a possible explanation. While the dynamics of the dust movement has\nbeen studied in detail for the LHC, these models have to be extended to lepton colliders to eval-\nuate the effect of beam-dust interactions on the protection, availability, and performance reach of\nFCC-ee.\n\u2013 Superconducting magnets\nA quench protection system will be required for the superconducting final focus magnets. A\ndetailed description of this system is provided in Section 3.11.\nThe impact of beam-related failures on the superconducting magnet structures has not yet been\nstudied. However, such failures are not expected to be critical due to the relatively long time\nconstants of superconducting circuits and the limited number of superconducting magnets.\nThe effects of the quench protection system on the beam, including potential erratic firing of\nquench heaters or CLIQ systems, must be modelled in detail.\nMachine protection system elements\nThe machine elements listed below are part of the machine protection system and prevent the machine\nto be damaged by the beams.\n\u2013 Machine interlock systems The dedicated hardware related to machine protection is described\nin Section 8.2. As in the current large CERN accelerators, the core of the machine protection\nsystem relies on the Beam Interlock System (BIS). This system connects user inputs that detect\nfailures or beam losses in the machine to the beam extraction systems. The Beam Interlock System\n(BIS) must be highly reliable and, for that reason, is fully redundant. Due to the large machine\ncircumference, a significant delay occurs between detecting a beam abort request and triggering\nthe beam extraction.\nThe cooling of the synchrotron radiation absorbers will need to be interlocked. This interlocking\ncan be based on thermal switching and cooling water flow measurements. Given the high segmen-\ntation of the synchrotron radiation absorbers, a cost-effective method for identifying locations with\n112\n\nexcessive temperature or reduced cooling flow must be developed, as running individual cables to\nnumerous controllers would be too expensive.\nThe main dipole circuits, along with other primary magnet circuits, will be water-cooled. While\nthe impact of a loss of water cooling requires further analysis, initial assessments suggest that\nit is not highly critical. Water cooling is primarily chosen due to its significantly higher energy\nefficiency compared to air cooling. If the thermal time constants in the absence of cooling are of\nthe order of days, it may be possible to operate without an interlock on magnet cooling, instead\nrelying solely on tunnel temperature monitoring. In such a scenario, temperature measurements\nwould need to be highly granular to accurately locate potential cooling issues.\nThe need of a fast magnet current change monitor (FMCM) can be determined through an analysis\nof powering failures across different systems. Strong, individual magnets with short time constants\nmay require FMCM protection. Preliminary analyses indicate that failures in the main magnet\ncircuits pose significant challenges, even when rapidly detected by an FMCM.\n\u2013 The beam extraction system must operate with extreme reliability to ensure the beam can be\naborted whenever required by the machine interlock system. Any degradation in the beam-dumping\nsystem, such as a reduction in redundancy or safety margins, must be detected early enough to al-\nlow safe beam disposal without losses. For this reason, the beam extraction system also functions\nas a machine protection system user.\nThe number and length of abort gaps are critical system parameters that influence the RF system\nand the reaction time to a beam dump request. Since beam stability is maintained through col-\nlisions, the dumping of both beams must be synchronised. The specifics of this synchronisation\nrequire further study.\n\u2013 The collimation system is described in detail in Section 1.5. In addition to cleaning the beam,\nit plays a crucial role in the machine protection system by safeguarding the machine aperture\nagainst irregular and accidental beam losses. The collimators must act as the aperture bottleneck,\nintercepting all primary losses. Depending on the analysis of failure scenarios, a distributed colli-\nmation system may need to be considered. This approach would represent a new regime compared\nto previous lepton colliders.\nParticular attention is required to prevent beam-induced damage to the collimators. Fast fail-\nures have been observed at SuperKEKB, where a beam with 100 times less stored energy caused\ndamage to the collimators within just 2 to 3 turns. For this reason, fast and sensitive beam loss\nmeasurements, integrated with the beam interlock system, are essential at the collimator locations.\n\u2013 Beam Instrumentation\nIdeally, any machine failure should be detected at the source, such as a power converter failure\nor an incorrect collimator position. A global safety net based on beam measurements is highly\nrecommended to enhance reliability and, in the case of beam instabilities, may serve as the only\nprotection. For this reason, highly reliable beam instrumentation systems, integrated with the beam\ninterlock system, are essential for the safe operation of the accelerator.\nHistorically this protection is based on a distributed system of fast beam loss monitors (BLMs),\nlike in the LHC. A scaling of the number of BLMs as presently installed in the LHC with the\nFCC-ee circumference would lead to a total of 12\u2019000 BLMs. Even larger numbers of BLMs have\nbeen proposed in initial studies. The BLM electronic systems will need to be extremely reliable to\nlimit the number of false dumps initiated by the BLM system.\nDue to the extremely small vertical beam size, detecting the onset of instabilities in the vertical\nplane is unlikely to be feasible using beam loss monitors. Instead, the use of fast, interlocked beam\nposition monitors must be studied in detail.\nA third layer of protection is the beam current change monitor, which aborts the beams upon\ndetecting a reduction in measured beam current. Further investigation is required to determine\nwhether this system is adequate for protecting against certain fast failure modes.\n113\n\nMachine protection system strategy\nSeveral FCC-ee failure modes with time scales of only a few turns have been identified. The reaction\ntime of the machine protection system can be slightly shortened by filling patterns with multiple abort\ngaps. The detection of the onset of failure modes will have to be optimised to detect any malfunctioning\nof equipment or the onset of instability as early as possible. As the vertical beam size is small, one can\nmost likely not rely on interlocking on beam losses in the vertical plane, since the limiting apertures will\nbe far away from the beam expressed in numbers of sigma. Fast interlocked beam position monitors will\nmost likely need to be distributed along the accelerator.\nProtection against fast failures is achieved through redundancy, segmentation and highly reliable\ndesigns. Also fixed absorbers are part of the protection against fast failure modes. These absorbers are\nchallenging due to the high beam brightness and shower development. Where no suitable materials can\nbe found, a possible remedy would be the use of disposable absorbers for rare failure cases.\nA full and complete analysis of failure modes of all FCC-ee components requires a more advanced\nhardware design. This will allow a detailed definition of mitigation steps, including the detection systems\nfor the various failures. At this stage in the machine protection study, not a single showstopper has been\nidentified.\n114\n\nChapter 3\nFCC-ee collider technical systems\n3.1\nMain magnets\n3.1.1\nIntroduction\nThe proposed collider magnet system meets the requirements of the FCC-ee V24.3 GHC optics. The\nmagnets have been designed to operate below iron saturation at t\u00aft, so that they behave linearly at all\nintermediate energy levels, Z, WW and ZH.\nThe regular FODO lattice of the collider ring features 2840 arc half-cells composed of a short\nstraight section (SSS) followed by a series of dipole magnets. Depending on the position along the\nlattice, the SSS hosts none, one or two sextupole magnets. Where there is either no sextupole or only\none sextupole, the total dipole length is adapted to occupy the space, maximising the dipole filling factor\nin the machine.\nThe dipole and quadrupole magnets are designed as twin aperture units, as was already proposed\nin the CDR [13].\nCompared to using separate magnetic elements, the twin-aperture solution significantly reduces\npower requirements by half, as the return ampere-turns in the coils supply the second aperture. Since\nthe dipoles and quadrupoles are powered in long series, they include locally powered trim windings\nthat enable independent adjustments of the magnetic field in each aperture. This allows fine-tuning,\ncorrections, and compensation for local beam energy losses caused by synchrotron radiation (SR).\nThe requirements for the arc magnets are based on the FODO lattice described in Section 1.2 and\nsummarised in Table 3.1. The total number of magnets in the lattice accounts for the arcs and long strait\nsections (LSS).\nTable 3.1: Magnet requirements for the FODO lattice V24.3 GHC.\nDipole\nQuadrupole\nSextupole\nTotal number in lattice. . .\n6128\n3324\n4672\n. . . of which in the arcs\n5680\n2836\n4672\nBore aperture\n74 mm\n74 mm\n66 mm\nMagnetic length\n9.7 - 11.2 m\n2.9 m\n1.3 m\nMax strength\u2020, arc (t\u00aft, 182.5 GeV)\n61.0 mT\n11.9 T m\u22121\n880 T m\u22122\n\u2020 Sextupole strength given as B\u2032\u2032(B\u2032\u2032 = 2S)\n3.1.2\nDipoles\nThe dipole yoke features an I-shape geometry corresponding to two back-to-back C-shape dipoles, with\na common powering circuit around the central part. It allows a compact design which can be built in a\ncost-efficient way. The assembly is composed of three parts that can be machined out of solid iron (low-\ncarbon steel) plates. As all three parts have a simple rectangular cross-section, the amount of machining\ncan be minimised by selecting raw material plates in a thickness close to the final dimensions.\nCurrently, it is planned to split the dipole section of each arc half-cell into two dipole units to\nminimise the number of interconnections while keeping a feasible and practical unit length for the man-\nufacture and transport of the magnet components and vacuum chambers.\n115\n\nThe use of solid iron material is possible since the magnets will be DC-powered during operation.\nCompared to a laminated assembly, this also helps to maximise the magnet stiffness limiting its natural\nsag, in particular for a 12-m-long magnet with low second moment of area.\nThe dipole is powered by two busbars made of extruded aluminium, one in each aperture. The\nground insulation around the busbars has to be radiation-hard due to the energy deposited by the syn-\nchrotron radiation. There are several options, such as inorganic coatings (e.g., hard anodisation), using\nthe surrounding air only, or a combination of both. The separation between the busbars and the sur-\nrounding components - magnet yoke, vacuum chamber and SR shielding - can be ensured by ceramic\nspacers placed at regular intervals along the magnet. The layer of air insulation has to be adapted to\nthe peak voltage of the circuit, which in the case of the collider dipoles is very low (only 210 volts),\nas a consequence of the low current density, the DC powering mode and the low resistance of the sin-\ngle busbars. Therefore, spacers between 3 and 5 mm thick are compatible with relaxed tolerances for\nmanufacturing the busbars at low cost and limiting the number of spacers along the magnets. A similar\ninsulation technology can also be used for the field tapering trim conductors wound around each pole.\nThe total field harmonics simulated in 2D are below 1 \u00d7 10\u22124 relative field error at the reference\nradius of 10 mm.\nThe general parameters of the dipole are summarised in Table 3.2.\nThe field map in the dipole cross-section at t\u00aft operation (peak field) is shown in Fig. 3.1.\nTable 3.2: General parameters of the arc dipole magnets.\nParameter\nUnit\nValue\nStrength, B, 45.6 \u2013 182.5 GeV\nmT\n15.2 - 61.0\nBore aperture\nmm\n74\nMagnetic length\nm\n9.7 to 11.2\nOuter envelope\nmm\n520 \u00d7 133\nPeak current\nA\n3665\nMagnet resistance (at 32\u00b0C op. temp.)\nm\u2126\n0.27\nPeak voltage, magnet\nV\n0.98\nPeak voltage, half-octant (incl. busbars) \u2020\nV\n420\nConductor (Aluminium)\nmm2, mm\n65 \u00d7 35, \u001f7.7\nTurns (busbar)\n-\n1\nTurns per coil (trim)\n-\n7\nCurrent density (busbar), t\u00aft\nA/mm2\n1.61\nTemperature rise (5 bar)\n\u25e6C\n14.5\nYoke active mass\nkg\n2621\nBusbar active mass\nkg\n131\nTrim coil active mass\nkg\n6.7\nMagnet active mass\nkg\n2909\n\u2020 One half-octant corresponds to one series circuit, which includes 355 magnets. The\ncircuit voltage will be balanced around the middle point of the circuit so that the voltage\nto ground will not exceed half the circuit voltage.\n3.1.3\nQuadrupoles\nThe quadrupole magnet is designed as two joined figure-of-eight units, which allows powering the two\napertures with only two simple racetrack coils. This approach minimises the production costs but im-\nposes opposite polarities seen by the e+ and e\u2212beams, as they travel through the magnet, a constraint\n116\n\nFig. 3.1: Field map in the dipole cross-section at t\u00aft operation.\nwhich has been included in the design of the beam line optics from the early stages of the study.\nFor cost reasons and due to the complex shape of the poles, a laminated construction of the yoke\nparts is planned. Each of the top and bottom yokes is split in two parts to allow the integration of the\nracetrack coils. The symmetry of the assembly is controlled by the tight tolerances on the mating faces\nand a system of V-grooves and pins for precise relative localisation of the assembled parts. Non-magnetic\nspacers are placed between the half-yoke assemblies to control the top-bottom pole symmetry.\nThe twin-aperture double figure-of-eight configuration generates coupling between the apertures\ndue to the left-right asymmetry of the magnetic circuits of each aperture. This translates into a shift\nof the magnetic at different powering levels (i.e., between different operation phases of the machine).\nThe geometry of the magnetic circuit has been designed with straight poles where the racetrack trim\ncoils for the field tapering circuits have been placed. This allows streamlining of the magnetic flux, and\nminimising the coupling so that the axis shift can be compensated by using adjacent horizontal orbit\ncorrection circuits.\nThe total field harmonics as simulated in 2D are below 2\u00d710\u22124 relative field error at the reference\nradius of 10 mm when only the main coils are powered. When, in addition, the field tapering trim coils\nare activated to the peak value of + 3.5 percent of the main field on one aperture and - 3.5 percent of the\nmain field on the other aperture, the b1 relative field harmonic is up to 12\u00d710\u22124, and the b3 relative field\nharmonic is up to 1.5 \u00d7 10\u22124, due to the cross-talk between apertures and the asymmetry created by the\nopposite field differences. These errors can be compensated by the adjacent horizontal orbit correctors\nfor the b1, and by the adjacent lattice sextupoles for the b3.\nThe parameters of the quadrupole magnet are summarised in Table 3.3. The field map in the\nquadrupole cross-section at t\u00aft operation (peak field) is given in Fig. 3.2.\n3.1.4\nSextupoles\nThe sextupole magnet is designed with a conventional geometry of 6 symmetrical poles and hosts trim\nwindings, which can be used for horizontal and vertical orbit correction, as well as to generate a skew\nquadrupole component like is done in synchrotron light sources. Although the sextupole pairs are not\nmagnetically coupled between beam lines, they will be assembled as a single mechanical unit, either\nby fixing them on a common crib, or by merging the adjacent poles in a single piece lamination. Both\nsolutions will be studied during the pre-TDR phase to determine the most cost-effective. The assembly\nof sextupole pairs will also minimise the fiducialisation and alignment operations during the construction\nand installation phases.\nThe magnet design is relatively compact since the sextupole pairs have to fit the 350 mm intra-\nbeam distance. Consequently, the flux density in iron and current density in the conductors are high. The\nmagnet operates below saturation at peak field, as the flux density does not exceed 1.6 T. This choice\nallows the trim circuits to be operated in a linear regime at all field levels.\nThe simulated 2D total field harmonics of the main circuit of the sextupole are below a 1 \u00d7 10\u22124\n117\n\nTable 3.3: General parameters for the quadrupole.\nParameter\nUnit\nValue\nStrength, B\u2032\nT m\u22121\n11.8\nBore aperture diameter\nmm\n74\nMagnetic length\nm\n2.9\nOverall width x height\nmm\n590 x 610\nPeak current, t\u00aft\nA\n366\nMagnet resistance (at 35\u00b0C op. temp.)\nm\u2126\n51.3\nPeak voltage magnet\nV\n18.8\nPeak voltage, half-octant (incl. cables) \u2020\nkV\n1.91\nConductor (copper)\nmm2, mm\n14.4 \u00d7 14.4, \u001f7.5\nTurns per coil (main)\n-\n36\nTurns per coil (trim)\n-\n26\nCurrent density, t\u00aft\nA/mm2\n2.25\nTemperature rise (5 bar)\n\u25e6C\n19.0\nYoke active mass\nkg\n5789\nMain coil active mass\nkg\n334\nTrim coil active mass\nkg\n9.7\nMagnet active mass\nkg\n6535\n\u2020 One half-octant corresponds to one series circuit (focusing or defocusing), which includes\n89 magnets. The circuit voltage will be balanced around the middle point of the circuit so\nthat the voltage to ground will not exceed half the circuit voltage.\nFig. 3.2: Field map in the quadrupole cross-section at t\u00aft operation.\n118\n\nrelative field error at the reference radius of 10 mm when only the main coils are powered.\nThe field quality of the correction circuits is naturally low, as expected since the field is generated\nby the six poles of the sextupole, which are significantly different from the ideal lines of the constant\nscalar potential of each correction field. Both the b5 field harmonic (relative to B1) of the horizontal orbit\ncorrection circuits and the a5 field harmonic (relative to A1) of the vertical orbit correction circuits reach\n60 \u00d7 10\u22124. For the skew quadrupole circuit, the a4 field harmonic (relative to A2) reaches 775 \u00d7 10\u22124.\nThe effect of these field errors on the beam dynamics is being evaluated to understand if the solution to\nembed the correction circuits in the sextupole is viable. Otherwise, separate corrector magnets will have\nto be designed and integrated in the lattice. They would be relatively short since the field strengths of\nthese correctors are relatively small.\nThe parameters of the sextupole magnet are summarised in Table 3.4. The field map in the sex-\ntupole cross-section at t\u00aft operation (peak field) is given in Fig. 3.3.\nTable 3.4: General parameters for the sextupole main circuit.\nParameter\nUnit\nValue\nStrength, B\u2032\u2032\nT m\u22122\n880\nBore aperture diameter\nmm\n66\nLength\nm\n1.3\nOverall width x height (one beam)\nmm\n350 x 350\nPeak current, t\u00aft\nA\n178\nMagnet resistance (at 35\u00b0C op. temp.)\nm\u2126\n274\nPeak voltage magnet\nV\n49\nPeak voltage, circuit (incl. cables) \u2020\nV\n284\nConductor dimensions (copper)\nmm2, mm\n6.15 \u00d7 6.15, \u001f4.0\nTurns per coil\n-\n24\nCurrent density, t\u00aft\nA/mm2\n7.0\nTemperature rise (6 bar)\n\u25e6C\n20\nYoke active mass\nkg\n498\nMain coil active mass\nkg\n14.6\nMagnet active mass (incl. trim coils)\nkg\n635\n\u2020 One circuit corresponds to 8 magnets. The circuit voltage will be balanced around the\nmiddle point of the circuit so that the voltage to ground will not exceed half the\ncircuit voltage.\nThe parameters of the sextupole correction circuits are summarised in Table 3.5. The field maps\nfor the sextupole correction circuits at peak correction field are given in Fig. 3.4.\n3.1.5\nCoils and busbars\nThe conductor materials, operational current densities, and number of turns of the coils and busbars have\nbeen selected based on global optimisation of the lifetime cost of the magnet system, in combination with\nother systems in the machine, in particular the electrical distribution, power converters, and technical\ninfrastructure. This optimisation has balanced the capital versus operational costs of the magnet system\nconsidering the powering needs and duration of each phase of the machine (from Z to t\u00aft), the integration\nconstraints and dissipated power of the cabling in the tunnel, and the integration of the power converters\nin the alcoves, as to minimise the total cost of all these systems over the lifetime of the machine. As\na result, the quadrupole and sextupole coils use copper conductors since they require a larger current\ndensity, whereas the dipole busbars use aluminium. Since aluminium and copper cannot be cooled\n119\n\nFig. 3.3: Left: Field map in the sextupole cross-section at t\u00aft operation (peak field). Right: Detailed\nview of a half-sextant. The conceptual positioning of the conductor has been generated from parametric\nmodelling for checking integration feasibility. It will be optimised for industrial production during the\npre-TDR phase.\nTable 3.5: General parameters for the sextupole correction circuits.\nParameter\nUnit\nH orbit\nV orbit\nSkew quad\nStrength, B.l\nmT m\n20\n20\n\u2013\nStrength, G.l\nmT\n\u2013\n\u2013\n600\nTurns per pole\n-\n54-27\n27\n43\nPeak current\nA\n8.3\n14.3\n9.9\nResistance per magnet\n\u2126\n2.15\n1.06\n0.84\nPeak voltage per magnet\nV\n17.8\n15.2\n8.4\nConductor dimensions (copper)\nmm2\n3.2 x 1.6\n3.2 x 1.6\n3.2 x 1.6\nCopper mass per magnet\nkg\n25.9\n12.9\n10.4\nFig. 3.4: Field maps of the correction circuits at peak correction fields. Left: horizontal orbit correction;\nmiddle: vertical orbit correction; right: skew quadrupole correction.\n120\n\nby water in a common cooling circuit due to galvanic corrosion, it is considered to cool the busbar\nwith a 1 mm thick copper tube embedded in the aluminium bulk. This solution avoids the need of a\ndedicated demineralised water-cooling network for aluminium. The global optimisation tool will be\nfurther developed during the pre-TDR phase also to include the cooling network costs. More details on\nthis global optimisation can be found in Section 3.8.1.\n3.1.6\nSupporting structures\nSSS units\nThe magnets in the short straight sections (SSS) - quadrupoles and sextupoles - are supported by a com-\nmon girder where they are pre-aligned and fixed, to guarantee the stability of their relative positioning\nand ease the global alignment of the beam line elements in the tunnel. The pre-assembly of the SSS\nmagnets is also necessary to install a common vacuum chamber across them and minimise the number\nof vacuum interconnections.\nThere are three versions of the Short Straight Sections (SSS), depending on whether they contain\nno sextupoles, one sextupole, or two. Two configurations are under consideration for the arc half-cell\nlayout. In the first option, the lengths of the SSS girder and dipoles are adapted to the number of sex-\ntupoles in the arc half-cell, resulting in three different variations of dipole and SSS lengths. In the second\noption, all SSS girders are manufactured at a uniform length, corresponding to the longest version capa-\nble of housing two sextupoles. When fewer than two sextupoles are required, a short dipole of equivalent\nlength replaces the missing sextupole.\nThe second option offers the advantage of standardising SSS and dipole lengths across the arcs,\nalong with their support structures. This approach also provides greater flexibility in redistributing SSSs\nif optical adjustments are needed during different operational phases of the machine. However, it intro-\nduces the drawback of requiring additional interconnections for SSSs that do not contain two sextupoles,\ncompared to the first option, leading to a slight reduction in the dipole filling factor.\nBoth options are technically feasible and will be evaluated in detail during the pre-TDR phase of\nthe project, taking into account functionality, machine performance, and cost.\nDipole units\nSimilar considerations apply to the dipole assemblies as to the SSS units. They will be pre-assembled\nat the surface, incorporating their vacuum chambers and synchrotron radiation (SR) shielding blocks,\nbefore being transported, installed, and aligned in the tunnel as individual units.\nThe dipole supporting scheme must ensure both precise alignment functionality and the minimi-\nsation of magnet sag due to its weight and the additional mass of shielding blocks surrounding the SR\nabsorbers, which are distributed approximately every five to six metres. This aspect is particularly crit-\nical, as the dipole magnets have a flat and elongated aspect ratio, resulting in relatively low mechanical\ninertia that makes them susceptible to deformation. Consequently, the supporting scheme must be de-\nsigned to align with the longitudinal distribution of the SR shielding along the dipoles, ensuring structural\nstability and optimal performance.\nMore information on the supporting structures can be found in Section 3.10.\n3.2\nVacuum system and electron cloud mitigation\n3.2.1\nIntroduction\nThe FCC-ee vacuum system design is rather challenging due to its sheer size and the fact that it must\ncope with a synchrotron radiation (SR) environment that changes significantly depending on the beam\nenergy.\n121\n\nThe Z machine at 45.6 GeV is characterised by an SR spectrum with a critical energy of only\n21 keV, while the highest energy t\u00aft machine at 182.5 GeV has a critical energy of 1.35 MeV. The Z ma-\nchine has a very large beam current, around 1.4 A, leading to a significant photon-stimulated desorption\n(PSD) rate. Since nearly all SR photons are absorbed in a very thin layer of the vacuum chamber walls,\nthey contribute locally to the PSD dynamic gas load.\nThe t\u00aft SR fan, on the other hand, penetrates deeply into the material of the vacuum chamber where\nit generates high-energy Compton showers, giant dipole resonance, and particle creation, necessitating\na thorough analysis of the related radiation field in the tunnel. Efficient solutions must be implemented\nto mitigate detrimental effects on accelerator and tunnel components, particularly shielding cables and\nelectronics in the tunnel, which has proven to be a challenging task.\nThe analysis and modelling carried out so far by the vacuum group have taken into account con-\ncerns raised by other groups, such as:\n\u2013 Machine physics group (e.g., beam-stay clear aperture, impedance contributions of all vacuum\ncomponents)\n\u2013 Magnet group (e.g., integration of vacuum chamber cross section and SR shielding within the\nmagnets\u2019 geometries)\n\u2013 FLUKA team (e.g., SR shielding, radiation protection, and related R2E issues)\n\u2013 Tunnel integration and logistics (e.g., total power dissipation in air and cooling water in the tunnel\narcs)\n\u2013 Cost estimation and machine installation planning\nThe beam parameters are chosen to maintain an SR power of 50 MW per beam across all beam\nenergies. Consequently, the linear SR power in the arcs is approximately 650 W/m, regardless of beam\nenergy.\nThis approach would also help contain high-energy Compton-scattered secondaries once the beam\nenergy is increased to 182.5 GeV later in the experimental programme. Additionally, the associated syn-\nchrotron radiation (SR) power is concentrated on the absorbers rather than being distributed throughout\nthe entire vacuum chamber, improving thermal management and overall system efficiency.\nThe design of the FCC-ee machines, including the full-energy booster, have provided valuable in-\nsights into the challenges ahead. In particular, the selection of suitable materials for the vacuum chamber\nand the adoption of a lumped SR absorber design have emerged as effective solutions to several critical\nissues related to vacuum performance and machine physics.\nThe following sections outline the proposed design and the analysis conducted thus far.\n3.2.2\nPressure Requirements\nThe FCC-ee is a powerful synchrotron radiation (SR) source, at all beam energies. From the point of\nview of the photon-stimulated desorption (PSD) gas load, the Z machine is the toughest one to deal with,\nsince it has the largest beam current. Basically, any photon in the Z SR spectrum below its critical energy\n(i.e., 91% of the total SR photon flux) can generate photoelectrons which are emitted within a very thin\nlayer of the internal surface of the vacuum chamber.\nIt is therefore necessary to maximise the pumping efficiency and minimise the PSD gas load, while\nfinding ways to speed up the vacuum conditioning as much as possible, so that vacuum quickly becomes\ngood enough to store nominal currents at the Z energy. The photoelectrons are very efficient at desorbing\nmolecules inside the vacuum and contribute to the electron cloud in the positron ring.\nThe pressure requirements, which stem mainly from beam-gas scattering arguments, mean that\nthe vacuum lifetime, \u03c4vac, should be much longer than the lifetimes of all other effects, such as Bhabha\nscattering, collisions burn up, beam-thermal photon scattering, etc.\n122\n\nExtensive experience for similar SR-dominated storage rings and colliders, e.g., SuperKEKB and\nlight sources, shows that an average pressure in the low 10\u22129 mbar range, nitrogen-equivalent, should\ngive a \u03c4vac of several tens of hours.\n3.2.3\nPhysical Aperture Requirements\nBased on geometric impedance arguments, a circular cross section of the vacuum chamber was requested\nat the beginning of the FCC-ee study. The internal diameter compatible with the design of the magnets\nand other machine components and diagnostics had initially been set at 70 mm. Later in the study, a\nreduction of the inner diameter (ID) of the magnet yokes became necessary, and the ID of the vacuum\nchamber was reduced to 60 mm.\nThe application of non-evaporable getter (NEG) coating makes this ID reduction irrelevant for\nvacuum since NEG coatings generate a rather uniform distributed pumping, contrary to a lumped pump-\ning design, which would need maximisation of the vacuum chamber conductance. A reduction from 70\nto 60 mm would mean a 37% loss of conductance loss (ratio of IDs cubed). All design and modelling are\ntherefore based on a 60 mm ID vacuum chamber.\nThe vacuum chamber is made of oxygen-free silver-bearing (OFS) copper and can be extruded up\nto 12 m. The cross section is shown in Fig. 3.5. The chamber has two appendages, called winglets, in the\nhorizontal plane to accommodate short, localised synchrotron radiation absorbers (SRAs) and pumping\nslots. These do not protrude inside the circular part of the chamber.\nFig. 3.5: Cross section of the FCC-ee arc vacuum chamber with winglets.\n3.2.4\nPumping System\nNEG-coating will be applied throughout the vacuum chamber. There have been tests at a KEK Photon\nFactory beamline of the effectiveness of \u2018thin\u2019 NEG-coatings. It was found that the NEG-coating is still\ncapable of being fully activated after 10 cycles of saturation and re-activation [239] for thicknesses down\nto 200 nm. For comparison, the standard NEG-coating thickness of the long straight sections of the LHC\nis 2 \u00b5m. The reduction to 200 nm is compatible with requirements of the resistive-wall impedance.\nOne more advantage of the application of NEG-coating is that \u223c90% of its PSD outgassing com-\nprises H2 , and the favourable effect on the beam-gas scattering of a dominant H2 becomes important.\nThe modelling and analysis carried out throughout the FCC study period have demonstrated that\nthe application of NEG-coating to 100% of the vacuum chamber\u2019s internal surface will drastically reduce\n123\n\nthe need for lumped pumps, therefore minimising the number and length of the expensive control and\npower cables for such pumps.\nHowever, a few lumped pumps are needed every 30-50 m to pump non-getterable gases (methane\nand inert gases such as He, Ar and Kr), although CH4 is effectively pumped by beam ionisation as\nsoon as e\u2212or e+ are injected. The lumped pumps which have been identified as suitable are integrated\nNEG-ion pumps. The readout of the 12 l/s ion pump will be used to get an estimate of the pressure\nat the pump\u2019s location by conversion of its ion-pump current. This methodology is both effective and\ncurrent, enabling the early detection of developing leaks, which are typically identified through changes\nin pressure, particularly under static vacuum conditions where no beam is stored. This is a crucial\noperational consideration, as locating leaks in a machine as large as the FCC-ee can be challenging and\ntime-consuming, as previously experienced during LEP operation. By facilitating early leak detection,\nthis approach helps to minimise machine downtime and improve overall operational efficiency.\n3.2.5\nNEG-Coating\nAs mentioned, detailed measurements have proved that a \u2018thin\u2019 NEG-coating can be envisaged for the\nFCC-ee collider rings. A thickness of 200 nm is deemed ideal [240].\nThe major drawback of the NEG-coating solution is that a reliable, radiation-resistant, in-situ\nbake-out system is needed. Prototyping of a solution based on a thin titanium track sandwiched between\ntwo plasma-sprayed ceramic insulation layers (see Fig. 3.6), gave a rather uniform vacuum chamber\ntemperature profile and reasonable electric power needs. The latter mainly depends on the efficiency of\nthe radiation-resistant thermal insulation layer, which is under study now. Cost-efficient optimisation of\nthis heating system is underway.\nFig. 3.6: Bake-out system based on cold-sprayed conductive tracks.\nThe detailed design of horizontal NEG-coating benches has not yet been done. However, experi-\nence with a similar coating setup developed for the HL-LHC stand-alone magnets provides confidence\nthat such a system can be implemented. The proposed approach involves a horizontally moving carriage\nequipped with a permanent magnet magnetron trap, which would travel along the axis of the chambers,\nup to 12 m in length, depositing NEG coating in localised sections of approximately 20 cm at a time.\nTransfer of this CERN-developed technology to industry for mass production for the two 91 km\nrings will be necessary.\n3.2.6\nVacuum Profiles\nExtensive modelling of the pressure profile along a representative length of the FCC-ee arcs has been\ncarried out. The comparison between a NEG-coating-based solution and one based on lumped pumps\nshows that the former is much more efficient at reducing the average pressure along the arcs, and it\n124\n\nconditions a long beam-gas scattering lifetime faster than the latter. The benefits of using the SRA and\nthe NEG coatings can be seen in Figs. 3.7 and 3.8.\nExtensive data from existing light sources, some with 100% NEG-coating (MAX-IV and SIRIUS)\nand some without NEG-coating, makes it clear that NEG-coating allows an almost immediate availability\nof long vacuum lifetimes, at least for the Z energy machine, which is the most demanding in vacuum\nterms.\nFig. 3.7: The pressure profiles assuming no NEG-coating are shown for different vacuum conditioning\nbeam doses of 1, 10, 100, and 1000 Ah. One of the two beams has lumped SRAs, the other one does not.\nIt is evident that for each beam dose, the pressure profile for the case with SRAs gives a lower pressure\nand, therefore, an advantage in terms of vacuum commissioning time.\n3.2.7\nSynchrotron Radiation Absorbers (SRA)\nThe current design of the SRA is displayed in Fig. 3.9. It is a 390 mm long copper component welded\ninto a dedicated aperture in the vacuum chamber. It needs to be actively cooled by specific water-cooling\ncircuits integrated in the absorber.\nThe channels have a twisted tape design, see Fig. 3.10, that significantly improves cooling capacity\nby enhancing turbulence mechanisms.\nThe synchrotron radiation absorbers (SRA) are produced using laser powder bed fusion (LPBF)\nadditive manufacturing technology.\nThis approach offers the advantage of enabling the fabrication\nof intricate internal structures, such as the complex twisted-tape design, which would be more time-\nconsuming and less refined if manufactured using traditional methods.\nCopper materials produced\nthrough 3D printing are currently being qualified for ultra-high vacuum (UHV) applications. A green\nlaser machine is employed to deposit copper alloy layer by layer, ensuring negligible degradation of\nits mechanical, thermal, and electrical properties. New machines with lower energy requirements and\nsmaller beam wavelengths are entering the market, promising a more cost-effective and energy-efficient\nsolution.\nA promising candidate for the absorber material is the copper alloy CuCrZr, which is undergoing\ndetailed thermal and mechanical testing to assess its performance and suitability for this application.\nBoth analytical and numerical analyses are being conducted to support the design of the syn-\nchrotron radiation absorber, particularly in relation to the twisted-tape cooling channels within it. The\n125\n\nFig. 3.8: The pressure profiles for the two rings, with and without SRAs, are shown here for the 1 Ah\nbeam conditioning dose, i.e., the initial condition of the rings. In this case, the two sets of curves allow\nthe comparison of adding NEG-coating to the two rings. The corresponding pressure curves drop by\napproximately two orders of magnitude, greatly shortening the vacuum commissioning time.\ndesign is based on implicit formulations by Manglik and Bergles [241], which show strong agreement\nwith experimental observations.\nThe geometric and fluid dynamics parameters for the internal cooling channels are shown in Ta-\nble 3.6.\nTable 3.6: Table of parameters and data for each absorber channel.\nParameter\nData per\nabsorber channel\nd\n7 mm\nH\n0.5 mm\nv\n30 mm\nRe\n3 m/s\nm\n2.1 \u00d7 104\nh\n115 g/s\n\u2206P\n0.2 bar\nThe absorbers intercept a high heat load from SR on their slanted surface. The temperature needs\nto be maintained below safety levels to ensure mechanical integrity and avoid water phase transitions.\nHowever, this also leads to an increased pressure drop that requires a design optimisation. The heat\nintercepted by the absorbers is not the same around the collider ring. The current worst-case scenario\nindicates a total power of 4471 W and a peak power density of 74.6 W/mm2. SR strikes a (< 2 mm wide)\nstrip horizontally across the middle of the absorber surface, see Fig. 3.11. This refers to the 91 GeV\ncentre-of-mass machine. For the t\u00aft machine configuration, the total power remains unchanged; however,\nthe power density is expected to increase, and the strip width to decrease. Due to the Compton effect, the\npower density transitions from a surface phenomenon to a volumetric distribution, potentially resulting\nin an equivalent surface density.\n126\n\n(a)\n(b)\n(c)\nFig. 3.9: (a) Synchrotron radiation absorber integrated in the vacuum chamber, (b) sawtooth profile\nhighlighted, and (c) cooling channels with twisted tape.\nTo accurately determine the volumetric power distribution, detailed simulations using FLUKA\nare required, as Synrad lacks the capability to model volumetric effects.\nThe synchrotron radiation (SR) power density peak is not constant but decreases with each suc-\ncessive sawtooth, as shown in Fig. 3.12. For the thermo-mechanical analysis, the SR power density\ncorresponding to the highest peak (from the first tooth) is used. This conservative assumption accounts\nfor fewer sawtooth impacts by SR than would occur in reality as the total power remains the same, i.e.,\n4471 W.\nThe temperature distribution of the absorber due to SR power is shown in Fig. 3.13. The maximum\ntemperature is 219\u00b0C.\nSawtooth profile\nIntroducing a sawtooth profile on the face of the SRA modifies the photon reflection and, thereby, it\npotentially reduces the fraction of photons which, after reflections, impinge on the central circular part\nof the vacuum chamber. Two cases, with and without a sawtooth profile on the SRA faces, have been\n127\n\nFig. 3.10: Twisted-tape design of the absorber channels.\nFig. 3.11: Synchrotron radiation strip in the absorber. The sawtooth structure alternates impacts, with\nevery other side of the tooth being struck, as highlighted in the red box.\nFig. 3.12: The SR power density peak along the tooth of the SRA.\ncompared. the images in Fig. 3.14 show the result, side by side, and the selection of facets relevant to the\nphotoelectron emission. The sawtooth case (on the left) decreases the amount of SR photons absorbed\nby the circular part of the dipole vacuum chamber segment (985 cm long) by 81%.\nIt can be seen that the sawtooth design removes the two reflected photon spots (in green-blue\ncolour) near the axis of the vacuum chamber, on the lower part of it.\nWithout sawtooth, the two spots would generate primary photoelectron, which would be trapped\nalong the vertical field lines along the dipole magnet and perturb the stored beam.\nThe trajectory of the beam is shown by the curved yellow line. Although these simulations had\nonly 2 SRA with sawtooth out of the 26 of the whole arc model ( 130 m-long), it is concluded that the\nintroduction of the sawtooth profile on the inclined surface of the SRA would be beneficial for a reduction\nof the primary photoelectrons. More refined simulations will be carried out shortly.\nAn optimisation for the position of the cooling channels was performed in a 2D approximation\n128\n\nFig. 3.13: Temperature distribution of the SRA with 2 cooling channels.\n(a) Case with 2 SRA with sawtooth pro-\nfiles\n(b) Case with \"regular\" SRA, one in-\nclined surface\nFig. 3.14:\nThe effect of sawtooth on synchrotron radiation power density. (a) Case with 2 SRA and\nsawtooth profiles and (b) Case with \u2018regular\u2019 SRA and one inclined surface\nwith the aim of lowering the temperature of the internal cooling channels. To this end, the SR power\ndistribution in a section perpendicular to the horizontal mid-plane was divided into small regions equal\nto the width of the sawtooth, as illustrated in Fig. 3.15.\nA third cooling channel is beneficial to lower the temperature of the internal channels and, in\ngeneral, of the whole absorber, as shown in Fig. 3.16. The temperature of the internal surface of the\ncooling channels, presented in Fig. 3.17, always stays below 70\u00b0C.\nThe Von Mises stress due to SR heat load is shown in Fig. 3.18. The maximum stress is 285 MPa\non the sawtooth receiving the highest SR power density. These values are below the elastic limit of the\ncopper alloy and are deemed safe. However, the material properties of the copper alloy must be measured\nexperimentally to validate the results of the thermal and mechanical simulations.\nThe cooling layout for the vacuum chamber in the half arc cell is illustrated in Fig. 3.19. A single\ncooling channel serves the vacuum chamber for the magnets on the girder (quadrupoles and sextupoles),\nwhich then splits into two channels for the dipole magnets.\nThe cooling channel on the opposite side of the absorbers ensures an even temperature distribu-\ntion around the absorber area, minimising differential deformations. To enhance cooling efficiency and\nachieve a more uniform outlet temperature and to equilibrate pressure drop, the two cooling circuits cross\nover between the dipoles before recombining at the water outlet.\nThe maximum pressure difference between the inlet and outlet of the cooling line should be around\n2-3 bar, and the inlet water temperature is around 27\u00b0C (EN/CV inputs). Considering a conservative case\naccounting for three absorbers per vacuum chamber (12 m long) and the total resistive losses [242] (150\n129\n\nFig. 3.15: Power density distribution in the absorber, plotted in a section perpendicular to the mid-plane.\nThe distribution is divided into seven regions, each 0.23 mm wide, with constant power density.\nFig. 3.16: Cross section of the SRA temperature distribution with 3 cooling channels.\nFig. 3.17: Temperature of the internal surface of the cooling channels of the SRA. These are numbered\nas in Fig. 3.16.\nW/m), total power of about 31 kW is generated per half arc cell, i.e., SRA = (4.5 kW \u00d7 6) + impedance\nlosses = (150 W/m\u00d728 m). The flow rate needed for the SRA would be 115 g/s\u00d73 =345 g/s. Considering\nthe parallel configuration of the two cooling tubes, the combined mass flow rate would be 690 g/s, leading\nto an average temperature difference of about 11\u00b0C between the inlet and outlet.\nThe pressure drop along the parallel smooth channel along the 12 m long vacuum chamber is 0.25\nbar for an internal diameter of 14 mm, without considering bends. The cooling channel on the absorber\nside incurs a pressure drop of 0.2 bar per absorber, resulting in a total pressure drop of 0.6 bar for all three\nabsorbers. The theoretical pressure drop in the dipole would then be 0.85 bar. Considering all the fittings\n130\n\nFig. 3.18: Von Mises stress distribution of the SRA.\nand bends, a pressure drop of 1.5/2 bars from the inlet to the outlet of the half arc cell is expected.\nFig. 3.19: The vacuum chamber cooling layout for the arc half cell.\nInterconnection modules, shown in Fig. 3.20, are implemented to cope with the thermal expansion\nof the vacuum chambers during bakeout, NEG activation thermal cycles, and beam operation. These\nmodules ensure that any resulting transversal misalignments of magnets and BPMs stay within the me-\nchanical alignment tolerances. To reduce the quantity of these critical assemblies, interconnection mod-\nules are placed only on either side of the quadrupole-sextupole magnet girder. This configuration min-\nimises the mechanical coupling between the dipole chambers and the quadrupole chamber integrating the\nBPM. An axial stroke of 65 mm is required, and a 3 mm transverse offset has been chosen as a design\nrequirement.\n131\n\nFig. 3.20: Interconnection modules.\n132\n\nThe interconnection modules are dismountable and are based on an external vacuum enclosure\nand a smooth internal RF transition to ensure electrical continuity for the image current, avoiding higher\norder modes. The vacuum enclosure integrates a thin-walled hydroformed bellows expansion joint which\nhas an axial and lateral stiffness of about 10 N/mm. A minimum length of 150 mm is needed for the bel-\nlows. Oval flanges are integrated on the module and chamber extremities and the leak tight connections\nare achieved by shape memory alloy rings and soft gaskets. Significant beam induced heat loads are\ngenerated in the module (a few 100s W) and an appropriate robust RF transition will be designed. Vari-\nous options are considered for the bellows shielding. The first one is based on a deformable RF bridge.\nThe concept is based on a thin bridge attached to the adjacent chamber extremities, stretched and almost\nstraight in operating conditions. This solution is used in LHC and HL-LHC. The second solution extends\nthe technical solution used at superKEK and is based on a comb design. A third one is being developed\nat CERN. In this solution, the shielding of the bellows is achieved by robust sliding RF fingers. A set of\nmachined copper parts is used to ensure a smooth transition between the vacuum chamber cross-section\nand the oval RF shielding.\n3.3\nRadiation shielding\n3.3.1\nDipole shielding\nThe emission of synchrotron radiation by the stored electron and positron beams in the collider can\nhave a significant impact on machine components and other equipment in the tunnel (see Section 1.9). A\ndedicated shielding must be installed on the dipoles, tightly enclosing the synchrotron radiation absorbers\ndescribed in Section 3.2. A preliminary conceptual shielding design for the collider arcs is shown in\nFig. 3.21. A first optimisation of the shielding geometry has been performed, but further iterations are\nneeded in the technical design phase. Several hundred kilograms of shielding material is needed for each\nsynchrotron radiation absorber in order to reduce the ionising dose in the tunnel sufficiently. The design\nof the shielding and its integration entails many technical challenges, which require detailed engineering\nstudies. This section highlights some of the main design considerations.\nThe selection of the shielding material is a trade-off between shielding efficiency, raw material\ncosts, material availability in the industry, engineering aspects (fabrication, machining), and radiologi-\ncal (operational and waste) considerations. High-density materials such as tungsten heavy alloys (17\u2013\n18.5 g/cm3) are very efficient in absorbing photons. However, the costs are prohibitive when considering\nthe large number of shielding units required. Lead-based alloys are less dense and, therefore, require a\nlarger shielding volume but are available at a fraction of the cost. The current baseline material for\nthe dipole shielding is based on a lead-antimony alloy, which is commonly used as shielding material\nfor photons. The antimony content is needed for structural reasons; it hardens the material, increasing\nits mechanical stability and machinability. Lead-antimony has a good corrosion resistance, which is\nan important factor in high-radiation environments. While lead alloys with different antimony content\nare available in the industry, an antimony fraction between 6 and 8% is considered sufficient for dipole\nshielding. The resulting material density of such a binary alloy (10.88 g/cm3) is only slightly reduced\ncompared to pure lead (11.35 g/cm3). The shielding might require a casing or coating to enable safe\nhandling during the installation or during maintenance work. Although lead antimony seems to be a\ngood candidate material, the final material selection for the shielding will be confirmed in the technical\ndesign phase.\nThe anticipated activation of the shielding material is a key factor in its life cycle and requires\na thorough assessment. Radionuclide production within the shielding is primarily driven by neutrons\ngenerated from photo-nuclear interactions, particularly in the synchrotron radiation absorbers. Initial\nstudies indicate that neutron production due to synchrotron radiation is expected to be minimal up to ZH\noperation, as photon energies remain largely below the (\u03b3,n) threshold. However, a significant neutron\nflux is expected during t\u00aft operation, as the synchrotron photon spectrum extends beyond the giant dipole\nresonance of most materials. A preliminary radiological assessment of antimonial lead as a shielding\n133\n\nmaterial suggests that it can be considered non-radioactive after a cool-down period of one to two years\nfollowing t\u00aft operation, with residual activity initially dominated by the antimony content. Further studies\nare required to evaluate potential contributions from other radiation sources, particularly beam-gas scat-\ntering, which can lead to shielding activation at all beam energies due to the emission of Bremsstrahlung\nphotons with significantly higher energies than synchrotron radiation.\nThe current shielding configuration represents only a preliminary conceptual design and must be\nrefined into a realistic technical solution using state-of-the-art engineering practices. Given that the\ncollider ring requires more than 20 000 shielding units, a careful balance between design optimisation\nand cost efficiency is essential. Assuming 20 synchrotron radiation absorbers per FODO cell for ZH\nand t\u00aft operation, and an estimated shielding weight of 400 kg per absorber, the total shielding material\nrequired for the arcs amounts to approximately, 10 400 tons, with an additional 1000 tons needed for the\nexperiment insertions. The sheer scale of the raw material required introduces a significant risk factor in\nterms of procurement, necessitating a well-defined strategic sourcing plan. Furthermore, a full life cycle\nassessment must be conducted to explore potential reuse options for the shielding material following the\ndecommissioning of the FCC-ee. The material could either be reintegrated into the market or repurposed\nfor use in other CERN facilities.\nIntegrating the shielding is a complex task and requires a coordinated design effort for the systems\nconcerned (shielding, vacuum chambers, synchrotron radiation absorbers, and magnets). Direct contact\nbetween shielding and vacuum system components must be avoided, since the shielding would act as a\nheat sink during the bake-out of the vacuum chambers. This requires a careful assessment of tolerances\nand alignment requirements and needs a detailed study of the assembly procedure for all components.\nConsidering the weight of the shielding (about 4 tons per 20 m dipole), the mechanical design of the\ndipole and its supporting scheme needs to be reassessed in order to the cope with the additional load\ngenerated by the shielding. Given the complexity of the shielding integration and assembly, a staged\nshielding approach for different operation modes is not favoured.\nAnother important aspect of the shielding design is the heat load management and the associated\nstructural stability at higher temperature. The shielding absorbs about 20% of the synchrotron radiation\npower during ZH and t\u00aft operation. (see Table 1.20).\nThis amounts to 20 MW for the full ring, or 2.5 MW per arc, which has to be dissipated by a\ndedicated cooling circuit embedded in the horizontal shielding inserts. For a single shielding element,\nthe power load can reach up to several hundreds of Watt and could give rise to higher than tolerable\npeak temperature (especially due to the low melting point of Pb-alloys). Detailed energy deposition and\nthermo-mechanical simulations and associated system engineering considerations are essential for the\ndesign optimisation of the shielding and routing of service systems, the dimensioning of the circuit, and\nFig. 3.21: Preliminary conceptual radiation shielding design for the collider dipoles in the FCC-ee arcs.\nThe shielding is assumed to be made of antimonial lead and has a weight of about 400 kg per synchrotron\nradiation absorber.\n134\n\nFig. 3.22: Possible electronics bunker (red circle) near the lattice quadrupoles in the FCC-ee arcs. In this\nvery first design, the bunker is assumed to be made of concrete (gray walls) and borated polyethylene\n(green sheets on the inside). The dimensions shown have to be revised once the number and size of the\nelectronics racks have been confirmed.\nthe definition of the corresponding infrastructure requirements.\n3.3.2\nElectronics bunker\nA conceptual design of a possible electronics bunker has been devised (see Fig. 3.22), in order to reduce\nthe radiation levels for electronics. In this very first design, the bunker is assumed to be made of 10\u2013\n20 cm-thick concrete walls, which are covered on the inside by borated polyethylene sheets. The latter\nare needed for moderating and capturing neutrons. The concrete walls can also be replaced by other\nmaterials, which can affect the required wall thickness. The actual bunker size will depend on the final\nspace requirements for electronics racks. The outer dimensions shown in Fig. 3.22 need to be adapted\nonce a complete inventory of the required racks has been established. It is presently assumed that one\nsuch bunker is needed per arc quadrupole in the collider, which amounts to more than 2800 units. The\nbunkers might also be needed in the insertion regions.\nThe technical implementation of such a bunker remains to be studied. In particular, the integration\nof the bunker inside or near the quadrupole girder has to be assessed. Another important aspect is the\naccessibility of electronics in case of interventions. The racks need to be accessible without the need\nof heavy lifting equipment in case an electronics card has to be exchanged. Furthermore, a suitable\nventilation system has to be designed for the bunkers to extract the heat generated by the systems inside\nthe bunker and to have precise temperature control.\n3.4\nRadio frequency system layout, configurations and parameters\n3.4.1\nIntroduction\nThe superconducting radio frequency (SRF) system of FCC-ee [13] accelerates two beams of particles\ncirculating in opposite directions. The system is designed to provide 50 MW of RF power in continuous\nwave (CW) to each beam in order to compensate synchrotron radiation (SR) losses. Beam currents and\nrequired RF voltages for four operating points are summarised in Table 3.7. At the Z operating mode\nthe beam current of 1.3 A is very high and the total RF voltage is only about 100 MV. When switching\nto the W and Higgs operating points, the beam currents are reduced by one order of magnitude and are\n135 mA and 26.7 mA respectively, while the total RF voltage is ten times higher, at 1.05 and 2.1 GV . In\nthe t\u00aft mode the beam energy is significantly increased (182.5 GeV). The beam current and RF voltage\nvary again by one order of magnitude and are 5 mA and 11.3 GV making the accelerator a very high\ngradient machine. The collider RF system requires a transverse feedback system to cure coupled bunch\ntransverse instabilities, as described in Section 1.4. Strip line kickers operating at a multiple of the bunch\nrepetition frequency are an obvious choice. For the collider, the function of depolariser and transverse\nfeedback can be combined as outlined in Section 1.7.\n135\n\nThe SRF system will be located in a single straight section at point PH, while the one for the\nbooster will be grouped in point PL. The requirement to locate all the RF at a single location rather than\nbeing more distributed around the ring is driven by the need for extremely precise centre-of-mass energy\ncalibration at the Z. This localisation also has the benefit of consolidating the cryogenics, electrical\ndistribution, and RF maintenance. The following sections describe the main aspects of the RF system\nand important changes since the CDR and mid-term report.\nTable 3.7: Main RF-related FCC-ee parameters.\nModes\nEnergy\n[GeV]\nCurrent\n[mA]\nRF Voltage\n[GV]\nZ\n45.6\n1292\n0.089\nWW\n80.0\n135\n1.049\nZH\n120.0\n26.8\n2.098\nt\u00aft\n182.5\n5\n11.300\n3.4.2\nBaseline FCC-ee collider SRF system layout\nTable 3.8: Evolution of FCC-ee collider RF system layout.\nOperating point\nZ\nWW\nZH\nt\u00aft\nConceptual design report\nRF frequency\n[MHz]\n400\n400/800\nCommon RF system for two beams\nno\nyes\nNumber of cavities\n104\n272\n272/372\nNumber of cells per cavity\n1\n4\n4/5\nRF power per cavity\n[kW]\n962\n368\n149/155\nFeasibility study mid-term report\nRF frequency\n[MHz]\n400\n400/800\nCommon RF system for two beams\nno\nyes\nNumber of cavities\n112\n264\n264\n264/488\nNumber of cells per cavity\n1\n2\n2/5\nRF power per cavity\n[kW]\n901\n378\n382\n78/163\nFeasibility study final report\nRF frequency\n[MHz]\n400\n400/800\nCommon RF system for two beams\nno\nyes\nNumber of cavities\n264\n264/408\nNumber of cells per cavity\n2\n2/6\nRF power per cavity\n[kW]\n380\n78/195\nDue to the large span in beam current and RF voltage of the four FCC-ee operating modes, it is\nvery challenging to design a unique RF system suitable for all the operating points. Nevertheless, several\nsteps were performed towards a more compact and efficient solution.\nThe main parameters of the RF system described in CDR [13] are summarised in Table 3.8. For\nthe Z operating point only, 1-cell elliptical cavities at 400 MHz with low shunt impedance were foreseen,\nwith a cavity RF shape carefully optimised to minimise the higher-order mode (HOM) power. The 4-cell\n136\n\ncavities were considered for WW and ZH operating points due to significantly higher RF voltages and\nlower beam currents. Thanks to the small number of bunches required for the highest energy operating\npoint (t\u00aft), it was assumed that there is a common RF system for both electron and positron beams that\nreuses all 400 MHz 4-cell cavities complemented by more compact 800 MHz 5-cell cavities [243].\nThe main RF system changes in the mid-term report concerned WW and ZH operating points.\nThe first considerations of 2-cell cavity scenario were described in Ref. [244] and highlighted a strong\nHOM damping efficiency compared to the 4-cell designs while still permitting a moderate accelerating\ngradient. On that basis and due to the increased RF voltage requirements for the WW operating point,\n2-cell cavities were chosen, and a common RF system for the ZH operating point was also adopted. This\nled to an increased number of high-gradient 800 MHz 5-cell cavities for the t\u00aft operating point.\nTwo additional modifications led to the present baseline RF system. The 2-cell cavities were also\nadopted for the Z operating point requiring the reverse phase operation (RPO) mode [245] discussed\nin the following section. In addition, 6-cell cavities at 800 MHz have been proposed instead of 5-cell\ncavities at the t\u00aft operating point, leading to a significant reduction of the total number of cryomodules\nthus a reduction of the investment costs. The main RF parameters for the collider are summarised in\nTable 3.9.\nTable 3.9: Main RF parameters of the FCC collider.\nParameters\nZ\nW\nZH\nt\u00aft\nCommon RF system for two beams\nno\nno\nyes\nyes\nRPO\nyes\nno\nno\nno\nTotal RF voltage [MV]\n89\n1049\n2098\n2098\n9202\nBeam current [mA]\n1283\n135\n53.6\n10\nRF frequency [MHz]\n400.79\n400.79\n801.58\nOperating temperature [K]\n4.5\n4.5\n2\nNumber of cells per cavity\n2\n2\n6\nQuality factor Q0\n2.7 \u00d7 109\n2.7 \u00d7 109\n3 \u00d7 1010\nCavity voltage [MV]\n7.95\n7.95\n22.5\nAccelerating gradient Eacc [MV/m]\n10.6\n10.6\n20.1\nRF power per cavity [kW]\n380\n78\n195\nCoupling factor QL\n9.2 \u00d7 105\n4.5 \u00d7 106\n4.1 \u00d7 106\nNumber of cryomodules\n66\n66\n102\nNumber of cavities\n264\n264\n408\n3.4.3\nReverse Phase Operation\nThe optimal cavity detuning, \u2206fopt = f0 \u2212fRF, and optimal quality factor, QL,opt, are commonly used\nto minimise RF power requirements in high-current synchrotrons. Assuming 132 2-cell cavities for the\nZ operating point, the lowest RF voltage per cavity, Vcav \u22480.7 MV results in \u2206fopt \u2248\u221270 kHz and\nQL,opt \u22485 \u00d7 103. Both are extremely difficult to achieve because of the enhancement of longitudinal\ncoupled-bunch instabilities due to fundamental mode (FM) modulations of bunch-by-bunch parameters\ndue to transient beam loading, as well as increased critical fields in a fundamental power coupler (FPC).\nAn alternative approach, the reverse phase operation (RPO) mode [245] was studied for the FCC RF\nsystem to overcome these challenges partially. The RPO was originally developed and tested in KEKB\nfor various scenarios [245\u2013247] and was adopted as a baseline solution for the electron storage ring of\nthe Electron-Ion Collider (EIC) [248]. It is based on introducing groups of focusing and defocusing\ncavities. They are de-phased with respect to the reference phase and provide accelerating voltage at the\nbeam phase, adding up to the required total RF voltage as illustrated in Fig. 3.23. In this case, Vcav can\n137\n\nbe chosen to be the same for the WW and ZH operating points, resulting in a common optimal quality\nfactor for three modes given by:\nQL,opt =\nV 2\ncavNcav\n2PSR(R/Q).\n(3.1)\nHere Ncav is the total number of cavities, PSR is the synchrotron radiation power, and (R/Q) is the ratio\nof the shunt impedance to the quality factor of the cavity FM expressed in circuit ohm. Although this\nsimplifies the fundamental power coupler design, the first drawback is that the total RF voltage can only\nbe changed in discrete steps of Nfoc \u2212Ndefoc, (see, e.g., Ref. [249]),\nVRF = U0\ne\nv\nu\nu\nt1 +\n \n1 \u2212e2N2\ncavV 2\ncav\nU2\n0\n!\n(Nfoc \u2212Ndefoc)2\nN2\ncav\n,\n(3.2)\nwhere U0 is the energy loss per turn due to synchrotron radiation. Therefore, the RF voltage has been\nincreased from 79 to 89 MV, which assumes Nfoc = 71 and Ndefoc = 61. The RPO mode needs to be\nused for the Z operating point of the collider and all cycles of the high-energy booster (see Section 6.3).\n0\n50\n100\n150\n200\nPhase (deg.)\n600\n400\n200\n0\n200\n400\n600\nRF voltage (MV)\nfoc\ndefoc\ns\nVfoc\nVdefoc\nVfoc + Vdefoc\n71 focusing cavities\n61 defocusing cavities\nBeam\n89 MV\nFig. 3.23: RF waves (left) and phasors (right) for the RPO mode.\n3.4.4\nInstabilities due to fundamental mode (FM) and transient beam loading\nCavity detuning leads to impedance asymmetry around the RF frequency, which can drive the coupled\nbunch instability. Direct RF feedback [250] (Fig. 3.24, left) is assumed to be implemented in the low-\nlevel (LL) RF system to reduce the effective impedance \u2019seen by the beam\u2019. The closed loop impedance\nis\nZcl(\u03c9) =\nZ(\u03c9)\n1 + GFBZ(\u03c9)e\u2212i\u03c4delay\u03c9+i\u03d5adj ,\n(3.3)\nwhere GFB is the feedback gain, \u03c4delay is the overall loop delay assumed to be 700 ns (similar to the LHC\nRF system [251]), and \u03d5adj is the phase adjustment required to correctly set the feedback negative at the\ndetuned cavity resonant frequency. The flat response is achieved for 1/GFB = 2(R/Q)\u03c9rf\u03c4delay. The\ninstability growth rates were computed assuming a uniformly filled ring for the Z, WW, and ZH operating\npoints (Fig. 3.24, right). The synchrotron radiation damping is sufficient to suppress any coupled-bunch\nmodes driven by fundamental cavity impedance for WW and ZH operating points, whereas direct RF\nfeedback is necessary for stability at the Z operation point.\nTo evaluate the transient beam loading, the small-signal (Pedersen) model [252] was extended to\nthe RPO case. The filling scheme assumed in the mid-term report considered 20 trains of 560-bunches\nwith the 25-ns bunch spacing resulting in about 1.2 \u00b5s gaps between bunch trains. In this case, the\nmodulation of the effective RF voltage reaches about 50% for the baseline VRF = 89 MV (Fig. 3.25,\nleft) resulting in the synchrotron tune spread of 30% (Fig. 3.25, right). This spread is not acceptable\n138\n\nRF cavity\nLoad\nCirculator\nGenerator\n\u03a3\n\u2013\n+\nCavity voltage\nForward wave \nReflected wave \nError signal\nDelay\nDirect RF \nfeedback\nPhase pickup\nLongitudinal \ndamper\nReference signal\nBeam\nTuner\n+\n\u03a3\n+\n400\n200\n0\n200\n400\nCBI mode number\n10\n2\n10\n1\n100\n101\n102\nGrowth rate (s\n1)\nSR damping rate at Z\nSR damping rate at WW\nSR damping rate at HZ\nZ, Imp. + DFB\nWW, Imp.\nHZ, Imp.\nFig. 3.24: Simplified block diagram of the LLRF system for the FCC-ee 400 MHz RF system (left) and\nGrowth rates of longitudinal coupled bunch instabilities due to fundamental cavity impedance (right).\nfor transverse beam stability due to limited space in the tune diagram (Section 1.4.3), and therefore, two\nmitigation schemes were proposed: a higher RF voltage or a shorter gap length.\nAfter a modification of the injection and extraction system layouts (Section 1.8), a new filling\nscheme of 40 trains of 280-bunches with 0.6 \u00b5s gaps was adopted, and a stable working point was found\nfor all bunches (see Fig. 1.17). The impact of low-intensity pilot bunches was also verified, and a uniform\nfilling of all gaps is recommended to avoid an additional 1% increase in the synchrotron frequency spread.\nFig. 3.25: Left: bunch-by-bunch modulation of the effective RF voltage with RPO for 20, 580-bunch\ntrains filling scheme (one train shown) as a function of the bunch number. Right: synchrotron tune\nspreads as a function of total RF voltage.\n3.4.5\nAnalysis of RF system trip\nA time-domain model based on [253] was developed to evaluate beam-cavity interaction in the event of\nan RF system failure. It solves differential equations describing the cavity-generator and LLRF building\nblocks (Fig. 3.24, left) coupled with the longitudinal equations of motion for centroids of all bunches\nsimilar to Ref. [254]. The two highest current FCC operating points were considered.\nZ operating point\nIt is assumed that the LLRF system is capable of detecting the event of a single RF cavity (or RF amplifier,\nLLRF system, etc.) trip within one turn (Fig. 3.26, top left, green trace). It then adapts the reference\nsignals of the remaining cavities (blue and orange traces) to compensate for missing RF voltage within\nthe following turn thanks to a strong direct RF feedback. In that case, the RF voltage of the tripped cavity\n139\n\novershoots for a short time by about 6% of the nominal RF voltage and then settles slightly below the\nnominal value. At the same time, the RF power (Fig. 3.26, top right) is modulated at the synchrotron\nfrequency due to the synchrotron oscillations excited of different bunches (Fig. 3.26, bottom). Although\nthe peak RF exceeds the nominal value by about 40% (shaded blue and orange areas), the total average\npower of all remaining cavities increases by less than 10% (solid black line). In this scenario, the RF\npower system adapts the high-voltage set point to efficiently cope with the corresponding overshoot\n(Section 3.4.12). The amplitude of bunch oscillations remains within a few ps, which is significantly\nsmaller than the rms bunch length. The beam, however, becomes unstable due to the increase of the\nimpedance around the FM (the direct RF feedback is no longer active). In particular, coupled-bunch\nmodes -2 or 2 become unstable depending on the type of cavity tripped. To suppress these instabilities,\na longitudinal damper system can be employed (Fig. 3.24, left) using the remaining RF cavities as the\nkicker cavities and providing the shortest damping time of the order of two synchrotron periods [255,\n256]. The algorithm needs to be adapted for the RPO case, and the potential increase of RF power\ntransients should be further studied. After that, a recovery scenario can be evaluated. For completeness,\nthe results of simultaneous trips of focusing and defocusing cavities were evaluated. In that case, the\nRF power modulations are unacceptably high (more than 70%) and the beams must be dumped. Note\nthat coupled-bunch instabilities due to the impedance of two tripped cavities of the same type can not be\nsuppressed by the longitudinal damper.\nFig. 3.26: Transients in the event of a single focusing RF cavity trip for Z operating point. Top left:\nevolution of RF voltages normalised by the nominal value of 7.95 MV as functions of time. Top right:\nevolution of the RF power normalised by the nominal value of 380 kW for the focusing, defocusing, and\ntripped RF cavities. Bottom: synchrotron oscillations of different bunches in a train.\nWW operating point\nA similar analysis was performed for the scenario with all cavities being in phase for the W operating\npoint. A tripped RF system cannot drive a coupled-bunch instability due to a lower beam current, higher\nenergy, and stronger synchrotron radiation (see Fig. 3.24). An example of simultaneous trips of six RF\nsystems is shown in Fig. 3.27. It is the worst-case scenario as the probability of this event is rather low\n140\n\nand sequential trips can appear instead. Applying a similar strategy of detecting missing RF cavities and\nadapting the total RF voltage, the power transients can be kept below 30% while the peak RF voltage\ncan increase by 15% with respect to the nominal value. This requires increasing the time of RF voltage\nadaptation by another turn at a cost of about 10 ps amplitude of the bunch oscillations (Fig. 3.27, bottom),\nwhich becomes comparable with the 18 ps rms bunch length. No coupled-bunch instability is expected\nin this case due to sufficiently fast synchrotron radiation damping.\nFig. 3.27: Transients in the case of six RF cavity trips for the WW operating point. Top left: evolution\nof RF voltages normalised by the nominal value of 7.95 MV as a function of time. Top right: evolution\nof the RF power normalised by the nominal value of 380 kW for the focusing and tripped RF cavities.\nBottom: synchrotron oscillations of different bunches in a train.\n3.4.6\nRF synchronisation aspects\nThe ring tunnel of the FCC-ee must also be compatible with the FCC-hh accelerator to be installed in\nthe same infrastructure once the lepton physics programme has been completed. Therefore, the tunnel\ncircumference, which will obviously remain an unchangeable parameter throughout the entire lifetime\nof the FCC, must be carefully chosen. Flexibility in terms of beam parameters and transfer schemes is\nkey to not exclude any possibilities even in the far future.\nFor the FCC-ee, there are only a few restrictions as long as the booster and collider rings have\nexactly the same circumference. RF frequencies for the ultra-relativistic leptons are moreover constant\nand synchrotron radiation naturally damps longitudinal oscillations of the bunches.\nThe choice of circumference is more constrained for FCC-hh, since protons will either be trans-\nferred from a high-energy booster (HEB) in the existing SPS or LHC tunnel. In this injector the hadrons\nmust be accelerated with beam control loops to mitigate common-mode dipole oscillations. These beam-\nderived corrections change the RF frequency during acceleration and hence modify the azimuthal posi-\ntion of the bunches at the arrival at the flat-top. This requires a cogging process to move them to the\ndesired azimuth prior to the bunch-to-bucket transfer. Additionally, following acceleration and synchro-\nnisation in the HEB, multiple transfers of batches of about 80 bunches to the collider cannot be avoided\n141\n\nbecause of the need to keep the stored energy of the injected beam at an acceptable level for protection\ndevices.\nThe first analysis to identify an FCC circumference compatible with the HEB in the SPS or LHC\ntunnel can be found in Ref. [257]. Once synchronised to the same RF frequency, two circular accelerators\ncan be modelled as cogwheels. For a circumference ratio of C2/C1 = h2/h1 = n1/n2, where h are\nthe harmonic numbers, the bunches in both rings are at the same azimuth only every n1 turns of the\nring with the circumference C1, which corresponds to n2 turns in ring with C2. This is also the basic\nperiodicity with which the beam transfer can take place. In the CDR, a 97 750 m circumference ring\nwas chosen as a baseline solution with the corresponding ratios with the HEB CFCC/CLHC = 11/3 and\nCFCC/CSPS = 99/7. The evolution of the placement required an additional detailed study [258]. For the\npresent FCC baseline circumference of 90 658.2 m the ratios with the HEB are CFCC/CLHC = 1010/297\nand CFCC/CSPS = 1010/77. This means that beam can only be transferred every 1010 turns in the\ninjector, corresponding to about 90 ms for the HEB in the LHC tunnel. While FCC circumferences of\n179.5 m shorter or longer would be ideal from the RF point of view, with much smaller numerators\nand denominators in the circumference ratios, and provide important flexibility at the transfer, they are\nexcluded based on the integration in the tunnel.\nThe baseline circumference ratio of the HEB in the LHC tunnel of 1010/297 \u22433.40067 is ex-\ntremely close to 17/5 = 3.4 [259]. A promising alternative in view of FCC-hh would therefore be an\n18 m shorter FCC circumference of 90 640.2 m, hence exactly 3.4 times the circumference of the LHC.\nIt would allow the injection of hadrons every 17 turns of the HEB, corresponding to only 5 turns in the\ncollider. Such low numbers of turns, with an almost instantaneous transfer, enable non-adiabatic RF\nmanipulations, like bunch rotation to compress or stretch bunches for the injection into the collider, in\ncombination with multiple transfers to limit the maximum stored energy for reasons of machine protec-\ntion. These manipulations are excluded with the present baseline scenario. To keep the baseline harmonic\nnumber of hFCC = 121 200 = 24\u00b73\u00b752\u00b7101 for the full flexibility with bunch spacings, the RF frequency\nof the FCC-ee would have to be increased by only 80 kHz, from 400.79 MHz to 400.87 MHz. This is\nsmall enough to stay within the frequency range of the operational cavity tuning systems. The impact of\na circumference change as small as 18 m on the tunnel integration would be minor. Table 3.10 compares\nthe baseline scheme with the proposed alternative circumference.\nTable 3.10: Summary of baseline and alternative tunnel circumferences. The length difference with\nrespect to the baseline circumference is indicated by CFCC.\nhFCC\nCFCC [m]\n\u2206CFCC [m]\nhFCC\nhLHC\nhFCC\nhSPS\nfRF [MHz]\nComment\n120 960\n90 478.6\n-179.5\n112/33\n144/11\n400.8\nIdeal for RF, too short\nfor tunnel integration\n110 160\n90 640.2\n-17.95\n17/5\n459/35\n364.4\nOption for FCC-hh\n121 200\n400.9\nProposal for FCC-ee,\nideal for RF with\nminimal change\n122 400\n404.8\nOption for FCC-ee\n146 880\n485.8\nOption for FCC-hh\n121 200\n90 658.2\n\u2013\n1010/297\n1010/77\n400.8\nBaseline\n121 440\n90 837.7\n+179.5\n92/27\n92/7\n400.8\nIdeal for RF, too long\nfor tunnel integration\n142\n\n3.4.7\nTechnological choices for the SRF cavities\nThe technological choices proposed for the two types of SRF cavities of the FCC-ee collider are driven\nby the experience of particle accelerators operating at similar parameters. The accelerating gradients\nare fixed to 10 MV/m at 400 MHz and 20 MV/m at 800 MHz. These accelerating gradients must be\nreached in operation and be very reliable. Thus, a 20% margin on the accelerating field Eacc and the\nunloaded quality factor Q0 is added between the values during qualification tests in a vertical cryostat\nand operation in the machine.\nIt is indeed important to remember that performance degradation occurs between cavity qualifi-\ncation in the vertical cryostat and cavity performance after cryomodule assembly. This is a well-known\nphenomenon in the SRF domain. Taking into account an additional margin for reliable operation, per-\nformance targets on Eacc and Q0 have been specified for all steps of the cavity lifetime (see Table 3.11).\nTable 3.11: Main RF performances targets of the 400 MHz and 800 MHz cavities.\nCavity configuration\nbare\ndressed\ncryomodule\noperation\nOrientation in test\nvertical\nvertical\nhorizontal\nhorizontal\nhelium tank\nFPC\nAdded elements\nHOM couplers\ntuner\nshieldings\n400 MHz\nEacc [MV/m]\n13\n12.4\n11.8\n10.6\nCavity\nQ0\n3.3 \u00d7 109\n3.15 \u00d7 109\n3 \u00d7 109\n2.7 \u00d7 109\n800 MHz\nEacc [MV/m]\n24.8\n23.6\n22.5\n20.25\nCavity\nQ0\n3.8 \u00d7 1010\n3.65 \u00d7 1010\n3.5 \u00d7 1010\n3 \u00d7 1010\nAt the Z, WW and ZH operating points, the 2-cell cavity technological design is inspired by the\n400 MHz LHC cavities accelerating a proton beam of about 0.5 A (1 A for HL-LHC) and operating at\n300 kW RF power in CW [260]. The cavity is heavily damped thanks to four coaxial couplers placed\nvery close to the accelerating cell. The cavity is made of copper and is coated with a superconducting\nniobium thin film, operating at the temperature of 4.5 K. Its very large aperture of 300 mm diameter\nallows the propagation of most of the high-frequency modes induced by the beam. The Nb/Cu version of\nthe 352 MHz - 5 mA multicell cavities used in LEP is also a good reference for the design of the 2-cell\nFCC-ee cavity [261] where some experience can be gained to push the accelerating gradient to 10 MV/m\nand above, while keeping the HOM damping properties very efficient.\nBulk niobium technology is very suitable for the 800 MHz 6-cell cavities used at the t\u00aft energy.\nSimilar 5-cell cavities of this type have already been developed for high-intensity proton accelerators\nlike the SNS linac at ORNL in Oak Ridge [262], the SPL project at CERN [263], the ESS accelerator\nin Lund [264], and the PIP-II linac at Fermilab [265]. It is also important to remember that a prototype\nFCC-ee 5-cell bare cavity was manufactured and successfully tested in a vertical cryostat by the Jefferson\nLaboratory in 2018 [266].\n3.4.8\nRF design of elliptical cavities\nA multi-objective optimisation was performed for the 2-cell 400 MHz cavity, targeting both the FM\nproperties, such as peak surface electric and magnetic fields, and the longitudinal impedance of the\nHOMs. At the Z operating point, the longitudinal impedance of the 0-mode in the fundamental passband\nbecomes critical for ensuring longitudinal stability, as this mode only couples to the power coupler with\na loaded quality factor of approximately 106. To address this, the (R/Q) of the 0-mode was incorporated\ninto the optimisation problem. As a result, the half-cell lengths were reduced from 187 mm to 180 mm,\n143\n\nFig. 3.28: Artist\u2019s view of the 2-cell 400 MHz (left) and 6-cell 800 MHz (right) SRF cavities.\nlowering the (R/Q) of the 0-mode to below 0.01 \u2126. This modification was achieved while maintaining\nthe FM figures of merit and HOM performance metrics at levels comparable to the previous design.\nThe design of the 6-cell 800 MHz cavity is based on the 5-cell design reported in the mid-term report,\nwith an additional mid-cell added to the structure. The mid-cells were optimised to reduce peak surface\nfields, enabling a higher accelerating gradient (Eacc) required for tt operation. Additionally, the end-cell\nwas designed to facilitate the damping of potentially harmful trapped modes. The parametrised model\nof a cavity-cell, along with the shapes adopted for the 2-cell 400 MHz and 6-cell 800 MHz cavities,\nare shown in Fig. 3.29. The corresponding geometrical parameters are given in Table 3.12 and some\nimportant figures of merit for the cavities are presented in Table 3.13.\n6-cell 800 MHz\n2-cell 400 MHz\nFig. 3.29: Parametrised model of the cavity\u2019s end-cell (left) and the shapes of the two FCC-ee cavities\n(right). The inner side of the end-cell has the same shape as the middle cells in the 6-cell cavity.\nTable 3.12: Geometric parameters of the FCC cavities.\nA/Ae [mm]\nB/Be [mm]\na/ae [mm]\nb/be [mm]\n2-cell 400 MHz\n94.06 / 102.81\n127.81 / 137.97\n77.19 / 61.11\n109.06 / 58.94\n6-cell 800 MHz\n67.72 / 66.5\n57.45 / 51.0\n21.75 / 17.0\n35.6 / 23.0\nRi/Rbp [mm]\nL/Le [mm]\nReq [mm]\n\u03b1/\u03b1e [\u25e6]\n2-cell 400 MHz\n125.58 / 150\n180 / 180\n351.041\n105.3 / 109.6\n6-cell 800 MHz\n60.0 / 78.0\n93.5 / 85.77\n166.591\n100.0 / 96.9\nFigure 3.30 presents the impedance spectrum of each cavity type up to 3.4 GHz without any damp-\ning features. For the 2-cell 400 MHz cavity, no critical modes with high longitudinal impedance (Z\u2225) are\nidentified. However, dipole modes near 530 MHz are trapped, leading to excessive transverse impedance\nabove the coupled bunch instability threshold. To mitigate this, two hook-type couplers are installed per\ncavity, reducing transverse impedance to approximately 60 k\u2126/m. A transverse feedback system with a\nmoderate damping rate (about 50 turns) can ensure stability at the Z operating point. The hook coupler\n144\n\nTable 3.13: Some figures of merit for the FCC-ee cavities, with the LHC cavity as a reference for\ncomparison.\nLHC (reference)\nFCC 2-cell\nFCC 6-cell\nf [MHz]\n400.79\n400.79\n801.58\n(R/Q)linac [\u2126]\n88.1\n182.7\n630.4\nG [\u2126]\n252\n232.7\n272.8\nEpk/Eacc [-]\n2.3\n2.0\n2.04\nBpk/Eacc [mT/MV/m]\n5.1\n5.33\n4.31\nk\u2225[V/pC]\n0.13\n0.26\n3.58\n(\u03c3z = 14.6 mm)\n(\u03c3z = 14.6 mm)\n(\u03c3z = 2.32 mm)\ngeometries are shown in Fig. 3.31(a). For the 6-cell 800 MHz cavity, two DQW-type HOM couplers, as\nshown in Fig. 3.31(b), suffice to meet stability requirements for tt working point.\nFig. 3.30: Longitudinal (left) and transverse (right) impedance of the two cavity types. The wakefield\nsimulations are conducted on the cavities without any damping coupler. Consequently, due to the trun-\ncation of the wake potential, the impedance peaks are not fully resolved.\n(a)\n(b)\nFig. 3.31: (a) Two hook-type couplers are used to damp the trapped dipole modes in the 2-cell 400 MHz\ncavity. (b) DQW-type HOM couplers are employed for HOM damping in the 6-cell 800 MHz cavity.\n3.4.9\nHOM power calculation\nA short bunch length of a few millimetres can excite high-frequency HOMs in the cavities, reaching up to\ntens of GHz. These high-frequency modes must be extracted from the cryomodules and dissipated in air-\ncooled or water-cooled RF loads. Several types of RF extractors have been studied, including rectangular\n145\n\nwaveguides, ridged waveguides, beam line absorbers and coaxial lines. A configuration with two coaxial\nwaveguides oriented at 90\u00b0 and connected to the beam pipe is chosen for its simplicity, its compactness\nand its ability to handle high RF power. Since the 2-cell cavities are designed to avoid trapped modes\nwith large longitudinal impedance in them, there is no need to place the HOM power extractors close\nto the cavity. Consequently, the coaxial lines, which also lack an FM rejection mechanism, must be\npositioned far from the cavity on the beam pipe to prevent the extraction of FM energy while absorbing\nHOM energy. Another advantage of this configuration is that it eliminates the creation of a transverse\nkick caused by the two couplers interacting with the FM field, as the influence of coaxial lines on the\nFM is minimal. However, this design choice comes at the cost of requiring a larger distance between the\ncavities to accommodate these couplers on the beam pipe.\nA similar coaxial line inter-cavity damping concept was considered for the 800 MHz cavity. Due\nto space limitations and the need to shorten 800 MHz cryomodules, studies are ongoing to eliminate the\ncoaxial line for the 800 MHz system. This appears feasible, with the two additional HOM ports near\nthe cavity utilised for HOM couplers to damp other dangerous HOMs mainly required for the booster\ncavities which have lower beam instability thresholds. Since neither the coaxial lines nor the HOM\ncouplers have broadband transmission capabilities up to tens of GHz, room-temperature high-power\nbeam line absorbers (BLA) are necessary between cryomodules to absorb HOM power above the beam\npipe cut-off frequency for both 400 MHz and 800 MHz cryomodules.\nFigure 3.32(a) shows the HOM power distribution for the Z operating point. Each coaxial line\nshould handle several kilowatts of HOM power, with up to 7 kW expected for the coaxial extractors\nlocated in the middle of the cryomodule. Additional margins must be considered, as some HOMs can\ngenerate up to 10 kW of additional HOM power if the beam spectral line aligns with a high-impedance\npeak. Depending on the mode excited and its coupling to the coaxial lines, this power can propagate into\ndifferent couplers. Therefore, to ensure reliability, the coaxial line extractors will be designed to handle\npower levels between 15 kW and 20 kW to accommodate such worst-case scenarios. Figure 3.32(b)\nillustrates the power distribution for collider cavities in t\u00aft operation without using inter-cavity coaxial\nlines. In this scenario, each DQW coupler absorbs, on average, 0.1 kW of HOM power, with most of the\npower propagating out of the cryomodule which has to be damped by inter-cavity BLAs.\nIt is important to highlight that, in the case of the bunch length without collisions (referred to as\nSR for the synchrotron radiation) there is a significant increase in the HOM power at the Z working point\ncompared to when beams are in collision, where beamstrahlung (BS) increases the energy spread and\nbunch length. Figure 3.33 illustrates the loss factor of the four-cavity module with tapers and without\ncouplers for both the BS and SR bunch lengths. The resulting HOM power at the Z operating point is\ncalculated using the formula PHOM = k\u2225,HOMQI, where k\u2225,HOM represents the longitudinal loss factor\nof HOMs, Q denotes the bunch charge, and I stands for the average beam current. Figure 3.33 also\npresents the HOM power levels, showing an increase by approximately a factor of 4.4 when transitioning\nfrom the BS to the SR bunch length. A significant portion of HOM power for the SR bunch length is\ncaused by 300 mm to 100 mm diameter tapers at the cryomodule ends. Removing these tapers reduces\nHOM power by 100.4 kW (SR) and 13.2 kW (BS). Replacing them with 300 mm to 160 mm diameter\ntapers reduces HOM power by 52.3 kW (SR) and 6.8 kW (BS).\n3.4.10\nFundamental Power Couplers\nA new family of fundamental power couplers (FPC) has to be developed for FCC-ee which all must\noperate reliably in CW mode. For the 400 MHz 2-cell cavities, the reverse-phase operation scheme\nreduces the input power requirement for the Z working point from 0.9 MW to approximately 400 kW,\nmatching the requirements for the WW and H working points at the same QL level of 9.2\u00d7105. However,\nadditional margins must be considered for the RF power modulations and failure scenarios, where one or\nmore cavities may trip, requiring the remaining cavities to compensate. An adjustable coupler is needed\nto cover a QL range from 9 \u00d7 105 to 4.5 \u00d7 106, as required for the t\u00aft working point, to minimise the\n146\n\nZ: \ud835\udc43HOM \u224863.2 kW\n2.1 kW\n4.0 kW\n6.0 kW\n4.4 kW\n6.4 kW\n5.1 kW\n6.9 kW\n5.1 kW\n6.6 kW\n4.0 kW\n5.5 kW\n6.5 kW\nBeam\n(a)\nt \u04a7t: \ud835\udc43HOM \u22482.8 kW\n0.98 kW 0.03 kW\n0.13 kW\n0.09 kW\n0.12 kW\n0.10 kW\n0.10 kW\n0.11 kW\n0.04 kW\n1.05 kW\nBeam\n(b)\nFig. 3.32: (a) The figure displays an approximation of the HOM power distribution at the Z operating\npoint in a cryomodule configuration consisting of four 2-cell 400 MHz cavities, each equipped with two\nhook-type couplers for trapped dipole mode damping, and two coaxial lines on the beam pipe for HOM\npower extraction. The total HOM power propagating through all eight hook-type couplers is approxi-\nmately 0.7 kW. (b) An approximation of the HOM power distribution in a cryomodule configuration\nwith four 800 MHz cavities at t\u00aft operation. Each cavity has two DQW HOM couplers. Most of the\nHOM power propagates out through the beam pipes, requiring beamline absorbers between modules. In\nboth cases, BS bunch length is considered for HOM power calculation.\n4\n6\n8\n10\n12\n14\n16\n18\n20\n0\n1\n2\n3\n4\n5\n6\n7\nZ: SR\nZ: BS\nFour 400 MHz 2-cell-cavity module with tapers\n4\n6\n8\n10\n12\n14\n16\n18\n20\n50\n100\n150\n200\nZ: SR\nZ: BS\nFour 400 MHz 2-cell-cavity module with tapers\nFig. 3.33: The figures show the loss factor (left) and HOM power (right) at the Z working point for 2D-\naxisymmetric modules consisting of four 2-cell cavities with tapers at both ends and no couplers. Circle\nmarkers highlight the loss factor and HOM power corresponding to the BS and SR bunch lengths at the\nZ working points.\ninput power to \u224880 kW (Table 3.9).\nAt 800 MHz, the couplers installed on the 6-cell cavities for the t\u00aft require QL,opt = 4.2 \u00d7 106 to\noperate at \u2248200 kW. The same concept of the adjustable FPC is foreseen to unify the coupler designs\nwith the collider and booster 800 MHz RF systems. The QL range is from 4.2 \u00d7 106 to 2.7 \u00d7 107, which\nis a compromise between the tuning capabilities and RF power overhead (see Section 6.3).\n147\n\n\ud835\udc3ftune\n(a)\n\ud835\udc3ftune\n(b)\nFig. 3.34: The RF models of the 400 MHz(a) and 800 MHz(b) power couplers, along with their mechan-\nical representation concepts. Ltune is used to adjust QL when transitioning between working points by\naltering a waveguide plate on the air side of the coupler.\nAt 400 MHz, with a nominal power of approximately 400 kW, the proposed design concept in-\ncorporates an alumina ceramic disc window positioned within the rectangular waveguide, following an\napproach similar to that developed for Linac4. This configuration includes a step transition to a vertically\nmounted coaxial coupler, which interfaces with both the cavity and the surrounding cryomodule. The\nplacement of the ultra-high vacuum (UHV) boundary within the rectangular waveguide presents logistic\nchallenges for assembly, as the insertion into the outer vacuum vessel is intended to occur outside the\nclean room. However, technical solutions involving localised enclosures are being explored to address\nthese constraints.\nAt 800 MHz, for a nominal power of 200 kW, the design adopts a more conventional annular\ndisc window within the coaxial section of the coupler. Integration with the conceptual design of the\n800 MHz cryomodule necessitates an innovative approach to the structural support system, ensuring that\nthe horizontally mounted coupler is adequately supported while avoiding hyperstatic constraints that\ncould impede thermal expansion. Engineering solutions to address these challenges are currently under\ndevelopment. The RF models of both couplers, along with their respective mechanical design concepts,\nare presented in Fig. 3.34.\n3.4.11\nSRF cryomodules\nTwo types of cryomodules are planned to accommodate the 400 MHz and 800 MHz cavity strings, cov-\nering the four operating modes of FCC-ee. The first type is designed for operation at 4.5 K and will\nhouse four 2-cell 400 MHz cavities, with a total length of 11.24 m. For the 6-cell 800 MHz cavities, the\ncryomodule will be designed to operate at 2 K, with an expected total length of 10.25 m.\nThe RF design of the cavity string has been refined through iterative development to optimise sev-\neral key aspects: improving the integration of mechanical elements such as bellows and flanges within\nthe string, enhancing the overall integration of the string within the cryomodule, including the orienta-\ntion of rigid components such as fundamental power couplers (FPC) and coaxial extractors, and ensuring\ncompactness and efficient longitudinal integration within the FCC tunnel.\nThe 400 MHz cryomodule conceptual design includes an isostatic supporting system for the cavi-\nties that allows free thermal contraction of the different elements, the weight of the FPC and the vacuum\nforces are intended to be discharged on the vacuum vessel. Helium tank, tuner and reinforcement struc-\ntures are still to be engineered. In the conceptual design, the space occupation has been identified by\nrescaling the correspondent elements of the LHC cryomodule. In Fig. 3.35 it can be seen that there is\nlimited clearance to integrate the actively cooled thermal shield and magnetic shield, not present in the\n148\n\nFig. 3.35: Lateral and front view of the 400 MHz cryomodule.\nLHC cryomodule. The cryomodule outer diameter is constrained by the length of the FPC outer conduc-\ntor, actively cooled with supercritical helium at 4.5 K. There is a margin to reduce this value towards a\nmore compact cryomodule design once the FPC maximum power and RF losses for the Z working point\nare finalised.\nThe current cryomodule design and assembly sequence are based on a cylindrical vacuum vessel,\nwhich is the preferred choice for maintaining structural integrity under vacuum forces. This design\nis commonly used in machines with a large number of cryomodules, such as XFEL and LCLS-II. A\ncylindrical vacuum vessel also presents a cost-effective solution in several respects. First, it simplifies\nmaterial procurement, as it allows the use of low-carbon steel tubular products. Second, it facilitates\nan industrialised assembly process, following established practices from previous machines, where the\ncavity string slides into the vacuum vessel without requiring the vessel itself to be cleaned to cleanroom\nstandards at any point.\nHowever, the new fundamental power coupler (FPC) design, which incorporates a ceramic window\nin the waveguide, necessitates a revision of the assembly process. The first integration approach, which\nis compatible with the current cryomodule conceptual design, involves inserting the coupler antenna\nand ceramic window in a second step\u2014after the cavity train has been placed inside the vacuum vessel.\nThis would be achieved using a local cleanroom or a glovebox. The local cleanroom approach has been\nsuccessfully employed for FPC maintenance in other facilities, such as ESS, XFEL, and SNS, but it poses\na potential risk of cavity contamination. Therefore, both the local cleanroom concept and the associated\nassembly procedure must be designed and thoroughly validated with prototype testing before finalising\nthe current cryomodule design.\nIf this integration method proves too complex or incurs excessive R&D costs, an alternative design\nis under consideration. This would involve a vacuum vessel composed of two separate sections, as used\nin other projects such as Crab cavities and SPL. In this configuration, the top part of the vessel would\nbe brought into the cleanroom along with the cavity string, enabling the FPC assembly to take place in\na fully controlled clean environment. While this solution minimises the risk of cavity contamination, it\nintroduces significantly greater complexity and increases the cost of the vacuum vessel.\nThe design of the HOM for the 400 MHz cryomodule is determined by the highest power extrac-\ntion requirements at Z operating point, the coaxial extractors in between cavities should be dimensioned\nto extract up to 6 kW-10 kW each. Thus, the coaxial extractors shall be rigid connectors (PHOM \u00d76\n> 1 kW) reducing the freedom in the port positioning across the vacuum vessel, with complications in\nmatching the routing and the assembly and maintenance needs. For the absorption of the HOM power\nleaking through the beam pipe, it is foreseen the integration of warm BLA in the cryomodule inter-\nconnection regions. Examples of water-cooled BLA have been tested for EIC, and their impact on the\nmachine reliability and cavity contamination is now under assessment.\n149\n\nThe 800 MHz cryomodule conceptual design, Fig. 3.36, is based on the PIP-II HB650 cryomodule,\nwith the strong back support for the cavity string, and has been developed in collaboration with FNAL.\nFig. 3.36: Lateral and front view of the 800 MHz cryomodule.\nThe parameters that require adjustment of the current PIP-II design are: (i) the power for the\nFPC, (ii) the presence of HOM extractors, (iii) the requirement of the design to be compatible with\nboth segmented and continuous architecture. The FPC of the HB650 cryomodule, designed for a peak\npower of 65 kW, has a bellows in the outer conductor to decouple thermo-mechanically the waveguides\nfrom the outer conductor, avoiding transmitting cantilever forces to the cavity string. The bellows must\nbe eliminated from the FCC FPC design, given the requirement of 250 kW of forward RF power to be\ntransmitted. Active cooling is preferred for the cooling of the FPC outer conductor, using supercritical\nhelium at 4.5 K to be able to adjust the cooling capacity by adjusting the helium flow rate in the different\nworking points and phases of machine operation. The requirements for the HOM extractors for the\n800 MHz cavity string are still under definition due to the necessity of introducing BLAs. The current\ndesign is compatible with a continuous machine architecture, although if the power to be extracted from\nthe BLAs is too high to be dumped in the cryogenic lines (XFEL design for 100 W) the requirement\nof warm BLA would push towards a segmented architecture for the 800 MHz cryomodule, as curently\ndefined for the 400 MHz. The conceptual design of both cryomodules is well advanced, in both cases\nthe FPC remains the most critical component to design and integrate and may require modifications to\nthe current models. The current design allows some space contingency: the next step will focus on the\nengineering and dimensioning of the components inside the cryomodules.\nTo address the definition of the RF cryogenic capacity needs, heat load budgets have been calcu-\nlated for both cryomodules. The values of static heat loads in Table 3.14 include a 50% margin to account\nfor the preliminary level of maturity of the two design concepts. This margin will likely decrease when\nTable 3.14: Cryomodules heat loads budget.\n400 MHz\n800 MHz\nMax. heat load to thermal shield per CM [W]\n327\n180\nMax. static heat load to 4.5 K / 2 K bath per CM [W]\n197\n56\nMax. dynamic heat load to 4.5 K / 2 K bath per CM [W]\n619.2\n130.2\nengineering the cryomodule internal components. The dynamic heat loads only account for the power\ndissipated by the cavity at the nominal values of Q0 and Eacc. The heat loads from power coupler, HOMs\nand non-superconducting elements of the beamline are not included. It is noted that the values of Q0 and\nEacc are target values of the R&D processes (Table 3.11). At present, there are no elliptical 2-cell and\n6-cell cavities with the stated performance at 400 MHz and 800 MHz, respectively, the specifications are\n150\n\nbased on the rescaling of performance obtained at different frequencies, with different surface treatment\nrecipes. The stated performances rely on the success of the R&D programmes.\nFor the dynamic loads, it was assumed that at least a 20% operational margin should be added to\nthe nominal value to ensure machine operation with up to 10% faulty or unpowered cavities, and voltage\nneeds being compensated by increasing the gradient of the remaining cavities. For both cryomodules\npreliminary cryogenic schemes have been defined, together with the dimensions of the cryomodule inner\npipes. The cavities are immersed in a saturated helium bath, the helium tanks are connected on top\nthrough a 2-phase tube, from which vapour pumping and pressure control ensures temperature control of\nthe helium bath. Cavity cool-down is done from a lower point through a valve-controlled line at 4.5 K.\nSteady-state operation filling is ensured by a valve directly feeding the 2-phase line. For the 800 MHz,\nFig. 3.37, the valve is a JT subcooling the liquid to 2 K. Helium level control in the 2-phase is ensured by\nliquid level measurement (LT) in a phase separator, connected to the bottom supply line, as in the helium\ntanks, so that the level can be measured in one point only (communicating vessels).\nFig. 3.37: Cryogenic scheme for the 800 MHz cryomodule.\nAn actively cooled thermal shield at 50 K is needed to intercept the conduction heat from the\nthermal bridges between ambient temperature and helium bath, such as the cold-to-warm transitions in\nthe beam tubes, cavities supporting system, etc. The static and dynamic heat loads linked to the FPC\nexternal conductor are gas-cooled through a double-walled heat exchanger; cold supercritical helium\nis injected at the coldest end of the FPC and is extracted at room temperature at the vacuum vessel\ninterface. Temperature-based mass flow regulation on each FPC is possible with warm valves outside\nthe CM. Finally, two burst disk exhaust lines protect the cavity circuit against overpressure in the worst-\ncase event of accidental venting of the cavity vacuum with air. For the less critical case of insulation\nvacuum break, only one of the two burst disks should be enough to evacuate the mass flow rate of\nhelium vapour. The scenarios in which the cryogenic supply is interrupted, or the machine is subjected\nto a power cut, are considered abnormal operating conditions which could happen frequently, not an\nemergency scenario. The limited mass flow will be recovered through the cryomodule return line \u2013 the\n151\n\nreturn valve default position is open in case of a power cut. If there are problems with the return line\nvalve, the helium mass flow will be released in the tunnel through a pressure relief valve, which ensures\nleak-tight reclosing. It is important to mention that this is a preliminary schematic, several components\nstill need to be included for cryomodule operation, for example the instrumentation, the valves and/or\nlines for individual cryomodule warm-up/cool-down,etc.\n3.4.12\nHigh power RF system\nThe high-power RF systems will comprise electrovacuum amplifiers and solid-state power amplifiers\n(SSPA), chosen to meet the RF power level required at different operating points and frequencies. For the\nFCC collider, the efficiency of electric power conversion from the grid to RF was considered a priority,\ntogether with cost-effectiveness and footprint minimisation. In the last three years, a novel concept of\nthe compact (3 m high) low voltage (<60kV) two-stage (TS) multi-beam klystron (MKB) [267] was\npioneered within CERN\u2019s High Efficiency klystron Project. Such a tube can generate CW RF power up\nto 1.2 MW at 400 MHz with very high efficiency \u2013 above 85%. TS MBK design was completed and\nis ready for prototyping in industry. TS MBK layout and the tube performance are shown in Fig. 3.38.\nIn the CDR and MTR, it was assumed that for the Z operating point, one tube would feed one cavity\nand then be reused for other operating points by splitting the RF output power. The novel TS MBK\ntechnology can be considered as an optimal choice for various high-energy colliders like CLIC, ILC and\nMuon Collider.\nFig. 3.38: Artist\u2019s view of TS MBK is shown on the left. Simulated RF power/efficiency performance of\nthe TS MBK operated at different High Voltage levels is shown on the right.\nThe present baseline FCC collider layout with a common 2-cell 400 MHz SRF cavity used for Z,\nWW, and ZH operating points reduces the maximum RF power needed for a single cavity from 1 MW\nto below 0.5 MW. In addition, the RPO mode leads to different RF power transient modulations for\nfocusing and defocusing cavities due to gaps in the beam filling schemes (Fig. 3.39). Thus, the single\n0.5 MW RF power source feeding one cavity was the solution that satisfied the requirements for all beam\nenergies.\nFollowing these changes, the TS MBK design was scaled down in RF power from 1 MW to\n0.5 MW, providing high efficiency as before with the original tube. However, analysis of the klystron\noperation with required RF power transient modulation regulated by the LLRF system brought the opera-\ntional efficiency of the tube down from 85% to 68%. The reason is that the highest efficiency is delivered\nby a klystron when it operates in saturation. Without changing the operating high voltage on a fraction of\nmicrosecond scale (not yet technically feasible), efficiency will be linearly degraded by reducing the RF\npower. CEPC adopted a possible solution using the depressed collector (5 stages) to recover the energy\nback into HV modulator [268]. At this point, klystrons will operate with an average efficiency of about\n152\n\nFig. 3.39: Transient RF power modulation profiles for two types of accelerating cavities (Z-pole).\n65%, but the overall RF system efficiency can be pushed up to 85%. This approach is not commonly used\nin industrial high-power klystrons, and it will result in a significant increase in the tube complexity and\ncost. Moreover, the transient nature of the recuperated beam power will require specialised electronics\nto return the energy to the DC modulator.\nA gridded tube, like an inductive output tube (IOT), is another class of electrovacuum device that\nis renown for their ability to operate efficiently in a wide range of output RF power levels regulated by\nthe input RF signals. For example, a 1.2 MW, 0.7 GHz multi-beam (10 beams) IOT was successfully\nprototyped in industry for ESS almost a decade ago [269], proving that powerful MB IOT is a mature\ntechnology. However, the practical efficiency in these tubes is limited to 70-75%. The extended IOT\nversion, called Tristron (a hybrid of triode and klystron) was proposed in the late 1960s, but it has never\nbeen commercialised. A tristron comprises an additional idler cavity located before the output cavity.\nThis cavity dramatically improves bunching quality and increases efficiency. A tristron was studied and\noptimised at CERN as a candidate for FCC RF power source [270]. The final MB (10 beams) tristron\ndesign at 400 MHz showed excellent performance in RF power range from 300 kW to 600 kW with effi-\nciency exceeding 90%. A snapshot of particle dynamics in the tristron and simulated RF power/efficiency\nperformance at different operating voltages are shown in Fig. 3.40. Compared to TS MBK, the tristron\nprovides a much more compact and cost-effective solution.\nFig. 3.40: Left: A snapshot of particle dynamics in the tristron simulated in 3D PIC CST. Right: RF\npower/efficiency performance at different operating voltages.\nThe RF power modulation waveform shown in Fig. 3.40 can be convoluted with the tube perfor-\nmance at a fixed voltage for the operational efficiency of the tristron at the Z operating point. , The\n153\n\ntristron transient efficiency simulated for the operating voltage of 46 kV is shown in Fig. 3.41. Despite\nthe very broad range of the RF power modulation required, a remarkably high average efficiency of\n88.7% can be obtained.\nFig. 3.41: Transient RF efficiency of the tristron when operated at the Z-pole.\nThe failure scenario of a single cavity trip was also studied. In this case, there must be a dramatic\nchange of the RF power modulation waveform, so that the peak RF power required can temporarily\nexceed 520 kW (Fig. 3.26). The proposed recovery scenario is based on the slow (200-300 \u00b5s) ramp-up\nof the tristron operating voltage from 46 kV to about 50 kV. At this new set point, the operating efficiency\nwill be slightly reduced: from 88.7% to 85.2%. For the WW and ZH poles the RF power transient sweep\nrequired will stay within 1%, thus, tristron will operate with an efficiency exceeding 90%, while similar\nperformance degradation is expected in failure scenarios. Finally, if a 1-cell 400 MHz cavity for the Z\noperating point is re-considered in the future, two tristrons can be combined through the 3-dB hybrid and\ndeliver 1 MW RF power. The booster and t\u00aft-pole will be operated with 800 MHz RF power sources.\nDirect scaling of 400 MHz of tristron to the higher frequency and reduced RF power (200 kW) is a\nstraightforward task, it will be initiated upon completion of the technical design of the 400 MHz tristron.\nThis 800 MHz tube will feed a different number of the cavities depending on its location: one tube per\ncavity t\u00aft collider and one tube per four cavities for the Z, WW and ZH poles and the booster.\nA preliminary 3D mechanical model of the tristron is shown in Fig. 3.42. The tristron development\nprogramme is separated into two phases. The first one is a technology demonstrator based on a retrofit\nand upgrade of the existing ESS MB IOT. This work will be done in a collaboration of CERN, ESS and\nThales. It is expected that the project can be completed on a short timescale of 12-18 months, providing\nESS with an additional option for the efficiency upgrades of their RF system in the future. The second\nphase is technical design and prototyping of a 400 MHz tristron for FCC. During this phase attention will\nbe focused on system optimisation and cost reduction. It is antcipated that a tristron prototype will be\nbuilt and tested 30-36 months after the formal project assignment between CERN and Thales.\nTristron technology will cover all the power and frequency ranges for FCC collider and booster\nat different energies. However, t\u00aft mode booster only requires 13 kW at 800 MHz to feed the cavity. It\nis then possible to split RF power into 10 cavities from the 200 kW tristron which is operated efficiently\nat a lower RF power of about 130 kW. However, the RF distribution system could be too bulky and\nexpensive. As an alternative, a 15 kW SSPA can be employed. There is no specific development of such\nan amplifier at CERN and most of the development is in industry. Recently it was reported that L-band\n6 kW GaN/SiC single transistors operated at 100 V are commercialised [271], providing drain efficiency\nof about 80%. So far these chips are operated at a low duty cycle (10%), but predictions are for further\nperformance improvements in the coming years.\n154\n\nFig. 3.42: Tristron 3D view (left) compared to TS klystron (right).\nThe RF power sources are grouped by RF units, each one being individually powered by a power\nconverter located at the surface. Fig. 3.43 summarises the distribution schemes for the collider and\nbooster at the different beam energy levels.\n3.4.13\nRF system integration in the tunnel\nThe integration studies of the RF system in the accelerator tunnel and in the klystron gallery were con-\nsidered as high priority and were completed to verify that: (i) the cryomodules and the dedicated services\nfit, with minor exceptions, in a tunnel with 5.5 m diameter, both for the collider and the booster ring (ii)\nthe RF equipment necessary for the t\u00aft mode working point fit in the 2032 m of the long straight section.\nThe civil engineering layout, transport constraints, cable trays and general services, as designed for the\narcs, were input to the study. The focus was the integration of the cryomodule, cryogenic distribution\nline and waveguide connection from the FPC to the klystron gallery. All the different working points\nwere considered to ensure feasible transitions from Z to t\u00aft and coherence in the beam positions between\nthe collider and booster rings, Fig. 3.44.\nThe cross section in Fig. 3.45 presents the 400 MHz cryomodule in point PH connected to the\ncryogenic distribution line (QRL) through the jumper. Some space was allocated along the QRL for the\nservice module containing the cryogenic valves and a local heat exchanger (if needed), in the sector with\nthe 800 MHz cryomodules at 2 K, in case the current baseline with a centralised heat exchanger is not\nviable.\nThe cryogenic services required for the t\u00aft working point will be installed at the beginning of\nmachine operation, including all the service modules and jumpers required to feed all the cryomod-\nules. A platform has been included on top of the QRL for the access and maintenance of the FPC and\nwaveguides. Access to both sides of the cryomodule is ensured for the maintenance of the HOM cou-\npler connectors and tuner in case of need. In point PH the 800 MHz cryomodules sit in the shadow of\nthe 400 MHz cryomodules, thus integration is less critical. The cross section in Fig. 3.46 presents the\n800 MHz cryomodule in point PL, the same cryomodule design will be compatible with installation on\nthe ground, for the collider, and installation on an elevated platform for the booster, for this reason the\nFPC is horizontally oriented.\n155\n\nFig. 3.43: High power RF distribution layouts for the collider and booster.\nFig. 3.44: RF longitudinal integration of the 400 MHz cryomodules in point PH, and waveguide system\nlayout from the FPCs to the klystron gallery\nThe clashes highlighted in dashed lines can be resolved with the adaptation of the general services,\npavement and false ceiling to the requirement of the RF straight section, different to what is required\nin the arcs. The beam height in the RF straight section should be increased, from the current value of\n980 mm in the arcs, to 1200 mm to accommodate the current design of the 400 MHz cryomodule to avoid\nthe clash between the cryomodule supports and the pavement. Several solutions are under evaluation,\nin case the diameter of the cryomodule cannot be reduced, a slope in the tunnel should be introduced to\nlower the pavement in only the collider straight sections. After the revision of all the civil engineering\nand the services, it will also be possible to refine the integration work by adding more details, i.e., patch\npanels for warm valves, water pumps for the FPC inner conductor cooling, HOM load dumpers and BLA\n156\n\nFig. 3.45: 400 MHz cryomodule, integration in point PH (collider). Non-accelerated beam on the right\nof the cryomodule is necessary for Z and WW working points only.\nFig. 3.46: 800 MHz cryomodule, integration in point PL (booster).\nwith the dedicated water cooled circuits, etc. In the following design stage, the integration work will be\nrefined to adjust the position of the non-accelerated beam, necessary for Z and WW working points, to\navoid it being in the transport/passage area.\nThe collider beam positions and spacing in the RF straight section at the various working points\nwill be achieved by a beam optics system for beam separation and recombination (see Fig. 3.47). It is\n157\n\nimportant to underline that, in point PH both collider beams need steering, the position of the incoming\nbeam needs to be adjusted compared to the arcs, otherwise, the cryomodule would be centred in the\nmachine tunnel, strongly protruding in the transport/passage area. It has been possible to maintain the\nbeam spacing in the collider at point PL at 350 mm, as in the arcs.\nFig. 3.47: Beam location required at the arc-RF interconnection region, in point PH (top and centre) and\nin point PL (bottom).\nThe longitudinal integration of the RF equipment along the long straight section was also con-\nsidered, in parallel with the disposition of klystrons and bunkers in the klystron gallery. A vertical\narrangement of the booster and main rings is chosen to ease the installation of the waveguide lines in\nthe ducts. Thanks to a concrete chicane located at the duct entrance, the level of X-rays in the klystron\ngallery will be limited, thus allowing personnel access to the klystron gallery during commissioning and\noperation. Seven 400 MHz cryomodules and eight 800 MHz cryomodules are placed between two con-\nsecutive quadrupole magnets, whose location vertically corresponds to the location of the bunkers in the\nklystron gallery. This choice for the longitudinal integration maximises compactness and accounts for\nthe constraint that every bunker can have a maximum of four klystrons on each side. The disposition of\nthe RF equipment, at the t\u00aft working point, on each side of the IP point is summarised by the scheme in\nFig. 3.48.\n158\n\nFig. 3.48: Scheme illustrating the distribution of cryomodules and quadrupoles in point PH (left) and\npoint PL (right).\n3.4.14\nR&D on SRF\nConsidering the timeline of the FCC-ee project, there is sufficient opportunity to conduct R&D aimed at\nenhancing the performance of SRF cavities. This would enable the optimisation of both the size and cost\nof the overall SRF systems [272].\nThe 400 MHz cavities built with the Nb/Cu technology require advanced engineering techniques\nfor the copper substrates. The design and fabrication of two bulk seamless 400 MHz copper cavities are\nongoing (see Fig. 3.49), allowing the ultimate SRF performance with this geometry and Nb/Cu copper\ntechnology to be assessed without the effect of welds in the equatorial area.\nFig. 3.49: Design and fabrication of the first 400 MHz 1-cell cavity machined from bulk copper.\nHydroforming technology, which is highly attractive for series production, is being explored in\ncollaboration with KEK. The development of internal welding techniques is also being pursued, in par-\nticular, the welding of the RF ports on the cavity beam tubes.\nElectropolishing is the best technique for preparing the surface of copper substrates for low surface\nroughness. The electropolishing setup has been available at CERN since 2022 and was successfully\nbenchmarked on smaller cavities. Some R&D is still needed to optimise the polishing parameters on\nlarger cavities, but a first successful attempt was on an LHC type 1-cell 400 MHz cavity with a simplified\ngeometry (without RF ports - see Fig. 3.50). The most promising coating approach of niobium on copper\n159\n\nis high-power impulse magnetron sputtering (HiPIMS), which has shown excellent results on several\n1.3 GHz 1-cell cavities. It was performed on a 400 MHz LHC type cavity in 2023 and the test results at\n4.5 K and 1.7 K were reported in the mid-term report.\nFig. 3.50: Electropolishing and niobium coating of a simplified LHC 400 MHz cavity.\nFor the 800 MHz cavities built in bulk niobium, the 5-cell bare cavity developed by JLAB on a\nsimilar RF design shape has already demonstrated that an accelerating gradient of 30 MV/m is achievable\nwith a quality factor of Q0 = 3.0\u00d71010 . To reach a Q0 = 3.8\u00d71010 or higher values, a dedicated R&D\nprogramme in collaboration with FNAL [273] is on going. It will be based on a combination of nitrogen\ndoping and mid-temperature bake-out, inherited from the 5-cell 650 MHz cavity R&D performed within\nthe PIP-II project.\nAn innovative concept of the slotted waveguide elliptical cavity (SWELL) is being developed [274\u2013\n276] in parallel to the baseline study. The design consists of elliptical cavities where longitudinal waveg-\nuide slots crossing perpendicularly to the RF surface are added to damp transverse HOMs. Thanks to\nthis approach, the cavity is seamless by its nature and can be built by sectors, which is very appropriate\nfor precise manufacturing techniques. This quadrant-based configuration allows direct access to the RF\nsurface when separated, thus facilitating the surface preparation, surface inspection and thin film depo-\nsition (with any kind of superconducting material). The cavity is also robust against frequency detuning\nby Lorentz forces or microphonics, and allows cryogenic cooldown with a significantly reduced volume\nof liquid helium.\nRF design efforts led to 400 MHz 2-cell and 800 MHz 6-cell SWELL cavities as alternatives\nwith almost one order of magnitude better transverse impedance damping. A prototype of a simplified\nSWELL version of a 1-cell 1.3 GHz elliptical cavity has been fabricated for a feasibility demonstration of\nthis new concept (see Fig. 3.51). The cavity was installed in a vertical cryostat at CERN in August 2024.\nThe Q0 factor was measured at 2.2 K using a self excited loop (SEL) digital LLRF system and the stan-\ndard decay time procedure. After tens of hours of RF conditioning of low-field multipacting barriers, the\naccelerating field has been gradually increased. At Eacc = 1.1 MV/m, the cavity quenched repetitively,\nmost likely due to the presence of a surface defect observed on one quadrant before cavity assembly.\nThe cavity reached a quality factor of Q0 = 1.0 \u00d7 1010 at 1 MV/m with a very good reproducibility.\nThis corresponds to a residual surface resistance of 20 n\u2126as shown on the plot in Fig. 3.51, which is\na remarkable result for such a complex RF structure. It demonstrates, in particular, that no RF leakage\noccurs through the slots and in the contact surfaces of the quadrants. Additional niobium re-coatings,\nsurface treatments and cold RF tests are planned in the next months to study and fully qualify this very\nattractive and innovative concept.\n160\n\nFig. 3.51: SWELL cavity prototype design, fabrication and test.\n3.5\nSurvey and alignment systems\nThe survey and alignment systems and strategy are based on the steps detailed in this section. Machine\nand detector components undergo fiducialisation and assembly measurements at the surface to ensure\nprecise alignment once installed in the tunnel. This process begins with marking the floor to indicate the\ndesignated positions for the jacks that will support each component. After placement, these jacks are\nsurveyed to confirm their correct positioning.\nFollowing this, absolute alignment is carried out relative to the underground geodetic network,\nestablishing a stable reference for all components. Once the components are interconnected, a process\nknown as smoothing is performed to refine their relative alignment, ensuring seamless integration.\nThe final and most time-consuming phase of alignment involves maintaining the initial precision\nover time. This aspect is particularly critical for a newly constructed tunnel, such as that of FCC-ee,\nwhere long-term stability must be carefully monitored and preserved.\n3.5.1\nAlignment tolerances for the FCC-ee machine\nThe initial mechanical alignment tolerances assumed for the FCC-ee arcs are described below. It is as-\nsumed that adjacent arc quadrupoles and sextupoles are pre-aligned at 50 \u00b5m accuracy with respect to\na common \u223c6 m long girder. In the tunnel, the alignment tolerances from girder to girder or between\ngirders are 200 \u00b5m over 50 m and 500 \u00b5m over 200 m. In the interaction regions (IR), transverse mis-\nalignment errors for quadrupole and sextupole reference axes are taken to be \u00b1100 \u00b5m (1\u03c3) (\u00b1 250 \u00b5m\n(1\u03c3) longitudinally, and \u00b10.25 mrad in roll). Current requirements regarding the alignment are of 30 \u00b5m\nfor the final focusing quadrupoles; the LumiCal will need to be aligned at 50 \u00b5m, and the screening and\ncompensation solenoids at 100 \u00b5m (all values referring to 1\u03c3).\nThe figures presented above represent misalignment errors at the level of the reference axis, in-\ncorporating both the fiducialisation process and the subsequent adjustment steps. To meet the specified\n161\n\nalignment requirements, position determination and adjustment solutions will need to achieve precision\nand accuracy at least three times higher than the stated tolerances.\nWith regard to fiducialisation, the required measurement tolerances are well within reach for syn-\nchrotrons operating under stable environmental conditions with rigid support structures. However, for\nFCC-ee, the process must be automated due to the large number of girders and components that require\nfiducialisation and pre-alignment.\nFurthermore, in a newly constructed tunnel such as that of FCC-ee, where stable and unstable\nareas have yet to be identified, a significantly greater number of components will require (re)alignment\ncompared to the LHC. The implementation of automated solutions will be essential in achieving and\nmaintaining the necessary alignment standards over the machine\u2019s operational lifetime.\n3.5.2\nAlignment tolerances of FCC-ee experiments\nThe alignment accuracy for the assembly of the experiment is assumed to be similar to those of the LHC\nexperiments, i.e., 0.5 mm with respect to the machine geometry. The positioning and stability tolerances\nand requirements of each sub-system of the FCC-ee experiments need to be identified in order to estimate\nthe means of adjustment.\n3.5.3\nTheoretical data\nThe spatial position and orientation data for the beamline elements including the FCC detectors need\nto be extracted from the beam optics calculations such as BEATCH/MADX beamline definition files.\nAdditional parameters necessary for geodetic metrology can be derived from the layout drawings of the\ndetectors.\n3.5.4\nMetrology\nIn addition to the metrological controls of detector and machine components throughout the manufactur-\ning and assembly process, the final transfer measurement of the component axis, called fiducialisation,\nis a major step in the metrologic controls and is mandatory for later alignment. This job is carried out\nfor each piece of equipment whose precise alignment parameters are to be determined. The proposed\ntechniques are similar to those proposed for the Compact LInear Collider (CLIC), i.e., laser tracker and\nclose-range photogrammetry. For smaller components, coordinate measuring machines (CMM) and new\ntechnologies such as frequency scanning interferometry (FSI) may be used, depending on the accuracy\nrequested.\nFor larger components, the effects of thermal expansion must be carefully accounted for and com-\npensated to ensure precise alignment. Metrology measurements should be conducted in a controlled\nenvironment to maximise accuracy. On-site measurements in the tunnel or experiment caverns should\nbe minimised, as they inherently introduce uncertainties that can reduce the overall precision of the\nalignment process.\nThe feasibility of metrology measurements within the tunnel or caverns must be thoroughly as-\nsessed, as factors such as environmental conditions, spatial constraints, supporting systems, and concur-\nrent activities can impact measurement quality and accuracy.\nThe placement, number, and distribution of alignment targets (fiducials) on the components play\na critical role and must be determined based on survey requirements, selected alignment technologies,\nand the specific constraints of the experiment caverns and accelerator tunnel. Additionally, the support-\ning system must adhere to alignment specifications and constraints while following established survey\nguidelines [277].\nDepending on the object, the parameters of the fiducialisation are stored in the survey reports or a\ndatabase and can originate from metrology reports, geometrical quality control measurements or from a\n162\n\nspecific fiducialisation operation. The external fiducials are supposed to stay visible and accessible for\nthe various measurement operations during the lifetime of the component.\n3.5.5\nAlignment of accelerator components\nIntroduction\nThe alignment of the beam components of future CERN accelerators will be achieved with various\ntechniques depending on the alignment tolerance (mainly depending on component type and physics re-\nquirements), the sector concerned (long straight sections, arcs, transfer lines, injection/extraction zones,\netc.), the geometric dimension of the components, and the phase of the project (initial installation of the\nmachine, a single isolated component alignment, voluntary displacement, smoothing campaign).\nThe radiation level will also influence the instrumentation and methods chosen for measurement\nand alignment.\nMarking the beam line and supporting system on the floor\nUsing the MAD-X sequence files transmitted by the physicists in charge of beam optics, and prior to\nthe installation of the first component in the tunnel, the vertical projection of the beam point assembly\nand the position of specific component supports such as jacks must be traced on the ground. This will\nbe based on the geodetic reference network of the tunnel. This tedious work, previously done manually,\nshould be automated in the future (see below). The ground marking prepares the floor for the installation\nof the equipment support systems and later the components.\nPosition control of supporting systems\nFollowing the installation of the supporting systems of the largest and most voluminous components\n(mainly jacks), their position must be verified to ensure safe installation and to detect any positioning\nerrors prior to the critical component installation step. The positioning accuracy of the supports can be\neasily achieved with well-known and standard 3D measurement systems.\nComponent pre-alignment\nThe pre-alignment phase in the tunnel (not to be confused with the pre-alignment of components on\ngirders before installation in the tunnel) consists of the initial alignment of the components after their\ninstallation. This activity is performed using the absolute reference frame, i.e., based on the geodetic\nreference network of the tunnel.\nDuring this phase, the tolerance required is slightly less stringent than in the relative alignment\nstage of the machine (smoothing phase), allowing the use of 3D polar measurement techniques such as\ntotal stations and laser trackers.\nA similar approach will be used when aligning an isolated component, for instance, when replacing\na unit with a spare. In such cases, the new component is typically positioned relative to the nearest\nreference component to ensure continuity in alignment.\nOnce all components have been pre-aligned, they can be mechanically interconnected, ensuring a\nstable and precise overall assembly.\nMachine smoothing\nSmoothing consists of refining the relative position of neighbouring components to meet relative align-\nment tolerances and avoid offset between adjacent components.\nThe first step is to precisely measure the vertical and radial position of the whole machine or\nsection concerned. In the following step, components outside the alignment tolerances are identified and\n163\n\nwill be displaced.\nThe initial machine smoothing after installation is distinguished from maintenance smoothing,\nwhich is repeated regularly to compensate for displacements due to mechanical constraints, geological\nmovements or support instability. The frequency of periodic maintenance smoothing depends mainly on\nphysics requirements, ground motion and time available during the technical stops.\nIt is a relatively time-consuming activity. Thus, during machine operation, where maintenance\ntime is limited to yearly technical stops, it is not possible to measure the entire machine. Smoothing is\nthen restricted to some sensitive portions of the machine.\nGenerally, the acquisition techniques depend on the machine plane to be measured (vertical, radial)\nand on the accuracy required. For radial measurements, wire offset measurements are favoured, while\ndirect levelling is used for vertical position determination.\nOutside the arcs and within much smaller volumes (a few dozen metres at most), 3D polar tech-\nniques can also be used for machine alignment.\nThe most restrictive areas in terms of precision will be equipped with permanent and automatic\nmeasurement systems. In addition, most of the machines could, in principle, be measured by the remote\nalignment system to be developed, which is described below.\nTransfer lines\nThe transfer lines are different from the main machine in terms of geometry (continuously changing\nslope and roll), topology (fewer components and greater spacing) and the alignment needs as the beam\npasses only once. The alignment techniques will need to be compatible with these different constraints\nand in particular offset measurements and direct optical levelling are much more difficult to realise.\nNotion of primary and secondary components\nSince the machine components are of all sizes and weights, their stability in time is also different. The\nlargest and heavier components are more stable. These are usually magnets, such as dipoles, which have\nan impact on the trajectory of particles and are considered as \u2018primary\u2019 elements. The other components\nare qualified as \u2018secondary\u2019 elements.\nFrom a practical point of view, the precise alignment of primary components is generally per-\nformed during the smoothing campaign (see above), while secondary components are mainly aligned\nwith respect to the primary elements in a second phase.\nFor the FCC-ee the alignment tolerances of the dipoles are quite loose, e.g., at the level of 1 mm\ntransversely. The relative alignment of quadrupole magnets, sextupole magnets, and beam-position mon-\nitors (BPMs) is more sensitive. These elements, forming the arc \u2018short straight sections\u2019, should be pre-\naligned on common girders prior to installation in the tunnel, as it is being done for modern light sources.\nThe closest of these girders, which are about 25 or 50 m apart in the tunnel, should then be aligned with\nrespect to each other.\nImpact of component type on alignment\nThere are several categories of components, each with specific alignment tolerances.\nMagnetic el-\nements, which actively influence the beam, typically require more precise alignment in at least one\nplane\u2014whether roll angle, horizontal, or vertical. This is particularly critical for dipole and quadrupole\nmagnets, where small misalignments can significantly affect beam dynamics.\nBeam diagnostic equipment forms another group of components with distinct alignment con-\nstraints. Some, such as beam position monitors (BPMs), require precise knowledge of their position\nrelative to the primary beamline. This can be achieved using beam-based alignment techniques, ensuring\noptimal accuracy in beam monitoring and control.\n164\n\nThe weight and dimensions of the components play a crucial role in determining the appropri-\nate supporting system and alignment strategy. Stability and safety considerations necessitate the use\nof isostatic supporting systems, which minimise structural deformations. Additionally, the mechanical\ndesign of the components must ensure that deformations remain negligible. The length of the compo-\nnents, along with associated lever arm effects, is a key factor influencing both alignment precision and\ninterconnections within the system.\n3.5.6\nInteraction regions including MDI\nThe alignment of the MDI is described further in Section 1.6.\nThe initial alignment in the interaction region, surrounding the MDI (\u00b1900 m around the IP) will\nbe performed with the rest of the collider.\nPosition monitoring is planned for the components for the incoming beam in this region, using a\ncombination of hydrostatic levelling systems (HLS), FSI distance measurements, wire positioning sys-\ntems (WPS), and inclinometers, resulting in a configuration similar to the HL-LHC. Knowledge gained\nduring CLIC studies (see [278] and [279]) could also be applied if needed. In addition, innovative sys-\ntems, such as the structured laser beam (SLB) [280], are being studied for use in this region.\n3.5.7\nRemote alignment and monitoring\nAlong the straight sections, for example, in the IR areas, the same alignment solutions as those proposed\nfor the implementation phase of the CLIC project can be used [138]. The solutions developed for CLIC\nwill certainly meet the FCC requirements. The transverse position of components will be measured\nwith regard to a long-range straight alignment reference over several hundreds of metres. Alignment\nsensors measuring the transverse offsets with respect to an alignment reference will be installed on the\ncomponents. Overlapping references will be used over very long distances, allowing a very accurate\ndetermination of one common straight reference. Two types of alignment references can be considered:\na structured laser beam (SLB), or a stretched wire. Both systems will have to be combined with a\nhydrostatic levelling system (HLS) which will provide relative vertical references.\nThe SLB can be defined as a pseudo non-diffractive optical beam, with a very bright central core,\nsharp boundaries, a minimal divergence and a theoretically infinite range (tested on 1 km). All of its\nproperties are under evaluation, and its application to the transverse alignment of components and, more\nparticularly, to the FCC-ee is the object of two PhD theses. The R&D on the SLB has just started.\nPreliminary studies indicate that maintaining the straightness of the SLB along its trajectory requires it\nto be enclosed within a vacuum pipe. However, due to the specific properties of the beam [281], the\nrequired pipe diameter is smaller compared to those used in optical-based alignment systems.\nStretched wires used as straight references are not at a development stage. They have been in use,\ncombined with WPS, for many years in the LHC for the continuous determination of the position of the\nlow beta quadrupoles. The same combination will be used for a full remote alignment system of the main\ncomponents of the long straight sections around IP1 and IP5 for the HL-LHC project. (see Refs. [282]\nand [283]). Their main drawback comes from the limited length of cables between each sensor and its\nremote electronics/acquisition system (maximum 120 m). Cables will be a great concern in the FCC-\nee tunnel, from the integration/space available and radiation perspective. One R&D development to\novercome this issue would be the development of WPS sensors based on FSI measurements (replacing\nthe current capacitive technology). A \u2018chained\u2019 optical fibre configuration could be developed that would\ntake far less space in the tunnel and could be compatible with the high level of radiation expected during\nthe machine\u2019s operation.\nExtrapolating such solutions to the arcs will require additional R&D as there is currently no solu-\ntion allowing the permanent monitoring of the position of components in the arcs. Alignment solutions\nhave been developed for straight portions, not circular ones and should be adapted, either using the spe-\n165\n\ncific properties of SLB, or developing a new configuration of alignment references based on \u2018broken\nlines\u2019 of wires.\nPosition adjustment is an activity that will be challenging to automate. Since 3D adjustments\nof components are required, continuous monitoring is essential when using actuators to perform these\nadjustments in all three dimensions. This ensures that the bellows at the extremities of the component\ncan accommodate the displacement without excessive stress or deformation. Additionally, for longer\ncomponents, even small movements can create significant lever arm effects, leading to unintended shifts\nat the opposite end. Real-time monitoring throughout the adjustment process is, therefore, necessary to\nmaintain alignment precision and prevent mechanical strain.\n3.5.8\nSurvey robot options\nGiven the size of the collider, many alignment steps will have to be automated, from the 3D scans to the\ninitial alignment. A few examples of robot options are provided below. 3D scans could be performed by\na \u2018dog robot\u2019, provided that there are permanent targets which define the underground network and allow\nthe geo-referencing of scans. For the step consisting of marking the beam axis and the jack position on\nthe tunnel floor, increasing numbers of floor marking robots piloted by tacheometers are now available\non the market. An automatic inspection of the position of components pre-aligned on girders could be\nperformed with high accuracy by a robot in the tunnel once the girder is at its final location. In all cases,\nadaptations to the specific tunnel configuration and the underground geodetic network will be necessary.\nThese may include increasing the density of the network and incorporating permanent targets that various\ntypes of instruments can measure to enhance alignment precision.\n3.5.9\nImpact of beam-based alignment on alignment system requirements\nThe FCC-ee design assumes one BPM close to each quadrupole. Beam-based alignment (BBA) will\ndetermine the BPM position offsets (reflecting both mechanical and electrical errors) with respect to\nthe magnetic centre of the nearby quadrupole and sextupole magnets, and it will help steer the beam\nthrough the magnetic centre of these elements by using orbit correctors along with dipolar and (skew)\nquadrupolar trim coils to minimise feed-down effects. Instead of relying on magnetic trims, Beam-Based\nAlignment (BBA) could also be carried out using movers. While movers are not included in the current\nbaseline scenario for the arcs, they could be a viable solution for the strong sextupole magnets in the\nexperiment insertions. If movers were to be implemented, their displacement range would determine\nwhether additional measurement systems are required to assess potential risks and ensure safe operation.\nSince BBA must be performed regularly to monitor and correct possible alignment drifts, the choice of\nadjustment mechanism should also consider long-term stability and operational efficiency.\n3.5.10\nExperiments\nIn the FCC-ee experiments, the geodetic metrology survey work will be performed in different steps:\ndesign, manufacturing construction, assembly and alignment of the detector elements. This means:\n\u2013 Participating in the project at an early stage, e.g., when collecting the geometrical parameters,\nalignment needs and discussing the integration of the survey needs in the design of the infrastruc-\nture, tools or detector elements.\n\u2013 Providing the necessary geometric data for adjustment and control of the assembly infrastructures.\n\u2013 Providing the position and orientation information related to the FCC-ee detector assembly and\ntests, i.e., the geometric information:\n\u2013 for the detector assembly tooling alignment,\n\u2013 for the geometrical follow-up and adjustment of the detector elements during assembly,\n\u2013 for the positioning of the detector elements for tests.\n166\n\n\u2013 Establishing, measuring, computing and maintaining geodetic networks or coordinate systems and\ndefining the parameters linking them when needed.\n\u2013 Providing surveyed position and orientation information to locate the detector in the CERN Coor-\ndinate System (CCS) and to link it to the accelerator geometry.\n\u2013 Providing, when necessary, metrology measurements for the fiducialisation of the detector ele-\nments as well as of module assemblies, as described in the metrology section above.\n\u2013 Providing, when and where necessary, geometric control and validation measurements for detector\nelements as well as of module assemblies.\n\u2013 Providing the control of the position and the alignment of elements and module assemblies in the\nexperiment area.\n\u2013 Participating in any upgrade projects at an early stage to ensure high-quality geometric information\nduring the lifetime of the detector.\n\u2013 Providing stability measurements of cavern walls and floor on demand.\nThis covers both the theoretical and the practical aspects of the geodetic metrology work for the FCC-ee\nproject. The theoretical positions of the beamline elements are provided by the accelerator optics team.\nIn-field measurements should be performed using suitable survey instrumentation and methods\nsuch as total stations, optical levelling, photogrammetry, 3D laser scanners or laser trackers.\n3.5.11\nLink of machine geometry to the experiment area\nThe very first geometric link between the tunnel geometry and the experiment cavern is expected to pass\ndirectly from the tunnel to the cavern while the access and visibility exist. In later stages, the geometric\nlink between the accelerator and the experiment area will be performed through the survey galleries using\ngeodetic methods and dedicated monitoring systems as described in the MDI section above.\nMarking out\nWith respect to the geodetic network, reference marks representing the projected beam line and the\nelements to be aligned can be painted on the floor and walls by the survey team. These marks help with\nthe installation of the services and beamline elements. Everybody working in their vicinity must ensure\nthat these marks remain visible. The marks and annotations required have to be defined in collaboration\nwith technical coordination.\nGeometric quality control measurement\nThe survey team should provide on-demand, where and when necessary, the geodetic measurements and\nanalysis for the geometrical and dimensional control of prototype and production elements.\nPositioning\nPrior to the installation of the detector elements, their supports are installed by others and pre-adjusted to\ntheir nominal position by the survey team. These survey interventions can also happen before the support\ninstallation if shims are required to overcome local floor deformations.\nOnce the detector elements are installed, their initial positioning will be carried out with respect\nto the geodetic network of the area. Precise survey methods and instrumentation have to be used, such\nas laser trackers, total stations and direct levelling.\nIn collaboration with the technical coordination of the experiment, the development and instal-\nlation of simple alignment systems for the positioning of the detectors after maintenance or equivalent\ncould be included.\n167\n\n3.5.12\nAs-built survey, 3D scans and measurements\nThe FCC-ee tunnel will have a diameter of 5.5 m. All services and cable paths will have to be optimised\ninside. Furthermore, the FCC project has a rather long lifetime: it is planned to dismantle the compo-\nnents of FCC-ee and replace them with a superconducting machine for the FCC-hh after 15\u201320 years\nof operation. It will be necessary to perform 3D scans of the empty tunnel as soon as possible, before\nany services are installed and subsequently perform 3D scans at well-defined milestones: all services in\nplace before the installation of components, all components in place, etc. The geo-referenced 3D point\nclouds obtained during the installation process will be highly valuable for verifying that components\nare positioned according to their theoretical locations and for identifying potential interferences between\nsystems. Additionally, these data will play a crucial role in facilitating the future installation of new\nequipment once the FCC-ee is in operation, ensuring seamless integration and minimising disruptions.\nIt is recommended to execute equivalent as-built measurements using 3D scans of the civil en-\ngineering structures in the experiment caverns, followed by as-built measurements of the infrastructure\ninstalled and, finally, the experiments in order to provide 3D documentation of the experiment areas\nof the FCC-ee and to save time during installation and future upgrade works. The survey team should\npre-process these measurements to give the geo-referenced point clouds and their 3D coordinates in the\nCCS, or a defined experiment coordinate system, to the integration team of the FCC-ee experiments.\nBy utilising 3D scans, a comprehensive digitisation strategy can be developed, incorporating data-\nto-cloud solutions for remote visualisation. This will enable access to detailed historical documentation,\nsuch as girder assembly records, while also supporting the implementation of digital twin technology. A\ndigital twin would allow real-time anomaly detection and advanced simulations, including studies on the\nimpact of temperature variations and other environmental factors.\n3.5.13\nSoftware\nThe Survey Database plays a critical role in storing all the parameters needed for surveyors to align and\ndetermine the position of accelerator components in the LHC era. This database stores the calibrated\ncomponent geometry (fiducialisation) as well as their theoretical positions within the global CERN Co-\nordinate System (CSS). It also contains an element\u2019s voluntary displacement (bump) and its measured\noffset to the theoretical position at a given date. Furthermore, it stores all the measurements acquired and\nother crucial information, such as calibration parameters of the instruments and sensors.\nFor the FCC-ee, the survey database will require similar capabilities, including the ability to handle\nan ever-increasing number of accelerator elements followed in 4D (3D position plus time). Additionally,\nfuture concepts such as girders housing elements and so-called cells will need to be accounted for in the\ndatabase.\nThe survey database will need to seamlessly interface with the digital twin framework and any\nBuilding Information Model (BIM) solutions implemented for the construction and maintenance of the\nFCC-ee accelerator infrastructure.\nTo support planned monitoring systems, the development of custom databases or integration into\na broader CERN-standard database will be essential. These databases must efficiently manage an ever-\ngrowing number of sensor parameters\u2014both existing and newly developed\u2014to ensure reliable data pro-\ncessing for computational models. Additionally, automated, robot-based, and as-built measurement data\nwill need to be incorporated, either within a dedicated system or as part of CERN\u2019s global database\ninfrastructure.\nMoreover, due to the inherent complexity of the data structure, dedicated APIs should be devel-\noped to enable secure and efficient access to internal data for various CERN applications, including\nsurvey-related tools. These interfaces will be designed using standard IT technologies, ensuring interop-\nerability with other systems and facilitating seamless data exchange across different platforms.\nGiven the sheer volume of data and the survey processes, special software will be needed for the\n168\n\ngeodesy, alignment, and survey processes. Commercial software may have serious limitations due to the\nspecificity of the alignment processes that involve combining several methods of observation, geodesy\naspects, and non-widely used sensors and instruments.\nEven though a significant level of automation is planned, in-field intervention of surveyors to ob-\nserve, check, and, in some cases, move an accelerator element will happen. As such, specific computing\ninterfaces will be needed to acquire geometrical observations from the survey instrument. In-house de-\nveloped solutions will provide the geometric data in a reliable and adapted way. New processes will\nrequire either the evolution of the current software such as SMART [284] and TSUNAMI [285] or the\ndevelopment of entirely new software adapted to the FCC-ee alignment strategy. Most likely, surveyors\nin the field will use a combination of existing commercial software that satisfies typical needs and fol-\nlows standard procedures, with in-house software that meets CERN and FCC-ee specific workflows and\ninstrumentation. Common rules, formats and standards should, therefore, be defined and implemented;\nthis strategy will involve strong and long-term industrial partnerships.\nMonitoring systems will also be put in place, and acquiring data from these systems will require\nspecial development to be integrated into future standards at CERN according to the evolution of the\ncontrol system IT-infrastructure (communication middleware and low-level framework controlling the\naccelerator equipment). Post-processing the permanently acquired data is a crucial step. It involves a va-\nriety of tools available to surveyors or machine-based routines to compute the positions and their related\nstatistics for numerous geometric elements such as points, planes, lines, or circles. In configurations\nwhere the monitoring system must provide real-time positions, for example, when synchronised with\nthe accelerator\u2019s timing system, optimisation strategies should be found and implemented in the global\ncalculation process. Collaborations with academic partners will be a key to success in developing new\nalgorithms and achieving the expected performance.\nThe main computation shell, LGC [286], will need to evolve or be re-developed to handle new\nmathematical models describing the behaviour of new instruments or sensors. It will need to be a single\npoint entry from across most of the survey, alignment, and geodesy projects. It will need to be able to\nhandle most of the survey processes and combine several sources of data in a reliable, fast, and integrated\nway.\nSpecial post-processing algorithms and dedicated routines, such as smoothing algorithms or best-\nfit processes for various geometric primitives will need to be available. Automated processes intended for\nfiducialisation, robot-based measurements or any other geometrical checks may also require dedicated\npost-processing tools and algorithms.\nIn summary, the feasibility study has provided valuable insights into the surveying, alignment, and\ngeodesy requirements for the FCC, highlighting the need for further analytical refinement and dedicated\ndevelopment to establish a robust software environment and adequate database. While many existing\nsolutions can be adapted, some aspects of the FCC-ee project will require the development of specialised\ntools or the evolution of current software. Particular attention must be given to data storage and manage-\nment strategies to ensure long-term accuracy, reliability, and interoperability with other systems.\n3.6\nBeam intercepting devices\nThe FCC-ee complex, including the collider, booster and injectors, will require several beam intercepting\ndevices to be installed in the various accelerators, covering a large variety of functionalities. At this point,\nthe following devices have been identified:\n\u2013 Positron target (injector)\n\u2013 Extraction dumps & spoilers (collider and booster)\n\u2013 Beamstrahlung (photon) dump\n\u2013 Betatron and momentum collimators\n169\n\n\u2013 Synchrotron radiation (SR) collimators\n\u2013 Interaction region (IR) masks and machine detector interface (MDI) devices\n\u2013 Injection protection devices (collider and booster)\n\u2013 Extraction protection devices (collider and booster)\n\u2013 Beam stoppers\n\u2013 Slits/scrapers\n\u2013 Collimators (booster)\nA detailed study and design process are required to ensure that all these devices meet their specific\noperational requirements. So far, three key components\u2014collimators, the positron target, and photon\ndumps\u2014have been identified as presenting significant technological challenges. Addressing these chal-\nlenges necessitates dedicated R&D efforts and prototyping to develop viable solutions.\nAs the functional requirements of additional components become fully defined, further challenges\nare expected to emerge. In particular, injection protection devices likely need to intercept a low-emittance\nbeam with high-energy density, a condition that could potentially damage or destroy conventional mate-\nrials. Therefore, advanced material research and innovative engineering solutions are critical.\nSimilarly, some of the interaction region (IR) and machine-detector interface (MDI) masks are\nexpected to experience substantial energy deposition, leading to significant thermo-mechanical loads.\nTheir design must adopt suitable materials and structural configurations capable of withstanding these\nconditions. In extreme cases, sacrificial protection devices may need to be incorporated to safeguard\ncritical elements and ensure long-term system integrity.\n3.6.1\nLepton dumps and spoilers\nSpecific dumps are necessary to safely absorb the beams from the collider and booster. There are two\ndumps for this purpose, one for positrons and one for electrons. Each dump will receive the beams from\nboth the collider and the booster. Preliminary estimates indicate that spoilers upstream of the dumps are\nnot required, as the beam will be sufficiently diluted that the dump can manage the thermo-mechanical\nloads safely.\nNevertheless, if, after detailed studies, spoilers are deemed necessary, they have already been\nstudied. The principle would be to use passive graphite cylinders some hundreds of metres upstream of\neach dump [287].\nThe design concept that is planned to be used for the dumps is similar to the current LHC dumps\n[288], i.e. a combination of different graphite and CfC grades, enclosed in a metallic, cylindrical vessel\n(Fig. 3.52). Also, the dimensions are expected to be similar to those of the LHC dumps (diameter in the\norder of 400-700 mm \u00d7 length \u223c5 m).\n3.6.2\nBeamstrahlung radiation dumps\nHigh-intensity beamstrahlung (BS) radiation is expected to be generated at the interaction points due\nto the synchrotron radiation emitted during the collision in the electromagnetic field of the opposing\nbeam. Dedicated devices are required to safely absorb the power carried by this beam, which can reach\nhundreds of kilowatts. One BS dump is required on each side of each interaction point; hence, a total\nof eight dumps are needed for the entire collider. One of the most efficient materials for absorbing this\ntype of radiation is lead. Moreover, in order to avoid thermal-stresses and unpredictable change of phase\nduring operation, liquid lead, circulated in a closed circuit, has been chosen as the baseline (Figs. 3.53 and\n3.54). Moreover, due to the strong dependence of the photon beam power to beam separation, a robust\nsystem capable of absorbing rapid power excursions is required. Research and development activity for\nthe optimisation of this device is ongoing, and a robust prototyping activity is envisaged in the next phase\nof the project.\n170\n\nFig. 3.52: Schematic diagram of the FCC-ee dump block design, showing the material for the dump core\nand the vessel.\nIn addition, a robust shielding enclosure needs to be installed around the liquid lead system so\nthat activation of the cavern and limitations to personnel access to the area are avoided. An alternative\ndesign using gas-cooled graphite discs is also being considered. Both design options are to be studied\nand prototyped to have a robust design for such a device.\nLd\nLinj\nWd\nHi\nHd\nHc\ndeff\nwindow\nPhoton\nwall\nArgon (cover gas)\nbeam\nPb inlet\noutlet\nEnergy Proj.\nFig. 3.53: Schematic of the FCC-ee beamstrahlung dump.\n3.6.3\nBetatron and momentum collimators\nThe design of these devices will depend on the operating requirements and the accident scenarios that\nthey may need to withstand. Since these devices are located in proximity (and even interact with) the\nbeam, special constraints are imposed so that their impedance is as low as possible.\nThe selected materials and geometries must preserve beam quality while ensuring that the devices\ncan withstand beam impacts under off-normal conditions, including potential accident scenarios.\nA total of 58 units will be required, covering all installations at point PF, within the experiment\ninsertions, and the shower absorbers. The design will incorporate key improvements based on operational\nexperience from the LHC and SuperKEKB collimation systems. Openable tanks will be implemented\nto facilitate maintenance and replacement, while optimised bellows movement will enhance mechanical\nflexibility and reduce wear. The use of high-performance absorbing materials will ensure the system can\nwithstand sustained beam loads without degradation, and enhanced radiation resistance will contribute to\nlong-term durability. Additionally, reliable actuation mechanisms will be developed to enable precise and\nrepeatable positioning. These design choices aim to maximise system robustness, ease of maintenance,\nand overall operational reliability.\n171\n\nFree-surface Pb\nFLUKA\nPhoton beam\nArgon medium\nWall\nLiquid Pb Flow\nVessel\nFig. 3.54: Preliminary simulation of liquid-lead beeamstrahlung dump.\n3.6.4\nSynchrotron radiation collimators\nThese devices have a different function to the betatron and momentum collimators. However, the design\nconsiderations and constraints are expected to be similar due to their proximity to the beam. The mate-\nrials and technologies selected for the hardware design will be based on the functional requirements. A\ntotal of 48 units will be required for operation.\n3.6.5\nInteraction region masks and absorbers\nAs their names suggest, these devices absorb secondary particle showers generated by upstream collima-\ntors and to protect sensitive hardware in the interaction regions.\nThe specific design of these components may vary depending on their exact function and installa-\ntion layout. They may incorporate either fixed or movable absorbing elements, depending on operational\nrequirements. Given the high-energy environment, high-density materials such as tungsten heavy alloys\nare preferred for their superior absorption properties.\nA total of 16 of these devices will be needed with two per beam positioned upstream of each\ninteraction point.\n3.6.6\nInjection protection devices\nThese devices protect the machine from any physical damage in case of injection failure (e.g., beam\non the wrong trajectory). These devices are expected to have a similar function to the TDIS for the\n(HL-)LHC machine (see Fig. 3.55).\nThe materials and design to be selected must fulfil the functional requirements whilst guaranteeing\nrobust protection of the machine elements that may be exposed to accidental injection failures. One\ndevice per injection point will be required (hence, a total of 2).\n3.6.7\nExtraction protection devices\nThese devices are responsible for protecting the machine from any physical damage in case of extraction\nfailure scenarios (e.g., a beam at the wrong trajectory). These devices are expected to hold a similar\nfunction as the TCDS/TCDQ system for the (HL-)LHC machine.\n172\n\nFig. 3.55: Front image of the (HL-)LHC injection protection device, the TDIS. It shows the two graphitic\nabsorbers, kept in place by a TZM back stiffener and TiGr5 clamps. The RF screen for the circulating\nbeam is visible on the right side.\nThe selected materials and design must meet the functional requirements while providing reli-\nable protection for machine elements that could be exposed to accidental injection failures. To ensure\nadequate safeguarding, one device will be required per extraction point, resulting in a total of two units.\n3.7\nBeam transfer systems and separators\n3.7.1\nBeam transfer\nThe concepts for the beam transfer systems of the collider and their associated requirements are discussed\nSection 1.8. This section focuses on a few systems but a comprehensive assessment of the technical\nchoices and specifications can be found in [178].\nThin septum\nFor collider injection, a very thin septum with an apparent blade thickness of up to 2.8 mm is required\n(see Table 1.18). The long pulse length of at least 304 \u00b5s prevents using an eddy-current, so the proposed\ntopology is a direct drive, under vacuum, septum. Figure 3.56 shows the mechanical concept for the\nseptum, with the thin blade carrying the drive current between the injected and circulating beam, shown\nin magenta. A circular perforated shield carries the image current of the circulating beam to minimise\nthe impedance.\nDuring injection, the distance between the blade and the circulating beam becomes very small.\nThe design will need to consider both synchrotron radiation and direct impact from the beam halo, with\nthe possible need for a specific mask to protect the thin blade of the septum.\nKicker systems\nFor the collider dump and injection systems, the kicker requirements are listed Tables 1.18 and 1.19.\nBenefiting from the design of a completely new accelerator complex, the same kicker hardware design\nwas selected for both systems. A ferrite-loaded lumped-inductance kicker magnet operating at relatively\n173\n\nFig. 3.56: Mechanical design concept for the collider thin, under vacuum, injection septum.\nlow current and voltage is selected. This choice of an out-of-vacuum magnet enhances reliability, reduces\ncosts, and simplifies maintenance, making it more favourable compared to other technologies, such as\nstriplines, considered during the feasibility study. Additionally, this magnet topology was previously\nimplemented in LEP, where it demonstrated reliable performance in a lepton collider environment.\nA primary constraint for the system presently considered is to rise and fall within the time between\ntrains, within less than 600 ns. This limits the maximum length of each kicker to 0.7 m and requires a\ntotal of 16 kickers for the injection and 18 for the dump. Every magnet will be connected to its generator\nwith a maximum cable length of approximately 250 m. Additionally, harmonising the systems across the\nFCC machine can lead to significant cost savings.\nFor the collider injection, two generator options are possible: a pulse forming network (PFN)-\nbased pulse generator or a Marx generator, with the latter being the preferred choice as it maintains a\nlower voltage. To compensate for the long flattop duration, a significantly large capacitor is required,\nnecessitating adequate space allocation in the service gallery. The magnets will operate in short-circuit\nmode for the dump system since there is no fall time requirement.\n3.7.2\nSeparators\n(a)\n(b)\nFig. 3.57: Schematic representation of the separator system function in PF (a) and the concept of an EM\nseparator combining electric and magnetic fields (b).\nAn electromagnetic (EM) separator is required at the entry and exit of the RF section to merge\nand separate beams travelling in opposite directions (see Fig. 3.57a). Operating for H and t\u00aft modes, they\nallow both beams to circulate on the same trajectory in the cavity.\nTo achieve this, perpendicular electric and magnetic fields are used to deflect the outgoing beam\nwhile allowing the incoming beam to maintain a straight trajectory, preventing synchrotron radiation\nfrom being directed towards the RF section. A key challenge lies in generating the extremely low mag-\n174\n\nnetic fields required to counteract the electric field in one direction, as remanent magnetisation can dis-\nrupt the delicate field balance. The current design concept [289], which explores shaping the end fields\nand potentially implementing an air-coiled dipole magnet, is under active investigation to ensure that the\nrequired field overlap is both technically feasible and stable (see Fig. 3.57b).\nAdditional design considerations include beam impedance, thermal loads, and the risk of high-\nvoltage sparks. To minimise impedance, the integration of ground electrodes along the length of the\nseparator has been proposed. However, synchrotron radiation striking these electrodes must be accounted\nfor in the cooling strategy. The potential for stray particles and electrical discharges further necessitates\na design that allows either collective or independent power regulation of the separators.\nMaintaining proper overlap of the electric and magnetic fields is another key challenge. Online\nmeasurements of the magnetic field or beam position could be incorporated into fast feedback loops,\nenabling real-time corrections to ensure field balance during operation. While the current design does not\ninclude active cooling for the electrodes, energy deposition due to RF heating and synchrotron radiation\nmust be carefully assessed. Although active cooling remains a viable option, its implementation would\nincrease both cost and system complexity [290].\nImportant uncertainties remain regarding the high voltage breakdown probabilities in the presence\nof synchrotron radiation. An R&D programme has been initiated to quantify this relation, but the present\nconcept addresses it by limiting the maximum electric field to 1.46 MV m\u22121. Electric breakdown during\nbeam operation will also need to be considered for interlocking and machine protection strategies, as the\nsudden loss of electric field will cause strong betatron oscillations of the circulating beam.\nDedicated DC septa magnets are needed towards the arc from this separator to further separate\nthe trajectories up to the nominal arc separations. Two groups with thin and thick septa will operate at a\nrelatively high field of up to 0.244 T for t\u00aft mode. The resulting high power of the synchrotron radiation\ngenerated will need specialised absorbers to protect other nearby components and downstream septa.\nThe combined system of EM separator and DC septa is required for the higher energy modes\nwhere the collider cavities are shared between the two beams. The present concept results from the initial\nstudies conducted [289,291] and a more detailed review of the overall implementation and operation of\nthe separator system will be needed in the technical design phase.\n3.8\nPowering systems\n3.8.1\nCollider Magnet Powering Systems\nGlobal optimisation of the magnet powering systems\nEvaluating cost-effective, efficient and reliable powering solutions is critical to assessing the feasibility\nof the FCC project. This requires balancing factors such as current density, number of turns, magnets\nin series, power converters location, energy storage systems and redundancy, while complying with\nconstraints like footprints, power losses, and machine performance.\nFor instance, increasing cable current density lowers capital cost by allowing smaller cross-section\ncables but raises operational costs due to higher power losses. Identifying a current density that min-\nimises total costs, both capital and operational, is crucial. Tunnel and alcove space must also be con-\nsidered: Is there room for larger cables, or should space prioritise high-current cables ? Could shorter\ncables reduce expenses further ?\nA comprehensive optimisation model addresses these complexities. This global model evaluates\ninterconnected systems/circuits configurations, machine placements, and constraints, providing action-\nable insights to guide design decisions. Sub-models for magnets, cables, trays, power converters, alcoves,\nand cooling systems were developed in collaboration with feasibility study teams. Figure 3.58 illustrates\ntheir interconnections, which are critical for global optimisation.\n175\n\nFig. 3.58: Interconnected sub-models within the global optimisation of the magnet powering systems.\nThe main output, total expenditure (TOTEX), combines capital (CAPEX) and operational (OPEX)\nexpenditures :\nTOTEX = CAPEX + \u03b1 \u00b7 OPEX\n(3.4)\nWhere TOTEX [CHF] is the total expenditure; CAPEX [CHF] is the capital expenditure; OPEX [CHF]\nis the operational expenditure; \u03b1 is the weighting factor, a parameter to balance the relative importance\nof CAPEX and OPEX.\nThe global model also outputs other important parameters such as power consumption, power\nlosses, material masses and carbon footprint. Key inputs include the number of alcoves, cable and\nmagnet current density, magnet turns and circuit configurations. Constraints include maximum voltage\ndrop and available cable trays.\nAn evolutionary optimisation algorithm, suited for multi-variable, non-linear and non-continuous\nsystems, iteratively determines the input parameters that minimise TOTEX while respecting constraints.\nThe model guided choices for magnet and cable parameters to identify cost-effective solutions.\nThe magnet parameters were refined by the magnet team to meet additional constraints and forms the\nbaseline of this report.\nCollider Magnet Circuits\nMagnet powering is performed by power converters in alcoves located either at the end of the straight\nsection or in the machine tunnel, called Big Electrical Alcove and Small Electrical Alcove respectively.\nThe installation of power converters in the machine tunnel is not considered due to space and radiation\nconstraints.\nThe location of the power converters is dictated by several factors, including the granularity of\ncontrol required, the maximum voltage tolerance of the cable insulation and the resulting impact on\nexpenditure for cables and converters. The granularity of control required by the optic layout :\n\u2013 Collider dipoles, as well as collider quadrupole focusing and defocusing magnets, can each be\npowered in series within their respective family.\n\u2013 Collider sextupoles need to be powered in groups of two or four (depending on the energy level).\n\u2013 Collider tapering magnets can be powered in groups of up to four consecutive magnets.\n\u2013 Collider correctors need to be powered individually.\nThe power converters for the collider dipoles and quadrupoles are installed in the big electrical\nalcoves at the end of the straight section.\nIn contrast, all other converters are located in the small electrical alcoves of the tunnel, as they\npower fewer magnets in series. Table 3.15 presents the quantity of magnets and circuits and the powering\nparameters.\n176\n\nMagnet specifications and quantities for the straight section and the injection is not yet defined,\nestimations were made.\nFor the Booster details, see Table 6.7 in Section 6.7.1\nTable 3.15: Collider Magnet Powering Circuits.\nMagnet\nCircuit\nPeak\nPeak\nQuantity\nQuantity\nCurrent (A)\nVoltage (V)\nDipole\n5680\n16\n3665\n420\nQuadrupole (F and D)\n2836\n32\n366\n1914\nSextupole (F and D)\n4672\n1168\n178\n284\nDipole Tapering\n5680\n710\n7\n148\nQuadrupole Tapering\n5672\n709\n9\n150\nHorizontal Corrector\n2824\n2824\n8\n47\nVertical Corrector\n2824\n2824\n14\n48\nSkew Quadrupole\n2824\n2824\n10\n44\n\u2020Straight Section\nn/a\n1666\nn/a\nn/a\n\u2020Injection\nn/a\nn/a\nn/a\nn/a\nCollider subtotal\n34 698\n12 773\n-\n-\nBooster Subtotal\n21 068\n7917\n-\n-\nTotal\n55 766\n20 690\n-\n-\n\u2020Magnet specifications not yet fully defined or nonexistent, values extrapolated\nPrecision of power converters\nConverter precision class is used to encapsulate metrics such as accuracy, reproducibility, stability, reso-\nlution and tracking. Depending on the precision class, the cost and complexity of the power converters\nvaries significantly. Table 3.16 shows the precision classes used for CERN power converters.\nCurrently power converters offering class 4 precision have been considered, but the current pre-\ncision requirements for the power converters remain unspecified. These requirements are essential to\ndetermine the precision class and, consequently, the cost implications of the converters.\nStandard precision converters (class 7) are readily available from manufacturers, offering a cost-effective\nsolution for most applications. However, a step higher in precision involves additional costs due to more\nstringent stability and resolution requirements, which remain manageable within standard practices. In\ncontrast, the highest precision converters, often required for the most demanding applications, are not\nonly difficult to manufacture but also come with substantial cost increases. Defining the precision class\nrequired is thus critical to accurately estimate the capital expenditure and to identify whether standard or\ncustom-designed converters will be necessary.\n177\n\nTable 3.16: HL-LHC Precision class and metrics.\nClass\n0\n1\n2\n3\n4\n5\n6\n7\nResolution [ppm]\n0.5 0.5\n1.0\n1\n1\n1\n1\n1\nInitial uncertainty after cal. [2x RMS ppm]\n2.0 2.0\n3.0\n7\n10\n50\n100\n200\nLinearity [max. ppm]\n2.0 2.0\n5.0\n8\n9\n20\n50\n100\nStability during fill (12 h) [2x RMS ppm]\n1.0 2.6 15.5 33\n39\n50\n100\n200\nShort term stability (29 min) [2x RMS ppm] 0.2 0.4\n1.2\n2\n5\n10\n20\n50\nNoise (< 500 Hz) [2x RMS ppm]\n3.0 5.0\n7.0 15\n19\n50\n100\n200\nFill to fill repeatability [2x RMS ppm]\n0.7 1.6 14.5 32\n38\n60\n100\n200\nLong term fill to fill stability [2x RMS ppm] 9.5 9.5 26.5 56\n64\n200\n500\n1000\nAvailability of Power Converters\nPlease see Section 2.4.4.\n3.8.2\nRF Powering\nThe RF systems of the FCC-ee machine will be distributed between point PH, which will host the col-\nlider RF, and point PL, which will house the booster RF. The RF infrastructure will evolve throughout\nthe operational lifecycle of FCC-ee, adapting to the different modes of operation. The primary RF am-\nplifiers will be tristrons (or potentially klystrons), while the booster in the t\u00aft phase will utilise solid-state\namplifiers (or possibly IOTs).\nThe tristrons will require a high-voltage DC supply, which will be provided by the RF main power\nconverter system. This system is planned to be located on the surface and will require a 40 kV AC supply.\nIn contrast, the solid-state amplifiers for the booster during t\u00aft operation will be installed underground in\nthe klystron galleries and will operate with a low-voltage AC supply.\nThe electrical infrastructure must be designed to accommodate all modes of operation, ensuring\nsufficient capacity for the t\u00aft phase, which has the highest power demand. Given the substantial energy\nrequirements of the RF systems, a dedicated branch of the machine\u2019s electrical network will be allocated\nto their supply, ensuring stable and efficient power distribution.\nPoint PH Layout\nThe number of RF cavities and RF amplifiers will increase with the beam energy, see Fig. 3.59. There\nwill be updates of the machine for each operating mode. The strategy is to increase the number of cavities\nand RF amplifiers within the operating year. The technical infrastructure to cover all modes of operation\nwill be installed from the beginning, see Fig. 3.60.\n178\n\nB2\n132 x 400 MHz Tristrons\u00a0500 kW\u00a0\n132 x 400 MHz Tristrons\u00a0500 kW\u00a0\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\nTristron/klystron Gallery\nB1\nB2\nZ, W Machines\n132 x 400 MHz Tristrons\u00a0500 kW\u00a0\n132 x 400 MHz Tristrons\u00a0500 kW\u00a0\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\nTristron/klystron Gallery\nB1\nH Machine\nB2\n102 x 400 MHz Tristrons\u00a0500 kW\u00a0\n102 x 400 MHz Tristrons\u00a0500 kW\u00a0\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\n400 MHz\nTristron/klystron Gallery\nB1\nttbar Machine\n800 MHz\n204 x 800 MHz\u00a0Tristrons\u00a0500 kW\u00a0\u00a0\nPoint H\nPoint H\nPoint H\nPoint H\nFig. 3.59: Collider RF amplifiers as a function of operating mode.\nFig. 3.60: Concept of electrical distribution at point PH.\n179\n\nPoint PL layout\nLike the collider, the booster will be upgraded with more cavities and RF amplifiers as the operating\nmode advances, see Fig. 3.61. The technical infrastructure will also be installed from the beginning to\ncover all operating modes, see Fig. 3.62.\n14/28 x 800 MHz Tristrons\u00a0500 kW\u00a0\n800 MHz\n800 MHz\n800 MHz\n800 MHz\nTristron/klystron Gallery\nBooster\nZ, W,H Machines\n14 x 800 MHz Tristrons\u00a0500 kW\u00a0\n800 MHz\n800 MHz\n800 MHz\n800 MHz\nTristron/klystron Gallery\nBooster\nttbar Machine\n224 x 800 MHz SSA 10 kW\u00a0\u00a0\n224 x 800 MHz SSA 10 kW\u00a0\u00a0\n800 MHz\n800 MHz\n800 MHz\n800 MHz\nPoint L\nPoint L\nFig. 3.61: Booster RF amplifiers in function of operation mode.\nFig. 3.62: Concept of Electrical distribution layout at point PL.\nRF high-voltage main power converters\nThe powering solution for the tristrons (or klystrons in case they are used) of the collider still needs to be\noptimised. However, a single and centralised high-voltage power converter installed on the surface has\nmany advantages. Figure 3.63 illustrates the principle of this case.\n180\n\nPoint H\nHV Bunker\n+Tristrons\nHV Bunker\n+Tristrons\nAC/DC\nFCC Tunnel\nVSC\nHV Bunker\n+Tristrons\nRF Amplifier\nGallery\nFig. 3.63: The principle of the integration of FCCee RF powering.\nEven with a centralised power converter solution, some RF powering equipment needs to be in-\nstalled in the klystron gallery (HV tank in Fig. 3.63):\n\u2013 Filtering capacitors in the proximity of the tristrons for DC filtering and DC bus decoupling.\n\u2013 If needed, a small power converter can be used to trim the voltage on each tristron (powering fine\ntune / klystron perveance drifts in case they are used, etc.)\n\u2013 A crowbar protection system (probably a series HV switch) to disconnect a klystron in case of a\nfault.\n\u2013 Small power converters for the tristron (or klystron) filament heater and solenoid.\nAs a first rough estimation, a volume of 1 m3 is to be reserved in the RF amplifier gallery for\neach tristron. The centralised RF high voltage power converter can be based on the so-called MMC\n(Modular Multilevel Converter), offering very high efficiency (97-98%) and high modularity. These\ntypes of converters are already deployed (e.g., for high-voltage DC transmission systems) at even higher\nvoltages and power. An illustrative draft layout of the 150 MW / 60 kV RF power converter is shown in\nFig. 3.64. The estimated total surface area for the collider RF power converter is 50 m\u00d730 m = 1500 m2.\n40 m\n25 m\nFig. 3.64: Centralised RF high-voltage power converter.\nThere can be a similar approach for the booster but with a smaller power level of around 10 MW.\n181\n\n3.9\nBeam diagnostics\nThe FCC-ee beam instrumentation (BI) will be composed of a very large number of devices that will\nprovide a means to measure relevant beam properties across the FCC complex (injector complex, booster\nand main ring). Table 3.17 shows the overview of the number and type of BI systems needed in the\ncomplex. A feasibility study was only carried out for specific systems in the main ring that are considered\nthe main challenges for the FCC BI. The section includes the requirements and design solutions for such\nsystems.\nTable 3.17: Number of BI systems in the FCC-ee complex\nDump\nline\nMain\nring\nBooster\nring\nInj.\nlines\nHE\nlinac\nComm.\nlinac\ne\u2212\nlinac\ne+\nDR\ne+\nTL\ne+\nlinac TOTAL\nBeam position\nQuad\nBPM\n20\n5800\n2944\n420\n82\n35\n11\n258\n30\n17\n9617\nSpecial\nBPM\n20\n5\n4\n29\nCollimator\nBPM\n66\n5\n71\nBeam loss\nFast BLM\nchannels\n34\n152\n126\n200\n512\nArc BLM\nchannels\n17616\n8808\n26424\nArc BLM\ncrates\n1468\n1468\nBeam intensity\nFast BCT\n& WCM\n3\n4\n2\n1\n2\n2\n2\n1\n4\n2\n23\nDC BCT\n4\n2\n1\n7\nTransverse profile\nImaging\nscreen\n6\n6\n2\n20\n2\n2\n2\n2\n4\n2\n48\nSR-based\n4\n1\n1\n6\nLaser Wire\nScanner\n2\n2\nLongitudinal profile\nb/b(EO/streak)\n2\n1\n1\n1\n1\n1\n1\n2\n10\nLuminosity / collision rate\nBeamstrahlung\n8\n8\n182\n\n3.9.1\nBeam position diagnostics\nThe R&D for the FCC-ee BPM systems is focused on the design, integration and alignment of button-\ntype BPM pickups for the arc and the interaction regions (IR) of the main rings, as well as R&D of the\nrelated signal processing electronics. Given the size of the system and its importance for FCC operation,\nthe reliability and potential repair strategies should be considered at all stages of the system design.\nFig. 3.65: Electrode arrangement of an FCC-ee main ring button BPM, along with lines of constant beam\nhorizontal (left) and vertical (right) displacement.\nFigure 3.65 illustrates the skewed arrangement of the BPM button electrodes to avoid the exposure\nof the synchrotron light fan.\nThe BPM system, with the button pickups as the signal source located at every quadrupole, has to\nmeet several challenging requirements, such as a turn-by-turn resolution of 10 \u00b5m and an orbit resolution\nbetter than 1 \u00b5m, with the relative accuracy and the alignment tolerances in the same range. A bunch-by-\nbunch measurement capability is required for the nominal FCC-ee bunch spacing of 25 ns. The BPMs\nwill also serve several feedback applications, thus the layout, segmentation, and data transmission need\nto be studied to minimise the latency of the BPM readings.\nTo tune and optimise the luminosity in the interaction points (IP), BPMs will be symmetrically\nlocated on each IP side. One pair of BPMs is planned in the combined beam vacuum chamber near the\nluminosity calorimeter to serve an IP luminosity feedback system. Another 3 - 5 BPMs accommodated\nin the IR cryostat with the beams in separate chambers will be mounted next to the segmented supercon-\nducting quadrupoles. These IR BPMs and associated signal cabling need to be particularly reliable, as\ntheir locations will be unreachable after the final assembly.\nRequirements and details of the BPM system are still being discussed. Current studies based on\nelectromagnetic simulations are targeted to find an optimal button electrode arrangement and size, ensur-\ning at the same time that there are sufficient signal levels to achieve the required resolution and the BPM\nbeam impedance within the limit assigned to the BPM system for all FCC-ee operational modes [292].\nPreliminary studies have been performed [293, 294], and the longitudinal beam coupling impedance of\n4000 BPM pickups with conical button electrodes was compared to other impedance contributing ele-\nments, such as the resistive wall (RW), bellows, RF cavities and taper section. So far, initial studies have\nshown that the BPM impedance budget of 40.1 V/pC should not be very difficult to fulfil and more chal-\nlenging could be thermal aspects related to beam heating and resulting changes of the BPM mechanical\ndimensions and material properties [13].\nIn many aspects, the performance required from the BPM systems for the FCC-ee and current\nsynchrotron light sources are quite similar, and therefore, technical solutions used in such systems could\nbe used as a reference. However, the size of the FCC-ee BPM systems, the radiation levels, and tun-\nnel temperature gradients are by far less favourable, therefore new design, production, installation and\nmaintenance challenges will have to be addressed.\n183\n\nEarly estimates for both the mechanical alignment of the BPMs required with respect to the\nquadrupoles and the alignment\u2019s long-term stability are of the order of 100 \u00b5m. Solutions used in syn-\nchrotron light sources suggest that the BPMs may have to be rigidly attached to their corresponding\nquadrupoles to meet this alignment requirement. The relative positions of the BPM and quadrupole geo-\nmetrical axes would need to be measured with even greater accuracy. As this requirement could influence\nthe design of the quadrupoles and alignment strategies, aspects related to BPM alignment should be stud-\nied at an early stage of the arc cell design. Given the importance of the BPM alignment for the FCC-ee\ncommissioning and subsequent operation, the solutions chosen should be confirmed by measurements\nperformed on an arc cell prototype.\nContrary to light sources, there will be high levels of ionising radiation in the FCC-ee tunnel. The\ncurrent experience with BPM electronics shows that they can be built from commercial off-the-shelf\n(COTS) components carefully selected and qualified with radiation tests when the integrated radiation\ndose over the whole lifetime of the project stays below some 1 kGy. Any higher radiation doses may\nrequire designing dedicated integration circuits, which would require significant financial and work-\nforce resources, especially since the CERN BI group currently has no experience in designing radiation-\ntolerant BPM electronics.\nTemperatures in the FCC-ee tunnel will have significant gradients and variations related to chang-\ning operational conditions, unlike in light sources. To achieve the beam position measurement accuracy\nrequired, it may be necessary for the BPM temperature drifts to be reduced by active cooling to ensure\nthat the BPM dimensions stay within the necessary margins. Similarly, the BPM electronics may also re-\nquire active cooling to stabilise their temperatures to a level that ensures the long-term accuracy required\nof the system. Such aspects will be studied in more detail once the temperature variations and gradients\nin the machine tunnel are better quantified, along with the temperature sensitivity of the prototypes of\nthe BPM electronics.\nBeam signals from FCC-ee arc BPM electrodes will not be able to be sent to the signal processing\nelectronics over long coaxial cables due to very limited space in the tunnel cable trays. Instead, the\nbeam signals must be treated close to the BPMs, so that the resulting beam data can be sent over optical\nfibres to an alcove. At this initial stage of the system design, it is expected that there will be a mini-rack\nlocated near each BPM pair (one BPM per beam, installed close to each arc quadrupole). This mini-rack\nwould accommodate BPM electronics, receive beam signals from the BPMs over short coaxial cables,\nand transmit results over optical fibres to an alcove. Racks to accommodate computers to process and\nconcentrate beam position data at rates adequate for sending it to the surface will be located in the\nalcoves.\nCurrently, the design effort is focusing on the arc BPMs, as they are most important for the design\nof the arc cell, which is a crucial part of the machine design. It is expected that the booster BPMs and\ntheir electronics will have a similar design.\nThe IR BPMs have stricter requirements for the measurement resolution and accuracy, therefore\ntheir mechanical design will be addressed separately. Also, the IR BPM processing electronics will need\nto fulfil very challenging requirements. It would be favourable to accommodate the IR BPM electronics\nin places free from high levels of ionising radiation so that the electronics can be based on the best\ncommercial components available on the global market. Otherwise, it might be very difficult to design\nand produce radiation-tolerant versions.\n3.9.2\nTransverse diagnostics\nTransverse profile measurements must be non-invasive during regular operation, whilst invasive mea-\nsurements may be considered in the initial stages of commissioning or dedicated low-intensity fills.\nMonitoring the relative evolution of the transverse emittance is the main priority for transverse di-\nagnostics, and the precision target is set to 2% in emittance, corresponding to 1% in beam size. Absolute\n184\n\naccuracy is less critical and not strictly necessary from the very beginning of the operation. The accuracy\ntarget is set at \u00b115% in emittance. These precision and accuracy targets apply to both transverse planes,\nirrespective of the machine\u2019s operation mode.\nMost machine operations require a relatively slow monitoring of the evolution of the average\nbeam emittance. Measuring the average emittance at a frequency of at least 1 Hz is desirable, as it can\nprovide input for feedback systems aimed at optimising luminosity. However, faster diagnostics enabling\nbunch-by-bunch measurements become necessary for studying effects like single bunch instabilities or\ndetecting any emittance patterns in the filling scheme. Bunch-by-bunch capabilities are not required\nfrom all instruments, but at least one system per beam must provide such measurements. Bunch-by-\nbunch measurements can be acquired by integrating tens or hundreds of revolutions to enhance the signal\nas needed. These measurements can occur either through a continuous bunch scan or with on-demand\nmeasurements. In both cases, the full-ring scan should not exceed a few minutes to ensure sufficient\nbeam stability. Single-bunch measurements recorded in a single-turn may be investigated but are not a\npriority.\nAs is customary in high-energy lepton machines, the transverse diagnostics for FCC-ee will pri-\nmarily rely on synchrotron radiation (SR). To achieve the resolution needed for picometre-level trans-\nverse emittance, diagnostics techniques operating in the x-ray domain become necessary.\nThe baseline locations for the SR diagnostics are downstream of the two major experiment inter-\naction points (PA and PG), just after the wiggler straight section. This location features a series of weak\ndipoles that are suitable candidates for the radiation source, with the photons emitted efficiently sepa-\nrated by the strong dipoles downstream that transport the beam towards the arc. The light will propagate\nto the instrumentation in a dedicated extraction line. Extraction lines approximately 100 m long will be\nrequired to transversely separate the light from the main beam and intercept the radiation at a distance of\n0.5 m.\nPlacing the diagnostics outside the arcs offers several advantages, including reduced radiation\nlevels, improved accessibility to the equipment, and more flexibility in adapting the machine design to\nmeet diagnostic requirements. Moreover, in the baseline GHC optics model, the location downstream\nof the interaction points is favourable due to relatively high betatron functions. These produce vertical\nbeam sizes exceeding 40 \u00b5m, thereby relaxing the resolution demands on the instrumentation.\nThe radiation energy range for diagnostics is expected to remain between 20 keV and 80 keV, well\nwithin the capabilities of existing diagnostic systems at modern light sources. To address variations\nin the synchrotron radiation spectrum across different beam energies, segmenting one of the existing\ndipoles into a sequence of tunable bends has been proposed. This approach minimises changes between\noperational modes while remaining transparent to the machine optics as long as the global bending angle\nof the dipole is preserved.\nA multilayer monochromator will be installed as the first element of the photon beamline, po-\nsitioned immediately after the vacuum exit window. Beyond its primary function of providing quasi-\nmonochromatic light for specific diagnostic techniques, this monochromator also bends the photon beam,\nreducing the transverse space occupied by the diagnostics line. Additionally, it absorbs the majority of\nsynchrotron radiation power emitted outside of the spectral range of interest, thereby reducing the ther-\nmal load on the detector.\nDue to their simplicity and robustness, X-ray pinhole cameras are identified as the baseline for\ntransverse diagnostics. These instruments will fulfil the requirement for precise average emittance mon-\nitoring. Bunch-by-bunch measurements can also be achieved with a fast gated detector. The optimised\npinhole width for a typical photon energy of 20 keV is 60 \u00b5m, which can be manufactured using the\nsame technologies as modern-day light sources. This configuration provides a theoretical resolution\nof 35 \u00b5m, comparable to the (vertical) beam sizes of interest, though not ideal for absolute beam size\nmeasurements.\n185\n\nTechniques based on synchrotron radiation interferometry (SRI) can improve resolution and com-\npensate for the limited accuracy of pinhole cameras when the beam size approaches its resolution limit.\nDiagnostics exploiting the Heterodyne Near-Field Speckles (HNFS) technique [295] is being developed\nas a potential SRI candidate, and Young\u2019s double-slit interferometers have also been studied for FCC-ee.\nAll interferometry-based devices could be installed on the same beamline as the pinhole camera, and the\nconfigurations could be switched as needed.\nAlongside SR-based techniques, scintillating screens for beam observation (BTVs) will be in-\nstalled in the transfer and dump lines. BTVs will also be placed in the main ring for beam detection\nduring the initial stages of machine commissioning.\n3.9.3\nBeam loss monitoring\nFor circulating machines, the main functionality of a beam loss system is to:\n\u2013 detect beam losses fast enough to protect accelerator components by triggering a beam extraction\nbefore the equipment is damaged and to\n\u2013 provide regular measurements of the amount and location of beam losses along the accelerator to\noptimise machine operation and assess its performance.\nHowever, the design of the beam loss monitoring (BLM) system depends on the knowledge of\nbeam losses that are expected to be detected. Beam losses could be classified as accidental (or also\nknown as irregular beam losses) and unavoidable (also known as regular beam losses). Regular beam\nlosses are those that can be minimised but not completely avoided; they correspond to beam debris from\ncollimation cleaning, physics collision debris, Touschek scattering along the accelerator or Coulomb\nscattering from residual gas interactions, among others. Therefore, continuous monitoring of beam losses\nwith a distributed BLM system is required. Irregular beam losses can appear as a result of equipment\nfailures, beam instabilities, micro-particles interacting with the beam or aperture restrictions, i.e., an\nobject inserted in the way of the beam. These are, to some extent, avoidable losses, but a beam loss\nsystem has to detect and define the levels allowed for such losses to protect the accelerator.\nStored energies in the FCC-ee collider ring are expected to be lower than present existing ma-\nchines like the LHC or its high luminosity upgrade (HL-LHC). However, as the beam size becomes very\nsmall, particularly for the vertical plane, the expected beam energy density is comparable to HL-LHC\nparameters. Assuming a beta function in the arc of 50 m (on average), beam sizes are expected to be of\nthe order of microns, and the beam energy deposition per surface can go up to 11 082 MJ/mm2 in the\nmost critical case of the Z-pole configuration, see Table 3.18.\nIonisation chambers have collection times of the order of \u00b5s for electrons and ms for ions, and\nalthough they perform very stably under radiation and could be very sensitive, they are not ideal for\nbunch-by-bunch measurements. Instead, solid-state detectors have risen and decay times of the order\nof ns, which will make them the most suitable candidates for fast loss detection. A new beam loss\ndetection technology under study is the use of large-core silica fibres to convert the secondary charged\nparticles from beam impacts into Cherenkov light. This process is instantaneous. The signal is then\ntransported to both fibre ends and read-out by photo-sensors. The photo-sensor choice defines the time\nresponse of the device. Regular photo-multipliers, can be fast, in the order of 1 \u22122 ns rise and decay\ntimes. Silicon photo-multipliers, are of the same magnitude although a bit slower, in the order of 10 \u2212\n20 ns.\nFinal specifications on minimum and maximum beam losses to be measured and the required\ntiming resolution will define the final choice of technology. In the meantime, R&D is needed to evaluate\nthe performance of such devices under the 50 MW synchrotron radiation levels per beam expected in the\ntunnel.\n186\n\nTable 3.18: Collider beam parameters.\nHL-LHC\nZ\nW\nZH\nt\u00aft\nBeam Energy [GeV]\n7000\n45.6\n80\n120\n182.5\nParticle\np\ne+e\u2212\nNo. bunches\n2748\n11200\n1780\n440\n60\nBeam current [mA]\n1090\n1270\n137\n26.7\n4.9\nBunch Intensity [1011]\n2.2\n2.14\n1.45\n1.15\n1.55\nStored beam energy [MJ]\n678\n17.5\n3.3\n0.97\n0.3\nGeom. emittance hor. \u03b5x [nm]\n0.34\n0.71\n2.17\n0.71\n1.59\nGeom. emittance ver. \u03b5y [pm]\n340\n1.9\n2.2\n1.4\n1.6\nHor. beam size \u03b2x = 50 m [\u00b5m]\n130\n188\n329\n188\n282\nVer. beam size \u03b2y = 50 m [\u00b5m]\n130\n9.7\n10.5\n8.4\n8.9\nEnergy density [MJ/mm2]\n40 118\n11 082\n682\n645\n87.2\nFast beam loss monitors\nWith unprecedented stored beam energies for an electron collider, up to 17.5 MJ in the Z-pole operations,\nthe electron/positron beams are highly destructive. A collimation system will be set in place in order to\nreduce the backgrounds to the experiments as well as to protect the machine from unavoidable losses.\nThere is one system in PF for global halo collimation (betatron and off-momentum) and a second system\naround the colliding points. Beam loss monitors need to be installed at each collimator, with the aim\nof measuring turn-by-turn losses or faster, if possible. With the presently proposed collimation system,\n27 collimators will be installed per beam, and thus 54 beam loss monitors covering both beams in the\ncollider ring.\nRegarding the synchrotron radiation collimation system, presently, six collimators and two masks\nper beam upstream of the interaction points are planned. To monitor the losses in these locations, a total\nof 16 beam loss monitors per collision point will be needed (corresponding to 64 beam loss monitors in\nthe collider ring).\nThe injection and extraction to the booster and collider rings will also need beam loss monitoring,\nin particular at the location of collimators, beam masks or absorbers, kicker magnets and septum magnets.\nTable 3.19 shows the present estimate of beam loss monitors to cover the collider ring collimation and\nthe injection/extraction needs for both rings.\nThe injectors to the Booster will need additional beam loss monitoring, and a first estimate of an\nadditional 200 monitors is being considered.\nArc cell beam loss monitors\nPotential beam losses occurring in the arc cells of the collider and booster rings need to be continuously\nmonitored. Beam loss monitors are typically located where losses are expected. In the case of the arc\ncells that correspond to near the arc quadrupoles, the aperture available is smaller. On the other hand, it\nis not predictable where micro-particles will interact with the beam.\nA generic beam loss system in the arc cell should be able to cover a distance of several metres\nand reconstruct the main beam loss location. The implementation of this beam loss system is still under\nR&D, but a minimum configuration with 3 monitors or channels distributed along that distance could\nprovide the location of the loss by triangulation. This number has been used to estimate the number\nof beam loss channels and read-out tunnel electronics needed to cover both the collider and the booster\nrings. Figure 3.66 shows a schema of the configuration of a generic beam loss system in the FCC-ee arc\ncell.\n187\n\nTable 3.19: Fast beam loss monitors for Colliding and Booster ring, excluding injectors.\nPurpose\nColliding ring\nBooster ring\nTotal\nCollimation Halo (PF)\n27/beam\n54\nCollimation SR (PA/PD/PG/PJ)\n32/beam\n64\nBooster injection region\n10/beam\n20\nBooster to Collider extraction\n15/beam\n30\nBooster to Dump extraction\n15/beam\n30\nBooster to Dump transfer line\n(12+5)/beam\n34\nBooster to Collider transfer line\n6/beam\n12\nCollider injection region\n2/beam\n4\nCollider to dump extraction\n15/beam\n30\nCollider dump line\n(12+5)/beam\n34\nTotal Injectors\n200\nTotal Ring\n93/beam\n63/beam\n312\nThe tunnel read-out electronics will be installed under the arc quadrupoles. A total of 18 BLM\nchannels per arc cell can be read-out with a single crate. This includes the beam loss monitors for the\ncollider and the booster rings. Table 3.20 shows the number of channels in both rings together with the\nnumber of crates needed in the tunnel. R&D is needed to develop radiation-tolerant electronics that are\nable to withstand the FCC-ee radiation level, which comes mainly from synchrotron radiation.\nFig. 3.66: Proposal of beam loss system in the arc cells, for Booster ring (on top) and Collider ring (on\nbottom), sharing the same read-out crate.\n3.9.4\nLongitudinal diagnostics\nLongitudinal profile monitoring is needed to assess the effect of beamstrahlung, which will increase\nbunch lengths depending on the charge balance between colliding bunches. A bunch-by-bunch measure-\nment of the bunch length is deemed crucial to determine the collision condition and the energy spread.\nTurn-by-turn measurement is not needed as the evolution of the bunch length will be in the order of the\nlongitudinal damping time (i.e., from 1320 turns at Z to 20 at t\u00aft). The precision of the order of 1%\nbetween bunches (both beams) is needed, while absolute accuracy is not strictly needed (still undefined).\nConsidering a minimum bunch length of 1.91 mm or 6.4 ps (t\u00aft) bunch length measurements must have\n188\n\nTable 3.20: Arc beam loss monitors.\nCollider\nBooster\nTotal\nBLM channels per quadrupole\n6\n3\n9\nBLM channels in the ring\n17 616\n8808\n26 428\nBLM crates per arc cell\n1\n0\n1\nBLM crates in the ring\n1468\n0\n1468\na precision of better than 60 fs. A bunch-by-bunch profile measurement on selected bunches is required\nduring commissioning and when requested to check the quality of top-up injected bunches, where fresh\nbunches at 10% nominal population are injected onto circulating bunches.\nAs part of this feasibility study, electro-optical spectral decoding (EOSD) is one of the candidate\ntechniques that could fulfil these requirements. The Karlsruhe Institute of Technology (KIT) is working\non the design of an EOSD system adapted to the FCC-ee environment and parameters that allow single-\nshot longitudinal measurement with sub-picosecond resolution and a repetition rate in the MHz range\n[296]. Simulations have been carried out to investigate its performance under FCC-ee conditions that\npresent significant challenges for EOSD measurements, especially the long bunches during Z operation\nwith \u03c3 ranging from 4.7 to 15.5 mm and the high bunch charge. A prototype was tested in the CLEAR\nfacility at CERN in 2024. Further studies will be needed to optimise thermal management of the EO\npick-up system under very high repetition rates, investigate the placement of monitor and laser/detection\nsystem and optimise the resolution to achieve 50 fs resolution.\nCherenkov diffraction radiation (ChDR) is an alternative to EOSD for longitudinal diagnostics\n[297,298]. ChDR is generated as a charged particle passes in the vicinity of a dielectric material with a\nvelocity which exceeds the speed of light in the given dielectric material. As the radiation is emitted at\nthe well-known Cherenkov angle, the extraction of the signal is simplified in comparison to diagnostic\ntechniques based on synchrotron radiation, which is emitted at a very small angle. For that reason,\nthe incoherent part of the ChDR spectrum is a promising candidate for measuring bunch length in the\nFCC-ee. However, two analytical models [299,300] predict a very different photon yield with very little\nexperimental data [301,302]. To assess the potential of incoherent ChDR for FCC-ee, a photon counting\nexperiment is being prepared to measure the photon yield in the visible spectrum. The ATF2 beamline\nat KEK [303] is a suitable candidate for these tests, as it provides high particle energy and charge and\na small beam size, which allows a beam-radiator distance in the sub-mm range, maximising the photon\nyield obtained.\n3.9.5\nLuminosity monitoring diagnostics for IP tuning\nAt each interaction point where the opposing beam is encountered, beamstrahlung emitted during the\nbeam-beam collision results in an intense flux of photons on both sides of the IP, that are extracted\nthrough a dedicated 500 m long dilution channel terminated by a liquid lead dump. Specific instrumen-\ntation dedicated to monitoring the beamstrahlung profile position and its intensity is under development.\nSince the position of the photon peak is sensitive to the beam-beam transverse distance in the nanometre\nrange as well as to residual optical aberrations at the IP, these signals are a valuable input for the IP\ntuning; see Fig. 3.67. The sensitivity range spans almost linearly over 200 nm and then saturates. This\nbeamstrahlung information is used, in particular, for precision IP tuning scans.\nA beam television screen (so-called BTV) is under development with the goal of imaging the\nbeamstrahlung photon profile. The scintillator technology used for this device should be optimised for\nproviding the best signal-to-noise ratio (i.e., synchrotron radiation vs beamstrahlung radiation) while\nkeeping the thermal load from the ultra-intense flux of photons acceptable. Considering the worst-case\nscenario, a hollow screen is being simulated such that the profile position is tracked by fitting the tails\n189\n\nFig. 3.67: Position of the beamstrahlung peak on the BTV screen installed at 400 m from the interaction\npoint. In blue is a Gaussian fit applied to a full-screen image. The Gaussian tails fit to a hollow screen\nimage are shown in red. The tail fit is based on the use of a 30 mm aperture.\nonly. The result obtained with a gap of 30 mm (equivalent to 1 sigma of the profile) is presented by the\nred curve in Fig. 3.67. It accurately follows the curve obtained by fitting the whole distribution (blue\ncurve). If a screen imaging technique cannot be employed due to the heat load, the ionisation of rest gas\nis a possible alternative means of measuring the beamstrahlung profile [304].\nAnother process of interest in measuring luminosity is the rate of radiative Bhabha scattering.\nSince the resulting off-energy leptons mainly hit the beam-pipe about 150 m from the interaction point,\na fast beam loss monitor installed at that location would allow monitoring bunch-by-bunch collision\nrate, complementing the beamstrahlung profile imaging technique. The latter might not be able to re-\nsolve individual bunch crossings. An example of a similar instrument is the BRAN developed for the\nLHC [305].\n3.9.6\nInverse Compton polarimeter for energy calibration\nA beam energy measurement based on resonant spin depolarisation will be implemented [306], providing\nprecise collision energy calibration for the Z and WW modes. This technique performs regular trans-\nverse beam excitation tune scans on a dedicated pilot bunch to identify the spin resonant depolarisation\nfrequency, which then provides the collision energy with great precision. The subject is covered in de-\ntail in the EPOL section of this feasibility report (Section 1.7). Here, the need for the inverse Compton\npolarimeter (IPC), which will perform the bunch polarisation measurement, is highlighted. The vacuum\nchamber for this 100 m long instrument must comply with the impedance budget of the machine, and a\ndesign study has been initiated. The simulation of the detector made good progress in building a digital\ntwin of the future instrument. The EPOL section of this document gives more insight into the whole\nenergy calibration procedure and the associated instrumentation.\n3.10\nArc region: integration and supporting systems\nThe current FCC-ee layout has a circumference of around 90 km, and about 85 % (i.e., 77 km) are taken\nby the arcs. Arcs are made of a sequence of FODO half-cells, about 3000 for the high-energy optics, and\nconsist of a short straight section (SSS) with quadrupole, sextupoles, beam instrumentation and correc-\ntors, followed by a long dipole length that can be achieved with a series of two or three interconnected\n190\n\nmagnets. This section describes the optimisation of the arc-supporting structures to maximise their per-\nformance, easing the installation and maintenance while minimising cost. The section also reports the\nstate of advancement of the construction of the arc half-cell mock-up.\n3.10.1\nCollider-Booster placement configurations\nThe placement of the booster and the collider must be optimised in the radial and vertical directions\nof the tunnel cross-section, with a hard constraint of a maximum tunnel inner diameter of 5.5 m. The\nlongitudinal positioning of the SSS of the collider relative to the position of the SSS of the booster also\nrequires optimisation. An optimised configuration of the tunnel cross-section, as described in Ref. [307],\nwith respect to that presented in the CDR [13] has the booster placed on top of the collider. This frees\nmore space for the services, especially the cooling and ventilation piping, the space reserved for trans-\nport vehicles, and the alignment system (Fig. 3.68). In addition to being more compact, the vertical\nconfiguration provides further advantages:\n\u2013 Permits a smaller tunnel diameter in the RF sections.\n\u2013 Same basement configuration as FCC-hh.\n\u2013 Easier access for handling and removal of booster magnets and SSS (when leaving enough vertical\nclearance to allow installing/uninstalling both machines once the supports are already in position).\n\u2013 Better from a radiation point of view, as the highest dose is generated on the outer side of the\ntunnel, which could be detrimental to the booster ring in case of a horizontal placement [308].\nFig. 3.68: Configurations for the relative placement between booster and collider. Left: horizontal con-\nfiguration. Right: vertical configuration.\nHowever, the vertical placement of the booster could raise dynamic stability challenges: due to the\nlonger lever arm between the ground and the magnet, the booster could oscillate further, exceeding the\ntight dynamic positioning tolerances, particularly in the SSS region. For this reason, a significant effort\nin design and simulations has been made to improve the supporting system and maximise the stability of\nthe two accelerators.\nGiven that the booster will be positioned above the collider, it is essential to maintain sufficient\nclearance with the collider underneath. This could be done by longitudinally shifting the SSS of the\ncollider with respect to the SSS of the booster, keeping the cell periodicity (i.e., the azimuthal distance\nbetween the booster SSS and the collider SSS is maintained constant along the arc). Since the SSS is the\nbulkiest section of the arc for both machines, the proposed modification allows the SSS of the collider\nto be longitudinally positioned corresponding to the location of the smaller and more compact booster\n191\n\ndipoles, and vice versa (example for ZH/t\u00aft phases with the Quad-Sext-Sext configuration of the collider\nFig. 3.69).\nFurther work will be required during a next phase of the project to optimise the interface and spac-\ning between the collider, the booster, and their support structures. Sufficient clearance must be ensured\nto facilitate handling procedures, allowing for the installation or removal of individual magnets from\neach accelerator without interfering with the magnets of the other machine. This must be achieved while\nkeeping the support structures in place, avoiding unnecessary disassembly and minimising operational\ndisruptions.\nFig. 3.69: Azimuthal shift between booster and collider - collider optics V24.3_GHC and booster optics\nV24_FODO.\n3.10.2\nArc cell configurations of the collider\nThe configuration of the collider arc cell changes from the low to the high energy phase. The number of\nquadrupoles per unit length is doubled between the Z/WW and ZH/t\u00aft phases as the length of the FODO\ncells is halved: the length of the half cell is 52 m for Z/WW phases and 26 m for the ZH/t\u00aft phases. As can\nbe seen in Fig. 3.70, there are two configurations for the Z/WW phase: 568 short straight sections with\none quadrupole and one sextupole and 856 short straight sections with a single quadrupole. Similarly,\nthere are two configurations for the ZH/t\u00aft phase: 1136 short straight sections with one quadrupole and\ntwo sextupoles, and 1704 short straight sections with a single quadrupole.\nFig. 3.70: Arc cell configurations for the collider, for the Z/WW phases and the ZH/t\u00aft phases - optics\nV24.3_GHC.\nAmong these different SSS configurations, the Quad-Sext-Sext configuration has been studied\n192\n\nin detail and will be installed in the mock-up. This SSS configuration is the bulkiest and the most\nchallenging for its integration. It is also the most complex in terms of static and dynamic stability.\nThe optics of the collider is still evolving. However, the reference optics for the first phase of\nthe mock-up was frozen at version V24.3_GHC by the end of 2024, to allow installation in the first\nhalf of 2025. To document this baseline solution, two drawings were produced, one of the cross-section\n(Fig. 3.81) and one longitudinal view representing an arc half-cell (Fig. 3.82), for the reference baseline\noptics V24.3_GHC. These two drawings, which constitute the baseline configuration for the mock-up,\nwill be versioned following the mock-up study and will evolve in the coming years.\nFurther work is needed to define the strategy for the modification of the FCC-ee between the\nZ/WW and ZH/t\u00aft phases. At first glance, a mechanical reconfiguration of the collider will be necessary\nbetween these phases. To understand this reconfiguration, consider an ensemble of five FODO cells at\nZ/WW phase, corresponding to 10 cells at ZH/t\u00aft, this forms a pattern that repeats 17.5 times in one arc,\nand over the eight arcs of the entire collider. In these five cells at Z/WW (i.e., 10 cells at ZH/t\u00aft), there\nare 20 slots where SSS can be installed (10 cells at ZH/t\u00aft multiplied by 2 SSS per cell). Over these 20\nslots, moving from the Z/WW to ZH/t\u00aft phase will involve:\n\u2013 2 slots are not changing\n\u2013 2 slots are for single quadrupoles at Z/WW phase, which change polarity at ZH/t\u00aft phase.\n\u2013 2 slots are for single quadrupoles at Z/WW phase, which will change slot location at ZH/t\u00aft phase.\n\u2013 6 empty slots at Z/WW phase will receive single quadrupole at ZH/t\u00aft phase.\n\u2013 4 slots are for quadrupole - sextupole at Z/WW phase, which will be removed at ZH/t\u00aft phase.\n\u2013 4 empty slots at Z/WW phase will receive quadrupole - sextupole - sextupole at ZH/t\u00aft phase.\n\u2013 4 occupied slots at Z/WW phase will receive quadrupole - sextupole - sextupole at ZH/t\u00aft phase.\nThe mechanical reconfiguration of the collider between the Z/WW phase and the ZH/t\u00aft phase\npresents many inconveniences and challenges. The number of SSS that would need to be dismounted,\nmoved or installed is very large, requiring a large number of activities in the tunnel, transport to and from\nthe access points and the surface, as well as breaking the vacuum of the collider beam pipes and proceed-\ning with full realignment of the collider. Another solution to alleviate most of these issues requires the\ninstallation of all SSS girders from the start, that is, installing the full contingent of elements required\nfor the ZH/t\u00aft operation, while less than half of these would be used for the Z/WW phase of operation. A\ncareful optimisation of the power converter circuits for the magnets in the arcs would allow a very fast\n(order of one hour) switch between the two modes of operation. This solution is being actively studied\nto avoid the mechanical and operational challenges linked to a collider reconfiguration.\n3.10.3\nOptimisation of the collider supporting structure - static and dynamic analyses\nOverview and principles\nFigure 3.71 shows the 3D model of an arc half-cell, with a focus on the short straight section of the\ncollider and booster. The supporting system of the booster shown in this picture is one of the possible\nsolutions under study, compared to the conceptual configuration reported in Section 8.2.7.\nThe principle for assembling, installing, aligning and maintaining the elements in the SSS on their\nsupporting system has been extensively analysed.\nUsing girders to support the common elements in the SSS offers significant practical advantages.\nThe SSS elements, magnets, and vacuum chambers can be pre-assembled and pre-aligned on a girder\nin a workshop at the surface with the proper tools and environment. The entire SSS module (girder\nwith quadrupole, sextupoles, alignment fiducials and vacuum system) can then be transported as a single\nobject to the tunnel, optimising the transport and maintenance operations. Hot spares of SSS modules\ncan be stored and rapidly prepared for installation in case of a major fault. Repair can then be done in\n193\n\nFig. 3.71: CAD model of an arc half-cell, with focus on the Short Straight Section.\nthe correct conditions at the surface. Finally, a pre-alignment of elements on the girder at the surface\nreduces the time required for the positioning and final alignment of the girder in the tunnel.\nFig. 3.72: CAD model of the optimised actual steel girder.\nHowever, a potential disadvantage of a girder is that it usually requires more space vertically, than,\nfor example, a supporting system with standard jacks for each magnet of the SSS. This means that the\nvertical position of the accelerators would be higher, with possibly a detrimental effect on the dynamic\nstability at the level of the beam axis. It is, therefore, important to maximise the girder stability by\noptimising its design and materials.\nSpecifications\nAn initial estimation of the acceptable vibrations in the SSS was defined in 2022, and is reported in\nTable 3.21. This specification did not distinguish between vertical and lateral motion and between booster\nand collider.\nTo consolidate the tolerance estimates, the sensitivity to vibrations of the GHC optics at the Z op-\nerating point was evaluated assuming a tolerance on the beam oscillation amplitude at the collision point\nof less than 5% relative to the collision point beam size [309]. Due to the small emittance ratio, verti-\ncal oscillations are more than an order of magnitude more critical than horizontal oscillations. Assuming\nthat an orbit feedback will efficiently damp beam oscillations with frequencies below 1 Hz, the integrated\nRMS motion for frequencies higher than 1 Hz is ideally around 10 (100) nm for the vertical (horizontal)\nplane. If the beam orbit feedback bandwidth can be extended above 1 Hz, it would be possible to set the\ntargets for the vertical (horizontal) plane to 20 (200) nm, in line with Table 3.21. It must be noted that\nthe sensitivity may evolve in the future with the optics and the machine layout. For the low-beta regions,\nthe tolerances are an order of magnitude tighter. These considerations are summarised in Table 3.22, the\nkey frequency of interest is 1 Hz, and tolerances are given at the quadrupole (SSS) magnetic axis.\n194\n\nTable 3.21: Proposed dynamic stability requirements in the arcs, presented at FCC IS workshop for the\narcs [310] in 2022.\nFrequency range\nTolerance\nCorrelation\n0.01 Hz < f < 1 Hz\n1 \u00b5m\n10 km\n0.01 Hz < f < 1 Hz\n100 nm\nnone\n1 Hz < f < 10 Hz\n20 nm\nnone\n10 Hz < f < 100 Hz\n5 nm\nnone\n100 Hz < f\n1 nm\nnone\nTable 3.22: Updated dynamic stability requirements in the arcs at the level of the quadrupole magnetic\naxis.\nTolerance at 1 Hz frequency\nCollider vertical direction\n20 nm\nCollider lateral direction\n200 nm\nBooster vertical direction\n40 nm\nBooster lateral direction\n400 nm\nHistorical background\nIt is interesting to compare the current stability specifications with what was studied in other projects\nor achieved in past CERN machines, such as the Large Hadron Collider (LHC/HL-LHC) and the future\nCompact LInear Collider (CLIC). For the LHC/HL-LHC quadrupoles [311]:\n\u2013 In standard operation, the root mean square (RMS) should be < 5 \u00b5m at 1 Hz;\n\u2013 Beam instabilities can be provoked if the RMS is between 5 \u00b5m and 20 \u00b5m at 1 Hz;\n\u2013 A beam dump is usually needed for an RMS > 20 \u00b5m at 1 Hz.\nOn the other hand, the future Compact LInear Collider (CLIC) has significantly more stringent specifica-\ntions: given its very small beam sizes, even minor oscillations of one quadrupole reduce the luminosity.\nIt has been estimated that in the vertical direction the RMS must be below 1 nm at 1 Hz and similarly,\nit must be below 5 nm at 1 Hz in the lateral direction to ensure sufficient performance [312]. A study\nhas demonstrated that these specifications can be achieved, albeit using active stabilisation based on\npiezo-actuators combined with a stiff and optimised design of the quadrupole support [313].\nHence, the FCC arc specifications are closer to those of a linear accelerator (CLIC) than those of\nexisting circular accelerators (LHC/HL-LHC), which illustrates their challenging aspects.\nNumerical methodology\nIt is possible to calculate the vibrations expected for a given configuration of the SSS numerically and\ncompare it with the specification above. A finite element method (FEM) has been defined and is de-\nscribed in the following steps:\n1. Definition of a baseline model (support and simplified magnets);\n2. Carry out static analysis of the system \u2192to assess the structural resistance and the static stability\nof the support;\n3. Carry out modal analysis \u2192to assess the rigidity of the system, study the dynamic characteristics\nof the system;\n195\n\n4. Identify the transfer function of the support from the ground to the magnet axis \u2192identify the\ncritical modes of the supports, carry out a comparative study between different supports;\n5. Conduct random vibration analysis in response to ground motion \u2192study the impact of the support\non the RMS at the magnetic centre, and obtain an estimate of this RMS;\n6. Add vibrational cross-talk between the booster and the collider, add excitation forces dependent\non the support environment such as pumps, water pipes, ventilation, etc.;\n7. Compare the results to the specifications.\nFor the moment, this methodology is being applied from step 1 to step 5. The vibrational cross-\ntalk between the booster and the collider, and how to account for it in the simulations, is currently being\nstudied [314]. Further investigations are required to determine and include excitation forces.\nFig. 3.73: Transfer function comparison for different girder geometries in the vertical and lateral direc-\ntions.\nAn example of a transfer function comparison for different geometries is shown in Fig. 3.73. The\nfirst graph displays the transfer functions obtained in the vertical direction and the second in the lateral\ndirection. Each plot represents the amplification or reduction of the input oscillation through the system\nover a given range of frequencies. The transfer functions provide insight into how the system behaves\nand reacts over a range of frequencies. The higher the natural frequencies and rigid body frequencies, the\nmore rigid the system is considered to be. Comparative studies can be carried out to analyse the impact\non stability of the geometry, materials, position, rigidity, number of feet, etc. and to determine the most\nsuitable geometry.\nKnowing the spectrum of the ground motion over the relevant range of frequencies, as well as\nthe transfer function of the supporting structure between the ground and the centre of the magnet, it is\npossible to estimate the displacement of the mechanical axis of the magnet in response to the ground\nmotion. As values of the estimated movement of the ground in the FCC tunnel are not yet available, the\npower spectral density (PSD) of the ground motion measured in the LHC tunnel [315] has been used\ninstead as an initial input. When performing a random vibration analysis of the system with such a\nground PSD as an input for the calculation, the PSD of the magnetic axis is obtained as an output, and\n196\n\nthe integrated root mean square (RMS) displacements at the level of the axis can then be computed. The\nmethodology is detailed in Fig. 3.74.\nFig. 3.74: Methodology to assess the stability of the supporting systems.\nExperimental benchmarking\nIt is important to note that the method described above is sensitive to several parameters that cannot be\nprecisely estimated at this stage of the study; similarly, the simulations contain approximations, such as\nsimplified magnets and interfaces (ground to support, support to magnets, etc.). It is thus of paramount\nimportance to experimentally benchmark and tune the simulations to acquire confidence in the numerical\nmodel. A simple 2.5 m-long Short Straight Section demonstrator (see Fig. 3.75) was therefore assembled\nto allow an understanding of how the different elements of the SSS affect the system stability. This SSS\nconsists of feet/jacks supporting a granite girder, on which the prototype quadrupole built by TE-MSC\nduring the CDR phase [316] was installed.\nFig. 3.75: 2.5 m long short straight section demonstrator and its equivalent in simulation.\nA multistep experimental characterisation of each element and, successively, of the full assembly,\nin terms of modal analysis and transfer function, was then performed. These measurements were car-\nried out at CERN in the Mechanical Measurement Laboratory of EN-MME. The experimental results\nare compared with the numerical analyses to gradually refine the simulations and to determine the dy-\nnamic stability of the different elements more accurately. The different steps and their key results are\nsummarised below.\n197\n\n1. Characterisation of the prototype quadrupole: the vibrational natural frequencies of the pro-\ntotype quadrupole, even after extrapolation for the 2.9 m-long quadrupole, are quite high, around\n100 Hz, and typical of a very stiff system. It will thus only marginally affect the vibrational be-\nhaviour of the SSS. Particular attention should be given to the interfaces between quadrupole and\ngirder, as these interfaces, depending on their stiffness, can be the source of rigid body modes, gen-\nerally at low frequencies, which have a major impact on stability. For more details, see Ref. [311].\n2. Characterisation of the 2.5 m long girder: the natural frequencies of the girder are above 400 Hz,\nwhereas the rigid body modes are below 100 Hz and even fall below 20 Hz for the first. The\nresults show that the frequencies associated to the girder rigid body modes are determined by the\nvibrational modes of the feet/jacks. The girder is therefore a rigid component, but the feet/jacks\nhave a significant effect on its stability, which is why it is important to work on the design of the\nfeet/jacks that will be used to support the girder. For more details, see [311].\n3. Characterisation of the 2.5 m long girder with the prototype quadrupole: the third step in-\nvolved characterising the 2.5 m long girder with three jacks and the 1 m long quadrupole prototype\non top. This configuration was chosen because it is the closest to that which is most likely to be\nadopted in the FCC-ee tunnel. The key results are presented below and details can be found in\nRef. [311].\nTo summarise, the measurements demonstrated that individual subcomponents such as the quadrupole\nand the girder are relatively stiff compared to the supports on which they are placed, i.e., the jacks and\nthe interface between magnets and girder.\nTable 3.23 displays the integrated RMS of the 2.5 m long girder with the prototype quadrupole,\nat the level of the ground, girder and quadrupole, in both vertical and lateral directions. This table also\ncompares experimental measurements with data obtained from simulations.\nTable 3.23: Experimental and simulation results for the 2.5 m long granite girder with the prototype\nquadrupole: Integrated Root Mean Square at 1 Hz at the level of the floor, the girder and the quadrupole\nin the vertical and lateral direction.\nIntegrated RMS\nvalues at 1 Hz\nVertical\ndirection EXP.\nVertical\ndirection SIMU\nLateral\ndirection EXP.\nLateral\ndirection SIMU\nOn the ground\n5 nm\n5 nm\n7 nm\n7 nm\nOn the girder\n12 nm\n10 nm\n162 nm\n124 nm\nOn the quadrupole\n13 nm\n15 nm\n309 nm\n220 nm\nDirect comparison of the values presented in Table 3.23 with the specifications presented in Ta-\nble 3.22 shows that with the 2.5 m long demonstrator, the specifications have been reached or even\nexceeded. However, the real SSS will be 6 m long instead of 2.5 m, which will have a detrimental effect\non stability.\nGiven the consistency found between the experimental results and the data obtained via simulation,\na first extrapolation was carried out: simulating a 6 m long granite girder with the simplified quadrupole\nand sextupoles (see Fig. 3.76). Table 3.24 presents the modal results following extrapolation. Given\nthe increase in mass and length of the system, there is a clear decrease in all mode frequencies: the\nsystem becomes less rigid. The refinement process on the simulations is still in progress to determine\nthe integrated RMS for the 6 m length of the short straight section.\nConclusions and highlights\nThe experimental measurements facilitate the understanding of how the different elements of the SSS\naffect the stability of the system and indicate an order of magnitude of the displacements expected in\n198\n\nFig. 3.76: 6 m long short straight section in simulation composed of the granite girder, the simplified\nquadrupole and sextupoles.\nTable 3.24: Simulation results of the modal analysis of the 2.5 m long granite girder with the prototype\nquadrupole vs. the 6 m long granite girder with the quadrupole and sextupoles\nModes\nFrequency for 2.5 m-long\nconfig. (simu. and exp. results)\nFrequency for 6 m-long\nconfig. (simu.)\nMode shape\nidentification\nS1\n14 Hz\n6 Hz\nTilting mode around X\nS2\n30 Hz\n16 Hz\nTilting mode around Y\nS3\n34 Hz\n12 Hz\nTilting mode around Z\nS4\n47 Hz\n26 Hz\nRotation mode around X\nS5\n55 Hz\n30 Hz\nUp and down mode\nthe frequency range of interest for FCC-ee. Individual subcomponents such as the quadrupole and the\ngirder are relatively stiff (vibrational natural frequencies are in the order of a few hundred Hz) compared\nto the supports on which they are placed, i.e., the jacks and interfaces girder/magnets. From the dynamic\nstability point of view, the latter thus requires more work, during the next project phase.\nThe measurements of integrated RMS on the 2.5 m long demonstrator show vibrations comparable\nto the current specifications. However, simulations performed so far on the 6 m length of the SSS demon-\nstrate that, with the current configuration of the systems, the specification will be exceeded. Moreover,\nfor the moment, the study considers only the ground motion and does not account for additional external\nvibration sources (such as pumps, cooling systems, and ventilation) or the vibration cross-talk between\nthe booster and collider structures through the ground. These additional sources will have a detrimental\neffect on the stability of the system, and they require further work.\nThe specifications appear challenging, and considerable work is required to optimise the system in\nterms of stability. This stability challenge must be taken into account by all stakeholders who will have\nequipment in the tunnel (pumps, ventilation, cooling, tunnel cross-section etc.) that will have a direct\nimpact on the stability of the supporting structure.\n3.10.4\nIntegration studies magnet/vacuum system\nThe design of key components, including magnets, the vacuum system, alignment mechanisms, and beam\ninstrumentation, is still in the early stages for both the collider and the booster. To advance this work,\na dedicated design study was initiated with the primary objective of refining the collider\u2019s integration\nmodel, with a particular focus on system interfaces. This study has proven to be crucial not only for\noptimising the integration layout but also for improving the optical design, as discussed in the following\nsections.\n199\n\nAs part of the study, several critical aspects were analyzed, including the integration of the vacuum\nabsorber cooling system, heating jackets, dipole-to-dipole and dipole-to-quadrupole interconnections,\nmagnet busbar insulation, vacuum shape-memory alloy (SMA) flange tooling, and overall accessibility\nto interconnections. More details on this work can be found in Refs. [317\u2013319]. The present discussion,\nhowever, focuses on one of the key outcomes of the study: the separation of the e+/e\u2212beams in the\ncollider.\nIn the CDR [13] and, still, at the beginning of the Arc Half-Cell Mock-up Project, the optics design\nof the collider had a 30 cm radial spacing between the e+ and the e\u2212beams. In light of the results of the\ninterfaces design study, this distance has been increased to 35 cm. The main reasons are the following:\n1. Integration of vacuum synchrotron radiation absorber cooling circuit, heating jackets and dipole\nbusbar insulation.\n(a) 300 mm e+/e\u2212separation results in jacket/busbar interference\n(b) 350 mm e+/e\u2212separation allows >25 mm radial clearance between the two systems, a part of\nwhich will host the connection fittings of the cooling water supply tubes of the SR absorbers\n2. Dipole to dipole interconnection (see Fig. 3.77).\n(a) 300 mm e+/e\u2212separation results in a clash between vacuum chamber flanges and busbar\ninsulation\n(b) 350 mm e+/e\u2212separation guarantees 24.5 mm clearance between vacuum chamber flanges\nand insulation, as well as a continuous dipole busbar interconnections (no need of jumpers)\n3. Vacuum chamber interconnection (see Fig. 3.78).\n(a) 350 mm e+/e\u2212separation provides more space for SMA flange tooling and general access to\ninterconnections\n(b) \u223c127 mm between flange-to-flange insulation (assuming \u223c10 mm insulation)\n(c) Enough space for BPM positioning (3\u00d7 vacuum chamber outer diameter from SMA flange\nconnection.)\nFig. 3.77: Relative position of vacuum flanges and busbar insulation. Top and bottom Left: 300 mm\ne+/e\u2212separation. Top and bottom Right: 350 mm e+/e\u2212separation.\n3.10.5\nArc half-cell mock-up: concept verification\nA mock-up of the arc half-cell is being built at CERN, on the Meyrin site and specifically in building\n355/358. Among its objectives, a distinction can be made between short-term (2025) and long-term ones:\n200\n\nFig. 3.78: 350 mm e+/e\u2212separation, vacuum interconnections and SMA flanges.\n\u2013 Short term objective: a mock-up allowing the testing of the integration of simplified elements\nwithin a short time-frame (detailed study of the integration of elements, analysis of access and\ncompatibility with safety requirements, test of alignment strategy and mechanical stability, etc.).\nThis mock-up will also be used for outreach, it is a \u2018visual\u2019 demonstrator for the stakeholders of\nthe FCC.\n\u2013 Long term objective: an evolving mock-up allowing equipment groups to install and test their\nequipment. The mock-up could, in the future, house the full-size/weight functional elements.\nThe mock-up will be 1:1 scale, meaning that the 5.5 m of the tunnel, and the half-cell length at\nhigh machine energy ( 30 m), will be accurately reproduced. The only area that will not be reproduced\nin the mock-up is the trench under the ground level.\nAs shown in Fig. 3.79, the mock-up structure will be made of steel, featuring an arch every 3\nmetres, reinforced by transverse beams. Wooden or aluminium panels will be attached to the structure\nand painted to replicate the appearance of concrete accurately. The main advantage of the steel structure\nis that it can be easily dismounted and remounted if needed, as well as updated and adapted to the\nevolution of the machine arc region.\nFig. 3.79: CAD of the mock-up structure in development.\nFor the 2025 installation, the initial mock-up will consist of a combination of real and dummy\nelements, with the flexibility to evolve over time. To facilitate integration testing and optimisation, the\nmagnets will be constructed from wood, while actual support structures, including jacks, girders, and pil-\nlars, will be installed. The arc envelope is designed to support the full weight of all real components from\nthe outset, ensuring that no structural modifications will be required when transitioning from dummy to\nreal elements.\n201\n\nA prototype of the remote maintenance and inspection system (RMIS) robot will be installed\nto evaluate various operational scenarios, including routine maintenance, emergency procedures, and\nleak detection. Additionally, a prototype of the fire door and its partition will be deployed to assess\nits positioning, integration, installation process, and interaction with the RMIS. Following these initial\ninstallations, all essential services\u2014including cooling and ventilation systems, electrical infrastructure,\nand IT networks\u2014will be implemented.\nFig. 3.80: CAD of the integration of the RMIS, CAD of the integration of the fire door and partition and\nservices, example of wooden magnets.\n3.10.6\nNext steps\nAs mentioned above, a significant amount of work still needs to be done before reaching a satisfactory\nsolution for the integration and stability of the arc half-cell elements. In particular, the following main\nactivities have been identified:\n\u2013 Install the first version of the mock-up, and test integration aspects.\n\u2013 Build an arc configuration compatible with the installation/uninstallation/handling procedures de-\nfined by the Handling Engineering team (see Section 8.6).\n\u2013 Develop and commission the mixed reality system in the mock-up region.\n\u2013 Continue the study and optimisation of the supports (jacks, girders, supporting structures) from\nthe stability and cost point of view, also via prototypes and dedicated experimental measurements\nin the mock-up (e.g., ground-induced vibrations on the 6 m SSS, random-vibrations effects).\n\u2013 Perform thermomechanical simulations to evaluate, for example, the thermal deformations induced\nby the tunnel temperature variation on the elements of the girder, also validating the proposed air\nflow cooling system.\n\u2013 Update and upgrade the mock-up main systems. In particular, the initial dummy structures (wooden\nmagnets, vacuum chambers) were replaced with the first prototypes produced by the equipment\ngroups while also adapting the mock-up to the changes of the arc region.\n3.11\nMachine protection hard- and software systems\nThis section describes the systems, hardware and software, closely related to the machine protection of\nthe accelerator. They are the systems which presently fall under the responsibility of the TE-MPE group.\n3.11.1\nInterlock systems\nInterlock systems are essential for the safe operation of the FCC-ee. The following interlock systems\nhave been identified for the FCC-ee collider and booster.\n\u2013 Warm magnet interlock controller (WIC). The system protects the warm magnets and the syn-\nchrotron radiation absorbers from over-heating because of missing (water) cooling and/or running\n202\n\nFig. 3.81: FCC-ee GHC Arc Half-Cell sectional drawing - EDMS 3180552 [320]\nat too high a load (magnet current or synchrotron radiation load). In case of a power converter\nfault, it can also act as an interface between the power converters and the beam interlock system.\nThe system is connected to thermal switches, flow meters of the water-cooling system, the power\nconverters and the beam interlock system.\nA diagnostic system that identifies which magnet or synchrotron radiation absorber segment has\nan over-temperature needs to be developed. The system should not require individual cables to be\ninstalled to these magnets; such a system does not exist at the moment. In the existing machines,\nindividual cables are installed, but this would be too expensive for a machine as large as the FCC-\nee.\n\u2013 Beam Interlock System (BIS). This is the core of the machine protection system and connects the\nmany Users (Power converters, RF, Beam Loss Monitors, Interlock Systems etc.) to the beam\ndumping system. There are dedicated BIS for the injection and extraction systems, which can\ninhibit injection or extraction.\nThe BIS is based on customised electronics and needs to be designed and developed based on the\nfailure cases and reaction times derived by detailed machine protection studies for the main ring,\nthe full energy booster-ring and the transfer lines. The current LHC system does not account for\nany especially fast interlock channels. Potential designs of extra fast interlock channels have to be\nstudied and the electronics required designed and developed in case the machine protection studies\nshow that reaction times in the microsecond range are required.\n\u2013 Safe Machine Parameters (SMP). The SMP is closely linked to the BIS. It provides flags to the\ndifferent BIS to allow masking of certain interlock channels when operating with low beam inten-\nsities and/or energies (needed for setting up the accelerator). It also provides beam parameters to\nmany different systems like the beam loss monitors and the experiments, all in a highly reliable\n203\n\nFig. 3.82: FCC-ee Conceptual layout Arc Half-Cell - V24.3_GHC Q-S-S configuration - EDMS 3180559\n[321]\nenvironment.\n\u2013 Fast Magnet Current Change Monitor (FMCM). For some normal conducting magnet systems the\nreaction time from the power converters to request a beam request in case of powering failures can\nbe too long. For those systems a dedicated system can be installed. The FMCM has a very fast\nreaction time to request a beam dump in case of fast magnet current changes (in general a power\nconverter trip).\n\u2013 Powering Interlock Controller (PIC). This system interfaces the protection of the super conducting\nmagnets (Quench Detection System) to the Beam Interlock System and requests a beam dump in\ncase of any problems related to the superconducting magnets. For this reason it also interfaces\nto the many systems to which the superconducting magnets are connected: power converters,\ncryogenics, UPS etc.\n3.11.2\nProtection systems for superconducting magnets\nThe FCC-ee will be dominated by normal conducting magnets and circuits. However, superconducting\ncircuits of the FCC-ee (e.g., the circuits of the final focusing magnets at the IPs) will require dedicated\nprotection systems to ensure their safe operation.\n\u2013 Quench detection and data acquisition system (QDS). The QDS is made of high-precision, fast,\ndedicated electronic boards for the detection of quenches in superconducting magnets, busbars,\nlinks and HTS current leads. It interfaces all superconducting magnet and circuit protection sys-\ntems (energy extraction system, local protection units, coupling loss induced quench systems), the\n204\n\npowering interlock controllers and the beam interlock system. If a quench is detected, the QDS\nwill send high-resolution data to the post-mortem system, which is crucial to validate the correct\nbehaviour of the circuit and the protection system before releasing them for re-powering.\n\u2013 Energy extraction systems (EE): These are clusters of racks with high-current switches, controls\nand extraction resistors. If there is a power failure or quench of a superconducting magnet, the\nEE systems are activated and they ensure the timely and safe extraction of the energy stored in\nthe circuit to the extraction resistor. The EE systems interface the QDS and the PIC and send\nhigh-resolution data to the post-mortem system.\n\u2013 Local protection units. These are quench heater power supplies, to protect superconducting mag-\nnets in case of a quench. They consist mainly of an energy storage system based on capacitor\nbanks, which discharge their energy into quench heater strips installed on or in the coils of the\nmagnets if there is a quench. They interface the QDS and the instrumentation feed boxes (IFS).\n\u2013 Coupling loss induced quench system (CLIQ). These are special double racks size systems, to\nprotect superconducting circuits in case of a quench or powering failure. They consist mainly of\nan energy storage system based on capacitor banks, which discharge their energy into the magnet\u2019s\ninductance, creating a high di/dt in the circuit. They interface the QDS and the Instrumentation\nFeed Boxes (IFS).\n\u2013 Cold diodes for circuit protection. These are radiation hard by-pass diodes required to divert the\ncircuit current around the quenching magnet. They are specially designed together with industry\nand need to be qualified for the integrated radiation dose expected, and the 1 MeV equivalent\nneutron fluence levels.\n\u2013 Warm diodes for circuit protection. These are warm by-pass diodes to ensure a discharge path of\nthe oscillating currents induced by the activation of the CLIQ systems around the power converter\nof a circuit. They are usually procured from industry.\n\u2013 Electrical quality assurance (ElQA). This is the dedicated high precision, high voltage (mobile)\nhard- and software for the ElQA testing of all superconducting circuit elements during production,\nreception and commissioning.\n\u2013 Proximity equipment (current lead heaters). These consist of regulators and power transformers\nwith support structures and controls racks. They are required to heat the normal conducting end\nof the HTS current leads to avoid the creation of condensation and ice. They are usually custom\ndesigns based on commercial components.\n\u2013 Instrumentation feed boxes (IFS). These boxes interface cables for discharge and instrumentation\nfrom the cold mass of superconducting magnets and links. They consist of dedicated PCBs for\ninterfacing the QDS, cryogenic and protection equipment (CLIQ, Local protection units) and are\ninstalled on top of the instrumentation flanges of the cryo-assemblies.\n3.11.3\nSoftware systems\nSoftware systems play an important role for interlocking, efficient and safe validation and safe operation\nof the FCC-ee.\n\u2013 Software Interlock System (SIS). The SIS completes the hardware interlock system. It generally\nreads the equipment status over software and is connected to the BIS to request a beam dump when\nneeded. It is less reliable and significantly slower in reaction than a full hardware system however\nit is more flexible. This system is presently developed mainly by the BE-CSS group. However, as\nit is important and related to machine protection, while very likely not listed in any other category,\nit has been added to the TE-MPE list of items.\n\u2013 Post mortem systems. The safety of the accelerators depends on the correct functioning of the\ncomplete chain of the machine protection system and the in-depth understanding of the reason for\n205\n\nbeam dump requests and powering failures. The post-mortem system receives and reliably stores\nhigh-resolution data from all relevant systems and performs automatic analyses of these data. It\ninterfaces with the SIS and can block beam operation if the analysis criteria are not met.\n\u2013 Accelerator testing (AccTesting) & analysis tools for commissioning and operation. These are\nsoftware systems running on top of the CERN IT infrastructure for scheduling, automatically\nperforming and evaluating hardware commissioning tests of the accelerator systems. They are\nessential for efficient and safe hardware commissioning and for validating the conformity and\ncorrect operation of the various hardware systems, many of which are related to the different\nelectrical circuits and to machine protection.\n\u2013 Fault tracking and machine availability. These are software tools for the simulation and the track-\ning of system and accelerator faults. They are very important during the design and operation of\nthe accelerators and their different hardware systems, especially those related to the safety of the\naccelerator. The machine availability needs to be studied and tracked to optimise performance and\ndetermine where investments are best placed to improve performance.\n3.11.4\nConclusion on machine protection hard- and software systems\nNew techniques and concepts will need to be developed for the WIC system to identify the faults\u2019 loca-\ntion, without having to pull individual cables to the sensors. In case required, special extra fast channels\nof the BIS will need new technologies. No specific new developments have been identified for all other\nsystems described in this chapter.\n3.12\nAn alternative arc magnet design\nFCC is also pursuing an alternative design for the magnets in the arc short straight sections, which could\nbring the following advantages compared to the baseline design:\n1. Lower power consumption and lower weight.\n2. More flexibility in optics design.\n3. An improved filling factor.\n4. State-of-the-art technology with increased societal impact.\nThe lower power consumption is achieved by replacing the main quadrupoles and sextupoles of the\narcs with superconducting ones. In the baseline scheme, about 80 MW of electrical power is consumed\nat top energy by the collider main magnets, the majority of which goes to power the quadrupoles and\nsextupoles. An estimated further 14 MW is consumed by the cooling and ventilation systems for these\nmagnets. By employing superconducting quadrupoles and sextupoles, one can dispense with ohmic\nlosses at the expense of cooling power, which is estimated to be only a fraction of the ohmic load.\nReplacing the normal conducting sextupoles and quadrupoles with magnets based on high-temperature\nsuperconductors (HTS) would result in the following gains:\n\u2013 Magnets can be nested, increasing the dipole filling factor;\n\u2013 Magnets for the electron and positron beams are independently powered, giving greater flexibility;\n\u2013 Power consumption for the relevant systems is significantly reduced;\n\u2013 The use of novel materials and techniques (HTS conductors) increases the relevance of FCC to\nsociety and its sustainability credentials.\nThe idea has led to the approval of two projects, named FCCee-HTS4 and FCCee-CPES, that have\nbeen financed through the CHART programme, a Swiss mission-oriented research network focused on\ntechnology development for the FCC.\n206\n\nHTS4 aims to investigate the nested magnet idea using HTS conductors. The end goal of the\nproject, a metre-class prototype, is supported by subscale sextupole demonstrators manufactured at\nCERN and PSI. The first two demonstrators investigate the options of using a wax-impregnated canted-\ncosine-theta (CCT) coils, based on insulated HTS tape, and a partial-insulation based cosine-theta (CT)\nconfiguration. The prototype will consist of a nested quadrupole-sextupole configuration.\nFig. 3.83: The three different types of short straight sections of the baseline design (left). On the right,\nthe single type using nested HTS magnets.\nThe minimum length of the short straight section (SSS), 3.5 m, is dictated by the minimum length\nof the quadrupoles, below which synchrotron radiation issues arise. This corresponds to a total magnetic\nlength of 3 m. To make the magnets as compact as possible, the sextupole can be nested in the same axial\nspace as the quadrupole.\nTwo cooling strategies are being considered. Both involve a dry, cryogen-free magnet. The first\nconsists of a cryogenic distribution line connected to several cryoplants located on the surface. The\ndistribution line services the HTS modules via Neon-based heat exchangers. This arrangement allows\nsimple installation and replacement of magnets.\nA second option is to give each magnet its individual cooling system in the form of multiple\nredundant cryocoolers. By utilising high-reliability single-stage coldheads, it is expected that such a\nconfiguration can achieve high overall system reliability and availability.\nFig. 3.84: Concept of cooling method based on cryogenic distribution line (left), and heat exchangers be-\ntween the line and the HTS SSS\u2019s (right). Sketches courtesy of J. Bessler, E. Rosenthal, Forschungszen-\ntrum J\u00fclich.\nThe optimum operating temperature of an HTS-based short straight section (SSS) is found by\nbalancing the operational costs (dominated by electricity use for cooling) with capital costs (dominated\nby HTS conductor). For the cryocooler-based cooling option, 40 K seems to be a sweet spot for a wide\n207\n\nrange of energy and conductor prices. It is expected that results from a conceptual design study of the\ndistributed cooling line would yield an overall lower total cost-of-ownership option, with the optimum at\na lower temperature.\nThe sextupole demonstrators (Fig.3.85) are designed to generate a gradient of 1000 T/m2 (the FCC\ndesign calls for a gradient of 820 T/m2) at a current of 250 A.\nFig. 3.85: The HTS4 sextupole demonstrator: left: CAD design; right: the magnet after winding, before\nthe assembly of its aluminium sleeve.\nThe improvement expected in the dipole filling factor over the baseline solution is 7%. This would\ntranslate to 7% higher luminosity at the same beam power or one year of running less in the FCC-ee\n14-year programme for the same physics output. This also translates to 7% less RF voltage needed at top\nrunning, and thus the number of 800 MHz cavities required is reduced.\nThe nesting of quadrupoles and sextupoles paves the way for nesting a dipole component as well\nsee, for instance, Ref. [322], increasing the filling factor to 120% of the baseline value. Such an inclusion\nin the HTS SSS is possible.\nHTS4 is also pursuing technologies of partially insulated HTS tapes. Partially insulated coils have\ndistinct advantages in robustness and effective current density, as they reduce the amount of stabilising\ncopper required in case of a quench. Developing such a technology is important for the future of HTS\naccelerator magnet technology and a coating station (Fig. 3.86) has been built at PSI to coat HTS tapes\nwith a partially insulated layer.\nThe CPES project at ETHZ designed a highly efficient power supply suitable for powering accel-\nerator magnets while operating inside the cryostat at cryogenic temperatures. In this way, the large heat\nload associated with the high-current conduction-cooled leads required to transfer the current from room\ntemperature to cryogenic conductions can be avoided. This is a key component in making cryogen-free\nmagnets energy efficient.\nCPES built a demonstrator (Fig. 3.87) with five full-bridge phase modules and up to 100 A output.\nTest results of this module at 100 A are extrapolated to a heat load of 4.4 W at 250 A. In comparison,\na pair of high-current conduction-cooled current leads would have 23 W of losses in the cryostat. For\ncryogenic power supplies to be viable in an accelerator environment, additional studies on component-\nand system-wide reliability and radiation hardness are required.\nFor the cryo-cooled approach, equipment needs to be placed in the collider tunnel (cryocooler and\nassociated electronics) or indeed inside the SSS cryostat (power supply). Therefore a radiation study\nhas been performed to ensure that equipment will continue functioning during the whole lifetime of the\nFCC. This study, that uses somewhat more shielding around the SR photon stoppers, shows that doses of\n1 kGy or less are possible for the equipment concerned (to be validated in the next phase).\nThe possibility of using HTS superconducting magnets operated at or below 40 K and replacing\n208\n\nFig. 3.86: Left: The coating station, with the uncoated tape-spool on the left and coated tape spool on the\nright. The coating occurs near the bottom of the setup, after which the tape is heated to be dried before\nre-spooling. Right: one CT sextupole coil wound using 4 mm coated dummy tape.\nFig. 3.87: The CPES demonstrator comprises five full-bridge phase modules using Gallium Nitride\n(GaN) transistors.\nthe baseline approach of iron-based non-superconducting magnets seems promising but also involves\nsome risks (mainly having to do with costs and the fact that this is a radically different approach) that\nneed to be understood. The HTS4 prototype will be tested in early 2026, at which point the technological\nreadiness level as well as integration into the FCC-ee tunnel and timeline will be reviewed.\n3.13\nDismantling FCC-ee\nIn order to make way for the FCC-hh, the FCC-ee machine and infrastructure will have to be removed.\nThis section presents a first look at the strategy and process for dismantling FCC-ee and identifies the\nmain cost drivers as well as logistics and planning constraints. Given that the details of the machine and\nits components are still being refined, it is clear that the considerations here can only be approximate\nbut can be refined as the project progresses. The dismantling study drew heavily on the experience of\ndismantling LEP [323].\n209\n\n3.13.1\nBasic strategy\nObjectives\nThe objective is to dismantle the FCC-ee machine and its specific infrastructure in order to leave the\nunderground areas in a state ready for the installation of the FCC-hh. Since the regular arcs account for\n80% of the FCC circumference and 90% of the mass, their clearing will dominate the overall dismantling\nprocess and drive the logistic constraints.\nFig. 3.88: Cross-section of the current FCC-ee tunnel integration in the regular arcs. The main areas to\nbe dismantled are circled in blue.\nFigure 3.88 shows the cross-section in the regular arc of the FCC-ee. The areas circled in light\nblue represent the principal areas that will be dismantled in the machine tunnel. The equipment consists\nof the collider and booster rings along with their metallic support and alignment structures, control and\nDC powering cables and piping for a variety of cooling circuits. It is assumed that the main ventilation\nsystem as well as safety systems, AC power cables and fibre optic cables will not require dismantling.\nIn addition to the main machine tunnel there are alcoves, located at about every \u223c1.5 km along the\ncircumference of the arc, housing local equipment, like low voltage distribution and repeaters. Much\nof this equipment will not be dismantled. However, the alcoves will also house the power converters\nfor some of the FCC-ee magnets. The removal of this equipment, along with the associated DC cabling\nrepresents a significant workload and logistic challenge.\nAssumptions for the study\nA number of assumptions were made for the study and these are listed below (in no particular order)\nalong with a brief explanation of the reason for the assumption and its impact.\n\u2013 FCC-ee operation will end with \u223c5 years of physics at the top energy (360 GeV). This is the most\nconstraining scenario from a radiological point of view as operation at this energy will produce the\nhighest levels of induced activity in some machine elements. It is assumed that the arc magnets and\nvacuum chambers of the collider and booster, as well as the photon stoppers will become activated.\nHowever, the materials chosen for these components will be selected so that the levels of activity\nare minimised, and it is expected that the activity will decay to below release levels within a few\nyears. In the straight sections, parts of the RF modules and individual components (such as beam\n210\n\ndumps and collimators) will also become activated. The levels will be determined from FLUKA\nsimulations as well as measurements in-situ (see Section 3.13.3) during and after operation. The\nremainder of the machine elements will be treated as conventional.\n\u2013 To determine the timescale of dismantling, it is assumed that the work will be done during two\n8-hour shifts per day, working five days a week. Such a schedule assumes that equipment mainte-\nnance can be carried out overnight and during weekends.\n\u2013 The machine shafts at all 8 points will be used to extract the equipment (although not necessarily\nat the same time). The dismantling of the experiments will be via the experiment cavern shaft(s)\nand kept separate from the machine dismantling.\n\u2013 As the bottleneck for dismantling is likely to be in the underground areas, the logistics of the\ndisposal of the equipment once at the surface are considered in less detail here. The main con-\nsideration given to the surface sites is to make some estimates of the needs in terms of temporary\nstorage.\nEquipment to preserve\nMost of the equipment removed from the machine will be treated as waste. After radiological checks, it\nwill be disposed of via the appropriate pathway. However, some of the equipment is of high value and\nhas potential for reuse. The major system in this class is the RF, with a total installed voltage of over\n23 GV, and a construction cost well in excess of 1 BCHF. Table 3.25 summarises the RF system installed\nfor the t\u00aft run.\nTable 3.25: RF system installed for t\u00aft running (180 GeV/beam).\nNumber of\nTotal\nFrequency\nMachine\ncryomodules\nVolume\n[MHz]\n[m3]\n400\nCollider\n70\n2519\n800\nCollider\n100\n4320\n800\nBooster\n124\n5357\nSum\n294\n13196\nPreserving the cryomodules in a way that would allow their re-use in another facility implies\nstoring them in appropriate conditions, with the cavities themselves either under vacuum or filled with\nan inert gas. Assuming that cryomodules can be stacked on top of each other to a maximum of 3\nmodules, the storage space needed would amount to a floor surface area of 4400 m2 (not including access\nspace). In addition to the cryomodules, there is the RF power system, consisting of klystrons, circulators,\nwaveguides and power supplies. With 2 klystrons per module a total of 140, 400 MHz klystrons and 288,\n800 MHz klystrons would need to be stored.\nFor this study, it is assumed that all RF related equipment apart from the waveguides is kept and\nstored, although in reality a much more detailed study will be required to determine which parts of the\nsystem to preserve and which to discard. Besides the RF system, there may be other pieces of equipment\nto be kept, but these are likely to be smaller, individual items (e.g., specific beam instruments) which are\nall installed in the long straight sections. None of the machine elements in the arcs will be preserved.\nIt is also assumed that the radioactivity of the arc components (magnets and vacuum vessels) will\ntake a few years to decay, and they will require interim storage for this period.\n211\n\n3.13.2\nRegulatory framework\nThe regulatory framework concerning the elimination of radioactive waste is currently defined by the\ntripartite agreement between CERN and the Host States as explained in Ref. [324]. The agreement\nallows CERN to eliminate radioactive waste in the two Host States by using the most technically and\neconomically advantageous pathways in both countries. This principle allows CERN to optimise its\nradioactive waste elimination by choosing the most appropriate solution corresponding to the type of\nwaste.\nConcerning the elimination of radioactive waste produced by CERN experiments, the principle is\nthat the collaborating institute remains the owner of the equipment they have provided (even if radioac-\ntive) and that they take it back unless otherwise agreed.\nThe cost estimate for the disposal of radioactive waste from CERN\u2019s facilities is based on an\ninventory indicating the amount and radiotoxicity of present and future radioactive waste, i.e. waste\nstored at CERN and waste that will be produced by preventive and corrective maintenance or by the\nupgrade of CERN\u2019s facilities or experiments. The estimate of future waste will not include an estimate\nof waste produced in case of the decommissioning of CERN\u2019s facilities until the decommissioning has\nbeen approved.\n3.13.3\nRadiological estimations and zoning\nThe radiological zoning is a key driving factor for the logistics of dismantling the machine. The aim\nof the process is to identify all components and structures which are likely to become radioactive. This\nwill be based on knowledge of the beam\u2019s behaviour and its interaction with matter and the history of\noperation. The classification of a zone determines the precautions and procedures which have to be\napplied. The synchrotron radiation emitted by the high-energy leptons will strike the localised absorbers\nin the vacuum chamber and will induce radioactivity. Other areas expected to become radioactive are\nbeam scrapers, collimators, shields, beamstrahlung, main beam dumps and, to some extent, the magnets\nthemselves. The vacuum vessels and magnets and, in particular, the absorbers, which are placed every\n4-5 m around most of the machine circumference, obviously present the largest volume of radioactive\nmaterial. Simulations show that the level of activity in the activated components will be very weak\n(TFA) and appropriate precautions will be taken in the dismantling process. Current studies indicate that\nthe magnets and vacuum vessels of both booster and collider will not become activated until the t\u00aft run.\nDuring dismantling, the most active components will be removed first unless they are in an area which\ncan be closed off until the rest of the machine has been removed. This could apply, for example, to the\nbeam dump where the tunnel containing the dump transfer line and radioactive dump block, could be\nsealed off.\nPredictions of the levels of activity are made by simulations using tools such as FLUKA and\nthese will form the basis of the initial zoning. Unexpected beam losses may lead to additional localised\nradioactivity, and this information will be incorporated in the overall picture. The operational zoning\nfor dismantling will be confirmed by radiation measurements carried out after the definitive stop of the\nmachine and before any dismantling is started.\n3.13.4\nDismantling process\nIt is assumed that the dismantling can be done from all 8 points. However, it is unlikely that all 8\npoints will be used at the same time. The activities will be split into a series of \u2018trains\u2019 that will move\nprogressively through the arcs. Each train will consist of the personnel, equipment, and transport vehicles\nneeded to remove a specific set of equipment or carry out specific actions. Each train will have to\ncomplete its work before the next train starts. However, some optimisation may be possible. The order\nof the activities is listed below:\n\u2013 Radiological measurements and zoning \u2013 measurements of radioactive activity. Final verification\n212\n\nof the zoning of the arcs.\n\u2013 Where essential systems and services (fire protection, communications, safety systems etc.) will\nbe interrupted or removed, compensatory measures will have to be installed before the start of\ndismantling activities.\n\u2013 Cryogenic systems will have to have the helium evacuated and be warmed up before the start of\ndismantling equipment in the affected areas.\n\u2013 Cooling circuits will have to be emptied.\n\u2013 Electrical safety: all elements to be removed have to be made electrically safe with an electrical\nlockout, followed by a definitive separation from the supply.\n\u2013 Radiation survey measurements of the equipment and its surroundings (checking for anomalies\nand contamination risks).\n\u2013 All of the equipment removed from the machine will undergo a triage measurement to determine its\nfurther destination: release, detailed free release measurement or further storage as a radioactive\nitem. There will have to be space and dedicated measurement equipment for this free release\nmeasurement.\n\u2013 Removal of radioactive components like collimators, which will be more highly activated.\n\u2013 Removal of booster magnets and vacuum chambers as activated materials.\n\u2013 Dismantling of the metallic structures supporting the booster as the last part of booster machine\nelement removal.\n\u2013 Removal of the collider vacuum chambers and magnetic elements together with the photon stop-\npers.\n\u2013 Dismantling of the remaining machine support structures (can probably be done in parallel with\nthe removal of the collider).\n\u2013 Removal of straight section elements and equipment.\n\u2013 Removal of unused piping.\n\u2013 De-cabling.\n\u2013 Final cleaning and floor/walls repair/repainting as necessary.\nCritical logistics paths for dismantling\nAs already mentioned, this analysis is based on dismantling two half-arcs from each point. Since the\nmain components to remove will be the arc magnets, this defines the scale and sets the limits of the\ndismantling process.\nTunnel transport of arc components\nThe average distance travelled will be 3 km each way from the loading location to the extraction point.\nBased on a vehicle speed of 10 kph loaded and 20 kph empty, the average travelling time for a round trip\nwill be \u223c30 minutes. Clearly, journeys to the beginning of the arc will be short, and those to mid-arc will\nbe longer, but the average time/distance was used in the calculations. Dismantling will start on one side\nwith the closest magnets and on the other at the 6 km mid-arc extremity. To be added to the travelling\ntime are the loading/unloading times: 45 minutes for loading (135 minutes for the 3-dipole trains) and\naround 30 minutes for unloading.\nTaking into account that there will be two 3-dipole trains for every three SSS trains, each side of\nthe arc would be capable of delivering 6 or 7 loads to be lifted within a double 8-hour shift. Therefore,\nit is assumed that only one transport vehicle will be needed on each side in the tunnel to deliver enough\nmagnets to saturate the crane capacity (see below).\n213\n\nArc equipment dismantling\nAs well as the transport team, each train will have a team at the worksite to cut or dismantle the equipment\nand prepare it for transport. It is assumed that enough time will be available between each transport to\nprepare the next load.\nLifts and cranes\nThe bottleneck in the extraction process is the crane lifting time. The depth of the shafts varies from\n180 m (PD) to 400 m (PF) giving an average shaft depth of 240 m. For heavier loads, assuming a lifting\nspeed of around 8 m/minute [325], a single hoist would take around 35 minutes to complete. Allowing\n30 minutes for loading and 30 minutes for unloading, an average single round trip to the surface (240 m)\nwill take \u223c1.8 hours. This sets an upper limit on the number of hoists during a double 8-hour shift in the\nrange 6 to 10, according to the depth of the shaft.\n3.13.5\nMaterial quantities\nArcs\nTable 3.26: Contents of a half-cell in the regular arc\nDescription\nQuantity\nLength\nApprox. Weight\n[m]\n[kg]\nBooster dipoles (2 sections)\n4\n5.55\n2500\nCollider main dipoles (2 sections)\n4\n5.55\n5000\nBooster short straight section\n1\n2\n4200\nCollider short straight section\n1\n6.3\n\u223c11 000\nMetallic support structures\n1\n10 000\nDetails of the quantities concerned have been addressed in a separate document [326], and only\nthe main conclusions are presented here. These numbers have been derived based on the current state\nof the design, which will certainly evolve but should not affect the conclusions by more than \u00b120%.\nTable 3.26 summarises the contents of the regular half cells; the weight of booster magnets has been\nassumed to be the same as those of the collider ring. For the support structures, an overall weight of 10\ntonnes per half-cell is assumed.\nExcluding the busbars, total material weight is 118.35 ktonnes for the arcs and 121.25 ktonnes for\nthe whole machine if the straight sections are included. If one assumes that copper cored cables are\nused, there will be around 2.4 ktonnes for the whole machine (0.8 ktonnes, if aluminium is used). Based\non cabling of the sextupole families using 120 mm2 section copper-cored cables, their weight will be\n1.6 ktonnes for the whole main ring. A similar value for the booster sextupole powering can be assumed\nand in both cases the weight will be reduced by a factor 3 if aluminium is used. Each half-cell will also\ncontain other equipment, which is cabled to the nearest alcove (orbit correctors, beam position monitors,\nbeam loss monitors, interlock cables and miscellaneous signals). It has been estimated that there will be\n\u223c31 000 km of these cables. It is assumed that the other cables for such things as AC power, fibre optics\nand the access system will not be removed as they will serve FCC-hh.\nThe collider and booster dipole magnets can be transported and lifted stacked in groups of 3 on\nthe transport trailer. The collider QSS girders are the heaviest elements and will be evacuated one at a\ntime. There will be 368 lifts for each of the quadrupole girders (QSS, QS and Q) and booster SSS and\n245 lifts for the collider dipoles and a similar number for the booster dipoles (see Table 3.27).\n214\n\nTable 3.27: Hoist inventory for one extraction point, assuming dipoles can be transported three at a time,\nworking for a minimum duration of 28, 5-day weeks with 2 shifts per day.\nElement\nQuantity\nNo. Hoists\nNo. per week\nper crane\nBooster dipoles\n736\n245\n11 (\u00d73)\nBooster SSS\n368\n368\n16\nCollider dipoles\n736\n245\n11 (\u00d73)\nCollider SSS\n368\n368\n16\nTotal\n1226\nLSS\nThe long straight sections of the collider and booster contain a further 520 quadrupoles and 200 sex-\ntupoles, and they have a total weight \u223c2900 tonnes.\nRF\nThere will be 170 cryomodules installed in the collider at PH and 124 in the booster at PL. These will be\npowered by the klystrons in the gallery above the tunnel and linked to the modules by the waveguides.\nCryogenics\nThe cryogenics equipment is located in the klystron galleries, the long straight sections, the service\ncaverns, shafts and surface buildings. The equipment to be removed the comprises control equipment,\ndistribution lines, cold boxes and storage vessels. Sensitive elements like instrumentation and valves\nwill be removed first. The cryogenic equipment associated with the machine-detector-interface, MDI,\nhas not been specified at the time of writing and its dismantling has not been considered. However, it is\nnot expected to have a significant impact on the overall timescale or cost.\nIt is assumed that both cryoplants at PH will be dismantled, although one may be kept for FCC-hh.\nAlcoves\nDetailed estimates of the equipment in the alcoves which has to be removed are given in Ref. [326].\nTable 3.28 presents an overview of this equipment and the associated cabling.\nTable 3.28: Summary of electrical equipment to be dismantled from the various alcoves.\nCables\nConverters\nNumber of\nNumber per\nLength per\nNumber of\nNumber of\nalcoves\nalcove\nalcove [m]\nconverters\nracks\nBig alcoves\n16\n460\n274 666\n228\n273\nSmall alcoves\n40\n880\n429 148\n440\n238\nGrand Total\n56\n42 560\n21 560 578\n21 248\n13 888\n215\n\n3.13.6\nTimescales\nArcs\nGiven the average 1.8 hours needed for a round trip of the crane hook, the time required to perform the\n1226 hoists corresponds to about 28 weeks working two shifts per day and five days per week.\nLSS\nIt is assumed that the machine elements in the LSS between the IP and the arc can be dismantled in\n\u223c4 weeks.\nRF\nThe rate of removal of RF cryomodules is limited by the time it takes to carefully dismantle and transport\nthem, and it is expected to take around the same time as the installation. The removal of klystrons and\nwaveguides should be \u223c50% faster than installation and can be done in the shadow of the cryomodule\ndismantling. The rate of dismantling cryomodules is expected to be around 16 stations per month, work-\ning two shifts, 5 days per week. Working in PH and PL in parallel, the time envelope determined by the\ndismantling of the 170 cryomodules in PH will be <12 months.\nCryogenics\nThe sensitive elements in the service caverns and tunnel will be removed first and the cold boxes will be\npurged and sealed before removal. Once connecting pipes have been removed, the boxes can be lifted\nand removed. At the surface, as many elements as possible will be carefully removed for potential reuse\nin FCC-hh. Dismantling at the surface can only start once all cryogens have been stored and underground\nelements have been disconnected.\nIt has been shown in Ref. [324] that if PH and PL are done in parallel, the cryogenics system can\nbe dismantled in <1 year allowing around 6 weeks for the initial preparatory stages.\nOverall timescale\nTime/week\n-\nPA\n+\n-\nPB\n+\n-\nPD\n+\n-\nPF\n+\n-\nPG\n+\n-\nPH\n+\n-\nPJ\n+\n-\nPL\n+\n4\n8\n12\n16\n20\n24\n28\nPreparatory phase\n32\n36\nArc Dismantling\n40\n44\nRF Dismantling\n48\n52\nLSS and cleanup\n56\n60\n64\n68\n72\n76\n80\n84\n88\n92\n96\n100\n104\nFig. 3.89: Schematic representation of a possible timeline of machine dismantling based on 2 shifts\nworking, 5 days per week. The arrows on PA indicate the direction of progress through the arc. The\npreparatory phase is only shown for the first two arcs.\nThe overall duration is governed by the rate at which the main arc components can be removed\n216\n\nfrom the tunnel. In the following, it is assumed that the overhead crane will be working continuously 5\ndays per week and 16 hours per day.\nTo be added to 28 weeks for arc equipment removal are the times needed for initial activities\nsuch as radiological zoning, electrical safety, implementation of compensatory systems for safety and\nservices, cryogenics warmup etc. as well as the dismantling of the straight sections and the de-cabling\nand de-piping activities which follow. It has been assumed that the LSS dismantling and cleanup will\nrequire around 3 months after the arc has been cleared. Careful overall planning should allow much\nof the work to be performed in the shadow of the overall dismantling of the machine elements in other\nareas. Smaller loads can be brought to the surface using the lifts, which have a 3 t capacity.\nBased on 5 days, two shifts working, and these assumptions, a possible timeline for dismantling\nis shown in Fig. 3.89. The direction of the trains\u2019 progression is indicated on PA, showing that one train\nstarts from mid-arc and the other at the IP end. The preparatory phase is only indicated for PA and PG\nas it will be in parallel with other activities for the other points. The total time required for this scenario\nis \u223c2 years. Adding two shifts and working at weekends would reduce it to a total of about 1.4 years.\n3.13.7\nSurface storage and logistics\nOnce the equipment reaches the surface, it will have to be transported from the shaft head to a temporary\nstorage where it can be re-checked for radioactivity before being prepared for onward transport. At this\nstage, traceability data will also need to be generated for each load. The preparations may include further\ndismantling and sorting of the material before loading into (new) specific transport containers. Cranes\nwill be needed for the new storage facilities.\nAfter t\u00aft running, the arc magnets and vacuum chambers will remain radioactive for a period of up\nto a few years. They should be stored on-site for the decay period before entering the disposal pathway.\nThe space requirement for this would amount to \u223c20 000 m2 if they are piled four high. This interim\nstorage could be in the form of tent-like structures.\nA tent-type structure which has no foundations but which could be heated to keep it above freezing\nshould also suffice for temporary surface storage (triage, etc.).\nTo set the scale on the size of the covered storage and preparation area, it can be assumed that it\nshould be capable of holding the material which comes out of the machine in 1 week, and there should\nbe sufficient space around each element to allow any dismantling/conditioning to take place. Based on\nthe numbers given in Table 3.27 and that dipoles will require a footprint of 11 m\u00d73 m (to allow access),\na covered area of 1500 m2 would be required for the 5-working day, two-shift scenario. To be added to\nthis will be space for loading and unloading the equipment. The installation of a temporary industrial\ntent/hanger of an appropriate size at each surface point will, therefore, be required. It should be noted\nthat during dismantling, equipment for FCC-hh will be arriving at CERN for assembly and testing, which\nwill put an additional strain on the space available on CERN. Site security is an important issue, given\nthe value of the materials being temporarily stored at surface sites, as well as the sensitive nature of\nlow-level radioactive elements. Additional security will, therefore, be necessary.\nFor equipment requiring long term storage in controlled conditions, a more substantial building\nwill be required. This type of building typically has large access doors, thermal insulation and a small\ncapacity crane. These lightweight buildings are limited to a span of around 20 m so it may be necessary\nto construct a number of them.\n3.13.8\nDismantling budget items\nAs much as possible of the work will be done by CERN staff and their regular support contractors so\nthat they are familiar with the equipment being dismantled. However, they will not be able to do all the\nwork and therefore additional contractors will be required. These contracts will also cover things such\nas operating the traceability system, removing cables and pipework, and ensuring safety supervision.\n217\n\nDetails of the costs for the various labour components have been given in the report of the FCC-ee\ndismantling study [324].\nEstimates of the cost of infrastructure changes and additional equipment, summarised in Ta-\nble 3.29, have also been included in Ref. [324].\nTable 3.29: Summary of equipment and infrastructure changes required for dismantling\nDescription\nNew temporary storage facilities (8\u00d71500 m2)\nNew storage facilities for radioactive decay (20 000 m2)\nNew long term storage facilities (5000 m2)\nTransport and handling materials (incl. cranes, vehicles, fuel etc.)\nTooling for dismantling\nTransport containers\nEquipment maintenance/consolidation (vehicles, cranes...)\nEquipment for traceability, safety, signage etc.\nInfrastructure modifications (access/safety systems, surface areas etc. )\n3.13.9\nPathways for FCC-ee components after removal\nAs mentioned above, high-value equipment that can be reused will be stored in storage. Materials that\nare not classified as radioactive (i.e., conventional waste) can be sold for recycling, and the remainder\nwill be treated as waste. Institutes in member states will be offered the possibility of receiving equipment\nwhich is not needed by CERN and that they can use at their facilities. Radioactive waste will be disposed,\nusing the Host State authorised facilities. The cost of this will be minimised by the appropriate choice\nof materials for components which will be activated, thereby limiting the volume of waste classified as\nradioactive. Both long-term and temporary storage will be required at CERN: the temporary areas will\nserve as buffer zones for equipment to be re-cycled and as intermediate storage for materials requiring\nprocessing before disposal. Long-term storage will be for equipment of high value which can be reused.\n3.13.10\nDismantling of the experiments\nThe FCC-ee detector systems resemble LEP detectors in the sense that they are optimised for electroweak\nprecision physics and precision measurements of the Higgs sector in a similar energy range. The overall\nsize of the detectors is comparable to the LEP experiments. The CLIC-like Detector (CLD), for instance,\nhas a height of 12 m and a length of 10.6 m, compared to DELPHI, which was \u223c10 m in both length\nand diameter. The typical mass of a LEP experiment was approximately 3000 tons (barrel + endcaps),\nconcentrated in the instrumented iron of the return yoke. Depending on the size and weight of the\nsolenoid magnets, their lowering/lifting may require dedicated lifting equipment exceeding the capacity\nof the overhead cranes in the assembly halls on top of the caverns. The FCC-ee caverns are equipped with\ntwo independent lifts capable of evacuating 300 people within 30 minutes. The occupancy of the caverns\nis therefore not expected to be a limiting factor for the dismantling schedule. A crucial difference between\nLEP and FCC-ee may be the radioactive activation of detector (and accelerator) hardware originating\nfrom the up to 105 times higher instantaneous luminosity.\nDismantling of the LEP experiments\nTraditionally, the detector systems and specific infrastructure are owned by the international collabora-\ntions that designed and built them, with CERN as a member of the collaborations. It is thus also the\n218\n\ncollaborations that are in charge of the preparation and implementation of the dismantling. Dismantling\nof FCC-ee experiments is expected to follow the LEP approach, which is outlined below.\nThe dismantling of the LEP experiments had to be integrated into the global LHC project plan\nand tightly coordinated with the accelerator dismantling. CERN, as the host lab, was in charge of the\nexperiment sites, logistics, radiological and general safety, planning, and coordination. The year before\nthe start of dismantling was dedicated to the preparation of the site, e.g., the mechanical workshop,\nsetting up storage area for sub-detectors and zones for the safe storage of activated materials, zones for\ntemporary storage of high-value waste, such as copper cables and pipes.\nThe dismantling teams of the four LEP experiments typically consisted of 10-15 persons. A small\ncore of experienced CERN technical staff (2-4 persons) with in-depth knowledge of the detector, its\ninfrastructure and the experiment site was reinforced by handling and electro-mechanical support per-\nsonnel (about 5 persons). The international collaborations assumed their responsibility and sent expert\nteams that, ideally, had been involved in the installation process of a sub-detector approximately 12 years\nearlier.\nA radiological zoning analysis based on detailed modelling of the detector and its environment\nwas performed well before the start of the dismantling. The main steps of dismantling were:\n\u2013 Making the areas safe (flushing detector gases, cutting electrical power, coolant supplies, removal\nof beam pipe and calibration sources)\n\u2013 Cutting and removing cables and pipework\n\u2013 Extraction of sub-detectors in the reverse order of installation\n\u2013 Removal of remaining components and materials\nThe overall dismantling budget of the 4 experiments was about 3 MCHF (in year 2000 prices).\nAbout 1 MCHF was contributed by CERN, mainly used for financing of additional handling person-\nnel, rental of cranes and special transports. Each of the 4 scientific collaborations foresaw a budget\nof about 0.5 MCHF. This covered the additional personnel for the systematic radioactivity monitoring,\nadditional personnel for the dismantling operations, purchase of special tools and infrastructure modifi-\ncations/preparations. The sales of the dismantled material brought a nett income of about 100 kCHF per\nexperiment. A big fraction of the sales price of the return yokes (corresponding to about 10 000 tons of\nsteel) was offset by the cost of cutting and transport (special heavy-load transports).\nThe unprecedented luminosity of the FCC-ee storage ring may lead to significantly higher activa-\ntion of the detector hardware and its infrastructure. Hardware close to the beam pipe, like the luminome-\nters, will be activated the most.\nConclusions from LEP dismantling\nPreliminary considerations suggest that the dismantling of the FCC-ee experiments can follow the same\napproach that was used for the four LEP experiments in 2001. The estimates of time and resources re-\nquired appear still valid. The degree of activation and the related classification of certain parts of the\ndetector need to be assessed with dedicated simulations based on realistic detector models and opera-\ntional scenarios. The amount of material declared as TFA may have an impact on the planning and cost\nof the dismantling.\n3.13.11\nRecycling of materials\nIt can be anticipated that there will be some offset in the costs from the sales of materials for recycling\nand some specialist equipment. In the case of LEP dismantling, the sales revenue corresponded to \u223c15%\nof the total cost of dismantling. The LEP dipole magnets, which formed the bulk of the materials, were\nmade from steel embedded in concrete, and at the time, it was not financially viable to sell them for\n219\n\nrecycling. However, the FCC-ee magnets will be made of steel, weigh a total of \u223c120 ketones, and\nwill form the bulk of the recyclable materials to be removed. Copper and aluminium cables/busbars, as\nwell as stainless steel pipework, will constitute further materials to be sold for re-cycling. Heavy metals\n(like lead and tungsten) will potentially be used for shielding, which will be available for recycling. The\nvacuum chambers in FCC-ee will be fabricated from high-purity copper and will, therefore, be of high\nvalue for recycling. There will be more copper and/or aluminium in the busbars and cables. A total\nof 3000 tonnes of copper or 1000 tonnes of aluminium will be required for magnet powering, further\nboosting the income from sales.\nPlanning\nFigure 3.89 presents a possible timeline for the dismantling process based on an initial preparatory phase\nof 20 weeks followed by 40 weeks of dismantling activities. The schema presented assumes that up\nto 4 arcs can be dismantled simultaneously. Such a scheme, however, will require additional transport\nequipment and larger facilities for triage, storage, and processing of the equipment than if only two arcs\nwere dismantled simultaneously. If the LSS could be done in parallel to an arc at another point and the\nsequence was, for example, to complete dismantling from PA and PG (28 weeks), then start PD and PJ\nand so on, the overall duration would increase to around 144 weeks, but the total labour costs would\nremain the same. The gain would come from a reduction in the quantity of transport equipment required\nand fewer infrastructure requirements.\n3.13.12\nConclusions\nThe general scheme for dismantling up to 8 half arcs through 4 access shafts concurrently has been\nanalysed and is feasible given the current design of the FCC-ee and its infrastructure. If it were necessary\nto only work through two shafts concurrently due e.g., to bottlenecks in the extraction channels, the total\ncost would not change very much, but the overall duration would increase from around two to three\nyears.\nThe collaborations will fund the dismantling of the experiments, but some support will be required\nfrom CERN staff. Once the design has been completed and the specifications of the materials are known,\nit should be possible to estimate the cost of the elimination of radioactive waste.\n220\n\nChapter 4\nFCC-ee booster design and performance\n4.1\nOptics design and Beam dynamics\n4.1.1\nBooster parameters\nThe booster is located in the same tunnel as the collider. To simplify its mechanical integration, the\nlength of one arc cell is set to 52 m, matching the short cell length in the collider. More precisely, the arc\nperiodicity corresponds to five short cells due to the non-interleaved sextupole scheme.\nHowever, the booster layout (see Fig. 4.1) differs in several aspects from the collider layout. These\ndifferences are highlighted in Fig. 4.2 and summarised below:\n\u2013 The booster beam runs at a radial offset of 8 m on the outer side relative to the interaction point\nnot to interfere with the experimental detector.\n\u2013 The booster beam pipe is positioned at the top level of the tunnel, with a vertical offset of 1030 mm\nand a horizontal offset of 161 mm towards the inner side. This offset ensures that the booster and\ncollider maintain exactly the same circumference. Additionally, the booster cells have a slight\nlongitudinal offset to enhance mechanical stability and facilitate tunnel integration. Due to minor\ndifferences in the arc cell patterns of the booster and collider, the distance between their reference\ntrajectories oscillates by approximately \u00b14 mm. This orbit variation is also influenced by the\ndipole arrangements in the arcs.\n\u2013 The RF cavities in the booster are positioned in the long straight section H, whereas in the collider,\nthey are located in section L.\nThe parameters for the booster are summarised in Table 4.1.\n4.1.2\nMain constraints\nAt injection energy, Transverse Coupled Bunch Instabilities (TCBIs) may limit the total beam current,\nwhile the Transverse Mode Coupling Instability (TMCI) may determine the maximum allowed bunch\ncharge. Both effects could, in principle, be mitigated by a larger momentum compaction factor.\nFor the ZH/t\u00aft modes, TCBI is not a concern due to the significantly lower average current. How-\never, TMCI remains a limiting factor because of the large bunch charge (4 nC) required during collider\nfilling. Studies on the filling scheme have shown that a bunch charge of 4 nC is not essential for all\noperations. A reduced bunch charge of 1.6 nC, which remains above the minimum required to miti-\ngate bootstrapping instability, has been identified as a viable alternative. This reduction has a negligible\nimpact on the collider filling time for the ZH/t\u00aft modes.\nFor the Z/W modes, collective effects studies have demonstrated that the beam pipe is the main\ndriver of TMCI. Two approaches were investigated to accommodate a bunch charge of 4 nC: increasing\nthe momentum compaction or reducing the transverse impedance. Increasing the momentum compaction\nwould lead to a larger equilibrium emittance, necessitate different optics for different operational modes,\nand require additional magnet families to operate the booster at different working points, similar to the\ncollider. Conversely, reducing the transverse impedance implies the need to minimise the contribution\nfrom the resistive beam pipe.\nThe proposed solution is to use a beam pipe made from copper or copper-coated stainless steel\nand to enlarge the inner diameter of the beam pipe from 50 mm to 60 mm. Studies have shown that\n221\n\nFig. 4.1: Layout of the booster and collider. The booster shares the tunnel with the collider. The RF\ncavities of the booster are located in point L.\nFig. 4.2: Layout of the booster and collider in the section A, left. The distance between the reference\naxis of the booster and collider arcs is shown on the right picture.\nfurther increasing the diameter beyond 60 mm would result in a significant rise in magnet costs. A\n60 mm diameter provides a reasonable compromise between the need for larger and heavier magnets and\nachieving lower transverse impedance.\nFinally, reducing the stored current in the booster by a factor of ten significantly alleviates the\nconstraints associated with TCBI, reducing the need for large momentum compaction. Consequently, the\ncurrent strategy is to adopt the same optics for all operation modes while increasing the inner diameter\nof the vacuum chamber.\nEnsuring beam stability in the booster requires chromaticity correction, which necessitates the use\nof sextupoles. The CDR compared three different sextupole schemes, where sextupoles separated by a\n222\n\nTable 4.1: Preliminary key parameters of the high-energy booster of FCC-ee. We consider here a linac\nof 20 GeV as a pre-injector and a high-energy damping ring.\nRunning mode\nZ\nWW\nZH\nt\u00aft\nCircumference\n[km]\n90.65871376\nInjection energy\n[GeV]\n20\nExtraction energy\n[GeV]\n45.6\n80\n120\n182.5\nNumber booster ramps per cycle\n10\n2\n1\n1\nNumber of stored bunches\n1120\n928\n300\n64\nParticle number/bunch (filling)\u2020\n[1010]\n2.725\n1.268\n1.268\n1.268\nParticle number/bunch (top-up)\u2020\n[1010]\n2.725\n1.035\n1.268\n1.125\nCollider top-up interval\n[s]\n43.405\n14.772\n11.286\n10.446\nRF frequency\n[MHz]\n800\nLattice version\nV24_FODO\nMomentum compaction\n7.12 \u00d7 10\u22126\nCoupling\n2 \u00d7 10\u22122\nInjection emittances (norm.)\n[\u00b5m]\n20 \u00d7 2\nExtraction horizontal equilibrium emittance\n[nm]\n0.087\n0.27\n0.61\n1.4\nExtraction vertical equilibrium emittance\n[pm]\n1.75\n5.37\n12.1\n28.0\nInjection Energy loss / turn\n[MeV]\n1.34\nExtraction Energy loss / turn\n[MeV]\n36.1\n342\n1730\n9270\nInjection bunch length\n[mm]\n4\nExtraction bunch length\n[mm]\n2.43\n2.56\n2.26\n1.98\nInjection RMS energy spread\n[10\u22123]\n1\nExtraction RMS energy spread\n[10\u22123]\n0.38\n0.67\n1.01\n1.53\nInjection Maximum relative energy acceptance\n[%]\n3\nExtraction Maximum relative energy acceptance\n[%]\n1\n1.01\n1.51\n2.29\nInjection RF voltage\n[MV]\n50.1\nExtraction RF voltage\n[MV]\n57.2\n402\n1960\n10200\nFilling time\n[s]\n2.8\n2.315\n3\n0.64\nUp-Ramp time\n[s]\n0.706\n0.857\n1.429\n2.321\nFlat top\n[s]\n0.1\n0.1\n0.1\n0.1\nDown-Ramp time\n[s]\n0.334\n0.689\n1.148\n1.866\nTotal cycling time\n[s]\n39.4\n7.922\n5.68\n4.927\n\u2020 The required particle numbers in the booster assume an injection efficiency into the collider of 80% as specified in 2.3.9\nphase advance of \u03c0 form a family:\n\u2013 Classical sextupole scheme. After every quadrupole a sextupole magnet is installed leading to a\nmaximum number of sextupoles. In this case there are two families per plane.\n\u2013 Interleaved sextupole scheme, consisting of paris of sextupoles separated by 180deg betatron phase\nadvance . The sextupoles are considered to mainly, or only, act in one plane, and the pair for one\nplance is interlaced with a pair of the other plane.\n\u2013 Completely non-interleaved sextupole scheme. In order to optimise the cancellation of the sex-\ntupole geometric effect, only linear elements are installed between two sextupoles forming a pair,\nand there is no interference between the pairs affecting one or the other plane.\nThe non-interleaved sextupole scheme was found to give the best dynamic aperture and momentum\nacceptance. Thus, this scheme has been retained.\n223\n\nTo further increase the momentum acceptance, we have also added some transparency conditions\non the dispersion suppressors and insertions to match the chromatic functions:\n\u2013 The phase advance between the sextupoles in the dispersion suppressor is \u03c0 in both planes to\nmaximize the geometric aberration cancellation.\n\u2013 The angles of some dipoles in the dispersion suppressors have been matched to cancel the second-\norder dispersion. However, the total angle of the dispersion suppressor stays unchanged.\n\u2013 The phase advance between the end of the upstream arc (or the beginning of the upstream disper-\nsion suppressor) and the beginning of the downstream arc (or the start of the downstream dispersion\nsuppressor) is equal to the phase advance of one arc cell plus an integer.\n\u2013 Although the insertions are not perfectly symmetric, we have preferred to keep some waist con-\nditions in the middle. In other terms, we ask to have \u03b1x = \u03b1y = D\u2032\nx = 0 at the middle of\nthe insertion. We also ask to keep the chromatic derivative of \u03b1 and the second-order dispersion\nderivative near 0: Ax \u2248Ay \u2248dD\u2032x/d\u03b4 \u22480.\n\u2013 We match the Twiss parameters but also the Montague functions Ax, Ay, Bx, By and second-order\ndispersion dDx/d\u03b4 and dD\u2032\nx/d\u03b4 at the entrance of the right arc.\n4.1.3\nFODO lattice\nThe starting configuration for the design of a booster cell is a sequence of five FODO cells with 90 degree\nphase advance, and each approximately 52 m long.\nThe booster cell must follow the geometry of the collider determined by the structure for the\ncollider short 90/90 FODO cell of the GHC optics. This condition requires the basic unit length of five\nbooster arc cells to be 260.554 m.\nTo maximise the cancellation of geometric aberrations introduced by the arc sextupoles, a phase\nadvance of \u03c0 in both planes between the sextupoles of a pair is required, imposing four constraints.\nAdditionally, the global tune of the machine is fine-tuned by adjusting the arc cells, adding two more\nconstraints. As a result, the arc cell tune is 1.25\u00b1\u03f5x,y with \u03f5x,y \u226a1. To accommodate these constraints,\nthe arc cell requires six quadrupole families to control the phase advances between sextupole pairs and\nthe global tune, along with two sextupole families to regulate the global chromaticity. The optical and\nchromatic functions of the arc cell, based on a FODO lattice, are shown in Fig. 4.3 (top).\nThe dispersion suppressor consists of 1.5 FODO arc cells followed by two additional FODO cells\nof the same type as the arcs, but with only one dipole per half-cell instead of two (see Fig. 4.3 (middle)).\nThe dipole lengths have been optimised to minimise second-order dispersion at the end of the dispersion\nsuppressor. The dispersion naturally damps along this section, requiring minor quadrupole adjustments\nin the dispersion suppressor to cancel the dispersion, correct second-order dispersion, and ensure a phase\nadvance of 180\u25e6between the last sextupole in the arcs and the entrance of the dispersion suppressor. This\nphase advance constraint allows the possible later insertion of an additional sextupole to further correct\ngeometric aberrations.\nThe dispersion suppressors and insertions have been optimised according to transparency condi-\ntions. The optical functions and second-order chromatic functions for one quarter of the booster, based\non a FODO lattice, are shown in Fig. 4.3 (bottom).\n4.1.4\nAlternative: HFD lattice\nThe Hybrid FODO (HFD) lattice is an alternative to the FODO cell. The main motivation of this cell is\nto reduce the anharmonicity and second-order chromaticity of the FODO cell to enlarge the momentum\nacceptance and dynamic aperture. The main difference between the HFD and FODO cells are:\n\u2013 The phase advances between the two sextupoles of the same pair are near \u03c0 (and not exactly \u03c0).\n224\n\nFig. 4.3: Optical functions (left) and second-order chromatic functions (right) in the arc cells (top), in the\ndispersion suppressor before section B (middle), or in one quarter of the booster (bottom) for the booster\nbaseline optics with FODO arc cells.\n\u2013 The dipoles do not have the same length, which enable a modulation of the distance between the\nquadrupoles. The total length of the dipoles stay the same, to keep the same curvature radius and\nthus radiated power per turn.\n\u2013 The horizontal and vertical tunes are quite different. In the case of the FODO cell, the tunes are\nabout 1.25 in both planes against 1.25/1.15 for the HFD cell.\nThe optical functions and second-order chromatic functions in the arc cell and in one-quarter of\nthe booster based on an HFD lattice are shown in Fig. 4.4.\n225\n\nFig. 4.4: Optical functions (left) and second-order chromatic functions (right) in the arc cells (top) and\nin one-quarter of the booster (bottom) with the version with HFD arc cells.\n4.1.5\nDynamic aperture and momentum acceptance\nOne of the main concerns is to ensure a sufficiently large dynamic aperture and momentum aperture to\nkeep the beam losses small at injection. The dynamic aperture without errors is calculated by scanning\nthe initial particle positions that are stable on the x and y axes after 1000 turns, without taking into\naccount synchrotron radiation damping. Different initial energy offsets between \u22122 % and +2 % are\nalso considered checking the momentum aperture. Figure 4.5 compares the horizontal and vertical stable\nregions as a function of the energy offset, illustrating the dynamic aperture of both the FODO and Hybrid\nFODO lattices.\nIn both cases, the margin is sufficient to ensure the stability of the injected beam. The target\ndynamic aperture of 15 \u03c3 is indicated by the dashed red line in Fig. 4.5.\nThe corresponding momentum aperture for the FODO lattice exceeds \u00b10.75 % in the horizontal\nplane and \u00b11 % in the vertical plane, equivalent to 5 \u03c3\u03b4 where \u03c3\u03b4 denotes the rms relative momentum\nspread of the injected beam. The HFD lattice exhibits a larger momentum aperture in the horizontal\nplane. However, this difference is partly thanks to the absence of an injection optics in one of the\ninsertions. This injection optics disrupts the superperiodicity of the FODO lattice. Injection has not yet\nbeen developed for the HFD lattice.\nThe impact of eddy currents on the dynamic and momentum aperture has also been investigated.\nThe cyan dashed lines in Fig. 4.5 represent tracking results for the FODO lattice, including a systematic\nb3 field error component applied to each dipole in the arcs.\nThe expected sextupole gradient in the dipoles due to eddy current effects is \u22120.015 T m\u22122, cor-\n226\n\nresponding to an integrated b3 of approximately \u22120.0025 m\u22122 at injection energy. To assess its impact,\nthe dynamic aperture was evaluated for ten different integrated b3 values over a range of 0.01 m\u22122.\nThe phase variation that corresponds to the \u2206p/p is shown on the top horizontal axis of Fig. 4.5\nand is calculated following section 3.4 of Ref [327]. The impact of the linear and random non-linear field\nerrors on the stability region and a possible mitigation strategy are the next steps of investigation.\nFig. 4.5: Horizontal (left) and vertical (right) Dynamic Aperture at injection as a function of momentum\ndeviation for the FODO and the HFD optics. The normalised horizontal and vertical emittances used to\ncompute the beam sizes are 20 \u00b5m and 2 \u00b5m, respectively. The dashed red line is the target value of 15 \u03c3\ntransverse dynamic aperture, the cyan dashed line show the effect of several values of the systematic b3\ncomponent due to eddy-current in the main dipole, as described in the text.\n4.1.6\nTapering\nThe energy lost per turn due to synchrotron radiation scales with the fourth power of the beam energy.\nConsequently, the relative energy loss per turn scales with the third power of the energy. As a result, the\nrelative energy lost per turn increases from 6.7 \u00d7 10\u22125 at injection to 5 \u00d7 10\u22122 at extraction for the t\u00aft\noperation.\nIn consequence, the beam energy varies around the ring with a maximum just after the RF section\nand a minimum, when the beam arrives again at the RF section one turn later. The magnetic fields have\nto be adjusted to ensure that the beam remains close to the center of the vacuum chamber.\nSince the arcs are individually powered, the dipoles in different arcs can be supplied with different\ncurrents, allowing for tailored magnetic field adjustments. Assuming a single power supply per arc, the\nmaximum beam deflection in the booster can be reduced to 553 \u00b5m (see Fig. 4.6). Further improvement\ncan be achieved using horizontal dipole correctors positioned near the focusing quadrupoles. In this case,\nthe maximum orbit variation is reduced to 55 \u00b5m, while the maximum integrated strength of the dipole\ncorrector remains at 6.3 mT m, which is below the specified dipole strength listed in Table 5.4.\nThese results indicate that a combination of varying the dipole field for each arc and employing\ndipole correctors is sufficient to maintain the orbit within the required tolerances. However, this study\ncould be further refined by increasing the number of sectors within the dipole arcs to achieve a finer\nmagnetic field distribution.\nAdditionally, while this analysis has focused on orbit correction, synchrotron radiation losses\nalso induce beta-beating and impact the equilibrium emittance. Further studies should investigate beta-\nbeating correction through arc rematching with the interaction region.\n227\n\nFig. 4.6: Left: Beam orbit around the booster at the extraction energy for the t\u00aft mode taking synchrotron\nradiation losses into account, and comparing the cases of a different magnetic field in each arc with the\nhorizontal correctors off (in blue) or on (in red). Right: Integrated field of the horizontal dipole correctors\nto minimise the orbit with synchrotron radiation.\n4.2\nCollective effects\n4.2.1\nBaseline assumptions for collective effects studies\nThe high-energy booster may be subject to impedance-induced instabilities, which depend on various\nfactors and can manifest as either short-range or long-range effects. Some of these factors, such as the\nnumber of bunches and the number of particles per bunch, are linked to the cycling and operational mode.\nIn contrast, others, like the momentum compaction factor, are determined by the optics design.\nAt this stage of the study, only resistive wall contributions and RF cavities have been taken into\naccount. While these do not represent the full spectrum of impedance effects, they are dominant and play\na crucial role in defining key physical parameters of the beam pipe, such as its diameter and material.\nThese parameters, in turn, influence other critical subsystems, including the vacuum system and magnet\ndesigns.\n4.2.2\nMismatched beams at injection\nThe high-energy booster serves as the intermediary between the high-energy LINAC and the main ring.\nIts ability to deliver a beam that meets the required specifications depends on multiple factors, including\nthe properties of the injected beam from the high-energy LINAC. While the booster design demonstrates\nrobustness to a range of transverse beam parameters at injection energy, the longitudinal parameters can\nintroduce significant mismatches and microwave instabilities. A study was conducted to ensure that the\ninjected beam does not induce instabilities. The injector complex is capable of providing beams with\nspecific bunch lengths and energy dispersion. A two-dimensional parametric scan was performed to\nfurther assess injection energy stability. The longitudinal mismatch \u03bez has been quantified in terms of:\n\u03bez = \u03c3eq\nz /\u03c3inj\nz ,\n(4.1)\nwhere \u03c3inj\nz is the bunch length at injection and \u03c3eq\nz is the bunch length at equilibrium. Figure 4.7 shows\nthat the baseline bunch lengths and energy dispersion requirements from the LINAC provide a significant\nsafety margin regarding longitudinal mismatch and microwave instabilities. Figure 4.7 also rules out a\nconfiguration where an energy compressor would not be used after the high-energy LINAC, resulting in\nan injection energy dispersion of 0.25 % and a bunch length of 1 mm. The figure shows that the present\nbaseline injection parameters from the high-energy LINAC, with \u03c3z = 4 mm and \u03c3e = 0.1 %, allow a\nsignificant margin to avoid mismatch and microwave instabilities at injection energy.\n228\n\n0.05\n0.10\n0.15\n0.20\n0.25\ne at injection (LINAC) [%]\n1\n2\n3\n4\nz at injection (LINAC) [mm]\n3.05\n7.34\n12.04\n16.37\n20.56\n24.43\n27.46\n30.32\n33.00\n35.87\nz\nFig. 4.7: Kernel density estimate of the longitudinal mismatch as a function of bunch length and energy\ndispersion at injection. The energy considered is 20 GeV, and the different booster parameters con-\nsidered are those of the Z-pole operation (see Table 4.1). The target circle shows the present baseline\ninjection parameters to the high-energy booster.\nAnother effect being studied is the result of a transverse jitter of up to 1 \u03c3 in the vertical and\nhorizontal planes. Present particle tracking studies do not show any effect at equilibrium. However,\namplitude detuning has not yet been taken into account, and these results need to be confirmed with\nmore realistic simulation parameters.\n4.2.3\nCoupled bunch instabilities\nTransverse coupled bunch instabilities due to resistive wall impedance\nTransverse resistive wall wakefields contain long range components.\nThese can lead to transverse\ncoupled-bunch instabilities that are destructive to the beam. Given the following assumptions, one can\nestimate analytically the transverse growth rate due to coupled bunches: 1. Equally spaced Gaussian\nbunches 2. Only coherent bunch modes 3. Only the most prominent radial mode in the longitudinal\nazimuthal mode.\nWith these assumptions, the transverse growth rate \u03c4\u22a5[328] can be expressed by:\n\u03c4\u22a5\u223c\nNp \u00b7 Nb\n4\u03c0 \u00b7 Qx,y \u00b7 E \u00b7 Re(Z\u22a5) \u00b7 G(Qx,y, \u03c3z, \u03c3e)\n(4.2)\nwhere Np is the number of particles per bunch, Nb is the number of bunches, Qx,y is the transverse tune,\nE is the energy, Z\u22a5is the transverse impedance, and G a factor which can be approximated by 1 in our\ncase. With the Z operation mode being the worst-case scenario, one can estimate the growth rate as a\nfunction of the mode numbers. By normalising the modes, one can compare the growth rate for two\ndifferent booster configurations, namely from 2023 and 2024, respectively. Figure 4.8 shows that the\ngrowth rate has been reduced in the new baseline design compared to the previous one. The most drastic\nchange is at the Z-pole operation, which represents the worst-case scenario. For this case, a reduction\nis observed from 374 s\u22121, i.e., (8.7 turns)\u22121 in the 2023 design to 10 s\u22121, i.e., (310 turns)\u22121 in the 2024\ndesign. This is due to several important changes, including the increase of the beam pipe diameter from\n50 mm to 60 mm and the reduction of the number of bunches from 15 880 to 1120 bunches. While the\nnew growth rates are still faster than the transverse synchrotron damping (\u223c30 000 turns), they reduce\nthe constraints on the dampers needed to mitigate such coupled-bunch instabilities.\n229\n\nFig. 4.8: Resistive wall transverse impedance induced transverse growth time constants as a function of\nthe mode number for the 2024 (hashed-red) and 2023 baseline (plain-blue).\nLongitudinal coupled bunch instabilities due to cavities high order modes\nThe higher order modes of the RF cavities are the main drivers of the longitudinal coupled bunch in-\nstabilities. The strategy to keep the RF system below the stability limit of longitudinal coupled bunch\ninstabilities is detailed in Section 6.3.3.\n4.2.4\nSingle Bunch instabilities\nSingle bunch instabilities that may arise in the high-energy booster and hinder achieving technical targets\nare of two types: microwave instabilities (MI) and transverse mode coupling instabilities (TMCI) (see\n[328]). The bunch population thresholds for these instabilities can be expressed as:\nNTMCI\np,th\n= Qx,y \u00b7 Qs \u00b7 E \u00b7 \u03c3z\nIm{Z\u22a5} \u00b7 e \u00b7 c ,\nNMI\np,th \u221dn \u00b7 \u03b1c \u00b7 E \u00b7 \u03c3e \u00b7 \u03c3z\n\f\fZ\u2225\n\f\f\n,\n(4.3)\nwhere Qx,y is the transverse tune, Qs is the synchrotron tune, E is the energy, \u03c3z is the bunch\nlength, Z\u22a5is the transverse impedance, \u03b1c is the momentum compaction factor, and Z\u2225is the longitudi-\nnal impedance.\nAlthough these two effects are interconnected, transverse mode coupling instabilities are partic-\nularly critical due to their potential to cause destructive transverse exponential growth in the beam. In\ncontrast, microwave instabilities primarily result in longitudinal emittance growth, which, given the in-\njected beam parameters, remains within the limits required for extraction to the main ring.\nThe design of the high-energy booster requires balancing multiple dominant effects, as outlined in\nEq. (4.3). Among these, resistive wall contributions are the primary source of impedance effects, while\nthe momentum compaction factor plays a crucial role in determining the optimal optical design.\n230\n\nThe following section examines the influence of these parameters on transverse mode coupling\ninstabilities.\nResistive wall contribution\nThe large circumference of the booster ring makes the resistive wall (RW) impedance the dominant\ncontributor to collective effects. In this study, the VACI SUITE [329] was used to analyse different\nmaterials and beam pipe radii. The resulting impedance calculations were directly incorporated into\nXSUITE [175] and PYHEADTAIL [330] for beam dynamics simulations. These tools enabled precise\nmodelling of beam behaviour and its interaction with the surrounding environment, ensuring accurate\npredictions and optimisations for the beam pipe design.\nA detailed study of beam pipe materials has been done for three cases: a copper beam pipe (Cu),\na stainless steel pipe (SS), and a stainless steel pipe with an internal copper coating (SS-Cu). Various\ncopper coating thicknesses were evaluated, and a 1 mm copper layer was identified as the optimal con-\nfiguration. The different material scenarios (Cu, SS, and SS-Cu) are illustrated in Fig. 4.9. The choice\nof materials played a crucial role in controlling RW impedance, directly impacting overall beam stability\nand performance.\n10\n2\n101\n104\n107\n1010\n1013\nfrequency [Hz]\n10\n7\n10\n5\n10\n3\n10\n1\n101\n103\n105\n Z [ ]\n(a)\nCu\nSS-Cu\nSS\n10\n2\n101\n104\n107\n1010\n1013\nfrequency [Hz]\n10\n7\n10\n5\n10\n3\n10\n1\n101\n103\n105\n Z [ /m]\n(b)\nCu\nSS-Cu\nSS\nFig. 4.9: (a) Longitudinal impedance and (b) Dipolar impedance for a pipe with R=30 mm and L=1 m,\nfor three different scenarios (Cu, SS, and SS-Cu).\nGiven that the beam pipe has a round geometry, no detuning (quadrupolar) impedance was ob-\nserved, even in the case of the coated pipe, which featured a narrow strip of missing copper on the inner\nsurface. While the absence of a continuous copper layer might have been expected to introduce a detun-\ning impedance, the VACI results indicated that the effect of this strip was negligible. Consequently, the\nfinal design adopts the SS-Cu configuration with a 1 mm copper coating, providing an optimal balance\nbetween material properties and impedance control.\nBeam-pipe radius and material\nTwo materials were considered for the beam vacuum chamber: stainless steel and copper. Stainless\nsteel offers advantages such as lower initial cost and reduced eddy currents induced by magnetic field\nramps during acceleration. However, it comes with increased longitudinal and transverse impedance (see\nFig. 4.9). Given the low magnetic fields involved, eddy currents are not a concern, allowing for a 1 mm\ncopper coating: beyond approximately 2 kHz, the skin depth ensures the beam interacts predominantly\nwith the copper layer.\n231\n\nThe impact on beam dynamics was assessed using the PYHEADTAIL1 tracking code [330].\n0.6\n0.8\n1.0\n1.2\n1.4\nMomentum compaction factor\n1e\n5\n3\n2\n1\n0\n1\n2\n3\nRe( Qy/Qs0)\n(a)\nPA31.0 h/tt\nPA31.0 z/w\n60\n70\n80\n90\n100\nBeam pipe diameter [mm]\n(b)\nFig. 4.10: Real part of the tune shift of the first azimuthal transverse coherent oscillation modes nor-\nmalised by the synchrotron tune as a function of the momentum compaction factor (left) and the beam-\npipe diameter (right) for the Z-operation mode. For (a), a copper beam-pipe of 50 mm diameter and a\nbunch population of 2.5\u00d71010 particles are considered. For (b), a stainless steel beam-pipe with a bunch\npopulation of 2.5 \u00d7 1010 particles and a momentum compaction \u03b1c = 7.34 \u00d7 10\u22126 are considered.\nA comparison was conducted on a circular beam pipe made of either copper or stainless steel,\neach with a diameter of 50 mm, using the PA31.0 baseline design (2023 CDR baseline) for the Z-\npole operation. A substantial increase in bunch length and longitudinal emittance was observed with\na stainless steel vacuum chamber of 50 mm diameter, necessitating an increase in the inner diameter\nof the beam pipe. To address this, an optimisation study was conducted to determine the ideal beam\npipe diameter for stainless steel. Modal analysis, following the methodology in Ref. [61], established a\nminimum of 70 mm, with a potential increase up to 100 mm to accommodate impedance margins.\nMomentum Compaction Variation\nFor a given bunch of particles, variations in the relative path length due to changes in momentum can\nsignificantly affect transverse mode coupling instability (TMCI) bunch population thresholds. This is\nquantified by the variation of the momentum compaction. Figure 4.10 (a) illustrates that the 2023 optics\nfor t\u00aft operation with \u03b1c = 7.34 \u00d7 10\u22126 and a 50 mm diameter copper beam pipe resides in an unstable\nregion. By contrast, the 2023 Z mode optics (\u03b1c = 1.49 \u00d7 10\u22125), with nearly twice the momentum\ncompaction, falls within a stable zone.\nBunch Population Variation\nA high-energy booster design featuring a 50 mm diameter beam pipe, whether made of copper or stain-\nless steel, coupled with an optics design featuring a momentum compaction of \u03b1c = 7.34\u00d710\u22126, proves\nimpractical. Conversely, adopting a single optics design instead of separate values for different operation\nmodes offers benefits. A compromise was reached, maintaining a single momentum compaction value\n(\u03b1c = 7.12 \u00d7 10\u22126) while increasing the beam pipe diameter from 50 mm to 60 mm and opting for\ncopper as the beam pipe material. Figure 4.11 demonstrates that this new baseline design increases the\nTMCI threshold bunch population from 2.5 \u00d7 1010 to 5.7 \u00d7 1010. Additionally, incorporating a 300-turn\ntransverse damper would further enhance the threshold and provide additional safety margins. These\nresults, however, require validation with a more comprehensive machine impedance model.\n1https://github.com/PyCOMPLETE/PyHEADTAIL\n232\n\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n4.5\n5.0\nBunch population [1010 particles]\n3\n2\n1\n0\n1\n2\n3\nRe( Qy/Qs0)\nNominal\nPA31.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\n4.5\n5.0\nNominal\nPA31.3\nFig. 4.11: Real part of the tune shift of the first azimuthal transverse coherent oscillation modes nor-\nmalised by the synchrotron tune as a function of bunch population for the PA31.0 2023 CDR baseline\n(left) and the PA31.3 2024 baseline design (right).\n4.3\nRadiation environment\nGiven the significant power dissipated by synchrotron radiation in FCC-ee, appropriate mitigation mea-\nsures must be implemented to prevent radiation-induced equipment failures and degradation of machine\nperformance. Although the radiated power is considerably higher in the collider than in the booster, the\nbooster\u2019s contribution must still be carefully evaluated, as no dedicated photon stoppers are foreseen,\nunlike in the collider ring.\nThis section examines the ionising dose generated by synchrotron photon emission in the booster\narcs and assesses the shielding efficiency of the dipole yokes. Other radiation effects, such as single-\nevent effects in electronics or radiation-induced corrosion, fall outside the scope of this section and\nwill be addressed in future studies. Additionally, other radiation sources in the booster, such as beam-\ngas scattering, must also be considered. However, the dose studies presented here provide an initial\nassessment of the shielding requirements for the booster.\n4.3.1\nSynchrotron radiation emission during a booster cycle\nThe primary source of radiation in the FCC-ee arc tunnel is synchrotron radiation emitted in the collider\nring. By design, this radiation is limited to 100 MW across all operating modes (50 MW/beam). In\ncontrast, the average synchrotron power emitted by the booster is significantly lower due to several\nfactors: the lower stored beam intensity, the strong dependence of synchrotron radiation power on beam\nFig. 4.12: Time evolution of the beam energy (left), critical energy of the synchrotron photon spectrum\n(centre) and emitted synchrotron radiation power (right) for a booster ramp from 20 GeV to 182.5 GeV\n(t\u00aft operation). The flat bottom and flat top plateaus are not shown.\n233\n\nenergy (\u221dE4), the relatively short duration of booster cycles, and the intervals without beam between\ncycles.\nFor top-up injection, the booster train intensity is expected to be lower than for full collider refills,\nas the bootstrap bunch charge can vary between 0 % and 100 %. However, top-up cycles are anticipated\nto have a greater impact on cumulative radiation effects because they will be executed more often.\nThe evolution of the radiated power and photon spectra during a booster cycle depends on the\nramp function. Figure 4.12 shows the time dependence of the beam energy, critical energy and emitted\npower during a ramp from 20 GeV to 182.5 GeV in t\u00aft operation. The figure assumes a bunch train of\n64 bunches, with a bunch intensity of 1010 e\u00b1, which is the maximum top-up intensity in t\u00aft cycles (see\nTable 4.1). At the end of the ramp, the power reaches about 3 MW, while the average power during the\n\u223c2 s-long ramp is about 1 MW. The presently foreseen repetition rate of booster cycles for t\u00aft operation is\n10.4 s, alternating between electrons and positrons. Taking into account the time without beam between\ncycles, the average power is less than 0.2 MW, i.e., more than 500 times lower than in the collider. This\nestimate can still slightly change depending on the need of a flattop plateau before beam extraction. The\npeak power and top-up interval is similar for ZH operation, but the radiation leakage from the magnets is\nexpected to be less compared to t\u00aft due to the lower critical energy at flattop. For the other beam modes\n(Z and WW), the top-up intervals are longer and the peak power and critical energies are lower. They are,\nhence, expected to be less relevant for cumulative radiation effects than the two higher-energy modes.\n4.3.2\nBooster contribution to the ionising dose in the arcs\nThe synchrotron radiation absorbers in the collider ring need to be surrounded by heavy shielding in order\nto sufficiently reduce the ionising dose in the tunnel (see Section 1.9). It is, therefore, highly desirable\nthat the booster contribution to the ionising dose remains as low as reasonably achievable. Contrary to\nthe collider, the synchrotron photons emitted in the booster impact directly on the vacuum chamber. The\nchamber walls are too thin to fully shield the photons and secondary particles, but the H-shaped yokes\nof the booster dipoles still provide a significant attenuation of the secondary radiation. The shielding\nefficiency required of the booster dipole yokes represents an important prerequisite for the magnet design.\nIn order to study the necessary yoke thickness, the radiation leakage from the magnets and the resulting\ndose in the tunnel was estimated by means of FLUKA Monte Carlo simulations [126, 127, 331]. In\nthis very first study, the booster was modelled as a series of 11 m-long dipoles with 30 cm drift spaces.\nThe studies will have to be repeated in the future with a more realistic simulation model that includes\nquadrupoles and sextupoles; nevertheless, the results obtained provide a first estimate of the booster-\ninduced radiation environment.\nFigure 4.13 compares the booster and collider contributions to the annual dose in the arc tunnel for\nt\u00aft operation. The simulation assumes 185 days of operation, with 75% machine uptime. The results for\nthe collider assume a 400 kg lead-alloy shielding around the photon stoppers, with a thickness of 10 cm\non the internal and external side of the magnets (see Section 1.9). For the booster, dipole iron yokes\nwith thicknesses of 2 cm and 4 cm were simulated. As a conservative assumption, each booster cycle\nwas modelled at maximum top-up intensity, corresponding to the highest bootstrap bunch charge. The\nresults indicate that, with the current collider shielding, the dose contribution from the collider remains\ndominant.\nAt the location of the upper cable trays on the walls (above 2 m from the floor), the radiation\ndose from collider operation reaches 2 \u2013 10 kGy/year, while the booster contributes up to approxi-\nmately 2 kGy/year when using 2 cm-thick dipole yokes. To maintain the dose at the cable trays below\n10 kGy/year, the booster\u2019s contribution cannot be entirely neglected. Reducing booster-induced radia-\ntion at the walls to below 1 kGy/year in t\u00aft operation can be achieved by increasing the booster dipole\nyoke thickness to 4 cm.\nThe results presented indicate that the booster\u2019s contribution to overall dose levels in the tunnel is\n234\n\nFig. 4.13: Annual ionising dose in the arc tunnel during t\u00aft operation, showing separately the contribu-\ntions of the collider (left) and the booster (middle: with a 2 cm-thick yoke, right: with a 4 cm-thick yoke).\nThe collider simulations assume a preliminary lead-based shielding around discrete photon stoppers (see\nSection 1.9). The studies were carried out using the FLUKA code. The FLUKA magnet models are\nshown at the top of the figure.\nnon-negligible and must be considered alongside collider shielding. Further studies are required for both\nthe collider and the booster to optimise the overall shielding strategy.\n4.4\nInjection and extraction\n4.4.1\nInjection\nThe beam is accelerated to 20 GeV in the high energy linac and transported from the injector complex\nto the collider complex close to point PA, through the injection transfer lines shown with bright green\ncolour in Fig. 4.1. The injection transfer-line tunnels merge with the collider tunnel on either side of\nthe PA experiment straight section, approximately 600 m from the IP. This layout is symmetric around\nthe interaction point (IP), and since the booster optics is also symmetric, the injection scheme described\nbelow for the clockwise direction applies equally to the counter-clockwise injection on the opposite side\nof the straight section.\nAt the junction with the collider tunnel, the current baseline design features an angle of approxi-\nmately 150 mrad between the injection and booster beamlines. While the precise geometry of the injec-\ntion line has not yet been finalised, the present concept envisions using approximately 10 m of dipoles\nto achieve a total deflection of 125 mrad, followed by a septum system providing an additional 25 mrad\ndeflection to align with the booster trajectory [332].\nThe design of the booster injection has primarily focused on the booster FODO lattice and on the\ninjection elements. The detailed trajectory and optical matching from the injection line will be addressed\nat a later stage, with no significant challenges identified so far.\nThe beam produced by the injector complex is composed of up to 4 bunches separated by 25 ns\nper batch, whose parameters are detailed in Table 4.1. The booster accumulates the injected batches at\na maximum rate of 100 Hz and for up to several seconds. The baseline uses a fast injection scheme,\nallowing consecutive batches to be injected between circulating ones. Therefore, the injection kicker has\nto provide a flattop of up to 80 ns.\n235\n\nFig. 4.14: Magnets layout, apertures, beam paths with envelopes and Twiss functions for the booster ring\nalong the PA straight section with the injection optics on the positron injection side and the nominal optics\non the electron injection side. The dipole position is shown in red, and the quadrupoles are depicted in\nblack.\nTaking advantage of the low field of the dipole magnets in the injection region close to an IP,\nwhere the average bending radius is twice as large as in the arcs (19.8 km), the current injection scheme\nremoves selected dipoles and redistributes their deflection among the adjacent ones. In total, six dipole\nmagnets are removed on each side of the PA section, with their deflection transferred to six neighbouring\ndipoles. This redistribution does not affect the reference trajectory outside each injection region and\nresults in a negligible impact on the ring circumference (28 \u00b5m). The dipoles are removed symmetrically\nwith respect to the FODO lattice to minimise optical perturbations, particularly in the dispersion func-\ntion. Some minor effects on the local dispersion remain, as seen around the electron injection point in\nFig. 4.14.\nThe second key requirement of the injection scheme pertains to the optical functions and phase\nadvances in the vertical plane at the injection devices. A high beta function at both the kicker and the\nsepta, combined with a phase advance close to 90\u25e6, enhances the kicker\u2019s efficiency and maximises the\nseparation between the circulating and injected beams at the septum. To achieve this while maintaining\nsymmetry in the lattice around the local FODO structure, two additional quadrupoles (inj0 and inj1)\nand independent powering of 2 \u00d7 11 existing quadrupoles are introduced.\nThe resulting injection optics, illustrated for the positron injection side in Fig. 4.14, features a\nvertical beta function of up to 250 m at the septum. While this optics modifies the phase advance and the\nlocal sextupole correction scheme, a global correction allows both effects to be compensated [333]. Once\nthe injection process is completed, at the start of the energy ramp the optics can adiabatically be reverted\nto the nominal configuration for the remainder of the booster cycle, thereby minimising the impact of the\ninjection optics on the booster beam dynamics.\nThe placement of the injection elements and the threading of the injected beam through the lattice\nelements can be seen in the close-up of the injection region in Fig. 4.15. Following the injected envelope,\na side channel in the horizontal plane will need to be installed between the poles of the quadrupole 065.\nThis seems feasible with the present quadrupole design in the grey part of the aperture, between 31.5 mm\n236\n\nFig. 4.15: Layout, apertures, Twiss functions, beam paths and envelopes in both planes around the\nclockwise injection point of the booster. Injected and circulating envelopes are defined by the \u00b115 \u03c3\nbeam size and the injected beam parameters.\nand 65 mm [334].\nIn the vertical plane, a closed orbit bump of 10 mm at the septum is foreseen to bring the circulating\ntrajectory closer to the injected one in order to reduce the required kicker strength. This bump is taken\ninto account only as a constant vertical orbit shift in Fig. 4.15, but properly modeled in beam dynamics\nsimulations. The inside edge of the septum is located 11.5 mm from the centre of the beam pipe and the\ninjected beam is placed closer to the blade with an envelope of \u00b13 mm to be compared with the blade\nthickness of 5 mm and the septum vertical aperture of 10 mm. At the septum, the vertical slope of the\ninjected beam is 260 \u00b5rad and reduced to 86 \u00b5rad after the quadrupole 066. Downstream, a fast kicker\nprovides an angle of 90 \u00b5rad.\nThe injection optics features optimised beta function and phase advance, but one may notice that\nthe vertical beta function at the kicker remains around 100 m. The low vertical beta function at the kicker\nallows relaxing the requirements on the kicker pulse flatness [178]. In practice, an active damper of the\ninjection oscillations is required but at this stage, only injection system and ring optics are considered.\nAnother source of injection offset may come from the high energy linac with up to 1 \u03c3 jitter in\neach transverse plane [335]. In the longitudinal plane, the maximum relative energy jitter is 3 \u00d7 10\u22123\n(see Table 7.13). Such a jitter should not impact the aperture requirement at injection but active damping\nmay need to be considered to avoid emittance growth.\nThis baseline injection scheme relies on a set of hardware requirements summarised in Table 4.2,\nconsidered achievable using existing technologies. A comprehensive discussion on the hardware choices\nis provided in Section 6. Further investigations are needed to advance this concept towards a technical\ndesign, focusing on error analysis and their impact, as well as the operational and performance optimi-\nsation of the scheme to maintain a reliable injection despite the various drifts that may occur.\n237\n\nTable 4.2: Summary of the booster injection scheme hardware requirements\nKicker\nSeptum\nBeam energy (GeV)\n20\nDeflection angle per system (mrad)\n0.09\n4.5\nMaximum repetition frequency (Hz)\n100\nDC\nRise/Fall time (ns)\n25\u2020\n\u2013\nflattop time (ns)\n80\n\u2013\nBlade thickness (mm)\n\u2013\n7\nAperture (H\u00d7V mm)\n\u2013\n5\u00d710\nLongitudinal available space (m)\n5.5\n20\n\u2020A 25 ns rise or fall time is not needed with the present filing schemes described in Section 2.3.8.\n4.4.2\nExtraction\nThe booster beam is extracted in the technical straight section in PB (see Fig. 4.1) towards the booster-\nto-collider beam transfer line. The structure of the circulating beam depends on the operation mode and\nthe required filling scheme of both booster and collider as well as collective effects considerations in\nboth synchrotrons [336]. However, the present concept is based on the most stringent requirements of a\nfast extraction of a full turn of 304 \u00b5s, with a rise time of the kicker system within the planned minimum\ncollider gap between trains of 600 ns 2.\nUnlike the experiment sections, the PB technical straight section of the booster is physically\nstraight and consists solely of quadrupoles. Due to the ample space available between these quadrupoles,\nno modifications to the layout are required to accommodate the extraction elements.\nTo facilitate the extraction of both electron and positron beams, a symmetric design is preferred.\nSince the collider injection system is positioned in the second half of the straight section (see Sec-\ntion 1.8.1), the booster extraction system is placed at the centre of the section. Figure 4.16 illustrates the\nlayout along the entire straight section, where the extraction scheme is centrally located and symmetri-\ncally configured to extract both beams towards the section\u2019s exit.\nThe extraction scheme operates entirely in the horizontal plane, with both the kickers and septa\nproviding a horizontal deflection.\nThe nominal optics follows a FODO structure without dispersion and features a strong beating\nover a period of two cells (see Fig. 4.16). The large beta function and near 90\u25e6phase advance per cell\nalready match the typical requirements of a fast extraction system. However, the optics was adjusted to\nrelax the requirement on the kicker pulse flatness to limit the extracted beam offset to 1 \u03c3. This extraction\noptics uses 9 independent power supplies, but no additional magnets will be needed. The injection optics\nis required only for a short time before extraction without perturbing the rest of the booster cycle.\nThe extraction layout is fully symmetric for electron and positron beams, with the kickers placed\nat the precise centre of the straight section on either side of the focusing quadrupole 022 (see Fig. 4.17a).\nAlthough the present concept considers dedicated kickers for electron and positron beam extraction, this\nplacement at the centre of the straight section could allow the reuse of the same kickers for the extraction\nof both beams.\nThe circulating beam is moved closer to the extraction septum using a closed-orbit bump of\n10 mm, although it is presently only modelled as a shift of the reference trajectory in Fig. 4.17a. The\n2For the baseline bootstrapping injection and filling scheme described in Section 2.3.8, the gaps in the booster are signifi-\ncantly larger than 600 ns.\n238\n\nFig. 4.16: Layout, apertures, beam envelopes, and Twiss functions for the booster ring along the PB\nstraight section, showing the extracted and stored beam. The envelopes are computed using the largest\nequilibrium beam parameters (reached for t\u00aft-mode).\nkicker system provides a total angle of 0.2 mrad to ensure the required clearance at the septum blade\nlocated upstream of the following focusing magnet. In this scheme, the septum blade has a thickness of\n8 mm, with its inside edge located 20 mm from the reference position of the booster beam. Downstream\nof the septum, the extracted beam envelopes pass through the quadrupole between its poles, within a side\nchannel that will need to be installed\u2014similar to the booster injection setup (Section 4.4.1).\nTable 4.3: Summary of the booster extraction scheme hardware requirements\nKicker\nSeptum\nBeam energy (GeV)\n45.6 \u2013 182.5\nDeflection angle per system (mrad)\n0.2\n2\nMaximum repetition frequency (Hz)\n0.3\n0.3\nRise/fall time (\u00b5s)\n1.1\nN/A\nflattop time (\u00b5s)\n304\nN/A\nBlade thickness (mm)\nN/A\n8\nAperture (H\u00d7V mm)\nN/A\n18\u00d710\nLongitudinal available space (m)\n15\n15\nThe hardware requirements for this extraction scheme are summarised in Table 4.3. This concept\nis based on realistic hardware specifications achievable with current technologies. A detailed discussion\nof the hardware choices is provided in Section 6. Comprehensive error studies and failure mode analyses\nare required to advance the present concept toward a technical design.\nPassive absorbers must be installed after the extraction kickers to protect the septum and the most\nexposed downstream components from potential failures that could result in miskicked bunches striking\nthe booster aperture. Likewise, a system of masks should be implemented in the transfer lines to the\ncollider to intercept particles with large oscillations, preventing them from reaching the collider aperture\nand shielding the transfer line itself.\n239\n\n(a)\n(b)\nFig. 4.17: Magnet layout, Twiss functions, beam paths and envelopes in the horizontal plane for the\nbooster extraction (a) and dump (b). The envelopes are computed using the largest equilibrium beam\nparameters (reached for t\u00aft-mode).\n4.4.3\nDump\nThe booster transfer dump system closely resembles the collider dump system described in Section 1.8.1.\nIt is positioned at approximately the same longitudinal location (see Fig. 4.16) and, like the collider\nsystem, extracts the beam at the entrance of the straight section towards its centre. The system must rise\nwithin the minimum possible gap between trains of 600 ns (or larger, for the present filling schemes) and\nextract the entire beam in a single turn. This necessitates a fast extraction scheme with a flattop duration\nof 304 \u00b5s, with both the kicker and septa designed to provide horizontal deflection.\nUnlike injection or extraction systems, a dump may be required anytime. As a result, the system\nmust be capable of safely extracting the circulating beam within a few turns. This requirement means\nthat the concept cannot depend on manipulating the optics or the closed orbit before the kicker system\nis triggered. Consequently, the optics in the extraction region remains unchanged, and the reference\nposition of the circulating beam stays at the centre of the vacuum chamber.\nThe kicker system provides a slightly larger deflection angle of 0.3 mrad compared to the extrac-\ntion scheme. Further downstream, the septum is positioned upstream of the next focusing quadrupole\n(see Fig. 4.17b) to take advantage of the approximately 90\u25e6phase advance per cell and the larger beta\nfunction. At the septum, the dumped beam is shifted by a total of 43 mm, allowing for a septum blade\nthickness of 25 mm and placing its inner edge 4 mm from the ring reference position. The total septum\ndeflection is 5 mrad, and the downstream quadrupole will need to be adapted to accommodate a side\nchannel for the dumped beam.\nSince the circulating beam energy varies continuously throughout the booster cycle, both the sep-\ntum power supply and the kicker charging system must adjust to match the beam energy, from injection\nat 20 GeV up to the maximum energy of 182.5 GeV. Additionally, specialised control systems will\nbe required to trigger a dump if any of these elements fails to follow their expected voltage or current\nprofiles.\nThe transport line to the dump consists solely of a drift tube, without dipoles or quadrupoles.\nSmall correctors may be considered at a later stage to fine-tune the beam trajectory. With a total distance\nof 1200 m from the dump kicker to the dump, the beam naturally expands to a 1 \u03c3 size of 3.5 mm in\nthe horizontal plane and 1 mm in the vertical plane. These beam sizes are calculated for the smallest\n240\n\npossible beam parameters, corresponding to the design equilibrium emittance in Z-mode.\nFor dump system, reliability is a critical factor, and one particular aspect must be addressed from\nthe earliest stages of development. The total deflection provided by the kicker system is typically dis-\ntributed across multiple independent magnets and generators, but the failure of at least one component is\nalways a possibility. Therefore, it is essential to ensure that beam extraction and transport to the dump\nremain functional even in the event of a missing kicker.\nIn the current design, a total of nine kickers are used, meaning that the loss of a single unit results in\nan overall deflection reduction of 11 %. The present concept guarantees that an extraction kick variation\nof up to \u00b120 % keeps the dumped beam envelope at the dump location within \u00b1150 mm, which is\nconsidered acceptable for the dump\u2019s size and design.\nAdditionally, to accommodate a \u00b120 % variation in kick strength, the horizontal aperture of the\nseptum must exceed 30 mm.\nTable 4.4: Summary of the booster dump scheme hardware requirements\nKicker\nSeptum\nBeam energy (GeV)\n20 \u2013 182.5\nDeflection angle per system (mrad)\n0.3\n5\nMaximum repetition frequency (Hz)\n0.3\n0.3\nRise/fall time (\u00b5s)\n\u223c1.5\nN/A\nflattop time (\u00b5s)\n304\nN/A\nBlade thickness (mm)\nN/A\n25\nAperture (H\u00d7V mm)\nN/A\n30\u00d710\nLongitudinal available space (m)\n20\n20\nThe hardware parameters required for this dump scheme are summarised Table 4.4 and a detailed\ndiscussion on the technology choice of the hardware system can be found in Section 6.4.\nTo develop this dump concept towards a technical design, a comprehensive review of the failure\ncases and mitigation measures, as well as possible errors in both the circulating beam and the dump line,\nwill need to be carried out. Similar considerations as those presented in the previous section hold for\nprotecting the booster aperture in case of failure of the dump extraction elements.\n4.5\nOngoing studies and possible upgrades\nSince the CDR, the booster has faced several major changes:\n\u2013 The layout has changed to follow the different changes on the collider layout (see Section 4.1.1:\nthe circumference has decreased; the length of the insertions has changed to go from a scheme\nwith 2 IPs to 4 IPs; the booster is located on top of the collider with a transverse offset in the arcs;\nthe location of the RF cavities has changed.\n\u2013 The baseline optics is based on FODO cells (Section 4.1.3. Maintaining the same optics for the dif-\nferent operation modes may reduce the costs. An alternative, based on hybrid cells (Section 4.1.4)\nhas been developed and compared. Improving the matching conditions, including second-order\nconsiderations, has enlarged the momentum acceptance and dynamic aperture.\n\u2013 The injection and extraction systems were developed. The placement of the transfer lines from the\npre-injector complex to the booster was optimised (Section 4.4.1). The extraction and dump lines\nare located in section B (see Section4.4.2). A baseline of the injection and extraction sections exists\nand this has been integrated in the booster FODO lattice. The baseline injection scheme requires\na slight modification of the PA section by changing a few dipoles, adding a couple of quadrupoles\n241\n\nand by adding 22 independent power supplies for existing quadrupoles. The injection and extrac-\ntion sections are able to transport the required envelopes of the circulating and injected/extracted\nbeams. The machine protection at extraction is highly challenging due to the high stored energy\nand has pushed the reduction of the total number of bunches at Z and WW operation. The hardware\nrequired for the injection, extraction, and dump have been listed.\n\u2013 The collective effects (see Section 4.2) have been studied for the updated optics and considered\ndifferent sources of instabilities: mismatching at injection, microwave, transverse mode coupling,\ntransverse and longitudinal coupled bunches. The studies have shown that present baseline injec-\ntion parameters from the high-energy LINAC allow a significant margin to avoid mismatch and\nmicrowave instabilities at injection energy (see Section 4.2.2). Studies on the coupled bunch insta-\nbilities have shown that the new parameters (especially the reduced number of stored bunched at\nZ-operation and the enlarged beam pipe) increase the threshold (see Section 4.2.3). Nevertheless,\na transverse damper (although with relaxed damping time) is still mandatory. Single-bunch insta-\nbilities were investigated for copper and stainless steel beam pipes of several diameters as well as\nfor different values of momentum compaction. The analysis has led to the choice of a copper beam\npipe with a diameter of 60 mm as the baseline. With such parameters and with only the beam pipe\nas an impedance contributor, the beam is stable for all operating modes with the baseline optics.\n\u2013 The synchrotron radiation power emitted from the booster during one cycle has been evaluated\n(see Section 4.3.1) to estimate the ionising dose in tunnel (see Section 4.3.2). The studies have\nshown that the contribution of the booster to the overall dose levels in the tunnel has to be studied\nin conjunction with the collider shielding. A recommendation is to increase the thickness of the\nbooster dipole yokes from 20 mm to 40 mm for better shielding efficiency.\nThere has been a lot of progress, and many changes have been made to the booster design since\nthe CDR. The current booster performance fulfills most of the requirements. Several additional studies\nremain to be done for a complete validation of the booster design. Among the different topics to be\naddressed are the following :\n\u2013 The placement of injection elements for the vertical injection scheme and threading of the injected\nbeam through the lattice elements is particularly challenging. It is necessary to undergo detailed\nstudies on the feasibility of the magnets and proposed channels for the injected beam. Some\ntechnical solutions are proposed for the septa and kickers and could be developed towards a tech-\nnical design but could also benefit from further R&D to apply newer technologies. The apertures\nand strengths used in the extraction and dump baseline concept are capable of transporting the\nenvelopes of the circulating and extracted beams, but a more detailed study, including kicker tech-\nnology choices and filling scheme requirements, will be needed to finalise the requirements and\nconverge on the technology choices. Despite the reduced beam intensity in the booster, such beams\nremain extremely critical and potentially destructive. Additional measures must be considered to\nensure the safety and integrity of all machine components in case of failure during the extraction\nand transfer processes. It is necessary to develop a dedicated system to monitor the position of the\nbeam in the extraction and dump regions, to evaluate the required reaction time to detect anomalies\nand safely dispose of the beam, and to have interlocks to avoid drifts beyond well-defined limits.\n\u2013 According to studies carried out so far, collective instabilities will not be a imitation with nominal\nbeams in the HEB with the foreseen larger Cu coated chamber and a transverse damper for TCBI.\nNevertheless, the studies have to be refined by taking all impedance sources into account, and the\ninstability thresholds need to be confirmed by self-consistent simulations, which include possibly\ncompounding effects, like intrabeam scattering and synchrotron radiation.\n\u2013 To further validate the booster dipole design, the next step is to produce and test a short prototype.\nThe optimisation of the magnets will be pursued in order to include in the process: (1) the yoke\nthickness of the dipole to provide additional radiation shielding, (2) the operational temperature of\n242\n\nthe magnets to improve the efficiency of waste heat recovery, (3) the industrialisation and design\nfor manufacture and assembly, and (4) detailed integration with the other technical systems.\n\u2013 The results presented demonstrate that the contribution of the booster to the overall dose levels in\nthe tunnel must be studied in conjunction with the collider shielding. In the next steps, it will be\nnecessary to perform further investigations in order to optimise the overall shielding strategy.\n243\n\n244\n\nChapter 5\nFCC-ee booster operation concept\n5.1\nOperation and performance\n5.1.1\nFilling scheme\nFollowing the 2023 mid-term review of the FCC Feasibility Study, a revised proposal for the injectors\nintroduces a Linac that produces and accelerates four pulses with a 25 ns spacing. The repetition fre-\nquency is set to 100 Hz for the Z and WW operation modes, and 50 Hz for the ZH and t\u00aft modes. The\ndamping ring now operates at 2.86 GeV and accommodates both electrons and positrons. The evolution\nof the damping ring (DR) bunch pattern is sketched in Fig. 5.1 for the old (left) and new (right) injector\nscheme.\nThis revised approach is now the new baseline, with the updated collider filling scheme fully\ndetailed in Section 2.3.7. The booster-filling scheme has been adapted to follow this new collider-filling\npattern.\nFig. 5.1: Pulse structure in the damping ring before injection into the linac of 20 GeV for an operating\nfrequency of 200 Hz (left) or 100 Hz (right).\nFor the Z mode, the new scheme implies that each booster cycle provides beam to only one tenth\nof the collider bunch positions. The smaller number of bunches in each booster cycle has several advan-\ntages:\n\u2013 Machine protection considerations only allow for about 1/10th of all bunches, i.e., 1120 (each with\nmax. 1/10th of nominal collider bunch intensity) injected into collider at once at Z energy.\n\u2013 The shorter booster injection plateau relaxes the vacuum quality required for tolerable emittance\ngrowth from rest gas collisions and reduces the impact of intra-beam scattering (IBS) and, thus,\nemittance growth on early injected bunches.\n\u2013 It allows the bunches to be distributed around the booster circumference. This relaxes the fast\nbeam ion instability and tune shifts for the electron beam, as well as the RF power required for\nbeam loading compensation. This distribution can also be exploited to optimise the filling of the\ncollider to mitigate e-cloud for positrons.\nHowever, the main drawback is the increase in the number of ramps, which in turn affects the time\nrequired for the top-up of all bunches (the effective cycle length), as illustrated in Fig. 5.2. In the new\n245\n\nscheme, the goal is to inject up to 1/10th of all collider bunches per booster cycle. c A consequence of the\nnew scheme that either the accelerating ramp in the booster must be shortened (for operational margin),\nas assumed in Table 5.1, or the full collider top-up duration length be slightly increased (e.g., the total\nramping time in the Z mode rising from 1.0 s to 1.14 s).\nFig. 5.2: Effective cycle time as a function of the ramping time and the number of bunches transferred\nper booster cycle. The brown dot corresponds to the scheme in presented in the mid-term review and the\nblue dot is for the new scheme.\nAn example of the filling pattern in the booster is shown in Fig. 5.3. It is worth noting that for Z\noperation, it is possible to choose which subset of bunches is injected from the booster to the collider.\nSuch a scheme provides flexibility in the accumulation phase of the collider for the creation of gaps in\nthe bunch train and possibly mitigates the electron cloud effect.\nThe three operation modes run with a smaller number of bunches and lower bunch intensity com-\npared to Z. The low bunch intensity needed from the injector (< 1 \u00d7 1010) resolves transverse coupled\nmode instabilities (TMCI) limitations in the booster (see Section 4.2). The three operation modes al-\nlow longer abort gaps, partly occupied by non-colliding bunches for energy calibration. There is still a\nmargin for reducing the injection rate (i.e., pausing between cycles) for energy saving in top-up mode or\nincreased booster cycle length (e.g., if beam injection in the collider needs to be done piecemeal). For\nWW operation, the transfer of half of the bunches at each injection is considered to limit the length of the\ninjection plateau. For the ZH and t\u00aft operation, one requirement for the filling scheme is to always have\nonly one beam present in the common RF section at a time. The number of bunches is small enough to\nrun the injector complex at 50 Hz with two bunches.\n5.1.2\nEmittance evolution\nThe transverse damping time is respectively 9 s, 0.763 s, 0.141 s, 0.0419 s and 0.0119 s at the injection\nenergy of 20 GeV and at the extraction energy of the 4 operating modes, respectively. The direct con-\nsequence is that the damping time at Z operation is of the same order of magnitude as the total ramping\n246\n\nTable 5.1: Filling parameters\nZ\nWW\nZH\nt\u00aft\nLinac repetition rate\n[Hz]\n100\n100\n50\n50\nBunches per Linac pulse\n4\n4\n2\n2\nLinac bunch spacing\n[ns]\n25\n25\n25\n25\nBooster accumulation time\n[s]\n2.8\n2.32\n3.0\n0.64\nBooster total ramping time\n[s]\n1.0\n1.6\n2.6\n4.3\nBooster cycle length\n[s]\n3.8\n3.92\n5.6\n4.94\nBunches per booster cycle\n1120\n928\n300\n64\nNumber of bunches in collider\n11 200\n1856\n300\n64\nMax. bunch intensity injected in collider\n1010\n2.725\n1.268\n1.268\n1.268\nNominal bunch intensity in collider\n1010\n21.5\n13.8\n16.9\n14.8\nAllowable charge imbalance\n[%]\n5\n3\n3\n3\nBeam lifetime: lumi 4 IPs, (q,BS,lattice)/4\n[s]\n916\n517\n428\n497\nFig. 5.3: Filling pattern for the different operation modes (from top to bottom): Z, WW, ZH, and t\u00aft. For\nthe Z mode, 4 bunch batches are separated by longer gaps, which is not visible on this scale.\n247\n\ntime given in Table 5.1 whereas the damping time is small for the other modes. Therefore, the emittance\nand energy spread at the extraction at the Z mode will depend on the initial injection parameters, whereas\nthe equilibrium emittance will be reached for the other modes. For this reason, only the Z mode has been\nconsidered for assessing whether the extracted emittance remains within the collider injection tolerances.\nThis study examines two injection scenarios:\nCase 1 (Linac alone for 20 GeV electrons) \u03b5x = 10 \u00b5m , \u03b5y = 10 \u00b5m , \u03c3\u03b4 = 1 \u00d7 10\u22123.\nCase 2 (Baseline: Damping ring) \u03b5x = 20 \u00b5m , \u03b5y = 2 \u00b5m , \u03c3\u03b4 = 1 \u00d7 10\u22123\nThe equilibrium emittance in the collider for Z operation, \u03f5x,RMS, is 0.71 nm \u00d7 \u03f5y,RMS = 1.9 pm \u00d7 \u03c3\u03b4 =\n1.09 \u00d7 10\u22123. A first study on the injection into the collider suggests that the collider can accept up\nto 5 times larger vertical emittance. That is why the target for the emittance at extraction, \u03f5x,target, is\n0.71 nm\u00d7\u03f5y,target = 9.4 pm. However, since the equilibrium horizontal emittance in the booster is lower\nthan in the collider for the Z and WW modes, the expected horizontal emittance at extraction is about\n0.12 pm (see Fig. 5.4).\nThe baseline energy ramp has a parabolic increase from 0 \u2013 80 GeV s\u22121, a linear ramp up to a\nmaximum energy higher than the extraction one (to speed up the radiation damping), a decrease back to\nthe extraction energy, a flat-top, and finally a ramp-down of the magnets. The current total time of the\nbooster ramp is 1.14 s, near the target of 1 s and can be shared between a ramp-up of 0.706 s, a flat-top\nof 0.1 s, and a ramp-down of 0.334 s. It is worth noting that the maximum slope for the magnetic field in\nthe dipole in the ramp-up is the same as in the ramp-down. However, it is likely that it will be possible\nto have a faster ramp-down since no beam is circulating during this time. The stability constraints and\nbeam loading in the RF cavities are not a concern during the ramp-down. Under these conditions, it is\npossible to reach a total ramp time of 1 s with a ramp-down of 0.194 s.\nThe evolutions of the beam energy, the radiated power, the minimum RF voltage, the horizontal\nand vertical RMS emittance of the energy spread are given in Fig. 5.4 for the baseline. The maximum\nenergy delivered by the cavities is 90.6 MeV/turn. In case 1, the final RMS vertical emittance is 30 pm,\nwell above the target of 9.4 pm. In case 2, the final vertical RMS emittance is 6.12 pm, which is above\nthe equilibrium emittance in the collider but within the injection acceptance.\nIf the ramp does not include an energy overshoot but maintains the same up-ramp, flat-top, and\ndown-ramp durations with a parabolic profile, the maximum energy delivered by the cavities is reduced\nto 51.7 MeV/turn. In this scenario, the final RMS vertical emittance reaches 55.4 pm and 11.2 pm\nin both cases\u2014significantly exceeding the target value of 9.4 pm. This highlights the clear advantage\nof increasing the energy to accelerate damping and achieve lower emittance values. Several mitigation\nstrategies have been evaluated to enhance damping during the ramp and achieve a smaller vertical emit-\ntance while maintaining a total ramping time of 1.14 s. In all cases, accelerating damping requires an\nincrease in radiated power, which in turn necessitates a higher cavity voltage.\nThree solutions are proposed to achieve a final smaller vertical emittance. The first possibility is to\nincrease the time allocated to the ramp-up by decreasing the time of the ramp-down. For instance, if the\nramp-down time is reduced by 170 ms, the ramp-up time increases to 876 ms. This also enables reaching\na higher maximum energy, thereby accelerating damping due to increased power consumption. The\nmaximum energy delivered by the cavities is then 130.0 MeV/turn. The final vertical RMS emittance\nis 9.27 pm and 1.99 pm for the two cases, respectively.\nThe second possibility is to achieve a higher energy by increasing the slope of the magnetic field\nfrom 80 \u2013 100 GeV s\u22121, for instance. In this case, the maximum energy delivered by the cavities is\n158.5 MeV/turn. The final vertical RMS emittance is 9.1 pm and 1.96 pm for the two cases, respec-\ntively. The third proposal is to insert a wiggler in one of the straight sections.\nFor these studies, the following parameters were assumed: a number of wigglers, nW = 2, each\n4.925 m long, with nP = 43 poles, each LP = 95 mm long, a magnetic field in the gap of BW = 1 T,\nand a gap between the poles of 20 mm. The wiggler parameters are preliminary and require further\n248\n\nrefinement. The aim in the framework of this study was to obtain an order-of-magnitude estimate of\nwhat is needed.\nThe parameters of the wiggler were calculated to go from I2 = 0.59 mm\u22121 to I2 = 2.36 mm\u22121\nand from I3 = 0.057 mm\u22122 to I3 = 27 mm\u22122 at an injection energy of 20 GeV. The evolution of the\nbeam energy, voltage, and beam emittance with an additional wiggler is given in Fig. 5.4. The emittance\nevolution takes into account that I\u2208and I\u220bvary in time since it is assumed that there is a constant\nmagnetic field in the wiggler. The maximum energy delivered by the cavities is then 122.5 MeV/turn.\nThe final RMS vertical emittance for the baseline case is 1.84 pm. Having a larger I3 significantly\nenlarges the final energy spread to 1.9 \u00d7 10\u22123, which is above the requirements. An optimisation of the\nwiggler parameters should enable a smaller final energy spread to be achieved.\nFig. 5.4: Evolution of the beam energy (first line), radiated power and RF voltage required (second line),\nthe horizontal RMS emittance (third line), vertical RMS emittance (fourth line), and RMS energy spread\n(last line) as a function of time for Z mode operation.\nIn summary, achieving the required final vertical emittance is only possible with the baseline\nscenario if two conditions are met: using a high-energy damping ring and maintaining a normalised\nvertical emittance of 2 pm throughout the linac. However, at the price of more RF power, it is possible to\nreach the target vertical emittance with a ramp of 1 s if it is possible to combine a shorter ramp-down with\na wiggler. Increasing the acceleration rate to reach higher energies more quickly can be beneficial, but\ncaution is needed to avoid excessively high energies, where the radiated power will increase significantly,\nleading to high power consumption.\n5.1.3\nRamping strategy\nFollowing an accumulation time, the booster will ramp the beam energy from the injection energy\n(20 GeV) up to extraction energy (45.6 GeV for Z, up to 182.5 GeV for t\u00aft). The optimisation strat-\n249\n\nFig. 5.5: Evolution of the beam energy (first line), the radiated power and required RF voltage (second\nline), the horizontal RMS emittance (third line), vertical RMS emittance (fourth line), RMS energy\nspread (fifth line), and synchrotron integrals I\u2208and I\u220bas a function of time, for Z mode operation with\na wiggler installed in one of the straight sections.\negy has to ensure beam stability and reach the target emittances.\n\u2013 The start of the ramp shall be adiabatic to avoid shaking the bunches.\n\u2013 The energy gain per turn is limited by eddy currents in the magnets. A conservative maximum\nramp rate of 80 GeV/s is considered.\n\u2013 When approaching high energies, the energy gain is dominated by the energy provided to compen-\nsate for losses due to synchrotron radiation. The extraction energy needs to be reached adiabati-\ncally.\nThe tracking simulation suite BLOND [337] was used to design the energy and RF voltage ramps for\nall four modes. The next sections give details of the energy ramps of the two extreme modes (the high\ncurrent mode Z and the high energy mode t\u00aft).\nZ mode ramp\nTo achieve the target emittances required by the collider (see Section 5.1.2), the ramping strategy includes\nan energy overshoot up to 53 GeV. Since energy loss due to synchrotron radiation scales with the fourth\n250\n\npower of the energy, the 8 GeV excess must be compensated by a high RF voltage.\nFor designing the voltage ramp, the phase-space longitudinal stability regions are considered at\nthree key points: the flat bottom, the overshoot maximum, and the flat top, as shown in Fig. 5.6. To\nmaintain a sufficiently small filling fraction (the ratio of bunch emittance to stability area), an RF voltage\nof at least 85 MV is required.\nFig. 5.6: Longitudinal phase space stability regions delimited by the separatrix (red curve). Blue lines\nshow curves of constant energy. Left panel corresponds to flat bottom, with an energy E = 20 GeV and\nvoltage VRF = 50.1 MV. Right panel corresponds to flat top, with an energy E = 45.6 GeV and voltage\nVRF = 57.2 MV. The middle panel corresponds to the maximum of the energy overshoot, E = 53 GeV,\nwith voltage VRF = 85 MV.\nA doubly parabolic voltage ramp up to 85 MV is proposed, see Fig. 5.7. The first 1 % voltage\nincrease is parabolic to avoid shaking the beam; then there is a steep linear part, and finally a parabolic\ncurve for the remaining 20 % of the voltage increase. From 85 MV, the voltage is ramped down to\n57.2 MV with a similar strategy, parabolic for the initial 20 %, then linear, then parabolic for the remain-\ning 40 %, before a 0.1 s flat top. The proposed ramp, based on considerations of longitudinal dynamics,\nwill be fine-tuned according to hardware considerations.\nFig. 5.7: Left: Energy and voltage ramping strategies for the Z mode. The total energy gain is plotted\nas a full green line; it is the sum of the energy gain needed for acceleration (light-blue dashed line) and\nthe energy required to compensate for synchrotron radiation losses (dark blue dashed line). The voltage\nis shown as a full orange line. Right: Synchronous phase, theoretical (full blue line) against simulated\nbunch position (dotted orange line).\nt\u00aft mode ramp\nThe t\u00aft mode ramp lasts 2.03 s, corresponding to 6713 turns in the booster ring, followed by a 0.1 s flat\ntop. The energy increases nine-fold, from 20 GeV to 182.5 GeV. At flat top, the energy loss due to\nsynchrotron radiation is substantial (over 10 GeV/turn). The top energy has to be reached as slowly as\n251\n\npossible. The proposed energy and voltage ramps are shown in Fig. 5.8. A preliminary solution with a\nlinear voltage increase from 50.1 MV up to 11.533 GV is proposed.\nFig. 5.8: Left: Energy and voltage ramping strategies for the t\u00aft mode. The total energy gain is plotted\nas a full green line; it is the sum of the energy gain needed for acceleration (light-blue dashed line) and\nthe energy required to compensate for synchrotron radiation losses (dark blue dashed line). The voltage\nis shown as a full orange line. Right: Synchronous phase, theoretical (full blue line) against simulated\nbunch position (dotted orange line).\n5.2\nRequirements\n5.2.1\nMagnets\nThe magnet design is based on the FODO lattice described in Section 4.1.3. The main cell of the arcs\nuses 1 dipole family, 6 quadrupoles circuits (to tune the phase advances between the sextupoles and also\nthe global tune of the cell), and 2 sextupoles families (to correct the chromaticity in both planes).\nEach quadrupole is combined with one dipole corrector. The correction plane is directly linked\nto the polarity of the quadrupole (horizontal if positive and vertical if negative). More details on the\ncorrection scheme in the booster are given in Section 5.2.6. The requirements for the main magnets of\nthe booster are summarised in Table 5.2.\nTable 5.2: Main magnet requirements for the booster.\nDipole\nQuadrupole\nSextupole\nCorrector\nFocusing\nDefocusing\nTotal number in lattice . . .\n6164\n3346\n576\n560\n3346\n. . . of which in arcs\n5536\n2768\n576\n560\n2768\nAperture [mm]\n65\n65\n65\n65\n65\nLength [m]\n11\n1.3\n0.7\n1.4\n< 0.3\nMax strength, arc at t\u00aft\n58.9 mT\n28.7 T m\u22121\n1147 T m\u22122\n1219 T m\u22122\n20 mT m\nMin strength, arc at 20 GeV\n6.45 mT\n2.8 T m\u22121\n126 T m\u22122\n134 T m\u22122\n20 mT m\n5.2.2\nInjection\nTo assess the injection requirements for the booster, the 6-D dynamic aperture was calculated at injection\nover 1000 turns. The calculation was performed by tracking a grid of macro-particles with initial actions\nranging from 1 \u2013 50 \u03c3 in 1 \u03c3 steps, considering four different angles in the x-y plane: 0\u25e6, 30\u25e6, 60\u25e6and\n90\u25e6.\n252\n\nMacro-particles were injected at the injection kicker with an initial time offset between \u2212250 \u2013\n250 ps and a relative energy spread between -2% and +2%. The maximum action for which a macro-\nparticle remains unlost after 1000 turns is shown in Fig. 5.9, with the 15 \u03c3 limit indicated in red.\nIf the RMS energy spread at injection is 10\u22123 and the RMS bunch size is 4 mm, the corresponding\nrequirements are a maximum time jitter of 50 ps and a relative energy spread tolerance of 5 \u00d7 10\u22123. It\nis worth noting that the injection transfer line to the booster requires a relative energy difference error of\n3 \u00d7 10\u22123. To summarise, the time jitter for the injection complex should be 50 ps and the relative energy\nerror should be less than 3 \u00d7 10\u22123.\nFig. 5.9: 6-D dynamic aperture, in units of rms beam size (\u03c3), at injection into the booster for 1000\nturns as a function of the initial time delay and relative energy difference. The injection emittances are\n20 \u00b5m \u00d7 2 \u00b5m. The red line gives the contour for a dynamic aperture of 15 \u03c3.\n5.2.3\nRF staging\nThe high-energy booster aims to accumulate and accelerate the bunches before injection into the two\ncollider rings. The RF system will be installed in point PL.\nIn the first stage, the RF system must operate at the Z, WW or ZH operating points without\nany hardware modification, allowing fast switching between the three different modes as is done in the\ncollider. This is achieved by installing 112 cavities which corresponds to 28 cryomodules with 4 cavities\nper cryomodule. Due to the large range in RF voltage between injection and extraction energy, reverse\nphase operation (RPO) [245] is planned (more details are given in Sections 3.4.3 and 6.3).\nThe second step will consist of adding 332 cavities (84 cryomodules) to have a total of 448 cavities\nto run at the t\u00aft energy, corresponding to a total of 112 cryomodules. This important installation sequence\nwill be performed during a year of shutdown after the last run at the Z, WW, ZH operating points and\nbefore the start of the t\u00aft run.\nThe same 6-cell 800 MHz elliptical cavities as designed for the collider t\u00aft mode will be used.\nAs a baseline, the cavity manufacturing technology is the standard bulk niobium technology which has\n253\n\na limitation restricting the usable accelerating gradient to 20 MV/m in operation, assuming that the\ncavities are qualified in a vertical cryostat at a 20 % higher gradient and Q0 (see Table 3.11).\n5.2.4\nVacuum\nCollective effects arising from the accumulation of oppositely charged particles in the beam can lead\nto various undesirable consequences. As these effects are highly sensitive to bunch spacing, they are\na primary concern at the Z operating point, where the collider will run with a large number of closely\nspaced bunches.\nIn particular, electron cloud build-up and photoelectron emission during operation with positrons\nand ion accumulation during operation with electrons may lead to beam instabilities, emittance growth\nand other detrimental effects in the high-energy booster. These effects can most effectively be mitigated\nby limiting the production of electrons and ions in the beam chamber environment, which sets require-\nments on the properties of the vacuum chamber surface as well as the vacuum level in the machine.\nIon accumulation and instabilities\nBeam-induced gas ionisation gives rise to electrons and ions along the beam path. The positive ions are\nattracted by the electron beam field and may be trapped in oscillation along the bunch train. Trapped\nions accumulate over the passage of a bunch train and can seed a coupled-bunch instability known as the\nfast beam-ion instability [338, 339]. Ions are trapped between bunches if their molecular mass number,\nA, exceeds a critical mass number, Ac, which in the linear approximation can be defined as [99]\nAc \u2261Nbrpc \u2206tsep\n2\u03c3y(\u03c3x + \u03c3y) ,\n(5.1)\nwhere Nb is the bunch intensity, \u2206tsep the bunch spacing and rp is the classical proton radius. Since the\ntrapping mass is inversely proportional to the beam size, the most critical conditions for ion trapping and\ninstabilities occur immediately after injection, when the beam sizes are at their largest, and relax as the\nemittance decreases during the booster cycle.\nThe following parameters are assumed: a bunch spacing of 25 ns, as in the collider filling scheme,\nthe critical mass number Ac \u22481, the transverse beta functions \u03b2x,y \u224340 m and the horizontal dispersion\nDx \u22430.125 m. In this case, even hydrogen gas, H2 (A = 2), would be trapped around the bunch train\nand avoiding instabilities in such conditions would set unrealistic constraints on the acceptable vacuum\nlevels, especially for an unbaked vacuum without active pumping from a NEG or similar surface. Follow-\ning the recent updates after the mid-term review, the proposed strategy for Z mode involves transferring\nonly one-tenth of the total number of bunches at a time from the booster to the collider. This allows the\nbunches to be distributed around the booster circumference, thereby increasing the bunch spacing.\nIf each group of four bunches from the linac is separated by the maximum possible distance\nof approximately 1 \u00b5s, the ion trapping mass between successive 4-bunch trains can reach Ac \u224835,\nsignificantly mitigating constraints. In this scenario, ions from the lightest and most abundant gases\nwould be trapped along the 4-bunch trains but would dissipate during the gaps before the next group,\nmaking them unlikely to cause detrimental effects. However, heavier gas species such as CO2 could still\nbe trapped from train to train, and their potential impact on vacuum level requirements will need to be\nstudied further.\nElectron cloud\nElectron clouds can be created by secondary electron emission through a beam-induced multipacting\nprocess, an accumulation of photoelectrons, or a combination thereof. Electron cloud formation through\nmultipacting depends strongly on the secondary electron yield (SEY) of the beam chamber surface, de-\nfined as the ratio between the emitted and the impinging electron currents. The risk of electron cloud\n254\n\nbuild-up for different values of the SEY has been assessed by simulating the process of electron cloud\nformation in the beam chamber at injection and extraction energy using the PYECLOUD code [73].\nAssuming the nominal collider filling pattern with uniform trains of bunches spaced by 25 ns, electron\ncloud build-up in drift spaces, as well as in the main dipolar, quadrupolar and sextupolar fields is sup-\npressed if the SEY is kept at the value of 1.5 or below. Here, the strongest constraints come from the\nsextupole magnets at extraction energy, whereas the requirement in other elements is more relaxed. Such\nvalues of the SEY are expected to be readily achievable after beam-induced conditioning for warm cop-\nper surfaces [340]. In addition, these requirements can be significantly further alleviated if the flexibility\navailable in the booster filling pattern for spacing the bunches over the entire ring, is employed.\nPhotoelectrons, produced through photoemission from the chamber walls due to the synchrotron\nradiation emitted by the circulating beam, can enhance the electron cloud build-up process, and in very\nlarge quantities can induce electron cloud effects even in the absence of beam-induced multipacting. The\namount of photoelectrons emitted is determined by the photoelectron yield (PY) of the beam chamber\nsurface, defined as the ratio between the emitted photoelectrons and the number of impinging photons,\nalong with the number and distribution of synchrotron radiation photons in the beam chamber. While\nbuild-up studies for the different photoemission levels have not been finalised for the booster, studies\nfor the collider can be used (see Section 1.4.4) for a first estimate of the acceptable level in the booster.\nFor the collider, build-up and ray-tracing studies imply that the photon absorbers need an efficiency well\nabove 90% to ensure beam stability. Since the beam current in the booster is around a factor 100 lower\nthan in the collider, the photon flux is lower by a similar factor and therefore effectively fulfils the collider\nconstraint. In addition, since electron multipacting is expected to be well suppressed in the booster, the\nrisk of photoelectrons enhancing the multipacting to a worrying degree is low. Therefore, the effect of the\nphotoemission is not expected to have a major impact on the beam quality. Detailed studies are pending.\n5.2.5\nMachine protection systems\nBeam intensity limitations for beam transfers\nEnsuring robust machine protection is a key priority when operating with the high-intensity and small-\nemittance beams of the Z mode. While the stored beam intensity in the booster is lower than in the\ncollider, uncontrolled beam losses could still pose a risk to equipment. In particular, beam loss incidents\nmay occur during the beam transfer process due to potential kicker failures or timing errors.\nGiven the large number of booster-to-collider transfers required for top-up injection, the reliability\nof the hardware systems involved is paramount. To further enhance safety, protection absorbers will be\nstrategically placed in critical areas, including the booster extraction region, the transfer lines, and the\ncollider injection region. These absorbers will ensure that any mis-steered beams are safely intercepted,\npreventing damage to the accelerator systems.\nSimilar protection measures are successfully implemented in other high-intensity accelerators,\nsuch as the SPS and LHC at CERN, providing a well-established foundation for ensuring safe operation.\nThe maximum acceptable load on protection absorbers poses a limitation for the beam intensity,\nwhich can be safely transferred from the booster to the FCC-ee collider. Some of the most robust absorber\nmaterials for protection absorbers used nowadays at CERN include isotropic graphite and Carbon/Carbon\ncomposites. Material tests with 440 GeV proton beams in the CERN HiRadMat facility showed that such\nmaterials can resist energy deposition densities as high as 5 kJ/g without sustaining any damage (5 kJ/g\ncorresponds to a peak temperature of roughly 3000 \u25e6C). The maximum acceptable energy density may\neven be higher, but firm limits can only be established once higher-intensity beams become available in\nHiRadMat or other facilities.\nIn order to provide a first order estimate of the expected intensity limitation for booster-to-collider\nbeam transfers in the Z mode, a generic beam loss scenario is considered, where a mis-steered 45.6 GeV\nbunch train is intercepted by a graphite or Carbon/Carbon absorber with a density of 1.8 g/cm3. The\n255\n\nenergy deposition in the absorber block is calculated with the FLUKA radiation transport code. It\nis assumed that all bunches impact on the same spot and have an emittance of \u03f5x,target = 0.71 nm in\nthe horizontal plane and \u03f5y,target = 9.4 pm in the vertical plane; these values are the target emittances\nfor booster extraction defined in Section 5.1.2. Assuming the bunch train corresponds to around 1% of\ncollider intensity (1200 bunches with a bunch intensity of 2.14\u00d71010 \u2013 2.68\u00d71010 e\u2212/+), the simulations\nsuggest that the maximum energy density in in the block can reach 5 \u2013 6 kJ/g if \u03b2x,y = 500 m at the\nabsorber location, and 3 \u2013 4 kJ/g if \u03b2x,y = 1 km (in both cases the possible contribution of the dispersion\nto the beam spot size was neglected). These results show that a transfer of 1% of the collider intensity\nmight be acceptable in the Z mode if large \u03b2-functions can be achieved at protection absorbers. On the\nother hand, transferring a train equivalent to 10% of the collider intensity, as originally envisaged in the\nmid-term report, is considered too high and poses a non-negligible risk for machine protection.\nThe presented numbers provide an initial estimate of intensity limitations, but a more comprehen-\nsive assessment will be necessary through detailed thermo-mechanical studies. These studies will enable\na thorough evaluation of material response to energy deposition and temperature gradients induced by\nparticle showers.\nAdditionally, refining the acceptable load on absorber materials will require dedicated beam im-\npact tests to ensure their resilience under operational conditions. The final intensity limits will also be\ninfluenced by the beam\u2019s emittance and optics.\nFurthermore, a systematic analysis of potential failure scenarios during beam transfer will be es-\nsential. This will allow more precise estimates of energy deposition in protection absorbers, ensuring\ntheir effectiveness in safeguarding machine components.\nOther machine protection aspects for the booster\nAccidental beam losses can occur not only during the transfer from the booster to the collider but also\nwithin the booster ring itself, due to factors such as beam instabilities, interactions with dust particles, or\nhardware failures. A thorough assessment of potential failure modes and their associated time scales is\nessential for defining the machine protection architecture of the booster.\nGiven the destructive potential of the booster beams at Z mode\u2014even at just 1% of the collider\u2019s\nintensity\u2014it is likely that a minimal collimation system will be required to protect the machine through-\nout the booster cycle. At top energy in Z mode operation (45.6 GeV), the stored beam energy in the\nbooster is comparable to that of SuperKEKB, where collimator jaws suffered damage from the beams.\nThis underscores the importance of machine protection in the booster, with the robustness of collimators\nbeing a key area of study, similar to the protection absorbers discussed previously.\nFor safe operation, a beam monitoring and loss detection system will also likely be necessary in the\nbooster. The specific requirements for booster beam instrumentation, such as beam loss monitors, beam\nposition monitors, and beam current monitors, will be determined based on the failure modes identified.\nIn cases of excessive beam loss, a rapid extraction system must be in place to remove the beam in a\nsingle turn. As outlined in Section 4.4, the current extraction system design assumes that the booster\nshares a beam dump with the collider. The required reaction time for triggering a beam abort remains to\nbe defined but is expected to be within a few turns.\nBeyond beam losses, the impact of synchrotron radiation-induced heating must also be carefully\nassessed. While the synchrotron power emitted in the booster ring is significantly lower than in the\ncollider (see Section 4.3), power deposition on equipment remains non-negligible. Detailed energy de-\nposition studies will be necessary to ensure that sensitive components are adequately protected from heat\ngenerated by synchrotron photons.\n256\n\n5.2.6\nCorrection strategy\nThe schematic workflow of the correction strategy is shown in Fig. 5.10 and is presented here for the\nFODO lattice described in Section 4.1.3. The emittance tuning is divided in two parts: one with the\nsextupoles turned off (or very low strength) and the other with the sextupoles ramped to full strength\nin 3 steps. The momentum aperture of the nominal lattice without errors reduces to \u00b10.3% when sex-\ntupoles are switched off. For the moment, this value is considered acceptable since the high-energy linac\ncan provide dedicated single bunches with an energy spread of 0.05%, during commissioning. Further\nstudies are required in the next phase, including the errors in the momentum aperture evaluation. It is\nassumed that all the orbit correctors of the booster are individually powered, and they are placed at each\nquadrupole together with the BPM (i.e., 1400 dipole correctors per plane as given in Table 5.2). Firstly,\nthe sextupoles are off. The orbit correction is applied segment-by-segment (SbS), i.e., in this case, arc by\narc, which is similar to the LHC commissioning [341]. After the SbS, two iterations of orbit correction\n(using the singular value decompositions method) are made on all arcs and in line in order to reduce the\nresidual orbit.\nThis is sufficient to reduce the orbit enough to locate the closed orbit. Following this step, multiple\niterations of orbit correction in the ring are performed until the residual RMS orbit falls below the ana-\nlytical value [342]. Finally, the sextupoles are set to 33% of their nominal strength, and a final iteration\nof orbit correction in the ring is carried out.\nFour iterations of orbit correction, coupling resonant driving terms (RDTs), horizontal and vertical\ndispersion correction, phase advance adjustments, and tune corrections are performed at this stage.\nA total of 560 normal quadrupole correctors are distributed within the F2D2 main quadrupole fam-\nily along the eight arcs. In comparison, 568 skew quadrupole correctors are positioned at the sextupoles\nin the eight arcs.\nThis procedure is then repeated with the sextupoles set to 66%, of their nominal strength before\nbeing performed at full sextupole strength.\nVarious case scenarios were studied for 100 seeds. The alignment and field errors used are re-\nported in Table 5.3. Assuming 200 \u00b5m misalignment from one girder to the other (about 25 m distance)\nand 50 \u00b5m misalignment for the elements placed on top of the same girder (BPM, Quadrupole, and\nSextupole).\nTable 5.3: Summary of the different error types and their values.\nError type (Gaussian RMS )\nValue\nUnit\nMB relative field error\n10\u22123\nMB main dipole roll error\n300\n\u00b5rad\nMQ offset (with respect to the girder)\n50\n\u00b5m\nMQ roll\n100\n\u00b5rad\nMS offset (with respect to the girder)\n50\n\u00b5m\nBPM offset (with respect to the girder)\n50\n\u00b5m\nGirder-to-girder offset\n200\n\u00b5m\nIt is worth noting that all the errors applied on the elements are randomly Gaussian distributed\nwithin \u00b13 RMS.\n5.2.7\nResidual orbit and corrector strength required\nFigure 5.11 shows the RMS values of the residual orbit for the 100 configurations of errors studied with\nthe correction procedure described in the previous section. The dashed red lines on the distributions\nrepresent \u00b13 times the RMS calculated analytically. The right panel of Fig. 5.11 shows the distribution\nof the RMS orbit corrector strength for the same 100 machine configurations.\n257\n\nFig. 5.10: Workflow chart of the tuning scheme of the booster.\nFig. 5.11: RMS values of the residual orbit (left) and of the corresponding corrector strengths (right) for\nthe different error configurations described in the text.\nThe RMS values of the correctors\u2019 strength for the same 100 different configurations are shown in\nFig. 5.12. As for the residual orbit both optics have similar RMS corrector strength values. The average\nvalues of the RMS residual orbit and of the maximum corrector strength are presented in Table 5.4.\n5.2.8\nEmittance evaluation\nThe final equilibrium emittance for the 100 converging machine configurations is evaluated at a beam\nenergy of 45.6 GeV. The distribution of the equilibrium emittance after orbit correction and before the\ncorrection of the coupling RDTs, dispersions, phase advances and tunes are shown in orange in Fig. 5.13.\n258\n\nFig. 5.12: RMS values of the normal and skew quadrupole correctors strength for the 100 configurations\nof errors, as described in the text.\nTable 5.4: Average RMS residual orbit and maximum RMS corrector strength values after correction for\nthe 100 configurations based on Table 5.3.\nPlane\n3\u00d7RMS\nAnalytic\nSeeds\nResidual orbit\n[\u00b5m]\nx\n253\n181\ny\n262\n160\nOrbit Corrector\n[mT.m]\nx\nt\u00aft\n20\n23\ninj\n2.2\n2.5\ny\nt\u00aft\n21\n24\ninj\n2.2\n2.6\nIntegrated Quadrupole\n[T.m\u22121.m]\nNormal\nt\u00aft\n-\n0.32\nCorrector\ninj\n-\n0.03\nSkew\nt\u00aft\n-\n0.13\ninj\n-\n0.02\nAfter the four iterations of orbit, coupling RDTs, dispersions, phase advances and tunes corrections the\nequilibrium emittance distributions are centred around the target values at Z energy.\n5.2.9\nPerspectives\nFuture studies can focus on reducing the number of independent correctors to simplify the correction\nprocess and enhance computational efficiency.\nTo achieve this, the autocorrelation of the trim (resp. skew) correctors, as well as the linear and\nnon-linear correlations between correctors around the ring, will be analysed.\nFinally, chromaticity correction will be implemented, and the dynamic aperture will be evaluated\nwhile accounting for various errors and their associated corrections.\n259\n\nFig. 5.13: Distribution of the equilibrium emittance in the horizontal (top) and vertical (bottom) planes\nat Z energy before (ante) and after (post) the four iterations of orbit and emittance correction described\nin Section 5.2.6.\n5.3\nAvailability\nThis section details results from the enhanced Monte Carlo simulation environment for FCC-ee avail-\nability described in Section 2.4, focusing on systems specific to the booster ring.\n5.3.1\nContributing Systems\nThe same general framework for availability approximation was applied as per the collider systems,\ndescribed in Section 2.4.1. The specifics of this process used for each booster system are described below.\nOnly faults leading to downtime in the representative system were considered, thereby assuming a similar\ndegree of redundancy for each basic component family as exists currently in the working accelerator.\nDetails of subsystems, scaling numbers, and any additional system-level redundancy implemented are\nprovided in Table 5.5. Fault data was taken from CERN\u2019s Accelerator Fault Tracking (AFT) database\n[235] and is specific to the LHC physics operation 2015-2024, unless otherwise stated.\n1. Beam Instrumentation: Beam instrumentation faults are given beam position monitor (BPM),\nbeam loss monitor (BLM) and \u201cother\u201d categories. These were scaled according to the relative\nnumber of monitors in the booster compared to the LHC.\n2. Beam Losses: Downtime due to Unidentified Falling Objects (UFOs) and beam instabilities.\nDumps in the former category were scaled with the length of the beam pipe, assuming similar\namounts of dust and beam interaction as in the LHC. Dumps due to beam instabilities were ap-\nplied without scaling. The LHC sees relatively long downtimes due to beam loss effects that cause\nquenches in nearby superconducting magnets, which is not representative of FCC-ee. Therefore,\ndowntime due to quench recovery was subtracted to calculate the MTTR. FCC-ee dumps due to\nbeam losses then appear frequently, with a short recovery time.\n3. Extraction: Describes systems required for beam abort. These include controls and kicker hard-\nware to divert the beam into the dump block. They appear twice in the LHC (one for each circulat-\ning beam), as for the booster, so they are applied without scaling. The dump blocks are excluded\nas these are shared with the collider rings.\n4. Injection Systems: This includes kickers, septa, and control systems needed to inject and extract\n260\n\nthe beam under regular operation. The LHC has two injection systems (one for each beam). The\nbooster has two injection systems from the injector complex and two extraction systems for the\ncollider.\n5. Machine Protection & Interlocks: Scaling for LHC subcategories is approximated from the\nrelative number of hardware instances foreseen in the FCC-ee.\n6. Magnets: Failure data from 3 532 normal-conducting magnets around the CERN complex was\napplied to 12 500 magnets in the booster.\n7. Power Converters: Failure data was taken from two families of power converters, each grouped\naccording to similar MTBF, to represent powering hardware for various magnet types. Only faults\nleading to downtime in the LHC were considered, thereby assuming a similar degree of redundancy\nfor each magnet group as currently exists in the LHC. Due to the large number of corrector magnets\nin the latest optics configuration, an MTBF of 9 days is observed in some categories.\n8. Radio Frequency (RF): The LHC has 16 accelerating superconducting RF cavities. The number\nin FCC-ee varies with energy mode. All cavities are horizontally tested to a margin 10 % above\ntheir nominal voltage so, theoretically, nominal beam energy can be preserved if no more than\n10 % of the cavities are unavailable. The effect of losing cavities on beam stability and hardware\nprotection has only been modelled in the collider so far, where it was determined that redundancy\nis severely limited in Z and W modes due to beam loading. In the booster, the transients required\ndue to energy ramping complicate beam stability calculations, and it is presently unclear whether\nthe beam could be preserved in the event of cavity loss. Pending further study, no redundancy was\nassumed in the lower energy (higher beam current) modes for the booster. In ZH and t\u00aft, 10 % is\ngiven as per the collider cavity circuits.\n9. Transverse Damper: The booster will have one transverse damper system. The failure rate is\nscaled down from the two dampers in the LHC.\n10. Vacuum: LHC vacuum faults are categorised according to the failed component (pump, gauge,\nvalve, controller). These are then scaled according to the relative number of components in the\nbooster vacuum system.\n5.3.2\nInherent Resilience to Shorter Fault Types\nIn the event of an outage in the booster and injector complex, stable beams can be maintained in the\nmain collider rings for a lifetime of 10-15 minutes, depending on energy mode (see Table 2.2). If top-up\ninjection can be restored at this time, normal physics can resume. This significantly reduces the FCC-\nee\u2019s sensitivity to short-duration fault types in the booster and injector complex and leads to an inherent\nadvantage for availability.\n5.3.3\nSimulation Results\nThe breakdown of unavailability and lost luminosity contribution from each booster system is shown in\nFig. 5.14. Contributions from the injector complex are also provided for illustration. For comparison\nwith collider and technical infrastructure systems, see Fig. 2.22.\nThe RF is the largest contributor to unavailability and lost luminosity in Z and WW modes, largely\nbecause it does not benefit from redundancy as it does in the collider. Power converters suffer from the\nsame challenges as identified for the collider in Section 2.4.1. Beam losses, although occurring at the\nsame rate per metre of beam pipe as the collider, are much less significant for lost luminosity as their\nrecovery time is relatively short.\n5.3.4\nR&D Opportunities\nSeveral R&D opportunities are identified to improve availability in the booster ring:\n261\n\nTable 5.5: Parameters used to simulate availability of systems and subsystems in the FCC-ee Booster.\nSystem\nSubsystem\nRepresentative FCCee Redundancy\u2217Location\nUnit\nGroup\nSystem\nMTBF\nMTBF\nMachine\n#\n#\n# (%)\nAP\ndays\ndays\nBeam\nInstruments\nBPM\nLHC\n1000\n3369\n0 (0)\nall\n20 671\n6.1\nBLM\n3600\n200\n0 (0)\nall\n36 632\n183.3\nOther\n1\n1\n0 (0)\nall\n24.5\nBeam Losses UFOs\nLHC\n54\n91\n0 (0)\nall\n2.4\nBeam Instability\n1\n1\n0 (0)\nall\n4.3\nExtraction\nControls\nLHC\n2\n2\n0 (0)\nPB\n36\n18.2\nHardware\n2\n2\n0 (0)\nPB\n65\n32.7\nOther\n2\n2\n0 (0)\nPB\n71\n35.6\nInjection\nSystems\nMKI\nLHC\n2\n4\n0 (0)\nPB\n20\n5\nTDI\n2\n4\n0 (0)\nPB\n71\n17.8\nMachine\nProtection\nFMCM\nLHC\n1\n10\n0 (0)\nall\n39.2\nBIS\n1\n2\n0 (0)\nall\n32.7\nSMP\n1\n1\n0 (0)\nall\n87.1\nPIC\n1\n0.2\n0 (0)\nall\n261.4\nWIC\n1\n6\n0 (0)\nall\n21.8\nMagnets\nNormal-conducting\nCERN\n3532 12 500\n0 (0)\nall\n71 \u00d7 106\n5681\nPower\nConverters\nDipole\nLHC\n194\n16\n0 (0)\nall\n3672\n229.5\nQuadrupole\n194\n32\n0 (0)\nall\n3672\n114.8\nSextupole Focusing\n194\n32\n0 (0)\nall\n3672\n114.8\nSextupole Defocusing\n194\n32\n0 (0)\nall\n3672\n114.8\nDipole Tapering\n1032\n346\n0 (0)\nall\n15 485\n44.8\nQuadrupole Tapering\n1032\n346\n0 (0)\nall\n15 485\n44.8\nHorizontal Corrector\n1032\n1672\n0 (0)\nall\n15 485\n9.3\nVertical Corrector\n1032\n1672\n0 (0)\nall\n15 485\n9.3\nQuadrupole Corrector\n1032\n1384\n0 (0)\nall\n15 485\n11.2\nSkew Quadrupole\n1032\n1384\n0 (0)\nall\n15 485\n11.2\nRadio\nFrequency\nCavity Circuit Z\nLHC\n16\n112\n0 (0)\nPL\n1462\n0.54\nCavity Circuit W\n16\n112\n0 (0)\nPL\n1462\n0.54\nCavity Circuit ZH\n16\n112\n11 (10)\nPL\n1462\n314.6\nCavity Circuit t\u00aft\n16\n600\n60 (10)\nPL\n1462\n465.2\nTransverse\nDamper\nLHC\n2\n1\n0 (0)\nPL\n65.4\n65.4\nVacuum\nPumps\nLHC\n891\n8360\n0 (0)\nall\n349 448\n41.8\nGauges\n1052\n904\n0 (0)\nall\n274 997\n304.2\nValves\n323\n226\n0 (0)\nall\n84 434\n373.6\nControllers\n789\n2328\n0 (0)\nall\n55 915\n20.8\n* System-level redundancy in addition to that already implemented in the component family of the representative system.\nRadio Frequency\nPresently, it is unclear whether redundancy could be implemented in the booster RF cavities as the tran-\nsients due to ramping lead to additional complications. However, the beam current within the booster is\nsignificantly lower than in the collider, suggesting beam loading effects should be less problematic. Im-\nplementation of redundancy in this system could significantly benefit the achieved integrated luminosity.\nPower Converters\nProposed solutions are treated in Section 2.4.4. Collaboration with the optics working group is required\nto consider how to preserve the beam if combinations of magnets fail. A system-level redundancy ap-\n262\n\nFig. 5.14: Unavailability and lost luminosity contribution of each system in the booster. Systems are\nordered according to Z mode lost luminosity contribution.\nproach could make significant gains in this case, besides reducing the number of families for the corrector\nmagnets.\nExploiting Resilience to Short Faults\nAdditional opportunities exist to exploit the booster\u2019s natural resilience to shorter fault types. A lengthy\nturnaround time may be avoided if a failed component can be brought back online before the beams in\nthe main collider expire. To this end, there are two parallel approaches:\n1. If the collider beam lifetime without top-up injection can be made longer, systems will have a\nbetter opportunity to recover before a beam abort is necessary. This requires intricate optimisation\nof the beam optics under various possible failure mechanisms; however, this could greatly alleviate\nthe design task on the collider technical systems.\n2. Measures to bring the recovery time of failed systems to below 10 minutes could be extremely\npowerful for the booster. For example, the automatic reset of recurring RF trips or the installation\nof redundant or back-up modules that can quickly be brought online to replace failed components.\n5.4\nConclusion\nThe results presented in this section demonstrate the feasibility of the Future Circular Collider (FCC)\ndesign, outlining the operational strategies, technical requirements, and performance benchmarks neces-\nsary for its successful implementation. Through detailed analysis, the revised filling scheme, ramping\nstrategy, and emittance evolution have been optimised to enhance collider efficiency while addressing\nchallenges related to beam stability and machine protection. The study has also highlighted key advances\nin magnet technology, RF staging, vacuum control, and correction strategies to mitigate instabilities and\nimprove overall reliability. Furthermore, availability assessments and R&D opportunities underscore\nthe importance of system redundancy and resilience to minimise downtime and maximise integrated\nluminosity. Moving forward, continued refinements and targeted technological developments will be es-\nsential to ensuring the FCC meets its scientific and operational goals, paving the way for groundbreaking\ndiscoveries in high-energy physics.\n263\n\n264\n\nChapter 6\nFCC-ee booster technical systems\n6.1\nMain magnets\nThe proposed booster magnet system meets the requirements of the booster FODO lattice V24 described\nin Section 4.1.3. The regular FODO lattice of the booster ring contains 2768 arc half-cells composed of\na short straight section (SSS) and two dipoles. There are three lengths of arc half-cell depending on the\ncomposition of the short straight section (SSS): one quadrupole and either no sextupole, or a focusing\nsextupole, or a defocusing sextupole. The arc-half cells are organised into a periodic structure of 5 cells\nevery 260.554 m, matching the collider. The positrons and electrons circulate in opposite directions in\nthe booster so the magnet polarity is the same for both filling cycles.\nIn this version, all arc dipoles are identical. The dipoles in the dispersion suppressors are slightly\nlonger and require different field levels but share a common cross-section with the arc dipoles. There\nare six main quadrupole circuits in the arcs, with strengths ranging from 24.9 \u2013 26.6 T m\u22121. Since the\nstrengths of the arc quadrupoles are similar, a single magnet design is proposed for all quadrupoles, with\nslight variations in powering. In the dispersion suppressors, strengths of up to 28.7 T m\u22121 are required.\nThe current proposal is to use similar magnets, with additional magnetomotive force provided by trim\ncircuits.\nFor the sextupoles, the dispersion in the defocusing sextupoles is half that of the focusing sex-\ntupoles. Consequently, the defocusing sextupoles require twice the integrated gradient. This has been\nachieved by using a common cross-section for both sextupoles while making the defocusing sextupoles\ntwice as long. The sextupole strengths in the dispersion suppressor region are lower than those in the\nmain arcs. The current proposal is to use the same magnets with a current bypass.\nThe requirements of the arc magnets are summarised in Table 6.1. A summary of the magnet\ncycles is given in Table 4.1. The relative field error dipole-to-dipole is required to be less than 1 \u00d7 10\u22123.\nThe relative harmonic field error is required to be better than 1 \u00d7 10\u22124 on a reference radius of 10 mm\nfor all magnets. The following section describes the technical solutions and performance of the main\nmagnets of the arcs: dipoles, quadrupoles, and sextupoles.\nTable 6.1: Magnet requirements for the booster FODO lattice V24.\nDipole\nQuadrupole *\nSextupole\nFocus\nDefocus\nTotal number in lattice. . .\n6146\n3346\n576\n560\n. . . of which in arcs\n5536\n2728\n528\n528\nAperture [mm]\n65\n65\n65\n65\nLength, arc [m]\n11\n1.3\n0.7\n1.4\nMax strength\u2020, arc at t\u00aft ext.\n58.9 mT\n26.6 T m\u22121\n1147 T m\u22122\n1219 T m\u22122\nMin strength\u2020, arc at 20 GeV in.\n6.45 mT\n2.7 T m\u22121\n126 T m\u22122\n134 T m\u22122\n* The ratio of min:max quadrupole strength does not match the beam rigidity as there are multiple families.\n\u2020 Sextupole strength given as B\u2032\u2032, B\u2032\u2032 = 2S.\n265\n\nFig. 6.1: Field map of the booster dipole at t\u00aft energy.\n6.1.1\nDipoles\nThe cross section of the proposed booster dipole is shown in Fig. 6.1, and its key parameters are sum-\nmarised in Table 6.2. The proposed dipole is an H topology with a laminated steel yoke and directly\ncooled aluminium busbars, the following paragraphs will discuss each of these key design aspects.\nThree topologies were initially considered: C, O, and H. A C topology is attractive from an inte-\ngration perspective as it gives easy access to vacuum components. However, early studies showed that a\nC topology was not able to effectively shield the earth\u2019s magnetic field and led to relative field errors of\n3 \u00d7 10\u22124 at injection energy (6.5 mT, 20 GeV) and therefore an O or H topology is necessary. It should\nbe noted that the beam may be impacted by the Earth\u2019s field in areas not shielded by the magnets. An H\ntopology is advantageous over an O topology as the poles can be used to optimise the field quality across\nthe full cycle. The H topology was further optimised for field quality across the full range of operations.\nThis optimisation led to a back leg that is wider than strictly necessary for magnetic return, 40 mm with\na peak field around 150 mT. A lower back leg peak field reduces the remanent magnetisation of the\nsteel, yielding a magnetic performance benefit. Additionally, the extra material removes the need for\ndedicated synchrotron radiation shielding and, therefore, represents a holistic design optimum. The yoke\nis laminated to reduce the eddy current during the ramp. The material chosen for the prototype is M270-\n50A, a 0.5 mm thick electrical steel with low coercivity that is readily available due to its prevalence\nin industrial applications. The lamination thickness is conservative, 1/15 of the skin depth, mitigating\nproblems from yoke eddy currents.\nBusbars have been used instead of coils for two key reasons: they allow end-to-end magnet in-\nterconnection, reducing transmission losses, and they simplify magnet construction. Aluminium is pre-\nferred over copper as it is cheaper for a given resistance per unit length. This choice is facilitated by the\nlow field requirement, the magnet envelope is still reasonable even with the larger busbar section. The\nground insulation will be an air gap set by 3 mm thick ceramic spacers. This solution is radiation hard\nand withstands voltages well in excess of the required 1 kV to ground. The root mean squared (RMS)\ncurrent density is low, 1.4 A mm\u22122 for the t\u00aft cycle. This current density has been shown to optimise the\ncombined total lifetime cost of the magnets and technical infrastructure. While a lower current density\nwould allow an air-cooled solution, it is preferable to dissipate heat from the tunnel using water rather\nthan air. Therefore, the magnets will be water-cooled.\n266\n\nTable 6.2: General parameters of the arc dipole magnets.\nParameter\nUnit\nValue\nStrength, B, 20 \u2013 182.5 GeV\nmT\n6.5 - 58.9\nAperture (horizontal \u00d7 vertical)\nmm2\n130 \u00d7 65\nMagnetic length\nm\n11\nOuter envelope\nmm2\n246 \u00d7 165\nPeak current\nA\n3065\nMagnet resistance\nm\u2126\n0.70\nMagnet inductance\n\u00b5H\n44\nPeak voltage, magnet\nV\n2.2\nConductor (Aluminium)\nmm2\n12 \u00d7 79, \u001f7\nTurns\n1\nRMS current density, t\u00aft\nA mm\u22122\n1.4\nMagnet active mass\nkg\n2452\nBusbar active mass (Al)\nkg\n54\nYoke active mass\nkg\n2398\nFig. 6.2: The short prototype booster dipole built and tested to demonstrate the feasibility of low field\nlevels. In this prototype, the busbars are substituted with a coil for compatibility with test facilities.\nOther water-cooled systems in the tunnel are made of copper. To avoid the risk of galvanic corro-\nsion or the need for multiple cooling circuits, the inner surface of the cooling tubes will be made of either\nstainless steel or copper. The baseline proposal is to use a mechanical assembly of a tube and a busbar;\nhowever, co-extrusion and electroplating are also being considered. This will be studied in detail during\nthe next phase.\nTest of short prototype dipole magnet\nThe main field of the booster dipole at injection is lower than previous machines at CERN, less than half\nof both the LEP (22 mT) and the SPS as LEP injector (15.7 mT). Additionally, hysteresis effects are\ncomplex to model as they depend on material characteristics and previous magnetic states. Therefore, a\n0.5 m long prototype booster magnet has been built to demonstrate the feasibility of the low field levels\nwith respect to the remanent effect in the iron yoke. The short prototype produced is shown in Fig. 6.2.\nThe allowed field harmonics measured during magnetic cycles from 6.5 \u2013 58.9 mT are presented\nin Fig. 6.3. The total field harmonics are below 1 \u00d7 10\u22124 relative field error up to a radius of 17 mm.\nThe results show that the magnet stabilises quickly after only a few pre-cycles, with only minor, non-\n267\n\n(a) Sextupolar component.\n(b) Decapolar component.\nFig. 6.3: 2D field harmonics in the short prototype booster dipole at the t\u00aft field levels. Values quoted at\nR = 10 mm in units of 1 \u00d7 10\u22124 [343].\nsystematic field distortions observed throughout the cycle.\nFor practical reasons, testing has so far been conducted in a quasi-static manner, meaning it does\nnot account for eddy fields from either the copper vacuum chamber or the magnet itself. Since the\nvacuum pipe is circular, the eddy fields have been calculated using analytical formulae and cross-checked\nwith numerical modelling, showing good agreement. The eddy currents in the vacuum tube will generate\na sextupole component of 15 mT/m2, corresponding to 0.15% of the total sextupole strength of the\nmachine at injection. Due to the relatively long ramp times, the modelled eddy field harmonics from the\nmagnet itself are 0.1 \u00d7 10\u22124 relative to the main field at injection.\nThe transfer function of the short prototype booster dipole is shown in Fig. 6.4. The remanent\nmagnetisation of the yoke contributes around 60 \u00b5T, or 1%, of the main field at injection. From vali-\ndated models, it can be seen that the remanent magnetisation is locally linear with material coercivity.\nIt is therefore readily concluded that the coercivity of the yoke must be controlled to at least 10% be-\ntween magnets to be within the currently allowed dipole-to-dipole relative field error of 1 \u00d7 10\u22123. This\nconsistency can be readily achieved by the use of a simple control on the steel supply1 and, potentially,\nshuffling. It seems likely that a magnetic length correction with end shims will be needed. However, this\nis not a foregone conclusion and remains to be studied in detail. The transfer function is inversely pro-\nportional to the aperture, so a tolerance of 1 \u00d7 10\u22123 in the main field implies a 65 \u00b5m aperture tolerance\nwithin range for a stamped and stacked yoke. Material controls, shuffling, and length correction were\nsuccessfully implemented with the SPS dipoles, which have a similar total weight of steel as the booster\ndipoles, though they are less numerous.\n6.1.2\nQuadrupoles\nThe parameters of the proposed quadrupole magnet are summarised in Table 6.3. The field map for the\nquadrupole magnet at t\u00aft energy is given in Fig. 6.5. To minimise the length of the short straight sections,\nthereby increasing the dipole filling factor and reducing the synchrotron radiation losses, the quadrupole\nhas been designed with a relatively high gradient and a pole tip field around 0.9 T. As the requirements\nare more typical, the quadrupole design is correspondingly more conventional than that of the dipole.\nThe coils will be simple racetrack-shaped windings made from hollow conductors, with copper used\n1The value of 10% is an upper bound of the variation seen even between completely different suppliers for a given electrical\nsteel grade.\n268\n\nFig. 6.4: The centered transfer function of the short prototype booster dipole at the t\u00aft field levels [343].\nfor compactness. The yoke will be laminated, as the booster operates in a cycled mode. The vacuum\nchamber diameter is constrained by impedance requirements, resulting in an aperture that is large relative\nto the good field region. Consequently, a relative harmonic distortion below 1 \u00d7 10\u22124 is achievable.\nTable 6.3: General parameters for the quadrupole magnet.\nParameter\nUnit\nValue\nStrength, main arc at t\u00aft ext.\nT m\u22121\n26.6\nUltimate strength, disp. sup. at t\u00aft ext.\nT m\u22121\n28.7\nAperture diameter\nmm\n65\nLength\nm\n1.3\nOuter envelope\nmm\n\u001f584\nCurrent, arc at t\u00aft ext.\nA\n939\nAdditional MMF for disp. sup. at t\u00aft ext.\nA\n1350\nMagnet resistance\nm\u2126\n11.4\nMagnet inductance\nmH\n13.3\nPeak voltage magnet\nV\n15.5\nConductor (copper)\nmm2\n14.3 \u00d7 18.25, \u001f2.8\nTurns\n13\nRMS current density, main arc at t\u00aft\nA mm\u22122\n1.5\nTemperature rise at 6 bar\n\u25e6C\n11.2\nMagnet active mass\nkg\n2070\nCoil active mass\nkg\n368\nYoke active mass\nkg\n1702\nCoil overhang\nmm\n140\nThe cross section of the quadrupole has been optimised to minimise the total lifetime cost of\nboth the magnet itself and the technical infrastructure. This optimisation began with a parametric cross-\nsection, which was then refined in two stages. First, the geometry inboard of the coil was adjusted to\n269\n\nFig. 6.5: Field map of the booster quadrupole magnet at 26.6 T m\u22121, main arc at t\u00aft extraction.\nmaximise the gradient delivered per ampere-turn. Next, a global optimisation was performed to de-\ntermine the number of turns, current density, and back leg thickness (see Section 3.8.1). These three\nparameters\u2014number of turns, current density, and back leg thickness\u2014are key trade-offs between capi-\ntal expenditure (CapEx), operational expenditure (OpEx), and infrastructure requirements and costs.\nTo facilitate such a complex optimisation, a parametric code was used to generate design space\nmaps, allowing for rapid interpolation during function calls. These maps plotted stored magnetic energy,\nmagnetic efficiency, and yoke cross-section as functions of current density and pole width. A design\ncould then be specified based on three interpolated variables and the number of turns. The required\nampere-turns were determined from efficiency and bulk current density, while the cooling hole diameter\nwas solved using Newton-Raphson for a given temperature rise and pressure. The resistance was calcu-\nlated based on the cooling hole diameter and filling factor, and the inductance was derived from magnetic\nenergy and the number of turns. Finally, the mass was determined from the yoke cross-section and the\ncoil. The recommended design was then manually reviewed to finalise the cross-section.\nThe magnet\u2019s current density is relatively low, at 1.5 A mm\u22122 RMS in the main arcs during the t\u00aft\ncycle, demonstrating that despite the fixed magnet lifetime, investing in larger coils remains beneficial to\nreduce power consumption and electrical infrastructure requirements.\nThere are 24 quadrupoles in the dispersion region that require ultimate strength. At this field\nlevel, the yoke begins to saturate, causing efficiency to drop from 96% at nominal to 93% at ultimate. A\nbespoke solution for these quadrupoles may be proposed at a later stage.\n6.1.3\nSextupoles\nThe parameters of the proposed sextupole magnet are summarised in Table 6.4. The field map for the\nsextupole magnet at t\u00aft energy is given in Fig. 6.6. The sextupole is again relatively strong with a pole tip\nfield of 0.7 T, and again a conventional design is proposed, with material and design choices similar to\nthose for the quadrupole. The total harmonic distortion is below 1 \u00d7 10\u22124 relative to the main field.\n270\n\nTable 6.4: General parameters for the sextupole magnet.\nParameter\nUnit\nSextupole\nDefocus\nFocus\nStrength, B\u2032\u2032\nT m\u22122\n1219\n1147\nAperture diameter\nmm\n65\nLength\nm\n1.4\n0.7\nOuter envelope\nmm\n\u001f305\nPeak current\nA\n595\n556\nMagnet resistance\nm\u2126\n51\n27\nMagnet inductance\nmH\n9.3\n4.7\nPeak voltage magnet\nV\n32\n16\nConductor (copper)\nmm2\n8.4 \u00d7 8.4, \u001f2.5\nTurns\n10\nRMS current density at t\u00aft\nA mm\u22122\n3.7\n3.5\nTemperature rise (6 bar)\n\u25e6C\n14\n4.6\nMagnet active mass\nkg\n614\n312\nCoil active mass\nkg\n105\n57\nYoke active mass\nkg\n509\n255\nCoil overhang\nmm\n50\nFig. 6.6: Field map of the booster sextupole magnet at t\u00aft energy, B\u2032\u2032 = 1219 T m\u22122.\n6.1.4\nSummary\nIn conclusion, the headline magnet requirements of v24 FODO optics are technically feasible including\nlow dipole field and lens strengths. For reference, the power consumption of the proposed magnets are\nsummarised in Table 8.15. There is a large design space of feasible magnets, giving an opportunity for\nholistic design and a cost optimised solution. Moving into the next phase the industrialisation, design for\nmanufacture and assembly, and detailed integration with the other technical systems will be performed.\n6.2\nBooster vacuum system\nThe booster chamber design is based on a round seamless tube in OFE copper. The inner diameter is\n60 mm and the thickness is 1.5 mm, see Fig. 6.7. A copper tube (size yet to be determined) is spot\nwelded on it for water cooling. No lump photon absorber is planned. There is no need for a bakeout\n271\n\nthermal cycle, and therefore, non-shielded bellows are used to compensate for mechanical and alignment\ntolerances. The chamber is neither coated nor baked.\nFig. 6.7: Cross section of the FCC-ee booster vacuum chamber.\n6.2.1\nInput parameters\nTo determine the pressure levels in the FCC-ee booster, the end-of-2024 state of the design has been used\nas a baseline, as summarised below: The vacuum chamber results in 26.6 l.m/s specific conductance (a\nvalue similar to the two storage rings).\nFig. 6.8: Representative section of the vacuum chamber in the FCC-ee booster, modelled over 12.5 m.\nIt is assumed that one pump is placed every 12.5 m around the ring. Consequently, a 12.5 m section\nwith periodic boundary corrections has been modelled (see Fig. 6.8). The section includes a single\nion pump, which is simulated to operate at a pumping speed of 40 l/s, accounting for the conductance\nlimitation of the orifice, despite its rated speed of 60 l/s.\nIn the following discussion, a distinction is made between static (background) gas, which is always\npresent in the system, and dynamic (time-dependent) gas, which arises during operation. Since their\ncalculation methods differ, they are addressed in separate sections. In both cases, the gas levels are\nestimated after 100 hours of conditioning.\n272\n\n6.2.2\nStatic pressure\nFor unbaked metals, the dominant gas to desorb is water vapour. Empirical tests show [344] that the\noutgassing rate is inversely proportional to the pumping time and can be estimated as:\nQH2O \u22483 \u00d7 10\u22129\nt\n(mbar.l/s/cm2)\n(6.1)\nwhich corresponds to a specific outgassing rate of 3 \u00d7 10\u221211 mbar.l/s/cm2 after 100 hours.\nA MOLFLOW simulation was performed on the model of the representative section for this out-\ngassing from the walls and the 40 l/s pumping speed on the pumping port.\nFig. 6.9: Static (background) pressure after 100 h of conditioning in a 12.5 m long representative section.\nThe resulting pressure profile, in Fig. 6.9, shows an average pressure in the 3 \u00d7 10\u22128 mbar range,\nwith the lowest pressure at the pump location, as expected.\n6.2.3\nDynamic vacuum\nHigh-energy photons are created by synchrotron radiation (SR) when the booster is operating. Estimating\nthe dynamic vacuum requires calculating the amount of SR, calculating the resultant outgassing through\nphoton-stimulated desorption (PSD), and then performing a vacuum simulation. As the booster is a\ncyclic machine, all quantities are time-dependent.\nThe SR photon flux scales linearly with the beam energy and current:\nFlux [photons/sec] = 8.08 \u00d7 1017 \u00d7 Ebeam[GeV] \u00d7 Ibeam[mA]\n(6.2)\nThe booster\u2019s operation parameters in the Z mode are as follows:\n\u2013 1120 bunches per cycle.\n\u2013 2.5\u00d71010 electrons per bunch.\n\u2013 Revolution frequency: 3.3 kHz.\n\u2013 Current: 14.8 mA.\n\u2013 Operation cycle:\n\u2013 0-2.8 s: Accumulation (linear increase from 0 to 14.8 mA at 20 GeV).\n\u2013 2.8-3.6 s: Ramp-up (energy increase from 20 GeV to 45.6 GeV).\n\u2013 3.6-3.8 s: Ramp-down (cycling magnets, no beam).\n273\n\nFig. 6.10: Energy ramp-up from 20 to 45.6 GeV with an overshoot.\n6.2.4\nSYNRAD simulations\nTo estimate the SR, the formula can be made more precise by applying the so-called SR_factor, which\nspecifies what portion of the SR spectrum has an energy over 4 eV. The reason is that photons below\nthat energy (equivalent to the work function for photo-electron generation on most metal alloys) are not\npowerful enough to desorb molecules from the surface.\nThe Monte Carlo simulation code SYNRAD was used to model and simulate four magnets in\na periodic setup (D1-D2-D3-D4, then D1 again, see Fig. 6.11). Each magnet is 11 m long, and the\nFig. 6.11: SYNRAD model representing the four booster dipoles creating SR, in a periodic setup.\nmagnetic field scales linearly with the energy, from 6.5 mT at 20 GeV.\nSYNRAD does not support time-dependent beam parameters, however, it is possible to obtain the\naverage SR factor by simulating 26 distinct energies equally spaced from 20.6 GeV to 45.6 GeV and\ntaking the average (see Fig. 6.12).\nFig. 6.12: Part of SR spectrum above 4 eV for beam energies at 20, 26, 32, 38 and 45.6 GeV.\n274\n\nAveraging the flux for the 26 energies at 14.83 mA, SYNRAD estimates the flux to be 2.24 \u00d7 1017\nphotons/s. Taking only the average SR factor of 88% from SYNRAD, and substituting in (6.2):\nFlux = 8.08 \u00d7 1017 \u00d7 32.8 \u00d7 14.83 \u00d7 0.88 \u00d7\n44\n64486 = 2.36 \u00d7 1017photons/s\n(6.3)\nwhere 32.8 GeV is the average energy during the ramp, and 64 486 m is the dipoles\u2019 magnetic length.\nThe SYNRAD and the theoretical results are thus very close.\nThe results of the 44 m length modelled in SYNRAD (for calculating the SR) to the 12.5 m length\nin MOLFLOW (for calculating the vacuum). The booster comprises more than just dipoles. It is estimated\nthat the total radiation from the dipoles is distributed over a 90 km arc length :\nFlux [12.5 m] = 8.08 \u00d7 1017 \u00d7 E \u00d7 I \u00d7 0.88 \u00d7 12.5 m\n90 km\n(6.4)\nThe following formula is used to convert the flux to outgassing:\nQ[molecules/sec] = Flux \u2217\u03b7\n(6.5)\nwhere \u03b7, the molecular yield, describes how many photons on average are desorbed by an absorbed SR\nphoton. This depends on the material and decreases over time as the surface is conditioned. The duration\nof this conditioning is estimated to be 100 h, based on data from an experiment performed at KEK [345]\nwhere 1.2 m long uncoated stainless steel vacuum chambers were irradiated with SR.\nFig. 6.13: Photon stimulated desorption yield of uncoated stainless steel.\nAs shown in Fig. 6.13, the dominant gas species are typically H2, CO, CO2, CH4, ordered by\nfraction (plus H2O, if unbaked, which can initially be the predominant gas species\u2013but the sample in\nthe figure was baked). In this case, CO was considered because it has an atomic number much higher\nthan that of hydrogen, and therefore its effect in terms of beam bremsstrahlung (BS) is approximately 56\ntimes bigger than for H2. The dependence for BS given by Zeff(Zeff + 1) , where Zeff is the weighted\neffective atomic number for C and O.\nCalculating with an average cycle current of 8 mA, 100 h of operation corresponds to a photon\ndensity of 1 \u00d7 1021 photons/m, resulting in a CO yield of 3 \u00d7 10\u22124 mol/photon. As a result, the\noutgassing is:\nQ = 8.08 \u00d7 1017 \u00d7 E \u00d7 I \u00d7 0.88 \u00d7 12.5\n90 000 \u00d7 kBT \u00d7 10\n(6.6)\n275\n\nwhere E is the energy in GeV, I is the beam current in mA, T the temperature in K and the kBT term\noriginates from the ideal gas equation, allowing conversion from molecules/s to Pa\u00b7m3/s, and the factor\nof 10 is the conversion from Pa\u00b7m3/s to mbar\u00b7l/s. A temperature of 300 K was assumed.\nFig. 6.14: Dynamic outgassing caused by PSD, over 6 booster cycles on a 12.5 m modelled region.\nDynamic vacuum simulations\nThe result of the equation (visualised in Fig. 6.14) was imported into MOLFLOW as a time-dependent\noutgassing parameter and applied it to the side wall of the modelled region, as the location of primary\nincidence of SR.\nAs the residence time of molecules in the booster is not negligible, the dynamic pressure builds up\nafter approximately 3 cycles when starting the booster from a static state, as can be seen in Fig. 6.15.\nFig. 6.15: Dynamic pressure, averaged over the 12.5 m modelled region, after starting the booster.\nThe average pressure, after reaching a periodic state, cycles between 1.7 \u00d7 10\u22128 mbar and 2.8 \u00d7\n10\u22128 mbar. The peak pressure was chosen to have a conservative estimate in the following stages.\n6.2.5\nComparison and conclusion\nThe pressures from the two sources, and their sum are plotted in Fig. 6.16. While the static pressure, due\nto thermal outgassing, is higher after 100 h, it also conditions faster:\n276\n\nFig. 6.16: Comparison of static and peak dynamic pressures after 100 h of conditioning.\n\u2013 Thermal outgassing decreases with t\u22121 [344]\n\u2013 Photon stimulated desorption of stainless-steel decreases with t\u22120.6 [345]\nAfter 100 h, the total pressure at the peak of a booster cycle is in the order of 4 \u00d7 10\u22128 mbar. The\nlatest beam-gas calculations estimate that the booster pressure needs to be below 30 nTorr [346], which\nis the expected level.\nIt would be preferable to have an in-situ bakeout system installed, and consequently NEG-coating\nof the vacuum chambers, as this would reduce the number of external pumps and their cabling by a\nfactor of about 5. Additionally, the NEG-coated solution would guarantee very fast reconditioning of\nany vacuum sector needing venting during operation.\n6.3\nRadio frequency system layout, configurations, and parameters\n6.3.1\nIntroduction\nThe high-energy booster SRF system accelerates the electron and positron bunches before injection into\nthe two collider rings. A booster transverse feedback system is required to cure coupled-bunch transverse\ninstabilities, as specified in Section 4.2.1 as well as damping injection oscillations. Both RF systems will\nbe installed in point PL.\n6.3.2\nParameter choices for the SRF system\nThe present baseline RF system requires flexibility for switching between Z, WW, and ZH operating\npoints. Then it needs to be upgraded for the highest energy t\u00aft operating point. The baseline solution\nassumes the same 6-cell 800 MHz elliptical cavities as in the collider. The main RF-related global\nparameters are summarised in Table 6.5. Note that the indicated maximum synchrotron radiation power\nincludes the energy overshoot for the Z operating point without wigglers. To avoid hardware modification\nTable 6.5: RF-related parameters for FCC-ee high-energy booster.\nOperating point\nZ\nWW\nZH\nt\u00aft\nMaximum beam current\u2217\n[mA]\n16.2\n6.2\n2.0\n0.4\nExtraction Energy loss / turn\n[MeV]\n36.1\n342\n1730\n9270\nInjection RF voltage\n[MV]\n50.1\nExtraction RF voltage\n[MV]\n57.2\n402\n1960\n10200\nMaximum synchrotron radiation power\n[MW]\n1.07\n2.13\n3.49\n3.99\n* Including 80% injection efficiency in the FCC-ee collider.\n277\n\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nQuality factor, QL\n1e8\n0\n1\n2\n3\n4\n5\n6\nTotal RF power (MW)\nSR power tt\nSR power ZH\nSR power W\ntt, Vcav = 22.8 MV\nZH, Vcav = 17.5 MV\nW, Nfoc\nNdefoc = 8, Vcav = 26.5 MV\nW, Nfoc\nNdefoc = 16, Vcav = 13.5 MV\nFig. 6.17: RF power requirements as a function of the cavity quality factor. Vertical lines indicate the\nchosen quality factors for the first (solid) and second (dotted) stages of HEB SRF systems.\nin the first stage, a common quality factor that minimises RF power requirements needs to be chosen.\nThe RPO scheme must be deployed at the injection energy. At higher energies, it remains active for\nthe Z and WW operating points, while the transition to the normal phase operation mode has to be\ndone for the ZH and t\u00aft ramps to achieve the maximum total RF voltage. It is assumed that the first\n112 cavities share a single RF power source per four cavities. Therefore, the difference between the\nnumber of focusing and defocusing cavities, Nfoc \u2212Ndefoc, can be changed in steps of eight cavities.\nSeveral scenarios for the WW operating points and corresponding RF power requirements were analysed\n(Fig. 6.17). Choosing Nfoc \u2212Ndefoc = 16 and QL = 107 (solid blue vertical line) seems to be a\ngood compromise that leads to a small RF power overshoot for both WW and ZH operating points\nand keeps the cavity bandwidth (half-height full-width) \u2206f = fRF/QL \u224880 Hz. Switching to the\nt\u00aft operating point, QL needs to be changed to reduce RF power requirement, which can be done by\nadjusting waveguide length as described in Section 3.4.10. The optimal QL = 9.2 \u00d7 107 results in\nan extremely small \u2206f \u22489 Hz which might be challenging to control in an accelerator environment.\nTherefore, the QL = 2.7 \u00d7 107 (\u2206f = 30 Hz) is chosen with a drawback of 43% more RF power than\nSR power at 182.5 GeV. The range QL = 4.2 \u00d7 106 \u22122.7 \u00d7 107 assumed to be covered by the common\n800 MHz FPC design for collider and booster.\nRF power requirements at injection energy\nThe RF power requirements during the injection process depend on the LLRF system details and the\nbeam loading compensation scheme in use. Extremely slow SR damping rate and very high impedance\nof the fundamental mode require a direct RF feedback system to suppress the longitudinal coupled-bunch\ninstability. The expected growth rate for the Z operating point at the end of the filling at the injection\nenergy is shown in Fig. 6.18. The stability can be improved by enhancement of the SR damping rate\nusing a wiggler as described in Section 5.1.2. The dynamic model, similar to the one of the collider\n(Section 3.4), was applied to evaluate RF power transients during injection (Fig. 6.19, left). The peak\nRF power increases significantly even after injection of the first four bunches due to the fast and strong\nreaction of the direct RF feedback, so its gain must be reduced. This can be acceptable since the in-\nstability growth rates shown in Fig. 6.18 are computed for the maximum beam current. The RF power\ncan be kept acceptable at the 50 kW limit if cavities are gradually detuned as the beam current increases\n278\n\nTable 6.6: Main RF parameters of the FCC booster.\nZ\nW\nZH\nt\u00aft\nRPO at extraction\nyes\nyes\nno\nno\nRF frequency [MHz]\n801.58\nOperating temperature [K]\n2\nNumber of cells per cavity\n6\nQuality factor Q0\n3 \u00d7 1010\nCavity voltage at extraction [MV]\n5.6\n13.5\n17.5\n22.8\nEacc [MV/m]\n4.9\n12.0\n15.6\n20.3\nMax. RF power per cavity [kW]\n42\n8.9 / 12.7\nCoupling factor QL\n1 \u00d7 107\n9.2 \u00d7 107 / 2.7 \u00d7 107\nNumber of cryomodules\n28\n112\nNumber of cavities\n112\n448\n50\n25\n0\n25\n50\nCBI mode number\n10\n2\n10\n1\n100\nGrowth rate (s\n1)\nImp. + DFB, Nfoc\nNdefoc = 8\nFig. 6.18: Growth rates of longitudinal coupled-bunch instabilities driven by the fundamental cavity\nmode for the Z operating point.\n(Fig. 6.19, right). At any moment the filling schemes should be maintained as uniform as possible to\nreduce modulations of beam and RF cavity parameters.\nThe development of a frequency tuning system able to operate in a pulsed regime with a resolution\nat the Hz level will be mandatory. It can be based on the elastic axial deformation of the cells by an\nelectromechanical system equipped with a stepping motor and a piezo-electric actuator. A new type\nof tuning technology can also be considered, for example, a non-mechanical tuner using ferroelectric\nmaterials [347,348].\n6.3.3\nLongitudinal coupled-bunch instabilities due to RF cavity HOMs\nThe low beam injection energy, combined with long longitudinal and transverse damping times, reduces\nthe beam stability limit at the booster injection phase. The simultaneous installation of all 112 cavities\nbrings the total beam impedance close to the stability threshold. To mitigate this, a transverse feedback\nsystem and wigglers can help improve stability.\n279\n\n0.00\n0.05\n0.10\n0.15\nTime (ms)\n0\n5\n10\n15\n20\n25\nRF power per cavity (kW)\nInjection\n0\n1000\n2000\nCycle time (ms)\n500\n250\n0\n250\n500\nDetuning (Hz)\nFoc. cav.\nDefoc. cav.\nFig. 6.19: Left: evolution of RF power before and after injection of the first four bunches at the Z\noperating point with parameters: Nfoc \u2212Ndefoc = 8, the feedback gain is 20% of the optimal value.\nRight: evolution of cavity detuning at 20 GeV for Z operating point.\nFrom a cavity design perspective, modifying one of the end cells can improve the damping of\nthe mode with the highest longitudinal impedance. Additionally, frequency spread in HOMs, caused\nby manufacturing imperfections, leads to resonance at different frequencies, which helps distribute and\nreduce peak impedance. A perturbation analysis, following the approach in Ref. [349], was conducted\non the 6-cell cavity to assess its effect on the total longitudinal impedance of the cavity chain.\nFigure 6.20(a) shows the longitudinal impedance of the lower-order modes within the fundamental\nmode (FM) passband for all 112 cavities, where the cavity geometries have been perturbed, and the total\nlongitudinal impedance has been calculated accounting for these perturbations. Since these five modes\nlie within or below the FM passband, they couple primarily to the power coupler rather than the HOM\ncouplers. Their coupling to the fundamental power coupler (FPC) depends on the target QL of the FM.\nHowever, for two different QL values, the frequency spread of the eigenmodes ensures that the longitu-\ndinal impedance peak remains below the Z-booster stability threshold. For the HOM with the highest\nlongitudinal impedance, an alternative end-cell design (V2) was investigated as a potential improvement\nover the current design (V1) to reduce mode trapping. Additionally, implementing cell sorting during\nassembly, as described in Ref. [349], can help prevent HOMs from being trapped at 2.37 GHz, as shown\nin Fig.6.20(b). The combined effects of the transverse feedback system, increased beam energy loss\nfrom wigglers, the asymmetric end-cell design and frequency spread due to manufacturing imperfec-\ntions should help keep the system below the stability limit, although with only a small safety margin.\n6.4\nBeam intercepting devices (halo collimators, beam dump)\nAs for any large accelerator, beam intercepting devices will be needed in the booster. At this stage\nthe studies are not mature enough to define the actual requirements; however, it is estimated that some\ncollimators will be needed, as well as extraction and injection protection devices, which will need to be\nable to withstand partial or full impacts of the high energy beams operated in the booster. Even though\nthe total energy potentially deposited by the booster beams will be lower than that in the collider the\nmaterials used in the beam intercepting devices will also be submitted to significant loads. In addition,\nthe other requirements (e.g., UHV compatibility, low impedance) will also make the design of these\ndevices challenging. Another important device required by the booster is a beam dump. As described in\nSection 1.8.1, the collider dumps will be designed also to absorb the beams extracted from the booster.\nAdditional requirements of beam intercepting devices, not foreseen at this stage, may be identified during\nthe functional studies of the booster.\n280\n\n785\n787\n789\n791\n793\n795\n797\n799\n801\nf [MHz]\n0\n2\n4\n6\n8\n10\nZk[M+]\nZk with =z = 1:51 s for ZB\nQ of FM=4.3e6\nQ of FM=1.1e7\nL\nL\n(a)\n2345\n2350\n2355\n2360\n2365\n2370\n2375\n2380\n2385\nf [MHz]\n0\n1\n2\n3\n4\n5\n6\nZk[M+]\nZk with =z = 1:51 s for ZB\nEnd-cell V1: Cell Sorting\nEnd-cell V2: Cell Sorting\nEnd-cell V1-V2: Cell Sorting\nEnd-cell V1-V2: No Cell Sorting\n(b)\nFig. 6.20: (a) Longitudinal beam coupling impedance at the FM passband for 112 cavities under ge-\nometrical perturbations, compared with the beam stability limit determined by synchrotron radiation.\nThe impedance is calculated by considering the average (R/Q) of the modes and the QL of the modes\nthrough their coupling with the FPC. (b) Longitudinal impedance for the 2.368 GHz mode, correspond-\ning to the HOM with the highest longitudinal impedance. The impedance for 112 cavities, with no HOM\ncoupler and damping occurring only through the open boundary condition, is calculated under geomet-\nrical uncertainties and compared to the stability limit (including a wiggler). Asymmetric end-cells and\ncell sorting during cavity assembly can reduce the impedance by a small margin below the stability limit.\n6.5\nBeam transfer systems\n6.5.1\nSepta\nInjection\nAs discussed in Section 4.4.1, the beam is transferred from the injector complex and injected into the\nbooster on either side of the PA experiment straight section. The hardware requirements for the present\ninjection concept are listed in Table 4.2. The operation mode of each system will see injection at up to\n100 Hz for up to \u223c30 s, followed by \u223c30 s without beam.\n(a)\n(b)\nFig. 6.21: Mechanical drawing of the Lambertson septum for booster injection in a cross-section side\nview (a) and isometric view (b).\nFor injection into the booster, several septa topologies have been studied, and a Lambertson septum\ndesign has also been selected for the present concept [178]. To keep the apparent septum thickness to a\n281\n\nminimum, the coil is located outside vacuum, but the second pole, including the septum, the magnet gap\nand the orbiting beam area are all under vacuum, see Fig. 6.21.\nExtraction\nThe septa used for extraction towards the collider will only extract one energy for each operation mode,\nand the list of requirements from the extraction design is summarised in Table 4.3. The leak field of the\nseptum is less critical than for the collider injection septa since they only have to be powered at extraction\nand are not required to track the beam energy like the booster dump septa. This opens the possibility\nof using a pulsed device, which is less challenging with respect to thermal dissipation. Another option\nthat was explored to achieve a more sustainable solution was the use of a permanent magnet. This latter\noption, however, would lead to an apparent septum thickness that exceeds the requirements.\nThe present baseline consists of 2 pulsed septa outside vacuum. The pulse length is chosen to\nbe relatively long to allow a flattop of >304 \u00b5s to allow extraction of the full circulating beam as well\nas to provide sufficient time for eddy currents in the extraction vacuum chamber to decay, preventing\nthe generation of a lower quality field. To limit design effort and benefit from economies of scale, this\nmagnet is chosen to be identical to the collider thick injection septum, albeit operating at a different\ncurrent. To optimise the cost, the two magnets of each system are connected electrically in series.\nDump\nThe booster dump septa shown in Fig. 6.22 are the same design as the collider dump septa described\nin Section 4.4.3. However, the following operational differences have an impact on the final design of\nthe booster dump septa. First, the field of the dump septa in the booster must follow the energy of the\nparticles in the booster during the ramp, making it a ramped device rather than a purely DC-operated\ndevice. Second, the dynamic range of the booster dump septa is larger, as the device will be used across\nthe energy range from booster injection energy level to top energy in the t\u00aft mode.\nDue to the first reason, the system will include a link to the Beam Energy Tracking System. Be-\ncause of the further increased dynamic range with respect to the collider dump septa, further development\nof the proposed low-power septa topology is needed to ensure the field homogeneity and leak field levels\nremain within specification throughout the dynamic range. For both extractions, the two septa will be\npowered electrically in series, i.e., one power converter per extraction.\nFig. 6.22: Mechanical drawing of the booster dump septum without its vacuum chamber.\n282\n\n6.5.2\nKickers\nInjection\nA stripline design has been chosen for the injection kicker system to meet the requirements listed in\nTable 4.2 and in particular the fast rise and fall times of 25 ns. Two systems are used, each consisting of\na single device.\nTo meet the field homogeneity requirements, the stripline must be carefully designed. Numerical\nfield simulations were carried out comparing several cross sections, finally resulting in a half-moon\nshaped electrode design offering the best field homogeneity parameters. To minimise the stripline\u2019s\nimpact on the circulating beam, it is essential to achieve the desired characteristic impedance in the even\nmode while maintaining the odd-mode characteristic impedance as close as possible to 50 \u2126to ensure\nthe required field quality.\nFurther optimisation studies on impedance matching will be conducted, such as considering a\ntermination network on the load side of the stripline. This termination method also requires a resistor\nbetween the electrodes, which presents some challenges. An in-vacuum design is difficult to implement\ndue to concerns about power losses and vacuum compatibility, whereas an outside-vacuum design would\nbe prone to parasitic inductance. In addition, mechanical design optimisation studies should commence\nsoon to ensure the design is capable of withstanding synchrotron radiation.\nFor the generator side, the short flattop duration of 80 ns allows the use of either an inductive adder\nor very short pulse forming lines (PFL). Separate generators deliver both positive and negative driving\npulses to the stripline via 50 \u2126coaxial cables.\nExtraction\nThe extraction of electron and positron beams from the booster is achieved through two systems, each\nconsisting of 14 kicker magnets and following the extraction scheme requirements listed in Table 4.3.\nThese systems employ the same lumped inductance topology used for collider injection and dump kick-\ners, leveraging the benefits of economies of scale. Each magnet could either be driven by a pulse-forming\nnetwork or a Marx generator and is operated in short-circuit mode. The Marx generator consists of a main\nhigh-voltage stage and a low-voltage stage. Both stages are composed of multiple units: the stages in\nthe high-voltage section are triggered throughout the entire pulse duration, while the low-voltage stages\nare triggered sequentially to compensate for voltage droop along the pulse. A matching resistor can be\nincluded on the generator side to address the mismatch between the magnet and the transfer cable. In or-\nder to provide the required flattop quality, the length of the cable connecting the magnet to the generator\nis limited to 100 m.\nThe cable length between each extraction kicker and its generator is defined by the pulse require-\nments. Thus, the location of the service galleries is affected by the required cable lengths. The required\ncable length is 100 m which includes the bending radius (1 m) and the handling path (15 m).\nDump\nThe booster beam dump system will be very similar to the collider dump (see Section 4.4.3), only requir-\ning adjustments for placement and control. The same magnet modules and generator topologies will be\nused. Compared to the collider dump, which operates at a fixed energy, beam energy tracking is required.\nThis feature can be achieved using commercially available power supplies.\nControls\nAn inductive adder (IA) pulse generator may be considered for some systems but would be a new tech-\nnology for CERN, requiring a thorough analysis of its impact on controls. The IA introduces challenges\nsuch as managing the 100 Hz repetition rate, which limits the time for tasks like post-operational checks.\n283\n\nRadiation to electronics (R2E) factors, including high-energy hadron flux and accumulated radiation\ndose, also need careful consideration to ensure the system\u2019s robustness.\nSimilarly, the Marx generator, another novel technology, requires a detailed evaluation of the\nimpact of its control system and offers potential synergies with collider injection systems to enhance\nefficiency. A generator based on the LBDS design is planned for the dump kickers, balancing reliability\nwith R2E considerations. An active or hybrid fail-safe retriggering architecture, akin to the SBDS system,\nis preferred to avoid complexities like signal reflections associated with passive systems.\n6.6\nBeam Instrumentation\nIn the course of the feasibility study, the type of beam diagnostics has been identified for the booster, with\nan estimation of the number of instruments needed as outlined in Table 3.17. Similar to the collider ring,\nbeam position monitors (BPMs) and beam loss monitors (BLMs) form the vast majority of the installed\nsystems. Presently, the overall concept for such systems is that they will share the acquisition scheme\nadopted for the main ring BPMs and BLMs, where signals will be acquired and digitised in shielded\nracks installed in the tunnel in each arc half cell.\nCurrent (DC and bunched) measurement, transverse and longitudinal profile measurement systems\nwill also be present and capable of measuring throughout the energy ramp. This will form one of the main\nchallenges of the next phase where a preliminary design for the booster BI systems will be produced,\nparticularly for monitors based on synchrotron radiation due to the changing spectrum as a function of\nthe beam energy.\n6.7\nPowering system\n6.7.1\nBooster Magnet Powering Systems\nGlobal optimisation of the Magnet Powering Systems\nPlease see Section 3.8.1.\nBooster Magnet Circuits\nMagnet powering is performed by power converters in alcoves located either at the end of the straight\nsection or in the machine tunnel, called Big Electrical Alcove and Small Electrical Alcove, respectively\nThe installation of power converters in the Machine Tunnel is not possible due to space and radiation\nconstraints.\nThe location of the power converters is dictated by several factors, including the granularity of\ncontrol required, the maximum voltage tolerance of the cable insulation and the resulting impact on\nexpenditure for cables and converters. The granularity of control is determined by the optics layout:\n\u2013 Booster dipoles, as well as booster quadrupole focusing and defocusing magnets, can be powered\nin series within their respective family.\n\u2013 Focusing and defocusing booster sextupoles can be powered by half-octant.\nThe power converters for the booster dipoles, quadrupoles, and sextupoles are installed in the big\nalcoves at the end of the straight section. All other converters are located in the small alcoves of the\ntunnel, as they power fewer magnets in series. Table 6.7 presents the quantity of magnets and circuits\nand the powering parameters.\nMagnet specifications and quantities for the tapering, correctors, dispersion suppressor, straight\nsection and injection are not yet defined and therefore estimations were made. A different powering\nscheme is needed for the dispersion suppressor which uses the same magnets as in the arcs, see Sec-\ntion 6.1.\n284\n\nFor the collider details, see Table 3.15 in Section 3.8.1.\nTable 6.7: Booster magnet powering circuits quantities and parameters\nMagnet\nCircuit\nPeak\nPeak\nQuantity\nQuantity\nCurrent (A)\nVoltage (V)\nDipole\n5536\n16\n3065\n851\nQuadrupole (F and D)\n2768\n32\n939\n1998\nSextupole Focusing\n576\n16\n525\n1002\nSextupole Defocusing\n560\n16\n595\n1492\n*Dipole Tapering\n2768\n346\n10\n396\n*Quadrupole Tapering\n2768\n346\n10\n382\n*Horizontal Corrector\n1672\n1672\n20\n68\n*Vertical Corrector\n1672\n1672\n20\n69\n*Quadrupole Corrector\n1384\n1384\n20\n65\n*Skew Quadrupole\n1384\n1384\n20\n65\n*Straight Section\nn/a\n1033\nn/a\nn/a\n*Injection\nn/a\nn/a\nn/a\nn/a\nBooster Subtotal\n21 068\n7917\n-\n-\nCollider subtotal\n34 698\n12 773\n-\n-\nTotal\n55 766\n20 690\n-\n-\n* Magnet specifications not yet fully defined or non-existent, values extrapolated.\nPrecision of Power Converters\nPlease see Section 3.8.1.\nAvailability of Power Converters\nPlease see Section 5.3.4.\n6.8\nArc region: integration and supporting systems\nThis section complements Section 3.10, which describes the integration and development of supporting\nsystems in the collider arcs. Arcs are made of a sequence of FODO half-cells, about 3000 for the\nhigh-energy optics, and consist of a short straight section (SSS) with quadrupole, sextupoles, beam\ndiagnostics and correctors, followed by a long dipole length that can be achieved with a series of 2 or\n3 interconnected magnets. This section describes the optimisation of the arc-supporting structures to\nmaximise their performance, easing the installation and maintenance while also minimising cost. This\nstudy is being conducted within the scope of the FCC-ee Arc Half Cell Mock-up Project, and of the\nFCC-ee design study. It is planned to study elements of the arc cell in a full-scale mock-up (detailed in\nSection 3.10.5).\nThe analysis of the relative placement between the collider and the booster is not detailed in this\nsection, as it has been covered in Section 3.10.1.\n6.8.1\nArc cell configurations of the booster\nThe configuration of the booster arc cell does not change from the low to the high energy mode. In\nfact, the length of the arc half-cell remains 26 m for all the phases. As can be seen in Fig. 6.23, there\n285\n\nare two configurations: 1136 half-cells with 1 quadrupole and 1 sextupole, and 1704 half-cells with 1\nquadrupole. It should be noted that in Fig. 6.23, the drift distances are not represented. In addition, for\nthe booster, the focusing and defocusing sextupoles are not of the same length: 1.4 m for the defocusing\nsextupole and 0.7 m for the focusing sextupole.\nFig. 6.23: Arc cell configurations for the booster, for all the phases - optic V24-FODO.\nAmong the different configurations, the FCC-ee Quad-Sext (defocusing) type has been studied in\ndetail and will be installed in the mock-up. This SSS configuration is the bulkiest and, therefore, the most\nchallenging in terms of integration. It is also the most complex in terms of static and dynamic stability.\n6.8.2\nOptimisation of the booster supporting structure - static and dynamic analyses\nOverview and principles\nAs discussed in Section 3.10.3, the goal is to optimise the design of the supporting structure by finding a\nbalance between static and dynamic structural stability, integration constraints, and cost, while ensuring\ncompliance with all safety requirements. This optimisation process is still ongoing, with alternative\ngeometries currently under evaluation.\nThe design of the booster supporting structures for the SSS, which is currently under study, is\nillustrated in Fig.6.24. This structure consists of two cantilever supports on which a girder is installed.\nFollowing the same principle as the collider\u2019s SSS, the use of girders to support the common elements\nin the SSS provides significant practical advantages. The SSS elements, including magnets and vacuum\nchambers, can be pre-assembled and pre-aligned on a girder in a clean room outside the tunnel, using\nthe appropriate tools and environment. The module can then be transported as a single unit to the tunnel,\nstreamlining transport and maintenance operations (for more details, see Section3.10.3).\nFig. 6.24: CAD model of a possible optimised version of the booster SSS.\n286\n\nSpecifications\nAn initial estimation of the acceptable vibrations in the SSS was defined in 2022, and is reported in\nTable 6.8. This specification did not distinguish between vertical and lateral motion, and between booster\nand collider.\nTo consolidate the tolerance estimates, the sensitivity to vibrations of the GHC optics at the Z op-\nerating point was evaluated assuming a tolerance on the beam oscillation amplitude at the collision point\nof less than 5% relative to the collision point beam size [309]. Due to the small emittance ratio, vertical\noscillations are more than an order of magnitude more critical than horizontal oscillations. Assuming\nthat an orbit feedback system will efficiently damp beam oscillations with frequencies below 1 Hz, the\nintegrated RMS motion for frequencies higher than 1 Hz is ideally around 10 (100) nm for the vertical\n(horizontal) plane. If the beam orbit feedback bandwidth can be extended above 1 Hz, setting the targets\nfor the vertical (horizontal) plane to 20 (200) nm, in line with Table 6.8 is possible. It must be noted that\nthe sensitivity may evolve in the future with the optics and the machine layout. For the low-beta regions,\nthe tolerances are an order of magnitude tighter.\nThese considerations are summarised in Table 6.9. The key frequency of interest is 1 Hz, and in\nthis frequency range:\n\u2013 The collider quadrupole acceptable vertical displacement is 20 nm.\n\u2013 Laterally, the acceptable displacement of the collider quadrupole is higher by roughly one order of\nmagnitude. Currently, a value of 200 nm is tentatively assumed.\n\u2013 It is very likely that the quadrupoles in the booster can accept larger displacements than in the\ncollider. It is, however, not evident to define how much the requirements can be relaxed. An\nincrease of the tolerance by a factor of two in vertical and lateral directions is currently tentatively\nassumed, resulting in values of 40 nm and 400 nm, respectively.\nTable 6.8: Dynamic stability requirements in the arcs proposed in 2022%, presented by T. Raubenheimer\nat FCC IS workshop for the arcs [310].\nFrequency range\nTolerance\nCorrelation\n0.01 Hz < f < 1 Hz\n1 \u00b5m\n10 km\n0.01 Hz < f < 1 Hz\n100 nm\nnone\n1 Hz < f < 10 Hz\n20 nm\nnone\n10 Hz < f < 100 Hz\n5 nm\nnone\n100 Hz < f\n1 nm\nnone\nTable 6.9: Updated dynamic stability requirements in the arcs at the level of the magnetic axis.\nTolerance at 1 Hz frequency\nCollider vertical direction\n20 nm\nCollider lateral direction\n200 nm\nBooster vertical direction\n40 nm\nBooster lateral direction\n400 nm\nHistorical background\nIt is interesting to compare the current stability specifications with what was studied in other projects\nor achieved in past CERN machines, such as the Large Hadron Collider (LHC/HL-LHC) and the future\nCompact LInear Collider (CLIC). Concerning the LHC/HL-LHC quadrupoles:\n287\n\n\u2013 In standard operation the root mean square (RMS) value should be < 5 \u00b5m at 1 Hz;\n\u2013 Beam instabilities can be provoked if the RMS is between 5 \u00b5m and 20 \u00b5m at 1 Hz;\n\u2013 A beam dump is usually triggered for an RMS > 20 \u00b5m at 1 Hz.\nOn the other hand, the future Compact LInear Collider (CLIC) has significantly more stringent specifica-\ntions: given its very small beam sizes, even minor oscillations of one quadrupole reduce the luminosity.\nIt has been estimated that in the vertical direction, the RMS must be below 1 nm at 1 Hz and similarly, it\nmust be below 5 nm at 1 Hz laterally to ensure sufficient performance [312]. A study has demonstrated\nthat these specifications can be achieved, albeit using active stabilisation based on piezo-actuators com-\nbined with a stiff and optimised design of the quadrupole support [313].\nHence, the FCC arc specifications are closer to those of a linear accelerator (CLIC) than those of\nexisting circular accelerators (LHC/HL-LHC), which illustrates their challenging nature.\nNumerical methodology\nAs explained and detailed in Section 3.10.3, the supporting structures of the collider and the booster are\nbeing optimised in terms of static and dynamic stability. For this scope, a finite element method (FEM)\nprocedure has been defined (see Section 3.10.3).\nFig. 6.25: Transfer function comparison for different supporting structure geometries in the vertical and\nlateral directions.\nAn example of a transfer function comparison for different geometries of the booster supports is\nshown in Fig. 6.25. Two graphs are presented: the first displays the transfer functions obtained vertically,\nand the second the transfer function obtained laterally. The transfer functions provide insight on how the\nsystem behaves and reacts over a range of frequencies. The greater the natural vibrational and rigid body\nfrequencies, the more rigid the system is considered to be. Comparative studies can be carried out to\nanalyse the impact on stability of the geometry, materials, position, rigidity and number of feet, etc. and\nto determine the most suitable geometry.\n288\n\nKnowing the spectrum of the ground motion over the relevant range of frequencies, as well as\nthe transfer function of the supporting structure between the ground and the centre of the magnet, it is\npossible to estimate the displacement of the magnet mechanical axis in response to the ground motion.\nSince the values of the estimated movement of the ground in the FCC tunnel are not yet available, the\npower spectral density (PSD) of the ground motion measured in the LHC tunnel [315] has been used as\nan initial input instead. When performing a random vibration analysis of the system with such ground\nPSD as an input for the calculation, the PSD of the magnetic axis is obtained as an output, and then\nthe integrated root mean square (RMS) displacements at the level of the axis can be computed. The\nmethodology is explained in Fig. 3.74.\nExperimental benchmarking\nIt is important to note that the method described above is sensitive to several parameters that cannot be\nprecisely estimated at this stage of the project. Similarly, the simulations involve certain approximations,\nsuch as simplified representations of magnets and interfaces (e.g., ground-support and support-magnet\ninteractions). Therefore, it is crucial to experimentally benchmark and refine the simulations to build\nconfidence in the numerical model.\nTo better understand how the different elements of the SSS influence system stability, a simple\n2.5 m long short straight section demonstrator was assembled (see Section 3.10.3). The design of this\ndemonstrator closely resembles what will be installed in the collider. However, during the next phase,\nthe plan is to extend these measurements to the booster\u2019s SSS as well.\n6.9\nMachine protection\nMachine protection hardware and software will be required. These protection elements are very similar\nto those described for the collider and are described in more detail in Section 3.11. As there are no\nsuperconducting magnets foreseen in the booster, there will be no such protection systems.\n289\n\n290\n\nChapter 7\nFCC-ee injector complex\n7.1\nInjector overview\nThe FCC-ee injector complex must provide the electron and positron bunch trains for alternating boot-\nstrapping injection during, both, top-up and filling-from-scratch operations. Given the charge per bucket\nand lifetime for this operational mode, an alternating injection of a train of positrons and electrons ap-\nproximately every few tens of seconds is required to ensure the correct balance between positron and\nelectron bunch charges during collider operation. It includes separate linacs for electrons and positrons\nup to a beam energy of 2.86 GeV \u2013 the electron linac (e-Linac) and the positron linac (p-Linac), respec-\ntively. Figure 7.1 shows the basic layout of the injector complex schematically. Following the positron\nPositron linac, 304 m, 2 GHz\n13.3 MV/m, 21 RF unit module\nEnergy \ncompressor\nPositron\nsource\nElectron transfer line\nDamping \nring,\n2.86 GeV\nHigh-energy Linac, 1080 m, S-band, \n21.1 MV/m, 72 RF unit module\nEnergy\ncompressor \nBunch \ncompressor\nto BR\n20 GeV\nOverall length including DR and transfer lines ~1200 m \ne+\ne-\ne+\ne-\nElectron linac, 215 m, S-band\n19.5 MV/m, 15 RF unit module\nElectron \nsource\nTransfer lines\nFig. 7.1: Baseline layout of the pre-injector complex, including the high-energy (HE) linac.\nand electron linacs, both species are injected into the damping ring (DR) for emittance reduction. The\nlayout also includes the high-energy (HE) linac, which boosts the beam energy from 2.86 GeV up to\n20 GeV in order to inject beams directly into the booster ring (BR). The baseline for the positron source\nis based on a conventional scheme using electrons from the e-Linac impinging on a tungsten target. This\napproach allows all linacs to operate at 100 Hz with 4 bunches per pulse to meet the collider ring filling\nspecification for the most demanding Z running mode.\nOperating at a 100 Hz repetition rate with four bunches per RF pulse, the linac system incorporates\nbeam-loading compensation and long-range wakefield suppression for enhanced stability. Although the\ninjector complex is now longer, this new layout improves reliability, featuring a damping ring at a higher\nenergy of 2.86 GeV and eliminates the need for a common linac, which would otherwise require doubling\nthe repetition rate. This revised concept provides a more efficient and sustainable solution aligned with\nperformance and operational goals.\nTable 7.1 lists the collider and booster parameters used as specifications for the injector design.\nIt is worth emphasising that the injector must operate continuously due to the short beam lifetime and\nthe strict requirement that the charge imbalance between the electron and positron beams in the collider\nremain within a narrow range of 3-5%. This constraint requires a precise and uninterrupted injection\nprocess to maintain beam-beam stability. For example, assuming a beam duration of about 1000 seconds,\n291\n\nTable 7.1: Collider and booster parameters used as specifications for the injector design. Bunch charge\nis the maximum bunch charge to be injected into the collider ring. Emittance, bunch length and energy\nspread are the specifications at the injection into the booster ring.\nRunning mode\nZ\nW\nZH\nt\u00aft\nUnit\nNumber bunches in collider\n11200\n1856\n300\n64\nNominal bunch charge in collider\n34.40\n22.08\n27.04\n23.68\nnC\nAllowable charge imbalance\n5\n3\n3\n3\n%\nBeam lifetime, lumi 4 IPs\n(q, BS, lattice)/4\n916\n517\n428\n497\ns\nTrains/Bunches per booster cycle\n40\u00d7280\n8\u00d7232\n2\u00d7150\n2\u00d732\nMax injected bunch charge\n3.43\n3.43\n1.60\n1.60\nnC\nNumber of bunches\n4\n4\n2\n2\nLinac rep. rate\n100\n100\n50\n50\nHz\nBunch spacing\n25\nns\nBeam energy at BR\n20\nGeV\nNorm. emittance (x, y) (rms) (BR)\n<20,2\nmm mrad\nBunch length (rms) (BR)\n\u223c4\nmm\nEnergy spread (rms) (BR)\n\u223c0.1\n%\nthe injector must alternate between injecting electrons and positrons at intervals of about 50 seconds.\nThis requirement imposes a significant operational challenge, particularly in the Z-mode, where any\ninterruption in injector functionality could severely impact the collider performance. Consequently, the\nreliability and availability of the injector are of critical importance, as any downtime could compromise\nthe overall efficiency of the collider. This issue represents a critical limitation presented in more detail in\nSection 7.9, where potential risks and mitigation strategies associated with injector failures are discussed\nin more detail.\nThe top-up operation for each operating mode requires the charge of the individual bunch in the\ntrain to vary from a few tens of pC to about 4 nC per injection, depending on the charge imbalance of\nelectrons and positrons of the individual bucket in the collider. This requirement results from the different\nlifetimes of the individual bunches in the collider rings, which will also determine the filling pattern for\neach injection. Regarding emittance, the specifications for injection into the BR require a beam with a flat\nnormalised emittance of 20 mm\u00b7mrad and 2 mm\u00b7mrad in the horizontal and vertical planes, respectively,\nto ensure a shorter cycle in the booster itself. This specification has an impact on both electron source\nand DR parameters. In particular, the electron source must guarantee this emittance even during the\nrequired charge variation for top-up operation, and this question has an impact on the optimisation of the\nphoto-cathode RF gun.\nIn order to achieve independent design specifications for the linacs in the injector from those of the\nBR, an energy compressor in the transfer line from the HE linac to the BR is planned. This arrangement\nis depicted in the left part of Fig. 7.1. By adopting this approach, the design of the linacs can converge\ntowards a solution for the beam length and energy spread at the linac end specified in Table 7.1, without\nconsidering more complex layouts that include compression and/or decompression of the beam along the\ndifferent linacs.\nTable 7.2 provides a comprehensive summary of the key parameters of the electron and positron\nbeams as they progress through the injector and booster up to the point of injection into the collider in\nZ-mode. This table serves as a crucial reference, consolidating the relevant beam characteristics at each\nstage of the acceleration and manipulation processes. By collecting these parameters in a structured man-\nner, Table 7.2 played a key role in coordinating the various simulation studies conducted on the different\n292\n\ninjector subsystems. It allowed the results to be systematically compared and validated, ensuring consis-\ntency between simulations. Furthermore, this collection was crucial to verify that the beam parameters\nremain within the specifications required for successful injection in both the booster and the collider.\nThe findings from the injector study have also been documented in four detailed scientific re-\nports submitted to CHART [350\u2013353]. These reports serve as a comprehensive record of the research\nconducted, encompassing various aspects of the injector\u2019s design, performance, and operational con-\nstraints. Additionally, these reports include an extensive list of references that provide further context\nand background to the study. This bibliography features a wide range of scientific publications, includ-\ning peer-reviewed journal articles, conference proceedings, and contributions presented at workshops\nand international conferences.\nThe following sections provide a summary of the key findings and achievements resulting from\nthe efforts to address the recommendations outlined in the mid-term review. These results highlight\nthe progress made in optimising the injector\u2019s design, performance, and integration within the overall\nsystem. Additionally, this discussion includes an overview of the proposed location of the injector on\nthe CERN site. The positioning of the injector is a critical aspect, as it directly influences factors such as\nbeam transport efficiency, infrastructure requirements, and operational feasibility.\nTable 7.2: Electron and positron bunch parameters along the injector and booster up to the injection\ninto the collider for the Z-mode. Some parameters still have to be calculated (tbc). LE=Low-energy,\nHE=High energy, DR=Damping ring.\nBeam\nEnergy\nBunch\ncharge\nTransm.\nBunch\nlength (rms)\nRel. energy\nspread (rms)\nNorm.\nemit. (rms)\nH/V\n[GeV]\n[nC]\n[%]\n[mm]\n1E-3\n[mm mrad]\nLE Linac injection\n0.2\n3.79\n1\n5\n3/3\nLE Linac exit\n2.86\n3.75\n0.99\n1\n6\n3.3/3/3\nPositron source target\n0.045\n26.53\n7.07\n1.34\n>100\n21 000/20 000\nPositron capture exit\n0.185\n14.81\n0.56\n9\n>100\n13 000/12 000\nPositron linac injection\n0.263\n12.06\n0.81\n8\n140\n13 000/12 000\nPositron linac exit\n2.86\n10.73\n0.89\n2.8\n8.7\n13 000/12 000\nEnergy Compressor\n2.86\n10.09\n0.94\n2.8\n8.7\n13 000/12 000\nDR injection\n2.86\n5.04\n0.5\ntbc\ntbc\n13 000/12 000\nDR extraction\n2.86\n4.99\n0.99\n4.8\n0.72\n10/1\nLE Linac injection\n0.2\n5.20\n1\n5\n3/3\nLE Linac exit\n2.86\n5.15\n0.99\n1\n6\n3.3/3.3\nTransfer line\n2.86\n5.09\n0.99\n1\n6\n3.3/3.3\nDR injection\n2.86\n5.04\n0.99\n1\n7\n5/5\nDR exit\n2.86\n4.99\n0.99\n4.8\n0.72\n10/1\nBunch Compressor\n2.86\n4.94\n0.99\n1\n7\n10/1\nHE Linac injection\n2.86\n4.89\n0.99\n1\n7\n12/1\nHE Linac exit\n20\n4.84\n0.99\n1\n6.1\n16/1.6\nEnergy Compressor\n20\n4.80\n0.99\n4\n1\n16/1.6\nTransfer line\n20\n4.56\n0.95\n4\n1\n16/1.6\nBooster injection\n20\n4.33\n0.95\n4\n1\n20/2\nBooster extraction\n45.6\n4.29\n0.99\n2.43\n0.38\n10.71/0.89\nCollider injection\n45.6\n3.43\n0.8\n2.43\ntbc\n10.71/0.89\n293\n\n7.2\nElectron source\nThe baseline configuration of the injector complex, illustrated in Fig. 7.2, includes a single electron\nsource for producing both the nominal electron beam and the driver electron beam for positron produc-\ntion. The electron source is composed of a photo-cathode 2.6 cell RF photo gun followed by three RF\naccelerating structures reaching the beam energy of approximately 200 MeV. The main requirement for\nthe electron source is to generate four bunches with a charge of 5 nC each, keeping the normalised emit-\ntance below 4 mm\u00b7mrad in order to have a margin in any emittance growth along the linacs and transfer\nlines between linacs.\nExtensive simulations have been conducted on the electron source and downstream linacs. Uni-\nform and truncated Gaussian initial distributions have been studied, and Table 7.3 lists the optimised\nbeam parameters that were achieved at the end of the electron source. These parameters and the simu-\nlated distributions have been used as input for the design and simulations of the subsequent linacs. In\nparticular, investigations into the yield of positron production indicate that 5 nC electron bunches are\nsufficient to achieve the desired positron bunch charge.\nFig. 7.2: Schematic layout of the 200 MeV pre-injector consisting of an RF-gun and 3 accelerating\nstructures. Here the option with two redundant laser systems is shown.\nTable 7.3: Electron source beam parameters at 200 MeV with a bunch charge of 5 nC.\nParameter\nUniform Distribution\nGaussian Distribution\nTransverse Emittance [mm\u00b7mrad]\n2\n3\nEnergy Spread rms [%]\n0.4\n0.25\nBunch Length rms (mm)\n0.98\n1.3\nOne of the most challenging aspects for the electron source is the top-up mode for the collider.\nIn this operational mode, the bunches circulating in the collider rings will be topped up with charge,\ncompensating for the charge decrease during collisions. Therefore, the injector has to deliver varying\nbunch charges in the range of 10-100% for each bunch. Nominal operation consists of a four bunch\nper RF pulse scheme, with a spacing of 25 ns. In theory, a single laser pulse could be split in 4 and\nthen individually manipulated, but using up to 4 lasers would allow more flexibility to change the charge\nindependently of a few hundred pC up to 5 nC. Several lasers may also be needed to achieve the required\n294\n\navailability (see Section 7.9). The source and the linac will work with a 100 Hz repetition rate, leaving\nonly 10 ms between pulses to adjust laser, RF or magnet parameters. A detailed beam dynamics study\nhas been started to determine which parameters need to be changed for different bunch charges to deliver\nbeams as similar as possible. The best option would be to leave RF and magnet parameters constant and\nonly change the laser spot size and intensity on the cathode so that the charge density stays as similar as\npossible. The spot size could be manipulated fast enough using a controllable mirror array. Simulations\nshow that, in this case, the beam parameter variation at the exit of the electron source is not too big (see\nFig. 7.3). More details on the electron source study can be found in Ref. [354].\nFig. 7.3: Beam parameter variation as a function of bunch charge simulating the top-up operation of the\nelectron source and pre-injector.\n7.3\nElectron linac\nThe electron linac accelerates electron beam of up to 4 bunches of 5 nC each from the energy of about\n200 MeV to 2.86 GeV at the repetition rate of 100 Hz for Z-mode, which presents the most critical case\nfor the linacs. The electron linac is located right after the electron source, as shown in Fig. 7.1. In the\nelectron production mode, the beam goes to the DR, and in the positron production mode, it goes to the\ntarget.\nBeam dynamics simulations have been done to study both longitudinal and transverse beam dy-\nnamics in the electron linac using the tracking code RF-TRACK [355]. The main purpose was to define\nthe specifications for RF structures in terms of iris aperture, working frequency, structure length, gradi-\nent, and lattice parameters, like quadrupole separation, kind of lattice, and phase advance. The following\nbeam parameters were used in the simulations: bunch length 1 mm, relative energy spread 0.25% and\nemittance 3.2 mm\u00b7mrad at the start of the electron linac for the case of the 5 nC electron bunch.\nThe linac comprises a FODO lattice with 90 degrees phase advance per cell with one quadrupole\nand one BPM per RF structure, with a total cell length of 7.5 m. The RF structures are operated on-\ncrest. This allows the accelerating efficiency to be maximised, and the beam quality degradation to be\nminimised.\nTracking simulations were conducted in terms of emittance growth to evaluate the robustness of\nthe linac design against static misalignments. Gaussian-distributed misalignments were assumed for the\nRF accelerating structures, quadrupoles, and BPMs; the corresponding rms values are summarised in\n295\n\nTable 7.4. A BPM resolution of 10 \u00b5m was also included in the computation of some of the steering\ncorrections applied.\nBased on these simulations, an RF structure aperture corresponding to a/\u03bb = 0.15 was deter-\nmined. To mitigate the effects of misalignments, a combination of one-to-one correction and dispersion-\nTable 7.4: RMS of the Gaussian random distributions assumed for the misalignments of the lattice\nelements for the static effect simulations.\nElement\nValue [\u00b5m]\nQuadrupoles\n50\nRF accelerating structures\n100\nBPM\n30\nfree steering (DFS) was applied sequentially, incorporating the randomly distributed errors. The min-\nimum RF aperture corresponding to < a > /\u03bb = 0.15 was determined by compromising the growth\nof transverse emittance from static effects with the efficiency of the RF structure. Finally, a maximum\nemittance growth of 0.3 mm\u00b7mrad was obtained at the end of the linac for 98 % or more of the simulation\nseeds assuming the optimised RF parameters (on-crest operating phase and aperture corresponding to\na/\u03bb = 0.15).\nDynamic effects were also investigated, focusing specifically on the amplification of the incoming\nbeam transverse jitter, whether in position, angle or a combination of both. To simulate transverse beam\njitter, the transverse phase space was painted following a circular path at the entrance of the linac. The\njitter amplification (JA) was then calculated as the square root of the ratio between the areas of the\ntransverse phase space at the entrance and at the exit of the section. The final jitter, in either position or\nangle, was determined by multiplying the incoming jitter by the computed amplification. This method\nprovides a quantitative measure of the robustness of the linac design to incoming beam transverse jitter\nand enables optimisation of parameters such as the RF structure aperture, the lattice phase advance per\ncell, and the spacing between quadrupoles linked in this design to the length of the RF structure. Both\nsingle- and multi-bunch effects were analysed following a different procedure. In the case of the single-\nbunch the JA was computed all along the linac varying the above-mentioned parameters. As an example,\nFig. 7.4 shows the dependence of the JA on the RF structure aperture. The aperture corresponding to\nFig. 7.4: Single-bunch jitter amplification along the electron linac at different RF apertures.\na/\u03bb = 0.15 produces a maximum final JA of approximately 1.2. Assuming an initial orbit jitter of\n0.12 \u03c3 (where \u03c3 is the transverse beam size), like for example, that measured in AWAKE for similar\n296\n\nbeam parameters, results in a jitter of 0.14 \u03c3.\nThe JA was also used to study multi-bunch dynamic effects, but assuming a variable kick imparted\nby the first bunch on the second bunch. Given the amount of jitter that can be accepted, the maximum\ntolerable kick was determined and used to determine the specification for the HOM dipole suppression\nin the RF structure. The results are shown in Fig. 7.5, demonstrating that the kick on the following bunch\nof 0.1 V/pC/mm/m corresponds to a JA of 1.02 at the exit of the linac, which is significantly smaller\nthan the single-bunch JA. From these simulations, the total JA, calculated as a product of single- and\nFig. 7.5: Multi-bunch JA at the exit of the electron linac versus transverse wakefield kick imposed by the\nfirst to the following bunch.\nmulti-bunch JAs, is 1.22. The corresponding total jitter is smaller than 0.15 \u03c3, assuming 0.12 \u03c3 as the\nincoming jitter. This value has a negligible impact on the positron production, and is expected to be in\nthe acceptance of the DR. The parameters obtained from the beam dynamics studies are summarised in\nTable 7.5 for convenience.\nTable 7.5: Summary of the optimised RF and lattice parameters based on the beam dynamics studies.\nParameter\nValue\nMean RF structure aperture (mm)\n16.1 (a/\u03bb = 0.15)\nRF structure length (m)\n3\nRF structure operating phase\non-crest\nPhase advance/cell (degrees)\n90\nNumber of BPM/RF structure\n1\nNumber of quadrupoles/RF structure\n1\nDistance between the quadrupoles (m)\n3.75\n7.4\nPositron source and linac\nThe production of positrons is always an extremely important topic for any electron-positron collider,\nespecially for future colliders like the FCC-ee, which are designed to operate at extreme parameters.\nFor the FCC-ee, a high-yield positron source is essential to provide the low-emittance positron beam\nwith sufficient intensity to reduce the injection time into the collider. Specifically, at Z-pole operation,\na positron bunch intensity of 2.14 \u00d7 1010 particles is required at injection into the collider rings. The\npositron rate for the FCC-ee is twice that achieved at the SLC at SLAC, while remaining an order of\nmagnitude lower than the values typically proposed for linear collider projects [356]. At the injector\n297\n\nlevel, the primary requirement for the positron source is to deliver a positron bunch charge of 5 nC,\nwhich must be accepted into the damping ring (DR), as indicated in Table 7.2. Based on the available\nexperience of designing and operating previous or current positron sources, a safety margin of 2.56\nhas been applied to the FCC-ee positron source design, requiring the delivery of a total positron bunch\nintensity of 12.8 nC at the injection into the DR.\n7.4.1\nPositron production and capture system\nA conventional positron source using 2.86 GeV electrons impinging on a 15 mm thick tungsten target\nis the basis for FCC-ee positron production. The bremsstrahlung radiation of the electrons in the field\nof the target nuclei is converted in e+e\u2212pairs. The target thickness has been optimised to maximise\nthe number of positrons produced at the target exit. This conventional production method has been\nsuccessfully employed in all the e+e\u2212colliders (ADA, ACO, DCI, SPEAR, ADONE, LEP, and also for\nthe first linear collider SLC).\nThe capture section includes an Adiabatic Matching Device (AMD) [357], followed by a capture\nlinac embedded in a DC solenoidal magnetic field to accelerate the positron beam to about 170 MeV.\nAt the end of the capture linac, positron and electron bunches are separated using a chicane at 170 MeV\nand the solenoid focusing is used up to a positron energy of 930 MeV. After the matching section\nat 930 MeV, the positron beam passes through quadrupole focusing and is accelerated up to the DR\nenergy 2.86 GeV. An energy compressor system (ECS) is used before the DR to increase the number of\npositrons within the DR energy acceptance. The DR is an important part of the positron source design\nas its dynamic aperture, longitudinal and transverse acceptance parameters define the final performance\nof the positron source. The baseline design of the DR is described in Section 7.5.\nTwo AMD designs were investigated during the Feasibility Study: one employing a flux concen-\ntrator (FC) based on pulsed magnet technology (currently used in the SuperKEKB collider [358]) and\nanother using a superconducting (SC) solenoid based on high-temperature superconducting (HTS) ma-\nterials. The latter, an innovative approach for positron sources, will also be tested in the PSI Positron\nProduction (P3) experiment at SwissFEL [359], which has been designed as a demonstrator for the FCC-\nee positron source technologies (see Section 7.4.6).\nFor the classical FC-based approach, several models were evaluated for the FCC-ee positron\nsource design. These included the one designed by BINP for the FCC-ee and ILC projects, the FC\ndeveloped by KEK for the ILC project, and the FC currently used in the SuperKEKB collider. Due to\nthe conceptual and mechanical constraints of the FC, the peak of the magnetic field is located down-\nstream the target and as a result, the available field on the target is reduced to \u223c3.5 T/\u223c1.1 T (for the\nBINP/SuperKEKB designs respectively) manifesting a significant drop in capture efficiency. Moreover,\nthe presence of a high transverse magnetic field component (with strong domination of dipole harmonic)\nmakes the trajectories of positrons strongly distorted. As a result, the positron beam receives an offset in\nthe vertical and horizontal planes. This must be mitigated for the positron beam transport in the capture\nline. Compared to the FC systems used in the SuperKEKB or BINP designs, the FCC-ee requires a higher\nrepetition rate (up to 100 Hz), ideally with stronger magnetic fields and larger apertures. These require-\nments pose substantial technological and engineering challenges, particularly for high-power sources.\nTo address these challenges, an SC solenoid based on HTS technology was proposed for positron\ncapture. The HTS solenoid offers several advantages over the FC design. It provides a significantly\nhigher magnetic field at the target exit surface, a larger aperture and greater flexibility in target position-\ning, as the target can be placed inside the magnet bore. The axial symmetry of the solenoid ensures zero\ntransverse magnetic fields at the magnet axis, eliminating beam distortion issues encountered with the FC\noption. The comparison of the field profiles for the FC and HTS solenoid designs, as used in the FCC-ee\npositron source studies, is shown in Fig. 7.6. Based on these considerations and simulation results, the\nAMD employing the HTS solenoid was selected as the baseline for the FCC-ee positron source.\n298\n\n-50\n0\n50\n100\n150\n200\nZ [mm] (z = 0 target exit) \n0\n2\n4\n6\n8\n10\n12\n14\nBz [T]\nTarget exit\nFC : ILC-BINP\nMax Bz = 5.00 T\nBz on the target = 0.84 T\nFC : ILC-KEK\nMax Bz = 5.07 T\nBz on the target = 0.75 T\nFC + BC : FCC-BINP\nMax Bz = 7.50 T\nBz on the target = 3.50 T\nFC + BC : SuperKEKB\nMax Bz = 4.40 T\nBz on the target = 1.14 T\nHTS : FCC\nMax Bz = 14.94 T\nBz on the target = 11.67 T\nFig. 7.6: Magnetic field profile of the AMD implemented in the form of the FC and HTS solenoid\nmagnet. BC refers to the bridge coils, which are solenoid magnets surrounding the FC. The following\nFC models were analysed: BINP design for the ILC, KEK design for the ILC, BINP design for FCC-ee,\nand KEK design for SuperKEKB. A dashed line indicates the target exit surface.\nThe capture linac consists of six 3 m long, travelling wave (TW) 2 GHz RF structures with large\niris apertures (2a = 60 mm), designed to provide enhanced transverse acceptance for positrons. The\nbaseline design assumes an average RF gradient of 13.3 MV/m. Each accelerating structure is em-\nbedded within ten solenoid magnets, forming a solenoidal magnetic channel with a field strength of\napproximately 0.5 T, which efficiently guides the positron beam through the capture linac aperture. An\nadditional solenoid magnet, referred to as the tuning solenoid, is placed between the AMD and the first\naccelerating structure. This solenoid increases the magnetic field experienced by the positron beam prior\nto entering the capture linac, further improving beam focusing and capture efficiency. The RF phases\nof the capture linac were optimised using the Xopt package [360] to maximise the final positron yield\naccepted by the DR. Figure 7.7 presents the key simulation results for the capture section, including the\nseparator chicane and the first two accelerating structures of the positron linac. At the beginning of the\ncapture section, a 33% drop in capture efficiency is observed, primarily due to the transverse acceptance\nof the accelerating structures. This is followed by a smaller 9% reduction in efficiency after the separator\nchicane.\n7.4.2\nRadiation load studies for target and capture system\nThe interaction of the electron drive beam with the positron production target gives rise to an intense\nflux of secondary particles. Only a fraction of the original drive beam energy contributes to the final\npositron yield, while most of the power is dissipated in the target, the AMD and the downstream capture\nlinac. The resulting thermal load and cumulative radiation damage in the different components require\na careful assessment in the engineering design process. This concerns in particular, the design of the\nproduction target and the optimisation of shielding components, which protect sensitive components like\nthe SC coils of the AMD.\nIn order to quantify the impact of secondary radiation fields, radiation transport studies were car-\nried out with the FLUKA Monte Carlo code. The FLUKA geometry model is illustrated in Fig. 7.8. The\ntarget was modelled as a stationary tungsten disk with a thickness of 15 mm. The target is surrounded\nby cylindrical tungsten shielding (13 cm long and 2 cm thick walls), which reduces the heat load and\n299\n\nFig. 7.7: Simulation results of the positron capture section, starting from the target exit surface. The plots\nillustrate: (a) the evolution of positron capture efficiency, (b) the positron beam energy, (c) the magnetic\nfield profile along the capture section, and (d) the schematic layout of the capture section.\nradiation damage in the AMD. The inner radius of the HTS coils of the AMD, placed in a cryostat, was\n6.1 cm. A second tungsten shielding with a tapered aperture was assumed to be located between the\nAMD and the tuning solenoid, and a third between the tuning solenoid and the first RF structure of the\ncapture linac.\nFig. 7.8: FLUKA geometry model of the positron production target, the AMD with SC solenoid, the\ntuning solenoid, and the downstream positron capture linac.\nThe radiation load studies assumed a 2.86 GeV electron drive beam with four bunches, a bunch\ncharge of 2.37 \u00d7 1010 e\u2212, and a repetition frequency of 100 Hz, which results in an average drive beam\npower of 4.3 kW (Z-pole). The simulated power density distribution in the target, shielding, AMD and\nthe first linac cells is illustrated in Fig. 7.9.\nWith such electron beam parameters, the target and surrounding shielding absorb around 1.3 kW,\n300\n\nFig. 7.9: Power density (Z-pole) in the target, AMD, shielding, tuning solenoid and the first RF cells of\nthe capture linac. The peak power density in the target reaches 10 kW/cm3 (out of the scale of the plot).\nwhich poses a challenge for the target design; possible engineering solutions and cooling options are\ndiscussed in the next section. Another issue is the atomic dislocations in the target, which are mostly\nconcentrated along the beam axis. Assuming 185 days of operation per year and a duty factor of around\n80%, the radiation transport simulations show that the displacement damage in the target can reach a\npeak value of 1\u20132 DPA/year for FCC-ee operation at the Z-pole. Possible mitigation measures need to\nbe determined, e.g., the design of a remote handling system, which would enable regular replacement of\nthe target assembly.\nThe power deposition in the AMD, including cryostat, HTS solenoid and support structures, is\nonly about 10 W, which demonstrates the effectiveness of the shielding. In particular, the power density\nin the HTS coils remains below 10 mW/cm3, which is considered acceptable and is safely below the\nquench level of the solenoid. The simulations also show that the cumulative displacement damage in the\nHTS tapes is less than 1 \u00d7 10\u22124 DPA/year (Z-pole), which is not expected to degrade their properties.\nFurthermore, the total radiation dose to the coils reaches about 6 MGy/year. Since no organic insulation\nmaterials are used in the coils, such dose values should not pose a problem for the HTS solenoid, but\nrequire further assessment. If needed, a slight increase in the shielding thickness can reduce the dose\nfurther.\nThe capture linac is assumed to consist of six RF structures with 44 cells, which are surrounded\nby solenoids. About 0.6 kW are deposited in the shielding between the AMD and the capture linac.\nAt the same time, most of the remaining power, i.e., about half of the power originally carried by the\nelectron drive beam, is lost in the linac, mainly in the first structure. The tungsten shielding between the\nAMD and the linac protects the front face of the linac, but cannot intercept the most energetic secondary\nparticles near the beam axis, which are then lost on the cavity walls. The highest radiation-induced\npower deposition in a single RF cell is about 70 W, but decreases to about 15 W at the end of the first RF\nstructure. The thermal load due to RF wall losses is estimated to reach similar (or even higher) values as\nthe average radiation-induced power deposition per cell. With an adequate cooling design, the radiation\nload in the linac is expected to be manageable. The solenoids around the RF structure are assumed to\nbe normal conducting. The integrated dose in the solenoids is estimated to be about 1 MGy/year for\noperation at the Z-pole, which is considered acceptable. However, the peak dose in the upstream tuning\nsolenoid reaches 5 MGy/year, which must be considered when choosing insulation materials. A better\nshielding of the tuning solenoid might be needed.\n301\n\n7.4.3\nDesign and integration of the positron source target\nThe current baseline design is based on a fixed target made of polycrystalline tungsten (W) with a thick-\nness of 15 mm. The selection of tungsten as a material for the target is due to its high atomic number\nand its remarkable thermo-mechanical properties at high temperatures. However, to properly dissipate\nthe thermal power produced by the beam impact, a thermal management strategy must be included in the\ndesign. For this purpose, a pressurised water cooling circuit is added in the target, as shown in Fig. 7.10a.\nThis consists of a pair of embedded tantalum pipes that transport water from an upstream source and cir-\nculate through a 180\u00b0 elbow inside the tungsten core. This setup will allow the beam-impacted region\nto properly transfer the 1.26 kW deposited on the target and its shielding and avoid the direct contact\nof water with bare tungsten. The power density distribution obtained from Monte Carlo simulations is\nshown in Fig. 7.10b, where the peak value is 10.4 kW/cm3 and it takes place along the primary beam\naxis (z-axis), close to the exit face of the target.\nbeam \ndirection\n15\nshielding\ntarget\ncooling pipe\nx\ny\nz\n(a)\n0\n50\n100\nZ axis (mm)\n0\n5\n10\n15\n20\n25\n30\n35\nY axis (mm)\n Beam \ndirection\n100\n102\n104\n106\n108\n1010\nPower density W/m3\n(b)\nFig. 7.10: FCC-ee e+ source target. (a) Baseline design geometry: the detailed zone shows the embedded\ntantalum cooling pipes. Only one half of the geometry is shown because it is symmetrical with respect\nto the x-axis and (b) power density deposition map obtained from FLUKA.\nFigure 7.11 shows the steady-state thermo-mechanical results. Note that the location of maximum\ntemperature (P1) is not coincident with the position of maximum equivalent thermal stresses (P2). While\nP1 is along the beam axis beneath the exit surface, P2 is located at the exit surface at a height above P1.\nThe maximum temperature at P1 is 284\u00b0C. This means that the target is working below the ductile-to-\nbrittle transition temperature (DBTT) for tungsten1. In terms of stresses at P1, the 99 MPa registered on\nthe design are due the constrained material surrounding the target. On the other hand, P2 reaches 166\u00b0C\nwith a maximum equivalent stress of 138 MPa located at the surface level and produced due to the strong\nthermal gradient. The resulting stress values are below the yield stress at the associated temperatures.\nThe thermal fatigue analysis performed using the Universal Slope method [362] showed that the target\nis capable of withstanding the extreme service conditions and coping with the expected lifetime of the\ndevice, set to 155.4 days/year, which corresponds to 1.34\u00d7109 thermal cycles2 with a duty factor of\n0.84 [363]. Then, the number of thermal cycles is obtained by including the primary beam frequency of\n100 Hz.\nFrom the integration standpoint, the positron source target is a subsystem and its interaction with\nthe required infrastructure is based on the mechanical layout of the P3 experiment. The current config-\nuration is being used to study the space requirements during the injector complex design. Figure 7.12\n1For the results presented in this document, the DBTT was set to 400\u00b0C, based on the behaviour of tungsten at high strain-\nrate loading conditions reported in [361].\n2The target lifetime is estimated assuming an operation cycle of 185 days/year [13]\n302\n\n\u25cf P1: 99 MPa\n\u25b2 P2: 138 MPa\n138 \nEq. Stress, \u03c3eq (MPa)\n0 \nTemperature, T (\u00b0C)\n284\n27\n\u25cf P1: 284 \u00b0C\n\u25b2 P2: 166 \u00b0C\nFig. 7.11: Steady-state thermo-mechanical results: temperature (left) and equivalent stress (right) distri-\nbutions for the baseline W target. Maximum temperature and stress points are marked with a circle and\ntriangle, respectively.\nshows the tunnel cross section with dimensions of 4\u00d74 m to host the expected services around the beam\nintercepting device. With the aim of allowing the installation and replacement of the target inside the\nHTS solenoid, a drift space of around 1.5 m is included. In addition, an overhead travelling crane with a\ncapacity of 500 kg to handle the target and the surrounding shielding is under consideration. In parallel,\na more detailed study of radiation protection where the use of mobile shielding is an option is being\ncarried out. At the same time, an evaluation of the utilities required (e.g., cooling, cabling, handling\nequipment) needs to be developed. Further integration studies are ongoing to define the requirements in\nterms of civil engineering. The results of these studies will be used in the model for general integration\nof the injector complex.\n4 \nA. Positron source target\nB. Transport passage\nC. Survey volume\nD. Compressed air circuit\nE. Cooling circuit\nF. Cable trays\nDimensions in metre (m) \nFig. 7.12: Current layout of the FCC-ee injector complex cavern: tunnel overview (left) and expected\nutilities around the positron source target (right).\n7.4.4\nPositron linac\nThe positron linac (p-Linac) begins with a chicane equipped with a collimator (beam stopper) at its centre\nto remove electrons and photons co-propagating with the positron beam. The p-Linac is divided into two\nsections, each with distinct layouts. In Section 1, the layout is the same as that of the capture linac, where\nthe accelerating structures are surrounded by solenoids. In contrast, Section 2 employs a simple FODO\nlattice, with each FODO cell containing two accelerating structures and a phase advance of 76.35\u00b0, opti-\nmised for minimum positron beam size. The accelerating structures and solenoids used in both sections\nare identical to those in the capture linac. The separator chicane is situated between the capture linac and\nSection 1, featuring a symmetric layout of four dipole magnets with identical designs but different cur-\nrent settings. A schematic diagram of the chicane, along with the collimator/beam stopper, is presented\nin Fig. 7.13a.\n303\n\n(a)\n(b)\nFig. 7.13: Separator chicane design. (a) Schematic layout of the chicane and collimator used to stop\nthe electron and photon beams. Sol. refers to Solenoid magnet; Dip. refers to Dipole magnet (ldip =\n180 mm) and Col. refers to Collimator (lcol = 120 mm) with d0 = d1 = 125 mm and d2 = 350 mm. (b)\nOn-axis magnetic field of the chicane, including three neighbouring solenoids on each side.\nThe dipole yoke in the chicane has a length of 180 mm and a vertical aperture of 70 mm. The beam\npipe within the dipoles assumes a rectangular aperture of \u2206x = 150 mm and \u2206y = 50 mm. The colli-\nmator is horizontally offset by \u221235 mm. To account for field crosstalk between the chicane and the up-\nstream and downstream solenoids, a 3D magnetic field simulation was performed using MAXWELL3D.\nThis simulation includes three solenoids upstream and three downstream of the chicane. The resulting\non-axis magnetic field is shown in Fig. 7.13b.\nSection 1 of the p-Linac contains 20 accelerating structures, with an average RF gradient of\n13.3 MV/m. The RF phase is set to -10\u00b0 off peak, optimised to maximise the final positron yield. At\nthe end of this section, the average energy of the positron beam around the bunch core is approximately\n932 MeV. Section 2 contains 52 accelerating structures, with an average RF gradient of 12.8 MV/m.\nHere, the RF phase is adjusted to 5\u00b0 off crest for optimal positron yield.\nBeam tracking throughout the p-Linac was simulated using RF-TRACK, including short-range\nwakefield and space charge effects. To estimate the effective positron yield accepted by the DR, particle\nselection was applied using energy and time cuts. For all results presented here, an energy window of\n\u00b1 2% around 2.86 GeV (i.e., 2.86 GeV \u00b1 57.2 MeV) and a time window of \u00b1 10 mm/c were used. In\nthe next phase of the FCC, positron tracking simulations in the positron linac followed by the injection\nin the DR should be carried out to have a more realistic estimate of the positron yield accepted.\n7.4.5\nSimulation Results and Final Performance\nComprehensive start-to-end tracking simulations were conducted to evaluate the performance of the\nFCC-ee positron source. The final longitudinal phase space of positrons at the end of the p-Linac is shown\nin Fig. 7.14. Approximately 99% of the positrons reaching the end of the p-Linac are accelerated in the\nfirst main RF bucket. Furthermore, about 88% of these positrons fall within the assumed DR acceptance\nwindow, demonstrating the effectiveness of the positron source and linac design. The evolution of the\npositron yield along the longitudinal axis, from the target exit to the end of the p-Linac, is depicted in\nFig. 7.15.\nTable 7.6 summarises the key parameters and simulation results for the baseline design of the\npositron source and linac. Beam dynamics simulations confirm that the proposed design ensures reliable\npositron production, achieving a final accepted yield of 3 Ne+/Ne\u2212. This meets the requirements set\nby the FCC-ee (Z-pole) with a safety margin of 2.56. To date, no critical issues have been identified\nthat would prevent the use of a superconducting solenoid as the AMD, along with the proposed capture\n304\n\nFig. 7.14: Longitudinal phase space at the end of the positron linac. The inset provides a zoomed view\nof the main RF bucket. The red region represents the energy and time cut window used to estimate the\nfraction of positrons accepted by the damping ring.\nFig. 7.15: Evolution of the positron yield along the longitudinal axis, from the target exit to the end\nof the positron linac. The dashed lines indicate the boundaries of the different sections of the positron\npre-injector up to the end of the positron linac.\nsystem and positron linac, in the baseline design. For comparison, in a similar layout using an FC-based\ncapture system (SuperKEKB model), the accepted positron yield is approximately 1.5 Ne+/Ne\u2212. This\nlower yield would likely result in use of a thermionic gun to deliver the required electron drive beam\nbunch charge (\u22655 nC), significantly increasing the target power load.\nSimulations incorporating imperfections in the positron source systems were also conducted. The\nimperfections considered, from the target to the end of the p-Linac, are summarised in Table 7.7, with\nRMS values reported. The impact of these imperfections is found to be negligible. The average positron\nyield accepted by the DR decreases by only 1.3%, while the average transverse emittances increase by\n0.4% horizontally and 0.8% vertically. These results indicate the robustness of the proposed design.\n305\n\nTable 7.6: Parameters and simulation results for the baseline design of the positron source and linac,\ndelivering a positron bunch charge of 5 nC accepted into the damping ring, including safety margins. CS\n(capture system), CL (capture linac), p-Linac (positron linac), DR (damping ring).\nParameter\nValue\nUnit\ne\u2212Drive Beam\nBeam energy\n2.86\nGeV\nRepetition rate\n100\nHz\nNumber of bunches per pulse\n4\nBunch charge\n3.8\nnC\nBunch length (rms)\n1\nmm\nBeam size (rms)\n1\nmm\nBeam power\n4.3\nkW\nTarget\nThickness\n15\nmm\nProduction rate\n7.07\nNe+/Ne\u2212\nDeposited power\n1\nkW\nPEDD\n5.8\nJ/g\nCapture System\nAMD peak field (@Target)\n15 (12)\nT\nSolenoid strength\n0.5\nT\nAMD/CS aperture\n60\nmm\nAverage energy @CL\n173\nMeV\nPositron yield @CS (before chicane)\n4.2\nNe+/Ne\u2212\nPositron Linac\nPositron yield @p-Linac\n3.4\nNe+/Ne\u2212\nPositron yield accepted @DR\n3.0\nNe+/Ne\u2212\nAverage energy\n2.87\nGeV\nBunch length (rms)\n2.84\nmm\nEnergy spread (rms)\n0.87\n%\nSpot size x/y (rms)\n5.28 / 2.78\nmm\nNormalized emittance x/y (rms)\n13.1 / 13.0\nmm\u00b7rad\nGeometric emittance x/y (rms)\n2.36 / 2.32\nmm\u00b7rad\nTable 7.7: Summary of imperfections considered from the target to the end of the positron linac, with\nRMS error values reported for each parameter.\nImperfection\nUnit\nValue\nTransverse position error\n\u00b5m\n100\nTransverse angular error (solenoids and dipoles)\n\u00b5rad\n200\nTransverse angular error (other elements)\n\u00b5rad\n100\nMagnetic strength error\n%\n0.1\nRF gradient error\n%\n1\nRF phase error\n\u25e6\n0.1\nBeam position error\n\u00b5m\n100\nBeam divergence error\n\u00b5rad\n100\n306\n\n7.4.6\nPSI Positron Production (P3) Project\nThe PSI Positron Production (P3) experiment is a demonstrator for the positron source and the goal is to\ndesign and install such a demonstrator in the SwissFEL facility, and experimentally validate a range of\nnovel techniques that, according to simulations, have proven potential to increase the positron yield by\none order of magnitude with respect to the state of the art [359]. The P3 project is driven by the high\nluminosity requirements of the FCC-ee collider ring and its results will be one of the key outcomes of the\nfeasibility study concerning the injector. The remarkable positron capture capabilities of P3 are enabled\nto a great extent, by the usage of a high-temperature superconducting (HTS) solenoid around the target\nregion, as well as a novel standing-wave solution for the RF cavities that provides a large iris aperture.\nHTS solenoid (12.7 T)\nTarget insertion \ndevice\n16 solenoids (0.45 T)\nTarget\n2 RF Cavities (40 mm aperture)\nSpectrometer\n2 scintillating fibers\n2 Faraday cups\nDiagnostics chamber\nBroadband pick-ups\nBroadband pick-ups\n6 GeV e-\ndrive beam\ne+\ne-\nFig. 7.16: Overview of the technology for the P3 experiment.\nFigure 7.16 presents a technical drawing of the experiment, illustrating all the technologies de-\nveloped or under development at PSI and CERN. These technologies have been carefully designed and\noptimised based on an in-depth study involving advanced beam dynamics simulations. This detailed\nsimulation work made it possible to model and predict the behaviour of particle beams under various\nconditions, thereby refining the experimental setup and ensuring the optimal performance of each com-\nponent. The figure also illustrates the integration of these technologies, highlighting key aspects such\nas the integration of the target in the cryostat that houses the HTS coils, the RF structures surrounded\nby normal conducting solenoids, and the diagnostics chamber that will allow measurement of the charge\nand energy spectrum of the positrons generated.\nThe procurement and assembly of most accelerator and diagnostic components are progressing\non schedule, ensuring the timely completion of the project milestones. A key achievement has been\nthe successful demonstration of the HTS solenoid at PSI, which achieved magnetic fields up to 18 T, a\nsignificant step forward for this advanced component.\nFigure 7.17 shows photos of the P3 component production process, including the HTS coils and\ntheir cryostat, the broadband pickups, and the first accelerating RF structure. Overall, the P3 experiment\nis making steady progress, with installation work at SwissFEL proceeding smoothly during scheduled\nshutdown periods, which take place three times a year. Essential infrastructure components, such as\nsegments of the extraction line and the high-voltage klystron-modulator system, are being installed in\nthe tunnel according to plan. The primary installation phase is expected to conclude by the end of 2025,\npaving the way for the experiment to begin positron operations in 2026. It is worth noting that the\nSwissFEL facility is an ideal location for hosting the P3 experiment, as it can deliver an electron beam\n307\n\nFig. 7.17: P3 components production and installation in SwissFEL.\nenergy of up to 6 GeV, matching the maximum drive beam energy required for the FCC-ee positron\nsource. Currently, two beamlines (Aramis and Athos) are operational at SwissFEL, and the accelerator\ntunnel has reserved space for a future third beamline (Porthos). This layout provides sufficient room for\nthe temporary installation of the P3 experiment and switchyard. Figure 7.18 illustrates the current design\nof the P3 experiment in its planned final configuration within the SwissFEL tunnel.\nFig. 7.18: The PSI Positron Production (P3) Experiment.\n7.5\nDamping ring and bunch compressor\nThe new optimised FCC-ee injector layout imposed a review of the intrinsic structure of damping ring\n(DR) Transfer Lines (TLs). The presence of two independent linacs for electron and positron beams,\nand the elimination of the common linac, naturally led to increased DR energy which, to avoid spin\nresonances, was set at the value of 2.86 GeV.\nThe main concept driving the DR and TLs design consists of achieving an overall efficiency of the\norder of 80 % in transporting electron and positron beams from the respective linacs, through the DR for\nemittance cooling, to the end of the TLs conveying extracted beams toward the collider booster. Electron\nand positron linacs produce beam pulses at 100 Hz, each pulse consists of 4 bunches spaced by 25 nsec,\neach bunch stores a variable charge intensity up to 5 nC. The DR is mainly needed to reduce the emittance\nof the incoming positron beam by more than three orders of magnitude, from 2.36\u00d710\u22126 m\u00b7rad to about\n1.8\u00d710\u22129 m\u00b7rad.\nHowever, in the latest injector layout, the DR will also be used for electron beam cooling to cure\n308\n\npossible emittance dilution induced by misalignments and space-charge effects. Several options have\nbeen studied and evaluated for the DR arcs, such as using multi-bend cells, and FODO cells. One of\nthe options studied is based on a 6-fold symmetry ring, and has multi-bend arc cells. This design is\npresented as the main option in the following section. An alternative design of the DR has also been\nstudied. A FODO cell is chosen and this alternative DR design, consists of three arcs and three straight\nsections that locate damping wiggler magnets, the RF cavity and injection/extraction equipment. The\nring is about 384 m long, and its energy is 2.86 GeV. The injected beam emittance could be reduced to\nthe required emittance value of 1.76 nm\u00b7rad, horizontal damping time is 6.4 ms and the energy loss per\nturn is 1.13 MeV. The total length of the damping wiggler magnets is about 36.45 m. They have a 2 T\nmagnetic field and are distributed in the three straight sections. It could be possible to lower the magnetic\nfield of the damping wiggler to 1.5 T for optimising the phase advance for minimum emittance (around\n135\u00b0). However, this may cause even more challenging dynamic aperture optimisation.\nFig. 7.19: Damping Ring layout. The six-fold symmetry allows having straight sections dedicated for\ndifferent equipment: RF cavity, injection/extraction septa and kickers and wigglers (to reduce damping\ntime and equilibrium emittance).\n7.5.1\nNew damping ring design\nThe new DR lattice features a six-fold symmetry, as shown in Fig. 7.19. It consists of six arc cells\nconnected by six straight sessions. Each straight session is used to host three wiggler magnet insertions,\none RF cavity module, and two independent injection/extraction sections. Injection and extraction will\nbe implemented in the same branch for the two-particle species in order to avoid changing the polarities\nof the DR magnets, thus ensuring fast and reliable operation modes for both electron and positron. The\ninjection will be performed using an on-axis scheme.\nArc cells are based on an achromatic multi-bend optics, symmetric with respect to the cell centre.\nEach half cell provides 30\u00b0 deflection angle, using 15 bends of five different types. This approach allows\nkeeping the maximum excursion of the horizontal dispersion, optimising damping time, and shaping the\nH5 function along the cell to achieve low emittance. A further reduction of the damping time is obtained\nusing three 3.5 m long wiggler magnets, each with a moderate magnetic field intensity of 1.8 T. Straight\nsections are based on the FODO structure and modified according to their function.\nThe DR optics is presented in Fig. 7.20, it features moderate betatron oscillation amplitudes\nachieved with a relatively weak focusing lattice producing low chromaticity per cell and, consequently,\nwide on- and off-momentum dynamic aperture. Limiting betatron oscillation amplitudes in the transverse\nplanes below a maximum value of the order of 10 m is also beneficial in keeping the ring requirement\nin terms of stay-clear aperture under control, which is crucial especially for DR operation with positron\nbeam. A complete list of the DR parameters is presented in Table 7.8.\n309\n\nFig. 7.20: Damping Ring optics: betatron amplitude (left) and dispersion (right).\nTable 7.8: Damping ring parameters.\nParameters\nValue\nEnergy [GeV]\n2.86\nCircumference [m]\n373.46\nArc Cell\nmulti-bend\nLattice shape\nsix-fold symmetry\nNat. emittance [nm rad] (WGL on/off)\n1.3 / 2.3\nBunch Length [mm]\n5.1\nDamping time \u03c4x,y (WGL on/off) [ms]\n16.9 / 29.4\nNat. Chromaticity (x/y)\n-38.2/-28.3\nNat. energy spread (WGL on/off) [10\u22124]\n7.1 / 5.2\nBetatron amplitude max (x/y) [m]\n9.66 / 6.49\nBetatron amplitude min (x/y) [m]\n0.5 / 1.1\nTune (Qx,Qy)\n27.8707 / 22.3728\nMomentum compaction (WGL on/off) [10\u22123]\n1.55 / 1.57\nRevolution period [\u00b5s]\n1.2457\nDipole #, length [m], field [T]\n180 , 0.7 1.13, 0.34 0.39\nWiggler #, length [m], field [T]\n3, 3.5 , 1.8\nCavity #, length, voltage [MV]\n1.5, 4\nMax. # Bunch stored, Bunch Curr. [mA]\n40 / 4\nStore time\n5 \u03c4y\nEnergy loss per turn (WGL on/off) [keV]\n422.2 / 246.7\nSR power loss wiggler [kW]\n27.83\nKicker rise time [ns]\n50\n7.5.2\nTiming\nThe maximum number of trains that could be simultaneously stored in the damping ring depends on the\nrevolution period (Tper), the train length (\u2206t) and the kicker pulse rise time (tK)\nntrain =\nTper\n\u2206t + tK\nThe storing time (Tstore) for each train of bunches it is fixed by the requirements imposed from the next\nsteps of the injector chain: the positron vertical emittance must be damped from 2.34 mm\u00b7mrad (\u03f5y\ninj) to\n0.18 nm\u00b7rad (\u03f5y\next);\n\u03f5y(t) \u223c\u03f5y\ninje\n\u22122t\n\u03c4y\nThe damping required implies:\nTstore = \u2212\u03c4y\n2 ln \u03f5y\next\n\u03f5y\ninj\n\u22435\u03c4y\n310\n\nUsing the values in Table 7.8 for the revolution period and the linac repetition rate of 100 Hz\n(TRepRate = 10 ms) gives:\n\u03c4y \u2264ntrainTRepRate\n5\n\u224320 ms\nwith ntrain \u224310 that corresponds to Tper \u22651.25 \u00b5s.\n7.5.3\nBunch compressor\nThe bunch compressor is designed to reduce the bunch length of the beam originating from the damping\nring, from an initial range of 4\u20135 mm to a final length of \u223c1 mm. Figure 7.21 (right) illustrates the\nschematic layout of the bunch compressor, which consists of a magnetic chicane formed by four C-\nshaped bending magnets. Each magnet has a magnetic length of 1.9 m and a maximum magnetic field\nstrength of 1 T. The momentum compaction factor R56 is -0.336 m, and the bending angle of each\nmagnet is 11 degrees, resulting in a maximum dispersion of 0.98 m. The distance between dipoles 1 (3)\nand 2 (4) is 2.9 m, while the separation between dipoles 2 and 3 is 2 m. To induce the necessary energy\nchirp for compression, two RF structures, providing a maximum accelerating voltage of 122 MV, are\nemployed. Additionally, four RF structures are utilised to partially remove the residual chirp in order to\nmeet the specifications of the high-energy linac (HE-linac). These structures operate with a maximum\naccelerating voltage of 256 MV. Beam dynamics simulations were performed using the ELEGANT code\nfor a bunch with a maximum charge of 5 nC. Figure7.21 (left) shows the longitudinal phase space after\nthe compression and de-chirping. The results indicate a residual energy spread of 0.7% after de-chirping,\na compression factor of 5.75, and a reduction in the bunch length from 4.6 mm to 0.8 mm. The horizontal\nemittance growth is approximately 20%, while the vertical emittance growth remains below 1%.\nBunch compressor, 50 m\nchirping\n122 MV \nde-chirping\n256 MV\nto HE linac\nfrom DR \nLong. phase space\nFig. 7.21: Bunch compressor at 2.86 GeV placed between the DR and the HE-linac. Left: longitudinal\nphase space after the compression and de-chirping. Right: schematic layout and overall length.\n7.6\nHigh energy linac and Energy Compressor\n7.6.1\nHigh energy linac\nThe high energy (HE) linac accelerates electron and positron beams from the exit of the chicane down-\nstream of the DR at 2.86 GeV energy up to the transfer line towards the booster ring injection at 20 GeV\nenergy.\nAnalogous to the e-linac, beam dynamics simulations have been done to study both longitudi-\nnal and transverse beam dynamics in the HE-linac. The following beam parameters were used in the\nsimulations: bunch length 1 mm, emittance 1 mm\u00b7mrad and 10 mm\u00b7mrad in the vertical and horizontal\nplane, respectively at the start of the HE-linac for a 5 nC electron bunch. The lattice is the same as the\nelectron linac: a FODO lattice with 90\u00b0 phase advance per cell, one quadrupole, and one BPM per RF\n311\n\nstructure. The RF structures operate at the peak of the RF electric field (on-crest) to maximise accelerat-\ning efficiency and minimise beam quality degradation. The beam tracking simulations described in this\ndocument were performed using RF-TRACK [355].\nTo evaluate the robustness of the linac design against static misalignments in terms of emittance\ngrowth, the same Gaussian-distributed misalignments assumed for the electron linac and reported in\nTable 7.4 and the BPM resolution of 10 \u00b5m were considered.\nTo mitigate the effects of misalignments, a combination of one-to-one correction and dispersion-\nfree steering (DFS) was applied sequentially, incorporating the randomly distributed errors. In this case,\nthe focus is on the vertical plane, which is much more critical due to the smaller margin between the start-\ning value and the value accepted by the booster. Finally, a maximum emittance growth of 0.6 mm\u00b7mrad\nin the vertical plane was obtained at the end of the linac for 98% or more of the simulation seeds, giv-\ning a final emittance of 1.6 mm\u00b7mrad below the maximum 2 mm\u00b7mrad required at the booster injection.\nA similar emittance increase is expected in the horizontal plane, which would give a final emittance\nsmaller than 15 mm\u00b7mrad, still satisfying the booster requirement (maximum emittance smaller than\n20 mm\u00b7mrad) in the horizontal plane. These results were achieved by varying the RF structure aperture\nand optimising the minimum number of sections (resulting in 8 for the HE-linac) in which the linac\nmust be divided to avoid propagating an error in the correction over a long distance. These simulations\ndetermined a minimum aperture of the RF structure corresponding to a/\u03bb = 0.12.\nThe dynamic effects were investigated using the same approach as the electron linac. The JA\nwas determined by tracking simulations varying the length of the RF structure, impacting the distance\namong the quadrupoles, the phase advance per cell, and the RF structure aperture. Figure 7.22 shows,\nfor example, the JA along the HE-linac assuming a constant RF structure length of 3 m (corresponding to\na distance among the quadrupoles of 3.75 m) for several RF structure apertures. In particular, for an RF\nFig. 7.22: Jitter amplification along the HE-linac for several RF structure apertures. The RF structures\nare operated on-crest, with a quadrupole spacing of 3.75 m (corresponding to the RF structure length of\n3 m).\naperture corresponding to a/\u03bb = 0.12, a final JA of 1.01 was obtained for 3 m RF structure length. The\nmulti-bunch effects were investigated by imposing a kick from the first to the following bunch, analogous\nto what was done for the e-linac. The results are shown in Fig. 7.23. The RF structure has been designed\nto provide a long-range wakefield corresponding to a maximum kick equal to 0.11 V/pC/m/mm for the\n5 nC bunch charge. This corresponds to a multi-bunch JA of 1.02.\nSingle- and multi-bunch JAs give a total JA of 1.03. This allows a very large transverse jitter\ncoming from the upstream sections to be tolerated. The latter is expected to be much smaller than the\none at the exit of the gun section, because of the damping in the DR (which is expected to reduce the\n312\n\nFig. 7.23: Multi-bunch jitter amplification at the end of the HE-linac.\nincoming jitter), and the kickers in current use (which introduce an angle jitter). Table 7.9 summarises\nthe most important lattice and RF structure parameters determined by the beam dynamics simulations. In\nTable 7.9: Summary of the optimised RF and lattice parameters based on the beam dynamics studies.\nParameter\nValue\nMean RF structure aperture (mm)\n13.9 (a/\u03bb = 0.12)\nRF structure length (m)\n3\nRF structure operating phase\non-crest\nPhase advance/cell (degrees)\n90\nNumber of BPM/RF structure\n1\nNumber of quadrupoles/RF structure\n1\nDistance between the quadrupoles (m)\n3.75\nsummary, the RF structure aperture, length, and lattice of the HE-linac fulfil the specifications determined\nby the transfer line and booster in terms of static and dynamic effects.\n7.6.2\nEnergy compressor\nThe Energy Compressor (EC) [364] at the end of the HE-linac is essential to achieve optimal performance\nalong the HE-linac and, at the same time, the beam parameters required by the transfer line and the\nbooster ring. This kind of system, previously utilised in accelerators such as SuperKEK-B to enhance\npositron capture efficiency in the damping ring (DR), consists of a magnetic chicane followed by RF\nstructures operated at zero-crossing phase. Using the EC presents several advantages:\n\u2013 Possibility to operate the RF structures of the HE-linac on-crest. This is advantageous for the\nmitigation of emittance growth and for accelerating efficiency.\n\u2013 It minimises the single-bunch energy spread due to the RF curvature and the longitudinal short-\nrange wakefields.\n\u2013 It reduces the bunch-to-bunch energy variation due to a very large variation from several nC down\nto nearly 0 nC bunch charge and associated beam loading effects when using a \u2018golden\u2019 RF pulse\nduring top-up mode operation.\n\u2013 It reduces the overall bunch-to-bunch energy jitter.\n\u2013 It manipulates the beam longitudinal phase space to match the booster requirements.\n313\n\nThe EC also has some drawbacks:\n\u2013 It requires more hardware and more space.\n\u2013 It converts energy jitter and offset to arrival time jitter and offset, which must be within the toler-\nance of the downstream sections.\nWhile the transfer line and booster requirements can be met without this system, its absence would lead\nto reduced performance along the HE-linac.\nThe EC may be utilised exclusively for single-bunch effects, as well as for both single- and multi-\nbunch effects. In the first case, the R56 of the chicane and the integrated voltage of the RF structures\nare determined by the target bunch length and energy spread, given the incoming chirp. The simulations\nalso incorporate a residual chirp resulting from compression downstream of the DR, estimated at 0.7%\nfor the 5 nC bunch charge. Table 7.10 summarises the results obtained for a maximum and minimum\ncharge of 5 nC and 5 pC, respectively. In this configuration, increasing the integrated voltage can reduce\nTable 7.10: Parameters of the high energy EC assuming the same machine settings for the maximum\n5 nC and a minimum 5 pC single-bunch charge. \u2018Initial\u2019 indicates that the parameter is computed at the\nentrance of the EC chicane and \u2018final\u2019 at the exit of the downstream RF modules. The voltage is 410 MV.\nParameter\nQ = 5 nC\nQ = 5 pC\nInitial rms bunch length (mm)\n1.00\n1.00\nInitial single bunch \u2206E/E (%)\n0.56\n0.20\nFinal rms bunch length (mm)\n4.00\n1.43\nFinal single bunch \u2206E/E (%)\n0.10\n0.12\nthe single-bunch energy spread by a factor of 3 to 4 while maintaining the bunch length. The booster\ninjection does not currently require this, but it is stressed that the system can, in principle, provide it.\nAlthough bunch-to-bunch beam loading compensation can be managed through a low-level RF\n(LLRF) system, this system must have the capability to modify the RF phase and/or amplitude for each\nof the infinite combinations of bunch charges in the timescale of the bunch separation (presently 25 ns)\nfor four bunches accelerated during the same RF pulse. Ongoing studies are therefore investigating\nwhether the EC fulfils this task by leveraging a single constant golden pulse optimised by the LLRF,\nwhich remains the same for all the possible charge combinations. In this context, the bunch length\nwas identified as a third degree of freedom to fine-tune the single-bunch properties. The bunch length\nselected is 0.8 mm rms instead of the 1 mm assumed so far. This modification is not detrimental to the\nother aspects of the design since a shorter bunch would even be advantageous for static and dynamic\neffects at the price of a slightly increased single-bunch energy spread of 0.05% at the EC entrance.\nLike the previous case, the simulations incorporate the residual chirp resulting from compression\ndownstream of the DR, estimated to be 0.7% for all bunches, and the beam loading effect as a function\nof the bunch charge calculated assuming the golden pulse discussed in this document, see Fig. 7.30.\nThe optimal R56 of the chicane is about 0.55 m and the voltage of the downstream RF structures is\nequal to 620 MV. This corresponds to a total EC length of less than 90 m including matching sections\nupstream and downstream of the chicane, the chicane itself, made of normal conducting dipoles, and\nthree RF modules. Table 7.11 summarises the results for the maximum single-bunch charge of 5 nC. The\nresults of the low-charge scenario simulations without modifying any machine parameters optimised for\nthe high-charge case are shown in Table 7.12. The shorter single-bunch length compared to the higher\ncharge mode appears to be acceptable for the booster, as lower charges are less susceptible to instabilities.\nIn conclusion, the EC enables the operation of the HE-linac at settings optimised for beam dy-\n314\n\nTable 7.11: Parameters of the EC for the maximum 5 nC bunch charge, assuming a target single-bunch\nenergy spread of approximately 0.1%. Bj corresponds to jth bunch along the train. The extra time delay is\ncomputed by subtracting an increasing integer number of RF structures periods. The voltage is 620 MV.\nB1\nB2\nB3\nB4\nInitial rms bunch length (ps)\n0.80\n0.80\n0.80\n0.80\nInitial single bunch \u2206E/E (%)\n0.61\n0.61\n0.61\n0.61\nInitial offset centroid \u2206E/E from B1 (%)\n0\n-0.31\n-0.59\n-0.93\nFinal rms bunch length (mm)\n4.06\n4.07\n4.09\n4.10\nFinal single bunch \u2206E/E (%)\n0.11\n0.11\n0.10\n0.09\nFinal offset centroid \u2206E/E from B1 (%)\n0\n-0.01\n-0.03\n-0.05\nFinal centroid \u2206t from B1 (ps)\n0\n5.7\n11.0\n17.3\nTable 7.12: Parameters of the EC for a 5 pC bunch charge, assuming the machine parameters optimised\nfor the 5 nC bunch charge (RF structures phasing and strength of the dipoles set using the 5 nC bunch as\na reference). The relative energy spread, energy offset, and extra time delay are computed with respect\nto the B1 of the 5 nC bunch charge.\nB1\nB2\nB3\nB4\nInitial rms bunch length (ps)\n0.80\n0.80\n0.80\n0.80\nInitial single bunch \u2206E/E (%)\n0.14\n0.14\n0.14\n0.14\nInitial offset centroid \u2206E/E from B1 at 5 nC (%)\n1.62\n1.97\n2.30\n2.54\nFinal rms bunch length (mm)\n1.04\n1.04\n1.03\n1.03\nFinal single bunch \u2206E/E (%)\n0.13\n0.13\n0.12\n0.12\nFinal offset centroid \u2206E/E reference B1 at 5 nC (%)\n0.14\n0.21\n0.29\n0.36\nFinal centroid \u2206t from B1 at 5 nC (ps)\n-29.0\n-35.2\n-41.0\n-44.9\nnamics and RF structures while ensuring that the target parameters for the downstream lines are matched\nat its output. The energy jitter and offset caused by substantial bunch charge variations ranging from a\nfew nC to nearly zero are converted into time delays and jitter, which are better tolerated by the transfer\nline and the booster ring compared to energy variations. Table 7.13 summarises the expected range of\nparameter variation for the final bunch. Some minor effects, like the variation of the bunch length and the\nTable 7.13: Spread of the beam parameters at the EC exit for the different charges (assuming the same\nbunch charge along the four bunches), and considering the maximum single-bunch variation from 5 nC\ndown to 5 pC. The peak-to-peak values are taken for the B4, which are the maxima.\nInitial\nFinal\nSingle-bunch rms energy spread @ 5 nC (%)\n0.61\n0.103\u00b10.009\nSingle-bunch rms bunch length @ 5 nC (ps)\n0.80\n4.08\u00b10.02\nSingle-bunch rms energy spread @ 5 pC (%)\n0.14\n0.125\u00b10.006\nSingle-bunch rms bunch length @ 5 pC (ps)\n0.80\n1.035\u00b10.006\nPeak-to-peak centroid energy offset variation from 0-5 nC (%)\n\u00b11.74\n\u00b10.21\nPeak-to-peak centroid \u2206t variation from 0-5 nC \u2206t (ps)\n0\n\u00b131\nresidual chirp from the bunch compressor before HE-linac for the 5 pC charge, are presently neglected.\n315\n\nOthers are overestimated, such as the single-bunch beam loading, which is included both in the golden\npulse calculation (solely the fundamental mode) and in the tracking code. Even with these assumptions,\nthe HE-linac and EC design fulfils the requirements of the downstream sections. Further studies are\nunderway to fine-tune the results.\n7.7\nTransfer lines from HE-linac to Booster\n7.7.1\nTransfer line geometry\nThe transfer line geometry has changed significantly between MTR and this report. The transfer lines at\nthe MTR stage passed close to the SPS to allow synergy with hadron transfer lines for FCC-hh and for the\nphysics programme in the SPS. The design suggested here provides a direct connection from the output\nof the HE-linac on the surface at the CERN Pr\u00e9vessin site, see P1 in Fig. 7.24 to the two extremities of\nthe collider tunnel straight section of PA, see P8 and P10, respectively. This design is driven mainly by\ncivil engineering constraints related to scheduling and shaft availability. It also features a symmetric line\ndesign for electrons and positrons, keeping the beam dynamics impact of synchrotron radiation in the\nfinal bending sections equal for both species. The location of the injector complex allows a very efficient\nconnection between HE-linac and the CERN North Area (NA); see beamlines close to P2 in Fig. 7.24. It\nremains to be discussed if a beam transfer in the reverse direction from the booster back to, e.g., the NA\nor a direct line from the HE-linac to the SPS is required and to design the transfer lines accordingly.\nFig. 7.24: Lepton transfer lines from the injector complex on the surface to the collider tunnel.\n7.7.2\nCell design and beam dynamics\nAs shown in Fig. 7.24, the high energy linac to booster transport has been designed with a constant\nnegative vertical slope of \u22123\u25e6in the CERN Coordinate System (CSS), combined with horizontal bending\nin sectors P2-P3, P4-P5, P7-P8 and P9-P10. The slope will be applied and removed at the first and last\ncells of the line, respectively. To maintain it along the line, the local bending plane must be progressively\ntilted following the expressions described in Ref. [365]. Figure 7.25 confirms that such a procedure yields\n316\n\nFig. 7.25: XSUITE survey output and reference trajectory provided by Civil Engineering. The colour bar\nshows the local roll angle \u03c8MADX, which is necessary to maintain a constant vertical slope in the global\nframe.\nthe correct beam trajectory. This twisting reference frame will introduce a coupling between horizontal\nand vertical motion. Skew quadrupoles may be needed to control such a coupling, although they have\nnot been included in this initial iteration.\nAdditionally, the beam transport from the high-energy linac to the booster must be designed to\nstay within the \u2018beam quality\u2019 budget specified in Table 7.14, which will drive the lattice design choices.\nTable 7.14: Summary of Sector Parameters.\nSector\nBunch len. (mm)\nRMS dp/p (10\u22123)\n\u03f5x,N (\u00b5m)\n\u03f5y,N (\u00b5m)\n(...)\nHE Linac\n1\n7.5\n16\n1.6\nE. Compressor\n4\n1.0\n16\n1.6\nTransfer\nTBD\nTBD\nTBD\nTBD\nBooster Inj.\n4\n1\n20\n2\n(...)\nFODO cells have been chosen to design the transfer line due to their simplicity. Later iterations\nmay explore other types of cells, which explicitly aim to minimise the impact of synchrotron radiation\n(such as theoretical-minimum-emittance cells). The chosen phase advance is 135\u00b0 as it is close to the\noptimum for minimising emittance blow-up [366], while remaining an easy number to work with when\ndesigning orthogonal correction schemes. Figure 7.26 shows the horizontal emittance blow-up as a func-\ntion of the cell length and the dipole fill factor for the sectors P2-to-P33 and P6-to-P7 (or equivalently\nP9-to-P10). The required quadrupole gradients, bending fields and apertures are also shown. The aper-\nture required has been calculated with the formula:\nAx,y = n\u03c3 \u2217\nr\n\u03b2x,y \u2217\u03f5norm,x,y\n\u03b3\n+ Dx,y \u2217(2 \u2217\u03b4p\np + \u03b4jitter) + traj \u2217\ns\n\u03b2x,y\n\u03b2max\n+ align\n(7.1)\n3P4-to-P5 has very similar behaviour to P2-to-P3.\n317\n\nFig. 7.26: Horizontal emittance blow-up, bending field, quadrupole gradient and aperture as a function\nof cell half length and dipole fill factor.\nwhere n\u03c3 = 6, \u03f5norm,x/y = 20/2 \u00b5m, the 1\u03c3 momentum spread \u03b4p\np is 0.1% (\u00b12 \u03c3 taken into account and\ndispersion contribution conservatively added linearly). The trajectory variation is assumed to be \u00b12 mm\nat the locations of maximum betatron functions, the momentum jitter \u03b4jitter is assumed to be a maximum\nof \u00b10.3 %, and there are \u00b12 mm taken into account for alignment errors.\nBased on the parametric scans above, two cells have been chosen to build the line: a long FODO\nfor the shared part of the transport (P1-to-P6) and a short FODO for the separate parts of the transport\n(P6-to-P8, P6-to-P10). The latter is required due to the tight bending radius of R = 300 m, which\nleads to significant synchrotron radiation. Table 7.15 lists the parameters for each FODO cell. The 135\u00b0\nphase advance is close to the optimum for minimising emittance blow-up [366], while remaining an easy\nnumber to work with when designing orthogonal correction schemes.\nTable 7.15: FODO cell parameters.\nAttribute\nLong FODO\n(P1-to-P6)\nShort FODO\n(P6-to-P8/P10)\nCell length (m)\n50\n18\nDipole fill factor\n0.5\n0.67\nDipole field (mT)\n130\n330\nDipole length (m)\n6\n6\nDipoles per half cell\n2\n1\nQuadrupole length (m)\n1\n1\nQuadrupole gradient (T/m)\n5\n14\nCell phase advance (deg)\n135\n135\nThe schematics and optics functions for both cell configurations are shown in Fig. 7.27. The\nnumber of magnets required has been documented in Ref. [367]. For the beginning and end of the line,\nthe bending magnets will bend vertically to introduce (and then remove) the -3\u00b0 slope present along the\nentire line descending from the HE-linac to the collider tunnel. In those cells, the dispersion will be\nvertical but similar in amplitude and shape to the one shown in Fig. 7.27. Under such a configuration,\ntracking simulations show that both the dp/p blow-up and the bunch length increase remain under 5%.\nHowever, further investigations might be needed when including matching sections and errors, which\n318\n\nFig. 7.27: Magnet layout and optics for long and short FODOs (quads in orange and dipoles in blue).\nOnly horizontal dispersion is shown, but a similar vertical dispersion is expected for the cells where the\n\u22123 deg. the vertical slope is applied.\nhave not been considered in this report.\n7.7.3\nMagnet technology and technical infrastructure needs\nThe magnet system of the transfer lines is specified in Table 7.16. The constant transfer energy of\n2 0 GeV opens the door to permanent magnet technology, thus both technologies, electro- and permanent\nmagnets were studied and documented in Ref. [368]. It can be concluded that both magnet technologies\nare technically feasible. The installation and running cost for the permanent magnet option is well below\nthe electromagnet option. The technical infrastructure needs are also much reduced, however the transfer\nlines as a whole, contribute less than 10% of the injector complex power requirements. The total power\nrequirements of the transfer lines amount to about 2 MW, compared to about 25 MW for the full injector\ncomplex. The permanent magnet option would require about a factor 10 less power for e.g., corrector\nmagnets and ventilation. Operational flexibility is the main aspect to consider when choosing between\nmagnet technologies. If the are beam stability issues in the booster, a transfer energy increase can be\nbeneficial. On the other hand, if the booster could accept a lower energy beam at injection, reducing\nthe transfer energy reduces the power consumption of the whole injector complex which is driven by\nthe HE-linac. The main field of permanent magnets can be tuned by about \u00b120% by increasing or\ndecreasing a leakage field via mechanical shunts. The shunt modification and subsequent magnetic field\nmeasurement require several weeks. Another argument for operational flexibility is the duty cycle of the\ninjector complex, which varies between 5 and 75% depending on the operation mode. In particular, in the\nlow-duty modes, the injector beam can be used for experiments beyond FCC physics and shot-to-shot\nvariability of beam parameters, including the transfer energy, open the door to a very diverse physics\nprogramme as discussed in Ref. [369]. At this stage, electromagnets have been chosen as the baseline\ntechnology due to the higher operational flexibility for the FCC and any science programme beyond the\nFCC.\n7.8\nRF system for linacs\n7.8.1\nRF accelerating structure\nThe RF design of the accelerating structures FCC injector complex is optimised to deliver efficient beam\nacceleration in all 3 linacs: the electron (e-)linac , the positron (p-)linac and the high-energy (HE)-linac.\n319\n\nTable 7.16: Summary of magnet specifications, assuming polarity switching and the FODO parameters\nfrom Table 7.15. For ease of manufacturing and costing, the 6 m dipoles have been split into 1 m seg-\nments. The number of dipoles quoted refers to the number of 1 m segments.\nUnit\nQuadrupoles\nDipoles\nCorrectors\nTotal number\n338\n286x6=1716\n224\n# magnets in common line\n162\n192x6=1152\n108\nLength\nm\n1\n1\ntbd\nAperture (diameter)\nmm\n30\n30\n30\nGradient\nT/m\n5-15\n-\n-\nField\nmT\n-\n150-400\ntbd\nDeflection\n\u00b5rad\nO(10)\nField homogeneity\nO(10\u22123)\nO(10\u22123)\ntbd\nPolarity switching time\ns\nO(1)\nO(1)\nTable 7.17: Accelerating structure parameters for e-, p- and HE-linacs.\ne-linac\np-linac\nHE-linac\nUnit\nFrequency\n2.8\n2\n2.8\nGHz\nLength\n3\n3\n3\nm\nAverage aperture\n0.15\u03bb\n0.2\u03bb\n0.12\u03bb\nCell aperture: first/last\n17.13/14.99\n30/30\n14.85/10.85\nmm\nIris thickness: first/last\n10.4/13.7\n14.3/20.0\n2.84/4.04\nmm\nVg/c: first/last\n3.14/1.38\n2.58/1.92\n3.92/1.25\n%\nr/Q: first/last\n3.28/3.67\n1.49/1.52\n3.63/4.38\nk\u2126/m\nQ: first/last\n14599/13668\n20977/19102\n16571/16039\nFilling time\n486\n447\n460\nns\nSLED coupling\n15\n17\n15\nRsh,eff (4 bunches)\n81.69\n36\n95.65\nM\u2126/m\nRepetition rate\n100\n100\n100\nHz\nKlystron power per structure\n14.2\n14.2\n14.2\nMW\nAverage power per structure\n3.76\n3.68\n3.72\nkW\nBunch charge\n5\n15\n5\nnC\nAverage loaded gradient (4 bunches)\n19.50\n13.31\n21.06\nMV/m\nEs,max (instant.)\n77\n55\n73\nMV/m\nSc,max (instant.)\n453\n298\n501\nmW/mm2\nWhile each linac has some unique operational parameters, they share several common design features:\nall have a RF structure of total length of 3 m, are configured to accelerate 4 bunches with a separation of\n25 ns, and operate with a repetition rate of 100 Hz. The HE- and e-linacs are designed to operate at a fre-\nquency of 2.8 GHz, with a bunch charge of 5 nC, while the p-linac operates at a lower frequency of 2 GHz\nto accommodate its higher bunch charge of 15 nC. This difference reflects the tailored optimisation of\neach linac to the specific beam dynamics requirements described above. The RF structures have tapered\ngeometries, which effectively balance beam transport with short- and long-range wakefield suppression\nrequirements, Wt < 0.1 V/pC/mm/m and a value specific to each linac of < a > /\u03bb. The detailed\nparameters and design specifications for all three linacs are summarised in Table 7.17. Similar design\nprinciples are applied to all 3 linacs, providing a uniform and scalable approach across all structures. The\nRF design of the HE-linac, is described as an example, in detail below.\nThe parametric sweep of iris aperture and thickness was utilised to identify structures that satisfy\nthe long-range transverse wakefield constraint Wt < 0.1 V/pC/mm/m for a given < a > /\u03bb = 0.12\n320\n\nrelated to the short-range wakefields, ensuring stable beam propagation. The long-range transverse\nwakefields were calculated using a lookup table, which employs frequency-domain parameters of the\n20 lowest higher-order modes (HOMs).\nTo achieve more realistic and accurate wakefield predictions and to benchmark the lookup table\ncalculations, the ECHO2D time-domain solver was used for the structure of the final choice. This\napproach is more accurate, accounting for an infinite number of HOMs and the coupling between cells.\nThe envelope-of-the-envelope approach was applied to the wakefield data from both ECHO2D and the\nlookup table to rigorously assess worst-case scenarios and long-range wakefield effects. The results are\nshown in Fig. 7.28.\nFig. 7.28: : Envelope-of-the-envelope of transverse wakefield potentials for the HE-linac structure, cal-\nculated over time using both the lookup table and ECHO2D methods\nIn the design of travelling wave accelerating structures, minimising bunch-to-bunch energy spread\nis a critical objective for ensuring high beam quality and stable accelerator performance. In operation\nduring the collider filling with nominal bunch charge, the input RF power pulse shape is optimised to\nminimise bunch-to-bunch energy spread, taking into account the beam loading effect. As shown in\nthe red trace in Fig. 7.29, the input RF power is modulated using a step-like amplitude modulation. This\napproach ensures a constant average loaded gradient for all four bunches. The gradients for unloaded and\nloaded conditions are represented by the blue and orange traces, respectively. The four red dots indicate\nthe temporal positions of the bunches. In Fig. 7.30(a), the unloaded and loaded gradients are shown in\nmore detail for comparison near the position of the 4 bunches, showing a maximum energy difference\nof 2.4% between unloaded and loaded gradients on the fourth bunch, highlighting the beam loading\neffect in HE-linac. However, in top-up operation, where bunch charges vary from 0 to 100% among the\nfour bunches, a single optimal input RF pulse must accommodate both extremes. The \u2018golden pulse\u2019\n321\n\nis introduced to address this by averaging the optimised RF pulses for unloaded and loaded voltages.\nWhile it does not individually minimise energy variation to \u223c0-level, it provides a balanced compromise,\nreducing energy spread across all possible charge variations. Figure 7.30(b) demonstrates the golden\npulse in top-up operation, reducing energy spread to +1.1% and -1.1% for unloaded (4 bunches at 0\nbunch charge, small red dots) and loaded cases (4 bunches at nominal intensity of 5 nC, large red dots),\nrespectively. This result underscores the golden pulse\u2019s ability to balance energy spread across bunches,\nensuring stable performance even under varying charge conditions in top-up mode.\nFig. 7.29: Input RF power and average gradients versus time.\n(a) Nominal charge condition.\n(b) Top-up operation.\nFig. 7.30: Bunch-to-bunch energy minimisation for the nominal bunch charge (a) and top-up operation\n(b).\n7.8.2\nRF module and RF power\nEach RF module of the electron and high-energy linacs consists of one high voltage modulator (HV),\none klystron operating at 2806 MHz, one pulse compressor (Barrel-Open Cavity or SLED type) and four\naccelerating structures with one quadrupole, one corrector magnet and one BPM between each structure.\nIts total length is 15 m. The choice of an RF module consisting of four structures results from cost and\npower consumption optimisation. Figure 7.31 shows the schematic layout of such an RF module.\nThe positron linac has two types of RF modules. The first type equips the end part of the capture\nlinac and the S1 linac. It is about 13 m long, since instead of 4 quadrupoles, it has 40 solenoids, i.e.,\n10 solenoids per structure for beam focusing. A schematic layout of this type of module is shown in\n322\n\nFig. 7.31: Schematic layout of an RF module for the electron, S2 positron and high-energy linacs.\nFig. 7.32: Schematic layout of the RF module for the positron capture and S1 linacs.\nFig. 7.32. The second type of RF module in the p-linac is similar to the electron and high-energy linac\nmodule (see Fig. 7.31). The klystron operates at 2004 MHz in the p-linac.\nFor the electron and the high-energy linacs, the peak power specification of each klystron is\n80 MW. Its repetition rate and RF pulse length are 100 Hz and 3 \u00b5s, respectively. For the positron linac,\nthe power specification of the klystron and its repetition rate are also 80 MW and 100 Hz, respectively,\nbut its RF pulse length is 5 \u00b5s. Although no klystron exists at the specific frequencies of 2806 MHz\nand 2004 MHz, many klystrons have demonstrated reliable performance at 2856 MHz with such a power\nspecification and RF pulse length. The development of a conventional klystron at 2806 MHz with a\n100 Hz repetition rate is straightforward by retuning its cavities and redesigning its collector. As for the\ndesign of a 2004 MHz klystron with such specifications, it would be a completely new development but\npresents no technical challenges. Several companies have indeed been contacted to assess the feasibility\nof such conventional klystrons and confirmed that such specifications are achievable. The RF efficiency\nof such klystrons would be 42%. Their parameters are summarised in Table 7.18.\nBoth types of klystron operate at 80% of their peak power specification, i.e., at 64 MW. For the\nelectron and high-energy linacs, it is assumed that the RF waveguide system comprises S-band WR284\nwaveguides and is 25 m long. Taking into account the waveguide losses, the klystron power per structure\n323\n\nTable 7.18: Klystron parameters.\nLinac\nFreq.\nPeak power\nspecification\nRep.\nrate\nRF pulse\nlength\nDuty\nfactor\nAverage\npower\nNumber\nrequired\n[MHz]\n[MW]\n[Hz]\n[\u00b5s]\n[10\u22123]\n[kW]\ne-Linac\n2806\n80\n100\n3\n0.3\n24\n15\np-Linac\n2004\n80\n100\n5\n0.5\n40\n21\nHE-Linac\n2806\n80\n100\n3\n0.3\n24\n72\nis then 14.2 MW before pulse compression. For the positron linac, the RF waveguide system comprises\nthe less lossy L-band WR510 waveguides. With a 25 m long waveguide system, the klystron power per\nstructure is 15.4 MW before pulse compression. The specifications of each RF module for all linacs are\nsummarised in Table 7.19.\nTable 7.19: RF module summary table for the injector linacs.\ne-Linac\np-Linac\nHE-Linac\nUnit\nRF frequency\n2.8\n2.0\n2.8\nGHz\nRepetition rate\n100\n100\n100\nHz\nModulator max. peak power\n190\n190\n190\nMW\nModulator max. average power\n114\n152\n114\nkW\nKlystron max. RF power\n80\n80\n80\nMW\nKlystron RF pulse length\n3\n5\n3\n\u00b5s\nStructures per klystron\n4\n4\n4\nKlystron power per structure\n14.2\n15.4\n14.2\nMW\nAverage loaded gradient\n19.5\n13.3\n21.1\nMV/m\nNumber of rf modules\n1+14\n1+6+14\n72\nModule Length\n15\n13, 14.8\n15\nm\nLength of all modules\n215\n304\n1080\nm\nIn recent years, research and development have been conducted on pulsed high-efficiency klystrons,\nand it is conceivable that more of these klystrons will be available in the near future. A comparison of\nthe plug power consumption for all linacs assuming 42% and 70% klystron efficiencies is shown in Table\n7.20. The advantage of operating with high-efficiency klystrons is remarkable for the electron and high-\nenergy linacs but less so for the positron linac since the power consumption of the structure solenoids in\nthe capture and S1 linacs is a substantial fraction of the positron linac total power consumption.\nTable 7.20: Comparison of the plug power consumption for the injector linacs assuming 42 % or 70 %\nklystron efficiencies.\nLinac\nPlug power [MW]\nKlystron efficiency [%]\n42\n70\ne-Linac\n2\n1.2\np-Linac\n8\n6.5\nHE-Linac\n9.5\n6\n7.9\nAvailability\nThis section details results from the enhanced Monte Carlo simulation environment for FCC-ee avail-\nability described in Section 2.4, focusing on systems specific to the injector complex.\n324\n\n7.9.1\nContributing Systems\nFor availability modelling, the injector chain is divided into two top-level accelerators. The statistical\nfailure rate and blocking duration from subsystems in each accelerator are taken from two representative\nmachines with similar performance characteristics. These are simulated in the injector complex of the\nFCC-ee to gauge the effect of equivalent availability on global physics performance.\n1. Lower Energy Injectors: The electron and positron source, linac and damping ring up to an\nenergy 2.86 GeV are modelled from fault data from the SuperKEK-B e\u2212/e+ source, injector linac\nand damping ring between 1998-2023, detailed in Ref. [370].\n2. High Energy (HE) Linac: with an energy up to 20 GeV is modelled using fault data from the\nLinac Coherent Light Source (LCLS) at SLAC [371].\nSubsystems within each accelerator have been re-categorised for illustration to preserve naming con-\nventions in the CERN complex. These include the relevant supporting technical infrastructure for each\naccelerator. Only faults leading to downtime in each accelerator were considered, thereby assuming a\nsimilar degree of redundancy in the FCC-ee as exists in practice for each representative subsystem.\n7.9.2\nInherent resilience to shorter fault types\nIn the event of an outage in the booster and injector complex, stable beams can be maintained in the\nmain collider rings for a lifetime of 10-15 minutes, depending on energy mode (see Table 2.2). If top-up\ninjection can be restored in this time, normal physics can resume. This significantly reduces the FCC-\nee\u2019s sensitivity to short-duration fault types in the injector complex and leads to an inherent advantage\nin availability. The contribution for lost luminosity of subsystems in the injector complex is therefore\nbiased towards those with longer-duration fault types.\n7.9.3\nResults\nThe overall contribution to downtime of each accelerator in the injector complex is compared with the\nbooster systems in Fig. 5.14. The lost luminosity contributions in the Z mode from the low energy\ninjectors and HE linac are significant, second only to the booster RF system. The availability of the\ninjector complex will be a challenge for overall FCC-ee performance.\nLower Energy Injectors\nThe contribution to unavailability and lost luminosity from each subsystem in the low energy injectors\nis shown in Fig. 7.33. These only contribute to downtime, as there is high redundancy in the relevant\nsystems, meaning that faults generally block the beam for only short durations. The majority of faults\nare due to RF breakdowns, which have a large contribution to lost luminosity in Z and W modes due to\nthe lengthy turnaround time needed to recover from dumps.\nHigh Energy (HE) Linac\nThe contribution to unavailability and lost luminosity from systems in the HE linac are shown in Fig-\nure 7.34.\nRF breakdowns are again the most problematic, representing contributions from S-band\nklystrons, high-power sub-boosters, waveguides and modulators. The control system is also a high\ncontributor, composed of micros and CAMAC crates as well as the MCC/VMS computing and tim-\ning systems. The access system is represented by the personnel protection system (PPS). Contribution\nfrom the gun laser system is also significant.\n325\n\nFig. 7.33: FCC-ee unavailability and lost luminosity contribution of the low energy injectors (up to\n6 GeV) determined by applying fault statistics from equivalent equipment at SuperKEK-B [370]. Sys-\ntems are ordered according to Z mode lost luminosity contribution.\nFig. 7.34: FCC-ee unavailability and lost luminosity contribution of the HE Linac determined by apply-\ning fault statistics from the Linac Coherent Light Source (LCLS) at SLAC [371]. Systems are ordered\naccording to Z mode lost luminosity contribution.\n7.9.4\nR&D Opportunities\nOpportunities exist for exploiting the injector complex\u2019s natural resilience to shorter fault types. If a\nfailed component can be brought back online before the beams in the main collider expire, a lengthy\nturnaround time may be avoided. This mirrors the opportunities already discussed for the booster in\nSection 5.3.4.\nThe short beam lifetime is especially significant for Z mode operation, where the charge imbalance\nbetween electron and positron beams in the collider must be less than 5%. Assuming a lifetime of 10-\n15 minutes, the injection of electrons and positrons must alternate for top-up every 50 seconds. This\n326\n\nplaces significant design constraints on the injector hardware and has profound implications for reliability\nand availability, as even short interruptions could impact the collider\u2019s performance. This requirement\nlimits the breakdown (BD) rate in the injector\u2019s accelerating structures. The time required to bring an\naccelerating structure back into operation after a BD is on the order of a minute. This poses a problem\nwith the injector\u2019s availability. An analysis of BDs in the SwissFEL linac is conducted in Ref. [372].\nDuring regular user operation, the RF modules failure rate began to reduce thanks to RF conditioning\nincidental to nominal operation. This incidental conditioning followed a power law trend that saw the\nBD rate decrease by over three orders of magnitude in the first three years of user operation, from 10\u22126\nto less than 10\u22129 BD per pulse per metre or about two BD per day in the entire linac. Nonetheless, RF\nBDs continue to account for about half of all broken interlocks in SwissFEL.\nGiven the number of RF structures planned for the FCC injector and scaling, the results obtained\nfor SwissFEL, translate into a reduction of the BD rate from about 850 events per day to about eight\nevents per day after the first four years of operation. The proposed solution, which is to be further\ninvestigated, to mitigate these events is to use some additional RF modules during these BD events. The\nlow probability of having more than two events simultaneously led to the adoption of one additional RF\nmodule for the positron and electron linacs and two additional RF modules in the HE linac. Thanks to\nthis approach, the injector\u2019s availability due to the BDs could be greater than 99% after a few years of\noperation.\n7.10\nCivil engineering\n7.10.1\nInjector complex\nThe preferred location for the FCC-ee injector complex is on the existing CERN Pr\u00e9vessin site. Several\noptions for the location of the high-energy linac were explored, with the preferred choice being near the\nnorthwest edge of the Pr\u00e9vessin site. A more detailed placement study considering also environmental\naspects will be performed in the next phase before confirming the location. The envisaged layout of the\nfacility is shown in Fig. 7.35.\nFig. 7.35: Plan view of high energy linac civil engineering.\nThe civil engineering for the high-energy linac will consist of four main elements, namely: the\nhigh-energy linac tunnel, the associated e+ and e\u2212tunnels, the damping ring and the transfer tunnel-\ns/structures to connect the damping ring to the rest of the facility. All these structures will consist of\n327\n\nreinforced concrete buried structures extending over a length of about 1.2 km. For shielding purposes,\nthese structures will be built in a series of trenches up to 15 m below the ground level. These so-called\n\u2018cut-and-cover\u2019 tunnels will be backfilled using the excavated material from the trench formation, and\nthen a surface hall will be constructed above the tunnels. A series of 6 m long vertical mini-shafts of about\n0.8 m diameter will connect the tunnels to the surface hall for connecting the klystrons and to allow for\nthe passage of services and cables. A schematic section of this arrangement is shown in Fig. 7.36.\nFig. 7.36: Cross-section of high energy linac civil engineering.\nCompared to the other options studied for the high energy linac, the preferred site has a number of\nsignificant advantages including:\n\u2013 The proposed location is quite flat with a total difference in ground level along the length of the\nHE-linac of about 5 m\n\u2013 The proposed location has minimal existing infrastructure. A small number of underground net-\nworks will need to be rerouted before construction, and two or three older structures on the\nPr\u00e9vessin site will be carefully dismantled or relocated as needed.\n\u2013 The location and orientation are well suited for a potential future connection of beam lines to the\nNorth Area of Pr\u00e9vessin, where fixed-target physics research is conducted.\n7.10.2\nTransfer Tunnel\nThe beam lines from the high energy linac will be connected to the FCC main accelerator tunnel through\na transfer tunnel. This transfer tunnel will consist of a single tunnel of internal diameter 3 m and total\nlength of 5 560 m. As this tunnel approaches PA of the FCC, the tunnel will bifurcate to provide a clock-\nwise and anti-clockwise link to the FCC. These two link tunnels will be symmetrical and each 747 m in\nlength. This arrangement is shown schematically in Fig. 7.37 and a plan view is given in Fig. 7.38.\nThe main characteristics of the transfer tunnel are:\n\u2013 Three horizontal curves with a minimum radius of 300 m are required\n\u2013 The tunnel will have a slope of 4.9%.\n328\n\nFig. 7.37: Schematic view of transfer tunnels.\n\u2013 Connection of the tunnel to the high energy linac will be made on the CERN Pr\u00e9vessin site at the\nend of the high energy linac.\n\u2013 Connections to the FCC main tunnel would be created with 0.8 m diameter drilled horizontal pas-\nsage for the clockwise and anti-clockwise beam lines. A small personnel access connection would\nalso be created between the FCC and transfer tunnels for emergency access and ventilation. These\nconnections would be constructed in the widened section of the accelerator tunnel either side of\nPA, where the span of the accelerator tunnel is 14.5 m.\n\u2013 A temporary shaft located within the existing Pr\u00e9vessin site would be built to provide access for\nthe construction of the transfer tunnel. This shaft would have a depth of 30 m and an internal\ndiameter of about 10 m to suit the contractor\u2019s plant and equipment. The shaft may not be needed\nfor the operation of the FCC. The transfer tunnel will be excavated from this shaft using either a\ntunnel boring machine or roadheader or a combination of the two.\n\u2013 A junction cavern of 30 m length and 9 m span will be necessary to accommodate the bifurcation\nof the tunnel for the clockwise and anti-clockwise injection into the FCC machine.\nGeological conditions for tunnelling this small-diameter tunnel are expected to be favourable,\nwith molasse strata serving as the tunnelling medium from the access shaft down to the FCC accelerator\ntunnel. The connections to the FCC tunnel will be made at a depth of approximately 200 m below ground\nlevel. Additional confidence in the feasibility of construction comes from CERN\u2019s extensive experience\nin underground civil engineering projects in this region, including the SPS, LHC, and CNGS, all of\nwhich were successfully constructed in the same general area. If a tunnel boring machine (TBM) is used\nfor excavation, reinforced concrete segments will likely be employed for support, similar to the main\nFCC accelerator tunnel. Alternatively, if a roadheader is used, a two-phase approach will be followed for\ntunnel support, consisting of an initial lining with rock bolts and shotcrete, followed by a secondary cast\nin-situ reinforced concrete lining.\n7.11\nTechnical infrastructure\nThe new injector complex will be integrated in CERN\u2019s Pr\u00e9vessin site, requiring additional energy\nand services. Initially constructed for the SPS accelerator and its fixed-target physics programme, the\nPr\u00e9vessin site hosts the SPS North Area and serves as a critical hub for CERN\u2019s technical infrastruc-\nture. This includes the 400 kV power lines from RTE (France\u2019s Transmission System Operator) that\n329\n\nFig. 7.38: Plan view of transfer tunnels.\nsupply power to the entire CERN complex, the CERN Control Centre (CCC) responsible for operating\nall CERN accelerators, the new data centre, and the Ethernet backbone hub. These infrastructures are\nregularly upgraded to support the evolving demands of CERN\u2019s programmes. The new injector complex\nwill become a significant addition to the existing layout. The injector complex consists of five main areas:\nthe e-linac, the p-linac, the damping ring, the HE-linac, and the transfer line to the booster. Each area\nincludes an accelerator tunnel and its associated surface building. Dedicated technical infrastructures\nwill be established to meet the needs of these areas, which can operate independently. For electricity\nand cooling, there will be a shared infrastructure. A new electrical substation will connect to the existing\nmain substation to supply power to the complex. Cooling towers, grouped in a dedicated building near\nthe end of the HE linac, will dissipate heat generated by the five areas. Each area will also have its own\nventilation systems.\nThe tunnels will house accelerator system components such as RF cavities, magnets, instrumenta-\ntion, and beam pipes. The surface buildings will accommodate RF klystrons, high voltage modulators,\nmagnet power supplies, vacuum control systems, and beam instrumentation electronics. These buildings\nwill require power distribution, water cooling, ventilation, control systems, and safety features such as\nfire detection and alarm systems. Services like electricity, cooling, and control will be distributed from\nthe tunnels to the surface buildings.\nAdditional technical infrastructures will support the complex, including access systems, smoke\nextraction, environmental monitoring, radiation protection systems, handling and transport systems, and\ncommunication systems. These systems will be integrated into the surface buildings above the tunnels.\nThe injector complex can be operated remotely from the existing CERN Control Centre. The estimated\nmain accelerator electrical loads for the injector complex are presented in Table 7.21. In addition to the\nmain loads, the power demand of the other systems is presented in Table 7.22. The injector complex will\n330\n\nTable 7.21: Main electrical loads from the accelerators of the injector complex.\nAccelerator loads\nArea\nPower rating\nRF\ne-linac\n2 MW\nRF\np-linac\n4 MW\nMagnets\np-linac\n4 MW\nRF\nHE-linac\n9.5 MW\nMagnets\nDamping ring\n2.5-4 MW\nMagnets\nTransfer line\n2 MW\nTotal\n24-25.5 MW\nTable 7.22: Additional loads of the injector complex.\nOther loads\nTypes\nPower rating\nAccelerator systems\nAuxiliary magnets, vacuum,\ninstrumentation, control...\n2 MW\nGeneral services\nAC plugs, lighting,safety\nsystems...\n2 MW\nCooling and ventilation\nPumps, motors, fan coils...\n3 MW\nTotal\n7 MW\nrequire a main electrical substation with a capacity of 40 MVA, and its annual energy consumption is\nestimated at 150 GWh. The cooling towers will have a capacity of approximately 25 MW, with an annual\nwater consumption of 200 000 m3. This water will be sourced from the existing distribution system,\nwhich uses water from Lake Geneva. From a technical infrastructure perspective, integrating the injector\ncomplex into the Pr\u00e9vessin site is feasible without affecting SPS operations.\n7.12\nOngoing studies and possible upgrades\nAs the study advances there is strong support from Switzerland and PSI to continue and strengthen the\nCHART collaboration. The injector project team, consisting of PSI and CERN members and external\npartners, is preparing a comprehensive proposal to be included in the CHART programme for the finan-\ncial period 2025-2028, complete with detailed resource and cost estimates, which should be completed\nin early 2025. In the next phase, several critical areas will require focused attention. The updated base-\nline design includes a 2.86 GeV damping ring, which must be integrated into the forthcoming technical\ndesign study.\nThe current baseline design assumes an RF frequency in the linacs compatible with the main rings\nto retain operational flexibility. However, the limited availability of suitable power sources on the market\npresents a challenge, prompting efforts to adopt a commercial S-band frequency for the RF system in\nthe linacs. Additionally, the positron linac will undergo optimisation to shift from the current 2 GHz\nsetup to a more widely available S-band frequency. Reliability and availability of the injector complex\nwill be key factors in the injector\u2019s design, particularly for continuous \u2018top-up\u2019 operation, which requires\na low-gradient injector configuration with an experimentally validated RF breakdown rate. Assessing\nthe impact of short interruptions caused by RF breakdowns in top-up operations will also be critical for\nensuring stable performance.\nThe involvement of international partners will remain crucial as the injector study progresses to-\n331\n\nwards the technical design and construction stages. A comprehensive technical design report could fol-\nlow the feasibility study phase, building on the SwissFEL linac technology for RF accelerating structures\nand related upgrade projects. This report will also benefit from the expertise of international partners who\nhave experience in synchrotron light and positron source operations. Its primary objective will be to es-\ntablish detailed specifications for the accelerator and technical infrastructure requirements necessary to\ninitiate civil engineering design. These specifications will ensure that all system and subsystem require-\nments are addressed, making the initial construction phase and mass production of critical components\nsmoother.\nA comprehensive TDR for the accelerator and the associated technical infrastructure will be com-\npleted should the project move to its next phase. This will be pivotal, enabling further engineering design\nefforts and finalising all necessary specifications for civil engineering work. This phase is essential to\nconfirm that all design elements undergo rigorous examination and are fully integrated into the project,\nensuring a seamless transition to the construction phase. A prototyping phase will be critical in this\ncontext. During this phase, RF accelerator structures will undergo exhaustive testing to validate their\nperformance and reliability. Additionally, based on a photo-cathode RF gun, the electron source con-\ncept will be demonstrated to support top-up operation for injection into the collider ring reliably. This\ndemonstration is essential to confirm that the chosen technology can meet operational requirements and\nintegrate smoothly into the overall system.\nFurthermore, the P3 positron production experiment at PSI will be completed and commissioned,\nwith subsequent development focusing on a hybrid scheme expected to reduce the power dissipated\non the target while keeping the efficiency of positron production. This development phase will refine\nthe specifications for the positron source, ensuring that all components meet the operational criteria for\nintegration into the injector complex.\n332\n\nChapter 8\nTechnical infrastructure for FCCs\n8.1\nRequirements and design considerations\nThe infrastructure requirements and the proposed technical solutions for FCC-ee have been defined for\nthe PA31-1.0 layout, which, as described above, features eight points with associated surface areas. Four\nof the points are experiment points, and four are technical points. The technical infrastructure systems\ndescribed here are electricity and energy management, cooling and ventilation, integration, geodesy and\nsurvey, cryogenic systems, transport and logistics, and computing infrastructures and robotics. The\npresent study focuses on the technical infrastructure related to FCC-ee, but wherever design choices\nare made which may impact FCC-hh (in particular, the space requirements and dimensions), constraints\nfrom and possible synergies with the hadron collider are taken into account.\n8.1.1\nAssignment of points\nFour of the eight FCC points are designated for experiments: PA, PD, PG, and PJ. Among these, PA and\nPG are considered as large experimental areas for FCC-hh, whereas PD and PJ are optional sites that\nmay accommodate smaller hadron collider detectors requiring less infrastructure. All four points can\naccommodate the much smaller experiments of the FCC-ee collider.\nThe remaining four points are technical. Point PB, the only one located in Switzerland, has been\nchosen to house the beam dump system. Points PL and PH have been selected to house the booster and\ncollider RF, respectively. Point PF was found less appropriate to house the RF due to difficult access\nconditions (the access shaft is displaced laterally w.r.t. the FCC ring by several hundred metres) [373],\nbut it could house the collimation system.\nThe assignment of points PL and PH was made based on constraints from accelerator physics\n(preference to concentrate the collider RF in one point only), constraints at the surface areas and infras-\ntructure constraints (accessibility, resources, electrical network connection and powering). Since point\nPL features a relatively complicated surface site with many constraints, it was decided to install the\nbooster RF 800 MHz cryomodules at this point. The Booster RF requires much less infrastructure than\nthe collider RF and can more easily be integrated. Point PH was designed to house the collider RF (400\nand 800 MHz cryomodules), which requires substantial infrastructure.\n8.1.2\nElectricity supply\nElectrical power will be provided by the French network and fed into the FCC at three points (PA, PH,\nand PD). Further distribution is then accomplished via the FCC tunnel. The electrical infrastructure is\ndesigned to support all FCC-ee configurations seamlessly, eliminating the need for additional substations\nbetween different operational stages. The proposed setup also includes the possibility of operating the\nmachine without one sub-station (PA or PD). The PH substation, which has the main RF loads (200 MW),\nis mandatory for beam operation. This setup will ease the maintenance and repairs as all substations will\nbe connected together through the HV network. RTE (R\u00e9seau de Transport d\u2019\u00c9lectricit\u00e9) has launched a\nstudy on how to connect the FCC to the French network. The requirements of the FCC project are not\nconsidered significant by RTE, and will not impact the French electrical network operation.\n333\n\n8.1.3\nCooling and ventilation\nThe potential sources of cooling water in the area are lake Geneva and the Rh\u00f4ne and Arve rivers. As\na baseline, the required cooling water will be taken from Lake Geneva via the existing infrastructure,\nwhich has enough capacity to supply the FCC. Pipework within the tunnel will connect the remaining\npoints to PA, PD, or PJ to ensure their respective water supply. The drainage flow rates, corresponds to\naround 30 m3/h in the RF points and a maximum of 11 m3/h in the remaining points.\nA semi-transverse ventilation scheme has been adopted for the FCC tunnel, with air supplied\nthrough a dedicated duct running along the entire sector and extracted either via the tunnel itself or\nthrough an emergency extraction duct. To ensure continuous airflow in case of a duct failure, air is\nsupplied to each sector from both endpoints, with the same configuration adopted for the extraction\nsystem.\n8.1.4\nCryogenic systems\nThe cryogenic system design of FCC-ee follows the requirements of the superconducting devices, which\nare distributed throughout the machine. Whilst the technical points PB and PF do not feature any cryo-\ngenic needs, the technical points PH and PL are associated with the radiofrequency (RF) system, which\nneeds to be operated at 2 K and at 4.5 K. These RF points have the largest cryogenic installations due\nto their high concentration of heat loads. Additionally, each experiment point \u2013 PA, PD, PG, and PJ \u2013\nrequires a dedicated cryoplant to support the cooling needs of the detector magnet and the magnets in the\nmachine detector interface (MDI) region.\n8.1.5\nTransport and logistics\nIn the first phase of the analysis, an inventory was established detailing the type, quantity, dimensions,\nand weight of the components to be transported. Simultaneously, the number of personnel requiring\ntransport to their workplace in the tunnel was determined, and evacuation studies were conducted.\nBased on these input data, two vehicle concepts have been studied: the first for the transport of the\nequipment, including the accelerator components, and a second for the transport of personnel throughout\nthe installation, operation and dismantling phases.\nThe vehicle for transporting materials will be electric, fed by batteries. Charging stations will be\ninstalled all along the tunnel. The design comprises a trailer carrying the material, pulled by a tractor\nhosting the batteries. The trailer is equipped with two robotic arms capable of handling and manoeuvring\nthe components up to their final location.\nAs the market already offers valid solutions, the personnel vehicle will be based on an existing\nsystem. This will then be customised to meet the specific requirements and constraints of the FCC\ntunnel. The personnel vehicles will be electric and powered by batteries. The personnel transport will\nconsist of a mixture of individual and scheduled transport systems. Its characteristics will be defined to\nguarantee the evacuation of the people present in a sector at a safe time.\nFor safety reasons, vehicle overtaking needs to be possible at any location in the tunnel, putting a\nconstraint on the width of the vehicles.\nIn addition to technical solutions for material and personnel transport, a logistics study is being\nconducted. This study develops logistics scenarios based on various boundary conditions, such as the\nnumber of shafts available for material transfer and the number of vehicles used for underground trans-\nport.\nFor each scenario, key performance indicators (KPIs) are generated, including the number of\nmagnets that can be installed per day and the total installation time required for the accelerator. Potential\nbottlenecks in material flow are also identified. These indicators serve as an objective tool for evaluating\nand comparing different scenarios, enabling the selection of the most suitable approach for the overall\n334\n\nproject.\n8.1.6\nGeodesy\nThe size of the FCC requires a refined and extended geodetic infrastructure, including reference frames\nand a gravity field model. The geodetic infrastructure must be compatible with each phase of the project.\nThis comprises the generation of a primary surface geodetic network. To this end, Swisstopo and IGN\nare increasing the density of their national geodetic networks. In order to meet the vertical alignment\naccuracy, a refined model of the gravity field is being prepared.\n8.1.7\nCommunications, computing and data services\nThree different infrastructures will be deployed to enable data, telephone and radio networks. They are\nall built on top of a fibre optics infrastructure. Regarding the IT infrastructure, the FCC will feature two\nredundant data centres on the Meyrin and Pr\u00e9vessin sites.\n8.1.8\nSurface areas\nBased on the design choices above, and input from the infrastructure and equipment groups, the needs\nfor infrastructure and buildings at the eight surface points have been compiled. The tables summarise\nthe key elements (element, location, construction type, size, capacity) by domain (safety, electricity,\nand energy management, cooling and ventilation, geodesy and survey, cryogenic systems, transport and\nlogistics, computing infrastructures). The contents of these inventory tables are the basis for the layout\nof the surface points [374].\n8.1.9\nUnderground areas\nIntegration of the underground areas, including the tunnel, main caverns and service caverns, shafts and\nalcoves, has been performed. Equipment sensitive to radiation will be placed in alcoves. There are seven\nalcoves per arc. The alcoves are linked to transport lay-by zones, which allow transport vehicles to park,\npass and overtake each other.\nIn addition to the alcoves, there are service caverns at the eight points. The current civil engi-\nneering design for the service caverns at technical areas is 60 m long, 25 m wide and 15 m high. These\ncaverns will each be divided into three levels to provide additional floor area on the upper levels. The\nservice caverns are mainly occupied by power supplies, cooling and ventilation equipment as well as\ncryogenics equipment.\n8.2\n3D Integration Studies\nThe 3D integration studies of the FCC-ee have been detailed for all the areas of the underground tun-\nnels and caverns, fitting the requirements from the work packages (e.g., civil engineering, infrastructure,\ngeneral services, transport, safety, optics, accelerators requirement, etc.). This section presents the re-\nsults of the configuration and layout of the accelerators and infrastructure systems that were studied for\nthe feasibility study report. This is an evolution of the previous studies made for the conceptual design\nreport. [13,307]. The 3D integration studies take into account the configurations of both the FCC-ee and\nthe FCC-hh to ensure space compatibility.\n8.2.1\nGeneral layout of the FCC\nThe FCC is a 90.6 km circumference tunnel including eight access points equally spaced above the accel-\nerator tunnel and currently named as point PA, PB, PD, PF, PG, PH, PJ and PL (see Fig. 8.1). The points\nPA, PD, PG and PJ will host the detectors in dedicated civil engineering areas. They are mentioned as\n335\n\nlarge experiment points for points PA and PG and small experiment points for points PD and PJ. The\npoints PB, PF, PH and PL are mentioned as technical points hosting different accelerators part.\nFig. 8.1: FCC-ee schematic view\nFor the FCC-ee machine,\n\u2013 The point PB will host the extraction system from the booster, transfer line and injection system\nto the collider, and the extraction systems and transfer lines to the dumps for both the collider and\nthe booster,\n\u2013 The point PF will host the collimation systems (betatron and momentum),\n\u2013 The point PH will host the collider RF system,\n\u2013 The point PL will host the booster RF system.\nFor the FCC-hh machine,\n\u2013 The point PB will host the collider injection lines and the extraction lines to the dumps,\n\u2013 The point PF will host the betatron collimation system,\n\u2013 The point PH will host the momentum collimation system,\n\u2013 The point PL will host the RF system.\n8.2.2\nIntegration of point PA and point PG\nPoint PA and point PG will serve as large experiment points, hosting detectors in the cavern in both the\nFCC-ee and the FCC-hh phases of operation. The cavern size and extent meet the needs of the detectors\nfor both FCC-ee and FCC-hh. In addition, for the FCC-ee, the long straight sections (LSS) on either side\n336\n\nof point PA and point PG will host the beamstrahlung dumps and the polarimeter system (see Fig. 8.2\nand Fig. 8.3). The LSS of point PA will also host the end of the transfer line from the injector linac, into\nthe booster.\nIP-A\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n438.5\n20\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 8.2: FCC underground - civil engineering in point PA.\nIP-G\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\n156.8\n10\n160\n5\n135\n5\n5 20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n438.5\n20\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 8.3: FCC underground - civil engineering in point PG.\nThe figures included in this section are the results of the 3D integration studies for the point PA\nand the point PG.\nFig. 8.4: FCC-ee point PA and point PG - general overview.\nFig. 8.5: FCC-ee point PA - top overview with optics.\n337\n\nFig. 8.6: FCC-ee point PA - experiment cavern cross-section.\nFig. 8.7: FCC-ee point PA - experiment cavern iso view.\n338\n\nFig. 8.8: FCC-ee point PA - shaft of the experiment cavern.\nFig. 8.9: FCC-ee point PA - shaft of the service cavern.\n339\n\nFig. 8.10: FCC-ee point PA - tunnel cross-section with booster.\nFig. 8.11: FCC-ee point PA - tunnel cross-section with dump.\n340\n\nFig. 8.12: FCC-ee point PA - booster injection tunnel.\n8.2.3\nIntegration of point PB\nPoint PB will house the FCC-ee beam dump and injection from the booster into the collider. In the next\nphase of operation, FCC-hh will house the beam dump system. The civil engineering volumes meet the\nneeds of FCC-ee (see Fig. 8.13).\nLONG STRAIGHT SECTION\nBEAM DUMP CAVERN\nSERVICE CAVERN\n2030\n708\n354\n354\n13.6\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nMIDPOINT OF LSS\n83\n5\n155\n5\n330\n5\n83\n5\n155\n5\n330\n5\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 3\nMAIN BEAM TUNNEL\n7.8\n7.25\n6.25\n5.5\n7.8\n7.25\n6.25\n5.5\nMAIN BEAM TUNNEL\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\nARC\n9670\nARC\nE\nE\nF\nF\nG\nG\nH\nH\nC\nC\nE\nE\nF\nF\nG\nG\nH\nH\nFig. 8.13: FCC underground - civil engineering in point PB\nThe figures included in this section are the results of the 3D integration studies for the point PB.\n341\n\nFig. 8.14: FCC-ee Point PB - general overview.\nFig. 8.15: FCC-ee Point PB - shaft of the service cavern.\n342\n\nFig. 8.16: FCC-ee Point PB - tunnel including the dump.\n8.2.4\nIntegration of point PD and point PJ\nPoint PD and point PJ will serve as small experiment points, hosting detectors in the cavern in both the\nFCC-ee and the FCC-hh phases of operation (see Fig. 8.17 and Fig. 8.18). The cavern size and extent\nmeet the needs of the detectors for both FCC-ee and FCC-hh. In addition, for the FCC-ee, the long\nstraight section (LSS) on either side of point PD and point PJ will host the beamstrahlung dumps.\nIP-D\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n16.4\n438.5\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 8.17: FCC underground - civil engineering in point PD.\nIP-J\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n16.4\n438.5\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 8.18: FCC underground - civil engineering in point PJ.\nThe figures included in this section are the results of the 3D integration studies for point PD and\npoint PJ.\n343\n\nFig. 8.19: FCC-ee point PD and PJ - general overview.\nFig. 8.20: FCC-ee point PD and PJ - shaft of the experiment cavern.\n344\n\nFig. 8.21: FCC-ee point PD and PJ - shaft of the service cavern.\nFig. 8.22: FCC-ee point PD and PJ - experiment cavern cross-section.\n345\n\nFig. 8.23: FCC-ee point PD and PJ - experiment cavern iso view.\n8.2.5\nIntegration of point PF\nPoint PF will house FCC-ee betatron and momentum collimation systems. In a next phase of operation,\nFCC-hh will house the beam dump systems. The civil engineering volume meet the needs of FCC-ee\n(see Fig. 8.24).\nLONG STRAIGHT SECTION\nSERVICE CAVERN\n2030\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nMIDPOINT OF LSS\n5.5\nMAIN BEAM TUNNEL\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n5.5\nMAIN BEAM TUNNEL\nACCESS TUNNEL\n9\n557\nARC\n9670\nARC\n9670\nPLAN VIEW\nFig. 8.24: FCC underground - civil engineering in point PF.\nThe figures included in this section are the results of the 3D integration studies for the point PF.\n346\n\nFig. 8.25: FCC-ee point PF - general overview.\nFig. 8.26: FCC-ee point PF - shaft of the service cavern.\n8.2.6\nIntegration of point PH and point PL (RF Systems)\nThe RF systems of the FCC-ee will be located in point PH for the collider and point PL for the booster\n(see Fig. 8.27 and Fig. 8.28).\n347\n\nLONG STRAIGHT SECTION\n2030\n2012\n1006\n1006\nMIDPOINT OF LSS\nSERVICE CAVERN\nKLYSTRON GALLERY\n5.5\n341\n3.3\n341\n341\n3.3\n10\nSTAIRWELL\nKLYSTRON GALLERY\nMAIN BEAM TUNNEL\n341\n5.5\nMAIN BEAM TUNNEL\nSTAIRWELL\n9670\nARC\n9670\nARC\nFig. 8.27: FCC underground - civil engineering in point PH\nLONG STRAIGHT SECTION\n2030\n1446\n723\n723\nMIDPOINT OF LSS\nSERVICE CAVERN\nKLYSTRON GALLERY\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\n5.5\n5.5\n354\n3.3\n354\n3.3\n10\nSTAIRWELL\nKLYSTRON GALLERY\nSTAIRWELL\n9670\nARC\n9670\nARC\nFig. 8.28: FCC underground - civil engineering in point PL\nConfiguration and layout of collider RF systems - point PH\nThe figures included in this section are the results of the 3D integration studies for point PH.\nFig. 8.29: FCC-ee point PH - general overview.\n348\n\nFig. 8.30: FCC-ee point PH - shaft of the service cavern.\nFig. 8.31: FCC-ee point PH - tunnel cross-section with FCC 800 MHz cavity.\n349\n\nFig. 8.32: FCC-ee point PH - tunnel cross-section with FCC 400 MHz cavity.\n350\n\nFig. 8.33: FCC-ee point PH - tunnel and gallery cross-section.\nFor radiation safety, the distance between the klystron gallery and the machine tunnel is 10 m\n(Fig. 8.33, Fig. 8.37) and shielding is installed in the klystron gallery. The vertical cores house the waveg-\nuides and electrical cables. For fire protection there are partition walls every 400 m in the klystron gallery,\nand a smoke extraction system on the ceiling. There is a stairway connection between the klystron gallery\nand the machine tunnel every 280 m.\nConfiguration and layout of booster RF systems - point PL\nThe figures included in this section are the results of the 3D integration studies for point PL.\n351\n\nFig. 8.34: FCC-ee point PL - general overview.\nFig. 8.35: FCC-ee point PL - shaft of the service cavern.\n352\n\nFig. 8.36: FCC-ee point PL - tunnel cross-section with booster 800 MHz cavity.\n353\n\nFig. 8.37: FCC-ee point PL - tunnel and gallery cross-section.\n8.2.7\nIntegration of the Arcs\nThe machine tunnels will house the FCC-ee accelerator and, in the following phase of operation, the\nFCC-hh accelerator. The civil engineering volume meet both accelerators needs.\n354\n\nSince the publication of the conceptual design report [13], the collider and booster have been lowered\nto give more space above the beam lines for safety requirements. After collecting updated requirements\nfrom all the stakeholders, the space requirements were reviewed with respect to installation and mainte-\nnance accessibility. A robot was added to the ceiling of the tunnel for better control of installation and\nmaintenance of both magnets and support services.\nThe graphics included in this section are the results of the 3D integration studies for the arcs based\non one of the baseline scenarios of a half-cell layout (see Fig. 3.81 and Fig. 3.82). The optimisation\nof the arc-supporting structures to maximise their performance, easing the installation and maintenance\nwhile minimising cost is facilitated by the FCC-ee Arc Half Cell Mock-up (see Section 3.10).\nFig. 8.38: FCC-ee layout in the arcs - longitudinal view.\nFig. 8.39: FCC-ee layout in the arcs - cross-section view.\n355\n\n8.2.8\nIntegration of the Alcoves\nIn addition to the technical and experiment points, there will be 56 alcoves distributed around the ring\n(7 per arc). These alcoves will mainly house electronics and power supplies which need to be shielded\nfrom ionising radiation. The alcoves integrate the electrical equipment to supply a sector of the FCC,\nincluding systems installed in the alcoves themselves, plus the tunnel infrastructure like lighting, general\nservices and a secured network. The entrance of the alcoves will also serve as a parking area for the\ntransport vehicles (see Figs. 8.40 and 8.41).\nThe drawings included in this section are the results of the 3D integration studies for the alcoves.\nFig. 8.40: FCC-ee alcove in the arcs with big parking area.\nFig. 8.41: FCC-ee alcove in the arcs with small parking area.\n356\n\nFig. 8.42: FCC-ee alcove at point PA and PG.\nFig. 8.43: FCC-ee alcove at point PB.\n357\n\nFig. 8.44: FCC-ee alcove at points PD and PJ.\nFig. 8.45: FCC-ee alcove at point PF\nThe integration of power converters in the alcoves and the routing of cables in the machine tunnel\npresent significant challenges due to space constraints and the high number of circuits involved. Power\nconverters are installed in both small and big alcoves. Table 8.1 provides an overview of the number of\nconverters in the alcoves and the number of cables in the cable trays.\nThere are five cables trays of varying sizes located above the booster supporting structure. The\nlayout of the cables in the cable tray must respect the normal cabling rules. The proposed radiation\nshielding must reduce the radiation level to be low enough for the cables to survive for the entire lifetime\nof operation.\n358\n\nTable 8.1: Quantities of converter racks in the alcoves and cables in cable trays at the exit of an alcove.\nMagnet\nQuantity of Racks in\nCables\nBig Alcove\nSmall Alcove\nSize (mm2)\nQuantity\nCollider Dipole\n27\n-\n1x500\n2\nCollider Quadrupole (F and D)\n46\n-\n1x300\n4\nCollider Sextupole (F and D)\n42\n84\n1x70\n28\nCollider Dipole Tapering\n1\n2\n1x6\n16\nCollider Quadrupole Tapering\n1\n2\n1x10\n16\nCollider Horizontal Corrector\n2\n3\n1x10\n60\nCollider Vertical Corrector\n2\n3\n1x16\n60\nCollider Skew Quadrupole\n2\n3\n1x10\n60\n*Collider Straight Section\n18\n-\n-\n-\n*Collider Injection\nn/a\nn/a\nn/a\nn/a\nBooster Dipole\n35\n-\n1x500\n2\nBooster Quadrupole (F and D)\n86\n-\n1x185\n8\nBooster Sextupole Focusing\n4\n-\n1x240\n2\nBooster Sextupole Defocusing\n11\n-\n1x185\n4\n*Booster Dipole Tapering\n1\n2\n1x4\n8\n*Booster Quadrupole Tapering\n1\n2\n1x6\n8\n*Booster Horizontal Corrector\n3\n6\n1x25\n36\n*Booster Vertical Corrector\n3\n6\n1x25\n36\n*Booster Quadrupole Corrector\n3\n5\n1x16\n30\n*Booster Skew Quadrupole\n3\n5\n1x16\n30\n*Booster Straight Section\n23\n-\n-\n-\n*Booster Injection\nn/a\n-\nn/a\nn/a\nTotal\n314\n123\n-\n410\n*Magnet specifications not yet fully defined or inexistent \u2013 values extrapolated\n8.2.9\nNext phase for the integration studies\nThe integration studies have been made with the pre-design of volumes and will evolve with detailed\ntechnical design in the next phase of the FCC studies. Optimisation of the 3D integration studies with\nrespect to the requirements from work packages will continue for all the areas following the identified\ntechnical and space needs:\n\u2013 Optimisation of the large experiment points PA and PG [375] [376] and small experiment points\nPD and PJ [377], integrating more detailed detectors design in the experiment caverns,\n\u2013 Optimisation of the technical point PB [378], integrating more detailed mechanical design of the\naccelerators and transfer lines,\n\u2013 Optimisation of the technical point PF [379], integrating more detailed mechanical design of the\ncollimation systems,\n\u2013 Optimisation of the technical point PH and PL [380] [381], integrating the more detailed mechan-\nical design of the radiofrequency and cryogenic systems and enlarging the space for transport and\nsafety in the passage part of the tunnel,\n\u2013 Optimisation of the arc half-cell [382], including the optimisation of the arc-supporting structures\nstudied by the FCC-ee Arc Half Cell Mock-up (Section 3.10) to maximise their performance, ease\nthe installation and maintenance while minimising cost.\n359\n\n\u2013 Optimisation of the alcoves [383], updating the control and powering racks layout with respect to\ntechnical specification evolutions.\n8.3\nCooling and ventilation\n8.3.1\nIntroduction\nThe cooling systems for the FCC mainly concern several water systems for the machine and its infras-\ntructure, including accelerator and detector equipment (electronic racks, cryogenic plants, water-cooled\nmagnets, RF equipment, etc.). Raw water will be used to fill the cooling circuits in some firefighting\nsystems and as make-up water for the cooling towers. Chilled water is needed to extract the heat load\nfrom air in ventilation systems. Demineralised water would be employed to cool sensitive equipment\nlike magnets, synchrotron radiation absorbers, and power converters.\nThe ventilation systems for the FCC should ensure the necessary conditions of humidity and tem-\nperature in the tunnel during operation, providing a supply of fresh air for personnel working within the\nfacilities and heating for the working environment. The extraction systems must be capable of purging\nthe air in the tunnel before access is allowed, as well as removing smoke and gases during an emergency.\nOther systems comprise several and varied applications, some unrelated to cooling and ventila-\ntion. The compressed air systems for the FCC would provide compressed air to end clients requiring it,\nincluding the dampers employed in the FCC tunnel. Effluent water from the cooling towers and filters\nwould be concentrated in salts and returned to a water treatment plant. Drinking water would be needed\nfor sanitary purposes. Finally, a drainage network would evacuate the water drained from the surface\nfacilities and underground areas.\nCooling systems\nWater supply\nThe FCC accelerator would need to be supplied with water at the eight surface points. The main water\nconsumers are the cooling towers, but water is also needed for the fire-fighting systems, the demineralised\nwater production plant and all the cooling plants in the surface buildings as well as in the tunnels and\ncaverns.\nAs a baseline, raw water is supplied from point PA to the rest of the accelerator, as represented in\nFig. 8.46. Lake Geneva, located near PA, also serves as a water source for other accelerators within the\nCERN complex. Pipes running through the FCC tunnel sectors distribute water to one or more contiguous\npoints: one branch supplies water from point PA to points PB, PD, PF, and PG, while another branch\nsupplies water from point PA to points PL, PJ, and PH. Table 8.2 presents the approximate maximum\nraw water flow rates required, along with the effluent water generated at the cooling towers and filters.\nAn alternative design to this baseline could include the Rh\u00f4ne and Arve rivers as potential water\nsources for the FCC. In that case, point PA would feed points PL and PB with water from Lake Geneva,\npoint PD would feed points PF and PG with water from the Arve river and point PJ would feed point PH\nwith water from the Rhone river. This would effectively decrease the piping and pumping system sizes.\nFirefighting water is available across each surface site, as well as in the service and experiment\ncaverns. An additional flow rate of 240 m3/h per point is allocated for firefighting purposes. Each surface\nsite is equipped with water tanks capable of storing the estimated water supply needed for one hour.\nIn addition to the cooling towers and firefighting systems, the demineralised and chilled water\ncircuits also require periodic refilling, with an estimated maximum demand of 0.5 m3/h.\nWater transfer between points is managed through a pumping station at point PA and booster\npumps positioned at the bottom of the shaft at point PF, as illustrated in Fig. 8.47, which also depicts the\napproximate surface and underground elevations, along with shaft depths.\n360\n\nFig. 8.46: Distribution of raw water coming from point PA, Lake Geneva.\nTable 8.2: Maximum make-up and effluent water of cooling towers (m3/h).\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nMake-up water for\n94\n13\n94\n13\n94\n192\n94\n36\ncooling towers\nEffluent water from\n13\n2\n13\n2\n13\n26\n13\n5\ncooling towers and filters\nFig. 8.47: Pumping stations and booster pumps of the raw water system.\n361\n\nPrimary cooling circuits.\nThe cooling towers will remove most of the heat generated by the accelerator equipment, the detectors\nand the technical areas. There will be a set of field erected, open wet cooling towers per surface site.\nThe evaporative cooling towers are of the mechanical-induced draft counter-flow type. Ventilation\nfans are positioned at the top of the cells, ensuring easy access for maintenance. Each tower consists\nof multiple cells with identical cooling capacity, with one cell per tower reserved for backup purposes\n(N+1 redundancy). The towers are designed to operate with water treated with anti-corrosion and biocide\nchemicals. The cooling towers comply with the following parameters and conditions:\n\u2013 Outside air wet bulb temperature: 21\u00b0C.\n\u2013 Cooling tower inlet temperature: 40\u00b0C.\n\u2013 Cooling tower outlet maximum temperature: 25\u00b0C.\nThe cooling power to be installed at each point has been determined based on the users\u2019 cooling\nrequirements. Certain equipment, particularly cryogenic systems, will be cooled directly by the primary\ncircuit, while other equipment will be connected to the primary systems via heat exchangers (secondary\ncircuits). In most cases, the secondary circuits will operate in a closed loop using demineralised water.\nTable 8.3 gives an overview of the cooling requirements by type of equipment: each row represents\na different type of equipment, except for the \u2018Underground\u2019 row, which groups all equipment cooled from\nthe same primary circuit and is located underground. In addition, Table 8.4 provides the cooling tower\ncomplex capacity per point, including the backup cells. Figure 8.48 shows the cooling tower complexes\nper point, including the backup cells.\nTable 8.3: Cooling demands (MW) of the primary circuit.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nCryogenics\n34.0\n10.0\nExperiments\n0.5\n0.5\n0.5\n0.5\nGeneral Services\n2.0\n2.0\n2.0\n2.0\n2.0\n2.0\n2.0\n2.0\nPower Converters\n4.5\n0.1\nChilled Water\n5.8\n5.2\n5.8\n5.2\n5.8\n11.3\n5.8\n5.8\nUnderground\n42.5\n1.0\n42.5\n1.0\n42.5\n48.9\n42.5\n2.7\nTotal power required\n50.8\n8.2\n50.8\n8.2\n50.8\n100.7\n50.8\n20.6\nTable 8.4: Cooling capacity (MW) of the primary circuit.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nNumber of cells per cooling tower\n6\n2\n6\n2\n6\n8\n6\n3\nCooling capacity per cell\n10.0\n10.0\n10.0\n10.0\n10.0\n15.0\n10.0\n11.0\nTotal cooling capacity\n60.0\n20.0\n60.0\n20.0\n60.0\n120.0\n60.0\n33.0\nThe cooling towers operate continuously in open air with the ambient conditions present in Geneva\nand its surrounding area, with only a short stoppage each year to carry out maintenance. The baseline\nstrategy implemented to reduce water consumption in the cooling tower is the recycling of its blowdown\nwater. To do so, its conductivity is first reduced to values of around 20 \u00b5S/cm. The resulting water is\nthen mixed with normal raw water, which is eventually used as a low-conductivity make-up water for the\ncooling towers.\n362\n\nAn alternative to the baseline design is the adoption of hybrid cooling tower technology, which\ncombines the advantages of both wet and dry cooling methods to enhance performance and reduce the\nenvironmental impact. In this system, the wet cooling tower - similar to the baseline design - uses\nwater to absorb heat from the process, releasing it through evaporation. Dry air-water heat exchangers\nsupplement this. The airflows from the wet and dry sections are mixed before reaching the fan stack,\nhelping to reduce or eliminate the visible water vapour plume typically observed in wet cooling towers,\nparticularly under certain weather conditions. However, hybrid cooling towers require a larger surface\narea and entail higher costs.\nFig. 8.48: Cooling tower complex for FCC-ee, including the backup cells.\nDemineralised water cooling circuits.\nThe secondary circuits are connected to the primary system through heat exchangers. In most cases, the\nsecondary circuits use demineralised water in a closed loop. Demineralised water cooling circuits are\ngrouped according to the typology of the equipment to be cooled and to the equipment pressure ratings.\nSince the underground areas are up to 400 m below ground level (case of point PF), it is necessary to\ninstall an underground cooling station in the service cavern at all points. Here, heat exchangers separate\nthe circuit coming from the surface (with a static pressure of up to 40 bar) from the underground distri-\nbution circuit. For operability and maintenance purposes, both surface and underground cooling stations\nare accessible during accelerator running. Figure 8.49 shows the demineralised water distribution in the\nFCC tunnel, the water being supplied at the experiment points. The types of underground equipment\ncooled by demineralised water are listed in Table 8.5.\nThe magnets, alcoves and SR absorbers rows\ncorrespond to equipment located in the tunnel. The other four columns refer to equipment located close\nto the access points.\nThe heat loads from the accelerator\u2019s radio frequency system come directly from the RF equip-\nment. Furthermore, the cryogenic installation, which cools part of the equipment to cryogenic temper-\natures, is cooled by primary water, not demineralised water. The first fill of the demineralised water\ncircuits can be done by a CERN-owned on-truck demineralised water production station and leave the\n363\n\nFig. 8.49: Demineralised water distribution in the FCC tunnel.\nTable 8.5: Demineralised water cooling demands (MW) per underground user.\nPoint /\nSector\nPA /\nPL-PA\nPA-PB\nPB\nPD /\nPB-PD\nPD-PF\nPF\nPG /\nPH-PJ\nPJ-PL\nPH\nPJ /\nPH-PJ\nPJ-PL\nPL\nMagnets\n2\u00d77.1\n2\u00d77.1\n2\u00d77.1\n2\u00d77.1\nAlcoves\n2\u00d70.9\n2\u00d70.9\n2\u00d70.9\n2\u00d70.9\nSR Absorbers\n2\u00d712.5\n2\u00d712.5\n2\u00d712.5\n2\u00d712.5\nExperiment Area\n0.5\n0.5\n0.5\n0.5\nPower Converters\n1.0\n1.0\n1.0\n1.0\n1.0\n1.0\n1.0\n1.0\nRF\n45.7\n0.7\nCryogenics*\n0.01*\n0.01*\n0.01*\n2.2*\n0.01*\n1.0*\nTotal power\n42.5\n1.0\n42.5\n1.0\n42.5\n48.9\n42.5\n2.7\n* Cryogenic equipment uses primary water quality in its secondary circuit.\ntopping up of the circuits to smaller local demineralisers at each point. Alternatives include renting an\non-truck production station or designing the local demineralisers to carry out the first fill too. In this\ncase, the production station would be underutilised, operating at reduced capacity most of the time.\nChilled water cooling circuits.\nChilled water at 6\u00b0C is needed for air dehumidification and cooling purposes and for the cooling of\nelectrical equipment with specific temperature requirements.\nThe water is cooled by industrial air-cooled or water-cooled chillers. The maximum heat load to be\nremoved by chilled water per point is given in Table 8.6, together with the flow needed for a temperature\ndifference of 6 K between the supply and return chilled water temperature. The number of chillers and\npower per chiller is shown in Table 8.7: all of them have similar cooling demands except for point PH,\n364\n\nwhich has a higher demand due to its hosting the most power-intensive RF section.\nThe distribution of chilled water in the tunnel is designed as shown in Fig. 8.50. The selection of\nrefrigerant for the chillers will be guided by both technological compatibility and environmental sustain-\nability, with careful consideration of ongoing research developments. This decision will be made at a\nlater stage, ensuring it reflects the latest advances and best practices. Additionally, the potential integra-\ntion of mixed water production at 12\u00b0C, which is not currently planned, will be assessed based on user\nrequirements and implemented if deemed necessary to optimise efficiency and performance.\nTable 8.6: Chilled water cooling demands (kW) and supply water flow rate (m3/h) per point.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nCooling power\n4895\n4322\n4875\n4322\n4895\n9367\n4875\n4757\nFlow rate\n703\n620\n700\n620\n703\n1345\n700\n683\nTable 8.7: Chilled water cooling capacity (kW) per point.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nNumber of chillers\n6\n6\n6\n6\n6\n7\n6\n6\nCooling power of chiller\n1000\n900\n1000\n900\n1000\n1800\n1000\n1000\nTotal cooling power\n6000\n5400\n6000\n5400\n6000\n12 600\n6000\n6000\nFig. 8.50: Chilled water distribution in the FCC tunnel.\n365\n\n8.3.2\nVentilation systems\nDesign principles and heat loads\nThe FCC ventilation systems supply a sufficient amount of fresh air to meet the air quality and thermal\nrequirements: the ambient temperature is suitable for the accelerator and auxiliary technical equipment.\nIn addition, the air supplied is dehumidified to prevent condensation on equipment and structures.\nIn the current design, the underground areas are generally ventilated by air-handling units located\non the surface, accessible at all times. Redundant units (N + 1) are planned everywhere to avoid affecting\naccelerator operation in case of breakdown. In addition, fancoils provide local cooling wherever neces-\nsary. Tables 8.8, 8.9 and 8.10 present the air heat loads in all surface sites, in the underground areas and\nfor each sector of the tunnel, respectively.\nTable 8.8: Heat loads on air (kW) on the surface, per point.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nCryogenics*\n13\n13\n13\n1400*\n13\n402*\nExperiment Areas\n50\n40\n50\n40\nGeneral Services\n500\n500\n500\n500\n500\n500\n500\n500\nPower Converters*\n2250*\n35*\nShaft pressurisation\n300\n150\n300\n150\n300\n150\n300\n150\nFresh air for Underground\n150\n50\n150\n50\n150\n150\n150\n150\nTotal heat load\n1013\n700\n1003\n700\n1013\n800\n1003\n800\nto Chilled water\n* Cryogenics and power converters heat loads that are extracted without chilled water.\nTable 8.9: Heat loads on air (kW) underground, per point.\nPoint\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nCryogenics\n10\n10\n10\n145\n10\n60\nRF\n4600\n75\nExperiment Areas\n50\n40\n50\n40\nPower Converters\n220\n220\n220\n220\n220\n220\n220\n220\nCV Zone Underground\n200\n200\n200\n200\n200\n200\nTotal heat load\n480\n220\n470\n220\n480\n5165\n470\n555\nto Chilled water\nTable 8.10: Heat loads on air (kW) for each arc of the tunnel.\nMagnets\nCables*\nSynchrotron radiation\nAlcoves\nTotal heat load\nabsorbers\nto Chilled water\n352\n2500\u2217\n250\n300\n3402\n* Heat load from the cables extracted without chilled water.\n366\n\nTunnel ventilation.\nFor the FCC tunnel, a semi-transverse ventilation scheme has been adopted. The air is supplied through\na specific duct running throughout the sector and extracted either through the tunnel itself or by an\nemergency extraction duct. Air is supplied to each sector from both endpoints to ensure air supply even\nin case of a duct failure; the same configuration has been adopted for the extraction (Fig. 8.51).\nThe air supply duct runs in the concrete floor slab and supplies air to the tunnel about every 100 m\nvia diffusers at floor level. A closed circular segment in the upper part of the tunnel is used for emergency\nextraction. The structure consists of 70 mm thick steel panels, secured to the tunnel lining using post-\ndrilled anchors, and is equipped with passive fire protection on both sides. Inlet diffusers and extraction\ngrills are strategically offset to ensure optimal air distribution within the tunnel and to prevent direct\nairflow shortcuts between supply and extraction points.\nFire-resistant dampers are installed at every connection between diffusers and extraction grills,\nenhancing ventilation control in the event of a fire or helium release. These dampers help manage airflow\nwithin the affected tunnel compartment, improving safety and containment.\nTo further control the spread of smoke and helium gas, each tunnel sector is divided into 28\ncompartments, separated by fixed fireproof panels and automatic doors. This design prevents smoke\npropagation in case of fire and mitigates the spread of helium gas in the event of an accidental leak from\naccelerator equipment.\nFig. 8.51: Operation of the ventilation elements in one sector of the tunnel during normal operation.\nSmoke and helium extraction in green, general extraction in red and air supply in blue.\nUnder normal conditions, there are four different working modes for tunnel ventilation.\n\u2013 Run mode: the accelerator is in operation, and most of the electrical systems are powered; a high\nheat load is transferred to the air in this mode. In addition,n radiation protection aspects are taken\ninto account.\n\u2013 Access mode: technical personnel can work in the tunnel and therefore occupational safety re-\nquirements are considered.\n\u2013 Economy mode: a minimum airflow is employed in situations without personnel access, reducing\nthe airflow. In this mode, the dew point of the air is controlled, but wider ranges of dry temperature\nare accepted to save energy.\n367\n\n\u2013 Flushing mode: used to renew the air underground completely and takes place when moving from\nRun to Access modes. The extracted volumes are filtered before release.\nTable 8.11: Airflow conditions for the tunnel ventilation.\nAir\nSupply\nRegular\nExtraction\nEmergency\nExtraction\nRun and\nAccess mode\n2\u00d727 000 m3/h\nper sector.\n2\u00d727 000 m3/h\nper sector.\nStandby under pressure\noperation, no extraction.\nFlushing\nmode\n100 000 m3/h\nper sector.\n100 000 m3/h\nper sector.\nStandby under pressure\noperation, no extraction.\nEmergency\nconditions\n10 000 m3/h in affected\ncompartments (max. 2).\n3500 m3/h in adjacent\ncompartments (max. 2).\n2160 m3/h in the rest\nof the compartments.\nMax. 54 000 m3/h\nSharing between\nthe two shafts\ndepends on affected\ncompartment location.\n10 000 m3/h in affected\ncompartments (max. 2).\n3500 m3/h in adjacent\ncompartments (max. 2).\nThe airflow requirements under normal and emergency conditions are presented in Table 8.11.\nWhen the accelerator is in operation with full heat loads, the maximum dry temperature is limited to\n32\u00b0C and the maximum dew point is limited to 12\u00b0C, inside the tunnel. In this mode, the nominal supply\ntemperature is of 17\u00b0C. In flushing mode, the minimum supply temperature is 15\u00b0C. If the external\ntemperature is below 0\u00b0C, the airflow will be reduced to maintain the 15\u00b0C supply temperature. For\nthe access mode, the temperature inside the tunnel is set between a minimum of 18\u00b0C and a maximum\nof 26\u00b0C, while respecting the regulations regarding air renewal. In all operating modes, environmental\nsustainability and energy efficiency are key priorities. As a general principle, the ventilation system is\ndesigned to minimise electrical consumption by incorporating free cooling and air recycling strategies.\nIn run and access modes, airflow is supplied through an inlet duct integrated into the tunnel floor\nslab. In flushing mode, however, air is not delivered via this duct but is distributed longitudinally across\nthe entire tunnel cross-section.\nAn alternative approach to tunnel ventilation would be to extend the longitudinal airflow concept\nof flushing mode to both run and access modes, resulting in a fully longitudinal ventilation scheme.\nThis solution would simplify system controls, enhance robustness, and free up space required for the\nintegration of the inlet duct. However, before implementation, the system\u2019s performance under degraded\nconditions and emergency scenarios must be carefully assessed to ensure full compliance with safety\nstandards.\nExperiment areas ventilation.\nThe ventilation system for the experiment areas (experiment caverns at points PA, PD, PG, and PJ)\nconsists of a ventilation system on the surface with a supply and extraction unit and the possibility of\nrecycling 100% of the air or the option to supply a controlled percentage of fresh air. The ventilation\nprinciple for the experiment caverns is represented in Fig. 8.52. No additional local cooling systems are\nplanned.\nThe nominal airflow conditions are presented in Table 8.12. During operation, the experiment\nareas will have a temperature distribution of 18/32\u00b0C from floor to ceiling. The same parameters as for\nthe FCC tunnel are applicable in flushing and access modes.\n368\n\nTable 8.12: Airflow conditions for the experiment areas ventilation.\nAir\nSupply\nRegular\nExtraction\nGas\nExtraction\nRun and\nAccess mode\n50 000 m3/h\nto 70 000 m3/h\n50 000 m3/h\nto 70 000 m3/h\nSwitched off\nFlushing\nmode\n50 000 m3/h\nto 70 000 m3/h\n50 000 m3/h\nto 70 000 m3/h\nSwitched off\nFire emergency\n(gas extraction)\nUp to 70 000 m3/h\nUp to 70 000 m3/h\nSwitched off\nGas emergency\n(gas extraction)\n20 000 m3/h\nSwitched off\n20 000 m3/h\nFig. 8.52: Ventilation systems of the experiment cavern. Smoke and helium extraction in orange, general\nextraction in red and air supply in blue.\nRF areas ventilation.\nThe RF system is cooled mainly by the demineralised water circuits in the underground klystron galleries\nof points PH and PL. A considerable heat load nevertheless remains to be extracted: 4600 kW in point\nPH and 75 kW in point PL.\nThe ventilation design has main ventilation from the surface, with a fresh air supply, plus local\ncooling with fan coils cooled with chilled water. Table 8.13 presents the airflow requirements for each of\nthe modes; flushing is not needed because contaminants are not present in the klystron gallery equipment.\nTechnical areas ventilation.\nDedicated ventilation systems serve the technical zones around each point and the connecting galleries\nbetween areas. These areas comprise the service caverns and connecting galleries at all points.\nThe design of each ventilation system is different because the general demands and heat loads\n369\n\nTable 8.13: Airflow conditions for the RF areas ventilation.\nAir\nSupply\nRegular\nExtraction\nEmergency\nExtraction\nRun and\nAccess mode\n30 000 m3/h\n30 000 m3/h\nSwitched off\nEmergency\nconditions\n<30 000 m3/h\n<30 000 m3/h\n10 000 m3/h in affected\ncompartments (max. 2).\n3500 m3/h in adjacent\ncompartments (max. 2).\ndiffer greatly between the points. A difference is made between the technical areas in experiment points\n(points PA, PD, PG, PJ), the technical areas in technical points (points PB and PF), and the technical\nareas in RF points (points PH and PL). The ventilation solutions proposed under normal and emergency\nconditions are presented in Table 8.14. Finally, other ventilation systems pressurise airlocks to create\npressure cascades for safety purposes.\nTable 8.14: Airflow conditions for ventilation of the technical areas.\nAir supply\nExtraction\nEmergency Extraction\nTechnical Areas\nin Experiment\npoints\nFresh air for UAs,\n20 000 m3/h.\nVentilation for\nService Cavern,\n40 000 m3/h.\nExtraction through\nthe Service Cavern,\n60 000 m3/h.\nEmergency extraction\nthrough the Ventilation\nsystem for Service\nCavern, 60 000 m3/h.\nTechnical Areas\nin Technical\npoints\nVentilation for\nService Cavern,\n40 000 m3/h.\nExtraction through\nthe Service Cavern,\n40 000 m3/h.\nEmergency extraction\nthrough the Ventilation\nsystem for Service\nCavern, 40 000 m3/h.\nTechnical Areas\nin RF points\nVentilation for\nService Cavern,\n40 000 m3/h.\nExtraction through\nthe Service Cavern,\n40 000 m3/h.\nEmergency extraction\nthrough the Ventilation\nsystem for Service\nCavern, 40 000 m3/h.\nSurface buildings ventilation\nEach surface building will be ventilated by a dedicated air-handling unit. Where the building size requires\nit, it is planned to have several units in the same building, each of them taking care of a part of the\nbuilding. At present, it is not considered necessary to have redundant units in these buildings. Should\nthis be needed, it can easily be implemented. All surface buildings will be equipped with a mechanical\nsystem on the roof to extract smoke, designed and certified for operation at 400\u00b0C for a minimum period\nof 2 h.\n370\n\n8.3.3\nOther systems\nDrinking water\nDrinking water will be used by personnel. It is planned that this will be provided by the local water\nnetwork at each point.\nReject water and sumps\nDischarging effluent water into local disposal networks or small water bodies presents challenges due to\nits high salinity levels. To address this, a centralised treatment system is proposed, in which all effluent\nwater is transported through the tunnel to a treatment plant at point PA.\nAn alternative approach would involve local treatment of effluent water at each point. Imple-\nmenting minimum or zero liquid discharge (ZLD) technologies could significantly reduce the volume of\neffluent by concentrating the salts into solid pellets. However, this solution would introduce higher costs\nand increased surface area requirements due to the complexity of these treatment systems.\nCompressed air\nThe compressed air for all equipment and actuators will be provided by compressed air stations located on\nthe surface at each point. These will supply both surface and underground areas. A level of redundancy\nof N +1 is planned to ensure the reliability and maintainability of the plant.\nSumps and clear water\nTwo separate pump systems to lift clear water and sewage will be installed underground at each point.\nThey will be connected to the point\u2019s local drainage network. All underground equipment (tunnel and\ncaverns) must have redundancy in order to avoid affecting operation in case of a breakdown. The sump\npumping capacities for the tunnel at the points are 30 m3/h, and the experiment caverns have an additional\n30 m3/h of sump pumping capacity. Alarms for \u2018high level\u2019 and \u2018level too high\u2019 will be implemented in\nall basins.\nThe key parameters of the clear water, including temperature and pH, will be systematically mon-\nitored prior to discharge. If the clear water fails to meet the required quality standards or poses a risk\nof environmental contamination, appropriate mitigation measures will be implemented. These measures\nmay include the activation of retention basins at designated discharge points to ensure compliance with\nenvironmental regulations.\n8.4\nPower consumption and electricity distribution\n8.4.1\nEnergy consumption of the FCC-ee machine\nOverall power Demand\nSince FCC-ee is a large-scale accelerator, accurately identifying and understanding its electrical loads\nis essential for designing a robust electricity infrastructure and assessing overall energy consumption.\nThe accelerator\u2019s main electrical loads include the radiofrequency (RF) systems, magnets, cryogenic\nsystems, cooling and ventilation, experiments, and general services, which cover all general-purpose\nenergy needs. The total power demand varies depending on the operation mode of the machine (Z, WW,\nH, and t\u00aft).\nThe collider radiofrequency system represents the largest electrical load, requiring 146 MW across\nall operation modes. It consistently supplies 50 MW per beam to compensate for synchrotron radiation\nlosses. The global efficiency of the RF chain is 68%, with the goal of having klystron amplifiers operating\nat 80% efficiency. The power demand for the magnets and their powering chains depends on the beam\n371\n\nenergy, starting from 6 MW in Z mode, increasing to 39 MW in H mode, and reaching 89 MW in t\u00aft\nmode.\nThe cryogenic power demand remains relatively low at 13 MW up to H mode but becomes signif-\nicant at 35 MW in t\u00aft mode. The cooling and ventilation systems require between 25 MW and 33 MW,\nwhile the power demand of the experiments and data centres is estimated to be 10 MW for all four ex-\nperiments, with an additional 4 MW allocated for local data centres, given that detailed technical designs\nare not yet available. Finally, general services are expected to require up to 26 MW, based on scaling\nfrom LHC consumption.\nThese estimates will form the basis for the development of the FCC-ee\u2019s electrical infrastructure,\nensuring it can accommodate the varying power demands while optimising efficiency and sustainability.\nTable 8.15 shows the estimate of the maximum power demand for the four different modes of operation.\nTable 8.15: Power demand by technical system, in MW.\nZ\nW\nH\nt\u00aft\nBeam energy, GeV\n45.6\n80\n120\n182.5\nCollider radiofrequency\n146\n146\n146\n146\nBooster radiofrequency\n2\n2\n2\n2\nCollider cryogenics\n1.2\n11.5\n11.5\n27.6\nBooster cryogenics\n0.35\n0.8\n1.5\n7.4\nCooling and ventilation\n25\n26\n28\n33\nCollider magnets\n6\n17\n39\n89\nBooster magnets\n1\n3\n5\n11\n4 experiments, PA, PD, PG, PJ\n10\n10\n10\n10\n4 datacenters, PA, PD, PG, PJ\n4\n4\n4\n4\nGeneral services\n26\n26\n26\n26\nTotal power during beam operation\n222\n247\n273\n357\nOperational model\nThe energy consumption is estimated based on the accelerator operational model. The power demand\ndepends on the period of the year and the state of the machine. The machine schedule defines the\ndifferent periods during the year and the power demand varies from the minimum during the shutdown\nto the maximum during beam operation.\nThe schedule consists of six distinct periods: shutdown, commissioning, physics operation, short\ndowntime (without access to the machine), technical stops (or long downtime), and machine develop-\nments. The power demand calculated for each period is shown in Table 8.16.\nTable 8.16: Power demand by operation mode, in MW.\nBeam energy mode\nZ\nW\nH\nt\u00aft\nShutdown\n30\n33\n34\n41\nTechnical stop\n67\n78\n81\n108\nShort downtime\n74\n98\n125\n209\nCommissioning\n144\n163\n177\n233\nMachine Development\n96\n121\n147\n231\nBeam operation\n222\n247\n273\n357\n372\n\nThe machine schedule comprises 120 days of shutdown, 30 days of commissioning, 20 days of\nmachine development, 10 days of technical stops and 185 days for physics, see Table 8.17.\nThe machine availability is expected to be at least 80%. Unlike other accelerators, FCC-ee does\nnot lose time for acceleration, meaning that its operational efficiency is determined solely by technical\ndowntime and the associated time required for beam refilling and recovery. Based on empirical data from\nsimilar machines, the effective efficiency factor is estimated to be approximately equal to the hardware\navailability (80%), with an additional 5% reduction to account for beam recovery after a failure.\nOf the 185 days allocated for physics operation, an estimated 46 days are lost due to downtime,\nleaving 139 days for colliding beams.\nThe downtime is categorised into three types: long stops due to major failures, such as the loss\nof cryogenic conditions or RF cavity conditioning; downtime with machine access, allowing repairs and\nmaintenance; and downtime between cycles, which includes beam dumps and refilling that do not require\nmachine access.\nTable 8.17: Distribution of operating modes in time.\nPeriod Type\nDuration\nShutdown\n120 days\nCommissioning\n30 days\nPhysics Operation\n185 days\nBeam colliding\n139 days\nDowntime\n46 days\nMachine development\n20 days\nTechnical Stops\n10 days\nPower demand by points\nAs the distribution of the power demand is not uniform across the points (see Table 8.18), the installed\npower and its position need to be known to be able to design the electrical infrastructure. The load survey\nperformed in the first phase of the study provided the following localised power requirements:\n\u2013 Surface at each point: between 6.1 and 42.2 MW,\n\u2013 Underground at each point: between 2.1 and 215 MW,\n\u2013 Tunnel between points: around 20.2 MW.\nThis first analysis allowed the creation of a load mapping of the FCC-ee machine for the design of its\nelectrical network, see Fig. 8.53.\nTable 8.18: Power demand by point, t\u00aft mode.\nPoint\nType\nMax Power [MW]\nPoint PA\nExperiment\n23\nPoint PB\n20\nPoint PD\nExperiment\n23\nPoint PF\n20\nPoint PG\nExperiment\n23\nPoint PH\nCollider RF\n194\nPoint PJ\nExperiment\n23\nPoint PL\nBooster RF\n30\n373\n\nFig. 8.53: Load mapping of the FCC-ee machine.\nEnergy consumption\nWith the schedule and the expected power demand for the various periods, the annual energy consump-\ntion can be calculated, see Tables 8.19 and 8.20 for Z and t\u00aft operation respectively. The energy con-\nsumption varies from 1.07 TWh/year for Z mode operation to 1.77 TWh/year for t\u00aft mode operation. For\ncomparison, the complete CERN complex energy consumption in 2024 was 1.3 TWh/year. This yearly\nconsumption is expected to increase after the completion of the HL-LHC project.\nTable 8.19: Energy Consumption, Z mode.\nZ mode\nDuration, Days\nPower, MW\nEnergy, GWh\nBeam colliding\n139\n222\n740\nDowntime\n46\n67\n75\nCommissioning\n30\n144\n103\nMachine development\n20\n96\n46\nTechnical Stops\n10\n67\n16\nShutdown\n120\n30\n86\nTotal Z mode operation\n1070\nTable 8.20: Energy consumption, t\u00aft mode.\nTT mode\nDuration, Days\nPower, MW\nEnergy, GWh\nBeam colliding\n139\n357\n1200\nDowntime\n46\n108\n157\nCommissioning\n30\n233\n168\nMachine development\n20\n231\n111\nTechnical Stops\n10\n108\n26\nShutdown\n120\n41\n117\nTotal t\u00aft mode operation\n1770\n374\n\nGrid Connections\nTo provide power to the machine which is spread over many points, the strategy is to connect three points\nto the high-voltage European grid and to create an internal transmission network through the tunnel to\ndistribute it to the other points. These connections will be rated at the same level of 220 MVA at each\npoint. These points are PH, PA, and PD (see Fig. 8.54) and will be connected to the French grid, operated\nby RTE. RTE confirmed that, beside a minimum additional infrastructure to connect the new FCC points,\nno further upgrades or power stations are required in the existing French grid.\nPH needs a dedicated substation for the collider RF systems. PA can be powered through an\nexisting CERN substation. PD is needed to cover the other parts of the machine, for redundancy with PA\nand for the future operation of FCC-hh.\nFig. 8.54: High Voltage grid connections, PDL as delivery points.\nIn addition to that, all the points will be connected at much lower power to the local distribution\ngrids: SIG (Services Industriels de Gen\u00e8ve) for the point in Switzerland (PB), and ENEDIS for points\nlocated in France, except for point PG which will be connected to Energie et Services de Seyssel. These\nconnections are needed for the civil engineering works, and later they will be used as backup sources. The\nvoltage level of these connections will be at medium voltage (20 kV in France, 18 kV in Switzerland),\nand they will be in general rated at 14 MW, to cover the TBM loads in the civil engineering works phase.\n8.4.2\nFCC electrical grid\nTransmission network\nThe FCC can be powered from the French national grid, operated by RTE (France\u2019s Transmission Sys-\ntem Operator, R\u00e9seau de Transport d\u2019\u00c9lectricit\u00e9), through three access points (PA, PD, and PH) at two\npossible voltage levels (400 kV or 225 kV). Power will be distributed to the other access points via an\ninternal high-voltage (HV) transmission network, which will be implemented using HV cables installed\nwithin the accelerator tunnel. These cables will link all access points, ensuring power transmission from\n375\n\none point to the adjacent ones.\nFollowing verification with RTE, it has been confirmed that operating two or three high-voltage\nsupplies of the FCC in parallel will not be permitted by the grid operator, as this would introduce the risk\nof uncontrolled or unwanted power transfers between connection points.\nAs a result, the option of operating the HV grid of the FCC as a closed loop, initially considered\nfeasible, has been discarded at this stage of the study. Instead, the three high-voltage supplies will\nbe operated in an antenna configuration, with each connection radially supplying other points in the\naccelerator. In the normal configuration, three distinct sectors have been defined, each powered by a\nsingle RTE connection: PA will supply PB, PJ, and PL; PD will supply PF and PG; while PH will\noperate standalone, as the RF systems at this location represent the largest power load of the machine.\nFig. 8.55: General single line diagram of the transmission network of FCC.\nEven if the HV cables between PB and PD, between PG and PH, and between PH and PG will not\nbe loaded during normal operation, they can be used as a backup supply in case part of the HV network\nis unavailable. The possible continuity of service based on the [N-1] principle has been analysed by\nsimulating different failures in the network and reconfigurations to overcome these failures have been\ndetermined. The only scenario in which the machine will cease operation without the possibility of\nnetwork reconfiguration is the loss of supply from PH, as the RF loads at this location are too high\nto be compensated by other power sources. Apart from this case, the network is designed to allow\nreconfiguration, ensuring that the accelerator can continue normal operation in the event of a failure of\none HV source or one HV branch. The list of possible HV network failures that the system can withstand,\nalong with the corresponding reconfiguration strategies, is summarised in Table 8.21.\n376\n\nTable 8.21: Transmission network configuration modes to overcome failures.\nPA - PB\nPB - PD\nPD - PF\nPF - PG\nPG - PH\nPH - PJ\nPJ - PL\nPL - PA\nNormal\nconfiguration\nON\nOFF\nON\nON\nOFF\nOFF\nON\nON\nLoss of PA\nON\nON\nON\nOFF\nON\nON\nOFF\nON\nLoss of PD\nON\nON\nON\nOFF\nON\nON\nOFF\nON\nLoss of PA - PB\nOFF\nON\nON\nON\nOFF\nOFF\nON\nON\nLoss of PD - PF\nON\nOFF\nOFF\nON\nON\nOFF\nON\nON\nLoss of PF - PG\nON\nOFF\nON\nOFF\nON\nOFF\nON\nON\nLoss of PJ - PL\nON\nOFF\nON\nON\nOFF\nON\nOFF\nON\nLoss of PL - PA\nON\nOFF\nON\nON\nOFF\nON\nON\nOFF\nThis analysis also provides the minimum criteria to dimension the sources and the lines of the HV\nnetwork, in addition to the load requirements. Finally, to also cope with the objective of keeping the\nsame HV grid for the future FCC-hh, it was decided that all the HV cables will be sized equally to a\nnominal rating of 115 MVA, to allow the infrastructure to be compatible with the FCC-hh load.\nSelection of the voltage level, the location and the technology of the HV transmission network\nThe selection of the operating voltage of the transmission network has been based on a study aimed to\noptimise infrastructure and operational costs. As a result, the voltage will be stepped down from 400 or\n225 kV, to a lower level, see Fig. 8.55.\nFor the radiofrequency (RF) systems, the voltage will be stepped down to the required level for the\nmain RF power conversion system, which is currently planned to be 40 kV. While adopting 40 kV for the\nentire transmission network would offer some benefits in terms of material uniformity, an initial analysis\nclearly indicated that this voltage level is not optimal due to the large cable cross-sections required,\nleading to high space occupancy in the tunnel and significant power losses. For these reasons, 40 kV was\ndiscarded from the beginning of the study.\nTo determine the most suitable internal transmission voltage, the analysis considered three refer-\nence voltages, selected from standard values used by European Grid Operators: 63 kV, 90 kV, and 132 kV.\nThe study was conducted for these three voltage levels, allowing extrapolation to evaluate performance\ntrends across different voltage ranges. For each voltage level, two options have been considered : i)\nsubstations installed on the surface or underground (in the technical galleries of the accelerator); ii)\nair-insulated substations (AIS) or gas-insulated substations (GIS).\nThe following parameters were included in the analysis, with the aim of evaluating the impact of\nthe different alternatives on all the main aspects of the total lifetime cost of the network:\n\u2013 OPEX1 of the HV lines: electrical losses of the lines depending on their operation over the full FCC\nmachine (based on the operating models of the phases of FCC-ee, and on a simplified estimation\nof the same models for FCC-hh).\n\u2013 CAPEX2 of the HV lines: initial cost of the cables, the accessories and the installation works\nrequired.\n\u2013 OPEX of the HV substations: electrical losses of the transformers depending on their operation\nover the full FCC machine programme and the cost of the maintenance of the substations.\n1Operational expenditure\n2Capital expenditure\n377\n\n\u2013 CAPEX of the HV substations: initial cost of the substations, and equivalent financial value of\ntheir space occupation.\nThe values of CAPEX and OPEX of each case have been assessed based on detailed studies of\nthe substations and the lines at the different voltage levels, but also with estimated financial values of the\nspace occupied and energy cost.\nThis comprehensive analysis gave the total lifetime cost for each scenario, with the variation trends\nillustrated in Fig. 8.56. The study concludes that selecting a 63 kV transmission voltage and using GIS\nsubstations installed on the surface are the optimal choices within the range analysed. Additionally, man-\nufacturers are demonstrating a clear trend toward reducing the greenhouse gases used in GIS mixtures,\nsignificantly improving the environmental sustainability of this technology. The final technical solution\nwas developed based on these findings.\nFig. 8.56: Trend of the variation of the total lifetime cost of the electrical grid for different voltage levels,\nlocations and technologies of the HV transmission network.\nThis analysis will be kept running in the future phases of the FCC study, as some parameters have\na significant impact and can change the conclusions.\nMain high voltage substations\nThe design of the HV substations has been developed according to the results of the analysis shown on\nFig. 8.56.\nA 400/63 or 225/63 kV GIS substation will be installed with a main stepdown transformer of\n220 MVA in the three points connected to the European grid. The main switchgears and auxiliary systems\nwill be housed inside a dedicated building, while the transformer will be installed nearby, protected by\nfirewalls and equipped with all necessary safety systems to manage potential oil spills. These include a\ncontainment pit, oil separator, retention basin, and fire protection measures to ensure safe operation and\nenvironmental compliance. It is worth noting that in PH an additional bay will be available in the 400 kV\nswitchgear, to supply an additional 150 MVA 400/40 kV transformer that will be dedicated to the power\nconversion system for the FCC-ee RF system.\nA 63 kV GIS substation will be installed at all the other access points, as shown in the single line\ndiagram of the transmission network in Fig. 8.58a. Also, in this case, the main switchgear will be housed\nwith the auxiliary systems in a building. At each point, the 63 kV GIS substation will supply two 40 MVA\n378\n\n63/20 kV transformers that will be the sources of the distribution networks for each point.\nIn each access point connected to the grid, the total surface area of the HV substation will be ap-\nproximately 10 000 m2; in each of the other points, it will be approximately 4000 m2, these requirements\nare already included in those considered by the civil engineering team for the surface occupation and the\nlayouts of the different sites.\n(a) Single line diagram.\n(b) Layout.\nFig. 8.57: Typical 400/63 kV substation\n(a) Single line diagram.\n(b) Layout.\nFig. 8.58: Typical 63 kV substation\n379\n\nInstallation of HV cables in the accelerator tunnel\nAs the installation of HV transmission networks rated at tens or hundreds of MVA is not a standard\nsolution adopted in the underground accelerator facilities (e.g., in LHC today only cables of up to 18 kV\nand rated at 15 MVA are installed for the electrical distribution), a detailed and specific feasibility analysis\nhas been performed, in order to confirm the absence of showstoppers and to provide requirements for\ncivil engineering.\nThe final report of this analysis confirms the feasibility of installing such cables in the underground\nareas of the accelerator. It provides models and datasheets of cables with their related losses, different\ninstallation methods with their constraints and the required space and civil engineering works to install\nand house the cables. It also includes a cost estimate and a tentative schedule for the installation. All the\ndetails can be found in Ref. [384], but a summary is presented in Table 8.22.\nTable 8.22: Summary table of the requirements of the HV lines.\n63 kV\n132 kV\nProposed cable\n3\u00d7 1200 mm2,\nAluminium cable\n3\u00d7 630 mm2,\nAluminium cable\nProposed space occupation\nin the tunnel\nConcrete duct of 520\u00d7500 mm.\nProposed quantity of\njunction chambers\n13 junction chambers (including 1 earthing junction chamber)\nProposed space occupation\nof junction chambers\nWith earthing of screens:\nduct of 1500\u00d7500 mm\nwith a length of 9.5 m.\nWith earthing of screens:\nduct of 1800\u00d7500 mm\nwith a length of 12 m.\nPreferred installation method\nWithin PEHD ducts with the so-called cable train pulling method.\nCost of installation\nLower cost\n+ 4% compared to 63 kV\nSchedule estimation of\ninstallation (per line\nbetween two points)\n160 days\n170 days\nLevel of magnetic field\nin the tunnel\nSee magnetic field graphs on Fig. 8.59.\nFig. 8.59: Comparison of magnetic field simulations for cables (63 kV in blue, 132 kV in red).\n380\n\nTwo important points deserve to be mentioned: the cable runs in a concrete duct of 520\u00d7500 mm\nin the machine tunnel requiring a specific volume, as can be seen in Fig. 8.61; and the cables along\na tunnel sector need junction chambers every approximately 1-1.5 km, requiring a significant space in\nthe tunnel of approximately 1200\u00d7500\u00d716 000(length) mm as shown in Fig. 8.62. This second point is\nimportant, as it was decided to create the junction chambers corresponding to each alcove (in the current\nbaseline, every 1.6 km ), housing them in the transport parking areas to ease their construction and future\naccessibility.\nFig. 8.60: Specification of the proposed 63 kV cable.\n381\n\nFig. 8.61: Proposed space occupation of the cables in the machine tunnel.\nFig. 8.62: Proposed space occupation of the junction chambers in the machine tunnel.\nDistribution networks\nThe power is locally dispatched to the electrical loads of the surface and underground facilities by the\nmedium and low voltage distribution networks available at each point.\nThe various loads can be classified based on their function and criticality, and each category has a\ndedicated distribution network with specific features, as shown in Table 8.23. The functional separation\nof the networks was one of the criteria in the study of the distribution at each point. This was to ensure\nusers\u2019 power quality (in particular, to minimise potential disturbances from power electronics) and to\nenhance reliability, operability and maintainability of the grid.\n382\n\nTable 8.23: Network types and characteristics.\nNetwork Type\nLoads type (non-exhaustive list)\nPower unavailability duration in\ncase of degraded scenario\nMachine\nPower converters,\nRF, cooling\npumps, fan motors, etc.\nUntil return of main supply\nGeneral\nServices\nLighting, outlets\nUntil return of main or secondary\nsupply\nSecured\nPersonnel\nsafety-related\nloads\n(lighting, pumps, elevators)\n10-30 s\nUninterruptible\nPersonnel safety (evacuation and\nanti-panic lighting,\nfire-fighting\nsystem, oxygen deficiency, evacu-\nation)\nInterruptions are not allowed; con-\ntinuous service is mandatory\nMachine safety (sensitive process-\ning and monitoring, beam loss,\nbeam monitoring, machine protec-\ntion)\nThe distribution network concept is the same for all points. The HV transmission network sup-\nplies two 63/20 kV transformers to create two main types of networks at 20 kV: General Services (GS)\nand Machine. The power is dispatched through two medium voltage substations (one in a surface build-\ning, the other in the underground service cavern) to 20/0.4 kV transformers that supply the low voltage\nswitchboards in charge of local distributing to the terminal loads.\nThe GS and machine networks can be coupled at the 20 kV substations to allow a backup supply:\nthe size of the main 20 kV transformers, busbars and links (primary and backup) has been set to allow\nfull reconfiguration and nominal operation in case one element of the network is unavailable as a result\nof maintenance or failure. For these reasons, and also to cope with the load forecast of the FCC-hh, the\ntwo main transformers of each point have been sized at 40 MVA, and the main 20 kV links at 20 MVA.\nAn example is shown in the single line diagram of the distribution network of point PA shown in\nFig. 8.63, and the layout of the 20 kV substations on the surface at the same point is shown on Fig. 8.64.\n383\n\nFig. 8.63: Conceptual electrical distribution for point PA.\n384\n\nFig. 8.64: Layout of the 20 kV substation of point PA.\nSecured and uninterruptible networks\nBased on the load categories of Table 8.23, there is a secured network with backup sources available at\neach point to power critical loads within a few seconds of the main supply becoming unavailable. The\nfirst priority backup sources have an emergency power station installed on the surface close to the substa-\ntion (the baseline is a diesel generator, alternatives like hydrogen-based groups are under evaluation). As\nan alternative, there will be a connection to the medium voltage utility deployed during the construction\nphase which will be kept available.\nThe backup sources will be at 20 kV and will be connected to the surface substation, on a busbar\nwhere only critical loads are hosted; from there, a cable running down the shaft will connect to the\nequivalent in the underground substation. From the underground substation, the secured network will be\ndistributed to each alcove through a 20 kV line, and each secured load in the tunnel will be powered from\nits closest alcove.\nThe distribution from the secured substation in the tunnel must be done at medium voltage, as\nstepping down to low voltage would mean having an excessive voltage drop in the circuits running along\nthe sector. In this sense, a possibility for optimisation was identified during the study, and to avoid\nduplicating the 20 kV cables in the tunnel (one for the normal network, one for the secured power), it is\nproposed to use the same link deployed for the general services, applying a load shedding logic in case\nof power outage. The aim is to minimise the space occupation and ease integration in this tight area.\nIn all the substations (surface, underground, alcoves) there will be a coupling between the critical\nloads 20 kV busbar and the general services busbar; in normal operation, the coupling will be closed,\nand the link between the substations will serve both critical and not-critical loads. In case of a failure,\nmaintenance or any other unavailability of the main source, the electrical network will be supplied using\nthe backup power sources: in this case, the couplings between the secured network and the general\nservices network will be automatically disconnected, and in the tunnel the same 20 kV link will only\nkeep the loads related to the safety of people live.\nThe secured network of one access point covers all the facilities of the point itself at medium\nvoltage and up to half a sector left and right in the tunnel. To enhance the reliability of the system, there\nis an MV coupling to the last alcoves of each half sector: this stays open during normal operations. If\n385\n\na part of the network connected to one point is not operational, all the secured network busbars can be\npowered from the adjacent points through the tunnels by closing this coupling.\nThe secured network described so far is specifically designed to support electrical loads related to\nthe safety of personnel. If a similar level of backup is required for systems associated with the accelerator\nor experiments, a parallel infrastructure with equivalent characteristics will need to be developed and\nimplemented. For loads that cannot accept a brief interruption of few seconds, whether they are safety-\nrelated or critical to operation, an uninterruptible power supply (UPS) system supported by batteries will\nbe made available. This system will be strategically installed in buildings, service caverns and alcoves,\nto ensure a continuous power supply with the necessary autonomy. This infrastructure will serve critical\nloads of systems like vacuum, machine protection, cryogenics, RF, control, IT.\n386\n\n(a) On surface,\n(b) underground,\n(c) in the tunnel.\nFig. 8.65: Conceptual electrical distribution for the secured network.\n387\n\n8.4.3\nRF Powering\nThe RF system requires a power source capable of delivering a stable, high-quality DC high voltage. In\nexisting implementations, such as the LHC and other accelerators, this is typically achieved by supplying\na small group of RF amplifiers with a power converter operating in the MW range. However, for FCC-\nee, this approach has been deemed economically unfeasible due to the large number of power converters\nand the extensive surface infrastructure that would be required at point PH. To address this challenge, a\ncentralised power conversion strategy has been adopted, utilising a modular multilevel converter (MMC)\nto efficiently meet the system\u2019s power requirements.\nGiven that the RF system\u2019s power demand exceeds 100 MW, a thyristor-based converter was con-\nsidered but ultimately found to be impractical due to power quality issues. If such a converter were\nimplemented, a large-scale reactive power and harmonic compensation system would be required to\nmaintain acceptable power quality. In contrast, the MMC solution offers significant advantages: it re-\nquires minimal or no harmonic filtering on the AC side and provides flexible reactive power control. This\ncapability could potentially be leveraged to partially compensate for the reactive power consumption of\nthe accelerator, further optimising energy efficiency.\n8.4.4\nArc powering and alcoves\nPower is distributed through the alcoves along the tunnel from the underground 20 kV substations. The\nalcoves serve multiple functions: they house equipment that must be protected from radiation, as well\nas local distribution systems for the arc, including accelerator systems, cooling and ventilation, safety\nsystems, lighting, and power boxes. Additionally, they accommodate the power converters responsible\nfor supplying the magnets in the arc.\nThe current baseline design includes seven alcoves per arc, with two larger alcoves positioned at\nthe ends of the LSS (long straight section) of each point. These larger alcoves will host the power con-\nverters for the main arc magnets (dipoles and quadrupoles), as they require more space. The remaining\nalcoves will be spaced every 1600 m, each covering a sector extending 800 m on either side, distributing\npower accordingly.\nThe machine and general service networks will be separately available only in the first alcoves\nat the LSS ends, as the power converters in these locations have significantly higher loads and must be\npowered using dedicated transformers connected to a separate machine network. However, for the other\nalcoves, where power requirements for converters and other accelerator systems are much lower, it has\nbeen decided to supply them only from the general service network to avoid installing two separate 20 kV\nlinks in the tunnel.\nTo achieve this optimisation, the functional separation criteria outlined in Table 8.23 has been sus-\npended for the alcoves. Instead, the choice is based on the assumption that the electrical parameters of\nthe installed systems, particularly the power converters, will comply with specific requirements for con-\nnection to the network, including resilience to voltage and frequency variations and low total harmonic\ndistortion (THD).\nA similar synergy has been adopted for the safety-related loads and the secured network in the\nalcoves. These will be supplied through the same 20 kV link running through the tunnel, using a load-\nshedding logic to prioritise general services when necessary.\nFollowing these technical choices, one 20 kV cable will run through the tunnel to the first smaller\nalcove from the alcoves at the end of the LSS at each access point, connecting it and continuing to the\nnext, up to the end of the arc at the next access point (see Fig. 8.66. In the nominal configuration,\neach access point will supply the alcoves of half sectors to the left and to the right, with the one in the\nmiddle having an open coupling between the two sides. Closing this coupling and having the 20 kV cable\nrunning from one point to the other, will allow re-supplying all the alcoves from only one point if the\nother is unavailable.\n388\n\nFig. 8.66: Arc and alcoves powering layout concept.\nElectrical equipment in the alcoves\nThe power distribution of the alcoves has been studied and sized based on the load requirements identi-\nfied for the FCC-ee arc. The 20 kV cable coming from the arc will arrive at a switchgear divided into two\nbusbars for secured and other loads. The switchgear will be connected to 20/0.4 kV transformers power-\ning various low voltage switchboards, from where all the circuits going to the alcove and the tunnel are\nsupplied. A redundant UPS will provide the required backup to create an uninterruptible network for the\ncritical loads, and a redundant power supply will be dedicated to the emergency lighting.\nIn addition to the power converters, a certain number of racks will be installed, supplied through\nad-hoc busbar trunking systems, and hosting the systems required for the accelerator and the services in\na sector. Today the number of these racks is estimated at 13 units but could evolve in accordance with the\nevolution of the systems\u2019 requirements. Figure 8.67 shows the typical single-line diagram of the power\ndistribution of an alcove.\nFig. 8.67: Typical single line diagram of the power distribution of an alcove.\nA preliminary study has been conducted for the so-called big alcoves at the end of the LSS, con-\n389\n\ncerning the powering of the power converters and of the loads of the half sector. The principles that have\nbeen applied are the same as used for the other alcoves, and the single line diagram is shown on Fig. 8.68.\nFig. 8.68: Typical single line diagram of the power distribution of a big alcove at the end of LSS.\nElectrical equipment in the arc\nThe list of the equipment and circuits for the powering of the arc includes:\n\u2013 One power outlet box on the general service network every 50 m, powered from only the closest\nalcove (maximum length of the circuit: 800 m), without redundancy.\n\u2013 One power outlet box on UPS network every 50 m, with secured redundant powering from both\nalcoves to the right and left (maximum length of the circuit: 1600 m).\n\u2013 One normal light every 5 m, powered from only the general service network of the closest alcove\n(maximum length of the circuit: 800 m), with a circuit connected in parallel to the secured switch-\nboard of the same alcove supplying 1 light out of 5 (to create a set of minimum lighting every\n20 m).\nIn addition, the list of the electrical equipment related to safety in the arc includes:\n\u2013 One electrical emergency button (AU) every 50 m.\n\u2013 One emergency light every 14 m, with secured redundant powering from both alcoves on the right\nand left (maximum length of the circuit: 1600 m).\n390\n\nFig. 8.69: Electrical distribution in the arc.\nThe list of the cables composing these circuits is given in Table 8.24.\nTable 8.24: Estimation of the power cables in the arc.\nUser\nLoad\nCable\ntray\nCable\ntype\nSize (mm)\nNumber of\nlines in\nthe tunnel\nPowering\nMV power of alcoves\nMV\n3\u00d7(1\u00d7400 mm2)\n+ (1\u00d7120 mm2) Cu\n3\u00d7d=50 + d=21\n1\nPower outlets\non GS network\nLV\n3\u00d7(1\u00d7150 mm2)\n+ (1\u00d795 mm2) Cu\n3\u00d7d=21 + d=18\n1\nPower outlets on UPS\nLV\n3\u00d7(1\u00d7150 mm2)\n+ (1\u00d795 mm2) Cu\n3\u00d7d=21 + d=18\n2\nClassic lighting\nLV\n(5\u00d710 mm2) Cu\nd=22\n1\nEmergency lighting\nSafety (5\u00d72.5 mm2) Cu, flat\n24x6\n2\nEmergency stops link (AU) Safety 14\u00d7(2\u00d71 mm2) Cu\nd=21\n2\nThe quantification of these cables is of great importance in the assessment of the space required\nfor the cable trays and other containment systems (e.g., cablofil, duct) that need to be installed in the arc.\nFor the same reason, the signal and control cables and the optical fibres used by other systems\nand installed in the arc have also been estimated. This process started from the various system\u2019s owners\nwhen available, or from extrapolation from previous accelerator projects at CERN when the information\nwas not available. The list of these cables is given in Table 8.25.\nThe collection of the powering and cables\u2019 requirements in the tunnel will be constantly updated in\nthe next stages of the study to consider every possible modified or new request and to adapt the technical\nsolution accordingly. Furthermore, the use of optical fibres should be prioritised over copper cables to\nminimise space occupancy when developing users\u2019 cable requirements.\n391\n\nTable 8.25: Estimation of the control and signal cables, and optical fibres crossing the arc.\nUser\nLoad\nCable tray Cable type\nSize (mm)\nNumber of\nlines in\nthe tunnel\nFibre optics\nBackbone\nFO\n3 cables (\u00d724 fibres)\nd=25\n1\nUnderground\nFO\n9 cables (\u00d724 fibres)\nd=25\n2\nBI (only BPMs)\nFO\n13 cables (\u00d712 fibres)\n+8 cables (\u00d724 fibres)\nd=25\n4\nSensing\nFO\n2 cables (\u00d76 fibres)\nd=25\n1\nVacuum\nion pumps\nSignals\n1\u00d70.63(HV)\n+ 2\u00d70.25 mm2 Cu\nd=10.7\n28\nNEG (power)\nSignals\n3\u00d72.5 mm2 Cu\nd=13\n16\nPenning\nSignals\n3-axis 0.8/8.4 mm Cu\nd=10.3\n12\nPirani\nSignals\n1\u00d7 (4\u00d71 mm2) Cu\nd=6.5\n12\nBA power\nSignals\n6\u00d7 (2\u00d70.75 mm2) Cu\nd=14.5\n6\nBA collector\nSignals\n3-axis 0.5/5.7 mm Cu\nd=7\n6\nSector valve\nSignals\n6\u00d7 (2\u00d70.75 mm2) Cu\nd=14.5\n6\nProfibus\nSignals\n2\u00d7 (1\u00d70.35 mm2) Cu\nd=8\n1\nSector doors\nSafety\n13\u00d7 2\u00d70.5\nd=17\n1\nFire doors - magnet\nSafety\n2\u00d71.5\nd=10.5\n3\nAccess\nFire doors - position contacts\nSafety\n2\u00d71\nd=5\n3\n&\nFire doors - flashing lights\nSafety\n4\u00d71.5\nd=10.5\n3\nAlarms\nCall points - break-the-glass\nSafety\n2\u00d71\nd=5\n2\nCall points - telephones\nSafety\n1\u00d7 4\u00d70.6)\nd=7.4\n2\nEvacuation - voice alarm\nSafety\n2\u00d72.5\nd=13\n2\nCooling\nFancoils\nSignals\n1\u00d770 mm2\nd=16.6\n16\n&\nDampers\nSignals\n1\u00d735 mm2\nd=12.1\n21\nVentilation Valves & other equipments\nSignals\n1\u00d735 mm2\nd=12.1\n3\nRadiation\nprotection\nRadiation detectors\n(t\u00aft phase only)\nSafety\n2\u00d7CEH50\n+ 2\u00d7 (2\u00d70.22 mm2)\nd=9.5\n2\nMagnet\nWIC fieldbus\nSignals\n1\u00d750 mm2\nd=14\n4\nProtection\nBIS fibres\nFO\n1 duct\nd=25\n1\nPower\nConverters\nDC cables\nOthers\nUnknown\nThe information summarised in Table 8.24 and Table 8.25 allows the selection and dimensioning\nof the cable containment systems to be installed (mainly cable trays). This is one of the most important\nfactors for the determination of the layout and cross section of the arc tunnel. The number and dimensions\nof cable trays are:\n\u2013 Twelve 500 mm wide and 60 mm high cable trays for: DC cables (five cable trays considered), MV\npower cables, LV power cables, signal cables and optical fibres.\n\u2013 Two 200 mm wide, 60 mm high and fire-resistant cable trays for safety systems.\n\u2013 One 520\u00d7500 mm concrete duct for the HV cables.\n392\n\n8.4.5\nControl of FCC grid\nAC Network Control Using Unified Power Flow Controllers\nUnified power flow controllers (UPFCs) are power-electronic-based network controllers capable of per-\nforming voltage control, power flow control, reactive power compensation, and protection against net-\nwork perturbations. The versatility of these systems makes them highly suitable for controlling and\nstabilising the FCC AC transmission network, offering an alternative to systems such as static var com-\npensators (SVCs) or DC networks.\nA UPFC consists of two back-to-back converters, each connected to the network via a transformer.\nOne converter is connected in parallel, enabling reactive power or voltage control at the associated net-\nwork node. The other converter is connected in series, allowing active and reactive power flow control,\nvoltage control, and voltage dip mitigation by injecting a specific voltage between the network and the\nloads. Figure 8.70 illustrates the basic structure of the UPFC.\nVDC\nAC\nAC\n+\nConverter 1\nConverter 2\nTransmission Line\nControl\nSeries\nTransformer\nParallel\nTransformer\nV+Vse\nV\nVse\nI\nMeasurements\nParameters\nVRef\nPRef\nQRef\nVse\nV\nV+Vse\nFig. 8.70: Diagram of a unified power flow controller (UPFC) used to enhance controllability of the FCC\nnetwork.\nThe application of UPFCs in the FCC network can be tailored to specific protection and reactive\npower compensation requirements. In the high-voltage transmission ring, UPFCs can be installed at each\nnetwork connection point to manage the accelerator\u2019s reactive power using the parallel converter. At the\nsame time, the series converter provides protection against voltage dips and prevents undesired power\nflows, particularly under closed-loop operation.\nAt the medium-voltage level, UPFCs enable voltage control and protect access points from voltage\ndips. To optimise equipment efficiency, protection can be focused on critical sections of the network by\nconnecting the series transformer to selected feeders. This approach creates a dedicated machine net-\nwork, effectively decoupling it from general services, following the model already employed in CERN\u2019s\nexisting infrastructure.\nCompared with existing compensating equipment such as SVCs, UPFCs offer enhanced function-\nality. While they perform the same tasks of reactive power compensation and voltage control, UPFCs\nare more robust to network perturbations, exhibit faster response times, and, through the series converter,\nprovide load protection against transients - an advanced feature not currently available in SVCs.\n393\n\nAt this stage of the project, the exact compensating requirements are not fully defined. However, it\nis anticipated that the reactive compensation needs for each access point will be approximately 10 MVAr.\nRegarding voltage dip compensation, most of the recorded voltage dips at CERN exhibit a depth of less\nthan 30% of the nominal voltage. With this figure in mind, and assuming a power rating of 10 MVA\nfor the loads to be protected at each access point, the UPFC must be designed to inject up to 3 MVA\nduring such events. Based on these considerations, the total installed UPFC power per access point can\nbe estimated at approximately 15 MVA.\nDC Distribution Alternative\nRecent developments in power electronics have enabled the use of DC for power transmission and dis-\ntribution. Compared with conventional AC distribution, DC networks offer lower transmission losses,\nas only active power flows through the cables and the skin effect is absent. Additionally, DC networks\nprovide precise power flow control and mitigate perturbations originating from the AC network.\nThe use of DC to transmit power from network connection points to accelerator loads is under\nconsideration. In this transmission scheme, loads are supplied by high-voltage converters with energy\nbuffers that decouple them from network dynamics. This configuration enables the local generation or\nabsorption of reactive power as required by the loads and protects them from network perturbations. To\nimplement these features, the network configuration shown in Fig. 8.71 is proposed.\nPH\nHVDC\nG-H\nPG\nHVDC\u00a0\nPD\n20 kV\u00a0\nPB\n20 kV\u00a0\nPB\nHVDC\nPA\nHVDC\nPF\nHVDC\nL-A\u00a0\nA-B\nB-D\u00a0\nD-F\u00a0\nH-J\nF-G\nRTE\n400 kV\nPJ\n20 kV\u00a0\nPG 20 kV\u00a0\nRTE\n225 kV\nPD\n225 kV\u00a0\nJ-L\u00a0\nPF\n20 kV\u00a0\nPJ\nHVDC\u00a0\nPL\n20 kV\u00a0\nPA\n400 kV\u00a0\nFCC HVDC\nTransmission\nRing\nPA\n20 kV\u00a0\nPD\nHVDC\nPH 20 kV\u00a0\nPH\n400 kV\u00a0\nRTE\n400 kV\nPL\nHVDC\u00a0\nFig. 8.71: High Voltage DC network used as an alternative to conventional AC distribution along the\naccelerator ring.\nIt consists of eleven power converters: three operating as rectifiers and eight as inverters. A key\nfeature of this configuration is the closed-loop operation of the transmission ring, which guarantees\n394\n\nprecise control of power flows. This operational mode enables adjustments to the power drawn from the\nmain connection points, optimising flow and ensuring resilience in the event of a feeder outage. In such\nscenarios, any point on the accelerator can still be supplied by at least two feeders located on opposite\nsides of the ring.\n8.4.6\nEnergy storage systems\nThe use of energy storage systems (ESS) is being evaluated for the FCCee and FCChh. The primary\nobjectives of ESS are:\n\u2013 Providing energy to critical systems (e.g., safety or cryogenics) during electrical outages lasting\nfrom minutes to hours (some of these systems currently rely on diesel generators).\n\u2013 Storing lower-cost energy from renewable sources (local or otherwise) for later use.\n\u2013 Temporarily storing the energy of FCC-hh magnets during the deceleration phase of the accelera-\ntion cycle and returning it during the next cycle.\nTechnologies such as batteries, supercapacitors, flywheels, electrolysers, fuel cells (hydrogen-\nbased), and gravitational energy storage systems have been preliminarily analysed and compared for the\nabove-mentioned applications.\nA collaboration has been established to explore the integration of hydrogen as an energy storage\nsystem (ESS) vector to support one or more functions within the accelerator complex. Hydrogen-based\nsystems are particularly well-suited for both short and long-term energy storage, offering the advantage\nof decoupling energy storage capacity - determined by the hydrogen mass - from charging speed, defined\nby electrolyser capacity, and power output, which is set by the fuel cell capacity.\nThe heat generated by electrolysers and fuel cells is available at high temperatures, which can\nenhance the usability of waste heat. For instance, this heat can be used to increase the temperature of\nwater used for cooling various equipment, thereby improving the efficiency and transportability of waste\nheat over longer distances. Additionally, the heat recovered can be leveraged to drive absorption cooling\ncycles, contributing to the cooling needs of magnets, power converters, tunnels, and other infrastructure.\nIn principle, hydrogen-based ESS technology offers high flexibility and adaptability across a wide\nrange of applications. However, it has some drawbacks, including relatively low conversion efficiency\nand the requirement for robust hydrogen storage systems. Nevertheless, the co-generation of usable heat\nand cooling can partially offset these efficiency limitations, making hydrogen a promising candidate for\nintegration into the FCC infrastructure. Studies on the feasibility and implementation of hydrogen ESS\nwithin the FCC are ongoing and will be further intensified in the future.\nFor the FCC-hh superconducting magnets, preliminary assessments suggest that batteries appear\nto be the most suitable ESS technology for recovering energy during the ramp-down phase of the cycle\nand re-injecting it into the magnets during the next acceleration cycle.\n8.5\nCryogenic systems\nCryogenic infrastructure is essential for various components of the accelerator. The experiment points\nPA, PD, PG, and PJ will each be equipped with two cryoplants: one dedicated to the detector magnet\n(detector cryoplant) and another to the machine detector interface (MDI) region magnets (interaction\nregion (IR) cryoplant). These systems ensure the required low-temperature environments for the sensitive\ncomponents in the experiment regions.\nWhile the technical points PB and PF do not require cryogenic refrigeration, the technical points\nPH and PL are associated with the radiofrequency (RF) system, which necessitates operation at 2 K\nand 4.5 K to efficiently accelerate particles to the required energies. Each technical point features a long\n395\n\nstraight section (LSS) of 2032 m, symmetrically distributed around the interaction point (IP). The RF sys-\ntem, composed of a string of superconducting cavities and klystrons, is housed within these LSS regions\nand requires dedicated cryogenic refrigeration to maintain the necessary low-temperature conditions for\nefficient operation.\nFig. 8.72: FCC-ee collider cryogenic system layout for t\u00aft operation.\nInstallation of the cryogenics for the cooling of the superconducting RF systems will follow the\nsame strategy defined for the cryomodules to be operated in the technical points PH and PL.\nA new RF layout was proposed in June 2024 with the aim of simplifying the overall installation\nof the SRF system. As described in Section 3.4.3, it consists of installing and, from the beginning,\noperating all the 2-cell 400 MHz cavities for the Z, WW and H mode, with each cavity powered at\n500 kW in continuous wave (CW) mode. In other words, all the cryomodules necessary for the operation\nof FCC-ee at the energies of Z, WW and H levels will be installed at once and operated with the heat\nloads corresponding to the Z energy. This is valid for both 400 MHz and 800 MHz cryomodules.\nThis new layout significantly simplifies the design and staging of the cryogenic system. There will\nonly be two stages: one for the Z, WW and H operation, with cryoplants operated to cover heat loads at\nH energy, and another one for t\u00aft operation, with the same cryogenics scenario. This major modification\ndrove the update of the cryogenic system with respect to the CDR, and the corresponding results can be\nfound in the following sections.\n8.5.1\nCryogenics for superconducting RF systems\nLayout and architecture\nThe general cryogenic layout of the FCC-ee RF system is shown in Fig. 8.73. Cryoplant locations are\nindicated using small circles near the experiment and technical points.\n396\n\nFig. 8.73: General cryogenic layout for the technical points.\nAiming to optimise the integration of the machine, the RF systems of the collider and the booster\nhave been split between two points. Point PH contains the collider RF, while point PL contains the\nbooster\u2019s. This separation is also optimised from the cryogenic point of view as the booster and the\ncollider present different heat load profiles. The booster ramps up the energy of the particles from\ninjection energy to collider energy while the collider maintains a constant energy. Both the dynamic and\nstatic loads vary greatly. Moreover, the booster is composed solely of bulk Niobium 800 MHz cavities\noperating at 2 K, whilst the collider is mainly composed of coated elliptical 400 MHz cavities operating\nat 4.5 K. For the collider at point PH, there is an exception at the t\u00aft stage, where 800 MHz cavities are\ninstalled to further increase the accelerating gradient achieved with the 400 MHz cavities.\nFigures 8.74 and 8.75 show the cryogenic plant architectures for point PH and PL respectively. For\ncertain stages that contain two cryoplants, the cryogenic plant architecture includes an interconnection\nbox (QUI) that couples the refrigeration equipment to the cryogenic distribution line. The interconnection\nbox facilitates a level of redundancy amongst the refrigeration plants and eases maintenance procedures.\nThe other elements that are shown in the figures are the warm compressor station (WCS) and the upper\ncold box (UCB), located on the surface. Also included is the lower cold box (LCB), located in the cavern.\nThis split box architecture has a temperature cut of 40 K between the two cold boxes, which reduces the\nhydrostatic losses incurred due to the depth of the tunnel.\n397\n\nFig. 8.74: Cryogenic plant architecture at point PH (RF collider).\nFig. 8.75: Cryogenic plant architecture at point PL (RF booster).\n398\n\nTemperature levels\nIn view of the high thermodynamic cost of refrigeration at 2 K and 4.5 K, the thermal design of cryogenic\ncomponents aims to intercept the largest fraction of heat loads at higher temperatures, hence the use of\nmultiple staged temperature levels. These are:\n\u2013 50 K \u2013 75 K for thermal shield as the first major heat intercept, sheltering the cavity cold mass\nfrom the bulk of heat inleaks from the environment.\n\u2013 4.5 K normal saturated helium for cooling 400 MHz superconducting cavities.\n\u2013 2 K saturated superfluid helium for cooling the 800 MHz superconducting cavities.\nThe cryomodules (CM) and cryogenic distribution line (QRL) combine several low temperature insula-\ntion and heat interception techniques which will have to be implemented on an industrial scale. These\ntechniques include low-conduction support systems made of non-metallic fibreglass/epoxy composite,\nlow impedance thermal contacts under vacuum for heat intercepts and multi-layer reflective insulation\nfor wrapping the cold surface.\nHeat loads\nInward static heat leaks (inleaks) arise from the ambient temperature environment and depend on the\ncryomodule design. The current design adopts a fully segmented architecture for both the booster and\nthe collider, where each cryomodule has an independent connection to the cryogenic distribution line.\nAdditionally, this distribution line is positioned externally to the cryomodule. The thermal calculations\nfor the cryomodules are based on the thermal performance data of similar cryogenic assemblies.\nThe heat loads in the RF cryomodules are dissipated in the cavity baths at 4.5 K and 2 K. These\nheat loads are determined by both the thermo-mechanical design of the cryomodule and the heat dissipa-\ntion from the cavities during operation.\nTable 8.26 presents the heat load values for point PH, while Table 8.27 provides the corresponding\nvalues for point PL. The reported values (excluding margins) originate directly from the SRF group. For\nthe booster, these values are expected to increase, as the final RF cavity voltage and duty cycle have not\nyet been determined. The heat loads given in Table 8.27 for the booster assume a duty cycle of 15%.\nHowever, duty cycle values across different working points will range between 15% and 90% and still\nrequire finalisation.\nAdditionally, the reported heat loads do not account for all margins or the dynamic heat loads\nresulting from dissipation in the fundamental power coupler and higher-order modes (HOMs). These\nvalues are valid for an installed quality factor of 3.0 \u00d7 1010 for the 800 MHz cavities and 2.7 \u00d7 109 for\nthe 400 MHz cavities.\nNotably, at the t\u00aft stage for both point PH (collider) and point PL (booster) there will be 800 MHz / 2 K\ncavities. These 800 MHz cavities have different heat loads at the different points. While the static heat\nloads are similar, the dynamic losses are very different with 27.1 W/cavcollider and 3 W/cavbooster. The\ndynamic losses are very different since the collider operates in continuous waves with 27.1 W/cavcollider\nwhile the booster dynamic losses are dependent on the duty cycle. This value is likely to increase fol-\nlowing the expected increase of the booster duty cycle.\n399\n\nTable 8.26: Collider heat loads at point PH (as of October\u201924).\nFCC-PH (collider)\nZ, WW, & H\nt\u00aft\nFreq [MHz]\n400\n400\n800\nTemperature [ K]\n4.5\n4.5\n2.0\nNo. of cryomodules\n66\n66\n102\nNo. of cavities (\u00d74)\n264\n264\n408\nStatic losses to the thermal shield / CM (no margins) [W]\n218\n218\n120\nStatic losses to the helium bath / CM (no margin) [W]\n131\n131\n37.3\nDynamic losses / cavity (no margins) [W]\n128\n129\n27.1\nDynamic losses / CM (no margins) [W]\n512\n516\n108.5\nTotal static losses to the thermal shield (with uncertainty factor) [kW]\n21.6\n21.6\n18.4\nTotal static losses to the helium bath (with uncertainty factor) [kW]\n13\n13\n5.7\nfTotal dynamic losses (with overcapacity factor) [kW]\n50.7\n51.1\n16.6\nTable 8.27: Booster heat loads at point PL with an assumed duty cycle of 15% (as of October\u201924).\nFCC-PL (Booster)\nZ, WW, & H\nt\u00aft\nFreq [MHz]\n800\n800\nTemperature [ K]\n2.0\n2.0\nNo. of cryomodules\n28\n112\nNo. of cavities (\u00d74)\n112\n448\nStatic losses to the thermal shield / CM (no margins) [W]\n103\n103\nStatic losses to the helium bath / CM (no margin) [W]\n37\n37\nDynamic losses / cavity (no margins) [W]\n3\n3\nDynamic losses / CM (no margins) [W]\n12\n12\nTotal static losses to the thermal shield (with uncertainty factor) [kW]\n4.3\n17.3\nTotal static losses to the helium bath (with uncertainty factor) [kW]\n1.6\n6.2\nTotal dynamic losses (with overcapacity factor) [kW]\n0.5\n2.0\nDimensioning the cryoplants requires adding margins to the raw heat loads, by defining and ap-\nplying two factors, the uncertainty and the overcapacity. The uncertainty, evolving during the project\nlifetime, is set to 50% for the feasibility study and covers the design uncertainties of the cryo facility. It\nis applied to the static heat loads. The overcapacity, stable during the project lifetime, is also set to 50%\nfor the feasibility study, and ensures nominal performance of the cryo facility by covering specific risks\nsuch as reduced performance induced by ageing and operational flexibility. The overcapacity is applied\nto both the dynamic heat loads and the static heat loads after the uncertainty factor. Figure 8.76 shows a\nvisual representation of how the margins were applied.\n400\n\nFig. 8.76: Uncertainty and overcapacity margins on the raw heat loads\n8.5.2\nCooling scheme and cryogenic distribution\nThe cooling scheme for the cryomodules is represented in Fig. 8.77. The 4.5 K cavity cold masses are\nimmersed in saturated helium baths, which are supplied by line C. The saturation pressure is maintained\nby line D, which recovers the evaporated vapour. The 2 K cavity cold masses are immersed in saturated\nhelium baths, which are supplied by line A. The low saturation pressure is maintained by pumping the\nvapour through line B. Each cryomodule has a dedicated thermal shield and heat intercept circuit cooled\nin parallel between line E and F.\nFig. 8.77: Cryogenic flow scheme for the cryomodules. Here the cryogenic plant is located to the right\nof the 800 MHz section.\nTable 8.28 gives the size of the main cryogenic distribution system components. The cryogenic\ndistribution line (QRL) was designed for the final t\u00aft stage, making it oversized for the Z, W, and H stages.\nThis design choice was made to lower installation complexity and costs. A visual cross-sectional view\nof the QRL can be seen in Fig. 8.78. A front view of the lengths of the QRL along with other connecting\ncomponents in the service cavern and LSS sections can be seen in Fig. 8.80 and Fig. 8.79.\n401\n\nTable 8.28: Dimensions of the main cryogenic distribution line components.\nComponent\nDiameter [mm]\nDiameter [mm]\nPoint PH\nPoint PL\nLine A: 1.3 bar, 2.2 K\n80\n60\nLine B: 30 mbar, 2.0 K\n345\n265\nLine C: 3 bar, 4.6 K\n120\n20\nLine D: 1.3 bar, 4.5 K\n200\n20\nLine E: 20 bar, 50 K\n80\n60\nLine F: 18 bar, 75 K\n80\n60\nVacuum jacket (400 MHz)\n550*\n-\nVacuum jacket (800 MHz)\n830*\n600*\n* +100 mm for bellows and flanges.\nE\nF\nDN850\nDN750\nB\nA\nC\nD\nE\nF\nDN550\nDN650\nC\nD\nB\nE\nF\nA\nDN850\nDN750\nC\nD\nb)\na)\nFig. 8.78: Cross sections of point PL (left) and point PH (right) cryogenic distribution line. a) for the\ncooling of 800 MHz cryomodules. b) for the cooling of 400 MHz cryomodules.\nFig. 8.79: Collider (point PH) cryogenic plant distribution architecture at the t\u00aft stage.\n402\n\nFig. 8.80: Booster (point PL) cryogenic plant distribution architecture at the t\u00aft stage.\n2 K system optimisation\nRefrigeration of the RF cavities in a 2 K saturated bath involves low-density helium (He) with process\npressures in the 30 mbar range. A series of compressors are required to achieve these pressure levels.\nWhenever high mass flow rates of helium need to be treated, performing a large fraction of the com-\npression at low temperatures allows operating with a higher density, effectively limiting the size of the\ncompressors. During t\u00aft operation of FCC-ee, about 550 g/ s or 250 g/ s [385] per train will need to be\npumped at points PH and PL, respectively. In both cases, a cold compressor system (CCS), composed of a\nseries of centrifugal compressors, will be required to provide the compression back to semi-atmospheric\nlevels (\u2248400 mbar). From previous studies, it is considered that a CCS of 12 kW at 1.8 K is feasi-\nble [386,387]. This translates into a mass flow rate of about 500 g/ s with one train of four compressors\nat a suction pressure of 16 mbar. Addressing FCC-ee needs, the suction pressure of such a CCS can be\nincreased as the saturation temperature desired is 2 K. This leads to slightly higher densities and, hence,\nallows operation with slightly more than 500 g/ s mass flow rates.\nThe lower the design suction pressure of a CCS is, the more compression stages may be required\nto reach semi-atmospheric levels, increasing the complexity of the system further. Since the cavities are\ncooled by a saturated He-II bath [388], the furthermost 2 K cryomodule will need to be at the saturation\npressure of helium at 2 K, that is, at 31 mbar. The pressure drop along the distribution line to that\ncryomodule needs to account for this and must be minimised so that the suction pressure at the inlet of\nthe CCS is kept as high as possible. The design goal is to limit the total pressure losses such that the\nsuction pressure of the CCS stays above 22 mbar. Out of the 9 mbar of available pressure drop, 7 mbar is\nleft as a margin for heat exchangers, elbows and valves, and 2 mbar is set as a design criterion for sizing\nthe very low pressure (VLP) return line or line B in Fig. 8.81. The choice of 2 mbar provides a good\ncompromise for the CCS suction pressure and the overall size of the VLP line. Limiting the pressure\ndrop further could hinder the already difficult distribution line integration in the 5.5 m diameter tunnel,\n403\n\nwhere the space is very limited due to the presence of both booster and collider machines.\nEnsuring a thermodynamically well-adapted architecture is essential to reduce the high cost asso-\nciated with such a system. Several architectures have been assessed and compared so far, with the goal\nof finding the optimum choice when considering both energy and integration constraints. Figure 8.81\nshows the two main options that are being considered.\nFig. 8.81: FCC-ee 2 K system distribution architecture options studied, a) and b). CCS being the Cold\nCompressor System, RM the Return Module, C-HEX the Centralised Heat Exchanger and D-HEX the\nDistributed Heat Exchanger.\nThe current calculations for the cryoplants and QRL are based on the preliminary architecture\nchoice of the C-HEX design. An energetic optimisation was performed [389] to justify the preliminary\narchitecture choice. The conclusions of the study showed that choosing a D-HEX based architecture\nmeans only a 1.3% increase in total cryoplant size and energy consumption of FCC-ee. The main gain\nof the C-HEX option is the smaller size of the VLP return line, as well as the central location of one\nsingle HEX, reducing the number of components in the tunnel and easing the overall integration. This\nconclusion is subject to achieving high-efficiency on a C-HEX twice as big as the current state of the art.\nThe current calculations for the cryoplants and QRL are based on the C-HEX design.\nHelium Recovery System\nThe latest available cryomodule inventory values are 55 kg of He at 2 K per 800 MHz cryomodule, and\n116 kg of He at 4.5 K per 450 MHz cryomodule [388]. Because the SRF cavities are low-pressure rated\ndevices, the risk of inventory loss in a non-nominal scenario is high. Without a recovery system the\npressure inside the helium tank of the cryomodules would start building up, in the case of non-nominal\noperation, eventually reaching the set pressure of the pressure relief valve first, then ultimately the burst\ndisc. The latter is the main safety component preventing the cavity from sustaining any mechanical\ndamage. The scenarios that could lead to such a situation are:\n\u2013 Scenario 1: Isolated cryomodule(s) from the cryoplant due to a malfunctioning valve.\n\u2013 Scenario 2: Loss of the full sector cooling capacity (e.g., due to a power outage).\n\u2013 Scenario 3: Beam vacuum break.\n\u2013 Scenario 4: Insulation vacuum break.\nScenarios 3 and 4 generate very high mass flow rates due to the large heat load that appears after\na vacuum break. Therefore, these are to be addressed with the pressure relief devices alone. The helium\n404\n\nrecovery system (HRS) will cover Scenario 1 and 2, which consist of only inherent static heat loads. The\nconcept proposed for such a system is depicted in Fig.8.82 and has been presented in detail in [389].\nFig. 8.82: FCC-ee proposed helium recovery system (HRS) concept.\n8.5.3\nCryogenic plants\nTable 8.29 and Table 8.30 below give the nominal cooling capacity per cryogenic plant required at the\nvarious temperature levels for the technical points, including an overcapacity margin factor of 1.5.\nTable 8.29: Point PH cryoplants and their staging, including an overcapacity margin factor of 1.5.\nZ, WW, & H\nt\u00aft\nType\nC1\nC1+ (Upgrade of C1)\nSchema\nSee Fig. 8.83 (a)\nSee Fig. 8.83 (b)\n50-75 K, kW per cryoplant\n23.7\n37.5\n4.5 K, kW per cryoplant\n36.4\n36.6\n2.0 K, kW per cryoplant\n-\n13.0\nNominal equivalent cooling capacity at\n4.5 K per cryoplant [kWeq]\n39.4\n82.0\nNumber of cryoplants required\n2\n2\n405\n\nFig. 8.83: Point PH cryoplant architecture at Z, WW and H (a), and t\u00aft (b).\nTable 8.30: Point PL Cryoplants and their staging, including an overcapacity margin factor of 1.5.\nZ, WW, & H\nt\u00aft\nType\nB1\nB2\nSchema\nSee Fig. 8.84 (a) See Fig. 8.84 (b)\n50-75 K, kW per cryoplant\n14.4\n16.9\n4.5 K, kW per cryoplant\n-\n-\n2.0 K, kW per cryoplant\n3.6\n6.1\nNominal equivalent cooling capacity at\n4.5 K per cryoplant [kWeq]\n13.3\n22.0\nNumber of cryoplants required\n1\n2\nFig. 8.84: Point PL cryoplant architecture at Z, WW and H (a), and t\u00aft (b).\n406\n\n8.5.4\nCryogen inventory and storage\nThe cryogenics system for the RF points will require helium and nitrogen. Nitrogen will only be needed\nfor the regeneration of absorbers and dryer beds. Consequently, one standard 50 m3 liquid nitrogen\n(LN2) reservoir is planned for each point PH and point PL. The helium inventory is mainly driven by\nthe cryomodule cold mass baths and the cryogenic distribution system. The combined helium inventory\nof point PH (collider) and point PL (booster) is 17.4 tons for the Z, WW, and H stage and 32.7 tons for\nthe t\u00aft stage. The storage will be provided using 250 m3 medium-pressure (MP, 18 bar) storage tanks, the\ntotal number of storage tanks required can be found in Table 8.31.\nTable 8.31: Inventory of helium and its storage for the FCC-ee RF points.\nMachine\nZ, WW & H\nt\u00aft\nCryomodules (t)\n9.2\n19.4\nDistribution (t)\n5.0\n6.0\nCryoplant (t)\n3.2\n7.2\nTotal (t)\n17.4\n32.7\nNo. of 250 m3 MP storage tanks at point PH (collider)\n21\n34\nNo. of 250 m3 MP storage tanks at point PL (booster)\n4\n12\nTotal No. of storage tanks (+1 auxiliary tank)\n26\n47\n8.5.5\nEconomic mode for energy savings\nOne of the particularities of the FCC-ee is the large difference between the static and the dynamic heat\nloads that the cryogenic system must handle. The dynamic heat loads represent between 22% and 68%\nof the total heat loads depending on the machine stage and RF point. See Table 8.32 below, where details\nare given.\nTable 8.32: Static and dynamic heat load sharing for the different FCC-ee phases.\nFCC-ee Machine\nZ, WW & H\nt\u00aft\nPoint\nPH\nPL\nPH\nPL\nStatic heat loads at 4.5 K [kWeq]\n24.8\n10.4\n54.8\n32.5\nDynamic heat loads at 4.5 K [kWeq] 54.0\n2.9\n109.2 11.6\nTotal heat loads at 4.5 K [kWeq]\n78.8\n13.3\n164.0 44.1\nDynamic heat load percentage\n68%\n22%\n67%\n26%\nDue to the proportion of large dynamic heat loads and the requirement to maintain the RF cavities\nat cryogenic temperatures (<5 K) throughout the years between the long shutdowns (LS), the cryo-\ngenic systems must be designed in such a way that the electrical and water consumptions are optimised\nthroughout the year.\nThe cryogenic system must deliver full power during the physics, commissioning, and machine\ndevelopment (MD) periods. During these periods the RF cavities need to be fully operational at top\nenergy. During the end-of-year technical stops (YETS) and the technical stops (TS), all RF cavities\n(including the 800 MHz cavities at 2 K) will be switched off and maintained at 4.5 K using an economic\nmode of the cryogenic plant. During this economic mode, there will be only static heat loads from the\nRF cavities. In the current evaluation of the FCC-ee yearly operation [4], around 36% of the time could\nbe operated with such a cryogenic economic mode as depicted in Fig. 8.85.\n407\n\nFig. 8.85: FCC-ee yearly cryogenic operation modes between long shutdown periods.\nTo allow these energy savings, the cryoplants must be designed taking into account these different\noperation modes. The coefficients of performance (COP) of the cryoplants must be optimised for the full\npower mode and the economic mode, where a reduced cryogenic power will be delivered. To achieve\nthis objective in partnership with the cryoplant manufacturers, different solutions will be studied and\ndeveloped. For instance, specific piping and some additional cryogenic equipment will be needed, such\nas smaller warm compressors with variable frequency drives and specific turbines that could be operated\nefficiently during this economic mode. A COP-1 of 220 Welec/W at 4.5 K for the full power mode and a\nCOP-1 of 250 Welec/W at 4.5 K for the economic mode were considered for this report.\nBecause of the economic mode, the cryogenic system will consume less power during the YETS\nand TS periods. The energy consumption per year for the FCC-ee cryogenic system is shown in Ta-\nble 8.33. The table includes both scenarios with and without the implementation of an economic mode.\nBy using the economic mode, electrical energy savings of up to 26% can be achieved. Note that the\ncooling water system dedicated to cryogenics will be also alleviated in about the same proportion.\nTable 8.33: Cryogenic system electrical energy consumption per year.\nPL and PH plants\nZ, WW & H\nt\u00aft\nFull power [MW elec]\n20.3\n45.8\nEco power [MW elec]\n7.6\n12.9\nElec energy/year [GWh] no eco mode\n177.4\n401.0\nElec energy/year [GWh] with eco mode\n138.1\n298.3\nElectrical energy savings per year\n22%\n26%\n8.5.6\nCryogenics for experiments and MDI region\nConcept\nThe experiment points PA, PD, PG and PJ each have a detector cryoplant that covers the needs of the\ndetector magnet, as well as a second IR cryoplant for the machine detector interface (MDI) region mag-\nnets.\nFigure 8.86 shows the loads expected for the detector and IR cryoplants. In yellow is the 2 T\ndetector solenoid, which will be cooled by a dedicated detector cryoplant. The other loads, represented\nin blue, will be covered by the IR cryoplant. These loads remain under study, but could include the MDI\n408\n\nmagnets, which contain focusing quadrupoles (QC**), compensating and screening solenoids, as well\nas the crab sextupoles (SY**). One of the detectors will also include a liquid argon calorimeter and its\nassociated liquid nitrogen cryoplant.\nFig. 8.86: Interaction Region superconducting electrical loads.\nBasic parameters\nThe current working scenario has the following cryoplants:\n\u2013 Four cryoplants for the detector solenoids. CMS-like 1.5 kWeq at 4.5 K plants are considered\nas an envelope case following the latest FCC experiment sites civil engineering and technical\ninfrastructure review\n\u2013 Four cryoplants for the IR area magnets. Further details on heat loads and the mechanical design\nof the cryostat will define the cryoplant size and architecture.\n\u2013 One nitrogen liquefier for the detector containing the liquid argon calorimeter. An ATLAS-like\n20 kW at 80 K plant is considered at this stage.\n8.5.7\nCryogenics for alternative solutions\nAn alternative solution currently under study aims to exchange all the short straight section (SSS) warm\nmagnets (arc quadrupoles, arc sextupoles and correctors) with superconducting ones based on ReBCO\nHTS tapes. The main goal of this alternative solution is power reduction. It also envisages nesting the\nquadrupoles and the sextupoles. Saving space and relaxing the RF system requirements and costs. The\nproposal involves 2900 distributed cryostats, each being 3.5 m long, affecting some 11% of the entire\nmachine. The operating temperature is currently defined at 40 K [390]. The adoption of this solution\nwould have a large impact on the amount of cryoplants and distribution lines that would be needed.\n8.6\nTransport\n8.6.1\nEquipment transport requirements\nThe transport of equipment within the underground facilities is a key activity during the installation\nphase. Given the current stage of the study, some of the data collected remain partial. Therefore, as-\nsumptions have been made based on similar existing projects. The identified requirements have been\nconsolidated in the document Transport Requirements [391].\nThe types of items considered in the preliminary transport study include:\n\u2013 Accelerator components (magnets, supports, beamstrahlung dump system);\n\u2013 Power converters;\n\u2013 Electrical equipment;\n\u2013 Cryogenic equipment;\n409\n\n\u2013 Cooling and ventilation equipment.\nAmong these, the collider and booster ring components have the greatest impact on the design of\nthe transport vehicles. To keep underground installation time as short as possible, certain components,\nsuch as quadrupoles and sextupoles, will be pre-assembled on a supporting structure at the surface and\nthen transported as a single unit (QSS unit), as illustrated in Fig. 8.87.\nFig. 8.87: Quadrupole with two sextupoles and the supporting girder (QSS unit)\nThe weight of the QSS unit is expected to be close to 14.5 t for a length of 7 m, which represents\nthe maximum load that the vehicle will lift. The dipoles will be transported stacked in groups of three,\nwith an overall weight close to 16 t and a length of approximately 12 m. The beamstrahlung dump system\nis also significant in terms of weight and dimensions, a specific preliminary study has been conducted on\nthis topic and is summarised in the present report Section 8.6.1 . The other elements considered are more\nstandard (mainly pipes, racks and cable reels) and will be transported by electric tractors and trailers as\nis usual for CERN accelerators.\nOverhead cranes and shafts\nOverhead cranes will be installed in almost every surface building and within the service caverns to\nfacilitate handling operations during both the installation and operation phases.\nThis type of equipment is generally preferred over floor-based handling machines, such as forklifts\nor telehandlers, as it offers several advantages. In terms of safety, the suspension point is located above\nthe object being handled, reducing the risk of accidental collisions or tipping. From an operational\nperspective, overhead cranes provide greater positioning precision, ensuring more controlled and efficient\nhandling. The use of overhead cranes eliminates the need for wide aisles for manoeuvring and high floor\nload capacities, leading to potential cost savings in infrastructure design and implementation.\nTable 8.34 contains the list of the overhead cranes foreseen to be installed in the facilities of the\nexperiment and technical points.\nThe overhead cranes will comply with the relevant European Directives (currently the Directives\n2006/42/EC [392], 2014/30/EU [393] and 2014/35/EU [394]) and the CERN Safety Rules. According\nto the expected frequency of use (intensive during the installation phase, very low during the opera-\ntion phase) and the load spectra (the maximum load will rarely be lifted), they will be considered as\nlight/medium duty overhead cranes and classified as A4-M4 according to the FEM (European Materials\nHandling Federation) guide 1.001.\n410\n\nTable 8.34: List of overhead cranes.\nBuilding\nLocation\nCapacity [t]\nAssembly hall SX\u2020\nSurface\n120\nHead-Shaft building SD\u2020\n75\nHead-Shaft building SD\u2021\n25\nTunnel and service areas ventilation building SU\n7.5\nExperiment ventilation building SUX\u2020\n7.5\nCooling plant SF\n3.5\nPower converters building SR\n5\nCompression station SH\u2020\n20\nService cavern\nUnderground\n20\n\u2020 Only in the experiment points\n\u2021 Only in the technical points\nThe hoist design will incorporate specific features to ensure that the crane is suitable for han-\ndling fragile components with high precision in positioning. The hoist will be equipped with two ropes,\nensuring that the hook is lifted and lowered without horizontal drift, thereby minimising the risk of unin-\ntended movement. Additionally, all motors will be driven by inverters, allowing for smooth acceleration\nand precise control during lifting and lowering operations.\nThe speed values will be set in the following ranges:\n\u2013 Lifting speed: 8 to 10 m/min;\n\u2013 Cross-travel speed: 12 to 15 m/min;\n\u2013 Long-travel speed: 15 to 20 m/min.\nEach building layout will ensure safe access to the cranes during preventive and corrective main-\ntenance (e.g., a walkway at the side of the railway). Access to any position where the crane may stop in\ncase of breakdown will be possible.\nShaft cranes\nThe overhead cranes installed in the assembly halls and in the shaft-head buildings will require a bespoke\ndesign due to their particular lifting heights, as shown in Table 8.35. The overhead cranes in the SD\nbuildings of the experiment points have a capacity of 75 t in order to allow the handling of the FCC-hh\nmagnets in the future. This will avoid expensive modifications of the cranes and buildings arising from\nincreasing the capacity from 25 t to 75 t.\nTable 8.35: Characteristics of shaft cranes.\nOverhead crane\nSites\nCapacity [t]\nLifting height [m]\nAssembly hall crane\nPA, PD, PG, PJ\n120\n253\nHead-shaft building crane type A\nPB, PH, PL\n25\n253\nHead-shaft building crane type B\nPF\n25\n400\nHead-shaft building crane type C\nPA, PD, PG, PJ\n75\n253\nTo minimise the overall dimensions of the hoist while accommodating the required rope length,\nthe cranes will be equipped with two trolleys, each capable of lifting approximately 55% of the crane\u2019s\n411\n\ntotal capacity. When handling a full-capacity load, both trolleys will operate together, using a spreader\nbeam (see Fig. 8.88).\nEach trolley will house two independent hoisting units (motor \u2013 gearbox \u2013 rope drum) that support\nthe hook block. Under normal operating conditions, both hoists will function simultaneously, with the\nrope winding evenly across both drums.\nThis configuration provides mechanical redundancy in the event of a hoist component failure. If\nany component of one hoist malfunctions and prevents normal operation, the other hoist will still be able\nto complete the lifting operation. In such a scenario, the rope will be wound on the functioning drum in\na double-layer configuration, ensuring continued operation and safety.\nFig. 8.88: Concept of shaft crane.\nThe design of the shaft cranes will also include the following specific features:\n\u2013 Emergency brake on each rope drum to avoid dropping the load should any element of the hoisting\ndrive chain fail;\n\u2013 FEM classification of the hoist gearboxes: M8\n\u2013 Hoisting speed at full load: 15 m/min - hoisting speed without load: 30 m/min\n\u2013 Laser sensors, encoders and a programmable logic controller (PLC) to control the hook position at\nany moment.\nThe cranes will also be equipped with a dedicated monorail, installed below one girder, hosting\na traversing trolley on which a platform is suspended. The platform allows personnel access inside the\nshaft in both the construction and operation phases to install or maintain the technical infrastructure (e.g.,\nventilation ducts).\nIn the coming five years, CERN will also test a new technology for the lifting ropes, based on\ntextile ropes instead of steel ropes, which reduces the overall weight suspended from the structure of the\ncrane and, therefore, optimising the overall crane design and cost.\nUnderground transport vehicles\nThe diversity of magnets to be transported creates a number of different requirements for the transport\nand handling technology in the tunnel. The basic principle will consist of two types of trailers, which are\nspecially equipped with the technology required for the particular magnet transport and magnet handling.\n412\n\nA detailed study is accessible in Ref. [395], based on QSS units of 11 t and dipoles of 3.7 t. In 2024 the\ndesign of the magnet has been updated with QSS units of 14.5 t and dipoles of 5 t, however, this change\ndoes not have a significant influence on the design of the vehicle, the main outcome being that the outer\nwidth may increase by 200 mm maximum, which still fits inside the transport volume.\nThe underground transport vehicles will be composed of convoys, each consisting of two tractors\nthat can move in both directions and a specialised trailer designed for transporting and handling magnets\nwithin the regular arcs. There are two main categories of magnets and assemblies to be transported, both\nfor the collider and the booster, each with specific weight distribution characteristics requiring adapted\ntrailers. The dipole magnets are long and relatively light, with a unit weight of 5 t and 12 m long, whereas\nthe QSS units are shorter and heavier, weighing up to 14.5 t and 7 m long.\nThe tractors and all actuators on the trailers will be fully electric, eliminating exhaust gas emis-\nsions and reducing noise in the tunnel during magnet assembly. The tractors and trailers will be powered\nby battery systems, requiring the installation of charging stations in the service caverns to allow recharg-\ning during vehicle downtime periods, such as magnet loading and maintenance. The battery-powered\napproach is preferred compared to a conductor rail system, as it provides greater flexibility, requires no\nadditional tunnel infrastructure, and enhances safety by eliminating exposed live electrical components.\nAdditionally, battery technology is expected to improve in capacity and reliability in the coming years,\nfurther strengthening this choice.\nThe specialised trailers will be loaded with magnets at the base of the service cavern shafts, which\nwill be equipped with the necessary infrastructure for lowering them into the tunnel. Autonomous driving\nwill be implemented for the journey from the shaft/loading area to the installation points in the tunnel,\nminimising personnel requirements and improving operational efficiency.\nTo accommodate vehicle movements, enlargements are planned at every alcove, following a fixed\npattern determined by the alcove locations. These enlargements will allow vehicles to pass or overtake\nwhen necessary, and can also serve as evacuation points in case of an emergency. However, the baseline\napproach for magnet transport is to operate overnight without personnel present in the tunnel, thereby\navoiding co-activity with workers. While interventions by personnel during magnet transport have not\nbeen entirely ruled out, additional compensatory safety measures would need to be implemented to\nensure proper evacuation procedures in such cases.\nThe handling technique relies on three-axis movement. First, the components are lifted vertically\nfrom the trailer. Once at the required height, a movable arm equipped with gripping technology places the\ncomponents onto jacks. Finally, a fine longitudinal adjustment can be made using the gripper, ensuring\nprecise positioning of the magnets.\nTransport of quadrupoles and sextupoles\nThe QSS unit represents the biggest weight requirement for the equipment. The special trailer (shown in\nFig. 8.89) which has the capability to carry the QSS unit is equipped with a damping system that protects\nthe load from small bumps in the surface of the carriageway during travel through the tunnel. Hydraulic\ncylinders (alternatively electric cylinders) will be used by the handling system to generate the necessary\nforce to move the load to its final destination. The hydraulic cylinders perform the main movements\nwhile placing the steel girder on top of alignment blocks.\nMotors on the gripping system will allow the final fine adjustment longitudinally, due to the limi-\ntation in accuracy of the positioning of the whole convoy (as shown in Fig. 8.90).\nTransport of dipoles\nThe dipoles are nearly 12 m long and are the longest items to be transported; they require dedicated\nequipment for their transport and handling. The trailer which is planned for carrying the dipoles has the\ncapability to carry three dipoles at one time, thereby increasing transport efficiency (see Fig. 8.91).\n413\n\n(a)\n(b)\nFig. 8.89: Transport and installation of a QSS unit.\n(a)\n(b)\nFig. 8.90: Detail of the gripping system.\n(a)\n(b)\nFig. 8.91: Transport and installation of 3 dipoles.\nTo enable the transport of three dipoles as one load, the dipoles will be stored in a special rack.\nThe rack can be raised and lowered by the spindle lifting gear so that the handling system can always\npick up the dipoles and place them in their final destination from the one position.\nTransport of booster ring components\nThe components of the booster ring are mounted above the collider ring. The trailers for the dipoles can\ninstall magnets on both the collider and the booster, the same strategy applies for trailers dedicated to the\nQSS units.\n414\n\nLifts\nThe lifts will comply with the relevant European Directives (currently 2014/33/EU [396]) as well as\nCERN Safety Rules and EN standards. The lifts will use state-of-the-art technologies like those used\nin high-rise buildings, which already cover heights of up to 450 m. Two lifts will be installed in each\nof the four shaft-head buildings at the technical points, while four lifts will be installed in each of the\nfour shaft-head buildings at the experiment points, within the service shafts. Lifts are the only authorised\nmeans of personnel access to and from the underground areas, making their reliability and safety criti-\ncal. To enhance safety, the lift shaft concrete modules will be over-pressured, preventing the ingress of\ncontaminants or smoke in case of an emergency.\nThe lifts will be powered by the secure power network, ensuring they remain fully operational\neven in the event of a failure of the standard electrical network. To further improve safety, operational\nefficiency, and maintenance availability, each lift shaft module will be equipped with two lifts, providing\nredundancy and easing access and maintenance operations.\nThe lift capacity and speed have been determined based on the results of evacuation simulations\n[397]. A maximum cycle time of 4 minutes has been defined, covering the entire process from people\nentering the lift, travelling from underground to the surface, and exiting the lift. This calculation assumes\na shaft depth of 400 m and a lift speed of 4 m/s.\nDuring the LHC programme, approximately 80% of the non-machine components were trans-\nported using lifts, suggesting that a similar proportion will apply to FCC. After evaluating different op-\ntions, lifts with a 3 t capacity were chosen as the baseline solution, as they offer the best cost-to-capacity\nratio while meeting the project\u2019s operational and logistic requirements.\nThe main characteristics of a lift are:\n\u2013 Speed : 4 m/s;\n\u2013 Capacity : 3000 kg/38 persons;\n\u2013 Shaft height : (up to) 400 m;\n\u2013 Car (length \u00d7 width \u00d7 height) : 2700 mm \u00d7 1900 mm \u00d7 2700 mm;\n\u2013 Door (width \u00d7 height) : 1900 mm \u00d7 2700 mm;\n\u2013 Shaft width : 2750 mm;\n\u2013 Shaft length : 3750 mm;\n\u2013 Headroom : 7700 mm;\n\u2013 Pit depth : 5900 mm.\nPreliminary detailed handling studies in LSS sections in PA and PB\nThe underground areas identified as \u2019Machine tunnel widening\u2019 areas in Fig. 8.92, are zones where\nhandling processes will be studied in detail since the configuration of the machine elements is different\nfrom the regular arcs. The input from the beam optics induces tunnels with specific configuration and\nhandling challenges.\nStudies based on the preliminary design of the beamstrahlung dump system, located 500 m away\nfrom the interaction point on each side of each experiment cavern, have been performed to determine\nthe possible handling process and equipment to install it. The same conceptual study was performed for\nPB, hosting the beam dump system of the collider and the booster. Details can be found in Ref. [398].\nThe handling and installation of the beamstrahlung dump system is feasible using a mobile crane and a\nstandard electric tractor pulling a trailer. This avoids the installation of an overhead crane above each\nsystem, allows the reuse of the mobile crane for the installation of several systems, and helps reduce the\nsize of the cavern required to install this system (see Fig. 8.93).\n415\n\nFig. 8.92: FCC-ee Layout including machine tunnel widening areas.\nFig. 8.93: Handling study for the beamstrahlung dump system.\nDue to the limited space between beam lines in the area, the handling and installation of compo-\nnents in PB will be done by overhead cranes above the beam lines and beam dumps. Specific overhead\ncranes with a capacity of 20 t will be installed above each beam dump system to allow their installation\nand maintenance, as their weight is significantly higher than the elements of the beam lines estimated to\nbe up to 5 t (see Fig. 8.94).\nOnce the final design of the machine components in this area is available, a detailed handling study\nwill be performed in order to determine the most optimised handling strategy both for the installation\nand operation phase.\n416\n\nFig. 8.94: Handling study in point PB, beam lines are highlighted in green.\nFig. 8.95: Tunnel model developed for logistics studies.\n8.6.2\nLogistics\nMaterial flow simulation\nLogistics is of great importance for the construction, assembly, and operation of the FCC. An event-\ndiscrete material flow simulation study has been conducted to integrate all the dynamic interdependencies\nto create a robust schedule, identify bottlenecks and potential improvements, and estimate the resources\nrequired. Figure 8.95 shows the tunnel model which was developed. In addition, the corresponding\nnecessary process flows and dependencies were defined and abstracted so that they could be integrated\ninto the digital model. The simulation was run using Tecnomatix Plant Simulation\u00a9.\nThe underlying input parameters and handling strategy are described in Ref. [395]. Several sets\nof simulations were developed, allowing the identification of the optimised scenario: the dipole magnets\nwill be handled through the experiments point service shafts, the QSS units will be handled through\n417\n\nthe technical points service shafts. This allows the workload of the shaft cranes to be balanced and\noptimisation of the overall arc transport time.\nThe main final outcome is that the effort required to handle the dipole magnets from experiment\npoints to their final location in the arcs is 1200 man-hours or 75 days working in two shifts. The effort\nrequired to handle the QSS assemblies from the technical points is 1392 man-hours or 87 days working\nin two shifts. This result is compatible with the original assumption of 100 days duration and provides\ncontingency in case of failure or logistic chain discontinuity. The workload of the shaft cranes allows\nthe installation of two arcs from the same surface point to be performed in parallel, if the final schedule\nrequires doing so. At the beginning of the simulation, it is assumed that the tunnel civil engineering\nhas been completed and the general services technical infrastructure (cooling and ventilation, cabling,\nsupporting jacks etc.) is installed so that the tunnel is ready for magnet transport. The logical flow of the\nprogrammed process can be seen in Fig. 8.96.\nFig. 8.96: Programmed logistic process.\nThe quadrupoles and sextupoles are pre-aligned on the girder and assembled into transport units.\nAs described earlier, three dipoles can be grouped and transported simultaneously as a dipole pack. The\nmagnet transport vehicle is designed to carry one QSS unit or one dipole pack at a time. During magnet\ntransport operations, no other traffic will be present in the tunnel to ensure safety and efficiency.\nTo enable continuous transport operations, a variable number of magnets can be stored under-\nground at the bottom of the shafts. Simulations indicate that a buffer of three QSS units or three dipole\npacks in the underground service cavern allows smooth operation. Expanding this buffer to 16 dipole\npacks and 8 QSS units would provide a one-day operational margin, mitigating potential disruptions in\nthe surface logistics chain.\nMagnet transports will not be scheduled to pass through areas where installation teams are actively\naligning and connecting the magnets, as this approach optimises transport times. While co-activity of\nsimultaneous transport and installation could be possible by reducing convoy speed to enhance safety, it\nis not included in the baseline plan due to its impact on efficiency.\nThe collider ring and booster ring can be installed simultaneously during the same installation\nphase, thanks to the flexibility of the trailers. On the surface sites, storage areas are planned near each\nshaft, with a capacity of two days (equivalent to 32 dipole packs or 16 QSS units) to facilitate direct\ncrane loading.\nIt is important to note that the time required for aligning and connecting the magnets is still an\nestimate at this stage. As a result, any conclusions drawn based on this parameter should be interpreted\nwith caution.\n418\n\nMagnet production flow simulations\nAs detailed in Ref. [399], the anticipated manufacturing timelines for dipoles, quadrupoles, and sex-\ntupoles are aligned with the current FCC-ee installation schedule. By targeting an average production\nthroughput of 18 magnets per day, manufacturing and installation can proceed in parallel, ensuring timely\ndeliveries while allowing sufficient time for R&D and procurement activities prior to full-scale produc-\ntion. This assessment confirms that the planned manufacturing rates are adequate to support the on-time\ninstallation phase, demonstrating the overall feasibility of the FCC-ee magnet production strategy.\nSurface transport of 240 t transformers and 60 t magnets\nThe transport of equipment exceeding 24 t in a single unit requires an exceptional convoy and, in some\ncases, modifications to public roads to ensure feasibility. The heaviest piece of equipment identified in\nthe project is the high-voltage transformers to be installed at sites PA, PD, and PH. A study [400] has\nconfirmed that these transformers can be transported to site PH via four different routes with exceptional\nconvoy procedures and limited modifications to public roads.\nThe second heaviest equipment in the project consists of the cryo-dipoles for the FCC-hh machine,\nwhich have according to today\u2019s estimates a unit weight of approximately 60 t and a length of 15 m. A\nseparate study [401] demonstrated the feasibility of transporting these magnets to their final destination\nalong the last kilometres leading to sites PA, PD, PG, and PJ, where service shafts are sufficiently wide\nto accommodate the handling of 15 m-long magnets.\nOverall surface road transport volumes for FCC-ee installation\nThe scenario involves logistical planning for the transport of equipment on public roads. A key consid-\neration is limiting the potential impact of daily transport operations. The most transport-intensive phase\nwill be the magnet installation, during which the daily traffic per site is expected to remain below 10\ntrucks per day under the current schedule. This corresponds to an average of approximately one truck\nper hour, ensuring a steady, manageable flow of transport. Further details on transport logistics and\nplanning can be found in Ref. [402].\nHandling for Experiments\nHandling activities in the experiment caverns will be conceptually similar to those currently carried\nout for the LHC Experiments. Detector components will be lowered to the cavern from the assembly\nhall through the shaft directly connecting the two facilities; this will be done with the overhead cranes\ninstalled in the surface hall. The components will then be handled with two overhead cranes installed\ninside the experiment cavern; each of them will have a capacity of 20 t. These overhead cranes will have\nthe same characteristics as described in Section 8.6.1 plus the additional features listed below:\n\u2013 the hoist gearbox will include a differential unit which allows the installation of a second hoist\nmotor; this motor will be used for operations at very low speed (of the order of 0.3 m/min) which\nis usually requested for the precise assembly of detector components;\n\u2013 an emergency brake on the rope drum to avoid dropping the load if any element of the hoisting\ndrive chain fails.\nPersonnel access to the various parts of the detectors will be facilitated by mobile elevating working\nplatforms (scissor and boom lifts).\n419\n\n8.6.3\nPersonnel transport\nRequirements for Personnel Transport Vehicle\nThroughout all stages of the life cycle, personnel will need to be transported from the vertical shafts to\ntheir designated workplaces. Following the handover of the shafts and tunnel from civil engineering, the\ninstallation of general infrastructure, such as electrical cabling, cooling, and ventilation, will take place,\nfollowed by the placement and connection of magnets. Various specialists will be required for these\ninstallation tasks, with the number of personnel varying depending on the specific phase of the project.\nOnce the collider is in operation, there will be technical and unplanned stops during which mainte-\nnance teams will enter the tunnel for repairs, inspections, and system upgrades. The safety requirements\nfor personnel transport are outlined in Section 9.4.1, and further details can be found in Ref. [395].\nThe maximum distance between two shafts is 11 km, meaning that when some shafts are closed\nfor access, the longest round-trip distance for personnel transport could be 22 km. To ensure efficient\ntransport and minimise travel time, vehicles should be capable of speeds up to 30 km/h.\nFire doors installed in the tunnel define the maximum permissible vehicle size. Personnel transport\nvehicles should be able to pass each other to avoid blockages during evacuations and provide operational\nflexibility. The maximum driveway width is 2.2 m, and the maximum allowable vehicle height is 2.25 m.\nThis allows vehicles to have a maximum width of 0.8 m, ensuring a 0.2 m clearance between vehicles as\nthey pass, as well as between the vehicles and tunnel walls or machine equipment (see Fig. 8.97).\n(a)\n(b)\nFig. 8.97: Concepts of vehicle circulation in the regular arc.\nBased on these requirements, a design of a vehicle for four people has been established (see\nFig. 8.98), the other constraint being the length of the vehicle to ensure maneuverability inside the tunnel\n(see Fig. 8.99).\nThe vehicles should be capable of autonomous driving using contour navigation, minimising the\nneed for additional infrastructure. However, manual steering should remain an option for emergencies,\nmaintenance, and operational flexibility. The vehicles will be battery-powered, with an estimated range\nof approximately 200 km based on an available volume of 216 L. This autonomy is sufficient, allowing\nfor over six hours of continuous operation at full speed or nine round trips along the maximum distance\nof 22 km. During peak times, up to 200 people may be present in a single sector, requiring 50 vehicles\nper arc, with designated parking positions in each alcove (see Fig. 8.99).\n420\n\n(a)\n(b)\nFig. 8.98: Dimensions of the conceptual design of the personnel transport vehicle.\n(a)\n(b)\nFig. 8.99: Illustration of manoeuvre of personnel transport vehicles in and out parking place\nOperation concept\nThe concept of operation requires a distinction between the installation and operation phases of the\naccelerator, as each has distinct conditions. During installation, large quantities of materials must be\ntransported to specific work sites, following a clear workflow. In contrast, the operation phase involves\nmaintenance and other tasks distributed throughout the entire tunnel.\nThe main challenge during the installation phase is the simultaneous transport of materials and per-\nsonnel within the tunnel. To minimise interference, the most effective approach is to prevent intersections\nof material flow. The baseline strategy for the magnet installation phase - the most transport-intensive\nphase - is to schedule material transport operations overnight while installation work takes place during\nthe day. This method ensures better coordination and reduces congestion in the tunnel.\nThis night-time transport strategy can also be selectively applied to other phases where material\nmovement is expected to be significant, such as the delivery of cables and pipes before their installation.\nHowever, in some cases, the presence of personnel near moving vehicles will be unavoidable during\ninstallation activities.\nTo enhance safety, personnel transport vehicles will be equipped with collision avoidance systems\nto detect and prevent accidents involving workers and obstacles within the transport zone. These sys-\ntems will account for potential hazards, including toolboxes, materials, or personnel, ensuring safe and\nefficient tunnel operations (see Fig. 8.100).\nThe speed of the vehicles will be reduced in zones where activity is detected, ensuring safe coex-\n421\n\nFig. 8.100: Obstacle detection systems.\nistence of movement and ongoing work. For both the installation and operation phases, two scenarios\nfor personnel transport can be defined:\n\u2013 Groups of people use a vehicle assigned to them, after drop-off the vehicle will park in the closest\nalcove during the whole stay in the tunnel;\n\u2013 Groups of people use a vehicle to get to their place of work, the vehicle then moves somewhere\nelse to pick up the next team.\nThe two scenarios will be used depending on the type of work to be performed. The first scenario\nwill be typically the one used for punctual work in several locations, the second being more dedicated to\nteams working in a fixed place.\nEvacuation concept\nThe personnel transport vehicles will be parked in the lay-by zones of the alcoves. The maximum number\nof workers per arc is limited to 200, meaning that up to 50 vehicles may be required per arc, ensuring that\neach worker always has an assigned seat in a vehicle for evacuation purposes. Figure 8.99 illustrates how\nseven vehicles can be parked in the small lay-by zones, providing a storage capacity of 49 vehicles per\narc. Additionally, 20 vehicles can be parked in the service caverns at each point, offering contingency\nparking spaces to support traffic management.\nThe current installation schedule foresees work being carried out simultaneously in all eight arcs,\nrequiring a maximum of 400 personnel transport vehicles across the entire accelerator. However, further\nstudies on detailed installation scenarios may help optimise this number, particularly if it is possible to\nreduce the number of personnel present in a single arc during certain phases. Such an optimisation would\nrequire a real-time personnel and vehicle tracking system, ensuring that each worker always has a seat\navailable in an evacuation scenario.\nCurrent state of investigation\nOngoing studies have led to the design of a vehicle that meets all dimensional, manoeuvrability, and au-\ntonomy requirements. The main challenges associated with these vehicles are their autonomous driving\ncapabilities and the management of the fleet, both for daily operations and emergency evacuations.\n422\n\nCERN has prior experience with autonomous driving technologies. In addition, the industry has\nmade significant advances in autonomous vehicle technology, with some manufacturers offering au-\ntonomous forklifts capable of operating safely alongside personnel. Modern factories, such as for ex-\nample car manufacturing plants, are today typically deploying autonomous vehicles alongside human\npersonnel. The challenge will be to integrate this autonomous functionality into a custom-designed per-\nsonnel transport vehicle.\nFleet management presents another key challenge, as it requires integrating data from multiple\nsystems, including safety systems, personnel tracking, and vehicle localisation. This integration will\nallow a centralised system to issue real-time instructions to each vehicle, ensuring efficient operations\nunder normal conditions and coordinated response in case of evacuation. The development of this system\nwill be addressed in a later phase.\n8.7\nCommunications, computing and data services\nThe following sections outline the key components required for the computing infrastructure of the FCC,\nbased on the Future Circular Collider Conceptual Design Report, Volume 3 [10]. These sections detail\nthe equipment and infrastructure necessary to support data, voice, and radio communications, as well as\nthe broader computing infrastructure. The document has been developed drawing on experience from\nprevious colliders, particularly the LHC, to ensure a robust and efficient design.\nThe set of services and users was introduced in Ref. [10]. For completeness, it is depicted in\nFig. 8.101.\nFig. 8.101: Users and services of communication services.\n8.7.1\nCommunication Services\nThe FCC will require the same communication services portfolio as provided at the LHC. These services\ninclude:\n\u2013 The site-wide campus network, including Wi-Fi coverage,\n\u2013 The high-performance data centre network,\n\u2013 The dedicated technical network supporting accelerator operations and control networks for ex-\nperiments,\n\u2013 CERN\u2019s fixed and mobile telephony services,\n\u2013 The TETRA digital radio service for the Fire Brigade and site guards, and\n\u2013 Support for IoT devices, including a LoRaWAN infrastructure.\n\u2013 WhiteRabbit network for timing distribution and synchronisation of all accelerator machines.\n\u2013 Access control and video surveillance systems\n\u2013 CERN Safety Alarms Monitoring (CSAM) system\n423\n\nTo support the diverse services and technologies required for communications, three independent\ninfrastructures will be deployed within the FCC facilities to enable data, telephony, and radio networks.\nWhile these three communication systems operate on separate network equipment, they will all rely on\na shared fibre infrastructure that will interconnect the FCC\u2019s surface and underground facilities with the\nrest of CERN.\nIt is important to note that the choice of fibre infrastructure will have a significant impact on the\nequipment and associated costs required to implement data, telephony, and radio services.\nThe following sections present the fibre infrastructure solutions currently under consideration for\nthe FCC, along with the requirements for data, telephony, and radio networks.\n8.7.2\nFibre network deployment\nThree different possibilities are being evaluated:\n\u2013 Deploy the cables on the surface. This might be very complicated, given the size of the FCC and\nthe distances between the points. Laying the cable on the surface will require agreements with\nmultiple entities.\n\u2013 Deploy the cables underground using the tunnel. The main issue with this approach is the level of\nradiation that will affect the cable. Presently, there are two types of fibre optic channels: the stan-\ndard one and a more radiation tolerant version. The price difference is very significant; therefore,\nplacing standard cables and shielding them behind concrete might be more economical.\n\u2013 Rely on existing telecommunication operators. This approach has issues regarding the manage-\nment of the network. The planning of interventions will also be more cumbersome. Moreover,\nthere is the risk of locking in with a single operator.\nAnother key aspect under study is the network topology. In the LHC, a star topology is used,\nwhere each point has direct and redundant access to the CERN Computer Centre. This design provides\na resilient and efficient architecture, simplifying traffic exchange at the data centre, which serves as the\ncentral hub for all infrastructures, including the internet, WLCG, experiments, and GPN. While this star\ntopology remains the preferred design for the FCC, the final decision will depend on the optical fibre\ndeployment strategy and whether the fibre infrastructure will be owned by CERN or an external entity.\nAdditionally, the connections between the alcoves and access points are being carefully designed.\nIn the LHC, each alcove is directly connected to the two access points of its sector. However, in the\nFCC, with seven alcoves per sector, an alternative approach is being considered: a daisy-chain topology,\nwhere each alcove is connected only to its two nearest alcoves or access points. This solution would\nsignificantly reduce the number of fibres required but would come at the cost of reduced resilience in\ncase of network failures.\n8.7.3\nTelephony and Radio Networks\nThis section covers the voice and radio communication services requirements for FCC\u2019s facilities and\nexperiments. The \u2018red phones\u2019 currently installed in the LHC are required, and a radiation resistance\nstudy should be carried out. The fixed telephony [403] is currently based on IP phones on the surface\nand the CERNPhone application [404].\nIn the LHC, CERN IT provides a mobile voice and data services [405], a TETRA [406] radio\nnetwork for the fire brigade, and a LoRaWAN network [407] for battery-powered wireless sensors to the\naccelerator chain and the experiments via a radiating cable. WiFi is only available on the surface, the\nalcoves and certain areas of the experiments, such as the WiFi access points, are not radiation-free, and\nthe WiFi frequencies are too high to be injected in the radiating cable.\n424\n\nThe deployment of the radiating cable is essential to ensure the availability of mobile and TETRA\nservices in the accelerators and experiment areas. Since the FCC environment may expose the cables\nto higher radiation levels than those currently supported, a study is underway to assess their long-term\ndurability. The cable must be installed in a way that provides a direct line-of-sight for service users\u2014such\nas personnel, robots, and sensors\u2014while also optimising its placement to extend its lifespan.\nBy the time the FCC could become operational, telecommunications technologies will have evolved\nfurther. Current trends suggest a convergence of mobile telephony, TETRA, and IoT services into future\nmobile network generations (5G and beyond). While the specific technologies may change, the core ser-\nvices - including mobile data, voice communication, IoT connectivity, and safety functions - will remain\nfundamental.\nFrom a deployment point of view, there are three points to be assessed:\n\u2013 Interconnection:\n\u2013 Fibres between one or several central points, today Meyrin and Pr\u00e9vessin, and all the FCC\naccess points.\n\u2013 Fibres between each FCC access point and its adjacent alcoves.\n\u2013 Radio equipment:\n\u2013 Mobile/TETRA/LoRaWAN radio emitters: 1 rack per access point, 1 per alcove and probably\n1 extra for each large experiment.\n\u2013 If safety is a concern for these services (as is the case today for TETRA), the racks should\nhave a secure supply with backup from diesel generator sets and/or UPS.\n\u2013 Antennae to emit the radio signals:\n\u2013 Radiating cable in all the tunnels and experiments..\n8.7.4\nData network\nThe data network design of the FCC will follow the same approach as the LHC, as described in the\nLHC Computing TDR [408]. It is based on a tiered structure, with CERN being the Tier-0, several\nremote sites, or Tier-1s, connect directly to CERN and store, analyse and redistribute the data to other\nTier-2 institutes. Connectivity from CERN to Tier-1\u2019s and other WLCG members is established through\nthe national research and education networks, and the FCC will not impact its structure, apart from the\nforeseeable increase in capacity and members.\nThe networks at CERN are composed of several independent infrastructures. Following today\u2019s\nLHC design, the FCC network will need to offer user connectivity to:\n\u2013 General Purpose Network (GPN): CERN\u2019s Campus Network offering Internet access, wired and\nwireless connectivity to users.\n\u2013 Technical Network (TN): Control network critical for the management and operation of the accel-\nerators.\n\u2013 FCC Computing Grid (equivalent to today\u2019s LCG): High-bandwidth network connecting the server\nfarms in the FCC experiments to the datacentres for data storage at the Tier-0 and communication\nwith the Tier-1 and Tier-2 centres.\nThe FCC network will be composed of passive and active equipment. The passive equipment,\nproviding the physical media to support data communication (mostly fibre and UTP), will include around\n260 starpoints with racks, patch panels, patches, and the fibre infrastructure to connect each starpoint to\nthe upper element in the topology, either FCC points or the datacentres. The starpoints will also house\nthe active network equipment.\n425\n\nThe active equipment, enabling data communication, will mainly include switches, wireless access\npoints and routers. Based on today\u2019s LHC scale and user density, 300 and 280 switches will be needed\nfor TN and GPN respectively. Around 600 access points will be needed to provide wireless coverage\nin the surface buildings, underground facilities and alcoves. To interconnect all FCC facilities to both\nTN and GPN networks, 34 routers will be required. While today the GPN and TN infrastructures are\ncompletely separated and use different passive and active equipment, some economies could be made in\nthe future by sharing the equipment and using virtualisation to implement the separation.\nAs mentioned in Section 8.7.2, the fibre network deployment will have an important impact on the\nway the network topology is built and how alcoves, buildings and FCC points will be interconnected.\n\u2013 Starpoints in the alcoves should, ideally, be connected to their closest FCC points to provide re-\ndundant TN and GPN access. Fibres could be direct to the points or patched between alcoves.\n\u2013 Starpoints in the surface buildings and underground facilities will use internal fibres to connect the\nwired and wireless network to GPN and TN.\n\u2013 FCC points will need redundant fibre connectivity to the datacentres to have access to GPN, TN\nand, in the case of experiments, to LCG.\nTo ensure redundancy and fault tolerance of the FCC network, the backbone equipment intercon-\nnecting all FCC points will be distributed between the datacentres in Building 513 (Meyrin) and Building\n775 (Pr\u00e9vessin). The Second Network Hub (Building 773) in Pr\u00e9vessin will also offer possibilities for\nincreased resiliency.\n8.7.5\nIT infrastructure\nAs described in the previous section, the FCC will combine computing resources distributed all over\nthe world. CERN will be the Tier-0. By the time the FCC starts, CERN will have two datacentres:\none in Meyrin and a second one in Pr\u00e9vessin. This redundancy will help with business continuity and\ndisaster recovery. The Pr\u00e9vessin datacentre is currently being built [409]. During 2025, it will provide\n12 megawatts of computing resources. It will use the latest cooling technologies, and it will recuperate\nheat for other buildings. The power usage effectiveness (PUE) is expected to be 1.1. For comparison, the\ncurrent PUE of the Meyrin datacentre is 1.5.\nThe LHC experiments follow the CERN Open Data Policy [410], which ensures a consistent\napproach towards the openness and preservation of experiment data. The experiments at the FCC will\ncontinue in this direction, ensuring the use cases of re-interpretation and re-analysis of physics results are\navailable to the public. The Data Preservation and Long Term Analysis in High Energy Physics Project\n(DPHEP) [411] identified four levels of data (published results, outreach and education, reconstructed\nand raw data). This goes in the direction of Open Science, which applies to multiple areas of the FCC\nand this Feasibility Study.\nGiven the distributed nature of the collaboration, cyber-security plays a critical role in the whole\ninfrastructure. It is of vital importance that all the components are secured from the first day and that\nthey can withstand the constant cyber attacks that target scientific infrastructures. Ensuring security,\ndata resilience and protection, and long-term data accessibility requires dedicated organisation from the\nbeginning of the project.\n8.8\nRobotics\nThe fourth industrial revolution drives automation and data interconnection across industries, includ-\ning space, warehouses, and harsh environments. Industry 4.0\u2019s pillars are IoT, Wireless Sensors, Cloud\nComputing, AI, ML, and Robotics. Robots are vital for tasks humans avoid due to danger, size con-\nstraints, or extreme environments. CERN has developed robots for accelerator maintenance, reducing\n426\n\nrisk and enhancing uptime. Envisioning advances over two decades, robots could revolutionise FCC\ntunnel interventions, replacing manual work or risky interventions.\n8.8.1\nRobotic impact\nRobotics can enhance machine availability by improving maintainability through both corrective and\npreventive maintenance, as well as by increasing reliability with predictive maintenance. Additionally,\nrobotics improves operational safety by reducing the need for workers to perform hazardous tasks and im-\nproves emergency safety with fast interventions by readily available robotic systems in the underground\nfacilities, able to provide situational awareness and support rescue teams [412].\nThe potential impact of robotics on the availability can be demonstrated by looking at the lumi-\nnosity of the particle accelerator, a metric that can be approximated as the volume of physics data it\ngenerates within a given time frame. To reach the luminosity targets [13] of the FCC, the machine avail-\nability must reach a minimum of 80 %, see Section 8.10. Recent studies, based on expert interviews and\nhistorical LHC data, have shown that this target can only be achieved by a 15-fold increase of the mean\ntime between failures of certain critical systems. Introducing a readily available robotic system in the\naccelerator and thus reducing the drive time to intervention locations, allows to relax this constraint by a\n10-fold, see Section 8.10.\nAs part of the safety concept for the FCC, robotics will enhance infrastructure and personnel safety\nduring emergency scenarios within the 91 km long FCC tunnel. A three step emergency response strategy\nincluding robotics has been proposed by the CFRS [413]:\n1. Response by trained workers on site\n2. Emergency response robots\n(a) Situation awareness\n(b) First intervention (fire fighting, search and rescue)\n3. Professional human responders\n(a) Verify situation\n(b) Second intervention (finalise situation awareness and fire fighting, specific damage control)\n8.8.2\nLevel of robotic automation\nAutomation has the potential to be a primary driver of cost reduction across all stages of the accelerator\u2019s\nlifecycle, particularly in sustaining high availability throughout years of operation - directly influencing\nthe organisation\u2019s data output and, consequently, its value and profit. It is therefore essential to deter-\nmine the optimal level of automation that maximises benefits, while identifying the point beyond which\nadditional automation leads to diminishing economic returns. The level of automation throughout the\naccelerator life cycle has to be identified in upcoming studies.\n8.8.3\nStandards, conventions, and guidelines towards efficient robotic automation\nIt is essential to emphasise that effective and economical robotics depends on incorporating automation\nrequirements from the earliest design stages. Hardware and software components must adhere to well-\ndefined standards, norms, and conventions, ensuring seamless integration of robotic automation. In the\nnear future, a central point of contact or service needs to provide guidance, support, and oversight on\nimplementing the conventions and guidelines for infrastructure and intervention procedures.\n427\n\n8.8.4\nRobotic R&D required\nThe initial focus of the robotic development will be on a system with the greatest potential to enhance\navailability and safety, targeting the largest area of the FCC complex\u2014the main tunnel. Previous studies\n[414] have identified a rail-based robotic system installed on the ceiling as the most efficient and robust\nsolution for the accelerator tunnel. However, robotic systems covering other areas are expected to further\nenhance machine availability and safety. The necessary developments for a rail-based robotic system for\nthe FCC tunnel area can be split into four phases:\n1. Definition of procedures and conventions\n(a) Defining required tasks and intervention procedures\n(b) Defining remote maintenance code of practice\n2. Integration\n(a) Define rail placement in regular tunnel cross section and parking locations\n(b) Design radiation safe spaces for parking and robot maintenance\n(c) Tool manager\n(d) Design of automated hatches in fire doors\n3. Technology R&D\n(a) Infrastructure (Energy management, logistics)\n(b) Locomotion\n(c) Manipulator\n(d) Control (Motion, grasping)\n(e) Human-robot interfaces (Tele-operation, proprioception, haptics, collaboration)\n(f) Recovery scenarios and emergency interventions\n(g) Tool manager\n(h) Localisation,mapping & perception\n(i) Cognition\n4. Proof of concept\n(a) Inspection and measurements in full autonomous mode\n(b) Teleoperation mode\n(c) Collaborative mode\n(d) Dipole alignment\n(e) Vacuum leak detection\n(f) Reconnaissance\nThe plan establishes progressive levels of capability:\n1. BASIC: Full operation with limitations in automation and safety, requiring substantial tele-operation.\n2. BASIC+: Emergency intervention capabilities added.\n3. MEDIUM: Tool Manager, improved Human-Robot Interface, and higher efficiency.\n4. ADVANCED: Semi-autonomy achieved, enabling collision avoidance and human-robot collabo-\nration.\n5. ADVANCED+: Full autonomy attained, introducing cognition and unforeseeable interventions.\nThis roadmap outlines the journey towards a comprehensive robotic solution for FCC. It addresses var-\nious technical challenges while highlighting the potential for enhanced safety, efficiency, and required\ninnovation in maintenance operations.\n428\n\nFig. 8.102: The current baseline of the rail-based FCC robotic system with one RMIS and two SES\nsystems.\n8.8.5\nDevelopment status\nThe study on a rail-based robotic system for the FCC tunnel area departed from the first phase of the\nimplementation plan outlined in the previous section. This rail-based robotic system, referred to as FCC\nrobotic system, consists of two subsystems: the Remote Maintenance and Inspection System (RMIS) and\nthe Surveillance and Emergency Shuttle (SES). The RMIS is designed to enhance machine availability\nand operational safety, while the SES focuses on improving emergency safety.\nIn Phase 1, requirements were gathered from stakeholders to enhance machine availability and\noperational safety [415], as well as emergency safety [416]. The requirements for emergency safety\nhave reached a high level of maturity, while those for machine availability and operational safety are\nstill in progress, as they are closely tied to the infrastructure design. Additionally, a draft for a Remote\nMaintenance Code of Practice has been developed, outlining conventions for infrastructure design and\nguidelines for intervention procedures [417].\nIn Phase 2, the integration of the rails beneath the ceiling of the accelerator has been finalised. A\ndesignated area within the tunnel\u2019s cross-section has been allocated for the robotic system, and radiation-\nshielded parking locations in the service caverns have been identified.\nIn Phase 3, a prototype of the 11-degree-of-freedom Remote Maintenance and Inspection System\n(RMIS) has been developed for proof-of-concept experiments in the FCC tunnel mock-up, with instal-\nlation scheduled for 2025. The design of the Surveillance and Emergency Shuttle (SES) remains at the\nconceptual stage. The current baseline designs for both the RMIS and SES are illustrated in Fig. 8.102.\nPhase 4, which begins in end of 2025, will focus on tests with functional infrastructure in the FCC\ntunnel mock-up.\n8.9\nGeodesy\nSince the FCC-ee will extend well beyond the current CERN site, spanning both Switzerland and France\nacross areas with diverse topographical and geological characteristics, an enhanced and extended geode-\ntic infrastructure will be required. This will include an evolution of existing reference frames and an\nupdated gravity field model to ensure precise positioning throughout the project.\nA robust geodetic foundation will support the planning, construction, alignment, and operation\nof the FCC-ee, accommodating different levels of accuracy. These range from the initial large-scale\nplacement studies to the final sub-millimetric precision alignment, which will continue to be refined\nthroughout the accelerator\u2019s lifetime. The geodetic infrastructure will be adaptable to meet the needs of\n429\n\neach project phase.\nDuring the preparatory phase, a primary geodetic network will be established as early as possible\nto provide a stable reference frame for all subsequent activities, including civil engineering. Once the\nFCC-ee layout is finalised and construction begins, the geodetic network will be extended underground\nthrough the shafts, forming a dedicated underground geodetic network to ensure precise alignment of the\ninfrastructure.\nThis section describes the core components of the geodetic infrastructure, while the alignment\nstrategy for the accelerator components and detectors is detailed in Section 3.5.\n8.9.1\nGeodesy\nDefinition of the coordinate reference systems for the FCC-ee\nA key component of the geodetic infrastructure will be a static coordinate reference system, established\nthrough the CERN Terrestrial Reference Frame (CTRF), along with a kinematic model (CKM) that rep-\nresents the temporal evolution of the CTRF\u2019s reference points. This system will enable connections\nbetween CERN\u2019s existing reference frames and international, national, and local reference frames, en-\nsuring compatibility and long-term stability. Additionally, it will serve as a foundation for analysing\ncrustal deformations in the region.\nFor civil engineering works, a compound Coordinate Reference System (CRS) will be used, con-\nsisting of a projected CRS for horizontal positioning and a vertical CRS for gravity-related height deter-\nmination. The horizontal coordinates will be defined through a CERN Projected Frame (CPF), while the\nVertical Reference Frame (CVF) will provide height information consistent with the gravitational field.\nFor alignment purposes, the CERN Coordinate System (CCS) - which is currently used for all\nCERN machines - will remain in use. This will ensure a consistent and reliable link between the FCC\ninfrastructure and the existing CERN facilities.\nSince the FCC is a cross-border project, existing geo-referenced data such as geological maps, dig-\nital terrain models, and aerial imagery are expressed in different geodetic horizontal and vertical datums.\nTo ensure compatibility, these datasets will be harmonised and transformed into the CTRF. Transforma-\ntion models and their associated uncertainties will be carefully computed to maintain consistency across\nall datasets. Additionally, dedicated geodetic transformation software will be developed and made avail-\nable to stakeholders to facilitate seamless integration.\nFigure 8.103 shows the connection amongst the different parts of the reference system infrastruc-\ntures. A detailed description of the coordinate reference systems is provided in Ref. [418].\nImplementation of the surface geodetic network\nSince it will be the reference for all survey and civil engineering work, a primary surface geodetic net-\nwork (P-SGN) will have to be created as soon as possible to implement the CTRF (see [419]). During the\nperiod of the FCC Feasibility Study, IGN and Swisstopo increased the density of their national geodetic\nnetwork (R\u00e9seau de Base Fran\u00e7ais and Points fixes planim\u00e9triques, respectively) over the FCC area and\nbuilt new geodetic pillars and installed a new continuously operating global navigation satellite system\n(GNSS) reference station at locations suitable for the FCC-ee (see Fig. 8.104). The coordinates of the\nP-SGN will be determined and tied in the latest implementation of the European Terrestrial Reference\nFrame using simultaneous GNSS observations, ensuring absolute accuracy of 3 to 5 mm.\nDuring the tunnel construction, the P-SGN would increase its density with auxiliary points, and a\nportal network would be created at each shaft to define the orientation of the tunnel. A surface levelling\nnetwork will also be created, linking the eight surface sites and access shafts.\n430\n\nFig. 8.103: Graphical outline of the coordinate reference systems for the FCC-ee.\nGravity field model\nTo meet the vertical alignment accuracy requirements and to overcome the differences between the\nFrench and the Swiss altimetric systems, the local variations of the gravity field must be known or\nmodelled with high accuracy and resolution (i.e., at a very short wavelength).\nA centimetric (1 cm) accuracy could be achieved for the civil engineering and tunnelling work and\nas a basis for computing the gravity field model at the tunnel level. The latter is required to align the\nmachine in an Euclidean plane. The computation of these models will require additional R&D.\nA control profile, composed of GNSS-levelling and astrogeodetic observations, has already been\ndetermined to control the different geoid solutions that will be computed [420].\nUnderground geodetic network\nOnce the tunnel shafts have been excavated, the coordinate reference system will be transferred under-\nground. At this stage, the coordinates of reference markers regularly spaced on the floor and on the wall\nof the tunnel will be computed (see Fig. 8.105).\nThe underground geodetic network will be the reference for all automatic or manual alignment\nactivities. Systems and instruments detecting the movements of the reference markers will be developed\nand installed to permanently or periodically monitor the stability of the reference network.\nThe development of the optimum methodology for the determination and monitoring of the un-\nderground geodetic network will require additional R&D efforts.\nA geodetic reference frame that includes the nominal beamline must be established for each of the\nFCC-ee experiment caverns. To achieve this, geodetic reference points will be installed within the ex-\nperiment caverns, typically implemented using wall brackets, nests, permanent tripods, or ground inserts\nequipped with CERN standard survey reference sockets. The entire geodetic network will be defined\nwithin the CERN Coordinate System (CCS) as part of the broader underground geodetic network. The\nnetwork will be measured using high-precision instrumentation, including laser trackers, total stations,\nand direct levelling techniques. To maintain accuracy and stability, the geodetic networks of the ex-\n431\n\nFig. 8.104: Primary Surface Geodetic Network for the Future Circular Collider.\nperiment caverns will be regularly updated, ensuring that alignment remains consistent throughout the\nlifetime of the FCC-ee.\nCalibration, checking and testing of the geodetic instruments\nTo meet surveying and alignment requirements, geodetic instruments, sensors, and tools used during the\nconstruction, installation and operation of the FCC must be regularly tested. A concept for calibration,\nchecking, and testing (CCT) of geodetic instruments for the FCC has been developed (see Ref. [421]). A\nmix of in-house activities and facilities as well as outsourcing to external service providers would cover\nthe needs. Dedicated spaces must be allocated at strategic locations for checking instruments like total\nstations, levels, laser trackers, 3D scanners prior usage. External service providers can be in charge of\nyearly maintenance and fixing identified defects.\n432\n\nFig. 8.105: Schematic representation of the coordinate transfer.\n8.10\nAvailability\nThis section details results from the enhanced Monte Carlo simulation environment for FCC-ee avail-\nability described in Section 2.4, focusing on systems specific to the Technical Infrastructure serving the\ncollider and booster. Infrastructure serving the injector complex is detailed in Section 7.9.\n8.10.1\nContributing Systems\nThe same general framework for availability approximation was applied to the collider systems, de-\nscribed in Section 2.4.1. Specifics of this process used for each technical infrastructure system are\ndescribed in the following paragraphs. Only faults leading to downtime in the representative system\nwere considered, thereby assuming a similar degree of redundancy for each basic component family as\ncurrently exists in the working accelerator. Details of subsystems and scaling numbers are provided in Ta-\nbles 8.36 and 8.37. Fault data was taken from CERN\u2019s Accelerator Fault Tracking (AFT) database [235]\nand is specific to the LHC physics operation 2015-2024, unless otherwise stated.\n1. Cooling & Ventilation: Fault rate was scaled using the number of critical circuits at each access\npoint, which is similar to the LHC (160 in LHC, 168 in FCC-ee). This does not consider the overall\nvolume served by these critical circuits, which is significantly larger in the FCC-ee.\n2. Electrical Network: The FCC-ee is connected to the PA, PD and PH external grid. The distribu-\ntion between PA and PD is connected such that one can power the other in the event of failure with\napproximately 15 minutes of changeover time following beam dump. At PH, there is no backup\nreconfiguration option due to the high power demand in the collider RF system. Any electrical\nnetwork failure at PH will, therefore, block the beam until failed hardware is restored. Two types\nof faults are categorised:\n(a) External network perturbations are a high contributor to downtime in the LHC, as they can\ntrigger child faults in sensitive hardware across the complex. Failure rate and downtime from\nthis category are applied without scaling to each of the three access points, assuming the\nsame resilience to glitches as the LHC.\n(b) Internal network faults occur due to hardware failure in the electrical distribution designed\nand managed by CERN. This is scaled according to the number of substations at each location\n433\n\n(PA: 4, PD: 3, PH: 1). This excludes the parallel power line feeding the collider RF at PH,\nwhich has not yet been modelled. A study to optimise the reliability of this parallel line\nagainst cost factors will take place in the pre-TDR phase.\n3. Cryogenics: The FCC-ee requires only two cryoplants to serve the collider and booster supercon-\nducting RF systems at PH and PL, respectively. In the absence of a detailed design to indicate the\nnumber of components, the failure rate at each point is assumed to scale with the reference 4.5 K\npower level relative to one LHC cropland at 144 kW. This is constant for lower energy modes (Z,\nW, ZH) at 80 kW (collider) and 9 kW (booster). During the long shutdown prior to t\u00aft operation,\neach cryoplant is upgraded to 168 kW and 53 kW, respectively.\n8.10.2\nSimulation Results\nThe breakdown of unavailability and lost luminosity contribution from each technical infrastructure sys-\ntem is shown in Fig. 8.106. The electrical network has the largest contribution to lost luminosity in Z,\nWW, and ZH operation due to its more frequent and shorter duration fault types. Cryogenics is the most\nsignificant contributor to unavailability and lost luminosity in t\u00aft mode due to the energy upgrade required\nfor additional cavities in the superconducting RF system.\nFig. 8.106: Contribution of technical infrastructure subsystems to unavailability and lost luminosity.\nSystems are ordered according to Z mode lost luminosity contribution.\n8.10.3\nR&D Opportunities\nSeveral areas for improvement are identified:\nInternal Electrical Network Faults\nThe internal electrical network significantly contributes to lost luminosity despite a 15-minute changeover\nredundancy between PA and PD. Designs must incorporate a more robust redundant connection between\nthese two points. An automatic switch could significantly reduce the changeover time. However, the\nlargest gains would be made by avoiding beam dumps altogether, as this eliminates lost luminosity due\nto turnaround time in the initial operation phases (see Section 2.3.2).\nReliability must get particular attention at PH, as this cannot be reconfigured to draw power from\nanother access point. Further, this means the parallel power line feeding the collider RF must be designed\nto a particularly high-reliability target.\n434\n\nTable 8.36: Parameters used to simulate availability of systems and subsystems in the collider Technical\nInfrastructure.\nSystem\nSubsystem\nLHC\nFCCee\nLocation\nGroup MTBF\nZ,WW,ZH / t\u00aft\nZ,WW,ZH / t\u00aft\n#\n#\ndays\nCooling &\nCritical circuits:\nVentilation\nPA\n200\n30\nPA\n111.3\nPB\n200\n20\nPB\n166.9\nPD\n200\n30\nPD\n111.3\nPF\n200\n20\nPF\n166.9\nPG\n200\n30\nPG\n111.3\nPH\n200\n25\nPH\n133.6\nPJ\n200\n30\nPJ\n111.3\nPL\n200\n25\nPL\n133.6\nElectrical\nInternal Network:\nNetwork\nPA\n1\n4\nPA\n3.6\nPD\n1\n3\nPD\n4.8\nPH\n1\n1\nPH\n14.3\nExternal Glitch\n1\n3\nPA, PD, PH\n7.7\nCryogenics\nTunnel:\n(collider)\nInstrumentation\n144\n80 / 168\nPH\n70.6 / 33.6\nPLC\n144\n80 / 168\nPH\n352.9 / 168.1\nProduction:\nTemperature\n144\n80 / 168\nPH\n47.1 / 22.4\nControls\n144\n80 / 168\nPH\n470.6 / 224.1\nInstrumentation\n144\n80 / 168\nPH\n74.3 / 35.4\nPLC\n144\n80 / 168\nPH\n235.3 / 112.0\nVacuum\n144\n80 / 168\nPH\n352.9 / 168.1\nOperation:\nPNO-SAM\n144\n80 / 168\nPH\n352.9 / 168.1\nPNO-BSCR\n144\n80 / 168\nPH\n235.3 / 112.0\nPNO-REF\n144\n80 / 168\nPH\n282.3 / 134.5\nPNO-DFB\n144\n80 / 168\nPH\n17.9 / 8.5\nPNO-HF\n144\n80 / 168\nPH\n282.3 / 134.5\nOther\n144\n80 / 168\nPH\n117.6 / 56.0\nSpecific Operation\n144\n80 / 168\nPH\n176.5 / 84.0\nUsers\n144\n80 / 168\nPH\n282.3 / 134.5\nExternal Electrical Perturbations\nThe simulation assumes that the same resilience to external network perturbations will occur in the FCC-\nee as currently appears in the LHC. This is a coarse assumption, as the resulting downtime is most\ncommonly due to child faults in sensitive accelerator systems, e.g., high-precision power converters, RF,\netc.; the number of which could be significantly higher in FCC-ee. Learning from LHC experience,\nall FCC-ee systems must be designed according to an established standard for resilience to electrical\nglitches.\n435\n\nTable 8.37: Parameters used to simulate availability of systems and subsystems in the booster.\nSystem\nSubsystem\nLHC\nFCCee\nLocation\nGroup MTBF\nZ,WW,ZH / t\u00aft\nZ,WW,ZH / t\u00aft\n#\n#\ndays\nCryogenics\nTunnel:\n(booster)\nInstrumentation\n144\n9 / 53\nPL\n627.4/ 106.5\nPLC\n144\n9 / 53\nPL\n3137 / 532.7\nProduction:\nTemperature\n144\n9 / 53\nPL\n418.3/ 71.0\nControls\n144\n9 / 53\nPL\n4183 / 710.3\nInstrumentation\n144\n9 / 53\nPL\n660.5 / 112.2\nPLC\n144\n9 / 53\nPL\n2091 / 355.2\nVacuum\n144\n9 / 53\nPL\n3137 / 532.7\nOperation:\nPNO-SAM\n144\n9 / 53\nPL\n3137 / 532.7\nPNO-BSCR\n144\n9 / 53\nPL\n2091 / 355.2\nPNO-REF\n144\n9 / 53\nPL\n2510 / 426.2\nPNO-DFB\n144\n9 / 53\nPL\n158.8/ 27.0\nPNO-HF\n144\n9 / 53\nPL\n2510 / 426.2\nOther\n144\n9 / 53\nPL\n1046/ 177.6\nSpecific Operation\n144\n9 / 53\nPL\n1569/ 266.4\nUsers\n144\n9 / 53\nPL\n2510 / 426.2\nCryogenics\nDespite the significantly smaller cryogenic load compared to LHC, this is the highest contributor to\ndowntime from the technical infrastructure systems. As designs develop, special consideration must be\ngiven to ensure availability.\n8.10.4\nOutlook\nTechnical infrastructure availability is of particular importance in the next phase as many of these systems\nhave significant footprints on the civil engineering layout, e.g., the size of alcoves and caverns, routing\nand location of cables and equipment, radiation protection, access, etc. The coming years must see a\nthorough reliability/availability analysis of these high priority systems to ensure performance ahead of\ncivil engineering procurements.\n436\n\nChapter 9\nFCC safety concepts\n9.1\nIntroduction\nThis chapter outlines the safety concept for FCC. Given the intricate nature of particle accelerators, which\ninvolve high-energy beams, radio frequency cavities, cryogenic systems, and sophisticated electromag-\nnetic equipment, a comprehensive safety strategy is essential to ensure operational integrity.\nKey safety considerations include identifying the scope of the concept, its objectives, as well\nas the underlying impact of domains such as deep underground siting, radiation protection, structural\nintegrity, fire and oxygen deficiency, and emergency response protocols. Integrating safety measures\ninto the FCC design has an impact on the layout of the facilities. This chapter underlines the specific\nstrategies and technologies employed, demonstrating our commitment to creating a safe and efficient\nresearch environment.\n9.1.1\nSafety considerations\nThe geographical distribution of surface sites and the time required to reach each site by road, the chal-\nlenges linked to the underground working conditions, and the diverse composition of technical equipment\nat surface sites require the systematic development of an integrated safety concept.\nThe results presented in this chapter are based on work that assumes the baseline layout and\nparameters outlined in this report. If future phases of the study introduce deviations from the baseline,\ntheir impact on the safety concept will have to be assessed. Certain safety systems form the foundation\nof the safety concept; therefore, any modifications to these systems may necessitate the development of\nan entirely new safety concept (see Section 9.3.4).\n9.2\nSafety goals & objectives\n9.2.1\nRegulatory framework\nCERN, an intergovernmental organisation established under international law by its Convention (1 July\n1953, amended 16 June 1972), is headquartered in Geneva and operates across the Franco-Swiss border.\nUnder its regulatory framework, CERN establishes safety rules as necessary for its functioning.\nThe CERN Safety Policy [422] defines the overarching principles governing safety at CERN and is\ncomplemented by CERN-specific rules tailored to its operational needs. Where specific rules are not\nestablished, national laws apply within their respective territories. This framework ensures that the rules\nare uniform throughout the site and adapted to the specific (particularly technical) requirements of the\norganisation.\nCERN collaborates with the Host States under domain-specific treaties and tripartite agreements,\ne.g., in efforts to minimise environmental impact and uphold best practices in radiation protection. While\nthe Host States facilitate its operations, CERN remains committed to limiting its impact on their territo-\nries and ensuring its activities do not compromise their security.\nThis regulatory framework reflects the current perspective and serves as the foundation for devel-\noping this safety concept.\n437\n\n9.2.2\nCERN safety policy\nCERN has a safety policy [422] in place that defines the safety objectives for every project and activity\nin order of priority:\n1. Life safety: ensure the best possible protection according to CERN\u2019s Safety Rules in health and\nsafety matters of all persons, irrespective of their status, participating in the organisation\u2019s activities\nor presence on its site, as well as of the population living in the vicinity of its installations.\n2. Environment protection: limit the impact of the organisation\u2019s activities on the environment.\n3. Asset protection and business continuity: guarantee the use of best practices in matters of safety.\nThe FCC feasibility study covers all these objectives, although the scope of the safety concept,\ndeveloped at this stage, focuses on the life safety objective. The environmental protection aspects are\ncovered in a dedicated stand-alone document, which is equally referenced in the third volume of the\nFeasibility Study Report.\nAlthough the safety concept described focuses on the FCC-ee accelerators (injector, booster, and\ncollider), possible incompatibilities with the civil engineering layout for FCC-hh are highlighted and\nintegrated based on the requirements for the feasibility study. Modifications to the technical infrastructure\nneeded for FCC-hh but which are not yet included in the design will be integrated in the safety concept\nwhen the infrastructure is being designed.\nThe transfer tunnels from the injector chain are not included in this concept, since safety aspects\ncan only be studied for those elements once a design baseline is developed. The impact on safety of this\npart of the infrastructure would therefore be analysed in the next phase of the project.\n9.2.3\nLifecycle phases\nThe Safety concept covers the following lifecycle phases:\n\u2013 Construction phase.\n\u2013 Installation phase.\n\u2013 Operation phase, including maintenance periods and repair activities.\nEach phase is characterised by different safety aspects, associated with the safety systems deployed\nand available, and with the time occupants are exposed to those conditions. The development of the safety\nconcept described in this section is based on analysis of the operation phase of the FCC.\n9.2.4\nSafety Organisation & Management Plan\nA safety management plan is required for ensuring the safe operation of such a large research infrastruc-\nture. This plan will not be limited to the respect of safety objectives but also safeguard the long-term vi-\nability of the facility by fostering a culture of safety, compliance, and continuous improvement. Through\nrisk assessment, planning, and the establishment of clear procedures, a management plan ensures that\nsafety is prioritised in all phases of the infrastructure.\nThe safety regulation on the \u2018Responsibilities and organisational structure in matters of safety at\nCERN\u2019 (SR-SO) [423] is based on the the CERN Safety Policy [422].\nCurrent practice at CERN foresees that the appointed project leader (PL) is responsible for safety\nwithin the project [423]. The PL may decide to appoint a project safety officer (PSO) with the mandate to\nsupport the project leader in meeting the obligations in matters of safety [424]. At the end of the project\nphase, safety responsibilities are transferred from the project leader to the organic units in charge of the\noperation.\n438\n\n9.3\nPlanning for safety\n9.3.1\nHazard Register\nA hazard register is the result of systematic identification of activities, equipment, and substances with\ntheir associated hazards for workers, the public, or the environment. A systematic inventory of hazards\nserves as a support not to overlook any danger and unifies the terminology among different assessors.\nSuch lists are available from different occupational safety organisms (see for example Ref. [425]). As\nthey target manufacturing and services, they must be modified for particle accelerators and for research\ninfrastructures in general to include hazards unique to these environments. Table 9.1 shows the head-\nlines of a hazard register for particle accelerators. Ref. [426] provides a hazard list, tailored to particle\naccelerators. The adaptation of the hazard list to the local workplace by adding or suppressing hazardous\nequipment, activities, or substances precedes establishing the register.\nThe focus of the hazard register depends on the lifecycle phase. In the planning stage, it identifies\nhazards which can be controlled by design, for example, by adopting standards. In this early stage,\norganisational and psychosocial hazards and risks have not yet been assessed. In the installation and\noperational phase, workplace hazards become more important, for example, related to the organisation\nof work or physiological constraints.\nTable 9.1: Hazard domains for a hazard register, with examples.\nHazard Domain\nExamples\nExternal\nEarthquake, climate, malicious action, cyber criminality\nPhysical\nTemperature, noise, electromagnetic fields\nIonising Radiation\nParticle beam, stray radiation, activation\nNon-ionising radiation\nStatic magnetic fields, UV light, microwaves, lasers, RF\nNoxious substances\nChemically or biologically harmful substances\nFire\nIgnition sources, flammable materials\nMechanical\nCutting, crushing, collision, fall of object\nElectrical\nElectrical shock, electrical arc\nWorking conditions\nTemperature, lighting\nPhysiological\nWorking posture, vibration, manual handling\nUnexpected events\nLoss of control, loss of power\nOrganisation\nConstraining schedule, lack of information\nPsycho-social\nIncomplete and monotonous activities\nThe equipment, activities, and substances are identified by location (surface site and building\nor underground areas) and lifecycle phase. The hazards emerging from each equipment, activity, and\nsubstance are identified with a specific list of hazards based on Ref. [425], modified and complemented\nfor accelerator facilities, and published in Ref. [426]. The hazard description links to relevant sources of\nstandard practice (see Section 9.3.2) at the time of the Feasibility Study. These sources must be updated\nregularly during the project life cycle.\nIn a large particle accelerator, most equipment, activity, and substance and their associated hazards\noccur repetitively at various locations and in different phases. To avoid tedious and error-prone updates of\na written document, the hazard register is kept in a relational database where every piece of information\nneeds to be updated only at a single location and is automatically propagated. Different types of database\nreports produce documents and reports summarising the hazards for a specific location and phase or the\nrecommended sources of appropriate standard practice (Section 9.3.2). Hazards for which no standard\npractice exists (or where standard practice from conventional industry is not applicable) require a detailed\nrisk assessment and identification of mitigation measures (see Section 9.3.3).\n439\n\n9.3.2\nStandard practices\nStandard practices are based on hazard identification, risk descriptions, and mitigating measures applying\nto technologies and related activities in industry that are similar to those encountered in an accelerator.\nExamples are electrical distribution of standard current and voltage and transport.\nSuitable sources of standard practice are national and international legislation on hazardous equip-\nment, activities, and substances. These documents are prescriptive, and their application is usually\nmandatory. A hazard is often considered under control when such mandatory regulations are imple-\nmented and applied.\nCERN\u2019s safety policy [422] is to apply European Directives and associated standards where avail-\nable. Numerous types of consumer and industrial products are subject to European Directives, which\ninclude chapters on Essential Health- and Safety Requirements (EHSR). Their purpose is to guarantee\nequal safety standards for workers and for consumers (who buy and use products) throughout the member\nstates of the European Union. Only under this condition can goods be freely traded within the European\nEconomic Area (EEA). Suppliers from third countries must also apply the European safety standards to\nintroduce their products into the common market.\nAnother source of standard practice is the publications by occupational health and safety organ-\nisms, e.g., SUVA1, INRS2, HSE UK3, CTPI-AEAI CH4, and of industrial associations e.g., BG ETEM5.\nTheir recommendations provide the practical elements required to meet the legal prescriptions at the\nworkplace. They are often borne from common sense and may be easy to apply, effectively eliminating\nthe hazard and making further risk assessment superfluous.\nProduct documentation by manufacturers is another source of standard practice. The manufacturer,\nhaving designed the equipment so that it meets legal requirements, gives the necessary information for\nsafe use in the form of user manuals, video tutorials, and other training materials. Over time, CERN\nhas built up a wealth of knowledge about safety, based on the experience from operating the existing\ninfrastructure. The source material defining standard practices is assembled and classified in the hazard\nregister.\n9.3.3\nPerformance-based design\nFor hazards for which standard practices are not available or are not fully applicable to the particularities\nof an underground accelerator complex, the study follows a performance-based design (PBD) approach.\nPBD is a state-of-the-art risk assessment approach, which is used in areas such as fire safety and\nintroduced in national legislation in several countries, including Switzerland [427]. It is a process of\ndefining alternative design options in an iterative way and assessing the impact against a predefined set\nof safety objectives. For this study, a PBD methodology introduced by the Society of Fire Protection\nEngineers (SFPE) [428] was adopted. According to SFPE, the PBD process can be divided into 6 steps\n(see Fig 9.1) after having defined the scope of the assessment:\n1. Identify the safety goals (see Section 9.2.2).\n2. Define the design objectives and develop the performance criteria (i.e., safety requirements).\n3. Develop the accident scenarios based on the system-level risk assessment.\n4. Develop the trial design with the proposed safety systems.\n5. Evaluate the trial design against the performance criteria.\n6. Create new trial designs until they meet the criteria - (iterative process).\n1https://www.suva.ch/\n2https://www.inrs.fr/\n3https://www.hse.gov.uk/\n4www.bsvonline.ch/fr/publications/det\n5https://www.bgetem.de/\n440\n\nThe process ends when a trial design that meets the safety objectives is retained as the baseline\nsolution.\nDifferent methodologies can be used for the evaluation of trial designs, ranging from simple as-\nsessments to highly complex algorithms [429] and numerical simulations. A qualitative analysis was\nperformed during the conceptual study phase (2014 to 2018). For the feasibility study, a more in-depth\nevaluation was performed using quantitative (i.e., worst credible scenarios) and probabilistic approaches.\nFig. 9.1: Performance-based design flowchart. Example for fire scenarios from SFPE [428]\n9.3.4\nSafety systems\nFor the safety concept described in this document, a safety system refers to a set of engineering con-\ntrols aimed primarily at ensuring life safety by incorporating both preventive and protective measures\nduring normal and accident scenarios. A system that is used primarily for technical purposes but also\nperforms safety functions can be considered a safety system, provided that it adheres to the required\nsafety standards.\nThe following Sections (9.4 and 9.5) provide a brief summary of the safety systems proposed as a\nresult of the study. Additional details are provided as references to reports, notes, etc.\n9.4\nSafety concept for the operation phase\nAs mentioned in Section 9.2.1, the strategy is to cover conventional hazards with standard practices\nand integrate accelerator-specific hazards in a performance-based design approach. The outcome is an\nintegrated approach towards safety for the project.\n441\n\n9.4.1\nSafety systems supporting the concept\nThe combination of the safety systems described hereafter constitutes the present safety concept. The\nsuppression and/or major modification of any given safety system will have an impact on the global\nsafety concept, which might require partial or total redesign of the concept.\nThe Safety concept is built on the following main pillars:\n\u2013 Static confinement.\n\u2013 Air management & dynamic confinement.\n\u2013 Personnel transport.\n\u2013 Emergency response.\n\u2013 Secure power network.\n\u2013 Access control.\nIn addition to these pillar systems, several high-integrity safety systems complement the safety\nconcept. They permanently monitor the safety conditions and trigger appropriate safety actions from\nother systems or personnel.\n\u2013 Access Safety System.\n\u2013 Hazard detection.\n\u2013 Emergency call.\n\u2013 Evacuation alarm.\nThe particle accelerators have the following modes:\n\u2013 Run mode: the beam is circulating or could be circulating; personnel can only be present in very\nlimited areas of the facility.\n\u2013 Access mode: beam cannot circulate. Personnel are authorised to access the facility. There are\ndifferent types of access periods:\n\u2013 Short access: for interventions over a period of typically one hour or more and less than a\nday.\n\u2013 Technical stop: for planned interventions over a period of several days up to a few months.\n\u2013 Long shutdown: for planned interventions lasting several years for major consolidation and\nupgrade works.\nCompared to other phases, the operation phase constitutes the longest part of the project\u2019s lifetime\nand during which the majority of occupational hazards (see Section 9.3.1) are present simultaneously.\nDepending on the state of the accelerators, the occupants may be exposed to different hazards. The\naverage occupancy density in underground facilities is low, although occupancy during technical stops\nand long shutdowns can be comparable to that of the installation phase.\nStatic confinement (Compartmentalisation)\nThe fire safety concept relies on passive fire compartments as the principal strategy to sectorise the\nfire load and prevent fire and smoke propagation across the facility whilst enabling safe evacuation of\noccupants and intervention of the emergency teams.\nThe concept has partitions along the main tunnel and in all areas with a specific fire risk (e.g., elec-\ntrical alcoves), using a dedicated fire-resistant partition. Moreover, protected areas for evacuation (e.g.,\nsafe areas6) will also be compartmentalised. Doors, dampers, and hatches installed in the compartment\n6Areas free from smoke and hazardous gases as a buffer for occupants to wait for the lift, not to be confused with a temporary\nrefuge shelter or equivalent.\n442\n\nmust also be fire-resistant and match the same resistance level as the fixed partition. For services pen-\netration of those partitions (e.g., pipes, cable trays), the openings must be effectively sealed, following\nsafety standards, to match the fire resistance required.\nAs a fundamental part of the fire safety concept, the fire rating of the compartments must guarantee\nthat the fire and smoke are contained for the time needed to enable safe evacuation and intervention.\nMoreover, to limit property losses and recovery time, the integrity of the compartments must withstand\nall foreseeable fire scenarios. For this, the rating will be based on various factors: the fire load, the\npossibility of reaching flashover conditions in the affected compartments, and the time needed to ensure\nthe safe evacuation and intervention of the emergency teams. The fire rating must also be consistent\nwith the minimum structural fire resistance requirements assigned by standard practices and Host State\nregulations (see Table 9.6).\nThe following fire-resistance rating is proposed as a baseline for the feasibility study of the under-\nground infrastructure. The resistance stated below is based on ISO 834 curves [430] for design purposes\nas defined in EN-13501-2 [431]. Section 9.4.3 provides more information on the difference between\nstandard and natural curve-based fire resistance.\n\u2013 Accelerator tunnel (arc and straight sections): EI90 partition (every 400 m) with interlocked door\nnormally open.\n\u2013 RF sector - connection between klystron gallery and accelerator tunnel: EI90 partition at the bot-\ntom and top of connection staircases.\n\u2013 Service caverns - safe area (lift shaft): EI120 partition.\n\u2013 Connection tunnels - connections between experiment and service caverns: EI120 .\n\u2013 Alcoves - connection to the accelerator tunnel: EI120 partition.\n\u2013 Other underground spaces with specific risks (UPS, transformers): EI120.\nIn the accelerator tunnel, fire compartments also serve as an important element of the evacuation\nstrategy by limiting the distances travelled within the affected compartment, and they allow occupants\nto quickly move into an adjacent (non-affected) compartment which serves as a safe area (free from\nsmoke, gas and fire consequences) to continue the evacuation until reaching the safe area joined to the\npressurised lift shaft and, ultimately, the assembly point at the surface.\nDifferent requirements in terms of evacuation distances exist for tunnels. Table 9.2 provides refer-\nences for railway and road infrastructures in Europe, as well as for other particle accelerator infrastruc-\ntures.\nTable 9.2: Overview of distances between emergency exits in transport, technical, and accelerator tun-\nnels. EU Regulation 1303/2014/EC and Directive 2004/54/EC apply to EU network of rail and road\ntunnels, respectively. XFEL compartments are made of solid fire-proof walls with a triple water mist\nenclosing system instead of a fire door.\nSource\nLength [m]\nComment\nEU road tunnels [432]\n500\nBetween emergency exits (if required)\nEU railway tunnels [433]\n500\nBetween connections to adjacent tube\nOLT4 [434]\n500\nBetween access shafts in non-frequented technical galleries\nNFPA 520 [435]\n610\nTo reach a safe exit, refuge, or portal\nXFEL [436]\n600\nBetween two compartments (wall + water curtain)\nILC [437]\n500\nPassage connecting the two galleries\nThese requirements are understood to be the distance to reach an area of relative safety where\nthe occupants are no longer exposed to untenable conditions. Moreover, once the occupants reach the\n443\n\nadjacent (unaffected) compartments, the remaining length needed to evacuate using motorised means\nis not considered in the maximum distance requirement. This is the case of the Gotthard and Lyon-\nTurin base tunnels [438] where evacuation is guaranteed through the adjacent (non-affected) double-tube\nconcept.\nThe distance between two compartments must consider the maximum acceptable length (Ta-\nble 9.2), as well as the layout constraints and practical aspects of the facility. For the FCC, this can\nbe summarised as:\n(\nd \u2264500 m\nd = distance between alvoves \u00f7 integer number of compartments between two alcoves\nSolving the system with 1600 m between two alcoves results in 4 compartments, hence one every\n400 m. With this layout, each alcove will house safety-related systems for two compartments to the left\nand two to the right. The final implementation of each individual compartment will depend on the exact\nlocation of the beamline elements of both the collider and the booster. For example, one should avoid\nthe installation of a compartment in the middle of a quadrupole girder, or close to a radiation absorber. A\ncompartment assembly is planned to be included in the arc half-cell mockup to test and identify the best\nlocation. Figure 9.2 shows a possible integration layout of such a partition. The challenges emerging\nfrom integrating such a compartment around different services, including the hatches for overhead robots,\nneed to be considered. A subsequent design phase has to develop detailed plans.\n(a) 2D view\n(b) 3D view\nFig. 9.2: Illustration of the integration of a fire compartment in the cross-section of the FCC tunnel. Light\nred: fixed partition walls; Purple: frames with grey fill: movable parts - fire door, robot hatch, installation\nhatch.\nAir management & dynamic confinement (ventilation)\nDue to the nature of underground facilities, adequate indoor air quality is required for both the occupants\nand the equipment. A robust ventilation system ensures the appropriate temperature and humidity con-\nditions in the tunnel during operation and when people are present. During access mode, it provides a\nsupply of fresh air for occupants with an appropriate air exchange rate.\nFive different working modes for the tunnel ventilation are envisaged:\n444\n\n\u2013 Run mode: the accelerators are in operation and most electrical systems are powered; a heat load\nis transferred to the air in this mode; radiation protection aspects are taken into account for the air\nflow. No personnel are present in the main tunnel, the alcoves, and the experiment caverns.\n\u2013 Access mode: the accelerators are not operational. Personnel can access and work in the tunnels.\nOccupational health & safety requirements must be considered.\n\u2013 Flushing mode: Completely renew the air underground when moving from the Run to Access\nmode. Personnel are not present in underground structures.\n\u2013 Economy mode: Reduced airflow for energy-saving reasons in situations other than Access mode,\nreducing the air exchange to a minimum. The presence of personnel is not foreseen in any under-\nground structures.\n\u2013 Emergency mode: activated in the event of a fire or gas release to guarantee dynamic confinement\nbetween the affected and adjacent compartments.\nTunnel arcs\nFor tunnel arcs, two technical solutions were studied [439]:\n1. Semi-transverse ventilation scheme where the air is supplied to each sector from both endpoints\nvia a specific duct throughout the sector below the transport zone, supplied to each compartment\ntransversely by air diffusers, and extracted either through the tunnel itself or by an emergency\nextraction duct on the ceiling of the tunnel;\n2. Longitudinal ventilation scheme where the air is supplied at one end of the sector and extracted at\nthe other end.\nIn addition to air management during nominal situations, an emergency extraction system is pro-\nposed for the main underground areas. This system will be activated in case of fire or cryogenic gas leak\nto:\n\u2013 Allow safe evacuation from the affected compartment while providing enough safety margin (Sec-\ntion 9.4.3).\n\u2013 Create a dynamic confinement to prevent smoke from spreading to adjacent compartments.\n\u2013 Remove heat and smoke in the affected compartment, reducing the risk of structural damage and\nreinforcing property protection.\n\u2013 Allow for a safe and efficient intervention from the emergency teams, allowing emergency respon-\nders the ability to manipulate and control the system to their advantage.\nSince there are still two concepts for the ventilation system being considered, there are also two\ndifferent concepts for the emergency extraction system under consideration, one for each ventilation\nscenario (semi-transverse & longitudinal).\nIn the semi-transverse ventilation concept, the sector between the two shafts is considered to be\nsplit in the middle. Air is supplied to the tunnel through four wall-mounted air diffusers in each compart-\nment. During access mode 54 000 m3h\u22121 (2 \u00d7 27 000 m3h\u22121) of fresh air is supplied to both halves of\nthe sector. In the event of a fire, the smoke and hot air are extracted from both ends of the sector and ex-\nhausted to the outside. In such emergency mode, the extraction dampers located under the ceiling of the\ntunnel are open in all three compartments (affected + two adjacent). The air in the affected compartment\nwill be extracted at a flow rate of 10 000 m3h\u22121 and 3500 m3h\u22121 in the adjacent compartments, which\nyields a total extraction flow rate of 17 000 m3h\u22121. In the event of an emergency (e.g., fire), the fire\ndoors of the affected compartment and the two adjacent ones are closed. Hence, to compensate for the\nextracted volume, an equal amount of fresh air (make-up air) is ensured via the nominal supply diffusers\nconnected to the slab duct (Fig. 9.3). This concept creates a pressure difference between the different\n445\n\ncompartments, ensuring that smoke and gas are confined, providing enough time for the occupants to\nevacuate from them (see Section 9.4.3).\nIn the case of longitudinal ventilation, under nominal conditions 54 000 m3h\u22121 of fresh air is sup-\nplied to the tunnel from one end of the sector and extracted at the other. In case of emergency, the\nsame extraction flow rates as per the semi-transverse are used in the affected and adjacent compart-\nments. The fire doors of the affected compartment and the two adjacent ones are also closed, but in\nthis case, the make-up air is supplied from both ends of the sector towards the adjacent compartments\n(2 \u00d7 8500 m3h\u22121), ensured via bidirectional dampers installed on the walls of the compartment. These\ndampers allow make-up air to enter the affected compartment, sweeping the smoke towards open extrac-\ntion dampers located under the vault, providing the necessary compensation. The isolation of the com-\npartments creates a pressure difference, ensuring the confinement of smoke/gas and providing enough\ntime for the occupants to evacuate.\nFig. 9.3: Semi-transversal ventilation mode (top) and emergency mode (bottom). The + and - signs\nillustrate the pressure cascade in the affected compartment and the adjacent ones.\nRegardless of the ventilation concept adopted, it is important to consider the full operability of\nthe fire compartment doors at all times. The risk of overpressure due to nominal, emergency or de-\ngraded modes will be carefully studied to ensure that the evacuation concept is not compromised if these\ndoors cannot be opened normally by applying a force less than 70 N. Compensatory measures, such as\ninstalling pressure-breaking systems, sliding fire doors, etc., must be considered if such a risk is non-\nnegligible.\nA comparison of smoke extraction system performance with respect to life safety of occupants is\ndiscussed in Section 9.4.3.\nAlcoves\nThe electrical alcoves are ventilated via dedicated ducts using the same system as the main tunnel. Emer-\ngency extraction is also available in these areas to support evacuation and intervention. However, due to\nthe reduced evacuation distance inside the alcove, this system is not deemed necessary for the life safety\nof occupants; hence, it is not expected to be triggered automatically. However, in case of a fire, the smoke\ndampers must isolate the normal ventilation to prevent any propagation outside the compartment.\n446\n\nFig. 9.4: Longitudinal ventilation mode (top) and emergency mode (bottom). The + and - signs illustrate\nthe pressure cascade in the affected compartment and the adjacent ones.\nExperiment caverns\nThe experiment caverns are ventilated by a dedicated system that also ensures dynamic confinement\nbetween the experiments and the accelerator tunnel, as well as providing the necessary airflow to ensure\nhygienic conditions and proper indoor air quality.\nSeveral Computational Fluid Dynamics (CFD) analyses of CMS and ATLAS [440, 441], experi-\nment detectors at the present LHC, have proven that the evacuation in experiment caverns can be safely\nperformed without any active smoke extraction system due to their large volumes and relatively short\nevacuation distances. The FCC experiment caverns will be even larger, hence an active emergency ex-\ntraction system for smoke is not required for life safety. However, the ventilation system should be able\nto support the extraction of cold smoke. In the case of particle (sub)detectors that require non-negligible\namounts of cryogenic fluids, a risk assessment will be performed to determine if a dedicated gas extrac-\ntion system is needed to cope with the Oxygen Deficiency Hazard (ODH).\nService caverns\nService caverns are ventilated with a dedicated system that ensures dynamic confinement between the ex-\nperiment cavern and the accelerator tunnel, as well as providing the necessary airflow to ensure hygienic\nconditions. Like the experiment caverns, a smoke extraction solution is required to support intervention\nand recovery time after a fire, but it is not deemed necessary for the occupants\u2019 life safety.\nSafe areas & protected staircases\nAs a basis of the safety concept, certain areas must be kept free of smoke. Consequently, safe areas,\nprotected lift shafts, klystron gallery staircases, and personnel tunnels connecting service and experiment\ncaverns will benefit from independent dynamic confinement. This over-pressurising system will, in\ngeneral7, be fed fresh air and designed to guarantee its performance throughout the duration of the worst\ncredible intervention case. Among other requirements, this implies that such a system must be supplied\n7Alternative solutions might be studied case-by-case, such as using air from adjacent areas.\n447\n\nby a safety power network with fire-rated cables and redundant fans.\nSurface buildings\nThe surface buildings are ventilated by dedicated air handling units designed according to state-of-the-art\nbest practices. Smoke extraction systems will be required for rooms with a floor area exceeding 300 m2\n(in France according to the \u2018Code de Travail\u2019 [442]) or 600 m2 (in Switzerland according to AEAI DPI\n21-15 [443]), in application of prescriptive design standards.\nPersonnel transport\nDue to the distances between the access shafts (11.4 km), occupants need to rely on a dedicated transport\nsystem to commute and evacuate the tunnel in an emergency. At any given time, the capacity of the\npersonnel transport system available underground must ensure the evacuation of all occupants. The same\ntransport system can be used during normal conditions for safe and efficient transport from the service\ncaverns to workplaces along the arcs, with the possibility of parking the vehicles at the entrance of the\nalcoves and in the service caverns. In some situations, autonomous vehicles can go directly to the location\nof the workplace, drop-off the occupants (and material) before driving to the nearest alcove where it will\nstay parked until the end of the shift/activity. In contrast to the nominal scenario, during an emergency\n(i.e., evacuation alarm), the occupants are requested to walk towards the nearest safe alcove and take a\nseat in one of the parked vehicles.\nThe parking capacity for these vehicles will be ensured by the lay-by zones at the entrance of the\nalcoves. The baseline layout has parking spaces for up to 7 vehicles per alcove.\nThe simultaneous circulation of pedestrians and vehicles in the transport zone requires robust\ndetection systems (e.g., stop in case of an obstacle or reduce speed near people or other vehicles) and a\ncentralised communication system to ensure full autonomous driving.\nThe study included the feasibility assessment of an autonomous vehicle (Fig. 9.5) with a bi-\ndirectional drive. It is narrow enough to allow meeting traffic and bypassing of other vehicles within\nthe 2.20 m wide transport zone of the cross-section [444].\n448\n\n(a) Transport vehicle with 4 seats.\n(b) Cross-section layout with the two vehicles passing\neach other within the 2.20 m transport zone.\nFig. 9.5: Personnel transport system [445].\nThe space on either side of a vehicle in the transport zone is \u224870 cm left and right. However,\nwhen two vehicles overtake or pass, the margin reduces to \u224820 cm [445].\nPersonnel transport to and from the surface is ensured by at least two independent lifts situated\nin an over-pressured elevator and stair compartment of the shafts. In the experiment points, two sets of\ntwo lifts are planned to provide the necessary reliability and ensure safe evacuation (see Sections 9.4.1\nand 9.4.4). As requested by the European Lift Directive and the associated harmonised standard [446],\naccess hatches connecting a staircase to the lift shaft must be installed every 11 m for rescue purposes.\nThe lifts must also conform with ISO 8100-1 [447].\nMeans of emergency response\nA simple scale-up of the current emergency response strategy in place for the LHC is not feasible due\nto the size of the infrastructure. A dedicated emergency preparedness and intervention concept will\nneed to be developed in a subsequent design phase as well as a further extension of the existing Mutual\nAssistance Agreements with the Host States [448]. The feasibility study prepared the basis and carried\nout a first analysis of the concept. It consists of the following approach (see also Section 9.4.5):\n1. A central emergency response coordination team.\n2. First response from trained personnel.\n3. Robotic intervention with firefighting capabilities.\n4. On-site support from local emergency services, particularly for surface incidents.\n5. Intervention from CERN Fire & Rescue Service (CFRS) and if relevant, other appropriately trained\nemergency services.\n449\n\nA dedicated approach is proposed for the installation and construction phases (see Sections 9.5.2\nand 9.5.3).\nSecure power network\nSafety systems must maintain their functions at all times. A loss of the general electrical network, e.g.,\ndue to a power cut, would lead to a loss of electrically powered safety systems, hence the need for a\nsecured power network to ensure the availability of safety systems at all times.\nThe secured power network is part of the global electrical network powered with backup sources\nin case the main power supply is lost, to allow the critical and safety-related loads to be powered at\nall times. To avoid duplicating medium voltage (MV) lines in the tunnel, it is proposed to optimise\nthe infrastructure using the same MV link in the tunnel for powering general services and the secured\nnetwork, applying a logic of load shedding in case of a power outage. The aim is to minimise the impact\nin the tightly integrated area and to avoid distributing the power at Low Voltage (LV), dedicated to safety\nsystems, from the surface to the middle of the tunnel, due to the large cable distances that can induce\nhigh power losses and critical voltage drops [449].\nTwo backup sources are planned for the secured power network:\n\u2013 A connection to an alternative public electrical utility.\n\u2013 Emergency power supplies on each surface site.\nIn case of a failure, maintenance, or any other unavailability of the general service network, the\nelectrical network is supplied using the backup power sources mentioned above. In this case, the cou-\nplings between the secured network and the general services network are automatically disconnected\nwhen the voltage from the main sources is no longer available. This logic of load shedding is used on the\nsurface and underground, all the way down to the electrical alcoves, providing power only to the safety\nsystems, leaving the other loads de-energised.\nAll active and passive components involved in the load shedding must be properly designed, main-\ntained, inspected, and tested regularly to ensure a level of reliability which is consistent with that of\nthe safety systems it serves. A description of the network and the single-line diagram is available in\nRef. [449].\nAccess control\nControl of access to the installations at CERN today is based on several layers of protection, each one\nonly allowing a more restricted number of people to enter. On-site access is permitted for identified\naffiliated personnel; entering a surface building housing an accelerator access point requires special\nauthorisations, and finally, entering a beam facility is subject to the most rigorous control.\nBefore granting access to a beam facility, and once a user is identified, several database verifica-\ntions are performed, which include:\n\u2013 Authorisation is granted by the facility responsible to a person recognised by the organisation and\nwith a professional need to access this facility.\n\u2013 All mandatory and specific Safety training for the facility is valid.\n\u2013 The activity has been declared and approved; the organisational unit in charge of works\u2019 coordina-\ntion keeps a detailed list of planned and approved activities together with the assigned personnel,\nas well as a list of on-call personnel likely to intervene at short notice.\nAccess control, therefore, constitutes the first element in the chain of personnel safety systems,\ninstalled to protect the personnel and guarantee that only identified, trained, and authorised personnel\nenter the underground premises.\n450\n\nAccess control is also used to ensure that the number of persons accessing the facility does not\nexceed the maximum number that has been set for safety or operational reasons. For example, the\npressurised safe zones at the bottom of the shafts can only host a limited number of people in case of\nemergency. Therefore, once this number is reached, further access is blocked until some personnel leave\nthe facility. Similarly, the limited capacity of the underground vehicle fleet limits the number of people\nallowed to enter, and this limit is also ensured by the access control system.\nAccess control is formed by two sets of access points; one at the surface and one underground.\nSurface access points\nThe access points at the surface, installed just before reaching the pressurised lifts, give access to\nthe underground areas that are accessible in both beam and access modes, i.e., the service caverns and\nthe klystron galleries.\nThese access points are composed of one or several personnel access devices (PAD) and a material\naccess device (MAD). The devices are linked with commercial access control products, such as access\nrights and biometry databases, using computer networks and state-of-the-art human-computer interfaces.\nA personnel access device (PAD) performs all the checks in one place. It is an inviolable barrier\nthat guarantees that only one identified person can enter at a time. The user\u2019s identity is confirmed\nby a biometric check, relevant access authorisations are verified, and equipment checks (for example,\npossession of passive or active dosimeters) are performed. All these actions take place while the user is\ninside the PAD.\nThe PADs are built using commercial-off-the-shelf components, integrated to form one system,\nfollowing the same principles that have been applied throughout the CERN accelerator complex for\nalmost 20 years. Future PADs, although conceptually similar to the PADs of existing CERN accelerators,\nwill leverage technological advances that can be seen, for example, in the domain of border control, with\nsimilar airlock-like booths installed in recent years at major international airports.\nIn addition to the PAD(s), each access point is equipped with at least one MAD. This device\nallows a safe way to bring bulky material in and out of the accelerator premises. The current concept\nuses a booth of the same size as the lift in the shaft. Its doors can only be operated from outside. After\nopening the doors on one side, the material is placed inside the device, the doors are closed and locked,\nand a scanning process ensures that no one is present within the device. Once scanning is completed\nsuccessfully, the door on the other side of the MAD can be opened and the material removed. The\nMADs at existing CERN facilities are equipped with a combination of standard volumetric detectors and\ncustom image processing algorithms. The MADs for a future project will certainly also benefit from\ntechnological advances, especially in the field of image processing.\nUnderground access points\nThe service caverns are sufficiently shielded from radiation emitted, while the collider is operated\nwith beams. However, access to the accelerator tunnels and experiment caverns requires passing through\nadditional access points, which are interlocked with the presence of beams and other specific hazards.\nConstructed with the same components as their surface counterparts, the underground access points\nleading to areas subject to the presence of beams will thus form part of the Access Safety system.\nGiven the size of the FCC and the distance between two adjacent sites, the granularity of the\naccess control system needs further enhancements. Having a detailed count of people inside the facility,\nas well as a good vision of their location within the facility, is important for safety. Individual tracking\ndevices will be worn by all personnel entering the underground premises. Antennas distributed at regular\nintervals (in each alcove and throughout the access tunnels and service caverns) will allow the emergency\nresponse team to locate people within the underground complex.\n451\n\nAccess Safety System\nThe Access Safety System is an interlock mechanism that acquires the status of and acts on elements\nimportant for safety (EIS) of two types: EIS-access and EIS-beam. It prevents the beam from being\npresent at the same time as personnel. The EIS-access consists of the personnel and material access\ndevices (access control components), emergency exit doors, movable shielding walls etc. The EIS-\nbeam consists of accelerator components that can stop the circulation and the injection of beams. These\ncomponents will include the beam dumps of the collider and the booster. Additional EIS-beam devices\nwill allow redundancy for each interlock chain with technological diversity (e.g., a bending magnet or\na moving stopper obstructing the beam aperture). A functional safety approach, e.g., following the IEC\n61511 [450] standard, will be used throughout the lifecycle of the system.\nThe main functions of the Access Safety System include the following:\nSearch mechanism. After a prolonged operation with access, the machine volumes must be visually\ninspected for the absence of human presence. To facilitate this task, each site is divided with doors into\nsmaller, more manageable units called access sectors. Once the patrol is completed, the search memory\nof each access sector is armed. The division of the FCC into access sectors takes into account the civil\nengineering constraints, accessibility of equipment, etc. Short accesses thereafter are permitted as long\nas members of the personnel are in possession of a safety token. Should an intrusion occur or access\nwithout a token take place, the search of the corresponding access sector is disarmed, and a new patrol is\nrequired. Unlike the preceding accelerators, the patrol will be largely automated, with the long portions\nof the tunnel swept by a robot equipped with a camera. Algorithms to detect the presence of humans,\ncombined with remote supervision, allow unambiguous confirmation of the absence of personnel.\nMonitoring of safe for beam conditions. Whenever equipment is powered and there is ongoing or\nimminent injection or circulation of beams, the system monitors the state of all EIS-access. The moment\nthe EIS-access quit their safe state, or there is a detected failure of the EIS-access equipment, the EIS-\nbeam of the corresponding interlock chain is systematically and automatically activated to stop the beam.\nEstablishing safe for access conditions. Prior to permitting access to the FCC, the accelerator equip-\nment is stopped using its conventional control system. The role of the access safety system is then to\ninhibit the possibility of starting the beam by interlocking the EIS-beam. Access can begin only when\nthe interlock actions have been confirmed.\nMonitoring of safe for access conditions. When access to the FCC is allowed, the safety system con-\ntinuously monitors the state of the EIS-beam. Degradation of the protection barriers results in actions\nranging from blocking access to launching evacuation and requesting the stoppage of an upstream accel-\nerator that could potentially inject a beam in a downstream accelerator.\nEstablishing safe for beam conditions. In order to permit the operation of the FCC with beam, it must\nbe empty of personnel and its search memories armed. To further secure the transition from access to\nbeam operation, an audible warning signal will sound to announce the imminent injection of beams. The\npersonnel are trained to press emergency power cut buttons if there is an audible beam imminent warning\nsignal. Only once the warning has correctly sounded and no abnormal presence in the facility is detected\nwill the conditions for removing the inhibition from EIS-beam be established.\nHazard detection\nThe access safety system prevents any human entry into certain zones in case of radiation and electrical\nhazards by blocking access while the accelerators are operated or are about to be operated with beam.\nAccess is only allowed when the beam is not present and when the pre-conditions for access are met. In\naddition, the access safety system monitors its own elements and launches evacuation alarms should a\nhazardous situation occur.\nHowever, even with a complete stop of beam operation, it is important to monitor the situation\nfor other hazards. The principal ones identified for the FCC accelerator are fire, oxygen deficiency, and\n452\n\nionising radiation.\nFire detection system\nThe Fire Detection (FD) system must satisfy the requirements resulting from fire risk studies. These\nimply generalised early fire detection. Several fire detection technologies meet this requirement, e.g.,\nsmoke detection with opacimeters or with laser beams. However, not all are well suited to be deployed in\nthe FCC tunnel (low height, material obstructing lines of sight, electronics sensitive to ionising radiation).\nThe baseline solution consists of equipping each alcove with aspirating smoke detectors (ASD). A variant\n\u2013 long range ASD (L-ASD) - which is suitable for the FCC, has been put in service at CERN in the SPS\nring. It is capable of detecting aspirated smoke with a 100 m long sampling segment that can be extended\nby up to 700 m of non-sampling tube.\nWith the proposal of having alcoves every \u223c1600 m, it is possible to install 16 L-ASDs in each\nalcove and aspirate air samples from the 800 m left and right of the alcove. Additional ASDs will be\ninstalled for detection within the alcoves themselves, as well as within the service and experiment cav-\nerns. Control and monitoring equipment racks, interconnected with optical fibres, will be installed in\neach alcove. All components of the fire detection system must meet the requirements of the applicable\nEuropean standard, EN 54 [451].\nIt should be noted that this solution requires about 400 km of aluminium aspirating tubes. Should\nfurther analysis prove that having thermal detection is sufficient in terms of performance, newer tech-\nnologies, more suited for long tunnels, will be considered. The thermal detection method most adapted\nto the accelerator environment consists of using distributed temperature sensing (DTS). It is based on\noptical fibre line-type temperature variation detection. This solution is particularly well suited for long\ntunnel sections, where an integrator unit connected to an optical fibre pulled inside the 11.4 km tunnel\nsegment can be installed in each service area. The spatial resolution of the detection is of the order of a\nfew metres and the algorithms can trigger an alarm both in case of a temperature rise (fire) or a tempera-\nture drop (e.g., due to cryogenic leak) of a few degrees. However, the suitability of the technology in an\nenvironment with high levels of ionising radiation must first be proven.\nOxygen deficiency hazard\nThe two technical sites PH and PL, where the superconducting RF cavities are located, require particular\nattention due to the presence of cryogenic coolants. Commercial oxygen deficiency hazard (ODH) detec-\ntors that are installed today in the LHC complex can be used to monitor the oxygen level in the vicinity\nof cryogenic installations at the two RF points of the FCC. They are based on electrochemical cell sen-\nsors installed inside the tunnel, connected to detector electronics which can be housed up to 900 m away.\nSignals from several detectors are then fed to the control and monitoring equipment rack.\nAlternative detection techniques can be used (aspirating detector, fibre sensors etc.). In addition\nto oxygen level monitoring in precise locations, larger parts of the FCC could be monitored for a sudden\ntemperature drop using the fibre-based distributed temperature sensing.\nRadiation monitoring system\nA radiation monitoring system will be installed to measure prompt radiation levels at the interfaces to the\naccelerator tunnel, the experiment caverns, and the injector complex. These detectors are equipped with\nalarm functions that will signal any increased ambient dose equivalent rates. Radiation detectors will be\ninstalled at strategic locations in the tunnel and experiments to continuously measure residual ambient\ndose equivalent rates after beam stop.\nDetectors will be installed to monitor the activation levels in the air of the tunnel. The radioactivity\nin the water circuits is expected to be negligible and will be checked during regular sampling campaigns.\nAir and water releases, radioactivity in the environment, and levels of stray radiation on surface sites will\n453\n\nbe surveyed by an environmental monitoring system with real-time monitoring where required.\nEmergency Call Points\nManual call points\nManual call points (break-the-glass devices) are installed throughout the facility. They will be on each\nside of an alcove entry door, as well as on each side of the fire partition doors in the tunnel. In addition,\nCERN best practices require placing manual call points at regular intervals in the tunnels, grouped with\nother safety equipment: emergency lights, evacuation loudspeakers, etc., fixed on easily identifiable\nmodular panels.\nEmergency communication system\nIn the past, the CERN underground facilities have been equipped with emergency telephone sets (known\nas red-telephones). Based on analogue technology, the devices contain no active electronic components\nand could, therefore, be even placed permanently in areas possibly exposed to high levels of ionising\nradiation. Mobile phones come with more functions, for instance, precise localisation and video trans-\nmission, but they rely on a communication infrastructure that comprises electronic equipment, which is\nnot radiation-hard.\nAlthough the need for reliable, safe communication is clear throughout the complex, no deci-\nsion has been made as to which specific technology is the most appropriate. The installation of fixed\nred-telephones could be one of the solutions. Having a leaky feeder cable with a fire-resistant jacket\nand circuit integrity properties (Pca90-PH90, [452]), and fed by a secure power network, would allow\nemergency communication with mobile telephony services throughout the subsurface infrastructure. To-\nday, this seems to be the most viable option. Such an approach could benefit from the developments\nrequired to provide secure data communication means to control autonomous vehicles as well as emer-\ngency surveillance robots. Moreover, this might also respond to the need for safe communication for\ninterventions. In this case, its performance and reliability must be compatible with the intervention time\n(see Section 9.4.1), and some adaptations would be necessary (double loop, additional fire rating, etc.).\nEvacuation alarms\nWhenever a hazardous situation (fire, oxygen deficiency, possible problem with access safety system) is\ndetected, the concerned zones of FCC are evacuated. To this end, the FCC tunnel will be equipped with\nloudspeakers placed every \u223c25 m connected to amplifier racks of a voice alarm system located in the\nalcoves.\nThe choice of voice alarm system is dictated by the added possibilities for emergency response\nteams to play pre-recorded messages or directly address the personnel underground with ad hoc in-\nstructions. An alternative solution, based on using more sparsely installed sirens, exists. Although less\nversatile, allowing only an evacuation siren with no accompanying voice messages, this solution is more\nsuited to very large (e.g., experiment caverns) or noisy (e.g., compressor room) locations.\nThe system control and monitoring equipment racks, installed at regular intervals, acquire evacu-\nation requests from the detection systems. The racks are connected by optical fibre and configured with\nappropriate evacuation matrices. Thus, in case of a hazardous event, evacuation is launched not only\nin the same location but also at other sites, as required by the evacuation matrices. This is possible as\nthe control racks communicate between themselves. The components of the evacuation system must be\ncompliant with the appropriate European standard EN 54 [451].\nDue to the circular shape of the underground structure, most locations can be evacuated in two\ndirections. However, in emergency situations, evacuating personnel can often use only one of the two\npossible escape routes. Despite the fact that most personnel movements (including evacuation) will be\n454\n\nmade using autonomous vehicles, all alcoves and fire compartment doors will be equipped with adaptable\ndirection signage. It must clearly indicate the direction in which to go to escape a detected danger.\nEmergency lighting and route guidance\nAll of the underground facility is equipped with emergency lighting as defined in the corresponding\nCERN safety guideline [453]. This includes:\n\u2013 A general ambient safety lighting, ensuring at least 5 lux (lm/m2) at floor level,\n\u2013 Marked evacuation routes (exit ways, doors, direction) with illuminated and luminescent signs.\nThis wayfinding (guidance) system will also be dynamic and inform occupants if an evacuation\nway is no longer safe (for example, smoke present in adjacent compartment).\nAll these systems need to be connected to the secure power network (see Section 9.4.1) or have an\nautonomy of at least 120 minutes to guarantee the life safety of occupants. They also need to be designed\nto ensure an overall system fire-rated integrity of at least 90 minutes (E90).\nMoreover, robotic systems can be deployed to guide the occupants in their evacuation, by pro-\nviding an indication of the safe direction to evacuate (projecting arrows on the floor of the transport\nzone) [454] and providing audio assistance to the emergency response team. Evacuation signs will also\nbe visible on the compartment doors.\n9.4.2\nOccupational hazards during nominal conditions\nWhile the facility is in operation, the occupants are exposed to the hazards that are present under nominal\nconditions. The hazards and safety requirements during nominal operation are mentioned here, whereas\nthe accident scenarios are discussed in Section 9.4.3.\nIonising radiation\nFor the mitigation of risks associated with ionising radiation, the standard prescriptive methods of the\nexisting CERN radiation protection rules and procedures are used. However, optimisation of the design\nof civil engineering infrastructure is more assimilated in a performance-based approach, where the pro-\nposed design has to be evaluated to see whether it will comply with the radiation protection objectives.\nRadiological hazards\nHigh-energy particle beams interact with each other in the experiments or with beamline components in\nthe accelerator, creating secondary particles that may pose radiological risks during operation (prompt\nradiation). This interaction also produces residual radioactivity that will present a potential hazard during\nmaintenance (residual radiation). Workers may be exposed to ionising radiation from activated equip-\nment, gases, or fluids by external exposure. The radioactive contamination hazards and the resulting\ninternal exposure from incorporation are expected to be negligible.\nThe FCC-ee will operate in four phases, with beam energies rising from 45 GeV in Z mode to\n182.5 GeV in t\u00aft mode, and beam currents dropping from 1.27 A to 4.9 mA. Thus, radiological risks vary\nwith the phase and the most conservative scenarios have been used for their assessments.\nAt the stage of the feasibility study, detailed integration, such as the routing of ventilation ducts\nand water pipes, is not yet done. Infrastructure integration will be optimised in later design phases. The\nsame is valid for the material moved from the accelerator to storage areas or workshops for maintenance\nand repair or for elimination. As in other industrial facilities, radioactive sources and X-ray generators\nmay be used for various purposes. These activities will follow standard prescriptive methods, as already\ncommonly applied at CERN or in industry.\n455\n\nAll results of the radiation transport simulations presented here were obtained using the FLUKA\ncode [331] with FLAIR [455].\nRadiation area classification\nDose constraints for the design of the infrastructure as well as active radiation monitoring will ensure\nthat radiation doses received by personnel working on site remain below the regulatory limits [456] under\nnominal and accident operating conditions.\nThe radiation area classification scheme [457] allows radiation risks to be managed and ensures\nthat optimisation processes, training, access control, and collective and personal protection means for\npersonnel intervening in the respective areas are adequate for the expected risks. A summary of the\nradiological area classification adopted at CERN is provided in Table 9.3 .\nTable 9.3: Synopsis of the work area classification at CERN [457].\nClassification\nAmbient dose equivalent rate limit\nAnnual effective dose limit\npermanent workplaces\nlow-occupancy areas\nNon-designated\n0.5 \u00b5Sv/h\n2.5 \u00b5Sv/h\n1 mSv\nSupervised\n3 \u00b5Sv/h\n15 \u00b5Sv/h\n6 mSv\nSimple controlled\n10 \u00b5Sv/h\n50 \u00b5Sv/h\n20 mSv\nLimited stay\nnot permitted\n2 mSv/h\n20 mSv\nHigh radiation\nnot permitted\n100 mSv/h\n20 mSv\nProhibited\nnot permitted\n-\n20 mSv\nProtection objectives\nThe risks resulting from ionising radiation are analysed very early in the design phase among others, with\nthe objective of developing mitigation approaches that ensure that accessibility requirements are met for\neach area.\nAreas with unacceptably high radiation levels from prompt radiation (high radiation and prohibited\nradiation areas) are inaccessible during operation, and essential risk control measures are employed as\ndescribed above. The access control system prevents entry to such hazardous areas, whereas an interlock\nsystem halts beam operation if unauthorised access occurs. An emergency stop system ensures the rapid\nand controlled termination of beam operation if necessary.\nWhere feasible, areas accessible during beam operation will generally be designed to allow a clas-\nsification as a non-designated area, avoiding any radiation protection restrictions. The planned civil engi-\nneering infrastructure complies with the radiation protection requirements for the operation of FCC-ee.\nHowever, the present infrastructure may not necessarily be ready in all parts for FCC-hh, especially\nwhere compliance can only be reached by significant costs at the current stage or where infrastructure\nis only required for FCC-hh. The required infrastructure modifications or additions will need to be im-\nplemented after the operation of FCC-ee. One example is the dedicated beam dump caverns that will be\nonly needed for FCC-hh and would not be used by the FCC-ee.\nResidual dose rates in the accelerator tunnel have been estimated for several areas, and these will\nallow a first evaluation of potential constraints on the operation of the facility and maintainability, as well\nas the related optimisation of the design of beamline components.\nInjector complex\nThe injector complex injects electron and positron beams alternately into the booster. Radiological\nhazards during nominal operation come mainly from prompt radiation from the positron source, beam\n456\n\ndumps, and loss locations in the linear accelerators and the damping ring. It is necessary to determine the\nminimum soil thickness needed to contain the prompt radiation, aiming to keep the klystron hall above\nthe accelerators as a non-designated area.\nAn initial set of beam parameters and assumed loss terms has been used to estimate the shielding\nthickness required above the injector complex. Figure 9.6 shows the ambient dose equivalent rates at 90\u00b0\nthrough shielding from a beam loss on a thin long target, indicating the thickness required to achieve the\ndose rate objectives. Approximately 6 m of soil cover is deemed adequate for the specified loss term.\nFig. 9.6: Ambient dose equivalent rate through rock (from 3.25 m distance onwards), resulting from a\ncontinuous beam loss in the FCC-ee injector complex based on initial assumptions for potential beam\nlosses.\nA conventional fixed target, where 2.86 GeV electrons interact in a tungsten rod, is used to produce\nthe positrons. The target station will have specific shielding. Activation of the target and downstream\naccelerator elements also generates sources of radiation which have an impact on workers during main-\ntenance work. These residual radiation levels are reduced by local shielding and optimisation of the\nelements concerned during the technical design phase.\nThe highest levels of activation in the injector complex will occur at the positron production target,\nand initial studies show that these levels will impose strict restrictions on access and maintenance, with\nextended cool-down times. Remote handling and shielding are indicated, aligned with intervention and\nmaintenance protocols.\nUnderground infrastructure\nThe collider will be housed in the tunnel with a limited number of access points and connection tunnels,\nminimising the interfaces between accessible and inaccessible areas that need to be studied and adapted\nin the design to meet radiation protection objectives. The lateral shielding of 10 m rock effectively\ncontains stray radiation during nominal operation and accident events for both FCC-ee and FCC-hh.\nMore penetrating radiation from loss points in the forward direction is effectively shielded by hundreds\nof metres of rock, ensuring protection for other potential underground infrastructures.\nThe general design assumptions taken for the underground infrastructure are as follows.\n457\n\n\u2013 The accelerator tunnel and experiment caverns are not accessible during beam operation.\n\u2013 The service caverns and klystron galleries must be accessible during beam operation for both\nFCC-ee and FCC-hh. The minimum shielding between the accelerator tunnel and accessible areas\nis about 10 m, as required by FCC-hh and also driven by stability considerations from civil engi-\nneering. Connection tunnels should be long (\u223chundreds of metres) or, if short (\u223ctens of metres),\ninclude chicanes and/or shielded doors. Chicanes are preferred over shielded doors which have a\nrisk of failure and because chicanes have fewer maintenance issues.\n\u2013 Service caverns should be non-designated areas (see Table 9.3) for unrestricted access.\n\u2013 Klystron galleries will be classified as non-designated areas or supervised radiation areas.\n\u2013 Access to the arcs must be possible without requiring passage through high-radiation areas.\n\u2013 Alcoves, i.e., technical areas attached to the accelerator tunnel, must be shielded to prevent activa-\ntion of the installed equipment and are inaccessible during beam operation.\n\u2013 Areas with high radiation and activation levels must be separated from low activation areas in\nterms of ventilation and cooling systems (compartments) and personnel access (bypass routes,\nlocal shielding).\n\u2013 The FCC-ee booster will be located on top of the collider ring. As it will operate at about only\n10% of the collider current and at varying energies, the studies conducted so far were limited to\nthe collider itself.\nThe items identified in the collider that will likely show higher activation levels and hence higher residual\ndose rates are:\n\u2013 The beamstrahlung dumps next to the interaction points; two dumps on each side of each experi-\nment in points PA, PD, PG, and PJ;\n\u2013 collimators and absorbers installed in a dedicated insertion region in point PF and next to the\ninteraction points;\n\u2013 the matching regions next to the interaction points impacted by scattered radiation from the beam\ncollisions in the experiments;\n\u2013 the main beam dumps in point PB;\n\u2013 the inner detectors in the interaction points;\n\u2013 the EM separators installed at point PH.\nThe following sections highlight some results of the radiation protection studies conducted during\nthe feasibility study phase.\nArc sections\nThe arc sections make up the largest part of the accelerator. Activation and average residual dose\nrate levels can have a potential impact on personnel, depending on the time it takes in the tunnel to reach\na particular workplace.\nThe main relevant source terms are beam interactions with the residual gas molecules in the vac-\nuum chamber and the synchrotron radiation. The latter contributes only significantly to activation in the\nt\u00aft mode, where synchrotron radiation is energetic enough to produce relevant photoneutron fluence and,\nthus, induced activity.\nFigure 9.7 illustrates the expected residual dose rates after t\u00aft operation. The dose rate levels\ninduced by the other modes are two to three orders of magnitude lower. In the t\u00aft mode, some waiting\ntime may be required before performing interventions in the tunnel to reduce the dose to personnel.\nHowever, the decay is relatively fast, and within a few days, it is down to very low levels acceptable\nfor long interventions. These figures show dose rates without any shielding installed around the photon\nabsorbers. It is now planned to install this shielding. It will have an important mitigating effect so that\ndose rates will be considerably lower in the t\u00aft phase.\n458\n\nThe ventilation system is designed to recycle air, limiting the release of short-lived radioisotopes\nduring operation. Inhalation and immersion doses were calculated for interventions immediately after\nthe beam stop without air renewal (worst case), with insignificant doses in all modes, except for t\u00aft, where\na few \u00b5Sv per hour of stay could be expected. However, flushing is always required for safety before\nentering the tunnel.\nIn conclusion, the FCC-ee arcs will exhibit some activation, but the low dose rates should not lead\nto significant doses to individuals passing or intervening in the arc sections.\n(a)\n(b)\nFig. 9.7: The graphs represent the distribution of the ambient dose equivalent rate (\u00b5Sv/h) in the arcs after the t\u00aft\noperation phase, averaged over the y-axis from -50 cm to +50 cm, approximately 1 m above the floor. (a): with\na decay time of 1 hour, (b): Average values after various decay times: 1 hour, 4 hours, 1 day, and 1 week. The\nirradiation profile considers all years of t\u00aft operation phase, taking into account shutdown periods.\nConnection tunnels between experiment and service caverns\nColliding beams at interaction points create secondary particles that spread throughout the exper-\niment cavern. Although the detector absorbs much of this radiation, some can reach areas such as the\nservice cavern, which must remain accessible during operation. It has been assessed whether access-\ning the service cavern is feasible during operation with measures such as shielding and chicanes in the\nconnection tunnels.\nThis study is for FCC-hh, as proton-proton collisions produce higher dose rates than the electron-\npositron collisions in FCC-ee. A layout compatible with FCC-hh will, therefore, be compliant with\nFCC-ee. This approach is justified because the caverns and connection tunnels will not change between\nthe two colliders.\nRadiation transport simulations were performed for the entire geometry, including the experiment\ncavern, the connection tunnels, and the service cavern. The assessment considered the most conservative\noperational FCC-hh scenario (\u2018ultimate\u2019), with a collision rate of 3.24 \u00d7 1010 p/s8.\nThe spatial distribution of the dose rate through the service tunnel and within the service gallery\nis shown in Fig. 9.8. The results demonstrate that the proposed design will meet the target ambient dose\nequivalent rate limit, i.e., <0.5 \u00b5Sv/h inside the service cavern, allowing access during operation with\npermanent occupancy (non-designated area classification).\nThe feasibility of designing and building the following mitigation measures was confirmed by\nintegration and civil engineering: (1) mobile shielded doors with a thickness of 1 m at the entrance of\nthe transport tunnel and (2) a two-legged chicane for the access tunnels for personnel. Additionally, the\n8Based on a peak luminosity of 30 \u00d7 1034 cm\u22122s\u22121\n459\n\ncurrent design includes a three-legged chicane (not included in the simulation studies shown here), for\nconnecting the main accelerator tunnel with the experiment service area, to minimise the dose rate con-\ntribution from the accelerator tunnel. The schematic layout proposed by civil engineering and integration\nincludes chicanes for direct access tunnels. This will ensure that the radiation protection objectives for\nthe service cavern are met.\nFig. 9.8: The plot shows the ambient dose equivalent rate averaged over 3 m in height at the FCC exper-\niment points from pp collisions along the transport tunnel between the service and experiment caverns.\nAt the tunnel-experiment cavern interface, a 1 m shielding wall and a two-legged chicane for personnel\npassage are implemented.\nBypass tunnels\nBypass tunnels allow access from the service cavern to the accelerator tunnel, bypassing the ex-\nperiment caverns. Bypass tunnels can be designed to allow access to areas with low activation levels\nwhile avoiding passing through areas of increased residual radiation risk. The bypass tunnels must re-\nduce prompt radiation streaming towards the service cavern down to acceptable levels, ideally without\nthe need for additional mobile shielding walls for easier access.\nTwo bypass tunnels are planned at each experiment point to connect the service cavern with the\naccelerator tunnel. FCC-ee and FCC-hh feature different radiation sources near the interaction regions,\nwith radiological hazards that must be considered when designing the layout of bypass tunnels and their\njunctions with the accelerator tunnel. The constraints must be assessed for both accelerators:\n\u2013 FCC-ee. Beamstrahlung, synchrotron radiation (SR), and radiative Bhabha (RBB) electrons in-\ncrease the residual radiation levels in the straight sections next to the interaction points. Resid-\nual dose rate levels in the personnel and transport passage are in the range between 0.1 and\n100 \u00b5Sv/h after decay times of 1 to 4 days, as determined in some preliminary simulation studies\n(see Fig. 9.9). The integration of SR and RBB shielding on the outgoing beamline, which is still\npending, will further help to reduce residual dose rates. The beamstrahlung dump must be shielded\nso that the impact on the personnel and transport passage is reduced to sufficiently low levels in\nthe passageway, located on the opposite side of the tunnel.\n\u2013 FCC-hh. Residual radiation levels are increased in the straight sections next to the IPs, from\ncollision debris in the IP. The ambient dose equivalent rate levels in the personnel and transport\n460\n\npassage range between 0.1 and 10 mSv/h after decay times of 1 day to 1 week (see Fig. 9.10).\nThe area has to be considered as a high radiation area. Given the enlarged tunnel cross section, it\nseems feasible to integrate additional shielding along the beam line, effectively reducing residual\ndose rates to acceptable levels in the personnel and transport passage. Alternatively, the bypass\ntunnels could be extended before the operation of the FCC-hh.\nFig. 9.9: The top and centre plots show residual dose rates averaged within the dashed lines in the straight\nsection geometry next to the FCC-ee IP (bottom plot, distance from the IP). These were computed for two\nradiation sources: (1) radiative Bhabha during Z pole and (2) synchrotron radiation during t\u00aft, assuming\none year of operation (185 days).\nBeam dump\nThe beam dumps will receive a rather small fraction of the accelerated particles, considering the\ntop-op operation mode and approximately only one dump per day, and will therefore become radioactive\nto a level that will likely not require a compartmentalisation of the area for separate ventilation. The\ndumps are shielded and placed in a section where the tunnel cross-section is increased. The passage for\ntransport and personnel in the straight section is sufficiently far from the dumps to achieve acceptable\ndose rate levels at the passage. Dedicated dump caverns and extraction beam lines will need to be added\n461\n\nFig. 9.10: Results showing residual dose rate at FCC-hh IP straight sections after an irradiation of 25 y,\nwith an average collision rate of 5.4\u00d7109 p/sec (10 y) + 3.2\u00d71010 p/sec (15y). Acceptable positions for\nthe connection of the bypass tunnel are at \u223c200 m and at \u223c450-500 m.\nfor FCC-hh.\nThe radiological study of the beam dumps examines the residual radiation levels next to the beam\ndumps and is based on a preliminary dump proposal that still lacks a detailed technical design. The study\nwas done for the Z pole scenario, which is considered to be the most conservative. Each beam dump is\ncomposed of a cylindrical graphite structure of a length of 600 cm. The structure consists of three layers\nof graphite with varying densities of 1.1 g/cm3 and 1.8 g/cm3. An additional layer consisting of a high-\ndensity absorber made of CuCrZr is integrated at the end of the structure. The dump is encapsulated with\na 1 cm thick layer of titanium alloy. The extraction line is equipped with three successive cylindrical\nspoilers made of graphite (with densities ranging from 1.7 to 1.8 g/cm3) and 3 cm thick. A first dump\nshielding was implemented, consisting of a first layer of iron (20 cm) and a second layer of concrete\n(40 cm). Although this is still a conceptual shielding design, it illustrates the expected effects of potential\nshielding.\nFLUKA Monte Carlo simulations were performed in order to assess the residual dose rate after\none year of operation (185 days), considering one beam dump per day, where all particles stored in the\ncollider are discharged. The number of particles dumped annually is 4.44 \u00d7 1017p/y (Z pole). The\nresults show that the residual dose rate reaches values around 45-50 \u00b5Sv/h, at a distance of 1-2 m from\nthe shielded dump, after 185 days of operation (one dump per day) and 1 hour of cool-down; after 1 day,\nit reduces to 15 \u00b5Sv/h. The dose rate values are relatively low, indicating that even a minimal shielding\naround the dumps effectively reduces residual radiation to almost acceptable levels.\nBeamstrahlung dump\nThe radiological impact of the beamstrahlung dump using liquid lead as an absorber was assessed.\nFLUKA Monte Carlo simulations were performed for the Z pole operation mode, as it generates the\nhighest beamstrahlung power among all operational modes. Initial simulations at t\u00aft mode indicate as\nwell considerable dose rates and more important activation due to the higher energetic beamstrahlung\nspectrum.\nThe model considered an inclined beam dump with a layer of liquid lead. An initial shielding\n462\n\ndesign was tested to mitigate the risks associated with residual radiation. The shielding is 1 m thick in\nall directions and extends 5 m upstream around the vacuum chamber to mitigate backscattering.\nFigure 9.11 shows the average dose rate values in the transverse plane across the tunnel, at the\nlevel of the beamstrahlung dump, considering an irradiation profile of 1 year at Z pole operation (185\ndays). Residual dose rate values, after 1 hour of cool-down time, may reach 7 Sv/h inside the shielding.\nApproximately 3 m away from the shielding, the dose rates decrease to below 100 \u00b5Sv/h.\nAt these very high dose rates, optimised shielding is mandatory to contain the residual dose rate\nat an acceptable level outside the dump. The current shielding must be enlarged and optimised to reduce\nthe dose rate to 1\u221210 \u00b5Sv/h in the passage area after 4 hours of cool-down time. Appropriate shielding\nwill certainly be more massive, but can be integrated. The dose rate from activated lead in the pumping\ncircuit and reservoir will be further assessed and included inside a shielded casing. Waiting times before\nmanual interventions on the dump will be considerable (days/weeks), and remote operation will be used\nto minimise doses to personnel while handling components and performing maintenance. The activation\nof the lead absorber will require particular attention and a dedicated study during the technical design\nphase to assess the radiological risks and implications for handling and elimination.\nFig. 9.11: Residual ambient dose equivalent rate profile at the FCC-ee beamstrahlung dump, after 185\ndays of Z pole operation, for different cool-down times. The profiles are averaged in the volume enclosed\nby the two dashed lines, which extends 1 m on Y-axis and Z-axis.\nCollimation\nFLUKA Monte Carlo simulations were conducted to evaluate residual radiation in the collimation\nsection (PF) and the potential impact on the design, integration, civil engineering and cooling/ventilation.\nThe model encompasses the positron betatron collimation section, including 12 quadrupole magnets, 6\ncollimators (both primary / secondary and horizontal / vertical) and 2 shower absorbers. A standard\ntunnel cross section is used without detailed integration of additional infrastructure, such as ducts, cables,\nand piping.\nThe Z pole is considered the operational mode with the highest loss rate of 8.5\u00d71011 p/s, based on\na beam lifetime of 30 minutes.\nFigure 9.12 presents the residual dose rate profiles along the straight section of the positron be-\n463\n\ntatron collimation after 185 days at Z pole operation, evaluated for different cool-down times (ranging\nfrom 1 hour to 1 year). The results indicate the highest peak occurring in front of the secondary horizon-\ntal collimator. The high dose rates span several tens to hundreds of metres, with maximum residual dose\nrate values reaching 1 mSv/h after one week of cool-down.\nBased on the parameters provided, the collimation section exhibits very high dose rates, mak-\ning immediate hands-on maintenance in this part of the tunnel impossible. Evaluating and improving\ncollimator shielding could help reduce activation levels in the surrounding infrastructure. With further\noptimisation of design parameters, the implementation of appropriate bypass tunnels, and a hybrid main-\ntenance approach (combining personnel and robotics), it appears feasible to allow access after one day\nof cool-down. This time frame is also essential to ensure the decay of short-lived radioactive isotopes in\nthe air, enabling safe ventilation and the controlled release of air into the environment through flushing.\nFig. 9.12: The plot displays the residual dose rate profiles along the positron betatron collimation straight\nsection after 185 days of Z pole operation, evaluated for different cool-down times (ranging from 1\nhour to 1 year). The labels correspond to the components on the beamline: PV (primary vertical),\nPH (primary horizontal), showabs1 (first shower absorber), showabs2 (second shower absorber), SV\n(secondary vertical), and SH (secondary horizontal).\nSurface Sites\nRadiological hazards at surface sites during nominal beam operation are potentially induced by prompt\nradiation that can propagate from the experiment cavern up through the shaft.\nThe same parameters and radiation sources used to calculate the prompt radiation in the connec-\ntion tunnels, described above, are applied to calculate the propagation of the prompt radiation from the\nexperiment cavern to the surface along the shaft. The study considers FCC-hh, where proton-proton\ncollisions (\u2018ultimate\u2019 scenario, with a collision rate of 3.24 \u00d7 1010 p/s) produce a dose rate higher than\nthat of electron-positron collisions in FCC-ee.\n464\n\nThe results are shown in Fig. 9.13. The colour map on the right displays the values of the ambient\ndose equivalent rate along the shaft using a colour gradient (in \u00b5Sv/h). The left graph depicts the profile\nof the ambient dose equivalent rate, with values averaged over the volume defined by the two dashed\nlines in the colour map on the right. The two horizontal red dashed lines represent the minimum and\nmaximum depths of the shafts for the four experimental points. This allows visualisation of the range of\nambient dose equivalent rates at the different surface sites.\nThe plot shows surface dose rates ranging from 10 to 70 \u00b5Sv/h. Shielding installed at the machine-\ndetector interface, and a 1-metre thick concrete shielding at the top of the shaft are adequate mitigation\nmeasures.\nFig. 9.13: Ambient dose equivalent rate through the shaft resulting from pp collisions in the experiment\ncavern.\nOther radiological hazards at the surface site may arise from the handling of activated material\nthat has been removed from the tunnel. Standard prescriptive methods are used to limit the radiological\nrisk to personnel by having dedicated areas to store and work on radioactive items. Buffer zones are\nestablished at the border between areas where activation can occur and non-activation areas to control\nthe flow of material and to guarantee the correct classification of items removed from the accelerator\nareas.\nThe release of radioactive air and water from the accelerator tunnel and the experiment cavern\nposes a negligible risk. This is mitigated by recycling the air during operation and having dedicated\nwater handling installations to avoid any potential contamination or uncontrolled releases.\nThe use of radioactive sources and X-ray-generating devices in surface facilities may occasionally\noccur during the construction and operation phases. These common practices are covered by standard\nprescriptive methods and rigorous regulations that have been widely applied at CERN and in industry.\nNon-ionising radiation (NIR)\nRisk of non-ionising radiation includes exposure to static magnetic fields, time-varying electromagnetic\nfields (e.g., RF), lasers and non-coherent light sources (e.g., UV & Infrared, light, LED). These risks\nare currently addressed by standard practices, namely by European Directives [458,459]. It is possible,\nat this stage, to conclude that the design of NIR-generating accelerator and detector components will\nrespect the exposure limit values of the directives.\nFor static magnetic fields (e.g., from permanent or electro-magnets), the exposure limit values\n(ELV) and action levels (AL) are given by CERN\u2019s General Safety Instruction GSI-NIR-1 [460].\n465\n\nStray magnetic field from experiment detectors\nA study was performed simulating typical fringe fields from the experiment cavern housing an FCC-hh\ndetector representing a worst-case scenario and concluded that the residual magnetic field at the surface\nof experiment points is well below current limits. At a distance of 200 m above the detector, the stray\nfield is of the order of 0.1 mT, whereas the limit for wearers of active medical devices is 0.5 mT [461].\nStray magnetic field from the collider\nA study was performed simulating the extent of stray fields for evaluation against the ELVs and ALs . All\nstray field envelopes at the ELVs stay within 1 m from the magnet\u2019s centre, except for the quadrupole,\nwhich emits a stray field envelope at 0.5 mT to most of the cross-section of the tunnel (Fig. 9.14). This\nis due to the fact that the quadrupole has substantial field strength (\u22480.45 T at the aperture) and an\nopen iron yoke. In comparison, the dipole yoke is also open but with low field in the aperture (60 mT),\nwhile the sextupole also has a relatively high field (0.5 T) but confined within a closed iron yoke. Since\nquadrupoles will be spread throughout the arc, people with active implantable medical devices (AIMD)\nwould not be able to access the tunnel, without a valid medical certificate [460]. Even when the magnets\nare not powered, there is still a residual risk of remanent fields stemming from magnetised metal in the\nsurroundings. Occasional access in specific areas may be granted, based on a risk assessment and fenced\noff from any individual 0.5 mT sources.\nAccess is possible for the public and workers without any particular risk9 (B < 40 mT). Any work\nnear the dipoles and quadrupoles when the magnetic source is on would require a specific workplace risk\nassessment and training.\nFig. 9.14: Simulation of stray field envelope at 0.5 mT for the FCC-ee collider arc. a) Dipole: (X1, Y1)\n= (1070, 980) mm; b) Quadrupole: (X2, Y2) = (2690, 2720) mm\n.\nLasers for beam polarisation\nFixed laser installations are planned in some alcoves for beam polarisation and energy calibration. The\nlaser installation will be installed within a dedicated designated laser area (DLA), with interlocks to\ncut off the source in case of unauthorised access. The classification of the laser systems, as well as\n9Such as wearers of passive metal implants and pregnant workers.\n466\n\nthe engineering control measures, will follow the applicable International Standards, i.e., IEC 60825\nseries [462].\nOptical fibre network\nThe infrastructure will deploy an optical fibre network (OFN) for internal communication and data trans-\nmission. Depending on the maximum output power of the transmitter (dB m), the OFN will be classified\nwithin a given hazard level in accordance with IEC 60825 [462]. For any given hazard level, a set of\nengineering control measures are required.\nElectrical safety\nThe electrical infrastructure will cover everything from low voltages (e.g., lighting) to high voltages\n(e.g., power transmission). Despite this wide range, electrical safety may still be covered by standard\npractices. Most of the electrical equipment will be housed in surface buildings, in the service caverns, and\nthe alcoves. The FCC accelerator and experiment detectors are expected to be designed according to the\nappropriate international standards (IEC) where they obey the safety by design principle, i.e., ensuring\na proper degree of inherent protection (e.g., IPx rating according to the IEC 60529 standard [463])\npreventing live parts being accessible. Any non-standard equipment will be subject to a rigorous risk\nassessment design process to ensure conformity with the applicable legislation. The electrical network\nwill be designed according to national and international standards for all voltage levels (low, medium,\nand high). A secure power network is foreseen as mentioned in Section 9.4.1. The location of cable trays\nin the tunnel arc and the alcoves is chosen to minimise interference with the occupants.\nOccupants and emergency teams will be authorised and required to activate an emergency stop in\ncase of an unsafe situation or incident, cutting off the electrical power to the general (non-safety-related)\nservices. In the LHC, this is achieved by a spatial distribution of general emergency stop (AUG) buttons\nalong the tunnels and caverns. The exact technical solution for the FCC will be studied in the next phases,\nduring the detailed design of the electrical network.\nFor works or activities in which the protection elements are temporally removed, there are a set of\ntechnical and administrative procedures to ensure the safe execution of such activities. For example, lock-\nout, tag-out and electrical work permits to ensure safety during interventions on electrical equipment. A\nsafety-by-design approach is enforced, considerably reducing the technical and administrative burden of\nspecific safety prescriptions.\nChemical safety\nOnly a few chemicals are required for the operation of the FCC infrastructure. Most of them will be used\nin the closed circuits of the cooling water network:\n\u2013 Biocides - chlorine dioxide, produced from hydrochloric acid and sodium chloride.\n\u2013 Corrosion inhibitors - mainly sulphuric acid.\nSignificant quantities of synthetic lubricants (e.g., BREOX) are expected on the surface sites for\nthe cryogenic compressors. Cooling refrigerants (coolants) are also needed for the fan coils in the tunnels\nand chillers on the surface. Some traces of oil are expected underground, but these will be in minimal\nquantities (e.g., vacuum pumps, motors, and other machinery).\nAt this stage, only standard chemicals are intended to be used, hence standard practices and reg-\nulations are applicable when handling these chemicals. For each chemical product, the supplier must\ndeliver a safety data sheet (SDS) or an extended safety data sheet (eSDS) and a technical data sheet\n(TDS) with information on product usage, on hazards during use and during emergency procedures.\n467\n\nMechanical safety\nThe feasibility study focused on the technical infrastructure at large and its possible impact on the civil\nengineering layout. The mechanical design of the beamlines and equipment inside the infrastructure\nwill be detailed in the next phases of the project. The necessary safety studies and assessments will be\nperformed in parallel.\nThe use of robotics (both overhead and floor-driven) will be widely present in the FCC infrastruc-\nture. The cohabitation of robots and personnel poses a safety hazard that will be dealt with during the\ndesign phase, where the robotic systems are designed and manufactured according to the EU Regulation\n2023/1230/EU on machinery [464] and associated harmonised standards.\nIndoor air quality\nThe indoor air quality in the underground infrastructure is guaranteed by the ventilation system described\nin Section 9.4.1. During access mode, the air renewal for hygienic purposes is guaranteed by the air\nexchange in the concerned sector. The values of the flow rates and air velocities in the tunnel are shown\nin Table 9.4. In the technical points (PB and PF), the supply flow rate for the service caverns and\nconnection tunnels is 20 000 m3 h\u22121. For the experiment points (PA, PD, PG and PJ), the supply flow\nrate for the service caverns and connection tunnels is also 20 000 m3 h\u22121, whereas the experiment caverns\nare supplied with 50 000 to 70 000 m3 h\u22121. The RF points (L and H), are supplied with 20 000 m3 h\u22121\nin the service areas (cavern and connections) and 30 000 m3 h\u22121 in the RF sector in the tunnel [439].\nThe ventilation of the underground infrastructure is a pre-condition for access. Hence the correct\nfunctioning of the ventilation system must be ensured before granting access to personnel.\nTable 9.4: Metrics of the ventilation system in the accelerator tunnel during access mode [439].\nScheme\nFlow rate\nVelocity\nACHa\n[m3 h\u22121]\n[m s\u22121]\n[h\u22121]\nSemi-transverse\n27 000 (per half arc)\n0.25\n0.3\n(54 000 per sector)\nfrom 0 (midpoint) to 0.5\nin a sector\nLongitudinal\n54 000 per sector\n1\n0.3\na Air changes per hour\nNoise\nAs far as reasonably possible, the owners of noise-generating equipment installed both in the under-\nground areas or surface sites must apply technical solutions to achieve a daily exposure level below\n80 dB(A) [465]. These limits are considered state-of-the-art and would avoid the mandatory use of per-\nsonal protective equipment (e.g., earplugs). In the case of specific equipment emitting higher sound\nlevels (e.g., cryogenic compressor building at the surface), specific engineering and personal protective\nmeasures must be put in place.\nWorkplace ergonomics\nDespite the fact that there are no permanent workplaces in the underground infrastructure, occupants may\nbe requested to spend considerable amounts of time performing repetitive tasks therein. The integration\nof the tunnel arc, as well as the experiment and services caverns, must take into account the requirements\nto ensure proper workplace ergonomics.\nIn the tunnel arc, the passage from the transport area towards the opposite side of the accelerator(s),\ni.e., the external side, passes underneath the beamline in between two beam elements (e.g., dipoles,\n468\n\ncorrector magnets, etc.). Such a passage must take into account the ergonomics of occupants crossing\nfrom one side to the other several times a day. Standard practices as used in industrial installations are\navailable in EN 547 [466] to cover this occupational hazard. If passage underneath the beamline remains\nthe baseline approach, the minimum vertical clearance from the floor to the vertical obstacle (i.e., the\nbeam pipe) is 1123 mm 10.\n9.4.3\nOccupational hazards during accident scenarios\nDuring the feasibility study phase, only some selected accident scenarios were analysed, mainly those\ndeemed to have an impact on the layout and civil engineering structure of the underground infrastructure.\nAdditional accident scenarios will be assessed during the next phases of the study.\nIonising radiation\nAccident scenarios that may be relevant in terms of radiological protection will not produce different\nhazards from those described for nominal operation, i.e., external exposure from prompt or residual ra-\ndiation or internal exposure from the incorporation of radioactive contamination. The relevant scenarios\nconsidered are the following.\n\u2013 Beam losses: refers to the inadvertent deviation or depletion of particle beams from their intended\ntrajectory within the accelerator, leading to secondary radiation from interactions with accelerator\ncomponents. A machine protection system must ensure that such events are detected and the beam\nwill be directed either to the beam dumps or absorbed by the collimation system or protection\ndevices.\n\u2013 Fire: fire can release radioactivity from combustible activated materials, with smoke that carries\nradioactive isotopes. As it spreads and settles, contamination may occur. The radioactivity content\nin combustible materials is low and will not lead to a relevant exposure of the intervening person-\nnel. The radiological risk to workers or emergency responders is negligible, given the greater risks\nthat such emergency situations present, such as oxygen deficiency, smoke toxicity, and fire.\n\u2013 Leakages: leaks from water circuits can release large amounts of water that may contain radioac-\ntive isotopes. The radioactive concentration of the water circuits is low and will not lead to any\nrelevant exposure scenarios.\nThe main accident scenario considered is an accidental beam loss, where the civil engineering\ninfrastructure is critical to contain prompt radiation and protect workers in adjacent areas. Although\nunlikely and mitigated by the machine protection system, such scenarios are considered in the design.\nBeam loss scenarios are assessed at critical locations, that are, the injector complex, bypass tunnels, and\nRF klystron galleries. The dose objective of 1 mSv per incident11 is respected in the following loss cases\nstudied.\nInjector complex\nDose equivalents from secondary radiation during full beam loss scenarios of one-hour duration remain\nlargely inferior to those of the continuous loss scenario with a limited loss rate, as described above.\nThe doses behind 6 m of soil will be less than 100 \u00b5Sv as shown in Fig. 9.15. Therefore, the\nconstraining scenario is determined by a sustained limited beam loss rate.\n10Based on the tallest population in CERN\u2019s members states, with a wrist to shoulder blade distance of 823 mm (95th\npercentile) and an additional 300 mm allowance covering the helmet, and head movement clearances.\n11Design target values for a non-designated area. It refers to the maximum effective dose per event with a probability <0.01\nper year.\n469\n\nFig. 9.15: Ambient dose equivalent through the shielding at the FCC-ee injector complex, resulting from\na 1-hour beam loss scenario.\nKlystron gallery\nDuring the operation of the collider and booster, the klystron galleries remain accessible. Given that\nradiation can propagate through waveguide ducts and emergency exit staircases, prompt radiation prop-\nagation was assessed in the event of an accident scenario, i.e., beam loss.\nIn the absence of well-defined beam loss scenarios, the study considers the most conservative case,\nwhich is the complete beam loss, where all the particles stored in the ring (both electrons and positrons)\nimpinge on a single cryomodule located below the waveguide duct. Although this scenario is highly\nimprobable, it can serve as an upper limit for the analysis of a catastrophic event. Radiation transport\nsimulations were performed to determine the ambient dose equivalent in the klystron gallery.\nThe beam loss scenario is analysed for the Z mode (beam energy 45 GeV) as it has the high-\nest beam intensity of all operational modes, which is not compensated for by the higher energy at t\u00aft\nmode. The resulting dose was normalised using the total number of particles stored in the ring, that is,\n15 800 bunches of 1.51 \u00d7 1011 particles per bunch, for 2 beams giving 4.8 \u00d71015 particles in total.\nThe results, shown in Fig. 9.16 and Fig. 9.17, include two types of plots: a 2D colour map illus-\ntrating the dose distribution within a specific tunnel subcell, highlighting the transverse cut used in the\nsimulation model, and a 1D profile averaging the values from the colour map along the waveguide duct\nprofile.\nThe results show that, during a full beam loss scenario in Z mode, the dose in the klystron gallery\nis of the order of 10 \u00b5Sv. This value is well below the annual dose limit of 1 mSv for a non-designated\narea, as indicated in Table 9.3.\nThe access requirement to the klystron gallery during FCC-hh operation still needs to be decided.\nIf the gallery remains accessible, the radiological conditions must be compatible with the radiation source\npresented by the FCC-hh.\n470\n\nFig. 9.16: The ambient dose equivalent is calculated for a catastrophic accident scenario, considering that\nall particles stored in the FCC-ee collider are lost against an RF cryomodule in a single event. The colour\nmap illustrates that the estimated ambient dose equivalent inside the klystron gallery is approximately\n10 \u00b5Sv.\n(a)\n(b)\nFig. 9.17: The plot presents the dose projected along the duct during a complete beam loss scenario at\nthe FCC-ee RF section. Prior to the second leg (at x = 10 m), the ambient dose equivalent reaches 2 mSv.\nThen, the values decrease down to 1 \u00b5Sv, due to the presence of the chicane. At the far end, the dose\nincreases again as a result of the contribution of radiation coming from the staircase.\nBypass tunnels\nThe S-shaped bypass tunnels at the experiment points, approximately 100 m in length, were evaluated\nfor their compatibility to ensure low doses in the service cavern during catastrophic beam losses in the\naccelerator tunnel. In the absence of defined beam loss scenarios, the study assumes the most conserva-\ntive case: a full beam loss of all stored particles of both beams impinging on an accelerator component in\nfront of the junction with the bypass tunnels. Figure 9.18 shows the results of the radiation transport sim-\n471\n\nulations, where the service cavern is connected to the bottom left, and the accelerator tunnel is running\nat the top of the plot. Ambient dose equivalents remain below 1 \u00b5Sv for FCC-ee in Z mode and at about\n10 \u00b5Sv for FCC-hh for a catastrophic full beam loss in the collider. The results demonstrate compliance\nwith the design objectives.\n(a)\n(b)\nFig. 9.18: These plots show the stray radiation scattering along a bypass tunnel from a full beam loss of\nboth beams in FCC-ee, Z-mode (beam energy 45 GeV) (a) and FCC-hh (b).\nFire and smoke\nFire and smoke propagation pose a significant risk to the FCC infrastructure, particularly in underground\nareas. The likelihood of a fire can vary based on factors such as location, activity, layout, fire load,\nand occupancy levels. However, fires in confined spaces are especially dangerous due to the accelerated\ngrowth caused by thermal radiation feedback and the rapid spread of smoke.\nAs an outcome of the initial hazard registry analysis, the following list describes possible ignition\nsources or fire-specific hazards across FCC areas:\n1. High and low voltage installation, including cables and power wet/dry transformers (overheat,\nshort-circuit, arc) (For LHC, the frequency of an electrical fire was estimated as \u22484 \u00d7 10\u22123/year\n[467])\n2. Transport vehicles (accident, battery malfunction)\n3. Hot works (welding, grinding)\n4. Cryogenic systems (oxygen enrichment of air, condensed air dripping on combustible materials)\n5. Pumps and mechanical devices (overheat)\n6. Flammable and explosive atmospheres (in surface building only)\n7. Glowing cigarette\n8. Arsonist (considered as unlikely for underground areas due to access control and active surveil-\nlance)\nThese hazards are mitigated by means of a fire safety concept that describes the coordinated set of\ncivil-engineering, technical and organisational measures to reduce fire risk to the level that meets safety\nobjectives (see Section 9.2.2).\n472\n\nThe fire safety concept follows two strategies:\n\u2013 prescriptive approaches based on Host States laws: this deem-to-satisfy solution ensures that at\nleast life safety criteria are met, and safety measures are commensurate with standard industrial\nfire risks. This will be the default strategy for surface buildings.\n\u2013 performance-based design: as explained in Section 9.3.3, whenever the technical prescriptions\ncannot be implemented, are not appropriate or simply out of scope, the safety objectives need to\nbe ensured by guaranteeing the safety performance of the facility in case of accidental scenarios.\nThe following subsections summarise the safety studies to characterise fire hazards in FCC and\ndescribe the prevention and mitigation measures included in the main areas of the infrastructure. Fire\nresistance, reaction to fire and organisational measures to ensure fire safety are discussed at the end of\nthe chapter. The proposed fire safety concept will be refined in the subsequent phases of the study and\nupdated to reflect any future changes to the baseline used in the feasibility study.\nTunnel Arcs\nThe accelerator tunnel represents the largest volume and floor area of the entire facility. Thus, specific\nattention has been devoted to studying how a fire will impact the evacuation and the life safety of the\noccupants. The entire analysis is available in a technical report [468], with a summary of the main\nassumptions and outcomes below.\nTo verify that the proposed compartmentalisation and smoke extraction strategies ensure life safety\nobjectives, computational fluid dynamics (CFD) simulations using the NIST\u2019s Fire Dynamics Simulator\n(FDS) (v6.8.0) [469] have been performed for a complete 400 m long compartment.\nThe tenability limits below (based on ISO 13571 [470]) define the performance criteria used\nthroughout the study:\n\u2013 Visibility of the evacuation path (at 2 m height) < 10 m\n\u2013 Fractional Effective Dose (FED) > 0.3\n\u2013 Temperature > 60 \u25e6C\nAdditional criteria are analysed for further comparison among trial designs such as: FED> 0.1,\nhot smoke layer temperature of 200 \u25e6C, smoke layer spread velocity and heat flux > 2.5 kW m\u22122.\nThe time to reach these untenable conditions constitutes the \u2018Available Safe Egress Time\u2019 (ASET).\nThe \u2018Required Safe Egress Time\u2019 (RSET) is defined as the time required for the occupants to leave the\ncompartment. The comparison of both times provides the safety margin used for the analysis of life\nsafety criteria, as illustrated in Fig. 9.19. The ASET > RSET condition is a safety requirement for all\nscenarios studied.\nFig. 9.19: Illustration of the different time stamps and input parameters to evaluate the ASET and RSET,\nstarting at the ignition (t = 0).\n473\n\nThe baseline pre-movement time and walking speed are taken from BS PD 7974-6 [471] and set\nas 30 s and 1.2 m s\u22121, respectively. The 90th (pre-movement) and 10th (walking) percentiles of the\nstandard distribution associated to those values (i.e., 120 s and 0.8 m s\u22121, respectively) have also been\nused to explore slower responses. Table 9.5 summarises the list of input parameters required to perform\nthe evaluation.\nTable 9.5: Input values to perform the ASET-RSET analysis. Occupants are considered to be awake and familiar\nwith the premises - Cat. A, and assumed to be trained to a high level of safety management - level M1 (ensured by\nappropriate training before access to underground facilities is granted (see Section 9.4.5). Whilst the complexity\nof the building is considerable, having a wayfinding system (see Section 9.4.1) and only two possible routes (left\nor right) allows the selection of a building level B2. Level A1 is considered since a robust detection system is to\nbe installed across underground premises. The occupants\u2019 location is relative to the location of the fire.\nParameter\nValue\nJustification\nDetection time\n120 s\nPerformance requirement for such fire\nPre-movement time\n30 s (120 s)\nBS PD 7974-6 [471]\nVentilation ramp up\n0 - 60 s\nVentilation design [439]\nWalking speed\n1.2 m s\u22121 (0.8 m s\u22121)\nBS PD 7974-6 [471]\nOccupant\u2019s location\n-100 m / 0 m / +150 m\nCredible scenarios\nSeveral design fire scenarios were developed during the conceptual study phase, during brain-\nstorming sessions conducted with accelerator safety experts and using reference data from the litera-\nture [472]. Among these, a fire developing from a transport vehicle loaded with pallets was shown to be\nthe worst-credible scenario with respect to life safety in the tunnel. The heat release rate (HRR) curve\nobtained shows a medium-fast growing phase that reaches a first peak of 4 MW in 8 min. After a short\ndip, the HRR continues to grow up to a 8 MW peak reached after 17 min, as shown in Fig. 9.20.\nFig. 9.20: Fire scenario of transport vehicle considered for PBD assessment against the life safety ob-\njective in the tunnel arc. Standard t2-curves (ISO 16733-1 [473]) are also depicted for comparison (from\nslow to ultra-fast growth). The analysis is stopped after 27 min to match the simulated time relevant for\nlife safety.\nThe study also investigated the two main ventilation strategies proposed above as well as the\nimpact on the final available safety margin time (ASET \u2212RSET) of several different design criteria such\n474\n\nas: smoke extraction flow, fresh air supply, door behaviour, delay times, background initial flow. All the\ncases (nominal and degraded) are described in a specific technical report [468].\nThe performance criteria are examined using time-position plots for all scenarios studied, as il-\nlustrated in Figs. 9.21 and 9.22. The evacuation time-position profiles (extensively used in tunnel fire\nsafety [474, 475]) allow the ASET > RSET condition to be verified as well as quantifying the safety\nmargin when the occupants reach the end of the compartment.\nThe analysis of all scenarios confirmed that both of the proposed smoke extraction concepts allow\nenough time to safely evacuate the compartment under nominal conditions. Some degraded modes (i.e.,\nno detection, and therefore no automatic activation of any action) do not meet ASET > RSET condition.\n(a) Semi-transverse Case 11C [468]\n(b) Longitudinal Case 25C [468]\nFig. 9.21: Visibility time-position plot for semi-transverse (ST) and longitudinal ventilation (LT) strate-\ngies. The 10 m visibility threshold is clearly depicted as well as different possible evacuation pathways\n(shown as dashed lines) for reduced and nominal human behavioural cases. Ventilation vector: left-to-\nright. Both strategies ensure that occupants can evacuate before reaching untenable visibility conditions;\nST is the most performant option, namely downstream the seat of the fire.\n(a) Semi-transverse Case 11C [468]\n(b) Longitudinal Case 25C [468]\nFig. 9.22: Fractional effective dose (FED) plot for semi-transverse (ST )and longitudinal (LT) ventilation\nstrategies. Ventilation vector: left-to-right. The FED 0.1 and 0.3 thresholds are clearly depicted, as well\nas evacuation lines for reduced and nominal human behavioural cases.\nFinally, the safety margin for nominal and reduced speed evacuees provided by nominal conditions\n(no degraded modes) of cross-sectional and longitudinal smoke extraction strategies are compared in\n475\n\nFig. 9.23. Several extraction capacities from 0 to 25 000 m3/h are also explored. The semi-transverse\nsolution shows better smoke-sweeping capacity, providing a better margin for the same extracted flow.\nThe comparison also demonstrates that the absence of smoke extraction induces a negative safety margin,\ni.e., the occupants are unable to reach the compartment due to the lack of visibility.\nIn conclusion, from a safety point of view, the dynamic confinement offered by the semi-transverse\nscheme is found to be more efficient and robust (including degraded modes) for the safe evacuation of\noccupants in case of an incident. Thus, for this feasibility study phase, the semi-transverse option is\nconsidered as the baseline for the FCC tunnel.\nFig. 9.23: Safety margin (ASET-RSET) available for reduced (120 s pre-movement time and 0.8 m s\u22121)\nand nominal (30 s pre-movement time and 1.2 m s\u22121) evacuees and different smoke extraction (and sup-\nply) flows.\nShafts and safe areas\nWithin the shaft and their waiting areas (see Section 9.4.4), the fire risk will be limited to fire loads\nstemming from the safety systems themselves. These areas are critical for safe evacuation and must not\nbe compromised; hence, no storage of combustibles is allowed. As mentioned above, the pressurised\nvolume and an EI120 compartment ensure that these areas are free of smoke at all times.\nConversely, the transport zone of the vertical shaft poses a significant fire risk. Due to its chimney-\ntype configuration, a fire at the bottom of the shaft will quickly propagate upwards, making it difficult\nto reach and extinguish. To mitigate this, additional fire safety measures should be considered, such as\ncable enclosures, fire protective barriers at regular intervals, etc. Although this scenario does not pose\na major threat to life safety (since the transport zone is separated from the lift shaft), it is important to\nconsider how safety systems are protected at the surface. In a later stage of the study, the impact on\nproperty protection and continuity of operation of such scenarios will be considered in a cost-benefit\nanalysis to identify the most appropriate measures.\nExperiment caverns\nFire risk in experiment caverns is primarily associated with the large quantity of data and power cables\nfeeding the detector and the ignition sources and combustibles integrated within its sub-systems.\nThe reaction to the fire of cables will be controlled to limit the energy, smoke, and acidity pro-\nduction and all the cable trays exiting in the experiment caverns (via the connection galleries) must\n476\n\n(a) FCC-ee\n(b) FCC-hh\nFig. 9.24: Illustration of the FCC detectors at the experiment point PG.\nbe sealed and covered with intumescent paint to prevent propagation. In localised areas with vertical\ndense cable tray arrangements, automatic extinguishing systems (e.g., water mist) will be considered as\na compensatory measure for property protection and business continuity.\nRegarding the detector, a dedicated risk assessment will be conducted for each detector sub-\nsystem, identifying the most appropriate compensatory measures to maintain the fire risk within ac-\nceptable limits. The LHC detectors currently employ several effective safety measures to mitigate the\nfire risks, including:\n\u2013 Inert nitrogen atmosphere: the inner detector volumes are filled with nitrogen to eliminate igni-\ntion sources in combustible areas.\n\u2013 Inert gas extinguishing systems: flooding systems are in place to suppress potential fires in outer\nlayers, with manual activation available from the control room.\n\u2013 Dedicated detection systems: localised detection systems monitor for anomalies and can trigger\npower cuts to prevent malfunctions. These systems utilise inner temperature monitoring and multi-\nparameter gas sampling to ensure precise oversight within the detector.\n\u2013 Over flooding foam system: a water-based foam system allows flooding of the cavern in case\nof extensive fire. This system is not aimed at life safety and might be destructive to the detector\nelectronics. Technical and cost-benefit analyses are required to evaluate the appropriateness for\nthe FCC detectors.\nFrom a life safety standpoint, the lower-level safe-passage connections to protected areas in the\nservice cavern (purple galleries in Fig. 9.24) allow quick evacuation in case of fire. Due to the volume\nof the FCC-ee detector compared to the large dimensions of the cavern and its shaft (Fig. 9.24), smoke\nextraction is not required for life safety. This was closely studied for ATLAS and CMS in the LHC\n[440, 441] and remains valid for the FCC experiment caverns at this stage. A smoke extraction system\nis still necessary to ensure safe and efficient fire-fighting intervention, as well as to reduce potential\nproperty loss in case of fire.\nService caverns\nThe service caverns house the majority of the technical infrastructure to feed the underground facilities.\nThey are areas with significant fire loads and ignition sources, such as power transformers, electrical\nracks, and computing rooms, which must be enclosed within equipment-specific EI120-rated fire com-\npartments. The proximity to pressurised safe areas and the efficient vertical means of evacuation (shafts)\nensure the life safety of the occupants, as verified by the studies performed for the LHC [440,441].\nThe evacuation passages from the experiment area and the main tunnel are also completely en-\nclosed within an EI120 fire-rated over-pressurised compartment and will not be impacted by any fire in\n477\n\nthe service cavern.\nA cost-benefit analysis will determine if dedicated extinguishing systems, such as inert gases or\nwater mist, will be needed to protect property in critical areas such as computing rooms or power trans-\nformer zones.\nKlystron galleries\nThe klystron galleries concentrate high electrical energy and combustible loads comprising power cables\nand the klystrons themselves. While dry technologies exist, the infrastructure is being designed for the\npossibility of hosting oil-filled klystrons. These galleries are equipped with a ceiling-mounted emergency\nextraction system, similar to the main tunnel, and evacuation distances are limited < 200 m (i.e., 400 m\nin between two exits). Several pressurised connection staircases to the main tunnel, are distributed along\nthe gallery, ensuring the evacuation of occupants in case of fire (see below).\nAlcoves\nAlcoves will contain large amounts of active equipment needed for the operation of the accelerator in a\nsmall volume: transformers, control and power racks, electrical components, etc. They are considered as\nhigh fire risk areas due to the combination of fire load with multiple electrical ignition sources. Hence,\nthey must be compartmentalised with respect to the accelerator tunnel, with a fire door, fire dampers and\nsealing of all services which cross.\nThe maximum combustion time of a 1 MW fire in the alcoves is \u22481 h 30 min. This is considering\nthe relatively small and enclosed volume (\u226440 m3) and the fact that fire cannot be sustained below 13%12\nO2 concentration [476]. Hence, the fire rating for the alcove compartments is EI120, considering that\nflashover conditions cannot be discarded at this stage.\nThe racks and services feeding the safety systems of the tunnel arc will be installed in the alcoves.\nThis equipment will be contained in separate volumes within the alcoves, protected with a dedicated\nfire compartment. This limits the risk of compromising those safety systems in case of a fire inside the\nalcove.\nThe evacuation distance to reach the fire door at the entrance of the alcove remains limited (below\n40 m), so the occupants can quickly reach the adjacent compartment in the main tunnel.\nThe smoke extraction ducts installed in the alcoves are connected to the tunnel smoke extraction\nsystem with fire-rated dampers. As mentioned above, smoke extraction from the alcoves is deemed not\nnecessary for life safety but is important for the emergency intervention teams, property protection and\nbusiness continuity in case of a fire.\nIn some specific alcoves, oil-filled transformers might be installed. In these cases, localised ex-\ntinguishing systems (e.g., CO2, inert gas, automatic powder extinguisher, water mist) will be considered\ncase by case to mitigate the impact on property protection and continuity of operations to an acceptable\nlevel. Moreover, the rail-mounted robotic intervention solution that is planned for the tunnel areas might\nnot be suited to the alcove geometry and justifies further study for automatic extinguishing of high-fire\nrisk-specific equipment.\nSurface buildings\nThe surface buildings will house most of the underground technical systems. The fire load is considered\nto be present in the form of electrical cables, racks, power transformers, and other industrial equip-\nment (oil compressors, pumps, fans, etc.). Prescriptive approaches for industrial facilities as per Swiss\nAEAI [443] and French Code du Travail [442] provide the design requirements to ensure life safety\ngoals. In addition to the minimum host state requirements, areas considered as high-risk (with high fuel\n12Conservative value to account for hydrocarbon fuels\n478\n\nload density or ignition sources) will be equipped with automatic fire detection systems, enabling the\nprompt detection and activation of first responders. In such cases, the evacuation alarms will also be\nautomatically triggered.\nReaction to fire\nThe underground inner lining will be made of non-combustible materials (A1/A2 as per EN 13501-\n1 [477]) and will not increase the fire load in the facility. Partitions must also be non-combustible\n(including sandwich panels, false ceilings/floors, and finishing). This is in line with the requirements for\nunderground transport tunnels [433,478,479].\nThe combustibility of material contained in the premises will be strictly controlled to limit com-\nbustibility and the consequences of any ignition. CERN Safety Instruction IS 41 [480] limits the spread\nof flames, droplets behaviour and smoke production of all materials to a minimum or low contribution to\nfire (i.e., A,B and C Euroclasses [477]) and prevents the use of halogenated materials. Whenever these\nprovisions cannot be met, a dedicated risk analysis is performed to determine compensatory measures to\nlimit such materials.\nSpecific attention is to be paid to the reaction to fire of cables. CERN Specific Safety Instruction\nSSI-FS-2-1 [481] already requires the installation of cables that are certified to, at least, Cca-s1,a2,d1\nclass or equivalent. Cca-s1,a2,d1 [452] must be retained as the minimum class for cables in the FCC, as\nit implies:\n\u2013 Limited self-propagation.\n\u2013 Low thermal energy released.\n\u2013 Low smoke production.\n\u2013 Limited fire growth rate.\n\u2013 Non-acidity of gases (i.e., halogen-free).\n\u2013 No sustained flaming droplets (>10 s).\nFire resistance\nIn the event of fire, the integrity of the underground structure must be maintained for the period of time\nrequired to:\n\u2013 Ensure self-rescue and complete evacuation of occupants.\n\u2013 Allow safe intervention of emergency responders.\n\u2013 Limit tunnel damage and recovery time.\nThis fire-resistant requirement must be applied to the civil structures as well as to the technical sys-\ntems that need to operate in case of fire (e.g., cables, cables trays, ventilation ducts). It will be evaluated\nusing natural curves13 and engineering methods. Natural curves will be developed with the worst pos-\nsible scenarios impacting the infrastructure (localised and distributed fires) and will consider all phases\n(growth, developed fire and decay). It is important to note that these natural curves might not be the same\nas used in Section 9.4.3 for life safety assessment due to the main safety objective being assessed: a criti-\ncal scenario for evacuation (a rapid growing fire) is not necessarily the most critical scenario for structural\nresistance (long-lasting fire). The resistance assessment must consider the serviceability limits for the\nload bearing and spalling requirements to ensure that the above-mentioned objectives are met, despite\n13Temperature-time curve that describes the behaviour of a fire in an uncontrolled or natural environment, without external\nintervention or standardised conditions. This curve is derived from real fire scenarios and reflects the actual growth, peak and\ndecay phases of a fire.\n479\n\nthe absence of extended collapse of the structure. For convenience, the final resistance can be expressed\nas per ISO 834 [430] using a time-temperature equivalent method as available in [482] and [483].\nTable 9.6 highlights the minimum prescriptive requirements for fire resistance used in the Host\nStates, as well as in other particle accelerator infrastructures. The risk levels N1, N2, and N3 for French\nroad tunnels are determined by the potential impact of structural collapse on both the infrastructure and\nits surroundings [484]. In particular, risk level N3 is indicated for immersed tunnels and when the risk of\nlocal collapse can represent a major risk of flooding. While the corresponding prescriptive fire resistance\n(R240 + HCM120) appears disproportionate for FCC due to the lack of comparable fire loads, the risk of\nwater intake as a consequence in case of local collapse will be studied in the next phases of the project.\nTable 9.6: Overview of minimum fire resistance prescribed in underground tunnels. R refers to fire resistance\nas per ISO 834 curve and EN 13501-2 [431]. RWS/HCM refer to the normalised hydrocarbon time-temperature\ncurves with faster growth and higher temperatures than the ISO-834 curve as depicted in Fig 9.25a. q stands for\nfire load density. Clearance is the maximum allowable height of the tunnel.\nSource\nFire Resistance [m]\nComment\nFR road\ntunnels [478]\nR60\nIf clearance < 3.5 m for all risk levels\nR120\nIf clearance > 3.5 m for risk levels N1\nHCM120\nIf clearance > 3.5 m for risk levels N2\nR240 + HCM120\nIf clearance > 3.5 m for risk level N3\nFR railway\nurban tunnels [485]\nR120\nfor public transportation\nCH Industrial\nBuilding [486]\nR60 (R90)\nHeight > 11 m < 30 m (if q > 1200 MJ/m2)\nR90 (R120)\nHeight > 30 m < 100 m (if q > 1200 MJ/m2)\nCH road\ntunnels [487]\nR60\nFor lightweight vehicles\nRWS/HCM 120\nIf heavy goods\nCH railway\ntunnels [488]\nHCM 120\nIf submerged or below water tables\nR120 (RWS/HCM 120)\nFor unstable tunnel (if >trains/day)\nR120\nFor stable ground\nXFEL [436]\nR90\nFor shaft and underground infrastructure\nHL-LHC [489]\nR60\ntunnel\nR120\nsafe areas and protected shaft\nAs indicated above, the proposed fire resistance for underground infrastructure expressed as per\nISO 834 is:\n\u2013 R90 for tunnel and experiment caverns.\n\u2013 R120 for alcoves, service caverns and areas with specific fire load.\n\u2013 R120 for safe areas and protected shafts.\nThe different fire scenarios studied in the tunnel areas show that even in degraded mode, tem-\nperatures remain below 300 \u25e6C for a large part of the tunnel (Fig. 9.25b). Close to the seat of the fire,\nthe maximum recorded air temperatures for most unfavourable scenarios remain below 600 \u25e6C. This\nis substantially below the ISO 834 curve (Fig. 9.25b), demonstrating that the proposed fire resistance\n480\n\nensures the life safety of occupants during the evacuation phase. The next phase of the study will eval-\nuate whether greater resistance is needed to ensure the objective of property protection and business\ncontinuity.\n(a) Temperature evolution for transport vehicle fire with three different ventilation condi-\ntions [468].\n(b) Temperature time-position plot for case 18A [468]. Ventilation vector: left-to-right.\nAir/smoke temperature is measured at 2.6 m from the ground. This case represents a failure\nof the smoke extraction system and maximises the thermal impact to the tunnel for the vehi-\ncle fire design. The black line corresponds to the 200 \u25e6C threshold. The red and green\ndashed/dotted lines are evacuation trajectories for worst and nominal human behaviour\ncases.\nFig. 9.25: Temperature profiles in the case of a fire in the tunnel.\nOrganisational measures for fire prevention\nThe following general requirements to prevent fires and limit their consequences will be implemented:\n481\n\n\u2013 All hot works are to be conducted under a fire permit approval stipulating preventive and compen-\nsatory measures to be put in place (most of them are already implemented in the current CERN\nsafety policy);\n\u2013 Smoking will be strictly forbidden in all buildings at CERN, including underground areas.\n\u2013 Fire safety awareness must be part of the access training ranks. This shall include instructions on\nprompt manual alarm triggering, behavioural reflex, and first response training.\n\u2013 Maintenance and control. Patrol (automated) will check for unusual cues (hot spots, improperly\nplaced material).\n\u2013 Regular tests and fire drills. Fire safety systems must be permanently monitored and checked.\nUnplanned evacuation drills will regularly verify that the global safety concept is successfully\nimplemented and if there are discrepancies, propose actions and update the concept.\nOxygen deficiency hazard (ODH)\nThe SRF cryomodules of the FCC-ee rely on liquid helium to reach their superconducting state. The\n400 MHz cavity cryomodule will be cooled using 115 kg of helium at 4.5 K (He-I), whereas the 800\nMHz cryomodule will use 55 kg of superfluid helium (He-II) at 2 K. Following a risk assessment [490],\na few accident scenarios were identified as potential sources of helium release in the FCC tunnel. Such\na release poses considerable risks for people working underground. The helium gas released into the\nenvironment would displace the air (i.e., the oxygen) and lead to a possible asphyxiation of occupants\nunderground; this is referred to as an Oxygen Deficiency Hazard (ODH). Moreover, low-temperature\nhelium flow can also cause severe internal/external cold burns. A performance-based design approach,\nusing numerical simulations in the form of computational fluid dynamics (CFD), provided an analysis of\nthe ODH in the RF section of the FCC-ee accelerators. The outcome of the safety studies is summarised\nbelow, based on a series of reports that contain the full details [491,492].\nFor simulations, a full fire compartment (400 m) in the RF sector at point PH was selected as the\ncontrol volume. The CFD simulations were performed in two dedicated batches, corresponding to the\ntwo accident scenarios chosen for the analysis: 1) sustained RF quench and 2) loss of beamline vacuum.\nThe FCC-ee SRF system will be designed to avoid a sustained RF quench, leaving the loss of beamline\nvacuum to be considered as the most credible incident (MCI) at this stage, with a mass flow rate of\n20 kg s\u22121 [490]. The scenarios studied are summarised in Table 9.7. The case and mesh settings for the\nCFD solver are detailed in [491,492].\nTable 9.7: List of simulation scenarios and the main input parameters.\nRef.\nScenario\nRelief points\nBurst disc\nMass flow\nPressure &\nTemperature\nSim time\n[per CM]\n\u03d5 [mm]\n[kg s\u22121]\n[bar(a)] / [K]\n[s]\nSC1\nSustained\nRF quench\n1\n100\n2.9\n2.0 /\n5.32\n57\nSC2\n2\n100\nSC3\n4\n50\nSRF01\nLoss of Beamline\nVacuum\n1\n100\n20\n26\nSRF02\n2\n100\nThe simulations were run on CERN\u2019s HPC cluster and post-processed, focussing on analysing the\nfollowing results:\n\u2013 Comparison between input scenarios.\n\u2013 Dynamic behaviour of the oxygen levels in the cross-section of the tunnel.\n482\n\n\u2013 Time needed to reach ODH conditions in the evacuation path.\n\u2013 Propagation speed of the Helium cloud front.\n\u2013 Propagation speed of the Helium Plug 14.\n\u2013 Longitudinal size of the Helium Plug.\nThe findings are summarised in Table 9.8, showing the time at which untenable conditions are\nreached in the transport/evacuation zone (i.e., O2 \u226418%), the propagation speed of the helium cloud\nfront, and the behaviour of the helium plug formed in the tunnel. This includes scenarios where gas is\nstill being relieved from the burst disk ( \u02d9mHe \u0338= 0) and when the inventory is empty ( \u02d9mHe = 0), along\nwith the size of the corresponding plug at the end of the simulation. Figure 9.26 illustrates the results of\nthe cross-section and longitudinal propagation of the helium cloud.\nTable 9.8: Results of the CFD simulations with the scenarios described in Table 9.7.\nRef.\nTime to reach\n18% O2\nPropagation speed [m/s]\nHe plug size\nCloud\nHe plug\nHe plug\n[s]\nfront\n( \u02d9mHe \u0338= 0)\n( \u02d9mHe = 0)\n[m]\nSC1\n7\n1.52\n0.66\n0.58\n32\nSC2\n10\n1.33\n0.57\n0.7\n29\nSC3\n15\n1.66\n0.63\n0.81\n35\nSRF01\n4\n3.3\n5.3\n3.3\n73\nSRF02\n2\n2.57\n3.8\n2.57\n53\nThe simulations confirm the turbulent flow effects observed in real-life scenarios [493]. Untenable\nconditions are reached as soon as 2 seconds after the opening of the pressure relief device, and after an\nadditional 4 seconds the cloud has propagated another 12 m downstream. The turbulent flow leads to\nthe creation of a helium plug, which was observed in all 5 scenarios, right next to the release point and\nextending up to 70 m in length within 26 seconds (Table 9.8). The plug can obstruct the entirety of\nthe transport zone, posing a heavy constraint for the evacuation of the occupants towards the adjacent\ncompartment where they would retrieve the transport vehicle to evacuate from the underground area.\nGiven these observations, with the cryomodules at nominal conditions (i.e., maximum inventory),\nthe access to the RF section of the tunnel must be blocked when the risk of such accident events is\npresent. Access to the klystron gallery is allowed, however, the bore holes for the wave guides need to\nbe leak tight. Additional future studies may determine if there is a minimum inventory where access to\nthe RF sector would be possible. In this case, occasional access might be granted with prior approval\n(i.e., procedures) and by requesting the use of personal protective equipment (PPE), such as self-rescue\nmasks. It is intended to extend these studies, for the further design of the FCC study to include the use\nof the emergency (smoke) extraction duct and measure the impact on the extent of the helium plug and\ncloud propagation, in view of iterating on the access conditions to the RF sector.\nIt is also preferable to have a cryomodule design with multiple release points, although a single\nrelease point might still be studied in more detail to improve the outcome compared to SRF01.\nThe ODH assessment for the experiment caverns will be performed in the next phase of the study,\nwhen the detector technologies are chosen and which cryogenic gas will be utilised (if any).\nSeismic hazard\nThe region is characterised by a moderate seismic level. With 11 earthquakes of magnitude > 5 estimated\nto have occurred within a radius of 100 km around Geneva in the last 500 years the hazard is considered\n14Area of the tunnel that is completely filled with helium gas\n483\n\n(a) t = 1 s\n(b) t = 3 s\n(c) t = 6 s\n(d) t = 26 s\n(e) He plug propagation at t = 6, 10, 26 s\nFig. 9.26: Results for of the CFD simulations of scenario SRF02 at a time t, following the opening of\nthe burst disk. a) - d): Cross-section view just 1 m away from the burst disk. e): longitudinal view of the\nhelium propagation. Colour scale shows the oxygen content in the 2D plane (passage from red to orange:\nthe transition to 18% and below). Ventilation flows right-to-left.\n484\n\nand analysed. At least two seismically active faults stretch about 10 and 30 km southwest of Geneva,\nwithin the area of the current reference implementation scenario. In order to provide suitable seismic\nsafety requirements for the design of the civil and mechanical structures, equipment, and installations\nforeseen in the underground facilities, subsequent preparatory phases need to assess seismic hazards at\nthe depths concerned. To do so, a collaboration with the Swiss Seismological Service (SED), hosted by\nthe Swiss Federal Institute of Technology Zurich (ETHZ), the University of Geneva (UNIGE), and the\nFrench Universit\u00e9 Grenoble Alpes (UGA) is proposed for further studies. So far, a simplified approach\nbased on the adaptation of the legal seismic safety requirements for ordinary surface buildings on French\nterritory was used to design and assess new mechanical structures and equipment in the Large Hadron\nCollider (LHC) and Super Proton Synchrotron (SPS) complexes, meaning that the structural elements\ncould be over- or under-sized to resist the required earthquake loads. This proposal will build upon\na project to draw a probabilistic-seismic-hazard-oriented and tailor-made assessment for the proposed\nunderground facilities. The main products of the projects are:\n\u2013 Seismic Hazard Curves: a family of seismic hazard curves that represent the annual frequency of\nexceeding different levels of ground motion, essential for designing earthquake-resistant structures\nand assessing the safety of existing facilities.\n\u2013 Site Response Analyses: uniform hazard spectra (UHS) and scenario earthquakes, including ac-\nceleration time-histories, for seismic design and safety evaluations of the civil infrastructure and\nthe equipment structures hosted there.\nThe overall study is planned for a 3-year period (2025 - 2028)15.\n9.4.4\nEvacuation\nA series of evacuation studies were undertaken for the underground infrastructure.\nGeneral requirements and considerations\nThe following list summarises the minimal requirements for all FCC areas, in line with the prescriptive\nrequirements in France\u2019s Code du Travail [442] and Switzerland\u2019s Norme de Protection Incendie [443]\nused for standard facilities:\n\u2013 At any given point, occupants must be able to choose at least two distinct evacuation paths. The\nmaximum dead-end evacuation distance is \u226440 m (e.g., in alcoves).\n\u2013 The width of any evacuation doors must be \u22650.9 m.\n\u2013 The maximum evacuation distance:\n\u2013 for surface buildings: in accordance with [442,443];\n\u2013 for underground installations: in accordance with performance-based design and inline with\nbest practices in other underground tunnel infrastructures.\n\u2013 Emergency shelters (refuges) without safe escape routes connecting to the surface are not consid-\nered in the safety concept for the operation phase. This is in line with the provisions of Directive\n2004/54/EC for road tunnels [432].\nTunnel arc: evacuation modelling\nThe evacuation from the underground infrastructure will rely on both horizontal and vertical means.\nPersonal transport vehicles will ensure the horizontal evacuation from the nearest alcove to the safe area\n15Note that the French and Swiss seismic hazard model currently in force for surface buildings will be superseded by the\nnew European Seismic Hazard Model (ESHM 2020) [494] that will be incorporated in the second generation of the Eurocode\n8 [495].\n485\n\nat the bottom of the access shaft. Vertical evacuation will be ensured via pressurised lift shafts equipped\nwith a secured set of lifts (composed of 2 lifts for redundancy and availability), to bring occupants to the\nassembly points at the surface.\nAt the bottom of every lift shaft a fire-, smoke- and gas-proof safe area is needed to ensure that\noccupants can safely wait for the arrival of the lift. Defining the size (surface area) of the safe area\nand its impact on tunnel occupancy is crucial to verify the safety concept during evacuation processes,\nultimately defining the maximum number of occupants allowed underground at the same time. For a safe\nevacuation, maximum admissible crowding in safe areas should be under 3 occupants/m2 [496].\nMany conditions with different probabilities (e.g., occupancy distribution in the tunnel, walking\nspeed or transportation speed) need to be evaluated in order to define the required surface area and reserve\nenough space near the shaft in the integration drawings. At this phase of the study these parameters are\nnot exhaustively known; hence a stochastic approach with random variables (in a given set ranges) is\nmore suitable. Therefore, to determine the size of the safe area, an evacuation model was developed\nusing plain Monte Carlo simulations.\nDepending on the location of the fire, one or more sectors of the tunnel arc will need to be evacu-\nated. A worst-case scenario is assumed where the fire is just next to the connection to a service cavern,\nblocking access from one sector only, which means that all occupants of an entire sector must evacuate\nvia the other access shaft (10 \u2013 11 km away). In addition, it is a common practice to also evacuate the\nadjacent sectors that are not affected by the fire (as in the LHC scenario). To summarise, occupants from\none and a half sector (1.5 sectors) will be evacuating through a single shaft (Fig. 9.27).\nFig. 9.27: Simplified schematic of the evacuation model.\nIn this model, the number and location of the alcoves are important, indicating the total parking\ncapacity. For the feasibility study, the baseline number of alcoves is 7 per sector, but alternative studies\nwere carried out assuming 9 alcoves.\nIt is assumed that all occupants inside the tunnel will have access to a transport vehicle. Therefore,\nthe maximum number of occupants allowed inside the sector is limited depending on the capacity of the\ntransport vehicles and the parking space in the sector. A total of 4 different simulation scenarios were\n486\n\ncreated (see Table 9.9) with 2 different distribution methods for the occupancy distribution in the tunnel.\nThe number of occupants per sector is comparable to a scale-up (factor 3) of the maximum number of\noccupants seen during Long-Shutdown 2 (LS2) in the LHC [497].\nTable 9.9: Evacuation scenario parameters.\nScenario\nNumber\nVehicle\noccupant\ncapacity\nOccupancy\ndistribution\nN. of alcoves\n(per Sector)\nVehicle Parking\nCapacity\n(Alcove/Shaft)\nOccupants\n/ 1.5 Sector\nOccupants\n/ Sector\n1\n2\nBinomial\n7\n10/20\n260\n174\n2\n3\nBinomial\n7\n10/20\n390\n260\n3\n4\nUniform\n7\n4/4\n192\n128\n4\n4\nUniform\n9\n4/4\n240\n160\nThe distribution of occupants in the tunnel is an important variable in determining the size of the\nsafe area. Since lone working is not allowed by default, it is assumed that occupants are working in\ngroups. The number of occupants per group and their position is treated as random. They are placed\neither in between two adjacent alcoves or between the service cavern (Shaft A) and the nearest alcove.\nAfter the evacuation alarm, both the occupants between Shaft A and Shaft B and the occupants in the\nhalf sector on the other side of Shaft A start to evacuate to the safe area in Shaft A (Fig. 9.27). To do\nthis, occupants between the two alcoves must first walk to the alcove where they parked their vehicles\nand then travel to the safe area of Shaft A with their vehicles. Occupants in the area between Shaft A\nand the nearest alcove will walk directly. Two different occupancy distributions (Fig. 9.28) were used to\nindicate the initial positions of groups.\n(a)\n(b)\nFig. 9.28: Example of occupant group distribution along 1.5 sectors. Shaft A location at position 0 m.\na) Binomial distribution, restricted to 2 and 10 occupants per group; b) Uniform random distribution,\nrestricted to groups of 4 occupants.\nThe simulations consist of 50 different random occupancy distribution scenarios, each run with\nMonte-Carlo (1 000 samples). The results are shown in Fig. 9.29, with an occupant walking velocity as\na normal distribution (mean(SD) of 1.2(0.3) m s\u22121) and a transport velocity as a uniform distribution\n([20 \u221230] km h\u22121). The maximum number of occupants that reached the safe area at the end of each\nsimulation (50 000 in total) is recorded and is also shown in Fig. 9.29. Scenarios 3 and 4 require the\nsmallest safe area size. This is mainly due to the uniform distribution of the occupant groups in the\ntunnel, meaning that they will all arrive at the safe area in a distributed fashion, thus crowding is limited\nby the travel time of the lift. Scenarios 1 and 2 have a binomial distribution with an agglomeration of\noccupants in the middle of the arc (this could be the case during a major repair or maintenance in a\n487\n\nparticular arc cell). This would lead to a higher crowding at the safe area once these occupants reach\nthe lift, hence a larger safe area is required to maintain a density below 3 occupants/m2. The results\nshow that having a minimum safe area of 50 m2 would be suitable safety. It is feasible to implement\nsuch an area near the lifts of all eight service caverns. Additional details are available in the technical\nreport [397].\nTechnical points: service caverns\nThe service caverns at the technical points are connected to the accelerator tunnel via compartmentalised\npassages that will be used as emergency escape routes. In some points (such as PF), the service shaft\nis not directly connected to the service cavern. Therefore, an additional horizontal connection tunnel is\nrequired. It will also be used as a safe evacuation path.\nThe service shafts at the technical points are equipped with one set of lifts to ensure the vertical\nevacuation to the surface. Each set is composed of two lifts for redundancy and availability. Lifts\nhave a dedicated pressurised fire-resistant compartment (lift shaft), separating the air volume from the\nsurrounding environment (i.e., service cavern) to protect the integrity of the evacuation to the surface in\ncase of emergency. The pressurised compartment is extended to the safe area, with its size as determined\nabove.\nExperiment points: experiment and service caverns\nThe experiment points will enable independent dedicated flows of occupants up to the surface, separating\nthose evacuating from the experiment and service caverns from those evacuating from the accelerator\ntunnel.\nThe experiment cavern is connected to the service cavern through three separate personnel pas-\nsages that can be used as emergency escape routes: two at the level of the beamline and one at the\nground floor. These personnel passages will contain little or no combustible material. Additional bypass\nchicanes are integrated whenever a personnel passage requires heavy mobile shielding for radiation pro-\ntection purposes. A second connection tunnel on the ground floor is only for the passage of material and\nwill not be considered a safe evacuation path.\nThe main tunnel is connected to the service cavern by two bypass tunnels about 100 m from the\ninteraction point and two connection tunnels at the end of the long straight section close to the experiment\ncavern (Fig. 9.30).\nAirlocks are planned in the connections between the tunnel/experiment cavern and the bypass tun-\nnels/ service cavern, separating and isolating the ventilation volumes to prevent the mixing of radioactive\nair with accessible areas.\nSimilar to the other points, the occupants rely on lifts for vertical evacuation to the surface site,\nwhich will be done by a single shaft located in the service cavern. This is a new concept, different from\nthe experiment points at LEP/LHC, which profited from more than one shaft. However, the separation\nof the flow from the accelerator tunnel and the experiment cavern is still ensured by having two sets of\ntwo lifts (four in total), in the shaft: one set to house the occupants evacuating from the experiment and\none set for occupants evacuating from the accelerator (Fig. 9.30). Each set is composed of 2 lifts for\nredundancy and availability. Each set of lifts has a pressurised fire-resistant compartment, separating\nthe air volume from the surrounding environment (i.e., shaft and service cavern) to protect the integrity\nof evacuation to the surface. The pressurised compartment is extended to the dedicated experiment and\naccelerator (machine) safe areas (Fig. 9.30). The safe area is where the occupants wait for the lift to\nevacuate to the surface. The size of the accelerator safe area, as previously mentioned, is a minimum of\n50 m2, while the exact footprint of the experiment safe area is yet to be integrated and will dictate the\nmaximum occupancy allowed in the experiment cavern (3 occupants / m2).\n488\n\n(a) Result of one simulation for scenario 2\n(b) Result of 50 000 simulation runs for each scenario.\nFig. 9.29: Simulation results of the evacuation study. a) results of one simulation run of scenario 2,\nwith the occupancy density (crowding) in the safe area over time; b) Maximum number of occupants\n(crowding) in the safe area for each scenario.\n489\n\nFig. 9.30: Integration of the evacuation flow of occupants in an experiment point. The illustration shows\nthe example of the experiment cavern housing an FCC-hh detector.\nKlystron galleries\nThe superconducting RF (SRF) cavities in the RF sections will be fed by waveguides coming from\nklystron galleries located above the main tunnel. The length of these klystron galleries is roughly 2010 m\nin point PH and 1445 m in point PL. A series of connections to the main accelerator tunnel via staircases\nare available at regular intervals and at both extremities, providing the necessary means of evacuation\nfrom the klystron galleries in case of emergency (e.g., fire in the modulators) and thus avoiding dead\nends. These connections are distributed as follows:\n\u2013 At PH, there are a total of 6 tunnel connection staircases, one every 341 m.\n\u2013 At PL, there are a total of 4 tunnel connections, one every 354 m.\n490\n\n(a) Point PH - 341 m in between staircases\n(b) Point PL- 354 m in between staircases\nFig. 9.31: Klystron galleries and their evacuation connections in point PH (a) and PL (b)\nThe frequency of these connections helps to minimise the distance that any occupant would need\nto walk to reach another fire compartment in the main tunnel. Each staircase will be equipped with fire\ndoors at both ends (tunnel and gallery). In addition to the static confinement properties, each connection\nwill also be pressurised, ensuring a dynamic confinement between the main tunnel and the gallery. A\nmore in-depth risk analysis will be conducted for this area during ta subsequent design phase to assess if\nthe distance and number of staircases are sufficient.\nIn addition to the staircases, at the two ends of each klystron gallery, lifts are available for trans-\nporting personnel and material, avoiding having to pass through the RF section to work in the arc. These\nlifts will not be used in an emergency (e.g., fire). Access to the Klystron gallery is also possible from the\nservice cavern in the middle of the RF sector.\nAlcoves\nAlcoves will be spread along the accelerator tunnel (minimum 7 alcoves per sector): two big alcoves\nand five small alcoves. These alcoves house electrical racks and equipment and will form a dedicated\nEI120 fire-rated compartment, separated from the main tunnel. They will have a single access (in and\nout), through a fire door connecting to the main tunnel, creating a dead-end in terms of evacuation. The\nmaximum allowable distance from the end of the alcove to the fire door must not exceed 40 m. This is\nbased on the maximum evacuation distance to reach a protected staircase in France [442], ensuring that\n491\n\nthe adjacent fire compartment (i.e., the main tunnel, relatively free from smoke) can be reached safely in\ntime.\nIn the baseline layout, all the alcoves comply with this maximum distance. The layout also in-\ncludes two mezzanines, one on each side of the alcove. Staircase connections from the mezzanine to the\nground floor will be installed at both extremities of the alcove to ensure that the evacuation length is not\ndoubled and to avoid being trapped on the mezzanine.\nSurface buildings\nThe surface buildings will rely on applicable national and international standard practices for the evacua-\ntion requirements applicable to industrial infrastructures within the Host States. For PB the Swiss AEAI\nDirectives 15-15 [486] and 16-15 [498] will apply. For all the other sites, the French Labour codes are\napplicable [499].\n9.4.5\nEmergency preparedness and intervention concept\nAn underground particle accelerator of 91 km in circumference presents unique challenges in terms of\nemergency response. The threefold size increase compared to the LHC presents challenges, including\nmuch larger distances between access points (11 km) and surface distance between shafts. Hence, a new\nemergency preparedness and intervention concept is required.\nThe emergency response concept proposed is divided into four distinct phases, starting from a\nconfirmed accident event (e.g., fire) [500]:\n\u2013 First Response: trained personnel or contractors at the accident site are responsible to raise an\nalarm, provide first aid, deliver first response (e.g., fire extinguishers) and initiate evacuation pro-\ncedures.\n\u2013 Robotic Intervention: remote-operated robotic vehicles gather situational data and conduct prelim-\ninary firefighting actions before human intervention. Ceiling-mounted and floor-based robots can\nfulfil these tasks, for example.\n\u2013 Local Fire Services: on-site support from local emergency services, primarily for surface-level\ninterventions.\n\u2013 CERN Fire & Rescue Service (CFRS): CFRS to coordinate emergency interventions, if relevant\nwith other emergency services, with the use of equipment stored both in surface and underground\nlocations. This includes for instance foam-based firefighting systems and compressed air foam\n(CAFS) units. Rapid-deployment solutions are required to ensure a quick intervention to all eight\nsurface sites.\nSupport infrastructure for emergency response\nThe concept will also rely on a robust support infrastructure for an efficient emergency response:\n\u2013 Surface site: landing zone in the vicinity for airborne emergency intervention, a command post, a\ncasualty room, and a logistical hub for storing specialised intervention vehicles, firefighting robots,\nand extinguishing agents.\n\u2013 Underground: compartments with designated safe waiting areas, compartmentalisation, smoke\nextraction (with CFRS override and remote control), priority intervention vehicles and robotic\nassistance units. A reliable communication system, vertical dry risers connecting the surface and\nservice cavern, and underground water reservoirs will ensure adequate firefighting resupply.\nUnlike current baseline practice in the LHC, the use of robots will play a critical role in the\nemergency response for the FCC by enabling the possibility of quick fire response within the underground\ninfrastructure, where human access may be restricted during accelerator operations.\n492\n\nTraining and implementation strategy\nTo fulfill the concept, all underground personnel will be trained in emergency response and first aid. A\nstructured transition plan will be developed to align with this new approach. CERN has already begun\ntesting robotic solutions to validate their potential in real emergency scenarios. Further technical details\nwill be made available in the relevant reports [500].\nGiven the critical partnership with the local fire services in fulfilling the concept, we emphasize\nthe importance of CFRS being actively involved in the joint work with these key partners. This includes\nthe establishment of joint training programmes, workshops, and drills building on the current practices.\nBy implementing these measures, the FCC will enhance its ability to manage emergency situations\nefficiently while prioritising the safety of personnel and infrastructure.\n9.5\nSafety during the construction and installation phases\n9.5.1\nSafety coordination\nThe baseline concept for safety coordination is based on French legislation, as 7 out of the 8 surface sites\nare located within French territory. For the surface site PB in Switzerland, Swiss legislation applies. The\ndetailed design will include a proposal to harmonise processes across all worksites to increase efficiency.\nIn accordance with French law [501], the project owner is responsible for safety coordination\nthroughout all phases of the project [423].\nSpecialised external service providers (i.e., safety coordinators) will assist the project owner in\nthis safety coordination mission.\nSafety coordinators are responsible for preparing coordination plans and the PGCSPS (Plan G\u00e9n\u00e9ral\nde Coordination en mati\u00e8re de S\u00e9curit\u00e9 et de Protection de la Sant\u00e9) for the relevant worksite(s). These\nplans must be provided to contractors during the tendering phase to clearly outline their safety obliga-\ntions and expectations, as well as to specify the applicable laws and regulations governing the project.\nAll worksite-related safety documents, procedures, and methods must be written in French to ensure\ncompliance with national regulations. Each contractor remains responsible for the safety of their own\nemployees, according to their operating methods. Any accident or incident occurring within the work-\nsites must be reported by the contractors using a form-based system. Today, at CERN, this reporting is\ngoverned by CERN\u2019s safety rule SR-SIM [502].\n9.5.2\nConstruction phase\nDuring the construction phase, civil engineering works on the surface and underground are executed by\nspecialised firms under contract with CERN. It ends with the handover of the buildings and underground\nstructures to CERN from the contractor.\nThe evacuation plan and emergency procedures in the event of incidents within the worksite(s),\nwill be included in the PGCSPS. Such procedures are developed in consultation with CERN, the con-\ntractor and the local emergency services. It indicates, among others, the assembly points for emergency\nservices, access conditions to the various zones means to evacuate victims and the need for specific fire-\nfighting / response equipment. Joint training, reconnaissance and drills should be organised with the\nCFRS to ensure a tailored response and strengthen the collaboration with the local services.\n9.5.3\nInstallation phase\nThe installation phase begins with the handover of the surface buildings and underground structures from\nthe civil engineering contractor to CERN.\nThis will happen at different moments for each access point and the associated tunnel sectors: in\nthe underground area of an access point, the installation phase can start after the total or partial release\n493\n\nof the adjacent tunnel sectors leading to the neighbouring access point with lift facilities. In a tunnel\nsector, installation activities are allowed as long as there are two adjacent access points from which the\noccupants can reach safely to evacuate. These rules will guarantee a two-way evacuation possibility, with\nsecured horizontal and vertical means of escape at all times. The technical and organisational details of\nsafety during the installation phase will be engineered in the project preparatory phase.\nTwo sub-phases of installation can be distinguished: the service installation (electricity, lighting,\nventilation, cooling, detection and alarm systems, and transport system) and the accelerator installation\n(beamline elements, magnets, RF cavities, cryogenic systems, power converters, and control systems).\nService installation\nService installation begins after the release (handover) of the civil engineering (CE) structures from the\ncontractor to CERN. The temporary lighting, ventilation, lifts and other services installed by the civil\nengineering contractor could potentially be taken over and used by CERN for the initial phases of the\nservice installation. Obviously, no work can be executed by CERN and its contractors without these\nessential services. It is therefore advisable to foresee the transfer of these assets to CERN at the time of\nhandover, saving the time and cost of CERN installing essential services in a provisional manner. The\ntransfer should include the assets, as well as the technical documentation and maintenance procedures.\nSimilarly, robust construction site access control devices (e.g., turnstiles) could be transferred from the\ncontractor and connected to the CERN access control system. This would allow verification of CERN\nimposed training, etc., access control and the enforcement of work coordination.\nSafety organisation during service installation\nThe services mentioned above are largely installed by contractors mandated by CERN. In order to co-\nordinate work and occupational safety coherently, experience from the High Luminosity LHC shows\nthat the work of a pairing (binome) consisting of an activity coordinator employed by CERN and an\nindependent safety coordinator (see Section 9.5.1) is very effective. The FCC project should adopt the\nsame approach. Given the geographical span of the facility and the unavailability of most of the safety\nand automation systems in this early phase of the installation works, each of the access point sites will\nbe permanently manned by guards. Their primary role will be to ensure smooth material entry without\ncompromising access control procedures. In addition, during working hours, a site supervisor will ensure\nthe respect of safety procedures and act as a liaison with service and equipment groups at CERN in case\nbehavioural or technical anomalies are observed.\nInstallation order during service installation\nThe underground ventilation system is essential for the well-being and safety of workers, especially in\nthe 11.4 km long tunnel sectors. The definitive ventilation system will be installed with priority. This\nincludes cooling water, which is required for the air-handling units along the tunnel. Once the smoke\nextraction duct is equipped, the dampers and extractors are powered and commissioned, local control of\nsmoke development is possible. At the same time, while avoiding co-activities, the definitive electrical\nsupply and lighting will be installed. This includes the installation of detection systems\u2019 control and\nindicating equipment (CIE) racks in the alcoves, high-voltage cables to the alcoves and transformers.\nCable trays will be installed to guide the numerous cables in an orderly manner.\nThe installation of definitive detection systems can proceed with lower priority. If smoke detection\nis performed by aspiration tubes, then this system can only be made operational after the accelerator\ninstallation, because of its sensitivity to dust and welding fumes, which would raise numerous false\nalarms. Manual call points distribution and a dedicated procedure will ensure prompt alarm activation\nduring this degraded phase.\nFor the FCC, the transport system has a safety role during evacuation, it is also indispensable for\n494\n\nthe next phase in which the accelerator is installed. As described in Section 9.4.1, the transport system\nis based on autonomous vehicles, both for the transport of personnel and for large and heavy loads. All\ninfrastructure to allow autonomous movement of the vehicles must be available at the end of the service\ninstallation phase.\nEmergency response during service installation\nDuring the service installation, a provisional alarm system is required since the automatic fire detection\nwould not yet be available. Manual call points (break-the-glass devices) and provisional evacuation sirens\nwill be installed and cabled to the CIE racks. Provisional communication infrastructure is necessary to\ntransmit the alarms to the central emergency coordination team.\nDue to the large distances in the tunnel, and on the surface between the surface sites and a CERN\nsite, where the emergency coordination takes place, the possibility for timely intervention of trained\nemergency services has to be implemented before the installation phase starts. Consequently, early\ndevelopment of the integrated emergency concept is needed.\nOccupational safety during service installation\nDuring service installation the safety systems may not be installed or not be fully operational, and strict\nmeasures for occupational safety must be implemented. According to preliminary estimates, up to 200\noccupants per sector are expected during the installation phase. This is significant but less than in the\nworst-case scenario during the operation phase that was studied (Section 9.4.4).\nThe focus is on the self-protection of the workers:\n\u2013 Access is only granted to trained personnel.\n\u2013 All workers must be trained in the use of the self-rescue mask (for use in case of fire or smoke),\nand the use of the transport vehicles for evacuation.\n\u2013 A sufficient number of certified first-aiders at the workplace 16 must be trained.\n\u2013 All workers must also be trained in raising an alarm by pressing the alarm button if there is a fire\nor smoke development and to react correctly to the evacuation sirens.\n\u2013 The installation schedule and planning must have shifts dedicated to high-risk activities where the\nhuman presence is limited to the absolute minimum. For example, using night shifts for heavy\ntransport activities, such as cable drums or other bulky loads, where the access to the sector con-\ncerned is restricted to the transport team only.\n\u2013 The underground worksites must be kept clear of combustible materials at all times. Any such\nmaterial (packaging, cable drums) must be evacuated to the surface immediately after its use.\n\u2013 The transport zone of about 2.5 m width must be kept free of stored material throughout the tunnel\nto permit evacuation.\nAccelerator Installation\nOnce the basic services - ventilation, lighting, electricity, smoke extraction, detection, and alarm systems\nand transport - are commissioned, the sub-phase of accelerator installation may begin.\nSafety organisation during accelerator installation\nThe same concept as the previous phase is assumed, with an update of the existing PGCSPS, if necessary.\n16A first-aid qualification with a focus on the most frequent types of personal accidents at industrial workplaces. The training\nlasts two days and is concluded by a proficiency test.\n495\n\nInstallation order during accelerator installation\nDrawing on experience from LHC, the accelerator will be installed in a sequence of\n\u2013 Transporting the magnets and other beamline elements like collimators, and RF cavities to their\ndesignated location.\n\u2013 Making provisional geometrical alignment.\n\u2013 Connecting the beamlines with each other.\n\u2013 Connecting the electrical supply and the controls to the magnets.\n\u2013 Concluding with a final geometrical alignment.\nThe partition walls separating the tunnel into 400 m long fire compartments can be installed as\nsoon as the magnets are placed. A phased approach, where only certain partitions are initially installed\nor where the partitions leave openings for the installation of further cables and services, allows the\nflexibility needed during installation while improving the safety of degraded modes. Passive protections\nin the form of partition walls are the most reliable system for this phase. Finally, the automatic detection\nand alarm system can be commissioned.\nSimilar to the service installation sub-phase, the planning will include shifts dedicated to high-\nrisk activities, such as magnet transport, and avoid co-activity by restricting access to only the teams\nconcerned.\nTransport during accelerator installation\nMagnets will be lowered underground with overhead cranes through the large shafts of the service cav-\nerns at sites PA, PD, PG and PJ. Then, a magnet transport vehicle will move them past the already\ninstalled magnets to their final location. During this journey, the magnet transport vehicle effectively\nblocks the transport zone of 2.20 m width, thus blocking the evacuation exit. Access during transport to\na sector will be restricted to the transport team, reducing the number of occupants underground during\nthis period. Once the magnet transport has passed the midpoint of the sector, a returning vehicle can pass\nan arriving one in the extended lay-by area at the central alcove. The same rule applies to the transport\nof other large items which are wider than 80 cm and thus cannot be bypassed by a personnel vehicle.\nFrom the moment when all magnets are positioned in a sector, the transport, and evacuation rules\napplicable during normal operation become valid, because only the transport zone is available. In partic-\nular, special, narrow personnel transport vehicles must be used for personnel and light loads.\nEmergency response during accelerator installation\nThe provisional alarm system with break-glass push buttons installed during the service installation sub-\nphase remains active until the automatic detection and alarm system has been commissioned. If the\ndetection technology chosen is aspiration smoke detectors, this can only be done after all dust and fume\ngenerating works are concluded. The alarm system must be configured to trigger the evacuation alarm\n(sirens or voice messages) and alert the central emergency coordination team, which will analyse the\nsituation and engage the most appropriate emergency response with the different emergency services.\nOccupational safety during accelerator installation\nThe type of work during accelerator installation is mostly of a mechanical and electro-mechanical nature.\nThis includes hot work (grinding, welding and brazing), which is a potential ignition source. The com-\npartment walls, installed after magnet placement, may have a higher leakage rate for smoke than in their\nfinal configuration because some openings for cables and other services cannot be tightened before all\ninstallation work is finished. The mitigating measures personnel have to apply to take account of this are\nidentical to those in the service installation sub-phase: minimisation of combustible material, rigorous\n496\n\ntraining of workers performing hot work in extinguishing and alarm procedures, self-rescue mask and\nevacuation training for all workers.\n9.6\nConclusion\nThe safety concept outlined in this report emphasises a comprehensive and integrated approach to safety\nthroughout all phases of the proposed facility. From the initial construction and installation phases to\nthe long-term operation of the collider, safety systems to manage risks associated with both normal and\naccident scenarios have been studied.\nThis concept demonstrates the feasibility, in terms of life safety, of the current baseline layout and\ndesign for the FCC-ee. However, any modification of the proposed baseline will require an update of the\nconcept and the re-assessment of its safety effectiveness.\nMoving forward, a continuous risk assessment and iterative enhancement of the concept is essen-\ntial for the evolving nature of the project. Additionally, it is crucial to address the remaining open points\nand research gaps that were identified during the development of the concept.\nAs the effort progresses, the safety concept will incorporate other safety objectives, maintaining a\nstrong safety-oriented approach in the design of this unprecedented facility.\n497\n\n498\n\nChapter 10\nFCC-hh collider design and performance\n10.1\nDesign and performance\nThe Future Circular Collider (FCC) integrated programme offers the most powerful post-LHC experi-\nmental infrastructure proposed to address key open questions in particle physics. It envisions an initial\nelectron-positron collider phase, FCC-ee, which will later be followed by a proton-proton collider, both\nof which will be installed in the same tunnel of approximately 91 km in circumference, close to CERN.\nThe hadron collider, FCC-hh, would operate at a centre-of-mass energy of about 85 TeV (or\nabove), extending the energy frontier by almost an order of magnitude compared with the LHC, and\nproviding a 5- to 10-times higher integrated luminosity than the upcoming High-Luminosity LHC. The\nmass reach for direct discovery at FCC-hh will amount to several tens of TeV, and it will allow, for\nexample, the direct production of new particles, whose existence could already be indirectly exposed\nby precision measurements at FCC-ee. The FCC-hh hadron collider can also accommodate ion and\nlepton-hadron collision options, allowing complementary physics explorations.\nThe FCC-hh accelerator configuration described in this chapter, including its layout and injector\noptions, preserves the rich potential for a diverse physics programme, ranging from heavy ion collisions\nto a dedicated flavour or forward physics programmes, as are familiar from the LHC. Examples of this\npotential were amply discussed in the CDR and are briefly reviewed in Section 1.2 of Volume 1. Fur-\nthermore, it is expected that the 4-fold symmetry of the interaction regions will add flexibility and boost\nperformance to the exploitation of the two lower-luminosity interaction points.\nThe FCC integrated programme follows the successful example of the past Large Electron Positron\nCollider (LEP) and Large Hadron Collider (LHC) projects at CERN, which used one and the same\ninfrastructure for successively realising two large collider projects. Inspired by the sequence of LEP and\nLHC, the comprehensive long-term FCC programme maximises the opportunities of physics. The lepton\nand hadron colliders, FCC-ee and FCC-hh, would profit from common civil engineering and also from\nsharing much of the technical infrastructure. The updated baseline layout of the FCC-ee electron-positron\ncollider and its injector design are fully compatible with the demands of the future hadron collider (FCC-\nhh), and do not compromise the latter\u2019s performance. The main ring optics and RF configurations for\nboth colliders were refined to simplify operation across the energy range of FCC-ee and to enable a\nsmooth transition to FCC-hh after the completion of the FCC-ee research programme.\nThe FCC-hh baseline assumes 14 T Nb3Sn magnets, that are compatible with a collision centre-\nof-mass energy of 85 TeV. An R&D path towards HTS magnets would enable higher collision energies.\nThe present design allows four collision points and experiments. The experience gained from the Phase II\nupgrades of the LHC detectors for the HL-LHC, developments for further exploitation of the LHC and\nongoing detector R&D for future Higgs factories will be important stepping stones for the development\nof the FCC-hh experiments.\nIn the next sections, the layout for the collider, the injector options, and the injection lines will be\ndescribed. Following this, Section 10.4 describes the pathway to developing the key technology required\nfor the FCC-hh: the development of high-field magnets based on both the 14 T Nb3Sn technology and\nhigher-field HTS, that could enable higher collision energies and/or cost savings. Teams around the\nworld are pursuing the development of the requisite magnet technology. The primary regions involved in\nthe advancement of magnet technology include the US, Europe, Japan, and China. In each region, there\nare growing efforts to coordinate and integrate research internally among universities, laboratories, and,\nto some degree, industry.\n499\n\nAn R&D plan is outlined which shall close the gap between the near- to medium-term scope\n(5\u201310 years) of the European High Field Magnet (HFM) Programme and the US Magnet Development\nProgramme on the one hand, and the long-term needs of the FCC integrated programme on the other\nhand. It complements the bottom-up, technology-driven approach of the HFM Programme with a top-\ndown, long-term strategic roadmap derived from the requirements of the FCC-hh. Moreover, this plan\nwill provide a framework for the coordination of R&D efforts on a global scale and over a sustained\nperiod of time.\nFinally, this chapter closes with a discussion of some other accelerator systems that would be\nrequired for the FCC-hh, including cryogenic plants and their distribution.\n10.2\nFCC-hh layout and optics\n10.2.1\nLayout of the FCC-hh ring\nSince the publication of the Conceptual Design Report (CDR) [10] several studies have been carried out\nto provide a revised and improved version of the ring layout. The key concepts that have been used\nto determine the main properties of the new layout can be summarised as follows: the outcome of the\nplacement studies; the proposal to equip the new layout of the FCC-ee ring with four experiment points;\nthe considerations on the harmonic number of the FCC-hh ring that should be made compatible with that\nof its injector.\nThe placement studies provided strong indications that the length of the FCC-hh ring had to be\nshortened to satisfy the multiple constraints that emerged during the investigations. Most of the reduction\ncompared with the CDR was achieved by reducing the lengths of the arcs, keeping the total length of the\nstraight sections constant. However, a final adjustment also reduced the length of the straight sections.\nThe FCC-ee design introduced the important constraint that the ring should assume a four-fold\nsymmetry and four-fold superperiodicity, to enable four experiment insertions with optimum luminosity\nperformance. This feature, which must also be fulfilled by \u2013 and may similarly benefit \u2013 the FCC-hh ring,\nradically changes the configuration with respect to what was presented in the CDR [10]. The functions\nof the various technical insertions had to be reviewed and different functions to be combined differently,\nwhich resulted in a modified layout and optics design for most of the insertions. Another major change\nin the layout is the radial displacement of the interaction points (IP) of the FCC-hh ring to align with the\nIP positions of the FCC-ee ring. This geometric modification has a significant impact, as the dispersion\nsuppressor is employed to control the new ring geometry. This adjustment must be implemented while\nensuring the feasibility of the optics, particularly maintaining proper dispersion matching. This change\nhas an important side effect on the optimisation of size and layout of the experiment caverns, with the\noption of sharing the detector\u2019s services, infrastructure, and possibly components between the lepton and\nthe hadron FCC colliders [503]. A further major modification to the ring layout is the reduction of the\nnumber of surface sites from twelve to eight, which is beneficial in terms of overall costs and which also\nfacilitated the placement. The last, but certainly not least, change with respect to the original baseline\nconfiguration is the proposal to locate the last part of the transfer lines inside the ring tunnel. This choice\nhas the benefit of reducing the length of the tunnel needed for the transfer lines from the injector to the\nFCC-hh.\nThe proposed layout of the FCC-hh ring is shown in Fig. 10.1. The circumference is 90.66 km,\nwith 2032 m long technical insertions and experiment insertions accommodated in a straight tunnel of\nlength of 1400 m, with approximately 965 m distance between the last dipole magnets on either side of\nthe IP. The experiment insertions are located in Point A (PA), Point D (PD), Point G (PG), and Point J\n(PJ). The IPs of the hadron and lepton rings are superimposed within a few millimetres.\nFigure 10.2 shows a comparison of the three rings on the right side of an experiment insertion.\nThe crossing angle between the two FCC-ee rings is clearly visible, with the FCC-hh straight section in\nbetween the two rings. Further away from the IP, the three rings converge and are fully compatible with\n500\n\nFig. 10.1: Overall view of the layout of the new FCC-hh ring configuration. The functions of the various\ninsertion regions are mentioned. The experiment straight sections are located with respect to the four-\nfold symmetry of the ring. The length of the straight sections is also mentioned.\na single tunnel. Detailed studies of the geometry of the hadron ring optimised the current layout so as\nto reduce the radial distance between the three rings, with a beneficial impact on the integration. This\nimportant result was achieved by carefully displacing the main dipoles in the region of the dispersion\nsuppressors (see the next section). Applying the same recipe, also in the technical insertions the geome-\ntries of the hadron and lepton rings were matched as closely as possible, with a radial distance between\nthe rings of approximately 30 cm).\nThe merging of secondary experiments with injection systems, which resembles the concept im-\nplemented in the LHC, was abandoned because it would have generated transfer lines that were too long.\nThe injection of the clockwise beam is performed in PB, and it is combined with the momentum colli-\nmation, whereas the injection of the counter-clockwise beam is performed in PL, and it is combined with\nthe RF system. The beam is always injected into the outer beam channel of the FCC-hh accelerator. The\ntwo other technical insertions, points PF and PH, each have a single role: to house the beam dump and\nthe betatron collimation systems.\nA review of the FCC-hh quadrupole families, including their magnetic properties and the mechan-\nical apertures, has been carried out. The list of magnet families used in the current layout of the FCC-hh\nring is presented in Table 10.1. Several of the proposed families in the insertions could still be further\noptimised as discussed below.\nBefore entering the details of the discussion of the design of the magnetic lattices of the new layout\nof the FCC-hh, it is important to mention a crucial change with respect to the CDR. The nominal field of\nthe main dipoles is 14 T, which corresponds to the centre-of-mass energies of 84.6 TeV. The geometry\nof the proposed layout is fully compatible with the new ranges of dipole field and centre-of-mass energy.\n501\n\nFig. 10.2: Comparison of the geometry of the FCC-hh ring and for the two FCC-ee rings in the vicinity\nof PA. The same situation occurs in the other three experiment insertions.\nIn the rest of the document, the strength of the quadrupoles is expressed for a beam energy of 45 TeV,\nwhich amounts to adding a 6% safety margin to the available magnetic strength. When citing minimum\nmagnet strengths, an injection energy of 3.3 TeV is considered, as had been adopted by the CDR. These\nvalue could be scaled linearly to alternative lower injection energies of 1.7 or 1.3 TeV.\n10.2.2\nDesign of regular arcs and dispersion suppressors\nThe review of the FCC-hh lattice imposed by the placement studies was used to reassess some of the\nprincipal assumptions made for the former CDR layout [10]. This is the case for the choice of regular arc\ncell length. For highest-energy hadron accelerators, designing the lattice with a longer regular cell offers\none clear advantage. Namely, the longer cell leads to an increase in the dipole filling factor (for the FCC-\nhh, this factor was increased from 0.8 as in the CDR to 0.82 at present), with an accompanying increase\nin the values of beta-functions and dispersion. The larger optical functions enhance the efficiency of\nthe correction systems, such as the chromatic sextupoles and Landau octupoles, but they also render\nthe beam more sensitive to magnetic field errors, in particular at injection, putting additional demands\non the magnet design and the correction systems. An obvious upper limit to the cell length is set by\nthe physical dimensions of the vacuum chamber, the injected beam emittance, and the required beam\naperture. In Ref. [504], the target aperture values are given as 13.4 \u03c3 at injection energy and 15.5 \u03c3 at\ncollision energy, where \u03c3 denotes the nominal rms beam size computed for a normalised rms emittance\nof 2.2 \u00b5m).\nIn Fig. 10.3, the regular cell with optical parameters and available beam aperture is shown for the\ncurrent layout. The number of main dipoles per cell has increased from 12 in the CDR [10] to 16. The\noverall cell layout with the dipole (blue) and quadrupole (red) magnets is indicated at the top. The phase\nadvance per cell was kept at 90\u25e6. The cell length is about 275.8 m, to be compared with about 213.0 m\nfor the CDR. The change in the arc cell results in a larger value of the beta-functions and dispersion,\nwhich has several positive and also a few negative side effects. Even for this longer cell, two cryo-\njumpers, connected to the quadrupole cryostats, are sufficient to feed all superconducting magnets from\nthe cryogenic line [505]. The beneficial increase in cell length and the induced increase in the values of\noptical parameters require a small adaptation of the dimensions of the beamscreen. Figure 10.3 shows\nthe cross section of the beam screen from the CDR [10] (dotted line) and a proposed new version with\n502\n\nTable 10.1: Main parameters of the dipole and quadrupole families used in the entire ring. All fields\nare referred to 45 TeV to include a safety margin on the required magnetic strength. Note that the\norientation of the various aperture types might change according to the polarity of the quadrupole, in\norder to optimise the beam aperture.\nNAME Magnetic 1 Nominal Nominal\nAperture\nAperture\nCoil\nNumber\nlength\nfield\ngradient\ncross section\ndimensions\naperture\nof\ndiameter magnets\n[m]\n[T]\n[T/m]\n[mm]\n[mm]\nMB\n14.187\n14\nNA\nBeamscreen 2\n\u2013\n50\n4464\nMBX\n10.0\n14.6\nNA\nOctagon 3\n33.1/33.1/13.5/76.5\n116\n8\nMBR\n13.0\n5.6\nNA\nOctagon\n33.1/33.1/13.5/76.5\n80\n24\nMBW\n14.0\n1.7\nNA\nEllipse 4\n29.5/22.0\n20\nMQ\n6.4\nNA\n375.0\nBeamscreen\n\u2013\n50\n536\nMQ\n9.6\nNA\n375.0\nBeamscreen\n\u2013\n50\n8\nMQ\n10.0\nNA\n375.0\nBeamscreen\n\u2013\n50\n8\nMQ\n12.0\nNA\n375.0\nBeamscreen\n\u2013\n50\n24\nMQM\n6.0\nNA\n375.0\nRectellipse 5\n15.0/13.2, 15.0/15.0\n50\n17\nMQ1\n14.3\nNA\n130.0\nCircle\n36.49\n164\n16\nMQ2\n12.5\nNA\n105.0\nCircle\n58.24\n210\n32\nMQ3\n14.3\nNA\n105.0\nCircle\n58.24\n210\n16\nMQ4\n12.0\nNA\n175.0\nRectellipse\n28.9/24.0, 28.9/28.9\n70\n8\nMQ5\n12.0\nNA\n260.0\nRectellipse\n20.0/18.2, 20.0/20.0\n60\n8\nMQR\n6.4\nNA\n280.0\nRectellipse\n20.0/18.2, 20.0/20.0\n60\n8\nMQY\n6.0\nNA\n200.0\nRectellipse\n28.9/24.0 - 28.9/28.9\n60\n2\nMQY\n9.1\nNA\n200.0\nRectellipse\n28.9/24.0, 28.9/28.9\n60\n14\nMQYL\n12.8\nNA\n200.0\nRectellipse\n28.9/24.0, 28.9/28.9\n60\n6\nMQW\n4.0\nNA\n40.0\nEllipse\n26.1/15.3\n44\n1 The specified magnetic length corresponds to an individual magnet. Multiple magnets may be concatenated to form a\nlonger structure if necessary.\n2 This cross-section corresponds to the shape depicted in Fig. 10.3 (right) and is defined by points.\n3 An octagon is defined by four numbers: the half width and half height along main axes, two angles sustaining the cut\ncorner in the first quadrant, given in radians and in order of increasing values.\n4 An ellipse is defined by two numbers specifying the horizontal ah and vertical av semi-axes, given in the form ah/av.\n5 A rectellipse is a shape obtained by the intersection of a rectangle and an ellipse [116,211] and is defined by four numbers\nspecifying the half-width rw and half-height rh of the rectangle, horizontal ah and vertical av semi-axes of the ellipse,\ngiven in the form rw/rh, ah/av. Note that, in general, the ellipse is replaced by a circle.\nlarger horizontal aperture (continuous line). These changes in the beamscreen dimensions will require a\nmore detailed design validation in the next study phase.\nThe performance of the corrector systems that are present in the arc was also evaluated and re-\nviewed [506], and the new layout of a short straight section of a periodic FODO cell is shown in Fig. 10.4.\nAs a direct consequence of the cell lengthening, each arc consists of fewer cells, reducing the number of\navailable slots for installing the required correctors. However, the larger beta-functions and dispersion\nenhance the effectiveness of some correctors in their roles. The properties of the correction circuits in\nthe arcs are listed in Table 10.2, where Nc represents the number of circuits per arc, while Nm stands\nfor the number of magnets per circuit. The symbol n in the units represents the order of the magnetic\nmultipole, which is 0 for a dipole.\nThe analysis of corrector efficiencies has identified several additional optimisations that can be\n503\n\nFig. 10.3: Layout, optical parameters, and dispersion of the 16-dipole periodic FODO cell design (left)\nand cross section of the beamscreen compatible with the aperture requirements of the arc cell (right).\nThe horizontal line in the aperture plot represents the minimum value acceptable.\napplied to the layout of the Short Straight Sections (SSS). These improvements will enhance the dipole\nfilling factor of the collider and will be incorporated into the next iteration of the FCC-hh ring lattice. In\ngeneral, a shortening of each SSS of about 4 m can be envisaged. Another possible source of gains in the\nenergy reach of FCC-hh can come from increasing the length of the main dipole. Even for this aspect,\nthe change in the design of the periodic FODO cell will be part of the next version of the magnetic lattice.\nFig. 10.4: Layout of the periodic FODO cell short straight section (left to right: sextupole spool piece\nMCS, beam position monitor BPM, chromatic sextupole MS, main quadrupole MQ, Landau octupole\nMO, trim quadrupole MQT, skew quadrupole MQS, orbit corrector MCB, and decapole spool piece\nMCD)\nThe dispersion suppressors (DS) were reviewed starting from the CDR design [10]. The presently\nproposed layouts are shown in Fig. 10.5, where the DS for the transition between the regular arc and\nexperiment insertion is displayed at the top, and the one connecting the regular arc and a technical\ninsertion at the bottom.\nThe complexity of the design of the DS for the experiment insertions resides in the need to control\nthe whole geometry and to radially displace the IP position. The control of the geometry is achieved by\n504\n\nTable 10.2: Correctors circuits properties and capabilities for the FCC-hh Ring. For the correction of the\nlinear coupling, the resonance strength indicated by C\u2212is defined as C\u2212=\n1\n2\u03c0\nR p\u03b2x\u03b2yksei(\u00b5x\u2212\u00b5y)ds,\nwhere \u03b2x,y, ks and \u00b5x,y are the beta functions, skew quadrupole gradient, and phase advances, respec-\ntively.\nLength\nStrength\nIntegral strength\nNc\nNm\nCorrectors\n[m]\n[Tm\u2212n]\n[Tm1\u2212n]\ncapabilities\nDipole orbit correc-\n1.2\n4.5\n5.4\n61\n1\nresidual rms orbit\ntors MCB\n\u22640.3 mm\nTrim quadrupoles\n0.5\n220\n110\n2\n8\nup to 0.15 tune shift\nMQT\nwith \u03b2-beating \u22641%\nSkew quadrupoles\n0.5\n220\n110\n2\n2\nC\u2212< 10\u22124\nMQS\nChromatic sextupoles\n1.2\n7000\n8400\n2\n28\ncontrol around Q\u2032 = 10\nMCS\nwith squeezed optics\nLandau octupoles\n0.5\n2.2 \u00d7 105\n1.1 \u00d7 105\n2\n18\nSame amplitude\nMO\ndetuning as in CDR\nFig. 10.5: Layout of the dispersion suppressor on the left of an experiment insertion (top) and technical\ninsertion (bottom).\nselectively displacing blocks of the main dipoles, whereas the quadrupoles are kept in regular positions\nto ensure control of the optics and dispersion. The DS starts just behind Q19 and ends with Q6, and\nits extent is an essential parameter to ensure optimal geometry control. The quadrupoles in the DS are\nassumed to have independent powering, which ensures enough optical flexibility. In practice, this can\nbe achieved with main quadrupoles, powered in series with the other main quadrupoles in the regular\npart of the arc, and trim quadrupoles to ensure independent control of the gradient generated at a given\nring location. This scheme has been successfully implemented in the LHC [116] and provides optimised\nhardware use (quadrupoles and power converters). However, on most occasions, these trim quadrupoles\nmust be set to the opposite polarity of that of the main quadrupole they accompany, trading efficiency for\nspace and simplicity. The details of the quadrupole families and their powering will be studied in more\ndetail at a later stage.\nThe DS for the technical insertions is shorter, running between, but not including, Q15 and Q7.\nIn this case, the main role of the DS is to control the dispersion since the ring geometry does not need\n505\n\nto be changed in the technical insertions. It should also provide enough optical flexibility to enable the\nmatching of the optical parameters of the regular arc with those of the various technical insertions.\nBoth types of DS have short gaps (of the order of 2 m) to allow the installation of collimators, the\nso-called TCLD collimators, which should absorb particles that have lost energy in interactions with the\nprimary and secondary collimators.\n10.2.3\nExperiment straight sections\nThe experiment insertions are the core of the FCC-hh ring design, both for the complex geometry needed\nto match the radial position of the IPs with those of the FCC-ee and for the requirement to achieve the\nlow \u03b2\u2217value needed to reach the target luminosity performance. At injection energy, \u03b2\u2217= 10 m (like\nthe LHC case [116]), which is then reduced to \u03b2\u2217= 30 cm at collision energy. The squeeze of \u03b2\u2217will\ntake place, at least partially, during the energy ramp, based on considerations of the available aperture\nthat indicate the minimum value \u03b2\u2217for a given beam energy.\nThe layout of the four experimental insertions is identical to maintain consistent optics. However,\nthe polarity of the separation dipoles varies, as both beams change between outer and inner magnet aper-\nture at the different insertions. This causes a slight variation in the horizontal dispersion function, which\nmanifests itself in two distinct forms. Two important differences with respect to the layout presented\nin Ref. [10] were implemented: the strictly straight beam-line section is about 965 m instead of 1400 m\nas a consequence of the radial displacement of the IP. Furthermore, the separation (MBX type) and re-\ncombination (MBR type) dipoles are superconducting to reduce their total length, which is important\ngiven the reduced length of the straight section. This set up resembles what is being implemented for the\nHL-LHC [8,9], where the normal-conducting D1 of the LHC will be replaced by a superconducting one.\nThe D2 recombination dipole is already superconducting in the LHC and will remain so in the HL-LHC,\nalthough with an increased coil aperture.\nIn terms of the magnetic field, the integrated strength of the separation and recombination dipoles\nis 146 Tm at 45 TeV, and the nominal fields of the D1 and D2 magnets are 14.6 T for and 5.6 T, respec-\ntively. The radius of the coil aperture has been determined and found to be 58 mm for D1 and 40 mm\nD2. For comparison purposes, the coil radius of the HL-LHC D1 and D2 separation and recombination\ndipoles is 75 mm and 52.2 mm, respectively.\nThe optical parameters, dispersion, and beam aperture for the layout of the PD experiment inser-\ntion are shown in Fig. 10.6 for the solution with \u03b2\u2217= 10 m for the injection energy (left) and \u03b2\u2217= 30 cm\nfor collision energy. The most striking difference is the maximum value of the beta-functions that reaches\nabout 2000 m and 70 000 m for injection and collision optics, respectively. The target aperture values\nfor the two cases differ and so do the bottleneck locations. For the injection optics, aperture limits ap-\npear in the dispersion suppressors surrounding the straight section. Conversely, for the collision optics,\nincluding the orbit from the crossing angle, the aperture limit is first reached in the separation dipole\n(D1), followed by the inner triplet, while the rest of the insertion provides aperture values that largely\nexceed the target. This suggests that, in the future, the aperture of the D1 separation dipole should be\nincreased. On the positive side, in view the available aperture margin in Q1, a further reduction of \u03b2\u2217\ncould be envisaged.\nNote that the ring chromaticity varies during the squeeze due to the contribution of the experi-\nmental insertions to the overall ring chromaticity. The strength of the chromatic sextupoles needed to\nobtain Q\u2032 = 10 when \u03b2\u2217= 10 m is approximately 19 % of that required to obtain the same Q\u2032 when\n\u03b2\u2217= 30 cm.\nA solution has been found for the squeeze from \u03b2\u2217= 10 m to \u03b2\u2217= 30 cm and the corresponding\nquadrupole strengths are shown in Fig. 10.7. The starting point for this transition is not compatible with\nthe aperture requirements at injection energy. Therefore, the transformation of the nominal injection\n506\n\nFig. 10.6: Optical parameters, dispersion, and beam aperture for the injection optics of the experiment\ninsertion at PA (left, \u03b2\u2217= 10 m) and the collision optics (right, \u03b2\u2217= 30 cm) including crossing angle.\nThe horizontal line in the aperture plot represents the minimum value acceptable.\noptics to the starting point of the squeeze sequence is envisioned during the energy ramp1, as the squeeze\nsequence satisfies the aperture requirements when the beam energy reaches 10 TeV or higher.\nFig. 10.7: Quadrupole strength during the \u03b2\u2217squeeze for the left and right sides of the experiment\ninsertion (left and right plots, respectively).\nThe strength values of the quadrupoles that generate the two optical configurations of the experi-\nment insertions are summarised in Table 10.3.\nA cornerstone feature for the performance of the experiment insertions is the crossing scheme. A\nset of correctors generates a local orbit bump around the IP to mitigate the effect of long-range beam-\nbeam interactions [10]. The orbit also separates the beams, preventing collisions until the beams are at\ntop energy and the optics is squeezed. Although the bump is fully corrected and, therefore, transparent\nto the rest of the ring, the horizontal and vertical dispersion generated must be taken into account. The\nstrategy followed is similar to that employed in the LHC [116]. At injection, the quadrupoles in the\ndispersion suppressors are used to rematch the horizontal dispersion to the neighbouring arcs, while\nthe standing vertical dispersion is small enough that it does not necessitate countermeasures. When\n1The duration of the energy ramp is approximately 20 min.\n507\n\nTable 10.3: Strength of the insertion quadrupoles for the injection optics of the experiment insertion at\nPA (second column, \u03b2\u2217= 10 m) and the collision optics (third column, \u03b2\u2217= 30 cm). All the gradients\ncorrespond to 45 TeV.\nNAME\nGradient\nGradient\nGradient\nGradient\nMaximum gradient\n[T/m]\n[T/m]\n[T/m]\n[T/m]\n[T/m]\nMQ.14L\n\u2212127.9\n\u2212172.3\n\u2212127.9\n\u2212172.3\n375.0\nMQ.13L\n119.9\n133.1\n119.9\n133.1\n375.0\nMQ.12L\n\u2212114.1\n\u2212102.9\n\u2212114.1\n\u2212102.9\n375.0\nMQ.11L\n94.9\n28.2\n94.9\n28.2\n375.0\nMQ.10L\n\u2212116.6\n\u221240.9\n\u2212116.6\n\u221240.9\n375.0\nMQ.9L\n190.9\n146.5\n190.9\n146.5\n375.0\nMQ.8L\n\u2212176.4\n\u221270.1\n\u2212176.4\n\u221270.1\n375.0\nMQ.7L\n222.7\n170.6\n222.7\n170.6\n375.0\nMQ.6L\n\u2212129.1\n\u2212311.2\n\u2212129.1\n\u2212311.2\n375.0\nMQY.5L\n149.3\n127.8\n155.1\n128.0\n260.0\nMQY.4L\n\u221288.0\n\u2212151.7\n\u221290.9\n\u2212151.6\n175.0\nMQXE.3L\n94.8\n94.8\n94.8\n94.8\n105.0\nMQXD.2L\n\u221292.9\n\u221292.9\n\u221292.9\n\u221292.9\n105.0\nMQXC.1L\n114.1\n114.1\n114.1\n114.1\n130.0\nMQXC.1R\n\u2212114.1\n\u2212114.1\n\u2212114.1\n\u2212114.1\n130.0\nMQXD.2R\n92.9\n92.9\n92.9\n92.9\n105.0\nMQXE.3R\n\u221294.8\n\u221294.8\n\u221294.8\n\u221294.8\n105.0\nMQY.4R\n60.0\n75.8\n60.0\n74.6\n175.0\nMQY.5R\n\u221272.7\n\u221264.8\n\u221270.0\n\u221263.5\n260.0\nMQ.6R\n124.4\n8.6\n124.4\n8.6\n375.0\nMQ.7R\n\u2212149.2\n\u2212187.9\n\u2212149.2\n\u2212187.9\n375.0\nMQ.8R\n166.7\n198.9\n166.7\n198.9\n375.0\nMQ.9R\n\u2212117.2\n\u2212140.0\n\u2212117.2\n\u2212140.0\n375.0\nMQ.10R\n85.4\n178.1\n85.4\n178.1\n375.0\nMQ.11R\n\u2212101.2\n\u221290.3\n\u2212101.2\n\u221290.3\n375.0\nMQ.12R\n108.2\n122.7\n108.2\n122.7\n375.0\nMQ.13R\n\u2212120.8\n\u2212146.0\n\u2212120.8\n\u2212146.0\n375.0\nMQ.14R\n107.2\n153.9\n107.2\n153.9\n375.0\ntransitioning to collision optics, a set of orbit correctors in the arc is used to create a closed-orbit bump\nthat exploits the field of the chromatic sextupoles to cancel the vertical dispersion. This is illustrated\nin Fig. 10.8, where the crossing and separation bumps are presented at injection energy (top) and at top\nenergy (bottom) for the nominal value of the half-crossing angle and half-separation that are 100 \u00b5rad\nand 1.5 mm, respectively.\nThe orbit bump at top energy that created the dispersion bump is clearly visible, and the overall\ncorrection of the spurious vertical dispersion is good. The primary constraint is the alternating cross-\ning plane between PA and PG. The crossing and separation schemes in all experimental insertions are\ndesigned to accommodate all possible combinations of crossing and separation planes while ensuring\ncompatibility with this constraint.\n508\n\nFig. 10.8: Closed dispersion and orbit with crossing angle and separation at injection (top) and collision\n(bottom) energies with a closer look at the experimental insertions.\n10.2.4\nBeam dump\nAs described above, changes in the ring layout with respect to CDR [10] reduced the length of the tech-\nnical straight sections from 2800 m to 2032 m. The new layout accommodates the dump systems for\nboth beams at PF, as a result of civil engineering considerations. At an intermediate stage [507], the\npossibility of merging the dump and injection systems for the clockwise beam in PB was considered.\nHowever, this option was deemed unfeasible, primarily due to machine protection concerns arising from\nthe complexities of handling combined failure scenarios for the injection and dump systems. The nec-\nessary layout modifications could only be resolved by dedicating a technical insertion exclusively to\nthe beam dump. The system is illustrated in Fig. 10.9 (left), where the circulating and extracted beam\nenvelopes are shown for the nominal extraction case, ensuring sufficient clearance.\nThe externally activated dumping system has the function to extract and dilute the beam, and to\ndispose the entire extracted beam onto an external absorber located 2.5 km from the extraction point in\n509\n\n0\n500\n1000\n1500\n2000\n2500\nbetx [m]\nbety [m]\n0\n300\n600\n900\n1200\n1500\n1800\n2100\n2400\n2700\nLongitudinal position [m]\n0.04\n0.02\n0.00\n0.02\n0.04\n0.06\nHor envelope [m]\nVer envelope (15sig) [m]\nExtracted beam (6sig) [m]\n0\n500\n1000\n1500\n2000\n2500\nbetx [m]\nbety [m]\n0\n300\n600\n900\n1200\n1500\n1800\n2100\n2400\n2700\nLongitudinal position [m]\n0.04\n0.02\n0.00\n0.02\n0.04\n0.06\nHor envelope [m]\nVer envelope (15sig) [m]\nMisfired inj/extr beam (6sig) [m]\nFig. 10.9: Left: Optics (top) and beam envelopes and active elements (bottom) for the extraction straight\nsection around PF. Right: Dump system failure scenario: asynchronous beam dump. The configurations\nshown refer to collision energy.\na dedicated cavern. The design of the complete dump system is driven both conceptually and hardware-\nwise by machine protection considerations [508].\nThe extraction system design had to be adapted to the reduced length of the straight section, lead-\ning to an increased length of the superconducting extraction septa (utilising superconducting shield and\ntruncated cosine-theta technologies), as well as higher switch voltage and an extended system length\nfor the extraction kickers. At this stage, it is challenging to predict the switch technology that will be\navailable on the FCC-hh timescale. However, if significant difficulties arise in achieving the required\nhardware parameters, an alternative approach could allow the extracted beam to pass through an aper-\nture in the cryostat of the downstream quadrupole, reducing the required septum deflection angle by\napproximately one-third of its nominal strength.\nThe design of systems involving fast pulsed devices acting in a single turn on a beam with un-\nprecedented power, such as that of the FCC-hh, is driven by their failure scenarios. A relevant failure\nscenario concerning the asynchronous beam dump is shown in Fig.10.9 (right), where the misfiring of\nan extraction or dilution kicker leads to an immediate trigger of the full system that, however, is not\nsynchronised with the beam abort gap. Dedicated protection absorbers are expected to protect the down-\nstream machine from particle spray. The damage limit of the absorbers drives the extraction kicker rise\ntime. This limit is most critical for global machine protection, in particular in the case that a beam abort\noccurs with the full beam at top energy. For this specific failure scenario, only a single dumped beam\nis shown. The systems for the other beam are arranged symmetrically around the centre of the straight\nsection.\nThe general optical parameters and the beam aperture are shown in Fig. 10.10\nThe strength and aperture values for the quadrupoles that generate the optical configuration of the\nbeam dump are summarised in Table 10.4.\n10.2.5\nRF and injection straight section\nThe technical insertion at PL is used to accommodate the RF system and the injection of the counter-\nclockwise beam. The main constraints imposed by the RF system are the increased inter-beam distance,\nwhich must reach 420 mm to accommodate the accelerating cavities, and the cancellation of dispersion\nin the straight section where the cavities are located to minimise synchro-betatron coupling. These\nconstraints are met by introducing two doglegs that both increase the inter-beam distance and ensure that\nthe dispersion and its derivative are zero in the central part of the insertion.\n510\n\nFig. 10.10: Optical parameters, dispersion, and beam aperture at injection of two configurations of the\ndump insertion with different settings in the dispersion suppressors to match the ring to injection (left)\nand collision (right) tunes. MKD and MSD positions are highlighted in black. The horizontal line in the\naperture plot represents the minimum value acceptable.\nThe beam is injected in the vertical direction, as the transfer line will run above the main ring\nmagnets, just on top of the external aperture of the circulating beam. Optimal injection conditions require\na phase advance of 90\u25e6between the kicker and the injection protection dump, and maximising the value\nof p\u03b2x\u03b2y at the location of the injection protection dump. An additional constraint in the design of the\ninjection of the counter-clockwise beam is to use the same hardware as installed in PB for the injection\nof the clockwise beam: this does not pose any serious challenge for the overall design of the insertion.\nFigure 10.11 shows the vertical trajectory of the injected beam, assuming a difference in height\nbetween the circulating and injected beams of 1250 mm. This first block of bending magnets represents\nthe end of the transfer line, followed by a downward bending dipole, a second dipole that starts to\ndeflect the trajectory to become parallel with the plane of the collider and then the septa, with a field that\ndecreases with the reduction of the thickness of the septum blade (the details are given in Table 10.5). The\nlast block of bending magnets represents the kickers that cancel the residual angle of the injected beam.\nThe second dipole is a recent addition to the magnetic sequence that helps to reduce the longitudinal\nfootprint of the insertion dedicated to the injection elements and is labelled MBWI in Table 10.5. It is\ninstalled in a region where the injected and the circulating beams are separated enough that a conventional\ndipole can be used rather than a septa-type magnet. This allows using a stronger magnetic field of 1.4 T\nto accelerate the geometrical transition between the plane of the transfer line to that of the collider.\nNote that the quadrupole located in between the two groups of bending devices is used to provide\nan additional dipole kick exploiting the off-axis traversal of the beam.\nFigure 10.12 shows the optical parameters, dispersion, and beam aperture at injection, correspond-\ning to the most critical configuration. The part of the insertion close to the DS on the right-hand side\n(light-blue box in the figure) is where the injection system is located: it is left empty here, as the injection\nelements are inactive for the circulating beam, and they do not affect the beam whose optics are shown\nhere. The section envisaged for the RF system (green box in the figure) has a length of approximately\n870 m.\n511\n\nTable 10.4: Strength of the insertion quadrupoles for the optics of the technical insertion at PF (beam\ndump) and its dispersion suppressors. All the gradients correspond to 45 TeV.\nNAME\nGradient\nMaximum gradient\n[T/m]\n[T/m]\nMQ.14LF.B1\n116.47\n375.0\nMQ.13LF.B1\n\u2212120.36\n375.0\nMQ.12LF.B1\n116.72\n375.0\nMQ.11LF.B1\n\u2212115.10\n375.0\nMQ.10LF.B1\n155.11\n375.0\nMQ.9LF.B1\n\u2212160.22\n375.0\nMQ.8LF.B1\n62.91\n375.0\nMQM.B7LF.B1\n\u2212151.48\n375.0\nMQM.A7LF.B1\n\u2212151.48\n375.0\nMQY.6LF.B1\n43.49\n200.0\nMQY.5LF.B1\n\u221247.69\n200.0\nMQY.4LF.B1\n24.98\n200.0\nMQY.4RF.B1\n\u221224.98\n200.0\nMQY.5RF.B1\n47.69\n200.0\nMQY.6RF.B1\n\u221243.49\n200.0\nMQM.A7RF.B1\n136.32\n375.0\nMQM.B7RF.B1\n136.32\n375.0\nMQ.8RF.B1\n\u221249.48\n375.0\nMQ.9RF.B1\n169.34\n375.0\nMQ.10RF.B1\n\u2212127.26\n375.0\nMQ.11RF.B1\n142.57\n375.0\nMQ.12RF.B1\n\u2212116.81\n375.0\nMQ.13RF.B1\n125.28\n375.0\nMQ.14RF.B1\n\u2212131.00\n375.0\nTable 10.6 summarises the strength of the quadrupoles that generate the optical configuration of\nRF and injection insertion.\n10.2.6\nBetatron collimation\nThe collimation system is meant to clean the betatron halo and off-momentum particles surrounding the\nmain beam. These two functions are performed by two subsystems located in two insertions to allow for\ndedicated optical conditions. Cleaning of the betatron halo requires small values of the dispersion func-\ntion and appropriate phase advances between the various collimation stages. Cleaning off-momentum\nparticles requires large normalised dispersion2 values and is discussed in further detail in Section 10.2.7.\nA side effect of the collimation system is the beam impedance originating from the jaws that\nare close to the beam edge. Recently, for the HL-LHC, mitigation measures for the beam impedance\nbased on local changes to the beam optics were proposed (see Ref. [509, 510] and references therein),\nwhich aim at increasing the beta functions at the collimators. This novel concept has also already been\nincorporated into the optics design of the FCC-hh betatron collimation insertion.\nTwo additional novel features were implemented in the layout of the collimation insertions, both\nrelated to the geometry of the doglegs that are part of the insertions. The main function of doglegs in the\n2The normalised dispersion is defined as Dx/\u221a\u03b2x.\n512\n\nFig. 10.11: Trajectory in the vertical plane of the injected counter-clockwise beam from the transfer line\narc to the injection kicker (left) and a detailed view of the path through the septa (right). Exceptionally,\nthe description of the layout is made using the counter-clockwise beam as a reference.\nTable 10.5: Electromagnetic and aperture parameters of the septa, dipole, and kickers assumed for the\ninjection of the counter-clockwise beam.\nNAME\nActive length\nBlade thickness\nMagnetic field\nAperture\nAperture dimensions\n[m]\n[mm]\n[T]\ncross section\n[mm]\nMSI1\n8.0\n8\n0.7\nEllipse\n12.0 / 11.0\nMSI2\n5.0\n12\n1.0\nCircle\n16.0\nMSI3\n20.0\n18\n1.2\nCircle\n16.0\nMBWI\n70.0\nNA\n1.4\nCircle\n16.0\nMKI\n40.0\nNA\n0.024\nCircle\n18.3\nLHC collimation insertions is to filter out the neutral particles generated by the beam-matter interaction\nin the jaws of the collimators [511]. Thanks to the doglegs, the neutrals are prevented from depositing\nenergy in the coils of the first superconducting dipole on the opposite side of the insertion, i.e., at the\nbeginning of the DS. Hence, the LHC collimation geometry need not be exported to the FCc-hh, by\nrescaling it to the higher beam energy. Instead, it is sufficient to introduce the minimum deflection that\nbrings the neutrals out of the cross-section of the coils of the first superconducting dipole at the beginning\nof the downstream DS. This approach simplifies the layout of the doglegs and relaxes the requirements\nin terms of dipole strength needed to generate the doglegs. Based on these considerations, each of the\ntwo doglegs of the PH insertion is made of two dipole blocks (composed of two MBW-type dipoles) with\nopposite polarities, and each block generates 46.0 Tm at collision energy.\nThe second change is keeping the inter-beam distance constant along the whole straight insertion.\nIn fact, in the LHC, the arc inter-beam distance of 194 mm is increased in the collimation insertions to\n224 mm by the geometry of the doglegs of the two counter-rotating beams. In the layout of the FCC-\nhh collimation insertions, the inter-beam distance remains constant and has the same value as in the\narcs, namely 250 mm. This choice has a fundamental consequence, as in this case, not only the optical\nparameters are the same for the counter-rotating beams, but also the dispersion functions are the same.\nHence, this design choice facilitates having exactly identical layouts and optics for the two beams.\nThe Q6 quadrupoles, previously composed of six MQTLH magnets as in the LHC [116], have\n513\n\nFig. 10.12: Optical parameters, dispersion and beam aperture at injection, corresponding to the most\ncritical configuration for the optics of the RF and injection insertion for the anti-clockwise beam. Sec-\ntions dedicated to a specific function are highlighted: the area where the RF cavities may be located\n(green), injection protection devices (orange) and injection elements (light blue). The horizontal line in\nthe aperture plot represents the minimum value acceptable.\nbeen replaced in the new layouts by a single MQY quadrupole. This change optimises the beam aperture,\neliminating an unnecessary bottleneck.\nAdditionally, to maximise the available beam aperture, the orientation of the elliptical beam pipe\nin the MQW quadrupoles is adjusted according to the quadrupole polarity.\nThe betatron collimation subsystem is located in PH, and the corresponding layout and optical\nfunctions are shown in Fig. 10.13. As discussed above, a novel optical configuration featuring high-beta\nvalues has been designed to mitigate the beam impedance generated by the collimators. However, this\noptics is not suitable for the injection energy because here it would violate the aperture requirements.\nFurthermore, cleaning performance is essential at collision energy and much less important at injection.\nTherefore, two optical configurations were designed: one with mid-range values of the beta-function\nto be used at injection, and one with large values of the beta-functions that should be used at collision\nenergy. These two configurations are those shown in Fig. 10.10 (left, for the injection configuration and\nright, for the collision configuration). An optical transition between the two configurations is envisioned\nduring the energy ramp. This same type of transition will first be tested at the LHC during Run 3, with\nthe goal of becoming operational for the HL-LHC. Consequently, the FCC-hh will benefit from existing\noperational experience with dynamic optical changes in the collimation insertions. It is important to\nhighlight that, in both LHC and FCC-hh, the target aperture differs between the two configurations, and,\nin all cases, the aperture requirements are satisfied.\nTable 10.7 summarises the strength and aperture values for the quadrupoles generating the two\noptical configurations of the insertion for betatron collimation.\n514\n\nTable 10.6: Strength of the insertion quadrupoles for the RF insertion at PL and its dispersion suppres-\nsors. All the gradients correspond to 45 TeV.\nNAME\nGradient\nMaximum gradient\n[T/m]\n[T/m]\nMQ.14LL.B1\n117.49\n375.0\nMQ.13LL.B1\n\u2212115.18\n375.0\nMQ.12LL.B1\n115.75\n375.0\nMQ.11LL.B1\n\u2212110.70\n375.0\nMQ.10LL.B1\n158.84\n375.0\nMQ.9LL.B1\n\u2212170.55\n375.0\nMQ.8LL.B1\n75.86\n375.0\nMQM.7LL.B1\n\u2212353.09\n375.0\nMQR.6LL.B1\n261.98\n280.0\nMQR.5LL.B1\n\u2212252.75\n280.0\nMQR.4LL.B1\n274.79\n280.0\nMQR.3LL.B1\n\u2212180.75\n280.0\nMQR.2LL.B1\n187.29\n280.0\nMQR.1LL.B1\n\u2212274.64\n280.0\nMQR.01LL.B1\n233.43\n280.0\nMQR.1RL.B1\n\u2212259.94\n280.0\nMQY.2RL.B1\n\u221278.80\n200.0\nMQY.3RL.B1\n71.95\n200.0\nMQYL.4RL.B1\n87.58\n200.0\nMQYL.5RL.B1\n\u2212132.28\n200.0\nMQY.6RL.B1\n67.81\n200.0\nMQYL.7RL.B1\n96.84\n200.0\nMQ.8RL.B1\n\u221248.36\n375.0\nMQ.9RL.B1\n150.32\n375.0\nMQ.10RL.B1\n\u2212113.83\n375.0\nMQ.11RL.B1\n139.02\n375.0\nMQ.12RL.B1\n\u2212100.32\n375.0\nMQ.13RL.B1\n116.73\n375.0\nMQ.14RL.B1\n\u2212116.30\n375.0\n10.2.7\nMomentum collimation and injection\nThe technical insertion at PB serves two functions, namely injection of the clockwise circulating beam\nand momentum collimation. A transition region of approximately 530 m (from the kicker to the pri-\nmary collimator) is used to match the optics between these two systems, while also providing shielding\nbetween the kickers and momentum collimation debris, particularly in the event of injection losses.\nThis insertion presents two main challenges from a beam optics perspective. First, the optimal\nbeam properties for maximising the performance of each system individually are conflicting. Ideally,\nthe injection region should have zero dispersion to prevent the need for very tight injection protection\nabsorber settings, which must otherwise account for momentum offsets while maintaining alignment\nwith the collimation hierarchy.\nConversely, a large value of the normalised dispersion is necessary for the momentum collimation\nsystems to function effectively. Additionally, to protect each system from potential losses originating\nfrom the other, the longitudinal footprint of each subsystem must be carefully allocated, including a\n515\n\nFig. 10.13: Optical parameters, dispersion and beam aperture for the low-beta optics (for injection) of\nthe betatron collimation insertion PH (left) and the high-beta (for collision) variant (right). The blue and\nthe red aperture regions indicate superconducting and normal-conducting magnets, respectively. The\nhorizontal line in the aperture plot represents the minimum value acceptable.\nbuffer area with shielding between them.\nThe first challenge is addressed by fine-tuning the upstream dispersion suppressor to ensure that\nthe residual dispersion from the arc meets these constraints. The second challenge is managed by opti-\nmising the injected beam trajectory, as discussed in the previous section.\nIn this insertion, the optics of the two beams can differ if necessary since the counter-clockwise\nbeam is not subject to injection constraints. This flexibility allows its optics to be configured in a way\nthat minimises the impact of momentum collimation losses on the injection elements.\nDoglegs are also needed for the momentum collimation system, and each block of dipoles (com-\nposed of three MBW-type dipoles) generates 69.0 Tm at collision energy.\nThe layout and hardware configuration of the injection system are identical, but mirror reflected,\nof that shown in Fig. 10.11 and Table 10.5.\nFigure 10.14 shows the optical parameters, dispersion, and beam aperture at injection that cor-\nresponds to the most critical configuration. The dispersion is matched so that it is small as the beam\nreaches the injection kicker and then grows as the beam reaches the dogleg where the primary collimator\nis located.\nThe strength values for the quadrupoles that generate the optical configuration of the insertion for\nthe off-momentum collimation are summarised in Table 10.8.\n10.2.8\nImpedance considerations\nBeam-coupling impedance remains largely unchanged with respect to the CDR [10, Section 2.4.7]). The\nmain implications from the change of layout are related to a shorter ring circumference, which implies a\nslightly larger revolution frequency and a reduced total length of beam screens and vacuum pipe, along\nwith lower maximum beam energy, a lower magnetic field on the beam screen at top energy, and possibly\na higher operating temperature of the beamscreen. The vertical dimension of the beam screen remains\nunchanged from the CDR, with a half height of 12.2 mm.\n516\n\nTable 10.7: Strength of the insertion quadrupoles for the betatron insertion at PH (second column, low-\nbeta, third column, high-beta) and its dispersion suppressors. All the gradients correspond to 45 TeV.\nNAME\nGradient\nGradient\nMaximum gradient\n[T/m]\n[T/m]\n[T/m]\nMQ.14LH.B1\n117.3\n127.6\n375.0\nMQ.13LH.B1\n\u2212103.8\n\u2212110.4\n375.0\nMQ.12LH.B1\n113.2\n116.3\n375.0\nMQ.11LH.B1\n\u2212105.7\n\u2212124.0\n375.0\nMQ.10LH.B1\n152.8\n168.7\n375.0\nMQ.9LH.B1\n\u2212115.9\n\u2212108.8\n375.0\nMQ.8LH.B1\n52.4\n61.4\n375.0\nMQM.7LH.B1\n\u221257.5\n\u2212206.0\n375.0\nMQY.6LH.B1\n28.3\n79.3\n200.0\nMQW.5LH.B1\n\u221225.5\n\u221228.5\n44.0\nMQW.4LH.B1\n38.6\n34.8\n44.0\nMQW.4RH.B1\n\u221233.2\n\u221231.9\n44.0\nMQW.5RH.B1\n38.2\n34.8\n44.0\nMQY.6RH.B1\n\u2212154.3\n\u221283.9\n200.0\nMQM.7RH.B1\n215.7\n207.8\n375.0\nMQ.8RH.B1\n\u221258.2\n\u221236.7\n375.0\nMQ.9RH.B1\n159.5\n142.6\n375.0\nMQ.10RH.B1\n\u2212114.2\n\u2212114.5\n375.0\nMQ.11RH.B1\n139.5\n140.0\n375.0\nMQ.12RH.B1\n\u221288.9\n\u221297.3\n375.0\nMQ.13RH.B1\n114.6\n113.5\n375.0\nMQ.14RH.B1\n\u2212103.9\n\u2212113.2\n375.0\nThe reduction in tunnel length results in an 8% increase in the revolution frequency, shifting the\nfirst unstable betatron line to higher frequencies. However, this has no significant impact on stability, as\nthe associated rigid-mode instability is effectively suppressed by the transverse feedback damper [10].\nAdditionally, the reduced tunnel length decreases the resistive-wall impedance of the vacuum struc-\nture\u2014particularly of the beam screens\u2014by the same 8%. The reduction of the magnetic field from 16 T\nto 14 T also leads to a reduction of the resistivity of the copper beam screens, through magnetoresistance,\nof about 8% (assuming a residual resistivity ratio of 70 as in the LHC beam screens [512], and standard\ncopper properties for magnetoresistance [513] and temperature dependency [514], as implemented in\nXWAKES [515]), which leads to a reduction of their resistive-wall impedance by 4%. 3 By contrast, the\nlower flat-top energy (42.3 TeV instead of 50 TeV) has a more pronounced effect, as both tune shifts and\ngrowth rates are inversely proportional to \u03b3, leading to an 18% increase.\nSince at top energy, the resistive-wall impedance of the beam screens accounts for only 10% of the\ntotal impedance [10], the stability at the flat top is degraded with respect to the CDR by approximately\n20%, primarily due to the lower beam energy. At injection energy, where the beam screen contributes\n50% of the total impedance, stability improves by 4% if the beam screen temperature remains unchanged.\nEven in a worst-case scenario, the increase in instability growth rates and tune shifts remains manageable\nat both injection and flat top [10]. If the injection energy is lowered to 1.3 TeV, the multi-bunch instabil-\n3If the beam screens were operated at 70 K instead of 50 K, their resistive-wall impedance would increase by 21% with\nrespect to the CDR configuration (50 K, 16 T). At injection energy (corresponding to a dipole field of 1.09 T, almost unchanged\nwith respect to the CDR), the corresponding increase due to temperature would be of 48%, as the temperature effect is more\npronounced at low values of the magnetic field.\n517\n\nFig. 10.14: Optical parameters, dispersion and beam aperture at injection for the momentum collimation\nand injection insertion PB for the clockwise beam. Sections dedicated to a specific function are high-\nlighted: injection elements (light blue), injection protection devices (orange) and momentum collimation\nelements (green). The horizontal line in the aperture plot represents the minimum value acceptable.\nity growth times decrease by a factor of almost three to 20\u201325 turns [10]. Also, here, a safety margin still\nexists since even faster multi-bunch instabilities, e.g. with rise times about 10 turns, could be damped by\nan LHC-type feedback system along with Landau octupoles and non-zero chromaticity [516].\n10.2.9\nOngoing studies\nThe cell magnet layout and the number of dipoles per cell are already optimised for maximum beam\nenergy. An even higher dipole filling factor might still be achieved by optimising the length of the main\ndipoles, which is subject to various constraints, such as the size of the shaft used to lower the dipoles.\nA non-standard option for the FCC-hh ring configuration utilises combined-function magnets [517].\nFurther investigations of this approach (see, e.g., Ref. [518]), including corrector systems and refined\nlength of the combined-function magnets, is essential for determining whether if this setup could serve\nas a viable alternative to the present baseline lattice.\n10.3\nFCC-hh injection\n10.3.1\nHadron injectors in the SPS or LHC tunnel\nMachines located in three different tunnels were initially considered as potential hadron injectors: a\nbooster within the collider tunnel, a modified LHC or a new superconducting machine in the LHC tunnel,\nand a superconducting SPS (scSPS) in the SPS tunnel. The option of placing a booster in the collider\ntunnel, using superferric magnets at 1.1 T with a 70% filling factor, was discarded at an early stage due\nto the need for long bypass tunnels \u2014approximately 15 km in length\u2014around the experiment caverns.\nThe remaining options, involving a machine in either the LHC or SPS tunnel, differ in their achiev-\n518\n\nTable 10.8: Strength of the insertion quadrupoles for the momentum collimation insertion at PB and its\ndispersion suppressors. All the gradients correspond to 45 TeV.\nNAME\nGradient\nMaximum gradient\n[T/m]\n[T/m]\nMQ.14LB.B1\n123.6\n375\nMQ.13LB.B1\n\u2212124.0\n375\nMQ.12LB.B1\n118.1\n375\nMQ.11LB.B1\n\u2212125.3\n375\nMQ.10LB.B1\n150.5\n375\nMQ.9LB.B1\n\u2212129.6\n375\nMQ.8LB.B1\n57.9\n375\nMQYL.7LB.B1\n\u221220.1\n200\nMQY.6LB.B1\n67.8\n200\nMQYL.5LB.B1\n\u2212122.6\n200\nMQYL.4LB.B1\n68.8\n200\nMQY.3LB.B1\n103.2\n200\nMQY.2LB.B1\n\u221256.8\n200\nMQM.1LB.B1\n\u2212131.8\n375\nMQY.1RB.B1\n1.6\n200\nMQW.2RB.B1\n\u221220.2\n44\nMQW.3RB.B1\n32.2\n44\nMQW.4RB.B1\n\u221231.3\n44\nMQW.5RB.B1\n27.8\n44\nMQY.6RB.B1\n\u2212169.8\n200\nMQM.7RB.B1\n231.0\n375\nMQ.8RB.B1\n\u221240.5\n375\nMQ.9RB.B1\n129.9\n375\nMQ.10RB.B1\n\u2212111.3\n375\nMQ.11RB.B1\n131.8\n375\nMQ.12RB.B1\n\u2212103.3\n375\nMQ.13RB.B1\n110.2\n375\nMQ.14RB.B1\n\u2212115.6\n375\nable injection energy for the collider. An scSPS limits the injection energy to 1.3 TeV, whereas a machine\nin the LHC tunnel could exceed the collider\u2019s baseline injection energy of 3.3 TeV.\nIn addition to the injection energy of 3.3 TeV the main requirements of the hadron injector are the\ndelivery of the beam parameters in intensity, emittance and bunch spacing, as well as a fill duration of\naround 30 min.\nA detailed study was carried out to evaluate the feasibility of modifying the existing LHC into\na fast-ramping 3.3 TeV injector. This analysis included assessing layout modifications in the straight\nsections, optimising the powering segmentation to enable faster ramping, and developing a simplified\noptics design [519]. The FCC-hh Conceptual Design Report [10] concluded that, at 3.3 TeV, the threshold\nfor FCC-hh injection absorbers to survive beam impact requires a burst-mode transfer of 130 batches\nfrom the modified LHC to the FCC-hh, each batch consisting of 80 bunches. This configuration would\nallow the full LHC beam to be transferred within a few seconds.\nAlternatively, the LHC could be replaced by a 4 T superconducting machine based on magnet\ndesigns from RHIC, Tevatron, or FAIR (SIS200/300). To avoid excessively long transfer lines, this\n519\n\nmachine would require either polarity reversal or a twin-aperture magnet design. The RF system is\nassumed to limit the ramp-up time to no more than 50 s, resulting in a total collider filling time of\n39 minutes. Additionally, this option would necessitate a burst-mode injection transfer lasting several\nseconds.\nAnother approach to replacing the current LHC within its tunnel involves a superferric, iron-\ndominated machine operating at 2T, capable of achieving a transfer energy of approximately 1.75 TeV.\nHowever, neither of these options has been studied in further detail at this stage.\nIf the collider can accommodate an injection energy of 1.3 TeV, a superconducting machine in\nthe SPS presents an intriguing option. This possibility has been explored at the conceptual level and is\ndocumented in Ref. [520].\nThis study considered following the present SPS lattice, which naturally is well-matched to the\nexisting tunnel geometry, using missing bend dispersion suppressors. A collimation system needs to be\nintegrated into the straight-section layout. The beam transfer from the scSPS to the collider is limited\nto 640 bunches per transfer due to absorber limits. In this case, no burst-mode transfer is required.\nThe filling time considered in Ref. [520] needs to be revised in view of the reduced number of collider\nbunches and a possibly higher ramp rate.\nOverall, the feasibility of an scSPS is mainly determined by the design of large aperture, fast ramp-\ning dipoles, and quadrupoles. The design study compares 2D designs of main dipoles and quadrupoles for\nboth single- and double-layer coil configurations. Among these, the 4.2 K-compatible double-layer coil\ndesign emerges as the most promising. The study also evaluated a challenging 80 mm aperture, primar-\nily motivated by also allowing a slow-extraction based fixed-target programme reaching up to 1.3 TeV.\nRecent advancements in crystal-assisted slow extraction provide confidence that the current spiral step\nof 20 mm could be reduced to approximately 5 mm, directly impacting the required magnet aperture.\nThe initial magnet study also highlights the significant benefits of doubling the injection energy in\nthe SPS to 50GeV, as this would reduce the critical energy/field swing and AC losses. In addition, this\napproach could eliminate the current need for transition crossing.Given that the PS will be more than\n100 years old at the time of FCC-hh, one might consider replacing the PS with a 50 GeV machine - a\nsuperconducting machine in the PS tunnel or a normal conducting PS2 (studied as an option to renovate\nthe LHC injector chain).\nInjector option summary and outlook\nThe three options for an FCC hadron injector are summarised in Table 10.9. All options can deliver the\nmain beam parameters required, such as intensity, emittance, and bunch spacing. The main difference\nis the implied FCC-hh injection energy. The modified LHC option stands out for the filling time, in\nparticular, since the filling time of the scSPS was calculated with a rather conservative ramp rate. The\nLHC would also need a large effort in continuous consolidation over decades before being repurposed as\nan FCC hadron injector.\nIf the collider injection energy stays above the reach of an scSPS, an attractive option seems to be\na new 4 T machine in the LHC tunnel. Another possibility, with an intermediate beam energy, is a 2-T\nsuperferric machine. If 1.3 TeV is acceptable for the collider, an scSPS becomes appealing, also in view\nof a possible synergy of beam transfer tunnels.\nGiven the timescale for all options, it seems valid to consider renovating the entire injector chain,\nallowing the removal of certain bottlenecks in beam production.\nFor the next study steps, it is planned to establish a parametric model for the main cost drivers of a\n3.3 TeV superconducting machine and a 1.75 TeV superferric machine in the LHC tunnel, and a 1.3 TeV\nsuperconducting machine in the SPS tunnel.\n520\n\nTable 10.9: Comparison of high-energy booster options, a superconducting machine in the SPS tunnel\n(scSPS), a modified faster-ramping LHC and a new 4 T machine in the LHC tunnel. A further option\n(not shown) with an intermediate energy of 1.75 TeV would be a superferric machine in the LHC tunnel.\nUnit\nscSPS\nmod. LHC\n4 T LHC\nCircumference\nkm\n6.9\n26.7\n26.7\nApertures\n1\n2\n1\nInjection energy\nGeV\n26\n450\n450\nExtraction energy\nTeV\n1.3\n3.3\n3.3\nInjection field\nT\n0.12\n0.6\n0.6\nMaximum field\nT\n6\n4\n4\nEnergy/field swing\n50\n7\n7\nIndividual dipole length\nm\n12\n14.3\n14.3\nDipole filling factor\n0.65\n0.66\n0.66\nNumber of dipoles\n372\n1232\n1232\nNumber of quadrupoles\n216\n480\n480\nNumber of bunches\n640\n2600\n2600\nStored energy\nMJ\n15\n167\n167\nBooster filling time\nmin\n0.5\n7.5\n3.8\nRamp rate\nT/s\n0.4\n0.026\n0.08\nCycle length\nmin\n1.1\n12\n4.9\nBooster cycles per FCC fill\n34\n4\n8\nCollider filling time\nmin\n37\n46\n39\n10.3.2\nLayout of the FCC-hh injection\nIn the case of using the present LHC or a new 4 T machine in the LHC tunnel as the FCC hadron\ninjector, the beam would be transferred at 3.3 TeV, which, in Ref. [10], was considered the baseline\ninjection energy.\nWith the new geometry of the lepton transfer lines from the surface to the collider tunnel (see\nSection 7.7), there is no longer a synergy between the lepton and hadron transfer tunnels to simplify the\ncivil engineering work for the lepton tunnels.\nFor hadron beams from the LHC tunnel, it is proposed that both beams be extracted from P8, as\nillustrated in Fig. 10.15. Compared to the current LHC dump system, designed for 7 TeV and operated\nat 6.8 TeV, an extraction system for FCC beams would require only half the deflection while benefiting\nfrom at least 50 years of technological advancements. Additionally, such an extraction system could be\ndesigned with a simpler triggering logic compared to a fail-safe dump system.\nTransfer lines from LHC P8 to the collider tunnel require superconducting magnets well within\nthe reach of current Nb-Ti technology (see Table 10.10). As soon as the transfer lines join the collider\ntunnel, the magnetic field required drops to the injection field of the collider magnets, as described in\ndetail in Section 10.3.1.\nTable 10.10: Lengths of transfer lines and tunnels from the LHC with the required magnet fields in the\nconnection tunnel and inside the collider tunnel, respectively.\nTL length [km]\nTunnel length [km]\nDipole fields [T]\nLHC P8 to PB\n9.5\n1.9\n6.6/1\nLHC P8 to PL\n7.5\n3.8\n4.7/1\n521\n\nFCC\nFig. 10.15: Transfer tunnels (blue dashed) for 3.3 TeV hadron beams from LHC P8 to the collider. The\ntransfer lines continue inside the collider tunnel for several km to reach the injection straights PB and\nPL.\nIn case a lower injection energy into the collider is attainable, the option of a super-ferric iron-\ndominated machine in the LHC tunnel allows a beam transfer at around 1.75 TeV. This option could use\nthe same extraction system layout as described above. The reduced transfer energy would be beneficial\nfor the system design. Also, the transfer line geometry could be the same as described above, with lower\nfields in the transfer dipoles.\n10.3.3\nLayout of the FCC-hh injection lines from a superconducting SPS\nFor a superconducting SPS, based on \u223c6 T magnets, the transfer energy is limited to 1.3 TeV. At this\nenergy, the use of the existing TI8 tunnel for hadron transfer is within reach of the current technology,\nwhich reduces the new tunnelling for the clockwise beam injected in PB by 3 km (see Fig. 10.16 and\nTable 10.11). The dipole fields required amount to 5.9, 2.3 and 7.4 T for the different arcs, respectively.\nAs soon as the transfer line is in the collider tunnel, a field of 0.44 T is required.\nFor the anti-clockwise beam injected in PL, the straight section 6 (LSS6) of the SPS is favoured\nto have a short connection of less than 1 km to the collider tunnel with dipole fields of 4.2 T.\n10.3.4\nTransfer lines in the ring tunnel\nTwo sections of the FCC-hh transfer lines are inside the collider tunnel, in the arcs that join PA and PB\n(for the clockwise beam) and PA and PL (for the counter-clockwise beam). The design of the transfer\nline will inherit the features of the regular arcs of the ring over this length. It is assumed that periodic\ncells of the transfer line will be copies of those in the hadron collider, with each containing 16 dipole\n522\n\n2000\n0\n2000\n4000\n6000\n8000\n8000\n6000\n4000\n2000\n0\n2000\nFCC PA\nFig. 10.16: Transfer tunnels (blue dashed) for 1.3 TeV hadrons from SPS LSS4 to the collider in clock-\nwise direction, and from SPS LSS6 to the collider in anticlockwise direction. The transfer line continues\ninside the collider tunnel for several km to reach the injection straights PB and PL.\nTable 10.11: Lengths of transfer lines and tunnels from the scSPS with the required magnet fields in the\nconnection tunnel and inside the collider tunnel, respectively.\nTL length [km]\nTunnel length [km]\nDipole fields [T]\nSPS-LSS4 to PB\n12.9\n1.6\n7.4/0.44\nSPS-LSS6 to PL\n6.9\n0.9\n4.2/0.44\nmagnets. Furthermore, the focusing structure will also be applied to the part of the transfer lines outside\nthe ring tunnel, whereas the geometry will impose a different choice of dipole magnets.\nTwo injection energies have been considered, 3.3 TeV, which is the baseline assuming the LHC as\nan injector, and an alternative of 1.3 TeV, assuming a superconducting SPS. The higher injection energy\nis considered for the magnet design parameters in Table 10.12).\nIn view of the large scale of production for the transfer line magnets, assembly and manufacturing\nwill be a key focus of future development efforts.\nThe aim of the following preliminary assessment was to consider existing magnets at CERN and\nelsewhere, firstly to generate multiple design concepts and secondly to make an initial assessment of\nwhether these could satisfy the transfer line requirements. Ultimately, three concepts, highlighted in\nFig. 10.17, were selected for further development. These three concepts will be developed until the\nmost suitable design can be identified, also taking into account resource effectiveness. Typically, this\n523\n\nTable 10.12: FCC-hh transfer line magnets parameters for injection energy of 3.3 TeV and for the section\nlocated inside the ring tunnel. The total length of the tunnel section of the two transfer lines is 19.6 km.\nSuch an estimate is an upper bound based on the FCC-hh arc length. The FCC-hh ring regular cell is\n276 m long.\nElectromagnet\nPermanent\nmagnet\nInterconnections\nLongitudinal gap (mm)\n550\n50\nAperture\nBeam pipe inner diameter (mm)\n30\nand\nGood field region (GFR) diameter (mm)\n20\nfield quality\nField linearity in GFR (units)\n2\nDipoles\nIntegrated dipole field per cell (T m)\n230\n230.4\nDipole magnet field strength (T)\n1\nMagnet magnetic length (m)\n5\n1.2\nNumber of magnets per cell\n46\n192\nTotal dipole length (km)\n8.51\n8.52\nQuadrupoles\nIntegrated quadrupole gradient per cell (T)\n118\nQuadrupole magnet gradient (T/m)\n20\n25\nMagnet magnetic length (m)\n3\n1.2\nNumber of magnets per cell\n4\n8\nTotal quadrupole length (m)\n444\n355.2\nFig. 10.17: Sketch of the possible conceptual designs for the transfer line magnets. The three magnet\ndesign concepts highlighted in red were selected.\nassessment will be based on lifetime cost, but it will also consider other factors, such as climate impact\nand ethical issues regarding where raw materials are sourced.\n524\n\nElectromagnet design concepts\nIron-dominated normal-conducting accelerator magnets are a mature and well-understood technology.\nFurthermore, the field strength required is compatible with the normal-conducting magnet capabilities,\nmaking them suitable for this application. The volume of the yoke will be optimised to reduce weight and\nmaterial cost while retaining sufficient torsional rigidity and magnetic performance. The most critical\noptimisation involves determining the optimal size of the coil cross-section to minimise the total lifetime\ncost. This requires balancing capital investment costs, primarily driven by the conductor, with overhead\nexpenses, mainly related to electrical power consumption.\nOne dipole magnet design provides a 1.2 T field in the 30 mm aperture and is largely inspired by\nthe TI2/TI8 transfer line magnets that connect the SPS ring to the LHC (see Fig. 10.18). An H-shaped\nyoke geometry was selected because it has better torsional rigidity and saturation performance compared\nto other options. This minimises the dipole cross-section dimensions, particularly the height. The exact\nlength of each magnet unit has not yet been determined, but a 5 m dipole would weigh 4600 kg.\nFig. 10.18: Photograph of a 6.3 m long dipole magnet (HCMBI_001) used in the LHC transfer line.\nThe yoke is made of laminated electrical steel. The laminations are punched and then stacked\ntogether, which is the most cost-effective assembly method for producing a large series of long magnets.\nThis configuration also minimises eddy current losses when the magnets are ramped, reducing running\ncosts.\nThe 58 kAturns required are provided by two bedstead coils. This coil shape reduces the inter-\nconnection length between magnets, thus maximising the longitudinal filling factor. The coils are wound\nwith a hollow copper conductor and cooled with demineralised water. Figure 10.19 (left) shows the 2D\nfield distribution in the yoke cross-section, while the 3D magnet geometry is visible in the right plot of\nthe same figure. Note the length of the magnet relative to its cross-section.\nThe quadrupole concept is also inspired by the TI2/TI8 transfer line magnets. It would be an as-\nsembly of laminated steel quadrants with water-cooled coils. Each of the four coils provides 7.4 kAturns,\nwhich produces a 25 T/m gradient in the 30 mm diameter aperture, with a 1.5 m long quadrupole weigh-\ning 1000 kg. The 2D field distribution in the yoke cross-section is shown in Fig. 10.20.\n525\n\nFig. 10.19: Left: Normal conducting dipole magnet 2D field distribution (four-fold symmetry). Right:\nNormal conducting dipole magnet 3D model.\nFig. 10.20: Normal conducting quadrupole magnet 2D field distribution (eight-fold symmetry).\nPermanent Magnet Solutions\nPermanent magnets (PM) for accelerators are especially well suited to the transfer line specifications.\nAs the FCC-hh beam will always be injected at the same energy, the magnet strength does not need\nto be varied. Additionally, the field quality requirements are less stringent than those in the collider\nring because the beam only makes a single pass. It is worth mentioning that PMs are already used in\naccelerators, albeit on a much smaller scale. For instance, at CERN, there are permanent accelerator\nmagnets in Linac4 [521] and the beamline of the FASER [522] experiment. At Fermilab, the 3.4 km\nrecycler ring is entirely based on PMs [523, 524]. Furthermore, PMs can also be found in insertion\ndevice magnets for electron synchrotrons around the world (see Ref. [525] for a review).\nNote that PM blocks/wedges are the magnetised elements that are assembled to create an accel-\nerator magnet (see Fig. 10.21). During their manufacture, they should gain homogeneous magnetisation\n(magnitude and direction) oriented relative to an external mechanical datum surface. However, man-\n526\n\nFig. 10.21: Samarium Cobalt permanent magnet wedge used in the FASER Halbach magnet at CERN.\nufacturing tolerances introduce magnetisation errors that must be monitored through quality assurance\ntesting and mitigated by the accelerator magnet designs.\nMagnetic forces between PM elements make it challenging to assemble them in a precise and safe\nway. However, the design concepts presented here are not novel, and multiple assembly techniques are\nalready available. More research is needed to determine whether these approaches are suitable for the\nindustrial scale required by the FCC-hh or whether new techniques will need to be developed.\nThe design of the transfer line will also include active correctors, i.e., normal-conducting mag-\nnets that are meant to compensate for, e.g., trajectory errors in the transfer lines due to the extraction\nconditions in the FCC-hh injector or magnetic-field errors from the PMs of the transfer line.\nRisks Associated with Permanent Magnets\nPMs have two key weaknesses: the magnetic field they produce is susceptible to radiation dose and\nvariations in temperature, both of which will affect the transfer lines. Therefore, it is important to exam-\nine these vulnerabilities and make an initial assessment of whether realistic operating conditions could\nprevent the transfer line magnets from functioning adequately.\nThe first vulnerability is the temperature dependence of PMs, which could cause a drift in magnetic\nfield strength as the ambient temperature varies. Annual temperature data from the LHC tunnel [526],\nwhich is assumed to behave similarly to the FCC-hh ring tunnel, and PM material data were used to\ncalculate the maximum possible integrated dipole error per cell (see Table 10.13). The magnitude is\nsmall enough to be managed using active corrector magnets.\nThe second vulnerability is PM demagnetisation due to irradiation. Demagnetisation mechanisms\nare complex, but damage is primarily a function of dose and energy [527], with different levels of PM\nhaving different susceptibilities. For this initial assessment, it is assumed that the PM elements of the\ntransfer line receive a uniform dose indirectly (i.e., from the collider beam). Moreover, the direct dose\nfrom the transfer line beam is neglected, and it is assumed that there is no realistic failure scenario where\nthe beam could be lost and dumped into the transfer line. This assumption will be reviewed when the\ndetails of the machine protection configuration are discussed. Another aspect that will be reviewed in\n527\n\nTable 10.13: Permanent magnet temperature dependence parameters with annual LHC tunnel tempera-\nture variation.\nUnit\nSmCo\nNdFeB\nTemperature dependence\n%/\u00b0C\n0.035\n\u22120.120\nTemperature variation (annual)\n\u25e6C\n\u00b10.87\nIntegrated dipole field per cell\nTm\n235\nCorrection field magnitude per cell\nTm\n0.716\n2.435\nlater studies is the possible impact of localised losses occurring in the collider ring, such as the so-called\nunidentified falling object (UFO) events that have been observed and studied in detail in the LHC (see,\ne.g., Ref. [528] and references therein for a review of this topic). Losses from these events are typically\non the order of 1 \u00d7 108 protons. While they could potentially trigger a quench in a superconducting\nmagnet, they may also impact the PMs. This possibility will be investigated further in future studies.\nThere are significant uncertainties in calculating an estimate for the accumulated lifetime dose.\nThree key variables are: residual gas density in the collider vacuum tube; longitudinal position (dose rate\nis higher between collider magnets); and number of years spent in commissioning vs. in operation (dose\nrate is lower in the latter phase). Using the FCC-hh particle transport simulation studies [529] and taking\nconservative assumptions, a lifetime dose of 1.7 kGy was calculated (see Table 10.14). For SmCo or\nNdFeB magnets, this dose should not alter the magnetic field on the axis by more than 1 unit (factor of\n10\u22124) so the transfer line requirements would still be satisfied. In conclusion, whilst radiation damage\ncan be considered a low risk, this assertion will need to be rigorously tested before committing to a PM\ntransfer line design. In addition, a comprehensive literature search will be conducted to understand the\nresistance of PMs to radiation. Potentially, the FCC will need to conduct its own PM irradiation test\ncampaign.\nTable 10.14: Radiation dose rate parameters for the assessment of the FCC-hh transfer line magnet.\nUnit\nValue\nCommissioning dose rate\nGy/year\n200\nCommissioning duration\nyear\n5\nOperation dose rate\nGy/year\n20\nOperations duration\nyear\n35\nTotal lifetime\nyear\n40\nLifetime dose\nkGy\n1.7\nAn additional risk of using a PM design is insufficient supply from manufacturers. For that rea-\nson, although they are more sensitive to temperature and less resistant to radiation [530], NdFeB PMs\nwere selected because they are produced at a lower cost and on a larger scale than SmCo PMs [531].\nTable 10.15 shows that the forecast global supply of NdFeB should be sufficient to cover the required\nvolume for both PMs concepts. Note that the iron-dominated permanent magnet design has not yet been\noptimised, so this value represents an upper limit.\nIron-Dominated permanent magnet design concepts\nIron-dominated permanent accelerator magnets generate a magnetic field using PM elements and func-\ntion similarly to conventional iron-dominated electromagnets. The iron yoke serves as a low-reluctance\npath, enhancing magnetic flux density. The pole helps shape the magnetic field distribution within the\naperture and can be shimmed to improve field quality. This is particularly beneficial in PM accelera-\n528\n\nTable 10.15: Permanent magnet material need and forecast supply.\nUnit\nNdFeB global\n2019\nk-tonnes/year\n130\nsupply\nForecast for 2030\nk-tonnes/year\n200\nRequired volume\nIron-dominated\ntonnes\n950\nof NdFeB magnet\nconcept designs\nblocks/wedges\nShimmed Halbach\ntonnes\n625\nfor concepts\nconcept designs\ntor designs, where magnetisation and assembly errors pose significant challenges. The iron also helps\nhomogenise the magnetic field, mitigating these errors.\nThe dipole and quadrupole design concepts both feature parallelepiped-shaped PM blocks. These\nare easier to produce and have better magnetisation direction tolerances compared to other geometries.\nFirst, the low-carbon steel yokes and non-magnetic components are assembled, and then the PM blocks\nare added one by one into the assembly. The blocks are inserted into cavities where some low-carbon\nsteel material is present on either side. This reduces magnetic forces, making the assembly process\nsimpler and faster.\nThe dipole design concept has an iron length of 1.2 m and an overall cross-section dimension of\n0.2\u00d70.2 m, it provides a field of 1 T in the aperture of 30 mm. The field integral can be adjusted by a\nfew percent by inserting magnetic shunts at the magnetic measurement stage, mainly to compensate for\nirregularities of PM blocks. The dipole magnet cross section is presented in Fig. 10.22 (left), and the 2D\nmagnetic field distribution is shown in the right part of the same figure.\nFig. 10.22: Left: Iron-dominated permanent dipole magnet cross-section. Right: Iron-dominated perma-\nnent dipole magnet 2D field distribution (four-fold symmetry).\nThe quadrupole concept design has an iron length of 1.1 m and an overall cross-section dimension\nof 0.2\u00d70.2 m. The gradient in the aperture diameter of 30 mm can be adjusted from 25 \u2013 30 T/m using\nradially adjustable shims. This operation is performed in the magnetic measurement stage. The cross\nsection is presented in Fig. 10.23 (left) and the 2D magnetic-field distribution is shown in the right part\nof the same figure.\nThe price of PM material will be a significant factor in the overall accelerator magnet cost. It is,\ntherefore, crucial to minimise the PM volume in each design, first by shimming/narrowing the poles, and\nsecondly by optimising the working point of the PM elements on their magnetic hysteresis curves.\n529\n\nFig. 10.23: Left: Iron-dominated permanent quadrupole magnet cross-section. Right: Iron-dominated\npermanent quadrupole magnet cross-section (four-fold symmetry).\nShimmed Halbach magnet design concepts\nIn Halbach arrays, PM elements are arranged to minimise the magnetic field on one side of the array\nwhilst maximising it on the other. Indeed, cylindrical Halbach arrays are an exceedingly compact con-\nfiguration of permanent multipole accelerator magnets, i.e., they require minimal PM element volume to\nproduce a given field strength over a circular aperture [532]. However, the absence of iron to homogenise\nthe magnetic field means that manufactured Halbach magnets are highly sensitive to PM magnetisation\nand assembly errors. Consequently, significant resources are typically invested in the manufacture and\nassembly of Halbach accelerator magnets to ensure satisfactory field qualities. This can include a range\nof measures: first, it requires extensive quality assurance, measuring the magnetic field of PM wedges\n(either individually or as a representative sample). Second, it may be necessary to match problematic\nPM wedges around the circumference of the cylinder to partially cancel field errors [532]. Finally, when\nassembling PM wedges, a mechanical structure may be needed to guide them in position; or mechanical\nshims might be used for small adjustments [533]. Both of these options reduce the PM packing factor,\nwhich affects magnetic performance. Even with these expensive mitigation measures, the field quality\nthat can realistically be achieved is limited. Based on CERN experience building Halbach accelera-\ntor magnets, it is anticipated that a standard design would not satisfy the current FCC-hh transfer line\nrequirements for field uniformity of about \u00b12 units.\nFortunately, cylindrical Halbach accelerator magnets can be shimmed to substantially decrease\nharmonic field errors. This technique was successfully developed and implemented in the CBETA 500\nMeV electron energy recovery linac at Cornell University [534]. Initially, conventional Halbach magnets\nwere manufactured with a slightly increased bore size to accommodate the shim assembly. Following\nthat, standard rotating coil measurements are used to evaluate the magnetic field error harmonics (see\nFig. 10.24 (left)).\nAn automated code was subsequently developed to optimise the distribution of magnetic shims\naround the bore circumference. These shims become magnetised, functioning as small dipole sources.\nFinally, the optimisation code determines the required length for each iron shimming rod before insertion\ninto the magnetically transparent collar (see Fig. 10.24 (right)).\nWorking with suppliers to create suitable processes, the CBETA team produced an initial produc-\ntion run of 216 magnets. Initially, the magnets had a relative field error of 18.2 units on average, which\ndecreased to 2.2 units after shimming. This gives confidence that by making the manufacturing toler-\nances less stringent during the initial build phase, the overall cost of production can be reduced without\nimpacting the quality of the magnetic field [534] (see Fig. 10.25).\nFigure 10.26 shows a cross section of the cylindrical FCC-hh transfer line Halbach dipole and\nquadrupole magnet concepts, respectively. Note that the inner bores of the magnets have been increased\n530\n\nFig. 10.24: Left: Performing rotating coil magnetic field quality measurements on an unshimmed Hal-\nbach magnet. Right: Shimmed Halbach magnet. Note the iron shimming rods of varying lengths (black)\nthat have been assembled and glued to the plastic collar (white).\nFig. 10.25: Flow chart describing the production of conventional and shimmed cylindrical Halbach mag-\nnets, respectively.\nbeyond what is required for the beam pipe to accommodate the shim assembly. The designs demonstrate\nthat the required field strengths can be achieved using sensible PM wedge geometries and volumes.\nHowever, it is more challenging to determine what level of field quality can realistically be achieved\nbecause this is a function of manufacturing tolerances that are not yet known. Currently, extrapolating\nfrom the initial production run of CBETA indicates that the FCC-hh field quality requirements can be\nmet. More research and development will be needed to confirm this statement. There are two main av-\nenues of investigation that need not be mutually exclusive. A prototyping campaign would have the joint\nbenefits of expanding knowledge of manufacturing processes and tolerances in the real world. Alterna-\ntively, stochastic modelling tools could be used to assess the sensitivity of the unshimmed Halbach field\nquality to different manufacturing tolerances, including PM wedge magnetisation magnitude/directional\nerrors and wedge radial/azimuthal positional errors. For example, the ROXIE 2D magnetic modelling\npackage [535] has a tool to perform randomised error studies. It is primarily used to investigate the effect\nof varying the azimuthal position of conductors in superconducting magnets but could also be used to\nstudy a range of Halbach parameters.\n531\n\nFig. 10.26: Halbach dipole (left) and quadrupole (right) for the FCC-hh transfer line magnet concepts.\nConclusions on FCC-hh transfer line magnets and future work\nAn initial assessment resulted in three viable candidate magnet concepts. The next phase of investigation\nwill develop these designs to a level where the most suitable can be evaluated. Given the large scale of\nFCC-hh compared to existing accelerators, a significant focus of this work will be on manufacturing and\nassembly challenges.\nObtaining accurate lifetime cost estimates will be key to making an informed choice. Currently,\nthere are too many uncertainties to perform reliable calculations. However, it is still useful to begin\nconsidering how the contribution of different capital and overhead costs will affect the final total, which\nis qualitatively shown in Fig. 10.27. Although it should not be used as a tool to evaluate each concept,\nthis information is useful to compare costs within each category.\nFig. 10.27: Qualitative considerations on the magnet costs for the various concepts considered.\nA permanent magnet research and development programme has the potential for significant ben-\nefits for accelerator engineering and beyond. Collaboration agreements can also accelerate progress,\nwith different partners contributing various expertise and capabilities. Collaborators at other research\ninstitutes could offer valuable contributions to the electromagnetic design of accelerator magnets. Mean-\nwhile, private-sector manufacturers are well-placed to develop new industrial-scale production processes.\nIntegration of the transfer lines in the FCC-hh tunnel was studied, considering the various options\n532\n\nfor the magnet design. The result of these studies is shown in Fig. 10.28, where the normal-conducting\n(left) and PM (right) solutions are presented. In both cases, the nominal tunnel size does not need to be\nincreased to allow the installation of the transfer lines. However, it is evident how the smaller size of the\ncross-section of the PMs renders this concept highly interesting, also with regard to integration.\nFig. 10.28: Cross-section of the FCC-hh ring tunnel with a sketch of the integration of the transfer lines\nfor the two options under study, namely with normal conducting magnets (left) and permanent magnets\n(right). Integration of the transfer lines into the ring tunnel does not require any increase in the tunnel\ncross-section.\n10.4\nHigh-field magnets\nThe following is organised in four sections. Section 10.4.1 provides an update to the baseline magnet\nparameters for FCC-hh dipoles, and outlines the changes with respect to the 2019 conceptual design re-\nport. Section 10.4.2 mentions alternative choices for the magnet system and how they would affect other\naccelerator subsystems; Section 10.4.3 presents design options that will validate key magnet parameters,\nplaces them in the context of past and present projects, and provides key figures for a block-coil design;\nfinally, opportunities and challenges of HTS options for FCC-hh dipole magnets are discussed in Sec-\ntion 10.4.4. Considerations of cost and timeline are not given here, but will be addressed by FCC and the\nHFM Programme in the input to the update of the European Strategy for Particle Physics.\n10.4.1\nBaseline with Nb3Sn magnets\nEvolution of main parameters\nThe main parameters of the FCC-hh with Nb3Sn main dipoles and its evolution with respect to the\ndesign report [10] is given in Table 10.16. As discussed in Section 10.2.1, from the point of view of the\nconceptual layout and optics, the main change is the 7% reduction of the accelerator circumference, from\n97.76 km to 90.66 km. The relevant parameter for the energy reach, i.e., the length of the arcs, is reduced\nby 5%. However, an iteration on the optics layout, thanks in particular to the use of longer cells, allows\nfor an increase of the arc filling factor by 4% from 0.80 to 0.83 [518].\n533\n\nTable 10.16: Parameters of the FCC-hh lattice, 2019 and 2025 values.\nCDR 2019\n2025 Nb3Sn\nDipole field\n(T)\n16.0\n14.0\nDipole aperture\n(mm)\n50\n50\nDipole magnetic length\n(m)\n14.3\n14.3\nOperational temperature\n(K)\n1.9\n1.9\nTunnel length\n(km)\n97.76\n90.66\nArc length\n(km)\n81.0\n76.9\nArc filling factor\n-\n0.80\n0.83\nC.m. energy\n(TeV)\n50+50\n42.5+42.5\nLoadline fraction\n-\n0.86\n0.80\njc at 16 T and 4.2 K\n(A/mm2)\n1500\n1200\nNumber of dipoles\n-\n4587\n4463\nNumber of quadrupoles\n-\n760\n520\nFor the magnet baseline parameters, the main change is the reduction of the operational field from\n16 T [536] to 14 T [537]. This choice enables the following accompanying measures, which together\nprovide a consistent baseline with high confidence level based on HL-LHC experience:\n\u2013 An increased margin for magnet operation: the loadline fraction (nominal current divided by max-\nimum theoretical current) is decreased from 86% [536] (the same value as for the LHC Nb-Ti\ndipoles at 7 TeV [538, 539], but considered risky for the production of more than 4000 Nb3Sn\ndipoles) to 80% (2% above the baseline for the HL-LHC Nb3Sn triplet). A discussion of the\nmargins associated to this loadline fraction is given in Section 10.4.1;\n\u2013 It is assumed that the conductor critical non-copper current density required to produce 14 T at 80%\nloadline fraction can be attained with the best Nb3Sn conductor available today, corresponding to\n1200 A/mm2 at 16 T, 4.22 K; see Section 10.4.3 for the fit and expected values at other fields\nand temperatures. The target defined for an FCC-hh conductor in 2015 of 1500 A/mm2 at 16 T,\n4.22 K [540] has been achieved and exceeded in laboratory samples. Development of usable wires\nfor magnets, based on this technology, is under way, but efforts have not yet started to industrialise\nthe technology.\n\u2013 EuroCirCol studies showed that the design of 16 T magnets is marginal with respect to the target of\nmaximum 200 MPa of stress in the coil [536]4; for a classical magnet design, the 12.5% reduction\nin field from 16 T to 14 T corresponds to a 25% reduction in stress, and therefore the 14 T magnet\ndesign can satisfy a condition of maximum stress of 150 MPa, which is more appropriate for a\nlarge scale production.\nOther relevant parameters such as operational temperature, aperture, inter-beam distance, maxi-\nmum size of the magnet, are unchanged. With the reduction of the magnetic field and of the arc length,\nand the increase of the arc filling factor, the centre of mass (c.m.) energy is 84.6 TeV.\nFilling factor, cell quadrupoles\nCell quadrupoles in the LHC lattice have a magnetic length of 3.15 m, and a gradient of 220 T/m, thus\nproviding \u223c700 T of integrated gradient [538]. The cell contains six dipoles, whose magnetic length is\n14.3 m, and total cell length is 107 m: the ratio between total magnetic length of the dipoles and cell\n4Note that the peak stress in the magnet coil is not a direct observable of the magnet; here, as in all the previous literature,\npeak stresses in the finite element model are referred to, with some assumptions on magnet preload, etc.\n534\n\nlength is the filling factor of the arc: 14.3\u00d76/107=0.80. The remaining 20% is left for interconnections\nand spool pieces (occupying 1.35 m for each dipole, i.e., about 10%), cell quadrupoles (5.9%) and other\nmagnets.\nFor the FCC-hh, the seven-fold increase in energy compared with the LHC would require a seven\ntimes larger integrated gradient, i.e., \u223c5000 T, and, using the same technology and cell layout, one\nwould need 22.5-m-long quadrupoles occupying nearly 50% of the arcs. To avoid this adverse effect\non the filling factor, one has to choose longer cells; this makes not only more space for dipoles because\nquadrupoles are more spaced, but also shortens the quadrupoles since the integrated gradient is inversely\nproportional to the cell length [537].\nIn the first version of the FCC-hh optics the number of dipoles per cell has been doubled w.r.t. the\nLHC from six to twelve, with a total cell length of 210 m [10]. A recent further step brought the number\nof dipoles to 16, with a total cell length of 276 m [541]: the 1600 T of integrated gradient can be achieved\nby 4.2-m-long quadrupoles giving 375 T/m [10], occupying 3% of the cell. In this way the filling factor\nis increased to 0.83, and the resulting energy with 14 T dipoles is 85 TeV COM; see Table 10.16, fourth\ncolumn. Further optimisations could give filling factors up to 0.87, thus reaching 90 TeV; this can be\nconsidered an upper limit, since the assumption for the distance between the magnetic lengths of two\nconsecutive dipoles is 1.5 m (10% larger than in the LHC, requiring more massive end supports for the\ncoil ends of 14 T magnets) and it appears difficult to reduce.\nInjection energy and magnet aperture\nA possible FCC-hh injection energy is 3.3 TeV as in the Conceptual Design Report [10]; this gives an\nenergy increase by a factor 14.2 between injection and collision energy, slightly smaller than in the LHC,\nwhere this factor is 15.6. The larger injection energy compensates for the larger beta functions due to the\nlonger cell length, and facilitates fitting the beam within a 50 mm aperture, and leaving space for a beam\nscreen to intercept the synchrotron radiation5. Since the beam size is proportional to the square root of\ncell length divided by the injection energy, compared to the LHC injection, the beam size in the FCC is\nreduced by 30%. Differently the LHC dipoles, thanks for the much larger bending radius, the FCC-hh\ndipoles do not require a curved geometry since the aperture gain would be negligible (of the order of\n1 mm). Protons at 3.3 TeV for injection into the FCC-hh could be provided either from a modified LHC\nor from a new 4 T machine in the LHC tunnel.\nAlternative FCC-hh injector options with 1.75 TeV and 1.3 TeV injection energy based on a su-\nperferric ring in the LHC tunnel or a faster cycling superconducting machine in the SPS tunnel are also\nbeing considered [10, Chapter 6.4]. However, these would pose major challenges for the accelerator and\nmagnet systems, with an unprecedented energy increase for a high-energy hadron collider (factors of 25\nor 33 from injection to top energy, respectively, to be compared with a record energy swing by a factor\nof 23 for the HERA proton ring), which would require a renegotiation of requirements on the control of\nfield quality and magnet reproducibility at injection. Moreover, these could also require a larger magnet\naperture (thus increasing the mass of the conductor), or a shorter cell length (thus reducing the filling fac-\ntor and the energy reach). Further studies are needed to converge on the choice of the optimum injector\nfor the FCC-ee.\nMain dipole margins\nThe short sample condition is defined as the combination of the peak field in the coil and the current\ndensity in the superconductor that corresponds to the measured critical surface of a strand short sample\nat the operational temperature: this is the maximum theoretical field achievable in the magnet. Super-\nconducting magnets operate at a fraction of this value, called loadline fraction. The loadline margin\n5Note that the beam screen presented in the baseline [10] corresponds to 100 TeV c.m. energy, with double the synchrotron\nradiation at 85 TeV.\n535\n\nFig. 10.29: Margins for Nb-Ti LHC dipoles at 7 TeV and 1.9 K (left) and for the HL-LHC quadrupoles\nat 7 TeV and 1.9 K (right).\nFig. 10.30: Margins for FCC-hh Nb3Sn dipoles at 1.9 K: baseline of 2019 (left) and of 2025 (right).\nis defined as one minus the loadline fraction. The current fraction is the ratio between the maximum\ntheoretical current that can be carried at the operational field and the operational current. The current\nsharing temperature is the temperature where the pair of nominal field and current density lie on the\ncritical surface. The temperature margin is the difference between the current sharing temperature and\nthe operational temperature.\nFigure 10.29 presents a visualisation of these margins for (HL-)LHC magnets based on two dif-\nferent types of Low Temperature Superconductor (LTS), namely for the LHC arc dipoles operating at\n7 TeV, and for the HL-LHC triplet quadrupoles at 7 TeV. LHC Nb-Ti dipoles have 14% loadline margin,\n43% current margin and 1.3 K temperature margin [538,539,542]. The HL-LHC Nb3Sn quadrupole pro-\nduction is proving that a 22% loadline margin can be achieved systematically, with very limited training\nand no retraining after a thermal cycle [543,544]; the current margin is 54%, and the temperature margin\nis 4.9 K, i.e., about three times larger than in the LHC dipoles. All quadrupoles systematically reach\noperational current at 4.5 K, thus proving the existence of a temperature margin larger than 2.6 K.\nMargins for the 2019 and 2025 baseline for the FCC-hh dipoles are shown in Fig. 10.30. The 2025\nbaseline for FCC-hh guarantees a 4.6 K temperature margin, cf. the previous value of 3.3 K, and a 60%\ncurrent margin. Margins for the 2019 and 2025 FCC-hh Nb3Sn dipoles are compared with those for the\nLHC Nb-Ti arc dipoles and for the HL-LHC Nb3Sn triplet magnets in Table 10.17.\nHypothesis on hysteresis losses\nIn the case of the FCC-hh Nb3Sn dipoles, the main source of the so-called AC losses are the hysteresis\nlosses due to the magnetisation of the superconductor (also called persistent currents); they are peculiar\nto superconductors, and they are proportional to the filament size. The energy dissipated over a full\ncycle is independent of the ramp rate, and therefore the power losses scale with the ramp rate dB/dt.\nNote that other sources of AC losses as currents induced in loops that are partially resistive through the\ninter-strand resistance in cables, or the inter-filament resistance are proportional to d2B/dt2. Losses are\n536\n\nTable 10.17: Margins for LHC dipoles at 7.0 TeV, HL-LHC triplet, FCC-hh dipoles, all operating at\n1.9 K.\nEnergy\nBore\nPeak\nLoadline\nCurrent\nTemperature\n(TeV)\nfield (T)\nfield (T)\nmargin (%)\nmargin (%)\nmargin (K)\nLHC dipole\n7.0\n8.3\n8.7\n14%\n43%\n1.3\nHL-LHC triplet\n7.0\n9.9\u2020\n11.3\n22%\n54%\n4.9\nFCC-hh dipole 2019\n50\n16\n16.5\n14%\n52%\n3.3\nFCC-hh dipole 2025\n42.5\n14\n14.5\n20%\n60%\n4.5\n\u2020 The quadrupole gradient times the aperture radius is given here.\ndissipated in the magnet coil during the ramp, and the cryogenic power needed to deal with them is\nrelated to the magnet temperature: higher operational temperatures imply lower power consumption for\ncryogenics. On the other hand, the magnet temperature has little influence on the power needed to deal\nwith synchrotron radiation, since this is intercepted on the beam screen at or above 50 K; see Table 10.20.\nFor the FCC-hh magnet, a target of 5 kJ/m over the ramp (i.e., 10 kJ/m for the complete cycle) has\nbeen set in the CDR [10]. With the present status of technology for Nb3Sn conductors, having filaments\nof the order of 50 \u00b5m, Nb3Sn dipoles at 14 T have about twice this, i.e., 20 kJ/m for the full cycle [545].\nSeveral paths are possible to close this gap between targets and technology:\n\u2013 Reducing the filament size; the drawback in this option is that it requires R&D on the conductor.\nThe need was identified [540, 546] and attempts in this direction were carried out. The resulting\ntechnology should clearly not increase cost or decrease critical current, which is not granted;\n\u2013 Using artificial pinning centre (APC) technology [547], that gives lower critical current density\nat low field, and therefore lower hysteresis losses, satisfies the 10 kJ/m target. APC also have the\npotential of giving larger current densities in the 14 T-18 T range, see next section;\n\u2013 Increasing the cooling power of the cryogenic system, that only has to absorb these losses during\nthe ramp;\n\u2013 Provide additional temperature margins so the magnet cold mass can buffer the energy deposited\nduring the ramp; superfluid helium in the cold mass plays an important role in the buffering mech-\nanism;\n\u2013 Doubling the ramping time, with a corresponding reduction of the integrated luminosity.\n10.4.2\nAlternative choices for the LTS magnet system\nSeveral alternative choices and how they would impact other accelerator subsystems are described below.\nThey are: (i) operation at 4.5 K, (ii) a combined function lattice, (iii) longer dipoles and (iv) a lower\noperational field of 12 T. More design options that meet the above baseline parameters and do not affect\nother accelerator subsystems are discussed in Section 10.4.3.\n4.5 K operation\nThe data of HL-LHC Nb3Sn quadrupole magnets shows that they can all operate at 4.5 K [543, 544].\nMoreover, instabilities limiting performance are more severe at 1.9 K than at 4.5 K. This could open the\npossibility of operating at 4.5 K. Keeping the same magnets with 20% loadline margin at 1.9 K would\nimply a reduced loadline margin of 10% at 4.5 K, and a current density margin of 42% and a temperature\nmargin of 1.9 K; see Fig. 10.31. Even though the HL-LHC magnets are routinely reaching this condition\nin individual tests, this baseline for the FCC-hh appears promising but extremely daring, given that the\n537\n\nFig. 10.31: A typical HL-LHC Nb3Sn quadrupole magnet training, reaching nominal current also at\n4.5 K (left) and margins for an option of FCC-hh Nb3Sn dipoles designed for 1.9 K operating at 4.5 K\n(right).\nmagnet system must also be robust against beam-induced effects that may be more severe than in the\nLHC due to the increased beam energy. The 4.5 K option is under study, and would present the following\nadvantages: (i) Reduced complexity of the cryogenic system and its cost; (ii) Reduction of the cryogenic\npower to remove heat from the cold mass of a factor two to three; since about half of the heat has to\nbe removed from the cold mass (the other half on the beam screen), this would imply a reduction of the\ncryogenic power by 30%.\nThe 4.5 K option could rely on dry magnets (cold mass not filled with liquid helium (LHe)); this\nwould reduce the He inventory; however, it would imply challenges to magnet cooling during the ramp,\nand to magnet insulation (LHe is a much more reliable insulator than vacuum because the Paschen\neffect in residual gas could lead to a dielectric breakdown during a quench). To prove the viability of this\noption it is necessary to develop a baseline for the cooling at 4.5 K, and determine whether the theoretical\ntemperature margin of \u223c2 K and \u223c40% in current density is sufficient to operate the \u223c4400 magnets in\nthe FCC, or whether to increase the margins. Note that in case of a 4.5 K baseline it is quite probable\nthat all magnets should be individually tested at 1.9 K before installation, since training is much faster at\n1.9 K, because during training at 4.5 K performance plateaus (that can be overcome at 1.9 K) may appear.\nCombined function Lattice\nA combined function lattice relies on removing the main quadrupoles and having a systematic quadrupole\ncomponent (b2) in the dipoles. This layout reduces the flexibility of operation, but it is used in some low-\nenergy accelerators. The main advantage is to remove the need for two families of quadrupole magnets,\neven if their number (500) is fairly moderate with respect to that of the dipoles. The combined function\nlattice implies more stringent requirements on dipole alignment, since it contains the quadrupolar com-\nponent; the option was considered, but eventually discarded for the LHC [548]. If the conductor peak\nfield is kept constant, the combined function option would allow a further increase in beam energy of\napproximately 0.5%. The reason is that the larger filling factor would be partially compensated by the\nneed to lower the main dipole field because part of the peak field would be created by the quadrupolar\ncomponent [549].\n20 m long magnets\nIn the late 2000s, the US LARP programme achieved the scaling of a Nb3Sn quadrupole from 1.5 m to\n3.4 m long magnets [550]; HL-LHC quadrupoles at CERN prove the scaling to 7.5 m [544]. Scaling in\nlength of FCC-hh dipoles is currently planned in two steps, first to 5 m (with the possibility of vertical\ntesting of the magnet) and a second to 14.3 m.\n538\n\nThe limit in magnetic length for LHC and FCC of 14.3 m is related to the European Union regula-\ntions for standard transport. For the SSC project, 17.5 m-long Nb-Ti dipoles were planned for the lattice\nand 15 were built and reached requirements [551]. Having 20 m-long magnets would have three positive\nconsequences:\n\u2013 A reduction of the total number of magnets to manufacture from \u223c4400 to \u223c3200 units, with, pos-\nsibly, a 30% shorter production (about two years), or 30% fewer production lines (see Table 10.16);\n\u2013 A reduction of the magnet cost; assuming 25% of the total cost is due to manufacturing and a\nreduction of 30% in the magnet number, the total cost of the dipoles would be reduced by 8%;\n\u2013 An increase of the filling factor of 3.5%, either used to increase the energy to 88 TeV COM, or to\nreduce the dipole cost (via a 0.5 T field reduction and less conductor).\nIn case this route is further pursued, detailed studies are required to assess the impact of 20 m long\nmagnets on several other areas, such as transport and integration.\n12 T magnets\nA layout based on a 12 T operational field would provide 73 TeV COM energy, with the same hypothesis\non the filling factor as in the baseline shown in Table 10.16. Using the same loadline margin as for the\n14 T baseline, 12 T dipoles would have a similar current and temperature margin, but require 30% less\nconductor. 12 T dipole short models are planned in the HFM programme, manufactured by INFN [552],\nas well as at CERN and PSI.\n10.4.3\nNb3Sn dipole designs\nRequirements\nBased on the experience of the HL-LHC triplet quadrupole magnets, the following targets have been set:\n\u2013 Field: To provide an operational field in the aperture of 14 T, short models must be able to system-\natically reach 15 T (so-called ultimate field). For the operational field of 12 T, an ultimate field of\nat least 13 T is required.6\n\u2013 Loadline and temperature margin: The dipoles operated at 1.9 K should provide a loadline margin\nof at least 20%, and a temperature margin larger than 2.6 K at operational field to reach operational\nfield also at 4.5 K.\n\u2013 Mechanics: The structure must be able to withstand forces corresponding to the ultimate field. The\ncoil, in the case of a design including a coil preload, must be not in tension at nominal field.7 The\ntarget maximum stress must not exceed 150 MPa in all phases (assembly, cool-down, and powering\nto nominal).\n\u2013 Protection: the hotspot temperature for the protection system in the nominal scenario (without\nfailures) must not exceed \u223c270 K. The system should guarantee a maximum hotspot temperature\nof 350 K in case of realistic and conservative failure scenarios.\nConductor properties\nThe parametrisation used for the Nb3Sn conductor is the following\n6Note that LHC dipoles, operating at 8.1 T in the LHC at an equivalent energy of 6.8 TeV, had short models systematically\nreaching 9.5 T.\n7Note that this is a less stringent requirement than previously used (10 MPa of compression at nominal or at ultimate field);\nthis is justified on the grounds that many experimental data show that partial unloading does not prevent reaching nominal field.\n539\n\nTable 10.18: Assumptions for critical current density of Nb3Sn superconductor.\nCritical current density in\n12 T\n15 T\n18 T\nsuperconductor (A/mm2)\n1.9 K\n3655\n2170\n1185\n4.22 K\n2800\n1515\n705\nJsc(T, B) = C0\nB\n \n1 \u2212\n\u0014 T\nTc0\n\u00151.52!0.96 \n1 \u2212\n\u0014 T\nTc0\n\u00152!0.96 \uf8eb\n\uf8ed\nB\nBc20\n\u0010\n1 \u2212[T/Tc0]1.52\u0011\n\uf8f6\n\uf8f8\n2.5\n(10.1)\nwith Tc0=16 K, Bc20=29.38 T, and C0 is the variable parameter to scale the conductor performance: C0=\n214 000 AT/mm2 for the improved HL-LHC considered as the baseline. The specification for HL-LHC\nhas been given at 12 T and at 15 T. For an FCC-hh dipole at 14 T, specifications should be given at 15 T\nand at 18 T (at 0.5 T larger than peak field in operational condition and at short sample field, respectively).\nThe critical current densities at different fields and temperatures are given in Table 10.18.\nQuantity of conductor\nThe driving term of the magnet cost is the quantity of conductor: it accounts for about one third of the\ncost for the LHC dipoles, and half of the cost for the HL-LHC magnets. The quantity of conductor is\nparametrised via the equivalent coil width weq, i.e., the width of the 60\u00b0 sector coil having the same\nsurface area as the insulated coil, see Fig. 10.32, left. This quantity has the advantage of being related to\nthe field and to the current density via the approximated expression\nB[T] \u22480.007 J[A/mm2]weq[mm].\n(10.2)\nThe volume of the insulated conductor is given by\nV \u22484\u03c0lm\n3\nh\u0000r + weq\n\u00012 \u2212r2i\n= 4\u03c0lm\n3\nh\n2rweq + w2\neq\ni\n(10.3)\nwhere lm is the magnet length, and r is the magnet aperture radius (see also Fig. 10.32, right). For FCC-\nhh, a coil width of up to 55 mm is considered, thus giving a quantity of conductor 2.5 times larger than\nin the LHC dipoles.\nPrevious achievements in bore field\nNb3Sn accelerator dipole models have been developed since the late 80\u2019s. A short summary of the\nachievements is given below. All cases refer to 1 to 2 m long magnets (usually called short models),\nexcept for the HL LHC magnets (11 T dipoles and final triplet quadrupole).\nIn 1990 the CERN-Elin dipole reached 9.5 T at 4.3 K in a 50 mm aperture, with a two-layer coil\nbased on cos(\u03b8) geometry and grading [541]. This option was not retained for the LHC due to the higher\ncost with respect to the Nb-Ti option at 1.9 K and the complexity of the technology.\nIn the 1990s the MSUT dipole reached 11.3 T at 4.5 K in a 50 mm aperture, with a two-layer coil\nbased on cos(\u03b8) geometry and grading [553]. The magnet was tested again in 2020 at 1.9 K, achieving\nthe power converter limit (11.8 T bore field).\nIn the 1990s the D20 LBNL dipole reached 13.4 T at 1.9 K in a 50 mm aperture, with a four-layer\ncoil based on cos(\u03b8) geometry and strong grading [554,555].\n540\n\nFig. 10.32: Coil layout for the LHC dipole, and equivalent coil width (width of the red sector, left) and\nquantity of conductor versus equivalent coil width (right).\nIn the 2000s the HD2 LBNL dipole reached 13.8 T at 4.5 K, with a novel coil configuration based\non a two-layer block design. Unlike to previous models, which all had an aperture of 50 mm, this magnet\nhas a free bore of 36/43 mm diameter [556].\nIn the second half of the 2010s, the Fresca2 CERN-CEA dipole reached 14.6 T at 1.9 K, with\na coil configuration based on a four-layer block design. This magnet, conceived as a cable test station\noperating at 13 T, has a free bore of 100 mm diameter [557,558]. All of its features conform to accelerator\nrequirements, except for the very large coil width (80 mm, see Fig. 10.33) that makes it unaffordable.\nIn the second half of the 2010s, some 11 T dipoles short models reached 12.0 T [559, 560] both\nat CERN and in FNAL in a 60 mm aperture at 1.9 K.8 Note that the coil has the same width as the\nLHC dipoles, and therefore the higher field is obtained by higher current density (540 A/mm2 rather than\n360/440 A/mm2 at nominal current), see Fig. 10.33. The scaling to 5 m showed degradation of perfor-\nmance after thermal cycles in the long magnets; nevertheless, the programme achieved two significant\nresults: (i) the first double aperture Nb3Sn dipole magnet, fully compatible with machine operation and\n(ii) the first scaling of Nb3Sn coils to 5 m lengths, reaching a bore field above 11 T.\nIn the second half of the 2010s, MDPCT1 dipole reached 14.5 T at 1.9 K in a 60 mm aperture. This\nmagnet, made at FNAL, is a four-layer cos(\u03b8) dipole with grading. This is the first dipole to reach fields\nabove 14 T at 4.5 K [561], and also the first to reach more than 14 T with a coil width of the order of\n50 mm (as compared to 80 mm of Fresca2). After reassembly and after a thermal cycle the performance\ndegraded irreversibly by more than 10% [561].\nSince 2015, the HL-LHC interaction region triplet quadrupoles [543,544,562] showed very good\nreproducibility of performance (11.3 T peak field in nominal conditions), nominal currents were also\nachieved at 4.5 K in all models, 13 T was achieved in many short models, scaling to 7.15 m lengths, and\nthere was no degradation of performance after thermal cycle. The project is halfway through production\nat the moment of writing.\nMagnet designs: cos(\u03b8), block coil, common coil\nAs shown during the EuroCirCol studies [536], the target magnetic field can be achieved with different\ndesigns, each one presenting opportunities and challenges. The more classical way is to follow the cos(\u03b8)\nconfiguration; a two-layer design can give 12 T dipoles [552] with a coil width of the order of 35-40 mm,\nand a third and fourth layer are needed to reach 14 T operational fields as in MDPCT1. The first option\nis being developed in INFN and at CERN (FalconD) and a proposal for a four layer coil was put forward\n8Note the possible confusion between the magnet name (11 T) and the maximum achieved field (12.0 T).\n541\n\nFig. 10.33: Operational and achieved field versus coil width in LHC and Tevatron colliders, and in Nb3Sn\nshort models (left), and 11 T, MDPCT1 dipoles, and in common coil and CCT demonstrators (right).\nFig. 10.34: Conceptual design of 14 T and 12 T magnets: BOND (left), FalconD (centre left), SMACC1\n(centre right), F2D2 (right).\nby INFN for EuroCirCol [563].\nThe design based on block coils holds the record in field today and therefore is a natural alternative\nto the cos(\u03b8) design. This option is being pursued by CERN, with a two-layer coil and a 25 mm wide\ncable (BOND [564]), and by CEA-Saclay with a four-layer coil including grading (F2D2 [565]) and an\nintermediary step with flat racetrack coils (R2D2 [566]). As an example, the cross-section and the main\nparameters of the BOND magnet are given in Fig. 10.34 and Table 10.19. The coil width, as for other\ndesigns, is of the order of 50-55 mm. This is a first list of parameters of a design that could be further\noptimised to reduce the conductor mass.\nThe main differences with respect to the designs presented in 2019 [536], are (i) 20% lower stored\nenergy due to the lower field, (ii) a maximum hotspot temperature of 270 K in case of a quench with\nnominal protection, and (iii) a coil stress below 150 MPa. The conductor mass is 10% lower, and current\ndensities of the 2025 baseline are very similar to the current densities of the 2019 baseline in the inner\nlayer (all 2019 designs use grading).\nA third option is the common coil design, which is an intrinsically double aperture magnet, based\non racetrack coils plus non-planar correction coils; the idea has been proposed in the 90\u2019s [567], and\ntoday is the design that has been adopted for the Chinese SppC dipole. In 2022, IHEP built a a hybrid\nNb3Sn/Nb-Ti technology demonstrator magnet called LFP1-U that reached 12.5 T in two small 14 mm\ndiameter apertures [568], and 90% of short sample at 4.5 K; see Fig. 10.33. The next step for IHEP is\nLFP3, aiming to produce 16 T, with 13 T obtained from Nb3Sn plus 3 T from HTS [569]. The common\ncoil path is being followed by CIEMAT, aiming at a 14 T operational field with Nb3Sn, based on a\ncommon coil design in a 50 mm aperture ( [570] and DAISY design [571]. Recently, the PSI team has\nmade a significant improvement in the design, finding an asymmetric configuration of the coil that allows\nhaving planar correction coils of the same type as the common coils [572]. This design will be applied\nto CIEMAT magnets.\n542\n\nTable 10.19: Parameters for possible designs of 12 T and 14 T, scaled to 14.3 m magnetic length.\nFalconD\nSMACC1\nBOND\nF2D2\nDAISY\nCoil type\ncos(\u03b8)\nStress-\nBlock\nBlock\nCommon\nManaged\nCoil\nCoil\nCoil\nCommon Coil\nGraded\nField\n(T)\n12\n12\n14\n14\n14\nCurrent\n(kA)\n19.9\n12.7\n19.3\n9.2\n15.4\nPeak field\n(T)\n12.5\n12.6\n14.8\n14.6\n14.6\nLoadline margin\n(%)\n25\n23\n18\n24\n19\nEquivalent coil width\n(mm)\n37.4\n20.1+19.1\n53.4\n23.9+27.5\n31.7+23.0\nJ overall\n(A/mm2)\n418\n411/603\n348\n299/438\n326/346\nJ superconductor\n(A/mm2)\n1204\n1205/2129\n967\n875/1968\n933/982\nJ copper\n(A/mm2)\n1337\n1339/1774\n1074\n973/1093\n1037/909\nStored energy\u2020\n(MJ)\n15.5\n22.9\n29.5\n30.0\n31.9\nInductance\u2020\n(mH)\n64\n266\n146\n692\n252\nCoil energy density\n(J/mm3)\n0.079\n0.109\n0.089\n0.098\n0.079\n\u2020 FalconD and F2D2 designs are single aperture; here stored energy and inductance are scaled to two apertures.\nMagnet designs based on stress management\nA stress managed magnet [573] design can be defined as a design where the supporting structure is not\nexternal, as in the cos(\u03b8) layout, or external and internal, as in the block and common coil designs, but\nit is spread within the coil as a metallic winding former. The advantage is twofold: (i) the structure can\nintercept forces and avoid stress accumulation and (ii) the winding former acts as a winding, reaction\nand impregnation tooling, thus, accelerating manufacturing processes. This can allow the use of higher\ncurrent densities in the windings, though this advantage is compensated by the winding former, which\ndilutes the effective current density. A disadvantage could be that after epoxy impregnation, bonded in-\nterfaces are loaded in tension and may break, leading to long training. Alternatives to epoxy impregnation\nare being studied.\nStress-managed structures may be the only way to reliably reach fields above 15 T. The US-MDP\nresearch programme is strongly investing in this direction [574\u2013576], proposing two designs both based\non stress management. A stress managed cos(\u03b8) , where a cos(\u03b8) coil is wound on a former that includes\nthe wedges, is being studied at FNAL. A Nb3Sn coil in mirror configuration has reached 12.7 T at 87%\nof short sample limit [576].\nA fully stress-managed magnet is the CCT (canted cosine theta) configuration, where each turn is\nsupported by a rib integrated to a former. This design, also called tilted solenoid or double helix, dates\nback to the early 1970s [577] and has been adopted by LBNL since the mid 2000\u2019s, aiming to reach fields\ntowards 20 T [578]. A drawback of CCT with respect to the previous option is that the use of conductor\nis less optimised, since part of it is used to generate a solenoidal field that is cancelled by the other coil.\nHowever, the structure is totally mixed with the coil \u2013 a kind of endoskeleton \u2013 making easier protection\nand mechanics and possibly allowing higher current densities.\nThe short model CCT5 built at LBNL reached 8.5 T with a Nb3Sn winding using a 10 mm cable\nover a 90 mm aperture [578]. At PSI, using a similar design and the same cable, 10.1 T were reached\nin a 60 mm aperture short model named CD1 [579]. In both cases the overall current densities (over the\ninsulated coil) are very large (800 and 1000 A/mm2 respectively): a field of 8-10 T is reached with an\nequivalent coil width of the order of 17 mm; see Fig. 10.33. PSI is currently pursuing a stress-managed\nasymmetric common coil as a candidate for 14 T (SMACC1) [572].\n543\n\nFig. 10.35: Critical (engineering) current densities of different HTS conductors, Nb3Sn, and Nb-Ti.\nReproduced from [581].\nHybrid Nb-Ti/Nb3Sn magnets\nMaterial grading is an option that consists of using a cheaper and less performant material in the low field\nregion. It has been used for the D19H magnet [580], and is being used in demonstrators (for instance\nLPF1 in the IHEP programme [568]). Unlike the current grading, where higher current density is used for\nlow field regions (as in CERN Elin, MSUT, D20, and in the LHC dipole), here similar current densities\nare used in the inner and outer layer, but the outer layer is made with Nb-Ti. Nb-Ti at 1.9 K with an\noverall current density of the order of 400 A/mm2 can be used in coil regions not exceeding 8 T; this\ncould lead to a significant reduction of the mass of Nb3Sn conductor (>30%); however, this prevents\noperating at 4.5 K, since the temperature margin of Nb-Ti at 80% of the loadline at 1.9 K is only about\n2 K.\n10.4.4\nHigh Temperature Superconductor: perspectives and challenges\nHigh Temperature Superconductor: opportunities\nHigh Temperature Superconductor (HTS), discovered in the mid 80\u2019s in the family of cuprates, has many\ninteresting features that make it a game changer in superconducting technology, see Fig. 10.35 [581]: (i)\nhigh values of critical current density (>2000 A/mm2) also above 20 T, opening the way to high fields, (ii)\nthe ability of sustaining high current densities and fields at and above 20 K, opening the path to cheaper\ncooling systems (even though liquid nitrogen cooling is still considerably out of reach for high field\nmagnets), and (iii) a much higher stability versus thermo-mechanical perturbation due to the increase\nin enthalpy margin at higher operating temperatures. The HFM programme is exploring the options of\ndipole magnets in the 14 to 20 T range, at temperatures between 4.5 K and 20 K, thus covering a COM\nenergy in the range of 85 to 120 TeV.\nTwo types of high-temperature superconductors are commercially available: BSCOO and RE-\nBCO. BSCOO [582], produced mainly by one company in the US, has the advantage of being available\nas round wire with small filaments. Its use is complex since, like Nb3Sn, it needs a reaction after wind-\ning, but at 900\u00b0C in oxygen rich \u223c50 bar atmosphere. A process-compatible electrical insulation system\nmust be selected. Moreover, BSCOO is brittle and, hence, requires careful handling in coil manufac-\nturing and appropriate mechanical structures to respect stress limitations. Several short magnet models\n544\n\nhave successfully been built in the US; see Section 10.4.4.\nREBCO [583] is produced by multiple suppliers worldwide; this conductor is produced in the\ngeometry of a tape, and its industrialisation recently profited from large private investments aiming at\nultra-compact magnet systems for fusion (solenoids and toroidal field coils) with \u223c20 T coil field. This\nhas reduced the price in the past ten years by a factor three. The conductor does not require a heat\ntreatment after winding. On the other hand, (i) unit lengths are still typically short ( 300 m) and longer\nlengths today affect the cost, (ii) REBCO is a highly anisotropic conductor (anisotropy factor of \u223c5).\nThe challenge is not only to make a fully transposed (Rutherford-like) cable from tape to wind a coil, but\nalso to deal with mechanical properties: while very robust against tension and transverse compressive\nstress, delamination of the tape under tensile transverse stress causes degradation. Another challenge is\nto control hysteresis losses and field quality as the equivalent filament size is very large in the plane of\nthe tape (typically 4-12 mm).\nDevelopment of iron-based superconductors [584, 585], is being strongly pursued in China. The\ncritical current density achieved is still lagging a factor 2-3 behind the expectations set ten years ago,\nbut based on raw-material prices the material has the potential of a very low cost; this could become a\nsignificant advantage for a high-field collider magnet, where about half of the price is the superconductor.\nGiven their potential, the HFM Programme is investing in REBCO tape technology development\nin the KIT/CERN Collaboration on Coated Conductor (KC4), as well as in iron-based superconductor\ntechnology (CNR-SPIN/CERN), aiming at a round wire with powder-in-tube layout [586].\nFields achieved in EuCARD2 and US-MDP dipole models\nBetween 2015 and 2020, three dipole magnets based on REBCO were built within the framework of FP7-\nEucard2 programme [587]. In CEA, a dipole technology demonstrator based on double REBCO ribbons\nand three racetrack coils, without aperture, reached 5.4 T [583]. In the same period, two magnets were\nbuilt with Roebel cable: in CEA a 40 mm aperture dipole was manufactured with a cos(\u03b8) configuration,\n12 mm coil width, reached 1.16 T due to one degraded coil [588]. This magnet will be re-tested with\na replacement coil. At CERN a dipole was built with the same cable, with an aligned block dipole\nconfiguration in a 40 mm aperture, reaching 3.35 T at 5 K and 4.3 T at 4.5 K (FeatherM2.12 and 2.34\n[587,589]).\nMore recently, the US programme, US-MDP, has developed several Bi-2212 racetrack coils and a\nCCT magnet (Bin5) which reached 1.6 T in a 31 mm aperture [590]. A CCT with a CORC\u00ae cable based\non a REBCO tape reached 2.9 T in a 65 mm aperture [591], with a more recent test exceeding 5 T.\nPlans for 20 T: hybrid or full-HTS?\nThe FP-7 Eucard2 programme aimed at an HTS insert for a Nb3Sn external coil [587]; the same strategy\nhas been adopted by US-MDP and IHEP. US-MDP proposes to achieve 20 T via a magnet using different\ndesigns [575]: on the one hand an all-CCT hybrid, and on the other hand a COMB (Conductor on Molded\nBarrel) HTS part, and stress managed cos(\u03b8) for the inner Nb3Sn layer and a classical cos(\u03b8) for the outer\nlayer. The IHEP common coil design is also based on an HTS inner coil and Nb3Sn outer coils [569],\nwith HTS contributing 5 T to the field.\nThe hybrid option HTS/Nb3Sn does not allow the higher operational temperature that would be\npossible with a full-HTS magnet (e.g., 20 K). For the time being, Nb3Sn is still much better mastered\nthan HTS, and therefore both US and China are working on the hybrid option, at least to make technology\ndemonstrators. It must be noted, though, that the performance-related cost for HTS at 20 K is today two to\nthree times larger than at 4.5 K, and since the conductor is the driving parameter of the estimated magnet\ncost, this can be a showstopper for the 20 K option. Improved performance at 20 K is a development\nobjective for REBCO conductor.\n545\n\nChallenges: field reproducibility, mechanics, hysteresis losses, protection\nA stringent requirement for accelerator main magnets is the precision and reproducibility of the transfer\nfunction not only at high field, but also at injection and during the ramp (10\u22124 to 10\u22125 needed relative to\nmain field). This aspect is strongly related also to the design of insulation and protection: some HTS coils\nthat are being made for fusion operate in DC mode and make use of non-insulated coils, allowing current\nredistribution that eases reaching higher fields. This option is not suitable for accelerator magnets, which\nrequire a dielectric insulation. Metal insulations are also being studied, but these are not yet proven to be\nsuitable for accelerator magnets in terms of field control, ramp losses, and protection.\nAnother issue is related to transverse (to the tape surface) tensile stress in the winding that causes\ndelamination of the superconducting layer from the supporting substrate, degrading the cable perfor-\nmance. Careful design may control this effect.\nThe high temperature margins of HTS have the drawback that quench velocities are slow, and the\nvoltage rise that is monitored to detect the quench can take too long. Consequently, quench protection\nand detection strategies need to significantly different from those of LTS magnets. Moreover, at 20 T the\nenergy density to be absorbed by the coil is well above the enthalpy limit: detection of, and protection\nfrom, quenches in HTS coils are still major challenges, and coils that reached 20 T for fusion applications\nwere lost during quenches. Systems that can provide a partial extraction of the stored energy for long\nmagnets are being studied. Another possibility would be to avoid quenches, i.e., having a system that,\nonce a temperature increase is detected, manages to prevent a resistive transition or at lest a thermal\nrunaway.\nFinally, stability can be achieved by very large filaments: HTS tapes used for fusion have a width\nof 4 to 12 mm. This width leads to a large magnetisation, giving rise to hysteresis losses, field quality\ndistortions, and field drifts, that are expected to be larger than for LTS, with long field quality drifts\nexpected in simple tape-stack cables. These effects should be included in the conception of a novel cable\nthat could make REBCO compatible with HEP requirements.\nIn conclusion, it can be said that the technological readiness level (TRL) of HTS technology for\naccelerators lags considerably behind that of LTS conductors. Vigorous R&D is therefore needed, also\nin concert with other fields and applications, over the coming years to demonstrate how HEP can benefit\nfrom the potential advantages of HTS technology.\n10.5\nFCC-hh accelerator systems and technical infrastructures\n10.5.1\nCryogenics requirements with 1.9 K Nb3Sn magnets\nIn the latest accelerator baseline, the tunnel length has been reduced to 90.7 km with eight access points,\nrequiring an update of the layout of the cryogenic system, which is proposed and described in Fig. 10.36.\nThe current cross-sectional view of the cryogenic distribution line (QRL), and the layout of the individual\npipes (lines) can be found in Fig. 10.37. Both figures refer to an FCC-hh operation scenario with 14 T\ndipole magnets [592].\nThe layout of the cryogenic system seen in the figure consists of two accelerator cryoplants at\npoints PB, PD, PF, PH, PJ, and PL. Each of these cryoplants has a cooling capacity of 53.1 kW at\n4.5 Keq, including 9.9 kW at 1.9 K.\nTwo cryoplants are foreseen in the high-luminosity insertion region at points PA and PG, each of\nthem with a capacity of 78.9 kW at 4.5 Keq, including 17.6 kW at 1.9 K. Detector cryoplants will be\ninstalled in PA, PD, PG and PJ, with a 1.5 kW at 4.5 Keq, similar to the existing helium cryoplant of the\nCMS experiment. The cryogenic system also includes twenty-four boil-off re-liquefiers.\nWithout considering detector cryoplants and the boil-off re-liquefiers, this represents a total cryo-\ngenic cooling capacity required of 950 kW at 4.5 Keq. It includes 100 kW at 4.5 Keq for the cryogenics\nof the 2 high-luminosity insertion regions (inner triplets).\n546\n\nFig. 10.36: Updated layout of the FCC-hh cryogenic system layout.\nThis translates into a total electrical power requirement of about 210 MW to operate the cryogenic\nsystems. Neglecting the two high-luminosity insertion regions, the total electrical power required for the\nFCC-hh cryogenic system decreases to 186 MW.\nThe advantage of this layout is the reduced cryogenic sector length, decreasing to 4.8 km of cool-\ning length per cryoplant compared to 8.4 km in the CDR. This reduction directly translates into a smaller\npumping line. Consequently, the cryogenic distribution line is reduced from DN1350 to DN1100 type.\nThe total helium inventory for the cryogenic system is estimated at 820 t.\nThe key parameters for the FCC-hh accelerator cryogenic system discussed above are summarised\nin Table 10.20 and neglect the detector needs and cryogenics associated with the high-luminosity inser-\ntion regions in PA and PG.\n10.5.2\nPower converters\nA preliminary study has been conducted to assess power converter requirements, focusing on the neces-\nsary footprints and volumes in alcoves and surface areas.\nThe study specifically examines the powering of the superconducting magnets. To stabilise power\nconsumption from the utility grid and minimise the sizing of upstream electrical components (e.g., trans-\nformers, cables), energy storage systems integrated with the power converters are required. These sys-\ntems store energy during the accelerator\u2019s ramp-down phase and supply it during beam acceleration.\nGiven their substantial space requirements, these storage elements must be placed in alcoves to minimise\npower losses from long cable runs.\nPreliminary findings, based on FCC-hh magnet specifications, suggest that the space allocated for\nFCC-ee power converters (in terms of footprint and volume) is comparable to what is needed for the\n547\n\nFig. 10.37: Layout of the cross section of the FCC-hh QRL as of the CDR (left) and in the current\nconfiguration (right). The line B represents the very low pressure helium return line; the line C represents\nthe supercritical helium supply line; the line D represents the low pressure helium return line; the line E\nrepresents the helium thermal shield supply line; the line F represents the helium thermal shield return\nline.\nTable 10.20: Key parameters for the cryogenic system of the FCC-hh. A safety factor of 1.2 is included\nin the helium cryogenic capacity. These figures do not include the high-luminosity insertion regions with\nthe triplet quadrupoles, or the requirements of the experiment detectors.\nFCC-hh Parameters\nCDR [2018]\nFSR [2025]\nCircumference [km]\n97.75\n90.7\nDipole field [T]\n16\n14\nCentre of mass energy [TeV]\n100\n85\nSynchr. radiation for two beams [MW]\n4.8\n2.4\nMagnet temperature [K]\n1.9\n1.9\nBeam screen temperature [K]\n[40 - 60]\n[40 - 60]\nHelium cryogenic capacity at 4.5 K equivalent [kW]\n1214\n947\nNumber of cryo islands\n6\n8\nTotal number of cryoplants\n10\n16\nArc cooling length [km]\n84\n76.8\nElectrical consumption [MW]\n266\n208\nHelium inventory [t]\n880\n820\nFCC-hh magnet powering including energy storage.\n10.5.3\nTechnical systems\nThe technical infrastructures described in this section, designed to meet the needs of the FCC-ee, also\nalready incorporate the requirements for FCC-hh.\nElectrical networks\nThe electrical connections to the 400 kV lines of RTE (France\u2019s Transmission System Operator) have\nbeen designed to accommodate the power demands of both FCC-ee and FCC-hh, with the latter requiring\n548\n\nabout the same power as the FCC-ee in the t\u00aft mode. Three connection points are planned, each rated at\n220 MVA, and will be interconnected through an internal high-voltage network.\nFor FCC-ee, the estimated peak power demand for t\u00aft operation is approximately 360 MW, which\nis well below the 660 MVA capacity of the grid connection. This setup provides redundancy in the power\nsources, ensuring reliable operation. However, the power demand is not evenly distributed between all\npoints. Specifically, PH, which houses the RF systems, has a substantial power requirement of 200 MW.\nTo address this, a dedicated 400 kV substation will be allocated for the RF power supply. The two\nremaining connection points, PA and PD, will handle all other loads via the internal high-voltage network\nand can operate redundantly.\nFor FCC-hh, the primary power consumers will be the cryogenic systems, with their load more\nevenly distributed across all three connection points. The eight points of the FCC-hh ring will require a\npower rating between 40 and 60 MW each.\nUnlike FCC-ee, all three grid connections will be essential for powering FCC-hh, leaving no\nredundancy in power sources. In the event of a power source failure, accelerator operation would not be\npossible. However, critical systems could continue running in a degraded mode to maintain minimum\ncryogenic conditions.\nCooling and ventilation\nThe redistribution of thermal loads from FCC-ee to FCC-hh will require the installation of some addi-\ntional cooling towers at most points, except for PH, where a lower capacity will suffice. However, the\noverall thermal load in the tunnel will be reduced as the new loads will be located mainly in service\ncaverns and surface buildings.\nThese adjustments will be limited to designated service areas, ensuring that modifications to cool-\ning networks remain localised. In addition, the tunnel ventilation systems will remain unchanged, with\nonly minor adaptations required for specific service and experiment caverns.\nSafety systems\nFor FCC-hh, additional safety measures will be necessary. Unlike FCC-ee, where oxygen deficiency\nis not a concern in the arc tunnel, the presence of cryogenic systems in FCC-hh requires dedicated\nmonitoring and protective measures. Consequently, oxygen deficiency hazard detection systems will be\ninstalled in the tunnel, alcoves, and service caverns to maintain a safe working environment.\n10.5.4\n3D integration studies\nThe 3D integration studies of the FCC-hh have been detailed for all areas of the underground tunnels and\ncaverns, fitting the requirements from the work packages. This section presents the results of the con-\nfiguration and layout of the accelerators and infrastructure systems that were studied for the feasibility\nstudy report. This is an evolution of the previous studies made for the conceptual design report. [13,307]\nThe 3D integration studies take into account both of the configurations of the FCC-ee and FCC-hh to\nensure space compatibility.\nIntegration of point PA and point PG\nPoint PA and point PG will serve as large experiment points, hosting detectors in the cavern in both the\nFCC-ee and the FCC-hh phases of operation. The cavern size and extent meet the needs of the detectors\nfor both FCC-ee and FCC-hh. In addition, for the FCC-ee, the long straight sections (LSS) on either side\nof point PA and point PG will host the beamstrahlung dumps and the polarimeter system (see Fig. 10.38\n549\n\nand Fig. 10.39). The LSS of point PA will also host the end of the transfer line from the injector linac,\ninto the booster.\nIP-A\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n438.5\n20\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 10.38: FCC underground - civil engineering in point PA\nIP-G\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\n156.8\n10\n160\n5\n135\n5\n5 20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n438.5\n20\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 10.39: FCC underground - civil engineering in point PG\nThe figures included in this chapter represent the results of the 3D integration studies for point PA\nand point PG.\nFig. 10.40: FCC-hh point PA - experimental cavern cross-section\n550\n\nFig. 10.41: FCC-hh point PA - experimental cavern iso view\nIntegration of point PD and point PJ\nPoint PD and point PJ will serve as small experiment points, hosting detectors in the cavern in both the\nFCC-ee and the FCC-hh phases of operation (see Fig. 10.42 and Fig. 10.43). The cavern size and extent\nmeet the needs of the detectors for both FCC-ee and FCC-hh. In addition, for the FCC-ee, the long\nstraight section (LSS) on either side of point PD and point PJ will host the beamstrahlung dumps.\nIP-D\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n16.4\n438.5\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 10.42: FCC underground - civil engineering in point PD\nIP-J\nEXPERIMENTAL\nCAVERN\n156.8\n10\n160\n5\n135\n5\n60\n5\n20\n14.5\n14.5\n14.5\n18.6\n14.8\n156.8\n10\n160\n5\n135\n5\n5\n20\n14.5\n14.5\n14.5\n18.6\n16.4\n14.8\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 4\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\nTUNNEL WIDENING\nSECTION 3\nTUNNEL WIDENING\nSECTION 2\nTUNNEL WIDENING\nSECTION 1\n1.6\n1.6\n0.8\n2.7\n1\n1.5\n1.6\n0.8\n2.7\n1\n1.5\n1400\nLONG STRAIGHT SECTION\n5\n100\nTUNNEL WIDENING\nSECTION 5\n60\nTUNNEL WIDENING\nSECTION 4\n5\n100\nTUNNEL WIDENING\nSECTION 6\nTUNNEL WIDENING\nSECTION 5\n16.4\n438.5\n438.5\nTUNNEL WIDENING\nSECTION 7\nTUNNEL WIDENING\nSECTION 7\nVariable\nVariable\n5.5\n5.5\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\nELECTRICAL ALCOVE\n(see drawing FCC-CE-11000000003)\n9670\n9670\nARC\nARC\nMAIN BEAM TUNNEL\nMAIN BEAM TUNNEL\nFig. 10.43: FCC underground - civil engineering in point PJ\nThe figures included in this chapter represent the results of the 3D integration studies for the point\nD and the point J.\n551\n\nFig. 10.44: FCC-hh point PD and PJ - experiment cavern cross-section\nFig. 10.45: FCC-hh point PD and PJ - experiment cavern iso view\nIntegration of the arcs\nThe FCC-hh superconducting magnets will have a maximum diameter of 1.2 m, regardless of the tech-\nnology used (Nb3Sn, HTS, etc.), resulting in the tunnel cross section shown in Fig. 10.46. For the FCC-ee\nring, the transport area is 2.2 m wide, allowing personal vehicles to pass each other freely throughout\nthe tunnel. In contrast, for FCC-hh, this area may be reduced to 2 m, restricting vehicle crossings to\ndesignated alcove lay-bys spaced out every 1.6 km. Consequently, traffic control will require a different\napproach compared to FCC-ee.\nThe figures included in this chapter represent the results of the 3D integration studies in the arcs.\n552\n\nFig. 10.46: Cross section of the tunnel for the FCC-hh layout in the arcs.\nNext phase for the integration studies\nThe integration studies have been made with pre-design of volumes and will evolve with detailed techni-\ncal design in the next phase of the FCC studies. Optimisation of the 3D integration studies with respect\nto the requirements from work packages will continue for all the areas following the identified technical\nand space needs:\n\u2013 Optimisation of the large experiment points PA and PG [375] [376] and small experiment points\nPD and PJ [377], integrating more detailed detectors design in the experiment caverns,\n\u2013 Optimisation of the arc half-cell [382].\n10.5.5\nFCC-hh power demand\nIn FCC-ee, the primary power-consuming systems are the RF systems, which compensate for syn-\nchrotron radiation losses.\nThese systems must supply approximately 100 MW to the beams across\ndifferent operating modes. In Z mode, RF power accounts for 65% of the total power demand, while\nin t\u00aft mode, it represents 37.5%. These values reflect the energy requirements necessary to sustain beam\nstability and luminosity performance.\nFor FCC-hh, the dominant power consumer will be the cryogenic systems required for magnet\ncooling. The cryogenic capacity is determined primarily by two factors: the static heat load of the\nmagnets and the synchrotron radiation deposited on the beamscreen. The cryogenic power demand\nvaries depending on the operating temperature of the magnets and the beamscreen. Table 10.21 presents\nthe power demand for the baseline scenario where 14 T Nb3Sn magnets are cooled to 1.9 K, with a total\nsynchrotron radiation power of 2.4 MW and a beamscreen temperature ranging in the interval 40 \u2013 60 K.\nThe cryogenic systems for the arc magnets alone require 185 MW of electrical power, with an\nadditional 22.5 MW needed for the high-luminosity insertions inner-triplet magnets (two sets for two\nexperiments). The RF power requirement is estimated at 23 MW during the energy ramp and decreases\nto 12 MW at flat top, during beam collisions.\n553\n\nTable 10.21: FCC-hh power demand by technical systems at 85 TeV beam centre-of-mass energy.\nSystem\n85 TeV\nRadio frequency [MW]\n17\nCryogenics [MW]\n207.5\nCooling & ventilation [MW]\n40\nMagnet powering [MW]\n33\nExperiments [MW]\n24\nData centre [MW]\n8\nGeneral services [MW]\n26\nTotal power [MW]\n355\nMagnet powering will be managed from alcoves with interconnection boxes, and power losses\nwill be minimised through short cable sections, reducing demand to 33 MW. The estimated power\nneeds for experiments are based on the LHC experiments (ATLAS and CMS), while general services\npower requirements have been extrapolated from LHC operations. Although some figures require further\nrefinement, these estimates align with expected scaling from the LHC.\nFor a configuration using Nb3Sn magnets cooled to 1.9 K and generating 2.4 MW of synchrotron\nradiation, the total power demand is approximately 360 MW, comparable to that of FCC-ee. The FCC-\nhh power demand might further be reduced to below 300 MW, if the magnet temperature can be raised\nto 4.5 K.\nOperational model\nThe accelerator operational model determines the energy consumption. The power demand varies de-\npending on the time of year and the operational state of the machine. The machine schedule defines\nsix operational periods: (1) Shutdown; (2) Commissioning; (3) Physics operation; (4) Short downtime\n(without machine access); (5) Technical stops (longer downtimes); and (6) Machine development. The\npower demand for each period is shown in Table 10.22.\nTable 10.22: FCC-hh power demand during different operational periods.\nPeriod\n85 TeV\nShutdown [MW]\n122\nTechnical stop [MW]\n122\nDowntime [MW]\n122\nCommissioning [MW]\n324\nMachine development [MW]\n324\nBeam operation [MW]\n355\nThe introduction of a eco-mode for the cryogenic systems during shutdown, reducing power con-\nsumption to 83 MW, significantly decreases the power demand during non-operational periods. The\nannual schedule consists of:\n\u2013 120 days of shutdown,\n\u2013 30 days of commissioning,\n\u2013 20 days of machine development,\n\u2013 10 days of technical stops, and\n554\n\n\u2013 185 days of physics (beam operation).\nThe FCC-hh machine availability is expected to be similar to that of LHC, with an operational efficiency\nof approximately 80%, corresponding to an expected period of beam collisions of 1700 hours.\nEnergy consumption\nBased on the operational schedule and the expected power demand throughout the FCC-hh programme,\nthe estimated annual energy consumption at 85 TeV is shown in Table 10.23.\nTable 10.23: FCC-hh annual energy consumption at 85 TeV collision energy.\nBeam Energy\n42.3 TeV\nAnnual energy consumption [TWh/y]\n2.34\nFor FCC-hh, total annual energy consumption is slightly higher compared to the energy consump-\ntion of FCC-ee because of the continuous operation of cryogenic systems. Furthermore, power demand\nremains relatively high even during shutdown periods. However, introducing an eco-mode has signifi-\ncantly reduced cryogenic power consumption during non-operational phases.\n10.5.6\nOther systems\nOther accelerator systems for the FCC-hh, e.g., beam-transfer systems, the cryogenic beam vacuum\nsystem, beam diagnostics, etc., are described in the Conceptual Design Report (CDR) [593].\n10.5.7\nOn-going studies\nA key feature highlighted during the CDR phase is the potential application of an HTS coating to the\nbeam screen. This approach was explored as a mitigation measure to address the increased resistivity of\nthe beam screen due to its higher operating temperature (around 50 K), which was chosen to reduce the\ndemands of cooling power.\nFollowing the publication of the FCC CDR, extensive research has focused on conducting com-\nprehensive analyses of the coating\u2019s performance, examining its electromagnetic properties and other\nrelated factors.\nA prototype beam screen incorporating the suggested HTS coating is currently under construction.\nThis will facilitate a comprehensive examination of its magnetic characteristics, such as the overall field\nquality of both the beam screen and the HTS coating. The tests will include dipole and quadrupole ex-\nternal magnetic fields. Impedance measurements will also be attempted, if feasible, to fully characterise\nthe HTS coating.\nThe application of an amorphous carbon coating to the HTS presents an opportunity to elevate the\nbeam screen\u2019s operating temperature, as it inherently resolves vacuum instability issues. The optimal\noperating temperature will be determined by balancing multiple factors, including HTS performance,\nbeamscreen resistivity, effects on beam dynamics, and benefits for the cryogenic system. These aspects\nwill be further studied in the next project phase to identify the optimum operating temperature.\nFinally, FCC-hh will require the installation of the cryogenic distribution line (QRL) that has a\ndiameter below 1.1 m regardless of the operational temperature of the magnets (1.9 K, or 4.5 K).\n555\n\nReferences\n[1] D. Shatilov, How to increase the physics output per MW.h for FCC-ee? - Parameter optimization\nfor maximum luminosity. Eur. Phys. J. 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IEEE Transac-\ntions on Applied Superconductivity 7(2), 547 (1997). https://doi.org/10.1109/77.614654\n587\n\n[581] N. Mounet (ed.), 2021 European Strategy for Particle Physics \u2013 Accelerator R&D Roadmap.\nCERN Yellow Reports:\nMonographs (CERN, 2022).\nURL https://arxiv.org/abs/\n2201.07895\n[582] D.C. Larbalestier, et al., High-Tc superconducting materials for electric power applications. Na-\nture 414, 368\u2013377 (2002). https://doi.org/10.1038/35104654\n[583] M. Durante, et al., Realization and first test results of the eucard 5.4-T REBCO dipole magnet.\nIEEE Transactions on Applied Superconductivity 28(3), 4203805 (2018). https://doi.org/\n10.1109/TASC.2017.2780080\n[584] G. Biswal, K.L. Mohanta, A recent review on iron-based superconductor.\nMaterials Today:\nProceedings 35, 207\u2013215 (2020).\nhttps://doi.org/10.1016/j.matpr.2020.03.211.\nURL\nhttps://doi.org/10.1016/j.matpr.2020.03.211\n[585] G.R. Stewart, Superconductivity in iron compounds. Reviews of Modern Physics 83, 1589 (2011).\nhttps://doi.org/10.1103/RevModPhys.83.1589\n[586] A. Malagoli, et al., Development of a scalable method for the synthesis of high quality (Ba,K)-122\nsuperconducting powders. IEEE Transactions on Applied Superconductivity (2025). Early Access\n[587] G. Kirby, et al., First Cold Powering Test of REBCO Roebel Wound Coil for the EuCARD2\nFuture Magnet Development Project. IEEE Transactions on Applied Superconductivity 27(4),\n1\u20137 (2017). https://doi.org/10.1109/TASC.2017.2653204\n[588] M. Durante, et al., Overview of HTS accelerator magnet developments at CEA saclay. IEEE\nTransactions on Applied Superconductivity 34(5), 4002905 (2024). https://doi.org/10.1109/\nTASC.2024.3045679\n[589] L. Rossi, C. Senatore, HTS Accelerator Magnet and Conductor Development in Europe. Instru-\nments 5(1), 8 (2021). https://doi.org/10.3390/instruments5020008\n[590] T. Shen, et al., Design, fabrication, and characterization of a high-field high-temperature supercon-\nducting Bi-2212 accelerator dipole magnet. Physical Review Accelerators and Beams 25 (2022).\nhttps://doi.org/10.1103/PhysRevAccelBeams.25.122401\n[591] Y.M. Wang, L. S\u00e1nchez, J. \u00c5gren, J. Huang, R. Forsberg, et al., Colorado geoid compu-\ntation experiment:\noverview and summary.\nJournal of Geodesy, 95, (12) 95(12) (2021).\nhttps://link.springer.com/article/10.1007/s00190-021-01567-9\n[592] F.\nZimmermann,\nScenarios\nfor\nthe\nFCC-hh.\nTech.\nrep.,\nCERN,\nGeneva\n(2024).\nURL https://indico.cern.ch/event/1439072/contributions/6106995/attachments/\n2917946/5120981/FCC_hh_scenarios.pdf\n[593] The FCC Collaboration, FCC-hh: The Hadron Collider. Eur. Phys. J. Spec. Top. 228 (2019). URL\nhttps://doi.org/10.1140/epjst/e2019-900087-0\n588\n\nAppendix A\nCosts\nA.1\nFCC-ee construction\nThe capital cost for construction of the FCC-ee is summarised in Table A.1. This cost includes construc-\ntion of the entire new infrastructure and all equipment for operation at the Z, WW and ZH working points.\nOperation of the FCC collider at the t\u00aft working point will require later installation of additional RF cav-\nities and associated cryogenic cooling infrastructure with a corresponding total cost of 1,260 MCHF.\nTable A.1: Estimated investment costs for different construction domains in 2024 Swiss Francs.\nDomain\nCost\n[MCHF]\nCivil engineering\n6160\nTechnical infrastructures\n2840\nInjectors and transfer lines\n590\nBooster and collider\n4140\nCERN contribution to four experiments\n290\nFCC-ee total\n14 020\n+ Four experiments (non-CERN part)\n1300\nFCC-ee total, including four experiments\n15 320\nThe costs indicated include materials and personnel costs of contractors and suppliers. They do not\ninclude the cost of scientific, engineering, technical and administrative personnel at the host organisation\nor at the collaborating institutes.\nThe total construction cost for CERN amounts to 14 020 MCHF (covering Z, WW and ZH working\npoints), dominated by 45% or 6160 MCHF by civil engineering, which also comprises all site-related\ninvestments. The capital cost for the technical infrastructures, including site-external connections, is\n2840 MCHF, corresponding to 20% of the total construction cost. Another 30%, or 4,140 MCHF, cor-\nresponds to the collider and full-energy booster construction. The cost estimate for the injector complex\nand transfer lines is 590 MCHF. In addition, the CERN contribution to the four experiments is estimated\nat 290 MCHF, while the non-CERN part of the total cost of these four experiments would amount to\napproximately 1300 MCHF, as shown in Table A.1. The investments are distributed over a time frame of\nabout 15 years.\nThe indicated figures include materials and personnel costs of contractors and suppliers. They do\nnot include the cost of scientific, engineering, technical and administrative personnel at the host organi-\nsation or the collaborating institutes. The engagement of this personnel directly leads to the generation of\nnoteworthy socio-economic benefits via the pathways of education, training, direct, indirect and induced\neconomic value added.\nA.2\nFCC-ee operation costs\nA.2.1\nAnnual cost of operations of each stage\nA material cost of 200 MCHF has been estimated by individually categorising each item of equipment\naccording to its nature: fixed installation (1% OPEX), technical infrastructure (5% OPEX), and con-\n589\n\nsumables (3% OPEX). The 200 MCHF figure represents the weighted sum of these categories across all\nsubsystems. Adding an annual electricity cost of 100 MCHF (with some variation depending on the col-\nlision energy point) and approximately 300 MCHF for personnel (1,400 FTEs), the total average annual\noperating cost of FCC-ee across all stages amounts to around 600 MCHF.\nA.3\nFCC-hh Construction and Operational Costs\nA.3.1\nFCC-hh construction\nTable A.2 splits the construction costs into the creation of the infrastructures (subsurface, surface and\nterritorial developments), the enabling technical infrastructures, and the accelerators.\nThe total construction cost amounts to 18 880 MCHF. It is dominated by the cost for the collider\nmagnets, amounting to about 10 000 MCHF. This cost, however, will need to be reviewed in light of\nongoing R&D efforts. In particular, further research into novel types of superconducting materials is\nessential\u2014not only to potentially reduce costs, but also to unlock broader technological benefits and\ncross-sectoral applications.\nThe cost of the four FCC-hh experiments can be estimated only at a later stage, once more detailed\ndesigns of the detectors exist. The construction investments are distributed over a time frame of about 15\nyears.\nTable A.2: Estimated investment costs for different construction domains in 2024 Swiss Francs.\nDomain\nCost\n(MCHF)\nCivil engineering\n520\nTechnical infrastructures\n3960\nInjectors and transfer lines\n1000\nCollider\n13 400\nFCC-hh total\n18 880\nThe costs indicated include materials and personnel costs of contractors and suppliers. They do not\ninclude the cost of scientific, engineering, technical and administrative personnel at the host organisation\nor at the collaborating institutes.\nA.3.2\nFCC-hh operation\nOperational costs for the FCC-hh phase foreseen as a second step in 2070 have not yet been determined.\n590\n\nAppendix B\nInstallation\nB.1\nInstallation planning\nB.1.1\nThe technically-limited timeline for FCC-ee construction\nPreparatory placement studies for the FCC are well advanced. The further timeline is mainly determined\nby the preparation of the civil engineering (subsurface investigations, civil engineering design and ten-\ndering, and the project authorisation processes with the host states, planned to advance in parallel), and,\nafterwards, by the civil construction and the subsequent installation of technical infrastructure and accel-\nerator components. The timeline of FCC-ee in Table B.1, including work already accomplished. More\ndetails on the construction and installation aspects are discussed below.\nTable B.1: Timeline for FCC-ee design, construction, and operation.\nMilestone / phase\nyears\nConceptual Design Study\n2014 \u2013 2018\nTerritorial implementation studies\n2016 \u2013 2025\nDefinition of the placement scenario\n2022\nFeasibility Report ready\n2025\nEarliest Project Approval by CERN Council\n2027/28\nEnvironmental evaluation & project authorisation processes\n2026 \u2013 2031\nMain technologies R&D completion\n2031\nTechnical Design Report ready\n2032\nCivil engineering - Collider\n2033 \u2013 2041\nTI Installation \u2013 Collider\n2039 \u2013 2043\nAccelerator Installation \u2013 Collider\n2041 \u2013 2045\nHW Commissioning \u2013 Collider\n2042 \u2013 mid 2046\nStart Beam Operation \u2013 Collider\nmid 2046 \u2013 2047\nNominal Beam Operation \u2013 Collider\n2048 \u2013 2062\nB.1.2\nFCC-ee technical infrastructure and machine\nThis section outlines a high-level schedule for installing the FCC-ee machine and its supporting infras-\ntructure. Based on the feasibility study, it adopts a 90.7 km circumference layout with eight surface sites.\nThe timeline extends from the start of civil engineering excavation scheduled for January 2033 to the\nanticipated readiness for beam commissioning in July 2046. The plan is divided into two main phases:\n\u2013 Civil construction phase 2033-2041\n\u2013 Installation phase 2038-2046\nCivil engineering strategy integration\nSynergies found between installation planning and civil engineering phase and updated civil engineering\nstrategy\nThe baseline presented in the midterm review outlined eight handovers of individual shaft sectors. Ini-\ntially, all installation work within an arc could only commence after the release of a single designated\n591\n\npoint (see Fig. B.1).\nTo enhance coordination, synergies between civil engineering and installation planning were ex-\nplored. As a result, the civil engineering team restructured the handover process, breaking down the\nsingular shaft-sector handover into multiple phased handovers. The revised civil engineering strategy\n(see Fig. B.2) involves removing the TBMs through the experiment shaft (PX), which allows an earlier\nrelease of the machine shaft (PM) at a technical point.\nAdditionally, a gradual handover approach for arc installation was introduced. The tunnel floor\nand smoke extraction duct will be the final construction activity completed by civil engineering along the\ntunnel arc. To coordinate with the machine installation, the tunnel arc is split into sectors corresponding\nto the alcove locations. Therefore, once civil engineering has completed construction activities up to an\nalcove, the sector can be released for the installation of machine infrastructure.\nFor each shaft sector, the following elements now have distinct release dates:\n1. PM of the experiment point\n2. PM of the technical point\n3. Staged release of the arc done alcove by alcove. 5 to 7 staged handovers are foreseen for one arc\nsector going from the technical point to the experiment point. A separating door will be moved at\nevery handover to separate the two worksites\n4. PX of the experiment point\nThe civil engineering construction durations across each of the sites vary primarily due to the\ndifferent structural layouts, depths and construction methods.\nImpact on installation organisation and planning\nBreaking down the handover process of civil engineering enables an earlier start for installation activities.\nThe early handover of the PM technical points allows for the installation of essential shaft components,\nincluding lifts, cranes, and technical infrastructure. Each staged release of the arc facilitates the progres-\nsive installation of technical infrastructure in the tunnel, shifting part of the work into the shadow of the\ncritical path.\nThe staged release of a sector between two access points means that, on the technical point side,\ntechnical infrastructure installation will be underway, while civil engineering work will still be ongoing\non the opposite side of the separating doors. Safety regulations require two evacuation routes in case\nof an emergency, which is ensured by the separating door between the two worksites. This door is\nexclusively for emergency evacuation. In such an event, personnel from the civil engineering side will\nbe responsible for assisting in the evacuation of those from the installation side.\nSince the overall arc and final ventilation equipment will not yet be in place during the staged re-\nlease, the installation of technical infrastructure will be carried out using a temporary ventilation system.\nHandover dates\nThe handover dates were provided by the civil engineering team based on the TBMs advancing at a rate\nof 16 m/day, which is 10% less than the previous civil engineering baseline.\nInstallation phase\nInstallation phase for a sector\nThe installation planning was developed through a bottom-up approach, beginning with a detailed anal-\nysis of the sequence and duration required for each sector. The installation process for each of the eight\n592\n\nFig. B.1: Civil engineering previous baseline: one shaft-sector release.\nsectors will be carried out in four distinct phases. First, the installation of technical infrastructure and\nlifting equipment inside the shaft. Second, the installation of the technical infrastructures in the tun-\nnel. Third, the installation of the accelerator itself. Fourth, the commissioning period of the technical\ninfrastructures and the accelerators (see Fig. B.3).\nThe technical infrastructure must be installed before the accelerator to ensure unobstructed access\nto the walls and floors and to prevent potential damage from heavy construction activities. Furthermore,\nmost of this infrastructure will remain in place throughout the entire lifespan of the FCC, from the\nelectron collider to the hadron machine. While the installation of technical infrastructure does not require\nimmediate ease of access, all maintenance constraints must be carefully considered.\nThe installation starts with the shaft which has to be equipped with all services (lifts, crane, venti-\nlation, electricity, pipes . . . ). This phase is quite slow due to the limited number of workers (expected to\nbe around 30) who can work inside the shaft, because they all depend on the shaft crane. The shaft instal-\nlation is expected to last for close to 12 months for a 250 m deep shaft. The duration of shaft installation\nworks depends on the shaft depth.\nDuring the installation phase, certain technical infrastructure elements, such as lighting and power\nsupply, will be commissioned progressively. However, a dedicated six-month period will be required\nat the end of the installation phase to conduct comprehensive testing and final commissioning of all\nsystems.\nOnce the technical infrastructure of an arc is fully completed, a thorough cleaning will be carried\nout before the installation of accelerator components begins. The magnet installation process is orga-\nnized into three shifts, with the shaft crane serving as the primary bottleneck, as each magnet requires\n90 minutes to be lowered. To complete magnet installation within a year, at least two trailers will be\nnecessary.\nAll cabling will be pre-installed, allowing for system connections to take place after the installation\nof magnets and vacuum systems. Fire safety doors will be installed at the final stage once all magnets\nand cavities at points PH and PL are in place. As a result, the final safety systems will only become\noperational after the full installation of the accelerator. Until then, only temporary safety systems will be\n593\n\nFig. B.2: Civil engineering current baseline: the staged handover of the arc.\nFig. B.3: Sector sequence for installation.\nin place during the installation phase.\nOnce all accelerator systems are installed, the commissioning phase will begin, starting with the\ntechnical infrastructure. The safety systems will be the first to undergo commissioning, with this phase\nexpected to take approximately six months. Following this, the accelerator commissioning will com-\nmence, which is also estimated to last around six months, after which the system will be ready for the\nfirst beam tests.\nExperiment point installation\nExperiment shaft installation mainly comprises the installation of the ventilation duct. The installation\nis expected to be completed within six months. The installation of the experiments is scheduled to take\nplace after the overall accelerator hardware commissioning. A minimum of two years has been allocated\nfor installing each experiment within the cavern. The total available time for the installation of each\nexperiment ranges between four and five years. Table B.3 provides an overview of the start dates and\nduration of the experiment installations.\n594\n\nTable B.2: Handover dates from civil engineering for the machine shaft (PM), experiment shaft (PX) and\nfirst alcove.\nLocation\nHandover to CERN\n(2025 update)\nPA PX\nMar - 41\nPA PM\nFeb - 39\nA - B Alcove\nJan - 39\nPB PM\nNov - 38\nB - D Alcove\nNov - 38\nPD PX\nMay - 40\nPD PM\nApril - 38\nD - F Alcove\nSep - 38\nPF PM\nSep - 38\nF - G Alcove\nJan - 39\nPG PX\nApr - 41\nPG PM\nFeb - 39\nG - H Alcove\nMay - 40\nPH PM\nDec - 39\nH - J Alcove\nSep - 39\nPJ PX\nSep - 40\nPJ PM\nJun - 38\nJ - L Alcove\nJun - 39\nPL PM\nJun - 39\nL - A Alcove\nJun - 39\nTable B.3: Experiment installation start date and duration.\nPoint\nStart date\nDuration in years\nPA\n11/09/2041\n4.4\nPD\n11/11/2040\n5.2\nPG\n12/10/2041\n4.2\nPJ\n14/03/2041\n4.8\nInstallation at points with radiofrequency systems\nRadiofrequency equipment will be installed in point PH and in point PL. The installation planning fo-\ncuses on two main areas: the klystron galleries and the long straight section (LSS). Cavities and klystrons\nwill be installed to support all stages of FCC-ee operation, ensuring readiness for the full accelerator life-\ncycle.\nIn the klystron gallery, the technical infrastructure will be installed first to ensure the availability of\ngeneral services in this area. The rate of installation is assumed to be the same as in the tunnel. Following\nthis, the cores will be equipped with waveguides and cable trays using the space from the centre of the\ngalleries to the edges. Two months after the start of core installation, klystron and the low-level RF and\ncontrol installation will commence.\nIn the LSS, once the technical infrastructure has been installed, the cryogenic distribution line\n(QRL) installation can start. Since the cavities will be delivered from point PJ and that the sector H-J\nis being installed from PH to PJ with magnets, the cavity installation will therefore only start when the\n595\n\ntransport of magnets has been completed for space reasons. Once the cavities have been placed, the\nconnection under clean room conditions between the cavities will take place and two weeks later, other\ngeneral connection work for the waveguides and controls will be done. Then, cryogenic hardware com-\nmissioning will be carried out. After the sector hardware commissioning of the technical infrastructure\nis completed, a one-year period is planned for cavity conditioning. The sequence is shown in Fig. B.4.\nThe duration depends on the number of systems to be installed at each point.\nFig. B.4: Radiofrequency equipment installation sequence.\n596\n\nStrategy for global installation schedule phase\nThe installation strategy involves deploying a maximum of four teams working in parallel on the same\ntype of task, such as shaft works, technical infrastructure, and machine installation. As a result, the start\nof certain activities may be delayed until the necessary resources become available.\nIn the previous baseline, the resource usage was organised on a first ready, first installed basis.\nIncluding the radiofrequency sequence into the overall schedule has an impact on the critical path and\nto optimise the latter, resources were allocated in priority to points PH, PJ and PL which will host\nradiofrequency installation or its transport.\nFor most sectors benefiting from the staged release for the installation of technical infrastructure,\nthe installation will proceed in the same direction as the civil engineering handover, moving from the\ntechnical point to the experiment point. The machine installation follows a sequential \u2018train\u2019 approach to\nstreamline transport logistics, adhering to the same direction\u2014from the technical point to the experiment\npoint.\nOverall planning installation\nFigure B.5 shows overall planning for FCC-ee with the location in the machine indicated across the top\nand the timeline on each side. Main blocks of activities shown are:\n\u2013 Civil engineering works.\n\u2013 Shaft and sector civil engineering release date.\n\u2013 Shaft works, technical infrastructure installation, machine installation and hardware commission-\ning depicted with a direction line.\nThe critical path is driven by two sequences:\n\u2013 The resource levelling from sectors J-L and L-A to sectors D-F and F-G\n\u2013 The handover date of PH PM and the RF installation at point PH\nThe current schedule gives the overall machine readiness for beam in July 2046. The durations of all\nactivities are provided as calendar days.\nB.1.3\nDismantling FCC-ee\nIntroduction\nThis section presents a high-level schedule for the period covering the dismantling of FCC-ee to the\ninstallation of the FCC-hh machine and its related infrastructure. The time period covered is from the\nstop of the beam at the end of 2062 to the readiness for beam commissioning in 2073. The key phases\nare the following:\n\u2013 Stop of FCC-ee beam at the end of 2062\n\u2013 Dismantling activities end 2063 \u2013 end 2065\n\u2013 Installation phase 2066 - 2073\nDismantling FCC-ee\nSince the FCC-ee and FCC-hh machines are different in terms of equipment inside the machine, the\nwhole machine in the arc, the LSS and the experiment will be dismantled. A specific study [324] ad-\ndressed the dismantling activities foreseen to transition from FCC-ee to FCC-hh. Figure B.6 from this\nstudy indicates that it is possible to complete the dismantling of FCC-ee in 2-years. The study also found\nthat it should be possible to dismantle the experiments within this time frame as well.\n597\n\nFig. B.5: Overall linear planning for FCC-ee. The durations of all activities are counted as calendar days.\nPM is the machine shaft and PX, the experiment shaft.\nFor the overall planning, a 2-year duration for dismantling was considered independently of the\nstudy. In the arc, most of the equipment will be removed from the tunnel: instrumentation, collider and\nbooster magnets, vacuum equipment, cabling for magnets, magnet supports and alignment structures,\npower converters and related cabling located in the alcoves and the cooling circuit for magnets. In the\nFCC-ee RF points, point PH and PL, the cavities and QRL will be dismantled.\n598\n\nTime/week\n-\nPA\n+\n-\nPB\n+\n-\nPD\n+\n-\nPF\n+\n-\nPG\n+\n-\nPH\n+\n-\nPJ\n+\n-\nPL\n+\n4\n8\n12\n16\n20\n24\n28\nPreparatory phase\n32\n36\nArc Dismantling\n40\n44\nRF Dismantling\n48\n52\nLSS and cleanup\n56\n60\n64\n68\n72\n76\n80\n84\n88\n92\n96\n100\n104\nFig. B.6: Planning for dismantling FCC-ee.\nCivil engineering construction\nTo support the operation of FCC-hh, additional civil engineering constructions will be undertaken.\n\u2013 Transfer lines\n\u2013 Beam dump at point PF\nCivil engineering has not yet conducted a detailed study of the durations, but the beam dump at point PF\nhas been identified as the most time-critical. As long as the beam dump at point PF is completed within\n3.5 years\u2014starting concurrently with dismantling at the end of 2063\u2014it will not impact the schedule.\nB.1.4\nInstallation of FCC-hh\nEquipment kept and updated from FCC-ee\nThe technical infrastructures (ventilation, power, network) from FCC-ee will remain for FCC-hh.\nInstallation of a sector\nGiven the long operational lifetime of FCC-ee, an upgrade of the safety systems will be required. This\nwill be followed by installation of specific cabling and piping for FCC-hh. Next the Quench Recovery\nLine (QRL) will be installed, to provide cryogenics for the superconducting magnets of the machine.\nThe magnet supports will be installed next, followed by the magnets and their interconnection.\nInstallation at an RF point\nIn point PL, which will be the point where the radiofrequency equipment will be installed, there will also\nbe an upgrade of safety systems, cabling and piping and then QRL installation followed by installation\nof the cavities.\nThere will be technical infrastructure hardware commissioning, cryogenic cool down in each sec-\ntor and in point PL cavity conditioning.\nTo finish installation activities, each sector will have accelerator hardware commissioning and\nfinally there will be global hardware commissioning for the whole machine.\n599\n\nFig. B.7: Installation sequence for FCC-hh.\nGeneral strategy for installation (priorities concerning civil engineering works)\nSimilar to the FCC-ee machine, a maximum of four teams can work on the same type of activity simul-\ntaneously. The planning is, therefore, driven by the resource levelling and the shift pattern it implies.\nPriorities for resource usage have been determined considering the radiofrequency equipment to\nbe installed in point PL and the beam dump (the most critical construction) in point PF. The first sectors\nto start installation activities are A-B, B-D, J-L and L-A, allowing point PL to be installed as soon as\npossible. Then sectors D-F, F-G, G-H and H-J can be installed once the resources are available.\n600\n\nThis plan creates some contingency for civil engineering to build the beam dump at point PF and\nlimits its potential impact on the readiness for beam commission.\nThere are 3.5 years starting from the dismantling activities at the end of 2063 which are idle time\nas a result of the resource levelling in point PF. These 3.5 years can be used to build the beam dump at\npoint PF without having an impact on the beam commissioning date.\nThe overall planning is divided into two phases:\n\u2013 Dismantling activities for 2 years\n\u2013 Installation activities for 8 years\nThe transition from FCC-ee to FCC-hh is planned to be completed within 10 years, ensuring a timely\nand efficient upgrade process.\nThe FCC-hh would be ready for beam commissioning in 2073.\n601\n", "Future Circular Collider\nFeasibility Study Report\nVolume 3\nCivil Engineering, Implementation\nand Sustainability\nMarch 31, 2025\nSubmitted to the European Physics Journal ST, a joint publication of EDP Sciences,\nSpringer Science+Business Media, and the Societ\u00e0 Italiana di Fisica.\narXiv:2505.00273v1 [physics.acc-ph] 25 Apr 2025\n\nNote from the Editors\nOne of the recommendations of the 2020 update of the European Strategy for Particle Physics was that\n\u201cEurope, together with its international partners, should investigate the technical and financial feasibility\nof a future hadron collider at CERN with a centre-of-mass energy of at least 100 TeV and with an\nelectron-positron Higgs and electroweak factory as a possible first stage.\u201d\nIn June 2021, the CERN Council launched the FCC Feasibility Study to be completed by 2025, in\ntime for the next update of the European Strategy for Particle Physics. The study results are made\npublicly available through this FCC Feasibility Study Report, as input to the European Particle Physics\nStrategy update process, initiated by the CERN Council in March 2024.The studies presented in this FCC\nFeasibility Study Report do not imply any commitment by the CERN Member or Associate Member\nStates to build the Future Circular Collider.\nThis report and the assumptions contained in it do not prejudge further territorial feasibility analysis by\nthe Host States, France and Switzerland, as well as the outcome of their respective public debate and\nconcertation processes, and future decisions of their relevant authorities.\nii\n\nAcknowledgements\nWe would like to thank the International Steering Committee members:\nF. Gianotti (Chair), CERN\nR. Bello, CERN\nP. Chomaz, CEA, France\nM. Cobal, INFN and University of Udine, Italy\nB. Heinemann, DESY, Germany\nT. Koseki, KEK, Japan\nM. Lamont, CERN\nL. Merminga, FNAL, United States\nJ. Mnich, CERN\nM. Seidel, PSI and EPFL, Switzerland\nC. Warakaulle, CERN\nand the Scientific Advisory Committee members:\nA. Parker (Chair), Cambridge University, UK\nR. Bartolini, DESY, Germany\nA. Chabert, SFTRF, France\nH. Ehrbar, Heinz Ehrbar Partners LLC, Switzerland\nB. Gavela Legazpi, UAM Madrid, Spain\nG. Hiller, TU Dortmund, Germany\nS. Krishnagopal, FNAL, U.S.\nP. Kri\u017ean, University of Ljubljana, Slovenia\nP. Lebrun, ESI, France\nP. McIntosh, STFC, ASTeC, UKRI, UK\nM. Minty, BNL, U.S.\nR. Tenchini, INFN Sezione di Pisa, Italy\nfor their continued guidance and careful reviewing that helped to complete this report successfully.\niii\n\nThe research carried out by the international FCC collaboration hosted by CERN, which\nled to this publication, has received funding from the European Union\u2019s Horizon 2020\nresearch and innovation programme under the grant numbers 951754 (FCCIS), 654305\n(EuroCirCol), 764879 (EASITrain), 730871 (ARIES), 777563 (RI-Paths) and from FP7\nunder grant number 312453 (EuCARD-2).\nThis work has also benefited from the support of CHART (Swiss Accelerator Research\nand Technology, founded in 2016 as an umbrella collaboration for accelerator research\nand technology activities. Present partners in CHART are CERN, PSI, EPFL, ETH-\nZurich and the University of Geneva.\nTrademark notice: All trademarks appearing in this report are acknowledged as such.\niv\n\nThis report was edited with the Overleaf.com collaborative writing and publishing system. Typesetting\nand final print preparation were performed using pdfTEX3.14159265-2.6-1.40.17\nCopyright CERN for the benefit of the FCC collaboration 2024\nCreative Commons Attribution 4.0\nKnowledge transfer is an integral part of CERN\u2019s mission.\nCERN publishes this volume Open Access under the Creative Commons Attribution 4.0 licence\n(http://creativecommons.org/licenses/by/4.0/) in order to permit its wide dissemination and\nuse. The submission of a contribution to the CERN document server shall be deemed to constitute the\ncontributor\u2019s agreement to this copyright and licence statement. Contributors are requested to obtain any\nclearances that may be necessary for this purpose.\nThis volume is indexed in: CERN Document Server (CDS):\nCERN-FCC-ACC-2025-0003\nDOI 10.17181/CERN.I26X.V4VF\nhttp://cds.cern.ch/record/2928194\nThis report edition should be cited as:\nFuture Circular Collider Feasibility Study Report Volume 3: Civil Engineering, Implementation and\nSustainability, preprint edition edited by M. Benedikt et al., CERN accelerator reports,\nCERN-FCC-ACC-2025-0003,DOI 10.17181/CERN.I26X.V4VF, Geneva, 2025.\nAvailable online: https://cds.cern.ch/record/2928194\nv\n\nList of Editors at 31 March 2025\nM. Benedikt1 (Study Leader), F. Zimmermann1 (Deputy Study Leader), B. Auchmann1,2,\nW. Bartmann1, J.P. Burnet1, C. Carli1, A. Chanc\u00e93, P. Craievich2, M. Giovannozzi1, C. Grojean4,5,\nJ. Gutleber1, K. Hanke1, A. Henriques1, P. Janot1, C. Louren\u00e7o1, M. Mangano1, T. Otto1, J. Poole1,\nS. Rajagopalan6, T. Raubenheimer7, E. Todesco1, L. Ulrici1, T. Watson1, G. Wilkinson1,8.\nList of Contributors at 31 March 2025\nA. Abada9,10,11, M. Abbrescia12,13, H. Abdolmaleki14,15, S.H. Abidi6, A. Abramov1, C. Adam9,16,17,\nM. Ady1, P.R. Ad\u02d8zi\u00b4c18, I. Agapov4, D. Aguglia1, I. Ahmed19, M. Aiba2, G. Aielli20,21, T. Akan22,\nN. Akchurin23, D. Akturk24, M. Al-Thakeel1,25,26, G.L. Alberghi25, J. Alcaraz Maestre27, M. Aleksa1,\nR. Aleksan3, F. Alharthi9,10,28, J. Alimena4, A. Alimenti29, S. Alioli30,31, L. Alix1,9,16,\nB.C. Allanach32, L. Allwicher4, A.A. Altintas33, M. Alt\u0131nl\u013133,34, M. Alviggi35,36, G. Ambrosio37,\nY. Amhis9,10,11, A. Amiri38,39, G. Ammirabile40, T. Andeen41, K.D.J. Andr\u00e91, J. Andrea9,42,43,\nA. Andreazza44,45, M. Andreini1, T. Andriollo46, L. Angel47, M. Angelucci48, S. Antusch49,\nM.N. Anwar12,50, L. Apolin\u00e1rio51, G. Apollinari37, R.B. Appleby52,53, A. Apresyan37, Aram Apyan54,\nArmen Apyan55, A. Arbey9,56,57, B. Argiento35,36, V. Ari58, S. Arias59, B. Arias Alonso1,\nO. Arnaez9,16,17, R. Arnaldi60, F. Arneodo61, H. Arnold62, P. Arrutia Sota1, M.E. Ascioti63,64,\nK.A. Assamagan6, S. Aumiller65, G. Ayd\u0131n66, K. Azizi38,67, P. Azzi68, N. Bacchetta68, A. Bacci44,\nB. Bai69, Y. Bai70, L. Balconi44,45, G. Baldinelli63,64, B. Balhan1, A.H. Ball1,71, A. Ballarino1,\nS. Banerjee72, S. Banik2,73, D.P. Barber4,74, M.B. Barbero9,75,76, D. Barducci40,77, D. Barna78,\nG.G. Barnaf\u00f6ldi78, M.J. Barnes1, A.J. Barr8, R. Bartek79, H. Bartosik1, S.A. Bass80, U. Bassler9,81,82,\nM.J. Basso83,84, A. Bastianin45,85, P. Bataillard86, M. Battistin1, J. Bauche1, L. Baudin1,\nJ. Baudot9,42,43, B. Baudouy3, L. Bauerdick37, C. Bay\u0131nd\u0131r87,88, H.P. Beck89, F. Bedeschi40, C. Bee62,\nM. Begel6, M. Behtouei48, L. Bellagamba25, N. Bellegarde1, E. Belli1,90, E. Bellingeri91,\nS. Belomestnykh37, A.D. Benaglia30, G. Bencivenni48, J. Bendavid1, M. Benmergui92, M. Benoit93,\nD. Benvenuti1,40, T. Bergauer94, N. Bernachot95, G. Bernardi9,96,97, J. Bernardi98, Q. Berthet99,100,101,\nS. Bertoni102, C. Bertulani103, M.I. Besana2, A. Besson9,42,43, M. Bettelini104, S. Bettoni2,\nS. Beuvier\u2020105, P.C. Bhat37, S. Bhattacharya106, J. Bhom107, M.E. Biagini48, A. Bibet-Chevalier108,\nM. Bicrel109, M. Biglietti110, G.M. Bilei63, B. Bilki111,112, K. Bisgaard Christensen1, T. Biswas113,\nF. Blanc114, F. Blekman4,115,116, A. Blondel9,101,117, J. Bl\u00fcmlein4, D. Boccanfuso35,118,\nA. Bogomyagkov119, P. Boillon108, P. Boivin100, M.J. Boland120, S. Bologna121, O. Bolukbasi33,\nR. Bonnet102, J. Borburgh1, F. Bordry1, P. Borges de Sousa1, G. Borghello1, L. Borriello35,\nD. Bortoletto8, M. Boscolo48, L. Bottura1, V. Boudry9,81,82, R. Boughezal122, D. Bourilkov123,\nM. Boyd83,124, D. Boye6, G. Bozzi125,126, V. Braccini91, C. Bracco1, B. Bradu1, A. Braghieri127,\nS. Braibant25,26, J. Bramante128, G.C. Branco129, R. Brenner130, N. Brisa102, D. Britzger131,\nG. Broggi1,90, L. Bromiley1, E. Brost6, Q. Bruant3, R. Bruce1, E. Br\u00fcndermann132, L. Brunetti9,16,17,\nO. Br\u00fcning1, O. Brunner1, X. Buffat1, E. Bulyak133, A. Burdyko44,134, H. Burkhardt1,135,\nP.N. Burrows136, S. Busatto44,90, S. Buschaert86, D. Buttazzo40, A. Butterworth1, D. Butti1,\nG. Cacciapaglia137,138,139, Y. Cai7, B. Caiffi140, V. Cairo1, O. Cakir58, P. Calafiura141, R. Calaga1,\nS. Calatroni1, D.G. Caldwell142, A. \u00c7al\u0131\u00b8skan143, C. Calpini144, M. Calviani1, E. Camacho-P\u00e9rez145,\nP. Camarri20,21, L. Caminada2,73, M. Campajola35,36, A.C. Canbay58, K. Canderan1, S. Candido1,\nF. Canelli73, A. Canepa37, S. Cantarella48, K.B. Cant\u00fan-Avila145, L. Capriotti146,147, A. Caram148,\nA. Carbone44, J.M. Carceller1, G. Carini6, F. Carlier1, C.M. Carloni Calame127, F. Carra1,\nC. Cartannaz86, S. Casenove1, G. Catalano149, V. Cavaliere6, C. Cazzaniga150, C. Cecchi63,64,\nF.G. Celiberto151, M. Cepeda27, F. Cerutti1, F. Cetorelli30,31, G. Chachamis51, Y. Chae4, F. Chagnet152,\nI. Chaikovska9,10,11, M. Chalhoub86, M. Chamizo-Llatas6, M. Champagne153, H. Chanal9,154,155,\nG. Chapelier108, P. Charitos1, C. Charles105, T.K. Charles156, C. Charlot9,81,82, S. Chatterjee4,\nA. Chaudhuri157, R. Chehab9,10,11, S.V. Chekanov158, H. Chen6, T. Chesne105, F. Chiapponi25,26,\nG. Chiarello159,160, M. Chiesa127, P. Chiggiato1, Ph. Chomaz3, M. Chorowski161, J.P. Chou162,\nvi\n\nM. Chrzaszcz107, W. Chung163, S. Ciarlantini68,164, A. Ciarma48, D. Cieri131, A.K. Ciftci165,\nR. Ciftci166, R. Cimino48, F. Cirotto35,36, M. Ciuchini110, M. Cobal167,168, A. Coccaro140,\nR. Coelho Lopes De Sa169, J.A. Coleman-Smith1, F. Collamati170, C. Colldelram171, P. Collier1,\nP. Collins1, J. Collot9,172,173, M. Colmenero1, L. Colnot149, G. Coloretti73, E. Conte9,42,43,\nF.A. Conventi35,174, A. Cook1, L. Cooley175,176, A.S. Cornell177, C. Cornella1, G. Cornette105,\nI. Corredoira178, P. Costa Pinto1, F. Couderc3, J. Coupard1, S. Coussy86, R. Crescenzi179,\nI. Crespo Garrido1,180, T. Critchley1,101, A. Crivellin73, T. Croci63, C. Cudr\u00e9105, G. Cummings37,\nF. Cuna12, R. Cunningham1, B. Cur\u00e91, E. Curtis181, M. D\u2019Alfonso182, L. D\u2019Aloia Schwartzentruber183,\nG. D\u2019Amen6, B. D\u2019Anzi12,13, A. D\u2019Avanzo35,36, D. d\u2019Enterria1, A. D\u2019Onofrio35, M. D\u2019Onofrio184,\nM. Da Col149, M. Da Rocha Rolo60, C. Dachauer185, B. Da\u02d8gli24, A. Dainese68, B. Dalena3,\nW. Dallapiazza186, M. Dam187, H. Damerau1, V. Dao62, A. Das188, M.S. Daugaard1, S. Dauphin108,\nA. David1, T. Dav\u00eddek189, G.J. Davies181, S. Dawson6, J. de Blas190, A. de Cosa150, S. De Curtis191,\nN. De Filippis12,50, E. De Lucia48, R. De Maria1, E. De Matteis44, A. De Roeck1, A. De Santis48,\nA. De Vita1,68,164, A. Deandrea9,56,57, C.J. Debono192, M. Deeb100, M.M. Defranchis1, J. Degens184,\nS. Deghaye1, V. Del Duca48, C.L. Del Pio6, A. Del Vecchio90, D. Delikaris1, A. Dell\u2019Acqua1,\nM. Della Pietra35,36, M. Delmastro9,16,17, L. Delprat1, E. Delugas149, Z. Demiragli193, L. Deniau1,\nD. Denisov6, H. Denizli194, A. Denner195, A. Denot108, G. Deptuch6, A. Desai196, H. Deveci1,\nA. Di Canto6, A. Di Ciaccio20,21, L. Di Ciaccio9,16,17, D. Di Croce1,114, C. Di Fraia35,36,\nB. Di Micco29,110, R. Di Nardo29,110, T.B. Dingley8, F. Djama9,75,76, F. Djurabekova197, D. Dockery37,\nS. Doebert1, D. Domange1,198, M. Doneg\u00e0150, U. Dosselli68, H.A. Dostmann1,199, J.A. Dragovich37,\nI. Drebot44, M. Drewes200, T.A. du Pree201, Z. Duan202, C. Duarte-Galvan203, O. Duboc204, M. Duda2,\nP. Duda161, H. Duran Yildiz58, H. Durand105, P. Durand105, G. Durieux200, Y. Dutheil1, I. Dutta37,\nJ.S. Dutta205, S. Dutta206, F. Duval1, F. Eder1, M. Eisterer98, Z. El Bitar9,42,43, A. El Saied207,\nM. Elisei44, J. Ellis1,208, W. Elmetenawee12, J. Elmsheuser6, V. Daniel Elvira37, S.C. Eno209,\nY. Enomoto210, B.A. Erdelyi68,164, O.E. Eruteya101,211, M. Escobar212, O. Etisken213, I. Eymard144,\nJ. Eysermans182, D. Falchieri25, C. Falkenberg204, F. Fallavollita1,131, A. Afalou1,9,10, J. Faltova189,\nJ. Fanini1, L. Fan\u00f263,64, K. Fanti105, R. Farinelli25, M. Farino163, S. Farinon140, H. Fatehi38,\nJ. Fatterbert105, A. Faure214, A. Faus-Golfe9,10,11, G. Favia1, L. Favilla35,118, W.J. Fawcett32,\nA. Federowicz37, L. Feligioni9,75,76, L. Felsberger1, Y. Feng23, A. Fern\u00e1ndez T\u00e9llez215, R. Ferrari127,\nL. Ferreira1, F. Ferro140, M. Fiascaris1, C. Fiorio45, S.A. Fleury1, L. Florez186, M. Florio45,149,\nA. Fondacci63, B. Fontimpe212, K. Foraz1, R. Fortunati2, M. Fouaidy9,10,11, A. Foussat1, A. Fowler1,\nJ.D. Fox216, M. Francesconi35, B. Francois1, R. Franqueira Ximenes1, F. Fransesini48, A. Frasca1,184,\nA. Freitas217, J.A. Frost8, K. Furukawa210, A. Gabrielli25,26, A. Gaddi1, F. Gaede4, A. Gall\u00e9n130,\nR. Galler218,219, E. Gallice105, E. Gallo4,115, H. Gamper1, G. Ganis1, S. Ganjour3, S. Gao6,\nA. Garand148, C. Garaus204, D. Garcia1, R. Garc\u00eda Al\u00eda1, R. Garc\u00eda Gil220, C.M. Garcia Jaimes1,114,\nH. Garcia Rodrigues2,221, C. Garion1, M. Garlasch\u00e81, D. Garnier152, M.V. Garzelli115,\nS. Gascon-Shotkin9,56,57, M. Gasior1, G. Gaudino35,118, G. Gaudio127, V. Gaur222, K. Gautam73,116,\nV. Gawas1, T. Gehrmann73, A. Gehrmann-De Ridder73,150, K. Geiger1, M. Genco149, F. Gerigk1,\nH. Gerwig1, A. Ghribi1,9,223, P. Giacomelli25, S. Giagu90,170, E. Gianfelice37, S. Giappichini132,\nD. Gibellieri1,224, F. Giffoni149, G. Gil da Silveira225, S.S. Gilardoni1, M. Giovannetti48, T. Girardet105,\nS. Girod1,105, P. Giubellino60, P. Giubilato68,164, F. Giuli20,21, M. Giuliani102, E.L. Gkougkousis1,73,\nS. Glukhov226, J. Gluza227, B. Goddard1, C. Goffing1,132, D. Goldsworthy1, T. Golling101,\nR. Gon\u00e7alo51,228, V.P. Gon\u00e7alves47,229, T. Gon\u00e7alves Da Silva212, J. Gonski7, R. Gonzalez Suarez130,\nS. Gorgi Zadeh1, S. Gori230, E. Gorini159,231, L. Gouskos232, M. Gouzevitch9,56,57, E. Granados1,\nF. Grancagnolo159, S. Grancagnolo159,231, A. Grassellino37, A. Grau132, E. Graverini40,77,114,\nF.G. Gravili159,231, H.M. Gray141,233, M. Grazzini73, Mario Greco29,110, Michela Greco60,234,\nA. Greljo49, J-L. Grenard1, A.V. Gritsan235, R. Gr\u00f6ber68,164, A. Grudiev1, E. Gschwendtner1, J. Gu236,\nD. Guadagnoli17,137,237, G. Guerrieri1, A. Guiavarch207, G. Guillermo Canton1,238, M. Guinchard1,\nY.O. G\u00fcnaydin239, K. Gurcel92, L.X. Gutierrez Guerrero240,241, D. Guti\u00e9rrez Rueda1,\nA. Guti\u00e9rrez-Rodr\u00edguez242, V. Guzey197,243, C. Haber141, T. Hacheney244, B. Hac\u0131\u00b8sahino\u02d8glu33,\nvii\n\nK. Hahn122, J. Hajer129, T. Hakulinen1, J.C. Hammersley245, M. Hance230, J.B. Hansen187,\nB. H\u00e4rer132, E. Hauzinger218, M. Haviernik189, B. Hegner1, C. Helsens114, Ana Henriques1,\nC. Hernalsteens1, H. Hern\u00e1ndez-Arellano215, R.J. Hern\u00e1ndez-Pinto203, M.A. Hern\u00e1ndez-Ru\u00edz242,\nJ. Hern\u00e1ndez-S\u00e1nchez215, J.W. Heron1, L.M. Herrmann1, R. Hirosky246, J.F. Hirschauer37,\nJ.D. Hobbs62, K. Hock6, S. H\u00f6che37, M. Hofer1, G. Hoffstaetter6,247, W. H\u00f6fle1, M. Hohlmann248,\nF. Holdener249, B. Holzer1, C.G. Honorato215, H. Hoorani250, A. Houver105, E. Howling1,8,136,\nX. Huang7, F. Hug251, B. Humann1, P. Hunchak120, Y. Husein1, A. Hussain1,252, G. Iadarola1,\nG. Iakovidis6, G. Iaselli12,50, P. Iengo35, A. Ilg73, M. Iodice110, A.O.M. Iorio35,36, V. Ippolito170,\nU. Iriso171, J. Isaacson37, G. Isidori73, R. Islam253, A. Istepanyan105, S. Izquierdo Bermudez1,\nV. Izzo35, P.D. Jackson196, R. Jafari1,38, S.S. Jagabathuni1,101, S. Jana254,255, C. J\u00e4rmyr Eriksson1,\nP. Jausserand152, M. Jensen256, J.M. Jimenez1, F.R. Joaquim129, O.R. Jones1, J. Joos108,\nE. Jourd\u2019huy9,257, E. Jourdan212, J.M. Jowett1,258, A. Jueid259, A.W. Jung205, M. Kagan7,\nI. Kahraman58, V. Kain1, J. Kalinowski260, J.F. Kamenik261,262, A. Kanso263, T. Kar264, S.O. Kara265,\nH. Karadeniz266, S.R. Karmarkar205, V. Karpati267, I. Karpov1, M. Karppinen1, P. Karst9,75,76,\nS. Kartal33, V.V. Kashikhin37, U. Kaya58, A. Kehagias1,268, J. Keintzel1, M. Kennouche1, M. Kenzie32,\nM. Kerr\u00e9veur-Lavaud46, R. Kersevan1,269, V. Keus197,270, H. Khanpour14,271,272, V.V. Khoze273,\nV.A. Khoze273, P. Kicsiny1, R. Kieffer1, C. Kiel114, J. Kieseler132, A. Kilic274, B. Kilminster73,\nS. Kim275, Z. K\u0131rca274, M. Klein\u2020184, A. Klimentov6, M. Klute132, V. Klyukhin119,276,\nM. Knecht137,277,278, B. Kniehl115, P. Ko279, S. Ko1, F. Kocak274, T. Koffas280, C. Kokkinos281,282,\nK. Ko\u0142odziej227, K. Kong283, P. Kontaxakis101, I.A. Koop119, P. Kopciewicz1, P. Koppenburg201,\nM. Koratzinos1,2, K. Kordas284, A Korsun9,10,11, O. Kortner131, S. Kortner131, B. Korzh101,\nT. Koseki210, J. Kosse2, P. Kostka1,184, S. Kostoglou1, A.V. Kotwal80, G. Kozlov1,276, I. Kozsar1,\nT. Kramer1, P. Krkoti\u00b4c1, H. Kroha131, K. Kr\u00f6ninger244, S. Kuday1,58, G. Kuhlmann285,\nO. Kuhlmann1,286, M. Kuhn287, A. Kulesza288, M. Kumar289, F. Kurian6, A. Kurtulus1,150,\nT.H. Kwok73, S. La Mendola1, M. Lackner98,290, T. \u0141adzi\u00b4nski1, D. Lafarge1, P. La\u00efdouni1,\nG. Lamanna9,16,17, N. Lamas19, G. Landsberg232, C. Lange2, D.J. Lange163, A. Langner1,\nA.J. Lankford291, L. Lari6, M.S. Larson292, K. Lasocha1, A. Latina1, S. Lauciani48, M. Laufenberg105,\nG. Lavezzari1, L. Lavezzi60, L. Lavezzo1, M. Le Garrec1,9,16, A. Le Jeune102, Ph. Lebrun1,293,\nY. L\u00e9chevin1, A. Lechner1, E. Lecointe105, J.S.H. Lee294, S.W. Lee295, S.J. Lee279,296, T. Lefevre1,\nC. Leggett141, T. Lehtinen297, S. Leone40, C. Leonidopoulos298, S. Leontsinis73,\nG. Leprince-Maill\u00e8re299, G. Lerner1, O. Leroy9,75,76, T. Lesiak107, P. Levai78, A. Leveratto91,\nR. Levi152, A. Li6, S. Li300,301, D. Liberati302, G.L. Lichtenstein47, M. Liepe247, Z. Ligeti141,\nH. Lin303, S. Linda144, E. Lipeles304, Z. Liu305, S.M. Liuzzo306, T. Loeliger287,\nA. Loeschcke Centeno307, A. Lorenzetti73, C. Lorin3, R. Losito1, M. Louka12,308,\nM.L. Loureiro Garc\u00eda180, I. Low122,158, K. Lubonis152, M.T. Lucchini30,31, V. Lukashenko73,\nG. Luminati48, A.J.G. Lunt1,309, A. Lusiani40,310, M. Luzum311, H. Ma6, A. Maas312,\nE. Macchia1,90,170, A. Macchiolo73, G.E. Machinet263, R. Madar9,154,155, T. Madlener4, C. Madrid23,\nA. Magalotti29, M. Maggiora60,234, A.-M. Magnan181, M.A. Mahmoud313, Y. Mahmoud314,315,\nF. Mahmoudi1,9,56, H. Mainaud Durand1, J. Maitre108, Y. Makhloufi101, B. Malaescu9,117,316,\nA. Malagoli91, C.H. Malan108, M. Malekhosseini38, A. Maloizel1,96,97, S. Malvezzi30, A. Malzac148,\nG. Manco127, L.S. Mandacar\u00fa Guerra163, P. Manfrinetti91,317, E. Manoni63, J. Mans305, L. Mantani318,\nS. Manzoni1, L. Marafatto167, C. Marcel1, T. Marcel109, R. Marchevski114, G. Marchiori9,96,97,\nF. Mariani44,90, V. Mariani63,64, S. Marin1, C. Marinas318, V. Marinozzi37, S. Mariotto44,45,\nC. Marquis105, J. Martelain319, G. Martelli63,64, A. Martens9,10,11, I. Martin-Melero1,\nV.I. Martinez Outschoorn169, F. Martinez215, C.M. Jardim27, L. Marzola320,321, S. Masciocchi258,264,\nA. Mashal14, A. Masi1, I. Masina146,147, P. Mastrapasqua200, V. Mateu322, S. Mattiazzo68,164,\nM. Maugis102, D. Mauree144, G.H.I. Maury-Cuna323, A. Mayoux1, E. Mazzeo1, S. Mazzoni1,\nM. McCullough1, M. Meena9,42,43, E. Meftah101, Andrew Mehta184, Ankita Mehta1, B. Mele170,\nR. Mena-Andrade1, M. Mentink1, D. Mergelkuhl1, V. Mertinger267, L. Mether1, S. Meylan105,\nT. Michel102, T. Michlmayr2, M. Migliorati90,170, A. Milanese1, C. Milardi48, G. Milhano51,\nviii\n\nM. Minty6, C. Mirabelli324, T. Miralles9,154,155, L. Miralles Verge1, D. Mirarchi1, K. Mirbaghestan73,\nN. Mirian4,325, V.A. Mitsou318, D.S. Mitzel244, M. Mlynarikova1, S. M\u00f6bius89,\nM. Mohammadi Najafabadi1,14, G.B. Mohanty326, R. N. Mohapatra209, S. Moneta63, P.F. Monni1,\nE. Monnier9,75,76, S. Monteil9,154,155, I. Le\u00f3n Monz\u00f3n203, F. Moortgat1,327, N. Morange9,10,11,\nM. Moretti146,147, S. Moretti71, T. Mori1,210, I. Morozov119, A. Morozzi63, M. Morrone1,\nA. Moscariello101, F. Moscatelli63,328, I. Moulin214, N. Mounet1, A. Mueller329, A.-S. M\u00fcller132,\nB.O. M\u00fcller285, J. Mundet220, E. Musa1,4, V. Musat1,8, R. Musenich140, E. Musumeci318, M. Mylona1,\nV.V. Mytrochenko9,10,133, B. Nachman141, S. Nagaitsev6, T. Nakamoto210, M. Napsuciale323,\nM. Nardecchia90,170, G. Nardini330, G. Narv\u00e1ez-Arango331, S. Naseem61, A. Natochii6,\nA. Navascues Cornago1, B. Naydenov1, G. Nergiz1, A.V. Nesterenko276, C. Neub\u00fcser332,\nH.B. Newman333, F. Niccoli1,334, O. Nicrosini127, U. Niedermayer226, G. Niehues132, J. Nielsen1,\nG. Nigrelli1,90,170, S. Nikitin119, I.B. Nikolaev119, A. Nisati170, N. Nitika167,168, J.M. No335,\nM. Nonis1, Y. Nosochkov7, A. Novokhatski1,7, J.M. O\u2019Callaghan336, S.A. Ochoa-Oregon203,\nK. Ohmi202,210, K. Oide1,101,210, V.A. Okorokov119, C. Oleari30,31, D. Oliveira Damazio1,6, Y. Onel112,\nA. Onofre337,338,339, P. Osland340, Y.M. Oviedo-Torres341,342,343, A. Ozansoy58, F. Ozaydin87,344,\nK. Ozdemir345, A. Ozturk1, M.A. P\u00e9rez de Le\u00f3n203, S. Pacetti63,64, H. Pacey8, J. Paciello108,\nC.E. Pagliarone346,347, A. Paillex105, H.F. Pais da Silva1, F. Palla40, A. Pampaloni140, C. Pancotti149,\nM. Pandurovi\u00b4c348, O. Panella63, G. Panizzo167,168, C. Pantouvakis68,164, L. Panwar9,117,316,\nP. Paolucci35, Y. Papa105, A. Papaefstathiou349, Y. Papaphilippou1, A. Paramonov158, A. Pareti127,350,\nB. Parker6, V. Parma1, F. Parodi140,317, M. Parodi1, B. Paroli44,45, J.A. Parsons351, D. Passarelli37,\nD. Passeri63,64, B. Pattnaik318, A. Patwa352, C. Paus182, F. Pauss150, F. Peauger1, I. Pedraza215,\nR. Pedro51, J. Pekkanen1, G. Peon1, A. Perez109, E. Perez1, F. P\u00e9rez171, J.C. Perez1, J.M. P\u00e9rez27,\nR. Perez-Ramos137,138,353, G. P\u00e9rez Segurana1, A. Perillo Marcone1, S. Perna35,36, K. Peters4,\nS. Petracca35,354, A.R. Petri44, F. Petriello122, A. Petrovic1, L. Pezzotti25, G. Piacquadio62,\nG. Piazza179, A. Piccini1, F. Piccinini127, A. Pich318, T. Pieloni114, J. Pierlot1, A.D. Pilkington52,\nM. Pillet324, M. Pinamonti167,168, N. Pinto235, L. Pintucci167,168, F. Pinzauti1, K. Piotrzkowski271,\nC. Pira48, M. Pitt1, R. Pittau190, S. Pittet1, P. Placidi63,64, W. P\u0142aczek355, S. Pl\u00e4tzer312,356,\nM.-A. Pleier6, E. Ploerer73,116, H. Podlech357,358, F. Poirier9,16,17, G. Polesello127, M. Poli Lener48,\nJ. Polinski161, Z. Polonsky73, N. Pompeo29, M. Pont171, G. Alexandru-Popeneciu359, W. Porod195,\nL. Porta1, L. Portales3, T. Portaluri307, M.A.C. Potenza45, C. Prasse285, E. Premat183, M. Presilla132,\nS. Prestemon141, A. Price355, M. Primavera159, R. Principe1, M. Prioli44, F.M. Procacci12,\nE. Proserpio44,134, A. Provino91,317, C. Pueyo1, T. Puig19, N. Pukhaeva276, S. Pulawski227,\nG. Punzi40,77, A. Pyarelal360, J. Qian303, H. Quack361, F. S. Queiroz47, G. Quintas-Neves299,\nH. Rafique71, J.-Y. Raguin2, J. Raidal320, M. Raidal320, P. Raimondi37, A. Rajabi4,\nS. Ram\u00edrez-Uribe203, S. Randles184, T. Rao6, C.\u00d8. Rasmussen6, A. Ratkus362, P.N. Ratoff53,363,\nP. Razis364,365, P. Rebello Teles1,366, M.N. Rebelo129, M. Reboud9,10,11, S. Redaelli1, C. Regazzoni105,\nL. Reichenbach1,367, M. Reissig132, E. Renou105, A. Renter\u00eda-Olivo318, J. Reuter4, S. Rey105,\nA. Ribon1, D. Ricci1, W. Riegler1, M. Rignanese68,164, S. Rimjaem368, R.A. Rimmer369, R. Rinaldesi1,\nL. Rinolfi1,293, O. Rios1, G. Ripellino130, B. Rivas370, A. Rivetti60, T. Robens371, F. Robert183,\nE. Robutti140, C. Roderick1, G. Rodrigo318, M. Rodr\u00edguez-Cahuantzi215, L. R\u00f6hrig154,155,244,\nM. Roig372, F. Rojat108, J. Rojo201,373, J. Roloff232, P. Roloff1, A. Romanenko37, A. Romero Francia1,\nH. Romeyer374, N. Rompotis184, N. Rongieras102, G. Rosaz1, K. Roslon375, M. Rossetti Conti44,\nA. Rossi63,64, E. Rossi35,36, L. Rossi44,45, A.N. Rossia68,164, S. Rostami38, G. Roy1, B. Rubik37,\nI. Ruehl1, A. Ruiz-Jimeno376, R. Ruprecht132, J.P. Rutherfoord360, L. Rygaard4, M.S. Ryu295,\nL. Sabato1,114, G. Sadowski9,42,43, D. Saez de Jauregui132,377, M. Sahin378, A. Sailer1, M. Saito379,\nP. Saiz1, G.P. Salam380,381, R. Salerno9,81,82, T. Salmi297, B. Salvachua1, J.P.T. Salvesen1,8,136,\nB. Salvi299, D. Sampsonidis284, Y. Villamizar137,138,139, C. Sandoval331, S. Sanfilippo2,\nE. Santopinto140, R. Santoro44,134, X. Sarasola114, L. Sarperi287, I.H. Sarp\u00fcn382, S. Sasikumar1,\nM. Sauvain383, A. Savoy-Navarro3,9, R. Sawada379, G. Sborlini384, J. Scamardella35,36, M. Schaer2,\nM. Schaumann1,4, M. Schenk1, C. Scheuerlein1, C. Schiavi140,317, A. Schloegelhofer1, D. Schoerling1,\nix\n\nA. Sch\u00f6ning264, S. Schramm101, D. Schulte1, P. Schwaller251,385, A. Schwartzman7, Ph. Schwemling3,\nR. Schwienhorst386, A. Sciandra6, L. Scibile1, I. Scimemi387, E. Scomparin60, C. Sebastiani1,\nB. Seeber388, J.T. Seeman7, F. Sefkow4, M. Seidel2,114, S. Seidel74, J. Seixas339,389,390, N. Selimovi\u00b4c68,\nM. Selvaggi1, C. Senatore101, A. Senol194, N. Serra73, A. Seryi369, A. Sfyrla101, Pramond Sharma391,\nPunit Sharma6, C.J. Sharp1, L. Shchutska114, V. Shiltsev392, M. Siano44,45, R. Sierra1, E. Silva29,\nR.C. Silva47,343, L. Silvestrini170, F. Simon132, G. Simonetti1, R. Simoniello1, B.K. Singh393,\nS. Singh6, B. Singhal79, A. Siodmok1,355, Y. Sirois9,81,82, E. Sirtori149, B. Sitar394, D. Sittard1,\nE. Sitti150, T. Sj\u00f6strand59, P. Skands395, L. Skinnari292, K. Skoufaris1, K. Skovpen327, M. Skrzypek107,\nP. Slavich137,138,139, V. Slokenbergs23, V. Smaluk6, J. Smiesko1,396, S.S. Snyder6, E. Solano171,\nP. Sollander1, O.V. Solovyanov1,9,154, M. Son397, F. Sonnemann1, R. Soos1,9,10, F. Sopkova189,\nT. Sorais398, M. Sorbi44,45, S. Sorti44,45, R. Soualah399, M. Souayah1, L. Spallino48, S. Spanier400,\nP. Spiller258, M. Spira2, D. Stagnara102, M. Stallmann186, D. Standen1, J.L. Stanyard1, B. Stapf1,\nG.H. Stark230, M. Statera44, C. Staudinger1,204, G. Streicher401, N.P. Strohmaier2, R. Stroynowski106,\nS. Stucci6, G. Stupakov7, S. Su360, A. Sublet1, K. Sugita258, M.K. Sullivan7, S. Sultansoy24,\nI. Syratchev1, R. Szafron6, A. Sznajder402, W. Tachon403, N.D. Tagdulang37,171,336, N.A. Tahir258,\nY. Takahashi123, J. Tamazirt9,10,11, S. Tang6, Y. Tanimoto210, I. Tapan274, G.F. Tassielli12,404,\nA.M. Teixeira9,154,155, V.I. Telnov119, H.H.J. Ten Kate1,405, V. Teotia6, J. ter Hoeve298, A. Thabuis1,\nG.T. Telles19, A. Tishelman-Charny6, S. Tissandier108, S. Tizchang14,406, J.-P. Tock1, B. Todd1,\nL. Toffolin1,167,407, A. Tolosa-Delgado1, R. Tom\u00e1s Garc\u00eda1, T. Tomasini408, G. Tonelli40,77, T. Tong409,\nF. Toral27, T. Torims1,362, L. Torino171, K. Torokhtii29, R. Torre140, E. Torrence410, R. Torres53,184,\nT. Mitsuhashi210, A. Tracogna149, O. Traver171, D. Treille1, A. Tricoli6, P. Trubacova1, E. Tsesmelis1,\nG. Tsipolitis268, V. Tsulaia141, B. Tuchming3, C.G. Tully163, I. Turk Cakir58, C. Turrioni63,\nJ. Tynan105, F.P. Ucci127,350, S. Udongwo411, C.S. \u00dcn274, A. Unnervik1, A. Upegui99,100,\nJ.P. Uribe-Ram\u00edrez203, J. Uythoven1, R. Vaglio36,91, F. Valchkova-Georgieva412, P. Valente170,\nR.U. Valente170, A.-M. Valente-Feliciano369, G. Valentino1,192, C.A. Valerio-Lizarraga203,323,\nS. Valette1, J.W.F. Valle318, L. Valle1, N. Valle127, N. Vallis1,2,114, G. Vallone141, P. van Gemmeren158,\nW. Van Goethem1, P. van Hees59, U. van Rienen411, L. van Riesen-Haupt1,114, P. Van Trappen1,\nM. Vande Voorde413,414, A.L. Vanel1, E.W. Varnes360, J.-L. Vay141, F. Veit285, I. Veliscek6, R. Veness1,\nA. Ventura159,231, M. Verducci40,77, C.B. Verhaaren415, C. Vernieri7, A.P. Verweij1, J.-F. Vian416,\nA. Vicini44,45, N. Vignaroli159,231, S. Vignetti149, M.C. Villeneuve218, I. Vivarelli25,26,\nE. Voevodina1,131, D.M. Vogt417, B. Voirin418, S. Voiriot105, J. Voiron144, P. Vojtyla1, V. V\u00f6lkl1,\nL. von Freeden1, Z. Vostrel1,419, N. Voumard1, E. Vryonidou52, V. Vysotsky119, R. Wallny150,\nL.-T. Wang420, Y. Wang9,10,11, R. Wanzenberg4, B.F.L. Ward421, N. Wardle181, Z. Wa\u00b8s107,\nL. Watrelot1, A.T. Watson422, M.F. Watson422, M.S. Weber89, C.P. Welsch53,184, M. Wendt1,6,\nJ. Wenninger1, B. Weyer1, G. White423, S. White306, B. Wicki1, M. Widorski1, U.A. Wiedemann1,\nA.R. Wiederhold52, A . Wiedl132, H.-U. Wienands158, A. Wieser150, C. Wiesner1, H. Wilkens1,\nD. Willi424, P.H. Williams53,425, S.L. Williams32, A. Winter422, R.B. Wittwer73, D. Wollmann1,\nY. Wu114, Z. Wu9,16,17, J. Xiao9,56,57, K. Xie386, S. Xie37,333, M. Yalvac22, F. Yaman425,426,\nW.-M. Yao141, M. Yeresko9,154,155, A. Yilmaz194, H.D. Yoo275, T. You208, F. Yu251,385, S.S. Yu79,\nT.-T. Yu410, S. Yue1, A. Zaborowska1, M. Zahnd105, C. Zamantzas1, G. Zanderighi65,131, C. Zannini1,\nR. Zanzottera44,45, P. Zaro102, R. Zennaro2, M. Zerlauth1, H. Zhang202, J. Zhang158, Y. Zhang202,\nZ. Zhang9,10,202, Y. Zhao1, Y.-M. Zhong427, B. Zhou303, D. Zhou210, J. Zhu303, G. Zick372,\nM.A. Zielinski1, E. Zimmermann105, A. Zingaretti68,164, J. Zinn-Justin3, A.V. Zlobin37, M. Zobov48,\nF. Zomer9,10,11, S. Zorzetti37, X. Zuo132, J. Zurita318, V.V. Zutshi392, M. Zykova2.\n\u2020 deceased\n1 Switzerland - CERN, European Organization for Nuclear Research\n2 Switzerland - PSI, Paul Scherrer Institute\n3 France - CEA/Irfu, Commissariat \u00e0 l\u2019Energie Atomique et aux Energies Alternatives, Institut de\nrecherche sur les lois fondamentales de l\u2019Univers\nx\n\n4 Germany - DESY, Deutsches Elektronen-Synchrotron\n5 Germany - Humboldt-Universit\u00e4t zu Berlin\n6 United States - BNL, Brookhaven National Laboratory\n7 United States - SLAC National Accelerator Laboratory\n8 United Kingdom - University of Oxford\n9 France - CNRS/IN2P3, Centre National de la Recherche Scientifique, Institut National de\nPhysique Nucl\u00e9aire et de Physique des Particules\n10 France - IJCLab, Laboratoire de Physique des 2 Infinis Ir\u00e8ne Joliot Curie\n11 France - Universit\u00e9 Paris-Saclay et Universit\u00e9 Paris-Cit\u00e9\n12 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bari\n13 Italy - Universit\u00e0 di Bari\n14 Iran - IPM, Institute for Research in Fundamental Science\n15 Iran - Malayer University\n16 France - LAPP, Laboratoire d\u2019Annecy de Physique des Particules\n17 France - Universit\u00e9 Savoie Mont Blanc\n18 Serbia - University of Belgrade\n19 Spain - ICMAB/CISC, Institut de Ci\u00e8ncia de Materials de Barcelona, Consejo Superior de\nInvestigaciones Cient\u00edificas\n20 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata\n21 Italy - Universit\u00e0 Roma Tor Vergata\n22 T\u00fcrkiye - Yozgat Bozok \u00dcniversitesi\n23 United States - Texas Tech University\n24 T\u00fcrkiye - TOBB ETU, TOBB Ekonomi ve Teknoloji \u00dcniversitesi\n25 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna\n26 Italy - Universit\u00e0 di Bologna\n27 Spain - CIEMAT, Centro de Investigaciones Energ\u00e9ticas, Medioambientales y Tecnol\u00f3gicas\n28 Saudi Arabia - KACST, King Abdulaziz City for Science and Technology\n29 Italy - Universit\u00e0 Roma Tre\n30 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano-Bicocca\n31 Italy - Universit\u00e0 di Milano-Bicocca\n32 United Kingdom - University of Cambridge\n33 T\u00fcrkiye - \u02d9Istanbul \u00dcniversitesi\n34 T\u00fcrkiye - Eski\u00b8sehir Teknik \u00dcniversitesi\n35 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli\n36 Italy - Universit\u00e0 di Napoli Federico II\n37 United States - FNAL, Fermi National Accelerator Laboratory\n38 Iran - University of Tehran\n39 Iran- FUM, Ferdowsi University of Mashhad\n40 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa\n41 United States - University of Texas Austin\n42 France - IPHC, Institut Pluridisciplinaire Hubert Curien\n43 France - Universit\u00e9 de Strasbourg\n44 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano\n45 Italy - Universit\u00e0 di Milano\nxi\n\n46 Switzerland - PIBG, P\u00f4le Invert\u00e9br\u00e9s du Basin Genevois\n47 Brazil - UFRN, Universidade Federal do Rio Grande do Norte\n48 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati\n49 Switzerland - UNIBAS, University of Basel\n50 Italy - Politecnico di Bari\n51 Portugal - LIP, Laborat\u00f3rio de Instrumenta\u00e7\u00e3o e F\u00edsica Experimental de Part\u00edculas\n52 United Kingdom - University of Manchester\n53 United Kingdom - CI, Cockcroft Institute\n54 United States - Brandeis University\n55 Armenia - A. Alikhanyan National Laboratory\n56 France - IP2I, Institut de Physique des 2 Infinis de Lyon\n57 France - Universit\u00e9 Claude Bernard Lyon 1\n58 T\u00fcrkiye - Ankara \u00dcniversitesi\n59 Sweden - Lund University\n60 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Torino\n61 United Arab Emirates - New York University Abu Dhabi\n62 United States - Stony Brook University\n63 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia\n64 Italy - Universit\u00e0 di Perugia\n65 Germany - Technische Universit\u00e4t M\u00fcnchen\n66 T\u00fcrkiye - Hatay Mustafa Kemal \u00dcniversitesi\n67 T\u00fcrkiye - Do\u02d8gu\u00b8s \u00dcniversitesi\n68 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Padova\n69 People\u2019s Republic of China - Harbin Institute of Technology\n70 United States - University of Wisconsin-Madison\n71 United Kingdom - RAL, Rutherford Appleton Laboratory, Science and Technology Facilities\nCouncil\n72 India - IMSc, Institute of Mathematical Sciences, Chennai\n73 Switzerland - Universit\u00e4t Z\u00fcrich\n74 United States - University of New Mexico\n75 France - CPPM, Centre de Physique des Particules de Marseille\n76 France - Aix-Marseille Universit\u00e9\n77 Italy - Universit\u00e0 di Pisa\n78 Hungary - HUN-REN Wigner Research Centre for Physics\n79 United States - Catholic University of America\n80 United States - Duke University\n81 France - LLR, Laboratoire Leprince-Ringuet\n82 France - \u00c9cole Polytechnique, Institut Polytechnique de Paris\n83 Canada - TRIUMF, Canada\u2019s National Laboratory for Particle and Nuclear Physics\n84 Canada - Simon Fraser University\n85 Italy - FEEM, Fondazione Ente Nazionale Idrocarburi (ENI) Enrico Mattei\n86 France - BRGM, Bureau de Recherches G\u00e9ologiques et Mini\u00e8res\n87 T\u00fcrkiye - I\u00b8s\u0131k \u00dcniversitesi\n88 T\u00fcrkiye - \u02d9Istanbul Teknik \u00dcniversitesi\nxii\n\n89 Switzerland - UNIBE, University of Bern\n90 Italy - Universit\u00e0 di Roma la Sapienza\n91 Italy - CNR-SPIN, Consiglio Nazionale delle Ricerche\n92 France - Expert naturaliste et entomologiste\n93 United States - ORNL, Oak Ridge National Laboratory\n94 Austria - HEPHY, Institut f\u00fcr Hochenergiephysik\n95 Switzerland - Geos, Bureau d\u2019ing\u00e9nieurs conseils en g\u00e9otechnique, g\u00e9nie civil, hydraulique et\nenvironnement\n96 France - APC, Laboratoire AstroParticule et Cosmologie\n97 France - Universit\u00e9 Paris Cit\u00e9\n98 Austria - TUWIEN, Technische Universit\u00e4t Wien\n99 Switzerland - HEPIA, Haute \u00c9cole du Paysage, d\u2019Ing\u00e9nierie et d\u2019Architecture de Gen\u00e8ve\n100 Switzerland - HES-SO University of Applied Sciences and Arts Western Switzerland\n101 Switzerland - UNIGE, Universit\u00e9 de Gen\u00e8ve\n102 France - SETEC ALS, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en infrastructures de transport, g\u00e9nie civil et\nenvironnement\n103 United States - East Texas A&M University\n104 Switzerland - Amberg Engineering Ltd\n105 Switzerland - ECOTEC Environnement SA, Bureau d\u2019\u00e9tudes et de conseil en environnement\n106 United States - Southern Methodist University\n107 Poland - IFJ PAN, Institute of Nuclear Physics, Polish Academy of Sciences\n108 France - Cerema, \u00e9tablissement public pour l\u2019\u00e9laboration, le d\u00e9ploiement et l\u2019\u00e9valuation de\npolitiques publiques d\u2019am\u00e9nagement et de transport\n109 United Kingdom - Rendel Ltd, Engineering design consultancy firm\n110 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre\n111 T\u00fcrkiye - \u02d9Istanbul Beykent \u00dcniversitesi\n112 United States - University of Iowa\n113 India - Indian Institute of Technology Kanpur\n114 Switzerland - EPFL, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne\n115 Germany - Universit\u00e4t Hamburg, Fakult\u00e4t f\u00fcr Mathematik, Informatik und Naturwissenschaften\n116 Belgium - VUB, Vrije Universiteit Brussel\n117 France - LPNHE, Laboratoire de Physique Nucl\u00e9aire et de Hautes \u00c9nergies\n118 Italy - Scuola Superiore Meridionale\n119 Affiliated with an institute formerly covered by a cooperation agreement with CERN\n120 Canada - University of Saskatchewan and the Canadian Light Source\n121 United Kingdom - University of Bristol\n122 United States - Northwestern University\n123 United States - University of Florida\n124 Canada - York University\n125 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari\n126 Italy - Universit\u00e0 di Cagliari\n127 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pavia\n128 Canada - Queen\u2019s University\n129 Portugal - CFTP-IST, Centro de F\u00edsica T\u00e9orica de Part\u00edculas, Instituto Superior Tecnico,\nxiii\n\nUniversidade de Lisboa\n130 Sweden - Uppsala University\n131 Germany - MPP, Max-Planck-Institut f\u00fcr Physik Garching\n132 Germany - KIT, Karlsruher Institut f\u00fcr Technologie\n133 Ukraine - NSC KIPT, National Science Center Kharkiv Institute of Physics and Technology\n134 Italy - Universit\u00e0 degli Studi dell\u2019Insubria\n135 Germany - Albert-Ludwigs-Universit\u00e4t Freiburg\n136 United Kingdom - JAI, John Adams Institute for Accelerator Science, University of Oxford\n137 France - CNRS/INP, Centre National de la Recherche Scientifique, Institut de Physique\n138 France - LPTHE, Laboratoire de Physique Th\u00e9orique et Hautes Energies\n139 France - Sorbonne Universit\u00e9\n140 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Genova\n141 United States - LBNL, Lawrence Berkeley National Laboratory\n142 Italy - IIT, Instituto Italiano di Tecnologia\n143 T\u00fcrkiye - G\u00fcm\u00fc\u00b8shane \u00dcniversitesi\n144 Switzerland - WSP Ing\u00e9nieurs Conseils SA\n145 Mexico - UADY, Autonomous University of Yucatan\n146 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara\n147 Italy - Universit\u00e0 di Ferrara\n148 France - MARCELEON, Cabinet d\u2019ing\u00e9nierie juridique et fonci\u00e8re\n149 Italy - CSIL (Economic Research Institute)\n150 Switzerland - ETHZ, Swiss Federal Institute of Technology Zurich\n151 Spain - UAH, Universidad de Alcal\u00e1 Madrid\n152 France - CIA, Conseil Ing\u00e9nierie Acoustique\n153 France - Evinerude, Bureau d\u2019\u00e9tudes environnementales\n154 France - LPCA, Laboratoire de Physique de Clermont Auvergne\n155 France - Universit\u00e9 Clermont Auvergne\n156 Australia - ANSTO, Australian Synchrotron\n157 India - Brahmananda Keshab Chandra College\n158 United States - ANL, Argonne National Laboratory\n159 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Lecce\n160 Italy - Universit\u00e0 di Palermo\n161 Poland - Wroc\u0142aw University of Science and Technology\n162 United States - Rutgers University\n163 United States - Princeton University\n164 Italy - Universit\u00e0 di Padova\n165 T\u00fcrkiye - IUE, \u02d9Izmir Ekonomi \u00dcniversitesi\n166 T\u00fcrkiye - Ege \u00dcniversitesi\n167 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Udine\n168 Italy - Universit\u00e0 di Udine\n169 United States - University of Massachusetts Amherst\n170 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma\n171 Spain - CELLS/ALBA, Consortium for the Construction, Equipment and Exploitation of the\nSynchrotron Light Laboratory\nxiv\n\n172 France - LPSC, Laboratoire de Physique Subatomique et de Cosmologie\n173 France - Universit\u00e9 Grenoble Alpes\n174 Italy - Universit\u00e0 degli Studi di Napoli Parthenope\n175 United States - National High Magnetic Field Laboratory\n176 United States - Florida State University\n177 South Africa - University of Johannesburg\n178 Spain - IGFAE, Instituto Galego de Fisica de Altas Enerx\u00edas, Universidade de Santiago de\nCompostela\n179 United Kingdom - LSE, London School of Economics\n180 Spain - Universidade de Santiago de Compostela\n181 United Kingdom - Imperial College London\n182 United States - MIT, Massachusetts Institute of Technology\n183 France - CETU, Centre d\u2019Etude des Tunnels\n184 United Kingdom - University of Liverpool\n185 Switzerland - Linde Kryotechnik AG\n186 Switzerland - ILF Consulting Engineers\n187 Denmark - NBI, Niels Bohr Institute\n188 Japan - Hokkaido University\n189 Czech Republic - CUNI, Charles University\n190 Spain - Universidad de Granada\n191 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Firenze\n192 Malta - University of Malta\n193 United States - BU, Boston University\n194 T\u00fcrkiye - IBU, Bolu Abant \u02d9Izzet Baysal \u00dcniversitesi\n195 Germany - Julius-Maximilians-Universit\u00e4t W\u00fcrzburg\n196 Australia - University of Adelaide\n197 Finland - HIP, Helsinki Institute of Physics, University of Helsinki\n198 Belgium - ULB, Universit\u00e9 Libre de Bruxelles\n199 Germany - IMA, Institut f\u00fcr Maschinenelemente, Universit\u00e4t Stuttgart\n200 Belgium - CP3, Centre de Cosmologie, de Physique des Particules et de Ph\u00e9nom\u00e9nologie,\nUniversit\u00e9 Catholique de Louvain\n201 Netherlands - NIKHEF, Nationaal instituut voor subatomaire fysica\n202 People\u2019s Republic of China - IHEP, Chinese Academy of Sciences\n203 Mexico - UAS, Universidad Aut\u00f3noma de Sinaloa\n204 Austria - BOKU, Universit\u00e4t f\u00fcr Bodenkultur Wien\n205 United States - Purdue University\n206 India - University of Delhi\n207 France - Ginger BURGEAP, bureau d\u2019\u00e9tudes en environnement\n208 United Kingdom - King\u2019s College London\n209 United States - University of Maryland\n210 Japan - KEK, High Energy Accelerator Research Organization\n211 Switzerland - Geoenergy, Reservoir Geology and Basin Analysis Group\n212 France - SETEC International, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie en charge des transports et des infrastructures\n213 T\u00fcrkiye - KKU, K\u0131r\u0131kkale \u00dcniversitesi\nxv\n\n214 France - SETEC LERM, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en mat\u00e9riaux de construction\n215 Mexico - BUAP, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla\n216 United States - Stanford University\n217 United States - University of Pittsburgh\n218 Austria - MUL, Montanuniversit\u00e4t Leoben, Lehrstuhl f\u00fcr Subsurface Engineering, Geotechnik\nund unterirdisches Bauen\n219 Austria - MUL-ZaB, Underground Research Center, Zentrum am Berg\n220 Spain - IFAE, Institut de F\u00edsica d\u2019Altes Energies\n221 Switzerland - FHNW, University of Applied Sciences Northwestern Switzerland\n222 India - UPES, University of Petroleum and Energy Studies\n223 France - GANIL, Grand Acc\u00e9l\u00e9rateur National d\u2019Ions Lourds\n224 France - Universit\u00e9 Caen Normandie\n225 Brazil - UFRGS, Universidade Federal do Rio Grande do Sul\n226 Germany - Technische Universit\u00e4t Darmstadt\n227 Poland - University of Silesia in Katowice\n228 Portugal - Universidade de Coimbra\n229 Brazil - UFPel, Universidade Federal de Pelotas\n230 United States - University of California Santa Cruz\n231 Italy - Universit\u00e0 del Salento\n232 United States - Brown University\n233 United States - University of California Berkeley\n234 Italy - Universit\u00e0 di Torino\n235 United States - Johns Hopkins University\n236 People\u2019s Republic of China - Fudan University\n237 France - LAPTh, Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique\n238 People\u2019s Republic of China - Dongguan University of Technology\n239 T\u00fcrkiye - Kahramanmara\u00b8s S\u00fct\u00e7\u00fc \u02d9Imam \u00dcniversitesi\n240 Mexico - UNACH, Universidad Aut\u00f3noma de Chiapas\n241 Mexico - MCTP, Mesoamerican Centre for Theoretical Physics\n242 Mexico - UAZ, Universidad Aut\u00f3noma de Zacatecas\n243 Finland - University of Jyv\u00e4skyl\u00e4\n244 Germany - Technische Universit\u00e4t Dortmund\n245 United Kingdom - Overleaf\n246 United States - University of Virginia\n247 United States - Cornell University\n248 United States - FIT, Florida Institute of Technology\n249 Switzerland - Shirokuma GmbH\n250 Pakistan - National Centre for Physics\n251 Germany - Johannes Gutenberg Universit\u00e4t Mainz\n252 Pakistan - PAEC, Pakistan Atomic Energy Commission\n253 India - Mathabhanga College\n254 India - Harish-Chandra Research Institute\n255 Germany - MPIK, Max-Planck-Institut f\u00fcr Kernphysik Heidelberg\n256 Sweden - European Spallation Source ERIC\nxvi\n\n257 France - Centre de calcul de l\u2019IN2P3\n258 Germany - GSI, Helmholtzzentrum f\u00fcr Schwerionenforschung GmbH\n259 Republic of Korea - IBS, Institute for Basic Science, Center for Theoretical Physics of the\nUniverse\n260 Poland - University of Warsaw\n261 Slovenia - University of Ljubljana\n262 Slovenia - Jozef Stefan Institute\n263 France - Microhumus, Bureau d\u2019\u00e9tude et d\u2019ing\u00e9nierie sp\u00e9cialis\u00e9 dans la gestion des sols d\u00e9grad\u00e9s\n264 Germany - Fakult\u00e4t f\u00fcr Physik und Astronomie, Universit\u00e4t Heidelberg\n265 T\u00fcrkiye - Ni\u02d8gde \u00d6mer Halisdemir \u00dcniversitesi\n266 T\u00fcrkiye - Giresun \u00dcniversitesi\n267 Hungary - University of Miskolc\n268 Greece - NTUA, National Technical University of Athens\n269 Switzerland - Transmutex SA\n270 Ireland - DIAS, Dublin Institute for Advanced Studies, School of Theoretical Physics\n271 Poland - AGH, University of Science and Technology\n272 Iran - University of Science and Technology of Mazandaran\n273 United Kingdom - IPPP, Institute for Particle Physics Phenomenology, Durham University\n274 T\u00fcrkiye - Bursa Uluda\u02d8g \u00dcniversitesi\n275 Republic of Korea - YU, Yonsei University\n276 Affiliated with an international laboratory covered by a cooperation agreement with CERN\n277 France - CPT, Centre de Physique Th\u00e9orique\n278 France - Aix-Marseille Universit\u00e9 et Universit\u00e9 du Sud Toulon Var\n279 Republic of Korea - KIAS, Korea Institute for Advanced Study\n280 Canada - Carleton University\n281 Greece - FEAC Engineering P.C.\n282 Greece - UPATRAS, University of Patras\n283 United States - University of Kansas\n284 Greece - AUTH, Aristotle University of Thessaloniki\n285 Germany - IML, Fraunhofer-Institut f\u00fcr Materialfluss und Logistik\n286 Germany - RWTH Aachen, Rheinisch-Westf\u00e4lische Technische Hochschule Aachen\n287 Switzerland - ZHAW, Zurich University of Applied Sciences\n288 Gernany - Universit\u00e4t M\u00fcnster\n289 South Africa - University of the Witwatersrand\n290 Austria - Fachhochschule Technikum Wien\n291 United States - University of California Irvine\n292 United States - Northeastern University\n293 France - ESI, European Scientific Institute\n294 Republic of Korea - UOS, University of Seoul\n295 Republic of Korea - KNU Kyungpook National University\n296 Republic of Korea - KU, Korea University\n297 Finland - Tampere University\n298 United Kingdom - University of Edinburgh\n299 Switzerland - BG Ing\u00e9nieurs Conseils\nxvii\n\n300 People\u2019s Republic of China - T.-D. Lee Institute\n301 People\u2019s Republic of China - Shanghai Jiao Tong University\n302 Italy - CNR, Consiglio Nazionale delle Ricerche\n303 United States - University of Michigan\n304 United States - University of Pennsylvania\n305 United States - University of Minnesota\n306 France - ESRF, European Synchrotron Radiation Facility\n307 United Kingdom - SUSSEX, University of Sussex\n308 Italy - Universit\u00e0 di Bari Aldo Moro\n309 United Kingdom - University of Bath\n310 Italy - Scuola Normale Superiore di Pisa\n311 Brazil - Universidade de S\u00e3o Paulo\n312 Austria - Universit\u00e4t Graz\n313 Egypt - Center for High Energy Physics, Fayoum University\n314 Egypt - Center of theoretical physics, British University in Egypt\n315 Egypt - Cairo University\n316 France - Sorbonne Universit\u00e9 et Universit\u00e9 Paris Cit\u00e9\n317 Italy - Universit\u00e0 di Genova\n318 Spain - IFIC-CSIC/UV, Instituto de F\u00edsica Corpuscular, Consejo Superior de Investigaciones\nCient\u00edficas/Universidad de Valencia\n319 Switzerland - Service de g\u00e9ologie, sols et d\u00e9chets du canton de Gen\u00e8ve\n320 Estonia - NICPB, National Institute for Chemical Physics and Biophysics\n321 Estonia - UT, University of Tartu\n322 Spain - Universidad de Salamanca\n323 Mexico - UGTO, Universidad de Guanajuato\n324 Switzerland - Edaphos engineering\n325 Germany - Helmholtz-Zentrum Dresden-Rossendorf\n326 India - Tata Institute of Fundamental Research Mumbai\n327 Belgium - Universiteit Gent\n328 Italy - CNR-IOM, Consiglio Nazionale delle Ricerche\n329 Austria - JKU, Johannes Kepler Universit\u00e4t Linz\n330 Norway - University of Stavanger\n331 Colombia - Universidad Nacional de Colombia\n332 Italy - Trento Institute for Fundamental Physics and Applications\n333 United States - Caltech, California Institute of Technology\n334 Italy - Universit\u00e0 dalla Calabria\n335 Spain - IFT, Instituto de F\u00edsica Te\u00f3rica, Universidad Aut\u00f3noma de Madrid\n336 Spain - UPC, Universitat Polit\u00e8cnica de Catalunya\n337 Portugal - Departamento de F\u00edsica, Universidade do Minho\n338 Portugal - Centro de F\u00edsica das Universidades do Minho e do Porto\n339 Portugal - LaPMET, Laboratory of Physics for Materials and Emergent Technologies\n340 Norway - University of Bergen\n341 Chile - SAPHIR, Instituto Milenio de F\u00edsica Subat\u00f3mica en la Frontera de Altas Energ\u00edas\n342 Chile - Universidad Andres Bello\nxviii\n\n343 Brazil - IIP, International Institute of Physics\n344 Japan - Tokyo International University\n345 T\u00fcrkiye - \u02d9Izmir Bak\u0131r\u00e7ay \u00dcniversitesi\n346 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso\n347 Italy - Universit\u00e1 degli Studi di Cassino e del Lazio Meridionale\n348 Serbia - Vin\u02d8ca Institute of Nuclear Sciences\n349 United States - Kennesaw State University\n350 Italy - Universit\u00e0 di Pavia\n351 United States - Columbia University\n352 United States - DOE, Department of Energy of the United States of America\n353 France - IPSA, Institut Polytechnique des Sciences Avanc\u00e9es\n354 Italy - Universit\u00e0 degli Studi del Sannio\n355 Poland - UJ, Jagiellonian University\n356 Austria - Universit\u00e4t Wien\n357 Germany - Goethe-Universit\u00e4t Frankfurt, Institut f\u00fcr Angewandte Physik\n358 Germany - HFFH, Helmholtz Forschungsakademie Hessen f\u00fcr FAIR\n359 Romania - INCDTIM, National Institute for Research and Development of Isotopic and\nMolecular Technologies\n360 United States - University of Arizona\n361 Germany - Technische Universit\u00e4t Dresden\n362 Latvia - RTU, Riga Technical University\n363 United Kingdom - Lancaster University\n364 Cyprus - University of Cyprus\n365 Cyprus - Cosmos Open University\n366 Brazil - CBPF, Centro Brasileiro de Pesquisas F\u00edsicas\n367 Germany - Universit\u00e4t Bonn\n368 Thailand - CMU, Chiang Mai University\n369 United States - JLAB, Thomas Jefferson National Accelerator Facility\n370 Ecuador - ESPOL, Escuela Superior Polit\u00e9cnica del Litoral\n371 Croatia - IRB, Rudjer Boskovic Institute\n372 France - Air Liquide Advanced Technologies\n373 Netherlands - VU Amsterdam\n374 France - ING\u00c9ROP ,Groupe d\u2019ing\u00e9nierie et de conseil en mobilit\u00e9 durable, transition \u00e9nerg\u00e9tique\net cadre de vie\n375 Poland - Warsaw University of Technology\n376 Spain - IFCA, Instituto de F\u00edsica de Cantabria\n377 Germany - Institut f\u00fcr Beschleunigerphysik und Technologie\n378 T\u00fcrkiye - U\u00b8sak \u00dcniversitesi\n379 Japan - ICEPP, International Center for Elementary Particle Physics, University of Tokyo\n380 United Kingdom - Rudolf Peierls Centre for Theoretical Physics, University of Oxford\n381 United Kingdom - All Souls College, University of Oxford\n382 T\u00fcrkiye - Akdeniz \u00dcniversitesi\n383 Switzerland - Latitude Durable SARL\n384 Spain - USAL, Universidad de Salamanca\nxix\n\n385 Germany - PRISMA+ Cluster of Excellence\n386 United States - Michigan State University\n387 Spain - Universidad Complutense Madrid\n388 Switzerland - scMetrology SARL\n389 Portugal - IST, Instituto Superior Tecnico, Universidade de Lisboa\n390 Portugal - CeFEMA, Center of Physics and Engineering of Advanced Materials\n391 India - Indian Institute of Science Education and Research Mohali\n392 United States - NIU, Northern Illinois University\n393 India - Banaras Hindu University\n394 Slovakia - Comenius University\n395 Australia - Monash University\n396 Slovakia - Slovak Academy of Sciences\n397 Republic of Korea - KAIST, Korea Advanced Institute of Science and Technology\n398 France - Amberg Engineering Chamb\u00e9ry\n399 United Arab Emirates - Khalifa University of Science and Technology\n400 United States - University of Tennessee\n401 Austria - WIFO, \u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\n402 Brazil - Universidade do Estado do Rio de Janeiro\n403 France - M\u00e9lica, NATURA SCOP, \u00c9tudes et expertises environnementales\n404 Italy - Universit\u00e0 LUM, Casamassima\n405 Netherlands - University of Twente\n406 Iran - Arak University\n407 Italy - Universit\u00e0 di Trieste\n408 France - ForestAllia, Cabinet de gestion et d\u2019expertise foresti\u00e8res\n409 Germany - Universit\u00e4t Siegen\n410 United States - University of Oregon\n411 Germany - Universit\u00e4t Rostock\n412 Switzerland - CEGELEC SA\n413 Sweden - KTH, Royal Institute of Technology, Stockholm\n414 Sweden - OKC, Oskar Klein Centre for Cosmoparticle Physics\n415 United States - Brigham Young University\n416 France - Expert foncier et agricole\n417 Germany - ITSM, Institut f\u00fcr Thermische Str\u00f6mungsmaschinen und Maschinenlaboratorium,\nUniversit\u00e4t Stuttgart\n418 France - \u00c9cole Normale Sup\u00e9rieure de Lyon\n419 Czech Republic - CTU, Czech Technical University\n420 United States - University of Chicago\n421 United States - Baylor University\n422 United Kingdom - University of Birmingham\n423 United Kingdom - University of Southampton\n424 Switzerland - Swisstopo, Federal Office of Topography\n425 United Kingdom - Daresbury Laboratory, Science and Technology Facilities Council\n426 T\u00fcrkiye - IZTECH, \u02d9Izmir Y\u00fcksek Teknoloji Enstit\u00fcs\u00fc\n427 Hong Kong - City University of Hong Kong\nxx\n\nAbstract\nVolume 3 of the FCC Feasibility Report presents studies related to civil engineering, the development\nof a project implementation scenario, and environmental and sustainability aspects. The report details\nthe iterative improvements made to the civil engineering concepts since 2018, taking into account sub-\nsurface conditions, accelerator and experiment requirements, and territorial considerations. It outlines a\ntechnically feasible and economically viable civil engineering configuration that serves as the baseline\nfor detailed subsurface investigations, construction design, cost estimation, and project implementation\nplanning. Additionally, the report highlights ongoing subsurface investigations in key areas to support\nthe development of an improved 3D subsurface model of the region.\nThe report describes development of the project scenario based on the \u2018avoid-reduce-compensate\u2019\niterative optimisation approach. The reference scenario balances optimal physics performance with terri-\ntorial compatibility, implementation risks, and costs. Environmental field investigations covering almost\n600 hectares of terrain\u2014including numerous urban, economic, social, and technical aspects\u2014confirmed\nthe project\u2019s technical feasibility and contributed to the preparation of essential input documents for the\nformal project authorisation phase. The summary also highlights the initiation of public dialogue as part\nof the authorisation process. The results of a comprehensive socio-economic impact assessment, which\nincluded significant environmental effects, are presented. Even under the most conservative and stringent\nconditions, a positive benefit-cost ratio for the FCC-ee is obtained. Finally, the report provides a concise\nsummary of the studies conducted to document the current state of the environment.\nxxi\n\nPreface from CERN\u2019s Director-General\nIn 2021, in response to the 2020 update of the European Strategy for Particle Physics, the CERN Council\ninitiated the Future Circular Collider (FCC) Feasibility Study.\nThis report summarises an immense amount of work carried out by the international FCC collabo-\nration over several years. It covers, inter alia, physics objectives and potential, geology, civil engineering,\ntechnical infrastructure, territorial implementation, environmental aspects, R&D needs for the acceler-\nators and detectors, socio-economic benefits and cost. It constitutes important input for the ongoing\nupdate of the European Strategy for Particle Physics.\nThe Feasibility Study required engagement with a broad range of stakeholders. In particular,\nthroughout the Study, CERN has been accompanied by its two Host States, France and Switzerland,\nand has been working with entities at local, regional and national level. I am very grateful to the Host\nState authorities and teams for their invaluable help. Furthermore, significant sections of the Study were\nsupported by the European Union under the Horizon 2020 and Horizon Europe framework programmes.\nThe Study also greatly benefited from contributions from accelerator laboratories and universities from\nacross Europe, such as the Swiss Accelerator Research and Technology (CHART) initiative, and from\nthe Americas, Asia, Africa and Australia.\nThe proposed FCC integrated programme consists of two possible stages: an electron\u2013positron\ncollider serving as a Higgs-boson, electroweak and top-quark factory running at different centre-of-mass\nenergies, followed at a later stage by a proton\u2013proton collider operating at an unprecedented collision\nenergy of around 100 TeV. The complementary physics programmes of each stage match the physics\npriorities expressed in the 2020 update of the European Strategy for Particle Physics.\nA major achievement of the Feasibility Study is the choice of placement of the collider ring and\nthe entire infrastructure, including the surface sites and the access shafts, which was developed and\noptimised over several years following the principle \u2018avoid, reduce, compensate\u2019. Sustainability studies\nhave assessed energy efficiency, land use, water and resource management, and socio-economic impact,\nensuring that the FCC is designed in accordance with the latest environmental and societal standards.\nI would like to thank all contributors to this report for their hard work and commitment, which\nallowed the outstanding results presented here to be achieved.\nFabiola Gianotti\nCERN, Director-General\nxxii\n\nPreface from the FCC Collaboration Board Chair\nBuilding on the earlier Future Circular Collider (FCC) Conceptual Design Study conducted between\n2014 and 2018, the FCC Feasibility Study (2021\u20132025) has been undertaken by a robust international\ncollaboration, now comprising over 160 institutes worldwide. The FCC \u2018integrated programme\u2019, de-\nveloped in the framework of the Feasibility Study, consists of an initial electron-positron collider, the\nFCC-ee, which could be followed by a proton-proton collider, the FCC-hh. This staging takes into ac-\ncount the physics priorities as formulated in the updates of the European Strategy for Particle Physics of\n2012 and 2020, as well as the relative technology readiness and costs of the FCC-ee and FCC-hh.\nOver the years, I have closely followed the steady progress of the study, representing the FCC\ncollaboration at the international steering committee and participating in annual FCC Week meetings,\nwhich include sessions of the International Collaboration Board. The commitment and enthusiasm of\nthe members of the collaboration has always been impressive. The collective effort is clearly visible.\nParticipation by students and early-career researchers is increasing. There is a shared determination and\nmomentum to move forward.\nThe strong international collaboration around the FCC and its global network provide a solid foun-\ndation for the future of this project. The FCC community continues to grow, with increasing engagement\nfrom new institutes and partners worldwide. This broad support will be essential as the project enters its\nnext phase.\nThe FCC Feasibility Study demonstrates not only the technical viability of the project, but also\nthe strength of the international community that supports it. As we move towards the next step in\nthe decision-making phase, this collective effort is key to showing a possible path forward. The FCC\npromises far-reaching scientific opportunities and long-term benefits for innovation, training, and global\ncollaboration in science and technology.\nPhilippe Chomaz\nCEA, Chair of the FCC International Collaboration Board\nxxiii\n\nContents\n1\nCivil engineering\n1\n1.1\nUnderground structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n2\n1.2\nSurface structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n22\n1.3\nStaged approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n37\n1.4\nSubsurface site investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n39\n1.5\nManagement of excavated materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n54\n2\nTerritorial implementation\n69\n2.1\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n69\n2.2\nMethodology to develop a sustainable project\n. . . . . . . . . . . . . . . . . . . . . . . .\n70\n2.3\nRequirements and invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n80\n2.4\nTerritorial constraints\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n89\n2.5\nInitial variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n97\n2.6\nReference scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103\n2.7\nTerritorial infrastructure needs\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130\n3\nEnvironment\n163\n3.1\nContext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163\n3.2\nEnvironmental aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165\n3.3\nCurrent state of the environment\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200\n3.4\nConclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263\n4\nSustainability\n265\n4.1\nContext . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265\n4.2\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265\n4.3\nMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274\n4.4\nSocio-economic sustainability enablers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275\n4.5\nComprehensive sustainability performance assessment based on Cost-Benefit Analysis . . . 281\n4.6\nLimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283\n4.7\nLifecycle analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286\n4.8\nSocio-economic performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291\n4.9\nReturns to participating countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312\n4.10\nRequirements and constraints for a preparatory phase\n. . . . . . . . . . . . . . . . . . . . 315\n4.11\nRecommendations for a preparatory phase project . . . . . . . . . . . . . . . . . . . . . . 316\nReferences\n333\nxxiv\n\nChapter 1\nCivil engineering\nIntroduction\nSince the completion of the FCC conceptual design in 2018, several significant modifications have been\nmade to civil engineering. They derive from the improved maturity of requirements for the systems that\ninterface with civil engineering, such as the accelerators, the detectors, and the technical infrastructure to\nbe housed within the underground and surface structures. Furthermore, more precise localisation of the\nsurface sites has facilitated a greater understanding of the geographical and environmental constraints to\nbe accounted for in the development of the civil engineering infrastructure. The main improvements that\nhave occurred since the conceptual design of the underground civil engineering required for the FCC-ee\ncollider was completed are as follows:\n\u2013 A reduction in the overall circumference of the accelerator tunnel from 97.8 km to 90.6 km.\n\u2013 A reduction in the number of surface sites (and access points to the underground) from 12 to 8.\n\u2013 A reduction in the number of permanent shafts needed for operation from 18 to 12.\n\u2013 A reduction of the depth to the deepest shaft from 578 m to 400 m.\n\u2013 Additional underground civil engineering for the RF systems at technical sites PH and PL.\n\u2013 A simplification of the civil engineering needed for the beam absorber system.\n\u2013 Simplification of the underground infrastructure required for the beam transfer lines, with the use\nof a single tunnel to house both clockwise and anti-clockwise transfer to the FCC.\nIn addition to the above, a more detailed\u2014yet still evolving\u2014understanding of the requirements\nfor surface civil engineering has been built up. Initial spatial arrangements for all eight surface sites\nhave been developed, with preliminary dimensioning of the necessary buildings, roads, and other surface\ninfrastructure providing a framework for further refinement. For two of the eight sites, and under a col-\nlaboration with the U.S. Fermi National Accelerator Laboratory, preliminary design studies for buildings\nhave been carried out. The results offer valuable insights into space requirements, user access needs and\ncost envelopes. They were mainly informed by the technical needs of the interfacing systems. The inte-\ngration of the \u2018Avoid, Reduce, Compensate\u2019 approach to develop the surface sites is an iterative process,\nrequiring continued efforts to understand the technical needs, the territorial requirements and constraints\nand the project cost and risk implications. Understanding the technical system requirements is an essen-\ntial guiding element. The analysis of the current state of the environment also carried out in the frame of\nthe feasibility study, is another aspect that will inform the subsequent activities.\nA staged approach to civil engineering has been studied. Infrastructure essential for the operation\nof the FCC-ee collider and its associated experiments is included within the initial stage, along with\nany civil engineering needed for FCC-hh for which it would be impossible, impractical, or inefficient to\nconstruct during a second stage. This staged approach primarily concerns the surface infrastructure since\nit is relatively straightforward to construct additional buildings in a second stage.\nThe civil engineering for the FCC-ee, as defined in this document, builds on the studies completed\nfor the conceptual design phase and carried out for the feasibility phase. The current design demonstrates\nthe technical feasibility of FCC civil engineering. It is to be noted, however, that there are still areas\nwhere further work needs to be done in order to reduce technical risks, in particular taking into account\nthe remaining data that will be provided upon completion of phase 1 of the sub-surface site investigations\nthat commenced in October 2024 and is expected to be completed before the end of 2025.\n1\n\nThe work carried out since the completion of the conceptual design has largely maintained similar\nspatial elements for the underground works (sizes of caverns, shafts, tunnels, etc.), and therefore, it has\nnot been necessary to undertake additional calculations for the overall structural stability of these ele-\nments. Furthermore, the construction methodologies remain largely as identified during the conceptual\ndesign phase, although the sequence for undertaking the works has now been revised, in particular, to\naccount for the reduced number of access points to the underground civil engineering.\nA key input to the feasibility study has come from the early interaction between the FCC civil\nengineering team and potential future stakeholders from the industry. CERN has held a number of\nmeetings and workshops with several major contractors specialising in underground civil engineering.\nThe feedback received has proved invaluable in developing not only robust technical solutions but also\na realistic and efficient schedule for the execution of civil engineering. Feedback from the industry has\nalso helped shape CERN\u2019s initial thinking on potential contractual routes for the delivery of the design\nand construction of civil engineering. The civil engineering schedule developed as part of the feasibility\nstudy has been integrated with the subsequent infrastructure and machine installation activities. The\nresulting integrated schedule results in a gradual handover of the civil engineering for each of the eight\nsectors, thus allowing parallel and more efficient execution of installation activities in the main tunnel.\n1.1\nUnderground structures\nSeveral improvements have been made to the underground structures since the conceptual design report\nwas completed. A thorough identification has been made of the underground structures necessary for the\nFCC-ee collider as well as those for the FCC-hh collider, which cannot be deferred. The latter will be\nconstructed as part of the civil engineering necessary for the FCC-ee collider and associated experiments.\nA Product Breakdown Structure (PBS) has been produced down to level 4, containing 205 uniquely\nidentified structures. Table 1.1 lists the PBS and associated structures for the sector PA to PB. The PBS\nof other sectors follow a similar structure. In total, the underground civil works consist of twelve per-\nmanent shafts for operation, one temporary shaft required only during the civil engineering construction,\ntwelve large caverns with spans exceeding 20 m as well as numerous smaller caverns, alcoves, connec-\ntion and bypass tunnels that collectively make up the underground civil engineering. Figure 1.1 shows a\nschematic arrangement of underground civil engineering.\nTable 1.1: PBS for sector PA to PB underground structures.\nPBS Level\nPBS Description\n0\n1\n2\n3\n4\n2\nCivil engineering\n2\n3\nUnderground structures\n2\n3\n1\nSite PA\n2\n3\n1\n1\nExperiment shaft\n2\n3\n1\n2\nService shaft\n2\n3\n1\n3\nExperiment cavern\n2\n3\n1\n4\nService cavern\n2\n3\n1\n5\nAlcoves\n2\n3\n1\n6\nBeam tunnel sector AB\n2\n3\n1\n7\nBypass tunnel AL\n2\n3\n1\n8\nBypass tunnel AB\n2\n3\n1\n9\nConnection tunnels and galleries\n2\n3\n1\n10\nTunnel widenings\nThe overall circumference of the accelerator tunnel that will house the colliders is 90.6 km, a\n2\n\nFig. 1.1: Schematic layout of FCC-ee underground civil engineering.\nreduction of about 7% compared to the 97.8 km tunnel developed at the conceptual design phase. The\naccelerator tunnel, which will house the collider, has an internal nominal diameter of 5.5 m. On the basis\nof the pre-existing and recent site investigation data, the average elevation is 300 m above datum and the\ninclination of the tunnel plane has been maintained at 0.1% and 0.4% in the two axes. This results in a\ntunnel depth that varies between 30 m where the tunnel passes under the Rh\u00f4ne river and 560 m where\nthe tunnel passes under the Borne plateau on the eastern side of the overall study site. The average depth\nof the tunnel is approximately 240 m below the ground surface.\nTwo sizes of experiment cavern complexes are envisaged; these are similar in layout and function.\nThe first type includes a cavern to house the largest planned FCC-hh detector with a 35 m span (similar\nto that of the existing ATLAS detector cavern) and the second type includes a cavern to house the smaller\nFCC-hh detectors with a span of 25 m (similar to that of the existing CMS detector cavern).\nA single transfer tunnel connecting the injection system to the FCC is envisaged. This tunnel\nstarts close to the surface of the existing CERN Pr\u00e9vessin site where it will connect to the cut and cover\ntunnel that will house the high-energy LINAC. The tunnel will descend over a distance of about 5 km at\nwhich point it will bifurcate at a location close to PA to allow symmetrical clockwise and anticlockwise\ninjection into the FCC. The injection will take place on either side of the experiment area located in PA.\nExpectations regarding the geology to be encountered during the civil engineering of the under-\nground structures are consistent with those established during the conceptual design phase of the FCC-ee\nstudy, providing a solid foundation for further refinement and risk mitigation in subsequent phases. The\ncurrent expectation is that the majority of the tunnels and the cavern complexes will be located within\nthe molasse rock, a low to medium-strength sedimentary rock made up of complex sequences of marls\nand sandstones. This material is well suited for tunnelling since it is typically watertight and can be\nsupported through the implementation of a range of standard rock support measures such as rock bolts,\nshotcrete, reinforced concrete segments etc. Larger caverns can become more challenging and will re-\nquire more complex methods for the excavation and support of the rock mass. This is further detailed in\n3\n\nSection 1.1.5.\nThe accelerator tunnel will pass through approximately 4.4 km of limestone rock. Whilst it will\ncertainly be possible to excavate the rock by either tunnel boring machine or traditional drill and blast\nmethods, this rock mass may contain large interconnected voids (karsts) with water and silt, potentially\nunder high pressure. Specific construction measures may be needed in this area, as presented in Sec-\ntion 1.1.1. Placement optimisation of the underground structures has ensured that the location of larger\nunderground structures, such as caverns and shafts, avoids areas where limestone formations are likely\nto be encountered. This will require careful review at the conclusion of the ongoing site investigation\ncampaign. The shafts will need to be excavated through varying depths of so-called moraine strata before\nthe molasse rock is reached. This stratum is a mix of clays, sands, gravels and boulders. It is known to\ncontain aquifers.\nCERN has over 40 years of experience in managing projects that involve the construction of tun-\nnels, shafts, and caverns in the molasse rock and, therefore, has the experience and knowledge to under-\ntake the FCC civil engineering. Some aspects, as listed below, will be challenging but nonetheless well\nwithin the capabilities of many Member States civil engineering contractors.\n\u2013 The average depth at which the underground structures will be constructed is about three times\ngreater than the average depth of the LHC tunnel. This will present higher ground stresses that\nwill need to be considered in the design of the underground structures and when selecting the\nconstruction methodologies to be used. Proven engineering solutions will be applied to effectively\nmitigate potential challenges, such as ground deformation, and ensure the smooth operation of the\ntunnel boring machine.\n\u2013 The tunnel will need to pass through a zone of so-called \u2018molasse charri\u00e9\u2019 a geological formation\nwith different characteristics compared to the molasse rock in which CERN\u2019s existing underground\nstructures were constructed. These factors will be carefully addressed in the design and construc-\ntion methodology to ensure a safe and efficient excavation process.\n\u2013 The tunnel will pass through several kilometres of limestone, which may contain water at high\npressure. Similar conditions were encountered during the construction of the LEP tunnel, pro-\nviding valuable insights into mitigation measures. Careful consideration will need to be given to\nthe tunnel design, selection of tunnelling methods and the provision of ground treatment ahead of\nthe tunnelling face in this zone of limestone rock. Modern engineering solutions, coupled with\nCERN\u2019s experience, ensure that potential challenges are well understood and can be managed\neffectively.\n\u2013 The tunnel will pass under Lac L\u00e9man. As far as possible, the tunnel horizon will be kept within\nthe molasse rock. If this is not possible then alternative tunnelling techniques for traversing water-\nbearing sands/gravel/silts will need to be used, such as earth pressure balance tunnel boring ma-\nchines or so-called slurry tunnel boring machines).\n\u2013 It is likely that during the construction of some shafts, water-bearing moraine strata will need to\nbe traversed before reaching the more favourable moraine rock. Again, this will require the use of\nspecialised construction methodologies such as diaphragm walls or ground freezing.\nAlthough some aspects of the civil engineering underground construction will be technically more\nchallenging than previous CERN construction projects, it is considered that the underground civil en-\ngineering structures can be designed and constructed using existing, proven, conventional techniques,\nincluding CERN\u2019s extensive experience in underground construction. This consideration is supported by\nthe technical discussions that CERN has held with tunnelling contractors.\nThe constraints arising from the large-scale geological environment on underground civil engi-\nneering, as described in the conceptual design report, are still largely valid. It is to be noted, however,\nthat the reduction in the circumference of the collider and accelerator tunnel has resulted in a higher\n4\n\nprobability that the tunnel can be predominantly located in the favourable molasse rock due to the gen-\neral displacement of the tunnel away from the limestone regions associated with the Jura, Vuache and\nMandallaz outcrops. Again, this should be confirmed with the completion of the ongoing site investiga-\ntions.\n1.1.1\nAccelerator tunnel\nThe majority of the 90.6 km circumference FCC tunnel alignment consists of a 5.5 m internal diameter\ntunnel, as illustrated in Fig. 1.2. There are eight sectors, each approximately 11.3 km in length. The\nmajority of each sector consists of an arc of a radius of 14.5 km.\nFig. 1.2: Accelerator tunnel cross-section.\nThe accelerator tunnel houses the beam and service infrastructure, as well as a transport corridor.\nThe current design of the tunnel assumes that where tunnel boring machines (TBMs) are used for exca-\nvation, a precast reinforced concrete segmental lining will be used to support the tunnel. In areas where\nTBMs will not be employed, primary support consisting of rock bolts and fibre-reinforced shotcrete will\nbe used with a secondary cast in-situ concrete lining. The tunnel floor is to be cast in-situ concrete\nand installed over void formers for the tunnel drainage and the fresh air duct. Access chambers for the\ndrainage network will be spaced every 100 metres along the tunnel. To ensure that the internal diameter\nis at least 5.5 m for the integration of technical infrastructure, the accelerator tunnel will be constructed\nwith a tolerance envelope of 100 mm.\n5\n\nThe installation of the precast segmental lining that supports the ground is carried out automat-\nically from within the TBM. CERN has discussed with a European TBM manufacturer the potential\nmachine requirements for the construction of FCC. They stated that either a double shield or single\nshield TBM could be utilised.\nFig. 1.3: Single shield TBM. Source: Herrenknecht\nA typical benefit of a double shield TBM over a single shield is the increased speed of construction,\nthis is because the machine can simultaneously excavate the ground and install the segmental tunnel\nlining. Conversely, a single-shield machine requires these two phases to occur sequentially. A double-\nshield machine is also better suited and more adaptable to variable geology and unstable ground.\nHowever, the increased complexity of the double shield machine TBM leads to greater capital\ncost, higher maintenance demand and increased risk of TBM breakdown, when compared to single shield\nTBM.\nFeedback from civil engineering contractors specialised in tunnelling indicates that in the rela-\ntively stable molasse rock of the FCC a single shield TBM could be a more cost-effective solution.\nFurthermore, the increased speed of construction offered by a double shield machine may not actually\nbe achieved, since the logistics of material delivery and spoil extraction at the shafts, and over the long\ntunnelling distances, would be more of a constraint to the TBM advance rate than the capability of the\nmachine itself.\nWhilst the majority of tunnel excavation will be within the molasse rock, which lends itself to\nTBM excavation, as detailed above, a specifically designed TBM may be used for the 4.4 km section\nof Mandallaz limestone likely to be encountered in the sector PG to PH. This TBM, which would be\ndesigned for soft and hard rock conditions, would also have the capability to probe ahead of the tunnel\nface and provide a real-time assessment of the ground conditions in front of the TBM. The machine\nwould have the capability to inject cement-based grout ahead of the excavation to reduce the risk of\nground collapse and water inflow. To take account of the potential difficulties that may be encountered\nin the limestone, the TBM advance rate has been reduced from an average of 16 m/day to 9 m/ day in the\nconstruction schedule.\nIf not excavated by a TBM, this section of limestone would need to be excavated by drill and blast.\nThis is a conventional tunnelling technique involving the use of explosives to excavate the rock face.\nDepending on the condition of the limestone in this area, additional ground treatment may be required\nahead of the tunnel face to prevent water ingress during excavation. The ongoing site investigations will\n6\n\ncharacterise the composition of the limestone along the FCC alignment and, therefore, provide greater\ncertainty of the tunnelling conditions.\nFor the current feasibility study, it has been assumed that a single-pass precast lining will be\nthe most efficient and effective ground support system, as this is the fastest and most cost-effective\nconstruction method. In the case that future site investigations reveal more challenging ground conditions\nthan those that have been assumed, then a review of the tunnel support system will need to be carried\nout. Where necessary, a more appropriate ground support system, consisting of a drained, reinforced\nconcrete in-situ lining, may be required.\nTable 1.2 shows the excavation and lining parameters assumed for the feasibility study.\nTable 1.2: Proposed TBM excavation and lining parameters.\nParameter\nProperties\nMinimum internal diameter (m)\n5.5\nCharacteristic concrete compressive strength for pre-cast\nconcrete, fck (MPa)\n50\nPre-cast concrete thickness (m)\n0.30\nReinforcement density for steel fibre reinforced pre-cast\nconcrete (kg/m3)\n35\nReinforcement density for steel bar reinforced pre-cast\nconcrete (kg/m3)\n80\nGasketed segments\nyes\nTotal radial construction tolerance (m)\n0.10\nExcavation diameter\n6.6\nThe current assumption for the start and finish sites for each of the TBMs is shown in Fig. 1.4.\nThe main advantage of this arrangement is that it allows an earlier completion of the technical sites\nbecause these do not have TBM installation or deinstallation activities associated with them. This is\na major benefit as it allows earlier installation of the infrastructure and accelerator components in the\nunderground areas. Further benefits of this approach are:\n\u2013 TBMs are large and heavy machines and as such cannot easily be manipulated in the confined\nspaces of an underground worksite. To install a TBM takes four to six months and requires a cavern\nlarge enough to allow the installation. At the four experiment sites, the two large caverns and the\nlong, widened sections of the main beam tunnel can be used for the installation and commissioning\nof the TBMs.\n\u2013 The presence of a shaft located directly above the axis of the main beam tunnel gives a significant\nadvantage for the installation of the TBM. It enables the TBM to be installed in relatively large\npieces, thereby reducing installation time.\n\u2013 Provision of two shafts, each capable of providing the necessary logistics and services to sup-\nport a TBM (transport of people, spoil removal, material, power, water etc.), provides a level of\nredundancy since, if one shaft is out of action, work can continue via the second shaft.\n\u2013 Two shafts provide better provision for the evacuation of people in case of an accident or an\nemergency when access to one shaft may not be possible.\n\u2013 Concentrating the underground civil engineering at the four experiment sites will allow the four\ntechnical sites to have a reduced impact on the local community and the local environment (less\ndust, noise, traffic etc.).\n7\n\nFig. 1.4: Proposed arrangement of TBM drives.\nCERN commissioned a study into the safety, ventilation, and logistics aspects of the FCC con-\nstruction to address concerns that the 5.5 m internal diameter tunnel and 11 km TBM drives would present\nsignificant safety and logistical risks, particularly with only a single means of access and egress. It was\ndemonstrated that using currently available technology, the tunnel could be constructed safely, and the\nassumed TBM advance rate could be achieved. Ventilation requirements were shown to be met over the\nfull length of the tunnel, with ducting and fan specifications calculated to supply adequate fresh air to\nthe excavation front. Finally, safety measures were outlined to ensure that construction activities would\nmeet the required standards both nationally and internationally. An example of the tunnel cross-section\nduring construction is shown in Fig. 1.5. An example of the safety refuge chambers specified in the study\nis shown in Fig. 1.6.\nTo accommodate the separation of the e+ and e\u2212beams of the FCC-ee machine near the detector\nlocations and the need to maintain space for the booster ring, the accelerator tunnel requires enlargement\non each side of the experiment caverns at PA, PD, PG, and PJ. There are a total of 8 tunnel enlargement\nareas, which extend for 1.1 km on either side of the experiment caverns. To minimise construction costs\nand optimise efficiency, the enlargements will be created in a stepped design, as shown in Fig. 1.7.\nThe widened tunnel sectors are split into 6 sections on either side of the experiment cavern, ranging\nfrom 18.6 m to 14.5 m in span and section lengths varying between 20 and 160 m. A seventh sector of\nwidening tapers from 14.5 m span to the regular 5.5 m diameter of the accelerator tunnel. This seventh\nsector commences from the end of the long straight section through into the arc section for a length of\n438.5 m. The beamstrahlung absorber will be located 500 m from the interaction point (IP) within section\n3 of the tunnel widening. A 20 m section of increased tunnel height may be required to provide space\nfor a crane around the beamstrahlung absorber. This is not currently incorporated in the feasibility study\nbaseline for civil engineering. If confirmed as necessary, this will be incorporated in the baseline during\nthe next design phase.\nThe construction of the tunnel-widening sections is proposed to be undertaken using conventional\nexcavation methods such as roadheader and/or hydraulic rock-breaker machines. A shotcrete final lining\nis proposed with the aim of reducing construction time, thereby enabling an earlier installation of the\n8\n\nFig. 1.5: Cross-section of the accelerator tunnel during construction. Credit: Amberg\nFig. 1.6: Example refuge chamber placed at the back of the TBM. Credit: mineARC\nTBMs, which will be carried out within the tunnel widening sections on either side of each experiment\ncavern.\n1.1.2\nBypass tunnels\nBypass tunnels are required at each of the four experiment areas to allow access for transport, personnel,\nand services directly from the service cavern to the accelerator tunnel, therefore bypassing the exper-\niment cavern and detector areas. These tunnels will have an internal diameter of 5.5 m, similar to the\ncross-section of the accelerator tunnel. The length of the bypass tunnels varies between 110 and 115 m,\ndepending on the experiment area. The 30 m radius bends allow transport vehicle movements as well\nas provide radiation protection between the accelerator tunnel and the service cavern. The bypass tun-\nnels connect the service cavern to the accelerator tunnel within the first section of the tunnel widening,\napproximately 74 m from the experiment cavern. The junction between the accelerator tunnel and by-\n9\n\nFig. 1.7: Plan view of the typical tunnel widening at an experiment cavern.\npass tunnel is at an angle of 45 degrees, for the purpose of civil engineering constructibility. However,\ntransport needs may require a shallower angle to be specified. In the next design phase, the details of the\njunctions between the two tunnels will be reassessed, and if required, a junction cavern or other more\neffective means of accommodating the connection will be implemented.\nThe bypass tunnels will be constructed using a roadheader machine and lined with in-situ concrete\nfor the final lining. The construction of these tunnels will be completed in parallel with the works for the\nconnection tunnels and tunnel-widening sections at each experiment point.\n1.1.3\nConnection tunnels\nThe connection tunnels between the service caverns and experiment caverns provide personnel access\nand materials/equipment transportation. These tunnels also house the service ducts, cables, and pipes\nlinking the service caverns to the detectors and accelerator tunnels. Figure 1.8 shows a typical layout\nof connection and survey galleries at an experiment point. Two 5.5 m diameter connection tunnels link\nFig. 1.8: Plan view of PA showing the layout of connection tunnels between the service cavern and\nexperiment cavern.\n10\n\neither end of the service cavern directly to the accelerator tunnel. These tunnels have an additional forked\nsection of tunnel, of 2.8 m span, to allow personnel access whilst the radiation shielding doors remain\nclosed across the full 5.5 m tunnel section. Two 3.3 m span evacuation tunnels provide a safe means\nof escape for personnel from the experiment cavern directly to the service cavern. These tunnels are\ndesigned with a chicane to provide radiation protection between the two caverns. At the lower level, a\n5.5 m diameter connection tunnel is required for service connections and personnel access to the floor\nof the experiment cavern. The transport tunnel is 10 m in span to accommodate the movement of large\nequipment, and the connection tunnel has a span of 5.5 m for personnel access and the conveyance of ser-\nvices between the two caverns. At each of the 4 experiment points, a 10 m internal diameter connection\ntunnel between the bottom of the access shaft and the experiment cavern is required to transport large\ndetector components to the areas inaccessible via the main shaft serving the experiment cavern.\n1.1.4\nShafts\nThere are thirteen shafts proposed for accessing the underground structures:\n\u2013 Four 12 m diameter shafts, one at each of the technical areas PB, PF, PH, and PL, for access and\nservice requirements.\n\u2013 Two 18 m diameter shafts, one at each of the experiment areas, PA, and PG, for access and instal-\nlation of the detector components in the experiment cavern.\n\u2013 Two 15 m diameter shafts, one at each of the experiment areas, PD, and PJ, for access and instal-\nlation of the detector components in the experiment cavern. Note that these smaller experiment\nshafts are dimensioned to accommodate the smaller detectors planned for PD and PJ.\n\u2013 Four 18 m diameter shafts, one at each of the service caverns at points PA, PD, PG, and PJ, for\naccess, service requirements and to facilitate the lowering of the largest accelerator components.\n\u2013 One 10 m diameter shaft on the CERN Pr\u00e9vessin site, to enable the construction of the transfer\ntunnel from the Injection Complex to the FCC. This shaft will only be used for construction, in\nparticular, to allow the assembly of the TBM to drive the 5 km transfer tunnel length.\nFig. 1.9: Cross-section through the 12 m diameter service shaft, as proposed at the four technical areas.\nThe service shafts at each of the eight points provide access to the service caverns. During the construc-\ntion phase, these will be used for the installation and commissioning of the infrastructure and accelerator\ncomponents. They will also be used during machine shutdowns for maintenance and upgrade of the\n11\n\naccelerator and supporting infrastructure. They will be equipped with two lifts and a stairwell located\nwithin a pressurised inner shaft, which provides a safe escape route in case of fire. The shaft also contains\na continuous vertical clear space for the crane to lower the equipment.\nAll four of the experiment caverns are served by either a 18 m or 15 m internal diameter shaft\ndirectly above the experiment cavern. These shafts primarily serve for the transportation of the detector\ncomponents, which will be lowered down the shafts from the Surface hall(SX) for installation in the\nunderground experiment caverns (UX). These shafts will also contain ventilation ducts and other services\nnecessary to support the operation of the detector within the UX caverns. As PA and PG are the larger of\nthe experiment areas, 18 m diameter shafts are required. Being the smaller experiment areas, PD and PJ\nonly require a 15 m experiment shaft at each location.\nThe construction shaft proposed for the TBM drives of the transfer tunnel may be used during\nthe infrastructure installation phase to transfer equipment and/or components from the surface into the\ntransfer tunnel.\nTable 1.3: Shaft depths at each site.\nSite\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nTransfer Tunnel\nMoraine Depth [m]\n54\n30\n25\n<5\n24\n20\n31\n40\n12\nMolasse Depth [m]\n147\n171\n156\n400\n202\n215\n222\n210\n17\nTotal Depth [m]\n201\n201\n181\n400\n226\n235\n253\n250\n29\nThe shafts have varying depths around the ring, ranging from 29 m to 400 m. Table 1.3 summarises\nthe depths of the shafts at each site, including the depths of the moraine and molasse geological layers.\nGenerally, the shafts are located directly above the corresponding cavern. However, at PF and PB, surface\nconstraints require the shaft to be offset from the service cavern. At PF, this is achieved by constructing\na 9 m internal diameter access tunnel 585 m in length, as shown in Fig. 1.10.\nAll the shafts will be excavated through the moraine strata. Historically, supporting methods\nsuch as diaphragm walls, secant piles, and ground freezing have all been used on CERN projects and,\ntherefore, will be appropriate for the construction of FCC shafts.\nThe shaft depths below the moraine strata will be located in molasse rock. Shafts in molasse\nhave historically been built most cost-effectively using conventional construction techniques (roadheader,\nhydraulic hammer) combined with shotcrete and rock bolts as primary support followed by a permanent\ncast in-situ reinforced concrete lining. Diaphragm wall construction consists of excavating a number of\nstraight sections of wall to form a quasi-circular shape. The sides of these excavations are supported\nwith a temporary bentonite slurry mix, which is replaced by reinforcement cages and concrete to form\nthe primary lining, inside which the shaft excavation can proceed. Figure 1.11 shows an example of the\ncross-section of a typical 12 m diameter service shaft in the moraine using the diaphragm wall technique.\nOnce stable rock (i.e., the molasse) is reached, the excavation is supported temporarily by rock\nreinforcement such as rock bolts and shotcrete, before installing a waterproof membrane and the perma-\nnent cast in-situ reinforced concrete lining. The slip-forming technique can be used for the permanent\nlining, where the concrete is poured into a continuously climbing formwork.\nThe staircases and lift shafts required within the service shafts for personnel and material access\nare constructed from prefabricated elements that are stacked on top of each other from the top of the\nshaft. These are placed as one of the final construction activities once all major civil engineering works\nare completed below ground and before the civil engineering structures are handed over to CERN.\nAs the shafts for FCC are deeper than any previously constructed at CERN, a specialist shaft-\nsinking consultant provided an assessment of possible excavation techniques suitable for these greater\ndepths. The study focused on the logistical considerations of the construction and the servicing of shafts\n12\n\nFig. 1.10: Plan view of the sub-surface arrangement at PF, showing the offset service shaft and access\ntunnel arrangement.\nto up to 400 m in depth (the deepest shaft at site PF). The assessment concluded that utilising current\ntechnologies and best working practices, the shafts as proposed are feasible to construct. They advised\nthat with all shafts being constructed in parallel, procurement of sufficient specialised labour and equip-\nment ahead of time would be key to ensuring that sufficient resources are available, thus minimising the\nrisk of a delay to the construction schedule. The study also highlighted that there would be potential\nfor equipment used during shaft sinking, also to be utilised during later cavern and tunnel excavation\nworks. This could offer benefits to both the cost and the construction schedule. Furthermore, CERN was\nadvised that advances in mechanisation and future shaft-sinking technologies could reduce construction\ndurations as well as project risks, in particular through the recent development of a vertical shaft-sinking\nmachine that does not require human intervention within the shaft itself.\n1.1.5\nCaverns\nLarge-span caverns are required at both experiments, PA and PG, to accommodate the FCC detectors\nand associated infrastructure. The proposed cavern dimensions are 66 m \u00d7 35 m \u00d7 35 m (L\u00d7W\u00d7H) and\nthe caverns will be constructed at a depth of up to 226 m in the molasse rock. Although these will be the\nlargest caverns ever constructed at CERN, they will not be significantly larger than the current ATLAS\ncavern of the LHC.\nThe construction sequence will consist of benched excavations using rock breaker and road-\nheader machines, with the primary support being provided by rock bolts, cable bolts and layers of\nsteel-reinforced shotcrete. During the widening of the crown area of the experiment cavern, additional\nlattice girders and layers of steel-reinforced shotcrete will be installed. The lattice girders for the vari-\nous excavation steps can be bolted together to ensure continuous rock support along the excavated area.\nThe secondary lining will be constructed from cast in-situ concrete to provide additional strength and\nprotection to the cavern walls. A waterproofing and drainage membrane will be installed between the\n13\n\nFig. 1.11: Cross-section of the 12 m diameter service shaft with diaphragm wall construction.\nFig. 1.12: Cross-section through the 3D model at PA, showing the service cavern (left) and experiment\ncavern (right).\nprimary and secondary linings to ensure that the cavern remains dry and that the structure is not subject\nto excessive water pressure arising from any groundwater that may be present.\nTwo smaller experiment caverns, 66 m \u00d7 25 m \u00d7 25 m (L\u00d7W\u00d7H), are required at PD and PJ.\nThese caverns will be constructed at up to 253 m depth using the same techniques for excavation and\nsupport as the experiment caverns situated at PA and PG.\nA service cavern at the same elevation as the accelerator tunnel with dimensions of 100 m \u00d7 25 m\n(L\u00d7W) is required adjacent to each of the four experiment caverns. Below the service shaft, the height\nof the service caverns is 22.4 m thereby providing direct access to the experiment cavern floor for large\nequipment and detector components. The remainder of the 100 m long service cavern has a height of\n15 m. Shorter service caverns of 60 m length are necessary at the remaining four technical points. The\nservice caverns will house infrastructure equipment such as electrical, cooling, ventilation and cryogen-\nics. Furthermore, the caverns will provide a safe refuge in the event of an emergency, with a dedicated\npressurised area at the bottom of the shaft. These caverns will be constructed in the same manner as\nthe experiment caverns. At the experiment sites, the spacing between the two caverns is approximately\n50 m, to mitigate electromagnetic effects from the detector on the nearby electrical components. This\nalso improves the overall structural efficiency by providing a sufficiently large rock pillar between the\n14\n\nexperiment and service caverns, thus minimising the structural support needed and reducing the risk and\ncomplexity of construction.\nThe service caverns will contain three floor levels, with steel structures providing the frame for\neach level. This greatly increases the usable space for technical infrastructure and services. Steel struc-\ntures will also be used to create the gallery levels around the detectors in the experiment caverns. These\nwill be similar to the galleries currently in place within the LHC experiment caverns, such as ATLAS\nand CMS.\nWhere tunnels of similar cross-section dimensions connect, a junction cavern is required. PF, PH\nand PL each require a junction cavern where the 7 m diameter connection tunnel from the service cavern\nintersects with the 5.5 m accelerator tunnel. Each cavern is 16 m long and at a span of 10 m.\nAn additional cavern for the FCC-ee machine beam absorber will be located at PB, and this will\naccommodate two beam absorbers, one for each of the two beam lines. Further details of this structure\nare provided in Section 1.1.8.\nSurvey galleries are required at each of the four experiment caverns to survey the beam alignment\non either side of the detectors. These consist of 1.5 m span tunnels of 60 m length, running parallel to the\naccelerator tunnel, with perpendicular connections made every 15 m into the tunnel widening section 1.\nThe possibility of incorporating these into the widened tunnel sections to reduce complexity and cost of\nconstruction will be studied in the next design phase.\n1.1.6\nUnderground structures for Radio Frequency Infrastructure\nFig. 1.13: 3D model view of the klystron gallery arrangement at PH.\nThe klystron galleries are an essential part of the FCC-ee civil engineering, as they will house the\nklystrons and other components of the Radio Frequency (RF) system. To accommodate the necessary\ninfrastructure, two separate galleries will be constructed, one at PH and the other at PL. The klystron\ngallery at PH (Fig. 1.13) will be 2012 m long for the collider RF system, while the gallery at PL will be\n1446 m long for the booster RF system. To allow access to the klystron galleries during the operation of\nthe FCC-ee machine, sufficient radiation shielding needs to be provided. To achieve this, 10 m of rock\nwill be maintained between the RF galleries and the accelerator tunnel. The internal dimensions of the\ngalleries are 10 m in span and 5.5 m high to accommodate the transport and placement of the equipment\nwithin the galleries, as well as allowing access for maintenance and repair during the operation phase.\n15\n\nThe galleries are sized with a 50 m extension in length at either end to incorporate the space for\nservice equipment. This is proposed instead of constructing the large alcoves along the accelerator tunnel,\nthereby enabling a more efficient use of tunnel excavation and space.\nThe galleries are connected directly to the accelerator tunnel via 1 m internal diameter wave-guide\nducts, spaced every few metres along the gallery (see Fig. 1.14. There will be 428 individual wave-guide\nducts at PH and 312 at PL.\nThe safety concept for FCC requires that for emergency egress, stairwell shafts are spaced at\nintervals of 341 m along the gallery to connect the galleries to the accelerator tunnel.\nFor access to the klystron galleries, a 7 m internal diameter connection tunnel links the upper level\nof the service cavern and the klystron gallery. This connection tunnel has a length of 62 m. The size of the\nconnection tunnel is designed to accommodate personnel access and the transport of the RF equipment\ninto the gallery.\nThe klystron galleries will be excavated using the same road header type machines that will be used\nfor the excavation of the caverns and connection tunnels at points PH and PL. Roadheader excavation\nis efficient and accurate, allowing precise excavation of the galleries. The klystron gallery lining will\nFig. 1.14: Cross-section through the klystron gallery and accelerator tunnel, including wave-guide duct\nbetween.\nconsist of a shotcrete primary lining and a cast in-situ concrete secondary lining. It may be feasible to\nuse shotcrete for the final lining of the gallery, as this would potentially offer faster construction and\nlower cost. This option will be studied during the next phase. The floor of the gallery will also be made\nof cast in-situ concrete and will include a drainage channel and the entry of the waveguide ducts up\nthrough the floor slab. The entry of the wave-guide ducts into the gallery will require the use of a chicane\nto provide radiation protection. This will likely be constructed with a precast concrete unit placed after\nthe final installation of the cryogenic line (QRL) infrastructure through the duct.\nThe wave-guide ducts, which will contain the wave-guides linking the klystrons to the RF cavities\nin the accelerator tunnel, will be excavated by raise boring. This process involves first drilling a pilot\n16\n\nhole and then attaching a reamer head at the bottom, which is pulled up, excavating the duct from below\nin a vertical direction. This method of excavation is efficient and minimises disruption to the surrounding\nrock. A steel or concrete lining will be grouted into the rock to provide a suitable finished surface and\nfinal lining.\n1.1.7\nAlcoves\nAt 1.6 km centres around the circumference of the machine, equipment alcoves, as illustrated in Fig. 1.15,\nare required to accommodate electrical equipment, services and transport needs. The majority of these\nalcoves are considered \u2018regular\u2019, measuring 40 m in length, 10.6 m in width, and 4.6 m in height. Posi-\ntioned on the inside of the ring, the alcoves are arranged perpendicular to the accelerator tunnel.\nFig. 1.15: Layout of alcoves around the FCC ring.\nIn addition to the regular alcoves, twelve \u2018large\u2019alcoves are needed on either side of each of the\nFCC access points to provide extra space for electrical equipment. These larger alcoves are 29 m in\nlength, 18 m in width and 8.3 m in height. These large alcoves will be located at the end of the long\nstraight sections on either side of the caverns. Two large alcoves are required at PA, PB, PD, PF, PG,\nand PJ, but not at PH or PL, because the additional size of the klystron galleries provides the necessary\nvolume for the equipment. An example of a large alcove is shown in Fig. 1.16. In total, the project\nrequires 40 regular alcoves and 12 large alcoves.\nAn access area to each alcove is provided to accommodate the radiation protection chicane walls.\nThis section is 6 m long and has a 10.6 m span at the entrance to both large and regular alcove types.\nA transport-passing bay is required at the entrance to each alcove. This will facilitate the passing\nof transport vehicles travelling in opposite directions through the tunnel. The passing bay also provides\nspace for the parking of transport vehicles during installation and shutdowns, with additional space for\nservicing/repairing the vehicles if necessary. The majority of the passing bays are accommodated in a\n17\n\nFig. 1.16: Model view of a large alcove and transport passing bay.\ncavern along the accelerator tunnel alignment and measure 16 m in length and 11 m in width. Additional\nlarger passing bays are required at the mid-section of each accelerator tunnel arc. There will, therefore,\nbe a total of 8 larger passing bay caverns, measuring 30 m by 11 m. These facilitate the passing of the\nmagnet delivery vehicles during the installation phase of the FCC-ee machine. An example of the large\npassing bay is shown in Fig. 1.17.\nFig. 1.17: Example of a regular alcove and large passing bay located at the centre of each arc sector.\nUnlike the caverns and tunnels in proximity to the FCC points, which can be at least partially\nexcavated in parallel with the TBM drives, excavation of the alcoves and passing bays will need to be\ncompleted after the TBM drive is complete. This is because the full tunnel section is required to support\nthe TBM (ventilation, conveyor for spoil removal, transport corridor for concrete segmented linings,\ncorridor for personnel etc.). It will, therefore, be necessary to break out the concrete tunnel lining and\n18\n\nexcavate the passing bay cavern and alcoves using roadheader excavation. The inner lining works for\nthe alcoves will then be carried out ahead of the relining of the accelerator tunnels. This will have to\nbe coordinated with the installation of the tunnel floor. The overall construction sequence and structural\ndesign will be similar to the caverns, as detailed in Section 1.1.5.\nThe complexity of the alcove construction and the associated logistical challenges have a major\nimpact on the construction schedule, since each alcove is potentially on the critical path for civil engi-\nneering. CERN has commissioned an additional study to investigate the optimal method of constructing\nthe alcoves in order to minimise the impact on the overall construction schedule. As a result, the current\nassumption in the schedule remains that alcoves can be constructed in parallel to one another, maintaining\nsufficient access, safety and logistical standards. By adopting an overlapping sequence of construction\nactivities, all alcoves of each sector can be constructed within a 12-month period, thereby achieving the\ntargeted handover date of each sector for the subsequent infrastructure and accelerator installation.\n1.1.8\nBeam absorber cavern\nThe absorbers for the FCC-ee beams will be located at PB. The beam absorber cavern layout includes a\n708 m long cavern with a span of 13.6 m, to house both the e+ and e\u2212absorber infrastructure. The size\nof the cavern has been dictated by the beam extraction length and angle, which requires a separation from\nthe accelerator line of at least 5.5 m and a septum/kicker angle of 10 mrad. The two beam extraction lines\nare arranged to cross at the centre of the cavern, adjacent to the centre of the PB long straight section.\nThis ensures that the beam absorber cavern volume is optimised.\nTo accommodate the separation of the two FCC-ee beams on the approach to PB, a series of tunnel\nwidening sections is required either side of the cavern. Three sections of tunnel widening, of lengths from\n83 to 330 m will be constructed either side of the cavern to increase the span of the accelerator tunnel\nfrom 5.5 to 7.8 m.\nThe absorber cavern will be excavated in the same manner as other caverns, using roadheader\nand/or rock breaker machines to excavate from the roof level down using a series of \u2018benches\u2019. Due to\nthe constraints at the surface, the service shaft and cavern will need to be offset from the centre point\nof the long straight section (LSS). The offset service shaft will, therefore, be positioned 350 m from the\ncentre of the LSS and connect to the beam absorber cavern via a connection tunnel of 97 m length.\nThe absorber cavern will be constructed as mentioned in Section 1.1.5. There will be a shotcrete\nand rock bolt primary lining with an in-situ concrete secondary lining. However, the option to create\nthe final lining from shotcrete will be considered in future design development to potentially reduce\ncosts and reduce the construction time. It is yet to be confirmed whether a shielding wall/structure is\nrequired within the cavern to shield the accelerator from the beam absorber apparatus; however, this\nwould be constructed with precast concrete blocks well after the civil engineering has been completed.\nA schematic view of PB including the beam absorber cavern is shown in Fig. 1.18.\n1.1.9\nExcavated material\nTo construct the subsurface structures, approximately 6.3 million m3(in-situ volume) of rock will be\nexcavated. This material will be extracted via the eight FCC access points. The predominant rock\ntype will be molasse, accounting for 96% of the total material. Moraine rock accounts for 1.5% of the\nexcavated material, and limestone makes up the remaining 2.5%.\nFigure 1.4 in Section 1.1.1 shows the baseline arrangement for the TBM drives. As mentioned, the\naccelerator tunnel sectors will be excavated using TBM. Shafts will be excavated by conventional mined\nexcavation or vertical shaft-sinking machines. The use of diaphragm walls will be necessary to support\nthe excavation of shafts through the initial moraine layer. All other excavations for subsurface struc-\ntures will be constructed by hydraulic hammer (rock breaker) and roadheader machines. The physical\ncharacteristics of the excavated material will differ according to the excavation method utilised.\n19\n\nFig. 1.18: Sub-surface structural layout at PB, service cavern (left) and beam absorber cavern (right).\nTable 1.4 provides a breakdown of the excavated material quantities extracted from each of the\neight sites and the transfer line between Pr\u00e9vessin and the FCC tunnel. The volumes are expressed as the\nin-situ volume i.e., the volume prior to excavation, the bulked volume i.e., the volume after excavation\nand the compacted volume i.e., the volume after the material has been re-compacted for example in a\nspoil deposit zone.\nTable 1.4: Excavation volumes for each FCC sector.\nIn-situ Vol,\nBulk Vol.,\nCompacted Vol.,\n% of Total\n10 3 m3\n103 m3\n103 m3\nPA\n1378\n2205\n1791\n22%\nPB\n148\n237\n192\n2%\nPD\n1274\n2038\n1656\n20%\nPF\n165\n264\n215\n3%\nPG\n1365\n2184\n1775\n22%\nPH\n312\n499\n405\n5%\nPJ\n1289\n2062\n1675\n20%\nPL\n241\n386\n313\n4%\nTransfer Tunnel\n122\n195\n159\n2%\nTwo TBM drives will commence at PA, one driven towards PB and the other driven towards PL.\nThe resulting total material extracted from PA will be almost 1.4 million m3, of which, 62 721 m3 is\nexpected to be moraine.\nNo TBM drives are planned from PB, the volume of excavated material, therefore, arises from the\nsubsurface structures at PB, including the beam absorber cavern. Of the total quantity of, 147 852 m3,\n10 473 m3 is expected to be moraine and the remainder is molasse.\nTwo TBM drives will commence at PD, one driven towards PB and the other towards PF. The\nresulting quantity of material to be extracted from PD is 1.3 million m3 of which, 24 925 m3 is expected\nto be moraine.\nNo TBM drives are planned from PF. As with PB, the excavated material at PF only arises from\nthe subsurface structures directly located at PF and not the accelerator tunnels either side. Almost all the\n20\n\nexcavated material at PF will be molasse as there are little or no quaternary deposits.\nTwo TBMs will be driven from PG, one driving towards PF and the other towards PH. The total\nquantity of material excavated from PG is almost 1.4 million m3. Moraine makes up 30 829 m3 of the\ntotal excavated material at PG. However, due to the 4.4 km long sector of limestone along the accelerator\ntunnel between PG and PH, 141 175 m3 of the total material will be limestone rock. The remaining\n1.2 million m3 of excavated material will be molasse.\nNo TBM drives are planned from PH, therefore all the excavated material comes directly from\nsubsurface structures at PH, including the klystron gallery and associated structures. 7482 m3 of the total\nexcavated material at PH is expected to be moraine, and the remainder is molasse.\nTwo TBMs will be driven from PJ, one driven towards PH and the other towards PL. Therefore,\nthe quantity of material extracted from PD is around 1.3 million m3 of which, 29 910 m3 is expected to\nbe moraine.\nNo TBM drives are planned from PL, the volume of excavated material is therefore attributed to\nthe subsurface structures at PL, including the klystron gallery and associated structures. Moraine rock is\nexpected to make up 13 468 m3 of the total excavated material at PL.\nThe Pr\u00e9vessin to SPS and SPS to FCC injection tunnels account for 122 329 m3 of excavated ma-\nterial, the majority of this material will be extracted from the Pr\u00e9vessin site, by means of the proposed\nconstruction shaft. A small proportion of the excavated material will be moraine, from the initial ex-\ncavation of the shaft, but the majority of the shaft and transfer tunnel excavation will be in molasse\nrock.\n1.1.10\nTunnelling in the molasse rock\nThe large-scale geological environment within which the FCC underground infrastructure will be ex-\ncavated is shown in Fig. 1.19, with most of the tunnel located within the Lower Freshwater Molasse\n(USM) and Lower Marine Molasse (UMM). The FCC will be excavated at depths of up to 560 m, with a\ntotal combined length of all excavations exceeding 100 km. Whilst the experience gained by CERN over\nthe previous 50 years for the construction of the LEP, LHC and Hi-Luminosity LHC has given valuable\ninsight into the likely characteristics and behaviour of the molasse rock, other projects excavated within\nthe molasse rock have also been the subject of a desktop study in order to improve the understanding of\nthe environment in which the FCC civil engineering will be constructed.\nMost of the projects reviewed were transport tunnels (road and rail) from a few hundred metres\nto a few kilometres in length at shallow depths. Tunnels were excavated by means of conventional\nexcavation, cut and cover, and TBM. One project in particular, the Moutier tunnel, was excavated by a\nsingle shield TBM in the Alsace tertiary molasse (a mix of marl, sandstone and limestone). Due to an\nunforeseen geological environment, the TBM became stuck 190 metres into the tunnel drive. As a result,\nthe remainder of the tunnel was excavated using conventional methods. This project highlights the need\nfor sufficient geotechnical investigations and appropriate analysis to be completed before construction\nbegins. At the greater depth of FCC, the molasse is likely to be more consolidated and unlikely to have\nbeen altered due to weathering. However, appropriate geotechnical investigations and numerical analysis\nwill be required to better predict the likely behaviour of rock and its influence on the performance of the\ntunnel boring machine.\nGenerally, the review confirms that excavations in molasse rock have been extensively conducted\nin Switzerland using both TBM and conventional methods. However, the FCC will require a compre-\nhensive geotechnical investigation to assess the characteristics of molasse as well as the in-situ stress\nregime. The investigation will address potential risks, including those arising from changes in pore water\npressure, rock squeezing, and geological faults.\nA tunnelling project has been identified in the UK with characteristics similar to those of the FCC.\nIt is currently under construction as part of a new Halite mine development. A single TBM excavates a\n21\n\nFig. 1.19: Geographical map of Switzerland. Credit: Philippos Garefalakis, F. S. (2019). Tectonic\nprocesses, variations in sediment flux, and eustatic sea level recorded by the 20 Myr old Burdigalian\ntransgression in the Swiss Molasse basin.\n37 km long tunnel with cross-sectional dimensions that are very similar to those of the FCC. Furthermore,\nthe tunnel is being excavated at comparable depths and within sedimentary geology that is not dissimilar\nto that expected for the FCC. An average tunnelling excavation rate of 20 m/day have been achieved.\nCERN will assess this project for lessons learned in more detail during the next phase of the FCC.\nIn conclusion, it is considered that underground civil engineering for the FCC is feasible and\nwithin the current experience and capabilities of many of the major designers and contractors currently\nactive within the CERN member states. Additional site investigations will be required to finalise the\nprecise depth and inclination of the FCC tunnel and to determine the geotechnical properties of the rock\nmass, which are necessary for CERN to move forward to the detailed design and construction phases.\n1.2\nSurface structures\nSince the completion of the conceptual design, there has been a rationalisation of the surface sites asso-\nciated with the FCC-ee civil engineering, with the number of surface sites reduced from twelve to eight.\n22\n\nThe eight surface sites will comprise four areas suitable for siting experiments and four assigned as tech-\nnical areas. The eight sites are spread evenly around the circumference of FCC-ee collider ring. The\nfour experiment areas are symmetrically distributed such that each site is diametrically opposite another\nexperiment site, as illustrated in Fig. 1.1. The experiment sites are at sites PA, PD, PG and PJ with the\ntechnical sites at the remaining sites PB, PF, PH and PL. The location of the four experiment surface\nsites are interdependent since the interaction points for each of the four sites define the location of the\nexperiment and service shafts at each site as illustrated in Fig. 1.20\nFig. 1.20: Options for experiment and service shaft locations relative to the interaction point.\nThe experiment access shafts can only be in one of two locations with respect to the interaction\npoint, and the machine access shafts should ideally be placed directly above the service cavern, which\nitself needs to be located approximately 50 m from the experiment cavern for structural stability of the\ntwo caverns and for electromagnetic shielding. Since each of the four interaction points associated\nwith the experiment areas is located precisely with respect to each other, the locations of the shafts\nat each experiment point are also fixed with respect to the shafts at the other experiment points. This\ninterdependency across the four experiment sites influences the layouts of the surface sites, since the two\nshafts are associated with specific building configurations.\nThe selection of surface site locations for the experiment areas requires careful coordination, as\neach site is interconnected with the location of the other three. For the technical sites, while proximity to\nthe centre of the associated long straight section (LSS) is a key factor, some flexibility exists. The single\nmachine access shaft can be linked to the accelerator tunnel via an access gallery, which, if required, can\nextend several hundred metres in length.\nFor a comprehensive discussion on environmental considerations, including landscape integration,\nreaders are referred to the relevant sections in Chapters 2 and 3 in this Volume.\nThe engineering designs of the surface site constructions that are eventually part of the project\nauthorisation files need respond to the requirements of the equipment that will eventually be housed at\neach site. Noisy equipment will be adequately noise insulated and placed in constructions that permit\ncontaining the residual noise within the applicable regulatory frameworks in place at the time. Examples\nof structures that may require such specific measures include:\n\u2013 Cryogenic plants comprising compressors.\n\u2013 Cooling and ventilation equipment with pumps, motors and fans.\n\u2013 Electrical equipment such as transformers.\nThe choice of construction materials and techniques for surface site buildings is guided by multiple\nfactors, including durability, safety, cost and environmental considerations such as landscape integration\nand regulatory constraints such as urbanism prescriptions. Newly emerging materials and technologies,\nas well as continuous monitoring of the environmental and regulatory prescriptions, including applicable\nenergy efficiency standards, will be considered during the subsequent design phase. In line with CERN\u2019s\n23\n\ngovernance framework, the territorial principle applies, i.e., the national laws and guidelines apply for\ninfrastructure on the surface sites in the Host States.\nAt this stage, no architectural strategies have been adopted. This will be done in the next design\nphase. The development of the architectural solutions will include a robust consultative process with the\nHost States, regional stakeholders and local communities. A more detailed discussion can be found in\nsection 2\nFor technical feasibility and costing purposes. the U.S. Fermi National Accelerator Laboratory has\nanalysed the technical needs of two of the eight surface sites in the framework of the international FCC\ncollaboration. The study used an experiment site (PA) and a technical site (PB) as generic examples. The\nwork resulted in the production of detailed drawings of the buildings at the sites. These designs were\nused as the basis for an initial cost estimate for the surface works. It should be stressed that these designs\nrepresent preliminary input for technical and financial feasibility and construction planning purposes\nonly and are not approved designs.\nThe subsections below present simplified versions of these concepts that permit further develop-\nment of site configurations and cost estimates.\nThe chapters 2 and Territorial implementation provide a further detailed examination of the con-\ntextual considerations, planning strategies, and logistical challenges associated with the surface sites,\noffering further insight into how these elements are being harmonized within the broader project vision.\n1.2.1\nSurface site - PA\nThe surface site PA will be the location for one of the four experiment areas. The site is located close\nto the existing CERN LHC surface site P8 which allows the re-purposing of some of CERN\u2019s existing\nLHC facilities and infrastructure to support the FCC-hh activities at site PA.\nThe buildings and other necessary civil engineering surface infrastructure for all surface sites have\nbeen identified and included within the civil engineering product breakdown (PBS) structure, which is\nshown for PA only in Table 1.5.\nA significant feature of this and all experiment area surface sites is the large assembly hall that\nwill be used for the sub-assembly and preparation prior to the transfer of the detector components to the\nunderground experiment cavern. It is to be noted that any future assembly hall for an FCC-hh detector\nmay need to be larger than that for an FCC-ee detector, and therefore, a footprint is reserved on the\nsite for such a future expansion/reconfiguration of the assembly hall. The final details of a conceptual\ndesign for this building at the FCC-hh phase will be determined in parallel with a future fabrication and\nassembly strategy for the associated detector.\nThe site location has some specific constraints, including:\n\u2013 The presence of a gas pipeline running adjacent to but outside the site. The layout of the buildings\nwithin the site takes into account the presence of this pipeline and, in the future development of\nthe design, how to cross the pipeline to allow services to connect to the existing LHC site P8 prior\nto the FCC-hh construction.\n\u2013 Likely urban development in the close vicinity of the proposed site, with direct views across\nGeneva to Mont Blanc. These views have been taken into account and building heights have\nbeen kept as low as possible, and the overall elevation of the platform has been minimised. To this\nend, the requirements brief included a target roof elevation no greater than that of the buildings\nlocated adjacent to the proposed site.\n\u2013 The presence of a protected environmental compensation area immediately to the north of the site,\nan existing development to the south of the site and a major arterial road to the west of the site\nrestricts the available area and layout of buildings within the surface site.\n24\n\nTable 1.5: PBS for PA surface structures.\nPBS Level\nPBS Description\n0\n1\n2\n3\n4\n2\nCivil Engineering\n2\n2\nSurface Structures\n2\n2\n1\nSite PA\n2\n2\n1\n1\nRoads, parking spaces, footpaths, fences, gates, landscaping, drainage\n2\n2\n1\n2\nTechnical galleries\n2\n2\n1\n3\nFire fighting equipment and medical station\n2\n2\n1\n4\nControl building\n2\n2\n1\n5\nAssembly hall\n2\n2\n1\n6\nMagnet storage\n2\n2\n1\n7\nShaft head building\n2\n2\n1\n8\nTunnel ventilation\n2\n2\n1\n9\nChilled water production facility\n2\n2\n1\n10\nExperiment cavern ventilation\n2\n2\n1\n11\nService cavern ventilation\n2\n2\n1\n12\nCooling plant and waste heat recovery\n2\n2\n1\n13\nSF annex\n2\n2\n1\n14\nWarm compressor\n2\n2\n1\n15\nHelium gas tanks foundations\n2\n2\n1\n16\nLiquid Nitrogen storage tank foundations\n2\n2\n1\n17\nPower converters building\n2\n2\n1\n18\nElectrical equipment building\n2\n2\n1\n19\nElectrical substation\n2\n2\n1\n20\nWaste material storage building\nThe functional requirements of the surface buildings at PA are similar to those built for previous CERN\nexperiment areas. Some key requirements are:\n\u2013 A large assembly hall for the pre-assembly of the detector. This building will house at least one\ncrane capable of lowering the detector subcomponents from the surface down to the underground\ncavern located about 200 m below. The precise crane dimensions and weight will need to be\nconsidered during the detailed design phase.\n\u2013 A shaft head building to accommodate the lifts, cranes, and staircases needed for personnel access\nto the underground areas and for the movement of material, equipment, and services between the\nsurface and underground areas. This building also houses an unloading bay for trucks transporting\nmaterial and equipment for installation in the underground areas.\n\u2013 Buildings to house the equipment necessary to ventilate the underground areas. The equipment\nfor ventilating the experiment cavern is housed separately from that for ventilating the rest of the\nunderground areas, since these two systems enter and exit the underground areas via different\nshafts. This equipment requires effective noise insulation, therefore these buildings will either be\nmade of reinforced concrete or have specific noise reduction measures incorporated or attached to\nthe building structure.\n\u2013 Buildings to accommodate the compressors and other equipment necessary for the cryogenic sys-\ntems that will be used by the detector. Similar noise abatement measures to those used for the\nventilation buildings will be necessary.\n25\n\nFig. 1.21: Preliminary simplified surface requirements for PA site.\nFig. 1.22: Preliminary cross-sectional diagram of PA site.\n\u2013 Cooling plant buildings will include the cooling towers and associated pump houses, basins etc.\nAlthough traditionally constructed in reinforced concrete, the use of prefabricated fibreglass rein-\nforced polyester (FRP) may be considered, in which case the civil engineering component would\nbe reduced to the provision of the cooling basin and appropriate supporting foundations, with the\ntowers themselves delivered as part of cooling, mechanical, and electrical infrastructure. In this\ncase, additional noise abatement measures may be needed around these pre-fabricated cooling\ntowers.\n\u2013 Control building to house offices and control room for the operation of the detector. This building\nwould also house areas for receiving visitors, noting that as PA is the closest FCC experiment area\nto the CERN main campus, it is likely to be an important focal point for CERN visitors.\n26\n\n\u2013 Buildings and support structures for transformers, switches, pylons etc. will be required for the\nelectrical infrastructure.\n\u2013 Other smaller buildings for various purposes as listed in the PBS given in Table 1.5.\nBased on initial conceptual layouts developed by the Fermi National Accelerator Laboratory and\nevolving requirements for the PA surface site, the conceptual designs have been further refined to de-\nvelop site layout scenarios, elevations, and earthwork estimates suitable for cost and schedule planning.\nIt should be noted that these representations merely serve early-stage feasibility inputs for planning\npurposes and have not been reviewed, validated and approved. Fig.1.21 presents a simplified view of\nthe proposed civil engineering buildings and associated works, while Fig.1.22 illustrates a streamlined\ncross-section of the site.\nOne aspect in which PA differs from the other three experiment sites, PD, PG and PJ, is the\npresence of an existing LHC surface site (P8) in the immediate vicinity. This presents an opportunity to\nreduce the land required for FCC-hh by re-purposing the existing LHC P8 site after the LHC finishes its\nphysics programme. A technical gallery from the existing site to PA would need to be constructed prior\nto FCC-hh to connect the services of the two sites together.\n1.2.2\nSurface site PB\nSite PB is a technical site. At this site, there will be no experiment area, and therefore, civil engineering\nis limited to the provision of buildings necessary to support the FCC-ee machine and the associated beam\nabsorber, which will be sited in the underground areas of PB. The site also reserves the necessary space\nfor the civil engineering required to accommodate a future hh machine, although these buildings will\nnot be constructed during the FCC-ee phase. The space reserved will be used temporarily during the\nconstruction phase to house the civil engineering contractors plant, equipment, material etc. This surface\nsite is the only one planned to be located on Swiss territory. The collaboration with the Fermi National\nAccelerator Laboratory also studied the need for a technical site, taking PB as an example. Building on\nthe initial work, CERN has developed further layout scenarios for cost and planning purposes.\nThe product breakdown structure (PBS) for the buildings and associated civil engineering works\nto be constructed at site PB is given in Table 1.6.\nSite PB is one of the smaller technical sites. Nonetheless, its location close to a protected water-\ncourse and within sight of nearby residential and agricultural properties will require rigorous integration\nstudies to be carried out. The smooth integration in the existing landscape will be further studied during\na subsequent project preparatory phase.\nAt FCC-ee phase, the principal surface infrastructure at site PB consists of:\n\u2013 A shaft head building to accommodate the lifts, cranes, and staircases needed for personnel access\nto the underground areas and for the movement of material, equipment, and services between the\nsurface and underground areas. This building also houses an unloading bay for trucks bringing\nmaterial and equipment for transportation via the shaft to the underground areas. This building\nmust be located directly over the associated shaft. The position of this building and the associated\nshaft could be adjusted within the site boundary to accommodate any changes or additions to the\nsurface requirements and constraints. This building would typically be constructed as a steel-\nframed building on reinforced concrete foundations and a reinforced concrete slab to sustain the\nload imposed by the vehicles entering the building for unloading. The building would include a\nsecure access area to ensure appropriate access control to the underground areas.\n\u2013 A building will be constructed to house the equipment necessary for ventilating the underground\nareas, including the shaft, access gallery, accelerator tunnel, and beam absorber cavern. As this\nequipment includes motorised components that may generate noise, the building design will incor-\nporate appropriate noise-reduction measures to ensure that noise levels at the site boundary remain\n27\n\nTable 1.6: PBS structure for surface site PB.\nPBS Level\nPBS Title\n0\n1\n2\n3\n4\n5\n5\n3\nPB Construction, testing, commissioning\n5\n3\n1\nSurface works\n5\n3\n1\n1\nRoads, footpaths, parking, fences, gates\n5\n3\n1\n2\nTechnical galleries\n5\n3\n1\n3\nAccess control building\n5\n3\n1\n4\nFire fighting equipment and medical station\n5\n3\n1\n5\nShaft head building\n5\n3\n1\n6\nVentilation building\n5\n3\n1\n7\nChilled water production building\n5\n3\n1\n8\nCold box and control Building\n5\n3\n1\n9\nCooling plant Building\n5\n3\n1\n10\nSF Annex (demineralised water)\n5\n3\n1\n11\nPower converters building\n5\n3\n1\n12\nElectrical building\n5\n3\n1\n13\nElectrical substation (foundations)\n5\n3\n1\n14\nWaste material storage\nFig. 1.23: Preliminary simplified area requirements for PB surface site.\nwithin the required limits. The choice of construction materials and noise mitigation solutions will\nbe determined based on technical and environmental considerations.\n\u2013 Cooling plant buildings, including the cooling towers and associated pump houses, basins and the\ndemineralised water plant building.\n28\n\nFig. 1.24: Preliminary simplified cross-section of PB surface site.\n\u2013 Various buildings and structures to house electrical equipment, including buildings for power con-\nverters and an emergency power system.\n\u2013 An access control building to house personnel undertaking security and safety operations at the\nsite.\nThe location of site PB in flat, open countryside requires careful consideration of its integration\ninto the surrounding landscape. To ensure minimal environmental impact, particular attention will be\ngiven to architectural and noise mitigation measures, both during the construction phase of FCC-ee and\nits subsequent operation.\nAs with site PA, the FCC-ee layout for site PB has taken into account the needs of a future FCC-hh\ncollider, and space has been reserved for the necessary civil engineering. The site boundary fence at the\nFCC-ee phase will already encompass these future needs.\nFigure 1.23 shows a simplified view of the PB surface site. The specific buildings required for\nFCC-ee are illustrated, along with the necessary space reservations for future FCC-hh civil engineering.\nA simplified cross-section is shown in Fig. 1.24.\n1.2.3\nSurface site PD\nSite PD has an identical function to site PA, namely, to house an experiment and provide support to the\naccelerator. As such, the requirements for civil engineering are almost identical, although the specificities\nof the local terrain and land plots require a different approach to the layout of the site.\nThe layout of the PD site has a number of constraints that need to be addressed. The main con-\nstraint is the planned future extension of the public road network in these areas, which reduces the\npotential land space for FCC at PD and requires a site access scenario that is compatible with the future\nlayout. After several iterations, a site layout that meets CERN requirements and is compatible with the\nroad development project has been developed. The proposed PD site is located on sloping agricultural\nland. The elevation change from one end of the site to another is about 20 m. This will require earthworks\nto be carried out to create a single flat platform on which to site the surface structures.\nOther specific features of the site which will need to be addressed after the feasibility study in-\nclude:\n\u2013 The scheduling compatibility of the FCC-ee civil engineering works with the planned road exten-\nsion project\n\u2013 The proximity of a medical facility to the site will be taken into account in the site\u2019s design.\nMeasures such as tree planting and landscaped features may be incorporated to ensure a well-\nintegrated and visually harmonious environment.\n29\n\nFig. 1.25: Preliminary simplified area requirements for PD surface site.\nFig. 1.26: Preliminary simplified cross-section of PD surface site.\n\u2013 The need to pass under bridges local to the site may result in a limitation on the height of oversized\ncomponents that can be transported to the site.\nA simplified view and section of the civil engineering structures at PD are given in Fig. 1.25 and\nFig. 1.26.\n30\n\n1.2.4\nSurface site PF\nPF is a technical access point with surface civil engineering structures similar in function to PB. In order\nto avoid siting surface buildings within an existing village, the PF surface site is offset by about 600 m\nfrom the axis of the accelerator tunnel.\nFig. 1.27: Preliminary simplified area requirements for PF surface site.\nFig. 1.28: Preliminary simplified cross-section of PF surface site.\nThe site is adjacent to a major road, minimising the need for new external roads to access the site.\nThe necessary platform needed for the surface buildings will be of sufficient size to accommodate the\n31\n\nfuture FCC-hh buildings. A simplified view and cross-section of the PF site are given in Fig. 1.27 and\nFig. 1.28.\nThe main constraints at PF relate to the presence of a so-called \u2018humid zone\u2019in the vicinity of\nthe proposed site. This will require specific attention during the detailed design of the civil engineering\nstructures to ensure that water run-off during the construction and operational phases does not impact\nthis zone.\nIn summary, the construction of the surface civil engineering required for FCC-ee at PF is con-\nsidered technically feasible. Particular attention will be given to implementing measures that ensure\nminimal environmental impact.\n1.2.5\nSurface site PG\nPG is an experiment point with civil engineering requirements similar to those of PA. The site is situated\non a plateau that is currently partially used for pasture and partially forested. To minimise the impact on\nthe forested area, the surface buildings associated with the cooling plant and some of the electrical sys-\ntems will be positioned in a secondary location approximately 300 m from the main site. This approach\nfollows the example of the existing CERN LHC Point 4, where cooling towers and pump stations are\nlocated in an area remote from the main site, in this case, to reduce their visual impact.\nFig. 1.29: Preliminary simplified area requirements for PG surface site.\nIn addition to mitigating visual impact, the layout of PG will be designed to ensure efficient use of\nspace while maintaining accessibility for operations and maintenance. Noise reduction measures will be\nimplemented where necessary to minimise any potential disturbances to the surrounding environment.\nFurthermore, efforts will be made to integrate the site harmoniously into the landscape.\n32\n\nFig. 1.30: Preliminary simplified cross-section of PG surface site.\n1.2.6\nSurface site PH\nPH will be a technical area that will support not only the access and ventilation systems necessary for\nthe accelerator tunnel, but also the infrastructure associated with the RF systems installed at this site.\nThe surface site will have a larger footprint than PB and PF, as the power and cryogenics associated\nwith the RF systems require additional buildings and dedicated foundations for infrastructure such as\ntanks and transformers.\nThe layout will be designed to optimise space efficiency while ensuring accessibility for mainte-\nnance and operations. Additionally, consideration will be given to minimising environmental impact and\nintegrating the site with its surroundings through appropriate architectural and landscaping measures.\nA preliminary simplified layout of PH is given in Fig. 1.31 and a simplified cross-section is given\nin Fig. 1.32\nSite PH is currently located on sloping ground within an agricultural and forested area, with some\nhouses in the near vicinity. This site will require specific studies into the visual impact of the site in order\nto identify measures that could be taken to reduce its visual impact on the surrounding area.\n33\n\nFig. 1.31: Preliminary simplified area requirements for PH surface site.\nFig. 1.32: Preliminary simplified cross-section of PH surface site.\n34\n\n1.2.7\nSurface site PJ\nPJ will be an experiment area with similar civil engineering structures to those described for site PD.\nThe site is located within agricultural land close to an autoroute. Beyond ensuring that the site is visually\nintegrated into its surroundings, no significant challenges have been identified at this stage. A simplified\nlayout for PJ is given in Fig. 1.33 and a simplified cross-section is given in Fig. 1.34\nFig. 1.33: Preliminary simplified area requirements for surface site PJ.\nFig. 1.34: Preliminary simplified cross-section of site PJ.\n1.2.8\nSurface site PL\nPL will be a technical area with similar requirements to PH due to the location of the Booster RF systems\nat this point. The potential presence of an aquifer linked to a potable water supply will need future\ninvestigation and if necessary, construction techniques and processes will need to be selected to ensure\n35\n\nthe aquifer is protected. . A simplified layout for PL is given in Fig. 1.35 and a simplified cross-section\nis given in Fig. 1.36\nFig. 1.35: Preliminary simplified area requirements for surface site PL.\nFig. 1.36: Preliminary simplified cross-section through site PL.\nIn summary, preliminary requirements for all eight surface sites have been gathered and prelimi-\nnary plan views and sections have been developed to a level sufficient for costing and planning purposes.\nThe construction of these sites is considered technically feasible. However, a project preparatory phase\nwill need to focus considerable effort to ensure that these sites are carefully integrated into their spe-\ncific local environments. This process will need to be carried out in close collaboration with appropriate\narchitectural specialists and must include a consultative process with the local inhabitants and other\nstakeholders. It may be necessary during this process to adjust and optimise the current preliminary\n36\n\nlayouts and locations to achieve an acceptable outcome for all stakeholders that conforms with technical\nrequirements.\n1.3\nStaged approach\nAn assessment has been made of both the underground and surface civil engineering to identify structures\nthat will only be needed for a subsequent FCC-hh machine and its associated detectors and to classify\nthe identified structures into those for which construction can be deferred until after the completion of\nFCC-ee physics and those which need to be constructed simultaneously with the civil engineering for\nthe FCC-ee machine. Consideration was given to both the cost and practicality of undertaking civil\nengineering for FCC-hh in a second stage after the operation of the FCC-ee machine.\n1.3.1\nUnderground structures\nSeveral underground civil engineering structures have been considered for staging as follows:\nExperiment detector caverns\nThe experiment detector caverns required for the FCC-hh are almost 100% larger by volume than those\nrequired for the FCC-ee detectors. The possibility of constructing the smaller experiment caverns in the\ninitial FCC-ee phase and then enlarging them prior to FCC-hh was investigated. However, this scenario\nwas eventually rejected as a feasible approach since very few of the first-phase structural elements of the\ncavern would be retained for the second phase, and it would be necessary to demolish the majority of\nthe first-phase works. This would not only be prohibitively expensive and create significant quantities of\nwaste material, but it would also represent a significant risk from a safety perspective since the reinforced\nrock around the periphery of the smaller FCC-ee cavern would need to be removed and re-supported for\nthe larger FCC-hh caverns.\nService caverns\nThe possibility of undertaking the construction of the service caverns that are adjacent to the experiment\ncaverns at points PA, PD, PG and PJ was also considered. The driver for this was the possibility of\nco-locating the systems that would traditionally be housed in the service cavern, such as air treatment\nand demineralised water systems, in the experiment cavern. Alternatively, it was considered only to\nconstruct a part of the service cavern for the FCC-ee phase and construct the remaining part necessary\nfor FCC-hh at a second stage. Constructing the second phase would require a complete re-mobilisation\nof the construction site at the surface and removing all systems from the service cavern and partially, at\nleast, from the machine access shaft. It was eventually concluded that neither a full nor partial staging\nof the service cavern would bring any major benefits since the cost of relocating the services from one\ncavern to another and the cost of remobilising the construction site would increase costs considerably\ncompared to completing the service cavern in one stage only.\nCivil engineering for beam absorber\nThe beam absorber system for FCC-ee requires only a localised enlargement of the beam tunnel over a\nlength of 708 m. This will be constructed at PB.\nThe FCC-hh beam absorber system, although not yet fully designed, will be more complex and\nlocated at PF. It will require the construction of over two kilometres of additional tunnels, two beam\ndump caverns and several junction caverns. Since none of the FCC-hh beam absorber structures can\nbe used at FCC-ee phase and given the criticality of PF for the overall construction schedule, it was\ndeemed preferable to defer the construction of the FCC-hh beam absorber civil engineering to a second\nstage. The downside to this approach will be the need to re-establish a construction site and remove all\n37\n\nservices from the beam tunnel over several hundred metres on either side of PB. Furthermore, it will not\nbe possible to transport personnel or equipment through the main tunnel in this area for a period of about\ntwo years while the FCC-hh beam absorber civil engineering is being carried out.\nFCC-hh transfer tunnels\nThe FCC-ee civil engineering includes a single transfer tunnel from the Pr\u00e9vessin site down to the FCC\nmachine. The tunnel bifurcates to provide clock-wise and anti-clockwise injection into the FCC-ee. For\na future FCC-hh machine, the pre-injection complex is likely to utilise either the current SPS or LHC\ntunnels with two new transfer tunnels for the clock-wise and anti-clockwise injection into FCC-hh. In the\ncase that the SPS tunnel is re-configured to house the FCC-hh injector system, then a single additional\ntransfer line with an approximate length of 3000 m and shaft for constructing the tunnel will be required.\nIn the case that the LHC tunnel is re-purposed then two transfer tunnels each of about 2500 m length will\nbe required, each with a single temporary shaft for construction purposes. A tunnel diameter of about\n4 m would be required, and connection caverns would be created to connect the transfer tunnels to the\nFCC main tunnel.\nAdditional by-pass tunnels\nThe FCC-ee civil engineering only includes by-pass tunnels at the four experiment sites PA, PD, PG,\nPJ. At the technical sites, by-pass tunnels are not required since a continuous transport corridor can be\nmaintained through the accelerator tunnel.\nFor FCC-hh there is a possibility that at PB and PH new by-pass galleries may be required in order\nto avoid the need for personnel to frequently pass through areas of higher radiation (due to the presence\nof collimators). If a definitive need for these additional by-pass tunnels can be confirmed prior to FCC-ee\ncivil engineering design works being completed, then it may be more efficient to include them at FCC-ee\nphase. In the case that the need is not fully confirmed, they can be constructed after the FCC-ee machine\noperation is complete. These would be constructed similarly to the additional by-pass tunnels that were\nconstructed for the LEP 200 upgrade in 1995.\n1.3.2\nSurface structures\nStaging of surface civil engineering for a future FCC-hh presents less technical difficulty than under-\nground civil engineering since access to the construction zones is readily achieved. Although detailed\nassessments of civil engineering requirements for all eight surface sites have not yet been fully com-\npleted, initial studies at points PA and PB suggest that the following buildings could be constructed after\nFCC-ee physics is completed and before FCC-hh commissioning and operation.\nAssembly halls for FCC-hh detectors elements\nAssessments of the assembly space needed for the larger FCC-hh detector elements, such as the super-\nconducting magnet coil, indicate that for at least the two larger detectors, some components will have\nphysical dimensions and weights that will make it impossible to transport them on the existing public\nroads without modifications to the existing public infrastructure. As such, it is likely that larger spaces\nand buildings will be required for the associated assembly activities.\nThis additional space would be required for manufacturing activities that would not normally be\ncarried out at the site, such as coil winding. Since the precise needs for a potential FCC-hh detector\nare not known at this stage and since there will be at least a 20-year gap between the facilities needed\nfor FCC-ee and FCC-hh detector assembly, it is not considered efficient or necessary to construct the\nlarger facilities already at FCC-ee phase. However, to avoid unnecessary demolition and re-construction\nwork in the future, the necessary space reservation for larger assembly halls will already be made at each\nof the four experiment sites. The space may be used for easily transferable facilities such as car parks\n38\n\nor storage areas, but no complex facilities will be installed within these reserved areas, and, as far as\npossible, underground utilities will be avoided, including technical galleries.\nCryoplants\nA future FCC-hh machine will require greater cryoplant capacity than during the FCC-ee phase. It is\ncurrently expected that the four experiment sites and sites housing RF systems will require cryoplant\nfacilities for the FCC-ee phase. However, a future FCC-hh would require upgraded larger plants at sites\nPA, PD, PG and PJ as well as new plants at Points PB and PF where no cryoplants are planned for FCC-\nee. The same approach as the one adopted for the assembly hall will be taken, whereby space will be kept\navailable and free of FCC-ee infrastructure for the currently expected FCC-hh cryogenics infrastructure.\nFurthermore, the landscaping and tree planting carried out for FCC-ee will, as far as possible, be executed\nin a manner that also serves the future FCC-hh needs.\nCooling and ventilation buildings\nAlthough cooling and ventilation systems will be required at all surface points for the FCC-ee phase, it\nis currently anticipated that cooling needs for the machine and experiments at FCC-hh will require plant\nupgrades including a possible increase in the cooling capacity and therefore number of cooling towers.\nThis will be accommodated in the same manner as the cryoplant, with due account taken of potential\nspace needs and visual/acoustic screening for the FCC-ee phase.\n1.4\nSubsurface site investigations\nA dependable and comprehensive 3D geological model is essential for assessing the feasibility of under-\nground civil engineering projects. Reliable geological and geotechnical data integrated into the model are\nrequired to design tunnels, caverns, and shafts. As the model evolves, the understanding of subsurface\ngeology improves, enabling the identification of potential risks and constraints that could affect these\nstructures. These factors may influence design, costs, and scheduling, making it vital to gather extensive\nsubsurface information during the early stages of planning.\nSince the autumn of 2024, CERN has been making a series of subsurface site investigations (SSI)\nusing a combination of data acquisition methods. Once complete, the information obtained from these\nSSI will be used to enhance confidence in the 3D geological model for the FCC study area. The phase\none SSI is currently about 40% complete, and the preliminary results are positive when compared to the\nmodel\u2019s predictions.\n1.4.1\nGeology in the region\nFor the purposes of the feasibility study and the targeted depths of the underground infrastructure, CERN\nhas considered that the Geneva region features three primary geological strata: moraines, molasse, and\nlimestone. A plan view of the Geneva basin geology is shown in Fig. 1.37.\nThe glacial moraines, characterised by their low strength, overlay the sedimentary molasse, which\nconsists of horizontally bedded layers of marl and sandstone that vary significantly in strength. The\nthickness of the moraines ranges from just a few metres to over 100 metres. Bordering and intersecting\nthe molasse are limestone formations, including the Alpine foothills and the Jura, Vuache and Sal\u00e8ve\nchains. Limestone in the Jura and Vuache foothills can potentially contain karsts caused by chemical\nweathering. These karsts, often filled with water and sediment, can lead to water inflow and structural\ninstability if encountered during excavation.\nBeneath Lake Geneva, prior investigations have revealed very soft deposits, including lacustrine\nclayey silts and glacial-lacustrine silts and clays, with compressive strengths ranging between 2 MPa and\n10 MPa. These deposits extend from the lakebed to approximately 260 metres in depth. Limited data\n39\n\nFig. 1.37: Geology of the Geneva area.\nexists for the Arve and Rh\u00f4ne Valleys, but soft deposits, including alluvial and alluvial-glacial moraines,\nare expected to reach depths of up to 100 metres. To mitigate construction risks and reduce water inflow\nchallenges, the tunnel alignment has been situated at a depth that is expected to remain entirely below\nthe moraines.\nThe molasse is composed of horizontally bedded layers of marl and sandstones. These layers\ncan vary in strength but are considered to be mostly stable and dry. Molasse is generally considered a\nfavourable geological stratum for tunnel boring machine excavation. For large-span caverns, constructing\nin stronger sandstone layers is preferable. The objective throughout the feasibility study has been to\nlocate underground infrastructure within the molasse, as can be seen in Fig. 1.38, wherever possible.\n40\n\nFig. 1.38: FCC long geological profile.\n1.4.2\nDevelopment of geological 3D model\nWithin the feasibility study, one of the primary objectives was to identify and locate the interfaces be-\ntween the moraines and the molasse, and between the molasse and the limestone more precisely. Al-\nthough data on the individual sub-strata of each layer exists, its quality is inconsistent and does not\ncurrently allow a clear separation of the moraines, molasse, and limestone into distinct sub-layers.\nIn collaboration with the University of Geneva (UNIGE) and specialist consultants from CERN\u2019s\nMember States, CERN has been developing a 3D geological model. This model is based on data from\nprevious borehole investigations, geophysical surveys in the study region and the ongoing SSI campaign.\nUrban areas such as Geneva and its suburbs benefit from numerous logged boreholes, which provide a\nhigh level of confidence for the upper 50 metres of the subsurface. In contrast, rural areas have fewer\nlogged boreholes, and certain locations, such as the foot of the Bornes and Mandallaz limestone outcrops,\nextend several kilometres without relevant geological data at the depths where the FCC underground\ninfrastructure is proposed.\nTo improve understanding of the geological conditions along the proposed FCC tunnel, a targeted\nsubsurface investigation campaign has been designed and is currently underway in areas of greatest\ngeological uncertainty. This campaign, which commenced in October 2024 and will continue until De-\ncember 2025, combines geophysical surveys with deep borehole drilling. Geophysical surveys are first\nconducted using seismic refraction to examine shallow strata and seismic reflection to explore deeper\nlayers. The collected data is then processed and interpreted to guide targeted drilling at depths ranging\nfrom 70 to 500 metres. By integrating these complementary methods, the reliability of the geological\nmodel in previously uncertain areas is significantly enhanced. This, in turn, increases confidence in the\nestimated construction costs and schedules, provides valuable information for the preliminary civil engi-\nneering design stage, and establishes key geological and geotechnical parameters prior to more targeted\ninvestigation campaigns.\nOnce the updated geological model is finalised, it, along with all individual borehole logs and\ngeophysical interpretations, will be made publicly available. This data will contribute to a broader un-\nderstanding of the geology in the region of the FCC, serve as a foundation for academic research, and\npotentially support future infrastructure projects beyond the FCC.\n1.4.3\nPhase 1 subsurface site investigations\nTo identify the site investigation to undertake in the first phase, three main criteria were considered:\n1. Areas where there is a risk of the tunnel crossing the molasse interface into moraines or limestones.\n2. Areas where crossing limestone is unavoidable.\n3. Areas where there is a complete lack of relevant geological information.\nUsing these three criteria, the phase one SSI campaign has been divided into nine separate sections\nnamely; Jura 1, Jura 2, Lake, Arve, Bornes, Mandallaz, Usses, Vuache and the Rh\u00f4ne.\n41\n\nThe individual sections depicted in Fig. 1.39 each present unique uncertainties and challenges.\nThe following sections will describe the current uncertainties in each area, explain the objectives of the\nsubsurface investigations, and present the preliminary results from the investigations already completed.\nFig. 1.39: Areas of geological uncertainty.\nJura 1\nSection Jura 1 is situated at the base of the predominantly limestone Jura mountain range, extending for\napproximately eight kilometres from Challex in France in the south to Satigny near CERN in Switzerland\nin the north. The proposed alignment is located at depths ranging from about 140 metres beneath the\nAllondon Valley at its shallowest point to 250 metres at its deepest on either side of the valley.\nThe understanding of the subsurface conditions in this section has been enhanced through recent\ninvestigations by other parties. In 2021, an extensive campaign of 2D and 3D geophysical investigations\nwas conducted by the Canton de Geneve and the Services Industrial de Geneve as part of the GEothermies\nprogramme. Additionally, borehole data obtained near Satigny clearly identified the molasse-limestone\n42\n\ninterface, and encountered artesian water flows near this interface. The data from this campaign was\nincorporated into a 3D geological model developed in collaboration with UNIGE, which allowed a re-\nduction in the planned scope of further investigations and provided an updated prediction that, in the\nnorthern part of the section, the limestone is located at a greater depth than previously expected.\nDespite these advances, residual uncertainties remain\u2014most notably in accurately defining the in-\nterface between the limestone and the molasse. As confidence in the updated data diminishes toward the\nsouthern portion of the section, further subsurface investigations remain necessary. Such investigations\nare required to confirm the current hypotheses and to ensure that the tunnel and associated underground\ninfrastructure avoid limestone wherever feasible, thus mitigating the risks associated with unforeseen\nhigh water pressures and challenges associated with tunnelling in limestone.\nThe SSI in Jura 1 are scheduled to begin in mid-2025 and will continue until the end of 2025. The\nfollowing is planned:\n\u2013 thirteen boreholes ranging from 230-270 m in depth:\n\u25e6one fully cored\n\u25e6twelve destructive and cored\n\u25e6three boreholes are optional, depending on the results achieved from geophysics and adjacent\nboreholes\n\u2013 13 high-resolution seismic reflection profiles with a total length of 23 510 m\nThe locations of the SSI in the section Jura 1 are shown in Fig. 1.40.\nJ U R\nA 1\nAvully\nSatigny\nBernex\nLaconnex\nChancy\nCartigny\nDardagny\nConfignon\nMeyrin\nVernier\nAire-la-Ville\nRussin\nThoiry\nFarges\nSergy\nSaint-Genis-Pouilly\nChallex\nCh\u00e9zery-Forens\nP\u00e9ron\nPr\u00e9vessin-Mo\u00ebns\nSaint-Jean-de-Gonville\nL\n0\n1\n2\n0,5\nKilom\u00e8tres\nFig. 1.40: Jura 1 section showing the locations of the investigations.\n43\n\nJura 2\nSection Jura 2 is located between Lake Geneva and the base of the Jura mountains, extending approx-\nimately three km from Meyrin in Switzerland to Ferney-Voltaire in France. The civil engineering in-\nfrastructure in this area is planned to be situated at about 200 m below the surface. At this depth, 3D\ngeological models indicate the potential for limestone to be present near the tunnel and primary infras-\ntructure, similar to the risks identified in Jura 1.\nRecent improvements in understanding have been achieved by incorporating seismic data from the\nnearby GEothermies programme into the geological models. This updated information suggests that the\ntop of the limestone is deeper than predicted.\nThe targeted SSI will enable further improvements to the understanding of the molasse-limestone\ninterface.\nThe following SSI is planned to start in mid-2025 and will last until late 2025:\n\u2013 three boreholes ranging from 240-250 m in depth.\n\u25e6one destructive and partially cored.\n\u25e6one fully cored.\n\u25e6one optional destructive and partially cored depending on the results of the geophysics and\nadjacent boreholes.\n\u2013 7300 m of high-resolution reflection seismic geophysics.\nThe locations of the proposed SSI are shown in Fig. 1.41.\nJ U\nR A 2\nSatigny\nBellevue\nGrand-Saconnex\nCollex-Bossy\nMeyrin\nOrnex\nFerney-Voltaire\nSaint-Genis-Pouilly\nPr\u00e9vessin-Mo\u00ebns\nA\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.41: Jura 2 section showing the locations of the investigations.\n44\n\nLake\nUnder Lake Geneva, the proposed FCC tunnel is at a depth of approximately 100 m below the bottom\nof the lake. The subsurface geology is characterised by moraines of mixed characteristics; however, the\nabsence of pre-existing borehole data in this area has led to uncertainty in the geological model.\nImprovements in understanding have been achieved by incorporating data from the GEothermies\nprogramme (acquired south of the proposed alignment) into the 3D geological model. Although this data\ndoes not clearly define the interface between the moraines and the underlying molasse to the north where\nthe proposed FCC tunnel is foreseen, it does indicate that the interface is located at a higher depth than\npreviously considered.\nAvoidance of the moraines is considered a key design priority, as tunnelling in water-bearing\nmoraines can be challenging. This will be confirmed after the SSI campaign.\nThe following SSI is planned to start in mid-2025 and will last until late 2025:\n\u2013 four fully cored boreholes ranging from 130-180 m in depth.\n\u2013 16 340 m of offshore seismic reflection.\nThe locations of the proposed SSI are shown in Fig. 1.42.\nL A K E\nBellevue\nGen\u00e8ve (Ville)\nChoulex\nVandoeuvres\nCorsier\nCologny\nMeinier\nPregny-Chamb\u00e9sy\nCollonge-Bellerive\nLac L\u00e9man\nGenthod\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.42: Lake section showing the locations of the investigations.\nArve\nThe Arve section, located at the eastern extremity of the proposed FCC tunnel, extends approximately\neight km in length, with the proposed FCC tunnel depth varying between 140 and 170 m. Situated within\nthe Arve Valley and adjacent to the Arve River, the area is known to be made up of a mixture of molasse\n45\n\nand glacial moraines near the surface, although geological data at the proposed FCC tunnel depths is\nlimited.\nFurther investigations will confirm the depth of the molasse-moraine interface and ensure that the\ntunnel remains within the molasse, thereby avoiding the potentially water-bearing moraines.\nThe following SSI is planned to start in early 2025 and will last until mid-2025:\n\u2013 five destructive and cored boreholes totalling 990 m in depth.\n\u25e6Up to three of these boreholes may not be undertaken following results from geophysics.\n\u2013 three high-resolution seismic reflection lines totalling, 13 150 m.\nThe locations of the proposed SSI are shown in Fig. 1.43.\nA\nR V\nE\nFaucigny\nLa Chapelle-Rambaud\nPers-Jussy\nAmancy\nArbusigny\nCornier\nEtaux\nLa Muraz\nLa Tour\nFillinges\nArthaz-Pont-Notre-Dame\nSaint-Jean-de-Tholome\nBonne\nFilli\u00e8re\nLa Roche-sur-Foron\nArenthon\nContamine-sur-Arve\nScientrier\nMarcellaz\nPeillonnex\nViuz-en-Sallaz\nMonnetier-Mornex\nBonneville\nNangy\nReignier-\u00c9sery\nSaint-Pierre-en-Faucigny\nVille-en-Sallaz\nD\n0\n1\n2\n0,5\nKilom\u00e8tres\nFig. 1.43: Arve section showing the location of the investigations.\nBornes\nThe area adjacent to the Bornes Plateau is the deepest section of the project, with depths ranging from\n500 to 560 m over five km. The deepest access shaft at PF, approximately 400 m deep, is also located\nwithin this section.\nThe proposed FCC tunnel will remain within the molasse, as the limestone is situated much\ndeeper\u2014nearly 1000 m below the surface. However, little is known about the characteristics and quality\nof the molasse. Additionally, thrusts, faults, and potential tectonic materials have been identified in the\nregion.\nGiven these factors and the high overburden, further investigations are required to obtain detailed\ninformation on the molasse and reduce geological uncertainties in this sector.\n46\n\nThe following SSI is planned to start in early 2025 and will last until mid-2025:\n\u2013 one fully cored borehole totalling 425 m in depth.\nThe locations for the SSI are shown in Fig. 1.44.\nB\nO\nR\nN E\nS\nAmancy\nEtaux\nSaint-Sixt\nFilli\u00e8re\nLa Roche-sur-Foron\nF\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.44: Bornes section showing the locations of the investigations.\nMandallaz\nThe Mandallaz is an anticline limestone range characterised by faulting and thrusting over the underlying\nmolasse on its western side. Little detailed geotechnical information was available prior to the start of\nthe SSI campaign. This presented uncertainties regarding the extent of the limestone and the nature of\nits structure.\nImprovements in understanding have been achieved through geophysical investigations as part of\nthe SSI. Data acquisition has been completed, and provisional interpretations indicate that the limestone\nat the depth of the proposed FCC tunnel is narrower than modelled before the campaign. This revised\ninterpretation suggests that the section requiring tunnelling through limestone is shorter than initially\nforeseen. Additionally, preliminary borehole data have revealed the presence of small karsts and traces\nof hydrocarbons, and provisional geophysical interpretations have identified an east-west strike-slip fault\nacross the Mandallaz mountains, although this has yet to be confirmed by the boreholes.\nThe following SSI has been carried out or is taking place:\n\u2013 three fully cored boreholes totalling 1240 m in depth\n\u25e6one of these boreholes is inclined at 30\u00b0from vertical\n47\n\n\u25e6one of these boreholes may not be required to be undertaken following the results of the first\ntwo boreholes.\n\u2013 three high-resolution seismic reflection lines totalling, 5100 m.\nThe locations for this SSI are shown in Fig. 1.45.\nM A N D\nA L\nL A Z\nLa Balme-de-Sillingy\nChoisy\nCercier\nFilli\u00e8re\nAllonzier-la-Caille\nVilly-le-Pelloux\nCuvat\nAnnecy\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.45: Mandallaz section showing the locations of the investigations.\nUsses\nThe Usses, a small section extending roughly one km, is where the proposed FCC tunnel is closest to the\nsurface, with about 50 m of cover above the tunnel at the lowest point in the Usses Valley.\nOn-site investigations have improved the understanding of the subsurface conditions in this sector.\nAll data acquisition has been completed, and the final interpretation of the geophysical data is under-\nway. Borehole results indicate that the moraine-molasse interface is encountered at 15 m, shallower than\nmodelled, suggesting that the proposed tunnel does not intrude into water-bearing moraines beneath the\nUsses River. This will be confirmed once the final geophysical interpretations are complete and compared\nagainst the borehole log.\nThe following SSI has been undertaken:\n\u2013 one fully cored borehole of 70 m.\n\u2013 two seismic refraction lines totalling 780 m, the first performed using an explosive source and the\nsecond utilising a weight drop source.\n\u2013 one very high-resolution seismic reflection of 770 m in length.\nThe locations for the SSI are shown in Fig. 1.46.\n48\n\nU S\nS\nE\nS\nContamine-Sarzin\nSallen\u00f4ves\nChoisy\nCercier\nChaumont\nChilly\nMinzier\nMarlioz\nCernex\nCopponex\nH\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.46: Usses section showing the locations of the investigations.\nVuache\nThe Vuache section at the southwestern extent of the proposed FCC tunnel extends over approximately\nfour km, with proposed tunnel depths ranging from 190 to 300 m and an average depth of around 250 m.\nThe Vuache mountain range, primarily an anticline structure bounded by thrust faults, underlies this\nsection, with the prominent Vuache Fault located to its south-west. The geology is dominated by Jurassic-\nCretaceous limestones and marls, overlain by the typical molasse found elsewhere in the Geneva basin.\nGeo-physical investigations carried out as part of the SSI have improved the understanding of the\nsubsurface conditions. One completed borehole has confirmed that molasse is present to about 30 m\nbelow the tunnel. The ongoing analysis of the geophysical data, along with additional borehole results,\nwill identify whether this is also the case for the remainder of the section.\nThe following SSI has been carried out or is taking place:\n\u2013 five destructive and partially cored boreholes totalling 1270 m in depth.\n\u25e6two of these will be optional, depending on the conclusions of the geophysics.\n\u2013 five high-resolution seismic reflection lines totalling, 9370 m.\nThe locations of the SSI are shown in Fig. 1.47.\nRh\u00f4ne\nIn the Rh\u00f4ne Valley, the proposed FCC tunnel is located approximately 50 m below the surface under the\nRh\u00f4ne River and the environmentally sensitive Marais de l\u2019Etournel. The overlying soils are predomi-\n49\n\nV U A C\nH\nE\nContamine-Sarzin\nVers\nSavigny\nVulbens\nChessenaz\nChavannaz\nChaumont\nCh\u00eanex\nJonzier-\u00c9pagny\nMinzier\nMarlioz\nClarafond-Arcine\nDingy-en-Vuache\nFrangy\nCernex\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.47: Vuache section showing the locations of the investigations.\nnantly composed of moraine or alluvial sands, gravels and boulders, and the area was formerly quarried\nas a source of gravel. These layers are saturated due to the influence of the Rh\u00f4ne River.\nThe current geological model predicts that the tunnel is situated entirely within the molasse, al-\nthough the interface between the molasse and the overlying moraine is predicted to be close. While\nlimited available data has allowed this initial interpretation, the scarcity of detailed geotechnical infor-\nmation limits its precision.\nAs a result, further investigations are required to accurately define the moraine\u2013molasse interface\nand confirm that the proposed FCC tunnel remains fully within the molasse, thereby mitigating potential\nrisks associated with the water-bearing overlying layers.\nThe following SSI could start in mid-2025 and finish by late-2025:\n\u2013 six destructive and partially cored boreholes totalling 765 m in depth.\n\u25e6Four of these boreholes may not be required following results from geophysics.\n\u2013 eleven geophysics seismic lines.\n\u25e6four profiles of high-resolution seismic reflection totalling 4920 m towards the upper part of\nthe valley.\n\u25e6four profiles of very high-resolution seismic reflection totalling 2990 m towards the bottom\nof the valley.\n\u25e6four profiles of seismic refraction at the bottom of the valley using a weight drop source,\ntotalling 240 m.\n\u2013 five high-resolution seismic reflection lines totalling 9370 m.\n50\n\nThe locations of the SSI are shown in Fig. 1.48.\nR\nH\nO N\nE\nChancy\nAvusy\nVulbens\nValleiry\nChevrier\nCh\u00eanex\nViry\nFarges\nPougny\nChallex\nCollonges\n0\n0,5\n1\n0,25\nKilom\u00e8tres\nFig. 1.48: Rh\u00f4ne section showing the location of the investigations.\n1.4.4\nPhase 2 sub-surface site investigations\nAfter the completion of the first phase of the SSI at the end of 2025, a geotechnical and civil engineering\nspecialist may be contracted in early 2026\u2014subject to the decision-making process\u2014to analyze the\ncampaign results and the corresponding geological model. Working in collaboration with CERN, this\nspecialist would define the scope and technical specifications for the second phase of the sub-surface site\ninvestigation and oversee the on-site operations.\nThis second phase would focus primarily on obtaining the necessary geotechnical data for the\ndetailed design of all underground and surface works to be undertaken. In particular, the second phase\nwould focus on the sites where experiment and service caverns are required since these require very\ndetailed knowledge of the lithology and rock engineering properties in order to undertake the complex\nnumerical analysis required to define the rock support necessary to create stable underground structures.\nDetailed Investigations Around Key Infrastructure\nPrecise geological, geotechnical, and hydrogeological data are essential for the effective design of both\nexperiment and service caverns, which are typically located at depths of several hundred metres. This\ninformation ensures structural integrity and supports the selection of appropriate construction method-\nologies. An indicative example of a typical drilling configuration can be observed in Fig. 1.49.\nThese boreholes will accurately characterise the molasse at the cavern depth, identifying structural\nfeatures such as fractures and weak zones that could affect cavern stability. Core samples and in-situ\n51\n\nFig. 1.49: Example of targeted borehole investigations for experiment cavern complexes.\ntesting will determine the molasse\u2019s strength, deformability, and stress state, enabling precise structural\nanalyses and the design of appropriate excavation and support systems. In addition, data on groundwater\nlevels, permeability, and pore pressures will inform dewatering plans and help manage water ingress -\nfactors critical to ensuring safety and stability during and after construction. Consequently, the bore-\nhole data from this campaign will be essential for optimising excavation methods, reducing risks, and\nestimating construction costs accurately.\n1.4.5\nFault Mapping and Seismic Modelling\nThe FCC study region is known to contain active or potentially active faults, including the Vuache Fault.\nHistorical seismic events have provided valuable insights into the area\u2019s seismic behaviour.\nWhile detailed study of seismic activity and structural faulting was not the primary focus of the\nfirst phase of the SSI, CERN, in collaboration with the University of Geneva, has utilised historical data\nto identify the main fault zones in the region, as shown in Fig. 1.50.\nThe proposed FCC tunnel is expected to pass through a zone with faulting, as illustrated in\nFig. 1.51. In areas such as the Mandallaz and Jura sections, where faults are known to be present,\nfurther refinement of fault characterisation will be possible once the fully processed results from the\nphase one SSI campaign become available. This will continue to be developed in collaboration with\nexternal partners over the coming years.\n52\n\nFig. 1.50: Fault map of FCC study area.\n1.4.6\nSummary of the Subsurface Site Investigations\nThe subsurface site investigations that have already been carried out as part of Phase One have improved\nthe reliability of the 3D geological model for the proposed FCC tunnel. The preliminary results from\ninvestigations in the key sections of Mandallaz, Usses, Vuache and Arve have been integrated into the\nmodel, and early results show promising signs that the FCC tunnel would be located within the molasse\nexcept in the Mandallaz section, where crossing the limestone is unavoidable.\nThe results from the remainder of the campaign will need to be fully acquired and processed\nbefore any definitive conclusions on the precise elevation of the tunnel can be made. However, current\nindications are that the tunnel might be shallower than currently planned. This would allow an overall\nreduction in shaft depth, reducing the impact and, therefore, have positive cost and schedule implications\n53\n\nFig. 1.51: FCC long profile with potential faults.\n1.5\nManagement of excavated materials\n1.5.1\nIntroduction\nBuilding the underground infrastructures of the Future Circular Collider (FCC) in the Franco-Geneva\nBasin would produce approximately 6.3 million cubic metres of excavated materials, mainly constituted\nby molasse, a soft heterogeneous rock (96%).\nThe management of excavated material stands as a key element in the realisation of the FCC within\nthe local region. Furthemore, it exemplifies a visionary investment designed to reduce environmental\nimpact and unlock benefits that extend well beyond the local context. Accordingly, from the earliest\nstages, an approach to the strategy for the excavated material management was incorporated into the\nfeasibility study as part of the FCCIS project, co-funded by the EU under the H2020 programme (grant\nagreement no. 951754).\nThe French tunnel design centre, (CETU), the Centre for studies and expertise on risks, environ-\nment, mobility and urban planning, (CEREMA), the Montanuniversit\u00e4t Leoben (Austria) collaborated\nwith the FCC study on this subject, with the technical support of the Swiss cantonal \u2018Service de g\u00e9olo-\ngie, sols et d\u00e9chets\u2019 (GESDEC).\nCurrent regulations still consider excavated materials as waste as soon as they exit the project\nboundaries, but the legislation is evolving in many European Countries. Excavated materials can be\nreused on-site (prevention of waste production) or recovered off-site. Final disposal as waste must be the\nlast option when no reasonable recovery (even after suitable preparation or treatment) is possible. The\nsuccessful management and use of excavated materials strongly depend on the early implementation of\na management strategy shared and agreed upon with the Host States by the project owner.\nThe presentation of a management plan of the excavated materials is considered to be the re-\nsponsibility of the future project owner, irrespective of who implements the actual tasks. To satisfy this\nrequirement, a report outlining the approach to the strategy for the management of the excavated material\n(in French \u2018Strat\u00e9gie de gestion et d\u2019usage des mat\u00e9riaux excav\u00e9s\u2019 [1] also available in English [2]) was\ndeveloped. The following aspects are included:\n\u2013 Quantities of excavated materials and current knowledge of the geological characteristics.\n\u2013 General principles for the management of the materials.\n\u2013 Identification of the potential risks.\n54\n\n\u2013 Legal framework in the two Host States.\n\u2013 Potential reuse cases.\n1.5.2\nThe excavated material quantities\nThe FCC excavation work is estimated to generate approximately 6.3 million cubic metres of excavated\nmaterial, equal to approximately 8.2 million cubic metres of expanded material over nearly a decade.\nThe quantities of excavated materials (see Table 1.4 ) were calculated on the planned design of the\nunderground structures (shafts, tunnels, caverns, alcoves, etc.). They correspond to the materials in place\nand the expanded materials (applying an expansion factor of 1.3).\n1.5.3\nThe excavated material characteristics\nThe material extracted will mostly comprise different types of heterogeneous soft rocks, called molasse\n(96%), along with limestone (2.5%) and quaternary deposits (1.5%).\nThe molasse is formed by a series of horizontal layers of cemented and silty sandstone interspersed\nwith layers of marl and argillaceous rocks. Geogenic anomalies such as the presence of natural hydrocar-\nbons or enhanced concentration of metals including nickel and chromium may exist naturally in varying\nquantities in parts of the various molasse layers.\nThe Lemanic basin features three main geological groups: quaternary formations (glaciolacus-\ntrine, fluvio-glacial and moraines), molasse and limestone bedrock. The reference placement proposed\nfor the FCC has been optimised to place the tunnel infrastructure in the Franco-Geneva molasse basin\n(Fig. 1.52). The limestone elements of the Jura and Vuache mountains, along with the Mandallaz and\nSal\u00e8ve ranges, skirt and intersect the molasse layers. It is hard to excavate limestone in the region due\nto its karstic characteristics caused by chemical alteration of the rock. These deep karsts are likely filled\nwith water and unconsolidated materials, which could penetrate the excavation because of strong water\npressure. CERN experienced these effects when conducting excavations in the limestone of the Geneva\nregion during previous projects (e.g., LEP in the \u201980s). Because of these difficulties, the design deliber-\nately avoids the Jura and the limestone of the Vuache. However, despite every effort to minimise crossing\nlimestone strata, one stretch of the proposed tunnel still passes through the Mandallaz limestone.\nFig. 1.52: Geological profile along the FCC path. The part of the tunnel under French territory is shown\nin blue; the part under Swiss territory is shown in red.\nThe molasse in the region is generally made up as follows:\n\u2013 30 to 50% clay,\n\u2013 10 to 15% silt,\n\u2013 10 to 15% sand, with a grain size of between 63 \u00b5m and 4 mm,\n\u2013 15 to 20% sandstone particles larger than 4 mm.\nThe sandstones (detrital sedimentary rocks formed from grains of sand cemented by silica, calcite\nand iron oxide) in the Lake Geneva region are mainly made up of:\n55\n\n\u2013 40 to 70% quartz,\n\u2013 20 to 45% calcite,\n\u2013 5 to 10% feldspar,\n\u2013 5 to 20% phyllosilicates (micas, chlorites, serpentinite, etc.)\nThe marls (sedimentary rocks containing clay and limestone) present in the region exhibit a wide\nvariety of compositions. Marls are ductile, micro-cracked and subject to swelling following contact with\nair or significant changes in soil moisture.\nThe nature of the excavated materials depends on the longitudinal profile of the geological struc-\ntures encountered. Different formations and different facies may be encountered. Homogeneity in terms\nof the nature and properties of the excavated materials is a key consideration, as it will determine their\nsubsequent use.\nA strategy will have to be devised during the construction phase to select the materials to be reused,\nbased on the following:\n\u2013 Initial visual selection at the face.\n\u2013 Tests on the geological formations and updates in case of changes in petrographic properties or\nindications of lithological changes.\n\u2013 Rapid and effective material quality control as soon as possible after the extraction of the material,\nor at the latest when the material reaches the surface.\nSpecific investigations would be required prior to the start of the excavation to determine the ge-\nological characteristics of the subsurface through which the FCC will pass and to assess the potential\ngeological risks. CERN is conducting an initial investigation campaign (2024 - 2025) as part of the FCC\nfeasibility studies. These first subsurface investigations could be later complemented by extensive sub-\nsurface investigations, devoted mainly to confirming the geological model and, therefore, to anticipating\nthe possible risks and preparing adequate mitigation. Laboratory tests are being conducted on core sam-\nples extracted during the subsurface investigations to identify and characterise the rocks in view of their\npotential for reuse and to analyse the presence of geogenic anomalies.\n1.5.4\nApproach to the management of excavated materials and associated risks\nDefining what could constitute a basis for a future strategy for managing and utilising excavated materials\nis a key feasibility criterion for the FCC study, reflecting both the alignment with the regulations of\nthe Host States and a broader commitment to sustainability and environmental stewardship. The basic\nconcept has been documented in a stand-alone deliverable of the FCCIS study [1]. The core principles,\nsummarised here, present the high-level aspects, related constraints and the opportunities identified for\ntreating the material as a resource instead of disposing of it as waste.\nThe approach to excavated materials management marks the initial step toward a comprehensive\napproach, conducted in accordance with the regulatory frameworks of both Host States. Its implemen-\ntation, in the form of a preliminary operational management plan, can only begin once the first set of\nsubsurface investigations is completed (by the end of 2025). Subsequently, this preliminary plan should\nbe revised whenever significant new information is obtained, following an iterative process that would\nculminate in a final operational management plan to be shared and agreed with the Host States, and\nshould be adopted before the start of excavation.\nApproach to the excavated material strategy\nThe studies carried out to develop an approach to the excavated material strategy were:\n\u2013 Iterative development of a 3D subsurface geological model (see Section 1.4.2).\n56\n\n\u2013 Inventory of the regional opportunities for reuse in France and Switzerland.\n\u2013 Investigation of the possible connection to the regional railway network.\n\u2013 Investigation of the possible connection of the railway sidings to the extraction sites by conveyor\nbelts, to avoid local nuisances due to truck transport.\nThe FCC schedule allows the possibility of optimising potential reuse scenarios. Accordingly,\nrather than centring on fixed solutions, the excavated materials management focuses on flexible ap-\nproaches and guiding principles that can be adapted to accommodate:\n\u2013 Evolutions in technology that could result in improvements in the techniques applied to the exca-\nvation and separation and treatment of the excavated materials.\n\u2013 New recovery pathways which are better suited to the characteristics of the extracted materials that\nmay become available in the future.\n\u2013 Evolution of regulations governing the management of excavated materials for specific applica-\ntions (e.g., use as soil improvers in agriculture).\nThe main parameters to be taken into consideration when building a strategy for the management\nof the excavated materials are:\n\u2013 TBM kinematics (Fig. 1.4) and the logistic aspects that determine the output and availability of\nexcavated materials within the area as well as the nearby storage and treatment areas required.\n\u2013 Identified uses and streams: specifications, demand (quantities and variation over time), location,\naccessibility and service, criteria for acceptance of the material.\n\u2013 Modes of transport and distances, as well as whether existing infrastructures can be used or\nwhether new infrastructures will need to be built.\nA schematic overview of the approach to the excavated materials management appears in Fig. 1.53.\nExperience from previous CERN projects shows that the proportion of materials affected by geogenic\nanomalies (such as hydrocarbons or elevated chromium and nickel levels) may vary, ranging from ap-\nproximately 15% to 45%, in part due to different regulatory thresholds of the Host States. For the record,\nexemptions have been granted for specific materials, for example, in 2019, during the HL-LHC project,\nto facilitate higher recovery rates in various recovery streams.\nEvaluation of risk in the management of excavated materials\nThe fraction of re-usable excavated materials depends on the geochemical, mineralogical and geotechni-\ncal properties of the materials excavated from the tunnel. When preparing a management plan for these\nmaterials, particular attention must be paid to the management of both technical and non-technical risks,\nwhich have a direct effect on limiting costs, optimising transport and avoiding compromising the sched-\nule. Typical technical risks relating to the external context for excavated materials are associated with:\n\u2013 The nature of the materials, which determines their classification as a specific type of material and\ntheir potential reuse;\n\u2013 The proportion of facies, in the case of a heterogeneous formation or a mixed facies with several\ntypes of material;\n\u2013 The position of the contacts between geological formations, which has an impact on the distribu-\ntion of the volume of material per formation.\nThe technical risks of the internal context, regarded as points to keep in mind by the project owner,\nare associated with:\n57\n\nExcavation material \nstrategy\nPolluted materials\nNon-polluted \nmaterials\nReused\nNot reused\nSpecific \nLandfill\nTreatment\nPollution \nremoval\nNormal \nLandfill\nNormal \nLandfill\nRecovery\n(inclusing \nrecycling)\nReuse on site\n% polluted \nmaterial\n% non polluted \nmaterial\nSpecific \nconditions\n% pollution \nremoved\nReduce transport \nnuisances and \nglobal footprint\nFig. 1.53: Schematic diagram of the scenarios defined for the excavated material strategy. (not including\ntransport).\n\u2013 The impact of the excavation methods, chosen according to the characteristics of the excavated ma-\nterials and, in particular, the additives necessary for the excavation, which can potentially pollute\nthe materials and hinder certain reuse cases.\n\u2013 The equipment used in the transport and in the treatment of the excavated materials, for the poten-\ntial of unforeseen mixing and potential pollution of the excavated materials.\n\u2013 The availability and extent of the temporary and final storage areas for excavated materials.\nAlong with the technical risks, non-technical challenges, such as political or administrative factors,\nshould also be taken into account in the development plan. For example, there may be modifications to\nenvironmental regulations. These non-technical challenges must be considered from the study phase.\nExcavation methods can have an impact on the potential use of molasse and other excavated ma-\nterials since they can alter their properties and quality. At this stage of the FCC study, the use of double-\nshield Tunnel Boring Machines (TBM) is likely to be possible for most of the main tunnel. Further\nstudies should provide more detail for the information provided in Table 1.7, specifying the impact of\nthe chosen excavation techniques on the quality of the excavated materials (type of TBM, explosives or\nroad header).\n1.5.5\nRegulatory frameworks\nIn France, AFTES recommendation GT35R1F2 on the management and use of excavated materials [3]\nand the CETU information document on naturally occurring geological materials excavated in under-\nground structures [4] are the main reference texts for the management of excavated materials.\nIn Switzerland, the ordinance on the avoidance and the disposal of waste [5], complemented by\nthe ordinance on the movement of waste [6], the \u2018Aide \u00e0 l\u2019execution relative \u00e0 l\u2019OLED\u2019 (help for the\nexecution of the ADWO, not available in English) and the \u2018Guide pour la r\u00e9utilisation des mat\u00e9riaux\nd\u2019excavation non pollu\u00e9s\u2019 (guide to the reuse of unpolluted excavated materials, OCEV), provide the\nframework for the subsequent steps.\nThe main regulations in force in the two Host States regarding the application of international\n58\n\nTable 1.7: Quantity of excavated material by excavation method.\nUsing TBMs\nUsing\nconventional\nmethod\nShafts\nTotal\nCollider infrastructure (m3, in situ)\n2 689 500\n2 828 500\n652 600\n6 170 600\nConnecting infrastructure\nto existing tunnels\n(injection) (m3, in situ)\n97 900\n9800\n14 600\n122 300\nTotal (m3, in situ)\n2 787 400\n2 838 300\n667 200\n6 292 900\nPercentage of Total\n44%\n45%\n11%\n100%\nagreements on the export of excavated materials are:\n\u2013 In Switzerland, Article 15, paragraph 1 of VeVA 814.610 requires that anyone exporting waste\n(including unpolluted excavated materials) must obtain authorisation from the Federal Office for\nthe Environment (VeVA 814.610, 2005).\n\u2013 In France, since 12 July 2007, the cross-border movement of waste has been subject to the provi-\nsions of Regulation (EC) No 1013/2006 of 14 June 2006, which incorporates the provisions of the\nBasel Convention [7]:\n\u2013 Article 43 permits the importing of waste for the purposes of recovery from countries which\nare Parties to the Basel Convention to a European country.\n\u2013 Articles 40 and 41 prohibit the importing of waste for the purposes of disposal from coun-\ntries which are Parties to the Basel Convention except where one of the countries (including\nSwitzerland) presents a prior duly reasoned request (paragraph 4).\nArticle 4.2 of the Basel Convention [7] states that each country must take measures to reduce the\ngeneration of waste and ensure the availability of adequate disposal facilities located, where possible,\nwithin the country, with a view to the environmentally sound management of dangerous waste and other\nwaste, whatever the place of its disposal.\nIn the north-west sector of the FCC, its path crosses the Franco-Swiss border at several points.\nIf the excavated materials were to be managed by each state, this would lead to the excavation of addi-\ntional shafts for the specific purpose of material evacuation, which is not realistic and does not respect\nthe \u2018avoid, reduce and compensate\u2019 approach because it would increase the quantity of materials to be\nmanaged and the number of nuisance zones on the surface due to the extraction points. For this reason,\nit would be desirable to propose the adoption of the principle of each state managing the equivalent mass\nof spoil excavated on its territory. This adjustment, which remains to be agreed with the two Host States\nand in association with CERN, would make it possible to deal with the small enclaves that cannot be\nmanaged by the TBMs without changing the principle of division laid down in the Basel Convention.\nA further point where an agreement between the project owner and the Host States seems appro-\npriate concerns the country in which the materials are extracted. In principle, according to the Basel\nConvention, each country is responsible for extracting and managing its share of the mass on its territory\nand for dealing with the associated adverse effects (dust, noise, traffic, etc.). The distribution of the\nTBMs, however, does not necessarily correspond to this mass distribution (e.g., no TBM launched from\nsite PB) for technical reasons. For such a scenario, compensatory measures will have to be agreed with\nand by the Host States.\n59\n\nVarious tools will have to be developed to ensure that the management of the materials respects an\nestablished and agreed management plan that is part of the project authorisation files. These will have to\nbe devised sufficiently early, in consultation with the Host States and relevant authorities, to ensure they\nare properly implemented when the time comes:\n\u2013 Administrative tools for the authorisation procedures for spoil transport and storage to enable\neffective recovery of the material.\n\u2013 Regulatory tools to enable the validation of the innovative processes, particularly in terms of char-\nacterisation, and to ensure they can be standardised.\n\u2013 Cross-border agreements: if relevant optimisations are identified, these will need to be made ex-\nplicit, substantiated and submitted for joint approval by the two Host States.\n\u2013 Agreements with offtakers of materials and owners of land plots that would receive materials\nbefore the start of the excavation process.\n\u2013 Logistics tools: an adequate traceability system is the responsibility of the owner and it provides\na useful way of improving the recovery of the materials and acts as a guarantee that the spoil is of\nsufficiently high quality.\nThe first three points could be governed by a bilateral international agreement.\nMaterials excavated during underground works are considered as \u2018waste\u2019 in the European Union\n(EU) countries and Switzerland unless they can be reused on the site of the project. The definition of the\nstatus of excavated soil and its classification as \u2018waste\u2019 or \u2018non-waste\u2019 are fundamental aspects, as they\ndetermine the legal framework to be followed for managing the excavated materials. The status of the\nexcavated soil must be specified according to the various on- and off-site management scenarios with the\nFrench and Swiss authorities.\nTo develop an integrated plan for the management of the excavated materials that is part of the au-\nthorisation process, it would be advisable that the FCC is treated as a single indivisible and transnational\nproject in the meaning of 1.c) of Article 2 of the \u2018waste\u2019 directive 2008/98/EC of 19 November 2008 [8].\nThe integrated approach facilitates the development of the agreements between the project owners and\nthe customers for the materials that must be in place before the construction works start. It also enables\nthe possibility to reuse materials on either side of the border, independent of their extraction site of the\nunique, indivisible project.\n1.5.6\nScenarios envisaged for the management of the excavated materials\nAs a long-term project offering sufficient lead time, the FCC may represent an opportunity to develop\ninnovative approaches for the management of excavated materials. For this reason, the study invested\nalready in launching the research and development of new technologies and solutions that have the po-\ntential to reduce the amount of waste that needs to be transported to deposit sites.\nThe identification of uses must comply with the waste hierarchy put forward by the European\nUnion parliament (\u2018waste\u2019 Directive 2008/98/EC) and implemented in the French and Swiss regulations.\nThe national policy for the prevention of waste production and reduction of waste impacts, outlined in the\nEnvironment Code (Art. L-541-1), supports the transition to a more sustainable management of the ex-\ncavated materials, by fostering the application of the waste hierarchy: avoid waste production (including\nreuse), preparation for reuse, recovery and disposal. It also includes achieving a total \u2018material\u2019 recovery\nof the waste stemming from the building and public works sector of 70%. This target is evaluated at the\nregional level.\nThe general principle of avoid/reduce/compensate will also be applied to the management of ex-\ncavated materials of the FCC: the \u2018avoid\u2019 and \u2018reduce\u2019 principles are applied mainly at the time of the\nsubsurface infrastructure planning (i.e avoiding producing unnecessary spoil and reducing the overall\n60\n\nexcavations by optimising location, design, and depth of underground infrastructures) and in the choice\nof the excavation methods (minimisation of pollutants during the excavation, thus reducing the quantities\nof excavated materials that will need specific land filling).\nThe various types of reuses and recovery call for material storage and treatment areas close to the\nextraction sites. The surface areas necessary depend on the detailed technical concept of the construction\nwork, the construction schedule and the dimensional design of the treatment unit on the sites. These\nelements will have to be developed at a later stage.\nAmong the identified pathways, the most likely to be realised are:\n\u2013 Use for development requirements within the project (e.g., FCC worksite tracks, landscaping\npurposes, etc.)\n\u2013 Use in earthwork (backfilling of quarries and mines and rewilding) and development projects.\nThis reuse case concerns most of the materials, as it can be applied for both the inert material and\nthe polluted excavated materials, after appropriate decontamination. As each quarry is subject to\nspecific environmental impact restrictions, specific acceptance criteria for the backfilling materials\nmust be respected. In total, it is estimated that all material that will not be addressed to specific\nland filling due to pollution can, in principle, be reused for quarry landscaping, after treatment.\nHowever, in order not to saturate the region, other reuse cases are investigated at the same time.\n\u2013 Use of the limestone fraction in concrete production and stabilisation of structures. The lime-\nstone, marl and clay deposits of the Jura and the northern Alps have provided the raw material for\nlime and cement since ancient times. Produced by calcining limestone, lime is used to improve\nsoils and whitewash walls; mixed with sand and water, it produces a mortar that is very easy to\nproduce and therefore very common. All limestone that will be extracted during the FCC construc-\ntion project will be destined to these reuse cases. Due to the costs of production of these resulting\nconstruction materials, it is assumed that the reuse of limestone is at zero gain and zero cost for\nthe project.\n\u2013 Use of the sand fraction in concrete production. Direct reuse of sand and gravel could be\nenvisaged, eventually after treatment of sieving and /or washing of the excavated materials. The\nuse of cyclones for the washing of excavated materials is an established treatment method that\nallows separation of the clay and other materials and obtains good-quality materials. The study on\nthe efficiency of this separation method remains to be performed.\n\u2013 Transformation of the molasse into fertile soil for applications in the development of brownfield\nsites, urban recreational areas and forest areas, as well as improving the fertility of acidified land\nand/or as technical areas along the verges of roads and motorways (pollutant filtration). The use\nof excavated materials transformed into reconstructed soil requires the identification of areas for\nbackfill in agricultural areas. The locations desired include hollows, slopes, areas of poor ground\nquality such as polluted or acidic soils, or of poor agronomic quality (e.g., low water retention\npotential). The application may be different depending on the type of land and topography. This\ntype of measure could be particularly suitable for certain rural areas in the Auvergne-Rh\u00f4ne-Alpes\nregion and in several cantons in Switzerland and would also allow deposits to be made near drilling\nsites. Due to the unknown topography of the chosen areas, it is currently difficult to identify the\nlocation and total areas. It is estimated that about 2 million cubic metres (about 4 million tons) of\nexcavated materials could be reused via this pathway, provided the appropriate areas are identified.\n\u2013 Use of a part of the molasses as technical materials: trench cover (e.g., roads), acoustic screens,\nfarm tracks, forest paths etc. Both the French and Swiss neighbouring landscapes are constituted\nby woods of different nature or of rural areas. In particular, the zone in the proximity of Annecy\nhas approximately 500 km of rural paths and tracks. In total, there are approximately 705 000\nkm of rural and forest paths in France. These paths and tracks must be maintained regularly; for\nthis, inert materials are necessary to ensure their stability. Raw molasse is also suitable for the\n61\n\nimplementation of vegetation-free strips near roads. With the installation of noise-reducing and\nprivacy-screening gabions, this scenario can generate significant savings in the development and\nmaintenance of public roads. Support from the relevant authorities is required to identify suit-\nable roads and locations near extraction sites, establish certifications, and grant permits necessary\nto carry out this type of application. A further application in the layout of roads is the use of\nreconstructed soil based on molasse as landscaping of trenches of covered streets or highways.\n\u2013 Development of building components by compression (bricks or compressed earth using \u2018sand-\nwich\u2019 technology) for use within the scope of the project where possible or outside the project\n(opportunities within the region to be investigated).\n\u2013 Development of new building materials containing a part of the molasse (e.g., shotcrete ingre-\ndients, supporting materials, insulating panels for surface buildings), to be used within the scope\nof the project where technically feasible or outside the project (opportunities within the region to\nbe investigated). Literature shows that considering excavated materials for the reuse as recycled\nconcrete aggregates (RCA) in the structural concrete of the tunnel or of the basement of the tunnel\ncould turn out to be not feasible because of the decreased strength and therefore further thorough\nstudies are required. A prudent approach, until more complete studies are performed, could be to\nuse RCA in shotcrete with fibre-reinforcement for non-structural parts only.\nSome of these pathways are listed in excavated material management guides used in France e.g.,\nfrom Cerema/UMTM (publication pending) and from the Minist\u00e8re de la transition \u00e9cologique et sol-\nidaire [9] and in Switzerland from the OCEV [10] and also in the AFTES recommendation GT35R1F2\n[3] (currently in revision). The other pathways must be identified and a framework for cross-border use\ncould be proposed to the respective authorities in the Host States.\nThe first four in the list correspond to traditional reuse cases already in use in other tunnel con-\nstruction projects. These are taken into consideration and will be applied in priority whenever the geo-\nmechanical, mineralogical and chemical characteristics of the material are suitable for these applications.\nIn addition to these traditional reuse cases, innovative reuse pathways were identified during the\n\u2018Mining the Future\u00ae\u2019 international competition carried out in 2021 and 2022. The competition aimed to\nidentify innovative pathways for excavated material from tunnel construction which could be profitable\nnot only to the FCC but to any further projects in the subalpine region. The competition was launched un-\nder the Horizon2020 project \u2018Future Circular Collider-Innovation Study\u2019 (Grant Agreement n. 951753)\nand was jointly organised by CERN and Montanuniversit\u00e4t Leoben. The submissions were scrutinised\nby a jury panel of international experts. The four finalists\u2019 concepts ranged from the manufacturing of\nsubstrates for agriculture and forestry to the production of raw construction materials like concrete and\nshotcrete, compressed earth bricks and other hydraulically bound building materials. They all need to\nanalyse and separate the materials during the tunnelling process in real-time, with subsequent on-site pre-\nprocessing directly on the excavation surface sites. Geogenic contamination by hydrocarbons and heavy\nmetals must be removed or at least be reduced to levels that are compatible with the proposed processes\nand end-use conditions. The consortium led by BG Engineering was selected as the most innovative and\ncomprehensive concept and won the competition.\nSome of the solutions are now being integrated into a unique design and evaluated in the field,\nin a project planned to reach maturity by 2030. The objectives of the evaluations are twofold. Firstly,\nto establish how to conduct the online identification, sorting and pre-treatment of the materials during\nthe excavation process. Secondly, to prepare different reuse pathways to sort and pre-treat materials,\nincluding transforming molasse into usable soil for forestry and rewilding applications, in line with the\nprinciples of a circular economy. The quality-assured creation of the reconstructed soil is a lengthy\nprocess spanning several years and has been chosen as the first large-scale experiment with field tests at\nOpenSkyLab.\nThe OpenSkyLab, is a project based on a plot of about 10 000 m2 located near LHC Point 5\n62\n\n(CMS, Cessy, France) that has been made available by CERN. Molasse extracted during the HL-LHC\nexcavations will be transported to this field to be used in the tests. Initial laboratory analyses will be\nperformed off-site to identify the most suitable mix of molasse and other natural additives (compost).\nThese will be followed by field tests in the OpenSkyLab\u2019s controlled environment (monitoring of the\nfield, weather, and plant growth conditions), using scientific protocols developed by a collaboration of\nuniversities working in this domain.\nIn keeping with CERN\u2019s long-standing tradition, this project relies on an open collaboration with\nacademia and industry. Currently, the collaboration includes university and research experts in agronomy,\npedogenesis and geology (HEPIA, BOKU, BRGM, Montan University Leoben) and industrial partners\nin soil engineering and phytoremediation (Microhumus, Edaphos), soil treatment techniques (WSP-BG)\nand monitoring and supervisory control systems (BECC).\nIn order to facilitate acceptance into the reuse pathways of the excavated materials, it will be\nnecessary to set up material-separating units during the tunnel construction phase, at the starting point\nof two TBMs as a minimum. These units could combine the screening, sorting, sieving and cleaning\noperations of the extracted materials.\nAssuming a two-shift 24-hour working day over 240 days per year, the consortium that won the\nMining the Future competition proposed a facility that could treat approximately 750 000 tonnes per year\nat an hourly rate of 200 tonnes. Each facility would employ a team of five people. A pilot project for the\ntesting of the efficiency of these sorting and treating facilities could be envisaged during the next phase.\nThe working hypothesis assumes that the previously listed solutions will account for a global reuse\nof about 70% of the overall excavated materials, among which the reconstructed soil reuse pathway could\namount to up to 2 million cubic metres (corresponding to about 25% of the total). The backfilling of\nquarries as well as more traditional reuse pathways (e.g., limestone and sand direct use) should overall\naccount for about 45%. These quantities remain to be confirmed during the next phase.\nRegional opportunities\nCERN commissioned a study to identify the regional opportunities available in France and Switzerland\nfor the evacuation of the excavated materials. This included:\n\u2013 A global inventory of the final storages and of the opportunities for landscaping of quarries and\nmines at the end of their operational lifetime, but holding a prefectural permit valid beyond 2033.\n\u2013 A study on potential industrial railway sidings for the evacuation of the materials.\nGlobal inventory of regional opportunities\nThis study started with a preliminary inventory of potential regional opportunities for landscaping (quar-\nries, mines) and storage, which was carried out at the start of the feasibility study (2021-2022) in France\nand Switzerland to provide initial indications of potential host sites and the capacities for excavated ma-\nterials of the various pathways. These detailed inventories list the existing and planned facilities (horizon\n2030) with sufficient capacity to receive and treat the excavated materials from the FCC. They will need\nto be repeated once the excavated material management plan has been defined to take account of the\nfinal material extraction fluxes and the possible availability of new reuse cases. Subject to updating and\noptimisation with respect to transport, these studies show that it is possible to find a pathway for all the\nmaterials excavated from the potential future FCC project and provide an initial estimate that can be used\nas a basis to begin the optimisation process according to the \u2018avoid, reduce, compensate\u2019 principle. It\nshould be underlined that the inventory of the potential recipients of the excavated materials was carried\nout with the aim of evaluating the financial envelope and identifying potential showstoppers for the FCC\nfeasibility. It is not possible at this stage to identify the specific recipients without engaging in contrac-\n63\n\ntual agreements. This step will be performed during the establishment of the final material management\nplan.\nFig. 1.54: Schematic diagram of the inventory of the regional opportunities for material reuse (status\n2021).\nRailway sidings\nThe study investigated the option of constructing industrial rail sidings near the surface sites to take away\nthe excavated materials. Potential locations near existing railway lines were identified, and the feasibility\nof creating sidings was examined. To supplement this study, the feasibility of a conveyor belt link has\nbeen assessed for the two sites deemed most appropriate for the installation of sidings: Vulbens (removal\nof materials from PJ) and Charvonnex (removal of materials from PG). This exploratory phase was\ncompleted by an initial assessment of greenhouse gas emissions from transporting excavated materials\nby road and/or by rail from the production site to the disposal site or to the location of the hypothetical\nreuse cases.\nThe feasibility study of railway sidings only took technical factors into account. The weighing of\ncertain factors linked to the acceptability of creating a railway siding (e.g., environmental aspects such\nas the nuisance factor in a densely populated area) must be carried out before a decision is reached.\nThe creation or refurbishment of railway access, already considered to lower the nuisances due to\ntruck transport, would further facilitate the use of quarries and reuse cases not in the immediate vicinity.\nA technical study could be conducted to analyse the possibility of cross-border transport by conveyor\nbelts from Challex (PL) to the railway network at La Plaine in Switzerland and from Ferney (PA) to the\nrail network at the Geneva Airport in order to use the existing railway infrastructure for the transport of\nthe materials to their final destination.\n1.5.7\nOutline of the next studies\nThe scenarios for the reuse of excavated materials are based on preliminary assumptions regarding the\nproportion of materials with geogenic or anthropogenic characteristics that may require specific handling.\nAt this early stage, and in the absence of more detailed geochemical analyses, a working assumption of\n30% of materials exhibiting natural geogenic variations appears to be the most reasonable.\nAs part of the FCC feasibility study, additional insights may be gained by examining recent\nprojects related to the enlargement of certain LHC accelerator caverns (HL-LHC project). Underground\nexcavations for this project indicated the presence of hydrocarbons in approximately 15% of the materi-\nals in France and nearly 50% in Switzerland. This difference is influenced not only by actual variations\nin subsurface conditions but also by differences in environmental regulations between the two countries.\n64\n\nFig. 1.55: Study of the potential locations for railway sidings.\nBased on these initial inventories, presented in Section 1.5.6, a preliminary approach to the man-\nagement of the excavated material was drawn up and used to assess the transportation costs from the\nextraction sites to the storage facilities and backfilling sites. The average transport distances are esti-\nmated to be 20 km in Switzerland and 40 km in France for uncontaminated materials and approximately\n100 km in both countries for materials requiring specific treatment. This is because treatment facilities\nare generally located outside the Lake Geneva region, where the FCC will be installed.\nFigure 1.56 presents the results obtained for uncontaminated materials. In this figure, the values\ndisplayed on black backgrounds indicate the quantities of material expected to be extracted per site,\nwhile the colours of the circles correspond to the quarries or backfilling sites designated for the disposal\nof outgoing materials. It should be noted that only quarries with a prefectoral permit valid beyond 2033\nhave been considered.\nThese scenarios will require updates, as the annual intake capacity of each site may be revised\nbased on regional requirements. The extracted quantities are provided as an indication of each quarry\u2019s\nbackfill capacity. However, further studies will be necessary to assess the feasibility of this operation,\nand agreements with quarry operators should be established in due course.\nSubject to updating and optimisation with respect to transportation, these studies show that it\nwould be possible to find a pathway for all the materials excavated from the potential FCC project sites\nand provide an initial financial estimate which could be used as a basis to begin the optimisation process\naccording to the \u2018avoid, reduce, compensate\u2019 principle.\n65\n\nFig. 1.56: Example of possible distribution of unpolluted excavation materials to the quarries nearest to the\nmaterial extraction sites (the figures in black are the value in tonnes). The colours of the circles link a given\nextraction site to one or more quarries or backfilling sites. The figures in yellow show the quantity of materials that\ncan be accepted by the quarries during the excavation. Swiss pathways are represented by a red dot, and French\npathways by a yellow dot.\nThe distribution of excavated materials should integrate the identified reuse cases as soon as the\ntechnical information on their feasibility becomes available. Therefore, the current distribution should\nbe viewed as a preliminary benchmark assessment, expected to evolve positively as studies progress.\nClose collaboration between the FCC and the Host State authorities is essential to refine and better adapt\nthe principles of the strategy of the excavation material management in alignment with the regional\nframework.\nA subsequent project preparatory phase should include the development of a roadmap along the\nfollowing points:\n\u2013 Confirmation of the characteristics of the excavated material and correlation to the potential reuses\nvia the analysis of the ongoing and future subsurface investigations;\n\u2013 Study of the technical methods for the real-time analysis of the materials and their sorting accord-\ning to their characteristics and potential reuse.\n\u2013 Pilot projects on the potential reuse cases: on the example of the ongoing OpenSkyLab project\nfor developing processes for using excavated materials for landscaping, other projects could be\nstarted for testing, for example, the possible reuse as construction or isolation materials. This\nstudy should include an evaluation of the environmental, economic and societal impact due to the\npotential injection on the market of the products based on excavated materials ;\n\u2013 Definition of the regulatory framework for the management of the excavated materials with the\n66\n\nhost States;\n\u2013 Update of the regional treatment and disposal opportunities (e.g., availability of quarries, final\ndeposits, treatment facilities) and related regulation;\n\u2013 Study on the excavation material logistics (traceability, fluxes, conveyors etc.), including the eval-\nuation of environmental and societal impacts and the potential limitations.\nCertain activities can be carried out in parallel. Others must follow a sequential process, leading to\nthe development of a preliminary excavation material management plan. Based on this plan, more con-\ncrete discussions can be initiated with the administrations of the Host States and the owners of potential\nfinal deposit and reuse sites.\n67\n\n68\n\nChapter 2\nTerritorial implementation\n2.1\nIntroduction\nTo be able to take an informed decision for a future particle-collider based research infrastructure and to\nundergo the necessary project authorisation process with national authorities, a specific implementation\nscenario needs to be conceived. Such a geo-localised scenario must be well-balanced, considering the\nthree main dimensions:\n1. Scientific excellence.\n2. Territorial compatibility.\n3. Risks related to the implementation that affect cost and schedule.\nWhile the exploratory phase of the FCC study between 2014 and 2018 [11] focused on the \u2018in\nprinciple\u2019 feasibility of the accelerator and the territorial boundary conditions, the studies between 2019\nand 2024 included the development of a well-balanced project scenario considering the three above-cited\ndimensions.\nThis chapter summarises the methodology adopted to carry out this work as documented in [12],\nsheds light on the variants considered and the evolution towards a reference scenario. The resulting sce-\nnario presented serves as a reference to design the various elements of the future circular collider-based\nresearch infrastructure if the global science community decides to make such a facility their priority.\nThe reference scenario presented is the result of a total of 10 years study of a large variety of\nscientific, technical, cost, societal and environmental aspects. It represents an infrastructure with a cir-\ncumference of approximately 91 km, including eight surface sites. It is conceived to be able to host\ntwo distinct particle colliders, a high intensity lepton collider first and a high energy hadron collider in\nsubsequent phases. The second machine and its experiments profit significantly from the assets put in\nplace for the first phase due to the residual asset value of that infrastructure, contributing to the overall\nsustainability of this long-term science programme. The iterative process that was used to develop the\nreference implementation scenario is summarised in the following sections.\nThe presence of a sufficiently large community of users committed to carrying out scientific re-\nsearch with the particle colliders for several decades is a prerequisite for justifying the construction of a\nresearch infrastructure of this scale. Scenarios involving a much smaller collider with a circumference\nof less than 90 km, would not allow the provision of a performance and a research programme that could\nattract a critical mass of scientists for a sustained period of time. The doubling of the interaction regions\nfrom two to four reflects the aim of attracting as many scientists as possible to such an infrastructure.\nThe size and the characteristics of the infrastructure also permit additional scientific activities with the\ninjector and particle colliders, as is the case today at CERN with the LHC programme.\nIn terms of compatibility with the geological conditions that affect the construction risks and\ncosts, only two types of configurations meet all requirements: an infrastructure with a circumference\nof between 89 and 91 km and eight surface sites, and a layout with a circumference of between 97 and\n98 km and twelve surface sites. Concerning the availability of suitable surface site locations, however,\nlayouts and placements suitable for scenarios involving a collider with a circumference well in excess of\n91 km and comprising more than eight surface sites turned out to entail unacceptable risks concerning\ntheir implementation.\nTo date, only scenarios around 91 km circumference and eight surface sites seem capable of satis-\n69\n\nfying the following three requirements:\n1. Good scientific performance of the particle collider and four experiment sites.\n2. Compatibility with territorial constraints at the surface and the subsurface.\n3. Understanding of the implementation conditions from cost and risk perspectives.\nOne of the scenarios named PA31 stands out from all of those iteratively developed following the\n\u2018Avoid-reduce-compensate\u2019 methodology [13] and analysed with a multi-criteria approach recommended\nfor industrial installations [14, 15]. It has been further studied and optimised in depth involving biblio-\ngraphic research, field work, and continuous discussions with the public administration services in both\ncountries involved and with key stakeholders in the implementation area. In case of a decision to move\nforward with the implementation of a project, the conditions for this scenario will have to be further\nanalysed, the scenario will have to be further improved, and detailed designs have to be developed before\nimplementation can start.\nTerritorial constraints and legal frameworks in host countries and within the European Union are\nconstantly evolving. Between 2014 and 2023, several layout and placement scenarios had to be ruled out\ndue to these changes. The information contained in this document and the working hypothesis described\nhere are therefore provisional. For the project to come to fruition, the validation and definitive freeze of a\nscenario securing the required surface areas and subsurface volumes should be done as soon as possible.\n2.2\nMethodology to develop a sustainable project\n2.2.1\nApproach\nFrom the outset, the objective of the study was to draw up a scientific research infrastructure that rec-\nonciles, in an eco-design approach [16, 17], i) scientific excellence, ii) territorial compatibility and iii)\nconsideration of acceptable risks associated with project implementation. A systematic process therefore\nhad to be set up to develop scenarios through an iterative approach, taking these three essential aspects\ninto account at all times. The eco-design approach adopts the \u2018Avoid-Reduce-Compensate\u2019 methodology\n(see Fig. 2.1), which takes into account both constraints and opportunities.\nThis process, which complies with the French Environmental Code, the Environmental Protection\nAct and the Swiss Federal Ordinance relating to the Environmental Impact Assessment Regulation, is\nperfectly in line with the desire and objective to arrive at a proposal based on a balanced scenario.\nIdeally, all stakeholders are involved in the process from the outset. However, an iterative approach\nhad to be taken given that in the beginning the placement of the infrastructure was not defined, the\nknowledge of evolving territorial conditions was incomplete, the possibilities of effectively involving\nstakeholders at all levels of society were limited, the knowledge of the technological choices to be made\nfor periods longer than twenty years is evolving, and the availability of resources for conceptual studies\nand personnel at this very early stage is limited.\nDespite these constraints, the international science community is committed to transparency and\npublic participation. The aim is to obtain a \"social licence to operate\" [18] by developing a scientific\npeaceful endeavour in the context of a systematic and structured public participation process. To this\nend, the feasibility study phase laid the foundation for the implementation of an approach in line with the\nregulatory frameworks and the best practices in France and in Switzerland. The approach goes beyond\ninforming the public, engaging affected stakeholders in the discussion of the various segments of the\nproject and, as far as possible, involving them in design. considerations that affect their territory. A\nconsultation process will therefore be carried out in an equitable manner on both sides of the border,\nrespecting the approaches and procedures specific to each country.\nThe scenario development process first used the bibliographic information available. It gradually\nintegrated further aspects as they became relevant and stakeholders as they were identified. This is the\n70\n\nImpacts of the\ninitial project\nscenario\nUnavoidable \nimpacts\nAvoidance\nmeasures\nResidual impacts\nReduction\nmeasures\nResidual impacts\nCompensation\nmeasures\nNet gain\nGain\nLoss\nInitial state\nof the\nenvironment\n> Development of the project scenario >\n\u2022\nAvoid:\nModify the project to suppress a negative impact.\n\u2022\nReduce:\nReduce as much the extent, duration and/or intensity of an impact that cannot be avoided.\n\u2022\nCompensate: Contribute with direct or indirect positive values to noteworthy negative effects that cannot\nbe avoided and sufficiently reduced.\nFig. 2.1: The \"avoid-reduce-compensate\" approach, known as \"\u00c9viter-r\u00e9duire-compenser (ERC) in\nFrance and anchored in the French environmental law that determines the project authorisation pro-\ncess.\ncase, for example, for the participation of local elected representatives (municipalities, intercommunal\nstructures, departments, regions). Depending on the layout, the number of surface sites and their loca-\ntion, between twelve and twenty communes were at any time directly concerned and had to be consulted.\nA further 30 or so municipalities could be indirectly affected, in terms of access needs or infrastruc-\nture connections, or simply because the tunnel passes under their territory. Other stakeholders will need\nto be added for the development of a detailed design scenario. These additional stakeholders include\nlocal infrastructure operators (e.g., water, canals or road networks), representatives of local authorities\nresponsible for certain subjects (e.g., traffic and nature) and associations (hunting, fishing, tourism, envi-\nronmental protection, heritage preservation, economic development, etc.). It is prudent to approach these\nrepresentatives as soon as the likelihood of their community being affected in some way is sufficiently\nhigh, i.e., when a specific scenario and an intent for a project exist. In this way, their availability to be\ninformed about the project vision can be taken into account, the relevant contacts can be designated and\nthe limited availability of the study group members can be taken into account. This study has involved\nselected elected representatives of directly affected locations. A systematic involvement of a wider do-\nmain of stakeholders is potentially appropriate at a subsequent phase, when a project intent is formulated\nand when a reference scenario that permits a useful involvement exists.\nThe international standards applicable, NF EN ISO 14001 (environmental management [19]) and\n(for eco-design) NF EN ISO 14006 [16] (see Fig. 2.2) require an iterative approach.\nThis approach is also set out in greater detail in the good practices guidelines for environmen-\ntal impact assessments, established by the French Ministry for the Ecological Transition, Biodiversity,\nForests, Marine Affairs and Fisheries, and in the NF EN ISO 31000 [20] standard on risk management\n(page 8 of the ISO standard) (see Fig. 2.3).\n71\n\nFig. 2.2: The Plan-Do-Check-Act approach for environmental management, defined in standard NF EN\nISO 14001, section 0.4, page vii, is the basis for \u2018eco-design\u2019.\n(1)\nEngage\nthe\npublic\nin the\ndevelopments\n(2) Identify the environmental\nstakes and challenges\n(3) Develop \nvariants and \nscenarios\n(4) Analyse \nthe initial \nstate\n(5) Assess \npotential \neffects\n(6) Improve \nusing Avoid-\nReduce-\nCompensate\n(7) Accompany and monitor the \nconstruction and operation\nFig. 2.3: Diagram from iterative impact study, French Ministry of Territorial Development and the En-\nvironment, 2001, p. 27, see footnote 6). Although this guide is from 2001 and specific regulations have\nchanged, the principles described in the diagram are still valid and recommended for use today.\n2.2.2\nIterative process\nThe scenario development process is based on the iterative Plan-Do-Check-Act (PDCA) approach, and\nincorporates the Avoid-Reduce-Compensate (ERC) approach.\n72\n\nThe process starts at a macroscopic level to identify the major constraints and opportunities. The\nconstraints are recorded in a geographical information system (GIS) so that a map-based identification\nof areas to be avoided and areas in which a surface site or a subsurface passage would need to be limited\ncan be rapidly identified. Such a system includes many data layers. Today, GIS-based Environmental\nInformation System (EIS) for the FCC study comprises more than 120 layers that contain detailed in-\nformation and are also used to build summary layers that are colour coded as shown in Table 2.1. The\nindividual territorial sensitivity grid levels differ for French and Swiss territories [21]. They are based\non national legal and regulatory constraints and concern particular regional and local constraints that are\nthe result of exchanges with expert companies in the areas of environmental impact studies and project\ndevelopment as well as with public administration services. Typically, the constraints considered for\nthe development of the future collider layout and placement scenario are highly conservative and some-\ntimes exceed required legal and regulatory constraints in several domains to ensure that good territorial\ncompatibility can be achieved by respecting known local and cultural heritage.\nScenarios were explicitly checked against such different interest zones, and a weighting took place\nwhether to continue considering locations with known constraints or to discard the scenario due to its\nparticular local high-value nature. The same strict constraint was applied to enlarged drinking water\nperimeters that were excluded as surface site locations, despite the fact that from a regulatory point of\nview, surface site constructions would be allowed in such zones.\nTable 2.1: Definition of the territorial sensitivity levels, representing constraints for determining the\nconfiguration and location. Each colour-coded level represents several data layers that can be shown on\na map in a geographical information system (http://cern.ch/fcc-sensitivity-grid).\nLevel\nDesignation\nDescription\n4\nUnacceptable\nThe level of constraint is such that the zone cannot be considered for a\nsurface site. These zones are considered to be exclusion zones and should\nbe avoided.\n3\nHigh\nThe zone is not recommended for the location of a surface site, but may be\nconsidered if it is decisive for the feasibility of the project, with additional\nreduction, compensation, or mitigation measures.\n2\nAcceptable\nThe zone is acceptable for the location of a surface site with appropriate\nreduction, compensation or mitigation measures.\n1\nLow\nThe zone can be considered for a surface site without further significant\nmeasures. Compensation may still be necessary.\nThis step permits the definition of entire classes for particle collider layout and placement candi-\ndates. Picking a representative candidate of a class permits the choices between the various configura-\ntions and locations under consideration to be progressively refined, introducing additional information\nobtained from the study of promising variants and discarding variants as soon as obstacles are detected.\nIf a scenario is discarded, the main exclusion reasons are analysed and the entire class of scenarios is\nanalysed with respect to those conditions. In many cases, this permits the elimination of an entire class of\nscenarios and the establishment of major exclusion criteria and constraints at the macroscopic level. The\napproach helps to reduce the solution space and to avoid further consideration of unfeasible scenarios in\nthe subsequent steps.\nScenarios that are considered potentially feasible are further analysed with more detailed informa-\ntion and further stakeholders are involved. The same elimination process as above is applied.\nThis approach leads to a gradual definition of exclusion criteria and zones, and to a selection of\nlikely layouts and placements that can eventually be optimised.\n73\n\nWith regard to the territorial analyses, the analysis process begins at a level that considers to-\npography, bathymetry, geology, hydrography, protection zones and urban development. It then gradually\nexpands to include additional aspects such as accessibility, transport, disturbances, potentially conflicting\nplanned developments and the availability of technical and natural resources (e.g., electricity or water).\nIt then incorporates additional elements, such as social factors, local preservation and development ob-\njectives, visibility, shared visibility, or disturbances for stakeholders affected directly (e.g., neighbours)\nand indirectly (e.g., communities affected by construction site traffic).\nThe scenario-building process requires a more detailed analysis phase, aimed at the direct par-\nticipation of stakeholders and local players in order to draw up a scenario adapted to the specific plot\nof land, always taking into account the three main issues (science, territory, implementation) within the\nframework of the iteratively improving avoid-reduce-compensate project development approach.\nWith the choice of a reference scenario as a prerequisite for field studies, environmental impact\nassessment, and technical design work, also the dialogue with public stakeholders could be gradually\ndefined and initiated. Considering the valuable accompaniment of the two CERN host states and their\nadvice in engaging the public in territorial development projects, the study collaboration requested CERN\nto consult the French \"Commission nationale du d\u00e9bat public (CNDP)\" (english: National Commission\nfor Public Debate) in 2024. A first analysis resulting in a list of recommendations were made public on\n6 March 2025 [22]. Taking account of these recommendations and considering the trans-border context\nof the particle collider scenario, it was decided to extend the collaboration with the CNDP to prepare\nsubsequent public engagement processes in case the international science collaboration expresses an\nintent to develop the study into a project and to enter a preparatory phase.\nInformal and formal processes engaging the public are ideally carried out as early as possible,\nand the French government reminds the principle and need of anticipation on various occasions. At the\nsame time, care must be taken to time engagement appropriately. This approach aims at assuring that the\nproject scenario can be adapted based on the involvement of stakeholders and having sufficient technical\ninformation at hand to inform he engaged stakeholders about the needs and constraints that govern the\nproject and the environment in which it would eventually be embedded.\nAs new information is integrated into this iterative process, automated and cartographic research\nmust be progressively completed, followed by manual research, interviews with people with good knowl-\nedge of the region, field visits and consultation with stakeholders (see Fig. 2.4).\nHigh level bibliographic and cartographic analysis. Semi-automated search.\nManual cartographic analysis of the surface and the subsurface 3D \nmodel, consultation of relevant geographical information systems, \nurbanistic and regional planification documents.\nDirect exchange with regional and local stakeholders \n(e.g. departments and municipalities), terrain and \nenvironment studies and subsurface investigations \ncarried out by expert companies.\nConsultation of regional and local public administration services \nin the two host states (e.g. DT and DDT), taking into \nconsideration of transport, resource, networks, local aspects. \nGathering of complementary information with field visits.\nStart\nFig. 2.4: As the layout and placement studies progress, additional information and stakeholders are\nincluded in the process to create a balanced scenario that meets the needs of all stakeholders.\n74\n\n2.2.3\nScenario assessment\nTo determine the value of a scenario, to assess if it should be further optimised or discarded and to be\nable to compare the merits of different scenarios among each other, a multi-criteria analysis scheme has\nbeen developed, based on an approach presented by the French organisation Cerema in its guidelines for\nthe environmental analysis of linear transport infrastructures [14]. This approach was completed using\nthe UNIDO International Guidelines for Industrial Parks, published in November 2019 [15].\nAs required by the regulatory environmental authorisation frameworks in France and Switzerland,\na development project is to be considered in broad terms, extending the analysis to various non-technical\nrelevant aspects such as indirectly affected stakeholders; legal, regulatory, social and economic factors;\nnetworks (roads, railways, water, electricity, canals, public service and safety infrastructures); heritage\nsites; visual aspects; disturbances (noise, dust, light, smells, pollution) and potential benefits. As recom-\nmended in the Cerema guide, this approach was used to assess the relative merits of each variant, and\ncontribute to the development of reduction, compensation, and support measures in an open and transpar-\nent process. In Switzerland, and more specifically in the canton of Geneva, a parallel can be drawn with\nthe cantonal guide for the strategic environmental assessment tool (EES) [23]. When plans, programmes\nor projects (PPPs) are drawn up, the EES is sometimes used to ensure that environmental and human\nhealth issues are taken into account systematically and at an early stage, as defined in the Environmental\nProtection Act [24]. As such, it can be used as a decision-making tool, assessing the merits of different\nscenarios.\nThe multi-criteria analysis results use standardised qualitative indicators to compare the suitability\nof different scenarios. Its application during the scenario-building process makes it possible to quickly\nidentify the types of scenarios that present significant advantages or disadvantages, and to determine\nwhether the differences between the scenarios are major or minor. This approach also offers the advan-\ntage of clarifying which elements have the greatest or least influence on the value of the scenario, and\nthus guides the development of new types of scenarios. This approach is then used in the subsequent\noptimisation stages, for example with regard to moving shaft and surface sites to more suitable locations\nand taking into account the availability of existing infrastructures (e.g., roads, railways, water supply\nand treatment, electricity), urban planning documents (PLU, PLUi, PADD, SCoT, PDcn, PDcom) and\nsynergies and opportunities (e.g., supply of residual heat, sharing of technical infrastructures, reduced\ntransport distances).\nThe criteria list is made up of nine topics, each comprising several detailed criteria. These criteria\ncover the various themes that are relevant for an implementation. 32 environmental factors, the scenario\nconfiguration determining the performance for scientific research, implementation costs and risks were\ntaken into account:\n1. Land status\n(a) Availability of plots\n(b) Clearly defined ownership\n(c) Plot price\n(d) Acquisition time and expected difficulties in obtaining rights\n(e) Plot development cost\n2. Road connections\n(a) Distance from transport, industrial and other infrastructures\n(b) Distance from populated areas\n3. Raw materials and services\n(a) Availability of raw materials for construction and resources for operation\n(b) Proximity to service providers\n75\n\n4. Physical characteristics\n(a) Plot size and shape\n(b) Topography\n(c) Shaft depth\n(d) Drainage and sanitation requirements for construction\n(e) Surface soil condition\n(f) Water resources\n(g) Accessibility\n(h) Subsurface conditions (physical)\n(i) Subsurface conditions (regulatory)\n5. Infrastructure\n(a) Accessibility of electrical power\n(b) Communication network\n(c) Water for industrial use\n(d) Drinking water\n(e) Waste water discharge, rainwater collection, disposal and treatment points\n(f) Temporary storage and processing areas during construction\n6. Environmental and social factors\n(a) Existing environmental constraints\n(b) Fauna and flora\n(c) Existence of construction constraints\n(d) Adjacent constraints\n(e) Disturbances\n(f) Availability and accessibility of workforce\n(g) Involvement of local authorities\n(h) Support from civil society\n7. Configuration\n(a) Geometry\n(b) Size\n(c) Transfer lines\n8. Implementation cost\n9. Risks related to the implementation\nFor each scenario, six sets of criteria were evaluated individually for each of the surface site\ncandidate locations for the surface sites in that scenario (land status, road connections, raw materials and\nservices, physical characteristics, infrastructure, environmental and social factors) and three high-level\ncriteria were considered for the overall scenario (configuration, costs, and risk).\nSpreadsheets for each scenario were created to assign each criterion a qualitative score between -2\nand +2, according to a pre-defined evaluation grid with standardised conditions. A score of \u20180\u2019 represents\na neutral assessment of the indicator. For each high-level criterion, the scores of its sub-criteria were\nadded together to provide an indicator for that criterion. The spreadsheet also shows the macro-criteria\nscores, and presents a final score for all criteria in the form of a percentage between 0 and 100. Lastly,\nthe values of the criteria are synthesised to provide indicators for 1) scientific excellence, 2) territorial\n76\n\naspects and 3) appropriateness of project implementation. This approach not only makes it possible to\nquickly estimate the value of a scenario and compare it with others, but also to highlight criteria that are\ninsufficiently known and require in-depth study.\nValues were assigned for the qualitative indicators through a collaborative process by the mul-\ntidisciplinary team, based on bibliographic and cartographic studies, database analysis, geographical\ninformation system queries, simulation and modelling. There were also field trips and field investiga-\ntions; interviews to discuss the most suitable footprint with staff from the administrative departments\nof the two host states (e.g., DT, GESDEC, OCEV, OCAN, OCT in Switzerland; DDT 01 and DDT 74\nin France); consultation with experts working in different technical fields (Cerema, Ecotec, HydroG\u00e9o,\nILF, GADZ, particle accelerator designers working in many partner institutes, geologists employed in\nmany partner universities); and feedback from local players during working meetings with municipali-\nties, inter-communal entities, and elected representatives.\nA disadvantage of this approach is that it simply adds up and averages all values. In some cases,\nthere may be an obstacle related to territorial or scientific aspects or to project implementation. However,\naveraging means that a single low value will just lower the overall ranking but will not necessarily\nshow the blocking point in the summary. The multi-criteria analysis was therefore complemented by\nan overall assessment of the scenario, which permitted the highlighting of the potential benefits of one\nscenario that make it particularly preferable to others or which indicate whether the scenario is difficult\nor not feasible. Thus, scenarios presenting obstacles continue to be analysed and recorded, but they\nare rejected even if the value of a thematic indicator (scientific performance, territorial compatibility\nor project implementation) is higher than the acceptable threshold value for that element. Examples\nof such situations include the strong probability of encountering geological features that would expose\nthe project to an unacceptably high risk (karst, potentially conflicting water-bearing layers, crossing a\nmajor fault, presence of high-pressure aquifers), patrimony sites that represent incompatibilities with a\ntechnical installation, too dense residential zones, incompatibilities with local or regional development\npolicies, a collider circumference that would not allow the scientific research programme to be conducted\nfor technical reasons or would not allow its operation to be viable (for example, a collider circumference\nsignificantly smaller than 90 km). The ranking is highlighted in summary diagrams such as the one\noutlined as an example in Fig. 2.5. The illustration also shows the limitations of multi-criteria analysis:\nfor example, two surface site locations in the PA0 scenario with twelve sites developed during the first\nexploratory phase are located in areas considered to be blocking points, but this is only visible in the\nindividual sheet for each site. The three-column summary alone, however, does not show these exclusion\ncriteria and must, therefore, be supplemented by a brief text description.\nTerritorial (T), implementation(I), and scientific (S) issues can, in fact, be easily visualised and\ncompared thanks to this standardised qualitative approach. Figure 2.6 highlights the merits of the cur-\nrent scenario working hypothesis PA31, which makes it a preferred scenario for the detailed territorial\nand technical analysis. Such overviews also helped to understand that scenarios involving twelve sites\ndo not meet the required conditions to undergo an in-depth study. The approach permitted further op-\ntimisation by understanding how the improvement on one site could potentially lower the performance\nof another and thus retain scenarios for further optimisation that improved all sites individually and the\nentire scenario as a whole.\nWith additional information becoming available, the assessment changes and therefore further\noptimisation of the scenario will be required until a decision to proceed with a construction project can\nbe taken. The advantage of the systematic approach is that it permits the demonstration that there is a\ncontinuous improvement of the project scenario based on the growing understanding of the boundary\nconditions and the consideration of stakeholder input during an environmental evaluation and project\nauthorisation process.\nAround a hundred different scenarios have been developed and individually analysed (see Fig. 2.7).\nEventually, the ten most promising scenarios (PA0-0.1, the scenario developed for the Conceptual De-\n77\n\nFig. 2.5: Example of a summary view of the multi-criteria analysis of an scenario (PA0-0.1). The scenario\nseems feasible, even if the territorial feasibility would be low. However, a closer look at each site reveals\nmany blocking points.\nFig. 2.6: : Summary of the multi-criteria analysis of reference scenario PA31-4.0.\nsign Report, turned out to be not feasible and serves as a performance reference baseline only) have\nbeen retained for a review with experts from different project development domains. The scenarios were\nranked using the VIKOR [25] quantitative method that was applied to the established multi-criteria anal-\nysis (see Fig. 2.8). The algorithm permits the evaluation of different multi-criteria factors with different\nunits and scales and with different, potentially even conflicting, minimisation and maximisation goals.\nThe following VIKOR criteria were set for the establishment of the ranking:\n1. Number of sites: An eight-site configuration offers four interaction points for the lepton collider,\ncompared with just two interaction points for the twelve-site configuration. Therefore, the goal\n78\n\nFig. 2.7: : Around one hundred different layout scenarios were studied and individually analysed.\nwas to minimise the number of sites with a weight contribution of 5%.\n2. Total length of curved sections: A longer circumference length provides higher scientific perfor-\nmance or simpler design. Therefore, the goal was to maximise the circumference with a weight\ncontribution of 5%.\n3. Territorial compatibility: Territorial compatibility, ease of implementation and scientific perfor-\nmance are given equal weights of 30% each. Each of these three pillars must be maximised, and all\nthree need to be balanced to ensure the feasibility of the scenario. The feasibility of each scenario\ncan only be determined through detailed analysis.\n4. Compatibility of technical implementation and construction with geological constraints, con-\nfiguration, and layout: Maximise with a weight of 30%.\n79\n\n5. Scientific performance, taking into account the configuration and technical difficulties of the\nscenario: Maximise with a weight of 30%.\nThe result was that the most promising scenario is an 8-site layout with a total circumference of the\norder of 91 km. This scenario gave sufficient residual margins for further optimisations. Meanwhile, all\nthe other scenarios developed are no longer considered feasible, either because of the loss of site locations\nduring the study years, because of unacceptable incompatibilities with territorial or geological conditions,\nor because their scientific performance is not sufficient to attract researchers from all over the world\nover the long term. Therefore, PA31 was considered for further detailed studies, in particular involving\nsubsurface investigations and detailed field studies concerning environmental aspects. Optimisations\nlead to the versions 3.0 and 4.0 for which the performance is also displayed.\n# Scenario \nNumber \nof sites \nArc length \n[km] \nTotal circum-\nference [km] \nResults of multi-criteria analysis \nT1) \nI2) \nS3) T1) \nI2) \nS3) Summary4) \nVIKOR5) \n1 PA0-0.1 \n12 \n83.750 \n97.750 53 \n75 \n83 \nD \nB \nB \nD \n7 \n2 PB17-0.8 \n12 \n81.193 \n96.093 58 \n81 \n79 \nC \nB \nB \nC \n4 \n3 PB19-0.3 \n12 \n77.784 \n91.324 69 \n25 \n63 \nC \nE \nC \nC \n11 \n4 PA21-0.3 \n8 \n82.045 \n95.845 80 \n37 \n65 \nB \nE \nC \nB \n5 \n5 PA38-0.1* \n12 \n75.228 \n89.228 57 \n81 \n67 \nC \nB \nC \nC \n9 \n6 PA33-0.13 \n8 \n79.377 \n93.377 50 \n81 \n83 \nD \nB \nB \nD \n8 \n7 PA35-0.6 \n8 \n78.637 \n92.637 54 \n75 \n83 \nD \nB \nB \nC \n6 \n8 PA37-0.3 \n8 \n80.823 \n94.823 54 \n62 \n53 \nD \nC \nD \nD \n10 \n9 PA31-1.0 \n8 \n76.932 \n91.172 74 \n87 \n80 \nB \nA \nB \nB \n3 \n10 PA31-3.0 \n8 \n76.929 \n90.658 76 \n87 \n78 \nB \nA \nB \nB \n2 \n11 PA31-4.0 \n8 \n76.929 \n90.658 78 \n87 \n78 \nB \nA \nB \nB \n1 \n1) Territorial compatibility, 2) Ease of project implementation, 3) Scientific performance, \n4) Ranking according to multi-criteria analysis, 5) Value of multi-criteria analysis according to the VIKOR method. \n*) The total length of the curved sections is considered to be too short. \nFig. 2.8: Multi-criteria analysis based ranking of the most promising implementation scenarios in 2022\nwith the performance of the gradual improvements of reference scenario class PA31.\n2.3\nRequirements and invariants\n2.3.1\nScience and technology motivated requirements\nLayout\nA set of parameters fundamental to particle accelerator design makes up the starting requirements for\nscenario development. The design parameters determining the overall size of the configuration cannot be\nchosen arbitrarily. These parameters include the geometry of the configuration (for example, a symmetry\nor periodicity of sectors involving a specific number of surface sites), the length of the basic curved cells,\n80\n\ncalled \u2018arcs\u2019 (which repeat like the parts of a chain, to build the curved sectors), the number of arc\naccelerator cells to be repeated and the lengths of the various types of straight sections between the\narcs. Figure 2.9 shows two basic configuration geometries used in configuration and layout studies.\nThe first geometry (image on the left) serves as a starting point: it groups together three experiment\nsites in the upper part of the geometry. It offers greater freedom in terms of moving the various surface\nsites but requires twelve surface sites. The second geometry (image on the right) represents the current\ndevelopment: the four experiment sites are evenly distributed (top, right, bottom, left), and only eight\nsurface sites are required. However, the freedom to move sites is less than with the first geometry.\nThe following requirements were initially set and had to be adapted during the development of a\nscenario that aimed at satisfying the territorial implementation constraints.\nFig. 2.9: Two different collider layouts. The image on the left shows a configuration comprising twelve\nsites based on a geometry with mirror symmetry. The image on the right shows an eight-site configuration\nbased on the repetition of a basic sector module. The arcs (blue) are separated by straight sections (green\nand red segments).\nThe initial simple mirror symmetry was discarded in favour of a 4 times repetition of a 90\u25e6sector,\ni.e., a four-fold symmetry. The initial configuration (12 sites) made it possible to group 3 experiment\nsites close to each other near the main CERN site, leading to shorter distances between surface sites and\ngreater flexibility to lengthen and shorten the north and south sides. The current geometry (8 sites) en-\nables a more regular design and thus facilitates performance optimisation processes. The lepton collider\ncan also have four interaction points.\nTotal circumference\nThe initial objective was to design a particle collider infrastructure with a circumference of around\n100 km. A reduction of 10%, to a circumference of 90 km, is considered to be the lower acceptable\nlimit, below which the performance obtained for scientific research would become too limited. The\nsmaller the circumference, the smaller the radius of the curved sections and the more pronounced the\ncurvature, resulting in greater energy losses, leading eventually to an unsustainable scenario from an en-\nergy efficiency perspective and the need for more powerful magnets for the hadron collider, which could\nthen become technologically unattainable.\n81\n\nNumber of surface sites\nThe initial 12 sites were reduced to 8 sites with the advent of the four-fold symmetry layout. It proved too\ndifficult to find a suitable layout scenario with 12 sites featuring intermediate access points compatible\nwith the territorial constraints and risks involved in implementing the project. A scenario with eight sites\noffers less flexibility for the layout study since the fixed interaction sites are geographically opposed.\nStill, the number of necessary suitable locations to be found is lower.\nNumber of interaction points\nFor the hadron collider, both geometries offer the possibility of four interaction points. However, only\nthe four-fold symmetry layout provides the possibility of having four interaction points with the lepton\ncollider. The 12-site scenario also proved difficult due to the need to combine experiments and injection\nat two points (PL and PB).\nArc cell length\nThe hadron collider arc cell length drove the overall circumference of the layout. Initially, a cell length\nof 213.03 m was considered. It was eventually extended to 275.79 m. The total circumference depends\non the multiples of that arc cell length and cannot, therefore, be arbitrarily chosen. In this case, the lepton\ncollider adapts to the more stringent requirement of the hadron collider.\nTotal number of arc cells\nThe size of the hadron collider curve can only be increased or decreased by inserting or removing an\narc cell in each curve. The overall configuration must remain symmetrical. The initial 12 site layout\nrequired 4 sectors of 19 short cells and 4 sectors of 73 long cells. The current 8 site layout requires 8\nsectors with 26 cells, i.e., a total of 208 cells. This requirement determines the total circumference of\nthe infrastructure. In this case, the lepton collider adapts to the more stringent requirement of the hadron\ncollider.\nTotal arc length\nThe 12-site configuration featured four short arcs and four long arcs. The long arcs were too long to\nremain without intermediate access points for technical and personnel safety reasons. Therefore, an\nadditional site had to be placed at the midway point, at a distance of around 8 to 10 km from each end.\nThe 8-site layout no longer has this requirement. The total arc length should, however, permit safe\noperation and the possibility to evacuate personnel in case of emergency efficiently. The current distance\nbetween access sites of about 11.5 km is considered acceptable.\nRadio frequency system harmonics\nThe stability and performance of the radio-frequency system used to accelerate the subatomic particles\ndepend on the circumference of the collider. It also concerns the transfer of particle beams from the\nexisting SPS and LHC tunnels. For a 91 km long collider, 3 possibilities have been identified, which\nprovide sufficient flexibility for the radiofrequency system design. A collider with a circumference of\nbetween 90.7 and 90.8 km is the best option. A length of 90.6 km is feasible but reduces the frequencies\nof the cavities in the radiofrequency system more than the others. In this case, the lepton collider adapts\nto the more stringent requirement of the hadron collider.\nLength of straight section at interaction points\nAt least 700 m are needed on either side of the interaction point to focus the collider beams to be able\nto achieve the high beam densities needed for high luminosities. The two colliders (lepton and hadron)\n82\n\nhave different space requirements for crossing the two beam lines, so the tunnel needs to be widened by\naround 10 m to a distance of 1400 m on either side of the interaction point.\nLength of straight section at radiofrequency locations\nA distance of 2800 m between 2 straight sections was initially deemed adequate to accommodate the\nradiofrequency equipment that accelerates the beams. After various equipment integration studies, it\nwas found that this value could be reduced. A distance of 2030 m is now considered the acceptable lower\nlimit required for the systems and the integration of the ancillary equipment.\nCooling water requirements\nWith the aim of conserving resources responsibly, ongoing studies have already helped to reduce re-\nquirements from an initial 4.9 million m3 per year to a range between 1.6 millionm3 (Z mode) and\n3.0 million m3 per year (t\u00aft mode). Further reductions can be expected due to the inclusion of the con-\ncept of heat reuse, taking into account technological developments and the development of water reuse\nsynergies.\nElectricity requirements\nInitial powering requirements of the lepton collider ranged between 1.2 and 2.0 TWh per year, depending\non the operation mode. Gradual advances in the concept development reduced these values to a range\nbetween 1.0 and 1.77 TWh per year. Since the current scenario has four interaction points rather than\ntwo, further reductions are possible by limiting the radiofrequency power if a reduction of the annual\nintegrated luminosity is acceptable for the scientific research programme. Further optimisations are to\nbe expected from an adaptive operation concept and energy consumption reduction of systems that are\npowered down or set to an energy-saving mode when not required for operation and maintenance.\nFor the hadron collider, an initial annual energy consumption estimate was based on current su-\nperconducting magnet technology at very low cryogenic temperatures. This estimate has been revised\nby developing a design that works at higher cryogenic temperatures to allow significantly lower en-\nergy consumption. Leveraging a high-temperature superconducting magnet technology would allow the\ncryogenic operation temperature to be further increased. Together with adapting the operation plan and\nintroducing an annual energy consumption ceiling, this would bring the annual energy consumption into\nthe range of the lepton collider. However, a focused R&D programme is required to develop the tech-\nnology. A window of opportunity in the range of more than 35 years is available to achieve this goal if a\ndecision to proceed is taken.\nSpace requirements of technical surface sites\nThe space requirements of the technical surface sites are determined by the technical infrastructures that\nboth particle colliders will need. Although the lepton collider has significantly fewer requirements than\nthe subsequent hadron collider, the surface sites must be able to host the additional equipment that will\nonly be put in place for the second phase.\nThe minimum equipment required on each site comprises an electrical substation, power con-\nverters to drive the particle accelerator equipment for the sectors in both directions of that site, power\namplifiers where there is a radiofrequency system, tunnel and cavern ventilation, raw water-based accel-\nerator cooling systems, raw water treatment systems, heat exchangers and refrigeration towers. Since the\nactual design of the particle accelerator is yet to come, it is challenging to estimate the space require-\nments for such systems. Therefore, the most advanced systems are used as a reference to estimate the\nspace requirements.\n83\n\nIn addition to the technical systems, space is required for temporary storage of the particle accel-\nerator systems to be installed underground and for the handling of the technical systems at the surface. In\nthe case of sites with a cryogenic refrigeration system, space is required to store the cryogens (liquid and\ngaseous helium as well as nitrogen). While the lepton collider will require only two sites with relevant\ncryogenic refrigeration systems for the radiofrequency systems, each site will host a cryogenic refriger-\nation plant for the hadron collider. Additional minor space requirements emerge from the roads on the\nsite, such as the need to provide limited office space and storage of spare parts, cranes, and handling\nequipment.\nThe working hypothesis is that in the order of 100 technicians and engineers per day can be\npresent during installation, major maintenance and upgrade interventions. During the operation phase,\nthe presence of personnel is limited to the strict minimum, leveraging remote operation and intervention\nas much as possible. No permanent presence of personnel is planned during ordinary operations.\nThe current lepton collider net space requirements for construction elements on technical sites\nare: 2.2 ha for PB, 2 ha for PF, 4.4 ha for PH and 2.6 ha for PL. Additional space is required for the\nhadron collider cryogenic refrigeration plants and cryogen storage, as well as for additional technical\nequipment. Including the requirements for green buffers and landscape integration bring the requirements\nto about 3.5 ha to 4 ha for the technical sites PB, PF, PL. About 8 ha are required for PH due to the\ninitial large cryogenic refrigeration system and the topographical challenges that call for a terrace-based\nlandscape integration. The indicated space requirements do not include the requirements emerging from\nthe need to accommodate the different topographical constraints, the need for green buffers and landscape\nintegration. Hence, the specific local requirements are higher.\nSubsequent architectural designs and landscape integration will aim to reduce land consumption\nas much as possible.\nSpace requirements of experiment surface sites\nIn addition to the requirements of the technical sites, each experiment site also requires a pre-assembly\nhall for the experiment detector. To limit the surface space requirements, the working hypothesis is that\nthe detector will be assembled underground. However, elements will need to be quality checked, pre-\nassembled and tested on the surface in a hall that measures about 1250 m2. Sufficient space of about\n1000 m2 for handling of parts and a temporary buffer for magnets to be installed is also required.\nAn experiment site typically also hosts a data centre, workspace for a group of about 50 scientists\nand engineers, meeting rooms and a few offices, small workshops, a data centre and visitor facilities.\nFor the hadron collider, the largest detector part, a superconducting magnet coil, cannot be trans-\nported directly to the sites. It needs to be manufactured on-site. For this process, about 7500 m2 are\nrequired in addition to each surface site. The space will remain untouched by construction during the\nfirst, lepton collider, phase, and it will be rewilded after the assembly and lowering of the magnet coil at\nthe end of the hadron collider installation phase.\nThe working hypothesis is that up to 300 scientists, technicians, and engineers can be present per\nday during installation and major maintenance and upgrade interventions. During operation, only a small\nteam of less than 20 people would be present on site. Additional personnel would be present to operate\nthe visitor facilities.\nThe current lepton collider net space requirements for construction elements on scientific sites are\nlisted below. 3 ha for site PA due to the possibility of leveraging the space of the existing LHC surface\nsite Pt8. Including the temporary space required for the production of the superconducting magnet coil\nof the hadron collider experiment, the space requirement increases to about 4 ha. The sites PD, PH and\nPJ require about 4 ha for the lepton collider phase and 5 ha for the hadron collider phase. The space\nrequirements indicated do not include the requirements emerging from the need to accommodate the\ndifferent topographical constraints, the need for green buffers and landscape integration. Hence, the\n84\n\nspecific local requirements are higher.\nSubsequent architectural designs and landscape integration will aim to reduce land consumption\nas much as possible.\n2.3.2\nInitial invariants\nA set of invariants was established in the beginning to guide the development of an implementation\nscenario to ensure that a minimum set of criteria concerning scientific excellence, territorial compatibility\nand project risk control can be satisfied. They are a combination of avoidance and reduction constraints,\ngoals and high-level requirements.\n\u2013 Avoid karstic limestone formations, risks of high-pressure water penetration, known major faults\nand areas of seismic instability, as well as significant overburden.\n\u2013 Place the underground structures in the molasse layer as much as possible.\n\u2013 Provide a technically feasible connection to CERN\u2019s SPS underground infrastructure and, if pos-\nsible, to the LHC infrastructure.\n\u2013 Dig the tunnel to a sufficient depth below the lake bed to ensure stability and long-term low main-\ntenance. The alignment can be optimised by identifying the minimum depth based on subsurface\ngeophysical and geotechnical investigations for a preferred scenario. The current assumption is\nthat the tunnel alignment crossing the Geneva lake is 100 m below the lake bed.\n\u2013 Dig the tunnel deep enough under the Arve, Rh\u00f4ne and Usses rivers to guarantee the micro-stability\nrequired for precise alignment of the accelerator and to avoid adverse effects with any, potentially\nexisting, surface constructions.\n\u2013 Limit overburden under the Mandallaz, Filli\u00e8re and Bornes zones (minimum depth to be defined\nby specific subsurface investigations).\n\u2013 Avoid elevations above 750 m for surface sites to limit the depth of shafts and ensure good site\naccessibility.\n\u2013 Aim for shaft depths of less than 250 m for scientific sites and 400 m for technical sites to avoid\nexcessive challenges for the installation of the accelerator equipment and the experiment detectors.\n\u2013 Avoid areas considered \u2018exclusion zones\u2019 in an established territorial sensitivity grid drawn up\nwith contracted organisation Cerema, Direction D\u00e9partementale du Territoire in France, collecting\ninformation from the Direction R\u00e9gionale de l\u2019Environnement, de l\u2019Am\u00e9nagement et du Logement\nand with contracted company Ecotec in Switzerland with additional information collected from\nthe cantonal DT services. This grid lists environmental, spatial planning, zoning and strategic\nconstraints, as well as public health and safety constraints with different relevance levels that lead\nto the definition of zones to be avoided and zones at surface and subsurface constructions will need\nto be limited if they cannot be avoided.\n\u2013 Give preference to proximity to strategic project infrastructures (e.g., grid power lines, certain\ntypes of roads, autoroute stations, railway lines) and stay clear of certain other infrastructures\n(e.g., geothermal probes, gas pipelines, oil pipelines).\n\u2013 Remain outside of town and village centres and hamlets to limit potential nuisances associated\nwith the construction and operation activities.\n\u2013 As far as possible, avoid areas subject to a set of less critical territorial constraints, and if avoidance\nis not possible, reduce surface areas in these zones.\n\u2013 Respect the fact that it is not possible to individually displace the locations planned for scientific\nsites where particle beams cross and where the experiment detectors are located.\n\u2013 Respect the limits for displacing technical sites along the straight sections of the ring within the\nlengths of those sections, according to the possibilities offered by the various technical systems\nrequired at the technical sites for the operation of the accelerators.\n85\n\n\u2013 Consider the constraint for positioning the shafts inside the ring to facilitate access to the transport\nzone in the tunnel.\n\u2013 Limit the length to around 400 m for the horizontal connection tunnels from the technical sites to\nthe shafts inside the ring. Building a longer tunnel is not out of the question, but it would entail\nadditional costs and difficulties.\n\u2013 If technically possible, limit the total occupied surface area of technical sites to 5 ha and the surface\narea of experiment sites to 8 ha. These areas include buffer zones, storage, and transport areas\nand take account of rewilding, reconstitution, replacement, or compensation measures. Wherever\npossible, seek synergies with existing infrastructures to reduce surface areas.\n\u2013 Avoid areas with difficult topography (steep and potentially unstable slopes, unstable soils, areas\nat risk of flooding, discontinuous terrain).\n\u2013 Ensure adequate road connections (7 m wide, 2 lanes, 20 m curvature radius, gradient well below\n10%, minimum clearance height of 4.4 m, compatibility with heavy goods vehicles of 44 t to the\nmain road network in accordance with article R312 of the French highway code).\n\u2013 Maintain a minimum distance of 100 m between residential areas and sites. Depending on topo-\ngraphical conditions and the site\u2019s noise and visibility attenuation features, this distance can be as\nmuch as 250 to 300 m.\n\u2013 Avoid protected agricultural areas unless they are essential to ensure technical feasibility.\n\u2013 Avoid natural and historic heritage sites, avoiding shared visibility between the sites.\n\u2013 Preserve the views and landscape protection zones as far as possible.\n\u2013 Avoid rivers and streams (to avoid having to modify or stabilise riverbanks).\n\u2013 Avoid wetlands and strictly protected areas.\n\u2013 Avoid protected forests because of the need to clear them and preserve existing biodiversity and\nbecause of their inaccessibility and topography, unless these areas are essential to ensure feasibility.\nIn the latter case, the land occupation should be limited.\n\u2013 Give preference to areas in proximity to high-capacity power lines (225 kV and 400 kV).\n\u2013 Look for opportunities with a connection or access to the autoroute system.\n\u2013 Look for opportunities with a connection or access to the railway system.\n\u2013 Consider the use of known brownfield sites for the installation of technical infrastructures that may\nbe remote from the sites (e.g., electrical substations, pumping stations, cooling towers) and for the\ndevelopment of compensation areas.\n\u2013 Look for scenarios that enable all surface sites to be reached within a reasonable time (30 minutes\nby car) from strategic service and supply points (e.g., CERN and CNRS/LAPP).\n\u2013 Avoid creating new border crossings and do not consider sites that straddle the border.\n\u2013 Avoid vineyards and areas with fruit trees.\n\u2013 Give preference to public land over private land, undeveloped land over developed land, unused\nland, overused land (special agricultural uses such as vineyards and protected fruit crops) and\nbrownfields.\n2.3.3\nVoluntary objectives\nThe multi-year study also led to the development of voluntary objectives that would help make the project\nmore territorially compatible. They have been taken into account in the evolutions of scenarios and in the\ndevelopment of a preferred layout scenario that serves as a reference, which is presented in later sections\nof this document.\n86\n\nSustainable operation and maintenance\nEnsure that the scenario can be operated and maintained sustainably. To achieve this, relevant technical\nfacilities (high-tech workshops, offices) must be in proximity to the sites. Therefore, give preference\nto scenarios that take advantage of synergies with existing CERN sites and/or are close to the LAPP of\nCNRS/IN2P3.\nProtecting farmland\nLimit the consumption of farmlands in both host states. Avoid protected agricultural areas, unless they\nare essential for feasibility.\nRoad access to surface sites\nTo limit the need to build new roads and to avoid consuming land, surface sites must either be located\ndirectly on existing departmental roads or only require an improvement to existing access roads. If new\nroads are essential, then the requirements should be minimised.\nDisturbances\nLimit direct disturbances for local inhabitants. Avoid proximity to residential areas, visibility, and shared\nvisibility. Avoid locations on roads passing through residential areas. Avoid proximity to natural and\nhistorical heritage sites. Provide means of evacuating spoil by conveyor belt to avoid truck traffic where\npossible.\nLandscape integration\nAim to preserve views and landscape protection zones wherever possible. Specific studies by landscape\narchitects are required for a preferred scenario during a subsequent design phase.\nProtection of water\nAvoid water protection zones, rivers, and streams. Do not take in water from water-bearing layers, and\navoid the use of drinking water for systems that require raw water. Avoid having to stabilise or modify\nriverbanks. Specific studies are required for a preferred scenario during a subsequent design phase.\nForests\nRespect protected forest zones and trees. Limit clearing forests or felling trees in both host countries to\nmaintain biodiversity. Avoid high-quality forest zones whenever possible. Improve climate resilience by\nrestoring impaired forests.\nSynergies\nGive preference to locations that can create synergies with nearby private and public facilities and in-\nfrastructures. This includes, for instance, the availability of emergency rescue stations and fire brigades,\nhospitals, commercial and industrial development zones, food processing companies, infrastructures that\nsupport public works, electricity lines, major transport axes, autoroute service stations, train lines and\nschool development projects. Identify the possibility of supplying residual heat within a 5 km radius,\npreferably to public facilities and major companies and residential housing. This is an approach that has\nalready been put in place by CERN in Ferney-Voltaire and such an infrastructure serves as a demonstrator\nfor the feasibility (see Fig. 2.10). Examples include, but are not limited to, milk processing companies\n(cheese production), hospitals and health service infrastructures, schools, fire brigades, prisons, offices,\nairports, train stations, and leisure facilities (pools and spas). Locating surface sites in the proximity\n87\n\nof public services can lead to tangible added value for the region. For example, the significantly en-\nlarged geographical extent triggered the need to develop an emergency intervention concept based on\ncooperation with regional fire departments and first-aid services. Other locations are particularly suited\nto foresee additional leisure activities around experiment surface sites that feature visitor centres. Ad-\nditional services including exhibitions, restaurants, and meeting facilities have potential for indirect and\ninduced economic value generation, but they need to be agreed with the local stakeholders to integrate\nwith the local economic and tourism development strategies and plans.\naz?J\n/o\n/*\nFERNEY\nVOTTAIRE\nOOOOEnergies\nLe r6seau de chaleur arrive dans votre vi[[e\nUn mode de chauffage\nsimple, 6conomique et 6cologique\nFig. 2.10: CERN powered heat network under construction in Ferney-Voltaire, France.\nReduced need for electrical infrastructure\nTo limit the effects and impacts of infrastructure development for electrical power, give preference to\nscenarios located near substations and high-capacity power lines.\nExcavated materials\nLimit the annually excavated volume of materials excavated and reduce road transport wherever tech-\nnically and economically feasible. Facilitate local reuse. The aim is to keep the volume of materials\nexcavated annually to less than 10% of the volumes generated in each region (Auvergne-Rh\u00f4ne-Alpes in\nFrance: 24.2 Mt in 2021 [26], cantons of Geneva [27] and Vaud [28] in Switzerland: 3.071 Mt in 2022).\nLand use\nThe goal for the scenario development is to develop a scenario that keeps land consumption as low as\npossible by still meeting the needs of the required surface site installations. The scenario development\nprocess avoids protected agricultural spaces, keeps interactions with multiple private landowners for land\nplot acquisition low, as a multitude of negotiations and complicated ownership situations can significantly\nimpact project implementation preparation and lead to unsatisfactory results for them. Consequently,\n88\n\nprioritise the use of public land over private property and steer clear of areas with planned development\nprojects and prefer non-protected agricultural spaces over protected ones.\nThe surface site candidate location in Switzerland is mainly located on publicly owned land. The\nsurface site candidate locations in France concern mainly privately owned land plots, subject to the typ-\nical urbanistic planning evolution. After exchanges with municipalities to determine the territorial con-\nditions and constraints of possible locations for surface sites, CERN asked the Prefect of the Auvergne-\nRh\u00f4ne-Alpes region in France to set aside the land plots to assure their availability for field studies. This\nprocess and the orders signed by the Prefect of the region mitigate the risk of unanticipated use of the\nland plots for other territorial developments for the study time period, permitting a comprehensive and\nexhaustive investigation of the environmental conditions. As a result, the land considered for the surface\nsites will not compete with other emerging projects. The solution was made possible thanks to the sup-\nport of France. It contributes to securing the studies while ensuring compliance with national legislative\nframeworks.\nBiodiversity and nature\nGive preference to sites with low-quality nature characteristics. Through the ERC approach, preserve the\nelements of interest in terms of biodiversity and nature within the perimeter as much as possible. Study,\ntogether with design offices, the existing and projected conditions of the sites concerned, and carry out\nenvironmental, flora, and fauna surveys on the proposed site to identify valuable elements and the site\u2019s\nrole in the ecological infrastructure. Propose appropriate restoration, replacement, and compensation\nmeasures based on the impacts identified by specialist consultants. Maintain or reinforce ecological\ninfrastructure, particularly wildlife corridors.\nThe work on these voluntary goals was also considered during the development of the eco-design\nstrategy and guidelines [29], which all project participants are required to consider during the subsequent\ndesign phase and which is also published in the report on the current state of the environment [30].\n2.4\nTerritorial constraints\n2.4.1\nTerritorial sensitivity grid\nThe development of a territorial sensitivity grid with its four levels (unacceptable \u2018red\u2019, high \u2018orange\u2019,\nacceptable \u2018yellow\u2019, and low \u2018green\u2019) served as a starting point to integrate the territorial constraints into\nthe implementation scenario development from the onset.\nBy applying the \u2018Avoid\u2019 approach, the analysis eliminated all the unacceptable zones to be avoided,\nshown in red (see Fig. 2.11), from the early development stages of the initial scenario at the macroscopic\nlevel. It should be emphasised that, in all cases, the scenario development process also aimed to avoid\nareas already developed if they were considered to be in active use (e.g., residences, farms, parking\nlots, industrial buildings and public infrastructures). Only brownfields or buildings that could be reliably\ndescribed as unused (ruined houses, abandoned industrial warehouses, etc.) were examined on a case-by-\ncase basis. In addition, for all the surface sites taken into consideration, choices have been made to avoid\nclearing protected forests, as well as avoiding the destruction of wetlands and hedgerows in agricultural\nareas.\nZones classified with high constraints, shown as \u2018orange\u2019 were generally avoided (see Fig. 2.12),\nbut a more detailed manual analysis of the underlying rationale for this classification was always con-\nducted to understand whether and under what conditions such a zone might be considered for certain\nparts of the research infrastructure. This step required a more detailed study of the different layers of\nconstraint that make up the overall layers. It also required additional information that the regional and\nlocal planning authorities of the two host states were best placed to provide (for example, the various\noffices of the D\u00e9partement du Territoire and the Infrastructure Department of the canton of Geneva, the\nDREAL, the DDT 74 and the DDT 01 in France).\n89\n\nFig. 2.11: : Zones in the scenario development perimeter classified as to be avoided (\u2018red\u2019). Note that\nthis map does not consider numerous other exclusion criteria such as slopes and high altitudes (see also\nonline at http://cern.ch/fcc-sensitivity-grid).\nIn France, the law of 22 August 2021, on combating climate change and strengthening resilience\nto its effects set a target of zero net artificialisation of soils (also known as ZAN). The ZAN initiative\nis a target set for 2050. It calls on local authorities, municipalities, departments, and regions to reduce\nthe rate of artificialisation and consumption of natural, agricultural, and forest areas by 50% by 2030,\ncompared to the consumption rate measured between 2011 and 2020. A similar instrument for crop\nrotation areas in Switzerland, \u2018surfaces d\u2019assolement\u2019 known as SDA exists.\nThe scenario development follows the regulatory frameworks in both host states regarding land\nuse efficiency. This concerns in particular the consideration of the principle of \"z\u00e9ro artificialisation\nnette (ZAN)\" (english: \"zero net land take\") in France and the principle of the \"Surfaces d\u2019Assolement\n(SDA)\" (english: crop rotation surfaces) in Switzerland. By considering these constraints in the \"avoid-\nreduce-compensate\" based development cycle, they support the development of projects that exhibit a\nhigh degree of territorial responsibility. The SDA imposed constraint was addressed by the development\nof an authorisation process for the territorial development of CERN at the federal level. Concerning ZAN\nit is noted that, on the recommendation of the prefect of the Auvergne-Rh\u00f4ne-Alpes region, the FCC seg-\n90\n\nFig. 2.12: : Zones in the scenario development perimeter classified as to be avoided (\u2018red\u2019) and with high\nconstraints (\u2018orange\u2019). Note that this map does not consider numerous other exclusion criteria such as\nslopes and high altitudes (see also online at http://cern.ch/fcc-sensitivity-grid).\nment on French territory is recognized among European and national large-scale projects (PENE) [31].\nConsequently, the land areas potentially consumed by surface sites would be outside the regional quota,\nin accordance with the decree of May 31, 2024 [32], concerning the national pooling of the consumption\nof natural, agricultural, and forest spaces for projects of major general interest. However, this exclu-\nsion from the regional quota would not exempt the FCC from complying with the principles of land use\nefficiency and compensation. Through its transversal and eco-responsible approach, the study demon-\nstrates its commitment in this area, thus affirming its intention to embed the project in a responsible and\nbalanced dynamic.\nRight from the start of the studies, it became clear that there were no areas with low constraints\nindicated with \u2018green\u2019 colour in the two host countries. The minimum number of constraints in both\ncountries corresponds to the \u2018yellow\u2019 class, i.e., acceptable zones. In addition, Switzerland has special\nrestrictions, imposed at the federal level, for a certain type of agricultural land, known as crop rotation\nareas (SDA), the best arable land in Switzerland. A federal sectoral plan sets a minimum surface area\n91\n\nto be maintained per canton (distributed among the cantons by quota). The Confederation monitors the\nmaintenance of the minimum SDA area. Under certain conditions, SDAs can be allocated to specific\nprojects, provided that all stakeholders at the federal and cantonal levels agree and that the minimum\nis maintained. This constraint is high, but the SDA spaces have been classified as an \u2018orange\u2019 zone to\nleave the possibility of downgrading open and to provide an option for the development of a layout and\nplacement scenario. Specific coordination at the federal and cantonal levels is nevertheless required to\nbe able to release such land for a development project. SDA spaces will have to be compensated on\na 1:1 basis by removing the topsoil and re-constructing the agricultural space on lower-quality plots or\nwastelands. Agricultural areas in the canton of Geneva outside the SDAs were classified as acceptable\n\u2018yellow\u2019 zones.\nThe initial classification of sensitivity layers is not fixed, but constantly changes as the territory\nevolves. Between 2014 and 2022, more than 1000 ha became \u2018red\u2019 exclusion zones (unacceptable con-\nstraints) in the Haute-Savoie department in France. In the canton of Geneva, around 100 ha have been\naffected by new restrictions and are now part of the exclusion zones, mainly due to stricter surface and\ngroundwater protection rules resulting from improved knowledge of the subsurface. This led to the re-\njection of several candidate sites proposing a configuration and location initially considered as possible.\nThese changes have made it even more difficult to continue developing scenarios, while at the same time\nhighlighting the iterative aspect of the process.\nFigure 2.13 shows two examples of these \u2018lost spaces for layout scenarios\u2019. The first concerns\nsectors of Ferney-Voltaire that are now intended for a development project (hospital project north of the\nD35, Route de Meyrin) and the classification of a sector as a compensation zone (south of the D35),\nwhich therefore cannot be compensated again. The second concerns a vast area north of the Rh\u00f4ne in\nFrance, which has been described as a \u2018peatland inventory\u2019.\nFig. 2.13: : Examples of regional changes. Left: 17 ha of new exclusion zones in Ferney-Voltaire (Ain,\nFrance). Right: 790 ha of peatland inventory on the banks of the Rh\u00f4ne in France: in light red, previously\norange zones that have become red zones.\n2.4.2\nSubsurface constraints\nSubsurface constraints, such as unfavourable geology, major faults, presence of strategic aquifers, drink-\ning water catchment areas and buffer zones, pipelines, power lines and gas mains, as well as reserved\nareas of public interest such as geothermal exploration zones or no-drilling zones due to superimposed\n92\n\naquifers or other information, were considered from the onset. Geological exclusion zones have been\ndefined by the geological consulting firms GADZ and ILF and the University of Geneva to take full ac-\ncount of geological conditions. These partners also examined the geological and hydrological situation\nbased on the following elements:\n1. Fault lines representing a high risk of seismic activity and that could cause tunnelling challenges.\n2. The interface between limestone and molasse.\n3. Potential high-pressure water penetrations or karstic formations that would expose the project to\nan unacceptable risk.\nAs a result, between 2014 and 2020, the project\u2019s initial study perimeter had to be significantly\nnarrowed (see Fig. 2.14) as additional knowledge was acquired and integrated into a 3D model of the\nsubsurface. Figure 2.15 shows two example images from the 3D subsurface model that was established\nto support the analysis of the subsurface constraints, to identify zones that are definitely to be excluded,\npreferred locations for the subsurface structures, and to identify zones with particular challenges or\ninsufficient data that require dedicated subsurface investigations.\nGiven the experience gained from the construction of the Large Electron Positron collider (LEP)\nunderground structure and from the construction of underground transport structures in the region (e.g.,\nthe Vuache road tunnel), the risks of building a large tunnel and caverns, which could be unstable,\nmove, collapse, or in which construction workers could be exposed to high-pressure water ingress that\ncould lead to fatal accidents, are considered unacceptable and must be avoided. As far as possible, all\nunderground structures should be located in the soft, stable molasse layer, which forms a reliable barrier\nagainst aquifers.\nAlthough maps and modelling work have provided additional information, reliable data on the\nexact depth of interfaces between different geological layers in the Vuache and Jura zones is still lacking.\nThe unavoidable limestone zones of Mandallaz have yet to be studied. Furthermore, little is known about\nconditions under the lake, as well as the Arve and the Rh\u00f4ne rivers. Since these conditions have a major\nimpact on the cost and schedule of the tunnel boring, more information about the subsurface in the key\nareas is being gathered with geophysical and geotechnical exploration between 2024 and 2025.\n2.4.3\nTopography, bathymetry, and other surface features\nInformation on topographical surface conditions has also been taken into account from the outset of the\nstudy. Steep slopes (Fig. 2.16) in excess of 30% presenting risks of unstable terrain and landslides are\nexcluded, as are cliffs, narrow valleys, and canyon-type formations. Since the tunnel must be placed\nat a sufficient depth below the lake bed, elevations above 750 m are an obstacle due to the depth of the\nshafts and unacceptable overloading (Fig. 2.17). High elevations also lead to high overburdens, which\ncan become challenging for tunnel boring activities, calling for more costly construction and slower\nprogress.\nThe bathymetry of the lake must be taken into account to ensure that the tunnel can be placed\nsufficiently below the lake bed with as short a crossing as possible. Lake Geneva is more than 50 m deep\nbeyond the Versoix-Corsier line (see Fig. 2.18). To avoid the tunnel becoming too deep over its entire\nfootprint, it is necessary to stay below this line. Crossing the lake where it is narrow avoids areas of\ninstability and minimises the risks associated with the presence of water. At the same time, other parts\nof the tunnel should not be located too deep under mountainous areas.\n2.4.4\nScenario development flexibility\nThe initial outline surface and subsurface constraints and many more constraints that are documented\nin detail in a specific report [12] provided a starting point for a semi-automated search to determine\napproximate exclusion and candidate zones. However, zones marked in orange (undesirable zones) and\n93\n\nFig. 2.14: : After several years of analysing the subsurface conditions based on bibliographic data and\nmodelling, the initial scenario development perimeter (yellow) had to be restricted (red) to assure com-\npatibility with the known subsurface conditions.\nyellow (acceptable zones), which at first glance appeared compatible with the location of a surface site,\nproved in various cases to be unacceptable due to restrictions that are not \u2018encoded\u2019 in the maps and\npublicly accessible documents which are available. This additional information was obtained in part\nby studying high-resolution maps, orthophotographs and data, by interviewing regional and local public\nadministration services and local stakeholders, domain experts and by means of walking tours (visual\ninspection of the surrounding area).\nSuch additional constraints included, but were not limited to, the following: unfavourably shaped\nland areas (surface available too small, too narrow, non-monolithic or too irregularly shaped), presence\nof adjacent constraints (nature protection areas requiring buffer zones, natural hazard areas such as flood\nzones or unstable banks, residential areas, sensitive areas), limited access (no road or no possibility\nof creating one due to topographical conditions or other restrictions, rudimentary road unsuitable for\nregular traffic and unable to be upgraded to meet requirements), likely opposition or known conflicting\ndevelopment policies, known conflicting projects.\n94\n\nFig. 2.15: : Example images from the 3D model (here molasse and cretaceous formations) used to\ndetermine the geological constraints.\nThe constraints and considering the currently known geological and topographical situation limits\nthe circumference of a future circular collider to less than 100 km. The layout studies conducted be-\ntween 2017 and 2021 concluded that to obtain a circumference of over 90 km that would deliver good\nperformance and therefore yield a research infrastructure of excellence, and given the various constraints\nthat the configuration must simultaneously meet in different locations, the available layout for the ring\nis limited to a strip with a width progressively reduced from 3000 m to 300 m depending on the area\nconcerned (see Fig. 2.19).\n95\n\nFig. 2.16: : Topography of the area. Red and orange colours indicate steep slopes.\n96\n\nFig. 2.17: : Relief of the area. White and red colours indicate high elevations.\nFig. 2.18: : Bathymetry of the Geneva lake.\n2.5\nInitial variants\n2.5.1\nIntroduction\nThis section provides the background which explains how the implementation scenario in the Franco-\nSwiss border region was developed. It explains why alternative scenarios to the west of the Jura were\nexamined and then discarded in favour of scenarios to the east of the Jura. It reviews how the layout and\nplacement considered during the exploratory phase of the FCC study (2014-2018) demonstrated the in-\n97\n\nPlaine du Genevois\n350 \u2013 550 m/mer\nMont Sal\u00e8ve\n550 \u2013 1380 m/mer\nVall\u00e9e de l\u2019Arve\n400 \u2013 600 m/mer\nMandallaz\nMont Vuache\n550 \u2013 1100 m/mer\nPlateau du Mont Sion\n550 \u2013 860 m/mer\nVall\u00e9e du Rh\u00f4ne\n~330 m/mer\nLac L\u00e9man\n300 \u2013 372 m/mer\nJura\n900 \u2013 1680 m/mer\nPlateau des Bornes\n600 \u2013 850 m/mer\nFig. 2.19: : Combination of subsurface and topographic constraints that lead to a ca. 300 m wide scenario\ndevelopment band and a diameter of about 28 km.\nprinciple feasibility of a new, large-scale research infrastructure and how the specific scenario examined\npresented prohibitive obstacles in certain locations. Finally, it mentions the variant involving a linear\ncollider, which was not selected for further studies.\nThe development of a scenario for the configuration in the Geneva region was based on the moti-\nvation of taking advantage of existing CERN infrastructures and assets built up over 70 years for a new\nproject. The construction of a circular collider requires existing particle accelerators in operation with\ntechnical infrastructures that can serve as injectors; the availability of workspace, workshops, equipment,\nand skilled workforce; as well as favourable legal, administrative, and project management frameworks.\nIt is, therefore, essential that the chosen layout remain within reasonable proximity to an existing CERN\nsite.\nIn addition, the particle collider must have a circumference greater than 90 km to accommodate\ntwo different particle colliders in the future (an electron-positron collider and a hadron collider), each\nof which must deliver the performance required to carry out the desired scientific research programme.\nThe immediate research zone would be located to the south of CERN\u2019s Meyrin and Pr\u00e9vessin sites, away\nfrom the Jura mountains. Indeed, during the Large Electron Positron collider (LEP) construction phase,\nmajor obstacles were already encountered due to the presence of karstic formations and high-pressure\nwater penetrations due to its proximity to the Jura mountains.\nNevertheless, as the next section highlights, an unbiased examination of the situation was con-\nducted so as not to overlook any other possible scenario.\n2.5.2\nScenarios west of the Jura\nA study [33] examined a layout in the Bresse plain (Dolois region), to the west of the Jura Massif (see\nFig. 2.20). These options had already been studied in 1997 and 2001 and were checked again between\n2014 and 2019. The ring would have been located outside the Jurassic formations, at a depth of around\n98\n\n40 metres. Still, in any case, the infrastructure would have encroached on existing national and regional\nparks and vast nature conservation areas. In addition, the required link to CERN\u2019s particle accelerator\ncomplex would have required a long tunnel of around 60 km for the transfer lines. This tunnel through the\nJura mountain range would have passed through very unfavourable geological formations with significant\noverburden. Given that the distance between the Jura mountains and the Petite Montagne du Jura is less\nthan 20 km, it is considered unfeasible to place a sufficiently large circular particle collider in this zone.\nFig. 2.20: Comparison of land areas and protection zones to the west and east of the Jura chain.\nThis variant was definitely dropped from further studies for the following reasons:\n\u2013 A long tunnel for the beam transfer line through the Jura mountain range would pose too many\ndifficulties, both from a civil engineering and a technical point of view. Construction times and\noverall costs would increase considerably, by at least 30%.\n\u2013 This scenario would require deep access shafts in difficult-to-access mountainous regions of the\nJura massif, which are largely nature conservation areas. The rock is highly unstable, and the\npenetration of high-pressure water is certain.\n\u2013 The loose soil in the Bresse region would require stabilisation and protection measures. Hy-\ndrophilic gypsum swells considerably (ground movements of roughly one metre recorded in the\nChienberg road tunnel), which is not compatible with large-scale cavern construction nor with the\nrequirement for a highly stable tunnel. Maintenance costs would be much higher than on stable\nground.\n\u2013 The installation would most likely interfere with nature protection constraints and cause significant\ndisturbances to local residents during the construction phase.\n\u2013 The space available between the Jura massif, its national park and the Petite Montagne du Jura\narea to the northwest is too small to accommodate a circular particle accelerator of sufficient size.\n\u2013 There is no reasonable way of operating and maintaining the infrastructure from CERN or any\nother suitable partner organisation nearby.\n99\n\n2.5.3\nRacetrack lakeside scenario\nThe conceptual feasibility investigations also comprised an analysis of the opportunities and constraints\nrelated to a racetrack layout with a lakeside placement of the particle collider ring that permits connecting\nthe infrastructure to CERN\u2019s particle accelerator complex [34].\nThe concept was based on having straight sections about 11 km long that could potentially also\nhouse a linear accelerator or collider. The motivation was to combine the possibilities of a linear electron-\npositron collider as a first stage with a circular hadron collider during a second stage. An alternative\nparticle acceleration concept with linear accelerators for a first-stage circular electron-positron collider\ncould also have been imagined.\nThe availability of long straight sections comes with advantages for the radiofrequency accelera-\ntion systems in terms of ample space and avoiding bending fields. A minimum crossing angle, 20 mrad\nin the case of CLIC, is required, however, in order to prevent collision debris passing through the op-\nposite linear accelerator arm. Realistically, some bended beam delivery section would be required for\ndispersion suppression, collimation and chromatic corrections. Such a layout would lead to a racetrack\nwith a total circumference of 90 km, permitting both, housing linear and circular accelerators (Fig. 2.21).\nFig. 2.21: Racetrack layout scenario with two 11 km long straight sections, leading to a total circumfer-\nence of 90 km.\nThis layout comes, however, with some significant disadvantages: It only permits up to two exper-\niments for the circular collider and also requires the inclusion of collimation, dumps, and beam transfer\nsections in the two straight sections.\nWhen it comes to placement options (Fig. 2.22) for such a layout, numerous geological and en-\nvironmental constraints are encountered: as with all circular scenarios, this one also needs to cross the\nMandallaz limestone sector. Some shafts could be very deep in their nominal locations (Fig. 2.23), i.e.,\nmore than 500 m, however, with a systematic optimisation process it is likely that acceptable alternatives\nfor displaced shafts can be found. In terms of traversal of the lake, the bathymetry starts to impose\nconstraints with depths of 65 m, which would need to be carefully evaluated.\nThe strongest limitations stem from the highly challenging needs to integrate 12 surface sites in\na highly urbanised area on one side and into a highly mountainous zone on the other side (Fig. 2.24).\nFor instance, a site PJ in Switzerland would be in the fully protected Allondon river zone, where any\nconstruction activities on the surface and subsurface are strictly forbidden. It remains unclear where and\nhow a feasible experiment site potentially covering up to 9 ha could be identified and rendered acceptable,\nconsidering that also major transport and electricity infrastructures would have to be created in this area\nwhich, is entirely natural. It is a highly protected nature zone. Site locations around PI in France in\nthe close vicinity of the river Rh\u00f4ne face similar constraints. Locations for a site PK in the Pr\u00e9vessin\nsector in France would fall in highly urbanised areas. Site locations in PL in Versoix in Switzerland are\n100\n\nCircular collider 90 km\nLinear accelerator/collider 11 km\nFig. 2.22: Placement option for a 90 km circular / 11 km linear racetrack scenario.\nSection for a linear\ncollider (11km)\nDeep shafts > 400 m\nFig. 2.23: Example racetrack alignment scenario.\nin fully protected lake border areas with absolute bans for subsurface activities and in highly urbanised\nlocations. Locations for site PB in Switzerland are in a large nature preservation zone, in particular the\nhome for amphibians which are highly protected. Potential locations could most likely be identified\nusing the Avoid-Reduce-Compensate sequence for other sites. In terms of cost, the scenario would lead\nto significant increases for the circular collider scenario, since it is not optimised for a circular collider\nlayout. The differences are in the order of 200 to 400 million CHF at least. Finally, the loss of at least\n20% of arc sections directly leads to a corresponding loss in the maximum achievable energy or, in the\ncase of a smaller radius in the curved sections, to significantly higher synchrotron radiation losses.\nA racetrack layout is neither optimised for a linear collider nor a circular collider. It, therefore,\ncreates additional complications and costs and leads to lower performance. The integration into the\nterritory is extremely challenging and significantly more complicated than the finally adopted circular\nlayout with eight surface sites. It will lead to higher environmental impacts and increased territorial\ndevelopment needs (e.g., access roads) and require more and deeper shafts. Therefore, further studies on\nthis scenario have been discontinued.\n2.5.4\nScenarios east of the Jura\nFor the zone to the east of the Jura, an initial large search perimeter was defined in 2014 based on the\nfollowing geological conditions [35\u201337]:\n\u2013 To ensure stability, the tunnel must cross Lake Geneva at a sufficient depth below the lake bed.\n101\n\nI\nJ\nK\nF\nG\nH\nL\nA\nB\nC\nD\nFig. 2.24: Example of the racetrack layout placement with the environmental constraints indicated. Site\nlocations I, J, L and B are in highly constrained zones, rendering the identification of a feasible and\nsocietally acceptable scenario highly challenging. The lake depth at the crossing between L and A is\nabout 65 metres deep.\nInitial ideas of placing the tunnel in unstable ground (moraines, quaternary glacial deposits) or\nin a construction on the lake bed had to be rejected due to a) insufficient stability and b) the\nimpossibility of creating suitable interfaces between the tunnel on either side of the lake and the\nconstruction in the lake.\n\u2013 In order to be located at an acceptable depth below the lake bed and to remain as far as possible\nwithin the impermeable molasse layer, underground structures should be located at around 250 m\nabove sea level, ideally avoiding crossing the limestone/molasse interfaces.\n\u2013 A boundary line was drawn to the northwest (Jura zone) and to the west (Vuache zone) to ensure\nsufficient distance from high elevations leading to unacceptable overburdens, inaccessible and\nprotected areas, unstable rocks, faults, seismically active zones, and unstable karstic formations\nwhere the penetration of high-pressure water is certain.\n\u2013 To the southwest, the Mandallaz mountainous zone forms a natural border. Its crossing cannot be\navoided. Consequently, the preferred scenarios are those for which the overburden and crossing\nlength are low.\n\u2013 To the south, a boundary line has been drawn northwest of the Montagne des Fr\u00eates nature reserve\nto avoid elevations above 750 m (unacceptable, as they would lead to excessively deep wells),\ninaccessible and topographically unacceptable zones, and protection zones to the south. This line\ncrosses the Filli\u00e8re valley at Thorens-Gli\u00e8res and spans the acceptable elevations of the Bornes\nplateau as far as La Roche-sur-Foron.\n\u2013 To the east, a boundary line has been drawn to avoid mountainous zones and thus remain in the\nArve River valley.\n102\n\nFig. 2.25: : Established study perimeter (red line). Exclusion zones and zones with too many difficulties\nfor surface sites are indicated in red; favourable zones are indicated in blue.\nThe perimeter obtained in this initial study turned out to be compatible with a circular infrastruc-\nture with a circumference of 90 to 100 km, and can meet geological, topographical, environmental and\nurban planning constraints (see Fig. 2.25). The maximum distance that can actually be used is 29 km\nfrom north to south and 30 km from west to east. The result is a zone capable of accommodating a circu-\nlar collider with a circumference of up to 92 km for a configuration comprising eight sites or up to 98 km\nfor a configuration comprising twelve sites.\n2.6\nReference scenario\n2.6.1\nIntroduction\nOf the about 100 scenarios analysed [12], based mainly on bibliographical data and field visits, it was the\nPA31 scenario that seemed the most interesting to retain for further in-depth studies and optimisation.\nThe trace of version 1.0 (PA31-1.0) stands out from the others. It proposes a balance between territorial\nplacement, scientific performance that the particle collider and the four interaction regions can offer and\ntechnical feasibility in terms of manageable risks and costs. This working hypothesis, developed based\non the Avoid-Reduce-Compensate (ERC) process described earlier, has made it possible to gain in-depth\nknowledge of the region, creating the basis for continuously improving the project considering territorial\nrequirements and constraints as well as technological advances.\nThe scenario version 4.0 (PA31-4.0) shown in Fig. 2.26, presented in this chapter, is established as\nthe reference scenario for a potential implementation project. It is the result of an optimisation process\napplied to the PA31-1.0 working hypothesis. It takes into account the progress made on design studies\nfor the FCC-ee and FCC-hh colliders, infrastructure and civil engineering studies, as well as territorial\ninformation collected from local stakeholders (concerned municipalities, departmental directorates of\nthe territories and the Direction R\u00e9gionale de l\u2019Environnement, de l\u2019Am\u00e9nagement et du Logement in\nFrance and the services of the Canton of Geneva). There still exists room for minor adjustments for some\ntechnical surface sites and the disposition of the experiment site shafts.\nThe technical feasibility of the project based on the so-called PA31-4.0 reference scenario could\n103\n\nFig. 2.26: The PA31-4.0 reference scenario that served as baseline for the subsurface investigations, the\nanalysis of the state of the environment and studies concerning connected infrastructure projects. An\ninteractive version can be consulted at https://cern.ch/fcc-overview.\nbe confirmed with the help of a diverse set of studies. However, it should be stressed that the territory and\nlegal frameworks in France, Switzerland and Europe are constantly evolving. Since 2014, a number of\nsurface site location candidates and scenario traces have no longer been feasible due to these evolutions.\nTherefore, the situation may further evolve and the conditions for implementing the reference scenario\nPA31-4.0 may also change. To ease the project authorisation process and to avoid potential interference\nwith future developments and spatial planning, it is advisable to obtain the rights on the required land\nplots as soon as possible.\n2.6.2\nScenario characteristics\nThe layout and functions of the PA31-4.0 reference scenario are shown in Fig. 2.27). The two shafts\nat the PA surface site (Ferney-Voltaire, France) were moved further north from the Route de Meyrin\nroad to maintain a safe distance, to provide space for traffic on the surface site around the experiment\nassembly hall and shafts, and to protect against direct visibility. Moving the locations of sites PD and\nPJ further northward would be favourable, but is ruled out due to the presence of the departmental road\nat the northern limit of site PA. Moving them further eastward is also ruled out due to the presence of a\ncompensation zone that is to be avoided and which will be turned into a fully functional wetland zone\nand natural habitat if the project is implemented. Such displacements would also move the surface site\nPG in Groisy and Charvonnex deeper into the forest and on a steep slope. Both are evolutions that are\nbetter avoided. The shafts at the PD surface site (Nangy, France) were rotated away from the autoroute\nto ensure compatibility with the RD 903 departmental road enlargement and integration with the A40\n104\n\nPA\nPG\nPD\nPJ\nPF\nPH\nPL\nPB\nExperiment site\nStraight section\nlength at IPs: 1400 m\nTechnical\nstraight section\nlengths: 2032 m\nExperiment site\nExperiment site\nTechnical site\nBooster RF\nTechnical site\nCollider RF\nTechnical site\nBetatron and\nmomentum\ncollimation\nTechnical site\nBeam extraction\nExperiment site\nFig. 2.27: The functions of the various sites in the PA31-4.0 scenario configuration.\nautoroute development project and to ensure the technical feasibility of creating a service shaft on the\nsite without installing an additional cavern between the service and the experiment caverns. A move of\nsite PA further southward is ruled out, as this would create incompatibility due to the presence of the\nA40 autoroute and the RD 903 road on the PD surface site, and topographical difficulties (steep slope)\ntowards the D 1203 departmental road to Annecy on the PG site in Charvonnex.\nThe shifting and rotating of the scenario took into account the objective of placing the PG surface\nsite in both the lower quality part of the forest affected and on the existing grassland plateau, where the\nsoil turned out to be of poor quality for agriculture. In addition, the shafts should be kept away from the\nsteep slope to the south to control construction risks and costs of building the shafts and buildings. It\nwas not possible to move the shafts further away from the forest, towards the plateau, without creating a\nconflict for the PD experiment site (Nangy) with the autoroute, and for the PJ experiment site (Dingy-en-\nVuache and Vulbens), due to the presence of a stream and topographical constraints. The PJ experiment\nsite is therefore kept at a distance from the A 40 to the south, and from the creek and topographical\nconstraints to the west. The wildlife corridor can be maintained. The placement of the PB technical\nsite (Presinge, Switzerland) was optimised by taking into account maps concerning biodiversity and\necological indicators made available by cantonal services, and the results of a study of possible access\nroutes carried out by a specialist firm in the canton of Geneva. The site would be located in Presinge,\ndirectly along the Route de Jussy road. A connection with the tunnel between the shaft and the service\ncavern, 98 m long, is required.\nThe working hypothesis of the location for the PF technical site is in \u00c9teaux (France), directly\nadjacent to the RN 203 national road. It includes a connecting tunnel between the 400 m deep shaft and\n105\n\nthe service cavern at the collider tunnel. A variant further south is currently not considered since the\ncreation of an inert waste deposit site (called I.S.D.I. in French) creates further constraints. However,\nin case the footprint of the main site is to be reduced, certain technical infrastructures that are limited\nto surface site constructions (e.g., ventilators, cooling towers, electrical substation) could be displaced\nto this area. The working hypothesis of the location for the PH technical site is across the border be-\ntween the two communes Cercier and Marlioz (France), directly adjacent to the D 203 departmental road\n(Route de Choisy). Taking into account the analysis of fauna, flora and biodiversity, the state of the for-\nest, topographical constraints and technical risks (gas pipeline north of the site), the site closely follows\nthe Route de Choisy road to the north and stretches into the forest down a slope to the west. Should an\nadjustment become necessary, an alternative site location exists 900 m in clockwise direction directly at\nthe D2 departmental road on a set of agricultural land plots. The significant displacement from the tech-\nnical straight section mid-point would require the development of a design for the fitting and installation\nof the radiofrequency ancillary systems (cryogenic refrigeration, powering). The preferred location for\nthe PL technical site (Challex, France) is on the nominal midpoint of the technical straight section to\nthe east of the town, on a field and a plot of land containing two single-family homes. Another possible\nlocation, 600 m west of the nominal point, has been studied and discussed with the municipality. It is\nslightly less preferred due to the higher visibility from residential zones of the commune. This option is\nalso characterised by additional technical challenges that would entail additional costs due to the need to\nbuild a shaft approximately 150 m outside the tunnel with additional civil engineering needs and more\ndifficult access to the machine.\n2.6.3\nScenario parameters\nThe geographical coordinates of the PA31-4.0 reference scenario resulting from this optimisation are\nshown in Table 2.2 for the scientific sites and in Table 2.3 for the technical sites.\nTable 2.2: Coordinates WGS84 of the theoretical beam interaction points for scientific sites.\nSite\nLocation\nLatitude\nLongitude\nPA\nFerney-Voltaire, Ain, France\n46.2480475\u25e6N\n6.0986019\u25e6E\nPD\nNangy, Haute-Savoie, France\n46.1453657\u25e6N\n6.3169260\u25e6E\nPG\nCharvonnex and Groisy, Haute-Savoie, France\n45.9938019\u25e6N\n6.1693009\u25e6E\nPJ\nDingy-en-Vuache and Vulbens, Haute-Savoie, France\n46.0962036\u25e6N\n5.9513024\u25e6E\nTable 2.3: Coordinates WGS84 of the theoretical beam interaction points for technical sites.\nSite\nLocation\nLatitude\nLongitude\nPB\nPresinge, Geneva, Switzerland\n46.2271027\u25e6N\n6.2374818\u25e6E\nPF\n\u00c9teaux, Haute-Savoie, France\n46.0490317\u25e6N\n6.2865850\u25e6E\nPH\nCercier and Marlioz, Haute-Savoie, France\n46.0146646\u25e6N\n6.0309816\u25e6E\nPL\nChallex, Ain, France\n46.1926255\u25e6N\n5.9810829\u25e6E\nTable 2.4 summarises the layout parameters of the particle colliders.\nThe functions of each surface site are shown in Table 2.5.\n2.6.4\nMulti-criteria performance of the reference scenario\nFigure 2.8 shows the performance of a number of shortlisted scenarios that were studied in more detail\nbefore the PA31 scenario was chosen as a reference for further optimisation. Fig. 2.28 shows the results\nof the multi-criteria analysis for this scenario in terms of territorial compatibility (T), implementation\nand risk management (I) and scientific value (S) for each site location and the entire trace.\n106\n\nTable 2.4: Layout parameters of the particle collider.\nParameter\nValue\nComment\nElevation of the tunnel under the PA\nsite shaft\n202 m above sea level\nThe elevation is subject to further op-\ntimisation after the availability of the\ngeophysical and geotechnical investi-\ngations.\nLength of straight sections at PA,\nPD, PG and PJ sites\n1400 m\nThese sections feature tunnel enlarge-\nments. The ee and hh machines may\nhave beam-optics dependent, differ-\nent machine straight section lengths\nin these sectors.\nLength of straight sections at PB, PF,\nPH and PL sites\n2032 m\nThis is the minimum space required\nto ensure that all radiofrequency sys-\ntems can reliably be fit. Subject to\noptimisation, not all available space\nmay be used after optimisation.\nEast-west rotation of the collider\naround the PA site\n10.97 degrees\nLength of one hadron collider arc\ncell in the arcs\n275.792 m\nNumber of cells in a curved section\n(arc) per octant\n26\nTotal length of the arcs\n78 684.476 m\nThe sum of the curved machine seg-\nments of the ee and hh machine may\nbe different\nTotal circumference of footprint\n90 658.745 m\nThe hh machine may be slightly\nshorter in the same tunnel (90,657.4\nm)\n2.6.5\nSite PA\nDescription of the site location\nThe main site is located in Ferney-Voltaire, Ain, France, south of the Route de Meyrin road, east of the\nEspace Candide shopping centre (see Fig. 2.29 and Fig. 2.30). The site would be connected to Point 8 of\nthe LHC by the Chemin des Pr\u00e9s Jins, a public road. An extension to the south of LHC Point 8, already\nplanned as part of the HL-LHC project, would make it possible to accommodate technical infrastructures\nto reduce the land take for the main site. The surface area of the site along the Route de Meyrin is 5.2 ha,\nand the surface area of the LHC Point 8 site extension is 2.7 ha.\nKnown constraints\nThe site is located in a protected agricultural (Ap) zone, close to an environmental compensation zone\nclassified as protected nature zone (Np). The water supply network passes close by Point 8 of the LHC.\nA gas pipeline runs along the boundary of the main surface site, before crossing the border between\nFrance and Switzerland. There is a network along the Route de Meyrin that supplies waste heat from\nLHC Point 8 to dwellings and to the commercial zone (ZAC, mixed development zone). Good urban and\n107\n\nTable 2.5: Layout parameters of the particle collider.\nSite\nFunction\nPA\nScientific site with one experiment, injecting the beam line from a linear\naccelerator at the CERN Prevessin site into the pre-accelerator (booster)\nlocated in the same tunnel as the collider.\nPB\nTechnical site with injection of booster beam line into the collider, ex-\ntraction of beam line from collider.\nPD\nScientific site with one experiment.\nPF\nTechnical site with betatron and momentum collimation.\nPG\nScientific site with one experiment.\nPH\nTechnical site with radiofrequency particle acceleration system for the\ncollider.\nPJ\nScientific site with one experiment.\nPL\nTechnical site with radiofrequency particle acceleration system for the\nbooster pre-accelerator.\n84.38\n69.53\n89.06\n79.69 79.69\n72.66\n75.00\n77.34\n82.00\n0.00\n20.00\n40.00\n60.00\n80.00\n100.00\nPA\nPB\nPC\nPD\nPE\nPF\nPG\nPH\nPI\nPJ\nPK\nPL\nTrace\nScore in % for each site of the scenario PA31-4.0\nFig. 2.28: Multi-criteria analysis percentage scores of each surface site location and the entire collider\ntrace of scenario PA31-4.0. Note that site locations PC, PE, PI and PK do not exist in 8 site scenarios.\nBlue lines indicate the individual performance thresholds (green, yellow, orange, red). Green indicated\nbars exhibit a very good performance and yellow indicated locations correspond to a good performance).\nlandscape integration is necessary to preserve the view facing the Alps. Due to heavy traffic in the area,\na concept must be developed together with the municipality\u2019s technical services for efficient site access.\nNo dedicated access road is required, though.\n108\n\nFig. 2.29: Aerial view of candidate location for surface site PA.\nSynergies and territorial potentials\nWaste heat from the particle collider cooling and the data centre can be recovered and supplied to the\nhomes and business parks around the site, including the Geneva airport and industrial zone, building on\nthe current heat supply network that has been put in place for the LHC programme. The existing but\nnon-functional environmental compensation area can be turned into a fully functional natural habitat and\nwetland, providing substantially increased environmental quality in that area. Treated residual water from\nthe cooling system can be used for this zone (the Poirier de l\u2019\u00c9pine zone) and potentially for agricultural\npurposes close to the site. Synergy with LHC Point 8 would permit a substantial reduction of the footprint\nof the PA site. This requires good planning and sequencing of the new collider project with the HL-\nLHC programme. Synergy with the CERN site in Pr\u00e9vessin and the Bois-Tollot substation provides the\nelectricity supply (existing 400 kV line to Pr\u00e9vessin and a dedicated 63 kV link from Pr\u00e9vessin to LHC\nPoint 8). A visitor centre could be created in synergy with LHC Point 8 to exploit the location fully.\n109\n\nPA31-4.0-PA\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.30: PA surface site location in Ferney-Voltaire, Ain, France. The hashed space in the south\nrepresents an annex that is an extension of the existing LHC P8 site.\n2.6.6\nSite PB\nDescription of the site location\nThe site lies in Presinge, canton of Geneva, Switzerland, to the south of the Nant du Paradis stream, on\na field classified as a protected crop rotation area (in French: \u2018Surface d\u2019Assolement\u2019 or in short SDA),\nbordering the Route de Jussy road (see Fig. 2.31 and Fig. 2.32). The surface area shown on the map\nindicates the site area covers 4.5 ha. The site is displaced south to the road, avoiding conflicts with nature\nprotection zones and providing for improved access. An underground connection tunnel of about 100 m\nin length is required to connect to the service cavern that is located inside the collider tunnel.\nKnown constraints\nThe prescribed protective distances between the Nant du Paradis creek that hosts an amphibian breeding\narea and the forest are respected. The environmental state analysis did not detect any interference with\nprotected environments in the vicinity of the location, in particular the amphibian breeding site. The\nimpact on the crop rotation area (SDA) should be kept to a minimum. The space consumed by SDA has\nto be compensated 1:1 by transporting the topsoil to another location that needs to be identified with the\nhelp of notified cantonal services. To blend in well with the surrounding landscape, the site needs to be\nas small and compact as possible and be ideally semi-underground. A study of the cooling system is\nnecessary to reduce noise and visual disturbances. It is also necessary to develop a concept for reducing\nlight pollution during the construction phase. The road access was studied by a specialised firm with\nin-depth knowledge of the sector. No new road needs to be constructed, but a junction would have to be\ncreated at the Route de Jussy. The detailed design and location of the recommended access option have\nto be validated by the notified bodies of the canton of Geneva once a construction project is proposed. A\ndetailed technical access plan should be drawn up at a later stage for this purpose.\n110\n\nFig. 2.31: Aerial view of candidate location for surface site PB.\nSynergies and territorial potentials\nAccording to the road access study carried out by the firm, direct access to the site from the Route de\nJussy is technically feasible and preferable from the project perspective. This scenario would avoid the\nneed to create a new access road. The green buffer zone around the site would reinforce and extend\nthe natural environment in the vicinity of the Nant du Paradis watercourse. Surface sites that are semi-\nunderground would not only improve the blending into the landscape but would also improve the overall\necological and biodiversity value of a non-agricultural habitat. The reinforcement of the local power\ngrid, necessary for the construction phase, is seen as an opportunity to improve the infrastructure for the\ninhabitants of the entire area. Improved public transport, including cross-border transport as part of the\nFCC, also represents an opportunity for the area. Several opportunities exist, and demand for supplying\nheat recovered from the particle accelerator nearby, for example, with HEPIA and a new correctional\ninstitution slated for construction by 2030 on the Champ-Dollon prison site.\n111\n\nPA31-4.0-PB\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.32: PB surface site location in Presinge, canton of Geneva, Switzerland.\n2.6.7\nSite PD\nDescription of the site location\nThe site is located in Nangy, Haute-Savoie, France (see Fig. 2.33 and Fig. 2.34) between the A40 au-\ntoroute and the RD903 departmental road on an agricultural field with zone \u2018A\u2019 classification in the local\nurban plan (in French: \u2018PLU\u2019). The surface area of the site is approximately 4.9 ha.\nKnown constraints\nThe site is subject to space constraints to the west, east and south due to existing roads and plans to build\na new connection between the roads. Road traffic is typically high, one reason for the road development\nproject that is expected to integrate the departmental road with the autoroute. A study for the development\nof different access scenarios was carried out by a specialised firm. The scenarios were discussed with\nthe Haute-Savoie department and with the mayor of the municipality. The commonly preferred scenario\nwith the lowest impact is one that comprises a dedicated access road to the surface site. The access to\nthe site would be via a roundabout, which would be built to the north at the D 1205 departmental road in\nFillinges.\nSynergies and territorial potentials\nThe site is only accessible via the dedicated, approximately 250 m long access road. The site is not\nvisible from residential areas, which facilitates its integration into the landscape. There are a number\nof possibilities for supplying residual heat from the cooling system, for example, to a nearby cheese\nfactory, to an industrial and business park, to hotels, medical facilities, neighbouring communes such as\nFillinges, Boringes, Scientrier, Contamine-sur-Arve and to the Alpes-L\u00e9man hospital complex. The heat\ncan also be used for biogas production in the waste water treatment facility in Scientrier. Currently, a\nstudy is ongoing to source water from the waste water treatment facility \u2018SRB\u2019 in Scientrier for use in\nthe accelerator cooling system. When the cleaned water is not used for the particle accelerator, it could\nbe made available for agricultural and industrial purposes. A direct connection by conveyor belt to the\n112\n\nFig. 2.33: Aerial view of candidate location for surface site PD.\nautoroute during the construction phase has been studied. It would facilitate the removal and possibly\nalso the supply of materials, thus largely avoiding the need for trucks. There are likely areas in the\nvicinity where excavated materials can be reused such as raised hedges, noise separation, covered trench\ncreation, landfill and transport to quarries for rewilding purposes. To be able to develop a solid excavated\nmaterials management plan, these opportunities need to be identified with the help of local authorities\nand notified bodies (e.g., SAFER, DDT, DREAL).\n2.6.8\nSite PF\nDescription of the site location\nA technical surface site at the nominal point PF in La Roche-sur-Foron, Haute-Savoie, France (see\nFig. 2.35 and Fig. 2.36) is not feasible because:\n\u2013 The site would be in the middle of a hamlet of single-family homes.\n\u2013 The presence of the Lavillat road in the direction of La Roche-sur-Foron is incompatible with the\nconstruction and installation of the accelerator site and equipment.\n113\n\nPA31-4.0-PD\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.34: PD surface site location in Nangy, Haute-Savoie, France.\n\u2013 The nominal point is located on high ground (755 m) leading to a shaft which is too deep and with\nan unfavourable topography.\n\u2013 A slight movement of the ring inwards is ruled out due to the presence of steep slopes and the risk\nof landslides.\nThe preferred alternative selected for a technical surface site PF is a location in \u00c9teaux, Haute-\nSavoie France (see Fig. 2.37), alongside the RD 1203 road, with a surface area of 4 ha. An underground\nconnection tunnel is required between the shaft to be located in the indicated surface site perimeter and\nthe service cavern at the inside of the collider tunnel.\nIf the surface site area needs to be reduced, made more compact or certain constructions cannot\nbe made compatible with the required landscape integration, then an annex to the south of the site,\nalongside the autoroute in La Roche-sur-Foron can be envisaged. The land is on the perimeter of a newly\nconstructed inert waste storage facility (in French: \u2018I.S.D.I.\u2019). Once the inert waste storage is full and no\nlonger in use, it can host constructions that are limited to the surface such as ventilation systems, cooling\ntowers and an electrical substation.\nKnown constraints\nMain site in \u00c9teaux:\nThe shaft of the site and the accelerator tunnel are 558.5 m apart, depending on the position of the shaft.\nThe wetlands to the east of the site must be maintained and could be integrated into the site. A certain\ndistance must be maintained between the site and the hamlet to the east. As a result, there is little space\nleft for the surface site, and the size of the site should be reduced. Work should be undertaken with\nthe local authority and government agencies (DDT, DREAL) to define zones for recycling excavated\nmaterials in the vicinity of the site. The area available for the surface site is very limited (4 ha). It may,\ntherefore, be necessary to relocate certain elements, such as an electrical substation or cooling towers, to\nthe south option for the site in La Roche-sur-Foron or to another nearby location.\n114\n\nFig. 2.35: Aerial view of candidate location for surface site PF.\nOption of an annex in La Roche-sur-Foron:\nThe technical site is located on the site of an inert waste storage facility (in France: \u2018I.S.D.I.\u2019), cur-\nrently under construction, with the status of a facility classified for environmental protection (in France:\n\u2018ICPE\u2019), i.e., subject to particular construction, operation and monitoring constraints. Following an anal-\nysis carried out by civil engineering contractors, the location was found, in principle, to be compatible\nwith the construction of a surface site. However, this choice would entail significant additional costs and\nadditional technical difficulties. For example, it would be necessary to employ pillars for construction on\ninert waste dumps to assure the stability of the groundworks and the construction of the shaft. It would\nbe necessary to create an access road 2.4 km long that crosses the existing railway line, and to build an\nunderpass under the autoroute. Lastly, this option is located in the immediate vicinity of an environmen-\ntal protection zone (in French: \u2018ZNIEFF\u2019), which is rich in biodiversity and includes a wildlife corridor\nthat must be preserved. The available surface area is roughly the same as for the location in \u00c9teaux (4.1\nha, versus 4.0 ha). However, if needed, the location could accommodate certain technical infrastructures\nthat are compatible with inert waste deposits, such as an electrical substation or cooling towers. Further\nanalysis will be carried out during the detailed technical design phase.\n115\n\nFig. 2.36: Nominal location of PF indicated with a spot on the collider trace. Two surface site candidate\nlocations requiring horizontal access tunnels are indicated with black arrows.\nPA31-4.0-PF\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.37: PF surface site location in \u00c9teaux, Haute-Savoie, France.\nSynergies and territorial potentials\nFor the location in \u00c9teaux, it is possible to supply residual heat from the cooling system to public facilities\nand businesses in a radius up to 3 km. A zone that qualifies as wetland, but which today is not well\npreserved, can be rewilded, protected, and be well preserved together with the habitat in the vicinity of\nthe Vuaz stream. Lastly, direct access from the main road is possible and would avoid the creation of\n116\n\na new access road. Electricity substations for the construction phase exist in the vicinity. If needed,\na connection to the nearby autoroute service station could be implemented to facilitate the transport of\nexcavated materials and the supply of construction materials.\n2.6.9\nSite PG\nDescription of the site location\nFig. 2.38: Aerial view of candidate location for surface site PG.\nThe experiment site PG lies to the north of the Route d\u2019Annecy road on a plateau, crossing the\nborder of the communes Charvonnex and Groisy, Haute-Savoie in France (see Fig. 2.38 and Fig. 2.39).\nThe main site is partly in a forest and partly on grasslands. It is approximately 800 m south of the A410\nautoroute area in Groisy. At this location, next to the autoroute service station, two smaller plots have\nbeen identified to host technical infrastructures that do not need to be close to the shaft. All plots are far\nfrom any dwellings. The area marked limits of the main site is 6.9 ha. However, only a fraction of that\narea would be constructed. Annexes of 1.9 ha and 1.7 ha for equipment storage, an electrical substation\nand cooling towers close to the autoroute are also indicated. An existing 800 m long, wide forest path\nhas to be refurbished to serve as an access road to the main site.\n117\n\nPA31-4.0-PG\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.39:\nPG surface site location in Charvonnex and Groisy, Haute-Savoie, France. the main site\nintersects the collider alignment, shown in blue. The two plots at the autoroute in the north serve for\nequipment that does not need to be necessarily located in the immediate proximity of the shafts. The areas\nalso serve for handover of incoming construction materials and the evacuation of excavated materials.\nKnown constraints\nThe forest is a classified wooded area (in France: \u2018EBC\u2019), heterogeneous, valued for its biodiversity in\nsome parts. The use of the forest for the site will be reduced and limited to the part with the lowest quality\nin terms of its natural environment. Clearing will be compensated for by, for example, reforesting the\nsouthern part of the plateau or existing brownfields in the forest. The site is on the edge of a steep slope\ntowards the Route d\u2019Annecy to the south, and must therefore remain on the top of the plateau. It is a\nquiet, natural area with exceptional views towards the Aravis mountain chain to the south. The location\nis exceptionally well suited to host a visiting facility with recreational facilities on the site. Measures\nwill need to be taken to reduce noise and light pollution during the construction and operating phases.\nSynergies and territorial potentials\nThe possibility of reforestation compensates for the clearing of approximately 1.5 ha of forest. A forest\nroad over flat land provides good access and makes it possible to create a route over approximately 800 m\nto the Groisy autoroute area and a wide road alongside the autoroute. Access to the autoroute during the\nconstruction phase for supplies and the removal of excavated materials has been studied and appears\nfeasible. The use of a conveyor belt removes the need for trucks. There are two temporary storage areas\nfor inert waste and other materials in the immediate vicinity of the site and the forest road. Annexes\nclose to the autoroute could accommodate those elements most likely to generate disturbances, such as\ncooling towers and an electrical substation. The supply of residual heat from the cooling system appears\nto be possible. Several potential consumers have been identified in the vicinity, including public facilities\n(elementary school, middle school, fire station), a commercial zone and a veterinary clinic. There is also\nthe possibility of creating a district heating network in Charvonnex and Groisy. The fire station can serve\nas a base for emergency services in the immediate vicinity of the site. Waste water from the cooling\nsystem could be used to feed the Fattes stream and wetlands in the forest. There is enough space on the\n118\n\nsite to build a visitor centre with recreational facilities that can be reached via the Groisy autoroute area\nor the Route d\u2019Annecy. The site is located near Annecy, within easy reach for CNRS/LAPP staff. Sites\nfor reusing excavated materials for agriculture and forestry have yet to be identified with the help of local\nauthorities and notified government agencies (e.g., SAFER, DDT, DREAL).\n2.6.10\nSite PH\nDescription of the site location\nFig. 2.40: Aerial view of candidate location for surface site PH.\nThe technical site PH is located right along the D203 road in Cercier, Haute-Savoie in France (see\nFig. 2.40 and Fig. 2.41). The site is located in the forest, straddling the municipalities of Cercier and\nMarlioz, stretching out to the west down a slope. It is far from dwellings and is not visible. It is in a\nnature setting. The defined area, located in an area with less biodiversity, is 8.2 ha.\nKnown constraints\nThe environmental field investigations revealed that the part of the forested sector to the north of the site\nis of great value (rich biodiversity, natural environment). Therefore, use of the forest needs to be min-\n119\n\nPA31-4.0-PH\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.41: PH surface site location in Cercier and Marlioz, Haute-Savoie, France.\nimised and the specific locations of buildings and accesses in the forest need to be carefully developed\nduring a subsequent design phase. The site will respect the buffer zone for the gas pipeline to the north.\nConsidering the quiet, natural setting, noise and light pollution must be given particular attention. A\ndwelling is located approximately 200 m to the south. There is no co-visibility between the site and the\ndwelling. Given the small size of the road, it is necessary to identify nearby reuse sites for excavated ma-\nterials, so that they can be used in agriculture or for reforestation. Materials would mainly be transported\naway to the north or the west by conveyor belt to avoid road constraints. The location is well suited to\nhost the radiofrequency system since a 400 kV grid line passes less than 2 km to the north. RTE, the\nnational grid operator will have to take into account the need to supply electricity via buried cables when\ncarrying out the study for the creation of a substation for access to the 400 kV line.\nShould for any reason the site preferred location at the nominal point not be considered feasible,\nan alternative placement about 900 m in the clockwise direction of the collider has been identified as\nan alternative. This site is located on agricultural fields next to the D2 departmental road. It would be\nsuitable as the location for the electrical substation in case of placement on the nominal point or when\ndisplaced since the electrical substation does not necessarily need to be in the immediate vicinity of the\nshaft.\nSynergies and territorial potentials\nThere is a great deal of interest in reusing water from the particle collider infrastructures for agricultural\nactivities around the site (e.g., apple and pear trees). A water basin exists nearby, to the northeast. In\ncase further, more detailed scenario developments are considered, a study will have to be carried out to\nfind a way of integrating those opportunities with the site. It is advisable to work with local stakeholders\nto identify potential consumers of the residual heat, for instance, in the fruit and vegetable sector.\n120\n\nFig. 2.42: Aerial view of candidate location for surface site PJ.\n2.6.11\nSite PJ\nDescription of the site location\nThe experiment site PJ is located in a field on a slope to the north of the A40 autoroute and to the west of\nthe Valleiry autoroute area, at the junction of the Chemin des Tattes and Chemin de Maigy roads across\nthe communes of Dingy-en-Vuache and Vulbens, Haute-Savoie, France (see Fig. 2.42 and Fig. 2.43). To\nthe west is a small stream. The site is far from any dwellings. The surface area of the site is 6.1 ha.\nThe site is accessible by the existing paved rural path Chemin des Tattes towards the north to\nVulbens. This path has to be enlarged and refurbished.\nKnown constraints\nA wildlife corridor exists that needs to be respected in the development of the surface site. If possible,\nthe corridor should be improved, as it currently functions poorly. An area with higher biodiversity in\nthe middle of the site will have to be re-created at the border of the site in conjunction with the wildlife\ncorridor. Site design will also have to take into account plans to improve soft mobility between Dingy-\nen-Vuache and Vulbens.\n121\n\nPA31-4.0-PJ\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nFig. 2.43: PJ surface site location in Dingy-en-Vuache and Vulbens, Haute-Savoie, France.\nSynergies and territorial potentials\nThe site is surrounded by numerous sloping farmlands. It will be necessary to work with local authorities\nand government notified bodies (e.g., SAFER, the agricultural chamber, DDT, DREAL) to determine\nwhere agricultural activities can benefit from the reuse of excavated materials. The site can also benefit\nfrom nearby developments to the south, over the same time frame (e.g., new national police station).\nIt seems feasible to make residual heat available to public institutions and nearby business districts in\nVulbens and Valleiry. In particular, it would be advisable to work with the department on integrating\neducational and training infrastructures with the surface site-related activities to generate local added\nvalue. The creation of a visitor centre would enable the development of high-quality, sustainable tourism.\nThe connection to the Valleiry autoroute service area for removing materials and receiving supplies via\nthe autoroute has been analysed and is feasible. To avoid trucks, a conveyor belt would be used to\ntransport the materials to the autoroute area. Incoming materials could be transported via a temporary\n700 m long road to the site. There is interest in developing synergies for the reuse of waste water to feed\nstreams and for crop irrigation.\n2.6.12\nSite PL\nDescription of the site location\nThe working hypothesis for the location of the technical site PL in Challex, Ain, France has been deter-\nmined through various iterations with the municipality in 2023 and 2024. The reference site location at\nthe nominal point can be seen in Fig. 2.44 and Fig. 2.45.\nThe site is at the nominal point in the middle of the technical straight section, near the border\nbetween France and Switzerland on an agricultural field. The perimeter includes two houses which\nwould have to be integrated in the surface site project. The location still needs to be optimised in close\ncooperation with the municipality and architects. This option, located far from the village, requires the\ncreation of an access road approximately 1.3 km long to the D89 departmental road. The route of this\nroad will be developed by an expert company in close cooperation with the commune, respecting the\n122\n\nFig. 2.44: Aerial view of candidate location for surface site PL.\nexisting environmental constraints. The area of the site is 5.5 ha. A large part of this space is foreseen\nfor rewilding.\nShould for any reason the implementation at the nominal point turn out to be unfeasible, an alter-\nnative location has been identified at a distance of 800 m in counter-clockwise direction along the straight\nsection. This location would require the creation of an access shaft about 150 m outside the line of the\ncollider and would therefore result in significantly higher costs (Fig. 2.46).\nKnown constraints\nOption with location at nominal point\nThe proximity of the Franco-Swiss border, close to vineyards, presents a challenge, as there are no roads\nor other infrastructure. However, one remote dwelling in the vicinity would be affected by disturbances\nand would therefore have to be acquired. This plot would be integrated into the surface site and serve\nfor rewilding and visibility protection. Access to the site through the village is ruled out. The roads\nare too narrow and the disturbance would be unacceptable. Building a new access route through the\nfields to the north of the village is complicated but feasible. The theoretical point is separated from the\n123\n\nPA31-4.0-PL\n0\n250\n500\n125\nm\nPoint nominal PA31-4.0\nTrac\u00e9 PA31-4.0\nSite de surface \u00e9tudi\u00e9\nChallex\nFig. 2.45: PL surface site options studies in Challex, Ain, France.\nFig. 2.46: Alternative location for site PL in Challex, Ain, France. The plot is located on the outside of\nthe collider tunnel, which calls for an underground connection tunnel and a more complicated access to\nthe radiofrequency gallery and the collider tunnel for equipment installation and maintenance.\nmain roads (Route de Greny and Rue de la Craz) at the entrance to the municipality by natural areas.\nThe forest to the north of Challex is a zone rich in biodiversity. On the Swiss side, the forest is a zone\nreserved for absolute protection (Ramsar site), the vineyards are protected, nature zones are protected,\nthe village is a cultural heritage indexed zone and the slope is too steep for surface site construction. A\n124\n\nsuspected, temporary, shallow water table was added to the Swiss maps in 2023. If this is the case, it\nwill be confirmed through ongoing geotechnical investigations. Technically, the creation of a shaft is\nfeasible, even if there is a temporary water table in this location. In the present, the investigations will\nalso determine its seasonal nature and the possibility of cross-border connections. The positioning of\nthe shaft and the entire site can be optimised according to the results of these subsurface investigations.\nFollowing an analysis conducted with the local municipality, it has been determined that this location\noption is preferred.\nOption for the location 800 m east of nominal point (not selected)\nA location 800 m east of the nominal point would not allow access inside the ring (see Fig. 2.46).\nThe site would be approximately 150 m from dwellings, 5 to 10 m lower than the municipality, on\na gentle slope of approximately 3%. It would be visible from certain dwellings. The site would partially\naffect the protected natural area, but the impact would remain limited since it is currently a field, and the\nbiological corridor passes further to the east of the site. It would be necessary to build an access road to\nthe D89 (approx. 400 m long) or to the Rue de la Craz road (approx. 300 m long). This scenario was\nused as a basis for discussions with the municipality to find an alternative to the location at the nominal\npoint.\nA technically feasible solution for access from the outside of the ring, albeit at a higher cost, has\nbeen developed. The shaft would be located about 150 m outside the ring (see Fig. 2.47). The verification\nregarding its visibility from isolated dwellings on the outskirts of the municipality has shown that this\nlocation should not be prioritised.\nFig. 2.47: Access to the main tunnel from the exterior via an underground connection. This approach is\nmore complicated and induces additional costs.\n125\n\nSynergies and territorial potentials\nThe proximity of the CERN sites (Pr\u00e9vessin in France and Meyrin in Switzerland) represents an excep-\ntional opportunity to benefit from synergies for the installation, operation, maintenance and repair of\nequipment in the shortest possible time. The fields to the north of the municipality appear to be suitable\nfor reusing excavated materials for agricultural purposes. There is no direct visibility from the village.\nThe proximity of the former Collonges train station at a distance of 12 km via the de-commissioned\nrailway tack represents an opportunity for removing materials and providing supplies, avoiding trucks\nas much as possible by using conveyor belts. A connection to the La Plaine train station in Switzerland\nwould be technically possible, but would be subject to an agreement between France and Switzerland. It\ncould also provide an opportunity for material removal via a combination of conveyor belts and railway\nsystems. The improvement of the local power grid, necessary for the construction phase, would benefit\nthe municipality and its residents. It would enable increased use of renewable energies and more robust\nvehicle recharging stations. Improving the public transport network, starting at the construction phase,\ncan also be of benefit to residents of the municipality, who currently mainly use private vehicles on the\nD884 in France and travel to Meyrin and La Plaine in Switzerland. Challex has traditionally been home\nto employees of international organisations, many of whom work at CERN. Strengthening the infrastruc-\nture would therefore benefit both the community and the project. Residual heat from the particle collider\ncould be used for heating individual and collective residences (e.g., the Les Cyclamens long-term care\ncentre), as well as for the Val Thoiry commercial centre approximately 7 km away. Other nearby commu-\nnities such as Greny, Saint-Jean-de-Gonville, P\u00e9ron and La Plaine (Switzerland) could also benefit from\nthis heat supply. The company Firmenich (perfumes and fragrances), based in La Plaine in Switzerland,\ncould also benefit from this heat. Heat could also be used in innovative ways for fish farming, aquaponics,\nmarket gardening, and greenhouses.\n2.6.13\nPr\u00e9vessin site\nThe aim of the placement studies for the injector facilities is to maximise the use of existing CERN\ninfrastructures. Considering the strong territorial constraints that have been identified and documented\nthroughout a 7-year period, the needs for electricity, raw water, a more than 1 km long space on the\nsurface for a linear accelerator and associated workshops, offices and storage zones, the existing CERN\nPr\u00e9vessin site emerged as the most suitable location for a working hypothesis. This site has the space\nto host the electron and positron sources, linear accelerators, damping rings and optional experimental\nfacilities to leverage the powerful electron-positron injector as an additional scientific instrument that\ncan be used even before the electron-positron collider enters operation. In addition, the site is at a rea-\nsonably close distance from the existing LHC surface site P8, which together with additional space in\nthe immediate vicinity, forms the surface site PA. Hence, the implementation of the transfer line, also\nleveraging the existing SPS subsurface structures, leads to an advantageous configuration. Numerous\ntechnical infrastructures such as the existing 400 kV grid connection, water supply and treatment, of-\nfices, computing facilities, room for construction activities permit the efforts that are typically linked to\nterritorial development for a new site to be kept within limits. At the current stage of conceptual develop-\nment, the injector would have a total length of approximately 1.2 km. It could almost fit into the fenced\nspace of the Pr\u00e9vessin site.\nCommon work with the authorities and further optimisation according to the \u2018avoid-reduce-com-\npensate\u2019 approach will be performed so that any unavoidable territorial extension will be kept as small\nas possible and to assure that ultimately a suitable reference scenario for the injector placement can be\nidentified.\nInitial explorations have excluded the possibility of extending the site towards the north and east\ndue to numerous nature, agriculture, and visibility constraints. The current, unfinished, working hypoth-\nesis shown in Fig. 2.48 is based on a placement between the \u2019Lion\u2019 creek and the North-Area beamline.\nThe requirements and constraints of various technical concept elements, such as the exact size and shape\n126\n\nof the damping ring, the widths and lengths of the accelerators and their integration, are today not yet\nat a level that permits freezing of the exact placement on the site. The analysis work carried out so far\npermitted, however, confirming the technical and territorial feasibility in principle and helped to identify\nthe constraints to be considered for subsequent activities.\nDuring a subsequent technical design phase, environmental analysis will guide the optimisation\nof the placement to ensure that natural constraints are respected, the required extension of the existing\nfenced domain is kept as small as reasonably possible, and that existing experimental facilities are not\nsignificantly impacted. A preliminary concept for the underground transfer line alignment avoids as\nmuch as possible conflicts with the projected construction areas on the surface. A definitive design\nwill require more detailed environmental analysis, including geology and hydrogeology. The estimated\nefforts for these analysis and design activities are in the order of two to three years. They need to be\nintegrated in the overall project environmental authorisation process.\nFig. 2.48: Sketch of the current working hypothesis for a linear-accelerator based injector that has a\nlength of about 1.2 km. A definitive placement remains to be developed in the frame of a design phase,\nconsidering environmental, existing experimental facility, territorial development and engineering con-\nstraints.\n2.6.14\nConclusion\nTable 2.6 shows the status of the feasibility analysis for the surface site locations in scenario PA31-4.0.\nTechnical feasibility was assessed using maps and data available to those working on the study and to\ncontractors. The assessment was also based on fieldwork and environmental studies carried out by spe-\ncialised companies, discussions with the relevant technical departments of the two host states, and with\nlocal elected officials (mayors, town councillors, departmental councillors, and regional councillors),\nwho represent the citizens and act in their interests.\nTable 2.6: Status of technical feasibility assessment for surface sites of PA31 scenario.\nSite\nLocation\nTechnical\nfeasibility\nFeasibility conditions\n127\n\nPA\nFerney-\nVoltaire,\nAin, France\nConfirmed\nLimit impact on the landscape, enhance the natural area\nand the existing compensation zone. Maximise synergy\nwith LHC point 8. Compensate for the loss of agricultural\nspace. Develop a visitor centre, for example, on the LHC\nPoint 8 site. Develop synergies based on heat recovery with\nmunicipalities within a 10 km radius, including Swiss mu-\nnicipalities and the Geneva airport.\nPB\nPresinge,\nGeneva,\nSwitzerland\nConfirmed\nDefine the exact location of the site on the plot and initi-\nate discussions with the municipality. Identify a location to\ncompensate for the loss of agricultural space. Limit impact\non the landscape. Take into account the sensitive location\nof the site in a natural setting. A detailed conceptual de-\nsign of the road access is to be developed and approved\nby the canton of Geneva. Reach an agreement to recycle\nexcavated materials, preferably locally. Develop synergies\nbased on heat recovery around the site with local stake-\nholders and authorities.\nPD\nNangy,\nHaute-\nSavoie,\nFrance\nConfirmed\nThere are no specific blocking points, but the major issues\nin this sector call for careful joint development of the site in\ncoordination with local stakeholders. Limit the loss of agri-\ncultural space by working on a smaller surface site. Com-\npensate for the loss of agricultural space. Maintain compat-\nibility with the proposed connection between the RD903\nand the A40. Estimated start of construction: first quarter\nof 2025. Develop a transport concept for the construction\nphase to limit impacts on a sector that is already overbur-\ndened. Develop synergies with the communities around the\nnearby hospital (CHAL), the Scientrier waste water treat-\nment plant (STEP) and the industrial zone to the north.\nPF\n\u00c9teaux,\nHaute-\nSavoie,\nFrance\nConfirmed\nThe north option along the RD1203 was confirmed, pro-\nvided that nearby wetlands are avoided. Limit the loss of\nagricultural space. For a potential southern extension op-\ntion, a decision would be required before the start of phase\n2 of the ISDI (inert waste storage facility) in La Roche-\nsur-Foron in 2027. This would allow earthworks to be car-\nried out on the western part for a smaller site, rather than\nwait for a complete development for the ISDI. Otherwise,\nannexes would need to be constructed on top of the inert\nwaste. An agreement must be reached with the ISDI oper-\nator and the landowners. The access layout should be de-\nveloped for this option. Any economic loss suffered by the\nISDI operator must be taken into account when developing\nsynergies between the site and the operator. Develop syn-\nergies with local authorities in terms of site development\nwith emergency services.\n128\n\nPG\nCharvonnex\nand\nGroisy,\nHaute-\nSavoie,\nFrance\nConfirmed\nThe site straddles the forest and the plateau, which includes\nunexploited grasslands. Two annexes close to the autoroute\narea will accommodate certain facilities (e.g., water cool-\ning system, electrical substation) to avoid any disturbance\nto the wooded area. Plan a visitor centre to develop high-\nquality, sustainable tourism. Develop synergies with the\nmunicipalities of Groisy and Charvonnex to develop the\nsite with neighbourhood services for on-site researchers\nand emergency services. The loss of woodland can be com-\npensated by reforestation around the site. The layout of the\nexisting access route to the north is suitable.\nPH\nCercier\nand\nMarlioz,\nHaute-\nSavoie,\nFrance\nConfirmed\nLimit the site\u2019s footprint and remain within the wooded\narea to avoid impacts on the dwellings to the south of the\nsite. Reduce the impact on natural habitats and biodiver-\nsity. Compensate for the impacts on woodland, habitat and\nbiodiversity that cannot be avoided and reduced. Respect\nthe easement for the gas pipeline near the site, and decide\nwhat distance to maintain between the pipeline and above-\nground infrastructure. Consider a split or displaced site\nlocation along the straight section.\nPJ\nDingy-en-\nVuache and\nVulbens,\nHaute-\nSavoie,\nFrance\nConfirmed\nCompensate for the loss of agricultural space. Preserve\necological corridors. Integrate the planned projects to de-\nvelop soft mobility between Dingy-en-Vuache and Vul-\nbens. Foresee a visitor centre to develop high-quality, sus-\ntainable tourism. Work with the municipalities to develop\nsynergy for the site with regard to neighbourhood services\nfor on-site researchers, emergency services and schools.\nPL\nChallex,\nHaute-\nSavoie,\nFrance\nConfirmed\nThe location at the nominal point has been discussed with\nthe municipality. Compensation for the loss of agricultural\nspace. A joint optimisation of the site with the municipality\nis in progress.\nCERN\nPr\u00e9vessin\nand\nSaint-\nGenis\nPouilly, Ain,\nFrance\nConfirmed\nThe location of the injector at the existing CERN Pr\u00e9vessin\nsite has been verified, and its technical feasibility has been\nconfirmed in principle.\nOptimisation of the placement\nwithin the site remains to be done based once detailed tech-\nnical requirements and invariants are available and the state\nof the environment has been analysed. Territorial devel-\nopment outside the fenced perimeter will be kept as low\nas reasonably possible. The alignment of the underground\ntransfer line to site PA will be designed considering geol-\nogy, hydrogeology and the project of constructed areas on\nthe surface.\n129\n\n2.7\nTerritorial infrastructure needs\n2.7.1\nIntroduction\nTo be able to construct, install and operate the particle-collider facility and its associated experiments,\na number of different territorial infrastructures are required. The development of the implementation\nscenario put an emphasis on leveraging existing infrastructures as much as possible (Fig. 2.49). The\nwell-developed transport, electricity, and water networks in the region around CERN are one of the\nmotivations to propose the facility in this region. The main infrastructures required and described in this\nsection are: roads that provide access to the surface sites, autoroutes to evacuate excavated materials and\nto supply construction materials and equipment, railway lines to support possible excavated materials\nand construction materials transport, electricity for the construction phase, direct access to the French\nhigh-capacity power grid for the operation, and raw water for cooling purposes.\nFig. 2.49: Noteworthy road, electricity, water treatment infrastructures, emergency services and border\ncrossings in the vicinity of the surface sites indicated by red circles.\n2.7.2\nRoad access\nThe road network is dense along the reference scenario footprint. For the site access roads, in order for\ntwo heavy goods vehicles to pass each other at reduced speed, a width of 5.50 m of roadway with two\n0.50 m shoulders is required. Subject to environmental constraints, the lanes of reinforced roads or new\nroads may be smaller: widths of 4.00 m for the roadway and 0.50 m for the shoulders are acceptable if\npossibilities for passage in both directions are foreseen. This reduced section will require instructions to\nbe given to the drivers of the vehicles concerned.\nSeveral surface sites can profit from direct road access (PA, PD, PF, PH) and some others require\nminor reinforcement of existing road access (800 m of forest path to be paved for PG, 600 m of rural path\nto be paved for PJ). Site PD requires the creation of a 300 m long dedicated access. Site PL requires the\ncreation of an approximately 1300 m long dedicated access. In total, less than 3 km of road have to be\ncreated.\n130\n\nFig. 2.50: Overview of the road and railway transport network in the perimeter of the reference scenario.\nRoad traffic analysis [38] has been carried out for all sites, and the feasibility of the construction\nwas verified with this work. Technical designs of road accesses have been developed for sites PB, PD\nand PF to ensure the feasibility in areas that are subject to particular road traffic constraints linked in PB\nto visibility and road safety, in PD due to a major road enlargement and autoroute development project\nand in PF to ensure road safety. Detailed road access designs have now to be carried out for all sites for\nthe development of a coherent design package that is required for environmental impact assessments and\nproject authorisation.\n131\n\nPB: Direct road access\nPD: Dedicated access road\nPA: Direct road access\nPF: Direct road access\nPG: Reinforcement of existing path\nPH: Direct road access\nPJ: Reinforcement of existing road\nPL: Dedicated access road\n(artistic conceptual path, not a design)\nFig. 2.51: Overview of road access concepts for each individual surface site.\n132\n\n2.7.3\nAutoroute access\nThe study examined the feasibility of connections to the autoroute network for the removal of materials\nand the supply of equipment during the construction phase [39]. The possibility of obtaining autoroute\nconnections, either directly, via conveyor belts or via temporary gravel paths during construction is a goal\nin the general interest, aimed at limiting the impact of the project, particularly during the construction\nphase. The specific technical choices will be made later, during the project development and preparation\nphase. To verify the technical, legal and financial feasibility of direct access to autoroutes, files with\nconceptual design plans and descriptions were compiled and submitted for review on 14 September,\n2022 to the competent authority for granting concessions: the Direction g\u00e9n\u00e9rale des infrastructures,\ndes transports et des mobilit\u00e9s (DGITM), Direction g\u00e9n\u00e9rale des infrastructures, des transports et des\nmobilit\u00e9s / Direction des mobilit\u00e9s routi\u00e9res / Sous-direction des financements innovants et du contr\u00f4le\ndes concessions autorouti\u00e8res / Chef du Bureau des services aux usagers et de la comodalit\u00e9 and the\nDirection g\u00e9n\u00e9rale des infrastructures, des transports et des mobilit\u00e9s / Direction des mobilit\u00e9s routi\u00e8res /\nSous-direction des financements innovants et du contr\u00f4le des concessions autorouti\u00e8res / Chef du Bureau\ndu patrimoine et de l\u2019am\u00e9nagement.\nThe feasibility of four new connections to the autoroute network was analysed and confirmed to\nbe in principle feasible (see Fig. 2.52) for the following sites:\n1. PD site in Nangy (on the A40 autoroute),\n2. PF site in \u00c9teaux/La Roche-sur Foron (on the A410 autoroute),\n3. PG site in Charvonnex/Groisy (on the A40 autoroute),\n4. PJ site in Dingy-en-Vuache/Vulbens (on the A410 autoroute).\nThe conclusions of the interactions with the DGITM were as follows:\n\u2013 The access concepts and loading/unloading areas provided are in principle acceptable.\n\u2013 Adjustments will be needed, with the final decisions to be made with the autoroute operator in the\nproject phase.\n\u2013 Detailed plans have to be developed and presented.\n\u2013 The procedure for submitting an application in the future was specified.\n\u2013 The proposed justifications, in the general interest, are acceptable;\n\u2013 Entrances and exits will need to be equipped with detection devices to manage tolls.\n2.7.4\nRailway access\nTo reduce the need for truck traffic, to generate further opportunities to supply quality construction\nmaterials from further distances and to open possibilities to transport excavated materials to appropriate\ndeposition sites and re-use locations in an environmentally friendly and high capacity way, railway access\nstudies have been carried out by a qualified domain-expert company [40\u201348].\nThe current reference scenario was taken as a working hypothesis for analysing the opportunities\nand feasibilities concerning accessing the railway system via existing installations (goods loading and\nunloading facilities) and concerning the creation of new accesses (so-called ITE, \u2018Installation Terminal\nEmbranch\u00e9e\u2019 in French).\nThe studies used a multi-criteria analysis that considered the following indicators:\n\u2013 Proximity of the surface site with a suitable railway track.\n\u2013 Technical and administrative compatibility for access with the French and Swiss railway infras-\ntructure.\n\u2013 Presence of an existing service or ITE that could be leveraged.\n133\n\nFig. 2.52:\nLocation of the autoroute connections, which were studied using existing service and rest\nareas. Blue dots correspond to autoroute rest areas, magenta dots indicate autoroute service stations and\ngreen dots indicate toll stations.\n\u2013 Feasibility of creating a transport connection between the site and the railway track access.\n\u2013 Minimum space requirements for railway access and available space.\n\u2013 Number of convoys required for evacuating all excavated materials.\n\u2013 Capacity availability and limitations on each railway line analysed.\nIt is important to keep in mind that each new railway access requires a space of about 400 m by\n40 m, i.e., 1.6 ha of land (see Fig. 2.53).\nThe train line 890000 through Meyrin, Collonges, today provides the necessary free capacity. Line\n902000 in Vulbens and line 897000 passing in \u00c9teaux and in Groisy have only limited capacities.\nThe analysis revealed the following \u2018in principle\u2019 opportunities for railway access:\nBased on the analysis, today, the most likely accesses to the railway system are the existing and\nunused train station in Collonges for site PL, new access north of Vulbens for site PJ and a new access\nwest of Groisy for site PG. While the old train station of Collonges is 13 km from the surface site PL in\nChallex, a connection with a conveyor belt can be a suitable approach, avoiding truck traffic.\nThe feasibility in principle for the creation of access in La-Roche-sur-Foron on the site of an\n134\n\nFig. 2.53: Minimum space requirements of a new railway access for goods transport.\nTable 2.7: Railway access opportunities for each surface site.\nSite\nDistance\nFeasibility\nDescription\nPA\nLess than 5 km\nUnsure\nRequires crossborder transport of materials\nPB\nLess than 5 km\nLow\nRequires crossborder transport of materials\nPD\nNo opportunity within 10 km\nUnfeasible\nPF\nLess than 1 km\nMedium\nSpace and ISDI constraints\nPG\nLess than 2 km\nMedium\nImplementation constraints\nPH\nNo opportunity within 10 km\nUnfeasible\nPJ\nLess than 5 km\nHigh\nPL\nLess than 10 km\nHigh\nVia existing, unused station at Collonges\ninert waste storage facility (I.S.D.I.) exists once that facility has been filled. However, the amounts of\nmaterials produced at site PF are limited compared to other sites, and the constraints due to the status\nof the facility (ICPE in France) and space limitations require a careful cost/benefit and administrative\nfeasibility analysis in addition to the technical analysis.\nThe technical and administrative feasibility of railway access at Geneva Airport in Switzerland\nfor site PA in France is subject to a specific analysis that will only be carried out in 2025. If it is\ntechnically feasible, an administrative challenge is to be addressed concerning the cross-border transport\nof materials in both directions: France to Switzerland for excavated materials and Switzerland to France\nfor construction materials and equipment.\nThe creation of a new ITE requires about 10 years of planning, detailed development of the variants\nto be presented for authorisation, an economic demand study concerning use beyond the FCC construc-\ntion phase, environmental impact assessment and the authorisation process. The implementation for use\nrequires about 2 years.\nIf train access is to be used for the evacuation of materials and the supply of construction materi-\nals and equipment, a detailed design and common project together with the French and Swiss national\nrailway network administration services would have to be started in a forward-looking way, starting in\n2025.\n135\n\n2.7.5\nConveyor belt links\nTo reduce the need for temporary paths and truck traffic due to excavated materials and construction\nmaterial-related transports between sites and autoroute accesses, example studies were performed to\ndetermine the feasibility of conveyor belt links [45,49] by an expert company in the domain. Two sites\nhave been selected for the case study: PJ (Vulbens and Dingy-en-Vuache, France) and PG (Charvonnex\nand Groisy, France). It is worth pointing out that the findings also apply to the other sites that were\nexamined at a high level, but no technical designs have been developed. If a preparatory project phase\nis launched, detailed technical design variants for traces and conveyor technologies for a construction\nhypothesis have to be drawn up for all eight sites and submitted for authorisation in the frame of the\nproject environmental authorisation process.\nConveyor belts would be operated with electricity with a capacity of 120 kW between the start and\nthe end of the construction activities. Based on a speed of 2 to 2.5 m/sec and a width of 650 to at most\n800 mm the following schedule has been established:\n\u2013 22 days per month.\n\u2013 226 days per year.\n\u2013 Up to 8 hours per day.\n\u2013 Operation between 08h00 in the morning and 18h00 in the evening.\n\u2013 No operation during the night, weekends or holidays.\nVarious technologies for conveyor systems have been analysed, and their costs have been esti-\nmated for the two specific locations PG and PJ. Depending on the environmental conditions (topography,\nterrain, vegetation, urban constraints) different footprint and noise-limiting systems can be considered.\nIn general, the choice is always determined by the goal to limit footprint and nuisances for the required\ncapacities, limited by the available technical constraints. Public spaces would be leveraged whenever\npossible. New routes would be limited to 3 m width. The maintenance of new routes is limited: they are\nnot permanent and the space used will be restored after use.\nThe feasibility of meeting the capacity requirements associated with a construction site that op-\nerates 2 tunnel boring machines (TBM) has been confirmed from a technical perspective and an envi-\nronmental perspective. Noise levels are between 65 dB(A) directly at the conveyor and 47 dB(A) at a\ndistance of 64 m with today\u2019s off-the-shelf technology. Example routes have been developed to confirm\ncompatibility with the noise regulations in France for both study sites.\nFor site PJ, the conveyor can be created to the autoroute service station in Valleiry (distance 700 m)\nand/or to new railway access north of Vulbens (1565 m) outside any residential area. It has to cross the\nRD 1206 departmental road. Disturbances due to noise can be avoided in both cases.\nFor site PG, the conveyor can be created to the autoroute service area in Groisy (distance of\nabout 800 m) and/or to new railway access at the north of the autoroute (925 m). The biggest challenge,\nalthough technically feasible (see Fig. 2.54) is the crossing of the A40 autoroute for a period of about 8\nyears. Residential areas are unlikely to be affected.\n2.7.6\nElectricity for the construction phase\nFor the supply of electricity during the construction phase, requests for hook-ups to local networks have\nto be made directly to the relevant national distributors (e.g., Enedis in France and SIG in Switzerland).\nAccording to information provided by company Herrenknecht, a leading TBM manufacturer, electricity\nrequirements are around 3.7 MVA for a construction site using a single TBM and around 7.4 MVA for\na construction site with two TBMs. The working hypothesis presented in Table 2.8 will be fine-tuned\nwith the civil engineering companies during a subsequent design phase before the start of construction.\nThis process will deliver the exact electrical power required during the construction phase. This will\n136\n\nFig. 2.54: Example of a conveyor crossing a major road.\ndepend on the number and configuration of the TBMs around the ring and the specific machinery used.\nAll that information will only be known with certainty shortly before the launch of the public works con-\ntracts. However, it has to be considered that planning, contracting, and implementing the local electricity\nconnections for the construction phase will require several years and will need to be part of the overall\nenvironmental authorisation process.\n2.7.7\nElectricity for the operation phase\nThe FCC-ee scientific research programme is based on different collider operating modes (Z, WW, ZH,\nt\u00aft and an optional HH mode). Each mode uses a different equipment configuration. This equipment (ac-\nceleration systems by superconducting radiofrequency cavity, electrical energy conversion systems and\ncryogenic cooling systems) will be installed progressively during the maintenance and upgrade phases\nplanned for these activities. One long shutdown (LS) is planned to install the radiofrequency systems\nfor the t\u00aft and optional HH operation modes. Each configuration is characterised by different electrical\npower needs (see Table 2.9), which serve as the basis for average consumption estimates.\nThe collider operates on a yearly schedule, with a limited period of beamline operation for physics\nresearch. The programme also includes phases for equipment testing and start-up, machine performance\noptimisation and routine maintenance. Depending on the operating mode, electrical energy consumption\nvaries from year to year.\nAt this stage of the study, it is only possible to provide approximate yearly consumption figures\n(see Fig. 2.55). The annual electricity consumption varies between 400 GWh/year for basic services that\nare in use also without beam operation and 1770 GWh/year for the t\u00aft operation phase. On average,\nthe annual electricity consumption over the operation period is slightly above 1200 GWh/year. The\ncapacities required to supply the particle collider with the required energy exist in France. However,\na plan for a specific power purchasing agreement portfolio will have to be established, allowing ample\n137\n\nTable 2.8: Working hypothesis for connection to local electricity networks during the construction phase.\nSite\nLocation\nOperator\nPower\nPA\nFerney-Voltaire, France\nEnedis\n7.0 - 13.8 MVA\n(= 400 A at 20 kV)\nPB\nPresinge, France\nSIG\n3.0 - 7.0 MVA\n(= 200 A at 20 kV)\nPD\nNangy, France\nEnedis\n7.0 - 13.8 MVA\n(= 400 A at 20 kV)\nPF\n\u00c9teaux, France\nEnedis\n3.0 MVA\n(= 100 A at 20 kV)\nPG\nCharvonnex, France\n\u00c9nergie et Services de Seyssel\n13.8 MVA\n(= 400 A at 20 kV)\nPH\nCercier, France\nEnedis\n3.0 MVA\n(= 100 A at 20 kV)\nPJ\nVulbens, France\nEnedis\n13.8 MVA\n(= 400 A at 20 kV)\nPL\nChallex, France\nEnedis\n3.0 MVA\n(= 200 A at 20 kV)\nTable 2.9:\nElectrical power need estimations for the operation phase. Technical feasibility studies\npermitted reducing power requirements by almost 45% between 2020 (initial hypothesis) and 2024.\nMode\nBeam energy\nOperation\nInitial capacity estimation\nCurrent capacity estimation\nZ\n45.5 GeV\n4 years\n65 MW - 240 MW\n30 MW - 222 MW\nWW\n80 GeV\n2 years\n70 MW - 265 MW\n33 MW - 247 MW\nZH\n120 GeV\n3 years\n70 MW - 294 MW\n34 MW - 273 MW\nt\u00aft\n175 GeV\n5 years\n80 MW - 350 MW\n40 MW - 350 MW\nHH\n182.5 GeV\n1 year\n50 MW - 384 MW\n41 MW - 357 MW\npreparation time before the energy is required to obtain favourable conditions and to contract a suitable\nenergy mix with a low carbon footprint [50,51].\nFollowing the preliminary and exploratory studies, more detailed concepts to optimise the energy\nperformance of the accelerator\u2019s equipment and to improve operations based on information provided by\nelectricity infrastructure operators and energy suppliers are required.\nThis approach will be based on the usual Avoid-Reduce-Compensate methodology.\n\u2013 Avoid: the overriding goal is to limit consumption according to a cost-benefit analysis, which\nincludes, for example: the research infrastructure layout of four experiments; limiting maximum\nannual power consumption, which will have impacts on luminosity and extending the duration of\nthe research programme; and ensuring that systems do not consume energy when not in use.\n\u2013 Reduce: this means to optimise system efficiency and reduce losses. This includes, for example,\nimproving the efficiency of electrical energy conversion for radiofrequency, reducing losses in\ninternal distribution and equipment, energy recovery and storage, smart consumption based on\nneeds (e.g., for ventilation and cooling), and developing systems that can switch more easily and\n138\n\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2046\n2047\n2048\n2049\n2050\n2051\n2052\n2053\n2054\n2055\n2056\n2057\n2058\n2059\n2060\n2061\n2062\n2063\nTWh\nFig. 2.55: Annual electricity requirements of the collider and its technical infrastructure. The average\nannual consumption over the programme is indicated by a blue horizontal line.\nquickly between operating modes (standby or operating mode).\n\u2013 Compensate: lastly, the goal of compensating is, on the one hand, to recover, store and supply\nrenewable energy for society, and on the other hand, to develop synergies for the transition to en-\nergy from renewable sources, increase renewable energy capacity and cooperate internationally for\nthe supply of renewable energy. Examples of compensation with direct economic benefits include\nthe creation of energy communities and pooling for pre-financial-investment-decision support to\nbuild up renewable energy sources, use of waste heat in industrial processes (e.g., cheese produc-\ntion), for greenhouse operations, crop cultivation and the heating of public establishments such as\nhospitals, schools, and shopping centres.\nAll these measures will need to be improved over the fifteen years of the technical design and\nconstruction phases. They are an effective way of limiting electricity consumption and its impact.\nWith regard to the various phases of the collider maximum power requirements are only necessary\nduring the t\u00aft operation phase, and during an optional phase at the end of the programme (hh) when all\nthe radiofrequency equipment is installed. On average, during the scientific research phase, the FCC-ee\nwould consume approximately 1.3 TWh per year. Over its entire lifetime, including shutdown periods\nand commissioning, its average electricity consumption would be around 1,3 TWh per year. To provide\na context for the impact of this electrical energy consumption, it can be compared to the electricity\nconsumption of a state-of-the-art data centre. For example, the Altoona (IA) data centre in the USA,\nowned by the Meta company, most known for the Facebook, Instagram and WhatsApp applications, has\nan annual consumption of 1.24 TWh [52]. The carbon footprint of this data centre is 532 158 tCO2(eq)\nper year. This corresponds to about the carbon footprint of the entire FCC infrastructure construction.\nThe consumption of all Meta company\u2019s data centres is 15 TWh/year, i.e., a factor ten higher than the\nannual energy need of the FCC-ee. The total annual carbon footprint of all Meta\u2019s data centres totals to\nabout 5 million tons CO2(eq).\nThe specific energy needs will only be known after the detailed technical development phase, so it\nwill be possible to take advantage of technical advances and development to improve energy efficiency.\n139\n\nRTE, which was entrusted with the task of managing the electricity transmission grid in France1\nthrough a public service contract dated 24 October 2005, which includes, among other things, the en-\nvironmental integration of the grid (consultation, protection of landscapes and natural and urbanised\nenvironments) and safeguarding the public grid, is responsible for analysing the connection while taking\ninto account technical choices; overseeing the hook-up process; and carrying out the necessary adminis-\ntrative procedures (connection agreement, grid access contract). RTE also carries out all works required\nto establish connections between surface site delivery points and the high capacity national electricity\ngrid once the hook-up agreement has been signed2.\nAccording to the results of the preliminary technical feasibility study carried out by RTE [53],\nwhich manages France\u2019s electrical grid, the connection to the high-power electrical infrastructure calls\nfor three supply points in France at this stage. A backup power supply point in Switzerland can be\nconsidered, but if required, its technical and administrative feasibility remains to be studied.\nAt this stage, the footprint of the reference scenario is crossed by various power lines, mainly\n63 kV and 225 kV. Two 400 kV lines cross the PA31 footprint from west to east (see Fig. 2.56). The\n400 kV lines pass close to the PL sites (Ain department in France) and the PF and PH sites (Haute-\nSavoie department, France). A major distribution station (Cornier) is located close to the PD and PF\nsites in France. Electricity needs are higher at the PL and PH sites, as these are designed to house the\nradiofrequency systems that accelerate particles in the collider.\nFig. 2.56:\nExisting or planned electricity grids in France and Switzerland within the FCC perime-\nter. Sources: Public layer CAD_ELEMENT_CONDUITE from SITG 2023 for Switzerland (https:\n//sitg.ge.ch/donnees/cad-element-conduite), available for consultation and extraction for free\nuse; for France, Open Data R\u00e9seaux \u00c9nergies (ODRE, https://opendata.reseaux-energies.fr).\nThree supply points are currently envisaged to achieve a well-balanced electricity supply scenario:\n1Decree no.\n2005-1069 of 30 August 2005 approving the status of the company RTE EDF Transport: https://\nwww.legifrance.gouv.fr/loda/id/JORFTEXT000000812363\n2RTE, Instruction des demandes de raccordement, version 2, 17 Octobre 2019, https://www.services-rte.com/files/\nlive/sites/services-rte/files/documentsLibrary/DTR%201.4.1%20Proc\u00e9dure%20Racc%20Conso%20L342-2%\n20v19%2010%2017_fr\n140\n\nOne in PL connecting to the nearby 400 kV line. One in PD connecting to the Cornier substation. One\nre-using the existing CERN grid connection in Bois Tollot (Ain, France). A detailed design study is\nrequired by RTE to determine the route and specificities of the new 400 kV connections. It may be\nadvantageous to connect site PF instead of site PD to the 400 kV line, leveraging the proximity of the\nRTE distribution point in Cornier and thus avoiding the need to cross the Arve river. It is worth noting\nthat the planning, authorisation, contracting and creation of grid power connections require substantial\nlead times. Ten years should be assumed for the entire process of one connection. In addition, for the\nentire particle collider project\u2019s environmental authorisation process, the availability of environmental\nimpact studies of the grid connections is required. Therefore, the detailed designs of the connections\nand their route variants based on the environmental constraints, technical feasibility and cost must be\ndeveloped with high priority now, even if, ultimately, the connections are only required after the civil\nconstruction phase.\n2.7.8\nRaw water supply\nThe particle accelerators need raw water mainly to cool the magnets. Synchrotron radiation is the main\nsource of heat in addition to numerous mechanical and electrical technical infrastructure components.\nAll raw water can be taken from an existing raw water supply line provided by the local Swiss company\nServices Industriels de Gen\u00e8ve (SIG) [54] that sources the water from Lake Geneva, as is the case with\nCERN today. No raw water will be consumed from drinking water reservoirs or subsurface water layers.\nThe technical solutions and equipment choices will not be known until shortly before the procure-\nment of the technical infrastructures, mid-way through the subsurface construction phase, in order to take\nfull advantage of technical advances, including those in cooling system efficiency. Estimates of the max-\nimum water requirements, based on consumption by CERN\u2019s existing accelerator cooling systems and\non the current technical concept developments, have been established (see Table 2.10. These values are\nthe result of a gradual development of a concept that permitted reducing the raw water requirements from\na maximum initial amount of 5 000 000 m3 per year for t\u00aft operation to about 3 000 000 m3 per year. The\ncurrent reference water capacity needs to assume the use of closed-circuit water cooling systems with\nevaporation towers. The raw water consumption stems from the need to make up for the evaporated\nwater in the secondary circuits of the cooling towers at each surface site.\nTable 2.10: Summary of the annual raw water needs.\nMode\nAnnual raw water\nrequirement\nYears\nZ\n1 604 861 m3\n4\nWW\n1 928 943 m3\n2\nHZ\n2 165 458 m3\n3\nL.S.\n163 817 m3\n1\nt\u00aft\n3 077 591 m3\n5\nFor comparison, the raw water consumption at CERN in 2022 was as follows:\nThe water supply scheme for raw water is based on the working hypothesis of using CERN\u2019s exist-\ning raw water supply, drawn from Lake Geneva by Services Industriels de Gen\u00e8ve (SIG) in Switzerland.\nThe available capacity of 604 m3/h leading to a total capacity of more than 5 000 000 m3 per year is\ncompatible with the needs of the FCC. This was confirmed by an exchange between CERN and SIG in\n2022. Then, in August 2023, SIG confirmed the technical feasibility of the supply within the existing\ncontractual framework either by building a new, short connection of around 200 m with a 500 mm nom-\ninal diameter between the Tuileries-La Berne pipe and Point 8 of the LHC in Ferney-Voltaire (France),\n141\n\nTable 2.11: Summary of the FCC raw water needs.\nItem\nRaw water need\nDescription\nSPS\n944 m3\nBA2, BA4, BA5, BE2\nLHC\n795 070 m3\nLHC complex, LHC2, LHC3.2, LHC 3.3,\nLHC4, LHC5, LHC6, LHC7, LHC8\nMeyrin,\nPr\u00e9vessin\n2 437 988 m3\nMeyrin and Pr\u00e9vessin sites main supply, SPS BA1 and BA6,\nLHC1 safe supply, clubs, Globe\nor by using two existing internal CERN lines which would require upgrading.\nTo make the distribution of water along the entire length of the accelerator technically easier and\neconomically more advantageous, two additional water supply points can be considered in France from\nthe Arve and/or the Rh\u00f4ne rivers. To this end, a specific territorial study would be needed, which would\nhave to integrate the quantitative management plans available for water resources (PGRE). Such water\nintakes would require the creation of water filtration and treatment plants.\nIn an effort to reduce further the water capacity needs, initial studies have been carried out to\nidentify promising levers (see Table 2.12). First, the introduction of waste heat recovery and supply from\nthe onset permits reducing the water intake needs significantly since less water needs to be evaporated if\nthe heat is supplied to consumers. The conservative scenario indicates the water-saving potential without\nadaptation of the classical operation schedule. Some commercial consumers need heat throughout the\nyear. It has to be pointed out that the realistic waste heat reuse indicated requires adaptation of the particle\ncollider operation to the season during which heat is required. Even higher saving potentials than the\nones indicated are possible, depending on the adaptation to seasonal territorial heat needs. Second,\nthe adaptive operation of the cooling system and the evaporation towers using advanced supervisory\ncontrol and potentially artificial intelligence would permit the reduction of consumption to the strict\nminimum required, compatible with the actual cooling needs. Third, the creation of an additional water\nintake next to site PD (Nangy, France) would ease the requirements on the overall system. Given that a\ndedicated water filtering and treatment facility would be required, an initial study aims to verify the use\nof waste water from the nearby Bellecombe/Scientrier waste water treatment plant (Syndicat des Eaux de\nRocailles et Bellecombe). This installation discharges treated water at an average rate of about 550 m3/h\ninto the Arve River. While in principle technically feasible and economically viable (the annual operation\ncost per m3 of water of a treatment plant required for the collider corresponds to the cost of a m3 of raw\nwater purchased from a water supplier), studies are currently ongoing to estimate the effort to reduce the\nresidual dissolved calcium carbonate (CaCO3) and germs in the water to render it compatible with use\nin the industrial cooling system.\nTable 2.12:\nWater-saving potentials with the introduction of waste heat supply scenarios and use of\ntreated waste water.\nMode\nConservative waste heat reuse\nRealistic waste heat reuse\nTreated waste water use\nZ\n356 800 m3/year\n476 800 m3/year\n685 000 \u22121 000 000 m3/year\nWW\n382 400 m3/year\n523 200 m3/year\n685 000 \u22121 000 000 m3/year\nHZ\n409 600 m3/year\n571 200 m3/year\n685 000 \u22121 000 000 m3/year\nL.S.\n96 000 m3/year\n96 000 m3/year\n685 000 \u22121 000 000 m3/year\nt\u00aft\n473 600 m3/year\n678 400 m3/year\n685 000 \u22121 000 000 m3/year\nAt this stage, from quantitative and commercial points of view, the reference scenario for water\nconsumption is technically, financially, and territorially feasible, since water extraction and consumption\n142\n\nrepresent quantities lower than CERN\u2019s actual past consumption. The availability of a supply represent-\ning twice the total maximum requirement was confirmed in 2023.\n2.7.9\nWaste water management\nConnections to the local sewage infrastructure are required at all sites for the management of drainage\nwater in the subsurface structures, rainwater collected and treated water that is purged from the raw-water\nbased cooling systems. The collected rainwater can also be reused on the sites for different project-related\npurposes and to maintain green spaces. Where possible, all collected water will be filtered and treated\non-site before it is released into the environment. From a territorial perspective, this approach is preferred\nover centralized wastewater management since it is beneficial for sustaining existing creeks, wetlands,\nand biodiversity in rewilding projects developed in association with the surface sites. Only where the\nwater does not qualify for free release would it be directed into the sewage system (e.g., due to a higher\npercentage of non-soluble residuals or during periods of heavy rain).\nAlternatively, a central waste water management concept based on returning all waste water to\na CERN site (e.g., LHC P8 and PA in Ferney-Voltaire) can be considered. For the management of\nthe cooling water, a \u2019zero liquid discharge\u2019 (ZLD) approach can also be considered. ZLD requires the\ncollection of solids from each surface site at regular intervals. A definitive choice of technology has yet\nto be taken and calls for a comprehensive, wider Cost-Benefit Analysis over the entire project period,\ncovering investments and operational factors. Water treatment technology is advancing rapidly due to\nenvironmental and sustainability constraints. It is, therefore, wise to consult experienced companies and\nconsider the various options in the frame of the environmental impact assessment before finalising the\ntechnology choice.\nWaste water from human activities (toilets, sinks, offices, visitor centres, caf\u00e9s and restaurants)\nwill be directly evacuated via connections to the public waste water system. The design for the waste\nwater network connections is to be developed in cooperation with local public administration services in\na subsequent preparatory phase, involving companies\u2019 experts in the domain. At this stage, the following\nconfiguration is envisaged for the local connections to the waste water networks:\n\u2013 Site PA: Connection to the waste water network via the LHC Pt8 in France.\n\u2013 Site PB: Connection to the local waste water network in Presinge, Switzerland.\n\u2013 Site PD: Direct connection to the waste water treatment station (\u2018STEP\u2019) SRB in Scientrier, France.\n\u2013 Site PF: Connection to the local waste water network in \u00c9teaux, France.\n\u2013 Site PG: Connection to the local waste water network via the Groisy autoroute station. Alterna-\ntively, connection to the network in Charvonnex at the D1203 in France.\n\u2013 Site PH: Creation of a new local waste water network to the nearest connection point at 250 to\n300 m distance in France. The waste water treatment station (STEP) in the vicinity of the site\nis not capable of accepting all of the waste water from the site in the most demanding cases.\nTherefore, either the STEP needs to be reinforced for the collider project or the excess water needs\nto be re-directed via a waste water network in the tunnel to sites PG and PJ. Developing the strategy\nis part of a subsequent design phase.\n\u2013 Site PJ: Connection to the local waste water network 500 m away in between Vulbens and Valleiry\nin France.\n\u2013 Site PL: Connection to the local waste water network in Challex, France.\n2.7.10\nEmergency services\nThe analysis of the different implementation scenarios revealed that the continuation of the existing ap-\nproach of serving surface sites of CERN\u2019s particle accelerators cannot be extended to the perimeter of\n143\n\nthe future particle collider without significant challenges. Although the surface sites are in the immediate\nvicinity of major road infrastructures, the distances and the traffic situation would call for intervention\ntimes, which would be too long if all sites had to be serviced from the CERN Meyrin site in Switzer-\nland. Locating dedicated emergency service personnel on each of the surface sites is prohibitive from\na financial point of view in terms of human resources and equipment, and would lead to challenges in\nthe operational management of the facility. Subsequent analysis of a single dedicated support pole pro-\nvides only limited improvements with respect to safety and emergency services. Therefore, a detailed\ngeographical analysis was carried out to identify alternative approaches (see Fig. 2.57).\nFig. 2.57: Fire-fighting and emergency services in the perimeter of the reference scenario.\nApart from site PH, the surface sites of the reference implementation scenario are close to fire-\nfighting and emergency service stations (see Table 2.13). Some of them have recently been constructed.\nTherefore, the project scenario can consider making use of support for emergency and firefighting per-\nsonnel at those stations, accompanied by regular common training and an emergency guidance centre\nat CERN. The strengthened collaboration of CERN with those services, the contribution of equipment,\nmaterials and training also leads to socio-economic benefits. These have been analysed and are part of\nthe wider socio-economic impact assessment.\nThe build up of these resources and the transition to a new operation scheme require several years\nof preparation. The ten years of construction phase provide an adequate window of opportunity to launch\n144\n\nTable 2.13: Selection of emergency services in the vicinity of surface sites.\nSite Distance Location\nCapacity Service\nPA\n1 km Pr\u00e9vessin, France\n66 persons Departmental fire fighting station CIS Est-Gessien\nPB\n5.8 km Ch\u00eane-Bougeries, Switzerland\n30 persons Cantonal fire fighting station\nPD\n0.3 km Contamine-sur-Arve, France\nn/a Hospital, Centre Hospitalier Alpes-L\u00e9man\nPD\n9 km Arenthon, France\n11 persons Fire fighting and first aid station\nPD\n12.1 km \u00c9teaux, France\n68 persons Regional fire fighting station\nPF\n3.2 km \u00c9teaux, France\n68 persons Regional fire fighting station\nPG\n2.3 km Groisy, France\n50 persons Regional fire fighting station, emergency service\nPH\n10 km Frangy, France\n37 persons Local fire fighting station\nPH\n14 km Epagny, France\n135 persons Regional fire fighting station, emergency service\nPH\n1.3 km Valleiry, France\n26 persons Regional fire fighting station, emergency service\nPL\n7.4 km Thoiry, France\n70 persons Regional fire fighting station, emergency service\nthis process, which requires agreements with the emergency and fire-fighting services.\n2.7.11\nTerritorial aspects for the management of excavated materials\nThe management of the excavated materials is treated as a project management and socio-economic chal-\nlenge rather than a civil engineering aspect. The availability of suitable deposits for inert waste decreases\ncontinuously, and prices for depositing materials continue to rise correspondingly. To provide an order\nof magnitude, the cost for the final deposit of the excavated materials can range between 385 million euro\nand 825 million euros depending on the possibilities to re-use materials or not [1].\nWhile the limestone fraction of the excavated materials can be re-used in the project, the majority\nof the 6 million m3 of in situ volume, 95% molasse and 3% morraines are the focus of the re-use pathway\ndevelopments. The aim is fourfold:\n1. Reduce the burden on the already tense situation. with respect to finding suitable deposits.\n2. Reduce the needs for long road transport.\n3. Reduce the overall project costs.\n4. Contribute to the creation of incremental socio-economic benefit generation by levering the project\nas a pilot for innovations in the area of excavated materials management.\nConcerning the aim to generate socio-economic benefits beyond the project, it has to be kept in\nmind that the molasse basin stretches north of the Alps from the Geneva region across Switzerland, Ger-\nmany, Austria up to Hungary. The use of novel methods to re-use such materials is therefore significant,\nand so are the socio-economic benefits potentials.\nIn the frame of the FCC feasibility study, leveraging the contributions of the European Commis-\nsion in the H2020 co-funded FCC Innovation Study project (FCCIS), an international, challenge-based\ncompetition called \u2018Mining the Future\u2019 was launched to explore credible, technically feasible and eco-\nnomically viable pathways for the development of molasse re-use on the 2030 timescale [55].\nDepending on the regulatory framework conditions in France and in Switzerland, between 15%\nand 30% of the molasse materials could be considered naturally polluted (e.g., naturally present hydro-\ncarbons, nickel, zinc and chromium). Hence, there will always be a residual quantity of materials that\nhas to be transported to deposits that accept such materials. It is assumed that a large amount of the other\nmaterials serves the refilling of quarries and the rewilding of the filled quarries.\nFurther pathways are currently being conceived in the frame of a field laboratory called \u2018Open-\nSyLab\u2019 (see Fig. 2.58) on CERN premises based on scientific protocols that permit the development of\nquality-managed processes and products, a legal prerequisite for the re-use of materials. Since this inno-\n145\n\nvation project only started in 2025 and much more extensive and detailed information is required about\nthe characteristics of the expected excavated materials by means of geotechnical sampling (extraction\nof borelogs in a representative set of locations along the collider tunnel alignment), a specific plan for\nthe management of excavated materials can only be drawn up at a later stage. It takes about 5 years\nto develop the processes and products to transform the molasse rock into soil that can be mixed with\nalready fertile soil and which can be effectively used for applications in agriculture, forestry, rewilding\nprojects, paths and roadside maintenance and further innovative applications such as thermal insulation\nand as construction material.\nFig. 2.58: The OpenSkyLab field laboratory on 1 ha of land marked with a red line, next to the CERN\nCMS Point 5 in Cessy, France, is developing quality managed processes for the transformation of exca-\nvated materials for use in rewilding and other societal applications. The field was prepared in the winter\nof 2025. The scientific development will last for at least four years.\nThe authorisations to implement these pathways in the frame of a new construction project can\nonly be requested from the national authorities in France and Switzerland once quality-managed pro-\ncesses and specific and localised descriptions of the re-use pathways exist and have been validated.\nExcavated materials have waste status in national legislation due to formal criteria, independent\nof their origin, treatment and degree of pollution. The application of these formal criteria renders the\nimplementation of ecological and economical meaningful principles of circular economy more difficult.\nOn 13 April 2021, Porr Bau GmbH appealed to the Court of Justice of the European Union (CJEU)\nto review a preliminary ruling under Article 267 TFEU from the Landesverwaltungsgericht Steiermark\n(Regional Administrative Court, Styria, Austria), made by decision of 2 April 2021 in the proceedings\nPorr Bau GmbH vs. Bezirkshauptmannschaft Graz-Umgebung concerning the conclusion of the Austrian\nnational court\u2019s finding that excavated materials discharged on cultivation areas constituted waste.\nIn case C-238/21, ECLI:EU:C:2022:885 [1], the Court (First Chamber) ruled:\nPoint 1 of Article 3 and Article 6(1) of Directive 2008/98/EC of the European Parliament and of the\nCouncil of 19 November 2008 on waste and repealing certain Directives, must be interpreted as preclud-\ning national legislation under which uncontaminated excavated materials, which, pursuant to national\n146\n\nlaw, are in the highest quality class,\n\u2013 must be classified as \u2018waste\u2019 where their holder neither intends nor is required to discard them and\nthose materials meet the conditions laid down in Article 5(1) of that directive for being classified\nas \u2018by-products\u2019, and\n\u2013 only loses that waste status when they are used directly as a substitute and their holder has satisfied\nthe formal criteria which are relevant for the purposes of environmental protection, if those criteria\nhave the effect of undermining the attainment of the objectives of that directive.\nAs a direct consequence of the judgement, non-contaminated excavated materials can be used\nfor ecological and economically meaningful applications if the materials meet the applicable quality\ncriteria. Formal criteria must not preclude and hamper the use of excavated materials and hinder the\nimplementation of circular economy principles. The end-of-waste status can be reached by mere quality\ntest. The pre-treatment, treatment, and transformation of the excavated materials have no impact on the\npossibility to use the materials, since they are integral parts of a production process described in EU\nDirective 2008/98/EC on waste Article 6.\nTherefore, re-use of excavated materials is possible in an EU country if one knows the quality\nof the excavated materials to a sufficient extent to organise the re-use before extraction and concludes\nagreements with customers for the materials for applications that are compatible with the materials\u2019\nquality that can be delivered including any potential processing before delivery and the re-use pathway\nis ecologically justified and economically viable.\nTo support this process, the project needs to implement a comprehensive monitoring system for\nthe analysis of the materials excavated, their treatment on the excavation site, their pre-processing and\nprocessing, the production of the end product, the transport to the customers (audit and traceability) and\nthe monitoring of the re-used materials after the customers have accepted them.\nFinally, the transnational transport must be carefully planned. Since the fair share principle yields\nan amount of materials under Swiss territory that is larger than the volume excavated on this territory,\na solution for either the repatriation of excavated materials from France to Switzerland or a form of\ncompensation needs to be developed before the excavation process can start.\nFor the refilling of quarries, the feasibility study has identified suitable locations on the 2030 time\nhorizon. However, it must be kept in mind that these locations are rapidly being consumed by other\nconstruction processes, and therefore, capacities must be reserved in good time via agreements between\nCERN and the quarries. While the study in France could be exhaustively carried out for the region\nconcerned (Fig. 2.59), data for potential quarries and mines that can be re-filled remain incomplete for\nSwiss territory today.\nWhile transport of the materials in the vicinity of the project by truck along major transport axes\nremains the primary assumption, transport between the excavation sites and the transport axes is prefer-\nably carried out with alternative means such as conveyor belts. Transport to re-use locations at further\ndistances is preferably carried out by train.\nAs a first step, a strategy for the management of excavated materials has been established as a joint\neffort of technical domain experts and organisations in host states that regularly accompany large-scale\nconstruction projects. Currently, processes and products are being developed to demonstrate the reuse\npotentials of molasse materials. At the same time, a baseline plan for the management of the expected\nmaterials has to be drawn up that confirms that the quarries and mines and the deposit availabilities can\nserve a conservative excavated materials scenario in both host countries. Work with host state author-\nities is needed to present the quality managed re-use processes and to obtain the authorisations for the\napplication of these processes. Agreements with customers need to be established in order to be able to\nimplement the re-use pathways. Significantly more samples and detailed analysis of geological samples\nneed to be taken along the tunnel alignment to come to a more precise estimate of a re-use scenario. To\n147\n\nFig. 2.59: Capacities of quarries that could be re-filled in the vicinity of the project on French territory\nand in the canton of Geneva in Switzerland. Capacities are indicated in tonnes.\ntechnically support the strategy, the online materials analysis during tunnelling and the on-site treatment\nand processing of the materials in a modular plant need to be demonstrated and brought to the industrial\napplication level (TRL level 9) within at most five years. The open question of railway transport, cross-\nborder traffic and repatriation of excavated materials needs to be resolved. Finally, alternative re-use\npossibilities at larger distances should be investigated, since once materials are on a railway track they\ncan be delivered with only a little additional carbon footprint. This opens up possibilities for re-uses that\nare currently not considered.\n2.7.12\nTransport and mobility\nConcerning transport of materials and equipment and mobility of persons, the following topics are iden-\ntified in the frame of the territorial implementation project development:\n1. Transport of construction materials to the construction sites.\n2. Evacuation of excavated materials from the construction sites.\n3. Commute of construction workers to and from construction sites.\n4. Transport of technical infrastructure and particle accelerator equipment to the surface sites.\n5. Transport of goods and consumables to the surface sites for operation, maintenance, and repair.\n6. Commute of personnel to and from surface sites for operation, maintenance, and repair.\n7. Visitor-induced traffic at experiment sites.\nThe most important contributor to additionally induced traffic is the evacuation of excavated ma-\n148\n\nterials. The strategy for a future project is to limit the use of trucks for transport from the sites and to rely\non alternative approaches such as conveyor belts and ropeways to create links to nearby major transport\naxes (e.g., autoroute service stations, railway terminals, multi-lane departmental roads). Such modalities\nare also suited for bringing in certain construction materials from the major transport routes to the sites.\nWhere this is not possible, trucks bring in equipment from the major transport axes via temporary routes,\ne.g., for pre-cast concrete elements and bulky particle accelerator and technical infrastructure equipment.\nOnly where such an approach cannot be avoided local roads will be used for limited construction and\ninstallation-related activities. Special transports will be unavoidable, but occur only very rarely and ac-\ncording to planned and authorised schedules and conditions. Construction materials-related traffic is very\nlimited, typically less than 10 deliveries per site that features a tunnel boring machine. The traffic during\nthe installation phase is of the order of 9 deliveries for a technical site and 18 deliveries for an experiment\nsite. The limiting factor is the amount of materials and equipment that can be transferred from the surface\nto the subsurface, as well as the limited transport and installation capacities in the underground structure.\nToday, a preliminary estimate of the number of construction workers per site shows that the pres-\nence varies between approximately 50 and 450 throughout the multi-year construction phase (Fig. 2.60).\nSignificant differences in workers on construction sites occur between sites with tunnel boring machines\n(PA, PD, PG, PJ) and sites without tunnel boring machines (PB, PF, PH, PL). Sites without tunnel boring\nmachines do not see the presence of more than 100 persons at a time. The amount of workers exceeds 250\npeople only during the peak activity period between 2035 and 2039. A specific personnel mobility plan\ncan only be developed once the construction activities are defined in greater detail during a preparatory\nphase project to prepare market surveys and tenders for the construction. To avoid that workers commute\nindividually between the construction sites and their residences, the construction plan will have organ-\nised shuttle transfers as is best practice in construction and industrial operation. The same approach will\nbe taken for the installation phase during which about 200 to 300 people would be active on experiment\nsites and about 100 people on technical sites. A small fraction of people will have to rely on individual\ncar transport. However, it is foreseen to keep such traffic limited to cases where such transport is needed.\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n2032\n2033\n2034\n2035\n2036\n2037\n2038\n2039\n2040\nPA\nPB\nPD\nPF\nPG\nPH\nPJ\nPL\nFig. 2.60: Example scenario of construction workers per construction site and year. A specific personnel\nand mobility plan has to be developed in the frame of a preparatory phase project when construction\nactivities are defined at a more detailed level.\nPersonnel commuting during operation is negligible. For maintenance and repair periods, shuttle\n149\n\ntransfer can again be foreseen. This also supports the participation of members of the international\ncollaboration who do not necessarily have individual transport means. No more than 10 to 30 people are\nexpected to be present on a surface site, depending on the type: a technical site or an experiment site.\nVisitor traffic to and from experiment sites is typically centrally organised with shuttles. If a site\nfeatures a visitor facility or additional cultural, educational, and leisure infrastructure, capacities for\nindividual traffic have to be planned. Assuming an expected presence of 25,000 visitors per year and per\nsite and 50% of individual visitors with 2 persons per vehicle, the individual traffic is in the order of 5 to\n10 vehicle round trips per site and day. It needs to be noted that visits only take place during about 250\ndays per year and during about 8 hours per day.\n2.7.13\nLandscape integration and architectural strategy\nContext\nGeneric technical designs of surface site buildings have been developed in the frame of the feasibility\nstudy to understand the space needs better, the compatibility of the required technical infrastructures\nwith the numerous surface site location constraints (e.g., topography, relief, visibility, nature, technolog-\nical risks, access, and many others) and the costs. These conceptual developments are not to be confused\nwith specific surface site designs that are eventually turned into plans to be included in the environmental\nauthorisation process. This activity also required and engagement of local stakeholders in participative\nworkshops, compliance with numerous applicable requirements and constraints such as functional and\nstructural performance requirements, zoning limitations (permitted land use), soil and subsurface pro-\ntection, urban planning documents and regulations, national and international norms, building codes and\nstandards, energy efficiency regulations, safety, emergency response, noise protection, containment of ar-\ntificial light pollution, accessibility, habitat and biodiversity protection (e.g., corridors and continuities),\ncultural and heritage considerations, landscape integration and ultimately, a societal licence to operate.\nFor these reasons and to prepare a potential subsequent project preparatory phase that needs to\ninclude the developments of the specific surface sites and the constructions on those sites, the feasibility\nstudy launched a first exploratory analysis to identify suitable components for an architectural toolkit\nthat can guide this subsequent work. The architecture concepts have been developed by an expert com-\npany with experience in the field of innovative architecture, building design and urban development and\nplanning. A multi-sectoral team of architects, planners, designers and urban planners came together to\ndraw up the seeds that need to be further developed into a comprehensive architectural toolkit for the\ndesign phase.\nThe elements of the architecture toolkit are all based on actually implemented projects Three\nnoteworthy examples (Fig. 2.61 developed by the contract company include:\n1. The Forest Tower3 at Camp Adventure Park in Gisselfeld Klosters Skove, Denmark. This project\nfeatures a 900-metre boardwalk connected to a 45-metre-tall observation tower, allowing visitors\nto experience the forest from a unique vantage point. The continuous ramp design ensures acces-\nsibility for all visitors, regardless of physical condition.\n2. The Living Places Copenhagen, which demonstrates a new way of building homes with a carbon\nfootprint of 3.8 kg/CO2/m2/year, three times lower than the current average. This project show-\ncases working sustainability and innovative designs.\n3. The Urban Village project develops a model for developing affordable and liveable homes. It\ncomprises the designs of modular, affordable and low-carbon footprint buildings that can be easily\nassembled in constrained, urban environments.\nAnother example is the project CO-EVOLUTION, a Danish/Chinese collaboration on sustainable\n3https://www.campadventure.dk/en/skovtaarnet/\n150\n\nurban development in China, which was awarded the Golden Lion in 2006 at the Venice Biennale of\nArchitecture.\nFig. 2.61: Three examples of innovative projects designed by the company that was engaged in the\nfeasibility study to develop and architecture guidance toolkit. From left to right: forest tower, living\nplaces, urban village.\nArchitectural toolkit\nThe motivation for the development of an architectural toolkit is to support the integration of surface sites\nas early as possible into their territorial contexts which differ from site to site. An additional question\nthat the toolkit aims to address is how new surface sites can create benefits to the territory and the local\ncommunities around the sites.\nThe toolkit builds on three pillars:\n1. Architecture concepts and elements,\n2. Landscape and\n3. Community\nThe three building blocks, architecture, landscape, and community (Fig. 2.62)) are the focus of\nthe integration strategies for the surface sites. The strategies aim to balance technical requirements with\nenvironmental sustainability and community engagement. The incorporation of architectural innovation,\nlandscape restoration, and public amenities seeks to minimise the ecological and visual footprint while\nfostering biodiversity and local engagement.\nArchitecture\nThe architectural design concepts emphasise sustainable and aesthetic integration into the environment.\nDesigners will adopt modern approaches such for instance green roofs, innovative construction tech-\nniques, and facade expressions to achieve these goals. These methods reduce the industrial structures\u2019\nvisual dominance. They facilitate a seamless transition between buildings and the surrounding landscape.\nDesigners are encouraged to explore novel materials and construction techniques that align with both en-\nvironmental and economic objectives. The incorporation of green roofs not only mitigates environmental\nimpacts but also enhances the visual cohesion between built and natural environments. An example for\na recent implementation of this concept is the one of Carlo Ratti for the Mutti food processing company\nin Italy [56] (See Fig. 2.63).\n151\n\nGreen roofs\nFacade expression\nInnovative construction\nNature restoration\nUtilising the terrain\nUninterupted landscape\nUse of excess energy\nEducation\nCommunity services\nFig. 2.62: Examples of elements from the architectural toolkit conceived as a basis to further develop\narchitectural guidelines for surface site developments.\nLandscape design\nThe project plans to employ strategies that prioritise ecological restoration and visual harmony. Key\ncomponents include:\n\u2013 Nature restoration: Restoration efforts enhance local ecosystems by promoting biodiversity and\nincreasing resilience against environmental changes. Utilisation of natural terrain: By embedding\nstructures into the existing landscape, designers minimise visual disruptions and maintain natural\nterrain continuity.\n\u2013 Utilising the terrain: Working with the natural terrain minimises the facilities\u2019 visual presence in\nthe surroundings.\n152\n\nFig. 2.63: The green roof created from the excavated materials of the construction site allows the building\nto blend with its natural surroundings. (Agnese Bedini and Melania Della Grave/DSL Studio)\n\u2013 Green buffers: The implementation of vegetative barriers reduces the visual and environmental\nimpact of facilities, supporting local flora and fauna. The landscape design ensures that facilities\nare integrated subtly into the environment, allowing nature to thrive while masking infrastructural\nelements from view.\n\u2013 Uninterrupted landscape: By embedding constructions into the relief and the landscape, nature can\nflow uninterrupted above, while the facilities can be partially hidden from view.\nCommunity engagement\nThe project is committed to actively involve local communities surrounding the sites by creating shared\nspaces, educational opportunities, cultural spaces and visit facilities. Depending on the community sup-\nport, professional and/or leisure services can be foreseen in the designs. Examples of specific actions\ninclude, for instance, the establishment of recreational areas such as community gardens, which utilise\nunused spaces while benefiting local populations. Providing educational platforms and visiting facilities\nallows the public to learn about the project\u2019s scientific objectives and technical achievements. They per-\nmit opportunities for direct engagements with scientists and the international engineering community.\nLeveraging excess energy for community purposes, such as heating public swimming pools, health and\nrelaxation facilities and supporting other leisure activities, are further possibilities that can be taken into\nconsideration. Through these initiatives, the project fosters a sense of inclusion and provides value to\nsurrounding communities beyond its core scientific mission.\nThe integration strategies for the FCC surface sites reflect a comprehensive approach to address-\ning environmental, technical, and social dimensions. By combining architectural innovation, ecological\n153\n\nrestoration, and community-centred design, the project ensures a sustainable and harmonious coexis-\ntence with its environment. These strategies not only aim at mitigating potential negative impacts but\nalso provide tangible and concrete actions to enhance local ecosystems and engage the public effectively.\nSite PA\nExperiment Site PA in Ferney-Voltaire (Fig. 2.64) is located in an already urban environment that con-\ntinues to see further constructions such as a commercial and high-tech innovation quarter, health-care\nproviders, residential buildings and commercial facilities. Located in a crossborder context with the\nGeneva airport and a border crossing in the immediate vicinity, the remaining open space would be par-\ntially occupied by the surface site. Therefore, a good integration and preservation of the view of the\nMont Blanc mountain chain need to be ensured. The surroundings of the site can be restored to create\nadded value for an existing habitat and nature corridor. The image below gives an impression of how the\nsite could embed into the open land, exploiting the immediate vicinity of the existing LHC point 8 (not\nshown) for any constructions and infrastructures that are not necessarily required to be in the immediate\nproximity of the two shafts.\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n10.\nHall d\u2019assemblage\n11.\nStockage Azote\n12.\nZone de fabrication des bobines\nSite Boundary\nGreen buffer - Trees Green\nbuffer - Meadow Wetland\nAccess road\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nbuilding\narea\nFig. 2.64: Space requirements for a site and landscape integration of experiment site PA in Ferney-\nVoltaire, France.\nSite PB\nTechnical site PB in Presinge, Switzerland, is located in an open agricultural landscape away from vil-\nlages. The area is, however, frequently used for leisure activities by residents, such as walking and\n154\n\nrunning. Together with the protected nature spaces in the immediate vicinity, the context calls for good\nlandscape integration. Conventional industrial buildings are not an option for this location. The architec-\ntural toolkit aims to provide guiding principles that need to be applied together with the local stakeholders\nto yield an acceptable site that provides the technical functionalities required for the science project. Fig-\nure 2.65 outlines the total space requirements for the FCC-ee and the FCC-hh phases. The envelope\nindicated can be kept as small as possible but as large as needed to develop appropriate landscape inte-\ngration based on an uninterrupted landscape and nature restoration. The aim is to create additional value\nby extending the nature preservation site and providing additional habitat to create improved conditions\nfor biodiversity growth and human leisure activities.\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\nSite Boundary\nGreen buffer - Trees \nAccess road\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nbuilding\narea\nFig. 2.65: Space requirements for a site and landscape integration of experiment site PB in Presinge,\nSwitzerland.\nSite PD\nExperiment site PD in Nangy, France is located between the A40 autoroute and the newly developed\nRD903 multi-lane departmental road that passses right outside the southern end of the site. The sur-\nroundings are dominated by the large regional hospital \u2018CHAL\u2019, an industrial zone in the north with a\nlarge milk processing facility and a mixed commercial and residential quarter on the opposite side of the\nmulti-lane departmental road. Although the area is large and open, the site is not highly visible, since\nit would be developed on a slope. The topographic conditions call for a terracing approach from north\nto south. Although buildings and equipment for the hadron collider phase do not need to be constructed\nfor the first, lepton collider phase, the site development and landscape integration call for a planned site\n155\n\ndevelopment of the terraces from the onset. Green spaces will, therefore, dominate the site during the\nfirst operation phase. Access to the site from the north is exclusive, so no additional traffic is generated.\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\n10.\nHall d\u2019assemblage\n11.\nStockage Azote\n12.\nZone de fabrication des bobines\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nSite Boundary\nGreen buffer - Trees Green\nbuffer - Meadow Access road\nbuilding\narea\nFig. 2.66: Space requirements for a site and landscape integration of experiment site PD in Nangy,\nFrance.\nSite PF\nTechnical site PF in \u00c9teaux, France is directly located on a national road with heavy traffic. A public\nworks company is established on the opposite side of the road. The area is characterised by an open\nview towards the Pre-Alp mountains and the slope falling off to a forest and small creek in the south\nat the A410 autoroute making the site partially visible from the national road. The architectural toolkit\nprovides means to foresee the restoration of nature in this location, thus creating added value despite the\nconsumption of agricultural space. Wetlands in the immediate vicinity of the site that are not adequately\npreserved today can be improved to create habitats and catalyse the lasting growth of biodiversity in\nthis area. Figure 2.67 shows the space requirements for the technical site and the opportunities for the\nwetland restoration in the west. The restored space is approximately as large as the constructed space.\nSite PG\nExperiment site PG spanning an area across the borders of Groisy and Charvonnex in France is located in\na mixed natural environment, a forest, and a pasture used for cattle. Avoiding the forest is not possible,\nsince the main shaft to the experiment cavern cannot be displaced and only little flexibility exists for\nadjusting the location of the shaft to the service cavern. The habitat and biodiversity constraints generated\n156\n\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\nSite Boundary\nGreen buffer - Trees \nWetland\nAccess road\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nbuilding\narea\nFig. 2.67: Space requirements for a site and landscape integration of technical site PF in \u00c9teaux, France.\nby the forest call for a reduction of woodland consumption as much as possible. Consequently, a split site\nlocation is envisaged that places visually and noise-impacting infrastructures close to the autoroute in the\nnorth, facilities that can be displaced to the open plateau outside the forest and keep only strictly needed\nequipment such as lifts and ventilation close to the shafts. The result is a site that covers a larger area but\nwhich impacts nature much less than a monolithic site. The configuration permits the creation of added\nvalue through a visiting facility. The first phase dedicated to the lepton collider would keep the spaces\nlargely free of construction and green. Only the second phase, dedicated to the hadron collider, calls\nfor temporary constructions for winding the coil of the detectors and permanent cryogenic refrigeration\nsystems. An area and trees equivalent to the cleared area and trees can be re-created on the site area that\nis currently open pasture and on clearings in the forest that have been created historically. This means\nthat the site development will eventually aim at an overall neutral balance with respect to habitat and\nbiodiversity preservation and it can create added value through visitor facilities. Figure 2.68 shows the\nspace requirements for constructions at the main site location (right) and the annex close to the autoroute\n(left). The green spaces for nature restoration and an example of a visitor facility can be seen in the\nbottom part of the main site.\nSite PH\nTechnical site PH in Cercier and Marlioz in France would be entirely located in a woodland on a rather\nsteep slope at the nominal location. In terms of integration, the main technical challenge is the slope that\ncalls for a terracing approach. The site would be entirely hidden in the forest. The technical require-\n157\n\nL\u00e9gende :\n1.\nCentre de visiteurs\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\n10.\nHall d\u2019assemblage\n11.\nStockage Azote\n12.\nZone de fabrication des bobines\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nSite Boundary\nGreen buffer - Trees Green\nbuffer - Meadow Access road\nbuilding\narea\nFig. 2.68: Space requirements for a site and landscape integration of experiment site PG in Charvonnex\nand Groisy, France. The right image concerns the main site around the shafts and the left image depicts\nthe annex close to the autoroute that helps to reduce the impacts on nature, habitat, biodiversity, visibility\nand noise.\nments for hosting all equipment to operate the radiofrequency system require, however, substantial space\n(Fig. 2.69). The major construction elements are the 400 kV electrical substation, the power converters,\nand the cryogenic refrigeration system.\nAlthough the location is technically feasible, environmental impact analysis and engagement with\nlocal stakeholders following the avoid-reduce-compensate scheme may still call for further reduction of\nspace consumption. In this case, splitting of the site into an electrical part that can be further displaced\nand elements that need to be close to the shaft (cryogenics, cooling, ventilation) can be re-considered.\nFrom an architectural perspective, the site buildings are less demanding than the others since the\nsite is invisible from the outside.\nSite PJ\nExperiment site PJ in Dingy-en-Vuache and Vulbens in France is located in an agricultural area just south\nof the A40 autoroute, with existing road access to Vulbens. The existence of a fauna corridor will need\nto be considered when developing the site integration. The site is not visible from the autoroute or the\ncommunes. It is remote from any hamlets or individual houses. The topographic and relief constraints\ncall again for a terracing approach that makes it necessary to prepare the entire site for both collider\nphases (ee and hh) from the onset. The terrain provides a good means to integrate the site visually and\nto foresee a visit facility. The existence of developing soft mobility connections between the communes\nin the vicinity can also be integrated in the site planning. Most of the surface would be kept as grassland\nuntil the second particle collider is installed. Several spaces that would be needed for this phase would\nalso be created already during the first phase, since the terracing approach permits the creation of covered\n158\n\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\n10.\nSyst\u00e8mes Radiofr\u00e9quence\n11.\nStockage Azote\nSite Boundary\nGreen buffer - Trees \nAccess road\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nbuilding\narea\nFig. 2.69: Space requirements for a site integration of technical site PH in Cercier and Marlioz, France.\nand half-buried volumes that can be used for different purposes at different times. As at other experiment\nsites, coil winding and detector assembly facilities would only be temporary. These areas would be\nrestored to green fields afterwards (Fig. 2.70).\nSite PL\nTechnical site PL in Challex, Ain department, France would be located on an open, flat, agricultural\nspace and the location of two individual houses. Vineyards in the vicinity on Swiss territory exist on\nslopes that fall steeply off to the Rh\u00f4ne river and to the Allondon river zone. The vicinity of the site\nlocation outside the village is used for leisure activities such as walking, hiking, running and visiting\nthe vineyards by local residents and by tourists. Full exploitation of the architecture guidance toolkit\nfor very good integration into the landscape is therefore a primary goal. Since the very even terrain\ncannot be effectively utilized to integrate the site into the landscape, lowering the site a little to avoid\ndisrupting the landscape can mitigate some of the visibility challenges. Facade expressions, natural\nconstruction materials, green facades and roofs, and visibility screens will be essential elements for the\nsite architecture and design. The surface area foreseen for this site includes an additional green buffer on\nspace that is unusable for agricultural exploitation to be able to ensure that the visibility of the site can be\nkept low and that the integration can be very well planned and implemented. Such integration also helps\nimprove the habitat value, supporting the thriving of biodiversity and making the area more attractive for\nleisure activities. Only a small difference between the lepton and the hadron collider phase constructions\nis planned, ensuring that the site is developed definitely as much as possible from the onset.\n159\n\nL\u00e9gende :\n1.\nCentre de visiteurs\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\n10.\nHall d\u2019assemblage\n11.\nStockage Azote\n12.\nZone de fabrication des bobines\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nSite Boundary\nGreen buffer - Trees Green\nbuffer - Meadow Access road\nbuilding\narea\nFig. 2.70: Space requirements for a site integration of experiment site PJ in Dingy-en-Vuache and Vul-\nbens, France. The architecture toolkit suggests centring the site between existing tree lines to ensure\nthat functional fauna corridors are created. Compared to today, they can lead to an improvement of the\nhabitat conditions.\nConclusions\nFigure 2.72 depicts the results of the application of the architectural toolkit on some of the surface site\nlocations. These works do not represent designs or specific architectural choices for the implementa-\ntion. They serve as a tool to engage with the local stakeholders to start a dialogue on the needs and\nconstraints in each location. They permit developing architectural concepts and designs as a cooperative\neffort, federating the scientists and engineers designing the research infrastructure, the architects and\nlandscape planners developing the sites, and the local stakeholders. The engagement first takes the form\nof collaborative workshops with representatives of the population and interested local stakeholders in\neach location. This phase also includes common field visits to get a better understanding of what can re-\nalistically be envisaged and what is needed both from technical and stakeholder sides. Requirements and\nconstraints from the technical project will be integrated in that activity. Once the boundary conditions\nare agreed upon and documented, a further, more detailed phase can start in which architect-engineers\ndevelop specific scenarios for the sites. The goal is to come to well-balanced and adequately integrated\nsite designs in a subsequent project preparatory phase. The results in the form of design plans, descrip-\ntions, and construction prescriptions will be included in the environmental authorisation process in each\nhost state.\nIt should be noted that the architectural concept and design developments of a public project of\n160\n\nL\u00e9gende :\n1.\nGu\u00e9rite d\u2019acc\u00e8s\n2.\nB\u00e2timent T\u00eate de puits\n3.\nSyst\u00e8mes Ventilation\n4.\nSyst\u00e8mes Refroidissement\n5.\nSyst\u00e8mes Cryog\u00e9nie\n6.\nStockage Helium liquide\n7.\nStockage Helium gazeux\n8.\nSyst\u00e8mes \u00e9lectriques\n9.\nSous-station \u00e9lectrique\n10.\nSyst\u00e8mes Radiofr\u00e9quence\n11.\nStockage Azote\nSite Boundary\nGreen buffer - Trees \nAccess road\nCode couleur :\nPhase 1 : FCC-ee \nPhase 2 : FCC-hh\nbuilding\narea\nFig. 2.71: Space requirements for a site integration of technical site PL in Challex, France.\nthis scale with eight new surface sites occupying several ha of space each call for a timely market survey\nand tendering process for a qualified partner. The availability of such an architectural company must\nbe ensured in terms of minimum personnel and uninterrupted time to work on the project. The entire\ndevelopment process is estimated to span several years.\n161\n\nApplication of the architectural language elements to the experiment site location PA in Ferney-Voltaire, France\nApplication of the architectural language elements to the experiment site location PD in Nangy, France\nApplication of the architectural language elements to the technical site location PL in Challex, France\nApplication of the architectural language elements for the concept of a visitor center at PG in Charvonnex/Groisy, France\nFig. 2.72: A collection of some artist concepts that result from the application of the architecture toolkit\nto individual site locations. Landscape integrated designs call for early preparation of the plots, and green\nbuffers will have to be prepared during the subsurface construction phase to be able to screen the sites\nfrom the beginning.\n162\n\nChapter 3\nEnvironment\n3.1\nContext\nThe international, collaborative FCC feasibility study created a basis for the subsequent environmental\nauthorisation processes of the project in the two Host States, aiming at a single permit for the project in\neach country. The term project, in agreement with the national and internationally applicable regulatory\nframeworks, refers to any intervention in the natural space including the soil. It requires three essential\nparts:\n1. An intent to construct that is communicated to authorities.\n2. A documented definition of the scope of the project, comprising indirect and induced connected\nprojects.\n3. A documentation of the project boundaries and interfaces.\nThe term project is to be understood in a broad sense. It embraces all elements that are required\nto construct and operate the particle-collider-based research infrastructure. It includes, therefore, (1)\nthe research infrastructure and (2) all territorial enabling developments and elements in France and in\nSwitzerland that are required to construct and operate the research infrastructure.\nThe research infrastructure, in turn, is composed of the subsurface and surface structures, all tech-\nnical infrastructure, the particle accelerators and the experiment detectors. The territorial development\nelements include, but may not be limited to: raw and drinking water supply; non-public sewage and\nwater treatment; low, medium and high voltage supplies; access roads; optional autoroute and railway\naccesses; facilities for waste treatment and management; excavated materials storage; final depot and\nre-use sites; compensation sites.\nTerritorial annex projects will need to be considered and developed collaboratively with the Host\nStates. For instance, these may include, but are not limited to, emergency and safety services, as well\nas temporary housing related to the construction phase, reinforcement of education facilities for workers\nand project participants (e.g., schools), health services for workers and project participants, district heat-\ning networks to supply the waste heat to consumers, water intakes that are shared with public clients, a\nregional geodetic network. Consequently, the project consists of segments that can ultimately be under-\ntaken by different organisations and may involve multiple actors with distinct responsibilities. Defining\nthe scope, boundaries, and interfaces will therefore be of utmost importance for a construction prepara-\ntory phase. This study was limited to the identification of the most relevant project segments and the\nlaunch of the process for gathering their requirements and key characteristics.\nThe term environment refers to all elements that surround the project (Fig. 3.1). According to\nthe EU regulation EC 2011/92/EU and the French \u2018Code de l\u2019environnement\u2019, articles L.122-1, R.122-\n2 and the European Norm EN 14001 section 3.2.1 the environment is to be understood in the largest\nsense. Specifically, the French Code de l\u2019environnement (article L110-1) includes aspects such as the\nspatial context, natural resources, habitats, noise, odour, sites, landscape, air quality, water quality, all\nliving species, biodiversity, soil, geodiversity (subsurface conditions), fauna, flora, climate, social coher-\nence, economy and the well-being of human beings. In Switzerland, the Manuel de l\u2019\u00c9tude d\u2019Impact\nsur l\u2019Environnement (Manuel EIE) guides environmental impact assessments under the Ordonnance sur\nl\u2019\u00e9tude d\u2019impact sur l\u2019environnement (OEIE), derived from the Loi sur la protection de l\u2019environnement\n(LPE) at federal level. It covers climate, sites, historical monuments, archaeology, natural dangers,\nterritorial and spatial development, air, noise, vibrations, energy, non-ionising and ionising radiation,\n163\n\nsubsurface water, surface water, aquatic ecosystems, water management, soil, polluted sites, waste, dan-\ngerous substances, dangerous organisms, prevention of major accidents, forests, flora, fauna, biotopes,\nlandscape, light immission, paths for pedestrians and hiking, cross-border effects, as well as cantonal\nenvironmental protection regulations as long as they do not disproportionately limit the implementation.\nFollowing the requirement to identify and understand the direct and indirect interactions of the\nsegments and the potential challenges that emerge from them, a variety of topics need to be considered.\nThese include, for instance, but are not limited to the geology, hydrogeology, urbanism, health and safety\nof people, the well-being of all living species concerned, traffic and mobility, services and infrastructures,\nnatural and cultural heritage, traded goods such as waste of all types, synergies, and conflicts with other\nplanned projects, material goods such as physical items that are privately or publicly owned, technical\nrisks, and many more.\nFig. 3.1: The environment refers to all elements that surround a project and their interactions with the\nproject and among them. It is to be understood in the largest sense.\nAn environmental aspect refers to any project element or process that interacts with the envi-\nronment. Identifying and prioritising these aspects hierarchically is a prerequisite for environmental\nimpact assessment. Several can be identified and quantified early; though eventually, they depend on\nrequirements and design choices. The challenge in large-scale particle collider projects is their iterative,\ndecades-long design process. While subsurface structures and construction are planned first, technical\ninfrastructures follow accelerator and experiment designs, with surface structures finalized later to incor-\nporate advanced techniques and stakeholder-driven landscape integration. This evolving process, guided\nby a plan-do-act-check cycle, generates a challenge for a timely impact assessment for long-term projects\nwith territorial implications.\nAn environmental impact is any change to the project environment resulting from an identified,\nrelevant environmental aspect. It emerges from the intersection of the environmental sensitivity in a cer-\ntain location (environmental issues and challenges) and the potential effects of an environmental aspect\nof a project element (Fig. 3.2). The impacts can, therefore, only be analysed and assessed for a spe-\ncific, localised project scenario. The impact assessment also requires a certain stability in the designs\nand a sufficient level of design detail. In practice, the following elements are required for the impact\nassessment:\n1. A specific project scenario (description, location, scope, boundaries, interfaces).\n2. Specific construction plans.\n3. Specific designs of the technical infrastructures, machine and experiment elements.\n164\n\n4. Descriptions of the construction processes.\n5. Detailed operation concepts.\n6. Prescribed procedures for operation, including the handling of failure cases and accidents.\n7. An analysis of the current (initial) state of the project environment (at least over four seasons).\n8. As a result of the initial state analysis, the prioritised issues and challenges of the locations in\nwhich the project will be embedded.\n9. The descriptions of the goods, products and resources (and their origins) used during all project\nphases, e.g., a procurement and transport scenario hypothesis.\n10. Relevant management concepts for all waste during all project phases.\nInitial state analysis to identify\nenvironmental issues and challenges\n+\n=\nIdentification of environmental \naspects to identify potential effects\nImpacts = issues \u00d7 effects\nFig. 3.2: Environmental impacts are a consequence of the environmental sensitivity at a certain location\n(issues and challenges) and the potential effects of environmental aspects of a project at that location.\nAssessing the environmental compatibility of the project involves an environmental impact study.\nIt is part of the single environmental authorisation process in each Host State. It concerns the analysis\nand assessment of the relevant environmental effects of aspects of the project by crossing them with the\nenvironmental issues and challenges (also called \u2018stakes\u2019) that have been identified and recorded in the\nframe of the initial state analysis in project-specific locations. This legally required process concerns\nthe verification of the project\u2019s compliance with the regulations. It includes an iterative improvement\nof the project scenario following the Avoid-Reduce-Compensate scheme that has already been adopted\nand used during the development of the layout and placement scenario. Public participation is a key\nelement of this process, in line with the Aarhus agreement [57], a UN convention that has been ratified\nby France in 2002 and Switzerland in 2014 to ensure access to information and public participation in\ndecision-making and access to justice in environmental matters. Additionally, the Espoo agreement [58],\nsigned by France in 2001 and by Switzerland in 1996, regulates the environmental impact assessment\nrequirements in a cross-border context, applicable as well to this project. Given that the project cannot be\nsubdivided and the authorisation applicants cannot be separated, a single unified project will be presented\nin both Host States during the authorisation process.\n3.2\nEnvironmental aspects\n3.2.1\nMethodology\nIdentifying and gathering the environmental aspects, i.e., any element of the project that can interact with\nthe environment, is a pre-requisite to be able to plan the environmental impact assessment during a sub-\nsequent project preparatory phase. This work started with the availability of technical design concepts in\n2024 and will continue after the end of the feasibility study. It permits the establishment of a baseline of\npotential environmental effects assuming current state-of-the-art technical choices, i.e., without optimi-\nsation and not foreseeing technical evolutions and improvements beyond what industrial partners expect\nthat they can deliver today.\n165\n\nThe identification of environmental aspects and the assessment of potential environmental effects\nare conducted systematically using configuration-managed system description sheets. These sheets are\njointly developed by environmental engineers and subsystem engineers for all project elements.\nHowever, technical infrastructures located outside the FCC site boundaries \u2014 such as access\nroads, highway connections, potential railway links, public electricity grids, and sewage and water net-\nworks \u2014 are not included in this approach. These elements are addressed in separate, dedicated environ-\nmental impact studies, instead.\nInformation systematically gathered and compiled in an environmental aspect report [59] serves\nthe following purposes:\n\u2013 Identify companies suitable to produce environmental impact studies;\n\u2013 Inform Host State environmental notified bodies about the project scope, contents, and interfaces\nin order to engage them effectively;\n\u2013 Inform the public about noteworthy project elements and their environmentally relevant elements;\n\u2013 Provides a baseline for the project engineers for the implementation of the eco-design approach;\n\u2013 Guides the environmental impact assessment;\nConsequently, all information gathered is documented in French and in a language that permits\nnon-experts to understand the project, the project\u2019s technical equipment, and the potential environmental\neffects linked to those elements.\nDepending on the potential environmental effects, the documentation concerns different project\nsegments at system or subsystem levels. Irrespective of the granularity of the element concerned, the\nfollowing information is gathered and documented:\n\u2013 Name of the system or subsystem;\n\u2013 Maturity level of the requirements and designs;\n\u2013 Linkages and connections to other systems such as a particle accelerator, a technical infrastructure\nor an experiment;\n\u2013 A short (around 80 words or one paragraph) non-technical description of the system\u2019s purpose:\nWhat does the system do and why does it exist;\n\u2013 A compact (up to one page) functional description of the system: what functions does the system\nimplement, how is it composed and how does it accomplish its purpose;\n\u2013 The system\u2019s capacity and performance including the following information: capacities in different\noperation modes with a description, number of units deployed, energy needs, resource and raw ma-\nterials needs, if and how the system transforms energy, types and quantities of emissions together\nwith an estimate of the environmental relevance (including a description of waste production re-\nlated to the system), known losses and inefficiencies in supplying the intended function, known\nspace requirements. For all system capacities and performance characteristics, an indication of the\nconfidence level and stability of the information is provided.\n\u2013 Locations at which the system is deployed.\nThis description is complemented by a structured summary of noteworthy environmental aspects\nand effects during normal operation, in degraded functioning, or in case of an accident. The following\ntypes of aspects are considered:\n\u2013 Release into water, soil, subsurface, air (including odour) ;\n\u2013 Waste production in terms of conventional and radioactive waste ;\n\u2013 Use of electrical and other sources of energy ;\n166\n\n\u2013 Consumption of raw materials ;\n\u2013 Consumption of natural resources: water, land, natural habitats, aquatic habitats, protected zones,\nprotected subsurface, agricultural space, protected agricultural space and others ;\n\u2013 Use of consumables (chemical products, for example) ;\n\u2013 Energy emissions such as non-ionising and ionising radiation, noise, vibration, heat, light or other\nforms of energy.\n\u2013 Effects on human environment, material goods and heritage such as traffic and transport ways,\nlandscape, visibility and co-visibility, health, increase of technological risks, agriculture and forestry,\nconstructed spaces, technical infrastructures, demographic development, territorial developments,\nurbanism, tourism and leisure activities.\nThe aspects are reported per project phase (construction, installation, operation, maintenance and\nrepair, decommissioning). For each aspect, the likelihood of occurrence is indicated and the potential\neffect in case it materialises. Its relevance is also indicated in order to be able to create a hierarchy of\nenvironmental aspects. Finally, the level of confidence is provided for that piece of information.\nThe descriptions are complemented with high-level functional diagrams and drawings and refer-\nences to supplementary information that provide evidence for the source of information and to permit\ntechnically interested readers to obtain further information.\n3.2.2\nScope\nThe systematic methodological approach to establishing a first inventory of environmental aspects of\nthe entire project comprises a large variety of project elements with the aim of being as exhaustive as\npossible given the constraint that the level of requirements and designs at this preliminary stage is still\nlow.\nThe following topics and elements are included in the inventory and report:\n1. Lepton injector: sources, positron production, linear accelerator and transfer lines to the booster.\n2. Lepton collider: the collider as a whole and indivisible entity, magnet circuits, magnet power sup-\nply, vacuum system, radiofrequency system, beam transfer systems, beam interception equipment.\nThe systems and equipment dealt with are also applicable to the environmental aspects of the\nbooster.\n3. Geodetic network and installations.\n4. Data communication networks in the entire perimeter of the project, including safety-related com-\nmunication equipment.\n5. Experiments: the research programme and its duration up to the end of the century, a generic de-\ntector and a working assumption for its subdetectors, the technical infrastructure systems required\nto operate the detector, the data acquisition and online computing infrastructure.\n6. Technical infrastructures: ventilation systems, compressed air production, connections to the French\nnational high capacity electricity grid for operation, local electricity distribution networks primar-\nily intended for construction, short-term energy buffering systems to ensure the stability of the\nelectricity supply, emergency energy supply, general communication networks, cryogenic refrig-\neration system, cryogen storage, drinking water supply, raw water supply, water cooling systems,\ndemineralised water production, chilled water production, cooling tower water management, un-\nderground water drainage recovery and evacuation, management of used water, clear water man-\nagement (including rainwater), and personal safety systems.\n7. Hadron collider: the research programme, the injectors, the collider, the experiments and the tech-\nnical infrastructures at a high level, with a baseline of today\u2019s technologies.\n167\n\n8. Subsurface structures with a focus on the construction: shafts, transfer line tunnels, caverns, ac-\ncesses, elevators, and subsurface transport systems.\n9. Surface sites with a focus on the construction: Site locations and functions, each individual net site\n(PA, PB, PD, PF, PG, PH, PJ, PL), the re-use of LHC point 8 for site PA, the Pr\u00e9vessin and Meyrin\nsites at a high level.\n10. Territorial developments in France: electricity supply for the construction, electricity supply for\noperation, drinking water, sewage, used water treatment, options for additional supply of cooling\nwater, access roads, access to autoroutes, options for railway accesses, emergency services, com-\nmunication network needs, needs concerning the management of excavated materials, require-\nments for the supply of waste heat, local transport needs for the construction, installation, and\noperation phases.\n11. Territorial developments in Switzerland: electricity supply for construction, electricity supply for\noperation, drinking water, sewage, used water treatment, raw water supply for cooling, site access,\noptions for railway access, emergency services, communication network needs, needs concerning\nthe management of excavated materials, requirements for the supply of waste heat, local transport\nneeds for the construction, installation, and operation phases.\n12. Construction phase: a dedicated description of the environmental aspects linked to the subsurface\nconstruction activities and the development of the surface sites, a preliminary schedule, descrip-\ntions of the construction sites, preparation of the sites before construction starts, management of\nthe construction sites, management of the personnel engaged in the construction, the supply of\nconstruction materials, resources required for the construction, shaft and cavern construction pro-\ncesses, tunnel construction processes, surface site civil structure construction approach, principles\nfor the management of the excavated materials, site restoration after construction.\n13. Installation phase: Installation of technical infrastructures, particle accelerators, the detectors, sup-\nply of the cryogens, transition of the technical infrastructures, the detectors, and the accelerators\ninto operation.\n3.2.3\nStatus and conclusions\nThe establishment of the comprehensive environmental aspects report [59] is currently in progress. It is\nan iterative work that advances with the gathering of requirements and suitable technologies to establish\na baseline and credible outlooks for future technologies and approaches.\nThe civil engineering construction phase (underground structures and surface sites), the technical\ninfrastructure systems, and the lepton collider systems are described according to the currently estab-\nlished baseline, along with the corresponding preliminary confidence and detail level. This preliminary\nanalysis will evolve as more detailed construction details and plans become available.\nRequirements for materials and resources that form the basis for an iteration of the environmental\naspects analysis must be understood to be approximate and linked to certain uncertainties. In particular,\nonly a high-level description of a generic experiment detector is available today as a baseline for further\nstudies. This description is based on current state-of-the-art technologies for detectors, typical detector\ntechnical infrastructures and data acquisition and processing. The subsequent design phase must at least\ninclude individual descriptions of four specific experiment detectors with more tangible and technical\ndesign assumptions based on a reasonable technological outlook for the coming years.\nConducting an environmental impact assessment requires detailed plans. If technical designs for\nparticle accelerators, experiment detectors, and their associated infrastructures are unavailable, voluntary\ncommitments on performance characteristics must be established.\nThe lepton injector and its systems and the installation phase, including commissioning, are cur-\nrently under pre-study. Descriptions are, therefore, not included at this stage. The territorial develop-\n168\n\nments in France and Switzerland have not yet been precisely defined. However, the minimum needs are\nknown and have been included. It should be noted that some adjustments of site locations may still be\nrequired, depending on the progress of the dialogue with local stakeholders in the vicinity of such sites.\nAt this stage, the main environmental aspects discussed in this chapter are linked to the construc-\ntion activities: the territorial development of some 50 ha of land spread over eight new surface sites,\nthe generation of \u223c6 million m3 (in situ) of excavated materials and the nuisances that are linked to any\nconstruction activity (e.g., noise, vibrations, dust, artificial light pollution, additional traffic).\nConsequently, the study anticipated a life-cycle analysis of the construction activities to gain a\nbetter understanding of other potential environmental effects on climate and the depletion of natural\nresources [60]. Contrary to conventional subsurface constructions, the creation of civil engineering\nstructures for a research infrastructure is less impactful. The LCA was based on actual available low-\ncarbon footprint products backed by EN 15804 certified Environmental Product Declarations (EPDs)\nand construction processes that foster short supply chains and construction prescriptions that consider\nresponsible use of resources. The resulting estimated carbon footprint covering the A1 to A5 lifecycle\nphases concerning the construction phase is about 0.53 million tCO2(eq). This value can be compared to\nCERN\u2019s current carbon footprint of 0.36 million tCO2(eq) in 2022, covering Scope 1, 2 and 3 emissions.\nIt must be noted that for carbon accounting the emissions must be distributed over the potentially con-\ntributing countries; consequently, the resulting annual impact per capita is about 0.11 kg, limited to the\nconstruction period. For comparison, the Paris Agreement defines a carbon budget of 2 000 kg per capita\nper year. The effects are mainly induced by two types of construction materials: ready-made concrete\nand steel. Design optimisations and technological progress will permit further lowering the footprint.\nAn update of the lifecycle analysis can be carried out during the technical design phase to quantitatively\nreport on the reduction effects. A dedicated environmental impact assessment will consider the directly\nrelated construction effects and their management. The planning of the construction process will have to\ninclude an environmental impact management plan that describes the responsible use of resources (e.g.,\nwater), the management of the construction activity-related waste production and the management of the\nconstruction-related traffic.\nConcerning the management of the excavated materials, the initial inventory of locations to permit\nrefilling quarries and deposit of non-reusable materials revealed the technical and managerial feasibility\nof the construction. However, in an effort to increase the reuse, a dedicated multi-year study has been\nlaunched in 2024 on CERN terrain with excavated molasse materials from the HL-LHC construction\nto develop quality-managed processes to transform the molasse into reusable materials. The pathways\ninclude rewilding projects (e.g., restoration of wasteland and preparation of the lower soil layers for new\nagricultural areas with fertile topsoil), the creation of raised hedges, the stabilisation of roadsides, the\ntreatment of rural and forest paths, the creation of parks and mini forests and the improvement of poor\nagricultural soil. Further applications, such as the production of insulation materials and non-structural\nconstruction materials, are being developed with industrial partners. The goal is to limit the pure deposit\nof non-reusable materials to 30%. It is important to recognize that, at this stage, no definite statements\nabout the re-use fraction can be provided due to the need to get an understanding of the excavated ma-\nterial\u2019s characteristics with dedicated subsurface investigations. However, FCC collaboration is actively\ninvesting in research and development of different innovative solutions to maximise material reuse and\nminimise environmental impact.\nAlthough the additional traffic induced by the construction activities is limited with respect to\nthe existing road traffic (between 2 and 15 transports per hour at the 8 sites during working hours,\nrepresenting an addition of 0.15 to 1.8% of the total traffic, depending on the site) in the immediate\nvicinity of the construction sites, care will have to be taken to develop a solid plan of the transport\nactivities. This will include the preference to transport excavated materials to the nearest major transport\naxe by conveyor belts and to optimise the supply of materials from the transport axes to the sites (e.g.,\nconveyor belts and optimised logistics). The goal is to avoid transit through residential neighbourhoods\n169\n\nand small roads as much as possible. The transport concept is part of the construction planning, the\nassociated authorisation process, and the subsequent requirements that are to be included in the tendering\nprocedures.\nThe artificialisation1 of land and the linked loss of habitat and biodiversity has been quantified\nand included in the socio-economic impact study. This effect is intended to be largely mitigated with\nrewilding projects around the sites and the re-creation of agricultural spaces. The environmental impact\nassessment will need to develop these measures in detail.\nDuring construction and exploitation, noise is a topic that can lead to notable effects in a few\nlocations where residential houses are within a perimeter of between 100 and 300 m around the sites. The\neffects have been quantified and are included in the socio-economic impact study. The environmental\nimpact assessment will have to include the development of adequate protection measures following the\navoid-reduce and compensate approach. So far, the potential effects revealed are limited to less than 10\nhouseholds in total for the entire project.\nThe effects of ionising radiation have also been quantified and have been found to be insignif-\nicant (actual annual dose in the vicinity of surface sites below 0.01 mSv/year well within the natural\nbackground radiation of about 0.8 mSv/year). This is because, based on CERN\u2019s multi-decade experi-\nence of operation, the scientific research installations generate additional ionising radiation far below the\npermitted thresholds with no health effects. Nevertheless, the applicable socio-economic quantification\nmethods have been used to cost the effects and report them. The environmental impact assessment will\nneed to include all the required monitoring and protection measures to ensure that the potential effects\nare maintained at an insignificant level.\nNoteworthy effects are expected to be primarily indirect, arising from the supply of raw and con-\nstruction materials, as well as off-site emissions. These include Scope 2 emissions, which result from\nthe electricity, heating, or cooling purchased to power project-related operations, and Scope 3 emis-\nsions, which encompass the broader environmental impact across the value chain, such as the production\nand transportation of materials, construction activities, and waste management. To address both aspects\nlinked to the construction of the facility and the scientific instruments and their operation, a procure-\nment plan that includes the environmental aspects will have to be developed and implemented. A first\nanalysis carried out with experts in the domain of energy procurement revealed that a large coverage\nof supply from renewable energy sources keeps the indirect emissions low. Privileging electrified con-\nstruction methods on a time horizon of 10 years can be foreseen. Entering operation on a 2050-time\nhorizon, in turn, offers the possibility for substantial energy supply coverage from renewable energy\nsources. Supply of waste heat, in particular when the research infrastructure operation is adapted to the\nlocal and seasonal needs, can largely help to reduce the carbon footprint by replacing conventional, fossil\nheat sources. The supply of raw and construction materials for the infrastructures and instruments will\nneed to be well-planned and included in the procurement and in-kind supply requirements. The mar-\nket is currently evolving fast in Europe towards fostering recycled materials (e.g., steel) and low-carbon\nproduction (e.g., concrete). The application and requirement of European Norms such as product com-\nparison based on EPD (Environmental Product Declarations) are needed to ensure a low environmental\nfootprint. Further lifecycle analysis for technical infrastructures, particle accelerator components and\nexperiment detectors are needed in the subsequent design phase to develop these requirements. Gases\nthat are harmful to the environment will need to be avoided if they have not already been taken off the\nmarket.\nThe surface sites lead to noteworthy environmental effects that are mainly linked to visibility.\nThese must be addressed in the design phase through the engagement of the public who is directly\naffected or concerned in cooperation with architects who have experience in landscape integration of\nindustrial and functional buildings. Preliminary studies have been carried out, and they confirm the\n1May be defined as: the transformation of a soil of agricultural, natural or forestry character by management actions, which\nmay result in its total or partial waterproofing.\n170\n\nexistence of suitable approaches and technologies today.\nEach site presents unique requirements and constraints that must be carefully considered. A key\nchallenge for the integrated project is the evolving definition of the space required to accommodate tech-\nnical equipment for the lepton collider, along with the long-term needs for a potential future hadron\ncollider. In locations where seamless landscape integration is a priority, constraints will play a deter-\nmining role in decision-making. A balance must be struck between minimising the site footprint for\nefficient land use and ensuring that the infrastructure can accommodate both the initial and potential\nsecond collider phases.\nThe consumption of agricultural space and forest not only leads to a reduction of habitat and bio-\ndiversity but also has tangible economic impacts. The loss of income (direct, upstream and downstream)\nhas been analysed and quantified and is included in the socio-economic study. Compensation proposals\nneed to be developed. While in Switzerland, only a one-to-one compensation of the space is acceptable,\nin France, collective compensation measures can also be jointly developed with affected stakeholders\nduring the environmental impact evaluation phase. The direct compensation for the loss of protected\nagricultural space involves the transfer of the high-quality topsoil to locations with either poorer soil\nquality or wasteland that will need to be refurbished. The loss of forests limited to France can for ex-\nample be partially compensated through re-forestation in the vicinity of the surface sites and at specific\nlocations. The notified bodies will be consulted for recommendations and validation for compensatory\nmeasures.\nWater consumption remains within current levels, as the requirements for the FCC-ee are similar\nto CERN\u2019s current needs. Recognising the importance of responsible resource management, efforts will\nbe made to limit water use. The FCC-ee replaces the Large Hadron Collider\u2019s water demand. Consid-\nering the continuous depletion of water resources, protection of water resources and reduction of water\nconsumption are part of the eco-design goals. Therefore, studies are underway to understand if and how\ntreated wastewater can be used for cooling purposes. The initial results confirm, in principle, its technical\nand financial feasibility. Local effects may remain with respect to water needed during the construction\nphase. The subsequent environmental impact study must therefore include a water sourcing and manage-\nment plan to ensure that there are no noteworthy local impacts due to the construction activities which\naffect the population and the existing economic activities.\nThe construction and operation of the research infrastructure entail generating significant amounts\nof conventional waste. The subsequent environmental impact study will detail the types and quantities.\nThe effect stems mainly from procured goods and therefore to manage this issue, waste avoidance and\nmanagement must be included in the procurement process. Since the operation of a new research infras-\ntructure replaces the operation of CERN\u2019s current flagship project and the number of persons involved is\nexpected to be stable over time, the daily waste production is not expected to grow. Continuous efforts\nto reduce waste generation, fostering reuse first and recycling in line with the Host State regulations is\nexpected to lead to a continuation of the waste reduction already engaged today.\nFinally, the aim to keep environmental impacts within acceptable limits calls for an adaptive op-\neration concept. Considering climate change effects and the need to generate environmental benefits to\nbalance negative externalities requires the inclusion of external constraints into the operation. For in-\nstance, the optimisation of the waste heat supply may call for a shift of operation into colder seasons.\nThe operation of the particle accelerators could be linked to the availability of abundant renewable energy\nvia online notifications received by a link with the energy supplier. The operation may also need to in-\nclude consideration of the changes in secondary circuit cooling water temperatures due to the long-term\nevolution of the climate. The presence of personnel also means having to consider seasonally changing\nworking conditions. For instance, it can be more sustainable to work during colder seasons than in hotter\nones since heating can be achieved by waste-heat recovery, but cooling requires additional energy.\nThe preliminary inventory and analysis of environmental aspects have led the environment con-\nsortium, composed of a number of companies, to develop a first version of an environmental strategy\n171\n\nthat is described in Section 3.2.4. The guidelines that this strategy includes are iteratively provided to the\ndesigners of the facility and are included in new procurement actions relating to studies and technical de-\nsigns. In this way, a culture of integrating the environmental impact into the design process is gradually\nbeing established. This eco-design approach is expected to play a fundamental role in the subsequent\ndesign, construction, and operation of the FCC.\n3.2.4\nEnvironmental strategy\nPurpose and scope\nThe purpose of the strategic vision [29] for the environment, eco-design, and sustainable development\nfor the project is to define and set guidelines in order to:\n\u2013 Set out the project owner\u2019s ambitions in relation to the environment, eco-design and sustainable\ndevelopment.\n\u2013 Steer and design the project to consider and integrate environmental aspects.\n\u2013 Embed the project in an overarching sustainable development approach based on the three sustain-\nability pillars: environmental, social and economic.\n\u2013 Establish a cross-disciplinary framework for the project, as well as for the international partners\nand collaborators, that can be applied to all phases of the project\u2019s development and operation.\nThe strategic vision applies to all phases of the project\u2019s development: planning, design, construction,\noperation, maintenance, and future development. It, therefore, concerns the construction of the infras-\ntructure, the particle accelerators, and the experiments that will be carried out there. From a geographical\npoint of view, the strategic vision is transnational in scope and incorporates the national and specific reg-\nulations applicable at every stage of the project.\nOrganisation and steering\nThe environmental strategy and its organisation and steering are based on the principles [61] already be-\ning followed at CERN as the project host. The strategy also incorporates the recommendations issued in\nthe context of the environmental standards that serve as guidelines [19,62], including the recommenda-\ntions relating to the key issues to be addressed. CERN\u2019s main objectives for the period 2021\u20132025 [63]\nand beyond place the environment at the top of the agenda. This 2E+SD (Environment, eco-design and\nSustainable Development) strategic vision reflects a strong commitment to design a new project that\nencompasses local and regional developments. To date, CERN\u2019s environmental objectives have been\nfocused on existing activities. An evolution is needed to meet the environmental challenges of building\nand then operating a new large-scale research infrastructure while taking into account the protection and\ndevelopment of the region. The project needs to be conceived considering the environment in which\nit will be embedded from the outset. To develop a scenario for a project, the project owner should set\nup an appropriate structure that is responsible for the integration of the 2E+SD strategy. This structure\nwill make it possible for the strategy and its implementation to be steered independently of the entities\nresponsible for the study, design, and implementation. It must report directly to the project management\nand have clearly identified reference people in all the entities involved in the various phases of the project.\nIt will help to define the project management procedures and will set requirements for the operational\nmanagement (organisational issues) and/or for the steering.\nCollective and individual responsibilities\nThe project management team develops the strategy, communicates it clearly, and ensures all interna-\ntional collaborators adhere to it. They establish an organisational structure and implement all necessary\nmeasures to achieve the objectives outlined in the 2E+SD strategic vision. To accomplish this, the fol-\nlowing actions will be taken:\n172\n\nShort term (2024-2030)\n\u2013 Understand the environmental and regulatory context in which the research infrastructure project\nand its related projects unfold.\n\u2013 Draw up an \u2018Environment, eco-design and Sustainable Development\u2019 roadmap to structure the way\nin which the environment is taken into account throughout the project and to identify and involve\nall stakeholders.\n\u2013 Set targets to be reached and continuous improvement objectives that are applicable to all stake-\nholders and to all phases of the project based on the UN\u2019s Sustainable Development Goals.\n\u2013 Engage in a systematic process of avoiding, minimising and offsetting the project\u2019s impacts through\nfollow-up and improvement measures.\n\u2013 Monitor regulatory and technical developments to anticipate changes in the fields of the environ-\nment, eco-design and sustainable development.\n\u2013 Integrate environmental and sustainable development objectives into all activities relating to the\nproject, in particular during the project design phase.\nMedium term (2030-2040+)\n\u2013 Steer the integration of environmental and sustainable development objectives into the construc-\ntion of infrastructure, technical equipment (particle accelerators, scientific experiments and all the\ntechnical infrastructure needed to operate them) and territorial development projects.\n\u2013 Develop partnerships with local stakeholders planned during the previous period (2024\u20132030).\n\u2013 Update the strategic vision and adapt it to changing circumstances based on environmental moni-\ntoring.\nLong term (2040+)\n\u2013 Continue to integrate the sustainability enablers, in particular solutions with the lowest energy\nconsumption and greenhouse gas emissions, provided that they are compatible with the scientific\noperation of the project and are economically viable.\nAll those involved in project-related activities actively contribute to the implementation of the\n2E+SD strategy through exemplary conduct and by keeping in mind the associated objectives and adopt-\ning best market practices on the basis of assessment of emerging technologies.\nAt every stage of the project, while pursuing the aim of achieving its scientific objectives, everyone\nmust actively seek out information enabling them to minimise the project\u2019s impact on the environment\nand must fulfil the environment, eco-design, and sustainable development responsibilities entrusted to\nthem.\nDecisions to adopt measures must be based on a cost\u2013benefit assessment of the various options,\nincluding lifecycle analysis where appropriate.\nIt is understood that actions to avoid and reduce impacts must be technically feasible, economically\nviable, and compatible with the need to deliver sustained scientific excellence on a global scale and with\nthe scientific goals of the new research infrastructure.\nPriority environmental themes\nAmong the many environmental aspects, the following eight topics have been assigned a priority for the\nsubsequent design phase:\n173\n\nWater\n\u2013 Limit water consumption, avoid sensitive periods and do not consume water from sensitive sites.\n\u2013 Monitor and control the quality of released water and how it is managed.\n\u2013 Optimise water use, recycling and reuse.\nWaste\n\u2013 Channel all waste to appropriate sorting facilities.\n\u2013 Repurpose to avoid and reduce final waste.\n\u2013 Use recycled and organic materials where possible.\nEnergy\n\u2013 Limit consumption and increase system efficiency.\n\u2013 Favour renewable energy sources.\n\u2013 Recover and store energy; supply residual heat.\nIonising radiation\n\u2013 Apply the standards and the agreement of CERN with the two Host States [64].\n\u2013 Study solutions to reduce and limit the generation of ionising radiation.\n\u2013 Identify and quantify local risks.\nBiodiversity\n\u2013 Identify and preserve sensitive sites.\n\u2013 Identify local protected and heritage species.\n\u2013 Take appropriate environmental offsetting measures.\nEmissions\n\u2013 Quantify emissions, including in terms of carbon footprint.\n\u2013 Develop recovery and management systems.\n\u2013 Monitor and control the quality of emissions and what happens to them.\nPlacement\n\u2013 Avoid sites that are sensitive or are subject to strong constraints.\n\u2013 Reduce surface areas and optimise the site layout.\n\u2013 Blend the infrastructure and activities into the environment.\nSocietal dimensions\n\u2013 Limit activities to necessary locations and periods.\n\u2013 Limit disruption and preserve the comfort of local residents.\n\u2013 Plan the creation of added value for society as part of the project.\n174\n\nSpecific guidelines\nAs a result of the development of the strategic vision, the following specific guidelines have been for-\nmulated. They are to be integrated in the subsequent design phases by all infrastructure and equipment\ndevelopers.\nWater\n\u2013 Avoid using drinking water for non-sanitary purposes.\n\u2013 Avoid extracting groundwater.\n\u2013 From the planning stage onwards, preserve the quality and quantity of groundwater.\n\u2013 Do not create interaction between layers of groundwater or mix their waters.\n\u2013 Put rainwater collection systems in place for purposes that do not require drinking water.\n\u2013 Limit evaporation by using closed circuits and, where possible, dry systems.\n\u2013 Optimise water use, in particular by recycling and reusing it.\n\u2013 Minimise direct extraction from watercourses.\n\u2013 Ensure that water released into the natural environment is of a quality at least equivalent to that of\nthe water quality of the environment.\n\u2013 Develop synergies for sharing water and reusing waste water for the benefit of other consumers,\nsubject to technical and regulatory feasibility.\n\u2013 Evaluate the use of waste water for industrial processes.\nWaste\n\u2013 Where possible, choose materials with a low impact on the environment (e.g., recycled, organic).\n\u2013 Include a requirement in tendering processes for companies to avoid packaging and to remove their\nwaste.\n\u2013 Channel all waste to the appropriate sorting facility.\n\u2013 Repurpose excavated materials, if possible, locally.\n\u2013 Avoid single-use and limited-use equipment and containers.\n\u2013 Share space and equipment.\nEnergy\n\u2013 Take the Host States\u2019 energy and climate goals into account when planning, building and operating\nfuture facilities.\n\u2013 Limit energy consumption to the quantities and durations required.\n\u2013 Recover and reuse as much energy as possible in the research infrastructure.\n\u2013 Take energy recovery measures.\n\u2013 Limit the use of fossil fuels.\n\u2013 Plan for the timely implementation of energy supply contracts or power purchasing agreements for\nthe supply of renewable energies.\n\u2013 Plan to recover, store and supply energy, including waste heat, first for use within the project, with\nthe possibility of subsequently making it available outside the project.\n\u2013 Avoid unnecessary consumption (e.g., by operating systems only where and when necessary,\navoiding systems that run in standby mode and assessing the possibility of switching systems\noff).\n\u2013 Increase the temperature of the cooling water and ambient air in areas requiring air handling.\n175\n\n\u2013 Limit the areas in which air handling is required and the duration thereof.\n\u2013 Avoid unnecessary lighting and operation of machinery.\n\u2013 Optimise schedules by striking a balance between different criteria, in particular by gearing con-\nsumption towards periods when cheap renewable energy is available and by making the best pos-\nsible use of recovered waste heat.\n\u2013 Optimise and pool means of transport (e.g., conveyors, trains, electric vehicles) and commuting\nbetween sites.\n\u2013 Adapt IT and data processing systems to requirements.\n\u2013 Design and construct buildings with ambitious energy performance targets.\nIonising radiation\n\u2013 Limit activities that produce ionising radiation.\n\u2013 Locate hazardous activities in non-sensitive areas.\n\u2013 Identify, quantify and control all radioactive emissions and immission in the environment and\nwaste.\n\u2013 Keep track of the locally applicable regulations.\n\u2013 Draw up risk management protocols.\nBiodiversity\n\u2013 Identify local biodiversity issues to avoid destroying sensitive sites, habitats and ecological corri-\ndors. Where avoidance is not possible, reduce and compensate.\n\u2013 Limit indirect impacts that disturb the environment (e.g., noise, light, vibration).\n\u2013 Contain unavoidable impacts (e.g., lighting intensity and colour, operating periods).\n\u2013 Plan measures to preserve flora and fauna and where not possible, develop mitigation measures to\naddress residual impacts.\n\u2013 Enhance biodiversity on and around the sites.\n\u2013 Plant only local species and avoid planting any undesirable ornamental species.\nEmissions\n\u2013 Take into account the climate goals set by Switzerland and France in line with the IPCC recom-\nmendations.\n\u2013 Identify all sources of emissions.\n\u2013 Treat emissions and immissions in the environment before release.\n\u2013 Determine the carbon footprint of emissions and immissions in the environment.\n\u2013 Keep all activities on a virtuous emission pathway.\n\u2013 Monitor and measure activities that are likely to pollute the air, soil and water.\n\u2013 Avoid gases that have a significant greenhouse effect (e.g., SF6) and use alternatives.\n\u2013 Opt for electricity and hydrogen (fuel cells) from renewable sources for the powering of machinery\nand the transport of equipment.\n\u2013 Encourage soft mobility and electric transport.\n\u2013 Remain below the thresholds in force for the immission of suspended dust (PM10) and nitrogen\ndioxide (NO2) around the perimeter of the future extensions.\n176\n\n\u2013 Identify and limit greenhouse gas emissions in the life cycle of the research infrastructure, taking\ninto account the scientific objectives, technical feasibility and economic sustainability, including\nduring equipment construction and procurement activities.\nPlacement\n\u2013 Avoid locations that present major concerns.\n\u2013 Reduce the footprint of surface sites to the absolute minimum, compliant with the requirements.\n\u2013 Optimise the use of space by increasing the density of sites and buildings.\n\u2013 Ensure that the infrastructure blends well into the landscape, the local environment and the urban\nsetting.\n\u2013 Avoid ground sealing and manage rainwater.\n\u2013 Incorporate islands of freshness.\n\u2013 Limit the impact of activities within the site.\n\u2013 Plan for the resilience of the sites.\nSocietal dimensions\n\u2013 Identify local sensitivities and issues.\n\u2013 Limit noise, odour and light pollution for local residents.\n\u2013 Integrate activities into the economic and social environment and develop synergies with local\nservices, such as the fire brigades and other emergency and security services.\n\u2013 As far as is compatible with the project plan, limit disturbance during rest periods (nights, week-\nends).\n\u2013 Minimise road traffic and put in place alternatives (e.g., pooled transport, public transport, rail\ntransport, conveyors).\n\u2013 Provide parking spaces and loading and unloading areas during the construction phase, based on\nrequirements identified and quantified in advance.\nRaw materials\n\u2013 Analyse the lifecycle of materials and infrastructure to anticipate the end of their life.\n\u2013 Favour the use of low-carbon construction materials (e.g., low-carbon concrete), where feasible.\n\u2013 Favour the use of recycled materials (e.g., steel, copper), where feasible.\n\u2013 Prioritise local sourcing and regional production.\n\u2013 Favour organic resources (e.g., wood), where feasible.\n3.2.5\nEnergy use\nThe project is committed to promoting and continuously increasing the use of renewable energy sources\n[65]. Fossil fuel-based energy will generally be avoided, and where its use is unavoidable, it will be min-\nimised as much as reasonably possible. The internal heating of the particle accelerator infrastructure will\nreuse waste heat and renewable energy sources whenever feasible and economically viable in the long\nterm. The use of fossil energy sources for backup electricity supply should be avoided. Instead, hydro-\ngen to power a fuel-cell based system can be a valid alternative in addition to the short-term electricity\nsupply via battery-based energy storage systems (BESS).\n177\n\nStudies carried out with external consultants to understand how far renewable energy sources\ncan be leveraged, show that a strategy based on sourcing the majority of electricity from renewable\nenergy sources at the national level can satisfy the project needs [50]. Continuous increase of renewable\nenergy sources and cross-border electricity transfer capacities pledged by the French government [66]\nsupport the validity of this concept [67]. In line with other European countries, the French electricity grid\nhas experienced a continuous reduction of its carbon intensity [68] and is today amongst the countries\nwith the lowest location-based electricity carbon intensity (Fig. 3.3, Sweden, France, Switzerland, and\nNorway). The long-term planning [69] published in early 2025 confirms the feasibility of the supply of\nthe required energy from the grid and via renewable energy sources.\ngCO\u0223eq/kWh\n0\n100\n200\n300\n400\n500\n600\n700\n800\nPologne\n762\n602\n587\n516\n487\n389\n425\n303\n436\n270\n173\n160\n249\n150\n246\n141\n248\n95\n324\n77\n95\n54\n41\n32\n9\n5\nPays-Bas\nR\u00e9publique\ntch\u00e8que\nAllemagne\nItalie\nBelgique\nGrande-\nBretagne\nDanemark\nEspagne\nPortugal\nAutriche\nSuisse\nNorv\u00e8ge\n-21 %\n-13 %\n-22 %\n-29 %\n-36 %\n-7 %\n-39 %\n-45 %\n-60 %\n-73 %\n-47 %\n54\n32\nFrance\n-40 %\n-22 %\n46\n40\nSu\u00e8de\n-58 %\n-44 %\nPays\nLecture :\nBaisse relative de l\u2019intensit\u00e9 \ncarbone de la production \nentre 2017 et 2023\nIntensit\u00e9 2017\n(gCO2eq/kWh)\nIntensit\u00e9 2023\n(gCO2eq/kWh)\nFig. 3.3: Evolutions of the carbon intensities of national grids in Europe. Source: RTE [68].\nThe studies permit expecting that by 2035 the energy needs relating to the construction activities\ncan be entirely satisfied by renewable energy sources. Implementing the approach via the local electricity\nsupplies requires, however, that dedicated renewable energy supply contracts with certificates of origin\nare settled. This in turn calls for a sufficiently exhaustive analysis of the energy needs at the construction\nsites over the construction years and a reliable construction planning that is sufficiently stable (planning\nsecurity).\nTo prepare the energy supply for the operation phase, up to ten years of preparatory time may\nbe required. This time frame serves well for defining the energy needs and consumption patterns, the\ninvariant energy needs, the development of concepts and techniques that permit adapting the research\ninfrastructure to supply possibilities in terms of changing availability and price. Furthermore, it allows\ntime to develop the portfolio of power purchasing agreements in terms of functions and capacities, the\ncontractual conditions and the tender processes. Eventually, the portfolio will lead to a mix of energy\nproduction technologies that match the needs of the research infrastructure, the ability of suppliers to\ngrant flexibility, the carbon footprint, and general contract-related conditions. While the studies with\nexternal consultants show that on the time scale of 2035 covering more than 1 TWh with renewable\nenergy in the region is feasible at the 60% level, significantly higher coverage will be feasible in the\n2050 time frame.\nIt is worth keeping in mind that the supply and consumption of energy from renewable sources\ndo not rely on a physical connection between the producer and the consumer. In an interconnected\nelectricity grid, electrons are fungible, i.e., indistinguishable and interchangeable. Therefore, any volume\nof purchased energy from renewable sources is accounted in the financial, societal and environmental\naccounting scheme that determines the sustainability level of the project. It is not relevant where the\nenergy has been physically produced and when it has been produced in the frame of a power purchasing\nagreement. It is, therefore, important to distinguish the carbon footprint of the power grid (location-\nbased carbon footprint of consumption) from the certificate of electricity origin carbon footprint of a\n178\n\nproject (market-based carbon footprint of consumption). Renewable energy certificates and guarantees\nof origin that are part of power purchasing agreements play a crucial role in the carbon accounting of a\nproject. The Greenhouse Gas Protocol Scope 2 Guidance explicitly states the requirement to report both\nfigures [70]. To achieve good financial performance, a more detailed forecast of the volumes required\nover an operating year and the possibility to adapt to the availability of renewable energy and its changing\nrewards are desirable. Consequently, a portfolio of renewable energy power purchasing agreements must\nbe developed with adequate preparation time. The portfolio will evolve during the operation phase since\nthe energy consumption needs to evolve according to different operation phases.\nFig. 3.4: Evolution of the levelized cost of electricity (LCOE, Source: Lazard\u2019s Levelized Cost of Energy\nVersion 17.0).\nBy 2023, the so-called levelized electricity costs (LCOE)2 of all renewable energy sources are\nbelow the production costs of electricity production from fossil fuels [71] (Fig. 3.4). Seasonal fluctua-\ntions in the daily electricity prices are a result of a complex interplay of production capacity (supply),\ndemand and non-technical factors. With respect to the pre-pandemic, electricity price evolution remains\nvolatile. The production location can be different from the consumption location in the interconnected\ngrid. Therefore, no general statement can be given, and the observation of large-volume electricity\nprices over multiple seasons did not permit an unambiguous seasonal cost variation pattern to be derived\n(Fig. 3.5). In particular, the production costs of electricity from renewable energy sources are diverse:\nwhile wind power is 10% cheaper in winter and 20% cheaper in spring than in summer, the situation\nfor production from photo-voltaic sources is, in general, the inverse. In continental climate zones, a\nquasi-equilibrium of supply and demand exists [72].\nSo far, it has not been possible to identify a significant difference in the cost of energy from\nrenewable energy sources between seasons.\nTo achieve good coverage with low-carbon electricity sources, off-site energy storage could be\nforeseen in the power purchasing strategy. For example, hybrid PPAs are rapidly entering the market\nand, by the 2040 to 2050 period, will be an integral part of large-volume power purchasing. Missing\nvolumes of renewable energy sources can be complemented with nuclear energy, which has a higher\nLCOE than renewable energy sources but is characterised by a very low carbon footprint.\nBy way of comparison, medium-sized offshore wind farms with a capacity of 600 MW, such\nas Kriegers Flak (Denmark) or Dunkerque, produce around 2.5 TWh of electricity per year at a cost\n2LCOE (Levelized Cost of Energy) is a metric used to assess the cost of generating electricity from different energy sources\nover their lifetime. It represents the per-unit cost (e.g., USD/MWh) of building and operating a power plant, considering all\ncosts and revenues.\n179\n\n0\n20\n40\n60\n80\n100\n120\n01.03.2023\n01.04.2023\n01.05.2023\n01.06.2023\n01.07.2023\n01.08.2023\n01.09.2023\n01.10.2023\n01.11.2023\n01.12.2023\n01.01.2024\n01.02.2024\n01.03.2024\n01.04.2024\nPrice (EUR/MWhe)\nFig. 3.5: Example of monthly electricity spot price in France between 2023 and 2024 (Source: Ember\nEnergy [73] ).\nof 44 euro/MWh at 2021 prices. Due to periods of economic crisis that caused an energy price in-\ncrease between 2020 and 2023, the auction prices for offshore renewable wind energy in France are\ndecreasing again. In France, auction prices for renewable wind power sources are currently, on average,\n69 euro/MWh. These auction prices are a suitable indicator for setting the electricity price to be assumed\nfor the annual energy costs in the overall sustainability assessment. Based on today\u2019s prices (Fig. 3.6)\nand environmental performances of energy production, an average price range of 70 to 80 euro/MWh and\na market-based carbon intensity of 15 to 25 gCO2(eq)/kWh of electricity is very conservatively assumed\ntoday.\n9\n9\n9\n9\n7\n6\n5\n5\n7\n6\n6\n8\n7\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n2010\n2012\n2014\n2016\n2018\n2020\n2022\n2024\n2026\nAverage Wind Auction Prize (Euro ct/kWh)\nFig. 3.6: Historic contract market prices of electricity from wind power in Europe in cents/kWh up to the\nend of 2024 (Source: graph derived from public European wind auctions).\nThis value is significantly higher than the price goal of 56 euro/MWh in 2030 in France, commu-\n180\n\nnicated in the public multi-annual energy planning of the government [66] (Fig. 3.7).\nFig. 3.7: Stated electricity market price targets for 2030 published by the French government in the pluri-\nannual energy programme [66]).\nTo maximise waste heat supply potential while maintaining reasonably-sized heat buffering sys-\ntems, operational flexibility and shifting operations to cooler seasons are preferred. Given the regional\nclimate patterns, working conditions are generally more favorable in autumn and spring compared to\nsummer.\nThe subsequent project preparatory phase must include the preparation of the power purchasing\nstrategy and a plan for the construction phase. This will serve as a learning experience to develop and\nnegotiate the power purchasing agreement portfolio for the operation phase, which is assumed to start\nafter 2045.\n3.2.6\nWaste heat use\nAlmost all of the energy used to operate the technical infrastructures and subsystems of a particle accel-\nerator is eventually converted into heat. Energy used to operate accelerator magnets, amplify radiofre-\nquency energy, absorb synchrotron radiation, air management systems, operate electronics and data pro-\ncessing equipment is almost entirely converted into low-grade heat, typically below 45 \u25e6C. Temperatures\nabove 50 \u25e6C, but still below 70 \u25e6C, can rarely be reached, for instance, when cooling cryogenic refriger-\nation system equipment and electrical transformers and substations. This heat is typically dissipated in\nthe ambient air via water-cooling and free-to-air cooling systems and is thus lost. Given the amount of\nheat that particle-accelerator based research infrastructures generate, there is an interest to explore ways\nto recover that heat and convert it into a valuable resource. The use of the heat for other purposes inside\nand outside the project boundaries has the following socio-economic benefit potentials:\n181\n\n\u2013 Reduction of electrical energy consumption and associated costs due to reduced cooling system\noperation requirements.\n\u2013 Reduction of raw water consumption and associated costs due to reduced cooling system operation\nrequirements.\n\u2013 Increased cooling system lifetime and reduction of associated maintenance and repair costs due to\nlower operational load on equipment.\n\u2013 Reduction of heat-generation-related carbon emissions due to the avoidance of dedicated heat\nproduction.\n\u2013 Lower heat costs for consumers.\n\u2013 Opportunities for creating new economic activities in the vicinity of the heat source.\nHowever, heat recovery and supply also require additional efforts and costs:\n\u2013 Additional components to recover the heat.\n\u2013 A dedicated network to transport the heat to where it is needed.\n\u2013 Potential additional components to raise the temperature of low-grade heat supplied for specific\nneeds.\n\u2013 Short-term and long-term heat storage systems to ensure supply stability and provide heat when\nneeded.\n\u2013 The need to refurbish existing buildings and the need for new buildings that are equipped with\nheating and cooling that function with the low-grade heat.\n\u2013 The need for a heat supply operator if the heat is used outside the research infrastructure bound-\naries.\nA technical-economic study has been carried out by an expert engineering company to create\nan inventory of the heat sources in the research infrastructure, to confirm the technical and financial\nfeasibility and, most importantly, to draw up a detailed cartography of the heat demand within the surface\nsites perimeters. The study also included an assessment of how far heat recovery and supply is technically\nfeasible and economically viable [74\u201376].\nThe information gathered was also integrated in the comprehensive, wider socio-economic impact\nanalysis, estimating the contribution to the net present value of the project and subsequently reporting on\nthe overall net benefit. This approach ensures that an informed decision-making process is implemented.\nIf the system is put in place, it is strongly advised that the heat supply is continuously monitored to report\non the efficiency of the approach and to be able to further optimise the waste heat recovery and supply\nprocess.\nWhilst retrofitting heat recovery and supply to existing cooling systems is technically possible,\nit can be more costly than planning the concept from the onset. Depending on the existing equipment,\ninfrastructures and environment around the particle accelerator facility, retrofitting may be less efficient\nsince the operating temperature of the equipment supplying the heat may not be matched to the consumer\nneeds e.g., magnet water cooling circuit temperatures too low, lack of data centre rack cooling infras-\ntructure, mismatch of the waste heat characteristics with existing district heating networks or missing\nlow-temperature district heating networks and finally lack of space and missing agreements with con-\nsumers. It is, however, preferred over no heat recovery. Therefore, from the outset, the FCC project has\nadopted an eco-design approach that integrates heat recovery and supply into the research infrastructure\nwhile embedding it within its broader socio-economic and environmental context.\nWaste-heat recovery and supply are already implemented at CERN in the frame of the LHC\nproject. One installation supplies waste heat from the cryogenic refrigeration system at LHC Pt8 in\nFerney-Voltaire. A district heating network developed by the company Dalkia for the municipality, sup-\nported by the state, the region, and the French environmental organisation ADEME, connects to this\n182\n\nsurface site. The surface site PA in Ferney-Voltaire is envisaged as an immediate extension of this LHC\nsite, leveraging not only the existing district heating network but also opening a window of opportunity\nto connect to structured heating networks [77] on the nearby Swiss territory that also supplies Geneva\nairport and major industrial and commercial facilities as well as residential buildings in the vicinity of\nthe surface site. The second example is the newly constructed data centre at the CERN Pr\u00e9vessin site.\nIts recovered waste heat will largely cover CERN\u2019s campus heating needs. A third example is the heat\nrecovery project at the CERN LHC surface site point 1 (ATLAS experiment) that will supply heat to the\nCERN Meyrin campus.\nThe following are examples of equipment that can serve as a starting point for the study of the\nfunctionality of integrating heat recovery and supply.\n\u2013 Normal conducting magnets (recovery of cooling water at temperatures between 25 \u221245 \u25e6C).\n\u2013 Normal conducting radiofrequency cavities (cooling water temperature between 25 \u221245 \u25e6C).\n\u2013 Synchrotron radiation absorbers (cooling water temperature between 25 \u221245 \u25e6C).\n\u2013 Rack mounted electronics (water cooled with a \u03b4T of 20 K and a temperature range between\n27 \u221249 \u25e6C on the outer circuit with a temperature range between 39 \u221260 \u25e6C on the rack cooling\ncircuit).\n\u2013 Radiofrequency amplifiers of different types e.g., solid state, klystrons, IOTs with a cooling water\ncircuit temperature range between 25 \u221235 \u25e6C with high stability and low-temperature fluctuation\nconstraint \u2013 depending on the case, as tight as 0.1 \u25e6C. By design, the maximum water temperature\nat the klystron\u2019s collector may be allowed to reach 63 \u25e6C, but so far, applications operating in this\nregime are not known.\n\u2013 Cryogenic refrigeration plants for superconducting components (e.g., magnets, radiofrequency\ncavities) with equipment cooling circuit water temperatures in the range of 50 \u25e6C (e.g., compres-\nsors) to 75 \u25e6C (e.g., oil separator).\n\u2013 Power electronics and converters (temperature range of circuits between 30 \u221260 \u25e6C for directly\nwater-cooled IGBT systems, for example).\n\u2013 Electrical transformer stations with water cooling-based systems in the range of 20 \u221270 \u25e6C (e.g.,\noil-based transformers).\n\u2013 Data centres [78] (recovery of 15 \u221220 \u25e6C air, 40 \u221250 \u25e6C heat from the CRAHs and 50 \u221260 \u25e6C\nfrom liquid cooling systems).\n\u2013 Ventilation and air management systems (e.g., heat from motors and air-to-air transfer) from 25 up\nto about 40 \u25e6C.\nThe initial equipment and heat load analysis will inform the designers which components are the\nones that produce most of the heat and with which characteristics (stability, temperature). This permits\nthe creation of a hierarchy of heat-producing components that can guide the development of the heat\nrecovery and supply concept. A multi-criteria analysis with different weights for the individual aspects\nis a suitable approach for this first step. The analysis process should at least include the following non-\nexhaustive list of aspects:\n\u2013 Operational temperature requirements and constraints from the equipment components to be cooled\nand their temperature variation tolerances.\n\u2013 Temperatures of the heat recovery potential for the different equipment to be cooled.\n\u2013 Variability and stability of the heat generation (hourly, daily, weekly, monthly).\n\u2013 Climatic and weather conditions in the environment of the research infrastructure (for instance,\na particle accelerator facility and a data centre operated in the north of Europe permit the use of\ndifferent heat recovery and supply technologies than in a southern European region).\n183\n\n\u2013 Use cases for the recovered heat inside the research infrastructure (e.g., pre-warming of water,\noffices, workshops, assembly halls, guest houses).\n\u2013 Demand of industrial heat consumers outside the research infrastructure (e.g., food production\nand processing industries, offices, hotels, airports, shopping malls, theatres, cinemas, congress\ncentres).\n\u2013 Demand for heating public spaces and institutions (e.g., schools and universities, hospitals, prisons,\ntrain stations)\n\u2013 Demand for heating of private spaces (e.g., apartment buildings and individual houses).\n\u2013 Demand for hot water production (the required temperature is above 55 \u25e6C for sanitary reasons\nand therefore priming with water boilers and heat pumps may be needed on an individual basis).\n\u2013 Distances between heat production and consumers (note that distances up to 10 km are feasible\nwith modern pipe technology for low-grade district heating systems in the 50 \u25e6C range).\n\u2013 Gap analysis concerning the need for heat buffering (e.g., capacity, space, duration, technology,\ninvestment costs, operation costs).\n\u2013 Investment costs for heat recovery, buffering and supply.\n\u2013 Operation costs for heat recovery, buffering and supply.\n\u2013 Capital and operation expenditures outside the system boundary (e.g., district heating network\noperation host, private heat pumps and priming equipment).\n\u2013 Public co-financing possibilities.\n\u2013 Duration and observation period envisaged for the heat recovery and supply.\n\u2013 Baseline for avoiding fossil energy sources for heating and the avoidance of primary energy for\nheating. Only the energy for stepping up the temperature for specific end-use cases needs to be\nconsidered.\n\u2013 Definition of the interface between the heat recovery and supply system that is part of the research\ninfrastructure and the segment that is outside the responsibility of the research infrastructure.\n\u2013 Conditions of the heat supply operator which provides the infrastructure up to the consumer and\nthat supplies the heat with guarantees or with contractual conditions that require the consumer to\ngenerate or obtain the gap between supplied and required heat.\n\u2013 The proposed heat supply technology (e.g., direct, indirect via a loop, indirect via heating the soil\nor other approaches).\nBased on technical designs in the subsequent development phase, all data need to be collected and\nthe most promising heat sources that qualify for a heat recovery case have to be identified. The viable\nheat consumers have to be confirmed in the frame of a territorial co-development activity. Eventually,\nthe following non-exhaustive list of aspects to tune the heat recovery and supply scenario should be\nconsidered:\n\u2013 Increase of the heat supplied by relaxing the equipment cooling requirements (e.g., water-based\nmagnet cooling up to 50 \u25e6C, increase of ambient air temperature inside the facility up to 40 \u25e6C and\npossibly beyond).\n\u2013 Validation that mission-critical systems remain within their required operation margins (e.g., in-\ncreasing the cooling water temperature of klystrons or relaxing their temperature stability may lead\nto unacceptable performance or render operation unfeasible).\n\u2013 Total amount of CO2 emission reduction potential as a result of avoidance of fossil fuel and any\nprimary energy, based on a credible estimate for the energy required to prime the heat for the\nend-use applications.\n\u2013 Optimisation of the heat supply by adjusting the operation schedule and introducing the possibility\nof reacting dynamically to heat needs.\n184\n\n\u2013 Adaptation of the particle accelerator operation schedule to the actual societal heat demand to\nincrease the overall socio-economic performance.\n\u2013 The potentially different energy costs for the research infrastructure operator when adjusting the\noperation schedule of the particle accelerator or when introducing the capability to dynamically\nreact to both electricity supply and heat demand constraints.\n\u2013 Additional societal and economic benefits that can be generated by creating new heat consumers\nin the vicinity of the supplied heat (e.g., food processing industries, agricultural producers, biogas\nproduction, thermal baths and recreational installations).\n\u2013 Introduction of temporary heat buffers (daily, weekly, monthly).\n\u2013 Availability of specific public co-financing facilities and loans with specific conditions.\n\u2013 Optimisation of the interface between research infrastructure, operator and heat consumers.\nThe recovered heat will not be consumed at all times and the consumption pattern will change.\nTherefore, care must be taken not to under-dimension the cooling, ventilation and evaporation systems\nfor the research infrastructure. If the heat is not consumed or cannot be delivered, it must be possible to\ncool all components reliably to ensure operation for scientific research purposes.\nThe techno-economic analysis permitted establishing the demand-based waste-heat supply scenar-\nios based on the three different assumptions shown in Table 3.1.\nTable 3.1: Waste heat supply potential according to local demand, supply scenario and operation mode.\nMode\nMinimum\nsupply potential\nAdaptation of operation\nschedule to demand\nAdaptation to demand\nand redistribution between sites\nZ\n223 GWh/year\n308 GWh/year\n414 GWh/year\nWW\n239 GWh/year\n339 GWh/year\n471 GWh/year\nHZ\n256 GWh/year\n371 GWh/year\n529 GWh/year\nL.S.\n60 GWh/year\n60 GWh/year\n60 GWh/year\nt\u00aft\n296 GWh/year\n441 GWh/year\n710 GWh/year\nBased on this scenario, the potential of avoiding carbon emissions in the region by substituting\nconventionally created heat with waste heat that is largely produced from renewable energy sources\ncan be estimated. Table 3.2 shows the estimates of carbon emissions avoided, based on the follow-\ning assumptions: an average market-based carbon footprint of 25 tCO2/GWh of electricity supplied\nto the FCC. A weighted average of about 190 tCO2 per GWh of conventional heat produced that can\nbe substituted with waste heat3. The resulting net carbon footprint avoided by supplying waste heat\nis 190-25 = 165 tCO2/GWh. Comparing the avoidable carbon emissions by supplying waste heat with\nthe range of total Scope 2 related carbon emissions of the collider operation between 305 000 and\n509 000 tCO2 shows that the supply of waste heat can be partially substitute conventional heat sources at\nthe same level, thus generating substantial positive environmental externalities that are made visible in\nthe comprehensive socio-economic impact assessment.\nThe \u2018minimum\u2019 scenario is based on the hypothesis that the particle collider starts operating in\nMarch and ends at the latest in November. Fig. 3.8 shows as an example the weekly overview of the\ncumulative heat demand around a perimeter of 5 km around each surface site.\nFigure 3.9 shows the heat demand and supply during the Z mode throughout the year, with a\nschedule that is better adapted to the heat demand.\n3Regional heat production mix: 36% electricity at 147 gCO2/kWh, 34% gas at 227 gCO2/kWh, 16% oil at 324 gCO2/kWh,\n11% wood at 30 gCO2/kWh, 0.3% heat at 49 gCO2/kWh leads to a total footprint of 186.7 gCO2/kWh = 186.7 tCO2/GWh\n185\n\nTable 3.2: One scenario outlining the potential for avoiding carbon emissions by supplying waste heat\nbased on an average of 165 t avoided CO2 per GWh of heat supplied.\nMode\nYears\nHeat supplied/year\nHeat supplied\nCO2 avoided/year\nCO2 avoided\nZ\n4\n308 GWh/year\n1232 GWh\n50 820 tCO2/year\n203 280 tCO2\nWW\n2\n339 GWh/year\n678 GWh\n55 935 tCO2/year\n111 870 tCO2\nHZ\n3\n371 GWh/year\n1113 GWh\n61 215 tCO2/year\n183 645 tCO2\nL.S.\n1\n60 GWh/year\n60 GWh\n9900 tCO2/year\n9900 tCO2\nt\u00aft\n5\n441 GWh/year\n2205 GWh\n72 765 CO2/year\n363 825 CO2\nTotal\n5288 GWh\n872 520 tCO2\nOperation Scope 2 emissions (for comparison, 20 350 GWh at 25 tCO2/GWh)\n508 750 tCO2\nFig. 3.8: Weekly heat demand and supply for an example schedule of the Z operation mode.\nFigure 3.10 shows the site PA in Ferney-Voltaire as an example for the heat demand study that\npermitted the development of the concept for the heat supply.\nSeveral industrial and public heat consumers were identified in the vicinity of several surface sites.\nThey include, for example, a hospital, a school, cheese production facilities, an airport, commercial zones\nand public housing. Such heat consumers are preferred over supply to individual houses that are more\ndifficult to connect. Public, industrial and commercial consumers typically have a higher and more stable\nheat demand. Site PD in Nangy (see Fig. 3.11) is one example where significant amounts of heat in the\n10 GWh/year range can be supplied in the close vicinity of the surface site.\nThe techno-economical study revealed that waste heat supply is challenging at site PH (Cercier and\nMarlioz) and would be modest at sites PL (Challex) and site PB (Presinge). Therefore, a redistribution\nof the heat from PH to PG, from PL to PA and between PB and PD could be considered to improve the\nyield.\nTable 3.3 gives an overview of the potential total waste heat demand that exists today in the perime-\n186\n\nFig. 3.9: Weekly heat demand and supply for an adapted schedule of the Z operation mode.\nters studied around each site. Waste heat is best re-used with the creation of new consumers, such as\nhealthcare facilities, thermal baths, greenhouses, industrial facilities, and residential buildings that are\nconnected to the new network from the outset.\nThe supply of residual heat (or waste heat) from the FCC creates windfalls in three ways:\n1. Balance the non-avoidable and non-reducible residual carbon footprint of electrical energy: sup-\nplying the FCC with electricity (the working hypothesis is based on using electricity partly from\nrenewable sources) would represent an average carbon footprint of around 40 000 tCO2(eq)/year.\nThe yearly supply potential from residual waste heat is around 320 GWh of energy per year. The\ntotal maximum residual heat capacity is around 1 600 GWh per year. Consequently the supply of\nwaste heat can substitute for the carbon footprint of the electrical energy consumed, provided that\nthis heat supply can be implemented and that the demand can be satisfied via a heat distribution\ninfrastructure. The technical-economic study [74\u201376] showed that 220 GWh to 300 GWh of heat\ncould be consumed within a radius of approximately 5 km around the surface sites. However, to\nincrease the efficacy of waste heat supply, the particle collider operation schedule needs to adapt\nwithin acceptable limits to the heat needs.\n2. Reduction of the carbon footprint of heating and cooling in the region: the supply of energy by a\nheating network using a high proportion of renewable energies (including residual heat) avoids the\nneed for other sources of heat. Based on the minimum reuse hypothesis (220 - 300 GWh/year),\nthe production of 27 500 to 38 500 tCO2(eq) could be avoided each year. Reasonable adaptation of\nthe operating schedule throughout the year would be required to make this approach an effective\nlever.\n3. Increasing the purchasing power of the local population: The organisation operating the FCC is\nnot a profit-making organisation. Energy can, therefore, be supplied by network operators at very\ncompetitive prices. According to the French multi-annual energy programme (PPE), waste-to-\nenergy plants (which recover waste heat) sell this heat at a very competitive price, between 10\n187\n\nFig. 3.10: Example from the heat demand study at site PA in Ferney-Voltaire, within a perimeter of\n\u223c5 km around the site.\nand C25/MWh. As a result, the heat supplied can then be the preferred choice for heating, hot\nwater, and cooling. In the Anergie network (Ferney-Voltaire), the price of waste heat supplied\nby CERN equipment is even lower. According to a study by AMORCE and ADEME, the aver-\nage selling price for networks supplied mainly by renewable and recovered energies (\u201cEnR&R\u201d)\nwas C78.2 /MWh, incl. tax, in 2020 (these prices do not take into account the initial investment\ncosts of the networks). According to the waste heat supply study carried out for this project by\nthe engineering firm Ginger BURGEAP, the average price was at the same level more recently.\nBased on this model, the potential savings are currently estimated at C50/MWh compared with\ngas heating and C140/MWh compared with electricity, using energy prices of 1st November 2023\nas a reference.\n4. Limiting water consumption: reusing residual heat would also reduce the need for cooling water.\nThe potentials are described in Section 3.2.9.\n3.2.7\nConstruction related carbon footprint\nAs the global focus on combating climate change intensifies, reducing greenhouse gas (GHG) emissions\nhas become a top priority. Infrastructures\u2014spanning transport, construction, and scientific instruments\n\u2014 play a critical role in this transition. Carbon budget analysis, as part of a more comprehensive Lifecy-\ncle Analysis (LCA) (see Fig. 3.12), has emerged as an essential tool for measuring and managing these\nemissions effectively.\nA comprehensive lifecycle analysis (LCA) conforming to the applicable ISO standards and Eu-\nropean Norms, EN 14040 and EN 14044, has been carried out [60]. For the construction sector, the\nEN 17472 norm has been followed. In addition to the use of generic databases, a specific procurement\nscenario has been analysed, based on currently available Environmental Product Declarations (EPD) con-\nforming to the European Norm, EN 15804+2, and the French \u2018Fiche de D\u00e9claration Environnementale\net Sanitaire\u2019 (FDES).\nThe goal of the work was firstly to identify the key drivers for quantitatively estimated environ-\nmental impacts of the construction and, secondly, to establish a credible reference scenario for the carbon\n188\n\nFig. 3.11: Example from the heat demand study at site PD in Nangy, concerning a nearby hospital\n(south), a cheese producer (north) and a mixed industrial/residential zone (north-east).\nbudget as a baseline for further designs and optimisations. It is important to note that a generic LCA can-\nnot provide adequate indications for the carbon footprint, but is limited to the capability of identifying\ndrivers. A specific and geo-localised project scenario with a particular sourcing scenario is necessary\nto be able to report absolute and credible estimates. The methodology adopted comprised the following\nsteps:\n1. Identification of components : a detailed inventory of materials was compiled based on the bill\nof quantities for the subsurface construction, the 4 experiment sites and the technical sites. The\nproducts concerned are used throughout the infrastructure\u2019s lifecycle.\n2. EPDs acquisition: EPDs were sourced for each material and product identified, ensuring com-\npliance with EN 15804+A2, the foundation of EN 17472. The materials were selected based on\n189\n\nTable 3.3: Overview of the total potential waste heat demand that exists today in the perimeters studied\naround each site\nSite\nPotential\nDemand\nConsumers\nPA\nHigh\n200 GWh/year\nSchools, commercial zones, residential\nPA Extended\nHigh\n1700 GWh/year\nExtension to Switzerland: airport, commercial and\nindustrial activities, residential, hospitals\nPB\nMedium\n30 - 200 GWh/year\nSchool, greenhouses, penitentiary,\nhospital, commercial activities, housing\nPB Extended\nHigh\n> 200 GWh/year\nCommercial and residential demands\nin nearby France, sector Annemasse\nPD\nLow\n14 GWh/year\nHospital, industrial\nPD Extended\nMedium\n50 GWh/year\nSchools, healthcare, residential\nPF\nMedium\n60 GWh/year\nSector La Roche-sur-Foron: industrial\nexpo center, schools\nPG\nLow\n16 GWh/year\nSchools, residential\nPG Extended\nMedium\n35 GWh/year\nSchools, residential\nPG Annecy\nHigh\n860 GWh/year\nAnnecy at distance of 7 km:\nIndustrial, commercial, residential\nPH\nVery low\n14 GWh/year\nAt 8 km distance: Retirement home, residential\nPJ\nLow\n20 GWh/year\nSchools, commercial, residential\nPL\nLow\n30 GWh/year\nSpread over 5 km: school, commercial, residential\nFig. 3.12: Stages considered for the LCA of the infrastructure construction.\nexpert knowledge of the local environment and state-of-the-art products. The availability of the\nproducts was confirmed by the suppliers.\n3. Software Tool: A certified tool compatible with French and Swiss Environmental Product Decla-\nration, ONE CLICK LCA, was chosen, ensuring robust and accurate calculations.\n4. Data Entry: data was imported into the tool and project-specific data was entered, including mate-\nrial quantities and lifecycle phases, transportation for excavated and construction material.\n5. Calculations: the tool was used to estimate the carbon budget, drawing on EPDs\u2019 data to evaluate\nGHG emissions for each lifecycle phase.\n6. Result Analysis: the results were analysed to pinpoint major emission sources, comparing them\n190\n\nagainst benchmarks and reduction targets.\n7. Guidance: the results were used to sensitise engineers and scientists to include a carbon budget\nas a further input to the subsequent design phase and to ensure that requirements are well for-\nmulated and justified so that the infrastructure corresponds to what is required, thus limiting the\nenvironmental impacts.\nThe analysis provided a breakdown of GHG emissions and additional quantitative potential envi-\nronmental impacts across the various lifecycle phases, products and materials. The key emission sources\nare reinforced steel (14%), precast concrete (49%) and concrete (23%). This highlights opportunities for\nemission reduction by designing the infrastructure with carbon reduction in mind, making careful mate-\nrial selection, optimising the construction process and making energy efficiency improvements. The most\neffective environmental impact management approach is a combination of the establishment of technical\nrequirements for the infrastructures with rationales for the requirement, design of the infrastructure based\non the requirements with carbon reduction in mind, careful material selection in agreement with the re-\nquirements, construction process optimisation, and energy efficiency improvements. The GHG impacts\nof the initial and benchmark scenarios are given in Table 3.4.\nTable 3.4: Reference carbon footprint of the FCC infrastructure construction for a period of 10 years\nbased on specific sourcing and procurement scenarios with EPDs.\nItem\nCarbon footprint\nSubsurface\n477 388 tCO2(eq)\n4 technical sites\n17 600 tCO2(eq)\n4 experiment sites\n31 200 tCO2(eq)\nTotal\n526 188 tCO2(eq)\nThe 526 188 tCO2(eq) carbon footprint of the construction over a period of 10 years can be com-\npared to CERN\u2019s current annual carbon footprint (184 173 tCO2(eq) [79]. Thus, the construction corre-\nsponds to about 3 years of CERN\u2019s annual footprint or about 30% of CERN\u2019s annual carbon footprint per\nconstruction year. The FCC construction carbon footprint can also be compared to that of the Olympic\nGames in Paris which had an estimated carbon budget of 1 580 000 tCO2(eq) [80].\nWith respect to conventional construction projects, the carbon footprint of a research infrastructure\nis significantly lower (see Fig. 3.13) than a small-scale metro line or a tramway line. For instance, the\nconstruction of the U5 Metro line in Berlin, Germany had a carbon footprint of 98 000 tCO2(eq) per\nkm [81]. On average, per km of underground transport line construction, the carbon footprint is 80 000\ntCO2(eq). The construction of a tram line has a carbon footprint between, 7 600 and 10 850 tCO2(eq) per\nkm.\nBased on the analysis, a number of recommendations were developed with the help of the expert\ncompany that carried out the LCA.\nAlthough CERN\u2019s annual carbon footprint will gradually be reduced, in line with the established\nenvironmental goals, national climate protection plans and IPCC recommendations, it would be advisable\nto limit adding construction-related climate impacts to the operation-related carbon budget. Hence, while\nthe construction of a new facility ramps up, it would be prudent to reduce the activities related to other\ncarbon-intense activities. With respect to the construction, the following strategies can help to reduce the\npotential impacts further:\n\u2013 Implementation of a thorough systems engineering methodology to develop well-justified and fully\ndocumented technical requirements for both subsurface and surface structural elements. These\nrequirements will represent the absolute minimum necessary to accomplish the scientific research\n191\n\n0\n10'000\n20'000\n30'000\n40'000\n50'000\n60'000\n70'000\n80'000\nMetro\nTram\nFCC\ntCO2(eq) footprint per km\nFig. 3.13: The construction-related carbon footprint per km of the FCC tunnel compared to typical public\ntransport linear structures [60]\nprogramme effectively (for example, determining the precise dimensions and volumes of structures\nthat meet the essential technical and physical requirements).\n\u2013 Integration of an eco-design in the comprehensive systems engineering process with carbon re-\nduction in mind that matches the established requirements (e.g., appropriate sizing of the caverns,\nshafts, alcoves).\n\u2013 Structural modification of the scenario by reducing the inner line thickness of subsurface structures\nby at least 5 cm, leading to a reduction of 16% for precast concrete and rebar steel.\n\u2013 Material substitution, considering low-impact materials which meet the established requirements\nand working with industrial partners to innovate and produce locally wherever possible.\n\u2013 Construction process optimisation to minimise emissions.\n\u2013 Reuse of excavated materials, for instance, in concrete production.\nWith respect to the initial baseline scenario, the reduction of the circumference to about 91 km and\nthe suppression of 4 shafts have led to a significant reduction of the construction-related carbon footprint\nduring the scenario development phase. Furthermore, the carbon footprint must be seen in the context\nof establishing an infrastructure that serves a worldwide community of about 15 000 scientists for two\nsubsequent particle colliders until the end of the century. Although according to international norms the\nquantities reported by the LCA must be entirely accounted for the first project phase only (FCC-ee),\nit can be seen as an investment that benefits the second phase, the high-energy hadron collider phase\n(FCC-hh).\n3.2.8\nOperation related carbon footprint\nDetectors\nWhile the carbon footprint of today\u2019s scientific research facilities, such as the LHC and its experiments,\nis largely caused by gases used in the detectors, this contribution will be only marginally relevant for the\nFCC era: gases with significant climate effects are already being banned, and the list of such products is\ngrowing rapidly.\n192\n\nToday\u2019s working gases will largely be unavailable by the year 2050 when the first collider enters\nits operation phase. The performance and long-term operation of gaseous detectors rely primarily on\nthe use of the optimal gas mixture, which is the active medium where the primary ionisation happens\nin the detector. Several gaseous detector technologies make use of gas mixtures containing expensive\nor greenhouse gases, which have specific properties that allow optimal detector performance and avoid\nageing effects. The GHGs most in use are the C2H2F4 (known as R134a, GWP of 1430) and SF6 (GWP\nof 23,900) for the Resistive Plate Chambers, the C4F10 (GWP of 8860) for Cherenkov detectors and\nthe CF4 (GWP of 7390) for wire chambers, Cherenkov detectors and micro pattern gaseous detectors\n(MPGDs). These gases are necessary to mitigate ageing phenomena, to act as a Cherenkov radiator and\nto contain charge development (thanks to their electronegative properties) or to improve time resolution.\nThe detector volumes range from a few m3 to hundreds of m3 making the use of gas recirculation\nsystems compulsory to reduce operational costs and GHG emissions. Even with the implementation\nof these systems, in some cases, emissions can be present mostly due to detector requirements or the\npresence of leaks. Residual leaks are mainly due to failures of plastic pipes and connectors that break\ndue to built-in fragility and mechanical stress. These leaks are not accessible during run periods and,\nin some cases, during regular technical stops. Big leak search and repair campaigns usually take place\nduring long shutdown periods, but leaks typically keep developing.\nTo reduce emissions, today\u2019s strategy [82] is based on three lines of action:\n\u2013 Gas Recirculation. The gas mixture is taken at the output of the detectors, purified and sent back\nto the detectors. It is technically possible to recycle 100% of the gas mixture.\n\u2013 Gas Recuperation. The gas mixture is sent to a recuperation plant where the GHG is extracted,\nstored and re-used. This system is always used in combination with a gas recirculation system to\nallow a further GHG reduction.\n\u2013 Alternative gases. Search for alternative gas mixtures suitable for particle detectors that do not\ncontain or have limited use of GHGs.\nThe substitution of fluorinated gases (F-gases) is fundamental because of the implementation in\nEurope of the F-gas regulation that will render such substances unavailable by 2050. Also in 2023 the\nEuropean Chemicals Agency (ECHA) released a proposal regarding restriction on PFAS, i.e., per- and\npolyfluoroalkyl substances, which contain at least one fully fluorinated methyl (CF3-) or methylene (-\nCF2-) carbon atom (without any H/Cl/Br/I attached to it). The proposal covers over 10 000 different\nPFAS, which are considered environmental pollutants with links to harmful health effects. Most of the\nso-called \u2018eco-friendly\u2019 gases belong to the PFAS family.\nIn addition, devices and circuits using gases either for cooling or for particle detection purposes\nmust be designed to be leak-tight and use a re-circulation principle.\nScope 2\nThe principal cause of carbon footprint will be the use of electrical energy.\nThe same approach will be used for the optimisation of all other resource use, such as electri-\ncal energy. The adoption of the hierarchical \u2018Avoid-Reduce-Compensate\u2019 principle guides the iterative\nplanning, implementation, checking and taking action cycle that leads to continuous optimisation.\nA comprehensive technical requirements gathering process has to be established to document and\nscrutinise where and when electrical energy is needed. Following a baseline scenario, the eco-design\napproach helps to conceive designs and choose products that lead to reduced energy consumption. A\nreview of the operation model that will be guided by overall sustainability goals integrating economic,\necological and societal aspects will guide the development of different scenarios. Some measures require\nanother iteration of the eco-design cycle by introducing new requirements that foster sustainability, such\nas the integration of waste-heat recovery and supply functionality. It permits, for instance, substituting\n193\n\nTable 3.5: Examples of some official electrical energy carbon footprint sources.\nCountry\nSource\nEnergy\nCarbon footprint\ngCO2/kWh\ntCO2/GWh\nYear\nFrance\nAdeme Base Empreinte\nOffshore wind\n15.6\n2023\nFrance\nAdeme Base Empreinte\nUnqualified energy mix\n52.0\n2022\nGermany\nUmweltbundesamt (UBA)4\nUnqualified energy mix\n380.0\n2023\nItaly\nISPRA\nUnqualified energy mix\n257.2\n2022\nSwitzerland\nBAFU/OFEV5\nUnqualified energy mix\n54.7\n2018\nSwitzerland\nBAFU/OFEV\nRenewable energy mix\n15.7\n2018\nfossil energy used inside and outside the project, but it comes with constraints such as additional in-\nvestment and operation costs, the necessity to buffer energy, the need to dynamically adapt operation,\nrequirements on financial and ecological accounting and the requirement to establish administrative and\ncommercial frameworks for successful implementation. All relevant ESG parameters need to be taken\ninto consideration, and it is therefore recommended that experienced companies be employed for the\noverall energy optimisation of the infrastructures.\nOfficial national values for the selected base year of the sustainability analysis must be used to\ndetermine the carbon footprint of the electricity consumed during the design and planning phases. Con-\nsequently, the carbon footprint depends on the technology (offshore wind, onshore wind, photovoltaic,\nhydro, nuclear) and the geographical location of the energy production. Even if all electricity is trans-\nported and supplied to the FCC by the French electricity grid, operated by RTE, this does not mean that\nthe electrical energy needs to be sourced solely from French territory. Studies carried out with experts in\nthe domain [51] showed that a comprehensive portfolio of energy supply contracts or power purchasing\nagreements (PPA) would be best established with sufficient lead time (order of 10 years). It must be able\nto respond to the evolving needs of the commissioning and operation phases. In order to foster the use\nof renewable energy sources and exploit the waste heat supply functionality, the particle collider would\nneed to adapt to the energy supply contract conditions that eventually are determined by commercial\nconditions on the one hand and by the availability of renewable energy capacities on the other.\nDepending on the country of origin, the carbon intensity of electricity is made available from\ndifferent sources. Table 3.5 provides an illustration.\nOnce a specific energy supply contract is active, emission accounting will be carried out using\nsupplier-provided emission information. For instance, a typical consumer-oriented electricity contract\nbased entirely on renewable energy sources (62% hydro, 31% wind and 7% PV, 100% are certified to be\nof renewable energy sources) in France today has an actual carbon footprint of 34 kgCO2(eq)/MWh [83].\nThis value is higher than the ADEME indicated emission factor for renewable energy sources to be used\nfor the planning and design phases since the consumption of electricity in the frame of a live contract\nincludes all emissions along the value chain and not only the production-related emissions. In addition,\nrenewable energy that is potentially sourced from physical PPAs is not accounted for in the carbon\nfootprint.\nDifferent assumptions were taken to estimate the Scope 2 carbon footprint related to the operation.\nOne assumption is based on today\u2019s energy mix, including nuclear energy and renewable energy sources\nwith a varying contribution of up to 75% and a carbon footprint of 24 gCO2/kWh. This configuration\nleads to an average annual indirect carbon footprint of about 500 000 tCO2 or approximately 35 000 tCO2\nper year depending on the renewable PPA and energy supply contract portfolio6.\n620 900 GWh * 24 tCO2(eq)/Gwh = 501 600 tCO2(eq).\n194\n\nTable 3.6: Lowest carbon footprint energy mix assumption used for the estimate of the carbon footprint\nfor operation on a 2050 time horizon. The carbon intensity figures were obtained from the Ademe Base\nEmpreinte database, 2023.\nEnergy Source\nContribution\nCarbon intensity\nNuclear\n10%\n3.7 gCO2(eq)/kWh\nOffshore wind\n55%\n15.6 gCO2(eq)/kWh\nOnshore wind\n10%\n14.1 gCO2(eq)/kWh\nPhotovoltaic\n15%\n25.2 gCO2(eq)/kWh\nHydro power\n10%\n6.0 gCO2(eq)/kWh\nTotal\n100%\n14.74 gCO2(eq)/kWh\nFor an optimistic reference estimate, it was assumed that an energy mix based on a portfolio of\nphysical and non-physical PPAs and energy supply contracts on the 2050 time horizon, entirely sourced\nfrom French territory via the national grid operated by RTE (see Table 3.6). Based on this mix, the total\ncarbon footprint of about 300 000 tCO2(eq) was estimated7 for the entire scientific research period over\n15 years. This corresponds to an annual average of about 20 500 tCO2(eq). Using a pessimistic estimate\nof 25 tCO2(eq)/GWh leads to a carbon footprint of 522 500 tCO2(eq) of an annual average of about\n34 800 tCO2(eq).\nThe residual carbon footprint can in principle also be offset by the supply of waste heat. Depend-\ning on the amount of waste heat re-used, this opens an opportunity to evolve towards net-zero operation\nscenario after 2050. Such a scenario requires the careful development of energy supply contracts and/or\nlong-term PPAs and the creation of district heating and industrial heat supply networks, with an adapta-\ntion of the accelerator operation to the energy supply and the heat demand. Introducing temporary heat\nbuffering will help achieve the goal.\n3.2.9\nWater use and saving\nDrinking water from the existing local distribution networks will only be used for drinking and sanitary\npurposes. All raw water required for industrial cooling systems will be sourced from CERN\u2019s existing\nwater supply (SIG) in Switzerland, which sources the water from Lake Geneva.\nFrom a quantitative point of view, the reference scenario for water consumption is technically,\nfinancially, and territorially feasible since water extraction and consumption represent quantities lower\nthan CERN\u2019s actual consumption in 2022. The availability of a supply representing twice the total needs\nwas confirmed by SIG in 2023.\nDuring the subsequent design phase, it will be necessary to verify aspects relating to the sharing\nof water with the other local stakeholders who use the same water sources, particularly with regard to\nrelated catchment areas which currently experience chronic deficits (Pays de Gex, La Roche-sur-Foron\nand possibly the Usses). Numerous synergies can be considered with local authorities in the vicinity of\nsurface sites in terms of the reuse of residual heat and released water.\nTherefore, a study has been launched recently to determine the feasibility and the conditions to\nalso source water from a water treatment station near the site PD in Nangy (STEP SRB in Scientrier, see\nTable 3.7). Initial results are promising, requiring, however, a reduction of the non-soluble content in the\nwater and an effective treatment of bacteria. A demonstration will be required for such an installation.\nIf considered viable, it can lead to substantial raw water reduction and can help supply treated water for\nother industrial purposes when the particle accelerator does not require it.\n720 900 GWh * 14.74 tCO2(eq)/GWh = 308 066 tCO2(eq).\n195\n\nTable 3.7: Overview of the raw water needs for cooling for each operation mode, waste water re-use\npotentials for sites PD, PF, PG and the residual treated water that can be made publicly available.\nMode\nYears\nInitial FCC\nwater need\nWaste water used\nat PD, PF, PG\nResidual\nwater needs\nTreated waste water\navailable to society\nZ\n4\n1 604 861 m3/year\n560 304 m3/year\n1 044 557 m3/year\n2 049 792 m3/year\nWW\n2\n1 928 943 m3/year\n619 017 m3/year\n1 309 927 m3/year\n1 991 080 m3/year\nZH\n3\n2 165 458 m3/year\n705 173 m3/year\n1 460 285 m3/year\n1 904 924 m3/year\nL.S.\n1\n163 817 m3/year\n78 840 m3/year\n977 m3/year\n2 531 256 m3/year\nt\u00aft\n5\n3 077 591 m3/year\n897 334 m3/year\n2 180 258 m3/year\n1 712 763 m3/year\nThe preliminary analysis has been carried out based on the water supplied to the treatment plant\nduring a typical year and an assumption of a treatment capacity of up to 400 m3/hour. Although a water\ntreatment plant has, in principle, the capacity to provide more water than is needed for the cooling of\nthe particle collider, it is prudent to assume that the water is mixed with ordinary raw water, that the\ntreated water is not always compliant with the needs, and that the treatment is not always fully efficient\nor available. Figure 3.14 gives an impression of the typical annual operation of the water treatment plant\nin Scientrier close to site PD and how wastewater recovery would map to the collider cooling needs for\nthe Z mode as an example.\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\n1.1 15.1 29.1 12.2 26.2 11.3 25.3 8.4 22.4 6.5 20.5 3.6 17.6 1.7 15.7 29.7 12.8 26.8 9.9 23.9 7.10 21.10 4.11 18.11 2.12 16.1230.12\nm3/h\nweek\nSTEP operation throught a year, water availability after treatment\nSTEP average wastewater flow\n[m3/h]\nAvailable water after treatment\n[m3/h]\nCERN reuse for cooling purposes\n[m3/h]\nPotential of reuse for other applications\n[m3/h]\nFig. 3.14: Operation of the STEP in Scientrier throughout a typical year, matching with FCC Z mode\nwater cooling needs and the capacities made available by water treatment to the FCC and society.\nIt should be noted that ultimately the feasibility of this approach and the actual capacities depend\non the technical designs and the possibility of implementing the concept in cooperation with the national,\nregional and local stakeholders in France.\nFurthermore, water reduction can be achieved with the recovery and supply of waste heat, since\n196\n\nless heat needs to be dissipated with evaporation towers. The reduction potential estimated in the dedi-\ncated engineering study was approximately 1.6 m3 of water per MWh of waste heat supplied. Table 3.8\noutlines the potential amount of cooling water savings for each operation mode and for one of three\ndifferent waste heat supply scenarios:\nScenario 1: the heat is distributed in a 5 km radius with no adaptation of the schedule. This means\nthat the FCC would be operated from April to September, when the heating needs are low.\nScenario 2: the heat is distributed in a 5 km radius with an adapted schedule. This means that the\nFCC would be operated from October to March, when the heating needs are high.\nScenario 3: the heat is distributed in a 5 km radius with an adapted schedule and distribution.\nThis means that the infrastructure would operate from October to March, when heating demand is\nhighest, and the heat would be distributed to areas where there is higher demand than in scenario 2.\nTable 3.8: Water saving potential related to waste heat supply (scenario 2, adapting the collider operation\nto seasonal demand).\nMode\nYears\nHeat supplied\nWater saved\nZ\n4\n308 GWh/year\n477 000 m3/year\nWW\n2\n339 GWh/year\n523 000 m3/year\nHZ\n3\n371 GWh/year\n571 000 m3/year\nL.S.\n1\n60 GWh/year\n96 000 m3/year\nt\u00aft\n5\n441 GWh/year\n678 000 m3/year\nTotal\n5288 GWh\n8 155 200 m3\nThe water savings also translate into a modest reduction of operating cost of about 6 million CHF.\nWhilst this is not a noteworthy financial sustainability contribution, together with some annual electricity\nsavings of 4 GWh per year, in total about 60 GWh which is worth another 5 million CHF, financially and\neconomically compensating the additional effort to operate the waste heat recovery system.\n3.2.10\nInduced road traffic\nTo estimate the additional traffic induced by the construction activities, a traffic analysis has been carried\nout using up-to-date traffic data in approximately 5 km wide perimeters around the surface site locations\nand comparing different standard trucks used for construction (Fig. 3.15). Based on this traffic analysis\n(Fig. 3.16) and the assumption of a worst-case scenario in which all materials need to be transported by\ntrucks on roads, it can be shown that the additional traffic induced by the project, distributed over nine\nconstruction sites and more than eight years is only marginal (Table 3.9). Traffic is assumed to be limited\nto working days and regular working hours, avoiding morning and evening peak hours.\nThe subsequent project design will emphasise reducing road-based transport requirements. The\ntraffic can be further reduced by using larger trucks (2+3 axles or 3+2 axles). Conveyor belts are the\npreferred means to bring excavated materials to major road and rail transport networks so that no local\ntraffic is induced. Where possible, construction materials are brought in via autoroutes to site connections\nor via major roads to avoid passing through residential areas.\nThe traffic for the five years of installation of the particle accelerator equipment is small. It ranges\nbetween 9 and 18 trucks per site and day, i.e., between 1 and 2 trucks per working hour. No traffic is\nforeseen during the night and non-working days. The limitation to traffic during the installation is due\nto the limited capacity of transferring equipment through the access shafts. The handling speed between\nsurface and underground and in the constrained underground environment determines the amount of\n197\n\n2 + 3\n3 + 2\n5\n4\nAxles\n40\n40\n40\n32\nTotal weight (t)\n24\n24\n17\n12\nCapacity (m3)\n25\n24\n24\n18\nCapacity (t)\nFig. 3.15: Capacities of different standard trucks used to analyse the construction site induced additional\nroad traffic.\nFig. 3.16: Perimeters of the traffic studies for each construction site. The bolder lines indicate the traffic\nrecorded on major transport routes.\nequipment that can be brought in. Between about 200 and 300 people per day are expected to be present\non experiment sites and about 100 people on technical sites (see Table 3.10). This leads to daily work-\nrelated traffic of about 100 to 200 cars. This traffic can be significantly reduced by organising the work\nand providing the possibility of carpools and bus transport.\nDuring operational periods, technical sites are expected to have minimal personnel presence, based\non system requirements, resulting in minimal traffic impact. For experiment sites, the highest projected\nstaffing scenario involves small teams of up to 20 people working across three shifts. Transportation\nshould be organized to limit daily vehicle movement to several dozen cars entering and exiting each site.\n198\n\nTable 3.9: Worst case scenario during the construction period for excavated material transport using\ntrucks only. The traffic can vary with different excavation scenarios, leading to less traffic at PL and PB\nand more traffic at PA.\nSite\nTraffic\nper day\nAdditional 5-axle\ntrucks per day\nAdditional traffic\nin percent\nAdditional 5-axle\ntrucks per hour\nPA\n7803\n46\n0.5 %\n4\nPB\n5918\n37\n0.6 %\n3\nPD\n20,475\n93\n0.4 %\n8\nPF\n11,331\n12\n0.1 %\n1\nPG\n13,681\n100\n0.7 %\n8\nPH\n1709\n23\n1.3 %\n2\nPJ\n13,954\n95\n0.7 %\n8\nPL\n3380\n46\n1.4 %\n4\nInjector\n7803\n9\n0.1%\n1\nHowever, visitor traffic at sites PA, PD, PG, and PJ may be substantially higher.\nTable 3.10: Number of people on-site during various different activity periods.\nSite\nInstallation\n5 years\nOperation\n10 months per year\nMaintenance\n2 months per year\nShutdown\nevery few years\nPA, PD, PG, PJ\n200 - 300 people\n15 to 20 people\n100 people\n200 - 300 people\nPB, PD, PH, PL\n100 people\n0 to 10 people\n15 - 30 people\nUp to 100 people\n3.2.11\nEnvironmental monitoring\nAn environmental monitoring system will be put in place once the new research infrastructure is com-\npletely constructed. Such a system will help track compliance with the initially set goals and support\nsafe operation. Such a system typically comprises the following functionalities:\n\u2013 Clear water monitoring: Measurement stations for effluent water integrate continuous monitor-\ning of temperature, pH, hydrocarbons, foam, turbidity, conductivity and flow rate. Alarms are\ntriggered based on threshold and trend conditions. Where a surface site is equipped with water\nretention facilities, additional monitors will be installed to activate retention when needed.\n\u2013 Sewage water monitoring: Measurement stations integrate continuous monitoring of temperature,\npH, conductivity and flow rate for water released into the public sewage network. Periodic sam-\npling is also implemented.\n\u2013 Process water sampling: Such stations serve periodic sampling of residual effluents from the pro-\ncesses such as for instance water recycling and treatment.\n\u2013 Air quality monitoring: Such stations continuously monitor the air, including oxides (nitrogen\noxides and ozone) that may be byproducts of the synchrotron operation. Those systems are coupled\nto air recycling functions. Continuous comparison with the existing background air conditions will\nbe implemented.\n\u2013 Noise monitoring: Such stations measure and record continuously the noise levels at the surface\nsite locations and in sensitive areas in the vicinity.\n\u2013 Meteorological monitoring: These stations are equipped with anemometers and pluviometers for\n199\n\nassessment of hazards due to potentially radioactive substances and fumes in case of fire. Cooper-\nation with the national metereological services will be considered for data exchange.\n\u2013 Radiological monitoring: Monitoring of radiological parame- ters during and after the operation\nto provide evidence for compliance with the dose constraints and limits. The system comprises\nequipment for on-site monitoring for the safety of workers and on and off-site monitoring for the\nenvironment.\nIn addition to the stationary environmental monitoring facilities, additional portable devices will\nbe used for periodic in-field monitoring. Samples such as water, soil and plants will be analysed regularly\nby environmental laboratories.\n3.3\nCurrent state of the environment\n3.3.1\nMethodology\nThe current state of the environment in the perimeter of the reference implementation scenario and at\nthe surface site candidates has been analysed following the national regulations in the two Host States,\nFrance and Switzerland. The resulting single, integrated report [30], complemented by interactive maps,\naudio, image and video materials as well as by an Environmental Information System based on the ESRI\ngeographical information system, is an essential preparation work for the subsequent environmental au-\nthorisation process that has to include an environmental impact assessment in a transnational context.\nThis work has been carried out between 2023 and 2025 with a consortium of expert companies. The fol-\nlowing section gives a glimpse of the scope of the work carried out and provides the basic conclusions.\nThe initial state of the environment is only valid for a limited period of time since the environment is con-\nstantly evolving. Therefore, further complementary studies (e.g., hydrogeological investigations, further\nstudies on fauna and flora, more comprehensive environmental measurements) and studies for poten-\ntial alternative site locations have to be engaged during a subsequent environmental impact assessment\nphase.\n3.3.2\nAir and climate\nClimate\nThe climatic conditions and their foreseeable evolution have to be considered for a long-term programme\nlike the FCC that will extend until the end of the century. The environmental state analysis includes\nthe collection of climate data from bibliographical sources and climate observation facilities in Geneva\n(Switzerland) and Annecy (France). Despite the limited distance of about 30 km between the extreme\nsites of the FCC, the climatic conditions are notably different. The north is characterised by a subcon-\ntinental climate with hot summers, but moderate weather conditions due to the protective effects of the\nmountains and the moderating effect of Lake Geneva water mass. The south experiences a mountain\ncontinental climate with greater weather and temperature differences between the summer and winter\nseasons. Winds are rather constant in all areas. The climate evolution shows a sustained and evolving\ntemperature anomaly between +1.7\u00b0 and +2.5\u00b0C compared to the pre-industrial period. The number of\nfrosty days has decreased significantly by 20% since 1950. Precipitation is highly variable, without note-\nworthy changes over the time period. Extreme heat conditions during summer periods are expected to\nevolve further until the end of the century. They are typically accompanied by dry periods with effects\non the soil and the amount of precipitation is expected to decrease. Rain is expected to intensify during\nthe wet periods.\nLake temperatures have risen in recent years due to climate change. Since 1980, the surface\nwater in most lakes has warmed by about 0.4\u00b0C per decade. The warming of the deep water is more\nvariable and mostly ranges between 0.0 and 0.2\u00b0C per decade in the deep lakes. A further increase in the\ntemperature of the surface water layer down to 1 m deep is expected in all Swiss lakes: for a scenario\n200\n\nwithout climate change mitigation of between 3 and 4\u00b0C in most lakes towards the end of the century.\nThe water temperature at depths where raw water intake occurs will only slightly increase.\nThe evolution of climatic conditions is, however, not expected to lead to noteworthy effects on\nthe particle collider, for instance the water cooling systems. Nevertheless, the FCC must account for\nclimate evolution in its design and the development of an operational concept. In the presence of an\naverage envisaged temperature increase of around 4\u00b0C until the end of the century, these steps concern\nin particular, the adoption of operation to conditions that permit efficient work (e.g., avoiding periods\nthat are too hot) and increasing the benefits of waste-heat reuse project, both internally and in the region\n(e.g., shift operation to a colder season).\nAir\nFig. 3.17: Air quality measurements carried out using monitoring equipment to assess atmospheric pol-\nlutants in the vicinity of the surface site.\nThe air condition within the perimeter of the FCC is generally good, and the air quality is improv-\ning constantly. The main cause of air pollution is road traffic, mainly diesel-powered trucks. Fine dust\nparticles have their origin mainly in the agricultural sector and industry, in particular construction and\n201\n\nquarries. All typical air pollutants have been studied to document baselines, and air quality measure-\nments have been carried out to establish references in the vicinity of the surface site. These references\nserve as valuable input for the development of the construction process and the design of the infrastruc-\ntures in order to be able to properly and adequately ensure the protection of the air quality and meet the\nEU zero pollution vision for 2050. If it is decided to go ahead with the project, continuous air monitoring\nhas to be implemented at the surface sites to monitor the evolution and to be able to control the impacts\non the air quality during the construction and operation phases.\nClimate protection plans\nFrance has reduced its emissions by 27% with respect to 1990, in line with an average reduction of\nthe emissions in Europe by about 31%. The per capita footprint in 2022 was about 6.5 tCO2(eq) per\nyear [84], a value that is below the European Union average of 8 metric tons per capita. While the energy\nand industry sectors were able to reduce their footprints considerably, the transport sector did not yet\nsee the same improvements. Emissions due to transport even slightly increased. This situation is also\nreflected at a regional scale, with the transport sector remaining the main producer of greenhouse gas\nemissions. France has adopted the 2015 Paris Agreement, aiming for a reduction of the net emissions by\n55% with respect to 1990 by the year 2030 and climate effect neutrality by 2050. Locally, the climate\nprotection goals can differ. For instance, for the Pays de Gex around CERN today, the goals established\nare -66% by 2050 with respect to the year 2015. For \u2018Grand Annecy\u2019 the goals are -55% by 2030 and\n-87% by 2050.\nIn Switzerland, greenhouse gas emissions have decreased continuously since 2010. Transport,\nagriculture, and industry remain the main emission contributors. As of 2025, two laws are in place that\nimpose requirements: the law on CO2 and the law on climate and innovation. The established goals are\na reduction of 60% of the greenhouse gas emissions by 2030 with respect to 1990. The long-term goal\nfor the country is to achieve net carbon neutrality by 2050. Also, at the cantonal level, an operational\nclimate protection plan is in place. It prescribes goals and 41 specific measures to be implemented by\n2030. The emission reduction objectives are in line with values established at the federal level.\nSummary and conclusions\nThe planning, construction and operation of a future research infrastructure at CERN takes into account\nthe plans and regulatory requirements that have been established at the national levels to achieve the\ngoals of the Paris Agreement. Aspects related to energy and greenhouse gas emissions are considered\naccording to the current policies established by CERN, aiming at keeping the energy required for its\nactivity as low as possible, ensuring that the established research programme goals can be achieved.\nThis includes continuous improvement of its energy efficiency, recovering and supplying waste heat and\nreducing greenhouse gas emissions. CERN is committed to demonstrating that appropriate measures\nare taken with respect to energy and greenhouse gas emissions during all phases of a future research\ninfrastructure, in line with the plans and regulatory requirements established by the Host States.\nAt the end of 2019, CERN established a target for the reduction of its direct CO2 emissions by\n28% with respect to 2018 (baseline year) by the end of the Large Hadron Collider Operation Run 3\n(around 2026). This target has been highlighted since September 2020 in the CERN public environment\nreports that are published biennially. Recently, CERN has adopted a target for the reduction of its direct\nCO2 emissions by 50% with respect to the baseline year 2018 for the year 2030 ( [85]. Indirect emissions\nrelated to electricity consumption and other emission categories, such as those related to procurement,\nare also reported and published. Associated reduction targets are under investigation.\nIf a new research infrastructure is approved and included in CERN\u2019s overall environmental perfor-\nmance management, emission reduction plans and goals, including the new research infrastructure, will\nbe set with respect to the corresponding updated envelope of policies.\n202\n\nFig. 3.18: Air quality measurements conducted to assess atmospheric pollutants in the vicinity of the\nsurface site.\nThe integration of a new research infrastructure into CERN\u2019s environment will generate additional\nemissions that the organisation will strive to minimise within the established goals to be achieved for the\nscientific research performance. A rigorous eco-design approach applied to the construction activities,\nthe technical infrastructures, the particle accelerators, and the detectors will be introduced at the level\nof the organisation and will be required from the entire international collaboration contributing to the\nproject, ensuring that in-kind contributions will comply with the relevant environmental rules and regu-\nlations.\nThe proposed particle collider will not operate concurrently with the Large Hadron Collider.\nTherefore, the emissions generated by the operation of the new collider and its experiments will replace\nthose linked to the LHC operation. The new collider and its experiments will technologically be signif-\nicantly more advanced, and the eco-design will make it a research infrastructure with lower emissions\nthan the LHC today.\nTogether with continued efforts to technologically upgrade other CERN research facilities and\nactivities, effective support of the Host States efforts to meet their climate protection goals remains\nachievable.\nIn the context of the environmental authorisation process, a climate protection plan integrating the\nnew project is expected to be included as part of the environmental impact assessment.\n3.3.3\nWater\nContext\nThe situation of surface and subsurface water within the perimeter of the scenario has been analysed\nbased on bibliographical data, databases, maps, and reports. The legal frameworks in France and Switzer-\nland are very different with respect to this topic, which makes the comparison and integration of data\nchallenging. Whilst in France, the European Union definitions and directives are applied, different water\nprotection frameworks exist in Switzerland at federal and cantonal levels. For this reason, the current\n203\n\nstate of the water has to be looked at separately for each of the two countries. In addition, subsurface\nwater tables have to be distinguished from surface water. However, both water masses, subsurface and\nsurface, extend across the national borders and lead to cross-border aspects with respect to subsequent\nanalysis of potential environmental aspects: effects and impacts that will need to be considered during a\nproject preparatory phase.\nSubsurface\nFrance\nConcerning subsurface water, five distinct relevant water masses have been identified. FRDG517 extends\nfrom Gex across the Geneva basin to the Grande C\u00f4te de Bonmont and the Usses sector. FRDG208 lies\nbelow the FRDG517, extending from the Jura to the lake and towards the Usses sector in a calcareous\ngeology. FRDG231 is located north of the Genevois zone in France, partially under the FRDG517,\npartially limited like a river between the Rh\u00f4ne and Divonne-les-Bains, touching the Swiss border at\nthe height of Versoix. FRDG511 is located in the Savoie alpine region, south of FRDG517. FRDG364,\ncorresponding to the Arve valley, passes at about 100 m of the site PD in Nangy.\nWith respect to the European legislation, a goal has been set to maintain the so-called \u2018good state\u2019\nlevel quality attained in 2015 of all water masses. The standard needs to be maintained both in qualitative\nand quantitative terms.\nWater-bearing layers exist in relation to these water masses. All apart from in the implementation\nperimeter are \u2018free\u2019, i.e., there are no water-tight layers towards the surface. None of the hydrogeological\nentities is characterised by an aquifer.\nBecause of the need to maintain the quality levels and the potential interactions between water\nmasses, particular protection measures are in place that will need to be observed with respect to subsur-\nface works.\nSwitzerland\nIn Switzerland, various types of water-bearing layers are distinguishable based on their water capacity\nand depth. Deep layers can also exist in the molasse layer which is preferred for tunnel construction.\nToday, four water-bearing layers are identified in the canton of Geneva, and two of them are used for\nproviding drinking water: Allondon and Genevois. Montfleury and Rh\u00f4ne are currently being studied\nin terms of capacities and quality with respect to serving as a drinking water supply. The deep layers\nare today not mapped and therefore dedicated subsurface investigations are required for a future particle\ncollider project. A multitude of shallow and temporary layers that are between 2 and 10 m below the\nsurface are spread over the entire canton. They need to be analysed where shafts and surface sites are\nplanned. One of them is at a distance of about 140 m from site PB in Presinge at a depth of 2 m. No\npotential mutual effects could be determined.\nAnother water-bearing layer is at about 90 m from site PA in France. The Montfleury layer at a\ndepth of about 45 m is located 800 m south of the main site. One shallow layer is directly at the surface\nsite location PL in Challex in France. It spans the border, and no information is available on this layer.\nSites PL and PA require particular analysis to take these layers into account for the choice of the shaft\nlocation and the shaft construction technique. All three sites, PL, PA and PB, need to consider the\npotential water layers in the vicinity of their surface site and consider cross-border aspects.\nSurface\nFrance\nFour main surface water bodies are within a radius of 1 km of the surface sites. Three of them are in\ngood state (FRDR11960, FRDR559, FRDR537) and one has moderate quality (FRDR555c) with a goal\n204\n\n0+000\n10+000\n20+000\n30+000\n40+000\n50+000\n60+000\n70+000\n80+000\n90+000\n522799\n411.3\n522801\n409.2\n522802\n409.3\n522804\n406.7\n522805\n411.8\n522812\n408.2\n332146\n426.1\n332149\n413.8\n332150\n413.4\n332151\n417.0\n332152\n427.8\n340816\n793.9\n530636\n801.75\n340818\n741.\n340823\n807.9\n340839\n795.4\n340842\n797\n340856\n834.4\n340876\n768.5\n340880\n827.3\n340881\n851.6\n340882\n838.3\n340793\n542.3\n340795\n550.1\n340802\n548.3\n340803\n542.7\n340804\n540.6\n340228\n384.5\n340267\n432.01\n340273\n433.1\n340274\n454.2\n340562\n452.3\n340317\n583.2\n340536\n523\n525309\n517.2\n340488\n459.5\n332264\n518.7\n332274\n652.7\n332275\n466.5\n340433\n476.9\n332236\n505.7\n332240\n525.0\n332301\n610.0\n332125\n504.3\n521856\n517.4\n332120\n501.1\n332138\n496.4\n539384\n481.0\n332369\n411.7\n332446\n419.3\n332447\n426.1\n332432\n420.8\n332439\n422.2\n332448\n423.9\n514713\n422.7\n332371\n421.6\n332742\n431.4\n332741\n462.9\n332745\n455.0\n332746\n459.7\n332772\n426.3\n332147\n426.7\n332148\n428.1\n \nLac L\u00e9man\n \n L'Arve\n \n La Filli\u00e8re\n \n La Filli\u00e8re\n \n Les Usses\n \n Le Flon\n \n Le Rh\u00f4ne\nL'Allondon\n250m\n300m\n400m\n250m\n300m\n400m\n500m\n600m\n700m\n800m\n \nPA PA\nAlt = 425.5m\nPB\nAlt = 430.5m\nPF\nAlt = 739m\nPG\nAlt = 600m\nPH\nAlt = 554m\nPJ\nAlt = 551m\nPL\nAlt = 477.5m\n387.1\n387.4\n421.5\n387.6\n387.2 388.5\n409.7\n402.6\n355.8\n397.0\n399.4\n389.7\n398.6\n417.3\n405.7\n801.75\n797.5\n543.3\n541.1\n531.65\n486.7\n429.6\n414.3\n485.3\n478.7\n501.9\n488.5\n426.5\nPD\nAlt = 465m\n0\n100 200m\nEchelle : 1/15 000\n500m\nSite de surface\nSondage g\u00e9otechnique\n (identifiant BRGM + altitude)\nNiveau d'eau mesur\u00e9\nLEGENDE :\nFig. 3.19: Overview of surface and subsurface water bodies in the scenario perimeter. In this conceptual\ndrawing, the subsurface structures are assumed to be at an elevation of 250 m. The uncertainty of the\nwater table heights is indicated in grey. The surface site locations and elevations are indicated.\nto achieve good quality by 2033. The site PF in \u00c9teaux is located in the vicinity of a stream (50 to 100 m).\nAlso, site PH is in the vicinity of a small creek (30 m). Other sites such as PD (600 m from the Arve) and\nPG (300 m from the Filli\u00e8re) are further from rivers.\nSwitzerland\nLake Geneva in Switzerland is the most important water body at the surface. It is 4 km from the PA and\nPB sites. Site PB is located in the vicinity of a small stream (30 m).\nSummary\nThe projection from the line of the implementation scenario to the subsurface intersects with the geo-\ngraphical location of numerous subsurface water bodies. However, the tunnel will be located signifi-\ncantly below them (see Fig. 3.19). No intake from any subsurface water-bearing layer is expected for\nthe construction and operation of the project. Water for drinking will be consumed from connections\nto the existing drinking water network. Raw water for cooling purposes will be taken from the existing\nwater supply network for CERN in Switzerland, which takes water from Lake Geneva. Drinking water\nprotection zones are largely avoided for the entire project so that any potential adverse effects can be\nexcluded.\nThe majority of subsurface layers are not located under a watertight layer. Thus, they are poten-\ntially subject to pollution. Also molasse layers may include water-bearing volumes. Therefore, dedicated\nhydrogeological investigations will be carried out to optimise the location of the shafts to avoid potential\nadverse effects with water-bearing layers in PA (Ferney-Voltaire, France) at a distance of 35 m from a\ndrilling ban zone (sector B in Switzerland) and PL (Challex, France). Particular attention will be devoted\nto avoid affecting nearby creeks and the biodiversity around sites PB (Presinge, Switzerland) and PH\n(Cercier and Marlioz, France). PH is, in addition, in an area with chronic lack of water and therefore\nsubsurface works such as the creation of a shaft will have adequate protection measures in their design\nin case there is a risk of affecting any water bearing layers.\nConcerning the release of water into the environment and particularly into nearby creeks, the\ndesign of the infrastructure will include filtering and cleaning before release. Connections to wastewater\nnetworks will ensure that all other water is released via the existing water treatment infrastructure at all\ntimes, ensuring compliance with the legal and regulatory frameworks in the two Host States.\n205\n\nFig. 3.20: Relief in the area of the FCC reference scenario.\n3.3.4\nSubsurface\nRelief\nThe FCC perimeter is constrained by noteworthy mountains (see Fig. 3.20). The Jura is located north\nand west of Lake Geneva with peaks of 1720 m. The south-east is characterised by the Bornes plateau\nevolving into the pre-alps that lead to Mont Blanc which has an elevation of 4806 m. The west is con-\nstrained by the Vuache mountain reaching 1112 m. The Sal\u00e8ve (1379 m) is located in the centre of the\nFCC circular alignment. The Aravis mountain range is located just south of sites PD, PF and PG. Mont\nSion (78t m) is located between the Vuache range and the Sal\u00e9ve . In the south, the tunnel crosses under\nthe Mandallaz range (923 m), also called Balme, that is part of the pre-Alps. The Massif du Chablais\nis northeast of Lake Geneva and east of the PB and PD sites. Despite the presence of the numerous\nmountain chains and peaks, all surface sites are located on lower ground in flat areas at between 400 and\n700 m elevation.\nTopography\nSite PA is located at an elevation of approximately 425 m in an open area with a very slight slope of\nabout 2 to 5%. Site PB is at an elevation of about 430 m on an even and open area. There are hills only\na few kilometres to the north. Site PD at an elevation of approximately 460 m is located on a slope of\nabout 5% towards the north. The zone is hilly in all directions, but the terrain is cut by major transport\nroutes (A40 autoroute, D903 departmental road). The absence of bushes and hedges makes the terrain\n206\n\nFig. 3.21: Geological profile of the Geneva Basin, illustrating stratigraphic units, tectonic features, and\nsedimentary formations shaping the region.\nvisible. Site PF reaches elevations of between 730 and 745 m on a slope of about 7% from west to east.\nThis makes the area very visible towards the mountains and from the RD1203 road. However, it is not\nvisible from the A410 autoroute. Site PG is separated from the A410 autoroute in the north by a forest\non a slight slope of 5% in north-south and west-east directions at about 600 m elevation. At the southern\nboundary, the slope starts to become steep \u2013 from 25% to 40% towards the RD1203,:Annecy road. this\narea is avoided. Site PH is located on a slope of 10 to 20% at an elevation of between 517 and 591 m,\nfalling off from the RD203 road. The entire area is located in a forest that covers the zone towards the\nUsses Valley in the west. The topography imposes a terracing approach for the site. The PJ site is located\non a wide and long slope of 6% at an elevation of between 496 and 532 m that falls off from the A40\nautoroute to the Rh\u00f4ne valley. This location also requires terracing. Tree lines that break the even space\nand slope exist in the vicinity. The PL site is located at 500 m elevation on a rather flat area. The absence\nof noteworthy trees or hedges in the vicinity makes the terrain highly visible. The land falls off steeply\ntowards the Rh\u00f4ne valley on the opposite side of the nearby pathway towards Switzerland.\nGeology\nThe geology is covered in greater detail in the sections on civil engineering since it determines the\nplacement of the subsurface works. Here, a general overview provides the context. The geological\nlandscape of the Gen\u00e8ve Basin spans between the Jura Mountains in the northwest and the Prealps in\nthe southeast, with a Tertiary molasse basin overlaying Cretaceous formations. Shaped by Quaternary\nglaciations, the basin features deep valleys and sedimentary deposits up to 400 m thick, especially in\nthe Grand-Lac, with Holocene sediments varying by river currents. The Rh\u00f4ne Delta sees Holocene\nsediments exceeding 100 m in thickness. The basin\u2019s geology includes three main units: Jura sedimentary\nrocks in the northwest, central Tertiary sandstone (molasse), and thrusted molasse with Prealpine units\nin the southeast.\n207\n\nThe Ain department is located on two very different geographical and geological domains with, to\nthe west, the large plains of Bresse and Dombes the western plains of Bresse and Dombes, a tectonic rift\nfilled with Tertiary deposits, and to the east, Jura mountains, marking the southwestern edge of the Swiss\nmolasse plain. In addition, the department is covered by three large geological units, Bresse and Dombes\nincluding C\u00f4ti\u00e8re and part of the Val de Sa\u00f4ne; Bugey and the southern part of Revermont and finally the\nPays de Gex. The Pays de Gex, where the PA and PL sites are located, features mountainous limestone\nformations (Middle and Upper Jurassic, Lower Cretaceous) with karst systems, bordered by faults and\nglacial deposits. Similarly, the surface sites PD, PF, PG, PH, PJ in Haute-Savoie in France and PB\nin Switzerland are part of the molasse basin and showcase diverse geological features from crystalline\nAlpine massifs to sedimentary molasse basins like the Plateau des Bornes. These molasse deposits,\nformed from Alpine erosion during the Oligocene to Miocene, vary in thickness and are tectonically\ninfluenced by Alpine uplift. The geological formations of the different surface sites are presented in\nTable 3.11 .\nTable 3.11: Geological formations present at surface sites.\nSite\nDeposits\nComposition of materials\nPA\nW\u00fcrmian glacio-lacustrine\nLayered clays and silts\nPB\nMorainic\nClays, silts, and sands\nPD\nGlacio-lacustrine\nClays and silts\nPF\nW\u00fcrmian to post-W\u00fcrmian morainic\nSilts, sands, pebbles, gravels, with\nlocalised presence of clays\nPG\nW\u00fcrmian morainic\nClays, sands, pebbles,\nstones,and boulders\nPH\nW\u00fcrmian to post-W\u00fcrmian morainic\nClays, sands, pebbles,\nstones, and boulders\nPJ\nW\u00fcrmian to post-W\u00fcrmian morainic\n(or colluvium)\nSilts, sands, pebbles, gravels, with\nlocalised presence of clays\nPL\nW\u00fcrmian morainic\nPebbles, gravels, sands, and limestone\nwith localised presence of clays\nSoil\nField soil investigations were carried out in July 2023 for site PD and in April 2024 for the sites PA, PB,\nPF, PG, PH, PJ and PL. The primary objective was to analyse the pedological characteristics of the soil\nof these sites to determine their suitability for agricultural activities and other potential uses.\nThe work consisted in the identification and description of existing vegetation and crops, as well\nas the assessment of factors impacting agricultural productivity, such as accessibility, topography, non-\ncultivable areas, wet zones, and irrigation infrastructure. Soil samples were collected using hand augers\nup to a depth of 120 cm to examine soil layers, coarse elements, and traces of waterlogging. The number\nof samples per site was determined based on plot size and soil diversity in order to ensure adequate\nrepresentation. A total of 48 samples were collected across the eight sites.\nThe PA site is dominated by deep loamy soils (neoluvisols) with a low content of coarse elements,\nalthough areas near roads feature shallower and rockier soil.\nAt the PB site, the surface horizon consists of clay-loamy soils with low amounts of coarse ele-\nments, but signs of pseudo-gleying appear in deeper layers.\n208\n\nFig. 3.22: The auger boring method used to obtain soil samples from different depths.\nPD site is characterised by deep loamy soils, healthy and well-drained, with low, coarse elements\nthroughout the soil profile and limited hydromorphy. The soil is highly suitable for agriculture due to its\ndeep, fertile, and easily mechanisable soils.\nAt the PF site, the surface layer consists of loamy neoluvisols with low rocky content, while clay\naccumulation begins at around 70 cm depth. These parameters are suitable for permanent grasslands.\nThe surveys carried out at the PG site and its annexes show that the present soil does not match the\nsoil recorded in the French GIS-Sol database. The soil of PG main site is deep, homogeneous, and range\nfrom clayey to clay-loamy textures, with low amounts of coarse elements and temporary hydromorphy\ntraces. Annex sites have lighter, powdery soils, moderately deep with a clay-loamy texture.\nThe PH site is covered by deep Brunisol-type soils with Redoxisol characteristics, where strong\nhydromorphic features are already apparent near the surface, indicating limited drainage. The survey\nconfirms that the permanent grassland at a small part of the PH surface site corresponds to the soil cover\nlisted in the database.\nPJ site is characterised by deep argilo-limoneux soils with minor coarse elements. Moderate hy-\ndromorphy is visible near the surface, with traces of altered limestone beyond 70 cm. The area is suitable\nfor both permanent and temporary grasslands.\nPL site at the border with Switzerland is predominated by calcosols with areas of colluviosols in\nsouthern regions. Soils vary from superficial to deep, with coarse elements more common in superficial\nareas. Hydromorphic features are less pronounced, and soils are generally suitable for agriculture.\n209\n\nFig. 3.23: Soil sample obtained by using auger boring method.\nOverall, most surface sites have deep soils with limited coarse elements, ensuring good agricul-\ntural potential, although hydromorphic tendencies and limited drainage at certain locations limits their\nagricultural use. Additional laboratory analyses of the soil are currently being conducted to assess its\nquality in terms of the presence of various mineral elements and their availability to plants, and potential\ncontaminants.\nSummary\nConcerning relief and topography only, site PH in Cercier and Marlioz exhibits significant issues due to\nthe slope in the forest. PJ in Dingy-en-Vuache and Vulbens is also located on a slope, but it is in an open\narea and significantly less steep with good access. Sites PA, PB and PL on very open and flat areas call\nfor particular integration with respect to visibility and co-visibility. Site PD and PF do not exhibit any\nparticular challenges, although good landscape integration is advisable to reduce visibility and to blend\ninto the terrain. Care needs to be taken at site PG to stay clear of the steep slope towards the Annecy\nroad.\nThe geological context of the study area highlights the diversity of formations across the Geneva\nBasin and the Ain and Haute-Savoie departments. The basin features sedimentary deposits influenced\nby quaternary glaciations, with thick holocene sediments in the Rh\u00f4ne Delta and Grand-Lac. The sites\nspan different geological units: Pays de Gex (limestone formations with karst systems) and molasse\nbasins (formed by Alpine erosion), showcasing a variety of materials, including glacio-lacustrine clays,\nmorainic sands, gravels, and silts. These variations underline the region\u2019s complex geological history,\nwhich is crucial for subsurface work placement and excavated material management.\nThe pedological surveys confirmed diverse soil characteristics, ranging from deep, fertile, and\nwell-drained loamy soils to hydromorphic and clayey profiles with drainage limitations. Sites such as\nPD and PL are highly suitable for agriculture due to their deep, fertile, and easily mechanisable soils. PA,\nPB, PF, and PJ show varying degrees of hydromorphy, particularly in deeper layers, making them more\nsuitable for grasslands or selective agricultural practices. PH and PG present significant hydromorphic\nconstraints, with PH showing pronounced surface water retention issues due to its altered limestone\nsubsurface. Variations in texture, depth, and coarse element content reflect the influence of local geology\n210\n\nand historical land use.\n3.3.5\nBiodiversity\nFig. 3.24: Fiery Clearwing Moth (Pyropteron chrysidiformis) feeding on a plant.\nBiodiversity refers to the diversity of species, ecosystems, habitats and ecological processes. It\nincludes both natural and human-modified environments, which together create the conditions for the\nexistence and functioning of various organisms. A variety of species in the natural spaces are not locally\nconfined. They extend across fauna corridors and ecologically coherent zones that comprise the terrestrial\nand aquatic species, namely plants, insects, mammals, amphibians and reptiles, which are considered as\nan integrated whole.\nTo assess potential impacts on biodiversity, the current situation was analysed for all candidate\nsurface site locations, first using bibliographical information. This includes, for example, the study of\nprotection zones at regional, national and international levels, inventories of natural heritage, ecological\ncorridors and their continuations. Then, field investigations were carried out by numerous experts over\na time frame of more than one year, covering the four seasons. They served not only to confirm and\ncomplement the existing bibliographic information but also as necessary input to establish a baseline for\nthe avoid-reduce-compensation approach, the optimisation of the sites and the subsequent environmental\nimpact assessment. The investigations were not restricted to the area within the perimeters of the surface\nsite locations. They were extended to a perimeter of up to several hundred metres larger, depending on\nthe topography, but the extension was investigated in less detail. An extended perimeter covering up to\n5 km was analysed at a high level with the help of existing databases and cartographic materials.\nSite PA in Ferney-Voltaire is in the vicinity of nature protection and humid zones as well as forests\nthat serve as cross-border corridors for animals. Amphibian breeding zones are noted in the enlarged\nperimeter on the Swiss side. The forests also serve as retreat areas for migrating birds. There are nature\nprotection and wetland zones, including amphibian reproduction zones, in the vicinity of the PB site\nin Presinge. There is a protection zone for migrating birds at some distance. For site PD in the Arve\narea there is a nature protection zone in the vicinity. Nature protection zones and ecological corridors\nhave been identified in the vicinity of site PF in \u00c9teaux. Several nature protection zones also exist in the\n211\n\nvicinity of site PG in Groisy and Charvonnex. Further away, there is a biotope protection zone. Nature\nprotection zones also exist in the vicinity of site PH in Cercier and Marlioz. At some distance, there is a\nbiotope protection zone. Rare species are found in the immediate vicinity of the site and partially at the\nlimit of the site, mainly close to a creek that passes at the site boundary to the north. There are nature\nprotection zones in the vicinity of site PJ in Dingy-en-Vuache and Vulbens. There are nature protection\nzones and cross-border ecological corridors, linking forest spaces and the Allondon zone with the Rh\u00f4ne\nriver zone in the immediate vicinity of site PL in Challex. Strict bird protection zones on the Swiss side\nof the border extend into the forest on the French side. There, biotope protection zones are known.\nNone of the sites is directly affected by a nature protection restriction, a national park or interna-\ntional biodiversity protection regulations (e.g., Natura 2000, RAMSAR, UNESCO or national parks).\nNatural habitats\nFig. 3.25: Bocage hay meadow photographed during the field investigations.\nIn the context of environmental analysis, a habitat refers to the natural environment or ecosystem\nwhere a particular species, community, or group of living organisms lives, grows, and thrives. It includes\nthe physical, chemical, and biological components that support life, such as soil, water, air, terrain, other\nplants and animals and the interaction among all those components. The studies carried out comprised\nestablishing an inventory of the existing habits at the surface sites, investigating the perimeters around\nthem, and evaluating their characteristics and qualities. This work helped to determine the sensitivity\nlevels associated with the larger zones concerned by the surface sites in order to apply the avoid-reduce-\ncompensate scheme for further optimisation of the project scenario.\nSite PA in Ferney-Voltaire, France is predominantly a peri-urban, open agricultural habitat of about\n70 ha that is also closely linked to Geneva airport, agricultural spaces in Switzerland and forest spaces\nbetween Switzerland and France. Its mainly formed by prairie, bushes, trees, monocultures and artificial\nhabitats (paths, roads, industrial and commercial buildings). The groves in the vicinity of the site exhibit\nhigh sensitivity. Overall, the sensitivity on the site is average to low, often only partially fulfilling the\nrequirements of a habitat.\nThe site PB in Presinge, Switzerland, is also an open agricultural space dominated by monocul-\ntures with some nearby woodlands and isolated hedges. Only a thin strip in the close vicinity of the\n212\n\nnearby creek exhibits a moderate to average habitat quality.\nSite PD in Nangy, France is located in a rural context, constrained at the side by an autoroute and\na departmental road and one side is bordered by a hamlet. Some isolated bushes and trees can be found\nin the vicinity. The habitat quality is very low to low. Only in a small patch at the southern end at the\nsurface site border, the bushes represent a high value in this much-constrained space.\nSite PF in \u00c9teaux, France is in a mixed agricultural and prairie zone. Woodland starts to appear\nat the borders. The north is limited by a heavily used national road. The enlarged investigation zone\nincludes a wetland. At the location of the surface site the habitat quality is low to average. The neigh-\nbouring wetlands and forest lands have a strong sensitivity.\nSite PG in Groisy and Charvonnex in France is located in a mixed environment consisting of\nprairie, woodland, grassland and rural/forest paths. The enlarged space close to the autoroute is domi-\nnated by artificialised spaces such as retention basins, temporary inert waste buffering, roads, paths and\nconstructed areas. The zone can, in general, be characterised as predominantly a forest habitat. On\naverage, the whole zone studied exhibits a low to average level of habitat quality. Where areas can be\nconsidered wetlands, both inside and outside woodlands, the habitat quality can be considered average.\nTwo forest areas that are outside the site perimeter, but in the immediate vicinity, have been identified to\nhave a high sensitivity due to the quality of the trees.\nSite PH in Cercier and Marlioz in France is almost entirely located in a woodland. There exist\nsome cleared spots that host prairies and grassland. Overall, the habitat quality is low and where mono-\ncultures exist, it is very low. A zone exists that can be considered a wetland due to its characteristics\nsouth of the site. Its effects extend to a 0.4 ha large part of the site, making this area a high-quality\nhabitat zone.\nSite PJ in Dingy-en-Vuache and Vulbens in France is located in an open rural, agricultural space\nthat is limited at two sides by treelines, a temporary creek, by an autoroute in the north and a rural path\nand further agricultural areas in the south. The extended study perimeter also includes zones that can be\ncharacterised as humid. The habitat quality is heterogeneous, ranging from very low to high. The space\noccupied by the surface site can be split in two halves: an area of low and an area of high habitat quality.\nThe half that is closer to the autoroute exhibits the higher value.\nSite PL in Challex in France is located in a rural context. The site and the larger study perimeter\nspanning 100 ha include agricultural fields, wasteland, bushes, and trees around houses that are on the\nsurface site. The herbaceous spaces carry characteristics of wetlands. The agricultural constructed spaces\nwith trees and gardens currently have a low to very low habitat quality. The humid prairies in the vicinity,\nbut not on the surface site, have an average habitat quality.\nWetlands\nWetlands provide numerous services for ecosystems, particularly in terms of regulation, water storage,\nand conservation of biodiversity. In the context of this study, investigations were carried out on the pres-\nence of wetlands in areas potentially affected by the surface sites. The study of wetlands is important en-\nvironmentally and also a regulatory requirement under French law. This study aims to assist in decision-\nmaking for the location of sites and their optimisation according to the avoid-reduce-compensate ap-\nproach. In France, in the case of the destruction of a wetland, the regulations impose compensatory\nmeasures with a ratio that can reach 1.5 to 2 times the wetland area impacted. Measures can include the\nimprovement of partially degraded wetland functions and monitoring over a defined period to evaluate\ntheir effectiveness.\nThe study of wetlands was carried out in the same way for Swiss and French territories to obtain\ncomparable and coherent data. In Switzerland, only wetlands listed in the federal inventories of low\nmarshes, riparian zones, OROEM, RAMSAR sites, and amphibian breeding sites are potentially pro-\ntected. In the absence of a direct equivalent of wetlands in Swiss legislation, this study was inspired\n213\n\nFig. 3.26: Wetland observed during the field investigations.\nby the definition of wetlands given in French legislation. According to Article L211-1 of the French\nEnvironment Code [86], \u201cWetlands are understood as areas, used or not, usually flooded or saturated\nwith freshwater, saltwater, or brackish water, permanently or temporarily; vegetation, when present, is\ndominated by hygrophilous plants for at least part of the year\u201d. Article R211-108 of the Environment\nCode specifies that: \u201cThe criteria to be retained for the definition of wetlands [...] relate to the soil\nmorphology linked to the prolonged presence of water of natural origin and the possible presence of\nhygrophilous plants. These are defined based on lists established by biogeographical regions. In the\nabsence of hygrophilous vegetation, the morphology of the soils is enough to define a wetland.\u201d Thus,\nFrench legislation defines wetlands based on floristic and/or pedological criteria.\nThe delineation of wetlands on surfaces concerned by the potential site locations was based on de-\npartmental/cantonal, Swiss, and French inventories, floristic criteria, and pedological inventories. Gov-\nernment inventories of the departments of Ain and Haute-Savoie allowed a first delineation of the known\nwetlands currently present on surface sites. Inventories of flora allowing a second delineation of wet-\nlands were carried out during the flowering period in spring 2023 and by an expert company to identify\nand delimit the types of habitats potentially present on the immediate and extended perimeters around\neach site. These inventories also highlighted \u2018pro parte\u2019 surfaces, i.e., surfaces where the habitat identi-\n214\n\nfied was not systematically or entirely characteristic of wetlands. Finally, pedological inventories were\nconducted by another expert company in 2023 and 2024. These inventories identified soils characteristic\nof wetlands for surfaces where the presence of wetland characteristics was eventually determined to be\nactually present or not in 2024 using shallow subsurface investigations (12 to 90 cm deep).\nAt the border of site PA in Ferney-Voltaire, two wetlands are known with a total size of 6.3 ha.\nThe site does not directly impact the zone. The concept for the site has a rewilding project to improve\nthe quality of this area and to make it a permanent and protected natural habitat with recreational charac-\nteristics. There are zones that are comparable to the French definition of wetlands in the vicinity of site\nPB in Presinge. None of these is in the immediate perimeter of the site, and the site will not impact any\nof these protection zones. The conceptual plan for the surface site includes the integration of one part\nof the nearby creek\u2019s area to rewild the space used for agricultural purposes today and to make it a fully\nprotected habitat.\nThree wetlands zones can be found in the extended perimeter of site PD in Nangy, separated from\nthe site by an autoroute. The site does not affect any of these wetlands. A number of wetland zones can\nbe found in the immediate vicinity of site PF in \u00c9teaux. The field investigations revealed that the zone\nis larger than registered in the regional inventory. The site does not impact these zones. However, the\nconceptual plan for the site concept includes the creation of a green buffer that includes one of the zones\ncurrently used for agricultural purposes to rewild it and to make it a protected habitat. There are also\nseveral wetland zones in the forest in the vicinity of site PG in Charvonnex and Groisy. The shape of\nthe site has been adapted to avoid potential negative effects on these zones. A wetland zone exists in the\nforest at the northern border of site PH in Cercier and Marlioz and cuts through the site towards the south.\nOut of 16 ha about 0.8 ha are in the perimeter of the currently indicated site boundary. Consequently, the\nsite will be further optimised during a subsequent design phase to either exclude significant effects on\nthe wetland zone or to develop appropriate compensatory measures where the effect cannot be avoided.\nFor example, a nearby area of land which has very poor biodiversity and habitat value has been identified\nand it can serve as an optional space in case the surface site equipment does not fit within the reduced\nsurface site geometry.\nThe vicinity of site PJ, in particular close to the autoroute, is characterised by extended wetland\nzones, covering 13.6 ha. 1.6 ha are on an agriculturally exploited area of the surface site. The subsequent\nsite design phase will take in account the presence of this zone to establish avoidance and reduction\nmeasures, including the possibility of creating an annex further in the north on land that is not affected.\nCompensation measures may have to be developed for the part that cannot be entirely avoided. Wetland\nzones also exist at some distance from site PL in Challex, in the forest. The site does not affect them.\nSumming up, none of the sites is directly affected by wetland induced constraints. The restoration\nof an ecological compensation zone in the immediate vicinity of site PA provides an opportunity to\nincrease the value of the zone and thus compensate for the loss of space by fostering the development\nof a natural habitat and the increase of biodiversity opportunities. Sites PH and PJ deserve particular\nattention during the further development of surface site designs due to zones that have characteristics of\nwetlands entering partially the site perimeters. Care also needs to be taken during the optimisation of the\nperimeter of site PG to ensure the avoidance of potential wetland-like areas outside the site limits.\nFlora\nOn-site field visits were conducted in 2023 to validate bibliographic data and inventory the species\npresent at the surface sites. These investigations aimed to confirm the presence of remarkable flora\nand invasive species and provide insights into local ecological contexts. \u201cRemarkable flora\u201d refers to\nplants that are notable or extraordinary due to their unique characteristics, ecological importance, rar-\nity, or cultural significance. These plants often stand out because of their striking appearance, unusual\nadaptations, or the critical roles they play in their ecosystems. The term can apply to native, endemic, or\neven cultivated plants. Invasive plants are non-native species that are introduced to a particular ecosys-\n215\n\nFig. 3.27: Military orchid (Orchis Militaris) observed during field investigations, providing valuable data\non local wildlife presence and ecosystem dynamics.\ntem, where they spread rapidly and often outcompete native plants. These plants typically lack natural\npredators, diseases, or other controls in their new environment, allowing them to thrive unchecked. As\na result, they can disrupt local ecosystems, reduce biodiversity, and cause environmental and economic\nharm.\nFor this study, remarkable species are those with legal protection status (national, regional, or\ndepartmental) in one of the two Host States and those listed as \u201cnear-threatened\u201d (NT) and those that\nappear in regional and national red lists.\nSpecial attention was given to invasive species, since soil that hosts invasive species must not be\nsimply transferred to land compensation areas in order to avoid spreading of such species. Risk levels\nestablished at regional and national criteria were considered to determine the sensitivity of areas with\nrespect to invasive species.\nThe habitats and floral compositions in the study area of site PA in Ferney-Voltaire, France are\ndominated by the agricultural space. During the field inventory, no remarkable species were observed.\nHowever, the municipal species list for Ferney-Voltaire identifies 3 noteworthy species that could in\nprinciple be encountered in the enlarged study area around the site. Complementary studies will be\nrequired during a project preparatory phase to confirm or exclude the presence in all areas that would\npotentially be affected by the surface site. Several species of invasive plants were observed in the PA\nstudy area that need to be considered when developing agricultural space compensation plans.\nThe habitats and composition in the Presinge study area in Switzerland concerning site PB are\nmainly agricultural. Woodland exists at a further distance and close to the Nant de Paradis creek, plants\n216\n\ntypical of wetlands (wetlands, riverside vegetation) are found. During the field visits, two remarkable\nspecies, protected at the cantonal and national level, were observed. Apart from these exceptions, no\nother important species listed in the bibliography were recorded. Several invasive species exist in the\nsurroundings, and there are even some exotic ones. The agricultural space is free from remarkable and\ninvasive species.\nFig. 3.28: Glutinous sage (Salvia glutinosa) observed during field investigations, providing valuable data\non local wildlife presence and ecosystem dynamics.\nApplying the municipal catalogue of remarkable species for site PD in Nangy, France does not\nlead to any significant sensitivity of the site. During the field inventory, no noteworthy species were\nfound. However, several invasive species were observed that may negatively affect agricultural cultiva-\ntion. Therefore, it remains to be studied if the soil can be transported for compensation purposes as is or\nif particular measures to eliminate those species will be required.\nNo remarkable species were recorded during the field inventory of the site PF in \u00c9teaux in France.\nThree noteworthy species listed in the bibliography may, in principle, occur in the enlarged study area\nincluding wet meadows and wooded areas, outside of the surface site perimeter.\nThe municipal species catalogue of Groisy and Charvonnex applicable to site PG in France men-\ntions three remarkable species that could be present in the study area. None of them were identified\nduring the field inventory and no other remarkable species from the bibliography were observed either.\nA few invasive species have been recorded in the study area and topsoil that is removed should be cleared\nof those species.\nThe list of flora species of the communes of Cercier and Marlioz applicable to site PH in France\nincludes a considerable number of remarkable species, but none of them is present in the study area, and\nno remarkable species were observed during the field visit.\nNone of the remarkable species listed in the bibliography for Dingy-en-Vuache and Vulbens for\nsite PJ in France occur in the study area and no remarkable species were observed during the field visits.\nSome remarkable species listed in the communal lists could, however, be potentially present in the area\nthat exhibit sufficient characteristics to support those species. They concern mainly humid zones at the\nedges of the surface site candidate perimeter.\nFor site PL in Challex, France, four species are highlighted as noteworthy in the bibliography.\n217\n\nTow out of them may potentially occur in the area of the PL site. However, none of them were observed\nduring the field visits. On the contrary, two invasive species were inventoried in the study area, which\nshould be taken into account in the case of reuse of agricultural topsoil.\nSumming up, no particular sensitivity of any surface site candidate could be established with\nrespect to remarkable flora. However, some sites will require attention with respect to the treatment\nof invasive species before the topsoil can be re-used for compensation measures. The PB surface site\ndesign requires attention due to two remarkable species observed during the field visit and the large\nnumber of potentially present species listed in the bibliography in the larger area. This site is, therefore,\nstill considered to have a strong sensitivity at its edges. No outstanding flora species were inventoried at\nthe PA, PG, PH, PJ, PL and PF sites, but these areas require complementary studies during a preparatory\nproject phase to confirm the state and to plan for the construction site activities. So in general, additional\nfield visits are required to reliably assess the environmental impacts. The sensitivity of site PF is also\nconsidered strong due to potential remarkable flora at the very edges of the site. Attention will need to\nbe paid to invasive species present in several locations, and this will need to be taken into account when\nconsidering the reuse of agricultural soil in other locations.\nFauna\nAmphibians\nFig. 3.29: Common toad (Bufo bufo) observed during field investigations, providing valuable data on\nlocal wildlife presence and ecosystem dynamics.\nFor some groups of amphibians, identification down to the species level cannot be carried out\nwithout genetic analysis due to the strong hybridisation within these groups. However, an inventory\nbased on bibliographical data and field investigations was established not only on the sites, but also\nfor the perimeters in the vicinity of the site. Investigations were done during the day and the night for\nseveral months. Amphibians are frequently found in the vicinity of water spaces, creeks, rivers, and\nwetland zones.\nAmphibians were observed in the vicinity of site PA in Ferney-Voltaire across the French and\nSwiss territories. Some of them are considered endangered in Switzerland. No amphibians are present\n218\n\non the surface site location. In the immediate vicinity of site PB in Presinge the bibliographic inventory\nwas confirmed by the field investigations and the issue8 is big, and therefore the river zone will be\nentirely avoided by the project. The integration of a rewilding project in the site will help to raise the\nprotection level of that zone further. The area is currently partially used as agricultural space. Site PD\nin Nangy and its vicinity have a low stake concerning amphibians. Although the site PF in \u00c9teaux is not\ndirectly concerned, the immediate vicinity revealed species with a high stake. At site PG in Charvonnex\nand Groisy several amphibians are confirmed in the vicinity and few on the site. The stake concerning\namphibians is also high in the vicinity of site PF. On the site, no issues could be identified. Some\namphibians were observed in the vicinity of site PJ, but the site did not reveal particular issues. Some\namphibians were observed in the larger area around site PL in Challex, including Switzerland. Some of\nthem are listed as endangered and protected. The site does not host amphibians.\nSumming up, the zones in the vicinity of sites PA and PD feature a few habitats that would give\nthem a high value. For sites PF and PJ, the availability of habitats also seems relatively limited, but the\nforest/hedge environment and the presence of streams give them a higher value. The vicinity of site PB,\nmeanwhile, has the particularity of being partly located on an amphibian reproduction site, that increases\nits value level, despite the lack of direct observation of high-valued species. The sites PG, PH, and\nPL have high values due to a high density of aquatic habitats and the observation of a large number of\nhigh-value species in their vicinities.\nBirds\nFig. 3.30: Reed warbler (Acrocephalus scirpaceus) observed during field investigations, providing valu-\nable data on local wildlife presence and ecosystem dynamics.\nOrnithological surveys were conducted using sound recorders and visually with binoculars and\ncameras. The survey period spanned 2023 and 2024. An inventory was carried out for the 8 surface site\nlocations over several seasons. Five ornithologists took part in the surveys. The inventories were con-\nducted under suitable weather conditions (no rain and little/no wind). Field observations were recorded\non-site using computer equipment. Observation intensity varied depending on the seasons. Increased\n8Environmental issues mentioned here and in the following sections may also be referred to as \u2018stakes\u2019 - an alternative\ntranslation of the French \u2018enjeux\u2019.\n219\n\nobservation intensity was applied to the spring inventories due to the sensitive period for breeding birds.\nA matrix was established using European guidelines for endangered species that is only applicable to the\nFrench territory. For Switzerland, the cantonal and federal protection lists were used to analyse the risks.\nBirds find living space in the vicinity of site PA in Ferney-Voltaire, mainly in trees, bushes, and\nhedges. Some noteworthy species have been found in the vicinity. Birds are also prevalent in the vicinity\nof the agricultural space in site PB in Presinge and next to the small creeks and rivers. Protected and\nendangered species were found in the extended zone around the site. Areas and trees in the vicinity of\nsite PD in Nangy provide protection spaces for birds. Some noteworthy species have been found on the\nsurface site location. The surface site PF in \u00c9teaux today includes several bushes that serve birds to find\nfood and rest during the migration. Some noteworthy species have been found on the site. The forest\non site PG in Charvonnex and Groisy provides living space for a variety of birds, and the bushes around\nserve as a retreat and reproduction space. Some noteworthy species have been found in the vicinity of\nthe site. Also the forest on site PH in Cercier and Marlioz provides space for birds. Some heritage\nspecies were found on the site. Site PJ is surrounded by bushes and hedges that serve birds as living\nand reproduction space and for rest during migration. Some heritage species were found on the site and\nin the immediate vicinity. Also the hedges nearby site PL provide protection for birds and noteworthy\nspecies were found there.\nFig. 3.31: European kestrel (Falco tinnunculus) observed during field investigations, providing valuable\ndata on local wildlife presence and ecosystem dynamics.\nA full database of species observed was established, and it has been integrated into a project-wide\ngeographical information system. The bird observations have limited validity and must be continued if a\ndecision to advance with a project design is taken.\nIn summary, the sites PD, PL, and PJ in France, as well as PB in Switzerland and their surround-\nings, contain hedgerows and open areas that support nesting species of high conservation value. The sites\nPF, PG, and PH in France feature hedges and forests adjacent to extensive pastures, which are crucial\nhabitats for uncommon species throughout the year. Site PA in France consists primarily of conventional\nagricultural land that becomes waterlogged in winter, serving as an important stopover site for waders.\nTo mitigate the environmental impact, dedicated measures will be implemented during the design\nphase to recreate bird nesting and living areas comparable to those lost, either within the green buffers of\n220\n\nthe sites or in their immediate vicinity. These efforts will be integrated into rewilding projects associated\nwith the development.\nMammals\nFig. 3.32: Red fox (Vulpes vulpes) observed during field investigations, providing valuable data on local\nwildlife presence and ecosystem dynamics.\nData on terrestrial mammals was collected during all naturalist assessments of other groups on the\nsurface sites. Therefore, data on terrestrial mammals were collected both day and night at all surface\nsites throughout four seasons. Terrestrial mammal species were recorded visually or through indicators\nsuch as tracks, faeces, burrows, etc. The particular attention given to weather conditions for other groups\nwas also applied during the assessments of terrestrial mammals. All observations were geolocalised and\nrecorded in the project-wide geographical information system.\nThe PA site in Ferney-Voltaire has been the subject of infrequent observations of terrestrial mam-\nmals during naturalist investigations. They include the European roe deer, wild boar, European badger,\nEuropean hare, brown rat, and greater white-toothed shrew. In the wider surrounding bibliographic data\nalso revealed the presence of species of medium concern, such as for instance the hedgehog and beaver.\nIn the vicinity of site PB in Presinge, two species with a high conservation priority in Switzerland\nwere observed: the beaver and the hare. Other species with a low priority that were encountered are the\nroe deer, badger and fox. Bibliographic data also provided information about species with a very high\npriority: the harvest mouse, polecat, weasel, wolf and the dormouse. Two species with a medium priority\nare the hedgehog and the stoat. However, these species were not observed.\nThe observations on site PD in Nangy of medium importance are the beaver and hedgehog. A\nspecies with lower importance, the fox was also observed. Bibliographic data also reports on the wildcat,\nthe polecat, the black rat, but they were not observed.\nSeveral observations have been recorded at the PF site at \u00c9teaux: the hedgehog, with medium im-\nportance, and the fox and the badger, with very low importance. Bibliographic data details the presence\nof four species of medium conservation concern, including the Alpine Ibex, European beaver, European\nrabbit and the wildcat.\nObservations at the PG site in Charvonnex and Groisy ranging from very low to low importance\n221\n\nare: European roe deer, fox, squirrel, wild boar, European hare, chamois. In the surroundings, the\nbibliography also reports species with high importance: European otter, polecat. The following species\nwith medium importance are reported: hedgehog and wildcat. However, these species were not observed.\nAt the PH site in Cercier and Marlioz the presence of species with medium importance such as\nthe beaver and the squirrel were recorded. Species of lower importance concern the red deer, roe deer,\nwild boar and fox. The bibliography also mentions the presence of species with very high concern such\nas the grey wolf, otter and medium concern such as the wildcat and the hedgehog. These species were,\nhowever, not confirmed.\nAt the PJ site in Dingy-en-Vuache and Vulbens several observations of mammals with medium\nimportance were made, such as the European beaver and the wildcat. Species with lower importance are\nthe squirrel and with even lower importance the red deer, roe deer, hare, wild boar, badger, fox and the\ngreater white-toothed shrew. The bibliography also mentions the presence of the lynx and the otter with\nvery high importance and the rabbit with medium importance, but they were not observed.\nObservations on site PL in Challex with a very low importance include the badger, fox, roe deer\nand hare. The analysis of the bibliography highlights four species with medium concern: wildcat, beaver,\nrabbit, and hedgehog. The polecat is cited with high importance and the lynx with very high importance.\nThese species have, however, not been observed.\nSumming up the bibliographic and field investigations of mammals carried out on all surface site\ncandidates and in extended perimeter around the sites shows that overall a strong sensitivity exists for\nall sites although on none of the sites direct observations of relevant species were confirmed. The reason\nis that mammals were observed in the vicinities and extended surroundings of the sites and they can\ntraverse the sites today, but they will face limitations during construction periods and when the sites are\nconstructed. However, no protected or endangered species would be affected directly by the surface sites.\nA subsequent preparatory project phase needs to consider the mammals in the surroundings of the site in\nthe design of the construction sites and the surface sites. Ecological corridors need to be considered and\npreserved. Where possible, green buffers and sites that can be traversed by mammals can preserve their\ncurrent behaviour. Embedding the presence of animals in general in the concepts of surface sites can also\nhelp to improve their habitats and eventually even support the increase of biodiversity and conditions for\nthem.\nChiropters\nChiropters (bats) are mammals. The name chiroptera comes from the Greek words cheir (hand) and\npteron (wing), meaning \u2018hand-wing\u2019. This reflects the unique structure of their wings, where elongated\nfingers are covered by a thin membrane of skin that allows them to fly. Chiropters are in the focus\nof environmental studies due to their ecological importance, vulnerability to habitat changes, and the\nlegal protections they enjoy in France and Switzerland through national laws, as well as in the frame of\nthe EU habitats directive, the \u2018EUROBATS\u2019 agreement, the \u2018Bern Convention\u2019 and \u2018Natura 2000 site\u2019.\nViolating protections of bats in France can result in significant penalties consisting of high fines and\nprison sentences.\nThis study comprised dedicated field investigations applying different techniques to establish an\ninventory of bats on and in the vicinity of candidate surface site locations to permit developing avoid-\nance, reduction, compensation, and accompanying measures during a subsequent project design and\npreparatory phase.\nBibliographic analysis could unfortunately not be carried out since it requires a detailed descrip-\ntion of the areas to be investigated, and the surface site locations were not sufficiently defined at the\ntime of making such inquiries for data, which are time-consuming processes with different data owners.\nTherefore, indirect (e.g., passive and active acoustic searches with ultrasound detectors and microphones,\nsearch for traces) searches were immediately carried out at the larger candidate surface site zones.\n222\n\nFig. 3.33: Bat detectors used to detect the presence of bats by converting their echolocation ultrasound\nsignals.\nOn site PA in Ferney-Voltaire, France, the existence of an ecological corridor renders the passing\nof chiropters likely in a band at the southern end of the surface site and outside that zone. 12 species were\nrecorded in the larger area around the surface site location, in particular in the neighbouring woodlands\nand groves. There were no sightings on the site itself, probably due to it being an open space currently\nsubject to light pollution during nighttime.\nOn site PB in Presinge, Switzerland, the zones at the borders of the surface site towards the Nant\nde Paradis creek represent an area of interest for chiropters for hunting. The same applies for individual\nbushes, the Seymaz zone and woodlands in the vicinity and garden areas in the Avenir hamlet. 2 species\nhave been observed at houses that would be removed for the construction of the site and 18 species were\nfound in the larger area. 7 of them have a preservation status. This makes the area sensitive and calls for\nmeasures to preserve the habitats and avoid and reduce light pollution as far as reasonably possible.\nOn site PD in Nangy, France, the larger zone is of interest for Chiropters for hunting where bushes,\ntrees and houses exist. 3 species were observed on the site and 8 in the extended investigation area. They\nhave protection status. As with site PB, the larger area is sensitive and calls for measures to preserve the\nhabitats and avoid and reduce additional light pollution as far as reasonably possible.\nOn site PF in \u00c9teaux, France, the neighbouring areas are of interest for chiropters, in particular\nzones with hedges and woodland. This concerns for instance the boundaries of the surface site, houses\nand gardens along the national road and the wetland zones. 13 species were observed on the larger area\nand some of them on the site close to trees. 3 enjoy a protection status. The larger area represents an\ninterest for this species and calls for measures to preserve the habitats and avoid and reduce additional\nlight pollution as far as reasonably possible.\nOn site PG in Groisy and Charvonnex, France, the woodland is of interest for chiropters. It extends\nto the autoroute zone in the north. 18 species have been observed in the larger area and 13 species were\nfound in some locations on the surface site, primarily in the forest. 8 enjoy a protection status. The\nstrong presence of chiropters in the forest calls for a minimisation of the impact on those zones during\nthe design phase and envisages compensation and accompanying measures.\nOn site PH in Cercier and Marlioz, France, chiropters find hunting areas and a corridor in and\nbetween the woodlands. 13 species have been observed within the site perimeter in the woodland. 5\nspecies enjoy a very high protection status and two are highly protected. The density and diversity\n223\n\ndiminishes as one approaches the road on the eastern side of the site. These findings call for further\noptimisation of the site, reduction, compensation and accompanying measures in the subsequent phase.\nOn site PJ in Dingy-en-Vuache and Vulbens, France, the woodlands at the creeks and the hedges\nat the limits of the surface site are interesting spaces for chiropters. Ten species were found on the border\nof the site and 16 in the larger area around the site. Some enjoy a particular protection status. The\ndensity and diversity are higher around hedges and trees close to the motorway. This location will need\nsome attention during the subsequent site design with respect to avoidance, reduction, compensation and\naccompanying. Artificial light pollution is one issue to be considered in this area.\nOn site PL in Challex, France, chiropters find suitable locations in the woods, hedges, hamlets and\nindividual houses, their gardens and the nearby vineyards. Two species with medium to low protection\nstatus were recorded at the houses that would have to be removed to construct the surface site.\nSumming up, the stakes with respect to chiropters directly on the surface sites are low in PA,\nPB, PD and PL. PJ has no particular sensitivity on the entire site, but a small sector that is close to the\nwoodlands requires particular attention. The stakes are average for PF, high for PG and very high for\nPH. The limitations of impacts on chiropters, the preservation and, where possible, the improvement of\ntheir habitats have to be included in the eco-design approach to be implemented in the subsequent phase.\nReptiles\nFig. 3.34: Common wall lizard (Podarcis muralis) observed during field investigations, providing valu-\nable data on local wildlife presence and ecosystem dynamics.\nField investigations on the candidate surface site locations focused on identifying reptile popu-\nlations in environments that are known to be favourable habitats for them. They include for example\nsemi-open areas, forest boundary zones, cavities and stone or woodpiles as well as constructed areas.\nThese inventories were carried out during the reptile\u2019s primary activity periods from May to June and\nfrom September to October. Each observation was geolocated. No intrusive methods were used to\navoid disturbance to the species. Several methodological limitations, an unfavourable rainy spring and\nan exceptionally hot summer as well as access limitations set limits on the quality and reliability of the\nresults. This concerns mainly the data for snakes that are more difficult to observe than other reptiles.\nFor a preparatory phase project and a comprehensive environmental impact assessment, the initial state\n224\n\nof reptiles has to be updated with complementary studies.\nThe natural habitats investigated for reptiles varied across the sites, leading to different levels of\nsuitability for living spaces and ecological corridors.\nAt site PA in Ferney-Voltaire, France, the forest edges and wood strips were identified as high-\nvalue habitats. Isolated trees and cultivated areas had a lower interest. Only one species with a low\nconservation value, the common wall lizard, was observed on the annex site south of LHC point 8.\nBibliographic data do not indicate the presence of species with high stakes.\nAt site PB in Presinge, Switzerland, the zones with vegetation at the nearby creek Nant de Paradis,\ngardens in the Avenir hamlet and small woods in the vicinity are of interest to reptiles, but not the surface\nsite location. Only a single species was found in the larger area around the site. No species were found\non the perimeter of the site.\nAt site PD in Nangy, France, interesting locations for reptiles are at the southern end of the site\nin the hedges and the borders of the autoroute, but not the surface site. Three species were found in the\nlarger area around the site and at the extreme edge in the south, outside the site.\nAt site PF in \u00c9teaux, France, the hedges at the border of the surface site are of interest for reptiles.\nOnly a single species was found in the larger environment around the site. No observations could be\nconfirmed on the site or in the immediate vicinity.\nAt site PG in Groisy and Charvonnex, France, the forest zone and the limits of the woodlands are\nof interest for reptiles. Also, areas close to the highway can be relevant spots. 2 species were found in\nthe larger area around the site, but no observations could be confirmed on the site directly.\nAt site PH in Cercier and Marlioz, France, the entire forest occupied by the surface site location is\nof interest for reptiles. 2 species were found in the area around the site, sometimes entering the perimeter\nof the site. However, no clear pattern of presence or movement could be determined that would permit\ndrawing sound conclusions on the permanent presence of reptiles on the site.\nAt site PJ in Dingy-en-Vuache and Vulbens in France, areas in the vicinity of the creeks, bushes,\ngroves and trees including the zone close to the motorway are of interest for reptiles. 7 species were\nfound in the larger area around the site, leading also to the conclusion that at the edges of the site, species\ncould be present.\nAt site PL in Challex, France, gardens, bushes, and trees are of interest for reptiles but not the\nmajority of the surface site. Only one species could be found at a distance of the site, close to the forest\nin the north. No observations on the site could be confirmed.\nSumming up, only very low sensitivity with respect to reptiles exists for sites PA, PB, PD and PL.\nIn the vicinity of PF some care needs to be taken to preserve the living spaces of reptiles. For PG and PH\nsensitivity may exist in some parts of the forest and the project design needs to respect this condition. An\nupdate of the initial state with complementary field investigations is required to optimise the integration\nof the surface site, applying avoidance and reduction measures. The architectural designs of the surface\nsite constructions should integrate concepts that favour the creation of habitats and thus help to increase\nthe presence of reptiles.\nInsects\nBibliographic research and field investigations of the sites and their vicinities by specialised companies\nwere used to identify the issues with respect to insects. Field investigations were carried out for several\nmonths during good weather conditions, low wind and during both day and night.\nDespite the highly urbanised environment, a strong population of insects was observed in the\nsurroundings of site PA in Ferney-Voltaire due to the favourable living and breeding spaces. The site\nitself, an agricultural area is not subject to a strong presence of insects and thus, therefore, has only a\nvery low sensitivity. The vicinity of the border between France and Switzerland towards the Geneva\n225\n\nFig. 3.35: Butterfly black-veined white (Aporia crataegi) observed during field investigations, providing\nvaluable data on local wildlife presence and ecosystem dynamics.\nairport may require the consideration of a cross-border impact since some species observed in this zone\noutside the site perimeter are protected in Switzerland. Complementary field investigations are required\nduring a project preparatory phase to reveal any such potential case.\nThe surroundings of site PB in Presinge feature an important population of insects, mainly those\nrelating to aquatic habitats. Some species observed in this area outside the site perimeter enjoy particular\nprotection status in Switzerland. The site itself is an agricultural space with low stakes apart from the\nareas that are close to the nearby creek.\nThe surroundings of site PD in Nangy are characterised by a few insect species. The site is an\nagricultural space and has low stakes with respect to insects. No species with protection status were\nobserved.\nThe extended surroundings of site PF in \u00c9teaux are attractive for insects. However, on the site and\nin the immediate vicinity, no relevant species were identified, and the sensitivity is low.\nThe forest at and around site PG in Charvonnex and Groisy is moderately attractive for insects, as\nare the surrounding hedges. The site itself does not show particular issues with respect to insects. Also,\nthe woodland spaces did not reveal the presence of relevant insects.\nThe forest spaces at and around site PH in Cercier and Marlioz provide, in principle, a favourable\nhabitat for insects. However, only little presence of insects was revealed within the candidate site perime-\nter. Due to some observations at the border of the site, the site has a medium level sensitivity.\nSite PJ in Dingy-en-Vuache and Vulbens, in principle, offers favourable conditions due to the trees\nand hedges around it. The stakes are high in the extended surroundings, but they are low on the site itself.\nThe hedges and bushes around site PL in Challex also, in principle, provide a favourable habitat\nfor insects. However, the site shows only low-level issues with respect to insects, though a presence\ncannot be entirely excluded. Some species are protected in the nearby Swiss territory. A preparatory\nproject phase will have to make complementary field investigations to consider potential cross-border\nimpacts.\nSumming up, none of the surface site candidates exhibits particular sensitivity with respect to\n226\n\nFig. 3.36: Golden-ringed dragonfly (Cordulegaster boltonii) observed during field investigations, pro-\nviding valuable data on local wildlife presence and ecosystem dynamics.\ninsect presence. The surroundings of site PB present a habitat with high sensitivity. The wider surround-\nings of site PF present, in principle, some sensitivity. For sites PG and PH, despite being woodland, the\nfavourable habitat for insects turns out to be less favourable than expected. The presence of some rele-\nvant species in the surroundings raises the sensitivity of the areas that are in the vicinity of the site. There\nwere observations of some species with medium sensitivity in the surroundings of site PJ, suggesting\nthat they might also be present on the site.\nAquatic\nFauna in the aquatic context has been analysed based on cartographic and orthophoto information. Sys-\ntematic investigations and water analysis for all aquatic aspects were not carried out at this stage. They\nare planned to be done if a design phase is launched. However, nearby surface water in the vicinity\nof sites PF, PG, PH and PJ was analysed. The stake concerning macroinvertebrates is often high in\nthe extended surroundings around surface sites. Aquatic benthic macroinvertebrates are insects in their\nnymph and larval stages, snails, worms, crayfish, and clams that spend at least part of their lives in water.\nFireflies are another important species that are sometimes encountered in the wider perimeters of the\nsites.\nAlthough the site PA and its immediate surroundings are not subject to aquatic fauna presence,\nthe wider environment is known to be a habitat for vulnerable and endangered species. Protected and\nendangered species are close to site PB, although the site does not affect their habitats. Sites PD and PF\nand their surroundings are not concerned by aquatic fauna. The vicinity of site PG is characterised by\nimportant aquatic habitats with vulnerable and endangered species that the project will avoid and aim not\nto affect. The site perimeter has already been adjusted as a result of various stakes identified during the\ninitial state analysis. Although site PH lies in the forest and close to a creek the presence of noteworthy\naquatic species is low and the site itself is not affected. Sites PJ and PL and their surroundings also have\nno issues with respect to aquatic fauna.\nSumming up, the PJ site does not present any observations of benthic macroinvertebrates. The\nwider surroundings of the PD, PF, and PL sites show a few habitats favourable to the development of\n227\n\nFig. 3.37: Stream photographed during the field investigations.\nbenthic macroinvertebrates, but only a few taxa are present. Also, the PH site does not present any\ntaxa with significance; however, the habitats are varied and the taxonomic diversity is high near the site,\nalthough with very low significance. The PG site hosts taxa with \u2018medium\u2019 significance, but the habitats\nare varied and taxonomic diversity is high near the site border. The wider PA site surroundings are\nsubject to an observation with \u2018high\u2019 significance, but the habitats are poor and have little interest for the\nbenthic macrofauna. The PB wider site surroundings have several observations of taxa with \u2018very high\u2019\nsignificance. No surface site has any relation with fis,h although some sites (PB, PF, PG, PH, PJ) are in\nthe vicinity of small creeks.\nForest\nDuring this study, expert companies and forest evaluation consultants have made a comprehensive and\ndetailed forest quality and value analysis. This included the potential loss of biodiversity, habitat and\neconomic income over a sustained period of several decades. The results are also integrated into the\ncomprehensive, wider socio-economic assessment. The French \u2018Indice de biodiversit\u00e9 potentielle\u2019 (IBP)\nmethodology was applied [87,88]. The project will not affect any existing forest spaces in Switzerland.\nForests are in the vicinities of sites PA, PB, PD, PF, PG, PJ and PL. Only sites PG and PH will require\nclearings.\nThe forest that would be affected by site PG has quite a diverse character. The xeric woodlands\nlocated in the southeast mainly consist of small-diameter oak woods, showing a strong to weak stake\ndepending on the area. The ravine woodlands in the west feature a composition of large and very large\ntrees rich in dendro-microhabitats, potentially hosting a rich and diverse biodiversity. The central area of\nthe forest presents a character more easily exploitable for forest owners. This leads to more or less diverse\n228\n\nFig. 3.38: Woodland photographed during the field investigations.\nstands depending on the plots. The presence of large dead wood is less important overall. The challenge\nin terms of biodiversity varies from strong to weak depending on the age of the trees. Consequently, the\nsurface site has been adapted to reduce the affected forest as much as possible and to select an area for\nthe access shaft locations that has a lower quality than the surroundings. In total about 2.4 ha of forest\nmay be affected by the surface site development.\nThe forest at PH features relatively young woodlands resulting from agricultural abandonment,\nthereby having few dendro-microhabitats. The woodlands located on the northern fringe of the site\nare the oldest and there is presence of a temporary watercourse. Medium wood is less conducive to\nsupporting forest biodiversity than large and very large wood. In total, up to 10 ha of forest may be\naffected in the communes of Cercier and Marlioz. Further surface site designs are needed to determine\nthe exact surface requirements, taking into consideration all the environmental issues that have been\nidentified.\nSummary\nDetailed data are included in specific paragraphs of the biodiversity section. To the east of the PA are\nwetlands that serve as a migratory stopover for bird species, and to the south, near LHCb Pt8, is a forest\nof ecological value due to the presence of bats and insects. Some agricultural patches near the site with\nisolated trees also play a valuable role for birds. The PA surface sites have low ecological stakes, however\nthe future construction must carefully consider the surrounding elements to maintain the key habitats and\nspecies.\nThe PB surface site presents low to moderate ecological stakes, however the presence of diverse\nbird species, aquatic insects and protected plants along the Nant du Paradis stream highlights the eco-\nlogical value of the site\u2019s nearby areas. The future construction must take into account the ecological\nsensitivity of these places to ensure the preservation of biodiversity and habitats.\nThe site PD is entirely covered by agricultural land which represents low-level stakes. Small areas\nof high ecological importance are located further north of the site. These include hedges and old trees\nthat provide habitat for birds and bats of low or moderate concern. Future construction in this area has to\ntake into consideration small fauna species that might be present on or crossing the site.\n229\n\nFig. 3.39: Italian locust (Calliptamus italicus) observed during field investigations, providing valuable\ndata on local wildlife presence and ecosystem dynamics.\nThe PF site is used as an agricultural meadow and presents moderate ecological states. How-\never, the site is located within the ecological corridor for wildlife movement, near the wetland area and\nforest with the stream providing habitats for a range of species, including birds, bats, and amphibians.\nThe site layout must be carefully planned to avoid disrupting the sensitive ecosystems and ensure good\nfunctionality of the fauna corridor.\nThe main PG surface site is partly in a forest area, which represents high stakes, and partly in\npasture land with low stakes. The annex site to the north, located near the highway, shows low ecological\nstakes. The main constraint rPG site is the valuable forests that hosts fauna and flora species, therefore\nthe effort has to be put into limiting deforestation and maintaining the current habitats.\nThe PH surface site is located in the forest with small clearings and wetland area. Part of the PF\nsurface site shows very high stakes, mainly in the north, due to the presence of bird species, including\nthose of high conservation concern, bat species with their ecological corridor as well as small fauna.\nStakes of strong character, with parts of medium and low are located in the southwestern part of the site.\nLimiting the use of areas with high stakes will be necessary to preserve its biodiversity and ecological\nvalue.\nMost of the PJ surface site presents low stakes, excluding an inventoried small wetland and\nhedgerow that are considered as strong stake. The current layout of the site already foresees the space\nfor an ecological corridor and grassy meadows in order to maintain connectivity between natural areas\nfor wildlife and to keep areas for birds to hunt.\nThe major part of the PL surface site is located on the agricultural land presenting low stakes.\nSome hedges within the site and in the vicinity of the site play an important role for bird species and\nmust be preserved whenever possible.\nTo ensure responsible development of the areas, site construction must be carefully planned to\nminimise habitat disturbance, maintain ecological corridors, and preserve biodiversity. By integrating\nthese considerations into project design plans at the early stage, it is possible to balance infrastructure\nneeds with the preservation of local biodiversity and ecological integrity.\n230\n\nFig. 3.40: Trees in the woodland photographed during the field investigations.\n3.3.6\nEcological functionality\nIn France, the ecological network, known as the \u2018Trame verte et bleue\u2019 (Green and Blue Framework),\nis a component of the national and regional planning framework. It integrates terrestrial and aquatic\necological continuity. This network comprises biodiversity reservoirs, ecological corridors, permeable\nterrestrial and aquatic spaces, and large agricultural areas. These elements collectively support species\nmovement, lifecycle completion, and biodiversity preservation. In Switzerland, the ecological network\nidentifies essential zones for nature and their connections. The REN\u2019s (R\u00e9seau \u00e9cologique national)\nframework includes nodal zones (vital habitats for species lifecycle completion), extension zones (lower-\nquality or smaller zones), continua (interconnected areas such as forests and wetlands), and development\nzones (partial habitats). The network also features ecological corridors linking key areas.\nThe difference in both countries lies in implementation and structure. In France, the ecological\nnetwork emphasises integrating green and blue corridors at a national scale under regional governance.\nIn contrast, Switzerland\u2019s REN adopts a more localised approach, focusing on specific ecological zones\nand their physical connectivity. Additionally, the French framework includes significant agricultural\nspaces and functions of water bodies while the Swiss REN categorises its zones with a greater focus on\ninter-zonal ecological dynamics.\nThe site PA and nearby area are permeable agricultural spaces that represent only limited interest\nin terms of ecological functionality. A regionally important ecological corridor was identified south of\nthe surface site. Wetlands in the vicinity of the surface site contribute to the ecological functionality\nin the context of the blue network. According to the local urban development plan, three isolated trees\nlocated to the east of the main surface site and trees to the south-east are considered a landscape element\nto be preserved. The layout and design of the surface site constructions will need to ensure that the\necological continuity is maintained.\nSite PB is located on large agricultural land with some extensive areas and a continuum of dry\ngrasslands. However, these areas which are conducive to biodiversity are not located within the surface\nsite. There are two locally important movement corridors for large fauna, one of which passes west to\nthe surface site without crossing it and the other through the eastern part of the surface site area, near\nthe hedgerows, which should be taken into account in the design phase. The PB surface site lies in the\nimmediate vicinity of the blue continuum, which follows the hedgerow line to the north-east. However,\nthe location of the site does not directly interrupt the functionality of this network.\nThe area of PD surface site is located on the permeable relay agricultural land. South of the PD\nsurface, under RD903, a secondary corridor of medium fauna that is to be considered in the design phase\n231\n\nwas identified. The surface site does not encroach on any element related to wetlands or water areas and\ntherefore does not affect the functionality of the region\u2019s blue network. According to the Nangy local\nurban plan, no element of biodiversity reservoirs or ecological corridors is present in the study area.\nThe PF surface site is located within permeable agricultural spaces and a forest ecological corridor\nconnecting the areas located to the north-west and south-west of the site. It is a remote area used by large\nfauna. The surface site is close to two wetland areas of the blue network, the functionality of which has\nnot yet been analysed. This aspect must be taken into account in the design phase of the surface site. It\nwill also be necessary to ensure the functionality of ecological corridors and large fauna movement routes\nbetween the forest areas to the north and south of the site surface, as required by the \u00c9teaux commune\u2019s\nlocal urban plan.\nTo the north of the PG surface site, across the highway, there are two forested corridors, while\nto the south there is a linear corridor, also forested. The PG area with its annex is located in permeable\nspaces, partly on agricultural and forest land, however the PG surface area is not located in any ecological\ncorridor and no biodiversity reservoir has been inventoried. The surface site does not concern any element\nof the blue network. According to the Groisy local urban plan, the surface site and the possible access\nroad are located on classified forested areas - Espaces Bois\u00e9s Class\u00e9s - which results in preservation or\nappropriate reforestation in the case of felling, depending on the agreed compensation method, therefore\nconstruction in the forested area will be limited to the minimum necessary.\nThe PH surface site is concerned only with permeable relay spaces and does not cross any eco-\nlogical corridors or biodiversity reservoirs. The surface site\u2019s proximity to the Tabass\u00e9 stream, which\njoins the Usses watercourse, is one of the main elements of the blue network of the area. During the field\nvisits, the wetland was inventoried on the perimeter of the surface site, but it does not seem to represent\na major functional role in the blue structure. The local urban development plan of Val des Usses and\nCercier also mentions a sector of ecological interest related to the watercourse to the north, which will\nbe taken into account when designing the layout of the infrastructure.\nThe PJ surface site is located on agricultural land with permeable relay spaces, as well as an\necological corridor connecting forested biodiversity reservoirs between the north and the south, which\nconnects with another ecological corridor in the further part. There are two small streams, west and east\nof the PJ site, and a wetland has been inventoried on the site itself, but its functionality has not yet been\nanalysed. In accordance with the local urban plans of two municipalities concerned, the surface site\nis located between wooded area ensuring the ecological continuity, and contains two lines of protected\nhedges. The preservation of ecological continuity and the ecological corridor will be taken into account\nduring the design phase.\nThe PL surface site is located on the relay permeable spaces and agricultural spaces. A regional\nwetland from departmental inventories and a corridor for the movement of large fauna are located to the\nnorth of the site, however, these structures do not cross the site. According to the local urban plan of the\nmunicipality of Challex, small hedges that are within the surface site perimeter and in close vicinity are\nconsidered natural structures and are to be preserved for ecological reasons.\nIn summary, the PA site includes a regional ecological corridor with wetlands and hedges that\nneed preservation to maintain ecological continuity. The PB site is near two fauna movement corridors\nand the blue network along the eastern side. Though the site does not directly impact the blue structure,\nthe surface site layout has to take it into consideration. The PD site consists of agricultural spaces with a\nsecondary fauna corridor in the south, near the RD903 but does not encroach on wetlands or biodiversity\nreservoirs. The PF site is located near two wetlands and within an ecological corridor, which will have\nto be taken into account in the design phase. Part of the PG site includes a classified forest area, and\nwood cutting should be minimised. The design of the site will have to ensure that the functionality of\nnearby ecological corridor and biodiversity reservoir is maintained. The PH site is close to the stream,\nand a larger watercourse is to be considered during the layout design. It also has some wetlands present\nbut these play a minor functional role. The PJ site lies in a large ecological corridor, including an area\n232\n\nof wetlands and hedgerows of ecological value. Lastly, the PL site consists of agricultural land with\nhedges that need preservation, while a regional wetland and fauna corridor further to the north remains\nunaffected. Overall, ecological continuity and protected elements must be carefully considered during\nthe design phase to ensure their functionality.\n3.3.7\nUrbanism\nThe urbanism aspects comprise all local and regional policies and plans for territorial developments. All\nland plots are subject to such plans, and they are regularly reviewed and updated at the municipality level\nand at the local and regional public administration levels.\nThe urban aspects of the perimeters of the surface sites, enlarged and extended zones of several\nkilometres around the surface sites have been analysed based on the relevant regional and local urban\nplans in France and in Switzerland. In addition, field visits permitted the publicly available informa-\ntion to be complemented and enriched with the up-to-date situation. This survey permits all regulatory\nconstraints with respect to the territorial development to be compiled and anticipating the planned evo-\nlution of the territory from an environmental point of view, considering all of the applicable laws and\nregulations. The relevant documents and associated geographical information systems and maps com-\nprise PLU, PLUi, PLUIh, PADD, SCoT in France and PDCn and PDCm of the canton in Geneva in\nSwitzerland.\nTable 3.12 shows that all extended or enlarged perimeters around the surface sites are subject to\nstrong or other urbanistic and territorial development issues. These issues have to be taken into account\nduring the detailed project plan development.\nTable 3.12: Summary of urbanism issues.\nTopic\nExtended perimeter around site\nDescription of stakes\nStrong urbanism stakes\nPA, PB, PD, PF, PG, PH, PJ, PL\nNature and agriculture protection zones,\nhumid zones.\nOther urbanism stakes\nPA, PB, PD, PF, PG, PJ, PL\nProtected or valuable architecture in the\nvicinity, sport facilities, agriculture,\nroads, highways.\nPublic utility servitude\nPB, PF, PH\nPipelines, electricity lines and protection\nbuffers around those infrastructures.\nUrban environment and\napplicable regulations\nPA, PB, PD, PG, PF, PJ, PL\nCo-visibility, requirement for integration\nin the urban context, topographic constraints.\nTable 3.13 shows that half of the sites are directly affected by urban constraints that need to be\nconsidered during the site design development and that require particular attention during the project\nauthorisation process.\n3.3.8\nMobility\nData about the public transport infrastructures and road traffic as well as soft mobility and multi-modal\nmobility within the perimeter of the project have been collected and analysed.\nPublic transport\nThe PA Site is well served by the Geneva public transport system (TPG) which operates across the\nSwiss/French border and serves the entire zone. The bus connection is direct, and there is a tramway\nconnection within a reasonable distance. Site PB in Switzerland is also served by the TPG network with\na bus station in the immediate vicinity and a tramway connection at a reasonable distance. The PD Site in\n233\n\nTable 3.13: Summary of urbanism topics by site.\nSite\nStakes\nUrbanism topics\nPA\nHigh\nProtected agriculture zone, gas pipeline at the site border\nPB\nHigh\nProtected agriculture zone (SDA), ecological corridor, landscape integration\nPD\nLow\nAgricultural space, road development project\nPF\nLow\nAgricultural space\nPG\nLow\nAgricultural space, nature zone (forest)\nPH\nHigh\nAgricultural space, nature zone (forest), pipeline at the northern site limit\nPJ\nHigh\nAgricultural zone, wetland zone, protected agricultural space, ecological corridor\nPL\nMedium\nProtected agricultural zone, nature protection zone\nFrance is well served by regional French bus lines, including a park+ride facility connecting to Geneva.\nThe presence of the large hospital (CHAL) ensures that the connections are maintained and potentially\nfurther developed. The location of site PF is poorly served by public transport. However, 2 km away,\nLa Roche-sur-Foron train station is an important multi-modal transport pole including a connection to\nGeneva via the L\u00e9man Express. The PG site is not served by public transport. However, the Groisy train\nstation is 2 km away and provides regular connections to Annecy and Geneva via the L\u00e9man Express\nline. The PH site is not served by public transport and no public transport exists in the vicinity. Site\nPJ is not served by public transport, but 2 km away, a Swiss TPG bus line connects to Vulbens and in\nValleiry, there is a train station on the line between Bellegarde and Evian via Annemasse. Although\nthere are Swiss TPG bus stops in Challex in the vicinity of site PL, the frequency is modest. Better\nconnections exist in nearby Dardagny in Switzerland. At a distance of 4 km in La Pleine, there are very\ngood connections to bus and train lines.\nSumming up, the experiment sites PA and PD are well served by public transport and the experi-\nment sites PG and PJ are reasonably connected at some distance. The technical sites PB, PF, PH and PL\nare not well served by public transport. An analysis of the demand from these sites would be required if\nfurther development of the public transport system is considered in relation to the FCC project. It could\nbe in the mutual interest of the project and the local stakeholders to develop public transport around the\nPG and PJ experiment sites at least.\nRoad network\nThe experiment sites PA, PD, PG and PJ are in the immediate vicinity of major roads and would profit\nfrom direct access to the autoroute infrastructure for construction and installation purposes. This would\neliminate any potential residual local traffic challenges around the sites during these phases. The PA\nsite is also well-connected to the CERN Pr\u00e9vessin and Meyrin sites via a major departmental road. In\naddition, the PL technical site is in the vicinity of a major departmental road and is also well-connected\nto the existing CERN sites. The PB Site is directly on a good road, but the traffic situation through\nGeneva and to nearby Annemasse in France is challenging. Technical site PF is also well-connected via\na major departmental road. Although site PH is directly located on a departmental road, it is isolated\nand is distant from major transport routes. The closest autoroute access is at a distance of 10 km in\nAllonzier-la-Caille. Installation of bulky equipment at this site needs to be carefully studied, developed\nand planned.\nOther transport modes\nThe study also included the analysis of dedicated bicycle tracks in France and Switzerland. Dedicated\nlanes and tracks have recently been constructed in the vicinity of site PA and these are expected to\nbe further developed. These span the Franco-Swiss border. A dedicated bicycle track is also being\n234\n\nFig. 3.41: Daily travel flows (all modes combined) in Grand Geneve (Source Grand-Gen\u00e8ve [89], based\non MRMT \u2013 EDGT 2015 - 2016) Although Geneva remains a central hub, the analysis of flows reveals\na more multipolar organisation, with a majority of internal travel within the large territories (Geneva,\nFrench Geneva, Nyon district).\nconstructed directly at the PB site. Sites PD and PF are not equipped for soft mobility. No dedicated\nbicycle lanes exist around site PG, but the road to Groisy is well-adapted for cyclists. Site PH has no soft\nmobility infrastructures. The surroundings of site PJ are being developed with a view to strengthening\nsoft mobility, aiming to link the nearby municipalities Vulbens and Valleiry. The creation of access to\nsite PJ also permits the connection of Dingy-en-Vuache to this system. PL is not particularly equipped\nfor soft mobility. Although walking and biking are easy in the commune, there are no dedicated links to\nother municipalities in France and Switzerland.\nForeseeable evolution\nThe Grand Gen\u00e8ve area is developing a multi-modal transport plan that aims to improve further the\ntransport infrastructure across the Franco/Swiss border. The continued housing development and demo-\ngraphic evolution of about +1.2% per year in the neighbouring French departments of Ain and Haute-\nSavoie, which is unrelated to CERN\u2019s activities, calls for such developments. There are about 1.2 million\njourneys today within the perimeter of the project, but about 4.2 million per day are expected by 2040.\nAs will be described later, the activities relating to the construction, installation, and operation of the\nproject are insignificant compared to the existing and future mobility in the region.\nThe extension of the Swiss railway system continues to increase its daily train capacity, mainly\n235\n\nFig. 3.42: Current and potential future extension of the Leman Express\ndue to the L\u00e9man Express lines (see Fig. 3.42). This also includes an improvement of the services to\nthe Arve valley (La Roche-sur-Forton), Groisy and Annecy for completion in 2030. In the longer term,\ndevelopments are planned for increasing the service to La Plaine and beyond to Bellegarde. Autoroute\nextension projects in Switzerland have been planned, but were recently put on hold. A project to connect\nboth sides of Lake Geneva sides by a tunnel under the lake has been studied, but any potential imple-\nmentation before 2050 is unlikely and therefore the project is not included in specific plans. In France,\nan autoroute is planned to connect the A40 (Arve valley) to the A412(Th\u00f4non) via a wide departmental\nroad (RD903) connecting to the A40 in Nangy. Bus line developments between major agglomerations\nand the hospital next to the PD site are likely.\nProject induced traffic\nProject induced traffic refers to the following types:\n1. Workers commuting to and from the construction sites during an approximately ten-year-long\n236\n\nconstruction phase.\n2. Evacuation of excavated materials from construction sites. While all sites require the evacuation\nof materials during the first two years, only four sites will see relevant transport of excavated\nmaterials during another 6 to 8 years due to the deployment of tunnel boring machines.\n3. Transport construction materials to the construction sites. All sites will see a moderate inflow of\nconstruction materials during the first two years, but only four sites will continue to have relevant\nconstruction materials inflow during the period when the tunnel boring machines are deployed.\nConstruction materials also need to be brought in when the surface site buildings are constructed.\n4. Transport of accelerator equipment during the six to eight-year installation phase that overlaps\npartially with the civil construction activities.\n5. Transport of the experiment detector equipment during experiment installation that overlaps with\naccelerator installation and testing phases.\n6. Commute of engineers and scientists during the installation and testing phases.\n7. Commute of engineers and scientists during the operation phase.\n8. Commute of engineers and scientists during regular maintenance periods and in the frame of repair\nactivities.\n9. Traffic induced by visitors to experiment sites during the operation and shutdown phases.\nThe main project-induced traffic is linked to the evacuation of the excavated materials. It will be\nconfined to major transport routes. The inflow of construction materials represents a minor additional\ncontribution to this traffic. Commute of workers is intended to be organised centrally, as is best practice\nfor construction sites. The installation of equipment for the particle accelerator represents a minimal\ncontribution to the traffic. The same is true for the transport of the experiment detector equipment. For\nthis case, some isolated, exceptional loads may be required due to the size of pieces manufactured off-\nsite. Once operational, only a few scientists and engineers commute daily to experiment sites. Technical\nsites are predominantly operated remotely and will see very little traffic for maintenance and repair. The\ntraffic of an estimated total number of 25 000 visitors per year to an experiment site during the operation\nphase can be compared to the traffic induced by a typical museum or archaeological site such as the\nGrottes de Cerdon in the region (about 50 000 visitors per year9) or the Ch\u00e2teau Voltaire in Ferney-\nVoltare (about 50 000 visitors per year [90]10 ). This traffic of individual visitors can be managed with\nappropriate directions to the site and through support by public transport. Visitors in groups arrive in\nbuses, presenting a minimal amount of additional traffic.\nMore information about the quantities and the additional traffic induced can be found in sections\nSection 2.7.2 and Section 2.7.12. A first quantitative traffic analysis has been carried out to confirm that\nthe traffic is manageable and that with respect to the nearby major transport routes, it represents only a\nminor addition.\n3.3.9\nHuman activities\nHuman activities\nThe analysis of the environmental state established the situation concerning human activities around the\nsurface sites. The environment around site PA in Ferney-Voltaire is dominated by commercial activities,\nthe LHC Pt8 surface sites and the airport. The presence of a surface site does not add to these activi-\nties. The environment around PB in Presinge is rural and characterised by small hamlets. The Geneva\nLandscape and Architecture School (HEPIA) is an academic activity zone in the vicinity. Towards the\nwest, the zone starts to be dominated by urban activities. The environment of site PD in Nangy is char-\n9https://www.ain.cci.fr/sites/g/files/mwbcuj1466/files/2024-02/Chiffres%20cles%202024%\n20AIN_.pdf\n10https://www.lemanbleu.ch/fr/Actualite/Archives/Le-chateau-de-Voltaire-entierement-renove.html\n237\n\nacterised by a mix of agricultural, commercial and industrial activities, residential zones and a major\nhospital (CHAL). Due to this mixed environment and the major transport routes available, the location\nis advantageous for an experiment site with a permanent presence of scientists and engineers. PF in\n\u00c9teaux is located on a main transport route with dispersed residential areas, small businesses and arti-\nsans and a major public works company opposite the site. PG in Groisy and Charvonnex does not have\nmajor human activities. The vicinity of Groisy, with schools and potential for local development, is an\nopportunity to develop a main experiment site with the presence of scientists and engineers. Site PH in\nCercier is very rural, with agricultural activities (fruit production) and some small hamlets. No major\nhuman activities are carried out in this area. The environment around the PJ site in Dingy-en-Vuache\nand Vulbens is agricultural with commercial activities to the north-east in Valleiry. PL in Challex is in\nan agricultural zone with low-density residential areas. Commercial activities take place at a distance in\nLa Plaine, Switzerland, which is not directly linked to the site.\nFig. 3.43: Commercial district near the PA site photographed during the field investigations.\nPoplulation\nThe population density around the eight surface sites varies significantly. Around PA, the area is mod-\nerately populated with about 34 000 inhabitants within a perimeter of 2 km. The major communes are\nFerney-Voltaire, Pr\u00e9vessin-Moens in France, Meyrin and Grand-Saconnex in Switzerland. The popu-\nlation growth in this area is 2.4% per year but this is unrelated to CERN\u2019s activities. Around PB the\nenvironment is sparsely populated, at most 6000 inhabitants can be counted in a perimeter of 2 km. The\nmain communes are Presinge, Pupling, Choulex, Meinier, Jussy in Switzerland and Ville-La-Grand in\nFrance. There is no annual population growth in Switzerland (between -0.3 and +0.3%). In neighbouring\nFrance, the annual growth is modest (+1.1%), comparable to the average in Haute-Savoie. Site PD is\nlocated in a moderately dense environment with about 4000 inhabitants in a perimeter of 2 km, the ma-\njority located in Nangy and Contamine-sur-Arve and Fillinges. The annual population growths in these\ncommunes are highly diverse, ranging from negative 0.5% in Nangy to +3% in Contamine-sur-Arve.\nThe PF site is located in a moderately populated zone with about 4000 inhabitants in a 2 km radius with\nthe majority of people in \u00c9teaux and La Roche-sur-Foron. The population evolution is stable, ranging\nbetween -0.6% and +1.0% per year. PG is located in a sparsely populated area with around 4000 in-\nhabitants in a perimeter of 2 km, mainly in Charvonnex and Groisy. However, the two communes see\nan annual population growth of between 2.2 and 3.2%. The environment around the PH site is very\nweakly populated. There are only 1500 inhabitants in a perimeter of 2 km in Cercier, Choisy and Mar-\nlioz. The population growth is around 1.5% per year. The area around PJ is also sparsely populated\n238\n\nwith about 6000 inhabitants in a perimeter of 2 km in Vulbens and Dingy-en-Vuache. Valleiry is a more\ndensely populated commune nearby. The annual population growth is 2 to 3.5%, higher than the aver-\nage in Haute-Savoie. PL in Challex is in a sparsely populated area with only about 3000 inhabitants in a\nperimeter of 2 km including Challex in France and Dardagny in Switzerland. Both communes experience\nan annual population growth of about 3% per year.\nHousing\nFig. 3.44: Residential district photographed during the field investigations.\nAs with the population, the housing situation also varies significantly amongst the surface site\nareas. In the immediate environment around PA, the housing sector is dominated by apartment buildings.\nPr\u00e9vessin is dominated by individual houses. The housing sector around PB is mixed with individual\nhouses in the closer vicinity and residential buildings further away. The communes in the vicinity of the\nsite are not dominated by individual houses, but see a mix of houses and residential buildings. The area\naround PD is dominated by individual houses. Individual houses are also predominantly found around\nsite PF. The entire area around PG is dominated by individual houses, as is the case with sites PH and\nPJ. Only Valleiry is an exception with a significant number of residential buildings and apartments. The\nsurroundings of site PL have a highly contrasting housing sector. Mainly individual houses are found in\nthe French communes of Challex, P\u00e9ron, Saint-Jean-de-Gonville. Residential buildings are predominant\nin the Swiss communes of Avully and Dardagny.\nEmployment\nAt a general level, the employment sector in the northern sectors of the FCC is dominated by Geneva and\nits surroundings on French territory (see also Fig. 3.45). The southern zone in Haute-Savoie is charac-\nterised by significantly fewer job opportunities and an overcapacity of available workforce. Depending\non the region, the tertiary sector is only weakly developed. The secondary sector (industrial activities)\noffers opportunities in selected locations. Like Geneva, the Department of Ain in France has many more\nemployment opportunities than the Haute-Savoie department.\nAround PA, employment opportunities are mainly found in the tertiary sector. In the Swiss terri-\ntory, the secondary (industrial) sector is also a major source of employment opportunities. Employment\naround PB is dominated by the primary sector (agriculture) and there is a slightly smaller number of job\nopportunities than people seeking work. PD has employment opportunities in the industrial sector and\nthe health sector (CHAL hospital), although the job opportunities are limited. The area around PF offers\nfew employment opportunities and those that exist are distributed between the secondary and tertiary\nsectors. The primary sector (agriculture) is rather weak in this area. There are fewer job offers than the\n239\n\nJura\nSavoie\nHaute-Savoie\nAin\nSite PL\nSite PJ\nSite PH\nSite PG\nSite PF\nSite PD\nSite PB\nSite\nPA\nEarthstar Geographics\nL\u00e9gende\nFronti\u00e8re\nD\u00e9partement\nTrac\u00e9\u00a0projet\nSite\u00a0de\u00a0surface\nP\u00e9rim\u00e8tre\u00a0d'\u00e9tude\n\u00e0\u00a02\u00a0km\n\u00e0\u00a0500\u00a0m\nNombre\u00a0d'emplois\u00a0pour\u00a0100\u00a0actifs\u00a0occup\u00e9s\u00a0en\u00a02021\n50\u00a0et\u00a0moins\nentre\u00a050\u00a0-\u00a085\nentre\u00a085\u00a0-\u00a0115\nentre\u00a0115\u00a0-\u00a0150\n150\u00a0et\u00a0plus\nPas\u00a0de\u00a0donn\u00e9es\nEmplois\u00a02021\n200000\n100000\n30000\n10000\n3000\n1000\n0\n3\u00a0000\n6\u00a0000\nM\u00e8tres\nEchelle\u00a0:\u00a01\u00a0/\u00a0150\u00a0000\n\u00b2\nFig. 3.45: Overview of the employment opportunities in the perimeter of the FCC reference scenario.\navailable workforce. Also around PG there are fewer job opportunities than available workforce. In par-\nticular,r the tertiary sector is only weakly developed. The same is true for site PH in which the primary\nsector (agriculture) is the main employer for almost one-third of the population. Also the area around\nPJ sees more job seekers than job offers. The main employment sector is agriculture. Around PL the\nsituation is mixed: residents find their employment in France and in Switzerland.\nAgriculture\nThe area used for agriculture in the Pays de Gex between the site PL in Challex and PA in Ferney-Voltaire\nhas been stable over the last 30 years. The evolution of plot ownership and agricultural exploitations in\nthe 1990s led to fewer but larger farms. The typical size of a single exploitation today is about 90 ha\nper farm, covering a total of about 3600 ha. The main product remains milk, although this sector is\ndecreasing. Cereals represent a minor contribution. Free trade zones between France and Switzerland in\nthis sector facilitate goods exchange, from which the sector for milk and milk-derived products profits\nmainly. Out of the 23 million litres produced in the Pays de Gex, 14 million are sold to cooperatives in\nGeneva. The volume of the milk production in the area is larger than the entire volume in Switzerland.\nThe cereals produced by about 90 producers are almost entirely sold in Switzerland. The production of\ncereals saw a constant increase with a growth of more than 60% between 2000 and 2010.\nMilk production is also an important agricultural sector in Haute-Savoie. Major, globally acting\nfirms and groups (e.g., Soci\u00e9t\u00e9 Laiti\u00e8re des Hauts de Savoie / Lactalis) are important economic players\nin the region who also produce milk derived products, in particular Reblochon and Abondance cheese.\nGreen spaces for feeding the cattle are important for this industry. Growing urbanisation puts this branch\nof the economy under pressure, although the economic potential is high. Production and sales of hay as\ncattle food is a related main economic branch.\nThe agriculture sector around PB in Switzerland is dominated by the production of cereals. Re-\ncently, following the construction of glass houses, different types of agriculture are fostering the local\nproduction of various products. Local agriculture is one of the economic pillars of the canton, although\nthe sizes of the individual operators are much smaller than in France (typically less than 50 ha). Vine-\n240\n\nFig. 3.46: Agricultural land photographed during the field investigations.\nyards are another relevant part of the cantonal agricultural sector. Land consumption creates pressure on\nthe agricultural sector: about 20 ha of agricultural space is lost every year.\nThe sector around PD in Haute-Savoie experiences different climatic conditions than the northern\nsector. The countryside is more mountainous and the agricultural activities are more diversified, although\nthe main product is hay and grass related to milk production. Almost 5000 ha are exploited in this area\nfor milk and cheese production. 17 million litres of milk are processed by a firm in Fillinges alone.\nMoving further south (sites PF and PG) shows that the importance of agricultural activities has\ndecreased over recent decades and small farms dominate. The activities are diverse, including cereals,\ncattle farming, meat production, hay production, vegetables, poultry and some local wine production.\nDairy production remains the dominant branch.\nTowards the south-east (PH) the activities are still milk and cheese production with a total area\nof more than 12 000 ha devoted to it. Other important activities are fruit (apples and pears) and cereals\n(including maize) production. The entire zone processes per year about 45 million litres of milk. The\neastern sector (PD) processes about 12 million litres of milk yearly and also sees dairy product industries\n(e.g., Baiko). Cattle farming for meat production is a related activity in the sector.\nForestry\nForestry is mainly important in the French Haute-Savoie department. About 150 000 ha are utilised in\nthe area. 70% of the forests are privately owned. Wood production comprises a variety of different tree\ntypes, both deciduous and conifer trees. Forestry in the French department of Ain is also well-developed,\nmainly supplying wood for carpentry and construction works.\nThe project scenario only affects forestry in a very limited way in PG (Groisy) and PH (Cercier\nand Marlioz) in the Haute-Savoie department in France. The economic loss has been quantified, and the\npotential effects on habitat and biodiversity have been analysed. Mitigation measures can be developed\nin a subsequent design phase based on this analysis.\n241\n\nViticulture\nFig. 3.47: Vineyards photographed during the field investigations.\nVineyards are present in the Ain and Haute-Savoie departments in France, as well as in the canton\nof Geneva. However, the implementation scenario does not affect any of them. Wine production exists\nin the vicinity of the PL site in Challex, on both the French and Swiss sides. Wine production also exists\nat some distance from the surface site PB in Switzerland.\nTourism\nTourism is already a major economic factor in Geneva and the immediate vicinity of CERN because of its\nScience Gateway visitor centre and the numerous exhibitions and guided tours that CERN offers. Every\nyear more than 400 000 people visit CERN either individually or as part of groups. The economic impact\ndue to local spending that creates indirect, direct and induced jobs is significant, since people typically\ncombine their visit with other activities in the region, on average for a stay of four days. For instance\nFerney-Voltaire (PA site) is known for the Ch\u00e2teau Voltiare, its typical weekly market and numerous\ntourist attractions in the immediate vicinity (e.g., the Jura mountains in France and Coppet and Nyon\nin Switzerland). Geneva and its numerous tourist attractions are not exhaustively listed here. However,\nthe United Nations, the International Red Cross Organisation, the old town, the Jet d\u2019Eau, the watch\nmuseums, the cathedral are some examples. The economic benefits in this area today have been recorded\nand estimations for the effects to be expected with a future collider projects have been estimated and are\nreported in the section on socio-economic impact (see Section sustainability:results). With the increase\nof CERN\u2019s activities in the region, high-quality science tourism is expected to expand into the Haute-\nSavoie region, contributing to the tourism development there as well.\nConcerning the new sites, PB in Presinge features a number of small, but relevant, tourist attrac-\ntions that invite pedestrian and bicycle tourists, extending their excursions through the vineyards to the\nlake or towards France to the Arve valley.\nThe area around the PD site in Nangy in France is mostly known for its bicycle tracks that will be\nsignificantly extended by 2030. A track from the lake to Mont-Blanc is planned.\nThe surroundings of the PF site in \u00c9teaux do not yet feature dedicated tourist attractions. However,\nseveral opportunities exist for discovering local cheese products between sites PD and PF. Together\nwith a visitor centre at PG in Charvonnex and Groisy the entire zone could profit from a well-planned\ndevelopment of high-quality tourism that links the lake through the Arve valley with the Annecy area,\nwhich is highly developed in terms of tourism. Numerous mountain walking tours can be included in\nthis programme.\n242\n\nThe area around site PH in Cercier and Marlioz is not currently developed touristically and does\nnot have noteworthy infrastructures.\nThe zone close to the Vuache next to site PD in Dingy-en-Vuache and Vulbens, on the contrary\nfeatures, numerous bicycle paths (including ViaRh\u00f4na) that are inviting for tourists interested in nature.\nThe site PL in Challex is embedded in a regional nature and bicycle tourism area, linking the\nJura mountains with the Rh\u00f4ne valley. It features hiking paths and trails through the vineyards. The\narea around the Swiss commune Dardagny is known as one of the most beautiful in Switzerland and is\ntherefore particularly protected along with the landscape that surrounds it.\nEconomic development projects\nDevelopment projects potentially relevant for the FCC scenario are included in the Geneva cantonal mas-\nter plan (Plan Directeur Cantonal, PDCn) and concern the period to 2030. A project for new apartments\non about 180 ha in the vicinity of the airport, involving major construction works and the employment\nof about 5700 workers, is potentially relevant for site PA in France. Also, about 1300 apartments are\nplanned to be constructed in nearby Grand-Saconnex, involving up to 2400 workers. No development\nprojects are registered in the vicinity of sites PL in Challex and PB in Presinge on the Swiss side.\nIn France, the potential main developments are in the vicinity of site PA in Ferney-Voltaire. A\nfuture commercial activity zone (ZAC) on about 65 ha and the creation of an additional 2500 apartments\nand educational facilities are planned for the period up to 2030.\nIn the vicinity of site PD in Nangy a new road widening project (RD903) and the intersection with\nthe A40 autoroute are scheduled to be implemented before 2030.\nScientific activities\nThe main scientific project in the region is the upgrade of the Large Hadron Collider, known as the\nHigh-Luminosity Large Hadron Collider (HL-LHC). It guarantees the continuation of the presence of\nscientists and engineers at today\u2019s level until the 2040s. The FCC implementation scenario builds on this\nactivity, leveraging the existing LHC Pt8 for the creation of surface site PA and hosting the injector on\nthe CERN Pr\u00e9vessin site. Also site PL in Challex profits from being in the vicinity of CERN Meyrin.\nFor site at PB, the presence of the Geneva Architecture and Landscape School (HEPIA) in Lullier\nmay be relevant. This facility is close to the site and potentially provides services that the surface site\ncan leverage to reduce its own requirements. HEPIA could also potentially profit from common devel-\nopments in different areas around the FCC, including agricultural studies and technical infrastructures.\nA collaboration already exists between the study, CERN and HEPIA to work on the re-use of excavated\nmaterials and agricultural aspects.\nThe national milk and meat industry school can be found in the vicinity of the PF site in \u00c9teaux in\nLa Roche-sur-Foron. The infrastructure also hosts a technical and scientific high-school. The school is\nactive in scientific partnerships with INRAE, CNRS, universities and national research centres. Potential\nsynergies can, for example, be found in the development of water and heat re-use.\n3.3.10\nHeritage\nThe analyses carried out in the frame of this study related to cultural, architectural and archaeological\nheritage first took into account all noteworthy elements that could be identified in a perimeter of 500 m\naround the surface sites. A subsequent, more detailed assessment focused on the elements in the imme-\ndiate vicinity of the surface site candidate locations. This choice of perimeter was established in order\nto understand the richness of each surface site which, subsequently, would need to be considered in the\ndesigns and territorial integration of the sites.\nBibliographic analyses did not reveal any registered archaeological sites or interest in archaeolog-\n243\n\nFig. 3.48: Architectural heritage photographed during the field investigations.\nical relevance at and in close proximity to the surface sites. There are no buildings or monuments of\nhistorical importance on the surface sites or directly affected by potential surface site constructions due\nto visibility or co-visibility. There are a few buildings of historical significance in the wider perimeters\nof some of the surface sites.\nThe sensitivity of the area of PA in Ferney-Voltaire, France with respect to heritage is low, par-\nticularly at the surface site itself. The site would be located on protected agricultural land. To the west\nof the study area, there is the protected woodland, Bois de la Mouille, also classified as wetland. To\nthe northeast, in the vicinity of the site, there are a few isolated protected trees and a wetland with low\nfunctionality. Nevertheless, the implementation of a surface site site avoids these classified and protected\nareas, despite the fact that some of them are on agricultural land.\nThe area around the site PB in Presinge, Switzerland has a strong heritage, architectural, cultural\nand landscape character. The surface site is relatively far from heritage sites but it remains partially\nvisible from the hamlets to the north as well as those to the south. The existing wooded strips partially\nprotect the views towards the villages of Choulex, Puplinge and Presinge, but remain open towards the\ncommunes of Jussy and Meinier. In order to preserve the rural character of the area, it is advisable to\nconsider good landscape integration, such as a semi-buried surface site so that visibility from nearby\nhamlets is limited.\nThe heritage sensitivity within the study area of the PD site in Nangy, France, is considered\nmedium to very high depending on the part of the site. The presence of the Ch\u00e2teau de Pierres and\na classified wood located to the north and west, 180 to 300 m from the surface site induced this rating.\nIn the area directly concerned by the site, the sensitivity is very low. The site is in the immediate vicinity\nof an autoroute and a departmental road which will be reorganised to improve traffic flow. No relevant\nvisibility issues are recorded in an area that is dominated by high traffic, a hospital, or industrial and\ncommercial facilities.\nSensitivity to heritage in the area of the PF surface site in \u00c9teaux in France is low. Very high\nissues are noted in the wider vicinity of the site to the south and the southeast due to a woodland around\na creek that is classified and protected. To the north-west, at a distance of about 400 m, there is a notable\nbuilding, constructed in 1923, which formerly housed a cheese factory. There are also several groups of\nisolated trees that are witnesses to the history of agriculture. However, the implementation of the surface\nsite avoids all sensitive spaces and stays close to the departmental road, directly opposite a public works\nconstruction company.\n244\n\nThe sensitivity related to heritage at site PG in Groisy and Charvonnex in France is considered to\nbe low. Some areas in the south of the main site are remarkable due to the presence of areas with wetland\ncharacteristics and unclassified but high-quality woodlands. There are a few old buildings linked to the\nnetworks of old mills located in the surrounding larger study area. The surface site does not directly\naffect any heritage elements.\nHeritage sensitivity in the immediate area of the PF surface site in Cercier and Marlioz, France is\nconsidered very low. This assessment is linked to the presence of the large forest (Grand Bois) and the\nTabass\u00e9 creek to the north of the surface site. Both present ecological interests, but are not considered\nheritage sites.\nThe heritage sensitivity of the PJ surface site in Dingy-en-Vuache and Vulbens in France is con-\nsidered medium to high due to the location of the site in an area classified as a protected agricultural area\nand an ecological corridor protection zone. The entire zone is of agricultural character. In the south-west,\nin the immediate vicinity, some areas exhibit very high sensitivity due to the presence of classified wood-\nlands along small creeks. The current shape of the surface site respects the integrity of the constraints.\nStill, particular attention will have to be paid for the specific design and integration of the surface site to\nmaintain the registered ecological corridor, ensuring the free movement of fauna in the area.\nThe heritage sensitivity for the PL surface site in Challex, France is considered to be medium to\nhigh. The area around the site consists largely of protected agricultural and, further away, natural lands.\nThere are several groups of isolated trees and alignments that bear witness to the history of agriculture.\nThe site itself is located in a protected agricultural area and borders a protected ecological corridor\nregistered in the municipal urban plan. The main issue is the visibility of the site from several locations\nin nearby villages. Therefore, care has to be taken for the specific design and landscape integration of\nthe surface site.\nIn summary, the main heritage constraints are mostly related to the rural and agricultural character\nof the areas, with the presence of historical buildings at some distance from the sites. Particular attention\nrelated to heritage has be paid during site design and landscape integration at the site locations PB, PJ\nand PL.\n3.3.11\nLandscape\nFig. 3.49: Mountainous landscape with agricultural fields documented during field investigations, high-\nlighting the interaction between natural and cultivated environments.\nThe initial state analysis included a detailed landscape analysis that was carried out with expert\ncompanies during field visits over an entire year. The landscape analysis extended up to 5 km around the\n245\n\nsurface sites, since the visibility of the sites depends significantly on the topography, urban and vegetation\nenvironment. Detailed landscape analysis and maps were developed that show the topography, the views\nfrom and to the sites and the visibility issues. They will serve as input for subsequent architectural design\nworks and landscape integration concepts.\nThe site PA and its surroundings in Ferney-Voltaire (France) are dominated by agricultural areas,\nGeneva airport, highly urbanised commercial surroundings and an ecological corridor between the resid-\nual forests that occupy the buffer along the Franco-Swiss border. The area is in an open landscape with\na view towards the Alps and Mont Blanc that has to be considered during the architectural design of the\nsurface site. The nearby LHC site Pt8 (LHCb) and its planned extension provide an excellent opportunity\nto reduce the PA site footprint as much as possible to preserve the view and the ecological corridor that\nalso stretches across the border.\nThe site PB in Presinge (Switzerland) is located in open countryside with valuable views towards\nthe Alps and the Sal\u00e8ve mountain. The landscape continuity is remarkable and the views from nearby\nhills over the landscape and its cultural and landscape heritage are highly valued. Much care must be\ntaken in the architectural designs of the site, ideally integrating the site in the landscape as much as\npossible, taking care that the view from the nearby villages towards the mountains remains unobstructed.\nThe PD site in Nangy (France) is located in a mixed urban, agricultural and industrial environment\nthat is dominated by major transport routes. Direct views to the sites are limited.\nThe PF site in \u00c9teaux (France) is located in a natural environment, directly on highly frequented\ntransport routes and commercial premises. No direct visibility from La-Roche-sur-Foron exists. How-\never, the mountain views towards the Alps need to be considered when developing the architectural\ndesign of the site.\nThe site PG in Charvonnex and Groisy (France) is located in a highly natural environment, partially\nforested and with grass fields. The mountain views from the site are highly valued. A direct, but limited\nview of the site only exists from the Oli\u00e8res plateau.\nThe PH site in Cercier and Marlioz (France) is located in a rural environment with a forest. Some\nhamlets exist in the vicinity, but due to the forest and the topography, no direct view of the site exists.\nThe PJ site in Dingy-en-Vuache and in Vulbens (France) is located in a mixed natural and agricul-\ntural environment. The landscape is open and the view from Vulbens must be taken into consideration\nduring the architectural design.\nThe site PL in Challex (France) is located in an agricultural/vineyard environment with views to\nthe Jura mountain, the Rh\u00f4ne valley and the Alps. The open views require careful landscape integration,\nconsidering in particular the site\u2019s visibility from the nearby hamlets.\n3.3.12\nNoise\nNoise, is considered to be unpleasant or annoying and is an environmental aspect that is relevant during\nthe construction of the surface and subsurface structures and during the operation of the particle collider.\nThe regulations concerning noise protection differ significantly between France and Switzerland. How-\never, in all cases the impact due to noise depends on the presence of people and animals that would be\naffected by the noise. The relevant indicators are not only frequency and amplitude, but also the time dur-\ning which an exposure to noise occurs and the duration of the exposure: during ordinary working hours,\nduring the night, on non-working days, the typical presence of people in their homes, the age, health\nand other social conditions of the potentially affected people (e.g., noise in the vicinity of a hospital, a\nschool or a retirement home). Typically, noise generated by machinery is considered to have noteworthy\nhealth effects from 40 dB(A) and higher. Noise up to 30 dB(A) is a level that is generally experienced by\npersons in a typical living environment (see Table 3.14).\nTherefore, the first step required is to establish the existing background noise in the vicinity of the\n246\n\nFig. 3.50: Field-based noise measurements conducted to assess ambient sound levels.\nFig. 3.51: Noise measurements taken near a residential area to understand the current noise level.\ncandidate surface sites. This activity is followed by estimations of noise generation without protection\nmeasures. This identifies sensitive areas. An eco-design is subsequently applied to reduce the noise\nwhere potential impacts on the environment are expected. The approach is to first work on low-noise\ndesigns. This also includes the relocation of noise-generating devices on the surface sites. Where this\nprocess turns out to be insufficient, noise protection measures to reduce the impacts are studied. Reloca-\ntion of noise-generating equipment or adjustment of an entire surface site is an option that is considered\nif no adequate mitigation measures can be identified.\nThe background noise was established by first consulting national noise emission databases and\nthen completing the data with field measurements. The measurements were carried out by expert com-\npanies on various days in 2024 at a selection of different locations and at different distances from the\nsurface sites. Detailed analysis of the frequencies, amplitudes, and directions of origins have been made\nto permit mixing potential noise sources at the surface sites with the ambient noise at a later stage. The\nnumber of potential residents that could be affected by noise has been obtained using an analysis of the\n247\n\nTable 3.14: Typical noise levels with practical examples.\nNoise\ndB(A)\nLevel\nConversation\nJet plane takeoff\n< 130\nAbove pain threshold\nImpossible\nJackhammer at 1 m\n< 110\nSupportable for a\nshort moment\nMotorcycle at 2 m\n< 90\nAnnoying\nPossible when shouting\nHeavy road traffic\n< 80\nVery noisy\nDifficult without shouting\nDwelling close\nto an autoroute\n<70\nNoisy\nPossible when\nspeaking loud\nWorking on a computer\n< 60\nModerate\nPossible with\nnormal voice\nNoise level in a\ncity during the day\n< 50\nRather quiet\nConstruction noise at\n100 to 200 m distance\nfrom a surface site\n40 - 45\n-\nPossible with quiet voice\nNoise level in the\ncountryside during\nthe day\n< 40\nQuiet\nNoise level in the\ncountryside during the\nnight without wind\n< 30\nVery quiet\nSnow falling in the\nmountains, recording studio\n< 15\nSilent\ndata collected with the geographical information system and statistical information (see Table 3.15).\nThe measurements indicate that the majority of sites are affected by significant background noise\nwith no people present in a perimeter of 200 to 300 m. Therefore, neither the noise from construction\nnor operation, that will be kept as low as possible with noise protection measures, are expected to impact\nthe population at sites PA (Ferney-Voltaire), PD (Nangy), PF (\u00c9teaux), PG (Charvonnex and Groisy),\nPJ (Dingy-en-Vuache and Vulbens). At the PL site (Challex), construction activities during the night\ncould lead to an excess of background noise, and therefore, the construction schedule would have to be\nadapted if a detailed technical design of the construction site in view of noise protection turns out to be\ninsufficient. At sites PB (Presinge) and PH (Cercier and Marlioz) the background noise is particularly\nlow with about 35 dB(A) compared to all other locations. In all cases, operation related noise can be kept\nbelow the threshold for residents potentially affected in the vicinity, but for the construction planning,\ncare must be taken to respect the times during which noise exposure is more impactful (e.g., during\nthe night, weekends and non-working days). For site PH, 3 to 4 houses at a distance of 100 m would\nbe affected, and at site PB, two houses at a distance of 200 m would be affected. The construction-\ninduced noise should, therefore, not significantly exceed the background noise during resting times in\nthese locations.\n248\n\nTable 3.15: Typical background noise measured in the vicinity of surface sites and the numbers of people\npotentially affected within the distances indicated from the site.\nSite\nBackground noise dB(A)\n7h-22h\nBackground noise dB(A)\n22h-7h\nPotentially\naffected people\nDistance to site\nPA\n55\n45\n0\n100 - 200 m\nPB\n36\n36\n0\u2020 (< 10\u2021)\n100 m\nPD\n48\n44\n0\n100 - 200 m\nPF\n48\n40\n~10\n100 - 200 m\nPG\n36 - 48\n37 - 45\n0\n100 - 300 m\nPH\n35\n29\n< 10\n100 m\nPJ\n39 - 47\n35 - 44\n0\n300 m\nPL\n40\n30\n< 5\n200 m\n\u2020 People exposed according to Swiss limits, DS III\n\u2021 People exposed according to permitted noise emissions in France\n3.3.13\nVibrations\nVibrations are rapid oscillating movements that propagate through solid paths and can be transmitted to\nthe human body, especially through direct contact with the ground or the structure concerned. They are\nthus physical phenomena characterised by a wave with its amplitude and frequency.\nThe risks associated with vibrations are mainly damage to buildings and disturbance of people.\nVibrations can occur due to seismic activities, ground movements, meteorological conditions and artifi-\ncial sources such as construction activities and machinery. The environmental analysis revealed that in\nthe entire perimeter of the project, seismic activities have a very weak to weak potential to create relevant\nvibrations, despite different occurrence probabilities for small-scale seismic events. Concerning vibra-\ntions caused by landslides surface site locations PA, PB, PD, PH, PJ and PL are at significant distances\nfrom risk zones and no subsurface cavities exist within a relevant distance of surface sites. A potential\nlandslide risk zone exists only at a distance of 500 m from the PF site, but the likelihood of an event is\nvery small. A cavity that is part of a defence infrastructure exists at a distance of 250 m. It is unlikely\nthat this cavity would collapse. Weather phenomena such as violent winds and lightning may cause vi-\nbrations that affect trees and building structures. However, such events are infrequent in the perimeter\nof the scenario. Various human-induced vibration sources over the coming ten years were identified in\nthe vicinity of surface sites PA, PD and PF. Road traffic is another source of ongoing vibration. It needs\nto be considered for sites PA, PD, PF, PG and PJ. No other noteworthy sources of vibrations could be\nidentified in the vicinity of surface sites.\n3.3.14\nLight\nLight pollution refers to the excess or poor management of artificial light in the nighttime environment.\nThis phenomenon is increasingly concerning, both for its effects on biodiversity and human health. There\nare two types of light pollution. First, direct light pollution relates to the impact of light directly produced.\nSecondly, indirect light pollution results from an accumulation of light, creating a halo that obscures the\nstars and degrades the quality of the night sky. With respect to the surface sites, light pollution is a\nrelevant environmental topic to be assessed during the detailed design phase concerning the construction\nactivities and the subsequent operation phase. Therefore, at this stage, the existing light pollution in\nthe vicinity of the candidate locations for surface sites has been analysed and documented to serve as a\nbaseline for the development of the detailed design.\nThe main source of light pollution in the areas concerned by the project is public lightning along\n249\n\nroads in residential areas. In addition, commercial zones are a source of artificial light, in particular when\nthey use large-scale public screens. Frequently, lights are not controlled. Some outdoor lights of private\nhouses contribute to light pollution. Finally, industrial installations for operation during nighttime and to\nensure safety are a strong source of light pollution.\nFor the current state, data have been purchased from various sources, and maps have been de-\nveloped using these data for the areas around the surface sites. The zone around site PA is strongly\nilluminated during the night. One source is the Geneva airport and another one is the commercial zone\nin the immediate vicinity. Road lighting and newly built residential houses also contribute. The Grand\nGen\u00e8ve plan foresees that the entire area is gradually restored to protect the ecological corridors and\nthe fauna. However, no protection measures are currently planned at local French urban planning level.\nSite PB in Switzerland is located in the countryside and only few buildings are found in the vicinity.\nIn the Grand Gen\u00e8ve plan, the perimeter is classified in order to protect the \u2018night\u2019. In particular, the\nzone close to the road is subject to refurbishment and the zone along the creek has a stake. However, no\nprotection measures are mentioned at local urban levels. Site PD is in the immediate vicinity of major\ntransport routes and industrial buildings on a field. No particular protection measures are planned at local\nurban planning level. Site PG is in a natural environment and in the forest with only little light pollution.\nAlthough no particular protection measures for the location exist, it can be assumed that preserving the\ncurrent situation is a priority. Also, site PH in the forest is in an area with very low light pollution.\nAlthough no particular protection levels are indicated it can be assumed that the current situation\nis to be preserved as much as possible. Site PJ in the countryside experiences small light sources in the\nvicinity from some distant urban constructions. The zone is classified to be preserved, and the ecological\ncorridors constitute a stake. General protection measures apply to forbid artificial light along the water\ncourses although at local urban planning level, no protection zones are indicated. Site PL is located\nin an agricultural zone and rather isolated next to fields, forests and vineyards. In Switzerland, nature\nprotection zones forbid artificial light. At the local urban level, no protections apply in France.\nSumming up, the site PD and its surroundings are located in an area where the night should be\npreserved with priority. However, no noteworthy species are affected and therefore the stake is average.\nThe PA site is, however, in an area with high light pollution and there are ecological stakes in the sur-\nrounding area. Therefore, there is a will to restore the night environment, and the stake is high. The stake\nis also high for the PB site in Switzerland, since the night is intended to be preserved and light pollution\nshould even be further reduced. Also, the stake for site PF is high since the site is located in an area\nwith almost no light pollution today. Similar conditions with high stakes apply to sites PJ and PL. The\nwider surroundings of sites PG and PH are in a forest with low light pollution and nearby noteworthy\nbiodiversity reservoirs. Therefore, the stakes with respect to light pollution are very high. These findings\nhave to be considered and integrated in the design and planning of the construction sites and a plan to\npreserve the night has to be developed for all sites concerning the operation phase.\n3.3.15\nRadiation\nPossible risks for the population and environment emerging from non-ionising and ionising radiation\nexposure at different locations on the surface were analysed based on available data in both Host States.\nFigure 3.52 shows the different types of radiation, non-ionising and ionising, that exist.\nThe Host States notified services in charge of carrying out measurements to establish national\ndatabases will require updated data before a particle accelerator is put into operation to establish a base-\nline for the ionising radiation.\nNon-ionising radiation\nIn France, exposure limits vary depending on the frequency range used, typically between 28 V/m and 87\nV/m for the electric field. The Swiss regulations distinguish between public areas in which the persons\n250\n\nFig. 3.52: Types of radiation (Source: IAEA [91]).\nstay only for brief intervals of time, such as roads or sports facilities, and sensitive areas, in which the\npersons may stay for a certain limited period of time including houses and apartments, schools, and hos-\npitals. Switzerland imposes stricter installation limits for radio equipment than France, with maximum\nelectric field values set at 4 V/m for 900 MHz, 6 V/m for 1800 MHz, and 5 V/m for installations oper-\nating across multiple frequencies. These Swiss regulations are designed to provide enhanced protection\nfor sensitive locations compared to the International Commission on Non-Ionizing Radiation Protection\n(ICNIRP) guidelines. Swiss limits with respect to immission, which represent the cumulative exposure\nfrom all emitters, align with European recommendations and are identical to those in France. Figure 3.53\nshows the values of the electric and magnetic fields measured under the line, as well as at 30 m and 100 m\nfrom the line, for very high voltage, high voltage and low voltage overhead lines.\nFig. 3.53: Average values of the electric and magnetic fields around overhead power transmission lines\nat 50 Hz (Source: DGS [92]).\nNo electricity lines are emitting low-frequency radiation in the vicinity of sites PB in Switzerland,\nPD, PG, PH, PJ and PL in France. A 63 kV line runs 250 m in the vicinity of the PF site in \u00c9teaux\nin France, which emits a negligible electromagnetic field onto the candidate surface site. The 66 kV\nunderground electricity line supplying LHC Point 8 in Ferney-Voltaire in France is just next to the PA\nsite. It induces a very weak electromagnetic field onto the site.\nSome radio stations that are sources of radio waves are present near the surface locations, but the\nrecorded exposure measurements are well below the reference levels. The data collected from measure-\nment stations near PA, PB, PD, PG, PJ show that all exposure measurements are significantly below\n251\n\nthe reference levels. No data was found for measurements within a 5 km radius of the PF, PH and PL\nlocations in France. Detailed measurements will have to be carried out before the installation is put into\noperation, but the risk of exceeding the limits for ionising and non-ionising radiation specified in the\nregulations is considered to be very low.\nIonising radiation\nIonising radiation carries sufficient energy to ionise atoms or molecules, leading to molecular changes.\nHigh doses can cause cellular damage and mortality, whereas controlled applications are pivotal in in-\ndustries, scientific research, and medicine. The sources of exposure are of natural and artificial origins:\n\u2013 Natural cosmic radiation: energetic particles from space contribute to exposure, influenced by\naltitude and geographic location. Terrestrial radiation: radioactive elements in the Earth\u2019s crust\n(e.g., uranium, thorium) emit radiation, varying regionally due to geological factors.\n\u2013 Natural radon gas: a significant contributor, radon accumulates in poorly ventilated indoor spaces.\nIt constitutes 33% of annual exposure in France. Incorporated radionuclides: naturally occurring\nradionuclides in food and water contribute 12% to annual exposure.\n\u2013 Artificial sources, nuclear accidents and testing: fallout from historical nuclear tests and accidents\nlike Chernobyl contributes marginally to current exposure.\n\u2013 Nuclear facilities: emissions from civilian and military installations are tightly regulated, with\nnegligible contributions ( 0.001\u20130.01 mSv/year near facilities).\n\u2013 Artificial sources, medical applications: diagnostic and therapeutic uses dominate artificial expo-\nsure, contributing 34% of total exposure in France.\n\u2013 Artificial sources, scientific research activities: the particle accelerators and colliders operated by\nCERN contributing less than 0.01 mSv/year.\nTable 3.16 gives an overview of the current ionising-radiation background conditions at the surface\nsite locations.\nTable 3.16: Level of exposure to ionising radiation at the surface site locations today (Source : Autorit\u00e9\nde s\u00fbret\u00e9 nucl\u00e9aire et de radioprotection (ASNR))\nNearest data entry\nAnnual exposure\nSurface site\nFerney-Voltaire\n5.2 mSv/year\nPA (Ferney-Voltaire, France)\nVille-la-Grand\n4.0 mSv/year\nPB (Presinge, Switzerland)\nNangy\n4.3 mSv/year\nPD (Nangy, France)\n\u00c9teaux\n4.4 mSv/year\nPF (\u00c9teaux, France)\nGroisy\n4.4 mSv/year\nPG (Charvonnex and Groisy, France)\nCharvonnex\n4.9 mSv/year\nPG (Charvonnex and Groisy, France)\nMarlioz\n4.9 mSv/year\nPH (Cercier and Marlioz, France)\nCercier\n5.0 mSv/year\nPH (Cercier and Marlioz, France)\nDingy-en-Vuache\n5.0 mSv/year\nPJ (Dingy-en-Vuache and Vulbens, France)\nVulbens\n5.8 mSv/year\nPJ (Dingy-en-Vuache and Vulbens, France)\nChallex\n5.5 mSv/year\nPL (Challex, France)\nExposure to cosmic radiation, originating from high-energy particles such as protons and heavy\nions from space, poses hazards due to its ionising nature, which can damage living tissues. The intensity\nof exposure increases with altitude, being roughly twice as high at 1500 metres compared to sea level and\nfurther elevated during air travel. While the Earth\u2019s magnetic field reduces exposure near the equator,\nhigher doses are received near the poles. In France, cosmic radiation accounts for about 7% of the\n252\n\naverage annual exposure to ionising radiation, with an effective dose at the surface sites between 0.32\nand 0.70 mSv/year. In Switzerland, the dose associated to cosmic rays in the vicinity of the site is about\n0.35 mSv/year.\nTelluric radiation refers to ionising radiation emitted by naturally radioactive elements like ura-\nnium, thorium, and potassium-40 found in the Earth\u2019s crust. Exposure levels vary depending on regional\ngeology, with areas rich in granitic or volcanic rock typically exhibiting higher radiation levels. In\nFrance, telluric radiation contributes approximately 14% of the average annual exposure to ionising ra-\ndiation, with an effective dose of around 0.51 to 0.55 mSv/year in the areas of the surface sites in France\nand 0.33 mSv/year in the vicinity of the surface site in Switzerland.\nExposure to natural radionuclides occurs through the ingestion of radioactive elements, such as\npolonium-210, present in food, water, and air, which originate from terrestrial rocks, soils, or cosmic\ninteractions. Foods like seafood are particularly rich in these radionuclides, and tobacco inhalation can\nalso contribute significantly. In France, this accounts for approximately 12% of the average annual\nexposure to ionising radiation, with an effective dose of about 0.55 mSv/year in France, varying between\n0.4 and 3.1 mSv/year depending on dietary habits. In Switzerland, the exposure is about 0.40 mSv/year.\nTobacco consumption accounts for about 0.04 mSv/year.\nExposure to radon, a naturally radioactive gas, varies between France and Switzerland due to\ndifferences in geology and measurement methodologies. In France, radon contributes 33% of the av-\nerage annual ionising radiation exposure, with a mean dose of 1.5 mSv/year, ranging between 0.54 and\n3.2 mSv/year. Specific areas concerned by the surface sites in Ain and Haute-Savoie report slightly lower\nexposures, around 1.47 and 1.14 mSv/year, respectively. In Switzerland, radon is the largest natural con-\ntributor to radiation, with an average dose of 3.3 mSv/year, reflecting a higher impact. This discrepancy\npartly arises from different dose conversion factors used; France employs the UNSCEAR coefficient,\nwhile Switzerland uses the CIPR\u2019s updated factors, which approximately double the estimated risks.\nConsequently, radon exposure is relatively more significant in Switzerland.\nExposure to ionising radiation from artificial sources in France and Switzerland includes contribu-\ntions from nuclear accidents, medical applications, nuclear installations and scientific research facilities.\nMedical applications in both France and Switzerland, are the largest contributors to artificial ionis-\ning radiation exposure. In France, they account for approximately 1.5 mSv/year per capita, representing\n34% of the total radiation exposure. Similarly, in Switzerland, medical applications contribute about\n1.49 mSv/year per capita, highlighting the widespread use of diagnostic and therapeutic procedures in-\nvolving ionising radiation in both countries.\nRadiation exposure due to past nuclear accidents and fallout, such as Chernobyl, and atmospheric\nnuclear tests is now minimal in both countries. In France, the average annual dose is 0.012 mSv/year,\nwith slightly higher doses in areas with significant fallout. In Switzerland, this exposure is even lower,\ncontributing only a few hundredths of a mSv annually, reflecting the diminished impact of residual fallout\nover time.\nExposure from nuclear facilities is negligible in both France and Switzerland due to strict regula-\ntory measures. In France, people living within 10 km of nuclear installations receive an annual dose of\n0.001 to 0.01 mSv under normal operational conditions. In Switzerland, exposure near nuclear facilities\nand the scientific facilities of CERN, is similarly low, with annual doses generally below 0.004 mSv,\ndemonstrating effective safety and monitoring measures.\nSumming up, the ionising radiation context at the surface sites is significantly larger than the\nresidual ionising radiation that is generated by CERN\u2019s scientific particle accelerators.\n253\n\n3.3.16\nTechnical risks\nNatural Hazards\nAs part of this study, several types of natural hazards that can potentially lead to interactions with the\nproject have been identified. These will be analysed in further detail during a subsequent environmental\nimpact assessment. The topics concern flooding, ground movement, seismic activities, avalanches, forest\nfires, cavities, radon, clay swelling and technological hazards. These natural hazards may also be caused\nby climate change effects. The evolution of the climate has been taken into consideration in the study\nof the current state of the environment, as well as the evolution of the environment in which the project\nwould be embedded.\nFlood and ground movement\nhazards that can be caused by numerous factors, such as rain, groundwater and rivers, are considered to\nhave low probability for all the locations. Effects due to unstable ground, such as landslides, mudflows\nand erosion have also been taken into account. Overall, no significant hazards or potential effects leading\nto relevant risks were identified in the concerned locations. No surface site on French territory is subject\nto a ground movement. For the site PB in Presinge in Switzerland, the closest potentially unstable ground\narea is located 700 m east of the site, however the landslide risk is superficial. The candidate surface site\nlocation is not subject to the hazards linked to flooding or earth movement.\nSeismic\nhazards vary depending on the location. France is divided into five seismic activity zones. The sites\nstudied are located in zones of moderate or medium seismic activity. In particular, sites PA, PL and PJ are\nlocated in zones of moderate (level 3) activity, while sites PG, PF and PD are located in zones of medium\n(level 4) activity. This requires the application of earthquake-resistant construction principles during the\nsurface site design development. In addition, some of the sites studied are located near active tectonic\nfaults. For example, site PA in Ferney-Voltiare is located about 400 m from a fault. In Switzerland, the\nseismic hazard model classifies locations into five zones, of which site PB in Presinge is located in zone\nZ1b (level 2), characterised by low seismic activity. Further field studies are needed, and cooperation\nwith scientific institutions to assess the local seismic risk in detail and develop specific engineering\nmodels will be undertaken.\nForest fires\nturn out to be a very low hazard in the zones concerned by the surface sites, although two locations are\nin forest zones. In France, the Forest Fire Risk Prevention Plan (PPRIF) established at the municipal or\ninter-municipal level, targets areas exposed to significant risk levels and strong land pressure. In addition,\nthe PPRIF may also impose clearing of areas in order to isolate the buildings. It may also require that\naccess roads be sized to allow fire trucks to pass and for people to evacuate in the event of a fire. No\nFrench municipality affected by the surface sites is subject to a forest fire risk prevention plan and none of\nthe areas surrounding the surface sites in France are subject to the legal obligation of clearing. Although\nthe site location PH in Cercier and Marlioz is not exposed to the natural forest fire hazard according to\nvarious regulatory and management tools, there always remains a residual and low hazard of forest fires\nin this area due to the presence of timber. In Switzerland and more specifically in the canton of Geneva,\nthere is no law, prevention plan or specific forest fire risk management plan. The site PB in Presinge is\nnot in the vicinity of a woodland that would generate a forest fire hazard to the site.\nAvalanches\nare not considered a relevant hazard for the surface sites due to relatively flat terrain and low forest\ndensity in the vicinity of the locations analysed.\n254\n\nCavities\nnatural or man-made voids can be considered hazards for construction activities. The analysis addressed\ntheir presence and potential effects with respect to the implementation of the surface sites. No cavities\nare located within a radius of 500 m around the French surface sites, except for the PG Charvonnex site\nwhere several cavities linked to military works are located within a radius of more than 250 m around this\nsite. Apart from their existence and location, no additional information is available. Thus, the potential\nhazard from underground cavities in this area requires additional data gathering.\nRadon\nis a colourless, odourless radioactive gas that originates from the decay chains of uranium and thorium,\nboth naturally present in the Earth\u2019s rocks. A key factor influencing radon concentration levels in build-\nings is the geology, in particular, the uranium content in the subsurface layers. In some areas, specific\nunderground features (e.g., faults, mining works, hydrothermal sources) can exacerbate radon transfer\nto the surface, locally increasing its potential. For new constructions, radon transfer can be limited by\nenhancing the building\u2019s seal between the ground and the structure. In France, the mapping method\nestimates the radon potential of geological formations by considering factors that influence both radon\nproduction in the subsurface and its transport to the surface. Zones are classified as having low, moderate,\nor high potential. All French surface sites studied are located in low radon potential zones.\nIn Switzerland, the radon map shows the probability in % of exceeding 300 Bq m\u22123 in buildings,\ndivided into four categories: \u22641%, 2 and 10%, 11 and 20%, and >20%. Unlike France, there is no\nnational campaign that estimates radon thresholds in buildings. The PB site in Presinge lies in a low-risk\narea, in the range of 2 to 10% probability of exceeding 300 Bq m\u22123.\nShrinking and swelling of clays\nis a natural hazard that has been assessed for all surface site locations. Superficial clay soils have the\nability to change consistency depending on their water content. When the water content of clay soil\nincreases, its volume expands, a phenomenon referred to as the swelling of clays. Conversely, a reduc-\ntion in water content causes the opposite effect, known as shrinkage of clays. Figure 3.54 explains the\nmechanism of the shrink-swell phenomenon. This shrinkage or swelling can cause structural damage to\nbuildings.\nFrom January 1, 2024, in France enforcement the of construction regulations has been tightened,\nand a new certificate for clay shrink-swell behaviour is now mandatory in zones subject to medium or\nhigh exposure. The surface sites located in France are subject to low to medium exposure to shrink-\nswell risks. Site PA in Ferney-Voltaire is mostly in a low hazard area, except for a small part of the\nsite near the LHC site point 8 (LHCb) where the exposure level is medium. Sites PD, PF, PG and\nPF are rates as low exposure. PH and PJ sites are located in zone with medium exposure. The PL\nsurface site in Challex is mainly located in the zone with low exposure, except for a small fragment\nin the southern part of the site with medium exposure, which is not foreseen to host constructions, but\na green buffer. In Switzerland, a lithological map that provides an overview of the subsoil classified\naccording to lithological and petrographic criteria indicates that the site PB in Presinge is located in\nsoils containing clays. However, the concentration and depth of this clay element in the soil are not\nprecisely described. Detailed soil investigations are required during a subsequent environmental impact\nand surface site design phase to clarify the conditions and, if needed, to take them into account during\nthe design of the surface site.\nTechnological hazards\nTechnological hazards linked to industrial, environmental, and infrastructural activities could potentially\nhave effects on human health, safety and the surrounding environment. Risks emerging from these\n255\n\nFig. 3.54:\nExpansion and shrinkage of clays. Damage to the building is caused by the rain induced\nexpansion on one side and shrinkage caused by removal of water by the tree on the other.\nhazards and effects arise from industrial installations, the transport of hazardous materials and other\nactivities involving dangerous substances. Therefore, their presence near candidate surface site locations\nhas been analysed.\nIn France, two categories of industrial facilities are considered to generate risk. The first group\nconcerns establishments reporting emissions and transfers of pollutants into the air, water or soil and the\nproduction of hazardous waste. This covers establishments such as large industrial installations, large\nmunicipal sewage treatment plants and certain livestock farms. Second, installations classified for en-\nvironmental protection (called ICPE) that are industrial or agricultural facilities subject to regulations\nfor the prevention of environmental risks and are classified according to regimes ranging from simple\ndeclarations to authorisations, depending on the risk. In addition, the SEVESO regulations (EU Direc-\ntive 2012/18/EU) impose strict controls on facilities processing hazardous chemicals in order to prevent\nserious accidents.\nIn Switzerland, the Ordinance on Major Accident Prevention (so called OPAM) seeks to protect\npeople and the environment from severe damage caused by extraordinary events in installations or during\nthe transport of hazardous materials. OPAM applies to businesses exceeding specific hazardous material\nthresholds, genetic organisms under strict confinement, and transport infrastructures like pipelines, rail-\nways, and highways used for dangerous goods. The planning authorities (cantons and municipalities) are\nresponsible for integrating aspects of major accident prevention into their plan for land use. Although\nSwitzerland does not apply the SEVESO directive, OPAM adopts even stricter thresholds for hazardous\nsubstances and includes transport routes, pipelines, and dangerous microorganisms within its scope.\n256\n\nA gas pipeline passes through the PA annex surface site near the LHCb, extending from Switzer-\nland and running along the edge of the main PA surface site towards the north. This installation must\nbe taken into account when designing the surface infrastructure; however, there are no hazardous indus-\ntrial installations located near the PA site, and the main threats might come from the proximity of major\ncommunication arteries (airport and departmental routes) that can transport dangerous goods.\nThere is a gas pipeline approximately 200 m south-west of the PB surface site which poses a po-\ntential risk of an accident involving hazardous materials. The Route de Jussy, classified as a major transit\nroute, runs alongside the eastern boundary of the site. This road is subject to regulations concerning the\ntransport of dangerous goods under the Swiss OPAM ordinance. Apart from these, there are no other\nindustrial installations, facilities declaring pollutant emissions, or safety perimeters within the vicinity of\nSite PB.\nThe PD, PF and PG surface sites are located near major transport routes (highways and departmen-\ntal roads) that are used for regional and national goods transport, including hazardous materials, creating\npotential risks of accidents or spillages. A railway line currently used for passenger transport passes near\nthe PG site. Neither the PD or PG sites have other classified industrial facilities or pollutant-emitting\nsources within a 500 m radius, ensuring a relatively low environmental risk. The classified installation\nfor environmental protection SARL Luc Maulet, which handles inert waste, is located 150 m from the PF\nsurface site near the A410 but poses no risk as its activities are related to the storage of non-recoverable\ninert waste.\nThere are no major roads or highways within a 500 m radius of PH surface site, there are just local\nroads and paths, which significantly reduces transport-related risks involving hazardous materials. There\nare also no classified installations, pollutant-emitting facilities, or other industrial sites in proximity.\nHowever, there is a gas pipeline near the PH site and special attention should be paid to heavy transport\nthat would cross the gas pipeline route.\nApart from the presence of the A40 autoroute located 50 m to the south of the PJ surface site and\nthe associated potential exposure to risks associated with the transport of dangerous goods, there are no\nclassified installations or establishments reporting releases and transfers of pollutants in the vicinity.\nAlso, for the PL surface site, apart from the proximity of the departmental road, no classified\ninstallations or establishments reporting releases and transfers of pollutants were identified within a\nradius of 500 m, including the Swiss territory.\nThe risk of the dam bursting has also been analysed. Such an event could cause water to leak from\nthe reservoir and flood the surrounding areas to a greater or lesser extent. None of the communes in\nFrance where the surface sites are located are at risk of dam failure. In the canton of Geneva, there are\ntwo dams, each downstream of the PB surface site thus, the site is not subject to the risk of dam failure.\nThere is no nuclear installation present near the surface sites, in France and Switzerland. Fur-\nthermore, there is no facility subject to the ICPE nomenclature for activities related to pyrotechnic risk,\nwithin a radius of 500 m around the sites, on French territory. In Lake Geneva, the entire geographical\narea of the Petit Lac is polluted by the presence of munitions dumped between 1948 and 1979. These\nare munitions such as shells, rifle cartridges, aircraft bombs and other explosive residues. The PA and\nPB sites are located 4 km from the shores of the lake. Thus, these surface sites are not subject to the\npyrotechnic risk associated with un-decommissioned munitions in the lake.\nIn summary, some sites are located near transport routes such as autoroutes, departmental roads\nand railways that carry or may carry dangerous goods. There is only a gas pipeline in close proximity\nto the PA, PB and PH sites, which needs to be considered when designing the surface site to minimise\nthe risk of an environmental accident. However, there are no nearby nuclear facilities, polluting facil-\nities or classified industrial facilities within 500m of any surface site, and the risk of a dam failure or\npyrotechnic hazards from munitions in Lake Geneva is minimal. Overall, these sites pose a relatively\nlow environmental and safety risk, with special consideration being given to infrastructure near transport\n257\n\nroutes.\nPolluted sites\nIn France, polluted sites and soils are described as locations that, due to past waste disposal or pollution\ninfiltration, pose ongoing risks to people or the environment. These issues often stem from outdated waste\ndisposal practices, chemical leaks, or accidents. Some areas also experience pollution from atmospheric\nfallout, which has accumulated over many years. It is different from diffuse pollution, like that from\nagricultural practices or car emissions near major roads. Industrial or agricultural activities that could\ncause pollution or risks to the local population are considered classified installations and are subject\nto regulations. The national policy aims to prevent future pollution while managing existing sites and\nensuring they are safe for their intended use. Three complementary databases (BASIAS, BASOL, SIS)\nprovide comprehensive pollution diagnostics, with detailed inventories of polluted sites and their risk\nlevels.\nIn Switzerland, polluted sites refer to locations where waste has been permanently stored, such\nas landfills, as well as areas where waste has been stored or infiltrated. Contaminated sites are those\nthat cause harmful or disruptive effects on the environment or have the potential to do so in the future.\nThanks to waste regulations established in the 1990s, Switzerland has prevented the creation of new\ncontaminated sites, by prohibiting hazardous waste landfills and untreated urban waste. It has put the\ninfrastructure for proper waste treatment in place, ensuring that any waste is handled responsibly.\nFor surface sites, PA, PD, PG, PH and PB there are sites listed in BASIAS, BASOL, SIS or Swiss\ndatabase located within a radius of 500m, however, none of the areas of PA, PB, PD, PF, PG, PH, PJ and\nPL have contaminated sites in immediate proximity.\n3.3.17\nOther projects\nIntroduction\nIn an environment that is subject to continuous development, urbanisation and demographic development\nin a cross-border context, the constraints and opportunities that can emerge from other projects must be\nconsidered when conceiving a new research infrastructure with significant territorial development needs.\nTherefore, the analysis of the initial state of the environment included the establishment of an inventory\nof projects that were planned and constructed and that were potentially relevant to the FCC. Continuous\nmonitoring needs to be implemented to keep this inventory up to date and to act rapidly in case a new\nproject concept is developed, in order to understand if synergies are possible and to avoid potential\nconflicts emerging.\nToday, the most relevant other projects to be considered are:\n\u2013 Geothermal exploitation\n\u2013 Lake crossing\n\u2013 Grand Gen\u00e8ve development project\n\u2013 Grand Annecy development project\n\u2013 Enlargement of the departmental road D903 and integration with the A40 autoroute in France\n\u2013 District heat network in Switzerland\n\u2013 Heat networks in France\n\u2013 Water networks in Switzerland\n\u2013 Water networks in France\n\u2013 Railway network development Nord Gen\u00e8ve\n\u2013 Railway network developments in France\n\u2013 Territorial development in the Dingy-en-Vuache, Vulbens, Valleiry sector\n258\n\n\u2013 Development of Groisy\n\u2013 Development of Ferney-Voltaire and Geneva international sector\nGeothermal exploitation\nThe energy provisioning strategy of the canton of Geneva foresees extensive further development of heat\nrecovery from geothermal sources that range from about 100 m depth to several hundred metres. The\ninvestigations carried out in the frame of the feasibility study reveal no incompatibilities between the\nFCC and existing geothermal installations today. Given the depth of the FCC subsurface structures, it\ncannot be excluded that further geothermal probes lead to potential conflicts. It is, therefore, of utmost\nimportance to implement an early warning system based on the current reference trace that permits\nCERN, as the project owner, to engage with the persons who plan to create such installations. A minor\ndisplacement of the probe can frequently resolve any incompatibility. Should a probe be built without\nknowledge or until the subsurface volumes are properly protected from other projects, the conflicting\ngeothermal probe would have to be removed, and the loss would need to be replaced. In France, no\ngeothermal probes are known in the vicinity of the current reference scenario and no knowledge of a\ndepartment or region-wide geothermal campaign exists. However, the need for reserving the subsurface\nvolumes is equally important on French territory.\nLake crossing\nVarious subsurface lake-crossing projects have been conceived on Swiss territory during recent decades\nin the sector of the FCC, but they are not in its immediate vicinity. Most recently, a metro railway\ntunnel project has been proposed. Such a project can lead to potential synergies as well as to potential\nconflicts. Synergies would exist around subsurface investigations, tunnelling technologies, and excavated\nmaterials management. Conflicts could arise from overlapping construction schedules that could lead\nto increased nuisances, increased difficulties for the management of excavated materials, availability\nissues for engineering companies and workers, and organisation of construction sites and activities. The\nconvolution of the authorisation processes of two almost concurrent projects could eventually generate\nsocietal acceptance issues for both projects. Care must also be taken to ensure appropriate designs for\nboth projects in case the two tunnelling projects overlap, although the depths differ.\nGrand Gen\u00e8ve development project\nTerritorial planning documents in both host countries integrate the continuous development of a \u2018Grand\nGen\u00e8ve\u2019 in their planning documents. In addition, it is a cross-border project that involves substantial co-\nordination. The project involves numerous improvements, such as road and railway mobility, urbanism,\neconomic development, environmental sustainability, housing, social cohesion and cross-border gover-\nnance. The project facilitates the extension of CERN\u2019s scientific activities in a larger zone. It also creates\nconstraints, since the urban development implies stricter preservation of natural and agricultural zones.\nThis rapid evolution needs to be considered in the further developments and authorisation processes of\nthe research infrastructure. The existing planning documents span a time horizon until 2030. Updates\nthat are imminent need to include a future particle collider project in the region. Therefore, the timeliness\nof deciding for an intent to advance with a construction project or not is important. As the example of the\ndepartmental road enlargement in the Nangy sector has shown, the improvement of mobility can be an\nopportunity. However, it can also rapidly jeopardise the feasibility of the current scenario when surface\nsite candidate locations are concerned.\nGrand Annecy development project\nThe regional development around Annecy is captured in numerous planning documents in France with\na long-term horizon of 2050. It concerns mobility, management of natural resources, common use of\n259\n\ninfrastructures and services, preservation of nature and agricultural spaces, support for innovation and\nenergy transition, development of eco-responsible tourism, development of education and training offers,\nsocial cohesion and solidarity, and the development of improved joint governance among municipalities,\npublic and private actors, associations, and the public. This development permits the development of\nsynergies with the FCC that for instance is also aiming at the development of innovation, education and\ntraining as well as high-quality tourism in the region, in particular in the sectors Groisy and Charvonnex\nthat would host an experiment site. Conflicts could potentially emerge from the increased protection\nmeasures.\nRD903 enlargement and A40 integration\nThe project to link the A40 autoroute with the 903 departmental road and to enlarge this road significantly\nin the immediate vicinity of the experiment site PD in Nangy was a potential risk for the feasibility.\nTimely interaction with the Host State administration permitted the development of a suitable solution to\nadapt the surface site to the road project. Depending on the start date and duration of the road construction\nworks, very good coordination between the two projects is required.\nDistrict heat network in Switzerland\nThe canton of Geneva has committed11 to substantially enlarge its heat distribution networks, in partic-\nular with major heat transport axes. The integration of geothermal heat, the GeniLac and the GeniTerre\nsystems ensure heating and cooling capabilities in view of supporting the achievement of climate pro-\ntection goals. This project leads to concrete synergies with the future research infrastructure that will be\nable to supply significant amounts of waste heat that can be injected into this network. No conflicts are\nidentified.\nHeat networks in France\nSeveral district heat networks are starting to be conceived and developed in the perimeters of various\ncandidate surface site locations in France. This concerns, but is not limited to, the PA site in Ferney-\nVoltaire, for example. This development does not generate conflicts, but as the case of Ferney-Voltaire\nshows, it creates concrete synergy potentials. The network in Ferney-Voltaire today profits from the heat\nsupplied by the Large Hadron Collider. A future particle collider would not only ensure continuity, but\nwould permit a significant increase in the heat supplied. Specific studies of the demand have been carried\nout in the frame of the feasibility study and these have confirmed this potential synergy.\nWater networks in Switzerland\nThe regional plans for water treatment in the Geneva region are currently under revision, but details are\nnot available. Although conflicts with the FCC project are unlikely, it is prudent to monitor the evolution\nof the regional water management plan developments. The raw water for cooling the particle collider\nmay have a high fraction of undissolved residuals after multiple recirculation. It is important to ensure\nthat the residual materials, including the total dissolved solids (TDS) in the cooling water, can and will\nbe accepted by the regional water treatment stations.\nWater networks in France\nSimilar to the situation in Switzerland, the knowledge of the planning and evolution of the local water\nnetworks and water treatment facilities is not centrally available. Although conflicts with the FCC project\nare unlikely, it is prudent to monitor the evolution of the regional water management plan developments.\n11https://www.ge.ch/installer-remplacer-chauffage/reseaux-thermiques-structurants-rts-0\n260\n\nFig. 3.55: Overview of the RD903 redevelopment project between the A40 Findrol interchange and the\nChasseurs crossroads.\nAs mentioned above, it is important to ensure that the cooling water can and will be accepted by the\nregional water treatment stations.\nThe water treatment facility in the vicinity of site PD represents an opportunity for the project.\nThe study included the verification of the feasibility of extending the water treatment facility with infras-\ntructures to accept the residual cooling water from the particle collider. In addition, the study revealed\nthat it is, in principle, technically and economically feasible to treat the waste water from the treatment\nplant and to use it for water cooling systems. This generates a potential to reduce raw water consumption\nand creates a socio-economic benefit potential for using treated waste water when the particle collider\ndoes not need it.\n261\n\nRailway network development Nord Gen\u00e8ve\nThe existing L\u00e9man Express is already reaching its maximum capacity and road traffic saturation calls\nfor further development of the railway infrastructure. The development of a north-south railway transport\naxis is a priority of the Geneva canton. A conflict with the FCC is unlikely and the additional transport\nmay, on the other hand, lead to potential synergies for the operation period of the new particle collider\ninfrastructure.\nRailway network developments in France\nThe continuous increase of road traffic, accompanied by traffic saturation and air quality impacts also\ncalls for a development of the railway infrastructure in France in the region concerned by the FCC. This\nmainly involves the L\u00e9man Express lines that pass in the vicinity of some of the FCC surface sites.\nTherefore, the development of the railway system presents opportunities for the project and potentially\nfor the territory.\nTerritorial development in the Dingy-en-Vuache, Vulbens, Valleiry sector\nThe modernisation of the A40 autoroute in the Dingy-en-Vuache, Vulbens and Valleiry sectors is planned\nby the operating company ATMB for between 2023 and 2028. It is important that the construction of the\nFCC starts after the tunnel through the Vuache has been refurbished to avoid limitations. If this is the\ncase, the planned autoroute works do not lead to a conflict with the FCC. However, timely design work\nmust be foreseen concerning the autoroute access for site PD for the FCC construction period. It would\ntake about 10 years to put such access in place.\nThe territorial developments around local mobility (e.g., bike paths), education (e.g., high school)\nand emergency services (e.g., fire brigade) represent attractive opportunities to develop synergies with the\nFCC. Timely engagement with the local, departmental and regional stakeholders is required to leverage\nthe FCC project, support these territorial development projects and integrate them into the surface site\nactivities at PJ.\nDevelopment of Groisy\nA school development project was validated by the department of Haute Savoie in 2023. There is no\nconflict with the FCC project. However, this and related further development projects in Groisy and\nCharvonnex represent attractive opportunities to generate synergies such as the supply of waste heat,\nhigh-quality tourism and the creation of apprenticeship programmes and other cooperation in the educa-\ntion domain.\nDevelopment of Ferney-Voltaire and Geneva international sector\nThe commune of Ferney-Voltaire has recently launched a large-scale redevelopment and modernisation\nprogramme around a new commercial activity zone (ZAC) in the vicinity of the PA surface site. The sup-\nply of waste heat from the existing CERN LHC point 8 (LHCb) site is also integrated in the development\nof a local district heating network. Developments that create synergies with the Geneva airport are also\nenvisaged in this sector. The plan also foresees the creation of high-tech and innovative facilities and a\nsignificant increase in housing capacity. At the same time, on the Swiss side of the border, significant\ndevelopment activities have started in Grand Saconnex. The development of the local tramway system\nconnecting the Geneva international sector (United Nations) with Ferney-Voltaire has been planned.\nAll these local economic development activities can potentially create conflicts with the FCC\nconstruction activities due to a local concentration of construction sites and construction-related traffic.\nA timely coordination with the local actors on the planning of an FCC construction is therefore needed.\n262\n\nFig. 3.56: The future Ferney Gen\u00e8ve ZAC project with an extension of the tram line and terminus located\nless than a kilometre from the PA site.\nOn the other hand, these developments can lead to significant cross-fertilisation in terms of waste\nheat supply, mobility, education and economic developments.\n3.4\nConclusion\nThe feasibility study phase anticipated studies and field investigations that are part of the environmental\nauthorisation process in both countries. Those include, for example, the establishment of an initial state\nof the environment, the identification and prioritisation of noteworthy environmental aspects, the identi-\nfication of indirect and induced connected enabling projects (road accesses, electricity, water and water\ntreatment) as well as informal engagements with the public and their representatives. The scenario de-\nvelopment process has been documented together with variants, and evolution of versions, the reference\nscenario and project invariants.\nThe studies permitted the identification of relevant issues and points requiring attention. The crit-\nical subsurface zones were located and the need for a continuation of subsurface investigations in order\nto establish a comprehensive and detailed 3D model was identified. The latter will serve as input to the\nconstruction process. The results of the preliminary subsurface investigations will provide information\nabout an improved depth and inclination of the tunnel alignment. The initial state analysis revealed that\ndifferent surface sites are subject to very different environmental constraints and present different op-\nportunities for the creation of synergies. The work on the description of the project elements and the\nenvironmental aspects showed that an iterative approach is required due to the long and iterative devel-\nopment of the technical designs. A detailed description of the subsurface construction works is needed as\n263\n\na first step to assess the environmental impacts of the construction phase. A plan for the adequate man-\nagement of the excavated materials according to industrial best practices and suitable for presentation to\nnotified bodies in both Host States needs to be established as soon as the preliminary subsurface inves-\ntigation results are available. The particle accelerator requirements need to be formally documented to\npermit a sufficiently detailed development of the technical infrastructure designs that are needed to assess\nthe environmental impacts. An eco-design strategy and guidelines have been developed that need to be\nintegrated in subsequent project development by putting a project-wide, transverse systems engineering\napproach in place.\nAlthough challenges and environmental sensitivities were revealed and documented, no funda-\nmental showstopper with respect to technical, engineering and environmental feasibility could be identi-\nfied.\nThe reference locations of the surface sites will require very different optimisation, reduction and\nintegration approaches. Where residual impacts cannot be mitigated with these approaches, compen-\nsatory measures may be required. Such measures can differ substantially in terms of type, size and\napproach among the site locations. For the loss of protected agricultural spaces, a 1-to-1 compensation\nby re-creating the lost area by transplanting the topsoil to wastelands or areas with poorer quality is\nenvisaged. Rewilding is another way of compensating for the loss of habitats and biodiversity.\nReforestation around surface sites where forests have been removed is an option, along with new\nforest establishment in previously non-forested areas. Landscape integration and preservation of visibil-\nity can be achieved by half-buried site elements, the separation of sites into different segments and by\nterracing.\nThe use of decarbonised, including renewable energies, aims at keeping Scope 2 emissions low.\nIncremental socio-economic benefits can, for example, be generated by entering energy supply contracts\nand agreements that include the creation of new renewable energy sources and by integrating waste heat\nrecovery and supply from the onset. Location-specific innovation projects can lead to further reductions\nof the environmental footprint and incremental socio-economic benefits such as the use of treated waste\nwater, the creation of soft mobility infrastructures, the development of high-quality tourism and local\nservices around some of the surface sites and the creation of training and education opportunities in the\nproject as a whole and at individual surface sites.\n264\n\nChapter 4\nSustainability\n4.1\nContext\nCERN\u2019s longstanding commitment to sustainability, integrating scientific, environmental, societal goals\nis a guiding principle in the development of a future particle collider infrastructure. The results presented\nin this chapter show the integration of strategies in the scenario development process that align with\nthe Organization\u2019s guiding principles and policies, ensuring that the FCC is conceived as a model of\nresponsible large-scale scientific infrastructure development.\nFrom the outset, the studies and developments for the FCC integrated CERN\u2019s existing guiding\nprinciples for the protection of the environment. It includes topics that extend beyond the biosphere, cov-\nering several aspects of the three sustainability dimensions. Examples include optimising resource use,\nlimiting greenhouse gas emissions, and prioritising sustainable excavation and material reuse. The fea-\nsibility study also considered CERN\u2019s ongoing biodiversity and land-use management efforts, ensuring\nthat construction and operational activities respect local ecosystems. It builds on the results and experi-\nence of CERN\u2019s past and present energy efficiency and waste heat recovery initiatives, aiming to reduce\noverall energy consumption, make responsible use of energy and contribute to regional energy networks.\nWater conservation, noise management, and emissions mitigation are further key elements of the study,\nreinforcing CERN\u2019s goal of balancing cutting-edge scientific progress with responsible environmental\nstewardship.\nAchieving these objectives requires close cooperation with the authorities in both Host States, as\nwell as meaningful engagement with the public. The feasibility study provides the foundation for the\ndialogue with national and regional regulatory bodies, ensuring that the FCC project aligns with envi-\nronmental legislation and sustainability goals in both France and Switzerland. Furthermore, open and\ncontinued discussions with local communities will be essential to address concerns, share best practices,\nand build a collaborative approach to come to an environmental, social, and governance (ESG) frame-\nwork that can ensure the long-term sustainability of such a new research infrastructure.\nBy incorporating lessons from past and existing projects at CERN and by leveraging the innova-\ntions adopted by other large-scale infrastructure projects in science and beyond, the FCC feasibility study\nseeks to set new standards for sustainability in large-scale scientific projects. It builds on the principles\nlaid out in international and national laws and regulations, best practices and CERN\u2019s published policies\nand strategies, integrating best practices in impact avoidance, reduction and mitigation, circular economy\nprinciples, and stakeholder engagement. As such, this chapter lays the groundwork for a potential FCC\nimplementation project that not only advances knowledge creation through fundamental physics research\nbut does so with a firm commitment to long-term sustainability that embraces scientific excellence, the\nenvironment and society.\n4.2\nIntroduction\n4.2.1\nSustainable research infrastructures\nResearch infrastructures (RI) are facilities that provide resources and services for research communities\nto conduct research and foster innovation [93]. An RI can be a single facility, such as, for example,\nthe European Spallation Source (ESS) or the European XFEL, or it can be a facility that is part of an\norganisation that hosts multiple facilities, such as the Large Hadron Collider (LHC) and other particle\naccelerators at CERN (e.g., Antiproton Decelerator, ELENA, PS, SPS) that offer dedicated scientific\n265\n\nresearch opportunities. The Future Circular Collider will be a research infrastructure that is hosted by\nCERN, conceived and constructed by an international collaboration, providing open access to a world-\nwide community of scientists.\nSustainability refers to the ability to maintain an activity at a certain rate or level. It integrates three\nstakes: Society, Economy and Environment(Fig. 4.1). A science programme or project can be considered\nsustainable if it is able to successfully address and complete its scientific core mission satisfying the\nrequirements of three stakes: it obtains a \u2018social license\u2019 to operate [94], it maintains an ecological\nbalance applying an avoid-reduce-compensate sequence [95], and it is affordable in the long term with\nwell-understood and managed risks.\nSociety\nEnvironment\nEconomy\nBearable\nViable\nEquitable\nSustainable\nFig. 4.1: Sustainability dimensions.\nAn appraisal process helps understanding if a programme or project is sustainable and provides\nmeans to identify pathways to make them more sustainable.\nThis process integrates financial and\nsocio-economic aspects. The latter comprise social and environmental benefits as well as negative ef-\nfects including environmental costs. The ISO standard for monetisation of environmental impacts (ISO\n14008 [96]) and the guidelines for determining environmental costs and benefits (ISO 14007 [97]) are\nevidence for the importance of applying such environmental unit costs in environmental and sustain-\nability reporting at the organisation and project levels. Science projects can achieve a positive socio-\neconomic net present value. If their financial performance is too low, the funding model needs to be\nrevised. Projects that are financially viable but have no or little socio-economic benefits need to be\nrevised. Projects that are financially and socio-economically positive can be sustainable (Fig. 4.2).\nEarly and accompanying socio-economic analysis that integrates all sustainability dimensions\nhelps to benchmark variants and versions of project scenarios and permits planning for long-term sus-\ntainability. An RI needs to periodically monitor and track the social, environmental, and economic\nperformance against the initial estimations in order to implement a continuous improvement process.\nIn line with the \u2018Ecodesign\u2019 EU Directive 2009/125/EC [17], sustainable development requires\nproper consideration of all three sustainability elements, including the identification and accounting of\npositive and negative impacts throughout the entire lifecycle of a programme or project. For RIs carrying\nout science missions, at least the following stakes should be considered:\n\u2013 Economy\n\u2013 Scientific excellence\n\u2013 Total costs (capital and operation expenditures)\n\u2013 Risks and residual risks after mitigation\n\u2013 Direct, indirect and induced \u2018value added\u2019 and employment\n266\n\nProject\nto be revised\nUnsustainable\nproject scenario\nGoal:\nSustainable\nproject\nFinancing \nmodel\nto be revised\nFinancial\nPerformance\n(Net Present Value F)\nSocio-economic performance\n(Net Present Value SE)\nNegative\nPositive\nNegative\nPositive\nFig. 4.2: Guidance for the sustainability of public investment projects. From Ref. [98].\n\u2013 Quantified incremental economic benefit potentials\n\u2013 Society\n\u2013 Quantified incremental social benefit potentials\n\u2013 Common good value (the value of the science mission as perceived by people)\n\u2013 Territorial compatibility\n\u2013 Social license\n\u2013 Environment\n\u2013 Quantified negative externalities\n\u2013 Quantified incremental environmental benefit potentials\n4.2.2\nApproach\nA new particle collider and its enabling technical infrastructure represent significant long-term invest-\nments for participating countries and funding partners. An appraisal process is necessary to gain an\nunderstanding of the cost drivers and benefit levers. Reducing the former, developing the latter and\nconceiving a long-term financing model that relies on international collaboration are required to ensure\nlong-term sustainability from the conceptual phase onwards. Funding agencies, science strategy bodies\n(e.g., ESFRI), national notified bodies in charge of issuing authorisations and investment banks who po-\ntentially grant long-term loans for publicly funded projects (e.g., EIB), request evidence for the project\u2019s\nviability. The structured process of assessing the case for proceeding with an implementation preparation\nproject and validating the project\u2019s viability is called \u2018project appraisal\u2019.\n267\n\nThis chapter also compiles a set of regulatory frameworks and appraisal guidelines that exist at the\nEuropean level, in France and in Switzerland to provide a landscape of the sustainability requirements\nthat govern the planning and implementation of new research infrastructure projects with strategic impor-\ntance and territorial development needs at CERN. In the countries that are part of the European Research\nArea (ERA), legal frameworks govern the compliance with sustainability aspects. Other countries such\nas Australia, the UK and the USA are still largely applying panel-based project decision taking, although\nthe UK does carry out ex-post evaluations on a case-by-case basis and Australia is evaluating the sustain-\nability of research infrastructures periodically. Sustainability and environmental criteria such as climate\nconsiderations are increasingly being incorporated into proposal design and assessment. Switzerland\nhas recently made sustainability aspects explicit for CERN\u2019s strategically important projects with terri-\ntorial development in the update of the law [99, 100] for the encouragement of research and innovation\nthat introduces an authorisation process at federal level. The \u2018Ordonnance concernant l\u2019approbation des\nplans des constructions et installations du CERN (OCIC)\u2019 [101], the prescription on how this plan for\nthe authorisation process is to be implemented, has been issued for public review in February 2025. In\naddition to the commonly known environmental topics (e.g., air, water and soil) it includes the need for\nthe assessment of the impacts on the climate and specific measures to comply with climate protection\nlaws.\nConsideration of quantitative environmental externalities1, both positive and negative, is still an\nemerging approach in the domain of research infrastructures unless it is explicitly required by national\nlegislations and governed by national guidelines. Such a \u2018wider\u2019 socio-economic analysis is, however,\nalready common practice in the general infrastructure project appraisal in numerous European countries\nsuch as France [102], Germany [103, 104], Italy and Switzerland and at EU level through EC funding\nconditions for numerous sectors, e.g., Connecting Europe [105], transport [106], energy [107], regional\ninvestment projects [108] as well as nature preservation and restoration [109].\nMethodologies for assessing public investment and assuring that a project contributes to the in-\ncrease of public welfare2 exist across different policy sectors and institutions [110, 111] including en-\nvironmental impacts [112] are already used for research infrastructure projects including particle ac-\ncelerators like the ALBA light source [113], the SOLEIL light source [114], the DESY/PETRA III\nsynchrotron [115], the CNAO hadron therapy facility [116], the LHC [117], High Luminosity LHC (HL-\nLHC) [118\u2013120] and the Compact Linear Collider (CLIC) study [121]. The Future Circular Collider\n(FCC) [122] study has, in particular, devoted significant resources to this topic over a time frame of al-\nmost ten years and has contributed to the advancement of the research infrastructure appraisal process at\nan international scale through scientific contributions to the field and participation in collaborative impact\nassessment projects at EU level. The approach is also used for other science facilities such as the Einstein\nTelescope [123], the Paris Saclay heat supply facility [124], the Nantes University hospital [125], and by\nthe Commonwealth Scientific and Industrial Research Organisation (CSIRO) [126] to evaluate a number\nof different science programmes. Ever more RIs, such as the Square Kilometre Array, are considering\nthe approach in view of planning for sustainability [127]. Environmental factors are increasingly being\nintegrated into these assessments [98, 128\u2013130]. A comprehensive socio-economic impact assessment\nis needed when a new research infrastructure project proposal requests being entered into the European\nStrategy Forum for Research Infrastructures (ESFRI) roadmap [131] as indicated by the 2026 roadmap\nguide (see page 25 of Ref. [132].\n1An environmental externality is a cost or benefit that affects a third party who didn\u2019t choose to incur that cost or benefit,\nspecifically in relation to the environment.\n2Public welfare refers to the collective well-being of society that is promoted through public services and institutions,\naiming to ensure equity, social cohesion, and access to essential goods and services for all. Paraphrased summary from Florio,\nM. (2019). Public Enterprises: Resurgence and the Future of the Public Sector. Springer.\n268\n\n4.2.3\nThe context in Europe\nResearch infrastructure long-term sustainability at European Research Area (ERA [133]) level is primar-\nily guided by the European Strategy Forum for Research Infrastructures (ESFRI) [134,135] 3\nEU regulation 2021/695 [136] defining the Horizon Europe Framework Programme for Research\nand Innovation explicitly includes requirements to address global challenges, including climate change\nand the United Nations Sustainable Development Goals (SDGs).\nEU member states typically translate and integrate the strategies, policies, and guidelines into their\nnational roadmaps and plans in addition to their existing national policies.\nA robust long-term vision is a prerequisite to successfully and sustainably operate a research in-\nfrastructure. Therefore, ESFRI issued a number of recommendations and actions [137].\nScientific excellence is the condition sine qua non. However, sufficient funding and sustainable\nfunding models, required across the entire life cycle, are indispensable for a successful strategy for a new\nresearch infrastructure. Together with adequate human resources, it is crucial for the operational phase.\nEffective governance is another key element for ensuring long-term sustainability. Moreover, RIs should\ncontribute to their sustainability by contributing to their carbon neutrality in order to support the carbon\nneutrality goals at the national level. It is worth mentioning that carbon neutrality accounting is taking\nplace at a national level.\nWhile the current recommendations place an explicit focus on scientific excellence, financial sus-\ntainability and societal acceptance, the call for comprehensive sustainability and impact assessment im-\nplicitly includes all environmental aspects. The recommendations also spell out that RIs should dedicate\nsufficient resources to periodically evaluate and communicate their socio-economic performance to var-\nious audiences. CERN\u2019s pioneering activities in this domain are explicitly mentioned by the ESFRI\nguide [138], encouraging national authorities to support the approach in cooperation with experts in the\nfield.\nThe ESFRI policy brief [139] details the need to tailor the impact assessment to the specific project\nand requests the inclusion in the roadmap of project proposals that aim for implementation on a ten-year\ntime frame that the wider socio-economic impact assessment is provided. Following the OECD defi-\nnition [140] these impacts comprise \u201cthe extent to which the intervention has generated or is expected\nto generate positive or negative, intended or unintended, higher-level effects\u201d. The European Commis-\nsion [141] states that \u201cThe term impact describes all the changes which are expected to happen due to the\nimplementation and application of a given policy option/intervention [such as investment in a Research\nInfrastructure and its activities]. Such impacts may occur over different timescales, affect different actors\nand be relevant at different scales (local, regional, national and EU)\u201d. Ex-post assessment is needed to\ndetermine whether the intended objectives and the ex-ante estimations have actually been achieved.\nEU Regulation 2021/1060 of the European Parliament and of the Council of 24 June 2021 lay\ndown common provisions on the European Regional Development Fund, the European Social Fund Plus,\nthe Cohesion Fund, the Just Transition Fund and the European Maritime, Fisheries and Aquaculture Fund\nand financial rules for those and for the Asylum, Migration and Integration Fund, the Internal Security\nFund and the Instrument for Financial Support for Border Management and Visa Policy. According to\nArticle 100 of Regulation (EU) No 1303/2013 [142], a major project is an investment operation com-\nprising \u201ca series of works, activities or services intended in itself to accomplish an indivisible task of\na precise economic or technical nature which has clearly identified goals and for which the total eligi-\nble cost exceeds EUR 50 000 000 [. . . ]\u201d. A socio-economic impact assessment of such major projects\nis recommended. The European Commission Economic Appraisal Vademecum 2021-2027 [143] cap-\ntures the general principles and provides sector application examples for impact assessment, including\n3ESFRI (https://www.esfri.eu) was established in 2002 with the purpose of developing a European approach to Re-\nsearch Infrastructure policy as a key element of the emerging European Research Area (ERA). Further Research Infrastructures\ncontribute to this effort in the frame of the EIROforum and the European Research Infrastructure Consortium (ERIC).\n269\n\nresearch and innovation in Annex I. It extends and complements the common provisions regulation that\nrecommends cost-benefit analysis in line with EU regulation (EU) No 207/2015 [144]. The methodol-\nogy is explained in detail in the \u2018European Commission Guide to Cost-Benefit Analysis of Investment\nProjects\u2019 [108].\nClimate change adaptation and mitigation and disaster resilience are covered by this regulation.\nFor instance, the volume of greenhouse gas (GHG) externality 4 and the external cost of carbon is ex-\nplicitly included, and alignment with the EU 2050 decarbonisation objectives is required. Concerning\nclimate adaptation, the costs of measures aiming at enhancing the resilience of the project to climate\nchange impacts that are duly justified in feasibility studies should be included in the economic analy-\nsis. The benefits of these measures, e.g., measures taken to limit the emissions of GHG or enhance the\nresilience to climate change, weather extremes and other natural disasters, should also be assessed and\nincluded in the economic analysis, if possible quantified; otherwise, they should be properly described.\nAn analysis of sustainable development (environmental protection, resources efficiency, climate\nchange mitigation and adaptation, biodiversity and risk prevention) should be covered. An analysis\nof the options considering technical, operational, economic, environmental and social criteria for the\nlocation of the infrastructure is requested to be in a feasibility study. This also describes the project\u2019s\nconsistency with the applicable environmental policy. Considerations should include resource efficiency,\npreservation of biodiversity and ecosystems, reduction of GHG emissions, and resilience to climate\nchange impacts. The process needs to fulfil the Directive 2011/92/EU, that defines the environmental\nimpact assessment (EIA) process, which ensures that projects likely to have significant effects on the\nenvironment are made subject to an assessment prior to their authorisation. Therefore, the total costs of\nthe negative environmental impacts and their compensation have to be included. Environmental benefits\ncan be assessed and added as well. They include, for instance, contributions to improve water supply and\nsanitation, waste management, energy capacity and stability, transport, ports (airports, seaports, inter-\nmodal), research and innovation and broadband communication.\nThe appraisal process aims to assess if a project will contribute to overall social welfare and\neconomic growth, taking into account benefits and costs to society. The EC [108] and UNIDO [145]\nhandbooks focus on economic and societal topics, although aspects such as assessment of the environ-\nmental externalities are typically part of project appraisal as required per EU regulation. For instance,\nthe shadow cost of carbon and the GHG emissions are shown in project appraisal examples. Eventu-\nally, the requirements for appraisal are defined for each project, specifically by the notified body for\nthat project. For instance, to obtain funds from the European Investment Bank (EIB), a comprehensive\nappraisal study including the positive and negative environmental externalities is required. The EIB pub-\nlished a guide [146] dedicated to this topic that includes references for the shadow cost of carbon and\nalso comprehensive calculation examples and guidelines for capturing environmental externalities.\nOther requirements emerge, for instance, from applying to the Connecting Europe Facility (CEF).\nThe InvestEU regulation introduces climate, environmental and social sustainability as elements in the\ndecision-making process when applying for the InvestEU Fund. The process is also a requirement in\nthe framework of the preparatory phase of ESFRI projects. The European Bank for Reconstruction\nand Development (EBRD) requires project assessment with potentially relevant greenhouse gas (GHG)\nemissions of more than 25 000 tonnes of CO2(eq) per year with respect to a baseline of 100 000 tonnes\nof CO2(eq) emissions per year. National requirements differ substantially from each other, requiring\nassessments for investment projects with public funding as low as for instance 300 000 euros in Lithuania.\n4An externality is a cost or benefit that is caused by one party but financially incurred or received by another. Externalities\ncan be negative or positive. A negative externality is the indirect imposition of a cost by one party onto another. A positive\nexternality, on the other hand, is when one party receives an indirect benefit as a result of actions taken by another.\n270\n\n4.2.4\nThe context in France\nIn France, the \u2018Code de l\u2019environnement\u2019 [147] guides the approach to develop a sustainable project\nscenario in the frame of an environmental evaluation process that is part of the authorisation of the\nproject. The term \u2018environment\u2019 is to be understood in its original meaning and in a wide sense: the\nsurroundings and conditions in which the project will be placed.\nThe goal of the process is to develop a feasible and sustainable project scenario following the\n\u2018avoid-reduce-compensate\u2019 method (French: \u00e9viter-r\u00e9duire-compenser, ERC), which is anchored in Eu-\nropean regulations and which is implemented in French law [148]. As a consequence, the project scenario\nto be authorised aims at a net positive value (see Fig. 4.3).\nImpacts of the\ninitial project\nscenario\nUnavoidable \nimpacts\nAvoidance\nmeasures\nResidual impacts\nReduction\nmeasures\nResidual impacts\nCompensation\nmeasures\nNet gain\nGain\nLoss\nInitial state\nof the\nenvironment\n> Development of the project scenario >\n\u2022\nAvoid:\nModify the project to suppress a negative impact.\n\u2022\nReduce:\nReduce as much the extent, duration and/or intensity of an impact that cannot be avoided.\n\u2022\nCompensate: Contribute with direct or indirect positive values to noteworthy negative effects that cannot\nbe avoided and sufficiently reduced.\nFig. 4.3: \u2018Avoid-Reduce-Compensate\u2019 approach for iterative development of a sustainable project sce-\nnario to achieve an ecological balance and, as far as possible, a net gain [13].\nThis approach of iterative development of variants and versions that are continuously improved is\nalso documented by the international standard ISO 14001 concerning environmental management. It de-\nscribes the Plan-Do-Check-Act (PDCA) model as an iterative process to ensure continuous improvement\n(ISO 14001, Step by Step, Chapter 1).\nConsidering that programme and project evaluation in France is compulsory for public investments\nthat exceed 20 million euros and a second assessment is required for investments that exceed 100 million\neuros, the national assembly tracks and reports on such projects every year using a standard information\nsheet approach that includes the net present value as an overall sustainability indicator and the greenhouse\ngas emissions avoided. Such information is published as an annex of the annual budget law [149]. In\n2023, 13 research investments were subject to comprehensive socio-economic evaluations.\nThe evaluation concerns the entire project throughout all life cycle phases. It is understood that\nthe level of description detail for individual phases and project segments can initially differ. The process\naccompanies the project throughout its entire lifetime. Consequently, the documentation needs to be\nregularly updated. The process records the initial state of the environment, including nature and a variety\nof other topics such as urbanism, public health, population safety and economic impacts.\n271\n\nThe process actively identifies and assesses relevant effects on the project environment (environ-\nmental impact analysis) and gives input to the design process following the avoid, reduce and compensate\nsteps. The process includes the involvement of the population via, for instance, an informal dialogue and\nparticipation phase and a formal public consultation processes (\u2018d\u00e9bat public\u2019) and public inquiry (\u2018en-\nqu\u00eate publique\u2019). The latter processes is carried out with national notified bodies.\nTo capture the sustainability performance properly, the French government requires a socio-economic\nevaluation for each project that is funded via public investments of more than 20 million euros. The eval-\nuation must be carried out according to the guidelines of the \u2018Secr\u00e9tariat g\u00e9n\u00e9ral pour l\u2019investissement\u2019\n(SGPI) [150]. Projects with a total public investment of more than 100 million euros are subject to a\nsecond expert assessment, on which the SGPI provides an assessment to the French parliament and the\nPrime Minister as well as to the minister under whose responsibility the project falls.\nThe socio-economic evaluation comprises a detailed description of the project, its variants and\nalternatives, the key characteristics, the implementation schedule, a list of relevant socio-economic indi-\ncators, a list of indicator values showing how the project performs with respect to public policies (e.g.,\nclimate impact reduction objectives), the financial plan, compliance with laws and regulations and a risk\nregistry.\nUntil 2020, socio-economic evaluations of programmes and projects included only limited envi-\nronmental aspects such as habitats and green spaces. The ever-growing importance of more global topics\nled to a broadening of the positive impacts and negative externalities covered. The 2023 impact assess-\nment guide in France [150] explicitly includes all environmental aspects that are project relevant such\nas CO2 equivalent emissions, noise, air pollution, water use and pollution, soil use and pollution and re-\nquires them to be associated with monetary values and to quantify the positive contributions in monetary\nterms. For instance, the legal value of one tonne of CO2 for the socio-economic evaluation has been set\nto \u20ac32 (base year 2010) in the 2023 guideline, which corresponds to about \u20ac40 in 2024. Despite this\nvalue, the annex that indicates the guidelines of converting non-tradeable goods and externalities into\nmonetary terms indicates a progression of the shadow cost of carbon \u20ac250 per CO2(eq) to 2030 and\n\u20ac775 per tCO2(eq) in the year 2050. This progression is in line with the EIB recommendations of the\nshadow cost of carbon.\nThe socio-economic evaluation of the FCC is based on a standard cost-benefit analysis, reporting\na net present value and a benefit/cost ratio based on the comparison of discounted total costs and benefits\nover a defined observation period. Costs and benefits were quantified with respect to a \"counterfactual\nscenario\" in which CERN operates the LHC until its expected end of life and continues to act as a\nscientific research platform with the existing particle accelerator complex. Noteworthy positive and\nnegative direct effects and externalities including environmental effects were taken into consideration for\nthe entire life cycle of the project.\nFor the social discount rate (SDR), the 2023 guidelines for socio-economic impact assessment in\nFrance [151] recommend using a value of 3.2% for projects with a lifetime up to the year 2070. However,\nfor very long-term and low-risk projects such as research infrastructures, a lower social discount rate in\nthe range of 2.5% can be justified. For the FCC CBA, economists selected a SDR of 2.8%, based\non the weighting of the SDRs in each individual CERN Member State considering its annual financial\ncontribution to CERN.\nIf there is a \u2018d\u00e9claration d\u2019utilit\u00e9 publique\u2019 (DUP), which governs the authorisation process for\npublic investment projects, the socio-economic evaluation is part of the legally required \u2018enqu\u00eate publique\u2019\nfiles to obtain project authorisation.\nThe socio-economic evaluation has to be updated regularly, following the iterative approach of\nrefining the project scenario and comparing expected effects to the actual effects once the project is\nimplemented (\u2018ex-post\u2019 analysis).\nA project can be considered sustainable if both the socio-economic and the financial net present\n272\n\nvalue are positive. In addition, the social discount rate applied should be larger than the average weighted\ncost of the capital needed to finance the project. This can be verified by determining the so-called Internal\nReturn Rate (IRR), which is closely linked to the calculation of the net present value. It expresses at\nwhich value of the social discount rate the net present value of the project would become zero. For\ninstance, if the loans for the project are granted at 3% but the net present value becomes zero at only 5%,\nthe condition would be satisfied.\nIf the project does not generate revenues, i.e., in the case of a research infrastructure for funda-\nmental scientific research, no financial net present value can be provided, a positive socio-economic net\npresent value and an internal return rate higher than the cost of the capital support the sustainability con-\ndition. If the socio-economic net present value is negative and the financial net present value is positive,\nthe investment may be financially viable, but it is not recommended from a societal point of view.\n4.2.5\nThe context in Switzerland\nThe authorisation process in Switzerland is based on guiding principles that require the demonstration of\ncompliance of the scenario with all applicable, individual laws and regulations. All laws and regulations\nthat would apply to the project need to be identified and explicitly listed. It is considered best practice\nto follow the Avoid-Reduce-Compensate approach as required in France and Europe with continuous in-\nvolvement of notified bodies, public administration services, and the population. It is to be accompanied\nby monitoring and continuous improvement measures.\nWith the recent update of the law for the encouragement of research and innovation (LERI) [152]\nand the development of a dedicated plan for new constructions and installations of CERN [153], guide-\nlines with respect to the sustainability of research infrastructures become more specific.\nThe consumption of land, in particular, high-quality crop-rotation arable land that is regarded as\na precious resource, needs to be avoided. Where this cannot be achieved, the residual consumption of\nsuch land that is registered in a national inventory needs, in principle, to be compensated. Therefore,\nalternatives and variants of the project need to be documented and assessed. Compensation can, for\ninstance, be achieved by stripping the topsoil of the original land affected and using that soil for creating\nhigh-quality arable land within an agreed geographical perimeter, for instance on wastelands or degraded\nsoil. The authorities facilitate the process of identifying suitable compensation areas and administrative\nprocesses.\nThe sector plan for CERN\u2019s constructions and installations with territorial needs (PS CERN) [154]\nhighlights a number of topics that need to be considered when developing new projects:\n\u2013 Water-bearing layers need to be protected and should not be used to provide raw water for cooling\npurposes. Care must be taken not to pollute water-bearing layers or to mix the water of superim-\nposed water-bearing layers.\n\u2013 Exclusion buffers next to watercourses protect the habitats.\n\u2013 Forest clearings are generally forbidden in Switzerland. An exemption can only be granted in\nexceptional cases for installations that are in the public interest.\n\u2013 Measures need to be taken to manage rainwater and used water to avoid flooding and polluting the\nenvironment. The same holds for the management of water used to extinguish fires.\n\u2013 Limitations for dust and particle emissions need to be respected.\n\u2013 Limitations for noise emissions need to be respected. Noise emission limits in Switzerland are\nabsolute and defined for different sensitivity zones as opposed to France, which considers noise\nlimitations in excess of existing background noise.\n\u2013 Measures need to be taken to manage waste of any kind during all phases of the project.\n\u2013 The national and cantonal energy and climate protection goals are to be taken into consideration\nduring the planning, construction and operation of future research installations. Energy consump-\n273\n\ntion is to be reduced to a minimum compatible with the capacity to fulfil the scientific research\ngoals.\n\u2013 The emission of greenhouse gases is to be minimised within the boundaries needed to meet the\nscientific goals and requirements of the project.\n\u2013 The design and implementation of technical systems have to integrate the optimisation of energy\nefficiency and the recovery and use of waste heat. The capacities and characteristics available for\ninternal and external use need to be identified and documented.\n\u2013 Buildings must comply with the national energy efficiency regulations.\n\u2013 In general, any optimisation and minimisation effort is understood to be conditioned by the techni-\ncal feasibility and economic viability. These efforts must always be compatible with the feasibility\nof achieving the specified scientific research goals.\n\u2013 A mobility plan that supports the national and cantonal climate plans is to be developed. Parking\nspaces are to be optimised, in line with the applicable regulations.\n4.3\nMethodology\nThe study adopted the approach and methodology to carry out a comprehensive, wider quantitative sus-\ntainability assessment based on the well-established cost-benefit analysis methodology [155] defined by\nthe European Commission, the European Investment Bank and as described by national guidelines such\nas the one in France [150]. Such an assessment includes the identification and quantification of costs,\nbenefits, and positive and negative externalities.\nThe goal is to present an implementation scenario that is likely to be long-term sustainable and for\nwhich sustainability level can be continuously improved with respect to an initial forecast that serves as\na baseline. The approach permits the analysis of variants and sustainability boundary conditions to be\nestablished.\nFollowing a lifecycle approach, it is a best practice to develop an initial cost-benefit assessment as\nearly as possible at the pre-feasibility stage and to update it regularly as long as the key project features\ncontinue to be adjusted during the design phase and even during the implementation. This approach\nhelps to deal with the challenge that exhaustive coverage of costs and benefits cannot be achieved and to\nfocus on gaining a good understanding of the key sustainability enablers and risks.\nSustainability analysis is an ingredient of informed decision-making. Project and sustainability\nappraisal of the scientific research project does not, however, capture the opportunity and value of the\nunderlying scientific mission. The indicators must therefore not be used to compare research projects or\nto make an investment choice between several projects.\nTo be useful during project authorisation, implementation and operation, the project must plan\nperiodic sustainability monitoring and tracking throughout its entire lifetime and implement an iterative\nimprovement process following the standard \u2018Plan-Do-Check-Act\u2019 principle either at the infrastructure\nlevel or for new programmes and projects.\nLife Cycle Assessment (or analysis) (LCA) [156, 157] is a methodology that is suitable for in-\ndividual project segments. It allows assessment of a set of environmental aspects that are relevant for\nachieving sustainability. Its goal and scope must be well-defined, and its results must be integrated in\nthe overall project and sustainability appraisal. When carrying out an LCA, care must be taken to be as\nspecific as possible and to exhaustively document the scenario variant and version assessed, the assump-\ntions, the input parameters, the data quality and the allocation procedure (algorithms and tools) to ensure\nthat the results have a meaningful value for appraisal. LCA is not able to capture all relevant environ-\nmental aspects and does not therefore replace an environmental impact evaluation. It can therefore not\nbe used to report on the overall environmental performance of a project.\nFor a comprehensive sustainability assessment, a quantitative Cost-Benefit Analysis (CBA) method\n274\n\nbased on state-of-the-art economic knowledge that integrates total costs, negative externalities (including\nenvironmental ones), industrial, social and environmental benefits is the preferred and adopted approach.\nA more complete description of the approach is provided in Section 4.5.\nProject developers have to keep up to date with national and international regulations and legal\nframeworks in the subsequent design and preparatory phase. They must continuously improve their\nknowledge about state-of-the-art project appraisal methods and the development of approaches to con-\nvert positive and negative impacts and externalities into quantitative terms suitable to report an overall\nsustainability indicator in the form of a project\u2019s net present value and benefit-cost ratio. For this reason,\nas long as additional knowledge and assumptions about the project scenario and the project\u2019s key features\nare developed, the Benefit-Cost Ratio (BCR) and the Internal Return Rate (IRR) evolve throughout the\nlifecycle phases.\n4.4\nSocio-economic sustainability enablers\n4.4.1\nImpact pathways\nSocio-economic impact pathways are a valuable inventory of sustainability enablers. Based on the con-\ncept of \u2018Theory of Change\u2019 [158], the RI-PATHS EU-funded project has developed a toolkit [159], fed-\nerating research infrastructures across various domains, including particle accelerator facilities such as\nALBA, CERN and DESY. The main pathways typical for particle accelerator-based facilities are shown\nin Fig. 4.4. This section outlines briefly how such pathways can lead directly to benefits and positive\nexternalities, and gives some specific examples.\nScience\nproducts\nTraining & \neducation\nIndustrial \nspillovers\nICT\nCultural \ngoods\nPositive\nenvironmental\nexternalities\nPublic\ngood\nvalue\nFig. 4.4: Main socio-economic impact pathways that are sustainability enablers of particle accelerator\nand particle physics research infrastructures.\nFuture projects are highly encouraged to carry out a comprehensive charting of the impact pathway\npotentials and develop sustainability-enabling measures around such a systematic exploration and design\nactivity.\nFundamental Physics Knowledge\nScience is formalised knowledge that is rationally explicable and tested against reality, logic and the\nscrutiny of peers, is a global public good [160]. Ultimately it is the main output of research infrastruc-\n275\n\ntures. In our transforming society, knowledge is about to become the basic economic resource, gradually\nreplacing capital, land and labour. There is evidence that the public sector has and is continuously fund-\ning much of the innovative science that stimulates private sector responses [161]. But what is the value\nof that knowledge that fundamental science projects generate? Are continued investments in new particle\naccelerator projects for scientific research sustainable in the perception of those people who do not di-\nrectly use those instruments and who do not directly profit from the generated knowledge? Which means\nexist to capture the value of such investments?\nParticle accelerators for fundamental science may or may not generate knowledge that can be di-\nrectly used by society. Other particle accelerators, such as synchrotron light sources, typically serve\napplied research. This means that a lower bound for the value of the knowledge generated can be quanti-\nfied in terms of the cost of the publications, the fees charged for the use of the facility and the resources\nthat the users invest in this research. The approach is based on the assumption that the research results\neventually end up in products and services that society uses. An example is the characterisation of the\nCOVID-19 virus structure at the BESSY-II synchrotron [162]. Particle accelerators and colliders that\nserve curiosity-driven research, such as the LHC or the Electron-Ion Collider, cannot use this model\nsince it is not obvious how the knowledge gain leads to direct societal applications. There exists, how-\never, no doubt that the scientific outcomes advance society. This view is shared by the majority of people,\neven if the asset is not directly used.5\nEvidence for the validity of the approach is available through the award of several Nobel Prizes in\neconomics for advances in this domain. It is proof that this value generation process is of fundamental\nimportance for society and welfare economics [163\u2013168].\nTo capture the value that science missions and research infrastructures represent to laypeople who\ncan not directly use them, methods that originally have been developed to elucidate the public good\nvalue of outdoor recreational spaces [169], to identify suitable value levels for environmental protection\nmeasures [170], to determine adequate levels of environmental incident mitigation measures [171] and\nto determine investment levels to protect natural and cultural heritage can be used. This approach has\nfirst been taken to estimate the value of the LHC project [172], then for the HL-LHC project [173]\nand now for the FCC [174]. The approach has recently also been adopted by an atmospheric research\ninfrastructure [175]. Briefly, the value that people associate with a science project can be captured by\nestimating their willingness to participate financially using well-established approaches in economics,\nsuch as contingent valuation, also referred to as \u2018stated preference\u2019.\nThe valuation of non-market impacts is challenging but could be undertaken wherever possible,\nand the \u2018EU better regulation toolkit\u2019 indicates the instruments for it [176]. This will enable a better un-\nderstanding of the public perception towards the science vision and test the validity of the public funding\nsustainability hypothesis, i.e., what level of periodic investment is justified in the public perception. To\ndesign, plan and carry out a public good value estimation, experts in the domain and qualified companies\nneed to be employed. It is important to ensure that such a willingness to participate in analysis, typically\nbased on surveys, is carried out independently, without the influence of the project owner and according\nto the internationally established guidelines on ethics and the quality standards required of survey-based\nanalytics. Examples of this approach can be found in Refs. [174,177].\nDepending on the number of countries or funding agencies that would carry out the project, such\na survey can require substantial resources. Economists, therefore, use techniques based on the \u2018Benefit\nTransfer Method\u2019 [178] to estimate the perceived value of a large population based on the identification\nof only a few significant parameters that can be derived from a limited number of samples. These\nparameters may be different for different projects. Therefore, such a study requires a pilot phase to\ndetermine the significant parameters, followed by a mass survey to determine the value that the public\n5The notion for this concept is the \u2018public good\u2019 as opposed to the \u2018common good\u2019 that is jointly used. Examples of common\ngoods are fish stocks in the ocean and public roads. Examples of public goods are knowledge, natural and cultural heritage,\nopen software and datasets and even tangible assets such as street lighting.\n276\n\nassociates with the investment.\nIf the estimated willingness to financially participate (WTP) is larger than the actual or expected\ncontribution to the planned new project, the public good value of the funded infrastructure can be con-\nsidered consistent with the financial participation and, therefore, can also be considered justified. If the\nWTP is less than the actual or planned contribution, there is a discrepancy between the value perceived\nby the people and the contribution supplied. In this case, the project should be revised.\nSustainability through education and training\nParticle accelerator and experimental physics research infrastructures offer the possibility to engage peo-\nple at all education and training levels, from apprentices to post-doctoral researchers. If people have the\nopportunity to actively participate in the design, construction and operation of such projects and pro-\ngrammes, they enjoy benefits that translate directly into a 2 to 10 % lifetime salary premium [122, 179]\ncompared to their peers who were enrolled in conventional training programmes at schools and univer-\nsities. A dedicated programme to integrate people after their active time in a research facility into the\nlabour market in their country or region of origin can significantly improve the return of investment for\nthe participating country or region [180].\nSustainability through participation of international science communities\nInvolving a significantly large and continuously growing community of scientists and engineers in the\nform of collaborative research projects over long periods of time ensures the long-term sustainability of\na science project or programme. The reasons are\n\u2013 The personnel costs are distributed over many contributing organisations and countries.\n\u2013 A stable generation of scientific products [181,182] (i.e., books, peer-reviewed articles, pre-prints\nand technical reports, proceedings and presentations) can be guaranteed.\n\u2013 The knowledge can be effectively transferred into lasting education curricula through publications\nand direct training over generations.\n\u2013 Impact can be generated through the training of early career professionals (see previous section).\nHigh value is mainly achieved by ensuring that the science products generated directly by the research\nproject or programme are taken up effectively and cited by an even larger second-tier community. Open\nAccess publication of trusted (peer-reviewed) publications is a pre-requisite to generating research in-\nfrastructure sustainability through scientific product generation. Finally, the concept of Open Innovation\nthat involves a large number of knowledge domains around a scientific core mission will ensure that the\nprobability of knowledge generation that is stimulated through the challenges of the science mission will\neventually spill over to society in domains that are immediately relevant to them [183].\nSustainability through industrial spillovers\nIndustrial spillovers from science projects generate benefits directly for industry and society [184\u2013186].\nThis impact pathway is most effective if science projects construct their instruments and infrastructures\nin collaboration with industrial partners [187\u2013189]. It works best when companies work closely with the\nresearch project to develop technologically intensive solutions and deliver non-standard services [190].\nThis approach is more laborious than a conventional client/supplier relationship since it requires ex-\nchanges of ideas and knowledge, the development of integrated processes, the mutual adaptation of\nworking methodologies, and risk sharing. This process, however, leads to the creation of lasting pro-\ncesses, products, and services that the industrial partners can leverage in other markets with earnings\nmultipliers above 3 and effects that can last between five and eight years. Lasting territorial effects have\nalso been reliably documented [191,192].\n277\n\nSustainability also depends on the design of the science mission: short-lived and non-upgradable\nprogrammes will lead to lower and shorter-lasting industrial spillovers than long-lasting programmes\nthat are characterised by periodic upgrades and operational efficiency improvement measures involving\nindustrial partners in continuous challenge-based activities.\nIndustrial spillovers can also lead to lasting positive environmental externalities. The challenge of\nreducing the carbon footprint and environmental impact of the construction of a new particle accelerator\nfacility creates an opportunity for industrial innovations in numerous construction-related domains. For\ninstance, it creates a potential of developing or putting in place low-carbon concrete and other construc-\ntion materials production facilities. It serves as a pilot platform for improved construction techniques,\nsuch as using natural resources such as wood and compressed earth. Showcasing the application cre-\nates market interest. Developing processes and products for the use of excavated materials can generate\nbenefits significantly beyond the needs of the research infrastructure project since the management of\nconstruction waste is a challenge that society faces and for which conventional construction projects typ-\nically have insufficient time and budget. Eco-design based industrial architecture is another emerging\ndiscipline for which particle accelerator facilities are suitable early adopters. Environmental benefits can\nalso be generated in the area of technical infrastructures that are developed with industrial partners. They\ninclude:\n\u2013 More efficient refrigeration systems which find their application, for example, in gas liquefaction\nand transport.\n\u2013 More efficient water cooling systems (adaptive water intake, use of waste water).\n\u2013 Improved electrical systems (loss reduction via DC-based systems.\n\u2013 High-speed power control management.\n\u2013 Short and medium-term energy storage.\n\u2013 Adaptive and machine learning infrastructure operations.\n\u2013 Waste heat buffering and supply.\nSustainability through open information and computing technologies\nThe development of Information and Communication Technology (ICT) and the generation of widely\navailable data not limited to scientific results (e.g., engineering test data, operation monitoring, system\ntests, etc.) are essential outputs of particle accelerator-based research infrastructures [193]. Putting a\nglobal data sharing- and processing infrastructure in place has already led to the creation of numerous,\nopenly accessible software packages, platforms and online services, which are also used in environments\noutside high-energy physics. They range from scalable data storage and distribution middleware through\ndata analysis and visualisation to data management and workflow systems. Also, openly accessible\nsoftware has been developed with a value that extends beyond scientific collaborations. Examples include\ninnovative Cloud computing services (e.g., Helix Nebula Science Cloud serving five scientific research\ndomains), meeting and event management software (e.g., Indico), particle/matter interaction modelling\nand analysis (e.g., GEANT4, FLUKA and ACTIWIZ) and electronic library and information access\nsoftware (e.g., Invenio and Zenodo). Long-term data preservation is another technological domain with\nhigh societal relevance that is gaining importance and is primarily driven by fundamental science research\ninfrastructures.\nParticle accelerator and high-energy physics research projects are strongly encouraged to create\nan inventory of potential ICT tools that can be made available openly and free-of-charge for societal\nuse. The feasibility of quantifying the societal impact of these solutions relies strongly on accounting\nfor the software uptake and use (e.g., number of installations, number of times it has been integrated\nin commercial and other open software packages) over sustained periods of time. Today, there is a\nlack of such accounting, which makes quantitative estimation of the societal impact challenging and\n278\n\nlabour intensive. However, it is important establish systematic monitoring and evaluation since ICT\ntools developed in the science environment have a major impact factor with significant and tangible\nvalue potentials [194,195].\nOpen and freely available software developed and maintained by science projects and programmes\nare sustainability enablers for research infrastructures. Their investment and continuous development\nand maintenance costs are marginal with respect to the societal benefits they can generate over decades.\nFuture particle accelerator projects and programmes should focus on properly managing and promoting\nICT developments and make sure they are taken up by society through a technological competence\nleveraging process and sustained online presence in potential user domains.\nSustainability through cultural goods\nCreating an interest in science among all citizens is part of the mission of any research infrastructure.\nProjects and organisations can develop a broad variety of activities to attract lay people, for instance,\nthrough permanent and travelling exhibitions, open days, guided tours, engagement with schools and\nteachers in joint workshops, citizen science projects, websites, social media, engagement with video\nbloggers, online and TV documentaries, art internships, common art projects, feature movies, books,\nscience fairs, presence in radio and TV shows and much more. The limit of cultural good creation is the\nlimit of the imagination of an ever-changing and diverse group of creative people that are best employed\nover sustained periods of time. Each of these cultural goods has the potential to generate value for\nsociety. Creating a sustained interest in the science project breaks down barriers and fear of people who\nare outside the science community.\nIt is important for particle accelerator and physics projects to engage lay people in playful and en-\ntertaining ways rather than aiming at education and teaching, which is a different socio-economic impact\npathway. The two should be kept separate, although effective cultural good creation and engagement\nraise the possibilities for explaining the underlying science in a second step.\nThe identification of value for cultural goods can be very different for each good. Therefore, future\nprojects and programmes will need to focus initially on a few cultural pathways. If the estimated value of\na pathway turns out to have sufficient potential, it should be further developed with a view to sustainable\nengagement. Continuous monitoring of the value should be carried out.\nThe value of on-site visits represents a cultural good of science infrastructures that can generate\nsubstantial tangible economic value in a sustainable way [196,197]. Such visits include the discovery of\nthe environment and nature [198,199]. It should, therefore, be the first to be considered for development.\nSocial media presence has the most impact on online cultural goods today and should therefore\nalso be considered with priority [118]. It is particularly important to create a sustained interest in science\nand to explain in which ways science impacts the environment and people\u2019s everyday lives. Different\nmeans of communication are needed for different generations and socio-economic groups [200].\nFinally, citizen science projects on the periphery of the physics science mission are effective tools\nto engage lay people and to reinforce the environmental and territorial compatibility of the research\ninfrastructure. An example is the initiatives to create biodiversity inventories of the surface sites, to\nimprove the quality of habitats on and around sites.\nSustainability through positive environmental externalities\nAny future particle-accelerator-based project has the potential to create positive environmental exter-\nnalities that can compensate for the residual, unavoidable negative environmental effects that cannot be\nreduced further. Before developing compensation and accompanying measures, negative effects on the\nenvironment have to be avoided. If they cannot be avoided, they should be reduced as far as is com-\npatible with achieving the goals and objectives of the infrastructure within accepted cost and schedule\nconstraints.\n279\n\nNational and international legal and regulatory frameworks define boundary conditions for the\navoidance, reduction, and compensation approach. The recently adopted update of the law for research\nand innovation in Switzerland, for instance, explicitly requires the consideration of the national and\nregional climate protection plans and energy-related aspects [201]. Other countries, such as France, have\nalready encoded the fight against climate change, resource and biodiversity protection, circular economy,\nand sustainable territorial development in the environmental protection laws (L110-1 of [147] and [202])\nthat govern the authorisation of new projects [202]. Hence, \u2018environmental\u2019 is always to be interpreted\nin a wide sense. The greenhouse gas emission reduction goals defined by the Paris Agreement are to be\nintegrated in new projects at EU level and following its translation into the national laws [203].\nIf properly planned, evaluated and monitored, collective compensation can even lead to a net\npositive effect [204]. Switzerland does not foresee such an approach and requires compensation based on\nequivalent surface and quality in principle within the affected canton [205\u2013207]. Despite this constraint,\nthe overall environmental performance may still be neutral or positive from a socio-economic assessment\npoint of view if the positive environmental externalities are properly evaluated and integrated in the net\npresent value of the project.\nSome typical examples of positive environmental externalities that particle-accelerator facilities\ncan integrate in their designs from the onset are:\n\u2013 Re-creation of agricultural spaces by transferring top soil to low quality land plots and wasteland.\n\u2013 Creation of green spaces with covered roads, fertilising wastelands and backfilled quarries, cre-\nation of parks, greening of roofs, reforestation around sites, creation and quality improvement of\nnatural habitats and wetlands.\n\u2013 Increase of biodiversity by the creation of new habitats on the research infrastructure\u2019s domain.\n\u2013 Improvement or creation of new ecological corridors, green and blue continuities.\n\u2013 Creation of forests with trees and plants adapted for climate change.\n\u2013 Introduction of forest management in view of protection from wildfires.\n\u2013 Improved water management of existing, but low-quality water courses.\n\u2013 Creation of water reservoirs.\n\u2013 Creation of raised hedges to fight soil erosion and create new habitats.\n\u2013 Creation of soft or multimodal mobility concepts for use beyond the research facility.\n\u2013 Creation and improvement of natural habitats and nature protection zones on the research infras-\ntructure sites.\n\u2013 Carbon footprint reduction by helping to avoid fossil fuel use through waste heat supply.\n\u2013 Supply of raw water for non-drinking purposes by supplying purified waste-water when not used\nby the research facility.\n\u2013 Increase of renewable energy resource capacities through long-term power purchase agreements\nand energy purchase communities.\n\u2013 Development of products and processes that leverage circular economy principles and low environ-\nmental impact technologies that spill over into the industrial domain (e.g., in the areas of electrical\nsubstations, construction materials, architecture solutions, power transmission and buffering, in-\ndustrial cooling).\n\u2013 Dismantling of infrastructures which are no longer used to create environmental and societal value.\n4.4.2\nInnovation and R&D\nParticle accelerators and experiment detectors at the collision points of particle colliders are projects\nwhich use cutting-edge technologies over periods spanning several decades. As a consequence, they\n280\n\ntend to develop and use technologies that do not exist at the time of design. This process continues for\nthe duration of the operation as detectors are upgraded. The required technical advances may be designed\nin-house and/or in partner institutions (such as universities) in conjunction with external companies. The\ndevelopment can take the form of joint design or procurement of technologies to be developed by the\ncompany. In both cases, industries profit from a technological knowledge transfer which may lead to\ntechnological breakthroughs, patents, or new business opportunities [208, 209]. Such processes are en-\ncouraged and accompanied by dedicated knowledge transfer (KT) centres at the participating organisa-\ntions. [210\u2013213] As enabler of the science mission, such technological advancement is a valuable output,\nwhich significantly affects the social sustainability of a project.\nOther sustainability potentials\nInternational science projects such as the FCC also provide possibilities to develop soft skills and in-\nternational cooperation. Such projects bring nations closer together as they aim to pursue a common,\npeaceful goal. As recently seen with the ceremonies of CERN\u2019s 70th anniversary, heads of state and\nministers come to visit the site and have bilateral discussions that may or may not be related to the scien-\ntific mission of the project or even to science. National news outlets have reported on the event, focusing\non the common project and these side aspects. Often, who discusses with whom is seen as more impor-\ntant than the event itself. Collaboration leading to more collaboration, there is a societal interest to bring\ndecision makers together to discuss issues of the world in an informal setting. Spinning off from particle\naccelerator scientific research, the SESAME project in Jordan [214] was set up with international collab-\noration in mind, as much or even more than the proposed scientific project. The Heidelberg, CNAO and\nMedAustron light-ion cancer therapy facilities are concrete examples of the direct transfer of knowledge,\nexpertise, skills, and technology from fundamental particle physics and particle accelerator research to\nmeaningful societal application. A future circular collider can achieve all this for Europe and beyond.\n4.5\nComprehensive sustainability performance assessment based on Cost-Benefit Analy-\nsis\nThe approach is to create an inventory of negative cost and positive benefit items including externalities\nand convert them into monetary terms that are combined to determine a net present value (NPV) of\nthe investment at the end of a chosen observation period (see Fig. 4.5). The ratio of the benefits of a\nproject relative to its costs (BCR) including externalities and the so-called internal return rate (IRR) are\ntwo measures that can be derived from this analysis to provide valuable insight in the sustainability of\nthe undertaking. The IRR is the discount rate that would bring the NPV of the entire project over the\nobservation period to zero. An investment can be considered sustainable if it is financially feasible (net\ncash flow is non-zero) and profitable from a socio-econonomic perspective. A positive BCR has been\ndetermined through a comprehensive socio-economic impact assessment under the most conservative\nassumptions, including total costs, externalities and benefits and an IRR that is greater than the cost of\nobtaining the capital required. These results support the overall sustainability of the project.\nNet\nPresent\nValue\nCAPEX\nOPEX\nValue of \nnegative \nexternalities\n=\n-\nBenefits\nResidual \nvalue\nValue of \npositive \nexternalities\nBenefits\nCosts\nFig. 4.5: Expression to determine the net present Value (NPV) of an investment project considering\neconomic, societal and environmental aspects.\n281\n\nIn line with the guidelines on cost estimation of research infrastructures [215], the following items\nneed to be established:\n1. Unit of analysis with clear scope and boundary descriptions.\n2. Reference period with a start and an end date of the observation based on the expected useful life\n(note that this period may be different from the physical life of the infrastructure and may lead to\nresidual asset values).\n3. Base year, i.e., the point in time when the quantitative estimation is made that does not necessarily\ncoincide with the start date of the investment or the project operation. Past values are capitalised\nand future values are discounted with respect to the base year using the same mathematical for-\nmula. Conversion rates of the unit of measure with respect to other relevant currencies are to be\nrecorded for the base year.\n4. Unit of measure for costs and benefits in a specific monetary currency.\n5. Approach for converting in-kind contributions in monetary terms.\n6. Definition and description of the counterfactual scenario.\n7. Project-specific Social Discount Rate that is justified by an economist expert advisory committee.\n8. Structure of capital and operation expenditures.\n9. Structure of negative externalities considered.\n10. Structure of positive impacts (benefits) considered.\nIn addition to full financial costs, negative externalities must be integrated in the assessment, as\nfar as they can be reasonably identified, accounted and converted in monetary terms.\nConcerning potential impacts on the climate, the methodology includes the accounting of project\nrelevant emission factors, the estimation of the net greenhouse gas (GHG) emissions (a negative external-\nity) and avoided emissions (positive impact or benefit) compared with a counterfactual baseline scenario.\nThe resulting amount of generated and avoided GHG emissions in tonnes of carbon dioxide equivalent\n(tCO2(eq)) has to be converted into monetary terms using a shadow price of carbon. In line with the EC\ntechnical guidance on the climate proofing of infrastructure, [216], for the shadow cost of carbon, it is\nrecommended to use the values established by the European Investment Bank (EIB) as the best available\nevidence on the cost of meeting the goals of the Paris Agreement [217].6\nInput-Output analysis [218] is a methodology that only captures economic linkages and deter-\nmines the value-added of an investment and can be used to estimate the effect on the job market and\nin which domains and geographical regions the economic activations take place. This tool is regularly\nused by governments and at the international level (e.g., EU, OECD) for empirical economic research\nand structural analysis and is therefore widely known. However, it is purely an economic instrument that\nshould only be used as follows:\n\u2013 As a complementary tool to document economic linkages, permitting the development of interna-\ntional in-cash and in-kind contributions.\n\u2013 To identify project-relevant industrial sectors.\n\u2013 To develop targeted common activities and synergies.\n\u2013 To understand the job market implications.\n\u2013 To develop regional specialisation policies.\n\u2013 To develop focused training and skilled labour mobility plans.\nRecently, the FCC study implemented the economists\u2019 recommendation to carry out a complemen-\ntary analysis of the public perception [177] using a stated preference and Willingness-To-Financially-\n6The Paris Agreement is a legally binding international treaty on climate change. It was adopted by 196 Parties at the UN\nClimate Change Conference (COP21) in Paris, France, on 12 December 2015. It entered into force on 4 November 2016.\n282\n\nParticipate (WTP) approach [219]. Such a survey can help to reveal if the full costs and cumulative\nimpacts of a research infrastructure or scientific investment are at least justified with respect to the per-\nception of the public.\nThe establishment of a risk registry, a risk assessment, and an evaluation of the residual risks is im-\nportant for new science missions and research infrastructure projects and programmes. It should include\neconomic, social, and environmental domains in addition to standard topics such as financial and project\nmanagement related matters. Selected chapters are to be analysed using a simplified appraisal process\nwith a limited and self-contained CBA or a multi-criteria analysis (MCA). Presenting several variants\nand versions of the project and individual segments together with their full financial costs, economic,\nsocial, and environmental performance levels is considered good practice in project appraisal and has\nbeen implemented by this study.\nThe results of the integrating and wider sustainability analysis are reported in a condensed sum-\nmary form using the following key performance indicators:\nNet Present Value (NPV) is the discounted sum of all future benefits less the discounted sum of\nall future costs over the appraisal period as a whole. To properly estimate the NPV, realistic estimates\nare required of the streams of benefits and costs over the appraisal period that can reasonably comprise\naround 30 years. Beyond this time frame, quantitative socio-economic estimates become challenging.\nThe key to determining both these streams is knowledge of the times at which the various elements would\ncome into play. Investment costs will typically be incurred prior to the date of opening, whilst operating\ncosts (for example, personnel and resources for operation and maintenance) and user benefits would\narise after the year of opening. User benefits, operating costs and revenues can be estimated from model\nruns for two or more years and the stream of benefits can be derived by interpolation and extrapolation\nbetween the benefits for the modelled years.\nBenefit/Cost Ratio (BCR) is given by the ratio of the discounted sum of all future costs and\nbenefits. The BCR is, therefore, a value-for-money measure, which indicates how much net social benefit\ncould be obtained in return for each unit of investment. Although the values are monetised, i.e., converted\ninto monetary units in this approach, they do not necessarily represent financial investments (e.g., the\nmonetary shadow cost of carbon is not a paid amount of money. It represents a monetary cost to restore\nthe effects linked to the quantified, potentially emitted carbon dioxide equivalent). Formulae for the NPV\nand BCR will be found in CBA textbooks, a good example of which is Pearce and Nash (1981).\nInternal Rate of Return (IRR). Whereas the NPV and BCR measures require a test discount rate\nto be specified, the IRR reports the average rate of return on investment costs over the appraisal period.\nThis can be compared with the test discount rate to see whether the project yields a higher or lower\nreturn than is required to break even in social terms. Calculation of the IRR and issues surrounding it are\ndiscussed in Pearce and Nash, Chapter 4 and in other cost-benefit textbooks.\n4.6\nLimitations\nParticle accelerator facilities are characterised by a diverse set of investment and operation cost items,\nnegative externalities, benefits and positive externalities. Research infrastructures dedicated to funda-\nmental science generally do not generate financial revenue. Unlike commercial ventures, research fa-\ncilities exploring fundamental questions about nature (like the origin of matter or the structure of the\nuniverse) don\u2019t sell a product or service that generates income. Consequently, they cannot generate\nprofit7. This makes it difficult to evaluate their performance using standard business metrics like return\non investment, earnings or profit.\nThis situation presents challenges for conducting comprehensive project appraisals and assessing\nlong-term sustainability through traditional financial metrics. In the absence of a direct positive financial\nreturn by definition, the value of these projects is primarily reflected in their broader socio-economic im-\n7Financial profit is the next income that is earned after deducing all explicit costs from the total revenue\n283\n\npact. Thus, the assessment of such infrastructures relies on identifying and, where possible, quantifying\nthe societal benefits in relation to the associated costs and externalities.\nThe public good value refers to the importance or benefit of a public good provided without profit\nto all members of a society. A science infrastructure such as particle collider are an example for a\npublic good. Elucidating its value as perceived by the public is an essential complementary ingredient\nto understand if society considers it worth investing in such scientific research activity. The total public\ngood value in the countries that would potentially financially contribute to a future particle collider-based\nresearch infrastructure was found to be larger than the sum of all known, identified, and quantified costs.\nThis result supports, at least from a societal point of view, the intent. Establishing the hypothesis that only\nCERN Member States contribute to the project implementation is not a likely scenario. An infrastructure\nof the scale of the FCC will attract participation and funding from beyond the European Research Area,\nas was the case with the Large Hadron Collider. Therefore, to estimate the public good value, those\ncountries have been selected that historically financially participated in CERN\u2019s international research\nprogrammes. An extremely conservative scenario can be built that includes only CERN Members and\nAssociated Member States. However, no less than those countries should be considered.\nAs recommended by the OECD [220,221], the French government [222], the UK government [223],\nand the European Commission [143,224], a comprehensive sustainability assessment should consider all\nof the above elements, i.e., total costs, total benefits, negative externalities, positive impact, and envi-\nronmental benefit potentials. In practice, not all contributing elements are relevant for a specific invest-\nment project, not all elements can be reliably quantified, and not all elements are known or understood\n(Fig. 4.6). Both cost and benefit items are affected by uncertainties (Fig. 4.7). The results presented in\nthis chapter must be interpreted in this light. An uncertainty analysis will eventually shed light on the\nranges. The EC CBA Guide [108] recommends a Monte Carlo based approach. However, this method\nalso relies on the knowledge of the probability distributions of the individual cost and benefit compo-\nnents, which are in turn challenging to obtain with a high degree of confidence.\nAs far as possible, the comprehensive socio-economic study report describes the scope of the study\nas precisely as possible, and the aspects considered are described together with the assumptions used for\nthe quantification of the aspects and their conversion into monetary terms.\nKnown Knowns\nCost and impact pathways\nthat can be measured and \nintegrated in research \ninfrastructure design.\nKnown Unknowns\nCosts and impact pathways\nthat are known to exist,\nbut for which no quantification \nmodel is known.\nUnknown Knowns\nThere are insufficient \nresources (time, people, \nmoney) to measure, analyse\nand integrate the cost and\nbenefit items.\nUnknown Unknowns\nCost and impact pathways\nthat we are neither aware of\nnor understand.\nFig. 4.6: The Rumsfeld matrix [225] applied to the identification of costs and benefits of research infras-\ntructures.\nRationalising comprehensive sustainability assessment using standard cost-benefit analysis [226]\nhelps to identify the sustainability limiting and enabling aspects and can guide the design and iterative\nevolution of the research infrastructure to increase long-term sustainability. In this approach, time is\n284\n\naccounted in a rigorous way, which is essential when considering effects on the environment at large.\nWhile methods to quantify cost items, including negative externalities, are typically well defined in the\nexisting guidelines, the approaches to quantifying and monetising benefits and positive externalities are\nnot exhaustively captured by a general catalogue or taxonomy. They are project-specific and need to be\nidentified and captured on a case-by-case basis using different methods and models. Still, not all cost\nitems and negative externalities are known at all times, and even if they are known, they cannot always\nbe reliably quantified, monetised, and assigned with uncertainty ranges. Much depends on the evolution\nof the economy and society, such as the availability and demand for excavated material deposits, the\nvaluation of climate impacts, the evolution of water supply and management, and the local and regional\ndemands for goods and services. An ex-ante analysis is, therefore, always only valid in the current\ncontext, projecting all potential future costs and benefits into today\u2019s socio-economic environment using\nthe currently known uncertainties. All assumptions underlying the cost and benefit quantification, the\nmodels used, and the monetisation methods need to be documented, together with the analysis results.\nCAPEX\nOPEX\nCO2eq\nSoil\nTraining\nICT\nWaste heat\nTourism\n?\n?\n0\n10\n20\n30\n40\n50\nCosts\nBenefits\nFig. 4.7: Examples for the accounting of full costs and benefits for an integrated sustainability analysis.\nOnly the identified cost and benefit items that can be converted to monetary terms were considered in\nthis specific assessment. Exhaustive coverage of all negative and positive externalities is challenging and\nand needs to be accepted in all socio-economic impact assessments.\nSustainability might refer narrowly to the internal sustainability of the project. In reality, it refers\nmore broadly to a whole range of external economic, social or environmental factors which can be influ-\nenced by the project. The 17 high-level development objectives (with more than 160 sub-objectives) of\nthe 2015 UN Sustainability Development Goals (SDGs) shown in Fig. 4.8 illustrate the breadth of these\nfactors. The ultimate goal is to identify and document quantified positive and negative impacts consider-\ning and leaning on the UN Sustainability Goals as a guiding principle for the topics [227] as a reference\nmatrix. Since quantitative sustainability analysis cannot provide full coverage, the UN SDGs can be\nregarded as a complementary catalogue of potential negative and positive impacts that can be looked at\nin terms of causal relationships with the project. The global indicators and monitoring framework for the\nSDGs [228] have been designed to help countries, not research organisations, develop strategies [229].\nThey are therefore not directly usable for reporting on scientific programmes and projects. A research\ninfrastructure can, however, report relevant positive and negative impacts in quantitative terms as far as\nthey have been assessed for each UN goal activity. This approach has for example, been implemented\nwith CERN\u2019s periodic environment report that relies on the GRI framework [230]. In the absence of es-\ntablished guidelines, the SDG tracker [231] and the European Commission SDG information site [232]\nprovide a good starting point for indicator recommendations based on the UN SDG goal specification.\nA full exploration of the FCC\u2019s contribution to the UN SDGs has not been done at this point. It should,\nhowever, be developed during the subsequent design phase that includes the project authorisation phase.\nSuch a qualitative analysis is not expected to give evidence of compliance with specific national or\n285\n\nFig. 4.8: The UN sustainability development goals (SDG).\ninternational targets. Rather, the goal is to show how the research infrastructure affects the environment\nat large in negative ways and how it contributes in very tangible ways to each of the goals.\nThe choice of the Social Discount Rate (SDR) affects the integration of cost and benefit items.\nUsing different SDR rates can be used to perform a sensitivity analysis and to show the robustness of the\noverall net present value. For this study only one SDR value has been used.\n4.7\nLifecycle analysis\n4.7.1\nContext\nAs the global focus on combating climate change intensifies, reducing greenhouse gas (GHG) emissions\nhas become a top priority. Infrastructures spanning transport, construction and scientific instruments\nplay a critical role in this transition. A lifecycle analysis is an essential tool to analyse the sources of\nemissions that affect the climate, to understand the drivers and to optimise the project in view of improved\nenvironmental compatibility.\nThe topic is comprehensive and complex, determined by many uncertainties and by the fact that\nthe different segments of the project are only gradually known as the concept development and design\nadvance. A long-term project like the future circular collider does not deliver detailed designs of the\ntechnical infrastructures and particle accelerator components until shortly before procurement. Detectors\nthat constitute the scientific experiments will only be built and procured as a collaborative effort at a much\nlater stage. To be able to leverage the technical advances, detailed designs are only developed when the\nparticle collider equipment is well known, procured and potentially already being installed.\nIn addition to this time dependency, LCA and the associated carbon budget assessment strongly\ndepend on the procurement scenario and the scenario of specific technologies. Therefore, the FCC study\nhas taken the approach of focusing first on the best-known project segment, the environmental footprint\nof civil construction based on the current concept.\nThe study also included the estimate of the Scope 2 footprint for operation, i.e., the carbon emis-\nsions that would be associated with the consumption of energy. Also, a specific procurement hypothesis\nhad to be assumed for this analysis.\nIt must be understood that the results presented herein are subject to further evolution through-\nout the lifecycle phases of the project, should a decision to pursue it be taken. In particular, they do\nnot consider certain negative externalities related to the construction of the particle accelerators and ex-\nperiments, optimisations, which are possible with the use of further advanced technologies, materials,\n286\n\nproducts, local production, responsible sourcing and procurement and the outcomes of commercial ne-\ngotiations during the procurement processes. Consequently, continuous socio-economic performance\nmonitoring, incorporating eco-design based on an iterative Plan-Do-Check-Act cycle, is important and\nshould be established before entering a preparatory project phase.\nThe analysis carried out using the European LCA Norms ISO/EN 14040 and ISO/EN 14044 aimed\nto estimate the carbon budget of the infrastructure construction that would serve two subsequently in-\nstalled particle colliders. It aims to establish a credible benchmark, leveraging the use of European norm\nEN 15804+A2 and French FDES norm standardised Environmental Product Declarations (EPDs) of ma-\nterials and products available today. This approach ensures a comprehensive assessment in line with\nthe European standard and norm EN 17472, which provides requirements and guidelines for calculating\nand reporting GHG emissions associated with infrastructure projects. The work also included the rec-\nommendations of Cerema for the evaluation of greenhouse gas emissions for road projects, the Swiss\n\u2018Koordinationskonferenz der Bau- und Liegenschaftsorgane der \u00f6ffentlichen Bauherren\u2019 (KBOB) and\nFrench \u2018Les donn\u00e9es environnementales et sanitaires de r\u00e9f\u00e9rence pour le b\u00e2timent\u2019 (INIES) databases\nfor ecological product footprints, and the ecoinvent (ecoinvent is an internationally active, mission-driven\norganisation devoted to supporting high-quality, science-based environmental assessments) database for\nproducts and materials where no EPDs were available. The work revealed some realistic pathways to\nfurther reduce the consequences of the construction and gave some recommendations on future aspects\nthat need to be considered during the subsequent design phase.\nThe results are integrated in the integrating, wider socio-economic impact assessment by convert-\ning the results of the LCA into monetary terms using the recommended approach of the EIB and the\nEuropean Norms EN 14007 and EN 14008.\n4.7.2\nMethodology\nThe work for the estimation of the construction-related greenhouse warming potential included the fol-\nlowing steps:\n1. Component identification: Compilation of the detailed inventory of materials based on the bill\nof quantities for the subsurface construction, the 4 experiment sites and the technical sites. The\ncurrent conceptual design was considered for this step. The products chosen are used throughout\nthe infrastructure\u2019s lifecycle.\n2. EPDs acquisition: Sourcing of EPDs for each material identified, ensuring compliance with EN\n15804+A2, the foundational basis for EN 17472. The materials are selected based on expert\nknowledge of the local environment and product availability and hence, represent state-of-the-art\nsolutions.\n3. Software tool: Selection of a certified tool compatible with French and Swiss Environmental Prod-\nuct Declaration - One Click LCA\u00ae, ensuring robust and accurate calculations.\n4. Data entry: Imported data into the tool and entered project-specific data, including material quan-\ntities and lifecycle phases, transport for excavated and construction material.\n5. Calculations: The tool was used to estimate the carbon budget, drawing on EPDs data to evaluate\nGHG emissions for each lifecycle phase.\n6. Result analysis: Analysed the results to pinpoint major emission sources, comparing them against\nbenchmarks and reduction targets.\n7. Formulation of recommendations: Based on the results and the identification of the key impact\ndrivers, a set of recommendations was formulated that is to be taken into consideration in the\nsubsequent design phase to further reduce the environmental footprint of the construction.\nFor the estimation of the Scope 2 emissions, the following steps were taken:\n287\n\n1. Consumption identification: estimation of the electricity consumption for the baseload and for\neach operational phase and establishment of an operational schedule.\n2. Procurement hypothesis: Establish a credible scenario for procuring the energy based on an exter-\nnal expert consultancy with a focus on sourcing energy from renewable energy sources.\n3. Quantification: Quantification of the associated climate effect by using the accredited French\nADEME 8 database.\n4. Formulation of recommendations: Based on the results and the identification of the key impact\ndrivers, a set of recommendations was formulated that are to be taken into consideration in the\nsubsequent design phase to further reduce the environmental footprint of the operation.\nIn both cases, the results were converted into monetary terms using the EIB-established shadow\nprice for carbon. The results were integrated over time and discounted using the 2.8% Social Discount\nRate established for the assessment project.\n4.7.3\nResults\nConstruction phase\nThe LCA [60] provided a breakdown of GHG emissions across various lifecycle phases and materials.\nIt must be stressed that the results were obtained with the most advanced, state-of-the-art products and\nmaterials on the market. The results are, therefore, credible, and the carbon-related climate footprint\ncan be further reduced as more advanced technology can be included in the project. The key emission\nsources are reinforced steel (14%), precast concrete (49%) and concrete (23%). The climate effects due\nto the use of electricity have been included in this analysis. It is assumed that the electricity required\nfor the entire construction process can be obtained from renewable energy sources via local suppliers in\nFrance and in Switzerland. The official carbon footprints of today\u2019s renewable energy mix in the two host\ncountries have been used in the study (see Table 3.5). The results obtained highlight opportunities for\nemission reduction by establishing technical requirements for the infrastructure with carbon reduction in\nmind, careful selection of materials which meet the requirements, construction process optimisation, and\nenergy efficiency improvements. The GHG impacts of the initial and benchmark scenarios are given in\nTable 4.1.\nTable 4.1: Summary of the LCA-based carbon budget of the construction process.\nItem\nFootprint\nSubsurface\n477 390 tCO2(eq)\n4 technical sites\n17 546 tCO2(eq)\n4 experiment sites\n31 735 tCO2(eq)\nTotal\n526 671 tCO2(eq)\nThe value obtained corresponds roughly to 3 years of CERN\u2019s annual carbon budget [79] or to\none-third of the carbon budget of the Olympic Games in Paris, 2024 [80].\nFurther environmental performance indicators obtained with the LCA are shown in Table 4.2.\nCompared to classical, non low-carbon construction processes, the most relevant indicator is marine\neutrophication, which can be linked to the use of recycled steel.\nThe results also allow a comparison to be made of the construction of subsurface structures with\nconventional structures, such as road and metro tunnels and tramway lines. The latter is characterised\n8ADEME stands for Agence de la Transition \u00c9cologique, which translates to Agency for Ecological Transition in English.\nIt is a French public agency under the supervision of the Ministry for the Ecological Transition and the Ministry for Higher\nEducation and Research.\n288\n\nTable 4.2: Summary of the LCA-based carbon budget of the construction process.\nIndicator\nValue\nPotential contribution to ozone layer depletion\n19.3 kg CFC 11 eq\nPotential acidification\n929 t SO2 eq\nPotential eutrophication - fresh water\n96 t (PO4)3\u2212\nPotential eutrophication - marine\n12 t N\nPotential eutrophication - land\n2.1 x 106 mol N\nby significantly higher carbon footprints as a result of the much stricter requirements that public use\nimposes. For comparison, the construction of the U5 underground line in Berlin (Germany), a typical\nsmall-scale metro line, has a carbon footprint of 80 000 tCO2(eq) per km. The footprint of a typical\ntramway line has between 7 600 and 10 850 tCO2(eq) per km. The linear part of a future circular collider\nsubsurface structures has a carbon footprint of about 5 300 tCO2(eq) per km (see Fig. 4.9).\n0\n10'000\n20'000\n30'000\n40'000\n50'000\n60'000\n70'000\n80'000\nMetro\nTram\nFCC\nFig. 4.9: Comparison of carbon footprint between a small-scale underground metro line, a tramway line\nand the FCC. [60]\nBased on the findings, the following levers were identified to reduce GHG emissions:\n\u2013 Document technical requirements for the structural surface and subsurface elements that capture\nthe strict minimum needs to fulfil the scientific research programme.\n\u2013 Develop an eco-design that meets the established requirements with carbon reduction in mind.\n\u2013 Make structural modifications by reducing the inner line thickness of subsurface structures by\n5 cm, leading to a reduction in the quantity of precast concrete and rebar steel of 16%.\n\u2013 Substitute materials, using low-impact materials wherever possible, leading to a further reduction\nof GHG emissions.\n\u2013 Optimise the construction process to minimise emissions, including local sourcing of raw and\nrecycled materials and production of construction materials.\n\u2013 Fully electrified construction processes and transport.\n\u2013 Reuse excavated materials, for instance, in concrete production.\n289\n\nClimate effects due to energy use during operation\nTo estimate the climate effects related to the use of energy (Scope 2) during the operation phase, the\nelectricity requirements have been estimated for the baseload and for each individual operation phase\n(Z, WW, ZH, t\u00aft). During the operation phase the energy needed to power the infrastructures, particle\naccelerators and experiments will be sourced entirely from the French electricity grid, managed by the\nnational grid operator RTE. A portfolio of multiple electricity contracts and power purchasing agree-\nments (PPA) facilitates the diversification of the electricity mix and sourcing it from different operators\nwho can provide certificates of origin, leading to market-based carbon footprint reporting. A prepara-\ntory study with two independent external consultants identified that on a short timescale, before 2030\n60% of the required energy could already be obtained from renewable energy sources and in a time\nframe of 15 years (around 2040) a portfolio to cover 80% of the needs with renewable energies can be\nestablished. For 2050, when the FCC is envisaged to operate, a coverage of 90% is assumed with a\nresidual supply of 10% nuclear energy. For the purpose of the socio-economic performance assessment,\na conservative maximum use of 80% energy from renewable energy sources has been used, thus over-\nreporting the carbon equivalent footprint. To estimate the carbon intensity of the project scenario, the\nofficial values of the French National Environment and Energy Management Organisation (ADEME)\nwere used, leading to a mix with a carbon intensity of about 15 tCO2(eq) per GWh. For the calculations\nin the socio-economic performance assessment, a more conservative degressive carbon intensity starting\nwith 26 tCO2(eq) per GWh in 2024, 19.10 in 2046 and 18.41 in 2050 assuming a constant decrease in\nthe emission factor of 4% have been used. Again, this approach leads to an over-reporting of the car-\nbon equivalent footprint. Table 4.3 below provides the Scope 2 indication of the carbon budget for each\nparticle collider operation phase with beam for scientific research and the total footprint for all operation\nand shutdown phases for two different carbon footprint assumptions leading to a range for the expected\ncarbon footprint: 15 tCO2(eq) per GWh and 25 tCO2(eq) per GWh.\nTable 4.3:\nSummary of the operation-related Scope 2 carbon emission footprint using two different\nmarket-based carbon intensity assumptions for the electricity purchased. Note that the integral carbon\nfootprint also covers Scope 2 emissions during shutdown periods.\nPhase\nDuration\nGWh/year\nFootprint all years\nat 15 tCO2(eq)/GWh\nFootprint all years\nat 25 tCO2(eq)/GWh\nZ\n4 years\n1 100\n66 000 tCO2(eq)\n110 000 tCO2(eq)\nWW\n2 years\n1 300\n39 000 tCO2(eq)\n65 000 tCO2(eq)\nHZ\n3 years\n1 500\n67 500 tCO2(eq)\n112 500 tCO2(eq)\nt\u00aft\n5 years\n1770\n132 750 tCO2(eq)\n221 250 tCO2(eq)\nTotal\n20 350\n305 250 tCO2(eq)\n508 750 tCO2(eq)\nIntegrating the energy consumption requirements over the years of operation leads to an integral\ncarbon budget that corresponds to about 2.5 years of CERN\u2019s annual carbon footprint today. For compar-\nison, the Meta company known for its products Facebook, Instagram and WhatsApp operates currently at\nleast three data centres in the United States with electricity consumptions between 1.2 and 1.4 TWh per\nyear [233]. Their individual, location-based Scope 2 emissions are significantly above, 350 000 tCO2(eq)\nper year.\nShadow cost of carbon\nThe conversion of the carbon budget respects the overall goals for climate protection and temperature\nlimits that were approved by a community of nations in the Paris Agreement. The European Investment\nBank (EIB) has calculated a so-called \u2018shadow price for carbon\u2019 that represents the costs that humankind\nneeds to associate with climate protection measures to achieve the agreed goal. The shadow price of\n290\n\nTable 4.4: Shadow cost of carbon under in currency unit per tonne CO2(eq) for various jurisdictions.\nRates in the first row are also published as European Union law 2021/C 280/01. Note that the 1.5%\nnear-term Ramsey Discount Rate is applied to the US indicated rates.\nOrganisation\nUnit\n2020\n2025\n2030\n2035\n2040\n2045\n2050\n2060\nSource\nEIB and EU\nEuro 2016\n\u20ac80\n\u20ac165 \u20ac250 \u20ac390 \u20ac525 \u20ac660\n\u20ac800\nn/a\n[234]\nEIB and EU\nEuro 2024\u2020\nn/a\n\u20ac208 \u20ac316 \u20ac492 \u20ac663 \u20ac833 \u20ac1010\nn/a\nSGPI France\nEuro 2018\n\u20ac87\nn/a\n\u20ac250\nn/a\n\u20ac500\nn/a\n\u20ac775\n\u20ac1203\n[150]\nUBA Germany Euro 2023\n\u20ac240\nn/a\n\u20ac254 \u20ac253\nn/a\nn/a\n\u20ac301\nn/a\n[235]\nUK (high)\nGBP 2020\n\u00a3361\n\u00a3390\n\u00a3420\n\u00a3453\n\u00a3489\n\u00a3527\n\u00a3568\nn/a\n[236]\nEPA USA\nUSD 2020\n$340\nn/a\n$380\nn/a\n$430\nn/a\n$480\n$530\n[237]\n\u2020 Adjusted based on EU-27 GDP deflator 100.0 in 2016 and 126.3 in 2023. It measures the amount to which\nthe real value of an economy\u2019s total output is reduced by inflation.\ncarbon increases over the years, making one tonne of CO2(eq) more expensive for society each year. The\ndiscounted value of the monetary conversion of the construction and operation-related carbon footprint\nis about 342 million euros. This amount is added to the integrated socio-economic assessment on the\ncost side of the balance and is used to estimate the net present value of the future research infrastructure\nat the end of its scientific operation programme. Table 4.4 shows the shadow cost of carbon currently\nrecommended for project appraisal by the European Investment Bank (EIB) and its time-adjusted value\nto be used in 2025.\n4.8\nSocio-economic performance\n4.8.1\nContext\nThe goal of the comprehensive socio-economic impact analysis including a wider set of components such\nas environmental externalities is to get a better understanding of the cost drivers and potential benefits.\nThis approach has been adopted to plan for a sustainable scenario. The analysis can also reveal under\nwhich conditions the overall socio-economic performance can be positive, i.e., represent a long-term\nsustainable investment for the society. Carrying out such analysis from the onset enables the project\nto incorporate the findings in the subsequent design phase, where it is easier to plan for sustainability\nenablers than during construction or when the infrastructure is already in operation.\nThe socio-economic analysis relies on a working hypothesis of the investments and resources en-\ngaged for the project by an international collaboration. Therefore, the work is based on a total project\ncost estimate including all investment costs, operation costs and relevant negative and positive external-\nities for the entire observation period carried out in 2024. This estimate may differ from project cost\nestimates carried out later or presented elsewhere, since it represents a snapshot of the estimates taken in\nJune 2024 and it includes global personnel engagements such as those of the international collaborations\nand monetised negative environmental externalities. The total costs required for the socio-economic\nanalysis include the investment costs (capital and operation expenditures) as well as monetised external-\nities such as environmental costs and the shadow cost of carbon. Therefore, those costs figures must not\nbe used to determine the financial needs to implement the project. They represent the total cost of the\nscience missions for society for the entire observation period. The same holds for the reported benefits:\nthey represent a collection of identified, quantified and monetised positive effects for society and are not\nlimited to direct economic effects. Neither costs nor benefits can be exhaustively covered due to uncer-\ntainties, available resources, and time limitations. However, the herein reported results are sufficiently\ncomprehensive and detailed to establish a stable Benefit-Cost Ratio that is unlikely to decrease further\nwith the introduction of additional, minor cost and negative externalities. The socio-economic perfor-\nmance requires periodic updates as the project is defined better and in more detail and as models and\n291\n\nresources to estimate additional benefits become available.\nA comprehensive report on the socio-economic performance analysis [122] details the data, as-\nsumptions, methodologies and outcomes of the first socio-economic impact analysis for the first phase\nof the integrated FCC research programme: the FCC-ee lepton collider based on only two interaction\npoints. The analysis spans the entire lifecycle of FCC-ee, encompassing its design, the construction of\nthe surface and subsurface structures, the creation of the technical infrastructures, the particle accelerator\nand experiment detector construction, the operation and the gradual beam energy upgrade phases. The\nentire analysis spans a duration of 41 years (2024 to 2064), starting with pre-investment study expenses,\nthe financial investment decision and lasting until the end of the operation phase. The methodologi-\ncal approach is based on the regulatory guidelines issued by the European Commission (EC) [238], the\nEuropean Investment Bank (EIB) [234], the European Strategy for Research Infrastructures (ESFRI)\nguidelines [215] and the French Secr\u00e9tariat g\u00e9n\u00e9ral pour l\u2019Investissement (SGPI) [150]. The guidelines\nadopted are compatible with those in other countries of the European Research Area, for instance, in the\nUK [223]. The study also considers the latest literature, works, and results of empirical research on the\neconomic quantification of impacts associated with research infrastructures.\nIn evaluating the FCC-ee project, costs and benefits are expressed in comparison to a scenario\nwhere the project is not implemented. In this counterfactual scenario, the LHC would continue its op-\neration until its anticipated end of life around 2040, and no new particle-collider would be constructed.\nCERN would continue its operation of the existing particle accelerators (e.g., AD, ELENA, LINAC4, PS)\nand the experimental infrastructures linked to them. It is based on the methods of standard cost-benefit\nanalysis (CBA). All costs and benefits are incremental, i.e., expressed as a difference between the costs\nand benefits of the operation of the existing infrastructure after the shutdown of the LHC and the costs\nand benefits that the FCC-ee would induce Consequently, the approach captures the net change, focusing\non causally related effects that can be reliably attributed to the FCC-ee project.\nThis social cost-benefit assessment carried out assumes an FCC-ee project with four experiments,\ncollectively involving approximately 260 000 person-years over the project\u2019s lifespan. The engagement\nof people is expected to reach its peak of about 15 500 people during the operation phase (Fig. 4.10).\nThis diverse group comprises scientists, engineers, technicians, administrative staff, doctoral and post-\ndoctoral researchers, undergraduate students, master degree level students and apprentices. Of the total\nparticipants, approximately 11% is assumed to be active on the particle accelerators and technical infras-\ntructures, while the remaining 89% will be engaged in the detectors and experimental physics.\nFig. 4.10: Number of persons engaged in the project over the years throughout all project phases.\n292\n\n4.8.2\nResults\nThe initial socio-economic impact assessment based on 2 experiment collaborations, limited to the in-\nvestment costs, operation costs, and core benefit pathways, yielded a positive net present value at the\nend of the FCC-ee operation phase [122]. The subsequent complementary assessment carried out in\n2024 [239] used an even more conservative calculation based on an update of the project configuration,\nconsidered only a reduced set of well-justifiable benefit pathways, and extended the analysis to wider\neffects and negative environmental externalities:\n\u2013 Revised investment and operation costs, reflecting the price evolution of goods and services be-\ntween 2018 and 2024.\n\u2013 Four experiment collaborations (instead of two as assumed in the initial assessment).\n\u2013 Revised social discount rate (2.8%).\n\u2013 Introduction of noteworthy environmental negative externalities.\n\u2013 Revision of major benefit pathway monetisation including additionally gathered data.\n\u2013 Strict limitation of benefits to core benefit pathways.\nTable 4.5: Social cost-benefit assessment of the FCC-ee project expressed as an incremental benefit\nwith respect to a counterfactual scenario in which no collider project is implemented after the end of\nthe HL-LHC operation. The results of the \u2019wider\u2019 socio-economic analysis include noteworthy negative\nexternalities and environmental benefits.\nCost/Benefit\nUndiscounted\nDiscounted\n(A) Costs\n19 666 MCHF\nInvestment costs (for 4 experiments, injector and t\u00aft stage)\n16 215 MCHF\n10 171 MCHF\nPersonnel costs\n16 802 MCHF\n7544 MCHF\nOperation costs (materials, consumables, services)\n4410 MCHF\n1879 MCHF\nDismantling costs\n228 MCHF\n72 MCHF\n(B) Negative externalities\n354 MCHF\nShadow cost of carbon\n634 MCHF\n342 MCHF\nLoss of agricultural income, biodiversity & habitat\n7.6 MCHF\n4.1 MCHF\nSocial cost of project-related, induced noise\n0.02 MCHF\n0.02 MCHF\nSocial cost of project-related, traffic-induced air pollution\n0.9 MCHF\n0.6 MCHF\nSocial cost of project-related, traffic-induced GHG externalities\n9.8 MCHF\n7 MCHF\nSocial cost of ionising radiation\n1.3 MCHF\n0.6 MCHF\n(C) Core benefits\n23 974 MCHF\nScientific production\n6507 MCHF\n2813 MCHF\nEarly career researcher training\n20 687 MCHF\n4986 MCHF\nIndustrial benefits for suppliers\n17 577 MCHF\n9569 MCHF\nOnsite visitors\n4538 MCHF\n2129 MCHF\nOnline and social media\n229 MCHF\n102 MCHF\nOpen software (experiments and detectors)\n7428 MCHF\n4375 MCHF\nTotal costs including negative externalities\n(A + B) 20 020 MCHF\nTotal core benefits\n(C) 23 974 MCHF\nReference net present value (NPV)\n(C) - (A + B)\n3954 MCHF\nReference Benefit Cost Ratio (BCR)\n1.20\nTable 4.5 presents the most certain and stable results of this additional social cost-benefit assess-\nment, showing the core cost and benefit pathways. A set of wider benefit pathways may occur, provided\n293\n\nTable 4.6: Additional benefit potentials not considered in the calculation of the reference net present\nvalue and benefit cost ratio.\nCost/Benefit\nUndiscounted\nDiscounted\n(D) Residual asset value for a subsequent collider project\n- 7911 MCHF\n- 2480 MCHF\n(E) Wider benefit potentials\n6916 MCHF\nOpen information platform\n5053 MCHF\n2681 MCHF\nOpen collaborative software\n7516 MCHF\n3487 MCHF\nICT spin-offs\n832 MCHF\n409 MCHF\nCreation of renewable energy sources through contracts\n227 MCHF\n117 MCHF\nSupply of waste heat\n313 MCHF\n132 MCHF\nAvoided greenhouse gas emissions (GHG) by supply of waste heat\n170 MCHF\n74 MCHF\nRewilding (habitats and biodiversity)\n0.4 MCHF\n0.2 MCHF\nContributions to regional emergency services\n31 MCHF\n16 MCHF\nNet present value including residual asset value\n(C) - (A + B + D)\n6 446 MCHF\nTotal core and wider benefit potentials\n(C+E) 30 890 MCHF\nthat dedicated planning and implementation are incorporated into the project designs and appropriate\ncontextual conditions are in place (see Table 4.6). To aggregate the value of measured benefits and com-\npare them with costs and negative externalities, a social discount rate (SDR) was established specifically\nfor the project. Instead of relying on existing SDRs suggested by international organisations, this project-\nspecific rate accounts for the level of development and preferences for consumption and investments in\ncountries contributing to the CERN budget and the very long duration of the project. The assumed SDR\nvalue is 2.8%. The result, strictly limited to costs, noteworthy negative externalities, and core benefits,\nshows a positive net present value of about 4 billion Swiss francs for the project, leading to a Benefit\nCost Ratio (BCR) of about 1.20. This value must not be interpreted as a fixed and certain number. A\npositive BCR under highly conservative assumptions provides confidence that the project scenario can\nachieve an overall beneficial contribution to the society. Depending on the project design and imple-\nmentation measures to support benefit generation and control costs and externalities, the BCR may be\nlower or higher. Continuous tracking of the impact generation throughout subsequent project phases and\nmonitoring during the project implementation and operation are required to assure an overall positive\nperformance.\nThe findings of the studies carried out over a time frame of about seven years suggest a positive\nsocio-economic net performance of the FCC-ee project. This result serves to demonstrate the long-term\nsocial sustainability of the proposed new scientific research infrastructure. The analysis so far has helped\nidentify the main impact pathways with the goal of supporting the design of the research infrastructure\nfor sustained socio-economic impact generation. The findings reported here are, however, not exhaustive.\nConcerning costs, the estimates are likely to evolve further during the design phase until an investment\ndecision is made provisional and subject to updates. The approach that was taken of integrating the\nanalysis of impacts for the environment, economy and society at large is in line with the EU practice\nin policy and infrastructure impact assessment. Further complementary socio-economic analysis, given\nadditional time and resources, would permit uncovering and quantifying additional positive impacts and\nstrengthen the robustness of the benefits already estimated. Studies by Flyvbjerg et al. [240\u2013242] high-\nlight a common trend of underestimating costs, overestimating revenues, and misjudging environmental\nand economic impacts and the unintentional introduction of bias. Literature, therefore, supports carrying\nout an uncertainty analysis, especially in large-scale infrastructure projects. To achieve this, the existing\ndeterministic framework of the CBA can be expanded with a probabilistic model, covering costs and\nbenefits. This approach will provide a more comprehensive view of the project\u2019s expected outcomes.\n294\n\n4.8.3\nCost and benefit coverage\nGood coverage of the main cost and benefit pathways has been achieved with the presented socio-\neconomic assessment, although exhaustive coverage of a large research infrastructure is limited by the\nknowledge about impact pathways, models to quantify them, time, personnel and budget. The assess-\nment carried out includes the full investment costs for the civil structures, the injectors, the booster, and\nthe collider up to t\u00aft stage and 4 experiment detectors. Full personnel costs comprising CERN paid and\npersonnel supplied by the international collaborations to the programme were accounted for. Full ma-\nterials, maintenance, consumables, and service costs for the operation phase were included in the costs.\nFinally, the dismantling costs of the main ring booster and collider were also included. This part does not\ninclude the disposal of equipment that would be classified as radioactive waste. Such an estimate can be\ndone only once the technical designs have been completed. It does also not consider the residual market\nvalue of the metals that would lead to a gain after dismantling.\nThe establishment of a proper residual value for a proposed investment is a key element for input\nto the financial sustainability analysis of such a project. According to the guide to the European Com-\nmission Cost-Benefit Analysis of investment projects, the discounted value of any net future revenue\nafter the time horizon of the project has to be included in the residual value. The guide indicates that it is\n\u201cthe present value at year n of the revenues, net of operation, costs, the project will be able to generate\nbecause of the remaining service potential of fixed assets whose economic life is not yet completely ex-\nhausted\u201d. In line with this EC guideline (p. 45, [224]) that economist practitioners use, the residual value\nis highlighted as a value with a negative sign in the cost account. If there is a \u2018use value\u2019 for the assets,\nthen the residual value is greater zero. If not, the residual value is considered zero. Both scenarios were\nconsidered in the analysis. Since the proposed infrastructure can serve two particle colliders in sequence,\nthe residual asset value is considered in this assessment. Due to the very long timespan associated with\nthe integrated programme, this social benefit-cost assessment, however, only concerns the first phase, the\nlepton collider FCC-ee. A residual asset value at the end of the FCC-ee operation phase is calculated\nthat can be made available as a \u2018gift\u2019 to a potential subsequent hadron collider project (FCC-hh). The\nresidual asset value becomes zero if no subsequent particle collider is installed that can profit from the\nbuilt-up assets. This approach has also been taken for the social cost-benefit assessment of the Large\nHadron Collider [193]. The calculation of the reference net present value (NPV) for the lepton collider\nFCC-ee project is carried out in a very conservative way: it does not include the residual asset value at\nthe end of the observation period. For the purpose of showing that further societal impacts are possible\nand that an integrated programme consisting of a lepton collider (FCC-ee) followed by a hadron collider\n(FCC-hh) is preferable, this benefit can be included in a wider NPV.\nThe materialisation of negative externalities and benefits depends largely on the design of an\nimpact-creation framework and external conditions.\nNegative externalities such as the carbon footprint and the associated shadow cost of carbon de-\npend on the procurement actions taken for the construction, the power purchasing agreements concluded\nfor construction and operation, and the national carbon pricing at the time of generating the carbon foot-\nprint. The indicated shadow cost of carbon considered the construction and operation of the research\ninfrastructure. The costs for the accelerators and detectors could not be included at this time since they\nrely on the availability of a technical design and a procurement scenario.\nThe effects of potential disturbances such as noise and induced traffic linked to the construction\ndepend significantly on the actual number of people that would be affected. Additionally, certain impacts\nare challenging to predict at this early stage because of a lack of forecast models for certain benefit\npathways, because they could not be identified, because of a lack of time and resources, or simply\nbecause of large uncertainties. Examples include the wider positive externalities that can emerge from\ndeveloping novel products and processes for re-using excavated materials, advancing technologies for\nlow-carbon construction materials, generating local synergies with the municipalities hosting surface\nsites, the unanticipated creation of high-value technology spin-offs, and the invention of entirely novel\n295\n\ntechnologies.\nThis analysis focused on the direct benefits currently known and foreseeable based on past fac-\ntual evidence, for instance, from the LHC and the European XFEL projects. It was concluded as soon\nas a high level of confidence was achieved in demonstrating a break-even point between benefits and\ntotal costs, including noteworthy negative externalities. Conservative assumptions were made for all es-\ntimates. Where a causal relationship between positive or negative effects and the project could not be\nreliably established, the item was entirely left out. For cost and benefit items for which commitments re-\nmain to be formulated (e.g., the development of dedicated open software platforms to support knowledge\ndissemination and international collaboration, the conclusion of renewable energy contracts or PPAs, the\nsupply of waste-heat, projects to re-create and strengthen the lost habitats, contributions to the operation\nof regional emergency services), the elements were labelled to be considered as a \u2018wider\u2019 societal impact.\nThey were included in the calculation of a wider net present value only.\nThe economic benefits of visitors rely on the existence of a visit programme, dedicated visit points,\ninfrastructures and guides. The reported benefits of onsite visitors are incremental with respect to the\ncounterfactual scenario in which no future particle collider project is implemented. This means, it cap-\ntures the likely benefits on top of the effects generated by visitors that come to CERN after the end of the\nHL-LHC programme. This counterfactual case is envisaged to be less impactful, since CERN without\na new flagship project at a global scale is assumed to be less attractive for visitors, as recent surveys of\nCERN visitors carried out in the first quarter of 2025 reveal. Some benefits are intangible in nature, such\nas advances in scientific knowledge, impacts related to science diplomacy, ethical considerations, and\ntrust in science. Although benefits created by open software and collaborative platforms have significant\nvalue potential, it is challenging to estimate which, when and in which ways such benefits reach society\nwithout a dedicated innovation creation and transfer programme in place for such technologies.\nSeveral further wider benefits have been envisaged, but were not further pursued at this stage due\nto resource and time constraints associated with unambiguously clarifying the demand. They include, for\ninstance, the strengthening of the local and regional electricity and communication networks, the creation\nof soft mobility, the contribution to the improvement of public transport, the creation of housing and\nschooling facilities, and the development of local businesses and services. However, the study included\nthe development of a framework to start elucidating the demands for such wider benefit potentials with\nthe municipalities in the perimeter of the project. Ongoing and future socio-economic analysis will shed\nmore light on those opportunities once the demands are better understood.\n4.8.4\nCost and negative externalities\nFor the cost-benefit calculations, the FCC has been considered as a design-to-cost project, with a total\ninvestment including 4 experiments and the t\u00aft stage, projected at approximately 16.2 billion Swiss francs\n(undiscounted) with an uncertainty range of -5% to +20%. This figure encompasses studies, preparatory\nactivities, design work, civil construction works, creation of technical infrastructures, all particle accel-\nerators (injectors, booster and collider) and all investment costs related to the four experiment detectors.\nPersonnel costs include all human resources involved in the project throughout all lifecycle phases,\nirrespective of the organisation employing them. The total personnel costs are composed of wages,\nindirect costs and employer-related costs without overheads. They are averages for different personnel\ncategories in the different countries participating in the project. In total, personnel costs make up about\n16.8 billion Swiss francs (undiscounted) and 7.5 billion Swiss francs (discounted).\nOperation costs refer to all expenses (both in-kind and outflows) that are needed for running,\nmaintaining, and repairing the research infrastructure throughout the entire scientific exploitation (e.g.,\nelectricity, water, spares, and human resources for maintenance and repair). The likely scenario for the\noperational costs amounts to a total of 4.4 billion Swiss francs undiscounted with a range due to uncertain\ncosts of resources (e.g., electricity and water), supplies and service contracts. The discounted costs are\n296\n\naround 1.9 billion Swiss francs. This corresponds to an average annual undiscounted cost of about 250\nmillion Swiss francs and about 105 million Swiss francs discounted over the operational time that spans\nfrom commissioning to the end of operation.\nThe cost figures used for this analysis, along with the projected number of project users must\nbe regarded as a working hypothesis that serves for estimating the socio-economic performance, that\nhelps to identify key impact pathways. It also helps in understanding which benefit potentials may still\nhave potential for further development. They are formulated based on the understanding of the project\nat the time of the analysis and are expected to undergo further revisions and refinements as the design\nprogresses.\nEstimates of the following cost items covering the period from the investment decision to the end\nof the FCC-ee operation phase have been included in the presented analysis:\n\u2013 Capital expenditures for civil construction, technical infrastructures, all particle accelerators (in-\njector, booster, collider) including the upgrade to t\u00aft operation and four experiments.\n\u2013 Cost of acquisition of all land for the surface sites, accesses and nature enhancement around the\nsites.\n\u2013 Cost of access road creation or refurbishing.\n\u2013 Creation of off-site infrastructures required for construction and operation (e.g., accesses, water\nsupply, water treatment, local electricity connections).\n\u2013 Full personnel cost estimates (CERN and the international collaboration) required for the design,\nconstruction and operation phases covering the particle accelerators, technical infrastructures and\nexperiments.\n\u2013 Typical operation costs (consumables, water and energy, maintenance, repair).\n\u2013 Dismantling cost of the lepton collider and its specific technical infrastructures that cannot be\nreused for a subsequent hadron collider.\n\u2013 Negative residual value of the infrastructures for a subsequent particle collider project.\nIn addition to the items mentioned so far, a portion of the investments involving reusable and\ndurable assets such as superconducting radiofrequency systems, electricity infrastructures, civil struc-\ntures, and basic technical infrastructures will last for use in a subsequent particle collider project. Ac-\ncording to the EC guidelines on Cost-Benefit Analysis (p. 45, [224]), this residual value is reported as a\ndiscounted value with a negative sign in the cost part. The residual value of the initial phase assets is sig-\nnificant and contributes to the sustainability of the integrated FCC programme. The estimated discounted\nvalue stands at approximately 2.5 billion Swiss francs, equivalent to 24% of the total investment.\nEstimates of the following negative externalities have been included in the presented analysis:\n\u2013 Cost of managing excavated materials as part of the investment cost.\n\u2013 Shadow cost of carbon for civil construction and the energy used for operation.\n\u2013 Cost of rewilding measures in the vicinity of the surface sites (e.g., preservation and improvement\nof wetlands, creation of trees to compensate for forest clearance and the creation of meadows and\ngrasslands) as part of the investment cost.\n\u2013 Economic loss (direct, indirect upstream and induced downstream) caused by the consumption of\nagricultural land for a period of 30 years.\n\u2013 Economic value of the cleared forest.\n\u2013 Economic value of loss of habitat and biodiversity.\n\u2013 Societal cost of construction and operation-related noise.\n\u2013 Societal cost of added traffic and air pollution induced by the transport of excavated materials.\n\u2013 Societal cost of additional ionising radiation.\n297\n\n\u2013 Societal cost of radioactive waste as part of the operation cost.\n4.8.5\nImpact pathways\nThe following impact pathways have been included in the analysis either as core elements or as potential\nwider benefits:\n\u2013 Value of scientific content production.\n\u2013 Increased market value of early-stage scientists and engineers.\n\u2013 Value of on-site tourism.\n\u2013 Value of online presence and social media activities.\n\u2013 Value of industrial spillovers involved in the construction of infrastructures, accelerators and ex-\nperiments.\n\u2013 Market value of ICT spin-offs based on the frequency of past and current spin-off company creation\nat CERN.\n\u2013 Societal value of open software products.\n\u2013 Market value of waste heat supplied and the societal value of carbon emissions avoided.\n\u2013 Market value of additional renewable energy sources created as a result of long-term power pur-\nchasing agreements.\n\u2013 Market value of treated waste water.\n\u2013 Societal value of improved and recreated wetlands, meadows, grassland and forests.\n\u2013 Economic value of compensated agricultural spaces.\n\u2013 Societal value of regional emergency and fire-fighting services required for the new research in-\nfrastructure.\nThe following impact pathways are considered highly reliable and form, therefore, a set of core\nbenefits on which the conservative net present value is based:\n1. Value of produced and cited scientific publications.\n2. Lifetime salary premium of early-career researchers and engineers aged under thirty.\n3. Incremental value for suppliers due to follow-up contracts that result from their activity in the\nproject.\n4. Value of on-site visitors based on the travel cost method and local spending.\n5. Leisure time value of people consuming project-related online and social media content.\n6. Estimated value of open software developed in the area of particle detectors and experiments, used\nby other scientific institutes and industries.\nThe first impact pathway assessed is the value derived from scientific content production. It stems\nfrom the knowledge flow generated by scientists and engineers engaged in the collider and its experi-\nments, resulting in diverse scientific products, ranging from journal articles and working papers to con-\nference proceedings and presentations. These products can have a lasting impact, extending beyond\nthe high-energy and particle physics community, potentially influencing other knowledge domains and\naddressing broader societal challenges. Scientometric techniques were employed to estimate scientific\nproduction and its propagation from the FCC-ee project. The methodology involved analysing historical\npatterns observed in comparable physics research programmes like Tevatron, LEP, and LHC. The eco-\nnomic concepts of opportunity cost and value of time were employed to determine the social value of\nscientific products. This approach considered the time spent by individuals, depending on their involve-\nment and responsibilities, in an experiment collaboration for producing these outputs and valued it based\n298\n\non their average hourly salaries. This method was applied to estimate the social value of scientific prod-\nucts produced by researchers directly involved in the research programme (so-called \u2018tier 0\u2019 products),\nthose citing the initial tier 0 knowledge (so-called \u2018tier 1\u2019 products), and products citing tier 1 outputs\n(so-called \u2018tier 2\u2019 products). Between 34 000 and 38 000 scientific products are expected to be directly\nproduced in the course of the FCC-ee project (tier 0 publications), with an additional 538 000 to 618 000\ntier 1 and 2 products likely to be generated based on that corpus until the year 2083 (see Fig. 4.11).\nFig. 4.11: Expected distribution of FCC-ee scientific products over time.\nConsidering that about 55% of the time spent by researchers is dedicated to scientific research ac-\ntivities and the production of the production of scientific outputs, but only about 22% can be attributed to\nFCC-ee specific scientific products, the estimated benefit from scientific production is around 6.51 billion\nSwiss francs undiscounted and about 2.8 billion Swiss francs discounted. This valuation accounts for\nthe diminishing value of tier 1 and tier 2 products compared to tier 0 products, as knowledge propagates\nthrough subsequent waves of production and the initial input from FCC-ee progressively diminishes.\nThe second impact pathway studied is the value of early career research and engineer training,\nwhich reflects the project\u2019s role in imparting knowledge, fostering skills development and building ca-\npacities for individuals actively engaged in the research programme throughout its lifecycle. The value\nstems from the fact that persons who were engaged in large-scale, multi-sectoral high-tech and science\nprojects at CERN represent a higher value to their eventual employers than persons who do not have\nsuch training experience. This is reflected by higher starting wages and faster-growing salaries. The\neffect remains until the person retires, and it leads to an overall incremental added value with respect to\npeers without such an experience. The analysis specifically evaluated the benefits accrued by technical\nstudents, doctoral students, post-doctoral researchers, and associated scientific and engineering person-\nnel up to a cut-off age of 30. The analysis did not include the training value for apprentices and other\nhighly qualified personnel with limited-term contracts, temporary labour and contracted workers. The\nbenefit has been quantified by estimating the lifelong career development improvements for participants\nupon entering the labour market after gaining work experience within the research programme. Previous\nstudies, further validated through a survey involving approximately 2600 individuals, indicate that the\nlifetime salary benefit for an early-stage researcher working at FCC-ee ranges from a minimum of 2% to\n10% for the average period of stay in the research infrastructure (3.78 years) (see Fig. 4.12). The total\nundiscounted socio-economic benefit is assessed at around 20.7 billion Swiss francs, and the discounted\nvalue is around 5.0 billion Swiss francs.\nThe third impact pathway explores the benefits generated by the project for industrial suppliers\nengaged in the construction of the infrastructure, the particle accelerators, and detectors. The benefit\nstems from increased financial performance of the suppliers a few years after they have received contracts\nin the frame of the project. The effect of being a supplier in a large-scale project, in particular in domains\nthat are characterised by project-specific designs, developments, and adaptations of off-the-shelf products\n299\n\nFig. 4.12: Lifetime salary of early-career researchers by sector of employment.\nand services, is linked to the gain of experience, increase in efficiency, and a broadened market access. In\nessence, the impact stems from a knowledge gain acquired through close collaboration with the research\ninfrastructure. This knowledge, in turn, contributes to the creation and improvement of new processes,\nproducts, and services that suppliers can leverage in other markets and domains. It leads to additional\ncontracts that the supplier is able to conclude because of that knowledge gained. This cause-effect-impact\nchain has been exhaustively analysed over some decades, and it has been found to be robust and stable.\nA profit multiplier has been determined, standing at 1.96 for procurement of items with low or moderate\nlevel of technology intensity and 3.06 for procurement with high level technology intensity. Applying\nthis multiplier to the investments that are likely to generate further industrial spillovers, the undiscounted\nbenefits are estimated at 17.6 billion Swiss francs. The discounted benefits are estimated at 9.6 billion\nSwiss francs (see Fig. 4.13).\nThe fourth impact pathway concerns the benefits generated by on-site visitors. Before 2020,\n150 000 visitors per year came to CERN. In 2024, after the opening of the new Science Gateway visitor\ncentre, the number increased to about 350 000 external visitors (not counting visits of persons partici-\npating in CERN projects, company visits and visits of employee families, accounting to about 40 000\nadditional persons). While in the period before the Science Gateway the participation was equally dis-\ntributed among group visits and individuals, the significantly increased capacity to welcome unguided\nvisits led to a change in the distribution. Today about 76% of people visit CERN individually and 24%\ncome as part of groups that enjoy the possibility to also visit experiment facilities, in particular the ones\nlinked to the LHC. 55% are classified as \u2018CERN motivated\u2019 visitors, whose primary purpose of the trip\nwas to visit CERN, while 45% are \"region motivated\" visitors, who travelled to the area for other reasons\nand took the chance to also visit CERN. The absolute number of persons that are part of visit groups\nremained relatively stable. Two campaigns of guided systematic interviews with on-site visitors before\nand after the opening of the Science Gateway permitted a robust multi-year spending behaviour of the\nvisitors to be established (see Fig. 4.14). In total, more than 4 000 individuals were interviewed, and\n300\n\nFig. 4.13: Time profile of FCC-ee industry benefits for suppliers, compared with the high-tech invest-\nments costs (Swiss francs, undiscounted - baseline scenario).\nonly about 3 550 responses with self-consistent and credible answers were retained for the analysis. The\naverage stay of persons in the region is 3.75 days, indicating that once they have visited CERN they\nextend their visit to further destinations in the vicinity.\nThe local spending associated with the visit ranged between 625 Swiss francs for group visitors\nand 713 Swiss francs for individual visitors, with a mean of 691 Swiss francs for all visitors. Based\non the survey, sampling from the obtained visitor spending distribution, the sum of the local spending\ndue to 350 000 annual on-site visitors translates to a tangible economic benefit for the region of about\n250 to 350 million Swiss francs per year. This figure does not, however, capture the socio-economic\nbenefit related to the FCC-ee. Based on this current survey, only a certain fraction of future visitors can\nbe attributed to an FCC. As outlined initially, the analysis limits benefit potentials to the incremental\neffects, i.e., the difference between the effects of on-site visitors that can be attributed to the existence of\nthe FCC and the evolution of CERN without the FCC. For this reason, the following assumptions were\napplied to estimate the incremental socio-economic benefit for the FCC-ee:\n\u2013 Conventional CERN visits: an increasing share of these visitors is attributed to FCC-ee, starting at\n0% in 2024 and gradually rising to 50% by 2064.\n\u2013 Visitors to the FCC-ee construction sites and the four experimental sites: these visitors are fully\nattributed to FCC-ee, as they would not have been accounted for in a scenario without FCC-ee.\n\u2013 Visits to the decommissioned LHC tunnel: adhering to a conservative approach, these are not\nattributed to FCC-ee since they would be justified even in the absence of the FCC-ee.\n\u2013 Visits to FCC experiment visitors centres.\n\u2013 About 10% of all visitors are coming to the CERN main site.\n\u2013 Open-day visitors: these are attributed to FCC-ee only for the additional capacity created by the\nnew accelerator; all other visitors are excluded from the count.\n\u2013\nBased on these assumptions, it is estimated that out of almost 19 million visitors throughout the\nentire observation period, only about 5.5 million are assumed to be attracted by FCC-ee (see Fig. 4.15),\nwhile the remaining will be motivated more by the overall CERN activity and longstanding worldwide\nreputation of scientific excellence.\n301\n\nFig. 4.14: Distributions of the spending of all on-site visitors, individual visitors and visitors that come\nto CERN as part of groups.\nConsidering that only the incremental benefit is reported here, the difference between the num-\nber of visitors that CERN would welcome without and with an FCC-ee is about 13.5 million over the\nobservation period.\nThe benefit for on-site visitors was monetised using the travel cost method, which incorporates the\ncosts borne by visitors to travel to CERN and FCC, the economic value of time spent travelling, along\nwith local expenditures connected to their visit based on two actual surveys carried out at CERN over\ntwo years (pre- and post COVID). The discounted benefit generated by about 5.5 million onsite visitors\nattributable to FCC-ee is estimated to be approximately 2.1 billion Swiss francs.\nThe fifth impact pathway analysed concerns virtual visitors who consume webpages and social\nmedia. Due to the limited availability of data, the analyses concerned only websites and social media\nchannels that are directly managed by CERN. The estimate, therefore, significantly underestimates the\nactual benefits generated by numerous online content that would be made available on a global scale.\nThe estimated number of online visitors is based on historical data collected by CERN\u2019s commu-\nnication group regarding visits to the main CERN website and social media accounts. Assumptions were\nmade about the number of visits specifically related to FCC-ee. This estimate has been revised to reflect\nchanges in the project\u2019s timeline and to ensure consistency with the revisions made in the estimation\nof onsite visitors, particularly regarding the share of FCC-ee attribution. It is assumed that the highest\nattributable share of visits is approximately 50%, aligning with the assumption made for CERN visitors.\nIn the scenario without the FCC, it is assumed that the number of online visits to websites and\n302\n\nFig. 4.15: Number of on-site visitors attracted by FCC-ee over the period 2024-2064 used for estimating\nthe impact estimation.\nsocial media will follow the same patterns as the on-site visitors in the absence of the FCC-ee. In\nthe scenario with the FCC, the number of online visits corresponds to the trend of growth of scientific\npublications due to the projected FCC-ee research programme. The share of online visits attributable to\nthe FCC-ee starts as a marginal share of the total CERN online visits. The main jump in online visits is\nexpected to occur with the start of operation. This share is expected to grow further during the operative\nphase. The number of online visitors is expected to reach its maximum several years after 2050 and\nthe end of operation. In these years, the share of the total CERN online visits associated with the FCC\nreaches conservatively about 50% and remains constant. This assumption is in line with survey results to\nonsite visitors about the reason to visit CERN today. Based on these assumptions, for the FCC-ee over\nthe 2024\u20132064 period, impressions are estimated at 1.7 billion, engagements at 79 million, and CERN\nwebsite visits at 175 million. These estimates are highly conservative and do not take into consideration\nfuture social medial developments and online platforms are likely to appear, but whose existence can\ntoday not be anticipated.\nThe monetisation of these visits is based on the actual observation of an online presence of a little\nover 3 minutes. Distributions are applied to different media types, such as social-media interactions\nand consuming online video snippets related to FCC. The value of time spent is determined using the\n\u2018opportunity cost\u2019 method, which suggests that time spent on social media and websites represents a\nmissed opportunity to engage in other potentially profitable activities. Since not all virtual visitors are\nnecessarily part of the economically active workforce, the opportunity cost of time was estimated by\nusing per capita GDP (instead of wages), adjusted based on the geographical distribution of virtual\nvisitors. The total undiscounted cultural benefit for online visitors is estimated to be approximately\n229 million Swiss francs, which corresponds to 102 million Swiss francs discounted.\n303\n\nThe sixth core impact pathway encompasses free and open-source software, systems, and plat-\nforms causally linked to the research programme. It is assumed that in particular software related to\nthe experiment and detector projects generates incremental societal value due to the adoption by other\nscience projects, research institutes, and companies with particular needs that cannot be easily satis-\nfied by commercially available software. While the first user base is typically found in the physics,\nastronomy, and medical research domains, companies using such software can be very diverse. Re-\ncent examples of using software from the LHC experiments range from space-borne earth observation\nsystems through medical imaging and mining to shipping container traffic and stock-market transaction\nanalysis. In essence, in any application where massive amounts of data need to be processed, patterns\nneed to be identified in background dominated environments, time-critical applications demand custom\nsolutions, and data processing efficiency is key to success, the developments of particle physics scientists\nand engineers are sought after.\nThe estimation of this benefit pathway is based on the use of actual particle detector modelling\nand simulation software, for which the use outside the core community could be tracked over the recent\nyears. It serves as a \u2018proxy\u2019 for comparable developments for which the need during the development\nof FCC detectors and experiments has been confirmed. Like software package analysis, new software\ncan find use beyond the core community, thereby generating a spillover benefit for society. A number\nof developments will concern the use of artificial intelligence in this area, configurable hardware, edge\ncomputing, and ever-evolving data communication technologies. Several of these developments are\nadmittedly associated with uncertainties, but as the past has shown, it is likely that the collaborations\naround the FCC-ee experiments will be able to make significant contributions in the ICT domain.\nFor detector modelling and simulation software, approximately 50 research centres, space agen-\ncies, and companies were identified using software developed for the LHC experiments. This included\n38 institutions beyond CERN that contributed in some way to the developments. Examples include but\nare not limited to the Fermi National Accelerator Laboratory, SLAC National Accelerator Laboratory,\nthe Centre for Medical Radiation Physics, and the European Space Agency. Additionally, 12 other lab-\noratories, institutes, and companies use such software without contributing to its development. They\ninclude, for example, NASA, General Electric, Philips, Siemens, Varian, Boeing, and General Motors.\nCERN does not systematically track the number of users and installations, but data available in 2023\nsuggest a current user community of about 95 contributing institutes (excluding CERN). Assuming the\nratio of 3:1 between contributing and non-contributing institutions remains stable, the total number of\nnon-contributing users is estimated to be around 30. In the absence of more reliable data, this estimate is\nconsidered reasonable and conservative.\nThe benefit is estimated as the avoided cost for the external users, and it is based on the cost of\nproduction of comparable new software. It was estimated that the production cost of existing detector\nmodelling and simulation software was about 44.2 million Swiss francs up to 2013, covering the first\n20 years of its development starting in 1994. CERN contributed about 50% of this cost (22 million\nSwiss francs), with the remaining amount funded by other external contributors. The estimates are\nbased on the hypothesis of comparable cost figures for FCC-ee related software and assuming CERN\u2019s\ncontribution remains at 50%. The avoided cost for each contributing organisation is the total estimated\nproduction cost minus their specific contribution, while the avoided cost for non-contributing users is the\nfull production cost. It is assumed that new software would be first released after 5 years of development\nwith developments continuing over the years, even during the operation phase, due to the continued\ninterest by academia and industry.\nIn this scenario, the total cumulated avoided cost representing the total undiscounted benefit is\nestimated to be about 7.4 billion Swiss francs. The discounted benefit is about 4.4 billion Swiss francs.\nThis benefit, in fact, would stand for a range of potential software developments that cannot be explored\nin detail at this early stage. It is advised that any future development foresees an open access mechanism\nfor such software, actively promotes such software in areas outside the particle physics community in\n304\n\nscience and industry and, most importantly, includes a systematic tracking of active users to help make\nsocio-economic impact estimates more accurate and reliable.\n4.8.6\nWider benefits\nA number of wider benefits have been analysed in detail in addition to the core benefits presented in the\nprevious section. Due to uncertainties that are linked with the possibilities to actually turn those wider\nbenefit potentials into tangible impacts, they are not considered in the calculation of the reference base-\nline net present value. The analysis and quantification of those benefit potentials is, however, based on\nfactual observations of past effects and outcomes and is therefore solid with respect to monetisation. As\nwith the core benefits, highly conservative working assumptions have been established, and only effects\nthat can be credibly justified have been included. Therefore, a second net present value is presented that\nincludes those wider benefits. To turn such potentials into tangible impacts, the preparatory implemen-\ntation phase of the future project needs to include dedicated work that plans for such benefit creation.\nVoluntary objectives and commitments are needed by the project owners to put instruments in place to\nactually turn the potentials into impacts. Last but not least, monitoring and tracking will need to be put\nin place to follow up on the impact generation.\nThe following wider benefits have been studied and are briefly presented in this section:\n1. Open information platform\n2. Open collaborative software\n3. Company spin-off generation in the information and communication technologies (ICT) sector\n4. Build-up of renewable energy sources\n5. Supply of waste heat\n6. Avoidance of greenhouse gases by substituting traditional heat energy sources with recovered and\nsupplied waste heat\n7. Improvement and creation of habitats and increase of biodiversity\n8. Strengthening of emergency services\nA future, global collaborative research project relies on a long-term, open scientific and technical\ninformation platform that permits the community to make their knowledge widely available so that it\nbecomes findable, accessible, interoperable and reusable (FAIR principle). CERN has a long-term track\nrecord in putting such infrastructures in place, the World Wide Web being the most prominent one. This\ntechnology subsequently permitted the development and making available of additional services, such as\nthe CERN Document Server (CDS), which is based on the in-house developed Invenio platform. This\ndevelopment has led to the creation of the Zenodo service, which the European Commission has endorsed\nas the catch-all repository for all EU-funded research. Today CERN operates this platform that is entirely\npart of the European Open Science Cloud (EOSC) for the European Commission. By continuing to\nbe at the forefront of big science, CERN can have a lead role in scientific and technical information\nprovision in Europe and at a global scale. The launch of a new large-scale science mission, the FCC,\njustifies not only the continuation of ongoing developments, but will likely also lead to the development\nand implementation of a new generation of information systems, in line with past occurrences. Such a\nplatform may offer functionalities that go beyond pure document and data management and long-term\ndata preservation. It may offer services that are today impossible to conceive. In order to estimate\nthe potential value of such a future development, the value of the Zenodo platform was estimated as a\nconservative reference with minimum functionality offered to society today. This was possible, because\nhistoric data of sufficient quality for relevant periods could be identified. An econometric model was\nconstructed to estimate the socio-economic impact of that virtual information repository, designed to\nfulfil collaborative information storage and usage requirements. The estimated monetised value is derived\n305\n\nfrom measurable benefits associated with comparable repositories, encompassing data storage, online\nusage, and downloads, net of the present value of its development, operation and maintenance costs.\nThe undiscounted value over the FCC-ee observation period of such a platform is 5 billion Swiss\nfrancs, and its discounted value is about 2.7 billion Swiss francs. To turn such an impact potential\ninto reality, several pre-conditions apply: the global community participating in the project has to have\na demand for such a platform, the community must be committed to use the platform, communities\nbeyond the high-energy and particle physics domain must adopt the platform (as was the case with\nthe Zenodo platform being endorsed by the European Commission). The fundamental requirements\nrely on an intent to play the role of developing and operating an information platform for several user\ncommunities. Long-term sustained resource engagement and a plan to disseminate the developments\nbeyond the core community are also needed.\nAnother typical case for open platforms in the history of CERN\u2019s large international collaborations\nis the creation of tools that support collaborative work. The \u2018Integrated Digital Conference\u2019 (Indico)\nevent management system is one example of such development. It revolutionised the management of\nphysical and virtual meetings, lectures, conferences and led to a comprehensive documentation of col-\nlaborative work and can be considered a key enabler of global collaborative projects. Since its start of\ndevelopment in 2002, the platform has spilled over to numerous academic and international organisations\nworldwide. A future large-scale project not only has very similar needs, but will create demands beyond\nthose that are satisfied with this platform today. The integration of collaborative writing, sketching, AI\nsupport for meetings and minute taking, translation among different languages, collaboration manage-\nment, video conferencing, recording and media publication, real-time messaging, shared workspaces,\nintegration with document management, approval and selected information distribution processes are\njust a few selected examples for which the need is already starting to appear in the frame of the studies\nrelated to the FCC.\nFor these reasons, the current Indico platform was chosen as a conservative, representative exam-\nple of a collaborative platform that can enable and improve future collaborative work in the frame of a\nlarge-scale project. The value generated from developing a new service to facilitate the worldwide col-\nlaboration involved in the FCC project in terms of meetings, calls, and event management was assessed\nby considering the willingness to pay (WTP) by private users for a comparable toolset, totalling 7.5 bil-\nlion Swiss francs undiscounted and 3.5 billion Swiss francs discounted. Since the potential of such a new\necosystem relies on a commitment for development, the adoption by communities beyond high-energy\nand particle physics, the value was only considered as a wider benefit.\nThe knowledge-transfer office records of the last two decades have shown that a stable number\nof companies have been created every year by persons who were engaged in CERN\u2019s flagship particle\ncollider project and the international experiment detector collaborations. A prominent example includes\nProton AG with over 400 employees and more than 100 million customers, offering secure e-mail and\nVPN as an unparalleled service to other providers. Other examples are Advacam which specialises\nin imaging devices for various industrial applications based on particle detector technology, LightEye\nworking on LiDAR technology for long-range wind speed measurements to improve aviation safety\nand PlanetWatch which specialises in data acquisition of environmental data. Based on these factual\nhistorical data, it is assumed that FCC-ee would generate approximately two new spin-off companies in\nthe information and computing technologies (ICT) sector alone each year from the design and preparation\nphase until the end of the observation period. Considering the probability of company survival each year\nand the annual market value of companies in the ICT sector, the socio-economic benefit is estimated to be\nat least 832 million Swiss francs undiscounted and 409 million Swiss francs discounted. This figure does\nnot include the economic benefits that are generated by numerous micro enterprises and independent\nconsultants that carry out their activities thanks to the experience and skills they acquired in the frame of\nlarge-scale particle accelerator and experiment detector projects.\nSome selected environmental benefits that the project could generate were also assessed. They\n306\n\ninclude the voluntary goal of supplying the infrastructure with electricity from renewable energy sources.\nEntering specific energy supply contracts and long-term power purchasing agreements (PPAs) can serve\nas a lever to build up new renewable energy sources since the power supplier can secure long-term\nfunding of new renewable energy investment projects before making a financial investment decision. A\nscenario of a portfolio of complementary energy supply contracts for the FCC construction and operation\nhas been analysed in terms of this value-generation pathway. Assuming that after 2050, society is largely\nde-carbonised and conservatively, no growing demand for such a funding instrument is assumed on a time\nhorizon of more than 30 years, the reported benefit remains limited: 227 million Swiss francs discounted\nand 117 million Swiss francs discounted. The development of a renewable energy portfolio can, in\nprinciple, begin with an investment decision for a new particle collider project and with a commitment of\nthe project to engage renewable energy sources. In this case, the potential benefit can rapidly turn into a\ntangible economic benefit. It is suggested that this benefit be revised by that time and reconsidered under\nthe evolving project implementation boundary conditions.\nA large part of the energy used to operate the particle collider and its experiments is converted into\nheat. Traditionally, the heat is dissipated via water-based cooling systems that connect to evaporation\ntowers. A study has been conducted to prove the feasibility of recovering and re-using waste heat.\nRecovery and supply of waste heat is a concept that is built into the design of the particle collider from\nthe onset. Recovered waste heat will be supplied via district heating networks to consumers in the\nvicinity of the FCC-ee sites. The environmental benefit stems from the fact that the energy used by the\nFCC research infrastructure is reused and supplied for heating and cooling purposes, avoiding the use\nof alternative, mainly non-renewable, sources with higher carbon intensity such as gas, wood, oil and\nconventional electricity mix. The environmental benefit of waste heat reuse is derived from the avoided\nGHG emissions in the project scenario, where CERN supplies waste heat\u2014produced using a cleaner\nelectricity mix\u2014to district heating networks serving consumers near the FCC-ee sites. This is compared\nto the emissions from alternative heating and cooling methods typically used in the CERN region. The\ntotal benefit is estimated at 170 million Swiss francs undiscounted, corresponding to 74 million Swiss\nfrancs after discounting.\nHowever, turning this potential benefit into tangible socio-economic impacts requires an adapta-\ntion of the operation schedule to the demand curve, agreements with district heating operators to put\nnetworks in place and to operate them, and customers who commit to take off the heat. Since such de-\nvelopments are typically time-consuming, entail territorial developments that last one to two decades,\nand depend also on local developments around the future surface sites, the benefits are not included in\nthe core net present value calculation. In addition, the potential benefits emerging from the avoidance\nof greenhouse gas emissions by replacing conventional heat sources are uncertain for the timescale after\n2050, when in principle the economy aims at being largely de-carbonised. Together the benefit potentials,\ni.e., the costs saved by using waste heat instead of conventional heat sources and avoiding greenhouse\ngas emissions, add up to about 313 million Swiss francs undiscounted and 132 million Swiss francs\ndiscounted. Once a decision to move forward with a project has been taken, a revision of those impacts\ncan take place, since a stronger commitment from the project owner also enables regional stakeholders\nto plan for waste-heat district heating networks and this eventually will lead to significantly increased\nbenefit potentials.\nThe project does only consumes land due to the development of eight surface sites, but it also opens\nopportunities to create new natural spaces in the immediate vicinity of the sites. Creating or improving\nthose habitats to integrate the surface sites well in their environments can strengthen the natural spaces\naround the sites, protecting them from further artificialisation and helping to improve the biodiversity,\npartially compensating for the effects of the loss of space. While today rewilding projects are foreseen\nin connection with the surface sites, they have not yet been discussed with the local stakeholders and\nthey have not yet been designed. Therefore, this benefit remains potential and is not included in the\ncalculation of the core net present value. The rewilding of habitats and biodiversity could represent an\n307\n\nundiscounted value of 0.4 million Swiss francs corresponding to 0.2 million Swiss francs discounted.\nThe future particle collider will be embedded in a territory that spans an area of roughly 30 \u00d7\n30 km. Care has been taken to select locations for surface sites that are in the vicinity of major trans-\nport routes. Nevertheless, the current concept implemented at CERN to provide emergency, rescue and\nfire-fighting services to surface sites of existing particle accelerators from a central fire brigade at CERN\nbecomes unfeasible for a future infrastructure of the FCC scale. Therefore, the safety concept foresees\na strong and lasting collaboration with local emergency services. This concept can be based on support\nwith equipment, training, and personnel made available by the research infrastructure. It could help to\nincrease the expertise and skills of local emergency services, contribute with state-of-the-art equipment,\nstrengthen the number of specialists in the region and increase the cooperation and coordination among\ndifferent emergency services. This benefit potential has an undiscounted value of about 30 million Swiss\nfrancs and represents a discounted value of about 16 million Swiss francs. Since it relies on the develop-\nment and implementation of a safety concept and plan at the territorial level which can require significant\namounts of time and adjustments that make the concept implementable, the benefit is not included in the\ncore net present value calculation today.\nFurthermore, two other classes of benefits described in the subsequent sections have not been di-\nrectly included in the overall formula to determine the project\u2019s net present value: the economic creation\nof value added and the public good value.\nComplementary analysis of economic value added\nThe economic value added has been estimated in addition to the socio-economic impact by analysing\nthe economic linkages (indirect, direct and induced) during the entire 30-year period covering design,\nconstruction and the operation phase of the FCC-ee using the established Input-Output Table method-\nology [243]. The study estimated the economic and employment effects that are connected to the con-\nstruction and operation of the new research infrastructure. They are not included in the incremental\ncost-benefit analysis, since they do not represent the creation of new economic goods and services be-\nyond the research infrastructure, but they lead to economic value added due to the activation of numerous\neconomic sectors in the frame of the research infrastructure-related activities.\nThese effects arise mainly from the construction of civil structures, particle accelerators and collid-\ners, technical infrastructures, experiments, operating expenses, and consumption related to the personnel\ninvolved. This economic analysis was only carried out for an infrastructure with two experiments and\nwas not updated to the current baseline.\nUsing an economic input-output model, the cumulated expenditure of about 21 billion Swiss francs\nover a 30-year construction and research operation period could be connected to some 800 000 person-\nyears of employment opportunities, corresponding to almost 30 000 jobs per year via global value-adding\nchains. In addition to about 6 000 directly project-related science, engineering, administration, and man-\nagement jobs globally, more than 20 000 jobs are needed to provide the goods and services for construc-\ntion and operation. The host countries, Switzerland and France, and especially the canton of Geneva\nand the Departments of Ain and Haute-Savoie could benefit most from the operation phase-related ex-\npenditures. In total, around 13 000 jobs would be filled or created annually on average in France and\nSwitzerland.\nAn initial, construction-related investment of 12.1 billion Swiss francs directly generates globally\n5.4 billion Swiss francs of value added, generating almost 80 000 person-years of employment, i.e., more\nthan 8 000 jobs per year over a ten-year investment period. Including the indirect effects in the production\nprocess, value added linked to the investment rises to 11.6 billion Swiss francs, leading to about 180 000\nperson-years of employment or 18 000 jobs per year during the investment period. Widening the system\nboundaries to include depreciation (i.e., the capital stock firms need to build up or replenish in order\nto cope with the FCC-related production), the FCC-related value added grows to more than 14 billion\n308\n\nSwiss francs and leads to more than 230 000 person-years of employment opportunities or 23 000 jobs\nper year during the investment phase. All types of companies, large, medium and small, can enjoy the\nbenefits from the value added. The countries that can profit from these benefits depend on the chosen\nprocurement strategy. The construction sector benefits most since almost half of the investment volume\ncan be attributed to civil engineering. Along the cycle, however, its share steadily falls, and most other\nsectors\u2019 shares rise.\nThe operation of the FCC generates value added by paying wages and social security contribu-\ntions and through the depreciation of the investment. No (net) operating surplus is considered since\nCERN, a purely scientific research organisation, is not profit-oriented. The direct value added during\nthe operation phase is estimated at around 455 million Swiss francs annually. For operation, a mix of\ninputs (intermediate goods and services) is needed, whose procurement will provide suitable firms with\nthe opportunity for sales and employment and thus generate about 165 million Swiss francs of indirect\nvalue added annually. The total direct, indirect and induced value added during the operation phase of\nmore than 620 million Swiss francs per year supports 8 400 jobs, the majority in France and Switzerland.\nThe buildup and supply of renewable energy sources for the operation of the research infrastructure\nwould raise Europe\u2019s value added by another 500 million Swiss francs, securing an additional 7 400\nperson-years of employment in Europe. By economic sector, the structure of the consumption effects is\nmarkedly different from the effects of the investment and operating expenditures: real estate activities,\n(retail) trade, personal services and the hospitality sector are the main beneficiaries of the consumption\nof project-related employees.\nThe lower limit for annual tourism spending due to the project in the wider Geneva region is at\nleast 130 million Swiss francs per year. Switzerland and France share the bigger part of the total effects,\nwith around 1 700 jobs linked to visitors only. Another 500 jobs are European; the rest \u2013 around 600 \u2013\nare filled outside Europe. Globally, tourism effects would sustain about 2 700 jobs.\nThe consumption of electrical energy in the frame of long-term power purchasing agreements\nwould generate a direct value added due to the capacity build-up activities of about 200 million Swiss\nfrancs, linked to 3 500 person-years of employment. Including intermediate inputs and investments\nneeded to produce and install the equipment, the contribution to Europe\u2019s value added rises to 510 million\nSwiss francs, securing 7 400 person-years of employment in Europe. Worldwide added value effects\nrelated to the electricity supply sector amount to 620 million Swiss francs or 11 600 person-years of\nemployment.\nThese figures must be interpreted with some caution. Most importantly, the indirect jobs are de-\nrived under a steady-state assumption. The estimates do not project major economic variables into the\nfuture (exchange rates, price levels and productivity being the most important ones). Therefore, the ef-\nfects are estimated as if the FCC was constructed and operated today. This should not be considered\na shortcoming, as it helps decision makers to grasp the effects of the estimates more easily when re-\nferring to a familiar frame of reference \u2013 the economy as it is today. The resulting figures on value\nadded are less compromised by this simplification, due to the fact that the evolution of economic key\nperformance parameters cannot be forecast on the timescale of an FCC project with construction starting\nin the mid-2030s and coming into operation in the late 2040s. The employment figures linked to the\nexpenditures represent reliable upper bounds since labour productivity is expected to rise. Even under\nchanging economic conditions, the FCC would remain what it is today \u2013 a major undertaking for the\nscientific community and society at large, with likely significant scientific, technological, engineering\nand economic impacts.\nThe analysis shows that the costs that a project like the FCC entails are also connected with\ntangible economic impacts in terms of sales opportunities for firms and employment opportunities for\nscientists and non-scientists alike. By concentrating on a core set of transmission mechanisms only, these\nresults constitute a lower bound for the expected economic effects. Therefore, even though the narrow\neconomic linkages of the construction and operation are not larger than would be expected for a project\n309\n\nof this size, the potential for spillovers into quite unrelated areas of technology and business are certainly\nmuch more pronounced \u2013 for example, only a few projects would have the touristic attractiveness, not to\nmention its technological and scientific potentials.\nAlso, by estimating the regional structure of the effects linked to the construction and operation of\nthe FCC, the analysis has shown that the connection between contribution to CERN, direct contracts and\nindirect benefits is not always clear-cut. For example, China and the United States, which are not member\nstates of CERN, are estimated to have sizeable economic benefits due to their prominent roles in global\nvalue chains. This information could form the basis for negotiations between CERN and countries such\nas China on intensifying and formalising closer collaborations in the future, which would be beneficial\nfor both parties.\nPublic good value\nTo gauge the volume of the societal benefits, a comprehensive survey was conducted among nearly\n10 500 individuals across nine countries [177], including both CERN member and non-member states\npotentially contributing to the future particle collider project at CERN. The survey aimed to assess pub-\nlic awareness of CERN and its research activities, to evaluate the perceived value of a new research\ninfrastructure, like FCC, to the public, and to compare this monetised value with the per-capita annual\ncontributions made by CERN member states.\nThe public good value should not be integrated in the estimate of the project\u2019s net present value,\nsince the perceived value of the project, i.e., the value that taxpayers associate with the project, is orthog-\nonal to the actually estimated incremental benefits. Measured through the willingness to pay, the public\ngood value also depends on the knowledge of the project, its costs, negative externalities and likely in-\ncremental benefits. Hence, the value of it is affected by some cognitive biases, such as, for instance, an\ninformation bias. The presence of such bias is not negative and cannot be avoided. They are part of the\nmechanism that permits people to associate a value to an asset to which they have no direct access.\nResults indicate that 41% of the respondents are aware of CERN and its mission, which, although\nlower than some other international organisations like NASA, remains generally positive. Over 80% of\nrespondents believe that scientific research at CERN advances our understanding of the universe and\ncontributes to improving quality of life. The hypothetical willingness to participate financially in the\ndevelopment of the new research infrastructure project was assessed, revealing varying distributions by\ncountry. Median values range from 2 Swiss francs per person per year in France to 20 Swiss francs in\nSwitzerland, both CERN member states. For non-member states, the median willingness to pay (WTP)\nvaries from zero in Japan to 24 in the USA (although the mean value for Japan is 10 Swiss francs, mean-\ning that a significant fraction of the Japanese adult population values that type of scientific research). The\ntotal value was estimated by multiplying the estimated per capita yearly WTP by a total adult population\nof about 380 million persons over 30 years in the CERN Member States, starting with the first relevant\ninvestments.\nIn all observed cases, the perceived public value in CERN\u2019s member states is higher than CERN\u2019s\nannual operational budget of 1.4 billion Swiss francs. The average per capita contribution in these states\nis approximately 2.5 Euro per year or about 5 Euro per income taxpayer per year. The total estimated\nWTP for a future collider project at CERN surpasses the estimated total costs of the FCC by a factor of\n20 and exceeds its quantified benefits by over 11 times.\nThese findings robustly support the conclusion that the decision to invest in a future particle col-\nlider programme at CERN can be considered justified from a societal perspective since the people who\npotentially fund the endeavour assign more value to it than it costs in total.\n310\n\n4.8.7\nConclusions\nThe socio-economic impact analysis is based on a social cost-benefit assessment conducted on the first\nphase of the FCC programme, spanning a time frame of 40 years from the financial investment deci-\nsion to the end of operation. The FCC-ee has quantified costs, negative externalities and conservative\nbenefit potentials and wider benefit potentials across various domains. Costs of about 20 billion Swiss\nfrancs discounted and negative externalities of about 354 million Swiss francs can be compared to the\nbenefits that this research infrastructure can generate. The total present value of the monetised core\nsocio-economic benefits associated with the FCC-ee research infrastructures has been conservatively es-\ntimated at a discounted value of 24 billion Swiss francs. Additional wider benefits amount to about 7\nbillion Swiss francs discounted. The infrastructures would represent a residual value of about 2.5 billion\nSwiss francs for a subsequent hadron collider, made available as a \u2018gift\u2019 to this second project.\nThe conservative estimate for the net present value (NPV) of the project over its entire observation\nperiod is about 4 billion Swiss francs, yielding a positive benefit-cost ratio of about 1.20. Including\nthe residual asset values can bring the NPV to about 6.5 billion Swiss francs. Extending the estimates\nwith wider benefit potentials, the project provides an opportunity to reach an even higher NPV. However,\nachieving such a performance requires the design, planning, and implementation of benefits, as well as\ngenerating measures with commitments and continuous monitoring and tracking at the level of CERN\nand international collaboration. Proper risk management and cost control must be in place to manage\ncosts and negative externalities.\nCosts were based on the currently available investment cost estimates and on the experience of op-\nerating CERN\u2019s particle accelerator and collider complex over the last two decades. The most noteworthy\nnegative externalities were identified, quantified and monetised using lifecycle analysis methodologies\nand guidelines at the European level for wider socio-economic impact assessment and project appraisal.\nCost values were currency and time value adjusted for 2024 as the base year.\nBenefits have always been appraised through a conservative methodology, drawing on the current\nunderstanding of the project, insights garnered from analogous past research infrastructures, and socio-\neconomic impact analyses on the LHC [193] and the HL-LHC [119] that were carried out as pre-cursors,\nanticipating the need to eventually produce an FCC socio-economic impact study.\nAdditionally, recent data collected between 2020 and 2024 has played a crucial role in shaping\nthese estimations. To ensure a comprehensive perspective, data gathering efforts included over 16 000 in-\ndividuals through online surveys. This diverse group included members of the public, visitors to CERN,\nusers of platforms like Zenodo and Indico, as well as former researchers.\nIn a likely scenario between optimistic and pessimistic assumptions, the quantified benefits exceed\nthe total costs associated with the design, construction, and operation of FCC-ee, resulting in a net\npositive socio-economic impact for the project.\nShould a financial investment decision be taken to proceed with a construction project, it will be\nnecessary to update the assessment during the coming years and to compile all the materials necessary\nto obtain funding from participating countries and seek authorisations from the host states.\nThe approach used in this analysis intentionally entirely excludes the uncertain and unforeseeable\nimpacts of knowledge increase generated by the science mission on society because of their inherent\nunpredictability.\nThe assessment of the public good value of the research infrastructure for the public offers an\ninsight into the overall benefits of a future particle collider project at CERN for society, gauged through\nthe public\u2019s perspective and willingness to financially contribute to a project\u2019s implementation. The\ninsight that the perceived value of a future research infrastructure project exceeds the costs of the FCC\nis important evidence that the public values such scientific research more than it actually costs and thus\nhelps obtain the Social Licence to Operate (SLO).\nWhile recognising the need for refinement, this analysis serves as a tool to inform decision-\n311\n\nmaking, optimise user engagement, identify and mitigate risks, and enhance social acceptability for the\nFCC-ee project. The findings emphasise that the FCC-ee project holds the promise of positive impacts\nnot only for the scientific community but for all of society, thereby contributing to the project\u2019s long-term\nsustainability.\n4.9\nReturns to participating countries\n4.9.1\nOverview\nSeveral economic analysis organisations (e.g., LSE [180], WIFO [244]) have been consulted to analyse\nhow potentially participating nations can increase the likelihood of benefiting from financially contribut-\ning to the project. An example set of those proposals is compiled in this section.\nThere exists a consensus among experts that international organisations, including CERN, gener-\nate significant economic and societal impacts beyond their core activities in their host countries and their\nparticipating nations.\nOne existing concept to ensure a continuous return to the participating countries is the International\nLiaison Officer (ILO) approach for integrating national companies in the procurement processes of the\ninternational organisation. This approach was studied by economists, and it was found that for a future\nlarge-scale project, a more structured and comprehensive approach could lead to better returns for the\nparticipating nations.\nThe recommended measures [180] to ensure good returns to the financially participating nations\nrevolve mainly around three topics:\n1. Industry benefits\n2. Training benefits\n3. Cultural benefits\nOne lever to ensure good returns is to increase the sustainability of spreading the benefits of pro-\ncurement, by enabling more firms across the various regions to successfully participate in future collider-\nrelated procurement and to tap into the value chain created by the contracts. This concerns:\n\u2013 Levelling the playing field so that more firms can participate in the procurement process.\n\u2013 Supporting SMEs as these are the firms that are most likely to face barriers in the procurement\nprocess.\n\u2013 Embedding more firms in the procurement value chain.\n\u2013 Decarbonising the procurement supply chain through aggregated energy supply contracts or power\npurchase agreements (PPAs) and energy communities that permit pooling renewable energy con-\ntracts for groups of suppliers and larger procurements.\nAnother lever is to foster brain circulation. CERN is an attractive place for people from across the\nworld to study and work. However, many of these talented individuals end up remaining abroad once\ntheir project involvement ends, leading to what is often referred to as a brain drain for their country of\norigin. In order to ensure that more places benefit from human capital formation in a virtuous process of\nbrain circulation, the following policies can help:\n\u2013 Understanding the local needs for talent so that Member States and their regions can target the\nrepatriation of people better.\n\u2013 Attracting CERN alumni through tailored initiatives.\n\u2013 Boosting connectivity so that sending and receiving regions benefit from human capital develop-\nment.\n312\n\nA further lever is to extend the benefits of tourism and to increase it to more regions. With the\nnew Science Gateway, each year 300 000 to 400 000 people visit CERN. However, most of the benefits\naccrue in a small geographic perimeter in Switzerland and France, where CERN is located. One way for\nmore regions to tap into this is to ensure that the larger FCC perimeter benefits from the on-site visits.\nThen, further developments can take place to turn CERN into a gateway for science tourism.\nEconomists have developed proposals that can be considered in the project development phase to\nhelp participating nations to reap the most from the opportunities that a new large-scale project offers.\nOne possibility for a contributing country would be to establish a national organisation with dedicated\nstaff that aims to develop the most suitable matches between the country\u2019s competencies and interests and\nthe project. This activity goes beyond classical industrial liaison. It aims to integrate schools, universities,\nresearch centres, companies of all sizes and national funding agencies through development policies\nand concrete actions with the project. This requires in-depth knowledge about the project, ensuring\nthat the organisation\u2019s personnel is involved long-term to be able to build up durable links and gain\ncomprehensive knowledge of the landscape of national competency and capacity. The direct revenue\nfrom procurement contracts is only considered the tip of an iceberg of potential impacts. Long-term\nreturns can exceed those from direct contracts by far. They include:\n\u2013 Repatriation of people and acquisition of highly skilled and trained personnel from the project.\n\u2013 Training nationals at all levels for limited periods abroad.\n\u2013 Using the project as a pilot factory, demonstrating technologies, bringing technologies to market\nand entering new markets.\n\u2013 Build durable transnational value chains, using the project as a motor for national innovation lever-\naging national funds.\n\u2013 Connect companies of different sizes.\n\u2013 Break up research silos by bringing universities and institutes from different disciplines together\naround a single science project.\nThe entire concept aims to overcome the information asymmetries that privilege only a few com-\npanies and universities that benefit from historical links, which enable them to benefit from CERN\u2019s\nlarge-scale science projects.\nAll efforts to plan for a good return for financially participating countries rely on a systematically\nestablished analysis, tracking and regular evaluation of socio-economic performance that can adapt the\nproject. Sufficient evidence exists about the socio-economic benefits of CERN\u2019s activities through dif-\nferent pathways, but there remains a gap in the understanding of what is needed to increase and sustain\nthese effects. Making data gathering and evaluation an integral part of the FCC project can help setting\ngoals for data collection and the methodological approaches to measure these effects.\nThe recommendations documented by LSE and WIFO for ensuring good returns for participat-\ning nations provide specific and tangible examples of successful cases for each policy recommendation\nbased on past initiatives. A significant advantage of several proposals is their standalone nature: they\ncan be implemented individually. Many of them can also be implemented by countries and regions in-\ndependently, allowing them to reap benefits from a project without having to involve other participating\nnations.\n4.9.2\nLocal employment opportunities\nA future research infrastructure with additional territorial development can lead to territorial benefits\nthrough direct employment, goods and services supply, indirect and induced job opportunities in a wider\nperimeter than covered by CERN\u2019s activities today. Indirect and induced impact do not only concern\nthe value chain of regionally supplied goods and services, i.e., further materials and service suppliers\n313\n\nto satisfy the needs of FCC suppliers and jobs that satisfy the needs that emerge from the presence of\npersonnel associated with the FCC construction and operation activities in the vicinities of the surface\nsites. The federation of certain activities that relate to the construction and operation, i.e., services\nthat are research infrastructure enablers at certain locations can also create new and durable territorial\nemployment opportunities. Such services include, for example, during the construction project planning,\nproject management, construction site preparation and operation, and business services (e.g., accounting,\nhuman resources, IT, land plot management). Services for the operation phase include, for instance,\nsurface site surveillance and safety, technical operation services, technical maintenance, operation of\nvisit facilities and general business services, as is the case of the construction phase.\nThe economic impact potentials, in particular the employment-related effects, are still under study\nand develop on the considered supplies and services as well as the locations where they would be sup-\nplied. Preliminary analysis points to opportunities in the range of 1 000 to 2 000 jobs over a sustained\nperiod of time until the end of the century. The effects are mainly linked to household expenses generated\nby those persons, representing per year about 219 million euro for the region Auvergne-Rh\u00f4ne-Alpes.\nDirect tax-related benefits are estimated to be in the range of 2.6 (regional) to 3.3 (national) million euros\nper year. Indirect and induced tax-related impacts range between 3.6 (regional) and 4.1 (national) million\neuro. The main sectors that would profit from those benefits are trade, housing, specialised construction\nworks, civil engineering and public works, commerce, manufacturing and specialised equipment, materi-\nals processing, financial and insurance services, chemical processing, energy production and distribution,\ncultural goods and services, restoration and telecommunications.\nThese preliminary results are to be taken with much care, since the project scenario, the construc-\ntion and operation organisation are at a very early stage and subject to development.\n4.9.3\nOpportunities for impact generation\nThe following policy recommendations are examples taken from the studies carried out by independent\neconomic research organisations to work towards generating regional returns in a global project.\n\u2013 Participating nations build up national support organisations to connect various actors (companies,\nuniversities, research centres, innovation hubs, national funding agencies) to the new research\nproject to leverage beyond pure contract acquisition as much as possible:\n\u2013 Piloting technologies.\n\u2013 Bringing technologies to market.\n\u2013 Training people.\n\u2013 Exploit the scientific research opportunities.\n\u2013 Leverage national funding for developments motivated by the new project.\n\u2013 Attracting highly qualified and trained people via job fairs.\n\u2013 Transferring knowledge from the project to universities and companies.\n\u2013 Move to a standard tendering approach, which includes adopting standard keywords and codes and\npublishing tendering opportunities to a wider audience, such as in the Supplement to the Official\nJournal of the European Union (TED). This can reduce search costs for firms and increase the\nopportunities for small and medium enterprises (SMEs).\n\u2013 Use the standard international NACE9 code system to ensure that companies receive requests for\nparticipation that match their competencies well and to ensure that countries can make an efficient\nmatch of their specialisations to the project\u2019s needs.\n9The Statistical Classification of Economic Activities in the European Community, commonly referred to as NACE (for the\nFrench term \u2018nomenclature statistique des activit\u00e9s \u00e9conomiques dans la Communaut\u00e9 Europ\u00e9enne\u2019), is the industry standard\nclassification system used in the European Union.\n314\n\n\u2013 Establish dedicated support centres within local business association offices in regions with con-\ncentrated clusters of firms active in the project relevant sectors. These centres will offer specialised\nsupport to regional SMEs aspiring to engage in the procurement process.\n\u2013 Unbundle large contracts to enhance the possibility of SMEs to participate in the procurement\nprocess while making the supply chain more resilient.\n\u2013 Set aside lower value contracts for SMEs, if they meet competitiveness criteria for quality and\nprice.\n\u2013 Conduct value chain mapping for the different technologies required to understand the spatial\ndistribution of procurement activities and for regions to understand the local competitiveness op-\nportunities better.\n\u2013 Set up Local Content Units (LCUs) as separate bodies or functions to be developed within existing\nregional development agencies in areas where important CERN suppliers are located. They may\nalso be established and coordinated directly by CERN as a \u2018local economic impact acceleration\nunit\u2019.\n\u2013 Create alliances between regions with project-relevant sectors to facilitate interregional collabora-\ntion and the sharing of knowledge.\n\u2013 CERN could facilitate energy supply contracts or aggregate power purchase agreements (PPAs)\nby acting as an anchor tenant or encouraging the creation of consortia. Alternatively, energy\nsupply contracts or PPAs can be created for larger procurements and groups of suppliers can be\ncreated in the frame of dedicated supplies. Also, energy communities that exist in other countries\nare an effective example of obtaining electricity for production and manufacturing purposes from\nrenewable energy sources. Conditions can be included in procurement requirements.\n\u2013 Regions identified as talent contributors should conduct a comprehensive analysis of the type of\nskills that the region needs to attract with a special focus on profiling homegrown talent that has\nleft the region to join CERN.\n\u2013 Create and promote opportunities through grants and fellowships targeting high-skilled individuals\nto move to their regions.\n\u2013 Provide repatriation incentives to return to their home region for individuals who stayed at CERN.\n\u2013 Engage with CERN staff and alumni abroad through knowledge exchange and entrepreneurship\nprogrammes, mentorship schemes and awards.\n\u2013 Together with tourism boards and other research facilities, develop science tour packages that\nfeature additional scientific attractions across Europe and technology hubs in combination with\nother activities.\n\u2013 Establish a funding stream for sustained socio-economic impact evaluation and data collection\nfrom the outset of the FCC project.\n\u2013 Operate an Open Data portal that attracts social scientists to use CERN to continue to evaluate the\nsocio-economic impact of investment in science.\n4.10\nRequirements and constraints for a preparatory phase\nThe subsequent design and preparatory phase calls for a more detailed design of the technical infrastruc-\ntures based on systematically identified and properly structured and documented requirements for the\nparticle collider and the experiments. This documentation has to be used to carry out an LCA according\nto the standards and best practices that were already used for the analysis of the construction footprint.\nDue to the absence of a detailed design, the long time scales, and the need to develop a particular\nprocurement scenario for a study, a more high-level approach can be taken for the estimation of the\npotential climate effects of the particle accelerators and experiments. However, much care must be taken\nto avoid an approach that is too simplistic and only focuses on the generic analysis of the carbon footprint\n315\n\nof the assumed materials. As far as possible, full systems should be considered, and where not possible,\nreasonable assumptions about the manufacturing, assembly, and installation process must be made and\nincluded in the analysis process.\nConcerning the use of renewable energy, it is important to establish an energy procurement team\nthat can anticipate the development of supply contracts or purchase agreements. The team needs to\ndevelop a strategy and prepare for the establishment of an energy supply portfolio in view of the test,\ncommissioning, and operation phases. The preparation for procuring energy for the construction phase\nis to be started as soon as possible. A time frame of ten years is considered adequate for the preparatory\nand procurement process of renewable energy for the operation phase.\nThe potentials of waste heat supply and water consumption reduction depend on national stake-\nholders putting district heating networks in place and working with CERN on water treatment and supply\nof treated water at a regional level. Therefore, dedicated local designs, operation plans and pilot schemes\nwill need to be put in place before the research infrastructure is assumed to enter the operation phase.\nA time window of 20 years is adequate, considering authorisations, financing, the establishment of local\noperators and the connection of consumers to the district heating network.\nWith respect to landscape integration, the development of rewilding projects, the use of excavated\nmaterials and the design of compensatory actions need ample time for working with local and regional\nstakeholders. This also requires the allocation of dedicated project-internal resources to establish con-\ntracts with external partners and to work together with them, the communities, and public administration.\nSeveral years should be allocated for building up these capacities. Hence, a schedule is needed that pro-\nvides flexibility in working with the local and regional stakeholders, avoiding the build-up of too much\npressure. Such pressure can be counterproductive to the achievement of mutual agreements and consen-\nsus about territorial development projects and the generation of socio-economic benefits at all levels.\n4.11\nRecommendations for a preparatory phase project\nThis section presents a set of recommendations that have been derived from the work presented in this\nanalysis. Their purpose is to ensure that the benefits can be monitored and regularly reported so that the\nupdated findings can be integrated in the infrastructure\u2019s design, construction, and operation phases.\nThe socio-economic study showed that a break-even of costs and benefits can be achieved with the\nFCC-ee research infrastructure with the impact pathways documented so far. However, the potential can\nonly be fully exploited if a continuous tracking of socio-economic impacts is integrated in the infrastruc-\nture\u2019s design, construction, and operation phases. To achieve this objective, nine recommendations have\nbeen made to the FCC project owners by the expert group of economists (CSIL, LSE, WIFO, University\nof Milano, Economic University of Vienna) who have been involved in the socio-economic studies so\nfar.\n1. Allocate adequate personnel and material resources for the impact identification, design,\nplanning, implementation, monitoring, and assessment to help fully leverage the impact po-\ntentials and make FCC a socio-economically sustainable endeavour. The personnel need to be\nempowered so that the results of the impact assessment and the impact generation recommenda-\ntions are accommodated in the design where appropriate, that they are implemented, and that they\nare continuously and systematically monitored. Also, the analysis should be carried out with the\nhelp of all participating project members. This requires that the socio-economic impact assess-\nment is implemented across the entire organisation, with the direct involvement of the highest\nmanagerial level and reporting directly to CERN\u2019s key stakeholder, the Council. This approach\nis expected to secure the sustainability and effectiveness of the process, as well as help enhance\nproject acceptance among financially contributing countries.\n2. Encourage participants that scientific and engineering works are published via gold open\naccess channels (as opposed to self-publishing) and reputable outlets (as opposed to depositing\n316\n\ninformation in preprint servers only). This ensures proper identification of work for tracking pur-\nposes and increases the likelihood of their uptake. This socio-economic impact assessment study\nhas revealed challenges in identifying all the scientific output associated with the research infras-\ntructure activities. It is essential to track the scientific production of researchers involved in experi-\nments and monitor citations across papers and other scientific products. However, scientific outputs\nlacking proper unique digital identifiers and citation references, as is often the case with workshop\nproceedings and presentations available on platforms like the CERN-developed Indico [245], can-\nnot be adequately identified and considered for socio-economic valuation. These types of outputs\nshould, whenever possible, be replaced or supplemented by citable reports or papers. Establishing\nstrategic partnerships with leading publishers, as exemplified by the SCOAP3 [246] project, is a\nsuitable approach to ensure the presence of citable publications. Open-access platforms used for\ndissemination could integrate download, citation and reference tracking if they do not already offer\nthose functions (e.g., Zenodo [247] and ArXiv [248] currently lack these functions). Furthermore,\nadditional research is necessary to expand the monitoring and tracking of scientific content be-\nyond scientific and engineering articles and presentations to include books to understand better the\nsocietal uptake of knowledge acquisition within the FCC programme.\n3. Foresee a framework to monitor the movement of people after they leave the project, to\nfacilitate the analysis of future career developments. Every individual contributing to the project\nfor a minimum duration should be encouraged, on a voluntary basis, to engage in a comprehensive\nmonitoring programme. Thanks to mechanisms to reconnect with them periodically, this initiative\nwould entail long-term follow-up and periodic collection of a set of basic information concerning\ntheir current work position.\n4. To ensure the effective analysis of industrial spillovers generated during project implementation,\nincorporate systematic monitoring of the incremental economic impacts on suppliers result-\ning from procurement actions over multi-year periods. Given that these effects may not manifest\nimmediately and can extend beyond the duration of the procurement contract, it is crucial to ob-\ntain feedback from the companies involved. This necessitates the establishment of a comprehen-\nsive procurement monitoring framework that facilitates ongoing engagement. Such a framework\nshould include provisions for storing information on the individuals initially involved in the con-\ntract, enabling periodic follow-up after the contract\u2019s conclusion. Additionally, it should facilitate\nthe collection of essential information regarding the spillover effects on the company generated\nby the procurement experience with CERN. This can be achieved through mechanisms such as\nshort online surveys designed to gather pertinent data. By implementing this approach, the FCC\nprogramme can gain valuable insights into the long-term economic impacts of its procurement\nactivities, fostering continuous improvement and enhancing collaboration with industrial partners.\n5. Information and Communication Technologies (ICT) have been identified as a key impact\npathway that should be better leveraged through targeted transmission actions to society, ac-\ncompanied by systematic monitoring of uptake. CERN and the FCC represent a globally unpar-\nalleled environment for the development of software and platforms to serve the needs of global\ncollaborations, which is in high demand across societal and industrial sectors, too. By identify-\ning the specific requirements of such collaborations and initiating dedicated development projects,\nthe potential for widespread adoption beyond the FCC project can be created. Examples include\ncollaborative event management, document creation, communication (both one-to-one and one-to-\nmany), file sharing, information management, social networks, remote operation, cybersecurity,\ndistributed computing, and data processing. CERN and the member states should ensure that the\ntechnologies developed are accessible free of charge to users outside the high-energy and parti-\ncle physics community while also guaranteeing long-term maintenance and improvement. This\nrequires making software and tools available on platforms that support download and installation\ntracking. The lack of such data has been identified as one of the limiting factors hindering the\n317\n\naccurate estimation of ICT impacts.\n6. With respect to the impact of spin-off companies, there is a need to establish a systematic\nmethod for tracking companies founded by former participants in the FCC programme,\nmonitoring their evolution over time, and assessing their economic value. The establishment\nof new companies leveraging knowledge acquired through the FCC programme represents an im-\nportant societal benefit. Notably, spin-offs often emerge from participants\u2019 amalgamation of dif-\nferent skills and experiences rather than the direct exploitation of a single licensed technology.\nIn particular, the technologies developed in collaborative R&D projects cannot be attributed to\nCERN alone, and CERN does not track the technologies of collaboration partners. However, to\naccurately gauge the economic and societal benefits generated, a voluntary, systematic tracking\nmechanism is essential. This tracking framework should facilitate a comprehensive assessment\nof the impact of spin-off companies. It could include the establishment of a centralised database\nto record information about spin-off companies (such as their founders, country, industry sector,\nproducts/services offered), and have the possibility to periodically contact them to provide updates\non their companies\u2019 progress.\n7. The study revealed the relevance of economic benefits due to on-site visitors. To ensure sustain-\nable monitoring of the on-site tourism impact pathway, CERN and the FCC collaboration should\nestablish a unified framework to continuously collect essential data on visitors to CERN\u2019s\nexhibition centres, the experiments and any other relevant visit site. A systematic tracking\nmechanism for visitors is indeed necessary to accurately report on the effects of on-site visitors.\nVisitors should be requested to provide a small set of basic information, including their country\nof origin, mode of transport to Geneva, the main purpose of the visit, duration of stay, visitor\nspending, and feedback on the exhibitions and the visit sites (e.g., their level of satisfaction). By\nimplementing this monitoring framework, it will be possible to effectively track and evaluate the\ncultural impact of on-site visitors, as well as enable continual enhancement of visitor experiences.\n8. The identification and quantification of environmental benefit potentials and the development\nof dedicated projects should be intensified. The identification and analysis of environmental\nbenefits are important for social acceptability and for achieving a net-zero balance of the scientific\nresearch activity for society. This requires the establishment and empowerment of economics and\nenvironmental experts in the coming project preparatory phase and intensified cooperation with\nindustrial partners and Host State services, for a reliable identification of potential environmental\nbenefits and costs associated with the project. In addition to the creation of renewable energy\nsources, the reuse of waste heat and the reuse of excavated materials, further opportunities may\nbe uncovered through additional research and extended discussions with project stakeholders. For\ninstance, impact pathways related to water usage, land management, biodiversity conservation, and\ntransport infrastructure need thorough investigation. Assessing potential negative environmental\nimpacts is equally important. Understanding and mitigating adverse effects such as pollution are\ncritical for achieving sustainable outcomes and ensuring the responsible use of natural resources.\n9. Continuous monitoring of the so-called \u2018common good value\u2019 has been identified as a suit-\nable approach to validate the investments against the expectations of funders, ultimately the\ntaxpayers. This approach should be further intensified through surveys conducted in all potential\nfunding countries and regularly repeated to enhance the understanding of how social acceptance\ncan not only be maintained but also be improved. A framework for streamlining this process\nhas been developed within this project, enabling the activity to continue with only marginal ad-\nditional resources. Expanding data collection to additional countries beyond those already sur-\nveyed can provide insights into the factors influencing the people\u2019s perception of the FCC science\nmission. 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Ginsparg, arXiv at 20.\nNature 476(7359), 145\u2013147 (2011).\nhttps://doi.org/10.1038/\n476145a\n333\n", "Future Circular Collider\nFeasibility Study Report\nVolume 1\nPhysics, Experiments, Detectors\nMay 2, 2025\nSubmitted to the European Physics Journal ST, a joint publication of EDP Sciences,\nSpringer Science+Business Media, and the Societ\u00e0 Italiana di Fisica.\narXiv:2505.00272v1 [hep-ex] 25 Apr 2025\n\nNote from the Editors\nOne of the recommendations of the 2020 update of the European Strategy for Particle Physics was that\n\u201cEurope, together with its international partners, should investigate the technical and financial feasibility\nof a future hadron collider at CERN with a centre-of-mass energy of at least 100 TeV and with an\nelectron-positron Higgs and electroweak factory as a possible first stage.\nIn June 2021, the CERN Council launched the FCC Feasibility Study to be completed by 2025, in\ntime for the next update of the European Strategy for Particle Physics. The study results are made\npublicly available through this FCC Feasibility Study Report, as input to the European Particle Physics\nStrategy update process, initiated by the CERN Council in March 2024. The studies presented in this\nFCC Feasibility Study Report do not imply any commitment by the CERN Member or Associate Member\nStates to build the Future Circular Collider.\nThis report and the assumptions contained in it do not prejudge further territorial feasibility analysis by\nthe Host States, France and Switzerland, as well as the outcome of their respective public debate and\nconcertation processes, and future decisions of their relevant authorities.\nii\n\nAcknowledgements\nWe would like to thank the International Steering Committee members:\nF. Gianotti (Chair), CERN\nR. Bello, CERN\nP. Chomaz, CEA, France\nM. Cobal, INFN and University of Udine, Italy\nB. Heinemann, DESY, Germany\nT. Koseki, KEK, Japan\nM. Lamont, CERN\nL. Merminga, FNAL, United States\nJ. Mnich, CERN\nM. Seidel, PSI and EPFL, Switzerland\nC. Warakaulle, CERN\nand the Scientific Advisory Committee members:\nA. Parker (Chair), Cambridge University, UK\nR. Bartolini, DESY, Germany\nA. Chabert, SFTRF, France\nH. Ehrbar, Heinz Ehrbar Partners LLC, Switzerland\nB. Gavela Legazpi, UAM Madrid, Spain\nG. Hiller, TU Dortmund, Germany\nS. Krishnagopal, FNAL, U.S.\nP. Kri\u017ean, University of Ljubljana, Slovenia\nP. Lebrun, ESI, France\nP. McIntosh, STFC, ASTeC, UKRI, UK\nM. Minty, BNL, U.S.\nR. Tenchini, INFN Sezione di Pisa, Italy\nfor their continued guidance and careful reviewing that helped to complete this report successfully.\niii\n\nThe research carried out by the international FCC collaboration hosted by CERN, which\nled to this publication, has received funding from the European Union\u2019s Horizon 2020\nresearch and innovation programme under the grant numbers 951754 (FCCIS), 654305\n(EuroCirCol), 764879 (EASITrain), 730871 (ARIES), 777563 (RI-Paths), 101086276\n(EAJADE), 101004730 (iFAST), 101131435 (iSAS), 101131850 (RF2.0) and from FP7 under grant\nnumber 312453 (EuCARD-2).\nThis work has also benefited from the support of CHART (Swiss Accelerator Research\nand Technology, founded in 2016 as an umbrella collaboration for accelerator research\nand technology activities. Present partners in CHART are CERN, PSI, EPFL, ETH-\nZurich and the University of Geneva.\nTrademark notice: All trademarks appearing in this report are acknowledged as such.\niv\n\nThis report was edited with the Overleaf.com collaborative writing and publishing system. Typesetting\nand final print preparation was performed using pdfTEX3.14159265-2.6-1.40.17\nCopyright CERN for the benefit of the FCC collaboration 2025\nCreative Commons Attribution 4.0\nKnowledge transfer is an integral part of CERN\u2019s mission.\nCERN publishes this volume Open Access under the Creative Commons Attribution 4.0 licence.\n(http://creativecommons.org/licenses/by/4.0/) in order to permit its wide dissemination and\nuse. The submission of a contribution to the CERN document server shall be deemed to constitute the\ncontributor\u2019s agreement to this copyright and license statement. Contributors are requested to obtain any\nclearances that may be necessary for this purpose.\nThis volume is indexed in: CERN Document Server (CDS):\nCERN-FCC-PHYS-2025-0002\n10.17181/CERN.9DKX.TDH9\nhttps://cds.cern.ch/record/2928193\nThis report edition should be cited as:\nFuture Circular Collider Feasibility Study Report Volume 1: Physics, Experiments, Detector, preprint\nedition edited by M. Benedikt et al., CERN physics reports,\nCERN-FCC-PHYS-2025-0002,DOI 10.17181/CERN.9DKX.TDH9, Geneva, 2025.\nAvailable online: https://cds.cern.ch/record/2928193\nv\n\nList of Editors at 31 March 2025\nM. Benedikt1 (Study Leader), F. Zimmermann1 (Deputy Study Leader), B. Auchmann1,2,\nW. Bartmann1, J.P. Burnet1, C. Carli1, A. Chanc\u00e93, P. Craievich2, M. Giovannozzi1, C. Grojean4,5,\nJ. Gutleber1, K. Hanke1, A. Henriques1, P. Janot1, C. Louren\u00e7o1, M. Mangano1, T. Otto1, J. Poole1,\nS. Rajagopalan6, T. Raubenheimer7, E. Todesco1, L. Ulrici1, T. Watson1, G. Wilkinson1,8.\nList of Chief Editors of Volume 1 Chapters at 31 March 2025\nP. Azzi9, G. Bernardi10,11,12, A. Blondel10,13,14, M. Boscolo15, D. d\u2019Enterria1, M. Dam16, J. de Blas17,\nB. Francois1, A. Freitas18, G. Ganis1, J. Keintzel1, M. Klute19, M. McCullough1, P.F. Monni1,\nF. Palla20, E. Perez1, M.-A. Pleier6, W. Riegler1, F. Sefkow4, M. Selvaggi1.\nList of Contributors at 31 March 2025\nA. Abada10,21,22, M. Abbrescia23,24, H. Abdolmaleki25,26, S.H. Abidi6, A. Abramov1, C. Adam10,27,28,\nM. Ady1, P.R. Ad\u02d8zi\u00b4c29, I. Agapov4, D. Aguglia1, I. Ahmed30, M. Aiba2, G. Aielli31,32, T. Akan33,\nN. Akchurin34, D. Akturk35, M. Al-Thakeel1,36,37, G.L. Alberghi36, J. Alcaraz Maestre38, M. Aleksa1,\nR. Aleksan3, F. Alharthi10,21,39, J. Alimena4, A. Alimenti40, S. Alioli41,42, L. Alix1,10,27,\nB.C. Allanach43, L. Allwicher4, A.A. Altintas44, M. Alt\u0131nl\u013144,45, M. Alviggi46,47, G. Ambrosio48,\nY. Amhis10,21,22, A. Amiri49,50, G. Ammirabile20, T. Andeen51, K.D.J. Andr\u00e91, J. Andrea10,52,53,\nA. Andreazza54,55, M. Andreini1, T. Andriollo56, L. Angel57, M. Angelucci15, S. Antusch58,\nM.N. Anwar23,59, L. Apolin\u00e1rio60, G. Apollinari48, R.B. Appleby61,62, A. Apresyan48, Aram Apyan63,\nArmen Apyan64, A. Arbey10,65,66, B. Argiento46,47, V. Ari67, S. Arias68, B. Arias Alonso1,\nO. Arnaez10,27,28, R. Arnaldi69, F. Arneodo70, H. Arnold71, P. Arrutia Sota1, M.E. Ascioti72,73,\nK.A. Assamagan6, S. Aumiller74, G. Ayd\u0131n75, K. Azizi49,76, N. Bacchetta9, A. Bacci54, B. Bai77,\nY. Bai78, L. Balconi54,55, G. Baldinelli72,73, B. Balhan1, A.H. Ball1,79, A. Ballarino1, S. Banerjee80,\nS. Banik2,81, D.P. Barber4,82, M.B. Barbero10,83,84, D. Barducci20,85, D. Barna86, G.G. Barnaf\u00f6ldi86,\nM.J. Barnes1, A.J. Barr8, R. Bartek87, H. Bartosik1, S.A. Bass88, U. Bassler10,89,90, M.J. Basso91,92,\nA. Bastianin55,93, P. Bataillard94, M. Battistin1, J. Bauche1, L. Baudin1, J. Baudot10,52,53, B. Baudouy3,\nL. Bauerdick48, C. Bay\u0131nd\u0131r95,96, H.P. Beck97, F. Bedeschi20, C. Bee71, M. Begel6, M. Behtouei15,\nL. Bellagamba36, N. Bellegarde1, E. Belli1,98, E. Bellingeri99, S. Belomestnykh48, A.D. Benaglia41,\nG. Bencivenni15, J. Bendavid1, M. Benmergui100, M. Benoit101, D. Benvenuti1,20, T. Bergauer102,\nN. Bernachot103, J. Bernardi104, Q. Berthet14,105,106, S. Bertoni107, C. Bertulani108, M.I. Besana2,\nA. Besson10,52,53, M. Bettelini109, S. Bettoni2, S. Beuvier\u2020110, P.C. Bhat48, S. Bhattacharya111,\nJ. Bhom112, M.E. Biagini15, A. Bibet-Chevalier113, M. Bicrel114, M. Biglietti115, G.M. Bilei72,\nB. Bilki116,117, K. Bisgaard Christensen1, T. Biswas118, F. Blanc119, F. Blekman4,120,121, J. Bl\u00fcmlein4,\nD. Boccanfuso46,122, A. Bogomyagkov123, P. Boillon113, P. Boivin106, M.J. Boland124, S. Bologna125,\nO. Bolukbasi44, R. Bonnet107, J. Borburgh1, F. Bordry1, P. Borges de Sousa1, G. Borghello1,\nL. Borriello46, D. Bortoletto8, L. Bottura1, V. Boudry10,89,90, R. Boughezal126, D. Bourilkov127,\nM. Boyd91,128, D. Boye6, G. Bozzi129,130, V. Braccini99, C. Bracco1, B. Bradu1, A. Braghieri131,\nS. Braibant36,37, J. Bramante132, G.C. Branco133, R. Brenner134, N. Brisa107, D. Britzger135,\nG. Broggi1,98, L. Bromiley1, E. Brost6, Q. Bruant3, R. Bruce1, E. Br\u00fcndermann19, L. Brunetti10,27,28,\nO. Br\u00fcning1, O. Brunner1, X. Buffat1, E. Bulyak136, A. Burdyko54,137, H. Burkhardt1,138,\nP.N. Burrows139, S. Busatto54,98, S. Buschaert94, D. Buttazzo20, A. Butterworth1, D. Butti1,\nG. Cacciapaglia140,141,142, Y. Cai7, B. Caiffi143, V. Cairo1, O. Cakir67, P. Calafiura144, R. Calaga1,\nS. Calatroni1, D.G. Caldwell145, A. \u00c7al\u0131\u00b8skan146, C. Calpini147, M. Calviani1, E. Camacho-P\u00e9rez148,\nP. Camarri31,32, L. Caminada2,81, M. Campajola46,47, A.C. Canbay67, K. Canderan1, S. Candido1,\nF. Canelli81, A. Canepa48, S. Cantarella15, K.B. Cant\u00fan-Avila148, L. Capriotti149,150, A. Caram151,\nA. Carbone54, J.M. Carceller1, G. Carini6, F. Carlier1, C.M. Carloni Calame131, F. Carra1,\nC. Cartannaz94, S. Casenove1, G. Catalano152, V. Cavaliere6, C. Cazzaniga153, C. Cecchi72,73,\nvi\n\nF.G. Celiberto154, M. Cepeda38, F. Cerutti1, F. Cetorelli41,42, G. Chachamis60, Y. Chae4, F. Chagnet155,\nI. Chaikovska10,21,22, M. Chalhoub94, M. Chamizo-Llatas6, M. Champagne156, H. Chanal10,157,158,\nG. Chapelier113, P. Charitos1, C. Charles110, T.K. Charles159, C. Charlot10,89,90, S. Chatterjee4,\nA. Chaudhuri160, R. Chehab10,21,22, S.V. Chekanov161, H. Chen6, T. Chesne110, F. Chiapponi36,37,\nG. Chiarello162,163, M. Chiesa131, P. Chiggiato1, Ph. Chomaz3, M. Chorowski164, J.P. Chou165,\nM. Chrzaszcz112, W. Chung166, S. Ciarlantini9,167, A. Ciarma15, D. Cieri135, A.K. Ciftci168,\nR. Ciftci169, R. Cimino15, F. Cirotto46,47, M. Ciuchini115, M. Cobal170,171, A. Coccaro143,\nR. Coelho Lopes De Sa172, J.A. Coleman-Smith1, F. Collamati173, C. Colldelram174, P. Collier1,\nP. Collins1, J. Collot10,175,176, M. Colmenero1, L. Colnot152, G. Coloretti81, E. Conte10,52,53,\nF.A. Conventi46,177, A. Cook1, L. Cooley178,179, A.S. Cornell180, C. Cornella1, G. Cornette110,\nI. Corredoira181, P. Costa Pinto1, F. Couderc3, J. Coupard1, S. Coussy94, R. Crescenzi182,\nI. Crespo Garrido1,183, T. Critchley1,14, A. Crivellin81, T. Croci72, C. Cudr\u00e9110, G. Cummings48,\nF. Cuna23, R. Cunningham1, B. Cur\u00e91, E. Curtis184, M. D\u2019Alfonso185, L. D\u2019Aloia Schwartzentruber186,\nG. D\u2019Amen6, B. D\u2019Anzi23,24, A. D\u2019Avanzo46,47, A. D\u2019Onofrio46, M. D\u2019Onofrio187, M. Da Col152,\nM. Da Rocha Rolo69, C. Dachauer188, B. Da\u02d8gli35, A. Dainese9, B. Dalena3, W. Dallapiazza189,\nH. Damerau1, V. Dao71, A. Das190, M.S. Daugaard1, S. Dauphin113, A. David1, T. Dav\u00eddek191,\nG.J. Davies184, S. Dawson6, A. de Cosa153, S. De Curtis192, N. De Filippis23,59, E. De Lucia15,\nR. De Maria1, E. De Matteis54, A. De Roeck1, A. De Santis15, A. De Vita1,9,167, A. Deandrea10,65,66,\nC.J. Debono193, M. Deeb106, M.M. Defranchis1, J. Degens187, S. Deghaye1, V. Del Duca15,\nC.L. Del Pio6, A. Del Vecchio98, D. Delikaris1, A. Dell\u2019Acqua1, M. Della Pietra46,47,\nM. Delmastro10,27,28, L. Delprat1, E. Delugas152, Z. Demiragli194, L. Deniau1, D. Denisov6,\nH. Denizli195, A. Denner196, A. Denot113, G. Deptuch6, A. Desai197, H. Deveci1, A. Di Canto6,\nA. Di Ciaccio31,32, L. Di Ciaccio10,27,28, D. Di Croce1,119, C. Di Fraia46,47, B. Di Micco40,115,\nR. Di Nardo40,115, T.B. Dingley8, F. Djama10,83,84, F. Djurabekova198, D. Dockery48, S. Doebert1,\nD. Domange1,199, M. Doneg\u00e0153, U. Dosselli9, H.A. Dostmann1,200, J.A. Dragovich48, I. Drebot54,\nM. Drewes201, T.A. du Pree202, Z. Duan203, C. Duarte-Galvan204, O. Duboc205, M. Duda2, P. Duda164,\nH. Duran Yildiz67, H. Durand110, P. Durand110, G. Durieux201, Y. Dutheil1, I. Dutta48, J.S. Dutta206,\nS. Dutta207, F. Duval1, F. Eder1, M. Eisterer104, Z. El Bitar10,52,53, A. El Saied208, M. Elisei54,\nJ. Ellis1,209, W. Elmetenawee23, J. Elmsheuser6, V. Daniel Elvira48, S.C. Eno210, Y. Enomoto211,\nB.A. Erdelyi9,167, O.E. Eruteya14,212, M. Escobar213, O. Etisken214, I. Eymard147, J. Eysermans185,\nD. Falchieri36, C. Falkenberg205, F. Fallavollita1,135, A. Afalou1,10,21, J. Faltova191, J. Fanini1,\nL. Fan\u00f272,73, K. Fanti110, R. Farinelli36, M. Farino166, S. Farinon143, H. Fatehi49, J. Fatterbert110,\nA. Faure215, A. Faus-Golfe10,21,22, G. Favia1, L. Favilla46,122, W.J. Fawcett43, A. Federowicz48,\nL. Feligioni10,83,84, L. Felsberger1, Y. Feng34, A. Fern\u00e1ndez T\u00e9llez216, R. Ferrari131, L. Ferreira1,\nF. Ferro143, M. Fiascaris1, C. Fiorio55, S.A. Fleury1, L. Florez189, M. Florio55,152, A. Fondacci72,\nB. Fontimpe213, K. Foraz1, R. Fortunati2, M. Fouaidy10,21,22, A. Foussat1, A. Fowler1, J.D. Fox217,\nM. Francesconi46, R. Franqueira Ximenes1, F. Fransesini15, A. Frasca1,187, J.A. Frost8,\nK. Furukawa211, A. Gabrielli36,37, A. Gaddi1, F. Gaede4, A. Gall\u00e9n134, R. Galler218,219, E. Gallice110,\nE. Gallo4,120, H. Gamper1, S. Ganjour3, S. Gao6, A. Garand151, C. Garaus205, D. Garcia1,\nR. Garc\u00eda Al\u00eda1, R. Garc\u00eda Gil220, C.M. Garcia Jaimes1,119, H. Garcia Rodrigues2,221, C. Garion1,\nM. Garlasch\u00e81, D. Garnier155, M.V. Garzelli120, S. Gascon-Shotkin10,65,66, M. Gasior1,\nG. Gaudino46,122, G. Gaudio131, V. Gaur222, K. Gautam81,121, V. Gawas1, T. Gehrmann81,\nA. Gehrmann-De Ridder81,153, K. Geiger1, M. Genco152, F. Gerigk1, H. Gerwig1, A. Ghribi1,10,223,\nP. Giacomelli36, S. Giagu98,173, E. Gianfelice48, S. Giappichini19, D. Gibellieri1,224, F. Giffoni152,\nG. Gil da Silveira225, S.S. Gilardoni1, M. Giovannetti15, T. Girardet110, S. Girod1,110, P. Giubellino69,\nP. Giubilato9,167, F. Giuli31,32, M. Giuliani107, E.L. Gkougkousis1,81, S. Glukhov226, J. Gluza227,\nB. Goddard1, C. Goffing1,19, D. Goldsworthy1, T. Golling14, R. Gon\u00e7alo60,228, V.P. Gon\u00e7alves57,229,\nT. Gon\u00e7alves Da Silva213, J. Gonski7, R. Gonzalez Suarez134, S. Gorgi Zadeh1, S. Gori230,\nE. Gorini162,231, L. Gouskos232, M. Gouzevitch10,65,66, E. Granados1, F. Grancagnolo162,\nS. Grancagnolo162,231, A. Grassellino48, A. Grau19, E. Graverini20,85,119, F.G. Gravili162,231,\nvii\n\nH.M. Gray144,233, M. Grazzini81, Mario Greco40,115, Michela Greco69,234, A. Greljo58, J-L. Grenard1,\nA.V. Gritsan235, R. Gr\u00f6ber9,167, A. Grudiev1, E. Gschwendtner1, J. Gu236, D. Guadagnoli28,140,237,\nG. Guerrieri1, A. Guiavarch208, G. Guillermo Canton1,238, M. Guinchard1, Y.O. G\u00fcnaydin239,\nK. Gurcel100, L.X. Gutierrez Guerrero240,241, D. Guti\u00e9rrez Rueda1, A. Guti\u00e9rrez-Rodr\u00edguez242,\nV. Guzey198,243, C. Haber144, T. Hacheney244, B. Hac\u0131\u00b8sahino\u02d8glu44, K. Hahn126, J. Hajer133,\nT. Hakulinen1, J.C. Hammersley245, M. Hance230, J.B. Hansen16, B. H\u00e4rer19, E. Hauzinger218,\nM. Haviernik191, B. Hegner1, C. Helsens119, Ana Henriques1, C. Hernalsteens1,\nH. Hern\u00e1ndez-Arellano216, R.J. Hern\u00e1ndez-Pinto204, M.A. Hern\u00e1ndez-Ru\u00edz242,\nJ. Hern\u00e1ndez-S\u00e1nchez216, J.W. Heron1, L.M. Herrmann1, R. Hirosky246, J.F. Hirschauer48,\nJ.D. Hobbs71, K. Hock6, S. H\u00f6che48, M. Hofer1, G. Hoffstaetter6,247, W. H\u00f6fle1, M. Hohlmann248,\nF. Holdener249, B. Holzer1, C.G. Honorato216, H. Hoorani250, A. Houver110, E. Howling1,8,139,\nX. Huang7, F. Hug251, B. Humann1, P. Hunchak124, Y. Husein1, A. Hussain1,252, G. Iadarola1,\nG. Iakovidis6, G. Iaselli23,59, P. Iengo46, A. Ilg81, M. Iodice115, A.O.M. Iorio46,47, V. Ippolito173,\nU. Iriso174, J. Isaacson48, G. Isidori81, R. Islam253, A. Istepanyan110, S. Izquierdo Bermudez1,\nV. Izzo46, P.D. Jackson197, R. Jafari1,49, S.S. Jagabathuni1,14, S. Jana254,255, C. J\u00e4rmyr Eriksson1,\nP. Jausserand155, M. Jensen256, J.M. Jimenez1, F.R. Joaquim133, O.R. Jones1, J. Joos113,\nE. Jourd\u2019huy10,257, E. Jourdan213, J.M. Jowett1,258, A. Jueid259, A.W. Jung206, M. Kagan7,\nI. Kahraman67, V. Kain1, J. Kalinowski260, J.F. Kamenik261,262, A. Kanso263, T. Kar264, S.O. Kara265,\nH. Karadeniz266, S.R. Karmarkar206, V. Karpati267, I. Karpov1, M. Karppinen1, P. Karst10,83,84,\nS. Kartal44, V.V. Kashikhin48, U. Kaya67, A. Kehagias1,268, M. Kennouche1, M. Kenzie43,\nM. Kerr\u00e9veur-Lavaud56, R. Kersevan1,269, V. Keus198,270, H. Khanpour25,271,272, V.V. Khoze273,\nV.A. Khoze273, P. Kicsiny1, R. Kieffer1, C. Kiel119, J. Kieseler19, A. Kilic274, B. Kilminster81,\nS. Kim275, Z. K\u0131rca274, M. Klein\u2020187, A. Klimentov6, V. Klyukhin123,276, M. Knecht140,277,278,\nB. Kniehl120, P. Ko279, S. Ko1, F. Kocak274, T. Koffas280, C. Kokkinos281,282, K. Ko\u0142odziej227,\nK. Kong283, P. Kontaxakis14, I.A. Koop123, P. Kopciewicz1, P. Koppenburg202, M. Koratzinos1,2,\nK. Kordas284, A Korsun10,21,22, O. Kortner135, S. Kortner135, B. Korzh14, T. Koseki211, J. Kosse2,\nP. Kostka1,187, S. Kostoglou1, A.V. Kotwal88, G. Kozlov1,276, I. Kozsar1, T. Kramer1, P. Krkoti\u00b4c1,\nH. Kroha135, K. Kr\u00f6ninger244, S. Kuday1,67, G. Kuhlmann285, O. Kuhlmann1,286, M. Kuhn287,\nA. Kulesza288, M. Kumar289, F. Kurian6, A. Kurtulus1,153, T.H. Kwok81, S. La Mendola1,\nM. Lackner104,290, T. \u0141adzi\u00b4nski1, D. Lafarge1, P. La\u00efdouni1, G. Lamanna10,27,28, N. Lamas30,\nG. Landsberg232, C. Lange2, D.J. Lange166, A. Langner1, A.J. Lankford291, L. Lari6, M.S. Larson292,\nK. Lasocha1, A. Latina1, S. Lauciani15, M. Laufenberg110, G. Lavezzari1, L. Lavezzi69, L. Lavezzo1,\nM. Le Garrec1,10,27, A. Le Jeune107, Ph. Lebrun1,293, Y. L\u00e9chevin1, A. Lechner1, E. Lecointe110,\nJ.S.H. Lee294, S.W. Lee295, S.J. Lee279,296, T. Lefevre1, C. Leggett144, T. Lehtinen297, S. Leone20,\nC. Leonidopoulos298, S. Leontsinis81, G. Leprince-Maill\u00e8re299, G. Lerner1, O. Leroy10,83,84,\nT. Lesiak112, P. Levai86, A. Leveratto99, R. Levi155, A. Li6, S. Li300,301, D. Liberati302,\nG.L. Lichtenstein57, M. Liepe247, Z. Ligeti144, H. Lin303, S. Linda147, E. Lipeles304, Z. Liu305,\nS.M. Liuzzo306, T. Loeliger287, A. Loeschcke Centeno307, A. Lorenzetti81, C. Lorin3, R. Losito1,\nM. Louka23,308, M.L. Loureiro Garc\u00eda183, I. Low126,161, K. Lubonis155, M.T. Lucchini41,42,\nV. Lukashenko81, G. Luminati15, A.J.G. Lunt1,309, A. Lusiani20,310, M. Luzum311, H. Ma6,\nA. Maas312, E. Macchia1,98,173, A. Macchiolo81, G.E. Machinet263, R. Madar10,157,158, T. Madlener4,\nC. Madrid34, A. Magalotti40, M. Maggiora69,234, A.-M. Magnan184, M.A. Mahmoud313,\nY. Mahmoud314,315, F. Mahmoudi1,10,65, H. Mainaud Durand1, J. Maitre113, Y. Makhloufi14,\nB. Malaescu10,13,316, A. Malagoli99, C.H. Malan113, M. Malekhosseini49, A. Maloizel1,11,12,\nS. Malvezzi41, A. Malzac151, G. Manco131, L.S. Mandacar\u00fa Guerra166, P. Manfrinetti99,317,\nE. Manoni72, J. Mans305, L. Mantani318, S. Manzoni1, L. Marafatto170, C. Marcel1, T. Marcel114,\nR. Marchevski119, G. Marchiori10,11,12, F. Mariani54,98, V. Mariani72,73, S. Marin1, C. Marinas318,\nV. Marinozzi48, S. Mariotto54,55, C. Marquis110, J. Martelain319, G. Martelli72,73, A. Martens10,21,22,\nI. Martin-Melero1, V.I. Martinez Outschoorn172, F. Martinez216, C.M. Jardim38, L. Marzola320,321,\nS. Masciocchi258,264, A. Mashal25, A. Masi1, I. Masina149,150, P. Mastrapasqua201, V. Mateu322,\nviii\n\nS. Mattiazzo9,167, M. Maugis107, D. Mauree147, G.H.I. Maury-Cuna323, A. Mayoux1, E. Mazzeo1,\nS. Mazzoni1, M. Meena10,52,53, E. Meftah14, Andrew Mehta187, Ankita Mehta1, B. Mele173,\nR. Mena-Andrade1, M. Mentink1, D. Mergelkuhl1, V. Mertinger267, L. Mether1, S. Meylan110,\nT. Michel107, T. Michlmayr2, M. Migliorati98,173, A. Milanese1, C. Milardi15, G. Milhano60,\nM. Minty6, C. Mirabelli324, T. Miralles10,157,158, L. Miralles Verge1, D. Mirarchi1, K. Mirbaghestan81,\nN. Mirian4,325, V.A. Mitsou318, D.S. Mitzel244, M. Mlynarikova1, S. M\u00f6bius97,\nM. Mohammadi Najafabadi1,25, G.B. Mohanty326, R. N. Mohapatra210, S. Moneta72,\nE. Monnier10,83,84, S. Monteil10,157,158, I. Le\u00f3n Monz\u00f3n204, F. Moortgat1,327, N. Morange10,21,22,\nM. Moretti149,150, S. Moretti79, T. Mori1,211, I. Morozov123, A. Morozzi72, M. Morrone1,\nA. Moscariello14, F. Moscatelli72,328, I. Moulin215, N. Mounet1, A. Mueller329, A.-S. M\u00fcller19,\nB.O. M\u00fcller285, J. Mundet220, E. Musa1,4, V. Musat1,8, R. Musenich143, E. Musumeci318, M. Mylona1,\nV.V. Mytrochenko10,21,136, B. Nachman144, S. Nagaitsev6, T. Nakamoto211, M. Napsuciale323,\nM. Nardecchia98,173, G. Nardini330, G. Narv\u00e1ez-Arango331, S. Naseem70, A. Natochii6,\nA. Navascues Cornago1, B. Naydenov1, G. Nergiz1, A.V. Nesterenko276, C. Neub\u00fcser332,\nH.B. Newman333, F. Niccoli1,334, O. Nicrosini131, U. Niedermayer226, G. Niehues19, J. Nielsen1,\nG. Nigrelli1,98,173, S. Nikitin123, I.B. Nikolaev123, A. Nisati173, N. Nitika170,171, J.M. No335,\nM. Nonis1, Y. Nosochkov7, A. Novokhatski1,7, J.M. O\u2019Callaghan336, S.A. Ochoa-Oregon204,\nK. Ohmi203,211, K. Oide1,14,211, V.A. Okorokov123, C. Oleari41,42, D. Oliveira Damazio1,6, Y. Onel117,\nA. Onofre337,338,339, P. Osland340, Y.M. Oviedo-Torres341,342,343, A. Ozansoy67, F. Ozaydin95,344,\nK. Ozdemir345, A. Ozturk1, M.A. P\u00e9rez de Le\u00f3n204, S. Pacetti72,73, H. Pacey8, J. Paciello113,\nC.E. Pagliarone346,347, A. Paillex110, H.F. Pais da Silva1, A. Pampaloni143, C. Pancotti152,\nM. Pandurovi\u00b4c348, O. Panella72, G. Panizzo170,171, C. Pantouvakis9,167, L. Panwar10,13,316,\nP. Paolucci46, Y. Papa110, A. Papaefstathiou349, Y. Papaphilippou1, A. Paramonov161, A. Pareti131,350,\nB. Parker6, V. Parma1, F. Parodi143,317, M. Parodi1, B. Paroli54,55, J.A. Parsons351, D. Passarelli48,\nD. Passeri72,73, B. Pattnaik318, A. Patwa352, C. Paus185, F. Pauss153, F. Peauger1, I. Pedraza216,\nR. Pedro60, J. Pekkanen1, G. Peon1, A. Perez114, F. P\u00e9rez174, J.C. Perez1, J.M. P\u00e9rez38,\nR. Perez-Ramos140,141,353, G. P\u00e9rez Segurana1, A. Perillo Marcone1, S. Perna46,47, K. Peters4,\nS. Petracca46,354, A.R. Petri54, F. Petriello126, A. Petrovic1, L. Pezzotti36, G. Piacquadio71,\nG. Piazza182, A. Piccini1, F. Piccinini131, A. Pich318, T. Pieloni119, J. Pierlot1, A.D. Pilkington61,\nM. Pillet324, M. Pinamonti170,171, N. Pinto235, L. Pintucci170,171, F. Pinzauti1, K. Piotrzkowski271,\nC. Pira15, M. Pitt1, R. Pittau17, S. Pittet1, P. Placidi72,73, W. P\u0142aczek355, S. Pl\u00e4tzer312,356,\nE. Ploerer81,121, H. Podlech357,358, F. Poirier10,27,28, G. Polesello131, M. Poli Lener15, J. Polinski164,\nZ. Polonsky81, N. Pompeo40, M. Pont174, G. Alexandru-Popeneciu359, W. Porod196, L. Porta1,\nL. Portales3, T. Portaluri307, M.A.C. Potenza55, C. Prasse285, E. Premat186, M. Presilla19,\nS. Prestemon144, A. Price355, M. Primavera162, R. Principe1, M. Prioli54, F.M. Procacci23,\nE. Proserpio54,137, A. Provino99,317, C. Pueyo1, T. Puig30, N. Pukhaeva276, S. Pulawski227,\nG. Punzi20,85, A. Pyarelal360, J. Qian303, H. Quack361, F. S. Queiroz57, G. Quintas-Neves299,\nH. Rafique79, J.-Y. Raguin2, J. Raidal320, M. Raidal320, P. Raimondi48, A. Rajabi4,\nS. Ram\u00edrez-Uribe204, S. Randles187, T. Rao6, C.\u00d8. Rasmussen6, A. Ratkus362, P.N. Ratoff62,363,\nP. Razis364,365, P. Rebello Teles1,366, M.N. Rebelo133, M. Reboud10,21,22, S. Redaelli1,\nC. Regazzoni110, L. Reichenbach1,367, M. Reissig19, E. Renou110, A. Renter\u00eda-Olivo.318, J. Reuter4,\nS. Rey110, A. Ribon1, D. Ricci1, M. Rignanese9,167, S. Rimjaem368, R.A. Rimmer369, R. Rinaldesi1,\nL. Rinolfi1,293, O. Rios1, G. Ripellino134, B. Rivas370, A. Rivetti69, T. Robens371, F. Robert186,\nE. Robutti143, C. Roderick1, G. Rodrigo318, M. Rodr\u00edguez-Cahuantzi216, L. R\u00f6hrig157,158,244,\nM. Roig372, F. Rojat113, J. Rojo202,373, J. Roloff232, P. Roloff1, A. Romanenko48, A. Romero Francia1,\nH. Romeyer374, N. Rompotis187, N. Rongieras107, G. Rosaz1, K. Roslon375, M. Rossetti Conti54,\nA. Rossi72,73, E. Rossi46,47, L. Rossi54,55, A.N. Rossia9,167, S. Rostami49, G. Roy1, B. Rubik48,\nI. Ruehl1, A. Ruiz-Jimeno376, R. Ruprecht19, J.P. Rutherfoord360, L. Rygaard4, M.S. Ryu295,\nL. Sabato1,119, G. Sadowski10,52,53, D. Saez de Jauregui19,377, M. Sahin378, A. Sailer1, M. Saito379,\nP. Saiz1, G.P. Salam380,381, R. Salerno10,89,90, T. Salmi297, B. Salvachua1, J.P.T. Salvesen1,8,139,\nix\n\nB. Salvi299, D. Sampsonidis284, Y. Villamizar140,141,142, C. Sandoval331, S. Sanfilippo2,\nE. Santopinto143, R. Santoro54,137, X. Sarasola119, L. Sarperi287, I.H. Sarp\u00fcn382, S. Sasikumar1,\nM. Sauvain383, A. Savoy-Navarro3,10, R. Sawada379, G. Sborlini384, J. Scamardella46,47, M. Schaer2,\nM. Schaumann1,4, M. Schenk1, C. Scheuerlein1, C. Schiavi143,317, A. Schloegelhofer1, D. Schoerling1,\nA. Sch\u00f6ning264, S. Schramm14, D. Schulte1, P. Schwaller251,385, A. Schwartzman7, Ph. Schwemling3,\nR. Schwienhorst386, A. Sciandra6, L. Scibile1, I. Scimemi387, E. Scomparin69, C. Sebastiani1,\nB. Seeber388, J.T. Seeman7, M. Seidel2,119, S. Seidel82, J. Seixas339,389,390, N. Selimovi\u00b4c9,\nC. Senatore14, A. Senol195, N. Serra81, A. Seryi369, A. Sfyrla14, Pramond Sharma391, Punit Sharma6,\nC.J. Sharp1, L. Shchutska119, V. Shiltsev392, M. Siano54,55, R. Sierra1, E. Silva40, R.C. Silva57,343,\nL. Silvestrini173, F. Simon19, G. Simonetti1, R. Simoniello1, B.K. Singh393, S. Singh6, B. Singhal87,\nA. Siodmok1,355, Y. Sirois10,89,90, E. Sirtori152, B. Sitar394, D. Sittard1, E. Sitti153, T. Sj\u00f6strand68,\nP. Skands395, L. Skinnari292, K. Skoufaris1, K. Skovpen327, M. Skrzypek112, P. Slavich140,141,142,\nV. Slokenbergs34, V. Smaluk6, J. Smiesko1,396, S.S. Snyder6, E. Solano174, P. Sollander1,\nO.V. Solovyanov1,10,157, M. Son397, F. Sonnemann1, R. Soos1,10,21, F. Sopkova191, T. Sorais398,\nM. Sorbi54,55, S. Sorti54,55, R. Soualah399, M. Souayah1, L. Spallino15, S. Spanier400, P. Spiller258,\nM. Spira2, D. Stagnara107, M. Stallmann189, D. Standen1, J.L. Stanyard1, B. Stapf1, G.H. Stark230,\nM. Statera54, C. Staudinger1,205, G. Streicher401, N.P. Strohmaier2, R. Stroynowski111, S. Stucci6,\nG. Stupakov7, S. Su360, A. Sublet1, K. Sugita258, M.K. Sullivan7, S. Sultansoy35, I. Syratchev1,\nR. Szafron6, A. Sznajder402, W. Tachon403, N.D. Tagdulang48,174,336, N.A. Tahir258, Y. Takahashi127,\nJ. Tamazirt10,21,22, S. Tang6, Y. Tanimoto211, I. Tapan274, G.F. Tassielli23,404, A.M. Teixeira10,157,158,\nV.I. Telnov123, H.H.J. Ten Kate1,405, V. Teotia6, J. ter Hoeve298, A. Thabuis1, G.T. Telles30,\nA. Tishelman-Charny6, S. Tissandier113, S. Tizchang25,406, J.-P. Tock1, B. Todd1, L. Toffolin1,170,407,\nA. Tolosa-Delgado1, R. Tom\u00e1s Garc\u00eda1, T. Tomasini408, G. Tonelli20,85, T. Tong409, F. Toral38,\nT. Torims1,362, L. Torino174, K. Torokhtii40, R. Torre143, E. Torrence410, R. Torres62,187,\nT. Mitsuhashi211, A. Tracogna152, O. Traver174, D. Treille1, A. Tricoli6, P. Trubacova1, E. Tsesmelis1,\nG. Tsipolitis268, V. Tsulaia144, B. Tuchming3, C.G. Tully166, I. Turk Cakir67, C. Turrioni72,\nJ. Tynan110, F.P. Ucci131,350, S. Udongwo411, C.S. \u00dcn274, A. Unnervik1, A. Upegui105,106,\nJ.P. Uribe-Ram\u00edrez204, J. Uythoven1, R. Vaglio47,99, F. Valchkova-Georgieva412, P. Valente173,\nR.U. Valente173, A.-M. Valente-Feliciano369, G. Valentino1,193, C.A. Valerio-Lizarraga204,323,\nS. Valette1, J.W.F. Valle318, L. Valle1, N. Valle131, N. Vallis1,2,119, G. Vallone144, P. van Gemmeren161,\nW. Van Goethem1, P. van Hees68, U. van Rienen411, L. van Riesen-Haupt1,119, P. Van Trappen1,\nM. Vande Voorde413,414, A.L. Vanel1, E.W. Varnes360, J.-L. Vay144, F. Veit285, I. Veliscek6, R. Veness1,\nA. Ventura162,231, M. Verducci20,85, C.B. Verhaaren415, C. Vernieri7, A.P. Verweij1, J.-F. Vian416,\nA. Vicini54,55, N. Vignaroli162,231, S. Vignetti152, M.C. Villeneuve218, I. Vivarelli36,37,\nE. Voevodina1,135, D.M. Vogt417, B. Voirin418, S. Voiriot110, J. Voiron147, P. Vojtyla1, V. V\u00f6lkl1,\nL. von Freeden1, Z. Vostrel1,419, N. Voumard1, E. Vryonidou61, V. Vysotsky123, R. Wallny153,\nL.-T. Wang420, Y. Wang10,21,22, R. Wanzenberg4, B.F.L. Ward421, N. Wardle184, Z. Wa\u00b8s112,\nL. Watrelot1, A.T. Watson422, M.F. Watson422, M.S. Weber97, C.P. Welsch62,187, M. Wendt1,6,\nJ. Wenninger1, B. Weyer1, G. White423, S. White306, B. Wicki1, M. Widorski1, U.A. Wiedemann1,\nA.R. Wiederhold61, A . Wiedl19, H.-U. Wienands161, A. Wieser153, C. Wiesner1, H. Wilkens1,\nD. Willi424, P.H. Williams62,425, S.L. Williams43, A. Winter422, R.B. Wittwer81, D. Wollmann1,\nY. Wu119, Z. Wu10,27,28, J. Xiao10,65,66, K. Xie386, S. Xie48,333, M. Yalvac33, F. Yaman425,426,\nW.-M. Yao144, M. Yeresko10,157,158, A. Yilmaz195, H.D. Yoo275, T. You209, F. Yu251,385, S.S. Yu87,\nT.-T. Yu410, S. Yue1, A. Zaborowska1, M. Zahnd110, C. Zamantzas1, G. Zanderighi74,135, C. Zannini1,\nR. Zanzottera54,55, P. Zaro107, R. Zennaro2, M. Zerlauth1, H. Zhang203, J. Zhang161, Y. Zhang203,\nZ. Zhang10,21,203, Y. Zhao1, Y.-M. Zhong427, B. Zhou303, D. Zhou211, J. Zhu303, G. Zick372,\nM.A. Zielinski1, E. Zimmermann110, A. Zingaretti9,167, J. Zinn-Justin3, A.V. Zlobin48, M. Zobov15,\nF. Zomer10,21,22, S. Zorzetti48, X. Zuo19, J. Zurita318, V.V. Zutshi392, M. Zykova2.\n\u2020 deceased\nx\n\n1 Switzerland - CERN, European Organization for Nuclear Research\n2 Switzerland - PSI, Paul Scherrer Institute\n3 France - CEA/Irfu, Commissariat \u00e0 l\u2019Energie Atomique et aux Energies Alternatives, Institut de\nrecherche sur les lois fondamentales de l\u2019Univers\n4 Germany - DESY, Deutsches Elektronen-Synchrotron\n5 Germany - Humboldt-Universit\u00e4t zu Berlin\n6 United States - BNL, Brookhaven National Laboratory\n7 United States - SLAC National Accelerator Laboratory\n8 United Kingdom - University of Oxford\n9 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Padova\n10 France - CNRS/IN2P3, Centre National de la Recherche Scientifique, Institut National de\nPhysique Nucl\u00e9aire et de Physique des Particules\n11 France - APC, Laboratoire AstroParticule et Cosmologie\n12 France - Universit\u00e9 Paris Cit\u00e9\n13 France - LPNHE, Laboratoire de Physique Nucl\u00e9aire et de Hautes \u00c9nergies\n14 Switzerland - UNIGE, Universit\u00e9 de Gen\u00e8ve\n15 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati\n16 Denmark - NBI, Niels Bohr Institute\n17 Spain - Universidad de Granada\n18 United States - University of Pittsburgh\n19 Germany - KIT, Karlsruher Institut f\u00fcr Technologie\n20 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa\n21 France - IJCLab, Laboratoire de Physique des 2 Infinis Ir\u00e8ne Joliot Curie\n22 France - Universit\u00e9 Paris-Saclay et Universit\u00e9 Paris-Cit\u00e9\n23 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bari\n24 Italy - Universit\u00e0 di Bari\n25 Iran - IPM, Institute for Research in Fundamental Science\n26 Iran - Malayer University\n27 France - LAPP, Laboratoire d\u2019Annecy de Physique des Particules\n28 France - Universit\u00e9 Savoie Mont Blanc\n29 Serbia - University of Belgrade\n30 Spain - ICMAB/CISC, Institut de Ci\u00e8ncia de Materials de Barcelona, Consejo Superior de\nInvestigaciones Cient\u00edificas\n31 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata\n32 Italy - Universit\u00e0 Roma Tor Vergata\n33 T\u00fcrkiye - Yozgat Bozok \u00dcniversitesi\n34 United States - Texas Tech University\n35 T\u00fcrkiye - TOBB ETU, TOBB Ekonomi ve Teknoloji \u00dcniversitesi\n36 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Bologna\n37 Italy - Universit\u00e0 di Bologna\n38 Spain - CIEMAT, Centro de Investigaciones Energ\u00e9ticas, Medioambientales y Tecnol\u00f3gicas\n39 Saudi Arabia - KACST, King Abdulaziz City for Science and Technology\n40 Italy - Universit\u00e0 Roma Tre\n41 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano-Bicocca\nxi\n\n42 Italy - Universit\u00e0 di Milano-Bicocca\n43 United Kingdom - University of Cambridge\n44 T\u00fcrkiye - \u02d9Istanbul \u00dcniversitesi\n45 T\u00fcrkiye - Eski\u00b8sehir Teknik \u00dcniversitesi\n46 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli\n47 Italy - Universit\u00e0 di Napoli Federico II\n48 United States - FNAL, Fermi National Accelerator Laboratory\n49 Iran - University of Tehran\n50 Iran- FUM, Ferdowsi University of Mashhad\n51 United States - University of Texas Austin\n52 France - IPHC, Institut Pluridisciplinaire Hubert Curien\n53 France - Universit\u00e9 de Strasbourg\n54 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Milano\n55 Italy - Universit\u00e0 di Milano\n56 Switzerland - PIBG, P\u00f4le Invert\u00e9br\u00e9s du Basin Genevois\n57 Brazil - UFRN, Universidade Federal do Rio Grande do Norte\n58 Switzerland - UNIBAS, University of Basel\n59 Italy - Politecnico di Bari\n60 Portugal - LIP, Laborat\u00f3rio de Instrumenta\u00e7\u00e3o e F\u00edsica Experimental de Part\u00edculas\n61 United Kingdom - University of Manchester\n62 United Kingdom - CI, Cockcroft Institute\n63 United States - Brandeis University\n64 Armenia - A. Alikhanyan National Laboratory\n65 France - IP2I, Institut de Physique des 2 Infinis de Lyon\n66 France - Universit\u00e9 Claude Bernard Lyon 1\n67 T\u00fcrkiye - Ankara \u00dcniversitesi\n68 Sweden - Lund University\n69 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Torino\n70 United Arab Emirates - New York University Abu Dhabi\n71 United States - Stony Brook University\n72 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia\n73 Italy - Universit\u00e0 di Perugia\n74 Germany - Technische Universit\u00e4t M\u00fcnchen\n75 T\u00fcrkiye - Hatay Mustafa Kemal \u00dcniversitesi\n76 T\u00fcrkiye - Do\u02d8gu\u00b8s \u00dcniversitesi\n77 People\u2019s Republic of China - Harbin Institute of Technology\n78 United States - University of Wisconsin-Madison\n79 United Kingdom - RAL, Rutherford Appleton Laboratory, Science and Technology Facilities\nCouncil\n80 India - IMSc, Institute of Mathematical Sciences, Chennai\n81 Switzerland - Universit\u00e4t Z\u00fcrich\n82 United States - University of New Mexico\n83 France - CPPM, Centre de Physique des Particules de Marseille\n84 France - Aix-Marseille Universit\u00e9\nxii\n\n85 Italy - Universit\u00e0 di Pisa\n86 Hungary - HUN-REN Wigner Research Centre for Physics\n87 United States - Catholic University of America\n88 United States - Duke University\n89 France - LLR, Laboratoire Leprince-Ringuet\n90 France - \u00c9cole Polytechnique, Institut Polytechnique de Paris\n91 Canada - TRIUMF, Canada\u2019s National Laboratory for Particle and Nuclear Physics\n92 Canada - Simon Fraser University\n93 Italy - FEEM, Fondazione Ente Nazionale Idrocarburi (ENI) Enrico Mattei\n94 France - BRGM, Bureau de Recherches G\u00e9ologiques et Mini\u00e8res\n95 T\u00fcrkiye - I\u00b8s\u0131k \u00dcniversitesi\n96 T\u00fcrkiye - \u02d9Istanbul Teknik \u00dcniversitesi\n97 Switzerland - UNIBE, University of Bern\n98 Italy - Universit\u00e0 di Roma la Sapienza\n99 Italy - CNR-SPIN, Consiglio Nazionale delle Ricerche\n100 France - Expert naturaliste et entomologiste\n101 United States - ORNL, Oak Ridge National Laboratory\n102 Austria - HEPHY, Institut f\u00fcr Hochenergiephysik\n103 Switzerland - Geos, Bureau d\u2019ing\u00e9nieurs conseils en g\u00e9otechnique, g\u00e9nie civil, hydraulique et\nenvironnement\n104 Austria - TUWIEN, Technische Universit\u00e4t Wien\n105 Switzerland - HEPIA, Haute \u00c9cole du Paysage, d\u2019Ing\u00e9nierie et d\u2019Architecture de Gen\u00e8ve\n106 Switzerland - HES-SO University of Applied Sciences and Arts Western Switzerland\n107 France - SETEC ALS, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en infrastructures de transport, g\u00e9nie civil et\nenvironnement\n108 United States - East Texas A&M University\n109 Switzerland - Amberg Engineering Ltd\n110 Switzerland - ECOTEC Environnement SA, Bureau d\u2019\u00e9tudes et de conseil en environnement\n111 United States - Southern Methodist University\n112 Poland - IFJ PAN, Institute of Nuclear Physics, Polish Academy of Sciences\n113 France - Cerema, \u00e9tablissement public pour l\u2019\u00e9laboration, le d\u00e9ploiement et l\u2019\u00e9valuation de\npolitiques publiques d\u2019am\u00e9nagement et de transport\n114 United Kingdom - Rendel Ltd, Engineering design consultancy firm\n115 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre\n116 T\u00fcrkiye - \u02d9Istanbul Beykent \u00dcniversitesi\n117 United States - University of Iowa\n118 India - Indian Institute of Technology Kanpur\n119 Switzerland - EPFL, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne\n120 Germany - Universit\u00e4t Hamburg, Fakult\u00e4t f\u00fcr Mathematik, Informatik und Naturwissenschaften\n121 Belgium - VUB, Vrije Universiteit Brussel\n122 Italy - Scuola Superiore Meridionale\n123 Affiliated with an institute formerly covered by a cooperation agreement with CERN\n124 Canada - University of Saskatchewan and the Canadian Light Source\n125 United Kingdom - University of Bristol\nxiii\n\n126 United States - Northwestern University\n127 United States - University of Florida\n128 Canada - York University\n129 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari\n130 Italy - Universit\u00e0 di Cagliari\n131 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Pavia\n132 Canada - Queen\u2019s University\n133 Portugal - CFTP-IST, Centro de F\u00edsica T\u00e9orica de Part\u00edculas, Instituto Superior Tecnico,\nUniversidade de Lisboa\n134 Sweden - Uppsala University\n135 Germany - MPP, Max-Planck-Institut f\u00fcr Physik Garching\n136 Ukraine - NSC KIPT, National Science Center Kharkiv Institute of Physics and Technology\n137 Italy - Universit\u00e0 degli Studi dell\u2019Insubria\n138 Germany - Albert-Ludwigs-Universit\u00e4t Freiburg\n139 United Kingdom - JAI, John Adams Institute for Accelerator Science, University of Oxford\n140 France - CNRS/INP, Centre National de la Recherche Scientifique, Institut de Physique\n141 France - LPTHE, Laboratoire de Physique Th\u00e9orique et Hautes Energies\n142 France - Sorbonne Universit\u00e9\n143 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Genova\n144 United States - LBNL, Lawrence Berkeley National Laboratory\n145 Italy - IIT, Instituto Italiano di Tecnologia\n146 T\u00fcrkiye - G\u00fcm\u00fc\u00b8shane \u00dcniversitesi\n147 Switzerland - WSP Ing\u00e9nieurs Conseils SA\n148 Mexico - UADY, Autonomous University of Yucatan\n149 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara\n150 Italy - Universit\u00e0 di Ferrara\n151 France - MARCELEON, Cabinet d\u2019ing\u00e9nierie juridique et fonci\u00e8re\n152 Italy - CSIL (Economic Research Institute)\n153 Switzerland - ETHZ, Swiss Federal Institute of Technology Zurich\n154 Spain - UAH, Universidad de Alcal\u00e1 Madrid\n155 France - CIA, Conseil Ing\u00e9nierie Acoustique\n156 France - Evinerude, Bureau d\u2019\u00e9tudes environnementales\n157 France - LPCA, Laboratoire de Physique de Clermont Auvergne\n158 France - Universit\u00e9 Clermont Auvergne\n159 Australia - ANSTO, Australian Synchrotron\n160 India - Brahmananda Keshab Chandra College\n161 United States - ANL, Argonne National Laboratory\n162 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Lecce\n163 Italy - Universit\u00e0 di Palermo\n164 Poland - Wroc\u0142aw University of Science and Technology\n165 United States - Rutgers University\n166 United States - Princeton University\n167 Italy - Universit\u00e0 di Padova\n168 T\u00fcrkiye - IUE, \u02d9Izmir Ekonomi \u00dcniversitesi\nxiv\n\n169 T\u00fcrkiye - Ege \u00dcniversitesi\n170 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Udine\n171 Italy - Universit\u00e0 di Udine\n172 United States - University of Massachusetts Amherst\n173 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Roma\n174 Spain - CELLS/ALBA, Consortium for the Construction, Equipment and Exploitation of the\nSynchrotron Light Laboratory\n175 France - LPSC, Laboratoire de Physique Subatomique et de Cosmologie\n176 France - Universit\u00e9 Grenoble Alpes\n177 Italy - Universit\u00e0 degli Studi di Napoli Parthenope\n178 United States - National High Magnetic Field Laboratory\n179 United States - Florida State University\n180 South Africa - University of Johannesburg\n181 Spain - IGFAE, Instituto Galego de Fisica de Altas Enerx\u00edas, Universidade de Santiago de\nCompostela\n182 United Kingdom - LSE, London School of Economics\n183 Spain - Universidade de Santiago de Compostela\n184 United Kingdom - Imperial College London\n185 United States - MIT, Massachusetts Institute of Technology\n186 France - CETU, Centre d\u2019Etude des Tunnels\n187 United Kingdom - University of Liverpool\n188 Switzerland - Linde Kryotechnik AG\n189 Switzerland - ILF Consulting Engineers\n190 Japan - Hokkaido University\n191 Czech Republic - CUNI, Charles University\n192 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Sezione di Firenze\n193 Malta - University of Malta\n194 United States - BU, Boston University\n195 T\u00fcrkiye - IBU, Bolu Abant \u02d9Izzet Baysal \u00dcniversitesi\n196 Germany - Julius-Maximilians-Universit\u00e4t W\u00fcrzburg\n197 Australia - University of Adelaide\n198 Finland - HIP, Helsinki Institute of Physics, University of Helsinki\n199 Belgium - ULB, Universit\u00e9 Libre de Bruxelles\n200 Germany - IMA, Institut f\u00fcr Maschinenelemente, Universit\u00e4t Stuttgart\n201 Belgium - CP3, Centre de Cosmologie, de Physique des Particules et de Ph\u00e9nom\u00e9nologie,\nUniversit\u00e9 Catholique de Louvain\n202 Netherlands - NIKHEF, Nationaal instituut voor subatomaire fysica\n203 People\u2019s Republic of China - IHEP, Chinese Academy of Sciences\n204 Mexico - UAS, Universidad Aut\u00f3noma de Sinaloa\n205 Austria - BOKU, Universit\u00e4t f\u00fcr Bodenkultur Wien\n206 United States - Purdue University\n207 India - University of Delhi\n208 France - Ginger BURGEAP, bureau d\u2019\u00e9tudes en environnement\n209 United Kingdom - King\u2019s College London\nxv\n\n210 United States - University of Maryland\n211 Japan - KEK, High Energy Accelerator Research Organization\n212 Switzerland - Geoenergy, Reservoir Geology and Basin Analysis Group\n213 France - SETEC International, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie en charge des transports et des infrastructures\n214 T\u00fcrkiye - KKU, K\u0131r\u0131kkale \u00dcniversitesi\n215 France - SETEC LERM, Soci\u00e9t\u00e9 d\u2019ing\u00e9nierie conseil en mat\u00e9riaux de construction\n216 Mexico - BUAP, Benem\u00e9rita Universidad Aut\u00f3noma de Puebla\n217 United States - Stanford University\n218 Austria - MUL, Montanuniversit\u00e4t Leoben, Lehrstuhl f\u00fcr Subsurface Engineering, Geotechnik\nund unterirdisches Bauen\n219 Austria - MUL-ZaB, Underground Research Center, Zentrum am Berg\n220 Spain - IFAE, Institut de F\u00edsica d\u2019Altes Energies\n221 Switzerland - FHNW, University of Applied Sciences Northwestern Switzerland\n222 India - UPES, University of Petroleum and Energy Studies\n223 France - GANIL, Grand Acc\u00e9l\u00e9rateur National d\u2019Ions Lourds\n224 France - Universit\u00e9 Caen Normandie\n225 Brazil - UFRGS, Universidade Federal do Rio Grande do Sul\n226 Germany - Technische Universit\u00e4t Darmstadt\n227 Poland - University of Silesia in Katowice\n228 Portugal - Universidade de Coimbra\n229 Brazil - UFPel, Universidade Federal de Pelotas\n230 United States - University of California Santa Cruz\n231 Italy - Universit\u00e0 del Salento\n232 United States - Brown University\n233 United States - University of California Berkeley\n234 Italy - Universit\u00e0 di Torino\n235 United States - Johns Hopkins University\n236 People\u2019s Republic of China - Fudan University\n237 France - LAPTh, Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique\n238 People\u2019s Republic of China - Dongguan University of Technology\n239 T\u00fcrkiye - Kahramanmara\u00b8s S\u00fct\u00e7\u00fc \u02d9Imam \u00dcniversitesi\n240 Mexico - UNACH, Universidad Aut\u00f3noma de Chiapas\n241 Mexico - MCTP, Mesoamerican Centre for Theoretical Physics\n242 Mexico - UAZ, Universidad Aut\u00f3noma de Zacatecas\n243 Finland - University of Jyv\u00e4skyl\u00e4\n244 Germany - Technische Universit\u00e4t Dortmund\n245 United Kingdom - Overleaf\n246 United States - University of Virginia\n247 United States - Cornell University\n248 United States - FIT, Florida Institute of Technology\n249 Switzerland - Shirokuma GmbH\n250 Pakistan - National Centre for Physics\n251 Germany - Johannes Gutenberg Universit\u00e4t Mainz\n252 Pakistan - PAEC, Pakistan Atomic Energy Commission\nxvi\n\n253 India - Mathabhanga College\n254 India - Harish-Chandra Research Institute\n255 Germany - MPIK, Max-Planck-Institut f\u00fcr Kernphysik Heidelberg\n256 Sweden - European Spallation Source ERIC\n257 France - Centre de calcul de l\u2019IN2P3\n258 Germany - GSI, Helmholtzzentrum f\u00fcr Schwerionenforschung GmbH\n259 Republic of Korea - IBS, Institute for Basic Science, Center for Theoretical Physics of the\nUniverse\n260 Poland - University of Warsaw\n261 Slovenia - University of Ljubljana\n262 Slovenia - Jozef Stefan Institute\n263 France - Microhumus, Bureau d\u2019\u00e9tude et d\u2019ing\u00e9nierie sp\u00e9cialis\u00e9 dans la gestion des sols d\u00e9grad\u00e9s\n264 Germany - Fakult\u00e4t f\u00fcr Physik und Astronomie, Universit\u00e4t Heidelberg\n265 T\u00fcrkiye - Ni\u02d8gde \u00d6mer Halisdemir \u00dcniversitesi\n266 T\u00fcrkiye - Giresun \u00dcniversitesi\n267 Hungary - University of Miskolc\n268 Greece - NTUA, National Technical University of Athens\n269 Switzerland - Transmutex SA\n270 Ireland - DIAS, Dublin Institute for Advanced Studies, School of Theoretical Physics\n271 Poland - AGH, University of Science and Technology\n272 Iran - University of Science and Technology of Mazandaran\n273 United Kingdom - IPPP, Institute for Particle Physics Phenomenology, Durham University\n274 T\u00fcrkiye - Bursa Uluda\u02d8g \u00dcniversitesi\n275 Republic of Korea - YU, Yonsei University\n276 Affiliated with an international laboratory covered by a cooperation agreement with CERN\n277 France - CPT, Centre de Physique Th\u00e9orique\n278 France - Aix-Marseille Universit\u00e9 et Universit\u00e9 du Sud Toulon Var\n279 Republic of Korea - KIAS, Korea Institute for Advanced Study\n280 Canada - Carleton University\n281 Greece - FEAC Engineering P.C.\n282 Greece - UPATRAS, University of Patras\n283 United States - University of Kansas\n284 Greece - AUTH, Aristotle University of Thessaloniki\n285 Germany - IML, Fraunhofer-Institut f\u00fcr Materialfluss und Logistik\n286 Germany - RWTH Aachen, Rheinisch-Westf\u00e4lische Technische Hochschule Aachen\n287 Switzerland - ZHAW, Zurich University of Applied Sciences\n288 Gernany - Universit\u00e4t M\u00fcnster\n289 South Africa - University of the Witwatersrand\n290 Austria - Fachhochschule Technikum Wien\n291 United States - University of California Irvine\n292 United States - Northeastern University\n293 France - ESI, European Scientific Institute\n294 Republic of Korea - UOS, University of Seoul\n295 Republic of Korea - KNU Kyungpook National University\nxvii\n\n296 Republic of Korea - KU, Korea University\n297 Finland - Tampere University\n298 United Kingdom - University of Edinburgh\n299 Switzerland - BG Ing\u00e9nieurs Conseils\n300 People\u2019s Republic of China - T.-D. Lee Institute\n301 People\u2019s Republic of China - Shanghai Jiao Tong University\n302 Italy - CNR, Consiglio Nazionale delle Ricerche\n303 United States - University of Michigan\n304 United States - University of Pennsylvania\n305 United States - University of Minnesota\n306 France - ESRF, European Synchrotron Radiation Facility\n307 United Kingdom - SUSSEX, University of Sussex\n308 Italy - Universit\u00e0 di Bari Aldo Moro\n309 United Kingdom - University of Bath\n310 Italy - Scuola Normale Superiore di Pisa\n311 Brazil - Universidade de S\u00e3o Paulo\n312 Austria - Universit\u00e4t Graz\n313 Egypt - Center for High Energy Physics, Fayoum University\n314 Egypt - Center of theoretical physics, British University in Egypt\n315 Egypt - Cairo University\n316 France - Sorbonne Universit\u00e9 et Universit\u00e9 Paris Cit\u00e9\n317 Italy - Universit\u00e0 di Genova\n318 Spain - IFIC-CSIC/UV, Instituto de F\u00edsica Corpuscular, Consejo Superior de Investigaciones\nCient\u00edficas/Universidad de Valencia\n319 Switzerland - Service de g\u00e9ologie, sols et d\u00e9chets du canton de Gen\u00e8ve\n320 Estonia - NICPB, National Institute for Chemical Physics and Biophysics\n321 Estonia - UT, University of Tartu\n322 Spain - Universidad de Salamanca\n323 Mexico - UGTO, Universidad de Guanajuato\n324 Switzerland - Edaphos engineering\n325 Germany - Helmholtz-Zentrum Dresden-Rossendorf\n326 India - Tata Institute of Fundamental Research Mumbai\n327 Belgium - Universiteit Gent\n328 Italy - CNR-IOM, Consiglio Nazionale delle Ricerche\n329 Austria - JKU, Johannes Kepler Universit\u00e4t Linz\n330 Norway - University of Stavanger\n331 Colombia - Universidad Nacional de Colombia\n332 Italy - Trento Institute for Fundamental Physics and Applications\n333 United States - Caltech, California Institute of Technology\n334 Italy - Universit\u00e0 dalla Calabria\n335 Spain - IFT, Instituto de F\u00edsica Te\u00f3rica, Universidad Aut\u00f3noma de Madrid\n336 Spain - UPC, Universitat Polit\u00e8cnica de Catalunya\n337 Portugal - Departamento de F\u00edsica, Universidade do Minho\n338 Portugal - Centro de F\u00edsica das Universidades do Minho e do Porto\nxviii\n\n339 Portugal - LaPMET, Laboratory of Physics for Materials and Emergent Technologies\n340 Norway - University of Bergen\n341 Chile - SAPHIR, Instituto Milenio de F\u00edsica Subat\u00f3mica en la Frontera de Altas Energ\u00edas\n342 Chile - Universidad Andres Bello\n343 Brazil - IIP, International Institute of Physics\n344 Japan - Tokyo International University\n345 T\u00fcrkiye - \u02d9Izmir Bak\u0131r\u00e7ay \u00dcniversitesi\n346 Italy - INFN, Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Gran Sasso\n347 Italy - Universit\u00e1 degli Studi di Cassino e del Lazio Meridionale\n348 Serbia - Vin\u02d8ca Institute of Nuclear Sciences\n349 United States - Kennesaw State University\n350 Italy - Universit\u00e0 di Pavia\n351 United States - Columbia University\n352 United States - DOE, Department of Energy of the United States of America\n353 France - IPSA, Institut Polytechnique des Sciences Avanc\u00e9es\n354 Italy - Universit\u00e0 degli Studi del Sannio\n355 Poland - UJ, Jagiellonian University\n356 Austria - Universit\u00e4t Wien\n357 Germany - Goethe-Universit\u00e4t Frankfurt, Institut f\u00fcr Angewandte Physik\n358 Germany - HFFH, Helmholtz Forschungsakademie Hessen f\u00fcr FAIR\n359 Romania - INCDTIM, National Institute for Research and Development of Isotopic and\nMolecular Technologies\n360 United States - University of Arizona\n361 Germany - Technische Universit\u00e4t Dresden\n362 Latvia - RTU, Riga Technical University\n363 United Kingdom - Lancaster University\n364 Cyprus - University of Cyprus\n365 Cyprus - Cosmos Open University\n366 Brazil - CBPF, Centro Brasileiro de Pesquisas F\u00edsicas\n367 Germany - Universit\u00e4t Bonn\n368 Thailand - CMU, Chiang Mai University\n369 United States - JLAB, Thomas Jefferson National Accelerator Facility\n370 Ecuador - ESPOL, Escuela Superior Polit\u00e9cnica del Litoral\n371 Croatia - IRB, Rudjer Boskovic Institute\n372 France - Air Liquide Advanced Technologies\n373 Netherlands - VU Amsterdam\n374 France - ING\u00c9ROP ,Groupe d\u2019ing\u00e9nierie et de conseil en mobilit\u00e9 durable, transition \u00e9nerg\u00e9tique\net cadre de vie\n375 Poland - Warsaw University of Technology\n376 Spain - IFCA, Instituto de F\u00edsica de Cantabria\n377 Germany - Institut f\u00fcr Beschleunigerphysik und Technologie\n378 T\u00fcrkiye - U\u00b8sak \u00dcniversitesi\n379 Japan - ICEPP, International Center for Elementary Particle Physics, University of Tokyo\n380 United Kingdom - Rudolf Peierls Centre for Theoretical Physics, University of Oxford\nxix\n\n381 United Kingdom - All Souls College, University of Oxford\n382 T\u00fcrkiye - Akdeniz \u00dcniversitesi\n383 Switzerland - Latitude Durable SARL\n384 Spain - USAL, Universidad de Salamanca\n385 Germany - PRISMA+ Cluster of Excellence\n386 United States - Michigan State University\n387 Spain - Universidad Complutense Madrid\n388 Switzerland - scMetrology SARL\n389 Portugal - IST, Instituto Superior Tecnico, Universidade de Lisboa\n390 Portugal - CeFEMA, Center of Physics and Engineering of Advanced Materials\n391 India - Indian Institute of Science Education and Research Mohali\n392 United States - NIU, Northern Illinois University\n393 India - Banaras Hindu University\n394 Slovakia - Comenius University\n395 Australia - Monash University\n396 Slovakia - Slovak Academy of Sciences\n397 Republic of Korea - KAIST, Korea Advanced Institute of Science and Technology\n398 France - Amberg Engineering Chamb\u00e9ry\n399 United Arab Emirates - Khalifa University of Science and Technology\n400 United States - University of Tennessee\n401 Austria - WIFO, \u00d6sterreichisches Institut f\u00fcr Wirtschaftsforschung\n402 Brazil - Universidade do Estado do Rio de Janeiro\n403 France - M\u00e9lica, NATURA SCOP, \u00c9tudes et expertises environnementales\n404 Italy - Universit\u00e0 LUM, Casamassima\n405 Netherlands - University of Twente\n406 Iran - Arak University\n407 Italy - Universit\u00e0 di Trieste\n408 France - ForestAllia, Cabinet de gestion et d\u2019expertise foresti\u00e8res\n409 Germany - Universit\u00e4t Siegen\n410 United States - University of Oregon\n411 Germany - Universit\u00e4t Rostock\n412 Switzerland - CEGELEC SA\n413 Sweden - KTH, Royal Institute of Technology, Stockholm\n414 Sweden - OKC, Oskar Klein Centre for Cosmoparticle Physics\n415 United States - Brigham Young University\n416 France - Expert foncier et agricole\n417 Germany - ITSM, Institut f\u00fcr Thermische Str\u00f6mungsmaschinen und Maschinenlaboratorium,\nUniversit\u00e4t Stuttgart\n418 France - \u00c9cole Normale Sup\u00e9rieure de Lyon\n419 Czech Republic - CTU, Czech Technical University\n420 United States - University of Chicago\n421 United States - Baylor University\n422 United Kingdom - University of Birmingham\n423 United Kingdom - University of Southampton\nxx\n\n424 Switzerland - Swisstopo, Federal Office of Topography\n425 United Kingdom - Daresbury Laboratory, Science and Technology Facilities Council\n426 T\u00fcrkiye - IZTECH, \u02d9Izmir Y\u00fcksek Teknoloji Enstit\u00fcs\u00fc\n427 Hong Kong - City University of Hong Kong\nxxi\n\nAbstract\nVolume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental pro-\ngramme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC\nwould address some of the most profound open questions in particle physics, from precision studies of\nthe Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model.\nThe report reviews the experimental opportunities offered by the staged implementation of FCC, begin-\nning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed\nby a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in\nterms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and\nconceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics\nprogramme imposes on the accelerator in the domains of the calibration of the collision energy, and the\ninterface region between the accelerator and the detector. The report also highlights advances in detector,\nsoftware and computing technologies, as well as the theoretical tools /reconstruction techniques that will\nenable the precision measurements and discovery potential of the FCC experimental programme. The\ncontent and structure of this report are guided by the scope and priorities defined in the mandate of the\nFCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics po-\ntential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated\nhere or are addressed only briefly, in alignment with the study\u2019s focus. This volume reflects the outcome\nof a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated\ncommunity-building coordination, and provides a targeted assessment of the scientific opportunities and\nexperimental foundations of the FCC programme.\nxxii\n\nPreface from CERN\u2019s Director-General\nIn 2021, in response to the 2020 update of the European Strategy for Particle Physics, the CERN Council\ninitiated the Future Circular Collider (FCC) Feasibility Study.\nThis report summarises an immense amount of work carried out by the international FCC collabo-\nration over several years. It covers, inter alia, physics objectives and potential, geology, civil engineering,\ntechnical infrastructure, territorial implementation, environmental aspects, R&D needs for the acceler-\nators and detectors, socio-economic benefits and cost. It constitutes important input for the ongoing\nupdate of the European Strategy for Particle Physics.\nThe Feasibility Study required engagement with a broad range of stakeholders. In particular,\nthroughout the Study, CERN has been accompanied by its two Host States, France and Switzerland,\nand has been working with entities at local, regional and national level. I am very grateful to the Host\nState authorities and teams for their invaluable help. Furthermore, significant sections of the Study were\nsupported by the European Union under the Horizon 2020 and Horizon Europe framework programmes.\nThe Study also greatly benefited from contributions from accelerator laboratories and universities from\nacross Europe, such as the Swiss Accelerator Research and Technology (CHART) initiative, and from\nthe Americas, Asia, Africa and Australia.\nThe proposed FCC integrated programme consists of two possible stages: an electron\u2013positron\ncollider serving as a Higgs-boson, electroweak and top-quark factory running at different centre-of-mass\nenergies, followed at a later stage by a proton\u2013proton collider operating at an unprecedented collision\nenergy of around 100 TeV. The complementary physics programmes of each stage match the physics\npriorities expressed in the 2020 update of the European Strategy for Particle Physics.\nA major achievement of the Feasibility Study is the choice of placement of the collider ring and\nthe entire infrastructure, including the surface sites and the access shafts, which was developed and\noptimised over several years following the principle \u201cavoid, reduce, compensate\u201d. Sustainability studies\nhave assessed energy efficiency, land use, water and resource management, and socio-economic impact,\nensuring that the FCC is designed in accordance with the latest environmental and societal standards.\nI would like to thank all contributors to this report for their hard work and commitment, which\nallowed the outstanding results presented here to be achieved.\nFabiola Gianotti\nCERN, Director-General\nxxiii\n\nPreface from the FCC Collaboration Board Chair\nBuilding on the earlier Future Circular Collider (FCC) Conceptual Design Study conducted between\n2014 and 2018, the FCC Feasibility Study (2021\u20132025) has been undertaken by a robust international\ncollaboration, now comprising over 160 institutes worldwide. The FCC \u201cintegrated programme\u201d, de-\nveloped in the framework of the Feasibility Study, consists of an initial electron-positron collider, the\nFCC-ee, which could be followed by a proton-proton collider, the FCC-hh. This staging takes into ac-\ncount the physics priorities as formulated in the updates of the European Strategy for Particle Physics of\n2012 and 2020, as well as the relative technology readiness and costs of the FCC-ee and FCC-hh.\nOver the years, I have closely followed the steady progress of the study, representing the FCC\ncollaboration at the international steering committee and participating in annual FCC Week meetings,\nwhich include sessions of the International Collaboration Board. The commitment and enthusiasm of\nthe members of the collaboration has always been impressive. The collective effort is clearly visible.\nParticipation by students and early-career researchers is increasing. There is a shared determination and\nmomentum to move forward.\nThe strong international collaboration around the FCC and its global network provide a solid foun-\ndation for the future of this project. The FCC community continues to grow, with increasing engagement\nfrom new institutes and partners worldwide. This broad support will be essential as the project enters its\nnext phase.\nThe FCC Feasibility Study demonstrates not only the technical viability of the project, but also\nthe strength of the international community that supports it. As we move towards the next step in\nthe decision-making phase, this collective effort is key to showing a possible path forward. The FCC\npromises far-reaching scientific opportunities and long-term benefits for innovation, training, and global\ncollaboration in science and technology.\nPhilippe Chomaz\nCEA, Chair of the FCC International Collaboration Board\nxxiv\n\nContents\n1\nOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n1\n1.1\nFCC-ee: A great Higgs factory, and so much more\n. . . . . . . . . . . . . . . . . . . . .\n2\n1.2\nFCC-hh: The energy-frontier collider with the broadest exploration potential\n. . . . . . .\n11\n2\nSpecificities of the FCC physics case . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n15\n2.1\nThe impact of FCC in particle physics . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n15\n2.2\nCharacterisation of the Higgs boson: role of EW measurements and of FCC-hh . . . . . .\n16\n2.2.1\nImpact of Z-pole measurements in Higgs couplings determination . . . . . . . . . . . .\n20\n2.2.2\nImpact of diboson measurements in Higgs couplings determination\n. . . . . . . . . . .\n22\n2.2.3\nComplementarity between Z-pole and higher-energy runs\n. . . . . . . . . . . . . . . .\n22\n2.2.4\nComplementarity and synergy between FCC-ee and FCC-hh . . . . . . . . . . . . . . .\n23\n2.3\nDiscovery landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n27\n2.3.1\nBSM exploration potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n27\n2.3.2\nTera-Z sensitivity to heavy new physics . . . . . . . . . . . . . . . . . . . . . . . . . .\n30\n2.3.3\nFlavour deconstruction at FCC-ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n37\n2.3.4\nHeavy Neutral Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n38\n2.3.5\nDark matter and dark sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n41\n2.3.6\nAxion-like particles\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n42\n2.3.7\nExotic decays of the Higgs and Z bosons\n. . . . . . . . . . . . . . . . . . . . . . . . .\n43\n2.3.8\nOther new physics searches\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n44\n2.3.9\nComplementarity and synergy between FCC-ee and FCC-hh . . . . . . . . . . . . . . .\n45\n2.4\nSelected topics in flavour physics\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n46\n2.4.1\nLepton universality tests in \u03c4 decays . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n47\n2.4.2\nLepton flavour violating \u03c4 decays\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n48\n2.4.3\nRare b-hadron decays with \u03c4+\u03c4\u2212pairs in the final state . . . . . . . . . . . . . . . . . .\n48\n2.4.4\nCharged-current b-hadron decays with a \u03c4\u03bd pair in the final state\n. . . . . . . . . . . .\n48\n2.4.5\nRare b- and c-hadron decays to di-neutrino final states . . . . . . . . . . . . . . . . . .\n48\n2.4.6\nRare decays and CPV studies with neutrals . . . . . . . . . . . . . . . . . . . . . . . .\n49\n2.4.7\nOn-shell Z, W, and Higgs flavour-changing decays . . . . . . . . . . . . . . . . . . . .\n50\n2.4.8\nCombined studies and synergy between the flavour and EW programmes . . . . . . . .\n50\n2.5\nFCC-hh specificities compared to high-energy lepton colliders . . . . . . . . . . . . . . .\n52\n2.5.1\nGeneralities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n52\n2.5.2\nResonance searches\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n53\n2.5.3\nPair production of new particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n55\n2.6\nPhysics reach of alternative FCC-hh \u221as options . . . . . . . . . . . . . . . . . . . . . . .\n56\n2.6.1\nHiggs properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n57\n2.6.2\nWIMP DM search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n58\nxxv\n\n2.6.3\nHigh-mass reach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n58\n2.7\nA forward-physics facility at FCC-hh\n. . . . . . . . . . . . . . . . . . . . . . . . . . . .\n59\n2.7.1\nNeutrino physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n60\n2.7.2\nBSM sensitivity\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n61\n2.7.3\nQCD and hadronic structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n61\n2.7.4\nSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n62\n3\nTheoretical calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n63\n3.1\nElectroweak corrections\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n64\n3.2\nQCD precision calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n66\n3.2.1\nQCD studies in Z/\u03b3\u2217\u2192jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n66\n3.2.2\nQCD aspects of Higgs physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n68\n3.2.3\nQCD modelling of the top-quark threshold\n. . . . . . . . . . . . . . . . . . . . . . . .\n69\n3.3\nMonte Carlo event generators\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n70\n3.3.1\nQCD aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n70\n3.3.2\nQED aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n71\n3.4\nOrganisation and support of future activities to improve theoretical precision\n. . . . . . .\n72\n4\nDetector requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n75\n4.1\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n75\n4.2\nBrief overview of the current detector concepts . . . . . . . . . . . . . . . . . . . . . . .\n75\n4.2.1\nThe IDEA detector concept\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n76\n4.2.2\nThe CLD detector concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n76\n4.2.3\nThe ALLEGRO detector concept\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n76\n4.3\nMeasurement of the tracks of charged particles\n. . . . . . . . . . . . . . . . . . . . . . .\n77\n4.3.1\nTrack momentum resolution: the measurement of the Higgs boson mass . . . . . . . . .\n77\n4.3.2\nTrack momentum resolution: the Z width and the stability of the momentum scale\n. . .\n78\n4.3.3\nAngular resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n79\n4.3.4\nNumber of tracker layers and highly-displaced vertices . . . . . . . . . . . . . . . . . .\n80\n4.3.5\nWork ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n81\n4.3.6\nPreliminary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n82\n4.4\nRequirements for the vertex detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n82\n4.4.1\nHeavy-flavour tagging and the Higgs boson coupling to charm quarks . . . . . . . . . .\n83\n4.4.2\nReconstruction of vertices and the measurement of the B \u2192K\u2217\u03c4\u03c4 branching fraction . .\n83\n4.4.3\nVertex resolutions and heavy-flavour electroweak precision observables . . . . . . . . .\n86\n4.4.4\nAlignment, overall scale of the detector, and the measurement of the tau lifetime . . . .\n87\n4.4.5\nPreliminary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n88\n4.5\nRequirements for charged hadron particle identification . . . . . . . . . . . . . . . . . . .\n88\n4.5.1\nStrange tagging and the Higgs boson coupling to strange (and charmed) quarks . . . . .\n89\n4.5.2\nSeparation of K\u00b1 from \u03c0\u00b1 and measurement of b \u2192s\u03bd\u03bd\n. . . . . . . . . . . . . . . .\n90\n4.5.3\nSeparation of K\u00b1 from \u03c0\u00b1 and measurement of Bs \u2192DsK\n. . . . . . . . . . . . . . .\n91\n4.5.4\nWork ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n92\n4.5.5\nPreliminary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n93\n4.6\nRequirements for electromagnetic calorimetry . . . . . . . . . . . . . . . . . . . . . . . .\n93\n4.6.1\nEnergy resolution and monophoton final states\n. . . . . . . . . . . . . . . . . . . . . .\n94\n4.6.2\nEnergy resolution and decays of heavy flavoured hadrons into photons or \u03c00 . . . . . . .\n95\nxxvi\n\n4.6.3\nRequirements on the geometrical acceptance for e+e\u2212\u2192\u03b3\u03b3 and \u2113+\u2113\u2212events at Z-pole\nenergies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n97\n4.6.4\nSensitivity to charged lepton flavour violation: Z \u2192\u00b5e and \u03c4 \u2192\u00b5\u03b3\n. . . . . . . . . . .\n99\n4.6.5\nBremsstrahlung recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100\n4.6.6\nPrompt decays of ALPs a \u2192\u03b3\u03b3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101\n4.6.7\nRequirements from \u03c00 \u2192\u03b3\u03b3 reconstruction in \u03c4 decays . . . . . . . . . . . . . . . . . . 102\n4.6.8\nWork ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103\n4.6.9\nPreliminary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104\n4.7\nRequirements for the hadron calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 104\n4.7.1\nReconstruction of Higgs boson hadronic final states . . . . . . . . . . . . . . . . . . . . 104\n4.7.2\nMeasurement of the Higgs boson invisible width . . . . . . . . . . . . . . . . . . . . . 105\n4.7.3\nSearch for heavy neutral leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106\n4.7.4\nWork ahead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107\n4.7.5\nPreliminary conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108\n4.8\nRequirements for the muon detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108\n4.9\nPrecise timing measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110\n4.9.1\nTime-of-flight measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110\n4.9.2\nTime measurements very close to the IP . . . . . . . . . . . . . . . . . . . . . . . . . . 111\n4.9.3\nTime measurements in the calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . 112\n4.10\nSelected studies with full simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112\n4.10.1\nMachine-learning event reconstruction\n. . . . . . . . . . . . . . . . . . . . . . . . . . 113\n4.10.2\nJet flavour tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114\n4.10.3\nHiggs boson mass determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115\n4.10.4\nTau polarisation\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116\n4.10.5\nSummary of detector requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117\n4.11\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120\n5\nMachine-detector interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121\n5.1\nInteraction region layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122\n5.2\nIntegration and alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125\n5.3\nMaintenance and detector opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126\n5.4\nBeam-induced backgrounds in the detectors . . . . . . . . . . . . . . . . . . . . . . . . . 128\n5.5\nImplementation tests and prototyping\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130\n5.6\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131\n6\nDetector concepts and systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133\n6.1\nDetector concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134\n6.2\nThe CLD and ILD detector concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134\n6.3\nThe IDEA detector concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135\n6.4\nThe ALLEGRO detector concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136\n6.5\nVertex detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137\n6.6\nMain tracking systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143\n6.6.1\nSilicon tracker\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143\n6.6.2\nDrift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144\n6.6.3\nStraw tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146\nxxvii\n\n6.6.4\nTime projection chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147\n6.7\nParticle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147\n6.7.1\nPrecision timing detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148\n6.7.2\nCompact RICH detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148\n6.8\nElectromagnetic calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150\n6.8.1\nSilicon pads, MAPS, scintillator strips . . . . . . . . . . . . . . . . . . . . . . . . . . . 150\n6.8.2\nNoble liquid\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150\n6.8.3\nSegmented crystals with dual-readout . . . . . . . . . . . . . . . . . . . . . . . . . . . 152\n6.8.4\nThe GRAiNITA ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153\n6.9\nHadron calorimeters\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154\n6.9.1\nScintillator tiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154\n6.9.2\nGaseous detectors\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156\n6.9.3\nDual readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156\n6.10\nCoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158\n6.11\nCryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159\n6.12\nMuon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160\n6.13\nLuminosity measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161\n6.13.1\nLumiCal design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161\n6.14\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163\n7\nFCC cavern infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165\n7.1\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165\n7.2\nThe FCC-hh reference detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165\n7.3\nFCC cavern infrastructure\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169\n8\nSoftware and computing\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171\n8.1\nThe FCC software ecosystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172\n8.2\nThe main components of KEY4HEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173\n8.3\nThe event data model EDM4HEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173\n8.3.1\nA specific use case: LEP data in EDM4HEP . . . . . . . . . . . . . . . . . . . . . . . . 174\n8.4\nIntegration of event generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174\n8.4.1\nEvent generators as packages\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175\n8.4.2\nCommon data formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175\n8.4.3\nConfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176\n8.5\nParametrised simulation\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176\n8.6\nFull simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177\n8.6.1\nDetector description and simulation strategy\n. . . . . . . . . . . . . . . . . . . . . . . 178\n8.6.2\nSub-detector models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178\n8.6.3\nFull detector models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179\n8.7\nDigitisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181\n8.8\nReconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182\n8.9\nAnalysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183\n8.10\nVisualisation\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184\n8.11\nComputing resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184\nxxviii\n\n8.11.1\nResource modelling\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185\n8.11.2\nModelling resources for FCC-ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187\n8.11.3\nMinimal baseline working scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188\n8.11.4\nOptimising resources: Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189\n8.11.5\nOptimising resources: Analysis techniques . . . . . . . . . . . . . . . . . . . . . . . . 190\n8.11.6\nOptimising resources: Workload and data management . . . . . . . . . . . . . . . . . . 190\n8.11.7\nIncreasing available resources: pledged resources . . . . . . . . . . . . . . . . . . . . . 191\n8.11.8\nIncreasing available resources: opportunistic resources . . . . . . . . . . . . . . . . . . 191\n8.11.9\nProjecting to the Z run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191\n8.12\nHuman resources: status and needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192\n8.13\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193\n9\nEnergy calibration, polarisation, monochromatisation . . . . . . . . . . . . . . . . . . . 195\n9.1\nOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195\n9.2\nInput from the experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196\n9.2.1\nThe crossing angle \u03b1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196\n9.2.2\nThe longitudinal boost and the collision-energy spread . . . . . . . . . . . . . . . . . . 196\n9.2.3\nRelative \u221as determination in the Z-resonance scan . . . . . . . . . . . . . . . . . . . . 196\n9.2.4\nAbsolute \u221as determination\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198\n9.3\nExpected precision on EW observables from the collision energy and its spread . . . . . . 199\n9.4\nProspects for monochromatisation and the measurement of the electron Yukawa coupling . 200\n9.5\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205\n10\nCommunity building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207\n11\nOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211\nReferences\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260\nxxix\n\nxxx\n\n1\nOverview\nThe particle physics landscape has been profoundly influenced by the discovery of a Higgs boson with\na mass around 125 GeV at the LHC [1, 2]. The long-predicted matrix of particles and interactions of\nthe Standard Model (SM) is now complete, and this consistent and predictive theory has so far been\nsuccessful at describing all phenomena accessible to collider experiments. After almost 15 years of LHC\noperation, the remarkable precision measurements and the many exploratory searches have demonstrated\nits validity and excluded signs of new physics across an order of magnitude of energies around the TeV\nscale. This notwithstanding, several fundamental experimental facts remain unexplained in the current\nframework, such as the abundance of matter over antimatter, the evidence for dark matter, or the non-\nzero neutrino masses, and many theoretical issues definitively also require physics beyond the present\nStandard Model (BSM), altogether calling for intensified collider exploration. For the first time since the\nFermi theory, however, the field of possible explanations to these unanswered questions provides little\nguidance for what form this exploration may take.\nThe confirmation by the LHC of the SM predictions up to the TeV range requires a different ap-\nproach to addressing these open questions. Solutions could exist at even higher energy, at the price of\neither an unnatural value of the weak scale or an ingenious but still elusive structure. Instead, radi-\ncally new physics scenarios have recently been devised, which often include light and feebly coupled\nstructures [3\u20135]. Neither the mass scale (from meV to ZeV) of this new physics nor the intensity of the\ncouplings to the SM (from 1 to 10\u221212 or less) are known, thus calling for a new, broad, and powerful tool\nof exploration. To experimentally push the limits of the unknown as far as possible with a real chance of\ndiscovery, this tool must be able to address the following goals in the broadest and deepest possible way.\n\u2013 Map the properties of the Higgs and electroweak (EW) gauge bosons, pinning down their interac-\ntions with accuracies order(s) of magnitude better than today, and acquiring sensitivity to, e.g., the\nprocesses that led to the formation of today\u2019s Higgs vacuum field during the time span between\n10\u221212 and 10\u221210 s after the Big Bang.\n\u2013 Sharpen our knowledge of already identified particle physics phenomena with a comprehensive\nand accurate campaign of precision electroweak, QCD, flavour, Higgs, and top measurements,\nsensitive to tiny deviations from the predicted Standard Model behaviour and probing energy scales\nfar beyond the direct kinematic reach. Such a campaign requires running at the intensity frontier\nwith large collected event samples, exquisitely precise experimental conditions and theoretical\ncalculations, as well as a maximal amount of synergies within the programme.\n\u2013 Improve by orders of magnitude the sensitivity to rare and elusive phenomena at low energies,\nincluding the possible discovery of light particles with very small couplings (e.g., massive neutri-\nnos, and/or axion-like particles). In particular, the search for dark matter should seek to reveal, or\nconclusively exclude, dark sector candidates belonging to broad classes of models.\n\u2013 Improve, by at least an order of magnitude, the direct discovery reach for new particles at the\nenergy frontier.\nThe entirely new context that led to these ambitious objectives calls for the highest integrated lu-\nminosities at the electroweak and Higgs scales, and for parton-parton collision centre-of-mass energies\nan order of magnitude above the TeV scale, already extensively probed by the LHC (and further so by the\nHL-LHC) direct searches. The 2021 update of the European Strategy for Particle Physics (ESPPU) [6]\nand the U.S. Community Study on the Future of Particle Physics (Snowmass \u201921) [7] now require an\ne+e\u2212Higgs factory with the highest priority, to complete and deepen the trailblazing Higgs boson mea-\nsurements performed at the LHC and HL-LHC. In addition, the 2021 ESPPU and the 2023 U.S. P5 report\nhave both highlighted the long-term vision [6,8] to operate a 10 TeV parton centre-of-mass energy (pCM)\ncollider following this e+e\u2212programme. Specifically, Europe\u2019s longer-term ambition [6] is to operate a\nproton-proton collider at the highest achievable energy, sensitive to energy scales an order of magnitude\n1\n\nhigher than those reached at the LHC. By providing considerable advances in sensitivity, precision, and\nenergy far above the TeV scale, the Future Circular Collider (FCC) matches the present landscape and the\nabove requirements to near perfection. Indeed, the FCC starts with a luminosity-frontier e+e\u2212machine\nspanning centre-of-mass energies from below the Z pole to beyond the top-pair production threshold\n(FCC-ee), later evolving to an energy-frontier hadron collider (FCC-hh). Both machines are strongly\nmotivated in their own right, as shown in the rest of this section. In particular, the full programme will\nprovide unique sensitivity to new physics in the Higgs sector: with almost three million Higgs bosons,\nFCC-ee will offer in a few years model-independent measurements of the Higgs boson mass, width, and\ncouplings to Z, W, \u03c4, b, c, order-of-magnitude more precise than today, to probe the possible BSM origin\nof Electroweak Symmetry Breaking. Ultimately, FCC-hh will produce 20 billion Higgs bosons and, in\ncombination with FCC-ee, provide incomparable measurements of the Higgs self-coupling, top Yukawa\ncoupling and of other rare or invisible modes probing in new directions the processes that led to the for-\nmation of today\u2019s Higgs vacuum field. Efforts to understand, analyse, and document the broad physics\npotential of such an ambitious programme started in 2012 [9] and culminated in the FCC Conceptual\nDesign Report (CDR) in 2018 [10\u201312].\nFrom the scale of Fermi interactions to that of the W and Z bosons, from the EW precision\nmeasurements to the observation of the top quark and of the Higgs boson, precision has always provided\nthe route to new discoveries; the FCC will be no exception in this respect. Any deviation from the SM\npredictions, interpreted as the manifestation of higher-dimensional operators, will point to a new energy\nscale that will be explored directly later on. Furthermore, correlations among several deviations will\nbe instrumental in characterising the structure of new physics and to reveal its exact or approximate\nglobal symmetries. In that regard, the fact that the SM features some a priori \u2018accidental\u2019 selection rules\n(lepton and baryon number conservation, custodial symmetry, suppression of flavour-changing neutral\ncurrents, smallness of the mixing among the different quarks, collective suppression of CP violation\neffects) that generic new physics scenarios do not share, is a welcome virtue and a promise for future\ndiscoveries or deeper understanding. The expected FCC precision is such that much will be learned,\nregardless of the outcome: theories beyond the SM will be very much constrained, even with a null\nresult, and will further guide new models from these precision measurements. When a new physics\nsignal is eventually observed, these precision measurements (whether they agree with or deviate from\nthe SM) will be precious in establishing the nature of the signal.\nThe presently proposed schedule of the FCC programme has 15 years of FCC-ee operation fol-\nlowed by 25 years of FCC-hh operation, interleaved with a shutdown of 10 years to dismantle the lepton\ncollider and install the hadron collider in the tunnel, for a grand-total of 50 years, a similar duration to\nthat of the current LEP + LHC programme (1989\u20132041). This sequence optimises the overall invest-\nment and its science value for several fundamental reasons: (i) the powerful physics complementarity of\nthe two machines, leading to a uniquely broad exploration potential; (ii) the synergy of the infrastruc-\nture, which leads to a considerable cost saving and reduces the financial burden; (iii) the implementation\nschedule, which opens a time window of at least 25 years for the development of the critical technology\nof high-field magnets for the hadron collider, reducing the financial and technological risks; and (iv) the\nduration of the programme and its strategic importance, which makes it conceivable to obtain the upfront\nfunding for the common infrastructure. The recyclable infrastructure and the large integrated luminosi-\nties also significantly improve the global sustainability of the particle physics worldwide endeavour over\nthe 21st century, by minimising the operation time, the electricity consumption, the cost, and the carbon\nemissions for a given scientific outcome [13,14].\n1.1\nFCC-ee: A great Higgs factory, and so much more\nWith its high luminosity, its clean experimental conditions, its multiple interaction regions, and a range\nof energies that cover the four heaviest elementary particles known today, FCC-ee offers a uniquely\nbroad and powerful physics exploration programme as a Higgs, electroweak, QCD, flavour, and top\n2\n\nfactory, with high potential for discoveries. The baseline plan, confirmed by the feasibility study mid-\nterm review recommendations, considers operating detectors at four interaction points (IPs), spanning\nthe e+e\u2212centre-of-mass energies around the Z pole, the WW threshold, the ZH production maximum,\nup to the tt threshold and just above. The current values for the luminosities expected at these energies\nare displayed in Fig. 1 and the envisioned 15-year experimental programme is summarised in Table 1,\ntogether with the numbers of events expected at each energy.\nFig. 1: The FCC-ee baseline design luminosity, summed over 4 IPs, displayed as a function of the centre-of-mass\nenergy, from the Z pole to the tt threshold and beyond (red curve). The luminosity typically achievable by linear\ne+e\u2212Higgs factories with a single IP in their baseline design between 250 and 380 GeV is also indicated (dash-\ndotted oval in the lower-right corner of the figure).\nTable 1: The baseline FCC-ee operation model with four interaction points, showing the centre-of-mass energies,\ndesign instantaneous luminosities for each IP, and integrated luminosity per year summed over 4 IPs. The integrated\nluminosity values correspond to 185 days of physics per year and a 75% operational efficiency (i.e., 1.2 \u00d7 107\nseconds per year) [15], in the Z, WW, ZH, and tt baseline sequence. The last two rows indicate the total integrated\nluminosity and number of events expected to be produced in the four detectors. The number of WW events\nincludes all \u221as values from 157.5 GeV up.\nWorking point\nZ pole\nWW thresh.\nZH\ntt\n\u221as (GeV)\n88, 91, 94\n157, 163\n240\n340\u2013350\n365\nLumi/IP (1034 cm\u22122s\u22121)\n140\n20\n7.5\n1.8\n1.4\nLumi/year (ab\u22121)\n68\n9.6\n3.6\n0.83\n0.67\nRun time (year)\n4\n2\n3\n1\n4\nIntegrated lumi. (ab\u22121)\n205\n19.2\n10.8\n0.42\n2.70\n2.2 \u00d7 106 ZH\n2 \u00d7 106 tt\nNumber of events\n6 \u00d7 1012 Z\n2.4 \u00d7 108 WW\n+\n+ 370k ZH\n65k WW \u2192H\n+ 92k WW \u2192H\nThe currently envisioned working hypotheses for the operation model [16], i.e. for the overall\nsequence and the duration of each step, will be continuously optimised in the coming years. An example\nof a baseline sequence is displayed in Fig. 2, with the Z, WW, and ZH runs assumed to happen in this\nchronological order. In reality, however, there will be quasi-total flexibility in the choice of the running\nsequence. (See inset below: \u2018A quasi total flexibility\u2019.) This flexibility will accommodate the likely\nrequests of the user community and will also fit the possible need for runs at different energies in view\nof complementary measurements.\n3\n\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\n15\nYears\n0\n100\n200\n]\n-1\nIntegrated luminosity [ab\nZ\nWW\n 10\n\u00d7\nZH\n 10\n\u00d7\nTop\n 10\n\u00d7\nQuasi-total order flexibility\nFig. 2: Baseline operation model for FCC-ee with four interaction points, showing the integrated luminosity at the\nZ pole (green), the WW threshold (blue), the Higgs factory (red), and the tt threshold (orange) as a function of\ntime. In this baseline model, the sequence of events follows the increase in collision energy, but there is quasi-total\nflexibility in the sequence all the way to 240 GeV (see inset). The integrated luminosities delivered during the first\ntwo years at the Z pole and the first year at the tt threshold are half of the annual design value. The hatched area\nindicates the shutdown time needed to prepare for the higher energy runs at the tt threshold and beyond.\nA quasi-total flexibility\nIn Ref. [17] it was deemed essential to establish the technical and financial feasibility of scheduling a Z pole run\nafter the ZH run or the WW threshold run, ideally with a first Z pole run during the initial period of FCC-ee opera-\ntion. Indeed, the Z pole run, while extremely fertile in physics opportunities, is undoubtedly the most ambitious and\ndemanding part of the programme from all perspectives (accelerator, energy calibration, detectors systematic biases,\ntheory calculations). It will be extremely challenging to achieve all the goals of the Z pole run during the first four\nyears of the collider operation.\nThis requirement from physics was compounded by a recommendation from the mid-term review committees to con-\nsolidate (and ideally simplify) the design of the RF system to allow efficient energy-staging, as well as to reduce\ncomplexity, risk, and cost; and to study options to avoid the 1-cell/2-cell RF cavity reconfiguration between Z and\nZH/W W running, in order to simplify the SRF system implementation and to improve flexibility in the physics pro-\ngramme. The new versatile RF system designed accordingly (see Ref. [18]) enables a quasi-total flexibility to choose\nthe running sequence. For example, it would allow for short (few weeks) initial Z pole and WW threshold runs, to\ncommission the collider and the detectors, to establish the resonant depolarisation procedures for centre-of-mass en-\nergy calibration, etc. The ZH run could then proceed early, before going back to the Z pole and the WW threshold,\nboth now at full luminosity, with fully functional resonant depolarisation and a complete understanding of the collider.\nIt will ultimately be up to the experimental collaborations and the relevant scientific committees to\noptimise the time flexibility and to tailor the FCC-ee operation scenario according to a number of factors\nthat cannot be mastered today. For example, external events such as the FCC-hh magnet readiness or\nthe CERN financial situation may call for a change in the overall duration of the FCC-ee running time.\nMeanwhile, new avenues will be explored during the next phase of the FCC study, between April 2025\nand the end of 2027, towards increasing the luminosities at all energies, as it would be highly beneficial\nacross the whole programme and would make a qualitative difference in a number of cases.\nThe original motivation for an e+e\u2212circular collider was to create a high-luminosity Higgs Fac-\ntory, operating at \u221as = 240 GeV in the LEP/LHC tunnel [19\u201321]. Choosing to build it in the 80\u2013100 km\ntunnel that would ultimately be hosting a 100 TeV hadron collider was cardinal in making this machine\nunique on the Higgs factory market. To start with, such a tunnel enables a highly versatile Higgs Factory\nthat extends much beyond the study of the Higgs boson alone, for three main reasons:\n4\n\n1. A circumference of 80\u2013100 km is required for an e+e\u2212circular collider to reach (for the first time\nin e+e\u2212collisions) the top-pair production threshold, making the FCC-ee energy range optimal to\nsharpen and challenge our current physics knowledge by studying all SM particles. In particular,\nenabling precise top quark measurements is essential for the overall FCC electroweak and Higgs\nprecision physics programme.\n2. For a given power and centre-of-mass energy, the luminosity of a circular collider is roughly pro-\nportional to the ring circumference. A circumference of 80\u2013100 km makes FCC-ee the e+e\u2212\nelectroweak, Higgs, and top factory project with the highest luminosity proposed to date, able to\nproduce, when summing all the data collected at the 4 IPs, 6 \u00d7 1012 Z bosons, 2.4 \u00d7 108 W pairs,\nalmost 3 \u00d7 106 Higgs bosons, and 2 \u00d7 106 top pairs, in as little as 15 years. (See also inset below:\n\u2018Rationale for the operation model\u2019).\nRationale for the operation model\n(From the mid-term review) It would also be interesting to add more information in the final Feasibility report about the\noptimisation of the durations of the various energy runs (Z, W W , ZH, tt) as well as a more detailed and quantitative\ndiscussion demonstrating the importance of the tt running.\nThe baseline set of centre-of-mass energies and integrated luminosities is found to be the most sensible way to distribute\nluminosity within the 15 years overall running constraint. It is deemed sufficient to establish a minimal, yet remarkable,\nphysics outcome for such a collider, with the smallest possible set of centre-of-mass energies that enables a study of\nall particles of the SM with a real chance of discovery.\n\u2013 At the Z pole (\u221as = 91.2 GeV), at least 5 \u00d7 1012 Z (in two years) enables otherwise unreachable flavour (b,\nc, \u03c4) physics, studies of QCD and hadronisation, the search for rare or forbidden decays, and the exploration\nof the dark sector. Together with the runs at \u221as \u224388 and 94 GeV, the Z pole data yield 50 to 1000-fold\nimproved measurements of the Z line-shape and many electroweak precision observables (EWPO), including\nthe Z invisible width. An integrated luminosity of at least 40 ab\u22121 at the two energies, just below and just\nabove the Z pole (one year each), was deemed appropriate for a direct, unique, and statistically limited deter-\nmination of \u03b1QED(mZ) and \u03b1S(mZ), which otherwise would greatly limit the new physics interpretation of all\nmeasurements of sin2 \u03b8eff\nW. One of the findings of the study has been the realisation of how rich the run at and\naround the Z pole is for the FCC-ee physics outcome.\n\u2013 An integrated luminosity of at least 20 ab\u22121 in two years around the W+W\u2212production threshold, evenly\nshared between \u221as = 157.5 and 162.5 GeV, is needed for the measurement of the W mass (and decay width)\nwith a statistical precision commensurate with the expected precision of the centre-of-mass energy determina-\ntion. These data are also important for, in particular, the determination of the number of neutrino species and\nfor an independent measurement of the strong coupling constant.\n\u2013 An integrated luminosity of at least 10 ab\u22121 in three years at \u221as = 240 GeV provides model-independent\nmeasurements of the Higgs boson couplings from a combination of its branching fractions and of the total ZH\nproduction cross section. In particular, a per-mil precision can be reached on the coupling of the Higgs boson\nto the Z, which greatly constrains new physics coupled to the Higgs boson.\n\u2013 A short run to scan the tt threshold (\u221as = 340\u2013350 GeV) allows the measurement of the top-quark mass,\na fundamental parameter of the Standard Model, with a precision of O(10 MeV), for which hadron colliders\ncannot compete. Because the prediction of EWPO\u2019s is, in various ways, sensitive to mtop, the discovery power\nof this EWPO exploration is limited by the uncertainty on mtop. For example, matching the precision of the\nSM predictions from the EWPO measurements to the 180 keV (resp. 4 keV) statistical uncertainty on the W\nmass (resp. Z width) requires a 20 MeV (resp. 15 MeV) knowledge of mtop. It is only when the mass of the top\nquark mass is measured with this precision that the FCC-ee EWPO measurements give their best sensitivity,\ntypically increasing the reach in new physics energy scale by 60%.\n\u2013 The ZH cross section dependence on \u221as provides sensitivity to the Higgs boson self-coupling when data at\n365 GeV are available, allowing a 5 \u03c3 discovery of this coupling to be contemplated. More importantly, the per-\ncent measurement of the top EW couplings (i) matches the EWPO ppm precision at the Z pole and the WW\nthreshold; and (ii) keeps the theoretical uncertainties on the top Yukawa coupling determination at FCC-hh at\nthe per-cent level, a pre-requisite for the model-independent determination of the Higgs boson self-coupling.\n5\n\n3. A circumference of 80\u2013100 km is also required for FCC-ee to offer unparalleled control of the\ncentre-of-mass energy, not only at the Z pole but also at the WW threshold, with the use of\nresonant depolarisation [22,23]. At the Z pole, the centre-of-mass energy scale should be known\nto 1 ppm or better, with a point-to-point residual uncertainty of 28 keV and a per-mil level spread.\nThese parameters are key inputs to the electroweak precision programme [24]. Details are given\nin Chapter 9. The resulting precisions on the Z mass and width, the forward-backward asymmetry\nof muon pairs around the Z pole, the electromagnetic coupling constant \u03b1QED(mZ), as well as on\nthe W mass, are listed in the first rows of Table 2.\nSeveral other fundamental aspects add to the uniqueness of FCC-ee.\n1. One of the findings of the FCC feasibility study has been the realisation of how rich the intensity-\nfrontier multi-Tera-Z run is for the FCC-ee physics outcome. It promises comprehensive measure-\nments of the Z lineshape and many EWPOs with at least fifty-fold improved precision, as well\nas direct and uniquely precise determinations of the \u03b1QED(mZ) [25, 26] and \u03b1S(mZ) interaction\ncouplings (Table 2), which would otherwise be dominant parametric uncertainties for virtually all\nprecision SM calculations. The comparison of these data with commensurately accurate SM pre-\ndictions is a way to reveal the existence of new physics (or to severely constrain its properties)\nthrough virtual loops or mixing: a factor of 50 in precision corresponds to a factor of 7 in energy\nscale, representing a step towards discovery (Section 2.3 and Refs. [27, 28]) similar to that from\nLHC to FCC-hh. This Z pole run offers more than \u2018just higher precision\u2019. It also enables other-\nwise unreachable flavour (b, c, \u03c4) physics, studies of QCD and hadronisation, the search for rare\nor forbidden decays, the exploration of the dark sector, and significantly increases sensitivity to\nnew feebly interacting particles, altogether further increasing the prospects for discovery.\n2. A unique feature of circular colliders is the ability to serve several IPs. Another finding of the\nFCC Feasibility Study has been the demonstration of the importance of operating four detectors\n(instead of only two in the 2014\u20132018 Conceptual Design Study), which led to an optimisation of\nthe ring layout with a new four-fold periodicity (further increasing the synergies with FCC-hh).\nIn a configuration with 4 IPs, the FCC science value for the investment is maximised in multiple\nways. (See inset below: \u2018The benefits of four interaction points\u2019.)\n3. Finally, FCC-ee stands out among the Higgs Factory projects for its unique opportunity to ac-\ncess the Higgs boson coupling to electrons [29\u201331], through the resonant production process\ne+e\u2212\u2192H at \u221as = 125 GeV [32]. This measurement relies on the combination of the high\nluminosity, the possibility of operating four detectors, the continuous ppm centre-of-mass energy\ncontrol, and the ability for centre-of-mass monochromatisation [33]. This is a unique opportunity\nfor FCC-ee, and one of its toughest challenges.\nAs a Higgs factory, FCC-ee has all the advantages of an e+e\u2212collider running in the vicinity of\nthe ZH cross section maximum: the measurement of this cross section by counting events with an iden-\ntified Z boson (and for which the mass recoiling against the Z gathers around the Higgs boson mass [34],\nindependently of the Higgs boson properties details) provides a precise and model-independent deter-\nmination of \u03baZ, the Higgs boson coupling to the Z. This absolute measurement can then be used as a\n\u2018standard candle\u2019 by all other measurements, including those made at hadron or muon colliders. The\nposition of the Z recoil mass peak also provides an accurate measurement of the Higgs boson mass from\nthe precise knowledge of the centre-of-mass energy. In combination with the measurement of the rate of\nZH events with a H \u2192ZZ\u2217decay, proportional to \u03ba4\nZ/\u0393H, a model-independent determination of the\ntotal width \u0393H can be obtained. The analysis of the other decays provides a set of model-independent\npartial width and coupling measurements.\n6\n\nTable 2: Experimental (statistical and systematic) precision expected for a selection of measurements accessible\nat FCC-ee, compared with the present world-average precision [35]. Some of the FCC-ee experimental systematic\nuncertainties (4th column) are initial estimates from early 2021 [36] and others have been improved and consol-\nidated during the Feasibility Study. A goal of further studies will be to improve them down to the level of the\nstatistical uncertainties (3rd column) with new ideas and innovative methods. This set of measurements, together\nwith those of the Higgs boson properties, achieves indirect sensitivity to new physics up to a scale \u039b of 100 TeV in\nan Effective Field Theory (EFT) description with dimension-6 operators (Chapter 2) and possibly much higher in\nspecific new physics (non-decoupling) models.\nObservable\npresent\nFCC-ee FCC-ee\nComment and\nvalue\n\u00b1\nuncertainty\nStat.\nSyst.\nleading uncertainty\nmZ (keV)\n91 187 600\n\u00b1\n2000\n4\n100\nFrom Z line shape scan\nBeam energy calibration\n\u0393Z (keV)\n2 495 500\n\u00b1\n2300\n4\n12\nFrom Z line shape scan\nBeam energy calibration\nsin2 \u03b8eff\nW (\u00d7106)\n231,480\n\u00b1\n160\n1.2\n1.2\nFrom A\n\u00b5\u00b5\nFB at Z peak\nBeam energy calibration\n1/\u03b1QED(m2\nZ) (\u00d7103)\n128 952\n\u00b1\n14\n3.9\nsmall\nFrom A\n\u00b5\u00b5\nFB off peak\n0.8\ntbc\nFrom A\n\u00b5\u00b5\nFB on peak\nQED&EW uncert. dominate\nRZ\n\u2113(\u00d7103)\n20 767\n\u00b1\n25\n0.05\n0.05\nRatio of hadrons to leptons\nAcceptance for leptons\n\u03b1S(m2\nZ) (\u00d7104)\n1 196\n\u00b1\n30\n0.1\n1\nCombined RZ\n\u2113, \u0393Z\ntot, \u03c30\nhad fit\n\u03c30\nhad (\u00d7103) (nb)\n41 480.2\n\u00b1\n32.5\n0.03\n0.8\nPeak hadronic cross section\nLuminosity measurement\nN\u03bd(\u00d7103)\n2 996.3\n\u00b1\n7.4\n0.09\n0.12\nZ peak cross sections\nLuminosity measurement\nRb (\u00d7106)\n216 290\n\u00b1\n660\n0.25\n0.3\nRatio of bb to hadrons\nAb,0\nFB (\u00d7104)\n992\n\u00b1\n16\n0.04\n0.04\nb-quark asymmetry at Z pole\nFrom jet charge\nApol,\u03c4\nFB\n(\u00d7104)\n1 498\n\u00b1\n49\n0.07\n0.2\n\u03c4 polarisation asymmetry\n\u03c4 decay physics\n\u03c4 lifetime (fs)\n290.3\n\u00b1\n0.5\n0.001\n0.005\nISR, \u03c4 mass\n\u03c4 mass (MeV)\n1 776.93\n\u00b1\n0.09\n0.002\n0.02\nestimator bias, ISR, FSR\n\u03c4 leptonic (\u00b5\u03bd\u00b5\u03bd\u03c4) BR (%)\n17.38\n\u00b1\n0.04\n0.00007\n0.003\nPID, \u03c00 efficiency\nmW (MeV)\n80 360.2\n\u00b1\n9.9\n0.18\n0.16\nFrom WW threshold scan\nBeam energy calibration\n\u0393W (MeV)\n2 085\n\u00b1\n42\n0.27\n0.2\nFrom WW threshold scan\nBeam energy calibration\n\u03b1S(m2\nW) (\u00d7104)\n1 010\n\u00b1\n270\n2\n2\nCombined RW\n\u2113, \u0393W\ntot fit\nN\u03bd (\u00d7103)\n2 920\n\u00b1\n50\n0.5\nsmall\nRatio of invis. to leptonic\nin radiative Z returns\nmtop (MeV)\n172 570\n\u00b1\n290\n4.2\n4.9\nFrom tt threshold scan\nQCD uncert. dominate\n\u0393top (MeV)\n1 420\n\u00b1\n190\n10\n6\nFrom tt threshold scan\nQCD uncert. dominate\n\u03bbtop/\u03bbSM\ntop\n1.2\n\u00b1\n0.3\n0.015\n0.015\nFrom tt threshold scan\nQCD uncert. dominate\nttZ couplings\n\u00b1\n30%\n0.5\u20131.5 % small\nFrom \u221as = 365 GeV run\n7\n\nThe benefits of four interaction points\n(From the mid-term review) The Scientific Advisory Committee recommends to construct 4 IPs for FCC-ee from the\nbeginning. The Scientific Policy Committee finds the proposal to include more than two IPs an attractive option.\nHowever, we expect, for the final Feasibility report, arguments focusing not only on the na\u00efive luminosity gain but also\non the overall physics optimisation.\nDetector Diversity The diverse set of demanding physics measurements and searches at FCC-ee leads to many dif-\nferent challenging detector requirements, which cannot be simultaneously satisfied by only one or even two detectors.\nInstead, four FCC-ee interaction points allow for a broader diversity of detector solutions to be explored and, therefore,\na wider community with diverse interests and skills to join the FCC-ee project, with a better perspective of optimally\ncovering all FCC-ee physics opportunities. Detector diversity also allows cross-checks of results across experiments: a\nsingle experiment is quite vulnerable to unforeseen effects, and consistency between two experiments can still happen\nby chance. Such bad luck is much less likely with four diverse detectors. (See remark about redundancy below.)\nImproved sustainability Operating FCC-ee with 4 IPs provides a net gain of luminosity (typically up to a factor 1.7\nwith respect to the 2 IP option) for a given electricity consumption. The physics outcome of 15 years operation with\n4 IPs would require 25 years with just 2 IPs. Running with four experiments would decrease the FCC-ee operation\ncarbon emissions in the same proportions. Folding in the construction carbon budget of the tunnel the additional two\nIPs and two detectors, it is found that operating FCC-ee with 4 IPs would reduce the total carbon footprint by \u223c15%\nfor the same physics outcome as with 2 IPs, both with today\u2019s figures and with those expected in the construction and\noperation times of FCC-ee.\nReduced and more robust systematic uncertainties In order to fully benefit from the considerable FCC-ee event\nsamples, especially at the Z pole, most of the work will focus on reducing the systematic uncertainties to match the\nstatistical precision. As a matter of fact, many key measurements are potentially affected by detector-related systematic\nbiases. These biases are uncorrelated between experiments, so that the related systematic uncertainties scale down as\n1/\np\nNexperiments. Precision is also about redundancy: measuring the same quantity in several experiments can reveal\nsources of errors that would have been overlooked otherwise. The illustrative example closest to FCC-ee comes from\nthe LEP measurement of the Z mass with the 1991 data, when a large discrepancy of \u223c20 \u00b1 5 MeV was noticed\nbetween the measurements from L3 and OPAL, on the one hand, and the measurements from ALEPH and DELPHI,\non the other. The investigation that followed identified and solved the origin of the issue, but it could have remained\nunnoticed for a long time (or forever) had there been only ALEPH and DELPHI (or only L3 and OPAL) around the\nring.\nCollider monitoring With the large collision rate at the Z pole, each detector will act as sophisticated beam instrumen-\ntation by allowing quick and high-quality measurements of many beam parameters: positions and sizes of the luminous\nregions; longitudinal and transverse boosts of the collision at the four IPs (beam energy difference, centre-of-mass en-\nergy spread, crossing angle); the dependence of these parameters on the exact position of the collision within each\nbunch; and other information we have not thought of yet. These measurements at four different points of the collider\nprovide a huge amount of information on the beam properties, which is useful for collider performance optimisation\nand, more specifically, on the \u2018energy model\u2019, which is the cornerstone of the precision programme at the Z pole, at\nthe WW threshold, and even more so at the Higgs boson resonance (\u221as = 125 GeV).\nTime flexibility The additional flexibility offered by two additional interaction points could be a game changer for the\nFCC-ee scientific outcome. For example, reaching the 5\u03c3 discovery level for the Higgs self-coupling, contemplating a\nfirst measurement of the electron Yukawa coupling, or securing a thorough search for sterile neutrinos, would simply\nbe missed opportunities with only two IPs (a little over 2 \u03c3 significance expected). The larger luminosity expected with\nfour IPs allows for a different time allocation to the different centre-of-mass energies, to be optimised when the time\ncomes, by the FCC-ee user community.\nCommunity building The FCC-hh will require the participation of an even larger community of users than the LHC.\nThe large collaborations operating the four detectors at FCC-ee would raise the overall profile of the worldwide high-\nenergy frontier community to a level more appropriate to support the ultimate high-energy proton collider.\nIntegrated luminosity gain Many FCC-ee measurements are statistically limited, either directly (e.g., the direct de-\ntermination of \u03b1QED(m2\nZ) from the muon forward-backward asymmetry measurements at \u221as = 88 and 94 GeV)\nor because their experimental systematic uncertainties would continue to improve with additional data, as is the case\nfor many critical observables (e.g., the Z width, the effective mixing angle, etc.). Any increase of integrated lumi-\nnosity is also welcome for searches for feebly interacting particles or for rare/forbidden processes. Therefore, these\nmeasurements and searches immediately benefit from four interaction points.\nThe FCC-ee best-measured Higgs boson couplings, \u03baZ and \u03baW, with a precision of 0.1% and\n0.23%, after eight years of operation at \u221as \u2265240 GeV, respectively, would require half a century to be\nreached with linear e+e\u2212Higgs factories running either at 250 and 500 GeV or at 380 and 1500 GeV,\nmaking FCC-ee the most time- and cost-effective, as well as the most sustainable, Higgs factory of all\n8\n\nproposed options [13,14]. More details on the physics programme are given in Chapter 2.\nThe many new opportunities of physics measurements and searches at FCC-ee create at least as\nmany challenges. Reaching experimental and theoretical systematic uncertainties commensurate with\nthe statistical precision of the many measurements feasible at FCC-ee requires a careful study of the\ndetector concepts, possibly of the mode of operation, and of theoretical developments.\nThe FCC-ee physics programme presents a number of key theoretical challenges [37]. Generally\nspeaking, the aim is either to provide the tools to compare experimental observations to theoretical pre-\ndictions at a level of precision similar or better than the (statistical) experimental uncertainties (Table 2),\nor to identify the additional calculations, tools, observables, or experimental inputs that are required to\nachieve this level of precision. Another essential line of research to be followed jointly by theorists and\nexperimenters is to identify observables, or ratios of observables, for which experimental and/or theo-\nretical uncertainties can be reduced. Finally, both for motivational purposes and for prioritisation, the\nrelative impact of the various measurements on the search for new physics should be evaluated. The\ntheoretical work motivated by the FCC programme can be organised as follows.\n\u2013 Calculation of QED (mostly), EW, and QCD corrections to (differential) cross sections, needed to\nconvert experimental measurements to so-called \u2018pseudo-observables\u2019: couplings, masses, partial\nwidths, asymmetries, etc., without altering significantly the possible new-physics contributions in\nthe original measurements. Appropriately accurate event generators are essential for the imple-\nmentation of these effects in the experimental procedures.\n\u2013 Calculation of the pseudo-observables with the precision required in the framework of the Standard\nModel so as to take full advantage of the experimental precision.\n\u2013 Identification of the limiting issues, such as the questions related to the definition of parameters,\nin particular the treatment of quark masses and, more generally, QCD objects.\n\u2013 Investigation of the sensitivity of the proposed (or new) experimental observables to the effect of\nnew physics in a number of important, specific scenarios. This essential work must be done at an\nearly stage, before the project is fully designed, since it potentially affects the priorities for detector\nconcepts and for the running plan.\nA community of theorists has already risen to the precision challenges, especially at the Z peak [38].\nAn evaluation of the options for the path ahead can be found in Refs. [37, 39, 40], and is developed in\nChapter 3.\nA complete set of detector specifications and their impact on the physics measurements is another\nmain deliverable of the feasibility study. The performance of a number of options for the various detector\ncomponents of possible future detectors: calorimeters [41], tracking and vertex detectors [42], muon\ndetectors [43], luminometers [44], and particle identification devices [45] are being studied to understand\nhow they could meet the requirements. More details are given in Chapter 6. The following gives a brief\nidea of the type of requirements that are under study.\n\u2013 Higgs and top physics A set of requirements have been established by past linear collider studies\nfor Higgs and top physics at 240 and 340\u2013365 GeV, arising in particular from the desired perfor-\nmance of particle-flow reconstruction, flavour tagging, or lepton momentum measurement. They\nneed to be adapted to take into account the cleaner FCC-ee experimental environment, the smaller\nbeam-pipe radius, and the smaller maximum operating energy [46]. Additional requirements arise,\nrelated to the need for a more accurate Higgs boson mass determination [34] prior to the s-channel\nHiggs boson production run, and for a more accurate ZH cross section measurement, to enable\na determination of the Higgs self-coupling. The s-channel Higgs boson production also leads to\ndemanding requirements on the centre-of-mass energy monochromatisation, while keeping a high\nluminosity and calling for the most sensitive analysis to separate Higgs boson decays from the\nhuge background of e+e\u2212annihilation events [32].\n9\n\n\u2013 Tera-Z challenges The high luminosity and large event rate at the Z pole (over 100 kHz), to\nwhich simulated data need to be added, turn into considerable challenges for data taking, storage\nand processing. The Z lineshape determination, which is based on cross section measurements\nas a function of the centre-of-mass energy for hadronic and leptonic decays of the Z, requires\naccurate mechanical construction and in-situ alignment of the luminometer and detector end-caps,\nin view of acquiring precise knowledge of the central tracker and calorimeter acceptance, for\nthe dilepton and diphoton events (and, to a lesser extent, for hadronic events). The point-to-\npoint centre-of-mass-energy uncertainties of the resonance scan, which can be verified in particular\nby means of the muon pair mass and boost reconstruction, are most relevant for the Z width\nand the forward-backward asymmetry measurements. The accuracy of the mass reconstruction\nneeded sets stringent constraints on the stability of the momentum reconstruction over time and\nscan points [24]. With a statistical precision of 4 keVfor both the Z mass and the Z width, the\ncentre-of-mass determination is critical for the physics output of the Tera-Z run [22,47].\n\u2013 Physics with W pairs The sub-MeV precision on the W mass expected from a scan of the WW\nproduction threshold seems, a priori, more demanding on the centre-of-mass energy calibration,\nand on the theoretical understanding of the cross section, than on the detector itself. At higher\nenergies, the requirements on jet angular calibrations and the possible dependence of the precise\nknowledge of the composition of hadrons in these jets, however, should be revisited. Similarly,\nrequirements on lepton angle, energy reconstruction, and energy scale, should be established [48],\nalthough they are probably covered by the requirements from the Z run.\n\u2013 Flavour challenges The formidable progress of the performance of vertexing devices in the past\ntwo decades, paired with the five times smaller beam-pipe diameter with respect to LEP, leads\nto unprecedented b- and c-tagging performance. The resulting expected statistical uncertainties\non the flavour EWPOs, such as Rb,c or Ab,c\nFB , allow for much larger improvements (by up to a\nfactor of 2000) with respect to the LEP measurements of other EWPOs. In addition, the rich\nFCC-ee flavour programme can be fully exploited only if the detector is equipped with hadron\nidentification covering the effective momentum range at the Z resonance [49] and electromagnetic\ncalorimetry with a superb energy resolution [50].\n\u2013 Tau physics The \u03c4 measurements listed in Table 2 (lifetime, mass, and branching fractions) have\nthe potential to achieve a determination of the Fermi constant at the level of a few 10\u22125. These\nmeasurements provide some of the most demanding detector requirements on momentum reso-\nlution (for the mass resolution), on the knowledge of the vertex detector dimensions (for the tau\nlifetime), and on e/\u00b5/\u03c0 separation over the whole momentum range (for the leptonic branching\nratios). The \u03c4-based EWPOs, RZ\n\u03c4 , Apol,\u03c4\nFB , and P\u03c4, as well as the detailed study of the hadronic\nspectral functions, require fine granularity and high efficiency in the tracker and electromagnetic\ncalorimeter [51].\n\u2013 Feebly interacting particles The current heavy neutral lepton (HNL) search strategy is based on\na rather conservative signal selection, requiring in particular an HNL decay less than 1 m away\nfrom the interaction point. With four IPs, the discovery region extends to the physical regions\nfavoured by the see-saw models of neutrino masses. It would be possible to extend it by detecting\nHNL decays further away from the IP, e.g., by making use of the large amount of cavern space\nsurrounding the detector [52]. Other feebly interacting particles, decaying into non-pointing or\ndelayed photons, pose a different set of challenges, which could possibly benefit from a high-\nprecision timing detector. See Section 2.3.4 for details.\nIntegrating all these (initial) detector requirements will be a considerable challenge, commensurate\nwith the unique set of measurement opportunities and with the discovery potential offered by FCC-ee.\nA refined list of detector requirements is being derived from a number of case studies inspired by the set\nof physics benchmark measurements at FCC-ee (encompassing those presented in Table 2), as described\nin Refs. [53,54]. The four FCC interaction points will not be too many to cover the resulting variety of\n10\n\ndetector requirements and physics opportunities. More details are given in Chapter 4.\nThe experimental environment at FCC-ee, where the incoming beams cross typically a few million\ntimes before interacting, is gentle and clean compared to hadron colliders, muon colliders and even linear\ne+e\u2212colliders. The main challenges have been extensively studied by the Machine Detector Interface\ngroup [55]:\n\u2013 The design of the e+ and e\u2212rings is asymmetric around each interaction region, in order to elim-\ninate the need for strong bending magnets upstream of the collision points and thus minimise the\nsynchrotron radiation background in the detectors.\n\u2013 The large number of bunches and the low level of beamstrahlung radiation result in a low rate of\npile-up events, typically 2 \u00d7 10\u22123 at the Z pole and less than 10\u22122 at the top energies.\n\u2013 The strong focusing optics requires a short free space (2.2 m) between the last beam elements. A\ncompensating solenoid and quadrupole assembly that fits in a forward dead cone of no more than\n100 mrad, has been designed and a complete mock-up is being prepared.\n\u2013 The luminosity monitors situated in front of this assembly could be adapted to the geometry with\ntwo beam pipes crossing at an angle of 30 mrad.\n\u2013 The small beam transverse dimensions allow for a beam pipe of 10 mm radius and for the first\nlayer of the vertex detector to be installed very close to the vacuum chamber.\n\u2013 In the current design with compensating solenoids, the detector solenoid magnetic field must be\nlimited to 2 T when operating at the Z pole, to avoid a blow up of the vertical beam emittance and\na resulting loss of luminosity. Alternative designs with non-local compensation are being studied.\nThese conditions are favourable on several accounts. The 100 mrad low angle dead cone offers\nthe possibility to extend the detector coverage down to a polar angle of cos \u03b8 \u22430.99, while the 10 mm\nradius beam pipe should be a prime starting point for high efficiency b- and c-flavour tagging against\nlight quarks and gluons. The 2 T magnetic field limit is not a significant handicap since the momentum\nof the produced partons is typically distributed around 50 GeV and does not exceed 183 GeV. If needed,\nan increase of the magnetic field to 3 T or more can be envisioned at higher energies, without loss of\nluminosity. More details about the challenges pertaining to the machine-detector interface and beam\nbackgrounds are given in Chapter 5.\nThe work for the particle physicists is now clearly cut out: design the experimental setup and\nprepare the theoretical tools that can, demonstrably, fully exploit the capabilities of FCC-ee. Experi-\nmentation at FCC-ee is both relatively easy and extremely demanding. The experimental conditions are\nclean, with essentially no pile-up, a well-defined and controllable centre-of-mass energy, and benign\nbeamstrahlung and synchrotron radiation effects. The sophistication arises from the very richness of\nthe programme. Matching the experimental and theoretical accuracy to the statistical precision, and the\ndetector configuration to the variety of channels and discovery cases, will be the real challenge.\n1.2\nFCC-hh: The energy-frontier collider with the broadest exploration potential\nThe physics landscape emerging from the FCC-ee, complemented by the HL-LHC exploration, will\nsignificantly raise the bar for the performance requirement of subsequent colliders. Several challenges\nremain open.\n\u2013 The extension of Higgs boson property measurements to several processes driven by smaller ef-\nfective couplings (e.g., rare decays such as H \u2192\u03b3\u03b3, \u00b5+\u00b5\u2212, Z\u03b3), and to processes requiring higher\nenergy (e.g., ttH and HH production).\n\u2013 The extension of studies of EW dynamics to a regime well beyond the scale of the EW symmetry\nbreaking.\n11\n\n\u2013 The direct exploration of the multi-TeV energy scale, to identify and directly study the sources of\npossible deviations found in the FCC-ee precision measurements, and to systematically extend the\nmass reach for a broad spectrum of BSM theories, particularly those whose impact on low-energy\nEW and Higgs observables is suppressed and those whose primary production processes require\ninitial-state gluons.\nThe 100 TeV FCC-hh provides the most complete and effective facility to tackle these challenges.\nThe study of the FCC-hh physics potential is very mature; it occupied the first phase of the efforts\ntowards the FCC CDR, thanks to a world-wide effort whose results have been documented in extensive\nreports [56, 57], partly summarised in Volumes 1 and 3 of the CDR [10, 12]. Some of the key results\nare recalled here. Recent preliminary studies of physics performance at different collider energies, in the\n80\u2013120 TeV range, have been done in the context of this feasibility study, and are reported in Section 2.6.\nSection 2.7 outlines the opportunities offered by a forward-physics facility, which would expand the\nlandscape of FCC-hh physics measurements presented in the CDR.\nOn the Higgs boson side, the data sample produced by FCC-hh of over 20 billion Higgs bosons\nwill bring the absolute determination of the couplings to muons, to photons, to the top quark, and to\nZ\u03b3 below the per-cent level. The large production yield of Higgs bosons at large transverse momentum\nallows measurements to be performed in kinematic regions with optimal signal-to-background ratios\nand reduced experimental systematic uncertainties. The possibility to accurately measure the ratio of\nthose couplings to couplings precisely measured at the FCC-ee (e.g., the HZZ\u2217and ttZ couplings),\nenables the FCC-hh to deliver sub-percent absolute measurements of those couplings, which are beyond\nthe reach of lepton colliders. The large HH production rate, furthermore, will bring the uncertainty\non the Higgs self-coupling below the 5% level, even with conservative estimates of the experimental\nsystematic uncertainties. The studies of Higgs boson production in very-high Q2 processes, whether in\ndirect, associated, or vector boson fusion/scattering production, test the existence of higher-dimensional\neffective operators in ways that are complementary to what is accessible even at the highest-energy lepton\ncolliders.\nThe direct search for new particles extends the mass reach to the several tens of TeV range, in\nparticular around 40 TeV for s-channel produced EW or coloured resonances, and in the 10\u201320 TeV\nrange for pair-produced strongly-interacting particles, such as squarks, stops, vector-like top partners,\nand gluinos. Weakly interacting particles can be probed up to 1.5\u20135 TeV, depending on their weak multi-\nplet assignment, allowing in particular the theoretically limited spectrum of possible WIMP dark-matter\ncandidates to be covered.\nLikewise, the search for partners of the Higgs boson extends to the multi-TeV region, a sensitivity\nthat, together with the precise determination of the Higgs boson self-coupling, constrains, in a unique\nway, extensions of the Higgs sector leading to a strong first-order EW phase transition in the early\nuniverse.\nLast but not least, the FCC-hh is a unique facility to extend the study of the less known manifesta-\ntion of the SM dynamics, namely the behaviour of high-density and high-temperature strongly interacting\nplasmas, through the analysis of data collected in central lead-lead collisions at nucleon-nucleon colli-\nsion energies up to \u221as \u224840 TeV [58]. Despite the significant progress made over the last decades at the\nSPS, at RHIC, and at the LHC regarding our understanding of the properties of the hot QCD medium\ncreated in high-energy heavy-ion collisions, grounded on increasingly precise and diverse experimental\nmeasurements, much remains unknown about the physics behind this most exotic area of QCD. Details\nof the concrete physics potential of heavy-ion running at the FCC-hh are provided in Refs. [57, 58].\nAside from its intrinsic and undisputed scientific value, this part of the physics programme, exclusively\naccessible at hadron colliders, offers the opportunity to enlarge the community of scientists attracted\nto the FCC, providing them the sole facility that can continue and extend the study of the high-density\nand high-temperature QCD medium produced in high-energy heavy ion collisions and the associated\n12\n\ncollective QCD phenomena, presently being actively pursued at the LHC.\nThe precision programme of the known elements of the SM should be complemented by a direct\nexploration of the unknown. Exploration requires breadth. To understand the properties of the visible\nUniverse, large-scale structure surveys are performed, gravitational waves with pulsar timing and much\nmore are sought. In the same vein, to understand the microverse this must be explored with as many\ndifferent microscopes as possible. The FCC-ee will directly explore the evasive and weakly-coupled\nlight new-physics frontier, while the FCC-hh will offer a direct way to scan the new energy frontier,\nabove the TeV scale. Together, the FCC-ee and the FCC-hh complement each other in this exploration\nof the unknown in a more comprehensive way than any other energy frontier projects presently under\nconsideration.\n13\n\n14\n\n2\nSpecificities of the FCC physics case\n2.1\nThe impact of FCC in particle physics\nParticle physics is the science of studying fundamental processes on the smallest accessible scales. The\nlast sixty years of particle physics have led to a radical overhaul of the understanding of the Universe,\nculminating in the landmark discovery of the Higgs boson in 2012. In this context, FCC may be viewed\nas a general-purpose particle physics facility, aimed at completing the extensive testing of the SM, ex-\nploring remaining open questions, and finding leads towards understanding the fundamental origins of\nthe Universe. The combination of the most powerful e+e\u2212Higgs and electroweak factory with the ul-\ntimate 100 TeV-class hadron collider is unique in its capacity to carry out a new phase of exploration\nin new regimes of precision and energy, and in a controlled and repeatable experimental environment.\nMore specifically, FCC will shed light on the many fundamental open questions about how the Universe\ncame to be.\nWhat is the origin of the Higgs boson? The Higgs boson discovered at LHC, with a mass\nof 125.20 \u00b1 0.11 GeV, is, so far, consistent with the SM version of Electroweak Symmetry Breaking\n(EWSB), which predicts the full Higgs phenomenology with no free parameter. These predictions must\nbe tested with the highest possible precision with FCC-ee and FCC-hh. Indeed, there are many reasons to\nbelieve that the underlying microscopic physics, from which the Higgs boson emerges, is associated with\nsome of the deepest mysteries in particle physics. One such mystery concerns the origin of the Higgs\nboson mass and the naturalness puzzle, which FCC is uniquely placed to address by a combination of\nprecision Higgs coupling measurements at the per-mil level and electroweak precision measurements\nimproved by a factor of 50 or much more with respect to the current precision, with direct high-energy\nexploration to comprehensively probe symmetry-based explanations for the electroweak hierarchy.\nWhat is the origin of the presence of matter in the Universe? The predominance of matter\nover antimatter, a.k.a. the baryon asymmetry of the universe (BAU), calls for both C and CP violation, as\nwell as an out-of-equilibrium epoch in cosmological history. The SM EWSB does not suffice to predict\na significant BAU, but particle physics can propose two hypotheses to accommodate this observation.\nA first possibility is that the Higgs potential is modified via a change of the Higgs self-coupling, lead-\ning to a first-order electroweak phase transition (EWPT). The FCC measurement of the Higgs boson\nself-coupling will reach a level of precision deemed adequate to clarify if the EWPT played a role in\nsetting an out-of-equilibrium phase, a necessary condition for creating the observed matter-antimatter\nasymmetry. Another possibility is that the Higgs boson couples to neutrinos, which would generate\na fermion-number-violating Majorana mass term, leading in turn to leptogenesis and, possibly, to the\nright amount of BAU. With its very high luminosity, FCC is best suited for the direct observation of the\nresulting heavy neutral leptons (HNL).\nWhat is the origin of mass and flavour? The Higgs mechanism is responsible for generating\nmass, but the reason for the pattern of Yukawa couplings is yet to be understood. The FCC unique\nexploration potential of flavour physics and of new symmetries and forces would lead to a deeper un-\nderstanding of approximate conservation laws, such as baryon and lepton number conservation (or the\nabsence thereof in case of Majorana neutrinos); would probe the limits of lepton flavour universality\nand violation; and could reveal new selection rules governing the fundamental laws of nature. A precise\ncomparison of the Yukawa couplings for the three fermion families will also be crucial in this endeavour.\nThe measurements of the muon and top Yukawa couplings at FCC-hh can be compared to the tau and\ncharm Yukawa coupling measurements at FCC-ee with sub-per-cent precision. A first measurement of\nthe strange Yukawa coupling is also possible at FCC-ee. Finally, an FCC-ee run at the s-channel Higgs\nresonance uniquely offers sensitivity to the electron Yukawa coupling, tantalisingly close to its SM value.\nWhat is the nature of dark matter? The unprecedented luminosity and detector environment of\nFCC-ee make it uniquely sensitive to exploring weakly-coupled dark sectors. Dark matter candidates,\nsuch as heavy axions, dark photons, etc., provide long-lived particle signatures. If dark matter is a doublet\n15\n\nor triplet weakly interacting massive particle (WIMP), FCC-hh will cover the entire parameter space up\nto the upper mass limit for a thermal relic. A range of complementary detector facilities could also be\nenvisioned to extend the FCC capabilities for neutrino physics, long-lived particles, and forward physics.\nWhat lies beyond the Standard Model? An impressive number of electroweak precision observ-\nables (EWPOs) will be measured by FCC-ee, with accuracies ranging from a factor 50 (e.g., for the W\nmass) to a factor 1000 (e.g., for Rb) better than today (Table 2). This new precision regime will allow\nthe effect of further weakly-coupled heavy particles to be detected up to masses of several tens of TeV\n(and much more in the non-decoupling configuration). Alternatively, this precision will bring sensitivity\nto particles mixing with the SM fermions in one part in 100 000, up to very high mass scales (more than\n1000 TeV for HNL). The SM, possibly extended with additional light degrees of freedom, might be a\nlow-energy effective field theory (EFT) approximation of a microscopic, ultraviolet (UV) theory from\nwhich it originates. The FCC-ee will improve the sensitivity to all EFT Wilson coefficients by one to sev-\neral order(s) of magnitude, while FCC-hh can further extend the reach of direct and indirect exploration\nin a complementary way. The combined FCC programme is the most powerful general survey of this\nuncharted EFT territory and of the existence of new particles beyond the known fermions and bosons.\nRelation with exotic astrophysical and cosmological signals Stochastic gravitational waves\nfrom cosmological phase transitions or astrophysical signatures of high-energy gamma rays are exam-\nples of phenomena that can arise due to exotic new physics which is, by contrast, directly accessible only\nto a facility offering the highest possible energy, such as FCC. Examples include confining new physics\nin a dark sector, decaying or co-annihilating TeV-scale WIMPs, or a modified EWPT. More precise top\nquark and Higgs boson mass measurements would also have important implications in the understanding\nof the SM vacuum metastability.\nAs an all-in-one-facility, FCC provides the versatility, redundancy, and cross-correlations ne-\ncessary to identify the fundamental origins of new phenomena. In general, its varied range of precise\nmeasurements of particle properties and interaction dynamics promises a set of guaranteed results with\nan unrivalled breadth with respect to other potential future facilities.\nThis chapter presents the unique role of FCC to address these fundamental questions, with a special\nfocus on: the combined characterisation of the Higgs boson at FCC-ee and FCC-hh (Section 2.2); the\ndirect discovery potential resulting from the FCC-ee clean environment, high integrated luminosity, and\nlarge acceptance rates of the detectors (Section 2.3); and the excellent opportunities in flavour physics\n(Section 2.4). The advantages of FCC-hh over multi-TeV lepton colliders to complement FCC-ee are\npresented in Section 2.5. Finally, the physics reach of FCC-hh as a function of its centre-of-mass energy,\nand the possibility of a forward-physics facility at FCC-hh, are briefly discussed in Sections 2.6 and 2.7.\n2.2\nCharacterisation of the Higgs boson: role of EW measurements and of FCC-hh\nThe Higgs boson is certainly a central piece of the current understanding of the fundamental structure\nof matter and physics laws. Its discovery in 2012, and the rich measurement programme over the past\nthirteen years, have been successful milestones in high-energy physics that, maybe more importantly,\nenabled the formulation of relevant questions about the nature of new physics beyond the weak scale,\nin very concrete and often quantitative terms. As already shown in various studies [59\u201361], FCC-ee\noffers fantastic opportunities for learning more about the Higgs boson, beyond what can be achieved at\nHL-LHC (Table 3) or at other proposed Higgs factories [14].\nIn a record time, FCC-ee will bring the Higgs programme into a sub-percent precision area, al-\nlowing the classical as well as the quantum mechanical effects of new physics on the Higgs couplings to\nbe probed and, from the pattern of the deviations, new selection rules distinguishing different models to\nbe discovered. Concrete examples proving the relevance of the sub-percent precision target can be found\nin Table 5 of Ref. [62], where several BSM models beyond the reach for direct discovery at HL-LHC\nare considered, and for which per-cent level deviations in the Higgs couplings are predicted. A sub-per-\n16\n\nTable 3: Expected 68% CL relative precision of the \u03ba parameters (Higgs couplings relative to the SM) and of\nthe Higgs boson total decay width \u0393H, together with the corresponding 95% CL upper limits on the untagged\n(undetected events), Bunt, and invisible, Binv, branching ratios at HL-LHC, FCC-ee (combined with HL-LHC), and\nthe FCC integrated programme. For the HL-LHC numbers, a |\u03baV | \u22641 constraint is applied (denoted with an\nasterisk), since no direct access to \u0393H is possible at hadron colliders; this restriction is lifted in the combination\nwith FCC-ee. The \u2018\u2013\u2019 indicates that a particular parameter has been fixed to the SM value, due to lack of sensitivity.\nFrom Ref. [59], updated with 4 IPs, the baseline luminosities of Table 1, and the most recent versions of the data\nanalysis. For some of the entries, the \u03ba precision starts being limited by the projected SM parametric uncertainties,\ne.g. in mb [40]. For these entries, the precision obtained by neglecting such parametric uncertainties is also\nreported (separated by a /).\nCoupling\nHL-LHC\nFCC-ee\nFCC-ee + FCC-hh\n\u03baZ (%)\n1.3\u2217\n0.10\n0.10\n\u03baW (%)\n1.5\u2217\n0.29\n0.25\n\u03bab (%)\n2.5\u2217\n0.38 / 0.49\n0.33 / 0.45\n\u03bag (%)\n2\u2217\n0.49 / 0.54\n0.41 / 0.44\n\u03ba\u03c4 (%)\n1.6\u2217\n0.46\n0.40\n\u03bac (%)\n\u2013\n0.70 / 0.87\n0.68 / 0.85\n\u03ba\u03b3 (%)\n1.6\u2217\n1.1\n0.30\n\u03baZ\u03b3 (%)\n10\u2217\n4.3\n0.67\n\u03bat (%)\n3.2\u2217\n3.1\n0.75\n\u03ba\u00b5 (%)\n4.4\u2217\n3.3\n0.42\n|\u03bas| (%)\n\u2013\n+29\n\u221267\n+29\n\u221267\n\u0393H (%)\n\u2013\n0.78\n0.69\nBinv (<, 95% CL)\n1.9 \u00d7 10\u22122 \u2217\n5 \u00d7 10\u22124\n2.3 \u00d7 10\u22124\nBunt (<, 95% CL)\n4 \u00d7 10\u22122 \u2217\n6.8 \u00d7 10\u22123\n6.7 \u00d7 10\u22123\ncent precision is a clear necessary target to expose such deviations. As mentioned in Section 1.1, the\nHiggs precision programme at 240 GeV (365 GeV) can be achieved within three (eight) years of opera-\ntion with FCC-ee, while other colliders considered at CERN would need half a century to reach a similar\nprecision [14].\nThese phenomenological projections are now being confirmed by independent experimental stud-\nies, with different detector set-ups [63\u201365]. Further directions in the Higgs precision programme also\nneed to be more systematically investigated beyond what was done so far, in particular in the context of\nspecific flavour scenarios or considering BSM sources of CP violation. This document, instead, empha-\nsises the benefit of the interplay between Higgs and electroweak measurements, a specificity of FCC-ee\nthat was not discussed in detail in the FCC CDR [10,11] and has been studied afterwards [60,61].\nThe interpretation of current Higgs boson measurements at LHC is so far not hindered by the\nlimited precision of the electroweak measurements at LEP and SLC. With FCC-ee targeting an order-\nof-magnitude improvement in the precision of Higgs boson properties in the main channels, the current\n(experimental and theoretical) precision on electroweak quantities would become a limitation. The Z-\npole run of FCC-ee is instrumental in avoiding contamination from electroweak coupling uncertainties\nin the Higgs boson characterisation. If the electroweak symmetry is linearly realised in the SM fields,\nthe interplay between the Higgs and electroweak sectors is even deeper [66]. Indeed, e+e\u2212\u2192W+W\u2212\nproduction is then sensitive to some of the same new-physics effects as Higgs boson production and\ndecay processes, making both types of measurements complementary.\nThe Standard Model Effective Field Theory (SMEFT) framework is adopted, truncated to opera-\ntors of dimension six [67,68]. The SMEFT is an appropriate framework for enumerating and quantifying\n17\n\n\u03b4gH\nZZ\n\u03b4gH\nWW\n\u03b4gH\n\u03b3\u03b3\n\u03b4gH\nZ\u03b3\n\u03b4g1,Z\n\u03b4\u03ba \u03b3\n\u03bbZ\n10- 4\n10- 3\n10- 2\n10- 1\n1\n10- 6\n10- 5\n10- 4\n10- 3\n10- 2\nHiggs couplings\naTGCs\nprecision reach on effective couplings from SMEFT global fit\nHL- LHC S2 + LEP/SLD\nFCC- ee Z/WW/240GeV\nFCC- ee Z/WW/240GeV+365GeV\nFree H Width\nno H exotic decay\nZ / WW denote Z-pole & WW threshold\n\u03b4gH\ngg\n\u03b4gH\ncc\n\u03b4gH\nbb\n\u03b4gH\n\u03c4\u03c4\n\u03b4gH\n\u03bc\u03bc\n\u03b4\u0393 H\n10- 3\n10- 2\n10- 1\n10- 3\n10- 2\n10- 1\nHiggs couplings\nHiggs couplings\n\u03b4gZ,L\nee\n\u03b4gZ,R\nee\n\u03b4gW\ne\u03bd\n\u03b4gZ,L\n\u03bc\u03bc\n\u03b4gZ,R\n\u03bc\u03bc\n\u03b4gW\n\u03bc\u03bd\n\u03b4gZ,L\n\u03c4\u03c4\n\u03b4gZ,R\n\u03c4\u03c4\n\u03b4gW\n\u03c4\u03bd\n10- 5\n10- 4\n10- 3\n10- 2\n10- 5\n10- 4\n10- 3\n10- 2\nVff couplings\nVff couplings\n\u03b4gZ,L\nuu\n\u03b4gZ,R\nuu\n\u03b4gZ,L\ndd\n\u03b4gZ,R\ndd\n\u03b4gZ,L\nbb\n\u03b4gZ,R\nbb\n10- 4\n10- 3\n10- 2\n10- 1\n10- 4\n10- 3\n10- 2\n10- 1\nVff couplings\nVff couplings\nimposed U(2) in 1&2 gen quarks\nFig. 3: Results of a global SMEFT fit to HL-LHC (grey) and FCC-ee (yellow, up to 240 GeV, and blue, up to\n365 GeV) data, interpreted in terms of the 68% probability sensitivity to Higgs and electroweak effective couplings.\nAdapted from Ref. [61].\nthe different possibilities in a relatively model-independent way. It assumes that new physics arises at a\nscale \u039b, significantly above the electroweak scale, with the Higgs boson embedded in a SU(2)L doublet.\nThe current status of the global SMEFT fit is shown in Fig. 3, adapted from Ref. [61]. In this figure,\nthe results of the fit for the different dimension-six operators affecting at leading order either the elec-\ntroweak processes (including anomalous triple gauge couplings, aTGCs, and boson-fermion couplings,\nVff) or the Higgs processes, or both simultaneously, are projected on a more physically meaningful set\nof effective couplings capturing the effects of new physics. More details can be found in Ref. [61].\nThe interplay between Higgs and electroweak measurements is illustrated in Fig. 4, which shows\nthe expected precision in the effective coupling determination. The correlations are displayed as internal\nlines of variable thickness and are visibly reduced when including Z-pole data at FCC-ee (dark blue) on\ntop of the current electroweak measurements (light blue). The importance of Z-pole measurements is\nsummarised below, followed by a discussion of the importance of the diboson process for Higgs physics.\nThe SMEFT results discussed in this section were obtained from fits with only linear effects in\n\u039b\u22122, consistently with the dimension-6 expansion. To estimate the theory uncertainty associated with\nthe neglected higher-order terms in the EFT expansion, Fig. 5 shows the ratio of the bounds on the\nWilson coefficients obtained in the linear case to those including quadratic contributions from dimension-\n6 operators, which are formally of the same order as dimension-8 contributions. These results derive\nfrom the HL-LHC+FCC-ee SMEFT fit of Ref. [69]. All the displayed operator coefficients can be\naccessed at FCC-ee, with the exception of the operators in the top-left quadrant, which enter in top-quark\n18\n\nFig. 4: Correlations between the determination of different EW/aTGC/Higgs interactions from a fit to future\nprojections at HL-LHC and FCC-ee within the SMEFT framework. The bars on the exterior of the circle indicate\nthe expected sensitivity in the determination of corresponding coupling (with different scales for the different\nsectors). The light/dark blue lines in the interior of the circle show the results excluding/including the FCC-ee\nprogramme of EW measurements at the Z pole. The Z-pole run is essential to isolate the Higgs measurements\n(there is no dark blue line connecting the Higgs and EW sectors) and to ensure that the extraction of the Higgs\ncouplings is not hindered by the uncertainties on the EW coupling determination. Adapted from Refs. [60,61].\nmeasurements at HL-LHC but do not contribute to FCC-ee observables at tree level. So, in almost all\ncases, the results of the linear fit are unchanged after the addition of quadratic effects. This observation\ncan be used as an indication that the uncertainty associated to effects of O(\u039b\u22124) is well controlled by\nFCC-ee precision measurements and is expected to be small. Another way to gauge the usefulness of\nthe SMEFT analysis is to compare the bound on the scale of new physics inferred from the fit of the\ndimension-6 Wilson coefficients to the actual limits set in explicit BSM models, as will be reported in\nthe next section. Of course, this does not exclude that (non-decoupling) new physics could still exist at\nmuch lower scales.\n19\n\nc1,8\nQq\nc1,1\nQq\nc3,8\nQq\nc3,1\nQq\nc8\ntq\nc1\ntq\nc8\ntu\nc1\ntu\nc8\nQu\nc1\nQu\nc8\ntd\nc1\ntd\nc8\nQd\nc1\nQd\ncc\u03d5\ncb\u03d5\nct\u03d5\nc\u03c4\u03d5\nctG\nctW\nctZ\nc(3)\n\u03d5q\nc(3)\n\u03d5Q\nc(\u2212)\n\u03d5q\nc(\u2212)\n\u03d5Q\nc\u03d5u\nc\u03d5d\nc\u03d5t\nc\u03d5l1\nc\u03d5l2\nc\u03d5l3\nc(3)\n\u03d5l1\nc(3)\n\u03d5l2\nc(3)\n\u03d5l3\nc\u03d5e\nc\u03d5\u00b5\nc\u03d5\u03c4\ncll\nc\u03d5\nc\u03d5G\nc\u03d5B\nc\u03d5W\nc\u03d5WB\ncWWW\nc\u03d5\u25a1\nc\u03d5D\n0.01\n0.05\n0.1\n0.2\n0.4\n0.6\n0.8\n0.05\n0.1\n0.2\n0.4\n0.6\n0.8\n0.05\n0.1\n0.2\n0.4\n0.6\n0.8\nRatio of the HL-LHC + FCC-ee SMEFT6 \ufb01ts performed at linear and quadratic order\nFig. 5: Impact of quadratic contributions from dimension-6 operators, i.e., at O(\u039b\u22124), in the SMEFT fit of\nRef. [69]. A U(2)Q \u00d7U(2)u \u00d7U(3)d \u00d7(U(1)L \u00d7 U(1)e)3 flavour symmetry is assumed. For each of the different\nWilson coefficients considered, the blue star indicates the ratio of the bound obtained in the pure dimension-6\n(linear) fit to that including quadratic dimension-six contributions. The difference between the two fits is minimal\nfor most operators entering in FCC-ee observables at tree level, i.e., leaving aside the purely hadronic top-quark\noperators in the top-left quadrant. The FCC-ee fit includes EWPOs at the Z-pole, light fermion-pair production,\nHiggs boson production (ZH+ VBF), diboson production, and top pair production.\n2.2.1\nImpact of Z-pole measurements in Higgs couplings determination\nThe importance of having precise Z-pole measurements for the extraction of Higgs couplings from\nfuture e+e\u2212Higgs data is clear, given that the Zee vertex also enters in ZH production. A precise-\nenough extraction of the Zee vertex is therefore needed to avoid extra uncertainties from new physics\neffects in these interactions. The left-handed and right-handed Zee couplings can be extracted from the\nZ \u2192e+e\u2212partial decay width and the left-right asymmetry parameter Ae, determined at FCC-ee from\nthe hadronic-to-leptonic cross-section ratios, the dilepton forward-backward asymmetries, and the tau\npolarisation forward-backward asymmetry, measured at the Z pole. This Zee coupling measurement\nalso helps mitigating the (centre-of-mass-energy growing) new-physics effects in the HZee interactions,\ndirectly correlated with the new-physics contributions to the Zee vertex in the SMEFT formalism.\nThe impact of Z-pole measurements in Higgs coupling fits was studied in Ref. [60] and, more\nrecently, in Ref. [61]. As a result of the reduced correlations between the HZZ and Zee couplings,\n20\n\ndisplayed in Fig. 4, and of the corresponding reduction of the uncertainty in the (H)Zee interactions,\nthe precision of the extraction of the Higgs couplings is improved, as illustrated in Fig. 6. In this figure,\nthe deterioration in the precision of the Higgs coupling extraction (with respect to an extraction with\nperfectly known Z couplings, dubbed perfect EW in the figure) is shown in two configurations: one\nwith the future FCC-ee Z-pole measurements, for which the Higgs coupling precision is close to the\nperfect EW case; and the other, limited to the precision of LEP/SLC Z-pole measurements, for which\na deterioration of up to a factor of two in precision would be observed (for the Higgs programme at\n240 GeV). Data at 365 GeV already significantly alleviate the impact of Z-pole measurements on most\ncouplings, though a 30\u201340% precision improvement is still observed for the Higgs couplings to the Z\nand W bosons.\n10\n2\n10\n2\nRatios real EW/perfect EW\n(no H exotic decay)\nw/o FCC-ee Z-pole\nFCC-ee Z/WW/240GeV\nFCC-ee Z/WW/240GeV+365GeV\n\u03b4gH\nZZ\n\u03b4gH\nWW\n\u03b4gH\n\u03b3\u03b3\n\u03b4gH\nZ\u03b3\n\u03b4gH\ngg\n\u03b4gH\ncc\n\u03b4gH\nbb\n\u03b4gH\n\u03c4\u03c4\n\u03b4\u0393H\n\u03b4g1,Z\n\u03b4\u03ba\u03b3\n1\n1.5\n1\n1.5\nFig. 6: Impact of Z-pole measurements on the Higgs coupling, Higgs decay width, and anomalous triple gauge-\nboson coupling (\u03b4g1,Z and \u03b4\u03ba\u03b3) precision from the SMEFT fit interpretation. The ratio to the precision that would\nbe obtained with infinitely precise Z-pole measurements is shown for fits that either exclude (\u2018T\u2019 bars) or include\n(solid bars) the projected FCC-ee Z-pole run measurements, with the Higgs programme at 240 GeV (yellow bars)\nand the additional data at 365 GeV (blue bars). The colour code is the same as in Fig. 3. Adapted from Ref. [61].\nNot all the 6 \u00d7 1012 Z bosons expected during the Z-pole run are needed to reach the precision\non the Zee vertex required to fully mitigate the EW contamination in the Higgs couplings determination.\nAn estimate of the number of events needed to reduce such contamination to a level that does not hinder\nthe Higgs couplings extraction is displayed in Fig. 7, which shows the deterioration in the precision of\nthe most precise HZZ and Hbb couplings with respect to the full statistics of the FCC-ee Z-pole run, as\na function of the number of events. From the perspective of Higgs couplings, a few 109 Z\u2019s, equivalent\nto less than a day of operation at the Z pole, are enough to saturate the Higgs coupling precision from\nthe 240 and 365 GeV runs.\n108\n5\u00b7108\n109\n5\u00b7109\n1010\n5\u00b71010\n1011\n5\u00b71011\n1012\nBaseline\n1.0\n1.1\n1.2\n1.3\n1.4\n# Z's\n\u03b4ghZZ/\u03b4ghZZ\n(Baseline)\nFCC-ee Z/WW/240GeV\nFCC-ee Z/WW/240+365GeV\n108\n5\u00b7108\n109\n5\u00b7109\n1010\n5\u00b71010\n1011\n5\u00b71011\n1012 Baseline\n1.00\n1.02\n1.04\n1.06\n1.08\n1.10\n# Z's\n\u03b4ghbb/\u03b4ghbb\n(Baseline)\nFCC-ee Z/WW/240GeV\nFCC-ee Z/WW/240+365GeV\nFig. 7: Estimated deterioration in the precision of the HZZ (left) and Hbb (right) couplings as a function of the\nnumber of Z\u2019s produced at FCC-ee, with respect to the baseline of 6 \u00d7 1012 events, for the FCC-ee programme up\nto 240 GeV (yellow) and up to 365 GeV (blue).\n21\n\n2.2.2\nImpact of diboson measurements in Higgs couplings determination\nTogether with gauge invariance, the assumption that electroweak symmetry is linearly realised in SMEFT\nimplies a series of correlations between the new-physics effects on the electroweak properties of the\nSM particles, for example the aforementioned correlation between contributions to the Zee and HZee\ninteractions. Another correlation relates modifications of the Higgs couplings to anomalous triple-gauge\ncouplings (aTGCs): two out of the three aTGCs (\u03b4g1,Z and \u03b4\u03ba\u03b3) are closely related to the Higgs couplings\nto vector bosons.\nAs shown in Ref. [70] for existing measurements and in Refs. [60, 61] for FCC-ee projections,\ndiboson and Higgs measurements are indeed sensitive to the same types of new-physics effects, so that\ndiboson measurements can help constrain Higgs couplings (and vice-versa). In the current SMEFT fits,\nall angular information available from the e+e\u2212\u2192W+W\u2212process is encoded in optimal observables,\nwhich bring a significant improvement [60] with respect to the fits performed in the FCC CDR [10,11],\nwhere only the (binned) W angular distribution was exploited to constrain the aTGCs. The inclusion of\nthe full diboson kinematic information in the SMEFT fit also constrains all other possible interactions\nthat can modify this process. The achieved relative precision on the Higgs couplings to gauge bosons\nand on the aTGCs is displayed in Fig. 8, for three assumed values of the selection efficiency for the\ne+e\u2212\u2192W+W\u2212events: 1%, 45% (default value in the following), and 100%. A detailed experimental\nstudy of the projected precision is required to assess the ultimate sensitivity of the diboson measurements.\n\u03b4gH\nZZ\n\u03b4gH\nWW\n\u03b4gH\n\u03b3\u03b3\n\u03b4gH\nZ\u03b3\n\u03b4g1,Z\n\u03b4\u03ba\u03b3\n\u03bbZ\n10-3\n10-2\n10-1\n1\n10-5\n10-4\n10-3\n10-2\nHiggs couplings\naTGCs\nprecision reach on effective couplings from SMEFT global fit\nFCC-ee Z/WW/240GeV\nFCC-ee Z/WW/240GeV+365GeV\nZ/WW denote Z-pole & WW threshold\nWW analysis efficiency\n\u03f5=1%\n\u03f5=45% (Default)\n\u03f5=100%\nFig. 8: Relative precision of the determination of the Higgs couplings and aTGCs in the SMFET fit, as a function\nof the selection efficiency assumed in the e+e\u2212\u2192W+W\u2212study: 1% (light shades), 45% (solid bars, chosen as\ndefault value), and 100% (triangles). The sensitivity comes mainly from the high-energy runs and the dependency\nat the WW threshold remains small. From Ref. [60].\n2.2.3\nComplementarity between Z-pole and higher-energy runs\nElectroweak precision physics at the Z pole is typically thought to mainly constrain the \u02c6S and \u02c6T oblique\nparameters characterising the gauge 2-point functions, and not be as sensitive as higher energy runs for\nthe \u02c6W and \u02c6Y parameters, the aTGCs, the Higgs self-energy and self-coupling, Higgs-vector-vector inter-\nactions, and a variety of four-fermion operators that, at tree-level, only enter off-pole observables [71].\nAll these interactions, however, enter at higher-orders in the Z-pole observable theoretical predictions.\nThe ultra-high precision provided by the Tera-Z event samples can overcome the extra loop-suppression\nfactor of these operators and actually provide relevant constraints, competitive and complementary to\nhigher-energy measurements where these interactions enter at leading order [72,73].\nThis statement is illustrated in Fig. 9, which shows the sensitivity (in terms of effective scale\nof new physics \u039b) to dimension-6 SMEFT operators entering in the four-fermion, gauge, and Higgs\nsectors, from the corresponding constraints in Z-pole observables on the one hand, and in higher-energy\n(denoted \u2018above-pole\u2019) observables on the other. Besides often being better, the on-pole bounds also\nconstrain different directions in the SMEFT space, as illustrated in Fig. 10 for two specific examples. As\n22\n\nR above-pole\nt\nR above-pole\nb\nR above-pole\nc\nR above-pole\ns\nR above-pole\n\u03c4\nR above-pole\n\u00b5\nR above-pole\ne\n\u03c3(Zh)\n\u03c3(WW)\n\u0393W\nmW\nAb\nAc\nA\u03c4\nA\u00b5\nAe\nRb\nRc\nR\u03c4\nR\u00b5\nRe\n\u03c3had\n\u0393Z\nA FB\nb\nA FB\nc\nA FB\n\u03c4\nA FB\n\u00b5\nA FB\ne\nAbove-pole\nOn-pole\nCH\nCH\nCHW\nCHB\nS3W\nSHW\nSHB\nS2W\nS2B\n[C(1)\nlq ]1133\n[C(1)\nlq ]3333\n[C(3)\nlq ]1133\n[C(3)\nlq ]3333\n[Clu]1133\n[Clu]3333\n[Ceu]1133\n[Ceu]3333\n[Cqe]3311\n[Cqe]3333\n[Cll]1122\n[Cll]1133\n[Cll]1331\n[Cll]3333\n[Cee]1133\n[Cee]3333\n[Cle]1133\n[Cle]3333\n[C(1)\nqq ]3333\n[C(3)\nqq ]3333\n[C(1)\nqu ]3333\n[C(1)\nqd ]3333\n[Cuu]3333\n[Cdd]3333\n[C(1)\nud ]3333\nHiggs\nGauge\n2Q2L\n4L\n4Q\n\u2190Above-pole On-pole \u2192\n0.3\n1\n2\n3\n4\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n\u039beff\ni [TeV]\nFig. 9: The 95% CL projected sensitivities at FCC-ee to four-fermion, gauge, and Higgs dimension-6 operators,\nin terms of the effective scale of new physics \u039b (in TeV), from measurements of Z-pole observables (right part of\nthe table) and of higher-energies observables (left part of the table). The rightmost two columns show the above-\nand on-pole combinations of all observables. Adapted from Ref. [72].\na consequence, the combination of on-pole and above-pole data very substantially reduces the overall\nvolume of parameter space and, accordingly, tightens the constraints on specific models. The scope of\nthe Tera-Z electroweak precision programme of FCC-ee is, therefore, far wider and more general than a\nna\u00efve extrapolation of the already amazingly accurate SM confirmation from LEP data would suggest.\n2.2.4\nComplementarity and synergy between FCC-ee and FCC-hh\nAs shown in Table 3, the precision of many Higgs boson couplings is expected to improve by about\none order of magnitude with respect to the (partial and not assumption-free) knowledge that will be\navailable at the end of the HL-LHC era. The precision of several couplings, such as H\u00b5\u00b5, Htt, H\u03b3\u03b3\nor HZ\u03b3, will however remain dominated by the HL-LHC knowledge, even if they will only be made\n23\n\nAbove-pole\nOn-pole\nCombined\n-0.3\n-0.2\n-0.1\n0.0\n0.1\n0.2\n0.3\n-10\n-5\n0\n5\n10\nCQ Model\nAbove-pole\nOn-pole\nCombined\n-0.010\n-0.005\n0.000\n0.005\n0.010\n-0.06\n-0.04\n-0.02\n0.00\n0.02\n0.04\n0.06\nFig. 10: Projected 68% CL sensitivities at FCC-ee, from measurements at the Z pole (orange) and in higher-\nenergy runs (blue), in the planes of Higgs self-energy vs. self-coupling (left) and of the \u02c6W oblique parameter\nvs. an operator modifying anomalous triple-gauge couplings (right). The overall combined sensitivities (green)\nare much more constraining than the individual bounds. In the right plot, S2W and S3W are the coefficients\nof the dimension-6 operators O2W = \u22121/2\n\u0000D\u00b5 W I\n\u00b5\u03bd\n\u0001 \u0000D\u03c1 W I\u03c1\u03bd\u0001\nand O3W = \u03f5IJK W I\u03bd\n\u00b5 W J\u03c1\n\u03bd\nW K\u00b5\n\u03c1\n, both\nnormalised with a scale of 1 TeV. In the left plot, the region between the dashed orange lines corresponds to\nlinearised on-pole constraints in the SMEFT operator coefficient and the solid black line corresponds to a weak\nquadruplet scalar model. Adapted from Ref. [72].\nassumption-free by the FCC-ee absolute determination of the HZZ coupling. The few per-cent HL-LHC\nprecision will be reduced by an order of magnitude at FCC-hh, by measuring ratios of branching ratios,\nfree of systematic uncertainties and normalised by the FCC-ee precise coupling determination [10]. The\nsuccessive improvements of the Higgs boson coupling precision when going from HL-LHC to FCC-hh,\nbenefitting on the way from the FCC-ee absolute and accurate coupling determination, are shown in\nFig. 11.\n\u03b4gH\nZZ\n\u03b4gH\nWW\n\u03b4gH\n\u03b3\u03b3\n\u03b4gH\nZ\u03b3\n\u03b4gH\ngg\n\u03b4gH\ntt\n\u03b4gH\ncc\n\u03b4gH\nbb\n\u03b4gH\n\u03c4\u03c4\n\u03b4gH\n\u03bc\u03bc\n\u03b4\u0393H\n10-4\n10-3\n10-2\n10-1\n1\n10-4\n10-3\n10-2\n10-1\n1\nHiggs couplings\nHiggs couplings\nprecision reach on effective Higgs couplings from SMEFT global fit\nHL-LHC S2 + LEP/SLD\nFCCee Z/WW/240GeV+365GeV\nFCCee+hh\nFree H Width\nno H exotic decay\nZ/WW denote Z-pole & WW threshold\nFig. 11: Higgs coupling precision improvements with the global SMEFT fit from HL-LHC to FCC-hh, benefitting\nfrom the FCC-ee accurate and absolute coupling determination to optimally exploit the hadron collider measure-\nments.\nThe FCC-ee role in the top Yukawa coupling determination is twofold. On the one hand, and as\nfor all other Higgs couplings, the HZZ absolute determination at 240 GeV enables a model-independent\ndetermination of the top Yukawa coupling from the HL-LHC data. On the other hand, the determination\nof the Ztt couplings from e+e\u2212\u2192tt at 365 GeV [74,75] can be used to normalise the measurement of\n24\n\n68% and 95% prob. regions\nNo FCC-ee\nHL+FCC-ee-hh\n-0.15\n-0.10\n-0.05\n0.00\n0.05\n0.10\n0.15\n-0.15\n-0.10\n-0.05\n0.00\n0.05\n0.10\n0.15\n\u03b4gHtt/gHtt\nSM\n\u03b4gZttL/gZttL\nSM\nFig. 12: Results from \u201ctoy\u201d fits to simulated data to illustrate the benefit of FCC-ee measurements in the FCC-hh\ndeterminations of the top Yukawa coupling (left) and of the Higgs self-coupling (right). In these fits, the total\nHH \u2192bb\u03b3\u03b3 cross section is used as a proxy to discuss the interplay between the two couplings, following the\nparameterisation of Ref. [77]. Simplifying assumptions are made on how the top EW couplings and the Higgs\ncouplings to bosons and fermions are measured with a standalone FCC-hh. The yellow (grey) areas show the 68%\nand 95% probability contours obtained assuming that the FCC-ee measurements are (are not) used in the coupling\nextraction from the FCC-hh data.\nthe ttH cross section at FCC-hh to that of the ttZ cross section, and to reduce the uncertainty in the top\nYukawa coupling down to the per-cent level [76], as illustrated in the left panel of Fig. 12.\nIn this discussion, it is assumed that contributions from, e.g., dipole or four-fermion interactions\nin e+e\u2212\u2192tt or pp \u2192ttX are negligible. The contributions of these four-fermion interactions to the\nttH cross section at FCC-hh could be constrained from tt measurements. To constrain the contributions\nof the eett four-fermion interactions to the e+e\u2212\u2192tt cross section, extra handles might need to be\nidentified, during the next phase of the study, to lift the approximate flat directions that could appear in a\nglobal top-quark analysis.\nThe Higgs boson self-coupling, \u03ba\u03bb, will start being probed at HL-LHC, with an uncertainty that\nwas estimated at the time of the 2020 ESPPU to be about 50%, in a fit where only deformations of \u03ba\u03bb are\nallowed. Since then, improved analysis techniques and the inclusion of additional decay channels have\nreduced this uncertainty to 26% [78]. The larger acceptance of the upgraded HL-LHC trackers is likely\nto bring it well below 25%. In e+e\u2212collisions, one-loop radiative corrections, that involve the Higgs\nself-coupling, to the Higgs boson production cross sections, are proportional to \u03ba\u03bb. These corrections\namount to several per-cent in the SM at 240 GeV and strongly depend on the centre-of-mass energy [79].\nWith this energy dependence, the sub-percent precision of the FCC-ee Higgs cross-section measurements\nat 240 and 365 GeV suffice to disentangle the effect of new physics in the HZZ coupling and in \u03ba\u03bb, and\nallows a stand-alone determination of \u03ba\u03bb with a precision of 28%, as shown in the left panel of Fig. 13.\nBesides being quantitatively competitive with HL-LHC projections, this precision is also qualitatively\ndistinct, as it is achieved within an SMEFT framework that accounts for a broad variety of potential new\nphysics effects.\nThe combination of FCC-ee with HL-LHC therefore lifts the assumption made for the sole HL-\nLHC extraction, and significantly improves the overall precision on \u03ba\u03bb to 18%, as shown in the right\npanel of Fig. 13. If deemed important, it would be possible to double the FCC-ee integrated luminosity\nat 240 and 365 GeV, and reach a precision close to 15% on \u03ba\u03bb, in a high-luminosity scenario dubbed\nHL-4 IP in Fig. 13. The doubling of the integrated luminosity can be achieved either by running twice as\nlong at these centre-of-mass energies, or by doubling the instantaneous luminosity, with a larger number\nof colliding bunches and/or a smaller vertical \u03b2\u2217(along with a smaller vertical emittance), but without\nany hardware modifications to the collider, as explained in Ref. [80].\n25\n\n0.17\n0.18\n0.2\n0.22\n0.25\n0.3\n0.4\n0.6\n0\n5\n10\n15\n20\n25\n30\n0\n2\n4\n6\n8\n10\nL240 GeV (ab-1)\nL365 GeV (ab-1)\nprecision reach on \u03b4\u03ba\u03bb from SMEFT global fit\nFCC-ee alone\n0.14\n0.15\n0.16\n0.17\n0.18\n0.19\n0.2\n0.22\n0\n5\n10\n15\n20\n25\n30\n0\n2\n4\n6\n8\n10\nL240 GeV (ab-1)\nL365 GeV (ab-1)\nprecision reach on \u03b4\u03ba\u03bb from SMEFT global fit\nFCC-ee + HL-LHC (0.25)\n4IP\n4IP\nHL-4IP\nHL-4IP\nFig. 13: The projected Higgs self-coupling relative precision from the SMEFT global fit, as a function of the\nintegrated luminosities of the 240 and 365 GeV runs, with FCC-ee alone (left) and FCC-ee combined with HL-\nLHC (right). The 4 IP and HL-4 IP dots represent the FCC-ee baseline scenario and an hypothetical scenario\n(described in the text) with doubled integrated luminosities at 240 and 365 GeV, respectively.\nRecent studies [81,82] have shown that other new physics interactions, entering at the same order\nin perturbation theory, but absent from the SMEFT framework considered in this report, could marginally\naffect the \u03ba\u03bb extraction from single-Higgs processes. In rare and extreme cases, the value of \u03ba\u03bb extracted\nfrom single production at FCC-ee data could differ from that with pair production at HL-LHC, a differ-\nence that would allow this new physics to be identified and constrained. More pragmatically, a global\nfit is needed to bound these other interactions and to mitigate their impact in the determination of \u03ba\u03bb.\nThe more operators are considered, the more observables are needed in the global fit. Some operators\ncurrently weakly bounded by experimental data, e.g., the four-fermion eett operator, will require further\ninvestigation in the next phase of the study.\nThis subtlety is anecdotal in the grand vision of the FCC integrated project. Indeed, the Higgs\nself-coupling will be uniquely and unambiguously probed at FCC-hh via Higgs boson pair (HH) pro-\nduction. Current estimates, combining the bb\u03b3\u03b3, bb\u03c4+\u03c4\u2212, bbZZ, and 4 b decay channels, suggest that\na precise determination, with an uncertainty as small as 3.4%, would be within the reach of a 100 TeV\npp collider [83], and probably better by a factor of two with progress similar to those made in the HL-\nLHC projections [78] and in recent FCC-hh studies [84,85]. The role of the different FCC stages in the\ndetermination of the Higgs self-coupling is summarised in Fig. 14.\nAs for HL-LHC, this FCC-hh precision refers to an exclusive determination of the Higgs self-\ncoupling, i.e., only considering deformations of \u03ba\u03bb. Other new physics interactions, however, could\nmodify the HH production or decay rates and it is important to keep their uncertainties under control.\nWhile an inclusive analysis taking into account all these effects has not yet been undertaken, an illus-\ntration of the impact of such effects is displayed in the right panel of Fig. 12. This figure shows how\nthe uncertainty in the top Yukawa coupling modifies the \u03ba\u03bb precision from the measurement of the total\ngg \u2192HH \u2192bb\u03b3\u03b3 cross section. The top Yukawa coupling enters with several powers in the different\ndiagrams, contributing to \u03c3(gg \u2192HH). As noted above, the precise determination of the top Yukawa\ncoupling at FCC-hh relies on the measurement of the \u03c3(pp \u2192ttH)/\u03c3(pp \u2192ttZ) ratio, where the ttZ\ncoupling itself should be allowed to vary within its experimental uncertainty, rather than being fixed to\nits assumed SM value. The plots in Fig. 12 show the impact of using, or not, the direct FCC-ee measure-\n26\n\n0.1\n0.2\n0.3\n0.4\n0.5\n0.1\n0.2\n0.3\n0.4\n0.5\nHL-LHC S2 + LEP/SLD\nFCC-ee Z/WW/240GeV\nFCC-ee Z/WW/240+365GeV (4IP/HL\u20134IP)\nFCC-ee+hh\nFig. 14: Improvement in the determination of \u03ba\u03bb at FCC-ee (the darker colours are for the HL-4 IP optimised\nscenario) and, subsequently, at FCC-hh.\nment of the ttZ coupling in the extraction of the top Yukawa coupling at FCC-hh (left panel) and the\nconsequent impact on the \u03ba\u03bb determination (right panel).\nFinally, a concern was expressed about the sensitivity of the \u03ba\u03bb determination at HL-LHC if its\ntrue value were about twice the SM value (\u03ba\u03bb = 2), for which the destructive interference between the\nbox and triangle diagrams of the HH production by gluon fusion in pp collisions would significantly\ndecrease the cross section. While the HL-LHC relative precision would actually not degrade for \u03ba\u03bb = 2,\nthe synergy with FCC-ee is, once more, remarkable here. Indeed, at FCC-ee the e+e\u2212\u2192ZH production\ncross section is a linear function of the true value of \u03ba\u03bb: \u03c3ZH = \u03c30 \u00d7 (1 + \u03b1 \u03ba\u03bb), with \u03b1 > 0 (i.e.,\nwith a constructive interference). The FCC-ee relative precision on \u03ba\u03bb, therefore, evolves as 1/\u03ba\u03bb when\nthe true value of \u03ba\u03bb increases. For \u03ba\u03bb = 2, a stand-alone precision of 14% would therefore be achieved\nat FCC-ee with an explicit EFT fit similar to that of Figs. 13 and 14, improved to less than 10% in the\nhigh-luminosity scenario.\n2.3\nDiscovery landscape\nThe discovery landscape for BSM physics at FCC-hh has been well documented in Ref. [57] and in the\nFCC CDR [10]. Here, instead, the FCC-ee discovery landscape is discussed. While several results were\nalready presented in the CDR, continuous work has taken place since, to refine or extend the scope of\nBSM searches, a notable example being the search for long-lived particles (LLPs) and heavy neutral\nleptons (HNLs).\n2.3.1\nBSM exploration potential\nThe capability and versatility of FCC-ee to explore open questions about the origins and nature of the\nUniverse is immense. In addition to probing the known elementary particles and fundamental forces with\nthe highest precision, it can survey uncharted territory both directly towards ultra-weak couplings and\nindirectly at very high energies, up to 100 TeV, for so-far unknown particles and interactions.\nAt the centre of many mysteries lies the Higgs boson. Besides enabling a much sharper picture of\nthe Higgs boson and testing its (non-)SM nature, the ZH run can also provide crucial model-independent\nsensitivity to its invisible decay mode(s), which probe the Higgs portal to dark sectors. Ultimately,\nan explanation for the origin of the Higgs mechanism itself is sought. From what underlying theory\ndoes the Higgs sector emerge? While this outstanding question is sufficient motivation in itself, a more\nfundamental description of the nature of electroweak symmetry breaking is, moreover, expected to be\nassociated with new theoretical principles addressing the hierarchy problem, a naturalness strategy that\n27\n\n0.5\n1.\n1.5\n2.\n2.5\n0.01%\n0.1%\n1%\n10%\n100%\nhhh coupling: \u03bb3/\u03bb3\nSM\nhZZ coupling: |ghZZ/ghZZ\nSM - 1|\nReal Scalar Singlet Model\ncurrent\nHL-LHC\nFCC-ee\nFCC-hh\nFCC-hh\nFig. 15: Scan of the parameter space for a real scalar singlet model, where all points shown have a first-order\nelectroweak phase transition, plotted in the plane of the fractional change in the Higgs coupling to a pair of Z\nbosons relative to its SM value (\u2018hZZ coupling\u2019) vs. the triple-Higgs coupling normalised to its SM value (\u2018hhh\ncoupling\u2019). The space outside the two FCC-hh lines and above the FCC-ee line can be covered at those facilities.\nAdapted from Ref. [91] and scaled to baseline luminosities.\nhas proven useful in the past and whose success or failure now would be of profound importance [86,87].\nThese theories typically extend the symmetries of the SM, for example in supersymmetric, composite,\nor extra-dimensional frameworks [88]. More recent proposals involving light new physics include novel\ntypes of cosmological dynamics [89]. Alternatively, something radically new altogether may manifest\nin direct searches, indirectly by measuring higher-dimensional operator coefficients or spectacularly in\nunforeseen types of exotic signatures. It is crucial to fully explore the Higgs boson as much as possible\nabove the TeV scale.\nA deeper understanding of the scalar sector of the SM can also show whether the early Uni-\nverse underwent a first-order electroweak phase transition (FOEWPT) or not, knowledge that is crucial\nfor understanding the matter-antimatter asymmetry. As an example, in the real scalar singlet model, a\nFOEWPT is correlated with a modification of the Higgs coupling to Z bosons in a way that can be ex-\nplored almost entirely by FCC-ee (Fig. 15). Furthermore, a FOEWPT can also lead to gravitational wave\n(GW) signatures, which could be detectable by future GW observatories, such as LISA. Since it will be\ndifficult to disentangle these signals from other astrophysical phenomena, precisely measuring the Higgs\nproperties at colliders could have an important role to play in settling this important question [90]. The\nsynergy between cosmology and particle physics has been fruitful in the past and may well lead to a\nmore profound understanding of the nature of the electroweak phase transition, exploring whether it had\na role to play in the origin of matter.\nThe power of FCC-ee to probe the Higgs boson at much higher resolution than accessible today\nis that it enables peering further into the cloud of quantum fluctuations surrounding it. The envisioned\nprecision indirectly opens a window onto physics at multi-TeV energies, around the level of current elec-\ntroweak precision observables from LEP but uniquely sensitive to the Higgs boson. Given the number of\npossible BSM Feynman diagrams contributing virtually to these quantum fluctuations, there is a tremen-\ndous variety of possible new physics scenarios solving shortcomings of the SM that cannot be tested by\n28\n\nother means. Similar to the past Fermi theory, the SMEFT is an EFT that maps out the path for continued\nexploration of what lies far beyond. For this essential programme of indirect BSM exploration through\nthe SMEFT, FCC-ee is just indispensable.\nNon-decoupling particles get most of their mass from the Higgs mechanism, requiring a more gen-\neral EFT framework than SMEFT, known as HEFT, to accurately capture their low-energy phenomenol-\nogy [92]. Their coupling to the Higgs boson has a lower bound and unitarity requires their mass to have\nan upper limit. Their parameter space is therefore finite and can be comprehensively covered by FCC-ee,\nas detailed in Ref. [93]. An interesting open question \u2014 is the Higgs responsible for most of the mass of\nany other particles beyond the SM ones? \u2014 could then be basically settled.\nA further qualitative leap in resolving power comes from studying the Z boson at the Z-pole run\nof FCC-ee. A Tera-Z factory, with five orders of magnitude more Z bosons than at LEP, is another truly\nexciting prospect in its breadth of SM physics and spectacular BSM sensitivity. While the measure-\nments at a Higgs factory bring the knowledge of the Higgs sector up to the high-precision standards of\nLEP electroweak precision observables, a new era of ultra-high precision observables will begin with\nTera-Z. This ultra-high precision gives FCC-ee an indirect sensitivity to scales of several tens of TeV for\nweakly-coupled new physics, while the sensitivity for strongly coupled physics can reach 100 TeV. To\nconsolidate this sensitivity, the statistical precision reached by the very large Tera-Z event samples must\nbe matched by a new generation of challenging theoretical calculations at higher electroweak loop orders,\nthe development of which is another benefit of the FCC-ee physics programme: pushing the boundaries\nof experiment also expands the frontiers of theory and the understanding of quantum field theory.\nAfter the Z boson, the W boson can also be used as a precision tool at FCC-ee. Its mass is\none of the most precisely measured parameters that can be calculated in the SM and is thus of utmost\nimportance. The production of almost 5 \u00d7 108 W bosons during the planned runs at the WW threshold\nand above will provide tests of the SM and of a plethora of BSM models with a precision at least one\norder of magnitude better than today. The combination of multi-Z and W production will measure\nthe gauge-boson sector with the sharpest cutting-edge precision, leading not only to an unprecedented\noverview at the microscopic scale of electroweak physics but also offering sensitivity to a far broader\nrange of physics intricately linked across the SM, and SMEFT more generally, by precision quantum\neffects.\nGoing to its highest energy, FCC-ee can explore physics associated with the heaviest known par-\nticle, the top quark, with the tt run. Its mass plays a fundamental role in the prediction of SM processes\nand for the cosmological fate of the metastable vacuum if the SM were extended up to 1010 GeV or\nhigher [94\u201397]. An improvement by more than an order of magnitude, achievable at FCC-ee [75], is\nnecessary to perform the above-mentioned precision tests at the quantum level. This improvement goes\nhand in hand with significant progress in the experimental determination of the strong coupling con-\nstant [98], one of nature\u2019s fundamental parameters. The large top quark mass suggests that it plays a\nunique role, not only in Higgs and flavour physics, but also in relation with new, so far unobserved, phe-\nnomena. Indeed, proposed solutions to important open questions motivate couplings of BSM physics to\nthe third generation, which also happens to be among the least constrained sectors of the SM. Therefore,\nthe precise measurements of the top quark mass and other top quark characteristics are crucial for BSM\nprecision exploration.\nAs a heavy flavour factory, FCC-ee can also investigate the other crucial third generation particles,\nthe tau lepton and the bottom quark. At the Z-pole run, a record number of \u2018clean\u2019 B mesons and \u03c4\nleptons are expected to be produced, the rare decays of which offer exceptional insight into flavourful\nprocesses beyond several tens of TeV in energy. Exploring the flavour structure of the SM in new regimes\ncan yield clues as to its origin and potentially reveal BSM symmetries and selection rules. In addition to\ntesting BSM flavour models, it provides a valuable experimental probe of CP violation and lepton flavour\nviolation/universality that can arise generically in BSM extensions.\nFinally, following the proposals and approvals at LHC of \u2018parasite\u2019 detectors that enhance its\n29\n\nphysics potential, it is possible to also envision additional experiments at FCC at different locations [99\u2013\n101]. Notably, the civil engineering provides FCC-ee with much bigger detector caverns (Chapter 7)\nthan needed for a lepton collider, in order to use them later for FCC-hh. It would then be possible to,\ne.g., install instrumentation in the cavern walls to search for new long-lived particles [52].\nEven in the absence of no-lose theorems for the discovery of BSM physics, whether in particle\nphysics or anywhere else, the case for a general-purpose particle observatory to carry out fundamental\nscience at the smallest accessible scales remains as strong as ever in the face of unanswered questions.\nThe purpose of FCC-ee is to improve the knowledge of the Universe and explore its fundamental origins.\nOn both these fronts, it is guaranteed to make significant progress.\n2.3.2\nTera-Z sensitivity to heavy new physics\nThe extensive physics programme and unprecedented precision of FCC-ee renders it uniquely suited\nto a general exploration of the zeptoscale. In particular, the understanding of the role of the Tera-Z\nprogramme at FCC-ee in discovering evidence for BSM physics has evolved significantly in recent years.\nThe picture that has emerged is that, if there is heavy new BSM physics coupled to the SM fields that\nmodifies SM observables, Tera-Z is well placed to find traces of it. This reasoning has been developed\nin the context of concrete models concerned with the flavour puzzle [102] and the microscopic origins\nof the Higgs boson [103, 104]. Even if a broad and agnostic view of the motivation for the presence of\nnew physics is taken, Tera-Z offers discovery potential for almost any scenario that leads to tree-level\nmodifications of the SM [27,28].\nWhen considering the possibility of new physics at the TeV scale, it is incumbent upon any\nmodel-builder to account for all aspects relating to flavour. Since precision flavour observables have,\nfor decades, provided a powerful indirect window onto physics at the shortest accessible distances, it\nis common that putative new physics scenarios fall foul of flavour constraints, requiring the mass scale\nof new states to greatly exceed the TeV scale. It is important, therefore, to identify and classify new\nphysics scenarios that can be consistent with the present suite of experimental constraints. In Ref. [102]\nit was reported that new physics with an approximate U(2)5 flavour symmetry could exist at very low\nscales whilst remaining consistent with constraints. The high energy states in such a scenario necessarily\ngive rise to modifications of the SM, with effects captured by families of dimension-6 SMEFT operators.\nThe coefficients of these operators are shown in Fig. 16, alongside present-day constraints from flavour,\nprecision EW, and high-energy collider probes.\nIt is clear that new physics states as low as the TeV scale are presently compatible with observa-\ntions. On the other hand, projections from a precision EW programme at FCC-ee, driven primarily by\nthe Tera-Z programme, are shown to probe significantly beyond this scale, as far as 10 TeV. Not only\nis the sensitivity of operators that enter electroweak precision at tree level enhanced to the tens of TeV\nscale, there are also many more third generation operators being constrained at loop level through RGE\nevolution. This observation would significantly impact the understanding of the new physics landscape\nat high energies and its interplay with flavour, providing opportunities to discover the effects of heavy\nnew physics.\nThe previous discussion concerns the flavour structure of new physics scenarios. In contrast,\nRef. [103] focuses specifically on the question of Higgs compositeness. Composite Higgs models are\na class of scenarios in which the Higgs boson is a composite bound state of a new strongly-coupled\ndynamics at the TeV scale and a potential precursor of extra spatial dimensions. These models offer\ncompelling answers to the question of the microscopic origins of the Higgs sector of the SM, in analogy\nwith the way in which QCD explains the existence and properties of the pions. However, a significant\nchallenge to such a scenario follows from the magnitude of the Higgs boson Yukawa coupling to the top\nquark. This large coupling is difficult to accommodate in the most basic realisations, but it can arise if\nthe left and/or right-handed top quarks are also partially composite. This observation thus brings flavour\nconsiderations to the fore when attempting to understand the origins of the Higgs sector.\n30\n\nFig. 16: The reach of FCC-ee precision electroweak observables (hatched) compared to present day flavour, elec-\ntroweak, and high energy collider constraints, for all operators consistent with U(2)5-symmetric flavour physics at\nthe new physics matching scale. The bounds are 3 \u03c3 single-parameter fits, obtained running from a scale of 3 TeV\nwith full resummation of the logarithmic terms. Taken from Ref. [102].\nReference [103] considers the role that an FCC-ee precision EW programme would play in probing\nthe possibility of partial top quark compositeness. A custodial symmetry is typically assumed of such\nmodels to evade current electroweak precision bounds from the T parameter, equivalent to a custodially-\nviolating dimension-6 operator. However, the SM violation of custodial symmetry itself leads to a next-\nto-leading-log RG running into the T parameter that can no longer be so easily evaded at FCC-ee. This\nrenders large swathes of parameter space accessible to FCC-ee, as shown in Fig. 17, where FCC-ee\nprojections are compared to nearer-term HL-LHC and flavour projections. A huge increase in projected\nreach is observed, to compositeness scales of at least 25 TeV.\n10\n20\n30\n40\n50\n60\n70\n0\n2\n4\n6\n8\n10\n12\n10\n20\n30\n40\n50\n60\n70\n0\n2\n4\n6\n8\n10\n12\n10\n20\n30\n40\n50\n60\n70\n0\n2\n4\n6\n8\n10\n12\nFig. 17: The FCC-ee reach for probing Higgs and top compositeness through the precision EW programme, as\ncompared to nearer-term HL-LHC and flavour measurements. Taken from Ref. [103]. Left, mixed, and right top\npartial compositeness are considered (left to right panels).\nA final consideration, developed in Refs. [27, 28], could be considered an \u2018informed agnostic\u2019\nperspective on the nature of heavy new physics. The leading low energy effects of any heavy new physics\n31\n\nscenarios with states whose mass does not depend significantly on the Higgs field can be captured in\nthe dim-6 operators of the SMEFT. However, that does not conversely mean that any pattern of dim-6\nSMEFT operators corresponds to a legitimate heavy new physics scenario. Thus, it is too simplistic to\nperform EFT fits in the context of future colliders without paying heed to concrete UV scenarios.\nTable 4: Heavy scalars, fermions, and vectors that can contribute to SMEFT at dimension-6 with corresponding\nrepresentations under SU(3)C \u00d7 SU(2)L \u00d7 U(1)Y . Taken from Ref. [105].\nScalar\nS\nS1\nS2\n\u03c6\n\u039e\n\u039e1\n\u03981\n\u03983\n(1, 1)0\n(1, 1)1\n(1, 1)2\n(1, 2) 1\n2\n(1, 3)0\n(1, 3)1\n(1, 4) 1\n2\n(1, 4) 3\n2\n\u03c91\n\u03c92\n\u03c94\n\u03a01\n\u03a07\n\u03b6\n(3, 1)\u22121\n3\n(3, 1) 2\n3\n(3, 1)\u22124\n3\n(3, 2) 1\n6\n(3, 2) 7\n6\n(3, 3)\u22121\n3\n\u21261\n\u21262\n\u21264\n\u03a5\n\u03a6\n(6, 1) 1\n3\n(6, 1)\u22122\n3\n(6, 1) 4\n3\n(6, 3) 1\n3\n(8, 2) 1\n2\nFermion\nN\nE\n\u22061\n\u22063\n\u03a3\n\u03a31\n(1, 1)0\n(1, 1)\u22121\n(1, 2)\u22121\n2\n(1, 2)\u22123\n2\n(1, 3)0\n(1, 3)\u22121\nU\nD\nQ1\nQ5\nQ7\nT1\nT2\n(3, 1) 2\n3\n(3, 1)\u22121\n3\n(3, 2) 1\n6\n(3, 2)\u22125\n6\n(3, 2) 7\n6\n(3, 3)\u22121\n3\n(3, 3) 2\n3\nVector\nB\nB1\nW\nW1\nG\nG1\nH\nL1\n(1, 1)0\n(1, 1)1\n(1, 3)0\n(1, 3)1\n(8, 1)0\n(8, 1)1\n(8, 3)0\n(1, 2) 1\n2\nL3\nU2\nU5\nQ1\nQ5\nX\nY1\nY5\n(1, 2)\u22123\n2\n(3, 1) 2\n3\n(3, 1) 5\n3\n(3, 2) 1\n6\n(3, 2)\u22125\n6\n(3, 3) 2\n3\n(\u00af6, 2) 1\n6\n(\u00af6, 2)\u22125\n6\nFig. 18: Projected bounds on the masses of new scalar fields (the bounds are 2 \u03c3 fits, obtained running with the\nleading-logarithmic terms from a scale of 2 TeV, at which the couplings to the SM particles are assumed to be unity,\ndown to the mass of the Z). \u2018Flavourless couplings\u2019 correspond to models in which couplings of the new states\nto fermions are absent, \u2018Universal couplings\u2019 correspond to equal couplings to all generations, and \u2018Third-gen\nonly\u2019 to new physics coupled only to the third generation fermions. The vertical dashed lines separate fields that\ncontribute to EWPOs at tree level (left), via one-loop RG evolution (middle), and via one-loop matching (right).\nFrom Ref. [27], scaled to baseline luminosities.\nAs an informed middle ground, Refs. [27,28] considered all possible new physics scenarios where\nany dim-6 SMEFT operators are generated at tree-level. The number of possibilities is large, but finite,\nas detailed in Table 4. If any such scenario exists and modifies SM properties in any sector of the SM at\ndim-6, the precision EW programme at FCC-ee has sensitivity, as shown in Figs. 18, 19, and 20.\n32\n\nFig. 19: Projected bounds on the masses of new vector fields. Same as for Fig. 18.\nFig. 20: Projected bounds on the masses of new fermion fields. Same as for Fig. 18.\nAs a matter of fact, FCC-ee can effectively probe virtually all heavy particles linearly coupled to\nthe SM, with a sensitivity that reaches up to 100 TeV at tree-level and O(1\u201310) TeV at the one-loop level\nfor O(1) couplings. This reach could extend even higher in the case of strongly-coupled new physics.\nQuantum RG effects are crucial. Any treatment that considers the SMEFT contributions of these states\nonly at tree-level would overlook the majority of the sensitivity of the FCC-ee Tera-Z programme to their\nexistence.\nReference [27] only considers the Tera-Z and WW runs. Recently, the SMEFit Collaboration\nstudied the impact of the various runs combined and individually. Details can be found in Refs. [69,\n106,107], including the slightly different EW-input scheme, which leads to some minor differences with\nrespect to the results of Ref. [27] for some models. Figure 21 demonstrates the exploratory power of\nthe various runs to a variety of models in which the full one-loop matching is performed at the matching\nscale. Figures 22, 23, and 24 consider selected scalar, fermion, and vector scenarios with RG-evolved\nWilson coefficients but not one-loop matching, as in Figs. 18, 19, and 20.\n33\n\nFig. 21: Sensitivity (95% CL) to a selection of models from Table 4 with Wilson coefficients fully matched at one-\nloop (the bounds are obtained from a \u03c72 fit and the couplings of the new particle are set to unity at the matching\nscale, taken to be the mass of this heavy particle, the different operators are then run down to the Z boson mass\nwith full numerical resummation of the logarithmic terms). In the case of new physics coupled to SM fermions,\nheavy scalar and fermions couple to the third generation only, while vectors couple to third-generation quarks and\nall generations of leptons. The starting scenario corresponds to all LEP/SLD and LHC constraints anticipated by\nthe end of HL-LHC operation. Additional combinations of FCC-ee runs are then shown. Black markers denote\nanticipated constraints were the theory uncertainties to remain as at present. The \u03981 + \u03983 model corresponds to\nthe custodial quadruplet model of Refs. [108\u2013110].\nFig. 22: As Fig. 21, but without the one-loop matched terms, for scalars.\nThe picture that emerges from Figs. 21, 22, 23, and 24 is that the Tera-Z programme of FCC-ee\nis, indeed, extremely powerful in searching for new physics, extending well beyond the scales probed at\nHL-LHC, and is also highly complementary to the Higgs run. The latter offers loop-induced sensitivity\nto the Higgs trilinear coupling [79], which could probe custodially symmetric models, as shown for the\n\u03981 + \u03983 model in Fig. 21. This weak custodial quadruplet scalar model and the Higgs trilinear coupling\ncan, moreover, be probed on the Z pole, as shown on the left plot of Fig. 25, with the combination\nsignificantly extending the coverage of the model parameter space [72].\n34\n\nFig. 23: As Fig. 21, but without the one-loop matched terms, for fermions.\nFig. 24: As Fig. 21, but without the one-loop matched terms, for vectors. The models B and W include flavour-\nuniversal couplings to leptons. See Ref. [106] for details.\nThe Tera-Z run is crucial to definitively answer the fundamental question of whether any particles\nother than the SM ones obtain most of their mass from the Higgs mechanism. Such so-called \u2018loryon\u2019\ncandidates have a finite parameter space that can be almost entirely probed by current and future colliders,\nwith a remaining open window for the elusive real singlet scalar model [93]. This window can potentially\nbe closed by precision measurements at the Z pole, as shown on the right plot of Fig. 25, from Ref. [72],\nthus allowing this important question to be definitively settled. The high sensitivity of FCC-ee to the\n\u02c6W and \u02c6Y parameters, both at the Z pole and in higher energy runs, also enables constraining elusive\nBSM candidates, such as weakly interacting massive particles. The combination of on-pole and above-\npole data, shown in Fig. 26, indeed gives a projected sensitivity beyond the indirect sensitivity reach of\nDrell\u2013Yan searches at HL-LHC [72].\n35\n\nAbove-pole\nOn-pole\n1000 2000 3000 4000 5000 6000 7000\n0\n2\n4\n6\n8\n10\n12\nAbove-pole\nOn-pole\n200\n400\n600\n800\n1000\n0\n2\n4\n6\n8\n10\n12\nFOPT\nLoryon\nFig. 25: FCC-ee sensitivity at 68% CL on the weak custodial quadruplet scalar (left) and real singlet scalar (right)\nmodels in the mass vs. coupling plane when combining Z pole data (orange) with ZH measurements (blue). For\nthe real singlet case, the constraints exclude a first order phase transition (FOPT) for the mass region shown. See\nRef. [72] for further information.\nFig. 26: Projected 95% CL for n-plet Dirac fermion and complex scalar weakly interacting massive particles with\nzero hypercharge. From Ref. [72].\nIt will be critical to reduce theory uncertainties (Chapter 3) in order to capitalise on the full po-\ntential of the FCC-ee data. Indeed, for a number of scenarios, the Tera-Z programme would probe the\nparameter space inaccessible to the runs at higher energies only in the context of improved theory uncer-\ntainties. An additional noteworthy aspect concerns the synergy with FCC-hh. Indirect probes at FCC-ee\napproach or exceed the 10 TeV scale. As a result, the only motivated successor to such a probe would be\na collider capable of directly probing beyond that parameter space or one capable of directly producing\nthe new states for which indirect evidence may have emerged at FCC-ee. In other words, a successor\ncollider would necessarily have to be capable of directly probing beyond the 10 TeV scale. The only such\nplausible facility is FCC-hh, strengthening the combined FCC physics case.\nIt should be noted that exceptions from the exploratory power of Tera-Z can exist. It was recently\nshown in Ref. [111] that a class of anomaly-free Z\u2032 models could exist in which the charge assignments\nlead to a suppression of electroweak-precision-sensitive operators at tree and one-loop level. Nonethe-\nless, such a scenario would be strongly constrained above the Z-pole, both at FCC-ee and HL-LHC,\ndemonstrating additional complementarity between runs and colliders.\n36\n\nThe individual models considered are, themselves, not being proposed as well-motivated in any\nsubjective sense. Rather, the collection of scenarios and the full family of Wilson coefficient patterns they\npopulate can be taken as being qualitatively representative of the broad family of Wilson coefficients\nthat could arise in UV scenarios. Thus the fact that the FCC-ee Tera-Z programme has sensitivity to\nthis wide class of models, whether at tree-level or one-loop, is indicative of the fact that it will have\nsensitivity to generic UV scenarios. To argue otherwise would require the construction of an explicit\ncounterexample model. Within the class of models considered in Ref. [27], the two counterexample\nstates are \u21264 and a special case for G, for which only the four top-right interaction is generated up\nto one loop. However, even BSM modifying four-top operators can be highly constrained through its\nnext-to-leading-log running into the T parameter at the Z pole [102,103], as also seen in Figs. 22 and 24.\nFinally, as another concrete UV scenario, supersymmetric models are a well-motivated approach\nto understanding the origin of the Higgs and addressing the hierarchy problem, where the BSM particles\nare, instead, typically expected to arise from new weakly-coupled dynamics. The Higgs couplings at one\nloop, in particular to gluons and photons, can probe the contributions of superpartners such as the stop,\nthe coloured scalar partner of the top. Such indirect probes are complementary to more model-dependent\ndirect searches and their sensitivity can reach around a TeV, as shown on the left plot of Fig. 27, taken\nfrom Ref. [112]. The right plot of Fig. 27, from Ref. [104], shows the projected Z branching ratio\nsensitivity at FCC-ee to the selectron and pure wino, together with the current direct search constraints\nat LHC.\n0\n1000\n2000\n3000\n4000\n5000\n6000\nmeL [GeV ]\n0\n500\n1000\n1500\n2000\n2500\n3000\nmf\nW [GeV ]\nFCC-ee Syst.\nFCC-ee Stat.\n103 \u00d7 |\u03b4 R\u2113|\n0.20\n0.05\n0.1\n1.0\nmf\nW = meL\nLHC\nLHC\n(Uncompressed)\nFig. 27: Left: Projected 2 \u03c3 sensitivity of Higgs couplings to stops at FCC-ee in the parameter space of stop\nmasses m\u02dct1 vs. m\u02dct2; from Ref. [112]. Right: FCC-ee Z branching ratio projected statistical and systematic 1 \u03c3\nuncertainties in the left-handed selectron mass vs. pure wino mass plane; from Ref. [104] scaled to the baseline\nluminosities.\n2.3.3\nFlavour deconstruction at FCC-ee\nTo give an example of concrete scenarios explored through a combination of the unprecedented precision\non Z-pole and WW-threshold observables with excellent capabilities as a flavour factory, a special class\nof theories based on \u2018flavour deconstruction\u2019 [113] is considered, whereby part of the electroweak sym-\nmetry is resolved into three generation-specific copies Gi (with the Higgs boson coupled to G3). This\nsymmetry, which arises, e.g., from gauge-flavour unification [114] or from extra-dimensions [115], is\nbroken to the SM in two steps that generate hierarchical fermion masses and mixings. The last breaking\nstep, G12 \u00d7 G3 \u2192G, should occur close to the TeV scale to avoid destabilising the Higgs potential,\ndelivering TeV-mass gauge bosons in the adjoint of G coupled mostly to the third generation.\n37\n\nTable 5: Constraints from flavour, high pT, and EWPOs on the mass of the gauge bosons predicted by flavour\ndeconstruction.\nDeconstructed SU(2)L\nDeconstructed U(1)Y\nElectroweak: Z-pole & WW-threshold\n9 TeV (5 TeV if exc. mW)\n2 TeV\nFlavour: Bs \u2192\u00b5\u00b5 (up-alignment)\n7.5 TeV\n2 TeV\nHigh pT: Drell\u2013Yan pp \u2192ee, \u00b5\u00b5, \u03c4\u03c4\n4.5 TeV\n3.5 TeV\nEW projection FCC-ee\n30 TeV\n7 TeV\n(on and above Z-pole & W-pole)\nThese electroweakly-charged and flavour non-universal gauge bosons give rise to a rich phe-\nnomenology across EWPOs, flavour observables, and high-energy LHC measurements, which has been\nquantified by considering deconstructed hypercharge [116] and deconstructed SU(2)L [117] (Table 5).\nFirstly, EWPOs are shifted at tree-level because the heavy gauge bosons directly couple to the Higgs\nboson. Constraints from LEP are already strong and the expected precision brought by FCC-ee would all\nbut cover the \u2018natural\u2019 regime in which these flavour models can be reconciled with the hierarchy prob-\nlem. Secondly, being intrinsically non-universal theories of flavour, many rare B- and \u03c4-decays receive\ntree-level shifts that will also be measured with excellent precision at Tera-Z. While more detailed stud-\nies are needed to fully assess these prospects, key processes will be B \u2192K(\u2217)\u03bd\u03bd, b \u2192s\u03c4\u03c4 transitions\nthat are a unique opportunity at FCC-ee, and LFUV measurements in \u03c4 decays. In these models, the shift\nin B \u2192K(\u2217)\u03bd\u03bd is directly correlated to that in Bs \u2192\u00b5\u00b5, which should be measured to few percent pre-\ncision at HL-LHC [118]. Lastly, these models are constrained by high-energy Drell\u2013Yan measurements\nof pp \u2192\u2113\u2113, that should improve by nearly a factor of two after HL-LHC.\nOther flavour deconstruction models have been proposed where, for instance, a new force-carrying\ngauge boson field is associated with a TeV-scale U(1)Y3 Z\u2032, coupling primarily to the third family of\nfermionic fields [119]. These models, currently favoured by measurements of B decays in tension with\nthe SM predictions, can be thoroughly tested by FCC-ee.\nTo summarise, FCC-ee is an optimal machine for probing theories of flavour deconstruction be-\ncause it achieves comparable sensitivity across diverse measurements traditionally separated into \u2018elec-\ntroweak\u2019 and \u2018flavour\u2019 categories, but whose effects in such flavour models are inextricably tied. View-\ning the electroweak and flavour programmes of FCC-ee together, and in combination with high-pT and\nlow-pT HL-LHC data, is therefore crucial to understanding its full power.\n2.3.4\nHeavy Neutral Leptons\nIn its minimal version, the SM Lagrangian does not accommodate neutrino masses, but this historical\naccident can easily be overcome by minimally extending the SM. Nonzero neutrino masses offer many\ntheoretical and phenomenological opportunities to address pending questions in the understanding of\nNature.\nMassive neutrinos can oscillate in flavour space, as experimentally observed since 1998. With\nthree families, this phenomenon naturally leads to the possibility of breaking CP symmetry in the leptonic\nsector. Furthermore, fermion (or lepton) number violation might be observed. In the SM, fermion number\nconservation (FNC) stems from charge conservation for charged fermions and from angular momentum\nconservation for massless neutrinos [120]. Thus, FNC is considered to be an accidental conservation law,\nwhich has no reason to hold if neutrinos are massive. The combination of the two possibilities opens the\ndoor to shedding light on the question of the existence of matter via leptogenesis.\nWhen the FNC rule is relaxed, active neutrinos can mix with right-handed neutrinos, via Yukawa\ninteractions mediated by the Higgs field. This minimal scenario is a concrete realisation of the (type-I)\n38\n\nsee-saw mechanism (Fig. 28). The right-handed neutrinos, which do not carry electric charge, weak\nisospin, or colour, have no interaction that would distinguish the particle from the antiparticle: they are\nnaturally Majorana particles. At energies much below the Majorana mass, the mixing is described by\nan effective dimension-5 Weinberg operator that, after electroweak symmetry breaking, generates an\neffective mass for the active neutrinos. Having two mass terms for each family, the neutrinos undergo\nlevel splitting thus the \u2018see-saw\u2019, with typically light active neutrinos and heavy sterile neutrinos. Unlike\nfor other SM fermions, the Yukawa coupling is not proportional to the mass of the light neutrinos, but\ncould either be made proportional to the geometric mean of the masses of the light and heavy particles, or\nbe enhanced with a symmetry that protects the masses of the light neutrinos [121]. The resulting heavy\nmass eigenstates are called Heavy Neutral Leptons (HNLs) and are nearly sterile particles. The ensuing\nrich phenomenology includes the possible observation of LLPs, for which, in the mass range 20\u201380 GeV,\na thorough and conclusive search can be performed at FCC-ee, during the Tera-Z run.\nLL\nLL\n'\n'\n'\n'\nNR\nYN\nY \u2020\nN\nMR\nLL\nLL\nY \u2020\nNYN\nMR\nFig. 28: Schematic illustration of the type-I see-saw mechanism. Left: The left-handed lepton EW doublets LL\nhave Yukawa-like interactions YN, with the Higgs EW doublet \u03c6, mediated by the heavy right-handed neutrinos\nNR. Right: At energies below the mass MR of these heavy neutrinos, an effective fermion-number-violating\ndimension-5 operator, involving two left-handed leptons and two Higgs fields, describes the low-energy degrees of\nfreedom. After electroweak symmetry breaking, a Majorana mass is generated for the active left-handed neutrinos.\nThis mass is proportional to the square of the original Yukawa coupling, to the squared Higgs vacuum expectation\nvalue v, and to 1/MR. Heavy Neutral Leptons (HNLs), aligned with the right-handed neutrinos in the limit\nMR \u226bv, complete the spectrum.\nGeneralising beyond this minimal scenario, FCC-ee can search for HNLs in the large sample of\nZ bosons produced resonantly. The Z decay to \u03bdL + HNL followed by the decays of the heavy neutral\nlepton HNL \u2192\u2113+ W\u2217, HNL \u2192\u03bd + Z\u2217, leads to a wealth of final state signatures that can be exploited\nat FCC-ee [122]. The Z branching ratio to HNLs is proportional to the squares of the mixing angles U2\nij\nbetween the SM neutrinos and the HNL, where i, j run over the three neutrino flavours.\nThe very large number of Z boson decays allows the exploration of very low U2\nij values, for HNL\nmasses below the Z mass. The explored values may result in HNLs with a measurable path in the\ndetectors, yielding spectacular signatures with jets or leptons produced far from the interaction vertex,\nwith no SM backgrounds. In particular, for decay lengths in the detector between 1 mm and 2 m, a\ndiscovery would be possible for HNL masses up to 60\u201370 GeV down to U2 values of O(10\u221211). For\nlarger HNL masses, up to the kinematic limit of the Z mass, a prompt analysis would be needed, which,\nbecause of significant SM backgrounds, would allow discovery for U2 values of O(10\u22129).\nDetailed simulation studies were performed to verify the experimental feasibility of these analyses\nand to determine the corresponding requirements on detector design. The reach in parameter space\nwas first studied in a toy model commonly used to compare different experimental approaches, rather\nthan a complete model for neutrino masses. The model features a single Majorana HNL mixing with\na single flavour of active neutrinos. The signal samples and all of the SM decays of the Z boson, as\nwell as four-fermion processes yielding the same final state as the HNL decays, were passed through\na parametrised simulation of the IDEA detector (Chapter 6) and then analysed. Both semi-leptonic and\nfully leptonic decays of the HNL were studied, for the cases of mixing with an electron neutrino and with\n39\n\na muon neutrino. The fully leptonic decay mode provides a clean experimental final state, with a good\nreach for long-lived decays, but with a significant price in branching fraction. The semileptonic decay\nHNL \u2192\u2113\u03bdjj has a branching fraction \u223c50%, allows full kinematic reconstruction of the neutrino decay,\nand was studied both for long-lived and prompt decays. The results are shown in Fig. 29 and documented\nin Refs. [123\u2013128].\n2\n5\n10\n50\n100\nMN1 [GeV]\n10\n12\n10\n10\n10\n8\n10\n6\n10\n4\n|U N|2\nFCC-ee LLP N1\njj\nFCC-ee prompt N1\njj\nFCC-ee LLP N1\nFCC-ee theo\nLHC prompt\nLHC LLP\nSHiP\nMATHUSLA\nFASER2\nAL3X\nFig. 29: Discovery potential in the mN \u2212|U\u00b5N|2 plane. The FCC-ee potential is based on the decay channel\nHNL \u2192\u2113\u03bdjj and is shown as a red (green) line for the prompt (long-lived) analyses described in the text. The blue\nline shows the reach of a search for long-lived particles in the decay channel HNL \u2192\u00b5+\u00b5\u2212\u03bd. The dashed green\nline bounds the area where, out of 6 \u00d7 1012 Z bosons, three events are produced with visible HNL decays inside\nan FCC-ee detector, i.e., with a displacement smaller than 5 m and larger than 0.5 mm (based on the analytical\nformulas in Ref. [129]). The requirement to explain the light neutrino masses imposes a lower bound, indicated as\na pink band, on the total HNL mixing (summed over flavours). The width of this band indicates the uncertainty\nin this lower bound due to the current lack of knowledge about the absolute scale and the ordering of the light\nneutrino masses. Light neutrino oscillation data can be explained anywhere above this band, in particular in\nmodels where the neutrino masses are protected by a symmetry related to approximate lepton-number conservation.\nFurthermore, this region could also accommodate the observed matter-antimatter asymmetry via a leptogenesis\nmechanism [130]. The existing limits from LHC searches are shown as turquoise areas. The expected discovery\npotential of projected experimental searches based on long baseline experiments are shown as green areas and are\ntaken from the website accompanying Ref. [131], where all the original works are cited.\nThe conclusion of these studies is that searches at FCC-ee enable the HNL discovery over a mass\nrange beyond the reach of specialised detectors for LLP searches being developed for HL-LHC and for\nmixing values much smaller than those covered by future searches at HL-LHC, for both prompt and\nlong-lived signatures. Besides the work based on parametrised detector simulations, the model is also\nbeing studied [132] through a detailed GEANT4 simulation of the ILD detector (Chapter 6).\nThe models featuring a single HNL are useful for assessing, in a simplified way, the parameter\nspace coverage of the experiments. In order to explain the observed neutrino oscillations, however, at\nleast two HNLs are needed. A realistic model [133] featuring two Majorana neutrinos with coupling to\nall three flavours of active neutrinos was studied in the fully leptonic final state featuring two electrons\n40\n\nor muons in the final state. The patterns of couplings were chosen such as to be compatible with neutrino\noscillation data based on the benchmarks proposed in Ref. [134]. As for the single-neutrino analyses,\nthe study was performed with the parametrised simulation of the IDEA detector and featured a full back-\nground analysis. An estimate of the reach was obtained for different coupling scenarios, corresponding\nto both normal and inverted neutrino mass hierarchy.\nThe phenomenology of the \u2018Symmetry Protected Seesaw Scenario\u2019 [135,136] has been presented\nin Refs. [137, 138]. This model adds two right-chiral neutrinos, required to explain the observed light\nneutrino mass squared differences, provided with a protective lepton number-like symmetry (LNLS) to\nensure that the two heavy neutral leptons form an almost degenerate pair of pseudo-Dirac neutrinos. The\nmain phenomenological signature of this model is the production of lepton flavour violating final states,\nwith a probability that oscillates with the length of the flight path of the HNL in the detector [139]. The\nregion in parameter space where this oscillation would be detectable at FCC-ee is mapped in detail in\nthe phenomenological study documented in Ref. [140]. An experimental study was performed based\non this work, with the same parametrised detector simulation and software as the studies described\nabove [141]. For HNL masses below 35 GeV, for favourable ratios of the HNL width and of the mass\ndifference between the two pseudo-Dirac states, a striking oscillation signal would be observed, allowing\nthe measurement of the mass difference.\nA large fraction of the model parameter space consistent with the see-saw mechanism, including\nthose with symmetry-enhanced neutrino masses, such as the inverse [142] or linear [143, 144] models,\nwould be probed. For masses around 40 GeV, the FCC-ee sensitivity would reach the smallest value of\nthe mixing angle theoretically compatible with the mass range experimentally still allowed for the active\nneutrinos.\nWith HNLs (as well as with other light and feebly-coupled particles, such as ALPs), FCC-ee is\nsimultaneously a discovery and a precision tool, in a single collider. In view of the cost and time scales\nassociated with the construction of each new collider, such an advantage cannot be overstated. Indeed,\nthe number of HNLs that can be detected during the Z-pole run grows as |U\u2113N|4 if their decay length in\nthe laboratory exceeds the detector size, or as |U\u2113N|2 if it is smaller than the effective detector dimensions\nAs a direct consequence, up to a million HNL decays can be observed during the Z-pole run if |U\u2113N| is\nnear the current upper experimental limits [129]. Such a large sample opens the way for the measurement\nof several quantities, from which important information about the underlying particle physics model can\nbe extracted, as the following. i) The branching ratios of HNL decays into different SM generations can\nbe measured with per-cent accuracy [145], which allows the consistency with neutrino oscillation data\nto be checked; many parameters of the see-saw model to be constrained [146] (including CP-violating\nphases and the absolute neutrino mass scale); the leptogenesis hypothesis [145] to be tested; and underly-\ning flavour and CP symmetries [147] to be probed. ii) The number of HNL events and the measurement\nof the HNL lifetime can reveal information about the violation of lepton number [126, 129] as well as\nunderlying flavour and CP symmetries [147]. iii) Finally, the angular distribution and the energy spec-\ntrum of the HNL decay products can provide information regarding the lepton number violation [148]\nand the HNL mass splitting [139\u2013141].\nThe combination of these observables may provide important information about the HNL role\nin particle physics and cosmology, in particular in the context of neutrino masses and leptogenesis. It\ncan also shed light on the properties of the underlying particle-physics theory within which the see-saw\nmodel is embedded (such as flavour and CP symmetries).\n2.3.5\nDark matter and dark sectors\nUnderstanding the origin / nature of dark matter (DM) is a central question in contemporary physics, con-\nnecting particle physics and astrophysics. Despite decades of searches across experiments, the favoured\nDM candidates, the WIMPs, have not been found, and the lower bounds on their masses are progressively\npushed beyond the reach of TeV-class e+e\u2212colliders.\n41\n\nMono-photon searches at FCC-ee can play a significant role in probing the so far unexplored\nparameter range allowed by the WIMP relic density constraints [149]. In particular, predictive models\nof leptophilic candidates with a thermal origin can be tested. Missing energy signatures at FCC-ee can\nprobe much of the parameter space for which DM direct annihilation into a dilepton yields the observed\nrelic density in Higgs-like models with mass-proportional couplings to charged leptons [150]. Models\nof asymmetric dark matter can also be probed at FCC-ee, with a sensitivity to DM-lepton interactions\nimproved by almost an order of magnitude [151]. Additionally, it would be possible to detect spin 0, 1,\nand 1/2 DM at FCC-ee in the context of simple, consistent, and renormalisable field theories that provide\nthe correct DM abundance and satisfy direct detection, indirect detection, and collider constraints [152].\nHidden sectors, consisting of new, invisible particles that interact almost imperceptibly with the\nSM, are rapidly gaining attention as they could hold the answer, not only to the dark matter problem\nbut also to a variety of other open questions in the field. The dark sector could contain a multitude of\nhidden particles. After all, the visible sector is non-minimal, so there is no good reason why the dark\nsector should contain only one type of dark matter particle and nothing else. Benefiting from a clean\nenvironment, high luminosity, and large acceptance, FCC-ee can directly scrutinise the O(1\u2013100) GeV\nmass range for so-far unknown particles, with interactions that would otherwise have been too feeble to\ndetect.\nDark sectors typically exhibit a stable particle, fundamental or composite, that could be a DM\ncandidate, and one or more mediator particles coupled to the SM via a neutral portal. The spin of the\nmediator particle defines the portal: vector, e.g., dark photon; scalar or pseudoscalar, e.g., Higgs portal; or\nfermion, e.g., sterile neutrino. These well-motivated dark sectors can be thoroughly explored at FCC-ee\nin a mass-coupling range that is inaccessible by any other means with the same sensitivity. Furthermore,\nsmall couplings of dark sector particles to SM particles could give rise to LLPs and other unconventional\ncollider signatures, such as dark showers.\nDark photons may mix kinetically with the SM hypercharge gauge boson. This possibility can be\nstudied in e+e\u2212\u2192A\u2032\u03b3 production, where the dark photon A\u2032 decays to \u00b5+\u00b5\u2212. The sensitivity to small\ncoupling values could be significant, reaching around \u223c2 \u00d7 10\u22124 for mA\u2032 ranging from 10 to 80 GeV at\nFCC-ee [153]. Alternatively, dark photons or dark Z\u2032 bosons can also be investigated via e+e\u2212\u2192A\u2032H\nor Z\u2032H production at the WW threshold or above [154].\nFinally, the associated production of a neutrino and a dark sector fermion can also be searched\nfor at FCC-ee in mono-photon signatures [155]. This kind of search has sensitivity up to mass values in\nexcess of 1 TeV. Other searches, such as invisible decays of a dark Higgs boson [156] or Z boson decays\nto an invisible dark photon [157] can also be exploited.\n2.3.6\nAxion-like particles\nAxion-like particles (ALPs) are generically expected in many BSM extensions, most famously in QCD\naxion models originally introduced to tackle the strong CP problem [158]. In these models, ALPs can\nbe heavier than the QCD axion and serve as mediators to the dark sector. Astrophysical and beam-dump\nexperiments constrain the ALP-photon coupling at low masses, but are less stringent in the 0.1\u2013100 GeV\nrange [121,159], potentially accessible at FCC-ee via e+e\u2212\u2192a\u03b3 [158] and e+e\u2212\n\u03b3\u03b3\n\u2212\u2192(e+e\u2212)a [160],\nwith the ALP a decaying as a \u2192\u03b3\u03b3. Various aspects of the ALP phenomenology at FCC-ee are ad-\ndressed in Refs. [161\u2013164]\nThe FCC-ee sensitivity to the e+e\u2212\u2192a\u03b3 channel was studied in Ref. [165] with the parametrised\nsimulation of the IDEA detector. Two final states were addressed: the \u2018prompt\u2019 case, where the ALP\ndecays near the interaction vertex, and the \u2018monojet\u2019 case, where the ALP decays outside the detec-\ntor, yielding the signature of a monochromatic photon recoiling against missing energy and mass. For\nboth channels, a full kinematic analysis was developed to separate the signal from irreducible SM back-\ngrounds.\n42\n\nSensitivity to photon couplings down to < 10\u22123 TeV\u22121 can be obtained at FCC-ee in the ma range\nfrom 0.1 to 100 GeV, extending current limits by more than two orders of magnitude in the Tera-Z run.\nIn particular, the \u2018monophoton\u2019 signature would cover a difficult region in the vicinity of 1 GeV, which\nis not accessible to beam dump experiments. In an intermediate region in mass and at small coupling\nvalues, the ALP lifetime is large enough to give rise to measurable paths inside the detector, providing\nLLP signatures that could be accessible by exploiting the pointing capabilities of the calorimeters.\nThe ALP coupling to Z and Higgs bosons can also be probed via e+e\u2212\u2192Za or Ha, with visible\nZ boson decays or H \u2192bb, and either a \u2192\u03b3\u03b3 or a \u2192\u2113+\u2113\u2212. Decays to SM particles other than photons\nare less constrained and provide an additional opportunity for ALP discovery at FCC-ee. A preliminary\nstudy of the sensitivity of FCC-ee to ALPs decaying into two gluons is presented in Ref. [166].\nThe projected sensitivity of the ALP search is illustrated in Fig. 30, where the importance of FCC-\nee is conspicuous in probing ALPs coupling to photons with a lifetime below cosmological/astrophysical\nscales, i.e., with a mass above 1 MeV.\nFig. 30: Projected sensitivity for ALPs in the photon coupling vs. ALP mass plane from the three following\nprocesses at FCC-ee: e+e\u2212\u2192\u03b3a \u21923\u03b3 (yellow area), photon-fusion \u03b3\u03b3 \u2192a \u21922\u03b3 (salmon area) [160], and\ne+e\u2212\u2192\u03b3a \u2192\u03b3 + INV (orange area). Existing limits (in grey) are adapted from Refs. [121, 131]. Also shown\nare projected exclusion limits at 95% C.L. on the ALP-photon coupling as a function of the ALP mass expected\nfrom searches for \u03b3\u03b3 \u2192a \u2192\u03b3\u03b3 in pp (violet), pPb (dark pink), and PbPb (orange) collisions at FCC-hh [167].\n2.3.7\nExotic decays of the Higgs and Z bosons\nThe large Higgs boson event sample at FCC-ee allows a direct search for exotic decays of the Higgs\nboson. Exotic decays are predicted by a variety of BSM theories [168\u2013171], including extended scalar\nsectors, SUSY, and dark sector models with Higgs or vector portals. Higgs branching ratios up to four\n43\n\norders of magnitude lower than the expected HL-LHC reach will be probed at FCC-ee, giving access to\nentirely new channels [172].\nSubstantial work in preparing searches for Higgs boson decays into long-lived particles (LLPs)\nis ongoing, focusing on signatures with displaced vertices [173]. The results suggest that FCC-ee is\nsensitive to long-lived scalars with decay lengths of order 1 mm to 10 m, with the peak sensitivity for\ndecay lengths around 0.3 m, as shown in Fig. 31. Additional studies, comparing different detector setups\nfor exotic Higgs decays, have also been initiated [174].\nmX=10 GeV\nmX=50 GeV\n10-5\n0.001\n0.100\n10\n5\u00d710-5\n1\u00d710-4\n5\u00d710-4\n0.001\n0.005\nDecay Length (m)\n95% BR(h\uf522XX) Limit\nFig. 31: Estimate of the sensitivity to LLPs in exotic Higgs portal decays; adapted from Ref. [171]. Solid (dashed)\nlines correspond to dedicated light (heavy) LLP search strategies.\nSearches for exotic Z decays to LLPs can also be carried out at FCC-ee during the Z pole run. In\nmodels of R-parity-violating supersymmetry, studied in Ref. [175], the FCC-ee sensitivity to long-lived\nlight neutralinos in Z decays exceeds that of hadron colliders or of future dedicated LLP experiments by\nthree orders of magnitude. Comparable gains in sensitivity can be obtained in other searches, such as Z\ndecays into hidden mesons [176].\nThe available parameter space of new SM-neutral vector bosons (Z\u2032) that couple exclusively to\nleptons could be significantly extended, offering the best performance of all future collider projects in\nthe kinematically allowed mass range (from 5 to 360 GeV) [177].\nIn brief, by taking full advantage of the large Tera-Z event samples, the dark sector programme at\nFCC-ee extends the intensity-frontier discovery potential significantly. It provides access to very-weakly-\ninteracting dark-sector particles with couplings so small that they are usually considered typical of beam-\ndump experiments, but in a mass range wholly inaccessible to any other intensity-frontier experiment.\nGiven that there is no preferred mass range for such states, this mass-range extension by more than two\norders of magnitude provides unique scientific opportunities in particle physics.\n2.3.8\nOther new physics searches\nOther possible studies at FCC-ee include, for example, searches for lepton-flavour violation (LFV) in\ndifferent manners [178\u2013183], compositeness [103], leptoquarks [184], new scalars [185], and more. In\nthis instance, the production of hidden-valley light quarks would perturb the QCD cascade, generating\ncorrelations among the final state particles that are absent in the SM. A detailed experimental study is in\nprogress.\n44\n\n2.3.9\nComplementarity and synergy between FCC-ee and FCC-hh\nThe FCC-hh will complement and substantially extend the FCC-ee physics reach in nearly all possible\ndirections. The seven-fold centre-of-mass energy increase with respect to LHC enhances the potential\nfor observing new particles at mass scales up to 40 TeV, as shown in Fig. 32. Indirectly, it will be\nsensitive to energies well above its kinematic reach of 100 TeV, for example in the tails of Drell\u2013Yan\ndistributions. Should any deviations from SM expectations be observed at FCC-ee, FCC-hh has the\npotential to pinpoint its microscopic origin. Some specific synergies between FCC-ee and FCC-hh in\nthis regard are highlighted in the next paragraphs.\nFig. 32: Summary of the 5 \u03c3 discovery reach, as a function of the resonance mass, for different FCC-hh luminosity\nscenarios. From Ref. [186].\nAs already alluded to in Section 2.2, there are many synergies between FCC-ee and FCC-hh that\ncome together to make the integrated FCC physics programme more than the sum of its parts. For ex-\nample, the absolute determinations of Higgs couplings and its total width at FCC-ee is necessary to fully\nexploit the potential of FCC-hh that is only able to measure relative coupling ratios. The clean environ-\nment of FCC-ee enables the precise determination of SM parameters necessary to reduce uncertainties\nfor FCC-hh. Moreover, certain types of BSM physics can only be accessed by FCC-ee and not FCC-hh,\nand vice versa. For instance, the nature of the electroweak phase transition will be probed by the precise\nmeasurement of the Higgs self-coupling and the search for additional Higgs partners at FCC-hh, together\nwith potential deviations in the Higgs couplings at FCC-ee.\nMore concretely, if a deviation in \u03baZ were observed at the level of 0.5%, this hint would be less\nthan half of one sigma at HL-LHC (with some unavoidable assumptions), but would correspond to an\nunambiguous 5 \u03c3 discovery at FCC-ee. In Ref. [187], it was shown that for a BSM modification of this\ncoupling new physics would have to show up at an energy scale of\nEMax \u2243\n1.1TeV\np\n|\u03baZ \u22121|\n.\n(1)\nThus, a deviation of 5 \u03c3 at FCC-ee would correspond to an energy scale of 15 TeV, essentially guaran-\nteeing that FCC-hh would be able to discover the heavy states ultimately responsible for the low energy\nHiggs coupling deviation, illustrating a compelling, dynamic, interplay between FCC-ee and FCC-hh.\n45\n\nThis synergy also extends to astrophysics and cosmology. Beyond-the-Standard-Model physics\nleading to a phase transition of some new sector, anywhere from the electroweak to the TeV scale, could\nyield gravitational wave signatures accessible to the next-generation gravitational wave observatories,\nsuch as LISA, the origin of which could then potentially be directly accessed at FCC-hh [90]. The\ndetection of high-energy gamma rays in astrophysical observatories such as CTA [188] may be due to a\nTeV-scale WIMP, but with a large degree of uncertainty inherent to such indirect observation methods.\nThe FCC-hh will be directly sensitive to the entire upper mass range, of around 1 and 3 TeV for triplet\nand doublet thermal WIMP dark matter, respectively [10], far beyond the reach of any conventional dark\nmatter direct detection experiment, as illustrated in Fig. 33. Cosmic-ray physics will furthermore benefit\nfrom hadron collision data at unprecedented energy and luminosity.\nFig. 33: The projected sensitivity of searches for a WIMP triplet DM candidate in final states with disappearing\ntracks at FCC-hh [10]. Adapted from Ref. [189].\nThe multiplicity of partons in the proton makes FCC-hh the most versatile high-energy parton\ncollider for the broadest possible exploration of elementary particle processes. Similarly to LHC, its\ncapabilities may be augmented by hosting complementary detectors for neutrino physics, dark sectors,\nand long-lived particles that may otherwise escape undetected. Together, FCC-ee and FCC-hh can truly\nenter the tens of TeV scale, indirectly and directly, to fully explore the open questions that LHC has only\nbegun to touch upon.\n2.4\nSelected topics in flavour physics\nThe peculiar structure of quark and lepton masses, as well as the quark mixing angles, is ad hoc within\nthe SM and is likely the low-energy imprint of some new dynamics. This structure implies approxi-\nmate flavour symmetries that give rise to the strong suppression of a series of flavour-changing processes\nwithin the SM, whose precise experimental study allows probing dynamics at scales well above the elec-\ntroweak scale. It is necessary to push the precision flavour frontier further and the FCC-ee programme\n46\n\noffers unique opportunities in this respect. Despite the fact that many tests in this sector have been per-\nformed in the recent past, without reporting significant deviations from the SM, the discovery potential\nremains high.\nOne class of unique opportunities concerns b-hadron and \u03c4 decays, and, in particular, b \u2192\u03c4\ntransitions. These processes directly test models where new physics is coupled mainly to the third gen-\neration \u2014 a general feature of many explicit BSM scenarios. Moreover, the class of models that can\nbe tested indirectly via such studies is also the one less constrained by direct searches (given the sup-\npressed couplings to light quarks). Here, the FCC-ee programme offers a particularly large margin of\nimprovement over the accuracy expected from currently approved flavour physics experiments, both at\nHL-LHC and at lower-energy e+e\u2212colliders (in particular Belle II at Super KEKB). The key features of\nthe flavour-physics programme during the Z-pole run at FCC-ee can be summarised as follows.\n\u2013 Clean environment (as in B-factories), with momentum and tagging efficiency of the pair-produced\nb\u2019s, c\u2019s, and \u03c4\u2019s from Z decays, with \u223c10 times more bb and cc pairs than the total collected by\nBelle II (Table 6).\n\u2013 Boosted b\u2019s and \u03c4\u2019s, leading to a significantly higher efficiency (compared to B-factories) for\nmodes with missing energy (especially multiple-\u03bd modes) and inclusive modes, as well as smaller\nuncertainties in lepton ID efficiencies.\nTable 6: Yields of heavy-flavoured particles produced at FCC-ee for 6 \u00d7 1012 Z decays [190].\nParticle species\nB0\nB+\nB0\ns\n\u039bb\nB+\nc\ncc\n\u03c4\u2212\u03c4+\nYield (\u00d7109)\n370\n370\n90\n80\n2\n720\n200\nThese features lead to to the identification of the following class of observables as particularly\npromising: i) neutral-current rare b- and c-hadron decays with \u03c4+\u03c4\u2212and \u03bd\u03bd pairs in the final state;\nii) charged-current b-hadron decays with a \u03c4\u03bd pair in the final state; iii) CP-violating observables in b-\nand c-hadron decays involving neutral particles in the final states (\u03c00, KS, \u03b3, ...); iv) lepton flavour\nviolating \u03c4 decays; v) precision tests of lepton universality in \u03c4 decays.\nIn addition to these classical flavour studies via low-energy probes, a truly unique opportunity of-\nfered by FCC-ee is the possibility of determining flavour parameters from W decays, as well as searching\nfor flavour-violating decays of Z and Higgs bosons. Within the SM, these processes are possibly too rare\nto be detected, but their search is an effective way to constrain or discover BSM dynamics. Some further\nideas uniquely relevant to the FCC-ee flavour programme are discussed in Refs. [190\u2013192]\nThe wide-ranging FCC-ee flavour physics programme cannot be easily summarised in a few pages.\nThe most interesting classes of observables are listed below, together with a discussion of a few examples\nthat illustrate the physics reach and the diversity of this programme.\n2.4.1\nLepton universality tests in \u03c4 decays\nThe major improvement expected at FCC-ee in the precision of measurements of the leptonic \u03c4 decay\nbranching fraction, the \u03c4 mass, m\u03c4, and the \u03c4 lifetime, \u03c4\u03c4, corresponds to a jump of more than one\norder of magnitude (from 10\u22123 to 10\u22124) in tests of universality between third-generation and light lep-\ntons [193,194]. An illustration of the FCC-ee reach on these measurements is shown in the left panel of\nFig. 34 [195]. With this level of precision, models addressing the hint of non-universality observed in\nb \u2192c\u03c4\u03bd decays [196] could either be unambiguously confirmed, leading to a major discovery, or ruled\nout. Theoretical work (on electroweak and radiative corrections), achievable with present knowledge but\nnot yet available, is needed to reduce the theoretical systematic uncertainties on these measurements well\nbelow the projected experimental systematic uncertainties.\n47\n\nFig. 34: Left: Direct measurements of B(\u03c4 \u2192\u2113\u03bd\u03bd) branching fraction and \u03c4 lifetime (ellipse) compared to the SM\nprediction (band); the width of the SM band is determined by the \u03c4 mass uncertainty. From Ref. [195]. Right: FCC-\nee impact in constraining, at 95% CL, the coefficients of representative dimension-six LFV operators normalised\nto the 1 TeV scale. Adapted from Ref. [197], scaled to the baseline FCC-ee luminosities.\n2.4.2\nLepton flavour violating \u03c4 decays\nSearches for LFV \u03c4 decays are null tests of the SM and, thus, are pristine targets for indirect NP searches.\nA variety of explicit models, predicting rates not far from current exclusion bounds, exist in the litera-\nture [197\u2013199], and FCC-ee will offer the ultimate experimental sensitivity on virtually all \u03c4 LFV decay\nmodes [194,200,201]. For example, the 90% CL projected limit on B(\u03c4 \u21923\u00b5) would be 2 \u00d7 10\u221211 in\nabsence of signal [195], which is three orders of magnitude below the current limit (2.1\u00d710\u22128 [35]) and\nmore than an order of magnitude better than the final Belle II projection (with 50 ab\u22121). The impact of\nsuch bounds is illustrated in the right panel of Fig. 34.\n2.4.3\nRare b-hadron decays with \u03c4+\u03c4\u2212pairs in the final state\nIn all these processes, there is an unexplored gap of about three orders of magnitude between SM predic-\ntions [202\u2013204] and experimental data [205,206] \u2014 a gap that represents a wide unexplored parameter\nrange of motivated new-physics models [207\u2013209]. At the SM predicted rates, FCC-ee is expected to be\nable to measure these decays, in particular B0 \u2192K\u22170\u03c4+\u03c4\u2212[210,211].\n2.4.4\nCharged-current b-hadron decays with a \u03c4\u03bd pair in the final state\nThe persisting anomalies in exclusive b \u2192c\u03c4\u03bd decays [212] give a strong phenomenological motiva-\ntion for deeper studies of these processes [181, 213\u2013215]. A unique opportunity offered by the FCC-ee\nprogramme would be the experimental access to the clean inclusive [216, 217] and leptonic [218, 219]\nmodes, as well as the suppressed b \u2192u transitions [220, 221]. For example, the measurement of the\nB \u2192\u03c4\u03bd branching ratio at FCC-ee [222] is expected to yield ultimate precision on |Vub|, with an esti-\nmated relative uncertainty of only 1%, which is a factor of three below current best estimates [212] and\nmore than a factor of two below the projected precision from the B \u2192\u03c4\u03bd measurement at Belle II [223].\n2.4.5\nRare b- and c-hadron decays to di-neutrino final states\nA recent sensitivity study [224] has shown that the branching ratios of the rare B0 \u2192K\u22170\u03bd\u03bd, B0 \u2192\nK0\nS\u03bd\u03bd, Bs \u2192K0\nS\u03bd\u03bd, and \u039b0\nb \u2192\u039b\u03bd\u03bd decays could be determined at FCC-ee with precisions of 0.53%,\n1.20%, 3.37%, and 9.86%, respectively, relative to the current SM estimates [225]. In particular, the\n48\n\nprecision on the B decay modes would exceed that expected from Belle II by an order of magnitude,\nwhile the Bs and \u039b0\nb modes, accessible at FCC-ee, would uniquely constrain possible new physics in\nb \u2192s\u03bd\u03bd transitions, as illustrated in the left panel of Fig. 35.\n\u221212\n\u221211\n\u221210\n\u22129\n\u22128\n\u22127\n\u22126\n\u22125\n\u22124\nCL\n\u22123\n\u22122\n\u22121\n0\n1\n2\n3\nCR\nEOS v1.0.10\nNZ = 6 \u00d7 1012\nSM\nB(B \u2192K\u03bd\u00af\u03bd) 2023\nB(B \u2192K\u03bd\u00af\u03bd)\nB(B \u2192K\u2217\u03bd\u00af\u03bd)\nB(Bs \u2192\u03c6\u03bd\u00af\u03bd)\nB(\u039bb \u2192\u039b\u03bd\u00af\u03bd)\n0\n10\u22123\n10\u22122\nyuc\n\u221210\u22124\n\u221210\u22123\n\u221210\u22122\n0\n10\u22124\n10\u22123\n10\u22122\nycu\nBh\u2192cu = 2.5 \u00d7 10\u22123\nBh\u2192cu = 2.9 \u00d7 10\u22123\nBh\u2192cu = 16%\nD \u2212\u00afD mixing\nFig. 35: Left: Comparison between the current constraint on the relevant effective b \u2192s\u03bd\u03bd transition operator\ncoefficients (CL,R) due to existing measurements [226] (cyan band) and the (systematic-error dominated) sensi-\ntivities predicted at FCC-ee (blue, orange, green, and red bands) [224]. The projected regions denote the 68%\nprobability of the marginal posterior density, assuming that all observables are SM-like. The Wilson coefficients\nare normalised to an effective scale of 6.5 TeV, up to the CKM factors Vts \u00d7 Vtb [224]. Right: Current (from D-D\nmixing) and projected (from FCC-ee searches for h \u2192cu) limits on effective charm-up flavour-changing Yukawa\ncouplings of the Higgs boson [183]. The 68%, 95%, and 99.7% CL regions allowed by D-D mixing data are\ndepicted from darker to lighter red.\nFurthermore, the large number of expected events could uniquely allow more detailed differential\nstudies of decay kinematics beyond simple branching ratios. Such measurements can also efficiently\nprobe possible BSM effects in terms of the production of light invisible particles in the final state, mim-\nicking the missing energy signature of the neutrino pair in the SM [227].\nIn the charm sector, processes mediated by the c \u2192u\u03bd\u03bd transition are unique probes of up-quark\nFCNCs because they do not receive long-distance QCD contributions plaguing related non-leptonic or\nrare semileptonic decays [228]. In addition, SM gauge invariance and approximate U(2) flavour sym-\nmetry relate these quark-flavour-changing processes to rare (semi)leptonic kaon decays [229\u2013231], thus\nmaking them crucial in (over)constraining BSM effects in FCNCs involving the first two quark genera-\ntions. Finally, the light dark sector coupling to c \u2192u quark currents [232,233] can be probed with the\nmissing energy signature, similar to the b \u2192s transition in the b-quark sector. Currently, the only exper-\niment probing these processes is BES III, which set the first upper limit, B(D0 \u2192\u03c00\u03bd\u03bd) < 2.1 \u00d7 10\u22124\nat 90% CL [234]. Based on na\u00efve luminosity scaling, this bound could be improved by more than two\norders of magnitude at FCC-ee and would thus make it relevant to probe flavour U(2) invariant BSM\nscenarios [231].\n2.4.6\nRare decays and CPV studies with neutrals\nThe discovery of CP violation in singly Cabibbo-suppressed D decays by LHCb [235] opened a new\nand largely unexplored venue for CPV studies. One of the outstanding puzzles is to understand whether\nthe observed size of CPV is due to SM effects enhanced by long distance QCD dynamics, or a possible\nsignal of NP [236,237]. Recent phenomenological studies using isospin [238,239] and U-spin [240,241]\nexpansions have shown that the measurements of decay rates and CP asymmetries in related D and Ds\ndecays to final states involving \u03c00 and K0\nS, which are not possible at LHCb but would be accessible\n49\n\nat FCC-ee, could yield a definite answer. Important representative studies also include CP violation in\nradiative singly Cabibbo suppressed modes [242\u2013244] and the doubly-radiative decay D0 \u2192\u03b3\u03b3 required\nfor the SM prediction of D0 \u2192\u00b5+\u00b5\u2212[245].\nIn the B sector, rates and CP asymmetries of rare radiative decays, mediated by the b \u2192s\u03b3\ntransition, such as B \u2192K\u2217\u03b3 and B \u2192Xs\u03b3, are most-sensitive probes of quark flavour violating dipole\ntransitions [246] in both minimally violating and U(2) flavour models; they are also crucial probes\nof flavour dynamics in composite Higgs models [247]. Improvements in the understanding of these\ndecays [248,249] are needed to fully leverage the prospective sizes of the FCC-ee event samples [250].\nRecent steps in this direction are documented in Refs. [251, 252]. Finally, time-dependent studies of\nrare decays, such as Bs \u2192\u00b5+\u00b5\u2212[253, 254], B \u2192KS\u2113+\u2113\u2212[255, 256], Bs \u2192\u03d5\u00b5+\u00b5\u2212[257], and\nB \u2192KS\u03bd\u03bd [258], offer novel and complementary probes of CP violation beyond the SM, some only\naccessible at FCC-ee.\n2.4.7\nOn-shell Z, W , and Higgs flavour-changing decays\nFlavour-changing decays offer unique novel probes of SM and BSM flavour dynamics and can be\nsearched for in inclusive final states (profiting from the unparalleled jet-flavour tagging capabilities of\nthe detectors) or in exclusive final states [259]. In particular, W \u2192bc decays could yield the ulti-\nmate precision on |Vcb|, with a relative uncertainty well below 1% [260,261]. Similarly, rare four-body\nZ decays could uniquely determine individual flavour neutrino couplings [262]. Furthermore, lepton-\nflavour-violating Higgs and Z decays involving \u03c4 leptons in the final state would improve existing LEP\nand LHC constraints by orders of magnitude [51, 263, 264]. Finally, FCC-ee could also directly probe\nFCNC decays of Z and Higgs bosons [183], possibly even reaching SM expectations for the former (in\nthe case of Z \u2192bs) and surpassing indirect constraints from neutral meson oscillation measurements for\nthe latter, as shown in the right panel of Fig. 35. Such direct measurements are also particularly important\nto lift degeneracies in BSM fits and disentangle possible UV sources of low energy FCNC effects [265].\n2.4.8\nCombined studies and synergy between the flavour and EW programmes\nBesides the interest of the specific observables illustrated above, probably the most interesting aspect\nof the FCC flavour programme lies in the possibility of combining several precision flavour-violating\nand flavour-conserving measurements. This combination offers a unique opportunity to characterise a\npossible NP signal, when it emerges, as illustrated in the next two paragraphs.\nNew-physics in B-B mixing\nMeasurements of \u03d5s from Bs \u2192J/\u03c8 \u03c6 and Bs \u2192\u03c6\u03c6 at FCC-ee could challenge present theory uncer-\ntainties [266,267]. Similarly, the full exploitation of experimental precision on \u2206ms will hinge upon the\ndetermination of |Vcb| at or below the sub-per-cent level [268,269] from either (inclusive) semileptonic\nB decays, leptonic Bc decays [218,219], or on-shell W+ \u2192bc decays [260,261]. As an illustration of\nthe increased sensitivity achieved by combining all these measurements, the NP reach in the Bs,d mixing\namplitudes is shown in Fig. 36. Mainly due to the increased precision on |Vcb|, the effective NP scale\nsensitivity would increase by a factor of three compared to current measurements and by a factor of 1.5\ncompared to the ultimate precision expected at Belle II. It is worth stressing that FCC-ee will also deliver\nthe ultimate determination of the CKM-matrix \u03b3 angle from B \u2192DK decays [270], allowing a per-mil\ntest of CKM unitarity in the b \u2192s triangle [271\u2013273] (one order of magnitude better than the current\nsensitivity), as well as the possibility to test the SM predictions for mixing-induced semileptonic CP\nasymmetries in both Bd and Bs decays [274\u2013276].\n50\n\nd\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\ns\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\np-value\nexcluded area has CL > 0.95\nCurrent\nCKM\nf i t t e r\nd\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\ns\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\np-value\nexcluded area has CL > 0.95\nPhase I\nCKM\nf i t t e r\nd\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\ns\nh\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\np-value\nexcluded area has CL > 0.95\nPhase III\nCKM\nf i t t e r\nFig. 36: Sensitivities to relative BSM amplitudes (hd and hs) in Bd and Bs mixings: current values (left), LHCb\n(50 fb\u22121) and Belle II (50 fb\u22121) projections (centre), and FCC-ee projections (right). From Ref. [269]. A limiting\nfactor of the FCC-ee sensitivity is the uncertainty on Vcb, expected to be reduced with the WW threshold run and\nfrom improved flavour-tagging algorithms.\nSynergy with the EW programme\nA particularly interesting synergy emerges when combining flavour-violating and EW observables. The\ndiscovery potential offered by this combination in a variety of NP models has only recently begun to be\nexplored [102,277,278]. An illustration of this potential is presented in Fig. 37 in the context of models\ndescribing generic NP coupled mainly to the third generation, as defined in Ref. [102].\nFig. 37: Constraints on semileptonic effective operators describing new physics coupled mainly to the third gen-\neration with minimal U(2) breaking [102]. The grey regions show the result of the current fit (68%, 95%, and\n98% CL), including flavour, electroweak, and Drell\u2013Yan data (the slight tension with the SM is driven by b \u2192c\u03c4\u03bd\ndata). The small ellipses are the result of an hypothetical fit with FCC-ee projected uncertainties on flavour and\nelectroweak observables, assuming a signal compatible with current data. The coloured bands are the individual\nconstraints of the observables in this scenario. The FCC constraints follow from the projections of a precision\nof 3%, 1.6%, 0.01%, and 20% on the B(B \u2192K\u03bd\u03bd), B(Bc \u2192\u03c4\u03bd), B(\u03c4 \u2192\u00b5\u03bd\u03bd), and B(B \u2192K\u03c4+\u03c4\u2212) values,\nrespectively. From Ref. [279].\nAs can be seen in this case, different observables probe the same parameter space in different\ndirections, and their combination is essential to fully characterise the hypothetical NP framework, with,\nin particular, the synergy between rare B decays, rare \u03c4 decays, and the flavour-conserving effective\ncouplings of the Z boson.\n51\n\n2.5\nFCC-hh specificities compared to high-energy lepton colliders\nWith operation expected to start in the mid-2040\u2019s, the guaranteed deliverables and primary targets of\nFCC-ee are the precise and model-independent measurement of a broad range of key couplings of the\nHiggs boson, a fifty- to thousand-fold improvement in the precision of EW parameters, and a precise\ndetermination of the top quark mass and EW couplings. A 3 TeV muon collider has also been proposed,\nfor a timescale similar to that of FCC-ee [280]. The best-measured Higgs couplings, \u03baZ and \u03baW, will\nbe measured at FCC-ee with expected uncertainties of 0.11% and 0.29%, respectively (Table 3), much\nbetter than the 0.9% and 0.4% uncertainties foreseen at a 3 TeV muon collider [281]. This observation,\ncombined with the Tera-Z programme and the 106 top pairs at FCC-ee, as compared to orders of mag-\nnitude fewer at a 3 TeV muon collider, renders FCC-ee the obvious priority for Higgs, electroweak, top,\nand flavour physics to follow HL-LHC. This section considers the question of what should follow FCC-\nee as a high-energy exploration facility, comparing and contrasting frontier (\u227310\u2019s TeV) lepton collider\noptions with FCC-hh.\n2.5.1\nGeneralities\nExploration in particle physics cannot be quantified by the volume of parameter space explored, nor by\nthe scale of the energy reached. Indeed, LHC has shown that the microscopic world that can be explored\nby hadron colliders is so multidimensional and rich that no metric can fairly convey the depth with which\nthe laws of nature are explored by colliding protons. Yet, looking to future high-energy facilities, this is\nprecisely what must be attempted.\nThe core attribute of a proton collider is that it does not simply collide a single particle and an\nantiparticle but, instead, collides anything found in the proton; any of the lightest five quarks and an-\ntiquarks, the gluons, the photon, and the EW gauge bosons. Thus, a proton collider has many particle\ncolliders in one, operating at the highest plausibly achievable energies, with an array of production chan-\nnels for discovery and exploration that is factorially greater than what can be achieved by colliding single\nfundamental particles \u2014 besides the additional possibility of colliding heavy ion in the same machine.\nThe price to be paid for this great leap in exploratory power is the inherent messiness of the final state\nfrom colliding composite objects. However, this challenge has been amply met at LHC and there is no\nreason to expect something else at a future proton collider.\nWere some hints for new physics at high energies to appear in the Run 3 of LHC or at HL-LHC, it\nis highly unlikely that identification of the microscopic production channel from which it emerged would\nbe possible at HL-LHC. Depending on the new physics at stake, the FCC-ee precision data may exhibit\ninteresting patterns of deviations that would refine the interpretation of these hints and give precious\ninformation about their quantum origin. At high energy, however, the only way to guarantee further\nexploration and characterisation of whatever may arise at LHC would be to collide protons once again,\nwith greater energy and larger collected event samples, possibly activating additional production channels\nand dynamical regimes: this is the only way to cover all possible production channels.\nAlso, it is worth noting that the discovery of the Higgs boson opened windows beyond the gauge\nparadigm to a new class of fundamental forces and to the flavour puzzle. Modern particle physics ex-\nploration should be equipped to navigate this new world. The case, for example, of a new neutral scalar\ncoupled to fermions with a strength proportional to their mass is enlightening. Clearly, the third gen-\neration quarks provide the most immediate access to such a sector, whether through production by bb\nannihilation or through gluon fusion via a top quark loop. This is, after all, how the Higgs boson was\ndiscovered. Such scenarios should not be blind spots for any future facility and, indeed, a future proton\ncollider would provide excellent discovery opportunities for states that do not carry electroweak charges.\nSome more concrete, yet still general, future discovery possibilities are considered below.\n52\n\n2.5.2\nResonance searches\nA key exploratory task for any high-energy exploration facility is to search thoroughly for new high-mass\nresonances. There are two complementary approaches to probe the existence of high-mass states: the\ndirect search for a mass peak and the indirect evidence emerging from deviations in precise measure-\nments of processes accurately predicted within the SM. The indirect approach extends the sensitivity\nof a collider well beyond its kinematic reach. As clearly shown by LEP2, the superior precision of a\nlepton collider can therefore match the sensitivity of direct searches at hadron colliders of much higher\ncentre-of-mass energies. The limitation of the indirect approach, however, is that the interpretation of\nsuch deviations is very much dependent on model assumptions. For example, the new state masses can\nvary significantly as a function of the assumptions on their couplings. Outside a well-defined theoretical\nBSM framework, for which there is no compelling prejudice today, this ambiguity significantly limits\nthe ability to point to new measurements that would clarify the source of new physics. Direct search,\nwhen possible, therefore provides a preferable (yet synergistic) approach, when the indirect and direct\nsensitivity of lepton and hadron colliders are numerically comparable.\nFor this reason, the focus here is on the comparison of FCC-hh and high-energy lepton colliders\nto the case of direct detection. Present theory priors do not favour any particular possibility, thus the\nbreadth of couplings that can be explored is a paramount consideration in planning for the future. For\nthis purpose, a proton collider has a further unique virtue, sampling a wide array of initial states, from\ngluons to photons or EW gauge bosons and quarks of a variety of flavours, and from neutral initial\nstates to charged or even coloured, any of which could lead to the formation of a new resonance. For\nexample, 15 qq(\u2032) initial states can create exotic bosonic resonances, both in flavour-conserving and\nflavour-violating channels. Besides, 20 V+q initial states could create excited quark states (with V = \u03b3,\ng), or new heavy quarks through charged (V = W) or neutral (V = Z) current transitions. Furthermore,\n8 VV\u2032 initial states can give rise to EW resonances or axion-like particles (V, V\u2032 = \u03b3, W, Z), or to gg\nresonances.\nAnother key component of exploration combines breadth with energy. As a figure of merit, pro-\nton colliders can be compared with lepton colliders to assess their relative reach in energy for reso-\nnances. Following Ref. [282], an optimistic scenario is considered, where a new high-energy resonance\n(serendipitously) resides at the kinematic limit of a lepton collider and can be produced by that initial\nstate 1. The energy of proton collisions that would be necessary to produce the same number of resonant\nevents, given the same integrated luminosity, is a natural figure of merit here.\nThe resulting equivalent CM energy is shown in Fig. 38, under the assumption that the parton-\nlevel production cross sections are a factor \u03b2 = 1, 10, 100 larger than the lepton-collider production\ncross section on resonance for qq and gg initial states. It is noteworthy that, even under the significant\nassumption that the production cross section via leptons matches that of quarks or gluons (\u03b2 = 1),\na 100 TeV proton collider significantly exceeds, for such a resonance, the reach of a 10 TeV lepton\ncollider. For larger parton production cross sections relative to leptons, the gap in coverage between the\ntwo classes of facilities further increases. Such a comparison, however, also conceals the richness of the\nphysics programme for such > 10 TeV resonances at a proton collider.\nTo go further, the direct discovery prospects for narrow resonances of mass MR > 10 TeV, which\nwould be inaccessible to a 10 TeV muon collider, is investigated. In the narrow width approximation, at\na proton collider operating at proton CM energy \u221as, the production cross section for a resonance R of\nspin S coupled to the initial state partons \u2018yy\u2019 and decaying into the final state \u2018xx\u2019 is\n\u03c3 = rCyy\ns\n,\n(2)\n1For lower masses, radiative-return production would be required to enable discovery.\n53\n\n\u0001\u0002\n\u0003\u0002\n\u0004\u0002\n\u0005\u0002\n\u0006\u0002\u0002\n\u0007\n\u0006\u0002\n\u0006\u0007\n\u0001\u0002\n\u0001\u0007\n\b\u0002\n\b\u0007\n\u0001\u0001 [\t\n\u000b]\n\u0001\u03bc [\u0001\u0002\u0003]\n\u2112pp=\u2112\u03bc\u03bc\ngg\nqq\n\u03b2=\u0001\n\u03b2=\u0001\u0002\n\u03b2=\u0001\u0002\u0001\nFig. 38: Energies of equivalent event numbers, assuming equal integrated luminosities, between a high-energy\nmuon collider and a proton collider; \u03b2 = 1 corresponds to the same partonic cross section between muons and\nproton partons while larger values of \u03b2 correspond to enhanced partonic cross sections for quarks and gluons, as\nwould be the case for resonances coupled primarily through QCD. Note that \u03b2 < 1 would require muons to be\nmore strongly coupled to new resonances than quarks, requiring muon flavour to play a role.\nwhere, for gluons and quarks, the factor Cyy is related to the parton luminosity as\nCgg = \u03c02\n8\nZ 1\n\u03c4\ndx\nx fg(x)fg(\u03c4x) ,\nCqq = 4\u03c02\n9\nZ 1\n\u03c4\ndx\nx\n\u0002\nfq(x)fq(\u03c4x) + fq(x)fq(\u03c4x)\n\u0003\n,\n(3)\nwhere \u03c4 = M2\nR/s and the parton distribution functions fg,q,q are evaluated at Q2 = M2\nR. The parameter\nr encodes all the model-dependent factors,\nr = (2S + 1)ByyBxx\n\u0393R\nMR\n.\n(4)\nThe width-to-mass ratio essentially encodes the microscopic coupling and hence parametrises the\nnature of the underlying theory. For these purposes, whenever \u0393R/MR \u22720.1, the theory is approxi-\nmately perturbative and the resonance effectively narrow. In Eq. (4), Byy is the branching ratio into the\npartons whose collision produced the resonance and Bxx is the branching ratio into whichever final state\nis under consideration. The latter could more prosaically be a pair of SM particles or something much\nmore exotic, such as pairs of long-lived particles.\nFigure 39 shows the number of pp \u2192R \u2192xx events for a variety of production channels\nat masses above 10 TeV. This number of events is weighted relative to the model-dependent factor r.\nSimply as an illustrative example, a scalar resonance could plausibly have r = 10\u22122. Thus, in this case,\nthe total number of events in Fig. 39 should be multiplied by 10\u22122. The number of events plausibly\navailable, hence the breadth of the exploration, to a 100 TeV proton collider for resonances above the\n10 TeV scale is vast. Smaller values of r are also possible, with events occurring above energies of\n10 TeV even for extremely narrow resonances, down to r \u223c10\u22128. For example, the SM Higgs boson\nhas r \u22483 \u00d7 10\u22125.\nIf the final states were rare collider objects, such as long-lived particles, then these many-orders\nof magnitude of events would be highly visible, offering a vast programme of not only discovery but\nalso characterisation. Presumably, for such exotic decays, the discovery reach would essentially saturate\nkinematic and PDF limits, up to \u223c50 TeV. On the other hand, if the final states were not rare but visible,\nsuch as to photons or leptons, then such a resonance would also stand out above the background. This is\n54\n\n\u0001\u0002\n\u0003\u0002\n\u0004\u0002\n\u0005\u0002\n\u0006\u0002\n\u0001\u0002\n\u0001\u0002\u0002\u0002\n\u0001\u0002\u0001\n\u0001\u0002\u0002\n\u0001\u0001 [\u0007\b\t]\n\u0002\u0003\u0003\n\u0003\n\u0001\u0001\n\u0002\u0002\n\u0003\u0003\n\u0004\u0004\u0004\u0004\n\u0005\u0005\n\u0006\u0006\n\u0002\u0001\n\u0003\u0002\n\u0007\b \t\u0006-\u0001\n \u000b\b\b \f\r\u000e\nFig. 39: The number of resonance-production events at a 100 TeV proton collider, relative to the model-dependent\nfactor r defined in Eq. (4). A non-exhaustive variety of initial states yy is considered and the final-state decay\nproduct xx is unspecified.\nconfirmed, for example, for the Sequential Standard Model scenario reach for leptonic decays shown in\nFig. 32, where the reach extends beyond 40 TeV. These are the easiest discovery opportunities that would\nmaximise the opportunities of the statistical reach of the large event samples.\nFinally, even in scenarios where the final state has a significant background, the number of events\nis large enough that a discovery would still be expected. This point is confirmed by detailed studies\nfor specific scenarios. For instance, Fig. 32 also shows the discovery reach for a variety of s-channel\nresonances. Even for a dijet final state, for which there is overwhelming background, the discovery reach\nextends to the 40 TeV scale.\n2.5.3\nPair production of new particles\nFigure 40 shows the result of a similar exercise as for the resonances, again following Ref. [282] and\nassuming the same integrated luminosity for each collider, and wondering what energy of muon collider\nwould produce the same number of pair-production events as a proton collider operating at a CM en-\nergy \u221asp. To do this, it is assumed that the muon collider can produce states close to threshold and,\nconsidering partonic cross sections\n\u02c6\u03c3ij\u2192xx(s\u00b5) = \u03b2\u02c6\u03c3\u00b5+\u00b5\u2212\u2192xx(s\u00b5)\n(5)\n(where ij = gg, qq are the initial state partons and xx are the pair-produced new states), it is also assumed\nthat the energy dependence of the cross section is inversely proportional to the partonic energy-squared.\nAs before, \u03b2 \u22481 qualitatively corresponds to new states that couple equally strongly to the muons and\nthe partons. Such scenarios would involve the production of purely electroweak states, or states with\nflavour-independent couplings. Instead, \u03b2 \u224810\u2013100 corresponds to states that may also carry colour.\nGoing beyond this, states that only couple to gluons or couple proportionally to fermion masses would\nhave \u03b2 \u226b100.\nIt can be seen from Fig. 40 that only for the case of \u03b2 \u22481, hence essentially only purely EW\nstates, does a 10 TeV muon collider have an estimated reach extending beyond that of a proton collider.\nThis is confirmed in the simple example of supersymmetry, where the estimated discovery reach for\ncoloured particles shown in Fig. 41 for a 100 TeV proton collider extends beyond 10 TeV, hence beyond\nthe kinematic limit of a 10 TeV muon collider. For purely electroweak particles, the proton collider reach\nsaturates at around the 5 TeV scale, close to the kinematic limit of a 10 TeV muon collider.\n55\n\n\u0001\u0002\n\u0003\u0002\n\u0004\u0002\n\u0005\u0002\n\u0006\u0002\u0002\n\u0007\n\u0006\u0002\n\u0006\u0007\n\u0001\u0002\n\u0001\u0001 [\b\t\n]\n\u0001\u03bc [\u0001\u0002\u0003]\n\u2112pp=\u2112\u03bc\u03bc\ngg\nqq\n\u03b2=\u0001\n\u03b2=\u0001\u0002\n\u03b2=\u0001\u0002\u0001\nFig. 40: Same as Fig. 38, but for pair-produced resonances.\nFig. 41: Summary of the 5 \u03c3 discovery reach for different SUSY particles. From Ref. [283].\nThis treatment has, however, been relatively na\u00efve in the sense that it is essentially rooted in the\ngauge paradigm. It can instead be assumed that, at these energy scales, the new physics couples only\nthrough dimension-6 contact interaction. In this case, the production cross section at the partonic level\nscales proportional to the partonic energy-squared. Such a possibility is plausible if the states that connect\nthe two sectors are heavy.\nFigure 42 shows the approximately equivalent colliders under this assumption, where the outcome\nis very different. In this case, a 100 TeV proton collider exceeds the reach of a 10 TeV muon collider\neven assuming comparable partonic cross sections at s\u00b5, which may not be the case.\n2.6\nPhysics reach of alternative FCC-hh \u221as options\nThe reduction of the FCC tunnel length, with respect to the CDR, from 100 to 90.7 km, and the range of\nvalues for the magnetic field strength of dipoles that might be ready for mass production on the timescale\nof the final definition of the FCC-hh accelerator, motivate a study of beam-energy scenarios alternative\nto the canonical \u221as = 100 TeV used for the CDR physics studies.\nThe first results of this study are presented here, considering the cases of \u221as = 80 and 120 TeV.\n56\n\n\u0001\u0002\n\u0003\u0002\n\u0004\u0002\n\u0005\u0002\n\u0006\u0002\u0002\n\u0007\n\u0006\u0002\n\u0006\u0007\n\u0001\u0002\n\u0001\u0007\n\b\u0002\n\u0001\u0001 [\t\n\u000b]\n\u0001\u03bc [\u0001\u0002\u0003]\n\u2112pp=\u2112\u03bc\u03bc\ngg\nqq\nDim-6 Contact\n\u03b2=\u0001\n\u03b2=\u0001\u0002\n\u03b2=\u0001\u0002\u0001\nFig. 42: Same as Fig. 40, but for production through a higher-dimension operator.\nThe former is motivated by the combined effect of a reduction in ring size and a less aggressive assump-\ntion, with respect to the CDR, for the strength of Nb3Sn dipoles finally available (14 T instead of 16 T).\nThe higher energy value is relevant in scenarios where high-temperature superconducting (HTS) dipoles,\nin the range of 20 T, become available. A more precise and detailed assessment of the full operational\nscenarios, including therefore the estimates of the collider luminosity, is underway. The definition of\nthese scenarios will be modulated by assumptions about, and interplay between, key elements such as\noverall power consumption and experimental pileup. The results of these more complete studies, and\ntheir impact on the physics programme, will be documented at a later stage.\nFor this report, the same luminosity setting is assumed for all three energies, 80, 100, and 120 TeV,\nnamely a total of 30 ab\u22121, obtained by combining the event samples collected by two general-purpose\ndetectors. The goal of the study is not to provide an accurate update of the 100 TeV results but rather\nto focus on the loss or gain in performance for some of the key deliverables highlighted in the FCC-\nhh CDR, namely the precision study of Higgs properties, the search for high-mass resonances, and the\npotential to discover or exclude scenarios of WIMP dark matter candidates. The chosen energies (80 and\n120 TeV) may not match precisely the values that will emerge from the more detailed accelerator studies.\nPreliminary indications suggest, however, that they provide a good reference for the physics performance\nwith dipole field strengths ranging between 12 and 20 T.\n2.6.1\nHiggs properties\nThe CDR has shown that the baseline FCC-hh programme can improve to sub-percent level the precision\nof Higgs decays such as \u03b3\u03b3, Z\u03b3, and \u00b5\u00b5, which are too rare to be detected with that kind of precision at\nFCC-ee or any other proposed e+e\u2212Higgs factory. This precision is achieved by considering the ratio\nof Higgs bosons produced above some pT threshold and decaying to a given channel, relative to those\ndecaying to four leptons. For the latter, the branching ratio is expected to be known from FCC-ee with\na per-mil precision. The ideal value of the pT cut is defined by the optimum balance between statistical\nand systematic uncertainties; typical values are in the 100 to 200 GeV range. In this pT range, the Higgs\nproduction rate is reduced (increased) by about 30% (35%), when changing \u221as from 100 to 80 (120) TeV.\nFolding this modified statistical uncertainty with the systematic uncertainties leads to the projections for\nthe measurement precision of Higgs couplings shown in Table 7. The 1% statistical precision expected at\n100 TeV for the determination of the ttH / ttZ production cross-section ratios is modified to 1.2% and\n0.85%, at 80 and 120 TeV, respectively.\nThe evolution of the Higgs self-coupling measurement is shown in Table 8. Three different sce-\n57\n\nTable 7: Projected uncertainties of Higgs coupling measurements at FCC-hh, for different \u221as scenarios, with an\nintegrated luminosity of 30 ab\u22121.\nCoupling\n100 TeV\n80 TeV\n120 TeV\nCDR baseline\n\u03b4gH\u03b3\u03b3/gH\u03b3\u03b3 (%)\n0.4\n0.4\n0.4\n\u03b4gH\u00b5\u00b5/gH\u00b5\u00b5 (%)\n0.65\n0.7\n0.6\n\u03b4gHZ\u03b3/gHZ\u03b3 (%)\n0.9\n1.0\n0.8\n\u03b4gH\u00b5\u00b5/gH\u00b5\u00b5 (%)\n0.65\n0.7\n0.6\nTable 8: Projected uncertainties of SM Higgs self-coupling measurements at FCC-hh, for different \u221as scenarios,\nunder different assumptions regarding the experimental systematic uncertainties, as defined in Ref. [83].\nSystematic uncertainties\n100 TeV\n80 TeV\n120 TeV\nscenario\nCDR baseline\nI (%)\n3.4\n3.8\n3.1\nII (%)\n5.1\n5.6\n4.7\nIII (%)\n7.8\n8.4\n7.3\nnarios for the systematic uncertainties are considered [83]: (I) corresponds to systematic uncertainties\ncomparable to those of the ATLAS and CMS experiments during the Run 2 of LHC; (III) is a conservative\nestimate based on 2019 projections for the HL-LHC performance; and (II) is an intermediate scenario.\nSignificant progress has been made since 2019 and the results, even for the baseline 100 TeV operations,\nwill be updated by the time of the ESPP discussions.\n2.6.2\nWIMP DM search\nA key result obtained for the CDR is the proof that an FCC-hh experiment could conclusively discover, or\nexclude, broad classes of dark matter candidates. For example, weakly interacting neutral components of\ndoublet or triplet weak isospin fermions, such as the higgsino and wino gauge fermions in supersymmet-\nric theories, are required by cosmology to have masses smaller than about 1 and 3.5 TeV, respectively.\nIt was shown in Ref. [284] that a search for disappearing charged tracks in events with large missing\ntransverse energy could fully cover these mass ranges (as shown by the red bands in the left-side plots\nof Fig. 43). The analysis has been repeated at 80 TeV, rescaling the signal strength while keeping the\nsame background level, leading therefore to a conservative extrapolation to lower energy. The results are\nshown in the right-side plots of Fig. 43. The O(10%) loss in reach still enables the 5 \u03c3 discovery up to\nthe cosmology limit, even for the more critical case of the higgsino. Is is expected that a re-optimisation\nof the analysis should cover the relevant mass range down to slightly smaller collision energies, possibly\nabove \u221as = 70 TeV.\n2.6.3\nHigh-mass reach\nThe general potential of FCC-hh to directly explore the existence of new large-mass particles is discussed\nabove. The beam energy is clearly the main driver for the mass reach. The detector performance and the\npileup environment have a minor impact on the energy-dependence of this reach, a dependence that can\nbe studied with a simple extrapolation based on the evolution with energy of the partonic luminosities,\nusing, e.g., the Collider Reach tool [285]. Table 9 shows the extrapolation to 80 and 120 TeV of the 5 \u03c3\nreach for several possible s-channel resonances. Details of the 100 TeV analysis and the definition of the\nvarious models listed here can be found in Ref. [186]. A reduction of the collision energy to 80 TeV leads\nto a 15\u201320% loss in mass reach, while running at 120 TeV would increase the reach by 10\u201315%. It goes\n58\n\nFig. 43: The 5 \u03c3 discovery reach for wino and higgsino dark matter candidates, via disappearing-track signals for\n\u221as = 100 (left) and 80 TeV (right). The red band corresponds to the alternative pixel-detector layout proposed in\nRef. [284], where the details of the analysis are discussed.\nTable 9: Beam-energy dependence of the projected 5 \u03c3 discovery reach, with the new particle mass in TeV, for s-\nchannel BSM resonances, in various decay modes. The definition of the various models can be found in Ref. [186].\nResonance\n100 TeV\n80 TeV\n120 TeV\nQ\u2217\n40\n33\n46\nZ\u2032\nTC2 \u2192tt\n23\n20\n26\nZ\u2032\nSSM \u2192tt\n18\n15\n20\nGRS \u2192WW\n22\n19\n25\nZ\u2032\nSSM \u2192\u2113\u2113\n43\n36\n50\nZ\u2032\nSSM \u2192\u03c4\u03c4\n18\n15\n20\nwithout saying that, to this date, there is no specific model that precisely requires the existence of such\nnew resonances in some of the mass ranges that would be (or not be) covered at the different energies.\nThe impact of the beam-energy change is reduced for particles well below the kinematic endpoint, whose\ndiscovery reach is mostly limited by weak couplings, backgrounds or systematic uncertainties (as, for\nexample, in the case of DM WIMPS discussed above).\n2.7\nA forward-physics facility at FCC-hh\nThe immense breadth of the physics programme available to a hadron-collider facility is well proven\nby LHC, with its programme of pp, pN, and NN collisions (where N stands for heavy ion). The four\n59\n\nlarge LHC experiments are accompanied by a multitude of smaller, dedicated experiments, which further\npush the exploitation of the scientific opportunities. A first exploration of the opportunities offered by\nthe programme of heavy ion collisions at FCC-hh was presented in Ref. [57] and in the CDR [10].\nThe additional unique opportunities that could arise from the exploitation of the high intensity beam\nof energetic particles, including neutrinos, produced by pp collisions in the forward region, is briefly\ndiscussed here. At LHC, these particles are studied with the far-forward experiments FASER(\u03bd) [286\u2013\n289] and SND@LHC [290,291], and new dedicated experiments have been proposed in the context of a\nforward physics facility (FPF) [292,293] operating concurrently with HL-LHC. A FPF-like suite of far-\nforward experiments integrated within FCC-hh would provide unique opportunities for neutrino physics,\nQCD studies, and BSM searches. Such FPF@FCC could be located around 1.5 km away from the IP\n(Fig. 44), where a dedicated cavern would be excavated aligned with the line-of-sight (LoS). It would\nhave a length between 100 and 500 m, depending on the detector setup. Representative applications of\nthe FPF@FCC experiments are summarised here. A more detailed discussion can be found in Ref. [294].\nFig. 44: High-energy light particles (neutrinos, LLPs/FIPs) produced in FCC-hh collisions could be detected at the\nFPF@FCC, located at around 1.5 km away from the IP, enabling sensitivity to a variety of SM and BSM signatures.\n2.7.1\nNeutrino physics\nFor neutrino detection, two options are considered: a FASER\u03bd2-like detector [292], dubbed FCC\u03bd, with a\nlength of 6.6 m, and a deeper variant, FCC\u03bd(d), with a length of 66 m. These detectors could collect [294]\nup to 109 electron/muon neutrinos and 107 tau neutrinos for Lpp = 30 ab\u22121, an increase of several orders\nof magnitude with respect to the (HL-)LHC yields. These neutrinos would exhibit the highest energies\never achieved in a laboratory (up to 40 TeV), overlapping with those from astrophysical sources. The\nevent yields forecast at the FPF@FCC would outperform all previous, ongoing, and future (proposed)\nneutrino experiments for all three generations, as indicated in Fig. 45. These unprecedented event rates\nallow the precise fingerprinting of neutrino properties, such as their flavour universality and non-standard\ninteractions.\nAs a representative application, the electromagnetic properties of neutrinos are considered, long\n60\n\n103\n104\n105\n106\n107\n108\n109\n dN/dlog10(E/GeV)\nenergy spectrum for \n+\nSHiP (6 1020 PoT)\nSND@LHC (250fb\n1)\nFASERv (250fb\n1)\nFASERv2 (3ab\n1)\nFCCv (30ab\n1)\nDUNE ND\nNuTeV\nCCFR\nNOMAD\nCDHS\nCHORUS\nMuCol 3TeV (1ton year)\nMuCol 10TeV (1ton year)\n1\n10\n102\n103\n104\n105\nNeutrino Energy E [GeV]\n101\n102\n103\n104\n105\n106\n107\ndN/dlog10(E/GeV)\nenergy spectrum for \n+\nSHiP (6 1020 PoT)\nSND@LHC (250fb\n1)\nFASERv (250fb\n1)\nFASERv2 (3ab\n1)\nFCCv (30ab\n1)\nDONUT\nFig. 45: The muon and tau neutrino scattering yields as a function of E\u03bd at FCC\u03bd and other experiments.\nrecognised as a window to new physics [295], in particular on the measurement of the neutrino charge\nradius \u27e8r2\n\u03bd\u27e9, which modifies the neutral-current DIS cross section for neutrinos. It can be extracted [296,\n297] by searching for deviations in the ratio between NC and CC DIS events as compared to the \u27e8r2\n\u03bd\u27e9= 0\nbaseline. The upper left panel of Fig. 46 shows the projected sensitivity to \u27e8r2\n\u03bd\u27e9at FPF@FCC considering\nonly statistical uncertainties. World-leading bounds would be achieved, measuring the (SM) neutrino\ncharge radius for \u03bde and \u03bd\u00b5, and reaching down to five times the SM value for \u03bd\u03c4. Realising this potential\nfor precision neutrino physics demands an excellent modelling of CC and NC neutrino DIS interactions\nwithin the detector, combined with high-precision event generators for neutrino DIS [298\u2013300].\n2.7.2\nBSM sensitivity\nThe FPF@FCC is sensitive to a variety of BSM models [294], including dark Higgs bosons [301],\nrelaxion-type scenarios, quirks [302\u2013305], and millicharged particles (mCPs). These BSM signatures\nfall, in most cases, outside the coverage of the main FCC-hh detectors, and hence such a far-forward\nfacility would markedly increase the discovery capabilities of FCC-hh. The sensitivity to dark Higgs\nbosons, D-type quirks, and mCPs of the FPF@FCC is summarised in Fig. 46. The enormous rates of\nforward Higgs production at 100 TeV enable the discovery of LLPs from Higgs decays with masses as\nlarge as 62 GeV (\u2243mH/2) and couplings as small as sin \u03b8 \u223c10\u22128 (beyond the reach of FCC-ee); of\nquirks with masses up to 14 TeV for a broad range of confinement scales \u039b; and of mCPs with masses up\nto several hundreds of GeV and charge q \u223c10\u22123e, closing the gap between (future) accelerator-based\nbounds and dark matter direct detection searches.\n2.7.3\nQCD and hadronic structure\nThe enormous samples of multi-TeV neutrinos available at the FPF@FCC (Fig. 45) enable high-resolution\nprobes of the unpolarised and polarised structure of protons and of heavy nuclei, as summarised by the\nrepresentative applications of Fig. 47.\nFirst, high-energy neutrino DIS structure functions [306, 307] provide a precise quark/antiquark\nflavour separation at large-x, which in turn reduces the theoretical uncertainties entering high-mass\nsearches at FCC-hh. Second, neutrino DIS on a polarised target [308, 309] resolves the spin structure\nof the proton [310, 311] with complementary information to related experiments, such as those at the\nElectron-Ion Collider [312]. Third, detecting neutrinos originating from proton-lead collisions provides\n61\n\n10\n34\n10\n33\n10\n32\n10\n31\n10\n30\nr2 [cm2] \nQ=0 GeV\nSM:Q\n30 GeV\nQ=0 GeV\nSM:Q\n30 GeV\nQ=0 GeV\nTEXONO\nCOHERENT\nLEP2\nCCFR\nCHARM\nLSND\nCOHERENT\nDUNE\ne\nSM:Q\n30 GeV\nCharge Radius Bounds\nFCC (d)\nFCC (w)\nFCC\nFASER 2\n0\n2000\n4000\n6000\n8000\n10000 12000 14000\nm [GeV]\n101\n102\n103\n104\n105\n106\n [eV]\nExcluded\nFASER(300fb\n1)\nFASER2(3ab\n1)\nFCC-LLP1(30ab\n1)\nFCC-LLP2(30ab\n1)\n quirk\nDT\nST\nDT\nST\nFig. 46: Top left: Sensitivity of the FCC\u03bd detectors to the neutrino charge radius. Top right: Reach for a dark Higgs\nboson \u03d5 at the FPF@FCC. Bottom left: Discovery potential for D-type quirks with mass mQ and confinement scale\n\u039b. Bottom right: Sensitivity to mCPs with mixing parameter \u03f5.\n10\u22121\n100\n101\nmX (TeV)\n0.96\n0.98\n1.00\n1.02\n1.04\n1.06\nLqq/L(ref)\nqq\n\u221as = 100 TeV\nNNPDF4.0\nNNPDF4.0 + FPF\nNNPDF4.0 + FCC\u03bd(d)\n10\u22124\n10\u22123\n10\u22122\n10\u22121\n100\nx\n\u22120.06\n\u22120.04\n\u22120.02\n0.00\n0.02\n0.04\nx\u2206s+(x, Q2)\nQ = MW\nNNPDFpol1.1\nNNPDFpol1.1 + FCC\u03bdpol\n10\u22129\n10\u22127\n10\u22125\n10\u22123\n10\u22121\nx\n0\n5\n10\n15\nxg(N/Pb)(x, Q2)\nQ = 2 GeV\nnNNPDF3.0\nnNNPDF3.0 + FCC\u03bd\nFig. 47: Projected constraints from the FPF@FCC experiments on the unpolarised (left) and polarised (middle)\nPDFs, and on the nuclear PDFs of lead nuclei (right).\ninformation on nuclear structure [313\u2013315] down to x \u223c10\u22129, where nuclear PDFs are unconstrained\nand novel dynamical regimes of QCD, such as the Colour Glass Condensate, are expected to dominate.\nThis kinematic region is also of prime importance for astroparticle physics experiments.\n2.7.4\nSummary\nIntegrating far-forward experiments into FCC-hh would extend its scientific potential in several syner-\ngetic directions from QCD and neutrino physics to BSM searches in a cost-efficient manner. While at this\nearly stage no attempt has been made to optimise the accelerator infrastructure or define the FPF@FCC\ndetector technology more precisely, the results shown here motivate further studies of how to fully realise\nthis unique physics potential.\n62\n\n3\nTheoretical calculations\nTo fully leverage the significantly improved experimental precision in Z-pole observables, W boson and\ntop quark masses, b and \u03c4 decays, as well as a broad array of Higgs observables, it is essential to ob-\ntain Standard Model predictions with an accuracy that matches the anticipated statistical uncertainties\nof FCC-ee. The expectation that most systematic experimental uncertainties can be reduced to the level\nof the statistical precision further underscores this requirement. Such theoretical predictions are neces-\nsary for both inclusive and exclusive processes, with the latter requiring integration with Monte Carlo\ngenerators. They encompass a wide range of technical aspects, including fixed-order perturbative correc-\ntions, resummation calculations, improved parton showers, non-perturbative hadronization effects, and\nlattice QCD. Any discrepancies between experimental data and Standard Model predictions (anomalies)\ncould provide crucial insights, potentially guiding the way towards new discoveries. In addition, detailed\nprecision analyses of BSM effects within concrete models and effective theories will open up a broad\nspectrum of new prospects.\nOn top of that, FCC-hh has unique capabilities for testing SM phenomena at ultra-high energies,\nparticularly the mechanism of electroweak symmetry breaking and broad coverage for direct particle\ndiscovery. Theory calculations are needed to evaluate (often large) backgrounds, expected signal rates,\nand to optimise the experimental search strategies. The high precision reached by the LHC, due to\nfurther improve in the HL-LHC era, has been and remains a powerful stimulus for the theory community\nto enhance the calculation reliability. This progress is fully aligned with the future needs of FCC-hh.\nA very active effort (in lattice and in perturbative calculations) is ongoing worldwide to improve\nthe theoretical control of flavour observables, in view of the current and forthcoming experimental\nprogress made by LHCb and Belle II. This effort will continue alongside the experimental advances\nmade by these experiments in the next decades, undertaking the required steps towards the ultimate\nprecision goals required by FCC. Suitably refined precision calculations for flavour observables should\nalso be identified and relevant actions must be planned accordingly. Present and future work focuses on\n(a) calculating higher-order perturbative QCD and EW corrections (including, for the latter, their match-\ning at the weak scale), and (b) understanding an order-of-magnitude better than before the separation and\ninterplay between perturbative and non-perturbative contributions with the goal of constraining the latter\nfrom data as much as possible. Improved lattice calculations, from algorithmic progress and hardware\ndevelopments, are a further essential ingredient.\nFor all the measurement areas where theoretical improvements are needed to match the FCC preci-\nsion goals \u2014 EW, QCD, flavour, BSM \u2014 the large interplay between the development of EW and QCD\ncalculations, in terms of impact on the total theoretical systematic uncertainties and of computational\nchallenges and tools, is remarkable. Two-loop QCD corrections are often of comparable size to one-loop\nEW corrections, and they both play a critical role at the required level of precision. Their interplay is\nthus essential, and often it is the source of added complexity when both EW and QCD corrections are\nmixed (e.g., in the presence of off-shell decays of weak bosons to quarks). On the formal side, progress\ntowards the understanding of multi-scale multi-loop diagrams is of common value to both EW and QCD,\nas well as to BSM studies. Techniques inspired by effective field theory (EFT) are becoming ubiquitous,\nand tools initially developed for flavour physics (soft-collinear effective theory, or SCET) are now rele-\nvant to describe QCD event shapes, resummations, jet-vetoed final states, and much more. This global\nsynergy of developments in different specific areas opens a whole new dimension for future coordinated\ntheoretical efforts.\nIf any deviation from the SM expectations were observed at FCC-ee/hh, the interpretation would\nrequire calculations to the requisite precision in BSM models or models with higher-dimensional EFT\noperators to the requisite precision. These higher-order corrections can be straightforwardly achieved by\nadapting the techniques developed for standard model (QED, EW, and QCD) calculations. Therefore,\nimproving the accuracy of SM predictions at large currently remains the main priority of the community\nof experts on radiative corrections. This chapter focuses on a brief review of the status, future needs and\n63\n\nprospects for theoretical improvements of relevance to EW, Higgs, jets, and top quark measurements,\nincluding the MC event-generator perspective, and the actions under way to support and coordinate such\nefforts.\n3.1\nElectroweak corrections\nTo meet the precision goals of FCC-ee, significant advances in calculations of higher-order radiative cor-\nrections and in MC generators will be needed [38,40,316]. For instance, electroweak NNLO corrections\nfor various pair production processes (e+e\u2212\u2192f\u00aff, e+e\u2212\u2192\u03b3\u03b3, e+e\u2212\u2192W+W\u2212, e+e\u2212\u2192ZH) are\nneeded, as well as MC tools for the simulation of multiple photon radiation beyond leading-logarithmic\n(LL) approximation. Even higher perturbative orders, including three-loop corrections in the full SM and\nleading four-loop corrections, are required to interpret precision measurements at the Z pole. Table 10\nprovides a few illustrative examples of precision quantities and the theory calculations required to extract\nthem from data.\nTable 10: A few sample precision quantities of interest for the FCC-ee programme, their current and projected\nexperimental uncertainties, and the required theory input for their extraction from the data. The last two columns\nshow the current state of the art for calculations of this theory input and higher-order calculations needed to reach\nthe FCC-ee precision target. More details can be found in Ref. [40].\nQuantity\nCurrent\nprecision\nFCC-ee stat.\n(syst.) precision\nRequired\ntheory input\nTheory status\nas of today\nNeeded theory\nimprovement\u2020\nmZ (MeV)\n2.0\n0.004 (0.1)\nnon-resonant\ne+e\u2212\u2192f\u00aff,\ninitial-state\nradiation (ISR)\nNLO,\nISR logarithms\nup to 6th order\nNNLO for\ne+e\u2212\u2192f\u00aff\n\u0393Z (MeV)\n2.3\n0.004 (0.012)\nsin2 \u03b8\u2113\neff\n1.6\u00d710\u22124\n1.2 (1.2) \u00d7 10\u22126\nmW (MeV)\n9.9\n0.18 (0.16)\nlineshape of\ne+e\u2212\u2192WW\nnear threshold\nNLO\n(e+e\u2212\u21924f\nor EFT\nframework)\nNNLO for\ne+e\u2212\u2192WW,\nW \u2192f\u00aff\u2032\nin EFT setup\nHZZ\ncoupling\n\u2013 \u2217\n0.1%\ncross section for\ne+e\u2212\u2192ZH\nNLO EW plus\npartial NNLO\nQCD/EW\nfull NNLO EW\nmtop (MeV)\n290\n4.2 (4.9)\nthreshold scan\ne+e\u2212\u2192tt\nN3LO QCD,\nNNLO EW,\nresummations\nup to NNLL,\nO(30 MeV)\nscale uncert.\nMatching fixed\norders with\nresummations,\nmerging with\nMC, \u03b1S (input)\n\u2020 The necessary theory calculations mentioned are a minimum baseline; additional partial higher-order contributions may also\nbe required.\n\u2217No absolute value for the HZZ coupling can be extracted from the LHC data without additional assumptions.\nAdditional theory input is necessary for the interpretation of the experimentally determined values\nof these quantities, i.e., to test the validity of the SM and probe possible physics beyond the SM, as\nillustrated in Table 11 for some of the same examples as above. In this context, the three-loop \u03b13\nS\ncorrections to the semileptonic b \u2192c decay [317] and the three-loop QED corrections to the muon\ndecay [317, 318] were recently calculated in the Fermi approximation. These results are a milestone in\nperturbative calculations and an important step towards precision calculations for FCC-ee. In particular,\n64\n\nTable 11: Required theory calculations for the prediction of the listed precision quantities within the SM. These\npredictions are needed for comparison with the quantities extracted from data (Table 10), for the purpose of testing\nthe validity of the SM and probing BSM physics. More details in Ref. [40].\nQuantity Required theory input\nTheory status\nas of today\nNeeded theory\nimprovement\u2021\n\u0393Z\nvertex corrections for\nZ \u2192f\u00aff\nNNLO + partial\nhigher orders\nN3LO EW + partial\nhigher orders\nsin2 \u03b8\u2113\neff\nmW\nSM corrections to the\nmuon decay rate\nNNLO + partial\nhigher orders\nN3LO EW + partial\nhigher orders\n\u2021 The mentioned needed theory calculations are a minimum baseline;\nadditional partial higher-order contributions may also be required.\nthe \u03b13 QED contribution translates to a shift of the muon lifetime of (\u22129 \u00b1 1) \u00d7 10\u22128 \u00b5s. With the\ncurrent measurement of \u03c4\u00b5 = 2.1969811 \u00b1 0.0000022 \u00b5s, the new correction terms are almost two\norders of magnitude smaller than the experimental uncertainty. Thus, an updated value of GF can only\nbe extracted once the latter has been improved.\nThe Fermi constant GF is one of several fundamental parameters that need to be precisely deter-\nmined in order to make quantitative predictions for electroweak precision observables (EWPOs) within\nthe SM or concrete BSM realisations through data-theory comparisons. Other examples of such quan-\ntities include the strong coupling \u03b1S and the top-quark mass mtop. Many of these parameters can be\nobtained from FCC-ee data with much reduced uncertainty compared to today (Table 2), but their extrac-\ntion from the experimental measurements requires significant theory input (as shown in Section 3.2 for\n\u03b1S and in the last row of Table 10 for mtop).\nSimilarly, the interpretation of cross section measurements requires the precise determination of\nthe luminosity through measurements of small-angle Bhabha scattering and/or large-angle photon-pair\nproduction (Section 6.13). For this purpose, the rates for these processes need to be computed at least\nwith NNLO QED corrections, logarithmically enhanced higher-order effects, and a careful treatment of\nvirtual hadronic corrections (which appear at NLO for Bhabha scattering and NNLO for two-photon\nproduction) [319,320].\nTo achieve the precision goals outlined in Tables 10 and 11, significant improvements in calcula-\ntion techniques for higher-order radiative corrections are required, including full two-loop corrections for\n2 \u21922 scattering processes, as well as decay processes with full three-loop corrections and approximate\nfour-loop contributions in a large-mass expansion.\nRecently, significant progress has been achieved in semi-numerical multi-loop calculation tech-\nniques based on dispersion relations [321, 322] and on series solutions of differential equations [323\u2013\n328]. These techniques have enabled the first calculations of electroweak two-loop corrections for the\nmain Higgs boson production process at FCC-ee, e+e\u2212\u2192ZH [322, 329], and they are expected to be\nuseful for calculations of NNLO corrections for other pair production processes as well.\nThe approach of Refs. [321,322] exploits dispersion relations and Feynman parameters to express\none subloop of a two-loop diagram in terms of integrals with up to three variables. Then the second\nsubloop becomes a simple one-loop integral, with well-known analytical results. For divergent diagrams,\nthe singularities can be removed with systematically constructed subtraction terms, which can also be\nevaluated analytically. These procedures lead to two- or three-dimensional finite numerical integrals that\ncan be evaluated with good precision within minutes on a single CPU core for a single diagram class.\nThe method does not use any reduction to master integrals, which saves computing resources.\nAnother powerful method for multi-loop integrals is the method of differential equations [330\u2013\n65\n\n334]. While it can be difficult to find analytical solutions to these equations, it was recently realised\nthat solutions can be efficiently obtained to arbitrarily high precision, using deep series expansions [323,\n324, 326\u2013328]. By matching series about different expansion points, solutions can be constructed that\nconsistently extend across thresholds and other singular points. To fully determine the differential equa-\ntion solutions, boundary values are also needed, and can be evaluated analytically or numerically for\nspecial kinematic points (such as zero momentum or unphysical Euclidean momentum). This step is\nmade particularly simple with the auxiliary flow method, which uses boundary conditions at infinity of\nan unphysical (auxiliary) variable, where they can be evaluated in terms of algebraic recurrence rela-\ntions [325].\nThe series expansion approach is not only restricted to two-loop integrals, but is also a promising\ntool for three-loop SM corrections. It requires a reduction to master integrals, which is the computa-\ntional bottleneck for this method. Recent developments in integral reduction methods [335\u2013337] can\nhelp to push the envelope on this front. In addition, the integral reduction can be performed numeri-\ncally with much lower computing resources, and the functional dependence on kinematic variables can\nbe reconstructed with suitable expansions or interpolations. Progress was also made towards analytical\nsolutions of differential equations for Feynman integrals, using functions beyond multiple polyloga-\nrithms [338,339].\nFor a reliable phenomenological description of e+e\u2212\u2192ZH, one of the next steps is to combine\nthe NNLO result with a calculation of the process e+e\u2212\u2192Hf\u00aff, where the fermion pair may be off the\nZ resonance. These off-shell contributions are important because of the relatively large decay width of\nthe Z boson. For the projected FCC-ee precision, it is sufficient to compute e+e\u2212\u2192Hf\u00aff at NLO, which\ncan be straightforwardly accomplished with existing automated tools.\n3.2\nQCD precision calculations\nThis section addresses some of the main theoretical challenges regarding Quantum Chromodynamics\n(QCD) calculations on the path towards FCC-ee. The considerations below are inspired by previous\nreviews [340] and largely by discussions that took place at topical FCC-ee workshops [316,341].\n3.2.1\nQCD studies in Z/\u03b3\u2217\u2192jets\nThe very large FCC-ee integrated luminosities at the Z boson pole and at higher energies provide an\nexcellent opportunity to expand the knowledge of strong interactions in QCD final states, both in the area\nof jet physics and for the extraction of the strong coupling constant, \u03b1S(m2\nZ), from hadronic observables\nin Z/\u03b3\u2217\u2192jets events.\nJet physics and shape observables\nFine details of QCD final states can be investigated through a range of jet observables such as event\nshapes (designed to describe the geometric properties of hadronic events), jet rates, and jet substructure\nobservables.\nOwing to their sensitivity to QCD radiation, these observables are widely used to extract \u03b1S [98],\ncalibrate non-perturbative hadronisation models [342], or study QCD dynamics within jets [343]. Fully\ndifferential calculations for the process e+e\u2212\u2192Z/\u03b3\u2217\u2192qq + X at N3LO in QCD (\u03b13\nS) for massless\npartons in the final state can be derived starting from the results of Refs. [344\u2013348] with the inclusive\ncross section at N3LO [349]. Similarly, the production of heavy (notably bottom) quarks, e+e\u2212\u2192\nZ/\u03b3\u2217\u2192Q\u00afQ + X, can be described at NNLO in QCD using the predictions of Refs. [350\u2013353]. For\nhigher jet multiplicities, the computation of QCD radiative corrections with massless final-state partons\nhas been extended to NLO for e+e\u2212\u2192Z/\u03b3\u2217\u2192n jets with n = 5 [354] and n = 6, 7 [355].\nThe essential NNLO QCD calculations for final states with four or five jets are beyond the current\nstate of the art. With the recent progress in the calculation of the necessary two-loop scattering ampli-\n66\n\ntudes (see, e.g., Refs. [356\u2013358] for the five-point case), these NNLO predictions will arguably become\navailable in the coming years. Future developments in the computation of such multi-scale amplitudes\nmay benefit from novel computational techniques discussed in Section 3.1 and in Refs. [324,359\u2013369].\nA recent review of modern computational methods can be found in Refs. [316,370].\nThe perturbative description of kinematic regimes that require the all-order resummation of radia-\ntive corrections has also improved substantially in the past decade, and the state-of-the-art calculations\nfor standard global event shapes and jet rates in e+e\u2212\u2192Z/\u03b3\u2217\u2192qq + X have reached NNLL order\nand beyond [371\u2013389]. Resummations for multijet final states are desirable for QCD phenomenology\nat FCC-ee, while currently only a limited number of predictions is available beyond the NLL order for\ne+e\u2212\u2192Z/\u03b3\u2217\u2192qqg + X observables [390\u2013393]. Further progress is therefore necessary in this area,\nrequiring dedicated analytical and numerical resummation techniques. Furthermore, the computation of\nnon-global observables [394,395], sensitive to the geometric pattern of soft QCD radiation, has recently\nbeen pushed to the NNLL order [396\u2013399], and a number of dedicated phenomenological applications\nto e+e\u2212collisions are becoming available [395, 397, 399\u2013406]. Computational techniques for jet sub-\nstructure observables have also witnessed outstanding progress in the last decade, resulting in an array of\napplications at lepton colliders to the study of observables measured on groomed jets [407\u2013410] or the\nstudy of fragmentation and spin correlations in jet physics [411\u2013417].\nMeasurements of the strong coupling constant\nAmong the main challenges to match FCC-ee experimental accuracy is the reduction of the uncertainties\nof the QCD parameters, and notably the strong coupling constant, \u03b1S(m2\nZ) [98]. The current world\naverage [35], which reaches a \u223c0.8% uncertainty (\u03b1S(m2\nZ) = 0.1180 \u00b1 0.0009), is mainly constrained\nby the precision of lattice calculations [418], expected to be improved by a factor of two in the next\ndecade [419,420].\nAt FCC-ee, a precision of 0.1% on \u03b1S(m2\nZ) can be contemplated (Table 2). The most precise\ndetermination comes from a combined fit of three EW pseudo-observables at the Z pole: the Z boson\nhadronic partial width, the total hadronic cross section at the resonance peak, and the ratio of hadronic\nto leptonic branching fractions. These inclusive quantities are particularly suitable to extract \u03b1S given\nthe small non-perturbative hadronisation corrections, which scale with the centre-of-mass energy Q as\n(\u039bQCD/Q)6 [421]. With the 6\u00d71012 Z bosons produced at FCC-ee, the total experimental uncertainty in\n\u03b1S extractions from fits of the above quantities is of the order of 0.1% [422], hence requiring a substantial\nreduction of the corresponding theoretical uncertainties. The status of theory computations for these\nobservables is well-advanced: QCD corrections are known up to N4LO [423\u2013425] and N3LO corrections\nfor massive bottom quarks are also known in a power series in m2\nb/Q2 [353]. On the other hand, EW\nand mixed QCD-EW corrections are available at least up to two loops (see, e.g., Refs. [426\u2013428] and\nreferences therein), as discussed in Section 3.1 of this report.\nOther very accurate extractions of \u03b1S at FCC-ee can be derived from \u03c4 [429, 430] and W [422,\n431] hadronic and leptonic decays, using high-order perturbative QCD computations. Existing stud-\nies on the \u03b1S extraction from the decay of EW bosons indicate that the calculation of higher-order\ncorrections2 up to O(\u03b15\nS), O(\u03b13), and O(\u03b1S, \u03b13) or O(\u03b12\nS, \u03b12) for QCD, EW, and QCD \u2295EW, re-\nspectively, are needed to match the expected statistical experimental precision on inclusive W and Z\nhadronic observables [422]. In the case of \u03c4 decays, open theoretical questions are related to the treat-\nment of non-perturbative effects [435\u2013437], as well as to the difference between extractions relying\non contour-improved (CIPT) [438,439] and fixed-order (FOPT) perturbative calculations adopted in the\nfits [440,441]. Recent investigations indicate that CIPT calculations might require a more robust estimate\nof non-perturbative corrections [440,442,443], with potential ways forward discussed in Refs. [444,445].\nGiven these open questions, \u03b1S fits based on CIPT have been excluded from the latest world average [35].\n2State-of-the-art calculations can be found in, e.g., Refs. [423,424,427,432\u2013434].\n67\n\nA deeper understanding of these aspects is necessary for robust determinations of \u03b1S from \u03c4 decays at\nFCC-ee.\nThe sensitivity to \u03b1S of differential observables, e.g., in the final states discussed in the previous\nsection, makes them also suitable for precise extractions of the strong coupling. Currently, different \u03b1S\ndeterminations from these observables are included in the world average [371\u2013373, 446\u2013460], and can\ndiffer from each other by up to a few standard deviations. Besides the high-accuracy perturbative ingredi-\nents described above, such fits require input on hadronisation effects. Non-perturbative radiation induces\nO(\u039bp\nQCD/Qp) changes in the observables (with typically p = 1) that must be estimated to achieve the\ndesired precision. Aside from the different observables considered in the fit, a central difference be-\ntween these different \u03b1S determinations lies in how hadronisation corrections are evaluated (with either\nMonte Carlo models or analytic techniques) [421,461\u2013472]. The yet suboptimal internal consistency of\n\u03b1S determinations in e+e\u2212jet observables hints at unsatisfactory modelling of non-perturbative QCD\ndynamics, which poses a major bottleneck for precision phenomenology at FCC-ee and requires sub-\nstantial improvements in our understanding of this kinematic regime. First innovative steps towards this\nambitious goal are being taken within a dispersive model of the QCD coupling, which has recently been\nused to extract the leading non-perturbative scaling in three-jet final states [473\u2013476].\nData from FCC-ee will be very beneficial for deepening the understanding of hadronisation cor-\nrections. On the one hand, energies higher than those of previous lepton colliders would arguably justify\nthe further development of analytic models based on a power expansion in \u039bQCD/Q. On the other\nhand, the energy span and experimental accuracy of FCC-ee are instrumental in gaining better control of\nnon-perturbative dynamics in MC generators, which will be beneficial in all measurements expected at\nFCC-ee, such as e+e\u2212\u2192tt, e+e\u2212\u2192W+W\u2212, and e+e\u2212\u2192ZH. A complementary approach is given\nby the design of observables with reduced sensitivity to hadronisation, e.g., through jet-substructure\ntechniques [407\u2013410], which open promising avenues for complementary extractions of \u03b1S [477]. An\nin-depth study of the effectiveness of these techniques at FCC-ee energies, as well as the estimate of the\nremaining hadronisation corrections, are highly desirable in the coming years [477,478].\n3.2.2\nQCD aspects of Higgs physics\nReaching theoretical uncertainties aligned with the projections of Table 3 for Higgs precision studies\nrequires dedicated developments in different areas of both QCD and EW calculations. While EW cor-\nrections are discussed in Section 3.1, this section focuses on QCD aspects. The clean experimental\nconditions at FCC-ee allow a detailed and exclusive study of the hadronic decays of the Higgs boson.\nPartial widths are currently theoretically known at the per-cent level, with a parametric uncertainty on\n\u03b1S(m2\nZ) that will be significantly reduced at FCC-ee with the expected 0.1% precision achieved in this\nparameter. More specifically, in the case of H \u2192bb, N4LO QCD corrections are known in the limit of\nmassless bottom quarks [425, 479, 480], and N4LO QCD corrections to H \u2192gg have been computed\nin the heavy-top-mass limit [425]. The simulation of Higgs decays is paramount both for correcting the\nfiducial acceptance of the experiments and for studying kinematic distributions of the decay products and\njet observables. These distributions are sensitive to quark Yukawa couplings [481,482] or to new physics\nstates [168, 172, 483\u2013485]. The sensitivity to light-quark Yukawa couplings can be enhanced by means\nof modern quark and gluon tagging techniques [486].\nA key application is the extraction of the strange-quark Yukawa coupling, for which preliminary\nstudies have shown promising results (Section 4.5.1). Among the challenges in the realisation of this\nmeasurement, a relevant theory bottleneck is the separation of the H \u2192ss decay from the Dalitz decay\nof a Higgs to a pair of either gluons (QCD mediated) or photons (EW mediated) followed by a glu-\non/photon splitting into strange quarks. Initial investigations [487] indicate that this background can be\ndrastically suppressed by a cut in the invariant mass of the pair of jets originating from the fragmentation\nof the two strange quarks, mj1j2 \u2273100 GeV. A robust theoretical control of the H \u2192ss signal in this\nregion requires accurate perturbative calculations as well as the resummation of logarithmic corrections\n68\n\nstemming from soft-gluon radiation off the final-state strange quarks near the Higgs mass threshold,\nmj1j2 \u223cmH. Together with advances in perturbative calculations, a second essential element in this\nendeavour is the development of improved hadronisation models to distinguish the non-perturbative frag-\nmentation of (strange) quarks from that of gluons. Such models are instrumental for the reliable training\nof jet taggers, and their calibration within future Monte Carlo generators will highly benefit from the\nprecise QCD data collected at FCC-ee.\nRecently, considerable steps have been taken in the calculation of theoretical predictions for Higgs\ndecays, which are essential for the implementation of the above ideas. The predicted kinematic distribu-\ntions of the H \u2192bb decay products are known up to N3LO in the limit of massless b quarks [488\u2013493]\nand NNLO (and partially beyond) mass corrections are available [494\u2013501]. Similarly, differential QCD\npredictions for H \u2192gg are now available up to N3LO in the large-top-mass limit [502]. Finite quark\nmass corrections to H \u2192gg are relevant at the level of precision foreseen at FCC-ee and could be\nincluded up to NNLO in QCD in the near future with state-of-the-art calculations [495,503\u2013509]. Cal-\nculations of hadronic event shapes and jet resolutions at NLO [510\u2013512] and NNLO [513] in QCD have\nalso been performed in recent years, including the treatment of mass logarithms in the relevant virtual\namplitudes [514\u2013522] and of Sudakov logarithms in event-shape distributions [523]. Similar to Z bo-\nson decays, the relatively low-energy scale involved in the Higgs boson decays (\u223cmH) implies that\nnon-perturbative QCD effects have a sizeable impact on most differential distributions of hadronic Higgs\ndecay products. Therefore, the considerations made in Section 3.2.1 apply here as well. The FCC-ee\nHiggs programme will benefit enormously from future developments in the modelling of hadronisation\neffects.\n3.2.3\nQCD modelling of the top-quark threshold\nThe properties of top quark, such as its mass, width, and EW couplings (Table 2) are scheduled to\nbe measured at FCC-ee with runs at centre-of-mass energies between 340 and 365 GeV. The top mass\ncan be extracted with high precision at FCC-ee through a threshold scan, where the top-quark pair is\nnon-relativistic. Suitable definitions of short-distance top-mass schemes unaffected by ambiguities re-\nlated to infrared physics are available [524\u2013528], and can be exploited for precise predictions of the \u03c3tt\nvs. \u221as lineshape. Although NNLO and N3LO fixed-order QCD calculations are available [529, 530],\n\u03c3tt receives a substantial contribution from Coulomb-type interactions in this non-relativistic kinematic\nregime. These effects can be accurately described in the context of effective field theories derived from\nnon-relativistic QCD [531\u2013533], valid when the top quark velocity is of order \u03b1S. A lot of effort has\nbeen devoted to computing predictions in this framework, including QCD effects up to N3LO [534]\n(see also Refs. [535, 536] and references therein), approximate NNLL renormalisation-group improved\ncorrections [537], and the inclusion of EW effects within an analogous EFT framework [538].\nThe description of the final state W+W\u2212bb + X requires the inclusion of non-resonant channels\nthat do not involve the creation of a pair of on-shell top quarks. These non-resonant channels critically\ndemand embedding the aforementioned non-relativistic EFT into the unstable particle EFT [539, 540],\nwhere current predictions reach NNLO accuracy for the non-resonant part [538]. Projections for FCC-ee\nquote an expected theoretical accuracy for the top mass of O(50) MeV [538] in the potential-subtracted\ntop-mass scheme [527] (see also Refs. [541, 542]), with O(30) MeV scale uncertainties [75, 543]. Im-\nproving further on these results represents a formidable challenge for the field of precision calculations,\nfar beyond the current state of the art. The main steps include the computation of N4LO corrections in the\nnon-relativistic EFT framework, as well as the description of QED effects at NNLL both in the collinear\nlimit (e.g., ISR [544, 545]) and in the soft limit (as discussed in Ref. [546]). Moreover, the optimal\nexploitation of the FCC-ee measurements might also require the N3LO calculation for the non-resonant\nchannels.\nThe theoretical description of differential distributions is less accurate than that of the inclusive\nquantities just discussed, and reaches either NLO or NNLO accuracy only for specific observables [547,\n69\n\n548]. Further progress is needed in these computations, which are central to controlling precisely the\neffect of experimental cuts. Some aspects of these calculations pose considerable theoretical challenges,\nfor instance, concerning the differential calculations in the non-relativistic limit, or the assessment of\nnon-factorisable radiative corrections to the decays of the two top quarks [549].\n3.3\nMonte Carlo event generators\nAmong the theoretical developments necessary for the FCC-ee physics programme, the area of Monte\nCarlo (MC) event generators (see, e.g., Ref. [550] for a review of the current state of the art) plays\na pivotal role. These tools are instrumental not only for the accurate simulation of QCD and QED\neffects, but also for the calibration of the detectors as well as the training of analysis tools. The precision\nexpected at FCC-ee requires a significant improvement in MC generators, with respect to their previous\ngeneration, far exceeding the current state of the art. The following paragraphs summarise some of the\ncorresponding challenges, regarding QCD and EW (notably QED) aspects.\n3.3.1\nQCD aspects\nMonte Carlo generators simulate QCD corrections in three stages: the hard scattering at high momentum\ntransfer; the parton shower stage, in which the system evolves towards low momentum scales; and the\nnon-perturbative stage, which implements the transition of final state partons into hadrons. A first area\nwhere substantial improvement is necessary concerns the formulation of parton shower algorithms, given\nthat current public tools are generally limited to leading logarithmic (LL) accuracy. The precision goals\nof FCC-ee arguably demand NNLL accuracy or beyond, which is currently the subject of widespread\ninvestigations within the community. Specifically, state-of-the-art algorithms achieving NLL accuracy\nfor broad ranges of observables have recently been formulated [414,551\u2013563] with novel techniques that\nhelp bridge the field of parton showers with QCD resummations [551\u2013554, 556, 557, 559]. Significant\nprogress has also been made in the formulation of amplitude-level evolution [564, 565], which would\nultimately allow a systematic treatment of soft quantum interference effects in parton showers. Beyond\nNLL, several conceptual and technical problems become relevant, spanning from the inclusion of higher-\norder matrix elements [566\u2013571], to the formulation of consistent schemes for the treatment of virtual\ncorrections in the soft and collinear limits [383,417,571\u2013574], and to the realisation of matching schemes\nto NLO matrix element corrections that preserve the shower accuracy [575]. The significant progress\nin the understanding of these aspects has recently resulted in the first class of NNLL parton-shower\nalgorithms [576] capable of achieving this perturbative accuracy for event-shape observables at lepton\ncolliders. This progress suggests that fully general NNLL parton showers may become available for\nphenomenology applications in the coming years.\nA second aspect with much scope for improvement is the matching of parton showers to higher-\norder calculations for the hard scattering. Presently, an array of techniques allows NLO [577\u2013582] or\nNNLO [583\u2013587] QCD calculations (and possibly beyond [588]) to be matched to LL parton showers.\nThese techniques have been applied to the differential simulation of Higgs boson decays [589,590], but\nwill arguably need to be revisited in light of the recent progress in advancing the accuracy of parton\nshowers [575].\nFurther necessary developments concern the accurate production of particle pairs at threshold\n(e.g., tt or W+W\u2212), for which significant challenges arise from the inclusion of effects related to\nnon-relativistic dynamics and unstable particle decay (Section 3.2.3) within event generators. Notable\nprogress in the development of resonance-aware matching has been made for top-pair production in\nhadronic collisions [548,591,592]. However, a full description of the hierarchy of scales involved in the\nprocess (top-quark velocity v, mtop, and width \u0393top) is not available in existing generators and requires\nsignificant conceptual advances.\nA final area that requires significant improvement in view of the precision required at FCC-ee is\n70\n\nthe modelling of non-perturbative corrections, especially in the fragmentation of light partons and heavy\nquarks, central in the simulated performance of flavour tagging algorithms. Possible advances may\ncome from a combination of generators with higher perturbative accuracy, as discussed above, and more\nversatile parametrisations and tuning of non-perturbative effects, for which the use of machine learning\ntechnology offers a promising alternative to current models [593\u2013595]. The tuning of these models bene-\nfit from the ability to select large high-purity data samples enriched with specific flavours (such as gluons\nand b quarks), essential for the direct training of jet taggers on experimental data. Valuable experimental\ndata for the calibration and testing of non-perturbative corrections could be collected from measurements\nof observables performed with hadronic invariant masses below the Z-boson resonance. Such measure-\nments are accessible either via dedicated runs at lower \u221as or from hard initial-state radiation away from\nthe Z-pole run. Preliminary feasibility studies [596, 597] indicate that O(109) events can be collected\nat various energy points over the 20\u201380 GeV hadronic mass range, enabling a variety of measurements\nuseful for the development and testing of non-perturbative models.\nFinally, the experimental accuracy expected in resonance production, such as e+e\u2212\u2192W+W\u2212\u2192\nqq\u2032q\u2032\u2032q\u2032\u2032\u2032 or e+e\u2212\u2192tt, will likely demand improved models of colour reconnection [598], which will\nbe calibrated with the accurate data available for these processes.\n3.3.2\nQED aspects\nThe tools based on Yennie, Frautschi, and Suura (YFS) exponentiation [599] provide a promising frame-\nwork for systematically improving the precision of QED (and QCD) radiative processes in MC gener-\nators. While the soft logarithms, arising from the real and virtual enhanced regions of phase space, are\nresummed to infinite order in the YFS formalism, the remaining collinear logarithms are not. These algo-\nrithms can be incorporated order by order, and the associated divergences can be regularised by including\nmasses for all leptons. The YFS treatment is completely exclusive for multiple photon emission.\nThe KKMC event generator uses a variant of YFS exponentiation called Coherent Exclusive Expo-\nnentiation (CEEX). The most recent version, 5.00.2, of the KKMC package [600] includes improvements\nfor the simulation of fermion pair production. Work is ongoing to include additional collinear con-\ntributions in the YFS framework [601], beam spread parametrisations, and better descriptions of tau\ndecays [602].\nYFS resummation has been implemented in the SHERPA-3 series in an automatic framework [603]\nfor both the initial (ISR) and final (FSR) state QED radiation. Initial-final state interference (IFI) QED ef-\nfects within the YFS framework are currently implemented in KKMC but not in SHERPA, for which they\nremain an essential target for future improvements, especially for the prediction of forward-backward\nasymmetries at FCC-ee. Using SHERPA\u2019s automated matrix element generators, the ISR resummation\ncan be applied to any e+e\u2212process, while final state radiation is currently restricted to leptonic states\nonly. The matching of this resummation to higher-order perturbative corrections is also automated within\nSHERPA, including the effects of collinear logarithms. The procedure renders finite the higher-order cor-\nrections, which by themselves can be infrared divergent. One-loop electroweak corrections are provided\nby automated tools such as RECOLA [604], while SHERPA automatically creates the YFS subtraction\nterm such that the end result is infrared finite. The real corrections can also be included in a similar\nfashion using internal automated tools. Since the subtraction has been automated within the SHERPA\nframework, the current limitation on the perturbative accuracy is missing higher-order corrections, in\nparticular multiloop calculations. However, as these calculations become available, it is relatively simple\nto include them within the YFS resummation framework.\nThese higher-order corrections can be provided by external electroweak libraries, which con-\ntain process-dependent multi-loop matrix elements and that can be interfaced with MC tools.\nThe\nDIZET 6.45 [605] package contains most of the currently known higher-order corrections for Z-pole\nphysics. For systematic extensions to higher levels of precision, however, a flexible object-oriented code\nlibrary would be more suitable, which is the goal of the new GRIFFIN project [606]. Its object-oriented\n71\n\nstructure also simplifies the interfacing with MC generators, fitting tools, and other external programs.\nThe study of aspects related to ISR has been the subject of recent work [607].\nAn alterna-\ntive approach to YFS factorisation for the description of ISR is based on collinear factorisation, as in\nRefs. [608\u2013610]. Unlike what happens in the YFS framework, a systematic resummation of collinear\nlogarithms is implemented, while soft corrections are only approximately described. Recent work has\nexpanded this formulation to the NLL order [544,545], which is relevant for the precision targets of FCC-\nee [610]. Such a formalism also offers a promising avenue for an alternative and independent simulation\nof QED radiation in parton showers.\n3.4\nOrganisation and support of future activities to improve theoretical precision\nAs discussed in Section 3.1, the important targets for FCC precision physics have been defined. Theo-\nretical progress is limited by several factors, ranging from the analytic control and classification of the\nintegral structures due to appear at higher-loop order to the numerical challenges of integration or event\ngeneration. A rather diverse expertise is needed to address all the different aspects of the problem. Most\ncalculations to improve the precision of EW and QCD observables at FCC-ee are therefore currently on-\ngoing as part of efforts by individual groups, historically engaged in this activity. The physics groups of\nthe FCC Feasibility Study are overseeing the coordination of the different efforts, via their regular meet-\nings and dedicated workshops. The workshops are an opportunity to discuss and share information on the\nprogress of the various groups, as well as to refine the definition of the precision targets and milestones.\nRecent examples of these workshops include \u2018Precision EW and QCD Calculations for the FCC Stud-\nies: methods and tools\u2019 [38], \u2018Precision calculations for future e+e\u2212colliders: targets and tools\u2019 [316],\n\u2018Parton Showers for future e+e\u2212colliders\u2019 [341], and, in 2024, \u2018Frontiers in precision phenomenology:\nresummation, amplitudes, and subtraction\u2019 [611].\nThe Future Colliders Unit at CERN has made resources available to host researchers engaged in\nFCC studies and, in particular, precision studies, either as long-term Scientific Associates (SASS) or as\nshort-term visitors (STV). These visitors interact with the current CERN Theory Group staff and fellows,\nproviding a constant presence of world experts on EW and QCD precision calculations.\nActivities related to HL-LHC and its precision goals are intimately connected with FCC studies:\nthe LHC precision needs are pushing both the fields of QCD, EW, and mixed QCD \u2295EW calculations.\nOn the QCD side, higher-order perturbative calculations develop technology that can be adapted to EW\nhigher-loop cases, in addition to pushing the precision of QCD predictions for FCC-ee at the Z peak. A\nmore profound understanding of non-perturbative effects of interest to the LHC (e.g., the study of lead-\ning and subleading power corrections) directly impacts the leading theoretical uncertainties ultimately\naffecting the precision of, for example, the extraction of \u03b1S at FCC-ee. The sensitivity of LHC mea-\nsurements to EW effects, furthermore, is pushing the development of higher-order EW calculations, with\ndirect benefit for the pure EW programme of FCC-ee. As a consequence, all the efforts of CERN and of\nthe wider community, dedicated to precision physics at the LHC must be seen as milestones towards the\nachievement of the FCC-ee precision goals.\nIn this context, a new initiative is being undertaken by the LHC Physics Centre at CERN (LPCC),\nwith the creation of a global effort dedicated to coordinate and support studies in the domain of event\ngenerators and multi-loop calculations, also building on the success of the former MCnet network [612].\nThis activity, in addition to continuing the coordinated Monte Carlo development work established by\nMCnet \u2014 opening it to MC codes not covered by MCnet so far and preserving the student mentoring\nand educational activities \u2014 will support research to improve the projected computing performance of\nevent generators and of multi-loop codes, exploring the opportunities offered by new hardware high-\nperformance computing architectures (e.g., GPUs). The numerical complexity and CPU cost are recog-\nnised as a limiting factor in implementing the highest-available theoretical precision in event generators\nthat can be used for realistic studies of the experimental data. These improvements are, therefore, a\ncritical step towards the realistic study of FCC-ee detector performance in the context of precision ob-\n72\n\nservables.\nTo summarise: the theoretical field of precision studies for FCC-ee is multifaceted, touching on\ndiverse challenges in both the formal and numerical fields and thus calling on diverse expertise. The\nstructures that have been put in place during the FCC feasibility study allow these developments to be\naddressed and coordinated, engaging the most qualified and experienced researchers in the community.\nThese steps towards the goal of matching theoretical and experimental uncertainties are important and\npromising, in order to optimally exploit the data from FCC-ee and, later, from FCC-hh. While it will be\nyears before the necessary precision goals are attained, the efforts initiated during the period of the FCC\nfeasibility study have began defining a clear roadmap. The approval of the FCC project will catalyse\nthe engagement of the theory community. The past and ongoing successes in enhancing the precision\nof LHC predictions, beyond any previous expectation, give confidence in the feasibility of attaining the\nFCC theory precision targets.\n73\n\n74\n\n4\nDetector requirements\n4.1\nIntroduction\nThe detector performance specifications required by the physics programme of a future electron-positron\nHiggs factory operating at the ZH production threshold and above, have been studied in the past for\nlinear colliders. The different FCC-ee experimental environment, on the one hand, and the rich FCC-ee\nelectroweak, QCD, and flavour physics programme offered by the very large event samples anticipated at\nthe Z resonance (the so-called \u2018Tera-Z\u2019 run), on the other, come with specific and entirely new challenges.\nThe statistical uncertainties expected on key electroweak measurements, both at the Z peak and at the\nWW threshold, call for a superb control of the systematic uncertainties, and put commensurate demands\non the acceptance, construction quality and stability of the detectors. The specific discovery potential of\nfeebly coupled particles in the huge FCC-ee event samples should also be kept in mind when designing\nthe detectors.\nGeneral considerations on the requirements for an FCC-ee detector were outlined in Refs. [36,54].\nIn this section, a few benchmark analyses [53] are selected and their sensitivity dependence on various\naspects of the detector performance are studied. In some cases, these studies result in a quantified per-\nformance requirement. It is understood that the extremely broad range of FCC-ee measurements has not\nyet been completely covered, and that some important requirements may be missing. The analyses per-\nformed for this report make use of the simulation of the performance of the detector concepts considered\nso far and described in Sections 6.2 (CLD), 6.3 (IDEA), and 6.4 (ALLEGRO). For the reader\u2019s conve-\nnience, a brief account of these three concepts is given below, in Section 4.2; they are an important input\nto further optimisations and to the development of new concepts that might be better adapted to parts of\nthe FCC-ee physics programme. As mentioned in Section 1, FCC-ee will accommodate four interaction\npoints. A single experiment may not be perfect in all aspects; a configuration with 4 IPs allows a range\nof detector solutions that will cover all physics opportunities.\nMost of the studies reported here have been performed using computer-generated events processed\nthrough a fast detector simulation performed with the DELPHES package. The chosen baseline is the\nIDEA detector [10] described in Section 6.3. More details about the DELPHES simulations used for the\nstudies reported here can be found in Section 8.5. To investigate the impact of the detector performance,\nvariations around this detector baseline have been studied, either by smearing the reconstructed objects\nat the analysis level or by producing dedicated event samples. For some tracker-related studies, the\nperformance expected with the CLD detector [613] has also been looked at. The CLD main tracker\nconsists of a set of layers of silicon sensors, in sharp contrast with the gaseous drift chamber of the\nIDEA detector. One study using a GEANT simulation of the ALLEGRO noble-liquid calorimeter has\nalso been made. A few preliminary performance studies or physics analyses have been performed using\na full simulation of the CLD detector, as shown in Section 4.10. After a brief overview of the detector\nbenchmarks implemented in the simulations used for the studies reported here, the following sections\naddress, in turn, the requirements on the various subdetectors.\n4.2\nBrief overview of the current detector concepts\nTwo detector concepts have been studied for FCC-ee at the time of the CDR: CLD, a consolidated option\nbased on the detector design developed for CLIC, with a silicon tracker and a 3D-imaging highly-granular\ncalorimeter; and IDEA, an innovative design developed specifically for FCC-ee, with a short-drift wire\nchamber and a dual-readout calorimeter. Since then, a third concept, ALLEGRO, has been proposed\nand is being developed, with an electromagnetic calorimeter based on a noble liquid. The three concepts\nconsidered so far have similar overall dimensions, with a length of 11\u201313 m and a height of 10\u201312 m.\nMore details on these detector concepts are given in Section 6.\n75\n\n4.2.1\nThe IDEA detector concept\nThe tracking system of IDEA3 includes a silicon vertex detector (VXD) surrounded by a low mass drift\nchamber and an external layer of silicon micro-strip detectors. In the version used for the studies reported\nhere, the VXD consists of a cylindrical \u2018barrel\u2019 section made of five single layers of sensors, at radii\nbetween R = 1.2 and 31.5 cm, and of two \u2018endcap\u2019 sections (one on each side of the interaction point),\neach made of three disks of single layers of sensors. The drift chamber (DC) has a total length of 4 m and\nconsists of 112 layers of wires, placed at radii between 35 and 200 cm. It allows \u2018continuous tracking\u2019\nand particle identification, as will be shown below. The total amount of DC material crossed by a particle\nemitted at 90\u25e6from the detector axis (defined by the bisector of the two beam axes) is 1.6% of a radiation\nlength. The DC is surrounded by a silicon wrapper that provides one precise spatial point at the end of the\nparticle trajectory and measures the time-of-arrival of charged particles. The tracking system is immersed\nin a 2 T magnetic field parallel to the detector axis, provided by a thin superconducting solenoid covering\nradii between 2.1 and 2.4 m. Outside the tracker, a preshower made of \u00b5RWELL detectors and a dual-\nreadout calorimeter of 2 m depth and 7 interaction lengths, made of lead and fibres, measure the position\nand energy of electromagnetic and hadron showers. The dual-readout calorimeter (DRC) is sensitive\nto the independent signals from scintillation and Cerenkov light production, resulting in an excellent\nenergy resolution for both electromagnetic and hadron showers. The simulations used here include\na modification of the CDR calorimeter design, in which a 20 cm deep (dual readout) electromagnetic\ncalorimeter made of crystals is added upstream of the DRC, following Ref. [614]. Finally, the muon\nsystem consists of layers of chambers based on \u00b5RWELL detectors embedded in the magnet return\nyoke.\n4.2.2\nThe CLD detector concept\nThe CLD4 detector has been adapted to the FCC-ee specificities from the CLIC detector model; it fea-\ntures a silicon pixel vertex detector and a silicon tracker, followed by a highly granular calorimeter. For\nthe simulations used here, the barrel section of the VXD consists of three double-layers of sensors, at\nradii ranging between 1.2 and 5.8 cm, and two endcap sections, consisting of three disks each, built as\ndouble-layer devices. The silicon tracker is made of six barrel layers, at radii from 12.7 cm to 2.1 m,\nand of two sets of eleven endcap disks. The material budget for the tracker modules is estimated to be\n1.1\u20132.1% of a radiation length per layer. The tracker is surrounded by a silicon-tungsten electromag-\nnetic calorimeter (ECAL), which is 30 cm or 22 X0 deep, and by a scintillator-steel hadron calorimeter\n(HCAL), that extends up to R = 3.6 m; the combined ECAL plus HCAL thickness corresponds to 6.5\ninteraction lengths. The very high granularity of the calorimeter makes it particularly well suited for\n\u2018particle flow\u2019 reconstruction techniques that, in CLD, are the key for reaching very good resolutions. A\nsuperconducting solenoid, delivering a 2 T magnetic field, surrounds the calorimeter, at a radius of about\n3.7 m. The iron return yoke is instrumented with resistive plate chambers (RPC) that form the muon\ndetection system. A detailed description of the CLD detector can be found in Ref. [613].\n4.2.3\nThe ALLEGRO detector concept\nThe design of ALLEGRO5 is more recent than the IDEA and CLD designs. Its tracking system consists\nof a silicon vertex detector and a main tracker, which could either also be made of silicon sensors or be\na gaseous detector. Surrounding the tracker is a high granularity noble-liquid ECAL, which could be\nmade of lead (or tungsten) and liquid argon or, alternatively, of tungsten and liquid krypton. The magnet\ncoil separates the ECAL from the high-granularity HCAL, which could be made of steel absorber plates\ninterleaved with scintillator tiles, as envisaged for the CLD calorimeter. For the muon system, several\noptions are under consideration.\n3Innovative Detector for an Electron-positron Accelerator.\n4CLIC-Like Detector.\n5A Lepton-Lepton collider Experiment with Granular Read-Out.\n76\n\n4.3\nMeasurement of the tracks of charged particles\nThe detection of charged particles and the measurement of their momenta before they traverse a large\namount of high density material is crucial for all physics analyses and for a successful particle-flow\nreconstruction [615]. This section deals with properties that are mostly related to the main tracker: the\nprecise measurement of the track momentum and angles, and the reconstruction of highly-displaced\nvertices. The determination of the track impact parameters, which is largely provided by the vertex\ndetector, is treated in Section 4.4. The measurement of quantities related to the ionisation energy per unit\nlength, useful to identify the nature of a charged particle, is covered in Section 4.5.\n4.3.1\nTrack momentum resolution: the measurement of the Higgs boson mass\nThe track momentum resolution is a key handle in many analyses. In particular, it directly impacts\nthe reconstructed masses, which are often used to suppress backgrounds. Both IDEA and CLD tracker\ndesigns would offer an excellent track momentum resolution. For example, for 10 GeV (50 GeV) muons\nemitted at an angle of 90\u25e6with respect to the detector axis, the momentum resolution is about 0.5h\n(1.5h) with the very light drift chamber of IDEA and about 2.5h (3h) with the heavier full silicon\ntracker of CLD, the latter being dominated by the effect of multiple scattering. Some examples from\nB physics, showing how the exceptional momentum resolution of the IDEA tracker separates the signals\nfrom the backgrounds, are presented in Sections 4.5.3 and 4.8.\nIn this section, the needs on the track momentum resolution are illustrated with the measurement\nof the Higgs boson mass, mH, which needs to be known to better than 4 MeV (its intrinsic width), in\nview of a potential run at the Higgs resonance (Section 9.4).\nThis measurement, described in detail in Ref. [63], exploits the Higgs-strahlung process, i.e.,\nthe associated production of a Z and a Higgs boson. Since, at a lepton collider, the total energy and\nmomentum of the final state are well known, the mass of the system that recoils against the Z, called\nrecoil mass and denoted mrecoil, can be reconstructed exclusively considering the Z decay products,\nirrespective of the Higgs boson decay. The mrecoil distribution exhibits a sharp peak at mH, so that a\nfit to this distribution provides a precise measurement of the Higgs boson mass. Experimentally, the\nchannel where the Z decays into a pair of muons offers the best resolution. A fit to the mrecoil distribution\nfor Z(\u00b5\u00b5)H events at \u221as = 240 GeV is displayed in the left panel of Fig. 48, for various assumptions\non the muon momentum resolution, while the right panel shows the result of a likelihood fit of the\ndistribution of signal events in the presence of background, with the same assumptions. Even with a\nperfect measurement of the momentum of the muons, the width of the mrecoil peak would be limited\nby the beam energy spread (BES), which amounts6 to 0.185% of the beam energy at \u221as = 240 GeV,\nso that mH would be determined with an uncertainty of 3.95 MeV (including the contribution of other\nsub-dominant systematic uncertainties [63]), for an integrated luminosity of 10.8 ab\u22121.\nThe decay muons, with typical momentum of O(50) GeV, should be measured with a momentum\nresolution better than the BES, so that the mass resolution be not limited by the momentum measure-\nment7. This goal is achieved with the IDEA detector (black curves in Fig. 48), only considering the\nmuon decay channel. The full silicon tracker of CLD, in its current implementation, performs less well\n(green curves) because of the larger amount of material, which leads to increased multiple scattering, the\nfactor that dominates the muon momentum resolution, even for the relatively high momentum range of\ninterest. However, the goal of 4 MeV on the measured Higgs boson mass would most likely be achieved\nby combining the muon and electron decay channels (Section 4.6). The blue curves in Fig. 48 show what\nwould be expected, with the IDEA tracker, if the detector magnetic field were increased from 2 to 3 T8;\n6The beam energy spread values used for the studies reported here are taken from Ref. [616].\n7Having a momentum resolution for O(50) GeV muons better than or comparable to the BES is also an important require-\nment in the search for Z \u2192\u03c4\u00b5 lepton flavour violating decays, at \u221as = 91 GeV. The analysis strategy requires a clear tau\ndecay in one hemisphere and a beam-energy muon in the other, in order to suppress the Z \u2192\u03c4\u03c4 background [194].\n8For the highest luminosity runs at the Z peak, the magnetic field of the detector is constrained to not exceed about 2 T,\n77\n\n122 123 124 125 126 127 128 129 130\n131 132\nRecoil (GeV)\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nEvents / 50 MeV\n)H\n\u2212\n\u00b5\n+\n\u00b5\nMuon final state Z(\nIDEA\nIDEA perfect resolution\nIDEA 3T\nIDEA CLD silicon tracker\n1\n\u2212\n = 240 GeV, 10.8 ab\ns\nSimulation\n \nFCCee\n124.99\n124.995\n125\n125.005\n125.01\n (GeV)\nh\nm\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nNLL\n\u2206\n-2\n)H (stat. + syst.)\n\u2212\n\u00b5\n+\n\u00b5\nMuon final state Z(\n) = 4.74 MeV\nh\n(m\n\u03b4\nIDEA \n) = 3.95 MeV\nh\n(m\n\u03b4\nIDEA perfect resolution \n) = 4.14 MeV\nh\n(m\n\u03b4\nIDEA 3T \n) = 5.73 MeV\nh\n(m\n\u03b4\nIDEA CLD silicon tracker \n1\n\u2212\n = 240 GeV, 10.8 ab\ns\nSimulation\n \nFCC-ee\nFig. 48: Left: Fits to the distribution of the Higgs boson recoil mass in ZH events, where the Z decays into muons,\nassuming an ideal momentum resolution (red), such that the resolution on the recoil mass is determined by the\nbeam energy spread, or the momentum resolution of the IDEA (black and blue) or CLD (green) detectors. The\nblue curve corresponds to a 3 T magnetic field, instead of the 2 T field used for the other distributions. Right:\nCorresponding Higgs boson mass measurements.\nthe result is a 33% improvement of the momentum resolution and a 14% improvement on the total mass\nuncertainty.\n4.3.2\nTrack momentum resolution: the Z width and the stability of the momentum scale\nThe point-to-point uncertainty on the centre-of-mass energy in the scan of the Z lineshape is, together\nwith the knowledge of the BES and the point-to-point uncertainty on the integrated luminosity, a dom-\ninant source of systematic uncertainty in the Z width measurement. The reconstructed peak position of\nthe dimuon invariant mass distribution in e+e\u2212\u2192\u00b5+\u00b5\u2212events provides a measurement of the centre-\nof-mass energy. As proposed in Ref. [22] and developed in Ref. [617], the aforementioned uncertainty\ncan be assessed from the difference in this reconstructed peak position between the energy points used\nin the lineshape scan. More details about the method are given in Section 9.2. Figure 49 shows the\nstatistical uncertainty with which the peak position is expected to be determined at \u221as = 87.9, 91.2,\nand 94.3 GeV, with the full FCC-ee event sample. With the track momentum resolution provided by the\nIDEA tracker, this precision reaches 20 keV for the two off-peak energies, such that the difference in\nthe collision energy at these two points can be measured with an uncertainty of about 28 keV, leading\nto an 11 keV uncertainty on the extracted Z width. With the resolution offered by the CLD tracker, this\ndifference is measured with two times larger uncertainty, resulting in an uncertainty of 22 keV in the Z\nwidth.\nSuch a precision, however, requires that the scale of the momentum measurements (and, in par-\nticular, of the magnetic field) be stable at the level of a few 10\u22127 (20 keV over \u221as, to ensure a 20 keV\nuncertainty on the peak position) or, at least, that its variations be monitored at that level. A monitoring\nat this level of precision may be difficult to achieve with magnetic NMR probes. However, the large sam-\nples of well-known resonances, in particular of KS decaying into \u03c0+\u03c0\u2212, provide an in-situ monitoring at\nas explained in Section 5. At \u221as = 240 GeV, the blow-up of the beam emittance that results from a higher magnetic field is\nnegligible and running, for example, with a 3 T field, which would provide a better track momentum resolution, is not ruled\nout.\n78\n\n87.9 GeV\n91.2 GeV\n94.3 GeV\n0\n10\n20\n30\n40\n50\n60\n70\n80\nUncertainty (keV)\nGen. level\nIDEA\nCLD\nFig. 49: Statistical uncertainty in the peak position of the measured dimuon invariant mass distribution, expected\nwith the full FCC-ee event sample of the Z lineshape scan (125 ab\u22121 at the Z peak and 40 ab\u22121 at each off-peak\nenergy). This uncertainty is shown assuming an ideal detector resolution (leftmost bars), the resolution of the\nIDEA tracker (middle bars), and that of the CLD tracker (rightmost bars).\nthis exceptional precision. An efficient and high purity algorithm that reconstructs KS \u2192\u03c0+\u03c0\u2212decays\nis presented below. It allows a KS to be reconstructed in about every second Z event, when the Z decays\nhadronically. With a mass resolution better than 400 keV with the IDEA detector, the position of the KS\nmass peak can be determined with a relative uncertainty of 2.3 \u00d7 10\u22129 with an integrated luminosity of\n40 ab\u22121 at \u221as = 87.9 GeV (and even better at \u221as = 94.3 GeV, given the larger cross section). This\ndataset could, hence, be split into, e.g., 100 subsamples in time, and the KS resonance be reconstructed\nin 100 bins, to ensure monitoring of the scale stability at the required level of 2.3 \u00d7 10\u22127.\n4.3.3\nAngular resolutions\nThe polar and azimuthal angles of the momentum of a prompt charged particle, at its production vertex,\nare given by the angles of the corresponding track at its distance of closest approach to the detector axis.\nThe angular resolutions in the two detector concepts considered so far vary between about 20 \u00b5rad for\nhigh momentum particles produced in the central region of the detector and a few mrad for soft forward\nparticles [613, 618]. The contribution of these angular resolutions to the uncertainty in the recoil mass\nshown above is negligible compared to that of the momentum resolution. For the reconstruction of\nthe mass of heavy-flavoured hadrons, the momenta of the daughter particles must be taken at the decay\nvertex of the hadron and the resolution of the azimuthal angle crucially relies on the reconstruction of this\ndecay vertex (see Section 4.4). Nevertheless, for all examples considered involving B mesons (see, e.g.,\nSections 4.5.3 and 4.8), the mass resolution remains completely dominated by the momentum resolution.\nA precise determination of the polar and azimuthal angles is crucial for exploiting the over-\nconstrained kinematics of many processes in e+e\u2212collisions. That is the case, in particular, of muon\npair production. As shown in Ref. [22], for e+e\u2212\u2192\u00b5+\u00b5\u2212(\u03b3) dimuon events, the crossing angle and the\nlongitudinal momentum imbalance can be reconstructed event-by-event from the sole measurement of\nthe polar and azimuthal angles of both muons. The BES, which is a crucial ingredient in the extraction\nof the Z width at Tera-Z, can then be derived from the width of the longitudinal momentum imbalance\ndistribution. To ensure that the BES uncertainty has a negligible effect on the extracted Z width, muon\ntracks from Z decays must be measured with an angular resolution of 0.1 mrad or better, a requirement\nfulfilled [613,618] by the detector concepts presented in the CDR. Moreover, the mean of the longitudi-\nnal momentum imbalance distribution provides the longitudinal boost. Its determination constrains the\nenergy losses of the beams in their separate rings [47] and, consequently, has a crucial influence on the\n79\n\nprecision of the Z and W mass measurements.\nAnother example that exploits the angles of dimuon events is the determination of the centre-of-\nmass energy well above the WW threshold, where the resonant depolarisation method cannot be applied.\nIn particular, at \u221as = 240 GeV, the centre-of-mass energy needs to be determined to O(1) MeV in order\nnot to spoil the Higgs boson mass determination from the recoil mass. The over-constrained kinematics\nof radiative return events e+e\u2212\u2192Z(\u03b3) with Z \u2192\u00b5+\u00b5\u2212(accompanied by an initial-state radiated photon\nalong the direction of one of the beams) allows the determination of \u221as from the precise knowledge of\nthe Z mass and the muon angles alone. The target precision for the \u221as measurement may set tighter\nrequirements on the angular resolutions than those given above.\n4.3.4\nNumber of tracker layers and highly-displaced vertices\nThe reconstruction of long-lived particles (LLPs) that decay into charged particles within the tracker\nvolume after having crossed the innermost layers of the vertex detector requires that the main tracker be\nable to efficiently identify such highly-displaced vertices. Typical use cases are the searches for LLPs\npredicted in many models that extend the Standard Model (Section 2.3 and Refs. [125, 173]) or the\nreconstruction of decays that involve KS or \u039b hadrons.\nAs an example, the case of KS mesons produced in B+ \u2192K+D0 decays, followed by the decay\nof the D0 meson into a KS\u03c00 pair, is considered here. The reconstruction of the KS \u2192\u03c0+\u03c0\u2212decay is\ndetailed in Ref. [271]. The KS candidates are built from pairs of opposite-charge particle tracks that do\nnot come from the primary vertex and that can be fitted to a common vertex, with a reconstructed mass\nclose to the nominal KS mass.\n of Ks vertex (mm) \nxyz\n L\n0\n500\n1000\n1500\n2000\n Reco Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n-\u03c0\n+\n\u03c0\n \n\u2192\n \ns\nK\nIDEA\n | < 0.95\n\u03b8\n | cos \n+\n K\nD\n )\n0\n\u03c0\n \ns\n ( K\n\u2192\n \n+\nB\nloose mass cut\n 5 MeV\n\u00b1\n mass \ns\nK\n 2.5 MeV\n\u00b1\n mass \ns\nK\n of Ks vertex (mm) \nxyz\n L\n0\n500\n1000\n1500\n2000\n Reco Efficiency\n0\n0.2\n0.4\n0.6\n0.8\n1\n-\u03c0\n+\n\u03c0\n \n\u2192\n \ns\nK\nCLD\n | < 0.95\n\u03b8\n | cos \nNhits >= 5\n+\n K\nD\n )\n0\n\u03c0\n \ns\n ( K\n\u2192\n \n+\nB\nloose mass cut\n 5 MeV\n\u00b1\n mass \ns\nK\n 2.5 MeV\n\u00b1\n mass \ns\nK\nFig. 50: The KS reconstruction efficiency for kaons emitted in B+ \u2192(KS\u03c00)D K+ decays, as a function of\nthe distance Lxyz between the KS decay vertex and the interaction point, for several thresholds on the KS mass\ncandidate, for the IDEA (left) and CLD (right) detector concepts.\nThe KS reconstruction efficiency obtained with the IDEA detector is shown in Fig. 50 (left), as\na function of the distance between the KS decay vertex and the interaction point, Lxyz. The efficiency\nis defined for the KS mesons that come from B+ \u2192(KS\u03c00)D K+ decays for which the daughter pions\nsatisfy the acceptance requirement | cos \u03b8| < 0.95. Within a mass window of \u00b15 MeV, the efficiency\nremains higher than 80%, as long as the KS meson decays within 1.5 m from the interaction point9. At\nlarger distances, the efficiency drops because the pion tracks only traverse a small fraction of the tracker.\n9The drop in efficiency observed at small flight distances is due to the correlation of the flight distance with the KS momen-\n80\n\nThe right panel of Fig. 50 shows the corresponding efficiency for events processed through a DELPHES\nsimulation of the CLD detector. As expected, the performance is much worse than that of IDEA. Steps\ncorresponding to the positions of the tracker layers are clearly visible. For example, since there are only\nfour barrel layers at a radial distance larger than 40 cm, the efficiency for selecting 5-hit tracks displaced\nby more than 40 cm vanishes in the central region, explaining the first step seen in the figure. Also, the\nKS mesons that decay within a few tens of centimetres from the IP have a lower detection efficiency\nthan that of the IDEA drift chamber, given the larger amount of material of the full silicon tracker and\nthe correspondingly larger multiple scattering and worse resolutions on the KS reconstructed vertex and\nmass.\nWhile some optimisations could be made to the full silicon tracker considered here, it is clear that\nan efficient reconstruction of KS \u2192\u03c0+\u03c0\u2212decays and, more generally, of long-lived particles that lead\nto late appearing tracks calls for a highly transparent tracker, a large tracking volume, and a considerable\nnumber of measurement layers.\n4.3.5\nWork ahead\nTracker acceptance and efficiencies\nThe search for the B \u2192K\u2217\u03c4\u03c4 rare decay, described in more detail in Section 4.4.2, sets requirements\non the track efficiencies. Demanding that both taus decay into three prongs is particularly useful for\nthis analysis and leads to a final state with six soft pion tracks. A momentum acceptance down to 100\u2013\n150 MeV is necessary to maintain a good signal efficiency. With a magnetic field of 2 T, the requirement\nof a minimum number of, e.g., 5 hits to reconstruct a track, implies that there be at least five measurement\nlayers at a radius smaller than 33 cm (50 cm) to reconstruct a track with a transverse momentum of\n100 MeV (150 MeV). This requirement on the position of the layers of the vertex detector and of the\ninnermost layers of the main tracker is fulfilled by both the IDEA and the CLD tracker designs [613,618].\nAs an illustration, the tracking efficiency as a function of transverse momentum is shown in Fig. 51 (left),\nfor tracks reconstructed with a novel machine-learning algorithm, discussed in Section 4.10. In addition,\nthe track reconstruction efficiency as a function of the distance to the closest charged hadron in a jet\nis shown in Fig. 51 (right). It indicates that CLD features a slightly larger efficiency in dense hadronic\nenvironments, possibly due to a better separation capability of two close-by tracks, driven by the superior\nsingle-point spatial resolution provided by silicon sensors.\nThe measurement of the luminosity from e+e\u2212\u2192\u03b3\u03b3 events (Section 4.6), to a precision of about\n10\u22125, requires a very precise knowledge of the large background from e+e\u2212\u2192e+e\u2212events. The\ntargeted precision will set a requirement on the e/\u03b3 separation that, in turn, will constrain the tracker\ninefficiency and the precision with which this inefficiency is known. In addition, the ratio of the partial\nwidth of the Z boson decay into hadrons to that into muons, R\u00b5, will be measured with a statistical\nprecision of about 5 \u00d7 10\u22126 at Tera-Z. Counting the number of \u00b5+\u00b5\u2212events with a similar level of\nsystematic uncertainty sets a very challenging requirement on the knowledge of the tracking (and muon\nchamber) efficiency.\nTrack angles\nThe angular resolutions provided by the current tracker designs comply, with a good safety margin,\nwith the requirements set by the studies done so far, as shown above. Further studies are needed to\ncheck if other measurements set tighter requirements. Beside the measurement of \u221as from the radiative\nreturn events previously mentioned, methods that are being developed to precisely determine dilepton\nacceptance in-situ (Section 4.6.3) may call for better angular resolutions.\ntum: the pion tracks from KS mesons that decay close to the IP are softer and more affected by multiple scattering or may lead\nto curling tracks (\u2018loopers\u2019).\n81\n\n10\u22121\n100\n101\npT [GeV]\n0.8\n0.9\n1.0\nTracking e\ufb03ciency\nZ/\u03b3\u2217\u2192q\u00afq(q = u, d)\n10 < \u03b8 < 170\u25e6,\nvertex R < 50 mm\n\u2206> 0.02 rad\nCLD\nIDEA\n10\u22122\n10\u22121\n100\n\u2206[rad]\n0.90\n0.92\n0.94\n0.96\n0.98\n1.00\nTracking e\ufb03ciency\nZ/\u03b3\u2217\u2192q\u00afq(q = u, d)\n10 < \u03b8 < 170\u25e6,\npT > 1 GeV, vertex R < 50 mm\nCLD\nIDEA\nFig. 51: Tracking efficiency evaluated with full simulation of the CLD and IDEA detectors using the ML-based\napproaches, as a function of pT (left) and of the angle \u2206MC to the closest generated charged particle (right).\n4.3.6\nPreliminary conclusions\nThe performance of a gaseous tracker and of a full silicon tracker have been shown and quantified with\nseveral examples.\n\u2013 Having a large number of measurement points along the tracks, as offered by a gaseous tracker, is\ncrucial for an efficient reconstruction of KS and \u039b hadrons or other long-lived particles that decay\ninto charged particles, and is a clear bonus for an experiment with a strong focus on flavour or\nBSM physics.\n\u2013 The momentum resolution offered by both designs looks adequate for Higgs boson measurements.\nThis statement probably holds as well for most electroweak measurements, with the notable ex-\nception of the Z width measurement. For flavour physics at the Z peak, where low momentum\ntracks are involved, a low mass gaseous tracker is advantageous since the momentum resolution is\nminimally affected by multiple scattering.\n\u2013 The tracker volume, extending to a radius of about 2 m, may have to be reduced a little in order\nto free some space to accommodate a detector dedicated to charged-hadron particle identification\n(which may be needed in particular for the CLD option, see Section 4.5). A reduction by O(20) cm\nwould degrade the momentum resolution by about 15%, as shown in Section 6.6. This effect might\nbe partly compensated by reducing the amount of material in the CLD tracker layers.\n4.4\nRequirements for the vertex detector\nThe measurement of the track impact parameters is driven by the performance of the vertex detector, as\nit provides very precise spatial points in the tracker layers closest to the beams. A precise measurement\nof these parameters is crucial for reconstructing vertices, for efficient identification of heavy quarks and\nof taus, and for accurate lifetime measurements. The resolution on these parameters typically scales as\n\u03c3(d0) = a \u2295\nb\np sin3/2 \u03b8\n,\n(6)\nwhere the asymptotic term, a, is driven by the single hit resolution, while the second term represents\nthe contribution of multiple scattering and depends on the material of the vertex detector layers and of\n82\n\nthe beam pipe. The radial distance of the first layer of the vertex detector is also crucial [486]. In the\nsimulations used for the studies reported here, the radius of the beam pipe is 1 cm, that of the innermost\nlayer of the vertex detector is 1.2 cm, and the material crossed by a particle emitted at a polar angle \u03b8\nbefore the first VXD measurement corresponds to 0.67% / sin \u03b8 of a radiation length.\n4.4.1\nHeavy-flavour tagging and the Higgs boson coupling to charm quarks\nPrevious flavour tagging studies made for linear colliders [619,620] colliders concluded that a \u22485 \u00b5m\nand b \u224815 \u00b5m/GeV (in Eq. 6) are adequate for measuring the Higgs boson couplings to bottom and\ncharm quarks. These requirements have been revisited in the context of the present study. In particular,\nmajor progress has been made in recent years in the field of flavour tagging algorithms. Machine-learning\napproaches, on one hand, and the ever increasing computing power, on the other, have significantly\nimproved the performance of flavour tagging with respect to that of the algorithms that were the state-of-\nthe-art a decade ago, so that more ambitious goals can be contemplated today. The algorithm developed\nfor the studies reported here is based on PARTICLENET [621] and uses state-of-the-art jet representations\nand an advanced graph neural network architecture. This algorithm is referred to as PARTICLENETIDEA\nand is described in more detail in Ref. [486]. With this new tool, an efficient and pure identification of\njets induced by gluons or even strange quarks (see Section 4.5.1) is available and the tagging efficiency\nof bottom and charm quarks is much larger than what was achieved with the previous generation of\nalgorithms, for the same purity.\nThis algorithm is a key ingredient in the measurement of the Higgs boson couplings to bottom,\ncharm, and strange quarks, as well as to gluons, as described in detail in Ref. [64]. The analysis exploits\nthe ZH events at \u221as = 240 GeV and considers the channels where the Z boson decays to pairs of\nmuons or electrons, to jets, or to neutrinos, the latter channel currently providing the best sensitivity.\nThe probabilities that each jet originates from a bottom, charm, or strange quark, or from a gluon, are\ndetermined by the PARTICLENETIDEA algorithm and are used to categorise events into orthogonal\ncategories, each enriched in one of the different Higgs boson decay modes and depleted in the others.\nThe branching ratios of the Higgs boson decays to bb, cc, ss, and gg pairs are measured in all\ncategories with a simultaneous fit to the recoil mass distributions (and, for the Z \u2192\u03bd\u03bd channel, to the\nvisible mass distributions).\nThe anticipated precision of the coupling measurements is summarised in Section 2.2. With an\nintegrated luminosity of 10.8 ab\u22121, the H \u2192bb and H \u2192cc event yields (cross section times branching\nratio) can be measured with a precision of 0.21% and 1.66%, respectively.\nThe dependence of this precision on alternative beam pipe and vertex detector configurations has\nbeen studied and compared to the sensitivity obtained with the baseline IDEA detector design. Beam\npipes with twice or half the nominal material budget have been studied. A vertex detector with the barrel\nlayers shifted by 0.5 cm towards larger radii and an option where the heavier beam pipe is complemented\nby a single-point resolution degraded by a factor of 2 have also been considered. The measurement of the\nH \u2192cc and H \u2192bb branching fractions is marginally improved or degraded for the assumed better or\nworse scenarios. A transverse impact parameter resolution of 2\u20133 \u00b5m is achieved with the baseline IDEA\nvertex detector. A resolution worsened by a factor of 2 remains largely sufficient to identify displaced\ntracks originating from boosted D and B meson decays produced in H \u2192bb and cc decays and has,\ntherefore, a small impact on the expected precision. A comprehensive discussion on the impact of vertex\ndetector assumptions on the tagging performance can be found in Ref. [622].\n4.4.2\nReconstruction of vertices and the measurement of the B \u2192K\u2217\u03c4\u03c4 branching fraction\nWith the current version of the IDEA detector, the primary vertex, for example in events where a Z\ndecays to hadrons, is typically reconstructed with a resolution of 2\u20133 \u00b5m in the x and z coordinates, and\nof a few tens of nm in the y direction (driven by the r.m.s. of the beam position in the vertical direction,\n83\n\nas shown in Table 14, Section 5), using a beamspot constraint in the vertex fit. For displaced vertices, the\nresolution depends very much on the track multiplicity of the vertex, on the track momenta and angles,\nand on the angular separation of the tracks. In the various B-physics processes that have been looked into\nso far, the resolution on the 3D distance between the interaction point and the displaced vertex typically\nvaries between \u223c10 and \u223c80\u00b5m. For example, in the Bs \u2192DsK decay, where the Ds decays to KK\u03c0,\nthe resolution of 15 \u00b5m obtained on the Bs decay vertex is sufficient for time-dependent CP violation\nmeasurements, since it is O(40) times smaller than the distance travelled by the Bs during one oscillation\nperiod.\nHowever, some processes of interest for flavour physics impose very strong demands on the recon-\nstruction of vertices. So far, the most stringent requirements on the performance of the vertex detector\ncome from the measurement of the branching ratio of the, yet unobserved, B \u2192K\u2217\u03c4\u03c4 decay. This\nbranching fraction is predicted to be very small in the Standard Model, at the level of O(10\u22127), and\nthe current experimental upper limit is larger than this prediction by three orders of magnitude. New\nphysics contributions can potentially result in a significant enhancement of this branching fraction. Con-\nsequently, its measurement is an important goal of the FCC-ee physics programme. A detailed analysis\nof the feasibility of this measurement at the Z pole is reported in Ref. [211], and is summarised below.\nFig. 52: Decay chain under study for a measurement of the B \u2192K\u2217\u03c4\u03c4 branching fraction.\nWhen both \u03c4 leptons decay into three charged pions and a neutrino, there are enough kinematic\nconstraints to completely reconstruct the decay, as illustrated in Fig. 52. The \u03c4 decay vertices (TV) are\nobtained from their daughter pion tracks. The secondary vertex (SV) is reconstructed from the two tracks\n(the kaon and the pion) produced by the K\u2217decay. The flight direction of each \u03c4 is then determined from\nthe line that joins the SV to each corresponding TV. The component of the neutrino momentum that\nis transverse to this flight direction is obtained as the opposite of the transverse component of the mo-\nmentum of the three charged pions. The \u03c4 mass constraint finally provides the remaining longitudinal\ncomponent of the neutrino momentum. Clearly, this reconstruction relies critically on the precise recon-\nstruction of the secondary and tertiary vertices.\nSeveral b \u2192ccs and b \u2192c\u03c4\u03bd transitions lead to final states that are similar to that of the signal,\napart from the presence of additional neutrinos and neutral pions; a powerful \u03c00 identification is needed\nto suppress these backgrounds. A \u03c00 identification efficiency of 80% is assumed here. A multi-variate\nanalysis allows the background to be reduced to a manageable, albeit still large, level. As an example,\nFig. 53 shows the distribution of the mass of the B candidates for a case where the resolution of the\nposition of the secondary and tertiary vertices is 20 \u00b5m in the longitudinal direction and 5 \u00b5m in the\ntransverse direction10. The remaining background under the B mass peak is dominated by irreducible\nbackground processes.\nThe numbers of signal (N) and background events are determined in the 5.0\u20136.0 GeV range of\n10For each tertiary or secondary vertex, the longitudinal direction is defined by the flight direction of the decaying particle.\n84\n\n4.6\n4.8\n5.0\n5.2\n5.4\n5.6\n5.8\n6.0\nm(K\u2217[3\u03c0]\u03c4[3\u03c0]\u03c4) [GeV]\n0\n20\n40\n60\n80\n100\n120\nCandidates / (0.030 GeV)\nPV (3.0\u00b5m, 0.0238\u00b5m, 3.0\u00b5m) & SV & TV (20.0\u00b5m, 5.0\u00b5m)\nProbability to identify a \u03c00 = 0.80\nBd \u2192K\u22170DsDs(Ds \u2192\u03c4\u03bd)\nBd \u2192K\u22170DsDs(Ds \u2192\u03c0\u03c0\u03c0\u03c00)\nBd \u2192K\u22170Ds\u03c4\u03bd(Ds \u2192\u03c4\u03bd)\nBd \u2192K\u22170DsDs(Ds \u2192\u03c0\u03c0\u03c0\u03c00\u03c00)\nBd \u2192K\u22170D\u2217\nsDs(D\u2217\ns \u2192Ds\u03b3, Ds \u2192\u03c4\u03bd)\nBd \u2192K\u22170DsDs(Ds \u2192\u03c4\u03bd, Ds \u2192\u03c0\u03c0\u03c0\u03c00)\nBd \u2192K\u22170D\u2217\ns\u03c4\u03bd(D\u2217\ns \u2192Ds\u03b3, Ds \u2192\u03c0\u03c0\u03c0\u03c00\u03c00)\nBd \u2192K\u22170DsDs(Ds \u2192\u03c4\u03bd, Ds \u2192\u03c0\u03c0\u03c0\u03c00\u03c00)\nBd \u2192K\u22170D\u2217\nsDs(D\u2217\ns \u2192Ds\u03b3, Ds \u2192\u03c0\u03c0\u03c0\u03c00\u03c00)\nsig\nsig + bkg\u2019s\nFig. 53: Distribution of the mass of the B candidates after the full selection, assuming that the secondary and\ntertiary vertices can be reconstructed with a resolution of 5 \u00b5m (20 \u00b5m) in the transverse (longitudinal) direction.\nThe normalisation corresponds to a total of 6 \u00d7 1012 produced Z bosons.\ninvariant mass from a maximum likelihood fit. The significance of the signal in this range is used as a\nconservative figure of merit of the reconstruction performance. This significance has been determined\nfor several assumptions on the vertex resolution. It shows a very strong dependence on the resolution of\nthe position of the secondary and tertiary vertices in the transverse direction11, as can be seen from the\nblack dots in Fig. 54. With an event sample corresponding to 6 \u00d7 1012 produced Z bosons, a resolution\nbetter than \u223c4.3 \u00b5m is needed to see evidence (3 \u03c3) of the decay mode under study and it should be\nbetter than \u223c2.2 \u00b5m for the observation (5 \u03c3) of this decay. With the version of the IDEA detector that is\nused as a baseline for this report this resolution is only 5 \u00b5m, as shown by the blue star symbol in Fig. 54.\nTo reach the evidence and observation thresholds, the resolution on the track impact parameters needs to\nbe improved by about 10% and 40%, respectively, with respect to the nominal IDEA resolutions12.\nIn order to investigate if and how these improvements can be achieved, additional DELPHES signal\nsamples have been produced, with an alternative tracker description, with less tracker material13 and an\nimproved single hit resolution. The results are shown in Fig. 54 by the additional star symbols. An\nimprovement of the single hit resolution in the VXD layers by 30% (i.e., from 3 to 2 \u00b5m in the barrel\nlayers) brings the sensitivity beyond the 3 \u03c3 evidence threshold, as shown by the yellow symbol. This\nthreshold is also reached with a 50% reduction of the VXD material, as shown by the magenta symbol.\nHowever, the impact of this sole improvement is limited by the material of the beam pipe, which causes\ncharged particles to experience multiple scattering before they enter the detector. Indeed, in the nominal\nIDEA simulations used here, the material of the beam pipe is twice that of a VXD layer, so that to\nprofit from the reduction in the material of the VXD layers the beam pipe transparency also needs to\nbe increased. The green symbol in Fig. 54 shows that, by reducing by 50% the material of both the\nbeam pipe and the VXD layers, the sensitivity increases to about 3.5 \u03c3, under the SM hypothesis for the\nconsidered branching fraction. Additional handles will be exploited to increase the sensitivity beyond\n11The dependence on the resolution in the longitudinal direction is much milder.\n12Restricting the invariant mass to the 5.2\u20135.6 GeV range would yield a local significance of the signal of about 5 \u03c3, but\nthis value is obtained assuming an accurate knowledge of the functional shapes of signal and background candidates, which\nrequires a study that goes beyond the scope of this work.\n13The decay of interest comprises eight charged particles plus two neutrinos and, hence, features low momentum charged\nparticles to be reconstructed. The reduction of the material is therefore one natural improvement to test, in view of minimising\nmultiple Coulomb scattering in the resolution sources.\n85\n\n0\n2\n4\n6\n8\nSV and TV transverse smearing in \u00b5m\n0.2\n0.3\n0.4\n0.5\n0.6\n\u03c3N/N\n2\u03c3\nEvidence (3\u03c3)\nObservation (5\u03c3)\nPrecision of BF measurement as function of the resolution\nSV and TV longitudinal smearing : 20 \u00b5m\nIDEA baseline\n50% reduced material budget in VXD layers\n30% better SH resolution\n50% reduced material budget in VXD layers and BP\nFig. 54: Statistical uncertainty on the B \u2192K\u2217\u03c4\u03c4 branching fraction expected from an event sample corresponding\nto 6 \u00d7 1012 Z bosons, as a function of the resolution of the position of the secondary and tertiary vertices, in the\ntransverse direction. The blue star shows the precision expected with the version of the IDEA detector used in the\nnominal simulations. The additional star symbols show how the sensitivity improves in alternative simulations of\nthe IDEA detector.\nthe 5 \u03c3 discovery level.\n4.4.3\nVertex resolutions and heavy-flavour electroweak precision observables\nThe FCC-ee operation at the Z-pole offers an immense potential for the measurement of the heavy-quark\nelectroweak precision observables, the partial decay-width ratios Rb(c) = \u0393(Z \u2192bb (cc)) / \u0393(Z \u2192\nhadrons), and the heavy-quark forward-backward production asymmetries Ab(c)\nFB . A huge improvement\nof the statistical uncertainty is expected, with respect to the LEP measurements (by up to a factor of\n2000), thanks not only to the large luminosity increase but also to the improvements in vertex detector\ntechnologies and tagging algorithms. Experimental strategies that go beyond the current state-of-the-art\nmethods also have to be developed, in order to reduce the systematic uncertainties in these measurements,\ndown to a level commensurate with the expected statistical precision. Earlier measurements have shown\nthat the contamination from light quarks is a large source of systematic uncertainty. Taking advantage\nof the very large number of Z bosons that will be produced at FCC-ee, a novel tagging technique has\nbeen pioneered in Ref. [623] for measuring Rb and Ab\nFB, which relies on the exclusive reconstruction of\na selected list of b-hadron decay modes. It allows hemispheres containing a b-hadron to be tagged with a\npurity larger than 99.8% and, using selected decay modes of charged B mesons, the charge of the hemi-\nsphere is determined unambiguously. After removing the contamination from light quark processes, the\nremaining source of systematic uncertainty for the Rb measurement is the correlation of tagging efficien-\ncies between the two hemispheres of an event. This uncertainty has been studied in detail in Ref. [623],\nusing generated events passed through a full simulation (including the reconstruction steps) of the CLD\ndetector. In particular, an improved selection of the b-hadron tracks based on their displacement with\nrespect to the luminous region has been shown to minimise the impact on the uncertainty of the ex-\nact knowledge of the correlation. The hemisphere correlation would need to be known with a relative\nprecision of only 10% to ensure that the corresponding systematic uncertainty on Rb is similar to the\nstatistical uncertainty, at the level of 0.015%. This results in a Rb determination that is 20 times more\nprecise than the current value, with a lot of potential to do even better. For the measurement of Ab\nFB, the\n86\n\n\u221220\n\u221215\n\u221210\n\u22125\n0\nlog(1 \u2212\u2126)\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\nA. U.\nZ pole, IDEA\nTrack IP resolution improved\nby 50 % and 25 %\nCuts for constant \u03b5c\nc\nSignal\nZ \u2192b\u00afb\nZ \u2192q\u00afq, q \u2208[u, d, s]\nFig. 55: Distribution of the pointing variable log(1 \u2212\u2126) for signal and background events, where D0 \u2192K+\u03c0\u2212\ndecays (and their charge-conjugates) are used to tag charmed hemispheres. The dashed and dash-dotted histograms\nshow how the discrimination improves when the resolution of track impact parameters is improved by 25% and\n50%, respectively, with respect to the nominal IDEA performance.\nremaining source of systematic uncertainty is the size of the QCD corrections. By exploiting acolinear-\nity [624] or b-hadron energy selection requirements, these corrections would need to be known with a\nrelative uncertainty of 1% for the statistical and systematic uncertainties to contribute equally to the total\nuncertainty. As a result, an improvement by a factor of 50 compared to the precision of the average of\nthe LEP measurements would be obtained.\nThese very small uncertainties motivate the use of exclusively reconstructed hadrons to measure\nRc as well. A first study, described in Ref. [625], exploits D0 \u2192K+\u03c0\u2212decays. The main contami-\nnation arises from Z \u2192bb events and needs to be reduced as much as possible to reach the expected\nstatistical precision of 5.3\u00d710\u22125 (corresponding to an improvement by a factor of about 60 compared to\nthe statistically most precise measurement from the SLD Collaboration [626]). This contamination can\nbe reduced by demanding that the \u2018pointing angle\u2019, i.e., the angle between the D0 momentum and the\nline that joins the primary vertex and the decay vertex of the D0, be close to zero. Figure 55 illustrates\nhow a cut on the cosine of this angle, \u2126, separates the signal from the background. The measurement\nof \u2126clearly depends on the reconstruction of the vertices, and the figure also shows how the discrimi-\nnation power increases when the resolution on the longitudinal and transverse track impact parameters\nimproves.\n4.4.4\nAlignment, overall scale of the detector, and the measurement of the tau lifetime\nPrecise measurements of the mass, the lifetime, and the leptonic branching fraction of the tau offer a\ncrucial test of lepton flavour universality (LFU) since, up to small radiative and electroweak corrections,\nthe following relation [435,627] holds between the muon and tau masses, their lifetimes \u03c4\u00b5 and \u03c4\u03c4, their\ncharged-current coupling constants g\u00b5 and g\u03c4, and their branching fractions into electrons and neutrinos:\n\u0012 g\u03c4\ng\u00b5\n\u00132\n\u2243\u03c4\u00b5\n\u03c4\u03c4\nB(\u03c4 \u2192e\u03bd\u03c4\u03bde)\nB(\u00b5 \u2192e\u03bd\u00b5\u03bde)\n\u0012m\u00b5\nm\u03c4\n\u00135\n.\n(7)\n87\n\nThis test, which can be seen as a determination of the Fermi constant from the tau, is currently limited\nby the precision of the \u03c4 lifetime, 290.3 \u00b1 0.5 fs, and by that of the B(\u03c4 \u2192e\u03bd\u03c4\u03bde) branching fraction,\n17.82\u00b10.04%. The measurement of B(\u03c4 \u2192\u00b5\u03bd\u03c4\u03bd\u00b5) allows additional similar tests of (g\u03c4/ge) and (g\u00b5/ge).\nWith the \u223c2 \u00d7 1011 tau pair events expected at Tera-Z, and a much improved determination of the\nthree key ingredients14 of Eq. (7), FCC-ee has the potential to test LFU at an unprecedented level. In\nparticular, the statistical uncertainty in the tau lifetime is expected to be about 15 ppm [195]. The current\nmeasurements, from the Belle and LEP experiments, are statistically limited and, for the two single\nmost precise measurements (Belle [628] and DELPHI [629]), the alignment of the vertex detector is\nthe dominant source of systematic uncertainty. While this alignment could, at first sight, appear to be a\nconcern in view of a lifetime measurement at the level of 15 ppm (which corresponds to a few tens of nm\non the flight distance of \u03c4 leptons produced at 91 GeV), a more careful investigation shows that this is not\nthe case [195]. Indeed, the offset on the decay length caused by misalignment effects averages to zero,\nto first order, when integrating over the azimuthal angle, as was first noted in Ref. [630]. The expected\nsystematic uncertainty due to misalignment, scaled from the value quoted by DELPHI according to the\nluminosity increase, is below 4 ppm. Other sources of systematic uncertainty have been considered in\nRef. [195]. One of them reflects the knowledge of the overall length scale of the vertex detector. For this\nuncertainty to be smaller than one half of the statistical uncertainty on the \u03c4 lifetime, that scale should\nbe known to better than 5 ppm. At LEP and at the B-factories this scale was only known to 100 ppm.\nHowever, recent developments made for the MUonE experiment indicate that a precision of 5 ppm is\nwithin reach, thanks to the use of optical techniques [631]. The leading systematic uncertainties are\nexpected to be due to the modelling of initial state radiation and to the knowledge of the tau mass, and a\ntotal systematic uncertainty of 16 ppm on the tau lifetime is deemed within reach [195].\n4.4.5\nPreliminary conclusions\n\u2013 One example has been shown where the physics outcome of FCC-ee would gain from having better\nvertex detector performance than the baseline detectors considered so far.\n\u2013 Minimising the amount of material in front of the vertex detector is important. Indeed, the material\nof the beam pipe is a limiting factor in some cases, in particular for observing the rare B \u2192K\u2217\u03c4\u03c4\ndecay.\n\u2013 It should be noted that these requirements, tighter than the ones presented for a linear collider de-\ntector, will have to be reached despite the additional constraints set by the FCC-ee environment on\nthe readout electronics of the detector: (i) its power budget is tighter than for a detector operating\nat a linear collider (since power-pulsing the electronics is not possible with collisions occurring\nevery \u223c20 ns), and (ii) it should handle a hit rate of about 200 MHz/cm2 in the innermost vertex\ndetector layer at the Z peak (Section 5.4).\n4.5\nRequirements for charged hadron particle identification\nCharged hadron particle identification (PID) is essential for the FCC-ee flavour physics programme and\nbrings significant benefits for other areas. The momentum range over which good PID capabilities are\nnecessary is broad, in sharp contrast with the PID needs of a B-factory. For flavour physics, for example,\nit extends from the lowest momentum of the reconstructed charged-particle tracks up to about 40 GeV. In\na gaseous tracker like the IDEA drift chamber, the determination of the number of ionisation clusters per\nunit length (dN/dx) is a promising approach that should allow charged kaons to be efficiently separated\nfrom charged pions in a large momentum range, from about 1.5 GeV to several tens of GeV. The expected\n14The knowledge of the \u03c4 lepton mass is also expected to be much improved from pair production threshold measurements\nat a next-generation tau-factory.\n88\n\nresolution on dN/dx is about 2%15, significantly better than that of the well-known measurement of\nionisation energy per unit length (dE/dx).\nTime-of-flight (TOF) measurements, in a single layer at a distance of about 2 m from the interac-\ntion point, fill the gap around 1 GeV16, where the average energy loss per unit length of kaons and pions\nis similar. However, they can only provide a 3 \u03c3 \u03c0/K separation at low momenta, up to about 3 GeV\nwith the 30 ps resolution assumed for the studies reported here17. Innovative solutions are being studied\nthat would provide good PID capabilities in the absence of a specific energy loss measurement, over the\nlarge momentum range of interest and despite the tight spatial constraints. A conceptual design exists for\na compact RICH detector, which looks promising and could comfortably cover the required momentum\nrange [632\u2013634]. An overview of the motivations for PID and of the possible detector solutions can be\nfound in Ref. [45]. This section illustrates the demands on PID performance with the measurement of\nthe Higgs boson coupling to strange quarks and with two B-physics processes.\n4.5.1\nStrange tagging and the Higgs boson coupling to strange (and charmed) quarks\nThe progress in the development of flavour-tagging algorithms in recent years allows, for the first time,\na relatively efficient and pure tagging of jets induced by strange quarks. Various analysis efforts are\nongoing within the circular and linear colliders communities. They all rely heavily on the identification\npower of state-of-the-art machine learning approaches.\n0\n0.2\n0.4\n0.6\n0.8\n1\njet tagging efficiency\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\njet misid. probability\nno PID\ndN/dx\n=30 ps)\nt\u03c3\ndN/dx + t.o.f ( \n=3 ps)\nt\u03c3\ndN/dx + t.o.f ( \nideal PID\n FCC-ee Simulation (IDEA)\n j j\n\u2192\n Z H , H \n\u2192\n -\ne\n+\n e\nj = u, d, s, c, b, g\ns tagging vs. ud\n0\n0.2\n0.4\n0.6\n0.8\n1\njet tagging efficiency\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\njet misid. probability\ns vs g\ns vs ud\ns vs c\ns vs b\n FCC-ee Simulation (IDEA)\ns tagging\n j j\n\u2192\n Z H , H \n\u2192\n -\ne\n+\n e\nj = u, d, s, c, b, g\nFig. 56: Performance of strange-quark tagging in jet samples from Z(\u03bd\u03bd)H events at \u221as = 240 GeV, where the\nHiggs boson decays into quarks of a well-defined flavour or into gluons. The left panel shows the impact of PID\non the separation power between jets induced by strange quarks and those induced by u or d quarks. The right\npanel shows how the algorithm separates strange jets from all other flavours. The \u2018s vs. ud\u2019 (black) curve in the\nright panel is identical to the red curve in the left panel.\nFigure 56 illustrates the performance of strange-quark tagging with the baseline IDEA detector\nused for this report, using the PARTICLENETIDEA algorithm [486]. As shown in the left panel, when\nno PID information is provided to the algorithm, the separation power between jets induced by strange\nquarks and those induced by u or d quarks is limited, as it mostly comes from the slightly harder energy\nspectrum of the constituents of a strange jet18. When the specific energy loss measured along the tracks\nwith the cluster counting technique is also used, the misidentification probability of jets induced by u\n15The promising performance of the dN/dx approach as determined from calculations, in particular the upper momentum\nbound, is being checked with test beam data.\n16This statement holds for a magnetic field of 2 T; the case of a higher field value is briefly considered in Section 4.9.1.\n17Even with a 10 ps resolution, the momentum range would only extend up to about 5 GeV.\n18The number of reconstructed KS \u2192\u03c0+\u03c0\u2212decays from displaced tracks associated with the jets (see Section 4.3.4) is not\nyet explicitly included in the set of variables used by the PARTICLENETIDEA algorithm; adding this variable may improve the\nperformance shown here.\n89\n\nor d quarks is reduced by about one order of magnitude, for the same s-quark tagging efficiency. In the\nkinematic range considered here, spanned by quarks produced in Z(\u03bd\u03bd)H(qq) events at \u221as = 240 GeV,\nthe time-of-flight information only brings a mild performance improvement. The right panel of Fig. 56\nshows how the algorithm separates strange jets from all other flavours, the separation from ud jets being,\nas expected, the most challenging. For a strange-quark tagging efficiency of 80% (90%), the mis-tag\nefficiency of ud jets reaches 20% (40%).\nThis tagging algorithm has been used to categorise Z(\u2113\u2113, jj)H(jj) events (where \u2113stands for e,\n\u00b5 or \u03bd) into mutually orthogonal categories enriched in one of the different Higgs boson decays (Sec-\ntion 4.4.1) and to extract the Higgs boson branching fractions to bb, cc, ss, and gg. With an integrated\nluminosity of 10.8 ab\u22121, the Higgs boson branching fraction to strange quarks would be measured with\na 105% uncertainty. More details can be found in Ref. [64].\nThe anticipated precision on the Higgs boson branching fractions to cc and ss has been explored\nfor several particle identification capabilities and the result is shown in Fig. 57. Given that charged\nkaons from strange quark hadronisation feature a hard momentum spectrum, it is crucial to have an\nefficient K/\u03c0 separation at large momenta, as provided by the dN/dx cluster counting technique. It is\nremarkable that the expected precision on the measurement of the H \u2192ss branching fraction, obtained\nby combining dN/dx with the time-of-flight technique, is almost identical to the asymptotic performance\nobtained with perfect PID capabilities. Conversely, if no PID is assumed, or only assuming ToF, the\nH \u2192ss branching fraction measurement cannot be performed, given an expected uncertainty in excess\nof 300%. The PID also plays a non-negligible role in the H \u2192cc branching fraction measurement, by\nenabling the identification of secondary charged kaons produced in D meson decays, as shown in the\nright panel of Fig. 57. A comprehensive discussion on the impact of PID on flavour tagging performance\ncan be found in Ref. [622].\nIDEA\nTruth PID\nonly dN/dX\n(no TOF)\nonly ToF (30 ps)\n(no dN/dX)\nNo PID\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\nuncertainty on BR(H \u2192s\u00afs)(%)\nPrecision of H \u2192s\u00afs vs. Particle ID assumptions\nIDEA\nTruth PID\nonly dN/dX\n(no TOF)\nonly ToF (30 ps)\n(no dN/dX)\nNo PID\n0.0\n0.3\n0.6\n0.9\n1.2\n1.5\n1.8\n2.1\n2.4\n2.7\n3.0\nuncertainty on BR(H \u2192c\u00afc)(%)\nPrecision of H \u2192c\u00afc vs. Particle ID assumptions\nFig. 57: Relative uncertainty in the H \u2192ss (left) and H \u2192cc (right) branching fractions, as expected for several\nassumptions on particle identification performance setups.\n4.5.2\nSeparation of K\u00b1 from \u03c0\u00b1 and measurement of b \u2192s\u03bd\u03bd\nThe trillions of bb events that will be collected, in a clean environment, during the Tera-Z run at FCC-ee\nmakes it the ideal facility to study rare decays of b hadrons. Among those, the modes corresponding to the\nb \u2192s\u03bd\u03bd transition are of considerable interest within the flavour physics community19. A first sensitivity\n19The first evidence for this transition has been recently obtained by the Belle II Collaboration in the B+ \u2192K+\u03bd\u03bd decay\nchannel [635]. In the future, with an integrated luminosity of 50 ab\u22121, Belle II is expected to measure the corresponding\nbranching fraction with O(10%) experimental precision [223].\n90\n\nstudy for FCC-ee, using the decays B \u2192K\u2217\u03bd\u03bd and Bs \u2192\u03c6\u03bd\u03bd, is detailed in Ref. [224]. According to the\nStandard Model, both decays should have branching fractions around 10\u22125. The current experimental\nupper limit on the branching fraction of B \u2192K\u2217\u03bd\u03bd is larger than this prediction by a factor of two,\nwhile for Bs \u2192\u03c6\u03bd\u03bd, the upper limit is two orders of magnitude larger. The study looks for a K\u2217or a\n\u03c6 resonance in a hemisphere with a large amount of missing energy and runs a multi-variate analysis,\nfollowing the strategy described in Ref. [222]. Assuming a perfect PID, the B \u2192K\u2217\u03bd\u03bd (Bs \u2192\u03c6\u03bd\u03bd)\nsignal can be selected with an efficiency of 3.7% (7.4%), for a signal-to-background ratio of 0.17 (0.13).\nWith 6 \u00d7 1012 Z bosons produced, this corresponds to a sensitivity of 0.5% for B \u2192K\u2217\u03bd\u03bd and of\n1.2% for Bs \u2192\u03c6\u03bd\u03bd. Here, sensitivity is defined as the relative precision expected on the branching\nfraction, computed as\n\u221a\nS + B/S, where S and B are the expected numbers of signal and background\nevents, respectively. The dependence of this sensitivity on the performance of the \u03c0/K separation that\nthe detector would achieve is shown in Fig. 58. With a separation power of 2 \u03c3, the loss in sensitivity,\ncompared to what is expected with perfect PID, is marginal, but it degrades quickly as the performance\nworsens. The momentum of the kaons involved in these decays peaks at about 3 GeV, but extends up to\n15\u201320 GeV, hence the PID performance offered by time-of-flight measurements alone is unlikely to be\nsufficient for this analysis.\n0\n1\n2\n3\n4\n5\nK-\u03c0 separation power [\u03c3]\n70\n75\n80\n85\n90\n95\n100\nSensitivity dilution [%]\n89.5%\n98.5%\n99.9%\n0\n1\n2\n3\n4\n5\nK-\u03c0 separation power [\u03c3]\n0\n20\n40\n60\n80\n100\nSensitivity dilution [%]\n81.1%\n97.6%\n99.9%\nFig. 58: Sensitivity to the B \u2192K\u2217\u03bd\u03bd (left) and Bs \u2192\u03c6\u03bd\u03bd (right) branching fractions, as a function of the \u03c0/K\nseparation power, with respect to the sensitivity assuming perfect PID.\n4.5.3\nSeparation of K\u00b1 from \u03c0\u00b1 and measurement of Bs \u2192DsK\nThe measurement of time-dependent CP asymmetries in the decay Bs \u2192DsK is a well-known method to\nextract the \u03b3 angle of the CKM matrix, which is currently only known with a precision of 4 degrees. The\nprospects for this measurement at FCC-ee have been first studied in Ref. [272], using the Ds \u2192\u03c6(KK)\u03c0\ndecay channel. The presence of the \u03c6 resonance and the absence of neutral particles among the final\ndecay products makes this signal easy to reconstruct. A precision on the \u03b3 angle of a few tenths of a\ndegree was shown to be within reach at FCC-ee, using only this decay mode20.\nThe study reported in Ref. [272], which considered a few exclusive background processes and\nused a simple parametrisation of the detector response, has been redone for this report with DELPHES\nto simulate the response of the IDEA detector and accounting for the inclusive Z \u2192bb and Z \u2192cc\nbackgrounds. The analysis starts by exploiting the mass resolution to reconstruct the \u03c6 candidates and,\nafterwards, the Ds candidates, without any PID requirement. In a second step, Bs candidates are built\n20A similar sensitivity is expected from the Phase-2 LHCb upgrade, with an integrated luminosity of 300 fb\u22121 [269]. The\nFCC-ee sensitivity can be improved by including other Ds decay modes, in particular those that include neutral particles (see\nSection 4.6.2).\n91\n\n5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.4 5.41\nK) (GeV)\ns\nm (D\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n6\n10\n\u00d7\n Entries\nK\ns\n D\n\u2192\n \ns\nB\n\u03c0\ns\n D\n\u2192\n \ns\nB\n\u03c0\ns\n D*\n\u2192\n \ns\nB\n cc\n\u2192\nZ \nOthers\n\u03c1\ns\n D\n\u2192\n \ns\nB\nK\ns\n D*\n\u2192\n \ns\nB\nK*\ns\n D\n\u2192\n \ns\nB\n\u03c0\ns\n D*\n\u2192\n \nd\nB\n-1\nK, 100 ab\ns\n D\n\u2192\n \ns\nB\n5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.4 5.41\nK) (GeV)\ns\nm (D\n0\n10\n20\n30\n40\n50\n3\n10\n\u00d7\n Entries\nK\ns\n D\n\u2192\n \ns\nB\n\u03c0\ns\n D\n\u2192\n \ns\nB\n\u03c0\ns\n D*\n\u2192\n \ns\nB\n cc\n\u2192\nZ \nOthers\n-1\nK, 100 ab\ns\n D\n\u2192\n \ns\nB\nFig. 59: Mass distributions of the Bs candidates in the Bs \u2192DsK \u2192\u03c6(KK)\u03c0K decay channel, prior to any PID\ncut (left) and after requiring that the \u2018bachelor\u2019 (the particle accompanying the reconstructed Ds) must be identified\nas a kaon (right). The momentum of the \u2018bachelor\u2019 is required to be larger than 1.5 GeV.\nby fitting the Ds and another track (the \u2018bachelor\u2019) to a common vertex [636]. The invariant mass of the\nBs candidates satisfying minimal kinematic and vertex \u03c72 cuts is shown in the left panel of Fig. 59. The\nsignal, shown in dark green, is very well separated from the ten times larger Bs \u2192Ds\u03c0 background,\nshown in red. However, running the same selection over the inclusive Z \u2192bb sample shows that there\nare other sources of backgrounds that contaminate the signal mass peak, in addition to the exclusive\nbackgrounds that were considered in Ref. [272] and that are also shown in Fig. 59. The right panel of\nthis figure shows that this background is largely suppressed by requiring that the \u2018bachelor\u2019 particle must\nbe identified as a kaon, which is done by using a PID cut that is 95% efficient on the signal. The PID\ncut uses the ratio of the likelihoods for the \u2018bachelor\u2019 to be a kaon or a pion and combines the dN/dx\nmeasurement of the track, determined with a resolution of about 2%, and the measurement of its TOF\nat 2 m from the interaction point, with a 30 ps resolution. Even for this mode with charged particles\nonly, PID capabilities appear to be mandatory to extract the signal with a decent signal-to-background\nratio. Since the momentum distribution of the kaons from Bs \u2192DsK decays is hard, time-of-flight\nmeasurements alone would not lead to an acceptable background suppression. For example, in a mass\nwindow that contains 95% of the reconstructed Bs candidates (the signal), the background contamination\ndecreases from 48%, without any PID, to 33% if only the TOF measurement is used, and to 19% if both\nthe dN/dx and TOF measurements are used (assuming the PID capabilities of IDEA). This last value\nwould degrade to 24% with a twice worse dN/dx resolution.\n4.5.4\nWork ahead\n\u2013 The measurement of time-dependent CP asymmetries in the Bs system requires the flavour of the\nmeson (Bs or Bs) to be tagged at the time of production. Various algorithms are typically com-\nbined to achieve this goal. A powerful method uses the charge of the kaons in the event that are\nnot associated with the signal decay, which typically have momenta well below 10 GeV. The per-\nformance of flavour tagging is studied in order to provide requirements on PID at low momentum.\nFor example, the determination of the angle \u03b3 of the CKM matrix, from the Bs \u2192DsK process,\nor of the phase \u03b2s, from the Bs \u2192J/\u03c8 \u03c6 decay, could serve as benchmark measurements. The\nidentification of very soft fragmentation kaons (produced when a b (anti-)quark hadronises into a\n92\n\nBs meson), for which the PID performance brought by TOF measurements is relevant, should also\nplay a key role in the measurement of the branching fraction of the Bs \u2192\u03bd\u03bd decay.\n\u2013 The determination of Vcs from W decays may benchmark the performance of strange-quark tag-\nging for working points with a much higher purity than that needed for the determination of the\ncoupling of the Higgs boson to the strange quark. Alternatively, Vcs may be measured in events\nwhere exclusive decays of charmed hadrons into kaons are selected, calling for a good \u03c0/K sep-\naration. More generally, electroweak measurements involving strange quarks, such as Rs or As\nFB,\nare studied for the requirements on the PID performance.\n\u2013 A very precise test of lepton flavour universality in the tau sector is provided by the simultaneous\nmeasurements, at the 10\u22125 level, of the tau lifetime and of the branching fraction of its decay to\nelectrons (Section 4.4.4). The latter requires a e/\u03c0 separation controlled at the 10\u22125 level, which\nmight be difficult to achieve from calorimetry measurements alone. The requirements on dE/dx\nor dN/dx measurements should also be studied in the context of e/\u03c0 separation.\n4.5.5\nPreliminary conclusions\n\u2013 It is not only for flavour physics that charged-hadron PID is needed. In particular, the potential\nfor constraining the coupling of the Higgs boson to the strange quark provides a strong motivation\nfor having PID, up to high momenta. Similarly, powerful strange tagging offers new prospects\nfor electroweak and top measurements in the strange sector, such as measurements of the Z \u2192ss\nbranching fraction [637] and forward-backward asymmetry, or of the Vts CKM element via rare\nt \u2192Ws decays [638].\n\u2013 The momentum range to be covered, extending from O(150) MeV to 40 GeV, is challenging. Cur-\nrent studies show that the \u03c0/K separation offered by the cluster counting approach, in the IDEA\ndrift chamber, is probably adequate. A degradation of the resolution of the energy loss measure-\nment by a factor of 2, with respect to what is expected from the baseline IDEA dN/dx performance,\nwould have a non-negligible impact on the determination of the Higgs coupling to strange quarks.\nSuch a degradation would correspond to the expected dE/dx performance.\n\u2013 In the absence of specific energy loss measurements in the tracker, there is a conceptual design for a\ncompact RICH detector that looks promising and could comfortably cover the required momentum\nrange. Detailed simulation studies are needed to evaluate the impact of such a detector on particle-\nflow reconstruction performance.\n4.6\nRequirements for electromagnetic calorimetry\nThis section summarises the needs for the measurement of electromagnetic (EM) showers, which may,\nbut does not have to, be performed in a dedicated electromagnetic calorimeter (ECAL). In the baseline\nIDEA concept, the EM showers are measured using a finely segmented crystal ECAL with dual readout\ncapabilities [614]. In a variant of this concept, considered in Ref. [10], the electromagnetic and hadron\nshowers are both measured in a dual readout (DR) calorimeter that uses scintillation and Cerenkov fi-\nbres. The CLD concept uses a high-granularity ECAL built as a sandwich of tungsten plates and silicon\nsensors. A high granularity noble liquid ECAL is also under consideration in ALLEGRO. These con-\ncepts have complementary strengths, ranging from an energy resolution of \u03c3E/E \u22433%/\n\u221a\nE for the\ncrystal-based ECAL to an extreme transverse resolution of \u223c2 \u00d7 2 mm2 for the fibre DR calorimeter, if\neach fibre is equipped with a SiPM readout device, or to a high longitudinal segmentation for the Si/W or\nnoble liquid solution. More details are given in Table 12. The next paragraphs illustrate the requirements\non electromagnetic calorimetry from representative analyses. Benchmark processes for which the per-\nformance is solely driven by the energy resolution are described first, followed by one case for which the\ntransverse granularity is crucial, and by examples that place stringent requirements on both the energy\nresolution and the granularity.\n93\n\nTable 12: Expected energy resolution of the different electromagnetic calorimeter options considered in the studies\nof Ref. [41].\nTechnology\nEM energy resolution\nstochastic term\nconstant term\nHighly granular Si/W based\n15\u201317%\n1%\nDual readout fibre (ECAL+HCAL)\n11%\n< 1%\nHybrid crystal (dual readout)\n3%\n< 1%\nHighly granular noble liquid based ECAL\n8\u201310%\n< 1%\n4.6.1\nEnergy resolution and monophoton final states\nFor final states that consist of a single photon and nothing else in the detector, the main handle to suppress\nthe backgrounds is the electromagnetic energy resolution. Two physics cases have been considered\nfor such final states: the determination of the Z\u03bde\u03bde coupling and the search for long-lived axion-like\nparticles.\nMeasurement of the Z coupling to the \u03bde\nAs described in Ref. [639], the e+e\u2212\u2192\u03bde\u03bde\u03b3 process at FCC-ee can be used to improve the precision\nmeasurement of the poorly known coupling of the Z to the \u03bde, currently known as g\n\u03bde\nZ = 1.06\u00b10.18 [35].\nThis is possible because of the presence of the t-channel W exchange in the e+e\u2212\u2192\u03bde\u03bde\u03b3 process,\ninterfering with e+e\u2212\u2192Z(\u03bde\u03bde)\u03b3. This interference slightly deforms the distribution of the missing\nmass M\u03bd\u03bd (or, equivalently, of the photon energy) in the vicinity of the resonant peak, M\u03bd\u03bd = MZ,\nincreasing (decreasing) the cross section above (below) the mass peak. The measurement is based on the\nasymmetry As of the photon energy spectrum in an interval of about \u00b11 GeV around the peak (where the\nphoton energy is approximately equal to \u221as/2\u00d7(1\u2212M2\nZ/s), i.e. 54 GeV at \u221as = 161 GeV) using event\nsamples generated with the KKMC [600,640] matrix element MC generator. At the WW threshold, with\nan integrated luminosity of 10 ab\u22121 and without considering any detector effects, this asymmetry would\nbe measured with a statistical uncertainty of 2 \u00d7 10\u22124, which translates into a 1% statistical uncertainty\non g\n\u03bde\nZ , as shown on the left panel of Fig. 60.\nTo evaluate the impact of a more realistic detector, the study was redone including the resolution\nfrom a homogeneous calorimeter with an energy resolution of \u03c3(E\u03b3) / E\u03b3 = 0.05/pE\u03b3 \u22950.002, re-\nsulting in a 50% degradation of the sensitivity to 1.4%, which remains an excellent performance. Should\nthe stochastic term be two times larger (i.e., 0.1/\n\u221a\nE, a value typical for a sampling calorimeter) the sen-\nsitivity would degrade to 2.4%. The right panel of Fig. 60 summarises the expected uncertainties. This\nstudy brings a clear constraint on the need for a very good calorimeter energy resolution and knowledge\nof photon energy calibration, to keep the uncertainty due to the calorimeter resolution at the per-cent\nlevel, as expected with a perfect detector.\nSearch for long-lived ALPs that decay outside the detector\nVery long-lived axion-like particles (ALPs) could be copiously produced at Tera-Z in Z decays (e+e\u2212\u2192\nZ/\u03b3\u2217\u2192a+\u03b3). When the ALP a decays outside the detector, the final state consists in a (monochromatic)\nsingle photon, with nothing else in the detector. The relevant mass range for such long-lived ALPs being\nbelow O(1) GeV, the photon energy is about 45 GeV. The sensitivity of FCC-ee to such particles has\nbeen studied in Ref. [165]. Simple kinematic cuts allow the reducible background (dominated by the\nassociated production of a photon with two fermions that escape detection) to be fully eliminated. Since\nthe irreducible background due to e+e\u2212\u2192\u03bd\u03bd\u03b3 production rises very steeply when the photon energy\ndecreases, the ECAL energy resolution is a key driver of the experimental sensitivity. Figure 61 shows\n94\n\nFig. 60: Left: Asymmetry As of the photon energy spectrum, at the WW threshold and without detector effects,\nafter subtracting the SM asymmetry predicted for g\n\u03bde\nZ = 1, as a function of the coupling. The yellow band represents\nthe statistical uncertainty expected with an integrated luminosity of 10 ab\u22121. Illustrative measurement points along\nthe prediction, with error bars that span the uncertainty band, are also shown. Right: Statistical uncertainty on the\ncoupling g\n\u03bde\nZ expected at the WW threshold, for two example values of the stochastic term of the electromagnetic\nenergy resolution (with a constant term of 0.2% added in quadrature). The uncertainty that would be obtained with\na perfect detector is also shown.\nthe 2 \u03c3 sensitivities expected for a crystal-based ECAL and for a dual-readout calorimeter, the former\nallowing significantly lower values of the ALP coupling to be probed. As was shown in Fig. 30, this\nanalysis would uniquely cover the range between \u22720.1 and \u223c1 GeV, which is beyond the reach of beam\ndump experiments.\n10\n2\n10\n1\n100\nma [GeV]\n10\n4\n10\n3\n10\n2\n10\n1\n|C\n|/ [TeV\n1]\nCrystal+Fibers\nFibers only\nFig. 61: Expected sensitivity, at the 2 \u03c3 level, of an FCC-ee experiment with a relative EM energy resolution of\n3%/\n\u221a\nE (blue curve) or 14%/\n\u221a\nE (orange curve), in the parameter space spanned by the mass of the ALP and its\ncoupling to two photons, from a search in the monophoton final state [165].\n4.6.2\nEnergy resolution and decays of heavy flavoured hadrons into photons or \u03c00\nThe FCC-ee flavour programme at the Z pole significantly expands beyond that of Belle II and LHCb,\nas described in Ref. [190]. In particular, for all decay modes common to the Bs and the Bd mesons, and\n95\n\nthat involve neutral particles, the Bd decays constitute an irreducible background to the Bs signal. In\nthat case, the mass resolution, driven by the electromagnetic calorimeter resolution, is the only handle\nto separate them. Two examples have been looked into: the radiative decay of B(s) into K\u2217\u03b3 and the\nBs \u2192DsK decay where the Ds decays into \u03c6\u03c1.\n4.8\n5.0\n5.2\n5.4\n5.6\n5.8\nm(K\u2217\u03b3) / GeV\n100\n103\n104\n105\n106\n107\nCandidates / 0.01 GeV\nZ pole, IDEA\n12 %/\np\nE\u03b3\nCombination\nB0\ns component\nB0\nd component\n5.1\n5.2\n5.3\n5.4\nm(K\u2217\u03b3) / GeV\n100\n103\n104\n105\n106\n107\nCandidates / 0.004 GeV\nZ pole, IDEA\n2 %/\np\nE\u03b3\nCombination\nB0\ns component\nB0\nd component\n2 %\n4 %\n6 %\n8 %\n10 %\n12 %\nPhoton energy-resolution/\np\nE\u03b3\n0.00\n0.25\n0.50\n0.75\n1.00\n1.25\n1.50\n1.75\n2.00\nRelative precision on\n\f\f\fVtd\nVts\n\f\f\f / %\nZ pole, IDEA\nExtracted from 100 pseudoexperiments\nCurrent precision from \u2206ms\n\u2206md\nFig. 62: Top: Mass distribution of B mesons decaying into K\u2217\u03b3 with an electromagnetic energy resolution of\n12%/\n\u221a\nE (left) or 2%/\n\u221a\nE (right). Bottom: Relative uncertainty on |Vts/Vtd| expected from the measurement\nof the ratio of the two branching fractions, as a function of the stochastic term of the EM energy resolution. The\ncurrent uncertainty is shown by the horizontal line.\nThe radiative decay of the B(s) meson to K\u2217\u03b3\nRadiative decays, such as Bd \u2192K\u2217\u03b3 (b \u2192s\u03b3) and Bs \u2192K\u2217\u03b3 (b \u2192d\u03b3), are a sensitive probe for\nphysics beyond the SM and can be used to place complementary constraints on the unitarity triangle.\nThe yet unobserved Bs \u2192K\u2217\u03b3 decay is an example of b \u2192d transitions that an experiment at a high-\nluminosity Z factory can probably uniquely study, provided that it can benefit from a precise photon-\nenergy measurement complementing an excellent reconstruction of displaced vertices. A first study of\nthe FCC potential to observe this decay has been reported in Ref. [641]. It assumes perfect charged\nhadron particle and photon identifications and ignores background contributions. The reconstructed\ncharged kaon and pion corresponding to the K\u2217\u2192K\u03c0 decay are combined with the generated photon\n(the energy of which is smeared to account for the detector resolution). The Bs signal yield is estimated\nfrom the CKM matrix elements and the corresponding hadronisation fractions fd and fs, leading to\nthe ratio NBd/NBs \u223c92. The distribution of the resulting K\u2217\u03b3 invariant mass is shown in Fig. 62 for\ntwo values of the stochastic term of the electromagnetic energy resolution. A sufficiently-high photon-\nenergy resolution is mandatory for the peak of the Bs signal to become visible and distinguishable from\nthe overwhelming B0\nd counterpart spectrum. With a stochastic term of 2%, the ratio of the two branching\n96\n\nfractions could be extracted with a relative statistical uncertainty better than 0.1%. Provided that the\nratio of the form factors of the two decays is well known, this opens the way to a very precise direct\nmeasurement of the |Vtd/Vts| ratio, as shown in the bottom plot of Fig. 62. A measurement may still\nbe possible with a resolution of 12%/\n\u221a\nE, but that would require an excellent control of the shapes of\nthe mass distributions, in particular of the tails (assumed here to be perfectly known), and the precision\nwould anyway degrade by at least an order of magnitude.\nThe Bs \u2192DsK decay\nThe copious Bs decay modes to neutral particles are inaccessible at Belle II and challenging at LHCb,\nand can be uniquely studied at FCC-ee. A few benchmark studies have been performed to extract the\nnecessary detector requirements for PID (Section 4.5) and calorimetry. One of them is the study of the\nBs \u2192DsK decay [50], where the Ds decays via D+\ns \u2192\u03c6\u03c1 \u2192K+K\u2212\u03c0+\u03c00, which could increase the size\nof the Bs sample by a factor of 3 with respect to that obtained with the single mode studied in Section 4.5.\nFigure 63 shows the impact on the mass resolution of the Bs system when a crystal-like calorimeter is\nemployed, improving the resolution of the calorimeter from \u03c3E / E = 0.15/\n\u221a\nE \u22950.005, corresponding\nto a resolution of 51 MeV, to \u03c3E / E = 0.03/\n\u221a\nE \u22950.005, corresponding to 14 MeV.\n5.20\n5.25\n5.30\n5.35\n5.40\n5.45\nm(K + K\n\u00b1\n0)D \u00b1\ns K\n) (GeV)\n0\n25\n50\n75\n100\n125\n150\n175\nnumber of events\nL = 1ab\n1 \n Ecm =45.6 GeV\nBs\nD \u00b1\ns K\n\u00b1 K\nK + K\n\u00b1\n0K\nfit DsK\nfit B0\nDsK\nDsK\nDs (\nK)\nB0\nDsK\nB0\nDs (\nK)\ndata error\n5.20\n5.25\n5.30\n5.35\n5.40\n5.45\nm(K + K\n\u00b1\n0)D \u00b1\ns K\n) (GeV)\n0\n100\n200\n300\n400\n500\n600\nnumber of events\nL = 1ab\n1 \n Ecm =45.6 GeV\nBs\nD \u00b1\ns K\n\u00b1 K\nK + K\n\u00b1\n0K\nfit DsK\nfit B0\nDsK\nDsK\nDs (\nK)\nB0\nDsK\nB0\nDs (\nK)\ndata error\nFig. 63: Distribution of the mass of the reconstructed Bs system (in GeV) for the process Bs \u2192DsK \u2192\u03c6\u03c1K \u2192\nKK\u03c0\u03c00K, on top of the main backgrounds, for a calorimeter with an energy resolution of 15%/\n\u221a\nE (left) or\n3%/\n\u221a\nE (right). PID is included. The resolution on the photon angles has a negligible effect on the resolution of\nthe mass of the Bs candidates.\n4.6.3\nRequirements on the geometrical acceptance for e+e\u2212\u2192\u03b3\u03b3 and \u2113+\u2113\u2212events at Z-pole\nenergies\nThe determination of the Z lineshape parameters requires the measurement of the hadron and lepton cross\nsections at and around the Z pole. With 1.5 \u00d7 1012 Z bosons produced at each FCC-ee interaction point,\nstatistical precisions of O(10\u22126) are within reach. Critical limiting uncertainties come from the counting\nof lepton pairs (e+e\u2212\u2192\u2113+\u2113\u2212, with \u2113= \u00b5, \u03c4) and from the integrated luminosity measurement. At\nFCC-ee, the wide-angle diphoton process e+e\u2212\u2192\u03b3\u03b3 becomes statistically relevant and offers prospects\nfor a safer determination (in terms of systematic uncertainties) of the integrated luminosity than the\ntraditional low-angle Bhabha scattering, e+e\u2212\u2192e+e\u2212.\nThe definition of the geometrical acceptance (defined, e.g., by a given polar angle lower cut in the\ncentre-of-mass frame of the collision) for both e+e\u2212\u2192\u03b3\u03b3 and e+e\u2212\u2192\u2113+\u2113\u2212is an obvious source of a\npotentially large systematic bias, which was dominant at LEP. Indeed, any global or local detector mis-\nalignment can generate a systematic bias on the acceptance. The tolerance on this bias can be calculated,\n97\n\n5\n10\n15\n20\n25\npolar angle cut (degrees)\n10\n15\n20\n25\n30\n35\n40\ntolerance (\u00b5m)\ne+e\u2212\u2192\u00b5+\u00b5\u2212\n0\n5\n10\n15\n20\n25\npolar angle cut (degrees)\n10\n20\n30\n40\ntolerance (\u00b5m)\ne+e\u2212\u2192\u03b3\u03b3\nstat\nstat + syst (corr.)\nstat + syst (uncorr.)\nFig. 64: Tolerance on the accuracy of the polar angle cut as a function of the polar angle cut in degrees, expressed\nas a radial accuracy for a detector situated at 2.5 m from the IP in the centre-of-mass of the collision. Left: For\ndilepton events, to ensure a systematic precision of 2.2 \u00d7 10\u22126. Right: For diphoton events, to ensure a systematic\nprecision of 1.5 \u00d7 10\u22125 (lower blue curve). Also indicated is the tolerance corresponding to having a systematic\nuncertainty equal to the statistical one, assuming either fully correlated (middle green curve) or uncorrelated (upper\nred curve) displacements in the two endcaps.\ne.g., either to match the resulting systematic uncertainty on the cross section to its statistical precision or\nto obtain a specific precision, as done in Ref. [642] and displayed in Fig. 64 for a polar angle cut between\n1 and 25 degrees.\nThe tolerance, expressed as the accuracy of the definition of the polar angle cut for a detector\nsituated at 2.5 m from the IP, is similar for dileptons and diphotons, and is in the 10\u201320 \u00b5m range for a\ncut between 10 and 20 degrees, corresponding to a required polar angle accuracy of 4 to 8 \u00b5rad.\nInspired by the work done for integrated luminosity measurements with low-angle Bhabha scat-\ntering at LEP, such a tight requirement calls for the design and the construction of the calorimeter (for\ndiphotons) and the tracker (for dileptons) endcaps with a mechanical precision ensuring the specified tol-\nerance of 10 to 20 \u00b5m, complemented by dedicated test-beam measurements and a survey/monitoring of\nthe distance between the two endcaps with a precision of 50 to 100 \u00b5m. While the task is challenging, it\nshould be kept in mind that for the luminosity monitor (LumiCal), situated at lower angles, the transverse\n(longitudinal) tolerance is of 1 \u00b5m (50 \u00b5m) at 1 m of the luminous region, for a precision of 10\u22124 on the\nintegrated luminosity measurement [44].\nWith respect to the LEP case, FCC-ee offers an additional totally new and possibly synergistic\napproach to a precise definition of the acceptance. Indeed, the large and constant beam crossing angle\nof 30 mrad provides an absolute angular scale to dilepton and diphoton events at all angles. Total energy\nand momentum conservation allows for the event-by-event determination of this crossing angle (together\nwith the constant longitudinal boost resulting from the specific positioning of the accelerating RF cav-\nities in the FCC tunnel) with excellent accuracy from the final state particle kinematic observables. A\nglobal fit of all events, constraining the crossing angle and the longitudinal boost to be constant, would\nthen provide an in-situ local \u2018calibration\u2019 of final state particle angles and, in particular, of the acceptance\ncut. The required statistical precision was demonstrated analytically [643] to be within reach with the\nFCC-ee dilepton and diphoton samples, but the actual fit procedure remains to be consolidated 21. The\nsensitivity of this approach is proportional to the magnitude of the crossing angle, and could not be used\nwith the LEP head-on collisions. At FCC-ee, it was already shown [643] that a (mechanical or otherwise)\n21It was already shown in Ref. [22] that this finite crossing angle and longitudinal boost could be used to find and monitor\nthe directions of the x, y, and z axes within a few \u00b5rad precision every hour at the Z pole with dimuon events.\n98\n\ntolerance of 100 \u00b5m in the r-\u03d5 direction would allow an acceptance definition of 3 to 12 \u00b5rad, irrespec-\ntive of the (global or local) endcap radial or longitudinal displacements, consistent with the tolerances\nmentioned above, as displayed in Fig. 65. More recent developments seem to indicate that the required\n\u03d5 tolerance can also be reached in situ.\nFig. 65: Analytically-predicted precision of the diphoton acceptance determination (in \u00b5rad) as a function of a\npolar angle cut applied in the event-by-event centre-of-mass frame, assuming a 100 \u00b5m tolerance in the azimuthal\ndirection, and exploiting the energy-momentum conservation and the constraints that the beam crossing angle and\nthe longitudinal boost are the same (on average) for all events and constant in time. This result is obtained with a\nreadout cell of 1\u25e6\u00d7 1\u25e6and position resolution of \u03c3x,y = 0.5 mm in the endcap calorimeter (commensurate with\nthe various proposed options).\nFurther work is needed to verify the feasibility of the second method beyond analytical computa-\ntions, as well as to evaluate the effect of the beam crossing angle on the acceptance determination with\nthe classical method. The large forward cross section of e+e\u2212\u2192e+e\u2212events will open the possibility of\nmutual in-situ alignment of the tracker and the calorimeter, offering a cross-check of the acceptance cut.\nIt will be important to check whether the second approach would also be suitable for the integrated lumi-\nnosity measurement with low-angle Bhabha scattering in the luminosity monitors. The two approaches\nare expected to help each other, either by reducing the mechanical constraints of the former or by im-\nproving the convergence of the latter, and most likely both. Their combination is expected to provide an\nexcellent understanding of the acceptance, a cross-check of their accuracy, and an explicit requirement\non the position and angular resolutions of the tracker and of the calorimeter.\n4.6.4\nSensitivity to charged lepton flavour violation: Z \u2192\u00b5e and \u03c4 \u2192\u00b5\u03b3\nWith its 6 \u00d7 1012 Z bosons, FCC-ee enables precise tests of charged lepton flavour violation (cLFV)\nprocesses. The Z \u2192\u00b5e process has an extremely clean signature \u2014 a beam-energy electron recoiling\nback-to-back against a beam-energy muon \u2014 with fully reducible background from the 2 \u00d7 1011 Z \u2192\n\u03c4+\u03c4\u2212events. It is estimated [51] that FCC-ee will improve by 2 to 3 orders of magnitude the current\nlimits of about 10\u22127 from the LHC [644]. The most dangerous background comes from the \u2018extreme\nbremsstrahlung\u2019 emission by a muon in a Z \u2192\u00b5\u00b5 event that creates a large deposit in the electromagnetic\ncalorimeter, faking an electron. This effect could be limited by improving the ECAL energy resolution\nand having the possibility of longitudinal segmentation to veto showers starting later in the calorimeter.\nThe sensitivity of FCC-ee to the LFV \u03c4 \u2192\u00b5\u03b3 decay was established in Refs. [51, 194] and the\nmajor detector effects on the measurement were evaluated. The analysis strategy requires the identifi-\ncation of a clear SM \u03c4 decay on one side (\u2018tag\u2019) so that the search for the LFV decay is performed in\nthe other hemisphere. The discriminant variables are the total energy and the invariant mass of the final\n99\n\nstate. As shown in Fig. 66 (left), the signal region is background dominated and the background density\nrises linearly away from the E\u00b5\u03b3 \u2212Ebeam = 0 line. This implies that the sensitivity (upper limit) scales\nlinearly with the E\u00b5\u03b3 resolution, which is dominated by the ECAL energy resolution. With the full event\nsample of 4 \u00d7 1011 \u03c4 decays, an expected 90% CL upper limit of 1.2 \u00d7 10\u22129 can be reached [195], as\nshown in Fig. 66 (right).\n2000\n2010\n2020\n2030\n2040\n2050\n2060\n1 \u00d7 10\n9\n2 \u00d7 10\n9\n5 \u00d7 10\n9\n1 \u00d7 10\n8\n2 \u00d7 10\n8\n5 \u00d7 10\n8\nupper limit\nBaBar 2010 90% CL\nBelle 2008 90% CL\nBelle 2021 90% CL\nBelleII 90% CL 50 ab-1, \n scaling\nSTCF 90% CL, 10y, \n scaling\nFCC-ee(Z) 90% CL, 6 1012 Z\n(\n), measured or expected upper limit\nMeasurement\nGuestimate\nFig. 66: Left: Reconstructed energy vs. mass for all \u00b5\u03b3 combinations in simulated Z \u2192\u03c4\u03c4\u03b3 background events with\none \u03c4 \u2192\u00b5\u03bd\u03bd decay. The signal region corresponding to 2 \u03c3 resolution is indicated by the red ellipse. Right: Present\nand expected upper limits for B(\u03c4 \u2192\u00b5\u03b3) [195]. The dates of the future measurements are mainly chosen for\nplotting purposes. The expected limits for Belle II and the Super Charm-Tau factories are conservative estimates,\nassuming that those searches will be mostly background-constrained.\nThis benchmark is particularly interesting because it also shows a requirement for the photon\nposition resolution, which contributes to the invariant mass calculation. In this example, where the\ncalorimeter has a resolution of about 16.5%/\n\u221a\nE (as in CLD) and a position resolution of 2 mm, the\ntwo contributions in the invariant mass calculation are similar. Therefore, for this measurement, while\nthe sensitivity is found to scale linearly (or slightly more strongly) with the photon energy resolution, a\nfine-grained crystal calorimeter with a 3%/\n\u221a\nE energy resolution would be particularly valuable. This\nis especially true since it would also provide a significantly better spatial resolution, of around 1 mm,\nleading to a fivefold improvement in sensitivity compared to the previous example.\n4.6.5\nBremsstrahlung recovery\nEven with an excellent EM calorimeter resolution, for 50 GeV central electrons the resolution of a calori-\nmetric measurement is worse than the resolution of the tracker determination of the momentum. Further-\nmore, the latter is not as good as that of muons since electrons emit bremsstrahlung radiation: even with\nthe light tracker of IDEA, corresponding to \u223c10% of a radiation length in the central region, the effective\nmomentum resolution of electron tracks is at least a factor of two worse than that of muons [645]. Sev-\neral measurements call for a better electron momentum resolution. For example, the determination of the\nHiggs boson mass from Z(\u00b5\u00b5)H events (Section 4.3.1) can gain from exploiting the Z \u2192e+e\u2212channel.\nA resolution improvement can be brought by the recovery of the bremsstrahlung photons in the calorime-\nter, if their energy can be added to the momentum of the track. An effective recovery requires that the\nshowers of the electron and of the radiated photon(s) be disentangled by the reconstruction algorithm.\nFor 50 GeV central electrons, in a 2 T magnetic field, photons radiated at small radii (where, in the IDEA\ntracker, most of the bremsstrahlung emissions happen) are separated by typically 2\u20133 cm from the elec-\ntron at the calorimeter entrance. The ability to separate showers that are so close to each other calls for a\ntransverse granularity of 1\u00d71 cm2 or better and may place some demands on the longitudinal segmenta-\ntion, which helps to disentangle showers that partially overlap. Detailed GEANT simulations and recon-\n100\n\nstruction algorithms are needed for a precise assessment of these constraints. Meanwhile, it is estimated\nthat, with the recovery of bremsstrahlung photons, the effective resolution of electrons would be 25%\n(45%) worse than the muon resolution for a calorimeter EM energy resolution of 3%/\n\u221a\nE (15%/\n\u221a\nE).\nMore details can be found in Ref. [645]. The DELPHES simulations used for the studies reported in this\ndocument rely on this estimation. With this bremsstrahlung recovery, the Z \u2192e+e\u2212channel signifi-\ncantly contributes to the determination of the Higgs boson mass from ZH events, as shown in Fig. 67,\nimproving the uncertainty by 22% compared to what is obtained from the muon channel alone [63].\n124.99\n124.995\n125\n125.005\n125.01\n (GeV)\nh\nm\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nNLL\n\u2206\n-2\n) = 4.74 MeV\nh\n(m\n\u03b4\n \n\u2212\n\u00b5\n+\n\u00b5\n) = 5.68 MeV\nh\n(m\n\u03b4\n \n\u2212\ne\n+\ne\n) = 3.97 MeV\nh\n(m\n\u03b4\n \n\u2212\ne\n+\n + e\n\u2212\n\u00b5\n+\n\u00b5\n1\n\u2212\n = 240 GeV, 10.8 ab\ns\nSimulation\n \nFCC-ee\nFig. 67: Likelihood scan of the Higgs boson mass with the recoil method, combining the muon and electron\nchannels. The uncertainties correspond to the quadratic sum of the statistical and systematic terms.\n4.6.6\nPrompt decays of ALPs a \u2192\u03b3\u03b3\nA search for ALPs produced in Z \u2192a\u03b3 decays, complementary to the one previously mentioned, consists\nin looking for ALPs that decay promptly into two photons, leading to a three-photons final state. The\nanalysis presented in Ref. [165] compares the sensitivities that are expected with the dual-readout fibre\ncalorimeter of IDEA and with the variant where crystals are placed in front of it.\nThe experimental sensitivity is driven by the ability to precisely reconstruct the invariant mass\nof the two photons coming from the ALP decay. For low masses, up to a few hundreds of MeV, the\nresolution on this diphoton mass is dominated by the resolution on the photon angles, hence by the\nprecision with which the impact point of the photons at the calorimeter entrance is determined. This\ncontribution decreases with increasing ALP mass and, above 10 GeV, the resolution depends only on the\nenergy resolution of the calorimeter. In addition, at low masses, below \u223c5 GeV, the two photons from\nthe ALP decay may not be resolved in the detector but be \u2018merged\u2019 into a single reconstructed object.\nDetailed GEANT simulations and reconstruction algorithms, still under development, are needed for a\nprecise understanding of these effects. A simplified approach is adopted for the current sensitivity study,\nwhereby the angular distance \u2206\u03b1 between the two photons is used to determine whether the photons\nare resolved. Taking into account the transverse granularity and the Moli\u00e8re radius of the detectors,\nit is assumed that photons with \u2206\u03b1 > 20 mrad can be reconstructed in the crystal calorimeter, which\ncorresponds to a separation of 4 cm (four calorimeter cells) of the two photons at the calorimeter entrance.\nFor the dual-readout calorimeter, photons are required to be separated by \u2206\u03b1 > 10 mrad to be resolved,\nwhich corresponds to the distance between 10 fibres of the detector.\nTaking into account the irreducible e+e\u2212\u2192\u03b3\u03b3\u03b3 background, the experimental reach expected\nfor the two calorimeter options is shown in Fig. 68. The crystal calorimeter has a better sensitivity for\n101\n\nhigh masses, where the sensitivity is driven by the energy resolution. The impact point resolution is very\nsimilar for the two calorimeters, but the better granularity of the fibre calorimeter is expected to provide\na better separation for collimated photons that emerge from the decay of ALPs at very low masses,\nresulting in a gain in sensitivity compared to that provided by the crystal detector.\n10\n1\n100\n101\n102\nma [GeV]\n10\n3\n10\n2\n10\n1\n|C\n|/ [TeV\n1]\nCrystal+Fibers \n>0.02 rad\nFibers only \n>0.01 rad\nFig. 68: Expected sensitivity at the 2 \u03c3 level of a FCC-ee experiment, in the parameter space spanned by the mass\nof the ALP and its coupling to two photons, from a search for ALPs that decay promptly into two photons. In the\nlegends, \u2206\u03b1 denotes (in rad units) the angular separation down to which the calorimeter is assumed to be able to\nresolve two photons.\nAs shown by Fig. 68, the parameter space covered by this analysis, that focuses on prompt decays\nof ALPs, nicely complements the one explored by a search or quasi-stable ALPs in the monophoton\nfinal state (Fig. 61). The sensitivity to ALPs with intermediate lifetimes, which are long-lived but decay\ninside the detector, is more difficult to assess. For ALPs that decay before reaching the calorimeter, it\ndepends on the ability to reconstruct the displaced decay vertex of the ALP into two photons. For ALPs\nthat decay inside the calorimeter, the sensitivity depends on the ability to identify late-starting showers.\nThe requirements that these analyses will place on the longitudinal segmentation of the calorimeter, on\nthe measurement of the timing of calorimeter signals, and on a potential preshower, remain to be studied.\n4.6.7\nRequirements from \u03c00 \u2192\u03b3\u03b3 reconstruction in \u03c4 decays\nThe reconstruction of \u03c00 \u2192\u03b3\u03b3 decays is a crucial component for several measurements of the FCC-ee\nphysics programme, such as the tau branching ratios or the tau polarisation. The kinematic of a \u03c4 \u2192\u03c1\u03bd\ndecay produced at the Z pole provides initial detector requirements [646]. For instance, the momentum\nof the \u03c00 produced in the \u03c1 decay is quite soft and its decay photons are even softer. The capability\nof identifying these low-energy photons requires a low noise and high energy resolution calorimeter.\nThe energy resolution is important also because it affects the \u03c00 identification itself, which relies on a\ncut on the diphoton invariant mass. The granularity is another important aspect that plays a role in the\nseparation of the two photons. The angular separation between the two photons, \u22482m\u03c00/E, is typically\n10 mrad, which leads to a separation of 2 cm at the calorimeter entrance; however, for the highest possible\nenergy (E\u03c00 = 45.6 GeV) the opening angle is reduced to 6 mrad, corresponding to 1.2 cm separation\nat the calorimeter entrance22. The granularity is also needed for the correct separation of the photons\nfrom charged pions in the decays. A study has been done comparing the performance of different noble\nliquid calorimeters (LAr and LKr) in \u03c00 events. Cases have been considered where the photons from\n22A large tracking volume, optimised for track momentum resolution, is also beneficial for the identification of collimated\nobjects such as \u03c00 decays.\n102\n\nthe \u03c00 decays can be reconstructed separately (resolved) or are reconstructed as a single EM object\n(unresolved). As seen in Fig. 69, the \u03c00 reconstruction efficiency and the \u03c00 mass resolution are better in\nthe LAr option with the finer granularity and improve further in the LKr option, given its smaller Moli\u00e8re\nradius.\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n in 2 cluster events [GeV]\ncl 1,cl 2\nm\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nCounts\n, E = 0-45.6 GeV\n0\nGaussian fit:\n = 0.137\n\u03bc\n = 0.011 \nECAL: Pb+LAr 3\nCells: 2x2x4 cm\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n in 2 cluster events [GeV]\ncl 1,cl 2\nm\n0\n200\n400\n600\n800\n1000\nCounts\n, E = 0-45.6 GeV\n0\nGaussian fit:\n = 0.137\n\u03bc\n = 0.009 \nECAL: Pb+LAr 3\nCells: 1x1x4 cm\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n in 2 cluster events [GeV]\ncl 1,cl 2\nm\n0\n100\n200\n300\n400\n500\nCounts\n, E = 0-45.6 GeV\n0\nGaussian fit:\n = 0.136\n\u03bc\n = 0.008 \nECAL: W+LKr\n3\nCells: 1x1x2.6 cm\nFig. 69: Invariant mass distributions of two-cluster \u03c00 mesons for different noble liquid calorimeter configurations.\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n energy (truth) [GeV]\n0\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\nProbability of finding \n0\nRes. and unres. \n0\nResolved \n0\nUnresolved \nECAL: W+LKr\n3\nCells: 1x1x2.6 cm\nECAL: W+LKr\n3\nCells: 1x1x2.6 cm\nFig. 70: Probability of \u03c00 identification as a function of its energy for a W+LKr calorimeter with a granularity of\n1 \u00d7 1 \u00d7 2.6 cm3.\nFigure 70 shows the \u03c00 reconstruction efficiency, as a function of its energy, all the way to 45 GeV.\nAbove 40 GeV, the transverse shape of an unresolved \u03c00 electromagnetic shower resembles more and\nmore that of a single photon and the identification efficiency progressively vanishes.\n4.6.8\nWork ahead\n\u2013 The measurement of tau polarisation in Z decays, from which the tau and electron asymmetries,\nA\u03c4 and Ae, are extracted, is a cornerstone of the Tera-Z physics programme. Experience from\nLEP shows that the precision of this measurement critically depends, in particular, on the design\nof the electromagnetic calorimeter. While the sizes of the event samples used by the four LEP\nexperiments were similar, the uncertainties differed by nearly a factor of two from one experiment\nto the other. As noted above, a high calorimeter transverse granularity is indeed crucial to identify\nand precisely reconstruct the \u03c00 mesons produced in \u03c4 decays. The precision that different detector\nconcepts can achieve on this measurement needs to be studied with a full simulation description,\nwhich also includes, besides the spatial and energy detector resolution, the effect of fake photons.\nWork in this direction has started, as is shown in Section 4.10.\n\u2013 The reconstruction of the events on fully simulated detector concepts will be crucial to extract\nfurther requirements on the detector performance. For instance, since photon energy contributes\n25% of the total energy of a jet, the ability to reconstruct low-energy photons is very important\n103\n\nin order to improve the jet energy resolution, which is crucial for Higgs boson hadronic final\nstates, such as H \u2192gg. Moreover, in a study considering multi-jet topologies [614] it has been\nshown that the absence of photon and \u03c00 identification prior to the jet particle-flow reconstruction\nwould worsen the resolution of the reconstructed hadronic objects in about one third of the cases.\nPreliminary studies will need to be updated once the reconstruction of full simulation detector\nconcepts become available in the coming months.\n\u2013 The measurement of long-lived particles decaying to photons relies on a precise standalone ECAL\nmeasurement of the direction of the shower. The impact of longitudinal segmentation on the\npointing capabilities and on displaced vertex reconstruction performance needs to be studied in\nfull simulation.\n4.6.9\nPreliminary conclusions\n\u2013 An electromagnetic calorimeter with excellent energy resolution (a few %) is required to optimise\nthe expected precision on the Z to \u03bde coupling via the e+e\u2212\u2192\u03bde\u03bde\u03b3 process, lepton flavour\nviolating decays such as Z \u2192\u00b5e and \u03c4 \u2192e\u03b3, decays of heavy flavoured hadrons to photons or \u03c00,\nand ALPs searches.\n\u2013 Excellent transverse granularity and resolution is needed for optimal Bremsstrahlung recovery and\n\u03c00 identification. Longitudinal segmentation and pointing capabilities are required for displaced\nphoton vertex identification, such as long-lived ALP decays.\n\u2013 A knowledge of the acceptance at the level required to match the statistical precision on the\ne+e\u2212\u2192\u03b3\u03b3 cross section for the absolute luminosity determination requires that the calorime-\nter be constructed with a mechanical precision of few tens of microns.\n\u2013 Reconstructing low energy photons from decays of \u03c00 mesons, either produced in B or D decays\nor in H \u2192gg, requires as little material in front the ECAL as possible, as well as a noise term as\nsmall as a few tens of MeV.\n4.7\nRequirements for the hadron calorimeter\nTo fully exploit the statistical power of FCC-ee, precise measurements of processes in their hadronic\nfinal states are crucial because of their typically large branching ratios. A clear advantage of e+e\u2212col-\nlisions over hadron collisions, such as at the HL-LHC, is the almost negligible pile-up and the absence\nof underlying event and initial-state QCD radiation, as well as the precise knowledge of the total energy-\nmomentum of the final state, resulting in cleaner data and improved jet energy resolutions. For FCC-ee,\nthe possibility of having a full GEANT simulation of the events in the new software has become available\nonly recently, so that a state-of-the-art event reconstruction based on the particle flow approach is not\nyet validated for complete physics studies. Since the reconstruction algorithm significantly impacts the\nfinal resolution on hadronic objects, it is challenging to determine specific requirements for the hadron\ncalorimeter performance from existing studies, performed with fast simulation DELPHES samples. Nev-\nertheless, valuable information can be derived regarding the overall impact that the performance of the\ncalorimeter has on the accuracy of the measurement, profiting from the particle-flow inspired reconstruc-\ntion available in DELPHES.\n4.7.1\nReconstruction of Higgs boson hadronic final states\nThe identification of H \u2192jj signal events relies on the resolution of the dijet system mass, which is in-\nfluenced by the performance of the calorimeter. Additionally, the precise separation of different flavours\ndepends on the effectiveness of the flavour tagging algorithm, which also imposes requirements on the\nvertex detector and on particle identification, as discussed in Sections 4.4.1 and 4.5.1. Assuming an ideal\n104\n\nparticle-flow algorithm, with perfect charged and neutral particle identification, the visible energy (and\nmass) resolution is dominated by the neutral hadron resolution, which is in turn driven by the HCAL\nstochastic term. A study has been performed to assess the impact of a degraded hadron calorimeter per-\nformance [622], by worsening the HCAL stochastic term (50% and 100%) and then compare the resulting\nH \u2192jj sensitivity to that of the IDEA detector baseline (which assumes dual-readout calorimetry with\na 30% stochastic term).\n30\n50\n100\nHadronic Calorimeter Stochastic Term (%)\n0\n10\n20\n30\n40\n50\nRelative Loss in Precision (%)\nH \u2192s\u00afs\nH \u2192c\u00afc\nH \u2192gg\nH \u2192b\u00afb\nFig. 71: Expected precision degradation of the branching ratio measurements for the H \u2192bb, cc, ss, and gg\ndecays as a function of the HCAL stochastic term. To guide the interpretation, the value 30% would correspond to\na dual-readout calorimeter as in the baseline IDEA simulation, 50% corresponds to an ATLAS-type calorimeter,\nand 100% to a CMS-type calorimeter.\nThe results are summarised in Fig. 71 for several Higgs boson decay channels. When the neutral\nhadron energy stochastic term is degraded to 50% (100%), the expected precision of the measurement\nof the H \u2192ss branching ratio degrades by about 20% (55%). The larger is the expected signal-to-\nbackground ratio in a given channel (the largest being for H \u2192bb), the smaller is the effect of the\ndegradation of the neutral hadron energy resolution on the expected precision. The visible mass resolu-\ntion is, therefore, particularly important for accurately measuring the H \u2192cc and H \u2192ss branching\nfractions.\n4.7.2\nMeasurement of the Higgs boson invisible width\nAs discussed in Section 4.3.1, FCC-ee offers a unique opportunity to use the \u2018recoil method\u2019 for pre-\ncise, model-independent measurements of Higgs boson properties. This method becomes particularly\nvaluable when studying the Higgs boson decay into an invisible final state. The Standard Model process\nH \u2192\u03bd\u03bd\u03bd\u03bd has a very small branching ratio, 1.06 \u00d7 10\u22123 [647], so that it is beyond the reach of the\nLHC programme and might only be observable at the FCC-hh. However, with possible extensions of\nthe Standard Model, such as the inclusion of a Higgs portal, the Higgs boson width to invisible final\nstates could be increased because of decays to non-SM particles, which could be potential dark matter\ncandidates [648,649], making the study of this channel highly relevant.\nIn a recent study [65], the DELPHES simulation of the IDEA detector was used, along with the\nstate-of-the-art flavour tagging algorithm PARTICLENETIDEA, described above. To maximise the size\nof the event sample, the analysis considers not only Z decays to ee and \u00b5\u00b5 but also to bb, cc, and qq. The\nvisible mass (Mvis) serves as the discriminant variable in the final fit (with no systematic uncertainties\nconsidered at this stage). The results indicate that, with an integrated luminosity of 10.8 ab\u22121 at \u221as =\n240 GeV and of 3 ab\u22121 at \u221as = 365 GeV, a measurement of the SM branching ratio with a precision\n105\n\nof 25% could be achieved. Furthermore, when accounting for the possibility of exotic decays, the study\nresults in the exclusion, at the 95% CL, of branching fractions lower than 0.05%, or a 5 \u03c3 observation if\ngreater than 0.13%. The Z \u2192qq decay channel was found to be the one with the best sensitivity, given\nits higher statistical power, and the run at \u221as = 240 GeV has much better sensitivity than the highest\nenergy run. A preliminary study performed with CLD full simulation can also be found in Ref. [622].\n120\n125\n130\n135\n140\n145\n150\n155\n160\n [GeV]\nmiss\nM\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nNormalised / 0.5 GeV\n\u00b5\n\u00b5\nee\nqq\nbb\ncc\nFCC-ee\nSimulation (Delphes)\n = 240 GeV\ns\ninv\n\u2192\nH\nFig. 72: The Mmiss distribution for several Z decay channels, corresponding to the Higgs boson signal, in HZ\nprocesses. The distributions are normalised to the same number of events and are shown after the Pmiss > 10 GeV\ncut and the Mvis selection around the Z mass.\nFigure 72 displays the normalised distribution of the missing mass, representing the Higgs boson,\nfor the various Z decay modes, allowing the comparison of resolutions between the lepton and hadron\nchannels. An investigation was also conducted into the effects of a poorer detector energy resolution on\nthe measurement, applying a simple additional Gaussian smearing to the four-vector of the hadronic final\nstate. As shown in Fig. 73, an additional smearing of 5% led to a 130% (80%) increase in the uncertainty\non the qq channel (combined result). The blue dashed curve in Fig. 73 represents the resolution of\nthe reconstructed Higgs boson mass for the case where the Z boson decays into hadronic modes, as a\nfunction of the additional smearing. It is important to note that this quantity includes other effects from\nbeam spread and ISR. In the future, it may be beneficial to use a better-defined quantity, such as the Z\nresolution itself, to further evaluate the dependence on the calorimeter performance.\n4.7.3\nSearch for heavy neutral leptons\nIt has been shown in Refs. [650,651] that an e+e\u2212machine like FCC-ee, with the potential to collect a\nvast event sample at the Z peak holds significant discovery potential for feebly interacting particles, such\nas heavy neutral leptons (HNL). Such a large dataset, covering a phase space at low coupling strengths, is\nunmatched by other proposed future colliders and could potentially reach the lower bounds set by theory.\nThe study reported in Ref. [125] focuses on the production of HNLs with masses between 20 and 80 GeV\nat \u221as = 91 GeV, with an integrated luminosity of 2.05\u00d7108 pb\u22121, corresponding to 6\u00d71012 e+e\u2212\u2192Z\nevents. In particular, the process e+e\u2212\u2192N\u00b5\u03bd\u00b5 \u2192\u00b5qq\u2032\u03bd\u00b5 has been investigated. This process has a\nsubstantial branching ratio of about 50% over the entire mass range of interest and complements other\nstudies in the leptonic channel with long lifetimes [134,651,652].\nIn a search for HNLs that decay promptly in the detector, the analysis applies selections on muons,\n106\n\nFig. 73: The effect of an additional smearing to the hadronic energy of the events on the expected uncertainty in a\nmeasurement of the branching fraction of the Higgs boson decay to invisible particles is shown for three individual\nchannels and for all channels combined. The root mean squared of the reconstructed Higgs boson mass is also\nshown, as a dashed blue line (corresponding to the vertical axis on the right side).\njets, and missing energy to minimise background contaminations. The discriminant variable used in this\nanalysis is the visible mass, which corresponds to the HNL mass, as shown in Fig. 74.\nThe final selection involves a sliding cut on the search HNL mass, taking into account the observed\nresolution (\u03c3 = 20%\u221amHNL). A study to evaluate the impact of varying the mass resolution has been\nperformed and the result is shown in Fig. 75, indicating a minimal effect at low masses, where the\nbackground from Z \u2192qq events is negligible, but becoming more relevant at higher masses, where the\nbackground is higher.\n4.7.4\nWork ahead\n\u2013 The total Higgs boson width measurement at \u221as = 240 GeV is statistically limited by the precision\non the H \u2192ZZ\u2217partial width, which crucially depends on identifying all the hadronic Z decay\nmodes. The separation of the W and Z mass peaks is driven by hadronic resolution and is required\nin order to suppress the overwhelming H \u2192WW\u2217background. The current detector proposals\nsatisfy this requirement in fast simulation studies, but this result has to be confirmed by constrained\nkinematic fits in full-simulation studies.\n\u2013 These preliminary studies have been performed using a fast simulation of the detector with close to\nideal particle-flow performance and can, therefore, only provide overall guidelines for the needed\nhadron calorimeter resolution.\nFull-simulation performance studies with particle-flow reconstruction using integrated tracking,\nECAL, and HCAL information, and kinematic fits constrained by the total energy and momentum\nconservation, are of paramount importance to consolidate the requirements on hadronic calorime-\nter technology, transverse and longitudinal granularity, and resolution.\n107\n\n0\n20\n40\n60\n80\n100\n [GeV]\nvis\nM\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nEvents/bin/6e12 Z\n qq\n\u03bd\n\u00b5\n uu,dd,ss\n\u2192\nz\n\u00b5\n\u00b5,\u03c4\n\u03c4\n\u2192\nz\n cc\n\u2192\nz\n bb\n\u2192\nz\n=20 GeV\nN\nM\n=50 GeV\nN\nM\n=80 GeV\nN\nM\nFig. 74: The Mvis distribution for background and HNL signal events after a preliminary selection.\n4.7.5\nPreliminary conclusions\n\u2013 The precision of the Higgs boson couplings to quarks and gluons, in particular the strange and\ncharm Yukawa couplings, as well as the Higgs to invisible one, drives the hadron calorimeter\nrequirements. Heavy neutral lepton hadronic decay modes also benefit from excellent visible\nenergy resolution.\n\u2013 In particular, assuming an ideal particle-flow reconstruction setup with highly-efficient tracking\nand neutral hadron identification capabilities, the neutral hadron resolution drives the sensitivity to\nthe strange Yukawa coupling. An excellent visible mass resolution, obtained through particle-flow\nreconstruction, is of paramount importance for the observation of this mode.\n4.8\nRequirements for the muon detector\nAt the FCC-ee energies, the muon momentum reconstruction is entirely driven by the tracking system\nand the main role of the muon detector is to identify muons with a very high efficiency and purity, as well\nas to serve as \u2018tail-catcher\u2019 for the hadron showers that may not be fully contained in the calorimeter.\nAn important figure of merit is the probability that a pion be misidentified as a muon. An example\nbenchmark measurement to set a requirement on the control of the pion contamination is that of the\nultra-rare B \u2192\u00b5+\u00b5\u2212decay. As illustrated in Fig. 76, the excellent mass resolution of the IDEA detector\noffers a very good separation of the B and Bs peaks. A significant background coming from B \u2192\u03c0+\u03c0\u2212\ndecays is, however, present under the B peak. Assuming a double \u03c0 \u2192\u00b5 mis-identification probability of\n2\u00d710\u22125, this background contribution (dashed histogram in Fig. 76) would be as large as the signal [190].\nWhile the measurement of the track momentum in the muon detector alone does not improve (in\nthe momentum range of interest) the excellent prompt muon momentum resolution already provided by\nthe tracker, a good standalone resolution is useful to reduce the pion contamination and to identify pions\n108\n\n20\n30\n40\n50\n60\n70\n80\nMN1 [GeV]\n10\n9\n10\n8\n10\n7\n|U N|2\nFCC-ee s = 91.2 GeV NZ = 6e12 95% CL HNL reach\n(E)/E = 10%/ E/GeV\n(E)/E = 20%/ E/GeV\n(E)/E = 30%/ E/GeV\nFig. 75: The 2 \u03c3 significance of an HNL signal for several visible mass width resolutions, from a search for HNLs\nthat decay promptly into a muon and two jets.\n5250\n5300\n5350\n5400\nm\u00b5+\u00b5\u2212(MeV)\n0\n20\n40\n60\n80\n100\n120\nCandidates / 5 MeV\nFCC-ee\nZ 0\nb\u00afb Delphes simulation\nTotal \ufb01t\nBs\n\u00b5+\u00b5\u2212\nB\n\u00b5+\u00b5\u2212\nB\n\u03c0+\u03c0\u2212\nSimulated data\nFig. 76: Mass distribution of B \u2192\u00b5+\u00b5\u2212and of Bs \u2192\u00b5+\u00b5\u2212as expected from the IDEA detector, with an event\nsample of 5 \u00d7 1012 Z decays. The background contribution from misidentified pions in B \u2192\u03c0+\u03c0\u2212decays is also\nshown, as the dashed curve. From Ref. [190].\nthat decay before the muon detector. In addition, the standalone performance of the muon detector is\nimportant in searches for long-lived particles that decay outside the tracker volume. The requirements\non the standalone momentum resolution need to be quantified and they are likely to have a significant\nimpact on the technologies that will be chosen for the muon system of an FCC-ee detector [43].\nThe FCC-ee could uniquely probe yet another suppressed b \u2192s transition, via the Bs \u2192\u03bd\u03bd\ndecay mode [653]. The main backgrounds for this search are the b \u2192\u03c4\u03bdX decays, where the \u03c4 decays\nsemi-leptonically and the decay lepton escapes detection. This configuration can occur when the muon\nis forward or too soft to reach the muon detector. In this case, a calorimeter equipped to perform muon\nidentification might help, together with a low detector magnetic field.\n109\n\n4.9\nPrecise timing measurements\nThe motivations for timing measurements at FCC-ee are outlined in this section. Quantified requirements\nare still to be assessed for most of the use cases.\n4.9.1\nTime-of-flight measurements\nAs mentioned in Section 4.5, charged hadron particle identification relying on the specific energy loss\nmust be complemented by other measurements in order to fill the gap around 1 GeV, where the Bethe\u2013\nBloch energy loss function is close to its minimum. Time-of-flight measurements, for example in a\nlayer of silicon sensors at 2 m from the interaction point, with a non-challenging resolution \u03c3t \u2243100 ps,\nare adequate for this purpose (with a magnetic field of 2 T or less). With a resolution of 30 ps, such\n(standalone) TOF measurements would allow charged kaons to be separated from charged pions up\nto O(3) GeV in momentum, while an excellent resolution of 10 ps would be needed 23 to extend this\nmomentum range up to 5 GeV.\nSuch TOF information could also be obtained in a silicon-tungsten CLD-like ECAL, where mea-\nsurements could be made in several layers, each with a resolution of, e.g., \u223c100 ps. Dedicated timing\nlayers made of inorganic scintillator offer another solution. For example, the calorimeter design proposed\nin Ref. [614] includes two such thin layers, upstream of the crystal-based ECAL mentioned earlier, which\ncould provide a 20 ps timing resolution.\nAnother well-known use-case of TOF measurements is the determination of the mass and lifetime\nof new massive particles. An example is provided by feebly coupled heavy neutral leptons that could be\ncopiously produced in Z \u2192\u03bdN decays at Tera-Z. In such decays, the energy of the new lepton N depends\nonly on its mass. In subsequent decays, such as N \u2192Z(\u2113\u2113)\u03bd or N \u2192W(qq\u2032)\u2113, the flight distance of\nN is obtained from the decay vertex of the Z boson and the TOF of the charged particles provides the\ntime at which N decayed, from which both the lifetime and the velocity (hence the mass) of N can be\nextracted [126]. The need for a large tracking volume, as well as a timing resolution in the ballpark of a\nfew tens of picoseconds, has so far placed the practical realisation of this idea out of realistic experimental\nreach. A first study of the expected performance of this measurement technique has been presented in\nRef. [654], in the context of FCC-ee. It uses as a benchmark the process e+e\u2212\u2192N\u00b5\u03bd\u00b5 \u2192\u00b5qq\u2032\u03bd\u00b5,\nalready considered in Section 4.7. A simple algorithm has been developed that allows the reconstruction\nof the time when N decays, despite the fact that the masses of the charged particles produced in the\nhadronic W decay are, a priori, unknown. Since there is no way to determine the \u2018event time\u2019 (t0) of the\ncollision for such interactions, with no primary tracks, it must be assumed that N was produced at the\nnominal beam crossing time. This leads to a smearing, of about 36 ps, of the reconstructed time of flight\nof N, from which its velocity is derived. Figure 77 (left) shows the relative resolution with which the mass\nof the HNL can be reconstructed with this method, as a function of its flight distance, for an HNL mass\nof 40 GeV and several assumptions on the resolution of the timing measurements, \u03c3t. The resolution is\ndefined as the width of the interval between the 16% and the 84% quantiles of the reconstructed mass\ndistribution. The aforementioned smearing prevents reaching the ideal resolution that would be obtained\nwith \u03c3t = 10 ps, if the event t0 was known, represented by the lowest curve in Fig. 77 (left). From the two\nupper curves it can be seen that, provided \u03c3t is smaller than 50 ps, the degradation due to the detector\nresolution is limited to 20%. For an HNL of mass 40 GeV that decays at 1.5 m from the interaction\npoint, this technique provides a mass resolution below 1%, which is significantly better than what can\nbe obtained by measuring the visible mass in the detector. The right panel of Fig. 77 shows that, in the\nparameter space that FCC-ee can probe and that extends beyond the sensitivity of the HL-LHC, timing\nmeasurements with \u03c3t = 30 ps would allow the HNL mass to be reconstructed at the per-cent level.\n23Such a resolution is smaller than the time it takes, at the Z peak, for the two bunches to cross each other (about 36 ps).\nHence, to be able to exploit a 10 ps resolution, the \u2018event time\u2019, t0, would need to be reconstructed. Simple algorithms should\nallow this t0 to be reconstructed, for most SM processes, with a resolution of \u03c3t/\n\u221a\nN for events with N primary tracks that\nreach the timing layer.\n110\n\nFig. 77: Left: Relative mass resolution of the HNL as a function of its flight distance, for an HNL mass of 40 GeV,\nusing a reconstruction technique exploiting timing measurements; two hypotheses on the resolution of the timing\nmeasurements are considered (\u03c3t = 10 and 50 ps). Right: Relative mass resolution expected at FCC-ee, as a\nfunction of the HNL mass and of its (squared) mixing with the \u03bd\u00b5, in the parameter space where FCC-ee could\nmake a discovery, for a timing resolution of 30 ps.\nIt should be noted that, should the magnetic field be increased to 3 T (as could be considered for\nthe runs at \u221as = 240 GeV and beyond), particles with a momentum of 1 GeV may not reach the outer\nradius of the tracker24 of about 2 m. Hence, to provide PID capabilities in the momentum range around\n1 GeV, where the measurement of ionisation energy per unit length does not provide any separation, the\nTOF measurements should be made either at a smaller radius or when the particle eventually reaches\nthe endcaps. In the latter case, in particular at normal incidence, it is essential to investigate the effects\nof multiple scattering and energy loss resulting from interactions with the beam pipe and the tracker\nmaterial. While this may pose less of an issue for a gaseous tracker, it remains important to study this\naspect in detail. In the former case and for the IDEA detector, the outermost layer of the vertex detector,\nat a radius of 35 cm from the beams, could be used for that purpose, at the expense of an increased\nmaterial budget. With a time resolution of 30 ps, such standalone TOF measurements would ensure a\nK/\u03c0 separation larger than 3 \u03c3 in the whole momentum range where PID based on dN/dx is ineffective.\nThe impact that the larger material would have on the measurement of the track parameters remains to\nbe studied. In a detector design with a full silicon tracker, the TOF measurements could be made in one\nof the layers of the outer tracker.\n4.9.2\nTime measurements very close to the IP\nAt FCC-ee, the distribution of the \u2018event time\u2019 (t0) of the collisions follows a Gaussian distribution to a\nvery good approximation, with a width ranging between 36 ps during the Tera-Z run and 6.5 ps during\nthe tt threshold run. The arrival time of a particle in the innermost layer of the vertex detector depends\nonly minimally on its nature (K, \u03c0, \u00b5, e, etc.), such that a measurement of this time provides (for primary\nparticles) a measurement of the particle production time and of the event time t0. For a given resolution\nof each measurement, \u03c3t, the event t0 can then be determined with a resolution of \u03c3t/\n\u221a\nN, with N\nbeing the number of charged primary particles crossing this layer. Measuring the event t0 offers several\nadvantages, as listed below.\n24Prompt particles with a curvature radius \u03c1 are confined to radial distances below 2 \u03c1 and, hence, need to have a transverse\nmomentum pT (GeV) > 0.3 \u00d7 R (m) \u00d7 B (T)/2 to reach a barrel layer situated at a radius R. Particles with a momentum of\n1 GeV and a polar angle of 45\u25e6only reach R \u223c1.6 m in a 3 T magnetic field.\n111\n\n\u2013 It provides a robust reference for some of the TOF measurements outlined above.\n\u2013 The spread of the t0 distribution being proportional to the beam energy spread, its measurement\nprovides an independent determination of the latter.\n\u2013 Because of the crossing angle, the t0 of a collision and the longitudinal position of the collid-\ning particles within their respective bunch are correlated. With respect to a time origin, defined\nas the time when the centres of the two bunches coincide with the IP, collisions that occur early\n(late) always involve particles that are in the head (tail) of both bunches. Collisions that happen\nat a time close to the origin involve particles that are in the middle of the bunches. Splitting the\nevents into early, central, and late collisions can provide relevant accelerator-related information.\nFor example, the mass distribution of dimuon events at Tera-Z would provide a check that there\nis no unexpected difference in the centre-of-mass energy between head and tail collisions. Alter-\nnatively, the longitudinal boost distribution of dimuon events at \u221as = 125 GeV would exhibit a\ncorrelation [655] between the centre-of-mass energy and the longitudinal position that could im-\nprove the effective monochromatisation (Section 9). Moreover, further checks of the beam-beam\neffects could be made, by exploiting the fact that these effects depend strongly on the longitudinal\nposition of the colliding particles [656].\nMoreover, the measurement of the production time of the particles complements the spatial recon-\nstruction of primary vertices in view of a direct pile-up measurement (expected to be at the per-mil level\nat Tera-Z). However, achieving precise timing measurements in the innermost layer of the VXD, without\nheavily compromising the material budget, will probably be a challenge.\n4.9.3\nTime measurements in the calorimeters\nBesides the TOF measurements mentioned earlier, time measurements in the calorimeters provide han-\ndles to exploit the shower development in space and time. The hadronic energy reconstruction, in par-\nticular in a non-compensating calorimeter, as in the CLD design, can benefit greatly from such measure-\nments, which allow the delayed signal from neutrons to be identified. The possible benefit of timing for\npattern recognition in high-granularity imaging calorimeters remains to be studied in detail.\nFinally, in the DR calorimeter of IDEA, a Fourier transform of the full signal from the SiPMs\nreading out the fibres would provide high precision (better than 100 ps) timing for the individual fibres\nand, in turn, longitudinal segmentation; the potential benefit in a particle-flow reconstruction algorithm\nadapted to the hybrid segmented crystal and fibre dual-readout calorimeter of Ref. [614] remains to be\nstudied. It could also benefit the identification of low energy neutral hadrons, potentially providing neu-\ntron vs. KL separation, assuming that the initial time t0 is known. However, a concrete implementation\nhas to be studied in detail.\n4.10\nSelected studies with full simulation\nMost of the requirements discussed in the previous sections have been obtained using fast parametrised\nsimulations. While a full simulation and event reconstruction with every detector concept is beyond the\nscope of this feasibility study, a few selected preliminary reconstruction performance and physics results\nobtained with full simulation are presented in this section. With the exception of ML-based tracking,\nall of them use the reconstruction of the CLD detector concept. A high-level machine-learning-based\nparticle-flow reconstruction algorithm is first discussed. An initial implementation of a full simulation\nflavour tagging algorithm in CLD is described next and the achieved performance is compared with the\nfast simulation results. Finally, the Higgs mass measurement using the recoil mass method and the \u03c4\npolarisation measurement at the Z pole are addressed.\n112\n\n4.10.1\nMachine-learning event reconstruction\nThe Higgs boson decays preferentially into hadrons. Therefore, the optimal identification and recon-\nstruction of hadronic jets is crucial for measuring Higgs boson properties. In particular, resolving the\nmass peaks from W, Z \u2192jj hadronic decays at the 3 \u03c3 level requires reconstructing the dijet masses\nwith a resolution \u03c3m at the \u0393/m \u22482.5% level, where \u0393 is the natural W or Z width. Moreover, the mea-\nsurement of rare hadronic Higgs decay rates, such as H \u2192cc and H \u2192ss, requires excellent dijet mass\nresolution, since the relative uncertainty on these modes scales with \u221a\u03c3m, as discussed in Section 4.7.\nThe visible energy of hadronic jets is roughly distributed as follows: f\u00b1 = 65% from charged\nhadrons (\u03c0\u00b1, K\u00b1, . . . ), f\u03b3 = 25% from photons originating from \u03c00 decays, and fn = 10% from neutral\nhadrons (n, KL, . . . ). The particle-flow approach relies on the tracking system to measure the momenta\nof charged particles, benefiting from its superior resolution, compared to the calorimeters, while the\nenergies of photons and neutral hadrons are measured with the calorimeters. In an ideal PF algorithm,\nthe visible mass resolution is dominated by the HCAL resolution, despite the neutral hadron energy\ncontent being subdominant. Achieving the best mass resolution requires efficiently identifying neutral\nhadrons and disentangling them from mismeasured clusters originating from charged hadron showers.\nAn optimal PF algorithm requires nearly 100% tracking efficiency and purity over the full mo-\nmentum range for an accurate measurement of the charged energy component. Fine transverse and lon-\ngitudinal calorimeter segmentation is necessary for optimal geometrical matching of extrapolated track\ntrajectories to electromagnetic and hadron showers. Additionally, low-noise high-resolution calorimetry\nand efficient clustering algorithms are essential for identifying and reconstructing individual photon and\nneutral hadron showers. Excellent electromagnetic and hadron calorimeter resolutions are crucial for\ncomparing tracking and calorimeter energy measurements after geometrical matching. A low material\nbudget in the tracker and before the calorimeter (e.g., pre-shower or solenoidal magnet) is desirable to\nminimise nuclear interactions and conversions that could compromise track, photon, and neutral hadron\nreconstruction efficiency. Moreover, the PF reconstruction performance depends critically on the trans-\nverse and longitudinal granularity for optimal track-cluster matching and neutral hadron identification.\nFinally, maximising the hermeticity and uniformity of the detector design is crucial for PF reconstruction.\nElectron and muon identification and momentum determination, whether isolated or within jets,\nalso benefit from a holistic treatment of all detector components [657, 658]. For example, as shown\nin Section 4.6, photon bremsstrahlung emissions within the tracker requires combining tracking and\nECAL information. Similarly, muons are identified by combining data from tracking, calorimetry, and\nmuon detectors. A comprehensive PF reconstruction should encompass a wide range of tasks, aiming at\nproviding an exhaustive list of identified final-state particles produced in the collisions and interacting\nwith the detector, along with accurate measurements of their momenta and origin vertices.\nA novel approach to full event reconstruction based on graph neural network (GNN) methods is\ndescribed in the following. The goal is to improve every aspect of the reconstruction process, from ef-\nficiency to resolution, and to enable rapid iterations over various detector concepts and geometries, so\nas to estimate performance and, hence, optimise detector technologies and design options. The effec-\ntiveness of this approach is shown in Fig. 78. The left panel displays the tracking efficiency achieved\nwith machine learning (ML) methods using the GGTF algorithm [659] for the CLD and IDEA detectors\nin Z \u2192jj events at the Z pole. The ML approach significantly improves the CLD performance with\nrespect to the standard tracking (a similar comparison for the IDEA case cannot be made because the\nbaseline reference is missing). It also shows that IDEA, with its superior number of track measurements,\ncan reconstruct much lower transverse momentum tracks, which are crucial for optimal PF reconstruc-\ntion since a significant portion of the visible jet energy is carried by soft charged particles. The right\npanel illustrates the visible mass resolution in ZH \u2192\u03bd\u03bdss events at \u221as = 240 GeV obtained with ML-\nbased PF (MLPF) compared to the PANDORA particle-flow reconstruction [660, 661], showing similar\nperformance. This result was obtained using GNN-based PF reconstruction, described in more detail\nin Ref. [615], taking as input reconstructed classical tracks and low-level calorimeter hit reconstruction.\n113\n\n10\u22121\n100\n101\npT [GeV]\n0.8\n0.9\n1.0\nTracking e\ufb03ciency\nZ/\u03b3\u2217\u2192q\u00afq(q = u, d)\n10 < \u03b8 < 170\u25e6,\nvertex R < 50 mm\n\u2206> 0.02 rad\nCLD\nIDEA\nCLD Conformal Tracking\n0.6\n0.8\n1.0\n1.2\n1.4\nMpred/Mtrue\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\nEvent fraction\nML\n\u03c3/\u00b5=0.05\nPandora\n\u03c3/\u00b5=0.05\nFig. 78: Left: Tracking efficiency in CLD and IDEA using the classical (Conformal Tracking) and ML-based\n(GGTF) approaches. Right: Visible mass resolution in H \u2192ss events using the classic PANDORA reconstruction\nand the ML-based particle flow approach.\nAlthough this is work in progress, it indicates that the established PF algorithm performance can already\nbe reproduced with this approach. Further improvements are foreseeable by optimising the clustering\nstep, enhancing the neutral hadron identification efficiency, and making use of further optimised tracking\nalgorithms.\n4.10.2\nJet flavour tagging\nThe first investigation of jet-flavour tagging performance with a full simulation of the CLD detector con-\ncept at FCC-ee is briefly presented here, and discussed in more details in Ref. [662]. As discussed in\nSections 4.4.1 and 4.5.1, jet-flavour tagging is essential for precision measurements of the Higgs cou-\nplings to quarks and gluons. A modified DELPHES configuration simulates the CLD detector geometry\nand resolutions in fast simulation, referred to as the CLD fast simulation. The full simulation uses the\nCLD conformal tracking (the baseline tracking reconstruction in CLD) to reconstruct charged particles.\nThe PANDORA particle flow algorithm [660, 661] is used for global event reconstruction, to build a\nparticle-level view of the event.\nJets are clustered with the kT Durham algorithm [390] using N = 2 exclusive clustering on\ne+e\u2212\u2192ZH \u2192\u03bd\u03bdjj events. The input to jet clustering are the reconstructed tracks and the neutral\nparticles reconstructed by PANDORA. The jet flavour tagger [486] is then applied to assign each jet a\nprobability of originating from a given flavour among seven possible categories: g, u, d, s, c, b, and \u03c4.\nThe tagger uses the information of all the input particles within a jet, including kinematic, displacement,\nand particle identification properties. Adding direct vertex information (positions and invariant masses of\nsecondary vertices) to the network does not improve performance, indicating that the model effectively\nlearns vertexing from the track displacement, the charged particle content, and the kinematic variables.\nThe implementation of the algorithm in DELPHES and its performance are described in detail\nin Ref. [486]. Both fast and full simulation datasets are trained using identical input features. For\nillustration purposes, Fig. 79 shows the charm and gluon score, defined as the monotonic transformation\nof the tagging probability log(P / (1 \u2212P)). The fast- and full-simulation output scores agree reasonably\nwell. Additional jet tagging scores and performance figures can be found in Ref. [662].\n114\n\n\u22126\n\u22124\n\u22122\n0\n2\n4\nc-jet discriminant\n0.0\n0.2\n0.4\n0.6\n0.8\nc\nb\ng\nFullSim CLD\nFastSim CLD\n\u22124\n\u22122\n0\n2\ng-jet discriminant\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\nu\nb\ng\nFullSim CLD\nFastSim CLD\nFig. 79: Flavour tagging output in the full (solid) and fast (dashed) CLD simulation for charm (left) and gluon\n(right) multi-variate discriminants for various jet species.\nIt is observed that fast simulation features better performance across all tagging categories. For\ninstance, in c-tagging, the efficiency of correctly identifying c-jets vs. misidentifying light-quark jets\ndecreases from 80% in fast simulation to 70% in full simulation, for a 1% light quark misidentification\nrate. This loss in performance is under investigation but can be largely explained by track reconstruction\ninefficiencies in full simulation and a sub-optimal particle-flow algorithm parameter tuning.\nThis study shows that initial jet-flavour tagging performance in full simulation in CLD is sub-\noptimal. Future work should focus on improving CLD reconstruction to mitigate the identified limi-\ntations, such as low tracking efficiency at low momentum and large neutral hadron mis-identification\nprobability. In addition, exploring the use of energy loss per unit length (dE/dx) information from the\nsilicon tracker may provide additional particle identification capabilities, which can be useful for strange\njet identification and can also provide additional exploitable information for charm, bottom, and tau\ntagging. Making progress in these areas is crucial to achieve the FCC-ee precision Higgs physics goals.\n4.10.3\nHiggs boson mass determination\nMeasuring the Higgs boson mass precisely at FCC-ee is important because it constitutes a limiting para-\nmetric uncertainty in the calculations of the branching ratios of the Higgs boson decay channels. Achiev-\ning a precision of 4 MeV makes this uncertainty negligible and leads to more accurate predictions of the\nHiggs boson decay properties. Also, knowing mH with a precision comparable to the Higgs boson\nnatural width is the minimum requirement for potentially measuring the electron Yukawa coupling at\n\u221as = 125 GeV, the Higgs boson pole (Section 9.4).\nThe Higgs boson mass measurement prospects have been studied in full simulation using the\nCLD detector [63]. Track reconstruction and muon identification are the main event reconstruction\nfeatures required for this measurement, which allows a straightforward comparison to fast simulation.\nThe Higgs boson mass recoil method and the resulting sensitivity obtained with fast simulation in the\ndimuon and dielectron channels are extensively discussed in Sections 4.3.1 and 4.6, assuming the IDEA\ndetector performance with a gaseous drift chamber or, alternatively, a CLD-like silicon tracker. The\ndriving experimental factor for the sensitivity is the track momentum resolution, ultimately limited by\nthe multiple scattering induced by the beam pipe and tracker material. A gaseous tracking device is,\ntherefore, preferred for this measurement. In this study, the recoil mass method has been applied to the\nCLD silicon tracking full simulation and compared to the CLD-like fast simulation results, as shown\n115\n\n122 123 124 125 126 127 128 129 130\n131 132\nRecoil (GeV)\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n0.014\nEvents\n)H\n\u2212\n\u00b5\n+\n\u00b5\nMuon final state Z(\nIDEA Si Tracker (Delphes)\nCLD (FullSim)\n1\n\u2212\n = 240 GeV, 10.8 ab\ns\nSimulation\n \nFCC-ee\n124.99\n124.995\n125\n125.005\n125.01\n (GeV)\nh\nm\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nNLL\n\u2206\n-2\n) = 5.11 MeV\nh\n(m\n\u03b4\nIDEA CLD silicon tracker (Delphes) \n) = 6.41 MeV\nh\n(m\n\u03b4\nCLD FullSim \n1\n\u2212\n = 240 GeV, 10.8 ab\ns\nSimulation\n \nFCC-ee\nFig. 80: Higgs boson mass determination using the recoil mass method in the dimuon channel in the full (red\ncurves) and fast (red curves) simulation. Left: The mrecoil distribution. Right: Likelihood scan of the Higgs boson\nmass and corresponding precision.\nin Fig. 80. The recoil mass distribution obtained in e+e\u2212\u2192ZH \u2192\u00b5+\u00b5\u2212H events is shown on the\nleft panel; it agrees at the 15% level with the fast simulation distribution. This small discrepancy is\nmost likely explained by a small difference in the tracker material description and is currently under\ninvestigation. The right panel shows the corresponding precision on the Higgs boson mass determination,\nobtained from a likelihood scan using different mass hypotheses, yielding a precision of 6.4 MeV for full\nsimulation, compared to 5.1 MeV in fast simulation.\nThis study shows that the full simulation of the CLD detector is available to perform a complete\nphysics benchmark study. Further work is needed to understand the discrepancy in the observed preci-\nsion between fast and full simulation, which may also point to shortcomings in the full event simulation\nand reconstruction. Extending the study to the dielectron final state, which requires the implementation\nof photon bremsstrahlung recovery to fully reconstruct the final-state electron momentum, will be an\nimportant step forward in the understanding of the CLD detector performance in this important measure-\nment.\n4.10.4\nTau polarisation\nThe Z-pole running will provide an unprecedented sample of 2 \u00d7 1011 clean \u03c4+\u03c4\u2212events and a unique\nopportunity for the determination of the tau polarisation, which is in turn very sensitive to the electroweak\ncouplings of the Z boson (sin2 \u03b8W). The tau polarisation is defined as P\u03c4 = (\u03c3+ \u2212\u03c3\u2212)/(\u03c3+ + \u03c3\u2212),\nwhere \u03c3+ and \u03c3\u2212are the production cross sections of left-handed and right-handed taus, respectively. It\ncan be expressed as a function of the electron and tau asymmetry parameters, Ae and A\u03c4, and it depends\non the angle \u03b8 between the tau momentum and the electron beam in the centre-of-mass frame of the\ncollision:\nP\u03c4(cos \u03b8) = \u2212A\u03c4(1 + cos2 \u03b8) + 2Ae cos \u03b8\n1 + cos2 \u03b8 + 2AeA\u03c4 cos \u03b8 .\n(8)\nThe measurement of P\u03c4(cos \u03b8) allows the determination of A\u03c4 and Ae, as a test of the universality\nof the Z boson couplings to electrons and taus. Integrating over cos \u03b8, one obtains Ptotal\n\u03c4\n= \u2212A\u03c4. At\nLEP, the uncertainty in Ae was statistically dominated [663], while for A\u03c4 systematic and statistical un-\ncertainties were at the same level. The large FCC-ee data samples and advanced detector capabilities are\n116\n\nexpected to significantly reduce these uncertainties. Assuming a factor 10 improvement in the system-\natic uncertainty with respect to LEP, the systematic uncertainty in A\u03c4 could be as low as 0.02%, with Ae\nhaving an even smaller uncertainty.\nTo confirm our expectations that this precision can be achieved, a full simulation study of the CLD\ndetector is underway, focusing on tau reconstruction and identification. Tau identification relies on re-\nconstructing charged hadrons and photons from \u03c00 \u2192\u03b3\u03b3 decays. About 65% of tau decays are hadronic,\ndecaying to one or three charged hadrons accompanied by photons from \u03c00 decays. An algorithm based\non the PANDORA particle-flow candidates has been developed to reconstruct the main decay modes:\n\u03c4 \u2192\u03c0\u03bd, \u03c4 \u2192\u03c1\u03bd \u2192\u03c0\u03c00\u03bd, and \u03c4 \u2192a1\u03bd. In parallel, a GNN method is being developed to improve the\nidentification performance.\nA first analysis limited to Z \u2192\u03c4\u03c4 events in which one of the taus decays leptonically in one\nhemisphere and the other decays hadronically in the other hemisphere has been performed [664].\nFigure 81 shows the optimal variables for the three main configurations considered in the analysis.\nThe first mode is designed to select \u03c4 \u2192\u03c0\u03bd decays. In this case the optimal variable is directly the energy\nfraction x\u03c0 = E\u03c0 / Ebeam. The other two configurations correspond to the \u03c4 \u2192\u03c1\u03bd \u2192\u03c0\u03c00\u03bd channel with\nthe reconstruction of either one or both of the \u03c00 decay photons. Here the optimal observable at LEP was\ndefined to be\n\u03c9\u03c1 = W+(\u03b8\u2217, \u03c8) \u2212W\u2212(\u03b8\u2217, \u03c8)\nW+(\u03b8\u2217, \u03c8) + W\u2212(\u03b8\u2217, \u03c8) ,\n(9)\nwhere W+ and W\u2212represent the angular distributions of the \u03c1 decay products for different helicity states,\nand \u03b8\u2217and \u03c8 are angles describing the decay products in the \u03c4 rest frame [665]. The reweighted P\u03c4 = \u00b11\nsignal templates are shown in comparison to the SM prediction. Additionally, the backgrounds coming\nfrom tau misidentification are also shown. No other backgrounds are considered at this stage. Further\nstudies of the full simulation samples and optimisation of the reconstruction algorithm are in progress.\nAn analysis aiming to extract A\u03c4 was performed using a log-likelihood fit of the optimal variable\nin the \u03c1 channel with two resolved photons. For an integrated luminosity of 17 ab\u22121, corresponding to\ndata collected by one FCC-ee experiment in a single year, the statistical uncertainty achieved is 7\u00d710\u22125.\nFuture work includes refining the tau reconstruction algorithms, expanding the analysis to cover more\ndecay channels and backgrounds, and performing a comprehensive extraction of the polarisation pa-\nrameters across multiple cos \u03b8 bins. In addition, focus will be placed on deriving explicit calorimeter\nrequirements to reduce the dominant systematic uncertainties reflecting the \u03c00 and fake photon identifi-\ncation efficiencies as close as possible to (or below) the statistical uncertainties.\n4.10.5\nSummary of detector requirements\nThe FCC-ee detectors are expected to perform precise measurements across a wide range of physics\nprocesses, requiring optimised designs. This summary provides a simplified overview of the key require-\nments, but it is important to recognise that these specifications often involve trade-offs, which should\nand will be studied in full simulation. For instance, incorporating a RICH or time-of-flight detector for\nparticle identification may negatively impact the resolution of visible energy measurements. Identifying\nlow-momentum muons effectively requires smaller detectors or a reduced magnetic field, which compro-\nmises the ability to accurately track high-momentum particles, impacting the overall physics programme.\nFinally, it should be noted that over-ambitious requirements could compromise the overall feasibility and\nthe reliable operation of the detector systems. It is therefore of the utmost importance that the contin-\nued and creative effort to soften certain detector requirements with in-situ methods be consolidated and\namplified.\nAn incomplete list of requirements is summarised in Table 13. For physics channels involving\ncharm, bottom, and tau production, the beam-pipe is required to have a minimal material budget, par-\nticularly critical for processes such as the B \u2192K\u2217\u03c4\u03c4 decay. The vertex detector must achieve a spatial\n117\n\n0\n0.2\n0.4\n0.6\n0.8\n1\nbeam\n/E\nmeson\nE\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\nEvents\n-1\n=91 GeV, 0.68 fb\ns\n channel\n\u03c0\nPseudodata, \nSM Template\n=+1 Template\n\u03c4\nA\n=-1 Template\n\u03c4\nA\nAll Tau MisId Background\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03c1\n\u03c9\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nEvents\n-1\n=91 GeV, 0.68 fb\ns\n) channel\n\u03b3\n (1\n\u03c1\nPseudodata, \nSM Template\n=+1 Template\n\u03c4\nA\n=-1 Template\n\u03c4\nA\nAll Tau MisId Background\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u03c1\n\u03c9\n0\n500\n1000\n1500\n2000\n2500\n3000\nEvents\n-1\n=91 GeV, 0.68 fb\ns\n) channel\n\u03b3\n (2\n\u03c1\nPseudodata, \nSM Template\n=+1 Template\n\u03c4\nA\n=-1 Template\n\u03c4\nA\nAll Tau MisId Background\nFig. 81: Optimal variables used to extract the \u03c4 polarisation in three decay modes: \u03c0 (top), \u03c1 with one identified\nphoton (bottom left), and \u03c1 with two identified photons (bottom right).\nresolution of 3 \u00b5m or better and a material thickness below 1% of a radiation length, to improve the\nprecision of certain important measurements, such as the measurement of Rc at the Z pole or that of\nthe branching fraction of the aforementioned B \u2192K\u2217\u03c4\u03c4 decay. The \u03c4 lifetime measurement requires\nthe knowledge of the length scale of the vertex detector to be monitored with optical techniques with a\nprecision of \u03b4\u03c4\u03c4 < 10 ppm. The momentum resolution in the tracking systems, \u03c3p / p, needs to be better\nthan 0.2% for O(50) GeV tracks in order to achieve a precision of 4 MeV on the Higgs boson mass.\nAchieving a precision of O(10) keV on the Z width requires an exceptional track momentum resolution\nfor such tracks, better than 0.1%. It also demands a precise knowledge of the BES, for which an angular\ntracking resolution \u03c3\u03b8 better than 0.1 mrad is needed. For flavour physics at the Z peak, where low mo-\nmentum tracks are involved, a low mass gaseous tracker is advantageous since the momentum resolution\nis minimally affected by multiple scattering. Having a highly-efficient and pure tracking from 100 MeV\nto tens of GeV is of crucial importance to improve the dijet energy and mass resolution with particle-flow\nreconstruction.\nElectromagnetic calorimetry with excellent energy resolution (few %) is required to improve the\n118\n\nTable 13: Summary of detector requirements.\nAggressive\nConservative\nComments\nBeampipe\nX/X0 < 0.5%\nX/X0 < 1%\nB \u2192K\u2217\u03c4\u03c4\nVertex\n\u03c3(d0) = 3 \u229515 / (p sin3/2 \u03b8) \u00b5m\nX/X0 < 1%\n\u2013\nB \u2192K\u2217\u03c4\u03c4\nRc\n\u03b4L = 5 ppm\n\u2013\n\u03b4\u03c4\u03c4 < 10 ppm\nTracking\n\u03c3p/p < 0.1%\nfor O(50) GeV tracks\n\u03c3p/p < 0.2%\nfor O(50) GeV tracks\n\u03b4MH = 4 MeV\n\u03b4\u0393Z = 15 keV\nZ \u2192\u03c4\u00b5\nt.b.d.\n\u03c3\u03b8 < 0.1 mrad\n\u03b4\u0393Z(BES) < 10 keV\nECAL\n\u03c3E/E = 3%/\n\u221a\nE\n\u03c3E/E = 10%/\n\u221a\nE\nZ \u2192\u03bde\u03bde coupling,\nB physics, ALPs\n\u2206x \u00d7 \u2206y =\n2 \u00d7 2 mm2\n\u2206x \u00d7 \u2206y =\n5 \u00d7 5 mm2\n\u03c4 polarisation\nboosted \u03c00 decays\nbremsstrahlung recovery\n\u03b4z = 100 \u00b5m,\n\u03b4Rmin = 10 \u00b5m (\u03b8 = 20\u25e6)\nIn-situ constraint with\ndilepton/diphoton events\nalignment tolerance for\n\u03b4L = 10\u22125 with \u03b3\u03b3 events\nHCAL\n\u03c3E/E = 30%/\n\u221a\nE\n\u03c3E/E = 50%/\n\u221a\nE\nH \u2192ss, cc, gg, invisible\nHNLs\n\u2206x \u00d7 \u2206y =\n2 \u00d7 2 mm2\n\u2206x \u00d7 \u2206y =\n20 \u00d7 20 mm2\nH \u2192ss, cc, gg\nMuons\nlow momentum (p < 1 GeV) ID\n\u2013\nBs \u2192\u03bd\u03bd\nParticle ID\n3 \u03c3 K/\u03c0\np < 40 GeV\n3 \u03c3 K/\u03c0\np < 30 GeV\nH \u2192ss\nb \u2192s\u03bd\u03bd, ...\nLumiCal\ntolerance \u03b4z = 100 \u00b5m, \u03b4Rmin = 1 \u00b5m\nacceptance 50\u2013100 mrad\n\u2013\n\u03b4L = 10\u22124 target\n(Bhabha)\nAcceptance\n100 mrad\n\u2013\ne+e\u2212\u2192\u03b3\u03b3\ne+e\u2212\u2192e+e\u2212\u03c4+\u03c4\u2212(cc)\nprecision on the Z \u2192\u03bde\u03bde coupling via the e+e\u2212\u2192\u03bde\u03bde\u03b3 process, on lepton flavour violating decays\nsuch as the Z \u2192\u00b5e and \u03c4 \u2192\u00b5\u03b3 decays, on decays of heavy flavoured hadrons to photons or to \u03c00 mesons,\nand on ALPs searches. The electromagnetic calorimeters must provide an energy resolution of \u03c3E / E =\n3% /\n\u221a\nE for aggressive scenarios and 10% /\n\u221a\nE for conservative ones, with spatial granularity between\n2 \u00d7 2 mm2 and 5 \u00d7 5 mm2. High granularity is crucial for \u03c4 polarisation measurements, boosted \u03c00\ndecays, and bremsstrahlung photon recovery. Additionally, alignment tolerances of \u03b4z = 100 \u00b5m and\n\u03b4Rmin = 10 \u00b5m (measured at a 20\u25e6polar angle) are essential for a precise calibration of the acceptance\nor, equivalently, of the luminosity. The large dilepton and diphoton samples will be instrumental to\nascertain in-situ the acceptance determination.\nA good particle identification performance is required to achieve 3 \u03c3 K/\u03c0 separation up to 30 GeV\nand is essential for studying H \u2192ss decays, to study rare decays such as b \u2192s\u03bd\u03bd, and, more generally,\nto maximise the FCC-ee flavour physics potential.\nHadron calorimeters with sufficient resolution and granularity are crucial for the success of the\nHiggs boson physics programme. In particular, the expected precision in the Higgs couplings to quarks\nand gluons is driven by the particle-flow global event reconstruction capabilities and the visible mass\n119\n\nresolution. The hadron calorimeters must feature a stochastic term of less than 30% in the aggressive\nscenario or less than 50% in the more conservative scenarios. The transverse granularity should range\nfrom 2 \u00d7 2 mm2 to 20 \u00d7 20 mm2. The luminosity monitors must have a spatial tolerance of, at least,\n\u03b4z = 100 \u00b5m and \u03b4Rmin = 1 \u00b5m, with an acceptance range of 50\u2013100 mrad. The detector must ensure\noptimal hermeticity. Requiring no gaps (and possibly a small overlap) between the LumiCal and the\ncombined tracker plus calorimeter system sets the requirement for the tracker and calorimeter acceptance\nat 100 mrad. Forward coverage is necessary for the detection and identification of photons produced in\nthe e+e\u2212\u2192\u03b3\u03b3 process, which promises to provide an independent measurement of the luminosity.\nProcesses involving the production of forward electrons, for example e+e\u2212\u2192e+e\u2212\u03c4+\u03c4\u2212(cc) might\nalso benefit from even more forward coverage.\nFinally, the muon systems will be used mainly to identify muons, given that their momenta will be\noptimally measured by the tracking system at FCC-ee. They should provide excellent identification for\npion rejection and standalone momentum measurement for long-lived particle searches.\n4.11\nOutlook\nBoth software and analysis tools have matured during the Feasibility Study, and the common software\nframework (Chapter 8) was instrumental in developing a number of key physics case studies in view\nof extracting some of the necessary detector requirements. So far, most of the studies have been per-\nformed with a fast simulation of the response of a few detector benchmarks, similar to those presented\nin the Conceptual Design Report. Variations around these baseline concepts were applied to quantify the\ngeneric sensitivity dependence of key observables on the detector performance. In the next phase of the\nstudy, more explicit requirements will be obtained with a (full) simulation, reconstruction, and analysis\nstrategy, optimised to the specific capabilities of the considered hardware, when the current R&D efforts\nstart converging in concrete and definite detector proposals.\nMatching experimental systematic uncertainties to the FCC-ee statistical precision will remain a\ncritical objective of the entire physics programme. This perspective constitutes a superb opportunity for\ndetector designers. It also continuously generates new and creative ideas from the analysts to control\nuncertainties from the data themselves: past experience has shown that a careful analysis of systematic\neffects and corrections almost always boils down to a statistical problem. This strategy will be gener-\nalised and will lead to a better precision for most observables, owing to the very large event samples\nexpected at FCC-ee.\nWith 6\u00d71012 Z and 3\u00d7108 W pairs, the leading challenge for the detector and analysis designs will\ncontinue to be the precision target with which the electroweak observables (Table 2) can be measured.\nWork on the hadronic, dilepton, and diphoton cross-section measurements has started, but much remains\nto be done, for example, to consolidate the in-situ acceptance determination method for lepton pairs\nand for the luminosity measurement with photon pairs and low-angle Bhabha scattering. The field of\nmeasurements at FCC-ee is huge, even when limited to the benchmark processes listed in Ref. [53].\nAn even stronger connection between theorists and experimentalists will help streamlining and refining\nthe list of observables and the parameter space to be explored. Clearly, the physics requirements will\ncontinue to be the driving factor in all efforts to design the most technologically-advanced (but also the\nmost realistic) FCC-ee detector concepts, to ensure the full coverage of this challenging and promising\nphysics programme.\n120\n\n5\nMachine-detector interface\nThe FCC-ee interaction region (IR) is designed to reach the highest luminosities at all centre-of-mass en-\nergies, from the Z pole to the tt threshold. This design is based on the crab-waist collision scheme, with\nnano-beams at the interaction point (IP), large horizontal crossing angle, and crab-waist sextupoles [666].\nThe Machine Detector Interface (MDI) of FCC-ee has a compact and complex design [18,667] that fulfils\nconstraints imposed by the machine [18] and detector requirements (Chapter 4).\nThe main beam parameters are recalled in Table 14, for the four main operational centre-of-mass\nenergies. In FCC-ee, the two beams circulate in different vacuum chambers, which merge at 1.3 m\nfrom the IP. The distance between the face of the superconducting final focus quadrupole (FFQ) and the\nIP (\u2113\u2217) is 2.2 m, well inside the detector volume (Section 6). In addition to the optics constraints on\nthe IR layout, physics considerations strongly advocate for hermetic detectors and for constraining the\naccelerator components within a cone of 100 mrad from the IP, along the z axis25. These requirements\ndemand a compact MDI design with tight space constraints.\nTable 14: Key collider parameters for the FCC-ee IRs with 4 IPs. The bunch length, \u03c3z, is different for non-\ncolliding bunches (determined by \u2018synchrotron radiation\u2019, SR) and colliding bunches (determined by \u2018beam-\nstrahlung\u2019, BS); \u03c3\u2217\nx and \u03c3\u2217\ny denote the bunch sizes at the IP in the (horizontal and vertical, respectively) transverse\ndirections, while \u03c3\u03b4 is the relative beam energy spread.\nZ\nW+W\u2212\nZH\ntt\nBeam energy (GeV)\n45.6\n80\n120\n182.5\nLuminosity / IP (1034 cm\u22122s\u22121)\n145\n20\n7.5\n1.41\nBeam current (mA)\n1 294\n135\n26.8\n5.1\nBunch number / beam\n11 200\n1 852\n300\n64\nBunch spacing (ns)\n27\n163\n1 008\n4 725\n\u03c3\u2217\nx (\u00b5m)\n9.5\n21.8\n12.6\n36.9\n\u03c3\u2217\ny (nm)\n40.1\n44.7\n31.6\n43.6\n\u03c3z (mm) SR / BS\n4.7 / 14.6\n3.46 / 5.28\n3.26 / 5.59\n1.91 / 2.33\n\u03c3\u03b4 (%) SR / BS\n0.039 / 0.121\n0.069 / 0.105\n0.102 / 0.176\n0.151 / 0.184\nThe crab-waist scheme requires a large horizontal crossing angle of 30 mrad. The incoming beams\npoint straight to the IP, while the outgoing beam trajectories are strongly bent from the IP, so that the\nbeams can successfully merge back close to the opposite ring [668]. This scheme ensures that most of\nthe synchrotron radiation (SR) generated at the IR magnetic elements does not strike the IR central beam\npipe. The intense radiation emitted during the collision in the electromagnetic field of the opposite beam,\nknown as beamstrahlung (BS), is mostly collinear with the outgoing beams, similarly to the SR [669].\nBoth the BS and SR photons are stopped at about 500 m downstream of the IP, in dedicated dumps [670].\nTo minimise the level of SR photons that reach the detectors, the closest bending magnet is located at\nmore than 100 m from the IP and those located up to 500 m have a SR critical energy below 100 keV.\nTo counteract the beam rotation and deflection that would be caused by the simultaneous effects of\nthe detector magnetic field of 2 T and the crossing angle, a compensating solenoid delivering a magnetic\nfield of \u22125 T is placed at 1.23 m from the IP, cancelling out the longitudinal magnetic field integral along\nthe z axis from the last focusing quadrupole to the IP. Consequently, the front face of the luminosity\ncalorimeter (LumiCal), placed in front of the compensating solenoid, is only 1 m from the IP. The Lu-\nmiCal is centred around the outgoing beam direction and measures the integrated luminosity from the\n25The coordinate system of the detector has the origin centred at the nominal collision point. The z axis is defined as the\nbisector of the axes of the incoming and outgoing beams, ideally in the direction of the axis of the experiment solenoid. The\nx axis is in the plane subtended by the two beams and pointing away from the centre of FCC. In this way, the positron beam\nis travelling towards positive values of z (mainly) and x (subordinately). Perpendicular to the (x, z)-plane, the y axis points\nupwards. The polar angle, \u03b8, is then measured with respect to the z axis and the azimuthal angle, \u03d5, with respect to the x axis\nin the (x, y) plane. The radial coordinate, r =\np\nx2 + y2, is the distance from the z axis.\n121\n\nrate of low-angle Bhabha events, e+e\u2212\u2192e+e\u2212. The first layer of the vertex detector must be placed\nas close as possible to the IP to optimise the precision of the primary and secondary vertex position de-\ntermination, with direct impact on the efficiency and purity of flavour tagging algorithms. The smallest\naffordable distance is set by the central beam pipe radius of 1 cm. The length of the vertex detector\n(1.86 m) is chosen to cover the angular region | cos \u03b8| < 0.99. A lightweight mechanical structure is\ndesigned for its support. To avoid any material in front of the LumiCal, all other detector elements must\nbe placed above 110 mrad with respect to the z axis.\nAn overall design of the interaction region is shown in Fig. 82. The next sections describe the\nmain features of the MDI. A more detailed discussion can be found in Ref. [671].\nSupport tube\nLumiCal\nInner Vertex\nCompensating \nsolenoid\nQC1\nOuter Vertex\nScreening solenoid\nFig. 82: Layout of the interaction region. The support tube allows the integration of the luminosity calorimeter\n(LumiCal) and the vertex detector. The three segments of the final focus quadrupoles (QC1) are shown with the\nscreening and compensating solenoids.\n5.1\nInteraction region layout\nThe mechanical layout of the IR comprises an 18 cm long central beam pipe with a 10 mm internal radius,\na pair of ellipto-conical beam pipes about 1064 mm long on either side, a silicon vertex detector covering\nthe radial range from 13.7 to 315 mm, and the LumiCal at 1074 mm from the IP, 190 mm thick, covering\nthe angular range between 50 and 134 mrad. All these elements are held in place by a lightweight carbon\nfibre and honeycomb rigid structure support tube, which allows the overall integration before the insertion\nin the experiment [672]. The vacuum chambers are made of AlBeMet162, an alloy of Aluminium (38%)\nand Beryllium (62%), chosen for its high elastic modulus and low density.\nThe central beam pipe has a double layer structure, cooled by liquid paraffin flowing between\nthe two layers, as displayed in Fig. 83. A cross-sectional view of the central beam pipe and of the\ncooling manifolds, also made of AlBeMet162, is shown in Fig. 83 as well. The double-layer structure is\nmade of two concentric cylinders, each one 0.35 mm thick and assembled with 1 mm gap for the paraffin\nflow, thus bringing the effective diameter of the central beam pipe and its cooling layer to 23.4 mm. An\ninternal 5 \u00b5m coating layer of gold ensures a good electrical conductivity to minimise the beam heat load\nto nearly 60 W [673] and to shield the vertex detector from residual high energy SR photons.\nThe ellipto-conical vacuum chamber, shown in Fig. 84, extends between 90 and 1154.5 mm from\nthe IP. Following a short transition from the central chamber, its thickness remains at a constant value\nof 2 mm. Water flows in the cooling channels to extract an expected heat load of about 130 W; an\nasymmetric design is needed to match the angular acceptance of the luminosity calorimeter.\nA thermo-structural analysis has been performed to calculate the temperature distribution, stress,\nstrain and displacement of the beam pipes. The maximum temperature of the central chamber reaches\n29 \u25e6C, cooled with paraffin entering at 18 \u25e6C , while it amounts to 50 \u25e6C for the conical chamber cooled\n122\n\nFig. 83: Left: The central chamber in AlBeMet162 with its cooling inlets and outlets, and its internal gold coating\nlayer. Right: Chamber cross section and zoom on the cooling channel for the paraffin flow.\nFig. 84: Ellipto-conical vacuum chamber.\nFig. 85: Left: Material budget of the beam pipe, in per cent of a radiation length, as a function of the cos \u03b8 polar\nangular. Right: Distribution of the material budget of the beam pipe in the transverse plane, in the 0 < \u03b8 < 0.2 rad\nangular range, at the entrance of the LumiCal. The red lines represent the LumiCal angular coverage.\nwith water entering at 16 \u25e6C. The maximum stress has been calculated considering the constraint con-\nfigurations of a cantilevered support, resulting in a maximum displacement of 0.5 mm and a maximum\nstress ten times lower than the AlBeMet162 yield strength (193 MPa). The resulting material budget\ndistribution for the vacuum chamber is shown in Fig. 85 as a function of the polar angle. The material\nencountered by a particle produced at normal incidence corresponds to 0.68% of a radiation length (X0).\nSeveral vertex detector designs are described in Section 6. The integration study performed here is\n123\n\nbased on the engineered version currently adopted by the IDEA concept (Section 6.5). This version fea-\ntures two main subsystems, of active elements based on 50 \u00b5m thick \u2018Monolithic Active Pixel Sensors\u2019:\nan inner vertex detector, composed of three barrel layers at a radial distance between 13.7 and 35.6 mm,\ncovering an angular acceptance of about | cos \u03b8| < 0.99; and an outer vertex detector, composed of two\nbarrel layers at 13 and 31.5 cm, and three disks on either side of the IP.\nMiddle vertex\nDisks\nBellows\nCooling cones\nLumiCal\nFig. 86: Layout of the vertex detector cooling cones assembly, together with the main elements to be integrated\naround it.\nThe inner vertex detector is cooled by flowing gas (air or helium) through a system of carbon\nfibre cones, shown in Fig. 86, that forces gas convection inside the detector volume. The same carbon\nfibre structure supports the power and readout circuits. The inner vertex detector is mounted on top of\nthe conical vacuum chamber by means of two thin peek-based rings, anchored on either side at about\n170 mm from the IP and soldered on a conical carbon fibre structure supporting three layers of silicon\nvertex ladders, also integrating the central beam pipe cooling circuits (Fig. 87). The outer vertex detector\nand disks are mounted on the inner surface of the support cylinder, by means of insert rings, and cooled\nby water pipes.\nParaffin cooling \ninlet-outlet \nLayer 1 and 2 cooling cone\nLayer 3 cooling cone\nSupport cone\nInner Vertex layers\nFig. 87: Longitudinal section of the beam pipe and inner vertex layers. The dark gray object is the conical support\nof the vertex detector, which is supported by the conical beam pipe. The inlet/outlet paraffin of the central chamber\ncooling manifolds are visible at the edge of the support cone. The orange structures represent the cooling cones.\nThe luminosity monitor is described in Section 6.13.1. It consists of two cylindrical devices,\n124\n\nplaced at about 1 m away from the IP, on either side of the IP. Each device spans a sensitive radial\ncoverage between 54 and 115 mm from the beamline plus a service region from 115 to 145 mm, which\nhouses the electronics readout, cables, and cooling. In order to achieve the desired accuracy of 10\u22124 in\nthe measurement of the luminosity, the calorimeter has a stringent requirement on the knowledge of its\nboundaries. In particular, the relative positioning of the two sides along the z axis needs to be known with\na precision of \u00b1100 \u00b5m and, once assembled, the calorimeter must be a rigid hollow cylinder. This is\nguaranteed by dimensioning the bellows of the beam pipe such that their external dimensions are smaller\nthan the internal calorimeter bore and such that it could possibly slide inside. The beam pipe has been\ncarefully designed to minimise the material effects on particles reaching the luminosity calorimeter. In\nfact, the material budget ranges from approximately 0.07 X0 to 0.5 X0 (Fig. 85). The maximum values,\ndriven by the AlBeMet cooling manifolds, are at a safe distance from the 50 mrad LumiCal acceptance\ncone. The design of the cooling manifolds has been optimised to limit the effects of showers originating\nfrom electrons scattering in the beam pipe. Ongoing studies show that the impact on the luminosity\nmeasurement is limited.\nThe IR magnet system [18] includes the final focus quadrupoles, the compensating solenoid, the\nscreening solenoid, and magnetic correctors for IR tuning. The limited space available constitutes a\nchallenge to the design of the IR magnet system, currently envisaged to fit in an envelope of 100 mrad\naround the z axis. The system design includes a cryostat partially located inside the detector, surrounding\nthe compensating solenoid and the first final focus quadrupole (QC1), which is itself embedded in the\nscreening solenoid (for the part inside the detector). It also includes the second final focus quadrupole\n(QC2), starting 0.30 m upstream of QC1.\n5.2\nIntegration and alignment\nThe accelerator and detector components that are placed within \u00b11.5 m from the IP are mounted in a\nsingle rigid structure, which provides a cantilevered support for the pipe and avoids loads on the thin-\nwalled central chamber during assembly. This rigid structure also supports the LumiCal and the vertex\ndetector (Fig. 88). The support tube is an empty cylindrical structure made of a 4 mm honeycomb struc-\nture interleaved within two 1 mm thick carbon fibre walls. It is longitudinally split in two halves and is\ncomplemented by two aluminium flanges and two endcaps that support the LumiCal and the beam pipe.\nSix aluminium ribs are fixed inside the tube in order to support the outer vertex layers.\nFig. 88: Support tube showing the beam pipes and bellows, the vertex detector with air-cooling cones, the lumi-\nnosity detector, and, in brown, the vacuum chambers internal to the cryostat (not shown).\nA structural analysis, performed to calculate the stress and displacement of each part of the support\n125\n\ntube taking into account the estimated weights of detector elements, including services material, shows\nthat the structural resistance is safely respected.\nThe insertion of the support tube in the detector is foreseen either with a few sleds or with longitu-\ndinal rails fixed to its external surface. A possible option could then be to slide these sleds (rails) inside\nhollow carbon fibre rails, permanently fixed on the inside wall of the tracker to guarantee the structural\nrigidity while inserting the support tube. The corresponding calculations and simulations are beyond the\nscope of this feasibility study.\nThe alignment and monitoring device [674] is composed of three main subsystems:\n\u2013 The deformation monitoring system is capable of monitoring the shape of the screening solenoid\nsupport, which is then used as a reference [675]. It exploits in-line multiplexed and distributed\nfrequency scanning interferometry (IMD-FSI) [676] to monitor sections of optical fibres firmly\ninstalled on the inner surface of the screening solenoid support. This system occupies no more\nthan 5 cm3 within the assemblage and requires an interface with the endcap of the first final focus\nquadrupole.\n\u2013 At the end of each fibre used in the deformation monitoring system, a mirror is installed to redirect\nthe laser beam towards the centre of the assemblage, targeting the final focusing quadrupoles, the\nbeam position monitors (BPMs), the LumiCal, and any other component that requires position\nmonitoring. This subsystem is very similar to the FSI heads installed on the low-\u03b2 quadrupoles in\nthe HL-LHC MDI [677]. The corresponding distance measurements monitor the position of the\ninner components relative to the cryostat.\n\u2013 Finally, to ensure the alignment of both sides of the MDI with respect to each other, a long-range\nalignment system is foreseen, also based on FSI but with a different optical setup to enable longer-\ndistance measurements.\nA dense network of such measurements around the detector provides a continuous link between\nthe endcaps of the QC1 on each side of the MDI, which serve as the reference surface for the cylinder\nmonitored by the deformation system. Reference points are placed on the supporting feet of the detector,\neasy to access for a technician or a robot, and used to link to the cavern survey network and the rest of\nthe accelerator.\nA network of Frequency Scanning Interferometry is proposed for the alignment of the inner\ntracker. This network will be implemented similarly to what has been done for the ATLAS SemiConduc-\ntor Tracker [678], but with the latest version of the technology, more compact and precise. This system\nalso allows the measurement of the positions of the LumiCal and of the beam pipe relative to the FFQs.\n5.3\nMaintenance and detector opening\nPeriodic (or exceptional) detector maintenance requires, in general, access to the internal subsystems,\nknown as \u2018opening the detector\u2019. The design of the MDI region must carefully anticipate the intertwined\nrequirements from the civil engineering, the machine, and the detector. Three opening scenarios, with\ntheir own advantages and drawbacks, have been examined.\n1. In a first scenario, the two endcap calorimeters are moved along the z axis to disengage them from\nthe barrel, as displayed in the left panel of Fig. 89, by a couple metres if only access to the central\ntracker is needed and by up to 7 m if the tube supporting the LumiCal, the vertex detector, and\nthe central vacuum chamber requires extraction (and re-insertion). The mechanical stability of the\nfinal focus quadrupoles requires rigid supports, as close as possible to the detector boundaries.\nThese supports, if fixed, would make the longitudinal opening of the detector endcaps impossible.\nRemovable supports would then need to be designed to allow safe removal of the FFQs, and a\nquick re-installation and alignment following the access to the inner detectors. In this scenario, in\n126\n\nFig. 89: Longitudinal (left) and short longitudinal plus transversal endcap (right) detector opening\naddition to the re-alignment issue, the beam-pipe vacuum is broken. As the removal of the FFQs\nfrom inside the detector would first require the removal of other machine elements just behind\nthem, this scenario can be envisaged only for medium or long machine shutdowns (several weeks\nor months), as done with the BELLE II detector at SuperKEKB.\n2. A second option involves vertically splitting the detector endcaps, allowing opening without re-\nmoving the FFQs. In this scenario, the two split endcaps are first moved longitudinally for about\n2 m and then moved from the beamline in the transverse direction, as shown in the right panel of\nFig. 89. The FFQs could stay cold, with the beam pipe under vacuum. This scenario could be very\neffective in the case of a quick access. The only constraint from the machine side is to keep all\nthe services needed by the FFQs (supports, vacuum, cryogenics, powering) in the shadow of the\nFFQs, i.e., inside the detector forward acceptance cone. The main drawback is the serious impact\non the detector acceptance, as splitting the endcaps creates a dead zone in the vertical plane and\nmay imply a complete recalibration of the calorimeter angular acceptance determination.\n3. A third, currently preferred, possibility consists of moving the complete detector along the x axis,\naway from the beamline. As in the first scenario, this requires a disconnection of the internal FFQs\nfrom the rest of the machine, but allows them to be kept inside the detector. The FFQs can then be\neasily removed without touching any other machine element, before proceeding to a longitudinal\nopening of the endcaps without any obstacle. The detector integrity is preserved and, although the\nbeam vacuum is broken and a re-alignment of the FFQs is needed, relatively short access periods\n(few weeks) can be envisioned. As the FCC-ee detectors have a diameter of typically 12 m, this\nscenario requires enough transverse free space on one side of the detector, which is currently not\navailable in the two small experiment caverns (Section 7). Another location for the balconies (in\ngreen on Fig. 122, Chapter 7) may have to be found in these caverns, e.g., by placing all of them on\nthe other side of the detector, and a small additional alcove (typically 25 m long and a few metres\ndeep) might also be needed, depending on the exact transverse size of the detector. Designing the\nsmall caverns so that their axis can be transversely displaced from the beamline by a few metres, if\ncompatible with the size of the specialised FCC-hh detectors (Section 7), would alleviate the need\nfor such an alcove.\nTechnical mitigation solutions for the drawbacks of these three scenarios will be investigated in\ndetail during the next phase of the study.\n127\n\n5.4\nBeam-induced backgrounds in the detectors\nThe beam-induced backgrounds in the detectors arise from two categories of sources: those generated by\nprocesses involving only a single beam, and those generated by the interactions between the two beams\nat each IP, usually called luminosity backgrounds.\nAlthough the collimation system and absorbers remove the bulk of the particles produced by sin-\ngle beams (electrons/positrons and photons) before they can hit the detectors, some background may\nremain because the particles can scatter off them. Elastic and inelastic interactions of the beam with the\nmolecules of the residual gas produce scattered particles, deviating from the original orbits, as well as\nphotons from inverse-Compton scattering. Showers may also be produced for a very small fraction of\nevents.\nIntra-beam particle interactions, also known as Touschek scattering, are negligible at FCC-ee,\ngiven that they are suppressed by a large energy factor in comparison to lower energy colliders, such as\nSuperKEKB and DA\u03a6NE. Synchrotron radiation [679] has been simulated with BDSIM [680] and the\nGEANT4 [681] toolkit. The bulk of SR is emitted almost collinearly with the beam, and the IR optics\nkeeps it away from the detector sensitive layers. Magnet misalignments, imperfections, and beam tails,\nhowever, may cause SR to reach the detector. Studies are ongoing to optimise the design and the position\nof dedicated masks (a few metres upstream of the detector) in order to minimise the effects of SR in the\ndetector.\nA variety of processes such as space-charge effects, beam instabilities, interaction with residual\ngas, intra-beam scattering, magnet misalignments, and magnetic field errors can lead to the population\nof a beam halo, potentially leading to beam particle losses. These particles are mostly intercepted by\nthe collimators located in the dedicated section of the collider [18], following the approach used for\nLHC [682]. The relevant studies have been performed with the XSUITE-BDSIM simulation tool [683,\n684]. The vast majority of the beam halo losses in the MDI are intercepted by the SR collimators, so\nthat no losses are observed beyond the last SR collimators before the IPs, in all cases. The background\ncontribution from beam halo particles that leak from the beam halo collimation system is, therefore, not\nexpected to be an issue. Tertiary collimators have been included upstream of the SR collimators, strongly\nfurther reducing the effects of residual losses.\nBeam-gas interactions depend on the residual gas pressure profile in the rings and on the out-\ngassing materials inside the vacuum chambers. Simulations of the beam-gas interactions have been\nperformed with MOLFLOW+ [685], with a residual gas pressure profile resulting from 1 h beam condi-\ntioning at a full nominal current of 1.27 A at the Z pole. Within \u00b1500 m from the IP, the gas composition\nis 85% hydrogen, 10% carbon monoxide, and 5% carbon dioxide, at an average pressure of 10\u221211 mbar\nand spikes of 10\u22128 mbar in the vicinity of the SR absorbers. This vacuum level, conservatively estimated\nat the beginning of the machine commissioning, is expected to progressively improve over time. Pre-\nliminary results obtained with FLUKA indicate that the dose and fluence due to beam-gas interactions\nwithin \u00b1500 m from the IP in the Z pole run are not the leading contributors: for a pressure profile re-\nsulting from only one hour of beam conditioning, the estimated dose and fluence in the innermost vertex\ndetector layers are as low as 3 kGy/year and \u223c7 \u00d7 1011 cm\u22122/year, further decreasing with increasing\nconditioning.\nThe most relevant luminosity background arises from incoherent pairs creation (IPC) [686], a\nclass of interactions between two photons emitted by a single electron and a single positron at the IP,\ne+e\u2212\u2192(e+e\u2212)e+e\u2212. The simulation of these backgrounds has been performed with GUINEAPIG [687]\nand interfaced to KEY4HEP (Section 8). The resulting e+e\u2212pairs are predominantly produced in the\nforward direction, with small transverse momenta. Although the production cross section is large, only a\nsmall fraction of these particles are in the detector acceptance, as shown in Fig. 90 for the Z-pole and tt\nruns; a few others hit the region where the two beam pipes bifurcate (crotch) and scatter off the detector.\nThe largest effect occurs in the Z-pole run, given its instantaneous luminosity, the highest of the\n128\n\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n [rad]\n\u03b8\n4\n\u2212\n10\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n10\n [GeV]\nT\np\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n10\nparticles / BX\nVXD\n= 91.2 GeV\ns\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n [rad]\n\u03b8\n4\n\u2212\n10\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n10\n [GeV]\nT\np\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n10\nparticles / BX\nVXD\n = 365 GeV\ns\nFig. 90: Number of IPC particles produced for each FCC-ee bunch crossing, as a function of their transverse\nmomentum and polar angle, for the Z (left) and tt (right) working points. The area limited by the red lines\nrepresents the acceptance of the vertex detector.\nFCC-ee programme. In the innermost layer of the IDEA vertex detector, the hit rate reaches about\n70 MHz/cm2, for an average of 5 pixels per cluster, which imposes a rather stringent requirement on the\nreadout electronics of the order of 200 MHz/cm2 with, conservatively, a safety factor of 3. In the IDEA\ndrift chamber, where the pairs created by several successive bunch crossings need to be integrated during\nthe drift time (400 ns), the occupancy is about 7%. Incoherent pairs may also reach larger radii and their\neffects have been studied for the ALLEGRO liquid Argon electromagnetic calorimeter. The first layers\nof the calorimeter are the most affected, but the effect can be largely mitigated by setting a minimum\nreadout energy threshold of 20% of the energy released by a minimum ionising particle, resulting in an\noccupancy of 0.03% in the barrel and 0.2% in the endcaps.\nRadiative Bhabha (RB) scattering, e+e\u2212\u2192e+e\u2212\u03b3, is another important luminosity background\nthat may severely affect the superconducting FFQs. Radiative Bhabha events were generated with BB-\nBREM [688] and GUINEAPIG, and processed by FLUKA [689\u2013691]. Their study shows that a substantial\nannual dose of power is deposited in QC1, which necessitates a tungsten shielding of approximately\n2 mm around the beam pipe to protect the superconducting magnets. This shielding decreases the annual\ndose power deposition peak value to about 3 MGy (a reduction by an order of magnitude) and the de-\nposited power density to about 1.5 mW/cm3. These values are compatible with the design dose limit of\n30 MGy for the full magnet lifetime and the quench limit of 10\u201320 mW/cm3 adopted at the LHC. Other\nradiation sources contributing to the energy deposition in QC1, like beam-gas scattering, incoherent pair\ncreation or synchrotron radiation, still need to be carefully evaluated at the FFQs. They are expected,\nhowever, to be much more benign than radiative Bhabha events. The integration of this shielding with\nthe design of QC1 will be performed in the next phase of the study.\nThe total ionisation dose (TID) and the 1 MeV neutron-equivalent (neq) fluence from the main\nradiation sources in the Z-pole operational mode (i.e., RB and IPC) have been estimated in the IDEA\ninteraction region with FLUKA, and are displayed in Fig. 91. The peak annual dose and fluence in\nthe inner vertex detector are at the level of a few tens of kGy and a few 1013 cm\u22122, respectively, for\nthe innermost layers. These numbers are compatible with most of the technologies currently under\nconsideration for the monolithic active pixel sensors. At higher centre-of-mass energies, the TID and\nfluence are expected to be smaller, given the reduced instantaneous luminosity.\n129\n\nFig. 91: Total ionisation dose (top) and 1 MeV neq fluence (bottom) in the interaction region of the IDEA detector.\n5.5\nImplementation tests and prototyping\nDesign and simulation studies must be complemented by actual prototyping and implementation tests,\nto develop dedicated setups and evaluate technical solutions to the integration challenges. The following\nactivities are proposed or planned; some are already ongoing.\n\u2013 The realisation of a full scale mock-up of the beam pipes of the IR is being carried out at INFN\n(LNF and Pisa). This study includes the integration of the vertex and LumiCal detectors in the\nsupport tube, with particular emphasis on the paraffin and water cooling of the pipes and on the air\ncooling of the inner vertex detector. This activity is fully integrated with the R&D carried out in\nthe ECFA DRD8 Working Group [692].\n\u2013 The experimental validation of the alignment system of the FFQ is ongoing with the FSI system at\nCERN, using a 1:2 mock-up of the beam pipes and cryostat.\n\u2013 The design of the screening anti-solenoid and and the production of QC1 corrector prototypes are\nproposed at the Brookhaven National Laboratory (BNL), leveraging their \u2018direct winding technol-\nogy\u2019 [693].\n\u2013 The fabrication of a High Temperature Superconducting (HTS) magnet is proposed by LAPP An-\nnecy for the final quadrupole QC1, together with its integration with the water-cooled beam-pipe.\nIn summary, a lot of progress has been made in the past years. The layout has been significantly\nimproved by reducing the material budget in front of the LumiCal and also through a careful design\nof the cooling manifolds, re-engineered in AlBeMet162 material. The feasibility of the inner vertex\ndetector cooling has been validated and the routings of its services have been designed and integrated\nwith those of the beam pipe. More studies are on the way to optimise the design and confirm its validity\nexperimentally. A careful analysis of the detector maintenance and FFQ integration has been performed,\nleading to the identification of the main optimisation issues to be tackled during the next phase of the\n130\n\nstudy. An alignment strategy has been outlined, based on the technology planned for HL-LHC. Finally,\nthe study of the beam-induced backgrounds and the evaluation of the main radiation doses and fluences\nin the IR region led to the development of mitigation measures, like the design of the collimation system\nand SR shielding.\n5.6\nOutlook\nStudies carried out during the Conceptual Design Study and the Feasibility Study have converged to a\nbaseline MDI design with satisfactory overall performance. Further investigations to consolidate this\ndesign and to improve its performance will be performed. Refinements will also be needed when actual\ndetector proposals are finalised.\nSeveral options are currently considered for the QC1 cryostat design. Most importantly, a choice\nwill be made for the operating temperature of the cooling scheme, among three options: 1.9-2.1 K in\npressurised He II; 4.5 K for supercritical He; or 10\u201320 K for He gas forced flow. Another important\ndesign decision concerns the dimensions of the cryostat, which currently covers a cone of 100 mrad\naround the z axis. While the forward acceptance of the detector calorimetry would benefit from a smaller\ncryostat, the operability of the collider, and the integrated luminosity, would advocate for more relaxed\ndimensions, calling for a complete optimisation study.\nIn the baseline MDI design, the detector solenoid field of 2 T is \u2018locally\u2019 compensated with \u22125 T\nsolenoids placed within \u00b1\u2113\u2217around the IP. The performance of an alternative \u2018non-local\u2019 scheme, with\n\u22122 T solenoids positioned outside the detector at about \u00b120 m from the IP [694], will be studied and\ncompared to that of the baseline. First observations show that the non-local scheme might achieve a\nbetter residual vertical emittance, opening the possibility to increase the strength of the detector solenoid\nfield to 3 T. An adverse consequence of the non-local scheme seems to be a higher spin depolarisation, so\nthat further investigations are needed to preserve the possibility of beam-energy calibration with resonant\ndepolarisation (Chapter 9).\nThe main beam-induced background sources have been studied during the Feasibility Study, with\nthe exception of the injection backgrounds and thermal photons, which will have to be included. The\nstudies of the impact of all backgrounds in the data taking and in the physics performance will be fi-\nnalised, and proposed mitigation solutions will be consolidated. To this aim, the FLUKA software in-\nterface between the simulation of the machine backgrounds and the simulation of the detector will be\nrefined. A deeper understanding will be sought of the synchrotron radiation background mitigation, in\nparticular the positioning of the SR masks or the tolerances of the machine elements that might impact\nthe detectors, such as the alignment of the FFQs, the collimators, and the vacuum system. More gen-\nerally, the effectiveness of the shielding elements to protect the detector and the superconducting FFQ\nmagnets will be thoroughly evaluated.\nAs the design of the sub-detectors (e.g., vertex detectors, luminometers, superconducting pipes,\nsupporting structures) and of the accelerator components (e.g., beam position monitors, vacuum pumps,\nremote vacuum connections, cryostat supporting structures) get finalised, their integration, as well as the\nimpact on the maintenance and assembly of the interaction region, will be established in more detail.\nFinally, methods for the alignment, the opening, and the maintenance of the detector and accelerator\nelements will be developed, and possible consequences on the cavern dimensions will be evaluated.\n131\n\n132\n\n6\nDetector concepts and systems\nThe development of detectors for FCC-ee represents a challenge that drives technological developments\nbeyond the present state of the art. The main challenge arises from the richness of the physics programme\nand the large number of events, especially at the Z pole run. Matching the experimental accuracy to\nthe statistical precision and the detector configuration to the variety of channels and discovery cases,\nlead to performance requirements (Chapter 4) that exceed those studied for TeV-class linear colliders\nover the past decades. To preserve the low emittance of the FCC-ee beams during the Z-pole run, the\nstrength of the detector magnetic field crossed by the beams under an angle of 15 mrad is limited to\n2 T (Chapter 5). This constraint calls for larger tracking volumes that can, in part, be compensated by\nshallower calorimeter systems, given the FCC-ee emphasis on the lower energies. In addition, with\ncontinuous bunch crossings at rates of up to 50 MHz, the front-end electronics needs to be permanently\npowered and, given the much higher bandwidth of data to be recorded, the instantaneous power (and\ncooling) demand is also higher than in cases where power pulsing can be applied. Meeting these demands\nwhile preserving the material budget of the tracking detectors, the compactness of the calorimeters,\nand therefore their performance, requires further developments. In order to fully exploit the excellent\nprecision potential, in particular at the Z resonance, events must be recorded at rates of about 100\u2013\n200 kHz, comparable to first-level trigger rates in the upgraded HL-LHC detectors.\nThese challenges motivate the development of new detector technologies, followed up in the\nframework of newly created CERN-anchored detector R&D Collaborations (DRDs). This framework\naims at maximising synergies with parallel or consecutive developments (\u2018stepping stones\u2019), such as the\ndevelopment of an ultra-lightweight Si-based tracking system for the ALICE experiment. Such innova-\ntive R&D efforts towards FCC-ee will be intensified in the coming years, as the major detector upgrades\nof the ATLAS and CMS multi-purpose experiments come to an end.\nThis chapter presents an overview of the currently proposed technologies for detector systems,\nand the status and plans for R&D. Detector concepts that, in this context, denote consistent and pre-\nliminary arrangements of detector systems in a full experiment, informed by engineering considerations\nand realised in a simulation software suite, are also introduced. These detector concepts may or may\nnot become proposals for future FCC-ee detectors, as the outcome of the ongoing and future innovative\nR&D efforts might well motivate new concepts and change the overall landscape very significantly. De-\ntector concepts are, however, indispensable to guide R&D efforts, to reveal typical system integration\nconstraints, to optimise the design and technology choices of detector systems, and to study their im-\npact on the overall physics performance in the interplay of all components, e.g., for flavour tagging or\nparticle-flow reconstruction.\nSome performance studies require a detailed implementation of the detector characteristics in full\nGEANT4 simulations. The related software developments have, therefore, been a strong focus of the de-\ntector concept work in the feasibility study, and will have to intensify during the next phase of the study.\nIn order to optimise the use of still sparse human and financial resources, and to maximise interchange-\nability, the software framework KEY4HEP (Chapter 8) is used throughout the FCC detector studies. For\nexample, the studies for the integration of the vertex detector and beam pipe into the interaction region\n(Chapter 5) are to be considered a generic proof-of-principle for the machine-detector interface of all\nfour experiments. In general, the combination of technologies for tracking, calorimetry, and particle\nidentification is still very much open. For example, the ALLEGRO concept considers both gaseous and\nsilicon-based tracking. The KEY4HEP framework [695] allows for different combinations in a \u2018plug-\nand-play\u2019 approach, without duplicating the sub-detector developments and simulation implementations\nfor each concept.\nThe presently considered detector concepts (CLD/ILD, IDEA, and ALLEGRO) are briefly de-\nscribed, before a discussion of the sub-system developments, within or beyond these concepts. The\nintegrated luminosity determination is discussed at the end of the chapter.\n133\n\n6.1\nDetector concepts\nA fundamental difference among the current concepts derives from their different approaches to calorime-\ntry, as this choice profoundly impacts the overall detector architecture. All concepts aim for a calorimeter\nsegmentation that allows for particle separation within jets, and consequently for particle-flow recon-\nstruction, but with different balances between spatial and energy resolutions. Hadron-shower tracking\ndemands the full calorimeter to be inside the coil, whilst such an arrangement is at variance with the\nlarger depth required by fibre-based dual read-out techniques, or with the cryogenic infrastructure re-\nquirements of liquid noble gases.\nThe coordinate system used for the description of detector concepts is as follows. The z axis\nis defined as the bisector of the axes of the incoming and outgoing beams. The x axis is in the plane\nsubtended by the two beams and pointing away from the centre of the FCC-ee ring. In this way, the\npositron beam travels towards positive values of z (mainly) and x (subordinately). Perpendicular to the\n(x, z) plane, the y axis points upwards. The polar angle, \u03b8, is measured with respect to the z axis and the\nazimuthal angle, \u03d5, with respect to the x axis in the (x, y) plane. The radial coordinate, r =\np\nx2 + y2,\nis the distance from the z axis.\n6.2\nThe CLD and ILD detector concepts\nThe CLIC-like detector CLD [613], illustrated in Fig. 92, is an adaption to the experimental conditions\nat FCC-ee of the CLIC detector model [620, 696], itself developed from the ILD [619] and SiD [619]\nconcepts, originally designed for linear colliders. Both ILD and SiD, and consequently CLD, have a de-\nsign driven by very-high-granularity calorimeters. They feature electromagnetic and hadron calorimeters\n(ECAL and HCAL), both located inside a solenoidal coil, to ensure continuous topological reconstruction\nof shower evolution. To achieve a fine 3D-imaging segmentation, their front-end read-out electronics is\nembedded in the active volumes of the sandwich structures. The CLD ECAL has tungsten as the absorber\nand is read out with silicon sensors, while the steel HCAL has scintillator tiles directly coupled to silicon\nphoto-multipliers (SiPMs) as the active medium. These technologies were originally developed by the\nCALICE Collaboration [697] and are presently being applied at large scale in the CMS high-granularity\ncalorimeter (HGCAL) upgrade [698].\nYoke\nCoil \nHCAL\nECAL \nFig. 92: The CLD concept detector: end-view cut through (left) and longitudinal cross section of the top right\nquadrant (right). The detector has an overall diameter of 12.0 m and an overall length of 10.6 m.\n134\n\nWith respect to the original CLIC detector, CLD has an interaction region adapted to the larger\ncrossing angle and the more invasive machine-detector interface (Chapter 5), a bigger tracking volume\nto compensate for the magnetic field limitation of 2 T, and the calorimeter depth adapted to the FCC-ee\nenergy range. The tracking system of CLD features a silicon pixel vertex detector (VXD) and a silicon\ntracker.\nA full simulation suite, including full-event reconstruction, already exists and provides realistic es-\ntimates of full-detector performance figures of merit, such as jet resolutions, flavour-tagging efficiencies\nand purities, background levels, etc. Recently, to provide additional handles on particle identification,\na novel ring-imaging Cherenkov system, ARC [632\u2013634], has been suggested as an extra barrel layer\nbetween the tracker and the ECAL; the tracking system has been correspondingly re-optimised, on the\nbasis of full simulations.\nThe ILD detector concept is also being studied for a tentative adaptation to FCC-ee. It is similarly\nbased on highly granular calorimeter technologies with embedded electronics, including silicon pads,\nmonolithic active pixel sensors (MAPS), scintillator strips for the ECAL, and scintillator tiles and various\ngaseous technologies (RPCs, MPGDs) for the HCAL. Like in the CLD concept, both sections are placed\ninside the magnet coil. The major distinction with CLD is that ILD focuses on a radically different\ntracking choice, a gaseous time projection chamber (TPC), favoured for its transparency and particle\nidentification capabilities, complemented by a surrounding silicon layer to maximise momentum and\ntiming precision.\nThe long signal collection times of a TPC, together with the beam-induced background, which\nscales with the high bunch crossing rate, raises the question of how reliably a TPC can be operated\nat FCC-ee, in particular during the Tera-Z run. This issue is currently being investigated with full-\nsimulation studies using a plug-and-play combination of CLD and ILD, which merges the interaction\nregion and inner tracking system of CLD with the ILD TPC and calorimeters. First results [699] indicate\nthat there are distortions due to space-charge effects in the centimetre range. Work is ongoing to mitigate\nthese effects and possibly demonstrate the feasibility of reaching the performance goals in the Z-pole run\nconditions.\n6.3\nThe IDEA detector concept\nThe Innovative Detector for e+e\u2212Accelerator (IDEA) [700\u2013702], illustrated in Fig. 93, is a detector con-\ncept specifically designed for FCC-ee, introduced during the Conceptual Design Study [11]. It is based\non a silicon pixel vertex detector, a gaseous central tracker, and a crystal-based electromagnetic calorime-\nter placed inside a superconducting solenoidal magnet, surrounded by a dual-readout fibre calorimeter\nand completed by a muon detection system placed in the iron yoke that closes the magnetic field.\nThe tracker is composed of a silicon pixel vertex detector, a large-volume extremely-light short-\ndrift wire chamber for central tracking and particle identification, and a surrounding wrapper made from\nsilicon micro-strip sensors for improved momentum resolution. The wire chamber provides up to 112\nspace-point measurements along a charged particle trajectory with particle-identification capabilities pro-\nvided by the cluster-counting technique. Energy resolution for electrons and photons is provided by a\nfinely-segmented crystal electromagnetic calorimeter. The particle identification capabilities of the drift\nchamber are complemented by a time-of-flight measurement, provided either by LGAD technologies in\nthe Si wrapper or by a first layer of LYSO crystals in the ECAL. Outside a thin (about 30 cm thick) low-\nmass (corresponding to less than 0.8% of a radiation length) superconducting solenoid, the calorimeter\nsystem is completed by a dual readout fibre calorimeter, providing enhanced energy precision for iso-\nlated hadrons and hadron showers, and a return path for the magnetic field. The muon detection system\nis based on the \u00b5-Rwell detectors, a recent micro-pattern gas detector that provides a space resolution\nof a few hundred microns, giving the possibility of reconstructing secondary vertices at a large distance\nfrom the interaction point.\n135\n\nacceptance, 100 mrad\nMuon chambers\nReturn yokes\nDR Fibre Calo\nCoil\nDR Crystal Calo\nSilicon Wrapper\nDrift Chamber\nVertex Detector\nr (m)\nz (m)\nFig. 93: Longitudinal cross section of the top right quadrant of the IDEA concept detector. The LumiCal, the com-\npensating solenoid, and the final-focus quadrupole are displayed along the z axis, below the 100 mrad acceptance\nline.\n6.4\nThe ALLEGRO detector concept\nThe ALLEGRO (A Lepton-Lepton collider Experiment with Granular Read-Out) detector concept is\nrelatively recent and under rapid development. Its design, illustrated in Fig. 94, is articulated around\na high-granularity noble liquid electromagnetic calorimeter in a cryostat made from novel lightweight\nmaterials, thus taking advantage of the excellent stability of this technology, and it capitalises on recent\nprogress in electronics integration and advanced mechanical structures. The inherent linearity, stability,\nand uniformity of noble liquid calorimeters allow exquisite control of systematic uncertainties, a unique\nasset for high-precision measurements.\nThe tracking system consists of a silicon vertex detector and a main tracker that remains to be\nidentified. The silicon vertex detector is expected to use MAPS or DMAPS technology, with the possible\ninclusion of an LGAD layer for precise timing measurements. Both a drift chamber and a straw layer are\nconsidered for the gaseous tracker option. If a gaseous tracker is chosen, a silicon wrapper is foreseen\nat the outer periphery of the tracking volume, to provide precise track measurements at the entrance of\nthe calorimeter and possibly a precise measurement of the time of flight by using LGAD technology. A\nfully silicon-based tracking system, like in CLD, is also being considered and is used in full-simulation\nparticle-flow studies.\nA high-granularity-sampling noble liquid ECAL surrounds the tracker. The options considered\nconsist of lead (or tungsten) and liquid argon, or tungsten and liquid krypton. The use of innovative, low-\npower, cold front-end electronics, placed inside the cryostat, could provide a noiseless readout, but the\noption of placing low-noise electronics outside the cryostat is also being studied. The thin, lightweight\ncoil is located around the ECAL, within the same cryostat. The high-granularity HCAL is made of steel\nabsorber plates interleaved with scintillator tiles, corresponding to at least 8 interaction lengths. Two\ndesign options are being considered, one with SiPMs directly coupled to the scintillating tiles (as for\nCLD), and the other with wavelength-shifting (WLS) fibres used to guide the light to SiPMs located\noutside the detector (as for the ATLAS HCAL). The HCAL also acts as a return yoke for the magnetic\n136\n\nTracker\nVertex Det.\nECAL EndCap\nHCAL Barrel\nHCAL EndCap\nMuon Tagger\nMuon Tagger\nSilicon Wrapper & ToF\nSilicon Wrapper & ToF\nECAL Barrel\nSolenoid\nFig. 94: Longitudinal cross section of the top right quadrant of the ALLEGRO concept detector. The LumiCal, the\ncompensating solenoid, and the final-focus quadrupole are displayed along the z axis.\nfield.\nThe geometry described above, with a barrel and two end-caps, is considered as a \u2018baseline\u2019. An\nalternative layout is also being considered, with a somewhat longer barrel and the end-caps replaced by\nsmaller radius end-plugs fitting in the barrel opening. This solution would provide several engineering\nadvantages, including the routing of the cables in and out of the barrel cryostat and the reduction of the\ngap-widening issue in the end-cap ECAL modules.\nFor the muon system, several options are under consideration, including drift tubes or chambers,\nresistive plate chambers (RPCs), and micromegas (MM). Here, the development of eco-friendly but\nperformant gas mixtures is a compelling line of R&D.\n6.5\nVertex detectors\nVertex detector design is undergoing a strong technological development that can be summarised by the\nterms lighter, closer, and more precise. The development is driven by upgrade activities in Belle II and in\nthe LHC experiments. The second and third generation ALICE vertex detectors, ITS2 and ITS3 [703], are\nof particular relevance for FCC-ee, with many common conditions and requirements, such as moderate\nradiation environments and the need for high resolution and low multiple scattering. The technology\nof choice, CMOS MAPS, can be thinned down to a thickness of 50 \u00b5m or less, so that the sensors can\nultimately be bent into cylindrical layers around the beam pipe with very little support material.\nA comprehensive description of the silicon vertex detector, considered for the IDEA and ALLE-\nGRO detector concepts, is presented in this section. This detector element is currently the most advanced\nfrom an engineering point of view, being already integrated in the complex Machine Detector Interface\nlayout (Chapter 5). A much briefer description of the vertex detector considered for CLD follows.\nThe vertex detector considered for IDEA and ALLEGRO features two main subsystems, whose\nactive elements are based on 50 \u00b5m thick MAPS:\n\u2013 an inner detector, located close to the beam pipe, at radii between 13.7 and 35.6 mm, covering an\nangular acceptance of about | cos \u03b8| < 0.99;\n\u2013 an outer detector, located at radii between 130 and 315 mm, composed of a middle barrel, an outer\n137\n\nbarrel, and three disks on each end-cap.\nTwo layouts are being explored for the inner vertex detector. The baseline layout uses a traditional\napproach, with modules mounted on a carbon fibre support structure. An alternative, less advanced,\nultra-light layout is based on curved detectors, using a concept similar to the ALICE ITS3 [703]. The\nbaseline layout of the vertex detector is displayed in Fig. 95.\nSection F-F\nSection G-G\nwithout \nOuter Vertex\nF\nF\nG\nG\n1\n1\n2\n2\n3\n3\n4\n4\n5\n5\n6\n6\nA\nA\nB\nB\nC\nC\nD\nD\nvertex_FCC 2_2\nFCC Vertex\nIstituto Nazionale di Fisica\nNucleare-Sezione di Pisa\nfbosi\n03/04/2023\nProgettato da\nControllato da\nApprovato da\nData\n1 / 1 \nEdizione\nFoglio\nData\nOUTER VERTEX= N.51 Staves\n16 Pixel detectors/stave\nSurface pixel detectors=42.2x40.6 mm2=17,21 cm2\nPower dissipated/pixel detector=1,72 W\nPower dissipated/stave=27,52 W\nOUTER VERTEX POWER DISSIPATED\n=1403,52 W\n \nMIDDLE VERTEX=N.23 Staves\n8 Pixel detectors/stave\nSurface pixel detector=42.2x40.6 mm2=17,21 cm2\nPower dissipated/pixel detector=1,72 W\nPower dissipated/stave=13,76 W\nMIDDLE VERTEX POWER DISSIPATED\n=316,48 W\n \nInner Vertex: N.3 layers of pixel detectors\nLayer 1: N.15 staves of 6 pixel detectors=90 pixel detectors\nLayer 2: N.24 staves of 10 pixel detectors=240 pixel detectors\nLayer 3: N.36 staves of 16 pixel detectors=576 pixel detectors\nSurface pixel detector=8,4x32mm2=2,68 cm2\nPower dissipated/pixel detector=0.134 W\nLayer 1: Power dissipated 12.06 W\nLayer 2: Power dissipated 32,16 W\nLayer 3: Power dissipated 77,18 W\nTotal power dissipated by the inner Vertex:121,4 W \n42,20\n42,20\n40,60\n8,40\n32,00\n193,00\n321,80\n515,00\n609,40\n1860,00\n652,60\n304,70\n304,70\n315,30\n310,00\n315,30\n310,00\n1240,00\nR=315.0\nR=130,0\nR=34,5 third layer\nR=23,7 second layer\nR=13,7 first layer\nOuter Vertex\nInner Vertex\nDisk 1\nDisk 2\nDisk 3\nDisk 1\nDisk 2\nDisk 3\n326,30\n326,30\nMiddle Vertex\n326,20\n40,60\nFig. 95: Engineered layout and main characteristics of the baseline vertex detector for the IDEA and ALLEGRO\ndetector concepts. Top-left: Cross sectional view showing the barrel layers. Top-right: Longitudinal view showing\nthe outer barrel and disks. Bottom-right: Longitudinal view with the inner and middle barrels, as well as the disks.\nAll dimensions are in mm. The bottom-left panel lists the main elements for the outer, middle, and inner barrel\ndetectors, together with the dissipated power.\nIn the baseline layout, the inner vertex detector is composed of three concentric barrel layers\nmounted on a carbon fibre structure. The elementary unit is a module of 32\u00d78.4 mm2 z\u00d7r\u03d5 dimensions.\nEach module has two chips abutted together in z, inspired from the ARCADIA R&D [704]. The chip\nactive area features 640 (z) \u00d7 256 (r\u03d5) pixels of 25 \u00d7 25 \u00b5m2 area. A 2 mm inactive space is envisaged\nin r\u03d5, corresponding to the periphery of the chip. A conservative power consumption of 50 mW/cm2\nis assumed, based on the \u223c30 mW/cm2 measured for the current ARCADIA prototype, read out at\n100 MHz/cm2, and considering the higher expected FCC-ee data rate. In order to allow for a 2 mm\nradial clearance in view of its insertion, the first layer is located at a radius of 13.7 mm. The length\nis constrained by the central beam pipe cooling manifolds. The first layer comprises 15 staves with 6\nmodules each, along z. The staves overlap in \u03d5, as shown in Fig. 96, to allow internal alignment.\nA lightweight support on each ladder provides rigidity and facilitates the mounting of the MAPS.\nThe structure is made of thin carbon fibre walls interleaved with Rohacell [705], which holds the sensors\n(facing the beam pipe) and two 1.8 mm wide buses (one for data, the other for power) at the edges of\n138\n\nView C\nC\n1\n1\n2\n2\n3\n3\n4\n4\n5\n5\n6\n6\nA\nA\nB\nB\nC\nC\nD\nD\nComplete layout layer 1\nIDEA-INNER VERTEX\nIstituto Nazionale di Fisica\nNucleare-Sezione di Pisa\nfbosi\n02/02/2023\nProgettato da\nControllato da\nApprovato da\nData\n1 / 1 \nEdizione\nFoglio\nData\n1,40\n8,40\n4,20\n0,20\n0,05\nRadius=13.70\nRadius=13.70\nMisalignment 2.5\n1,40\n0,20\n0,20\n2,00\n2,20\nOverlap 0.504\nOverlap 0,477\n0,05\n0,05\n8,40\n227,40\n193,00 active part\n32,00\n32,00\n32,00\n32,00\n32,00\n32,00\n17,00\n17,00\n0,20\n0,20\n0,20\n0,20\n0,20\n0,20\n0,20\nInner Vertex\nLayer 1 : N.15 staves pinwheel of 6 pixel detectors = 90 \npixel detectors\nLayer 1 Power dissipated :\nN.1 pixel detector = 0.84x3.2 cm2 =2.69 cm2. \nPower dissipated /pixel= 50 mW/cm2\nPower dissipated /pixel detector=0.134,5 W\nTotal Power dissipated = 12.105 W\n5,00\n1,80\n0,20\n0.20\n1,80\n0,20\n5,00\n0,20\n1,00\nFig. 96: First layer of the baseline inner vertex detector for the IDEA and ALLEGRO detector concepts. Transverse\n(top-left) and longitudinal (top-right) cross sections of the assembly; 3D view (bottom-left); and detailed view\nshowing the overlaps and the different structures (bottom-right). All dimensions are in mm. The 50 \u00b5m thick\nMAPS sensors face the centre of the structure. The brown structures are the buses and the golden parts are the\nelectronic hybrid circuits for readout.\nthe structure. The thickness of the bus comprises 200 \u00b5m Kapton and 50 \u00b5m aluminium, for a total of\n0.09% X0. The ladders are arranged in a pin-wheel geometry.\nThe second layer, with a structure similar to the first, is made of 24 ladders of 10 modules each,\nat a radius of 23.7 mm, arranged in a pin-wheel geometry opposite in orientation to that of the first layer,\nto mitigate possible charge-dependent effects on charged-particle track reconstruction. The third layer\nhas 36 ladders, each composed of 16 modules. The ladders are arranged in a \u03d5-symmetric lampshade\nfashion: half of the ladders are located at a radius of 34 mm, the other half at 35.6 mm. Each layer\ncontributes 0.25% X0 at normal incidence, about one fifth of it coming from the overlap between staves\nof the same layer. The vertex detector layers are mounted on conical carbon fibre support structures using\ntwo rings of peek material for thermal isolation during bakeout. The conical support structures also guide\ncooling gas inside the detector volume and support the power and readout circuits. The middle barrel\nand the disks, together with the support cones, are shown in Fig. 86 (Chapter 5). The amount of detector\nmaterial crossed by a particle originating from the main IP (\u2018material budget\u2019) is shown in Fig. 97, for\nthe inner vertex layers and for the complete vertex detector.\nThe main geometric dimensions of the vertex detector, together with the power dissipated by each\nlayer, are reported in Table 15. The inner vertex detector is planned to be cooled with gas passing through\nchannels embedded in the conical support structure. Both atmospheric air and helium are considered as\ncoolant gases. The gas is contained in a cylindrical, 200 \u00b5m thick, carbon fibre envelope surrounding\nthe detector. The cooling performance has been analysed using computational fluid dynamics (CFD)\n139\n\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0 0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n0\n1\n2\n3\n4\n5\n6\n] \n0\nMaterial budget [% of X\nSilicon\nGlue\nPCB\nKapton\nRohacell\nCarbon Fibre\nAluminium\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0 0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n] \n0\nMaterial budget [% of X\nSilicon\nWater\nGlue\nPCB\nPEEK\nKapton\nRohacell\nCarbon Fibre\nCarbon Fleece\nAluminium\nFig. 97: Material budget (expressed as a percentage of a radiation length) for the silicon vertex detector considered\nfor ALLEGRO and IDEA for the inner vertex detector (left) and for the complete vertex detector (right), in the\nbaseline design, as a function of the cosine of the polar angle.\nTable 15: Main parameters of the baseline vertex detector considered for the IDEA and ALLEGRO detector\nconcepts.\nSubsystem\nLayer ID\nRadius (mm)\n|z| (mm)\nNo. staves\nNo. modules / stave\nPower (W)\nInner barrel\n1\n13.7\n< 96.5\n15\n6\n12\nInner barrel\n2\n23.7\n< 160.9\n24\n10\n32\nInner barrel\n3\n34 and 35.6\n< 257.5\n36\n16\n77\nMiddle barrel\n1\n130\n< 163.1\n23\n8\n316\nOuter barrel\n2\n315\n< 326.3\n51\n16\n1400\nDisks\n1\n34.5 < r < 275\n304.7\n56\n2\u20136\n135\nDisks\n2\n70 < r < 315\n620\n48\n3\u20137\n420\nDisks\n3\n105 < r < 315\n930\n40\n4\u20137\n370\nsimulation models, and the result is that the largest temperature difference between the modules along a\nstave is less than 15 \u25e6C. Although this is considered an acceptable level, further optimisations are ongoing\nto reduce this temperature difference. A mechanical vibration analysis based on Finite Element Analysis\n(FEA) in ANSYS showed a maximum displacement amplitude in the radial direction of about 1.5 \u00b5m\nfor a nominal air flow of 0.7 g/s, resulting in a negligible effect on the impact-parameter resolution.\nA second, ultra-light layout for the inner vertex detector is being explored, albeit with a less\nadvanced system engineering. The layout is based on a concept similar to the ALICE ITS3 curved sensor\ntechnology, which facilitates a self-supporting structure with essentially no material besides that of the Si\nsensors. The ITS3 uses a stitching technique to form wafer-scale sensors from multiple repeated sensor\nunits (RSUs). Each layer comprises two half-cylindrical sensors featuring ten RSUs in z and three, four,\nor five in \u03d5 for the first, second, and third layers, respectively. Unlike ITS3, a vertex detector for FCC-ee\nmust have the largest possible polar-angle coverage. The inner vertex detector has four layers, of which\nthe first three are arranged to have approximately the same angular acceptance while the fourth has the\nsame length as the third. The first layer, at 13.7 mm radius, uses two \u03d5 rows of 10 RSUs in z and is\nsupported by only two carbon foam longerons and rings. The spacing between the two half-shells is\n1.25 mm, thus leaving a gap in the \u03d5 acceptance. This gap is recovered by a rotation in \u03d5 of 1.25 mm of\nthe second layer, although with a worse impact parameter resolution. The second layer is composed of\n140\n\nthree \u03d5 rows of 13 RSUs. The first two layers are read out and powered from both ends. For the third\nand fourth layers, the use of two sensors in z per half-layer is foreseen to circumvent the limitation of\nthe 12-inch wafer diameter. The third layer uses 8 layers on the \u2212z side and 10 on the +z side, while\nthe fourth layer has a reversed distribution (10 on the \u2212z side and 8 on the +z side); in this way, the\nacceptance gap in z of one layer, of about 10 mm, is covered by the other. For these layers, the readout\noccurs only at the far ends in z. This layout design is illustrated in Fig. 98. Integration studies are\nongoing to validate its technical feasibility. The material budget is very much reduced with respect to the\nmore classic design, as shown in Fig. 99.\nLayer 3\nLayer 4\nRSU\nFlex circuit\n(power & R/O)\nLongeron \nRing \nLayer 1\n281.7 mm \nR=20.35 mm\nLayer 2\n216.7 mm \nR=13.7 mm\n216.7 mm \n173.3 mm \n1.25 \nmm\nR= 27 mm\nR= 33.65 mm\nFig. 98: Ultra-light inner vertex detector layout for the IDEA and ALLEGRO detector concepts. The four half-\nlayers are shown separately in the top-left and in the bottom. The arrangement of the first two layers is shown in\nthe top-right view.\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0 0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n0\n1\n2\n3\n4\n5\n6\n] \n0\nMaterial budget [% of X\nCarbon Fibre\nSilicon\nKapton\nCarbon Foam\nAluminium\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0 0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n] \n0\nMaterial budget [% of X\nSilicon\nWater\nGlue\nPCB\nPEEK\nKapton\nRohacell\nCarbon Foam\nCarbon Fibre\nCarbon Fleece\nAluminium\nFig. 99: Material budget (expressed as a percentage of a radiation length) for the silicon vertex detectors considered\nfor ALLEGRO and IDEA, for the inner vertex detector (left) and for the complete vertex detector in the ultra-light\ndesign (right), as a function of the cosine of the polar angle.\n141\n\nA single layer contributes only about 0.07% X0, a reduction by about a factor three compared to\nthe traditional design. Furthermore, the material is more uniformly distributed in \u03d5, given the absence\nof overlapping structures in the same layer, as can be seen by comparing the left and right panels of\nFig. 100.\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n] \n0\nMaterial budget [% of X\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0\n0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n3\n\u2212\n2\n\u2212\n1\n\u2212\n0\n1\n2\n3\n\u03c6\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n] \n0\nMaterial budget [% of X\n1\n\u2212\n0.8\n\u2212\n0.6\n\u2212\n0.4\n\u2212\n0.2\n\u2212\n0\n0.2 0.4 0.6 0.8\n1\n\u03b8\ncos\n3\n\u2212\n2\n\u2212\n1\n\u2212\n0\n1\n2\n3\n\u03c6\nFig. 100: Material budget (expressed as a percentage of a radiation length) for the silicon vertex detectors con-\nsidered for ALLEGRO and IDEA in the baseline (left) and the ultra-light designs (right), for the complete vertex\ndetector, as a function of the azimuthal angle vs. the cosine of the polar angle.\nFor both alternatives, the outer vertex detector is composed of two barrel layers and three disks\non each side. The elementary unit is a module of area 40.6 (z) \u00d7 42.2 (r\u03d5) mm2. Each module has\nfour hybrid pixel sensor chips, inspired by the ATLASPIX3 R&D [706]. The 50 \u00b5m thick sensor has\n372 \u00d7 132 pixels of 50 \u00d7 150 \u00b5m2 area. The power consumption is assumed to be 100 mW/cm2, half of\nthe level observed at the current stage of development, but still too high (by at least a factor of two) to\nbe handled by air cooling. The modules are placed on a lightweight triangular truss structure. The staves\nare mechanical structures that hold the modules. A stave is composed of a carbon-fibre multilayered\nstructure, consisting of 120 \u00b5m thick carbon fibre KDU13 and two carbon fleeces of 65 \u00b5m in total,\nto support two 90 \u00b5m thick polymide tubes of 2.2 mm diameter, where demineralised cooling water\ncirculates. An electronic bus, providing power distribution and readout and control signals, runs along\nthe entire stave length and is placed on top of the modules. It is terminated, at the end of both sides, by a\nhybrid circuit.\nThe middle barrel layer is positioned at a radius of 130 mm and is composed of 22 ladders, each\nwith 8 modules. The outer barrel layer is placed at a radius of 315 mm and is composed of 51 ladders, of\n16 modules each. The outer and middle barrels are supported by a flange attached to an external support\ntube. The flange also supports the two innermost disks. Three disks per side, located at |z| = 304.7, 620,\nand 930 mm, complete the outer vertex tracker. The inner disk is located inside the barrel. Each disk\nis composed of eight petals, four facing the IP and four facing the opposite direction, made of modules\nof the same type as those of the barrels. The support structure of each disk is made of a sandwich of\nthin carbon fibre walls (each 0.3 mm thick) interleaved with 5.4 mm thick Rohacell [705]. The material\nbudget of the outer vertex detector is about 1% of a radiation length at normal incidence, increasing to\nabout 3% at the edges of the middle and outer barrel, because of the supports and hybrid circuits.\nThe vertex detector of the CLD concept [613], composed of a cylindrical barrel and forward disks,\nis located at radii below 112 mm. The layout is based on double layers of ultralight MAPS fixed on a\ncommon support structure that includes cooling circuits. The 125 mm long barrel comprises three double\nlayers (0.63% X0 each) at radii 12.5\u201313.5, 37\u201338, and 57\u201358 mm. Three disks on each side (0.70% X0\neach), at distances from the IP of 160, 230, and 300 mm, complete the detector. For simulation studies,\na point resolution of 3 \u00d7 3 \u00b5m2 is assumed.\n142\n\nFull simulation studies [707] with the smaller radius beam pipe introduced since the publication of\nRef. [613] (the inner radius decreased from 15 to 10 mm) and a corresponding reduction of the radius of\nthe inner barrel layer confirm earlier conclusions from fast simulations [613] of a better impact parameter\nresolution and a significantly improved flavour-tagging performance. Even with a simultaneous increase\nof the beam-pipe material budget from 0.45% to 0.61% X0, the studies show, for example, an impact\nparameter resolution improved by 20% for 10 GeV tracks.\n6.6\nMain tracking systems\n6.6.1\nSilicon tracker\nThe CLD concept features an all-silicon tracker, complementing the vertex detector (briefly described at\nthe end of the previous section) with a \u2018main tracker\u2019, itself divided into inner and outer sections by a\nlightweight (1.25% X0) carbon-fibre support tube, at a radius of 690 mm. The inner tracker comprises\nthree barrel layers and seven forward disks on each end-cap, while the outer tracker has three more barrel\nlayers and four disks on each side. The material budget of the modules (200 \u00b5m of silicon sensors, or\n0.21% X0, including electronics), plus cooling and connectivity, is estimated to range between 1.1%\nand 1.3% X0. In addition, carbon-fibre support structures, which differ from layer to layer, contribute\nbetween 0.13% and 0.37% X0. For simulation studies, point resolutions of 5 \u00d7 5 \u00b5m2 and 7 \u00d7 90 \u00b5m2\nare assumed for the innermost disk of the inner tracker and for all other layers, respectively. The material\nbudget of the complete CLD tracking system, including the vertex detector and the main tracker (plus\nthe beam pipe), is shown in Fig. 101.\n]\u00b0\n [\n\u03b8\n0\n20\n40\n60\n80\n [%]\n0\nMaterial Budget x/X\n0\n10\n20\n30\nFCC\u2212ee CLD\nOuter tracker\nInner tracker\nVertex detector\nBeam pipe\nFig. 101: Stacked material budget (expressed as a percentage of a radiation length) of the different parts of the\nCLD tracking system (plus the beam pipe), as a function of the polar angle and averaged over the azimuthal angle,\nincluding contributions from sensitive layers, cables, supports, and cooling.\nFull-simulation studies to assess the performance of the CLD tracker are reported in Ref. [613].\nFigure 102 shows some essential performance figures for single muons: the momentum and impact\nparameter resolutions, as well as the polar and azimuthal angular resolutions. For pT > 100 GeV,\nthe momentum resolution curves start to flatten out, reaching an asymptotic value of \u03b4(1/pT) \u22431 \u00d7\n10\u22125 GeV\u22121. For lower momenta, the momentum resolution is dominated by multiple scattering. More\nstudies are needed to further reduce the material budget, in particular for the support structures and\nservices.\n143\n\np [GeV]\n1\n10\n2\n10\n]\n-1\n) [GeV\nT,true\n2\n/p\nT\np\n\u2206\n(\n\u03c3\n5\n\u2212\n10\n4\n\u2212\n10\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\n-\n\u00b5\nSingle \n = 10 deg\n\u03b8\n = 30 deg\n\u03b8\n = 50 deg\n\u03b8\n = 70 deg\n\u03b8\n = 89 deg\n\u03b8\n)\n\u03b8\n3/2\n b / (p sin\n\u2295\na \n[deg]\n\u03b8\n20\n40\n60\n80\nm]\n\u00b5\n) [\n0\nd\n\u2206\n(\n\u03c3\n1\n10\n2\n10\n3\n10\n-\n\u00b5\nSingle \np = 1 GeV\np = 10 GeV\np = 100 GeV \nFig. 102: Top-left: Transverse momentum resolution for single muons as a function of momentum at five fixed\npolar angle values. Polar-angle dependence of the impact parameter resolution in the transverse plane (top-right), of\nthe polar angle resolution (bottom-left), and of the azimuthal angle resolutions (bottom-right), for muon momenta\nof 1, 10, and 100 GeV. From Ref. [613].\nA smaller tracker outer radius would, in particular, allow for the insertion of a compact RICH\ndetector, such as the ARC detector (Section 6.7.2), which could provide improved particle identification\nperformance at the cost of a worse momentum resolution. A recent full-simulation study [707] confirms\nfast-simulation indications that a reduction of the tracker outer radius from 2.31 to 1.80 m leads to a\ndegradation of the momentum resolution by about 15%, showing that the momentum resolution scales\nroughly like 1/R, where R is the outer tracker radius. This observation is compatible with expectations\nin cases where multiple scattering is the dominant effect (otherwise, a 1/R2 dependence would be ex-\npected). The study also confirms that an increase of the magnetic field strength from 2 to 3 T would lead\nto a \u223c30% improvement of the pT resolution.\n6.6.2\nDrift chamber\nThe IDEA concept features the InTrEPId (Inner Tracking Equipped with Particle Identification) drift\nchamber, designed to provide tracking with high-precision momentum measurement and particle iden-\ntification by cluster counting. A high transparency is obtained by a novel approach for the wiring and\n144\n\nassembly procedures [708]. The total amount of material is about 1.6% X0 at normal incidence (dom-\ninated by the outer container material), increasing to about 5.0% X0 in the forward direction (the end\nplates instrumented with front-end electronics contributing 75% of that value). The drift chamber is a\nsingle-volume, high-granularity, all-stereo, short-drift, low-mass cylindrical wire chamber, co-axial with\nthe 2 T magnetic field. It extends from an inner radius of 0.35 m to an outer radius of 2 m, has a length\nof 4 m along the z axis, and consists of 112 co-axial layers, at alternating-sign stereo angles, arranged\nin 24 identical azimuthal sectors. The angular coverage extends down to \u223c13\u25e6(227 mrad). The size\nof the approximately square cells ranges between 12 and 14.5 mm, for a total of 56 448 drift cells. The\nchallenges potentially arising from a large number of wires (about 350 000 in total) are addressed by the\ndesign of the wiring procedures, successfully exploited during the recent construction of the MEG2 drift\nchamber [709].\nA very light gas mixture, 90% He and 10% iC4H10, corresponding to a maximum drift time of\n\u223c400 ns, is expected to be used in operation. The number of ionisation clusters generated by a minimum\nionising particle is about 12.5 cm\u22121, allowing cluster counting/timing techniques to be exploited, to\nimprove both the spatial resolution (better than 100 \u00b5m) and the particle identification resolution (\u223c3%).\nA spatial resolution around 120 \u00b5m has been achieved in the 7 mm cell size MEG2 drift chamber with\nthe same gas mixture and very similar electrostatic configuration [710]. An even better spatial resolution\nis expected in InTrEPId, with the application of cluster timing techniques on the one hand and with the\nlonger drift on the other, which mitigates, on average, the effects of the short-drift stochastic behaviour.\nFast simulation studies have been performed with DELPHES to evaluate the tracking performance,\nwith the vertex detector, the drift chamber, and a surrounding double layer of silicon microstrip detectors.\nThis \u2018Si wrapper\u2019 provides an additional accurate space point with an assumed resolution of 7(r\u03d5) \u00d7\n90(z) \u00b5m2, and a precise definition of the tracker acceptance. Details of ionisation clustering to exploit\nthe cluster counting/timing technique were not simulated, conservatively limiting the spatial resolution of\nthe drift chamber to 100 \u00b5m. The resulting momentum resolution is displayed in Fig. 103. For transverse\nmomenta in excess of \u223c20 GeV, the resolution is well described by \u03b4pT/p2\nT = 3\u00d710\u22125 GeV\u22121. Angular\nresolutions better than 0.1 mrad are obtained in both the azimuthal and polar angles.\n20\n40\n60\n80\n100\n0\n0.0005\n0.001\n0.0015\n0.002\n0.0025\n0.003\n0.0035\n0.004\n0.0045\n0.005\n\u00b0\n = 90\n\u03b8\nIDEA full tracker - \nMultiple scattering only \nIDEA no Si wrapper \n/ p\np\n\u03c3\nT\nT\np (GeV)\nT\nFig. 103: Transverse momentum resolution as a function of pT, for tracks at a polar angle of 90\u25e6, in the IDEA\ntracking system (full red curve). The contributions from multiple scattering (dot-dashed red curve) and the impact\nof the silicon wrapper (dash-dotted blue curve) are also illustrated.\nCluster counting and timing provide a \u03c0/K separation better than three standard deviations up to\nmomenta about 30 GeV, except in a narrow gap between 0.9 and 1.6 GeV, where the Bethe\u2013Bloch energy-\nloss curves for the two particle types cross. These values were obtained with a fast simulation study that\nparametrised GARFIELD++ [711] results within DELPHES. As illustrated in Fig. 104, the gap can be\nadequately covered with a time-of-flight measurement over a distance of 2 m, with a non-challenging\nresolution of O(100) ps.\n145\n\n1\n10\n50\nmomentum [GeV/c]\n0\n2\n4\n6\n8\n10\n12\n14\nsigni\ufb01cance (K/\u03c0)\ntime of \ufb02ight (\u03c3t = 100 ps)\ndN/dx (He 90% \u2212Isobutane 10%)\ncombined\nFig. 104: Significance (in standard deviations) of the \u03c0/K separation in the IDEA drift chamber, from a fast\nDELPHES simulation study, with the cluster counting performance parametrised from GARFIELD++ results (yellow\ncurve). A better than 3 \u03c3 separation is obtained up to momenta \u223c30 GeV. The p < 1.6 GeV region is covered by a\ntime-of-flight system, extending over a distance of 2 m and with a timing resolution assumed to be 100 ps (orange\ncurve). The combination of the drift chamber and the time-of-flight system is represented by the dashed red curve.\n6.6.3\nStraw tracker\nA straw tracker with thin Mylar walls may also be a promising option to meet the stringent FCC-ee\ndetector requirements, when combined with a pixel detector near the beam pipe and a silicon wrapper\nas an outer layer. A straw tracker can provide a spatial resolution of 100\u2013120 \u00b5m per straw and a low\nmaterial budget of 1.2% X0 at \u03b8 = 90\u25e6for 100 layers of straws made with 12 \u00b5m-thick Mylar walls.\nWith O(100) hits per track, such a straw tracker is well suited for both pattern recognition and searches\nfor long-lived particles. In addition, it can provide excellent particle identification capabilities, such as\n\u03c0/K and K/p discrimination, across a wide momentum range and could also be used for triggering\npurposes, making it valuable for both collider data taking and cosmic ray studies.\nEach straw functions as an independent channel, providing significant flexibility for design optimi-\nsation. The operational robustness also benefits from the fact that each straw can be easily disconnected\nif its wire breaks. The electric charges generated within a straw remain confined to that specific unit.\nThe electric field within a straw is radially symmetric, making the resolution independent of the parti-\ncle incident angle and leading to a good single-hit resolution. Straws with different radii can be used\nin various detector regions to optimise hit occupancy, material budget, and channel counting. The gas\nmixture can be optimised to enhance particle identification capabilities and different gas mixtures can be\nsimultaneously used for straws in different layers.\nFigure 105 shows an example layout of a straw tracker implemented in a GEANT4 simulation,\nfeaturing O(60 000) straws with a diameter of 1 to 1.5 cm and a length of 5 m, arranged in ten concentric\nsuperlayers. Straws are arranged in both axial and stereo layers with a stereo angle of a few degrees to\ndetermine the hit position with an accuracy of a few mm along the z direction. Initial simulations [712]\npredict similar momentum resolutions as with the InTrEPId drift chamber.\nSignificant R&D is required to realise such a detector design. Close collaboration with straw\nmanufacturers is essential to produce O(12) \u00b5m-thick-walled aluminium-coated straws with high yields.\nOptimising the detector layout and developing a robust mechanical design for the end-plates and support\nstructure of these 5 m-long straws are critical tasks. Further investigations into gas mixtures, GARFIELD\nsimulations, and front-end electronics are important for dE/dx and dN/dx measurements. Fast algo-\n146\n\nFig. 105: (Left) An example layout of the straw tracker with ten superlayers, each superlayer containing ten\nsublayers. (Right) Simulated hits from 5000 muons, revealing the layout of the straw tracker in the GEANT4\nsimulation.\nrithms need to be developed and implemented in the front-end ASIC or FPGA in order to effectively\nidentify individual clusters. In the coming years, prototype chambers will be built and tested with cosmic-\nray muons and with beams, in view of validating the simulated performance.\n6.6.4\nTime projection chamber\nTime projection chambers (TPCs) provide continuous 3D tracking over a large volume with minimal\nmaterial interference, while also enabling particle identification via energy deposition in the gas. The gas\nchoice is critical to maximise ionisation signal yield and minimise transverse diffusion, which strongly\ndepends on the magnetic field strength and on the drift velocity. Minimising transverse diffusion calls\nfor a \u2018hot gas\u2019, commonly achieved so far with a small admixture of CF4. Given that CF4 has a strong\ngreenhouse effect, a replacement gas will have to be identified. For particle identification via cluster\ncounting, dN/dx, small, sub-millimetre pad sizes are needed, in which case digital readout is sufficient.\nMechanical alignment must be precise, within a few tens of microns, to avoid systematic errors.\nElectric and magnetic fields must be parallel, to prevent E \u00d7 B distortions, calling for a highly uniform\nmagnetic field. Minimising space-charge build-up is essential, as transverse electric field components\ndistort electron drift paths. Hence, beam backgrounds (such as low-energy X-rays and muons from beam-\nhalo interactions, both generating low-pT particles that curl and deposit significant ionisation) must be\ncontrolled, or corrective strategies must be implemented. First estimates of the effect of beamstrahlung\nbackgrounds were recently presented [699], with the conclusion that distortions expected with the FCC-\nee Tera-Z luminosities are at the same level as those observed in ALICE. Ion feedback, where ions from\nthe amplification process drift towards the cathode (over \u223c0.5 s), must be carefully managed. Operating\nat low gain with effective passive backflow mitigation, such as double misaligned meshes or graphene\nfilters, would be necessary. If space charge effects are unavoidable, correction techniques (built on the\nexperience of ALICE) should be employed. The operability of a TPC at FCC-ee luminosities is still\nunder discussion in the community and is being actively investigated.\n6.7\nParticle identification\nThe identification of charged hadrons (\u03c0, K, p) significantly enhances the physics potential of experi-\nments at FCC-ee, as discussed in Section 4.5. In particular, it improves the flavour-tagging performance\nin the selection of Higgs boson decays to cc or ss, and is crucial for the extensive flavour physics pro-\ngramme with the Z-pole data. From simulation studies, the momentum region to be covered is up to\n147\n\na few tens of GeV. For experiments with gaseous trackers, the specific energy loss (dE/dx) provides\nseparation power up to moderate momenta, in conjunction with time-of-flight to cover the overlap region\naround 1 GeV, where the dE/dx separation is poor. As already mentioned for drift chambers or straw\ntrackers, the performance can be enhanced with cluster counting, dN/dx. For experiments with silicon-\nbased tracking, however, neither dE/dx nor dN/dx would provide the required level of performance.\nThere, ring-imaging Cherenkov (RICH) detectors could deliver particle identification over a very wide\nmomentum range. The following two sections describe the use of precision timing and RICH detectors\nto enable the required particle identification performance.\n6.7.1\nPrecision timing detector\nThe identification of charged hadrons based on their specific energy loss must be complemented by\nother measurements to fill the gap around 1 GeV, where the Bethe\u2013Bloch energy-loss curves for the\ndifferent particle types cross over. Time-of-flight measurements, for example in a layer of silicon sensors\nat 2 m from the interaction point, with a non-challenging resolution of \u223c100 ps, are adequate for this\npurpose. With a resolution of 30 ps, time-of-flight measurements alone would allow kaons to be separated\nfrom pions up to O(3) GeV in momentum, while an excellent resolution of 10 ps would be needed to\nextend this momentum range up to 5 GeV. Such TOF information could also be obtained in a silicon-\ntungsten ECAL, where measurements, each of a resolution of, e.g., 100 ps, could be made in several\nlayers. Dedicated timing layers made of inorganic scintillator offer another solution. An example is the\nsegmented crystal ECAL design of MAXICC (described in Section 6.8), which includes two such thin\nlayers, potentially providing a 20 ps timing resolution.\nBecause of the finite length of the colliding bunches, the \u2018event time\u2019, t0, has a natural spread of\nabout 36 ps at the Z pole. To exploit timing resolutions better than that value, t0 needs to be determined\non a event-by-event basis. In events with a high charged-particle multiplicity, it is possible to reconstruct\nt0 from the timing measurement of the other tracks. For lower multiplicity events, e.g., Z \u2192\u03c4\u03c4, this\nmethod is less effective. As an alternative, an additional timing measurement close to the interaction\npoint could be established, possibly in the form of an LGAD silicon sensor layer at low radius. This\nsolution would allow a direct track-by-track time-of-flight measurement independent of t0. Studies are\nneeded in order to quantify the implications of such a layer in terms of additional material for readout\nelectronics and cooling.\n6.7.2\nCompact RICH detector\nStudies are underway to develop a compact RICH detector for inclusion in CLD, with the goal of fitting\nit in a 20 cm radial envelope and contributing less than 10% of a radiation length to the material budget,\nhence limiting its impact on the other subsystems of the experiment, such as tracking and calorimetry.\nIt is enabled by the new generation of photodetectors, in particular silicon photomultipliers (SiPM), that\nhold the promise of providing high detection efficiency and spatial granularity in a low thickness. A\nfocusing geometry has been developed, where the surface of the detector is tiled with a large number\nof similar RICH detector elements, in a cellular approach, a concept named ARC, for \u2018Array of RICH\nCells\u2019 [632\u2013634].\nThe components of an ARC cell are shown in the top panel of Fig. 106. The lightweight vessel\nis made of carbon-fibre composite, with a wall thickness that depends on whether the contained gaseous\nradiator needs to be pressurised. The RICH uses dual radiators, silica aerogel and gas, with Cherenkov\nphotons from both radiators focused via a spherical mirror onto a common SiPM detector plane. The\nbaseline choice for gaseous radiator is C4F10 at atmospheric pressure, given its attractive optical prop-\nerties, as used for example in the RICH1 detector of LHCb, aiming for a leak-free closed circulation\nsystem. With the high photon-detection efficiency achievable with SiPMs, this option can provide a suf-\nficient number of detected photons, about 16 for a high-momentum particle, despite the limited radiator\nlength of only around 15 cm. On the timescale of FCC, however, such fluorocarbons may be banned,\n148\n\nMomentum (GeV)\nNumber of standard deviations\nFig. 106: Top: Schematic cross section through the ARC barrel detector, showing the various components of a\nsingle cell. Bottom left: ARC barrel and end-cap as described in the detector geometry of the simulation, with\ncolours used to distinguish the cells. Bottom right: Momentum dependence of ARC\u2019s K/\u03c0 separation (in standard\ndeviations), with two radiator options.\nso that R&D is required to find alternative gases, such as xenon with mild pressurisation, to ensure a\nsufficient yield of detected photons. The aerogel radiator extends the particle identification performance\nto low momenta, while also serving as an efficient thermal insulator, separating the gas radiator from the\nSiPM detector plane, which is likely to need cooling to limit the dark-count rate (although the option of\nsuppressing noise with timing cuts will also be investigated). This insulator would allow the SiPMs to be\noperated at around \u221240 \u25e6C, e.g., with mixed-phase CO2 circulation, while maintaining the radiator gas\nat room temperature to prevent condensation.\nThe performance of such a RICH concept has been evaluated with full simulation studies [713].\nThe geometry of each cell, in terms of mirror and photodetector position and angle, depends on the posi-\ntion of the cell in the detector. Given symmetry considerations, there are about 40 unique cell geometries\nacross the detector, which have been optimised in an automated procedure. The resulting detector de-\nscription has been implemented in the KEY4HEP software framework (Chapter 8), with DD4HEP for\nthe geometry and GEANT4 for the simulation, as illustrated in the bottom-left panel of Fig. 106. Tak-\ning the integration into CLD as an example, 10% of the original tracker volume has been reassigned\nto ARC, the tracker dimensions being adapted to fit in the remaining space. Studies are underway to\ndevelop pattern recognition and particle identification algorithms, as well as to check the impact on the\nexperiment, e.g., on the performance of the tracking and particle-flow calorimetry. Meanwhile, the per-\nformance has been studied using standalone ray-tracing software, as shown in the bottom-right panel of\nFig. 106. The overall resolution per detected photon is around 2 mrad, balanced between contributions\nfrom the chromatic dispersion, focusing errors, and pixel size, where mm-scale pixelisation of the SiPMs\nhas been assumed. Excellent K/\u03c0 separation is achieved for momenta above 2 GeV. For lower momenta,\na TOF system would provide complementary information. The development of ARC is established as a\n149\n\ntask within the newly formed DRD4 collaboration [714], with the milestone of a full conceptual design\nwithin a year and a prototype of a single ARC cell to be delivered within three years. Such a prototype\nwill provide an excellent test-bed for the study of the key developments required for this detector, as well\nas the possibility of including RICH detectors as integral parts of the FCC-ee tracking detectors.\n6.8\nElectromagnetic calorimeters\n6.8.1\nSilicon pads, MAPS, scintillator strips\nElectromagnetic calorimeter technologies with embedded front-end electronics and high 3-dimensional\nsegmentation have been studied extensively [697]. They include silicon pads, MAPS sensors and scin-\ntillator strips, and capitalise on the possibility of power-pulsing and overall modest bandwidth require-\nments. Adapting them to a circular collider such as FCC-ee, with continuous readout and high rates,\nposes challenges for data concentration, powering, and cooling, requiring a full re-optimisation to max-\nimally preserve their compactness.\nSilicon diodes are currently implemented in the CMS end-cap\ncalorimeter upgrade, but the FCC-ee goals in terms of compactness (Moli\u00e8re radius), energy resolution,\nand granularity are considerably more ambitious.\nRelated R&D has begun, in the framework of the DRD6 Collaboration. As a first step, quantitative\nrequirements are being studied in simulations. Tools have been developed to evaluate hit occupancy,\nbandwidth and, with model assumptions on the embedded electronics, power consumption as a function\nof position in the detector [715].\n6.8.2\nNoble liquid\nThe proposed ALLEGRO noble-liquid electromagnetic calorimeter is a sampling detector using liquid\nargon as active medium and lead/steel absorbers as passive material. The absorbers and electrodes are\nstraight, and inclined (in the barrel) in the (x, y) plane by 50\u25e6with respect to the radial direction. The\ndetector has both transverse and longitudinal segmentation. Alternative design options include liquid\nkrypton as active medium and tungsten for passive material, as well as trapezoidal absorbers to maintain\nthe sampling fraction constant as a function of depth.\nThe calorimeter is located inside a cryostat, made of 33.8 mm-thick aluminium in the current\nsimulations while novel, lightweight materials are being considered (Section 6.11). The 2 mm-thick\nabsorber plates are composed of a sandwich of lead (1.8 mm) with steel sheets glued on either side.\nBetween adjacent absorbers are two equal-size liquid argon gaps, separated from each other by a 1.2 mm-\nthick electrode, realised as a multilayer PCB. The use of multilayer PCBs as readout electrodes allows\nfor great flexibility in the choice of granularity as a function of depth. In the present geometry, the liquid\nargon gaps have thicknesses, projected along the direction orthogonal to the electrode, of 2\u00d71.25 mm at\nthe inner radius and 2\u00d72.43 mm at the outer radius. The electrodes are segmented longitudinally into 11\nlayers. The first layer, about half as thick (1.5 cm) as the others (3 to 5 cm), is used as a presampler. To\nachieve a \u03d5-uniform response of that first layer, the absorber does not contain lead, to form a \u2018LAr-only\u2019\nhomogeneous presampler. The sampling fraction is about 38% in the presampler layer and increases\nfrom 13.5% to 17.3% throughout the other 10 layers. A depth of 22 X0 is achieved in a thickness of\n40 cm for the Pb\u2013LAr solution and about two thirds of that for denser solutions based on W and LKr.\nThe segmentation in \u03d5 is naturally provided by the absorbers. The baseline is to read out two gaps\ntogether, forming a single cell spanning \u2206\u03d5 = 2\u03c0/768 = 8 mrad. The segmentation along the electrode\nand in \u03b8 is formed by cells on the readout electrode. It amounts to \u2206\u03b8 = 0.56\u25e6, except in one of the\nfirst layers, where a four-times finer granularity (\u2206\u03b8 = 0.14\u25e6) is implemented, to discriminate between\nsingle showers from prompt photon and collimated pairs of showers from neutral pion decays. The total\nnumber of readout channels for the barrel part of the calorimeter is around 2 million. The expected\nsampling term of the resolution ranges from \u223c7.5%/\n\u221a\nE for a solution based on LAr, down to below\n5%/\n\u221a\nE, for a denser solution based on LKr.\n150\n\nAn adapted geometry is needed for the detector end-caps. The inclined absorber and electrode\nplanes of the barrel calorimeter are replaced by \u2018blades\u2019 arranged in a turbine-like structure. In order to\navoid having too large variations of gap sizes and sampling fractions between the inner and outer radii,\nthe detector is assembled as three nested wheels, with similar gap sizes at the inner radius of each wheel.\nThe geometries of both the barrel and the end-cap sections are implemented in the GEANT4 full\nsimulation of the KEY4HEP software framework. Algorithms for digitisation and clustering (fixed-\nsize sliding-window and topological clusters) are also implemented. Example displays of reconstructed\nclusters from single-photon and single-\u03c00 events are shown in Fig. 107.\nFig. 107: Event displays in the (r, z) view for clusters reconstructed in the ECAL barrel of ALLEGRO, for a\nphoton (left) and a \u03c00 \u2192\u03b3\u03b3 (right), both coming from the main IP at normal incidence with an energy of 10 GeV.\nThe particles impinge on the detector from the bottom. Clustered cells are shown in brown, with lighter tones\ncorresponding to higher cell energies. The yellow dots are placed in the cell centres. Noise is not simulated. In\nthis simulation, the strip layer is the first one.\n0\n20\n40\n60\n80\n100\nEtrue [GeV]\n2.5\n5.0\n7.5\n10.0\n12.5\n15.0\n17.5\nResolution [%]\nEM SW clusters, noise on\nResolution\n0.04\nE\n7.7%\np\nE\n0.5%\nResponse bias\n2.0\n1.5\n1.0\n0.5\n0.0\n0.5\n1.0\n1.5\n2.0\nResponse bias [%]\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \nArea under curve (AUC) when \ndifferent ECAL layers (1-5) have finely \nsegmented \u201cstrip\u201d cells\nFig. 108: Left: Simulated energy response and resolution of the LAr ECAL barrel calorimeter, including noise,\nfor reconstructed (sliding window) photon clusters as a function of the true photon energy. Right: ROC curves of\na BDT trained to discriminate between photons and neutral pions with momenta between 1 and 100 GeV, using\ninput features calculated from the clustered cell energies.\nExamples of performance studies are illustrated in Fig. 108, where the energy resolution and\nresponse expected with the (LAr plus tungsten) baseline model are shown, together with the ROC curves\nfor a simple BDT-based photon/\u03c00 discrimination algorithm exploiting the shower shapes computed from\nthe cell energies. The latter, which shows the area-under-curve (AUC) of the efficiency vs. rejection curve\nof the BDT algorithm for various alternative configurations corresponding to different positions of the\nstrip layer, demonstrates how the simulation can help design choices.\n151\n\nSustained R&D on noble liquid calorimeters is carried out in the framework of the WP2 of DRD6.\nOngoing activities focus on the optimisation of the detector material, geometry and segmentation, overall\ndetector mechanical structure and integration, readout electronics, as well as on prototyping and testing\nthe various detector elements. On a longer timescale, the plan is to build a prototype and test it with\nbeam, around 2027\u20132028.\n6.8.3\nSegmented crystals with dual-readout\nThe Maximum Information Crystal Calorimeter (MAXICC) is a homogeneous electromagnetic calorime-\nter concept optimised for FCC-ee, made of longitudinally segmented crystals with embedded dual-\nreadout and precise timing capabilities. An overview of its design can be found in Ref. [614]. This\ncalorimeter offers an electromagnetic energy resolution of 3%/\n\u221a\nE, crucial for studies of heavy-flavour\nphysics with low-energy final-state photons [716] and to improve the resolution of the mass recoiling\nagainst Z \u2192e+e\u2212in ZH events with a recovery of bremsstrahlung photons. Furthermore, it enables an\nefficient clustering of photon pairs from \u03c00 decays, which can effectively reduce the splitting of the two\nphotons across different jets in multi-jet events [614].\nThe MAXICC calorimeter design is optimised for integration with a dual-readout hadron calorime-\nter section to provide an energy resolution for charged and neutral hadrons of about 27%/\n\u221a\nE \u22952%, by\ncorrecting each shower individually using its estimated electromagnetic fraction, simultaneously mea-\nsured with different techniques, thereby reducing the impact of shower fluctuations on the resolution.\nThe inclusion of longitudinal segmentation and the enhancement of transverse granularity with \u223c1 cm2\ncells (compared to the previous generation of crystal calorimeters) provide a powerful handle for particle\nidentification and association of charged-particle tracks with calorimeter clusters in particle-flow jet re-\nconstruction, with the potential to achieve an energy resolution of 4.5% for 45 GeV jets [717], as shown\nin Fig. 109. A complete simulation of the detector integrated with other IDEA sub-detectors, within the\nKEY4HEP framework, is in progress, to allow more detailed physics studies [718].\n0\n20\n40\n60\n80\n100\n120\n140\n [GeV]\n\u232a \njet\n E\n\u2329\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n/E\nE\n\u03c3\n 0.027\n\u2295\n \nE\n/E = 0.34/\nDRO\nE\n\u03c3\n 0.015\n\u2295\n \nE\n/E = 0.29/\nPFA\nE\n\u03c3\n 0.042\n\u2295\n \nE\n/E = 0.36/\nRAW\nE\n\u03c3\nw/o DRO, w/o pPFA\nw/ DRO, w/o pPFA\nw/ DRO, w/ pPFA\n jj\n\u2192\n \n\u03b3\n Z*/\n\u2192\n -\ne\n+\ne\nJet energy resolution\nFig. 109: Jet energy resolution vs. jet energy, with or\nwithout a dual-readout particle flow algorithm.\nFig. 110: Segmented crystal calorimeter prototype cell\nand module with SiPM dual-readout.\nAs shown in Fig. 110, the baseline calorimeter design features two longitudinal layers of high-\ndensity crystals (such as PWO or BGO), with 6 X0 in the front layer and 16 X0 in the rear layer, for a\ntotal of 22 X0 to ensure full containment of electromagnetic showers. The light from the crystals is read\n152\n\nout with silicon photomultipliers (SiPMs) of active area in the range between 4 \u00d7 4 and 6 \u00d7 6 mm2. One\nSiPM is glued on the front side of the front layer and two are glued on the rear face of the rear layer.\nOne of the rear SiPMs embeds an optical filter that cuts out the scintillation light based on wavelength\ndiscrimination and detects a pure Cherenkov signal for dual-readout corrections. An alternate approach\nalso uses pulse shape analysis to differentiate scintillation and Cherenkov components. The front-end\nboards, electronics, and cooling services are located in the front and rear parts of the calorimeter to\nminimise the impact of passive material on energy resolution.\nThe MAXICC calorimeter can provide a time resolution better than 30 ps for electromagnetic\nshowers with energy of 20 GeV or higher, as obtained from beam tests with similar calorimeter proto-\ntypes [719]. In addition, two thin and highly segmented layers of LYSO:Ce crystals, for a total of 1 X0,\ncould be added in front of the PWO crystals for time tagging of minimum ionising particles, using a\ntechnology similar to that used by the CMS MTD [720], with a time resolution of 20 ps.\nThe required technological R&D, prototyping, and simulation are progressing steadily, through\na coordinated effort of many international collaborators within the DRD6 WP3 (task 3.1.2). Single\ncalorimetric cells have been tested with beam in 2024 and full containment calorimeter prototypes (one\nusing PWO and the other using BGO) are being built for beam tests in 2025. Each prototype will\ninstrument \u223c100\u2013200 channels for readout, covering a transverse size of at least five times the Moli\u00e8re\nradius and a depth of 22 X0.\n6.8.4\nThe GRAiNITA ECAL\nThe GRAiNITA concept features a novel electromagnetic calorimetry design, with a detection volume\nfilled with millimetric grains of high-Z and high-density inorganic scintillator crystals immersed in a\nbath of transparent high-density liquid. The multiple refractions of the light on the grains ensure the\nstochastic confinement of the light, as in the LiquidO detection technique [721]. The scintillation light\ncan be collected towards the photodetectors by means of WLS fibres, regularly distributed in the detec-\ntion volume as for a conventional Shashlik detector, allowing a potentially-large transverse granularity.\nThis extremely-fine sampling of the electromagnetic shower promises an excellent energy resolution,\ncomparable to what is known from crystal calorimeters.\nThe main high-Z and high-density inorganic scintillator crystal considered for GRAiNITA is\nZnWO4 [722], providing a light yield of \u223c10 000 photons per MeV. A considerable advantage is that\nZnWO4 can be successfully grown in the form of transparent granules of the desired size, with the method\nof spontaneous crystallisation from a flux melt [722], significantly reducing the cost of the calorimeter.\nSuch a high energy-resolution granular calorimeter would then meet the requirements, from physics and\notherwise, of an FCC-ee experiment. It would, moreover, be particularly useful to address a compre-\nhensive flavour physics programme with rare decays involving photons or neutral pions in the final state.\nGiven that the Z production rate at FCC-ee is of the order of 100 kHz and since these events should\ntypically hit less than 1% of the calorimeter cells, the 20 \u00b5s signal decay time of the ZnWO4 should not\nbe a concern. Nevertheless, the possible use of other types of crystals will be investigated.\nMeasurements with a small prototype (2.8 \u00d7 2.8 \u00d7 5.5 cm3) equipped with a green LED confirm\nthat, as expected, the signal remains confined in the vicinity of its production point [723]. From the\nanalysis of cosmic-ray muons [723] and of data from a muon beam test performed in summer 2024 at\nCERN with the same small prototype, it is clear that the collection of about 10 000 photo-electrons per\nGeV is within reach with a GRAiNITA-like calorimeter. This result paves the way for a statistical fluctu-\nation of 1%/\n\u221a\nE on the energy resolution from photo-electrons (Fig. 111). The next steps, following this\nproof-of-principle, include the system aspects, including a mechanical configuration and an electronics\nread-out concept.\n153\n\n200\n400\n600\n800\n1000\n1200\nSum of 16 channels\n0\n20\n40\n60\n80\n100\n120\n \n / ndf \n2\n\u03c7\n 53.28 / 39\nWidth \n 1.70\n\u00b1\n 14.92 \nMPV \n 3.1\n\u00b1\n 403 \nArea \n 7.339e+02\n\u00b1\n 2.282e+04 \nGSigma \n 2.99\n\u00b1\n 55.86 \n \n / ndf \n2\n\u03c7\n 111.8 / 86\nWidth \n 0.58\n\u00b1\n 25.24 \nMPV \n 0.7\n\u00b1\n 443.9 \nArea \n 1.263e+03\n\u00b1\n 1.503e+05 \nGSigma \n 0.95\n\u00b1\n 42.09 \n0\n200\n400\n600\n800\n1000\nNPhe\n0\n100\n200\n300\n400\n500\n600\n700\n \n / ndf \n2\n\u03c7\n 111.8 / 86\nWidth \n 0.58\n\u00b1\n 25.24 \nMPV \n 0.7\n\u00b1\n 443.9 \nArea \n 1.263e+03\n\u00b1\n 1.503e+05 \nGSigma \n 0.95\n\u00b1\n 42.09 \n \nFig. 111: Number of photo-electrons recorded in a small GRAiNITA prototype, where the ZnWO4 grains are\nimmersed in a heavy liquid to increase the density of the medium. Left: Cosmic-ray muons with ZnWO4 grains\nimmersed in ethylene-glycol (from Ref. [723]). Right: Muon tracks from a beam test at CERN with ZnWO4 grains\nimmersed in LST Fastloat (density = 2.8 g/cm3) [724].\n6.9\nHadron calorimeters\n6.9.1\nScintillator tiles\nOne of the considered hadron calorimeter designs is a non-compensating sampling calorimeter based on\nthe ATLAS TileCal [725], with steel as absorber and plastic scintillating tiles as active material. The\nlight from the scintillator is collected and transported to the SiPMs located outside the calorimeter via\nWLS fibres, as shown in Fig. 112.\n4 \u00d7 5 cm\n6 \u00d7 10 cm\n3 \u00d7 20 cm\nsource tubes\nscintillator\niron\nwavelength-shifting fiber\nsilicon photomultiplier\nbeam axis\nFig. 112: HCAL tile module concept. Each module consists of 13 radial layers of scintillating tiles with different\nradial extension (5, 10, and 20 cm), and each radial layer is divided into two tiles in azimuth (hatched red). Scin-\ntillation light is brought to SiPMs at the outer radius via WLS fibres. In the z direction, tiles are read out in groups\nof 3 or 4.\nThe radial orientation of the tiles and the light collection via the WLS fibres along the tile edges\nallow a hermetic implementation in \u03d5. The location of the photodetectors and their associated electronics\nin the modules\u2019 girder at the outside radius makes them serviceable during collider shutdown periods. It\nalso embeds the calibration system with movable radioactive 137Cs photon sources that can pass through\nall calorimeter cells [726].\n154\n\nThe proposed design uses 5 mm low-carbon steel absorber plates interleaved with 3 mm plastic\nscintillating tiles. The barrel is segmented into 128 modules in \u03d5 and 13 radial layers (of different\ndepths: four of 5 cm, six of 10 cm, and three of 20 cm, as shown in Fig. 112). Each layer is divided in\n\u03d5 in two longitudinal read-out compartments. In each compartment, the tiles are read out in groups of\nthree or four along the z axis, which leads to a cell granularity \u2206\u03d5 \u00d7 \u2206\u03b8 of 24.5 \u00d7 22 mrad2 at normal\nincidence. Steel-scintillator technology is also being considered for the end-cap hadron calorimeter.\nThe performance of the tile HCAL, evaluated with a sliding window clustering algorithm, is shown\nin Fig. 113. The optimisation of the calorimeter details, including the choice of the absorber and scin-\ntillating materials, as well as their segmentation, is ongoing. These R&D studies are coordinated by the\nDRD6 WP3 (task 3.3.2), including the characterisation of perspective scintillating materials, like PEN\nand PET [727], and the light collection from scintillating tiles via WLS fibres with SiPM photodetec-\ntors [728].\nFig. 113: HCAL tile energy resolution for hadron clusters.\nA complementary approach is also being explored, with the so-called SiPM-on-Tile technology\nand with front-end electronics embedded into the active layers of a steel sandwich structure. The SiPMs\nare integrated into the electronics PCBs, which also hold read-out ASICs, power distribution, and a LED-\nbased calibration system. Reflector-wrapped scintillator tiles are glued onto the PCB, with a dimple\nleaving space for the SiPMs underneath, which read each tile individually.\nWhile the ATLAS-style geometry offers easier access and space for service routing, including\ncooling for a calorimeter placed outside the coil, the SiPM-on-Tile approach is the natural choice for\ncalorimeter systems entirely inside the solenoid, such as in the CLD concept, where radial compactness\n(especially in the barrel) is strictly mandated by cost considerations. The technology was originally\ndeveloped by the CALICE Collaboration; a scalable prototype with 22 000 channels was built and has\nbeen successfully tested in beams since 2018 [729]. The main challenge in the adaptation to FCC-ee\nlies in coping with the continuous readout (i.e., without power-pulsing) and with the much higher rate,\nbandwidth, power, and cooling requirements, without compromising granularity and compactness.\nThe R&D has common challenges with other concepts based on embedded electronics and is\npursued in the framework of the WP1 of the DRD6 Collaboration. The SiPM-on-Tile technology is\ncurrently being applied in a large scale in the CMS HGCAL, a detector with 280 000 tiles. Although\nthe CMS HGCAL has to address radiation hardness and other challenges not present at FCC-ee, it has\n155\n\nmore relaxed performance and compactness requirements, and remains more than an order of magnitude\nsmaller in terms of channel count than, e.g., the CLD HCAL.\n6.9.2\nGaseous detectors\nGaseous detector technologies with two-dimensional transverse segmentation are also pursued as read-\nout options for hadron calorimeters. Proof-of-principle elements have been tested using GEM and mi-\ncromegas detectors, and larger prototypes with glass RPCs have been built and successfully tested, with\nup to 500 000 channels [730,731]. Granularities finer than with tiles are easily achievable, but to maintain\nthe designs cost-effective and to limit read-out power consumption, trade-offs must be found between\nenergy and space information. The channel amplitude is encoded in one or two bits only, hence the name\ndigital or semi-digital HCAL.\nThe related R&D is pursued both in the DRD6 (\u2018calorimeters\u2019) and in the DRD1 (\u2018gas detectors\u2019)\nprojects. The challenges of data concentration, powering, and cooling are shared with other ECAL\nand HCAL technologies with embedded readout. The quest for improving the detection technologies\nthemselves, in terms of rate capability and stability, is common with R&D for muon detectors, and both\nface the imperative of replacing the currently used gas mixtures with high global warming factors by\nmore eco-friendly solutions.\n6.9.3\nDual readout\nA fibre-sampling Dual-Readout (DR) calorimeter [732] can, in principle, be used as a single system\nfor electromagnetic and hadron showers. This option is considered in the IDEA concept, with a calori-\nmetric section made of a dual-readout, longitudinally unsegmented and fully projective, fibre-sampling\ncalorimeter, providing both electromagnetic and hadron shower measurements. Another option is to use\nthis technology as a hadron calorimeter behind an electromagnetic section based on crystals, as discussed\nin Section 6.8.3.\nAlternate rows of scintillating and Cherenkov (clear) fibres are inserted in capillary tubes made of\nbrass or iron. Each fibre is individually read out with a SiPM. In order to significantly reduce the number\nof readout channels, the analogue grouping of 4\u20138 SiPM signals is foreseen. The optimal granularity is\ndifferent if the detector has to provide both electromagnetic and hadronic shower measurements or just\nthe latter. The present choice (1 mm fibres in 2 mm capillary tubes) is designed to address both.\n60\n70\n80\n90\n100\n110\n120\n130\n140\n150\n160\nMass (GeV)\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nArbitrary units\nFig. 114: From Ref. [733]. Invariant mass distributions of W (blue), Z (red), and H (green) hadronic decays,\nfrom e+e\u2212\u2192W+W\u2212and ZH events fully simulated and reconstructed at \u221as = 240 GeV in a dual-readout\nfibre-sampling calorimeter. To highlight the detector performance, semileptonic b decays are excluded.\nThe hadron energy resolution is estimated to be about 30%/\n\u221a\nE, with a negligible constant term.\nThe expected separation reachable for the W, Z and H hadronic decays is shown in Fig. 114, obtained\n156\n\nwith a stand-alone simulation and subsequent reconstruction of the DR calorimeter, and excluding semi-\nleptonic decays [733]. Similar studies show that this detector can provide excellent stand-alone electron-\npion separation. Moreover, the RD52 lead prototype obtained an efficiency of about 99% in identifying\nelectron showers, for a rejection ratio of charged-pion showers higher than 500 [734].\nAdvances in solid-state light sensors, such as SiPMs, have opened the way for high transverse\ngranularity, which gives the detector the capability to determine shower angular positions at the mrad\nlevel, or better. In the present design, without a crystal-based electromagnetic calorimeter in front, the\n1 mm diameter fibres are placed in an iron absorber matrix, at a distance (apex to apex) of 1.5\u20132 mm.\nThe lateral segmentation could be pushed down to the mm level, largely enhancing the resolving power\nfor close-by showers, with a significant impact expected, for example, on the isolation and reconstruction\nof \u03c4 \u2192\u03c1\u03bd final states. For the setup with crystals in front, the segmentation of the DR sections remains\nto be optimised.\nThe high photo-detection efficiency of SiPMs should lead to light yields of O(100) photo-electrons\nper GeV, for both the scintillation and Cherenkov signals, which guarantees a stand-alone EM resolution\nclose to 10%/\n\u221a\nE. Readout ASICs providing time information with about 100 ps resolution may allow\nthe reconstruction of the longitudinal shower position with a resolution of about 5 cm.\nOn the other hand, the large number and density of channels require an innovative readout archi-\ntecture for efficient information extraction. Both charge integration and waveform sampling ASICs are\navailable on the market and candidates for early testing have been identified. A first implementation of a\nscalable readout system is well-advanced. Looking further ahead, digital SiPMs (dSiPMs) should allow\na significant simplification of the readout architecture, but the technology is not yet sufficiently mature.\nA specific R&D programme has been approved for the 2025\u20132026 period.\nThe mechanical assembly and integration of a system with O(108) sensitive elements require the\ndevelopment of a robust and engineered procedure. A scalable mechanical solution has been conceived\nfor both non-projective and projective modules. A small (\u223c10 \u00d7 10 \u00d7 100 cm3) EM prototype has been\nbuilt, based on the gluing of capillary tubes. This procedure is being used for the construction of a hadron\ncalorimeter prototype (of size \u223c60 \u00d7 60 \u00d7 250 cm3) that should be completed by mid 2025. Alternative\napproaches, for both mechanical assembly and readout architecture, are being investigated within DRD6.\n0\n5\n10\n15\n20\n25\nDistance from shower axis [mm]\n3\n\u2212\n10\n2\n\u2212\n10\nFraction of total SiPM signal in fiber\nScintillation, 20 GeV e+ (CERN-SPS)\nCherenkov, 20 GeV e+ (CERN-SPS)\nScintillation, GEANT4.10.7.p03\nCherenkov, GEANT4.10.7.p03\nFig. 115: Lateral shower profile of positrons with an energy of 20 GeV. The black circles (triangles) refer to\nthe scintillation (Cherenkov) options. The red and blue bands correspond to the simulation predictions for the\nscintillation and Cherenkov signal, respectively.\nThe EM prototype was tested with beam at the CERN SPS and the results (Fig. 115) show that\n157\n\nsimulations model the instrumental effects well. The performance in the reconstruction of the properties\nof both hadron and EM showers is sufficient to retain the possibility of an integrated dual-readout solution\nbased on fibre-sampling only, for the calorimetric system of an FCC-ee experiment. The huge amount of\ninformation made available by the fibre SiPM readout is well suited to take advantage of deep-learning\nalgorithms.\n6.10\nCoil\nConceptual studies of 2 T superconducting solenoid variants have been concluded for the CLD, IDEA,\nand ALLEGRO FCC-ee detector concepts. From a conceptual perspective, the CLD solenoid is similar\nto that of CMS, with the calorimeters located inside the solenoid bore. A relatively high energy density\nis targeted, for the purpose of limiting the weight of the cold mass, with various benefits, in particular\nregarding the overall cost and easier transport from the manufacturer to CERN. For the IDEA and AL-\nLEGRO concepts, the solenoid is located inside the hadron calorimeter and the free-bore diameter is\nsubstantially smaller. The advantage of this variant is that the cold-mass weight is reduced, albeit at the\ncost of requiring high particle transparency of the cold mass, thermal shields, and vacuum vessel. The\ndesign of thin, low-mass magnet systems is discussed in Ref. [11]. Representative field maps are shown\nin Fig. 116 and typical design parameters are shown in Table 16.\nFig. 116: Field maps of the CLD (left) and IDEA (right) detector magnets in the (r, z) view, featuring 2 T in the\nfree bore.\nTable 16: Overview of typical design parameters of the different solenoid variants.\nVariant\nStored magnetic\nCold mass\nEnergy density\nenergy (MJ)\nweight (t)\n(kJ/kg)\nCLD\n590\n52\n11.4\nIDEA\n130\n10.6\n12.3\nAllegro\n250\n22\n11.4\nFor each variant, a relatively high energy density, of about 12 kJ/kg, is targeted, a value compara-\nble to what was previously shown in the CMS solenoid and the Bess\u2013Polar solenoid [735]. This energy\ndensity poses challenges for quench protection and cold-mass mechanics but, relying on technological\nsolutions previously demonstrated for the ATLAS, CMS, and Bess\u2013Polar solenoids, no setbacks were\nidentified. The baseline is to build the solenoids with reinforced aluminium-stabilised low-temperature\nsuperconductors. These conductors have been successfully applied in many detector magnet projects\nworldwide over the past decades and they meet the technical requirements of the FCC detector magnets,\nregarding the field ranges, the free bores, the transparency to particles, and the mechanics and stabil-\nity. The preferred technology is co-extrusion of Nb-Ti/Cu Rutherford cable in a high purity aluminium\n158\n\nstabiliser. This technology offers the best characteristics for coil quench protection and coil stability,\nwith an indirect cooling. Strong mechanical properties can be reached using either Ni-doped high-purity\naluminium stabiliser, or aluminium alloy profiles electron-beam-welded to the coextruded aluminium-\nstabilised superconductor. It should be noted that this assumes the commercial availability of reinforced\naluminium-stabilised Nb-Ti conductor. At the time of the conclusion of the conceptual cold-mass stud-\nies, it became clear that companies that had historically made this conductor type commercially available\nhad discontinued production.\nAs an alternative to aluminium-stabilised Nb-Ti conductor technology, preliminary studies were\nmade concerning the implications of aluminium-stabilised high-temperature-superconducting (HTS) con-\nductors. The use of HTS brings interesting benefits, such as potentially allowing a higher operating\ntemperature and, thus, reduced cryogenic operating costs. The implications for capital costs, cold mass\nmechanics, quench detection and protection are, however, not yet fully understood and characterised.\nThis technology requires further R&D before it can be concluded that it is a reliable alternative to the\nNb-Ti conductor. Two manufacturing methods are considered for the aluminium-stabilised HTS: co-\nextrusion in high-purity aluminium profiles and soft soldering in copper-plated aluminium profiles. As\nthe HTS are produced in thin tapes, several HTS conductor technologies are envisaged: stacks of tapes,\nRoebel cables, and conductor on round core (CORC\u00ae) conductors.\nAn Experimental Magnets Committee was established by CERN in 2023 to address the R&D\nneeds of detector magnet projects and to resolve identified issues regarding the availability of technolo-\ngies and facilities needed to manufacture superconductors for detector magnets. An ongoing programme\nis targeting to establish access to a co-extrusion line that would allow R&D and prototyping, both with\nlow- and high-temperature aluminium-stabilised superconductors. In addition to the CERN effort, spe-\ncific R&D for an HTS solenoid for IDEA/ALLEGRO is currently in progress at INFN-LASA.\n6.11\nCryostat\nThe use of carbon composite technologies for cryostat construction is being studied in an R&D pro-\ngramme in the CERN EP Department. In collaboration with industry, a 1 m carbon composite cryostat\nprototype has recently been developed, as shown in Fig. 117. The manufacturing procedure, based on a\nwet filament winding process, ensures helium leak-tightness at cryogenic temperatures without the need\nfor a metallic liner.\nFig. 117: Full liner-less tank demonstrator, 1 m length, 0.3 m diameter, and 5 mm wall thickness. Manufacturing\nprocess: filament wet-winding, non-crossing, out-of-autoclave curing.\nRecent developments to support large-scale production (larger than 5 m in diameter and length),\ninclude the refinement of the winding process and the development of a toughened epoxy resin to en-\nhance resistance to microcracking. Additionally, a novel technique has been developed to wind each ply\nof material without fibre crossings, minimising porosity and further improving microcrack resistance.\nPromising helium leak tests at low temperatures indicate that strict cryogenic standards can be met for\ndetector operations.\nThe ability of cryostat vessels to resist structural instability (buckling) under compressive loads\n159\n\nposes an additional challenge. The use of a full carbon honeycomb as a replacement for aluminium\nhoneycomb is being explored. Initial prototypes have undergone extensive testing, including thermal\nexpansion and dimensional stability assessments, underscoring the suitability of carbon honeycomb for\nlarge, buckling-sensitive cryostat walls.\nThe combination of a leak-tight carbon wall with the full carbon honeycomb core represents a\npromising design direction for next-generation HEP cryostats. A preliminary study, using the ALLEGRO\ndetector concept as an example, revealed a 64% reduction in the material budget and a 30% reduction in\nwall thickness for buckling-sensitive cryostat walls compared to an aluminium sandwich design, with a\nthermal expansion coefficient one order of magnitude lower while maintaining comparable mechanical\nproperties.\n6.12\nMuon system\nSeveral technologies are under consideration for use in detector muon systems at FCC-ee, including\n\u00b5-RWELL [736], resistive plate chambers [737], resistive Micromegas [738], scintillators, drift tubes,\nand combinations thereof. Apart from muon identification, these systems can offer capabilities for tail\ncatching of calorimeter showers, identification of long-lived particles by providing tracking with good\nposition resolution, or independent triggers.\nThree \u00b5-RWELL layers are currently implemented in the IDEA design, in both the barrel and end-\ncap regions, housed within the iron yoke that closes the detector magnetic field. The \u00b5-RWELL chambers\nprovide 2D space point measurements with a few hundred micron precision. In order to benefit from\nindustrial production capabilities of this technology, a modular design is adopted with basic \u00b5-RWELL\n\u2018tiles\u2019 with an active area of 50 \u00d7 50 cm2 and a readout strip pitch of about 1 mm, enabling a sufficient\nspatial resolution of about 400 \u00b5m while limiting the number of readout channels to 1000 per tile. The\nchoices of detector tile size, strip pitch and width are a compromise between the largest \u00b5-RWELL\ndetector that can be industrially mass-produced and the maximum input detector capacitance that can be\ntolerated in terms of signal over noise ratio by the front-end electronics.\nTable 17 lists the dimensions, the number of basic \u00b5-RWELL tiles, and the readout channels of the\nthree muon stations of the IDEA detector. In total, including the barrel and the end-cap muon stations,\nthe system comprises about 5800 \u00b5-RWELL tiles with about 6 million readout channels.\nTable 17: Dimensions of the three IDEA barrel muon stations, together with the number of detector tiles and the\ncorresponding number of readout channels.\nStation\nRadius\n(m)\nLength\n(m)\nStrip pitch\n(mm)\nStrip length\n(mm)\nArea\n(m2)\n# of\ntiles\nChannels\n1\n4.52\n9.0\n1\n500\n260\n1040\n1 040 000\n2\n4.88\n9.0\n1\n500\n280\n1120\n1 120 000\n3\n5.24\n10.52\n1\n500\n350\n1400\n1 400 000\nThe geometries and material of both the barrel and the end-caps have been implemented in the\nGEANT4 full simulation of the muon system. The implementation of algorithms for digitisation and\nclustering will follow in the next step of the study. Since the \u00b5-RWELL technology has not yet been used\nto build a full detector system, a vigorous R&D programme to study integration issues will be carried\nout in the coming years. The detailed layout of the detector, together with all its services, will have\nto be accurately developed. The optimisation of the basic \u00b5-RWELL tile, including gas gap, diamond\nlike carbon layer resistivity, and gas amplification, has started [739,740] and is expected to be finalised\nto match the requirements of the IDEA muon system by 2027. The \u00b5-RWELL R&D is performed in\nsynergy with the WP1 of DRD1 [741]. Another important aspect of this R&D programme is the design\nand development of dedicated front-end electronics based on a custom-made ASIC.\n160\n\n6.13\nLuminosity measurement\nFor the precise measurement of cross sections, the integrated luminosity must be determined with high\nprecision. Ambitious goals have been formulated on the measurement precision: 10\u22124 or better on the\nabsolute luminosity and 5 \u00d7 10\u22125 or better on the relative luminosity between energy scan points. At\nFCC-ee, the wide-angle diphoton process, e+e\u2212\u2192\u03b3\u03b3, is statistically relevant and provides a promising\ncomplement to the traditional low-angle Bhabha scattering process, e+e\u2212\u2192e+e\u2212. For both processes,\nthe definition of the geometrical precision constitutes an important source of systematic uncertainty.\nAs discussed in Section 4.6.3, the \u03b3\u03b3 final state places a requirement on the accuracy of the lower\nlimit of the polar angle acceptance at the 8 \u00b5rad level, corresponding to 20 \u00b5m at 2.5 m from the IP.\nFor each of the proposed ECAL solutions, R&D is needed on how to obtain such construction preci-\nsion. Complementary methods to determine the acceptance in-situ with this precision or better are under\ndevelopment and alluded to in Section 4.6.3. Likewise, studies are needed on how to ensure that the effi-\nciency of observing the \u03b3\u03b3 final state can be understood to the required precision over the wide detector\nacceptance.\nFor the measurement of low-angle Bhabha scattering, the luminosity calorimeters (LumiCals) are\nlocated close to the beam pipe, where they are neighbouring the complex Machine Detector Interface\nregion (Chapter 5). Placed in front of the compensating solenoids, the LumiCals are at only \u223c1.1 m\nfrom the IP. In this region, space is severely limited and a very compact design is called for. The Bhabha\ncross section falls very steeply, as 1/\u03b83, with \u03b8 being the scattering angle, resulting in very challenging\ntolerances on the definition of the geometrical precision at the O(1 \u00b5m) level.\n6.13.1\nLumiCal design\nBased on experience from LEP [742, 743] and from past linear collider studies [619, 744, 745], com-\npact SiW sandwich calorimeters are proposed as luminosity monitors for the measurement of low-angle\nBhabha scattering. The calorimeters are designed as cylindrical devices assembled from stacks of iden-\ntical SiW layers. This simple geometry facilitates the control of construction and metrology tolerances\nto the necessary micron level, as emphasised by the OPAL experiment [742]. The monitors are centred\naround the outgoing beam directions in the severely limited space available, in front of the compensating\nsolenoids, which extend to |z| \u22431.2 m from the IP. The monitor design is illustrated in Fig. 118, where\nthe main physical dimensions are also given. The design includes 25 layers, each comprising a 3.5 mm\ntungsten plate, equivalent to one radiation length, and a Si-sensor plane inserted in the 1 mm gap. In\nthe transverse plane, the Si sensors are finely partitioned into pads. The proposed segmentation fea-\ntures 32 divisions, both radially and azimuthally, for 1024 readout channels per layer, or 25 600 channels\nin total for each calorimeter. A solution with a four times finer azimuthal segmentation is also under\nconsideration.\nA 30 mm uninstrumented region at the outer circumference is reserved for services (front-end\nelectronics, cables, and cooling), as well as for the physical structures (likely including precision dowels\nand bolts) needed for the assembly of the SiW sandwich. Overall, the proposed design is very compact,\neach calorimeter weighing only about 65 kg. An example of the integration of the LumiCals with the\nMDI and the detector system is shown in Figs. 86 and 88, in Chapter 5.\nThe Si-sensor pads are connected to front-end electronics positioned at radii immediately outside\nthe sensors. To minimise the occurrence of pile-up events, it is desirable to read out the sensors at the\nbunch-crossing rate. This constraint calls for the development of readout electronics with an O(20 ns)\nshaping time. From experience with similar electronics development [746], a power budget of 5 mW per\nreadout channel has been estimated, for a total of 130 W per calorimeter, to be removed by cooling. For\nthe required geometric precision, the temperature needs to be controlled to within a tolerance of 1 \u25e6C.\nThe goal of 10\u22124 precision on the absolute luminosity measurements translates into a required\nprecision of O(1 \u00b5m) on the radial dimensions of the calorimeters and of O(100 \u00b5m) on the distance\n161\n\n\u221225\n0\n25\n50\n75\n100\n125\n150\n\u2212150\n\u2212125\n\u2212100\n\u221275\n\u221250\n\u221225\n0\n25\n50\n75\n100\n125\n150\nmm\nmm\n1050\n1075\n1100\n1125\n1150\n1175\n1200\n\u2212150\n\u2212125\n\u2212100\n\u221275\n\u221250\n\u221225\n0\n25\n50\n75\n100\n125\n150\nmm\nmm\n55 mm\n115 mm\n135 mm\n145 mm\n1074 mm\n1190 mm\nelectronics + assembly\ncables + cooling\nFig. 118: Front view (left) and top view (right) of the luminosity calorimeter, centred around the outgoing beam\ndirection (shown as a red arrow). A possible segmentation of the Si pads is seen in the front view. Surrounding the\nsensitive region are regions for front-end electronics (red), and for cables and cooling (blue). The top view shows\nthe interleaved silicon-tungsten layer structure.\nbetween the two calorimeters.\nFirst full simulation studies of the LumiCals have been performed using 45.6 GeV electrons. They\nshow that the proposed geometry covers the polar angle region between 53 and 98 mrad for fully con-\ntained showers, corresponding to a cross section of 28 nb at the Z-pole energy. With a sampling fraction\nof 1.1%, the calorimeters have an energy resolution of 3.2%, corresponding to 22%/\n\u221a\nE. The intrin-\nsic resolution on the radial coordinate of showers is found to be 75 \u00b5m at a z = 1100 mm reference\nplane, considerably better than the contribution of about 120 \u00b5m from multiple scattering of the primary\nelectrons in the 2 mm of beam pipe material traversed at shallow angles.\nThe feasibility of the proposed design has been demonstrated in part, over the last two decades,\nby work of the FCAL R&D Collaboration, which had been specialising in technologies for very-forward\ncalorimeters at linear colliders. A five-layer prototype with a similar sandwich structure was built and\nsuccessfully tested in a beam test [745], and a dedicated readout system based on a custom-designed\nreadout chip was prepared [746,747].\nMuch work is needed towards a consolidated LumiCal design that satisfies the many severe re-\nquirements. Important future steps include:\n\u2013 Engineering-level study of the proposed detector assembly method, which involves precision dow-\nels and through-going bolts. This study must take into account the required O(1 \u00b5m) geometrical\nprecision on the radial coordinate.\n\u2013 Realistic estimate of the space needed for services at radii outside the sensitive region. This region\nshall be kept as transparent as possible by the use of lightweight materials, to minimise particle\ninteractions.\n\u2013 Design of a procedure for maintaining and monitoring the geometric accuracy of the monitors via\n162\n\nprecise metrology and alignment.\n\u2013 Design of a cooling system allowing control of a constant and uniform temperature over the mon-\nitors. The required tolerances have to be developed.\n\u2013 Re-evaluation of the expected radiation dose based on the final collider parameters and assessment\nof whether existing sensor technologies are adequate or further sensor R&D is required.\n\u2013 Design of compact low-power readout electronics that preferentially allows readout at the 50 MHz\nbunch-crossing rate, including transmission of signals away from the detectors. The system devel-\noped by the FCAL Collaboration may be a good starting point.\n\u2013 Further full simulation studies to optimise the design of the detector.\n6.14\nOutlook\nDuring the Feasibility Study, the detector designer community confirmed and enhanced its engagement\nand commitment to support a few complete detector concepts and to develop innovative detectors capa-\nble of delivering the required physics performance. The FCC-ee detectors have to meet unprecedented\nperformance requirements in order to match the expected statistical precision and discovery physics po-\ntential. These requirements are, in many respects, complementary to what was needed at HL-LHC: while\nradiation tolerance is not an issue, with few exceptions close to the beams, the demands on precision,\nefficiency, purity, transparency of trackers, and compactness of calorimeters are considerably more chal-\nlenging. Even though the readout bandwidth requirements appear relaxed when compared to the situation\nat HL-LHC, the required rate capabilities far exceed those from past linear collider studies. These con-\nstraints significantly magnify the system design and integration challenges especially if material budget\nand dead space are to be kept at minimum.\nThe detector R&D community has undergone a restructuring process, leading to the formation of\nDRD Collaborations to address these demands. While it is clear that these Collaborations will only be\nable to unfold their potential with an adequate ramp-up of resources, it is also important to emphasise\nthat they must benefit from proper guidance through the detector conceptual activities in the FCC effort.\nIn particular, it is crucial to continue to develop and maintain a powerful common software framework\n(Chapter 8), including full-simulation tools, in view of establishing and evolving the link between the\ndetector concepts, on the one hand, and technological R&D, prototype design and construction, and ulti-\nmately test-beam data analysis, on the other. It will be essential that this common framework be adopted\nby the DRD teams, to optimise the subsystem inclusion in the FCC-ee detector simulation studies. In-\ndeed, realistic geometries and digitizers will be essential to assess physics performance, as well as to\ncompare with prototypes and test-beam data.\nThe detector community is well connected worldwide. The US and European roadmap processes,\nfor example, have been well informed of each other and led to the formulation of overarching themes that\nare aligned to a large extent. This process is reflected in the ongoing integration of international groups\nand projects into the new DRD structure. Many of the proposals submitted to the DRD Collaborations\ntarget future Higgs factories and, among those, many specifically target FCC-ee. Given the current\nFCC-ee timeline, the R&D in the 2025\u20132027 period will give priority to conceptual and component\nstudies, with system aspects in focus from the beginning, preparing the way to the possible development\nof prototypes and demonstrators during the subsequent three-year period (2028\u20132030), followed by the\nconstruction and test of realistic modules by 2035.\nThe next phase of the FCC study will first capitalise on the developments made during the Feasibil-\nity Study regarding the full-simulation of the existing proto-detector concepts, to confront their simulated\nperformance with the detector requirements from physics. This work will clarify if those physics-driven\nrequirements are matched by the current proto-detector concepts and will point the way to alternative\ndetector solutions. Different detector configurations will then be studied to optimise both performance\nand cost. In parallel, the links to the DRD Collaborations will be tightened. Work towards the common\n163\n\ngoal of developing FCC-ee detector concepts will be encouraged, by giving the R&D groups the neces-\nsary inputs and requirements from the FCC Feasibility Study, and by identifying their needs in terms of\nguidance and software tools.\nSeveral challenges, specifically needed for FCC-ee but maybe not included in the DRD pro-\ngramme, will also need to be addressed. For example:\n\u2013 How to monitor the time-stability of the magnetic field map in the experiments at the 10\u22127 level\n(taking into account all magnetic elements, including compensating solenoids, etc.)?\n\u2013 How to achieve, possibly using a set of geometry systems, the accuracy on the knowledge of the\nalignment and surveying fiducials required for precision measurements (such as the luminosity\nmeasurement at low angles, the dilepton/diphoton cross section measurements at large angles, or\nthe tau lepton lifetime measurement)?\n\u2013 Can cosmic-ray muons continue to be used for the global alignment of FCC detectors, despite the\nfact that they will operate in much deeper caverns than those of previous colliders?\n\u2013 Are there new detector technologies or configurations that would be particularly well-suited for\nspecific FCC-ee measurements or that would be beneficial in view of improving the performance-\nto-cost ratio?\nIn the next few years, regular workshops will be organised with the DRD Collaborations, to eval-\nuate possible design choices for detector subsystems, including their simulation, optimisation, demon-\nstrators, and key engineering aspects, as well as to foster interactions and cross-fertilisation between\ninterested institutes. Issues ranging from low-level readout architectures and engineering resources to\nlarger-scale system integration, full-simulation-based optimisation, and high-level event reconstruction,\nwill be addressed. The goal will be to quantify the cost and performance (including flexibility aspects) of\neach specific design choice, always retaining a physics-driven perspective, towards the timely delivery\nof conceptual design reports and full detector concepts proposals shortly after 2030. Reaching this am-\nbitious goal will require an appropriate re-organisation and a significant injection of more (human and\nfinancial) resources in the project.\n164\n\n7\nFCC cavern infrastructure\n7.1\nIntroduction\nFour experiment caverns are foreseen at FCC. During the FCC-ee operation, all these caverns will house\ngeneral-purpose detectors, with various degrees of specialisation, aimed at exploiting the full physics\npotential of this collider. During the FCC-hh operation, a layout similar to the present LHC is foreseen:\ntwo caverns will house general-purpose detectors that cover the entirety of the proton-proton physics\nprogramme, similar to ATLAS and CMS, and the other two will house detectors more specialised to\ndedicated physics topics, on the model of ALICE and LHCb. It would be highly inefficient, impractical,\nand costly to modify the caverns at the end of the FCC-ee phase. A common cavern infrastructure that\nwill serve equally well FCC-ee and FCC-hh must therefore be designed ahead of time.\nMost aspects of the FCC experimental cavern infrastructure are defined by requirements for the\nFCC-hh detectors, given their much larger size, the extreme radiation environment and related shielding,\nas well as larger magnetic stray fields. A reference detector, conceived as a general-purpose detector\nable to fully exploit the physics potential of FCC-hh, was studied in detail in Ref. [748]. A cavern size\nof L66 m \u00d7 W35 m \u00d7 H35 m with a shaft diameter of 18 m is deemed sufficient to install and house\nsuch a detector. The cross section of this cavern is very similar to that of the ATLAS experiment. Two\ncaverns of this size and two smaller caverns for the specialised experiments have therefore been assumed\nto define the corresponding civil-engineering operations and costs.\nTo evaluate their size, the two smaller caverns were assumed to house a detector specialised in\nB-physics, on the one hand, and a detector specialised in heavy-ion physics, on the other. Preliminary\nstudies [749, 750] have shown that a detector with transverse and longitudinal sizes not significantly\nlarger than the dimensions of LHCb (10 m and 20 m, respectively) would have the same acceptance and\nresolutions as LHCb, in spite of the much larger energies. A more compact design, inspired from that of\nthe BTeV detector [751], would allow a two-arm spectrometer to be built in the same spatial envelope.\nSimilarly, a heavy-ion experiment would need to be more granular and have better performance, but\nits overall size would not have to be different from that of ALICE (the ALICE cavern dimensions are\nL53.5 m \u00d7 W15.5 m \u00d7 H22.7 m).\nA transverse cavern size similar to that of the CMS experiment would therefore be sufficient\nfor both specialised detectors, leading to a L66 m \u00d7 W25 m \u00d7 H24.5 m cavern and a shaft diameter\nof 15 m for those two caverns. Such four caverns will definitely be more than adequate to house the\nFCC-ee detectors, which have typical diameters and lengths of 12\u201314 m. The possibility of detector\nopening for maintenance in these caverns, especially the smaller ones, still need to be fully understood\nand ascertained.\nIn the following sections, the specifications and the layout of the FCC-hh reference detector are\nsummarised, and more details on the cavern layout are given.\n7.2\nThe FCC-hh reference detector\nThe FCC-hh parameters allow the direct exploration of particles with mass up to around 40\u201350 TeV [283],\napproximately an order of magnitude over the LHC sensitivity to heavy resonant states. During its life-\ntime, the FCC-hh is also expected to produce trillions of top quarks and tens of billions of Higgs bosons,\nallowing for rich SM precision measurement campaign [10,752] and rare-decay study programme [259].\nMost importantly, FCC-hh is the only machine under study today that can provide a few per-cent level\nmeasurement of the Higgs boson self-coupling [83,752].\nAn experimental apparatus that operates at FCC-hh must, hence, perform optimally on two main\nfronts (see Ref. [748] for a thorough discussion). Firstly, physics at the EW and Higgs boson scale will\nproduce objects in the detector with momenta in the pT range 20\u2013100 GeV; the LHC detectors were built\nto produce an optimal response in such an energy range. Secondly, a new regime, at the energy frontier,\nwill be characterised by the energy scale of decay products originating from highly boosted SM particles\n165\n\nand heavy resonances (potentially with mass as high as 50 TeV). An FCC-hh detector must therefore be\ncapable of reconstructing leptons, jets, top quarks, and Higgs and W/Z bosons with momenta as large as\npT = 20 TeV. In short, the detector must provide accurate measurements in the full energy range between\ntens of GeV and tens of TeV.\nFig. 119: Schematic of the FCC-hh reference detector.\nFigure 119 shows the layout of the FCC-hh reference detector. This detector concept does not rep-\nresent the final design, but rather a concrete example that suits the performance and physics requirements,\nand allows the identification of areas where dedicated further R&D efforts are needed. The detector has\na diameter of 20 m and a length of 50 m, comparable to the dimensions of the ATLAS detector but much\nheavier. The central detector, with a pseudorapidity coverage of |\u03b7| < 2.5, houses the tracking, electro-\nmagnetic calorimetry, and hadron calorimetry, inside a 4 T solenoid with a free bore diameter of 10 m.\nIn order to reach the required performance over the 2.5 < |\u03b7| < 6 pseudorapidity range, the forward\nparts of the detector are displaced along the beam axis by 10 m from the interaction point. Two forward\nmagnet coils with an inner bore of 5 m provide the required bending power. These forward magnets\nare also solenoids with 4 T field, providing a total solenoid volume of 32 m length for high precision\nmomentum spectroscopy up to |\u03b7| \u22484 and tracking up to |\u03b7| \u22486. As an option, replacing the forward\nsolenoids with two forward dipoles is also being considered. The tracker cavity has a radius of 1.7 m with\nthe outermost layer at around 1.6 m from the beamline in the central and forward regions, providing the\nfull spectrometer arm up to |\u03b7| = 3. The electromagnetic calorimeter (ECAL) has a thickness of around\n30 radiation lengths (X0). The overall calorimeter thickness, including the hadron calorimeter (HCAL),\nexceeds 10.5 nuclear interaction lengths (\u03bb), ensuring 98 % containment of high energy hadron showers\nand limiting punch-through to the muon system. The ECAL is based on liquid argon (LAr) given its\n166\n\nintrinsic radiation hardness. The barrel HCAL is a scintillating tile calorimeter with steel and lead ab-\nsorbers that uses wavelength shifting (WLS) fibres and silicon photomultipliers (SiPMs) for the readout.\nIt is divided into a \u2018central barrel\u2019 and two \u2018extended barrels\u2019. The HCALs for the endcap and forward\nregions are also based on LAr. The requirement of calorimetry acceptance up to |\u03b7| \u22486 translates into\nan inner active radius of only 8 cm at a z-distance of 16.6 m from the IP. The transverse and longitudinal\nsegmentation of both the electromagnetic and hadronic calorimeters is \u223c4 times finer than the present\nATLAS calorimeters.\nThe muon system is placed outside the magnet coils. The barrel muon system provides muon\nidentification, stand-alone muon spectroscopy by measurement of the angle of the muon track, as well\nas precision muon spectroscopy by combining the tracker measurement with the measured space points\nin the muon chambers. The forward muon system can only provide spectroscopy if forward dipoles are\nused.\nThe reference detector does not assume a magnet yoke, i.e., there is no shielding of the magnetic\nfield. Figure 120 shows the magnetic stray field as a function of radial distance from the beamline. The\nstray field still amounts to 100 mT at the cavern wall (R = 17.5 m), which has to be considered for the\nimplementation of access structures and services. The 5 mT level is achieved at a distance of 55 m from\nthe beamline, still outside of the service cavern. Clearly, it would be more convenient to have a shield\nfor the magnetic field, but to arrive at a level of 5 mT at the cavern wall, which was the specification for\nCMS, an iron yoke of 4 m thickness would be required, weighing a total of 52 kt.\nFig. 120: Radial magnetic field for the FCC-hh reference detector, without magnet yoke. The stray field is around\n100 mT at the cavern wall, while in the service cavern (50 m from the experimental cavern wall), it amounts to less\nthan 3 mT.\nAs can be seen in Fig. 119, embedding the muon system inside a yoke of 4 m radial thickness\nwould lead to a total detector radius of around 11 m, similar to the ATLAS detector. Such a yoke is\nprobably excessive in terms of cost and construction. With the radial extent of around 10 m for the\nFCC-hh reference detector, a cavern cross section of 35 m \u00d7 35 m is appropriate. If needed, such a\ncavern could even house the magnet yoke. For illustration, Fig. 121 shows an FCC-ee detector and\nthe FCC-hh reference detector in this large cavern, while Fig. 122 shows an FCC-ee detector and a\n167\n\nFig. 121: An FCC-ee detector (left) and the FCC-hh reference detector (right) in a large cavern of 35 m \u00d7 35 m\ncross section.\nFig. 122: An FCC-ee detector (left) and the FCC-hh reference detector (right) in a small cavern of 24.5 m \u00d7 25 m\ncross section.\nspecialised FCC-hh detector of 14 m-diameter, similar to CMS, in the smaller caverns.\nIn FCC-hh, the longitudinal extent of the detector is limited by the machine elements and the\nrelated shielding. The last magnetic elements in the final focusing magnets of FCC-hh are at \u2113\u2217= 40 m\nfrom the interaction point. In order to shield these magnets from the collision debris originating from the\ninteraction point, the so-called \u2018TAS absorbers\u2019 are placed at a distance of around 35 m. The absorption of\nthese high energy hadrons produces a significant amount of neutrons that \u2018diffuse\u2019 out of this absorber,\nas can be appreciated in Fig. 123. The concrete cavern wall at z = 33 m stops these neutrons from\nentering the cavern, defining the maximum possible cavern length to be 66 m. Altogether, these basic\nconsiderations converge to a cavern size of L66 m \u00d7 W35 m \u00d7 H35 m for the FCC-hh reference detector.\n168\n\nFig. 123: Radiation load for the FCC-hh detector and the final focusing magnets in the machine tunnel.\n7.3\nFCC cavern infrastructure\nThe FCC-hh cavern infrastructure is shown in Fig. 124. Since the service cavern is at a distance of\naround 50 m from the detector cavern and between 60 and 70 m away from the beamline, the stray field\ntherein is below 5 mT (Fig. 120) and standard equipment can be placed at this location. Besides, the\nradiation shielding provided by this distance suffices to allow permanent access to the service cavern. A\nmain shaft of 18 m diameter gives access from the surface to the experiment cavern. It houses only some\nventilation pipes but no other services or elevators, and is only foreseen for the transport of equipment.\nThe personnel access and the detector services are housed in the service shaft, which connects to the\nservice cavern. Three connection tunnels, represented in Fig. 124, connect the service and experiment\ncaverns: a central one, of 10 m diameter, for services, and two others, of 5.5 m diameter, placed on each\nof the two ends of the detector. They are complemented by two evacuation tunnels, also represented in\nthe figure.\nFig. 124: FCC-hh cavern infrastructure.\n169\n\nThe principal dimensions of the FCC cavern infrastructure are summarised in Table 18.\nTable 18: Requirements and key numbers for the FCC-ee and FCC-hh detectors.\nItem\nSize of large caverns\nL66 m W35 m H35 m\nShaft diameter of large caverns\n18 m\nSize of small caverns\nL66 m W25 m H24.5 m\nShaft diameter of small caverns\n14 m\nFCC-hh reference detector diameter without yoke\n20 m\nFCC-hh reference detector diameter with yoke\n22 m\nStray field at cavern wall (R = 17.5 m)\n100 mT\nDistance for stray field < 5 mT\n55 m\nFCC-ee detector diameter\n12\u201314 m\n170\n\n8\nSoftware and computing\nEver since the launch of the FCC conceptual design study in 2014, one of the primary objectives has been\nto design and develop a unified, synergistic, and adaptable software \u2018ecosystem\u2019, to serve as a foundation\nfor all future experiments at FCC-ee and FCC-hh. With its data processing framework and all the nec-\nessary tools inspired by the advanced software of running experiments and ongoing R&D initiatives, the\nresulting ecosystem is aiming at addressing all future experiment\u2019s use cases, based on modern software\ntechnology. While this transformative approach required significant time to gain general acceptance,\nand even if the level of completeness is not anywhere close to that of running experiments, this new\necosystem is now regularly used by the FCC particle physicists in their daily work. The performance of\nsome tools, such as flavour tagging algorithms, already far surpasses that of the algorithms used for past\nlinear collider studies [753]. Needless to say, further work is needed to fully enable all studies targeted\nby the FCC-ee scientific programme. For example, the following tasks (among many other necessary\ndevelopments) were identified as priorities for the FCC Feasibility Study:\n\u2013 Proceed with the full and parametrised simulations (and their interplay) of the sub-detectors cur-\nrently considered (Section 6), including digitisation and sub-detector interchange with a \u2018plug-\nand-play\u2019 framework, towards enabling the study of the performance (Section 4) of a large variety\nof detector concepts.\n\u2013 Develop and implement the various reconstruction and analysis tools for use by all collaborators,\nreaping the benefits from LHC experience and, whenever relevant, from past linear collider studies.\n\u2013 Complete the simulation of the interaction region, also known as machine detector interface (MDI,\nSection 5), in view of the final evaluation and mitigation of beam-related backgrounds in the\ndetectors. This task includes streamlining the access to the Monte Carlo codes that simulate the\nrelevant backgrounds.\n\u2013 Provide the technology needed to improve the accuracy of the simulation of beam-related quan-\ntities (such as the beam-energy spread, crossing-angle spread, bunch length and transverse size,\nfinal state particle deflection by the colliding bunches, etc.) as well as initial state and final state\nradiation (and their interference) to match the statistical precision expected at FCC-ee, in partic-\nular at the Z pole. Ensure that these technologies are usable in all Monte Carlo generator codes\nrelevant for FCC-ee, in close interaction with the code authors.\n\u2013 Continue to drive the development of the common software framework (KEY4HEP) and common\ndata format (EDM4HEP), ensuring that they meet the requirements of FCC, both in terms of func-\ntionality and of infrastructure building, testing and deployment.\n\u2013 Evaluate the need for computing resources and proceed with regular simulated data production.\nThe computing needs for FCC-ee are dominated by the Z-pole run, both online and offline. The\ncorresponding demands are significant, even when compared to HL-LHC. By the time FCC-ee\noperations start, it will be crucial to leverage the advances and insights gained from HL-LHC,\nalso in terms of resource sustainability. Even during the next phase of the study, the needs for\nfully simulated and reconstructed event samples, and for their analysis, are potentially challenging\nand require detailed identification, evaluation, and purchase of the necessary computing resources.\nCoordination with resource providers, which include CERN, WLCG grid sites involved in FCC\nresearch, and HPC centres, is required to identify ways to guarantee access to these resources.\n\u2013 Last but not least, provide the users with detailed documentation and regular pedagogical tutorials,\nas has been the case in the past decade.\nThis chapter reviews the progress made towards achieving the tasks listed above. The results\npresented and discussed reflect the collaborative efforts of the \u2018Software and Computing work package\u2019,\nin conjunction with other work packages within the FCC PED feasibility study. A key factor in this\nprogress has been the strong software core team at CERN, which provides the overall vision, delivers the\ndaily technical coordination, and ensures the timely development of essential common tools.\n171\n\n8.1\nThe FCC software ecosystem\nDuring the FCC feasibility study, the focus has been to deliver the components deemed essential to meet\nthe challenges of FCC-ee and to assess the physics potential of the proposed experimental infrastructure:\na comprehensive suite of e+e\u2212event and beam-background generators; a proper handling of the com-\nplex interaction region and associated backgrounds; an infrastructure that facilitated the implementation\nof detector subsystems and detector concepts (i.e., their geometries, their simulation, and the develop-\nment of versatile reconstruction algorithms); and tools for event analysis, visualisation, and resource\nmanagement. The corresponding workflows are illustrated in Fig. 125.\nFig. 125: Workflows to be supported during the project design and FCC Feasibility Study.\nBecause this ambitious plan required human resources far beyond those available during this phase\nof the project, a proposal was made to other e+e\u2212particle physicist communities to join forces and\nexplore the possibility of developing a common software solution that could be adapted to the needs of\nall collider and detector geometries. Based on the initial FCC software framework developed during\nthe Conceptual Design Study, nicknamed FCCSW, and driven by the belief that the high-energy physics\ncommunity was ready to further expand the number and role of shared components between experiments,\nthe KEY4HEP initiative was launched after two founding workshops held in 2019 and early 2020 [754,\n755].\nLike any other large-scale software development, KEY4HEP is inherently a collaborative effort.\nIt builds on the experience of the LHC experiments, is integrated with community R&D projects, and\nmaximises the reuse of established solutions and packages, allowing experiments to benefit from existing\ncommunity developments. Notable examples include the common core framework GAUDI [756]), de-\nveloped and used by LHCb and ATLAS following the positive experience of BELLE, the DD4HEP [757]\nR&D project for detector geometry, and other well-known packages like ROOT [758], GEANT4 [759],\nor PODIO [760]. By leveraging and contributing to these experiment-independent software packages, the\nKEY4HEP initiative aims at fostering a broader ecosystem of HEP software, enhancing collaboration and\ninnovation across the field.\nAfter recalling the main concepts of KEY4HEP in Section 8.2, the current status in each of the main\nareas is summarised in the following sections: common event data model (Section 8.3); event generators\n(Section 8.4); parametrised (Section 8.5) and full (Section 8.6) simulation; digitisation (Section 8.7) and\nreconstruction (Section 8.8); event analysis (Section 8.9); visualisation (Section 8.10); and resources\n(Section 8.11).\n172\n\n8.2\nThe main components of KEY4HEP\nThe KEY4HEP ecosystem has been designed to address core requirements common to all experiments\nin a sufficiently robust manner, while allowing specific extensions to meet individual demands. High-\nenergy physics data processing consists of several basic components that need to be chosen carefully, the\nmost important of which are listed below.\n1. A data processing framework provides the structure for integrating and steering all other com-\nponents. For example, past linear collider studies used the MARLIN [761] framework for many\nyears. In KEY4HEP, GAUDI [756] was chosen because of its widespread adoption by the LHC\nexperiments, its broader user and developer communities, and its recognised potential for future\nevolution, which includes support for accessing heterogeneous resources, accommodating differ-\nent architectures, and enabling task-oriented concurrency.\n2. A detector geometry description tool, chosen to be DD4HEP [757] because of its already widespread\nuse in the relevant communities. In addition to providing a comprehensive detector description for\nevent simulation, reconstruction, and analysis, DD4HEP is now also used in production by the CMS\nand LHCb collaborations. This adoption drives a consolidation and development process that is\nhighly advantageous for future experiments, in particular in critical areas, such as alignment and\ncalibration.\n3. A common event data model, called EDM4HEP (Section 8.3).\n4. An infrastructure to build, test, and deploy the required software with minimal effort, automat-\ning the installation and ensuring a consistently linked set of packages with correct dependency\nresolution. The LHC Collaborations addressed this challenge independently, without converg-\ning on a unified solution. The HEP Software Foundation\u2019s packaging working group identified\nthe scientific package manager SPACK [762] as a potentially promising common solution worth\nfurther exploration for use in HEP. In line with the KEY4HEP philosophy, SPACK was evalu-\nated and successfully used to build KEY4HEP, despite certain limitations [695]. These challenges\ninclude limited support for development workflows and deployment capabilities, requiring cus-\ntom in-house workarounds, such as those required to deploy build artifacts on CERNVM-FS, the\nwidely-adopted technology for software distribution in HEP.\n8.3\nThe event data model EDM4HEP\nThe event data model defines the structures needed to describe the required event information in the\npersistent store. While, in principle, this model can be different from what is used in the transient store\nseen by the data processing algorithms, and also from algorithm to algorithm, adopting the same event\nmodel everywhere reduces the need for conversions, enhances generality, and improves interoperability.\nSince the launch of the FCC studies, the choice has been for an event data model managed by\nPODIO [760], a toolkit that generates the data model implementation from templates. With this choice,\nthe high-level description in YAML files using Plain-Old-Data (POD) simple types are separated from\nthe low-level persistency layer, which can be optimised according to the back-end. Once the required\nclasses are defined in the YAML file, the PODIO tool creates the source code automatically. The same\ntechnology has been chosen for KEY4HEP, with an event data model referred to as EDM4HEP, initially\nbased on the event data models used in past linear collider studies (LCIO [763]) and in the FCC conceptual\nstudies (FCCEDM [11]) classes, and improved from there as needed.\nThe underlying assumption is that the same event data model can be used for all types of HEP\nexperiments, which is well-suited to the integrated FCC programme, with a lepton collider followed by\na hadron collider. This requirement appears to be fulfilled by EDM4HEP, although a more definitive\nassessment will become available only when the FCC-hh investigations are extended to more use cases.\n173\n\n8.3.1\nA specific use case: LEP data in EDM4HEP\nIn the context of the LEP data preservation efforts, an initiative has been launched to migrate those data to\nEDM4HEP, in a pioneering attempt to analyse these real, non-simulated data in the FCC software ecosys-\ntem. Beyond the clear advantage of preserving the ability to extract new scientific insights from LEP data\nfor future generations, this effort has several key objectives relevant to FCC-ee. Most interestingly, LEP\nand FCC-ee share the same collision type and several centre-of-mass energies. This initiative therefore\nopens a unique opportunity to FCC physicists to gain hands-on experience with real data, thereby prepar-\ning them for future analyses within the FCC-ee scientific programme. It can also provide a platform to\nvalidate and improve simulation, reconstruction, and analysis tools, thus enhancing their reliability for\nfuture collider studies.\nA preliminary migration feasibility study is currently underway with data from the ALEPH ex-\nperiment. The project aims at establishing a conversion workflow that integrates both the experiment\nlegacy software, executed within dedicated containers with the latest operating systems and validated by\nthe experiment, and KEY4HEP-based applications. The initial approach involves extracting data at the\nanalysis level26 into an operating system-agnostic ASCII format, which can then be used to reconstruct\nthe EDM4HEP structures for FCC analyses. Additionally, the project seeks to recreate a bookkeeping\ndatabase containing relevant ALEPH metadata.\nThe status of the project was presented in the autumn of 2024 [765, 766]. The current findings\nprovide encouraging evidence of the overall feasibility of the approach, despite difficulties in recovering\ncomprehensive documentation, retrieving detailed information about the data that are often hardcoded\nwithin the legacy software, and reconstructing detailed metadata about the data samples. These findings\nhighlight the importance of generalising this effort as part of a more structured and systematic project.\n8.4\nIntegration of event generators\nEvent generators are a crucial component of the software infrastructure in any HEP experiment, to design\noptimal data analysis strategies, evaluate detector performance requirements, and compare them with the\nresponse of different detector solutions, ultimately maximising the physics potential of the project. The\nrichness of the FCC physics programme introduces new challenges for event generators across multiple\ndimensions. The unprecedented statistical precision expected at the Z pole for FCC-ee, and the expanded\nenergy range of FCC-ee and FCC-hh, call for substantial theoretical advances (Section 3). These very\nprecise calculations need to be translated into similarly accurate, computationally efficient, and easily\nmaintainable software packages.\nMany event generators are already included in KEY4HEP. The first set of event generators was\nderived from the \u2018LCG stacks\u2019, i.e., software stacks developed and maintained in the EP-SFT group at\nCERN targeting the cases of ATLAS and LHCb. These stacks are, however, more and more used by\nnon-LHC projects, and have been progressively expanded to include event generators not used at the\nLHC, such as WHIZARD [767], a general purpose event generator used for past linear collider studies.\nToday, KEY4HEP includes an extended set of generic event generators, able to cover most of the initial\nneeds of future projects, such as PYTHIA8 [768].\nThe increasing interest for FCC-ee has brought in the need for more specific and more accurate\nevent generators. State-of-art generators for high-energy e+e\u2212collisions, however, date from the LEP\nera and have been minimally maintained since. One of the first tasks to be addressed in the FCC fea-\nsibility study was the recovery of the still very relevant LEP event generators, such as KKMC [769],\nBHLUMI [770], and BABAYAGA [771]. The generators and related tools available in KEY4HEP at the\ntime of writing are listed in Table 19.\n26For ALEPH, the initial focus is on the MINI format [764] however, the methodology under development is designed to be\nadaptable and could also be extended to the more comprehensive DST data format.\n174\n\nTable 19: List of generators and related tools available in KEY4HEP at the time of writing. Most of the generators\nare available in the upstream SPACK repository; the ones added by the KEY4HEP-SPACK repository are indicated\nwith an asterisk.\nGenerators\nBABAYAGA*\nBAURMC\nBHLUMI*\nCRMC\nEVTGEN\nGENIE\nGOSAM\nGUINEA-PIG*\nHERWIG3\nHERWIGPP\nKKMC*\nMADGRAPH5AMC\nPHOTOS\nPYTHIA6\nPYTHIA8\nSHERPA\nSTARLIGHT\nSUPERCHIC\nTAUOLA\nVBFNLO\nWHIZARD\nGenerator tools\nAGILE\nALPGEN\nAMPT\nAPFEL\nCCS-QCD\nCHAPLIN\nCOLLIER\nCUBA\nDIRE\nFEYNHIGGS\nFORM\nHEPMC\nHEPMC3\nHEPPDT\nHOPPET\nHZTOOL\nLHAPDF\nLHAPDFSETS\nLOOPTOOLS\nOPENLOOPS\nPROFESSOR\nPROPHECY4F\nQD\nQGRAF\nRECOLA\nRIVET\nSYSCALC\nTHEPEG\nUNIGEN\nYODA\n8.4.1\nEvent generators as packages\nWithin the software ecosystem, generators are software packages that come with their own build, test,\nand deploy recipes. The recipes allow KEY4HEP to build in share installation mode, run the built-in test\nprograms, and install the binaries into a distributed shared file system (CernVM-FS).\nThe generated events need to be injected into the simulation workflow, which requires a low level\nof interoperability between the event generator and the rest of the chain, named Common Data Formats.\nThis level ensures that the applications exchange information files that are understood by all relevant pro-\ncesses, even on different hardware.27 The event generators are indeed typically stand-alone applications\nproducing files with the generated events, in ASCII or binary data format. These event data formats have\nevolved in time following the requirements set by the community and are briefly reviewed in the next\nsection. Some recent event generators offer enhanced interoperability with Callable Interfaces, i.e., an\nAPI of functions streamlining the exchange of information among various components and increasing\nflexibility. These APIs can also be used as interface to a framework, as is described in the next section.\n8.4.2\nCommon data formats\nThe data formats produced by event generators provide structures to store the lists of particles per event,\nwith their momenta and type, information relevant to the event, such as its weight(s), and information\nrelevant to the run, such as the configuration and version of the generator. Several formats serving similar\npurposes appeared in the years ahead of the LHC. Among these, STDHEP [772] and HEPEVT [773] are\nfirst attempts to create standards, a challenge that has been assumed by HEPMC [774], the latest version\nof which (version 3) includes readers for most of the available formats. The complexity of the generators\ndeveloped for LHC brought in new needs, essentially to store information about matrix elements and\nalike. They have been included in the \u2018Les Houches Event format\u2019 (LHEf). This format had initially\nbeen designed to transfer the matrix-element information to the parton shower component, but has since\nbeen used as a generic format at LHC and beyond, including FCC.\nTo handle the plethora of formats, KEY4HEP ensures that readers for all the formats required by\nthe event generators of interest are available for all the simulation chains in use, based either on GAUDI\nor with standalone applications. For GAUDI applications, such as those using the framework compo-\nnents provided by K4SIMDELPHES [775] and/or K4SIMGEANT4 [776], the readers are implemented\n27Passing information through files might impact performance. However, reading Monte Carlo events from files is not a\nlimiting factor at the LHC and will likely not be at FCC either.\n175\n\nas GAUDI algorithms and transform the input from the files into EDM4HEP structures in memory that\ncan be parsed by the next simulation algorithm. For standalone applications, such as those provided by\nK4SIMDELPHES (Section 8.5) or DDSIM (Section 8.6.1), support for the formats is implemented within\nthe applications.\nIn the context of the ongoing ECFA activities for electroweak and Higgs factories, the HEPMC3\nand EDM4HEP formats were recommended for the next versions of event generators, and the latter is\ndeemed more suitable to meet the needs of the community. These recommendations were discussed at a\ndedicated event in June 2024 [777].\n8.4.3\nConfiguration\nThe configuration of generators for Monte Carlo simulations often involves redundant efforts, as differ-\nent generators aim at the same physics processes. To streamline this process and improve efficiency, the\nK4GENERATORCONFIG [778] package provides a unified approach to generator inputs. The package,\nwhich is already included in KEY4HEP, addresses essentially two challenges: lack of standardisation\n(each generator requiring a specific input format despite simulating, in principle, the same physics pro-\ncesses), and author involvement (relying on authors to adopt a common input format is impractical, as\nthey are unlikely to change existing workflows or agree on a unified approach). The proposed solution\nconsists in the creation of a master input card defining the required parameters and configuration for\nsimulations, which is then converted by a dedicated Python module into generator-specific runcards,\nensuring compatibility across different MC tools. This approach will automate the creation of inputs\ntailored to each generator while maintaining consistency with the master card.\nThe targetted benefits are reproducibility and error minimisation, as a unified configuration pro-\ncess inherently reduces discrepancies and manual errors in input preparation, and minimises the potential\nfor mistakes that can arise from manual handling of generator-specific configuration cards. The solution\nalso provides a way to improve legacy preservation, as the system also supports the older \u2018LEP era gen-\nerators\u2019, ensuring continued usability, even when there is no active development by the original authors.\nAn initial set of generators has already been integrated in the system and an infrastructure has been\nset up to enable running and comparing benchmarks of the tools. A status report was presented at the 3rd\nECFA workshop, in October 2024 [779].\n8.5\nParametrised simulation\nThe DELPHES parametrised simulation toolkit [780] is integrated into KEY4HEP. By applying resolu-\ntion and efficiency functions to generator-level objects, DELPHES offers a high-level approximation of\nthe detector response in a highly flexible and lightweight tool. Its capabilities encompass the propaga-\ntion of charged (and neutral) particles in a magnetic field, the modelling of electromagnetic and hadronic\ncalorimeters, and the parametrisation of muon identification efficiencies. Basic elements like charged-\nparticle tracks and calorimeter energy clusters are reconstructed from the simulated detector response. A\nsimplistic particle-flow reconstruction combines tracks and calorimeter information to form a list of par-\nticle candidates in a global event description. These particles are then used as input to form higher-level\nobjects such as isolated leptons, jets, and total/missing energy and momentum. Although the physics per-\nformance obtained from DELPHES represents the best that could be achieved with nominal sub-detector\nresolutions, this tool shows a reasonable agreement with the more detailed full simulation, as discussed\nin Section 4.10, and can thus be used to establish detector requirements and to provide rather robust\nestimates of the FCC-ee physics potential.\nThe DELPHES toolkit was enhanced with several new features, which include an algorithm recon-\nstructing the charged-particle track parameters and covariance matrix for arbitrary tracking geometries;\na module for deriving time-of-flight measurements; and a tool that parametrises the number of ionisation\nclusters associated with the trajectory of a charged particle in a gaseous detector, based on simulations\n176\n\nfrom GARFIELD [711]. These tools have been incorporated into the central DELPHES package and are\nemployed, in particular, to train a graph neural network for jet flavour identification [781]. Illustrating\ndistributions produced with these new modules are shown in Fig. 126.\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nMomentum (GeV)\n7000\n8000\n9000\n10000\n11000\n12000\n13000\ntime of flight [ps]\n\u03c0\nK\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nMomentum (GeV)\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n2400\n]\n-1\ndN/dx [m\n\u03c0\nK\n1\n10\n2\n10\nMomentum (GeV)\n0\n2\n4\n6\n8\n10\n12\n14\n significance\ntime of flight\ndN/dx\ncombined\nFig. 126: Particle identification metrics for charged kaons and pions emitted at \u03b8 = 90 \u25e6, as derived from the IDEA\ndetector DELPHES parametrisation. From left to right, the plots display, as a function of the particle momentum,\nthe time-of-flight in the tracker, the number of ionisation clusters per unit length for a gas mixture of 90% He and\n10% Isobutane, and their respective or combined separation power in terms of standard deviations.\nA DELPHES configuration card simulating the expected performance of the IDEA detector con-\ncept, with a detailed layer-by-layer description of its tracking system, has been implemented and added\nto the central repository [782]. An alternative version of this parametrisation, featuring a full silicon\ntracking system, was also developed to emulate physics performance closer to what is anticipated from\nthe CLD detector concept. The integration of CLD calorimeter parametrisations into this card is under\ndevelopment. More information on these parametrisations can be found in Ref. [618].\nThe DELPHES integration into KEY4HEP is achieved through the K4SIMDELPHES package [775],\nwhich wraps the core components of DELPHES and adds the functionality to convert its output into\nthe EDM4HEP data model. Several command-line tools (DELPHES*_EDM4HEP) simplify the use of\nthese extensions in stand-alone mode, while the K4SIMDELPHESALG GAUDI algorithm enables full\nintegration of DELPHES simulations within a KEY4HEP workflow, allowing users to benefit from features\nsuch as the generator functionalities described in Section 8.4.\nTo enhance flavour physics studies in parametrised simulations, an interface between PYTHIA8\nand EVTGEN is implemented, and is fully integrated with the DELPHES applications. This interface\nenables efficient generation of background contributions in regions of phase space where specific signals\nare expected (e.g., rare hadron decays or long-lived particles). Users must apply a posteriori normalisa-\ntions \u2018manually\u2019 to ensure consistency between the generated number of events and the reported cross\nsections.\n8.6\nFull simulation\nSome applications require simulations with a higher level of detail than DELPHES. For example, R&D\nefforts and physics analyses that access detector-level information demand a more detailed description\nof the detector geometry and response. To address these needs (and, incidentally, to validate the detector\nparametrisation outlined in the previous section), a detailed modelling of all the (sub-)detectors consid-\nered for FCC is actively being developed. This section provides an overview of the current status of\ngeometry implementation, along with existing examples of full detector configurations using different\ncombinations of sub-detectors.\n177\n\n8.6.1\nDetector description and simulation strategy\nThe DD4HEP toolkit [757] (Section 8.2) is used to model FCC detector geometries. This modern commu-\nnity standard hides the geometry complexity and allows high-level aspects (such as sub-detector dimen-\nsions, shape and materials, or the list of sub-detectors to be combined into a complete detector concept)\nto be configured by non-expert users with simple XML (\u2018compact\u2019) files in a flexible plug-and-play ap-\nproach, crucial for detector optimisation efforts. This approach allows the optimisation of (sub-)detector\nvariants without the need for recompilation and without an in-depth understanding of the technical de-\ntails of the geometry implementation. It is essential, however, that the developer of the C++ detector\nbuilder (also called \u2018detector driver\u2019) incorporates the necessary prescriptions and safeguards to ensure\nthat a \u2018sane\u2019 geometry be implemented under all circumstances. Several tools are available in DD4HEP\nto validate the resulting geometries, such as checks to ensure that detector volumes do not overlap.\nWhile implementing a completely new sub-detector geometry is a more complex task, numerous\nexamples and a wealth of community expertise greatly facilitate this process. Adding the newly created\nsub-detector to an existing concept, or building a new concept using existing sub-detectors, is straight-\nforward using the \u2018master\u2019 XML files that manage the list of sub-detectors and their envelope dimensions.\nThis, again, assumes that the C++ drivers are designed to adapt dynamically to changes in outer envelope\ndimensions. A policy has been set in place to document XML parameters that require additional prescrip-\ntions before modification, complementing the sanity check tools to reduce the risk of creating ill-defined\ngeometries.\nThe DD4HEP framework is also well-suited for the modelling of individual modules used in test\nbeams. Implementing test-beam geometries into this framework for the upcoming R&D activities would\nbe highly advantageous, as it would provide a basis for preparing complete sub-detectors, in view of their\nintegration into full detector concepts. Occasionally, the availability of complete sub-detector geometries\npredates the test-beam campaigns. In such cases, R&D teams could simplify and adapt the more complex\nfull geometry to create the individual module.\nThe GEANT4 simulations are run on these models through the DDSIM tool provided by DD4HEP.\nThis tool provides many functionalities that help the simulation configuration through command-line\narguments or Python steering files (or a combination thereof), and can be run with simple particle guns or\nby providing input files containing the particles from Monte Carlo generators. Most common formats are\nsupported: HEPMC(3), HEPEVT, STDHEP, and the so-called \u2018pair\u2019 files produced by GUINEAPIG++\n(in addition to the LCIO format). The output format can be EDM4HEP, LCIO, or the DD4HEP native\nformat.\n8.6.2\nSub-detector models\nSub-detector geometries are available in the K4GEO GITHUB package [783]. The currently available\nDD4HEP drivers, relevant for FCC-ee, are listed below. A more thorough description of their implemen-\ntation details can be found in Ref. [618].\n\u2013 Beam-pipe and related MDI components. Two different models exist: one based on \u2018native\u2019\nGEANT4 shapes with a simplified geometry and the other exploiting the ability of DD4HEP to\ndirectly import the CAD-based technical drawings, thus providing a much higher level of detail at\nthe expense of poorer computing performance.\n\u2013 Vertex detectors. The driver used to model, for instance, the CLD vertex barrel detector, builds\nan arbitrary number of layers made of staves parallel to the z axis with two different materials (one\nfor the sensitive layers and the other for the support). The endcaps are constructed with simple\noctagonal plates perpendicular to the z axis, made of an arbitrary number of slices with different\nthicknesses and materials. Another detector builder was recently developed to model the IDEA\nvertex detector. This driver offers a higher level of detail: it accounts for non-sensitive edges of\n178\n\nthe modules and includes staves/petals internal structures, together with support components. A\nswitch in this driver allows the modelling of a geometry with almost support-free curved sensors.\n\u2013 Main Trackers. Two versions are available: the former modelling a full silicon tracker, following\nan approach similar to that of the CLD vertex detector builder, described above, and the latter\nmodelling a full stereo gaseous drift chamber. The latter features hyperboloid layers and twisted\ntubes to emulate the cell volume hosting the sense and field wires. The full geometry is built with\na handful of user-provided parameters: global dimensions, number of (super)layers, number of\ncells in the first layer and its increment from one layer to the next, etc. A third model, describing\na straw-tube tracker, is under preparation.\n\u2013 Dedicated particle identification detector. A first version of the Array of RICH Cells (ARC)\nconcept, described in Section 6, is implemented. The driver builds both the barrel and the endcaps,\nand omits, for now, the cells in the transition region, given their higher complexity. This detector\nbuilder includes the radiator gas and aerogel, the mirrors, the sensitive silicon sensors, the cooling\nplates and the outer vessel. The mirror positions and inclinations are set according to Ref. [634].\nThe material budget of the full sub-detector implementation corresponds to approximately 5% of\na radiation length and can be easily tuned.\n\u2013 Calorimeters. The following drivers are available: SiW luminosity calorimeter, noble liquid\ncalorimeter with inclined absorber/readout planes, scintillating tile calorimeter (\u2018tileCal\u2019), and two\nfibre dual readout calorimeters, one with a capillary tube-based geometry and one where the fi-\nbres are directly inserted into metallic towers. A detector driver modelling a segmented crystal-\nbased dual readout calorimeter is being integrated in KEY4HEP. The simulation of dual readout\ncalorimeters is especially challenging, in particular because of the number of scintillating photons\ngenerated, and requires special prescriptions [618]. The high-granularity calorimeters proposed\nfor CLD are built with the generic driver described below.\n\u2013 Generic detector builders. Some drivers have been designed generically to serve multiple pur-\nposes. For example, GENERICCALBARREL_O1_V01 and GENERICCALENDCAP_O1_V01, are\nused, e.g., to build the ECAL, HCAL, and muon system of CLD. These drivers arrange user-\ndefined layer sequences, either radially or along the z-axis, forming a polyhedron with a customis-\nable number of sides, set in the compact file. Another example of a generic detector builder is\nMUONSYSTEMMURWELL_O1_V01, which defines stacks of layers made of user-defined tiles\n(e.g., PCB\u2019s) and also provides flexibility on the number of sides, as illustrated in Fig. 127. This\nflexibility is an appealing feature at this stage of the project, as it allows the software implementa-\ntion to smoothly and rapidly adapt to detector R&D choices. Unlike the formerly described drivers\nbuilding the CLD calorimeters and muon system, MUONSYSTEMMURWELL_O1_V01 allows the\nuser to define some overlap between the tiles (e.g., to account for their possibly non-sensitive\nedges) and stagger each side of the polyhedron to ensure a fully hermetic coverage. This construc-\ntor is used to model the IDEA \u00b5RWELL-based muon system and pre-shower sub-dectectors.\n8.6.3\nFull detector models\nThe availability of these sub-detector geometries along with the plug-and-play philosophy of DD4HEP fa-\ncilitates the creation and implementation of full detector concept alternatives. These models are hosted in\nthe K4GEO GITHUB package [783] and take the MDI components (beam-pipe, compensating solenoids,\nshields, LumiCal, etc.) from a central place, to ease the software maintenance. Pictures of three detector\nconcepts, as they are currently implemented in DD4HEP, are shown on Fig. 128.\nA complete model of the CLD detector is available [784]. The main change with respect to the\noriginal geometry is the adaptation of the vertex detector to the most recent beam-pipe design (Sec-\ntion 5). Based on this model, an alternative option including a dedicated PID detector, named ARC, was\nprepared. This version of CLD features a reduced-size outer tracker in order to fit the ARC between the\n179\n\nFig. 127: Illustration of the flexibility provided by the detector driver that builds \u00b5RWELL-based muon systems:\ndifferent barrel implementations with 6, 12, and 4 sides (from left to right). The grey layers represent the sensitive\ndetector components, while the return yokes are shown in red.\nFig. 128: Pictures of three detector concepts (ALLEGRO, CLD, and IDEA) implemented in DD4HEP.\nmain tracker and the (unchanged) ECAL, as shown in Fig. 129. This enables comprehensive studies to\nevaluate the benefits of enhanced particle identification capabilities, as well as any potential impact on\nthe performance of the particle-flow reconstruction.\nA first complete model of the IDEA detector is also available. It consists of a detailed inner ver-\ntex detector with straight staves; a full stereo drift chamber with all wires included; a silicon wrapper\nconstructed with the same driver as that used for the inner vertex detector;28 a solenoid and an end-plate\nabsorber described as simple cylinders with a thickness 0.75%X0; a pre-sampler; a fibre-based \u2018mono-\nlithic\u2019 dual-readout calorimeter; and a \u00b5RWELL-based muon system. Based on this implementation,\nan alternative version of the IDEA detector, featuring an additional crystal-based ECAL, is now being\ndeveloped.\nThe ALLEGRO detector concept is implemented as follows: a tracking system (inner vertex de-\ntector, drift chamber, and silicon wrapper) directly imported from the IDEA implementation; a noble\nliquid ECAL inside a lightweight cryostat whose outer wall also accounts for the solenoid material bud-\nget; and a tile HCAL, placed inside a muon system place-holder made of two nested layers of sensitive\ncylinders.\nThe GEANT4 toolkit is used to simulate the passage of particles through matter. Its raw simulation\noutput requires further processing to create data objects suitable for analysis. The processing workflow\nincludes two key stages: digitisation, which transforms simulated detector hits into realistic detector re-\nsponses, and reconstruction, which interprets these responses to identify and characterise the underlying\n28With the options of changing the definition of the staves in the compact file to have sensitive components on both sides,\nusing strips instead of pixels, and a reduction in the level of details being modelled to reach a computationally affordable\ndescription.\n180\n\nFig. 129: Picture of the CLD detector concept model with enhanced particle identification capabilities. This variant\nof CLD includes the ARC sub-detector between the outer tracker and the ECAL. The other subsystems (HCAL,\nmuon chambers, etc.) are present in the model but not shown here.\nphysics objects. The next two sections provide an overview of the capabilities currently available in the\ncentral FCC software, with ongoing developments and future directions. A more detailed discussion can\nbe found in Ref. [618].\n8.7\nDigitisation\nFor silicon trackers and muon systems, a straightforward and generic digitisation approach is currently\nimplemented. The simulated hit positions and time are smeared with Gaussian uncertainties, keeping\nthe digitised hit position within the sensitive volume and applying an optional time window cut. The\nspatial smearing is performed in the local coordinate system of the sensitive module and allows for two\ndistinct Gaussian widths. For strip-based sensors, the position along the strip direction is set in the\nmiddle of the sensor and the related uncertainty is defined as the wafer length divided by\n\u221a\n12. This\nsimple method allows a flexible and generic software implementation, making it applicable to various\nsub-detector types. An enhanced digitisation model that includes, in particular, charge-sharing effects, is\nunder development. This new model will enable more detailed studies and simulations.\nThe digitisation of the drift chamber sub-detector follows a similar methodology. In this case, the\ntwo variables subject to Gaussian smearing are the distance from the simulated hit to the nearest wire\nand the position along the wire. In addition to producing digitised hits with smeared positions, the algo-\nrithm calculates the associated number of interactions (clusters) and the number of electrons emitted per\ninteraction. This calculation is based on a parametrised model using the GARFIELD++ simulation frame-\nwork [785]. A more detailed drift chamber digitisation, which will include the generation and analysis\nof full waveforms, is under development. This evolution will enable more reliable assessments of, e.g.,\nthe impact of beam-induced backgrounds on the drift chamber occupancy and on track reconstruction\nefficiency and purity.\nA different approach is required for calorimeters: the simulated energy deposits corresponding\nto the same readout cell are aggregated and a calibration factor (sampling fraction) is applied alongside\nother specific processes, as outlined below.\n\u2013 The digitisation of CLD calorimeters is based on the original ILCSOFT implementation, interfaced\nwith GAUDI wrappers and data format converters to EDM4HEP. This implementation supports\nper-layer sampling fractions, operates in both analogue and digital modes, and includes zero-\nsuppression emulation.\n\u2013 The ALLEGRO calorimeter digitiser is a \u2018KEY4HEP-native\u2019 solution (i.e., a GAUDI algorithm with\nEDM4HEP input and an output that does not require wrappers or converters) that handles radial-\n181\n\nlayer-dependent calibration, zero suppression, noise addition, and cross-talk emulation. The cross-\ntalk emulation is performed in two steps: (1) the derivation of a detector-specific map that encodes\nwhich cells \u2018communicate\u2019 with each other and the associated cross-talk coefficients (sourced\nfrom measurements for the ALLEGRO ECAL); (2) the detector-agnostic energy distribution across\ncells, following the guidelines set by the map.\n\u2013 The fibre dual-readout calorimeter digitiser accurately emulates the response of the silicon pho-\ntomultiplier, generating full waveforms based on photon arrival times using the SIMSIPM [786]\npackage. This digitisation depends on parameters that can be obtained from vendors\u2019 data sheets\nand accounts for a variety of effects, including wavelength-dependent efficiency, dark counts, after-\npulsing, and cross-talk.\n8.8\nReconstruction\nThe EDM4HEP digitised objects produced by the algorithms mentioned in the previous section are sub-\nsequently processed through various reconstruction routines. Two tracking solutions are currently used\nin the FCC software: one based on a conformal tracking implementation from ILCSOFT [787], suitable\nfor silicon tracking systems, and another based on a graph neural network [659], successfully applied\nto both silicon and gaseous trackers, as detailed in Sections 4.10 and 4.3.3. The graph neural network\nsolution currently covers only track finding; ongoing developments will extend its capabilities to track\nfitting. Other \u2018classical\u2019 approaches are also investigated, both for gaseous and silicon-based tracking\nsystems.\nCalorimeter clustering can be performed using three different KEY4HEP-native solutions: one\nbased on a fixed-size sliding window for finding local maxima, another based on ATLAS topological\nclustering [788], and the third using the CMS CLUE algorithm, which has been ported to KEY4HEP in\nthe K4CLUE package [789]. A fourth option for calorimeter clustering, used by the CLD detector, is\navailable through the particle flow algorithm described below.\nA particle-flow-based global event reconstruction is available in the PANDORASDK [661] frame-\nwork, which is integrated into ILCSOFT and accessible in KEY4HEP via wrappers and converters. A\ncomplete particle-flow-algorithm sequence is in place for the CLD detector, adapted from the ILD so-\nlution [660]. While this implementation already demonstrates excellent performance [784], further op-\ntimisation is underway. The particle flow approach is expected to deliver the highest performance, in\nparticular for jet energy and angular resolutions, making it the preferred tool for detector optimisation.\nConsequently, dedicated efforts are focused on several key areas:\n\u2013 re-implementing the interface to PANDORASDK as a GAUDI algorithm with EDM4HEP input and\noutput, eliminating the reliance on data converters and wrappers;\n\u2013 developing PANDORASDK sequences for the ALLEGRO and IDEA detectors, adapted to and\nexploiting the specificities of their trackers and calorimeters;\n\u2013 implementing machine learning-based particle flow algorithms using graph neural networks, as\ndescribed in Ref. [615].\nThe clustering of EDM4HEP::RECONSTRUCTEDPARTICLECOLLECTION particle-flow particle can-\ndidates into jets is managed through a standard interface to the FASTJET [790] package. An additional\nFASTJET-based interface is available for the clustering of calorimeter-only objects and can be used for\ndetector setups that do not yet provide reconstructed particle candidates.\nSeveral particle identification algorithms are, or will be, developed to further extend particle-\nflow capabilities with additional particle identification algorithms. These algorithms include a RICH\npattern recognition [791] for the ARC detector (Section 6.7.2), a cluster-counting technique for gaseous\ntrackers with dN/dx measurement (Section 6.6), and a jet flavour tagging using the deep-learning-based\nParticleNet [792] model. The latter is already implemented within the analysis framework described in\n182\n\nthe next section and is being migrated to a GAUDI algorithm for integration into the central reconstruction\nchain.\n8.9\nAnalysis tools\nTo maximise synergies and enhance the productivity of the FCC particle physicist teams, the analysis\ntools are centrally developed and maintained in KEY4HEP. The samples generated for FCC studies are\nstored using the ROOT-based EDM4HEP data model, both for the parametrised and full simulation work-\nflows. Since this data model is built with the PODIO library, EDM4HEP files can be analysed using the\nautomatically generated helper methods (Section 8.3) in C++ or through the associated PYTHON bind-\nings. Although this is not the intended usage, those files can also be processed using \u2018plain\u2019 (PY)ROOT,\ni.e., without going through the PODIO layer. A third solution, relying on RDATAFRAMES [793], is avail-\nable through KEY4HEP. This package, called FCCANALYSES, has been central to most of the physics\nanalyses presented in this report and is described below.\nThe FCCANALYSES package equips analysers with a comprehensive and efficient toolkit built\naround RDATAFRAME.\nBy leveraging the RDATAFRAME framework, it provides automatic multi-\nthreading, with object relations from EDM4HEP maintained in a structured tabular format through an\nRDATASOURCE instance implemented in PODIO. Event selection and high-level computations follow\nthe standard RDATAFRAME syntax, while FCCANALYSES includes a set of general-purpose functions\nfor added convenience. Samples and their metadata (cross sections, event counts, normalisation fac-\ntors, etc.) are managed via JSON files, with centrally-produced samples browsable through a web inter-\nface [794] and available on EOS. A plotting utility facilitates process normalisation, stacked histograms,\nand background vs. signal comparisons. In FCCANALYSES, histograms can be produced directly from\ninput samples in a single step, but a \u2018staged\u2019 workflow, allowing resource-intensive steps to be isolated\nfor efficiency, is also supported. To enhance analysis capabilities, FCCANALYSES provides additional\nfeatures, including the following ones.\n\u2013 Job submission through HTCONDOR [795] to CERN batch system.\n\u2013 Jet clustering via FASTJET [790] and functionalities to perform jet-parton matching.\n\u2013 Machine learning integration using ONNX [796], TMVA [797] or XGBOOST [798].\n\u2013 Flavour tagging with the deep-learning based PARTICLENET [792] model.\n\u2013 Automated yield table production for arbitrary cut-flows.\n\u2013 Direct creation of ROOT files and associated data cards in a format suitable for the COMBINE [799]\nstatistical analysis and combination tool.\n\u2013 Smearing tools to generate new object collections from existing DELPHES samples under different\ndetector performance assumptions.\nA more detailed overview is given in Ref. [618].\nIn addition to this well-established toolkit, new initiatives aim at expanding the technology op-\ntions offered to the analysers. For instance, the COFFEA [800] PYTHON-based framework, known for\nscalable, efficient processing of large HEP datasets, now supports EDM4HEP. The FCC software team is\nalso exploring future-proof solutions, acknowledging shifts in paradigms akin to the HEP community\u2019s\ntransition from Fortran to C++. In this regard, the Julia [801] language, celebrated for its speed, ease\nof use, and expressive syntax, could address the \u2018two-language problem\u2019 (i.e., the reliance on C++ for\nperformance-intensive tasks and Python for user interface). To test Julia\u2019s suitability, an EDM4HEP for-\nmat reader was developed as part of the JULIAHEP [802] project, which aims to consolidate Julia-based\ntools for HEP.\n183\n\n8.10\nVisualisation\nVisual renderings of the software processes and outputs are crucial for purposes such as debugging, vali-\ndation, physics interpretation, and outreach. A variety of related tools have been developed or integrated\ninto the FCC software ecosystem, as described below.\nTo enable visualisation of FCC events and detectors, an experiment-independent web-based event\ndisplay tool, Phoenix [803], was extended to support the EDM4HEP data model. Leveraging this technol-\nogy, a dedicated web interface, PHOENIX@FCC [804], was created to host the central versions of FCC\ndetector geometries. This interface allows users to overlay event data onto a 3D view of the detector,\nwith the flexibility to easily incorporate custom detectors. An example of an event display generated\nwith this tool is shown in Fig. 130.\nFig. 130: Visualisation of a tt event within the CLD detector, displayed using the PHOENIX@FCC web-based\nevent display.\nBeyond the FCC-specific implementation, several other tools are available for displaying detector\ngeometries and event content. These include the JSROOT web interface [805], the QT plugin integrated\nwith GEANT4 (accessible through DDSIM), and the CED event display from ILCSOFT [806].\nAnother visualisation tool was developed as part of the FCC studies, to render the content and\nrelationships between objects in EDM4HEP-based events. This tool, called the EDM4HEP Event Data\nExplorer (EEDE) [807], visualises EDM4HEP objects as boxes that display the values of their various\nfields and are connected to related objects (e.g., a calorimeter cluster will be linked to its associated\nindividual cells). The displayed content can be tuned by applying filters on the objects. Figure 131\nshows a screenshot of this tool in use, with an excerpt of a Monte Carlo generator particle tree.\n8.11\nComputing resources\nThe computing resource requirements of a project include the processing power necessary to manage the\ndata generated by its activities and the storage capacity needed to maintain those data samples at various\nstages of processing. During the Feasibility Study, the work of particle physicists has primarily focused\non \u2018offline\u2019 activities, which correspond to the workflows in Fig. 125. These activities are expected to\nremain central during the next phase of the study. An initial analysis of the FCC offline computing needs\nis presented in Ref. [808]. This section builds upon and expands that analysis, with further insights.\nThe FCC PED activities to date have primarily relied on resources provided by CERN, as dis-\nplayed in Table 20. These resources represent approximately 0.1% of those currently available to the\n184\n\nFig. 131: Visualisation of the Monte Carlo particle tree for an e+e\u2212\u2192Z \u2192bb event, generated using the\nEDM4HEP Event Data Explorer [807].\nTable 20: Resources available at CERN for FCC physics, experiments and detectors studies as of October 2024.\nThe (old) benchmark HepSpec06 (HS06) is still used to facilitate comparison with LHC numbers; for the purpose\nof this analysis, HS06 and HS23 are numerically equivalent.\nStorage on EOS\n600 TB\nfor central productions\n100 TB\nfor analysis\nProcessing power\n9000 HS06 / HS23\nCPU on lxbatch\n3 GPU\nnodes on CERN Openstack\nSome GPU\nnodes on EuroHPC (via CERN OpenLab)\nLHC experiments, and will need to substantially increase. The main purpose of this section is to give\nenough elements to provide reasonable projections of the needs, as a function of parameters that will be\nbetter defined as the project progresses. Current ideas to ensure that an adequate amount of resources is\navailable for the studies are also presented. The target timescale is that of the next phase of the study\n(2025\u20132027), possibly extending to the first years of the proto-collaboration forming phase (2028\u20132030).\nA projection to the needs of the actual Z-pole operations, in two decades from now, is also presented.\n8.11.1\nResource modelling\nReliable projections require a model for the resource needs. When discussing the computing resource\nneeds, it is necessary to treat the two main phases of the project separately: design and preparation on\nthe one hand, and data taking on the other. During the design and preparation phase, the studies are per-\nformed with simulated and test-beam data, with needs increasing with time, based on expected integrated\nluminosities that define the statistical framework, and with many moving targets and unstructured activ-\nities (such as the number and type of detector concepts, data formats, algorithms, and levels of software\noptimisation). During the collider operation, both collected and simulated data need to be processed\ncontinuously, with more stable versions of detector implementations, data formats, and core-software,\nalbeit with quasi-stable algorithms that will continue to be refined during the operations phase.\n185\n\nThe significant and sustained effort dedicated to modelling the computing resource needs in AT-\nLAS and CMS has been thoroughly documented, and has quantified both the short- and long-term projec-\ntions for the high-luminosity LHC programme. An example can be found in Ref. [809]. The most recent\nupdate is shown in Fig. 132, from the latest CMS [810] and ATLAS [811] approved figures, with similar\nreal and simulated data samples. Not surprisingly, the projected needs are shown to decrease with more\naggressive R&D efforts. In particular, past investments in R&D, software quality/performance improve-\nment, and optimal use of storage in the past decade, have proven to be critical in reducing the HL-LHC\ncomputing needs of the experiments. The projected needs are compared to the extrapolated available\ncomputing capacities under a sustainable flat budget model. From theses numbers, it is possible to derive\nthat both ATLAS and CMS will have storage needs of the order of a few EB and computing needs of the\norder of a few MHS06.29\n2020 2022 2024 2026 2028 2030 2032 2034 2036\n0\n10\n20\n30\n40\n50\nyears]\n\u22c5\nAnnual CPU Consumption [MHS06\n=55)\n\u03bc\nRun 3 (\n=88-140)\n\u03bc\nRun 4 (\n=165-200)\n\u03bc\nRun 5 (\n2022 Computing Model - CPU\nConservative R&D\nAggressive R&D\nSustained budget model\n(+10% +20% capacity/year)\nATLAS Preliminary\n2020 2022 2024 2026 2028 2030 2032 2034 2036\nYear\n1\n2\n3\nDisk Storage [EB]\n=55)\n\u03bc\nRun 3 (\n=88-140)\n\u03bc\nRun 4 (\n=165-200)\n\u03bc\nRun 5 (\n2022 Computing Model - Disk\nConservative R&D\nAggressive R&D \nSustained budget model\n(+10% +20% capacity/year)\nATLAS Preliminary\nFig. 132: Projections of CMS (left) and ATLAS (right) computing (top) and storage (bottom) resource needs for\nHL-LHC. In both cases, the demands in case of no or conservative R&D and planned or aggressive R&D are\ncompared with projections of future pledged resources. From Refs. [810] and [811]. For ATLAS and CMS, the\ndata and Monte Carlo samples have roughly the same size [812].\nThe basic concepts of resource modelling employed by the LHC experiments can be applied to\nthe FCC case, which boils down to identifying the activities and the corresponding set of objectives and\nrequired workflows. The detailed activities and objectives depend on the phase of the project, although\nmacro-activities can be present at all stages. Today, and in the near future, the identified macro-activities\ninclude data analysis, sub-detector development and optimisation, and algorithm design and optimisa-\ntion.\n29An HS06 = HEPSpec06 is a benchmark to measure the computing capacity of a Computing Element. The rule of thumb\n\u2018core = 10 HS06\u2019 is used for the hardware available (at the time of writing) at, for example, the CERN facilities.\n186\n\nData analysis\nThis activity will always be present, in all phases of the project. During the design phase, the goal is to\nstudy the potential of the project with a level of accuracy that depends on the aspect being investigated. A\nfirst feasibility study of a measurement is typically done using a parametrised simulation of the response\nof a given detector concept, to identify critical points that would require a more accurate simulation.\nParametrised (or fast) simulation is also required for an experiment during data taking, e.g., for a rapid\nexploration of large portions of parameter space. As the studies progress, the need for accuracy increases,\nwhich calls for fully-simulated and properly-reconstructed events. Therefore, the analysis activity will al-\nways bring requirements for adequate samples of parametrised and fully simulated-reconstructed events,\ntheir relative importance depending on the phase of the project. An example of a presently ongoing\nanalysis macro-activity with full simulation is discussed in Section 4.10.\nSub-detector development and optimisation\nThis activity is specific to the design phase, during which the detector response is simulated, primarily\nusing particle guns to generate particles of a specific type, within a given region of phase space. Addi-\ntionally, samples of simulated events may prove useful and serve as benchmarks for the design process.\nWhile the size of these samples is usually not enormous, they may require a higher level of detail than\nis typical for standard physics analyses, potentially resulting in large data volumes. Examples of such\nactivities are discussed in Chapter 6.\nAlgorithm design and optimisation\nThis activity is present during all phases of a project. During the design phase, a minimal set of al-\ngorithms is identified to evaluate the performance of the proposed (sub)detectors, and to subsequently\nimprove and tune their design. During later stages, when the detector design is frozen (or when the\ndetector is built), the algorithms are continuously developed for improved performance. This activity\nmakes use, in particular, of particle guns and simulated events enriched in certain topologies. Examples\nof such activities are presented in Chapter 4. Advanced AI approaches, such as ML-based tracking and\nparticle flow algorithms, are complementary to more classical approaches in both the design and produc-\ntion phases. During the design phase, they offer a rapid re-optimisation of varying designs and concepts;\nduring the production phase, they are expected to deliver better performance.\n8.11.2\nModelling resources for FCC-ee\nAt this stage, quantitative predictions are only possible for the analysis macro-activity. The necessary\nbasic ingredients are the event sizes and the event processing time. The current activities mostly use\nparametrised simulations, hereafter labelled DELPHES, for which rather complete sets of events have\nbeen produced. The numbers presented in the following are taken from the Winter 2023 production cam-\npaign. For the full simulation, some measurements have been performed with the simulation of selected\nsamples with CLD, taken as a reference. It is assumed that the event sizes and the event processing times\nscale in the same way as for DELPHES. This assumption is based on the fact that these numbers depend\nmostly on the number and type of particles, and that they affect the sizes and processing time in the same\nway in DELPHES and full simulation. The resulting event sizes and processing times are reported in\nTable 21.\nTo project the needs in the years to come, an assumption on the needs in terms of sizes of the\nsimulated samples has been made. A rule of thumb often used to get approximate values is to assume\nsimulated samples corresponding to the expected integrated luminosity at each centre-of-mass energy,\nas displayed in Table 1 of this report. Table 22 shows the corresponding needs, for one experiment, in\nterms of computing resources.\nReconstruction and analysis requirements are not included in Table 22 because of the lack of\n187\n\nTable 21: Baseline event sizes and processing times. Parametrised simulation and full simulation with GEANT4 are\ndenoted DELPHES and FULL, respectively. For FULL, the values are extrapolated from measurements performed\nwith Z \u2192qq events, under the assumptions described in the text.\nProcess\n\u221as\nSize / event\nProcessing time / event\ne+e\u2212\u2192\n(GeV)\nDELPHES (kB)\nFULL (MB)\nDELPHES (ms)\nFULL (s)\nZ \u2192qq, \u2113+\u2113\u2212\n91.18\n8.3, 1.2\n1.1, 0.16\n14, 0.5\n11, 1.6\nW+W\u2212\u2192all, \u03bd\u03bd\u2113+\u2113\u2212\n157\u2013163\n9.5, 1.2\n1.3, 0.16\n16, 0.5\n13, 1.6\nHZ \u2192\u03bd\u03bdbb, bbbb\n240\n8.9, 13\n1.2, 1.8\n15, 23\n12, 18\nZZ \u2192all\n240\n10\n1.4\n17\n13\ntt \u2192all\n365\n18\n2.3\n30\n23\nTable 22: Projected needs for the nominal integrated luminosity, for one experiment. The amount of HS06 is\nshown for a reference period of three years, i.e., roughly the duration of the next phase of the study.\nDELPHES\nFULL\nRun\nProcess\nNumber\nStorage\nCPU\nStorage\nCPU\nof events\n(PB)\n(HS06)\n(PB)\n(HS06)\nZ\nqq\n1500 G\n12.5\n2.2 k\n1650\n2 M\n\u2113+\u2113\u2212\n225 G\n0.275\n12\n40\n40 k\nW\nW+W\u2212\n60 M\n\u223c10\u22123\n0.075\n72\nHZ\nHZ\n500 k\n\u223c10\u22125\n\u223c10\u22123\n\u223c1\nVBFH\n16 k\n\u223c10\u22126\n\u227210\u22123\ntop\ntt\n500 k\n\u223c10\u22125\n\u223c10\u22122\n\u223c1\nHZ\n90 k\n\u223c10\u22126\n\u227210\u22123\nVBF H\n23 k\n\u223c10\u22126\n\u227210\u22123\nTotal\n1725 G\n13\n2.2\n1690\n2 M\nsufficient quantitative information. However, the size of the DELPHES output, designed to emulate the\nreconstruction process, can serve as a basis for estimating the reconstruction needs. While the actual\nreconstruction may require more detailed information than what is currently provided by DELPHES, it is\nunlikely to significantly impact the overall resource demands. This conclusion is even clearer for the final\nanalysis ntuples, which represent a condensed version of the DELPHES output. The processing power\nneeds are more difficult to quantify. For reference, at LEP and Belle II, the reconstruction step took\nabout 30% of the full simulation CPU time [808], which can be taken as a conservative estimate, given\nthat (opportunistic) heterogeneous resources can play a relevant role in here. The numbers reported for\none experimennt in Table 22 give therefore a reasonable estimate of the scale of the problem.30 These\nnumbers show that the computing needs for the Z run are of the same order of magnitude as those of\nATLAS and CMS for HL-LHC. For the other runs, instead, the table shows that full nominal integrated\nluminosity samples are achievable today.\n8.11.3\nMinimal baseline working scenario\nThese considerations enable the design of a minimal working scenario to serve as a baseline target. This\nscenario includes, as a minimum, full nominal integrated luminosity samples for the W, HZ, and tt\n30It should be noted that, for DELPHES, in principle the sample can be reused for a different detector concept on the fly with\nminimal use of additional processing resources.\n188\n\ndatasets, as well as \u2018sufficiently large\u2019 samples for the Z run, where the precise definition of \u2018sufficiently\nlarge\u2019 remains to be determined. Table 23 reports the values, assuming that \u2018large enough\u2019 means 100\ntimes the LEP event samples. The total values per detector and for all four detector concepts are also pro-\nvided, assuming that they have similar average demands. These numbers are not far from the resources\ncurrently available and are well within the range of what can be realistically achieved, as discussed later.\nConsequently, the baseline \u2018100\u00d7LEP\u2019 scenario appears to be a realistic and achievable target.\nTable 23: Projected needs for one experiment, for the scenario with nominal integrated luminosity samples for the\nW, HZ and tt runs, and event samples 100 times larger than the LEP samples for the Z run. The total corresponds\nto four experiments requiring the same resources. The amount of HS06 is shown for a reference period of three\nyears, i.e., roughly the duration of the next phase of the study. The totals in bold are beyond today\u2019s availability.\nDELPHES\nFULL\nRun\nProcess\nNumber\nStorage\nCPU\nStorage\nCPU\nof events\n(TB)\n(HS06)\n(TB)\n(HS06)\nZ\nqq\n400 M\n3.25\n\u223c1\n440\n475\n(100\u00d7LEP)\n\u2113+\u2113\u2212\n42.5 M\n0.05\n6.5\n7\nW\nW+W\u2212\n60 M\n0.6\n75\n72\nHZ\nHZ\n500 k\n0.0065\n1\n\u223c1\nVBF H\n16 k\n\u223c0.001\n0.25\ntop\ntt\n500 k\n0.009\n9\n\u223c1\nHZ\n90 k\n\u223c0.001\n0.2\nVBFH\n23 k\n\u223c0.001\n0.25\nTotal\n500 M\n4\n\u223c1\n530\n550\n4 experiments\n2000 M\n16\n\u223c4\n2100\n2200\nEfficiently managing limited computing resources requires a three-fold optimisation approach for\nthe software, the analysis techniques, and the workload and data management. A proactive approach\nto resource management is essential for securing ongoing support from official bodies, especially as\ncomputing needs continue to grow. The following paragraphs discuss the current (or planned) pertinent\ninvestigations.\n8.11.4\nOptimising resources: Software\nSoftware quality and efficiency improvements\nUpgrading the code quality and efficiency is fundamental, though it often involves a considerable in-\nvestment in time and expertise. By continually using the latest software versions, projects can leverage\noptimisations and new capabilities. For instance, recent updates to GEANT4 have nearly doubled the\nspeed of simulation for the ATLAS experiment, illustrating the potential performance gains achievable\nthrough modernised codebases. Moreover, new, faster simulation techniques are emerging and being\nintegrated in the software frameworks for use in production31, and may offer further efficiency improve-\nments. End-to-end fast simulation based on Machine Learning techniques are also being developed,\nwhich could provide interesting ways to test very large event samples [813].\nSelective and filtered simulation approaches\nAnother opportunity for optimisation lies in selective or filtered simulations. By applying filters at the\ngeneration stage, simulations can focus only on event components relevant to specific analyses, reduc-\n31Parts of the electromagnetic calorimeter of ATLAS are simulated with Machine Learning techniques.\n189\n\ning unnecessary computation. For example, simulating only sub-detectors relevant for a given study\ncould save substantial processing power. This strategy requires a careful balance between computational\nsavings and scientific accuracy, but could significantly improve throughput.\nLeveraging heterogeneous resources for reconstruction and analysis\nHeterogeneous computing environments, combining CPUs, GPUs, and other accelerators, offer signif-\nicant opportunities for resource optimisation, particularly for computationally intensive tasks such as\nreconstruction and analysis. This approach has already proven highly valuable at the LHC, where the\nuse of GPUs and specialised hardware for suitable tasks has improved efficiency, freeing traditional CPU\nresources for other activities. Extensive R&D programmes are underway to develop the potential of\nthese technologies in view of HL-LHC.32 Integrating these advances into the FCC software ecosystem\nto ensure seamless compatibility and optimal performance across diverse processing architectures is of\ncritical importance for the FCC project.\n8.11.5\nOptimising resources: Analysis techniques\nEnhanced interplay between full and parametrised simulation\nIn scenarios where full simulation is unnecessary, parametrised simulations, such as those provided by\nDELPHES, can produce sufficiently accurate results with far lower resource demands. Facilitating inter-\naction between full and parametrised simulations allows researchers to switch between these approaches\nas needed, optimising resource use for each stage of an analysis. Developing automated or optimised\nconfigurations for DELPHES would further support this flexibility, making it easier to adapt simulations\nbased on the specific needs of each analysis.\nAdvancing beyond traditional statistical methods\nBy default, HEP analyses rely on a straightforward rule of thumb: generating MC samples at least as\nlarge as the expected data sample. While simple, this approach is resource-intensive, particularly in\nscenarios with high data volumes and complex simulations. Alternative statistical methodologies that\nallow similar statistical power with fewer simulated events are already explored in some fast simulation\ndomains with promising results [815]; these variance reduction techniques should be further investigated\nto optimise computational resources.\n8.11.6\nOptimising resources: Workload and data management\nA home-made solution effectively supported the production on the local CERN HTCONDOR and EOS\nresources until the time of writing. The increasing complexity and scale of FCC projects necessitate a\nmore robust and distributed infrastructure. The primary requirements for the updated system include:\na centralised file catalogue to organise and track data; data replication to ensure redundancy and ac-\ncessibility across sites; and remote access capabilities to facilitate seamless interaction with distributed\nresources.\nTo address these FCC needs, ILCDIRAC, the instance of the DIRAC framework used in past linear\ncollider studies, has been adopted. This framework is widely recognised for its workload management\nand file catalogue capabilities, and is already employed by several high-energy physics experiments, such\nas LHCb, Belle II, BES III, JUNO, etc. Through this integration, the FCC Virtual Organisation (FCC VO)\nhas become part of ILCDIRAC. The CERN HTCONDOR and EOS resources have been associated with\nthe FCC VO within ILCDIRAC. In addition, steering applications tailored to FCC workflows have been\nintegrated into the framework to support specialised production needs.\n32An example is the Next Generation Trigger project [814].\n190\n\nProduction with ILCDIRAC has begun, marking significant progress in adopting the distributed\nmodel. Efforts to include external storage elements (SE) have been initiated with sites at CNAF, Bari,\nand Glasgow. While these integrations are still in the testing phase, they represent an essential step\ntowards expanding the infrastructure capacity and flexibility. This approach ensures that FCC projects\nbenefit from a scalable and distributed workload management system, ready to handle the challenges of\nfuture production and analysis tasks.\n8.11.7\nIncreasing available resources: pledged resources\nAt CERN, FCC currently obtains computing resources from quotas reserved for the \u2018Small and Medium\nExperiments\u2019 (SME) projects. These resources, while sufficient for initial activities, are limited and\ncannot realistically be increased by a large factor in the SME context.\nTo address future needs, discussions are ongoing with the WLCG and CERN resource manage-\nment teams to integrate FCC into the WLCG computational infrastructure. This integration, which\nshould begin as early as 2025, would establish a reliable framework for resource allocation and en-\nable a steady increase in computing and storage capacity over time. Current projections suggest that,\nby the end of the next phase of the study, in 2027, a tenfold increase in resources should be achievable,\nequivalent to approximately 5 PB of storage and 100 kHS06 of CPU power. These resources would be\nsufficient to support the minimal baseline \u2018100\u00d7LEP\u2019 scenario discussed earlier, while also providing\ncontingency for targeted studies requiring larger data samples.\n8.11.8\nIncreasing available resources: opportunistic resources\nTo enhance resource availability for FCC projects, leveraging opportunistic resources is a key strategy,\nwhich includes high-performance computing (HPC) facilities, national resources, and advanced devel-\nopment initiatives.\nOn the HPC front, discussions are ongoing with CERN OpenLab to exploit EuroHPC resources for\nFCC needs. The focus is on providing transparent access through the CERN OpenLab interface, which is\nbeing developed to support diverse hardware architectures, such as AMD, Intel, and ARM CPUs, as well\nas NVIDIA and AMD GPUs. Initial estimates suggest access to substantial computing resources over\nperiods ranging from six months to one year, which would support specific, time-limited studies requir-\ning intensive computational power. Investigations are underway to integrate these HPC resources into\nDIRAC, ensuring streamlined access for FCC workflows. The HPC resources are particularly suitable for\nspecialised use cases that demand intense but temporary computational efforts, such as AI and machine\nlearning (ML) developments, and physics-specific simulations or statistical studies requiring short-term\nbursts of computing power.\nResources available at individual institutes or through national departments could significantly\ncontribute to FCC workloads. These resources can potentially be included within the FCC VO through\nintegration with the DIRAC framework, enhancing the overall pool of accessible computational power.\n8.11.9\nProjecting to the Z run\nAll the above provides a basis for understanding the computing needs during the Z run. The analysis\nfocuses on storage requirements, likely to be the most critical aspect. The squares in Fig. 133 show\nthe projected FCC storage requirements for the real data collected during the Z-pole run,33 with four\nexperiments and the assumption of four identical runs in four years. Also shown are the projections\nfor simulated data with size identical to the real data (triangles), four times larger than the real data\n(stars) and ten times larger than the real data (circles). The horizontal band indicates the HL-LHC\u2019s\n33A similar situation applies to CPU needs, though it is important to consider the previously mentioned challenge of adapting\nto heterogeneous resources. Nonetheless, it is anticipated that by 2045 this issue will likely no longer be a significant obstacle.\n191\n\n2044\n2045\n2046\n2047\n2048\n2049\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nCumulative storage [EB]\n+10%/y\n+20%/y\n+15%/y\nZ run data storage projection\nZ run: data + MC ~ data\nZ run: data + MC ~ 4 x data)\nZ run data + MC ~ 10 x data\nProjection of LHC storage needs\nProjection of WLCG resources\nFig. 133: Projection of the current storage resources to the FCC-ee Z-pole run with four experiments collecting\nequal amounts of data in four successive years (squares) and varying amounts of simulated data (triangles, stars,\ncircles). The figure also includes the projected resource needs of the LHC and a hypothetical evolution of WLCG\nresources, under different scenarios for sustained annual budget increases.\nprojected storage requirements, as derived from Fig. 132 assuming that ATLAS and CMS account for\napproximately 90% of the total.\nThe storage resources required for FCC-ee data during the Z run are comparable to the projected\nrequirements of the LHC. The inclusion of simulated samples, however, will substantially increase the\nstorage demands, even in the minimal scenario, in which the simulated samples have a size similar to\nthat of the real data samples. A dedicated computing infrastructure, similar to the World LHC Comput-\ning Grid (WLCG) for the LHC, is therefore required to meet the computing demands of the FCC. As\npreviously mentioned, this could possibly be a natural extension of the WLCG. The projected storage\ncapacity of the WLCG during the years of the FCC-ee Z-pole run, under various assumptions regarding\nsustained annual budget increases, is also shown in Fig. 133. While provided for illustrative purposes\nonly, this projection suggests that a natural evolution of the current model could effectively supply the\nrequired resources.\n8.12\nHuman resources: status and needs\nThe substantial progress achieved in the software ecosystem during the FCC Feasibility Study has\ndemonstrated that a dedicated software core team at CERN is pivotal in driving and coordinating the\nmajority of FCC activities. This team has evolved over time, initially operating within the CERN EP-\nSFT group and then, in September 2024, moved to the newly-established CERN EP-FCC group. The\ncurrent workforce at CERN includes (in FTEs) 1.4 staff members, providing leadership and continuity, 3\nfellows, and 3 students (technical and doctoral). Additionally, the CERN EP R&D program has been in-\nstrumental in providing fellow support, particularly for the development and advancement of KEY4HEP,\na critical component for the FCC activities. Contributions from external institutes have increased, in\nparticular from collaborators in France, Italy, and the United States. This expanding network of exter-\nnal contributors strengthens the FCC effort by bringing diverse expertise, resources, and perspectives,\ncomplementing the core team\u2019s efforts at CERN.\nConsolidating and expanding the team is essential to sustain progress, address emerging chal-\n192\n\nlenges, and capitalise on synergies with other initiatives. To strengthen this team, efforts are being made\nto secure two additional staff positions for long-term stability and expertise; two continued fellows to\nretain knowledge and maintain operational continuity; two technical students, providing critical support\nfor development tasks and creating a pipeline of future talent. In addition, a dedicated IT contact would\nbe beneficial to foster strong relationships with the CERN IT service groups, and ensure streamlined\naccess to IT services and infrastructure critical to the FCC activities.\nThe software ecosystem central to FCC workflows, KEY4HEP, requires permanent development,\nconsolidation, and maintenance. Establishing long-term support mechanisms is crucial to ensure the\ncontinued relevance and effectiveness of KEY4HEP . Discussions with CERN EP management are un-\nderway, to secure a sustainable future for the project as it evolves from its current R&D phase into a\nbaseline activity.\n8.13\nOutlook\nBefore and during the Feasibility Study, a constant concern has been to overcome the challenges of\nlimited resources, while being able at all times to evaluate the FCC detector requirements and physics\npotential, with a robust software and computing infrastructure. It was therefore strategically decided to\nmaximize the use of already existing solutions in a common software framework, while broadening the\napplicability of common tools and frameworks to meet the evolving needs of the project. The resulting\nKEY4HEP ecosystem is now routinely used by FCC particle physicists in their daily work. To fully\nreap the rewards of such a transformative approach, it will be essential to further generalise its use, in\nparticular in the scope of the ongoing DRD efforts and, later, within the experimental Collaborations.\nThe long-term viability and adaptability of the framework will require continuous consolidation\nand harmonisation, to efficiently support the required workflows. To maximise the effectiveness of the\navailable computing resources, robust support for multi-threading must be guaranteed, and mechanisms\nto handle heterogeneous resources should be implemented wherever applicable. These efforts are closely\naligned with HL-LHC developments, making it imperative to ensure the seamless integration of these\nadvances into KEY4HEP. As KEY4HEP transitions out of the R&D phase, it will be crucial to establish\na sustainable support model with contributions from collaborating institutes.\nSignificant progress has been made in the development of full simulation tools, including the es-\nsential plug-and-play capability, but much remains to be accomplished in this domain. A critical task\nwill be the implementation of detailed signal digitisers, where the DRD teams are expected to play an\nimportant role. To consolidate the conclusions of the Feasibility Study, from beam-induced background\nsimulations to detector requirements and physics potential, the complete SIM-DIGI-RECO chain must\nbe established for all present and future detector subsystems and concepts. As new sub-detector tech-\nnologies emerge, new detector configurations, distinct from those studied during the Feasibility Study,\nwill be explored. More flexible geometry implementations and improved sub-detector interoperability\nwill be required. The generalisation of common reconstruction algorithms, e.g., for tracking, particle\nidentification, and particle-flow reconstruction, will empower the community to identify optimal detec-\ntor designs with a minimal investment of human resources. Advanced AI approaches will play a pivotal\nrole in this effort.\nFuture full simulation studies will demand a significant increase of both computing and human\nresources. Meeting these growing computational needs involves pursuing multiple avenues inspired by\nthe LHC model, with integration into the WLCG resource pool, leveraging HPC calls, and exploring op-\nportunistic use of available resources. Should the acquisition of additional resources prove challenging,\nmitigation techniques have been identified and will need to be implemented. Improving the interface\nbetween centrally-produced samples and analysis frameworks, including Python-based frameworks, is\nessential.\nCloser ties with the LHC community will need to be developed, as they can unlock mutual bene-\n193\n\nfits, by leveraging shared technologies that advance both the FCC and LHC objectives. In this respect,\npromoting positions shared between LHC and FCC might foster joint development efforts and enhance\nexpertise exchange. Finally, to broaden the project resource base, continued efforts are required to attract\nmore external contributors from institutes worldwide, to raise awareness and interest in FCC among the\nbroader scientific community, and to encourage partnerships and resource sharing.\n194\n\n9\nEnergy calibration, polarisation, monochromatisation\n9.1\nOverview\nExcellent knowledge of the collision energy, \u221as, is vital for many of the most important measurements\nthat will be performed at FCC-ee, in particular the determination of the Z-resonance parameters, and the\nmass and width of the W boson. To achieve this goal requires calibrating the mean energy of each beam\naround the ring, Eb, in principle not identical for electrons and positrons but here designated with a single\nsymbol for simplicity. The collision energy \u221as can then be calculated, provided there is sufficiently good\nknowledge of the crossing angle of the two beams and all effects that give rise to local shifts of the energy\nat each interaction point.\nCircular colliders have the unique attribute that transverse polarisation naturally accumulates\nthrough the Sokolov\u2013Ternov effect, and the spin tune, which is the ratio of the precession frequency\nto the revolution frequency, is directly proportional to Eb. The spin tune can be directly measured by\nthe procedure of resonant depolarisation (RDP), in which the frequency of a depolarising kicker mag-\nnet is adjusted until the polarisation is found to vanish. This technique, which has an intrinsic relative\nprecision of 10\u22126 or better, has been exploited at many facilities, most notably at LEP in scans of the Z\nresonance [816] and more recently at VEPP4 in the determination of the J/\u03c8 and \u03c8(2S) masses [817].\nAlternatively, in a free spin precession (FSP) measurement the depolariser may be used to rotate the spin\nvector into the horizontal plane, and the precession frequency measured directly. The self-polarisation\nof the beams can be used for these measurements, but this will only be possible for Z-pole operation and\nat energies up to and including the W+W\u2212threshold. At energies higher than these, the polarisation\nlevel will be too small for RDP and FSP measurements to be practical and the energy scale will have to\nbe determined from physics processes at the experiments, such as e+e\u2212\u2192Z(\u03b3), ZZ and W+W\u2212pro-\nduction. Here, the Z and W masses measured with high precision at lower energies with RDP provide a\nnormalisation that can then be applied at higher energies.\nThe calculation of \u221as at each interaction point requires good knowledge of the crossing angle of\nthe two beams, which must be measured by the experiments in real time. In addition, it is necessary to\naccount for local energy variations from synchrotron radiation, the RF system and impedance, and to\nconsider the effects of opposite-sign vertical dispersion.\nThe knowledge of Eb at LEP was ultimately limited by the sampling rate of RDP measurements,\nwhich were performed outside physics operation with a periodicity of around once per week. The energy\nwas found to vary significantly between measurements due to several effects, for example earth tides and\nstray ground electric currents [816]. In order to enable the much greater degree of systematic control\nthat the vastly larger event samples at FCC-ee warrant, the operational strategy will be very different to\nLEP. Measurements of Eb will be performed several times per hour on non-colliding pilot bunches. In Z\nrunning, around 160 pilot bunches will be injected at start of fill, and wiggler magnets will be activated\nto speed up the polarisation time. One to two hours will be required for the polarisation to build, after\nwhich the wigglers will be turned off and physics (colliding) bunches injected. The RF frequency will be\ncontinually adjusted to keep the beams centred in the quadrupoles, thus suppressing tide-driven energy\nchanges, which would otherwise be O(100 MeV). A model will be developed to track residual energy\nvariations between measurements.\nA more detailed discussion on the machine aspects concerning the \u221as calibration can be found in\nthe Volume 2 of this Report [18]. The contribution of the experiments to those studies and the current\nlevel of understanding of the expected performance are summarised here. Also included below is a\nbrief discussion of the studies that are underway for monochromatisation of the collision energy when\noperating at \u221as \u2248125 GeV, corresponding to the mass of the Higgs boson. Monochromatisation is\nmotivated by the need to reduce the spread of \u221as to a value similar to the Higgs width (around 4 MeV),\nthereby improving the sensitivity to direct Higgs production and allowing tight constraints to be placed\non the electron-Yukawa coupling.\n195\n\n9.2\nInput from the experiments\nThe experiments operating at FCC-ee will themselves provide measurements that are essential input to\nthe calibration of the collision energy and related quantities. A full discussion of these measurements\ncan be found in Ref. [22]. Here, a brief summary is given, together with some recent updates. The\nprincipal data set for performing these measurements is the very large sample of dimuon events that\neach experiment will collect, arising from the process e+e\u2212\u2192\u00b5+\u00b5\u2212(\u03b3), where \u03b3 indicates the possible\npresence of initial-state radiation (ISR). Analysis of the topology of these events, constrained by the\ntotal energy and momentum conservation in the final state, allows several important quantities to be\ndetermined. This analysis is, in general, based on the knowledge of the muon directions, which in turn\nimposes demands on the performance of the tracking system (see Section 4.2).\n9.2.1\nThe crossing angle \u03b1\nThe nominal value of the crossing angle is \u03b1 = 30 mrad, but the true value must be determined through-\nout data-taking so that the collision energy can be calculated to the required precision. At the Z pole,\nmore than 106 dimuon events will be collected every 10 minutes in each detector, which will allow this\nparameter to be measured with a statistical uncertainty of 0.3 \u00b5rad, which is sufficient for the physics\ngoals, since a precision of 15 \u00b5rad leads to an uncertainty of 10 keV on \u221as. The statistical precision\nwill be worse at higher energies, where the production rate is lower, but will not compromise the physics\nmeasurements that are targeted in these regimes.\nThere is an important subtlety in the crossing-angle determination that must be accounted for. The\nelectron and positron bunches experience mutual electric and magnetic fields that accelerate (decelerate)\nthe bunches before (after) the collision and also increase (decrease) the crossing angle. The collision\nenergy is invariant, but the change in crossing angle from this effect (estimated to be a relative 0.6%\nmodification) must be known so that the measured crossing angle can be corrected back to the unaffected\nquantity and used together with beam energies as determined from RDP to calculate \u221as.\nThe magnitude of the variation in \u03b1 depends on parameters such as the bunch population and the\nspread in collision energy \u03b4\u221as. It is found empirically, from simulation studies, that \u03b1 is proportional to\nL1/2 / \u03b4\u221as\n1/6. By measuring L, \u03b1, and \u03b4\u221as from dimuon events for different bunch intensities, it will be\npossible to extrapolate to zero intensity and determine the value of \u03b1 in the absence of these effects. A\ngood opportunity to perform these measurements would be in the period that top-up injection is taking\nplace. It is therefore important that the detector can operate during this period and that the beams are\nstable. A simulated study of the measurement of \u03b1 against L1/2 / \u03b4\u221as\n1/6 is presented in Fig. 134.\n9.2.2\nThe longitudinal boost and the collision-energy spread\nThe dimuon topology allows the longitudinal boost to be determined on an event-by-event basis. When\naveraged over a suitable sample size, this provides invaluable information to constrain the model of the\nenergy loss around the ring and to calculate the local collision energy at each interaction point. The\nwidth of this distribution (Fig. 135) is a measure of \u03b4\u221as, which is an essential input to the measurement\nof certain observables, such as the Z and W widths. Again, the foreseen statistical precision on these\nquantities is excellent. For example, the energy spread can be measured to one part in a thousand with\none million dimuon events. Recent work [818] has investigated how sensitive the determination of \u03b4\u221as is\nto the knowledge of the ISR corrections in dimuon production. The conclusion is that the measurement\nis robust; even if it is assumed that the second-order corrections from ISR are unknown (which is not the\ncase), the resulting bias on the extraction of \u03b4\u221as is far smaller than the statistical uncertainty.\n9.2.3\nRelative \u221as determination in the Z-resonance scan\nThe reconstructed peak position of the dimuon invariant-mass distribution provides an excellent proxy for\nthe collision energy. The difference in this reconstructed position between the points of the Z-resonance\n196\n\nL1/2/\u03b4\n1/6\n\u221as\nFig. 134: Change in the measured crossing-angle \u03b1 vs. L1/2 / \u03b4\u221as\n1/6, at various points during the top-up injection.\nExtrapolation down to L1/2 / \u03b4\u221as\n1/6 = 0 allows the crossing-angle to be determined in the absence of bunch-bunch\neffects [22].\n\u03b3\nLongitudinal Boost, x\n5\n\u2212\n4\n\u2212\n3\n\u2212\n2\n\u2212\n1\n\u2212\n0\n1\n2\n3\n4\n5\n3\n\u2212\n10\n\u00d7\nEvents\n2\n10\n3\n10\n4\n10\n5\n10\nSpread (no BS)\nSpread (BS)\n = 0.1 mrad\n\u03c6\n,\u03b8\n\u03c3\nWith ISR\n 0.1%\n\u00b1\nAsymmetry = \nOne million dimuon events\nFig. 135: Fitted value of longitudinal boost from one million dimuon events at one of the FCC-ee IPs [22]. Once\nthe ISR is unfolded, this distribution can be used to measure the energy spread. The magenta line shows the impact\nof a centre-of-mass boost on the distribution. The shift can be measured with a statistical precision of 40 keV. The\nother curves indicate the impact of beamstrahlung, angular resolution on the track directions, and ISR.\nscan provides a measure of the change in collision energy, which is a critical input for several analyses,\nin particular the measurement of the Z boson width. The distribution is fitted in bins of the polar angle\nfor back-to-back events. An example fit is shown in Fig. 136 (left). The statistical precision on this\npseudo-\u221as measurement, when summing the samples from four experiments, is around 20 keV for each\nof the two off-peak running points, assuming the momentum resolution of the IDEA detector. So that the\ndetector does not introduce a bias in the measurement larger than the statistical precision, the momentum\nscale stability must be controlled at this level.\nThe field stability can be tracked with NMR probes and the momentum scale can be directly\n197\n\n93.5\n94\n94.5\nM (GeV)\n0\n10\n20\n30\n40\n50\n60\n3\n10\n\u00d7\nEvents\n85\n90\n95\n (GeV)\ns\n10\n\u2212\n8\n\u2212\n6\n\u2212\n4\n\u2212\n2\n\u2212\n0\n2\n bias (MeV), shifted\nFig. 136: Left: Example fit to the dimuon invariant-mass distribution at \u221as = 94.3 GeV, where the peak is\nmodelled with the superposition (blue) of a Gaussian function (red) and two exponential functions (black). Right:\nThe difference (bias) between the \u221as extracted from the dimuon invariant-mass fit and the true value. Results are\nshown for the simulated performance of the IDEA detector (red points) and for the expected dependence, including\n(black points) or not (black curve) ISR/FSR effects. Each set of results also has an overall overset of a few MeV,\nwhich is energy independent and, hence, not relevant for the determination of the Z width. A single shift has been\napplied to the bias, to correct for these offsets, so that the bias is zero at 87.9 GeV, for all sets of results.\nmonitored through the reconstruction of low-mass resonances. However, even with a perfect detector,\nthere is a bias in the pseudo-\u221as measurement in the Z resonance scan arising from ISR/FSR effects,\nand from the product of the Breit\u2013Wigner shape of the resonance and the Gaussian distribution of the\nenergy spread of the colliding beams. The value of this bias varies by about 8 MeV when going from\n\u221as = 87.9 to 94.3 GeV, as can be seen in Fig. 136 (right). This difference must be corrected for in\nthe measurement, which requires a good understanding of the ISR/FSR effects. In a generator-level\nstudy, disabling ISR/FSR changes the difference in the bias between the two off-peak points by around\n500 keV. Therefore, the theoretical prediction of these ISR/FSR effects to the 1% level would be sufficient\nto render their impact negligible for the Z-width measurement.\n9.2.4\nAbsolute \u221as determination\nAt collision energies above the Z boson mass, the dimuon events may be used to provide an absolute\nmeasurement of \u221as. Radiative returns, in which the emission of an initial-state photon means that\nthe dimuon has the Z mass, allows for the calibration of events unaffected by ISR. The method can be\nextended to also include multihadron final states. This method can be calibrated at the W-pair production\nthreshold with RDP, and is of great value for physics studies in the regime where no RDP is possible, i.e.,\ncollision energies above 200 GeV. This approach also provides a useful complementary measurement\nof \u221as in the intermediate energies where RDP is possible but challenging. The foreseen statistical\nuncertainty is around 280 keV for 6 ab\u22121 of integrated luminosity at \u221as = 125 GeV and 260 keV for\n20 ab\u22121 at \u221as = 160 GeV. The performance of the tracking system must be sufficiently good that the\nprecision is not compromised.\n198\n\n9.3\nExpected precision on EW observables from the collision energy and its spread\nSeveral of the most important electroweak observables are expected to have a dominant or significant sys-\ntematic uncertainty associated with the knowledge of the collision energy and collision-energy spread.\nThe collision-energy uncertainties can be classed in three distinct categories, itemised below. These un-\ncertainties propagate to the physics results in an observable-dependent manner, as discussed in Ref. [22].\n\u2013 Uncertainties that are fully correlated between measurements propagate to the knowledge of the\nabsolute energy scale. Examples include the values of the anomalous magnetic moment and the\nmass of the electron, the frequency of the RF system, and any other systematic bias that occurs at\nall times and all energies. At this stage in the studies, it is estimated that this uncertainty will be\naround 100 keV on the collision energy at the Z pole and 300 keV at the W+W\u2212threshold. This\ncontribution is expected to be the dominant systematic uncertainty in the measurements of the Z\nand W boson masses.\n\u2013 A point-to-point contribution comprises biases that occur at all times, or lead to an average shift,\nbut are different for each energy setting. The principal method of determining this uncertainty\nwill be based on the dimuon invariant-mass distribution, as reconstructed by the experiments.\nThe estimated magnitude of this uncorrelated uncertainty is 20 keV for each off-peak point of the\nZ-resonance scan. The understanding gained at the Z pole and complementary measurements will\nlead to a corresponding uncertainty of around 100 keV at the W+W\u2212threshold. The point-to-\npoint uncertainty is expected to be the dominant contribution in the measurement of the Z width.\n\u2013 The uncertainty on each individual RDP measurement is dominated by an uncertainty that is set by\nthe frequency of the polarimeter sampling or the size of the energy bins where the depolarisation\ncan be located. A reasonable estimate of this uncertainty is 200 keV at the Z pole and 300 keV\nat the W+W\u2212threshold. As this component is statistical in nature, its impact decreases with\nthe square-root of the number of events. As it is planned to collect \u223c104 measurements at each\nenergy point, the final uncertainty from this source will be essentially negligible, compared to\nother contributions. However, the importance of making each measurement as precise as possible,\nand of collecting the largest possible number of measurements, will become more evident when\nthe data set is split into smaller samples to perform systematic checks.\nTable 24: Current projected \u221as-related uncertainties on selected electroweak observables.\nObservable\nUncertainty\nmZ (keV)\n\u0393Z (keV)\nsin2 \u03b8eff\nW (\u00d710\u22126)\n\u2206\u03b1QED(m2\nZ)\n\u03b1QED(m2\nZ) (\u00d710\u22125)\nmW (keV)\nAbsolute\n100\n2.5\n\u2013\n0.1\n150\nPoint-to-point\n14\n11\n1.2\n0.5\n50\nSample size\n1\n1\n0.1\n\u2013\n3\nEnergy spread\n\u2013\n5\n\u2013\n0.1\n\u2013\nTotal \u221as-related\n101\n12\n1.2\n0.5\n158\nFCC-ee statistical\n4\n4\n1.2\n3.9\n180\nThe contributions from each uncertainty category, and their quadratic sum, are listed in Table 24\nfor several key electroweak observables. This table also shows the contribution from the uncertainty in\nthe knowledge of the energy spread, which affects quantities with a strong quadratic dependence on the\ncollision energy. Observables that are most susceptible to this uncertainty include the Z cross section and\nthe Z width. A collision-energy spread of 70 MeV, determined with a precision of \u00b1 0.05 MeV, leads to\na sub-dominant systematic uncertainty in the measurement of these observables.\n199\n\nWith the current expectations, it will be possible to reduce the uncertainty from energy-related\nquantities by an order of magnitude or more with respect to what was achieved at LEP, such that they\nwill be smaller than, or similar to, the statistical uncertainty for all observables apart from mZ. Indeed,\nthe entries in Table 24 for the \u221as-related systematic uncertainties can be compared to the corresponding\nLEP values of 1.7 MeV for mZ, 1.2 MeV for \u0393Z, and 9 MeV for mW.\n9.4\nProspects for monochromatisation and the measurement of the electron Yukawa coupling\nThis section describes the tantalising possibility, unique to FCC-ee, to observe the s-channel process\ne+e\u2212\u2192H, and thereby determine the electron Yukawa coupling. The challenges are very demanding\nand progress is required from both the accelerator and the experimental analyses, but the current studies,\ndescribed below, are encouraging.\nThe electron Yukawa via resonant Higgs production at 125 GeV\nConfirming the mechanism of mass generation for the stable visible elementary particles of the universe,\ncomposed of u and d quarks plus the electron (and neutrinos), is experimentally very challenging because\nof the low masses of the first-generation fermions and, thereby, their small Yukawa couplings to the\nHiggs field. (The neutrino mass generation remains a BSM problem in itself.) In the SM, the Yukawa\ncoupling of the electron is ye =\n\u221a\n2 me/v = 2.8 \u00b7 10\u22126, for me(mH) = 486 keV and Higgs vacuum\nexpectation value v = (\n\u221a\n2 GF)\u22121/2 = 246.22 GeV. Measuring it via H \u2192e+e\u2212appears hopeless at\nhadron colliders because the decay has a tiny partial width, proportional to the electron mass squared,\n\u0393(H \u2192e+e\u2212) =\nGF mH m2\ne\n4\n\u221a\n2 \u03c0\n \n1 \u2212\n4 m2\ne\nm2\nH\n!3/2\n= 2.14 \u00d7 10\u221211 GeV ,\n(10)\nwhich corresponds to a branching fraction B(H \u2192e+e\u2212) \u22485 \u00d7 10\u22129 for the SM Higgs boson. At LHC\nand FCC-hh, such a final state is completely swamped by the Drell\u2013Yan e+e\u2212continuum. The current\nLHC searches [819,820], exploiting about 140 fb\u22121 of pp data at \u221as = 13 TeV, reach an observed upper\nlimit on the branching fraction of B(H \u2192e+e\u2212) < 3.0 \u00d7 10\u22124 at 95% CL. This value translates into\nthe current upper bound on the Higgs boson effective coupling modifier to electrons of |\u03bae| < 240.\nAssuming that the sensitivity to the H \u2192e+e\u2212decay scales simply with the square root of the integrated\nluminosity, the HL-LHC phase with a Lint = 2 \u00d7 3 ab\u22121 data sample (combining the ATLAS and CMS\nresults) will result in ye \u2272100 ySM\ne . Based on searches for the similar H \u2192\u00b5+\u00b5\u2212channel, one can\nexpect upper limits on B(H \u2192e+e\u2212) to be further improved by factors of about four, by adding more\nHiggs production categories and using advanced multivariate analysis methods, eventually reaching ye \u2272\n50 ySM\ne\nat the end of the HL-LHC.\nAbout ten years ago, it was first noticed that the unparalleled integrated luminosities of Lint \u2248\n10 ab\u22121/year expected at \u221as = 125 GeV at the FCC-ee would make it possible to attempt an observation\nof the direct production of the scalar boson and, thereby, a direct measurement of the electron Yukawa\ncoupling [821,822]. Subsequently, several theoretical studies [30,823\u2013826], simulated data analysis [32],\nand accelerator studies [827\u2013829] have explored the various aspects connected to the e+e\u2212\u2192H mea-\nsurement.\nThe Feynman diagrams for s-channel Higgs production (and its statistically most significant decay\nat FCC-ee, H \u2192gg, see below) and dominant backgrounds are shown in Fig. 137 (left). The resonant\nHiggs cross section in e+e\u2212collisions as a function of \u221as is theoretically given at Born level by the\nrelativistic Breit\u2013Wigner (BW) expression:\n\u03c3ee\u2192H = 4 \u03c0 \u0393H \u0393(H \u2192e+e\u2212)\n(s \u2212m2\nH)2 + m2\nH\u03932\nH\n.\n(11)\n200\n\n124.99\n124.995\n125\n125.005\n125.01\n (GeV)\ns\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n(s) (fb)\n H\n\u2192\nee\n\u03c3\nEnergy spread:\n = 0\n\u03b4\n = 4.1 MeV\n\u03b4\n = 7 MeV\n\u03b4\n = 15 MeV\n\u03b4\n = 30 MeV\n\u03b4\n = 100 MeV\n\u03b4\nFig. 137: Left: Diagrams for the s-channel production of the Higgs boson decaying into two gluon jets (top) and\nreducible Z\u2217quark dijet backgrounds (bottom) in e+e\u2212at \u221as = 125 GeV. Right: Resonant Higgs production cross\nsection at \u221as = 125 GeV, including ISR effects, for several e+e\u2212collision energy spread values: \u03b4\u221as = 0, 4.1, 7,\n15, 30, and 100 MeV [823].\nAn accurate knowledge of mH is, therefore, critical to maximise the resonant cross section. An O(4 MeV)\nprecision on the Higgs boson mass can be achieved (Section 4.3) before any dedicated e+e\u2212\u2192H run.\nIn addition, the FCC-ee beam energies will be monitored with a relative precision of 10\u22126, providing a\nsub-MeV accuracy on the exact point in the Higgs lineshape being probed at any moment.\nFor mH = 125 GeV, Eq. 11 gives \u03c3ee\u2192H = 4 \u03c0 B(H \u2192e+e\u2212)/m2\nH = 1.64 fb as peak cross sec-\ntion. Two effects, however, lead to a significant reduction of the Born-level prediction: (i) ISR depletes\nthe cross section and generates an asymmetry of the Higgs lineshape; and (ii) the actual beams are never\nperfectly monoenergetic, i.e., the collision \u221as has a spread \u03b4\u221as around its central value, further leading to\na smearing of the BW peak. For FCC-ee operating at 125 GeV, the natural spread in collision energy due\nto synchrotron radiation will be around 70 MeV. Monochromatisation aims at reducing \u03b4\u221as to the few\nMeV scale, while still delivering moderately large (few ab\u22121) integrated luminosities, Lint [827\u2013829].\nThe reduction of the BW cross section due to initial-state photon emission(s) alone is of a factor of 0.35\nand leads to \u03c3ee\u2192H = 0.57 fb [823].\nThe additional impact of a given energy spread on the Higgs BW shape can be quantified through\nthe convolution of BW and Gaussian distributions, i.e., a relativistic Voigtian function. Figure 137 (right)\nshows the Higgs lineshape for various \u03b4\u221as values. The combination of ISR plus \u03b4\u221as = \u0393H = 4.1 MeV\nreduces the peak Higgs cross section by a total factor of 0.17, down to \u03c3ee\u2192H = 0.28 fb. Though tiny,\nthe cross section for any other e+e\u2212\u2192H production process, through intermediate W or Z bosons, is\nmuch further suppressed by the electron mass for on-shell external fermions (chirality flip) [31] and is\nnegligible as well as any other loop-induced Higgs production mechanisms at \u221as = 125 GeV that is not\nsensitive to ye [830].\nThe strategy to observe the resonant production of the Higgs boson [32] is based on identify-\ning final states consistent with any of the H decay modes that lead to small (but statistically significant\nwhen combined together) excesses over the expected backgrounds (orders-of-magnitude more abundant\nthan the signal). In Ref. [32], a detailed study was performed with large simulated event samples of\nsignal and associated backgrounds generated with PYTHIA 8 [768] for eleven Higgs boson decay chan-\nnels. A benchmark monochromatisation point of (\u03b4\u221as, Lint) = (4.1 MeV, 10 ab\u22121), corresponding to\n2800 Higgs bosons produced, was assumed for the signal. A simplified description of the expected ex-\nperimental performance was considered for the reconstruction and (mis)tagging of heavy-quark (c, b),\nlight-quark (uds), and gluon (g) jets, as well as photons, electrons, and hadronically decaying tau lep-\n201\n\ntons. Generic preselection criteria were defined to suppress reducible backgrounds while keeping the\nlargest fraction of the signal events. A subsequent multivariate analysis of O(50) kinematic and global\ntopological variables, defined for each event, was carried out. Boosted Decision Tree (BDT) classifiers\nwere trained on signal and background events to maximise the signal significance for each individual\nchannel. The most significant Higgs decay channels are found to be H \u2192gg (for a gluon efficiency of\n70% and a uds-for-g jet mistagging rate of 1%), and H \u2192WW\u2217\u2192\u2113\u03bd jj. The digluon final state is the\nmost sensitive channel to search for the resonant Higgs boson production (Fig. 137 left, upper diagram)\nbecause it has a moderately large branching fraction (B \u22488%) while the Z\u2217\u2192gg decay is forbidden\nby the Landau\u2013Yang theorem. The most important experimental challenge is to reduce the light-quark\nfor gluon mistagging rate to the 1% level (while maintaining the efficiency for the H \u2192gg channel at\n70%) to keep the overwhelming Z\u2217\u2192uu, dd, ss backgrounds (Fig. 137 left, lower diagram) under\ncontrol. Such a mistagging rate is a factor of about seven times better than the current state-of-the-art for\njet-flavour tagging algorithms [486], but it is a realistic goal given all the experimental and theoretical\nimprovements in the understanding of parton radiation and hadronisation expected at the FCC-ee [831].\nCombining all results for an accelerator operating at (\u03b4\u221as, Lint) = (4.1 MeV, 10 ab\u22121), a 1.3 \u03c3\nsignal significance can be reached for the direct production of the Higgs boson, corresponding to an\nupper limit on the electron Yukawa coupling at 1.6 times the SM value: |ye| < 1.6 |ySM\ne | at 95% CL for\neach detector in one year. Based on this benchmark result and the dependence of the resonant Higgs cross\nsection on \u03b4\u221as (Fig. 137, right), bidimensional maps of e+e\u2212\u2192H significance and electron-Yukawa\nsensitivities have been determined in the (\u03b4\u221as, Lint) plane.\nFig. 138: Upper limit contours (at 95% CL) on the electron Yukawa ye (coloured bands) in the collision-energy\nspread \u03b4\u221as vs. integrated luminosity Lint plane. The red star over the \u03b4\u221as = \u0393H = 4.1 MeV red-dashed line\nindicates the reference point assumed in the physics simulation analysis [32]. The black cross indicates the previ-\nously achieved working point with self-consistent parametric monochromatisation [829,832]. The red and yellow\nsquares indicate the monochromatisation points based on simulations of the \u2018GHC V22 Z\u2019 and \u2018GHC V22 tt\u2019\noptics, respectively (see text for details) [833].\nFigure 138 shows the 95% CL upper limit contours on the electron Yukawa coupling strength as\na function of the energy spread and integrated luminosity with the red star (on the red-dashed line cor-\nresponding to a reference monochromatised collision-energy spread equal to the Higgs boson width),\nindicating the result of this benchmark study. The next section discusses the results of the current\nmonochromatisation simulation studies, shown with red and yellow squares in this figure.\n202\n\nFCC-ee monochromatisation\nMonochromatisation is necessary to reduce \u03b4\u221as to the few MeV level of the natural SM Higgs width and\nthereby increase the sensitivity of the electron-Yukawa measurement via e+e\u2212\u2192H. This strategy was\nfirst proposed 50 years ago [834] and relies on creating opposite correlations between spatial position\nand energy deviations within the colliding beams with nominal beam energy E0. Figure 139 shows\na schematic of the principle of monochromatisation for beams that collide head on (left) and with a\ncrossing angle \u03b1 (right). The current baseline design of FCC-ee corresponds to the latter configuration.\nIn both configurations, the correlations between transverse (either horizontal or vertical) position in the\nbeam and energy lead to a lower spread in collision energy than in the uncorrelated case.\nFig. 139: Schematic of the principle of monochromatisation for head-on collisions (left) and collisions with a\ncrossing angle (right). In both cases, opposite-sign correlations between the transverse position in the beam and\nthe energy lead to a reduction in the collision-energy spread, compared with the uncorrelated case.\nMonochromatisation can be achieved by adding dedicated components at the interaction region\n(IR) to generate a non-zero dispersion function with opposite signs for the two beams at the IP. A non-\nzero dispersion function at the IP in the horizontal and/or vertical directions (D\u2217\nx,y \u0338= 0) enlarges the IP\ntransverse beam size (\u03c3\u2217\nx,y), which in turn affects the luminosity, L \u221d1/(\u03c3\u2217\nx\u03c3\u2217\ny). The monochromatisa-\ntion factor is defined as\n\u03bb =\ns\n1 + \u03c32\n\u03b4\n\u0012 D\u22172\nx\n\u03b5x \u03b2\u2217x\n+ D\u22172\ny\n\u03b5y \u03b2\u2217y\n\u0013\n,\n(12)\nwhere \u03c3\u03b4 is the relative energy spread, \u03b5x,y the transverse emittances, and \u03b2\u2217\nx,y the betatron functions at\nthe IP. For any value of \u03bb achieved, \u03b4\u221as and L in the monochromatisation operation mode are\n\u03b4\u221as =\n\u221a\n2 E0 \u03c3\u03b4\n\u03bb\nand\nL = L0\n\u03bb ,\n(13)\nwhere L0 represents the luminosity for the same values of \u03b2\u2217\nx,y but without D\u2217\nx,y. Consequently, the\ndesign of a monochromatisation scheme requires considering both the IR beam optics and the optimi-\nsation of other collider parameters to maintain the highest possible luminosity. Possible approaches to\nmonochromatisation for FCC-ee have been studied for several years, starting from self-consistent para-\nmetric studies [827, 829, 832, 835]. Recent developments [833, 836] comprise a detailed study of the\nIP-region optics required for monochromatisation, exploring different potential configurations and their\nimplementation in the FCC-ee global lattice, along with beam-dynamics simulations and performance\nevaluations including the impact of beamstrahlung.\nThe baseline FCC-ee standard lattice design is the so-called \u2018Global Hybrid Correction\u2019 (GHC)\noptics [668, 837, 838]. It allows for four IRs, where the e+ and e\u2212beams are brought to collision with\nan \u03b1 = 30 mrad angle in the horizontal plane, as well as a potential vertical crab-waist scheme. The\nresults of the monochromatisation studies shown in Fig. 138 are based on two versions of this optics:\n\u2018GHC V22 Z\u2019, where the lattice is optimised for operation at the Z pole, and \u2018GHC V22 tt\u2019, which is\noptimised for operation above the tt threshold (in both, \u2018V22\u2019 designates the 2022 configuration). Three\n203\n\napproaches to monochromatisation have been investigated. In the first, the horizontal dipoles used for the\nlocal-chromaticity-correction system are reconfigured to generate a non-zero D\u2217\nx of size \u223c10 cm, while\nmaintaining the same \u03b1 value. Given the values of the other parameters in Eq. (12) [837], it follows that\nmonochromatisation factors in the range \u03bb = 5\u20138 are achievable.\nThis study was performed both to provide monochromatisation in all four IRs and then repeated\nto give monochromatisation in only two IRs. The second method introduces a non-zero value of D\u2217\ny by\nadjusting the strengths of the skew quadrupoles in the interaction region. The very low vertical emittance\nin FCC-ee implies that similar monochromatisation factors as in the horizontal case can be achieved with\nD\u2217\ny \u22481 mm. Finally, schemes involving non-zero values of both D\u2217\nx and D\u2217\ny have been explored. In all\ncases, the layout of the components around the IR and the parameter values were adjusted to satisfy the\nboundary conditions in the machine and deliver optimum performance.\nSimulations were performed with GUINEA-PIG [687] to determine the performance of the dif-\nferent monochromatisation schemes, taking into account the impact of beamstrahlung. The particle\ndistribution at the IP was simulated as an ideal Gaussian distribution, comprising 40 000 particles and\ndefined by the following global optical performance parameters: E0, \u03c3\u03b4, \u03b5x,y, \u03b2\u2217\nx,y, D\u2217\nx,y, \u03c3z, and \u03b1. For\neach configuration, the \u03b4\u221as (from the distribution of the collision energy) and L were calculated. The\nresults are presented in Tables 25 and 26 for the \u2018GHC V22 Z\u2019 and \u2018GHC V22\u2019 tt optics, respectively.\nTable 25: Values of \u03b4\u221as, L, and Lint for five setups of the \u2018GHC V22 Z\u2019 monochromatisation IR optics [833]:\nwithout monochromatisation (\u2018Std. ZES\u2019), with D\u2217\nx \u0338= 0 in four and two IPs (\u2018ZH4IP\u2019 and \u2018ZH2IP\u2019), with D\u2217\ny \u0338= 0\n(\u2018ZV\u2019), and with D\u2217\nx,y \u0338= 0 (\u2018ZHV\u2019).\nStd. ZES\nZH4IP\nZH2IP\nZV\nZHV\nCM energy spread \u03b4\u221as (MeV)\n69.52\n26.80\n24.40\n25.25\n20.58\nLuminosity / IP L (1034 cm\u22122s\u22121)\n44.8\n15.0\n18.4\n1.46\n1.42\nIntegrated luminosity / IP / year Lint (ab\u22121)\n5.38\n1.80\n2.21\n0.18\n0.17\nTable 26: Same as previous table, but for the \u2018GHC V22 tt\u2019 monochromatisation IR optics [833].\nStd. TES\nTH4IP\nTH2IP\nTV\nTHV\nCM energy spread \u03b4\u221as (MeV)\n67.20\n27.10\n23.16\n20.23\n21.24\nLuminosity / IP L (1034 cm\u22122s\u22121)\n71.2\n17.9\n24.5\n1.37\n1.42\nIntegrated luminosity / IP / year Lint (ab\u22121)\n8.54\n2.15\n2.94\n0.16\n0.17\nAll the investigated monochromatisation schemes are successful in reducing \u03b4\u221as by a factor of\ntwo or more with respect to the value without monochromatisation. As expected, this reduction in energy\nspread is accompanied by a reduction in luminosity, which is more marked for the configurations with\nD\u2217\ny \u0338= 0 and combined D\u2217\nx,y \u0338= 0, where the beamstrahlung leads to a blow up in \u03f5y. The corresponding\nphysics performance is plotted as red (yellow) squares for the \u2018GHC V22 Z\u2019 (\u2018GHC V22 tt\u2019) setups in\nthe (\u03b4\u221as, Lint) plane in Fig. 138, from which the corresponding 95% CL upper limit contours for the ye\ncoupling can be read off. The physics performance of all designed monochromatisation IR optics with\nnon-zero D\u2217\nx are comparable to, or even exceed, those of the previous FCC-ee self-consistent parameters\n(black cross). The \u2018MonochroM TH2IP\u2019 optics achieves the best \u03b4\u221as vs. Lint benchmark, with \u03b4\u221as =\n23.16 MeV and Lint = 2.94 ab\u22121. This corresponds to an upper limit (at 95% CL) of |ye| < 3.2 |ySM\ne | for\nthe Higgs-electron coupling, for each detector in one year. With four experiments running at the same\nluminosity with the \u2018TH4IP\u2019 scheme in the \u2018GHC V22 tt\u2019 optics with crossing angle, one should be able\nto set an upper limit (at 95% CL) of about 2.5 times the SM value in one year of operation. This is to be\ncompared with about 4 times the SM value when operating without monochromatisation. Prospects for\nimprovements in the monochromatisation performance are briefly alluded to in Section 9.5.\n204\n\n9.5\nOutlook\nThe studies performed before and during the Feasibility Study established a baseline scheme for calibra-\ntion of the collision energy, ensuring that the physics goals of FCC-ee can be met. Nevertheless, these\nstudies must be refined in certain areas and alternative schemes should be considered to further improve\nperformance and operational efficiency.\nThe absolute uncertainties in \u221as arising from RDP are the dominant systematic uncertainties in\nthe measurements of the Z and W masses. Future studies will investigate whether these uncertainties\ncan be reduced beyond the currently assumed values: 100 keV at the Z pole and 300 keV at the W+W\u2212\nthreshold.\nThe measurements of energy-related quantities made by the experiments using dimuon events\nare a critical ingredient in the \u221as calibration, at all centre-of-mass energies. Recently, several of these\nstudies have been deepened to validate their robustness with respect to the uncertainties in the knowledge\nof higher-order ISR/FSR effects; this work will be extended further. It is also important to consolidate\nthe strategy for understanding how the measurement of the crossing angle is affected by changes in the\nbunch intensity. The impact of detector performance and the interplay with alignment studies will be\nanother focus of attention. Finally, the use of other categories of physics events, beyond dimuons, will\nbe investigated.\nIt is important to have a reliable procedure to accurately translate the mean beam energy, measured\nby RDP, to the local collision energy, relevant for the physics measurements. Full simulations of this\nprocedure will be conducted, at each interaction point, incorporating the in-situ measurement of the\nlongitudinal boosts of the collisions and the knowledge of the machine impedances. Attention will also\nbe paid to the control of energy shifts from possible dispersion effects at each interaction point, as well\nas to the related requirements on the precision of the system of beam-position monitors.\nMore detailed simulations of the level and lifetime of transverse polarisation will be performed,\nin parallel with changes to account for any evolution in the proposed optics of the accelerator. A deeper\nunderstanding will be sought of any effects that might bias the assumed proportionality between the\nspin tune and the mean beam energy. It will be particularly important to monitor the expected level of\npolarisation at the W+W\u2212threshold and the RDP strategy in this challenging regime. Detailed technical\ndesigns will be made of the polarimeter and depolariser systems.\nSo far, the baseline strategy to get transversally polarised pilot bunches has been to inject unpo-\nlarised beams and to stimulate the growth of polarisation by activating wigglers at the start of each fill.\nThis is a robust approach but has the disadvantage of introducing dead-time, during which no collisions\nare possible. To overcome this inconvenient, studies will investigate the possibility of injecting already-\npolarised pilot bunches, for which the design of the injection system must be modified. Simulations will\nbe required to validate that the bunches retain their polarisation throughout the injection step and while\ntravelling in the booster ring.\nFurther investigations will also take place regarding the feasibility of the electron Yukawa mea-\nsurement. In particular, new and refined schemes will be investigated with the aim of improving the\nmonochromatisation of the collision energy. It will also be necessary to develop and simulate a pro-\ncedure to monitor and adjust the collision energy in real time, to ensure that it remains centred at the\nHiggs pole. Further physics studies will be performed to improve the signal yield and the signal-to-\nbackground discrimination. Investigations will be performed to evaluate if the significance of the signal\ncan be improved with differential measurements, accounting for the expected correlations between the\nmonochromatisation and the longitudinal coordinate of the e+e\u2212collision.\n205\n\n206\n\n10\nCommunity building\nCommunity building is critical for the success of the FCC project, because it fosters political, public, and\nfinancial support, encourages scientific collaboration and interdisciplinary innovation, promotes educa-\ntion and outreach, and helps ensure the project\u2019s long-term impact and sustainability. By creating an\nengaged, well-informed, and enthusiastic community, FCC can position itself not only as a groundbreak-\ning scientific endeavour but also as a global, inclusive project with far-reaching benefits for humanity.\nThis aspect has been given high priority ever since the beginning of the Conceptual Design Study, in\n2014, in several directions:\n\u2013 Global scientific networks: The FCC project will be one of the largest scientific endeavours ever\nattempted and its success crucially depends on the cooperation of a broad international scien-\ntific community. Engaging researchers, engineers, and institutions worldwide in discussions and\ncollaborations, early on, will ensure that FCC leverages the best scientific expertise, knowledge,\ntraining, and innovation from across the globe, from the preparation of the theory and experimental\ntools to the actual operation of the collider and the detectors, culminating in the data analysis and\ninterpretation.\n\u2013 Transdisciplinary collaboration: The FCC project encompasses a wide range of disciplines, from\nparticle physics theory to detector design and R&D, from computing to engineering, from accel-\nerator physics to machine-detector interface, etc. A well-established community always encour-\nages cross-disciplinary collaboration and cross-fertilisation, enabling experts from various fields\nto contribute their knowledge and solve complex problems together. It also provides the resilience\nnecessary to overcome setbacks, adapt to new circumstances, keep pushing the project forward to\nits implementation.\n\u2013 Inspiring the next generation of scientists and engineers: Community engagement will help\ninspire the next generation to pursue careers in high-energy physics, and to build and operate the\ncollider and the experiments. The FCC project must be a focal point for educational programmes,\nworkshops, and professional training that generate interest and excitement in scientific discovery.\nThe work done today will likely benefit future generations in ways that cannot yet be predicted. By\ncreating a strong, multi-generational community, the project ensures that these long-term benefits\nare recognised, advocated for, and maximised over time.\n\u2013 Funding: Last but not least, the FCC project will require funding from multiple sources, including\ngovernments, private donors, and international organisations. A strong, active community can\nadvocate for the project, raising awareness about its scientific and societal benefits. Demonstrating\nbroad support and interests from the community and advocacy of the long-term scientific benefits\nis required to establish credibility and increase the likelihood of securing the necessary resources\nfor the project.\nAs a matter of fact, the FCC feasibility study midterm review committees issued a number of\nrecommendations to this effect. In particular, they recommended:\n\u2013 to work with the scientific community, institutes, laboratories, and funding agencies to ensure sup-\nport and resources for four experiments, facilitating the exploitation of the full scientific potential\noffered by the large investment in the FCC facility;\n\u2013 to dedicate additional human and financial resources to the project, with a resource-loaded sched-\nule of work and clear priorities;\n\u2013 to develop the coordination and structure required to enable the theoretical progress needed to\nmatch the anticipated experimental precision of the FCC data, both at CERN (fellows, scientific\nassociates, visitors) and by engaging collaborating institutes (including, for instance, the creation\nof European networks); and\n207\n\n\u2013 to establish a dedicated FCC team in the research sector at CERN, with specific new positions\nassociated, and to quantify its size and makeup in terms of seniority so that the resources required\ncan be estimated.\nSuch actions have been (at least partially) anticipated a decade ago during the Conceptual Design\nStudy (2014-2019), and intensified during the Feasibility Study (2021\u20132025). The three volumes of the\nFCC Conceptual Design Report [10\u201312], released in January 2019, have been signed by 1364 authors,\ndistributed in about 140 institutions, which had become members of the FCC Collaboration with the\nsignature of Memoranda of Understanding (MoU) during this first phase. To comply with the recom-\nmendations of the 2021 European Strategy Update, the FCC Collaboration was reinforced by inviting\nmore institutions to join and carry out the FCC Feasibility Study. One of the goals was to gather a ma-\njority of particle physicists behind the project, able to build a consensus in the community at the next\nEuropean Particle Physics Strategy update that FCC is, indeed, the post-LHC collider option with the\nbroadest scientific impact, at the intensity and the energy frontiers.\nDuring the five years of the Feasibility Study, the expansion of the Collaboration was pursued in\ntwo different ways.\nA. At the Collaboration level, the FCC Global Collaboration (FGC) Working Group continuously en-\ngages with current and new participants \u2014national institutes, laboratories and universities, as well\nas industry\u2014 to encourage an expanded membership through Memoranda of Understanding. The\nFGC explores opportunities for future prospective participants, supports new participants in the\napplication process, and assists the new participants in defining areas of collaboration, in particu-\nlar for the accelerator. It then concludes relevant agreements to facilitate the integration process. It\nalso prepares the foundations for R&D and contributions by industry, as well as fostering interest\nin geology, geodesy, logistics, materials science, and other areas that, while not being at the core\nof CERN activities, are critical for the success of the FCC feasibility study and its implementation\non the ground.\nB. From the side of the FCC Physics, Experiments, and Detectors (PED) group, one of the six pil-\nlars of the FCC Feasibility Study, contacts are established with all high-energy physics groups in\nEurope and around the world, to invite them to join and contribute to the FCC project, in parallel\nto their current activities. To this effect, an International Forum of National Contacts (IFNC) was\ncreated, chaired by two national contacts, with the mandate of attracting the different HEP groups,\ncountry by country. The quasi-complete list of European states (around 30) are represented in the\nIFNC, which meets regularly to reinforce the collaboration. The IFNC also reaches out to the rest\nof the world. The United States of America are now strongly involved in the Collaboration, fol-\nlowing the recent Snowmass process and the positive recommendation of the U.S. Particle Physics\nProject Prioritization Panel (P5) to engage in an off-shore Higgs Factory. Most of the other large\nnon-European countries are also active and represented in the IFNC (including Argentina, Brazil,\nCanada, Chile, India, Mexico, Pakistan, South Korea, Thailand, and Turkey) and the list continues\nexpanding.\nThe cases of Japan and China, currently considering projects for colliders on their soil, are treated\nseparately. With the goal to integrate teams from these countries in the near future, scientific\nexchanges with the Japanese and Chinese communities already occur in the FCC/CEPC/LC/ECFA\nand other national workshops. Informal discussions with early-career Japanese physicists have also\nbeen organised.\nTo build an extensive community of HEP physicists, the IFNC is also developing a finer structure,\nidentifying institutional contacts for the participating institutes inside a country (up to 20 or 30\nindividuals for certain countries, such as France, Germany, Italy or the UK, and even more for\nthe US), the goal being to have a vast majority of HEP institutes contributing, or on the verge of\ncontributing, to the project by the end of the next European Strategy Update (2026).\n208\n\nIn parallel, the PED group has also launched a call for Expressions of Interests (EoI\u2019s), in October\n2024, to encourage the different institutes to get together and collaborate on innovative FCC sub-detector\nR&D within the DRD Collaborations, and on detector concept studies, with the FCC integration as\nmain objective. A first version of these sub-detector EoI\u2019s will be submitted as input to the European\nStrategy Group by March 31st, 2025, and will be the basis for continuing development and consolidation\nduring the next phase of the FCC study, until the end of 2027, with more R&D, prototype construction,\ndetailed simulation, test beams, etc. Detector concepts EoI\u2019s will follow a similar development. Different\ncombinations of sub-detectors will be integrated and tested in the common software to reach optimal\nperformance, possibly as a function of the many physics objectives. Further steps are also envisioned,\nsuch as documenting, as an additional input to the European Strategy, the potential contribution of the\ndifferent countries to FCC in the coming years, should the project be recommended and then approved.\nThe work with the scientific community progresses on a daily basis in the working groups of the\nPED pillar and gets a broader exposure twice a year during the \u2018FCC Collaboration Weeks\u2019 in Spring\n(2021 at CERN; 2022 in Paris; 2023 in London; 2024 in San Francisco; 2025 in Vienna) and the \u2018FCC\nPhysics Workshops\u2019 in Winter (2022 in Liverpool; 2023 in Krakow; 2024 in Annecy; 2025 at CERN),\nallowing the community to be reinforced and new scientific collaborations to emerge. A strong FCC\nparticipation in the US Community Study on the Future of Particle Physics (\u2018Snowmass 2021\u2019) acted as\na decisive seed for the FCC effort in the US and was followed by three US-FCC workshops in 2023, 2024,\nand 2025. Besides, many national FCC Collaboration workshops have taken place, in essentially all large\ncountries or regions of Europe and in the US, with active participation from the PED coordination group,\nyielding a significant growth of the PED part of the Collaboration in the past five years.\nSeveral funding agencies have already reacted very positively to this evolution, decisively sup-\nported by substantive diplomatic work from the CERN management. The most resounding three exam-\nples are listed below.\n1. In April 2024, the White House and CERN signed a joint statement of intent [839] saying, in\nparticular, \u201cShould the member states determine that FCC-ee is likely to be CERN\u2019s next world-\nleading research facility, the US intends to collaborate on its construction and physics exploitation,\nsubject to appropriate domestic approvals\u201d.\n2. In June 2024, the CERN Council approved the Medium Term Plan (MTP) for the period 2025\u2013\n2029 [840], including the funding of a bottom-up resource request for FCC-specific new positions.\n3. In September 2024, the EU Competitiveness Report [841] was publicly released, with the follow-\ning statements: \u201cOne of CERN\u2019s most promising current projects, with significant scientific po-\ntential, is the construction of the Future Circular Collider (FCC): a 90-km ring designed initially\nfor an electron collider and later for a hadron collider. [...] Refinancing CERN and ensuring its\ncontinued global leadership in frontier research should be regarded as a top EU priority\u201d.\nFollowing the approval of the CERN MTP in June 2024, CERN created a dedicated FCC group\nin the EP department, effective since September 2024, with dedicated new positions (fellows, students,\nscientific associates, visitors) over the next three years. This sends another strong signal to the HEP\ncommunity worldwide, regarding the host-lab commitment to FCC. Past experience has shown that even\na moderately-sized host-lab group provides a significant leverage on contributions from the particle-\nphysics community at other institutes. It is now anticipated that the creation of this group will be a\nstrong incentive for CERN contract holders to reassign part of their time to the FCC project, starting\nwith the supervision of the new recruits. As the project moves to the next phase, many more engineers\nand detector physicists will be needed soon. The current situation is being carefully monitored and\nit is expected that a significant pool of these engineers and physicists will transition to FCC detector\ndevelopment as the construction for the HL-LHC upgrades begins to wind down.\n209\n\nAssuming a positive recommendation of the CERN Council at around 2028, the FCC Collabora-\ntion expects that an FCC Committee (equivalent to the LHCC for the LHC experiments) will be formed\nby the CERN management and that a call for FCC detector Conceptual Design Reports will be issued\nsoon after. Proto-collaborations (in particular, subsets of the FCC Collaboration, but not only) could then\nanswer this call shortly after 2030 with full detector concept proposals.\nFinally, the coordination and structuring of the theoretical work needed to match the anticipated\nexperimental precision of the FCC data has started during the Feasibility Study. Several successful mini-\nworkshops were organised (Targets and Tools, Flavour Physics Programme, BSM Physics Programme,\nHiggs/Top/EW Physics Programme, Parton Shower, Phenomenology) with between 100 and 350 partic-\nipants. The CERN/TH FCC team currently consists of three physicists, with the occasional participation\nof up to eight staff members and fellows, reflecting a genuine academic interest in working on the FCC\nphysics among theorists. Needless to say, more dedicated resources will be needed for a worldwide\norganisation during the next phases of the FCC study.\n210\n\n11\nOutlook\nThe alignment of stars that led, in 2011/2012, to the concept of a \u223c100 km electron-positron collider\nin the same tunnel as a future 100 TeV proton-proton collider in the Geneva basin and, in 2020, to the\nupdate of the European Strategy for Particle Physics (ESPPU) endorsing the FCC feasibility study as\na top priority for CERN and its international partners, has presented the global HEP community with\na unique and exceptional opportunity to advance the field. After almost five years of Feasibility Study\nperformed by a worldwide consortium of scientists and engineers, the particle physicists \u2014including the\nearly-career contingent\u2014 are now steadily coalescing around the initial-stage machine (FCC-ee) as the\nfirst priority for a post-LHC collider at CERN.\nThe FCC-ee offers ideal conditions (high luminosity, centre-of-mass energy calibration, possibly\nmonochromatisation, and moderate beam-induced backgrounds) for the intensity-frontier study of the\nfour heaviest particles of the Standard Model, accumulating enormous samples (6 \u00d7 1012 Z bosons at\n88\u201394 GeV, 5\u00d7108 W bosons at and above 157 GeV, 2.8\u00d7106 Higgs bosons at and above 240 GeV, and\n4 \u00d7 106 top quarks at and above 340 GeV) in only a few years of operation at each energy point. With a\nwealth of opportunities for precision electroweak, QCD, flavour, and Higgs measurements, searches for\nrare or forbidden processes, and the possible discovery of feebly coupled particles, FCC-ee is sensitive\nto essentially any kind of new physics from a few GeV up to scales of 10 to 100 TeV, over an extremely\nbroad range of couplings. These studies may help address the most profound questions of particle physics\ntoday. What is the nature of dark matter? How did the antimatter disappear? What is responsible for the\nnon-zero neutrino masses? Even if FCC-ee were to \u2018only\u2019 confirm the Standard Model with a precision\nup to three orders of magnitude better than today, theories that propose solutions to these fundamental\nquestions would become very tightly constrained, thus guiding the development of new models and\nimproving significantly the understanding of the creation of the Universe. It is instructive to recall that\none of the foundation stones of modern physics is a null experiment: the absence of discovery of the\nEther by the Michelson\u2013Morley experiment in 1887.\nThe FCC-ee is also the perfect springboard for a 100 TeV hadron collider (FCC-hh), for which it\nprovides a major fraction of the infrastructure. The complementary and synergistic exploratory physics\nprogrammes of these two machines offer a uniquely powerful long-term vision. In a way not too dis-\nsimilar from the discovery of Neptune in 1846, which was predicted by the precise measurement of the\norbit of Uranus in 1843 (inconsistent with Newton\u2019s laws applied to the solar system of the seven planets\nobserved at that time), any deviation with respect to the Standard Model predictions observed at FCC-ee\nis testable directly with FCC-hh, up to a scale of 40 TeV. When a new physics signal is eventually ob-\nserved at FCC-hh or elsewhere, the FCC-ee precision measurements \u2014whether they agree or not with\nthe Standard Model\u2014 will be an invaluable resource in establishing the nature of the underlying physics.\nThe FCC integrated project is also able to measure the Higgs boson interactions with fermions\nand gauge bosons with high precision (down to a part in a thousand) without theoretical hypotheses. The\nHiggs potential, modelled by the Higgs boson self interactions, plays a fascinating and central role in\nthe cosmological history of the universe. A first determination of the trilinear Higgs boson self-coupling\nwith a precision of the order of 25% will be provided by HL-LHC through the measurement of the\nHiggs-pair production cross section. A qualitatively different and complementary determination with a\nsimilar precision will exploit the per-mil-level measurement of the single-Higgs production cross section\nat FCC-ee, yielding a combined precision better than 20%. A unique per-cent level measurement of the\ntrilinear Higgs self-coupling will only become available with FCC-hh.\nTo date, there is no other collider project that can even remotely compete with such an exploratory\nbreadth and depth: the most complete understanding of the Higgs sector; the unique interplay between\nthe electroweak, flavour, and Higgs measurements at the intensity frontier; the multiple synergies be-\ntween FCC-ee and FCC-hh; the access to the smallest couplings and the highest energy scales; in all\naspects, the FCC integrated programme offers outstanding physics prospects. The FCC project, with its\nfour interaction points, therefore suits to perfection the scientific ambitions of CERN and of its worldwide\n211\n\ncommunity of 15 000 users. It is also remarkable that the overall duration; the electricity consumption;\nthe total cost; and the life-cycle carbon footprint of the FCC-ee construction and operation are all very\nsignificantly smaller [14] than those of other (lower luminosity) Higgs factory options at CERN once\nnormalised to their physics output (i.e., once the running time of these alternative projects is extended to\nmatch the same Higgs-coupling precision as FCC-ee, and yet, disregarding the richness of the remain-\nder of the FCC-ee physics programme, which lies beyond these other options). Furthermore, the FCC\nintegrated project minimises the carbon emissions on the road to the highest energies, as the FCC-ee\ninfrastructure will be fully recycled for FCC-hh. The FCC infrastructure could also be repurposed to\nhouse a fast accelerator and injector for a very high energy muon collider in the LEP/LHC tunnel.\nThe delivery of this Feasibility Study marks the completion of the first phase of an extended and\nintensive programme of work. Even though the e+e\u2212collider is currently scheduled to deliver its first\ncollisions in the second half of the 2040\u2019s, the timeline of the project, displayed in Fig. 140 for both the\naccelerator and the experiments, is tightly filled with important deadlines that must be met and critical\nmilestones that cannot be missed.\nFig. 140:\nPossible timeline of the FCC-ee project between the end of the feasibility study and the start of the first\nFCC-ee physics run, with key dates for the project as a whole (pink), and separately for the accelerator (left side,\ngreen) and for the detectors (right side, blue). (The acronym FC3 stands for \u2018FCC Committee\u2019.)\nStart of FCC-ee physics run\nFCC-ee Accelerator\nKey dates\nFCC-ee Detectors\nFCC Approval: Start of prototyping work .\nEuropean Strategy Update: FCC Recommendation\nFC3 formation, call for CDRs, collaboration forming\nEnd of HL-LHC upgrade: more ATS personnel available .\nDetector CDRs (>4) submitted to FC3\nDetector component production\nFour detector TDRs completed\nStart detector installation\nStart detector commissioning\nEnd of HL-LHC\nStart of ground-breaking and CE at IPs\nIndustrialisation and component production\nTechnical design & prototyping completed\nStart accelerator installation\nStart accelerator commissioning\nEnd of HL-LHC upgrade: more detector experts available\nDetector EoI submission by the community\n\u2013 2047\n\u2013 2046\n\u2013 2045\n\u2013 2044\n\u2013 2043\n\u2013 2042\n\u2013 2041\n\u2013 2040\n\u2013 2039\n\u2013 2038\n\u2013 2037\n\u2013 2036\n\u2013 2035\n\u2013 2034\n\u2013 2033\n\u2013 2032\n\u2013 2031\n\u2013 2030\n\u2013 2029\n\u2013 2028\n\u2013 2027\n\u2013 2026\n\u2013 2025\nFCC Feasibility Study Report\n2047 \u2013\n2046 \u2013\n2045 \u2013\n2044 \u2013\n2043 \u2013\n2042 \u2013\n2041 \u2013\n2040 \u2013\n2039 \u2013\n2038 \u2013\n2037 \u2013\n2036 \u2013\n2035 \u2013\n2034 \u2013\n2033 \u2013\n2032 \u2013\n2031 \u2013\n2030 \u2013\n2029 \u2013\n2028 \u2013\n2027 \u2013\n2026 \u2013\n2025 \u2013\n212\n\nThe first of these milestones has been for the particle physics community to prepare expressions of\ninterest (EoIs) for critical detector components towards the realisation of up to four experiments, in time\nfor the forthcoming European Strategy Update. More EoIs are foreseen if FCC-ee is recommended as the\npreferred post-LHC project at CERN by the European Strategy Group. Should the project be approved\nby CERN Council on the basis of this recommendation, a formal call for the creation of experiment\nproto-collaborations will be launched, towards the submission of Detector Conceptual Design Reports\n(CDRs) a few years later, followed by detector Technical Design Reports (TDRs) in the mid-2030\u2019s.\nAchieving these ambitious goals will require an appropriate and timely re-organisation of activities over\nthe coming couple of years, and a significant injection of (human and financial) resources in the project.\nIn parallel with detector design, construction, installation, and commissioning, the road towards\nthe first collisions is paved with many other exigencies to respond to, a partial list of which follows.\n\u2013 First and foremost, the effort towards the goal of matching theoretical calculation uncertainties\nto the expected statistical power of the collider (and propagating these calculations to technically\naccurate Monte Carlo generators), so as to optimally exploit the data from FCC-ee and, later, from\nFCC-hh, needs to be immediately structured and sustained with appropriate resources, from the\nclear roadmap established during the Feasibility Study.\n\u2013 In the coming few years, the requirements from detailed physics case studies will continue to be\nthe driving factor in efforts to design the most technologically-advanced (but also the most real-\nistic) FCC-ee detector concepts, to ensure the full coverage of the wide and challenging physics\nprogramme. These efforts will have to be intensified, in particular at the Z pole, where the require-\nments from physics are expected to be the most demanding.\n\u2013 These physics studies will need to be backed up with a versatile and reliable software ecosystem,\nfrom accurate Monte Carlo event generators to modern event reconstruction and analysis software,\npassing through detailed detector simulation. Achieving this will demand a significant increase of\nboth computing and human resources, which were a limiting factor during the Feasibility Study.\nTo broaden the project resource base, continued efforts are required to attract (many) more external\ncontributors from institutes worldwide. Promoting positions shared between LHC and FCC will\nalso foster joint development efforts and enhance expertise exchange.\n\u2013 Regarding the interaction region, the integration strategy of the inner sub-detectors (e.g., vertex\ndetectors, luminometers, superconducting pipes, supporting structures) with the accelerator com-\nponents will be established, as their designs are finalised. Methods for opening and maintenance\nof the detector elements, together with their alignment with respect to the beams will be further\ndeveloped, and possible consequences on the cavern dimensions will be evaluated. Most impor-\ntantly, the studies of the impact of all beam-induced backgrounds on the detector performance and\nmitigation solutions will need to be consolidated for all sub-detectors.\n\u2013 The measurement and monitoring of the centre-of-mass energy will be one of the cornerstones of\nthe whole physics programme. The baseline scheme presented in this Volume must be refined and\nmade fully reliable, and alternative schemes will be considered. Specifically, the possibility of in-\njecting already polarised electron and positron bunches will be thoroughly investigated. Improved\nschemes for monochromatisation will be systematically studied in view of proposing a sustainable\nmethod for the electron Yukawa coupling measurement.\n\u2013 Finally, detailed studies of the physics programme of FCC-ee on the one hand, and groundwork\nstudies of physics and detectors at FCC-hh on the other, will continue to further extend the explo-\nration of the standalone potential of each collider, and the synergies between them. These efforts\nwill also reflect the guidelines that will emerge from the review of the Feasibility Study Report\nand from the ESPPU discussions.\nWhile it will be years before all these goals are attained, there is no doubt that the recommendation of the\nFCC project by the forthcoming ESU will catalyse the engagement of the particle physics community\n213\n\nat large on FCC-ee. The growing interest from young scientists in the project must be recognised with\nappropriate career opportunities.\nThe baseline choice of collision energies and running sequence (Z pole, WW threshold, ZH maxi-\nmum, and tt threshold, as shown in Fig. 141) with four interaction points is sufficient to demonstrate that\nFCC-ee offers an extraordinary list of opportunities (and associated challenges) for milestone measure-\nments with a real chance of discovery. Looking ahead, this list will only become richer as the investiga-\ntions deepen, and it is already clear that more integrated luminosity and the extension of the programme\nto encompass additional energy points would increase the FCC science value still further [17]. In paral-\nlel, the FCC-ee machine parameters are now different from those that prevailed at the time of the CDR,\nand will continue to evolve in the next phase of the study, while the understanding of the physics per-\nformance of the experiments is progressing. This perspective may significantly modify, or enrich, the\ndesirable scientific programme, as pictured in Fig. 141.\nFig. 141:\nPotential physics programme for FCC-ee, ordered by increasing centre-of-mass energy, without indication of\na specific chronological sequence. The events highlighted in red indicate the minimal programme with fifteen years of\nrunning, and with the corresponding integrated luminosities and physics outcome. The numbers of Z, WW, ZH, and tt\nevents delivered to four interaction points are indicated. A possible wider physics programme, with additional centre-of-mass\nenergies, is highlighted in blue.\nTotal \nintegrated \nluminosity \n(ab-1)\nEnergy \n(GeV)\nAdditional opportunities\nCDR baseline runs (4IPs)\nFCC-ee Physics Runs Ordered by Energy\nEW sector\nsensitivity to Higgs self-coupling via quantum effects\nHiggs sector\nindirect sensitivity \n to new physics \nby probing \nSM predictions\nPhysics \nhighlights\n# events \n(4 IPs)\nO(2\u00d7106)\nO(2\u00d7106)\nO(108)\nO(1013)\n240\nHiggs couplings \n\ud835\udf0eZH\n10.8\nZH\n157.5\n162.5\n19.2\nW mass and width \nN\ud835\udf08 \n\ud835\udefcS \nflavour (e.g. Vcb)\nWW\n340\n350\n0.4\nmtop\n365\n2.7\ntop EW couplings \nHiggs VBF production \n(\u0393H and Higgs couplings improved) \n\u2026\n91.2\n125\n88\n94\n40\n40\nZ lineshape \nQCD \nflavour \nrare decays \ndark sector\nZ\nQCD \nprecision \nstudies\nO(1)\n40\n60\n\u2026\n125\nelectron \nYukawa\n30\n217\nHiggs mass\n5\ntt\n\u2026\n214\n\nFor example, the possibility to run at \u221as = 125 GeV, with a centre-of-mass energy spread of\nthe order of the Higgs boson width, is under consideration, towards a 3 \u03c3 evidence for the electron\nYukawa coupling. Precision QCD studies with a few ab\u22121 at centre-of-mass energies of 20, 30, 40,\n. . . , 80 GeV are very appealing to a significant fraction of the HEP community. Because the study\nof the monochromatisation schemes required for the electron Yukawa measurement are not yet at a\nmature stage; and because Z-pole data with energetic initial-state radiation can in principle also explore\nlower centre-of-mass energies; no proposal is made yet to include these energy points in the baseline\nprogramme.\nThese additional possibilities and corresponding science value further demonstrates the flexibility\nand breadth of the FCC-ee physics potential. An increase of the FCC-ee specific luminosity would\nenable the physics programme to be extended to encompass at least some of these possibilities within the\ncurrently envisaged 15-year timescale. It will ultimately be up to the experimental collaborations and the\nrelevant scientific committees to optimise the time flexibility and to tailor the FCC-ee operation scenario\naccording to a number of factors that cannot be controlled today. For example, external events such as the\nFCC-hh magnet readiness or the CERN financial situation may call for a change in the overall duration\nof the FCC-ee running time. Furthermore, intriguing early results may motivate additional running at a\ngiven working point. Meanwhile, new avenues will be explored towards increasing the luminosities at\nall energies.\nAt the end of the HL-LHC operation, the LEP-LHC integrated programme will have delivered sus-\ntained scientific excellence for over 50 years, and greatly advanced our understanding of the fundamental\ninteractions. The succession of FCC-ee and FCC-hh in a common tunnel will replicate and magnify this\nsuccess, with vastly better precision and increased energies. The FCC integrated programme offers out-\nstanding prospects for progress in a wealth of topics, including Higgs, electroweak, and flavour physics,\nas well as remarkable sensitivity in direct searches for both feebly coupled low-mass particles and those\nthat may exist up to many tens of TeV. The upcoming ESPPU provides an opportunity for the global HEP\ncommunity to endorse this vision, and then to work together so as to enable the first stage of this project,\nFCC-ee, to be realised in a timely fashion. Seizing this opportunity will be an important step forward in\nthe journey towards a more complete understanding of the laws of nature.\n215\n\nReferences\n[1] CMS Collaboration, \u201cObservation of a new boson at a mass of 125 GeV with the CMS\nexperiment at the LHC\u201d, Phys. Lett. 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Andrade,34\nN. Andres,25 M. Andr\u00e9s-Carcasona,35 T. Andri\u0107,36 S. Ansoldi,37, 38 J. M. Antelis,39 S. Antier,40 M. Aoumi,41\nT. Apostolatos,42 E. Z. Appavuravther,43, 44 S. Appert,1 S. K. Apple,45 K. Arai,1 A. Araya,46 M. C. Araya,1\nJ. S. Areeda,47 M. Ar\u00e8ne,48 N. Aritomi,19 N. Arnaud,32, 49 M. Arogeti,50 S. M. Aronson,8 K. G. Arun,51\nH. Asada,52 G. Ashton,53 Y. Aso,19, 54 M. Assiduo,55, 56 S. Assis de Souza Melo,49 S. M. Aston,57 P. Astone,58\nF. Aubin,56 K. AultONeal,39 S. Babak,48 A. Badalyan,59 F. Badaracco,60 C. Badger,61 S. Bae,62\nS. Bagnasco,22 Y. Bai,1 J. G. Baier,63 L. Baiotti,64 J. Baird,48 R. Bajpai,65 T. Baka,66 M. Ball,67\nG. Ballardin,49 S. W. Ballmer,68 G. Baltus,69 S. Banagiri,70 B. Banerjee,36 D. Bankar,12 P. Baral,7\nJ. C. Barayoga,1 J. Barber,16 B. C. Barish,1 D. Barker,71 P. Barneo,34, 72 F. Barone,73, 4 B. Barr,23\nL. Barsotti,74 M. Barsuglia,48 D. Barta,75 S. D. Barthelmy,76 M. A. Barton,23 I. Bartos,77 S. Basak,18\nA. Basalaev,78 R. Bassiri,79 A. Basti,80, 17 M. Bawaj,81, 43 J. C. Bayley,23 A. C. Baylor,7 M. Bazzan,82, 83\nB. B\u00e9csy,84 V. M. Bedakihale,85 F. Beirnaert,86 M. Bejger,87 A. S. Bell,23 V. Benedetto,88 D. Beniwal,89\nW. Benoit,27 J. D. Bentley,78 M. Ben Yaala,90 S. Bera,91 M. Berbel,92 F. Bergamin,10, 11 B. K. Berger,79\nS. Bernuzzi,93 M. Beroiz,1 C. P. L. Berry,23 D. Bersanetti,94 A. Bertolini,29 J. Betzwieser,57\nD. Beveridge,24 N. Bevins,95 R. Bhandare,96 A. V. Bhandari,12 U. Bhardwaj,97, 29 R. Bhatt,1\nD. Bhattacharjee,63 S. Bhaumik,77 A. Bianchi,29, 98 I. A. Bilenko,99 M. Bilicki,100 G. Billingsley,1\nS. Bini,101, 102 O. Birnholtz,103 S. Biscans,1, 74 M. Bischi,55, 56 S. Biscoveanu,74 A. Bisht,10, 11 B. Biswas,12\nM. Bitossi,49, 17 M.-A. Bizouard,40 J. K. Blackburn,1 C. D. Blair,24, 57 D. G. Blair,24 R. M. Blair,71\nF. Bobba,104, 105 N. Bode,10, 11 M. Bo\u00ebr,40 G. Bogaert,40 G. Boileau,106, 40 M. Boldrini,107, 58\nG. N. Bolingbroke,89 L. D. Bonavena,82 R. Bondarescu,34 F. Bondu,108 E. Bonilla,79 G. S. Bonilla,47\nR. Bonnand,25 P. Booker,10, 11 R. Bork,1 V. Boschi,17 N. Bose,109 S. Bose,12 V. Bossilkov,24 V. Boudart,69\nY. Bouffanais,82, 83 A. Bozzi,49 C. Bradaschia,17 P. R. Brady,7 M. Braglia,110 A. Branch,57\nM. Branchesi,36, 111 J. E. Brau,67 M. Breschi,93 T. Briant,112 A. Brillet,40 M. Brinkmann,10, 11 P. Brockill,7\nA. F. Brooks,1 J. Brooks,49 D. D. Brown,89 S. Brunett,1 G. Bruno,60 R. Bruntz,113 J. Bryant,114 F. Bucci,56\nJ. Buchanan,113 O. Bulashenko,34, 72 T. Bulik,115 H. J. Bulten,29 A. Buonanno,116, 117 K. Burtnyk,71\nR. Buscicchio,114, 118, 119 D. Buskulic,25 C. Buy,120 R. L. Byer,79 G. S. Cabourn Davies,121 G. Cabras,37, 38\nR. Cabrita,60 L. Cadonati,50 S. Caesar,16 G. Cagnoli,122 C. Cahillane,71 J. Calder\u00f3n Bustillo,123\nJ. D. Callaghan,23 T. A. Callister,124, 125 E. Calloni,26, 4 J. B. Camp,76 M. Canepa,126, 94\nG. Caneva Santoro,35 M. Cannavacciuolo,104 K. C. Cannon,33 H. Cao,89 Z. Cao,127 L. A. Capistran,128\nE. Capocasa,48 E. Capote,68 G. Carapella,104, 105 F. Carbognani,49 M. Carlassara,10, 11 J. B. Carlin,129\nM. Carpinelli,118, 130, 49 J. J. Carter,10, 11 G. Carullo,80, 17 J. Casanueva Diaz,49 C. Casentini,131, 132\nG. Castaldi,133 S. Y. Castro-Lucas,134 S. Caudill,29, 66 M. Cavagli\u00e0,135 R. Cavalieri,49 G. Cella,17\nP. Cerd\u00e1-Dur\u00e1n,136 E. Cesarini,132 W. Chaibi,40 W. Chakalis,124, 125 S. Chalathadka Subrahmanya,78\nE. Champion,137 C. Chan,33 C. L. Chan,138 K. Chandra,109 I. P. Chang,139 W. Chang,139 P. Chanial,49, 48\nS. Chao,139 C. Chapman-Bird,23 E. L. Charlton,113 P. Charlton,140 E. Chassande-Mottin,48 L. Chastain,5\nC. Chatterjee,24 Debarati Chatterjee,12 Deep Chatterjee,7 M. Chaturvedi,96 S. Chaty,48 K. Chatziioannou,1\nD. Chen,141 H. Chen,139 H. Y. Chen,74 J. Chen,74 K. H. Chen,142 X. Chen,24 Y.-R. Chen,139 Y. Chen,143\nH. Cheng,77 P. Chessa,80, 17 H. Y. Cheung,138 H. Y. Chia,77 F. Chiadini,144, 105 C-I. Chiang,145 C. Chiang,142\nG. Chiarini,83 A. Chiba,146 R. Chiba,147 R. Chierici,148 A. Chincarini,94 M. L. Chiofalo,80, 17 A. Chiummo,49\nS. Choudhary,12 N. Christensen,40 S. S. Y. Chua,9 K. W. Chung,61 G. Ciani,82, 83 P. Ciecielag,87 M. Cie\u015blar,87\nM. Cifaldi,131, 132 A. A. Ciobanu,89 R. Ciolfi,149, 83 F. Clara,71 J. A. Clark,1, 50 T. A. Clarke,5\nP. Clearwater,150 S. Clesse,151 F. Cleva,40 E. Coccia,36, 111 E. Codazzo,36 P.-F. Cohadon,112 M. Colleoni,91\nC. G. Collette,30 A. Colombo,118, 119 M. Colpi,118, 119 C. M. Compton,71 L. Conti,83 S. J. Cooper,114\nP. Corban,57 T. R. Corbitt,8 I. Cordero-Carri\u00f3n,152 S. Corezzi,81, 43 N. J. Cornish,84 A. Corsi,153\nS. Cortese,49 A. C. Coschizza,154 R. Cottingham,57 M. W. Coughlin,27 J.-P. Coulon,40 S. T. Countryman,155\nJ.-F. Coupechoux,148 B. Cousins,6 P. Couvares,1 D. M. Coward,24 M. J. Cowart,57 B. D. Cowburn,137\nD. C. Coyne,1 R. Coyne,156 K. Craig,90 J. D. E. Creighton,7 T. D. Creighton,157 A. W. Criswell,27\nJ. C. G. Crockett-Gray,8 M. Croquette,112 S. G. Crowder,158 J. R. Cudell,69 T. J. Cullen,1 A. Cumming,23\nR. Cummings,23 E. Cuoco,49, 159, 17 M. Cury\u0142o,115 P. Dabadie,122 T. Dal Canton,32 S. Dall\u2019Osso,58 G. D\u00e1lya,86\nB. D\u2019Angelo,126, 94 S. Danilishin,28, 29 S. D\u2019Antonio,132 K. Danzmann,10, 11 K. E. Darroch,113\nC. Darsow-Fromm,78 A. Dasgupta,85 L. E. H. Datrier,23 Sayantani Datta,51 V. Dattilo,49 I. Dave,96\nA. Davenport,134 M. Davier,32 D. Davis,1 M. C. Davis,95 E. J. Daw,160 M. Dax,117 D. DeBra,79, \u2217\narXiv:2302.03676v1 [gr-qc] 7 Feb 2023\n\n2\nM. Deenadayalan,12 J. Degallaix,161 M. De Laurentis,26, 4 S. Del\u00e9glise,112 V. Del Favero,137 F. De Lillo,60\nN. De Lillo,23 D. Dell\u2019Aquila,162, 130 W. Del Pozzo,80, 17 F. De Matteis,131, 132 V. D\u2019Emilio,16 N. Demos,74\nT. Dent,123 A. Depasse,60 R. De Pietri,163, 164 R. De Rosa,26, 4 C. De Rossi,49 R. DeSalvo,133 R. De Simone,144\nS. Dhurandhar,12 R. Diab,77 P. Z. Diamond,63 M. C. D\u00edaz,157 N. A. Didio,68 T. Dietrich,117 L. Di Fiore,4\nC. Di Fronzo,30 C. Di Giorgio,104, 105 F. Di Giovanni,136 M. Di Giovanni,36 T. Di Girolamo,26, 4 D. Diksha,29, 28\nA. Di Lieto,80, 17 A. Di Michele,81 S. Di Pace,107, 58 I. Di Palma,107, 58 F. Di Renzo,49, 17 Divyajyoti,165\nA. Dmitriev,114 Z. Doctor,70 E. Dohmen,71 P. P. Doleva,113 L. Donahue,166 L. D\u2019Onofrio,26, 4 F. Donovan,74\nK. L. Dooley,16 T. Dooney,66 S. Doravari,12 O. Dorosh,167 M. Drago,107, 58 J. C. Driggers,71 Y. Drori,1\nJ.-G. Ducoin,168, 48 L. Dunn,129 U. Dupletsa,36 O. Durante,104, 105 D. D\u2019Urso,162, 130 P.-A. Duverne,32\nS. E. Dwyer,71 C. Eassa,71 P. J. Easter,5 M. Ebersold,169 T. Eckhardt,78 G. Eddolls,23 B. Edelman,67\nT. B. Edo,1 O. Edy,121 A. Effler,57 J. Eichholz,9 M. Eisenmann,19 R. A. Eisenstein,74 A. Ejlli,16\nE. Engelby,47 A. J. Engl,79 L. Errico,26, 4 R. C. Essick,170 H. Estell\u00e9s,117 D. Estevez,171 T. Etzel,1\nC. Evans,16 M. Evans,74 T. M. Evans,57 T. Evstafyeva,13 B. E. Ewing,6 F. Fabrizi,55, 56 F. Faedi,56\nV. Fafone,131, 132, 36 H. Fair,68 S. Fairhurst,16 P. C. Fan,166 X. Fan,172 A. M. Farah,173 B. Farr,67\nW. M. Farr,124, 125 E. J. Fauchon-Jones,16 G. Favaro,82 M. Favata,174 M. Fays,69 J. Feicht,1 M. M. Fejer,79\nE. Fenyvesi,75, 175 D. L. Ferguson,176 A. Fernandez-Galiana,74 I. Ferrante,80, 17 T. A. Ferreira,15\nF. Fidecaro,80, 17 P. Figura,115 A. Fiori,17, 80 I. Fiori,49 M. Fishbach,70 R. P. Fisher,113 R. Fittipaldi,177, 105\nV. Fiumara,178, 105 R. Flaminio,25 S. M. Fleischer,179 L. S. Fleming,180 E. Floden,27 H. K. Fong,33\nJ. A. Font,136, 181 B. Fornal,182 P. W. F. Forsyth,9 A. Franke,78 S. Frasca,107, 58 F. Frasconi,17\nJ. P. Freed,39 Z. Frei,183 A. Freise,29, 98 O. Freitas,184 R. Frey,67 P. Fritschel,74 V. V. Frolov,57\nG. G. Fronz\u00e9,22 Y. Fujimoto,185 I. Fukunaga,186 P. Fulda,77 M. Fyffe,57 H. A. Gabbard,23 W. E. Gabella,187\nB. U. Gadre,117, 66 K. Gaglani,39 J. R. Gair,117 J. Gais,138 S. Galaudage,5 S. Gallardo,188 R. Gamba,93\nD. Ganapathy,74 A. Ganguly,12 D. Gao,79 S. G. Gaonkar,12 B. Garaventa,94, 126 J. Garcia-Bellido,110\nC. Garc\u00eda-N\u00fa\u00f1ez,180 C. Garc\u00eda-Quir\u00f3s,91 K. A. Gardner,154 J. Gargiulo,49 F. Garufi,26, 4 C. Gasbarra,131, 132\nB. Gateley,71 V. Gayathri,77, 7 G. Gemme,94 A. Gennai,17 J. George,96 O. Gerberding,78 L. Gergely,189\nS. Ghonge,50 Abhirup Ghosh,117 Archisman Ghosh,86 Shaon Ghosh,174 Shrobana Ghosh,16 Tathagata Ghosh,12\nL. Giacoppo,107, 58 J. A. Giaime,8, 57 K. D. Giardina,57 D. R. Gibson,180 C. Gier,90 P. Giri,17, 80 F. Gissi,88\nS. Gkaitatzis,49 J. Glanzer,8 A. E. Gleckl,47 F. Glotin,32 J. Godfrey,67 P. Godwin,1 E. Goetz,154 R. Goetz,77\nJ. Golomb,1 B. Goncharov,36 G. Gonz\u00e1lez,8 M. Gosselin,49 R. Gouaty,25 D. W. Gould,9 S. Goyal,18\nB. Grace,9 A. Grado,190, 4 V. Graham,23 M. Granata,161 V. Granata,104 S. Gras,74 P. Grassia,1 C. Gray,71\nR. Gray,191 G. Greco,43 A. C. Green,77 R. Green,16 S. Green,121 S. R. Green,117 A. M. Gretarsson,39\nE. M. Gretarsson,39 D. Griffith,1 W. L. Griffiths,16 H. L. Griggs,50 G. Grignani,81, 43 A. Grimaldi,101, 102\nH. Grote,16 A. S. Gruson,47 D. Guerra,136 D. Guetta,58 G. M. Guidi,55, 56 A. R. Guimaraes,8 H. K. Gulati,85\nF. Gulminelli,192, 193 A. M. Gunny,74 H. Guo,182 Y. Guo,29 Anchal Gupta,1 Anuradha Gupta,194 Ish Gupta,6\nN. C. Gupta,85 P. Gupta,29, 66 S. K. Gupta,109 J. Gurs,78 Y. Gushima,195 E. K. Gustafson,1 N. Gutierrez,161\nF. Guzman,128 L. Haegel,48 G. Hain,113 S. Haino,145 O. Halim,38 E. D. Hall,74 E. Z. Hamilton,169\nG. Hammond,23 W.-B. Han,196 M. Haney,169 J. Hanks,71 C. Hanna,6 M. D. Hannam,16\nO. A. Hannuksela,138, 66, 29 H. Hansen,71 J. Hanson,57 R. Harada,33 T. Harder,40 K. Haris,29, 66\nT. Harmark,197 J. Harms,36, 111 G. M. Harry,45 I. W. Harry,121 D. Hartwig,78 B. Haskell,87 C.-J. Haster,74\nJ. S. Hathaway,137 K. Haughian,23 H. Hayakawa,41 K. Hayama,195 F. J. Hayes,23 J. Healy,137 A. Heffernan,91\nA. Heidmann,112 M. C. Heintze,57 J. Heinze,10, 11 J. Heinzel,74 H. Heitmann,40 F. Hellman,198 P. Hello,32\nA. F. Helmling-Cornell,67 G. Hemming,49 M. Hendry,23 I. S. Heng,23 E. Hennes,29 J.-S. Hennig,28, 29\nM. Hennig,28, 29 C. Henshaw,50 F. Hernandez Vivanco,5 M. Heurs,10, 11 A. L. Hewitt,13 S. Higginbotham,16\nS. Hild,28, 29 P. Hill,90 Y. Himemoto,199 A. S. Hines,128 N. Hirata,19 C. Hirose,200 J. Ho,142 S. Hochheim,10, 11\nD. Hofman,161 J. N. Hohmann,78 D. G. Holcomb,95 N. A. Holland,29, 98 K. Holley-Bockelmann,187\nI. J. Hollows,160 Z. J. Holmes,89 K. Holt,57 D. E. Holz,173 Q. Hong,139 J. Hornung,67 S. Hoshino,200\nJ. Hough,23 S. Hourihane,1 D. Howell,124, 125 E. J. Howell,24 C. G. Hoy,16, 121 D. Hoyland,114 B.-H. Hsieh,147\nH.-F. Hsieh,139 C. Hsiung,201 H. Hsu,142 P. Hu,187 Q. Hu,23 H.-Y. Huang,145, 142 Y.-J. Huang,6 Y. Huang,74\nY. T. Huang,202 M. T. H\u00fcbner,129 A. D. Huddart,203 B. Hughey,39 D. C. Y. Hui,204 V. Hui,25 S. Husa,91\nS. H. Huttner,23 R. Huxford,6 T. Huynh-Dinh,57 J. Hyland,23 A. Iakovlev,205 G. A. Iandolo,28\nB. Idzkowski,115 A. Iess,159, 17 K. Inayoshi,206 Y. Inoue,207 G. Iorio,82 P. Iosif,208 J. Irwin,23 M. Isi,124, 125\nM. A. Ismail,142 Y. Itoh,186, 209 B. R. Iyer,18 V. JaberianHamedan,24 T. Jacqmin,112 P.-E. Jacquet,112\nS. J. Jadhav,210 S. P. Jadhav,12 D. Jain,5 T. Jain,13 A. L. James,16 A. Z. Jan,176 K. Jani,187 L. Janiurek,23\nJ. Janquart,66, 29 K. Janssens,106, 40 N. N. Janthalur,210 S. Jaraba,110 P. Jaranowski,211 S. Jarov,154\nP. Jasal,34 R. Jaume,91 W. Javed,16 A. C. Jenkins,61 K. Jenner,89 A. Jennings,71 W. Jia,74 J. Jiang,77\nJian Liu,24 H.-B. Jin,212, 213 K. Johansmeyer,174 G. R. Johns,113 N. A. Johnson,77 R. Johnston,23 N. Johny,10, 11\nA. W. Jones,24 D. H. Jones,9 D. I. Jones,214 P. Jones,114 R. Jones,23 P. Joshi,6 L. Ju,24 K. Jung,215\nJ. Junker,10, 11 V. Juste,171 T. Kajita,216 C. Kalaghatgi,66, 29, 217 V. Kalogera,70 B. Kamai,1 M. Kamiizumi,41\nN. Kanda,209, 186 S. Kandhasamy,12 G. Kang,218 J. B. Kanner,1 S. J. Kapadia,18 D. P. Kapasi,9 S. Karat,1\nC. Karathanasis,35 S. Karki,135 D. Kasamatsu,146 Y. A. Kas-danouche,59 R. Kashyap,6 M. Kasprzack,1\nW. Kastaun,10, 11 J. Kato,146 S. Katsanevas,49 E. Katsavounidis,74 J. K. Katsuren,59 W. Katzman,57\nT. Kaur,24 K. Kawabe,71 K. Kawazoe,195 F. K\u00e9f\u00e9lian,40 D. Keitel,91 I. Kellard,16 J. Kelley-Derzon,77\n\n3\nJ. Kennington,6 J. S. Key,219 S. Khadka,79 F. Y. Khalili,99 S. Khan,16 T. Khanam,153 E. A. Khazanov,205\nM. Khursheed,96 N. Kijbunchoo,9 C. Kim,220 J. C. Kim,221 K. Kim,220 M. H. Kim,222 P. Kim,222 S. Kim,204\nW. S. Kim,223 Y.-M. Kim,215 C. Kimball,70 N. Kimura,41 M. Kinley-Hanlon,23 R. Kirchhoff,10, 11 J. S. Kissel,71\nT. Kiyota,186 S. Klimenko,77 T. Klinger,16 A. M. Knee,154 N. Knust,10, 11 Y. Kobayashi,185 P. Koch,10, 11\nS. M. Koehlenbeck,10, 11 G. Koekoek,29, 28 K. Kohri,224 K. Kokeyama,16 S. Koley,36 N. D. Koliadko,59\nP. Kolitsidou,16 M. Kolstein,35 V. Kondrashov,1 A. K. H. Kong,139 A. Kontos,225 M. Korobko,78\nR. V. Kossak,10, 11 N. Kouvatsos,61 M. Kovalam,24 N. Koyama,200 D. B. Kozak,1 L. Kranzhoff,10, 11\nS. L. Kranzhoff,28, 29 V. Kringel,10, 11 N. V. Krishnendu,10, 11 A. Kr\u00f3lak,226, 167 G. Kuehn,10, 11 P. Kuijer,29\nM. Kukihara,195 S. Kulkarni,194 A. Kumar,210 Praveen Kumar,123 Prayush Kumar,18 Rahul Kumar,71\nRakesh Kumar,85 J. Kume,33 K. Kuns,74 S. Kuroyanagi,110, 227, 228 S. Kuwahara,33 K. Kwak,215 G. Lacaille,23\nP. Lagabbe,25 D. Laghi,120 M. H. Lakkis,30 E. Lalande,229 M. Lalleman,106 A. Lamberts,40, 230 M. Landry,71\nB. B. Lane,74 R. N. Lang,74 J. Lange,176 B. Lantz,79 A. La Rana,58 I. La Rosa,25 A. Lartaux-Vollard,32\nP. D. Lasky,5 J. Lawrence,153 M. Laxen,57 A. Lazzarini,1 C. Lazzaro,82, 83 P. Leaci,107, 58 S. Leavey,10, 11\nS. LeBohec,182 Y. K. Lecoeuche,154 E. Lee,147 H. M. Lee,231 H. W. Lee,221 K. Lee,222 R.-L. Lee,14 R. Lee,74\nS. Lee,232 I. N. Legred,1 J. Lehmann,10, 11 L. Lehner,170 A. Lema\u00eetre,233 M. Lenti,56, 234 M. Leonardi,19\nE. Leonova,97 N. Leroy,32 N. Letendre,25 M. Lethuillier,148 C. Levesque,229 Y. Levin,5 K. Leyde,48\nA. K. Y. Li,1 K. L. Li,235 T. G. F. Li,138 X. Li,143 C.-Y. Lin,142, 236 E. T. Lin,139 F-K. Lin,145 F-L. Lin,237\nF. Lin,142 H. L. Lin,207 H. Lin,142 L. C.-C. Lin,235 F. Linde,217, 29 S. D. Linker,133, 188 T. B. Littenberg,238\nA. Liu,138 G. C. Liu,201 F. Llamas,157 R. K. L. Lo,1 T. Lo,139 L. T. London,74, 97 A. Longo,239 D. Lopez,169\nM. Lopez Portilla,66 M. Lorenzini,131, 132 V. Loriette,240 M. Lormand,57 G. Losurdo,17 T. P. Lott,50\nJ. D. Lough,10, 11 H. A. Loughlin,74 C. O. Lousto,137 G. Lovelace,47 M. J. Lowry,113 H. L\u00fcck,10, 11\nD. Lumaca,131, 132 A. P. Lundgren,121 Y. Lung,138 A. W. Lussier,229 J. E. Lynam,113 L. Ma,139 S. Ma,143\nM. Ma\u2019arif,142 R. Macas,121 M. MacInnis,74 D. M. Macleod,16 I. A. O. MacMillan,1 A. Macquet,35\nI. Maga\u00f1a Hernandez,7 C. Magazz\u00f9,17 R. M. Magee,1 R. Maggiore,114, 29, 98 M. Magnozzi,94, 126 M. Mahesh,78\nS. Mahesh,241 M. Maini,156 E. Majorana,107, 58 C. N. Makarem,1 S. Maliakal,1 A. Malik,96 N. Man,40\nV. Mandic,27 V. Mangano,107, 58 B. Mannix,67 G. L. Mansell,68, 74 G. Mansingh,45 M. Manske,7\nM. Mantovani,49 M. Mapelli,82, 83 F. Marchesoni,44, 43, 242 D. Mar\u00edn Pina,34, 72, 243 F. Marion,25 S. M\u00e1rka,155\nZ. M\u00e1rka,155 C. Markakis,191 A. S. Markosyan,79 A. Markowitz,1 E. Maros,1 A. Marquina,152 S. Marsat,120\nF. Martelli,55, 56 I. W. Martin,23 R. M. Martin,174 B. B. Martinez,128 M. Martinez,35 V. A. Martinez,77\nV. Martinez,122 K. Martinovic,61 D. V. Martynov,114 E. J. Marx,74 H. Masalehdan,78 K. Mason,74\nA. Masserot,25 M. Masso Reid,23 M. Mastrodicasa,58 S. Mastrogiovanni,40 M. Mateu-Lucena,91\nM. Matiushechkina,10, 11 K. Matsunaga,146 N. Mavalvala,74 R. McCarthy,71 D. E. McClelland,9\nP. K. McClincy,6 S. McCormick,57 L. McCuller,1 G. I. McGhee,23 J. McGinn,23 C. McIsaac,121 J. McIver,154\nA. McLeod,24 T. McRae,9 S. T. McWilliams,241 D. Meacher,7 M. Mehmet,10, 11 A. K. Mehta,117 Q. Meijer,66\nA. Melatos,129 G. Mendell,71 A. Menendez-Vazquez,35 C. S. Menoni,134 R. A. Mercer,7 L. Mereni,161\nK. Merfeld,67 E. L. Merilh,57 J. D. Merritt,67 M. Merzougui,40 C. Messenger,23 C. Messick,74\nP. M. Meyers,143 F. Meylahn,10, 11 A. Mhaske,12 A. Miani,101, 102 H. Miao,244 I. Michaloliakos,77 C. Michel,161\nY. Michimura,1, 33 H. Middleton,114 D. P. Mihaylov,117 A. Miller,188 A. L. Miller,60 B. Miller,97, 29\nS. Miller,1 M. Millhouse,50, 129 J. C. Mills,16 E. Milotti,245, 38 Y. Minenkov,132 N. Mio,246 Ll. M. Mir,35\nM. Miravet-Ten\u00e9s,136 A. Mishra,12 C. Mishra,165 T. Mishra,77 T. Mistry,160 A. L. Mitchell,29, 98 S. Mitra,12\nV. P. Mitrofanov,99 G. Mitselmakher,77 R. Mittleman,74 O. Miyakawa,41 S. Miyoki,41 Geoffrey Mo,74\nL. M. Modafferi,91 E. Moguel,63 S. R. P. Mohapatra,74 S. R. Mohite,7 M. Molina-Ruiz,198 C. Mondal,192\nM. Mondin,188 M. Montani,55, 56 C. J. Moore,114 J. Moragues,91 D. Moraru,71 F. Morawski,87 A. More,12\nS. More,12 C. Moreno,39 G. Moreno,71 S. Morisaki,7 Y. Moriwaki,146 G. Morras,110 A. Moscatello,82\nB. Mours,171 C. M. Mow-Lowry,29, 98 S. Mozzon,121 F. Muciaccia,107, 58 D. Mukherjee,238 Soma Mukherjee,157\nSubroto Mukherjee,85 Suvodip Mukherjee,170, 97, 247 N. Mukund,10, 11 A. Mullavey,57 J. Munch,89\nE. A. Mu\u00f1iz,68 P. G. Murray,23 J. Murray-Dean,16 S. Muusse,89 S. L. Nadji,10, 11 A. Nagar,22, 248 T. Nagar,5\nN. Nagarajan,23 K. Nakamura,19 H. Nakano,249 M. Nakano,57 Y. Nakayama,250 V. Napolano,49\nI. Nardecchia,131, 132 T. Narikawa,147 H. Narola,66 L. Naticchioni,58 R. K. Nayak,251 B. F. Neil,24\nJ. Neilson,88, 105 A. Nelson,128 T. J. N. Nelson,57 M. Nery,10, 11 S. Nesseris,110 A. Neunzert,219 K. Y. Ng,74\nS. W. S. Ng,89 C. Nguyen,48 P. Nguyen,67 R. Nguyen,16 T. Nguyen,74 L. Nguyen Quynh,252 S. A. Nichols,8\nG. Nieradka,87 Y. Nishino,19, 253 A. Nishizawa,33 S. Nissanke,97, 29 E. Nitoglia,148 W. Niu,6 F. Nocera,49\nM. Norman,16 C. North,16 J. Novak,254, 255, 256, 257 J. F. Nu\u00f1o Siles,110 G. Nurbek,157 L. K. Nuttall,121\nJ. Oberling,71 J. O\u2019Dell,203 E. Oelker,23 M. Oertel,254, 255, 256, 258, 257 G. Oganesyan,36, 111 J. J. Oh,223\nK. Oh,204 S. H. Oh,223 T. O\u2019Hanlon,57 M. Ohashi,41 T. Ohashi,185 M. Ohkawa,200 F. Ohme,10, 11 H. Ohta,33\nA. S. Oliveira,155 R. Oliveri,254, 255, 256 K. Oohara,259, 260 B. O\u2019Reilly,57 R. G. Ormiston,27 N. D. Ormsby,113\nM. Orselli,43, 81 R. O\u2019Shaughnessy,137 E. O\u2019Shea,261 Y. Oshima,262 S. Oshino,41 S. Ossokine,117 C. Osthelder,1\nD. J. Ottaway,89 H. Overmier,57 A. E. Pace,6 R. Pagano,8 M. A. Page,19 A. Pai,109 S. A. Pai,96 S. Pal,251\nO. Palashov,205 M. P\u00e1lfi,183 C. Palomba,58 K. C. Pan,139 P. K. Panda,210 P. T. H. Pang,29, 66\nF. Pannarale,107, 58 B. C. Pant,96 F. H. Panther,24 F. Paoletti,17 A. Paoli,49 A. Paolone,58, 263\nE. E. Papalexakis,31 G. Pappas,208 A. Parisi,17, 159 J. Park,232 W. Parker,57 D. Pascucci,86 A. Pasqualetti,49\nR. Passaquieti,80, 17 D. Passuello,17 M. Patel,113 M. Pathak,89 A. Patra,16 B. Patricelli,80, 17 A. S. Patron,8\n\n4\nS. Paul,67 E. Payne,1 T. Pearce,16 M. Pedraza,1 R. Pedurand,105 R. Pegna,17, 80 M. Pegoraro,83 A. Pele,1\nF. E. Pe\u00f1a Arellano,41 S. Penn,264 A. Perego,101, 102 A. Pereira,122 C. J. Perez,71 C. P\u00e9rigois,149\nC. C. Perkins,77 A. Perreca,101, 102 S. Perri\u00e8s,148 J. W. Perry,29, 98 D. Pesios,208 J. Petermann,78\nC. Petrillo,81 H. P. Pfeiffer,117 H. Pham,57 K. A. Pham,27 K. S. Phukon,29, 217 H. Phurailatpam,138\nO. J. Piccinni,35 M. Pichot,40 M. Piendibene,80, 17 F. Piergiovanni,55, 56 L. Pierini,107, 58 G. Pierra,148\nV. Pierro,88, 105 G. Pillant,49 M. Pillas,32 F. Pilo,17 L. Pinard,161 C. Pineda-Bosque,188\nI. M. Pinto,88, 105, 265, 26, 49 B. J. Piotrzkowski,7 K. Piotrzkowski,60 M. Pirello,71 M. D. Pitkin,13\nA. Placidi,43, 81 E. Placidi,107, 58 M. L. Planas,91 W. Plastino,266, 239 R. Poggiani,80, 17 E. Polini,25\nL. Pompili,117 D. Y. T. Pong,138 S. Ponrathnam,12, \u2020 E. Porcelli,29 J. Portell,34, 72, 243 E. K. Porter,48\nC. Posnansky,6 R. Poulton,49 Jade Powell,150 Jonathan Powell,16 M. Pracchia,25 T. Pradier,171\nA. K. Prajapati,85 K. Prasai,79 R. Prasanna,210 G. Pratten,114 M. Principe,133, 88, 265, 105 G. A. Prodi,267, 102\nL. Prokhorov,114 P. Prosposito,131, 132 L. Prudenzi,117 A. Puecher,29, 66 J. Pullin,8 M. Punturo,43\nF. Puosi,17, 80 P. Puppo,58 M. P\u00fcrrer,117 H. Qi,8 V. Quetschke,157 P. J. Quinonez,39 R. Quitzow-James,135\nF. J. Raab,71 G. Raaijmakers,97, 29 N. Radulesco,40 P. Raffai,183 S. X. Rail,229 S. Raja,96 C. Rajan,96\nK. E. Ramirez,57 T. D. Ramirez,47 A. Ramos-Buades,117 D. Rana,12 J. Rana,6 E. Randel,134\nP. R. Rangnekar,79 P. Rapagnani,107, 58 A. Ray,7 V. Raymond,16 N. Raza,154 M. Razzano,80, 17 J. Read,47\nT. Regimbau,25 L. Rei,94 S. Reid,90 S. W. Reid,113 D. H. Reitze,1 P. Relton,16 A. Renzini,1 P. Rettegno,21, 22\nB. Revenu,48, 268 A. Reza,29 M. Rezac,47 A. S. Rezaei,58, 107 F. Ricci,107, 58 D. Richards,203 J. W. Richardson,31\nA. Rijal,39 K. Riles,269 H. K. Riley,16 S. Rinaldi,80, 17 C. Robertson,203 N. A. Robertson,1 F. Robinet,32\nA. Rocchi,132 S. Rodriguez,47 L. Rolland,25 J. G. Rollins,1 M. Romanelli,108 R. Romano,3, 4 C. L. Romel,71\nA. Romero,35 I. M. Romero-Shaw,5 J. H. Romie,57 S. Ronchini,36, 111 T. J. Roocke,89 L. Rosa,4, 26\nT. J. Rosauer,31 C. A. Rose,7 D. Rosi\u0144ska,115 M. P. Ross,202 M. Rossello,91 A. Roussel,16 S. Rowan,23\nS. J. Rowlinson,114 S. Roy,66 A. Royzman,182 D. Rozza,162, 130 P. Ruggi,49 E. Ruiz Morales,110\nK. Ruiz-Rocha,187 K. Ryan,71 S. Sachdev,7, 50 T. Sadecki,71 J. Sadiq,123 P. Saffarieh,29, 98 S. S. Saha,139\nS. Saha,14 Y. Saito,270 K. Sakai,271 M. Sakellariadou,61 T. Sako,146 S. Sakon,6 O. S. Salafia,118, 119, 272\nF. Salces-Carcoba,1 L. Salconi,49 M. Saleem,27 F. Salemi,101, 102 M. Sall\u00e9,29 A. Samajdar,119 E. J. Sanchez,1\nJ. H. Sanchez,70 L. E. Sanchez,1 N. Sanchis-Gual,273, 136 J. R. Sanders,274 A. Sanuy,34 T. R. Saravanan,12\nN. Sarin,5 A. Sasli,208 P. Sassi,43, 81 B. Sassolas,161 H. Satari,24 O. Sauter,77 R. L. Savage,71 V. Savant,12\nT. Sawada,209, 186 H. L. Sawant,12 S. Sayah,161 D. Schaetzl,1 M. Scheel,143 S. J. Scherf,79 J. Scheuer,70\nM. G. Schiworski,89 P. Schmidt,114 S. Schmidt,66 S. J. Schmitz,63 R. Schnabel,78 M. Schneewind,10, 11\nR. M. S. Schofield,67 A. Sch\u00f6nbeck,78 H. Schuler,6 B. W. Schulte,10, 11 B. F. Schutz,16, 10, 11 E. Schwartz,16\nJ. Scott,23 S. M. Scott,9 T. C. Seetharamu,23 M. Seglar-Arroyo,25 Y. Sekiguchi,275 D. Sellers,57\nA. S. Sengupta,276 D. Sentenac,49 E. G. Seo,138 V. Sequino,26, 4 A. Sergeev,205 G. Servignat,255\nY. Setyawati,66 T. Shaffer,71 M. S. Shahriar,70 M. A. Shaikh,231 B. Shams,182 L. Shao,206 P. Sharma,96\nS. Sharma Chaudhary,135 P. Shawhan,116 N. S. Shcheblanov,277, 233 A. Sheela,165 B. Shen,116 K. G. Shepard,59\nE. Sheridan,187 Y. Shikano,278, 279 M. Shikauchi,33 H. Shimizu,270 K. Shimode,41 H. Shinkai,280\nD. H. Shoemaker,74 D. M. Shoemaker,176 S. ShyamSundar,96 A. Sider,30 H. Siegel,124, 125 M. Sieniawska,60\nD. Sigg,71 L. Silenzi,43, 44 L. P. Singer,76 D. Singh,6 M. K. Singh,18 N. Singh,115 A. Singha,28, 29 A. M. Sintes,91\nV. Sipala,162, 130 V. Skliris,16 B. J. J. Slagmolen,9 T. J. Slaven-Blair,24 J. Smetana,114 J. R. Smith,47\nL. Smith,23 R. J. E. Smith,5 J. Soldateschi,234, 281, 56 S. N. Somala,282 K. Somiya,2 K. Soni,12 S. Soni,74\nV. Sordini,148 F. Sorrentino,94 N. Sorrentino,80, 17 H. Sotani,283 R. Soulard,40 T. Souradeep,284, 12\nE. Sowell,153 V. Spagnuolo,28, 29 A. P. Spencer,23 M. Spera,82, 83 P. Spinicelli,49 A. K. Srivastava,85\nV. Srivastava,68 C. Stachie,40 F. Stachurski,23 D. A. Steer,48 J. Steinlechner,28, 29 S. Steinlechner,28, 29\nN. Stergioulas,208 M. StPierre,156 L. C. Strang,129 G. Stratta,285, 286, 58, 287 M. D. Strong,8 A. Strunk,71\nR. Sturani,288 A. L. Stuver,95 M. Suchenek,87 S. Sudhagar,12 N. Sueltmann,78 T. Sugiyama,147 H. G. Suh,7\nA. G. Sullivan,155 T. Z. Summerscales,59 L. Sun,9 S. Sunil,85 A. Sur,87 J. Suresh,33, 60 P. J. Sutton,16\nTakamasa Suzuki,200 Takanori Suzuki,2 B. L. Swinkels,29 A. Syx,171 M. J. Szczepa\u0144czyk,77 P. Szewczyk,115\nM. Tacca,29 H. Tagoshi,147 S. C. Tait,23 H. Takahashi,289 R. Takahashi,19 A. Takamori,46 S. Takano,262\nH. Takeda,290 M. Takeda,186 C. J. Talbot,90 C. Talbot,74 M. Tamaki,147 N. Tamanini,120 D. Tanabe,142\nK. Tanaka,291 T. Tanaka,290 A. J. Tanasijczuk,60 S. Tanioka,68 D. B. Tanner,77 D. Tao,1 L. Tao,77\nR. D. Tapia,6 E. N. Tapia San Mart\u00edn,29 R. Tarafder,1 C. Taranto,131 A. Taruya,292 J. D. Tasson,166\nM. Teloi,30 R. Tenorio,91 J. E. S. Terhune,95 L. Terkowski,78 H. Themann,188 M. P. Thirugnanasambandam,12\nL. M. Thomas,114 M. Thomas,57 P. Thomas,71 S. Thomas,68 J. E. Thompson,16 S. R. Thondapu,96\nK. A. Thorne,57 E. Thrane,5 Shubhanshu Tiwari,169 Srishti Tiwari,12 V. Tiwari,16 A. M. Toivonen,27\nA. E. Tolley,121 T. Tomaru,19 K. Tomita,186 T. Tomura,41 M. Tonelli,80, 17 A. Torres-Forn\u00e9,136\nC. I. Torrie,1 I. Tosta e Melo,130 E. Tournefier,25 A. Trapananti,44, 43 F. Travasso,44, 43 G. Traylor,57\nJ. Trenado,34 M. Trevor,116 M. C. Tringali,49 A. Tripathee,269 L. Troiano,293, 105 A. Trovato,38, 245\nL. Trozzo,4 R. J. Trudeau,1 K. W. Tsang,29, 294, 66 T. Tsang,295 M. Tse,74 R. Tso,143 S. Tsuchida,296\nL. Tsukada,6 T. Tsutsui,33 K. Turbang,297, 106 M. Turconi,40 C. Turski,86 D. Tuyenbayev,41 H. Ubach,34, 72\nA. S. Ubhi,114 N. Uchikata,147 T. Uchiyama,41 R. P. Udall,1 T. Uehara,298, 299 K. Ueno,33\nC. S. Unnikrishnan,247 T. Ushiba,41 A. Utina,28, 29 H. Vahlbruch,10, 11 N. Vaidya,1 G. Vajente,1 A. Vajpeyi,5\nG. Valdes,128 M. Valentini,101, 102 S. Vallero,22 V. Valsan,7 N. van Bakel,29 M. van Beuzekom,29\n\n5\nM. van Dael,29, 300 J. F. J. van den Brand,28, 98, 29 C. Van Den Broeck,66, 29 D. C. Vander-Hyde,68\nM. van der Sluys,29, 66 A. Van de Walle,32 J. van Dongen,29, 98 H. van Haevermaet,106 J. V. van Heijningen,60\nJ. Vanosky,1 M. H. P. M. van Putten,301 Z. van Ranst,28 N. van Remortel,106 M. Vardaro,217, 29\nA. F. Vargas,129 V. Varma,117 M. Vas\u00fath,75 A. Vecchio,114 G. Vedovato,83 J. Veitch,23 P. J. Veitch,89\nJ. Venneberg,10, 11 G. Venugopalan,1 P. Verdier,148 D. Verkindt,25 P. Verma,167 Y. Verma,96\nS. M. Vermeulen,16 D. Veske,155 F. Vetrano,55 A. Vicer\u00e9,55, 56 S. Vidyant,68 A. D. Viets,302 A. Vijaykumar,18\nV. Villa-Ortega,123 M. Vina,16 E. T. Vincent,50 J.-Y. Vinet,40 S. Viret,148 A. Virtuoso,245, 38 S. Vitale,74\nH. Vocca,81, 43 D. Voigt,78 E. R. G. von Reis,71 J. S. A. von Wrangel,10, 11 C. Vorvick,71 S. P. Vyatchanin,99\nL. E. Wade,63 M. Wade,63 K. J. Wagner,137 R. C. Walet,29 M. Walker,113 G. S. Wallace,90 L. Wallace,1\nH. Wang,262 J. Z. Wang,269 W. H. Wang,157 R. L. Ward,9 J. Warner,71 M. Was,25 T. Washimi,19\nN. Y. Washington,1 K. Watada,113 D. Watarai,33 J. Watchi,30 K. E. Wayt,63 B. Weaver,71 C. R. Weaving,121\nS. A. Webster,23 M. Weinert,10, 11 A. J. Weinstein,1 R. Weiss,74 C. M. Weller,202 R. A. Weller,187\nF. Wellmann,10, 11 L. Wen,24 P. We\u00dfels,10, 11 K. Wette,9 J. T. Whelan,137 D. D. White,47 B. F. Whiting,77\nC. Whittle,74 O. S. Wilk,63 D. Wilken,10, 11 K. Willetts,16 D. Williams,23 M. J. Williams,23\nA. R. Williamson,121 J. L. Willis,1 B. Willke,10, 11 C. C. Wipf,1 G. Woan,23 J. Woehler,10, 11\nJ. K. Wofford,137 D. Wong,154 H. T. Wong,142 I. C. F. Wong,138 M. Wright,23 C. Wu,14 D. S. Wu,10, 11\nH. Wu,14 D. M. Wysocki,7 L. Xiao,1 V. A. Xu,74 N. Yadav,87 T. Yamada,270 H. Yamamoto,1 K. Yamamoto,146\nM. Yamamoto,146 T. Yamamoto,41 T. S. Yamamoto,228 K. Yamashita,250 R. Yamazaki,303 F. W. Yang,182\nK. Z. Yang,27 Y.-C. Yang,139 M. J. Yap,9 D. W. Yeeles,16 A. B. Yelikar,137 T. Y. Yeung,59 J. Yokoyama,33\nT. Yokozawa,41 J. Yoo,261 Hang Yu,143 Haocun Yu,74 H. Yuzurihara,41 A. Zadro\u017cny,167 A. J. Zannelli,113\nM. Zanolin,39 M. Zeeshan,137 S. Zeidler,304 T. Zelenova,49 J.-P. Zendri,83 M. Zevin,173 J. Zhang,9 L. Zhang,1\nR. Zhang,77 T. Zhang,114 Y. Zhang,128 C. Zhao,24 Yue Zhao,182 Yuhang Zhao,147, 19 Y. Zheng,135 H. Zhong,27\nR. Zhou,198 X. J. Zhu,5 Z.-H. Zhu,127, 172 A. B. Zimmerman,176 M. E. Zucker,1, 74 J. Zweizig,1\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n2Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n6The Pennsylvania State University, University Park, PA 16802, USA\n7University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n8Louisiana State University, Baton Rouge, LA 70803, USA\n9OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n10Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n11Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n12Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n13University of Cambridge, Cambridge CB2 1TN, United Kingdom\n14\n15Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n16Cardi\ufb00University, Cardi\ufb00CF24 3AA, United Kingdom\n17INFN, Sezione di Pisa, I-56127 Pisa, Italy\n18International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n19Gravitational Wave Science Project, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n20Advanced Technology Center, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n21Dipartimento di Fisica, Universit\u00e0 degli Studi di Torino, I-10125 Torino, Italy\n22INFN Sezione di Torino, I-10125 Torino, Italy\n23SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n24OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n25Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n26Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n27University of Minnesota, Minneapolis, MN 55455, USA\n28Maastricht University, 6200 MD Maastricht, Netherlands\n29Nikhef, 1098 XG Amsterdam, Netherlands\n30Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n31University of California, Riverside, Riverside, CA 92521, USA\n32Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n\n6\n33University of Tokyo, Tokyo, 113-0033, Japan.\n34Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e8s, 1, 08028 Barcelona, Spain\n35Institut de F\u00edsica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n36Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n37Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n38INFN, Sezione di Trieste, I-34127 Trieste, Italy\n39Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n40Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire C\u00f4te d\u2019Azur, CNRS, Artemis, F-06304 Nice, France\n41Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 238 Higashi-Mozumi, Kamioka-cho, Hida City,\nGifu 506-1205, Japan\n42Department of Physics, National and Kapodistrian University of Athens, 15771 Ilissia, Greece\n43INFN, Sezione di Perugia, I-06123 Perugia, Italy\n44Universit\u00e0 di Camerino, I-62032 Camerino, Italy\n45American University, Washington, DC 20016, USA\n46Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan\n47California State University Fullerton, Fullerton, CA 92831, USA\n48Universit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France\n49European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n50Georgia Institute of Technology, Atlanta, GA 30332, USA\n51Chennai Mathematical Institute, Chennai 603103, India\n52Department of Mathematics and Physics, Graduate School of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki,\nAomori 036-8561, Japan\n53Royal Holloway, University of London, London TW20 0EX, United Kingdom\n54The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka City, Tokyo 181-8588, Japan\n55Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n56INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n57LIGO Livingston Observatory, Livingston, LA 70754, USA\n58INFN, Sezione di Roma, I-00185 Roma, Italy\n59Andrews University, Berrien Springs, MI 49104, USA\n60Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n61King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n62Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n63Kenyon College, Gambier, OH 43022, USA\n64International College, Osaka University, 1-1 Machikaneyama-cho, Toyonaka City, Osaka 560-0043, Japan\n65School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba City,\nIbaraki 305-0801, Japan\n66Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n67University of Oregon, Eugene, OR 97403, USA\n68Syracuse University, Syracuse, NY 13244, USA\n69Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n70Northwestern University, Evanston, IL 60208, USA\n71LIGO Hanford Observatory, Richland, WA 99352, USA\n72Departament de F\u00edsica Qu\u00e0ntica i Astrof\u00edsica (FQA), Universitat de Barcelona (UB), c. Mart\u00ed i Franqu\u00e9s, 1, 08028 Barcelona, Spain\n73Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno,\nItaly\n74LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n75Wigner RCP, RMKI, H-1121 Budapest, Hungary\n76NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n77University of Florida, Gainesville, FL 32611, USA\n78Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n79Stanford University, Stanford, CA 94305, USA\n80Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n81Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n82Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n83INFN, Sezione di Padova, I-35131 Padova, Italy\n84Montana State University, Bozeman, MT 59717, USA\n85Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n\n7\n86Universiteit Gent, B-9000 Gent, Belgium\n87Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n88Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n89OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n90SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n91IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n92Departamento de Matem\u00e1ticas, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n93Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n94INFN, Sezione di Genova, I-16146 Genova, Italy\n95Villanova University, Villanova, PA 19085, USA\n96RRCAT, Indore, Madhya Pradesh 452013, India\n97GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n98Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n99Lomonosov Moscow State University, Moscow 119991, Russia\n100Center for Theoretical Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland\n101Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n102INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n103Bar-Ilan University, Ramat Gan, 5290002, Israel\n104Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n105INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n106Universiteit Antwerpen, 2000 Antwerpen, Belgium\n107Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n108Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-35000 Rennes, France\n109Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n110Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid, 28049 Madrid, Spain\n111INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n112Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n113Christopher Newport University, Newport News, VA 23606, USA\n114University of Birmingham, Birmingham B15 2TT, United Kingdom\n115Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n116University of Maryland, College Park, MD 20742, USA\n117Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n118Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n119INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n120L2IT, Laboratoire des 2 In\ufb01nis - Toulouse, Universit\u00e9 de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n121University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n122Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n123IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n124Stony Brook University, Stony Brook, NY 11794, USA\n125Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n126Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n127Department of Astronomy, Beijing Normal University, Xinjiekouwai Street 19, Haidian District, Beijing 100875, China\n128Texas A&M University, College Station, TX 77843, USA\n129OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n130INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n131Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n132INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n133University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n134Colorado State University, Fort Collins, CO 80523, USA\n135Missouri University of Science and Technology, Rolla, MO 65409, USA\n136Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n137Rochester Institute of Technology, Rochester, NY 14623, USA\n138The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n139National Tsing Hua University, Hsinchu City, 30013 Taiwan\n140OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n141Kamioka Branch, National Astronomical Observatory of Japan, 238 Higashi-Mozumi, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n\n8\n142National Central University, Taoyuan City 320317, Taiwan\n143CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n144Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n145Institute of Physics, Academia Sinica, 128 Sec. 2, Academia Rd., Nankang, Taipei 11529, Taiwan\n146Faculty of Science, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n147Institute for Cosmic Ray Research, KAGRA Observatory, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba\n277-8582, Japan\n148Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n149INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n150OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n151Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\n152Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n153Texas Tech University, Lubbock, TX 79409, USA\n154University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n155Columbia University, New York, NY 10027, USA\n156University of Rhode Island, Kingston, RI 02881, USA\n157The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n158Bellevue College, Bellevue, WA 98007, USA\n159Scuola Normale Superiore, I-56126 Pisa, Italy\n160The University of She\ufb03eld, She\ufb03eld S10 2TN, United Kingdom\n161Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n162Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n163Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n164INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n165Indian Institute of Technology Madras, Chennai 600036, India\n166Carleton College, North\ufb01eld, MN 55057, USA\n167National Center for Nuclear Research, 05-400 \u015awierk-Otwock, Poland\n168Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00e9, CNRS, UMR 7095, 75014 Paris, France\n169University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n170Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n171Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n172School of Physics and Technology, Wuhan University, Bayi Road 299, Wuchang District, Wuhan, Hubei, 430072, China\n173University of Chicago, Chicago, IL 60637, USA\n174Montclair State University, Montclair, NJ 07043, USA\n175Institute for Nuclear Research, H-4026 Debrecen, Hungary\n176University of Texas, Austin, TX 78712, USA\n177CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n178Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n179Western Washington University, Bellingham, WA 98225, USA\n180SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n181Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n182The University of Utah, Salt Lake City, UT 84112, USA\n183E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n184Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n185Department of Physics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City, Osaka\n558-8585, Japan\n186Department of Physics, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto-cho, Sumiyoshi-ku, Osaka City,\nOsaka 558-8585, Japan\n187Vanderbilt University, Nashville, TN 37235, USA\n188California State University, Los Angeles, Los Angeles, CA 90032, USA\n189University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n190INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n191Queen Mary University of London, London E1 4NS, United Kingdom\n192Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n193Laboratoire de Physique Corpusculaire Caen, 6 boulevard du mar\u00e9chal Juin, F-14050 Caen, France\n194The University of Mississippi, University, MS 38677, USA\n\n9\n195Department of Applied Physics, Fukuoka University, 8-19-1 Nanakuma, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n196Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China\n197Niels Bohr Institute, Copenhagen University, 2100 K\u00f8benhavn, Denmark\n198University of California, Berkeley, CA 94720, USA\n199College of Industrial Technology, Nihon University, 1-2-1 Izumi, Narashino City, Chiba 275-8575, Japan\n200Faculty of Engineering, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n201Department of Physics, Tamkang University, No. 151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan\n202University of Washington, Seattle, WA 98195, USA\n203Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n204Department of Astronomy and Space Science, Chungnam National University, 9 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of\nKorea\n205Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n206Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Road 5, Haidian District, Beijing 100871, China\n207Department of Physics, Center for High Energy and High Field Physics, National Central University, No.300, Zhongda Rd, Zhongli\nDistrict, Taoyuan City 32001, Taiwan\n208Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n209Nambu Yoichiro Institute of Theoretical and Experimental Physics, Osaka Metropolitan University, 3-3-138 Sugimoto-cho,\nSumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n210Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n211University of Bia\u0142ystok, 15-424 Bia\u0142ystok, Poland\n212National Astronomical Observatories, Chinese Academic of Sciences, 20A Datun Road, Chaoyang District, Beijing, China\n213School of Astronomy and Space Science, University of Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing,\nChina\n214University of Southampton, Southampton SO17 1BJ, United Kingdom\n215Department of Physics, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea\n216Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa City, Chiba 277-8582, Japan\n217Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n218Chung-Ang University, Seoul 06974, Republic of Korea\n219University of Washington Bothell, Bothell, WA 98011, USA\n220Ewha Womans University, Seoul 03760, Republic of Korea\n221Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n222Sungkyunkwan University, Seoul 03063, Republic of Korea\n223National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n224Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki\n305-0801, Japan\n225Bard College, Annandale-On-Hudson, NY 12504, USA\n226Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n227Instituto de F\u00edsica Te\u00f3rica UAM-CSIC, Universidad Auton\u00f3ma de Madrid, C/ Nicolas Cabrera, 13-15, 28049 Madrid, Spain\n228Department of Physics, Nagoya University, ES building, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n229Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n230Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire C\u00f4te d\u2019Azur, CNRS, Lagrange, F-06304 Nice, France\n231Seoul National University, Seoul 08826, Republic of Korea\n232Technology Center for Astronomy and Space Science, Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu,\nDaejeon 34055, Republic of Korea\n233NAVIER, \u00c9cole des Ponts, Univ Gustave Ei\ufb00el, CNRS, Marne-la-Vall\u00e9e, France\n234Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n235Department of Physics, National Cheng Kung University, No.1, University Road, Tainan City 701, Taiwan\n236National Center for High-performance computing, National Applied Research Laboratories, No. 7, R&D 6th Rd., Hsinchu Science\nPark, Hsinchu City 30076, Taiwan\n237Department of Physics, National Taiwan Normal University, 88 Ting-Chou Rd., sec. 4, Taipei 116, Taiwan\n238NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n239INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n240ESPCI, CNRS, F-75005 Paris, France\n241West Virginia University, Morgantown, WV 26506, USA\n242School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n243Institut d\u2019Estudis Espacials de Catalunya, c. Gran Capit\u00e0, 2-4, 08034 Barcelona, Spain\n244Tsinghua University, Beijing 100084, China\n245Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n\n10\n246Institute for Photon Science and Technology, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan\n247Tata Institute of Fundamental Research, Mumbai 400005, India\n248Institut des Hautes Etudes Scienti\ufb01ques, F-91440 Bures-sur-Yvette, France\n249Faculty of Law, Ryukoku University, 67 Fukakusa Tsukamoto-cho, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n250Graduate School of Science and Engineering, University of Toyama, 3190 Gofuku, Toyama City, Toyama 930-8555, Japan\n251Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n252Department of Physics and Astronomy, University of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556, USA\n253Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n254Centre national de la recherche scienti\ufb01que, 75016 Paris, France\n255Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n256Observatoire de Paris, 75014 Paris, France\n257Universit\u00e9 PSL, 75006 Paris, France\n258Universit\u00e9 de Paris Cit\u00e9, 75006 Paris, France\n259Graduate School of Science and Technology, Niigata University, 8050 Ikarashi-2-no-cho, Nishi-ku, Niigata City, Niigata 950-2181,\nJapan\n260Niigata Study Center, the Open University of Japan, 754 Ichibancho, Asahimachi-dori, Chuo-ku, Niigata City, Niigata 951-8122,\nJapan\n261Cornell University, Ithaca, NY 14850, USA\n262Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan\n263Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n264Hobart and William Smith Colleges, Geneva, NY 14456, USA\n265Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n266Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n267Universit\u00e0 di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n268Subatech, CNRS/IN2P3 - Institut Mines-Telecom Atlantique - Universit\u00e9 de Nantes, 4 rue Alfred Kastler BP 20722 44307 Nantes\nC\u2019EDEX 03, France\n269University of Michigan, Ann Arbor, MI 48109, USA\n270Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba City, Ibaraki 305-0801, Japan\n271Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, 888 Nishikatakai, Nagaoka City,\nNiigata 940-8532, Japan\n272INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n273Departamento de Matem\u00e1tica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\n3810-183 Aveiro, Portugal\n274Marquette University, Milwaukee, WI 53233, USA\n275Faculty of Science, Toho University, 2-2-1 Miyama, Funabashi City, Chiba 274-8510, Japan\n276Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n277Laboratoire MSME, Cit\u00e9 Descartes, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vall\u00e9e Cedex 2, France\n278Graduate School of Science and Technology, Gunma University, 4-2 Aramaki, Maebashi, Gunma 371-8510, Japan\n279Institute for Quantum Studies, Chapman University, 1 University Dr., Orange, CA 92866, USA\n280Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata City, Osaka 573-0196,\nJapan\n281INAF, Osservatorio Astro\ufb01sico di Arcetri, I-50125 Firenze, Italy\n282Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n283Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), The Institute of Physical and Chemical Research\n(RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan\n284Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n285Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany\n286Istituto di Astro\ufb01sica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n287INAF, Osservatorio di Astro\ufb01sica e Scienza dello Spazio, I-40129 Bologna, Italy\n288Universidade Estadual Paulista, 01140-070 Campinas, S\u00e3o Paulo, Brazil\n289Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 8-15-1 Todoroki, Setagaya, Tokyo\n158-0082, Japan\n290Department of Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n291Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, The University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa\nCity, Chiba 277-8582, Japan\n292Yukawa Institute for Theoretical Physics, Kyoto University, Kita-Shirakawa Oiwake-cho, Sakyou-ku, Kyoto City, Kyoto 606-8502,\nJapan\n\n11\n293Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit\u00e0 di Salerno, I-84084 Fisciano,\nSalerno, Italy\n294Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG Groningen, Netherlands\n295Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n296National Institute of Technology, Fukui College, Geshi-cho, Sabae-shi, Fukui 916-8507, Japan\n297Vrije Universiteit Brussel, 1050 Brussel, Belgium\n298Department of Communications Engineering, National Defense Academy of Japan, 1-10-20 Hashirimizu, Yokosuka City, Kanagawa\n239-8686, Japan\n299Department of Physics, University of Florida, Gainesville, FL 32611, USA\n300Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n301Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 143-747, Republic of Korea\n302Concordia University Wisconsin, Mequon, WI 53097, USA\n303Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara City, Kanagawa 252-5258, Japan\n304Department of Physics, Rikkyo University, 3-34-1 Nishiikebukuro, Toshima-ku, Tokyo 171-8501, Japan\nABSTRACT\nThe global network of gravitational-wave observatories now includes \ufb01ve detectors, namely LIGO\nHanford, LIGO Livingston, Virgo, KAGRA, and GEO 600.\nThese detectors collected data during\ntheir third observing run, O3, composed of three phases: O3a starting in April of 2019 and lasting six\nmonths, O3b starting in November of 2019 and lasting \ufb01ve months, and O3GK starting in April of\n2020 and lasting 2 weeks. In this paper we describe these data and various other science products that\ncan be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The\nmain dataset, consisting of the gravitational-wave strain time series that contains the astrophysical\nsignals, is released together with supporting data useful for their analysis and documentation, tutorials,\nas well as analysis software packages.\n1. INTRODUCTION\nGravitational-wave (GW) detectors develop through successive generations of instruments with increasing sensitivity\n(Abbott et al. 2020a). The US-based Advanced LIGO1 detectors (Aasi et al. 2015) were the \ufb01rst two instruments of\nthe current generation to begin operation, collecting data during the \ufb01rst observing run (O1) from September 2015 to\nJanuary 2016, including the \ufb01rst direct detection of gravitational waves (Abbott et al. 2016). The second observing\nrun (O2) followed from November 2016 to August 2017, with the European detector Advanced Virgo (Acernese et al.\n2015) joining in August 2017. The GEO 600 detector in Germany (Dooley et al. 2016) serves as a center of research and\ndevelopment, and is used to test a number of critical detector technologies. Another GW detector, the Japan-based\nKAGRA (Akutsu et al. 2021), has also been rapidly developing.\nThis article focuses on the data collected during the third observing run, O3, that took place from April 1 2019 to\nApril 21 2020. The bulk of this observing run collected data only from LIGO and Virgo, and is divided into two main\noperational phases: O3a from April 1 2019 to October 1 2019, and O3b from November 1 2019 to March 27 2020,\nwith a one-month maintenance break between the two phases. KAGRA was expected to join O3, but this initial plan\nchanged due to the outbreak of COVID-19. Instead, KAGRA and GEO 600 operated during an extended observing\nphase, O3GK, from April 7 to April 21 2020 (Abbott et al. 2022a).\nThe analysis of the O3 data has led to numerous publications. Those include several updates to the GWTC (GW\nTransient Catalog; Abbott et al. 2021a,b,c) that compiles transient sources analyzed and reported by the combined\nLIGO-Virgo-KAGRA Collaboration (LVK). The cumulative GWTC catalog currently includes nearly 100 candidate\nsources (with a probability of astrophysical origin > 50 %), all associated with the coalescence of compact star binaries\ncomposed of either neutron stars, black holes, or both.\nFollowing the policy de\ufb01ned in the LIGO Data Management Plan (LIGO Laboratory 2022a) and a Memorandum\nof Understanding (LIGO Scienti\ufb01c Collaboration and Virgo Collaboration 2019), the O3 data set and associated\nscience products are published through the Gravitational-Wave Open Science Center (GWOSC) at https://gwosc.org\n\u2217Deceased, December 2021.\n\u2020 Deceased, March 2022.\n1\nLaser Interferometer Gravitational-Wave Observatory\n\n12\n2 allowing the reproducibility of the analyses performed by the LVK and increasing the impact of the data through its\nwider use. This paper provides a description of the publicly released data (LIGO Scienti\ufb01c Collaboration and Virgo\nCollaboration 2021a,b; LIGO Scienti\ufb01c Collaboration, Virgo Collaboration and KAGRA Collaboration 2022a) along\nwith additional information on their usage.\nTo date hundreds of scienti\ufb01c articles have been written using the data available from the GWOSC website (all\ndatasets combined) 3. These analyses con\ufb01rm, complement, and extend the results published by the LVK Collaboration,\ndemonstrating the impact on the scienti\ufb01c community of the GW data releases.\nThis paper is organized as follows. Section 2 summarizes the status of the detectors during the observing run O3,\ntogether with high-level indicators such as their distance reach and duty cycle of operation. This section also provides\ninsights about how the data are collected and calibrated, about data quality and about simulated signal injections.\nSection\n3 describes the format, content and provenance of the strain data \ufb01les distributed through the GWOSC,\nincluding the nomenclature used for the calibration versions and channel names. Section 4 describes the Event Portal,\na searchable GW event database accessible online. Details about the technical validation and review of the data and\ndocumentation are given in Section\n5. Finally, Section 6 provides some guiding principles to the novice user and\nsuggests software tools that can be used to analyze the data.\n2. INSTRUMENTS\nThe Advanced LIGO (Aasi et al. 2015) and Advanced Virgo (Acernese et al. 2015) detectors are enhanced Michelson\ninterferometers with arm lengths of 4 km and 3 km, respectively. Advanced LIGO comprises two detectors located at\ntwo di\ufb00erent sites in the US, namely, in Hanford, WA and Livingston LA, while Advanced Virgo has a single site in\nCascina, close to Pisa, Italy. The various instrument upgrades realized between the science runs O2 and O3 for the\nLIGO and Virgo detectors are described in (Buikema et al. 2020; Abbott et al. 2021a,c; Acernese et al. 2022a). They\ninvolve many parts of the instruments, including the main laser source and the core optics along with the installation\nof mitigation systems for a range of technical noises. One of the major novelties in O3 both for LIGO and Virgo is\nthe use of squeezed light sources (see Tse et al. (2019) for LIGO and Acernese et al. (2019) for Virgo), a technique\n(Schnabel et al. 2010; Barsotti et al. 2019) that signi\ufb01cantly reduces quantum noise, thus enhancing the sensitivity at\nhigh frequency.\nGEO 600 (Dooley et al. 2016) is a British\u2013German interferometric GW detector with 600 m arms located near\nHannover, Germany. As in LIGO and Virgo, quantum squeezing is used to reduce noise in the output measurement\nquadrature (Lough et al. 2021). This technique was \ufb01rst demonstrated by GEO 600 (Abadie et al. 2011). KAGRA\nis an underground laser interferometer with 3-km arms, located underground at the Kamioka Observatory in Gifu\nPrefecture, Japan. An important feature of its design is the cooling system intended to bring the large mirrors of the\ninterferometer to cryogenic temperature (around 20 K) in order to reduce thermal noise (Akutsu et al. 2016; Chen\net al. 2014). During the O3GK run however, the detector was operated at room temperature (Akutsu et al. 2018,\n2021).\n2.1. Detectors performance\nA GW detector\u2019s performance is often globally characterized by two measures: its duty factor, de\ufb01ned as the fraction\nof time the detector is recording observational quality data, and its distance reach, conventionally measured as the\nbinary neutron star (BNS) inspiral range (Finn & Cherno\ufb001993; Chen et al. 2021), the distance to which a BNS\ninspiral could be detected with signal-to-noise ratio of 8, assuming 1.4 solar mass component objects and averaging\nover source position and orientation. The choice of this metric is a standard convention. The value of 1.4 solar masses\nis close to the measured masses of the stars in the Hulse\u2013Taylor binary (Weisberg & Huang 2016) and within the\nnarrow range predicted by stellar evolution for neutron-star masses. The distance reach of the detectors strongly\ndepends on the source mass. For example, binary black-hole (BBH) systems can typically be detected at much greater\ndistances, up to several Gpc (e.g., Abbott et al. 2021c, Table IV).\nThe GWOSC website hosts summary pages for O3a4 and O3b5 which describe the LIGO and Virgo operations and\nsensitivity. The duty factors during O3a are 71% for LIGO Hanford (H1), 76% for LIGO Livingston (L1) and 76% for\n2\nThis website is also accessible at https://gw-openscience.org.\n3\nSee https://gwosc.org/projects for a list of articles that refer to the data published on the GWOSC website.\n4\nhttps://gwosc.org/detector_status/O3a\n5\nhttps://gwosc.org/detector_status/O3b\n\n13\nNetwork duty factor for O3a\nNo detector [3.2 %]\nSingle detector [15.0 %]\nDouble detector [37.4 %]\nTriple detector [44.5 %]\nNetwork duty factor for O3b\nNo detector [3.4 %]\nSingle detector [11.2 %]\nDouble detector [34.3 %]\nTriple detector [51.0 %]\nNetwork duty factor for O3GK\nNo detector [13.7 %]\nSingle detector [39.6 %]\nDouble detector [46.8 %]\nFigure 1. Duty factors for the LIGO and Virgo detector network during O3a (left) and O3b (center) and for the KAGRA and\nGEO 600 detector network during O3GK (right). These factors measure the fraction of time spent as a function of the number\nof detectors in operation. The same plots (caveat a di\ufb00erence in the color code) can be found on the GWOSC web summary\npages for O3a4 and O3b5 and have been produced from Abbott et al. (2022a) for O3GK.\nVirgo (V1). During O3b, the corresponding percentages are 79%, 79% and 76%, respectively. Those translate into the\nobserving factors shown in Fig. 1 that quantify the fraction of observing time spent with one, two or three instruments\nin operation.\nDuring the O3GK run, the duty factors of KAGRA (K1) and GEO 600 (G1) are 53% and 80% respectively, leading\nto a coincident observing factor of 47% (Abbott et al. 2022a). The lower duty cycle of KAGRA is due to the fact that\nalignment sensing and control with wavefront sensors was not yet implemented at the time of the run, leading to a\nhigher susceptibility to microseismic ground vibrations.\nThe median values of the BNS range over the whole observing run are 108 Mpc, 135 Mpc and 45 Mpc for H1, L1\nand V1 respectively during O3a, and 115 Mpc, 133 Mpc and 51 Mpc during O3b for the same detectors. The median\nvalues of the BNS range over the O3GK period are 0.66 Mpc for KAGRA and 1.06 Mpc for GEO 600. Fig. 2 displays\nthe median BNS range computed over regular intervals (5-minute scale for LIGO and Virgo and 20-minute scale for\nGEO 600 and KAGRA). The drops that can be observed in both plots are due to transient noise artifacts (discussed in\nSec. 2.3) reducing the detector sensitivity temporarily. The BNS range shown in the recent GWTC publications such\nas Abbott et al. (2021a) (Fig. 3) and Abbott et al. (2021c) (Fig. 3) are averaged over a longer period (1 hour) and\nare thus less a\ufb00ected by transient noise. The longer gaps in the BNS inspiral range are due to maintenance intervals,\ninstrumental issues, and earthquakes.\n2.2. Calibration\nThe GW strain h(t) is obtained and calibrated from variations of the optical power measured at the output port\nof each detector. The calibration procedure and the corresponding characterization of the systematic and statistical\nuncertainties are described in Viets et al. (2018); Sun et al. (2020, 2021) for Advanced LIGO and Acernese et al.\n(2022b) for Advanced Virgo. Calibration is performed in two stages: an initial, online calibration used for low-latency\nanalysis, and a \ufb01nal, o\ufb04ine calibration that applies any needed corrections to the initial result. The o\ufb04ine calibration\nmay correct for computer failures, incomplete modelling of the detectors, or any systematic errors characterized after\nthe observing period. The uncertainties in the calibration procedure for both the magnitude and phase of h(t) as a\nfunction of frequency are documented (LIGO Scienti\ufb01c Collaboration & Virgo Collaboration 2021).\nThe calibration process also includes a noise subtraction step based on independent measurements of a range of noise\nsources by witness sensors, as described in Davis et al. (2019); Vajente et al. (2020a); Mukund et al. (2020); Estevez\net al. (2019); and Acernese et al. (2022b). For the last two weeks of O3a, the Virgo data were reprocessed with a new\ncon\ufb01guration of the noise subtraction (Rolland et al. 2019; Acernese et al. 2022b) so a di\ufb00erent calibration is available\njust for this period (see Table 1).\nGWOSC releases two types of strain data: bulk data spanning an entire observing run, and smaller data snippets\naround the time of each GW event.\nData snippets are based on the calibration version available at the time of\npublication of the related GW event. Events that appear in multiple publications may have multiple data snippets\navailable, sometimes with di\ufb00erent calibration versions. Naturally, the time segments released as data snippets are\nalso available in the bulk data set, but the bulk data of the entire O3a, O3b and O3GK observation runs provided\nthrough GWOSC correspond to the \ufb01nal (most up-to-date) calibration. These di\ufb00erences in calibration can lead to\ndiscrepancies between the data snippets and the corresponding data in the bulk data release, potentially leading in\nturn to di\ufb00erences in the source parameter values that can be estimated from the data. However, as discussed in\nSec. 3.3, in addition to the main bulk data release, several alternate strain channels with di\ufb00erent calibration versions\nare also made public.\n\n14\nFigure 2. Binary neutron star ranges for O3a (upper plot), O3b (middle plot) with LIGO Hanford (red), LIGO Livingston\n(blue) and Virgo (purple) and for O3GK (bottom plot) with GEO 600 (black) and KAGRA (yellow). Similar plots (besides\nstyle di\ufb00erences) can be found on the GWOSC web pages for O3a 4 and O3b 5 and in Abbott et al. (2022a) for O3GK.\n\n15\nThe detector strain h(t) in O3 is calibrated only between 10 Hz and 5000 Hz for Advanced LIGO, between 20 Hz\nand 2000 Hz for Advanced Virgo, between 30 Hz and 1500 Hz for KAGRA and between 40 Hz and 6000 Hz for\nGEO 600. Any apparent signal outside these ranges cannot be trusted because it is not a faithful representation of\nthe GW strain at these frequencies. In addition, Advanced Virgo data between 49.5 Hz and 50.5 Hz are characterised\nby a large increase of calibration errors because of e\ufb00ects related to the mains power lines (Acernese et al. 2022b).\nBecause of this increased systematic error, data in this narrow frequency band were considered to be uninformative\nfor source-parameter estimation (see Appendix E of Abbott et al. (2021c) for relevant methods).\n2.3. Detector noise characterization and data quality\nThe data are dominated by instrumental noise that can be well described as Gaussian and stationary over limited\ntime scales and frequency ranges. The data also contain intermittent short-duration noise artifacts, or glitches, that\ncontribute to the noise background as well. Any analysis of GW data must account for the presence of these various\nnoise components (see Sec. 6 for more information about using the data). A summary of e\ufb00orts to characterize data\nquality in O3 can be seen in Davis et al. (2021) for Advanced LIGO, Acernese et al. (2022a) for Advanced Virgo, and\nAbe et al. (2022) for KAGRA. The overall quality of data for transient searches is recorded as data quality segments,\ndescribed in more detail in Sec. 3.2.\n2.4. Signal injections\nHardware injections are simulated GW signals added by physically displacing the test masses (i.e. the interferometer\nmirrors) (Biwer et al. 2017). The simulated signal initiates a response that mimics that of a true GW. By looking for\ndiscrepancies between the injected and recovered signals, it is possible to characterize the performance of analyses and\nthe coupling of instrumental subsystems to the detectors\u2019 output channels.\nDuring the third observing run O3, hardware injections were performed in the Advanced LIGO and Advanced Virgo\ndetectors. The record of all injections is available through GWOSC web pages.6\nThis list is provided to prevent\npotential confusion with an actual astrophysical signal. For Virgo, those injections were removed post-facto when\nproducing the calibrated strain (see Acernese et al. (2022b) for details on this subtraction), so the injection times are\nnot marked in the GWOSC \ufb01les. On the other hand, in the case of Advanced LIGO the injections are still present in\nthe calibrated data, and their times are marked in the GWOSC \ufb01les (see Sec. 3.2).\nNo injections were performed during O3GK.\n3. STRAIN DATA\nAll O3 open data are distributed under the Creative Commons Attribution International Public License 4.0,\nincluding strain data from O3a (LIGO Scienti\ufb01c Collaboration and Virgo Collaboration 2021a), O3b (LIGO Scienti\ufb01c\nCollaboration and Virgo Collaboration 2021b) and O3GK (LIGO Scienti\ufb01c Collaboration, Virgo Collaboration and\nKAGRA Collaboration 2022a).\nSmall batches of \ufb01les can be conveniently downloaded from the GWOSC website\ndirectly.7 However, when downloading large amounts of data (such as an entire observing run) the use of the distributed\n\ufb01le system CernVM-FS (Weitzel et al. 2017) is recommended.8 Once con\ufb01gured, CernVM-FS allows access to all GWOSC\ndata locally on the user\u2019s computer.\nThe O3 calibrated strain data are distributed in \ufb01les that contain 4096 seconds of data. Published GW signals are\nalso released in separate \ufb01les containing data snippets of 4096 seconds or 32 seconds, centered on the event\u2019s detection\ntime and released under the GWOSC Event Portal.9 The description of the data records that follows is valid both for\nsingle event releases and for bulk data releases.\nGWOSC calibrated strain data are repackaged from data stored in the LVK archives. The data source is uniquely\nidenti\ufb01ed by a channel name and a frame type (see Table 1). At times when data are unavailable or of quality too\npoor to be analyzed, the strain values are represented with NaNs. Strain data are made available both at the sampling\nrate of 16384 Hz, and at a downsampled rate of 4096 Hz10. Down-sampling is achieved using the standard decimation\nmethod implemented in scipy.signal.decimate11 from the Python package SciPy (Virtanen et al. 2020). The highest\n6\nhttp://gwosc.org/O3/o3_inj\n7\nhttps://gwosc.org/data\n8\nFor CernVM-FS installation instructions, see https://gwosc.org/cvmfs.\n9\nSee https://gwosc.org/eventapi.\n10\nFor simplicity, in the rest of the paper the sampling rates will be indicated in kHz and rounded to the closest integer, i.e. 4 and 16 kHz\nmeans 4096 and 16384 Hz, respectively.\n11\nThis method applies an anti-aliasing \ufb01lter based on an order-8 Chebychev type I in\ufb01nite impulse response (IIR) \ufb01lter (Ellis 2012) before\ndecimation.\n\n16\nfrequency available is determined by the Nyquist\u2013Shannon sampling theorem (Nyquist 1924), and is equal to half the\nsampling rate speci\ufb01ed in a particular dataset. This is an important consideration to keep in mind when deciding\nwhich sample rate to download from GWOSC. Because the anti-aliasing \ufb01lters used in resampling roll-o\ufb00at the upper\nend of the working frequency interval, the valid frequency range is reduced to a bit less than the Nyquist frequency.\nSo, for the 4 kHz data the maximum usable frequency is approximately 1700 Hz. Higher sample rate data will require\nmore hard-drive space to store and longer times to download. The user can decide which dataset meets their needs.\nTable 1. The channel names and frame types listed in this table are unique identi\ufb01ers in the LIGO, Virgo, GEO 600 and\nKAGRA data archives that allow tracing the provenance of the strain data released on GWOSC. H1 and L1 indicate the two\nLIGO detectors (Hanford and Livingston respectively), V1 refers to Virgo, G1 refers to GEO 600 and K1 refers to KAGRA.\nThe attribute CLEAN-SUB60HZ in H1 and L1 indicates that the noise subtraction procedure described in Vajente et al. (2020b)\nwas used. The attributes C01, V1Online and V1O3Repro1A refer to the calibration version.\nRun\nDet.\nChannel name\nFrame type\nO3a\nH1\nH1:DCS-CALIB_STRAIN_CLEAN-SUB60HZ_C01\nH1_HOFT_CLEAN_SUB60HZ_C01\nO3a\nL1\nL1:DCS-CALIB_STRAIN_CLEAN-SUB60HZ_C01\nL1_HOFT_CLEAN_SUB60HZ_C01\nO3a\nV1\nV1:Hrec_hoft_16384Hz\nV1Online\nO3a(last two weeks)\nV1\nV1:Hrec_hoft_V1O3ARepro1A_16384Hz\nV1O3Repro1A\nO3b\nH1\nH1:DCS-CALIB_STRAIN_CLEAN-SUB60HZ_C01\nH1_HOFT_CLEAN_SUB60HZ_C01\nO3b\nL1\nL1:DCS-CALIB_STRAIN_CLEAN-SUB60HZ_C01\nL1_HOFT_CLEAN_SUB60HZ_C01\nO3b\nV1\nV1:Hrec_hoft_16384Hz\nV1Online\nO3GK\nG1\nG1:DER_DATA_HD_CLEAN\nG1_RDS_C02_L3\nO3GK\nK1\nK1:DAC-STRAIN_C20\nK1_HOFT_C20\n3.1. GWOSC \ufb01le formats\nThe GWOSC open data are delivered in two di\ufb00erent \ufb01le formats: hdf and gwf. The Hierarchical Data Format hdf\n(Koziol & Robinson 2018) is a portable data format readable by many programming languages. The Frame format\ngwf (LIGO Scienti\ufb01c Collaboration and Virgo Collaboration 2009) is a specialized format used by the gravitational\nwave community. Data associated with GW events are also released as plain text \ufb01les containing two columns with\nthe global positioning system (GPS) time in the \ufb01rst column and the corresponding strain value in the second column.\nFor both formats the \ufb01le naming follows the naming convention,\nobs\u2014FrameType\u2014GPSstart\u2014duration.extension\nwhere FrameType for the main O3 data release is\nifo_GWOSC_ObservationRun_sKHZ_Rn\nand\n\u2022 obs is the observatory, i.e. the site, so can have values L, H, V, G or K;\n\u2022 ifo is the interferometer and can have values H1, L1, V1, G1 or K1;\n\u2022 ObservationRun encodes the observing run name, so in this case is O3a, O3b, or O3GK;\n\u2022 s is the sampling rate in kHz with either a value 4 or 16 (4096 Hz or 16384 Hz);\n\u2022 n is the version number of the \ufb01le (typically 1);\n\u2022 GPSstart is the starting time of the data contained in the \ufb01le, as a 10-digit GPS value (in seconds);\n\u2022 duration is the duration in seconds of the \ufb01le, typically either 4096 or 32 seconds;\n\n17\n\u2022 and extension represents the \ufb01le format and can be gwf or hdf.\nThe folders (or groups) included in the hdf \ufb01les are:\n\u2022 meta: metadata of the \ufb01le containing the following \ufb01elds:\n\u2013 Description, e.g. \u201cStrain data time series from LIGO\u201d,\n\u2013 DescriptionURL: URL of the GWOSC website,\n\u2013 Detector, e.g. L1, and Observatory, e.g. L,12\n\u2013 Duration, GPSstart, UTCstart: duration and starting time (using GPS and UTC standards, respectively)\nof the segment of data contained in a \ufb01le.\n\u2013 StrainChannel: channel name used in the LVK archives\n\u2013 FrameType: frame type used in the LVK archives\n\u2022 strain: array of h(t), sampled at 4 or 16 kHz depending on the \ufb01le. For the times when the detector is not in\nscience mode or the data does not meet the minimum required data quality conditions (see next section), the\nstrain values are set to NaNs. The strain h(t) is a function of time, so it is accompanied by the attributes Xstart\nand Xspacing de\ufb01ning the starting GPS time of the data contained in the array and the corresponding distance\nin time between the points of the array.\n\u2022 quality: this folder contains two sub-folders, one for data quality and the other for injections, each including a\nbitmask to indicate at each second the status of the data quality or the injections and the description of each\nbit of the mask (see Section 3.2 for details).\nThe gwf \ufb01les have a similar content but with a di\ufb00erent structure. They contain 3 channels, one for the strain data,\none for the data quality and one for the injections. The channel names are described in Table 2. The original \ufb01les\nproduced internally, whose channel names are listed in Table 1, contain only the strain channel, while the GWOSC\n\ufb01les conveniently combine the strain data with the data quality and injection information in the same \ufb01le.\nTable 2.\nChannel names of the GWOSC frame \ufb01les (format gwf).\nIn this nomenclature, ifo is a place holder for the\ninterferometer name, i.e. H1, L1, V1, G1 or K1, and s = 4 or 16 kHz denotes the sampling rate. The R1 sub-string represents\nthe revision number of the channel name so it will become R2 in case there is a second (revised) release, and so on.\nChannel name\nStrain\nifo:GWOSC-sKHZ_R1_STRAIN\nData quality mask\nifo:GWOSC-sKHZ_R1_DQMASK\nInjections mask\nifo:GWOSC-sKHZ_R1_INJMASK\n3.2. Data quality and injections in GWOSC \ufb01les\nSeveral types of searches are performed on the LIGO, Virgo, GEO 600, and KAGRA data. Those searches are\ndivided into four families named after the types of signals they target: Compact binary coalescences (CBC), GW\nbursts (BURST), continuous waves (CW) and stochastic backgrounds (STOCH). As each type of search has a unique\nsensitivity to instrumental artifacts, a detailed characterization of detector noise and data quality is essential to\neliminate spurious signals of terrestrial origin found by the searches.\nLIGO, Virgo, GEO 600 and KAGRA have\ndedicated teams responsible for detector characterization and data quality, as described in Davis et al. (2021); Acernese\net al. (2022a); Abbott et al. (2022a), and Abe et al. (2022).\nCBC analyses (Abbott et al. 2021a,b,c) seek signals from merging neutron stars and black holes by \ufb01ltering the data\nwith waveform templates. BURST analyses (Abbott et al. 2021e,f) search for generic GW transients with minimal\n12\nThe observatory refers to the site and it is indicated by one letter, like L for Livingston. The addition of a number after the letter to\nindicate the detector, e.g. L1, could be useful if multiple detectors are installed in the same site, as was the case for Initial LIGO (Abbott\net al. 2009).\n\n18\nassumptions on the source or signal morphology by identifying excess power in the time-frequency representation of\nthe GW strain data. CW searches (Abbott et al. 2022b) look for long-duration, continuous, periodic GW signals from\nasymmetries of rapidly spinning neutron stars.\nSTOCH searches (Abbott et al. 2021g,h) target the stochastic GW\nbackground signal which is formed by the superposition of and unresolved sources from various stages of the evolution\nof the universe.\nBecause of fundamental di\ufb00erences in the search methodologies, certain noise types are relevant to speci\ufb01c searches.\nCBC and BURST searches look for short, transient signals, with durations from less than a second to several tens of\nseconds. Data quality information for these searches is recorded as sets of time intervals when data are relatively free\nof corruption, known as segment lists. This information is provided inside the GWOSC \ufb01les for the two GW transient\nsearches CBC and BURST. The data quality information most relevant for CW and STOCH searches is in the frequency\ndomain and it is provided as lists of instrumental lines in separate \ufb01les, available for download on GWOSC13.\nData quality and signal injection information for a given GPS second is indicated by bitmasks with a 1-Hz sampling\nrate. The bit meanings are given in Tables 3 and 4 for the data quality and injections, respectively. To describe data\nquality, di\ufb00erent categories are de\ufb01ned. For each category, the corresponding bit in the bitmask shown in Table 3 has\na value of 1 (good data) if in that second of time the requirements of the category are ful\ufb01lled, otherwise 0 (bad data).\nTable 3.\nData quality bitmasks description.\nFor O3, the CBC_CAT1 and BURST_CAT1 segment lists are equivalent (see the\nde\ufb01nition of CAT1 in the text). Note that any data that are not present are replaced by NaN values in the corresponding strain\ntime series. In each bit mask, a value of 1 corresponds to the data quality check passing (good data), and a zero means the\ncheck has failed (bad data). The CBC_CAT3 and BURST_CAT3 are equivalent to CBC_CAT2 and BURST_CAT2 in O3.\nBit\nShort name\nDescription\n0\nDATA\nData present\n1\nCBC_CAT1\nPass CAT1 test\n2\nCBC_CAT2\nPass CAT1 and CAT2 test for CBC searches\n3\nCBC_CAT3\nPass CAT1 and CAT2 and CAT3 test for CBC searches\n4\nBURST_CAT1\nPass CAT1 test\n5\nBURST_CAT2\nPass CAT1 and CAT2 test for BURST searches\n6\nBURST_CAT3\nPass CAT1 and CAT2 and CAT3 test for BURST searches\nTable 4. Meaning of the injection bits. A value of 1 indicates TRUE (no injection), while a value of 0 is FALSE (injection is\npresent).\nBit\nShort name\nDescription\n0\nNO_CBC_HW_INJ\nNo CBC injections\n1\nNO_BURST_HW_INJ\nNo burst injections\n2\nNO_DETCHAR_HW_INJ\nNo detector characterization injections\n3\nNO_CW_HW_INJ\nNo continuous wave injections\n4\nNO_STOCH_HW_INJ\nNo stochastic injections\nThe meaning of each category is described in Davis et al. (2021) and Acernese et al. (2022a). Here, we provide a\nbrief summary of each category:\nDATA: Failing this level indicates that strain data are not publicly available at this time because the instruments were\nnot operating in nominal conditions. For O3, this is equivalent to failing Category 1 criteria, de\ufb01ned below. For\nintervals of bad or absent data, NaNs have been inserted in the corresponding strain data array.\n13\nSee https://gwosc.org/O3/o3speclines for L1, H1 and V1, https://gwosc.org/O3/O3GKspeclines for K1 and https://gwosc.org/O3/\nO3GK_GEO_speclines for G1.\n\n19\nCAT1: (Category 1) Failing a data quality check at this category indicates a critical issue with a key detector component\nnot operating in its nominal con\ufb01guration. GWOSC data during times that fail CAT1 criteria are replaced by\nNaN values in the strain time series. For O3, CBC_CAT1, BURST_CAT1, and DATA lead to identical segment lists.\nCAT2: (Category 2) Failing a data quality check at this category indicates times when excess noise is present in a\nsensor with an understood physical coupling to the strain channel (LIGO Scienti\ufb01c Collaboration and Virgo\nCollaboration 2016). The fraction of time removed by this category is less than 1% of the data, and is detailed\nin Table 6.\nCAT3: (Category 3) Failing a data quality check at this category indicates times when there is statistical coupling\nbetween a sensor/auxiliary channel and the strain channel which is not fully understood. This category was not\nused in O3 LVK searches, although it was used in previous observing runs (Abbott et al. 2021d).\nTable 5. Total time satisfying the data quality criteria for each SEARCH type (= CBC or BURST) and each CATEGORY (= CAT1,\nCAT2 or CAT3) spanning the full DURATION of each observing RUN (= O3a, O3b or O3GK) and each DETECTOR (= H1, L1, V1,\nG1 or K1). DURATION includes all time in seconds between the o\ufb03cial start and end of each RUN, including times when the\ninstruments are not collecting data for astrophysical analysis. When the criteria for a given \ufb02ag is satis\ufb01ed, the corresponding\nbit will have the value 1 (good data by these criteria); otherwise, it will have the value 0 (bad data). The data in the table can\nbe retrieved at https://gwosc.org/timeline/show/[RUN]_16KHZ_R1/[DETECTOR]_[SEARCH]_[CATEGORY].\nData Quality Flags (Total time in seconds)\nRUN\nDURATION\nDETECTOR\nDATA\nCBC_CAT1\nCBC_CAT2\nCBC_CAT3\nBURST_CAT1\nBURST_CAT2\nBURST_CAT3\nH1\n11218675\n11218675\n11177046\n11177046\n11218675\n11125849\n11125849\nO3a\n15811200\nL1\n11956179\n11956179\n11943913\n11943913\n11956179\n11879365\n11879365\nV1\n12038929\n12038929\n12038929\n12038929\n12038929\n12038929\n12038929\nH1\n9967195\n9967195\n9964945\n9964945\n9967195\n9915276\n9915276\nO3b\n12708000\nL1\n9810816\n9810816\n9782946\n9782946\n9810816\n9760960\n9760960\nV1\n9591207\n9591207\n9591207\n9591207\n9591207\n9591207\n9591207\nO3GK\n1180800\nG1\n940133\n940133\n940133\n940133\n940133\n940133\n940133\nK1\n628055\n628055\n628055\n628055\n628055\n628055\n628055\nTable 6. Fraction of observing time removed by applying CAT2 vetoes. The percentages represent the amount of time in the\nDATA segment list relative to the total duration of observing time. CAT2 vetoes were not used for Virgo, KAGRA, or GEO 600.\nDetector\nO3a\nO3b\nCBC\nBURST\nCBC\nBURST\nH1\n0.37%\n0.83%\n0.02%\n0.52%\nL1\n0.01%\n0.64%\n0.28%\n0.51%\nData quality categories are cascading: a time which fails a given category automatically fails all higher categories.\nSince CAT3 \ufb02ags were not used in O3, the CAT3 segment lists are identical to the corresponding CAT2 lists. However,\nthe di\ufb00erent analysis groups qualify the data independently: failing BURST_CAT2 does not necessarily imply failing\nCBC_CAT2. See Table 5 for the amount of time associated with each category.\nSimulated signals added to the detectors for testing and calibration are referred to as hardware injections. GWOSC\ndata releases provide a time series with each one second sample representing a bit mask vector of the state of\nthe injection at that time. The injections are categorized according to the type of injected signal relevant to each\nastrophysical search. There are also injections used for detector characterization (DETCHAR). The injection bitmask\nmarks the injection-free times. The bit corresponding to a given type of injection is de\ufb01ned in Table 4. A bit is set to\n1 if there is no injection, otherwise it is set to 0. The full details of the complete set of hardware injections for O3 can\nbe found at https://gwosc.org/O3/o3_inj.\n\n20\nA CBC signal was injected on one occasion in each of the LIGO detectors during O3a, but not in coincidence. The\n(CBC) injection for H1 took place between GPS 1251662270 (2019-09-04T19:57:32 UTC) and GPS 1251662279 (2019-\n09-04T19:57:41 UTC), which was during observing mode. The CBC injection for L1 did not take place during observing\nmode and is thus not present in the released data. No CBC injections were performed during O3b.\nNo injections of BURST signals were performed during O3a and O3b.\nSome signal injections of the DETCHAR type were injected during O3a and O3b for both H1 and L1, while there were\nnone for Virgo. The waveform model used for those injections is h(t) = a e\u2212(t\u2212t0)2/\u03c4 2 sin [2\u03c0f(t \u2212t0) \u2212\u03c6], where t0\nis the time of the injection. The signal parameters \u03c4, \u03c6 and f were randomly chosen and are documented in separate\ndatabases for H114 and for L115.\nFour STOCH signals were injected during O3.\nThese hardware injections consisted of a simulated stochastic\ngravitational-wave background of 13 minutes long duration and were generated using the NAP package (Acernese\net al. 2005) and rescaled to have an amplitude of \u21260 = 2.0 \u00d7 10\u22125 with the default Hubble constant value\nH0 = 100 km s\u22121 Mpc\u22121. Two of these injections were added only in H1 starting at GPS 1249200018 (2019-08-\n07T08:00:00 UTC) and GPS 1258273818 (2019-11-20T08:30:00). The other two injections were performed coherently at\nL1 and H1 during O3b starting at GPS 1258345818 (2019-11-21T04:30:00) and GPS 1258353018 (2019-11-21T06:30:00).\nThe detectors were in observing mode for all of these stochastic injections.\nCW injections were performed in H1 and L1 during both O3a and O3b, using a set of pulsar parameters provided\non the GWOSC website16. Those injections are always present except during de\ufb01ned intervals for O3a17 and O3b18.\nNo CW injections were performed in V1 during O3a, but there were CW injections in V1 during O3b between GPS\n1263945616 (2020-01-24 23:59:58 UTC) and GPS 1266019220 (2020-02-18 00:00:02 UTC). The injected signal was\nremoved a posteriori in the strain data as described in Acernese et al. (2022b). A residual signal after removal may\nstill be present with an amplitude between 20 and 100 times lower than that of the injection. The residual amplitude\nis smaller than or at most the same order as the calibration uncertainty.\nNo signal hardware injections of any type were performed during O3GK.\n3.3. Alternate versions of the strain data\nTable 7. Names of alternate strain channels in the O3 data release. ifo is a place holder for the name of the LIGO interferometer,\ni.e. H1 or L1.\nChannel name\nDescription\nifo:DCS-CALIB_STRAIN_C01_AR\nLIGO calibrated strain, o\ufb04ine calibration\nifo:DCS-CALIB_STRAIN_CLEAN_C01_AR\nLIGO calibrated strain,\nafter applying linear noise\nsubtraction\nifo:DCS-CALIB_STRAIN_CLEAN_SUB60HZ_C01_AR\nLIGO calibrated strain, after applying both linear and\nnon-linear noise subtraction. This is the recommended\nchannel (main release)\nV1:Hrec_hoft_16384Hz_AR\nVirgo calibrated strain for most of O3a and O3b (main\nrelease)\nV1:Hrec_hoft_V1O3ARepro1A_16384Hz_AR\nVirgo calibrated strain for the last two weeks of Sep 2019,\nnear the end of O3a with an enhanced noise subtraction\n(main release)\nIn addition to the main strain data release described above, the O3 data release includes several alternate strain\nchannels, as described at https://gwosc.org/O3/O3alt. This alternate data release is available via both CernVM-FS or\nstreaming via a network data server (NDS2) (Zweizig et al. 2021). The alternate strain channels re\ufb02ect di\ufb00erent choices\nfor how aggressively to apply noise subtraction strategies to remove di\ufb00erent sources of contamination. Some LVK\n14\nSee https://gwosc.org/static/injections/o3a/H1_detchar_inj.txt for O3a and https://gwosc.org/static/injections/O3b/inj_o3b_H1.txt\nfor O3b.\n15\nSee https://gwosc.org/static/injections/o3a/L1_detchar_inj.txt for O3a and https://gwosc.org/static/injections/O3b/inj_o3b_L1.txt\nfor O3b.\n16\nhttps://gwosc.org/O3/O3April1_injection_parameters\n17\nhttps://gwosc.org/timeline/show/O3a_16KHZ_R1/H1_NO_CW_HW_INJ*H1_DATA*L1_NO_CW_HW_INJ*L1_DATA/\n1238166018/15811200\n18\nhttps://gwosc.org/timeline/show/O3b_16KHZ_R1/H1_NO_CW_HW_INJ*H1_DATA*L1_NO_CW_HW_INJ*L1_DATA/\n1256655618/12708000\n\n21\nanalyses used di\ufb00erent versions of the strain channels. The alternate strain channel release was designed to re\ufb02ect the\ninternal formatting used by the LVK as much as possible. In particular, the release uses only the GWF \ufb01le format, does\nnot include any NaN values, and does not include any data quality information. The channels found in the alternate\ncalibration release are described in Table 7.\n4. ONLINE EVENT CATALOGS\nNinety-three GW transient events or notable candidates were discovered based on the LVK\u2019s analyses of the O3\ndata (Abbott et al. 2021a,b,c). Data associated with these signals are available online through the GWOSC Event\nPortal19, along with other scienti\ufb01c products. For all events in the Event Portal, snippets of strain data are released\nin the form of a segment of 4096 seconds around the time of the event. The data snippets are made available no later\nthan when the event discovery becomes public in a refereed, scienti\ufb01c journal. In addition, the Event Portal includes\na concise summary of the source properties (i.e., parameters of the compact star binaries associated with each of the\ndetected signals), links to a number of science products (posterior samples), links to any associated low-latency alerts,\nand a documentation page for each release containing publication information. The list of O3 event data releases is as\nfollows:\nO3_Discovery_Papers: Notable events \ufb01rst published individually (Abbott et al. 2020b,d,e,f, 2021i). Associated data\nreleases may contain preliminary versions of data quality segments and calibration\nO3_IMBH_marginal: Marginal candidates associated with the search for Intermediate Mass Black Hole (IMBH) binary\nmergers\nGWTC-2: Con\ufb01dent events from the O3a observation run (\ufb01rst search)\nGWTC-2.1-confident: Con\ufb01dent events from the O3a observation run (updated search)\nGWTC-2.1-marginal: Marginal candidates from the O3a observation run (updated search)\nGWTC-2.1-auxiliary: Candidates from GWTC-2 which, based on the updated analysis presented in the GWTC-2.1\ncatalog paper, do not satisfy the criteria for inclusion in the GWTC-2.1-con\ufb01dent or GWTC-2.1-marginal releases\nGWTC-3-confident: Con\ufb01dent events from the O3b observing run\nGWTC-3-marginal: Marginal candidates from the O3b observing run\nSome events are listed in the database with multiple versions, typically corresponding to the event\u2019s inclusion in\nmultiple releases. The cumulative GWTC catalog includes all con\ufb01dent GW events published by the LVK collaboration,\nand currently includes 93 events.\nEvents in the GWTC-2.1-confident and GWTC-3-confident releases all have a\nprobability of astrophysical origin greater than 0.5 20 in at least one of the search pipelines, and are included in the\ncumulative GWTC.\nThe online catalogs are searchable via a web user interface. The Event Portal database can be queried based on\nspeci\ufb01c source properties, namely the primary mass, secondary mass, total mass, chirp mass, \ufb01nal mass (of the merger\nremnant), luminosity distance, redshift, e\ufb00ective inspiral spin, or other properties associated with the observed signal,\nsuch as UTC or GPS event time, detector frame chirp mass, network SNR, false alarm rate and the posterior probability\nof astrophysical origin. The events can also be selected by identi\ufb01cation such as partial event name, release catalog or\ngroup of catalogs. The output format can be one of the following: HTML, JSON, CSV or plain ASCII text.\nTo ease the analysis of multiple events, the catalogs can be queried programmatically with scripts using the REST\nAPI that returns all catalog lists in a JSON format. Catalogs can be queried with a GET request. As an example,\nto request all merger events for which the primary mass is less than 3M\u2299, the URL for the GET request would be\nhttps://gwosc.org/eventapi/html/query/show?max-mass-1-source=3. A detailed explanation of the query API nodes\ncan be found on the GWOSC website21.\n19\nhttps://gwosc.org/eventapi\n20\nSee Abbott et al. (2021c), App. D. 7 for a de\ufb01nition and details about its estimation.\n21\nhttps://gwosc.org/apidocs\n\n22\n4.1. Parameter estimation\nFor each detected source the Event Portal displays the 90% credible intervals for a selection of parameters that\nre\ufb02ect the values given in the relevant publication. Those credible intervals are computed from the posterior samples\nresulting from Bayesian inference algorithms applied to the data.\nIn addition to the information provided by GWOSC, the posterior samples are distributed through the Zenodo open\nrepository (LIGO Scienti\ufb01c Collaboration, Virgo Collaboration and KAGRA Collaboration 2021; LIGO Scienti\ufb01c\nCollaboration and Virgo Collaboration 2021c).\nThey are provided from the single event web page and through the JSON API as downloadable links to the \ufb01les\non Zenodo. The parameter names follow a standard nomenclature22 (Hoy & Raymond 2021). Parameter estimates\nmay change with di\ufb00erent version of the event or catalog release. The parameter sets are denoted by a set of version\nnumbers for each event (depending on the number of releases in which that event appears).\n4.2. Low-latency alerts\nDuring O3, public alerts were communicated with low latency to report the occurence of a notable trigger detected\nin the data23.\nThe alerts are sent with a latency of few minutes after detection.\nThey include a number of\npreliminary parameter estimations that are useful for the localization of the source through a probability skymap.\nThis information can be used by other, non-GW, instruments to search for potential electromagnetic counterparts in\nfollow-up observations. The complete list of alerts sent during O3 can be found publicly in the GraceDB website24\nand, as described below, in GWOSC.\nThe Event Portal references the GraceDB entry for the original trigger alert of the event. Links to GraceDB entries\nare available through the GWOSC web interface and the JSON API. Events \ufb01rst detected o\ufb04ine do not trigger\nlow-latency alerts and thus lack a GraceDB entry.\n5. TECHNICAL VALIDATION\nThe O3 GWOSC data release is reprocessed for the broader user community beginning with the internal strain\ndata products used for data analysis by the LIGO, Virgo, and KAGRA Collaborations for publication purposes. The\nreprocessing produces new GWOSC gwf and hdf5 \ufb01les containing the previously discussed strain, data quality and\nhardware injection information for each detector. In addition, versions of these GWOSC \ufb01les at a reduced sampling\nrate of 4096 Hz for the strain channel of each detector are also produced. All data for the release are carefully reviewed\nby the internal GWOSC team and then reviewed by an independent review team made up of members from the LIGO,\nVirgo, and KAGRA Collaborations. This review process checks that:\n\u2022 the strain vectors at the maximum sample rate (16 kHz) in the GWOSC hdf and gwf \ufb01les are identical to\nmachine precision to the corresponding strain vectors of the LVK main archives;\n\u2022 the strain vectors after resampling at 4 kHz do not have numerical artifacts that may arise from the resampling\ntechnique;\n\u2022 the data quality and injection information located in either the GWOSC hdf and gwf \ufb01les or the online Timeline\ntool described in detail in Section 6, agree with all available records.\n\u2022 the documentation associated with the O3 data products found online is correct and contains comprehensive\ninformation for the broader user community.\nThe data \ufb01les and accompanying documentation are released to the public on the GWOSC website once all checks\nhave passed at the designated date and time agreed to by the LIGO, Virgo and KAGRA Collaborations.\n6. USAGE NOTES\n6.1. Salient features of GW data\n22\nSee https://lscsoft.docs.ligo.org/pesummary/unstable_docs/gw/parameters.html.\n23\nSee https://emfollow.docs.ligo.org/userguide for more details. This userguide is a living document that is being updated in preparation\nfor the upcoming science run O4. Therefore, the informations in this guide may not be necessarily relevant for O3 data.\n24\nhttps://gracedb.ligo.org/superevents/public/O3\n\n23\nWorking with GW data requires an awareness of the presence of noise in the data. An overview of LIGO/Virgo\ndetector noise and some applicable signal processing methods are described in Abbott et al. (2020c); see also above\nin Sec. 3.2 and 2.3 for a brief introduction to various classes of detector noise. In addition, as mentioned previously,\nthe data are only valid within a \ufb01xed frequency range due to the limits of calibration (Sec. 2.2) as well as due to\nartifacts from the down-sampling process (Sec. 3). All of these complications need to be considered when searching\nfor astrophysical signals.\n6.2. List of observing segments\nSegment lists describe times when GW detectors are collecting data and are operating in a normal condition, as\ndescribed in Section 3.2. The GWOSC website provides an online app called Timeline to discover, plot, and download\nsegment lists25. The Timeline query page allows users to select observing runs from a drop-down menu, and then view\nthe names of segment lists associated with the selected run. Segment lists may be downloaded as ASCII text \ufb01les or\nin a JSON format. Alternatively, segment lists may be displayed in an interactive plot, as seen in Fig. 3. To explore\ntimes within a run, a visitor can use the mouse to scroll and zoom on the Timeline plots. Hovering the mouse over a\nsegment displays a tool-tip with the exact start and stop time, in both GPS and UTC time.\n6.3. Software and Support\nThe GWOSC website provides a number of resources for helping investigators learn to work with GW data, including:\n\u2022 Software libraries26: A number of software packages developed for GW analysis are open source. The GWOSC\nwebsite provides a suggested list of packages, many of which were created by members of the LIGO, Virgo, and\nKAGRA collaborations. Links to source code and documentation are provided for each package.\n\u2022 Tutorials27: GWOSC provides tutorials to demonstrate the basics of GW data analysis. Most tutorials are in\nPython, and provided in notebooks that can be run in the cloud to avoid the necessity for the user to install\nsoftware.\n\u2022 Workshops and online course28: Annual Open Data Workshops provide a complete course in working with\nGW data, including lectures, software tutorials, and challenge problems. Materials from past workshops are\navailable as a free online course; students can enroll at any time.\nFuture workshops will be posted on the\nGWOSC website, and are open to any interested participants.\n\u2022 Discussion forum29: A public discussion forum for GW topics provides space to ask for help with GW data\nanalysis, discuss LVK papers, post questions about GW science, and connect with other researchers in the \ufb01eld.\n7. SUMMARY\nThe O3 data set described in this paper represents the most sensitive gravitational-wave observations to date. The\ndata contain over 80 compact object merger signals, as described in a number of catalog releases, including GWTC-2\n(Abbott et al. 2021a), GWTC-2.1 (Abbott et al. 2021b) and GWTC-3 (Abbott et al. 2021c). O3 includes three main\nphases: O3a, O3b, and O3GK. O3a and O3b are both joint runs of LIGO and Virgo, while the O3GK run involved\nKAGRA and GEO 600. Data and documentation for all O3 data are available from the GWOSC website.\nLooking ahead, LIGO, Virgo, and KAGRA are planning an O4 run, scheduled to begin in 2023, with improved\nsensitivity. Data from events discovered in O4 will be released as the events are published, and release of the next\nlarge strain data sets are planned for 2025 (LIGO Laboratory 2022b). This will be followed by the O5 observing run,\nanticipated to be the \ufb01rst extended observing run with a span of over two years (LIGO Scienti\ufb01c Collaboration, Virgo\nCollaboration and KAGRA Collaboration 2022b). Planned instrument upgrades should increase the sensitivity of the\nnetwork and thus extend the volume of space over which signals may be observed, so that future data sets will include\nmore frequent detections and a corresponding expanded depth of science in this rapidly evolving \ufb01eld.\n25\nSee https://gwosc.org/timeline.\n26\nhttps://gwosc.org/software\n27\nhttps://gwosc.org/tutorials\n28\nhttps://gwosc.org/workshops\n29\nhttps://ask.igwn.org\n\n24\nLIGO H\nLIGO L\n0\n3\n6\n9\n12\n15\n18\n21\n24\nTime [weeks] from 2019-04-01 15:00:00 UTC (1238166018)\nVirgo\nLIGO H\nLIGO L\n0\n3\n6\n9\n12\n15\n18\n21\nTime [weeks] from 2019-11-01 15:00:00 UTC (1256655618)\nVirgo\nGEO600\n0\n2\n4\n6\n8\n10\n12\n14\nTime [days] from 2020-04-07 08:00:00 UTC (1270281618)\nKAGRA\nFigure 3. Timelines for the full O3a (top) and O3b (middle) and O3GK (bottom) observing runs based on the data quality\nbitmask CBC_CAT1 for each detector (see Tab. 3). Colored bars represent times when data are available, and white areas show\ntimes when data are not available. Similar plots can be generated from the GWOSC web pages25.\n\n25\nACKNOWLEDGEMENTS\n1\nCalibration of the LIGO strain data was performed with GstLAL-based calibration software pipeline (Viets et al.\n2018). Calibration of the Virgo strain data was performed with C-based software (Acernese et al. 2022b). Data-\nquality products and event-validation results were computed using the DMT (John Zweizig 2006), DQR (LIGO\nScienti\ufb01c Collaboration and Virgo Collaboration 2018), DQSEGDB (Fisher et al. 2021), gwdetchar (Urban et al.\n2021), hveto (Smith et al. 2011), iDQ (Essick et al. 2020) and Omicron (Robinet et al. 2020) software packages\nand contributing software tools. Analyses relied upon the LALSuite software library (LIGO Scienti\ufb01c Collaboration\n2018). PESummary was used to post-process and collate parameter-estimation results (Hoy & Raymond 2021). For\nan exhaustive list of the softwares used for searching the GW signals and characterizing their source, see (Abbott\net al. 2021c). Plots were prepared with Matplotlib (Hunter 2007), seaborn (Waskom 2021) GWSumm (Macleod et al.\n2021a) and GWpy (Macleod et al. 2021b). NumPy (Harris et al. 2020) and SciPy (Virtanen et al. 2020) were used in\nthe preparation of the manuscript.\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\nThis material is based upon work supported by NSF\u2019s LIGO Laboratory which is a major facility fully funded\nby the National Science Foundation.\nThe authors also gratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of\nNiedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the\nGEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The\nauthors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National\nde la Recherche Scienti\ufb01que (CNRS) and the Netherlands Organization for Scienti\ufb01c Research (NWO), for the\nconstruction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors\nalso gratefully acknowledge research support from these agencies as well as by the Council of Scienti\ufb01c and Industrial\nResearch of India, the Department of Science and Technology, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigaci\u00f3n\n(AEI), the Spanish Ministerio de Ciencia e Innovaci\u00f3n and Ministerio de Universidades, the Conselleria de Fons\nEuropeus, Universitat i Cultura and the Direcci\u00f3 General de Pol\u00edtica Universitaria i Recerca del Govern de les Illes\nBalears, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8ncia i Societat Digital de la Generalitat Valenciana and the\nCERCA Programme Generalitat de Catalunya, Spain, the National Science Centre of Poland and the European\nUnion \u2013 European Regional Development Fund; Foundation for Polish Science (FNP), the Swiss National Science\nFoundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European\nCommission, the European Social Funds (ESF), the European Regional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scienti\ufb01c Research Fund\n(OTKA), the French Lyon Institute of Origins (LIO), the Belgian Fonds de la Recherche Scienti\ufb01que (FRS-FNRS),\nActions de Recherche Concert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen (FWO), Belgium,\nthe Paris \u00cele-de-France Region, the National Research, Development and Innovation O\ufb03ce Hungary (NKFIH), the\nNational Research Foundation of Korea, the Natural Science and Engineering Research Council Canada, Canadian\nFoundation for Innovation (CFI), the Brazilian Ministry of Science, Technology, and Innovations, the International\nCenter for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research\nGrants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the\nResearch Corporation, the Ministry of Science and Technology (MOST), Taiwan, the United States Department of\nEnergy, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN and\nCNRS for provision of computational resources.\n13\n14\n15\n16\n17\n18\n19\n20\n21\n22\n23\n24\n25\n26\n27\n28\n29\n30\n31\n32\n33\n34\n35\n36\n37\n38\n39\n40\n41\nThis work was supported by MEXT, JSPS Leading-edge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-inAid for Scienti\ufb01c Research on Innovative Areas 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-to-Core Program A. Advanced Research Networks, JSPS\nGrantin-Aid for Scienti\ufb01c Research (S) 17H06133 and 20H05639 , JSPS Grant-in-Aid for Transformative Research\nAreas (A) 20A203: JP20H05854, the joint research program of the Institute for Cosmic Ray Research, University of\nTokyo, National Research Foundation (NRF), Computing Infrastructure Project of Global Science experimental Data\nhub Center (GSDC) at KISTI, Korea Astronomy and Space Science Institute (KASI), and Ministry of Science and\nICT (MSIT) in Korea, Academia Sinica (AS), AS Grid Center (ASGC) and the National Science and Technology\nCouncil (NSTC) in Taiwan under grants including the Rising Star Program and Science Vanguard Research Program,\nAdvanced Technology Center (ATC) of NAOJ, and Mechanical Engineering Center of KEK.\n42\n43\n44\n45\n46\n47\n48\n49\n50\n51\n\n26\nREFERENCES\nAasi, J., et al. 2015, Class. 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Abe,27 F. Acernese,28, 29 K. Ackley,30 N. Adhikari,31 R. X. Adhikari,26 V. K. Adkins,32\nV. B. Adya,33 C. Affeldt,34, 35 D. Agarwal,36 M. Agathos,37, 38 K. Agatsuma,39 N. Aggarwal,40 O. D. Aguiar,41\nL. Aiello,42 A. Ain,43 P. Ajith,44 T. Akutsu,45, 46 S. Albanesi,47, 48 R. A. Alfaidi,49 A. Allocca,50, 29 P. A. Altin,33\nA. Amato,51 C. Anand,30 S. Anand,26 A. Ananyeva,26 S. B. Anderson,26 W. G. Anderson,31 M. Ando,52, 53\nT. Andrade,54 N. Andres,55 M. Andr\u00b4es-Carcasona,56 T. Andri\u00b4c,57 S. V. Angelova,58 S. Ansoldi,59, 60\nJ. M. Antelis,61 S. Antier,62, 63 T. Apostolatos,64 E. Z. Appavuravther,65, 66 S. Appert,26 S. K. Apple,67 K. Arai,26\nA. Araya,68 M. C. Araya,26 J. S. Areeda,69 M. Ar`ene,70 N. Aritomi,45 N. Arnaud,71, 72 M. Arogeti,73\nS. M. Aronson,32 K. G. Arun,74 H. Asada,75 Y. Asali,76 G. Ashton,77 Y. Aso,78, 79 M. Assiduo,80, 81\nS. Assis de Souza Melo,72 S. M. Aston,82 P. Astone,83 F. Aubin,81 K. AultONeal,61 C. Austin,32 S. Babak,70\nF. Badaracco,84 M. K. M. Bader,85 C. Badger,86 S. Bae,87 Y. Bae,88 A. M. Baer,89 S. Bagnasco,48 Y. Bai,26\nJ. Baird,70 R. Bajpai,90 T. Baka,91 M. Ball,92 G. Ballardin,72 S. W. Ballmer,93 A. Balsamo,89 G. Baltus,94\nS. Banagiri,40 B. Banerjee,57 D. Bankar,36 J. C. Barayoga,26 C. Barbieri,95, 96, 97 B. C. Barish,26 D. Barker,98\nP. Barneo,54 F. Barone,99, 29 B. Barr,49 L. Barsotti,100 M. Barsuglia,70 D. Barta,101 J. Bartlett,98\nM. A. Barton,49 I. Bartos,102 S. Basak,44 R. Bassiri,103 A. Basti,104, 43 M. Bawaj,65, 105 J. C. Bayley,49\nM. Bazzan,106, 107 B. R. Becher,108 B. B\u00b4ecsy,109 V. M. Bedakihale,110 F. Beirnaert,111 M. Bejger,112\nI. Belahcene,71 V. Benedetto,113 D. Beniwal,114 M. G. Benjamin,115 T. F. Bennett,116 J. D. Bentley,39\nM. BenYaala,58 S. Bera,36 M. Berbel,117 F. Bergamin,34, 35 B. K. Berger,103 S. Bernuzzi,38 C. P. L. Berry,49\nD. Bersanetti,118 A. Bertolini,85 J. Betzwieser,82 D. Beveridge,119 R. Bhandare,120 A. V. Bhandari,36\nU. Bhardwaj,63, 85 R. Bhatt,26 D. Bhattacharjee,121 S. Bhaumik,102 A. Bianchi,85, 122 I. A. Bilenko,123\nG. Billingsley,26 S. Bini,124, 125 R. Birney,126 O. Birnholtz,127 S. Biscans,26, 100 M. Bischi,80, 81 S. Biscoveanu,100\nA. Bisht,34, 35 B. Biswas,36 M. Bitossi,72, 43 M.-A. Bizouard,62 J. K. Blackburn,26 C. D. Blair,119 D. G. Blair,119\nR. M. Blair,98 F. Bobba,128, 129 N. Bode,34, 35 M. Bo\u00a8er,62 G. Bogaert,62 M. Boldrini,130, 83 G. N. Bolingbroke,114\nL. D. Bonavena,106 F. Bondu,131 E. Bonilla,103 R. Bonnand,55 P. Booker,34, 35 B. A. Boom,85 R. Bork,26\nV. Boschi,43 N. Bose,132 S. Bose,36 V. Bossilkov,119 V. Boudart,94 Y. Bouffanais,106, 107 A. Bozzi,72\nC. Bradaschia,43 P. R. Brady,31 A. Bramley,82 A. Branch,82 M. Branchesi,57, 133 J. E. Brau,92 M. Breschi,38\nT. Briant,134 J. H. Briggs,49 A. Brillet,62 M. Brinkmann,34, 35 P. Brockill,31 A. F. Brooks,26 J. Brooks,72\nD. D. Brown,114 S. Brunett,26 G. Bruno,84 R. Bruntz,89 J. Bryant,39 F. Bucci,81 T. Bulik,135 H. J. Bulten,85\nA. Buonanno,136, 137 K. Burtnyk,98 R. Buscicchio,39 D. Buskulic,55 C. Buy,138 R. L. Byer,103\nG. S. Cabourn Davies,77 G. Cabras,59, 60 R. Cabrita,84 L. Cadonati,73 M. Caesar,139 G. Cagnoli,51 C. Cahillane,98\nJ. Calder\u00b4on Bustillo,140 J. D. Callaghan,49 T. A. Callister,141, 142 E. Calloni,50, 29 J. Cameron,119 J. B. Camp,143\nM. Canepa,144, 118 S. Canevarolo,91 M. Cannavacciuolo,128 K. C. Cannon,53 H. Cao,114 Z. Cao,145 E. Capocasa,70, 45\nE. Capote,93 G. Carapella,128, 129 F. Carbognani,72 M. Carlassara,34, 35 J. B. Carlin,146 M. F. Carney,40\nM. Carpinelli,147, 148, 72 G. Carrillo,92 G. Carullo,104, 43 T. L. Carver,42 J. Casanueva Diaz,72 C. Casentini,149, 150\nG. Castaldi,151 S. Caudill,85, 91 M. Cavagli`a,121 F. Cavalier,71 R. Cavalieri,72 G. Cella,43 P. Cerd\u00b4a-Dur\u00b4an,152\nE. Cesarini,150 W. Chaibi,62 S. Chalathadka Subrahmanya,153 E. Champion,154 C.-H. Chan,155 C. Chan,53\nC. L. Chan,156 K. Chan,156 M. Chan,157 K. Chandra,132 I. P. Chang,155 P. Chanial,72 S. Chao,155\nC. Chapman-Bird,49 P. Charlton,158 E. A. Chase,40 E. Chassande-Mottin,70 C. Chatterjee,119\nDebarati Chatterjee,36 Deep Chatterjee,31 M. Chaturvedi,120 S. Chaty,70 C. Chen,159, 155 D. Chen,78\nH. Y. Chen,100 J. Chen,155 K. Chen,160 X. Chen,119 Y.-B. Chen,161 Y.-R. Chen,155 Z. Chen,42 H. Cheng,102\nC. K. Cheong,156 H. Y. Cheung,156 H. Y. Chia,102 F. Chiadini,162, 129 C-Y. Chiang,163 G. Chiarini,107 R. Chierici,164\nA. Chincarini,118 M. L. Chiofalo,104, 43 A. Chiummo,72 R. K. Choudhary,119 S. Choudhary,36 N. Christensen,62\nQ. Chu,119 Y-K. Chu,163 S. S. Y. Chua,33 K. W. Chung,86 G. Ciani,106, 107 P. Ciecielag,112 M. Cie\u00b4slar,112\nM. Cifaldi,149, 150 A. A. Ciobanu,114 R. Ciolfi,165, 107 F. Cipriano,62 F. Clara,98 J. A. Clark,26, 73 P. Clearwater,166\nS. Clesse,167 F. Cleva,62 E. Coccia,57, 133 E. Codazzo,57 P.-F. Cohadon,134 D. E. Cohen,71 M. Colleoni,168\nC. G. Collette,169 A. Colombo,95, 96 M. Colpi,95, 96 C. M. Compton,98 M. Constancio Jr.,41 L. Conti,107\nS. J. Cooper,39 P. Corban,82 T. R. Corbitt,32 I. Cordero-Carri\u00b4on,170 S. Corezzi,105, 65 K. R. Corley,76\nN. J. Cornish,109 D. Corre,71 A. Corsi,171 S. Cortese,72 C. A. Costa,41 R. Cotesta,137 R. Cottingham,82\narXiv:2308.13666v1 [astro-ph.HE] 25 Aug 2023\n\n2\nM. W. Coughlin,172 J.-P. Coulon,62 S. T. Countryman,76 B. Cousins,173 P. Couvares,26 D. M. Coward,119\nM. J. Cowart,82 D. C. Coyne,26 R. Coyne,174 J. D. E. Creighton,31 T. D. Creighton,115 A. W. Criswell,172\nM. Croquette,134 S. G. Crowder,175 J. R. Cudell,94 T. J. Cullen,32 A. Cumming,49 R. Cummings,49\nL. Cunningham,49 E. Cuoco,72, 176, 43 M. Cury lo,135 P. Dabadie,51 T. Dal Canton,71 S. Dall\u2019Osso,57 G. D\u00b4alya,111, 177\nA. Dana,103 B. D\u2019Angelo,144, 118 S. Danilishin,178, 85 S. D\u2019Antonio,150 K. Danzmann,34, 35 C. Darsow-Fromm,153\nA. Dasgupta,110 L. E. H. Datrier,49 Sayak Datta,36 Sayantani Datta,74 V. Dattilo,72 I. Dave,120 M. Davier,71\nD. Davis,26 M. C. Davis,139 E. J. Daw,179 R. Dean,139 D. DeBra,103 M. Deenadayalan,36 J. Degallaix,180\nM. De Laurentis,50, 29 S. Del\u00b4eglise,134 V. Del Favero,154 F. De Lillo,84 N. De Lillo,49 D. Dell\u2019Aquila,147\nW. Del Pozzo,104, 43 L. M. DeMarchi,40 F. De Matteis,149, 150 V. D\u2019Emilio,42 N. Demos,100 T. Dent,140 A. Depasse,84\nR. De Pietri,181, 182 R. De Rosa,50, 29 C. De Rossi,72 R. DeSalvo,151, 183 R. De Simone,162 S. Dhurandhar,36\nM. C. D\u00b4\u0131az,115 N. A. Didio,93 T. Dietrich,137 L. Di Fiore,29 C. Di Fronzo,39 C. Di Giorgio,128, 129 F. Di Giovanni,152\nM. Di Giovanni,57 T. Di Girolamo,50, 29 A. Di Lieto,104, 43 A. Di Michele,105 B. Ding,169 S. Di Pace,130, 83\nI. Di Palma,130, 83 F. Di Renzo,104, 43 A. K. Divakarla,102 A. Dmitriev,39 Z. Doctor,40 L. Donahue,184\nL. D\u2019Onofrio,50, 29 F. Donovan,100 K. L. Dooley,42 S. Doravari,36 M. Drago,130, 83 J. C. Driggers,98 Y. Drori,26\nJ.-G. Ducoin,71 P. Dupej,49 U. Dupletsa,57 O. Durante,128, 129 D. D\u2019Urso,147, 148 P.-A. Duverne,71 S. E. Dwyer,98\nC. Eassa,98 P. J. Easter,30 M. Ebersold,185 T. Eckhardt,153 G. Eddolls,49 B. Edelman,92 T. B. Edo,26 O. Edy,77\nA. Effler,82 S. Eguchi,157 J. Eichholz,33 S. S. Eikenberry,102 M. Eisenmann,55, 45 R. A. Eisenstein,100 A. Ejlli,42\nE. Engelby,69 Y. Enomoto,52 L. Errico,50, 29 R. C. Essick,186 H. Estell\u00b4es,168 D. Estevez,187 Z. Etienne,188\nT. Etzel,26 M. Evans,100 T. M. Evans,82 T. Evstafyeva,37 B. E. Ewing,173 F. Fabrizi,80, 81 F. Faedi,81\nV. Fafone,149, 150, 57 H. Fair,93 S. Fairhurst,42 P. C. Fan,184 A. M. Farah,189 S. Farinon,118 B. Farr,92\nW. M. Farr,141, 142 E. J. Fauchon-Jones,42 G. Favaro,106 M. Favata,190 M. Fays,94 M. Fazio,191 J. Feicht,26\nM. M. Fejer,103 E. Fenyvesi,101, 192 D. L. Ferguson,193 A. Fernandez-Galiana,100 I. Ferrante,104, 43\nT. A. Ferreira,41 F. Fidecaro,104, 43 P. Figura,135 A. Fiori,43, 104 I. Fiori,72 M. Fishbach,40 R. P. Fisher,89\nR. Fittipaldi,194, 129 V. Fiumara,195, 129 R. Flaminio,55, 45 E. Floden,172 H. K. Fong,53 J. A. Font,152, 196 B. Fornal,183\nP. W. F. Forsyth,33 A. Franke,153 S. Frasca,130, 83 F. Frasconi,43 J. P. Freed,61 Z. Frei,177 A. Freise,85, 122\nO. Freitas,197 R. Frey,92 P. Fritschel,100 V. V. Frolov,82 G. G. Fronz\u00b4e,48 Y. Fujii,198 Y. Fujikawa,199\nY. Fujimoto,200 P. Fulda,102 M. Fyffe,82 H. A. Gabbard,49 W. E. Gabella,201 B. U. Gadre,137 J. R. Gair,137\nJ. Gais,156 S. Galaudage,30 R. Gamba,38 D. Ganapathy,100 A. Ganguly,36 D. Gao,202 S. G. Gaonkar,36\nB. Garaventa,118, 144 C. Garc\u00b4\u0131a N\u00b4u\u02dcnez,126 C. Garc\u00b4\u0131a-Quir\u00b4os,168 F. Garufi,50, 29 B. Gateley,98 V. Gayathri,102\nG.-G. Ge,202 G. Gemme,118 A. Gennai,43 J. George,120 O. Gerberding,153 L. Gergely,203 P. Gewecke,153\nS. Ghonge,73 Abhirup Ghosh,137 Archisman Ghosh,111 Shaon Ghosh,190 Shrobana Ghosh,42 Tathagata Ghosh,36\nB. Giacomazzo,95, 96, 97 L. Giacoppo,130, 83 J. A. Giaime,32, 82 K. D. Giardina,82 D. R. Gibson,126 C. Gier,58\nM. Giesler,204 P. Giri,43, 104 F. Gissi,113 S. Gkaitatzis,43, 104 J. Glanzer,32 A. E. Gleckl,69 P. Godwin,173\nE. Goetz,205 R. Goetz,102 N. Gohlke,34, 35 J. Golomb,26 B. Goncharov,57 G. Gonz\u00b4alez,32 M. Gosselin,72\nR. Gouaty,55 D. W. Gould,33 S. Goyal,44 B. Grace,33 A. Grado,206, 29 V. Graham,49 M. Granata,180 V. Granata,128\nA. Grant,49 S. Gras,100 P. Grassia,26 C. Gray,98 R. Gray,49 G. Greco,65 A. C. Green,102 R. Green,42\nA. M. Gretarsson,61 E. M. Gretarsson,61 D. Griffith,26 W. L. Griffiths,42 H. L. Griggs,73 G. Grignani,105, 65\nA. Grimaldi,124, 125 E. Grimes,61 S. J. Grimm,57, 133 H. Grote,42 S. Grunewald,137 P. Gruning,71 A. S. Gruson,69\nD. Guerra,152 G. M. Guidi,80, 81 A. R. Guimaraes,32 G. Guix\u00b4e,54 H. K. Gulati,110 A. M. Gunny,100 H.-K. Guo,183\nY. Guo,85 Anchal Gupta,26 Anuradha Gupta,207 I. M. Gupta,173 P. Gupta,85, 91 S. K. Gupta,132 R. Gustafson,208\nF. Guzman,209 S. Ha,210 I. P. W. Hadiputrawan,160 L. Haegel,70 S. Haino,163 O. Halim,60 E. D. Hall,100\nE. Z. Hamilton,185 G. Hammond,49 W.-B. Han,211 M. Haney,185 J. Hanks,98 C. Hanna,173 M. D. Hannam,42\nO. Hannuksela,91, 85 H. Hansen,98 T. J. Hansen,61 J. Hanson,82 T. Harder,62 K. Haris,85, 91 J. Harms,57, 133\nG. M. Harry,67 I. W. Harry,77 D. Hartwig,153 K. Hasegawa,212 B. Haskell,112 C.-J. Haster,100 J. S. Hathaway,154\nK. Hattori,213 K. Haughian,49 H. Hayakawa,214 K. Hayama,157 F. J. Hayes,49 J. Healy,154 A. Heidmann,134\nA. Heidt,34, 35 M. C. Heintze,82 J. Heinze,34, 35 J. Heinzel,100 H. Heitmann,62 F. Hellman,215 P. Hello,71\nA. F. Helmling-Cornell,92 G. Hemming,72 M. Hendry,49 I. S. Heng,49 E. Hennes,85 J. Hennig,216 M. H. Hennig,216\nC. Henshaw,73 A. G. Hernandez,116 F. Hernandez Vivanco,30 M. Heurs,34, 35 A. L. Hewitt,217 S. Higginbotham,42\nS. Hild,178, 85 P. Hill,58 Y. Himemoto,218 A. S. Hines,209 N. Hirata,45 C. Hirose,199 T-C. Ho,160 S. Hochheim,34, 35\nD. Hofman,180 J. N. Hohmann,153 D. G. Holcomb,139 N. A. Holland,33 I. J. Hollows,179 Z. J. Holmes,114 K. Holt,82\nD. E. Holz,189 Q. Hong,155 J. Hough,49 S. Hourihane,26 E. J. Howell,119 C. G. Hoy,42 D. Hoyland,39 A. Hreibi,34, 35\nB-H. Hsieh,212 H-F. Hsieh,155 C. Hsiung,159 Y. Hsu,155 H-Y. Huang,163 P. Huang,202 Y-C. Huang,155 Y.-J. Huang,163\nYiting Huang,175 Yiwen Huang,100 M. T. H\u00a8ubner,30 A. D. Huddart,219 B. Hughey,61 D. C. Y. Hui,220 V. Hui,55\nS. Husa,168 S. H. Huttner,49 R. Huxford,173 T. Huynh-Dinh,82 S. Ide,221 B. Idzkowski,135 A. Iess,149, 150\nK. Inayoshi,222 Y. Inoue,160 P. Iosif,223 M. Isi,100 K. Isleif,153 K. Ito,224 Y. Itoh,200, 225 B. R. Iyer,44\nV. JaberianHamedan,119 T. Jacqmin,134 P.-E. Jacquet,134 S. J. Jadhav,226 S. P. Jadhav,36 T. Jain,37 A. L. James,42\nA. Z. Jan,193 K. Jani,201 J. Janquart,91, 85 K. Janssens,227, 62 N. N. Janthalur,226 P. Jaranowski,228 D. Jariwala,102\nR. Jaume,168 A. C. Jenkins,86 K. Jenner,114 C. Jeon,229 W. Jia,100 J. Jiang,102 H.-B. Jin,230, 231 G. R. Johns,89\nR. Johnston,49 A. W. Jones,119 D. I. Jones,232 P. Jones,39 R. Jones,49 P. Joshi,173 L. Ju,119 A. Jue,183 P. Jung,88\nK. Jung,210 J. Junker,34, 35 V. Juste,187 K. Kaihotsu,224 T. Kajita,233 M. Kakizaki,213 C. V. Kalaghatgi,42, 91, 85, 234\nV. Kalogera,40 B. Kamai,26 M. Kamiizumi,214 N. Kanda,200, 225 S. Kandhasamy,36 G. Kang,235 J. B. Kanner,26\nY. Kao,155 S. J. Kapadia,44 D. P. Kapasi,33 C. Karathanasis,56 S. Karki,121 R. Kashyap,173 M. Kasprzack,26\n\n3\nW. Kastaun,34, 35 T. Kato,212 S. Katsanevas,72 E. Katsavounidis,100 W. Katzman,82 T. Kaur,119 K. Kawabe,98\nK. Kawaguchi,212 F. K\u00b4ef\u00b4elian,62 D. Keitel,168 J. S. Key,236 S. Khadka,103 F. Y. Khalili,123 S. Khan,42\nT. Khanam,171 E. A. Khazanov,237 N. Khetan,57, 133 M. Khursheed,120 N. Kijbunchoo,33 A. Kim,40 C. Kim,229\nJ. C. Kim,238 J. Kim,239 K. Kim,229 W. S. Kim,88 Y.-M. Kim,210 C. Kimball,40 N. Kimura,214 M. Kinley-Hanlon,49\nR. Kirchhoff,34, 35 J. S. Kissel,98 S. Klimenko,102 T. Klinger,37 A. M. Knee,205 T. D. Knowles,188 N. Knust,34, 35\nE. Knyazev,100 Y. Kobayashi,200 P. Koch,34, 35 G. Koekoek,85, 178 K. Kohri,240 K. Kokeyama,241 S. Koley,57\nP. Kolitsidou,42 M. Kolstein,56 K. Komori,100 V. Kondrashov,26 A. K. H. Kong,155 A. Kontos,108 N. Koper,34, 35\nM. Korobko,153 M. Kovalam,119 N. Koyama,199 D. B. Kozak,26 C. Kozakai,78 V. Kringel,34, 35\nN. V. Krishnendu,34, 35 A. Kr\u00b4olak,242, 243 G. Kuehn,34, 35 F. Kuei,155 P. Kuijer,85 S. Kulkarni,207 A. Kumar,226\nPrayush Kumar,44 Rahul Kumar,98 Rakesh Kumar,110 J. Kume,53 K. Kuns,100 Y. Kuromiya,224 S. Kuroyanagi,244, 245\nK. Kwak,210 G. Lacaille,49 P. Lagabbe,55 D. Laghi,138 E. Lalande,246 M. Lalleman,227 T. L. Lam,156\nA. Lamberts,62, 247 M. Landry,98 B. B. Lane,100 R. N. Lang,100 J. Lange,193 B. Lantz,103 I. La Rosa,55\nA. Lartaux-Vollard,71 P. D. Lasky,30 M. Laxen,82 A. Lazzarini,26 C. Lazzaro,106, 107 P. Leaci,130, 83 S. Leavey,34, 35\nS. LeBohec,183 Y. K. Lecoeuche,205 E. Lee,212 H. M. Lee,248 H. W. Lee,238 K. Lee,249 R. Lee,155 I. N. Legred,26\nJ. Lehmann,34, 35 A. Lema\u02c6\u0131tre,250 M. Lenti,81, 251 M. Leonardi,45 E. Leonova,63 N. Leroy,71 N. Letendre,55\nC. Levesque,246 Y. Levin,30 J. N. Leviton,208 K. Leyde,70 A. K. Y. Li,26 B. Li,155 J. Li,40 K. L. Li,252 P. Li,253\nT. G. F. Li,156 X. Li,161 C-Y. Lin,254 E. T. Lin,155 F-K. Lin,163 F-L. Lin,255 H. L. Lin,160 L. C.-C. Lin,252 F. Linde,234, 85\nS. D. Linker,151, 116 J. N. Linley,49 T. B. Littenberg,256 G. C. Liu,159 J. Liu,119 K. Liu,155 X. Liu,31 F. Llamas,115\nR. K. L. Lo,26 T. Lo,155 L. T. London,63, 100 A. Longo,257 D. Lopez,185 M. Lopez Portilla,91 M. Lorenzini,149, 150\nV. Loriette,258 M. Lormand,82 G. Losurdo,43 T. P. Lott,73 J. D. Lough,34, 35 C. O. Lousto,154 G. Lovelace,69\nJ. F. Lucaccioni,259 H. L\u00a8uck,34, 35 D. Lumaca,149, 150 A. P. Lundgren,77 L.-W. Luo,163 J. E. Lynam,89 M. Ma\u2019arif,160\nR. Macas,77 J. B. Machtinger,40 M. MacInnis,100 D. M. Macleod,42 I. A. O. MacMillan,26 A. Macquet,62\nI. Maga\u02dcna Hernandez,31 C. Magazz`u,43 R. M. Magee,26 R. Maggiore,39 M. Magnozzi,118, 144 S. Mahesh,188\nE. Majorana,130, 83 I. Maksimovic,258 S. Maliakal,26 A. Malik,120 N. Man,62 V. Mandic,172 V. Mangano,130, 83\nG. L. Mansell,98, 100 M. Manske,31 M. Mantovani,72 M. Mapelli,106, 107 F. Marchesoni,66, 65, 260 D. Mar\u00b4\u0131n Pina,54\nF. Marion,55 Z. Mark,161 S. M\u00b4arka,76 Z. M\u00b4arka,76 C. Markakis,37 A. S. Markosyan,103 A. Markowitz,26\nE. Maros,26 A. Marquina,170 S. Marsat,70 F. Martelli,80, 81 I. W. Martin,49 R. M. Martin,190 M. Martinez,56\nV. A. Martinez,102 V. Martinez,51 K. Martinovic,86 D. V. Martynov,39 E. J. Marx,100 H. Masalehdan,153\nK. Mason,100 E. Massera,179 A. Masserot,55 M. Masso-Reid,49 S. Mastrogiovanni,70 A. Matas,137\nM. Mateu-Lucena,168 F. Matichard,26, 100 M. Matiushechkina,34, 35 N. Mavalvala,100 J. J. McCann,119\nR. McCarthy,98 D. E. McClelland,33 P. K. McClincy,173 S. McCormick,82 L. McCuller,100 G. I. McGhee,49\nS. C. McGuire,82 C. McIsaac,77 J. McIver,205 T. McRae,33 S. T. McWilliams,188 D. Meacher,31 M. Mehmet,34, 35\nA. K. Mehta,137 Q. Meijer,91 A. Melatos,146 D. A. Melchor,69 G. Mendell,98 A. Menendez-Vazquez,56\nC. S. Menoni,191 R. A. Mercer,31 L. Mereni,180 K. Merfeld,92 E. L. Merilh,82 J. D. Merritt,92 M. Merzougui,62\nS. Meshkov,26, \u2217C. Messenger,49 C. Messick,100 P. M. Meyers,146 F. Meylahn,34, 35 A. Mhaske,36 A. Miani,124, 125\nH. Miao,39 I. Michaloliakos,102 C. Michel,180 Y. Michimura,52 H. Middleton,146 D. P. Mihaylov,137 L. Milano,50, \u2020\nA. L. Miller,84 A. Miller,116 B. Miller,63, 85 M. Millhouse,146 J. C. Mills,42 E. Milotti,261, 60 Y. Minenkov,150\nN. Mio,262 Ll. M. Mir,56 M. Miravet-Ten\u00b4es,152 A. Mishkin,102 C. Mishra,263 T. Mishra,102 T. Mistry,179 S. Mitra,36\nV. P. Mitrofanov,123 G. Mitselmakher,102 R. Mittleman,100 O. Miyakawa,214 K. Miyo,214 S. Miyoki,214\nGeoffrey Mo,100 L. M. Modafferi,168 E. Moguel,259 K. Mogushi,121 S. R. P. Mohapatra,100 S. R. Mohite,31\nI. Molina,69 M. Molina-Ruiz,215 M. Mondin,116 M. Montani,80, 81 C. J. Moore,39 J. Moragues,168 D. Moraru,98\nF. Morawski,112 A. More,36 C. Moreno,61 G. Moreno,98 Y. Mori,224 S. Morisaki,31 N. Morisue,200 Y. Moriwaki,213\nB. Mours,187 C. M. Mow-Lowry,85, 122 S. Mozzon,77 F. Muciaccia,130, 83 Arunava Mukherjee,264 D. Mukherjee,173\nSoma Mukherjee,115 Subroto Mukherjee,110 Suvodip Mukherjee,186, 63 N. Mukund,34, 35 A. Mullavey,82\nJ. Munch,114 E. A. Mu\u02dcniz,93 P. G. Murray,49 R. Musenich,118, 144 S. Muusse,114 S. L. Nadji,34, 35 K. Nagano,265\nA. Nagar,48, 266 K. Nakamura,45 H. Nakano,267 M. Nakano,212 Y. Nakayama,224 V. Napolano,72\nI. Nardecchia,149, 150 H. Narola,91 L. Naticchioni,83 B. Nayak,116 R. K. Nayak,268 B. F. Neil,119 J. Neilson,113, 129\nA. Nelson,209 T. J. N. Nelson,82 M. Nery,34, 35 P. Neubauer,259 A. Neunzert,236 K. Y. Ng,100 S. W. S. Ng,114\nC. Nguyen,70 P. Nguyen,92 T. Nguyen,100 L. Nguyen Quynh,269 J. Ni,172 W.-T. Ni,230, 202, 155 S. A. Nichols,32\nT. Nishimoto,212 A. Nishizawa,53 S. Nissanke,63, 85 E. Nitoglia,164 F. Nocera,72 M. Norman,42 C. North,42\nS. Nozaki,213 G. Nurbek,115 L. K. Nuttall,77 Y. Obayashi,212 J. Oberling,98 B. D. O\u2019Brien,102 J. O\u2019Dell,219\nE. Oelker,49 W. Ogaki,212 G. Oganesyan,57, 133 J. J. Oh,88 K. Oh,220 S. H. Oh,88 M. Ohashi,214 T. Ohashi,200\nM. Ohkawa,199 F. Ohme,34, 35 H. Ohta,53 M. A. Okada,41 Y. Okutani,221 C. Olivetto,72 K. Oohara,212, 270\nR. Oram,82 B. O\u2019Reilly,82 R. G. Ormiston,172 N. D. Ormsby,89 R. O\u2019Shaughnessy,154 E. O\u2019Shea,204 S. Oshino,214\nS. Ossokine,137 C. Osthelder,26 S. Otabe,27 D. J. Ottaway,114 H. Overmier,82 A. E. Pace,173 G. Pagano,104, 43\nR. Pagano,32 M. A. Page,119 G. Pagliaroli,57, 133 A. Pai,132 S. A. Pai,120 S. Pal,268 J. R. Palamos,92 O. Palashov,237\nC. Palomba,83 H. Pan,155 K.-C. Pan,155 P. K. Panda,226 P. T. H. Pang,85, 91 C. Pankow,40 F. Pannarale,130, 83\nB. C. Pant,120 F. H. Panther,119 F. Paoletti,43 A. Paoli,72 A. Paolone,83, 271 G. Pappas,223 A. Parisi,159 H. Park,31\nJ. Park,272 W. Parker,82 D. Pascucci,85, 111 A. Pasqualetti,72 R. Passaquieti,104, 43 D. Passuello,43 M. Patel,89\nM. Pathak,114 B. Patricelli,72, 43 A. S. Patron,32 S. Paul,92 E. Payne,30 M. Pedraza,26 R. Pedurand,129\nM. Pegoraro,107 A. Pele,82 F. E. Pe\u02dcna Arellano,214 S. Penano,103 S. Penn,273 A. Perego,124, 125 A. Pereira,51\nT. Pereira,274 C. J. Perez,98 C. P\u00b4erigois,55 C. C. Perkins,102 A. Perreca,124, 125 S. Perri`es,164 D. Pesios,223\n\n4\nJ. Petermann,153 D. Petterson,26 H. P. Pfeiffer,137 H. Pham,82 K. A. Pham,172 K. S. Phukon,85, 234\nH. Phurailatpam,156 O. J. Piccinni,83 M. Pichot,62 M. Piendibene,104, 43 F. Piergiovanni,80, 81 L. Pierini,130, 83\nV. Pierro,113, 129 G. Pillant,72 M. Pillas,71 F. Pilo,43 L. Pinard,180 C. Pineda-Bosque,116 I. M. Pinto,113, 129, 275\nM. Pinto,72 B. J. Piotrzkowski,31 K. Piotrzkowski,84 M. Pirello,98 M. D. Pitkin,217 A. Placidi,65, 105\nE. Placidi,130, 83 M. L. Planas,168 W. Plastino,276, 257 C. Pluchar,277 R. Poggiani,104, 43 E. Polini,55\nD. Y. T. Pong,156 S. Ponrathnam,36 E. K. Porter,70 R. Poulton,72 A. Poverman,108 J. Powell,166 M. Pracchia,55\nT. Pradier,187 A. K. Prajapati,110 K. Prasai,103 R. Prasanna,226 G. Pratten,39 M. Principe,113, 275, 129\nG. A. Prodi,278, 125 L. Prokhorov,39 P. Prosposito,149, 150 L. Prudenzi,137 A. Puecher,85, 91 M. Punturo,65\nF. Puosi,43, 104 P. Puppo,83 M. P\u00a8urrer,137 H. Qi,42 N. Quartey,89 V. Quetschke,115 P. J. Quinonez,61\nR. Quitzow-James,121 F. J. Raab,98 G. Raaijmakers,63, 85 H. Radkins,98 N. Radulesco,62 P. Raffai,177 S. X. Rail,246\nS. Raja,120 C. Rajan,120 K. E. Ramirez,82 T. D. Ramirez,69 A. Ramos-Buades,137 J. Rana,173 P. Rapagnani,130, 83\nA. Ray,31 V. Raymond,42 N. Raza,205 M. Razzano,104, 43 J. Read,69 L. A. Rees,67 T. Regimbau,55 L. Rei,118 S. Reid,58\nS. W. Reid,89 D. H. Reitze,26, 102 P. Relton,42 A. Renzini,26 P. Rettegno,47, 48 B. Revenu,70 A. Reza,85 M. Rezac,69\nF. Ricci,130, 83 D. Richards,219 J. W. Richardson,279 L. Richardson,209 G. Riemenschneider,47, 48 K. Riles,208\nS. Rinaldi,104, 43 K. Rink,205 N. A. Robertson,26 R. Robie,26 F. Robinet,71 A. Rocchi,150 S. Rodriguez,69\nL. Rolland,55 J. G. Rollins,26 M. Romanelli,131 R. Romano,28, 29 C. L. Romel,98 A. Romero,56\nI. M. Romero-Shaw,30 J. H. Romie,82 S. Ronchini,57, 133 L. Rosa,29, 50 C. A. Rose,31 D. Rosi\u00b4nska,135 M. P. Ross,280\nS. Rowan,49 S. J. Rowlinson,39 S. Roy,91 Santosh Roy,36 Soumen Roy,281 D. Rozza,147, 148 P. Ruggi,72\nK. Ruiz-Rocha,201 K. Ryan,98 S. Sachdev,173 T. Sadecki,98 J. Sadiq,140 S. Saha,155 Y. Saito,214 K. Sakai,282\nM. Sakellariadou,86 S. Sakon,173 O. S. Salafia,97, 96, 95 F. Salces-Carcoba,26 L. Salconi,72 M. Saleem,172\nF. Salemi,124, 125 A. Samajdar,96 E. J. Sanchez,26 J. H. Sanchez,69 L. E. Sanchez,26 N. Sanchis-Gual,283\nJ. R. Sanders,284 A. Sanuy,54 T. R. Saravanan,36 N. Sarin,30 B. Sassolas,180 H. Satari,119, 42 O. Sauter,102\nR. L. Savage,98 V. Savant,36 T. Sawada,200 H. L. Sawant,36 S. Sayah,180 D. Schaetzl,26 M. Scheel,161 J. Scheuer,40\nM. G. Schiworski,114 P. Schmidt,39 S. Schmidt,91 R. Schnabel,153 M. Schneewind,34, 35 R. M. S. Schofield,92\nA. Sch\u00a8onbeck,153 B. W. Schulte,34, 35 B. F. Schutz,42, 34, 35 E. Schwartz,42 J. Scott,49 S. M. Scott,33\nM. Seglar-Arroyo,55 Y. Sekiguchi,285 D. Sellers,82 A. S. Sengupta,281 D. Sentenac,72 E. G. Seo,156\nV. Sequino,50, 29 A. Sergeev,237 Y. Setyawati,34, 35, 91 T. Shaffer,98 M. S. Shahriar,40 M. A. Shaikh,44 B. Shams,183\nL. Shao,222 A. Sharma,57, 133 P. Sharma,120 P. Shawhan,136 N. S. Shcheblanov,250 A. Sheela,263 Y. Shikano,286, 287\nM. Shikauchi,53 H. Shimizu,288 K. Shimode,214 H. Shinkai,289 T. Shishido,79 A. Shoda,45 D. H. Shoemaker,100\nD. M. Shoemaker,193 S. ShyamSundar,120 M. Sieniawska,84 D. Sigg,98 L. Silenzi,65, 66 L. P. Singer,143 D. Singh,173\nM. K. Singh,44 N. Singh,135 A. Singha,178, 85 A. M. Sintes,168 V. Sipala,147, 148 V. Skliris,42 B. J. J. Slagmolen,33\nT. J. Slaven-Blair,119 J. Smetana,39 J. R. Smith,69 L. Smith,49 R. J. E. Smith,30 J. Soldateschi,251, 290, 81\nS. N. Somala,291 K. Somiya,27 I. Song,155 K. Soni,36 S. Soni,100 V. Sordini,164 F. Sorrentino,118 N. Sorrentino,104, 43\nR. Soulard,62 T. Souradeep,292, 36 E. Sowell,171 V. Spagnuolo,178, 85 A. P. Spencer,49 M. Spera,106, 107\nP. Spinicelli,72 A. K. Srivastava,110 V. Srivastava,93 K. Staats,40 C. Stachie,62 F. Stachurski,49 D. A. Steer,70\nJ. Steinlechner,178, 85 S. Steinlechner,178, 85 N. Stergioulas,223 D. J. Stops,39 M. Stover,259 K. A. Strain,49\nL. C. Strang,146 G. Stratta,293, 83 M. D. Strong,32 A. Strunk,98 R. Sturani,274 A. L. Stuver,139 M. Suchenek,112\nS. Sudhagar,36 V. Sudhir,100 R. Sugimoto,294, 265 H. G. Suh,31 A. G. Sullivan,76 T. Z. Summerscales,295 L. Sun,33\nS. Sunil,110 A. Sur,112 J. Suresh,53 P. J. Sutton,42 Takamasa Suzuki,199 Takanori Suzuki,27 Toshikazu Suzuki,212\nB. L. Swinkels,85 M. J. Szczepa\u00b4nczyk,102 P. Szewczyk,135 M. Tacca,85 H. Tagoshi,212 S. C. Tait,49 H. Takahashi,296\nR. Takahashi,45 S. Takano,52 H. Takeda,52 M. Takeda,200 C. J. Talbot,58 C. Talbot,26 K. Tanaka,297\nTaiki Tanaka,212 Takahiro Tanaka,298 A. J. Tanasijczuk,84 S. Tanioka,214 D. B. Tanner,102 D. Tao,26 L. Tao,102\nR. D. Tapia,173 E. N. Tapia San Mart\u00b4\u0131n,85 C. Taranto,149 A. Taruya,299 J. D. Tasson,184 R. Tenorio,168\nJ. E. S. Terhune,139 L. Terkowski,153 M. P. Thirugnanasambandam,36 M. Thomas,82 P. Thomas,98\nE. E. Thompson,73 J. E. Thompson,42 S. R. Thondapu,120 K. A. Thorne,82 E. Thrane,30 Shubhanshu Tiwari,185\nSrishti Tiwari,36 V. Tiwari,42 A. M. Toivonen,172 A. E. Tolley,77 T. Tomaru,45 T. Tomura,214 M. Tonelli,104, 43\nZ. Tornasi,49 A. Torres-Forn\u00b4e,152 C. I. Torrie,26 I. Tosta e Melo,148 D. T\u00a8oyr\u00a8a,33 A. Trapananti,66, 65\nF. Travasso,65, 66 G. Traylor,82 M. Trevor,136 M. C. Tringali,72 A. Tripathee,208 L. Troiano,300, 129 A. Trovato,70\nL. Trozzo,29, 214 R. J. Trudeau,26 D. Tsai,155 K. W. Tsang,85, 301, 91 T. Tsang,302 J-S. Tsao,255 M. Tse,100 R. Tso,161\nS. Tsuchida,200 L. Tsukada,173 D. Tsuna,53 T. Tsutsui,53 K. Turbang,303, 227 M. Turconi,62 D. Tuyenbayev,200\nA. S. Ubhi,39 T. Uchiyama,214 R. P. Udall,26 A. Ueda,304 T. Uehara,305, 306 K. Ueno,53 G. Ueshima,307\nC. S. Unnikrishnan,308 A. L. Urban,32 T. Ushiba,214 A. Utina,178, 85 G. Vajente,26 A. Vajpeyi,30 G. Valdes,209\nM. Valentini,207, 124, 125 V. Valsan,31 N. van Bakel,85 M. van Beuzekom,85 M. van Dael,85, 309\nJ. F. J. van den Brand,178, 122, 85 C. Van Den Broeck,91, 85 D. C. Vander-Hyde,93 H. van Haevermaet,227\nJ. V. van Heijningen,84 M. H. P. M. van Putten,310 N. van Remortel,227 M. Vardaro,234, 85 A. F. Vargas,146\nV. Varma,137 M. Vas\u00b4uth,101 A. Vecchio,39 G. Vedovato,107 J. Veitch,49 P. J. Veitch,114 J. Venneberg,34, 35\nG. Venugopalan,26 D. Verkindt,55 P. Verma,243 Y. Verma,120 S. M. Vermeulen,42 D. Veske,76 F. Vetrano,80\nA. Vicer\u00b4e,80, 81 S. Vidyant,93 A. D. Viets,311 A. Vijaykumar,44 V. Villa-Ortega,140 J.-Y. Vinet,62 A. Virtuoso,261, 60\nS. Vitale,100 H. Vocca,105, 65 E. R. G. von Reis,98 J. S. A. von Wrangel,34, 35 C. Vorvick,98 S. P. Vyatchanin,123\nL. E. Wade,259 M. Wade,259 K. J. Wagner,154 R. C. Walet,85 M. Walker,89 G. S. Wallace,58 L. Wallace,26\nJ. Wang,202 J. Z. Wang,208 W. H. Wang,115 R. L. Ward,33 J. Warner,98 M. Was,55 T. Washimi,45\nN. Y. Washington,26 J. Watchi,169 B. Weaver,98 C. R. Weaving,77 S. A. Webster,49 M. Weinert,34, 35\n\n5\nA. J. Weinstein,26 R. Weiss,100 C. M. Weller,280 R. A. Weller,201 F. Wellmann,34, 35 L. Wen,119 P. We\u00dfels,34, 35\nK. Wette,33 J. T. Whelan,154 D. D. White,69 B. F. Whiting,102 C. Whittle,100 D. Wilken,34, 35 D. Williams,49\nM. J. Williams,49 A. R. Williamson,77 J. L. Willis,26 B. Willke,34, 35 D. J. Wilson,277 C. C. Wipf,26\nT. Wlodarczyk,137 G. Woan,49 J. Woehler,34, 35 J. K. Wofford,154 D. Wong,205 I. C. F. Wong,156 M. Wright,49\nC. Wu,155 D. S. Wu,34, 35 H. Wu,155 D. M. Wysocki,31 L. Xiao,26 T. Yamada,288 H. Yamamoto,26 K. Yamamoto,213\nT. Yamamoto,214 K. Yamashita,224 R. Yamazaki,221 F. W. Yang,183 K. Z. Yang,172 L. Yang,191 Y.-C. Yang,155\nY. Yang,312 Yang Yang,102 M. J. Yap,33 D. W. Yeeles,42 S.-W. Yeh,155 A. B. Yelikar,154 M. Ying,155\nJ. Yokoyama,53, 52 T. Yokozawa,214 J. Yoo,204 T. Yoshioka,224 Hang Yu,161 Haocun Yu,100 H. Yuzurihara,212\nA. Zadro\u02d9zny,243 M. Zanolin,61 S. Zeidler,313 T. Zelenova,72 J.-P. Zendri,107 M. Zevin,189 M. Zhan,202 H. Zhang,255\nJ. Zhang,119 L. Zhang,26 R. Zhang,102 T. Zhang,39 Y. Zhang,209 C. Zhao,119 G. Zhao,169 Y. Zhao,212, 45 Yue Zhao,183\nR. Zhou,215 Z. Zhou,40 X. J. Zhu,30 Z.-H. Zhu,145, 253 A. B. Zimmerman,193 M. E. Zucker,26, 100 and J. Zweizig26\nThe LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805, USA\n2NASA Marshall Space Flight Center, Huntsville, AL 35812, USA\n3Department of Space Science, University of Alabama in Huntsville, Huntsville, AL 35899, USA\n4Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35899, USA\n5Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n6Dipartimento Interateneo di Fisica, Politecnico di Bari, Via E. Orabona 4, 70125, Bari, Italy\n7INFN - Sezione di Bari, Via E. Orabona 4, 70125, Bari, Italy\n8Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA\n9Jacobs Space Exploration Group, Huntsville, AL 35806, USA\n10Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35899\n11Department of Space Science, University of Alabama in Huntsville, 320 Sparkman Drive, Huntsville, AL 35899, USA\n12Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA\n13International Space Science Institute (ISSI), Hallerstrasse 6, 3012 Bern, Switzerland\n14Max-Planck-Institut f\u00a8ur extraterrestrische Physik, Giessenbachstrasse 1, D-85748 Garching, Germany\n15Department of Astronomy, University of Maryland, College Park, MD 20742, USA\n16Center for Research and Exploration in Space Science and Technology, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n17Stockholm University and The Oskar Klein Centre for Cosmoparticle Physics, Alba Nova, 10691 Stockholm, Sweden\n18Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA\n19Department of Physics, Pennsylvania State University, University Park, PA 16802, USA\n20Center for Multimessenger Astrophysics, Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA\n16802, USA\n21Department of Astronomy & Astrophysics, University of Toronto, Toronto, Ontario M5S 1A1, Canada\n22Astrophysics Science Division, NASA Goddard Space Flight Center, MC 661, Greenbelt, MD 20771, USA\n23Joint Space-Science Institute, University of Maryland, College Park, MD 20742, USA\n24Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n25Center for Space Science and Technology, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA\n26LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n27Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan\n28Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n29INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n30OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n31University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n32Louisiana State University, Baton Rouge, LA 70803, USA\n33OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n34Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n35Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n36Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n37University of Cambridge, Cambridge CB2 1TN, United Kingdom\n38Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n39University of Birmingham, Birmingham B15 2TT, United Kingdom\n40Northwestern University, Evanston, IL 60208, USA\n41Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n42Cardiff University, Cardiff CF24 3AA, United Kingdom\n43INFN, Sezione di Pisa, I-56127 Pisa, Italy\n\n6\n44International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n45Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n46Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n47Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n48INFN Sezione di Torino, I-10125 Torino, Italy\n49SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n50Universit`a di Napoli \u201cFederico II\u201d, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n51Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n52Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n53Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n54Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona, C/ Mart\u00b4\u0131 i Franqu`es 1, Barcelona, 08028, Spain\n55Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n56Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n57Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n58SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n59Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n60INFN, Sezione di Trieste, I-34127 Trieste, Italy\n61Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n62Artemis, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n63GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, Science Park\n904, 1098 XH Amsterdam, Netherlands\n64National and Kapodistrian University of Athens, School of Science Building, 2nd floor, Panepistimiopolis, 15771 Ilissia, Greece\n65INFN, Sezione di Perugia, I-06123 Perugia, Italy\n66Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n67American University, Washington, D.C. 20016, USA\n68Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan\n69California State University Fullerton, Fullerton, CA 92831, USA\n70Universit\u00b4e de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France\n71Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n72European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n73Georgia Institute of Technology, Atlanta, GA 30332, USA\n74Chennai Mathematical Institute, Chennai 603103, India\n75Department of Mathematics and Physics, Graduate School of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki,\nAomori 036-8561, Japan\n76Columbia University, New York, NY 10027, USA\n77University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n78Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan\n79The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan\n80Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n81INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n82LIGO Livingston Observatory, Livingston, LA 70754, USA\n83INFN, Sezione di Roma, I-00185 Roma, Italy\n84Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n85Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands\n86King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n87Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n88National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n89Christopher Newport University, Newport News, VA 23606, USA\n90School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki\n305-0801, Japan\n91Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands\n92University of Oregon, Eugene, OR 97403, USA\n93Syracuse University, Syracuse, NY 13244, USA\n94Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n95Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n96INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n97INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n\n7\n98LIGO Hanford Observatory, Richland, WA 99352, USA\n99Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n100LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n101Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl\u00b4os \u00b4ut 29-33, Hungary\n102University of Florida, Gainesville, FL 32611, USA\n103Stanford University, Stanford, CA 94305, USA\n104Universit`a di Pisa, I-56127 Pisa, Italy\n105Universit`a di Perugia, I-06123 Perugia, Italy\n106Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n107INFN, Sezione di Padova, I-35131 Padova, Italy\n108Bard College, Annandale-On-Hudson, NY 12504, USA\n109Montana State University, Bozeman, MT 59717, USA\n110Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n111Universiteit Gent, B-9000 Gent, Belgium\n112Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n113Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n114OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n115The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n116California State University, Los Angeles, Los Angeles, CA 90032, USA\n117Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, Edificio C Facultad de Ciencias 08193 Bellaterra (Barcelona),\nSpain\n118INFN, Sezione di Genova, I-16146 Genova, Italy\n119OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n120RRCAT, Indore, Madhya Pradesh 452013, India\n121Missouri University of Science and Technology, Rolla, MO 65409, USA\n122Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n123Lomonosov Moscow State University, Moscow 119991, Russia\n124Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n125INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n126SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n127Bar-Ilan University, Ramat Gan, 5290002, Israel\n128Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n129INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n130Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n131Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France\n132Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n133INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n134Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n135Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n136University of Maryland, College Park, MD 20742, USA\n137Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n138L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n139Villanova University, Villanova, PA 19085, USA\n140IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n141Stony Brook University, Stony Brook, NY 11794, USA\n142Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n143NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n144Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n145Department of Astronomy, Beijing Normal University, Beijing 100875, China\n146OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n147Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n148INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n149Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n150INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n151University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n152Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n\n8\n153Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n154Rochester Institute of Technology, Rochester, NY 14623, USA\n155National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China\n156The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n157Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n158OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n159Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan\n160Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City\n32001, Taiwan\n161CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n162Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n163Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan\n164Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n165INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n166OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n167Universit\u00b4e libre de Bruxelles, Avenue Franklin Roosevelt 50 - 1050 Bruxelles, Belgium\n168IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n169Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n170Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n171Texas Tech University, Lubbock, TX 79409, USA\n172University of Minnesota, Minneapolis, MN 55455, USA\n173The Pennsylvania State University, University Park, PA 16802, USA\n174University of Rhode Island, Kingston, RI 02881, USA\n175Bellevue College, Bellevue, WA 98007, USA\n176Scuola Normale Superiore, Piazza dei Cavalieri, 7 - 56126 Pisa, Italy\n177E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n178Maastricht University, P.O. Box 616, 6200 MD Maastricht, Netherlands\n179The University of Sheffield, Sheffield S10 2TN, United Kingdom\n180Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n181Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n182INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n183The University of Utah, Salt Lake City, UT 84112, USA\n184Carleton College, Northfield, MN 55057, USA\n185University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n186Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n187Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n188West Virginia University, Morgantown, WV 26506, USA\n189University of Chicago, Chicago, IL 60637, USA\n190Montclair State University, Montclair, NJ 07043, USA\n191Colorado State University, Fort Collins, CO 80523, USA\n192Institute for Nuclear Research, Bem t\u2019er 18/c, H-4026 Debrecen, Hungary\n193University of Texas, Austin, TX 78712, USA\n194CNR-SPIN, c/o Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n195Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n196Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n197Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, Campus de Gualtar, PT-4710 - 057 Braga, Portugal\n198Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan\n199Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n200Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n201Vanderbilt University, Nashville, TN 37235, USA\n202State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement\nScience and Technology (APM), Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, China\n203University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n204Cornell University, Ithaca, NY 14850, USA\n205University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n206INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n\n9\n207The University of Mississippi, University, MS 38677, USA\n208University of Michigan, Ann Arbor, MI 48109, USA\n209Texas A&M University, College Station, TX 77843, USA\n210Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n211Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China\n212Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n213Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n214Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205,\nJapan\n215University of California, Berkeley, CA 94720, USA\n216Maastricht University, 6200 MD, Maastricht, Netherlands\n217Lancaster University, Lancaster LA1 4YW, United Kingdom\n218College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan\n219Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n220Department of Astronomy & Space Science, Chungnam National University, Yuseong-gu, Daejeon 34134, Republic of Korea\n221Department of Physical Sciences, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan\n222Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian District, Beijing 100871, China\n223Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece\n224Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan\n225Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sumiyoshi-ku, Osaka City, Osaka\n558-8585, Japan\n226Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n227Universiteit Antwerpen, Prinsstraat 13, 2000 Antwerpen, Belgium\n228University of Bia lystok, 15-424 Bia lystok, Poland\n229Ewha Womans University, Seoul 03760, Republic of Korea\n230National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, China\n231School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, China\n232University of Southampton, Southampton SO17 1BJ, United Kingdom\n233Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n234Institute for High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands\n235Chung-Ang University, Seoul 06974, Republic of Korea\n236University of Washington Bothell, Bothell, WA 98011, USA\n237Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n238Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n239Department of Physics, Myongji University, Yongin 17058, Republic of Korea\n240Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki\n305-0801, Japan\n241School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, UK\n242Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n243National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n244Instituto de Fisica Teorica, 28049 Madrid, Spain\n245Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n246Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n247Laboratoire Lagrange, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n248Seoul National University, Seoul 08826, Republic of Korea\n249Sungkyunkwan University, Seoul 03063, Republic of Korea\n250NAVIER, \u00b4Ecole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00b4ee, France\n251Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n252Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan\n253School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China\n254National Center for High-performance computing, National Applied Research Laboratories, Hsinchu Science Park, Hsinchu City\n30076, Taiwan\n255Department of Physics, National Taiwan Normal University, sec. 4, Taipei 116, Taiwan\n256NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n257INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n258ESPCI, CNRS, F-75005 Paris, France\n259Kenyon College, Gambier, OH 43022, USA\n\n10\n260School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n261Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n262Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan\n263Indian Institute of Technology Madras, Chennai 600036, India\n264Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n265Institute of Space and Astronautical Science (JAXA), Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan\n266Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n267Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n268Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n269Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA\n270Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n271Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, Piazzale Aldo Moro 5, I-00185 Roma, Italy\n272Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea\n273Hobart and William Smith Colleges, Geneva, NY 14456, USA\n274International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n275Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n276Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n277University of Arizona, Tucson, AZ 85721, USA\n278Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n279University of California, Riverside, Riverside, CA 92521, USA\n280University of Washington, Seattle, WA 98195, USA\n281Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n282Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, Nagaoka City, Niigata 940-8532,\nJapan\n283Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\nCampus de Santiago, 3810-183 Aveiro, Portugal\n284Marquette University, Milwaukee, WI 53233, USA\n285Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan\n286Graduate School of Science and Technology, Gunma University, Maebashi, Gunma 371-8510, Japan\n287Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA\n288Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n289Faculty of Information Science and Technology, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan\n290INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy\n291Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n292Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n293Istituto di Astrofisica e Planetologia Spaziali di Roma, Via del Fosso del Cavaliere, 100, 00133 Roma RM, Italy\n294Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City,\nKanagawa 252-5210, Japan\n295Andrews University, Berrien Springs, MI 49104, USA\n296Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, Setagaya, Tokyo 158-0082, Japan\n297Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo, Kashiwa City,\nChiba 277-8582, Japan\n298Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n299Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n300Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n301Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, Netherlands\n302Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n303Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium\n304Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n305Department of Communications Engineering, National Defense Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan\n306Department of Physics, University of Florida, Gainesville, FL 32611, USA\n307Department of Information and Management Systems Engineering, Nagaoka University of Technology, Nagaoka City, Niigata\n940-2188, Japan\n308Tata Institute of Fundamental Research, Mumbai 400005, India\n309Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, Netherlands\n310Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea\n311Concordia University Wisconsin, Mequon, WI 53097, USA\n\n11\n312Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan\n313Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan\n(Dated: August 29, 2023)\nABSTRACT\nWe present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-\nBAT) searches for gamma-ray/X-ray counterparts to gravitational wave (GW) candidate events iden-\ntified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using\nFermi-GBM on-board triggers and sub-threshold gamma-ray burst (GRB) candidates found in the\nFermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether\nthere are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data\naround the GW times to determine whether a GRB counterpart is present. No counterparts are found.\nUsing both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper lim-\nits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we\nconstrain theoretical models for the emission of gamma-rays from binary black hole mergers.\n1. INTRODUCTION\nThe detection of GW170817 (Abbott et al. 2017) co-\nincident with the short gamma-ray burst GRB 170817A\n(Goldstein et al. 2017; Savchenko et al. 2017) was a\nground-breaking discovery for the multimessenger era.\nNot only was it the first binary neutron star (BNS)\nmerger detected by the gravitational-wave (GW) instru-\nments Advanced LIGO (Aasi et al. 2015) and Advanced\nVirgo (Acernese et al. 2014), it was also the first, and to\ndate only, GW detection with a confirmed electromag-\nnetic (EM) counterpart. Since then, the search for EM\nemission from more of these extreme events has been\nat the forefront of multimessenger astronomy, particu-\nlarly in the gamma-ray energy band since GRB 170817A\ndemonstrated that BNS mergers are a progenitor of\nshort gamma-ray bursts (GRBs) (Abbott et al. 2017).\nGWs have also been observed from the mergers of other\ncompact objects, such as binary black hole (BBH) and\nneutron star\u2013black hole (NSBH) systems (Abbott et al.\n2019; Abbott et al. 2021; Abbott et al. 2021; Abbott\net al. 2021); however, no additional EM counterparts\nhave been confirmed as they have been inconclusive\n(Connaughton et al. 2016; LSC and Virgo and Fermi-\nGBM Team 2019a,b) or are still under debate (Graham\net al. 2020; Ashton et al. 2021; Bustillo et al. 2021; De\nPaolis et al. 2020; Palmese et al. 2021).\nGRB 170817A was first reported by the Fermi\nGamma-ray Burst Monitor (GBM; Meegan et al. 2009),\na space-based gamma-ray instrument sensitive from 8\nkeV to 40 MeV. This wide energy range of Fermi-\nGBM combined with its large field-of-view (FoV) and\nrapid alert abilities make it an ideal platform to search\n\u2217Deceased, August 2020.\n\u2020 Deceased, April 2021.\nfor gamma-ray counterparts to GWs in real time.\nFermi-GBM also provides continuous time tagged event\n(CTTE) data with a 6-hour latency that enables sen-\nsitive searches for short GRBs on the ground. Two of\nthese searches are the Untargeted Search, a blind search\nof Fermi-GBM data for short GRBs, and the Targeted\nSearch, which uses an external time to search for a short\nGRB (Blackburn et al. 2015; Goldstein et al. 2019).\nBoth were previously used to look for sub-threshold\nGRBs coincident with GWs from the first two LIGO-\nVirgo observing runs.\nAdditionally,\nthe\nBurst\nAlert\nTelescope\n(BAT;\nBarthelmy et al. 2005) on-board the Neil Gehrels Swift\nObservatory (hereafter referred to as Swift) provides ex-\ncellent sensitivity to detecting hard X-ray and gamma-\nray transients (Gehrels et al. 2004). Swift-BAT primar-\nily runs in a survey mode that continuously evaluates\nphoton rate increases and potential GRB triggers. An\nincrease in the observed photon rate can trigger the\non-board image-processing algorithms which can yield\n\u223carcminute GRB localizations.\nIdeally, Swift-BAT would detect and localize a GRB\nproduced by a binary merger independently of the GW\ndetection. If a GRB does not trigger an on-board de-\ntection, continuous count rate lightcurves are still avail-\nable for offline ground searches. Although Swift-BAT\nhas been used to search for public and sub-threshold\nGWs during the LIGO-Virgo observing runs, this work\npresents the first systematic search of Swift-BAT data\nfrom a LIGO-Virgo observing run.\nThe first observing run (O1) operated from Septem-\nber 2015 to January 2016, producing the first detec-\ntion of GWs from a BBH merger (GW150914; Ab-\nbott et al. 2016). Burns et al. (2019) used the Fermi-\nGBM Targeted Search to identify both triggered and\nsub-threshold GRB candidates in coincidence with GW\n\n12\ncandidates from O1.\nThe most significant gamma-\nray candidate found by the search was within 0.4 s of\nGW150914; however, it could not be confirmed as a\ncounterpart due to its weak signal and poor localiza-\ntion (Connaughton et al. 2016; Greiner et al. 2016; Con-\nnaughton et al. 2018).\nThe second observing run (O2) took place from\nNovember 2016 to August 2017, resulting in the de-\ntections of GW170817, GRB 170817A, and the kilo-\nnova AT2017gfo (Chornock et al. 2017; Cowperthwaite\net al. 2017; Nicholl et al. 2017; Soares-Santos et al.\n2017; Tanvir et al. 2017; Margutti & Chornock 2021).\nFollowing O2, the LIGO Scientific and Virgo Collabo-\nration published its first catalog of GW signals called\nthe Gravitational-Wave Transient Catalog 1 (GWTC-1;\nAbbott et al. 2019) using a re-analysis of data from both\nO1 and O2. Hamburg et al. (2020) searched for GRBs\ncoincident to the GWs reported in GWTC-1, using\nFermi-GBM triggers as well as sub-threshold GRB can-\ndidates from the Untargeted and Targeted Searches, but\nfound no additional counterparts beyond GRB 170817A.\nThe third observing run (O3) occurred from April\n2019 to March 2020 with a month-long commissioning\nbreak during October 2019. It benefited from improve-\nments to the sensitivity and duty cycle of the GW detec-\ntors made after O2 (Buikema et al. 2020; Abbott et al.\n2021; Acernese et al. 2019). This observing run provided\n56 public GW candidates in real-time with information\nfrom their preliminary analysis. More detailed analy-\nses were published by the LIGO, Virgo, and KAGRA\n(LVK) Collaboration in a series of GWTCs (GWTC-\n2; Abbott et al. 2021, GWTC-2.1; Abbott et al. 2021,\nGWTC-3; Abbott et al. 2021) with GWTC-3 providing\na cumulative list of 79 GW signals from O3 with a prob-\nability of astrophysical origin (pastro) > 0.5 \u2013 an 8-fold\nincrease relative to O2.\nAmong these candidates was\nthe detection of a second confident signal classified as a\nBNS merger, GW190425, whose total mass is larger than\nthat known from Galactic neutron star binaries (Abbott\net al. 2020).\nAdditionally, GW191219 163120 and GW200115 042309\nprovided the first detections of NSBH systems with\npastro > 0.5. Another possible NSBH, GW200105 162426,\nfell just outside the pastro > 0.5 criterion in the\nGWTC-3 analysis (Abbott et al. 2021).\nThere were\nalso two confident detections with ambiguous clas-\nsifications,\nGW190814 (Abbott et al. 2020b) and\nGW200210 092254, that represent a black hole merging\nwith either a light black hole or a heavy neutron star.\nAn overwhelming majority of the remaining candidates\nare most likely BBH in origin.\nIn this paper, we search Fermi-GBM and Swift-BAT\ndata for short GRB counterparts to GW candidates\nfrom O3, discussed in Section 2.1. Section 2.2 provides\nan overview of the Fermi-GBM Untargeted Search as\nwell as improvements made to the Fermi-GBM Tar-\ngeted Search. Section 2.3 describes the Swift-BAT sub-\nthreshold search. We present the results of the search\nwith Fermi-GBM triggers and the Untargeted Search in\nSection 3.1; with the Fermi-GBM Targeted Search, in-\ncluding a new joint ranking statistic that takes the spa-\ntial coincidence into account, in Section 3.2; and with\nthe Swift-BAT sub-threshold search in 3.3. Section 3.4\npresents the results from both Fermi-GBM and Swift-\nBAT for the marginal GWs identified in Section 2.1.\nFurthermore, Section 4 divides the discussion of GWs\nwith pastro > 0.5 into two groups depending on their\nestimated secondary component mass m2.\nFor merg-\ners with a possible neutron star component, we present\nthe flux and isotropic equivalent luminosity upper lim-\nits from both Fermi-GBM and Swift-BAT (Section 4.1).\nFor the BBH mergers, we compare the lack of observed\ngamma-ray emission to that predicted by theoretical\nmodels (Section 4.2).\nWe discuss upper limits to the\nmarginal GWs in Section 4.3. Finally, in Section 5 we\nsummarize our results and discuss future plans for using\nthe sub-threshold searches for GWs.\n2. METHOD\nIn this section, we summarize the set of GW signals\nthat we analyze from O3. We also present the search\nmethods used to find coincident gamma-ray and hard\nX-ray emission with Fermi-GBM and Swift-BAT.\n2.1. GW Trigger Selection\nThe analysis reported here focuses on GW candidates\nidentified during O3. These were selected by four sepa-\nrate analysis pipelines (i.e., GstLAL, Multi-Band Tem-\nplate Analysis (MBTA), PyCBC, and cWB) and pub-\nlished in GWTC-3 (Abbott et al. 2021). Each pipeline\ncalculates both a false alarm rate (FAR) from a back-\nground noise hypothesis and a pastro for each candidate\nassuming a compact binary coalescence source. Candi-\ndate signals with pastro > 0.5 in any pipeline are selected\nfor detailed analysis with a full estimation of the poten-\ntial astrophysical source parameters. The one exception\nis GW candidates identified by the minimally modeled\ncWB pipeline, which requires a time-matched confirma-\ntion with pastro > 0.1 in one of the other pipelines in\norder to ensure they originated from a compact binary\ncoalescence. In total, there were 79 GWs identified with\npastro > 0.5 during O3.\nTable 1 shows the candidate\nidentifier, date, time, and pastro for these GWs.\n\n13\nThe remaining subset of GW signals with a FAR below\n2 yr\u22121 and pastro \u22640.5 in a given pipeline are consid-\nered marginal GW candidates. As of GWTC-3, there\nare 6 marginal candidates which cannot be attributed\nto instrumental or environmental causes (Table 2). We\nexclude these candidates from our main analysis; how-\never, since the existence of a gamma-ray counterpart\ncould potentially prove an astrophysical origin, we per-\nform separate searches around each marginal candidate.\n2.2. Fermi-GBM Searches\nFermi-GBM has 12 sodium iodide (NaI) and 2 bis-\nmuth germanate (BGO) detectors that are strategically\npositioned to cover the full sky, unocculted by the Earth\n(Meegan et al. 2009).\nThe flight software on-board\nFermi-GBM triggers on an event when there is an in-\nflux of gamma rays at a level greater than 4.5\u03c3 above\nthe background rate in at least two NaI detectors (Pa-\nciesas et al. 2012). Additionally, the downlink of CTTE\ndata enables searches for GRBs below Fermi-GBM\u2019s on-\nboard triggering threshold using ground-based comput-\ning resources. With 2 \u00b5s timing resolution and full cov-\nerage of the unocculted sky over the energy range from 8\nkeV to 40 MeV, CTTE data has significantly expanded\nthe sensitivity of the Fermi-GBM instrument and its\nsub-threshold searches.\n2.2.1. Untargeted Search\nThe Fermi-GBM Untargeted Search is a blind search\nthat automatically scans the CTTE data for significant\ncount rate increases in at least two NaI detectors. The\nalgorithm was originally developed for detecting terres-\ntrial gamma-ray flashes (Briggs et al. 2013) and has\nsince been adapted to search for short GRBs with fluxes\nbelow the on-board triggering threshold.\nThe Untar-\ngeted Search runs through eighteen timescales ranging\nfrom 64 ms to 31 s and five energy bins from 27 keV to\n985 keV, and short GRB candidates are identified when\nat least two detectors exceed 2.5\u03c3 and 1.25\u03c3 above the\nbackground rate. Each candidate is given a reliability\nscore based on whether the geometry of the detectors\nwith significant flux is consistent with the observation\nof a distant astrophysical source. Currently, short GRB\ncandidates with durations less than 2.8 s and reliabil-\nity classifications of low, medium, and high are publicly\ndistributed via GCN.1\nIn this work, we combine short GRB candidates de-\ntected by the Untargeted Search with GBM-triggered\nGRBs and examine their temporal offsets from the GWs\nlisted in Table 1. Theoretical models predict the tem-\n1 https://gcn.gsfc.nasa.gov/fermi gbm subthresh archive.html\nporal offset between merger time and the production\nof gamma-rays to range from 0.01 s to 10 s depend-\ning on the conditions producing the gamma-ray emis-\nsion (Zhang 2019). For GRB 170817A, the only known\nshort GRB associated with a GW, the temporal offset\nwas 1.7 s with a duration (T90) over which 5\u201395% of\nthe GRB flux (50-300 keV) was detected of 2 s (Abbott\net al. 2017). This is consistent with a range of physi-\ncally viable scenarios (e.g., Lin et al. 2018; Salafia et al.\n2018; Zhang et al. 2018) where the temporal offset is\ncorrelated with burst duration. We therefore choose to\nsubtract the burst duration timescale from the temporal\noffset when performing our analysis. Doing so increases\nthe observed significance of simulated short GRB coun-\nterparts and yields no loss in detection sensitivity at the\n3\u03c3 level in alternative scenarios where the temporal off-\nset is the same for all simulated GRBs.\nAfter calculating the time offsets for each GW\u2013GRB\npair minus the burst duration, the smallest resulting\ntime offset for each GW is taken. For GBM-triggered\nGRBs, we use the T90 as a measure of the duration. For\nGRB candidates from the Untargeted Search, we use\nthe most significant timescale over which the GRB can-\ndidate was detected, which scales linearly with T90 for\non-board triggered GRBs. A background distribution\nis produced in the same way by replacing the observed\nGW times with random times during which there are\nno reported GW signals. This yields a distribution of\ntemporal offsets minus the burst duration between un-\nrelated GWs and the GRB sample. In both the search\nand background samples, positive and negative time off-\nsets are allowed, with no maxima imposed. GW triggers\noccurring during Fermi passage through South Atlantic\nAnomaly (SAA) are also included. See the results pre-\nsented in Section 3.1 for a comparison of the cumulative\nsignal and background distributions.\n2.2.2. GBM Targeted Search\nThe Fermi-GBM Targeted Search was developed for\nmultimessenger follow-up observations (Blackburn et al.\n2015). It uses CTTE data to scan around an external\ntrigger time for gamma-ray emission typical of a short\nGRB. For follow-up of the GWs in Table 1, we search\nfrom \u22121 s to +30 s around the GW time to ensure we\ndo not miss unexpectedly delayed gamma-ray emission\nfrom a counterpart short GRB, even after accounting\nfor temporal offsets up to 10 s relative to the GW time.\nStarting 1 s before the GW time provides a comfortable\nbuffer to account for the fact that the trigger times can\nvary by a few milliseconds for GW signals that are iden-\ntified by multiple pipelines.\nThe scan is repeated for\neight characteristic emission timescales which increase\n\n14\nTable 1. GW candidates from O3 with pastro > 0.5 (Abbott et al. 2021).\nEvent Name\nDate\nTime (UTC)\npastro\nEvent Name\nDate\nTime (UTC)\npastro\nGW190403 051519\n04-03-2019\n05:15:19\n0.60\nGW191103 012549\n11-03-2019\n01:25:49\n0.94\nGW190408 181802\n04-08-2019\n18:18:02\n>0.99\nGW191105 143521\n11-05-2019\n14:35:21\n>0.99\nGW190412\n04-12-2019\n05:30:44\n>0.99\nGW191109 010717\n11-09-2019\n01:07:17\n>0.99\nGW190413 052954\n04-13-2019\n05:29:54\n0.92\nGW191113 071753\n11-13-2019\n07:17:53\n0.68\nGW190413 134308\n04-13-2019\n13:43:08\n0.99\nGW191126 115259\n11-26-2019\n11:52:59\n0.70\nGW190421 213856\n04-21-2019\n21:38:56\n>0.99\nGW191127 050227\n11-27-2019\n05:02:27\n0.74\nGW190425\n04-25-2019\n08:18:05\n0.69\nGW191129 134029\n11-29-2019\n13:40:29\n>0.99\nGW190426 190642\n04-26-2019\n19:06:42\n0.73\nGW191204 110529\n12-04-2019\n11:05:29\n0.74\nGW190503 185404\n05-03-2019\n18:54:04\n>0.99\nGW191204 171526\n12-04-2019\n17:15:26\n>0.99\nGW190512 180714\n05-12-2019\n18:07:14\n>0.99\nGW191215 223052\n12-15-2019\n22:30:52\n>0.99\nGW190513 205428\n05-13-2019\n20:54:28\n>0.99\nGW191216 213338\n12-16-2019\n21:33:38\n>0.99\nGW190514 065416\n05-14-2019\n06:54:16\n0.75\nGW191219 163120\n12-19-2019\n16:31:20\n0.82\nGW190517 055101\n05-17-2019\n05:51:01\n>0.99\nGW191222 033537\n12-22-2019\n03:35:37\n>0.99\nGW190519 153544\n05-19-2019\n15:35:44\n>0.99\nGW191230 180458\n12-30-2019\n18:04:58\n0.96\nGW190521\n05-21-2019\n03:02:29\n>0.99\nGW200112 155838\n01-12-2020\n15:58:38\n>0.99\nGW190521 074359\n05-21-2019\n07:43:59\n>0.99\nGW200115 042309\n01-15-2020\n04:23:09\n>0.99\nGW190527 092055\n05-27-2019\n09:20:55\n0.83\nGW200128 022011\n01-28-2020\n02:20:11\n>0.99\nGW190602 175927\n06-02-2019\n17:59:27\n>0.99\nGW200129 065458\n01-29-2020\n06:54:58\n>0.99\nGW190620 030421\n06-20-2019\n03:04:21\n0.99\nGW200202 154313\n02-02-2020\n15:43:13\n>0.99\nGW190630 185205\n06-30-2019\n18:52:05\n>0.99\nGW200208 130117\n02-08-2020\n13:01:17\n>0.99\nGW190701 203306\n07-01-2019\n20:33:06\n>0.99\nGW200208 222617\n02-08-2020\n22:26:17\n0.70\nGW190706 222641\n07-06-2019\n22:26:41\n>0.99\nGW200209 085452\n02-09-2020\n08:54:52\n0.97\nGW190707 093326\n07-07-2019\n09:33:26\n>0.99\nGW200210 092254\n02-10-2020\n09:22:54\n0.54\nGW190708 232457\n07-08-2019\n23:24:57\n>0.99\nGW200216 220804\n02-16-2020\n22:08:04\n0.77\nGW190719 215514\n07-19-2019\n21:55:14\n0.91\nGW200219 094415\n02-19-2020\n09:44:15\n>0.99\nGW190720 000836\n07-20-2019\n00:08:36\n>0.99\nGW200220 061928\n02-20-2020\n06:19:28\n0.62\nGW190725 174728\n07-25-2019\n17:47:28\n0.96\nGW200220 124850\n02-20-2020\n12:48:50\n0.83\nGW190727 060333\n07-27-2019\n06:03:33\n>0.99\nGW200224 222234\n02-24-2020\n22:22:34\n>0.99\nGW190728 064510\n07-28-2019\n06:45:10\n>0.99\nGW200225 060421\n02-25-2020\n06:04:21\n>0.99\nGW190731 140936\n07-31-2019\n14:09:36\n0.83\nGW200302 015811\n03-02-2020\n01:58:11\n0.91\nGW190803 022701\n08-03-2019\n02:27:01\n0.97\nGW200306 093714\n03-06-2020\n09:37:14\n0.81\nGW190805 211137\n08-05-2019\n21:11:37\n0.95\nGW200308 173609\n03-08-2020\n17:36:09\n0.86\nGW190814\n08-14-2019\n21:10:39\n>0.99\nGW200311 115853\n03-11-2020\n11:58:53\n>0.99\nGW190828 063405\n08-28-2019\n06:34:05\n>0.99\nGW200316 215756\n03-16-2020\n21:57:56\n>0.99\nGW190828 065509\n08-28-2019\n06:55:09\n>0.99\nGW200322 091133\n03-22-2020\n09:11:33\n0.62\nGW190910 112807\n09-10-2019\n11:28:07\n>0.99\nGW190915 235702\n09-15-2019\n23:57:02\n>0.99\nGW190916 200658\n09-16-2019\n20:06:58\n0.62\nGW190917 114630\n09-17-2019\n11:46:30\n0.74\nGW190924 021846\n09-24-2019\n02:18:46\n>0.99\nGW190925 232845\n09-25-2019\n23:28:45\n0.99\nGW190926 050336\n09-26-2019\n05:03:36\n0.51\nGW190929 012149\n09-29-2019\n01:21:49\n0.86\nGW190930 133541\n09-30-2019\n13:35:41\n>0.99\n\n15\nTable 2. Marginal GWs from O3 without clear instrumental or environmental causes (Abbott et al. 2021; Abbott et al. 2021)\nEvent Name\nDate\nTime (UTC)\npastro\nGW190426 152155\n04-26-2019\n15:21:55\n0.14\nGW190531 023648\n05-31-2019\n02:36:48\n0.28\nGW191118 212859\n11-18-2019\n21:28:59\n0.05\nGW200105 162426\n01-05-2020\n16:24:26\n0.36\nGW200201 203549\n02-01-2020\n20:35:49\n0.12\nGW200311 103121\n03-11-2020\n10:31:21\n0.19\nby factors of 2 from 64 ms to 8.192 s. Each emission\ntimescale begins the search centered at the start of the\nscan window and then advances until the end using a\nfixed time step size. Emission timescales greater than\n256 ms use a time step equal to one-eighth the total\nemission duration. The remaining emission timescales\nuse a 64 ms step size to limit both the additional trials\nand the additional computational time associated with\nthe shorter emission timescales.\nThe Targeted Search achieves greater sensitivity than\nthe on-board triggering algorithm by processing the data\nfrom all 14 detectors coherently rather than focusing on\nsignificant signals present in detector pairs. This allows\nfor the detection of weaker signals below the Fermi-\nGBM on-board triggering threshold (Kocevski et al.\n2018). To do this, three spectral templates represent-\ning spectrally hard, normal, and soft GRBs (Table 3)\nare folded through the GBM detector responses to pro-\nduce an expected count rate for a given astrophysical\nsource location and flux. This expected count rate is\nthen compared to the observed counts through a log-\nlikelihood ratio,\nLj(d, s) =\nX\ni\nh\nln\u03c3ni\n\u03c3di\n+\n\u02dcd2\ni\n2\u03c32ni\n\u2212( \u02dcdi \u2212ri,js)2\n2\u03c32\ndi\ni\n,\n(1)\nwhere \u02dcdi represents the background-subtracted measure-\nments in each detector, \u03c3n is the standard deviation of\nthe background measurement, \u03c3di is the standard de-\nviation of the expected data (background+signal), ri,j\nis the location-dependent instrumental response for the\nspectrum denoted by index j, and s is the intrinsic\nsource photon flux at the Earth. See Blackburn et al.\n(2015) for a full derivation.\nThe log-likelihood ratio quantifies the probability that\nan astrophysical source is present versus a background-\nonly hypothesis. It is first computed separately for each\npoint on the sky and spectral template at a given time\nand emission duration. During this process we estimate\nthe best-fit photon flux for each spectral template by\nfinding the value sbest that maximizes the log-likelihood\nratio. Since the best-fit photon flux maximizes the like-\nlihood, which is effectively a product of Gaussian dis-\ntributions, the variance on this photon flux equals the\nvariance of the likelihood:\n\u03c32\nLj =\n1\nP r2\ni,j/\u03c32\ndi\n,\n(2)\nwhere \u03c3di includes both background and source contri-\nbutions, with the latter evaluated at sbest. Signal injec-\ntion studies using the normal spectral template demon-\nstrated that this formulation yields the expected er-\nror coverage levels for true source fluxes near 1 \u00d7 10\u22127\nerg cm\u22122 s\u22121 and below, which is the relevant flux range\nfor this sub-threshold analysis in Fermi-GBM.\nWe marginalize the log-likelihood ratio over all possi-\nble source amplitudes using a modified power law prior\ndesigned to both avoid divergence and to produce a lu-\nminosity distribution for the observed source flux that\nis invariant with respect to source distance (Blackburn\net al. 2015):\nP(s) =\nh\n1 \u2212e\u2212(s/2.5\u03c3L)\u22121i\ns\u22121 .\n(3)\nThe net result is a hypothesis test formulation following\nBayes\u2019 theorem.\nThe amplitude-marginalized log-likelihood ratios for\nindividual spectral templates, L\u2032j(d), at each time and\nduration are then averaged over all sky positions and\ntemplates using a uniform prior to formulate the full\nmarginal log-likelihood ratio,\n\u039b =\n3\nX\nj=1\n1\n3\nZ L\u2032j(d)\n4\u03c0\nd\u2126,\n(4)\nwhere the sum over j covers the hard, normal, and\nsoft spectral templates. The marginal results from all\nscanned times and durations are then sorted according\nto the largest value of \u039b after filtering out known detec-\ntor effects.\nLocalization maps estimating the probability of find-\ning the true source location at each point on the sky\nare produced for the top ranking candidates using the\nlog-likelihood ratio of the best-fitting spectrum for each\ncandidate. This is done by noting that the log-likelihood\n\n16\nTable 3. Spectral templates used by the Fermi-GBM Targeted Search.\nTemplate\nType\nParameters\nhard\nCut-off Power-law (Goldstein et al. 2016)\nEpeak = 1500 keV, \u03b1 = \u22121.5\nnormal\nBand (Band et al. 1993)\nEpeak = 230 keV, \u03b1 = \u22121.0, \u03b2 = \u22122.3\nsoft\nBand (Band et al. 1993)\nEpeak = 70 keV, \u03b1 = \u22121.9, \u03b2 = \u22123.7\nratio asymptotically approaches the behavior of a \u03c72 dis-\ntribution according to Wilks\u2019 theorem (Wilks 1938) with\na statistical probability given by\nP \u221dexp[L\u2032\nj(d)].\n(5)\nThe statistical probability is then convolved with Gaus-\nsian kernels to account for systematic errors, which\nare predominantly induced by the difference between\nthe true source spectrum and the three spectral tem-\nplates, imperfect knowledge of the detector response,\nand whether atmospheric scattering is taken into ac-\ncount for a given spacecraft rocking angle. As a final\nstep, we set the region blocked by the Earth in Fermi-\nGBM to zero and re-normalize the map to account for\nthe fact that gamma-ray sources are not visible through\nthe Earth and an implicit assumption that the signal\nhas a non-terrestrial origin.\nThe Targeted Search method was previously used to\nsearch for sub-threshold counterparts to GWs identified\nduring the O1 and O2 observing runs (Hamburg et al.\n2020). A number of improvements were made to it in\npreparation for O3 (Goldstein et al. 2019):\n1. Removal of the lowest 4\u201312 keV energy channel\nin the NaI detector data helped remove detector\nnoise as well as Galactic transients.\n2. Better background fitting during approach and\nexit from the SAA. This reduces local particle\nbackground triggers that were present in about\n1% of searches and formed the dominant non-GRB\nbackground in the high log-likelihood ratio param-\neter space.\n3. Better detector response models with a more\ncomplete treatment of the effects from the back-\nscattering of high energy gamma-ray photons off\nthe Earth\u2019s atmosphere. The atmospheric scatter-\ning effects are currently applied when the zenith of\nFermi-GBM is within \u00b15\u25e6of its nominal rocking\nangle of 130\u25e6with respect to the Earth\u2019s geocen-\nter, which occurs for \u223c70% of measurements.\n4. Decreasing the resolution from 1\u25e6to 5\u25e6for the grid\nof sky positions analyzed during the search. This\nprovided an order of magnitude improvement in\nexecution time with no notable loss in sensitivity\nor degradation of localization capability.\nThese changes necessitated a recalculation of the esti-\nmated systematic uncertainty applied to the localization\nmaps generated for the top-ranking search candidates.\nAn initial study of 34 sub-threshold short GRB detec-\ntions modeled this uncertainty as a 2.7\u25e6Gaussian sys-\ntematic (Goldstein et al. 2019). A more detailed model\nwas developed for this work using a larger sample of\n3,000 simulated short GRB detections. It consists of a\nweighted pair of Gaussian shapes normalized over the\nsky with the standard deviation \u03c31 of the first Gaus-\nsian always smaller than that of the second Gaussian,\n\u03c32. The parameters of each Gaussian were determined\nas functions of the most probable zenith angle for each\ncandidate and the spacecraft rocking angle relative to\nthe Earth. They range from 1.6\u25e6\u20136.0\u25e6for \u03c31 and 6.4\u25e6\u2013\n60.4\u25e6for \u03c32, with the fractional contribution of the first\nGaussian spanning 0.42\u20130.77.\n2.2.3. GBM Targeted Search Ranking Statistic\nWe use a ranking statistic R to characterize the sig-\nnificance of a coincidence between the GW candidates\nfrom the catalog and the short GRB candidates found\nby the Targeted Search. Following the formulation in\nHamburg et al. (2020), the statistic takes into account\nthe probability of astronomical origin of the GW, pastro;\nthe fraction of the GW localization not occulted by the\nEarth for Fermi-GBM, pvisible; the time offset of the\nGRB candidate from the GW time, \u2206t; and the FAR\nfrom the best-fitting spectral template of the GRB can-\ndidate, FARGBM. We update the formulation to include\nthe spatial association probability passoc and the dura-\ntion D of the gamma-ray emission:\nR = pastro \u00d7 pvisible \u00d7 passoc\n|\u2206t \u2212D| \u00d7 FARGBM\n.\n(6)\nThe spatial association probability passoc quantifies\nwhether the localizations of a sub-threshold gamma-ray\ncandidate and GW are consistent with being produced\nby the same source. It is computed according to\nS =\nZ\n\u03c1GBM \u03c1GW d\u2126, B =\nZ\n\u03c1GBM \u03c1uniform d\u2126,\n(7)\npassoc =\nS\nS + B ,\n(8)\nwhere S represents a signal hypothesis with both local-\nizations produced by the same source and B denotes a\n\n17\nbackground hypothesis where the localizations are un-\nrelated. Both S and B are constructed from integrals\nover all sky positions. In this context, \u03c1GBM is the prob-\nability density per unit area reported by the localization\nmaps produced for gamma-ray candidates identified by\nthe Targeted Search. Likewise, \u03c1GW is the probability\ndensity of the localization maps produced for each GW\nand \u03c1uniform = 1/4\u03c0 is the unit density of a uniform\nspatial distribution on the sky.\nThe duration of gamma-ray emission D is incorpo-\nrated into the temporal weight,\n1\n|\u2206t \u2212D|,\n(9)\nwhere \u2206t is the temporal offset between the GW time\nand the start of the candidate gamma-ray emission iden-\ntified by the Targeted Search and D is the candidate\nemission timescale. As discussed in Section 2.2.1, this\nis designed to account for scenarios where the observed\ntemporal offset scales with burst duration, which is ex-\npected from a broad range of models describing the\nobservations of GW170817/GRB 170817A. The best-fit\nvalue of D, given by the candidate with the largest value\nof \u039b, is a good proxy for burst duration because it scales\nproportionally with T90 when the Targeted Search is ap-\nplied to confirmed short GRBs in Fermi-GBM.\nWe enforce a minimum value of |\u2206t \u2212D| = 1 ms to\navoid divergence and account for the millisecond scale\nuncertainty between the GW merger times of signals\nidentified by multiple pipelines. We also apply a mini-\nmum value of FARGBM = 6.43\u00d710\u22126 Hz. This is equal\nto observing a single GRB candidate over the length of\nthe background sample used to compute FARGBM.\nWe tested the impact of these updates to the ranking\nstatistic by using the Fermi-GBM response generator2\nto inject short GRBs into CTTE data from the locations\nof modeled BNS mergers in Abbott et al. (2020a). The\nstart time of each GRB was offset from the GW time\nusing the duration of each burst, as given by T90. We\nthen applied the Targeted Search to this dataset and\nranked the candidates according to Equation 6 as well as\nthe older method from Hamburg et al. (2020). Doing so\nresulted in a factor of 1.7 increase in the number of joint\ndetections relative to the ranking statistic formulation\nfrom our older method.\nSince the true time offset model is not known, we re-\npeated the GRB injection study using the following al-\nternative models for the start time of the injected GRB\nrelative to the GW:\n2\nhttps://fermi.gsfc.nasa.gov/ssc/data/analysis/rmfit/\nDOCUMENTATION.html\n1. Offset of half T90 to test a scaling factor less than\nthe total burst duration.\n2. No time offset to bound emission scenarios where\nthe GRB occurs a few ms after the GW (Zhang\n2019).\n3. Fixed offset of 0.5 s assuming most gamma-ray\ncounterparts have a characteristic time delay\nwhich is half the median T90 of short GRBs ob-\nserved in Fermi-GBM.\nThese models were chosen with a bias towards testing\ntime offsets shorter than the typical duration of a short\nGRB since the inclusion of D in the updated temporal\nweight naturally performs better at longer time offsets\nthan the 1/|\u2206t| weight used in Hamburg et al. (2020).\nThe updated ranking statistic outperformed the older\nmethod in all scenarios, albeit with a smaller increase\nin the relative number of joint detections compared to\nthe scenario where temporal offset scales with burst du-\nration.\n2.2.4. Fermi-GBM Flux Upper Limits\nFor GW signals without a significant counterpart de-\ntection in Fermi-GBM we compute the gamma-ray flux\nupper limits as a function of sky position using the Tar-\ngeted Search because it is the most sensitive analysis\nmethod employed by Fermi-GBM. To do this, we use\nthe normal spectral template from Table 3 and the 1 s\ngamma-ray emission duration from the Targeted Search\nsince they are characteristic of typical short GRBs (von\nKienlin et al. 2020; Poolakkil et al. 2021). This results\nin a set of upper limits for each sky position at times\nranging from \u22121 s to +30 s around the GW time. We\nthen choose the maximum observed upper limit mea-\nsurement for each sky position, guaranteeing that the\nspecified confidence level of the upper limit applies over\nthe entire search period.\nWe construct the upper limits from the best-fit photon\nflux amplitude sbest and its Gaussian error \u03c3L discussed\nin Section 2.2.2 according to\nSUL = sbest + N \u00d7 \u03c3L,\n(10)\nwhere N is the significance level of the upper limit. We\nuse a 3\u03c3 upper limit level for reporting upper limits over\nthe full 10\u20131000 keV energy range of standard GRB flux\nmeasurements in Fermi-GBM following the convention\nestablished in Goldstein et al. (2019).\nWe also com-\npute a second 5\u03c3 upper limit over a 15\u2013350 keV range\nto match the convention used by Swift-BAT (see Sec-\ntion 2.3.3) when combining the upper limits from both\ninstruments.\n\n18\n2.3. Swift-BAT Searches\nSwift-BAT is a coded-aperture, large FoV (2.2 sr at\n10% coding fraction), hard X-ray instrument on-board\nSwift. Its detector plane contains 32,768 CZT detector\nelements, positioned under a coded aperture mask and a\ngraded-Z fringe shield that helps lower the background\nrate (Barthelmy et al. 2005). The BAT covers an en-\nergy range from 15 keV to 350 keV and monitors large\nportions of the sky with the goal of detecting GRBs.\nOnce triggered, the BAT can localize a GRB to 1\u20133 ar-\ncmin accuracy, prompting the Swift spacecraft to slew\nand point its two narrow-field instruments\u2014the X-ray\nTelescope (XRT; Burrows et al. 2005) and the Ultravio-\nlet/Optical Telescope (UVOT; Roming et al. 2005)\u2014for\nfollow-up observations. The BAT\u2019s localization accuracy\nis quantified by the instrument\u2019s partial coding fraction,\ni.e. the fraction of detectors exposed to an event at a\ngiven time and sky position. If the coding fraction for\na given trigger is 0%, then BAT will not be able to lo-\ncalize the event. The BAT averages \u223c90 GRB on-board\ntriggers per year, among which \u223c10% are short in dura-\ntion (Gehrels et al. 2009). The on-board GRB triggers\nare complemented by subsequent on-ground rates and\nimage data processing, in turn allowing for dedicated\nsearches for GRB emission. With no GWs from Table 1\ntriggering an on-board BAT detection, we conduct an\noffline follow-up analysis from the ground to search for\nthe corresponding hard X-ray counterpart emission.\n2.3.1. Swift-BAT Rates Data Search\nThe BAT flight software continuously assesses the\nsignal-to-noise ratio (SNR) of the observed count rates.\nIf an SNR exceeds the given threshold value determined\nby a number of rate-trigger criteria (Fenimore et al.\n2004), the triggering algorithm subsequently checks the\ncorresponding image data for the final confirmation and\nthe localization of the potential burst. The detection is\nconfirmed only if the image SNR threshold is surpassed\n(\u22736.5) and no other sources have been previously re-\nported at the event localization. For every confirmed\ndetection, BAT records event data containing counts\u2019 ar-\nrival times, location on the detector plane, and energy.\nWith its large effective area (\u223c2600 cm2 for 100 keV\nphoton detection at launch), the event data volume col-\nlected by BAT is too big to be stored on-board and, due\nto the limitations of the Swift downlink bandwidth, it is\nnot possible to transfer all the event data to the ground.\nAs such, until recently, the only way to conduct an of-\nfline, on-ground follow-up analysis of untriggered and\nsub-threshold events relied upon the rates light curves\nin four energy channels (15\u201325 keV, 25\u201350 keV, 50\u2013\n100 keV, and 100\u2013350 keV) with three time binnings\n(64 ms, 1 s, and 1.6 s) and their corresponding 64 s im-\nages in a single energy bin (15\u201350 keV). The recently\ndeveloped Gamma-ray Urgent Archiver for Novel Op-\nportunities (GUANO) technique circumvents this issue\nby retrieving BAT event data extending to \u223c200 s long\nwindows surrounding the trigger times from various as-\ntrophysical events (e.g., GWs, GRBs, fast radio bursts,\nneutrinos, etc.; Tohuvavohu et al. 2020). However, in\nthis paper we do not use the GUANO technique since a\nsignificant number of the considered GW triggers were\ndetected prior to the GUANO deployment in December\n2019. Instead, we conduct the analysis using the regu-\nlar rates data from BAT and leave the analogous study\nusing the GUANO data for the future GW observing\nruns.\nTo conduct the untriggered and sub-threshold search\nfor hard X-ray counterparts coincident with the LVK\ntriggers in Table 1, we developed a code analogous to\nLien et al. (2014). The search process begins by extract-\ning the raw light curves from within the central region of\nthe BAT FoV binned in 64 ms, 1 s, and 1.6 s time inter-\nvals. We opt to use the 1 s binned data to calculate the\naverage background rate and standard deviation, \u03c3bg,\nstarting at \u22121 s before the GW trigger time, and ex-\ntending to +30 s after. Using the raw light curves, we\ncompute the average background rate, rbg, spanning a\ntime window outside the signal interval, and spanning\n\u223c800 s (excluding the instrument slews or SAA). The\nsignal significance, S, is then computed from \u03c3bg, using\nS = (rsig \u2212rbg)/\u03c3bg,\n(11)\nwhere rsig is the threshold signal rate. The background\nuncertainty is estimated as \u03c3bg =\nq\n1\nN\nPN\ni=1(rbg,i \u2212rbg)2,\nwhere N is the number of data points in the considered\nportion of the lightcurve, rbg,i is the ith background\nrate measurement, and rbg is the mean background rate\nover the considered time interval. Furthermore, we vi-\nsually inspect each light curve to ensure that no peaks\noriginate from detector noise.\nOnce this is done, we\ncheck whether there are any potential counterparts to\nthe GW, defined as a \u22655\u03c3 detection above background.\n2.3.2. NITRATES Response Functions\nTo produce the BAT instrument response func-\ntions appropriate for converting from photon counts\nto a source flux in the rate data domain, we use the\nNon-Imaging Transient Reconstruction And TEmporal\nSearch (NITRATES; DeLaunay & Tohuvavohu 2021).\nThe NITRATES response modeling takes into account\nboth coded and uncoded parts of the detector, and thus\nincludes responses appropriate for all counts recorded\nin the rates data. In addition, these responses allow for\n\n19\npotential GRB detection from outside the BAT\u2019s coded\nFoV, as well as higher sensitivity across the entire FoV.\nThe instrument responses were created by simulating\nphoton beams onto the Swift Mass Model (SwiMM)\nusing Geant4, a particle-interaction simulator soft-\nware toolkit (Allison et al. 2016). We produce Detector\nResponse Matrices (DRMs) for 31 different incident di-\nrections, covering the \u223c2.2 sr sky area (corresponding\nto the 10-% coding fraction) where the responses are\nwell calibrated. For a complete description of the BAT\ninstrument response modeling, see Sec. 5 and Appendix\nA in DeLaunay & Tohuvavohu (2021).\n2.3.3. Swift-BAT Flux Upper Limits\nFor GWs without a 5\u03c3 detection above background in\nSwift-BAT, we estimate the flux upper limit from the\nobserved photon counts. We compute these limits for\neach time bin in the search by calculating the necessary\nnumber of counts that would result in a 5\u03c3 detection at\nthat time from the estimated background uncertainty\n\u03c3bg, assuming a 1 s emission duration. We then select\nthe largest counts value obtained in the search bins for\neach GW since this is guaranteed to satisfy the 5\u03c3 crite-\nria over the full search window. We convert the photon\ncounts to flux upper limits within the partially coded\nBAT FoV, over a 15\u2013350 keV energy range as a function\nof sky position by applying the NITRATES instrument\nresponse functions using the normal spectral template\n(Table 3) employed for upper limits computed with the\nFermi-GBM Targeted Search in Section 2.2.4. This is\ndone over 31 locations in a grid covering the \u223c2.2 sr\nBAT FoV.\n2.4. Combined & Marginal Flux Upper Limits\nFor GWs without a detected counterpart in Fermi-\nGBM or Swift-BAT, we combine the 5\u03c3 confidence level\nflux upper limits described in Sections 2.2.4 & 2.3.3 to\nproduce joint flux upper limits as a function of sky posi-\ntion using both instruments. We do this by selecting the\nmore constraining upper limit at each position since the\nindividual limits result from independent measurements.\nThis allows us to provide a single upper limit map for\neach GW that simultaneously leverages the wide FoV\nprovided by Fermi-GBM as well as the additional cov-\nerage and enhanced sensitivity of Swift-BAT.\nWe\nalso\nprovide\nmarginalized\nflux\nupper\nlimits\n(SUL,marg) that we compute by integrating the upper\nlimits over the sky using the probability density of the\nGW localization as a prior\nSUL,marg =\nZ\nSUL \u02dc\u03c1GW d\u2126,\n(12)\nwhere SUL is the position-dependent upper limit at a\ngiven confidence level and \u02dc\u03c1GW is the probability den-\nsity of the GW localization normalized over the visible\nportion of the sky. This reduces the set of upper limits\nfor each GW to a single, characteristic upper limit that\naccounts for the most likely location of the GW source.\n2.5. Isotropic-Equivalent Luminosity Upper Limits\nWe compute upper limits on the isotropic-equivalent\ngamma-ray luminosity Liso in the cosmological rest-\nframe energy range of 1 keV\u201310 MeV for GWs without\na detected counterpart in Fermi-GBM or Swift-BAT ac-\ncording to\nLiso = 4\u03c0 D2\nL SUL,marg, k,\n(13)\nwhere DL is the median luminosity distance of the GW,\nSUL,marg is the marginalized confidence level flux upper\nlimit described in Section 2.4, and k is the standard\nbolometric correction factor given by\nk \u2261\nR 10 MeV/1+z\n1 keV/1+z\nE dN\ndE (E) dE\nR 350 keV\n15 keV\nE dN\ndE (E) dE\n,\n(14)\nwhere z is the redshift inferred from DL.\nIn this\ncase, dN\ndE (E) represents the normal spectral shape from\nTable 3, which is used to generate the marginalized\nflux upper limit.\nWe chose to use the median DL\nand the marginalized flux upper limit for each GW\nrather than marginalizing Liso from the values esti-\nmated at each sky position in order to exclude the low-\nlikelihood modes of the distance luminosity posteriors\nfor GW200308 173609 and GW200322 091133, as dis-\ncussed in Abbott et al. (2021).\nAll other GWs yield\nsimilar values for Liso regardless of whether we use the\nindividual or median values for DL in the calculation.\n3. RESULTS\nThis section presents the results for the searches from\nFermi-GBM and Swift-BAT for coincident gamma-ray\nemission to the GW candidates presented in Tables 1\nand 2.\n3.1. Triggered and Untargeted Search Results\nWe compare the distribution of temporal offsets be-\ntween the GWs listed in Table 1 and the closest gamma-\nray signal in Fermi-GBM, minus its burst duration,\nshown in Figure 1.\nThe GRB sample here comprises\n214 GRBs triggered by Fermi-GBM during O3 and\n479 short GRB candidates detected by the Untargeted\nSearch. The background distribution was composed by\nchoosing \u223c104 random times in O3 during which there\nwere no reported GWs.\nConfidence intervals for the\n\n20\nFigure 1.\nThe cumulative distribution for the minimum\ntime offsets between the O3 GW triggers and GRBs found\nby either the GBM on-board triggering algorithms or the\nUntargeted Search. Confidence intervals for the search sam-\nple were determined by Monte Carlo sampling of the back-\nground.\nsearch sample were determined empirically by Monte\nCarlo sampling of the background distribution.\nThere are no significant deviations from the back-\nground, with the search sample lying largely within the\n68% confidence interval. The shortest temporal offset\ngiven by the sample distribution is approximately 10\nminutes and is within the 95% confidence interval. Such\nlarge offsets are not expected for on-axis prompt emis-\nsion from GRBs associated with binary mergers (Ve-\ndrenne & Atteia 2009; Zhang 2019); therefore, we find\nno further evidence for a GW/gamma-ray association.\n3.2. Targeted Search Results\nWe ran the Targeted Search on the 79 GWs shown in\nTable 1. Fermi-GBM was in the SAA for 15 of those\ntimes, therefore the detectors were turned off and no\ndata were obtained. Figure 2 shows the cumulative rate\nabove a given value of the marginalized log-likelihood\nratio \u039b separated according to the best-fitting spectral\ntemplate. The background distribution is determined by\nrandomly selecting times during the O3 livetime with-\nout known GW triggers.\nThis represents the FAR of\nthe search and describes the frequency of expected false\npositives as a function of \u039b. No significant gamma-ray\nsignals were found in coincidence with GWs.\nFigure 3 shows the ranking statistic R from Sec-\ntion 2.2.3 mapped to a p-value, defined as the number\nof more highly ranked background candidates as com-\npared to the total number of background candidates or\npi = N(R > Ri)/N, where N is the number of back-\nground gamma-ray candidates and i is the candidate in-\ndex within the search sample. The plots show no signif-\nicant deviations from background, yielding no evidence\nfor a GRB counterpart to the GW signals.\n3.3. Swift Results\nWe ran the pipeline described in Section 2.3 on the\n1 s binned light curves from Swift-BAT for the 79 can-\ndidates listed in Table 1. The goal of the pipeline is to\nexamine whether any emission surpasses the 5\u03c3 thresh-\nold above the observed background rate level. We visu-\nally inspect each light curve to ensure that no detector\nnoise or malfunction affects the reported results.\nWe\nidentify detector noise as a fast duration peak seen only\nin some of the energy channels.\nOnce identified, the\ndetector noise is subtracted down to the level of the av-\nerage background rate. There are 14 GWs for which the\ndata are either unavailable or background dominated be-\ncause they occurred during either the Swift-BAT SAA\npassage or a slew. Separately, 13 GWs were within the\nBAT FoV (>10% partial coding) and had image sur-\nvey data available at the time of interest. We report no\nsignificant hard X-ray detection in the Swift-BAT rate\ndata coincident with the reported GW triggers at the\n5\u03c3 level.\nWe also ran the standard BAT analysis on\nthe survey data (longer timescales, \u223c300 s) for the 13\ninside-BAT-FoV candidates and also report no excess\nX-ray emission.3\n3.4. Results for Marginal GW Canidates\nThe Fermi-GBM and Swift-BAT searches were ap-\nplied separately to the 6 marginal GW signals from\nTable 2 in an effort to identify EM counterparts,\nthat could prove an astrophysical origin.\nThe clos-\nest time offset from the GBM Triggered and Untargeted\nSearches was observed for GW191118 212859, which oc-\ncurred 42 minutes before the on-board trigger of GRB\n191118A and corresponds to a p-value of 0.1. The most\nsignificant Targeted Search candidate was found for\nGW200105 162426 using the hard spectral template. It\nhas a pre-trial p-value of 0.1 as estimated by the ranking\nstatistic distribution for background described in Sec-\ntion 2.2.3. Applying a trials factor of 3 to account for\nthe 3 spectral templates used by the Targeted Search\nincreases the p-value to 0.3.\nNo 5\u03c3 detections were\nfound for any marginal candidates using the Swift-BAT\nrates data search.\n4. SCIENCE DISCUSSION\nCompact binary mergers containing a neutron star\ncomponent are likely candidates for gamma-ray emis-\n3\nhttps://heasarc.gsfc.nasa.gov/ftools/caldb/help/batsurvey.\nhtml\n\n21\nFigure 2.\nThe cumulative rate above a given value of the marginalized log-likelihood ratio \u039b, separated into three plots\naccording to the best fitting spectral template, found in the Targeted Search. The orange line is the foreground distribution\nof GRB candidates found with the Targeted Search around the given GW merger time. The black dotted line is the randomly\nselected background sample and the green shading represents the 68%, 95% and 99.7% confidence intervals around it.\nsion, particularly if the inspiral process results in tidal\ndisruption of the neutron star (Burns 2020). In contrast,\nBBH mergers are not expected to produce gamma-rays\noutside of a few exotic scenarios (e.g., Loeb 2016a; Perna\net al. 2016; Zhang 2016; Dai et al. 2017).\nTherefore,\nusing the standard convention of m1 > m2, we divide\nour discussion into two sections based on the secondary\ncomponent mass m2:\n1. Mergers with a possible neutron star: m2 \u2264\n3 M\u2299(5% credible level)\n2. Probable BBH mergers: m2 > 3 M\u2299(95%\ncredible level)\nThe cut m2 \u22643 M\u2299was chosen to include all systems\nwith at least one neutron star component up to the max-\nimal allowed neutron star mass of 2.16\u20133.0 M\u2299(Bombaci\n1996; Kalogera & Baym 1996; Margalit & Metzger 2017;\nRezzolla et al. 2018). It may include a few ambiguous\nBBH mergers due to the uncertainty on the maximum\nallowed neutron star mass. We favor this approach over\na stricter cut due to the limited number of systems in\nO3 with light secondary component masses. Addition-\nally, the discussion of possible BBH mergers does not\nsuffer from the loss of a few ambiguous candidates, par-\nticularly given the large number of systems with m2 >\n3 M\u2299.\nIn Section 4.1 we discuss the absence of GRB detec-\ntions in coincidence with the 6 GWs classified with a\npossible neutron star component and present flux upper\nlimits from Fermi-GBM and Swift-BAT. In Section 4.2\nwe discuss the BBH mergers, providing flux upper lim-\nits and exploring how these limits may rule out certain\ntheoretical models.\n4.1. Possible Neutron Star in the System\n\n22\nFigure 3.\nCumulative fraction versus p-value of the updated ranking statistic R.\nThe solid black line is the foreground\ndistribution of GRB candidates found with the Targeted Search around the given GW merger time. The dashed black line is\nthe randomly selected background sample and the blue, green and orange lines represent the 68%, 95% and 99.7% confidence\nintervals for background, respectively.\nThere are 6 GWs (i.e.,\nGW190425,\nGW190814,\nGW190917 114630,\nGW191219 163120,\nGW200115\n042309, and GW200210 092254) where \u22655% of poste-\nrior probability lies below the dashed red line in Figure\n4. GW190425 is the least massive system from O3 and\nthe second BNS merger detected by LIGO-Virgo.\nIt\nhas a primary mass m1 = 2.1+0.5\n\u22120.4 M\u2299and a secondary\nmass of m2 = 1.3+0.3\n\u22120.2 M\u2299(Abbott et al. 2021, 2020).\nGW190814 has a low mass secondary component, esti-\nmated at m2 = 2.6+0.1\n\u22120.1 M\u2299, while its primary compo-\nnent has an estimated mass of m1 = 23.3+1.4\n\u22121.4 M\u2299. It is\nunclear whether this source is a BBH or a NSBH merger,\nsince the secondary component could either be a light\nblack hole or a heavy neutron star (Abbott et al. 2021).\nGW190917 114630 was identified as a BBH merger by\nthe GstLAL pipeline, but its secondary component mass\nof m2 = 2.1+1.1\n\u22120.4 M\u2299is a strong indicator for a NSBH ori-\ngin (Abbott et al. 2021). GW191219 163120 has a large\nprimary component mass of m1 = 31.1+2.2\n\u22122.8 M\u2299and the\nlowest secondary component mass m2 = 1.17+0.07\n\u22120.06 M\u2299\nof all the GWs with a possible neutron star (Abbott\net al. 2021); it represents a potential NSBH merger.\nGW200115 04230 has a primary mass of m1 = 5.9+2.0\n\u22122.5\nM\u2299suggesting a low-mass black hole, and a secondary\nmass of m2 = 1.44+0.85\n\u22120.29 M\u2299which is consistent with a\nneutron star (Abbott et al. 2021). GW200210 092254\npossesses a primary component mass of m1 = 24.1+7.5\n\u22124.6\nM\u2299and a secondary component mass of m2 = 2.83+0.47\n\u22120.42\nM\u2299that could either be a light black hole or a heavy\nneutron star (Abbott et al. 2021). It is unclear if this\nsource is a BBH or NSBH merger.\nAll GWs except GW191219 163120 were observ-\nable by both Fermi-GBM and Swift-BAT (Table 4).\nGW191219 163120 was observed by Fermi-GBM but no\nSwift-BAT data are available due to a slewing behavior\nof the spacecraft at the GW time. Neither instrument\n\n23\nFigure 4. The inferred 90% credible regions of the compo-\nnent masses for all GWs with pastro > 0.5 from O3 are shown\nin grey (Abbott et al. 2021; Abbott et al. 2021; Abbott et al.\n2021). The red dashed line marks the upper bound of m2\nallowed for our classification of systems with a possible neu-\ntron star component, which are marked by colored contours.\nFigure 5. The 5\u03c3 upper-limits on isotropic-equivalent lu-\nminosity Liso for the 6 GWs in O3 identified with a possible\nneutron star component and pastro > 0.5. The black data\npoint is the measured Liso from GRB 170817A and the black\ndashed line is the approximate lower bound for Liso of GRBs\ndetected on-board Fermi-GBM (Abbott et al. 2017).\nTable 4.\nFlux upper limits for the 6 GWs from O3 with pastro > 0.5 that are classified with a possible neutron star component.\nThe 3\u03c3 upper limits are computed for the 10\u20131000 keV energy range over the FoV of Fermi-GBM. The 5\u03c3 upper limits are\ncomputed for the combined coverage of Fermi-GBM and Swift-BAT with both instruments matched to the 15\u2013350 keV energy\nrange of Swift-BAT. The columns labeled Min and Max correspond, respectively, to the minimum and maximum upper limits\nobtained for points within the 90% credible region of the GW localization. The Marginal upper limit is computed by integrating\nthe upper limits produced at individual locations over the full sky using the GW localization as a weighted prior, normalized to\nthe visible portion of the sky. Also shown is the visible coverage percentage of the full GW localization for Fermi-GBM alone,\nSwift-BAT alone, and the combined FoV from both instruments.\n3\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\n5\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\nCoverage [%]\n10\u20131000 keV\n15\u2013350 keV\nEvent Name\nGBM\nBAT\nCombined\nMin\nMax\nMarginal\nMin\nMax\nMarginal\nGW190425\n56.70\n10.81\n57.81\n1.37\u00d710\u22127\n2.47\u00d710\u22127\n1.66\u00d710\u22127\n6.12\u00d710\u22128\n2.31\u00d710\u22127\n1.51\u00d710\u22127\nGW190814\n100.00\n100.00\n100.00\n1.17\u00d710\u22127\n1.26\u00d710\u22127\n1.21\u00d710\u22127\n4.71\u00d710\u22128\n7.64\u00d710\u22128\n6.26\u00d710\u22128\nGW190917 114630\n88.92\n6.56\n95.07\n1.48\u00d710\u22127\n4.33\u00d710\u22127\n2.33\u00d710\u22127\n5.26\u00d710\u22128\n3.83\u00d710\u22127\n2.08\u00d710\u22127\nGW191219 163120\n61.06\nN/A\n61.06\n1.03\u00d710\u22127\n2.36\u00d710\u22127\n1.20\u00d710\u22127\n1.00\u00d710\u22127\n2.27\u00d710\u22127\n1.15\u00d710\u22127\nGW200115 042309\n96.26\n4.80\n96.26\n1.31\u00d710\u22127\n2.83\u00d710\u22127\n1.78\u00d710\u22127\n8.53\u00d710\u22128\n2.56\u00d710\u22127\n1.60\u00d710\u22127\nGW200210 092254\n61.79\n50.55\n65.85\n1.28\u00d710\u22127\n3.13\u00d710\u22127\n2.01\u00d710\u22127\n4.41\u00d710\u22128\n1.47\u00d710\u22127\n9.00\u00d710\u22128\ndetected an EM counterpart to these GWs. Therefore,\nwe compute flux upper limits for each GW using the\nmethods described in Section 2. Table 4 presents the\nminimum and maximum flux upper limits from Fermi-\nGBM and Swift-BAT over the 90% credible regions\nof the GW localizations, as well as sky-marginalized\nflux upper limits. Incorporating the combined measure-\nments from Fermi-GBM and Swift-BAT, we also use\nthe sky-marginalized 5\u03c3 flux limits to generate upper\nlimits on the isotropic-equivalent luminosity (Figure 5).\nThe combined 5\u03c3 flux upper limits over the 15\u2013350 keV\nenergy range can be seen in Figure 6.\nThe lack of a gamma-ray counterpart to BNS merger\nGW190425 has three plausible explanations. First, the\ncombined coverage of \u223c60% of the total GW localization\nimplies that the GW source may not have been visible\nto Fermi-GBM and Swift-BAT. Second, GW190425 has\nan estimated luminosity distance of DL = 0.15+0.08\n\u22120.06 Gpc\nwhich is 4 times larger than that to GW170817 (Ab-\nbott et al. 2019).\nAt this distance, the luminosity of\nGW170817 would fall well below the upper limit for\nGW1904254 (Fletcher et al. 2019). (Figure 5), indicat-\n4 Note, the luminosity upper limit for GW1901425 is also con-\nsistent with that found in Hosseinzadeh et al. 2019, which uses\n\n24\ning that a counterpart similar to the one for GW170817\nwould have been unobservable to Fermi-GBM or Swift-\nBAT. Finally, the inclination angle of this GW is poorly\nconstrained, with the 90% credible level extending to a\nviewing angle of 70\u25e6with respect to the jet axis. This\nencompasses scenarios where the observed off-axis flux\nwould be below the detection limits, even if the central\nengine of GW190425 was powerful enough to be detected\non-axis by Fermi-GBM and Swift-BAT at its measured\ndistance.\n4.2. Probable BBH Mergers\nThere are a total of 73 GWs with the criterion of\nm2 > 3 M\u2299in > 95% of the posterior probability. All\nof these have estimated primary and secondary compo-\nnent masses much larger than the maximum expected\nneutron star mass of 3 M\u2299. Therefore, they are most\nlikely GW signals from BBH mergers.\nOf these GWs, 10 occurred during SAA for Fermi-\nGBM, but had data from Swift-BAT. Likewise, Swift-\nBAT does not have data for 9 GWs, either because\nSwift-BAT was in the SAA or slewing, but data are\navailable from Fermi-GBM. Finally, there are 5 GWs\nthat do not have data from either Fermi-GBM or Swift-\nBAT due to being in the SAA and/or slewing. Neither\ninstrument identified an EM counterpart for the GWs\nwith data coverage. As a result, we compute flux upper\nlimits for each GW according to the methods described\nin Section 2. Table 5 presents the minimum and max-\nimum upper limits over the 90% credible region of the\nGW localization as well as the marginalized flux up-\nper limits. Joint flux upper limits as a function of sky\nposition and the corresponding isotropic-equivalent lu-\nminosity limits for the GWs that have data coverage\nare provided in a separate data release (Wood et al.\n2023). For the GWs with Fermi-GBM data, we look\ninto constraining theoretical models of gamma-ray emis-\nsion from BBHs using the 3\u03c3 flux upper limits, as they\nprovide broad spectral coverage over the 10\u20131000 keV\nenergy range.\n4.2.1. Constraining gamma-ray emission models from\nBBH mergers\nEM radiation from BBH mergers is not expected due\nto the challenges associated with forming an accretion\ndisk during the merger process.\nNevertheless, Con-\nnaughton et al. (2016) reported GW150914-GBM, a\nweak gamma-ray signal following the first LIGO\u2013Virgo\ndetection of BBH GW150914 (Abbott et al. 2016), and,\npreliminary Fermi-GBM flux upper limits reported during the O3\nonline analysis\nmore recently, the Zwicky Transient Facility identified\na potential EM counterpart to GW190521 (Graham\net al. 2020). While the associations between these de-\ntections and the corresponding GWs remain nebulous\n(Connaughton et al. 2018; Ashton et al. 2021; Bustillo\net al. 2021; De Paolis et al. 2020; Palmese et al. 2021), a\nwide spectrum of models have been developed to invoke\nEM emission from BBH-mergers, all with non-negligible\ndifficulties (e.g., Loeb 2016b; Perna et al. 2016; Zhang\n2016; Perna et al. 2018).\nTo test the association between GW150914 and\nGW150914-GBM, Veres et al. (2019) assumed some\nof these BBH emission models and derived a model-\ndependent BBH-to-GRB ratio which represents the ex-\npected number of BBH mergers to be detected by LVK\nbefore a gamma-ray counterpart might be observed by\nFermi-GBM. Since the number of LVK BBH merger\ndetections has reached the BBH-to-GRB ratio for a few\nmodels reported by Veres et al. (2019), we attempt to\nconstrain them by computing gamma-ray flux upper\nlimits for each model and examining the implications\nwith respect to individual BBH mergers.\nWe consider four models for relating potential gamma-\nray emission to the energy present in BBH mergers: a\nneutrino\u2013antineutrino annihilation powered jet mecha-\nnism (\u03bd\u00af\u03bd; Ruffert & Janka 1998), a charged BH (Q;\nZhang 2016), the Blandford\u2013Znajek mechanism (BZ;\nBlandford & Znajek 1977), and a model where the\ngamma-ray energy is proportional to the emitted GW\nenergy (EGW).\nA detailed summary of these mod-\nels and their parameters can be found in Veres et al.\n(2019). We note that all of the above scenarios suffer\nfrom non-trivial critiques but are used here to be widely-\ninclusive of the broad spectrum of proposed mechanisms\nfor gamma-ray production.\nThe intrinsic properties\nof each model (e.g., magnetic field strength, charge of\nthe black hole, etc.)\nare determined by setting them\nto values consistent with the observed luminosity of\nGW150914-GBM (Connaughton et al. 2016).\nFor each GW, we use the posterior distributions of\nBBH parameters (e.g., final mass, distance, inclination,\nrotation parameter, etc.) from GWTC-3 and derive a\ndistribution of gamma-ray fluxes for the different mod-\nels. We then compare the distribution of fluxes to the 3\u03c3\nmarginalized flux upper limit from Fermi-GBM, shown\nin Table 5. This is performed for three GRB jet geome-\ntries: an isotropic emitter (i.e., an opening angle of 90\u25e6),\nan opening angle distributed uniformly between 10\u201340\u25e6,\nand a fixed 20\u25e6opening angle. All jets are assumed to\nhave a top-hat angular structure and are assigned point-\ning directions by sampling from the inclination posterior\nof each GW. Due to relativistic beaming, emission is\n\n25\nFigure 6. The 5\u03c3 flux upper-limit as a function of sky position for the 6 GWs from O3 identified with a possible neutron star\ncomponent and pastro > 0.5. The purple gradient represents the combined Fermi-GBM and Swift-BAT flux upper limits for\nsource positions at each point on the sky. The star symbol represents the zenith direction of Fermi-GBM, the square symbol\nrepresents the center of the Swift-BAT FoV, and the green contour represents the 90% credible area of the LVK localization.\nThe blue region is the non-visible portion of the sky which is occulted by the Earth for Fermi-GBM and outside the Swift-BAT\nFoV.\n\n26\nFigure 5 continued.\n\n27\nFigure\n7.\nExample of gamma-ray flux expected\nfor\nthe\n4\ndifferent\nmodels:\ncharged\nBH\nmodel\n(Q),\nneutrino\u2013antineutrino annihilation powered jet model (\u03bd\u00af\u03bd),\nBlandford\u2013Znajek (BZ), and gamma-ray energy as a fraction\nof GW energy (EGW) in the case of GW191216 213338. The\n3\u03c3 (10\u20131000 keV) marginalized flux upper limit is indicated\nby the vertical line. The legend contains the fraction of cases\nabove the 3\u03c3 upper limit; note that for the jetted emission\nmodels (uniform, fixed), cases with zero expected flux are not\nshown. Here the limit is violated in 100% and >99% of cases\nfor the \u03bd\u00af\u03bd and Q models, respectively (assuming isotropic\nemission).\nstrongly suppressed for GRBs with jet opening angles\nsmaller than the viewing angle. In order to simplify the\ntreatment of such cases, we assign zero flux to jets whose\ninclination is larger than the opening angle.\nFigure 7 shows an example of the flux distribu-\ntion for the four different models and the three jet\ngeometries compared to the GBM upper limits for\nGW191216 213338.\nThere is a dearth of jetted cases\n(green, red) compared to isotropic emission (light blue)\nat higher fluxes.\nThis is explained by the inclination\nangle-distance degeneracy of the GW parameter esti-\nmation.\nPoint estimates with smaller distances and\nthus higher flux will preferentially have jets pointed\naway from our line of sight.\nWhen we impose a jet\nopening angle \u227240\u25e6on such systems, they will not\ninclude the observer within their aperture in most of\nthe cases. Conversely, the point estimates with largest\ndistances point preferentially towards the observer, thus\nthere will be no strong differences between the jetted\nand isotropic cases at low flux values.\nWe classify GW191216 213338 as noteworthy because\nthe predicted gamma-ray flux distribution from at least\none model violates the GBM flux upper limit by more\nthan 10%. The 10% limit in the rest of this section refers\nto the isotropic emission model.\nOf the 58 probable\nBBH mergers with Fermi-GBM data coverage described\nin Section 4.2, 18 are considered noteworthy according\nto this criterion. The remaining 40 did not yield the\nnecessary number of cases above the GBM flux upper\nlimit in any of the models.\nOut of the four models considered here, the \u03bd\u00af\u03bd model\nviolates the Fermi-GBM flux upper limit in most of\nthe cases.\nOf the noteworthy GWs (denoted by \u2217in\nTable 7, Appendix A), 15 exceed the GBM limit in\nmore than 10% of cases for this model. In particular,\nGW190924 021846, GW191216 213338 (Figure 7) and\nGW200202 154313 exceed the GBM limit in {100, 30,\n20}%, {100, 31, 19}% and {100, 36, 24}% of the cases re-\nspectively (the 3 numbers represent the 3 different open-\ning angle choices). Interestingly, for these three events,\nin the isotropic emission scenario the \u03bd\u00af\u03bd can be ruled\nout, and the non-detection in gamma-rays can constrain\nthe jet geometry.\nThis is due to GW191216 213338\nand GW200202 154313 being the two closest BBH sig-\nnals observed during O3 with luminosity distances of\n0.34+0.12\n\u22120.13 Gpc and 0.41+0.15\n\u22120.16 Gpc, respectively (Abbott\net al. 2021).\nIn addition to being nearby (luminosity\ndistance of 0.55 \u00b1 0.22 Gpc), GW190924 021846 has a\nrelatively low final mass (13.9+2.8\n\u22120.9 M\u2299), which leads to\nhigher flux in the \u03bd\u00af\u03bd model.\nFor the Q model, the most constraining GWs are also\nGW191216 213338 and GW200202 154313. They vio-\nlate the GBM flux upper limit for the different jet ge-\nometries in {100, 31, 19}% and {96, 33, 22}% of cases,\nrespectively. In total, 12 of the probable BBH mergers\nhave larger than 10% of their flux estimates above the\nupper limit for this model.\nGW191109 010717 is the most constraining for the\nBZ scenario.\nIt violates the gamma-ray upper limit\nin {26, <0.1, <0.1}% of cases for the 3 different open-\ning angle choices. It has the fourth-highest total mass\nM = 112+20\n\u221216 M\u2299in O3 and is reasonably close at DL =\n1.29+1.13\n\u22120.65 Gpc (Abbott et al. 2021). The only other GW\nwith more than 10% of the flux estimates above the up-\nper limit for the BZ mechanism is GW190521 074359.\n\n28\nFor the EGW scenario, GW191216 213338 is again the\nmost constrained. It violates the gamma-ray upper limit\nin {27, 1.8, 0.7}% of the cases for the three jet opening\nangle choices. There are 3 GWs with 10% of the flux\nestimates from this model above the GBM flux upper\nlimit (Table 7 continued, Appendix A).\nIn summary, we provide constraints on theoretical\nmodels of gamma-ray emission from BBH mergers using\nthe flux upper limits from Fermi-GBM. We find that for\nmost BBH mergers the models considered here do not\npredict gamma-ray flux over the upper limit. Under our\nmodel assumptions, this can be understood as a conse-\nquence of the larger average distance of BBH mergers\nduring O3 compared to that of GW150914.\nWe also\nfind that the \u03bd\u00af\u03bd model is the most constrained. This\nmodel has the lowest BBH-to-GRB ratio in Veres et al.\n(2016), and indeed, observations reveal that 18 out of 58\ncases for the \u03bd\u00af\u03bd model yield an appreciable flux above\nthe upper limit. The expected flux in this model is in-\nversely proportional with the final mass; the average\nBBH merger in O3 was less massive than GW150914,\nresulting in larger predicted gamma-ray flux.\n4.3. Marginal GWs\nAlthough all 6 marginal GWs from Table 2 have\npastro < 0.5 they are of interest for EM follow-up.\nThis is because GW200311 103121 may have a possi-\nble BNS origin and the remaining 5 candidates have\npossible NSBH origins (Abbott et al. 2021; Abbott\net al. 2021). In particular, the possible NSBH merger\nGW200105 162426 was noted as a clear outlier from\nexperimental backgrounds despite not satisfying the\npastro > 0.5 criteria used to identify GW signals with\na likely astrophysical origin. It also has the highest ob-\nserved pastro of all the marginal GWs.\nThe 5 marginal GWs with possible NSBH origins\nwere visible to Fermi-GBM while the remaining one,\nGW200311 103121, occurred when Fermi-GBM was in\nthe SAA. None of the marginal GWs have apprecia-\nble coverage in Swift-BAT. No significant counterparts\nwere found. As with GW190425, this may be due to\nunfavorable viewing angles with respect to the jet axis,\nlarger observational distances such as the 0.27+0.12\n\u22120.11 Gpc\ndistance to GW200105 162426 (Abbott et al. 2021),\nand partial sky coverage for candidates other than\nGW190426 152155.\nIt therefore remains ambiguous\nas to whether these signals are real compact binary\ncoalescences. Nevertheless, we provide in Table 6 the\nflux upper limits for each marginal GW calculated ac-\ncording to the same methods described in Section 4.1\nsince they may provide emission model constraints if\nfuture analyses can identify an astrophysical progeni-\ntor with a favorable viewing angle with respect to the\njet axis. Figure 8 displays the 5\u03c3 confidence level flux\nupper limit map for GW200105 162426 since it is the\nmarginal GW with the highest probability of having\nan astrophysical origin. The marginalized 5\u03c3 flux upper\nlimit of GW200105 162426 yields an isotropic-equivalent\nluminosity upper limit of Liso = 2.1 \u00d7 1048 erg s\u22121\nwhen combined with its 0.27 Gpc distance. The data\nrelease (Wood et al. 2023) associated with this work\nprovides flux upper-limits as a function of sky position\nfor the remaining marginal GWs.\n5. SUMMARY AND FUTURE DIRECTIONS\nUsing the 79 GW candidates with pastro > 0.5 from\nO3 that were reported in GWTC-3, we searched for co-\nincident EM counterparts with Fermi-GBM and Swift-\nBAT. This represents the most comprehensive follow-up\nto date of the O3 run in the hard X-ray and gamma-ray\nregime. We found no significant counterparts in either\ninstrument. For the one BNS merger, GW190425, with\npastro > 0.5 there are several possible reasons for the\nnon-detection of a counterpart:\n\u2022 The combined Fermi-GBM and Swift-BAT cover-\nage of the GW localization area was \u223c60%, mean-\ning that the GW source may have been outside the\nFoV for both instruments.\n\u2022 The distance to GW190425 was four times larger\nthan the estimated distance for GW170817, caus-\ning the observed flux to be below the detec-\ntion threshold in both instruments if it had the\nsame intrinsic luminosity and viewing angle as\nGW170817.\n\u2022 The viewing angle may have been too far away\nfrom the jet axis to detect emission under scenarios\nwith a clean or structured jet.\nGW190425 is therefore unconstrained by our observa-\ntions.\nIn contrast to GW190425, the large number of BBH\ndetections in this sample allowed us to begin placing\nconstraints on certain models of gamma-ray emission\nfrom BBH mergers, despite the larger average distance\nfor this class compared to the BNS mergers. The most\nconstrained model was the \u03bd\u00af\u03bd model where two GWs,\nGW191216 213338 and GW200202 154313, were pre-\ndicted to produce an observable flux in Fermi-GBM.\nWith the number of GWs from BBH mergers to increase\nin the fourth LVK observing run (O4), we expect this\nmodel to become more constrained and ruled out as a\npotential explanation of EM emission from BBH merg-\ners.\n\n29\nFigure 8. The 5\u03c3 upper-limits as a function of sky position for GW200105 162426, the marginal GW with the highest pastro.\nThe purple gradient represents the combined Fermi-GBM and Swift-BAT flux upper limits for source positions at each point\non the sky. The star symbol represents the zenith direction of Fermi-GBM, the square symbol represents the center of the\nSwift-BAT field-of-view, and the green contour represents the 90% credible area of the LVK localization. The blue region is the\nnon-visible portion of the sky which is occulted by the Earth for Fermi-GBM and outside the Swift-BAT FoV.\nWith O4 having begun on May 24, 2023, we expect\nan increase in GW detections by a factor of 5 (Abbott\net al. 2018; Petrov et al. 2022) and a bountiful regime of\nEM follow-up data. This will greatly increase the need\nfor further instantaneous, wide FoV gamma-ray/X-ray\nobservations in order to detect the EM counterparts to\nthese GWs and localize them, especially given the ab-\nsence of a counterpart detection during O3. Towards\nthis end, the Fermi-GBM Targeted Search updates pre-\nsented in this paper will be used in future LVK observ-\ning runs. In the absence of detections, flux upper limits,\nboth marginalized and as a function of sky position, will\nbe provided to the community. Additionally, Swift-BAT\nGUANO and NITRATES will be used during the next\nobserving run.\nACKNOWLEDGEMENTS\nThe USRA co-authors gratefully acknowledge NASA\nfunding through contract 80MSFC17M0022. R.H. ac-\nknowledges funding from the European Union\u2019s Hori-\nzon 2020 research and innovation programme under the\nMarie Sk lodowska-Curie grant agreement No 945298-\nParisRegionFP. The UAH co-authors gratefully ac-\nknowledge NASA funding from co-operative agreement\n80MSFC22M0004.\nThe NASA authors gratefully ac-\nknowledge NASA funding through the Fermi GBM\nproject. This research also made use of Astropy, a com-\nmunity developed core Python package for Astronomy\n(Astropy Collaboration et al. 2022); NumPy (Harris\net al. 2020); SciPy (Virtanen et al. 2020) and mat-\nplotlib, a Python library for publication quality graphics\n(Hunter 2007).\nThe Swift authors acknowledge the use of public data\nfrom the Swift data archive. MC acknowledges support\nfrom NASA under award number 80GSFC21M0002\nand from Vetenskapsr\u02daadet through project number\n31004019.\nJD acknowledges support by the NSF un-\nder award numbers PHY-1913607 and PHY-2209445.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO 600 detector. Additional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scientifique\n(CNRS) and the Netherlands Organization for Scien-\ntific Research (NWO), for the construction and oper-\nation of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agencies\nas well as by the Council of Scientific and Industrial Re-\nsearch of India, the Department of Science and Technol-\nogy, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource De-\nvelopment, India, the Spanish Agencia Estatal de In-\nvestigaci\u00b4on (AEI), the Spanish Ministerio de Ciencia e\nInnovaci\u00b4on and Ministerio de Universidades, the Con-\n\n30\nTable 5. Flux upper limits for possible EM counterparts to probable BBH candidates detected during O3 with pastro > 0.5.\nThe 3\u03c3 upper limits are computed for the 10\u20131000 keV energy range over the FoV of Fermi-GBM. The 5\u03c3 upper limits are\ncomputed for the combined coverage of the Fermi-GBM and Swift-BAT with both instruments matched to the 15-350 keV\nenergy range of Swift-BAT. The columns labeled Min and Max correspond, respectively, to the minimum and maximum upper\nlimit values obtained for points within the 90% credible level of the GW localization. The Marginal upper limit is computed by\nintegrating the upper limits produced at individual locations over the full sky using the GW localization as a weighted prior,\nnormalized to the visible portion of the sky.\n3\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\n5\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\nCoverage [%]\n10\u20131000 keV\n15\u2013350 keV\nEvent Name\nGBM\nBAT\nCombined\nMin\nMax\nMarginal\nMin\nMax\nMarginal\nGW190403 051519\n76.61\n24.76\n82.91\n1.07\u00d710\u22127\n3.09\u00d710\u22127\n1.78\u00d710\u22127\n3.67\u00d710\u22128\n2.80\u00d710\u22127\n1.50\u00d710\u22127\nGW190408 181802\nSAA\n0.00\n0.00\n-\n-\n-\n-\n-\n3.50\u00d710\u22127\nGW190412\n97.27\n3.45\n99.80\n1.00\u00d710\u22127\n1.22\u00d710\u22127\n1.11\u00d710\u22127\n9.81\u00d710\u22128\n1.15\u00d710\u22127\n1.07\u00d710\u22127\nGW190413 052954\n33.38\n0.05\n33.42\n1.21\u00d710\u22127\n1.97\u00d710\u22127\n1.36\u00d710\u22127\n1.15\u00d710\u22127\n2.12\u00d710\u22127\n1.28\u00d710\u22127\nGW190413 134308\nSAA\n6.94\n6.94\n-\n-\n-\n7.40\u00d710\u22128\n2.10\u00d710\u22127\n1.25\u00d710\u22127\nGW190421 213856\n65.97\n40.81\n99.97\n1.38\u00d710\u22127\n1.58\u00d710\u22127\n1.44\u00d710\u22127\n5.02\u00d710\u22128\n2.04\u00d710\u22127\n1.30\u00d710\u22127\nGW190426 190642\n88.70\nSAA\n88.70\n1.10\u00d710\u22127\n2.48\u00d710\u22127\n1.34\u00d710\u22127\n1.09\u00d710\u22127\n2.29\u00d710\u22127\n1.31\u00d710\u22127\nGW190503 185404\n96.59\nSAA\n96.59\n1.32\u00d710\u22127\n1.36\u00d710\u22127\n1.33\u00d710\u22127\n1.25\u00d710\u22127\n1.28\u00d710\u22127\n1.26\u00d710\u22127\nGW190512 180714\n30.95\n0.00\n30.95\n1.65\u00d710\u22127\n1.79\u00d710\u22127\n1.76\u00d710\u22127\n1.54\u00d710\u22127\n1.66\u00d710\u22127\n1.64\u00d710\u22127\nGW190513 205428\n84.97\n0.00\n84.97\n1.07\u00d710\u22127\n1.31\u00d710\u22127\n1.13\u00d710\u22127\n1.06\u00d710\u22127\n1.19\u00d710\u22127\n1.09\u00d710\u22127\nGW190514 065416\n83.33\n68.64\n83.75\n1.09\u00d710\u22127\n3.03\u00d710\u22127\n1.35\u00d710\u22127\n3.89\u00d710\u22128\n2.79\u00d710\u22127\n8.77\u00d710\u22128\nGW190517 055101\n6.81\n4.07\n10.57\n1.32\u00d710\u22127\n1.35\u00d710\u22127\n1.34\u00d710\u22127\n4.41\u00d710\u22128\n1.26\u00d710\u22127\n1.02\u00d710\u22127\nGW190519 153544\n40.53\n0.00\n40.53\n1.13\u00d710\u22127\n1.61\u00d710\u22127\n1.26\u00d710\u22127\n1.06\u00d710\u22127\n1.54\u00d710\u22127\n1.18\u00d710\u22127\nGW190521\n58.61\n61.27\n99.98\n1.64\u00d710\u22127\n3.54\u00d710\u22127\n2.19\u00d710\u22127\n4.20\u00d710\u22128\n3.20\u00d710\u22127\n1.35\u00d710\u22127\nGW190521 074359\n100.00\n0.00\n100.00\n1.20\u00d710\u22127\n1.61\u00d710\u22127\n1.51\u00d710\u22127\n1.16\u00d710\u22127\n1.48\u00d710\u22127\n1.40\u00d710\u22127\nGW190527 092055\n72.51\n0.05\n72.51\n1.14\u00d710\u22127\n3.30\u00d710\u22127\n1.91\u00d710\u22127\n1.10\u00d710\u22127\n2.96\u00d710\u22127\n1.74\u00d710\u22127\nGW190602 175927\n65.84\nSAA\n65.84\n1.53\u00d710\u22127\n2.08\u00d710\u22127\n1.89\u00d710\u22127\n1.51\u00d710\u22127\n1.92\u00d710\u22127\n1.76\u00d710\u22127\nGW190620 030421\nSAA\n4.10\n4.10\n-\n-\n-\n8.21\u00d710\u22128\n1.79\u00d710\u22127\n1.39\u00d710\u22127\nGW190630 185205\n78.32\nSAA\n78.32\n1.17\u00d710\u22127\n2.16\u00d710\u22127\n1.30\u00d710\u22127\n1.08\u00d710\u22127\n1.97\u00d710\u22127\n1.20\u00d710\u22127\nGW190701 203306\n100.00\n99.51\n100.00\n1.27\u00d710\u22127\n1.33\u00d710\u22127\n1.28\u00d710\u22127\n1.01\u00d710\u22127\n1.20\u00d710\u22127\n1.15\u00d710\u22127\nGW190706 222641\n66.90\n12.80\n73.80\n1.03\u00d710\u22127\n2.95\u00d710\u22127\n1.63\u00d710\u22127\n4.66\u00d710\u22128\n2.79\u00d710\u22127\n1.53\u00d710\u22127\nGW190707 093326\n42.31\nSAA\n42.31\n1.38\u00d710\u22127\n2.34\u00d710\u22127\n1.60\u00d710\u22127\n1.30\u00d710\u22127\n2.12\u00d710\u22127\n1.48\u00d710\u22127\nGW190708 232457\n56.01\nSAA\n56.01\n1.28\u00d710\u22127\n4.24\u00d710\u22127\n1.93\u00d710\u22127\n1.22\u00d710\u22127\n3.77\u00d710\u22127\n1.75\u00d710\u22127\nGW190719 215514\n74.97\n15.00\n89.79\n1.17\u00d710\u22127\n3.74\u00d710\u22127\n1.85\u00d710\u22127\n3.65\u00d710\u22128\n3.40\u00d710\u22127\n1.60\u00d710\u22127\nGW190720 000836\n87.90\nSAA\n87.90\n1.08\u00d710\u22127\n2.64\u00d710\u22127\n1.19\u00d710\u22127\n1.01\u00d710\u22127\n2.46\u00d710\u22127\n1.12\u00d710\u22127\nGW190725 174728\nSAA\nSAA\n-\n-\n-\n-\n-\n-\n-\nGW190727 060333\n61.20\n0.01\n61.20\n1.61\u00d710\u22127\n1.93\u00d710\u22127\n1.74\u00d710\u22127\n1.49\u00d710\u22127\n1.72\u00d710\u22127\n1.58\u00d710\u22127\nGW190728 064510\n74.03\n71.13\n74.03\n1.07\u00d710\u22127\n2.36\u00d710\u22127\n1.21\u00d710\u22127\n6.33\u00d710\u22128\n2.28\u00d710\u22127\n9.27\u00d710\u22128\nGW190731 140936\n61.08\n3.17\n61.08\n1.20\u00d710\u22127\n1.99\u00d710\u22127\n1.40\u00d710\u22127\n1.13\u00d710\u22127\n1.88\u00d710\u22127\n1.32\u00d710\u22127\nGW190803 022701\nSAA\n47.43\n47.43\n-\n-\n-\n7.34\u00d710\u22128\n1.47\u00d710\u22127\n1.16\u00d710\u22127\nGW190805 211137\n91.07\n7.64\n98.63\n1.15\u00d710\u22127\n1.60\u00d710\u22127\n1.43\u00d710\u22127\n4.04\u00d710\u22128\n1.48\u00d710\u22127\n1.27\u00d710\u22127\nGW190828 063405\n90.53\n24.93\n90.53\n1.34\u00d710\u22127\n2.01\u00d710\u22127\n1.81\u00d710\u22127\n8.58\u00d710\u22128\n1.83\u00d710\u22127\n1.56\u00d710\u22127\nGW190828 065509\n12.79\n8.82\n12.79\n1.60\u00d710\u22127\n2.98\u00d710\u22127\n2.00\u00d710\u22127\n5.19\u00d710\u22128\n2.67\u00d710\u22127\n1.32\u00d710\u22127\nGW190910 112807\nSAA\n34.37\n34.37\n-\n-\n-\n3.85\u00d710\u22128\n1.77\u00d710\u22127\n8.11\u00d710\u22128\nGW190915 235702\n94.82\n76.04\n94.87\n1.59\u00d710\u22127\n2.15\u00d710\u22127\n1.86\u00d710\u22127\n5.59\u00d710\u22128\n1.74\u00d710\u22127\n1.13\u00d710\u22127\nGW190916 200658\n56.57\n0.00\n56.57\n1.20\u00d710\u22127\n1.61\u00d710\u22127\n1.31\u00d710\u22127\n1.12\u00d710\u22127\n1.42\u00d710\u22127\n1.21\u00d710\u22127\nGW190924 021846\n100.00\n92.40\n100.00\n1.39\u00d710\u22127\n1.61\u00d710\u22127\n1.47\u00d710\u22127\n4.25\u00d710\u22128\n1.43\u00d710\u22127\n8.43\u00d710\u22128\nGW190925 232845\nSAA\nSAA\n-\n-\n-\n-\n-\n-\n-\nGW190926 050336\n60.68\n0.02\n60.68\n1.53\u00d710\u22127\n2.84\u00d710\u22127\n2.10\u00d710\u22127\n1.43\u00d710\u22127\n2.57\u00d710\u22127\n1.88\u00d710\u22127\nGW190929 012149\n73.05\n34.84\n73.05\n1.35\u00d710\u22127\n2.25\u00d710\u22127\n1.75\u00d710\u22127\n4.79\u00d710\u22128\n2.14\u00d710\u22127\n1.59\u00d710\u22127\nGW190930 133541\n63.05\n0.56\n63.05\n1.55\u00d710\u22127\n2.87\u00d710\u22127\n2.39\u00d710\u22127\n1.46\u00d710\u22127\n2.71\u00d710\u22127\n2.25\u00d710\u22127\ncontinued on next page\n\n31\nTable 5 continued.\n3\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\n5\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\nCoverage [%]\n10\u20131000 keV\n15\u2013350 keV\nEvent Name\nGBM\nBAT\nCombined\nMin\nMax\nMarginal\nMin\nMax\nMarginal\nGW191103 012549\n76.96\n56.21\n97.35\n1.57\u00d710\u22127\n3.60\u00d710\u22127\n1.98\u00d710\u22127\n1.25\u00d710\u22127\n3.24\u00d710\u22127\n1.65\u00d710\u22127\nGW191105 143521\n77.45\n8.05\n80.39\n1.35\u00d710\u22127\n2.01\u00d710\u22127\n1.69\u00d710\u22127\n1.06\u00d710\u22127\n1.91\u00d710\u22127\n1.58\u00d710\u22127\nGW191109 010717\n89.38\n29.05\n89.38\n1.29\u00d710\u22127\n2.22\u00d710\u22127\n1.55\u00d710\u22127\n1.25\u00d710\u22127\n2.05\u00d710\u22127\n1.47\u00d710\u22127\nGW191113 071753\n72.98\n2.27\n73.00\n1.53\u00d710\u22127\n2.27\u00d710\u22127\n1.72\u00d710\u22127\n1.45\u00d710\u22127\n2.08\u00d710\u22127\n1.61\u00d710\u22127\nGW191126 115259\n59.81\n7.88\n59.81\n1.12\u00d710\u22127\n2.09\u00d710\u22127\n1.36\u00d710\u22127\n7.09\u00d710\u22128\n1.96\u00d710\u22127\n1.25\u00d710\u22127\nGW191127 050227\n89.03\n77.16\n89.04\n1.12\u00d710\u22127\n2.42\u00d710\u22127\n1.40\u00d710\u22127\n3.94\u00d710\u22128\n2.23\u00d710\u22127\n8.96\u00d710\u22128\nGW191129 134029\nSAA\nSAA\n-\n-\n-\n-\n-\n-\n-\nGW191204 110529\n48.10\n25.20\n66.23\n1.09\u00d710\u22127\n2.77\u00d710\u22127\n1.42\u00d710\u22127\n3.10\u00d710\u22128\n1.43\u00d710\u22127\n1.07\u00d710\u22127\nGW191204 171526\nSAA\n87.15\n87.15\n-\n-\n-\n2.02\u00d710\u22127\n9.13\u00d710\u22127\n3.97\u00d710\u22127\nGW191215 223052\n51.87\n21.09\n51.87\n1.41\u00d710\u22127\n1.69\u00d710\u22127\n1.53\u00d710\u22127\n4.40\u00d710\u22128\n1.55\u00d710\u22127\n1.29\u00d710\u22127\nGW191216 213338\n94.70\n1.76\n94.76\n1.40\u00d710\u22127\n1.64\u00d710\u22127\n1.48\u00d710\u22127\n1.26\u00d710\u22127\n1.50\u00d710\u22127\n1.33\u00d710\u22127\nGW191222 033537\nSAA\n0.89\n0.89\n-\n-\n-\n1.84\u00d710\u22127\n1.92\u00d710\u22127\n1.89\u00d710\u22127\nGW191230 180458\n40.80\n0.00\n40.80\n1.09\u00d710\u22127\n1.72\u00d710\u22127\n1.39\u00d710\u22127\n1.09\u00d710\u22127\n1.60\u00d710\u22127\n1.33\u00d710\u22127\nGW200112 155838\nSAA\nSAA\n-\n-\n-\n-\n-\n-\n-\nGW200128 022011\n45.58\n23.04\n45.58\n1.22\u00d710\u22127\n3.08\u00d710\u22127\n1.42\u00d710\u22127\n3.29\u00d710\u22128\n2.83\u00d710\u22127\n1.07\u00d710\u22127\nGW200129 065458\n1.36\n1.16\n1.36\n-\n-\n1.42\u00d710\u22127\n-\n-\n6.49\u00d710\u22128\nGW200202 154313\n99.99\nSAA\n99.99\n1.18\u00d710\u22127\n1.26\u00d710\u22127\n1.21\u00d710\u22127\n1.10\u00d710\u22127\n1.18\u00d710\u22127\n1.14\u00d710\u22127\nGW200208 130117\n99.70\n0.00\n99.70\n1.33\u00d710\u22127\n1.36\u00d710\u22127\n1.36\u00d710\u22127\n1.22\u00d710\u22127\n1.25\u00d710\u22127\n1.25\u00d710\u22127\nGW200208 222617\nSAA\n5.85\n5.85\n-\n-\n-\n6.09\u00d710\u22128\n1.77\u00d710\u22127\n1.06\u00d710\u22127\nGW200209 085452\n61.47\n7.05\n61.63\n1.27\u00d710\u22127\n1.69\u00d710\u22127\n1.35\u00d710\u22127\n3.71\u00d710\u22128\n1.28\u00d710\u22127\n1.17\u00d710\u22127\nGW200216 220804\nSAA\n38.42\n38.42\n-\n-\n-\n8.98\u00d710\u22128\n1.71\u00d710\u22127\n1.47\u00d710\u22127\nGW200219 094415\n20.36\nSAA\n20.36\n1.37\u00d710\u22127\n1.73\u00d710\u22127\n1.52\u00d710\u22127\n1.29\u00d710\u22127\n1.58\u00d710\u22127\n1.41\u00d710\u22127\nGW200220 061928\n99.63\n0.05\n99.65\n1.33\u00d710\u22127\n2.12\u00d710\u22127\n1.65\u00d710\u22127\n1.22\u00d710\u22127\n1.87\u00d710\u22127\n1.48\u00d710\u22127\nGW200220 124850\n63.37\n21.46\n80.25\n1.10\u00d710\u22127\n2.34\u00d710\u22127\n1.28\u00d710\u22127\n3.07\u00d710\u22128\n2.18\u00d710\u22127\n1.10\u00d710\u22127\nGW200224 222234\nSAA\n98.76\n98.76\n-\n-\n-\n1.13\u00d710\u22127\n1.40\u00d710\u22127\n1.27\u00d710\u22127\nGW200225 060421\n87.61\n1.30\n87.61\n1.37\u00d710\u22127\n3.32\u00d710\u22127\n2.36\u00d710\u22127\n1.28\u00d710\u22127\n3.10\u00d710\u22127\n2.23\u00d710\u22127\nGW200302 015811\n67.41\n23.35\n67.92\n1.04\u00d710\u22127\n3.40\u00d710\u22127\n1.62\u00d710\u22127\n3.27\u00d710\u22128\n1.77\u00d710\u22127\n1.19\u00d710\u22127\nGW200306 093714\n72.37\n30.46\n90.36\n1.18\u00d710\u22127\n2.54\u00d710\u22127\n1.46\u00d710\u22127\n5.38\u00d710\u22128\n2.40\u00d710\u22127\n1.33\u00d710\u22127\nGW200308 173609\n70.53\n4.40\n70.89\n1.19\u00d710\u22127\n3.39\u00d710\u22127\n1.92\u00d710\u22127\n8.13\u00d710\u22128\n3.20\u00d710\u22127\n1.77\u00d710\u22127\nGW200311 115853\nSAA\nN/A\n-\n-\n-\n-\n-\n-\n-\nGW200316 215756\n15.69\n13.49\n15.69\n1.14\u00d710\u22127\n1.51\u00d710\u22127\n1.34\u00d710\u22127\n1.09\u00d710\u22127\n1.36\u00d710\u22127\n1.22\u00d710\u22127\nGW200322 091133\n75.18\n13.82\n89.00\n1.06\u00d710\u22127\n3.70\u00d710\u22127\n1.54\u00d710\u22127\n4.49\u00d710\u22128\n3.38\u00d710\u22127\n1.39\u00d710\u22127\nselleria de Fons Europeus, Universitat i Cultura and the\nDirecci\u00b4o General de Pol\u00b4\u0131tica Universitaria i Recerca del\nGovern de les Illes Balears, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the National Science Centre\nof Poland and the European Union \u2013 European Re-\ngional Development Fund; Foundation for Polish Science\n(FNP), the Swiss National Science Foundation (SNSF),\nthe Russian Foundation for Basic Research, the Rus-\nsian Science Foundation, the European Commission,\nthe European Social Funds (ESF), the European Re-\ngional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scientific Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scientifique\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the\nNational Research, Development and Innovation Office\nHungary (NKFIH), the National Research Foundation\nof Korea, the Natural Science and Engineering Research\nCouncil Canada, Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoreti-\n\n32\nTable 6. Flux upper limits for possible EM counterparts to marginal GW candidates with (FAR < 2 yr\u22121, pastro < 0.5). The\n3\u03c3 upper limits are computed for the 10\u20131000 keV energy range over the FoV of Fermi-GBM. The 5\u03c3 upper limits are computed\nfor the combined coverage of Fermi-GBM and Swift-BAT with both instruments matched to the 15\u2013350 keV energy range of\nSwift-BAT. The columns labeled Min and Max correspond, respectively, to the minimum and maximum upper limits obtained\nfor points within the 90% credible level of the GW candidate localization. The Marginal upper limit is computed by integrating\nthe upper limits produced at individual locations over the full sky using the GW localization as a weighted prior, normalized to\nthe visible portion of the sky. Also shown is the visible coverage percentage of the full GW localization for Fermi-GBM alone,\nSwift-BAT alone, and the combined FoV from both instruments.\n3\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\n5\u03c3 Flux U.L. [erg s\u22121 cm\u22122]\nCoverage [%]\n10\u20131000 keV\n15\u2013350 keV\nEvent Name\nGBM\nBAT\nCombined\nMin\nMax\nMarginal\nMin\nMax\nMarginal\nGW190426 152155\n100.00\nSAA\n100.00\n1.03\u00d710\u22127\n1.65\u00d710\u22127\n1.30\u00d710\u22127\n1.00\u00d710\u22127\n1.53\u00d710\u22127\n1.21\u00d710\u22127\nGW190531 023648\n86.90\n0.03\n86.91\n1.35\u00d710\u22127\n2.63\u00d710\u22127\n1.74\u00d710\u22127\n1.26\u00d710\u22127\n2.42\u00d710\u22127\n1.60\u00d710\u22127\nGW191118 212859\n93.63\nSAA\n93.63\n1.07\u00d710\u22127\n2.93\u00d710\u22127\n1.19\u00d710\u22127\n1.05\u00d710\u22127\n2.71\u00d710\u22127\n1.13\u00d710\u22127\nGW200105 162426\n53.57\n3.01\n54.36\n1.13\u00d710\u22127\n1.53\u00d710\u22127\n1.26\u00d710\u22127\n1.06\u00d710\u22127\n1.69\u00d710\u22127\n1.18\u00d710\u22127\nGW200201 203549\n86.01\nSAA\n86.01\n1.17\u00d710\u22127\n1.80\u00d710\u22127\n1.31\u00d710\u22127\n1.09\u00d710\u22127\n1.64\u00d710\u22127\n1.22\u00d710\u22127\nGW200311 103121\nSAA\n0.01\n0.01\n-\n-\n-\n-\n-\n1.09\u00d710\u22127\ncal Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council\nof Hong Kong, the National Natural Science Founda-\ntion of China (NSFC), the Leverhulme Trust, the Re-\nsearch Corporation, the National Science and Technol-\nogy Council (NSTC), Taiwan, the United States De-\npartment of Energy, and the Kavli Foundation.\nThe\nauthors gratefully acknowledge the support of the NSF,\nSTFC, INFN and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-inAid for Scientific Research on Innovative Ar-\neas 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grantin-Aid for Scientific Research (S)\n17H06133 and 20H05639 , JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203:\nJP20H05854,\nthe joint research program of the Institute for Cos-\nmic Ray Research, University of Tokyo, National Re-\nsearch Foundation (NRF), Computing Infrastructure\nProject of Global Science experimental Data hub Cen-\nter (GSDC) at KISTI, Korea Astronomy and Space\nScience Institute (KASI), and Ministry of Science and\nICT (MSIT) in Korea, Academia Sinica (AS), AS Grid\nCenter (ASGC) and the National Science and Technol-\nogy Council (NSTC) in Taiwan under grants includ-\ning the Rising Star Program and Science Vanguard Re-\nsearch Program, Advanced Technology Center (ATC) of\nNAOJ, and Mechanical Engineering Center of KEK.\nAdditional LSC-Virgo-KAGRA acknowledgements for\nsupport of individual authors may be found in the fol-\nlowing document:\nhttps://dcc.ligo.org/LIGO-M2300033/public.\nREFERENCES\nAasi, J., Abbott, B. 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They assume the spectral shape of potential emission\nfollows the normal spectral template from Table 3 with a 1 s emission duration.\n\n36\nName\nWaveform (visible frac.)\nFQ\nF\u03bd\u00af\u03bd\nFBZ\nFGW\nUL\nGW190403 051519\nIMRPhenomXPHM (49, 36)\n74, 70, 67\n7.3, 6.7, 6.4\n7.3, 5.8, 5.6\n2.5, 1.8, 1.7\n178\nGW190403 051519\nSEOBNRv4PHM (39, 30)\n44, 35, 35\n5.0, 4.0, 3.8\n6.5, 4.6, 4.5\n3.4, 1.9, 1.7\n178\nGW190412\nIMRPhenomXPHM (6, 0)\n*137, 83, 95\n*299, 165, 173\n59, 30, 25\n64, 28, 22\n111\nGW190412\nSEOBNRv4PHM (12, 4)\n*148, 85, 82\n*356, 178, 172\n48, 25, 23\n70, 29, 25\n111\nGW190413 052954\nIMRPhenomXPHM (30, 19)\n11, 5.8, 5.2\n10, 5.7, 5.2\n10, 4.4, 4.0\n10, 4.2, 3.6\n136\nGW190421 213856\nIMRPhenomXPHM (23, 14)\n21, 8.1, 7.5\n14, 6.1, 5.8\n36, 13, 12\n27, 10, 9.6\n144\nGW190426 190642\nIMRPhenomXPHM (22, 14)\n32, 31, 29\n2.7, 2.3, 2.1\n75, 24, 22\n26, 8.0, 7.1\n134\nGW190503 185404\nIMRPhenomXPHM (30, 20)\n50, 20, 18\n38, 16, 15\n68, 29, 28\n54, 20, 18\n133\nGW190503 185404\nSEOBNRv4PHM (25, 16)\n42, 22, 21\n32, 17, 16\n53, 25, 24\n44, 19, 18\n133\nGW190512 180714\nIMRPhenomXPHM (27, 17)\n49, 24, 24\n107, 55, 54\n20, 7.2, 6.6\n28, 10, 9.2\n176\nGW190512 180714\nSEOBNRv4PHM (22, 13)\n45, 18, 17\n104, 46, 43\n18, 6.1, 5.2\n28, 9.5, 8.2\n176\nGW190513 205428\nIMRPhenomXPHM (31, 19)\n42, 24, 23\n35, 21, 20\n16, 9.2, 8.4\n17, 8.2, 7.5\n113\nGW190513 205428\nSEOBNRv4PHM (30, 19)\n52, 26, 24\n36, 20, 19\n15, 8.3, 7.9\n17, 8.0, 7.0\n113\nGW190514 065416\nIMRPhenomXPHM (24, 15)\n12, 5.1, 4.8\n7.8, 3.8, 3.7\n21, 8.7, 7.3\n14, 6.0, 5.4\n135\nGW190514 065416\nSEOBNRv4PHM (21, 13)\n12, 6.9, 6.1\n7.5, 4.4, 4.2\n17, 8.0, 7.8\n12, 6.0, 5.5\n135\nGW190517 055101\nIMRPhenomXPHM (10, 5)\n*485, 198, 173\n*202, 85, 74\n48, 10, 7.9\n60, 18, 14\n134\nGW190517 055101\nSEOBNRv4PHM (14, 8)\n*360, 171, 145\n*142, 70, 62\n29, 9.3, 7.6\n53, 16, 14\n134\nGW190519 153544\nIMRPhenomXPHM (6, 3)\n49, 19, 19\n14, 6.1, 5.8\n47, 12, 9.7\n32, 7.1, 5.5\n126\nGW190519 153544\nSEOBNRv4PHM (5, 2)\n49, 21, 17\n12, 6.3, 4.9\n38, 17, 14\n26, 9.6, 7.7\n126\nGW190521 074359\nIMRPhenomXPHM (7, 3)\n*222, 58, 49\n142, 44, 38\n*259, 76, 69\n*228, 65, 57\n151\nGW190521 074359\nSEOBNRv4PHM (25, 14)\n*99, 51, 47\n62, 31, 29\n*94, 37, 35\n*87, 35, 31\n151\nGW190521\nIMRPhenomXPHM (19, 11)\n15, 3.4, 3.2\n2.9, 0.77, 0.72\n121, 21, 18\n38, 6.9, 5.9\n219\nGW190527 092055\nIMRPhenomXPHM (21, 13)\n44, 16, 15\n31, 14, 13\n27, 13, 12\n23, 9.5, 8.7\n191\nGW190527 092055\nSEOBNRv4PHM (22, 14)\n34, 16, 15\n29, 15, 14\n23, 10, 9.7\n24, 10, 10\n191\nGW190602 175927\nIMRPhenomXPHM (31, 20)\n24, 14, 13\n6.8, 4.2, 3.9\n61, 33, 32\n29, 13, 12\n189\nGW190630 185205\nIMRPhenomXPHM (21, 14)\n*225, 75, 70\n*215, 78, 73\n145, 56, 51\n167, 56, 51\n130\nGW190630 185205\nSEOBNRv4PHM (26, 18)\n*195, 93, 88\n*185, 89, 83\n131, 56, 53\n145, 60, 57\n130\nGW190701 203306\nIMRPhenomXPHM (32, 20)\n20, 11, 10\n10, 6.0, 5.5\n51, 26, 24\n31, 15, 13\n128\nGW190701 203306\nSEOBNRv4PHM (35, 23)\n21, 14, 14\n9.7, 6.9, 6.7\n48, 29, 26\n29, 16, 15\n128\nGW190706 222641\nIMRPhenomXPHM (20, 12)\n53, 37, 34\n11, 8.4, 8.2\n63, 43, 40\n31, 19, 18\n163\nGW190706 222641\nSEOBNRv4PHM (19, 10)\n41, 27, 29\n9.1, 6.9, 7.5\n62, 44, 46\n33, 22, 23\n163\nGW190707 093326\nIMRPhenomXPHM (37, 26)\n174, 114, 109\n*961, 632, 602\n21, 13, 12\n63, 38, 35\n160\nGW190707 093326\nSEOBNRv4PHM (31, 20)\n151, 76, 70\n*821, 429, 389\n20, 9.8, 8.9\n57, 27, 24\n160\nGW190708 232457\nIMRPhenomXPHM (39, 26)\n152, 96, 91\n*415, 260, 248\n35, 20, 18\n70, 39, 36\n193\nGW190708 232457\nSEOBNRv4PHM (36, 25)\n125, 74, 72\n*338, 203, 197\n37, 19, 19\n64, 34, 34\n193\nGW190719 215514\nIMRPhenomXPHM (25, 16)\n51, 29, 28\n25, 13, 13\n16, 10, 9.2\n14, 7.2, 6.4\n185\nGW190720 000836\nIMRPhenomXPHM (44, 32)\n*261, 234, 266\n*1054, 759, 785\n19, 12, 12\n54, 28, 26\n119\nGW190720 000836\nSEOBNRv4PHM (35, 24)\n*194, 126, 119\n*852, 555, 515\n19, 11, 10\n51, 28, 26\n119\nGW190727 060333\nIMRPhenomXPHM (30, 19)\n23, 11, 10\n14, 7.8, 7.3\n16, 6.8, 6.1\n15, 6.1, 5.4\n174\nGW190727 060333\nSEOBNRv4PHM (25, 16)\n21, 12, 11\n12, 7.8, 7.3\n14, 6.8, 6.3\n14, 6.1, 5.6\n174\nGW190728 064510\nIMRPhenomXPHM (32, 21)\n*253, 125, 125\n*1130, 462, 459\n21, 8.4, 7.6\n58, 17, 15\n121\nGW190728 064510\nSEOBNRv4PHM (30, 19)\n*208, 79, 75\n*1015, 408, 388\n17, 6.0, 5.6\n54, 18, 16\n121\nGW190731 140936\nIMRPhenomXPHM (28, 18)\n20, 11, 10\n12, 7.4, 6.8\n24, 11, 10\n19, 9.3, 8.7\n140\nGW190731 140936\nSEOBNRv4PHM (27, 18)\n26, 17, 16\n13, 9.4, 9.1\n24, 12, 10\n20, 11, 9.9\n140\nGW190805 211137\nIMRPhenomXPHM (22, 14)\n28, 13, 12\n8.7, 4.8, 4.6\n7.4, 2.2, 1.9\n7.3, 2.2, 1.9\n143\nGW190805 211137\nSEOBNRv4PHM (18, 11)\n21, 13, 13\n6.6, 4.7, 4.8\n7.9, 2.6, 2.2\n6.9, 2.4, 2.3\n143\nTable 7. Table showing the 0.95 percentile fluxes from different models of BBH emission. The two numbers after the waveform\nnames indicate the percentage of the cases where the jet is pointing towards Earth in the uniform 10-40 degree opening angle\nand in the fixed 20 degrees opening angle case respectively. Flux units are 10\u22129 erg cm\u22122 s\u22121. The three numbers in each cell\nrepresent the isotropic emission, the uniform-distributed jet opening angle and the fixed jet opening angle. The upper limits\n(UL) are the 3\u03c3, 10\u20131000 keV range values from Table 5. Stars mark instances where the isotropic emission exceeds the UL in\nmore than 10% of the cases.\n\n37\nName\nWaveform (visible frac.)\nFQ\nF\u03bd\u00af\u03bd\nFBZ\nFGW\nUL\nGW190828 063405\nIMRPhenomXPHM (31, 21)\n58, 25, 23\n48, 22, 21\n27, 7.7, 6.8\n33, 9.9, 8.5\n181\nGW190828 065509\nIMRPhenomXPHM (22, 12)\n43, 19, 18\n103, 48, 44\n16, 6.4, 5.4\n23, 7.6, 6.3\n200\nGW190915 235702\nIMRPhenomXPHM (18, 10)\n39, 17, 14\n37, 18, 16\n28, 11, 10\n29, 11, 10\n186\nGW190915 235702\nSEOBNRv4PHM (20, 12)\n42, 25, 24\n39, 23, 22\n31, 12, 10\n32, 13, 11\n186\nGW190916 200658\nIMRPhenomXPHM (28, 18)\n13, 6.6, 6.2\n6.8, 3.5, 3.2\n8.4, 4.0, 3.6\n6.7, 2.3, 2.0\n131\nGW190916 200658\nSEOBNRv4PHM (25, 16)\n12, 6.1, 6.0\n6.1, 3.4, 3.4\n8.4, 4.9, 4.2\n5.9, 2.4, 2.2\n131\nGW190924 021846\nIMRPhenomXPHM (32, 22)\n*351, 258, 281\n*3217, 1887, 1884\n21, 12, 12\n78, 31, 28\n147\nGW190924 021846\nSEOBNRv4PHM (25, 16)\n*317, 131, 120\n*3158, 1364, 1253\n17, 6.4, 5.8\n75, 28, 25\n147\nGW190926 050336\nIMRPhenomXPHM (10, 6)\n14, 2.9, 2.6\n11, 3.3, 3.0\n21, 3.9, 3.5\n13, 2.5, 2.2\n210\nGW190929 012149\nIMRPhenomXPHM (9, 5)\n12, 2.8, 2.6\n4.9, 1.5, 1.4\n34, 14, 12\n14, 4.3, 3.7\n175\nGW190930 133541\nIMRPhenomXPHM (34, 23)\n*363, 236, 252\n*1483, 790, 776\n23, 12, 12\n69, 26, 23\n239\nGW190930 133541\nSEOBNRv4PHM (32, 21)\n*264, 141, 136\n*1086, 566, 534\n24, 11, 11\n60, 26, 24\n239\nGW191103 012549\nIMRPhenomXPHM (34, 23)\n*332, 234, 230\n*1349, 831, 801\n15, 9.3, 8.6\n53, 27, 24\n198\nGW191103 012549\nSEOBNRv4PHM (27, 18)\n*303, 164, 158\n*1355, 764, 710\n16, 8.6, 8.3\n58, 28, 26\n198\nGW191105 143521\nIMRPhenomXPHM (35, 24)\n86, 43, 42\n*509, 262, 247\n8.5, 3.5, 3.3\n26, 10, 9.5\n169\nGW191105 143521\nSEOBNRv4PHM (27, 17)\n84, 35, 31\n*509, 229, 208\n8.3, 3.0, 2.7\n26, 9.8, 8.6\n169\nGW191109 010717\nIMRPhenomXPHM (5, 2)\n169, 11, 10\n43, 5.5, 5.0\n*437, 54, 43\n217, 27, 22\n155\nGW191109 010717\nSEOBNRv4PHM (16, 10)\n47, 24, 22\n16, 10.0, 9.5\n*198, 113, 102\n89, 50, 43\n155\nGW191113 071753\nIMRPhenomXPHM (15, 8)\n35, 20, 20\n86, 53, 51\n25, 8.3, 7.3\n16, 5.9, 5.3\n172\nGW191113 071753\nSEOBNRv4PHM (15, 9)\n74, 42, 35\n118, 72, 62\n17, 8.6, 8.0\n14, 6.3, 5.7\n172\nGW191126 115259\nIMRPhenomXPHM (36, 25)\n103, 68, 68\n*394, 252, 244\n5.6, 2.9, 2.7\n18, 9.1, 8.4\n136\nGW191126 115259\nSEOBNRv4PHM (28, 18)\n104, 58, 52\n*419, 234, 214\n6.5, 3.1, 2.7\n21, 9.8, 8.8\n136\nGW191127 050227\nIMRPhenomXPHM (29, 19)\n59, 58, 61\n15, 11, 11\n48, 44, 41\n11, 8.8, 8.8\n140\nGW191127 050227\nSEOBNRv4PHM (17, 10)\n32, 15, 16\n16, 7.4, 7.1\n20, 10, 11\n13, 4.8, 4.5\n140\nGW191204 110529\nIMRPhenomXPHM (22, 13)\n107, 56, 51\n118, 68, 64\n46, 26, 25\n57, 32, 30\n142\nGW191204 110529\nSEOBNRv4PHM (15, 9)\n119, 78, 70\n121, 84, 82\n42, 29, 31\n55, 35, 36\n142\nGW191215 223052\nIMRPhenomXPHM (15, 8)\n34, 14, 11\n54, 22, 18\n19, 5.2, 4.1\n25, 6.5, 5.4\n153\nGW191215 223052\nSEOBNRv4PHM (14, 8)\n31, 13, 12\n49, 21, 19\n17, 4.9, 4.3\n22, 6.7, 5.8\n153\nGW191216 213338\nIMRPhenomXPHM (31, 19)\n*1097, 696, 684\n*5893, 3599, 3466\n96, 60, 54\n*287, 152, 140\n148\nGW191216 213338\nSEOBNRv4PHM (25, 15)\n*1180, 586, 545\n*6516, 3304, 3024\n93, 45, 40\n*311, 150, 135\n148\nGW191230 180458\nIMRPhenomXPHM (21, 13)\n10, 3.2, 2.9\n4.6, 1.8, 1.7\n18, 5.5, 4.9\n11, 3.5, 3.1\n139\nGW191230 180458\nSEOBNRv4PHM (23, 14)\n8.4, 4.2, 4.1\n3.8, 2.1, 2.1\n14, 5.1, 4.5\n9.3, 3.5, 3.0\n139\nGW200128 022011\nIMRPhenomXPHM (20, 12)\n35, 13, 11\n18, 8.1, 7.0\n32, 11, 9.8\n27, 9.5, 8.3\n142\nGW200128 022011\nSEOBNRv4PHM (26, 15)\n36, 29, 21\n15, 13, 9.6\n26, 18, 11\n23, 17, 10\n142\nGW200129 065458\nIMRPhenomXPHM (33, 18)\n*220, 149, 145\n170, 108, 105\n113, 64, 59\n128, 62, 57\n142\nGW200129 065458\nSEOBNRv4PHM (18, 9)\n*235, 108, 103\n211, 96, 88\n165, 60, 59\n188, 75, 71\n142\nGW200202 154313\nIMRPhenomXPHM (37, 25)\n*666, 364, 350\n*4383, 2342, 2214\n50, 23, 21\n*174, 78, 71\n121\nGW200202 154313\nSEOBNRv4PHM (32, 21)\n*703, 330, 300\n*4700, 2248, 2051\n50, 22, 20\n*185, 80, 72\n121\nGW200208 130117\nIMRPhenomXPHM (31, 20)\n18, 9.3, 8.4\n16, 8.7, 7.9\n25, 11, 9.6\n21, 9.3, 7.8\n136\nGW200208 130117\nSEOBNRv4PHM (31, 20)\n17, 11, 11\n14, 9.8, 9.2\n22, 11, 10\n19, 10, 9.0\n136\nGW200209 085452\nIMRPhenomXPHM (22, 13)\n21, 4.4, 4.0\n16, 4.6, 4.3\n25, 4.8, 4.2\n21, 4.4, 4.0\n135\nGW200209 085452\nSEOBNRv4PHM (22, 14)\n10, 5.7, 5.6\n8.4, 4.9, 4.8\n12, 4.5, 3.9\n10, 4.0, 3.7\n135\nGW200219 094415\nIMRPhenomXPHM (18, 11)\n11, 3.1, 2.7\n8.9, 3.1, 2.8\n16, 3.6, 3.2\n13, 3.2, 2.7\n152\nGW200219 094415\nSEOBNRv4PHM (22, 14)\n10, 4.9, 4.6\n7.7, 3.9, 3.7\n11, 4.1, 3.8\n9.7, 3.4, 3.2\n152\nGW200220 061928\nIMRPhenomXPHM (22, 14)\n8.3, 3.3, 3.1\n1.3, 0.63, 0.61\n52, 11, 10\n12, 4.1, 3.4\n165\nGW200220 061928\nSEOBNRv4PHM (22, 14)\n10, 6.2, 5.3\n1.4, 0.88, 0.8\n34, 12, 10\n12, 4.6, 4.1\n165\nGW200220 124850\nIMRPhenomXPHM (20, 13)\n13, 4.4, 4.3\n8.8, 3.6, 3.5\n16, 6.3, 6.0\n12, 5.0, 4.8\n128\nGW200220 124850\nSEOBNRv4PHM (17, 12)\n11, 4.8, 5.3\n8.0, 3.8, 3.9\n18, 6.2, 7.5\n13, 4.9, 5.5\n128\nTable 7 continued.\n\n38\nName\nWaveform (visible frac.)\nFQ\nF\u03bd\u00af\u03bd\nFBZ\nFGW\nUL\nGW200225 060421\nIMRPhenomXPHM (16, 8)\n97, 45, 40\n224, 114, 107\n33, 16, 14\n53, 26, 24\n236\nGW200225 060421\nSEOBNRv4PHM (22, 13)\n71, 43, 47\n174, 97, 102\n25, 12, 12\n43, 18, 20\n236\nGW200302 015811\nIMRPhenomXPHM (15, 8)\n62, 27, 26\n60, 29, 29\n62, 27, 26\n53, 23, 22\n162\nGW200302 015811\nSEOBNRv4PHM (20, 12)\n66, 35, 35\n58, 30, 30\n54, 22, 21\n48, 20, 18\n162\nGW200306 093714\nIMRPhenomXPHM (28, 18)\n133, 73, 67\n113, 60, 56\n19, 10, 9.7\n24, 9.9, 9.1\n146\nGW200306 093714\nSEOBNRv4PHM (25, 16)\n132, 86, 82\n102, 63, 61\n20, 9.3, 8.1\n23, 10, 9.5\n146\nGW200308 173609\nIMRPhenomXPHM (18, 11)\n51, 55, 51\n24, 24, 22\n74, 19, 12\n7.3, 2.2, 2.2\n192\nGW200308 173609\nSEOBNRv4PHM (14, 8)\n71, 66, 67\n32, 26, 25\n13, 2.8, 3.3\n4.7, 2.1, 2.1\n192\nGW200316 215756\nIMRPhenomXPHM (21, 11)\n112, 68, 62\n*482, 258, 237\n13, 6.3, 5.3\n29, 10, 9.2\n134\nGW200316 215756\nSEOBNRv4PHM (24, 15)\n103, 45, 41\n*484, 223, 205\n10, 3.6, 3.2\n28, 10, 9.1\n134\nGW200322 091133\nIMRPhenomXPHM (14, 9)\n147, 476, 499\n72, 58, 64\n42, 26, 27\n8.7, 3.3, 3.7\n154\nGW200322 091133\nSEOBNRv4PHM (4, 4)\n3.7, 3.3, 0.22\n2.0, 0.45, 0.17\n4.8, 0.48, 0.37\n0.77, 0.27, 0.26\n154\nTable 7 continued.\n", "The Physics of the B Factories\n\nii\nForeword\n\u201cThe Physics of the B Factories\u201d describes a decade long\ne\ufb00ort of physicists in the quest for the precise determina-\ntion of asymmetry \u2014 broken symmetry \u2014 between par-\nticles and anti-particles. We now recognize that the mat-\nter we see around us is the residue \u2014 one part in a bil-\nlion \u2014 of the matter and antimatter that existed in the\nearly universe, most of which annihilated into the cosmic\nbackground radiation that bathes us. But the question re-\nmains: how did the baryonic matter-antimatter asymme-\ntry arise? This book describes the work done by some 1000\nphysicists and engineers from around the globe on two\nexperimental facilities built to test our understanding of\nthis phenomenon, one at the SLAC National Accelerator\nLaboratory in California, USA, and a second at the KEK\nLaboratory, Tsukuba, Japan, and what we have learned\nfrom them in broadening our understanding of nature.\nWhy is our universe dominated by the matter of which\nwe are made rather than equal parts of matter and anti-\nmatter? This question has puzzled physicists for decades.\nHowever, this was not the question we addressed when we\nwrote the paper on CP violation in 1972. Our question\nwas whether we can explain the CP violation observed in\nthe K meson decay within the framework of the renor-\nmalizable gauge theory. At that time, Sakharov\u2019s seminal\npaper was already published, but it did not attract our\nattention. If we were aware of the paper, we would have\nbeen misled into seeking a model satisfying Sakharov\u2019s\nconditions and our paper might not have appeared.\nIn our paper, we discussed that we need new parti-\ncles in order to accommodate CP violation into the renor-\nmalizable electroweak theory, and proposed the six-quark\nscheme as one of the possible ways introducing new parti-\ncles. We thought that the six-quark scheme is very inter-\nesting, but it was just a possibility. The situation changed\nwhen the tau-lepton was found and it was followed by\nthe discovery of the Upsilon particle. The existence of\nthe third generation became reality. However, it was still\nuncertain whether the mixing of the six quarks is a real\norigin of the observed CP violation. Theoretical calcula-\ntion of CP asymmetries in the neutral K meson system\ncontains uncertainty from strong interaction e\ufb00ects. What\nsettled this problem were the B Factories built at SLAC\nand KEK.\nThese B Factories are extraordinary in many ways. In\norder to ful\ufb01ll the requirements of special experiments, the\nbeam energies of the colliding electron and positron are\nasymmetric, and the luminosity is unprecedentedly high.\nIt is also remarkable that severe competition between the\ntwo laboratories boosted their performance. One of us (M.\nKobayashi) has been watching the development at KEK\nvery closely as the director of the Institute of Particle and\nNuclear Studies of KEK for a period of time. As witnesses,\nwe appreciate the amazing achievement of those who par-\nticipated in these projects at both laboratories.\nThe B Factories have contributed a great deal to our\nunderstanding of particle physics, as documented in this\nbook. In particular, thanks to the high luminosity far ex-\nceeding the design value, experimental groups measured\nmixing angles precisely and veri\ufb01ed that the dominant\nsource of CP violation observed in the laboratory exper-\niments is \ufb02avor mixing among the three generations of\nquarks. Obviously we owe our Nobel Prize to this result.\nNow we are awaiting the operation of the next-\ngeneration Super B Factories. In spite of its great suc-\ncess, the Standard Model is not an ultimate theory. For\nexample, it is not thought to be possible for the matter\ndominance of the universe to be explained by the Stan-\ndard Model. This means that there will still be unknown\nparticles and unknown interactions. We have a lot of the-\noretical speculations but experimental means are rather\nlimited. There are great expectations for the Super B Fac-\ntories to reveal a clue to the world beyond the Standard\nModel.\nMakoto Kobayashi\nHonorary Professor Emeritus\nKEK\nToshihide Maskawa\nDirector General\nKobayashi-Maskawa Institute for the Origin of Particles\nand the Universe\nNagoya University\n\niii\nPreface\nThe inspiration for this book came from Fran\u00b8cois le Diberder.\nDuring his term as spokesperson for BABAR he laid down\na vision for the two B Factory detector collaborations,\nBABAR and Belle, to work together on a book that would\ndescribe the methodologies used and physics results ob-\ntained by those experiments. A key ideal emphasized from\nthe outset was that this book should be written from a\npedagogical perspective; it should be of interest to the\nstudent and expert alike. This vision was presented dur-\ning a BABAR collaboration meeting on the island of Elba\nin May 2008 and a follow up Belle collaboration meeting\nat KEK, with visiting colleagues from the BABAR collab-\noration, and was embraced by the community. A number\nof workshops involving people from the theoretical com-\nmunity as well as the two collaborations were held on four\ncontinents over the following years. The resulting book,\n\u201cThe Physics of the B Factories\u201d, is a testament to the\nway that this concept captured the zeitgeist on both sides\nof the Paci\ufb01c Ocean.\nThis book is divided into three parts, the \ufb01rst of which\nprovides a brief description of the B Factories, including\na short (though not exhaustive) historical perspective, as\nwell as descriptions of the detectors, ancillary data acqui-\nsition systems and data (re)processing systems that were\nbuilt by the two detector collaborations in the late 1990\u2019s.\nThe second part of the book discusses tools and meth-\nods that are frequently used when analyzing the data col-\nlected. These range from details of low level reconstruction\nalgorithms and abstract summaries of statistical methods\nto high level prescriptions used when evaluating system-\natic uncertainties on measurements of observables. The\nthird part of the book is devoted to physics results. This\nincludes su\ufb03cient theoretical discussion in order for the\nreader to understand the context of the work being de-\nscribed. We are indebted to our colleagues from the the-\noretical community who have helped us achieve our goal\nof explaining the physics of the B Factories in a broader\ncontext.\nIt should be noted that both B Factory experiments\nare still actively publishing results and as a result the work\npresented here is a snapshot of the output of the B Fac-\ntories up to some point in time. Where appropriate, mea-\nsurements from other experiments have been mentioned,\nhowever the focus of this book is on the output of the B\nFactories. As a result, any brief description of important\nwork by others should be interpreted as a suggestion for\nfurther reading on a given topic.\nJust as there are two B Factories, many of the observ-\nables studied or used in this book have a dual notation in\nthe literature. While preparing this book we have placed\nthe emphasis on the physics rather than trivialities such as\nconvention. The most notable instance of this issue found\nhere is that of the nomenclature used for the angles of\nthe Unitarity Triangle. In order to retain a pedagogical\napproach we chose a method for selecting between the\ntwo notations that is symbolic of their equivalence from\nthe perspective of physics. This choice was decided on the\noutcome of a coin \ufb02ip.\nIt has been a privilege for us to work with our col-\nleagues from the experimental and theoretical communi-\nties while compiling this book. The journey of preparing\nthis tome has been as rewarding as being a part of the\nindividual collaborations. This book has come into exis-\ntence because of the e\ufb00orts of the many people who have\ndevoted their time and e\ufb00ort writing contributions found\nherein, and it belongs to the community who helped create\nit.\nAdrian Bevan\nQueen Mary University of London\nBo\u02c7stjan Golob\nUniversity of Ljubljana\nJo\u02c7zef Stefan Institute\nThomas Mannel\nUniversity of Siegen\nSoeren Prell\nIowa State University\nBruce Yabsley\nUniversity of Sydney\n\niv\nHow to cite this work:\nThe journal version of this book should be used as the correct citation, and the full citation reference is\n\u201cEd. A.J. Bevan, B. Golob, Th. Mannel, S. Prell, and B.D. Yabsley,\nEur. Phys. J. C74 (2014) 3026, SLAC-PUB-15968, KEK Preprint 2014-3.\u201d\nPlease note that this is the o\ufb03cial version of The Physics of the B Factories. An auxiliary version of this book will\nbe made available online, both on arXiv and the INSPIRE database, under the same entry as the o\ufb03cial version of\nthe book. The o\ufb03cial version of the book uses the notation \u03c61, \u03c62, \u03c63 for the angles of the Unitarity Triangle, and\nthe auxiliary version uses the notation \u03b2, \u03b1, \u03b3.\nA note on conventions:\nThis book follows common practice in particle physics by using a relaxed system of natural units. The reduced\nPlanck constant \u210fis set to unity, and electromagnetic expressions include the \ufb01ne structure constant \u03b1 rather than\ndimensionful constants. Nevertheless, the units of energy (GeV, MeV, etc.) are distinguished from those of momentum\n(GeV/c, MeV/c) and mass (GeV/c2, MeV/c2); when length and time are explicitly mentioned, and especially in detector-\nrelated discussions, meters and seconds are used rather than the reciprocal of energy.\nThe treatment of charge conjugation depends on the context. Many analyses are motivated by possible di\ufb00erences\nbetween the behaviour of B0 and B0: in such cases, samples of the two states are distinguished. When describing the\nmethod, however, if the text speci\ufb01es reconstruction of B0 \u2192\u03c0+D\u2212with D\u2212\u2192K+\u03c0\u2212\u03c0\u2212, it is usually implied that\nthe equivalent procedure is followed for the charge conjugate mode B0 \u2192\u03c0\u2212D+ with D+ \u2192K\u2212\u03c0+\u03c0+. From time to\ntime, explicit statements are made to resolve potential ambiguities.\nCitations follow the author-year format, used in a \ufb02exible way. The most common form is surrounded by parenthe-\nses (Kobayashi and Maskawa, 1973). However, about 20% of cases incorporate the names of the authors into the\ngrammar of the sentence, as when referring to the classic paper of Kobayashi and Maskawa (1973). Variant forms are\nused within the text of a parenthesis; all should be clear from the context.\nThe only unusual feature is the use of three bibliographies: one for BABAR papers (page 806), one for Belle papers\n(page 822), and one for other references (page 835). To avoid tedium, the \u201cet al.\u201d is omitted for B Factory papers,\nciting only the \ufb01rst author of full BABAR Collaboration authorlists (Aubert, 2001e), and either the \ufb01rst member (Choi,\n2011) or the whole of the \ufb01rst-authorship group (Mizuk, Danilov, 2006) for full Belle Collaboration authorlists. Long\nauthorlists for \u201cother\u201d references are treated normally. The great majority of BABAR papers have either Aubert, del\nAmo Sanchez, or Lees as \ufb01rst author; most early Belle papers have Abe, but from 2002 onwards show great variety.\nResults are described as being from BABAR or Belle if the responsible experiment is not already apparent from the\ncontext. Occasionally, a BABAR paper and a Belle paper will be cited together, for example in a quoted average or in\nthe body of a table. It should always be clear which bibliography is meant.\nIn such a long work, there is inevitably some variation in style and usage. As editors, we have endeavoured to keep\nthis to a minimum.\n\nA. J. Bevan\u22171, B. Golob\u22172,3, Th. Mannel\u22174, S. Prell\u22175, B. D. Yabsley\u22176,\nK. Abe\u00a77, H. Aihara\u00a78, F. Anulli\u00a79,10, N. Arnaud\u00a711, T. Aushev\u00a712, M. Beneke\u00a713,14, J. Beringer\u00a715, F. Bianchi\u00a716,17,\nI. I. Bigi\u00a718, M. Bona\u00a716,17, N. Brambilla\u00a713, J. Brodzicka\u00a719, P. Chang\u00a720, M. J. Charles\u00a721, C. H. Cheng\u00a722,\nH.-Y. Cheng\u00a723, R. Chistov\u00a712, P. Colangelo\u00a724, J. P. Coleman\u00a725, A. Drutskoy\u00a712,26, V. P. Druzhinin\u00a727,28,\nS. Eidelman\u00a727,28, G. Eigen\u00a729, A. M. Eisner\u00a730, R. Faccini\u00a710,31, K. T. Flood\u00a722, P. Gambino\u00a716,17, A. Gaz\u00a732,\nW. Gradl\u00a733, H. Hayashii\u00a734, T. Higuchi\u00a735, W. D. Hulsbergen\u00a736, T. Hurth\u00a733, T. Iijima\u00a737,38, R. Itoh\u00a77,\nP. D. Jackson\u00a710,31, R. Kass\u00a739, Yu. G. Kolomensky\u00a715, E. Kou\u00a711, P. Kri\u02c7zan\u00a72,3, A. Kronfeld\u00a740, S. Kumano\u00a741,42,\nY. J. Kwon\u00a743, T. E. Latham\u00a744, D. W. G. S. Leith\u00a745, V. L\u00a8uth\u00a745, F. Martinez-Vidal\u00a746, B. T. Meadows\u00a747,\nR. Mussa\u00a716,17, M. Nakao\u00a77, S. Nishida\u00a77, J. Ocariz\u00a748, S. L. Olsen\u00a749, P. Pakhlov\u00a712,50, G. Pakhlova\u00a712,\nA. Palano\u00a724,51, A. Pich\u00a752, S. Playfer\u00a753, A. Poluektov\u00a727,28, F. C. Porter\u00a722, S. H. Robertson\u00a754, J. M. Roney\u00a755,\nA. Roodman\u00a745, Y. Sakai\u00a77, C. Schwanda\u00a756, A. J. Schwartz\u00a747, R. Seidl\u00a757, S. J. Sekula\u00a758, M. Steinhauser\u00a759,\nK. Sumisawa\u00a77, E. S. Swanson\u00a760, F. Tackmann\u00a761, K. Trabelsi\u00a77, S. Uehara\u00a77, S. Uno\u00a77, R. van der Water\u00a740,\nG. Vasseur\u00a762, W. Verkerke\u00a763, R. Waldi\u00a764, M. Z. Wang\u00a720, F. F. Wilson\u00a765, J. Zupan\u00a73,47, A. Zupanc\u00a73,\nI. Adachi\u00b67, J. Albert\u00b655, Sw. Banerjee\u00b655, M. Bellis\u00b666, E. Ben-Haim\u00b648, P. Biassoni\u00b667,68, R. N. Cahn\u00b615,\nC. Cartaro\u00b645, J. Chauveau\u00b648, C. Chen\u00b65, C. C. Chiang\u00b620, R. Cowan\u00b669, J. Dalseno\u00b670, M. Davier\u00b611,\nC. Davies\u00b671, J. C. Dingfelder\u00b645,72, B. Echenard\u00b622, D. Epifanov\u00b68, B. G. Fulsom\u00b645, A. M. Gabareen\u00b645,\nJ. W. Gary\u00b673, R. Godang\u00b674, M. T. Graham\u00b645, A. Hafner\u00b633, B. Hamilton\u00b636, T. Hartmann\u00b664, K. Hayasaka\u00b637,38,\nC. Hearty\u00b675, Y. Iwasaki\u00b67, A. Khodjamirian\u00b64, A. Kusaka\u00b68, A. Kuzmin\u00b627,28, G. D. La\ufb00erty\u00b676, A. Lazzaro\u00b667,68,\nJ. Li\u00b649, D. Lindemann\u00b645, O. Long\u00b673, A. Lusiani\u00b677,78, G. Marchiori\u00b648, M. Martinelli\u00b624,51, K. Miyabayashi\u00b634,\nR. Mizuk\u00b612,50, G. B. Mohanty\u00b679, D. R. Muller\u00b645, H. Nakazawa\u00b680, P. Ongmongkolkul\u00b622, S. Pacetti\u00b681,82,\nF. Palombo\u00b667,68, T. K. Pedlar\u00b683, L. E. Piilonen\u00b684, A. Pilloni\u00b610,31, V. Poireau\u00b685, K. Prothmann\u00b670,86,\nT. Pulliam\u00b645, M. Rama\u00b69, B. N. Ratcli\ufb00\u00b645, P. Roudeau\u00b611, S. Schrenk\u00b647, T. Schroeder\u00b687, K. R. Schubert\u00b688,\nC. P. Shen\u00b689, B. Shwartz\u00b627,28, A. So\ufb00er\u00b690, E. P. Solodov\u00b627,28, A. Somov\u00b647, M. Stari\u02c7c\u00b63, S. Stracka\u00b667,68,\nA. V. Telnov\u00b691, K. Yu. Todyshev\u00b627,28, T. Tsuboyama\u00b67, T. Uglov\u00b612,26, A. Vinokurova\u00b627,28, J. J. Walsh\u00b677,92,\nY. Watanabe\u00b693, E. Won\u00b694, G. Wormser\u00b611, D. H. Wright\u00b645, S. Ye\u00b695, C. C. Zhang\u00b696,\nS. Abachi97, A. Abashian\u202084, K. Abe98, K. Abe75, N. Abe99, R. Abe100, T. Abe7, T. Abe32, G. S. Abrams15,\nI. Adam45, K. Adamczyk19, A. Adametz101, T. Adye65, A. Agarwal55, H. Ahmed55, M. Ahmed102, S. Ahmed102,\nB. S. Ahn94, H. S. Ahn49, I. J. R. Aitchison45, K. Akai7, S. Akar48, M. Akatsu38, M. Akemoto7, R. Akhmetshin27,\nR. Akre\u202045, M. S. Alam102, J. N. Albert11, R. Aleksan62, J. P. Alexander7, G. Alimonti103, M. T. Allen45,\nJ. Allison76, T. Allmendinger39, J. R. G. Alsmiller104, D. Altenburg105, K. E. Alwyn76, Q. An106, J. Anderson36,\nR. Andreassen47, D. Andreotti107, M. Andreotti107,108, J. C. Andress109, C. Angelini77,92, D. Anipko27,\nA. Anjomshoaa53, P. L. Anthony45, E. A. Antillon32, E. Antonioli110, K. Aoki7, J. F. Arguin111, K. Arinstein27,28,\nK. Arisaka97, K. Asai34, M. Asai112, Y. Asano113, D. J. Asgeirsson75, D. M. Asner114, T. Aso115, M. L. Aspinwall116,\nD. Aston45, H. Atmacan73, B. Aubert85, V. Aulchenko27,28, R. Ayad117, T. Azemoon45, T. Aziz79, V. Azzolini46,\nD. E. Azzopardi1, M. A. Baak118, J. J. Back44, S. Bagnasco119,120, S. Bahinipati121, D. S. Bailey76, S. Bailey122,\nP. Bailly48, N. van Bakel45, A. M. Bakich6, A. Bala123, V. Balagura12, R. Baldini-Ferroli9, Y. Ban124, E. Banas19,\nH. R. Band125, S. Banerjee79, E. Baracchini10,31, R. Barate85, E. Barberio126, M. Barbero103, D. J. Bard45,\nT. Barillari32, N. R. Barlow76, R. J. Barlow76, M. Barrett103,127, W. Bartel61, J. Bartelt45, R. Bartoldus45,\nG. Batignani77,92, M. Battaglia15, J. M. Bauer128, A. Bay129, M. Beaulieu111, P. Bechtle45, T. W. Beck30,\nJ. Becker32, J. Becla45, I. Bedny27,28, S. Behari7, P. K. Behera21,130, E. Behn36, L. Behr131, C. Beigbeder11,\nD. Beiline27, R. Bell\u202045, F. Bellini10,31, G. Bellodi1, K. Belous132, M. Benayoun48, G. Benelli39, J. F. Benitez45,\nM. Benkebil11, N. Berger45, J. Bernabeu46, D. Bernard131, R. Bernet53, F. U. Bernlochner55, J. W. Berryhill63,\nK. Bertsche45, P. Besson\u202062, D. S. Best133, S. Bettarini77,92, D. Bettoni107, V. Bhardwaj34, W. Bhimji116,\nB. Bhuyan134, B. Bhuyan135, M. E. Biagini9, M. Biasini81,82, K. van Bibber136, J. Biesiada91, I. Bingham25,\nR. M. Bionta136, M. Bischofberger34, U. Bitenc3, I. Bizjak3, F. Blanc32, G. Blaylock137, V. E. Blinov27,28,138,\nE. Bloom45, P. C. Bloom32, N. L. Blount139, J. Blouw117, M. Bly65, S. Blyth140, C. T. Boeheim45, M. Bomben48,\nA. Bondar27,28, M. Bondioli133, G.R. Bonneaud48, G. Bonvicini141, M. Booke\u2020128, J. Booth133, C. Borean142,143,\nA. W. Borgland15, E. Borsato144,145, F. Bosi77, L. Bosisio142,143, A. A. Botov27, J. Bougher146, K. Bouldin45,\nP. Bourgeois62, D. Boutigny85, D. A. Bowerman116, A. M. Boyarski45, R. F. Boyce45, J. T. Boyd109, A. Bozek19,\nC. Bozzi107, M. Bra\u02c7cko3,147, G. Brandenburg\u2020122, T. Brandt88, B. Brau39, J. Brau139, A. B. Breon15, D. Breton11,\nC. Brew65, H. Briand48, P. G. Bright-Thomas148, V. Brigljevi\u00b4c136, D. I. Britton54, F. Brochard131, B. Broomer32,\nJ. Brose88, T. E. Browder103, C. L. Brown149, C. M. Brown55, D. N. Brown15, D. N. Brown146, M. Browne45,\nM. Bruinsma133, S. Brunet111, F. Bucci77,92, C. Buchanan97, O. L. Buchmueller45, C. B\u00a8unger64, W. Bugg150,\nA. D. Bukin\u202027,28, R. Bula102, H. Bulten118, P. R. Burchat66, W. Burgess45, J. P. Burke25, J. Button-Shafer15,\nA. R. Buzykaev27, A. Buzzo119, Y. Cai45, R. Calabrese107,108, A. Calcaterra9, G. Calderini48, B. Camanzi127,\nE. Campagna77,92, C. Campagnari63, R. Capra119,120, V. Carassiti107, M. Carpinelli77,92, M. Carroll25,\nG. Casarosa77,92, B. C. K. Casey103, N. M. Cason18, G. Castelli144, N. Cavallo151, G. Cavoto10, A. Cecchi107,\n\nvi\nR. Cenci77,92, G. Cerizza67,68, A. Cervelli77,92, A. Ceseracciu45, X. Chai21, K. S. Chaisanguanthum122, M. C. Chang152,\nY. H. Chang80, Y. W. Chang20, D. S. Chao22, M. Chao133, Y. Chao20, E. Charles15, C. A. Chavez25, R. Cheaib54,\nV. Chekelian70, A. Chen80, A. Chen117, E. Chen22, G. P. Chen96, H. F. Chen106, J. -H. Chen20, J. C. Chen96,\nK. F. Chen20, P. Chen20, S. Chen32, W. T. Chen80, X. Chen125, X. R. Chen153, Y. Q. Chen20, B. Cheng125,\nB. G. Cheon154, N. Chevalier109, Y. M. Chia76, S. Chidzik91, K. Chilikin12, M. V. Chistiakova15, R. Cizeron11,\nI. S. Cho43, K. Cho155, V. Chobanova70, H. H. F. Choi55, K. S. Choi43, S. K. Choi156, Y. Choi157, Y. K. Choi157,\nS. Christ64, P. H. Chu20, S. Chun97, A. Chuvikov91, G. Cibinetto107, D. Cinabro141, A. R. Clark15, P. J. Clark53,\nC. K. Clarke1, R. Claus45, B. Claxton65, Z. C. Clifton32, J. Cochran5, J. Cohen-Tanugi131, H. Cohn150, T. Colberg88,\nS. Cole6, F. Colecchia144,145, C. Condurache65, R. Contri119,120, P. Convert62, M. R. Convery45, P. Cooke25,\nN. Copty153, C. M. Cormack1, F. Dal Corso144, L. A. Corwin39, F. Cossutti142, D. Cote111, A. Cotta Ramusino107,\nW. N. Cottingham109, F. Couderc85, D. P. Coupal45, R. Covarelli81,82, G. Cowan149, W. W. Craddock45,\nG. Crane45, H. B. Crawley5, L. Cremaldi128, A. Crescente144, M. Cristinziani45, J. Crnkovic158, G. Crosetti119,120,\nT. Cuhadar-Donszelmann75, A. Cunha63, S. Curry133, A. D\u2019Orazio10,31, S. D\u02c6u11, G. Dahlinger88, B. Dahmes63,\nC. Dallapiccola137, N. Danielson91, M. Danilov12,26, A. Das79, M. Dash84, S. Dasu125, M. Datta125, F. Daudo16,\nP. D. Dauncey116, P. David48, C. L. Davis146, C. T. Day15, F. De Mori16,17, G. De Domenico62, N. De Groot65,\nC. De la Vaissi`ere48, Ch. de la Vaissi`ere48, A. de Lesquen62, G. De Nardo151,159, R. de Sangro9, A. De Silva160,\nS. DeBarger45, F. J. Decker45, P. del Amo Sanchez85, L. Del Buono48, V. Del Gamba77,92, D. del Re10,31,\nG. Della Ricca142,143, A. G. Denig33,161, D. Derkach11, I. M. Derrington32, H. DeStaebler\u202045, J. Destree32,\nS. Devmal47, B. Dey73, B. Di Girolamo16, E. Di Marco10,31, M. Dickopp88, M. O. Dima32, S. Dittrich64,\nS. Dittongo142,143, P. Dixon1, L. Dneprovsky\u202027, F. Dohou131, Y. Doi7, Z. Dole\u02c7zal162, D. A. Doll22, M. Donald45,\nL. Dong5, L. Y. Dong96, J. Dorfan45, A. Dorigo144, M. P. Dorsten22, R. Dowd126, J. Dowdell65, Z. Dr\u00b4asal162,\nJ. Dragic7, B. W. Drummond95, R. S. Dubitzky101, G. P. Dubois-Felsmann45, M. S. Dubrovin47, Y. C. Duh152,\nY. T. Duh20, D. Dujmic69, W. Dungel56, W. Dunwoodie45, D. Dutta134, A. Dvoretskii22, N. Dyce109, M. Ebert45,\nE. A. Eckhart117, S. Ecklund45, R. Eckmann163, P. Eckstein88, C. L. Edgar76, A. J. Edwards164, U. Egede116,\nA. M. Eichenbaum125, P. Elmer91, S. Emery62, Y. Enari38, R. Enomoto7, E. Erdos32, R. Erickson45, J. A. Ernst102,\nR. J. Erwin22, M. Escalier62, V. Eschenburg128, I. Eschrich133, S. Esen47, L. Esteve62, F. Evangelisti107,\nC. W. Everton126, V. Eyges5, C. Fabby47, F. Fabozzi151, S. Fahey32, M. Falbo165, S. Fan45, F. Fang103, F. Fang22,\nC. Fanin144, A. Farbin36, H. Farhat141, J. E. Fast114, M. Feindt161, A. Fella110, E. Feltresi144,145, T. Ferber61,\nR. E. Fernholz91, S. Ferrag131, F. Ferrarotto10, F. Ferroni10,31, R. C. Field45, A. Filippi16,17, G. Finocchiaro9,\nE. Fioravanti107, J. Firmino da Costa11, P.-A. Fischer5, A. Fisher45, P. H. Fisher69, C. J. Flacco30, R. L. Flack116,\nH. U. Flaecher149, J. Flanagan7, J. M. Flanigan63, K. E. Ford148, W. T. Ford32, I. J. Forster25, A. C. Forti76,\nF. Forti77,92, D. Fortin55, B. Foster109, S. D. Foulkes73, G. Fouque131, J. Fox45, P. Franchini107, M. Franco Sevilla63,\nB. Franek65, E. D. Frank166, K. B. Fransham55, S. Fratina3, K. Fratini10, A. Frey167, R. Frey139, M. Friedl56,\nM. Fritsch33, J. R. Fry25, H. Fujii7, M. Fujikawa34, Y. Fujita7, Y. Fujiyama99, C. Fukunaga168, M. Fukushima7,\nJ. Fullwood76, Y. Funahashi7, Y. Funakoshi7, F. Furano144, M. Furman15, K. Furukawa7, H. Futterschneider88,\nE. Gabathuler25, T. A. Gabriel104, N. Gabyshev27,28, F. Gaede32, N. Gagliardi144,145, A. Gaidot62, J.-M. Gaillard85,\nJ. R. Gaillard116, S. Galagedera65, F. Galeazzi144,145, F. Gallo16,17, D. Gamba16,17, R. Gamet25, K. K. Gan39,\nP. Gandini67,68, S. Ganguly141, S. F. Ganzhur62, Y. Y. Gao169, I. Gaponenko45, A. Garmash27,28, J. Garra Tico170,\nI. Garzia107, M. Gaspero10,31, F. Gastaldi131, C. Gatto151, V. Gaur79, N. I. Geddes65, T. L. Geld47, J.-F. Genat48,\nK. A. George1, M. George25, S. George149, Z. Georgette62, T. J. Gershon7,44, M. S. Gill15, R. Gillard141,\nJ. D. Gilman32, F. Giordano158, M. A. Giorgi77,92, P.-F. Giraud62, L. Gladney166, T. Glanzman45, R. Glattauer56,\nA. Go80, K. Goetzen87, Y. M. Goh154, G. Gokhroo79, P. Goldenzweig47, V. B. Golubev27,28, G. P. Gopal65,\nA. Gordon126, A. Gori\u02c7sek3, V. I. Goriletsky171, R. Gorodeisky90, L. Gosset62, K. Gotow84, S. J. Gowdy45, P. Gra\ufb03n62,\nS. Grancagnolo142,143, E. Grauges170, G. Graziani62, M. G. Green149, M. G. Greene172, G. J. Grenier21, P. Grenier45,\nK. Griessinger33, A. A. Grillo30, B.V. Grinyov171, A. V. Gritsan169, G. Grosdidier11, M. Grosse Perdekamp57,158,\nP. Grosso16, M. Grothe30, Y. Groysman15, O. Gr\u00a8unberg64, E. Guido119,120, H. Guler103, N. J. W. Gunawardane116,\nQ. H. Guo166, R. S. Guo173, Z. J. Guo169, N. Guttman90, H. Ha94, H. C. Ha94, T. Haas45, J. Haba7, J. Hachtel32,\nH. K. Hadavand174, T. Hadig45, C. Hagner84, M. Haire175, F. Haitani98, T. Haji8, G. Haller45, V. Halyo45,\nK. Hamano55, H. Hamasaki7, G. Hamel de Monchenault62, J. Hamilton45, R. Hamilton21, O. Hamon48, B. Y. Han94,\nY. L. Han96, H. Hanada176, K. Hanagaki91, F. Handa176, J. E. Hanson22, A. Hanushevsky45, K. Hara7, T. Hara7,\nY. Harada100, P. F. Harrison44, T. J. Harrison148, B. Harrop91, A. J. Hart148, P. A. Hart76, B. L. Hart\ufb01el97,\nJ. L. Harton117, T. Haruyama7, A. Hasan45, Y. Hasegawa177, C. Hast45, N. C. Hastings8, K. Hasuko57,\nA. Hauke105, C. M. Hawkes148, K. Hayashi7, M. Hazumi7, C. Hee45, E. M. Heenan126, D. He\ufb00ernan178, T. Held87,\nR. Henderson160, S. W. Henderson69, S. S. Hertzbach137, S. Herv\u00b4e62, M. He\u00df64, C. A. Heusch30, A. Hicheur85,\nY. Higashi7, Y. Higasino38, I. Higuchi176, S. Hikita179, E. J. Hill174, T. Himel45, L. Hinz129, T. Hirai99, H. Hirano179,\nJ. F. Hirschauer32, D. G. Hitlin22, N. Hitomi7, M. C. Hodgkinson76, A. H\u00a8ocker11, C. T. Hoi20, T. Hojo178,\nT. Hokuue38, J. J. Hollar125, T. M. Hong63, K. Honscheid39, B. Hooberman15, D. A. Hopkins149, Y. Horii37,38,\nY. Hoshi98, K. Hoshina179, S. Hou20,80, W. S. Hou20, T. Hryn\u2019ova45, Y. B. Hsiung20, C. L. Hsu20, S. C. Hsu20,\nH. Hu125, T. Hu117, H. C. Huang20, T. J. Huang20, Y. C. Huang173, Z. Huard47, M. E. Hu\ufb00er45, D. Hufnagel39,\n\nvii\nT. Hung45, D. E. Hutchcroft25, H. J. Hyun180, S. Ichizawa99, T. Igaki38, A. Igarashi113, S. Igarashi7, Y. Igarashi7,\nO. Igonkina139, K. Ikado38, H. Ikeda7, H. Ikeda7, K. Ikeda34, J. Ilic44, K. Inami38, W. R. Innes45, Y. Inoue181,\nA. Ishikawa7, A. Ishikawa176, H. Ishino99, K. Itagaki176, S. Itami38, K. Itoh8, V. N. Ivanchenko27, R. Iverson45,\nM. Iwabuchi43, G. Iwai100, M. Iwai7, S. Iwaida113, M. Iwamoto182, H. Iwasaki7, M. Iwasaki8, M. Iwasaki139,\nT. Iwashita34, J. M. Izen95, D. J. Jackson178, F. Jackson76, G. Jackson76, P. S. Jackson149, R. G. Jacobsen15,\nC. Jacoby129, I. Jaegle103, V. Jain102, P. Jalocha19, H. K. Jang49, H. Jasper105, A. Jawahery36, S. Jayatilleke47,\nC. M. Jen20, F. Jensen15, C. P. Jessop18, X. B. Ji96, M. J. J. John48, D. R. Johnson32, J. R. Johnson125, S. Jolly127,\nM. Jones103, K. K. Joo7, N. Joshi79, N. J. Joshi79, D. Judd175, T. Julius126, R. W. Kadel15, J. A. Kadyk15, H. Kagan39,\nR. Kagan12, D. H. Kah180, S. Kaiser88, H. Kaji38, S. Kajiwara178, H. Kakuno168, T. Kameshima113, J. Kaminski45,\nT. Kamitani7, J. Kaneko99, J. H. Kang43, J. S. Kang94, T. Kani38, P. Kapusta19, T.M. Karbach105, M. Karolak62,\nY. Karyotakis85, K. Kasami7, G. Katano7, S. U. Kataoka34, N. Katayama7, E. Kato176, Y. Kato38, H. Kawai182,\nH. Kawai8, M. Kawai7, N. Kawamura183, T. Kawasaki100, J. Kay65, M. Kay25, M. P. Kelly76, M. H. Kelsey45,\nN. Kent103, L. T. Kerth15, A. Khan127, H. R. Khan99, D. Kharakh45, A. Kibayashi7, H. Kichimi7, C. Kiesling70,\nM. Kikuchi7, E. Kikutani7, B. H. Kim49, C. H. Kim49, D. W. Kim157, H. Kim45, H. J. Kim180, H. J. Kim43,\nH. O. Kim180, H. W. Kim94, J. B. Kim94, J. H. Kim155, K. T. Kim94, M. J. Kim180, P. Kim45, S. K. Kim49,\nS. M. Kim157, T. H. Kim43, Y. I. Kim180, Y. J. Kim155, G. J. King55, K. Kinoshita47, A. Kirk148, D. Kirkby133,\nI. Kitayama95, M. Klemetti54, V. Klose184, J. Klucar3, N. S. Knecht75, K. J. Knoepfel18, D. J. Knowles148,\nB. R. Ko94, N. Kobayashi99, S. Kobayashi185, T. Kobayashi7, M. J. Kobel88, S. Koblitz70, H. Koch87, M. L. Kocian45,\nP. Kody\u02c7s162, K. Koeneke69, R. Ko\ufb02er137, S. Koike7, S. Koishi99, H. Koiso7, J. A. Kolb139, S. D. Kolya76, Y. Kondo7,\nH. Konishi179, P. Koppenburg7, V. B. Koptchev137, T. M. B. Kordich172, A. A. Korol27,28, K. Korotushenko91,\nS. Korpar3,147, R. T. Kouzes114, D. Kovalskyi63, R. Kowalewski55, Y. Kozakai38, W. Kozanecki62, J. F. Kral15,\nA. Krasnykh45, R. Krause88, E. A. Kravchenko27,28, J. Krebs45, A. Kreisel32, M. Kreps161, M. Krishnamurthy150,\nR. Kroeger128, W. Kroeger45, P. Krokovny27,28, B. Kronenbitter161, J. Kroseberg30, T. Kubo7, T. Kuhr161,\nG. Kukartsev15, R. Kulasiri47, A. Kulikov45, R. Kumar186, S. Kumar123, T. Kumita168, T. Kuniya185, M. Kunze87,\nC. C. Kuo80, T. -L. Kuo20, H. Kurashiro99, E. Kurihara182, N. Kurita45, Y. Kuroki178, A. Kurup149, P. E. Kutter125,\nN. Kuznetsova63, P. Kvasni\u02c7cka162, P. Kyberd127, S. H. Kyeong43, H. M. Lacker184, C. K. Lae169, E. Lamanna10,31,\nJ. Lamsa5, L. Lanceri142,143, L. Landi107,108, M. I. Lang69, D. J. Lange136, J. S. Lange187, U. Langenegger101,\nM. Langer62, A. J. Lankford133, F. Lanni67,68, S. Laplace11, E. Latour131, Y. P. Lau91, D. R. Lavin53, J. Layter73,\nH. Lebbolo48, C. LeClerc15, T. Leddig64, G. Leder56, F. Le Diberder11, C. L. Lee122, J. Lee49, J. S. Lee157,\nM. C. Lee20, M. H. Lee7, M. J. Lee49, M. J. Lee15, S.-J. Lee21, S. E. Lee49, S. H. Lee49, Y. J. Lee20, J. P. Lees85,\nM. Legendre62, M. Leitgab158, R. Leitner162, E. Leonardi10, C. Leonidopoulos91, V. Lepeltier\u202011, Ph. Leruste48,\nT. Lesiak19,188, M. E. Levi15, S. L. Levy63, B. Lewandowski\u202087, M. J. Lewczuk55, P. Lewis45, H. Li125, H. B. Li96,\nS. Li45, X. Li49, X. Li137, Y. Li84, Y. Li146, L. Li Gioi10,31, J. Libby45,189, J. Lidbury65, V. Lillard36, C. L. Lim43,\nA. Limosani126, C. S. Lin137, J. Y. Lin152, S. W. Lin20, Y. S. Lin20, B. Lindquist45, C. Lindsay55, L. Lista151,\nC. Liu106, F. Liu73, H. Liu153, H. M. Liu96, J. Liu102, R. Liu125, T. Liu91, Y. Liu47, Z. Q. Liu96, D. Liventsev7,12,\nM. Lo Vetere119,120, C. B. Locke55, W. S. Lockman30, F. Di Lodovico1, V. Lombardo67,68, G. W. London62,\nD. Lopes Pegna91, L. Lopez24,51, N. Lopez-March46, J. Lory48, J. M. LoSecco18, X. C. Lou95, R. Louvot129, A. Lu63,\nC. Lu91, M. Lu139, R. S. Lu20, T. Lueck55, S. Luitz45, P. Lukin27,28, P. Lund150, E. Luppi107,108, A. M. Lutz11,\nO. Lutz161, G. Lynch15, H. L. Lynch45, A. J. Lyon76, V. R. Lyubinsky171, D. B. MacFarlane45, C. Mackay109,\nJ. MacNaughton7, M. M. Macri119, S. Madani65, W. F. Mader88, S. A. Majewski66, G. Majumder79, Y. Makida7,\nB. Malaescu11, R. Malaguti107, J. Malcl`es48, U. Mallik21, E. Maly88, H. Mamada179, A. Manabe7, G. Mancinelli47,\nM. Mandelkern133, F. Mandl56, P. F. Manfredi190, D. J. J. Mangeol54, E. Manoni81, Z. P. Mao96, M. Margoni144,145,\nC. E. Marker149, G. Markey65, J. Marks101, D. Marlow91, V. Marques62, H. Marsiske45, S. Martellotti9,\nE. C. Martin133, J. P. Martin111, L. Martin48, A. J. Martinez30, M. Marzolla144, A. Mass109, M. Masuzawa7,\nA. Mathieu131, P. Matricon131, T. Matsubara8, T. Matsuda191, T. Matsuda7, H. Matsumoto100, S. Matsumoto192,\nT. Matsumoto168, H. Matsuo\u2020193, T. S. Mattison75, D. Matvienko27,28, A. Matyja19, B. Mayer62, M. A. Mazur63,\nM. A. Mazzoni10, M. McCulloch45, J. McDonald45, J. D. McFall109, P. McGrath149, A. K. McKemey127,\nJ. A. McKenna75, S. E. Mclachlin\u202054, S. McMahon25, T. R. McMahon149, S. McOnie6, T. Medvedeva12, R. Melen45,\nB. Mellado125, W. Menges1, S. Menke45, A. M. Merchant15, J. Merkel105, R. Messner\u202045, S. Metcalfe45, S. Metzler22,\nN. T. Meyer21, T. I. Meyer66, W. T. Meyer5, A. K. Michael32, G. Michelon144,145, S. Michizono7, P. Micout62,\nV. Miftakov91, A. Mihalyi125, Y. Mikami176, D. A. Milanes46, M. Milek54, T. Mimashi7, J. S. Minamora22,\nC. Mindas91, S. Minutoli119, L. M. Mir15, K. Mishra47, W. Mitaro\ufb0056, H. Miyake178, T. S. Miyashita66, H. Miyata100,\nY. Miyazaki38, L. C. Mo\ufb03tt126, G. B. Mohanty44, A. Mohapatra130, A. K. Mohapatra125, D. Mohapatra114, A. Moll70,\nG. R. Moloney126, J. P. Mols62, R. K. Mommsen133, M. R. Monge119,120, D. Monorchio151,159, T. B. Moore137,\nG. F. Moorhead126, P. Mora de Freitas131, M. Morandin144, N. Morgan84, S. E. Morgan148, M. Morganti77,92,\nS. Morganti10, S. Mori113, T. Mori38, M. Morii122, J. P. Morris39, F. Morsani77, G. W. Morton116, L. J. Moss45,\nJ. P. Mouly62, R. Mount45, J. Mueller60, R. M\u00a8uller-Pfe\ufb00erkorn88, M. Mugge136, F. Muheim53, A. Muir25,\nE. Mullin73, M. Munerato107,108, A. Murakami185, T. Murakami7, N. Muramatsu194, P. Musico119, I. Nagai38,\nT. Nagamine176, Y. Nagasaka112, Y. Nagashima178, S. Nagayama7, M. Nagel32, M. T. Naisbit76, T. Nakadaira8,\n\nviii\nY. Nakahama8, M. Nakajima176, T. Nakajima176, I. Nakamura7, T. Nakamura99, T. T. Nakamura7, E. Nakano181,\nH. Nakayama7, J. W. Nam157, S. Narita176, I. Narsky22, J .A. Nash116, Z. Natkaniec19, U. Nauenberg32,\nM. Nayak189, H. Neal45, E. Nedelkovska70, M. Negrini107, K. Neichi98, D. Nelson45, S. Nelson45, N. Neri67,\nG. Nesom30, S. Neubauer161, D. Newman-Coburn\u20201, C. Ng8, X. Nguyen111, H. Nicholson195, C. Niebuhr61,\nJ. Y. Nief11, M. Niiyama193, M. B. Nikolich116, N. K. Nisar79, K. Nishimura103, Y. Nishio38, O. Nitoh179,\nR. Nogowski88, S. Noguchi34, T. Nomura193, M. Nordby45, Y. Nosochkov45, A. Novokhatski45, S. Nozaki176,\nT. Nozaki7, I. M. Nugent55, C. P. O\u2019Grady45, S. W. O\u2019Neale\u2020148, F. G. O\u2019Neill45, B. Oberhof77,92, P. J. Oddone15,\nI. Ofte45, A. Ogawa57, K. Ogawa7, S. Ogawa196, Y. Ogawa7, R. Ohkubo7, K. Ohmi7, Y. Ohnishi7, F. Ohno99,\nT. Ohshima38, Y. Ohshima99, N. Ohuchi7, K. Oide7, N. Oishi38, T. Okabe38, N. Okazaki179, T. Okazaki34,\nS. Okuno93, E. O. Olaiya65, A. Olivas32, P. Olley65, J. Olsen91, S. Ono99, G. Onorato151,159, A. P. Onuchin27,28,138,\nY. Onuki8, T. Ooba182, T. J. Orimoto15, T. Oshima38, I. L. Osipenkov15, W. Ostrowicz19, C. Oswald72,\nS. Otto88, J. Oyang22, A. Oyanguren46, H. Ozaki7, V. E. Ozcan45, H. P. Paar174, C. Padoan107,108, K. Paick175,\nH. Palka\u202019, B. Pan102, Y. Pan125, W. Panduro Vazquez116, J. Panetta166, A. I. Panova171, R. S. Panvini\u2020197,\nE. Panzenb\u00a8ock34,167, E. Paoloni77,92, P. Paolucci151, M. Pappagallo24,51, S. Paramesvaran149, C. S. Park49,\nC. W. Park157, H. Park180, H. Park32, H. K. Park180, K. S. Park157, W. Park153, R. J. Parry25, N. Parslow6,\nS. Passaggio119, F. C. Pastore119,120, P. M. Patel\u202054, C. Patrignani119,120, P. Patteri9, T. Pavel45, J. Pavlovich146,\nD. J. Payne25, L. S. Peak6, D. R. Peimer90, M. Pelizaeus87, R. Pellegrini67,68, M. Pelliccioni16,17, C. C. Peng20,\nJ. C. Peng20, K. C. Peng20, T. Peng106, Y. Penichot62, S. Pennazzi81,82, M. R. Pennington44, R. C. Penny148,\nA. Penzkofer32, A. Perazzo45, A. Perez77, M. Perl45, M. Pernicka\u202056, J.-P. Perroud129, I. M. Peruzzi9,82, R. Pestotnik3,\nK. Peters87, M. Peters103, B. A. Petersen66, T. C. Petersen11, E. Petigura15, S. Petrak45, A. Petrella107, M. Petri\u02c7c3,\nA. Petzold105, M. G. Pia119, T. Piatenko22, D. Piccolo151,159, M. Piccolo9, L. Piemontese107, M. Piemontese45,\nM. Pierini125, S. Pierson45, M. Pioppi81,82, G. Piredda10, M. Pivk48, S. Plaszczynski11, F. Polci10,11,31, A. Pompili24,51,\nP. Poropat\u2020142,143, M. Posocco144, C. T. Potter139, R. J. L. Potter1, V. Prasad135, E. Prebys91, E. Prencipe33,\nJ. Prendki48, R. Prepost125, M. Prest142, M. Prim161, M. Pripstein15, X. Prudent85, S. Pruvot11, E. M. T. Puccio66,\nM. V. Purohit153, N. D. Qi96, H. Quinn45, J. Raaf47, R. Rabberman91, F. Ra\ufb00aelli77, G. Ragghianti150, S. Rahatlou174,\nA. M. Rahimi39, R. Rahmat139, A. Y. Rakitin22, A. Randle-Conde58, P. Rankin32, I. Rashevskaya142, S. Ratkovsky45,\nG. Raven118, V. Re190, M. Reep128, J. J. Regensburger39, J. Reidy128, R. Reif45, B. Reisert70, C. Renard131,\nF. Renga10,31, S. Ricciardi65, J. D. Richman63, J. L. Ritchie163, M. Ritter70, C. Rivetta45, G. Rizzo77,92, C. Roat66,\nP. Robbe85, D. A. Roberts36, A. I. Robertson53, E. Robutti119, S. Rodier11, D. M. Rodriguez32, J. L. Rodriguez103,\nR. Rodriguez45, N. A. Roe15, M. R\u00a8ohrken161, W. Roethel65, J. Rolquin62, L. Romanov27, A. Romosan15,\nM. T. Ronan\u202015, G. Rong96, F. J. Ronga7, L. Roos48, N. Root27, M. Rosen103, E. I. Rosenberg5, A. Rossi81,\nA. Rostomyan61, M. Rotondo144, E. Roussot131, J. Roy32, M. Rozanska19, Y. Rozen63, Y. Rozen198, A. E. Rubin5,\nW. O. Ruddick32, A. M. Ruland163, K. Rybicki19, A. Ryd22, S. Ryu49, J. Ryuko178, S. Sabik111, R. Sacco1,\nM. A. Saeed102, F. Safai Tehrani10, H. Sagawa7, H. Sahoo103, S. Sahu20, M. Saigo176, T. Saito176, S. Saitoh199,\nK. Sakai7, H. Sakamoto193, H. Sakaue181, M. Saleem127, A. A. Salnikov45, E. Salvati137, F. Salvatore149, A. Samuel22,\nD. A. Sanders128, P. Sanders116, S. Sandilya79, F. Sandrelli77,92, W. Sands91, W. R. Sands91, M. Sanpei98, D. Santel47,\nL. Santelj3, V. Santoro107, A. Santroni119,120, T. Sanuki176, T. R. Sarangi199, S. Saremi137, A. Sarti107,108, T. Sasaki7,\nN. Sasao193, M. Satapathy130, Nobuhiko Sato7, Noriaki Sato38, Y. Sato176, N. Satoyama177, A. Satpathy47,163,\nV. Savinov60, N. Savvas76, O. H. Saxton45, K. Sayeed47, S. F. Scha\ufb00ner91, T. Schalk30, S. Schenk101, J. R. Schieck36,\nT. Schietinger45,129, C. J. Schilling163, R. H. Schindler45, S. Schmid56, R. E. Schmitz30, H. Schmuecker87,\nO. Schneider129, G. Schnell200,201, P. Sch\u00a8onmeier176, K. C. Scho\ufb01eld25, G. Schott161, H. Schr\u00a8oder\u202064, M. Schram54,\nJ. Schubert88, J. Sch\u00a8umann7, J. Schultz133, B. A. Schumm30, M. H. Schune11, U. Schwanke174, H. Schwarz45,\nJ. Schwiening45, R. Schwierz88, R. F. Schwitters163, C. Sciacca151,159, G. Sciolla69, I. J. Scott125, J. Seeman45,\nA. Seiden30, R. Seitz111, T. Seki168, A.I. Sekiya34, S. Semenov12, D. Semmler187, S. Sen32, K. Senyo202, O. Seon38,\nV. V. Serbo45, S. I. Serednyakov27,28, B. Serfass62, M. Serra10, J. Serrano11, Y. Settai192, R. Seuster103,\nM. E. Sevior126, K. V. Shakhova171, L. Shang96, M. Shapkin132, V. Sharma174, V. Shebalin27,28, V. G. Shelkov15,\nB. C. Shen\u202073, D. Z. Shen203, Y. T. Shen20, D. J. Sherwood127, T. Shibata100, T. A. Shibata99, H. Shibuya196,\nT. Shidara7, K. Shimada100, M. Shimoyama34, S. Shinomiya178, J. G. Shiu20, H. W. Shorthouse1, L. I. Shpilinskaya171,\nA. Sibidanov6, E. Sicard111, A. Sidorov27, V. Sidorov\u202027, V. Siegle57, M. Sigamani1, M. C. Simani136, M. Simard111,\nG. Simi144, F. Simon70,86, F. Simonetto144,145, N. B. Sinev139, H. Singh153, J. B. Singh123, R. Sinha204, S. Sitt48,\nYu. I. Skovpen27,28, R. J. Sloane25, P. Smerkol3, A. J. S. Smith91, D. Smith148, D. Smith116, D. Smith45,\nD. S. Smith39, J. G. Smith32, A. Smol16, H. L. Snoek118, A. Snyder45, R. Y. So75, R. J. Sobie55, E. Soderstrom45,\nA. Soha45, Y. S. Sohn43, M. D. Sokolo\ufb0047, A. Sokolov132, P. Solagna144, E. Solovieva12, N. Soni123,148, P. Sonnek128,\nV. Sordini11,10,31, B. Spaan105, S. M. Spanier150, E. Spencer30, V. Speziali190, M. Spitznagel69, P. Spradlin30,\nH. Staengle137, R. Stamen7, M. Stanek45, S. Stani\u02c7c205, J. Stark48, M. Steder61, H. Steininger56, M. Steinke87,\nJ. Stelzer45, E. Stevanato144, A. Stocchi11, R. Stock206, H. Stoeck6, D. P. Stoker133, R. Stroili144,145, D. Strom139,\nP. Strother1, J. Strube139, B. Stugu29, J. Stypula19, D. Su45, R. Suda168, R. Sugahara7, A. Sugi38, T. Sugimura7,\nA. Sugiyama185, S. Suitoh38, M. K. Sullivan45, M. Sumihama207, T. Sumiyoshi168, D. J. Summers128, L. Sun29,\nL. Sun47, S. Sun45, J. E. Sundermann88, H. F. Sung20, Y. Susaki38, P. Sutcli\ufb00e25, A. Suzuki15, J. Suzuki7,\n\nix\nJ. I. Suzuki7, K. Suzuki38,45, S. Suzuki185, S. Y. Suzuki7, J. E. Swain53, S. K. Swain45,103, S. T\u2019Jampens131,\nM. Tabata182, K. Tackmann15, H. Tajima8, O. Tajima7, K. Takahashi99, S. Takahashi100, T. Takahashi181,\nF. Takasaki7, T. Takayama176, M. Takita178, K. Tamai7, U. Tamponi16,17, N. Tamura100, N. Tan208, P. Tan125,\nK. Tanabe8, T. Tanabe15, H. A. Tanaka45, J. Tanaka8, M. Tanaka7, S. Tanaka7, Y. Tanaka209, K. Tanida49,\nN. Taniguchi7, P. Taras111, N. Tasneem55, G. Tatishvili114, T. Tatomi7, M. Tawada7, F. Taylor69, G. N. Taylor126,\nG. P. Taylor116, V. I. Telnov27,28, L. Teodorescu127, R. Ter-Antonyan39, Y. Teramoto181, D. Teytelman45, G. Th\u00b4erin48,\nCh. Thiebaux131, D. Thiessen75, E. W. Thomas32, J. M. Thompson45, F. Thorne56, X. C. Tian124, M. Tibbetts116,\nI. Tikhomirov12, J. S. Tinslay45, G. Tiozzo144, V. Tisserand85, V. Tocut11, W. H. Toki117, E. W. Tomassini32,\nM. Tomoto7, T. Tomura8, E. Torassa144, E. Torrence139, S. Tosi119,120, C. Touramanis25, J. C. Toussaint62,\nS. N. Tovey126, P. P. Trapani16, E. Treadwell210, G. Triggiani77,92, S. Trincaz-Duvoid11, W. Trischuk91, D. Troost15,\nA. Trunov45, K. L. Tsai20, Y. T. Tsai20, Y. Tsujita113, K. Tsukada7, T. Tsukamoto7, J. M. Tuggle36, A. Tumanov91,\nY. W. Tung20, L. Turnbull175, J. Turner45, M. Turri30, K. Uchida103, M. Uchida99, Y. Uchida199, M. Ueki176,\nK. Ueno7, K. Ueno20, N. Ujiie7, K. A. Ulmer32, Y. Unno154, P. Urquijo126, Y. Ushiroda7, Y. Usov27,28, M. Usseglio62,\nY. Usuki38, U. Uwer101, J. Va\u2019vra45, S. E. Vahsen103, G. Vaitsas149, A. Valassi11, E. Vallazza142, A. Vallereau48,\nP. Vanhoefer70, W. C. van Hoek32, C. Van Hulse200, D. van Winkle45, G. Varner103, E. W. Varnes91, K. E. Varvell6,\nG. Vasileiadis131, Y. S. Velikzhanin20, M. Verderi131, S. Versill\u00b4e48, K. Vervink129, B. Viaud111, P. B. Vidal1, S. Villa129,\nP. Villanueva-Perez46, E. L. Vinograd171, L. Vitale142,143, G. M. Vitug73, C. Vo\u00df64, C. Voci144,145, C. Voena10,\nA. Volk88, J. H. von Wimmersperg-Toeller125, V. Vorobyev27,28, A. Vossen211, G. Vuagnin142,143, C. O. Vuosalo125,\nK. Wacker105, A. P. Wagner45, D. L. Wagner32, G. Wagner64, M. N. Wagner187, S. R. Wagner32, D. E. Wagoner175,\nD. Walker109, W. Walkowiak30, D. Wallom109, C. C. Wang20, C. H. Wang140, J. Wang124, J. G. Wang84, K. Wang73,\nL. Wang30, L. L. Wang11, P. Wang96, P. Wang96, T. J. Wang96, W. F. Wang45, X. L. Wang84, Y. F. Wang106,\nF. R. Wappler102, M. Watanabe100, A. T. Watson148, J. E. Watson53, N. K. Watson148, M. Watt65, J. H. Weatherall76,\nM. Weaver45, T. Weber45, R. Wedd126, J. T. Wei20, A. W. Weidemann153, A. J. R. Weinstein45, W. A. Wenzel15,\nC. A. West63, C. G. West32, T. J. West76, E. White47, R. M. White153, J. Wicht7, L. Widhalm\u202056, J. Wiechczynski19,\nU. Wienands45, L. Wilden88, M. Wilder30, D. C. Williams30, G. Williams95, J. C. Williams76, K. M. Williams84,\nM. I. Williams1, S. Y. Willocq137, J. R. Wilson153, M. G. Wilson30, R. J. Wilson117, F. Winklmeier117,\nL. O. Winstrom30, M. A. Winter149, W. J. Wisniewski45, M. Wittgen45, J. Wittlin137, W. Wittmer45, R. Wixted91,\nA. Woch111, B. J. Wogsland150, E. Won122, Q. K. Wong39, B. C. Wray163, A. C. Wren149, D. M. Wright136,\nC. H. Wu20, J. Wu122, S. L. Wu125, H. W. Wulsin45, S. M. Xella65, Q. L. Xie96, Y. Xie53, Y. Xie9, Z. Z. Xu106,\nCh. Y`eche62, Y. Yamada7, M. Yamaga176, A. Yamaguchi176, H. Yamaguchi7, T. Yamaki212, H. Yamamoto176,\nN. Yamamoto7, R. K. Yamamoto\u202069, S. Yamamoto168, T. Yamanaka178, H. Yamaoka7, J. Yamaoka103, Y. Yamaoka7,\nY. Yamashita213, M. Yamauchi7, D. S. Yan203, Y. Yan45, H. Yanai100, S. Yanaka99, H. Yang49, R. Yang91, S. Yang22,\nA. K. Yarritu45, S. Yashchenko61, J. Yashima7, Z. Yasin73, Y. Yasu7, S. W. Ye106, P. Yeh20, J. I. Yi76, K. Yi45,\nM. Yi69, Z. W. Yin203, J. Ying124, G. Yocky45, K. Yokoyama7, M. Yokoyama8, T. Yokoyama179, K. Yoshida38,\nM. Yoshida7, Y. Yoshimura7, C. C. Young45, C. X. Yu96, Z. Yu125, C. Z. Yuan96, Y. Yuan96, F. X. Yumiceva153,\nY. Yusa100, A. N. Yushkov27, H. Yuta183, V. Zacek111, S. B. Zain102, A. Zallo9, S. Zambito16,17, D. Zander161,\nS. L. Zang96, D. Zanin16, B. G. Zaslavsky171, Q. L. Zeng117, A. Zghiche85, B. Zhang48, J. Zhang7, J. Zhang32,\nL. Zhang73, L. M. Zhang106, S. Q. Zhang96, Z. P. Zhang106, H. W. Zhao96, H. W. Zhao128, M. Zhao69, Z. G. Zhao106,\nY. Zheng69, Y. H. Zheng103, Z. P. Zheng96, V. Zhilich27,28, P. Zhou141, R. Y. Zhu22, Y. S. Zhu96, Z. M. Zhu124,\nV. Zhulanov27,28, T. Ziegler91, V. Ziegler45, G. Zioulas133, M. Zisman15, M. Zito62, D. Z\u00a8urcher129, N. Zwahlen129,\nO. Zyukova27,28, T. \u02c7Zivko3, and D. \u02c7Zontar3\n\u2217General Editor\n\u00a7 Section Editor\n\u00b6 Additional Section Writer\n\u2020 Deceased\n1 Queen Mary, University of London, London, E1 4NS, United Kingdom\n2 Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia\n3 J. Stefan Institute, 1000 Ljubljana, Slovenia\n4 Theoretische Physik 1, Naturwissenschaftlich-Technische Fakult\u00a8at, Universit\u00a8at Siegen, Walter-Flex-Stra\u00dfe 3, D-57068 Siegen,\nGermany\n5 Iowa State University, Ames, Iowa 50011-3160, USA\n6 School of Physics, University of Sydney, NSW 2006, Australia\n7 High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan\n8 Department of Physics, University of Tokyo, Tokyo 113-0033, Japan\n9 INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy\n10 INFN Sezione di Roma, I-00185 Roma, Italy\n11 Laboratoire de l\u2019Acc\u00b4el\u00b4erateur Lin\u00b4eaire, IN2P3/CNRS et Universit\u00b4e Paris-Sud 11, Centre Scienti\ufb01que d\u2019Orsay, F-91898 Orsay\nCedex, France\n\nx\n12 Institute for Theoretical and Experimental Physics, Moscow 117218, Russia\n13 Physik Department, James-Franck-Stra\u00dfe 1, Technische Universit\u00a8at M\u00a8unchen, D-85748 Garching, Germany\n14 Institut f\u00a8ur Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, D-52056 Aachen, Germany\n15 Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA\n16 INFN Sezione di Torino, I-10125 Torino, Italy\n17 Dipartimento di Fisica, Universit`a di Torino, I-10125 Torino, Italy\n18 University of Notre Dame, Notre Dame, Indiana 46556, USA\n19 H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland\n20 Department of Physics, National Taiwan University, Taipei 10617, Taiwan\n21 University of Iowa, Iowa City, Iowa 52242, USA\n22 California Institute of Technology, Pasadena, California 91125, USA\n23 Institute of Physics, Academia Sinica, Taipei, Taiwan 115, Republic of China\n24 INFN, Sezione de Bari, via Orabona 4, I-70126 Bari, Italy\n25 University of Liverpool, Liverpool L69 7ZE, United Kingdom\n26 Moscow Institute of Physics and Technology, Moscow Region 141700, Russia\n27 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia\n28 Novosibirsk State University, Novosibirsk 630090, Russia\n29 University of Bergen, Institute of Physics, N-5007 Bergen, Norway\n30 University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA\n31 Dipartimento di Fisica, Universit`a di Roma La Sapienza, I-00185 Roma, Italy\n32 University of Colorado, Boulder, Colorado 80309, USA\n33 Johannes Gutenberg-Universit\u00a8at Mainz, Institut f\u00a8ur Kernphysik, D-55099 Mainz, Germany\n34 Nara Women\u2019s University, Nara 630-8506, Japan\n35 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan\n36 University of Maryland, College Park, Maryland 20742, USA\n37 Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan\n38 Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan\n39 Ohio State University, Columbus, Ohio 43210, USA\n40 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA\n41 KEK Theory Center, Institute of Particle and Nuclear Studies, KEK 1-1, OHO, Tsukuba, Ibaraki, 305-0801, Japan\n42 Particle and Nuclear Physics Division, J-PARC Center 201-1, Shirakata, Tokai, Ibaraki, 309-11-6, Japan\n43 Yonsei University, Seoul 120-749, South Korea\n44 Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom\n45 SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA\n46 IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain\n47 University of Cincinnati, Cincinnati, Ohio 45221, USA\n48 Laboratoire de Physique Nucl\u00b4eaire et de Hautes Energies, IN2P3/CNRS, Universit\u00b4e Pierre et Marie Curie-Paris6, Universit\u00b4e\nDenis Diderot-Paris7, F-75252 Paris, France\n49 Seoul National University, Seoul 151-742, South Korea\n50 Moscow Physical Engineering Institute, Moscow 115409, Russia\n51 Dipartmento di Fisica, Universit`a di Bari, I-70126 Bari, Italy\n52 Departament de F\u00b4\u0131sica Te`orica, IFIC, Universitat de Val`encia \u2013 CSIC\nApt. Correus 22085, E-46071 Val`encia, Spain\n53 University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom\n54 McGill University, Montr\u00b4eal, Qu\u00b4ebec, Canada H3A 2T8\n55 University of Victoria, Victoria, British Columbia, Canada V8W 3P6\n56 Institute of High Energy Physics, 1050 Vienna, Austria\n57 RIKEN BNL Research Center, Brookhaven, NY 11973, USA\n58 Southern Methodist University, Dallas, Texas 75275, USA\n59 Institut f\u00a8ur Theoretische Teilchenphysik, Karlsruher Institut f\u00a8ur Technologie, D-76131 Karlsruhe, Germany\n60 University of Pittsburgh, Pittsburgh, PA 15260, USA\n61 Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany\n62 CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France\n63 University of California at Santa Barbara, Santa Barbara, California 93106, USA\n64 Universit\u00a8at Rostock, D-18051 Rostock, Germany\n65 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom\n66 Stanford University, Stanford, California 94305-4060, USA\n67 INFN Sezione di Milano, I-20133 Milano, Italy\n68 Dipartimento di Fisica, Universit`a di Milano, I-20133 Milano, Italy\n69 Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA\n70 Max-Planck-Institut f\u00a8ur Physik, 80805 M\u00a8unchen, Germany\n71 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK\n\nxi\n72 University of Bonn, 53115 Bonn, Germany\n73 University of California at Riverside, Riverside, California 92521, USA\n74 University of South Alabama, Mobile, Alabama 36688, USA\n75 University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1\n76 University of Manchester, Manchester M13 9PL, United Kingdom\n77 INFN Sezione di Pisa, I-56127 Pisa, Italy\n78 Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy\n79 Tata Institute of Fundamental Research, Mumbai 400005, India\n80 National Central University, Chung-li 32054, Taiwan\n81 INFN Sezione di Perugia I-06123 Perugia, Italy\n82 Dipartimento di Fisica, Universit`a di Perugia, I-06123 Perugia, Italy\n83 Luther College, Decorah, IA 52101, USA\n84 Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA\n85 Laboratoire d\u2019Annecy-le-Vieux de Physique des Particules (LAPP), Universit\u00b4e de Savoie, CNRS/IN2P3, F-74941 Annecy-\nle-Vieux, France\n86 Excellence Cluster Universe, Technische Universit\u00a8at M\u00a8unchen, 85748 Garching, Germany\n87 Ruhr Universit\u00a8at Bochum, Institut f\u00a8ur Experimentalphysik 1, D-44780 Bochum, Germany\n88 Technische Universit\u00a8at Dresden, Institut f\u00a8ur Kern- und Teilchenphysik, D-01062 Dresden, Germany\n89 Beihang University, Beijing 100191\n90 Tel Aviv University, Tel Aviv, 69978, Israel\n91 Princeton University, Princeton, New Jersey 08544, USA\n92 Dipartimento di Fisica, Universit`a di Pisa, I-56127 Pisa, Italy\n93 Kanagawa University, Yokohama 221-8686, Japan\n94 Korea University, Seoul 136-713, South Korea\n95 University of Texas at Dallas, Richardson, Texas 75083, USA\n96 Institute of High Energy Physics, Beijing 100039, China\n97 University of California at Los Angeles, Los Angeles, California 90024, USA\n98 Tohoku Gakuin University, Tagajo 985-8537, Japan\n99 Tokyo Institute of Technology, Tokyo 152-8550, Japan\n100 Niigata University, Niigata 950-2181, Japan\n101 Universit\u00a8at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany\n102 State University of New York, Albany, New York 12222, USA\n103 University of Hawaii, Honolulu, HI 96822, USA\n104 Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA\n105 Technische Universit\u00a8at Dortmund, Fakult\u00a8at Physik, D-44221 Dortmund, Germany\n106 University of Science and Technology of China, Hefei 230026, PR China\n107 INFN Sezione di Ferrara, I-44100 Ferrara, Italy\n108 Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara, I-44100 Ferrara, Italy\n109 University of Bristol, Bristol BS8 1TL, United Kingdom\n110 INFN CNAF I-40127 Bologna, Italy\n111 Universit\u00b4e de Montr\u00b4eal, Physique des Particules, Montr\u00b4eal, Qu\u00b4ebec, Canada H3C 3J7\n112 Hiroshima Institute of Technology, Hiroshima 731-5193, Japan\n113 University of Tsukuba, Tsukuba 305-0801, Japan\n114 Paci\ufb01c Northwest National Laboratory, Richland, WA 99352, USA\n115 Toyama National College of Maritime Technology, Toyama 933-0293, Japan\n116 Imperial College London, London, SW7 2AZ, United Kingdom\n117 Colorado State University, Fort Collins, Colorado 80523, USA\n118 NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands\n119 INFN Sezione di Genova, I-16146 Genova, Italy\n120 Dipartimento di Fisica, Universit`a di Genova, I-16146 Genova, Italy\n121 Indian Institute of Technology Bhubaneswar, SatyaNagar, 751007, India\n122 Harvard University, Cambridge, Massachusetts 02138, USA\n123 Panjab University, Chandigarh 160014, India\n124 Peking University, Beijing 100871, PR China\n125 University of Wisconsin, Madison, Wisconsin 53706, USA\n126 School of Physics, University of Melbourne, Victoria 3010, Australia\n127 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom\n128 University of Mississippi, University, Mississippi 38677, USA\n129 \u00b4Ecole Polytechnique F\u00b4ed\u00b4erale de Lausanne (EPFL), 1015 Lausanne, Switzerland\n130 Utkal University, Bhubaneswar, India\n131 Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France\n132 Institute for High Energy Physics, Protvino 142281, Russia\n\nxii\n133 University of California at Irvine, Irvine, California 92697, USA\n134 Indian Institute of Technology Guwahati, Assam 781039, India\n135 Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India\n136 Lawrence Livermore National Laboratory, Livermore, California 94550, USA\n137 University of Massachusetts, Amherst, Massachusetts 01003, USA\n138 Novosibirsk State Technical University, Novosibirsk 630092, Russia\n139 University of Oregon, Eugene, Oregon 97403, USA\n140 National United University, Miao Li 36003, Taiwan\n141 Wayne State University, Detroit, MI 48202, USA\n142 INFN Sezione di Trieste, I-34127 Trieste, Italy\n143 Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n144 INFN Sezione di Padova, I-35131 Padova, Italy\n145 Dipartimento di Fisica, Universit`a di Padova, I-35131 Padova, Italy\n146 University of Louisville, Louisville, Kentucky 40292, USA\n147 University of Maribor, 2000 Maribor, Slovenia\n148 University of Birmingham, Birmingham, B15 2TT, United Kingdom\n149 University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom\n150 University of Tennessee, Knoxville, Tennessee 37996, USA\n151 INFN Sezione di Napoli, I-80126 Napoli, Italy\n152 Department of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan\n153 University of South Carolina, Columbia, South Carolina 29208, USA\n154 Hanyang University, Seoul 133-791, South Korea\n155 Korea Institute of Science and Technology Information, Daejeon 305-806, South Korea\n156 Gyeongsang National University, Chinju 660-701, South Korea\n157 Sungkyunkwan University, Suwon 440-746, South Korea\n158 University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA\n159 Dipartimento di Scienze Fisiche, Universit`a di Napoli Federico II, I-80126 Napoli, Italy\n160 TRIUMF, Vancouver, BC, Canada V6T 2A3\n161 Universit\u00a8at Karlsruhe, Institut f\u00a8ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany\n162 Faculty of Mathematics and Physics, Charles University, 121 16 Prague, The Czech Republic\n163 University of Texas at Austin, Austin, Texas 78712, USA\n164 Harvey Mudd College, Claremont, California 91711, USA\n165 Elon University, Elon University, North Carolina 27244-2010, USA\n166 University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA\n167 II. Physikalisches Institut, Georg-August-Universit\u00a8at G\u00a8ottingen, 37073 G\u00a8ottingen, Germany\n168 Tokyo Metropolitan University, Tokyo 192-0397, Japan\n169 Johns Hopkins University, Baltimore, Maryland 21218, USA\n170 Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain\n171 Institute for Single Crystals, National Academy of Sciences of Ukraine, Kharkov 61001, Ukraine\n172 Yale University, New Haven, Connecticut 06511, USA\n173 National Kaohsiung Normal University, Kaohsiung 80201, Taiwan\n174 University of California at San Diego, La Jolla, California 92093, USA\n175 Prairie View A&M University, Prairie View, Texas 77446, USA\n176 Tohoku University, Sendai 980-8578, Japan\n177 Shinshu University, Nagano 390-8621, Japan\n178 Osaka University, Osaka 565-0871, Japan\n179 Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan\n180 Kyungpook National University, Daegu 702-701, South Korea\n181 Osaka City University, Osaka 558-8585, Japan\n182 Chiba University, Chiba 263-8522, Japan\n183 Aomori University, Aomori 030-0943, Japan\n184 Humboldt-Universit\u00a8at zu Berlin, Institut f\u00a8ur Physik, D-12489 Berlin, Germany\n185 Saga University, Saga 840-8502, Japan\n186 Punjab Agricultural University, Ludhiana 141004, India\n187 Justus-Liebig-Universit\u00a8at Gie\u00dfen, 35392 Gie\u00dfen, Germany\n188 T. Ko\u00b4sciuszko Cracow University of Technology, Krakow 31-342, Poland\n189 Indian Institute of Technology Madras, Chennai 600036, India\n190 Universit`a di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy\n191 University of Miyazaki, Miyazaki 889-2192, Japan\n192 Chuo University, Tokyo 192-0393, Japan\n193 Kyoto University, Kyoto 606-8502, Japan\n194 Research Center for Electron Photon Science, Tohoku University, Sendai 980-8578, Japan\n\nxiii\n195 Mount Holyoke College, South Hadley, Massachusetts 01075, USA\n196 Toho University, Funabashi 274-8510, Japan\n197 Vanderbilt University, Nashville, Tennessee 37235, USA\n198 Technion, Haifa, Israel\n199 The Graduate University for Advanced Studies, Hayama 240-0193, Japan\n200 University of the Basque Country UPV/EHU, 48080 Bilbao, Spain\n201 Ikerbasque, 48011 Bilbao, Spain\n202 Yamagata University, Yamagata 990-8560, Japan\n203 Chinese Academy of Science, Beijing 100864, PR China\n204 Institute of Mathematical Sciences, Chennai 600113, India\n205 University of Nova Gorica, 5000 Nova Gorica, Slovenia\n206 University of Frankfurt, 60318 Frankfurt am Main, Germany\n207 Gifu University, Gifu 501-1193, Japan\n208 Tokyo University of Science, Chiba 278-8510, Japan\n209 Nagasaki Institute of Applied Science, Nagasaki 851-0123, Japan\n210 Florida A&M University, Tallahassee, Florida 32307, USA\n211 Indiana University, Bloomington, IN 47408, USA\n212 Sugiyama Jogakuen University, Aichi 470-0131, Japan\n\nxiv\nContents\nForeword\nii\nPreface\niii\nHow to cite this work\n. . . . . . . . . . . . . . . . .\niv\nA note on conventions . . . . . . . . . . . . . . . . .\niv\nAuthors . . . . . . . . . . . . . . . . . . . . . . . . .\nv\nA\nThe facilities\n1\n1\nThe B Factories\n. . . . . . . . . . . . . . . . . . . .\n1\n1.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n1\n1.1.1\nTesting the KM idea\n. . . . . . . . . .\n1\n1.1.2\nThree miracles . . . . . . . . . . . . . .\n1\n1.2\nThe path to the B Factories . . . . . . . . . .\n2\n1.2.1\nRequirements for a B Factory . . . . .\n2\n1.2.2\nEarly proposals . . . . . . . . . . . . .\n3\n1.2.3\nAsymmetric colliders . . . . . . . . . .\n3\n1.2.4\nA di\ufb00erent approach\n. . . . . . . . . .\n4\n1.3\nPEP-II and KEKB\n. . . . . . . . . . . . . . .\n5\n1.4\nDetectors for the B Factories . . . . . . . . . .\n6\n1.4.1\nThe BABAR detector collaboration . . .\n7\n1.4.2\nFormation of the Belle collaboration\n.\n9\n1.4.3\nBuilding the BABAR detector . . . . . .\n10\n1.4.4\nBuilding the Belle detector . . . . . . .\n14\n1.5\nPhysics at last . . . . . . . . . . . . . . . . . .\n16\n1.5.1\nEstablishing CP violation in B meson\ndecay . . . . . . . . . . . . . . . . . . .\n17\n1.5.2\nThe premature end of BABAR data taking 17\n1.5.3\nThe \ufb01nal Belle data taking runs . . . .\n17\n2\nThe collaborations and detectors . . . . . . . . . . .\n18\n2.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n18\n2.1.1\nThe BABAR and Belle collaborations . .\n20\n2.1.2\nThe BABAR detector . . . . . . . . . . .\n21\n2.1.3\nThe Belle detector\n. . . . . . . . . . .\n21\n2.2\nBABAR and Belle comparative descriptions\n. .\n23\n2.2.1\nSilicon detector . . . . . . . . . . . . .\n23\n2.2.2\nDrift chamber . . . . . . . . . . . . . .\n26\n2.2.3\nCharged particle identi\ufb01cation . . . . .\n28\n2.2.4\nElectromagnetic calorimeter . . . . . .\n30\n2.2.5\nMuon detector . . . . . . . . . . . . . .\n32\n2.2.6\nTrigger . . . . . . . . . . . . . . . . . .\n34\n2.2.7\nOnline and DAQ\n. . . . . . . . . . . .\n35\n2.2.8\nBackground and mitigation\n. . . . . .\n36\n2.2.9\nConclusion: main common points, main\ndi\ufb00erences . . . . . . . . . . . . . . . .\n38\n3\nData processing and Monte Carlo production . . . .\n40\n3.1\nIntroduction: general organization of the data\ntaking, data reconstruction and MC production\n40\n3.2\nData taking\n. . . . . . . . . . . . . . . . . . .\n41\n3.2.1\nIntegrated luminosity vs. time; luminos-\nity counting . . . . . . . . . . . . . . .\n42\n3.2.2\nMajor hardware/online upgrades which\nmodi\ufb01ed the quality of BABAR data . .\n43\n3.2.3\nMajor hardware/online upgrades which\nmodi\ufb01ed the quality of Belle data . . .\n44\n3.3\nData Reconstruction\n. . . . . . . . . . . . . .\n46\n3.3.1\nIntroduction . . . . . . . . . . . . . . .\n46\n3.3.2\nThe BABAR prompt reconstruction . . .\n46\n3.3.3\nThe Belle data reconstruction . . . . .\n46\n3.4\nMonte Carlo simulation production . . . . . .\n47\n3.4.1\nIntroduction . . . . . . . . . . . . . . .\n47\n3.4.2\nEvent generators\n. . . . . . . . . . . .\n48\n3.4.3\nDetector Simulation . . . . . . . . . . .\n48\n3.4.4\nMC production systems\n. . . . . . . .\n49\n3.4.5\nDi\ufb00erences between BABAR and Belle sim-\nulations\n. . . . . . . . . . . . . . . . .\n49\n3.5\nEvent skimming . . . . . . . . . . . . . . . . .\n51\n3.5.1\nIntroduction: purpose of event skimming 51\n3.5.2\nSkimming in BABAR . . . . . . . . . . .\n51\n3.5.3\nSkimming in Belle . . . . . . . . . . . .\n52\n3.6\nData quality and B counting . . . . . . . . . .\n53\n3.6.1\nThe control of data quality . . . . . . .\n53\n3.6.2\nB-counting techniques\n. . . . . . . . .\n55\n3.7\nLong Term Data Access system\n. . . . . . . .\n57\n3.7.1\nThe BABAR approach . . . . . . . . . .\n57\n3.7.2\nThe Belle approach . . . . . . . . . . .\n58\nB\nTools and methods\n59\n4\nMultivariate methods and analysis optimization . . .\n59\n4.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n59\n4.2\nNotation . . . . . . . . . . . . . . . . . . . . .\n59\n4.3\nFigures of merit . . . . . . . . . . . . . . . . .\n59\n4.4\nMethods . . . . . . . . . . . . . . . . . . . . .\n60\n4.4.1\nRectangular cuts\n. . . . . . . . . . . .\n61\n4.4.2\nLikelihood method\n. . . . . . . . . . .\n61\n4.4.3\nLinear discriminants\n. . . . . . . . . .\n62\n4.4.4\nNeural nets\n. . . . . . . . . . . . . . .\n62\n4.4.5\nBinary decision trees . . . . . . . . . .\n63\n4.4.6\nBoosting . . . . . . . . . . . . . . . . .\n63\n4.4.7\nBagging and random forest . . . . . . .\n64\n4.4.8\nError correcting output code . . . . . .\n64\n4.5\nAvailable tools . . . . . . . . . . . . . . . . . .\n65\n5\nCharged particle identi\ufb01cation\n. . . . . . . . . . . .\n67\n5.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n67\n5.1.1\nDe\ufb01nitions . . . . . . . . . . . . . . . .\n67\n5.1.2\nSubdetectors providing PID information\n67\n5.2\nPID algorithms and multivariate methods\n. .\n67\n5.2.1\nBelle algorithms . . . . . . . . . . . . .\n68\n5.2.2\nBABAR algorithms . . . . . . . . . . . .\n68\n5.3\nBABAR PID performance and systematics . . .\n69\n5.3.1\nHistory of PID performance in BABAR .\n69\n5.3.2\nSystematic e\ufb00ects . . . . . . . . . . . .\n69\n5.4\nBelle PID performance and systematics . . . .\n70\n6\nVertexing . . . . . . . . . . . . . . . . . . . . . . . .\n73\n6.1\nThe role of vertexing in the B Factories . . . .\n73\n6.2\nTrack parameterization and resolution\n. . . .\n73\n6.3\nVertex \ufb01tting by \u03c72 minimization . . . . . . .\n75\n6.4\nPrimary vertex reconstruction and beamspot\ncalibration . . . . . . . . . . . . . . . . . . . .\n77\n6.5\n\u2206t determination . . . . . . . . . . . . . . . .\n79\n6.5.1\nReconstruction of the Btag vertex . . .\n79\n6.5.2\nFrom vertex positions to \u2206t . . . . . .\n80\n6.5.3\n\u2206t resolution function\n. . . . . . . . .\n81\n7\nB-meson reconstruction . . . . . . . . . . . . . . . .\n83\n7.1\nFull hadronic B-meson reconstruction . . . . .\n83\n7.1.1\nKinematical discrimination of B mesons\n84\n\nxv\n7.2\nSemileptonic B-meson reconstruction . . . . .\n87\n7.3\nPartial B-meson reconstruction\n. . . . . . . .\n88\n7.3.1\nB \u2192D\u2217\u00b1X decays . . . . . . . . . . .\n88\n7.3.2\nB \u2192D\u2217\u00b1\u2113\u03bd\u2113decays . . . . . . . . . . .\n90\n7.4\nRecoil B-meson reconstruction . . . . . . . . .\n90\n7.4.1\nHadronic tag B reconstruction . . . . .\n92\n7.4.2\nSemileptonic tag B reconstruction . . .\n95\n7.4.3\nInclusive Btag reconstruction . . . . . .\n96\n7.4.4\nDouble tagging\n. . . . . . . . . . . . .\n97\n7.5\nSummary . . . . . . . . . . . . . . . . . . . . .\n99\n8\nB-\ufb02avor tagging\n. . . . . . . . . . . . . . . . . . . .\n100\n8.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n100\n8.2\nDe\ufb01nitions . . . . . . . . . . . . . . . . . . . .\n100\n8.3\nTagging categories . . . . . . . . . . . . . . . .\n101\n8.4\nDilution factor and e\ufb00ective tagging e\ufb03ciency\n101\n8.5\nPhysics sources of \ufb02avor information\n. . . . .\n102\n8.5.1\nLeptons\n. . . . . . . . . . . . . . . . .\n102\n8.5.2\nKaons\n. . . . . . . . . . . . . . . . . .\n102\n8.5.3\nSlow pions . . . . . . . . . . . . . . . .\n102\n8.5.4\nCorrelation of kaons and slow pions . .\n103\n8.5.5\nHigh-momentum particles\n. . . . . . .\n103\n8.5.6\nCorrelation of fast and slow particles .\n103\n8.5.7\n\u039b baryons . . . . . . . . . . . . . . . .\n103\n8.6\nSpeci\ufb01c \ufb02avor tagging algorithms\n. . . . . . .\n104\n8.6.1\nMultivariate tagging methods . . . . .\n104\n8.6.2\nSystematic e\ufb00ects . . . . . . . . . . . .\n104\n8.6.3\nFlavor tagging in BABAR\n. . . . . . . .\n104\n8.6.4\nFlavor tagging in Belle . . . . . . . . .\n106\n9\nBackground suppression for B decays\n. . . . . . . .\n109\n9.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n109\n9.2\nMain backgrounds to B decays . . . . . . . . .\n109\n9.3\nTopological discrimination . . . . . . . . . . .\n109\n9.4\nBABAR strategy\n. . . . . . . . . . . . . . . . .\n110\n9.4.1\nLinear discriminants\n. . . . . . . . . .\n111\n9.4.2\nNonlinear discriminants\n. . . . . . . .\n112\n9.4.3\nIncluding additional sources of background\nsuppression\n. . . . . . . . . . . . . . .\n113\n9.5\nBelle strategy\n. . . . . . . . . . . . . . . . . .\n114\n9.5.1\nSFW . . . . . . . . . . . . . . . . . . .\n114\n9.5.2\nKSFW\n. . . . . . . . . . . . . . . . .\n114\n9.5.3\nAdditional variables and neural network 115\n9.6\nSummary . . . . . . . . . . . . . . . . . . . . .\n117\n10\nMixing and time-dependent analyses\n. . . . . . . .\n119\n10.1\nNeutral meson mixing . . . . . . . . . . . . . .\n119\n10.2\nTime-dependent evolution\n. . . . . . . . . . .\n122\n10.3\nUse of \ufb02avor tagging\n. . . . . . . . . . . . . .\n123\n10.4\nResolution of \u2206t . . . . . . . . . . . . . . . . .\n124\n10.5\nModeling the \u2206t distribution for background\nevents\n. . . . . . . . . . . . . . . . . . . . . .\n126\n10.6\nParameter extraction from data . . . . . . . .\n126\n11\nMaximum likelihood \ufb01tting . . . . . . . . . . . . . .\n128\n11.1\nFormalism of maximum likelihood \ufb01ts . . . . .\n128\n11.1.1 Probability Density Functions . . . . .\n128\n11.1.2 Maximum Likelihood estimation of model\nparameters . . . . . . . . . . . . . . . .\n128\n11.1.3 Estimating the statistical uncertainty\nusing the likelihood . . . . . . . . . . .\n129\n11.1.4 Hypothesis testing and signi\ufb01cance . .\n130\n11.1.5 Computational aspects of maximum like-\nlihood estimates . . . . . . . . . . . . .\n130\n11.2\nStructure of models for signal yield measure-\nments and rare decay searches . . . . . . . . .\n131\n11.2.1 Extended ML formalism . . . . . . . .\n132\n11.2.2 Extending a model to multiple dimensions132\n11.2.3\nsPlots . . . . . . . . . . . . . . . . . .\n133\n11.3\nStructure of models for decay time-dependent\nmeasurements . . . . . . . . . . . . . . . . . .\n134\n11.3.1 Visualization of p.d.f.s of decay time\ndistributions . . . . . . . . . . . . . . .\n135\n11.4\nTechniques used for constraining nuisance pa-\nrameters from control samples . . . . . . . . .\n136\n11.4.1 Simultaneous \ufb01ts to control regions . .\n136\n11.4.2 Simultaneous \ufb01ts to multiple signal re-\ngions . . . . . . . . . . . . . . . . . . .\n136\n11.5\nMiscellaneous issues . . . . . . . . . . . . . . .\n137\n11.5.1 Background subtraction and weighted\nevents\n. . . . . . . . . . . . . . . . . .\n137\n11.5.2 Validation of ML \ufb01ts on complex models 138\n11.5.3 Computational optimizations of likeli-\nhood calculations . . . . . . . . . . . .\n139\n12\nAngular analysis . . . . . . . . . . . . . . . . . . . .\n140\n12.1\nFormalism . . . . . . . . . . . . . . . . . . . .\n140\n12.1.1 Spin and helicity\n. . . . . . . . . . . .\n140\n12.1.2 Angular bases . . . . . . . . . . . . . .\n140\n12.1.3 Angular distributions in the helicity basis141\n12.1.4 Angular distributions in the transver-\nsity basis . . . . . . . . . . . . . . . . .\n141\n12.1.5 CP violation . . . . . . . . . . . . . . .\n142\n12.1.6 Time dependence . . . . . . . . . . . .\n142\n12.2\nList of modes\n. . . . . . . . . . . . . . . . . .\n143\n12.2.1 V \u2192PP . . . . . . . . . . . . . . . . .\n143\n12.2.2 P \u2192V P , V \u2192PP . . . . . . . . . . .\n143\n12.2.3 P \u2192V \u03b3 , V \u2192PP and P \u2192T\u03b3 , T \u2192\nPP . . . . . . . . . . . . . . . . . . . .\n144\n12.2.4 P \u2192V V , V \u2192PP . . . . . . . . . . .\n144\n12.2.5 P \u2192V V , V1 \u2192P\u03b3 , V2 \u2192PP\n. . . .\n144\n12.2.6 P \u2192V V , V \u2192P\u03b3 . . . . . . . . . . .\n145\n12.2.7 P \u2192V V , V1 \u2192PP , V2 \u2192ll\n. . . . .\n145\n12.2.8 P \u2192V V , V1 \u2192PP , V2 \u2192V \u03b3\n. . . .\n145\n12.2.9 P \u2192TV , T \u2192PP , V \u2192PP . . . . .\n146\n12.3\nAnalysis details . . . . . . . . . . . . . . . . .\n146\n12.3.1 Generators . . . . . . . . . . . . . . . .\n146\n12.3.2 Experimental e\ufb00ects\n. . . . . . . . . .\n146\n12.3.3 Caveats\n. . . . . . . . . . . . . . . . .\n146\n12.4\nAngular \ufb01ts\n. . . . . . . . . . . . . . . . . . .\n147\n12.4.1 Dedicated or global \ufb01ts . . . . . . . . .\n147\n12.4.2 Partial and complete angular analyses\n147\n12.4.3 Other angular analyses . . . . . . . . .\n148\n13\nDalitz-plot analysis . . . . . . . . . . . . . . . . . .\n149\n13.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n149\n13.1.1 Three-body decay phase space . . . . .\n149\n13.1.2 Boundaries, kinematic constraints . . .\n149\n13.2\nAmplitude description\n. . . . . . . . . . . . .\n150\n13.2.1 Isobar formalism\n. . . . . . . . . . . .\n150\n13.2.2 K-matrix formalism . . . . . . . . . . .\n151\n13.2.3 Nonresonant description\n. . . . . . . .\n153\n13.2.4 Time-dependent analyses . . . . . . . .\n153\n13.3\nExperimental e\ufb00ects . . . . . . . . . . . . . . .\n154\n13.3.1 Backgrounds . . . . . . . . . . . . . . .\n154\n13.3.2 E\ufb03ciency\n. . . . . . . . . . . . . . . .\n154\n13.3.3 Misreconstructed signal . . . . . . . . .\n155\n13.4\nTechnical details . . . . . . . . . . . . . . . . .\n155\n13.4.1 Square Dalitz plot . . . . . . . . . . . .\n155\n13.4.2 Complex coe\ufb03cients\n. . . . . . . . . .\n156\n\nxvi\n13.4.3 Fitting . . . . . . . . . . . . . . . . . .\n157\n13.4.4 Fit fractions . . . . . . . . . . . . . . .\n158\n13.5\nModel uncertainties . . . . . . . . . . . . . . .\n158\n13.5.1 Estimation of model uncertainties . . .\n158\n13.5.2 Model-independent analysis\n. . . . . .\n159\n13.5.3 Model independent partial wave analysis 159\n14\nBlind analysis . . . . . . . . . . . . . . . . . . . . .\n160\n14.1\nDe\ufb01nition and brief history . . . . . . . . . . .\n160\n14.2\nSetting upper limits: a quantitative example .\n160\n14.3\nPrecision measurements . . . . . . . . . . . . .\n161\n14.4\nExamples from Belle\n. . . . . . . . . . . . . .\n161\n14.5\nExamples from BABAR . . . . . . . . . . . . . .\n162\n15\nSystematic error estimation\n. . . . . . . . . . . . .\n164\n15.1\nDi\ufb00erences between data and simulation\n. . .\n164\n15.1.1 Track reconstruction\n. . . . . . . . . .\n164\n15.1.2 K0\nS and \u039b reconstruction . . . . . . . .\n167\n15.1.3 Particle identi\ufb01cation . . . . . . . . . .\n168\n15.1.4 \u03c00 reconstruction . . . . . . . . . . . .\n168\n15.1.5 High-energy photons\n. . . . . . . . . .\n170\n15.2\nAnalysis procedure\n. . . . . . . . . . . . . . .\n170\n15.2.1 External input . . . . . . . . . . . . . .\n171\n15.2.2 Modeling of background\n. . . . . . . .\n171\n15.2.3 Fit bias . . . . . . . . . . . . . . . . . .\n171\n15.3\nSystematic e\ufb00ects for time-dependent analyses\n172\n15.3.1 Alignment of the vertex detector\n. . .\n172\n15.3.2 Beamspot position, z scale and boost .\n172\n15.3.3 Resolution function and \ufb02avor tagging\nparameters . . . . . . . . . . . . . . . .\n173\n15.3.4 The e\ufb00ect of physics parameters . . . .\n173\n15.3.5 CP violation in background components 173\n15.3.6 Tag-side interference\n. . . . . . . . . .\n174\n15.4\nSummary . . . . . . . . . . . . . . . . . . . . .\n175\nC\nThe results and their interpretation178\n16\nThe CKM matrix and the Kobayashi-Maskawa mech-\nanism\n. . . . . . . . . . . . . . . . . . . . . . . . . .\n178\n16.1\nHistorical background . . . . . . . . . . . . . .\n178\n16.2\nCP violation and baryogenesis . . . . . . . . .\n180\n16.3\nCP violation in a Lagrangian \ufb01eld theory . . .\n180\n16.4\nThe CKM matrix . . . . . . . . . . . . . . . .\n181\n16.5\nThe Unitarity Triangle . . . . . . . . . . . . .\n182\n16.6\nCP violation phenomenology for B mesons . .\n183\n17\nB physics\n. . . . . . . . . . . . . . . . . . . . . . .\n185\n17.1\nVub and Vcb\n. . . . . . . . . . . . . . . . . . .\n186\n17.1.1 Overview of semileptonic B decays\n. .\n186\n17.1.2 Exclusive decays B \u2192D(\u2217)\u2113\u03bd\n. . . . .\n189\n17.1.3 Inclusive Cabibbo-favored B decays . .\n194\n17.1.4 Exclusive decays B \u2192\u03c0\u2113\u03bd . . . . . . .\n200\n17.1.5 Inclusive Cabibbo-suppressed B decays\n209\n17.1.6 Evaluation of the results . . . . . . . .\n215\n17.2\nVtd and Vts . . . . . . . . . . . . . . . . . . . .\n216\n17.2.1 Bd,s mixing\n. . . . . . . . . . . . . . .\n216\n17.2.2 B \u2192X(s, d)\u03b3 . . . . . . . . . . . . . .\n217\n17.2.3 Summary\n. . . . . . . . . . . . . . . .\n219\n17.3\nHadronic B to charm decays . . . . . . . . . .\n221\n17.3.1 Introduction . . . . . . . . . . . . . . .\n221\n17.3.2 Theory overview . . . . . . . . . . . . .\n221\n17.3.3 Decays with a single D decay (D, D\u2217, Ds)225\n17.3.4 Decays with 2 D\u2019s . . . . . . . . . . . .\n227\n17.3.5 Decays to charmonium . . . . . . . . .\n232\n17.3.6 Summary\n. . . . . . . . . . . . . . . .\n235\n17.4\nCharmless B decays . . . . . . . . . . . . . . .\n236\n17.4.1 Introduction . . . . . . . . . . . . . . .\n236\n17.4.2 Theoretical overview\n. . . . . . . . . .\n237\n17.4.3 Experimental techniques . . . . . . . .\n241\n17.4.4 Two-body decays . . . . . . . . . . . .\n245\n17.4.5 Quasi-two-body decays . . . . . . . . .\n248\n17.4.6 Dalitz experimental techniques\n. . . .\n263\n17.4.7 Three-body and Dalitz decays . . . . .\n268\n17.4.8 Summary\n. . . . . . . . . . . . . . . .\n272\n17.5\nB-meson lifetimes, B0 \u2212B0 mixing, and sym-\nmetry violation searches\n. . . . . . . . . . . .\n274\n17.5.1 B-meson lifetimes . . . . . . . . . . . .\n274\n17.5.2 B0 \u2212B0 mixing . . . . . . . . . . . . .\n280\n17.5.3 Tests of quantum entanglement . . . .\n289\n17.5.4 Violation of CP, T, and CPT symme-\ntries in B0 \u2212B0 mixing\n. . . . . . . .\n292\n17.5.5 Lorentz invariance violation in B0 \u2212B0\nmixing . . . . . . . . . . . . . . . . . .\n298\n17.6\n\u03c61, or \u03b2\n. . . . . . . . . . . . . . . . . . . . .\n302\n17.6.1 Overview of \u03c61 measurement at the B\nFactories . . . . . . . . . . . . . . . . .\n302\n17.6.2\nTransitions and formalism\n. . . . . .\n304\n17.6.3\n\u03c61 from b \u2192c\u00afcs decays\n. . . . . . . .\n305\n17.6.4\n\u03c61 from b \u2192c\u00afcd decays\n. . . . . . . .\n308\n17.6.5\n\u03c61 from b \u2192c\u00afud decays . . . . . . . .\n311\n17.6.6\n\u03c61 from charmless quasi-two-body B\ndecays\n. . . . . . . . . . . . . . . . . .\n312\n17.6.7\n\u03c61 from charmless three-body decays\n314\n17.6.8\nResolving discrete ambiguities in \u03c61\n.\n317\n17.6.9 Time-reversal violation in b \u2192ccs decays322\n17.6.10 \u03c61 summary\n. . . . . . . . . . . . . .\n326\n17.7\n\u03c62, or \u03b1\n. . . . . . . . . . . . . . . . . . . . .\n328\n17.7.1 Introduction . . . . . . . . . . . . . . .\n329\n17.7.2 Event reconstruction . . . . . . . . . .\n333\n17.7.3 B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c1 . . . . . . . . . .\n333\n17.7.4 B0 \u2192(\u03c1\u03c0)0\n. . . . . . . . . . . . . . .\n338\n17.7.5 B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213\n. . . . . . . . . . .\n339\n17.7.6 SU(3) constraint using B0 \u2192\u03c1+\u03c1\u2212,\nand B+ \u2192K\u22170\u03c1+ . . . . . . . . . . . .\n341\n17.7.7 Summary\n. . . . . . . . . . . . . . . .\n342\n17.8\n\u03c63, or \u03b3 . . . . . . . . . . . . . . . . . . . . . .\n345\n17.8.1 Introduction . . . . . . . . . . . . . . .\n345\n17.8.2 GLW method\n. . . . . . . . . . . . . .\n345\n17.8.3 ADS method . . . . . . . . . . . . . . .\n347\n17.8.4 Dalitz plot (GGSZ) method . . . . . .\n350\n17.8.5 sin(2\u03c61 + \u03c63)\n. . . . . . . . . . . . . .\n360\n17.8.6 Determination of \u03c63 and discussion . .\n363\n17.9\nRadiative and electroweak penguin decays\n. .\n365\n17.9.1 Theoretical framework . . . . . . . . .\n365\n17.9.2 Inclusive b \u2192s\u03b3 . . . . . . . . . . . . .\n370\n17.9.3 Exclusive b \u2192s\u03b3\n. . . . . . . . . . . .\n377\n17.9.4 Exclusive and inclusive b \u2192d\u03b3\n. . . .\n379\n17.9.5 Rate asymmetries in b \u2192s(d)\u03b3\n. . . .\n382\n17.9.6 Time-dependent CP asymmetries . . .\n385\n17.9.7 Electroweak penguin decays b \u2192s(d)\u2113+\u2113\u2212387\n17.9.8 Electroweak penguin decays b \u2192s(d)\u03bd\u03bd 393\n17.10 B+ \u2192\u2113+\u03bd(\u03b3) and B \u2192D(\u2217)\u03c4\u03bd\n. . . . . . . .\n395\n17.10.1Overview . . . . . . . . . . . . . . . . .\n395\n17.10.2B+ \u2192\u2113+\u03bd(\u03b3) . . . . . . . . . . . . . .\n396\n17.10.3B \u2192D(\u2217)\u03c4\u03bd . . . . . . . . . . . . . . .\n404\n17.10.4Discussion and future prospects . . . .\n407\n17.11 Rare and forbidden B decays . . . . . . . . . .\n410\n\nxvii\n17.11.1B0 \u2192\u2113+\u2113\u2212(\u03b3) . . . . . . . . . . . . . .\n410\n17.11.2B0 \u2192invisible\n. . . . . . . . . . . . .\n413\n17.11.3B0 \u2192\u03b3\u03b3 and B0\ns \u2192\u03b3\u03b3\n. . . . . . . .\n414\n17.11.4Lepton \ufb02avor violating modes . . . . .\n416\n17.11.5Lepton number violating modes . . . .\n418\n17.11.6Lepton/baryon number violating modes 420\n17.11.7Summary\n. . . . . . . . . . . . . . . .\n421\n17.12 B decays to baryons\n. . . . . . . . . . . . . .\n422\n17.12.1Inclusive decays into baryons\n. . . . .\n422\n17.12.2Two-body decays . . . . . . . . . . . .\n423\n17.12.3Decays to baryon antibaryon plus mesons428\n17.12.4Radiative decays into baryons . . . . .\n439\n17.12.5Semileptonic decays with a baryon-antibaryon\npair . . . . . . . . . . . . . . . . . . . .\n440\n17.12.6Summary\n. . . . . . . . . . . . . . . .\n440\n18\nQuarkonium physics\n. . . . . . . . . . . . . . . . .\n441\n18.1\nIntroduction to quarkonium\n. . . . . . . . . .\n441\n18.1.1 Quantum numbers and spectroscopy\n.\n441\n18.1.2 Potential models\n. . . . . . . . . . . .\n442\n18.1.3 Quarkonium as a multiscale system . .\n443\n18.1.4 E\ufb00ective Field Theories . . . . . . . . .\n444\n18.1.5 Lattice calculations . . . . . . . . . . .\n447\n18.1.6 Applications . . . . . . . . . . . . . . .\n447\n18.2\nConventional charmonium\n. . . . . . . . . . .\n449\n18.2.1 New conventional charmonium states .\n449\n18.2.2 New decay modes of known charmonia\n457\n18.2.3 Measurements of parameters . . . . . .\n459\n18.2.4 Production . . . . . . . . . . . . . . . .\n462\n18.2.5 Concluding remarks . . . . . . . . . . .\n468\n18.3\nExotic charmonium-like states . . . . . . . . .\n469\n18.3.1 Theoretical models . . . . . . . . . . .\n469\n18.3.2 The X(3872) . . . . . . . . . . . . . . .\n470\n18.3.3 The 3940 family . . . . . . . . . . . . .\n476\n18.3.4 Other C = +1 states . . . . . . . . . .\n477\n18.3.5 The 1\u2212\u2212family . . . . . . . . . . . . .\n478\n18.3.6 Charged charmonium-like States . . . .\n480\n18.3.7 Summary and outlook\n. . . . . . . . .\n482\n18.4\nBottomonium\n. . . . . . . . . . . . . . . . . .\n485\n18.4.1 Introduction . . . . . . . . . . . . . . .\n485\n18.4.2 Common techniques\n. . . . . . . . . .\n485\n18.4.3 e+e\u2212energy scans\n. . . . . . . . . . .\n486\n18.4.4 Spectroscopy . . . . . . . . . . . . . . .\n487\n18.4.5 Discovery of charged Zb states . . . . .\n496\n18.4.6 Transitions and decays . . . . . . . . .\n498\n18.4.7 Physics beyond the Standard Model\n.\n506\n19\nCharm physics . . . . . . . . . . . . . . . . . . . . .\n515\n19.1\nCharmed meson decays . . . . . . . . . . . . .\n516\n19.1.1 Introduction . . . . . . . . . . . . . . .\n516\n19.1.2 Branching ratio measurements . . . . .\n520\n19.1.3 Cabibbo-suppressed decays . . . . . . .\n524\n19.1.4 Dalitz analysis of three-body charmed\nmeson decays\n. . . . . . . . . . . . . .\n530\n19.1.5 Semileptonic charm decays . . . . . . .\n543\n19.1.6 D+\ns leptonic decays . . . . . . . . . . .\n551\n19.1.7 Rare or forbidden charmed meson decays554\n19.1.8 D0 \u2192\u2113+\u2113\u2212\n. . . . . . . . . . . . . . .\n555\n19.1.9 Search for rare or forbidden semilep-\ntonic charm decays . . . . . . . . . . .\n558\n19.1.10Summary of charmed meson decays . .\n560\n19.2\nD-mixing and CP violation . . . . . . . . . . .\n561\n19.2.1 Introduction . . . . . . . . . . . . . . .\n561\n19.2.2 Hadronic wrong-sign decays . . . . . .\n567\n19.2.3 Decays to CP eigenstates . . . . . . . .\n573\n19.2.4 t-dependent Dalitz analyses\n. . . . . .\n578\n19.2.5 Semileptonic decays . . . . . . . . . . .\n580\n19.2.6 t-integrated CP violation measurements 584\n19.2.7 t-dependent CP violating asymmetries\n594\n19.2.8 Summary\n. . . . . . . . . . . . . . . .\n596\n19.3\nCharmed meson spectroscopy\n. . . . . . . . .\n599\n19.3.1 Introduction . . . . . . . . . . . . . . .\n599\n19.3.2 Production of charmed mesons at B Fac-\ntories . . . . . . . . . . . . . . . . . . .\n604\n19.3.3 Non-strange charm spectroscopy . . . .\n604\n19.3.4 Charmed-strange mesons . . . . . . . .\n610\n19.3.5 Conclusions\n. . . . . . . . . . . . . . .\n622\n19.4\nCharmed baryon spectroscopy and decays\n. .\n623\n19.4.1 Spectroscopy . . . . . . . . . . . . . . .\n623\n19.4.2 Weak decays . . . . . . . . . . . . . . .\n631\n19.4.3 Applications to light baryon spectroscopy635\n20\nTau physics\n. . . . . . . . . . . . . . . . . . . . . .\n637\n20.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n637\n20.2\nMass of the tau lepton\n. . . . . . . . . . . . .\n637\n20.3\nTests of lepton universality . . . . . . . . . . .\n639\n20.3.1 Charged current universality between\n\u00b5-e . . . . . . . . . . . . . . . . . . . .\n639\n20.3.2\nCharged current universality between\n\u03c4-\u00b5 . . . . . . . . . . . . . . . . . . . .\n640\n20.4\nSearch for lepton \ufb02avor violation in tau decays\n640\n20.4.1 Tau lepton data samples and search strate-\ngies . . . . . . . . . . . . . . . . . . . .\n640\n20.4.2 Results on LFV decays of the tau from\nBelle and BABAR . . . . . . . . . . . . .\n642\n20.4.3 Future Prospects\n. . . . . . . . . . . .\n644\n20.5\nCP violation in the tau lepton system . . . . .\n644\n20.5.1 Electric dipole moment of the tau lepton 645\n20.5.2 CP violation in tau decay\n. . . . . . .\n648\n20.6\nHadronic tau decays\n. . . . . . . . . . . . . .\n651\n20.6.1 Theory . . . . . . . . . . . . . . . . . .\n651\n20.6.2 Tau lepton branching fractions . . . . .\n655\n20.6.3 Hadronic spectral functions: Cabibbo-\nfavored modes . . . . . . . . . . . . . .\n655\n20.6.4 Hadronic spectral functions: Cabibbo-\nsuppressed modes . . . . . . . . . . . .\n659\n20.6.5 Inclusive non-strange spectral function\n660\n20.6.6 Inclusive strange spectral functions . .\n660\n20.6.7 Search for second-class currents . . . .\n661\n20.7\nTests of CVC and vacuum hadronic polariza-\ntion determination\n. . . . . . . . . . . . . . .\n662\n20.7.1\nCVC and vacuum hadronic polariza-\ntion contribution in (g \u22122)\u00b5 . . . . . .\n663\n20.7.2\nCVC and \u03c0\u03c0 branching fraction\n. . .\n664\n20.8\nMeasurement of |Vus| . . . . . . . . . . . . . .\n664\n20.9\nSummary of the tau section\n. . . . . . . . . .\n665\n21\nInitial state radiation studies . . . . . . . . . . . . .\n667\n21.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n667\n21.2\nThe Initial State Radiation method . . . . . .\n667\n21.2.1 Radiator function and Monte Carlo gen-\nerators . . . . . . . . . . . . . . . . . .\n668\n21.2.2 Cross section\n. . . . . . . . . . . . . .\n669\n21.2.3 Mass resolution and energy scale\n. . .\n670\n21.2.4 Comparison of tagged and untagged ISR\nmeasurements with direct e+e\u2212mea-\nsurements\n. . . . . . . . . . . . . . . .\n671\n21.3\nExclusive hadronic cross-sections\n. . . . . . .\n672\n\nxviii\n21.3.1 Common analysis strategy . . . . . . .\n672\n21.3.2 Hadronic vacuum polarization . . . . .\n672\n21.3.3 Measurement of e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3) . . .\n674\n21.3.4 Impact of ISR results on (g \u22122)\u00b5 and\n\u03b1(MZ) . . . . . . . . . . . . . . . . . .\n676\n21.3.5 Light meson spectroscopy\n. . . . . . .\n679\n21.3.6 Search for fJ(2220) . . . . . . . . . . .\n685\n21.3.7 Measurement of time-like baryon form\nfactors . . . . . . . . . . . . . . . . . .\n686\n21.4\nOpen charm production . . . . . . . . . . . . .\n690\n21.4.1 Measurement of exclusive D(\u2217)+D(\u2217)\u2212\nproduction far from threshold . . . . .\n690\n21.4.2 Measurement of the DD cross section\nvia full reconstruction\n. . . . . . . . .\n691\n21.4.3 Partial reconstruction of D(\u2217)+D\u2217\u2212\ufb01-\nnal states\n. . . . . . . . . . . . . . . .\n693\n21.4.4 e+e\u2212\u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\n. . . . . . . . . .\n694\n21.4.5 Three-body charm \ufb01nal states . . . . .\n695\n21.4.6 Charm baryon production in e+e\u2212an-\nnihilation . . . . . . . . . . . . . . . . .\n696\n21.4.7 Sum of exclusive vs inclusive cross section696\n21.5\nSearch for exotic charmonium . . . . . . . . .\n696\n21.5.1 Y family states in ISR \u03c0+\u03c0\u2212J/\u03c8\n. . .\n697\n21.5.2 Y family states in ISR \u03c0+\u03c0\u2212\u03c8(2S) . .\n700\n21.6\nDark force searches . . . . . . . . . . . . . . .\n700\n21.6.1 Searches for a dark photon . . . . . . .\n701\n21.6.2 A search for dark gauge bosons\n. . . .\n701\n21.6.3 A search for dark Higgs bosons\n. . . .\n702\n22\nTwo-photon physics . . . . . . . . . . . . . . . . . .\n703\n22.1\nDescriptions of two-photon topics to be covered 703\n22.1.1 Introduction for two-photon physics . .\n703\n22.1.2 Cross section for \u03b3\u03b3 collisions (zero-tag) 703\n22.1.3 Resonance production\n. . . . . . . . .\n704\n22.1.4 Single-tag measurements . . . . . . . .\n704\n22.1.5 Monte-Carlo Techniques . . . . . . . .\n704\n22.2\nPseudoscalar meson-pair production . . . . . .\n705\n22.2.1 Light-quark meson resonances . . . . .\n705\n22.2.2 Comparison with QCD predictions at\nhigh energy\n. . . . . . . . . . . . . . .\n707\n22.3\nVector meson-pair production\n. . . . . . . . .\n709\n22.4\n\u03b7\u2032\u03c0+\u03c0\u2212production . . . . . . . . . . . . . . .\n712\n22.5\nBaryon-pair production . . . . . . . . . . . . .\n713\n22.6\nCharmonium formation . . . . . . . . . . . . .\n713\n22.7\nForm factor measurements with single-tag pro-\ncesses . . . . . . . . . . . . . . . . . . . . . . .\n714\n22.7.1 The \u03b3\u03b3\u2217\u03c00 transition form factor\n. . .\n715\n22.7.2 The \u03b3\u03b3\u2217\u03b7 and \u03b3\u03b3\u2217\u03b7\u2032 transition form fac-\ntors . . . . . . . . . . . . . . . . . . . .\n718\n22.7.3 The \u03b3\u03b3\u2217\u03b7c transition form factor\n. . .\n719\n22.7.4 Summary\n. . . . . . . . . . . . . . . .\n720\n23\nB0\ns physics at the \u03a5(5S)\n. . . . . . . . . . . . . . .\n721\n23.1\nIntroduction . . . . . . . . . . . . . . . . . . .\n721\n23.2\nBasic \u03a5(5S) properties and beauty hadronization722\n23.2.1 Event classi\ufb01cation . . . . . . . . . . .\n722\n23.2.2 Choice of CM energy for data taking at\nthe \u03a5(5S)\n. . . . . . . . . . . . . . . .\n723\n23.2.3 Calculation of the number of B0\ns mesons\nin a data sample\n. . . . . . . . . . . .\n723\n23.2.4 bb cross section at the \u03a5(5S) . . . . . .\n724\n23.2.5 Fraction of bb events with B0\ns mesons .\n724\n23.2.6 Exclusive B0\ns and B decay reconstruc-\ntion technique . . . . . . . . . . . . . .\n726\n23.2.7 Fractions of events with B mesons\n. .\n727\n23.3\nMeasurements of B0\ns decays at \u03a5(5S) . . . . .\n729\n23.3.1 B0\ns semileptonic branching fraction . .\n729\n23.3.2 Cabibbo favored decays B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+(\u03c1+)730\n23.3.3 Cabibbo favored decays B0\ns \u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\n732\n23.3.4 Color suppressed decays B0\ns \u2192J/\u03c8\u03b7(\u2032)\nand B0\ns \u2192J/\u03c8f0(980)\n. . . . . . . . .\n734\n23.3.5 Charmless decays B0\ns \u2192hh, h = \u03c0, K .\n735\n23.3.6 Penguin decays B0\ns \u2192\u03c6\u03b3, B0\ns \u2192\u03b3\u03b3 . .\n736\n23.4\nConclusion . . . . . . . . . . . . . . . . . . . .\n737\n24\nQCD-related physics\n. . . . . . . . . . . . . . . . .\n739\n24.1\nFragmentation . . . . . . . . . . . . . . . . . .\n739\n24.1.1 Introduction . . . . . . . . . . . . . . .\n739\n24.1.2 Unpolarized fragmentation functions\n.\n741\n24.1.3 Polarized fragmentation functions\n. .\n752\n24.1.4 Summary on fragmentation functions .\n758\n24.2\nPentaquark searches . . . . . . . . . . . . . . .\n759\n24.2.1 Theoretical studies on pentaquarks . .\n759\n24.2.2 Positive claims in 2003\u20132005 . . . . . .\n761\n24.2.3 Inclusive production searches\n. . . . .\n762\n24.2.4 Searches in B decays . . . . . . . . . .\n763\n24.2.5 Searches using interactions in the de-\ntector material\n. . . . . . . . . . . . .\n763\n24.2.6 Summary\n. . . . . . . . . . . . . . . .\n766\n25\nGlobal interpretation . . . . . . . . . . . . . . . . .\n767\n25.1\nGlobal CKM \ufb01ts . . . . . . . . . . . . . . . . .\n768\n25.1.1 Introduction . . . . . . . . . . . . . . .\n768\n25.1.2 CP violation in the era of the B Factories768\n25.1.3 Methodology . . . . . . . . . . . . . . .\n768\n25.1.4 Experimental inputs\n. . . . . . . . . .\n770\n25.1.5 Theoretical inputs: derivation of hadronic\nobservables . . . . . . . . . . . . . . . .\n772\n25.1.6 Results from the global \ufb01ts . . . . . . .\n774\n25.1.7 Conclusions\n. . . . . . . . . . . . . . .\n774\n25.2\nBenchmark new physics models\n. . . . . . . .\n777\n25.2.1 Short description of NP models . . . .\n778\n25.2.2 Detailed description of NP models . . .\n781\n25.2.3 Summary\n. . . . . . . . . . . . . . . .\n792\nAppendices\n793\nA\nGlossary of terms\n. . . . . . . . . . . . . . . . . . .\n793\nB\nThe BABAR Collaboration author list . . . . . . . . .\n796\nC\nThe Belle Collaboration author list\n. . . . . . . . .\n801\nD\nAcknowledgments\n. . . . . . . . . . . . . . . . . . .\n805\nBABAR publications\n806\nBelle publications\n822\nBibliography\n835\nIndex\n899\n\n1\nPart A\nThe facilities\nChapter 1\nThe B Factories\nEditors:\nDavid Leith (BABAR)\nKazuo Abe, Stephen L. Olsen (Belle)\nAdditional section writers:\nPeter Kri\u02c7zan, Leo Piilonen, Blair Ratcli\ufb00, Guy Wormser\n1.1 Introduction\nIn their classic paper, Kobayashi and Maskawa (1973,\n\u201cKM\u201d) pointed out that CP violation could be natu-\nrally incorporated into the Standard Model (SM) as an\nirreducible complex phase in the weak interaction quark-\n\ufb02avor-mixing matrix if the number of quark \ufb02avors was\nsix. This was remarkable because at that time only the\nthree quarks of the original Gell-Mann (1964) and Zweig\n(1964a) quark model \u2014 i.e., the u-, d- and s-quarks \u2014\nwere experimentally established. The situation changed\ndramatically in late 1974 with the discovery of the c-\nquark at Brookhaven (Aubert et al., 1974) and SLAC (Au-\ngustin et al., 1974) and the 1977 discovery of the b-\nquark at Fermilab (Herb et al., 1977). By 1980, the\nKM idea, by then embodied in the Cabibbo-Kobayashi-\nMaskawa (CKM) quark \ufb02avor mixing matrix (Cabibbo,\n1963; Kobayashi and Maskawa, 1973), was accepted as an\nintegral component of the Standard Model, even though\nits raison d\u2019etre, the CP-violating complex phase, had not\nbeen measured (Kelly et al., 1980).\n1.1.1 Testing the KM idea\nIn the early 1980\u2019s, when the experimental state-of-the-art\nin B meson physics was de\ufb01ned by the CLEO experiment,\nwhere the measurements were based on data samples of\na few tens of events (Bebek et al., 1981; Chadwick et al.,\n1981), Bigi, Carter, and Sanda published papers exploring\nthe possibilities of using B meson decays to test the valid-\nity of the KM six-quark mechanism for CP violation (Bigi\nand Sanda, 1981, 1984; Carter and Sanda, 1980, 1981).\nThey concluded that for a relatively small range of the\nCKM-matrix parameter-space that was allowed at that\ntime \u2014 a range that corresponds to a substantial prob-\nability for B0 \u2212B0 mixing and a long B meson lifetime\n\u2014 large CP violation might be observable in neutral B\nmeson decays to CP eigenstates, such as B0 \u2192J/\u03c8K0\nS.\nHowever, in the early 1980\u2019s, no decays of this type had\nbeen seen; we now know that their branching fractions are\n\u223c0.1% or less. A reasonable conclusion that could be de-\nrived from these papers at that time was that de\ufb01nitive\ntests of the KM idea were hopelessly impractical.\n1.1.2 Three miracles\nSubsequently, three remarkable developments occurred\nthat completely turned the tables. These included the \ufb01rst\nemergence of evidence of a long B meson lifetime from\nexperiments at SLAC (Fernandez et al., 1983; Lockyer\net al., 1983), and the unexpected discovery by the AR-\nGUS experiment at DESY in 1987 of a substantial rate for\nB0 \u2212B0 mixing (Albrecht et al., 1987b). These measure-\nments indicated that the CKM-matrix parameters are, in\nfact, in the range that is accessible to tests of the KM\nidea. This was helped along by many well-attended in-\nternational workshops1 developing each of the di\ufb00erent\ntechnical approaches and re\ufb01ning the requirements and\nspeci\ufb01cations for each. It became clear that CP violation,\nat the level manifest in the Standard Model, could be ex-\nperimentally observable somewhere other than in neutral\nkaons: namely, in the B0 \u2212B0 system. Moreover large CP\nviolation was expected, rather than the one-in-a-thousand\ne\ufb00ect seen in K decay. In addition, Bigi and Sanda (1981)\nhad shown that a measurement of CP violation in neutral\nB meson decays to CP eigenstates could be clearly in-\nterpreted without theoretical uncertainties. However, an\nexperiment to observe CP violation in B decays would\nrequire about a thousand-fold larger data samples of B\nmesons than had been gathered heretofore.\nThe two fortuitous circumstances mentioned above\nwere accompanied by a third \u201cmiracle\u201d: extraordinary\nimprovements in the performance of e+e\u2212storage rings,\nwith order-of-magnitude luminosity improvements occur-\nring approximately every seven years. In 1980, the original\nCESR collider typically produced \u223c30 BB meson pairs\nper day; thirty years later, the two B Factories, KEKB\nand PEP-II, routinely produced more than one million BB\nmeson pairs per day, a nearly \ufb01ve orders-of-magnitude im-\nprovement! The B Factories built on the success of CESR\nat Cornell and DORIS-II at DESY to achieve these pro-\nduction rates. These developments were accompanied by\nless miraculous, but still impressive, advances in the capa-\nbilities of large solid-angle detectors, especially in the abil-\nity of data acquisition systems to handle the huge event\nrates associated with the available luminosities, precision\ntracking and vertexing devices, and the software and stor-\nage technologies required to deal with these large data\nsamples.\n1 The main workshops include: Heidelberg (Schubert and\nWaldi, 1986), Stanford (Bloom, Friedsam, and Fridman, 1988;\nHitlin, 1990), Courmayeur (De Sanctis, Greco, Piccolo, and\nTazzari, 1988), Zuoz (Locher, 1988), Los Angeles (Cline\nand Fridman, 1988; Cline and Stork, 1987), Blois (Cline\nand Fridman, 1991), Syracuse (Goldberg and Stone, 1989),\nTsukuba (Kikutani and Matsuda, 1993; Ozaki and Sato, 1991;\nYoshimura, 1989), Vancouver (MacFarlane and Ng, 1991), and\nHamburg (Aleksan and Ali, 1993).\n\n2\nThe remainder of this chapter discusses the historical\nroute taken to develop the ideas necessary to build a B\nFactory (Section 1.2), followed by an overview of the two\nstorage rings that were built to provide a source of B0B0\nmeson pairs to explore the B Factory scienti\ufb01c program\n(Section 1.3). A review of general issues concerning the\ndetector requirements for a B Factory is presented in Sec-\ntion 1.4; a more detailed discussion of the two detectors\nrealized can be found in Chapter 2. We conclude with a\nbrief look at the early physics discoveries of the B Facto-\nries (Section 1.5).\n1.2 The path to the B Factories\n1.2.1 Requirements for a B Factory\nThe time-dependent method for testing the KM idea is\nbased on the fact that there are decays with interfering\namplitudes (see Fig. 1.2.1) where the interference term\ncontains V \u2217\ncdVcbVtdV \u2217\ntb. The phase of this quartet of CKM\nmatrix elements is \u03c61 = \u03b2. Note that the BABAR exper-\niment uses \u03b2 to denote this angle, whereas the Belle ex-\nperiment reports results in terms of \u03c61; further notational\ndi\ufb00erences are discussed in Chapter 16. In the following\nwe will use the \u03c61 notation for this phase. The \u201cgolden\nobservable\u201d for its determination is the CP asymmetry\nbetween B0 \u2192J/\u03c8K0\nS and B0 \u2192J/\u03c8K0\nS. At the B Fac-\ntories, neutral B mesons are created in pairs at a center-\nof-mass energy corresponding to the \u03a5(4S). As a result\nthe wave function of the B0B0 pairs is in a P-wave en-\ntangled state, until one of the mesons decays. A further\ncomplication arises as neutral B mesons mix with a char-\nacteristic frequency \u2206md, so one computes the asymme-\ntry as a function of the proper time di\ufb00erence between\nthe decays of two mesons in an event, and uses knowl-\nedge of B0B0 mixing to infer the \ufb02avor of one of the B\nmesons (decaying into a CP eigenstate) relative to that\nof the other B decaying into a \ufb02avor speci\ufb01c \ufb01nal state.\nThis initial state preparation at the \u03a5(4S) enables one to\ndetermine the \ufb02avor of the b quark for the \ufb02avor speci\ufb01c\n\ufb01nal states with a high e\ufb03ciency.\nThe amplitude for the direct decay B0 \u2192J/\u03c8K0\nS,\nshown in the upper right panel of Fig 1.2.1, is proportional\nto the Vcb CKM matrix element. The decay can also pro-\nceed via the two-step process B0 \u2192B0 \u2192J/\u03c8K0\nS, shown\nin the bottom-right panel of the \ufb01gure. The phase di\ufb00er-\nence between these two amplitudes is 2\u03c61.\nThe technique for performing the interference mea-\nsurement is illustrated in Fig. 1.2.2. A B0B0 pair pro-\nduced via \u03a5(4S) \u2192B0B0 decay is entangled in a coherent\nquantum state until one of the mesons decays. Most B0\nmeson decays produce \ufb02avor-speci\ufb01c \ufb01nal states, i.e., the\n\ufb01nal-state particles can be used to determine whether the\ndecaying meson was a B0 or a B0. For example, a K+\nmeson in the \ufb01nal state signals a high likelihood for the\nB \u2192D \u2192K+ decay chain and, thus, a higher probability\nthat the parent meson was a B0 rather than a B0. Such\na decay is called a \u201c\ufb02avor-tag\u201d decay. At the time this\nB meson decays (t1 in the \ufb01gure), the accompanying B\nmeson\u2019s \ufb02avor is speci\ufb01ed as being the opposite.\nFigure 1.2.2. An illustration of the B Factory \ufb02agship mea-\nsurement of sin 2\u03c61 = sin 2\u03b2.\nThis accompanying meson then propagates in time and\nthe quark \ufb02avor content can oscillate from an unmixed\nstate into a mixed one, until it decays (at time t2). If it de-\ncays into a CP eigenstate such as J/\u03c8K0\nS, the unmixed and\nmixed \ufb02avor components interfere, producing di\ufb00erent de-\ncay rates for B0-tagged and B0-tagged mesons. A similar\npattern occurs for those cases where the CP eigenstate de-\ncay occurs before the \ufb02avor tag decay (i.e. t2 \u2264t1) except\nthat in this case the common phase from the mixing dia-\ngram has opposite sign. Thus, for B0-tagged events, the in-\nterference is destructive for negative values of \u2206t = t2 \u2212t1\nand constructive for positive \u2206t values, as indicated in\nthe graph in the lower part of the \ufb01gure, where the \u2206t\ndependence for B0-tagged events is shown in units of \u03c4B,\nthe B0 lifetime (\u22481.5 ps). The time-integrated asymme-\ntry is zero; asymmetries only show up in the decay-time-\ndependence of the \ufb02avor-tagged distributions. The inter-\nference in B0-tagged events has the opposite pattern, i.e.,\nconstructive interference for negative \u2206t and destructive\ninterference for positive \u2206t. Detailed discussions of \ufb02avor\ntagging and time-dependent CP asymmetry measurement\ntechniques used by the B Factories can be found in Chap-\nters 8 and 10, respectively.\nThese considerations set the base-line requirements for\nan experiment to measure the CP-violating phases us-\ning the time-dependent CP asymmetry technique at the\n\u03a5(4S):\nHigh luminosity: The branching fraction for the B0 \u2192\nJ/\u03c8K0\nS decay, the most prominent mode that is use-\nful for these measurements, is \u223c0.04% and that for\nJ/\u03c8 \u2192\u2113+\u2113\u2212(where \u2113= e, \u00b5) is \u223c12%. Thus, tens\nof millions of B0B0 pairs are needed. For an e+e\u2212col-\nlider operating at the \u03a5(4S), this requires integrated\nluminosities of \u223c30 fb\u22121 or more.\nBoosted B0B0 pairs: The B0 and B0 mesons must have\ndecay lengths in the laboratory that are su\ufb03ciently\n\n3\nd\nd\nt\nVtb*\nVcb*\nVtd\nd\nb\nt\nb\nd\nB0\nd\nb\n \n*\nB0\n \nVtd Vtb*\nVtb Vtd\nW\n \nB0\n \nKS\ns\nJ/\u03a8\nb\nc\nc\nW\nb\nW\nd\nB0\nd\nb\n \n*\nB0\nW\n \nVtd\nVtb Vtd\nt\nW\nB0\n \nB0\nW\n \nVtd\nb\nd\nKS\nc\nc\ns\nd\nJ/\u03a8\nW\nW\nt\nFigure 1.2.1. (left) The dominant quark-line diagrams for B0 \u2212B0 mixing. (right) The interfering diagrams used for the \u03c61\nmeasurement. As the direct B0 decay produces K0, and the B0 decay produces K0, the relative phase between B0 \u2192B0 \u2192\nJ/\u03c8K0\nS and B0 \u2192J/\u03c8K0\nS contains an additional term due to K0 \u2212K0 mixing (not shown).\nlong so that the time sequence of their decays can be\nmeasured. Also it should be noted that \u03a5(4S) mesons\nproduced in symmetric colliders are almost at rest in\nthe laboratory frame, and as a consequence one can\nonly measure functions of t1 + t2, for which any CP\nasymmetry vanishes. Both of these reasons impose the\nrequirement of an asymmetric energy e+e\u2212collision in\nthe laboratory frame of reference (see Section 1.2.3).\nHigh-resolution and large-coverage detector with\nexcellent particle identi\ufb01cation: The measured am-\nplitude of the CP-violating asymmetry is directly\nproportional to the detector\u2019s ability to reconstruct\nand \ufb02avor-tag the accompanying B meson.\n1.2.2 Early proposals\nAt the time, the most successful studies of B mesons were\nbeing performed at the CESR and DORIS II e+e\u2212col-\nliders operating at the center-of-mass (CM) energy corre-\nsponding to the \u03a5(4S) resonance, which, because it decays\ninto BB (and nothing else) nearly 100% of the time, is a\ncopious source of B mesons in a clean, low-background en-\nvironment. Also, luminosities of \u223c1032 cm\u22122 s\u22121, while a\nsigni\ufb01cant advance over previous machines, are two orders-\nof-magnitude too low to provide samples of B meson de-\ncays that are adequate for the CP violation measurements.\nDuring the late 1980\u2019s a very large number of concepts\n(twenty-two in all) emerged on the international scene to\ntest CP violation in B mesons. Both Hitlin (2005) and\nSchubert (2007) have presented detailed reviews of these\nproposals, and how they synergistically evolved to the two\nB Factories that were eventually built.\n1.2.3 Asymmetric colliders\nIn the late 1980s, as the TRISTAN program at KEK (High\nEnergy Accelerator Research Organization, Tsukuba,\nJapan) and the SLC program at SLAC (SLAC National\nAccelerator Laboratory, Stanford, USA) were winding\ndown, workshops and task forces were formed at both labs\nto investigate possible facilities to attack the CP violation\nproblem. In 1987, at a specialized workshop at UCLA that\nwas focused on possibilities for using linear e+e\u2212colliders\nfor B physics, Pier Oddone proposed a novel concept of an\nasymmetric-energy, circular e+e\u2212collider. This would op-\nerate at the \u03a5(4S) and produce B mesons with a lab-frame\nboost su\ufb03cient to enable decay-time-dependent measure-\nments (Oddone, 1987), as discussed in Section 1.2.1. The\nexperimental and analysis details on how one might e\ufb00ec-\ntively detect CP violation in such asymmetric decays are\ndescribed in Aleksan, Bartelt, Burchat, and Seiden (1989).\nWithin the US, the 1990 HEPAP Panel on \u201cThe HEP\nResearch Program for the 1990\u2019s\u201d (Sciulli et al., 1990),\nrecommended that the US should study the science op-\nportunities and technical requirements of a B Factory as a\npossible component of the future US accelerator program,\nand vigorously support the necessary R&D funding. Two\nyears later, the next HEPAP Panel (Witherell et al., 1992)\nrecommended that a B Factory be constructed in the US\nunder all budget scenarios under consideration. In the fall\nof 1992 the O\ufb03ce of Management and Budget (OMB)\nand the White House were assembling the budget proposal\nfor \ufb01scal year 1994, and included possible initial funding\nfor a B Factory. Both California and New York congres-\nsional delegates were working towards the interests of their\nconstituencies. In April 1993 the OMB asked the DOE\nand NSF to convene a joint review of the two projects,\nboth having already done careful reviews of their respec-\n\n4\ntive proposals \u2014 SLAC by DOE and Cornell by NSF.\nThis review (Kowalski et al., 1993) was charged to look at\nboth projects separately and non-competitively, and as-\nsess their suitability for the task ahead and the risks that\neach project posed with respect to achieving the goals, the\nschedule, and the cost. That fall, Congress recommended\nincremental growth for HEP funding, including $36 mil-\nlion to start the construction of a B Factory, with the\nchoice of site awaiting the decision from this review. In Oc-\ntober 1993 on the basis of this review Secretary of Energy\nHazel O\u2019Leary made the decision to go ahead with the con-\nstruction of the SLAC facility (O\u2019Leary, 1993), and that\nsame month President Clinton announced the construc-\ntion of a B Factory at SLAC, as a Presidential Initiative,\nwith a four year \ufb01nancial pro\ufb01le (Clinton, 1993). A man-\nagement team was immediately formed to design and build\nthe PEP-II collider under the leadership of Jonathan Dor-\nfan (SLAC), together with Tom Eliof (LBL) and Robert\nYamamoto (LLNL). Complementing this team, an Interim\nInternational Advisory Committee was formed by the lab\nmanagement to advise on the formation of the BABAR\ncollaboration\u2019s \ufb01rst committees. The detector evolution\nfrom this point onward is discussed in more detail in Sec-\ntion 1.4. In the shadow of the cancellation of the Super-\nconductiong Super Collider (SSC) project in Texas in Oc-\ntober, 1993, the HEPAP Panel on \u201cThe Vision for the\nFuture of HEP\u201d (Drell et al., 1994) was quickly assembled\nand charged; it met through the short period December\n1993 and March 1994. They presented HEPAP, DOE, and\nCongress with a strong vision of how to pull the US HEP\nprogram back from the brink caused by the SSC cancel-\nlation decision, and set a path to a healthy, competitive\ninternational research program. This plan strongly recom-\nmended continuing forward with both the main Injector\nproject at FNAL and the B Factory at SLAC. The three-\nlab (SLAC, LBL, LLNL) B Factory team worked well to-\ngether, smoothly solving the problems that arise in all\nhigh-tech construction projects, and bringing the project\nin \u201con-time\u201d and \u201con-budget\u201d. The high energy ring was\ncompleted and beam stored by mid 1997, and the low en-\nergy ring was completed, with beam stored, a year later.\nFirst collisions were observed that same month, and \ufb01rst\ncollisions with the BABAR detector in place were observed\nin May 1999. Design luminosity was achieved in the fall\nof 2000.\nIn Japan, the \ufb01rst o\ufb03cial presentation for a B Factory\nconstruction took place at the TRISTAN Program Advi-\nsory Committee (TPAC) in March 1991. The committee\nmembers heard the progress report on the feasibility stud-\nies for the machine design and detector con\ufb01guration that\nwere accumulated from the past several year\u2019s work. The\ncommittee was convinced that constructing a B Factory\nat KEK was su\ufb03ciently feasible and the project should\nnicely \ufb01t in as a third stage of the TRISTAN project. The\ncommittee recommended that KEK should proceed with\nits construction and, due to the highly competitive situa-\ntion worldwide, aim for the earliest possible completion of\nthe project. With this o\ufb03cial TPAC recommendation, and\nexpression of support from the international community in\nthe form of letters from prominent \ufb01gures and presence at\nwell-attended meetings, the KEK management began to\ntalk to the funding agency of the Japanese Government\nand to rearrange the laboratory resources toward the new\nproject.\nOf the original leading B Factory proposals mentioned\nin Section 1.2.2 above, only these two B Factory projects,\nboth based on the Oddone concept of asymmetric energy\nelectron-positron storage rings, PEP-II (PEP-II, 1993) and\nKEKB (Abe et al., 1993), were to survive. BABAR at PEP-\nII was approved in 1993, and Belle at KEKB was approved\nthe following year, in 1994.\n1.2.4 A di\ufb00erent approach\nMeanwhile a di\ufb00erent approach, aimed at using B mesons\nproduced in hadron collisions, was pursued by HERA-\nB (Hartouni et al., 1995; Padilla, 2000). Here, the plan\nwas to place thin metal targets inside the halo of the\nproton beam in the HERA electron-proton collider and\nrun parasitically with other HERA experiments. A draw-\nback was that the cross section for producing B mesons\nin proton-nuclear collisions at the available CM energy is\na tiny fraction (\u223c10\u22126) of the total hadronic cross sec-\ntion. Although serious di\ufb03culties were anticipated with\nthis approach, the project was approved in 1995 with an\nexpected data-taking start in 1998, one year ahead of the\nexpected start-up of PEP-II and KEKB. Ultimately, how-\never, the huge non-B meson background turned out to\nbe too di\ufb03cult to contend with and this approach proved\nnot to be competitive with the asymmetric e+e\u2212collider\napproach.\nIn 1994, the year that the SLAC and KEK B Factories\nwere approved, three sets of proponents for a dedicated B\nphysics experiment at the LHC were encouraged to \u201cjoin\ntogether to prepare a letter of intent for a new collider\nmode b experiment to be submitted to the LHCC\u201d (Kirse-\nbom et al., 1995). The three projects were called COBEX,\nGAJET, and LHB, and the merger resulted in the LHCb\nexperiment. The experimental design for LHCb is similar\nto that of HERA-B, in that it is a single-arm spectrom-\neter. Unlike HERA-B, which relied on a target to cre-\nate B mesons, LHCb relies on production of B mesons\nfrom pp collisions at the LHC. A dedicated spectrometer\nin the forward region is chosen to take advantage of the\nlarge cross section in the forward-backward direction. The\nLHCb experiment started taking data in 2008, when the\nLHC started collisions. Another proposed experiment to\nstudy CP violation in a hadronic environment was put\nforward, with the aim of using the Tevatron at Fermilab.\nThis was called the BTeV experiment and it was to have\nbeen a two-arm spectrometer, each arm being similar in\ndesign to LHCb (Santoro et al., 1999). Only the HERA-B\nand LHCb experiments were constructed and took data.\n\n5\n!\nFigure 1.3.1. Schematic view of the PEP-II (left) and KEKB (right) rings. At PEP-II, the two beams are stacked one on top\nof the other; the BABAR experiment is located in an experimental hall at the single interaction region, within region 2 of the\nPEP-II complex. At KEKB, the two beams are side-by-side, and intersect in the Tsukuba area experimental hall where the\nBelle detector was placed.\n1.3 PEP-II and KEKB\nPEP-II was located in the tunnel that had housed the\n32 GeV center-of-mass energy PEP e+e\u2212storage ring,2\nwhile the KEKB ring was in the 64 GeV center-of-mass\nenergy e+e\u2212TRISTAN storage accelerator tunnel. Fig-\nure 1.3.1 shows a schematic overview of the PEP-II and\nKEKB rings.\nBoth projects included conversions to meet the B Fac-\ntory requirements, namely an instantaneous luminosity in\nexcess of 1033 cm\u22122 s\u22121 and a boost factor (of the CM\nframe relative to the laboratory) su\ufb03cient for observing\nthe time evolution of B decays. To achieve these require-\nments, however, some considerable challenges had to be\naddressed.\nAsymmetric energies mean a dedicated ring for each\nbeam. In order to reach a high integrated luminosity one\nrequires an intense positron source and on-energy injec-\ntion for both rings. For KEKB, this meant that the in-\njection linear accelerator (Linac) energy had to be raised\nfrom 2.5 GeV to 8 GeV in order to provide for on-energy\ninjection of 8 GeV electrons and su\ufb03cient production of\n3.5 GeV positrons. PEP-II had the advantage of the ex-\nisting powerful SLAC Linac, which could provide the re-\nquired electron and positron beams with minimal modi-\n\ufb01cations. Both facilities used high-energy electron beams\n2 A maximum center-of-mass energy of 29 GeV was achieved\nduring the lifetime of PEP.\nand low-energy positron beams in order to avoid beam-\ninstability problems due to ion trapping, which are most\nserious at lower energies. Both facilities had only one in-\nteraction region (IR) for the detector in order to optimize\nthe luminosity. The luminosity of an e+e\u2212storage ring is\ngiven by\nL = Nbne\u2212ne+f\nAe\ufb00\n(1.3.1)\nwhere the numbers of electrons and positrons in each bunch\nare given by ne\u2212and ne+, Nb is the number of bunches,\nf is the circulation frequency, and Ae\ufb00is the e\ufb00ective\ncross-sectional overlapping transverse area of the beams at\nthe interaction point (IP). While the \ufb01ve parameters are\nindependent at lower beam currents, at high beam cur-\nrents Ae\ufb00becomes strongly beam-current dependent. As\nthe product Nbne\u2212ne+ is increased, Ae\ufb00increases, thereby\nlimiting the luminosity.\nParticles inside a beam bunch are de\ufb02ected when they\npass through the collective electromagnetic \ufb01elds of the\noncoming beam bunch at the IP; as a result, the on-\ncoming bunch collectively acts as a focusing lens. How-\never, these beam-beam e\ufb00ects are highly non-linear and\nproduce spreads in the operating point in the betatron-\noscillation tune plane, causing considerable complications\nin the machine operation. These beam-beam interactions,\nwhich become larger as the bunch charges are increased,\nalso limit the luminosity by enlarging Ae\ufb00.\nAttempts to raise the luminosity by raising Nb, the\nnumber of bunches in each ring, face a di\ufb00erent prob-\n\n6\nlem. When a beam bunch circulates with small separa-\ntion intervals from other bunches, it feels some e\ufb00ects of\nthe other bunches caused by residual oscillating electro-\nmagnetic \ufb01elds produced in the beam chambers and other\nring components by the preceding bunches. These e\ufb00ects\ncan drive coupled-bunch instabilities throughout the en-\ntire ring that grow as the beam currents increase. Coupled-\nbunch instabilities in the electron ring are also caused by\nthe presence of residual-gas ions and, for the positron ring,\nclouds of photoelectrons generated by synchrotron X-rays\nhitting the beam chamber walls and by photoelectrons\nreaccelerated by the beam striking the walls to make sec-\nondary yields.\nIn addition to driving coupled-bunch instabilities, the\npresence of ions and electron clouds enlarges the beam\nsizes, sometimes leading to beam losses throughout the\nring. In fact, this e\ufb00ect turned out to be the most se-\nrious problem for both projects, especially \u201cblow-up\u201d of\nthe positron beam caused by the photoelectron clouds.\nLarge beam currents also imposed serious challenges\nfor the hardware components along the rings. A high-\nquality vacuum had to be kept in the beam chambers to\nensure reasonably long beam lifetimes in an environment\nwhere the chamber walls were constantly bombarded by\nhuge \ufb02uxes of synchrotron X-rays. Heat energy accumu-\nlated in the ring components had to be removed e\ufb03ciently.\nTireless e\ufb00orts were made throughout the entire period of\noperation to keep improving the performance of critical\nhardware components and for \ufb01nding optimum operating\nconditions, which were often far from those carefully de-\nveloped during the design stage. Movable masks used to\nscrape away unwanted beam-halo particles turned out to\nbe a particularly di\ufb03cult challenge.\nA background simulation e\ufb00ort started in BABAR im-\nmediately to focus on the ingredients that should be inte-\ngrated in the PEP-II machine design, namely collimators\nand synchrotron radiation masks.\nThe conclusions of these early simulations were clear:\n\u2013 The background would be severe.\n\u2013 The uncertainties in the simulation were very large due\nto many reasons (incomplete knowledge of the physical\nsources, incomplete description of the machine, crude\nassumptions on the machine vacuum, etc.).\n\u2013 An experimental approach to try to control all these\napproaches was mandatory. This led to the creation of\na commissioning detector which started in 1996 (see\nSection 1.4.3.1).\n\u2013 The detector design, which was proceeding, had to\nadopt a safety factor of 10 relative to all background\npredictions. This \u201cadministrative\u201d rule turned out to\nbe extremely di\ufb03cult to meet initially, and led to\nchanges in the technical implementation of several de-\ntector components, but turned out to be very wise and\nhad many pay-o\ufb00s in the long term.\nMany collimators were proposed, with \ufb01xed or movable\njaws, for inclusion at key locations. It turned out that it\nwas di\ufb03cult and very costly to implement them all, so\nonly a select few were installed. At Belle, several versions\nof movable masks were used, each version being a gradual\nimprovement on the previous one.\nIn a two-ring machine with small bunch spacings, a\nbeam-separation scheme is needed to divert the beams\nas they leave the IP in order to avoid parasitic interac-\ntions. PEP-II used a head-on collision scheme with near-\nIP bending magnets to steer the e+ and e\u2212beam bunches\naway from each other as soon as possible after the colli-\nsion. KEKB, on the other hand, used a scheme in which\nthe two beams collide with a small (\u00b111 mrad) crossing\nangle. While this scheme had the considerable merit of al-\nlowing for shorter bunch spacing and more available space\nfor the detector components near the IP, it was not with-\nout risk. A previous attempt to use a small but \ufb01nite-angle\ncrossing scheme in the DORIS ring at DESY (Piwinski,\n1977) had problems that were attributed to beam insta-\nbilities from unwanted couplings between betatron and\nsynchrotron motions caused by the crossing angle, and it\nwas generally believed that this e\ufb00ect would get worse\nat larger crossing angles. However, a theoretical study\n(Hirata, 1995) concluded that a large horizontal cross-\ning angle in KEKB would, in fact, not be very harmful;\nbased on this, a \ufb01nite crossing angle was incorporated at\nan early stage of the design process. Ultimately, crossing-\nangle-induced transverse-longitudinal couplings were can-\nceled by the use of the world\u2019s \ufb01rst operational set of su-\nperconducting crab cavities that realign the directions of\nthe beam bunches so they pass through each other head-\non (Hosoyama et al., 2008). These were installed in Jan-\nuary 2007; with the cavities, and with chromatically cor-\nrected IP beta functions, KEKB eventually reached a peak\nluminosity of 2.1 \u00d7 1034 cm\u22122 s\u22121, more than twice the\noriginal design goal.\nAs a result of due care and attention in the design\nof the machines, the excellent performance of the KEKB\nand PEP-II colliders was comfortably su\ufb03cient to allow\nBABAR and Belle to verify the Kobayashi-Maskawa theory\nof CP violation, and, in addition, provide opportunities for\na number of other measurements and discoveries, many of\nwhich were well beyond the scope of the original physics\ngoals listed in the 1994 Belle Letter of Intent (Cheng et al.,\n1994) and the BABAR Physics Book (Harrison and Quinn,\n1998). The machine parameters for the two B Factories\nduring the \ufb01nal stages of their operation are given in Ta-\nble 1.3.1.\n1.4 Detectors for the B Factories\nThe B Factories have a common set of design require-\nments which are driven by the physics goals laid down in\nSection 1.2. The resulting detector designs for BABAR and\nBelle are, broadly speaking, quite similar, with similar op-\nerational performance. Any di\ufb00erences resulted from con-\nditions expected from the PEP-II and KEKB accelerator\ncomplexes and the technical competences and available re-\nsources of the groups who built the various sub-systems.\nThe main requirements are as follows\nLight material (i.e. high X0) for the inner detector:\nThe beam pipe, for the length corresponding to the\n\n7\nTable 1.3.1. Machine parameters of PEP-II and KEKB during the last stage of their operation.\nParameters\nPEP-II\nKEKB\nBeam energy\n(GeV)\n9.0 (e\u2212), 3.1 (e+)\n8.0 (e\u2212), 3.5 (e+)\nBeam current\n(A)\n1.8 (e\u2212), 2.7 (e+)\n1.2 (e\u2212), 1.6 (e+)\nBeam size at IP\nx\n(\u00b5m)\n140\n80\ny\n(\u00b5m)\n3\n1\nz\n(mm)\n8.5\n5\nLuminosity\n(cm\u22122 s\u22121)\n1.2 \u00d7 1034\n2.1 \u00d7 1034\nNumber of beam bunches\n1732\n1584\nBunch spacing\n(m)\n1.25\n1.84\nBeam crossing angle\n(mrad)\n0 (head-on)\n\u00b111 (crab-crossing)\nsolid angle subtended by the active region of the\nB Factory detectors, was made of beryllium with\na cooled channel between inner and outer walls.\nBeryllium was chosen to minimize the amount of ma-\nterial in terms of radiation length, to reduce multiple\nscattering and energy loss of particles crossing the\nbeam pipe.\nVertexing capability: The key to measuring CP vio-\nlating asymmetries is the precise determination of the\ndecay vertex of each B meson in an event. The only\nviable technology to use at the time the B Factories\nwere being constructed was a silicon-strip-based vertex\ndetector.\nParticle identi\ufb01cation: In order to classify particles in\nthe \ufb01nal states of interest, over a broad range of mo-\nmentum, it is not possible to rely on a single parti-\ncle identi\ufb01cation technology. Both experiments con-\nstructed drift chambers with su\ufb03ciently good speci\ufb01c\nenergy loss (dE/dx) measurement capability to per-\nform charged particle identi\ufb01cation for low momen-\ntum tracks. This was supplemented at Belle by a\nTime-Of-Flight system, and an aerogel-based Cheren-\nkov detector for characterizing high momentum parti-\ncles. At BABAR, high momentum track identi\ufb01cation\nwas achieved via the Detector of Internally Re\ufb02ected\nCherenkov light (DIRC), which was proposed by Blair\nRatcli\ufb00(Ratcli\ufb00, 1993; Schwiening et al., 2001).\nElectromagnetic calorimetry: Many \ufb01nal states of in-\nterest, including B0 \u2192J/\u03c8K0\nS where J/\u03c8 \u2192e+e\u2212,\nrequire that one is able to measure the energy of\nboth electrons and neutral particles. The technology\nadopted by the B Factories was inspired by the CLEO\nelectromagnetic calorimeter (Kubota et al., 1992):\nboth experiments used CsI(Tl) crystal calorimeters.\nK0\nL and muon identi\ufb01cation: The expected CP asym-\nmetries in B0 \u2192J/\u03c8K0\nS and B0 \u2192J/\u03c8K0\nL are equal\nin magnitude and opposite in sign: it was realized that\nto verify any observation of CP violation in B de-\ncays, it would be important to measure both of these\nmodes. Given the lifetime di\ufb00erence between K0\nS and\nK0\nL mesons, the K0\nS mesons would be expected to de-\ncay in the beam pipe or silicon detector, whereas most\nK0\nL mesons would pass through the inner part of the\ndetector without decaying. Detection requirements for\nK0\nL mesons were similar to those required for e\ufb03cient\nmuon identi\ufb01cation, which was important in order to\ndetect the J/\u03c8 \u2192\u00b5+\u00b5\u2212contributions for CP asymme-\ntry measurements. As a result, the outer parts of the\ntwo B Factory detectors were instrumented with layers\nof active detector sandwiched between absorber ma-\nterial. Belle adopted \ufb02oat-glass based Resistive Plate\nChambers (RPCs) operating in limited-streamer mode.\nBABAR initially adopted a Bakelite-based RPC solu-\ntion for its K0\nL and muon identi\ufb01cation. However, soon\nafter operation started it was clear that this needed to\nbe replaced, and a system of Limited Streamer Tubes\n(LST\u2019s) was successfully installed to replace the RPCs\nfor the remainder of BABAR\u2019s operational lifetime (see\nSections 1.4.3.6 and 2.2.5).\nData handling capability: The design goals of the B\nFactories were ambitious. If these were to be met, then\na signi\ufb01cant amount of data would have to be trans-\nferred from the detector system front-end, classi\ufb01ed\nby a trigger system, and stored for subsequent process-\ning. As the B Factory design luminosity was surpassed,\nthe data \ufb02ow and o\ufb04ine computing systems had to be\nadapted in order to keep up with the output of the\nmachine, and allow members of the Collaborations to\nproduce the physics results that appear in this book.\nA more detailed discussion on the B Factory detectors\nand readout can be found in Chapter 2, and an overview\nof data taking and Monte Carlo production required for\nphysics analysis can be found in Chapter 3.\n1.4.1 The BABAR detector collaboration\nThe SLAC management decided that with the approval\nof the B Factory as a new element of the national HEP\naccelerator program, it should explore how CERN had\nmanaged the growing of the large, international collabo-\nrations which had designed, built and operated the large\ndetectors at that laboratory. CERN Research Directors\nPierre Dariullat and Lorenzo Foa were very generous in\nproviding access to the lab archives, and engaged in full\ndiscussions on the CERN procedures and processes, iden-\ntifying both the strengths and weaknesses. These visits\n\n8\nwere very helpful in guiding the initial planning at SLAC.\nSeveral other visits to Europe allowed gathering a \u201ctem-\nporary international advisory committee\u201d (see below) to\nlisten to their collective wisdom, and advice on moving\nforward with the formation of national core groups for\nthe detector communities within Italy, France, Germany,\nUK and the US.\nThe CERN discussions emphasized the central impor-\ntance of gathering representatives of all the international\nagencies involved, to oversee their investments in the sci-\nenti\ufb01c collaboration. It was the \ufb01rst time that SLAC, or\nindeed any DOE O\ufb03ce of High Energy Physics (OHEP)\nlab, organized an external group of representatives of fund-\ning agencies from around the world to regularly review one\nof its experiments, and the \ufb01rst time that major construc-\ntion and operational funding from non-DOE sources came\nto a SLAC experiment. All of this was done through the\nInternational Finance Committee (IFC), which will be de-\nscribed later. This committee was a major player in the\nstory of the construction of the BABAR experiment, but\nalso in continuing operational support, and indeed was a\ncentral \ufb01gure in solving the serious computing problem in\n2001 that was caused by the accelerator team outperform-\ning the PEP-II design luminosity (Section 1.4.3.5).\nThe international community working on the detector\ndesign for the SLAC-hosted asymmetric B Factory held\nits inaugural gathering at the end of 1993, as the culmina-\ntion of a two year period of many workshops and detector\nmeetings preparing for a B Factory, hopefully to be built\nat SLAC. Over the next year there were seven more col-\nlaboration meetings preparing the Letter of Intent and the\nTechnical Design Report, and working through the \ufb01nal\nchoices of technology and performance speci\ufb01cations for\neach detector sub-system. SLAC management recruited\na short-lived, yet very important, Interim International\nAdvisory Committee in 1993, to advise the lab on for-\nmation of the BABAR collaboration\u2019s \ufb01rst committees and\nidentify and recruit those top level scientists. The target\ncommittee was an Interim International Steering Commit-\ntee formed in early 1994 with a very important charge. It\nwas to advise the laboratory on creating a detector R&D\nprogram (which was funded originally by SLAC, but later\nsubstantially supplemented by DOE/OHEP); to select an\ninitial Executive Board of the collaboration; to write the\noriginal governance document and socialize it within the\ncollaboration; and to choose the \ufb01rst Collaboration Coun-\ncil. This they did in short order and, having completed\ntheir job, the group just as quickly dissolved, with the\nthanks of the laboratory management.\nThe \ufb01rst Collaboration Council, in May 1994, quickly\ngave formal blessing to the collaboration\u2019s Governance\ndocument, and chose a Nominating Committee to search\nfor the \ufb01rst spokesperson of the detector collaboration, fol-\nlowing the search process de\ufb01ned in the newly passed gov-\nernance rules. The Council rati\ufb01ed the Executive Board\nselection, and voted on the name for the collaboration,\nestablishing the little French Elephant BABAR on \u201chis\u201d\nway to having an impressive citation count.3 It was a pro-\nductive \ufb01rst Council meeting, and a great kick-o\ufb00for the\nBABAR collaboration. Just seven weeks later, at the July\n1994 Collaboration Meeting, the Council formally rati-\n\ufb01ed the nomination of David Hitlin as the \ufb01rst BABAR\nSpokesperson. Indeed, he had been \ufb01lling the role of in-\nterim spokesman of this proto-BABAR community since\nthe late 1980\u2019s, and had coordinated and led the \ufb01rst \ufb01ve\nformal meetings of the collaboration.\nThe detector collaboration had a single spokesperson\nthrough the entire construction and commissioning peri-\nods, and through the \ufb01rst years of data taking. From that\npoint forward a new spokesperson was chosen from the col-\nlaboration every two years.4 This group of seven individ-\nuals were able stewards of the scienti\ufb01c life of the BABAR\ncollaboration. Their distinct visions on how to guide the\nexperiment forward, their use of the associated strong\nmanagement teams and their scienti\ufb01c judgment was no\nsmall part of the scienti\ufb01c success of BABAR. Within the\nBABAR collaboration the spokesperson is the chief o\ufb03cer\nof the collaboration, responsible for all scienti\ufb01c, technical,\norganizational, and \ufb01nancial a\ufb00airs of the collaboration,\nand represents the collaboration to the SLAC laboratory,\nto the DOE/OHEP, and to the international funding agen-\ncies, represented by the IFC. The spokesperson is assisted\nin this heavy responsibility by a Senior Management Team\nfor day-to-day decisions, and by an Executive Board which\nthe spokesperson chairs. The Senior Management Team is\nchosen by the Spokesperson and rati\ufb01ed by the Executive\nBoard and the Council.5 The Executive Board is repre-\nsentative of the regional composition of the collaboration,\nand consists of members distinguished by their scienti\ufb01c\njudgment, their technical expertise, and their commitment\nto the experiment, and is chosen by the Council through\nan election process. The technical life of the collaboration\nwas managed by the Technical Coordinator, who chaired\nthe Technical Board. This was normally a twenty mem-\nber group comprised of the detector system managers,\nthe lead engineering sta\ufb00, the computing leadership, and\nrepresentatives from the accelerator collider team. For an\nimportant period of the life of BABAR, starting in 1999\nfor about two years, this group was expanded to include\n3 The name BABAR is derived from B and B-bar. The BABAR\nelephant and the many distinctive likenesses of that character,\nare used with permission of Laurent de Brunho\ufb00, negotiated\nby David Hitlin. All copyrights were reserved to the owner,\nwhich changed to Nelvans after the late 1990\u2019s.\n4 BABAR Detector Spokespersons: David Hitlin (1993\u20132000),\nA. J. Stewart (Stew) Smith (2000\u20132002), Marcello Giorgi\n(2002\u20132004), David MacFarlane (2004\u20132006), Hassan Jawah-\nery (2006\u20132008), Fran\u00b8cois Le Diberder (2008\u20132010), J. Michael\nRoney (2010\u2013).\n5 As part of the transition from detector construction to op-\neration and data taking and physics analysis, a Senior Manage-\nment team was formed in 2000, which included the Spokesper-\nson, the Technical Coordinator, a senior technical advisor and\nlab contact if not covered by the Technical Coordinator, the\nPhysics Analysis Coordinator, the Computing Coordinator and\ndeputy, the past Spokesperson, and the Spokesperson-elect.\n\n9\na much broader membership and called the Augmented\nTechnical Board, which included all of the old Technical\nBoard but also all of the leaders from electronics, online\nand o\ufb00-line monitoring, computing, physics planning, and\nanalysis machinery \u2014 a cadre of about 50 sta\ufb00. For these\ntwo years this body worked hard and was a very important\npart of the BABAR story; they can take a lot of the credit\nfor bringing the detector operations and the physics pro-\nduction activity into a true \u201cfactory mode,\u201d alongside the\noperations of the PEP-II accelerator complex. The collab-\noration has been well served by the \ufb01ve strong scientists\nwho served as the BABAR Technical Coordinator6 provid-\ning sound technical judgment and strong commitment to\ntop level detector performance and to high e\ufb03ciency up-\ntime.\nThe collaboration is represented by a Council7 with an\nelected chair and deputy, and made up of representatives\nfrom each institution participating in the detector collab-\noration. The Council is the principal governing body of\nthe collaboration. The Council selects the Spokesperson\nNominating Committee, rati\ufb01es the Spokesperson nom-\nination, and the selection of the Executive Board. The\nCouncil appoints the operating committees of the collabo-\nration \u2014 Membership, Speakers Bureau, and Publications\nBoard. The Council has the unusual power to request a\nfull review from the Spokesperson of any decision or action\nfor which it deems such accountability was necessary, and\ncould remove the Executive Board, or even the Spokesper-\nson, under very strict conditions, if this unlikely situation\nshould occur. This served as a balance to the strong and\nindependent authority given to the BABAR Spokesperson\nunder the collaboration\u2019s governance (see above).\nThe experiment began in 1993 and by 1995 had 483\nmembers from 77 institutions, drawn from 10 countries \u2014\nCanada, China, France, Germany, Italy, Norway, Russia,\nTaiwan, the UK, and the US. By 2005, the collaboration\nhad grown to 625 members, from 80 institutions and 12\ncountries \u2014 with Israel, India, Netherlands and Spain hav-\ning joined in the meantime, and China and Taiwan leav-\ning. By January 2013 the active membership was still 325,\nof whom 51 were postdoctoral researchers and 56 graduate\nstudents. The experiment has produced 505 PhD theses,\na number which is still growing, and is a remarkable tes-\ntament to the intellectual life of the experiment and the\nbreadth of its academic reach. The collaboration has pro-\nduced more than one paper each week during a six year\nperiod (2004 through 2009) in the world\u2019s leading peer-\nreviewed journals, and a total by fall 2012 of 507 papers.\n6 BABAR Technical Coordinators: Vera L\u00a8uth (1994\u20131997),\nJonathan Dorfan (1997\u20131999), A. J. Stewart (Stew) Smith\n(1999\u20132000), Yannis Karyotakis (2000\u20132003), Bill Wisniewski\n(2003\u20132011).\n7 The BABAR Collaboration Council was formed under action\nof the Steering Committee (chaired by Pier Oddone), in May\n1994 with the \ufb01rst chair being Livio Piemontese (1994), fol-\nlowed by Bob Wilson (1996), Erwin Gabathuler (1998), Patri-\ncia Rankin (2000), Klaus Schubert (2002), Frank Porter (2004),\nGerard Bonneaud (2006), David Leith (2008), George La\ufb00erty\n(2010), Brian Meadows (2012), and Fabrizio Bianchi (2014).\nWe can celebrate that not only have both the BABAR and\nBelle experiments been \u201cfactories\u201d of physics, producing\nnew results over a broad spectrum of topics, but they have\nbeen veritable factories in producing candidates for new\nacademic appointments for universities around the world\nfrom the pool of graduate students and post doctoral re-\nsearchers who received their training on the BABAR and\nBelle experiments. They have outstanding training with\nboth technical and operational experience with large de-\ntectors and running accelerators, and computing and data\nproduction on a factory scale, and hands-on development\nof creative data analyses in a small group environment.\nIn order for collaborators to be considered as authors\non BABAR, they \ufb01rst must perform a substantial service\nto the experiment, either through the construction or op-\neration of hardware, or by taking on some technical or\nadministrative role required to maintain the quality of\nphysics output from the experiment. Having quali\ufb01ed for\nauthorship, a BABAR collaborator automatically signs pa-\npers. The authors appear in the author-list in alphabet-\nical order by institute. As a result there is, in general,\nno direct correlation between the lead authors of a given\nanalysis and the initial authors of a given BABAR paper.\nOn occasion, where non-BABAR collaborators (mainly stu-\ndents) have made signi\ufb01cant contributions to an analysis,\nrequests have been made for those people to be added to\nthe author list on the paper describing that analysis in\ndetail. Such requests, while never a foregone conclusion,\nwere generally granted.\n1.4.2 Formation of the Belle collaboration\nThe Belle collaboration was o\ufb03cially formed at a one-\nday meeting held at Osaka University on October 7, 1993,\nwhere it was formally decided that the results of the previ-\nously held workshops (Abe et al., 1993) were encouraging\nenough to merit proceeding towards the development of a\nLetter of Intent during the next year (Cheng et al., 1994).\nThis was followed by a series of meetings at which details\nof the detector design and issues of collaboration gover-\nnance were discussed.\nThe collaboration organization was discussed at a sec-\nond meeting at KEK on November 19\u201320, 1993. Here, it\nwas decided that there would be three co-spokespersons,\none representing each of the major constituencies of the\ncollaboration: the KEK group, non-KEK Japanese groups,\nand groups from outside of Japan. All three spokesper-\nsons were elected by the full collaboration. In the begin-\nning they served for a three year term that could be re-\nnewed. This rule was later changed to a two year term and\nlimiting renewals to a single term. In addition, it was de-\ncided to have an Institutional Board (IB) comprised of the\nspokespersons and one representative from each of the col-\nlaborating institutions,8 to deal with organizational and\npersonnel issues, and an Executive Board (EB) consisting\n8 Belle Institutional Board chairs: Yasushi Watanabe (1994\u2013\n2000), Seishi Noguchi (1994\u20132000), Leo Piilonen (2000\u20132012),\nChristoph Schwanda (2012\u2013).\n\n10\nof about ten members selected by the spokespersons to\nadvise them on technical and scienti\ufb01c issues.9 Important\nmatters are discussed in the IB or EB and then proposed\nto a general meeting of the collaboration. The general or-\nganizational principle has been that, insofar as possible,\ndecisions are made at general group meetings, either by\nconsensus or by a vote of those present. Urgent decisions\nare made by the spokespersons in consultation with the\nEB. This organization proved to be reasonably success-\nful; when the experiment switched from the construction\nto the operating phase in 1999, a task force was formed\nto re-examine the organizational structure, but eventually\nonly minor changes in the basic structure were adopted.\nThe name \u201cBelle\u201d (proposed by A. Abashian, Virginia\nTech) was adopted by a group vote at the third group\nmeeting held in January 1994 at Nara Women\u2019s Univer-\nsity.10 The Belle logo (proposed by T. Matsumoto, To-\nhoku) was selected by a vote at the sixth group meeting\nat Tohoku University in February 1995.\nThe experiment began in late 1993 with 136 members\nfrom 39 institutions from 7 countries \u2014 Japan, China, In-\ndia, Korea, Russia, Taiwan and the US. The \ufb01rst spokesper-\nsons11 were F. Takasaki, S. Suzuki, and S. Olsen. By 2008,\nthe Collaboration had grown to 275 members, from 60\ninstitutions and 15 countries \u2014 with Australia, Austria,\nCzech Republic, Germany, Italy, Poland, Slovenia, and\nSwitzerland having joined in the meantime. Up to fall\n2012, the Collaboration published 370 papers in scienti\ufb01c\njournals.\nTwo unique features of the Belle publication policy,\ndeveloped after considerable discussion and \ufb01nalized at a\nmeeting at KEK in November 2001, are worth noting:\nAuthorship con\ufb01rmation: In Belle, there is no default\nauthor list and authorship on a Belle paper is not auto-\nmatic. An important rule is that after a paper draft has\nreceived approval from its internal referees and the rel-\nevant physics conveners, it is posted for general review\nby all eligible authors.12 During the review period, a\n9 Belle Executive Board chairs: Kazuo Abe (1994\u20132000), Dan\nMarlow (2000\u20132002), Alex Bondar (2002\u20132010), Simon Eidel-\nman (2010\u20132012), Tom Browder (2012\u20132013), and Toru Iijima\n(2013\u2013 ).\n10 The name Belle is a pun on beauty, the quark of primary\ninterest for the B Factories, which led to a natural choice for\nthe name of the commissioning detector discussed later in this\nchapter: BEAST. The name can also be decomposed as B-el-le\nimplying electrons (el) and their opposite \u2014 positrons (le) \u2014\ncolliding to produce B mesons.\n11 Belle Detector Spokespersons: Fumihiko Takasaki (1994\u2013\n2003), Shiro Suzuki (1994\u20132000), Steve Olsen (1994\u20132006), Hi-\nroaki Aihara (2000\u20132006), Masanori Yamauchi (2003\u20132009),\nTom Browder (2006\u20132012), Toru Iijima (2006\u20132012), Yoshihide\nSakai (2009\u2013), Leo Piilonen (2012\u2013), Hisaki Hayashii (2012 \u2013).\n12 Eligible authors are those members of the collaboration\nthat actively contributed to Belle for at least six months in\nform of construction, maintenance or operation of the detector,\nsoftware development, contributing to ongoing analyses, etc.\nThey are also required to take a certain number of experimental\nshifts.\ncollaborator is required to con\ufb01rm his/her authorship\nby submitting the statement: \u201cI have read this paper\nand agree with its conclusions. Please include me as\nan author.\u201d Only then is he/she included in the au-\nthor list.\nAuthor-list name order: In principle, the order of the\nnames in the author list is alphabetic. However, the\npersons responsible for preparing a paper can propose\nto the spokespersons that a single person or a small\ngroup of people be listed as \ufb01rst authors. In general,\nthe spokespersons have approved such requests, the\nexceptions being for important papers central to the\nmain goals of the Belle program (e.g., precision mea-\nsurements of sin 2\u03c61) or cases where the proponents\ncannot agree on the speci\ufb01c name order. In these cases,\nthe author list is strictly alphabetic.\nWhen this policy was adopted, it was with the explicit\nproviso that it could be re-examined and modi\ufb01ed at any\ntime. However, it has proven to be quite popular among\nBelle collaboration members and has never been modi\ufb01ed.\nAlmost all Belle papers since 2002 have had a \ufb01rst-author\ngroup, with up to seven collaborators appearing out of\nalphabetical order at the start of the list; the number of\ncon\ufb01rming authors has been, on average, about half of the\ntotal number of eligible authors.\n1.4.3 Building the BABAR detector\nThe BABAR collaboration faced a set of design challenges\nas they prepared their Letter of Intent (LOI) during the\nperiod spring 1993 through summer 1994. These included\na long list of issues demanding detailed analysis to arrive\nat conclusions \u2014 inheriting an Experimental Hall which\nwas smaller, and had too low a beam height, for an opti-\nmal \u201cstart-from-scratch\u201d design; determining how to meet\nthe stringent speci\ufb01cations for the silicon vertex detector\nand drift chamber tracker to manage both the spatial res-\nolution to measure the separated B decay vertices and\nat the same time handle measuring with adequate pre-\ncision the broad momentum spectrum of the produced\ntracks; meeting the strong speci\ufb01cations for the charged\nparticle identi\ufb01cation along with good photon detection\nfor both position and energy measurement, and for reli-\nable muon and K0\nL detection. The actual LOI document\nwas produced over a few months, was completed in June\n1994, and quickly approved by the SLAC Experimental\nProgram Advisory Committee (EPAC) in July, only one\nmonth later.\nAs with all high tech projects, the detector design, con-\nstruction, and commissioning came along with its prob-\nlems. Fitting the collaboration\u2019s ambitions to the avail-\nable budget was a stringent constraint at the outset. A\ngreat deal of hard work went into de\ufb01ning the technical\ndetails for the \ufb01nal sub-systems in the short nine month\nperiod between the submission of the BABAR Letter of In-\ntent and the submission of the Technical Design Report, in\nFebruary 1995. The TDR had essentially the \ufb01nal vertex\ndetector geometry and technical description, a new Drift\n\n11\nChamber design with \ufb02at aluminum end plates instead of\na cleverly shaped carbon \ufb01ber construction, the choice of\nthe internally re\ufb02ected Cherenkov detector, DIRC, and its\nquartz bar radiators for the particle identi\ufb01cation system,\nand \ufb01nalizing the choice of the muon detector technology\nas Resistive Plate Chambers, RPC\u2019s. Later on there were\nother surprises that emerged and had to be dealt with\npromptly; the \ufb02ux return iron for the magnet had produc-\ntion schedule problems from the Japanese supplier as did\nthe superconducting magnet coil from Italy, but the IFC\ncame through with an added incentive clause to the mag-\nnet steel contract, and the lab management\u2019s connections\nto the US Air Force helped bring the delayed supercon-\nducting coil to SLAC on time, via \u201cair mail\u201d on a C5A,\nas part of a crew training \ufb02ight. Learning how to grow\nthe cesium iodide crystals and managing the salt deliv-\nery schedule for the large electromagnetic calorimeter, and\nhow to successfully polish the quartz bars for the DIRC\nparticle identi\ufb01cation system to the exacting dimensional\noptical speci\ufb01cations, were time-consuming problems that\nemerged during construction, looked as though they might\ncause serious schedule problems, required creativity and\nfocused commitment, but were \ufb01nally solved in time for\ndetector turn-on.\n1.4.3.1 The PEP-II commissioning run\nImmediately after PEP-II approval in June 1993, it was\nrealized that, because of the existence of the PEP tunnel\nand the signi\ufb01cant reuse of PEP machine components,\nthat PEP-II machine would be ready one or two years be-\nfore the BABAR detector would be. This was considered as\na good opportunity to be able to tune the machine without\nthe complications of detector protection and to provide a\nfast start for BABAR. The machine had to reach a lumi-\nnosity 100 times higher than previously achieved and was\ndoing so with much higher currents. The potential threat\nposed by backgrounds induced by such currents was con-\nsiderable. A few years previously at SLAC, muons from\nthe SLC tunnel had been compromising the Mark-II/SLC\ndetector performance, and therefore there was a high de-\ngree of consciousness of these issues among members of\nthe PEP-II machine group.\nIn 1996 there was a call proposing the instrumenta-\ntion, at minimal costs, of the PEP-II IR in the absence\nof BABAR during two running campaigns: a short one, in\n1997, where only the HER ring would be available, and\nanother one in 1998 with both rings. The goal of this in-\nstrumentation was manifold:\n\u2013 understand and quantify the various background sources\nin both rings,\n\u2013 provide to the machine reliable background sensors,\nso background could be reduced while tuning the ma-\nchine,\n\u2013 test prototypes of \ufb01nal BABAR elements to understand\ntheir sensitivity to background,\n\u2013 test the radiation protection and abort mechanism sys-\ntem.\nIt was of course not possible to cover all these issues\nwith a very small number of detectors since some of the\nrequirements were potentially con\ufb02icting with each other.\nBABAR therefore adopted a \u201cwideband\u201d approach where\na variety of detectors were assembled for the commission-\ning detector. PIN-diodes, silicon strip detector modules,\nsimilar to the \ufb01nal BABAR ones, a newly built mini-TPC,\nand reused straw tubes were used to understand the back-\nground resulting in charged particles, whereas a newly\nbuilt movable ring of thallium-doped CsI (or CsI(Tl)) crys-\ntals, similar to the BABAR ones, were used to monitor\nneutral background. DIRC and IFR prototypes comple-\nmented this equipment.\nThis set-up and the 1997 and 1998 campaigns turned\nout to be successful. The large backgrounds observed were\nmostly due to the not-yet-scrubbed state of the rings; their\nvarious sources were understood, and their variation with\ncurrent properly measured. After the required tuning, sim-\nulations were able to reproduce the observed background\nto within 50%. The correct strategy for a fast start to the\nBABAR experiment in 1999 was established, together with\na \ufb02exible and reliable abort system.\n1.4.3.2 The BABAR background remediation e\ufb00ort and\ndetector commissioning\nSince BABAR\u2019s high potential vulnerability to PEP-II back-\nground had been demonstrated both from simulations and\nfrom the 1997\u20131998 background measurement campaign\ndescribed above, in 1998 a background remediation e\ufb00ort\nwas set up to precisely quantify the adverse e\ufb00ects en-\ngendered by high background on the BABAR detector and\nphysics analysis. Four areas were identi\ufb01ed:\n1. long term degradation due to integrated dose,\n2. immediate damage due to a radiation burst,\n3. high occupancy in the detectors leading to ghosts or\nto ine\ufb03ciency,\n4. large dead-time in electronics read out leading to dead\ntime and/or ine\ufb03ciency.\nThis remediation group took many important decisions to\nprotect BABAR in both the short and long term, based\non background extrapolations taking account of future\nrunning conditions: a very comprehensive set of dosime-\nters were installed throughout the detector, and an abort\nstrategy was put in place to avoid item (2). The weakest\npoints in the data acquisition (DAQ) chain were identi-\n\ufb01ed as bottlenecks two years before they needed upgrad-\ning. As a result the DIRC and drift chamber electronics\nwere partially upgraded in good time and without lim-\niting data taking. Good running conditions were de\ufb01ned\nin order that BABAR did not accumulate data that would\nprove not to be useful.\nA strict policy to use up allowed radiation exposure\nas a function of the integrated luminosity was de\ufb01ned. A\n10% occupancy limit in the drift chamber and the vertex\ndetector were thus de\ufb01ned so as to guarantee good physics\noutput, and were correlated to real time background sen-\nsors incorporated in the machine diagnostics system to\nprevent running in worse conditions.\n\n12\nAnother crucial aspect of this task force was to prepare\na set of 25 machine-detector interface experts that pro-\nvided 24-7 support in the PEP-II control room, during the\n\ufb01rst four years of BABAR data taking. These background\nshifts proved invaluable to further the understanding and\ncontrol of the background issues and to disseminate back-\nground related issues to the PEP-II operations crew.\nThe \ufb01rst short run took place in May 1999, to be\nfollowed by a short shut-down to install the full DIRC\nsystem, and then operations began again in late Octo-\nber. Physics running began in late 1999 and continued\nthrough 2008, when the experiment was turned o\ufb00with\nthe PEP-II collider having achieved design luminosity\n(3 \u00d7 1033 cm\u22122s\u22121) within one year of operation. Dur-\ning its \ufb01nal year the PEP-II collider ran regularly at a\ndaily integrated luminosity of over seven times the design\nvalue, with record high circulating currents of both elec-\ntrons and positrons, and accumulating 557 fb\u22121 of data\nin the BABAR detector. Background issues were always\npresent during the lifetime of BABAR, but these were suc-\ncessfully managed to prevent them from seriously damag-\ning the experiment. Once routine operation of PEP-II and\nBABAR had been achieved, the background remediation\ne\ufb00ort underwent a transition to the Machine-Detector-\nInterface (MDI) working group that was responsible for\nmaintaining a watchful eye on the background conditions\nexpected within the detector, and over time learned (with\nthe help of accelerator physicists from PEP-II) to use\ndata from both the machine and the detector to measure\nbeam parameters such as emittances, the betatron oscilla-\ntion amplitude at the IP, and estimates of the beam sizes\nfor bunches of electrons and positrons (Kozanecki et al.,\n2009). This background remediation and MDI e\ufb00ort was\nkey to BABAR\u2019s high luminosity running and was the re-\nsult of the hard work of many people from all parts of the\nPEP-II and BABAR teams.\n1.4.3.3 Other beam-related backgrounds encountered\nIn addition to the expected background e\ufb00ects dominated\nby beam-gas terms, some unexpected sources came along\nthe way:\n\u2013 A luminosity term was readily observed in addition\nto single beam backgrounds and to backgrounds in-\nduced by beam-beam e\ufb00ects. This luminosity term was\ntraced to the presence of o\ufb00-momentum electrons or\npositrons after radiative Bhabha scattering. The un-\nfortunate presence of a dipole magnetic \ufb01eld at the IP\nmade BABAR very sensitive to these luminosity terms\nthat became relatively more and more important as\nthe machine was getting scrubbed and its peak lumi-\nnosity increased.\n\u2013 Electron cloud e\ufb00ects were analyzed in early studies\nin 1993-1994: they cause bunch-to-bunch instabilities\nbelieved to be damped by the proposed feedback sys-\ntems. In 1999 electron cloud e\ufb00ects were experimen-\ntally observed by huge pressure increases in the LER\nabove thresholds and by intra-bunch size enlargement\nuna\ufb00ected by bunch-by-bunch feedbacks. The machine\nwas immediately equipped wherever possible with ca-\nble coils around the beam pipe providing a 50 Gauss\nprotecting \ufb01eld that pushed the current thresholds far\naway. Nevertheless, the electron cloud e\ufb00ect was re-\nsponsible for a signi\ufb01cant increase of the positron beam\nsize with current that would \ufb01nally limit the maximum\nachievable luminosity.\n\u2013 Neutron induced background, where neutrons are pro-\nduced by few-MeV gamma photonuclear reactions, were\nfound to be quite signi\ufb01cant in some sub-detectors and\neven dominant in the case of the IFR.\n1.4.3.4 BABAR reviews and oversight committees\nThe detector design and construction were formally over-\nseen by two committees that were standard to the normal\nSLAC way of doing things \u2014 a DOE Lehman Review\nprocess for agency oversight of construction readiness and\nbudget soundness, and the usual laboratory Experimen-\ntal Program Advisory Committee, which had stewardship\nover the SLAC experimental program. There were two\nother new, and very important, very helpful, international\ncommittees as partners in the detector building story \u2014\na Technical Review Committee (the Gilchriese Commit-\ntee), and the International Finance Committee, the IFC.\nThe Technical Review Committee worked closely with\nthe Detector collaboration, met twice per year through\nthe construction period, and provided advice to both the\nSpokesperson and the laboratory. The committee worked\nin sub-committees on speci\ufb01c aspects of the detector con-\nstruction, or as requested by either the Spokesperson or\nthe Research Director. In practice, the collaboration used\nthis committee in its preparation for the formal techni-\ncal reviews by DOE \u2014 the Lehman Reviews. The IFC\nmet twice per year to review progress of the construction,\ndiscuss with the lab management and the Spokesperson\nprogress and concerns, and to set homework for lab and\ncollaboration. Members of the group were very used to\nworking together from many years doing just this same ex-\nercise at CERN, trusted each other and the agencies they\nrepresented, and took a strong, stewarding responsibility\nfor their new charge \u2014 the \ufb02edgling North American-\nhosted BABAR experiment. They met by phone in be-\ntween regular face-to-face sessions when serious, time-\nurgent problems came up, and were very e\ufb00ective in \ufb01nd-\ning solutions to the unexpected problems when they arose.\nThe IFC were able to ensure that BABAR could draw to-\ngether a critical mass of manpower and institutional sup-\nport from each of the regions working on the experiment,\nto ensure success on the central areas of the experiment\nconstruction. They, as a group, appreciated that SLAC\nand the US would carry the largest share of the expenses\nfor building and operating the experiment, but partici-\npated in solving all of the many problems that arose as\n\u201cour joint problem\u201d. Largely because of their long history\non other experiments at CERN, and the mutual trust they\nhad built up, they were a very important component in\nguiding and enabling an extraordinary experiment. Both\n\n13\ncommittees continued their important stewardship roles\nbeyond the end of the construction.\nThe Technical Review Committee was called back when\nthe lab and the experiment ran into computing problems\nbecause the machine performance surpassed the design\nluminosity, causing a computing load that could not be\nhandled by the laboratory alone, without severe \ufb01nancial\nhardship. They were also called to help as the detector\nproposed hardware upgrades to several sub-systems. They\nperformed spectacularly, once again.\nThe IFC, by the constitution, continued the twice-a-\nyear oversight of the detector collaboration through the\noperational phase of the BABAR experiment. Again, this\nwas a familiar role, as they worked in a similar way at\nCERN.\nThe IFC determined the Common Fund component of\nthe construction budget and the operating budget, and\nnegotiated with the lab and the Spokesperson on both of\nthese important, but thorny issues. The \ufb01nancial needs\nof the collaboration were presented by the Spokesperson\nafter discussion with the laboratory management, while\nthe decision making on what \ufb01nancial support would ac-\ntually be provided was the IFC\u2019s job. They also de\ufb01ned\nhow each region would meet their share of these costs.\nTypically this was by a negotiated mix of head-count and\nsystem responsibility determining the cost sharing in the\nconstruction phase, and essentially it was by participating\nhead-count for the operational phase. During construction\nthis Common Fund was around $4 M per year, totaling\n$15.4 M over the construction period, and about $2.7 M\nper year during the operations period, until the computing\ncrisis (see the following two sections).\nThe DOE Lehmann Committee formally base-lined the\ndetector budget in late 1995. Each member of the Tech-\nnical Review Committee had an individual system assign-\nment, and through the full construction and commission-\ning schedule these connections were maintained and pro-\nvided timely advice to the construction team and up-to-\ndate information to the review panel as a whole, and to the\nlab management. The IFC was a very helpful resource for\nboth the laboratory and for the experiment. They brought\na di\ufb00erent kind of management layer into the lab \u2014 a tech-\nnically savvy group, and a small enough group to have\nstrong working relationships between each other, in com-\nmand of substantial \ufb01nancial resources, and very commit-\nted to the success of the BABAR project. The Technical\nReview Committee was rather stable in its membership\nthroughout the period of construction, with only a few\npeople stepping down and requiring replacement. How-\never the IFC was rather di\ufb00erent, in that the heads of\neach of the international partner agency o\ufb03ces rotated\nquite frequently.\n1.4.3.5 Computing\nFrom the beginning SLAC had proposed that the lab would\nprovide the computing hardware resources, both process-\ning and data storage, for the BABAR experiment. The\ncollaboration, on their part, was to provide the required\ntrained manpower needed to create the software tools and\nhandle the data analysis. Early on, the IFC agreed to sup-\nport a model for computing where computer profession-\nals were hired to work alongside computer-savvy collab-\noration physicists. This was a very important early in-\nvestment that strategically enabled the rest of the BABAR\ncomputing story and bolstered the scienti\ufb01c output of the\nexperiment. The cost of this manpower was borne by the\nCommon Fund.\nComputing became a serious problem around the year\n2000 as the PEP-II collider luminosity climbed past the\ndesign luminosity and eventually grew to three times that.\nThe cost of upgrading the BABAR computing center to\nhandle the increased data analysis and data processing\nwas more than the lab budget could handle. In addition,\nthe existing BABAR computing model did not scale to the\nlarge number of machines that would be required to keep\nup with the data taking. The IFC was sympathetic, but\nrequested that the Technical Review Committee examine\nthe problem, and carefully review the technical details of\nthe collaboration\u2019s proposal along with the proposed cost\nmodel. The new costs were much too large for the non-\nUS countries to support directly with cash. This turned\nout to be a blessing in disguise because the European IFC\nmembers proposed an alternative in which the computing\nload would be distributed among several \u201cTier A\u201d com-\nputing centers in Europe, in addition to SLAC. Europe\nhad built up a large computing capacity in anticipation\nof the coming LHC experiments, most of which was ly-\ning fallow as the LHC turn-on was delayed. The proposed\nBABAR computing model successfully passed the techni-\ncal review by the Technical Review Committee, and at a\nspecial meeting in Paris in January 2001 the IFC formally\nagreed that the costs of computing for the BABAR experi-\nment, beyond those to support the original PEP-II design\nluminosity, should be shared by the whole collaboration.\nIn retrospect this spark of creativity not only saved the\nBABAR experiment, but helped set the stage for interna-\ntional grid computing in HEP.\nAs part of the examination of the computing crisis, the\ncollaboration rethought the needed changes to the existing\ncomputing model, and a small, passionate, very focused\ngroup worked to implement an entirely new computing\nmodel. The largest change was moving from the Objectiv-\nity data base system to a Root-based system, which was\ndone in 2003-2004, but beyond that there were continued\noptimizations over the following years. The implementa-\ntion of the new arrangement for handling computing at\nthe distributed agency computing centers was put in place\nin 2003, with the international Tier A site system set up\nwith SLAC, CCIN2P3 Lyon (France), INFN Padova and\nCNAF (Italy), GridKa (Germany), RAL (UK) and lat-\nterly U. of Victoria (Canada) making up the nodes. The\ncore computing (CPU and disk) came two thirds from\nSLAC and one third from the other sites. Two years later,\nthis sharing was \ufb01fty-\ufb01fty through the intense analysis pe-\nriod. This high volume, distributed computing environ-\nment was the \ufb01rst successful example of large scale pro-\nduction distributed computing (also known as Grid Com-\n\n14\nputing) in HEP in an actual data-taking experiment. The\nBABAR collaboration set up a Computing Steering Com-\nmittee, which twice a year examined the foreseen needs\nfor processor power and storage, and reported to the IFC.\nThis ranks among the great achievements of the collab-\noration and of the funding agencies within the IFC. It\nbuilt on the large international investment in Grid com-\nputing, and on very good international networking. The\nnew computing model, including the change to the Root\ndata analysis framework, was in operation by mid 2003\n(well ahead of schedule), and allowed the experiment to\nkeep processing the data, even at the higher luminosities.\n1.4.3.6 Sub-system upgrades\nBABAR, the lab, and the Technical Review Committee en-\ngaged in a review of each of the detector sub-systems in\nthe 2003, with the outcome that all of the systems were\nexpected to manage the increases in luminosity promised\nby the accelerator team, with just nominal improvements\n(even the expected increased backgrounds), with one ex-\nception \u2014 the muon system\u2019s IFR chambers. The IFR\nsub-system had become a serious problem around 2001,\nwith dropping e\ufb03ciency as the accumulated radiation dose\nincreased. New muon chambers had to be designed and\nbuilt, and then the installation of the new technology suc-\ncessfully implemented without an undue hit to data tak-\ning. This was another multi-lab and multi-nation e\ufb00ort\nto execute this detector upgrade rapidly while still taking\ndata. The collaboration made a heroic e\ufb00ort and made\nvery good progress in production of replacement detec-\ntors \u2014 this time LST\u2019s, which were essentially completed\nby the end of 2004. Installation in the detector was not\ncompleted until 2006, due to a chain of unfortunate ac-\ncidents unrelated to BABAR. The new chambers worked\nvery well, and for the remaining running BABAR had high\ne\ufb03ciency muon tagging.\n1.4.4 Building the Belle detector\nAs with BABAR, the construction phase of the Belle de-\ntector had to resolve a number of technical challenges in\norder to provide a design that would work su\ufb03ciently well\nto deliver the physics goals of the B Factory. As is typical\nwith particle physics experiments, some of the sub-systems\nunder consideration for Belle had proposed variants that\nhad to be studied in detail (Section 1.4.4.1). Along the way\nthe Belle detector team were also presented with several\nunexpected problems that required timely resolution (Sec-\ntion 1.4.4.2). The commissioning period and the \ufb01rst years\nof full Belle operation are discussed in Sections 1.4.4.3\nand 1.4.4.4 respectively.\n1.4.4.1 Design choices and related issues\nBeam pipe: The beryllium beam pipe section is made\nof two concentric cylinders and an intermediate cool-\ning channel. The only supplier for beryllium in such a\ncon\ufb01guration was Electrofusion in California. Because\nof its toxicity, it was only with considerable di\ufb03culty\nthat the import of beryllium was allowed by Japan\nCustoms o\ufb03cers.\nSilicon: The silicon detector \u2014 a key component for the\nsuccess of a B Factory experiment \u2014 was originally\nplanned to use a custom designed Application Spe-\nci\ufb01c Integrated Circuit (ASIC), however as discussed\nin Section 1.4.4.2, the then-standard Honeywell tech-\nnology for radiation-hard ASIC design could not be\nused for a project in Japan. As a result, the choice of\nwhich ASIC to use had to be changed to allow a work-\ning vertex detector to be assembled and installed in\ntime for data taking, while a suitable radiation-hard\ndesign was developed for a subsequent detector.\nDrift chamber: The Central Drift Chamber (CDC) de-\nsign originally envisaged two chambers: an inner \u201cpre-\ncision chamber\u201d with two wire layers and three cathode-\nstrip readout surfaces that focused on high spatial res-\nolution and the provision of z-direction information for\ntriggering and an outer 48-layer closed-cell drift cham-\nber for momentum and dE/dx measurements.\nSince most of the particles produced in B meson decays\nhave relatively low momentum, multiple scattering is\na major contributor to momentum measurement pre-\ncision. Because of this, and in order to maximize the\nchamber\u2019s transparency to synchrotron X-rays, consid-\nerable e\ufb00ort was made to increase the e\ufb00ective radia-\ntion length of the chamber. This included the use of a\nhelium-based chamber gas and aluminum \ufb01eld wires\nwith no gold plating, both unique features at that\ntime (Uno et al., 1993). Eventually, the inner precision\nchamber and the outer tracker were both incorporated\ninto a single, common gas vessel and their intervening\ngas barrier was eliminated.\nParticle identi\ufb01cation: A number of technologies were\ninvestigated for an e\ufb03cient charged particle identi\ufb01-\ncation system for higher momentum tracks. These in-\ncluded a Time-Of-Flight (TOF) system, an array of\naerogel radiators (ACC) developed in collaboration\nwith Matsushita Electric (Enomoto et al., 1993), and\nDIRC for the barrel region following the design concept\ndeveloped for BABAR (Ratcli\ufb00, 1993) and a focusing\nDIRC for the forward end-cap region (Kamae et al.,\n1996; Lu et al., 1996). The choice of aerogel for both\nthe barrel and end-cap was \ufb01nally made by an ad-hoc\ntask force appointed by the spokespersons. Their main\nreason for the selection of the aerogel option was its\noverall simplicity and minimal impact on the design\nof the accelerator and other detector components. The\naerogel system served the Belle experiment well.\nIn addition to a cylindrical array of 128 4-cm-thick\nscintillators as a TOF system, for additional charged\nparticle identi\ufb01cation capability, it was also decided\nto include a second layer of 64 4-mm-thick counters\n(the TSC) to form a track-trigger. The TSC-TOF was\ninitially considered to be a unnecessary redundancy.\nThe subsequent issues with regard to de-scoping the\nSVX trigger capability (Section 1.4.4.2) meant that\n\n15\nthe provision of this redundancy proved to be a wise\nchoice. The fast L0 triggers generated from TSC-TOF\ncoincidences are an essential part of the Belle DAQ\nsystem.\nK0\nL-muon detector: For the detection technology of the\n\u201cKLM\u201d (Belle\u2019s instrumented return yoke) LST\u2019s and\nRPC\u2019s were considered; RPCs were \ufb01nally selected be-\ncause of their robustness and simplicity. The key com-\nponents in an RPC are the highly resistive planar elec-\ntrodes that require very smooth surfaces in order to\navoid non-particle induced electromagnetic discharges.\nVarious electrode materials were studied including oil-\ncovered Bakelite, dry Bakelite, ABS and PVC plas-\ntic, and \ufb02oat glass. It was found that ABS plastic\nand \ufb02oat glass had acceptable e\ufb03ciency and lifetime\nproperties and glass electrodes were selected because\nof their availability and low price (Morgan, 1995). This\nwas the \ufb01rst use of glass electrodes in a large-scale RPC\nsystem. These worked well as long as care was taken\nto avoid any moisture contamination in the operating\ngas.\n1.4.4.2 Belle construction: two major crises\nThe Belle and KEKB Letters of Intent, submitted in\nApril 1994, resulted in the approval of the project by\nthe Japanese government, and construction started soon\nthereafter. The detector construction had two major\ncrises: the failure of the initially planned technology for\nthe silicon vertex detector and the collapse of the support\nstructure for the CsI crystals of the barrel electromagnetic\ncalorimeter.\nSVX failure\nA complication arose in the design of the ASIC chip,\ncalled SMAASH (with both analog and digital pipelines,\non-board data sparsi\ufb01cation, and trigger signals derived\nfrom 32-bit digital OR circuits; Yokoyama et al., 1997),\nintended for front-end readout of the SVX detector. US\nexport restrictions meant that the chip design program\nalso had to incorporate the development of the required\nradiation-hard techniques for the SMAASH ASIC chip. In\nearly 1997, technical problems with the chip development\ncaused the SVX subsystem project to fall well behind the\nschedule needed to be ready in time for the August 1998\ninstallation date. Following a June 1997 recommendation\nof a review panel of international experts chaired by P.\nWeilhammer of CERN, Belle abandoned the SVX and re-\ndesigned the entire system, settling for a more modest ar-\nrangement, SVD1, based on commercially available, non-\nradiation-hard components, that met the angular accep-\ntance and signal-to-noise requirements, but with no trig-\ngering capability and a marginally acceptable data acqui-\nsition rate. SVD1 (Alimonti, 2000) was a three-layer array\nof double-sided silicon detectors (DSSD) that were fabri-\ncated by Hamamatsu Photonics using a design that was\noriginally developed for the DELPHI experiment\u2019s micro-\nvertex detector. The readout was based on the VA1 front-\nend chip that was commercially available from the IDE AS\ncompany in Oslo, Norway. In a crash program involving\na close collaboration among thirteen di\ufb00erent groups in\nBelle and the KEK mechanical shop, SVD1 was designed\nand constructed and ready to be installed in Belle by the\nbeginning of October 1998. By that time, the Belle roll-in\ndate had been shifted to February 1999. To compensate\nfor SVD1\u2019s lack of internal trigger capabilities, a fast L0\ntrigger derived from TSC-TOF coincidences was used to\nlatch the SVD response for potentially interesting beam-\ncrossings while the slower L1 trigger decision was being\nmade.\nBecause it was a relatively primitive system, enough\nspare parts and a prototype frame were available to per-\nmit the assembly of a spare device, SVD1.1. During all\nof the data-taking prior to the installation of SVD2 in\n2003 (Natkaniec, 2006), Belle maintained a spare, replace-\nment vertex detector that was ready to be installed. The\noriginal version was eventually replaced after radiation\ndamage in summer 1999, and was replaced again by a\nmore radiation-hard version a year later.\nCollapse of the CsI crystal support frame\nIn the Belle calorimeter design, the crystals are supported\nby a honeycomb cell structure formed by 0.5-mm-thick\naluminum \ufb01ns stretched between a 1.6-mm-thick aluminum\ninner cylinder and an 8-mm-thick stainless steel outer\ncylinder. The \ufb01ns and the inner cylinder were originally\nwelded together and bolted to the outer supporting cylin-\nder.\nIn May 1998, when the loading of the crystals into\nthe structure and the associated cabling was nearly com-\nplete, and just weeks before the scheduled date for instal-\nlation of the ECL into the Belle structure, severe defor-\nmations to the structure were evident and loud ominous\nsounds were heard when the partially \ufb01lled support struc-\nture was rotated. These were caused by failures of many\nof the welds between the thin aluminum vanes and the\ninner cylinder. After removing all of the crystals and ca-\nbles, a major renovation of the structure was undertaken\nthat sti\ufb00ened the outer support cylinder and used bolts\nand washers to connect the aluminum vanes to the inner\ncylinder. This required a delay of the Belle roll-in date\nfrom August 1998 until February 1999. The modi\ufb01cations\nto the support structure were completed by mid-August\nand crystal re-installation and re-cabling were completed\nin September.\n1.4.4.3 KEKB/Belle commissioning and early running\nThe original schedule, in which Belle and KEKB were\ncommissioned at the same time, was changed. The initial\nKEKB commissioning occurred without Belle in place. In-\nstead, a modest commissioning detector, called BEAST,\nwas installed to provide feedback to KEKB on background\n\n16\nconditions during the machine study and tuning period.\nDuring the initial KEKB beam commissioning period, the\nfully assembled Belle was commissioned in the rolled-out\nposition using cosmic rays.\nKEKB commissioning run\nThe initial KEKB commissioning run started in Decem-\nber 1998 and was reasonably successful, but not with-\nout mishap. The injection system, including the positron\nsource, worked well, although sometimes positron injec-\ntion produced large radiation doses in BEAST. The closed-\norbit deviations in both rings were corrected to less than 1\nmm, which indicated that the magnets were well aligned.\nIn the high-energy ring (HER), a 250 mA electron beam\n(\u223c0.25 times the design value) was stored with a re-\nspectable 60 minute lifetime. In the low-energy ring (LER),\na 370 mA positron beam was stored (\u223c0.15 times the de-\nsign value).\nIn February, during high-current operation of the HER,\nthe intense synchrotron radiation fan generated in the\ndownstream superconducting IR quadrupoles \u2014 through\nwhich the exiting electron beam passes o\ufb00-axis and, thus,\nin a region of high \ufb01eld \u2014 burned a hole through a down-\nstream section of the aluminium beam-pipe, causing a\ncatastrophic vacuum system failure. A replacement pipe\nsection, made from aluminum, was quickly fabricated and\ninstalled. Subsequent simultaneous running of both the\nLER and HER produced collisions with a luminosity that\nwas estimated to be \u223c1030 cm2 s\u22121. BEAST measure-\nments indicated that the SVD occupancy rates would prob-\nably be tolerable, but the large radiation doses that some-\ntimes occurred during positron injection posed some dan-\nger. In addition, BEAST results indicated that the CDC\noccupancy levels and CsI pedestal widths would be very\nhigh during high-current operation of the HER.\nBelle commissioning run\nThe commissioning of the fully assembled Belle detector\nand solenoid with cosmic rays in the rolled-out position\nalso started in December 1998. This allowed for a complete\nrelative alignment in space and time of all the detector\nsubsystems and exposed some problems with the detector\nand the data acquisition system. The SVD1 and CDC spa-\ntial resolutions and the overall pT resolution of the CDC\nwere measured to be near the design value. The other sub-\nsystems, including the trigger and the DAQ software, also\nperformed well. One major problem was an e\ufb03ciency drop\nin the resistive-plate chambers of the K0\nL-muon detector,\nwhich was caused by minute levels of water vapor contam-\nination in the chamber gas. This was cured by replacing\nall 5 km of polyole\ufb01n tubing in the gas distribution system\nwith copper.\n1.4.4.4 Early operation\nBelle rolled into place on May 1, 1999 and saw \ufb01rst col-\nlisions (25 mA positron beam on a 9 mA electron beam)\non June 1. Early running was plagued by high occupancy\nin the CDC caused by synchrotron radiation produced\nby the electron beam. The origin of this problem was\ntraced to back-scattered X-rays from the aluminum sec-\ntion of the down-stream beam-pipe that was installed dur-\ning the KEKB commissioning run. In addition, in July,\nthere was an abrupt deterioration in the performance of\nthe inner-most layer of SVD1.0. This was found to be due\nto low-energy synchrotron X-rays produced in one of the\nupstream correction magnets in the HER.\nThe \ufb01rst run managed to map out the \u03a5(4S) peak, and\nwas then terminated in August. In the ensuing two-month\nshutdown, the downstream aluminum pipe was replaced\nwith a copper version, SVD1 was replaced by the SVD1.1\nspare, the CDC grounding was improved and additional\nbeam halo masks were incorporated inside the HER to\nreduce backgrounds from spent electrons. Software cur-\nrent limits were established on the upstream correction\nmagnets to prevent a repetition of the conditions that\ndestroyed SVD1.0. Although the front-end electronics for\nSVD1.1 were not radiation hard, subsequent versions of\nthe VA1 chip were fabricated with smaller feature sizes,\nand these were found to be quite radiation hard (Taylor,\n2003).\nElectron cloud instability\nThese \ufb01xes were e\ufb00ective and in the next run\u2014Belle\u2019s \ufb01rst\nphysics run\u2014Belle collected a 28 pb\u22121 data sample at the\n\u03a5(4S) peak containing 76k hadronic events with all de-\ntector sub-systems operating at near-design performance\nlevels. The peak machine luminosity was 3.1\u00d71032 cm2s\u22121\nbut attempts to go above this level were stymied by a\nblow-up of the positron beam size. This was traced to the\nelectron cloud instability, in which photo-electrons from\nthe vacuum chamber wall produced by synchrotron X-rays\nfrom one positron bunch experience a Coulomb attraction\nto the following positron bunch. The cure for this was the\nestablishment of a weak magnetic \ufb01eld near the vacuum\nchamber wall that bends the photo-electrons back into the\nwall. The \ufb01rst attempt at doing this in the LER involved\nattaching a large number of small permanent magnets to\nthe beam pipe, which was only modestly successful. The\nreal cure to the problem was achieved by the painstaking\nwrapping of solenoidal coils around all exposed sections of\nthe LER beam pipe, as was the case with PEP-II.\n1.5 Physics at last\nThe KEK and SLAC B Factories were under constant\nexamination to improve the respective accelerator teams\u2019\nunderstanding of beam optics, accelerator controls, and\nall aspects of collider operations; the instantaneous lumi-\nnosity increased gradually and steadily with the passage\nof time. Both machines quickly passed their design lumi-\nnosities. The PEP II luminosity passed 1 \u00d7 1033 cm2 s\u22121\nin 1999, and reached 2 \u00d7 1033 cm2 s\u22121 early in 2000. The\n\n17\nKEKB peak luminosity passed 1 \u00d7 1033 cm2 s\u22121 in Febru-\nary 2000 and reached 2 \u00d7 1033 cm2 s\u22121 by the summer,\nlater reaching 3.4\u00d71033 cm2 s\u22121 in April 2001, the largest\nluminosity then achieved in colliders. Over the life of the\nB Factories there was a further improvement by a factor\nof six at both facilities: see Table 1.3.1.\nThere were two very di\ufb00erent kind of collaborations\ngoing on between the two B Factory communities: the\ncollaboration between the accelerator groups, and that be-\ntween the detector and physics analysis groups. The accel-\nerator collaboration was both close and collegial. On each\noccasion when one or the other group were faced with a\nnew phenomenon on their suite of accelerators or control\nsystems or simulation systems, they would be in touch,\nand most often a small crew of experts from the \u201cother\nteam\u201d would appear in their control room trying to help\ndiagnose the new behavior. This joint facing of each new\nproblem was certainly a component of the increased per-\nformance of both machines. The competition between the\ntwo teams was also very important in motivating careful\nattention to up-time, and to optimum performance. The\ndetector/physics teams, by contrast, were relatively sep-\narate. One explanation of this comes from the desire not\nto share \u201ctoo much\u201d the details of data analysis, so that\nany discovery made would be independently veri\ufb01ed by\nthe other experiment. A secondary concern was to ensure\nthat knowledge of analysis techniques and systematic un-\ncertainties from one experiment did not unintentionally\nlead to a bias on the results, and \u201ctoo good\u201d agreement\nbetween Belle and BABAR. In any case, while there were\noccasional requests for help or advice on problems, details\nof on-going analyses were treated as con\ufb01dential.\nThe initial aim of both experiments was to present\n\ufb01rst results at the ICHEP 2000 meeting in Osaka, Japan.\nBelle submitted 17 papers to this conference, most of\nthese using 5.6 fb\u22121 of data, whereas BABAR submitted\n15 papers based on a data sample of 9.8 fb\u22121. Belle\u2019s\n\ufb01rst journal paper, a measurement of the B0 \u2212B0 mix-\ning parameter \u2206md, was submitted to Physical Review\nLetters in November 2000 (Abe, 2001b) and the \ufb01rst\nBABAR paper accepted for publication was measurement\nof time-dependent CP asymmetries in B0 meson decay\nand was submitted to Physical Review Letters in Febru-\nary 2001 (Aubert, 2001a). These \ufb01rst publications were a\ntaste of things to come.\n1.5.1 Establishing CP violation in B meson decay\nFollowing the initial results shown in Osaka, the two B\nFactories continued to work in competition with one an-\nother toward the goal of determining the level of CP vi-\nolation manifest in B meson decay. The two experiments\nhad similar strategies: to accumulate as much data as pos-\nsible in time for the next summer conference season. By\nthe time of the 2001 summer conference season BABAR and\nBelle had accumulated, and processed for physics analysis,\napproximately 29 fb\u22121 of data each at the \u03a5(4S) peak.\nAt the 2001 Europhysics Conference on HEP BABAR\nannounced the result sin 2\u03b2\n=\n0.59 \u00b1 0.14(stat) \u00b1\n0.05(syst), a 4.1\u03c3 deviation from the CP conserving solu-\ntion of sin 2\u03b2 = sin 2\u03c61 = 0. At the same time this result\nwas submitted for publication. A few weeks later at the\n2001 Lepton-Photon conference, Belle announced their re-\nsult sin 2\u03c61 = 0.99\u00b10.14(stat)\u00b10.06(syst), a 6\u03c3 deviation\nfrom the CP conserving solution. These BABAR (Aubert,\n2001e) and Belle (Abe, 2001g) results were published as\nback-to-back articles in the August 27, 2001 issue of Phys-\nical Review Letters. The Belle and BABAR central values\nstraddled predictions based on the KM model \u2014 and they\nwere consistent with each other. Together the B Factory\nresults clearly established the existence of CP violation in\nthe B meson system. More details of these and subsequent\nmeasurements of \u03c61 = \u03b2 can be found in Chapter 17.6.\n1.5.2 The premature end of BABAR data taking\nAs a result of budgetary decisions within the US, data tak-\ning with BABAR was curtailed and the experiment stopped\nrunning in 2008. However, the BABAR management, sup-\nported by SLAC, was able to work with the funding agency\nrepresentatives in order to ensure that a series of planned\nspecial runs at center-of-mass energies away from the \u03a5(4S)\nwould be allowed to go ahead before the shut-down. As a\nresult BABAR accumulated data at the \u03a5(3S) and \u03a5(2S),\nand performed an energy scan above the \u03a5(4S). The most\nsigni\ufb01cant result from these runs was the discovery of the\n\u03b7b, the long-sought-after ground state of the bb system\n(Section 18.4). The measurement of the ratio of hadrons\nto di-lepton pairs can be used to obtain a precision de-\ntermination of the b quark mass as discussed in the same\nsection.\n1.5.3 The \ufb01nal Belle data taking runs\nThe \ufb01nal beam abort ceremony of KEKB/Belle took place\nat KEK on June 30, 2010. The last data taking period\nwas devoted mainly to an energy scan around the \u03a5(5S),\ncollecting more than 21 fb\u22121 of data (see Section 3.2 for\ndetails on data taking).\nThe end of Belle data taking was triggered by two\nconsiderations. First, Belle accumulated data in excess of\n1 ab\u22121 in accordance with the plan put forward before the\nstart of operation. Second, it was time to start work on\nthe upgrade of the facility, both the accelerator (to Super-\nKEKB) and the detector (to Belle II).\n\n18\nChapter 2\nThe collaborations and detectors\nEditors:\nNicolas Arnaud (BABAR)\nHiroaki Aihara, Simon Eidelman (Belle)\nAdditional section writers:\nI. Adachi, D. Epifanov, R. Itoh, Y. Iwasaki, A. Kuzmin,\nL. Piilonen, S. Uno, T. Tsuboyama\n2.1 Introduction\nThe BABAR and Belle detectors have been primarily de-\nsigned to study CP violation in the B meson sector. In ad-\ndition, they aimed to precisely measure decays of bottom\nmesons, charm mesons and \u03c4 leptons. They also searched\nfor rare or forbidden processes in the Standard Model. As\ndescribed in detail in this book, all these original goals\nhave been reached and in many cases exceeded, thanks to\nthe very high integrated luminosity delivered by the two\nB Factories (PEP-II and KEKB, see Chapter 1), to the\nquality of the physics analysis stimulated by the fruitful\ncompetition between the two experiments, and, last but\nnot least, to the excellent performance of the two detec-\ntors, maintained over almost a full decade-long operation\nperiod. In the following, the main characteristics of BABAR\nand Belle are reviewed and compared, while the main in-\nformation about the evolution of these detectors during\nthe data taking period can be found in Section 3.2. These\ntwo chapters, however, only provide an introduction to\nthe two B Factory detectors and to their years of opera-\ntion. For more details, the reader should consult speci\ufb01c\ndetector papers from BABAR (Aubert, 2002j, 2013) and\nBelle (Abashian, 2002b; Brodzicka, 2012), as well as the\nreferences therein. A summary of the two detector main\ncharacteristics can be found in Table 2.2.1 located at the\nend of this chapter.\nBoth e+e\u2212colliders operated mainly at the center-of-\nmass energy of 10.58 GeV which corresponds to the mass\nof the \u03a5(4S) resonance which decays almost exclusively\n(with branching fraction greater than 96%) to charged or\nneutral B meson pairs (Beringer et al., 2012).\nIn a \u03a5(4S) decay, neutral B mesons are produced\nin a coherent quantum state |B0, B0\u27e9= (|B0\u27e9|B0\u27e9\u2212\n|B0\u27e9|B0\u27e9)/\n\u221a\n2, which means that, until one meson decays,\nthere is always one B0 and one B0 in spite of B0 \u2212B0\nmixing. Studying their decays often requires one to recon-\nstruct B decay vertices and to measure the \ufb02ight times\nof these mesons \u2013 in particular for time-dependent CP vi-\nolation analysis. As they are produced almost at rest in\nthe \u03a5(4S) rest frame \u2013 the mass of the resonance is just\nabove the BB production threshold \u2013 the only way to\nhave B vertices displaced from the e+e\u2212collision point\nis to boost these particles. This is achieved by choosing\ndi\ufb00erent energies for the two beams \u2013 see Table 2.1.1.\nNeglecting a very small beam crossing angle (in KEKB),\nthe kinematic parameters of \u03a5(4S) in the laboratory frame\n(i.e. detector rest frame) are:\n\u03b2 = p\u03a5 (4S) \u00d7 c\nE\u03a5 (4S)\n= E\u2212\u2212E+\nE\u2212+ E+\n(2.1.1)\n\u03b3 =\n1\np\n1 \u2212\u03b22 = E\u2212+ E+\n2\np\nE\u2212E+\n(2.1.2)\n\u03b2\u03b3 = E\u2212\u2212E+\n2\np\nE\u2212E+\n(2.1.3)\nAsymmetric colliders require asymmetric detectors, de-\nsigned to maximize their acceptance. By convention, their\n\u2018forward\u2019 and \u2018backward\u2019 sides are de\ufb01ned relative to the\nhigh energy beam. With the large boost, more particles are\nproduced on average in the forward direction, as shown on\nthe BABAR and Belle protractors displayed in Figure 2.1.1.\nTherefore, both detectors have more instrumentation on\nthe forward side (extended polar angle coverage including\na forward electromagnetic calorimeter) and they are o\ufb00-\nset relative to the interaction point (IP) by a few tens of\ncentimeters in the direction of the low energy beam.\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nBaBar\nBelle\n)\nlab\n\u03b8\ncos(\n*)\n\u03b8\ncos(\nForward side\nBackward side\nFigure 2.1.1. This plot shows the relationship between polar\nangles in the center-of-mass and laboratory frames for BABAR\n(red curve, solid line) and Belle (blue curve, dotted line). The\ncorresponding vertical lines de\ufb01ne the angular acceptance of\nthe two detectors.\nThe Belle and BABAR detectors must ful\ufb01ll stringent\nrequirements imposed by the physics goals of the two ex-\nperiments.\n\u2013 An acceptance close to 4\u03c0 and extended in the forward\nregion, as explained above.\n\u2013 An excellent vertex resolution (\u223c100 \u00b5m), both along\nthe beam direction and in the transverse plane.\n\u2013 Very high reconstruction e\ufb03ciencies for charged par-\nticles and photons, down to momenta of a few tens\nof MeV/c.\n\u2013 Very good momentum resolution for a wide range of\nmomenta, to help separating signal from background.\n\n19\nTable 2.1.1. Beam energies, corresponding Lorentz factor, and beam crossing angle of the B Factories for the nominal \u03a5(4S)\nrunning.\nB Factory\ne\u2212beam energy\ne+ beam energy\nLorentz factor\ncrossing angle\nE\u2212(GeV)\nE+ (GeV)\n\u03b2\u03b3\n\u03d5 (mrad)\nPEP-II\n9.0\n3.1\n0.56\n0\nKEKB\n8.0\n3.5\n0.425\n22\n\u2013 Precise measurements of photon energy and position,\nfrom 20 MeV to 8 GeV in order to reconstruct \u03c00\nmesons or radiative decays.\n\u2013 Highly e\ufb03cient particle identi\ufb01cation for electrons and\nmuons, as well as a \u03c0/K separation over a wide range\nof momenta \u2013 from \u223c0.6 GeV/c to \u223c4 GeV/c.\n\u2013 A fast and reliable trigger, and online data acquisition\nsystem able to acquire good quality data, to process\nthe data live, and \ufb01nally to store it pending o\ufb04ine\nreconstruction\n\u2013 A high radiation tolerance and the capability to oper-\nate e\ufb03ciently in the presence of high-background lev-\nels.\nBoth detectors have the same structure with a cylindri-\ncal symmetry around the beam axis. They are of compact\ndesign with their size being a trade-o\ufb00between the need\nfor a large tracking system and the need to minimize the\nvolume of the calorimeter, by far the most expensive sin-\ngle component of the detector. The forward and backward\nacceptances are constrained by the beamline geometry. Al-\nthough the BABAR and Belle collaborations made di\ufb00erent\ntechnological choices for their detector components, they\nhave similar subdetectors, each with well-de\ufb01ned func-\ntions. Going from the inside to the outside of the BABAR\nand Belle detectors, one \ufb01nds successively:\n\u2013 A charged particle tracking system, made of two com-\nponents.\n\u2013 A silicon detector, known as the SVT (\u2018Silicon Ver-\ntex Tracker\u2019) in BABAR, and the SVD (\u2018Silicon Ver-\ntex Detector\u2019) in Belle, made of double-sided strip\nlayers to measure charged particle tracks just out-\nside the beam pipe. This detector is used to recon-\nstruct vertices (both primary and secondary), mea-\nsures the momentum of low-energy charged parti-\ncles which do not reach the outer detectors due to\nthe strong longitudinal magnetic \ufb01eld and provide\ninputs (angles and positions) to the second tracking\ndetector, a drift chamber, which lies just beyond its\nouter radius \u2013 see below for details.\n\u2013 A drift chamber, known in BABAR as DCH (\u2018Drift\nCHamber\u2019) and in Belle as the CDC (\u2018Central Drift\nChamber\u2019), which measures the momentum and\nthe energy loss (dE/dx) of the charged particles\nwhich cross its sensitive volume. The latter infor-\nmation is useful for particle identi\ufb01cation (PID).\n\u2013 A solenoid cryostat located between the electromag-\nnetic calorimeter and the instrumented \ufb02ux return \u2013\nthese two detectors are described below. The cryostat\nis needed by the superconducting solenoid that pro-\nvides a 1.5 T longitudinal magnetic \ufb01eld in which both\ntracking devices are embedded.\n\u2013 PID detectors designed to distinguish the numerous\npions from the rarer kaons from a momentum of about\n500 MeV/c to the kinematic limit of 4.5 GeV/c.\n\u2013 BABAR is using a novel device called DIRC (Adam,\n2005) \u2013 \u2018Detector of Internally Re\ufb02ected Cherenkov\nlight\u2019 \u2013 which covers the barrel region.\n\u2013 Belle has two types of PID detectors: Aerogel Che-\nrenkov Counters (\u2018ACC\u2019) covering both the bar-\nrel and the forward regions; additional Time-Of-\nFlight (\u2018TOF\u2019) counters in the barrel region with\na \u223c100 ps resolution which makes them e\ufb03cient in\nseparating charged particles up to 1.2 GeV/c, as\nthe particle \ufb02ight path from the IP to the TOF\ncounters is about 1.2 m.\n\u2013 The BABAR (EMC) and Belle (ECL) calorimeters;\nthese are highly-segmented arrays of thallium-doped\ncesium iodide \u2013 in short CsI(Tl) \u2013 crystals assembled\nin a projective geometry. The BABAR EMC consists of\na barrel and a forward end cap while the Belle ECL in-\ncludes a barrel, a forward end cap and a backward end\ncap. Both calorimeters cover about 90% of the total\nsolid angle. In addition to the ECL, Belle developed a\nspecial extreme forward calorimeter (the EFC), made\nof radiation-hard BGO (Bismuth Germanate Oxide or\nBi4Ge3O12) crystals. Mounted on the \ufb01nal quadrupoles\nclose to the beam pipe, it provided information on the\ninstantaneous luminosity and the machine background\nwhich helped optimize KEKB operation.\n\u2013 An instrumented \ufb02ux return, designed to identify\nmuons and to detect neutral hadrons (primarily K0\nL\nand neutrons), and divided into three regions: central\nbarrel, forward and backward end caps. The BABAR\nIFR (\u2018Instrumented Flux Return\u2019) consists of alterna-\ntive layers of glass-electrode-resistive plate chambers\n(RPC\u2019s) and steel of the magnet \ufb02ux return. Origi-\nnally, there were 19 RPC layers in the barrel and 18 in\nthe end caps. Second-generation RPCs were installed\nin the forward end cap in 2002 while RPCs were re-\nplaced by Limited Streamer Tubes (LSTs) in the barrel\nin the period 2004-2006. Belle K0\nL and Muon detec-\ntion system (KLM) was designed designed similarly\nand employed alternating layers of RPC\u2019s (15 in the\nbarrel and 14 in the end caps) and 4.7 cm-thick iron\nplates.\n\u2013 A two-level trigger with a hardware Level-1 (L1) fol-\nlowed by a software Level-3 (L3). The L1 trigger com-\n\n20\nbines track and energy triggers with information from\nthe muon detectors and the decision to accept/reject\nan event is taken by a central trigger system called\nGLT (\u2018GLobal Trigger\u2019) by BABAR and GDL (\u2018Global\nDecision Logic\u2019) by Belle. The L3 trigger level runs\non the online computer farm. The two trigger systems\nhave similar design characteristics: a L1-accepted rate\nof O(kHz) and L3-accepted rate of O(100 Hz), for a few\npercent dead time and an event size of about 30 kB.\nObviously these parameters have evolved during the\ndata taking as luminosity and backgrounds increased.\nBoth the BABAR and Belle triggers have been found\nto be robust, reliable and e\ufb03cient in a wide range of\ndata taking conditions, including runs at lighter \u03a5 res-\nonances or at \u03a5(5S) and above.\n2.1.1 The BABAR and Belle collaborations\nBABAR\nThe size of the BABAR collaboration reached a maximum\nin 2004-2005 with more than 600 collaborators. At the end\nof 2012, there were still 325 BABAR collaborators belonging\nto 73 institutions.\nThe BABAR collaboration is led by a spokesperson\nwhose term is three years. He/she is selected by an ad hoc\nsearch committee whose choice is then validated by the\nBABAR Council. The Council is the main body of the col-\nlaboration and gathers representatives from all BABAR in-\nstitutions. All important decisions (changes in the BABAR\nmanagement, turnovers in the various BABAR committees,\napplication of a new institution wishing to join BABAR,\netc.) are subject to rati\ufb01cation by the Council. During\nthe \ufb01rst year following his/her election, the spokesperson-\nelect works in the senior management team with the cur-\nrent spokesperson who is ending his/her term. The other\nmembers of the senior management are the technical co-\nordinator, the physics analysis coordinator (PAC) and the\ncomputing coordinator. The PAC and computing coordi-\nnator are usually aided by a deputy who is expected to\nbecome the head of the corresponding o\ufb03ce later. The\ntwo other BABAR boards are the Executive Board which\nincludes representatives from the di\ufb00erent countries in-\nvolved in BABAR and the Technical Board (TB). The TB\nfocuses on the detector running; each BABAR system (the\nvarious sub-detectors, the online and trigger groups, the\nmachine detector interface, etc.) is represented there by\ntwo system managers, at least one of whom is based at\nSLAC.\nThe physics analysis organization is led by a PAC and\na deputy-PAC (DPAC). The PAC term is two years: one\nas DPAC, the other as PAC on charge. Analysis Work-\ning Groups (AWGs), led by up to three people depending\non the workload, gather together analysis topics which\nbelong to the same \ufb01eld, e.g. \u2018charmonium\u2019 or \u2018charm-\nless B-decays\u2019. Analysts regularly report the progress of\ntheir work at AWG meetings during which group discus-\nsions help the analysis to move forward. Analysis develop-\nments and details are described in BABAR Analysis Doc-\numents (a.k.a. \u2018BADs\u2019) stored in the BABAR CVS repos-\nitory. Usually, an analysis has one or more \u2018supporting\nBADs\u2019 (which are private BABAR documents) and one\njournal draft BAD which will ultimately be submitted for\npublication. Readers from within the AWG are chosen to\nread in detail the supporting BAD(s) of an analysis once\nit is in an advanced stage. When this part is completed,\na Review Committee (RC) made up of three people (not\nall from the AWG) is formed. The RC and the analysts\nthen work in close contact (phone or in-person meetings,\nexchanges on internal forums, etc.) to \ufb01nalize the analysis,\nvalidate its results and complete the journal draft.\nThe BABAR collaboration as a whole has two main\nways to get involved with the review of an analysis which\nis close to completion. One is the \u2018Collaboration Wide\nTalk\u2019 (CWT) which is held during either a physics meet-\ning or a plenary session of a BABAR quarterly collaboration\nmeeting. The CWT describes the whole analysis, usually\nincluding systematic uncertainties and the unblinded re-\nsults \u2013 the permission for unblinding is given by the RC\n(see Chapter 14 about blind analysis). The last global\nstep is the \u2018Collaboration Wide Review\u2019 (CWR), a two\nweek-period during which BABAR collaborators proof read\nthe draft of the written document which summarizes the\nwhole analysis \u2013 either a journal paper or a physics note\nif the result is initially only to be shown at conferences.\nFinally, a journal draft is examined by two \u2018Final Read-\ners\u2019 (FR) prior to being submitted. The PAC and the\nDPAC follow all the on going analyses in parallel and can\nstep in at any time to request more information, clarify a\npotential issue, remind about the coming deadlines, etc.\nThe CWR and FR steps are managed by the \u2018Publica-\ntion Board\u2019 which also follows the correspondence between\nanalysts and journal referees. Finally, the assignment of\nBABAR talks (obtained by the PAC who is in direct con-\ntact with conference organizers) is the responsibility of the\n\u2018Speakers Bureau\u2019.\nThe analysis review process described above has been\ncontinued since the completion of the data taking so as\nto maintain the high quality of the BABAR scienti\ufb01c pro-\nduction. An internal forum system and various databases\nprovide permanent documentation of the on-going analy-\nses and of their review process, to the whole collaboration.\nThe Authorship of each paper is automatically granted to\nall current members of the BABAR collaboration; people\nwho contributed signi\ufb01cantly to this paper without being\no\ufb03cial BABAR members are added to that particular au-\nthor list. People usually start signing BABAR papers one\nyear after becoming a BABAR member, and remain author\none year after leaving the collaboration.\nBelle\nThe size of the Belle collaboration grew with time and\nreached a maximum in 2012, two years after data taking\nended, with about 470 collaborators from 72 institutions\nin 16 countries.\nThe Belle collaboration is led by three spokespersons\nwhose term is two years with a maximum of three con-\n\n21\nsecutive terms. One spokesperson is from KEK, one from\nJapanese Universities and one from the non-Japanese in-\nstitutions. The spokespersons are elected by the sta\ufb00mem-\nbers of the whole collaboration. Spokespersons are respon-\nsible for running the collaboration, representing its inter-\nests in the institutions and with national funding agencies,\nand for allocating the available resources among the dif-\nferent subgroups.\nThe main body of the collaboration assembles three\ntimes a year at the Belle General Meeting (BGM), and\nbetween BGMs, decisions are enacted by the spokesper-\nsons and the Executive Board (EB). The role of the Exec-\nutive Board, which is made up of the three spokespersons,\nthree members from KEK, three members from Japanese\ninstitutions, and three members from institutions outside\nJapan, is to advise the spokespersons on scienti\ufb01c and\ntechnical matters, and to ratify all important decisions.\nThe EB usually meets monthly.\nEach collaborating institution selects a representative\nto sit on the The Institutional Board (IB), which meets\nat each BGM. The IB deals with organizational, manage-\nment, and personnel issues, including admitting new col-\nlaborators, modi\ufb01cations of the group\u2019s organization, initi-\nating the spokespersons\u2019 selection process, etc. The IB also\nmakes recommendations concerning potential new mem-\nbers during a general meeting. The resignation of mem-\nbers or institutions is treated similarly. The IB also func-\ntions as a \u201cKEKB users\u2019 organization\u201d. It gathers com-\nplaints and/or suggestions regarding KEK and asks KEK\nfor improvements. Various institutional matters are also\ndiscussed by the IB, i.e. items concerning each institu-\ntion\u2019s interest, such as students\u2019 thesis topics, etc. The\nBelle management also includes two physics analysis co-\nordinators and the computing coordinator.\nThe organization of the physics analysis is similar to\nBABAR. Working Groups (WG) led by one or two per-\nsons gather together analyses that belong to the same\n\ufb01eld, e.g., charmonium or charmless B decays. Analysts\nreport regularly the progress of their work at WG meet-\nings during which group discussions help the analysis to\nmove forward. Analysis developments and details are de-\nscribed in written documents - so called Belle Notes. Usu-\nally, an analysis has one or more supporting Belle Note\nresulting in a journal draft to be submitted for publica-\ntion. When an analysis is judged to be mature enough,\na refereeing committee (RC) of three collaboration mem-\nbers is formed. The RC and the analysts then work in close\ncontact (phone or in-person meetings, E-mail exchanges,\nvideoconferences etc.) to \ufb01nalize the analysis, validate its\nresults and complete the journal draft.\nIn addition to BGMs the results of analyses close\nto completion are discussed at Belle Analysis Meetings\n(BAM) usually held three times a year. When the RC\nand the analysts decide that the analysis is complete, a\ncollaboration-wide review starts, a two week-period dur-\ning which Belle colleagues proof read the \ufb01nal document,\na draft of a journal publication. These steps are managed\nby the Publication Council which follows up on the corre-\nspondence between analysts and journal referees and has\nthe general task of maintaining high quality of the Belle\npapers. Finally, a so called authorship con\ufb01rmation pro-\ncedure is started by the general consent of the referees.\nAuthorship of each paper is not automatic in Belle. Those\neligible for authorship are supposed to read the \ufb01nal draft\nand choose one of the three possibilities: agreement with\nthe paper conclusions and willingness to become an au-\nthor, non-authorship because of disagreement with the\nconclusions or because of insu\ufb03cient contribution.\nThe assignment of Belle talks is the responsibility of\nthe spokespersons who are in direct contact with confer-\nence organizers and inform the collaboration about the\nforthcoming scienti\ufb01c meetings.\n2.1.2 The BABAR detector\nFigure 2.1.2 (Aubert, 2002j) shows longitudinal and end\nviews of the BABAR detector. The end view shows the\nforward side of BABAR; on the backward side one would\nsee the toroidal water tank (also called \u2018StandO\ufb00Box\u2019, in\nshort SOB) which contains the 10,752 DIRC photomulti-\npliers (PMTs) detecting the Cherenkov photons created in\nthe quartz bars. The right-handed BABAR coordinate sys-\ntem is shown on both pictures: the z-axis coincides with\nthe axis of the DCH, which is o\ufb00set by about 20 mrad rela-\ntive to the beam axis in the horizontal plane \u2013 this rotation\nhelps to minimize the perturbation of the beams by the\nBABAR solenoidal \ufb01eld which is parallel to the axis of the\nDCH. The y-axis is vertical and points upward while the x-\naxis points away from the center of the PEP-II rings. One\ncommonly uses another coordinate system as well, with z\nunchanged, \u03b8 the polar angle de\ufb01ned with respect to this\naxis (\u03b8 = 0 corresponds to the most forward direction),\nand \u03c6 the azimuthal angle \u2013 unless otherwise stated, the\nBABAR detector is assumed to have a cylindrical symme-\ntry. Figure 2.1.3 shows photographs of the BABAR detector\nseen from the backward end (left picture) and of the SVT\n(right picture).\n2.1.3 The Belle detector\nThe schematic longitudinal cross section of the Belle de-\ntector is shown in Figure 2.1.4. Individual subdetectors\nas listed in Section 2.1 are denoted in the \ufb01gure. The full\ndetector is composed of the barrel part and of the forward\n(in the direction of the incoming e\u2212beam) and the back-\nward (in the direction of the incoming e+ beam) endcaps.\nThe coordinate system used is similar to that of BABAR;\nthe z-axis is in the opposite direction of the e+ beam (note\nthat this is not exactly the same as the direction of the\ne\u2212beam due to a \ufb01nite crossing-angle of the beams), the\ny-axis is vertical and the x-axis horizontal away from the\ncenter of the KEKB ring.\nPhotographs of the Belle detector are shown in Fig-\nure 2.1.5.\n\n22\nFigure 2.1.2. (top) Longitudinal and (bottom) end view of the BABAR detector (Aubert, 2002j).\n\n23\nFigure 2.1.3. (left) View of the BABAR detector from the backward end, with the magnetic shield rolled out of the way to\nreveal the PMTs of the DIRC. The central support tube, with the SVT as well as the B1 and Q1 (dipole and quadrupole)\nmagnets of the interaction region beam delivery system (right) was removed from the detector for maintenance at the time this\nphotograph was taken.\n2.2 BABAR and Belle comparative descriptions\nThis section provides a comparison of the di\ufb00erent BABAR\nand Belle components, classi\ufb01ed by function: \ufb01rst the sub-\ndetectors, then the trigger, the online and Data AcQui-\nsition (DAQ) systems and \ufb01nally the background protec-\ntion system. As previously mentioned, the detector journal\npublications from each collaboration should be consulted\nfor more detailed explanations of the detectors discussed\nbelow. Information about the PEP-II trickle injection sys-\ntem can be found in Section 3.2.2. Also, a casual reader not\ninterested in the technical details of the detector setup and\nperformances can move directly to Section 2.2.9 in which\na summary of the comparison between the two detectors\nis provided.\n2.2.1 Silicon detector\nBABAR\nAs shown on Figure 2.2.1, the BABAR SVT is made of\n\ufb01ve layers: three close to the beryllium beam pipe to per-\nform impact parameter measurements and two at a larger\nradius to help pattern recognition in the tracking system\n(SVT and DCH) and to perform stand-alone low-pT track-\ning: only tracks with momentum greater than 120 MeV/c\ncan be reliably measured in the DCH. The inner three lay-\ners are primarily used for vertex measurements while the\nouter two, located much further away, help the track ex-\ntrapolation to the DCH. The end view in Fig. 2.2.1 shows\nthe number of SVT modules: 6, 6, 6, 16 and 18 for layers\n1 to 5 respectively. It also shows that the two outer layers\nare divided into two sub-layers each, located at slightly\ndi\ufb00erent radii to ensure a small azimuthal overlap be-\ntween modules. A similar overlap exists for the inner 3\nlayers which are tilted by 5\u25e6. The three inner layers are\nstraight while the outer two are arch-shaped to minimize\nthe amount of silicon required to cover the solid angle and\nhence the amount of silicon that a track would have to\npass through in the forward or backward regions of the\nSVT: only about 4% X0.13 The angular coverage is from\n20 degrees to 150 degrees in the laboratory frame: 90%\nof the solid angle is covered in the center-of-mass frame.\nThe total active area of silicon is close to 1 m2 for about\n150,000 channels. Each SVT module is divided electrically\nin two half-modules which are readout at the ends. All sen-\nsors are double-sided: on one side, the strips are parallel\n13 The quantity X0 is called the radiation length.\nFigure 2.2.1. Longitudinal \u2013 unless otherwise mentioned,\nall subdetectors are axially symmetric around the detector\nprinciple axis \u2013 and transverse sections of the 5-layer BABAR\nSVT (Aubert, 2002j). The 27.9 mm diameter beampipe visible\nin the center of the SVT is composed of two beryllium layers\nwith a water channel between them for cooling purpose.\n\n24\nCDC\nECL\nKLM\nTOF\nACC\nSVD\nEFC\ne-\n8.0 GeV\ne+\n3.5 GeV\nSCALE\n0 1 2 3 m\nKLM\nCDC\nMoveable\nACC\nSVD\nECL\nendyoke\nFigure 2.1.4. Longitudinal (top), adapted from (Abashian, 2002b), and transverse (bottom) cross sections of the Belle detector.\nto the beam and measure the azimuthal angle \u03c6 and the\nradius of the hit r; on the other side the strips are trans-\nverse and measure the z coordinate. The SVT consists of\n340 sensors which are aligned in situ relative one-another\nusing dimuon and cosmic ray events. This local alignment\nis quite stable over time: it only needs to be updated when\nsomething \u2018signi\ufb01cant\u2019 occurs in the BABAR detector hall:\na detector access or a quench of the superconducting coil\n\n25\nFigure 2.1.5. Left: View of the Tsukuba detector hall with the Belle detector. The beamline enters from the bottom left\nthrough the detector end cap. Right: Beamline view of the detector. From the outer to the inner part the KLM modules, ECL\nmodules, ACC PMT\u2019s and the CDC end \ufb02ange can be seen (see the text for description of subdetectors).\nfor instance. Once this is done, the SVT is considered as\na rigid single body and one can check its alignment with\nrespect to the DCH. This global alignment is updated af-\nter every run (about once an hour): the newly computed\nalignment constants are then used to reconstruct tracks\nduring the following run, data from which a new set of\nconstants is extracted and so on. This procedure, called\nrolling calibration, is used by most of the BABAR systems\nand allows one to monitor changes in detector calibration\nwhich occur for the whole detector about once a day, be-\ntween two successive periods of data taking.\nObviously the SVT is a very sensitive device which\ncould be damaged by radiation as it is very close to the IP.\nDamage could come from two e\ufb00ects: either a huge burst of\nradiation destroying instantaneously some channels, or the\nintegrated dose exceeding the SVT radiation budget and\nleading to permanent damage. To mitigate such problems,\na dedicated system called SVTRAD has been developed:\nthis continuously monitors the radiation levels in the SVT\nand can either temporarily inhibit the injection or even\nforce a beam abort if the instantaneous dose is deemed to\nbe too high. More information about the SVTRAD system\ncan be found in Section 2.2.8 below.\nDuring the whole data taking period, the SVT perfor-\nmance was constantly monitored while studies were done\nregularly to predict future performance based on the ex-\npected increase of the beam currents and of the luminosity.\nThe main e\ufb00ects of the evolving running conditions to the\nSVT were twofold: occupancy-induced damage and radia-\ntion damage. While the former is an instantaneous e\ufb00ect\nwhich can be mitigated by limiting the occupancy in the\nmost a\ufb00ected layers, the latter gets integrated over time.\nBoth the modules and the front-end electronics su\ufb00er from\nthis degradation. There is no way to recover the lost per-\nformance, except by replacing any damaged components \u2013\nwhich was not attempted on the SVT. The consequences\nof these e\ufb00ects are the reduction of the collected charge\nand the increase of the noise. Both e\ufb00ects limit the SVT\nperformance and have been taken into account to de\ufb01ne\nthe operating mode of this sub-system.\nOver the nine years of operation, the average e\ufb03ciency\nof the SVT modules (computed for each half-module by\ndividing the number of hits associated to tracks with the\nnumber of tracks crossing that particular module) was\nabove 95%, excluding a few percent of defective half-\nmodules. Some half-modules had issues with individual\nchannels; however, these had no signi\ufb01cant impact on the\noverall e\ufb03ciency as usually two or more strips are used to\ndetect charge in a given layer crossed by a charged parti-\ncle. The z and r\u03c6 resolutions range from \u223c15 to \u223c40 \u00b5m\ndepending on the layer and on the measured quantity. The\nbest results are obtained for tracks with a polar angle close\nto 90\u25e6while resolution degrades slowly in the forward and\nbackward directions. Measurements of dE/dx allow the\nSVT to achieve a 2\u03c3 separation between kaons and pions\nup to a momentum of 500 MeV/c.\nBelle\nThe Belle SVD has been improved step by step after the\ncommissioning of the Belle detector in 1999. In the \ufb01rst 3\nyears, the \ufb01rst system, called SVD1, which consisted of 3\nlayers of AC coupled double-sided silicon-strip detectors\n(DSSD) read out with VA1 readout chip (Gamma-Medica,\n1999), was used. As SVD1 was the \ufb01rst silicon vertex de-\ntector built at KEK, a conservative design was chosen. Its\ncoverage was 23\u25e6< \u03b8 < 140\u25e6while the full acceptance of\nthe Belle detector was 17\u25e6< \u03b8 < 150\u25e6. The limited radi-\nation hardness of the VA1 chip AMS 1.2 \u00b5m (200 krad)\n\n26\nand its long shaping time (2.8 \u00b5sec) discouraged aggres-\nsive operation of the KEKB collider. In addition, since the\nBelle readout electronics were set to the ground level, and\nthe bias voltage was applied across the dielectric in the\ncoupling capacitor of the DSSD, a few pinholes appeared\nin the dielectric each year.\nBecause of these problems, the Belle collaboration\nstarted the upgrade of the SVD before the start of KEKB\noperation. In 2000, all SVD ladders were replaced utiliz-\ning an upgraded VA1 AMS 0.8 \u00b5m chip (Aihara, 2000b)\nwhose radiation tolerance improved to 1 Mrad.\nA major upgrade was done in summer 2003. The sec-\nond generation silicon vertex detector, SVD2 (Natkaniec,\n2006), consisting of 4 layers of DSSD and covering the\nfull angular acceptance (17\u25e6< \u03b8 < 150\u25e6), was installed\n(Fig. 2.2.2). The inner radius of the beam pipe was re-\nduced from 20 mm to 15 mm (Abe, 2004i). The radii of\nthe SVD2 layers are 20 mm, 44 mm, 70 mm and 88 mm. As\nthe KEKB luminosity increased after SVD2 was installed,\n85 % of Belle data were taken with SVD2.\nFigure 2.2.2. The longitudinal cross section of Belle\u2019s SVD2\n(Natkaniec, 2006). The layer 1 and layer 4 ladders are also\ndepicted. The radii of layers 1 to 4 are 20, 44, 70 and 88 mm,\nrespectively. SVD2 covers the whole Belle acceptance (17\u25e6<\n\u03b8 < 150\u25e6) shown by dashed lines.\nSVD2 also utilized a newly-developed chip, VA1TA,\nwhich had a 0.8 \u00b5sec peaking time and a radiation toler-\nance of 20 Mrad (AMS 0.35 \u00b5m technology) (Yokoyama,\n2001). The control register was made of triple-module-\nredundancy logic to avoid and detect single-event upsets\n(SEUs). Thanks to the short shaping time, the contribu-\ntion of the dark current to the overall noise was not sub-\nstantial. The voltage from the low-voltage power supply\nwas increased to be above the bias voltage and the rate of\npinhole appearance was reduced dramatically. SVD2 was\noperated for eight years without major problems.\nThe material in front of the CDC innermost layer is\nthe beam pipe (0.62% X0), four layers of strip sensors\n(1.71% X0), the SVD CFRP (carbon \ufb01ber reinforced poly-\nmer) cover (0.23% X0) and the CDC inner CFRP cylinder\n(0.17% X0) totaling 2.73% X0. The SVD sensor align-\nment is done among DSSDs (internal) and with respect to\nthe CDC (global). Both internal and global alignment pa-\nrameters are determined for every KEKB run period. No\nsigni\ufb01cant change in alignment parameters was observed\nthroughout the experiment.\nThe impact parameter resolution in r-\u03c6 and r-Z was\nmeasured to be \u03c3r = 21.9 \u229535.5/p \u00b5m and \u03c3Z = 27.8 \u2295\n31.9/p \u00b5m, respectively, where p represents the track mo-\nmentum in GeV/c and the \u2295sign denotes summation in\nquadrature (Abe, 2004h).\nThe hit occupancy in the inner most layer remained in\nthe range 5-7% at the highest luminosity of 2\u00d71034/ s/ cm2\nwithout degradation of the detector performance.\nThere is an important di\ufb00erence in the positioning of\nthe silicon detector and hence its role as a part of the\ntracking system between BABAR and Belle. In the case of\nBABAR\nthe SVT is installed inside a support tube. As a\nresult, the innermost radius of DCH is 236 mm and the ra-\ndius of the outermost layer of the SVT is 140 mm. There-\nfore, e\ufb03cient low-momentum track-reconstruction capa-\nbility of the SVT was required and the 5-layer design was\na natural choice. In the case of Belle, the SVD is supported\nby the CDC, with the radii of the outermost SVD layer\nand the innermost CDC layer being 90mm and 110mm, re-\nspectively. The reconstruction of low pt tracks can be done\nby the CDC. Thus, the main purpose of the Belle SVD is\nto extrapolate the tracks reconstructed in the CDC to\nthe decay vertices inside the beam pipe. The reconstruc-\ntion of low pT tracks with the CDC is e\ufb03cient down to\n70 MeV/c (Dungel, 2007).\n2.2.2 Drift chamber\nBABAR\nFigure 2.2.3. Longitudinal section of the BABAR DCH (Au-\nbert, 2002j) with the principal dimensions given in millimeters.\nLike the whole BABAR detector, the 40-layer drift chamber is\no\ufb00set by 370 mm from the IP. The electronics are located be-\nhind the backward end plate. The DCH coverage, de\ufb01ned by\nrequiring that at least half of the layers are traversed by the\ntracks, extends from 17.2\u25e6to 152.6\u25e6in polar angle.\nFigure 2.2.3 shows a longitudinal section of the BABAR\nDCH which performs both the tracking and part of the\nPID for charged particles \u2013 the latter is possible thanks to\nmeasurements of track ionization losses (dE/dx). Indeed,\nlow momentum tracks do not reach the DIRC and so only\nthe tracking system can help identify them. Moreover, the\n\n27\nDIRC only covers the BABAR barrel section which means\nthat the DCH is the only detector available to perform\nPID on the forward side of BABAR. The DCH is also a key\ncomponent of the L1-trigger level. The DCH readout elec-\ntronics, mounted on the backward end plate of the cham-\nber, were upgraded in 2004-2005 to cope with the trigger\nrate increase associated with the increase of the PEP-II\nluminosity and with the corresponding increase of back-\nground. In particular, the new readout boards included\nFPGAs responsible for performing the feature extraction\nstep (extraction of physical signals from the raw data; gain\nand pedestal corrections; data sparsi\ufb01cation and data for-\nmatting) prior to transferring the data from the front-end\nboards to the DAQ modules. Previously, feature extrac-\ntion was performed in the DAQ modules. These new chips\nwere sensitive to SEUs occurring at a rate of a few per day\nin the whole DCH electronics. Therefore, a dedicated sys-\ntem was set up to monitor the behavior of the new DCH\nfront-end boards and to reload in a few seconds the chip\n\ufb01rmware, should errors be detected.\nThe DCH counts 40 layers of small hexagonal cells\nof which 24 are placed at small stereo angles (about 50-\n70 mrad) to provide z information. The \ufb01eld wires are\nmade of aluminum and the gas mixture is 80:20 He-\nlium:Isobutane in order to minimize multiple scattering\ninside the DCH (the material inside the chamber only\ncounts for 0.2% X0). The 40 layers are gathered in 10 \u2018su-\nperlayers\u2019 in which all layers have the same orientation.\nLabeling \u2018A\u2019 an axial DCH superlayer (which stereo angle\nis null), \u2018U\u2019 a superlayer with positive stereo angle and\n\u2018V\u2019 a superlayer with negative stereo angle, the pattern of\nthe BABAR DCH can be written: \u2018AUVAUVAUVA\u2019. This\nparticular alternation optimizes the performance and the\nreliability of the DCH.\nLike the SVT, the DCH is a delicate system which\nmust be monitored continuously and carefully to detect\nany unsafe condition and mitigate it in the appropriate\nway. Particular examples of monitoring (with hardware\nand software systems) included the DCH gas mixture com-\nposition and potential gas leakage, and the high-voltage\n(HV) settings of each group of wires. The monitoring sys-\ntems were continuously improved over the years to mini-\nmize the dead time of the DCH without bypassing safety\nrequirements. In the \ufb01nal implementation, if the current\nof a given channel was found to be too high, the corre-\nsponding voltage was reduced until the current fell below\na safe threshold, at which point the HV would be ramped\nup again. During this process, all the other HV settings\nwere unchanged, allowing data taking to proceed. In ad-\ndition, a real time software process was able to predict\nthe DCH current during running, using several monitoring\nvariables that were independent (beam currents, various\nbackground levels readout by sensors, etc.). In this way,\nthe DCH would only switch from the injectable voltage\nlevel to the running one if the beam conditions were good\nenough to ensure a safe operation of the chamber when it\nwould reach its working point. Apart from a small number\nof wires which were damaged by a HV incident during the\nBABAR commissioning phase, the whole DCH worked well\nduring the whole data taking period. The DCH nominal\nHV was regularly raised during the data taking to correct\nfor gain losses due to aging: while the nominal HV level\nwas 1960 V, the initial setting was 1900 V; by the end\nof data taking, it had been raised to 1945 V \u2013 one volt\ncorresponds to about 1% on the gain. Loss of gain due to\nwire aging was 11% over the life of the chamber. The DCH\nperformed as expected during all the BABAR data taking,\nboth as the main component of the tracking system and\nas an important contributor to BABAR PID, with a mea-\nsured dE/dx resolution of about 8%, close to the design\nvalue of 7%.\nBelle\nThe Belle Central Drift Chamber (CDC) plays several im-\nportant roles. First, it reconstructs charged particle tracks,\nprecisely measures their hit coordinates in the detector\nvolume, and enables reconstruction of their momenta.\nSecond, it provides particle identi\ufb01cation information us-\ning measurements of dE/dx within its gas volume. Low-\nmomentum tracks, which do not reach the particle iden-\nti\ufb01cation system, can be identi\ufb01ed using the CDC alone.\nFinally, it provides e\ufb03cient and reliable trigger signals for\ncharged particles.\nSince the majority of the particles in B meson decays\nhave momenta lower than 1 GeV/c, minimization of multi-\nple scattering is important for improving the momentum\nresolution. Therefore, a gas mixture of 50% He and 50%\nC2H6 was chosen, which, because of the low Z nature of\nthe gases, provided optimal momentum resolution while\nretaining good energy loss resolution.\nThe structure of the CDC is shown in Fig. 2.2.4. It is\nasymmetric in the z direction with an angular coverage of\n17\u25e6\u2264\u03b8 \u2264150\u25e6and has a maximum wire length of 2400\nmm. The inner radius of the CDC lies at 80mm, and the\ndetector has no inner wall in order to minimize multiple\nscattering in the material that lies within the radius of\nthe \ufb01rst wire layer and to ensure good tracking e\ufb03ciency\nfor low-pt tracks. The outer radius is 880 mm. In the for-\nward and backward directions at small r, the CDC has the\nshape of a truncated cone. This allows for the necessary\nspace to accommodate the accelerator components while\nkeeping the maximum available acceptance. The chamber\nhas 50 cylindrical layers, each containing between three\nand six either axial or small-angle stereo layers, and three\ncathode strip layers. The CDC has total of 8400 drift cells.\nThe two innermost super-layers are composed of three lay-\ners each and the three outer stereo super-layers are com-\nposed of four layers each. When combined with the cath-\node strips, this provides a high-e\ufb03ciency fast z-trigger.\nFor each stereo super-layer, the stereo angle was deter-\nmined by maximizing the z-measurement capability while\nkeeping the gain variations along the wire below 10%. The\nsense wires are made of gold-plated tungsten and have the\ndiameter of 30 \u00b5m, while the aluminum \ufb01eld shaping wires\nhave the diameter of 126 \u00b5m.\nIn all layers, except the three innermost, the maximum\ndrift distance is between 8 mm and 10 mm. In the radial\n\n28\ndirection the thickness of drift cells ranges from 15.5 mm\nto 17 mm. In the innermost layers the cells are smaller\nand signals are read out by cathode strips. Staggering of\nthe neighboring radial layers within a super-layer in the \u03c6\ndirection by half cell helps in resolving left-right ambigu-\nities.\nThe CDC read-out electronics consists of Radeka-type\npre-ampli\ufb01ers which amplify the signal and send it to mod-\nules performing shaping, discrimination and charge(Q)-to-\ntime(T) conversion. These modules are placed in the elec-\ntronics hut and are connected to pre-ampli\ufb01ers via \u223c30 m\nlong twisted pair cables. The technique used is a simple\nextension of the ordinary TDC/ADC readout scheme, but\nallows Belle to measure both, timing and charge of the sig-\nnals, using multi-hit TDC\u2019s only.\nIn summer 2003, the cathode part, which corresponds\nto the inner most three layers, was replaced with a new\nchamber in order to provide space for SVD2. The new\nchamber consists of two layers with smaller cells about\n5 mm \u00d7 5 mm due to limited space and reducing the\noccupancy. The maximum drift time becomes shorter; less\nthan 100 nsec in the 1.5 T magnetic \ufb01eld.\nThe high voltage applied to the sense wires was kept for\n11-years of operation without serious radiation damage.\nAfter detailed alignment and calibration, the overall spa-\ntial resolution is around 130 \u00b5m, as expected. The track-\ning system consisting of the SVD and CDC provides rather\ngood momentum resolution, especially for low-momentum\ntracks thanks to the minimization of material inside the\ninner radius of the CDC:\n\u03c3pT /pT = 0.0019pT \u22950.0030/\u03b2 [pT : GeV/c].\nThe resolution on dE/dx, which is important for PID,\nwas 7% for minimum-ionizing particles. The r \u2212\u03c6 trigger\nof the CDC provides a highly e\ufb03cient and reliable trigger\nsignal. The z trigger that uses the cathode strips works\nwell in reducing the rate of the charged trigger by a factor\nof three without sacri\ufb01cing any physics events.\n747.0\n790.0\n1589.6\n880\n702.2\n1501.8\nBELLE Central Drift Chamber\n5\n10\nr\n2204\n294\n 83\nCathode part\nInner part\nMain part\nForward\nBackward\ne\ne\nInteraction Point\n17\u00b0\n150\u00b0\ny\nx\n100mm\ny\nx\n100mm\n-\n+\nFigure 2.2.4. Belle CDC structure.\n2.2.3 Charged particle identi\ufb01cation\nPrinciples of the charged particle identi\ufb01cation and their\ntechnological realization used in both detectors are de-\nscribed in the following. Readers interested mainly in the\nmethods and performance of the PID systems may obtain\nmore details from a separate chapter on charged particle\nidenti\ufb01cation, Chapter 5.\n2.2.3.1 BABAR\nFigure 2.2.5. Principle of the BABAR DIRC (Aubert, 2002j) \u2013\nnote that this schematic is inverted with respect to the other\npictures showing longitudinal sections of BABAR or of one of its\ncomponents: the forward (backward) side of the detector is on\nthe left (right) side of the picture.\nMany detectors contribute to the BABAR PID system:\nthe SVT and DCH via measurements of the speci\ufb01c en-\nergy loss dE/dx for charged particles crossing their active\narea; the EMC for electron identi\ufb01cation and the IFR for\nthe muons. But its main component is the DIRC which\ndominates the \u03c0/K separation power at high momentum\nby measuring the emission angle \u03b8C of the Cherenkov light\nproduced by a charged particle crossing a quartz bar ra-\ndiator (see Fig. 2.2.5). The dimension of each quartz bar\nis 4.9 m \u00d7 6 cm2.\nCharged tracks crossing a quartz bar at a velocity\ngreater than the speed of light in that medium produce\nlight through the Cherenkov e\ufb00ect. A fraction of these\nphotons propagate to the backward bar end through total\ninternal re\ufb02ection \u2013 the forward bar end is instrumented\nwith a mirror to re\ufb02ect forward photons backward. Then,\nthey exit the quartz bar through the quartz wedge which\nre\ufb02ects them at a large angle with respect to the bar axis.\nTraveling through the ultra-pure water contained in the\nSOB, they are \ufb01nally detected by one of the 10,752 PMTs\nlocated about 1.2 m away from the bar end (located be-\nyond the backward end of the magnet). Not only the po-\nsitions of the detected photons but also their arrival times\nare used to reconstruct the Cherenkov angle at which they\nwere emitted.\nThe large water tank of the BABAR DIRC was sensitive\nto backgrounds resulting mainly from neutrons interact-\ning with the H2O molecules. Moreover, it was a permanent\n\n29\nconcern as water could leak in the boxes containing the\nDIRC quartz bars (called \u2018barboxes\u2019) and from there reach\nother parts of the BABAR detector, causing serious and\npermanent damage to the apparatus. Therefore, the DIRC\ngroup had to design a sophisticated system monitoring in\nreal time the humidity outside the SOB and triggering a\nquick water dump, should a leak be detected. In addition,\nN2 was continuously \ufb02owing in the DIRC barboxes to keep\nthe quartz bars dry \u2013 drops of water would have spoiled\nthe quartz optical properties. Lastly, the SOB was full of\nultra-pure water (a potential environmental hazard) run-\nning in closed circuit and which had to be continuously\npuri\ufb01ed by a dedicated water plant.\nThe DIRC reconstruction associates PMT hits with\ncharged tracks crossing the quartz bars with a momentum\nabove the Cherenkov threshold. In addition to background\nhits which can potentially \u2018hide\u2019 the image of the Cheren-\nkov ring on the PMT array, a complication arises from the\nfact that the actual path of a given photon between its\norigin, somewhere along the charged particle track in the\nquartz, and its detection is unknown. For each detected\nphoton, there are 16 ambiguities coming from our igno-\nrance in the number and of the nature of the re\ufb02ections\nundergone by the photon in the quartz. Fortunately, most\nof them can be rejected as un-physical or leading to an\ninconsistent timing for the hit \u2013 the DIRC is truly a 3D-\nimaging device, which uses both the position and timing\ninformation to reconstruct its data. The ambiguities re-\nduce typically to three and are used in the reconstruction\nalgorithms based on an unbinned maximum likelihood for-\nmalism \u2013 see Chapter 11. Their outputs are usually a like-\nlihood value for each of the \ufb01ve \u2018stable\u2019 charged particle\ntypes (e, \u00b5, \u03c0, K and p) plus an estimation of the Cheren-\nkov angle \u03b8C and of the number of signal and background\nphotons, if enough photons have been found for that par-\nticular track. The angle resolutions achieved are typically\n10 mrad per photon and 2.5 mrad per track, a level only\n10% larger than the DIRC design goal. This is su\ufb03cient to\nseparate kaons from pions by more than 4 \u03c3 at 3 GeV/c.\n2.2.3.2 Belle\nParticle identi\ufb01cation at Belle, in particular for kaons and\npions, is performed by combined information from three\ndetector elements; the time-of-\ufb02ight detector (TOF), aero-\ngel Cherenkov counter (ACC) and dE/dx in the CDC. In\nthis section, brief speci\ufb01cations of two of these detectors\n(TOF and ACC) are summarized. A description of the\nCDC is given in Section 2.2.2.\nTime-of-\ufb02ight system\nThe time-of-\ufb02ight (TOF) system consists of a barrel of 128\nplastic scintillator counters and can distinguish between\nkaons and pions for tracks with momenta below 1.2 GeV/c.\nThe system is designed to have time resolution of 100 ps\nfor muon tracks (Kichimi, 2000).\nOne TOF module (the entire system comprises 64 mod-\nules) is shown in Figure 2.2.6. Each module consists of two\nTOF counters and one thin trigger scintillation counter\n(TSC). Fine-mesh PMTs are attached to the both ends\nof the TOF counter and the backward end of the TSC\ncounter. The acceptance is 33\u25e6- 121\u25e6in the laboratory\npolar angle, and the minimum transverse momentum to\nreach a TOF counter is 0.28 GeV/c. The two-layer con-\n\ufb01guration of TSC and TOF counters with 1.5 cm air gap\nremoves photon-conversion triggers due to a huge photon\nbackground caused by spent particle hits on the beam pipe\nnear the interaction region.\nFigure 2.2.6. One TOF module consisting of two TOF coun-\nters and one TSC counter. The scales are in mm.\nThe TOF readout system records a set of charges Qi\nand timings Ti from the rising edges of discriminator out-\nputs for each PMT signal from the TOF detector. Fig-\nure 2.2.7 shows the block diagram of the timing measure-\nment utilizing the Time Stretcher (TS) circuit. The cir-\ncuit \ufb01nds the \ufb01rst rising edge T2 of the TS reference clock\n(reduced radio-frequency - RF - signal of the KEKB ac-\ncelerator with a frequency of 508.9 MHz) following the\nrising edge T1 of the TOF signal, and expands the time\ninterval (T2 \u2212T1) by a factor of 20, for the timing of the\nfollowing pulse (T3 \u2212T2). These measured times are read\nout with Belle standard FASTBUS TDCs with a 0.5 ns\nleast signi\ufb01cant bit (LSB), providing a 25 ps LSB as a re-\nsult. A further time-walk correction is applied for timing\nvariation due to a pulse charge, \u2206Ti\u223c1/\u221aQi.\nThe TOF system measures time of \ufb02ight for charged\ntracks reconstructed by the CDC and requires addition-\nally the beam collision time for each event, tIP. It is deter-\nmined by the RF clock signal used as a reference, and the\ntime o\ufb00set is calibrated o\ufb04ine on a run-by-run basis using\na large sample of \u00b5-pair events (\u03b3\u03b3 \u2192\u00b5+\u00b5\u2212) with a pu-\nrity better than 98%. The expected TOF for each muon\ntrack is calculated, taking into account its \ufb02ight length\nmeasured by the CDC, and the o\ufb00set is tuned to give a\nzero deviation on average between the calculation and the\nTOF measurement for each PMT.\nDetermination of the collision timing for TOF mea-\nsurement has an ambiguity of an integer multiple of 1.96 ns\nin each event corresponding to the period of the RF clock.\nThis ambiguity can be solved in almost all cases, assigning\nthe velocity of light to high momentum tracks in an event\n\n30\nTime Stretcher \noutput\n16 ns\nPMT signal\n508.9 MHz\nRF clock\n 2 ns\nCollision Time\nTS clock\nTDC Stop\nf x \nT4\nT3\nT2\nT1\nT\nT\nTS Clock Edge\nFigure 2.2.7. Time Stretcher TDC scheme for Belle\u2019s TOF\nsub-system. The TS reference clock of approximately 8 ns is\ngenerated from the KEKB RF signal of 508.9 MHz (Abashian,\n2002b).\n(or, equivalently, assigning the pion mass to the tracks).\nWhen the pion-mass assumption fails, the kaon or proton\nmass is tried.\nLong-term variation of the time resolution of the TOF\nsystem was monitored using the \u00b5-pair samples. The res-\nolution of 110 ps measured in 2008 (Kichimi, 2010) was\ndegraded from the initial resolution of 96 ps obtained in\n1999. The 110 ps resolution includes a systematic error\nof 40 ps in total from timing jitters in the detector and\naccelerator electronics, calculation from \u00b5-track informa-\ntion, and the collision position spread due to a beam bunch\nlength. The degradation in timing performance is mainly\ndue to aging, a reduction of the attenuation length and\nlight yield in the TOF scintillation counters over the ten\nyear running period. Pion tracks have a slightly worse av-\nerage time resolution, typically by 10 ps, due to a nuclear\nscattering e\ufb00ect.\nAerogel Cherenkov counters\nFigure 2.2.8 shows the con\ufb01guration of the Belle Aerogel\nCherenkov counter (ACC; Iijima, 2000). The polar angle\ncoverage is 33.3\u25e6< \u03b8 < 127.9\u25e6in the barrel, and 13.6\u25e6<\n\u03b8 < 33.4\u25e6in the forward endcap. The detector is built from\naerogel modules of ten distinct types, varying in refractive\nindex (n = 1.010, 1.013, 1.015, 1.020, 1.028, or 1.030), and\nin the number (one or two) and size (2-, 2.5-, or 3-inch\ndiameter) of photomultiplier tubes used to detect photons,\naccording to their position in polar angle.\nThe barrel device consists of 60 identical sectors in the\n\u03c6 direction, and 16 modules are arranged in each sector.\nThe typical size of one module is approximately 120 \u00d7\n120\u00d7120 mm3, occupied with a silica aerogel radiator. The\naerogel radiator volume is covered with a white re\ufb02ector\nwith high re\ufb02ectivity (larger than 93%); it is supported\nby a 0.1 mm thick aluminum wall.\nEach counter is viewed by one or two \ufb01ne-mesh PMT(s)\nto detect Cherenkov light in an axial magnetic \ufb01eld of\n1.5 T. The PMT diameters were chosen to be either 2\u201d,\n2.5\u201d, or 3\u201d, depending on refractive indices since larger\nindex aerogel generates more photons and the acceptance\nof a PMT can be smaller as a result.\nn=1.028\n60 mod.\nn=1.020\n240 mod.\nn=1.015\n240 mod.\nn=1.013\n60 mod.\nn=1.010\n360 mod.\nB (1.5Tesla)\nBarrel ACC\n3\" FM-PMT\n2.5\" FM-PMT\n2\" FM-PMT\n17 \u00b0\n127 \u00b0\n34 \u00b0\nEndcap ACC\nn=1.030\n228 mod.\n885\nR\n(BACC/inner)\n1145\nR\n(EACC/outer)\n1622 (BACC)\n1670 (EACC/inside)\n1950\n(EACC/outside)\n854\n(BACC)\n1165\nR\n(BACC/outer)\n0.0m\n1.0m\n2.0m\n3.0m\n2.5m\n1.5m\n0.5m\n3.5GeV/c e+\n2\n8GeV/c e\n2\n-\nFigure 2.2.8. From (Abashian, 2002b). Layout of the ACC\nsystem consisting of 16-module lineup for the barrel and 5-layer\nmodules for the end cap regions of the Belle detector.\nThe end cap device is divided into 12 identical sectors\nin \u03c6, and each sector contains 19 modules, which are con-\n\ufb01gured to have 5-layer structure in the radial direction.\nEach counter module contains a \u223c100 \u00d7 100 \u00d7 100 mm3\nradiator volume followed by an air light-guide, and then\none 3\u201d PMT is attached. This module is made of 0.5 mm-\nthick CFRP to reduce material while remaining rigid. The\nCFRP inner wall is covered with the same white re\ufb02ector\nas used for the barrel. As there is no TOF coverage in the\nendcap regions, in order to achieve the required K\u2013\u03c0 sep-\naration for tracks with momenta < 1.5 GeV/c, the ACC\nendcap aerogel system has a refractive index of 1.03.\nOutput signals are ampli\ufb01ed by front-end electronics\nattached to the PMT backplane and are sent to a charge-\nto-time conversion circuit and subsequently digitized using\na TDC.\nThe calibration constants for all PMTs are obtained\nby \u00b5-pair events collected in the beam collisions and daily\nPMT responses during experiments are monitored by the\nilluminating LED system, which is installed on all counter\nmodules. The e\ufb00ective number of photoelectrons extracted\nfrom LED data as a function of the integrated luminosity\nfor a typical PMT is plotted in Figure 2.2.9. The luminos-\nity range plotted (up to 300 fb\u22121) corresponds to almost\n6 years from the beginning of operation. The variation is\nless than 5% over this period and this stability is found to\nbe su\ufb03cient.\n2.2.4 Electromagnetic calorimeter\nBABAR\nFigure 2.2.10 shows the longitudinal cross-section of the\nBABAR EMC. Its polar angle coverage ranges from 15.8\u25e6to\n141.8\u25e6which corresponds to around 90% of the solid angle\nin the center-of-mass system. The cylindrical barrel is di-\nvided into 48 rings of 120 CsI(Tl) crystals each while the\nend cap holds 820 crystals assembled in eight rings. These\n\n31\nFigure 2.2.9. The relative pulse height as a function of inte-\ngrated luminosity for a typical PMT of ACC.\nFigure 2.2.10. Longitudinal section of the BABAR EMC (Au-\nbert, 2002j) showing the arrangement of the 56 CsI(Tl) crystal\nrings: 48 for the barrel and 8 for the forward end cap. All di-\nmensions quoted on the drawing are in mm.\nadd up to a total of 6,580 crystals among which only three\nhad their readout chain permanently broken by the end of\nthe data taking period. The penetrating particles \u2013 in par-\nticular electrons and photons \u2013 initiate showers in crystals\nand cause the CsI to scintillate; the amount of light de-\npends on the energy deposited in the calorimeter by each\nparticle. The crystals are supported at the outer radius to\navoid pre-showers (i.e. particles producing showers in the\nmaterial in front of the calorimeter). It is worth noting\nthat the crystals are organized in a quasi-projective ge-\nometry: they all point to a position near the IP, o\ufb00set just\nenough to avoid the possibility of having particles going\ncompletely through non-instrumented gaps of the EMC.\nThe amount of material between the IP and the EMC\nranges between 0.3 and 0.6 X0 except for the 3 most for-\nward rings of the forward end cap, which see elements of\nthe beamline and of the SVT readout system. These rings\nare shadowed by up to 3 X0 and have been mainly in-\ncluded to ensure shower containment close to the end of\nthe calorimeter acceptance.\nThere are two kinds of calibration for the EMC: a\nlow-energy calibration using a 6.13 MeV radioactive pho-\nton source (\ufb02uorinert irradiated by neutrons) and a high-\nenergy calibration using reconstructed Bhabha events. The\nsource (Bhabha) calibration was performed about once ev-\nery 1-2 weeks (a few times a year). In addition, a light\npulser was used to monitor the light response of each in-\ndividual crystal on a daily basis in order to identify po-\ntential problematic areas. The radiation dose received by\nthe EMC over the years of data taking had no signi\ufb01cant\nimpact on its performance.\nThe EMC energy resolution \u03c3E/E varies from 5% at\n6.13 MeV to about 2% at 7.5 GeV, an energy probed us-\ning Bhabha events. The angular resolution is 12 mrad\n(3 mrad) at low (high) energy. The \u03c00 measured mass\nis in agreement with the PDG value and has a resolu-\ntion of about 7 MeV/c2. Finally, the EMC provides the\nmain discrimination variable to identify electrons: the ra-\ntio E/p of the shower energy to the track momentum \u2013\nother PID inputs are the DCH dE/dx and the \u03b8C value\nmeasured by the DIRC. The electron identi\ufb01cation proba-\nbility is around 90% on average with a pion contamination\nof 15\u221230%, depending on the track momentum and polar\nangle.\nBelle\nThe overall con\ufb01guration of the Belle calorimeter, ECL,\nis shown in Figure 2.2.11.\nThe ECL consists of a barrel section and two end caps\nof segmented arrays of CsI(Tl) crystals. The former part\nis 3.0 m long and has an inner radius of 1.25 m. The end\ncaps are located at z = +2.0 m and z = \u22121.0 m. The\nECL is composed of 8736 CsI(Tl) crystals in total. The\nscintillation light produced by particles in the crystals is\ndetected with silicon photodiodes.\nEach crystal has a tower-like shape and points almost\nto the interaction point. The crystals are tilted by a small\nangle in the \u03b8 and \u03c6 directions to prevent photons escaping\nthrough the gaps between the crystals. The angular cov-\nerage of the ECL is 17.0\u25e6< \u03b8 < 150.0\u25e6(total solid-angle\ncoverage of 91% of 4\u03c0). Small gaps are left intentionally\nbetween the barrel and end cap crystals providing the nec-\nessary space for cables and supporting parts of the inner\ndetector (these gaps result in a loss of acceptance at the\nlevel of 3%).\nThe amount of material in front of the ECL ranges\nbetween 0.3 to 0.8 X0.\nThe calorimeter is calibrated using Bhabha scatter-\ning and e+e\u2212\u2192\u03b3\u03b3 events. For the two innermost layers\nof crystals in the forward and backward end caps, cos-\nmic ray interactions are used for calibration. The Bhabha\ncalibration is performed once every 1-2 months. The elec-\ntronic channel transition coe\ufb03cients are monitored every\nday with a test pulse generator.\nThe radiation dose received by the ECL varies from\n100 rads for barrel crystals to about 700 rads for forward\nend cap crystals. The degradation of the light output due\nto the overall dose was less than 5% and had no signi\ufb01cant\nimpact on ECL performance.\nThe ECL energy resolution varies from 4% at 100 MeV\nto about 1.6% at 8 GeV. The angular resolution is about\n13 mrad (3 mrad) at low (high) energies. Such an energy\nand angular resolution provides a \u03c00 mass resolution of\n\n32\nFigure 2.2.11. From (Abashian, 2002b). Overall con\ufb01guration of the Belle ECL.\nabout 4.5 MeV/c2. The ECL provides the main parame-\nter for electron/hadron separation: the ratio E/p of the\nshower energy to the track momentum.\nIn addition the ECL is used to provide the Belle online\nluminosity monitoring system. The rate of Bhabha events\nis measured using geometrical coincidences of high energy\ndeposits in the forward and backward ECL. This system\nprovides a stable accurate luminosity measurement during\nan experimental run as well as during injection periods.\n2.2.5 Muon detector\nBABAR\nFigure 2.2.12. Overview of the BABAR IFR at the end of the\ndata taking period (Aubert, 2013): the barrel sextants made\nof 12 LST layers are visible in the left picture while the for-\nward and backward end doors appear on the right. The forward\nRPCs (16 layers) have all been changed whereas the backward\nones are still the original detectors.\nThe \ufb01nal layout of the BABAR IFR \u2013 with, in particu-\nlar, LST modules in all sextants of the barrel region \u2013 is\nshown in Figure 2.2.12.\nThe steel of the magnet \ufb02ux return is \ufb01nely segmented\ninto 18 plates of increasing thickness: from 2 cm for the\nnine inner plates to 10 cm for the outermost ones. When\ndata taking started, the BABAR IFR was instrumented\nwith more than 800 RPCs, organized in 19 layers in the\nbarrel region (divided itself into six sextants) and 18 in the\nend doors. These detectors quickly showed serious aging\nproblems (Anulli, 2002, 2003; Piccolo, 2002, 2003) and the\ndeterioration of their performance lead directly to a reduc-\ntion of the BABAR muon identi\ufb01cation capability. Overall,\n6-17% of the muons were lost due to problems in the IFR.\nAlthough several attempts were made to \ufb01x the RPCs\nand to limit the rate of degradation, it was \ufb01nally decided\nto replace most of these detectors. This was by far the\nlargest BABAR upgrade and it was successfully completed\nin a 4-year period in various steps.\nThe RPCs in the backward end cap were never re-\nplaced. Due to the boost, they had low rates and covered\na small solid angle. In 2002, more than 200 new RPCs were\ninstalled in the forward end cap (Anulli, 2005a). Their per-\nformance was signi\ufb01cantly improved with respect to the\noriginal RPCs (Anulli, 2005b). These detectors neverthe-\nless required constant maintenance and upgrades (Band,\n2006; Ferroni, 2009) until the end of the data taking, in or-\nder to maintain their e\ufb03ciency and their reliability while\nthe luminosity was increasing. In particular, the chambers\nwith the highest rates were operated in avalanche mode\nfrom 2006.\nThe \ufb01rst two barrel sextants were replaced during the\nsummer 2004 shutdown, only one and a half years after\nthe decision to proceed with this upgrade had been taken.\nAn extensive review process lead to the choice of the Lim-\nited Streamer Tube (LST) (Andreotti, 2003) technology\n\n33\nto replace the existing RPCs. The procedure consisted of\nreplacing 12 RPC layers by LSTs and to \ufb01ll the remaining\ngaps with brass \u2013 the outermost layer (#19) could not be\ninstrumented due to a geometrical interference. Increasing\nthe total absorber thickness allowed the improvement of\nthe pion rejection of the muon PID algorithms. The last\nfour barrel sextants were replaced during the fall 2006\nshutdown.\nThe LST e\ufb03ciency was measured using di-muon events.\nOn average, it was 88% at the end of the data taking,\nslightly below the geometrical acceptance of 92%. The dif-\nference was mainly due to a few misfunctioning or broken\nchannels.\nBelle\nThe muon and KL detector subsystem of Belle identi\ufb01es\nKL mesons and muons above 600 MeV/c with high e\ufb03-\nciency. The barrel-shaped region around the interaction\npoint covers a polar angular range of 45\u25e6to 125\u25e6while\nthe forward and backward end caps extend this range to\nbetween 20\u25e6and 155\u25e6.\nThis system consists of alternating layers of double-gap\nresistive plate counters and 4.7 cm thick iron plates. There\nare 15 detector layers and 14 iron layers in the octagonal\nbarrel region and 14 detector layers and 14 iron layers in\neach end cap. The iron plates provide a total of 3.9 interac-\ntion lengths of material (in addition to the 0.8 interaction\nlengths in the ECL) for a hadron traveling normal to the\ndetector planes. The hadronic shower from a KL interac-\ntion determines its direction (assuming an origin at the\ne+e\u2212interaction point) but not its energy. The range and\ntransverse de\ufb02ection of a non-showering charged particle\ndiscriminates between muons and hadrons (\u03c0\u00b1 or K\u00b1).\nThe active elements are double-gap glass-electrode\nRPCs operating in limited streamer mode. Each 2 mm\ngas gap is sandwiched between \ufb02oat-glass electrodes with\na bulk resistivity of 1012\u221213 \u2126\u00b7 cm (Figure 2.2.13). The\nnon \ufb02ammable gas mixture consists of 62% HFC-134a,\n30% argon, and 8% butane-silver.14 An ionizing particle\ntraversing the gap initiates a streamer in the gas that\nresults in a local discharge of the electrodes. This dis-\ncharge is limited by the high resistivity of the glass and\nthe quenching characteristics of the gas. A discharge in\neither gas gap induces signals on both of the orthogonal\nexternal copper-strip planes. Each \u223c5 cm wide strip forms\na \u223c50 \u2126transmission line with an adjacent ground plane.\nIn the barrel (but not the end caps), a 100 \u2126resistor con-\nnects the pickup strip to ground at the readout end to\nminimize re\ufb02ections; it also reduces the pulse height into\nthe front-end electronics by a factor of two.\nThe barrel RPCs, made in the US, use 2.4 mm thick\n\ufb02oat glass (73% SiO2, 14% Na2O, 9% CaO, and 4% trace\nelements). The end cap RPCs, made in Japan, use 2.0 mm\nthick \ufb02oat glass (70\u201374% SiO2, 12\u201316% Na2O, 6\u201312% CaO,\n0\u20132% Al2O3, and 0\u20134% MgO).\n14 Butane-silver is a mixture of approximately 70% n-butane\nand 30% iso-butane.\nFigure 2.2.13. Exploded cross section of a Belle superlayer\ndouble-gap RPC module.\nThe VISyN system by LeCroy (now Universal Voltron-\nics) is used to distribute high voltage, with Model 1458\nmainframes and 1468P and 1469N modules. For each RPC,\na positive voltage of +4.7 kV (+4.5 kV) is applied to the\nbarrel (end cap) anode plates and \u22123.5 kV to the cathode\nplates. Eight (\ufb01ve) anode plates in the barrel (end cap)\nare driven by a common HV channel while each cathode\nplane is driven by its own HV channel. The dark current\nis approximately \u223c1 \u00b5A/m2 or 5 mA total; most of this\n\ufb02ows through the noryl spacers.\nPulses travel from the 38,000 RPC cathode strips along\ntwisted-pair cables, between 3 and 6 meters long, to front-\nend electronics on the magnet yoke periphery. The typical\n100 mV pulse has a FWHM of under 50 ns and a rise time\nof under 5 ns. The dark rate in a typical detector module is\nunder 0.03 Hz/ cm2 with few spurious discharges or after\npulses. The signal threshold for discriminating these pulses\nis 40 mV (70 mV) in the barrel (end caps). The double-\ngap design results in a superlayer e\ufb03ciency of over 98%\ndespite the lower (90% to 95%) e\ufb03ciency of a single RPC\nlayer. Robustness against several failure modes is achieved\nby having independent gas and high voltage supplies for\neach RPC layer within a module. Hit position is resolved\nto about 1.1 cm when either one or two adjacent strips\n\ufb01re, resulting in an angular resolution of under 10 mrad\nfrom the interaction point.\nThe Belle RPCs have performed reliably and without\nevidence of failures or physical deterioration throughout\nBelle\u2019s lifespan. However, the RPCs are rate-limited by the\nglass-electrode resistivity, so the e\ufb03ciency of the modestly\nshielded end cap RPCs su\ufb00ered during high-luminosity\noperation from soft neutrons produced in beamline struc-\ntures. This was mitigated by the addition of external\npolyethylene shielding outside the end caps in Belle\u2019s later\nyears, but more such shielding would have been needed to\neliminate the e\ufb03ciency drop.\n\n34\n2.2.6 Trigger\nBABAR\nAs already discussed above, the BABAR trigger is imple-\nmented as a two-level hierarchy, with the L1 (hardware)\nfollowed by the L3 (software). Its combined e\ufb03ciency at\nthe \u03a5(4S) resonance energy matches its requirements:\nmore than 99% for BB decays, more than 95% for con-\ntinuum decays (uu, dd, ss cc) and still around 92% for \u03c4\u03c4\nevents. This trigger was very \ufb02exible, as illustrated by the\nquick and complex modi\ufb01cations of the L3 trigger lines\nimplemented during the last few months of the BABAR\nrunning, when data were taken at the \u03a5(2S) and \u03a5(3S)\nresonances and a \ufb01nal energy scan above the \u03a5(4S) was\nperformed. It was also robust against background: trigger\nrates much higher than the design values for both L1 and\nL3 were achieved as luminosity was increasing, while the\ndead-time remained relatively constant, around the 1%\ndesign value.\nThe BABAR L1-trigger uses information coming from\nthe DCH for charged tracks, from showers in EMC and\nfrom the IFR. The corresponding \ufb01rst two triggers \u2013\nDrift Chamber Trigger (DCT) and ElectroMagnetic Trig-\nger (EMT) \u2013 ful\ufb01ll all trigger requirements independently\nand are highly redundant, which boosts the global L1 ef-\n\ufb01ciency and allows one to measure the e\ufb03ciency of these\ncomponents using data. Originally, the DCT only pro-\nvided r and \u03c6 information; in 2005, 3D-tracking was im-\nplemented in L1 to add z-information which allowed one\nto reject background events (scattered beam-gas particles\nhitting the beam pipe) where tracks were produced tens\nof centimeters away from the IP. This upgrade gave the\nsystem more headroom to follow the increases of luminos-\nity and background without generating a signi\ufb01cant dead\ntime, especially during the \ufb01nal period of data taking. The\nthird L1 input trigger, the IFR Trigger (IFT), is mostly\nused for tests: IFR plateau measurements, cosmics trigger,\netc. Some work was required after the IFR barrel upgrade\nto align in time the RPC and LST signals, the latter com-\ning in about 0.6 \u00b5s later.\nInformation coming from the three components de-\nscribed above are received by the GLT which processes\nall these primitives and sends out some triggers to the\ncentral BABAR DAQ system. At this stage, a trigger can\nbe masked (for instance if it corresponds to a known tem-\nporarily noisy EMC crystal) or prescaled (meaning that\nnot all selected events are registered; in particular, events\nidenti\ufb01ed as Bhabha at the trigger level are prescaled).\nIf a valid trigger remains at this stage, the DAQ system\nissues a L1 Accept signal and the entire event is readout.\nThe BABAR L3-trigger re\ufb01nes and augments the L1\nselection methods. It has been implemented in such a\nway that a wide range of algorithms can be used to se-\nlect events independently of one another. Their logic and\ntheir parameters are set in software and these \ufb01lters have\naccess to the full event to make their decision. First, L3 in-\nput lines are de\ufb01ned by using a logical OR of any number\nof L1 output lines. Then, one or more scripts are executed\nfor each \ufb01ring L3 input line and return a yes/no \ufb02ag de-\npending on whether the event passes this step. Finally,\nL3 output lines are the logical OR of selected L3 script\n\ufb02ags; these \ufb02ags can also be used as vetoes, for instance\nto reject Bhabha events which would have been accepted\notherwise. Thanks to the spare capacity planned for at the\ntime the L3 system was designed, it could log data at a\nmuch higher rate than anticipated: close to 800 Hz at the\nend of the \u03a5(3S) data taking, to be compared with the\ninitial expectation of 120 Hz.\nMoving from the regular \u03a5(4S) data taking to the\n\u03a5(3S) run during which new physics (NP) decays were\nsought after, the trigger had to identify completely di\ufb00er-\nent topologies of events. Indeed, part of the signal decays\nwere containing particles invisible to BABAR which would\ntake away a signi\ufb01cant fraction of the energy-momentum\navailable for the collision. Whereas BB events exhibit\nlarge visible energy, high multiplicity or high transverse\nactivity, the decays of interest of the \u03a5(3S) are charac-\nterized by low visible energy and low multiplicity. This\nnew approach was implemented in three successive steps\nwhich required the design of new L1 and L3 trigger lines,\nsuch as new L3 \ufb01lters. These updates were done carefully,\nchecking at each step that the trigger rates would not ex-\nceed the capabilities of the system. They were successful,\nallowing the BABAR collaboration to collect large datasets\nat the \u03a5(2S) and \u03a5(3S) resonances.\nBelle\nThe trigger system of the Belle detector consists of sub-\ntriggers and the global decision logic (GDL) - constituents\nof the Level 1 (L1) hardware trigger - and of Level 3 (L3)\nsoftware trigger. The sub-triggers are formed by signals\nfrom the CDC, ECL, TOF, and KLM sub-detectors. The\nGDL receives summary information from each sub-trigger,\nthen makes a logical combination of sub-trigger informa-\ntion to trigger on hadronic (BB and continuum) events,\nBhabha and \u00b5+\u00b5\u2212pair events, etc. Three independent\ntriggers are prepared for the hadronic events; they require\neither three or more charged track candidates, high lev-\nels of deposited energy in the ECL (with a veto on the\nECL trigger for Bhabha events) or four isolated neutral\nclusters in the ECL. The L3 software trigger ran on the\nonline computer farm (see Section 2.2.7). Events triggered\nby L1 as Bhabha, \u00b5+\u00b5\u2212pairs, two-photon events, cosmic\nrays or events with high deposited energy in the ECL, by-\npass the L3 trigger decision. The events triggered by the\npresence of charged track candidates are passed to the L3\ntrigger to determine the presence of actual good charged\nparticle tracks, thus reducing the size of the raw data be-\ning recorded.\nThe e\ufb03ciencies of the L1 triggers for hadronic events\ncan be measured using the redundancy of the three se-\nlection requirements mentioned above because they are\nalmost independent. The overall e\ufb03ciency for hadronic\nevents is estimated to be more than 99%.\nAt the beginning of the experiment Belle experienced a\nhigh trigger rate caused by the beam background. Signals\n\n35\narising from this background caused the trigger rate to\nbe nearly the DAQ upper limit of 200 Hz even while run-\nning at very low luminosity. The rate of the two-charged-\ntrack trigger was especially high because of the low pt\ntracks originating from the beam-nucleus interactions. To\nreduce such a high trigger rate, the requirement of coinci-\ndence with outer sub-triggers, such as a TOF hit and/or\nan ECL isolated cluster, was added. Figure 2.2.14 shows\nthe average trigger rate as a function of the experiment\nnumber.15 The green curve shows the average total current\nof KEKB. The highest total current was 3000 mA around\nexperiment 50. The sudden drop of the total current at\nexperiment 57 was due to the crab cavity installation at\nKEKB. The red curve shows the average trigger rate. It\nwas as high as 500 Hz around experiment 50, which cor-\nresponds to the highest total current and luminosity. In\nearly experiments, high background was indicated by the\nnormalized trigger rate, the blue curve in Figure 2.2.14,\nde\ufb01ned as the the average trigger rate divided by the av-\nerage luminosity (called the e\ufb00ective cross section). This\n0\n200\n400\n600\n800\n1000\n1200\n1400\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\nexp.13 exp.21 exp.31 exp.39 exp.47 exp.55 exp.63\nTrigger rate\nNormalized trg\nTotal current\nTrigger rate (Hz)\nTotal current (mA)\nFigure 2.2.14. Average trigger rate as a function of the ex-\nperiment number for Belle.\nrate is normalized to the trigger rate with the luminosity\n1\u00d71034 cm\u22122 s\u22121. It was higher than 1200 Hz at the begin-\nning of operation, and dropped dramatically as the total\ncurrent increased (and hence the luminosity increased).\nAfter experiment 33 the rate was stable below 400 Hz,\nwhich was interpreted as an amelioration of the vacuum\naround the IP with the higher beam current. In a special\nrun in experiment 47, the luminosity components in the\ntrigger rate were measured to be about 190 Hz in the nor-\nmalized trigger rate. The noise-to-signal ratio (N/S) was\ncalculated to be about 5.6 in experiment 7, and about 1 or\nsmaller after experiment 37, an indication of the cleaner\nenvironment of KEKB operation.\n15 An extended period of operation is referred to as an exper-\niment within Belle, see Chapter 3. The corresponding nomen-\nclature on BABAR is a Run.\n2.2.7 Online and DAQ\nBABAR\nThe high-level design of the BABAR online system (Au-\nbert, 2002j) remained unchanged during the whole data\ntaking period. The DAQ chain starts from the common\nfront-end electronics, includes the embedded processors\nin the readout modules (which start processing the data\nfragments coming from the detector after a Level 1 ac-\ncept), the network event builder, the Level 3 trigger and\nthe event logging system. While the design remained con-\nstant, the system itself evolved signi\ufb01cantly over the time\nto follow the progress in hardware technology, and to cope\nwith the changes in data taking conditions: higher lumi-\nnosity, larger backgrounds, longer periods of data taking\nthanks to the trickle injection mode (see Section 3.2.2 for\ndetails), and so on. Several other developments were made\nwith the intent of making the overall system more robust,\nbetter performing, and easier to use. For all upgrades, the\nphilosophy was \ufb01rst to maximize the performance of the\nexisting hardware, and only then to plan a hardware up-\ngrade.\nWith PEP-II operated in trickle injection mode, data\ntaking could occur continuously during one day or more.\nTherefore special emphasis was put on the data taking\ne\ufb03ciency. The aim was to minimize the time spent by the\ndetector in any non-data-taking state (calibration, error\nrecovery, transition from \u2018injectable\u2019 mode to \u2018runnable\u2019\nmode, procedure to begin a new run, etc.). Maximizing\nthe BABAR duty cycle required a continuous monitoring\nof the whole system and attention to detail. While the\nonline system had already been designed to minimize the\nDAQ dead time, new features were introduced, parts of\nthe system were improved, and procedures modi\ufb01ed to\nincrease the detector uptime despite the more challenging\nenvironment. One concrete example of this evolution was\nthe reduction of sta\ufb03ng for the detector operation, as the\nonline control and monitoring system was simpli\ufb01ed and\nautomated.\nMoreover, as explained in Chapter 3, the PEP-II op-\neration in trickle injection mode required developments in\nthe trigger and the DAQ, in order to make the detector\ninsensitive to the background bursts associated with the\ncontinuous injection. Dedicated monitoring was added to\nallow detailed data quality analysis in real time.\nThe CPUs and the operating system used by the\nBABAR online system evolved over the years, switching\nfrom vendor-speci\ufb01c products to commodity systems. This\nallowed control of the cost of the upgrades of the online\nsystem and to provide enough headroom to anticipate the\nincrease of luminosity and background. Most of the online\nsoftware was written in C++; various scripting languages\nwere used as well, such as Java for graphical tools.\nAn important evolution of the online system was the\nreplacement of Objectivity-based databases by Root-based\nones. Several reasons explain this migration, which culmi-\nnated in 2006 with the decision to stop using Objectivity\nin BABAR. Indeed, there were many concerns regarding\nthe support and the maintenance cost of this software,\n\n36\nplus some technical issues. All these changes were care-\nfully planned to make sure they would have no impact on\nthe data taking.\nBelle\nThe original requirement for the Belle Data Acquisition\nSystem (Belle DAQ) was to read out event fragments from\n8 detector subsystems with a total data size of 40 kbytes\nat a maximum rate of 500 Hz, and to record the data after\nevent building and data reduction by real time processing.\nFigure 2.2.15 shows the con\ufb01guration of the DAQ sys-\ntem at the beginning of the experiment. The readout sys-\ntem is designed to utilize the uni\ufb01ed technology based on\nthe Q-to-T conversion combined with the common FAST-\nBUS multi-hit TDC (LeCroy 1877S), except for the SVD\nreadout. The data are read by the VME processor and\ncollected by the specially-designed event builder, and then\nprocessed by the online computer farm equipped with a\nlarge number of VME processor modules where high level\nsoftware triggering is performed. The data are \ufb01nally sent\nto the KEK Computer Center via \u223c2 km optical \ufb01ber\nlinks and recorded on digital video tapes.16\nFigure 2.2.15. The con\ufb01guration of the Belle DAQ system at\nthe beginning of the experiment.\nHowever, since the system was implemented using\n1990\u2019s-era information technology, maintenance of the sys-\ntem was di\ufb03cult in the long run. In addition, the FAST-\nBUS based readout system is not pipelined and it has a\nreadout dead time of more than 10% at the design max-\nimum trigger rate of 500 Hz. The trigger rate at the be-\nginning of data taking was\n200 Hz and the dead time\nwas manageable, but the rate increase was foreseen as the\nluminosity improves.\nBelle started the \u2018continuous\u2019 upgrade of the system\nto keep up with the luminosity increase. The \ufb01rst step\nwas made in 2001 to replace the event builder and VME\nbased online computer farm with a set of Linux PC servers\n16 These are the same tape format as previously used by some\nTV broadcasting companies.\n(EFARM) connected via Fast Ethernet \ufb01bers. The level\n3 data reduction which was performed in VME proces-\nsors was ported to the EFARM. The system became more\nmaintainable for a longer term operation as a result of this\nupgrade.\nIn 2003, the real time reconstruction farm (RFARM)\nwas introduced. The system is a large scale PC farm di-\nrectly fed by the event builder, and real time full event\nreconstruction is performed utilizing parallel processing of\nevents. The processing results such as the reconstructed\nIP position were also fed back to the accelerator control,\nwhich greatly contributed to the improvement of luminos-\nity. In the same year, the improvement of the FASTBUS\nreadout was also made so as to reduce the readout dead\ntime by a factor of four.\nAn improvement to the back-end system was made in\n2005, when a second EFARM and RFARM were added in\norder to have su\ufb03cient bandwidth and processing power\nto cope with the expected increase in luminosity.\nFor further reduction of the readout dead time, an up-\ngrade of the FASTBUS readout system, to a pipelined\nversion, was started. A new TDC was developed based on\nCOPPER, a common pipeline readout module developed\nat KEK (Figure 2.2.16). The TDC is designed to be plug-\ncompatible with LeCroy 1877S, allowing the use of the\nsame detector front-end electronics without any modi\ufb01-\ncations. The upgrade was performed detector by detector\nstarting from the CDC in 2007 utilizing the short shut-\ndown time during summer and winter. By 2009, \ufb01ve de-\ntector subsystems were upgraded resulting in a reduction\nin dead time to less than 1%. Figure 2.2.17 shows the Belle\nDAQ con\ufb01guration at the end of data taking.\n2.2.8 Background and mitigation\nBABAR\nPredicting accurately the background level using dedi-\ncated simulations is not an easy task, whether the detector\nplans to run at the intensity or at the energy frontier. Yet,\nbackground is a major concern for any HEP experiment\nas it can severely impact the data taking: \ufb01rst, by slowing\ndown the acquisition system and creating dead time; then,\nby decreasing the quality of the logged data when signal\nsignatures get lost in a mass of random hits; \ufb01nally, by\ndegrading or even destroying detector components. There-\nfore, special care is given to design detectors able to handle\nbackground levels corresponding to the predictions (with\nsigni\ufb01cant safety margins added), while numerous probes\nmonitor the background during the data taking. When\nthe conditions become unsafe for the detector, automated\nsystems make its HV ramp down to safer levels and can\neven dump the beams.\nFigure 2.2.18 shows an overview of the BABAR back-\nground monitoring system: several probes monitor quanti-\nties sensitive to background (radiation doses, rates recorded\nby scaler boards, channel currents, etc.) in real time and\ncompare the measured values with pre-de\ufb01ned alarm lev-\nels. The status of each variable (in alarm or not) is indi-\n\n37\nData Taking System\nRUNSUM\nMOND\nECL_BHA\nKEKB\nMonitors\nBELBMIF\n Trigger frontend \nLevel-1 Trigger\nSystem\nKLMTRG\nGDL\nevdisp\nDQM1\nCDC frontend\nCOPPER TDC\nTOF frontend\nFASTBUS TDC\nSVD frontend\nflashADC\nACC frontend\nECL frontend\nFASTBUS TDC\nKLM frontend\nFASTBUS TDC\nEFC frontend\nFASTBUS TDC\nEFCFBVME\nControl System\nMASTER\nexpertwin\nlocalwin\nlocal CDC HV\nlocal TOF HV\nlocal SVD HV\nlocal ACC HV\nlocal KLM HV\nTXSEQ\nrunwin\nlogwin\n(SVD trigger)\nCDC trigger\nTOF trigger\nx8\nECL_BH2\nENVMON\nCOPPER TDC\nEFC\nPC\nDQM2\nBOLD font - NSM nodes\nItalic font - non NSM components\nThick arrow - data flow\nMid arrow - trigger flow\nThin arrow - HV control\nRFARM2\nRFARM1\nE1TRK\nE1VXA\nE1VXB\nE1NEU\nE2NEU\nE2VTX\nE2TRK\nE3\nEFARM2\nE1TRK\nE1VXA\nE1VXB\nE1NEU\nE2NEU\nE2VTX\nE2TRK\nE3\nEFARM1\nx8\nx8\nx8\nOffline Data Processing\nHV System\nHVC\nSEQ\nTTD\nCOPPER TDC\nECL1 VME\nECL2 VME\nECL3 VME\nACC\nPC\nSVD\nTOF\nVME\nCDC\nPC\nECL trigger\nCOPPER TDC\nTRG\nPC\nKLM VME\nPC00 ... 05\nPC06 ... 11\nFigure 2.2.17. The con\ufb01guration of the Belle DAQ system at the end of data taking.\nFigure 2.2.18. Snapshot of the global BABAR background display (Aubert, 2013) taken at a time when the background was\nlow: all but a couple of probes are green which, in the BABAR framework, means \u2018safe level\u2019 \u2013 alarm states are indicated by\nyellow (warning level reached) and red (concern) colors. This display was available 24/7 in the control room to help shifters\nget a real time overview of the background levels around the BABAR detector. The longitudinal and end cross-sections show the\nlocations of the background probes which survey all systems: SVT radiation monitors, current levels in the DCH superlayers,\nrates in the DIRC, EMC and IFR or neutron rates on both ends of the beampipe.\ncated by the color of the display. New alarms produce vi-\nsual and audio alerts in the control room while automated\nsystems can modify the detector state or even abort the\nbeams if the background becomes worrisome.\nThere were two main active detector protection sys-\ntems in BABAR to ensure a safe operation of the sensi-\ntive tracking system. First, the SVTRAD which monitored\nboth the instantaneous and the integrated radiation doses\nreceived by the SVT. Originally, rates were measured by\n12 PIN diodes located on both ends of the SVT in three\nhorizontal planes (one at the beam level, the other two\n3 cm above/below it) and on the inside and outside of\n\n38\nFigure 2.2.16. A pipeline TDC module based on COPPER.\nthe PEP-II rings. As expected, the middle-plane diodes\naccumulated the highest radiation doses and started to\nbecome less reliable due to damage. Therefore, in 2002\ntwo diamond sensors were added to the SVTRAD sys-\ntem \u2013 this was the \ufb01rst time such sensors were used in\na HEP experiment \u2013 and they worked well until the end\nof the data taking. Another advantage of these detectors\nwith respect to the PIN diodes is that they are insensitive\nto temperature \ufb02uctuations. The maximum total dose af-\nter nine years of operations was measured to be around\n4 MRad, i.e. less than the SVT radiation budget, set to\n5 MRad. The SVTRAD was also able to abort the beams,\neither when instantaneous doses were too high or because\nthe integrated dose was consistently above some thresh-\nold during 10 consecutive minutes. Beam aborts induced\nby the SVTRAD protection system occurred a few times\na day on average. When PEP-II started to deliver beams\nin trickle injection mode (particles are injected in existing\nbunches at a few Hz frequency, see Section 3.2.2 for de-\ntails), the SVTRAD was modi\ufb01ed to monitor in addition\nthe dose associated with each injection of particles in the\ncollider rings. This provided a complementary feedback on\nthe trickle injection quality. The second active protection\nsystem was based on the monitoring of the DCH currents\nand was used to prevent damage to the drift chamber wires\nand the associated front-end electronics; it is described\nabove in Section 2.2.2.\nThe main BABAR background probes were also dis-\nplayed in the accelerator control room, providing valuable\ninformation about the beam status and helping operators\nreduce the background levels. For instance, the accelerator\ncrew was noti\ufb01ed when the SVTRAD 10-minute counter\nwas enabled; this signal would tell them that the beams\nwere to be tuned and that they also had some time to try\nand \ufb01x the problem before a beam abort would be issued.\nIn addition to the real-time monitoring and protec-\ntion system, various shieldings around BABAR have been\nbuilt and improved over the years. The main additions\nwith respect to the original detector design have been a\nDIRC shielding around the beamline components at the\nbackward end and shielding walls on the forward side of\nBABAR to protect the outer IFR layers.\n2.2.9 Conclusion: main common points, main\ndi\ufb00erences\nTable 2.2.1 summarizes in a single page the typical perfor-\nmances of the BABAR and Belle detectors. Of course the\nsignals detected by the individual subdetectors need to be\ncombined and converted into data used for physics mea-\nsurements. Various methods and tools are used for this\ndata reconstruction which are beyond the scope of this\nbook. Typical performances of combined tracking, charged\nparticle identi\ufb01cation and neutral particle reconstruction\nare also given in Table 2.2.1. More information can be\nfound in the detector articles published by the two col-\nlaborations and in this book, in particular for PID \u2013 see\nChapter 5 \u2013 and for tracking and vertexing \u2013 see Chap-\nter 6.\nBoth detectors reached their design performance and\nwere robust enough to keep them almost constant while\nthe luminosity delivered by the colliders was increasing.\nBoth data taking periods were about a decade long, al-\nlowing BABAR and Belle to collect huge datasets which\nmade possible the impressive harvest of physics results\nachieved by the two collaborations. The detector upgrades\ndescribed in Section 3.2 were mainly driven by the lumi-\nnosity increase although both experiments had a subdetec-\ntor weaker than the others: the silicon tracker for Belle and\nthe muon detector for BABAR. Several technological and\nconceptual breakthroughs were made by the B Factories,\namong which the BABAR DIRC (a new concept of ring-\nimaging Cherenkov PID detector), the use of the object-\noriented language C++ for the experiment software, or\nthe development of distributing computing. Now, they all\nare well-established in the HEP community.\n\n39\nTable 2.2.1. Summary of the BABAR and Belle detector main characteristics. The BABAR numbers provided in this table are representative of the detector performances;\nthey vary with the type of events reconstructed. Moreover, the PID selectors can be tuned depending on the analysis requirements \u2013 looser or tighter cuts. aUntil\nsummer 2003 Belle used a 3 layer SVD. bNumber of photo-electrons. cFor Bhabha events. dL3 trigger was operated partially from 2004 to 2007. eThe maximal trigger\nrate is determined at the end of the DAQ chain. fFor BB events. gFor momenta above 0.8 GeV/c. hFor \u03c00\u2019s reconstructed from photons in hadronic events.\nDetector type\nBelle\nBABAR\nabbreviation\nType\n\u03b8 Coverage\nIllustrative\nabbreviation\nType\n\u03b8 Coverage\nIllustrative\nPerformance\nPerformance\nTracking\nSVD\nSilicon\n[17\u25e6; 150\u25e6]\nSingle hit resolution:\nSVT\nSilicon\n[20.1\u25e6; 150.2\u25e6]\nSingle hit resolution:\n3/4 layersa\n12 \u00b5m (R\u03c6)\n5 layers\n\u223c10-15 \u00b5m (inner)\nTwo-sided\n19 \u00b5m (z)\nTwo-sided\n\u223c40 \u00b5m (outer)\nCDC\nDrift\n[17\u25e6; 150\u25e6]\nSingle hit resolution:\nDCH\nDrift\n[17.2\u25e6; 152.6\u25e6]\nSingle-cell hit\nchamber\n130 \u00b5m (R\u03c6)\nchamber\nresolution: \u223c100 \u00b5m\n200-1400 \u00b5m (z)\n(center of the cell)\n\u03c3(dE/dx)\u223c7%\n\u03c3(dE/dx)\u223c8%\nParticle ID\nTOF\nTime of \ufb02ight\n[34\u25e6; 130\u25e6]\n\u03c3t = 100 ps\nDIRC\nCherenkov\n[25.5\u25e6; 141.4\u25e6]\n\u03c3\u03b8C \u223c2.4 mrad\nscintillator\nACC\nThreshold Cherenkov\n[17\u25e6; 127\u25e6]\nNp.e. \u22656b\n\u2013\n\u2013\n\u2013\n\u2013\nwith aerogel\n\u2013\n\u2013\n\u2013\n\u2013\nCalorimetry\nECL\nCsI(Tl)\n[12.4\u25e6; 31.4\u25e6]\n\u03c3E/E\u223c1.7%c\nEMC\nCsI(Tl)\n[15.8\u25e6; 140.8\u25e6]\n\u03c3E/E\u223c3%\n[32.2\u25e6; 128.7\u25e6]\n[130.7\u25e6; 155.1\u25e6]\nMuon and K0\nL\nKLM\nRPC\n[20\u25e6; 155\u25e6]\n\u03c3\u03b8 = \u03c3\u03c6 = 30 mrad\nIFR\nRPC, LST\n[20\u25e6; 154\u25e6]\nLST layer e\ufb00. \u223c88%\ndetector\nfor K0\nL\nTrigger\nL1\nHardware\nFull\nL1\nHardware\nFull\nMax. rate \u223c5 kHz\nL3d\nSoftware\nBelle\nL3\nSoftware\nBABAR\nMax. rate \u223c1 kHz\nL1+L3\nacceptance\nMax. rate \u223c0.5 kHze\nL1+L3\nAcceptance\nPhysics mode e\ufb00. \u223c99%\nPhysics mode e\ufb00. > 99%f\n\u00b5\u00b1\n\u27e8\u00b5 e\ufb00\u27e9= 90%g\n\u00b5\u00b1\n\u27e8\u00b5 e\ufb00\u27e9= 59 \u221265%\n(KLM)\n\u27e8\u03c0 misID\u27e9= 2%\n\u27e8\u03c0 misID\u27e9= 1.4 \u22120.8%\nPID\nK/\u03c0\n\u27e8K e\ufb00\u27e9\u226585%\nK/\u03c0\n\u27e8K e\ufb00\u27e9= 84%\nAlgorithms\n(TOF,ACC,CDC)\n\u27e8\u03c0 misID\u27e9\u226410%\n\u27e8\u03c0 misID\u27e9= 1.1%\ne\u00b1\n\u27e8e e\ufb00\u27e9= 90%\ne\u00b1\n\u27e8e e\ufb00\u27e9= 90 \u221295%\n(CDC,ECL)\n\u27e8\u03c0 misID\u27e9\u223c0.3%\n\u27e8\u03c0 misID\u27e9< 0.2%\nTracking\n(CDC,SVD)\n\u03c3pT /pT = 0.0019pt [ GeV/c ]\nSVT + DCH\n\u03c3pT /pT \u223c0.5%\n\u22950.0030/\u03b2\nNeutrals\n(ECL)\n\u03c3(m\u03c00) = 4.8 MeV/c2 h\nEMC\n\n40\nChapter 3\nData processing and Monte Carlo\nproduction\nEditors:\nFabrizio Bianchi and Nicolas Arnaud (BABAR)\nShoji Uno (Belle)\nAdditional section writers:\nConcetta Cartaro, Christopher Hearty, Ryosuke Itoh, Leo\nPiilonen, Teela Pulliam, Dennis Wright\n3.1 Introduction: general organization of the\ndata taking, data reconstruction and MC\nproduction\nThe BABAR and Belle experiments have collected around\none Petabyte of raw data each. These data have been cal-\nibrated, the events reconstructed, and collections of se-\nlected events produced. Monte Carlo events (MC) have\nbeen generated and reconstructed with the same code used\nfor the detector data. The total amount of data produced\nby BABAR and Belle were over six Petabytes and over three\nPetabytes respectively. Over the years, both collabora-\ntions have developed computing models that have proven\nto be highly successful in handling the amount of data\nproduced, and in supporting the physics analysis activi-\nties. The main elements of the two computing models are\noutlined in this introductory section and will be described\nin more detail in the remainder of this chapter.\nThe \u2018raw data\u2019 coming from the detectors have been\npermanently stored on tape, calibrated, and reconstructed\nusually within 48 hours of the actual data taking. Recon-\nstructed data have been permanently stored in a format\nsuitable for subsequent physics analysis.\nMany samples of Monte Carlo events, corresponding\nto di\ufb00erent sets of physics channels, have been generated\nand reconstructed in the same way. In addition to the\nphysics triggers, the data acquisition also recorded ran-\ndom triggers that have been used to create \u2018background\nframes\u2019 that have been superimposed on the generated\nMonte Carlo events to account for the e\ufb00ects of the ma-\nchine background and of electronic noise, before the re-\nconstruction step.\nDetector and Monte Carlo data have been centrally\n\u2018skimmed\u2019 to produce subsets of selected events, the \u2018skims\u2019,\ndesigned for a speci\ufb01c area of analysis. Skims are very con-\nvenient for physics analysis, but they increase the storage\nrequirements because the same event can be present in\nmore than one skim.\nThe quality of the detector data and of the simulated\nevents has been monitored through all the steps of pro-\ncessing.\nFrom time to time, as improvements in detector cali-\nbration constants and/or in the code were implemented,\nthe detector data have been reprocessed and new samples\nof simulated data generated. When sets of new skims be-\ncome available, an additional skim cycle has been run on\nall the events.\nBABAR has been one of the \ufb01rst experiments to adopt\nthe C++ programming language to write o\ufb04ine and on-\nline software. In the mid-nineties, when this decision was\ntaken, the dominant language in the High Energy Physics\n(HEP) community was Fortran 77. However, problems\nand limitations associated with this language were becom-\ning very clear and BABAR chose early to commit to the\nC++ technology because there was the perception that\nthe HEP computing model was a very good match to an\nobject-oriented design. At \ufb01rst, the C++ expertise was\nlimited to few collaborators, who started o\ufb00ering tutorials.\nStarting in 1996, formal training courses were o\ufb00ered to\nthe collaboration members and rapidly produced a shared\nvocabulary and set of concepts that were immensely help-\nful in the actual software development. The \ufb01nal outcome\nof this e\ufb00ort was the over 3 million lines of code that today\nconstitutes the BABAR o\ufb04ine software.\nBelle data processing and analysis code (called Belle\nAnalysiS Framework - basf) was developed in C++ with\nan extensive use of adjoined tools (e.g. the CLHEP library\n(CLHEP, 2008) for which some of the Belle members were\nthe initial developers). The simulation tool, GEANT3 (Brun,\nBruyant, Maire, McPherson, and Zanarini, 1987), on the\nother hand, was written in Fortran.\nBelle data were stored using the PANTHER banks event\nstore based on the entity-relationship model (Putzer,\n1989) and developed speci\ufb01cally for this experiment.\nPANTHER banks (Adachi, 2004) o\ufb00ered a satisfactory stor-\nage throughout the data taking and reliable usage in the\ndata analysis process. Due to the large volume of recorded\ndata centralized skimming was used (see Section 3.5) in\norder to facilitate subsequent analysis of events. Further-\nmore, at the level of speci\ufb01c analysis, additional skimming\nwas performed, resulting in the so called index \ufb01les, pro-\nviding unique event identi\ufb01ers that enable processing of\nselected events only.\nSimilarly large data volumes produced by BABAR were\nanticipated to make it impossible to routinely run on all\nthe data. At \ufb01rst, BABAR decided to use an event store\nbased on the object-oriented database technology that was\nexpected to solve the problem of an e\ufb03cient and scal-\nable access to the data. The end result of this work was\nwhat, at the time, was the world\u2019s largest object-oriented\ndatabase. Unfortunately, it soon became clear that data\nvolumes and usage patterns were exceeding the capabili-\nties of the technologies that were available at that time.\nA lot of e\ufb00ort went into mitigating these problems. Fi-\nnally, the working solution identi\ufb01ed was to handle data\npersistency using Root I/O which o\ufb00ers the advantages\nof its lightweight interface and built-in data compression.\nIn this context, client/server data access was a very im-\nportant issue and the bundled data server, rootd, was in-\nsu\ufb03cient for BABAR\u2019s need. A better performing solution\nwas developed starting from rootd and taking advantage\nof the experience made with the object-oriented database.\n\n41\nThe result of this e\ufb00ort was a data server named XRootD\n(Furano and Hanushevsky, 2010).\nBABAR was the \ufb01rst HEP experiment to e\ufb00ectively use\ngeographically distributed resources, because the amount\nof computing needed to satisfy the production and anal-\nysis requirements exceeded what was possible at SLAC.\nGrid computing tools became available too late for the B\nFactories and BABAR solved the problem by assigning spe-\nci\ufb01c production tasks and datasets to di\ufb00erent computing\ncenters. Only 20-30% of Monte Carlo data where produced\nusing Grid resources with the aid of speci\ufb01c software tools.\nBelle (re-)processed the recorded data centrally at KEK\nwhile the production of simulation was dispersed among\nthe collaborating institutions. As with BABAR, a signi\ufb01-\ncant part of MC simulation was produced at remote sites.\n3.2 Data taking\nBABAR started taking physics data in October 1999 after\nan extensive period of commissioning of both the collider\nand the detector. The data taking ended on April 7th 2008,\nabout six months earlier than planned, due to budget con-\nstraints at the US Department Of Energy (DOE) level.\nThe BABAR data taking can be divided into seven main\nperiods, called \u2018Runs\u2019,17 for which details are given below.\nThe equivalent of the BABAR Run is called \u2018Experiment\u2019\nat Belle.\nTwo consecutive BABAR Runs are separated by a shut-\ndown period usually lasting a few months and during\nwhich various operations are performed by the PEP-II\nand BABAR teams: repairs, \ufb01xes and maintenance, both\nat the hardware and software levels. The longest BABAR\nshutdown took place between Runs 4 and 5 (from August\n2004 to April 2005) as the start of the new data taking\nperiod was delayed due to an electrical accident at SLAC:\nall work procedures had to be reviewed and improved in\norder to reinforce the site-wide safety best practice.\nBABAR Runs 1 to 6 data were taken at (or near) the\nenergy of the \u03a5(4S) resonance (10.58 GeV). About 90% of\nthese data were taken at the peak of the resonance (\u2018on-\nresonance\u2019 data) to maximize the number of produced BB\npairs. The remaining \u223c10% were taken about 40 MeV be-\nlow (\u2018o\ufb00-resonance\u2019 data) to study non-B backgrounds,\nin particular the production of light quark and \u03c4 pairs\ncalled \u2018continuum\u2019. Taking advantage of years of contin-\nuous improvements and upgrades, both on the machine\nand detector sides, Run 7 was expected to increase the\nsize of the BABAR dataset by 50% in about a year. Once\nthis goal would have been achieved, it was planned to\nend the data taking by running at other energies, below\nand above the \u03a5(4S) resonance. When it became clear\nshortly before Christmas 2007 that Run 7 was going to be\nmuch shorter than anticipated due to the lack of funding,\nthe BABAR management reacted quickly and decided to\n17 In the following the word \u201crun\u201d is used to identify a small\ndata acquisition batch up to a few hours long, i.e. the basic\nunit of the BABAR and Belle data taking system, not to be\nconfused with the \u201cRun\u201d de\ufb01ned here.\nstop the \u03a5(4S) resonance data taking \u2013 which had just\nrestarted a week earlier. Instead, data were taken at the\n\u03a5(3S) resonance during two months; then, the collision en-\nergy was moved to the \u03a5(2S) resonance for about a month.\nIn both cases, on- and o\ufb00-resonance data were recorded.\nFinally, the energy region above the \u03a5(4S) resonance up\nto 11.2 GeV was scanned during the last 10 days of data\ntaking.\nAlthough originally designed to be a \ufb01xed-energy ma-\nchine, PEP-II performed remarkably well during Run 7\nand all of the CM energy changes were done by moving\nthe energy of the HER beam, keeping the LER one \ufb01xed.\nAt the \u03a5(2S) energy (10.02 GeV), the HER orbit was\nquite close to the vacuum beam pipe in the interaction\nregion (IR), leading to a trade-o\ufb00between luminosity and\nbackground. At 11 GeV and above, synchrotron radiation\nbecame the dominant issue and the HER current had to\nbe decreased, which had a direct impact on the delivered\nluminosity. On the BABAR side, the trigger was the main\nsystem impacted by the changes of the running energy as\nthe data taking goal moved from selecting BB events with\nlarge visible energy, high multiplicity and/or high trans-\nverse energy to looking for decays with low visible energy\nand low multiplicity. These changes had to be made while\nthe data taking was ongoing and occurred thanks to the\n\ufb02exibility of the BABAR trigger design.\nBelle started taking data on June 1st 1999. After that,\ndata taking has been continuous for 6-9 months every year\nuntil the \ufb01nal shutdown on June 30th 2010. After each ma-\njor shutdown a new \u201cExperiment\u201d started. Hence the Belle\ndata are grouped into experiments 7 to 73, where only odd\nnumbers are used.18 Experiments 7 - 27 are recorded us-\ning the \ufb01rst Silicon Vertex Detector (SVD1) and the rest\nwith the second (SVD2) detector (see Section 2.2.1). There\nwere two scheduled shutdowns every year, in summer and\nwinter. The summer shutdown took about three months or\nmore for maintenance and hardware replacements within\nthe Belle detector as well as in the KEKB accelerator. The\nwinter shutdowns were shorter, typically one month long.\nIn the last three years of operation, the winter shutdowns\nwere slightly extended due to budget constraints. Beside\nthese shutdowns one day every two weeks was devoted to\nmaintenance of the accelerator and detector. Typically af-\nter each experiment cosmic ray data was taken with the\nBelle solenoid turned o\ufb00for the purpose of detector align-\nments. Belle took data mostly at the energy of the \u03a5(4S)\nresonance in order to study B meson decays. For the pur-\npose of the background estimation arising from the non-B\nmeson events the o\ufb00-resonance data was collected 60 MeV\nbelow the resonance peak energy, for around 10% of the\nrunning time, approximately every two months. Similar\no\ufb00-resonance data taking was performed also for the data\ntaken at other \u03a5 resonances. Note that the BABAR o\ufb00-\nresonance data taking was performed 40 MeV below the\n\u03a5(4S) mass, a di\ufb00erence which has no impact on the usage\nof this data.\n18 For various reasons some experiment numbers are not used:\nexperiment 29, 57 and 59.\n\n42\nThe \ufb01rst Belle non-\u03a5(4S) data was taken at the energy\nof \u03a5(5S) resonance for 3 days in 2005. During the following\nyear in the last week of February, \u03a5(3S) resonance data\nwas taken to enable the search for invisible particles from\ndecays of the \u03a5(1S) resonance. The last \u03a5(4S) resonance\ndata was taken in June 2008. After that, \u03a5(1S) (second\nhalf of June 2008), \u03a5(2S) (December 2008 and November\n2009) and \u03a5(5S) resonance data were taken, and energy\nscans between the \u03a5(4S) and \u03a5(6S) were carried out in\nthe last two years of operation. The \u03a5(1S) The CM en-\nergy change was rather smoothly performed, keeping the\nsame ratio of the beam energies in the KEKB rings. Dur-\ning that time, the magnetic \ufb01elds of the Belle solenoid\nand super-conducting \ufb01nal focusing magnet were kept at\nthe same values. The luminosity decreased at lower CM\nenergies for reasons which have not been well understood.\nThe beam background did not change by a large amount\nwhen running at di\ufb00erent energies. The same was true for\nthe trigger rates, where the increase of the cross-section\nat lower energy resonances was canceled by a lower lumi-\nnosity. Looser trigger requirements were adopted for two\ncharged track events in the case of the \u03a5(3S) data taking\nto achieve the physics goals of the \u03a5(3S) programme.\n3.2.1 Integrated luminosity vs. time; luminosity\ncounting\nThe integrated luminosity collected by Belle for each CM\nenergy is listed in Table 3.2.1 and is calculated using\nBhabha events, where the \ufb01nal state electrons are de-\ntected in the barrel part of the detector, and after re-\nmoving runs deemed to be unusable for physics studies\n(so-called bad runs) because of detector-related issues.\nThe Belle integrated luminosity as a function of time is\nshown in Fig 3.2.1. As well as the luminosity measure-\nment, the counting of recorded \u03a5(nS) events is done using\nthe method described in Section 3.6.2. The yields obtained\nare presented in Table 3.2.2.\n0\n200\n400\n600\n800\n1000\n1200\n1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010\nIntegrated Luminosity (fb -1)\nYear\nTotal \nOff-resonance \n1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010\nBelle logged luminosity\nFigure 3.2.1. Evolution of the Belle integrated luminosity. A\ndetailed breakdown of datasets is given in Table 3.2.1.\nThe systematic error on the luminosity measurement\nis about 1.4% and the statistical error is usually small\ncompared to the systematic error. The latter is dominated\nby the uncertainty of the Monte Carlo generator used to\ncalculate the cross-section for Bhabha events. The \u03a5(4S)\ndataset is split into two periods, named SVD1 and SVD2,\nwhich correspond to di\ufb00erent con\ufb01gurations of the Silicon\nVertex Detector, as explained in the following section. All\nother resonance and scan data were taken in the SVD2\ncon\ufb01guration.\nLees (2013i) describes the methods used to measure\nthe BABAR time-integrated luminosities at the \u03a5(2S),\n\u03a5(3S), and \u03a5(4S) resonances, as well as in the contin-\nuum regions below each of these resonances. For each\nrunning period at \ufb01xed energy, the luminosity was com-\nputed o\ufb04ine, using Bhabha (e+e\u2212\u2192e+e\u2212) and di-\nmuon ( e+e\u2212\u2192\u00b5+\u00b5\u2212) events for Runs 1-6 and only\nBhabha events for Run 7 \u2013 due to uncertainties in the\nlarge \u03a5 \u2192\u00b5+\u00b5\u2212background. No detailed analysis could\nbe performed for the \ufb01nal scan data because of the short\nduration of the running at each scan point (only about\n5 pb\u22121). Therefore, the corresponding luminosity is only\nan estimation taken from (Aubert, 2009x). The systematic\nerror on the luminosity measurement is about 0.5% for the\ndata collected at the \u03a5(4S) and 0.6% (0.7%) for data col-\nlected at the \u03a5(3S) (\u03a5(2S)). Table 3.2.1 and Fig. 3.2.2\nshow the luminosity integrated by BABAR, broken down\nby CM energy.\nIn addition to measuring the luminosity, the number\nof \u03a5 particles in the di\ufb00erent datasets is also computed\nusing a common method referred to as \u2018B-counting\u2019 for\nthe \u03a5(4S) running. This number is found by counting\nthe hadronic events in the on-resonance dataset and sub-\ntracting the contribution coming from the continuum, es-\ntimated using o\ufb00-resonance data and properly scaled to\nthe peak energy \u2013 see Section 3.6.2 for details. The \ufb01nal\nresults are shown in Table 3.2.2.\nTable 3.2.2. Number of \u03a5 particles in the di\ufb00erent BABAR and\nBelle datasets\nExperiment\nResonance\n\u03a5 number\nBABAR\n\u03a5(4S)\n(471.0 \u00b1 2.8) \u00d7 106\n\u03a5(3S)\n(121.3 \u00b1 1.2) \u00d7 106\n\u03a5(2S)\n(98.3 \u00b1 0.9) \u00d7 106\nBelle\n\u03a5(5S)\n(7.1 \u00b1 1.3) \u00d7 106\n\u03a5(4S) - SVD1\n(152 \u00b1 1) \u00d7 106\n\u03a5(4S) - SVD2\n(620 \u00b1 9) \u00d7 106\n\u03a5(3S)\n(11 \u00b1 0.3) \u00d7 106\n\u03a5(2S)\n(158 \u00b1 4) \u00d7 106\n\u03a5(1S)\n(102 \u00b1 2) \u00d7 106\n\n43\nTable 3.2.1. Summary of the luminosity integrated by BABAR and Belle, broken down by CM energy.\nExperiment\nResonance\nOn-resonance\nO\ufb00-resonance\nLuminosity (fb\u22121)\nLuminosity (fb\u22121)\nBABAR\n\u03a5(4S)\n424.2\n43.9\n\u03a5(3S)\n28.0\n2.6\n\u03a5(2S)\n13.6\n1.4\nScan > \u03a5(4S)\nn/a\n\u223c4\nBelle\n\u03a5(5S)\n121.4\n1.7\n\u03a5(4S) - SVD1\n140.0\n15.6\n\u03a5(4S) - SVD2\n571.0\n73.8\n\u03a5(3S)\n2.9\n0.2\n\u03a5(2S)\n24.9\n1.7\n\u03a5(1S)\n5.7\n1.8\nScan > \u03a5(4S)\nn/a\n27.6\nCalendar Year\n1999\n2000\n2001\n2002\n2003\n2004\n2005\n2006\n2007\n2008\n)\n-1\nIntegrated luminosity (fb\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n(4S) Onpeak\n\u03a5\n(4S) Offpeak\n\u03a5\nBABAR data taking periods\nDate\n)\n-1\nIntegrated luminosity (fb\n0\n5\n10\n15\n20\n25\n30\n2007 December\nJanuary\nFebruary\nMarch\nApril\n2008\n(3S) Onpeak\n\u03a5\n(3S) Offpeak\n\u03a5\n(2S) Onpeak\n\u03a5\n(2S) Offpeak\n\u03a5\n(4S)\n\u03a5\nAbove \nFigure 3.2.2. Evolution of the di\ufb00erent BABAR datasets with\ntime. The top plot shows the luminosity integrated during\nthe \u03a5(4S) running periods, on-resonance (blue curve) and\no\ufb00-resonance (red curve) operation. The bottom plot focuses\non the last BABAR running period (Run 7) which lasted less\nthan four months and during which three di\ufb00erent data tak-\ning phases occurred: \u03a5(3S) (red curve shows the on-resonance\ndataset; the purple one the o\ufb00-resonance), \u03a5(2S) (blue curve\nfor the on-resonance data, black for the o\ufb00-resonance) and \ufb01-\nnally a scan between the \u03a5(4S) energy and 11.2 GeV (green\ncurve).\n3.2.2 Major hardware/online upgrades which modi\ufb01ed\nthe quality of BABAR data\nThis section summarizes the upgrades to the BABAR de-\ntector and also describes the \u2018trickle injection\u2019 mode which\nallowed PEP-II to keep the luminosity (and hence the de-\ntector data taking conditions) stable during most of the\nrun. In the following, the \u2018forward\u2019 and \u2018backward\u2019 sides of\nthe detector are de\ufb01ned relative to the high energy beam.\nDetector upgrades\nOver the years, the main BABAR activities during the shut-\ndowns between Runs were related to the Instrumented\nFlux Return (IFR). Indeed, from the very beginning of the\ndata taking, the resistive plate chambers (RPCs) showed\nsevere aging all around the detector. Attempts were made\nto slow down the performance degradation but it became\nclear soon enough that the whole system needed an up-\ngrade involving the replacement of most of the muon cham-\nbers. This project was completed with the following se-\nquence:\n\u2013 12 forward RPCs were replaced between Run 1 and\nRun 2.\n\u2013 The remaining forward RPCs were replaced between\nRuns 2 and 3. Brass was installed in the forward IFR\nto increase the total absorber thickness.\n\u2013 The \ufb01rst two Limited Streamer Tube (LST) sextants\nwere installed between Runs 4 and 5 and the last four\nbetween Runs 5 and 6.\nAnother important area of detector-related work was\nbackground mitigation and system upgrades, to cope with\nthe instantaneous luminosity increase over the years \u2013\nPEP-II exceeded its design luminosity goal by a factor\nfour. These issues were addressed in various ways:\n\u2013 Addition of shielding in various places around the de-\ntector (inside the PEP-II tunnel entrance on the back-\nward side, in front of the IFR end-cap, etc.).\n\u2013 Replacement of the Detector of Internally Re\ufb02ected\nCherenkov light (DIRC) and Drift Chamber (DCH)\n\n44\nfront-end electronics to deal with the increase of the\ninstantaneous luminosity over time.\n\u2013 Online software developments (mainly for the Silicon\nVertex Tracker (SVT), the DIRC and the EMC) to\nspeed up the readout of the detector after a L1-accept\nand hence to be able to run at higher trigger rate while\nkeeping the DAQ dead time low.\nThe trigger system also underwent upgrades, primarily\nthe inclusion of 3D-tracking information in the L1 DCT\ntrigger to remove background events in which scattered\nbeam-gas particles would hit the beam pipe about 20 cm\naway from the IP. This new system was tested in parallel\nto the old one at the end of Run 4 and was used from Run\n5 onwards. The IFR component of the trigger also had\nto be updated when RPCs were replaced by LSTs which\nhad a di\ufb00erent latency. Finally, as explained above, sev-\neral changes were made to the trigger system (both to L1\nand L3) in early 2008 during Run 7, as the characteristics\nof the events needed for the physics analysis during this\nperiod were completely di\ufb00erent from those recorded at\nthe \u03a5(4S) resonance.\nTrickle injection\nWhen BABAR started taking data, PEP-II was operat-\ning in \ufb01ll-and-coast mode during which the injection and\ndata taking periods were clearly separated. No attempt\nwas made to inject the beams during a data taking run.\nTherefore, both currents (and consequently the instanta-\nneous luminosity) were slowly decreasing over time. When\nthey had dropped by about 30-50%, data taking was ended\nand the detector HV ramped down. Once BABAR was in\na safe mode insensitive to the potentially-high injection\nbackgrounds, the beams were replenished. Then, the HV\nwere raised again and the DAQ restarted when they had\nreached their nominal values. The whole procedure (end\nof the actual run; BABAR transition from runnable to in-\njectable states; beam injection; BABAR transition from in-\njectable to runnable; beginning of a new run) would take\naround 5 minutes. The duration of each \ufb01ll was adjusted\ndepending on the machine conditions, in order to maxi-\nmize the amount of integrated data. But the average lu-\nminosity delivered by PEP-II was only \u223c70% of the peak\nluminosity.\nA major improvement took place in 2004 when a new\nmode of operation called \u2018trickle injection\u2019 was introduced.\nThe beam currents were kept constant thanks to a con-\ntinuous injection of particles into the least \ufb01lled bunches,\nwithout interrupting the data taking. The average lumi-\nnosity immediately grew up by about 40% and the increase\nof the integrated luminosity was even larger than the gain\ndirectly provided by improving the duty cycle of the ma-\nchine. Indeed, operating the accelerator near the peak lu-\nminosity at all times and with constant currents, allowed\nthe PEP-II crew to improve the tuning of the beams and\nto reach new standards of performance and stability from\nwhich BABAR bene\ufb01ted as well.\nThe main challenge of this new running mode (\ufb01rst\nestablished with one beam, some months later with both)\nwas to inject enough particles into the rings, while keep-\ning the background levels low for BABAR. Quickly, it be-\ncame clear that the newly-injected bunches were causing\nbackground bursts: events with many hits in all detector\ncomponents were saturating the DAQ and causing high\ndead time. This background in phase with the injected\nbunch lasted up to a few thousands revolutions after the\ninjection, until the excitations induced by the particles\nadded to the bunch got damped. As it was possible to\nknow exactly which bunches had been recently re\ufb01lled and\nwhere they were located in the ring at any time (techni-\ncally speaking, the BABAR clock was locked to the PEP-II\ntiming system and markers were recorded for each injected\nbunch), the solution to this problem was to inhibit the\ntrigger when one such bunch was close enough to the de-\ntector. These online vetoes were extended o\ufb04ine when the\ndata were reconstructed, to make sure that the trickle in-\njection background would not impact the physics. Indeed,\nno signi\ufb01cant di\ufb00erence was ever found between events\nrecorded just outside the trickle injection inhibit windows\nand those selected far away from any injected bunch. The\ntrickle injection frequency was 5 Hz for the HER and 10\nHz for the LER, resulting in a dead time of 1.4% for the\nHER and 1.9% for the LER, 3.3% in total.\nAt the end of the commissioning phase which lasted a\nfew months in total, the trickle injection mode became the\ndefault con\ufb01guration for PEP-II. A constant and detailed\nmonitoring, both on the detector and machine sides, al-\nlowed to operate the B Factory safely in these conditions\nuntil the end of the data taking, not only at the \u03a5(4S) res-\nonance, but also from the \u03a5(2S) energy up to 11.2 GeV.\nThe veto regions did not change over time and induced a\ndead time of \u223c1% (\u223c0.5%) for the LER (HER) beam. As\nthe HER and LER inhibit windows did not overlap due\nto the low injection frequencies, the total dead time was\nthe sum of the two contributions, a small price to pay for\nthe signi\ufb01cant increase in integrated luminosity described\nabove. As described in Section 2.2.7, the BABAR online\nsystem had to be signi\ufb01cantly modi\ufb01ed to follow this sig-\nni\ufb01cant change of the machine operations: not only had\nthe detector control system to allow injection during data\ntaking, but the DAQ system also had to accommodate\nmuch longer periods of continuous data taking.\nSummary\nBoth the detector improvements and the PEP-II trickle\ninjection mode allowed BABAR to accumulate good data\nat a rate which increased over the years. More informa-\ntion about these di\ufb00erent types of upgrades can be found\nin (Aubert, 2013).\n3.2.3 Major hardware/online upgrades which modi\ufb01ed\nthe quality of Belle data\nDetector upgrades\nBelle encountered serious beam background in the begin-\nning of the experiment. The radiation damage on the read-\n\n45\nout electronics chips of the silicon vertex detector (SVD1)\nwas serious and the detector was replaced several times.\nFinally, the second type of silicon vertex detector (SVD2),\nwhich used so-called radiation hard electronics, was in-\nstalled during the summer of 2003. At the same time,\nthe inner part of the central drift chamber was also re-\nplaced with a compact small cell type drift chamber in\norder to make space for four instead of only three SVD\nlayers. The diameter of the beam pipe was changed from\n40 mm to 30 mm enabling the radius of the innermost\nSVD layer to be reduced to 20 mm in order to achieve a\nbetter vertex resolution; also the angular coverage of the\nsilicon vertex detector was matched to that of other detec-\ntors (17\u25e6\u2264\u03b8 \u2264150\u25e6). This was the only major hardware\nchange in the whole running period of the Belle detector\nand more information can be found in Chapter 2.\nOther detector modules have been used without any\nmajor replacement. Unfortunately, the outermost two lay-\ners of the 14 resistive plate chambers used in the muon\nand KL detector could not be operated due to the neu-\ntron background created by the radiative Bhabha events.\nHowever, the muon identi\ufb01cation capability was not sig-\nni\ufb01cantly a\ufb00ected. After the summer of 2003 the beam\nbackground was not so serious despite an increase of the\nluminosity to twice the design value.\nApart from the silicon vertex detector, the Belle data\nacquisition system used one type of multi-hit TDC mod-\nule. The module did not have a pipe-line readout scheme.\nTherefore, the readout dead time was larger than at BABAR.\nSeveral e\ufb00orts have been made in order to reduce the dead\ntime. Finally, the readout modules were replaced gradu-\nally with a pipe-line TDC for most of the sub-detectors\nrather late in the running period.\nContinuous injection and Crab cavities\nBelle turned o\ufb00the detector high voltage during beam\ninjection as commonly done at other experiments. The in-\njection time took slightly longer than at PEP-II causing a\nslightly lower average luminosity. In order to reduce such\na time loss, a continuous injection scheme was adopted\nfrom January of 2004. The detector high voltage was kept\non and the trigger signals were vetoed for 3.5 ms just after\neach beam injection. The scheme caused 3.5% dead time\nonly in the case of a 10 Hz injection rate. After adopt-\ning continuous injection, the KEKB machine beams be-\ncame stable and the peak luminosity was improved due to\nthe constant beam currents. The obvious di\ufb00erence in the\nbeam currents and luminosity before and after adoption\nof the continuous injection scheme is shown in Fig. 3.2.3\n(Abe et al., 2013). The e\ufb00ect of the scheme can also be\nseen in Fig. 3.2.1 as an increased slope of the integrated\nluminosity after the beginning of 2004.\nAnother important upgrade of the beam optics took\nplace in February 2007. At that time Crab cavities (Ya-\nmamoto et al., 2010) were introduced. These are RF de-\n\ufb02ectors providing the electron and positron bunches inside\nthe KEKB accelerator rings, which at the interaction point\nhave a crossing angle of 22 mrad, with a rotational kick\nFigure 3.2.3. Comparison of beam currents and luminosity of\nKEKB before (top) and after (bottom) adoption of the contin-\nuous injection scheme. The top two panels of each plot show\nthe electron and positron beam currents (red) and the third\npanel shows the luminosity (yellow). From (Abe et al., 2013).\nin order to undergo a head-on collision. The schematic\nprinciple of the Crab cavities operation is shown in Fig.\n3.2.4. The installation of the cavities into the KEKB was\nnot without problems, as can be also observed by a short-\nlasting plateau at the beginning of 2007 in the integrated\nluminosity curve (Fig. 3.2.1). While the increase in the\nluminosity after the installation was modest, the beam\ninduced backgrounds were reduced.\nFigure 3.2.4. Schematic principle of Crab cavities opera-\ntion leading to head-on collisions in KEKB despite the \ufb01nite\ncrossing-angle of electron and positron bunches.\n\n46\n3.3 Data Reconstruction\n3.3.1 Introduction\nBoth BABAR and Belle developed tools to process raw data\nin a timely way. The reconstruction also provides another\nlayer of data quality checks besides those performed in the\ncontrol room by looking at strip charts and histograms\n\ufb01lled during data collection.\n3.3.2 The BABAR prompt reconstruction\n3.3.2.1 Data processing\nThe BABAR data are processed in a two pass Prompt Re-\nconstruction (PR) system. The raw data (XTC \ufb01les) are\nread in each pass, once to compute time-dependent or\ndetector speci\ufb01c calibration constants, and then again to\nfully reconstruct the data. The system is named Prompt\nsince the calibration pass is done within a few hours of\ncollecting data and the reconstruction pass is completed\nwithin 12 hours.\nThe \ufb01rst pass, the Prompt Calibration (PC) fully re-\nconstructs a representative subset of the raw data. The\nactual percentage of data used depends on the number\nof events in the XTC \ufb01le. The PC pass computes vari-\nous calibration constants which are recorded in the Con-\nditions Database (CDB). The CDB tracks information re-\nlated to the detector systems and the beam conditions as\na function of data-collecting time. Most calibrations are\ncalculated for each run, but a subset of these calibrations\nneeds information collected over multiple runs and were\nthen called Rolling Calibrations. A separate database was\nused to collect inputs from each run for the Rolling Cali-\nbrations. When enough statistics were collected, or some\nother criteria met, a Rolling Calibration was performed.\nAn example of this procedure is the determination of the\nbeamspot rolling calibrations described in Section 6.4. The\noutput of both single run and rolling calibrations are writ-\nten to the CDB with a validity period corresponding to\nthe span of runs used. A copy of the updated conditions\ndatabase is made available for the full event reconstruc-\ntion (the second PR pass), for more speci\ufb01c physics event\nselection (skimming) and for general data analysis.\nThe second pass, the Event Reconstruction (ER), reads\nthe raw data from the XTC \ufb01les, the conditions and cal-\nibrations from the CDB, and performs the full physics\nevent reconstruction; track \ufb01nding, vertexing, PID, etc.\nInterleaved with this processing are two stages of event-\n\ufb01ltering. The \ufb01rst uses only L3 output-line information\n(Section 2.2.6) to reduce the contribution of events col-\nlected solely for diagnostic or detector-calibration pur-\nposes (e.g., Bhabha events, used for EMC calibration, etc.,\nare reduced by a factor of 15 beyond the factors already\napplied in L3). The second, which follows DCH-track and\nEMC-cluster reconstruction, tests events against about a\ndozen physics-motivated \ufb01lters. One \ufb01lter is highly e\ufb03-\ncient for BB \ufb01nal states, but much less e\ufb03cient for some\nother processes. Hence additional \ufb01lters address particular\nlow-multiplicity states relevant to tau physics, two-photon\nphysics, and so on. If an event satis\ufb01es any of these \ufb01lters,\nor the earlier L3-based \ufb01lter stage, it is saved. Reasons for\nsaving it are recorded with the event.\nThe output of the ER pass, the reconstructed events,\nis written to data collections which are archived and then\nmade accessible to the skimming system and to the ana-\nlysts. BABAR originally used an object-oriented database\ntechnology (Objectivity/DB) to store both the conditions\nand the reconstructed events, but later switched to a \ufb01le-\nbased Root I/O system (XRootD), \ufb01rst migrating the data\nstorage (2003) and then also the conditions database (2007).\n3.3.2.2 Reprocessing\nDuring the life of BABAR, as in any active experiment,\nthe data reconstruction algorithms and the detector cal-\nibrations are constantly being improved. In order for the\nphysics analysis to bene\ufb01t from these improvements, it is\nnecessary to reprocess the accumulated dataset, starting\nfrom the raw data. In BABAR, this reprocessing was done\nabout once a year, in parallel with the prompt processing\nof the incoming data. The total throughput and resources\nneeded for the reprocessing often exceeded the correspond-\ning need for the current data. The allocation of resources\nneeded to perform a reprocessing of the BABAR dataset\nwas driven by several facts: \ufb01rst, the moment when a sta-\nble and improved reconstruction framework was available;\nthen, the deadline by which to make the reprocessed data\navailable for physics analysis, in order to prepare results\nfor the next round of conferences; \ufb01nally, the size of the\nparticular dataset to reprocess.\nThe optimization of resources for the reprocessing is\naccomplished by breaking the conditions time-line into in-\ntervals and running separate instance of the two-pass pro-\ncessing system for each interval. The calibrations are com-\nputed within each separate interval and data run ranges\ncorresponding to each interval can be processed in paral-\nlel. The reprocessed condition intervals are then merged\ninto the Master CDB covering the whole time-line. The\nMaster CDB is then used for accessing the current and\nreprocessed data.\nA comprehensive bookkeeping system, based on a re-\nlational SQL database (Oracle or MYSQL), keeps track of\nall processing and reprocessing jobs indexed by run num-\nber. It records the date, time, software release and cal-\nibration used for that (re)processing of the data run, as\nwell as status of the job (completed, failed, etc.) and other\nstatistical quantities.\n3.3.3 The Belle data reconstruction\n3.3.3.1 Data processing\nThere are three major periods in the Belle data processing\nscheme, designed to cope with increasing event rate as well\nas to monitor data quality more reliably.\n\n47\nIn the 1st period from 1999 to 2003, raw data acquired\nin the Belle DAQ system are recorded to tape. Then, once\na tape becomes full and is released from the drive, o\ufb00-\nline processing starts reading raw data to perform event\nreconstruction (Adachi, 2004). This method only allows\none to monitor data quality with a delay of several hours\nsince one has to wait for a tape release to trigger the pro-\ncessing. In this \ufb01rst processing step, detector calibration\nconstants are not updated and are usually taken from the\nprevious experimental period with some necessary extrap-\nolations applied. If one needs to process a run immediately\nafter it has \ufb01nished, that is possible, but only by forcing\na change of tape. The delay in having processed data is\nreduced for that run at a cost of adding an overall delay,\ncorresponding to the tape change, for processing all data.\nThe reconstructed data are written to tape as a data sum-\nmary tape (DST). Then the next step called \u201cskimming\u201d is\ndone by reading DST (see Section 3.5.3), where one cre-\nates datasets containing physics events such as Bhabha\nevents, \u00b5-pair events, and hadronic events on disk which\ncan be accessed by users. Those physics datasets are used\nfor checking detector response and producing calibration\nconstants.\nTo improve the reconstruction chain, a computing clus-\nter (PC farm) for a real-time reconstruction (RFARM)\nwas introduced in 2003. Data sent by the DAQ system\nare received by the PC farm and reconstruction is done in\nparallel to the data acquisition (Itoh, 2005a). Output data\nare written in a hierarchy mass storage system (HSM) con-\nsisting of disks with a tape library as backend (Katayama,\n2005). This upgrade enables Belle to obtain reconstructed\nevents shortly after online data-taking, and precise data\nmonitoring becomes much more reliable. The data quality\nassurance is one of the duties of persons on shift during\nthe data taking. The skimming to select physics events\nis also carried out in the same way as before to provide\ncalibration data for detector experts.\nFollowing the initial success of the \ufb01rst RFARM sys-\ntem, the computing power in the RFARM doubled in or-\nder to be able to keep up with increasing luminosities in\n2005. This con\ufb01guration can process events at the highest\nKEKB luminosity without delay.\nThe Belle experiment employs a unique software frame-\nwork basf (Belle AnalysiS Framework) and traditional\ndata manipulation system with a zlib compression capa-\nbility (PANTHER ) throughout for all phases in event pro-\ncessing and this simple management was scalable using the\nprocessing scheme mentioned above (Adachi, 2004). The\nsoftware has been widely used not only for event recon-\nstruction, but for all physics analyses without any serious\nissues.\n3.3.3.2 Reprocessing\nBelle reprocesses all of the raw data once the detector\ncalibration constants are obtained (Ronga, Adachi, and\nKatayama, 2004). Usually the \ufb01rst half of the annual data\nrecorded from spring to summer is reprocessed to produce\nanalysis datasets used to obtain new results to be pre-\nsented in the summer conferences and the rest of raw data\nfrom autumn to winter is reprocessed for the winter con-\nferences. The calibration constants used for reprocessing\nare computed by the detector experts using the physics\nevents described above, once the experimental period (a\ncouple of months) is completed, and another set of con-\nstants computed directly from data. Once constants for all\ndetector elements are updated in the database (based on\nPostgreSQL) the reprocessing is carried out. In this step,\noutput data are recorded in a compact form e\ufb00ectively\nused for physics analysis (mini-DST, MDST) on disk. Ma-\njor physics analysis skims such as events containing J/\u03c8\ncandidates from B decays are produced in an organized\nfashion to speed up individual analysis. More background-\ntolerant tracking algorithms (combination of Hough and\nconformal transformation) and improved calibration con-\nstants (polar angle dependent threshold for shower clus-\nters in the ECL, new SVD alignment resulting in smaller\n\u2206z bias for several experiments - see Section 6) are devel-\noped using a large amount of data, making detailed stud-\nies of detector response possible. These new features are\napplied in a consistent way by reprocessing the raw data\nsample of \u223c560 fb\u22121 (experiment 31 to 55) taken with the\nSVD2 vertex detector (see Section 2.2.1), in the so called\n\u201cgrand reprocessing\u201d, and the data processing of later ex-\nperiments. The \u201cgrand reprocessing\u201d was started in July\n2009 and completed (including the calibration part) by\nFebruary 2010. Due to lack of time and manpower avail-\nable, many shorter runs of the earlier part of the Belle\ndata sample, taken with the SVD1 vertex detector, were\nnot included in this e\ufb00ort. At the same time new sets of\nMonte Carlo events are simulated with up-to-date decay\ninformation to improve the understanding of the nature of\nbackground. All Belle \ufb01nal physics results are in principle\nobtained from datasets produced in the grand reprocess-\ning.\n3.4 Monte Carlo simulation production\n3.4.1 Introduction\nSeveral Monte Carlo event generators are used to simulate\nthe \ufb01nal states of e+e\u2212collisions. A \ufb01nal state is repre-\nsented by a set of four-vectors originating from a com-\nmon vertex near the e+e\u2212interaction point or from the\nsource of a particular background. Once produced, the\nfour-vectors are passed by the software framework to the\ndetector simulation where they are tracked in the detec-\ntor, taking into account the interaction between the parti-\ncles and the di\ufb00erent materials, and the electronic signals\nwhich mimic the detector response are computed.\nIn the following sections the Monte Carlo simulation\nproduction at BABAR is described, followed by Section 3.4.5\ndetailing some di\ufb00erences in the approach taken by Belle.\n\n48\n3.4.2 Event generators\nThe generators depend on theoretical models of inter-\nactions to calculate the four-vectors. A combination of\nevents from both signal and background generators is re-\nquired in order to produce a simulated event stream real-\nistic enough to be essentially indistinguishable from real\ndata. A variety of generators makes this possible, as well\nas allowing individual sources of signal or background to\nbe studied independently.\n3.4.2.1 Signal generators\nThe production of hadronic events from the e+e\u2212collision\nthrough the decay of the Upsilon resonances and the direct\nproduction of uu, dd, ss and cc pairs, is handled by the\nEvtGen (Lange, 2001) package and the Jetset generator,\notherwise known as Pythia (Sj\u00a8ostrand, 1995). Collision\nvertices are sampled from beam parameters in the PEP\nconditions database or ASCII \ufb01les. These parameters in-\nclude beam energies, boosts and spot sizes.\nB decays, including CP-violating and other complex\nsequential decays are simulated using EvtGen. EvtGen is a\nframework in which new decay simulations can be added\nas modules. It uses decay amplitudes instead of probabil-\nities for each node in the decay tree in order to simulate\nthe entire decay chain, including all angular correlations.\nIt also has detailed models for semileptonic decays and an\ninterface to Jetset for the generation of continuum events\n(uu, dd, ss and cc production), and for generic hadronic\ndecays including those of B mesons.\nLepton pair events were simulated with KK2F (Jadach,\nWard, and Was, 2000), which is a high precision elec-\ntroweak Standard Model generator for e+e\u2212\u2192\u03c4 +\u03c4 \u2212\nand e+e\u2212\u2192\u00b5+\u00b5\u2212events, amongst others. It takes into\naccount QED radiative corrections (up to second order),\nincluding hard bremsstrahlung. When \u03c4 pair events are\nproduced, the \u03c4 decays are handled by the TAUOLA gen-\nerator (Davidson, Nanava, Przedzinski, Richter-Was, and\nWas, 2012).\nAfkQed (Czyz and K\u00a8uhn, 2001) was used to generate\nhard photons from initial and \ufb01nal state radiation using\nlowest-order QED calculations. Other generators used in-\ncluded Gamgam, which produces exclusive 2-photon decays\nof B0\u2019s, Diag36 (Berends, Daverveldt, and Kleiss, 1986),\nwhich generates 4-lepton \ufb01nal states, and SingleParticle,\nwhich generates one particle per event, using user-speci\ufb01ed\nparameters.\nTo compute the PEP luminosity and the Bhabha scat-\ntering cross section BHWIDE (Jadach, Placzek, and Ward,\n1997), a wide-angle Bhabha generator which has a the-\noretical accuracy of 0.5%, and BHLUMI (Jadach, Placzek,\nRichter-Was, Ward, and Was, 1997), a small-angle Bhabha\ngenerator, were used.\n3.4.2.2 Background generators\nIn real data, several background processes contribute to\nevents and mimic (or hide) real signals. Some of these\nbackgrounds may be removed during the data analysis,\nwhile others may not. In either case, it is necessary to sim-\nulate them in order to aid background subtraction or to\nmix them with the simulated signal. These backgrounds\ninclude Bhabha scattering, bremsstrahlung, QED back-\nground, initial state radiation, machine background, and\ncosmic rays.\nLuminosity backgrounds from electrons or positrons\nstriking the beamline or other machine elements outside\nthe nominal detector acceptance, were simulated using\nBHWIDE and BHLUMI .\nLepton pair and two-photon events from QED back-\nground were generated by Bkqed (Berends and Kleiss,\n1981) which also includes e\ufb00ects from radiative photons.\nMachine backgrounds due to electrons and positrons\nstriking apertures and photons from Compton scatter-\ning and bremsstrahlung from beam gas are simulated by\nTurtleRead (Barlow et al., 2005) which reads ASCII \ufb01les\nwritten by the Decay Turtle ray-tracing program.\nCosmic ray muons were another source of background\ntriggers for BABAR. To estimate this, the HemiCosm code\nshot muons inward from the upper hemisphere surround-\ning the volume of the simulated detector. The muons were\nsampled from the usual zenith angle distribution and one\nof three available momentum spectra.\nAll these background generators where mostly used\nduring the design and construction phase of the BABAR\ndetector. After the start of the data-taking the e\ufb00ect of the\ndi\ufb00erent backgrounds processes, including machine back-\nground and background hits from the detector electronic\nnoise, was simulated by superimposing recorded random\ntriggers to the signal events.\n3.4.3 Detector Simulation\nThe purpose of the BABAR detector simulation is to take\nfour-vectors from the generator stage and transport them\nthrough the detector geometry, where energy loss, pro-\nduction of secondaries, multiple scattering and decays can\noccur. As these particles pass through sensitive regions of\nthe detector, their energy, charge and angle information\nis collected in order to generate raw, idealized hits, which\nconsist of positions and energy deposits in the detector.\nThese quantities are stored in persistent containers in the\ndatabase for later use in the simulation of the detector\nresponse where idealized information is converted to re-\nalistic detector hits, blended with background data, and\ndigitized. The resulting realistic hits are then passed to\nthe reconstruction code where the full simulated event is\nbuilt for later comparison with real events.\n3.4.3.1 Bogus, SimApp, and GEANT4\nThe software package which handled the generation of the\nraw hits on BABAR is called Bogus. It was an applica-\ntion layer built on top of the GEANT4 simulation toolkit\n(Agostinelli et al., 2003) and was designed to model the\n\n49\nBABAR detector geometry and materials, propagate par-\nticles through a varying magnetic \ufb01eld, perform particle\ninteractions and decays, and provide scoring of detector\nhits.\nBogus was integrated into the BABAR software frame-\nwork and designed to be fully compatible with its event\nscheme, allowing Monte-Carlo truth information to be ad-\nded to the simulated BABAR event. The code which accom-\nplished this, BfmModule, initialized the GEANT4 kernel, ex-\ntracted event generator tracks from the framework event,\ninvoked GEANT4 to propagate these tracks through the de-\ntector and wrote the propagated tracks and produced sec-\nondaries into the event framework.\nThis event was then passed to SimApp, the package re-\nsponsible for simulating the detector response. Beginning\nwith hits from Bogus, it converted them to digitizations\nwhich mimicked the real electronic output of the detector,\nthat is, the ADC and TDC words. These were then mixed\nwith corresponding digitizations from background frames\nobtained from random triggers recorded by the data ac-\nquisition.\nTrigger conditions corresponding to a particular month\nof data-taking (see Section 3.4.4) were \ufb01nally applied to\nthe full event which was then sent to the reconstruction.\n3.4.3.2 Physics and transport processes\nThe physics of the initial e+e\u2212collisions and the decays\nof short-lived hadrons were handled by the event gen-\nerators discussed above. All other physics processes, in-\ncluding Ks and \u039b decays, and \u03c0 and K decays in \ufb02ight,\nwere supplied by GEANT4. In terms of shower development\nin the detector, by far the most important are the stan-\ndard electromagnetic processes of multiple scattering, ion-\nization, bremsstrahlung, pair production, Compton scat-\ntering and photoelectric e\ufb00ect. These processes are su\ufb03-\ncient to describe accurately the energy distribution in the\nEMC. Hadronic processes, though less frequent, are im-\nportant for the propagation of hadrons produced in the\ninitial interaction and the hadronic secondaries they in\nturn produce. The processes used included elastic scatter-\ning and capture, as implemented by the GEANT4 version\nof the Gheisha hadronic code (Fesefeldt, 1985), and in-\nelastic scattering as implemented by the GEANT4 version\nof the Bertini cascade (Bertini and Guthrie, 1971). The\nlatter was especially useful for a reasonable propagation\nof kaons from B decays.\nThe decay of long-lived particles was also handled by\nGEANT4, which used PDG (Beringer et al., 2012) branching\nratios to determine the \ufb01nal state of the decays.\nThe default particle transport code in GEANT4 is a\nRunge-Kutta stepper, but for BABAR this was deemed too\nslow. It was replaced by a specialized helical stepper which\ntook advantage of the near-uniform BABAR magnetic \ufb01eld\nby taking large steps and using exact calculations of the\nintersection of helical tracks and volume boundaries.\n3.4.4 MC production systems\nQuite early in the history of the BABAR experiment, the\nsimulation production used computing resources coming\nfrom over 17 production sites across the globe. Such dis-\ntributed production was possible because the only data\nthat needed to be available at the production sites were\nthe background event collections and the conditions. More-\nover, a missing production due to failed jobs was simply\nreplaced with a new production of the same decay mode,\nbut with di\ufb00erent random number generation seeds. All\nthis resulted in simple production management tools that\nwere easy to install at production sites.\nIn BABAR, simulation production is done on a \u2018per\nmonth\u2019 basis, using background frames and conditions and\ncalibrations corresponding to a speci\ufb01c month of data tak-\ning. Conditions and calibrations are read from the MySQL\nconditions database and were previously computed during\nthe prompt calibration pass of the reconstruction of raw\ndata or with a special o\ufb04ine analysis of the raw data for\nthose conditions that require data samples larger than a\nsingle run.\nThe production is carried out in cycles correspond-\ning to major updates in the simulation or reconstruction\ncode. In all cycles, the number of Monte Carlo events\nwas much larger than the number of events collected by\nBABAR. In the \ufb01nal cycle, the number of bb and cc events\ncorresponded to a luminosity ten times higher than the\nluminosity of the detector data and to a luminosity three\ntimes higher for continuum events.\nUnlike the detector data, the simulated data are auto-\nmatically marked \u2018good\u2019 in the bookkeeping database.\nBefore simulation production at a site can start, a\ntest production must be run and compared to the exact\nsame production performed at SLAC. This tests the re-\nlease installation, the accuracy of the conditions exported\nto the site, and the availability of the background collec-\ntions. Recently, most of the major simulation productions\nhave been done o\ufb00-site while specialized productions were\nmostly done at SLAC (for maximum control). However,\nhaving multiple sites has been very useful when several\nvarieties of production needed to be done at the same\ntime.\nAll the Monte Carlo event collections are imported at\nSLAC and stored in a High Performance Storage System\n(HPSS, a large tape storage robot). From SLAC, they are\nexported to the remote sites according to the requests of\nthe Analysis Working Groups (AWGs) that are doing their\nanalysis at that site.\nCurrently, simulation production remains distributed\nalthough an eventual collapse back onto SLAC is foreseen.\n3.4.5 Di\ufb00erences between BABAR and Belle simulations\nRather than implement stand-alone programs for event\ngeneration and simulation in Belle, these codes were in-\ntegrated into the basf as user modules. In this way, a\nuser could run an entire Monte Carlo production sequence\n\u2014 generation, simulation, reconstruction, skimming, and\n\n50\nanalysis \u2014 in one basf job and therefore is able to take\nadvantage of the parallel-processing of events built into\nbasf if desired.\nIn practice, event generation in Belle was done in\nsingle-processing mode to avoid inadvertent repetition or\noverlap of random number sequences. The output \ufb01les\nfrom this generation step were fed to the subsequent\nparallel-processing job for simulation and analysis (gen-\nerated events were processed by several processors, one\nevent at a time by each processor).\n3.4.5.1 Generators\nIn addition to EvtGen (Lange, 2001), Belle used the qq98\n(CLEO, 1996) event generator in the early years for B de-\ncays. Other generators used by Belle included CTOY (writ-\nten for Belle based on the HemiCosm code) for cosmic\nray muons, SG for single tracks (including cosmic rays),\nBHLUMI (Jadach, Placzek, Richter-Was, Ward, and Was,\n1997) for lepton pairs (with TAUOLA (Davidson, Nanava,\nPrzedzinski, Richter-Was, and Was, 2012) for subsequent\n\u03c4 decays), KK (Jadach, Ward, and Was, 2000) for fermion\npairs, and AAFH (Berends, Daverveldt, and Kleiss, 1986)\nfor two-photon production of fermion pairs.\n3.4.5.2 Detector simulation\nBelle used the Fortran-based GEANT3 (Brun, Bruyant,\nMaire, McPherson, and Zanarini, 1987) toolkit for de-\ntector simulation (this was the dominant motivation for\nBelle\u2019s continued support of Fortran, alongside C++, in\nits software library). C++ wrappers were incorporated\naround the GEANT3 toolkit to embed it within the basf.\nGEANT3 was supplemented with a Cherenkov-light simula-\ntion (written in C++) to model light propagation within\nthe Aerogel Cherenkov Counters (ACC). Four-vectors of\nthe generated particles in an event were passed to GEANT3,\nwhich then pass them through the model of the Belle ge-\nometry and generate hits in the sensitive elements. Decays\nof long-lived particles such as K0\nS mesons were handled by\nGEANT3. The simulation accounted for the evolution of the\nreal detector\u2019s behavior (dead or hot channels, e\ufb03ciency\nchanges, geometry changes, and trigger-parameter tuning)\nvia information tabulated in the master database by ex-\nperiment and run number. Through user hooks provided\nin GEANT3, these hits were digitized (simulated ADC, TDC\nand latch responses) tailored to the detector element so\nthat the output data stream would mimic the appearance\nof the real data, supplemented with the additional \u201ctruth\u201d\ninformation from the simulation. At the conclusion of the\nsimulation of each event, additional hits from real back-\nground events (recorded with a random trigger and \ufb01ltered\nto avoid any events with reconstructed tracks or clusters)\nwere superimposed on the event to mimic the background\nactivity in each detector element. The method developed\nconsists of overlaying a random-triggered real beam back-\nground event to a simulated signal event. The random-\ntriggered event is taken during a beam run with a typical\nrate of 1-2 Hz. The beam background \ufb01le, the collection of\nthe random-triggered events, is created for each run. The\nbeam background overlay procedure is applied to the out-\nput after the detector simulation. Thanks to this method,\nthe run-dependent beam background e\ufb00ects can be repro-\nduced in the simulation. However, because this overlay\nprocess is done after the digitization step, it is not pos-\nsible to consider a pile-up e\ufb00ect of electric charge before\nthe digitization. A data \ufb01le containing these background\nevents was recorded for each run. Background events were\nselected at random from the \ufb01les for a given Experiment\nwhen simulating Monte Carlo data early on within Belle.\nLater in the life of the experiment background events were\nselected sequentially from the corresponding background\n\ufb01le for a given run.\n3.4.5.3 Geometry\nThe detailed Belle detector geometry was modeled for\nGEANT3 in a manner similar to that of BABAR for GEANT4.\nThe magnetic \ufb01eld in Belle\u2019s interior was obtained from a\ntabulated map of the \ufb01eld\u2019s radial and axial components\nthat extended from the beamlines to the yoke\u2019s exterior\nsurface; this \ufb01eld was used by GEANT3 for charged particle\npropagation. No uniform-\ufb01eld approximations were made\nin the Belle simulation.\n3.4.5.4 Physics and transport processes\nPropagation, decay and interactions of all particles ex-\ncept the Cherenkov photons in the ACC were handled\nby the GEANT3 toolkit. Also for the most demanding\npart, the Belle electromagnetic-calorimeter (ECL) simu-\nlation, no fast (i.e., parametric) simulations were used.\nThe Fluka (Fasso, Ferrari, Ranft, and Sala, 1993) code\nembedded in GEANT3 was used to simulate hadronic inter-\nactions.\n3.4.5.5 Post-simulation track extrapolation\nIn the analysis phase of each event, whether simulated or\nreal, Belle utilized the GEANT track-extrapolation pack-\nage distributed with GEANT3 to extrapolate each recon-\nstructed charged track from the outer surface of the Cen-\ntral Drift Chamber (CDC) through the outer detectors;\nACC, Time-of-Flight (TOF), ECL, and K0\nL and \u00b5 detec-\ntor (KLM). This proved quite useful in matching tracks\nto hits in these outer detectors.\n3.4.5.6 MC production systems on Belle\nGeneration, simulation, and reconstruction of e+e\u2212\u2192\n\u03c4 +\u03c4 \u2212(\u03b3) was done for the most part at Nagoya University\nand the output data \ufb01les were stored there.\nMonte Carlo production of generic BB decays, con-\ntinuum (e+e\u2212\u2192qq) processes, and other speci\ufb01c signal\n\n51\nprocesses were handled by KEK and the other institutions\nwith signi\ufb01cant computing resources. Grid computing be-\ncame available for Belle\u2019s use fairly late in its lifetime and\ntherefore did not play a signi\ufb01cant role in Monte Carlo\nproduction. In Belle, the Monte Carlo Production Man-\nager utilized a web-based production scheme that har-\nnessed the CPU and storage capabilities at the remote\ninstitutions; the grid was treated as one of these 22 re-\nmote sites.\nEach production cycle was de\ufb01ned by a set of exper-\niments (and all of the real-data runs within each experi-\nment) and the Belle software library that had been used\nto process the real data therein. Ten times the real inte-\ngrated luminosity in bb events and six times that in contin-\nuum events (with cc handled separately from the lighter\nquarks) were produced in each MC production cycle. For\ndata samples taken at energies other than \u03a5(4S) six times\nthe accumulated luminosity in the data were simulated.\nThe Production Manager would \ufb01rst coordinate with\neach of the Site Managers to ensure that the remote site\nhad the proper Belle software library installed and oper-\nating properly; this was done by exercising the remote\nlibrary via several test jobs and then comparing sev-\neral thousand output histograms with the reference his-\ntograms at KEK. The Site Manager at each validated\nsite was then permitted to request the simulation of a\nsequence of experiments and runs via the web interface,\nupon which the KEK-generated event \ufb01les and the cor-\nresponding background-event \ufb01les were delivered to the\nremote site for MC production. Each job\u2019s simulated, re-\nconstructed, analyzed and \ufb01ltered outputs were delivered\nto KEK and tracked by the Site Manager, who was re-\nsponsible for restarting any failed jobs. Each output \ufb01le\nwas read back in entirety upon delivery to KEK to ver-\nify its integrity. Once all jobs in the requested sequence\nwere completed and delivered successfully, the Site Man-\nager would record this via the web interface. On rare oc-\ncasions when a site fell behind signi\ufb01cantly in its commit-\nment to deliver the requested sequence, the Production\nManager would consult with the other Site Managers and\nthen transfer the sequence to another site with spare ca-\npacity. KEK produced about half of Belle\u2019s generic-MC\nevents; the other institutions produced the remainder (see\nFig. 3.4.1).\n3.5 Event skimming\n3.5.1 Introduction: purpose of event skimming\nThe amount of detector and Monte Carlo data is such that\nit would be highly ine\ufb03cient to have all analysts reading\nthe full data sample. The identi\ufb01ed solution was to cen-\ntrally run an extra production step, the skimming, where\nevents passing di\ufb00erent sets of physics-motivated criteria\nwere written to separate streams, the skims.\nEach skim was optimized for a group of analyses us-\ning common sets of selected events as input. The fact\nthat some analyses reached completion and new analy-\nses started, resulted in skim de\ufb01nitions that were chang-\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nVPI\nLausanne\nNagoya\nTokyo\nGrid\nKorea\nHawaii\nVienna\nTIT\nPrinceton\nLjubljana\nTohoku\nKrakow\nYonsei\nCincinnati\nRIKEN\nITEP\nOsaka\nMelbourne\nKyungpook\nNCU\nNTU\nNumber of MC events (billions)\nFigure 3.4.1. Generic MC production in Belle at remote sites\n(circa 2008).\ning with time, new skims being added to production while\nothers became obsolete and were removed. The two experi-\nments adopted di\ufb00erent skimming philosophies, BABAR in-\ntroduced a large number of skims speci\ufb01c to analysis top-\nics, whereas Belle had a limited number of skims strongly\nrelated to the selection of events produced in a type of pro-\ncess. The BABAR methodology is described below, and is\nfollowed by a more detailed description of the Belle skims\nas an illustration of how one can identify events of a given\ntype.\n3.5.2 Skimming in BABAR\nBABAR analysis e\ufb00ort is organized into AWGs and each\nAWG is assigned to a particular site for the bulk of their\nanalysis work. The skims relevant to a speci\ufb01c AWG are\nexported to the site of the AWG.\nEvents are organized into lists referred to as \u2018collec-\ntions\u2019. Events from the full reconstruction steps go into\nthe \u2018AllEvent\u2019 collections. The outputs of the skimming\nstep consist of the \u2018AllEventSkim\u2019 collections (with all the\nevents that passed the skimming step) and of a set of col-\nlections for each skim. Skims can either be a full copy of\nthe selected events (deep copy skims) or pointers to the\nevents in the \u2018AllEventSkim\u2019 collections (pointer skims).\nThe choice of the type of skims used depends on the frac-\ntion of selected events, on the need for detailed detector\ndata, and on the availability of the \u2018AllEventSkim\u2019 collec-\ntions at the AWG site.\nSkim production was done in Skim Cycles and a cou-\nple of cycles had more than 200 output streams. Each \u2018Al-\nlEvents\u2019 collection, corresponding to a single run, was bro-\n\n52\nken into pieces and each piece was skimmed. The output\nstreams coming from the pieces of the same \u2018AllEvents\u2019\ncollection are then merged. Finally, in order to create\nskimmed collections with a reasonable number of events,\nstreams coming from di\ufb00erent AllEvents collections were\nmerged.\nOnly the \u2018AllEvents\u2019 collections declared \u2018good\u2019 by the\n\u2018Data Quality Group\u2019 (see Section 3.6) were used as input\nfor the skimming procedure. All the skim jobs must have\nbeen completed and the output streams merged success-\nfully to declare the skimming of several AllEvents collec-\ntions which are part of the same skimming job as good.\nTo have an e\ufb03cient skimming production, monitoring, job\ncrash recovery, disk clean up, and e\ufb03cient data distribu-\ntion are all critical elements. A set of software tools was\ndeveloped to make this production possible.\nAs mentioned above, the level of analysis pre-selection\nthat is available in skimming depends on the AWG re-\nquirements. To illustrate this one can consider the example\na number of di\ufb00erent Charmless B decays to four-particle\n\ufb01nal states (where each particle is one of the following: \u03c0\u00b1,\nK\u00b1, \u03c00, K0\nS) which are studied within the so-called Quasi-\nTwo-Body AWG within BABAR. A set of skims associated\nwith these \ufb01nal states was developed by members of that\nworking group to isolate B decays of particular interest.\nWhile each of the possible \ufb01nal states is topologically sim-\nilar, and in turn the analysis strategies for these decays are\nsimilar, there are di\ufb00erent requirements placed on di\ufb00erent\nchannels. Hence analyses would use dedicated skims for a\ngiven combination of topology and \ufb01nal state. The decay\nB0 \u2192\u03c1+\u03c1\u2212has two charged and two neutral pions in\nthe \ufb01nal state. This used the \u2018BFourHHPP\u2019 skim variant,\nwhere H denotes a charged hadron (without any PID con-\nstraints imposed), while P denotes a neutral pion decaying\ninto two photons. Similarly the decays to the four charged\ntrack \ufb01nal states B0 \u2192\u03c10\u03c10 and B0 \u2192K\u2217K\u2217(with sub-\nsequent K\u2217\u2192K\u03c0 decay) used the \u2018BFourHHHH\u2019 skim. In\nthis way each of these skims can be used to study a number\nof similar \ufb01nal states minimizing the time required by the\ndata analyst to process the data. The ensemble of similar\nfour body skims was also made available as the \u2018BFour-\nBody\u2019 skim. This skim methodology is applied across the\nBABAR AWG system, where some skims are speci\ufb01c to the\nanalysis of a given decay, while others are usable for a set\nof similar decays.\n3.5.3 Skimming in Belle\nAfter data processing, events taken by Belle are classi-\n\ufb01ed into several categories. Some of the categories such\nas Bhabha events, muon pair events and \u03b3 pair events\nare used for detector calibration, while the following three\ncategories are used for physics analyses:\n1. a skim for hadronic events, called HadronBJ, which is\nmainly used for analyses of B and charm mesons,\n2. a skim for \u03c4-pair events, called TauSkim, which is\nmainly used for analyses of \u03c4 leptons, and\n3. a skim for low multiplicity events, called LowMult,\nwhich is mainly used for two photon analyses\nFurther skims that contain smaller categories of physics\nevents are made from these three basic skims and provided\nto individual analyses, so that users usually do not need\nto run over a huge number of events in the basic skim. De-\ntails of the second stage skim are described in the section\nof each analysis. Classi\ufb01cation conditions for the three ba-\nsic skims are described in the rest of this subsection.\nHadronic event skim:\nHadronBJ events are selected primarily based on track\nmultiplicity and visible energy: the event must have at\nleast three charged tracks with a transverse momentum\ngreater than 0.1 GeV/c that originate from the vicinity\nof interaction point (|\u2206r| < 2 cm and |\u2206z| < 4 cm), and\nthe sum of the energy of charged tracks and reconstructed\nphotons (E\u2217\nvis) must be greater than 20% of \u221as. Note that\nall observables denoted by an asterix are measured in the\nCM frame.\nThese two selection criteria remove the majority of\nbeam gas background and two-photon events. Beam gas\nbackground is further reduced by requiring the primary\nvertex position of the event, when the vertex is well-\nreconstructed, to be |\u2206r| \u22643.5 cm and |\u2206z| \u22641.5 cm.\nBackground events from radiative Bhabha and higher mul-\ntiplicity QED processes are suppressed by requiring that\ntwo or more ECL clusters are detected at large angle\n(\u22120.7 < cos \u03b8\u2217< 0.9), the average ECL cluster energy\nbelow 1 GeV, and the total ECL cluster energy (E\u2217\nsum)\nto be below 80% of \u221as. E\u2217\nsum is also required to be\ngreater than 18% of \u221as since there are \u03c4-pair, beam gas\nand two photon events that have low energy sum. How-\never, this condition is rather tight for light quark pair\nproduction events (e+e\u2212\u2192q q with q = u, d, s, c), and\nhence a conditional selection is applied: E\u2217\nsum > 0.18\u221as\nor HJM > 1.8 GeV/c2, where HJM stands for heavy\njet mass, which is the invariant mass of particles found\nin hemispheres perpendicular to the event thrust axis.\nThe HJM is the most e\ufb00ective variable to remove \u03c4-pair\nevents, and it is required to exceed 25% of E\u2217\nvis. However,\nin order to regain qq events, a conditional selection is re-\nquired: HJM/E\u2217\nvis > 0.25 or HJM > 1.8 GeV/c2. These\ngeneral conditions to select hadronic events turned out\nnot to be very e\ufb03cient for inclusive \u03c8 events. Therefore,\nthe events with J/\u03c8 and \u03c8(2S) candidates are explicitly\nadded to HadronBJ.\nTau pair events: TauSkim\nSignatures of the \u03c4-pair production, e+e\u2212\u2192\u03c4 +\u03c4 \u2212(\u03b3), are\nlow-multiplicity and missing-momentum. Since at least\ntwo-neutrinos are missing in \u03c4-pair events, tight kinematic\nconstraints can not be applied. So TauSkim is designed\nto reduce well de\ufb01ned Bhabha, qq/BB, two-photon and\nbeam-gas background.\nTauSkim events are selected primarily based on track\nmultiplicity and the position of the event vertex: the num-\nber of charged tracks in an event must be at least two\n\n53\nand less than 8, where each track must have a trans-\nverse momentum greater than 0.1 GeV/c and originate\nfrom the vicinity of the interaction point (|\u2206r| < 2 cm\nand |\u2206z| < 5 cm). The net charge of the event Q must be\n|Q| \u22642. Beam gas background is reduced by requiring the\nprimary vertex position of the event to be |\u2206rv| \u22641.0 cm\nand |\u2206zv| \u22643.0 cm.\nBackground from (radiative) Bhabha events is sup-\npressed by requiring the sum of ECL clusters in CM (E\u2217\nsum)\nto be below 11 GeV, and the polar angle of the missing\nmomentum in the CM frame to be between 5\u25e6and 175\u25e6\nfor two track events.\nBackground from two-photon events is reduced by re-\nquiring the maximum of the transverse momentum of the\ncharged tracks (P max\nt\n) to be greater than 0.5 GeV/c and\nthe sum of the visible energy E\u2217\nvis greater than 3 GeV,\nwhere E\u2217\nvis is the sum of the absolute momentum of charged\ntracks multiplied by c and the photon-cluster energies in\nthe CM: the photon cluster is the ECL cluster to which\nno charged tracks are associated. Even if E\u2217\nvis is less than\n3 GeV, the events are accepted if P max\nt\n> 1.0 GeV/c.\nIn order to further reduce the (radiative) Bhabha events,\nevents with 2-4 charged tracks are rejected if the total en-\nergy E\u2217\ntot is greater than 9 GeV and the number of clusters\nin the barrel region (30\u25e6< \u03b8\u2217< 130\u25e6) is less than two,\nwhere E\u2217\ntot is the sum of of the visible energy and the\nabsolute value of the missing momentum (E\u2217\ntot = E\u2217\nvis +\nc|p\u2217\nmiss|). This condition reduces (radiative) Bhabha events\nwhere one electron or positron is detected in the Bar-\nrel calorimeter, but the energies of the other electron or\nphotons are not measured correctly either by starting to\nshower in the tracking volume or missing energy from the\nshower in the gap between the barrel and end cap of the\ncalorimeter.\nWith these selection criteria, about 80% of tau-pair\nevents are kept while Bhabha and two-photon events are\nreduced to an acceptable level. If the events are passed by\nboth the TauSkim and HadronBJ conditions, the events\nare kept in HadronBJ, while the remaining ones are kept in\nTauSkim. As a result both HadronBJ and TauSkim events\nare processed in physics analyses using the TauSkim sam-\nple.\nThe low-multiplicity skim\nThe low-multiplicity (LowMult) skimming of Belle data\nprocessing provides event-data collections mainly for anal-\nyses of zero-tag two-photon processes with an exclusive\n\ufb01nal-state system, \u03b3\u03b3 \u2192X, including charged tracks in\nthe \ufb01nal state (see Chapter 22 for the description of two-\nphoton processes). The charged multiplicity of the target\nevents is required to be two or four because of charge con-\nservation, and the total visible energy is expected to be\nmuch smaller than the energy of the e+e\u2212collision.\nThe minimum requirement of the transverse momen-\ntum pt for charged tracks in two track events is chosen\nto be 0.3 GeV/c. Tracks must originate from the vicin-\nity of the interaction point, which is |\u2206r| < 1 cm and\n|\u2206z| < 5 cm. For the four track events the additional\ntwo tracks are required to satisfy looser selection crite-\nria, pt > 0.1 GeV/c, |\u2206r| < 5 cm and |\u2206z| < 5 cm. For\nthe four-track events, a looser constraint for the impact\nparameter of tracks is adopted to collect the K0\nSK0\nS \ufb01nal-\nstate events.\nOnly events with smaller visible energy, with the sum\nof absolute momentum of tracks \u03a3|p| < 6 GeV/c and the\nsum of calorimeter cluster energies E\u2217\nsum < 6 GeV, are\ncollected, thus rejecting QED backgrounds with the full\nenergy of beam collision deposited in the detector.\nA further requirement on the missing-mass squared\nMM 2 > 2 GeV2/c4 is imposed to reject radiative events\nsuch as \u00b5\u00b5\u03b3 where the photon travels in the forward direc-\ntion and remains undetected. Any constraints originating\nfrom the trigger or particle-identi\ufb01cation are not included\nin the requirements, in order to avoid introducing system-\natic uncertainties on the skimming e\ufb03ciency from these\nsources.\nIn two photon events an approximate transverse-\nmomentum (pt) balance is expected. This was used in\nskimming of events with two charged tracks, applying\nloose selection on pt balance (where in the calculation\nof pt one also takes into account the calorimeter energy\ndeposits for any number of \u03b3 or \u03c00 candidates).\nIn addition, to salvage physics events where a track is\nmis-reconstructed or originates from noise (or from sec-\nondary interactions), a sub-category of events is skimmed\nusing a condition on the visible energy E\u2217\nvis < 4 GeV,\nwhen the event has at least two tracks. Processes with\nsix tracks, such as D+D\u2212production, can be explored\nin this sub-category, although the skimmed data must be\nused together with the TauSkim and/or HadronBJ skims\nto recuperate events with the visible energy exceeding the\nabove condition.\n3.6 Data quality and B counting\n3.6.1 The control of data quality\nData quality control is crucial at each step of the data ac-\nquisition, from the initial readout of the detector following\na positive trigger, to the \ufb01nal physics analysis. Therefore,\nBABAR and Belle have de\ufb01ned detailed procedures to val-\nidate each step of the data processing and to identify as\nquickly as possible any new hardware or software problem.\nThese prescriptions have evolved over the years while the\nexperiments were gaining experience. In the following, we\nwill mainly focus on the \ufb01nal versions of the data qual-\nity procedures which were in use at the end of the data\ntaking.\n3.6.1.1 Online data quality control in BABAR\nThe \ufb01rst level of data quality control is done in the control\nroom. The shift crew relies on information from the slow\ncontrol monitoring and DAQ systems to make sure that\nthe detector is taking good data in a smooth way. Should\nan unexpected event occur, the diagnostics of the situation\n\n54\nand the following actions are guided by well-established\nrecovery procedures. If needed, the shift crew can also seek\nhelp by contacting a team of on-call experts \u2013 at least one\nper critical system of the experiment.\nIn BABAR, the standard shift crew was made of two\npeople: the \u2018pilot\u2019, in charge of controlling the \ufb02ow of the\nmain data acquisition elements, and the \u2018Data Quality\nManager\u2019 (DQM), whose main task was to check moni-\ntoring plots continuously. These histograms, classi\ufb01ed by\nsubsystem (SVT, DCH, etc.), accumulated data in real\ntime during a run (usually about an hour long, unless a\nbeam abort or some hardware problem ended it prema-\nturely). About 15-20% of the events accepted by the L1\n(hardware) trigger level were used for this fast monitor-\ning. Most histograms could be directly compared with ref-\nerence ones, automatically selected by the control system\ndepending on the data taking conditions (colliding beams,\nsingle beam or cosmic events). Detailed guidance was also\nprovided by each BABAR system to help the shift crew as-\nsess the quality of the runs. Therefore, it was very easy to\nspot a change in the behavior of a given hardware compo-\nnent (readout section with an occupancy unusually low or\nhigh, noisy channels, etc.) and to react appropriately. This\ninformation, combined with the detector status provided\nby the slow monitoring system (high voltage, low voltage,\ngas \ufb02ow, temperature, etc.), allowed the shift crew to \ufb02ag\neach run after it had ended. Flags assigned at the subsys-\ntem level included \u2018good\u2019, \u2018bad\u2019, \u2018unknown\u2019, and \u2018\ufb02awed\u2019.\nThe \ufb01rst three have obvious meanings while the fourth one\nwas used to mark data in which the quality was not per-\nfect, but would be worth processing for o\ufb04ine checks by\nexperts. The global run \ufb02ag was the worst among the sub-\nsystem \ufb02ags: for instance, one subsystem \ufb02agged \u2018\ufb02awed\u2019\nwhile the other ones got the mark \u2018good\u2019 would result with\nthe run being assigned \u2018\ufb02awed\u2019 as global \ufb02ag. Shift crews\nhad two hours to \ufb02ag a run after its end. This delay gave\nshifters the opportunity to get expert advice when needed.\nTo avoid PC processing delays, it was crucial to give the\nright \ufb02ag to each run in a timely manner as only colliding\nbeam runs with \u2018good\u2019 or \u2018\ufb02awed\u2019 \ufb02ag were automatically\nprocessed. Runs initially marked \u2018bad\u2019 and re-quali\ufb01ed as\n\u2018good\u2019 later could only be processed during the next round\nof reprocessing; in the meantime, their data were unavail-\nable.\nMost of the raw data that was marked \u2018bad\u2019 su\ufb00ered\nfrom hardware failure. Although such a failure may have\noccurred in the \ufb01nal part of a run, all its data were po-\ntentially lost as the entire run would not be processed. In\nthe worst case, up to an hour of BABAR data would be\ndeclared unusable, even if the failure occurred only in the\nlast few seconds of data taking. Therefore, a software tool\nwas developed during the \ufb01nal reprocessing to truncate\nthese problematic runs and recover some good data. This\nprocedure was conceptually simple, but involved signi\ufb01-\ncant bookkeeping subtleties. Ultimately, this tool added\nabout 1 fb\u22121 to the \ufb01nal \u03a5(4S) dataset.\n3.6.1.2 Control of the data processing quality in BABAR\nData processing procedures could be subject to various\nproblems, even when working with raw data designated\nas \u2018good\u2019. To handle such complexities, this stage required\ndedicated quality assurance (QA) procedures which had to\nbe (re)done for a given run each time it was (re)processed.\nOnly runs that were declared good after data processing\nwere included in the datasets used for physics analysis.\nThe two steps of the BABAR processing (PC and ER)\ngenerated a large number of Root histograms. The Data\nQuality Group (DQG), led by an experienced BABAR mem-\nber, analyzed the primary histograms produced by the\nprocessing, and was responsible for the quality control of\ndata produced by the experiment. This group also checked\nthe consistency of the skimmed data, and validated soft-\nware releases used to generate Monte-Carlo events. The\nDQG met weekly at SLAC \u2013 to facilitate face-to-face col-\nlaboration between the online and o\ufb04ine teams \u2013 to assess\nthe quality of the runs processed in the past week. Experts\n(one per subsystem) used logbook entries and QA his-\ntograms to \ufb02ag each processed run. They could also look\nat stripcharts showing the run-by-run evolution of key QA\nquantities (both at the detector level and after the event\nreconstruction) versus time. These were very useful to help\nidentify trends which could indicate a developing problem.\nThe processing classi\ufb01cation was similar to the one used\nfor online data: a run could be declared \u2018good\u2019, \u2018\ufb02awed\u2019\n(meaning worth reprocessing, either immediately or after\nsome further data correction) or \u2018bad\u2019. This global \ufb02ag,\nwith optional related comments, was added to a database\nwhich kept track of all these checks and ensured that at\nmost a single processing of a given run was used by ana-\nlysts. Selecting good runs was of course a key task for the\nDQG group; but experts were also working hard to distin-\nguish runs which were bad for well-identi\ufb01ed and perma-\nnent reasons from those which might be later reprocessed\nsuccessfully. To give an idea of the amount of work per-\nformed by the DQG, one can note that the whole BABAR\ndataset (\u03a5(4S), \u03a5(2S), \u03a5(3S) and the \ufb01nal energy scan)\ncontains more than 35,000 physics runs in total. Only the\ncommon and constant e\ufb00orts of both the operations and\ncomputing teams allowed BABAR to log 95% of the lumi-\nnosity delivered by PEP-II and to give the analysts 99%\nof this dataset for physics. Indeed, a few fb\u22121 of data\nwere recovered during the \ufb01nal reprocessing of the \u03a5(4S)\ndataset in 2008.\n3.6.1.3 Data quality monitoring in Belle\nThe monitoring of data quality was done in two levels\nat Belle. The \ufb01rst was the real time monitoring of de-\ntector signals based on sampled level 1 triggered events,\nwhich is called the Data Quality Monitor (DQM). The\ndata of 10-20% of triggered events were sampled at the\nevent builder and sent to the monitor PCs. The data were\nanalyzed to examine the detailed operating status of each\ndetector, and histograms were accumulated including the\ndetector hit-map, the gain variation, etc. The histograms\n\n55\nwere placed in a shared memory so that the contents could\nbe referred to without interrupting the data taking and\nare transferred to the browsing PC on request over the\nnetwork. The task of monitoring the data was performed\nevery 15 minutes by one member of the Belle shift crew,\nthe so called \u201cnon-expert\u201d shifter. Of course the title is\nmisleading since the physicist on shift needed to be well\nacquainted with the detector in order to observe any de-\nviation of the monitored distributions of recorded events\nfrom the expected ones. However it is true that the second\nshift member, the \u201cexpert\u201d shifter, was usually a more se-\nnior member of the collaboration responsible for the data\nacquisition and the slow control monitors. In case of de-\nviations evident in the DQM which the \u201cexpert\u201d shifter\nwas unable to resolve the corresponding detector experts\nwere called in order to resolve any issues.\nThe second level of data quality check is the monitor-\ning of data quality of the full event reconstruction and\nevent classi\ufb01cation. During the DST production, various\nhigher level quantities were accumulated in histograms to\nfacilitate maintaining a high data quality for physics anal-\nysis. This system is called the Quality Assurance Monitor\n(QAM), and is maintained by the QAM group. The his-\ntograms are checked whenever the DST for one run was\nmade. At the beginning of the experiment, the DST pro-\nduction was performed o\ufb04ine and it took a few days to to\nobtain the result from the QAM. Therefore, timely feed-\nback to the team responsible for data taking was di\ufb03cult.\nAfter the introduction of RFARM in 2003, the DST pro-\nduction was fully integrated as a real time processing step,\nand the QAM was merged with the DQM. The RFARM\nwas capable of full event reconstruction together with the\nevent type classi\ufb01cation, and the versatile monitoring of\nspeci\ufb01c physics quantities became possible.\nA mechanism to collect histograms from nodes pro-\ncessing data in parallel was implemented in RFARM and\nthe histograms were collected and merged every 3 min-\nutes during data taking. The resulting histograms were\nsent to the monitor PC of the DQM over the network so\nthat they could be treated as a part of DQM histograms.\nThe shifters checked both of DQM and QAM histograms\nin real time to verify and ensure the high quality of data\nbeing recorded.\nThe real time monitoring of QAM provided by RFARM\nwas a powerful tool for the special runs such as the energy\nscan. For example, the distribution of the Fox-Wolfram\nmoment ratio (R2, see Chapter 9) could be obtained for\nhadronic events during data taking, giving the fraction of\nBB events in the sample in real time, and it was possible\nto know the beam energy of the current scan point pre-\ncisely. It enabled \u201con-the-\ufb02y\u201d determination of next scan-\nning point so that the energy scan could be performed\ne\ufb03ciently.\n3.6.2 B-counting techniques\nKnowing with the best possible precision and with well\nunderstood errors the number of B meson pairs in the\nused data sample is of paramount importance for many of\nthe analyses performed at the B Factories. The techniques\ndeveloped by BABAR and Belle to compute this number for\na given set of data were made part of the central produc-\ntion activities to enforce quality control and consistency\nof the results.\n3.6.2.1 B-counting in BABAR\nFor the \u03a5(4S) running periods, the number of BB events\nin BABAR was computed by subtracting the number of\nhadronic events due to continuum interactions from the\ntotal number of the events in the on-resonance data set:\nNBB = (NH \u2212N\u00b5 \u00b7 Roff \u00b7 \u03ba)/\u03f5BB\n(3.6.1)\nwhere\n\u2013 NH is the number of events satisfying the hadronic\nevent selection in the on-resonance data;\n\u2013 N\u00b5 is the number of events satisfying muon pair selec-\ntion criteria in the on-resonance data;\n\u2013 Roff is the ratio of selected hadronic events to se-\nlected muon pair events in the o\ufb00-resonance (contin-\nuum) data;\n\u2013 \u03ba \u2261\n\u03f5\u2032\n\u00b5\u00b7\u03c3\u2032\n\u00b5\n\u03f5\u00b5\u00b7\u03c3\u00b5 \u00b7\nP\ni \u03f5i\u00b7\u03c3i\nP\ni \u03f5\u2032\ni\u00b7\u03c3\u2032\ni corrects for the changes in con-\ntinuum production cross section (\u03c3) and e\ufb03ciency for\nsatisfying the selection criteria (\u03f5) between on and o\ufb00-\nresonance center-of-mass energies. O\ufb00-resonance quan-\ntities are denoted by a prime. The subscript \u00b5 refers to\nmuon pair events; the various contributions to the con-\ntinuum hadronic cross section, primarily e+e\u2212\u2192qq,\nare denoted by the subscript i. Since the muon pair\nand qq cross sections vary similarly with \u221as (0.7% dif-\nference between on- and o\ufb00-resonance), \u03ba has a value\nclose to 1. The quantity N\u00b5 \u00b7 Roff \u00b7 \u03ba is then the num-\nber of continuum hadronic events in the on-resonance\ndataset.\n\u2013 \u03f5BB = 0.940 is the e\ufb03ciency for produced BB events\nto satisfy the hadronic event selection, calculated un-\nder the assumption that\nB(\u03a5(4S) \u2192B+B\u2212) = B(\u03a5(4S) \u2192B0B0) = 0.5.\n(3.6.2)\nVariations in the amount of non-BB decays of the\n\u03a5(4S), and in the branching ratios of B+B\u2212and B0B0,\nare included in the systematic error, but are not sig-\nni\ufb01cant.\nThe numbers of hadronic events and muon pairs for\neach run was found as part of the skimming process (see\nSection 3.5 above). The hadronic event selection was based\non the number of charged tracks (\u22653), the total measured\nenergy, the event shape, the location of the event ver-\ntex, and the momentum of the highest momentum track.\nMuon pair events were selected using the invariant mass\nof the two tracks, the angle between them, and the energy\nassociated with each track in the calorimeter. When no\nenergy was associated with either track, at least one of\nthe tracks was required to be identi\ufb01ed as a muon in the\nIFR. This happened in roughly the 0.5% of the events,\n\n56\nwhen backgrounds in the calorimeter (such as out-of-time\nBhabha events) would cause a timing mismatch between\nthe calorimeter and the tracking system.\nThe selection criteria were tuned to maximize e\ufb03ciency\nfor BB and \u00b5+\u00b5\u2212events while minimizing sensitivity to\nbeam backgrounds. In particular, the analysis minimized\nthe time variation of the e\ufb03ciency for simulated qq and\n\u00b5+\u00b5\u2212events.\nThe residual non-statistical time variations of the e\ufb03-\nciencies result in an uncertainty in \u03ba and a corresponding\n0.27% systematic error on NBB. The other signi\ufb01cant con-\ntributions to the overall 0.6% uncertainty on NBB include\n0.36% from the uncertainty in the fraction of events that\nfail the selection criteria, mostly low multiplicity BB de-\ncays that fail the requirement on the number of charged\ntracks, and 0.40% from the uncertainty in the modeling\nof the total energy distribution that translates into an un-\ncertainty on the fraction of the events that fail the energy\ncut.\nThe total number of BB events (McGregor, 2008) in\nthe nominal full dataset is NBB = (471.0 \u00b1 2.8) \u00d7 106. In\naddition to the overall number quoted above, NBB was\ntabulated for each run so that analysts could obtain B-\ncounting and luminosity values for any subset of the full\n\u03a5(4S) dataset.\nThe numbers of \u03a5(3S) and \u03a5(2S) mesons produced\nin data sets collected at these resonances have been found\nusing a similar analysis. In this case, the o\ufb00-resonance con-\ntinuum scaling was performed using e+e\u2212\u2192\u03b3\u03b3 events,\ndue to the non-negligible \u03a5 \u2192\u00b5+\u00b5\u2212branching fraction.\nThe hadronic selection criteria were also modi\ufb01ed for these\nanalyses.\nThe \u03a5(3S) and \u03a5(2S) datasets contain (121.3 \u00b1 1.2)\u00d7\n106 and (98.3 \u00b1 0.9) \u00d7 106 Upsilons, respectively. These\nnumbers are calculated using hadronic events, with a cor-\nrection for the fraction of leptonic decays that fail the\nhadronic selection.\nThe primary contributions to the systematic errors are\nuncertainties on the e\ufb03ciency of the total energy selection\n(0.6%), the requirement on the number of tracks (0.4%),\nand the uncertainty on the \u03a5 \u2192\u2113+\u2113\u2212branching fractions\n(0.5%).\n3.6.2.2 B-counting in Belle\nThe \ufb01nal Belle \u03a5(4S) dataset contains (771.6 \u00b1 10.6)\u00d7106\nBB events. As in the BABAR B-counting scheme, this\nnumber is obtained by a subtraction of o\ufb00-resonance ha-\ndronic contributions, as measured by the number of events\nin the previously described HadronBJ skim, from the to-\ntal number of on-resonance hadronic events. In the Belle\ncase, this is calculated as:\nNBB = Non \u2212r(\u03f5q\u00afq)\u03b1N off\nq\u00afq\n\u03f5BB\n(3.6.3)\nwhere\n\u2013 Non is the number of events satisfying the hadronic\nevent selection in the on-resonance data;\n\u2013 r(\u03f5q\u00afq) is the ratio of e\ufb03ciency for q\u00afq events o\ufb00-resonance\nto the e\ufb03ciency for those on-resonance;\n\u2013 \u03b1 is the ratio of the number of Bhabha (e+e\u2212) events or\n\u00b5-pair events observed on-resonance to those observed\no\ufb00-resonance. This is described in more detail below;\n\u2013 N off\nq\u00afq\nis the number of events satisfying the hadronic\nevent selection in the o\ufb00-resonance data;\n\u2013 \u03f5BB is the e\ufb03ciency of the \u03a5(4S) \u2192BB event selec-\ntion criteria for on-resonance data.\nThe values of \u03f5BB remained relatively stable through-\nout the lifetime of Belle. Although it was evaluated on\nan experiment-by-experiment basis, typical values were\naround 99% and di\ufb00ered by less than 0.5% over all ex-\nperiments. The e\ufb03ciency for q\u00afq events showed no strong\ndependence on energy, so r(\u03f5q\u00afq) was determined to be very\nnear to 1, with variations of less than 0.3% over all data\ntaking periods.\nAside from di\ufb00erences in these numerical constants,\nthere is a notable di\ufb00erence from the BABAR approach. For\nmost data taking periods, the o\ufb00-resonance contributions\nare scaled using Bhabha events, rather than \u00b5-pair events.\nOriginally, the average of \u03b1 as calculated with Bhabha\nevents and \u00b5-pair events was used for the \ufb01nal calcula-\ntion. However, for data taken after spring of 2003, the\n\u00b5-pair e\ufb03ciency became signi\ufb01cantly less stable. This is\nattributed multiple e\ufb00ects, including changes to the trig-\nger masks used in the dimuon event identi\ufb01cation, as well\nas some inherent instability due to intrinsic timing varia-\ntions in a subset of these trigger masks. For data following\nthis period, only Bhabha events are used to calculate the\nvalue of \u03b1.\nSince the rate of fermion pair production is identical\nregardless of the type of fermion produced, the approach is\ne\ufb00ectively equivalent, regardless of whether e+e\u2212or \u00b5+\u00b5\u2212\nevents are considered. However, the periods when both\nmethods can be used to calculate \u03b1 allow an estimate of\nsystematic uncertainty on this value. This was determined\nto be a 0.5% uncertainty. This value is considered repre-\nsentative of the uncertainty on \u03b1, even during data taking\nperiods when \u00b5-pair events were not used for this calcula-\ntion.\nSystematic uncertainties are also assigned on the value\nof r(\u03f5q\u00afq), but these are a minor contribution to the overall\nerror, less than 0.2% for all experiments. This uncertainty\nis consistent with the level of variation seen in q\u00afq e\ufb03ciency\nas a function of run range during a single experiment, as\nevaluated by Monte Carlo events generated with condi-\ntions matched to those of the corresponding running pe-\nriod. A sideband in the z-position of the measured event\nvertex is used to study systematic uncertainties due to the\ninclusion of beam gas events, but such uncertainties are\nbelow 0.1%.\nUltimately, the uncertainty on NBB is dominated by\nthe systematic uncertainty from \u03b1, and is approximately\n1.5% for most of the Belle data.\nThe B-counting and b cross section measurement\nmethodology used by Belle in the context of B0\ns mesons\ncollected at the \u03a5(5S) is discussed in detail Chapter 23.\n\n57\nSLAC\nLDAP,NTP,DNS,DHCP \n(Primary)\nbbrltda01\nBBR-LTDA-VM\nBBR-LTDA-SRV\nBBR-LTDA-LOGIN\nVM Guest \nSL4/SL5/SL6\nx54\nbbrltda02\nbbrltda03\nMySQL\n(Master)\nPBS, Maui, \nXROOTD, TRScron\nNIC\nVM\nVirtual Bridge\nNIC\n2TB\nIaaS Client\nx24\nx20\nBatch and XROOTD servers \nInfrastructure servers\nBBRLTDA \nLogin Pool\nMySQL\n(Slave)\nNIC\nVM\nVirtual Bridge\nNIC\n24TB\nIaaS Client\nx22\nXROOTD\nTest\nRed Hat 6 Hosts\n(Centrally Managed) \nCode Repositories, \nHome Directories\nUser and \nProduction Areas\nCron and Batch\nServer \nIdentification and \nNetwork Services \nServers\nDatabase Servers\nNFS Servers\nTest Server\nLDAP,NTP,DNS,DHCP\n(Secondary)\nRouter/\nFirewall\nFigure 3.7.1. The LTDA cluster provides both storage and CPU resources in order to support analysis of BABAR data in\nthe future. It includes database servers, code repositories, user home directories, working areas, production areas, and XRootD\ndisk space. The isolation of back versioned components running on the batch system is implemented with \ufb01rewall rules: virtual\nmachines (VM\u2019s) are not allowed to connect to either the SLAC network or the world, and only well de\ufb01ned services are allowed\nbetween the VM network and the service network \u2013 see text for details.\n3.7 Long Term Data Access system\n3.7.1 The BABAR approach\nThe Long Term Data Access (LTDA) system is designed\nto preserve the capability of analyzing the BABAR data\nuntil at least the end of 2018. This requires the support\nof code, repositories, data, databases, storage, and CPU\ncapacity. Special attention has to be devoted to the docu-\nmentation. The system maintenance e\ufb00ort has to be min-\nimized, including hardware maintenance, operating sys-\ntems (OS) upgrades, tool upgrades, code validation, etc.\nThe use of a contained system o\ufb00ers a controlled environ-\nment and simpli\ufb01es documentation and user support. The\nBABAR analysis environment is supported with a frozen\noperating system infrastructure rather than actively mi-\ngrating to future software environment as needed. The\nBABAR framework preserves its full capability of expan-\nsion and development, and is able to support future new\nanalyses.\nA long-lived frozen BABAR environment has to be\nmaintained despite the evolving nature of hardware and\nOS. Also the support of back versioned OS is di\ufb03cult,\nbecause future security exploits will require unknown\npatches. Hardware virtualization solves the hardware sup-\nport problem for the foreseeable future and the use of OS\nimages on virtual machines (VM\u2019s) solves the system ad-\nministration problem, replacing it with the easier manage-\nment of a small number of OS images.\nThe design of the LTDA cluster architecture takes into\naccount the possibility that systems can be compromised\nfrom the security point of view and, in order to reduce\nrisk to an acceptable level, a risk-based approach has been\ntaken:\n\u2013 Assume that systems that can be compromised, are\nactually compromised.\n\u2013 Compromised components of the LTDA will be de-\ntectable by logging and monitoring.\n\u2013 The LTDA will prevent accidental modi\ufb01cation or dele-\ntion of the data.\n\u2013 The dynamic creation of VM\u2019s from read-only images\nadds a small layer of security, by avoiding the compro-\nmised elements from being persisted beyond the de-\nstruction of the VM.\nA representation of the cluster together with the lay-\nout of the network is shown in Figure 3.7.1. All sessions\nrequiring back versioned platforms, including interactive\nsessions for debugging, run in VM\u2019s on the batch system.\nThe isolation of the back versioned components is realized\n\n58\nthrough \ufb01rewall rules that are implemented in the LTDA\nswitch. The LTDA network is composed of three subnets\nto which di\ufb00erent elements of the cluster are attached. All\nthe back versioned components (VM\u2019s) are connected to\na VM subnet (BBR-LTDA-VM) and connection rules are\nenforced with the service network, (BBR-LTDA-SRV) in-\ncluding the VM\u2019s physical hosts and other infrastructure\nservers (always patched and up to date), and the login\nnetwork (BBR-LTDA-LOGIN, always patched and up to\ndate). The login pool is the only point of access for the\nusers.\nThe LTDA batch resources are managed by PBS Torque\n(Torque, 2012) and Maui Scheduler (Adaptive Comput-\ning, 2012) is used as the job scheduler. The virtualiza-\ntion layer is implemented using QEMU (Qemu, 2012) and\nKVM (KVM, 2012). The data to which the user jobs need\nto access are managed by XRootD and staged on the disks\nof the batch servers on demand. Each batch and XRootD\nserver has 12 disks of 2 TB, 11 of which are dedicated\nto XRootD. The last 2 TB disk of each server is used as a\nscratch area by the VM\u2019s running on the node. Each batch\nserver has 12 physical cores of which one is dedicated to\nthe host itself and the XRootD service. The other 11 cores\nare used to run virtual machines. With hyper-threading\non, each node can run up to 22 VM\u2019s. The cluster also\nincludes 20 servers used uniquely as a batch resource.\nThe LTDA cluster has been running in production\nmode since March 2012. All the active BABAR users have\nan account on the cluster with a 1GB NFS home direc-\ntory. So far about 50 users have run jobs on the system\nwhile about 15 of them have made heavy use of the sys-\ntem. About 2 million jobs have been completed in the last\nyear.\nIn almost one year of active use some \ufb01ne tuning has\nbeen necessary. NFS connection parameters have been\nadapted to handle the high number of NFS accesses occur-\nring when the queues are \ufb01lled to their maximum capacity.\nOn two occasions an upgrade of the host kernels has dis-\nrupted the system network. We have now established a\nvalidation procedure which allows us to test all the up-\ngrades on a test machine, con\ufb01gured exactly like a batch\nserver, before they are deployed to the entire cluster.\nMonitoring of the servers, the services and the batch\nqueues is also implemented. So far the cluster has met and\nexceeded the expectations.\n3.7.2 The Belle approach\nThe Belle group recently discussed their policy on data\npreservation (Akopov et al., 2012). It was decided that the\nBelle data will not be released to the public domain until\nthe time the statistics of Belle II supersedes the Belle data\nand all Belle members (and Belle II members) lose inter-\nest in Belle data. This situation will likely occur around\n2017-2018, a couple of years after the commissioning of\nthe SuperKEKB accelerator. Two approaches are consid-\nered to provide an environment to access Belle data even\nin the Belle II experiment period. One is porting the Belle\nsoftware to the new computing system for the Belle II ex-\nperiment. The other is converting the Belle data to the\ndata format adopted in Belle II so that it can be read\nin the Belle II software framework. The former approach\ndoes not require signi\ufb01cant modi\ufb01cations of the current\nsoftware. However, every time the computing system is\nreplaced with a new one (which typically takes place ev-\nery three or four years at KEK) the portability of the\ndata has to be con\ufb01rmed. For the latter case, one needs\nto prepare conversion software from the Belle data format\nto the Belle II one. Furthermore, the Belle data conver-\nsion has to be done in a systematic manner considering\nthe available hardware and human resource. But once it\nis converted, Belle users can keep using it in the Belle II\nsoftware framework. In both cases, the current Belle data\nhas to be migrated to a new format.\n\n59\nPart B\nTools and methods\nChapter 4\nMultivariate methods and analysis\noptimization\nEditors:\nFrank Porter (BABAR)\nAdditional section writers:\nPiti Ongmonkolkul\nMultivariate analysis (MVA) is widely used to extract\ndiscriminating information from data. This chapter pro-\nvides a general discussion of the most relevant MVA tools\nused by BABAR and Belle, their mathematical proper-\nties, and optimization methods. Speci\ufb01c multivariate al-\ngorithms used for charged particle identi\ufb01cation (PID),\nB-\ufb02avor tagging and discrimination against background\nare described in Chapters 5, 8, and 9, respectively.\n4.1 Introduction\nThe goal of analysis optimization is to make optimal use\nof the available data to perform a measurement of phys-\nical interest. Depending on the circumstance, the exact\nmeaning of \u201coptimal\u201d may di\ufb00er. However, the essential\nnotions are those of e\ufb03ciency (minimizing variance) and\nrobustness. The goal of e\ufb03ciency must be interpreted in\nthe context of being unbiased, or negligibly biased. Ro-\nbustness is used here in the broader sense, including both\nsensitivity to model errors and sensitivity to statistical\noutliers. An analysis that minimizes statistical uncertain-\nties may not be optimal if the systematic uncertainties are\nlarge.\nWith the large, complex event samples from present\nexperiments, plus the improvements in computing tech-\nnology, analysis methods have evolved. This evolution has\nbeen aided by advances in the available statistical method-\nologies.\nThe optimization problem may be viewed as a problem\nin classi\ufb01cation: For example, we wish to classify a set of\nevents according to \u201csignal\u201d or \u201cbackground\u201d. Thus, we\nhave the problem of optimizing a binary decision process.\nThis may be generalized to more than two classes, but\nthe binary decision covers much of what we do. Another\npossible approach is to de\ufb01ne some weight, or probability\nfor each event to belong to the various classes. The tech-\nnique of\nsPlots, discussed in Chapter 11, provides such\nan example.\nIt should be remarked that there are many variations\non the methods presented. The discussion here is introduc-\ntory rather than comprehensive. The reader is referred to\nthe text by Hastie, Tibshirani, and Friedman (2009) for a\nmore complete treatment of most of this material.\n4.2 Notation\nAs is common in physics, we adopt an informal notation\neschewing a notational distinction between a random vari-\nable and an instance. Our variables may be discrete or\ncontinuous, but for convenience the treatment here is in\nterms of continuous variables. The particle physics notion\nof an \u201cevent\u201d maps easily onto the statistical concept of\n\u201cevent\u201d.\nWe suppose that each event corresponds to an inde-\npendent identical random sampling in an \u2113-dimensional\nsampling space. An event is described by the vector x =\n(x1, . . . , x\u2113). The variables used to optimize the selection\nof events are called \u201cselection variables\u201d. We\u2019ll denote\nthese with the symbol s = (s1, . . . , sk). These are func-\ntions of the sampling vector, s = s(x). In some cases, s\nis simply a subset of the x variables. The dimension, k,\nof s may itself be varied during the optimization process.\nThe term multivariate is used to describe situations where\nwe analyse a multi-dimensional hyperspace s, using some\nwell de\ufb01ned methodology.\nThe means of the selection variables are denoted \u03be =\n(\u03be1, . . . , \u03bek). The covariance matrix is\n\u03a3 = E\n\u0002\n(s \u2212\u03be)(s \u2212\u03be)T \u0003\n,\n(4.2.1)\nwhere the \u201cE\u201d denotes expectation value. Uncertain pa-\nrameters of the distribution of the selection variables are\ndenoted with \u03b8. If there are r such parameters, we de-\nnote them as \u03b8 = (\u03b81, . . . , \u03b8r). The quantities \u03be and \u03a3\nmay be functions of \u03b8. Estimators for \u03b8 are denoted b\u03b8.\nIf the sampling distribution for the selection variables is\nmultivariate normal, the corresponding density is\nN(s; \u03be, \u03a3) \u2261\n1\np\n(2\u03c0)k det \u03a3\nexp\n\u0014\n\u22121\n2(s \u2212\u03be)T \u03a3\u22121(s \u2212\u03be)\n\u0015\n.\n(4.2.2)\n4.3 Figures of merit\nWe often reduce the optimization of an analysis to the\nproblem of maximizing or minimizing the expected value\nof a \ufb01gure of merit (FOM). \u201cLoss functions\u201d, typically\nmaking some estimate of error rate, are often used for\nthis, and are discussed, for example, in Hastie, Tibshirani,\nand Friedman (2009). Here, we mention some of the more\ncommon FOMs used speci\ufb01cally in particle physics.\nIf we are looking for some yet unobserved new e\ufb00ect,\nwe might optimize on the expected signi\ufb01cance of that\nnew e\ufb00ect. Suppose S is the expected number of signal\nevents after selection (depending on the analysis), and B\nis the expected number of background events, which we\nassume we can estimate from known processes. The to-\ntal number of events observed is N, including both signal\n\n60\nand background. The size of a possible signal is estimated\naccording to bS = N \u2212B. An estimate for the size of \ufb02uctu-\nations in background is\n\u221a\nB. Thus, S/\n\u221a\nB is related to the\nsigni\ufb01cance of a possible signal. In such a measurement,\nthis provides a \ufb01gure of merit to be maximized. The left\nside of Fig. 4.3.1 shows an example of this (with detection\ne\ufb03ciency substituting for S, that is, the e\ufb03ciency is S\ndivided by expected number of produced signal events in\nthe dataset) in the Belle analysis searching for \u03c4 \u2192\u2113hh\u2032\nlepton \ufb02avor violating decays (Miyazaki, 2013). Another\nexample can be found in Section 18.4.4.2, where the anal-\nyses that resulted in the observation of \u03b7b(1S) and \u03b7b(2S)\nmesons used the test statistic S/\n\u221a\nB to optimize event\nselection criteria.\nAnother approach to a \ufb01gure of merit for the case of\na search for a new e\ufb00ect has been suggested by Punzi\n(2003b). This approach de\ufb01nes a \u201csensitivity region\u201d for\nthe possible parameters, m, of the new e\ufb00ect. This def-\ninition is based on the con\ufb01dence level of the region for\nm that will be quoted if evidence for a new e\ufb00ect is not\nclaimed. The \ufb01gure of merit then corresponds to maximiz-\ning the size of the sensitivity region. A simple form of this\n\ufb01gure of merit is\n\u03f5\nn\u03c3/2 +\n\u221a\nB\n,\n(4.3.1)\nwhere \u03f5 is the e\ufb03ciency to observe a signal event, B is the\nexpected background, and n\u03c3 is the desired one-tailed sig-\nni\ufb01cance (in order to claim a discovery) of an observation\nexpressed in standard deviations of a Gaussian probability\ndistribution. This FOM has been used in some analyses,\nfor example, in BABAR\u2019s search for for B+ \u2192\u2113+\u03bd\u2113recoil-\ning against B\u2212\u2192D0\u2113\u2212\u00af\u03bdX (Aubert, 2010a).\nOn the other hand, we may wish to get the most pre-\ncise measurement of some known process. In this case,\nthe signal is proportional to S, and the estimated error\non the signal is\n\u221a\nS + B (i.e., the expected \ufb02uctuation on\nthe total number of events). Thus, to optimize on preci-\nsion (of signal yield), we wish to maximize the expected\nvalue of S/\n\u221a\nS + B. This can be viewed in an equivalent\nform: suppose that there are a total of NS signal events\nin the dataset before event selection. Selection involves\nsome e\ufb03ciency, \u03f5, to select signal events, so that we ex-\npect S = \u03f5NS. Then this FOM may be expressed as\n\u221aNS\np\n\u03f5 \u00b7 S/(S + B), where the factor S/(S + B) is the\nsignal purity in the selected sample. This makes explicit\nthe trade-o\ufb00between e\ufb03ciency and purity in the opti-\nmization.\nOf course, the idea of optimizing precision applies more\ngenerally than measurements of signal strength, for exam-\nple in the measurement of CP asymmetries. An example\nof optimizing on expected precision is shown in the right\nside of Fig. 4.3.1, for the Belle analysis measuring yCP in\nD0 \u2212D0 mixing (Staric, 2007).\nIn practice, in a complicated analysis, the optimization\nprocess is usually broken into more-or-less disjoint aspects,\nsuch as topological background suppression (e.g., Chap-\nter 9) or particle identi\ufb01cation (Chapter 5). For these sit-\nuations we often optimize on the signal purity, S/(S +B),\nor equivalently, the \u201csignal-to-noise\u201d: S/B. For example,\nin the optimization of PID, the goal is to get the best\ne\ufb03ciency for the desired particle type for a given con-\ntamination probability, or variations on this idea. A use-\nful graphical tool is known (from its engineering origins)\nas the \u201creceiver operating characteristic\u201d, a plot showing\nthe trade-o\ufb00between e\ufb03ciency and purity, or variants.\nFig. 4.4.1 provides an example in the context of PID, dis-\ncussed later in this chapter. The idea is used as well in B\nmeson reconstruction, for example in Fig. 7.4.3. Depend-\ning on the application, it may be acceptable to have a\ngreater or lesser contamination. That is, we may not op-\ntimize strictly on the particle identi\ufb01cation purity in the\ncontext of a given analysis. This leads to the provision of\nseveral PID selectors. In principle, the particle identi\ufb01ca-\ntion could be optimized along with the subsequent analy-\nsis, but this is unwieldy, and the provision of a choice of se-\nlectors approximates this. Providing pre-de\ufb01ned selectors\nalso facilitates re-use of work done to estimate systematic\nuncertainties.\nThere are still other \ufb01gures of merit that may be\nused in classi\ufb01cation problems. The misclassi\ufb01cation error,\nequal to the fraction of the sample that is incorrectly clas-\nsi\ufb01ed may be used. In building decision trees, two variants\nof this idea are commonly adopted, the \u201cGini index\u201d and\nthe \u201ccross-entropy\u201d. These FOMs are available in most\nmultivariate classi\ufb01cation packages in use in HEP and are\nde\ufb01ned below in the discussion on decision trees, although\ntheir application is not limited to decision trees.\n4.4 Methods\nStatistical methods and tools of increasing sophistication\nused to optimize analyzes are described in the remainder\nof this chapter. Beforehand, it is important to stress that\nfor many methods to be successful, two mandatory steps\nare required : training and validation. There are a few ex-\nceptions to this rule, where one can analytically compute\nthe parameters required to perform an optimization.\nIt is dangerous to optimize a selection with the ac-\ntual data that is to be used in the measurement. Such\nan approach is prone to tuning on \ufb02uctuations and the\nproduction of biases. For a simple example, suppose we\nare tuning an analysis for a particular signal, using the\nactual data. If we try to optimize S/B, say, we will \ufb01nd\nselection criteria that tend to favor signal-like events, tun-\ning on any upward \ufb02uctuations. This will tend to bias our\nmeasurement of the signal strength toward high values.\nNevertheless, this has been done extensively in particle\nphysics, sometimes successfully, but sometimes with dis-\nastrous results. With an awareness of the issues, BABAR\nand Belle have gone to some length to avoid relying on the\nmeasurement data for the optimization. Note that these\nissues are discussed in a somewhat di\ufb00erent context in\nChapter 14.\nThus, BABAR and Belle take the approach of using a\ntraining dataset for the optimization. This could be simu-\nlated data, sidebands to the data that will not be used in\nthe measurement, or a dataset that has similarities with\nthe measurement data. A feature of the training dataset is\n\n61\n0\n0.005\n0.01\n0.015\n0.02\n0.6\n0.8\n1\n\u01eb/\n\u221a\nB\ncos \u03b8\n0.82\n\u2206q (MeV)\nExpected uncertainty on yCP (%)\n0\n0.1\n0.2\n0.3\n0.4\n0\n1\n2\nFigure 4.3.1. Examples of \ufb01gures of merit used in optimization of Belle analyses. Left: Optimization on \u03f5/\n\u221a\nB in the search for\nthe lepton \ufb02avor violating decay \u03c4 \u2192\u00b5\u03c0\u03c0 (see Chapter 20). The horizontal axis is the cosine of the angle between the missing\nmomentum vector and the direction of the tagging charged particle, in the CM frame. Belle internal, from the (Miyazaki, 2013)\nanalysis. Right: Optimization on expected uncertainty in the measurement of the yCP parameter in D0 \u2212D0, see Section 19.2.3.\nThe horizontal axis is the measured kinetic energy released in the candidate D\u2217decay. Belle internal, from the (Staric, 2007)\nanalysis.\nthat it is known (or known well enough) which class each\nevent belongs to, so that the FOM may be computed. The\nselection criteria are optimized using the training dataset,\nthen applied to perform the desired measurement.\nA further re\ufb01nement in method is the notion of val-\nidation. It is possible that the training dataset contains\n\ufb02uctuations that result in criteria that are not broadly\noptimal. This is related to the problem of \u201cover-training\u201d,\nin which the training provides a model exquisitely tuned\nto the training sample, but with no real advantage on an\nindependent sample. E\ufb00ectively, the model is made very\ncomplicated when the underlying distribution is simpler.\nSince the training must be useful on an independent sam-\nple (it has to \u201cgeneralize\u201d), this erratic tendency has to\nbe regularized in some way. For example, another dataset\nmay be used to \u201cvalidate\u201d the selection and stop the op-\ntimization procedure (training) when no further improve-\nment is obtained. This helps to avoid the phenomenon\nof over-training. A variant on this is \u201ccross-validation\u201d,\nin which the training dataset is split into multiple equal\nsubsets, and each of the subsets is used to validate the\ntraining on the remaining (aggregated) subsets.\nThe estimate of the e\ufb03ciency obtained using the train-\ning/validation datasets may be biased too high. This is be-\ncause the \ufb01nal selection criteria actually depend on both\nthe training and validation datasets, and \ufb02uctuations in\neither dataset may a\ufb00ect the tuning in the optimization.\nTo avoid this, a further independent \u201ctest\u201d dataset, not\nused in the optimization process, may be used to obtain\nan unbiased e\ufb03ciency estimate.\nSome classi\ufb01cation methods lend themselves more eas-\nily than others to interpretation, for example, in deciding\nhow important the various inputs are. However, for a com-\nplicated problem a dedicated procedure may be required\nto understand which variables are most important, and\nperhaps eliminate ones that are not useful. A simple ap-\nproach is to remove one or more variables at a time to see\nthe e\ufb00ect of this on the classi\ufb01er performance.\n4.4.1 Rectangular cuts\nWhen variables are uncorrelated, a selection may be op-\ntimized by looking at the e\ufb00ect of each variable in turn.\nThis gives a selection region that is a hyper-rectangle in\nthe space of selection variables, with sides aligned with\nthe coordinate axes of the selection variables. Such selec-\ntion criteria are known as rectangular cuts. They have the\nmerits of ease of application, optimization, and interpre-\ntation. They are widely used, especially in \u201cpre-selection\u201d\n(e.g., skim production) where the selection is still rela-\ntively inclusive, and more sophisticated optimization is\nnot essential.\nThis simple approach may be used even if variables\nare correlated, however the result may no longer be op-\ntimal. In this case it may be possible to do considerably\nbetter with more sophisticated methods. For example, a\nre\ufb01nement is possible, in which arbitrary regions of sample\nspace may be approximated by sequences of rectangular\ncuts. A form of this approach is the technique of the de-\ncision tree, described further below.\nWhen there are correlations among variables, we may\nalso look for transformations that produce a set of uncor-\nrelated variables, and then apply rectangular cuts in the\ntransformed space.\n4.4.2 Likelihood method\nThe likelihood function provides a mapping of the obser-\nvations with often bene\ufb01cial properties. This is employed,\n\n62\nfor example, in the \u201clikelihood method\u201d for particle iden-\nti\ufb01cation (Chapter 5). In this approach, detector measure-\nments such as dE/dx, time-of-\ufb02ight, calorimeter response,\nand muon detector response are combined by multiplying\ntheir likelihoods for a given particle type interpretation.\nThen rectangular cuts are applied to ratios of these likeli-\nhoods for di\ufb00erent particle hypotheses. This approach to\ncombining the available information has the merits of ease\nof application and interpretation. It also has some moti-\nvation from the fact that the likelihood ratio provides a\nuniformly most powerful test in the case of simple hy-\npotheses. Table 5.2.1 shows a comparison of \u201ccut-based\u201d\n(that is, making rectangular cuts on the basic detector\nquantities) and \u201clikelihood based\u201d muon selection: for an\ne\ufb03ciency loss of less than 10%, the likelihood method de-\ncreases the pion contamination by approximately 30%.\nThe likelihood function is constructed from the sam-\npling p.d.f., so the form of the distribution must be known\nincluding any correlations among variables. This can be a\ndi\ufb03culty with this approach if this information is not read-\nily available. The \u201csupervised learning\u201d methods (neural\nnetworks and decision trees) described below have an ad-\nvantage in this respect, because subtle features, includ-\ning correlations, are usually included automatically in the\ntraining samples. Maximum likelihood \ufb01ts have been used\nwidely at the B Factories and are discussed in Chapter 11.\n4.4.3 Linear discriminants\nA linear discriminant is some linear function of the sample\nevent variables:\nL = A + B \u00b7 s,\n(4.4.1)\nwhere A and B are independent of s. The idea here is that\nL may be such that it tends to take on di\ufb00erent values for\ndi\ufb00erent classes (i.e., signal or background) of event. Thus,\nL may be useful for event classi\ufb01cation. The optimization\nprocess here is to select those values of A and B that\nproduce the best FOM.\nThe most commonly used linear discriminant is the\n\u201cFisher discriminant\u201d (Fisher, 1936), motivated in the\ncase of multivariate normal sampling. If signal is described\nby fS(s) = N(s; \u03beS, \u03a3S) and background by fB(s) =\nN(s; \u03beB, \u03a3B), we may form the logarithm of the likeli-\nhood ratio for an event to be signal or background:\nln \u03bb = ln wSfS(s)\nwBfB(s)\n= ln wS\nwB\n\u22121\n2 ln det \u03a3S\ndet \u03a3B\n\u22121\n2\n\u0000\u03beT\nS \u03a3\u22121\nS \u03beS \u2212\u03beT\nB\u03a3\u22121\nB \u03beB\n\u0001\n+sT \u0000\u03a3\u22121\nS \u03beS \u2212\u03a3\u22121\nB \u03beB\n\u0001\n\u22121\n2sT \u0000\u03a3\u22121\nS\n\u2212\u03a3\u22121\nB\n\u0001\ns,\n(4.4.2)\nwhere wS and wB are the probabilities (weights) for an\nevent to be signal or background, respectively. If the co-\nvariance matrices for signal and background are the same,\n\u03a3S = \u03a3B = \u03a3, then\nln \u03bb = ln wS\nwB\n\u22121\n2\n\u0000\u03beT\nS \u03a3\u22121\u03beS \u2212\u03beT\nB\u03a3\u22121\u03beB\n\u0001\n+ (\u03beS \u2212\u03beB)T \u03a3\u22121s.\n(4.4.3)\nThis is now a linear expression in s, referred to as the\n\u201cFisher discriminant\u201d.\nIf any of \u03beB,S or \u03a3B,S are unknown, they must be esti-\nmated, for example with a least-squares or maximum like-\nlihood \ufb01t to the entire dataset. It is important to remem-\nber the assumption that \u03a3B = \u03a3S. There is no general\nreason why this should be true. If not equal, improve-\nment (possibly substantial) in the analysis may some-\ntimes be obtained with the full \u201cquadratic discriminant\u201d\nof Eq. (4.4.2). This is discussed and demonstrated with\na simple example in Narsky (2005b, Section 2.1). Linear\ndiscriminants have been used widely at the B Factories,\nfor example see Section 9.5 which contains a detailed de-\nscription of the Belle strategy for continuum background\nsuppression for B meson decay analyses.\n4.4.4 Neural nets\nThe basis of the neural net (see, for example, Haykin\n(2009); MacKay (2003) for thorough developments) is a\nmodel for biological neurons, in which the \ufb01ring of a neu-\nron occurs once the summed \u201cinputs\u201d cross some thresh-\nold. In practice, this discontinuous behavior is smoothed\nout to a continuous function such as the sigmoid:\n\u03c3(X) =\n1\n1 + e\u2212X ,\n(4.4.4)\nwhere X is a parameterized function of the inputs (for\nexample, Eq. (4.4.5) below). As with other classi\ufb01cation\nmethods, the neural net is trained, validated, and tested\non datasets with known outcomes. The training involves\noptimizing the values of parameters in the net to, for ex-\nample, minimize classi\ufb01cation error.\nThe simplest neural net consists of one \u201cneuron\u201d. Sup-\npose the function X is of the linear form X = Pk\ni=1 wisi+b\n(which is the same form as a Fisher discriminant). To use\nthis net as a binary classi\ufb01er, we choose a threshold Xc\nsuch that if X > Xc, the net returns a one, otherwise it\nreturns a zero. Such a basic element is called a \u201cpercep-\ntron\u201d, which represents a decision boundary in the prob-\nlem space. Complex networks may be built out of these.\nNote that the function of the parameters w is to assign\nweights to the di\ufb00erent inputs, and the parameter b acts\nas a \u201cbias\u201d, changing the location of the decision threshold\nbut not the relative weightings.\nA feed-forward neural net (or \u201cmultilayer perceptron\u201d)\nconsists of layers \u2013 an input layer, an output layer, and\nany number of \u201chidden\u201d layers in between. Each layer has\na number of nodes that take inputs from the next lower\nlayer and provide outputs to the next higher layer. The\ninput layer consists simply of the k selection variables\nsi, i = 1, . . . , k, each variable represented by a node. Let\n\n63\nus suppose for this discussion that our network has a sin-\ngle hidden layer. Each node in the hidden layer represents\na numeric value obtained by a non-linear transformation\non a linear combination of the input nodes. For example,\nusing the sigmoid, the hidden nodes h1, . . . , hp compute\nthe values:\nhi = \u03c3\n\uf8eb\n\uf8ed\nk\nX\nj=1\nwijsj + bi\n\uf8f6\n\uf8f8,\ni = 1, . . . , p.\n(4.4.5)\nThe inclusion of a constant bias term, bi, may be thought\nof as including a linear term corresponding to an addi-\ntional input equal to the constant one.\nThe output layer may consist of multiple nodes for\nmultiple classes; often we have two output nodes, which\nlogically may be taken as a single output, as appropriate\nfor the two-class \u201csignal\u201d vs \u201cbackground\u201d selection. We\nwill assume this case here. The output is computed from\nthe hidden layer by taking linear combinations of the hid-\nden layer results,\nyj = aj +\np\nX\ni=1\ncjihi,\nj = 1, 2.\n(4.4.6)\nWe may then obtain a number between 0 and 1 expressing\nthe output of the neural net, for example, by\nt = ey1/ (ey1 + ey2) ,\n(4.4.7)\nwhere y1 is the \u201csignal\u201d class output. In the two class\nproblem, a single output is often taken using the sigmoid\nwhere t \u2261\u03c3(y2 \u2212y1); Eq. (4.4.7) is a generalization that\nmay be extended to an arbitrary number of classes. Once\nthe neural net is trained, large values of t indicate signal;\nan analysis can make an event selection based on t. It\nmay be remarked that the di\ufb00erence between the neural\nnet and a linear model is the use of non-linear \u201cactivation\nfunctions\u201d; in the present example, the sigmoid.\nTraining of the neural net consists in searching for opti-\nmal values of the net parameters, where optimal is de\ufb01ned\nin terms of minimizing a measure of the classi\ufb01cation er-\nror rate. For the example net, this training corresponds to\n\ufb01nding values for the p \u00d7 k parameters w, the p parame-\nters b, the two parameters a, and the 2 \u00d7 p parameters c.\nThe optimal values are often found by a gradient descent\nmethod, referred to as \u201cback propagation\u201d in this context.\nA popular methodology is the Bayesian neural net-\nwork (for example see the discussion on hadronic tag re-\nconstruction for Belle in Section 7.4.1). In this case, the\noutput of the net is interpreted as a posterior probability\nto be, e.g., signal. Regularization of the network may be\nachieved with the help of prior distributions (often Gaus-\nsian) in the parameters.\n4.4.5 Binary decision trees\nThe idea of a binary decision tree [see for example Hastie,\nTibshirani, and Friedman (2009, Chapter 9)] is a recur-\nsive search for the best binary selection over the set of\nvariables. Given a (training) dataset, we search for the\nvariable and a selection (or \u201ccut\u201d) value which provides\nthe best FOM. This split results in two \u201cnodes\u201d, one classi-\n\ufb01ed as \u201csignal\u201d, the other as \u201cbackground\u201d. A new search\nis applied to each of these nodes, resulting in two further\nsplits. The process is repeated until further splits do not\nimprove the FOM or fall below a speci\ufb01ed minimum num-\nber of events. Trees that are grown by the latter criteria\nmay be \u201cpruned\u201d to eliminate splits that fail some worthi-\nness criterion. The result is a set of rectangular regions in\nour selection variable space, each classi\ufb01ed as either signal\nor background. In the tree analogy, the set of \ufb01nal nodes\nat the end of the chain are called \u201cleaves\u201d\u2019.\nIn binary decision trees, a commonly used FOM, be-\nsides simply computing the average error (misclassi\ufb01ca-\ntion error), is the \u201cGini index\u201d, G(p) = \u22122p(1\u2212p), where\np is the fraction of correctly classi\ufb01ed events at the given\nnode. For example this FOM has been used in a num-\nber of inclusive B \u2192X\u2113+\u2113\u2212analyses described in Sec-\ntion 17.9. A similar alternative is the \u201ccross-entropy\u201d,\nQ(p) = p log p+(1\u2212p) log(1\u2212p). At each split, the values\nof Q of the two daughter nodes are added, weighted by\nthe numbers of events (or other weights). The split that\nmaximizes this sum is chosen. However, these FOMs are\nnot necessarily the ones we really wish to optimize on, and\nsome available tools permit user-de\ufb01ned FOMs.\nAn individual decision tree is a \u201cweak\u201d classi\ufb01er (or\n\u201cweak learner\u201d) in general. That is, it has a probability\ngreater than random of making a correct classi\ufb01cation,\nbut possibly not much greater. It has been trained with a\nparticular set of assumptions, such as the relative impor-\ntance of training events. Better predictive power may be\nobtained with methods that combine decision trees trained\nin di\ufb00erent ways. We introduce some of these techniques\nbelow.\nA feature of decision trees is that they are intuitive. We\ncan follow the progress along the tree and see how deci-\nsions are being made as well as see the relative importance\nof the di\ufb00erent inputs as discriminators. By studying the\ntrees produced in a given problem, we may eliminate vari-\nables that have little separation power, or are redundant\nwith other variables.\n4.4.6 Boosting\nThe idea of boosting [see for example Hastie, Tibshirani,\nand Friedman (2009, Chapter 10)] is to take a set of weak\nlearners and combine them in such a way as to obtain\na \u201cstrong learner\u201d: roughly, a classi\ufb01er whose output er-\nror can be made arbitrarily small in a computationally\ne\ufb03cient manner. Here, we introduce the technique in the\ncontext of boosting decision trees, although it can be used\nas well with other classi\ufb01ers, such as neural nets.\nIn boosting trees, we take the results of training a tree\nand increase the weight (\u201cboost\u201d) of misclassi\ufb01ed events in\nforming a new tree. This process is repeated, and the out-\nputs of the trees combined. For example, we consider the\npopular adaptive \u201cAdAboost\u201d methodology (Freund and\nSchapire, 1997; Hastie, Tibshirani, and Friedman, 2009):\n\n64\n\u2013 Start by assigning an equal weight to each event.\n\u2013 Train a tree with these weights.\n\u2013 Compute the weighted average error \u03f5 over all events.\n\u2013 Compute \u03b1 = log [(1 \u2212\u03f5)/\u03f5].\n\u2013 Increase the weight of misclassi\ufb01ed events by a factor\nof e\u03b1.\n\u2013 Repeat the training with these weights, using the same\nclassi\ufb01cation algorithm.\nAfter some desired number of iterations, the classi\ufb01cation\nof an event is computed as an average over all of the trees,\nweighted by their values of \u03b1. The AdAboost is set as\na default option within Toolkit for Multivariate Analysis\n(TMVA) and is used for the \ufb01nal BABAR PID algorithm\ndiscussed in Chapter 5.\n4.4.7 Bagging and random forest\nIn \u201cbagging\u201d [Bootstrap AGGregatING; see, e.g., Hastie,\nTibshirani, and Friedman (2009, Chapter 8)] decision trees\n(or other classi\ufb01ers in general) are constructed many times\non bootstrap replicas of the training data. A bootstrap\nreplica is a sampling, with replacement (that is, the da-\ntum is \u201creturned\u201d to the sample before the next sampling),\nof events from the training dataset. An event may appear\nmultiple times in the replica. The point of the bootstrap\nis that the dataset itself is used as an empirical estimator\nfor the underlying sampling distribution. Hence, multi-\nple occurrences of an event are simply a consequence of\nidentically distributed, independent samplings from this\ndensity estimator. The bootstrap replication results in an-\nother training dataset of the same size as the original. The\n\ufb01nal classi\ufb01er is obtained by taking the majority vote of\nthe individual classi\ufb01ers.\nIf each bagging replica is passed through the same\ntraining algorithm, there will generally be signi\ufb01cant cor-\nrelations among the resulting decision trees. This tendency\ncan be mitigated by the \u201crandom forest\u201d. In a random for-\nest, each decision begins with choosing a random subset of\nthe selection variables to be used in determining the split\nfor that node. The sum of exclusive b \u2192s\u03b3 analysis from\nBABAR described in Section 17.9.2.4 uses two random for-\nest classi\ufb01ers, one to perform best candidate selection and\na second to provide background suppression.\n4.4.8 Error correcting output code\nWe may consider the situation with multiple output classes,\nbut where one is still interested in the binary question\nof determining whether the event belongs to a particular\nclass or not. For example, suppose we have the classes e,\n\u03c0, K, p. There may be discriminants among all of these,\nand we may train classi\ufb01ers to distinguish among binary\npartitions of this set of classes. That is, we might have\na classi\ufb01er that preferentially returns a 1 for classes e or\n\u03c0 and a \u22121 for K, or p. We could train di\ufb00erent classi-\n\ufb01ers for every such partition of the classes, resulting in an\n\u201cexhaustive matrix\u201d. The aggregate of these classi\ufb01ers is\nused in classifying an event. The technology of digital er-\nror correction may be used for this, in a method referred\nto as \u201cerror-correcting output codes\u201d (ECOC) (Dietterich\nand Bakiri, 1995).\nAn event is classi\ufb01ed by evaluating each of the classi-\n\ufb01ers to give a vector consisting of the numbers \u22121 and 1 for\nthe event. The soft Hamming distances (Hamming, 1950)\nbetween this vector and the expected vectors for each class\nare calculated, where the soft Hamming distance between\ntwo binary strings of equal length is the sum of squares of\nthe di\ufb00erences at each position of the vector. This yields\na vector of numbers with length equal to the number of\nclasses. In the simplest case we can take the class with\nminimum soft Hamming distance to be the resulting class.\nThe idea is that an individual classi\ufb01er might make an er-\nror, but this error may be corrected by the redundancy in\nthe combination of the classi\ufb01ers. For instance in BABAR\nmany analyses have di\ufb00erent PID requirements on the e\ufb03-\nciency and mis-identi\ufb01cation rate implying di\ufb00erent levels\nof tightness in the selection. Instead of assigning the class\nwith the minimum soft Hamming distance, a cut is applied\nbased on the soft Hamming for the particular class and the\nratios of soft Hamming distance of the particular class to\nthose of the other classes. For example, for electron selec-\ntion, we cut on Se and Se/SK, Se/S\u03c0, Se/Sp where Sx is\nthe soft Hamming distance for class x. The disadvantage\nof the ECOC approach is in the need to build the classi-\n\ufb01ers for the exhaustive matrix, which becomes daunting\nif the number of classes becomes large.\nBABAR eventually applied the ECOC approach in the\nevolution of its particle identi\ufb01cation algorithm (Chap-\nter 5), where the results of several bagged decision tree\nclassi\ufb01ers are combined. We may get an idea of the impact\nfrom Fig. 4.4.1, which compares three methods for particle\nidenti\ufb01cation: a likelihood-based selector (Section 4.4.2);\na selector using bagged decision trees (Section 4.4.7) with\na non-exhaustive error correction matrix; and a selector\nusing bagged decision trees with an exhaustive error cor-\nrection matrix. In the case of the non-exhaustive matrix,\nthe classi\ufb01ers used are one-vs-one classi\ufb01ers, comparing\nthe pion with kaon hypothesis, pion with electron, etc.\nIn Fig. 4.4.1, top (for \u03c0\u2212K separation), we see that the\nnon-exhaustive ECOC performs similarly with the likeli-\nhood selector. When we go to an exhaustive ECOC selec-\ntion we \ufb01nd a notable improvement in mis-identi\ufb01cation\nfor the same e\ufb03ciency. In the bottom plot (for e \u2212\u03c0 sep-\naration) the non-exhaustive ECOC is tuned to somewhat\nhigher e\ufb03ciency, but yields much poorer mis-identi\ufb01cation\nthan the likelihood selector. Note that this is in contrast\nwith the situation for the \u03c0 \u2212K separation: relative clas-\nsi\ufb01er performance can depend substantially on the prob-\nlem. Finding the optimal approach may require extensive\nstudy, including consideration of systematics as well as\nperformance. However, in this case tuning an exhaustive\nECOC to the same e\ufb03ciency as the likelihood selector\nagain provides a lower misidenti\ufb01cation for the same e\ufb03-\nciency.\n\n65\nMomentum (GeV)\n0\n1\n2\n3\n4\n5\n 4\n\u00d7\nEfficiency or Misidentification \n0\n0.2\n0.4\n0.6\n0.8\n1\nExhastive Matrix Efficiency\nLikelihood Method Efficiency\n1vs1 Matrix Efficiency\nExhaustive Matrix MisID\nLikelihood Method MisID\n1vs1 Matrix MisID\nMomentum (GeV)\n0\n1\n2\n3\n4\n5\n 50\n\u00d7\nEfficiency or Misidentification \n0\n0.2\n0.4\n0.6\n0.8\n1\nExhastive Matrix Efficiency\nLikelihood Method Efficiency\n1vs1 Matrix Efficiency\nExhaustive Matrix MisID\nLikelihood Method MisID\n1vs1 Matrix MisID\nFigure 4.4.1. Performance of various particle identi\ufb01cation selections in BABAR. The horizontal axis is momentum, and the\nvertical axis is either e\ufb03ciency (circles) or a factor (for visibility) times the mis-identi\ufb01cation probability (triangles). Gray\nsymbols indicate a selector based on a likelihoods; open symbols indicate a selector based on bagged decision trees with a\nnon-exhaustive error correction matrix (see text); black symbols indicate a selector based on bagged decision trees with an\nexhaustive error correction matrix. Top: Performance of kaon selection. The pion mis-identi\ufb01cation probabilities are multiplied\nby four. Bottom: Performance of electron selection. The pion mis-identi\ufb01cation probabilities are multiplied by \ufb01fty.\n4.5 Available tools\nThere are two general purpose toolkits implementing many\nof these algorithms that have become the most widely used\nin our analyses:\n\u2013 StatPatternRecognition (Narsky, 2005b)\n\u2013 TMVA (\u201cToolkit for Multivariate Analysis\u201d; Hoecker\net al., 2007)\nFor neural nets, popular packages are:\n\n66\n\u2013 Stuttgart Neural Network Simulator (SNNS; Zell et al.,\n1995)\n\u2013 NeuroBayes (Feindt and Kerzel, 2006; Phi-T, 2008)\nImplementations of various classi\ufb01ers may be found as well\nin the broader toolkits:\n\u2013 The R project (R Project Contributors, 1997)\n\u2013 S-PLUS (TIBCO, 2008) (a commercial alternative to\nR)\n\u2013 MATLAB (MathWorks, 1984)\nThese should not be taken as exhaustive lists, only pro-\nviding those packages most commonly seen in the present\ncontext.\n\n67\nChapter 5\nCharged particle identi\ufb01cation\nEditors:\nAlessandro Gaz (BABAR)\nShohei Nishida (Belle)\n5.1 Introduction\nIn this chapter we present the implementation and per-\nformance of charged particle identi\ufb01cation (PID) at Belle\nand BABAR.\nAfter a brief introduction, the algorithms and statisti-\ncal tools used by the two experiments are discussed (Sec-\ntion 5.2). The PID algorithms that give the ultimate per-\nformance are based on multivariate techniques, described\nin detail in Chapter 4. Some examples of the typical per-\nformance of the particle identi\ufb01cation algorithms (PID se-\nlectors) are then given, along with a discussion on PID-\nrelated error sources, for both BABAR (Section 5.3) and\nBelle (Section 5.4).\nThe identi\ufb01cation of charged particles stable enough to\nbe detected (electrons, muons, pions, kaons, and protons)\nplays a central role in the physics program of the BABAR\nand Belle experiments. Not only are very good PID capa-\nbilities required for separating hadronic \ufb01nal states of B\ndecays such as \u03c0+\u03c0\u2212, K\u00b1\u03c0\u2213, K+K\u2212, and many others,\nbut the PID performance is crucial for the \ufb02avor-tagging\nof the B mesons (see Chapter 8). B0 candidates are dis-\ntinguished from B0 candidates based on the identi\ufb01cation\nof their decay products such as high-momentum charged\nleptons (e or \u00b5) or charged kaons. More generally PID very\noften provides powerful tools to reduce the backgrounds\narising from \ufb01nal states which di\ufb00er from that under study\nby swapping one of its particles with one of di\ufb00erent \ufb02avor.\n5.1.1 De\ufb01nitions\nThe performance of a PID selector dedicated to the identi-\n\ufb01cation of charged particles of type \u03b1 (\u03b1 = e, \u00b5, \u03c0, K, p)\nis characterized by an e\ufb03ciency and a set of mis-identi\ufb01ca-\ntion probabilities.\nThe PID e\ufb03ciency of particle type \u03b1 is computed as\nthe fraction of successfully identi\ufb01ed \u03b1 tracks among all\nthe \u03b1 tracks reconstructed and selected for a particular\nanalysis, while the mis-identi\ufb01cation probabilities are the\nprobabilities that particles of type \u03b2, \u03b3, . . . , are incorrectly\nidenti\ufb01ed as \u03b1.\nIn many cases the quantities de\ufb01ned above depend on\nthe momentum and on the polar and azimuthal angles of\nthe tracks. Therefore the performance of PID selectors is\nstudied and determined in bins of (p, \u03b8, \u03c6).\n5.1.2 Subdetectors providing PID information\nBABAR uses the information from all of its subdetectors as\ninputs for the PID selectors. Measurements of the energy\nloss dE/dx of a charged track are provided by the SVT\nand the DCH. The number of Cherenkov photons and the\nmeasurement of their angle with respect to the incident\ntrack are provided by the DIRC, while the EMC is respon-\nsible for the measurement of the deposited energy and of\nquantities describing the shape of the shower associated\nwith a track (such as the lateral and the Zernike moments\n(Zernike, 1934)), which can be used to distinguish lep-\ntonic and hadronic tracks. Finally most information (such\nas the number of iron layers traversed by the candidate\ntrack, and variables related to the shape of the cluster)\nrelevant to the identi\ufb01cation of muons is provided by the\nIFR.\nBelle uses similar input information. Measurements of\nthe dE/dx of a charged track are provided by the CDC. A\nTOF counter measures the time of \ufb02ight of a charged par-\nticle from the interaction point to the counter, from which\nthe velocity of the particle can be measured (Kichimi,\n2000). The number of Cherenkov photons at the ACC pro-\nvides separation for higher momenta (Iijima, 2000). Infor-\nmation from the ECL, together with that from the CDC\nand ACC, is used for electron identi\ufb01cation (Hanagaki,\nKakuno, Ikeda, Iijima, and Tsukamoto, 2002). The KLM\nis responsible for muon identi\ufb01cation (Abashian, 2002a).\n5.2 PID algorithms and multivariate methods\nIn the most simple method, PID selectors are based on\ncuts applied to the most relevant variables for every par-\nticle type (e.g. E/p for electrons, the distance traveled in\nthe return yoke for muons, the Cherenkov angle for K/\u03c0\nseparation, ...). Better performance is obtained with the\nuse of likelihood based selectors, in which the information\nfrom the various subdetectors is used to compute a set of\nlikelihoods Lk that the measured properties of the charged\ntrack in question would be produced by a true k-particle.\nFor an example of implementation of a selector based on\nlikelihood ratios, see Eq. (5.2.1). Belle has always used\nselectors based on likelihood ratios throughout the whole\nlife of the experiment.\nCut and likelihood based selectors are very stable over\nthe data-taking periods and do not need re-tuning to com-\npensate for the aging of the detectors and the changes\nintroduced by the reprocessing of the data. However, sig-\nni\ufb01cant improvements can be achieved by considering a\nlarger set of variables, even some with very mild discrim-\nination power, in the implementation of PID selectors.\nBABAR uses more sophisticated statistical tools such as\nNeural Networks (NN), Bagged Decision Trees (BDT),\nand Error Correcting Output Code (ECOC) algorithms,\nto accommodate a large number of input variables (up to\n36) and the signi\ufb01cant correlations among them.\nDue to their higher sensitivity to variations in the per-\nformance of the detector, the selectors based on multivari-\nate methods need to be re-trained on data control samples\n(see Section 5.3) after every major change in the recon-\nstruction algorithms. Particularly important for BABAR,\nwhich was a\ufb00ected by large variations in the performance\nof the IFR, is the inclusion of the data taking period as\n\n68\none of the input variables, in order to take into account\nthe loss of e\ufb03ciency in speci\ufb01c regions of the detector.\nIn the following sections the more re\ufb01ned algorithms\nimplemented at Belle and BABAR will be described.\n5.2.1 Belle algorithms\nThe PID at Belle is based on likelihood ratios. For hadron\nidenti\ufb01cation, likelihoods for a candidate particle \u03b1 are\ncalculated based on dE/dx information from the CDC\n(LCDC\n\u03b1\n), time of \ufb02ight from the TOF (LTOF\n\u03b1\n) and the num-\nber of photons from the ACC (LACC\n\u03b1\n), respectively. Then,\nthe likelihood ratios\nL(\u03b1 : \u03b2) =\nLCDC\n\u03b1\nLTOF\n\u03b1\nLACC\n\u03b1\nLCDC\n\u03b1\nLTOF\n\u03b1\nLACC\n\u03b1\n+ LCDC\n\u03b2\nLTOF\n\u03b2\nLACC\n\u03b2\n(5.2.1)\nare calculated and used for identi\ufb01cation. For example,\npions (kaons) can be selected by requiring a low (high)\nvalue of L(K : \u03c0), and protons are typically identi\ufb01ed\nwith requirements on both L(p : K) and L(p : \u03c0). The cut\nvalue applied to the likelihood ratios can be optimized\ndepending on the analysis.\nFor electron identi\ufb01cation, in addition to LCDC\n\u03b1\nand\nLACC\n\u03b1\n, information from the ECL (matching of the posi-\ntions of the track and the energy cluster, E/p, and trans-\nverse shower shape) is used to form likelihood ratios. There\nis a small region around \u03b8 \u223c125\u25e6with low electron iden-\nti\ufb01cation performance because of a small gap between the\nbarrel ECL and backward endcap ECL. For muon identi\ufb01-\ncation, reconstructed hits in the KLM are compared to the\nextrapolation of the CDC track, using the di\ufb00erence \u2206R\nbetween the measured and expected range of the track,\nand the statistic \u03c72\nr constructed from the transverse de-\nviations of all hits associated to the track, normalized by\nthe number of hits. Likelihoods for the muon, pion, and\nkaon hypotheses are formed based on p.d.f.s in \u2206R and\n\u03c72\nr. The likelihood ratio L\u00b5/(L\u00b5 + L\u03c0 + LK) is then used\nas a discriminating variable.\n5.2.2 BABAR algorithms\nIn BABAR, the ultimate performance in the selection of\nmuons is achieved with an algorithm based on Bagged De-\ncision Trees (Narsky, 2005a; also discussed in Section 4.4.7\nof this Book). The algorithm takes as input 30 variables:\nin addition to variables related to the length and the shape\nof the IFR cluster associated to the candidate track and\nthe measurement of the energy deposited in the EMC,\nthe variables related to the shape of the cluster in the\ncalorimeter, the number of Cherenkov photons, the open-\ning angle of the Cherenkov cone, and the number of DCH\nhits and the dE/dx measured in the DCH are also used.\nThe training of the selectors is performed on high pu-\nrity data samples of muons and pions, subdivided in 720\nbins of p, \u03b8, and charge. Candidate tracks are randomly\ndiscarded in order to have the same number of muons and\npions in the same bin. This allows the use of the p, \u03b8, and\ncharge variables in the tree without introducing any bias\ndue to the di\ufb00erent (p, \u03b8) spectrum of the source sample.\nThe source sample is then randomly split into a training\nand a testing sample. Four di\ufb00erent levels of tightness are\ndesigned for the muon selector (VeryLoose, Loose, Tight,\nand VeryTight); the cuts on the output of the classi\ufb01er are\ndesigned such that either the muon selection e\ufb03ciency or\nthe pion mis-identi\ufb01cation probability are kept constant.\nThe target e\ufb03ciencies (besides the very low-momentum\npart of the spectrum, where few muons can be identi\ufb01ed)\nare 90%, 80%, 70%, and 60% and the target pion mis-\nidenti\ufb01cation probabilities are 5%, 3%, 2%, and 1.2%. Two\nadditional selectors, optimized for muons in the momen-\ntum range [0.3, 0.7] GeV/c, with a target e\ufb03ciency of 70%\nand 60% have been developed. With roughly the same ef-\n\ufb01ciency, the BDT based muon selectors are signi\ufb01cantly\nmore e\ufb00ective in rejecting the pion contamination with\nrespect to the selectors based on Neural Networks, as can\nbe seen from Table 5.2.1.\nFor the other charged particles (electrons, pions, kaons,\nand protons), a class of selectors based on the Error Cor-\nrecting Output Code algorithms (Dietterich and Bakiri,\n1995) is used. The discrimination is based on 36 variables\nfrom the four inner subdetectors: SVT, DCH, DIRC, and\nEMC. Candidate e, \u03c0, K, and p are separated by means\nof several binary classi\ufb01ers (in our case BDT\u2019s) combined\nthrough an exhaustive matrix (see Chapter 4). The use of\nthe exhaustive matrix ensures the robustness of this type\nof selector against potential mis-classi\ufb01cations of some of\nthe binary classi\ufb01ers. The selectors are trained on high\npurity data samples (see Section 5.3) and the cuts on the\noutputs of the binary classi\ufb01ers are tuned in such a way\nthat the selection e\ufb03ciency matches that of the analogous\nlikelihood based selectors. Six levels of tightness are pro-\nvided (SuperLoose, VeryLoose, Loose, Tight, VeryTight,\nand SuperTight). At the same level of e\ufb03ciency, the mis-\nidenti\ufb01cation rate for the ECOC algorithms is signi\ufb01cantly\nlower than that of the likelihood based selectors (see Table\n5.2.1).\nTable 5.2.1. E\ufb03ciencies and mis-identi\ufb01cation rates (aver-\naged over the momentum and polar angle spectra) for di\ufb00erent\nkinds of muon and kaon BABAR PID selectors, all using Tight\nrequirements. The quoted uncertainty represents the typical\nstatistical uncertainty in each bin of the tables that measures\nthe performance of the supported selectors. No systematic un-\ncertainty has been included.\nMuon selector\ne\ufb03ciency (%)\n\u03c0 mis-id rate (%)\nCut based\n65.0 \u00b1 0.5\n1.43 \u00b1 0.05\nNN\n60.5 \u00b1 0.5\n0.97 \u00b1 0.05\nBDT\n59.4 \u00b1 0.5\n0.76 \u00b1 0.05\nKaon selector\ne\ufb03ciency (%)\n\u03c0 mis-id rate (%)\nCut based\n80.2 \u00b1 0.2\n1.39 \u00b1 0.07\nLikelihood based\n83.0 \u00b1 0.2\n1.47 \u00b1 0.07\nECOC\n84.2 \u00b1 0.2\n1.10 \u00b1 0.07\n\n69\n5.3 BABAR PID performance and systematics\nThe tuning of the PID selectors and the assessment of\ntheir performance takes advantage of high purity samples\nof tracks selected from the data. A large number of elec-\ntron and muon tracks is selected from e+e\u2212\u2192e+e\u2212(\u03b3),\n\u00b5+\u00b5\u2212(\u03b3) processes, with minimal cuts on the kinematics\nof the event, on the quality of both the candidate track\nand of the other track in the event, and on the basic PID\nproperties (to distinguish electrons from muons). For some\nlow-statistics cross-checks, a sample of electrons (muons)\nfrom the decays B \u2192J/\u03c8K(\u2217), J/\u03c8 \u2192e+e\u2212(\u00b5+\u00b5\u2212) has\nalso been used.\nK and \u03c0 candidates are selected from D\u2217+ \u2192D0\u03c0+,\nD0 \u2192K\u2212\u03c0+. The K/\u03c0 assignment is done based on the\ncharge of the soft pion from the D\u2217+ decay. The purity\nof the sample is increased by applying quality cuts on the\nreconstructed tracks, and rejecting fake D0\u2019s using cuts\non the invariant mass of the reconstructed D0 candidate\nand on the likelihood that the K and \u03c0 tracks originate\nfrom a common vertex. Additional \u03c0 samples, especially\nimportant for measuring the mistagging of pions as muons\nat high momentum (where the population of D0 \u2192K\u2212\u03c0+\nis low) are obtained from K0\nS \u2192\u03c0+\u03c0\u2212decays and from\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212events where one \u03c4 (tag) has one charged\nparticle among its decay products and the other decays to\na \ufb01nal state with three charged particles. Finally a high-\npurity sample of protons is obtained from \u039b0 \u2192p\u03c0\u2212de-\ncays, by taking advantage of the long lifetime of the \u039b0\nbaryon. The purity of the sample is enhanced by apply-\ning cuts on the quality of the candidate tracks and on\nthe probability that the proton and pion tracks are con-\nsistent with originating from the same displaced vertex.\nSome examples of performance of the BABAR selectors are\ndisplayed in Table 5.2.1 and in Figure 5.3.1.\nThese high purity samples are utilized in the training\nof the more advanced PID algorithms and in establish-\ning the performance of all the selectors. Depending on the\navailable statistics, the control samples are divided into\nseveral bins with di\ufb00erent (p, \u03b8). In the case of the muon\nselectors at BABAR, the samples are also subdivided in 6\nbins of \u03c6, to better characterize the degradation of the\nRPC chambers and the staged upgrade of the barrel sec-\ntion with LST detectors (see Chapter 2). Each of the se-\nlectors is applied to every bin of the control samples and\nthe e\ufb03ciencies for both the data (\u03b5data) and the simulation\n(\u03b5MC) are computed. The tables of e\ufb03ciencies thus built\nare then used to correct the simulation so that its PID per-\nformance matches that of the data. One of the most widely\nused algorithms to apply this correction in BABAR is the\nso-called PID-tweaking. In the case where \u03b5data = \u03b5MC,\nno correction is applied, whereas if \u03b5data < \u03b5MC a MC\ntrack that passes the selector is randomly discarded with\nprobability\n\u03b5data\n\u03b5MC\n.\n(5.3.1)\nIn the case \u03b5data > \u03b5MC, a MC track that does not pass\nthe selection is accepted with probability\n(\u03b5data \u2212\u03b5MC) 1\n\u03b5MC\n.\n(5.3.2)\nData taking period\nRun1 Run2 Run3 Run4 Run5 Run6 Run7\ncut based efficiency (barrel only)\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n+\n\u00b5\n \n-\u00b5\n \nFigure 5.3.2. Muon selection e\ufb03ciencies for a typical BABAR\ncut-based muon selector as a function of the data taking period.\nThe e\ufb03ciencies are computed only for the barrel region. The\nloss in performance due to the degradation of the RPC detector\nduring the early phases of the data taking is evident, as is the\nfull recovery with the installation of the LST\u2019s, completed after\nthe end of Run5.\nAt the end of the BABAR experiment, the size of the typi-\ncal correction applied by the PID-tweaking algorithm was\nabout one percent.\n5.3.1 History of PID performance in BABAR\nFor the BABAR experiment, the most important issue af-\nfecting the stability of PID performance was the degrada-\ntion of the e\ufb03ciency of the RPC chambers (see Chapter 2).\nThis is visible from Fig. 5.3.2, which shows the e\ufb03ciency\nof one of the cut-based muon selectors as a function of the\ndata-taking period. This loss of performance was also one\nof the main motivations to develop muon selectors relying\non variables in addition to those measured by the IFR.\n5.3.2 Systematic e\ufb00ects\nBoth experiments rely on high-purity data samples to as-\nsess the performance of PID selectors and correct the sim-\nulation so that it matches the data as much as possible.\nSeveral ways exist to estimate the systematic uncertainty\nin a measurement related to PID requirements. It is not\npossible to establish a recommended way to proceed for all\nanalyses, since in general the performance of each selector\ncan be sensitive to the charged and neutral multiplicity\nof the events studied. For example, the performance of\nelectron and muon selectors is studied in low multiplicity\nevents, thus some care must be taken when applying these\nselectors to B-decays, where the multiplicity of the \ufb01nal\nstates is substantially higher.\n\n70\n (GeV/c)\nLab\np\n0\n1\n2\n3\n4\n\u03b5\n0.75\n0.8\n0.85\n0.9\n0.95\n1\n )\n fake\n\u03b5\n( 1 - \n0.99\n0.992\n0.994\n0.996\n0.998\n1\ne efficiency\n mis-id rate\n\u03c0\n (GeV/c)\nLab\np\n0\n1\n2\n3\n4\n\u03b5\n0.4\n0.6\n0.8\n1\n )\n fake\n\u03b5\n( 1 - \n0.9\n0.92\n0.94\n0.96\n0.98\n1\n efficiency\n\u00b5\n mis-id rate\n\u03c0\n (GeV/c)\nLab\np\n0\n1\n2\n3\n4\n5\n\u03b5\n0.7\n0.8\n0.9\n1\n)\n fake \n\u03b5\n( 1 - \n0.8\n0.85\n0.9\n0.95\n1\n efficiency\n\u03c0\nK mis-id rate\n (GeV/c)\nLab\np\n0\n1\n2\n3\n4\n5\n\u03b5\n0.6\n0.7\n0.8\n0.9\n1\n )\n fake\n\u03b5\n( 1 - \n0.85\n0.9\n0.95\n1\nK efficiency\n mis-id rate\n\u03c0\n (GeV/c)\nLab\np\n0\n1\n2\n3\n4\n5\n\u03b5\n0.6\n0.7\n0.8\n0.9\n1\n )\n fake\n\u03b5\n( 1 - \n0.95\n0.96\n0.97\n0.98\n0.99\n1\np efficiency\n mis-id rate\n\u03c0\nFigure 5.3.1. Performance of some typical BABAR PID selectors for electrons (top left plot), muons (top right), pions (middle\nleft), kaons (middle right), and protons (bottom) as a function of the momentum of the candidate charged track. The solid\n(black) dots represent the e\ufb03ciency, which can be read o\ufb00the left axis, of the particular selectors, while the empty (red) squares\nshow the complement (e.g. kaon for the pion selector, and pion for all other selectors) mis-identi\ufb01cation probability (right axis).\nNote that the vertical scale di\ufb00ers from plot to plot.\nIn BABAR, many of the analyses estimate the system-\natic uncertainty on the PID performance by taking the dif-\nference of the signal reconstruction e\ufb03ciency in the simu-\nlation obtained by applying or not applying the correction\n(usually the PID-tweaking) based on the e\ufb03ciency tables\ndescribed above. For some analyses where the relative con-\ntribution of the PID to the total systematic uncertainty is\nlarge, or there is a sizable dependence on the multiplici-\nties and the topologies of the events, alternative strategies\nhave been applied, and where possible the performance of\nthe chosen selector(s) has been checked in control sam-\nples with similar track multiplicities and topologies of the\nchannel under study.\n5.4 Belle PID performance and systematics\nIn Belle, the PID performance of the kaon and pion iden-\nti\ufb01cation algorithm is estimated using the decay D\u2217+ \u2192\n\n71\nD0\u03c0+ followed by D0 \u2192K\u2212\u03c0+, similar to BABAR. Fig-\nure 5.4.1 (a) and (b) shows typical curves of the e\ufb03ciencies\nand mis-identi\ufb01cation rates for the kaon and pion iden-\nti\ufb01cation in the barrel region, studied with this control\nsample. Discrepancies between data and MC can be seen,\nespecially in the mis-identi\ufb01cation.\nIn the study of the kaon and pion identi\ufb01cation, the\ncontrol sample is divided into 384 bins, i.e. 32 momen-\ntum (p) bins and 12 polar angle (\u03b8) bins. The momen-\ntum range is divided into 100 (200) MeV/c bins below\n(above) 3 GeV/c. The polar angle subdivision is based\non the structure of the ACC: one \u03b8 bin for the backward\nendcap (with no ACC), and one bin for each of the ten\ntypes of aerogel counter module in the barrel and forward\nendcap, except for the large polar angle range covered by\nthe n = 1.010 modules, which is divided in two (see Fig-\nure 2.2.8, and the accompanying text in Section 2.2.3).\nFor each bin, the e\ufb03ciency and mis-identi\ufb01cation rate\nfor K and \u03c0 are estimated both for the data and the MC\nfor di\ufb00erent PID selections. The relevant value for general\nanalyses is the ratio of the e\ufb03ciency or mis-identi\ufb01cation\nrate between the data and the MC: Rl = \u03f5data\nl\n/\u03f5MC\nl\nand\nits uncertainty, where l is the bin index. These quantities\nare provided as a look-up table for general use in Belle\nanalyses. The e\ufb03ciency (mis-identi\ufb01cation rate) ratio and\nits uncertainty for a given analysis, which is quoted as the\nsystematic uncertainty from PID, can then be calculated\nby\nR = 1\nN\nX\nl\nnlRl,\n(5.4.1)\nand\n\u03b4R = 1\nN\n\uf8eb\n\uf8ed\nsX\nl\n(nl\u03b4Rstat\nl\n)2 +\nX\nl\nnl\u03b4Rsyst\nl\n\uf8f6\n\uf8f8+ \u03b4Rconst,\n(5.4.2)\nwhere Rl is the e\ufb03ciency ratio in bin l, nl is the number\nof tracks in that bin (analysis dependent), and N = P nl.\nThe parameters \u03b4Rstat\nl\nand \u03b4Rsyst\nl\nare respectively the sta-\ntistical and systematic uncertainties in bin l obtained from\nthe control sample study; \u03b4Rconst is an additional system-\natic uncertainty, independent of (p, \u03b8), based on variations\nin e\ufb03ciency between di\ufb00erent data taking periods (\u201cexper-\niments\u201d in Belle nomenclature: see Section 3.2). In this\nway, the correction factor and the systematic error can be\nautomatically calculated. The typical systematic uncer-\ntainty \u03b4R for kaon and pion identi\ufb01cation at Belle is 0.8%.\nIn physics analyses that measure a direct CP asymmetry,\nthe systematic error due to an asymmetry in the PID e\ufb03-\nciency between positive and negative charged tracks needs\nto be estimated. This error can be calculated by using the\ntables for Rl, \u03b4Rstat\nl\n, and \u03b4Rsyst\nl\n, which are provided sep-\narately for positive and negative particles.\nThe study of the proton identi\ufb01cation is performed\nwith \u039b \u2192p\u03c0\u2212, using the same binning for \u03b8 as above,\nbut with only 12 bins for momentum. The typical proton\ne\ufb03ciency is shown in Fig. 5.4.1 (c).\nFor the study of the lepton identi\ufb01cation, the two-\nphoton process e+e\u2212\u2192e+e\u2212\u2113+\u2113\u2212(\u2113= e, \u00b5) is used to\nobtain high statistics electron and muon samples. The con-\ntrol sample is divided into 70 bins (10 momentum bins in\n500 MeV/c steps and 7 polar angle bins). The e\ufb03ciencies\nof the lepton identi\ufb01cations estimated using this process\nare shown in Fig. 5.4.1 (d) and (e). Since the above pro-\ncess leads to low track-multiplicity events, inclusive J/\u03c8\nevents (J/\u03c8 \u2192\u2113+\u2113\u2212) are also used as a control sample,\nmainly for the estimation of a possible performance di\ufb00er-\nence between low-multiplicity events and hadronic events.\nThe mis-identi\ufb01cation rates of the lepton identi\ufb01cation for\npions and kaons, are studied using a control sample of\nK0\nS \u2192\u03c0\u03c0 and D\u2217+ \u2192D0\u03c0+ \u2192K\u2212\u03c0+\u03c0+.\n\n72\nMomentum (GeV/c)\n0\n1\n2\n3\n4\n0\n0.2\n0.4\n0.6\n0.8\n1\nKaon efficiency (data)\nKaon efficiency (MC)\nPion mis-ID (data)\nPion mis-ID (MC)\nEfficiency\n(a) Kaon identi\ufb01cation.\n0\n0.2\n0.4\n0.6\n0.8\n1\nEfficiency\nMomentum (GeV/c)\n0\n1\n2\n3\n4\nPion efficiency (data)\nPion efficiency (MC)\nKaon mis-ID (data)\nKaon mis-ID (MC)\n(b) Pion identi\ufb01cation.\nMomentum (GeV/c)\n0\n1\n2\n3\nEfficiency\n0.6\n0.7\n0.8\n0.9\n1\nData\nMC\n(c) Proton identi\ufb01cation.\nMomentum (GeV/c)\n0\n1\n2\n3\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nData\nMC\n(d) Electron identi\ufb01cation.\nMomentum (GeV/c)\n0\n1\n2\n3\nEfficiency\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nData\nMC\n(e) Muon identi\ufb01cation\nFigure 5.4.1. Performance of the PID at Belle as a function of the momentum of the candidate charged track for the data and\nMC-simulated events. (a) Performance of kaon identi\ufb01cation: kaon e\ufb03ciency and pion mis-identi\ufb01cation rate. (b) Performance\nof pion identi\ufb01cation: pion e\ufb03ciency and kaon mis-identi\ufb01cation rate. (c) Performance of proton identi\ufb01cation. (d) Performance\nof electron identi\ufb01cation. (e) Performance of muon identi\ufb01cation. In (c), (d) and (e), only e\ufb03ciencies respectively for protons,\nelectrons and muons are shown for the data and MC simulated events.\n\n73\nChapter 6\nVertexing\nEditors:\nWouter Hulsbergen (BABAR)\nTakeo Higuchi (Belle)\nAdditional section writers:\nMaurizio Martinelli\n6.1 The role of vertexing in the B Factories\nA vertex algorithm is a procedure by which the param-\neters of a decay vertex or interaction vertex are deter-\nmined from the reconstructed parameters of the outgoing\nparticles. In the simplest case the outgoing particles are\ncharged particles that are either stable or have a large c\u03c4\n(where \u03c4 is the particle lifetime) compared to the dimen-\nsions of the detector, namely electrons, muons, protons\nand charged pions and kaons. These particles are recon-\nstructed as charged particle trajectories (or \u2018tracks\u2019) in the\ntracking detectors and their reconstructed parameters are\nthe track parameters. More complicated vertex algorithms\ninvolve \ufb01nal states that include not only tracks, but also\nphotons or other decaying particles.\nThe role of vertexing algorithms in the B Factory ex-\nperiments can roughly be divided in three parts. First,\nvertex \ufb01ts are used to obtain the parameters of recon-\nstructed \u2018composite\u2019 particles from their decay products,\ni.e. charged particle trajectories and photon calorimeter\nclusters. These parameters are usually the vertex position,\nmomentum and invariant mass of the decaying particle.\nHowever, also the decay length of an unstable particle in-\nside a decay chain (such as the D meson in a B \u2192D\u03c0 de-\ncay), or the decay time di\ufb00erence \u2206t of the two B mesons\nfrom an \u03a5(4S) decay, can be computed with a vertex \ufb01t.\nSecond, the \u03c72 of a vertex \ufb01t is used to suppress com-\nbinatorial background in the selection of composite par-\nticles. Apart from a few cases of decays in \ufb02ight (pions\nand long lived strange hadrons), the decay products from\nmost composite particles all originate from a small region\naround the interaction point. The track parameter resolu-\ntion of B Factories is just su\ufb03cient to separate the decay\nvertices of bottom and charm mesons. When searching\nfor exclusive decays a requirement on the vertex \u03c72 pro-\nvides an e\ufb03cient way to reject wrong combinations from\nthe composite particle candidates. The \u03c72 plays a simi-\nlar role in the reconstruction of the primary interaction\nvertex or in the reconstruction of the \u2018second\u2019 B vertex\nfor the determination of B meson decay time di\ufb00erence.\nIn that case the contribution of individual tracks to the\nvertex \u03c72 is used to select the subset of tracks that best\ndetermines the vertex position.\nFinally, vertexing is used in the calibration and mon-\nitoring of the position and size of the interaction region.\nAs we shall see, information on the average position of the\nprimary vertex can be used as a constraint in vertex \ufb01ts.\nIn the BABAR and Belle experiments the beam parame-\nters are also fed back in real time to the accelerator for\ndiagnostics.\nThis chapter is organized as follows. The parameteri-\nzation of reconstructed tracks, which de\ufb01nes the input to\nthe vertex algorithms, is described in Section 6.2. Vertex\n\ufb01tting algorithms are discussed in Section 6.3. The cali-\nbration of the interaction region for use in vertex \ufb01ts is de-\nscribed in Section 6.4. An important application of vertex\n\ufb01ts is the determination of decay times, in particular the\nB meson decay time di\ufb00erence \u2206t. The demands on ver-\ntex resolution in the B Factory experiments are primarily\ndetermined by the requirement that \u2206t be measured with\nsu\ufb03cient precision to probe B0B0 oscillations. The proce-\ndures by which the decay time di\ufb00erence is estimated and\nits resolution calibrated are discussed in Sections 6.5.\n6.2 Track parameterization and resolution\nIf stochastic processes like energy loss and multiple scat-\ntering in detector material are ignored, the trajectory of\na charged particle in a magnetic \ufb01eld can be described by\n\ufb01ve parameters. In a uniform magnetic \ufb01eld the trajectory\nfollows a helix. The helix axis is parallel to the magnetic\n\ufb01eld, which in the B Factory solenoids is almost parallel\nto the e+-e\u2212beam axis.\nEven in the case that the \ufb01eld is not uniform or ma-\nterial e\ufb00ects cannot be ignored, the track can locally be\nparameterized as a helix. With respect to a conveniently\nchosen pivot point, the parameters can be de\ufb01ned as (see\nChapter 2 for the de\ufb01nition of the coordinate system)\nd\u03c1 or d0\nsigned distance in the x-y plane from the\npivotal point to the helix,\n\u03c60\nazimuthal angle from the pivotal point to\nthe helix center,\n\u03ba or \u03c9\ninverse of the track transverse momentum\ntimes charge of the track, \u03ba = e/pt\ndz or z0\nsigned distance along the z axis from the\npivotal point to the helix,\ntan \u03bb\ntangent of the dip angle.\nThe two experiments follow a slightly di\ufb00erent notation\nand de\ufb01nition. When two names are shown in the \ufb01rst\ncolumn of the table above, the \ufb01rst is for Belle and the\nsecond for BABAR . The sign of the inverse transverse mo-\nmentum \u03ba coincides with the sign of the charge of the\nparticle. If the pivot point is the origin, then d\u03c1 is the\n(signed)19 minimum distance to the z-axis and dz is the\nz-coordinate of the point-of-closest approach to the origin.\nThe azimuthal coordinate \u03c6 is the angle of the transverse\nmomentum vector with the x axis in BABAR while the co-\nordinate \u03c6 + \u03c60 is the angle of the transverse momentum\nvector with the y axis in Belle. In the following we use\nthe Belle de\ufb01nition, illustrated in Fig. 6.2.1. The BABAR\nde\ufb01nition can be found in (Hulsbergen, 2005).\n19 Sign of d\u03c1: for e > 0 and the pivot point lying outside\nthe helix projection to the (x, y) plane then d\u03c1 > 0; for the\npivot point inside the helix projection d\u03c1 < 0. For e < 0 this\nde\ufb01nition is reversed.\n\n74\nvv\nwv\nprv\n0\u03c6\ntpv\nt0\npv\n\u03c6\n(\n)\np\np y\nx ,\n(\n)\ny\nx,\ny\nx\n0\n>\ne\nvv\nwv\nprv\n0\u03c6\ntpv\nt0\npv\n\u03c6\n(\n)\np\np y\nx ,\n(\n)\ny\nx,\ny\nx\n0\n<\ne\nFigure 6.2.1. Schematic representations of the helix pa-\nrameterization for a positively (top) and negatively (bottom)\ncharged track in the (x, y) plane used at Belle. Magnetic \ufb01eld is\nin the direction of the z-axis. Vector rp determines position of\nthe pivot point. Other vectors in the \ufb01gure are de\ufb01ned as r =\nrp+sgn(e)w\u2212v, where w = sgn(e)(d\u03c1+\u03c1)(cos \u03c60, sin \u03c60), v =\n\u03c1(cos (\u03c60 + \u03c6), sin (\u03c60 + \u03c6)).\nThe charged particle position along the track trajec-\ntory can be represented using a running parameter \u03c6 as\nx(\u03c6) = xp + d\u03c1 cos \u03c60 + \u03c1{cos \u03c60 \u2212cos(\u03c60 + \u03c6)},\ny(\u03c6) = yp + d\u03c1 sin \u03c60 + \u03c1{sin \u03c60 \u2212sin(\u03c60 + \u03c6)},\nz(\u03c6) = zp + dz \u2212r\u03c6 tan \u03bb,\n(6.2.1)\nwhere (xp, yp, zp) is the pivot point and \u03c1 = 1/Bz\u03ba is\nthe (signed) curvature radius with Bz representing the\nstrength of the magnetic \ufb01eld. Using pt = e/\u03ba the mo-\nmentum vector along the trajectory is given by\npx(\u03c6) = \u2212pt sin(\u03c60 + \u03c6),\npy(\u03c6) = pt cos(\u03c60 + \u03c6),\n(6.2.2)\npz(\u03c6) = pt tan \u03bb.\nm) \n\u00b5\n) (\n0\n(z\n\u03b4\n-200\n-100\n0\n100\n200\nEntries\n0\n200\n400\n600\nm) \n\u00b5\n) (\n0\n(d\n\u03b4\n-200\n-100\n0\n100\n200\nEntries\n0\n200\n400\n600\nrad) \n\u00b5\n|) (\n\u03c6\n(|\n\u03b4\n-4000\n-2000\n0\n2000\n4000\nEntries\n0\n200\n400\n600\n800\n) \n-6\n)) (10\n\u03b8\n/2-\n\u03c0\n(tan(\n\u03b4\n-4000\n-2000\n0\n2000\n4000\nEntries\n0\n200\n400\n600\n800\nFigure 6.2.2. Measurements of the di\ufb00erences between the \ufb01t-\nted track parameters of the top and bottom stubs of cosmic ray\nmuons with a momentum above 2 GeV/c in BABAR. The data\nare shown as points, Monte Carlo simulation as histograms.\nThe (blue) smooth curves are the results of a Gaussian \ufb01t to\nthe data. From (Brown, Gritsan, Guo, and Roberts, 2009).\nExpressions for the inverse transformation \u2014 from posi-\ntion and momentum vector to helix parameters \u2014 and\nthe corresponding Jacobian can be found in (Hulsbergen,\n2005).\nThe helix track parameters are determined by a \ufb01t to\nthe measured hit coordinates along the track. Both Belle\nand BABAR use a track \ufb01t based on a Kalman \ufb01lter (Fruh-\nwirth, 1987). The BABAR track \ufb01t is described in (Brown,\n1997). The track parameter resolution is determined by\nthe number of hits and the hit resolution, and by multi-\nple scattering and energy loss. For the resolution on the\ndirection and position of the track the \ufb01rst two layers in\nthe vertex detector are most important. However, for the\nextrapolation to the interaction point the curvature res-\nolution is relevant as well. Both B Factory experiments\nfeature a multi-layer vertex detector (Section 2.2.1) with\na hit resolution in the range 10\u221250 \u00b5m to precisely mea-\nsure impact parameters. A precise curvature resolution is\nfacilitated by a large drift chamber.\nAn estimate of the track resolution in data can be ob-\ntained from cosmic ray events. The muon trajectory is\nreconstructed as two separate segments in the top and\nbottom halves of the tracking detector. The di\ufb00erence or\n\u2018residual\u2019 between the reconstructed parameter of the seg-\nments at their point of closest approach is representative\nfor the actual parameter resolution, after a correction with\na factor\n\u221a\n2. The distribution of the residuals is shown\nin Figure 6.2.2 for muons with momenta above 2 GeV/c\nin BABAR data and Monte Carlo. From a \ufb01t with a sin-\ngle Gaussian to these distributions the single-track reso-\nlution in data is estimated as 29 \u00b5m for z0, 24 \u00b5m for d0,\n0.45 mrad for \u03c60 and 0.53\u00b710\u22123 for tan \u03bb (Brown, Gritsan,\nGuo, and Roberts, 2009) (see Chapter 2 for a discussion\nof the pT resolution). The parameter resolution in Belle\n\n75\nis similar. It should be noted, however, that due to the\ncontribution from multiple scattering the resolutions are\na rather strong function of momentum. For example, in\nBABAR the d0 resolution at pT \u22480.1 GeV/c2 is over a\nfactor 5 worse than at pT \u22483 GeV/c2 (Aubert, 2002j).\nBesides the track parameters the track \ufb01t also com-\nputes a track parameter covariance matrix, which can be\nused in vertex \ufb01ts. The covariance matrix is among oth-\ners a function of the estimated uncertainty in the hit co-\nordinates and the estimated RMS of the scattering angle\ndistribution. Due to pattern recognition mistakes and sim-\npli\ufb01cations in the track model, the estimated track param-\neter uncertainty may not perfectly re\ufb02ect the RMS of the\nerror distribution. In Belle these imperfections are com-\npensated by scale factors that depend on track pT and\ntan \u03bb. The scale factors are calibrated with cosmic ray\nevents and simulations. In Babar such scale factors are\nnot used.\n6.3 Vertex \ufb01tting by \u03c72 minimization\nThe B Factory experiments have deployed several imple-\nmentations of vertex \ufb01ts. A complete description of these\nalgorithms is outside the scope of this book. In the fol-\nlowing we sketch the formalism of a generic minimum \u03c72\nvertex algorithm. A pedagogical introduction to vertex \ufb01t-\nting can be found in the lectures by P. Avery (Avery, 1991,\n1998).\nTo start, we consider a collection of N charged tracks\nand use a \u03c72 minimization algorithm to determine the\nbest vertex out of which they emerge. Once that is done,\nthe vertex can be improved by adding neutral particles,\nenforcing mass constraints to the in-going or some of the\noutgoing composite particles, and requiring consistency of\nthe vertex location with the collider luminous region. The\ngoodness of a \ufb01t is measured by testing the compatibility\nof the minimum \u03c72 with the expected probability distri-\nbution of a \u03c72 with the relevant number of degrees of\nfreedom.\nFollowing the notation in (Fruhwirth, 1987) we denote\nthe reconstructed helix parameters of track i by pi and\nthe corresponding covariance matrix by Vi. Given a set of\nN outgoing tracks each labeled with an index i, the \u03c72 of\nthe vertex can be generically written as\n\u03c72 =\nN\nX\ni=1\n[pi \u2212hi(x, qi)]T V \u22121\ni\n[pi \u2212hi(x, qi)]\n(6.3.1)\nwhere x is a 3D vector representing the \ufb01tted vertex po-\nsition, qi is the \ufb01tted momentum vector of the outgoing\ntrack and hi, the measurement model, is a function of x\nand qi that expresses the parameters of the helical tra-\njectory of the charged particle emerging from the vertex\nwith momentum qi.\nThe solution to the vertex \ufb01t is the set of parameters\nb\u03be \u2261(x, q1 . . . qN) that minimizes the \u03c72. In case the func-\ntion hi is linear in the parameters \u03be, the solution can be\nexpressed generically as\nb\u03be = \u03be0 \u2212\n\u0014d2\u03c72\nd\u03be2 (\u03be0)\n\u0015\u22121 d\u03c72\nd\u03be (\u03be0)\n(6.3.2)\nwhere \u03be0 is an arbitrary starting point for \u03be. The inverse\nof the second derivative matrix on the right hand side is\nalso half the covariance matrix for b\u03be. If the derivative of hi\nis denoted by Hi, this leads to the well known expression\nfor the linear least squares estimator,\nb\u03be = \u03be0 \u2212C\nX\ni\nHT\ni V \u22121\ni\n[pi \u2212hi(x, qi)]\n(6.3.3)\nwith the covariance matrix\nC =\n X\ni\nHT\ni V \u22121\ni\nHi\n!\u22121\n.\n(6.3.4)\nFor vertex \ufb01ts to helix trajectories the function hi is not\nlinear and hence its derivative Hi not constant. In that\ncase the minimum is obtained by starting from a suitable\nexpansion point \u03be0 and iteratively applying Eq. (6.3.2)\nuntil a certain convergence criterion is met, usually a min-\nimum change in the \u03c72.\nThere are two \ufb02avors of measurement models for tracks\nin vertex \ufb01ts: If the parameters pi are helix parame-\nters, the measurement model is given by the inverse of\nEq. (6.2.1) and Eq. (6.2.2) above. Alternatively, the track\nparameters can also be translated into position and mo-\nmentum space using Eq. (6.2.1) and Eq. (6.2.2). In this\ncase the measurement model is trivial, but has one dimen-\nsion more than the original \ufb01ve parameter helix. Further-\nmore, since the transformation only applies to a particular\npoint on the helix, it needs to be repeated if the vertex\nposition estimate changes between iterations.\nThe number of degrees of freedom of the computed \u03c72\nis NDOF \u22612N \u22123, i.e. the di\ufb00erence between the num-\nber of measurements, 5N (5 helix parameters per track)\nand the number of \ufb01tted parameters 3(N + 1) (3 vertex\ncoordinates and 3 momentum components per track). As-\nsuming that the uncertainties on the track parameters are\ncorrectly estimated i.e. that they are representative of the\nRMS of the error distribution, the minimum \u03c72 follows\nthe probability distribution of a \u03c72 variate with NDOF\ndegrees of freedom whose expectation value equals NDOF .\nA goodness of \ufb01t requirement is usually derived from \u03c72\nand NDOF to retain the acceptable N-prong vertices e.g.\nin the selection of event data samples.\nThe vertex \ufb01tting formalism can be extended with ad-\nditional constraints, such as prior knowledge of the vertex\nposition (for example from knowledge of the interaction\npoint, IP) or the known mass of the decaying particle.\nSuch constraints always take the form of a constraint equa-\ntion\nf(\u03be) = 0.\n(6.3.5)\nA distinction can be made between exact constraints and\nconstraints that have an associated uncertainty. The latter\nare sometimes called \u2018\u03c72 constraints\u2019. Mass constraints are\n\n76\nusually (but not always) implemented as exact constraints\nwhile IP constraints are an example of a \u03c72 constraint. Ex-\nact constraints can be implemented by using a Lagrange\nmultiplier. They add a term to the \u03c72\n\u2206\u03c72 = \u03bbf(\u03be)\n(6.3.6)\nwhere the Lagrange multiplier \u03bb is treated as an addi-\ntional parameter in the vertex \ufb01t. An alternative (more\ne\ufb03cient) method to deal with exact constraints is dis-\ncussed in (Hulsbergen, 2005). For one-dimensional con-\nstraints with an uncertainty \u03c3 the \u03c72 contribution is\n\u2206\u03c72 = f(\u03be)2\n\u03c32\n.\n(6.3.7)\nThis expression can be generalized to more than one di-\nmension by writing it in a matrix notation. Note that each\nindependent constraint adds one degree of freedom to the\n\u03c72.\nThe vertex \ufb01t can also be extended to include re-\nconstructed neutral particles. Photons reconstructed as\ncalorimeter clusters do not add position information to\nthe vertex, but they contribute to the momentum, and\na\ufb00ect the \u03c72 minimization once mass constraints are ap-\nplied.\nSeveral vertex \ufb01ts are implemented in sequence to re-\nconstruct decay trees that involve more than one decay\nvertex, e.g. B \u2192DX transitions. Such decay trees are\nusually reconstructed by starting from the most down-\nstream vertex and working towards the mother of the de-\ncay trees: \ufb01rst \ufb01t the D vertex, then use the result to \ufb01t\nthe B (this approach is sometimes called leaf-by-leaf \ufb01t-\nting). Other more global associations of constraints are\nimplemented for decay trees with leaves or branches with\nmany neutral particles (Hulsbergen, 2005).\nThe vertex \ufb01ts applied in the B Factory experiments\nare essentially extensions of the scheme above \u2013 see in par-\nticular (Tanaka, 2001) for Belle and (Hulsbergen, 2005) for\nBABAR. Implementations of the vertex \ufb01tting algorithm\ndi\ufb00er both in the parameterization of the problem and in\nthe way the \u03c72 is minimized. As outlined above, tracks\ncan be parameterized in terms of helix coordinates or (lo-\ncally) in terms of Cartesian coordinates. The latter leads\nto simpler expressions for derivatives, but may lead to\nslower convergence because derivatives vary more rapidly\nalong the track.\nFor the minimization both the global \u03c72 \ufb01t technique\ndescribed above and the Kalman \ufb01lter are used. Even\nfor algorithms that seemingly use the same minimization\nscheme, the implementations may di\ufb00er. To our knowl-\nedge, the most e\ufb03cient method to \ufb01t tracks to a common\nvertex is the algorithm developed by Billoir, Fruhwirth,\nand Regler (1985), presented in slightly di\ufb00erent from in\n(Fruhwirth, 1987). This algorithm was extended with a\nmass constraint in (Amoraal et al., 2013).\nNot all algorithms are applicable to all vertexing prob-\nlems. The general leaf-by-leaf approach for decay tree \ufb01t-\nting cannot easily be applied to the reconstruction of e.g.\nK0\nS \u2192\u03c00\u03c00 or B0 \u2192K0\nS\u03c00. For these types of decay\ntrees a \u2018global\u2019 decay tree \ufb01t can be used (Hulsbergen,\nf1 =0.76\u00b10.02\n\u00b51= 1.0\u00b10.5\n\u03c31=41.4\u00b10.9\n\u00b52= 2.9\u00b12.4\n\u03c32= 118\u00b16\nf1 =0.84\u00b10.03\n\u00b51=0.01\u00b10.01\n\u03c31=0.97\u00b10.02\n\u00b52=0.21\u00b10.06\n\u03c32=1.96\u00b10.10\n\u2206z residual (cm)\nevents\n\u2206z pull\nevents\nFigure 6.3.1. Residual (left) and pull (right) of the decay\nvertex z position of reconstructed B0 \u2192J/\u03c8 K0\nS candidates in\na BABAR simulated data sample. Fits to a double Gaussian are\nsuperimposed.\n2005). The latter also has the advantage that one has ac-\ncess to the vertex-constrained parameters of all particles\nin the decay tree. However, this algorithm computes a\nsingle covariance matrix for all of the parameters in the\ndecay tree, making it noticeably slower than a leaf-by-leaf\napproach. The CPU consumption of vertex algorithms is\noften a concern because of the combinatoric background\nin the reconstruction and selection of composite particles.\nA strict control on the accuracy of the vertex recon-\nstruction is mandatory for the B Factory experiments\nwhere the primary goal is to determine time-dependent\nCP asymmetries from the distance between two vertices.\nThis is illustrated in Figure 6.3.1 which shows the resid-\nuals and pull20 for the decay vertex z position of recon-\nstructed B0 \u2192J/\u03c8K0\nS (J/\u03c8 \u2192\u00b5+\u00b5\u2212) candidates from\na sample of simulated data taken from BABAR. The ver-\ntex resolution depends on the topology of the decay and\nthe direction and momenta of the \ufb01nal state particles and\nespecially on whether the K0\nS particles decays inside or\noutside the vertex detector volume. These e\ufb00ects are ac-\ncounted for in the per-event reconstruction uncertainty,\nthe estimate of which is computed by the vertex \ufb01t al-\ngorithm. Due to spread in the estimated uncertainty, the\nvertex resolution is not a Gaussian distribution. However,\nthe pull distribution is reasonably Gaussian with an RMS\nvalue close to unity, indicating that the uncertainties are\ncorrectly estimated.\nFor this decay the z residual distribution has an RMS\nof about 70 \u00b5m. A double Gaussian \ufb01t returns a core com-\nponent, which corresponds to about three quarters of the\ndistribution, with a standard deviation equal to 40 \u00b5m.\nThe resolution in the transverse coordinates is compara-\nble to that in z: about 50 \u00b5m.\nFigure 6.3.2 shows the reconstructed mass of B\u00b1 \u2192\nJ/\u03c8K\u00b1 decays in data, from BABAR, \ufb01tted both with and\nwithout a mass constraint on the J/\u03c8 \u2192\u00b5+\u00b5\u2212decay.\nThe mass constraint improves the accuracy of the derived\nJ/\u03c8 momentum and this leads to a large improvement\nin the B\u00b1 invariant mass resolution. The improvement in\nmass resolution is comparable to what one would obtain\n20 A \u2018pull\u2019 is a residual divided by its estimated uncertainty.\nSee also Section 11.5.2.\n\n77\n)\n2\n mass (GeV/c\n\u00b1\nB\n5.2\n5.25\n5.3\n5.35\n5.4\n)\n2\nEvents/(3 MeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\nno constraint\n mass con.\n\u03c8\nJ/\nFigure 6.3.2. Distribution of the reconstructed invariant mass\nof B\u00b1 \u2192J/\u03c8 K\u00b1 decays in BABAR data with and without en-\nforcement of a mass constraint on the J/\u03c8 \u2192\u00b5+\u00b5\u2212decay\nvertex leaf.\nby considering the B\u00b1-J/\u03c8 mass di\ufb00erence instead of the\nB\u00b1 mass. However, the advantage of applying the mass-\nconstrained vertex \ufb01t is that the resolution on both the\nvertex position and on the B momentum are improved.\n6.4 Primary vertex reconstruction and\nbeamspot calibration\nThe majority of beam-beam collisions occur in a tiny re-\ngion in the center of the detectors, the interaction region or\nbeamspot. The size of the interaction region is determined\nby beam optics and has varied through the B Factory\nruns. It is typically 1 mm along the beam (z), 100 \u00b5m in\nthe horizontal direction (x) and a few \u00b5m in the vertical\ndirection (y).\nThe position and size of the beamspot are used as a\nconstraint in the reconstruction of the B0B0 decay time\ndi\ufb00erence \u2206t. Since the beamspot is smallest in the verti-\ncal plane, the vertical coordinate is the most constraining.\nIn the directions along x and z the beamspot is not smaller\nthan a typical B decay length, which is about 25 \u00b5m in\nthe transverse plane and about 200 \u00b5m along the z-axis,\nand its constraint plays a marginal role.\nThe position and shape of the interaction region vary\nwith time and needs to be carefully calibrated and moni-\ntored. The calibration is based on the spatial distribution\nof reconstructed primary vertices (PVs). In the produc-\ntion of a B0B0 or B+B\u2212pair at the \u03a5(4S) resonance\nthere are no particles originating from the primary col-\nlision point other than the B mesons themselves. Con-\nsequently, the primary vertex cannot be directly recon-\nstructed in these decays and the beamspot calibration in-\nstead relies on continuum events. Bhabha and di-muon\nevents have the advantage that there are only two tracks\nin the event, that have both relatively high momentum\nand are guaranteed to originate from the PV. Hadronic\nevents have more tracks and consequently a smaller sta-\ntistical per-event uncertainty on the vertex position, but\nthey are polluted by a b\u00afb contribution. The calibration\nx\n0\n500\n1000\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\nEntries\nMean\nRMS\n 7282\n-0.5021\n 0.1718\n[mm]\n[entries/0.06 mm]\ny\n0\n500\n1000\n1500\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\nEntries\nMean\nRMS\n 7282\n 0.4819\n 0.1305\n[mm]\n[entries/0.04 mm]\nz\n0\n500\n1000\n-30\n-20\n-10\n0\n10\n20\n30\nEntries\nMean\nRMS\n 7282\n -1.913\n 3.169\n[mm]\n[entries/1.2 mm]\nFigure 6.4.1. Distribution of the x (top), y (middle), and z\n(bottom) position of reconstructed primary vertices in a typical\nBelle run (Exp. 5, run 333). From (Tomura, 2002a).\nin BABAR relies both on two-prong events and on multi-\nhadron events with at least 5 tracks. The calibration pro-\ncedure in Belle uses only multi-hadron events (Tomura,\n2002a).\nAn example of the distribution of the position of recon-\nstructed primary vertices in hadronic events in a typical\nBelle run is shown in Figure 6.4.1. In the y direction the\nRMS of the distribution is dominated by the vertex reso-\nlution. In the z direction it is dominated by the beamspot\nsize, while in the x direction it is a combination of both.\nThe distribution of PV positions is characterized by an\naverage position, the direction of its three principal axes\n(which are close, but not identical to the x, y and z axis;\nsee Chapter 2) and the RMS along each axis. The cali-\nbrated position, rotation and sizes are determined from\nmoments of (BABAR) or \ufb01ts to (Belle) the (x, y, z) distri-\nbution of PVs.\nTo determine the size of the beamspot the vertex reso-\nlution must be \u2018subtracted\u2019. In the vertical direction since\nthe resolution is so much wider than the beam size, the\nbeam spread must be estimated by other means. In BABAR\nthe size in y is computed from the luminosity reported by\nthe accelerator (Chapter 1). In Belle it is obtained from\nmeasurements of the size of the HER and LER beams by\nthe accelerator (Tomura, 2002a). When the beamspot is\nused as a constraint in vertex \ufb01ts, its size always appears\nin quadrature with the actual vertex resolution. Hence,\nit is important to know the size in the vertical direction\nprecisely.\n\n78\nFigure 6.4.2. Average primary vertex position in x (top), y\n(center) and z (bottom) as a function of run number in Belle\ndata. From (Tomura, 2002a).\nTo accommodate variations over time the calibration\nprocedure is performed in time slices. Belle \ufb01ts the mean\nposition with the other parameters (the widths and the\nrotation angles) \ufb01xed for every O(104) events. BABAR up-\ndates all parameters every \u223c10 minute interval, corre-\nsponding to approximately the same number of selected\nevents. Figure 6.4.2 shows the average primary vertex po-\nsition as a function of run number in the early days of\nBelle. In this period the typical duration of a run was\nabout 2 hours. Under stable conditions, the variation of\nthe position within a run is much smaller, typically of the\norder of 10 \u00b5m in x, 1 \u00b5m in y and 100 \u00b5m in z in both\nexperiments.\nIn vertex reconstruction the average beamspot can be\nused as a constraint on the production vertex of the B (or\nD, or \u03c4) particle. The \u03c72 contribution takes the form, cf.\nEq. (6.3.7),\n\u2206\u03c72 =\n\uf8eb\n\uf8ed\nxp \u2212xIP\nyp \u2212yIP\nzp \u2212zIP\n\uf8f6\n\uf8f8\nT\nV \u22121\nIP\n\uf8eb\n\uf8ed\nxp \u2212xIP\nyp \u2212yIP\nzp \u2212zIP\n\uf8f6\n\uf8f8\n(6.4.1)\nwhere xp are the parameters of the production vertex in\nthe vertex \ufb01t, xIP is the position of the center of the\nbeamspot and VIP is a 3 \u00d7 3 covariance matrix, represen-\ntative of the size of the beamspot. In Belle the constraint\nis only applied to the coordinates in the transverse plane;\nin BABAR both the 2D and 3D constraint are used, de-\npending on the vertex algorithm. Figure 6.4.3 shows the\nD\u2217+ \u2212D0 mass di\ufb00erence in e+e\u2212\u2192D\u2217+X continuum\nevents where we have selected D\u2217+ \u2192D0\u03c0+ decays with\nD0 \u2192K\u2212\u03c0+ with and without the constraint that the\nD\u2217+ originates from the beamspot. Due to its low mo-\nmentum the direction of the soft pion is very sensitive\nto multiple scattering. Requiring it to originate from the\ninteraction region substantially improves the mass resolu-\ntion.\n)\n2\n) (MeV/c\n0\n)-M(D\n+\nM= M(D*\n\u2206\n142\n144\n146\n148\n)\n2\nEvents/(70 keV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n3\n10\n\u00d7\nno constraint\nbeam spot con.\nFigure 6.4.3. Distribution of the reconstructed D\u2217+ \u2212D0\nmass di\ufb00erence in D\u2217+ \u2192D0\u03c0+ decays with D0 \u2192K\u2212\u03c0+\nfrom BABAR continuum data with and without a primary vertex\nconstraint.\nIn some applications, such as for D\u2217from B decays or\nthe reconstruction of the associated B vertex for \u2206t recon-\nstruction in Belle, the beamspot is used as a constraint on\na decay vertex. In this case the size of the beamspot must\nbe increased with the e\ufb00ective width of the decay length\ndistribution of the (mother) particle, schematically,\nVIP,tot = VIP + V\ufb02ight .\n(6.4.2)\nBoth experiments add the RMS of the B decay length dis-\ntribution in the transverse plane (about 25 \u00b5m, see Fig-\nure 6.4.4) in quadrature with the calibrated beamspot size\nto obtain an e\ufb00ective size appropriate for B decay prod-\nucts. This mostly a\ufb00ects the size in y.\nFinally, although these quantities do not directly per-\ntain to the vertex algorithms, it is convenient in the char-\nacterization of the beamspot, to mention the calibration\nof the beam kinematics. The beam energies are used in\nthe computation of e.g. the beam-energy-constrained mass\n(Chapter 9) and the proper decay time. In principle, there\nare six unknown parameters related to the incident beams,\nnamely the 3-momenta of the electron and positron beam.\nIn practice, the beam-directions are close enough to their\nnominal direction that only the relative direction matters,\nreducing the number of degrees of freedom to four. These\nare parameterized by the center-of-momentum energy \u221as\nand by the boost vector.\nBoth experiments calibrate \u221as with the kinematics of\nfully reconstructed hadronic B decays. In particular, a\n\n79\n0\n1000\n2000\n3000\n4000\n5000\n6000\n-50\n50\n0\n100\n150\n-100\n-150\nB meson flight length in y (\u00b5m)\nFigure 6.4.4. Distribution of the B meson \ufb02ight length in the\ny direction in Belle simulated data. A \ufb01t to a single Gaussian\n(red), with a width of 25 \u00b5m, is superimposed.\ndeviation of \u221as from nominal can be directly inferred from\na shift of the beam-energy-constrained mass relative to\nthe nominal B mass. The uncertainty is dominated by the\nuncertainty on the nominal B mass.\nIn Belle the boost vector is su\ufb03ciently constant that\nit has been \ufb01xed to its nominal value for the entire period\nof data taking. In BABAR the boost vector is calibrated\non a run-by-run basis using the four-momentum sum in\ndimuon events. Note that due to e\ufb00ects of initial and \ufb01nal\nstate radiation, the latter is not a very sensitive probe of\n\u221as.\n6.5 \u2206t determination\nThe analysis of time-dependent CP violation in decays\nof neutral B mesons at the e+e\u2212B Factories requires\nmeasurement of the decay time di\ufb00erence \u2206t of the two\nB mesons in the event (see Chapter 10). The procedures\nto reconstruct the vertex of the \u2018tagging\u2019 B and extract\nthe decay time di\ufb00erence are described in (Tajima, 2004)\nfor Belle and (Aubert, 2001c, 2002a) for BABAR, to which\nthe reader is referred for details.\nWe denote the reconstructed B meson that decays to\nthe \ufb01nal state of interest as Brec. We label the other B\nmeson by Btag, because its decay products are used to\ndetermine the \ufb02avor of Brec at \u2206t = 0. In an asymmet-\nric e+e\u2212B Factory the determination of \u2206t is derived\nfrom the measurement of the di\ufb00erence in the decay ver-\ntex positions of Brec and Btag along the boost axis, which\nis approximately the z axis. Consequently, we talk about\nthe \u2206z measurement and the \u2206z to \u2206t conversion.\nBy far the dominant contribution to the resolution on\n\u2206t is the \u2206z resolution. For most analyses the latter is in\nturn dominated by the Btag vertex resolution. The deter-\nmination of the Brec vertex position is performed with a\nstandard vertex \ufb01t, as described above. The reconstruc-\ntion of the Btag vertex position is more complicated since\nit requires the selection of the subset of tracks that directly\noriginate from the Btag vertex.\n6.5.1 Reconstruction of the Btag vertex\nFigure 6.5.1 shows schematically the topology of an event\nwith the Brec and Btag decays. Since there are no other\nparticles in the event beside the two B mesons, all tracks\nthat are not associated to Brec, i.e. tracks from the rest\nof the event (ROE), necessarily originate from the Btag\ndecay. However, a couple of experimental complications\nmake the reconstruction of the Btag vertex position non-\ntrivial. First, in only a small fraction of events, are all the\ndecay products of the Btag inside the acceptance of the\ndetector, hence a strategy based on a full reconstruction\nis excluded.21\n \nFigure 6.5.1. Schematic view of the geometry in the yz plane\nfor a \u03a5(4S) \u2192BB decay. For fully reconstructed decay modes,\nthe line of \ufb02ight of the Btag can be estimated from the (reverse)\nmomentum vector and the vertex position of Brec, and from\nthe beamspot position in the xy plane and the \u03a5(4S) average\nboost. Note that the scale in the y direction is substantially\nmagni\ufb01ed compared to that in the z direction. From (Aubert,\n2002a).\nSecond, most Btag mesons decay to an open-charmed\nparticle with at least one additional vertex after a \ufb02ight\nlength comparable to the decay length of a B meson. The\nconfusion in the assignment of the tracks between these\nvertices biases the measurement of the Btag position and\ndegrades the Btag vertex resolution.\nThe strategy to select the optimal set of tracks is sim-\nilar in both experiments. First, from the tracks in the\nROE a subset is selected that satis\ufb01es requirements like a\nminimum number of vertex detector hits and a maximum\ntransverse distance to the interaction region. Tracks from\nreconstructed photon conversions and V 0 decays (a neu-\ntral particle decaying into two charged tracks, for exam-\nple K0\nS \u2192\u03c0+\u03c0\u2212) are either removed or replaced with the\nmother particle. Subsequently, all tracks are combined in\na single vertex using the interaction region as a constraint.\nIf the \u03c72 of the vertex is larger than a certain criterion,\nthe worst track is removed and the vertex re\ufb01tted. This\nprocedure is repeated until the criterion is satis\ufb01ed or no\ntracks are left. In BABAR the criterion is a maximum con-\ntribution to the \u03c72 of 6 for each track, while in Belle the\n21 Also the sum of branching fractions of decays used in typ-\nical full reconstruction, see Chapter 7, is small.\n\n80\ncriterion is a maximum vertex \u03c72 of 20 per degree of free-\ndom (since a track contributes two degrees of freedom, the\nBABAR criterion is substantially tighter than the Belle cri-\nterion). In Belle tracks that have been identi\ufb01ed as high\npT leptons by the \ufb02avor tagging algorithm are always kept\nsince those have a large probability to originate from the\nBtag vertex.\nIf the beamspot is used as a constraint in the Btag ver-\ntex reconstruction, even vertices with a single track can\nbe reconstructed. The experiments exploit the beamspot\ndi\ufb00erently. In Belle the constraint is an ellipsoid in the\nxy plane, increased in size to account for the Btag trans-\nverse motion, as explained in Section 6.4. This use of the\nbeamspot leads to a small bias that is proportional to the\nBtag decay time and is treated as a systematic uncertainty.\nIn BABAR the Btag direction and origin are reconstructed\nwith a vertex \ufb01t using the Brec vertex and momentum and\nthe calibrated beamspot position and \u03a5(4S) momentum.\nThis Btag \u2018pseudo-particle\u2019 is subsequently used as any\nother track in the Btag vertex reconstruction. The advan-\ntage of this approach is that there is no bias due to the\nbeamspot constraint. However, it can only be applied to\nanalyses with a fully reconstructed Brec.\nSince the Btag vertex has in general fewer tracks than\nthe Brec vertex and may be contaminated by D daughter\ntracks, the \u2206z resolution is dominated by the Btag z po-\nsition resolution. The latter is in the range 100 \u2212200 \u00b5m,\nwhich has to be compared to a typical resolution of the\nBrec vertex of 50 \u00b5m. As the total resolution is of the or-\nder of the B mixing period, accurate knowledge of the\nresolution is essential when \u2206t is used in maximum like-\nlihood \ufb01ts to extract the parameters for time-dependent\nCP violation. The calibration of the so-called resolution\nfunction is discussed below.\n6.5.2 From vertex positions to \u2206t\nTo be sensitive to time-dependent CP violating e\ufb00ects the\nvertex resolution must be su\ufb03cient to resolve the oscilla-\ntions due to B0B0 mixing in the decay time distribution.\nGiven a proper decay time t and a momentum vector p,\nthe di\ufb00erence between the production and decay vertex\npositions of a B meson is given by\nxdecay \u2212xprod =\npc\nmc2 c t\n(6.5.1)\nwhere we have explicitly included factors c to express\nmomentum and mass in units of energy. At the \u03a5(4S)\nresonance the B momentum in the \u03a5(4S) rest frame is\np\u2217\nB \u2248340 MeV/c. With a lifetime of 1.5 ps, the B0 decay\nlength in the \u03a5(4S) frame is only \u223c30 \u00b5m, small com-\npared to the typical resolution of vertex detectors. This\nis the main motivation for constructing an asymmetric B\nFactory: the boost of the \u03a5(4S) system increases the de-\ncay length, making the measurement of the decay time\npossible.\nIf the z-axis is chosen along the boost direction, the\nexperimental resolution on the B meson decay time dif-\nference is dominated by the resolution on the decay vertex\nz position. The displacement in z of one of the B mesons\nis related to its proper decay time t by\nzdecay \u2212zprod = \u03b3\n\u0010\n\u03b1 cos \u03b8 + \u03b2\np\n1 + \u03b12\n\u0011\nct (6.5.2)\nwhere \u03b3 and \u03b2 are the boost parameters from the \u03a5(4S)\nframe to the lab frame and \u03b8 and \u03b1 = p\u2217\nBc/mBc2 are the\npolar angle and boost factor of the B in the \u03a5(4S) frame.\nSince no tracks originate from the production vertex,\nthe sensitivity to the decay time di\ufb00erence of the B mesons\ncomes mainly through the di\ufb00erence in the z positions of\nthe decay vertices. As the polar angles of the two B mesons\nare exactly opposite, the di\ufb00erence in the z positions can\nbe expressed as\nz1\u2212z2 = \u03b3\u03b2\np\n1 + \u03b12c(t1\u2212t2)+\u03b3\u03b1 cos \u03b8c(t1+t2). (6.5.3)\nIf the small parameter \u03b1 \u22480.06 is ignored, one obtains\nthe well known approximation\n\u2206t = \u2206z/\u03b3\u03b2c.\n(6.5.4)\nThis expression is used for all time-dependent analyses in\nBelle and for those without a fully reconstructed Brec in\nBABAR. The average value for the boost factor is \u03b2\u03b3 = 0.55\nin BABAR and \u03b2\u03b3 = 0.42 in Belle. It is calculated directly\nfrom the beam energies and has a typical uncertainty of\n0.1%. For a typical \u2206z resolution of 100 \u00b5m, the \u2206t res-\nolution is 0.6 ps, a bit less than half the B lifetime and\nsmall compared to the B0 oscillation period of \u223c12.5 ps.\nIgnoring the second term in Eq. (6.5.3) leads to a\ncos \u03b8 and decay time dependent bias. If the detection ef-\n\ufb01ciency is symmetric in cos \u03b8, the expectation value of\nthe bias is zero.22 Ignoring the acceptance and taking\nP(cos \u03b8) \u221d1\u2212cos2 \u03b8, the RMS of this term is 2\u03b3\u03b1c\u03c4B0/\n\u221a\n5,\nor about 30 \u00b5m (taking \u27e8t1 + t2\u27e9\u223c2\u03c4B0). Consequently,\nits contribution to the resolution is small but not negligi-\nble.\nIn the case of a fully reconstructed Brec the momentum\ndirection is measured with su\ufb03cient precision to correct\nfor the B momentum in the \u03a5(4S) frame. However, as can\nbe seen in Eq. (6.5.3) the correction depends on the sum of\nthe decay times, t1+t2, which can only be determined with\nvery poor resolution. BABAR has used the estimate t1 +\nt2 = \u03c4B+|\u2206t| to correct for the measured Brec momentum\ndirection and extract \u2206t from Eq. (6.5.3), giving\n\u2206t = \u2206z/c \u2212\u03b3\u03b1 cos \u03b8 \u03c4B\n\u03b3\u03b2 + s\u03b3\u03b1 cos \u03b8\n(6.5.5)\nwhere s is the sign of \u2206z and terms quadratic in \u03b1 have\nbeen ignored. The distribution of the event-by-event dif-\nference between \u2206t computed with Eq. (6.5.4) and Eq.\n(6.5.5) has an RMS of 0.20 ps. Therefore, for a typical\nresolution of 0.6 ps, the cos \u03b8 correction improves the \u2206t\nresolution by about 5% (Aubert, 2002a).\nEquation (6.5.5) is used for most B decays to hadronic\n\ufb01nal states in BABAR, while Eq (6.5.4) is used for semi-\nleptonic modes. In Belle the correction is not applied, but\n22 Assuming that also the distribution of events is symmetric\nin cos \u03b8, which is valid in the case of BB events.\n\n81\nincluded in the resolution model. The contribution to the\nresolution is computed on a per-event basis for fully recon-\nstructed \ufb01nal states and empirically parameterized from\nsimulated events for the semi-leptonic modes.\nThe time-dependent analysis of decays B0 \u2192K0\nS\u03c00\nand B0 \u2192K0\nS\u03c00\u03b3 is particularly challenging because there\nare no tracks directly originating from the Brec vertex. In\nearly analyses in BABAR (Aubert, 2004q), the Brec vertex\nposition was estimated from the intersection of the tra-\njectories of one or both K0\nS daughters with the beamspot.\nThe implementation was similar to the reconstruction of\nBtag vertices with a single track and the standard \u2206z to\n\u2206t conversion (see above) was used. This method su\ufb00ers\nfrom a bias, small compared to the resolution, but irre-\nducible.\nEventually BABAR developed a third method that\nmakes use of a decay tree \ufb01t (Hulsbergen, 2005) which was\napplied to a number of decays including B0 \u2192K0\nSK0\nSK0\nS.\nIn this algorithm the decay time di\ufb00erence \u2206t is extracted\nfrom a single vertex \ufb01t to the \u03a5(4S) \u2192B0B0 decay tree,\nusing all reconstructed particles associated with Brec and\nBtag and knowledge of the average interaction point and\n\u03a5(4S) momentum. The particles missing from the Btag\nvertex are parameterized as a single unconstrained four-\nvector at the Btag vertex. This algorithm maximally ex-\nploits all available information from reconstruction and\nbeam parameter calibration. It is interesting that it ob-\ntains a competitive resolution only if a constraint on the\nB decay time sum is applied. The latter is implemented\nas a \u03c72 constraint t1 + t2 = 2\u03c4B with (RMS) uncertainty\n\u221a\n2\u03c4B. Note that this approach is similar but not identical\nto the substitution t1 + t2 = \u03c4B + |\u2206t| applied in the \u2018mo-\nmentum corrected\u2019 method described above. It has been\nveri\ufb01ed that such a constraint does not bias the \u2206t mea-\nsurement. However, since this method does not lead to\na signi\ufb01cant improvement in resolution, it has only been\napplied to studies of B0 \u2192K0\nS\u03c00 and alike.\n6.5.3 \u2206t resolution function\nTo account for the \ufb01nite decay time resolution the p.d.f.\ndescribing the physical time evolution in a time-dependent\nanalysis is convolved with a resolution function which is\nthe response function that describes the distribution of the\nobserved decay time as a function of the true decay time\n\u2206ttrue. To \ufb01rst order the resolution function is a Gaus-\nsian function with zero mean and a width corresponding\nto the average resolution. In practice, the deviations from\na Gaussian are important. The parameterization and cal-\nibration of the resolution function is described in detail\nin Section 10.4. Here, we brie\ufb02y emphasize features of the\nvertex resolution that impact the \u2206t resolution in time-\ndependent analyses.\nThe estimated uncertainty in the Btag vertex z posi-\ntion is a function of the number of tracks assigned to the\nvertex and the direction and momentum of those tracks.\nIt di\ufb00ers substantially between events, leading to a large\nvariation in the estimated uncertainty on \u2206t, as shown in\n0\n50\n100\n0\n0.5\n1\n1.5\n2\n\u03c3 (ps)\n\u2206t\nEntries/0.06 ps\nB0 \u2192 J/\u03c8KS\n0\nB0 \u2192 \u03c8(2S)KS\n0\nB0 \u2192 \u03c7c1KS\n0\nB0 \u2192 J/\u03c8K*0\nb)\nFigure 6.5.2. Distribution of event-by-event uncertainty on\n\u2206t for the J/\u03c8 K0\nS, \u03c8(2S)K0\nS, \u03c7c1K0\nS and J/\u03c8 K\u22170 events. The\nhistogram corresponds to Monte Carlo simulation and the\npoints with error bars to BABAR data. From (Aubert, 2002a).\nFig. 6.5.2. The estimated event-by-event uncertainty on\n\u2206t is denoted by \u03c3\u2206t.\n (ps)\nt\n\u2206\n\u03c3\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nt residual RMS (ps) \n\u2206\n0.5\n1\n1.5\n2\n2.5\na)\nFigure 6.5.3. RMS of the \u03b4t = \u2206t \u2212\u2206ttrue distribution in\nBABAR simulated events as a function of the estimated event-\nby-event uncertainty in \u2206t. From (Aubert, 2002a).\nTo bene\ufb01t statistically from this variation the esti-\nmated uncertainty is used in the parameterization of the\nresolution function. Fig. 6.5.3 shows the actual \u2206t resolu-\ntion \u2014 de\ufb01ned as the RMS of the error distribution \u2014 in\nsimulated BABAR events as a function of the estimated un-\ncertainty \u03c3\u2206t. The linear correlation illustrates that \u03c3\u2206t\nis a good measure for the actual resolution, although a\nscaling factor of approximately 1.1 must be applied to ob-\ntain pulls with unit RMS. Therefore, the parameterization\nof the resolution function typically uses a width that is\nproportional to \u03c3\u2206t. The proportionality factor is derived\nfrom the data.\nThe bias due to tracks from D daughters depends on\nthe direction of the D meson in the B rest frame: If the D\nmeson moves approximately perpendicular to the z axis,\nthe z positions of D and B vertices coincide and the bias\nis small. Due to the boost of the D meson in the B frame,\nin such events the D daughter trajectories also have a\nrelatively large angle with respect to the beam direction,\nleading to a small vertex position uncertainty. It is for this\nreason that both experiments observe that the bias from\nD daughter tracks is roughly proportional to the per-event\nestimated uncertainty on the Btag vertex z position, as il-\n\n82\n (ps)\nt\n\u2206\n\u03c3\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nt residual (ps) \n\u2206\nMean of \n-0.35\n-0.3\n-0.25\n-0.2\n-0.15\n-0.1\nb)\nFigure 6.5.4. Mean of the \u03b4t = \u2206t \u2212\u2206ttrue distribution in\nBABAR simulated events as a function of the estimated event-\nby-event uncertainty in \u2206t. From (Aubert, 2002a).\nlustrated in Figure 6.5.4. Therefore, the parameterization\nof the resolution function for B decays often also uses a\nmean that is proportional to \u03c3\u2206t.\n\n83\nChapter 7\nB-meson reconstruction\nEditors:\nPaul Jackson (BABAR)\nAn\u02c7ze Zupanc (Belle)\nAdditional section writers:\nJos\u00b4e Ocariz\nThe BABAR and Belle detectors were designed and\nbuilt to detect and reconstruct particles produced in e+e\u2212\ncollisions and their decay products. Particles with long\nenough lifetimes or stable particles that deposit signals\nin subdetectors which in turn allow the measurements of\ntheir momenta or energies and consequently their four-\nmomenta (see Chapters 2 and 5 for more details) are: e\u00b1,\n\u00b5\u00b1, \u03c0\u00b1, K\u00b1, p, p, \u03b3, and K0\nL and are commonly collec-\ntively referred to as \ufb01nal state particles. Particles such as\nB mesons and charm mesons decay inside the beam pipe\nclose to the interaction point. In order to study the proper-\nties of B mesons, or other short-lived particles, they must\n\ufb01rst be reconstructed from their \ufb01nal state particles.\nReconstruction of B mesons proceeds via summing the\nmomenta of all \ufb01nal state particles to check for consis-\ntency with speci\ufb01c exclusive B-meson decays. The goal is\nto measure the four-momentum vector of a reconstructed\nB meson, or to at least identify particles in an event aris-\ning from the same B meson. Candidates are identi\ufb01ed by\nutilizing discriminating variables sensitive to the B-meson\nproperties. The building of these candidates from their\n\ufb01nal state particle momenta is referred to as exclusive\nB-meson reconstruction or also full hadronic reconstruc-\ntion and is described in detail in Section 7.1. Full recon-\nstruction of (semi-) leptonic B-meson decays is not possi-\nble because the neutrinos leave the detectors undetected\nand hence the momentum they carry is not measured\ndirectly. However, due to the experimental setup of B\nFactories additional kinematic constraints can be applied\nwhich allow us to infer the neutrino or semi-leptonically\ndecaying B-meson momentum indirectly. The constraints\nand methods are described in more detail in Sections 7.2\nand 7.4. As explained in Section 7.3 the unique kinematic\nproperties of B-meson decays to D\u2217\u00b1 mesons permit a\npartial reconstruction approach, without recourse to con-\nstraining the entirety of the B decay. As a consequence\nthe partial reconstruction e\ufb03ciency of B mesons is much\nhigher than that achieved by more exclusive techniques.\nThe choice of the most suitable reconstruction method in\nany given analysis depends on the studied decay mode and\nthe physics parameters of interest.\nThe rest of this chapter describes the methods \u2013 proce-\ndures and main kinematical constraints \u2013 used by BABAR\nand Belle to reconstruct and identify decays of B mesons.\nIn each subsection example B-meson decay modes are\nused for illustration of the reconstruction procedures. The\ntechniques relevant to the reconstruction of charm, tau\nand other events are described in other chapters.\n7.1 Full hadronic B-meson reconstruction\nIn most of the analyses we wish to extract some physics pa-\nrameters of interest for a given speci\ufb01c exclusive B-meson\ndecay mode, meaning that the entire B-meson decay chain\nfrom intermediate particles to all \ufb01nal state particles is\nreconstructed. For example, B0 \u2192D\u2217\u2212\u03c0+ decays can be\nreconstructed from \ufb01nal state particles produced in the\nfollowing exclusive decay chain:\nB0 \u2192D\u2217\u2212\u03c0+\n,\u2192D0\u03c0\u2212\n,\u2192K+\u03c0\u2212\u03c00\n,\u2192\u03b3\u03b3.\n(7.1.1)\nIn exclusive reconstruction the reconstruction of the de-\ncay chain proceeds from bottom up. First the selection\nof tracks and clusters not associated with any track is\nperformed. The former are used to construct \ufb01nal state\ncharged particle candidates (i.e. to determine their four-\nmomentum vector), K\u00b1 and \u03c0\u00b1 in the above example, and\nthe latter to construct photon candidates as described in\nChapter 2. In the next stages all decaying particles in the\ndecay chain are reconstructed: two photon candidates are\ncombined to form \u03c00 meson candidates; D0 candidates are\nformed by combining K+, \u03c0\u2212and \u03c00 candidates; D\u2217\u2212by\npairing D0 candidates from the previous level and a neg-\natively charged pion; and \ufb01nally the D\u2217\u2212and \u03c0+ candi-\ndates are combined to form the B0 candidates. At each\nstage the four-momentum of a decaying particle is given\nby the sum of the four-momenta of its decay products\nfollowing the momentum conservation rule.\nNot all combinations of two or more particles which\nform the \u2018mother\u2019 particle candidates are correct. Wrong\ncombinations (or background candidates) can be roughly\ndivided into two categories:23 combinatorial background\nand physics background. Combinatorial background can-\ndidates are random combinations of particles which are\nnot produced in a decay of the same particle. For example,\nin an event two \u03c00 mesons are produced and both decay\ninto two photons. If all four photons are detected then six\ndi\ufb00erent \u03c00 candidates (two photon combinations) can be\nreconstructed in total \u2013 two of them represent correctly re-\nconstructed \u03c00 mesons (signal candidates) while the other\nfour represent combinatorial background candidates. Sim-\nilarly, the B0 candidate in our example can be a combi-\nnation of correctly reconstructed D\u2217\u2212and \u03c0+ candidates,\nwhere the former originates from one B-meson decay and\nthe latter from the decay of the second B meson produced\nin the same event. Another large source of combinatorial\nbackground are events in which a light quark\u2013anti-quark\npair is produced instead of a pair of B mesons \u2013 so called\ncontinuum events (see Chapter 9). The \u2018continuum\u2019 back-\nground is usually the dominant background for rare B-\nmeson decay studies (decays of B mesons that do not\nproceed through the dominant b \u2192c transition). Much\ne\ufb00ort has therefore been invested in the development of\n23 Background composition strongly depends on the studied\nB-meson decay mode. Here only a general overview is given.\n\n84\n]\n2\n) [GeV/c\n0\n\u03c0\n+\n\u03c0\n-\nm(K\n1.8\n1.82\n1.84\n1.86\n1.88\n1.9\n1.92\n2\nEntries per 0.001 GeV/c\n0\n50\n100\n150\n200\n250\n300\n3\n10\n\u00d7\n]\n2\n) [MeV/c\n0\n\u03c0\n+\n\u03c0\n-\n)-m(K\n+\n\u03c0\n0\nD]\n0\n\u03c0\n+\n\u03c0\n-\nm([K\n140 142 144 146 148 150 152 154\n2\nEntries per 0.001 MeV/c\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n3\n10\n\u00d7\nFigure 7.1.1. Invariant mass distribution of D0 candidates\nreconstructed in K\u2212\u03c0+\u03c00 (left) and D\u2217+ \u2212D0 mass di\ufb00erence\nfor D\u2217+ candidates reconstructed in D0\u03c0+ and D0 in K\u2212\u03c0+\u03c00\ndecay modes (right) in simulated events. The correctly recon-\nstructed D0 (D\u2217+) candidates peak at the nominal D0 mass\n(D\u2217+ \u2212D0 mass di\ufb00erence) indicated by vertical dashed lines.\nFull histograms show the contribution of background candi-\ndates. The signal regions are indicated by the two vertical lines.\ncontinuum suppression techniques. They are described in\ndetail in Chapter 9.\nThe physics background originates from speci\ufb01c B-\nmeson decays to \ufb01nal states which can be easily misiden-\nti\ufb01ed as the \ufb01nal state under study. For example, consider\nthe charmless B+ \u2192K+\u03c0\u2212\u03c0+ decays. The same or a\nvery similar \ufb01nal state can also be achieved in many other\nB-meson decays, like for example: the B+ \u2192D0\u03c0+ \u2192\nK+\u03c0\u2212\u03c0+ decay chain leads to the same \ufb01nal state; B+ \u2192\nD0\u03c0+ \u2192K+K\u2212\u03c0+ and B+ \u2192K+J/\u03c8 \u2192K+\u00b5\u2212\u00b5+,\nwhere in the former case the K\u2212from the D0 decay is\nmis-identi\ufb01ed as \u03c0\u2212and in the latter the two muons as\npions, respectively; B+ \u2192D0\u03c0+ \u2192K+\u03c0\u2212\u03c0+\u03c00, B+ \u2192\nD0\u03c1+ \u2192K+\u03c0\u2212\u03c0+\u03c00 and B+ \u2192K+\u03b7\u2032 \u2192K+\u03c0\u2212\u03c0+\u03b3 de-\ncays have four-body \ufb01nal states but can still contaminate\nsignal candidates when the \u03c00 or \u03b3 are not reconstructed.\nPhysics backgrounds are potentially more dangerous than\ncombinatorial background because their distributions of-\nten peak around same values as distributions of the signal\ndecay mode.\nIn the rest of this section most commonly used kine-\nmatical constraints which can help to reduce the contribu-\ntion of combinatorial as well as physics backgrounds are\ndiscussed.\n7.1.1 Kinematical discrimination of B mesons\n7.1.1.1 Invariant mass and mass di\ufb00erence\nIn the case of B-meson decays via intermediate resonances,\nas shown in Equation (7.1.1), the most straightforward\nway to suppress the contribution of combinatorial back-\nground is to select only candidates populating the regions\naround the nominal masses (signal regions) of the decay-\ning particles in the invariant mass distributions. Figure\n7.1.1 shows for example the invariant mass distribution of\nD0 candidates reconstructed in the K\u2212\u03c0+\u03c00 decay mode\n(charge conjugation is implied). In this example a clear\nsignal peak is visible over the smooth contribution of com-\nbinatorial background candidates. By selecting candidates\nthat populate the signal region, indicated by two vertical\nlines, large amounts of combinatorial background are re-\njected while retaining almost all signal D0 candidates. The\nsignal region varies for di\ufb00erent particles and even for the\nsame particle reconstructed in di\ufb00erent decay modes. In\ngeneral, the invariant mass distribution of signal candi-\ndates is given by a convolution of the particle\u2019s true line-\nshape (usually a relativistic Breit-Wigner) and a detector\nresolution (usually described by the Gaussian function)\nstemming from the experimental uncertainty in the deter-\nmination of momenta of the particle\u2019s decay products. It\ntherefore depends on the resolution achieved in a given\ndecay mode and the natural width of the reconstructed\nparticle, if it\u2019s comparable or larger to the resolution. In\ncase of D0 mesons the natural width is negligible com-\npared to the detector resolution which ranges from around\n5-6 MeV/c2 in decay modes to charged \ufb01nal state par-\nticles only (e.g. K\u2212\u03c0+, K\u2212\u03c0+\u03c0+\u03c0\u2212) and up to around\n12 MeV/c2 in decay modes with one neutral pion. Com-\nposite particles whose natural width is much larger than\nthe invariant mass resolution are for example K\u2217(892) and\n\u03c1(770) with natural widths around 50 and 150 MeV/c2,\nrespectively.\nIn the example B-meson decay the D\u2217+ mesons are re-\nconstructed in the D0\u03c0+ decay mode. The energy release\nin the D\u2217+ \u2192D0\u03c0+ decay is very small (The D\u2217+ mass\nis only about 6 MeV/c2 above the D0\u03c0+ threshold). The\nD\u2217+ momentum measurement is dominated by the D0\nmomentum. The pion has low momentum, whose magni-\ntude and direction are well measured. Therefore, most of\nthe uncertainty in the D\u2217\u2019s momentum results from the\nmeasurement resolution of the D0 momentum. This in-\ntroduces a correlation between the measured D0 and D\u2217\ninvariant masses. Due to this correlation, the experimen-\ntal smearing of the D0 momentum (partly) cancels in the\nD\u2217+ \u2212D0 mass di\ufb00erence, \u2206m = m(D\u2217+) \u2212m(D0). The\nmass di\ufb00erence has a much better resolution and discrimi-\nnates more e\ufb00ectively between signal D\u2217+ and background\nthan the D\u2217+ invariant mass. Figure 7.1.1 shows the mass\ndi\ufb00erence distribution for D\u2217+ \u2192D0\u03c0+ decays, where\nthe D0 is reconstructed in the K\u2212\u03c0+\u03c00 mode. As can be\nseen the mass di\ufb00erence is about an order of magnitude\nbetter resolved than the mass of the D0. The mass di\ufb00er-\nence is commonly used to discriminate between the signal\nand background for particles reconstructed from compos-\nite particles with small energy released in the decay; apart\nfrom D\u2217mesons, such cases include also excited charm\nbaryons decaying to \u039bc, charmonium(-like) states decay-\ning to J/\u03c8, etc.\nKinematic \ufb01tting can improve the momentum (invari-\nant mass) resolution of reconstructed particles and there-\nfore also the signal and background discrimination. Details\nof kinematic \ufb01tting and performance improvements that\ncan be achieved are described in Chapter 6.\n\n85\n7.1.1.2 Energy di\ufb00erence \u2206E and beam-energy substituted\nmass mES\nIn principle, the invariant mass of B mesons could also\nbe used to distinguish between signal and background B-\nmeson candidates. However, as it will be explained in what\nfollows, the experimental setup of the B Factories allows\none to set additional kinematical constraints which im-\nprove the knowledge of the B-meson\u2019s momentum and\nhence allow for better signal and background discrimina-\ntion.\nThe \u03a5(4S) decays in two same-mass particles, B and\nB, thus imposing two constraints in the CM frame. If the\nB meson is correctly reconstructed, the energy of its decay\nproducts has to be equal to half the CM energy or equal\nto the beam energy in the \u03a5(4S) rest frame,24 and its\nreconstructed mass has to be equal to that of the B meson:\nE\u22c6\nrec = E\u22c6\nbeam = \u221as/2,\n(7.1.2)\nmrec = mB.\n(7.1.3)\nIn order to exploit the speci\ufb01cs of B-meson decay kine-\nmatics, two variables are de\ufb01ned, the beam-energy substi-\ntuted mass, mES, and the energy di\ufb00erence, \u2206E. They\ntogether exploit in an optimal way the information con-\ntained in the equations above.\nThe energy di\ufb00erence \u2206E can be expressed in a\nLorentz-invariant form as\n\u2206E = (2qBq0 \u2212s) /2\u221as,\n(7.1.4)\nwhere \u221as = 2E\u22c6\nbeam is the total energy of the e+e\u2212system\nin the CM frame, and qB and q0 = (E0, p0) are the Lorentz\nfour-vectors representing the energy-momentum of the B\ncandidate and of the e+e\u2212system, q0 = qe+ + qe\u2212. In the\nCM frame, \u2206E takes the more familiar form\n\u2206E = E\u22c6\nB \u2212E\u22c6\nbeam,\n(7.1.5)\nwhere E\u22c6\nB is the reconstructed energy of the B meson.\nThe uncertainty of \u2206E originates from the error in the\nB-meson energy measurement, \u03c32\nE\u22c6\nB, and the beam energy\nspread, \u03c32\nE\u22c6\nbeam:\n\u03c32\n\u2206E = \u03c32\nE\u22c6\nB + \u03c32\nE\u22c6\nbeam.\n(7.1.6)\nThe \u2206E resolution receives a sizable contribution from\nthe beam energy spread, but is generally dominated by\ndetector energy resolution (this being the dominant term\nfor modes involving photons). Figure 7.1.2 (a and b) shows\nthe \u2206E distributions for two cases: B+ \u2192K0\nS\u03c0+, K0\nS \u2192\n\u03c0+\u03c0\u2212and B+ \u2192K+\u03c00, \u03c00 \u2192\u03b3\u03b3. A clear di\ufb00erence in\nthe \u2206E resolution is seen between decay modes with and\nwithout photons in the \ufb01nal state. The long tail at low\n\u2206E for the B0 \u2192K+\u03c00 signals comes from the photon\nshower leakage in the calorimeter crystals.\nThe measurement error \u03c3E\u22c6\nB receives contributions\nfrom the errors in the absolute values of the momenta\n24 All quantities with a star symbol (\u22c6) are estimated in the\nCM frame unless otherwise stated.\n0\n10000\n20000\n30000\n40000\n50000\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n(a)\nentries\n\u0394E(GeV)\n0\n5000\n10000\n15000\n20000\n25000\n30000\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n\u0394E(GeV)\n(b)\nentries\n0\n10000\n20000\n30000\n40000\n50000\n60000\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nmES(GeV/c2)\n(c)\nentries\n0\n10000\n20000\n30000\n40000\n50000\n60000\n70000\n80000\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n(d)\nmES(GeV/c2)\nentries\nFigure 7.1.2. The \u2206E and mES distributions for (a and c)\nB+ \u2192K0\nS\u03c0+ and (b and d) B+ \u2192K+\u03c00. Solid line his-\ntograms are signal events generated using GEANT Monte Carlo\nand dotted histograms are from the continuum MC. The signal\nresolution in \u2206E is much worse for B+ \u2192K+\u03c00, due to the\nneutral pion present in the \ufb01nal state, but the di\ufb00erence is less\npronounced in mES as explained in the text.\nof the decay products. The momenta of the B-meson de-\ncay products can be combined in a second variable that\nis only weakly correlated to \u2206E. This is possible if the\nvariable depends on the small three-momentum of the B\nmeson to which the larger momenta of the B decay prod-\nucts contribute with opposing signs in the CM frame. The\npioneering experiments invented for this purpose a beam-\nenergy constrained mass. While ARGUS did actually a\n\ufb01t of the B-meson four momentum with the B-meson\nenergy constrained to the beam energy, CLEO used a\nsimpler approach adopted also at Belle, substituting the\nB energy with the beam energy, which is what we call\nthe beam-energy substituted mass or beam-energy con-\nstrained mass25\nmCLEO\nES\n= mbc =\nq\nE\u22c62\nbeam \u2212p\u22c62\nB ,\n(7.1.7)\nwhere p\u22c6\nB is the CM momentum of the B meson, derived\nfrom the momenta of their decay products, and the B-\nmeson energy is substituted by E\u22c6\nbeam.\nThe idea behind \u2206E is di\ufb00erent and complementary\nto that of mES. Whereas the latter is by construction in-\ndependent of the mass hypothesis for each of the particles,\n\u2206E depends strongly on them. If, for example, a kaon is\nmisidenti\ufb01ed as a pion, its energy, and consequently that\nof the B candidate, will be smaller than its true energy.\nThe event then will be shifted towards negative values of\n\u2206E. In contrast, the distribution for signal events peaks\n25 Since only the three-momentum of the B-meson candidate\nis used, this quantity is not Lorentz-invariant.\n\n86\nat zero as expected, making \u2206E especially helpful for dis-\ncriminating from physics background events involving mis-\nidenti\ufb01cation. On the other hand, mES will not change if\na particle is misidenti\ufb01ed, leading to peaking background\nfrom true B decays with incorrectly assigned particle iden-\ntities.\nWhile this is true for symmetric-energy e+e\u2212collid-\ners operating at the Y(4S) (such as CLEO), where the\nlaboratory system and the CM system are identical, it\ndoes not hold for the asymmetric B Factories. The B mo-\nmentum vector can only be boosted to the CM frame af-\nter masses have been assigned, and the result depends on\nthese mass assignments, although much weaker than for\n\u2206E. To strictly keep mass independence, BABAR is using a\nmodi\ufb01ed variable, which makes use of the three-momenta\nin the laboratory system and of the beam energy in the\nCM system:\nmES =\nq\n(s/2 + pBp0)2 /E2\n0 \u2212p2\nB.\n(7.1.8)\nwhere (E0, p0) is the four-momentum of the CM system in\nthe laboratory. This de\ufb01nition is identical with Eq. (7.1.7)\nif the laboratory system is the CM system, i.e., at a\nsymmetric-energy collider. But due to the weak mass de-\npendence, the behavior of mES and mbc are largely the\nsame even at asymmetric colliders and therefore through-\nout this book the common notation mES will be used for\nboth of them. When presenting beam-energy substituted\nmass or beam-energy constrained mass distributions the\nreader should keep in mind that Belle uses the de\ufb01nition\ngiven in Eq. (7.1.7) while BABAR uses the de\ufb01nition given\nin Eq. (7.1.8).26\nTo appreciate this subtlety, we approximate mES \u2248\nmbc, where the approximation arises from the uncertainty\nin the B momentum measurement (boosted to the CM\nframe), \u03c32\np\u22c6\nB, and the beam energy spread, \u03c32\nE\u22c6\nbeam:\n\u03c32mES \u2248\u03c32\nE\u22c6\nbeam +\n\u0012 p\u22c6\nB\nmB\n\u00132\n\u03c32\np\u22c6\nB.\n(7.1.9)\nAs the B mesons are almost at rest in the CM frame,\np\u22c6\nB/mB \u22480.06, the second term in the above equation\ngets small and the resolution in mES is dominated by\nthe spread in the beam energy. This is illustrated in Fig-\nure 7.1.2 (c and d) which shows the mES distributions\nfor B+ \u2192K0\nS\u03c0+ and B+ \u2192K+\u03c00. The signal resolu-\ntion in mES is much less a\ufb00ected by the uncertainty in\nthe measured B-meson four-momentum compared to \u2206E.\nFor signal events, mES yields the mass of the B meson and\nshows a clean peak. For continuum events, composed of\nlight quarks, the only way of reaching the B rest mass\nis by arti\ufb01cially associating random particles. As a conse-\nquence, their distribution displays a slowly varying shape,\nas expected from their combinatorial nature.\nThe mES resolution is around 3 MeV/c2 when no neu-\ntral particles contribute to the \ufb01nal state. The resolution\n26 As to any rule there is also an exception to this one: In the\nmeasurement reported by Belle in Abe (2001f) the de\ufb01nition\nEq. (7.1.8) is used.\nfor \u2206E more strongly depends on the B-meson decay\nmode: it is much larger for low mass \ufb01nal states such as\n\u03c0+\u03c0\u2212(Lees (2013b) quotes \u03c3\u2206E \u223c29 MeV) than for\nhigh mass \ufb01nal states such as D(\u2217)D(\u2217)K (del Amo San-\nchez (2011e) quotes \u03c3\u2206E between 6 and 14 MeV for modes\nwith zero or one D\u22170 meson in the \ufb01nal state).\nThe energy di\ufb00erence and beam substituted mass, de-\n\ufb01ned in Eqs (7.1.5) and (7.1.8), exploit optimally the kine-\nmatical constraints from the \u03a5(4S) decay to two B mesons.\nA small correlation between the \u2206E and mES variables fol-\nlows from their common inputs \u2013 the beam energy, mea-\nsured momentum of charged particles and energy of neu-\ntrals. The correlation from the energy measurement be-\ncomes severe if the \ufb01nal state particles contain high energy\nphotons, as shown in the top scatter plot in Figure 7.1.3.\nThe correlation coe\ufb03cient is +18% for mES and \u2206E in\nB+ \u2192K+\u03c00. The correlation can be reduced by calcu-\nlating mES after modifying the magnitude of the \u03c00 mo-\nmentum but retaining its direction to constrain the recon-\nstructed B energy to be the beam energy.27 The bottom\nscatter plot in Figure 7.1.3 shows that the correlation be-\ntween the modi\ufb01ed mES and \u2206E is reduced and the corre-\nsponding correlation coe\ufb03cient is \u22124% (Duh, 2012). This\ntechnique is found useful only for two-body B decays with\na hard photon, \u03c00 or \u03b7 \u2192\u03b3\u03b3 meson in the \ufb01nal state. For\nother B decays with soft photons only, the modi\ufb01ed mES\nhas similar distribution as that of mES because the mES\nresolution is dominated by the beam-energy spread. Fur-\nthermore, the modi\ufb01cation does not arti\ufb01cially create an\nenhancement in mES for the continuum background.\nFor \ufb01nal states with heavy particles, in particular B\ndecays to baryons, the correlation becomes strong since\nthe beam energy spread \u03c3E\u22c6\nbeam dominates in both vari-\nables. The di\ufb00erence between the mean beam energy used\nin the calculation of \u2206E and mES and the true beam en-\nergy of the event is the same, hence this contribution alone\nwould lead to 100% correlation. Therefore, in these analy-\nses other pairs of variables are preferred. If \u2206E is replaced\nby the invariant mass\nmB =\nq\nE2\nB \u2212p2\nB\n(7.1.10)\nof the reconstructed B candidate, this variable will not de-\npend on the beam energy at all and the correlation with\nmES becomes again very small, as shown in Fig. 7.1.4: dis-\ntributions from simulated events B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212in \u2206E\nvs mES with a correlation coe\ufb03cient of \u221229% compared to\nmB vs mES with a correlation coe\ufb03cient of (\u22122.3\u00b10.5)%\n(Lees, 2013h).\n27 In the calculation of the modi\ufb01ed mES (using Eq. 7.1.7)\nthe momentum of the B meson given as pB = pK+ + p\u03c00 is\nreplaced with pB = pK+ +\nq\n(E2\nbeam \u2212EK+)2 \u2212M 2\n\u03c00 \u00b7\np\u03c00\n|p\u03c00 |,\nwhere M\u03c00 is the nominal mass of \u03c00, and pK+ (p\u03c00) is the\nmeasured K+ (\u03c00) momentum.\n\n87\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n)\n2\n(GeV/c\nbc\nm\nE(GeV)\n\u0394\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n)\n2\n(GeV/c\nbc\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nE(GeV)\n\u0394\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\nFigure 7.1.3. The \u2206E vs mES (= mbc) distributions for the\nB+ \u2192K+\u03c00 signals. The top plot is for the original mES\nde\ufb01nition and the bottom is for the modi\ufb01ed mES case. Belle\ninternal, from the Duh (2012) analysis.\n7.1.1.3 Signal yield extraction\nAfter the reconstruction and selection of a speci\ufb01c exclu-\nsive B-meson decay is performed the next step is to de-\ntermine the number of correctly reconstructed B-meson\ncandidates. Most often the signal yield is extracted by per-\nforming an extended maximum likelihood \ufb01t to the two di-\nmensional \u2206E-mES distribution. In studies in which there\nis negligible correlation between the two variables the dis-\ntribution of events can be modeled by a product of two\none dimensional probability density functions. The \u2206E\nand mES distributions of signal B-meson candidates are\noften modeled with a Gaussian function (or sum of two\nor more Gaussian functions). The background candidates\nare modeled in mES with an empirical function introduced\nby the ARGUS collaboration (Albrecht et al., 1990a):\nArgus(mES|mthr, c) = mES\ns\n1 \u2212\n\u0012 mES\nmthr\n\u00132\n\u00d7\nexp\n\"\n\u2212c\n \n1 \u2212\n\u0012 mES\nmthr\n\u00132!#\n, (7.1.11)\nwhere mthr represents the endpoint in mES distribution\nand c is a free shape parameter. Background in \u2206E is\n)\n2\n(GeV/c\nES\nm\n5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29 5.295\n5.3\nE(GeV)\n\u0394\n-0.04\n-0.02\n0\n0.02\n0.04\n0\n20\n40\n60\n80\n100\n120\n140\n160\n5.25 5.255 5.26 5.265 5.27 5.275 5.28 5.285 5.29 5.295\n5.3\n)\n2\n(GeV/c\ninv\nm\n5.23\n5.24\n5.25\n5.26\n5.27\n5.28\n5.29\n5.3\n5.31\n5.32\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n)\n2\n(GeV/c\nES\nm\nFigure 7.1.4. Distributions from B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212events\n(Monte Carlo). The top plot is for \u2206E vs mES showing a\nstrong correlation, and the bottom is for the invariant mass\nmB vs mES which is only weakly correlated through measure-\nment errors. BABAR internal, from the Lees (2013h) analysis.\nusually modeled with a polynomial function. The choice of\nsignal and background models given above is very general\nand depends on the properties of the studied decay mode\nand background composition. The models used in speci\ufb01c\nstudies are provided in relevant sections and details about\nmaximum likelihood \ufb01tting are provided in Chapter 11.\n7.2 Semileptonic B-meson reconstruction\nAnalyses of B-meson decay modes containing leptons pre-\nsent one of the richest means of extracting information\nabout the CKM matrix, along with an understanding of\nproperties of the b quark bound in a meson. These probes\nare used in a variety of \ufb01nal states where the measurement\nstrategy can be more or less inclusive. Decays of the form:\nB \u2192X\u2113\u03bd, are used to measure |Vcb|, |Vub| and to extract\nbranching fractions of B transitions to charm-type and\nup-type mesons. For semileptonic decays involving charm\nstates (denoted B \u2192Xc\u2113\u03bd), the \ufb01nal state can be recon-\nstructed from the particles produced in a typical exclusive\n\n88\nFigure 7.2.1. The cos \u03b8B,D\u2217\u2113distribution for B0 \u2192D\u2217\u2212e+\u03bde\ndecays (Dungel, 2010). The points with error bars are data and\nfull histograms are, top to bottom, the signal component and\ndi\ufb00erent types of background. Signal decays are constrained to\nlie in the interval (\u22121, 1), while background decays populate a\nmuch wider region.\ndecay chain:\nB0 \u2192D\u2217\u2212\u2113+\u03bd\n,\u2192D0\u03c0\u2212\n,\u2192K+\u03c0\u2212\u03c00\n,\u2192\u03b3\u03b3.\n(7.2.1)\nThe reconstruction of the decay chain proceeds from\nthe identi\ufb01cation of the charged lepton. In tandem with\nthis, the reconstruction of a D meson occurs, most com-\nmonly a suitable ground state neutral or charged meson\n(D0, D0, D+, D\u2212). This ground state D meson may then\nbe combined with soft a \u03c0\u00b1 or \u03c00 in an attempt to form\na D\u2217\u00b1 or D\u22170. A tight constraint on \u2206m is applied to ev-\nidence such transitions. Higher resonant states of charm\nmesons (e.g. D\u2217\u2217) are usually examined in a combination\nof angular and mass distributions.\nUnder the assumption that the neutrino is the only\nmissing particle, the cosine of the angle between the in-\nferred direction of the reconstructed B and that of the\nD(\u2217)\u2113system is\ncos \u03b8B,D(\u2217)\u2113= 2E \u2217\nBE \u2217\nD(\u2217)\u2113\u2212m2\nB \u2212m2\nD(\u2217)\u2113\n2|p \u2217\nB||p \u2217\nD(\u2217)\u2113|\n,\n(7.2.2)\nwhere E \u2217\nB is half of the CM energy and |p \u2217\nB| is\np\nE \u22172\nB \u2212m2\nB.\nThe quantities E \u2217\nD(\u2217)\u2113, p \u2217\nD(\u2217)\u2113and mD(\u2217)\u2113are calculated\nfrom the reconstructed D(\u2217)\u2113system. This cosine is also\na powerful discriminator between signal and background:\nsignal events should strictly lie in the interval (\u22121, 1), al-\nthough \u2013 due to \ufb01nite detector resolution \u2013 about 5% of\nthe signal is reconstructed outside this interval. The back-\nground on the other hand does not have this restriction\nand populates a much wider region (see Fig. 7.2.1).\nThe experimental techniques used in reconstruction of\nsemileptonic B-meson decays are described in more details\nin Section 17.1.1.3.\n7.3 Partial B-meson reconstruction\nThe term partial reconstruction refers to a reconstruction\ntechnique in which not all of the \ufb01nal state particles are\nrequired to be detected and identi\ufb01ed, as is the case in ex-\nclusive (full) reconstruction described in Section 7.1. Par-\ntial reconstruction of the B meson can therefore result in\nsubstantially larger e\ufb03ciency, albeit with reduced purity\nresulting from higher backgrounds.\nBABAR and Belle use the partial reconstruction tech-\nnique mainly in time-dependent studies of B0 \u2192D\u2217\u2212X+\n(where X represents some hadronic state like \u03c0, \u03c1 or D)\nand B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113decays. In these measurements the\nB mesons are reconstructed using only the hadronic state\nX (or charged lepton) and the soft pion from the D\u2217\u2212\u2192\nD0\u03c0\u2212decay. The D0 decay is not reconstructed which in-\ncreases the acceptance.\nThe remainder of this section describes the kinematic\nconstraints and variables used to distinguish between par-\ntially reconstructed signal and background B0 \u2192D\u2217\u2212X+\nand B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113candidates. Physics use cases are de-\nscribed in Sections 17.5 and 17.8.\n7.3.1 B \u2192D\u2217\u00b1X decays\nThe partial reconstruction technique was originally ap-\nplied by CLEO (Brandenburg et al., 1998; Giles et al.,\n1984) to\nB0 \u2192D\u2217\u2212\u03c0+\nf\n(7.3.1)\n,\u2192D0\u03c0\u2212\ns\ndecays, where \u03c0f and \u03c0s are referred to as \u201cfast\u201d and\n\u201cslow\u201d pions, respectively. BABAR and Belle applied this\ntechnique to generic B \u2192D\u2217\u00b1X decays. In principle, X\nmay be any single-particle state (e.g. \u03c0, \u03c1, D, D(\u2217)\ns ) as\nlong as it can be exclusively reconstructed. For simplicity\nthe discussion is restricted only to B \u2192D\u2217\u00b1\u03c0 decays.\nIn this mode the D\u2217\u00b1 meson is created in a helicity zero\nstate and the characteristic angular distributions of the\nD\u2217+ decay products (see Chapter 12 for more details) can\nbe exploited for background suppression.\n7.3.1.1 Kinematic Variables\nThe decay chain given in Eq. (7.3.1) involves 5 particles\n(B0, D\u2217, D0, \u03c0s and \u03c0f), each determined by it\u2019s four-\nmomentum. There are thus 20 parameters in total which\ndescribe the entire decay chain. The experimentally mea-\nsured inputs to the partial reconstruction are only the\nthree-momenta of the fast and slow pion, p\u03c0f and p\u03c0s,\nrespectively. In principle, it is possible to determine all\n\ufb01ve four-momenta from the measured p\u03c0f and p\u03c0s using\nenergy-momentum conservation in the B0 and D\u2217decays\n(8 constraints), the known particle masses of B0, D\u2217\u2212,\nD0, \u03c0s and \u03c0f (5 constraints), and the fact that the en-\nergy of the B0 in the CM frame is equal to the half of\n\n89\nthe beam energy (1 constraint). However, since the B-\nmeson mass and the beam-energy constraints are imposed\nto determine the B-meson four-momentum the signal and\nbackground B-meson candidates cannot be separated by\nkinematic variables used in exclusive studies, like \u2206E and\nmES given in Eqs (7.1.5) and (7.1.8), respectively. Instead,\nvariables which can be used to identify signal events from\nthe decay kinematics are utilized. Many di\ufb00erent possible\nkinematic variables have been used in analyses of partially\nreconstructed B0 \u2192D\u2217\u03c0 decays performed by BABAR and\nBelle.\nThe measured28 p\u03c0f and p\u03c0s represent six independent\nvariables which can be used to distinguish signal events\nfrom background. Consider three of these as p\u03c0f in spher-\nical polar coordinates: magnitude (p\u03c0f ), polar (\u03b8\u03c0f ) and\nazimuthal (\u03c6\u03c0f ) angle. Since the fast pion has no pre-\nferred direction (distribution of signal decays is uniform\nin \u03b8\u03c0f and \u03c6\u03c0f ), only the magnitude, p\u03c0f , is useful. Signal\ndecays are uniformly distributed within a small window\nin p\u03c0f , smeared by the B0 momentum in the CM frame,\nas the fast pion is mono-energetic in the B rest frame.\nBackground events are distributed predominantly outside\nthis window. The three remaining degrees of freedom can\nbe considered as the magnitude of the slow pion momen-\ntum, p\u03c0s, the angle between the slow pion direction and\nthe opposite of the fast pion direction, \u03b4fs, and the az-\nimuthal angle of the slow pion direction around the fast\npion direction. The last of these three provides no useful\ninformation. The cos \u03b4fs peaks sharply at +1 for signal,\nas the slow pion follows the D\u2217direction due to the small\nenergy released in the D\u2217decay, while the background\nevents populate the entire physical region. Instead of the\nslow pion magnitude the cosine of the angle between the\nslow pion direction in D\u2217rest frame and the D\u2217direction\nin CM frame, cos \u03b8hel, is used since the former is correlated\nwith the p\u03c0f for signal events, while the latter is not. For\npartially reconstructed D\u2217\u03c0 events the cos \u03b8hel is given by\ncos \u03b8hel =\n1\np\u22c6\u03c0s\n\u0012E\u03c0sED\u2217\u2212E\u22c6\n\u03c0smD\u2217\npD\u2217\u03b3D\u2217\n\u2212\u03b2D\u2217E\u22c6\n\u03c0s\n\u0013\n,\n(7.3.2)\nwhere the energy and magnitude of the D\u2217momentum\nare given by ED\u2217= EB \u2212\nq\n|p\u03c0f |2 + m2\u03c0f and pD\u2217=\np\nE2\nD\u2217\u2212m2\nD\u2217, respectively, and \u03b3D\u2217= ED\u2217/mD\u2217and\n\u03b2D\u2217=\np\n1 \u22121/\u03b32\nD\u2217. The B-meson energy is taken to be\nhalf of the CM energy, EB = \u221as/2. The quantities de-\nnoted with asterisks in the above equation are calculated\nin the D\u2217rest frame. The distribution for signal events\nin cos \u03b8hel is proportional to cos2 \u03b8hel, as the B0 \u2192D\u2217\u03c0\ndecay is a pseudoscalar to vector pseudoscalar transition.\nThe cos \u03b8hel is calculated using kinematic constraints valid\nonly for signal decays so the background events can popu-\nlate also the unphysical region | cos \u03b8hel| > 1. Figure 7.3.1\nillustrates the discriminating power of the p\u03c0f , cos \u03b4fs\nand cos \u03b8hel kinematic variables for partially reconstructed\nB0 \u2192D\u2217\u2212\u03c0+ decays (Ronga, 2006).\n28 All momenta in the partial reconstruction section are eval-\nuated in the CM frame unless stated otherwise.\n [GeV/c]\nf\n*\np\n2\n2.1\n2.2\n2.3\n2.4\nEvents/0.008 GeV/c\n0\n1000\n2000\n3000\n4000\n\u03c0\n*\nD\n\u03c1\n*\nD\nCorrelated bkgd.\nUncorrelated bkgd.\n [GeV/c]\nf\n*\np\n2.2\n2.3\n2.4\nEvents/0.008 GeV/c\n0\n500\n1000\n1500\n2000\n\u03c0\n*\nD\n\u03c1\n*\nD\nCorrelated bkgd.\nUncorrelated bkgd.\nfs\n\u03b4\ncos\n0.85\n0.9\n0.95\n1\nEvents/0.005 \n0\n5000\n10000\n15000\nfs\n\u03b4\ncos\n0.94\n0.96\n0.98\n1\nEvents/0.005 \n0\n2000\n4000\n6000\n8000\n*\u03b8\ncos\n-1\n0\n1\nEvents/0.056 \n0\n1000\n2000\n3000\n4000\n*\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/0.056 \n0\n1000\n2000\nFigure 7.3.1. The p\u03c0f (top), cos \u03b4fs (middle), and cos \u03b8hel\n(bottom) distributions of partially reconstructed D\u2217\u03c0 candi-\ndates showing selection regions (left) and signal region (right).\nThe arrows indicate the borders of the signal region. Points\nwith error bars show the observed data distribution, while the\nempty histograms show the distribution of signal D\u2217\u03c0 can-\ndidates, and the hatched histograms show the contributions\nof background candidates originating from di\ufb00erent sources\n(Ronga, 2006).\nIn quite few measurements, the cos \u03b4fs variable is re-\nplaced by the \u2018missing mass\u2019,29 mmiss, which should be\nequal to the D0 meson mass for signal B0 \u2192D\u2217\u03c0 de-\ncays. The four-momentum of the missing D0, pD0, can\nbe obtained from the four-momentum conservation in the\ndecay of the B0 and D\u2217. The magnitude of the B-meson\nmomentum in the CM frame, pB, is given by the known\nB-meson energy, EB = \u221as/2, and the known B-meson\nmass: pB =\np\nE2\nB \u2212m2\nB. From the angle between the B\nand \u03c0f, given by,\ncos \u03b8B\u03c0f = m2\nB + m2\n\u03c0\u00b1 \u2212m2\nD\u2217\u00b1 \u22122EBE\u03c0f\n2pBp\u03c0f\n,\n(7.3.3)\nand the measured slow and fast pion momenta, the B\nfour-momentum may be calculated up to an unknown az-\nimuthal angle \u03c6 around p\u03c0f . Depending on the value of\n29 The variables mmiss and cos \u03b4fs are strongly correlated.\n\n90\n)\n2\n(GeV/c\nmis s\nm\n1.82\n1.84\n1.86\n1.88\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\n2\nEvents/(0.7 MeV/c )\nFigure 7.3.2. The mmiss distributions. The curves show, from\nbottom to top, the cumulative contributions of continuum,\npeaking BB, combinatorial BB, and B0 \u2192D\u2217\u2212\u03c1+ back-\nground, and B0 \u2192D\u2217\u2212\u03c0+ signal events (Aubert, 2004p).\n\u03c6, the expected D0 momentum can then be calculated as\np2\nD0(\u03c6) = m2\nB + (p\u03c0f + p\u03c0s)2 \u22122EB(E\u03c0f + E\u03c0s)\n+2pBp\u03c0f cos \u03b8B\u03c0f + 2pBp\u03c0s cos \u03b8B\u03c0f cos \u03b8fs\n+2pBp\u03c0s sin \u03b8B\u03c0f sin \u03b8fs cos \u03c6.\n(7.3.4)\nThe \u03c6-dependent missing mass is then calculated as, m(\u03c6) =\nq\np2\nD0(\u03c6). The value of \u03c6 is not constrained by kinemat-\nics and may be chosen arbitrarily: BABAR de\ufb01nes in Au-\nbert (2004p) the missing mass for partially reconstructed\nB0 \u2192D\u2217\u2212\u03c0+ decays to be mmiss =\n1\n2[mmax + mmin],\nwhere mmax and mmin are the maximum and minimum\nvalues of m(\u03c6), while in analysis of partially reconstructed\nB0 \u2192D\u2217+D\u2217\u2212decays BABAR chooses the value for which\ncos \u03c6 = 0.62, which is the median of the correspond-\ning Monte Carlo distribution for signal events obtained\nusing generated momenta, and de\ufb01nes the missing mass\nmmiss = mmiss(cos \u03c6 = 0.62) (Lees, 2012k). For signal can-\ndidates, the mmiss variable peaks at the nominal D0 mass\nmD0, with a spread of about 3 MeV/c2, while the back-\nground is smoothly distributed, dropping o\ufb00just above\nthe D mass due to lack of phase space. The distribution\nof mmiss for partially reconstructed B0 \u2192D\u2217\u2212\u03c0+ decays\nis shown in Fig. 7.3.2 (Aubert, 2004p).\n7.3.2 B \u2192D\u2217\u00b1\u2113\u03bd\u2113decays\nThe partial reconstruction technique of semileptonic\nB0 \u2192D\u2217\u2212\u2113+\u03bd\u2113\n(7.3.5)\n,\u2192D0\u03c0\u2212\ns\ndecays was \ufb01rst applied by ARGUS (Albrecht et al., 1987a,\n1994a) and later used by other experiments, including\nBABAR and Belle. The signal events are selected using only\nthe charged lepton from the B0 decay and the slow pion\nfrom the D\u2217decay. Due to the undetected neutrino in the\n\ufb01nal state, the kinematics of these decays di\ufb00er from the\npartial reconstruction of hadronic B \u2192D\u2217\u00b1X decays.\nAs a consequence of the limited phase space available\nin the D\u2217decay, the slow pion is emitted within a one-\nradian wide cone centered about the D\u2217direction in \u03a5(4S)\nrest frame. The D\u2217four-momentum can therefore be com-\nputed by approximating its direction as that of the slow\npion, and parameterizing its momentum as a linear30 func-\ntion of the slow pion\u2019s momentum, p\u03c0s:\npD\u2217= \u03b1 + \u03b2p\u03c0s,\n(7.3.6)\nED\u2217=\nq\np2\nD\u2217+ m2\nD\u2217,\n(7.3.7)\nwhere the o\ufb00set and slope parameters \u03b1 and \u03b2 are taken\nfrom the simulation. The approximations used in the de-\ntermination of the D\u2217four-momentum result in an un-\ncertainty in the D\u2217energy of about 400 MeV. The miss-\ning momentum carried by the neutrino is then given by\nenergy-momentum conservation in the B \u2192D\u2217\u2113\u03bd\u2113decays\np\u03bd = pB \u2212pD\u2217\u2212p\u2113.\nOne requires knowledge of the B-meson four-momentum,\npB, to solve this equation. The direction of the motion\nof the B is not known, but it\u2019s momentum is su\ufb03ciently\nsmall (on average 0.34 GeV/c) compared to the typical\nvalues of the magnitudes of lepton and D\u2217momenta so\nthat the three-momentum of the B meson can be set to\nzero. The neutrino invariant mass can then be computed\nas\nM 2\n\u03bd =\n\u0012\u221as\n2 \u2212ED\u2217\u2212E\u2113\n\u00132\n\u2212(pD\u2217+ p\u2113)2 ,\n(7.3.8)\nwhere the energy of the B meson is taken to be half of the\nCM energy. Figure 7.3.3 shows the distribution of partially\nreconstructed B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113decays (\u03c0s\u2113combinations)\nfrom Aubert (2006s). The signal events produce a promi-\nnent peak at M 2\n\u03bd \u22480 with spread around 0.850 GeV2/c4\nwhile background events are distributed in a wide range,\ndropping sharply to zero where there is a lack of phase\nspace.\n7.4 Recoil B-meson reconstruction\nB-meson decays to a \ufb01nal state with one or more neu-\ntrinos o\ufb00er very little or even no kinematic constraints\nwhich are usually exploited in B decay searches in order\nto distinguish these decays from continuum and BB back-\ngrounds, as described in Sections 7.1 and 7.3 and Chapter\n9. Prominent examples of such decays are:\nB0 \u2192\u03bd\u03bd,\nB+ \u2192K+\u03bd\u03bd,\nB0 \u2192D\u2212\u2113+\u03bd\u2113.\n30 BABAR uses in (Aubert, 2006s) a third order polynomial.\n\n91\n0\n200\n400\n600\n800\n1000\n1200\n1400\nx 10 2\nentries /(0.2 GeV2/c4)\nM\u03bd2 (GeV2/c4)\n0\n10000\n20000\n30000\n40000\n50000\n-10\n-8\n-6\n-4\n-2\n0\n2\nFigure 7.3.3. M 2\n\u03bd distribution for right-charge, \u2113\u00b1\u03c0\u2213\ns , (top)\nand wrong-charge, \u2113\u00b1\u03c0\u00b1\ns , (bottom) events. The points corre-\nspond to on resonance data. The distributions of continuum\nevents (dark histogram), obtained from luminosity-rescaled o\ufb00-\nresonance events, and BB combinatorial background events\n(hatched area), obtained from the simulation, are overlaid.\nMonte Carlo events are normalized to the di\ufb00erence between\non-resonance and rescaled o\ufb00peak data in the region M 2\n\u03bd <\n\u22124.5 GeV2/c4 (Aubert, 2006s).\nThe above decays cannot be measured by reconstructing\nall the decay products since the neutrinos cannot be de-\ntected in detectors like BABAR and Belle. A di\ufb00erent ap-\nproach is taken instead, which is referred to as recoil B-\nmeson reconstruction and is described in detail in the rest\nof this subsection. Herein, speci\ufb01c reference will be made\nto the searches for above example decays, to elucidate the\nnecessity of the recoil method, although the techniques of\nstudying the system recoiling against a reconstructed B\nmeson, referred to as the \u201ctag\u201d-B (Btag31), can be applied\nto any analysis. The full list of measurements utilizing the\nrecoil method performed by BABAR and Belle is given in\nTable 7.4.1.\nSeveral di\ufb00erent approaches are used in the recoil B-\nmeson reconstruction technique. These can be separated\naccording to the method used to reconstruct the decay\nof the B meson accompanying the signal B-meson decay.\nThe accompanying B meson can be reconstructed either\ninclusively or exclusively. In the exclusive reconstruction\nthe accompanying B meson is reconstructed in several spe-\nci\ufb01c decay modes. It is further divided into the hadronic\nand semileptonic reconstruction, depending whether the\ndecay modes used are hadronic or semileptonic, respec-\n31 The same notation, Btag, is also used in Chapter 8 where\nit represents a \ufb02avor tagged B-meson.\nTable 7.4.1. List of measurements performed by BABAR and\nBelle using the B recoil techniques.\nHadronic Btag\nB \u2192Xu\u2113\u03bd\n(Bizjak, 2005; Urquijo, 2010)\n(Aubert, 2008ac)\nB \u2192Xc\u2113\u03bd\n(Schwanda, 2007; Urquijo, 2007)\n(Aubert, 2010c,e)\nB \u2192D(\u2217)\u03c0\u2113\u03bd\n(Abe, 2005d)\nB \u2192D\u2217\u2217\u2113\u03bd\n(Liventsev, 2008)\n(Aubert, 2007z, 2008s)\nB \u2192\u03c0\u2113\u03bd\n(Aubert, 2006r)\nB \u2192Xs\u03b3\n(Aubert, 2008q)\nB \u2192\u03c4\u03bd\n(Adachi, 2012b; Ikado, 2006)\n(Aubert, 2005ae, 2008c; Lees, 2013a)\nB \u2192h(\u2217)\u03bd\u03bd\n(Chen, 2007b)\n(Aubert, 2008an)\nB \u2192invisible\n(Hsu, 2012)\nB \u2192D(\u2217)\u2113\u03bd\u2113\n(Aubert, 2008h,y, 2010e)\nB \u2192D(\u2217)\u03c4\u03bd\u03c4\n(Aubert, 2008al; Lees, 2012e)\nB \u2192K\u03c4\u00b5\n(Aubert, 2007au)\nB \u2192\u2113\u03c4/\u2113\u03bd\n(Aubert, 2008az)\nB \u2192\u03c4\u03c4\n(Aubert, 2006b)\nSemileptonic Btag\nB \u2192K\u03bd\u03bd\n(Aubert, 2005b, 2008an)\n(del Amo Sanchez, 2010p)\nB \u2192invisible (+\u03b3)\n(Aubert, 2004y)\nB \u2192\u03c0\u2113\u03bd\n(Hokuue, 2007)\nB \u2192\u03c1\u2113\u03bd\n(Hokuue, 2007)\nB \u2192\u03c4\u03bd\n(Hara, 2010)\n(Aubert, 2005ae, 2006a, 2007a, 2010a)\nB \u2192\u2113\u03bd\n(Aubert, 2010a)\nInclusive Btag\nB \u2192D(\u2217)\u03c4\u03bd\u03c4\n(Bozek, 2010; Matyja, 2007)\nB \u2192D(\u2217)\ns K\u2113\u03bd\u2113\n(Stypula, 2012)\ntively. In the inclusive reconstruction all detected particles\nwhich are not assigned to the signal B-meson are used to\nreconstruct the accompanying B-meson, without testing\nwhether the assigned particles are consistent with a spe-\nci\ufb01c B-meson decay chain. In all cases the recoil B-meson\nreconstruction relies on the following unique properties of\nexperimental setup of the B Factories (see Chapters 1 and\n2 for more details):\n\u2013 the BB pairs are produced without any additional par-\nticles,\n\u2013 the detectors enclose the interaction region almost her-\nmetically,\n\u2013 the collision energy (or initial state energy) is precisely\nknown.\nThe most commonly used strategy in the recoil B-\nmeson reconstruction is to reconstruct exclusively the de-\ncay of one of the B mesons (Btag) in the event. The re-\nmaining particle(s) in the event (detected as tracks or\nenergy deposits in the calorimeter) must therefore orig-\ninate from the other B-meson decay, referred to as the\n\n92\n (GeV)\nECL\nE\n0\n0.5\n1\nArbitrary units\n0\n0.1\n0.2\n0.3\nSignal\nBackground\nFigure 7.4.1. The Eextra(= EECL) distribution of simulated\nsignal and background events. Belle internal, from the B+ \u2192\n\u03c4 +\u03bd\u03c4 Adachi (2012b) analysis.\n\u201crecoil\u201d-B (Brecoil) or \u201csignal\u201d-B (Bsig),32 and are com-\npared with the signature expected for the signal mode. In\nstudies of the example decay, B+ \u2192K+\u03bd\u03bd the presence of\nexactly one charged track (positively identi\ufb01ed as a kaon)\nnot used in the reconstruction of the Btag is required. An\nadditional powerful variable which allows for separation\nof signal and background is the remaining energy in the\ncalorimeter, denoted as Eextra at BABAR or as EECL at\nBelle. It is de\ufb01ned as the sum of the energy deposits in\nthe calorimeter that cannot be directly associated with the\nreconstructed daughters of the Btag or the Brecoil. Figure\n7.4.1 shows a typical distribution of simulated signal and\nbackground events. For signal events (e.g. example decays\ngiven in beginning of this subsection), Eextra must be ei-\nther zero or a small value arising from beam background\nhits and detector noise, since neutrinos do not loose any\nenergy in the calorimeter. On the other hand, background\nevents are distributed toward higher Eextra due to the\ncontribution from additional clusters, produced by unas-\nsigned tracks and neutrals from the mis-reconstructed tag\nand recoil B mesons. For signal B-meson decays to a \ufb01-\nnal state with only one neutrino (like the example de-\ncay B0 \u2192D\u2212\u2113\u03bd\u2113) where the Btag is reconstructed in a\nhadronic decay mode, the neutrino momentum can be in-\nferred using the momentum conservation relation from the\nmeasured momenta of Btag, D\u2212and \u2113, and known initial\nstate: p\u03bd\u2113= pe\u2212+pe+\u2212pBtag\u2212pD\u2212\u2212p\u2113. This allows for the\nconstruction of a powerful kinematic constraint \u2013 missing\nmass squared, de\ufb01ned as MM 2 = |p\u03bd|2, which peaks at\nthe neutrino mass (MM 2 = 0) for correctly reconstructed\nevents.\nIn studies of B-meson decay modes using the exclusive\nrecoil B-meson reconstruction technique the number of\nreconstructed signal decays is linearly proportional to the\ne\ufb03ciency of the Btag reconstruction, which is given by\n\u03b5Btag =\nX\nf\n\u03b5fBf,\n(7.4.1)\n32 The terms used for this B meson in the various BABAR and\nBelle papers are not consistent. Elsewhere in this book we use\nthe term Bsig.\nand the sum runs over the B-meson decays to the exclu-\nsively reconstructed \ufb01nal states f. The \u03b5f are the corre-\nsponding reconstruction e\ufb03ciencies and the Bf are the\nbranching fractions of the B \u2192f decays. In order to\nachieve as high e\ufb03ciency as possible a large number of\nB-meson decay modes are used for the Btag reconstruc-\ntion. On the quark level B mesons decay dominantly via\nb \u2192cW + transitions, where the virtual W materializes ei-\nther into a pair of leptons \u2113\u03bd\u2113(semileptonic decay), or into\na pair of quarks, ud or cs, which then hadronize. The most\ncommon choice for exclusive Btag reconstruction are there-\nfore semileptonic B \u2192D(\u2217)\u2113\u2212\u03bd\u2113decays (semileptonic Btag\nreconstruction) and hadronic B \u2192D(\u2217)n\u03c0, D(\u2217)D(\u2217)\ns\nor\nB \u2192J/\u03c8Km\u03c0 (hadronic Btag reconstruction), where n\nand m indicate any number (n, m \u226410) of charged or\nneutral pions and kaons, respectively. The branching frac-\ntions of these hadronic decay modes are between 10\u22123\nand up to 10\u22122, and the branching fraction for inclusive\nsemileptonic decays33 of a B meson to a D meson plus\nanything else is around 20%. The two analysis techniques\nare complimentary and non-overlapping and, as such, can\nbe readily combined to improve the sensitivity of any re-\ncoil B analysis. This essentially doubles the size of the\navailable Btag sample.\nMany decay modes for which the B meson cannot be\nexclusively reconstructed rely on these methods to make\nmeasurements feasible. For the proposed high luminosity\nasymmetric e+e\u2212super \ufb02avor factories, measurements of\nB decays, not related to CP violation or the CKM picture\nof the Standard Model, will bene\ufb01t from recoil methods.\nThis corresponds to a wide program of purely leptonic,\nsemileptonic and radiative penguin34 B decays. Further-\nmore, with a huge dataset the recoil methods will provide\na clean \u201csingle B beam\u201d which will permit the extraction\nof hadronic B decay branching fractions using a missing\nmass technique.\nIn this section the general idea behind the recoil B-\nmeson reconstruction has been presented. In addition the\nvariables or constraints which can be imposed in studies\nof B-meson decays involving one or more neutrinos with\nrecoil B-meson technique have been brie\ufb02y described. The\nrest of this section is devoted to the description of di\ufb00erent\napproaches to Btag reconstruction. More details on anal-\nyses of decay modes utilizing the recoil B-meson recon-\nstruction (given in Table 7.4.1) can be found in Sections\n17.9, 17.10 and 17.11.\n7.4.1 Hadronic tag B reconstruction\nThe full reconstruction of one B meson, decaying hadron-\nically, has been utilized in a multitude of analyses by the\nB Factories (see Table 7.4.1). The approaches of BABAR\nand Belle di\ufb00er somewhat, providing samples which vary\n33 Semitauonic decays are not included in this case.\n34 A penguin decay is represented by a higher order Feynman\ndiagram including a loop with a W or Z boson; a quark in the\nloop undergoes a tree process - either a strong interaction one,\nor electroweak one.\n\n93\nin e\ufb03ciency and purity. The optimization of these choices\ndepends primarily on the signal mode in the recoil sys-\ntem and the available kinematic constraints which can be\nimposed.\n7.4.1.1 BABAR\nBABAR opts for a semi-exclusive approach where hadronic\nB decays are reconstructed by seeding the event with a\ncharm meson, and combining it with a number of pions\nand kaons. The algorithm underwent a major expansion\nin 2008 doubling its reconstruction e\ufb03ciency. The start-\ning point is the creation of a list with all the possible\nseeds in the event. In the original algorithm, D0, D+,\nD\u22170 and D\u2217+ mesons were used as seeds, reconstructed in\nthe following decay chains: D\u2212\u2192K+\u03c0\u2212\u03c0\u2212, K+\u03c0\u2212\u03c0\u2212\u03c00,\nK0\nS\u03c0\u2212, K0\nS\u03c0\u2212\u03c00, K0\nS\u03c0\u2212\u03c0\u2212\u03c0+; D0 \u2192K+\u03c0\u2212, K+\u03c0\u2212\u03c00,\nK+\u03c0\u2212\u03c0\u2212\u03c0+, K0\nS\u03c0+\u03c0\u2212; D\u2217\u2212\u2192D0\u03c0\u2212; and D\u22170 \u2192D0\u03c00,\nD0\u03b3. The 2008 expansion added the decay chains D\u2212\u2192\nK+K\u2212\u03c0\u2212, K+K\u2212\u03c0\u2212\u03c00; D0 \u2192K0\nS\u03c0\u2212\u03c0\u2212\u03c00, K+K\u2212, K0\nS\u03c00,\n\u03c0+\u03c0\u2212\u03c00, \u03c0+\u03c0\u2212; D\u2217\u2212\u2192D\u2212\u03c00, and the new seeds D+\ns \u2192\n\u03c6\u03c00, K0\nSK+; D\u2217+\ns\n\u2192D+\ns \u03b3 and J/\u03c8 \u2192e+e\u2212, \u00b5+\u00b5\u2212.\nSubsequently, each one of the reconstructed seeds is\ncombined with up to 5 charmless particles to form a Btag \u2192\nDseed Y candidate, where Dseed refers to the charm meson\nused to seed events. The Y system represents a collection\nof hadrons composed of n1\u03c0\u00b1 + n2K\u00b1 + n3\u03c00 + n4K0\nS\n(n1 = 1, ..., 5, n2 = 0, ..., 2, n3 = 0, ..., 2 and n4 = 0, 1)\nand having total charge equal to \u00b11. In the expansion,\nfour neutral Y systems, K+\u03c0\u2212, \u03c0+\u03c0\u2212, K+K\u2212and \u03c00,\nwere added. Overall, the original algorithm reconstructs\nBtag candidates in 630 di\ufb00erent decay chains, and the ex-\npansion in 1768.\nThe Btag candidates thus formed are accepted if they\nsatisfy some loose requirements that ensure kinematic con-\nsistency with a B meson: the beam-energy substituted\nmass, mES, has to be greater than 5.18 GeV/c2, and \u2206E\nhas to satisfy \u22120.12 < \u2206E < 0.12 GeV. Correctly recon-\nstructed events should have the mES and \u2206E distributions\npeak at the B-meson mass and at zero, respectively.\nThese algorithms provide several Btag candidates per\nevent. One of the most extended methods to choose a\nunique candidate selects the decay chain with the high-\nest purity, de\ufb01ned as the fraction of B candidates that\nare correctly reconstructed for mES > 5.27 GeV/c2 in each\nparticular chain. The purity is determined from a \ufb01t to the\nmES spectrum of a data sample, where the signal distribu-\ntion is described by a Crystal Ball function (Skwarnicki,\n1986), named after the Crystal Ball collaboration, de\ufb01ned\nas\nCB(m|\u03b1, n, m0, \u03c3) =\n(\ne\u2212(m\u2212m0)2/2\u03c32,\nif m\u2212m0\n\u03c3\n< \u2212\u03b1\nA\n\u0000B \u2212m\u2212m0\n\u03c3\n\u0001\u2212n , otherwise,\n(7.4.2)\nwhere A = (n/|\u03b1|)ne\u2212|\u03b1|2/2 and B = n/|\u03b1| \u2212|\u03b1|. The\nbackground distribution is described by an ARGUS func-\ntion as de\ufb01ned in Eq. (7.1.11). The purity can also be\nused to reject combinatorial background by selecting only\ndecay chains with a minimum value of purity, typically\nbetween 30% and 55%.\nIn more recent analyses, the best Btag candidate tends\nto be selected together with the rest of the event. For in-\nstance, in B \u2192D\u2217\u2113\u03bd, each Btag candidate is combined\nwith D\u2217and \u2113candidates. The best BtagD\u2217\u2113candidate is\nselected maximizing the energy measured in the calorime-\nter that is used in the reconstruction.\nIn the \ufb01nal selection the kinematic requirements on\nBtag are tightened, candidates are selected with mES >\n5.27 GeV/c2 and narrower \u2206E windows (\u221290 < \u2206E <\n60 MeV is typically used). Events outside these regions\nmay be used to study the combinatorial background.\nWhen all the Btag decay chains are used in the analy-\nsis, the e\ufb03ciencies of the original algorithm, de\ufb01ned as\n\u03b5B0\ntag = N(B0\ntag)\nN(BB) ,\n(7.4.3)\n\u03b5B+\ntag = N(B+\ntag)\nN(BB) ,\n(7.4.4)\nreaches typically 0.2% (B0B0) and 0.4% (B+B\u2212).\n7.4.1.2 Belle\nBelle developed two versions of hadronic Btag reconstruc-\ntion algorithms in the course of its history. In both versions\nthe Btag mesons are reconstructed in a set of exclusive \ufb01-\nnal states, although the approach is slightly di\ufb00erent from\nthe one used by BABAR described above. The di\ufb00erence\nbetween the two versions is in the selection of Btag candi-\ndates. In the \ufb01rst version a set of rectangular cuts is im-\nposed on Btag candidates (referred to as cut-based selec-\ntion), while in the second the selection of Btag candidates\nis made using a NeuroBayes neural network (referred to\nas NB selection) (Feindt, 2004) (see Section 4.4.4 for more\ndetails on neural nets). The latter version is mostly used\nin the measurements using the full data sample collected\nby Belle at the \u03a5(4S). At the end of this section a com-\nparison between the two versions in terms of performance\nis provided.\nIn the cut-based approach Belle reconstructs a set of\nthe following exclusive decay modes: B+ \u2192D(\u2217)0(\u03c0, \u03c1,\na1, D(\u2217)\ns )+ and B0 \u2192D(\u2217)\u2212(\u03c0, \u03c1, a1, D(\u2217)\ns )+. D0 mesons\nare reconstructed in 7 decay modes: K+\u03c0\u2212, K+\u03c0\u2212\u03c00,\nK+\u03c0\u2212\u03c0\u2212\u03c0+, K0\nS\u03c00, K0\nS\u03c0\u2212\u03c0+, K0\nS\u03c0\u2212\u03c0+\u03c00 and K\u2212K+.\nD\u2212mesons are reconstructed in 6 decay modes: D\u2212\u2192\nK+\u03c0\u2212\u03c0\u2212, K+\u03c0\u2212\u03c0\u2212\u03c00, K0\nS\u03c0\u2212, K0\nS\u03c0\u2212\u03c00, K0\nS\u03c0\u2212\u03c0\u2212\u03c0+ and\nK+K\u2212\u03c0\u2212, and the D+\ns mesons are reconstructed in two\ndecay modes: K0\nSK+ and K+K\u2212\u03c0+. The D candidates\nare required to have an invariant mass mD within (4\u22125)\u03c3\nof the nominal D mass value depending on the decay\nmode, where \u03c3 represents the D mass resolution. The D\u22170,\nD\u2217\u2212and D\u2217+\ns\nmesons are reconstructed in D\u22170 \u2192D0\u03c00,\nD0\u03b3, D\u2217\u2212\u2192D0\u03c0\u2212, D\u2212\u03c00 and D\u2217+\ns\n\u2192D+\ns \u03b3 modes, re-\nspectively. D\u2217\n(s) candidates are required to have a mass\ndi\ufb00erence \u2206m = mD\u03c0\u2212mD within \u00b15 MeV/c2 of its nom-\ninal mass or \u2206m = mD(s)\u03b3 \u2212mD(s) within \u00b120 MeV/c2.\n\n94\nThe \u03c10, \u03c1+ and a+\n1 are reconstructed in \u03c0+\u03c0\u2212, \u03c0+\u03c00 and\n\u03c10\u03c0+ modes, respectively. The invariant mass of the \u03c0\u03c0\npairs is required to be within \u00b1225 MeV/c2 of the nominal\n\u03c1 mass, and the \u03c1\u03c0 combinations are required to have in-\nvariant mass between 0.7 and 1.6 GeV/c2 (a1 mass region).\nIn order to obtain reasonable purity of the Btag sample\n(e.g. above 20% in the mES > 5.27 GeV/c2 region) the\ndecay chains with a high multiplicity of tracks and neu-\ntrals (and hence with a large contribution of combinatorial\nbackground) in the \ufb01nal state are excluded. Therefore in\nthe B \u2192D(\u2217)a1 decay modes only the D\u2212\u2192K+\u03c0\u2212\u03c0\u2212,\nK0\nS\u03c0\u2212and D0 \u2192K+\u03c0\u2212modes are used. The selection of\nBtag candidates is based on mES and \u2206E. The de\ufb01nition\nof the signal region in the \u2206E \u2212mES plane depends on\nthe studied signal decay mode. If an event has multiple\nBtag candidates the one with the smallest \u03c72 is selected\nbased on deviations from the nominal values of \u2206E, the\nD(s) candidate mass and the D\u2217\n(s) \u2212D(s) mass di\ufb00erence,\nif applicable. The e\ufb03ciencies as de\ufb01ned in Eqs (7.4.4) and\n(7.4.3) of B0\ntag and B+\ntag are found to be 0.10% and 0.14%,\nrespectively.\nIn the second approach Belle increased the number of\nreconstructed exclusive B decay modes and used a neural\nnetwork in their selection in order to increase the hadronic\nBtag reconstruction e\ufb03ciency (Feindt et al., 2011). In ad-\ndition to the decay modes used in the cut-based selec-\ntion the Btag candidates are reconstructed also in the fol-\nlowing decay modes: B+ \u2192D\u22170\u03c0+\u03c0+\u03c0\u2212\u03c00, D\u2212\u03c0+\u03c0+,\nD0K+, J/\u03c8K+, K+\u03c00, K0\nS\u03c0+, K+\u03c0+\u03c0\u2212, and for neu-\ntral B mesons via B0 \u2192D\u2217\u2212\u03c0+\u03c0+\u03c0\u2212\u03c00, D0\u03c00, J/\u03c8K0\nS,\nK+\u03c0\u2212, and K0\nS\u03c0+\u03c0\u2212.35 The D meson decay modes used\nin the reconstruction of Btag are D0 \u2192\u03c0\u2212\u03c0+, K0\nSK\u2212K+,\nD\u2212\u2192K+K\u2212\u03c0\u2212\u03c00 and D+\ns \u2192K+\u03c0+\u03c0\u2212, K+K\u2212\u03c0+\u03c00,\nK0\nSK+\u03c0+\u03c0\u2212, K0\nSK\u2212\u03c0+\u03c0+, K+K\u2212\u03c0+\u03c0+\u03c0\u2212and \u03c0+\u03c0+\u03c0\u2212\nin addition to the modes used by Belle in the cut-based\nreconstruction, given above. The J/\u03c8 is reconstructed in\ne+e\u2212and \u00b5+\u00b5\u2212modes. The sum of branching ratios of\nreconstructed decay modes adds up to around 12% for\nB+, 10% for B0 (not taking into account branching frac-\ntions of D(\u2217), J/\u03c8, and other intermediate states), 38%\nfor D0, 29% for D+, 18% for D+\ns and 12% for J/\u03c8. The\nreconstruction and selection proceeds in four stages. At\neach stage all available information on a given candidate\nis used to calculate a single scalar variable (referred to\nas network output) using the NeuroBayes neural network\nwhich can be by construction interpreted as a probability\nthat a given candidate is correctly reconstructed (Feindt,\n2004). The network output for each reconstructed particle\nis used as an input to other neural networks in the later\nstage(s). In the \ufb01rst stage \u03c0\u00b1, K\u00b1, K0\nS, \u03b3 and \u03c00 candi-\ndates are reconstructed and classi\ufb01ed, in the second D0,\nD\u00b1\n(s) and J/\u03c8, in the third D\u22170 and D\u2217\u00b1\n(s), and \ufb01nally in\nthe last, fourth stage the B\u00b1 and B0 candidates are re-\nconstructed and classi\ufb01ed. The neural networks of the \ufb01rst\n35 The B \u2192D(\u2217)(\u03c1, a1)+ modes are reconstructed as B \u2192\nD(\u2217)(\u03c00\u03c0+, \u03c0+\u03c0\u2212\u03c0+) in the network based Btag selection\nmeaning that there are no explicit restrictions made on the\ninvariant masses of the two or three pion systems.\nstage particles include measurements of time-of-\ufb02ight, the\nenergy loss in the CDC and Cherenkov light in the ACC\nfor the charged particles, and shower shape variables for\nphotons (see Chapter 2 for subdetectors description). The\nvariables with the largest separation power in the second\nstage, e.g. classi\ufb01cation of D(s) mesons, are the network\noutputs of the daughters (charged or neutral kaons and\npions), the invariant masses of daughter pairs (in case of\nmulti-body decay modes), the angle between the momen-\ntum of the D(s) meson and the vector joining the D(s)\ndecay vertex and interaction point and the signi\ufb01cance\nof the distance between the decay vertex and the inter-\naction point. In the last stage, the B-meson stage, the\nvariables providing good discrimination between correctly\nreconstructed B mesons and background candidates are\nagain the network outputs of the daughters (D(\u2217), J/\u03c8,\npions, kaons), the mass of the D(s) or mass di\ufb00erence\nbetween D\u2217\n(s) and D(s), \u2206E, and the angle between the\nB-meson momentum and the beam. A large fraction of\nBtag candidates are background candidates from contin-\nuum events. As explained in detail in Chapter 9 contin-\nuum background can be quite successfully suppressed at\nB Factories by exploiting event shape variables, such as\nthe reduced second Fox-Wolfram moment, R2, thrust an-\ngle and super Fox-Wolfram moments. In the default Btag\nnetworks these variables are excluded, but outputs of some\nadditional neural networks, which take also the continuum\nsuppression variables into account (with R2 and thrust an-\ngle only, or with R2, thrust angle and super Fox-Wolfram\nmoments), are provided.\nIn an ideal case, one would reconstruct all possible Btag\ncandidates in the given decay modes without making any\nselections (cuts) between the stages. No signal candidates\nwould be lost, i.e. the e\ufb03ciency is maximized. Postponing\nthe moment of the selection to the latest possible stage\nis always the preferred strategy in data analyses, since at\nthe end more information is available which can be used\nto more successfully separate signal and background can-\ndidates. However this procedure is limited by combina-\ntorics and computing resources. Events with many recon-\nstructed particles lead to a large number of possible Btag\ncandidates which of course require more computing time.\nLoose cuts between the reconstruction stages are there-\nfore required in order to keep computing time at a bear-\nable level. These cuts on the network output for a given\ncandidate are not performed at the end of each stage in\nwhich the candidate is reconstructed and classi\ufb01ed but it is\nperformed at the next stage and depends on the complex-\nity of the decay mode in the next stage. As an example,\nthe amount of combinations of the decay B \u2192D\u03c0\u03c0\u03c0 is\nmuch higher then that of the decay B \u2192D\u03c0 given the\nsame number of D candidates. Therefore, a tighter cut on\nthe signal probability of D candidates is performed only\nwhen necessary, e.g. when the reconstruction of all candi-\ndates would require too many resources, as in the case of\nB \u2192D\u03c0\u03c0\u03c0 decays.\nAt the end the kinematic consistency of a Btag can-\ndidate with a B-meson decay is checked using the beam\nconstrained mass, mES, as described previously. Since the\n\n95\n]\n2\n[GeV / c\nbc\nm\n5.24\n5.25\n5.26\n5.27\n5.28\n2\nEvents per 0.5 MeV / c\n0\n50\n100\n150\n200\n250\n300\n350\n3\n10\n\u00d7\ncut-based\nNB\nBackground\nData\nBtag\n+\n5.24\n5.25\n5.26\n5.27\n5.28\n2\nEvents per 0.5 MeV / c\n0\n20\n40\n60\n80\n100\n120\n140\n3\n10\n\u00d7\ncut-based\nNB\nBackground\nData\nBtag\n0\n]\n2\n[GeV / c\nbc\nm\nFigure 7.4.2. The mES (= mbc) distribution of hadronic B+\ntag\n(top) and B0\ntag (bottom) samples obtained by Belle with cut-\nbased (red) and NB selection (blue) (Feindt et al., 2011). In\ncase of the B+\ntag sample the cut on the network output in the\nNB selection is chosen to give equal purity as the cut-based\nselection in mES > 5.27 GeV/c2. In case of the B0\ntag sample\nthe cut on the network output in the NB selection is chosen\nto give equal B-meson signal yield as the cut-based selection.\nThese cuts are arbitrary and are chosen only for the purpose\nof comparing the NB and cut-based Btag selections.\nnetwork output can be interpreted as signal probability\nthe candidates which are reconstructed in di\ufb00erent decay\nmodes can be easily compared to one another. In case\nmultiple Btag candidates are found in an event the one\nwith highest signal probability is taken as the best one.\nThe mES distributions of B+\ntag and B0\ntag samples obtained\nby Belle with cut-based and NB selections are shown in\nFig. 7.4.2. In order to compare the performance in terms\nof Btag e\ufb03ciencies and purities of the NB and cut-based\nselections the network output cuts in the NB selection\nare chosen is such a way that equal purities (in mES >\n5.27 GeV/c2 region) or equal e\ufb03ciencies are obtained in\nboth selections. As can be seen from Fig. 7.4.2 at the same\npurity the signal yield (and hence e\ufb03ciency) is approxi-\nmately two times larger. The NB selection with e\ufb03ciency\nequal to the cut-based selection will result in a much purer\nsample: nearly 90% versus 25% (reducing the background\nlevel by more than a factor of 20). The NB selection used\nin Fig. 7.4.2 is arbitrary and is chosen only for the purpose\nof comparing the NB and cut-based Btag selections. The\n\ufb01nal selection depends on the studied decay mode and can\nbe selected either to give maximal possible Btag e\ufb03ciency\nor high purity. Figure 7.4.3 shows purity-e\ufb03ciency plots\nfor B+\ntag and B0\ntag for the default NB selection and the\none including continuum suppression. The highest pos-\nsible e\ufb03ciency that can be achieved with the NB selec-\ntion at Belle is around 0.18% for B0\ntag and 0.28% for B+\ntag\nwith around 10% purity. This corresponds to an improve-\nment in e\ufb03ciency by roughly a factor of two comparing to\nBelle\u2019s cut-based Btag selection.\n7.4.2 Semileptonic tag B reconstruction\nThis method of semi\u2013exclusive B reconstruction involves\nthe selection of a D meson and suitable lepton candidate,\n\u2113, which are then combined into a D\u2113candidate.\nThe Btag is reconstructed in the set of semileptonic B\ndecay modes B\u2212\u2192D0\u2113\u2212\u03bd\u2113X, where \u2113denotes an e or\n\u00b5, and X can be either nothing or a transition particle\nfrom a higher mass charm state decay, which one does not\nnecessarily need to reconstruct. This methodology natu-\nrally includes the B\u2212\u2192D0\u2113\u2212\u03bd\u2113and B\u2212\u2192D\u22170\u2113\u2212\u03bd\u2113\nmodes and also retains those modes with excited D me-\nson states which decay, via the emission of soft transitions\nparticles, to a D0. The technique can be similarly applied\nto the tagging of neutral B mesons where one would recon-\nstruct B0 \u2192D(\u2217)+\u2113\u2212\u03bd\u2113for a combination of all possible\nB0 \u2192D+\u2113\u2212\u03bd\u2113and B0 \u2192D\u2217+\u2113\u2212\u03bd\u2113states reconstructed\nexclusively. The main loss in e\ufb03ciency arises from the B\nand charm decay branching fractions while further selec-\ntion criteria must be applied in order to suppress non-B\ndecay backgrounds (continuum) and fakes from hadronic\nB decays.\nThe D0 decay is reconstructed by BABAR in the four\ncleanest hadronic modes: K\u2212\u03c0+, K\u2212\u03c0+\u03c0\u2212\u03c0+, K\u2212\u03c0+\u03c00,\nand K0\ns\u03c0+\u03c0\u2212. The K0\ns is reconstructed only in the mode\nK0\ns \u2192\u03c0+\u03c0\u2212. Belle reconstructs D0 candidates in ten de-\ncay modes (Hokuue, 2007): in addition to the four de-\ncay modes above, the K0\ns\u03c00, K0\ns\u03c0+\u03c0\u2212\u03c00, K\u2212\u03c0+\u03c0+\u03c0\u2212\u03c00,\nK+K\u2212, K0\nsK+K\u2212and K0\nsK\u2212\u03c0+ modes are also included.\nThe added bene\ufb01t of reconstructing the low momentum\ntransition daughter in D\u22170 decays is to provide a more\ncomplete and exclusive tag B selection. Indeed if one ne-\nglects to reconstruct these \u03c00 or \u03b3 daughters (from D\u22170 \u2192\nD0\u03c00/\u03b3) then they will be considered in the reconstruc-\ntion of the signal B target mode. However, it is observed\nthat the semi-exclusive reconstruction of B \u2192D0\u2113\u03bdX\nprovides a higher e\ufb03ciency with some loss of purity.\nFor neutral B tags the selection becomes that of either\nB0 \u2192D+\u2113\u2212\u03bd\u2113or B0 \u2192D\u2217+\u2113\u2212\u03bd\u2113. The D+ decays are\nreconstructed at Belle in seven decay modes K\u2212\u03c0+\u03c0+,\nK0\nS\u03c0+, K\u2212\u03c0+\u03c0+\u03c00, K0\nS\u03c0+\u03c00, K0\nS\u03c0+\u03c0+\u03c0\u2212, K0\nSK+ and\nK+K\u2212\u03c0+ (Hokuue, 2007), while BABAR uses only the \ufb01rst\ntwo decay modes. The D\u2217+ decays can be reconstructed\nas both D0\u03c0+ and D+\u03c00. The mass di\ufb00erence between D\u2217\nand D provides a powerful constraint as does the invariant\nmass of the D0 or D+ candidate.\nThe center-of-mass lepton momentum (p\u2217\n\u2113) for both\nelectrons and muons is selected to be greater than 0.8\n(1.0) GeV/c at BABAR (Belle). This is the lower end of\nmuon identi\ufb01cation for the current B Factories and there\nis commonly non-B background below p\u2217\n\u2113\u223c1 GeV/c. The\n\n96\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nPurity [%]\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\nEfficiency [%]\nNB without continuum suppression\nNB with simple continuum suppression\nNB with continuum suppresion with SFWM\ncut-based selection\nBtag\n+\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nPurity [%]\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\nEfficiency [%]\nBtag\n0\nNB without continuum suppression\nNB with simple continuum suppression\nNB with continuum suppresion with SFWM\ncut-based selection\nFigure 7.4.3. Purity-e\ufb03ciency plots for hadronic B+\ntag (left) and B0\ntag (right) as obtained by Belle with neural network based\nselection (NB) and cut-based selection (Feindt et al., 2011). The network based selection can include no continuum suppression\nvariables (blue), only simple ones (green) or Super-Fox-Wolfram moments (SFWM; red).\nreconstructed D mesons are required to be within \u00b13\u03c3\n(\u00b12.5\u03c3) at BABAR (Belle) of their nominal mass value. As\nexplained in Section 7.2 the cosine of the angle between\nthe B meson and the D(\u2217)\u2113candidate momenta, cos \u03b8B,D\u2113\nde\ufb01ned in Eq. (7.2.2), is a powerful discriminant. In case\nthe D\u2113and the neutrino are the only decay products of\nthe B then cos \u03b8B,D\u2113must lie in the physical region be-\ntween \u00b11. If additional decay products from the cascade\nof a higher mass charm state down to the D0 go unre-\nconstructed then this will force the value of cos \u03b8B,D\u2113to\nbe smaller. In order to keep such candidates events with\ncos \u03b8B,D\u2113between \u22122.5 and +1.1 are usually accepted.\nThe positive limit is allowed to be slightly outside of the\nphysical region to account for detector and reconstruc-\ntion e\ufb00ects. Of course, for the reconstruction of exclusive\nchannels (B\u2212\u2192D0\u2113\u2212\u03bd\u2113, B\u2212\u2192D\u22170\u2113\u2212\u03bd\u2113, B0 \u2192D+\u2113\u2212\u03bd\u2113\nand B0 \u2192D\u2217+\u2113\u2212\u03bd\u2113), the selection is tightened to only\nconsider the physical region.\nA typical B\u2212\u2192D0\u2113\u2212\u03bd\u2113X selection at BABAR yields\nan e\ufb03ciency of approximately 6 \u00d7 10\u22123 with a mode de-\npendent purity which averages to \u223c60%. For the neutral\nB reconstruction the e\ufb03ciency is typical half that of a\nsimilar charged B selection.\nThe loss of a neutrino in the semileptonic tagging mode\nlimits the constraints that can be imposed compared to\nthe case when all of the B meson decay products are\nreconstructed. For example the signal B direction can-\nnot be found as is possible for hadronic B reconstruction.\nHowever, this constraint is not of paramount importance\nin the analysis of signal decay modes to \ufb01nal state with\nmore than one neutrino like for example B+ \u2192\u03c4 +\u03bd\u03c4 or\nB0 \u2192\u03bd\u03bd). The knowledge of signal B momentum enables\ncalculation of missing mass which is a very powerful vari-\nable to separate signal B decays with a single neutrino in\nthe \ufb01nal state from background decays, but becomes weak\nwhen multiple neutrinos are present in the signal B decay.\n7.4.3 Inclusive Btag reconstruction\nAs discussed in the previous two sections the reconstruc-\ntion of the recoil B meson using the hadronic and semi-\nleptonic Btag samples has many bene\ufb01ts, however su\ufb00ers\nfrom low reconstruction e\ufb03ciencies. To increase the statis-\ntics Belle adopted an inclusive Btag reconstruction (Bozek,\n2010; Matyja, 2007) in studies of semitauonic B \u2192D(\u2217)\u03c4 \u2212\u03bd\ndecays (see Section 17.10). In contrast to the measure-\nments utilizing the hadronic or semileptonic recoil Btag\nreconstruction technique the procedure in this case is \ufb01rst\nto reconstruct the signal side (pairs of a D(\u2217) and a lep-\nton or pion from tau decay). In the second step the Btag\nis inclusively reconstructed from all remaining particles\npassing certain selection criteria however without checking\nconsistency with any speci\ufb01c B-meson decays. The num-\nber of neutral particles on the tagging side N\u03c00 + N\u03b3 < 6\nand N\u03b3 < 3. The quality of Btag reconstruction and sup-\npression of background is further improved by requiring\nzero total charge and net proton/antiproton number, no\nleptons on the tagging side and extra energy to be close\nto zero (less then 350 MeV). These criteria reject events\nin which some particles from the signal or tagging side\nwere undetected and suppress events with a large number\nof spurious showers. The consistency of Btag with a B-\nmeson decay is checked using the beam constrained mass,\nmES, and the energy di\ufb00erence, \u2206E. The simulation and\nreconstruction of the inclusive Btag sample is checked us-\ning a control sample of events, where the B \u2192D\u2217\u2212\u03c0+\ndecays (followed by D\u2217\u2212\u03c0\u2212, D0 \u2192K+\u03c0\u2212) are recon-\nstructed on the signal side. Figure 7.4.4 shows the mES\nand \u2206E distributions of the control sample for data and\nthe MC simulation. The good agreement of the shapes\nand of the absolute normalization demonstrates the valid-\nity of the MC-simulations for Btag decays. While the mES\ndistribution shows a clear peak at the B-meson mass, the\n\u2206E distribution is very broad. On the negative side events\nwith undetected particles contribute and the main source\nof the events with \u2206E > 0 are spurious showers in the\nelectromagnetic calorimeter from secondary interactions\nof hadrons. These clusters add linearly to \u2206E, but tend\nto average in the vector sum of their momenta that enters\nthe calculation of mES, see Eq. (7.1.8).\n\n97\n0\n5\n10\n15\n20\n25\n30\n35\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nmbc [GeV/c2]\nN / 5 MeV/c2\n0\n2.5\n5\n7.5\n10\n12.5\n15\n17.5\n20\n22.5\n25\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n\u0394E[GeV]\nN / 60 MeV\nFigure 7.4.4. The mES (= mbc) (a) and \u2206E (b) distribu-\ntions for inclusively reconstructed Btag using a B0 \u2192D\u2217\u2212\u03c0+\nrecoil control sample from data (points with error bars) and\nMC (histograms) (Matyja, 2007). The \u2206E (mES) of Btag can-\ndidates is required to be between \u22120.25 and 0.05 GeV (larger\nthen 5.27 GeV/c2) when plotting mES (\u2206E).\n7.4.4 Double tagging\nThere are two assumptions made when using the recoil\nmethod: the \ufb01rst is that the B reconstruction e\ufb03ciency is\nwell modeled by the Monte Carlo simulations of generic\nB decays and continuum events. The hadronic Btag re-\nconstruction e\ufb03ciencies de\ufb01ned in Eqs (7.4.4) and (7.4.3)\ndepend on the decay rates of B-meson decays to \ufb01nal state\nincluded in the reconstruction. Some of them are poorly\nknown and hence the Btag reconstruction e\ufb03ciencies de-\ntermined on simulated samples need to be validated or cal-\nibrated using the real data sample. The second is that for\nanalyses with few reconstructed particles from the signal\nB, the extra energy used to discriminate signal from back-\nground events is also well-modeled. These assumptions can\nbe checked by using control samples which test both the\ntag B reconstruction e\ufb03ciency and the description of ex-\ntra energy in a fully-reconstructed event. Both BABAR and\nBelle use double-tagged samples, in which both B mesons\nare fully reconstructed either in semileptonic or hadronic\n\ufb01nal states, as such a control.\nThe crosscheck using the double-tag approach was \ufb01rst\napplied by BABAR (Aubert, 2004y), using double semilep-\ntonic B decays. For the semileptonic Btag technique de-\nscribed in Section 7.4.2 this means the reconstruction of\ntwo oppositely charged and non-overlapping B \u2192D0\u2113\u03bd\u2113X\ncandidates with little other detector activity. Both BABAR\nand Belle have also used \u201chybrid double-tags\u201d, where one\nB is reconstructed in a hadronic \ufb01nal state while the\nsecond B is reconstructed in a semileptonic \ufb01nal state\n(B \u2192D(\u2217)\u2113\u03bd\u2113). These samples vary in size, depending\non the \ufb01nal states used, but given a semileptonic tag re-\nconstruction e\ufb03ciency (quoted by BABAR) of \u223c0.7% and\na hadronic tag e\ufb03ciency of \u223c0.2%, one expects to \ufb01nd\napproximately 50 semileptonic double-tagged events per\nfb\u22121, 30 hybrid tags per fb\u22121, and 4 hadronic double-\ntagged events per fb\u22121. Given the large datasets of the B\nFactories, and the expected dataset at future super \ufb02avor\nfactories, these are signi\ufb01cant samples which can be used\nas important cross-checks of the assumptions in the recoil\nmethod.\nThe double-tagged events have two important features.\nThe \ufb01rst is that one expects na\u00a8\u0131vely the yield to be propor-\ntional to \u03b52\ntag, which is the basis of the cross-check of the\ntag e\ufb03ciency. The second is that the complete reconstruc-\ntion of both B mesons creates an environment in which\nthe extra energy in a given event should represent the ef-\nfect of energy deposits unassociated with the B decays\nthemselves. This latter feature is an important ingredient\nin the cross-check of the extra energy modeling in signal\nevents, where it is also assumed that all detected particles\nassociated with the B decays have been reconstructed.\nThe cross-check of the tag e\ufb03ciency is currently only\nused in the semileptonic approach, and only by BABAR.\nThe early approach to the double-tag sample\n(Aubert,\n2006a) made two assumptions. Given an e\ufb03ciency, \u03b5tag,\nfor reconstructing one of the two Bs in an event in a se-\nmileptonic \ufb01nal state, the number of double tags (N2) is\ngiven simply by\nN2 = \u03b52\ntag \u00d7 NB+B\u2212\n(7.4.5)\nwhere NB+B\u2212is the number of charged B pairs originally\nproduced by the B Factory or generated in Monte Carlo\nsimulations. The tag e\ufb03ciency cross-check was performed\nby taking the ratio of the above equation in data and in\nMC simulation and assuming that the double-tag sample\nis dominated by charged B mesons so that NB+B\u2212can-\ncels, yielding the correction factor (ctag) for the tagging\ne\ufb03ciency in MC,\nctag = \u03b5data\ntag\n\u03b5MC\ntag\n=\ns\nN data\n2\nN MC\n2\n.\n(7.4.6)\nWhile MC studies of the double-tags suggest that the con-\ntamination from neutral B decays, or other backgrounds,\nis very small, the second assumption - that the reconstruc-\ntion of the \ufb01rst B does not bias the reconstruction of the\nsecond - is not addressed. The closeness of the correction\nto 1.0, as cited by BABAR, does suggest that also the sec-\nond assumption is essentially correct.\nA second approach to the e\ufb03ciency correction attempts\nto address some of the potential de\ufb01ciencies of the \ufb01rst\nmethod outlined above. In the alternative approach (Au-\nbert, 2007a), the data/MC comparison is performed using\nthe ratio of single-tagged to double-tagged events. If the\ne\ufb03ciency of reconstructing the \ufb01rst tag is \u03b5tag,1 and the\ne\ufb03ciency of reconstructing the second tag is \u03b5tag,2, then\nthe single-tag and double-tag yields, N1 and N2, are given\nby\nN1 = \u03b5tag,1 \u00d7 NB+B\u2212\n(7.4.7)\nN2 = \u03b5tag,1 \u00d7 \u03b5tag,2 \u00d7 NB+B\u2212.\n(7.4.8)\nThe ratio of the two cancels some of the common factors,\nyielding the following quantity to be determined in both\ndata and MC simulations,\n\u03b5tag,2 = N2\nN1\n(7.4.9)\nBABAR determines the number of single-tagged events\nby subtracting the combinatorial component under the D0\n\n98\nmass distribution using an extrapolation of events from\nthe D0 mass sideband. This leaves a sample of events con-\ntaining correctly reconstructed events, mis-reconstructed\nevents from neutral B semileptonic decay, and events from\ne+e\u2212\u2192cc continuum background events with real D0\nmesons paired with a combinatorial lepton. The correc-\ntion to the tag e\ufb03ciency is assumed to be equal for either\nthe \ufb01rst or second tag, and is computed from the data and\nMC as,\nctag = \u03b5data\ntag,2\n\u03b5MC\ntag,2\n= N data\n2\n/N data\n1\nN MC\n2\n/N MC\n1\n(7.4.10)\nThe correction is computed using only events in which the\nD0 meson in the \ufb01rst Btag decays into the K\u2212\u03c0+ \ufb01nal\nstate. This is cross-checked using a sample in which the\nD0 meson from the \ufb01rst tag decays into the K\u2212\u03c0+\u03c0\u2212\u03c0+\n\ufb01nal state only, yielding complementary results.\nIn both of the above methods, and across several it-\nerations of semileptonic recoil-based analyses, BABAR has\nfound the correction to be very close to 1.0. This sug-\ngests both that the assumptions in the above two meth-\nods are largely accurate, and also that existing simulations\nof these and the background decays are adequate for the\npurposes of modeling the decays. The correction has an\nassociated systematic error, which is typically determined\nby propagating the statistical uncertainty due to the \ufb01nite\nsample sizes of the double-tag and single-tag samples. The\nuncertainty of the correction is about 4%.\nBelle (Sibidanov, 2013) uses fully reconstructed events\nto calibrate the e\ufb03ciency of the NB-based Btag reconstruc-\ntion. One of the produced B mesons is reconstructed as\nhadronic Btag while the other B meson is reconstructed in\nthe semileptonic decay mode Bsl \u2192D(\u2217)\u2113\u03bd. The number\nof double tagged events is therefore given by:\nN(BtagBsl) = NBB \u00d7 B(Btag \u2192f)\u03b5Btag\u2192f \u00d7\nB(Bsl \u2192D(\u2217)\u2113\u03bd)\u03b5Bsl,\n(7.4.11)\nwhere B(Btag \u2192f)\u03b5Btag\u2192f is the product of branching\nfraction and reconstruction e\ufb03ciency of the speci\ufb01c decay\nBtag \u2192f and B(Bsl \u2192D(\u2217)\u2113\u03bd)\u03b5Bsl is the corresponding\nproduct for the semileptonically decaying B meson, which\nis well modeled in the simulation. The correction factor\nfor Btag \u2192f is then obtained by measuring the ratio of\nthe numbers of reconstructed double tagged events in real\ndata and MC samples\ncf\ntag =\nBdata(Btag \u2192f)\u03b5data\nBtag\u2192f\nBMC(Btag \u2192f)\u03b5MC\nBtag\u2192f\n= N data(BtagBsl)\nN MC(BtagBsl) \u00b7\nN MC\nBB BMC(Bsl \u2192D(\u2217)\u2113\u03bd)\nN data\nBB Bdata(Bsl \u2192D(\u2217)\u2113\u03bd).\n(7.4.12)\nIn this method of the Btag e\ufb03ciency calibration it is as-\nsumed that the Bsl \u2192D(\u2217)\u2113\u03bd modes are well modeled in\nthe MC sample and hence the \u03b5data\nBsl\n= \u03b5MC\nBsl . The overall\ncorrection factor (averaged over all Btag modes) is found\n (GeV)\nECL\nE\n0\n0.5\n1\nNumber of events\n0\n50\n100\n150\n200\n250\n300\n350\n (GeV)\nECL\nE\n0\n0.5\n1\n (data/MC)\nevents\nRatio of N\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\nFigure 7.4.5. Extra energy distribution for double-tagged\nB+\ntagB\u2212\nsl events (left plot), where the semileptonically decaying\nB meson is reconstructed in the D\u22170\u2113\u2212\u03bd\u2113decay mode. Black\nand red data points show the distribution obtained in data\nand in a sample of simulated events, respectively. The right\nplot shows the ratio of the two distributions \ufb01tted with a lin-\near function. Belle internal, from the Adachi (2012b) analysis.\nto be around 0.7 and consistent between di\ufb00erent Bsl de-\ncay modes. The total uncertainty of the calibration is es-\ntimated to be 4.2% for B+\ntag and 4.5% for B0\ntag.\nThe second application of the double-tagged sample is\nto test the modeling of extra particles left in the detec-\ntor after both B mesons have been reconstructed. In the\ncase of signal events, this typically means that the tag B\nis reconstructed up to any neutrinos in the \ufb01nal state (as\nin semileptonic tags), and that the signal B is also recon-\nstructed up to possible neutrinos in its \ufb01nal state. After\nreconstruction of both B mesons the remaining particles\nleft in the event are assumed to come from several sources:\nneutrals, such as photons, which arise from the electron-\npositron beams but not the interaction point; some low\nmomentum charged particles associated with interactions\nbetween the beam and the beampipe; neutral clusters from\nhadronic showering in the calorimeter which fail to asso-\nciate with a track; and detector noise. These sources would\ntypically lead to a few extra neutral particles left in a sig-\nnal event in about 20-30% of the reconstructed events.\nDouble-tagged events are used to test the simulation of\nthese extra neutral particles by fully reconstructing both\nB mesons either semileptonically, hadronically, or in a hy-\nbrid con\ufb01guration. An example of the use of the double-\ntags to test the extra energy simulation is the Belle col-\nlaboration\u2019s hadronic-tagged search for B+ \u2192\u03c4 +\u03bd\u03c4. Belle\nconstructs a hybrid double-tag sample (one hadronic B\nand one semileptonic B per event in the sample), and as-\nsumes that the extra neutral clusters remaining in these\nevents comes from the same sources as in signal events.\nThey compare the extra energy in data and MC (Fig.\n7.4.5) and use the di\ufb00erence as a variation on their p.d.f.\nmodel for signal events. Comparisons show that existing\ndetector simulations at the B Factories handle the vari-\nety of sources of extra neutral clusters fairly well, even in\nmoderate to high multiplicity \ufb01nal states of B decay.\n\n99\n7.5 Summary\nB-meson reconstruction is crucial for the broad physics\nprogram performed at Belle and BABAR. All of the tech-\nniques presented in this chapter utilize unique constraints\nprovided by the experimental setup of B Factories. They\neither improve the resolution (e.g. mES and \u2206E versus\nB-meson invariant mass in full hadronic reconstruction),\nincrease reconstruction e\ufb03ciency (partial reconstruction)\nor make possible studies of B-meson decays with multiple\nneutrinos in the \ufb01nal state (recoil reconstruction). Some\nof the B reconstruction methods presented herein were\nalready used by experiments prior to Belle and BABAR.\nOthers, in particular recoil techniques using fully- or semi-\nexclusive B-meson reconstruction, were pioneered in the\nB Factories era and proved invaluable to access rare pro-\ncesses where the kinematics of the signal B meson could\nnot be fully constrained. Together with background dis-\ncrimination (see Chapter 9) B reconstruction techniques\nhave been constantly improved over the past ten years\nwhich has enabled studies of less clean modes and in-\ncreased sensitivity to rare decays.\n\n100\nChapter 8\nB-\ufb02avor tagging\nEditors:\nJuerg Beringer (BABAR)\nKazutaka Sumisawa (Belle)\nAdditional section writers:\nRobert Cahn, Simone Stracka\n8.1 Introduction\nThe goal of B-\ufb02avor tagging is to determine the \ufb02avor of\na B meson (i.e. whether it contains a b or a b quark) at\nthe time of its decay. At the B Factories, \ufb02avor tagging\nis needed for most measurements of time-dependent CP\nasymmetries and B meson mixing. As will be discussed\nin Chapter 10, these measurements usually require full re-\nconstruction of the decay of one of the B mesons (referred\nto as Brec or \u201csignal\u201d B), measurement of the decay time\ndi\ufb00erence \u2206t between the two B meson decays, and \ufb02avor\ntagging of the other B meson (referred to as Btag in the\nfollowing).\nAt the B Factories, in contrast to hadron colliders,\nB meson pairs are produced in isolation (apart from any\ninitial-state radiation), since there is no \u201cunderlying event\u201d\nand the fraction of events with multiple e+e\u2212interactions\n(\u201cpile-up\u201d) is negligible. Therefore, if a Brec decay is fully\nreconstructed, the remaining tracks in the event can be\nassumed to come from the Btag decay. In this case \ufb02a-\nvor tagging is to a good approximation independent of\nthe speci\ufb01c Brec decay mode reconstructed (but of course\nstill depends on whether decays of B0/B0, B+/B\u2212or,\nwhen running at the \u03a5(5S), B0\ns/B0\ns are tagged), and the\n\ufb02avor tagging performance can be measured using fully\nreconstructed \ufb02avor-speci\ufb01c Brec decays. For inclusive re-\nconstruction of the signal B, \ufb02avor tagging in general de-\npends on the speci\ufb01c Brec reconstruction since the remain-\ning tracks in the event cannot be unambiguously assigned\nto either the Brec or Btag meson.\nThe tagging of neutral B0/B0 mesons from \u03a5(4S) de-\ncays assuming a fully reconstructed Brec decay is the pri-\nmary use case for \ufb02avor tagging at the B Factories. This\nis the situation considered in the following.\nFlavor tagging relies on the fact that a large fraction\nof B mesons decay to a \ufb01nal state that is \ufb02avor speci\ufb01c,\ni.e. to good approximation, can only be reached either\nthrough the decay of a b quark, or through the decay of\na b quark. Because of the large number of decay chan-\nnels, full reconstruction of a su\ufb03ciently large number of\n\ufb02avor-speci\ufb01c Btag decays is not feasible. Instead inclu-\nsive techniques are employed that make use of di\ufb00erent\n\ufb02avor-speci\ufb01c signatures of B decays. For example, in se-\nmileptonic decays B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113the charge of the lepton\nunambiguously identi\ufb01es the \ufb02avor of the decaying B me-\nson as long as the lepton can be clearly associated with the\nsemileptonic B decay and does not come from a secondary\nD meson decay.\nThe \ufb02avor tagging algorithms developed by BABAR and\nBelle proceed in two stages. In the \ufb01rst stage, individual\n\ufb02avor-speci\ufb01c signatures are analyzed, each of which pro-\nvides a signature-speci\ufb01c \ufb02avor tag that by itself could be\nused for \ufb02avor tagging. In the second stage, the results\nfrom the \ufb01rst stage signatures are combined into a \ufb01nal\n\ufb02avor tag. Both stages rely on multivariate methods in\norder to optimally combine all available information.\nThe outline of this chapter is as follows. After de\ufb01ning\nthe relevant quantities characterizing the performance of\nB-\ufb02avor tagging and discussing the choice of tagging cat-\negories, the di\ufb00erent sources of \ufb02avor information and the\ncorresponding discriminating variables are reviewed. Sec-\ntion 8.6 describes the speci\ufb01c \ufb02avor tagging algorithms\nused by the BABAR and Belle experiments and quotes\nthe performance of these algorithms. The method used\nto measure the \ufb02avor tagging performance is described\nelsewhere (see Section 10.6).\n8.2 De\ufb01nitions\nThe \ufb01gure of merit for the performance of a tagging algo-\nrithm is the e\ufb00ective tagging e\ufb03ciency Q,\nQ = \u03b5tag(1 \u22122w)2,\n(8.2.1)\nwhere \u03b5tag denotes the fraction of events to which a \ufb02avor\ntag can be assigned, and the mistag probability w is the\nfraction of events with an incorrectly assigned tag. The\nterm\nD = 1 \u22122w\n(8.2.2)\nis called the dilution and is the factor by which measured\nCP and mixing asymmetries are reduced from their physi-\ncal values due to incorrectly assigned \ufb02avor tags. The def-\ninition of Q is motivated by the fact that the statistical\nuncertainties \u03c3 on such asymmetry measurements gener-\nally scale approximately as (see Section 8.4)\n\u03c3 \u221d\n1\n\u221aQ.\n(8.2.3)\nTagging e\ufb03ciencies and mistag fractions are not a pri-\nori the same for tagging B0 and B0 decays because the\ndetector performance may not be completely charge sym-\nmetric. Therefore the averages\n\u03b5tag = \u03b5B0 + \u03b5B0\n2\n(8.2.4)\nw = wB0 + wB0\n2\n(8.2.5)\nand di\ufb00erences\n\u2206\u03b5tag = \u03b5B0 \u2212\u03b5B0\n(8.2.6)\n\u2206w = wB0 \u2212wB0\n(8.2.7)\nare de\ufb01ned where the subscript refers to the true decay.\nFor example, wB0 refers to the fraction of neutral Btag\nmesons that decay as B0 but are tagged as B0.\n\n101\n8.3 Tagging categories\nThe e\ufb00ective tagging e\ufb03ciency Q can be improved (and\nhence the statistical uncertainty of a measurement de-\ncreased) by grouping events into mutually exclusive tag-\nging categories according to their mistag probabilities w\n(or dilutions D). For tagging categories c with fractions of\nevents \u03b5c, dilutions Dc, total tagging e\ufb03ciency \u03b5 = P\nc \u03b5c\nand average dilution D = P\nc \u03b5cDc/\u03b5 one \ufb01nds\nQ =\nX\nc\n\u03b5cD2\nc = \u03b5D2 +\nX\nc\n\u03b5c(Dc \u2212D)2.\n(8.3.1)\nThus the resulting Q is always larger or equal to the one\nobtained when all events are treated as a single category.\nOne gains most from dividing events into categories when\nthe di\ufb00erences in dilution (or mistag fraction) between\ncategories can be made large. However, the characteris-\ntics and any systematic e\ufb00ects, such as correlations with\nthe tag vertex resolution, tag-side interference (see Sec-\ntion 15.3.6), or background levels, are expected to be de-\ntermined by the di\ufb00erent \ufb02avor-speci\ufb01c signatures. For\nthis reason one would prefer a grouping of events accord-\ning to di\ufb00erent signatures over a category de\ufb01nition based\non w.\nThe mistag probability w that can be achieved for a\ngiven set of Btag decay modes is determined by the \ufb02avor-\nspeci\ufb01c signatures present in these decays. Fortunately,\nthe mistag probabilities of di\ufb00erent \ufb02avor-speci\ufb01c signa-\ntures tend to be di\ufb00erent. For example, in semileptonic\ndecays the charge of a reconstructed high-momentum elec-\ntron or muon gives a much better indication of the correct\ntag than the charge of a low momentum pion (\u201cslow pion\u201d)\nfrom a secondary D\u2217decay.\nTherefore a grouping of events into tagging categories\naccording to the mistag probability naturally provides a\ngrouping according to the di\ufb00erent signatures of the cor-\nresponding Btag decays. Conversely, a grouping according\nto di\ufb00erent signatures leads to an approximate grouping\naccording to mistag probabilities. As a result it is possible\nto de\ufb01ne tagging categories that both optimize the tag-\nging performance and group events according to di\ufb00erent\nsignatures.\n8.4 Dilution factor and e\ufb00ective tagging\ne\ufb03ciency\nAs mentioned above, a CP asymmetry Arec measured us-\ning \ufb02avor tagging is reduced from the physical asymmetry\nby a factor D due to incorrectly assigned \ufb02avor tags. This\nscaling is easy to see by writing the measured asymmetry\nArec as\nArec = N \u2212N\nN + N ,\n(8.4.1)\nwhere N and N denote the number of reconstructed B\ndecays\nN = \u03b5tag(1 \u2212w)N0 + \u03b5tagwN 0\nN = \u03b5tag(1 \u2212w)N 0 + \u03b5tagwN0\n(8.4.2)\ntagged as B0 and B0, respectively. N0 and N 0 are the cor-\nresponding number of reconstructed B decays of a certain\ntype before tagging is applied. Substituting Eq. (8.4.2)\ninto (8.4.1) one directly obtains\nArec = (1 \u22122w)A0 = DA0,\n(8.4.3)\nwhere A0 = (N0\u2212N 0)/(N0+N 0) denotes the true physical\nasymmetry.\nThe statistical uncertainty in A0 is\n\u03c3A0 =\n\u03c3Arec\n1 \u22122w .\n(8.4.4)\nUsing Eq. (8.4.1) and denoting the total number of tagged\nevents by Ntag = N+N, assuming a small asymmetry (i.e.\nN \u2248N = Ntag/2), one \ufb01nds\n\u03c3Arec \u221d\n1\np\nNtag\n.\n(8.4.5)\nTogether with Eq. (8.4.4) it follows\n\u03c3A0 \u221d\n1\n\u221a\u03b5tag(1 \u22122w) =\n1\n\u221aQ .\n(8.4.6)\nIn general, this scaling of \u03c3A0 with Q is only approxi-\nmate. For a likelihood-based analysis and assuming a su\ufb03-\nciently large number of events, the expected uncertainty in\nan estimated CP or mixing asymmetry bA can be obtained\nfrom the maximum-likelihood estimator for the variance\non bA (see Section 11.1.3),\n\u03c3( bA)2 = V ( bA) =\n\u0012d2 log(L(A))\nd2A\n\u0013\u22121\nA= b\nA\n.\n(8.4.7)\nThis was calculated (Cahn, 2000; Le Diberder, 1990) for\nthe case of a measurement of a time-dependent CP asym-\nmetry with no direct CP violation such as e.g. the mea-\nsurement of A = sin 2\u03c61. Using several tagging categories\nc, ignoring e\ufb00ects of resolution and background, and with\nxd = \u2206m/\u0393, the approximation\n\u03c3( bA) \u2248\n\"\nN\n2x2\nd\n1 + 4x2\nd\nX\nc\n\u03f5cD2\nc\n\u0012\n1 + 12x2\ndD2\ncA2\n1 + 16x2\nd\n\u0013#\u22121/2\n,\n(8.4.8)\nwas derived. This leads to an improved de\ufb01nition Q\u2032 of\nthe e\ufb00ective tagging e\ufb03ciency,\nQ\u2032 =\nX\nc\n\u03b5cD2\nc\n\u0012\n1 + 12x2\ndD2\ncA2\n1 + 16x2\nd\n\u0013\n(8.4.9)\nwith \u03c3( bA) \u221d1/\u221aQ\u2032.\nQ\u2032 depends on the true asymmetry A and reduces to\nthe standard de\ufb01nition of Q for A = 0. For large asym-\nmetries (A \u22481) and for the most powerful tagging cate-\ngories used by the BABAR or Belle tagging algorithms with\nwc \u22482%, the factor\n1 + 12x2\ndD2\ncA2\n1 + 16x2\nd\n(8.4.10)\n\n102\namounts to a correction of more than 60%. This e\ufb00ect\nwas clearly observed when the scaling of the uncertainties\nof di\ufb00erent BABAR sin 2\u03c61 results with e\ufb00ective tagging\ne\ufb03ciency was analyzed.\n8.5 Physics sources of \ufb02avor information\nIn the following the di\ufb00erent \ufb02avor-speci\ufb01c signatures are\ndiscussed in more detail. Since the focus of this chapter\nis on tagging for fully reconstructed Brec decays, it is as-\nsumed that only tracks from the Btag decays are consid-\nered in the calculation of any of the discriminating vari-\nables described below.\n8.5.1 Leptons\nElectrons and muons produced directly in semileptonic B\ndecays (primary leptons) provide excellent tagging infor-\nmation. The charge of a lepton from a b \u2192c \u2113\u2212\u03bd transi-\ntion is directly associated to the \ufb02avor of the B0 meson:\na positively charged lepton indicates a B0, a negatively\ncharged lepton indicates a B0.\nLeptons from cascade decays (secondary leptons) oc-\ncurring via the transition b \u2192W \u2212c (\u2192s \u2113+ \u03bd) carry tag-\nging information as well: their charge is opposite to that\nof primary leptons from Btag and they are characterized\nby a much softer momentum spectrum.\nThe following kinematical variables are useful to iden-\ntify primary and secondary leptons:\n\u2013 q, the charge of the track.\n\u2013 p\u2217, the center-of-mass momentum of the candidate\ntrack. Combined with the charge of the track this is\nthe most powerful discriminating variable.\n\u2013 \u03b8lab, the polar angle in the laboratory frame.\n\u2013 EW\n90 , the energy in the hemisphere de\ufb01ned by the direc-\ntion of the virtual W \u00b1 in the semi-leptonic Btag decay.\nEW\n90 is calculated in the center-of-mass frame under the\nassumption that the Btag is produced at rest. The sum\nof energies for EW\n90 extends over all charged and neutral\ncandidates of the recoiling charm system X that are\nin the same hemisphere (with respect to the direction\nof the virtual W \u00b1) as the lepton candidate:\np\u00b5\nB = p\u00b5\nW + p\u00b5\nX \u2248(mB0, 0)\np\u00b5\nW = p\u00b5\n\u2113+ p\u00b5\n\u03bd\np\u00b5\nX =\nX\ni\u0338=\u2113\np\u00b5\ni\nEW\n90 =\nX\ni\u2208X, pi\u00b7pW >0\nEi\n(8.5.1)\n\u2013 pmiss, the missing momentum given by:\npmiss = pB \u2212pX \u2212p\u2113\u2248\u2212(pX + p\u2113).\n(8.5.2)\n\u2013 cos \u03b8miss, the cosine of the angle between the lepton\ncandidate\u2019s momentum p\u2113and the missing momentum\npmiss is calculated in the \u03a5(4S) center-of-mass frame\n(again with the approximation of the Btag being pro-\nduced at rest).\n\u2013 Mrecoil, mass recoiling against pmiss + p\u2113in the Btag\nframe. The Mrecoil distribution for semileptonic B de-\ncays peaks around the D mass and has a tail toward\nthe lower side due to missing particles, while that for\nsemileptonic D decays is more broad with a tail up to\n5 GeV/c2.\nThe above kinematical variables can be combined with\nparticle identi\ufb01cation (PID) information and applied only\nto selected electron or muon candidate tracks. Or they\ncan be applied to all tracks in order to recover the tag-\nging information from leptons that fail the PID selection\n(\u201ckinematically identi\ufb01ed leptons\u201d).\n8.5.2 Kaons\nThe dominant source of charged kaons are b \u2192c \u2192s tran-\nsitions (B0 \u2192D(\u2192K+X\u2032)X decays), where the charge\nof the kaon tags the \ufb02avor of Btag. Kaons from such de-\ncays are referred to as \u201cright sign\u201d kaons (a K+ indicates a\nB0 decay). The high average multiplicity of charged kaons\nof 0.78 \u00b1 0.08 (Beringer et al., 2012), combined with the\nhigher multiplicity of right sign vs wrong sign kaons of\n0.58 \u00b1 0.01 \u00b1 0.08 vs. 0.13 \u00b1 0.01 \u00b1 0.05 (Albrecht et al.,\n1994b) make kaons overall the most powerful source of\ntagging information.\nThe following discriminating variables are useful for\n\ufb02avor tagging with kaons:\n\u2013 q, the charge of the track.\n\u2013 LK, the kaon likelihood obtained from PID informa-\ntion.\n\u2013 If more than one charged kaon is identi\ufb01ed, it is useful\nto combine the information (q \u00b7 LK) from up to three\ncharged kaons.\n\u2013 nK0\nS, the number of K0\nS mesons reconstructed on the\ntag side. A kaon produced together with one or more\nK0\nS tends to originate from a strange quark in a b \u2192\ncc(d, s) decay or from the appearance of ss out of the\nvacuum, while one without an accompanying K0\nS has a\nhigher probability to come from the b \u2192c \u2192s cascade\ndecay.\n\u2013 The sum of the squared transverse momenta of charged\ntracks on the tag side. A large total transverse\nmomentum squared increases the likelihood that a\ncharged kaon was produced from a b \u2192cW \u2212, c \u2192\ns \u2192K\u2212transition, rather than the transition b \u2192\nXW \u2212, W \u2212\u2192cs/d, c \u2192s \u2192K+, which would give a\n\u201cwrong-sign\u201d kaon.\n\u2013 p\u2217, the center-of-mass momentum of the candidate\ntrack.\n\u2013 \u03b8lab, the polar angle in the laboratory frame.\n8.5.3 Slow pions\nLow momentum \u03c0\u00b1 from D\u2217\u00b1 decays (slow pions) pro-\nvide another source of tagging information. The substan-\n\n103\ntial background from low momentum tracks can be re-\nduced by correlating the direction of the slow pion and\nthe remaining tracks from the Btag decay. Since the slow\npion and the D0 are emitted nearly at rest in the D\u2217\u00b1\nframe, the slow pion direction in the Btag rest frame will\nbe along the direction of the D0 decay products and op-\nposite to the remainder of the Btag decay products. This\ndirection can be approximately determined by calculating\nthe thrust axis of the Btag decay products. The thrust is\ncalculated using both charged tracks and neutral clusters\nnot used in the reconstruction of Brec.\nThe following variables provide useful discriminating\npower:\n\u2013 q, the charge of the track.\n\u2013 p\u2217, the momentum of the slow pion candidate in the\n\u03a5(4S) center-of-mass frame.\n\u2013 plab, the momentum of the slow pion candidate in the\nlaboratory frame.\n\u2013 \u03b8lab, the polar angle in the laboratory frame.\n\u2013 cos \u03b8\u03c0T, the cosine of the angle between the slow pion\ndirection and the Btag thrust axis in the \u03a5(4S) center-\nof-mass frame.\n\u2013 LK, the PID likelihood of the track to be a kaon. PID\ninformation helps to reject the contribution from low\nmomentum kaons \ufb02ying in the thrust direction.\n\u2013 Le, the PID likelihood of the track to be a electron.\nThis helps to reject background from electrons pro-\nduced in photon conversions and \u03c00 Dalitz decays.\n8.5.4 Correlation of kaons and slow pions\nIn events where both a charged kaon and a slow pion can-\ndidate (e.g. from a D\u2217+ \u2192D0(\u2192K\u2212X)\u03c0+ decay) are\nfound, the corresponding \ufb02avor tagging information can\npotentially be improved by using the angular correlation\nbetween the kaon and slow pion. A kaon and a slow pion of\nopposite charge (i.e. agreeing \ufb02avor tag) that are emitted\nin approximately the same direction in the \u03a5(4S) center-\nof-mass frame can provide a combined tag with a relatively\nlow mistag fraction.\nIn addition to the information used to identify kaons\nand slow pions, the following discriminating variable can\nbe used:\n\u2013 cos \u03b8K,\u03c0, the cosine of the angle between the kaon and\nthe slow pion momentum calculated in the \u03a5(4S) center-\nof-mass frame.\n8.5.5 High-momentum particles\nA very inclusive tag can be obtained by selecting tracks\nwith the highest momentum in the \u03a5(4S) center-of-mass\nframe and using their charge as a tag. Given the other sig-\nnatures discussed above, the aim of such a tag is to iden-\ntify fast particles coming from the hadronization of the\nW boson produced in the decay b \u2192c W \u2212(for example\nfast pions from B0 \u2192D\u2217+ \u03c0\u2212) as well as high momentum\nleptons that may have failed the selection for the lepton\ntag signature. Direct hadrons or leptons with a positive\n(negative) charge indicate a B0 (B0) tag. These particles\nare produced at the Btag decay vertex and, in the \u03a5(4S)\ncenter-of-mass frame, are energetic and \ufb02y in a direction\nopposite to the charm decay products of Btag.\nUseful discriminating variables are:\n\u2013 q, the charge of the track.\n\u2013 p\u2217, the momentum of the track in the \u03a5(4S) center-of-\nmass frame.\n\u2013 d0, the impact parameter in the xy plane.\n\u2013 The angle between the particle and the Btag thrust\naxis in the \u03a5(4S) center-of-mass frame.\n8.5.6 Correlation of fast and slow particles\nThe angular correlations between slow charged pions from\nD\u2217\u00b1 decays and fast, oppositely charged particles origi-\nnating from the W \u2213hadronization in the decay b \u2192c W\ncan be exploited for \ufb02avor tagging. Since the W \u2213and the\nD\u2217\u00b1 are emitted back-to-back in the Btag center-of-mass\nframe, the slow pion and the fast tracks are expected to\nbe emitted at a large angle.\nThe following discriminating variables are useful:\n\u2013 p\u2217\nSlow, the center-of-mass momentum of the slow track.\n\u2013 p\u2217\nFast, the center-of-mass momentum of the fast track.\n\u2013 cos \u03b8SlowFast, the cosine of the angle between the slow\nand the fast track.\n\u2013 cos \u03b8SlowT, the cosine of the angle between the slow\ntrack and Btag thrust axis.\n\u2013 cos \u03b8FastT, the cosine of the angle between the fast\ntrack and Btag thrust axis.\n\u2013 LKSlow, the PID likelihood for the slow track to be a\nkaon.\n8.5.7 \u039b baryons\nThe \ufb02avor of a \u039b baryon produced in Btag decays carries\ntagging information because it contains an s quark that\nwas likely produced in the cascade decay b \u2192c \u2192s.\nTherefore, the presence of a \u039b (\u039b) will indicate a B0 (B0).\n\u039b \u2192p\u03c0 decays on the tag side are reconstructed by\ncombining charged tracks with tracks that are identi\ufb01ed\nas protons (or antiprotons). Although \u039b candidates are\nfound in a small fraction of events, they provide relatively\nclean \ufb02avor tags that are fully complementary to the other\nsignatures.\nUseful discriminating variables include:\n\u2013 q, the \ufb02avor of \u039b (\u039b or \u039b).\n\u2013 M\u039b, the reconstructed mass of the \u039b.\n\u2013 \u03c72\n\u039b, the \u03c72 probability of the \ufb01tted \u039b decay vertex.\n\u2013 cos \u03b8\u039b, the cosine of the angle between the \u039b momen-\ntum and the direction from the primary vertex to the\n\u039b decay vertex.\n\u2013 s\u039b, the \ufb02ight length of the \u039b candidate before decay.\n\u2013 p\u039b, the momentum of the \u039b candidate.\n\u2013 pproton, the momentum of the proton candidate used\nfor the \u039b reconstruction.\n\n104\n\u2013 nK0\nS, the number of K0\nS mesons reconstructed on the\ntag side.\n\u2013 \u2206z, di\ufb00erence between the z coordinate of the two\ntracks at the \u039b vertex point.\n8.6 Speci\ufb01c \ufb02avor tagging algorithms\nIn this section the tagging algorithms developed by BABAR\nand Belle are discussed. In both experiments these algo-\nrithms have been improved greatly during the lifetime of\nthe experiment, resulting in a substantial performance in-\ncrease. In the following only the \ufb01nal versions of the tag-\nging algorithms are discussed.\n8.6.1 Multivariate tagging methods\nThe BABAR and Belle tagging algorithms both use multi-\nvariate methods: BABAR uses an arti\ufb01cial neural network,\nwhile Belle\u2019s tagger is based on a multi-dimensional look-\nup table. Both algorithms provide not only a \ufb02avor tag\nbut also an estimated mistag probability for each event.\nBoth tagging algorithms were trained using large sam-\nples of simulated events. Imperfections in the simulation\nof particle decays (e.g. due to incomplete knowledge of\nbranching fractions) or detector response may lead to in-\naccurate estimates of the per-event mistag probability by\nthe tagging algorithm. Therefore both algorithms use the\nestimated per-event mistag probabilities only when sepa-\nrating events into tagging categories. For each category,\nw and \u2206w are measured using a sample of events where\nthe signal B decays into a self-tagging decay mode (B\ufb02av\ncontrol sample, see Section 10.6). As a result, inaccuracies\nin the simulation of the training sample can only lead to\na non-optimal tagging performance but will not introduce\nany systematic errors. The loss in tagging performance\nthat results from using tagging categories rather than per-\nevent mistag probabilities was found to be small both for\nthe BABAR and the Belle tagging algorithms.\n8.6.2 Systematic e\ufb00ects\nSystematic e\ufb00ects associated with tagging are discussed\nin Chapter 15; only a brief overview is given here. As dis-\ncussed above, by using tagging categories whose w and\n\u2206w are measured on data, systematic e\ufb00ects that could\narise from imperfections in the tagging algorithm or its\ntraining are replaced by the statistical uncertainties of the\nmeasurements of w and \u2206w. The remaining systematic ef-\nfects associated with \ufb02avor tagging arise from\n\u2013 potential di\ufb00erences in the tagging performance for sig-\nnal events and for the B\ufb02av control sample used to\nmeasure w and \u2206w, and\n\u2013 tag-side interference (see Section 15.3.6).\n8.6.3 Flavor tagging in BABAR\nThe BABAR tagging algorithm (Aubert, 2005i, 2009z; Lees,\n2013c) is a modular, multivariate \ufb02avor-tagging algorithm\nthat analyses charged tracks on the tag side in order to\nprovide a \ufb02avor tag and a mistag probability w. The \ufb02avor\nof Btag is determined from a combination of nine di\ufb00erent\n\ufb02avor-speci\ufb01c signatures, which include charged leptons,\nkaons, pions and \u039b baryons (see Section 8.5).\nFor each of these signatures, properties such as charge,\nmomentum, and decay angles are used as input to a spe-\nci\ufb01c neural network (NN) or \u201csub-tagger\u201d. Three sub-\ntaggers are dedicated to charged leptons, making use of\nidenti\ufb01ed electrons (Electron), muons (Muon) and kine-\nmatically identi\ufb01ed leptons (Kin. Lepton). The Kaon sub-\ntagger combines the information from up to three kaons\ninto a single tag. Slow pions are used both by a dedi-\ncated slow pion sub-tagger (Slow Pion) and in correla-\ntion with kaons (K-Pi). The Max p* sub-tagger analyzes\nhigh-momentum particles. The correlation of fast and slow\nparticles is exploited by the FSC sub-tagger. The Lambda\nsub-tagger looks at \u039b baryons.\nThese sub-taggers are combined by a single \ufb01nal neu-\nral network (BTagger) that is trained to determine the\ncorrect \ufb02avor of Btag. Based on the output of this NN and\nthe contributing sub-taggers, each event is assigned to one\nof six mutually exclusive tagging categories. The overall\nstructure of the BABAR tagging neural network is shown\nin Figure 8.6.1.\nFigure 8.6.1. Schematic overview of the BABAR tagging algo-\nrithm. Each box corresponds to a separate neural network.\nThe use of sub-taggers dedicated to speci\ufb01c signatures\nallows one to keep track of the underlying physics of\neach event and simpli\ufb01es studies of systematics. For ex-\nample, events with an identi\ufb01ed electron or muon from a\nsemi-leptonic Btag decay can be separated from other de-\ncays and assigned to the Lepton tagging category. The\nLepton category does not only have a low w but also\nmore precisely reconstructed Btag vertices, is less sensi-\n\n105\ntive to the bias from charm on the tag side, and is im-\nmune to the intrinsic mistagging associated with doubly\nCabibbo-suppressed decays (see tag-side interference in\nSection 15.3.6).\nThe training and validation of each of the sub-tagger\nNNs is based on the Stuttgart Neural Network Simulator\n(Zell et al., 1995). Extensive studies have been performed\nfor each sub-tagger, including a wide search for the most\ndiscriminating input variables. NN architectures and the\nnumber of training cycles are optimized to yield the most\ne\ufb03cient \ufb02avor assignment. The NNs are feed-forward net-\nworks with one hidden layer. The weights and bias values\nof the logistic activation functions are optimized during\ntraining using standard back-propagation.\nThe NNs are trained using a simulated sample of about\n500,000 B0B0 pairs in which one meson (Brec ) decays\nto a \u03c0+\u03c0\u2212\ufb01nal state while the other (Btag) decays to\nany possible \ufb01nal state according to known or expected\nbranching fractions. Half of this sample is used for training\nthe NN, while the other half is used as a test sample for an\nunbiased evaluation of the performance. Each sub-tagger\nis trained separately before the training of the BTagger\nnetwork.36\nDetails of the architecture of the di\ufb00erent neural net-\nworks used by the BABAR tagging algorithm are given in\nTable 8.6.1. For each of the nine sub-taggers and for the\n\ufb01nal BTagger NN the table lists all input variables and\nthe training target. Some of the sub-taggers are trained\nto separate B0 from B0 decays, while others are trained\nto discriminate true from fake signatures.\nThe output yBTagger of the \ufb01nal BTagger NN is mapped\nto values between \u22121 (for a perfectly tagged B0) and +1\n(B0). The distribution of this output for the B\ufb02av control\nsample is shown in Figure 8.6.2. Excellent agreement is\nobserved between data and simulation.\nThe estimated probability p of a correct tag assignment\nis given by the BTagger NN output\np = 1 \u2212w = (1 + |yBTagger|)/2,\n(8.6.1)\nand the probability of a given Btag being a B0 is\npBtag=B0 = (1 + yBTagger)/2.\n(8.6.2)\nThe correctness of these probabilities can be checked\nwith the B\ufb02av control sample. For example, one can plot\nthe probability of observing a B0 on the B\ufb02av side as\na function of the estimated probability pBtag=B0. Tak-\ning into account the time-integrated mixing probability\n\u03c7d = 0.1862 \u00b1 0.0023 (Beringer et al. (2012)), one expects\nfor a perfectly trained tagging algorithm\npBflav=B0 = (1 \u22122\u03c7d)pBtag=B0 + \u03c7d\n(8.6.3)\n= (1 \u22122\u03c7d)(1 + yBTagger)/2 + \u03c7d.\n(8.6.4)\n36 Simultaneous training of all sub-taggers and the BTagger\nNN has been shown not to result in a signi\ufb01cantly better clas-\nsi\ufb01cation performance.\nAs can be seen from Figure 8.6.3, the probabilities ob-\ntained from the BTagger NN output are in very good\nagreement with the expectations for both data and sim-\nulation. Nevertheless, as discussed in Section 8.6.1, these\nestimated probabilities are only used to separate events\ninto tagging categories.\nFraction per 0.02\n0.01\n0.02\n0.03\n0.04\n0.05\nMC\nData\nBTagger\ny\n-1\n-0.5\n0\n0.5\n1\nData - MC\n0\n0.002\nFigure 8.6.2. Distribution of the output of the \ufb01nal BTagger\nNN (yBTagger) on the B\ufb02av control sample for data and simu-\nlation, using the full BABAR data sample. A contribution of up\nto 22% from combinatorial background is subtracted in each\nbin based on a \ufb01t to the mES distribution. The di\ufb00erence be-\ntween data and simulation (with statistical uncertainties added\nin quadrature) is also shown.\nThe tagging algorithm assigns each event to one of\nsix hierarchical and mutually exclusive tagging categories:\nLepton, Kaon I, Kaon II, Kaon-Pion, Pion or Other. The\nname given to each category indicates the dominant\nphysics processes (or sub-tagger) contributing to the \ufb02a-\nvor identi\ufb01cation. For most categories, this classi\ufb01cation\nis based on yBTagger. For the Lepton category, which sin-\ngles out events with a cleanly identi\ufb01ed primary lepton,\nadditional cuts are made on the output of the electron or\nmuon sub-taggers. Over 95% of events in the Lepton cat-\negory contain a semileptonic Btag decay. The de\ufb01nition of\nthe tagging categories is summarized in Table 8.6.2.\nThe \ufb01nal version of the BABAR tagging algorithm37\n(Lees, 2013c) achieves an e\ufb00ective tagging e\ufb03ciency Q =\n(33.1 \u00b1 0.3)% on the full BABAR data set. The breakdown\nof this performance into the di\ufb00erent tagging categories is\nshown in Table 8.6.3.\n37 Improvements in the particle identi\ufb01cation algorithms used\nfor the \ufb01nal version of the BABAR tagging algorithm (Lees,\n2013c) lead to a higher Q value of (33.1 \u00b1 0.3)%, compared\nto Q \u224831% achieved by the previous version (Aubert, 2005i).\nThe tagging algorithm itself did not change.\n\n106\nTable 8.6.1. Overview of the neural networks used by the BABAR BTagger and its sub-taggers. For each sub-tagger the network\narchitecture is shown in the second column according to the notation Ninputs : Nhidden nodes : Noutputs. The input variables are\nlisted in the third column while the fourth column describes the goal of the NN training.\n(Sub-)Tagger\nNetwork architecture\nDiscriminating input variables\nTraining goal\nElectron\n4:12:1\nq, p\u2217, EW\n90 , cos \u03b8miss\nClassify B0 versus B0\nMuon\n4:12:1\nq, p\u2217, EW\n90 , cos \u03b8miss\nClassify B0 versus B0\nKin. Lepton\n3:3:1\np\u2217, EW\n90 , cos \u03b8miss\nRecognize primary leptons\nKaon\n5:10:1\n(qLK)1, (qLK)2, (qLK)3, nK0\nS, \u03a3p\u22a5\nClassify B0 versus B0\nSlow Pion\n3:10:1\np\u2217, cos \u03b8\u03c0T, LK\nRecognize slow pions from D\u2217\u00b1 decays\nMax p\u2217\n3:6:1\np\u2217, d0, cos \u03b8\nRecognize direct B daughters\nK\u2013Pi\n3:10:1\n(qLK), SlowPion tag, cos \u03b8K,\u03c0\nRecognize K-\u03c0 pairs from D\u2217\u00b1 decays\nFSC\n6:12:1\ncos \u03b8SlowFast, p\u2217\nSlow, p\u2217\nFast, cos \u03b8SlowT,\ncos \u03b8FastT, LKSlow\nRecognize fast-slow correlated tracks\nLambda\n6:14:1\nM\u039b, \u03c72, cos \u03b8\u039b, s\u039b, p\u039b, pproton\nRecognize \u039b decays\nBTagger\n9:20:1\nAll of the above tags\nClassify B0 versus B0\nTable 8.6.2. De\ufb01nition of tagging categories for the BABAR \ufb02avor tagging algorithm. Events with |yBTagger| < 0.1 are classi\ufb01ed\nas Untagged and are not used to extract time-dependent information from data.\nCategory\nDe\ufb01nition\nLepton\n(|yElectron| > 0.8 or |yMuon| > 0.8) and |yBTagger| > 0.8\nKaon I\n|yBTagger| > 0.8\nKaon II\n0.6 < |yBTagger| < 0.8\nKaon-Pion\n0.4 < |yBTagger| < 0.6\nPion\n0.2 < |yBTagger| < 0.4\nOther\n0.1 < |yBTagger| < 0.2\nTable 8.6.3. Performance of the \ufb01nal BABAR tagging algorithm on data.\nCategory\n\u03b5tag(%)\n\u2206\u03b5tag(%)\nw(%)\n\u2206w(%)\nQ(%)\n\u2206Q(%)\nLepton\n9.7 \u00b1 0.1\n0.2 \u00b1 0.2\n2.1 \u00b1 0.2\n0.2 \u00b1 0.5\n8.9 \u00b1 0.1\n0.1 \u00b1 0.4\nKaon I\n11.3 \u00b1 0.1\n\u22120.1 \u00b1 0.2\n4.1 \u00b1 0.3\n0.2 \u00b1 0.6\n9.6 \u00b1 0.1\n\u22120.1 \u00b1 0.4\nKaon II\n15.9 \u00b1 0.1\n\u22120.1 \u00b1 0.2\n13.0 \u00b1 0.3\n\u22120.2 \u00b1 0.6\n8.7 \u00b1 0.2\n0.0 \u00b1 0.5\nKaon-Pion\n13.2 \u00b1 0.1\n0.4 \u00b1 0.2\n23.0 \u00b1 0.4\n\u22121.3 \u00b1 0.7\n3.9 \u00b1 0.1\n0.5 \u00b1 0.3\nPion\n16.8 \u00b1 0.1\n\u22120.3 \u00b1 0.3\n33.3 \u00b1 0.4\n\u22122.7 \u00b1 0.6\n1.9 \u00b1 0.1\n0.6 \u00b1 0.2\nOther\n10.6 \u00b1 0.1\n\u22120.5 \u00b1 0.2\n41.8 \u00b1 0.5\n5.9 \u00b1 0.7\n0.28 \u00b1 0.03\n\u22120.4 \u00b1 0.1\nTotal\n77.5 \u00b1 0.1\n\u22120.3 \u00b1 0.5\n33.1 \u00b1 0.3\n0.7 \u00b1 0.8\nThe contribution of each of the nine sub-taggers to the\noverall tagging performance can be evaluated in two ways:\n\u2013 the absolute e\ufb00ective tagging e\ufb03ciency obtained by\nusing only one sub-tagger (Qabs);\n\u2013 the incremental e\ufb00ective tagging e\ufb03ciency (Qincr), de-\n\ufb01ned as the improvement in Q associated with adding\na single sub-tagger on top of all the others.\nTable 8.6.4 shows Qabs and Qincr for the nine sub-\ntaggers. In most events multiple \ufb02avor tagging signatures\nare present and contribute to the \ufb01nal tag as can be seen\nfrom the fact that Qincr is small for most sub-taggers. The\nexception is the Kaon sub-tagger which is the only tagger\nwhose presence is essential to maintain a high tagging per-\nformance. The fact that in most cases several sub-taggers\ncontribute to the \ufb01nal tag helps to ensure the robustness\nof the tagging algorithm.\n8.6.4 Flavor tagging in Belle\nThe \ufb02avor tagging method used by Belle (Kakuno, 2004) is\nbased on a multi-dimensional look-up table. A schematic\ndiagram of the algorithm is shown in Figure 8.6.4.\nThe algorithm provides two parameters as the \ufb02avor\ntagging outputs: q denoting the \ufb02avor of Btag (+1 for B0,\n\u22121 for B0), and r is an expected \ufb02avor dilution factor\nthat ranges from zero for no \ufb02avor information (w \u22430.5)\n\n107\nTable 8.6.4. Contribution of the nine sub-taggers to the BABAR tagging algorithm for the version of the algorithm used in\n2004. The \ufb01nal version of the algorithm has the same architecture of the sub-taggers and BTagger but uses an improved kaon\nidenti\ufb01cation, leading to a slightly larger tagging performance. The determination of Qabs on data was made using the B\ufb02av\ncontrol sample, assuming a time-integrated mixing probability of \u03c7d = 0.182 and correcting for background. See text for the\nde\ufb01nition of Qabs and Qincr.\nSub-tagger\nQabs on MC (%)\nQabs on data (%)\nQincr on MC (%)\nElectron\n6.1 \u00b1 0.1\n5.0 \u00b1 0.2\n1.14\nMuon\n4.0 \u00b1 0.1\n3.3 \u00b1 0.2\n1.0\nKin. Lepton\n2.9 \u00b1 0.1\n2.6 \u00b1 0.2\n0.36\nKaon\n18.8 \u00b1 0.1\n18.3 \u00b1 0.4\n9.91\nSlow Pions\n5.2 \u00b1 0.1\n6.1 \u00b1 0.4\n0.47\nK-Pi\n9.3 \u00b1 0.1\n10.0 \u00b1 0.4\n0.25\nMax p\u2217\n11.0 \u00b1 0.3\n9.7 \u00b1 0.5\n0.06\nFSC\n6.0 \u00b1 0.1\n6.6 \u00b1 0.4\n0.08\nLambda\n0.3 \u00b1 0.1\n0.2 \u00b1 0.1\n0.38\n) \n0\nB\n = \nflav\np (B\n0.2\n0.4\n0.6\n0.8\n1\nMC\nData\nExpected\n) / 2\nBTagger\n(1 + y\n0\n0.2\n0.4\n0.6\n0.8\n1\nResiduals\n-0.02\n0\n0.02\nFigure 8.6.3. Probability of observing a fully reconstructed\nB0 on the B\ufb02av side as a function of the probability pBtag=B0 =\n(1 + yBTagger)/2 of having a B0 on the Btag side. The dotted\nline shows the dependence expected for a perfectly trained tag-\nging algorithm. The solid points are from the full BABAR B\ufb02av\ncontrol sample, the open circles are obtained from simulation.\nA contribution of up to 22% from combinatorial background is\nsubtracted in each bin based on a \ufb01t to the mES distribution.\nThe residuals with respect to the expectation are shown at the\nbottom.\nto unity for an unambiguous \ufb02avor assignment (w \u22430).\nIn order to obtain a high overall e\ufb00ective tagging e\ufb03-\nciency Q, an estimated \ufb02avor dilution factor is assigned to\neach event based on multiple discriminants. Using a multi-\ndimensional look-up table prepared from a large sample of\nsimulated events and binned by the values of the discrim-\nSlow pion\nKaon\nLepton\nInformation on charged tracks\nLambda\nTrack-level \nlook-up tables\nFlavor information \"q\" and \"r\"\nEvent-level look-up table\nq.r\nq.r\n(q.r)K/\u039b\nSelect track\n with \nlargest \"r\"\nCalculate\ncombined \"q.r\"\nSelect track\n with \nlargest \"r\"\nFigure 8.6.4. Schematic diagram of Belle\u2019s two-stage \ufb02avor\ntagging algorithm. See the text for the de\ufb01nition of the param-\neters \u201cq\u201d and \u201cr\u201d.\ninants, the signed probability, q \u00b7 r, is given by\nq \u00b7 r = N(B0) \u2212N(B0)\nN(B0) + N(B0),\n(8.6.5)\nwhere N(B0) and N(B0) are the numbers of B0 and B0\nin the corresponding bin of the look-up table.\nThe \ufb02avor tagging algorithm proceeds in two stages:\nthe track stage and the event stage. In the track stage,\neach pair of oppositely charged tracks is examined to sat-\nisfy criteria for the \u039b-like particle category. The remaining\ncharged tracks are sorted into slow-pion-like, lepton-like\nand kaon-like particle categories. The b \ufb02avor and its di-\nlution factor of each particle, q \u00b7r, in the four categories is\nestimated using the discriminants shown in Table 8.6.5.\nIn the second stage, the results from the \ufb01rst stage are\ncombined to obtain the event-level value of q \u00b7 r. From the\nlepton-like and slow-pion-like track categories, the track\nwith the highest r value from each category is chosen as\nthe input to the event level look-up table. The \ufb02avor dilu-\ntion factors of the kaon-like and \u039b-like particle candidates\nare combined by calculating the product of the \ufb02avor dilu-\ntion factors in order to account for the cases with multiple\n\n108\nTable 8.6.5. Discriminants used in the Belle tagging algo-\nrithm.\n(Sub-)Stage\nVariables\nNumber of bins\nLepton\nq, e or \u00b5, L\u2113, p\u2217, \u03b8lab, Mrecoil, p\u2217\nmiss\n31680\nKaon\nq, nK0\nS\n, p\u2217, \u03b8lab, LK\n19656\nLambda\nq, nK0\nS\n, M\u039b, \u03b8\u039b, \u2206z\n32\nSlow pion\nq, plab, \u03b8lab, cos \u03b8\u03c0T, Le\n7000\nEvent\n(q \u00b7 r)\u2113, (q \u00b7 r)K/\u039b, (q \u00b7 r)\u03c0s\n16625\ns quarks in an event. The product of \ufb02avor dilution fac-\ntors gives better e\ufb00ective e\ufb03ciency than taking the track\nwith the highest r. Using the \ufb02avor dilution factor r deter-\nmined from Monte Carlo (MC) simulation as a measure of\nthe tagging quality is a straightforward and powerful way\nof taking into account correlations among various tagging\ndiscriminants.\nBy using two stages, the look-up tables can be kept\nsmall enough to provide su\ufb03cient statistics for each bin.\nFour million B0B0 MC events are used to generate the\nparticle-level look-up tables. To reduce statistical \ufb02uctu-\nations of the r values in the particle-level look-up tables,\nthe r value in each bin is calculated by including events\nin nearby bins with small weights. The event-level look-up\ntable is prepared using MC samples that are statistically\nindependent of those used to generate the track-level ta-\nbles to avoid any bias from a statistical correlation be-\ntween the two stages. Seven million B0B0 MC events are\nused to create the event-level look-up table. The perfor-\nmance of individual tagging categories as obtained in MC\nsimulation is shown for illustration in Table 8.6.6.\nTable 8.6.6. Performance of sub-taggers in the Belle \ufb02avor\ntagging algorithm in terms of e\ufb00ective tagging e\ufb03ciency Qabs\nin simulated events.\nSub-tagger\nQabs on MC\nLeptons\n12%\nKaons and \u039b\u2019s\n18%\nSlow Pions\n6%\nAll tagged events are sorted into seven subsamples ac-\ncording to the value of r: 0 \u2264r \u22640.1, 0.1 < r \u22640.25,\n0.25 < r \u22640.5, 0.5 < r \u22640.625, 0.625 < r \u22640.75,\n0.75 < r \u22640.875 and 0.875 < r \u22641. For each subsam-\nple l, the corresponding average wrong tag fraction wl\nis determined. For events with r \u22640.1, there is negligi-\nble \ufb02avor discrimination available and w0 is set to 0.5.\nFor the other six subsamples, the average wrong tag frac-\ntions wl (l = 1, 6) are measured directly from data using\nsamples of semi-leptonic (B0 \u2192D\u2217\u2212\u2113+\u03bd) and hadronic\n(B0 \u2192D(\u2217)\u2212\u03c0+ with D\u2217\u2212\u03c1+) B meson decays. These\ndecays are fully reconstructed and the \ufb02avor of the asso-\nciated B mesons is tagged. A total of 1461983 events are\nused to evaluate the performance of the tagging algorithm.\nAn e\ufb00ective tagging e\ufb03ciency of Q = (30.1 \u00b1 0.4)% is ob-\ntained. The wrong tag fractions, di\ufb00erences and tagging\ne\ufb03ciencies for each subsample are shown in Table 8.6.7.\nThe average value of r for each region (rl) and the mea-\nsured wrong tag fraction (wl) should satisfy rl \u22431 \u22122wl\nif the MC simulation used for constructing the look-up\ntables simulates generic B decays correctly. The degrada-\ntion from the subdivision into r bins and use of the cor-\nresponding measured wrong tag fractions wl is estimated\nto be about \u223c0.5%, according to a Monte Carlo study.\nTable 8.6.7. Tagging e\ufb03ciencies (\u03b5tag), wrong tag fractions\n(w) and their di\ufb00erences (\u2206w) for each r-interval for data tak-\ning with the SVD2 by Belle.\nr \u2212interval\n\u03b5tag\nw\n\u2206w\n0.000 \u22120.100 0.222 \u00b1 0.004\n0.5\n0.0\n0.100 \u22120.250 0.145 \u00b1 0.003 0.419 \u00b1 0.004 \u22120.009 \u00b1 0.004\n0.250 \u22120.500 0.177 \u00b1 0.004 0.319 \u00b1 0.003 +0.010 \u00b1 0.004\n0.500 \u22120.625 0.115 \u00b1 0.003 0.223 \u00b1 0.004 \u22120.011 \u00b1 0.004\n0.625 \u22120.750 0.102 \u00b1 0.003 0.163 \u00b1 0.004 \u22120.019 \u00b1 0.005\n0.750 \u22120.875 0.087 \u00b1 0.003 0.104 \u00b1 0.004 +0.017 \u00b1 0.004\n0.875 \u22121.000 0.153 \u00b1 0.003 0.025 \u00b1 0.003 \u22120.004 \u00b1 0.002\n\n109\nChapter 9\nBackground suppression for B decays\nEditors:\nJos\u00b4e Ocariz (BABAR)\nPaoti Chang (Belle)\nAdditional section writers:\nJacques Chauveau\n9.1 Introduction\nWhile the physics program of the B Factories is not lim-\nited to B physics, this chapter focuses on the techniques\nused to discriminate B decay events from backgrounds:\ndetails on speci\ufb01c background-suppression techniques for\ncharm, \u03c4 lepton and other decay modes are described in\nthe relevant chapters of this book. For both BABAR and\nBelle, most analyses of B decays use the kinematical con-\nstraints from the e+e\u2212collision at the \u03a5(4S) resonance to\nidentify signal events; additional discrimination can be ob-\ntained from information based on the \u201cevent shape\u201d, that\nis the phase-space distribution of decay particles detected\nin the event, and are the main topic of this chapter.\n9.2 Main backgrounds to B decays\nThe production cross-section from e+e\u2212collisions at the\n\u03a5(4S) resonance receives sizable contributions other than\nBB, and so the event rate is dominated by non-B events.\nThe identi\ufb01cation of speci\ufb01c B decay channels therefore\nhas to deal with a potentially large number of backgrounds\nfrom various sources. The dominant source of combina-\ntorial background comes from e+e\u2212\u2192qq events, which\nare usually referred to as \u201ccontinuum background\u201d. To\nstudy this background using real data, in addition to us-\ning signal sidebands (for example by requiring mES to\nlie safely below the B mass peak), the B Factories have\nalso dedicated a signi\ufb01cant fraction of o\ufb00-resonance data-\ntaking, at a center-of-mass energy slightly below the \u03a5(4S)\npeak: 40 MeV for BABAR, 60 MeV for Belle (see Chap-\nter 3). Also depending on the decay channel under con-\nsideration, other backgrounds (either from other B de-\ncays or from other processes) may also contribute, and\nneed to be addressed correspondingly. For example, B de-\ncay modes with only charged particles su\ufb00er backgrounds\nfrom QED processes (Bhabha scattering e+e\u2212\u2192e+e\u2212,\ne+e\u2212\u2192\u00b5+\u00b5\u2212, and e+e\u2212\u2192\u03c4 +\u03c4 \u2212) which can usually\nbe suppressed by taking advantage of their clean leptonic\nsignatures.\nIn the case of charmless b \u2192u and b \u2192s decay chan-\nnels, background rates outnumber the signal by orders of\nmagnitude, so combinatorial background from continuum\nevents is most often the dominant source of background:\nrandom combinations of particles in the \ufb01nal state may\nmimic the kinematical signatures of the signal. Thus back-\nground suppression is a crucial issue in the analysis tech-\nniques. While the signal-to-background rates are usually\nmore favorable in b \u2192c decay modes, background sup-\npression can play an important role in controlling poten-\ntial systematic uncertainties in precision measurements of\ncharmed B decays. Also, rejection of backgrounds from\nother B decay modes can play a signi\ufb01cant role in the\nanalysis results, as decay rates of such backgrounds, or\ntheir CP nature, can be poorly known.\n9.3 Topological discrimination\nFor simplicity, the discussion in this chapter is restricted\nto fully-reconstructed B decays; while most of the tools\nand techniques described here can be easily implemented\nor adapted to partly-reconstructed B modes, for a discus-\nsion of speci\ufb01c issues related to such modes, the reader is\nreferred to the relevant chapters.\nAs discussed in Chapter 7, one fundamental di\ufb00erence\nbetween B meson signal and combinatorial background is\nthe kinematics of their underlying production at the B\nFactories, so essentially all B meson analyses performed\nby BABAR and Belle take advantage of this information\nto identify the signal decay modes. After kinematic se-\nlection, additional background rejection is ensured by ex-\nploiting di\ufb00erences in the angular distributions of the par-\nticles produced in e+e\u2212\u2192\u03a5(4S) \u2192BB and background\nprocesses. For instance in a BB event, both B mesons are\nproduced almost at rest in the \u03a5(4S) frame, as the \u03a5(4S)\nmass is barely above the BB production threshold; as a\nresult, the B decay products are distributed isotropically\nin the e+e\u2212\u2192\u03a5(4S) \u2192BB rest frame. In contrast for qq\nevents, the quarks are produced with a large initial mo-\nmentum, and yield a back-to-back fragmentation into two\njets of light hadrons. For the same reason in BB events,\nthe angular distribution of decay products from the two\nB mesons are uncorrelated, while for continuum a size-\nable correlation arises, as the decay particles from each B\ncandidate tend to align with the direction of its jet.\nInformation based on the phase-space distribution of\ndecay particles can be quanti\ufb01ed in many di\ufb00erent ways.\nEarly BABAR and Belle physics analyses used methods ini-\ntially developed by the ARGUS and CLEO collaborations;\nthey then moved to develop more re\ufb01ned background-\nsuppression techniques. We recall these methods in this\nsection, and proceed to the description of those developed\nby BABAR and Belle in the next two sections. The BABAR\nPhysics Book (Harrison and Quinn, 1998) is a useful refer-\nence for background suppression tools and methods avail-\nable on the eve of B Factories; for consistency, a few def-\ninitions and variables inherited prior to the advent of the\nB Factories are summarized here:\n\u2013 Variables related to the B meson direction: the spin-1\n\u03a5(4S) decaying into two spin-0 B mesons results in a\nsin2 \u03b8B angular distribution with respect to the beam\naxis; in contrast for e+e\u2212\u2192f \u00aff events, the spin-1/2\nfermions f, and its two resulting jets, are distributed\n\n110\nfollowing a 1+cos2 \u03b8B distribution. Using the angle \u03b8B\nbetween the reconstructed momentum of the B candi-\ndate (computed in the \u03a5(4S) reference frame) and the\nbeam axis, the variable |cos \u03b8B| allows one to discrim-\ninate between signal B decays and the B candidates\nfrom continuum background.\n\u2013 Thrust and related variables: for a collection of N mo-\nmenta pi (i = 1, \u00b7 \u00b7 \u00b7 N), the thrust axis T is de\ufb01ned\nas the unit vector along which their total projection is\nmaximal; the thrust scalar T (or thrust) is a derived\nquantity de\ufb01ned as\nT =\nPN\ni=1 |T \u00b7 pi|\nPN\ni=1 |pi|\n.\n(9.3.1)\nA useful related variable is |cos \u03b8T|, where \u03b8T is the an-\ngle between the thrust axis of the momenta of the B\ncandidate decay particles (all evaluated in the \u03a5(4S)\nrest frame), and the thrust axis of all the other par-\nticles in the event (we call the set of those particles\nnot associated with the B candidate, \u201cthe rest-of-the-\nevent\u201d, or ROE). For a BB event, both B mesons are\nproduced almost at rest in the \u03a5(4S) rest frame, so\ntheir decay particles are isotropically distributed, their\nthrust axes are randomly distributed, and thus |cos \u03b8T|\nfollows a uniform distribution in the range [0, 1]. In\ncontrast for q\u00afq events, the momenta of particles fol-\nlow the direction of the jets in the event, and as a\nconsequence the thrusts of both the B candidate and\nthe ROE are strongly directional and collimated, yield-\ning a |cos \u03b8T| distribution strongly peaked at large val-\nues. Altogether, these arguments bring a qualitative\ndescription of the discriminating power provided by\n|cos \u03b8T|.\nAnother thrust-related variable is \u03b8T,B the angle be-\ntween the thrust axis of the B decay particles and\nthe beam axis; for signal, | cos \u03b8T,B| is uniformly dis-\ntributed, while for continuum events, the thrust of\nparticle momenta from the B candidate tends to be\naligned with the 1 + cos2 \u03b8T,B distribution followed by\nthe jets.\n\u2013 Sphericity and related variables: sphericity and thrust\nare strongly correlated concepts, nonetheless both are\ncommonly used. For a collection of momenta pi, the\nsphericity tensor S is de\ufb01ned as\nS\u03b1,\u03b2 =\nPN\ni=1 p\u03b1\ni p\u03b2\ni\nPN\ni=1 |pi|2 ,\n(9.3.2)\n(with \u03b1, \u03b2 = x, y, z) and provides a three-dimensional\nrepresentation of the spatial distribution of the pi col-\nlection. For an isotropic distribution, its three eigenval-\nues \u03bbk have similar magnitude; while for a planar dis-\ntribution, one of the eigenvalues is signi\ufb01cantly smaller,\nwith its eigenvector orthogonal to that plane; and \ufb01-\nnally for a very directional distribution, the eigenvector\noriented in that preferred direction has an eigenvalue\nconsiderably larger than the two others. Useful quan-\ntities derived from sphericity are the sphericity scalar\n(or sphericity), and the sphericity axis. The sphericity\nscalar S is de\ufb01ned as\nS = 3\n2 (\u03bb2 + \u03bb3) ,\n(9.3.3)\n\u03bb2 and \u03bb3 being the two lowest eigenvalues; values\nof S close to 1 correspond to isotropically distributed\nmomentum collections, while very collimated distribu-\ntions yield sphericity values close to zero. The spheric-\nity axis is collinear with the sphericity eigenvector hav-\ning the largest eigenvalue. In the same spirit as |cos \u03b8T|,\nthe variable | cos \u03b8S| is often used, where \u03b8S is the an-\ngle between the sphericity axes of the B candidate and\nthe ROE.\n\u2013 The Fox-Wolfram moments: another useful parameter-\nization of phase-space distribution of momentum and\nenergy \ufb02ow in an event, was introduced in (Fox and\nWolfram, 1978): for a collection of N particles with\nmomenta pi, the k-th order Fox-Wolfram moment Hk\nis de\ufb01ned as\nHk =\nN\nX\ni,j\n|pi| |pj| Pk (cos \u03b8ij) ,\n(9.3.4)\nwhere \u03b8ij is the angle between pi and pj, and Pk is\nthe k-th order Legendre polynomial. Notice that in\nthe limit of vanishing particle masses, H0 = 1; that is\nwhy the normalized ratio Rk = Hk/H0 is often used,\nso that for events with two strongly collimated jets, Rk\ntakes values close to zero (one) for odd (even) values\nof k. These sharp signatures provide a convenient dis-\ncrimination between events with di\ufb00erent topologies.\nThe variables and tools described in the list above do\nnot necessarily provide the optimal background discrimi-\nnating power, and for channels su\ufb00ering from large back-\nground rates, additional speci\ufb01c tools are developed. One\nsuch example is provided by a multivariate discriminant\nvariable introduced by the CLEO collaboration (Asner\net al., 1996) in the context of charmless B decays; it is\na Fisher combination (see Chapter 4 for the description of\nthe Fisher discriminant) of nine variables corresponding\nto the momentum \ufb02ow around the thrust axis of the B\ncandidate, binned in nine cones of 10\u25e6around the thrust\naxis as illustrated in Figure 9.3.1. The linear coe\ufb03cients\nassigned to the combination of these nine variables are\nextracted from MC generated events for the signal, and\neither B mass sidebands or events collected o\ufb00-resonance\nfor continuum. The Fisher used by CLEO has often been\nreferred to as \u201cthe CLEO Fisher\u201d by the B Factories.\n9.4 BABAR strategy\nFor BABAR, a typical analysis strategy is based on a two-\nstep approach: \ufb01rst, variables using the complete set of\nparticles in the event are built to reject copious back-\ngrounds while maintaining high e\ufb03ciency for signal. In the\nsecond step, variables are built separately, using informa-\ntion from the decay particles of the signal B candidate\n\n111\nh+\nh,-\nFigure 9.3.1. A graphical illustration of the CLEO Fisher\ndiscriminant, from (Asner et al., 1996). The h+, h\u2032\u2212arrows\nindicate the momenta of the two charged hadronic tracks in\na B0 \u2192h+h\u2032\u2212candidate; the momentum of ROE particles\nwithin each cone (the \ufb01rst three cones around its thrust axis\nbeing drawn in the \ufb01gure) are summed and combined to give\nthe Fisher discriminant.\nand of the ROE, to further reject backgrounds through\nadditional requirements on the selection, and/or as inputs\nto a maximum-likelihood \ufb01t (see Chapter 11 for the de-\nscription of maximum-likelihood \ufb01ts) at later stages in the\nanalysis.\nFigure 9.4.1 illustrates two typical variables used in the\n\ufb01rst step. A simple requirement on the number of charged\ntracks per event can provide highly e\ufb03cient background\nsuppression. Also, in this \ufb01rst step, a simple requirement\non the normalized second Fox-Wolfram moment ratio R2\nis applied; a loose cut on the value of R2 has negligible\nimpact on signal, while e\ufb03ciently removing a substantial\nfraction of diphoton or dilepton backgrounds. In this \ufb01rst\nstep, typical BABAR analyses also combine information\nboth from the decay particles of the B meson candidate\nand from the ROE, and use them to achieve additional\nbackground rejection. For example, Figure 9.4.2 shows the\ndistributions of |cos \u03b8S|, both for signal (from simulated\nB decays) and for continuum events (from sidebands on\ndata, by requiring mES to be in the 5.20 \u22125.26 GeV/c2\nrange). A simple per-event requirement on the value of\n| cos \u03b8S| is applied to de\ufb01ne the \ufb01nal analysis sample.\nAn important advantage of variables based on the ROE\nis that for the signal B decays, their correlation is small\nor negligible with the variables built out of the B candi-\ndate observables. Therefore it is appropriate to construct\na joint likelihood function from the product of their p.d.f.s\nto use in a \ufb01t.\n9.4.1 Linear discriminants\nFor typical BABAR analyses, several combinations of vari-\nables from the ROE are built, and combined in multi-\nvariate discriminants. A general description of linear dis-\ncriminants in the optimization of the analyses is given in\nBB\n\u2212\nqq\n\u2212 continuum\n\u03c4+\u03c4-\n\u00b5+\u00b5-(\u03b3)\ne+e-(\u03b3)\n\u03b3\u03b3\nNumber of tracks\nArbitrary units\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0\n2\n4\n6\n8\n10\n12\n14\n16\nBB\n\u2212\nqq\n- continuum\n\u03c4+\u03c4-\n\u00b5+\u00b5-(\u03b3)\ne+e-(\u03b3)\n\u03b3\u03b3\nR2\nArbitrary units\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 9.4.1. Two examples of global variables, used as a \ufb01rst\nstep in background suppression in most BABAR analyses of B\ndecays. The top plot shows the number of charged tracks per\nevent for various processes; the bottom plot is the distribution\nof the normalized second Fox-Wolfram moment ratio R2, for\nvarious processes. The \ufb01gures are from a BABAR Thesis (Ra-\nhatlou, 2002).\nChapter 4. Many of these discriminants use the so-called\n\u201cmonomials\u201d Ln, de\ufb01ned as\nLn =\nX\ni\u2208ROE\npi \u00d7 |cos \u03b8i|n ,\n(9.4.1)\nwhere pi is the momentum (computed in the \u03a5(4S) ref-\nerence frame) of particle i belonging to the ROE, and \u03b8i\nis the angle between its momentum and the thrust axis of\nthe B candidate. Dedicated studies concluded that the L0\n\n112\n)|\nS\n\u03b8\n|cos(\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n(a.u.)\n0\n0.2\n0.4\n0.6\n0.8\n1\nB\nB\nContinuum\nFigure 9.4.2. The signal (solid blue line) and continuum back-\nground (dashed red line) distributions of | cos \u03b8S|, a variable\noften used as a \ufb01rst step in background suppression for charm-\nless two-body B decays. | cos \u03b8S| is uniformly distributed for\nthe signal, while for continuum it is sharply peaked at large\nvalues. The \ufb01gure is adapted from a BABAR Thesis (Malcl`es,\n2006). The vertical scale is in arbitrary units (a.u.).\nand L2 pair provides most of the discriminating power to\nseparate signal from continuum background; for instance,\na bi-variate linear (Fisher) combination F = c0L0 + c2L2\n(using L0 and L2 only) reaches a signal-to-background\nseparation comparable to a Fisher using the nine vari-\nables in the CLEO Fisher. Figure 9.4.3 illustrates the\ncontribution from a single 1 GeV particle to both dis-\ncriminants, as a function of its angle with respect to the\nthrust axis. That same \ufb01gure shows the contribution from\na three-variable Fisher discriminant (including also the\nL1 monomial), that exhibits an almost equivalent angular\ndependence to the nine-variable CLEO discriminant, thus\nshowing that a comparable discriminating power can be\nachieved with a smaller number of variables.\nFor most charmless B decay analyses, the optimization\nalgorithm returns values very close to F = L2 \u22122 \u00d7 L0\n(i.e. c0 = \u22122c2, up to arbitrary o\ufb00set and scale parame-\nters) for the Fisher coe\ufb03cients. To a certain extent, this\ntwo-variable Fisher discriminant can be thought of as a\nsimple, continuous extension of the CLEO discriminant,\nthat can be explained in terms of the relative sign and\nratio of the c0 and c2 coe\ufb03cients described above. For\nan isotropically distributed collection of particles, the to-\ntal F value will be close to zero, as particles with angles\ncollinear/orthogonal to the B candidate thrust axis con-\ntribute with opposite signs, and tend to cancel out in the\nsum. In contrast, contributions from a collection of parti-\ncles collinear with the thrust axis will mostly sum up to\ngive a positive value.\nFigure 9.4.4 shows the distributions of this bi-variate F\ndiscriminant, with coe\ufb03cients evaluated both before and\nafter a \ufb01rst-step cut on | cos \u03b8S| < 0.8 (c.f. Figure 9.4.2).\nBefore the \ufb01rst-step selection, the F discriminant pro-\nvides a \u223c1.6\u03c3 separation between signal and background.\nThe \ufb01rst-step cut on | cos \u03b8S| rejects \u223c65% of all con-\n (degrees)\n\u03b8\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nValue (a.u.)\n-2\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n2\nCones\n Fisher\n2\n,L\n0\nL\n Fisher\n2\n,L\n1\n,L\n0\nL\nFigure 9.4.3. The contribution to the BABAR and CLEO\nFisher discriminants, for a single 1 GeV particle, as a func-\ntion of the angle of its momentum and the thrust axis of the B\ncandidate. The nine-step line indicates the values of the nine\ncone coe\ufb03cients in 10\u25e6bins for the CLEO Fisher, while the\ncontinuous blue line is the resulting function for the F used by\nBABAR. The dash-dotted line corresponds to a three-variable\nFisher (shown for illustration only, not used in actual BABAR\nanalyses). The coe\ufb03cients for these Fisher discriminants were\noptimized using samples of charmless two-body B decays for\nsignal, and data events from mES sidebands for background.\nThe \ufb01gure is adapted from a BABAR Thesis (Pivk, 2003). The\nvertical scale is in arbitrary units (a.u.).\ntinuum background, while retaining \u223c80% of signal; for\nthe signi\ufb01cantly signal-enriched remaining selected events,\nF still provides a \u223c1.2\u03c3 separation. This remaining dis-\ncriminating power is e\ufb03ciently exploited in the maximum-\nlikelihood analysis.\nThe monomial L0 is the total momentum \ufb02ow observed\nin the detector, and L2 is a direction-weighted sum of con-\ntributions to the total momentum \ufb02ow. Hence the ratio\nL2/L0 is expected to be rather insensitive to the actual\nper-event value of the total momentum \ufb02ow, which largely\ncancels in the ratio. The relative sign of the c0, c2 coe\ufb03-\ncients in F expresses the same cancellation. As a result,\nthe simulated distributions of both F and L2/L0 are found\nto be in excellent agreement with data. Some BABAR anal-\nyses have therefore preferred to use the simpler L2/L0 ra-\ntio. Simplicity over complexity (i.e. adding L1 or splitting\nthe ROE between charged and neutral particles) has been\nprivileged by most BABAR analyses because the discrimi-\nnating gain was found to be marginal.\n9.4.2 Nonlinear discriminants\nMany BABAR analyses combine the information from the\nmonomials with other variables to further enhance their\ndiscriminating power and the resulting performance in\nbackground suppression. As already mentioned, there are\nsigni\ufb01cant correlations among event-shape variables (since\nthey all quantify in di\ufb00erent ways the spatial distribution\nof momentum \ufb02ow). To better exploit such potentially\n\n113\nF\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n(a.u.)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nB\nB\nContinuum\n)|\nS\n\u03b8\nno cut on |cos(\nF\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\n(a.u.)\n0\n0.2\n0.4\n0.6\n0.8\n1\nB\nB\nContinuum\n)|<0.8\nS\n\u03b8\n|cos(\nFigure 9.4.4. The signal (solid blue line) and background\n(dashed red line) distributions of the Fisher discriminant F\nbased on the L0 and L2 monomials, used for continuum back-\nground suppression in several BABAR charmless B decay anal-\nyses. To illustrate the two-step procedure, the distributions\nare shown both before (top) and after (bottom) a \ufb01rst-step\ncut of | cos \u03b8S| < 0.8. The \ufb01gures are adapted from a BABAR\nThesis (Malcl`es, 2006). The vertical scale is in arbitrary units\n(a.u.).\nnonlinear correlations, neural networks (NN, see Chap-\nter 4 for a description of multivariate methods) and other\nnonlinear discriminant algorithms are used. As an illustra-\ntion, typical charmless 3-body analyses use, in addition\nto the L0 and L2 monomials, variables such as |cos \u03b8B|\nand |cos \u03b8T| in their \ufb01nal MVA. Figure 9.4.5 illustrates\nthe discriminating power achieved with a NN based on\nthese four variables, used in several Dalitz-plot analyses\nof charmless 3-body B decays in BABAR (see Chapter 13\nfor a description of Dalitz-plot analyses). In these analy-\nses, the NN output is used both for selection and in the\nmaximum-likelihood \ufb01t. At the \ufb01rst stage, this NN pro-\nvides a \u223c1.9\u03c3 separation between signal and background.\nA cut at NN > \u22120.4 is then applied to remove roughly\n75% of continuum background while retaining a 90% sig-\nnal e\ufb03ciency; on top of enhancing its signal-to-background\ncontent, this cut also reduces the sample size to a value\nthat is suitable for the CPU constraints a\ufb00ecting multidi-\nmensional amplitude \ufb01ts in Dalitz-plot analyses. Then, at\nthe amplitude analysis stage, the NN is implemented in\nthe likelihood function, where its remaining \u223c1.4\u03c3 sep-\naration is exploited in the maximum-likelihood \ufb01t. Two\nspeci\ufb01c features, relevant to the implementation of a NN\nin a Dalitz analyses are worth mentioning:\n\u2013 For continuum background, the NN is correlated with\nthe Dalitz variables. This feature can be qualitatively\ndescribed as follows: for continuum event candidates\npassing all selection criteria, and belonging to the cen-\nter of the Dalitz plot, the angular distribution of par-\nticles tends to exhibit a more isotropic distribution,\nsince already the three particles composing the signal\ncandidate have similar momenta and roughly equidis-\ntant angular separation. In order to include the NN\nin the likelihood function, a parameterization of this\ncorrelation as a function of Dalitz masses, has to be\ne\ufb00ectively implemented for its continuum component.\n\u2013 In light of the aforementioned systematic sensitivity\nto the simulation of the total momentum \ufb02ow, some\nBABAR analyses have opted for not allowing the L0\nand L2 monomials to be independently optimized in\nthe training stage of the NN, and used instead a linear\ncombination with \ufb01xed coe\ufb03cients or the L2/L0 ratio\nin the NN training.\nNN\n-1\n-0.8 -0.6 -0.4 -0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n(a.u.)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n hhh signal MC\n\u2192\nB\noff-resonance data\nFigure 9.4.5. An example of a multilayer perceptron out-\nput NN, used to discriminate between the signal B decay and\ncontinuum background in the charmless 3-body analysis of\nB0 \u2192K0\nS\u03c0+\u03c0\u2212decays. The solid blue histogram is the NN\noutput evaluated on signal Monte-Carlo, and the dashed red\nhistogram uses o\ufb00-resonance data. This neural network uses\nfour variables as inputs : L0, L2, | cos \u03b8B| and | cos \u03b8T |. The \ufb01g-\nure is adapted from a BABAR Thesis (P\u00b4erez, 2008). The vertical\nscale is in arbitrary units (a.u.).\n9.4.3 Including additional sources of background\nsuppression\nIn addition to the \u201cevent-shape\u201d variables discussed in the\nprevious sections, various other sources of discriminating\n\n114\ninformation are also available in B decay analyses: in par-\nticular, decay-time information extracted from vertexing\n(discussed in Chapter 6), kinematical variables extracted\nfrom B meson reconstruction (Chapter 7), and the out-\nput of B-\ufb02avor tagging (Chapter 8), can all contribute to\nbackground suppression. As described in more detail in\nChapter 11, a generic time-dependent analysis combines\nall this information in a maximum-likelihood analysis.\nFor speci\ufb01c analyses, only a subsample of this infor-\nmation is e\ufb00ectively used in the likelihood function; for\ninstance, timing information is not necessary to perform\na time-independent \ufb01t, and analysis of a \ufb02avor-speci\ufb01c de-\ncay (like charged B modes, or \u201cself-tagging\u201d neutral decay\nmodes), does not require tagging. In such scenarios, some\nBABAR analyses (particularly in searches of rare decay\nchannels) exploit this available background-suppressing\npower, by combining event-shape variables with the tag-\nging index output and/or the time di\ufb00erence signi\ufb01cance\n\u2206t/\u03c3(\u2206t) into a linear Fisher discriminant, which is in\nturn used in the likelihood function.\n9.5 Belle strategy\nFor Belle, the correlated shape variables are \ufb01rst combined\nto form a Fisher discriminant and then other uncorrelated\nvariables are included with the Fisher variable to form a\nsignal-to-background likelihood ratio R. The numbers of\nsignal and background events can be extracted by either\napplying a cut on the likelihood ratio and then performing\na \ufb01t using mES and \u2206E, or by requiring a loose cut on R,\nand then performing a \ufb01t using the variables mES, \u2206E and\nR. Later in the lifetime of Belle, more analyses employ the\nneural network technique to combine correlated variables\nwith the Fisher discriminant and other uncorrelated vari-\nables. One can make a requirement on the neural network\noutput to suppress the background or include the output\nafter a loose requirement in a multi-dimensional likelihood\n\ufb01t to extract the signal.\n9.5.1 SF W\nThere are two kinds of Fisher discriminant used to study\ncharmless B decays on Belle. All reconstructed particles\nin an event are divided into two categories: B candidate\ndaughters (denoted as s) and the ROE (denoted as o). Two\nFisher discriminants are constructed using the energy and\nmomentum of each particle in the e+e\u2212center-of-mass\nframe. The \ufb01rst Fisher discriminant is composed of several\nFox-Wolfram moments hkl\nj and is de\ufb01ned as\nSFW = a2hso\n2 + a4hso\n4 +\n4\nX\nj=1\nbjhoo\nj ,\n(9.5.1)\nwhere a2, a4 and bj are the Fisher coe\ufb03cients determined\nto separate signal and backgrounds in an optimal way us-\ning the signal and continuum MC events. The SFW vari-\nable is colloquially referred to as the \u201cSuper Fox-Wolfram\nMoment\u201d. In order to avoid the data-MC discrepancy in\nevent shapes, data in regions dominated by continuum are\noften used to determine the coe\ufb03cients. Variables hso\ni (i =\n2, 4) and hoo\nj\nare the normalized Fox-Wolfram moments,\nde\ufb01ned as\nhk\nl =\nX\nm,n\n|\n\u2192\npm ||\n\u2192\npn |Pl(cos \u03b8mn)\nX\nm,n\n|\n\u2192\npm ||\n\u2192\npn |\n,\n(9.5.2)\nwhere\n\u2192\npm and\n\u2192\npn are the momenta of particles m and n;\nPl(cos \u03b8mn) is the l-th order Legendre polynomial of cosine\nof the angle (\u03b8mn) between\n\u2192\npm and\n\u2192\npn; k categorizes the\ntype of Fox-Wolfram moment, so and oo, where m is from\nB signal daughters and n is from the ROE for so, and both\nm and n are from the ROE for oo. If B daughter particles\nthemselves decay into several particles, the event shape is\nmore isotropically distributed. However, the B candidates\nfrom the continuum are also more isotropically distributed\nto mimic the BB events. For two-body or three-body B\ndecays, the signal-to-background separation is therefore\nbetter if the SFW variable is computed using the particles\ndirectly from B decays. For instance, in the decay B \u2192\n\u03c9K with \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00, the Fox-Wolfram moment hso\nl\nin\nEq. (9.5.2) is calculated using the \u03c9 momentum instead of\nthe momenta of its daughter pions. The di\ufb00erence of the\nseparation power between the two di\ufb00erent treatments is\nless pronounced for multi-body B decays.\n9.5.2 KSF W\nTo further improve the continuum suppression, a second\nFisher discriminant was developed by Belle:\nKSFW =\n4\nX\nl=0\nRso\nl +\n4\nX\nl=0\nRoo\nl\n+ \u03b3\nNt\nX\nn=1\n|(Pt)n|, (9.5.3)\nwhere Rso\nl\nand Roo\nl\nare modi\ufb01ed Fox-Wolfram moments\nsimilar to hso\nl\nand hoo\nl\nin Eq. (9.5.2), respectively; the third\nterm is the scalar sum of the transverse momentum of\neach particle multiplied by a free parameter \u03b3 and Nt is\nthe total number of particles. The expressions of Rso\nl\nand\nRoo\nl\nare described as follows:\n\u2013 Rso\nl\nIn constructing Rso\nl , the missing momentum of an event\nis treated as an additional particle and the moment is\ndecomposed into three categories: a charged particle\npart (c), neutral particle part (n), and missing particle\npart (m). The variable Rso\nl\nis expressed as\nRso\nl\n= \u03b1clHso\ncl + \u03b1nlHso\nnl + \u03b1mlHso\nml\nE\u2217\nbeam \u2212\u2206E\n.\n(9.5.4)\nFor odd l, we have\nHso\nnl = Hso\nml = 0\nand\n(9.5.5)\nHso\ncl =\nX\ni\nX\njx\nQiQjx|pjx|Pl(cos \u03b8i,jx), (9.5.6)\n\n115\nwhere i runs over the B daughters; jx indexes the ROE\nin the category x (x = c, n, m); Qi and Qjx are the\ncharges of particle i and jx, respectively; pjx is the\nmomentum of particle jx; and Pl(cos \u03b8i,jx) is the l-th\norder Legendre polynomial of the cosine of the angle\nbetween particles i and jx.\nFor even l,\nHso\nxl =\nX\ni\nX\njx\n|pjx|Pl(cos \u03b8i,jx),\n(9.5.7)\nwhich is similar to Eq. (9.5.6) except for the charge\nfactors. There are two free parameters for l = 1, 3 and\nnine (3 \u00d7 3) for l = 0, 2, 4.\n\u2013 Roo\nl\nThe de\ufb01nition of the second term of Eq. (9.5.3) is sim-\npler.\nFor odd l, we have\nRoo\nl\n=\nX\nj\nX\nk\n\u03b2lQjQk|pj||pk|Pl(cos \u03b8j,k),(9.5.8)\nwhere j and k run over the ROE and other variables\nare the same as used in Eq. (9.5.6).\nFor even l, we have\nRoo\nl\n=\nX\nj\nX\nk\n\u03b2l|pj||pk|Pl(cos \u03b8j,k).\n(9.5.9)\nThere are \ufb01ve Fisher coe\ufb03cients (\u03b2l) to be determined.\nThe total number of Fisher coe\ufb03cients in KSFW is\n17, determined using the signal and continuum MC events.\nTo further improve the background suppression, the 17\ncoe\ufb03cients are obtained in seven missing mass squared\n(M 2\nmiss) bins, where M 2\nmiss is de\ufb01ned as\nM 2\nmiss =\n \nE\u03a5 (4S) \u2212\nNt\nX\nn=1\nEn\n!2\n\u2212\nNt\nX\nn=1\n|pn|2, (9.5.10)\nwhere E\u03a5 (4S) is the energy of \u03a5(4S) and En and pn\nare the energy and momentum of particle n, respectively.\nTherefore, there are seven sets of 17 Fisher coe\ufb03cients\nin KSFW. In general KSFW, compared to SFW, pro-\nvides better signal-background separation for charmless\ntwo-body and three-body B decays, but the improvement\nis less pronounced for the B decays into a \ufb01nal state with\nmore than three particles.\nTwo other variables that can distinguish between sig-\nnal and continuum are cos \u03b8B (as mentioned in Section 9.3)\nand \u2206Z, where the former is the cosine of the angle be-\ntween the B momentum and the beam direction in the\nCM frame and the latter is the distance in the beam direc-\ntion between the B vertex and the vertex from the ROE.\nFigure 9.5.1 shows the cos \u03b8B and \u2206Z distributions for\nthe B+ \u2192K+\u03c00 signal and the continuum events. Since\n\u03a5(4S) produced at e+e\u2212resonance is transversely polar-\nized, the B moving distribution behaves as sin2 \u03b8B while it\nis more or less \ufb02at for the continuum background.38 The\n\u2206Z distribution is broader for BB events due to the rel-\natively longer lifetime of B mesons. Signal B vertices are\nconstructed using the charged tracks of the B daughters.\nFor a decay mode with only one charged track in the \ufb01nal\nstate, for instance B+ \u2192K+\u03c00, the z vertex position is\nobtained by projecting the single track trajectory to the\nbeam axis. Obviously the \u2206Z resolution is better if there\nis more than one charged particle used to reconstruct the\ndecay vertex. The \u2206Z variable is not applicable for the\ndecay modes with only photons in the \ufb01nal state, for in-\nstance B0 \u2192\u03c00\u03c00. It is possible to use photon conversions\nto obtain the B vertex in a future super \ufb02avor factory. The\nprimary aim for this case is to perform a time-dependent\nmeasurement.\nFinally all the shape information is combined to form\na signal-to-background likelihood ratio (R), de\ufb01ned as\nR =\nLS\nLS + LB\n,\n(9.5.11)\nLS/B = P(KSFW)S/B \u00d7 P(cos \u03b8B)S/B \u00d7 P(\u2206Z)S/B,\n(9.5.12)\nwhere PS/B is the probability density function for signal\n(S) and background (B). Continuum suppression can be\nachieved by applying a cut selection on R based on a \ufb01gure\nof merit or requiring a loose selection and including R in\na multi-dimensional likelihood \ufb01t. To avoid poor modeling\nof the rising edges as shown in the top plot of Fig. 9.5.2,\nin some analyses a modi\ufb01ed likelihood ratio R\u2032 can be\nde\ufb01ned as\nR\u2032 = log R \u2212lb\nub \u2212R,\n(9.5.13)\nwhere lb is the lower bound of R, which is the loose R\nselection value to reduce the background, and ub is the\nupper bound (usually 1.0). The bottom plot of Fig. 9.5.2\nshows the R\u2032 distribution with lower R bound at 0.2 for\nB+ \u2192K+\u03c00 signal and the continuum background. The\nsignal and background R\u2032 distributions may be described\nby a single or double Gaussian, which can be used as p.d.f.\nrepresentations of R\u2032 in the multi-dimensional \ufb01t.\n9.5.3 Additional variables and neural network\nAdditional background discrimination is provided by B-\n\ufb02avor tagging. As described in Chapter 8, events with\ngood \ufb02avor tags usually contain high momentum leptons\nand are more likely to be BB events. The top plot of\nFig. 9.5.3 shows the normalized signed probability (q \u00b7 r)\ndistributions for B signal and the continuum background\nfrom MC. Note that the q \u00b7 r de\ufb01nition for the tag B\n38 The distribution of the angle between f and the beam axis\nfor e+e\u2212\u2192f \u00aff (continuum) events has a 1 + cos2 \u03b8B shape.\nHowever, the reconstructed \u03b8B in continuum events is a conse-\nquence of random combinations of tracks. The distribution is\nalso a\ufb00ected by acceptance e\ufb00ects. The resulting distribution\nturns out to be almost uniform.\n\n116\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\ncos\u03b8B \n \n( a.u. )\n0\n0.025\n0.05\n0.075\n0.1\n0.125\n0.15\n0.175\n0.2\n0.225\n-0.1 -0.075 -0.05 -0.025\n0\n0.025 0.05 0.075 0.1\n\u2206 z\n( a. u. )\nFigure 9.5.1. The cos \u03b8B (top) and \u2206Z (bottom) distributions\nfor the B+ \u2192K+\u03c00 and continuum MC events. Solid red\nlines are B signal candidates and dashed blue lines are the\ncontinuum background. These \ufb01gures are Belle internal, from\nthe (Duh, 2012) analysis. The vertical scale is in arbitrary units\n(a.u.).\ndescribed in Eq. 8.6.5 is also valid for the charged B me-\nson system by replacing B0(B0) with B+(B\u2212). It is easy\nto understand that the majority of the continuum events\npopulate the central q \u00b7r region, where the \ufb02avor informa-\ntion is poorly known, while sizable fractions of B signal\nevents have q \u00b7 r \u223c\u00b11. If the signal B decays into a \ufb02a-\nvor speci\ufb01c state, one can use the product of the signal\nB-\ufb02avor (qB) and q \u00b7 r to distinguish between signal and\nbackground. As shown in the bottom plot of Fig. 9.5.3, a\nlarge fraction of signal events populate the region around\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nR\n( a. u. )\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n-15\n-10\n-5\n0\n5\n10\n15\nR'\n( a. u. )\nFigure 9.5.2. The R (top) and modi\ufb01ed R (bottom) distri-\nbutions for the B+ \u2192K+\u03c00 and continuum MC events. Solid\nred lines are B signal candidates and dashed blue lines are\nthe continuum background. The modi\ufb01ed R (R\u2032) is de\ufb01ned\nafter requiring R > 0.2. These \ufb01gures are Belle internal, from\nthe (Duh, 2012) analysis. The vertical scale is in arbitrary units\n(a.u.).\nqB \u00b7 q \u00b7 r = \u22121 and the distributions for both signal and\nthe continuum events in the B+ \u2192K+l+l\u2212study become\nasymmetric. The asymmetric qB \u00b7 q \u00b7 r distribution for the\ncontinuum is due to the correlation of strangeness between\nthe tag and signal sides. To utilize all available informa-\ntion, the quantity qB \u00b7 q \u00b7 r (q \u00b7 r for the CP eigenmodes)\ncan be used in the likelihood for background suppression,\nor alternatively the original R selections can be optimized\ndepending on the value of qB \u00b7q \u00b7r. The latter method has\nbeen used in many Belle analyses.\nTo utilize all the available information, in some Belle\nanalyses the variables described above were combined us-\n\n117\nq r \n0\n0.02\n0.04\n0.06\n0.08\n0.1\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1.\n( a. u. )\nqB q r\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\n..\n( a. u. )\nFigure 9.5.3. The q\u00b7r (top) and qB\u00b7q\u00b7r (bottom) distributions\nfor signal (solid red) and continuum MC (dashed blue) events.\nSignal B events are generated to decay into a \ufb02avor speci\ufb01c\nstate. These \ufb01gures are Belle internal, from the (Wei, 2009)\nanalysis. The vertical scale is in arbitrary units (a.u.).\ning the neural network technique. One of the popular\npackages used in Belle is the NeuroBayes package (Feindt\nand Kerzel, 2006; Phi-T, 2008). For instance, the sup-\npression of the continuum background in the Belle anal-\nyses of B0 \u2192D0K\u22170, D0 \u2192K\u2212\u03c0+\n(Negishi, 2012) and\nB\u2212\u2192DK\u2212, D \u2192K+\u03c0\u2212(Horii, 2011) was achieved us-\ning several variables as the NeuroBayes inputs: such as\nKSFW, cos \u03b8T, cos \u03b8B, \u2206Z, \ufb02avor tagging information q\u00b7r,\nand the cosine of the angle between the momentum of the\nkaon candidate from the D decay and the B momentum\nin the D rest frame. Three more variables are included\nin the B0 \u2192D0K\u22170 search: (1) the distance of closest\napproach between the trajectories of the K\u2217and D can-\ndidates; (2) the di\ufb00erence between the sum of the particle\ncharges in the D hemisphere and the sum in the opposite\nhemisphere, excluding those used in the reconstruction of\nthe B meson; and (3) the angle between the D and \u03a5(4S)\ndirections in the rest frame of the B candidate. The ad-\nvantage of employing the neural network technique is that\nvariables having correlations with each other can be added\nand their correlations are considered non-linearly. As with\nthe signal-background likelihood ratio, one can make a re-\nquirement on the NeuroBayes output to suppress the con-\ntinuum background or include it in a multi-dimensional\nlikelihood \ufb01t to extract the signal yield.\nNeuroBayes is widely used in many high energy exper-\niments. The application, to name a few, ranges from Higgs\nsearch (Aaltonen et al., 2009d), studies of single top pro-\nduction (Aaltonen et al., 2010; Chatrchyan et al., 2012a),\nmeasuring B and D meson properties (Aaij et al., 2012l;\nAaltonen et al., 2011d), and full B meson reconstruction\nat B factories (Feindt et al., 2011).\n9.6 Summary\nIn summary, various techniques of background suppres-\nsion, mostly inspired by charmless B decay analyses suf-\nfering from huge backgrounds, are described in this chap-\nter.\nAs an illustration, for an analysis of B \u2192\u03b7\u2032h (h =\n\u03c1, K\u2217, \u03c9, \u03c6) (Schumann, 2007) in Belle, the continuum\nbackground is suppressed by imposing q \u00b7 r dependent se-\nlections on R. The signal e\ufb03ciency due to the suppression\nis (42\u201388)% and the background is reduced by (98\u201345)%,\ndepending on the decay mode. The possible improvement\nby including the variable R\u2032 in the \ufb01t for signal extraction\nis investigated in the B+ \u2192K+\u03c00 analysis in Belle. With\na lower bound (lb) value chosen to be 0.2, the signi\ufb01cance\n(the signal yield from the \ufb01t divided by its uncertainty)\nof the extracted signal is improved by 15%. Note that\nthere may be correlations between R\u2032 and other variables.\nFor instance, the variables R\u2032 and \u2206E for the continuum\nbackground is found to be correlated in the B \u2192hh\u2032\nanalysis (Duh, 2012). Hence, di\ufb00erent \u2206E p.d.f.s in dif-\nferent R\u2032 regions are implemented in the analysis. Exam-\nples of using the NeuroBayes package to include various\ncorrelated variables are described in Section 9.5.3. A re-\nquirement on the NeuroBayes output in the analysis of\nB\u2212\u2192DK\u2212, D \u2192K+\u03c0\u2212(Horii, 2011) retains 96% of the\nsignal and rejects 74% of the background. In the search\nof B0 \u2192DK\u22170, D \u2192K\u2212\u03c0+, the NeuroBayes output,\nranging from \u22121 to 1, is \ufb01rst required to be greater than\n\u22120.6 to suppress the background, and is then included\nin the multi-likelihood \ufb01t after being transformed using\nEq. (9.5.13) with the NeuroBayes output R, lb = \u22120.6\nand ub = 1.0. The loose cut (lb = \u22120.6) rejects 70.5% of\nthe background, while the signal loss is 3.9%.\nFor BABAR, most analyses of B \u2192hh channels (h =\n\u03c0, K) (see Chapter 17.4) followed strategies in line with\nthe generic approach described in Section 9.4.1: a two-step\nbackground suppression, starting with simple loose cuts on\n\n118\nstrongly discriminating variables, then using Fisher dis-\ncriminants as a discriminating variable in a likelihood \ufb01t.\nAt the selection step, signal e\ufb03ciencies were often adapted\nto the speci\ufb01c signal-to-background rates for the \ufb01nal state\nbeing considered; for example in (Aubert, 2007ay), the cut\non the | cos \u03b8S| value applied in the B+ \u2192h+\u03c00 study was\nchosen to retain about \u223c80% of signal while rejecting\n\u223c65% of continuum; in contrast, a tighter selection was\napplied for B0 \u2192\u03c00\u03c00, as a consequence of its smaller\nsignal-to-background rate. In the same spirit, the \ufb01nal\nupdate of the B0 \u2192\u03c0+\u03c0\u2212, K+\u03c0\u2212study (Lees, 2013b)\napplied a looser cut on | cos \u03b8S|, achieving close to \u223c90%\nsignal e\ufb03ciency. Owing to its larger signal purity, in this\nstudy both the signal and background parameters of the\nFisher p.d.f. were extracted from the signal sample itself in\nthe maximum-likelihood \ufb01t (instead of being extrapolated\nfrom sidebands or simulation control samples), thus min-\nimizing the corresponding systematic uncertainties. The\nobservation of the rare B+ \u2192K+K0 and B0 \u2192K0K0\ndecays (Aubert, 2006ai) is another useful illustration of\nlinear discriminants in BABAR; the enhancement of signal\nsensitivity provided by a similar Fisher discriminant was\ninstrumental in establishing the observation of these two\nrare channels. Concerning nonlinear discriminants, most\nBABAR analyses of charmless B \u2192hhh decays (h = \u03c0, K)\nimplemented NN discriminants in line with the generic\nstrategy discussed in Section 9.4.2; at the selection level,\ntypical cuts on the NN value were chosen to retain some\n\u223c90% of signal, while rejecting up to \u223c75% of contin-\nuum. For Dalitz-plot analyses such as (Aubert, 2009av),\nnon-negligible correlations between the NN and the Dalitz\nvariables for continuum events were observed, and ad-\ndressed with a dedicated parameterization; in this way,\nthe \u223c1.4\u03c3 separation provided by these NN discriminants\ncould be implemented in the likelihood function, and used\nin the amplitude \ufb01ts.\n\n119\nChapter 10\nMixing and time-dependent analyses\nEditors:\nAdrian Bevan (BABAR)\nThomas Mannel (theory)\nThis Chapter introduces neutral meson mixing, as well\nas the principles and methods underlying time-dependent\nanalyses in B meson decays. A detailed discussion of ex-\nperimental concerns for a time-dependent analysis follows\non from a theoretical introduction of mixing and time-\ndependent formalism (Sections 10.1 and 10.2). The ex-\nperimental aspects discussed here include the use of \ufb02a-\nvor tagging methods introduced in Chapter 8 and the in-\nevitable dilution of information when the tagging assign-\nment is incorrect (Section 10.3). The impact of the de-\ntector resolution on the reconstructed value of the proper\ntime di\ufb00erence between the decays of two neutral mesons\nand on the measurement of physical observables is raised\nin Section 10.4. The corresponding time evolution of back-\nground events is discussed in Section 10.5. The \ufb01nal part\nof this chapter discusses how parameters required to de-\nscribe the mixing and time-evolution of B mesons can be\nextracted from the data (Section 10.6). Systematic un-\ncertainties common to all time-dependent analyses of B\ndecays are discussed in Section 15.3.\nMixing in the neutral B meson system was discovered\nby the ARGUS Collaboration (Albrecht et al., 1987b),\nand Section 17.5 summarizes the measurements of B mix-\ning performed by BABAR and Belle. An understanding\nof mixing in B mesons is one of the ingredients in the\nstudy of time-dependent CP asymmetries: in particular,\nit is crucial for the measurement of the angles of the\nUnitarity Triangle introduced in Chapter 16, and discus-\nsion of measurements of the angles can be found in Sec-\ntions 17.6 through 17.8. Tests of quantum entanglement,\nthe CPT symmetry, and Lorentz covariance using neutral\nB mesons, discussed in Sections 17.5.3 through 17.5.5, also\nrely on a good understanding of mixing. Neutral meson\nmixing in charm decays was discovered at the B Facto-\nries: this is discussed in Section 19.2.\n10.1 Neutral meson mixing\nMeson mixing is a phenomenon that only occurs for the\nweakly-decaying, open-\ufb02avor (i.e. not qq pairs) neutral K,\nD, and B0\nd,s mesons. Collectively we can refer to these\nmesons as P when describing the formalism common to all\nthree systems. The e\ufb00ective Hamiltonian describing neu-\ntral meson mixing is given by\nHe\ufb00= M \u2212i\u0393\n2\n=\n\u0014\u0012\nM11 M12\nM21 M22\n\u0013\n\u2212i\n2\n\u0012\n\u039311 \u039312\n\u039321 \u039322\n\u0013\u0015\n, (10.1.1)\nwhere M and \u0393 are two-by-two Hermitian matrices de-\nscribing the mass and decay rate components of He\ufb00, re-\nspectively.\nThe CPT symmetry imposes that the matrix elements\nin Eq. (10.1.1) satisfy M11 = M22 and \u039311 = \u039322. In the\nlimit of CP or T invariance in mixing, \u039312/M12 = \u039321/M21\nis real. Figure 10.1.1 shows the short-distance box dia-\ngrams responsible for (top) D and (bottom) B0\nd,s mixing\ntransitions in the SM. For the cases of kaons and D mesons\nthese diagrams are dominated by long-distance contri-\nbutions that are di\ufb03cult to compute. The long-distance\npieces are strongly CKM suppressed only in the case of B\nmesons for which M12 can be computed in perturbation\ntheory. Long-distance contributions are due to real inter-\nmediate states whereas the short-distance contributions\narise from heavy quark transitions (in particular, the top\nquark).\n0\nui*\nVci\nVuj*\nVcj\nW+\nW\u2212\nc\nd,s,b\nu\nu\nd,s,b\nc\nD0\nD\nV\nd (s)\nid(s)\nW+\nW\n0\n0\nB\nB\nu,c,t\nu,c,t\nb\nb\nVjb*\nVib*\nVjd(s)\n\u2212\nd (s)\nV\nFigure 10.1.1. Box diagrams corresponding to the short-\ndistance contributions to neutral meson mixing for (top) D and\n(bottom) B0\nd,s mesons. Each of these contributions is matched\nby a diagram where the quark triplet, and W bosons are in-\nterchanged. The Vij are CKM matrix elements discussed in\nChapter 16.\nSolving the time evolution represented by the e\ufb00ec-\ntive Hamiltonian of Eq. (10.1.1) amounts to determining\nits eigenstates; however, the eigenvalue problem is non-\nHermitian, hence the eigenvalues will be complex and the\neigenstates will not be orthogonal. This non-Hermiticity\nand thus the imaginary parts of the eigenvalues lead to\na non-unitary time evolution in the two-dimensional sub-\nspace spanned by the Bd and the Bd. As a consequence,\nprobability is not conserved in this subspace, which de-\nscribes the fact that both mesons will eventually decay\nand hence disappear from this two-dimensional space.\n\n120\nThe eigenstates of the e\ufb00ective Hamiltonian can be\nrepresented as an admixture of the \ufb02avor eigenstates via\n|P1,2\u27e9= p|P 0\u27e9\u00b1 q|P 0\u27e9,\n(10.1.2)\nwhere |q|2 + |p|2 = 1 to normalize the wave function, and\nq\np =\ns\nM \u2217\n12 \u2212i\n2\u0393 \u2217\n12\nM12 \u2212i\n2\u039312\n,\n(10.1.3)\nand the corresponding eigenvalues read\nm1 \u2212i\n2\u03931 = M11 \u2212i\n2\u039311 + p\nq\n\u0012\nM12 \u2212i\n2\u039312\n\u0013\n(10.1.4)\nm2 \u2212i\n2\u03932 = M11 \u2212i\n2\u039311 \u2212p\nq\n\u0012\nM12 \u2212i\n2\u039312\n\u0013\n(10.1.5)\nwhere m1,2 are the masses and \u03931,2 are the widths of\nthe two e\ufb00ective Hamiltonian eigenstates. These states are\ngraphically depicted for various neutral meson systems in\nFig. 10.1.2, illustrating their mass and width di\ufb00erences.\nThese two parameters determine the time evolution of a\nneutral meson that oscillates between the particle and the\nanti-particle state, as explained in more detail below.\nAssuming m2 > m1 we de\ufb01ne \u2206m = m2 \u2212m1 > 0 and\n\u2206\u0393 = \u03932 \u2212\u03931, and then write the time evolved state that\nhad been a |P 0\u27e9at t = 0 as\n|P 0(t)\u27e9= g+(t)|P 0\u27e9+ q\npg\u2212(t)|P 0\u27e9\n(10.1.6)\nwith\ng\u00b1(t) = e\u2212im1te\u22121\n2 \u03931t 1\n2\nh\n1 \u00b1 e\u2212i\u2206m te\n1\n2 \u2206\u0393 ti\n.\n(10.1.7)\nFrom these relations we can compute the time-dependent\ndecay rates for both P 0 and P 0. If |fCP \u27e9is a common \ufb01nal\nstate for both P 0 and P 0, we denote the corresponding\ndecay amplitudes as\nAf = \u27e8f|H\u2206F =1|P 0\u27e9\n(10.1.8)\nAf = \u27e8f|H\u2206F =1|P 0\u27e9\n(10.1.9)\nwhere H\u2206F =1 is the Hamiltonian for transitions involving\na \ufb02avor change of one unit. De\ufb01ning\n\u03bb = q\np\nAf\nAf\n(10.1.10)\nand \u2014 following the textbook (Bigi and Sanda, 2000) \u2014\nthe auxiliary variables K\u00b1(t) and L(t)\nK\u00b1(t) = 4 e\u03931 t|g\u00b1(t)|2\n(10.1.11)\n= 1 + e\u2206\u0393 t \u00b1 2e\n1\n2 \u2206\u0393 t cos(\u2206m t)\nL(t) = 4 e\u03931 tg\u2217\n\u2212(t)g+(t)\n(10.1.12)\n= 1 \u2212e\u2206\u0393 t \u22122i e\n1\n2 \u2206\u0393 t sin(\u2206m t)\none arrives at\n\u0393(P 0(t) \u2192f) \u221d|\u27e8f|H\u2206F =1|P 0(t)\u27e9|2\n(10.1.13)\n= e\u2212\u03931 t|Af|2\n\u0014\nK+(t) + |\u03bb|2K\u2212(t) + 2Re\n\u001a\n\u03bbL\u2217(t)\n\u001b\u0015\n\u0393(P 0(t) \u2192f) \u221d|\u27e8f|H\u2206F =1|P 0(t)\u27e9|2\n(10.1.14)\n= e\u2212\u03931 t|Af|2\n\u0014\nK+(t) +\n1\n|\u03bb|2 K\u2212(t) + 2Re\n\u001a 1\n\u03bbL\u2217(t)\n\u001b\u0015\n.\nThese expressions \u2014 as well as the resulting CP asym-\nmetries \u2014 simplify considerably in the cases where some\nof the parameters are small. For comparison we list the\nvalues for the relevant parameters for the various neutral\nmeson systems in Table 10.1.1 The width di\ufb00erence \u2206\u0393\nin the kaon system is large compared to the average decay\nwidth \u0393 (= (\u03931 + \u03932)/2 = 1/\u03c4) and the mass di\ufb00erence\n\u2206m; hence, the above expressions are typically expanded\nin a di\ufb00erent way. In the system of neutral D mesons, both\nthe oscillation frequency \u2206m and the width di\ufb00erence \u2206\u0393\nare very small compared to the average decay width \u0393.\nThe resulting expressions are given in Section 19.2.\nFurthermore, for kaons and D mesons, the expressions\nfor M12 and \u039312 are dominated by long-distance contri-\nbutions. This makes the theoretical estimates of \u2206m and\n\u2206\u0393 in these systems di\ufb03cult to compute.\nThe situation is simpler for B mesons. The matrix el-\nement \u039312 is strongly CKM suppressed, and thus \u2206\u0393 is\nsmall compared to \u2206m, and can be set to zero. Further-\nmore, \u2206m is dominated by the short-distance top quark\ncontribution. We relate \u2206m and \u2206\u0393 to M12 and \u039312 using\nEqs (10.1.4) and (10.1.5)\n\u2206m2\nd,s \u2212(\u2206\u0393d,s/2)2 = 4\n\u0002\n|M12|2 \u2212|\u039312/2|2\u0003\n\u2206md,s\u2206\u0393d,s = 4Re(M12\u0393 \u2217\n12) .\n(10.1.15)\nNeglecting |\u039312| in the above expressions and explicitly\ncalculating the box diagram amplitude for Bd leads to\n\u2206md \u22432|M12|\n(10.1.16)\n= 2 G2\nF M 2\nW\n16\u03c02mBd\nS0|VtdV \u2217\ntb|\u03b7B\u27e8Bd|(\u00afbd)(\u00afbd)|Bd\u27e9\n(10.1.17)\nwhere S0 is a function of m2\nt/M 2\nW whose leading term\nbehaves as m2\nt/M 2\nW , re\ufb02ecting the Glashow-Iliopoulos-\nMaiani (GIM) mechanism (Buras and Fleischer, 1998; In-\nami and Lim, 1981), \u03b7B are the perturbative QCD cor-\nrections known to next to leading order (NLO) precision,\nand (\u00afbd)(\u00afbd) is a local (V \u2212A) \u00d7 (V \u2212A) operator with\n\u2206B = 2.\nFor the small width di\ufb00erence \u2206\u0393d, it follows from\nEqs (10.1.15) that\n\u2206\u0393d \u22432|M12| Re\n\u0012 \u039312\nM12\n\u0013\n.\n(10.1.18)\nRecall that \u2206md was de\ufb01ned to be positive; the sign of\n\u2206\u0393d must be determined by experiment.\n\n121\nK0 - K0\nE A10-12 MeV]\n-4\n-2\n2\n4\n0.2\n0.4\n0.6\n0.8\n1.0\n( )\nPIX 0(t) X 0)\nt/\u03c4\nK0 - K0\n0\n1\n2\n3\n4\n5\n0.2\n0.4\n0.6\n0.8\n1.0\nD0 - D0\nE A10-9 MeV]\n-4\n-2\n2\n4\n0.2\n0.4\n0.6\n0.8\n1.0\n( )\nPIX 0(t) X 0)\nt/\u03c4\nD0 - D0\n0\n1\n2\n3\n4\n5\n10-10\n10-7\n10-4\n0.1\nBd0 - Bd0\nE A10-10 MeV]\n-4\n-2\n2\n4\n0.2\n0.4\n0.6\n0.8\n1.0\n( )\nPIX 0(t) X 0)\nt/\u03c4\nBd0 - Bd0\n0\n1\n2\n3\n4\n5\n0.2\n0.4\n0.6\n0.8\n1.0\nBs0 - Bs0\nE A10-9 MeV]\n-10\n-5\n0\n5\n10\n0.2\n0.4\n0.6\n0.8\n1.0\n( )\nPIX 0(t) X 0)\nBs0 - Bs0\nt/\u03c4\n0\n1\n2\n3\n4\n5\n0.2\n0.4\n0.6\n0.8\n1.0\nFigure 10.1.2. Left: Illustration of mass and width di\ufb00erences of the eigenstates (one denoted by full (red) line and the other\nby dashed (blue) line) for various neutral meson systems. Right: Probabilities for an initially produced neutral meson to be\nfound after the time t in a particle (full (blue) line) or an anti-particle state (dashed (red) line).\n\n122\nTable 10.1.1. Values of the mixing parameters for the di\ufb00erent neutral mesons. All numbers are approximate to illustrate the\nrelative sizes.\nMeson\nM/MeV\n\u2206m/MeV\n\u0393/MeV\n\u2206\u0393/MeV\nK0\n497.6\n3.48 \u00d7 10\u221212\n3.68 \u00d7 10\u221212\n7.34 \u00d7 10\u221212\nD0\n1864.9\n9.45 \u00d7 10\u221212\n1.6 \u00d7 10\u22129\n2.57 \u00d7 10\u221211\nBd\n5279.6\n3.34 \u00d7 10\u221210\n4.43 \u00d7 10\u221210\n\u223c0\nBs\n5366.8\n1.16 \u00d7 10\u22128\n4.39 \u00d7 10\u221210\n6.58 \u00d7 10\u221211\nWith the same assumption |\u039312| \u226a|M12|, it also fol-\nlows from Eq. (10.1.3) that\n\u0012q\np\n\u0013\nd\n= e\u2212i\u03c6M12,\n(10.1.19)\nwhere \u03c6M12 is the complex phase of M12.\n10.2 Time-dependent evolution\nNeutral Bd mesons (from now on referred to as B0 mesons)\nare produced via e+e\u2212\u2192\u03a5(4S) \u2192B0B0 transitions at\nBABAR and Belle. The wave function for the \ufb01nal state\nB meson pair is prepared in an anti-symmetric coherent\nP-wave (L = 1) state \u03a8, where\n\u03a8 =\n1\n\u221a\n2\n\u0000|B0\u27e9|B0\u27e9\u2212|B0\u27e9|B0\u27e9\n\u0001\n.\n(10.2.1)\nThe Bd mesons remain in this coherent state, where there\nis always exactly one B0 and one B0, until one of them\ndecays. When the \ufb01rst B meson decays, the wave func-\ntion collapses and the remaining un-decayed B meson will\ncontinue to propagate through space-time and oscillate be-\ntween a B0 and B0 state, with a characteristic frequency\n\u2206md, until it also decays. This assumes that the BB pair\nis successfully described by quantum mechanics, despite\nthe macroscopic extent of the state; aspects of this as-\nsumption can be tested at the B Factories, as discussed\nin Section 17.5.3.\nIf one of the B mesons decays into a \ufb01nal state that can\nbe used to unambiguously determine the \ufb02avor of the B\nat the time it decayed, we refer to that as a Btag. The set\nof decay modes of interest as a Btag candidate are referred\nto as \ufb02avor-speci\ufb01c \ufb01nal states. An example of a \ufb02avor-\nspeci\ufb01c decay is B0 \u2192D(\u2217)\u2212\u2113+\u03bd\u2113, where \u2113= e, \u00b5. The\nCP-conjugate process has a \u2113\u2212in the \ufb01nal state, so the\ncharge of the \ufb01nal-state lepton is used to identify the \ufb02avor\nof the Btag with a B0 (B0) tag originating from a decay\nwith a \u2113+ (\u2113\u2212). Similarly, if the other B decays into a CP-\neigenstate or admixture thereof, we refer to that as the\nBCP . Events with one Btag and one BCP are of interest in\nthe study of time-dependent CP violation. This sequence\nis illustrated in Fig. 10.2.1 as seen from the laboratory\nframe of reference: in this frame, the center-of-mass frame\nis boosted forward in the direction of the electron (high\nenergy) beam. The B mesons are created almost at rest\nin the center-of-mass frame.\nHaving identi\ufb01ed the \ufb02avor of Btag, one can infer the\n\ufb02avor of BCP at the instant the \ufb01rst B meson decays, and\nthe correlated wave function collapses, using the time evo-\nlution of the B0B0 system. The detailed study of this sys-\ntem leads to the measurement of so-called time-dependent\nasymmetries.\nThe decay times of BCP and Btag in the center-of-mass\nframe of reference can be labeled as t1 and t2, respectively,\nand the time evolution of the B0B0 system is a function\nof t1 + t2 and t1 \u2212t2 in general. Assuming a negligible\ndi\ufb00erence between the decay rates of the mass eigenstates\n(i.e. \u2206\u0393d = 0), the BCP decay rate distribution for BCP\ndecaying into a CP eigenstate for a B0 (B0) tagged event is\ngiven by f+ (f\u2212), following from g\u00b1 de\ufb01ned in Eq. (10.1.7)\nf\u00b1(\u2206t) = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\"\n1 \u00b1\n2Im\u03bb\n1 + |\u03bb|2 sin(\u2206md\u2206t)\n\u22131 \u2212|\u03bb|2\n1 + |\u03bb|2 cos(\u2206md\u2206t)\n#\n,\n(10.2.2)\nwhere \u03c4B0 \u22611/\u0393d is the B0 meson lifetime and \u03bb is given\nin Eq. (10.1.10). The sign of sine and cosine terms indi-\ncated in Eq. (10.2.2) is for a CP odd \ufb01nal state such as\nJ/\u03c8K0\nS. CP even \ufb01nal states, such as \u03c0+\u03c0\u2212have the oppo-\nsite sign conventions for the sinusoidal terms. The proper\ntime di\ufb00erence t1 \u2212t2 between the decay times of the two\nB mesons is denoted by \u2206t (see Section 6.5), and terms\ninvolving t1 + t2 drop out. One can compute the time de-\npendence of neutral mesons decaying into \ufb02avor-speci\ufb01c\n\ufb01nal states (so called B\ufb02av events), where \u03bb = 0. These\nevents are used to provide an experimental cross check of\nthe time-dependent measurement and input parameters\nrequired to perform time-dependent \ufb01ts to data (see Sec-\ntion 10.6). Analysis of such decays enables one to measure\n\u2206md, where the time dependence becomes\nh\u00b1(\u2206t) = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n[1 \u2213cos(\u2206md\u2206t)] . (10.2.3)\nIt has been pointed out that, while the assumption \u2206\u0393d =\n0 is valid at the B Factories, improved constraints on this\nwill be required at future experiments in order to verify\nif one can continue to use this approximation (Bevan, In-\nguglia, and Meadows, 2011).\nThe coe\ufb03cients of the sine and cosine terms in equa-\ntion (10.2.2) are often referred to in terms of the param-\neters S and C by the BABAR experiment and in terms of\n\n123\n t\n\u2206\n \u03b3 \u03b2 \u2248\n z \n\u2206\n(4S)\n\u03d2\n+\ne\n_e\ntag\nB\nCP\nB\n\u03c8\nJ/\n0\nS\nK\nFigure 10.2.1. An illustration (not to scale) of a B meson pair decaying in the laboratory frame of reference. On the left hand\nside of the \ufb01gure, the initial e+e\u2212pair collides producing an \u03a5(4S). This subsequently decays into two B mesons described\nby the wave function given in Eq. (10.2.1), one decaying into a Btag \ufb01nal state and the other into a BCP \ufb01nal state. Once the\n\ufb01rst B meson decays, the remaining one oscillates with the characteristic frequency \u2206md before \ufb01nally decaying. The spatial\ndistance \u2206z between the decay vertices of the Btag and BCP as measured in the laboratory frame of reference is related to the\nproper time di\ufb00erence \u2206t between the decays of these particles in the center-of-mass frame of reference (see Section 6.5). In\nthis example the BCP \ufb01nal state is J/\u03c8K0\nS.\nS and \u2212A by Belle, where\nS = 2 Im\u03bb\n1 + |\u03bb|2 ,\n(10.2.4)\nC = \u2212A = 1 \u2212|\u03bb|2\n1 + |\u03bb|2 .\n(10.2.5)\nNote that S and C are related through\n\u0010 S\nsin \u03b8\n\u00112\n+\n\u0000C\n\u00012 = 1 ,\n(10.2.6)\nwhere \u03b8 is the phase of \u03bb.39 For brevity, we use the nota-\ntion S and C to refer to these coe\ufb03cients in the remainder\nof this book.\nAn asymmetry between f+(\u2206t) and f\u2212(\u2206t) is con-\nstructed in order visualize possible CP violation. If we\nneglect experimental e\ufb00ects for the moment, this time-\ndependent decay-rate asymmetry is given by\nA(\u2206t) = f+(\u2206t) \u2212f\u2212(\u2206t)\nf+(\u2206t) + f\u2212(\u2206t),\n(10.2.7)\nwhich reduces to the form\nA(\u2206t) = S sin(\u2206md\u2206t) \u2212C cos(\u2206md\u2206t).\n(10.2.8)\n39 Often the relation between parameters S and C is written\nin a form of inequality S2 + C2 \u22641.\nIn certain modes, the \ufb01tted parameters S and C are\nrelated to fundamental parameters of the SM, the angles\nof the Unitarity Triangle. As discussed in Chapter 16, two\nnotations are used in the literature for these angles. The\nBABAR experiment uses \u03b2, \u03b1, and \u03b3 to denote the angles,\nwhereas the Belle experiment reports results in terms of\n\u03c61, \u03c62, and \u03c63, respectively. In this book, we use the sec-\nond notation for brevity.\n10.3 Use of \ufb02avor tagging\nThe purpose of \ufb02avor tagging is to classify the Btag either\nas a B0 or as a B0 (see Chapter 8). The performance of the\n\ufb02avor tagging algorithm determines how well the values of\nS and C can be extracted from the data.\nThe BABAR experiment classi\ufb01es events according to\nthe information content used in determining the \ufb02avor\nof the Btag meson. These categories of events are ranked\nin order of decreasing contribution to the total tagging\ne\ufb03ciency Q (see Eq. 8.2.1). Thus, the BABAR classi\ufb01ca-\ntion is e\ufb00ectively one based on the Btag decay mode. The\nBelle experiment\u2019s algorithm uses the same information\nbut, instead of having distinct categories of events, that\nalgorithm computes a continuous variable that assigns a\ndilution factor for a given event.\n\n124\nAs discussed in Section 8.2, the algorithm for assign-\ning a \ufb02avor tag to an event, thus categorizing the tag-side\nB meson as a B0 or as a B0, is not perfect. There is\na \ufb01nite probability to incorrectly tag an event and thus\ndilute measurements that rely on this information. The\nmistag probability is denoted by wB0 (wB0) for a B0 (B0)-\ntagged event. The value of the mistag probability depends\non the Btag \ufb01nal state used, and results in a dilution factor\n\u27e8D\u27e9= 1\u22122\u27e8w\u27e9given by Eq. (8.2.2), where \u27e8w\u27e9is the aver-\nage mistag probability for B0 and B0 events (which is of-\nten just written as w). This dilution factor reduces the am-\nplitude of oscillation from the ideal level (with D = 1 when\nwB0,B0 = 0) by some value D < 1 for a non-zero mistag\nprobability. The time-dependent formalism developed in\nSection 10.2 needs to be modi\ufb01ed to account for the di-\nlution; indeed one should also account for possible di\ufb00er-\nences in mistag probability between B0- and B0-tagged\nevents, denoted by \u2206w = wB0 \u2212wB0. Such a di\ufb00erence\ncould be manifest through asymmetries in particle identi-\n\ufb01cation, as well as the intrinsic di\ufb00erence in cross section\nbetween particles and anti-particles interacting with the\nmatter of the detector. On allowing for dilution e\ufb00ects,\nthe rates of tagged B0 and B0 events are given by\nf Phys\n+\n= (1 \u2212wB0)f+ + wB0f\u2212,\nf Phys\n\u2212\n= (1 \u2212wB0)f\u2212+ wB0f+.\n(10.3.1)\nTaking dilution into account, the time dependence of\nthe physical states given by Eq. (10.3.1) becomes\nf Phys\n\u00b1\n(\u2206t) = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n[ 1 \u2213\u2206w\n(10.3.2)\n\u00b1\u27e8D\u27e9S sin(\u2206md\u2206t)\n\u2213\u27e8D\u27e9C cos(\u2206md\u2206t)].\nThe observed amplitudes of the sine and cosine terms in\nthe time-dependent asymmetry are suppressed by the av-\nerage dilution factor \u27e8D\u27e9for B and B. As \u2206w is small, this\nfactor is sometimes omitted for analyses with a low num-\nber of signal events. The analog of the asymmetry given\nby Eq. (10.2.8) is\nA(\u2206t) = f Phys\n+\n(\u2206t) \u2212f Phys\n\u2212\n(\u2206t)\nf Phys\n+\n(\u2206t) + f Phys\n\u2212\n(\u2206t)\n(10.3.3)\n= \u2212\u2206w + \u27e8D\u27e9[S sin(\u2206md\u2206t)\n\u2212C cos(\u2206md\u2206t)].\n(10.3.4)\nThus, a non-zero mistag probability \u2206w results in a small\no\ufb00set in A(\u2206t) at \u2206t = 0. Figure 10.3.1 shows the distri-\nbution of A(\u2206t) for S = 0.7, C = 0.0, and \u2206w = 0.0. The\namplitude of the sinusoidal oscillation is given by the mag-\nnitude of S in the case of a perfectly tagged asymmetry.\nIn reality, dilution e\ufb00ects reduce the measured amplitude\nrelative to the physical one, as illustrated in the \ufb01gure\nbelow with the case of \u27e8w\u27e9= 0.2.\nThe time dependence of events that one typically uses\nto study mixing (C = 1, S = 0), allowing for mistagged\n t (ps)\n\u2206\n-10\n-5\n0\n5\n10\n t)\n\u2206\nA(\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\nFigure 10.3.1. Distributions of the time-dependent CP asym-\nmetry with S = 0.7, C = 0, and \u2206w = 0 for (solid) perfect tag-\nging, and (dashed) the corresponding distributions after taking\ninto account dilution with \u27e8w\u27e9= 0.2.\nevents, is given by\nhPhys\n\u00b1\n(\u2206t) = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n[1 \u2213\u2206w\n(10.3.5)\n\u00b1\u27e8D\u27e9cos(\u2206md\u2206t)],\nwhere the \u00b1 index refers to mixed (\u2212) and unmixed (+)\nevents. Unmixed events have a B0B0 \ufb01nal state whereas\nmixed events are either B0B0 or B0B0 \ufb01nal states. Given\nthat the distribution is symmetric about \u2206t = 0, the mod-\nulus of this distribution is shown sometimes when illus-\ntrating neutral meson oscillation.\n10.4 Resolution of \u2206t\nA number of factors contribute to the resolution of the\nreconstructed value of \u2206z, and hence to that of the com-\nputed value of \u2206t \u2243\u2206z/\u03b2\u03b3. The experimental resolution\nR(\u03b4t, \u03c3\u2206t), as a function of \u03b4t = \u2206t\u2212\u2206ttrue and the uncer-\ntainty on \u2206t, \u03c3\u2206t, can be accounted for when measuring\ntime-dependent CP asymmetry parameters by convolut-\ning R(\u03b4t, \u03c3\u2206t) with f Phys\n\u00b1\n(\u2206t), giving\nF Phys\n\u00b1\n(\u2206t) =\n\u221e\nZ\n\u2212\u221e\nf Phys\n\u00b1\n(\u2206ttrue)R(\u03b4t, \u03c3\u2206t)d\u2206ttrue,\n= f Phys\n\u00b1\n(\u2206t) \u2297R(\u03b4t, \u03c3\u2206t).\n(10.4.1)\nTherefore, one can replace f Phys\n\u00b1\nwith F Phys\n\u00b1\nin Eqs (10.3.3)\nand (10.3.4) to obtain the corresponding equations that\naccount for both dilution and resolution e\ufb00ects. Factors\ncontributing to the resolution of \u2206t include:\n\u2013 Btag vertex resolution, which is a combination of track-\ning e\ufb00ects and, for a sub-sample of Btag mesons, the\n\ufb01nite lifetime of D mesons;\n\u2013 BCP vertex resolution, which is a superposition of track-\ning e\ufb00ects; and\n\n125\n\u2013 resolution of the measurement of the boost factor \u03b2\u03b3\ndetermined from the energy of the e+ and e\u2212beams.\nIt is important to understand the \u2206t resolution in detail\nas this is of a similar magnitude to the average separation\nbetween the BCP and Btag proper decay times. Thus, this\nresolution has a signi\ufb01cant e\ufb00ect on the extraction of S\nand C from a time-dependent analysis.\nDi\ufb00erent approaches are used to understand resolu-\ntion e\ufb00ects at the B Factories. BABAR adopts a paramet-\nric approach to describe the \u2206t resolution, whereas Belle\ncharacterizes resolution e\ufb00ects according to their physical\nsource. Both approaches work well and provide a good de-\nscription of resolution for use in time-dependent analyses.\nThe nominal BABAR \u2206t resolution function has a triple\nGaussian form, where the mean \u00b5i and width si of the\ntwo central Gaussian components are scaled by \u03c3\u2206t on an\nevent-by-event basis. The three Gaussians are denoted by\nGi, where i = core, tail, and outlier, in order of increasing\nwidth. The resolution function is given by\nRsig(\u03b4t, \u03c3\u2206t) = fcoreGcore (\u03b4t, \u00b5core\u03c3\u2206t, score\u03c3\u2206t) +\nftailGtail (\u03b4t, \u00b5tail\u03c3\u2206t, stail\u03c3\u2206t) +\nfoutlierGoutlier (\u03b4t, \u00b5outlier, soutlier) .\n(10.4.2)\nThe parameters stail, soutlier and \u00b5outlier are set to 3.0, 8.0\nps and 0.0 ps, respectively, and the other parameters are\ndetermined from reference samples of fully reconstructed\nB meson decays as described in Section 10.6. The tail\nwidth was determined from Monte Carlo simulated data,\nand the outlier mean was taken as unbiased, with a width\nvarying from 4 \u221212 ps. The mean of this range was taken\nas the nominal value for soutlier. As the physical tagging\ncategories for BABAR have di\ufb00erent purities and dilutions,\nthe values of \u00b5i and si for the core Gaussian contribution\nto the resolution function depend on the \ufb02avor category\nof an event. This di\ufb00erence is taken into account when\nanalyzing data. For early analyses, each of the BABAR \ufb02a-\nvor tagging categories had a separate value for \u00b5core and\nscore; in later iterations, the distinction was only made\nbetween Lepton and non-Lepton tagging categories. For\nBABAR data, score is typically 1.01 \u00b1 0.04 (1.10 \u00b1 0.02) for\nLepton (non-Lepton) events.\nThe Belle \u2206t resolution function (Tajima, 2004) ac-\ncounts for four di\ufb00erent physical e\ufb00ects\n\u2013 Btag vertex resolution,\n\u2013 BCP vertex resolution,\n\u2013 shift in the Btag vertex position resulting from sec-\nondary tracks from charm meson decays, and\n\u2013 kinematic approximation that the B mesons are at rest\nin the center-of-mass frame.\nThe Btag and BCP vertices are described by (i) a Gaus-\nsian resolution function in the case of multi-track vertices,\nand (ii) a sum of two Gaussians in the case of single-track\nvertices. The widths of these Gaussians are scaled by the\nuncertainty on the reconstructed vertex being described.\nThe resolution function resulting from non-prompt tracks\nassociated with a decay in \ufb02ight of charm mesons is de-\nscribed by the sum of a delta function and exponentials.\nThe kinematic approximation is described by a resolution\nfunction dependent on the polar angle of Btag as recon-\nstructed in the center-of-mass frame of reference. Given\nthat a BCP or B\ufb02av candidate is fully reconstructed, and\ndecays opposite the Btag in the center-of-mass frame of ref-\nerence, whereas the Btag may not be, the polar angle of the\nBtag candidate is determined from the fully reconstructed\nBCP or B\ufb02av decay. The physical time dependence f Phys\n\u00b1\nis convoluted by each of these resolution functions in turn\nin order to obtain the resultant F Phys\n\u00b1\n.\nFigure 10.4.1 shows the f Phys\n\u00b1\nand F Phys\n\u00b1\ndistributions\nfor S = 0.7 and C = 0.0, where both dilution and res-\nolution e\ufb00ects are considered. The distribution f Phys\n\u00b1\nis\nsmeared out considerably as a result of experimental reso-\nlution when computing F Phys\n\u00b1\n. The e\ufb00ect of dilution serves\nto reduce the reconstructed asymmetry between B0- and\nB0-tagged events. This can be seen as a reduction in the\nasymmetry between F+ and F\u2212in comparison with the\ntrue distributions f+ and f\u2212.\n t (ps)\n\u2206\n-10\n-5\n0\n5\n10\nArbitrary scale\n t (ps)\n\u2206\n-10\n-5\n0\n5\n10\nArbitrary scale\nFigure 10.4.1. Distributions of (top) f Phys\n\u00b1\n(\u2206t) with S = 0.7,\nand C = 0.0 for (solid) B0- and (dashed) B0-tagged events for\nperfectly reconstructed decays, and (bottom) the correspond-\ning distributions F Phys\n\u00b1\nafter taking into account typical dilu-\ntion and resolution e\ufb00ects.\n\n126\n10.5 Modeling the \u2206t distribution for\nbackground events\nGenerically, one can categorize three types of background\nthat are encountered in time-dependent analyses at the B\nFactories: (i) continuum events, (ii) B background includ-\ning charm mesons that decay in \ufb02ight, and (iii) other B\nbackground categories. The e\ufb00ect on the time-evolution\nof each of these types of events from the resolution of \u2206t\nneeds to be considered. The following describes the general\napproach adopted for each of these types of background.\n\u2013 The hadronization processes resulting from continuum\ne+e\u2212\u2192qq background, where q = u, d, s, or c, oc-\ncur on a time scale too small to measure. As a result,\nthe time dependence for this type of background is\nassumed to be a prompt distribution modeled using\na \u03b4 function convoluted with the resolution function.\nThe resolution function typically adopted for contin-\nuum background is a simpli\ufb01ed version of Eq. (10.4.2),\nwhere the scale factors stail and soutlier are set to 2.0\nps and 8.0 ps, respectively, and only the core Gaussian\nmean and scale factor are weighted by \u03c3\u2206t. The re-\nmaining parameters of the background resolution func-\ntion are obtained from \ufb01ts to data.\n\u2013 The time evolution of B background events that con-\ntain charm particles is biased as a result of the assump-\ntion that all tracks in the BCP vertex originate from\nthe same point whereas, in reality, the tracks from the\ncharm meson in the event originate from a secondary\nvertex that is displaced from the BCP vertex. This type\nof background can occur in the analysis of charmless\nB decays and, where necessary, the time dependence\nis assumed to be similar to the signal one, except that\nthe lifetime is taken to be di\ufb00erent from \u03c4B0. An e\ufb00ec-\ntive lifetime is extracted from samples of Monte Carlo\nsimulated data and used in place of \u03c4B0 for this type\nof background. Cross checks using control \ufb01ts to data\nvalidate the approximation of using Monte Carlo simu-\nlated data to determine the e\ufb00ective lifetime. A signal\nresolution function is assumed to be valid for this cat-\negory of events.\n\u2013 The time evolution of B background events that do\nnot contain charm particles is assumed to be the same\nas that for signal. Such backgrounds occur in time-\ndependent measurements of charmless B decay pro-\ncesses. While these events will be mis-reconstructed\nas a given hypothesized signal mode, the di\ufb00erences\nobserved between the resolution functions for signal\nMonte Carlo simulated data and B background Monte\nCarlo simulated data are small. Some analyses perform\nsystematic cross checks where the time dependence is\ngiven by a kernel estimation p.d.f. corresponding to the\n\u2206t distribution observed for Monte Carlo simulated\ndata in order to account for any bias. Such a distri-\nbution is formed from the sum of kernels, one for each\nevent in a control sample. In this case Gaussian kernels\nare used with a mean corresponding to the value of \u2206t\nof a given event, and a width given by the RMS of\nthe ensemble of data in the control sample. As such a\nmodel neglects the per-event uncertainty on \u2206t, when\nthis approach is used, a systematic cross check is per-\nformed where the kernel estimation p.d.f. is replaced\nwith a signal-like time dependence.\nBoth B Factories categorize continuum background\nwith a prompt distribution as described above. BABAR\ntreats background from di\ufb00erent types of B decays as in-\ndicated above, whereas Belle assigns an exponentially de-\ncaying distribution convoluted with the resolution func-\ntion as the p.d.f. for B background events. The lifetime\nassumed for the Belle B background p.d.f. is an e\ufb00ective\none determined from Monte Carlo simulated data.\nIt is possible that background events may themselves\nbe CP violating. In such cases, one can account for the\nlevel of CP violation by ensuring that the time depen-\ndence incorporates the asymmetry given in Eq. (10.2.8)\nfor neutral B decays, or the corresponding time-integrated\nasymmetry for charged B decays. This issue is discussed\nin Section 15.3.5.\n10.6 Parameter extraction from data\nIn order to perform a time-dependent analysis, one needs\nto determine the values of w, \u2206w, and the tagging e\ufb03-\nciencies, which are collectively referred to as tagging pa-\nrameters, and the resolution function parameters required\nto evaluate the convolution of f\u00b1(\u2206t) with R(\u03b4t, \u03c3\u2206t). A\nsample of neutral B mesons decaying into \ufb02avor-speci\ufb01c\n\ufb01nal states is used to determine these parameters. Sev-\neral hundred thousand events were in the control sam-\nples used by the B Factories. The set of modes used by\nBABAR for this is B0 \u2192D(\u2217)\u2212(\u03c0+, \u03c1+, a+\n1 ), whereas Belle\nuses B0 \u2192D(\u2217)\u2212\u03c0+, D\u2217\u2212\u03c1+, D\u2217\u2212\u2113+\u03bd as well as the char-\nmonium decays J/\u03c8K0\nS, and J/\u03c8K\u2217(892)0. No \ufb02avor tag\ninformation is used by Belle when extracting the param-\neters using the charmonium decays. BABAR only uses the\nB \u2192D\u2217\u2113\u2212\u03bd sample to perform a cross-check as there\nis a larger background in that mode than the other con-\ntrol sample channels. Collectively, this ensemble of \ufb02avor-\nspeci\ufb01c decay modes is referred to as the B\ufb02av control sam-\nple in the following. In addition to determining tagging\nand resolution function parameters for use in extracting\ninformation on CP asymmetries from neutral B\ufb02av modes,\na set of charged control samples is also used to perform a\nnumber of independent validation checks. One of these val-\nidations is the determination of S for a sample of charged\nB decays. As S is physically related to the B0\u2212B0 mixing\namplitude, the \ufb01tted value for this parameter in a sample\nof charged B decays should be consistent with zero. The\ncharged B control sample is formed using B+ \u2192J/\u03c8K+,\nJ/\u03c8K\u2217(892), \u03c8(2S)K+, \u03c7c1K+, and \u03b7cK+ in the case of\nBABAR, while B+ \u2192J/\u03c8K+ and D0\u03c0+ are used by Belle.\nThe corollary of using a set of control modes is that, for\neach mode used to determine the parameters of interest,\none introduces additional parameters relating to the shape\nof distributions of signal and background events, and the\npurity of each control channel in the signal region. Having\ndetermined the purities for each B\ufb02av mode, one can use\n\n127\nthese events to extract estimates of tagging and resolution\nparameters. This procedure implicitly assumes that there\nis no signi\ufb01cant interference on the tag side of the event\n(see Section 15.3.6), so that the mistag probabilities com-\nputed from the B\ufb02av sample are the same as those on the\nBCP side of the event. While this assumption was valid for\nthe B Factories, the precision of measurements at a super\n\ufb02avor factory may require that one formally accounts for\ntag-side interference in the time dependence of the neutral\nmeson system.\nIn order to determine tagging e\ufb03ciencies, one simply\nneeds to determine the fractions of the B\ufb02av sample recon-\nstructed in each of the physical categories; to determine\nthe mistag probabilities and di\ufb00erences, one needs to ac-\ncount for B0 \u2212B0 mixing in the B\ufb02av control sample.\nThe time evolution of these decays, neglecting resolution\ne\ufb00ects, is given by Eq. (10.3.5). One can account for ex-\nperimental resolution by convoluting h\u00b1 with a resolution\nfunction as described in Section 10.4:\nHPhys\n\u00b1\n(\u2206t) =\n\u221e\nZ\n\u2212\u221e\nhPhys\n\u00b1\n(\u2206ttrue)R(\u03b4t, \u03c3\u2206t)d\u2206ttrue,\n= hPhys\n\u00b1\n(\u2206t) \u2297R(\u03b4t, \u03c3\u2206t).\n(10.6.1)\nTherefore, it is possible to not only extract the tagging pa-\nrameters but also the resolution function parameters from\nthe B\ufb02av sample, where one assumes that the \u2206t resolu-\ntion function is the same for the B\ufb02av and BCP events.\nThere are many more events in the B\ufb02av sample than the\nBCP sample; hence, a more precise determination of the\nresolution function parameters can be obtained using the\nB\ufb02av data. Tagging performance is discussed in Chapter 8,\nand vertex resolution is discussed in Chapter 6.\nGiven the complexity of the situation, the extraction\nof parameters related to the tagging performance and \u2206t\nresolution is done in a two-step process. The \ufb01rst step\ninvolves extracting the purity of each of the B\ufb02av decay\nmodes used. Having done this, one determines the tag-\nging and resolution function parameters from the ensem-\nble of B\ufb02av modes. The result of this process is a set of\nparameters and the corresponding error matrix that can\nbe subsequently used as input parameters for the time-\ndependent analyses described in Chapter 17. In a number\nof cases, the time-dependent asymmetry parameters are\nextracted from a simultaneous \ufb01t to both the BCP and\nB\ufb02av samples so that tagging and resolution parameters\nare transparently propagated into the CP analysis.\n\n128\nChapter 11\nMaximum likelihood \ufb01tting\nEditors:\nWouter Verkerke (BABAR)\n11.1 Formalism of maximum likelihood \ufb01ts\nThe \ufb01nal step in a physics analysis, after appropriate event\nselection and reconstruction steps have been performed, is\nextracting a statement on a physics parameter of interest\nfrom the observed distribution of events in the data. To\nmake such an estimation, a model must be formulated\nthat describes the expected distribution of the observable\nquantities x for a given set of physics parameters of inter-\nest p. Then, given an observed data sample x0 one uses\nthe relation between x and p described by the model to\ninfer a statement on the value p for which the observed\ndata is most likely. A standard technique to make such\nan inference is a maximum likelihood estimator. In this\nsection the basics of this technique are described, start-\ning with a description of probability density function as\na means to model the observed data density, followed by\na brief description of the maximum likelihood formalism\nand a discussion on the structure of typical models used\nfor B-physics data modeling.\n11.1.1 Probability Density Functions\nFor many analyses, the models of observable distributions\nare described with a probability density function (p.d.f.)\nfor the observable quantities x:\nf(x; p).\n(11.1.1)\nSuch a probability density function is positive de\ufb01nite,\nand normalized to unity over the allowed range of the\nobservable x for any value of p, i. e.\n\u2200p :\nZ\nf(x; p)dx \u22611,\n(11.1.2)\nwhere the integral is over the allowed domain of the ob-\nservables x.\nIn addition to the parameter(s) of interest p, realis-\ntic models often incorporate a set of additional \u2018nuisance\nparameters\u2019 q that represent quantities that a\ufb00ect the re-\nlation between p and x that are not a priori known and\nmust be simultaneously inferred from the data. Examples\nof such nuisance parameters are resolution parameters and\n\ufb02avor tagging e\ufb03ciencies (see Section 10 for details). The\nmodel is thus de\ufb01ned as\nf(x; p, q).\n(11.1.3)\n11.1.2 Maximum Likelihood estimation of model\nparameters\nThe basis of parameter inference using a model F and\nobserved data is the likelihood, de\ufb01ned as the probability\ndensity function evaluated at the measured data point x0:\nL(p, q) = f(x0; p, q).\n(11.1.4)\nThe likelihood is then treated as a function of the param-\neters p and q.\nFor measurements consisting of an ensemble of data\npoints the likelihood of the ensemble is simply the product\nof the likelihood of each observation:\nL(p, q) =\nY\ni=0,...,N\nf(xi; p, q),\n(11.1.5)\nwhere xi represent independent and identically distributed\nmeasurements of the observable x. In practice one often\nuses the negative log-likelihood\n\u2212log L(p, q) = \u2212\nX\ni=0,...,N\nlog f(xi; p, q),\n(11.1.6)\ninstead of the likelihood as this is numerically easier to\ncalculate.\nEquation (11.1.5) de\ufb01nes an unbinned likelihood - the\nlikelihood is evaluated at each data point and no binning\nof the data is needed. The (unbinned) maximum likelihood\nestimator bp for a parameter vector p is de\ufb01ned as the value\nof p for which the likelihood is maximal or, equivalently,\nthe negative log-likelihood is minimal.\nFor an analysis with a very large number of observed\nevents and a small number of observables, it can be e\ufb03-\ncient to minimize a binned log-likelihood instead, de\ufb01ned\nas\n\u2212log L(p, q) = \u2212\nX\ni=0...N\nni \u00b7 log f(xi; p, q),\n(11.1.7)\nwhere xi and ni represent the bin center and event count\nof bin i of a histogram with N bins. The computation time\nscales with the number of bins N rather than the num-\nber of events. A binned likelihood is a priori less precise\nthan an unbinned likelihood as the information of the pre-\ncise position of the event in each bin is discarded, but at\nsmall bin sizes this may be a negligible loss of precision.\nIn practice, the prediction f(xi; p, q) in each bin is often\napproximated with the value of the probability density\nfunction at the bin center, where the integral of the p.d.f.\nover the bin volume should be used. This approximation\nhas little impact if the bin size is chosen su\ufb03ciently small,\nbut can otherwise result in biases in sharply falling or ris-\ning distributions, e. g. in the \ufb01tted lifetime of exponential\ndecay distributions.\nThe traditional \u03c72 \ufb01t is related to the binned max-\nimum likelihood (ML) \ufb01t by inserting the additional as-\nsumption that the uncertainty can be interpreted as Gaus-\nsian, however, this assumption is a poor approximation of\nreality for bins with low statistics (roughly n < 10).\n\n129\nThe properties of likelihood estimators are extensively\ndescribed in the literature (Edwards, 1992). In the asymp-\ntotic limit of in\ufb01nite statistics maximum likelihood es-\ntimators (ML estimators) are so-called ideal estimators:\nthey are consistent, meaning that they give the correct\nanswer in the limit of in\ufb01nite statistics, unbiased, mean-\ning that they give the correct answer on average for \ufb01-\nnite statistics, and e\ufb03cient, meaning that the variance of\nthe estimated parameter values is equal to the bound of\nthe expectation value of the variance predicted by the sec-\nond derivative of the log-likelihood. On \ufb01nite samples, ML\nestimators are not ideal, but nevertheless generally well\nbehaved if samples statistics are su\ufb03ciently large. How-\never, some particular care must be exercised when using\nML estimators for problems with very small (signal) event\ncounts: in these cases bias terms appear in the likelihood,\nwhich are generally proportional to 1/Nobs, where Nobs is\nthe number of observed events, and may be non-negligible\ncompared to the statistical uncertainty, which is approxi-\nmately proportional to 1/\u221aNobs.\n11.1.3 Estimating the statistical uncertainty using the\nlikelihood\nThe simplest way to measure the statistical uncertainty\n\u03c3(bp) on the estimate of a single parameter bp is to esti-\nmate the variance V (bp) of that parameter and calculate\nthe uncertainty as the square-root of the variance. The\nML estimator for the variance on bp is given by the second\nderivative of the log-likelihood at p = bp:\n\u03c3(bp)2 = V (bp) =\n\u0012d2 log(L(p))\nd2p\n\u0013\u22121\np=bp\n.\n(11.1.8)\nIn case there are multiple parameters, the variance of the\nensemble of parameters is represented by the covariance\nmatrix de\ufb01ned as\nV (p, p\u2032) = \u27e8pp\u2032\u27e9\u2212\u27e8p\u27e9\u27e8p\u2032\u27e9,\n(11.1.9)\nand can be estimated as\nbV (p, p\u2032) =\n\u0012\u22022 log(L(p, p\u2032)\n\u2202p\u2202p\u2032\n\u0013\u22121\np=bp,p\u2032=bp\u2032\n,\n(11.1.10)\nA multivariate covariance can also be expressed in terms\nof scalar variances and a correlation matrix\nV (p, p\u2032) =\np\nV (p)V (p\u2032) \u00b7 \u03c1(p, p\u2032).\n(11.1.11)\nHere \u03c1(p, p\u2032) expresses the linear correlation between pa-\nrameters p and p\u2032 and has values in the range [\u22121, 1] by\nconstruction.\nAn alternative estimator for the uncertainty on a pa-\nrameter is based on an interval de\ufb01ned by the log-likelihood\nratio\n\u03bb(p) = log L(p)\nL(bp),\n(11.1.12)\nwhere L(p) is the likelihood for a given value p, bp is the\nvalue of p for which the likelihood is maximal and L(bp)\nis therefore the maximum value of the likelihood. An in-\nterval in p de\ufb01ned by a rise in the log-likelihood-ratio of\nhalf a unit from zero corresponds to nominally a 68% con-\n\ufb01dence interval. Intervals de\ufb01ned this way are related to\nclassic frequentist con\ufb01dence intervals \u2014 under the con-\ndition that Wilks\u2019 theorem40 (Wilks, 1938) holds.\nWhen nuisance parameters are present, an interval can\nbe de\ufb01ned for each parameter replacing the likelihood ra-\ntio with the pro\ufb01le likelihood ratio\n\u03bbP (p) = log L(p, bbq(p))\nL(bp, bq) ,\n(11.1.13)\nwhere bp and bq represent again the ML estimates of pa-\nrameters p and q and bbq(p) represents the conditional ML\nestimate of parameters bq for a given value of p.\nFigure 11.1.1. Illustration of the de\ufb01nition of parameter un-\ncertainties in an example log-likelihood ratio (blue solid curve).\nThe variance estimator (HESSE , see Section 11.1.5.2) of Eq.\n(11.1.8) uses the second derivative at bp (here bp = 5) and cor-\nresponds to assuming a parabolic log-likelihood ratio shape\n(red dashed curve) and de\ufb01ning the interval by the intersection\npoints of the parabola with the horizontal line at +0.5 units.\nThe likelihood ratio estimator (MINOS , see Section 11.1.5.2) of\nEq. (11.1.12) de\ufb01nes the interval using the intersection of the\nactual log-likelihood ratio curve with a horizontal line at +0.5\nunits (blue curve, long dashes).\nThe di\ufb00erence between the variance-based uncertainty\nand the likelihood-ratio-based uncertainty is visualized in\nFig. 11.1.1. If the log-likelihood has a perfectly parabolic\nshape, as is expected in the limit of in\ufb01nite statistics (un-\nder certain regularity conditions), both uncertainty esti-\nmates will give the same interval.41 At low statistics di\ufb00er-\nences may occur due to the di\ufb00erent methods of estimating\n40 Wilks\u2019 theorem states that the likelihood ratio \u03bb(p) will be\nasymptotically \u03c72 distributed under certain regularity condi-\ntions as the samples sizes approaches in\ufb01nity.\n41 The 2nd derivative will perfectly predict the value of the\nparameter where the log of the likelihood ratio has increased\nby half a unit from zero in this case.\n\n130\nthe uncertainty. In particular, the pro\ufb01le likelihood-based\nintervals can yield asymmetric intervals around the central\nvalues.\n11.1.4 Hypothesis testing and signi\ufb01cance\nMost measurements of CP-violating parameters are ex-\npressed as interval estimates. Conversely, the result of a\nsearch for a rare signal is usually not expressed as an in-\nterval on a signal (strength) parameter, but rather as a\ntest of the background-only hypothesis.\nThe signi\ufb01cance of the observation is the probability of\nthe background-only hypothesis to result in the observed\nsignal strength, or larger. This probability is known as the\np-value. A p-value threshold of 1.2\u00b710\u22127 \u2013 corresponding to\nthe probability of a 5\u03c3 Gaussian \ufb02uctuation \u2013 is conven-\ntionally taken to reject the background-only hypothesis,\nand to declare the discovery of a new signal.\nTo calculate the p-value one must construct a test\nstatistic as function of the data that distinguishes the\nbackground-only hypothesis (the \u2018null hypothesis\u2019) from\nthe signal-plus-background hypothesis (the \u2018alternate hy-\npothesis\u2019). A common choice is \u03bbP (0) of Eq. (11.1.13),\nwhere p is the signal strength, so that \u03bbP (0) becomes\nthe ratio of the maximum likelihood of the background-\nonly model and the maximum likelihood of the signal-\nplus-background model. A dataset that is perfectly con-\nsistent with the background-only hypothesis will thus have\n\u03bbP (0) = 0, as the numerator and denominator of Eq.\n(11.1.13) are equal, whereas datasets with increasing sig-\nnal strength will result in increasing values of \u03bbP (0). The\np-value is then calculated as the fraction of experiments\nsampled from the background-only hypothesis that result\nin a value \u03bbP (0) that is as large as the observed value or\nlarger:\np =\nZ \u221e\n\u03bbobs\nP\n(0)\nf(\u03bbP (0)|p = 0)d\u03bbP (0),\n(11.1.14)\nwhere \u03bbobs\nP (0) is the value of \u03bbP (0) observed in the data,\nand f(\u03bbP (0)|p = 0) is the expected distribution of \u03bbP (0)\nvalues for the background-only hypothesis.\nCustomarily the signi\ufb01cance is re-expressed as a Gaus-\nsian \ufb02uctuation of Z\u03c3 that results in the same p-value,\nwhere Z is de\ufb01ned as\np =\nZ Z\u03c3\n\u2212\u221e\n1\n\u221a\n2\u03c0\u03c3 e\u2212x2/(2\u03c32)dx,\n(11.1.15)\nand can be calculated from p using the inverse of the error\nfunction.42\nIn the asymptotic regime of large statistics, and under\ncertain regularity conditions (Wilks\u2019 theorem), f(\u03bbP (0)|0)\nbecomes a log(\u03c72) distribution with one degree of freedom\nfor each parameter-of-interest. The signi\ufb01cance expressed\n42 In Root this calculation is easily accessible as function\nRooStats::PValueToSignificance(double pvalue)\nin Gaussian standard deviations can in that case be di-\nrectly related to the value of \u03bbobs\nP (0):\n\u03bbobs\nP (0) = 1\n2Z2.\n(11.1.16)\nFinally, for the speci\ufb01c and simple case of a likelihood\ndescribing a counting experiment with an expected sig-\nnal count s and background count b, both with Gaussian\nuncertainties, the value of Z can be directly expressed as\nZsb =\ns\n\u221a\ns + b,\n(11.1.17)\nbut it should be noted that the assumption of Gaussian\nuncertainties for s < 10 or b < 10 is poor.\n11.1.5 Computational aspects of maximum likelihood\nestimates\nFor all but a handful of textbook examples, the expres-\nsion for maximum likelihood estimator for bp cannot be\nexpressed analytically, hence the maximum likelihood es-\ntimate is computed numerically. The computational prob-\nlem factorizes into two pieces: de\ufb01nition of the likelihood\nfunction for a given problem, and heuristic searches for\nthe maximum of the likelihood function.\n11.1.5.1 Likelihood de\ufb01nition\nThe de\ufb01nition of the likelihood involves coding the de\ufb01-\nnition of the probability density function that is used to\nmodel the data, and then evaluating the natural log of\nthis p.d.f. for each observed data point.\nThe Root framework (Brun and Rademakers, 1997)\nimplements de\ufb01nitions of basic functional shapes such as\npolynomials and Gaussian distributions, but the complex-\nity of models used in typical B Factory analyses is such\nthat they cannot be expressed in terms of this limited\nset of basic functions. For the \ufb01rst round of B Factory\nmeasurements custom software packages were developed\nthat implemented the probability density functions rep-\nresenting the physics models as Fortran, LISP, or C++\nfunctions.\nIn the next iteration, the RooFit toolkit (Verkerke and\nKirkby, 2003) was developed by the BABAR collaboration\nthat allowed one to build probability density functions\nof arbitrary complexity inside the Root framework with a\nminimum amount of custom code. To this end, RooFit de-\n\ufb01nes generic software objects that represent observables,\nprobability density functions de\ufb01ning basic shapes as well\nas B-physics speci\ufb01c shapes, and operator objects that\nallow a user to combine basic shapes through addition,\nmultiplication and convolution. Over time a large number\nof analyses have migrated to using RooFit to encode their\nlikelihood functions. The package has been available in the\nRoot framework since 2005. Such models were either coded\n\u2018by hand\u2019, or for certain complicated models constructed\nby higher level packages that automate building of RooFit\np.d.f.s with a certain structure from an con\ufb01guration \ufb01le.\n\n131\n11.1.5.2 Likelihood minimization\nThe standard tool used by the HEP community for nearly\nforty years for minimization and uncertainty estimation\nis the Minuit package (James and Roos, 1975), originally\nwritten in Fortran. A version translated in C++ is now\navailable in the Root analysis framework, as well as a\nnew version, Minuit2, that was written from scratch in\nC++ by the original authors. The main components of\nthe Minuit package are three algorithms that operate on\nan user-de\ufb01ned (likelihood) function: MIGRAD , HESSE , and\nMINOS .\nMIGRAD is a heuristic algorithm that searches for min-\nima in externally provided multi-variate functions and\nfollows mostly a strategy based on a steepest descent\nalgorithm following a numerically calculated gradient of\nthe input function. Convergence is declared when the in-\nput function is within a preset estimated distance from\nthe function value in the nearest minimum assuming a\nquadratic form. The algorithm has been demonstrated to\nwork well on problems with a very large number of dimen-\nsions (> 100), but computational cost increases with the\ndimensionality.43 An inherent di\ufb03culty with a heuristic\nsearch algorithm is distinguishing between local minima\nand the global minimum. In most cases, the algorithm\nwill settle on the \ufb01rst minimum it \ufb01nds along its search\ntrajectory, even if this is not the true global minimum.\nThe odds of \ufb01nding the true global minimum increase if\nthe search is started at a point close to where it is ex-\npected to be, putting a premium on an educated guess by\nthe analyzer for the starting values of the algorithm. It is\nalmost impossible to prevent the \ufb01nding of local minima.\nHESSE calculates the covariance matrix by sampling\nthe likelihood in small steps around the minimum found by\nMIGRAD and calculating the second derivative from these\nsamples. Its output is the covariance matrix as de\ufb01ned in\nEq. (11.1.10). The calculation takes 1\n2N 2 likelihood sam-\nplings, where N is the number of parameters allowed to\nvary, which for large N may exceed the calculation spent\nin MIGRAD minimization.\nMINOS performs the calculation of the uncertainty in-\nterval de\ufb01ned by an increase in the negative log-likelihood\nof half a unit44 with respect to the assumed global min-\nimum. When a MINOS error calculation is requested for\nall N parameters of a \ufb01t, a N \u22121 dimensional hypersur-\nface is \ufb01rst reconstructed that is de\ufb01ned by \u03bb(p) = 0.5.\nThe N-dimensional hyper-cube that encloses this hyper-\nsurface de\ufb01nes the MINOS uncertainty on each parameter.\nThrough geometrical arguments it can be shown that the\nuncertainty de\ufb01ned this way is identical to that of Eq.\n43 The cost of numeric derivative calculations increases lin-\nearly with the number of parameters. The number of descent\nsteps required to \ufb01nd the minimum typically increases also\nwith the number of parameters, but is strongly dependent on\nthe shape of the likelihood.\n44 The default MINOS value of the increase is 1 unit, as built-in\nRoot \ufb01tting functions pass two times the value of the negative\nlog-likelihood. Conversely, Minuit instances owned by RooFit\nrecon\ufb01gure the MINOS error de\ufb01nition to half a unit.\n(11.1.13) for each parameter. MINOS calculations can be\nprohibitively time consuming for a large number of pa-\nrameters (roughly N > 30), but it is also possible to per-\nform a MINOS calculation on any subset of the parameters.\nIn such cases MINOS uses Eq. (11.1.13) to reduce the pa-\nrameter space to the desired subset.\n11.2 Structure of models for signal yield\nmeasurements and rare decay searches\nThe probability density functions used as models in B Fac-\ntory analyses serve two main goals: analysis of the data\nin terms of a signal and a background component, and\nif needed inference of the physics parameters of interest.\nThis section covers techniques used to describe the data\nin terms of signal and background.\nThe simplest model M to extract a signal yield from\nthe data in the presence of background is a model that\ndescribes the data sample as a sum of a signal and back-\nground components.\nm(x; p, q) = f \u00b7 s(x; p) + (1 \u2212f) \u00b7 b(x; q).\n(11.2.1)\nIn this equation, s(x; p) is the model of a signal distribu-\ntion in the observables x, b(x; q) is a model of the back-\nground distribution, and f is the fraction of signal in the\ndata.\nFigure 11.2.1. A simple composite probability density model\n(solid line) consisting of a background component de\ufb01ned by an\nArgus function (dashed line) plus a signal component de\ufb01ned\nby a Gaussian function.\nFigure 11.2.1 shows an example of a simple version of\nsuch a model where the signal is described by a Gaus-\nsian distribution of the energy-substituted mass mES and\nthe background by an Argus function (Albrecht et al.,\n1990a) that models the kinematics of continuum back-\nground events for this observable. See Section 9 for more\ndetails on p.d.f. choices to describe signal and background.\n\n132\nWith su\ufb03cient statistics, the shape parameters p and\nq of both signal and background can be constrained from\nthe data, in addition to the parameter of interest f: the\nfraction of signal events in the data. The estimate of the\nnumber of signal events in data is then f times the total\nnumber of observed events.\nIn the model of Eq. (11.2.1) the p.d.f. only models the\nshape of the distribution of the observed events and not\nits count, hence the parameter of interest can only be a\nfraction, and not a yield. As one is usually interested in\nthe latter in the context of a measurement, the likelihood\nformalism can be extended to also include the event count\nof the sample so that a yield can be obtained straight from\nthe \ufb01t.\n11.2.1 Extended ML formalism\nIn\nthe\nextended\nmaximum\nlikelihood\nformalism\n(EML) (Barlow, 1990) the normalization of the model is\nnot \ufb01xed to one, but to a parameter Nexp, so that the\nlikelihood expression e\ufb00ectively becomes\nL(p, q) =\n \nY\ni=0...Nobs\nf(xi; p, q)\n!\n\u00b7Poisson(Nobs|Nexp(p, q)),\n(11.2.2)\nwhere Nobs is the observed event count, modeled by a Pois-\nson distribution with the expected event count Nexp(p, q)\nas mean. The likelihood of a composite model with a signal\nand background term can then be rewritten in the EML\nformalism taking\nm(x; p, q) =\nNS\nNS + NB\n\u00b7 s(x; p) +\nNB\nNS + NB\n\u00b7 b(x; q),\n(11.2.3)\nas the probability density function and\nNexp = NS + NB,\n(11.2.4)\nas the expression for the expected event count. A mini-\nmization of the extended likelihood will now directly re-\nturn the estimates for the signal and background event\nyields NS and NB.\nOften, we may assume that the shapes of the compo-\nnent distributions and the numbers of events are uncor-\nrelated. That is, NS etc are not dependent on p and q.\nIn this case the extended likelihood information does not\nimprove the precision of the measurement of NS and NB,\nas the \ufb01t can always tune Nexp to match Nobs exactly for\nevery possible value of p, q and f \u2261NS/(NS + NB).\nThe extended ML formalism in this form is thus mostly\nused for notational convenience in B Factory analyses,\nallowing one to directly extract signal event yields from\nthe \ufb01ts, and to write sums of more than two components\nin a straightforward form with yield parameters for every\ncomponent\nm(x; ...) = NS \u00b7 s(x; p) +\nX\ni\nN i\nBbi(x; qi),\n(11.2.5)\nwhere the index i runs over all background components\nand bi denotes the model for background component i,\nwith parameters qi.\n11.2.2 Extending a model to multiple dimensions\nIn searches for rare decays, a single observable often does\nnot contain su\ufb03cient information to distinguish signal from\nbackground and the information of multiple observables\nmust be used. Several strategies can be followed to include\nthe information contained in additional observables. One\nway is to preselect events using cuts in these additional\nobservables in order to obtain a subsample enriched in\nsignal events, and to restrict the signal extraction \ufb01t to\nthe original observable. Another strategy \u2013 one that is of-\nten used for B Factory analyses and which maximizes the\nstatistical precision \u2013 is to extend the signal and back-\nground models to describe the distributions in these addi-\ntional observables, e\ufb00ectively constructing a multidimen-\nsional probability density function that is \ufb01t to the full\nevent sample.\nFor observables that are uncorrelated, a multidimen-\nsional model can be constructed as a simple product of\none-dimensional p.d.f.s, e.g.\nf(x, y, z; p) = f1(x; p1) \u00b7 f2(y; p2) \u00b7 f3(z; p3),\n(11.2.6)\nwhere the f1, f2, f3 represent normalized one-dimensional\nprobability density functions. In case there are expected\ncorrelations between observables, e.g. between x and y,\nthese must be modeled inside a higher-dimensional p.d.f.\nf(x, y). This may be accomplished, for example, through\nthe inclusion of conditional probability density functions\nf(x, y; p) = f1(x|y; p1) \u00b7 f2(y; p2),\n(11.2.7)\nwhere f1(x|y) is the conditional probability density in x\nfor a given value of y, i.e.\n\u2200y, p1 :\nZ\nf1(x|y; p1)dx \u22611,\n(11.2.8)\nwhich describes the distribution of x for each given value\nof y, and f2(y) describes the distribution in y. Advan-\ntages of the formalism with conditional p.d.f.s are that\ncorrelations are often easier to formulate in this way and\nthat all normalization integrals remain one-dimensional.\nThe latter is of particular importance if numeric integra-\ntion is needed, which is substantially more di\ufb03cult in two\nor more dimensions at the level of precision required for\nMinuit minimization. The downside of conditional p.d.f.s\nis that the normalization integral must be calculated for\neach value of y separately, which may be computationally\nexpensive, in case the integration needs to be performed\nnumerically.\nApart from their construction, the use of multi-\ndimensional probability density functions presents no new\ntechnical or conceptual issues in ML estimation, but visu-\nalization and validation of multidimensional p.d.f.s intro-\nduce some additional issues.\nA multi-dimensional model can be most simply visu-\nalized by projecting it on one of its observables:\nPyz(x) =\nZ\nf(x, y, z)dydz.\n(11.2.9)\n\n133\nIn the case of a factorizing model as de\ufb01ned in Eq. (11.2.6)\nthe projection integral simply reduces to f1(x) and is triv-\nial to calculate. If correlations are present, the integral\nmust be explicitly calculated.\nFigure 11.2.2. A two-dimensional probability density func-\ntion consisting of a linear background and a Gaussian signal.\nOn the left the probability density of the model is shown as a\nfunction of x and y. On the right the projection of the model on\nthe observable x is overlaid on the distribution of a simulated\ndata sample.\nA conceptual issue with plain projection plots is that\nthey include the full background and are not suitable to\nvisualize the presence of a small signal in the data that is\nconcentrated in a restricted region of the observable phase\nspace. This is demonstrated in Fig. 11.2.2, which visual-\nizes a two-dimensional model with a linear background\nand a Gaussian signal concentrated in the central region:\nwhile the signal is clearly visible in the central region, it\nis washed out in the projection plot. This can be miti-\ngated by only projecting a \u2018signal region\u2019 de\ufb01ned in the\nprojected observable x\nPySR(x) =\nZ ymax\nSR\nymin\nSR\nF(x, y)dy,\n(11.2.10)\nwhere the interval ymin\nSR\nto ymax\nSR\nrepresents the region in\nthe observable y that is enhanced in the signal.\nLikelihood ratio plots. In the search for rare decays\nmany observables are typically used and the signal may\nnot be con\ufb01ned to an easily de\ufb01nable signal region as was\npossible in the example of Fig. 11.2.2. In these cases, pro-\njections of the data and model on a single observable can\nbe de\ufb01ned using a likelihood ratio, rather than a series of\ncuts on each of the projected observables.\nFor such a plot, the signal and background models are\n\ufb01rst integrated over the plotted observable x to obtain\nthe signal and background probabilities according to these\nmodels using only the information contained in the pro-\njected observables y and then combined in a likelihood\nratio as follows:\nLR(y) =\nR\nS(x, y)dx\nR\n(f \u00b7 S(x, y) + (1 \u2212f)B(x, y)) dx.\n(11.2.11)\nA likelihood ratio projection plot is then constructed by\ntaking all parameters (f in the example above) at their\nestimated values from the data, and by only plotting the\ndata that meet a criterion LR(y) > \u03b1, where \u03b1 is a thresh-\nold in the predicted signal probability (between 0 and 1),\nand projecting the model with corresponding selection\nP LR\ny\n(x) =\nZ\nLR(y)>\u03b1\nF(x, y)dy.\n(11.2.12)\nThe integral over the region de\ufb01ned by LR(y) > \u03b1 is\nclearly not calculable analytically, even if the model itself\nis, but can be approximated with a Monte Carlo integra-\ntion technique as follows\nC(x; p, q) = 1/ND\nX\nDLR(y)\nF(x; y, p, q),\n(11.2.13)\nwhere DLR(y) is a pseudo-experiment dataset with ND\nevents, sampled from the p.d.f. F(x, y) from which all\nevents that fail the requirement LR(y) > \u03b1 have been\nremoved. Figure 11.2.3 shows an example of a likelihood\nratio plot de\ufb01ned using a three-dimensional extension of\nthe model shown in Fig. 11.2.2 projecting over the y and\nz dimensions using a likelihood ratio cut with a value of\n0.7.\nFigure 11.2.3.\nVisualization of a three-dimensional model,\nsimilar to that of Fig. 11.2.2. On the left a contour plot with\nconstant values of likelihood ratio de\ufb01ned by Eq. (11.2.11) of\na model in the observables y and z is shown. On the right the\nprojection of the model on the observable x is shown, requir-\ning LR(y, z) > 0.7 for both data and model to enhance the\nvisibility of the signal.\n11.2.3 sPlots\nA challenge in multi-dimensional models with a large num-\nber of observables is to verify that each component de-\nscribes the data well in all observables. For factorizing\np.d.f.s, Eq. (11.2.6), a new technique named\nsPlot has\nbeen developed at the B Factories (Pivk and Le Diberder,\n2005) to facilitate such studies.\nIn the sPlot technique the distribution in observable\nx is predicted using the distribution in all of the other\nvariables, y, which must be uncorrelated to y, and can be\n\n134\ncompared to the direct model prediction in x. The central\nconcept in sPlot is the de\ufb01nition of the sWeight\nsPn(y) =\nPnc\nj=1 V \u22121\nnj \u00b7 Fj(y)\nPnc\nk=1 Nk \u00b7 Fk(y) ,\n(11.2.14)\nwhere n is the selected component of a model consisting of\nnc components (e.g. signal and one or more backgrounds).\nIn this expression the indices j, k run over the nc model\ncomponents, Fj is the p.d.f. for component j in the ob-\nservables y, Nk is the expected number of events for the\nkth component, and V \u22121\nnj\nis the inverse of the covariance\nmatrix Vnj in these yield parameters. The matrix Vnj is\nobtained from the data, either through a numeric summa-\ntion over the per-event contributions using Eq. (11.1.10),\nor from HESSE following a maximum likelihood \ufb01t to the\ndata. Note that sWeights can be negative, as Vnj is not\npositive de\ufb01nite. The predicted distribution for any com-\nponent j in observable x is given by the histogram of\nevents in x where each event contributes with a weight\nsPn(y).\nAn example is shown in Figure 11.2.4, where for a 3-\ndimensional model in observables mES, \u2206E, F, the p.d.f.\nin mES for signal and background are compared with the\nsPlots in this observable, calculated using sWeights that\nuse exclusively the data and the model prediction in ob-\nservables \u2206E, F. In this example the data was simulated\nand has been sampled from the model itself and perfect\nagreement is observed between the p.d.f. and the\nsPlot\nprediction. When applied on samples of observed data,\ndiscrepancies between the sPlot and the direct model pre-\ndiction may occur, which may be indicative of disagree-\nments between data and model.\n11.3 Structure of models for decay\ntime-dependent measurements\nMuch of the interesting physics of the B-analyses is en-\ncoded in the distribution of the decay-time di\ufb00erence \u2206t\nbetween B0 and B0 mesons, and connected to the phe-\nnomena of B0 \u2212B0 \ufb02avor oscillations (see also Chapter\n10 and Section 6.5). The time scale of \ufb02avor oscillations\nis close to the decay time of B0 mesons and to the exper-\nimental resolution of the B Factory detectors. Thus it is\nimportant to precisely model both the physics e\ufb00ects en-\ncoded in the decay time distribution, as well as the e\ufb00ect\nof the detector resolution on this distribution, of which\nthe e\ufb00ect may vary on an event-by-event basis.\nA priori, the observed inclusive decay-time distribu-\ntion is expected to be modeled by the convolution of the\nphysics distribution, a pure exponential decay law, and a\ndetector resolution function:\nf(\u2206t; \u03c4, q) =\nexp(\u2212|\u2206ttr|/\u03c4) \u2297r(\u2206t \u2212\u2206ttr; q)\nR\nexp(\u2212|\u2206ttr|/\u03c4) \u2297r(\u2206t \u2212\u2206ttr; q)d\u2206t,\n(11.3.1)\nwhere \u2206t is observed decay time di\ufb00erence, \u2206ttr is the true\ndecay time di\ufb00erence, which is the integration variable\nFigure 11.2.4.\nDemonstration of\nsPlot concept using a\nmodel in three observables mES, \u2206E, F with a signal and\nbackground component. The top and bottom plot show the\nestimated signal and background shape in mES, respectively.\nIn either plot the line represents the model prediction in the\nobservable mES, and the histogram is the\nsPlot de\ufb01ned as\nweighted sum over the data using sWeight sPn(y) calculated\nfrom the model prediction using only the observables \u2206E and\nF.\nof the convolution integral, and \u03c4 is the lifetime of B0\nmesons. Fig. 11.3.1 illustrates the shape of the convoluted\np.d.f. of Eq. (11.3.1) and of its components.\nFigure 11.3.1.\nVisualization of exponential decay time dif-\nference distribution before (blue dashed) and after (blue solid)\nconvolution with a Gaussian resolution function (red, long\ndashes).\nThe resolution model of Eq. (11.3.1) is usually empir-\nically described as a sum of Gaussians, describing a \u2018core\u2019\n(C) and a \u2018tail\u2019 (T) resolution, and often includes a very\nwide \u2018outlier\u2019 (O) term to account for the possibility that\n\n135\noutlier events can occur in the data:\nr(\u2206t; \u00b5, \u03c3) =fC \u00b7 Gauss(\u2206t; \u00b5C, \u03c3C)+\n(1 \u2212fC \u2212fO) \u00b7 Gauss(\u2206t; \u00b5T , \u03c3T )+\nfO \u00b7 Gauss(\u2206t; 0, \u03c3O),\n(11.3.2)\nwhere \u00b5C,T and \u03c3C,T,O represent the means and widths\nof the corresponding Gaussian distributions, respectively,\nand fC and fO represent the fraction of events in the core\nand outlier component, respectively. While very few events\nare expected that are not described by the convolution of\nthe physics model with a core and tail Gaussian resolu-\ntion term, it is important to include a wide outlier term\nin the resolution model, as otherwise a single event that\nis \u2018far\u2019 from both core and tail models has the potential\nto contribute disproportionally to the likelihood and can\nstrongly and unduly in\ufb02uence the \ufb01t result, even when\noutliers only contribute at the permille level to the event\nsample. A common pragmatic choice for the outlier term\nis a very broad Gaussian distribution, as shown in the\nexample of Eq. (11.3.2), but other shapes have also been\nused.\nThe resolution model of the previous example describes\nthe average performance of the decay-time reconstruction.\nSince the decay-time di\ufb00erence is calculated from the dis-\ntance between two decay vertices, the resolution in the\ntime di\ufb00erence will depend on the number of tracks used\nin the vertex \ufb01ts as well as their con\ufb01guration, and the ver-\ntex \ufb01t procedure returns an estimate of the uncertainty on\nthe decay-time di\ufb00erence for each event.\nA more precise inference on the physics parameter \u03c4 of\nthe model f can be made by taking into account this per-\nevent uncertainty on the decay time di\ufb00erence \u2013 weighting\nevents with a precise measurement of \u03c3\u2206t more strongly\nthan those with a poorer measurement by modifying the\nresolution model as follows\nr\u2032(\u2206t|\u03c3\u2206t; \u00b5, \u03c3) = Gauss(\u2206t; \u00b5C, S \u00b7 \u03c3\u2206t),\n(11.3.3)\nwhere \u03c3\u2206t is the estimate of the uncertainty on \u2206t for\neach event. In this form the mean and width parameters\nof the resolution model r\u2032 describes an a posteriori shift\n\u00b5C and scaling S of the per-event error \u03c3\u2206t that is needed\nto match the model to the data. If the per-event uncer-\ntainty estimated by the vertex \ufb01t is correct, the mean and\nwidth will be 0 and 1, respectively, and r\u2032 will be a unit\nGaussian. In practice, this is often not the case due to the\ncomplexity of the underlying vertex \ufb01tting procedure and\na more complex p.d.f. is needed to describe the shape of\nthe resolution function. Here one can either take an em-\npirical form for r\u2032, e.g. a sum of two or three Gaussians,\nor try to construct a form that parameterizes the e\ufb00ect of\nthe leading underlying causes explicitly. Various choices\nof resolution models used for time-dependent analyses at\nthe B Factories are described in more detail in Section\n6.5. Inserting r\u2032 in Eq. (11.3.1) results in a conditional\nprobability density function\nf(\u2206t|\u03c3\u2206t; \u03c4, q) =\ne\u2212|\u2206ttr|/\u03c4 \u2297r\u2032(\u2206t \u2212\u2206ttr; \u03c3\u2206t, q)\nR\ne\u2212|\u2206ttr|/\u03c4 \u2297r\u2032(\u2206t \u2212\u2206ttr; \u03c3\u2206t, q)d\u2206t,\n(11.3.4)\nwhere \u2206ttr is again the integration variable of the convo-\nlution integral, and which describes the distribution of \u2206t\nfor a given value of \u03c3\u2206t, but not the distribution of \u03c3\u2206t\nitself. Such a conditional p.d.f. can be \ufb01t directly to the\ndata, or be multiplied with another (empirical) p.d.f. that\ndescribes the distribution of the per-event uncertainty on\n\u2206t:\nF \u2032(\u2206t, \u03c3\u2206t|\u03c4; q) = F(\u2206t|\u03c3\u2206t; \u03c4, q) \u00b7 Gauss(\u03c3\u2206t; q).\n(11.3.5)\nIn realistic models that account for the presence of back-\nground in the data, a separate decay-time distribution is\nde\ufb01ned for signal and background, each multiplied with\none or more probability density functions in other ob-\nservables that primarily serve to distinguish signal from\nbackground events. This approach to model building is\nstraightforward except for one aspect related to condi-\ntional models: The p.d.f. of Eq. (11.3.4) makes no assump-\ntions on the distribution of \u03c3\u2206t in the data, but does as-\nsume that signal and background events have the same\ndistribution, whereas the p.d.f. of Eq. (11.3.5) allows for\ndi\ufb00erent distributions of \u03c3\u2206t for signal and background,\nbut requires an explicit description of both. The most ap-\npropriate form depends on the speci\ufb01cs of the analysis.\nUsing Eq. (11.3.4) in cases where it is not appropriate,\ne.g. when distributions of \u03c3\u2206t for signal and background\nare expected to be di\ufb00erent, is referred to as the \u201cPunzi\nproblem\u201d (Punzi, 2003a) in HEP statistics literature, and\nmay lead to biased \ufb01t results.\nFinally, the physics of interest in the decay time dis-\ntribution is exposed by splitting the event sample in two\nmore categories, e.g. same-\ufb02avor and opposite-\ufb02avor B0\nmeson pairs to expose \ufb02avor oscillations:\nF(\u2206t, f; \u03c4, q) =\n\uf8f1\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f3\n(e\u2212|\u2206ttr|/\u03c4 cos(\u2206m\u2206ttr))\u2297R(...)\nR (e\u2212|\u2206ttr|/\u03c4 cos(\u2206m\u2206ttr))\u2297R(...)d\u2206t : f \u2261\u22121\n(e\u2212|\u2206ttr|/\u03c4 (1\u2212cos(\u2206m\u2206ttr))\u2297R(...)\nR (e\u2212|\u2206ttr|/\u03c4 (1\u2212cos(\u2206m\u2206ttr))\u2297R(...)d\u2206t : f \u2261+1\n(11.3.6)\nde\ufb01ning a two-dimensional p.d.f. in a continuous observ-\nable \u2206t and a discrete observable f that distinguishes\nsame-\ufb02avor from opposite-\ufb02avor events. The techniques il-\nlustrated on inclusive decay time distributions apply trans-\nparently to models modi\ufb01ed in this way.\n11.3.1 Visualization of p.d.f.s of decay time\ndistributions\nModels describing measurements of time-dependent CP-\nviolating decay processes commonly have two or three\ncontinuous observables: the decay time and one or two\nkinematic variables, such as mES or \u2206E, to distinguish\n\n136\nB decays from continuum background. These observables\nare usually uncorrelated and the kinematic variables have\na well-de\ufb01ned \u2018signal\u2019 range that allows one to plot the\ndecay time distribution of these events inside this signal\nrange only, using Eq. (11.2.10).\nIn the case that the p.d.f. contains a conditional ob-\nservable, such as \u03c3\u2206t, a di\ufb00erent technique is required to\nproject the conditional observable, as the p.d.f. does not\ncontain information on the distribution of that observable.\nAn average curve C is constructed from curves represent-\ning the projection over the non-conditional observables\ntaken at the values \u03c3\u2206t found in the data:\nC(\u2206t; p, q) = 1\nn\nX\ni=0,...,n\nZ\ndyF(\u2206t; \u03c3i\n\u2206t, y, p, q).\n(11.3.7)\nFigure 11.3.2.\nDistribution of the conditional decay time\nmodel F(\u2206t|\u03c3\u2206t) of Eq. (11.3.4) with values of \u03c3\u2206t of 0, 2,\n4, 6, 8 ps (red dashed, ordered high to low at \u2206t = 0) and\ndistribution of the data overlayed with the weighted average of\nthe conditional model using the \u03c3\u2206t values of the data sample.\nwhere n is the number of events in the data. Figure 11.3.2\nshows an example of a decay-time distribution: the red\ndashed curves illustrate the shape of the model at various\nvalues of \u03c3\u2206t, and the blue curve represents the weighted\naverage using the \u03c3\u2206t values of the dataset. Note that in\nthe limit of the data \u03c3i\n\u2206t describing the true distribution\nof \u03c3\u2206t Eq. (11.3.7) amounts to the Monte-Carlo integral\n(given by Eq. 11.2.13) over observable \u03c3\u2206t. For computa-\ntional e\ufb03ciency the summation of the data \u03c3i\n\u2206t is some-\ntimes approximated by a summation over a histogram of\nthe data.\n11.4 Techniques used for constraining\nnuisance parameters from control samples\n11.4.1 Simultaneous \ufb01ts to control regions\nAs a general analysis strategy it is preferable to constrain\nthe nuisance parameters q, such as the decay time resolu-\ntion model parameters, as much as possible from the data\nitself, instead of inferring them from simulation studies.\nIn many cases this can be accomplished by simply \ufb02oat-\ning the nuisance parameters in the ML \ufb01t. This will worsen\nthe estimated uncertainty on the physics parameter of in-\nterest, as the values of nuisance parameters are no longer\nassumed to be known exactly, instead their statistical un-\ncertainties, as inferred by the ML \ufb01t from the data, are\npropagated to the uncertainty on the physics parameter\nof interest.\nIn many B-physics analyses additional high-statistics\ncontrol samples exist that can constrain these nuisance\nparameters with greater precision than the signal sam-\nple. For example, for decay-time dependent CP violation\nmeasurements high statistics control samples from the B0\n\ufb02avor tagged samples can be used to measure the nui-\nsance parameters originating from the description of the\n\ufb02avor tagging performance as well as the modeling of the\ndetector decay time resolution.\nThe most straightforward way to incorporate the knowl-\nedge on nuisance parameters \u2013 their uncertainties and\ntheir correlations \u2013 in a measurement is to perform a joint\nlikelihood minimization:\n\u2212log L(p, q, q\u2032) = \u2212log LSIG(p, q) \u2212log LCTL(q, q\u2032),\n(11.4.1)\nwhere LSIG(p, q) is the likelihood for the signal region in\nterms of parameters of interest p and nuisance parameters\nq and LCTL(q, q\u2032) is the likelihood for the control region\nin terms of nuisance parameters q that are shared with the\nsignal region and nuisance parameters q\u2032 that are unique\nto the control region. Equivalently, this construction can\nbe expressed as a joint probability density function\nF(x|i; p, q, q\u2032) =\n\u001a\nFSIG(x; p, q)\nif (i = SIG)\nFCTL(x; q, q\u2032) if (i = CTL)\n(11.4.2)\nthat is conditional on a newly introduced discrete observ-\nable i that has states SIG and CTL, which label the events\nin the signal and control samples respectively.\nA minimization of a joint likelihood ensures that the\nfull information in both samples is taken into account, and\nthe estimated uncertainty of parameters and their corre-\nlations re\ufb02ect the information from both samples, as is\nillustrated in Fig. 11.4.1. The p.d.f.s describing the sig-\nnal and control sample can be very dissimilar in shape\nand structure, the only requirement is that the common\nparameters have the same physics interpretation in both\nmodels.\n11.4.2 Simultaneous \ufb01ts to multiple signal regions\nA mathematically similar, but conceptually di\ufb00erent ap-\nplication of joint \ufb01ts is to perform a joint likelihood \ufb01t\nto multiple signal regions, with similar p.d.f.s. If a signal\nregion can be split into regions with di\ufb00erent expected\nsignal purities, a split into these regions will exploit this\ndi\ufb00erence in purity without the need to provide an explicit\nparameterization of the change in purity over the phase\nspace of the original signal sample.\n\n137\nFigure 11.4.1.\nVisualization of the e\ufb00ect of a simultaneous\n\ufb01t. On the left a \ufb01ctitious low statistics signal sample is shown\n(modeled by a \ufb02at background and a Gaussian signal). The\nmodel uncertainty from the \ufb01t to the signal sample only is\nvisualized with the light orange band. On the right a \ufb01ctitious\nhigh statistics control sample is shown (modeled by a sloped\nbackground and the same Gaussian signal). The uncertainty on\nthe control sample model is visualized with the dark red band.\nThe reduced uncertainty on the signal sample by performing\na joint \ufb01t with the control sample is shown also in dark red in\nthe left plot.\nA prime example of this technique is splitting a signal\nmodel according to the \ufb02avor tagging technique (see also\nChapter 8) that was used to tag a particular event. Dif-\nferent tagging techniques are expected to result in quite\ndi\ufb00erent purities. The original model\nF(x; p, q) = F(x; p, q, wtag)\n(11.4.3)\nis substituted with\nF(x|c; p, q) =\n\uf8f1\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f4\n\uf8f4\n\uf8f3\nFtag1(x; p, q, wtag1)\nif (c = tag1)\nFtag2(x; p, q, wtag2)\nif (c = tag2)\nFtag3(x; p, q, wtag3)\nif (c = tag3)\n...\nFtagn(x; p, q, wtagn) if (c = tagn)\n,\n(11.4.4)\nwhere c is a discrete observable that labels which \ufb02avor\ntagging technique was used (here these are labeled tag1\nthrough tagn, for illustration). The component models\nFtagi(x; p, q, wtagi) are structurally identical to the origi-\nnal F(x; p, q, wtag), and expressed in terms of the same ob-\nservables and parameters, except for the parameter w that\ndescribes the mistag probability, which is now uniquely\nde\ufb01ned by wtagi for each state tagi rather than being a\nglobal parameter w. At the likelihood level, the original\nlikelihood L(p, q, wtag) is now reparameterized for each\nregion as L(p, q, wtag1, wtag2, wtag3, ..., wtagn).\nSince the model of Eq. (11.4.4) is de\ufb01ned conditionally\non the discrete split observable c, the model makes no as-\nsumptions on the distribution of events over the de\ufb01ned\nsubsets, and since each subset is equipped with its own\nnuisance parameter wtagi, also no assumption is made on\nthe variation of the mistag rates over the subsets. The split\nlikelihood is generally expected to improve the statistical\nuncertainty on the parameter of interest: in the above ex-\nample, events with better than average mistag properties\nwill now weigh more strongly in the likelihood than events\nwith less than average mistag properties, when compared\nto the original likelihood de\ufb01nition.\nWhile the signal splitting technique can quickly in-\ncrease the number of parameters allowed to vary in the \ufb01t,\nthe likelihood tends to be uncorrelated between the \u2018split\u2019\nparameters and the minimization stability in Minuit is\nnot as strongly impacted as one might a priori expect. The\ncalculation of the covariance matrix by HESSE will never-\ntheless be more time consuming, as HESSE is not aware\nof this block-diagonal form and will simply calculate all\ncovariance matrix elements.\n11.5 Miscellaneous issues\n11.5.1 Background subtraction and weighted events\nAn alternative approach to extracting signal properties\nfrom a data sample with a known background contribu-\ntion is to subtract the background in the data, using an\nestimate from a sideband region, and then \ufb01tting the back-\nground subtracted data samples with a signal-only model.\nAn advantage of the subtraction approach is that no\nparametric form is needed to describe the distribution of\nthe background. Background subtraction can be applied\nin both binned and unbinned ML estimates. In the latter\ncase, background events are added to the unbinned dataset\nwith negative weights. Another form of background sub-\ntraction is to reweight the data, using the sWeights de-\n\ufb01ned in Eq. (11.2.14), in such a way that the sum of\nweights re\ufb02ects only the signal component. sWeights can\nbe either positive or negative.\nIn all cases of event weighting the distribution of the\nexpected event count in any given region is modi\ufb01ed from\na Poisson distribution to a distribution that re\ufb02ects the\ne\ufb00ect of the subtracted background distribution. In a \u03c72\n\ufb01t, the (squared) uncertainty associated with each bin is\nthe calculated with the sum of the squares of the weights\nof the events in the bin, using the prescription for the\nvariance with weighted events:\n\u03c32 = V =\nN\nX\ni=1\nw2\ni ,\n(11.5.1)\nwhere wi is the weight of the i-th of N events contributing\nto a given bin. For example in a bin containing 20 events\nwith weight +1 and 10 events of weight \u22121, the uncer-\ntainty on the weighted sum of 10 events is estimated as\n\u221a\n30, compared to\n\u221a\n10 for a bin containing 10 events with\nonly positive weights.\nIn the likelihood formalism, the de\ufb01nition of the like-\nlihood of Eq. (11.1.6) can be modi\ufb01ed to include event\nweights\n\u2212log L(p, q) = \u2212\nX\ni=0,...,n\nwi \u00b7 log F(xi; p, q),\n(11.5.2)\nso that the ML estimators for the parameters p, q will take\nthe weights into account. The likelihood of Eq. (11.5.2) is\n\n138\nhowever not directly suitable for variance estimators: un-\nlike a \u03c72 \ufb01t, where the uncertainty associated with each\ndata point can be externally speci\ufb01ed according to Eq.\n(11.5.1), the variance estimator for these parameters will\nnot re\ufb02ect the increased uncertainty and will simply (in-\ncorrectly) assume Poisson uncertainties with \u00b5 = P wi.\nand will thus \u2013 in case of datasets with events that have\nweights less than unity \u2013 underestimate the uncertainty.\nNevertheless it is possible to extract an approximately\ncorrect covariance matrix by combining the ML estimate\nof variance V given by Eq. (11.5.2) with another ML es-\ntimate of the variance (C) for which the weight wi in Eq.\n(11.5.2) was substituted by w2\ni :\nV \u2032 = V \u00b7 C\u22121 \u00b7 V.\n(11.5.3)\nThe estimation of errors using Eqs (11.5.2) and (11.5.3)\nis not restricted to cases where event weights are \u00b11, but\ncan also be more generally applied to event samples with\narbitrary event weights.\n11.5.2 Validation of ML \ufb01ts on complex models\nMaximum likelihood \ufb01ts on complex models can be vali-\ndated by studying their behavior on simulated data that\nare sampled from the model itself. A typical study consists\nof simulating many (of order 1000) data samples accord-\ning to the model under study, and \ufb01tting the model to\neach of these datasets. For every estimated parameter in\nthe \ufb01t, the distribution of its pull, de\ufb01ned as\npull(p) = bp \u2212ptrue\n\u03c3(bp)\n(11.5.4)\ncan be examined. If the estimator bp is free of bias, i.e.\nit will estimate the true value correctly on average, the\nmean of the pull distribution will be consistent with zero.\nIf the estimator b\u03c3(p) represents the uncertainty correctly\nthe variance of the pull distribution will be consistent with\none. A too narrow pull distribution indicates that b\u03c3(p)\noverestimates the uncertainty. Conversely, a too wide pull\ndistribution indicates that b\u03c3(p) underestimates the uncer-\ntainty. Veri\ufb01cation of the absence of bias is of particular\nimportance for estimators of small yields for which ML\nestimators can be rather imperfect. Studies on simulated\ndata can also be used to determine the expected spread\nin (statistical) uncertainties on the physics parameter-of-\ninterest, indicating whether the uncertainty obtained on\nthe measured data was \u2018lucky\u2019 or not. For these studies,\nin particular when studying the aspect of expected statis-\ntical uncertainties, it is important to draw event samples\nfrom a conditional model evaluated at the observed values\nof the conditional observables (such as \u03c3\u2206t in decay time\ndependent \ufb01ts), to get a maximally relevant answer.\nAnother aspect of validation of ML estimates is to\nmeasure the goodness-of-\ufb01t of the model f(x) with re-\nspect to the data x. To do so, a test statistic T(x) must\nbe de\ufb01ned to quantify the agreement between data and\nmodel in some way. A common test statistic for this pur-\npose is Pearson\u2019s \u03c72, which divides the data in bins and\nmeasures the distance between the model prediction and\nthe data in each bin. The goodness-of-\ufb01t is then expressed\nby the p-value of the hypothesis that model f(x) is true,\ncalculating Eq. (11.1.14) using the chosen test statistic. If\nthe p-value is low, one may need to reject the model f as\na valid model.45 The \u03c72 test statistic is popular, despite\nits requirement that the data must be binned, because\nthis test statistic is distribution-free: in the limit of su\ufb03-\ncient event counts in all bins the distribution of \u03c72 values\nis independent of the distribution of the data predicted\nby model f, simplifying the interpretation of \u03c72 values in\nterms of probabilities.\nEstimating the goodness-of-\ufb01t for complex likelihood\nmodels with multiple observables constitutes a more di\ufb03-\ncult problem: due to the large number of empty bins that\narise in binning multi-dimensional observables distribu-\ntions the \u03c72 test statistic is no longer in the distribution-\nfree regime. Various unbinned multidimensional goodness-\nof-\ufb01t tests have been developed over the years (Aslan and\nZech, 2002), but are not as easy to use as the \u03c72 test in\nthe high-statistics regime for various reasons, e.g. because\nthey are not distribution-free either, and have not been\nroutinely used at the B Factories.\nIt should be noted that the unbinned maximum likeli-\nhood itself is not a reliable goodness-of-\ufb01t estimator. One\nreason for this is that this test statistic does not generally\nprovide a sane de\ufb01nition of agreement between data and\nmodel. For example, for a likelihood assuming an exponen-\ntial decay law distribution, the maximum log-likelihood is\nsimply proportional to average lifetime of the events in the\ndata. Thus, all data samples with the same average life-\ntime will result in the same goodness-of-\ufb01t independent of\nthe observed distribution of events. Another problem with\nthe maximum likelihood as goodness-of-\ufb01t test statistic\nis in obtaining the distribution of the test statistic: ML\nestimates are not distribution free, unlike likelihood ra-\ntios, so the expected distribution of ML values under the\nhypothesis that model f is true, must be obtained from\nan ensemble of pseudo-experiments. For models f(\u03b8) with\nparameters \u03b8 this poses a challenge as the true values of\nthe parameters are unknown. Instead, the distribution is\nusually obtained from pseudo-experiments sampled from\nthe model f(b\u03b8) using the ML estimates of the parameters\nb\u03b8. In the example of the decay law distribution, where\nthe maximum likelihood is simply proportional to the es-\ntimated lifetime b\u03c4, the p-value for the hypothesis f(b\u03c4) will\nthen be close to 50% by construction and thus not provide\nmeaningful information on the goodness-of-\ufb01t.\n45 Note that since a goodness-of-\ufb01t test is a hypothesis test in\nwhich the alternate hypothesis is the set of all possible alter-\nnatives to the hypothesis f being tested, one cannot formulate\nthe alternate hypothesis, and thus not quantify the power of\nthe test: the probability that the hypothesis f is false and the\nalternate hypothesis is true. One should therefore not conclude\nfrom a high p-value that the hypothesis f is true.\n\n139\n11.5.3 Computational optimizations of likelihood\ncalculations\nUnbinned maximum likelihood \ufb01ts are computationally\nintensive, and the \ufb01ts underlying many of the B Factory\nresults have taken many hours or even days to complete.\nE\ufb03cient computation of the likelihood is thus important.\nIn this section we discuss a number of the techniques that\nare applied in many of the B Factory likelihood \ufb01ts to op-\ntimize computational e\ufb03ciency. The techniques discussed\nhere are applied automatically in all RooFit-based like-\nlihood implementations and have often been applied by\nhand in custom likelihood implementations.\nConstant term pre-calculation. In many models (partial)\nexpressions occur that do not depend on any \ufb02oating\nmodel parameter. These terms can be identi\ufb01ed and pre-\ncalculated once at the beginning of the \ufb01t.\nCaching and lazy evaluation. Expensive objects such as\nnumeric integrals over functions, may not need to be re-\ncalculated every time their value is needed. By explicitly\ntracking if input variables have changed and caching the\nvalue of the previous outcome of the calculation, unnec-\nessary repeated calculations can be prevented. For simul-\ntaneous \ufb01ts, this strategy is also applied to components\nof the likelihood, so that these are only recalculated if a\nparameter on which the component actually depends is\nchanged.\nAnalytical (partial) integrals. For many functions, analyt-\nical expressions are known for their integrals. By using\nthe analytical forms, expensive numeric integration can\nbe avoided. For multi-dimensional functions, knowledge\nof partial analytical integrals can be used to reduce the\ndimensionality of the numeric integration that is needed.\nThis is particularly e\ufb03cient in cases where the dimension\nof the numeric integral is reduced to one, as numeric in-\ntegrals in one dimension can be calculated much more\ne\ufb03ciently and with accurate convergence estimates than\nmulti-dimensional integrals.\nApproximation of the complex error function. Many time-\ndependent B-physics models that involve convolution with\nGaussian resolution models are expressed in terms of the\ncomplex error function. Standard calculation of the com-\nplex error function can take O(100) complex number mul-\ntiplications to estimate its value. Instead, inside p.d.f.s\ninterpolation in a 2-dimensional lookup table is used to\nspeed up the calculation.\nParallelization of the likelihood calculation. The calcula-\ntion of the likelihood is by its nature very suitable for\nparallelized calculation. The wall-time of execution of ML\n\ufb01ts can be decreased by roughly a factor N by paralleliz-\ning the likelihood calculation over all N available cores on\na multi-core host, or alternatively over multiple hosts.\n\n140\nChapter 12\nAngular analysis\nEditors:\nGeorges Vasseur (BABAR)\nAn angular analysis uses the information coming from\nthe angular distributions of the \ufb01nal state particles. These\ndistributions depend on the spin and polarization of all\nthe particles involved in the decay chain. Consequently\nan angular analysis may determine the spin of a particle\nif unknown, and the polarization of the particles in a given\ndecay chain.\nFurthermore, the angles of the Unitarity Triangle\nhave been determined, in several B-meson decay modes,\nthrough the measurement of time-dependent CP asymme-\ntries in vector-vector \ufb01nal states, such as J/\u03c8K\u2217, D\u2217D\u2217,\nand \u03c1\u03c1, which have both CP-even and CP-odd compo-\nnents. These components need to be disentangled in order\nto extract the value of the CP asymmetry. This can be\nachieved by performing an angular analysis.\nIn this chapter the angular analysis is described. The\nformalism is presented in Section 12.1. An overview of the\nmain modes studied at the B Factories that require an\nangular analysis is given in Section 12.2. Several analysis\ndetails are discussed in Section 12.3. Finally angular \ufb01ts\nare described in Section 12.4.\n12.1 Formalism\n12.1.1 Spin and helicity\nThe spin is a quantum number characterizing a particle.\nIt is a positive half-integer for particles called fermions\n(for example, electrons, muons, and protons have a spin\nof 1\n2) or integer for particles called bosons (for example,\nmesons). The spin J of a given particle and its parity P\nare often given using the notation JP . According to the\nvalues of JP , particles are referred to as scalars (0+: f0,\na0, K\u2217\n0, ...), pseudoscalars (0\u2212: \u03c0, \u03b7, \u03b7\u2032, K, D, \u03b7c, B, ...),\nvectors (1\u2212: \u03c1, \u03c9, \u03c6, K\u2217, D\u2217, \u03c8, ...), axial vectors (1+: a1,\nK1, ...), or tensors (2+: a2, K\u2217\n2, ...).\nThe helicity h of a particle of spin J corresponds to the\nprojection of its spin along its momentum. For particles\nwith mass, it can be one of 2J + 1 values: \u2212J, \u2212J + 1,\n..., J \u22121, J. For massless particles, only two values are\nallowed: \u2212J and J. For example, photons, of spin 1, can\nhave two helicities, \u22121 and +1. More information on the\nhelicity formalism can be found in (Jacob and Wick, 1959).\n12.1.2 Angular bases\nLet us consider a spin 0 particle M0 (for example a B\nmeson or a D meson) decaying to two particles M1 and\nM2. Since the spin of M0 is zero, the spin projection of\nthe \ufb01nal state on the decay axis in the M0 rest frame\nhas to be zero. In other words, M1 and M2 must have\nthe same helicity. For example, if one of the \ufb01nal state\nparticles has spin 0 and hence its helicity is 0, the helicity\nof the other \ufb01nal state particle must also be equal to 0: it\nis longitudinally polarized.\nLet us now focus on the case where at least one of the\ndirect decay products of M0 has spin 1 (a vector or axial\nvector particle) and the other a spin greater or equal to\n1. If M1 or M2 is of spin 1, h can take three values: \u22121,\n0, and +1. There is one complex amplitude Ah associated\nwith each case: the longitudinal amplitude A0 and the\ntransverse ones A+1 and A\u22121. The three amplitudes (A0,\nA+1, A\u22121) correspond to helicity eigenstates and de\ufb01ne\nthe helicity basis.\nFor a CP eigenstate, the longitudinal amplitude is CP-\neven, while the transverse ones are an admixture of CP-\neven and CP-odd components. In the transversity basis\n(AL, A\u2225, A\u22a5), the amplitudes correspond to CP eigen-\nstates:\nCP-even longitudinal\n: AL\n= A0\n,\nCP-even transverse\n: A\u2225\n=\nA+1+A\u22121\n\u221a\n2\n,\nCP-odd transverse\n: A\u22a5\n=\nA+1\u2212A\u22121\n\u221a\n2\n.\nBoth \u201c0\u201d and \u201cL\u201d subscripts are commonly used for\nthe longitudinal amplitude. In what follows, the latter\nnotation is used. Additional information on the subject\ncan be found in (Kramer and Palmer, 1992), in (Dunietz,\nQuinn, Snyder, Toki, and Lipkin, 1991), and in the review\nof polarization in B decays of (Beringer et al., 2012).\nThe fractions of each polarization amplitude are de-\n\ufb01ned as fL,\u2225,\u22a5=\n|AL,\u2225,\u22a5|2\n\u03a3|Ah|2 , where h runs on the three po-\nlarization eigenstates. They satisfy the relation fL + f\u2225+\nf\u22a5= 1. The phase di\ufb00erences of the two transverse ampli-\ntudes with respect to the longitudinal one are de\ufb01ned as\n\u03c6\u2225,\u22a5= Arg(A\u2225,\u22a5/AL). As the decay is described by three\nindependent complex amplitudes, AL, A\u2225, and A\u22a5, there\nare six independent real parameters, often chosen as fL,\nf\u22a5, \u03c6\u2225, \u03c6\u22a5, the total decay rate \u0393, and an overall phase\n\u03b40.\nThis overall phase is meaningless in most cases. It is\nrelevant when there exists an external amplitude which\ncan be used as a reference to measure it. This is the case,\nfor example, if one of the B-meson daughters is a K\u2217. In\naddition to the three amplitudes, AL, A\u2225, A\u22a5, describing\nthe decay mode with the K\u2217, there is another amplitude\nA00 associated with the related decay mode where the K\u2217\nis replaced by the J = 0 (K\u03c0) wave, K\u2217\n0. The overall phase\ncan be de\ufb01ned as \u03b40 = Arg(A00/AL). As both the K\u2217and\nK\u2217\n0 decay to the same \ufb01nal state K\u03c0, the \u03b40 phase can be\nmeasured through interference between the B \u2192M1K\u2217\nand B \u2192M1K\u2217\n0 decays (Aubert, 2008bf).\nThe total amplitude may also be expressed as a func-\ntion of S, P, or D partial waves, characterized by the rel-\native orbital angular momentum L between M1 and M2,\nL being equal to 0, 1, and 2 for S, P, and D waves re-\nspectively. The partial wave basis is used for example in\n(Chung, 1997).\n\n141\nThe expressions for the angular dependence are rela-\ntively simple in the helicity and transversity bases. They\nare given in the next subsections.\n12.1.3 Angular distributions in the helicity basis\nv\n/\n/\n/\nl\nl\nc\nd\n/\ne2\ne1\nq\nk \n< \n+ \nk \n+\n<\nFigure 12.1.1. The three angles in the helicity frame: \u03b81,\n\u03b82, and \u03c6, shown in the example of B \u2192\u03c1\u2212\u03c1+ decays. The\nB \u2192\u03c1\u2212\u03c1+, \u03c1\u2212\u2192\u03c0\u2212\u03c00, and \u03c1+ \u2192\u03c0+\u03c00 decays are repre-\nsented in the B, \u03c1\u2212, and \u03c1+ rest frames respectively. The unit\nvector v de\ufb01nes the direction of the \u03c1\u2212in the B rest frame,\nor equivalently the direction of (opposite to) the line of \ufb02ight\nof the B in the \u03c1+ (\u03c1\u2212) rest frame. The decay plane of the \u03c1\u2212\n(\u03c1+) is de\ufb01ned by the c (d) and v unit vectors. Here \u03c6 is the\nangle between the two decay planes and \u03b81 (\u03b82) is the polar\nangle of the \u03c0\u2212(\u03c0+) with v (\u2212v).\nIn the helicity frame, in the case of the M0 \u2192M1M2\ndecay with M1 and M2 each subsequently undergoing a\ntwo-body decay, the relevant angles are the polar angle\n\u03b81 of a decay product of M1 with respect to the direc-\ntion opposite to the line of \ufb02ight of M0 in the M1 rest\nframe, the angle \u03b82 for M2 (same as \u03b81 for M1), and the\nangle \u03c6 between the decay planes of M1 and M2 in the\nM0 rest frame. The choice of the decay product of M1\n(M2) used to de\ufb01ne \u03b81 (\u03b82) is arbitrary, but it must be\nconsistent throughout the analysis. Figure 12.1.1 shows\nthe three angles in the case of B \u2192\u03c1\u2212\u03c1+ decays, with\n\u03c1\u2212\u2192\u03c0\u2212\u03c00 and \u03c1+ \u2192\u03c0+\u03c00. If Mi (i = 1 or 2) undergoes\na three-body decay, \u03b8i is de\ufb01ned as the angle between the\nnormal of the decay plane of Mi with respect to the di-\nrection opposite to the line of \ufb02ight of M0 in the Mi rest\nframe.\nThe di\ufb00erential decay rate in the helicity frame can be\nexpressed as:\n1\n\u0393\nd3\u0393\nd cos \u03b81 d cos \u03b82 d\u03c6 =\n9\n8\u03c0 \u03a3 \u03b1i gi(cos \u03b81, cos \u03b82, \u03c6) .\n(12.1.1)\nThe gi functions depend on the quantum numbers of\nthe particles in the decay chain and are given for the most\ncommon cases in the next section. The \u03b1i are real param-\neters, which can be expressed as functions of the fractions\nfL, f\u2225, f\u22a5and of the phase di\ufb00erences \u03c6\u2225, \u03c6\u22a5Beringer\net al. (2012):\n\u03b11 = |AL|2\n\u03a3|Ah|2 = fL ,\n\u03b12 = |A\u2225|2 + |A\u22a5|2\n\u03a3|Ah|2\n= 1 \u2212fL ,\n\u03b13 = |A\u2225|2 \u2212|A\u22a5|2\n\u03a3|Ah|2\n= f\u2225\u2212f\u22a5,\n(12.1.2)\n\u03b14 =\nIm(A\u22a5A\u2217\n\u2225)\n\u03a3|Ah|2\n=\nq\nf\u22a5f\u2225sin(\u03c6\u22a5\u2212\u03c6\u2225) ,\n\u03b15 = Re(A\u2225A\u2217\nL)\n\u03a3|Ah|2\n=\nq\nf\u2225fL cos(\u03c6\u2225) ,\n\u03b16 = Im(A\u22a5A\u2217\nL)\n\u03a3|Ah|2\n=\np\nf\u22a5fL sin(\u03c6\u22a5) .\n12.1.4 Angular distributions in the transversity basis\nThe angles used in the transversity frame are illustrated\nin Figure 12.1.2 for the decay mode B \u2192\u03c1+\u03c1\u2212. The angle\n\u03b81 has the same de\ufb01nition as in the helicity frame. In the\nM2 rest frame, the axes (x,y,z) are de\ufb01ned such that the\nx-axis has the direction opposite to the momentum of the\nM1 particle, the z-axis is normal to the decay plane of the\nM1 particle, and the projection of the momentum along\nthe y-axis is positive for the decay product of M1 that is\nused to de\ufb01ne \u03b81 (the \u03c0\u2212in the example of Figure 12.1.2).\nThen \u03b8tr and \u03c6tr are the polar and azimuthal angles of\none decay product of M2. They are called the transversity\nangles.\n1\nqtr\netr\nl+\nl-\n/+\n/\no\n/\no\n/\ne\n-\ny\nz\nx\nFigure 12.1.2. The three angles in the transversity frame: \u03b81,\n\u03b8tr, and \u03c6tr, shown in the example of B \u2192\u03c1+\u03c1\u2212decays. Here\n\u03b81 is the angle of the \u03c0\u2212with the \u03c1\u2212direction. And \u03b8tr (\u03c6tr)\nis the polar (azimuthal) angle of the \u03c0+ in the \u03c1+ rest frame.\nIt is convenient to write the di\ufb00erential decay rate, as\nin the helicity frame, as the sum of six terms:\n\n142\n1\n\u0393\nd3\u0393\nd cos \u03b81 d cos \u03b8tr d\u03c6tr\n=\n9\n8\u03c0 \u03a3 \u03b1tr\ni gtr\ni (cos \u03b81, cos \u03b8tr, \u03c6tr) ,\n(12.1.3)\nwith \u03b1tr\ni = \u03b1i, except for\n\u03b1tr\n2 = \u03b12 + \u03b13\n2\n=\n|A\u2225|2\n\u03a3|Ah|2 = f\u2225,\n\u03b1tr\n3 = \u03b12 \u2212\u03b13\n2\n= |A\u22a5|2\n\u03a3|Ah|2 = f\u22a5.\n(12.1.4)\n12.1.5 CP violation\nIf both the M0 decay and its charge conjugate M 0 decay\nare considered, there are now six complex amplitudes or\ntwelve real parameters to describe the two decays. They\ncan be chosen as the six parameters, \u0393, fL, f\u22a5, \u03c6\u2225, \u03c6\u22a5,\nand \u03b40, already given for the M0 decay, and the corre-\nsponding ones, \u0393, f L, f \u22a5, \u03c6\u2225, \u03c6\u22a5, and \u03b40, for the M 0\ndecay. Alternatively they can be de\ufb01ned as the six aver-\nages of the M0 and M 0 parameters and the six di\ufb00erences\nbetween M0 and M 0 parameters, written below:\nACP = \u0393 \u2212\u0393\n\u0393 + \u0393 ,\nAL\nCP = f L \u2212fL\nf L + fL\n,\nA\u22a5\nCP = f \u22a5\u2212f\u22a5\nf \u22a5+ f\u22a5\n,\n(12.1.5)\n\u2206\u03c6\u2225= 1\n2(\u03c6\u2225\u2212\u03c6\u2225) ,\n\u2206\u03c6\u22a5= 1\n2(\u03c6\u22a5\u2212\u03c6\u22a5\u2212\u03c0) ,\n\u2206\u03b40 = 1\n2(\u03b40 \u2212\u03b40) .\nThe quantity \u03c0, introduced in the de\ufb01nition of \u2206\u03c6\u22a5,\nis the phase di\ufb00erence between A\u22a5and A\u22a5if CP were\nconserved. CP violation can be established in an angular\nanalysis if one measures a non-zero value for any of these\nlast six parameters.\n12.1.6 Time dependence\nThe transversity basis is most suited to study CP vio-\nlation in time-dependent asymmetries in neutral B de-\ncays. Where \u03c4 is the B0 lifetime, \u2206md is the mass dif-\nference responsible for the B0-B\n0 oscillations, and \u2206t is\nthe proper time di\ufb00erence between the decay times of the\ntwo B mesons (see Section 10), the time-evolution for each\namplitude is given by:\nAL(\u2206t) = AL(0) e\u2212im\u2206t e\u2212|\u2206t|/2\u03c4\n\u00d7\n\u0012\ncos \u2206md\u2206t\n2\n+ i\u03b7\u03bbL sin \u2206md\u2206t\n2\n\u0013\n,\nA\u2225(\u2206t) = A\u2225(0) e\u2212im\u2206t e\u2212|\u2206t|/2\u03c4\n(12.1.6)\n\u00d7\n\u0012\ncos \u2206md\u2206t\n2\n+ i\u03b7\u03bb\u2225sin \u2206md\u2206t\n2\n\u0013\n,\nA\u22a5(\u2206t) = A\u22a5(0) e\u2212im\u2206t e\u2212|\u2206t|/2\u03c4\n\u00d7\n\u0012\ncos \u2206md\u2206t\n2\n\u2212i\u03b7\u03bb\u22a5sin \u2206md\u2206t\n2\n\u0013\n.\nThe \u03b7 parameter equals 1 for B decays and \u22121 for B\ndecays. The parameter \u03bb, introduced in Section 10, may\nhave three values, \u03bbL, \u03bb\u2225, and \u03bb\u22a5, which are in general dif-\nferent from each other. The total amplitude is the sum of\nthe three amplitudes, and the time-dependent total neu-\ntral B-meson decay rate is expressed as:\n\u0393(\u2206t) = |AL(\u2206t) + A\u2225(\u2206t) + A\u22a5(\u2206t)|2\n(12.1.7)\n= |AL(\u2206t)|2 + |A\u2225(\u2206t)|2 + |A\u22a5(\u2206t)|2\n+2Re(A\u2225(\u2206t)A\u2217\nL(\u2206t) + A\u22a5(\u2206t)A\u2217\nL(\u2206t)\n+A\u22a5(\u2206t)A\u2217\n\u2225(\u2206t)) .\nThus the time-dependence of the various terms enter-\ning the di\ufb00erential decay rate needs to be obtained. Since\nequivalent expressions describe the two CP-even ampli-\ntudes AL and A\u2225, the \u201c+\u201d subscript is used to denote\nboth \u201cL\u201d and \u201c\u2225\u201d to minimize the number of relations to\nbe used:\n\n143\n|A+(\u2206t)|2 = |A+(0)|2 e\u2212|\u2206t|/\u03c4\n\u00121 + |\u03bb+|2\n2\n+1 \u2212|\u03bb+|2\n2\ncos(\u2206md\u2206t)\n\u2212\u03b7 Im\u03bb+ sin(\u2206md\u2206t)\n\u0013\n,\n|A\u22a5(\u2206t)|2 = |A\u22a5(0)|2 e\u2212|\u2206t|/\u03c4\n\u00121 + |\u03bb\u22a5|2\n2\n+1 \u2212|\u03bb\u22a5|2\n2\ncos(\u2206md\u2206t)\n+\u03b7 Im\u03bb\u22a5sin(\u2206md\u2206t)\n\u0013\n,\nA\u2225(\u2206t)A\u2217\nL(\u2206t) = A\u2225(0)A\u2217\nL(0) e\u2212|\u2206t|/\u03c4\n\u00121 + \u03bb\u2225\u03bb\u2217\nL\n2\n+1 \u2212\u03bb\u2225\u03bb\u2217\nL\n2\ncos(\u2206md\u2206t)\n+i\u03b7\n2 (\u03bb\u2225\u2212\u03bb\u2217\nL) sin(\u2206md\u2206t)\n\u0013\n,\nA\u22a5(\u2206t)A\u2217\n+(\u2206t) = A\u22a5(0)A\u2217\n+(0) e\u2212|\u2206t|/\u03c4\n\u00121 \u2212\u03bb\u22a5\u03bb\u2217\n+\n2\n+1 + \u03bb\u22a5\u03bb\u2217\n+\n2\ncos(\u2206md\u2206t)\n\u2212i\u03b7\n2 (\u03bb\u22a5+ \u03bb\u2217\n+) sin(\u2206md\u2206t)\n\u0013\n.\n(12.1.8)\nThese general expressions are rather complex. How-\never, they can be simpli\ufb01ed under certain assumptions.\nIf the \ufb01nal state interactions can be neglected, the three\nparameters, \u03bbL, \u03bb\u2225and \u03bb\u22a5are equal to a common value\n\u03bb. If direct CP-violation e\ufb00ects can also be neglected, \u03bb\nsatis\ufb01es |\u03bb| = 1. The expressions for the time-dependent\nterms then become:\n|A+(\u2206t)|2 = |A+(0)|2 e\u2212|\u2206t|/\u03c4 (1 \u2212\u03b7 Im\u03bb sin(\u2206md\u2206t)) ,\n|A\u22a5(\u2206t)|2 = |A\u22a5(0)|2 e\u2212|\u2206t|/\u03c4 (1 + \u03b7 Im\u03bb sin(\u2206md\u2206t)) ,\nRe(A\u2225(\u2206t)A\u2217\nL(\u2206t)) =\nRe(A\u2225(0)A\u2217\nL(0)) e\u2212|\u2206t|/\u03c4 (1 \u2212\u03b7 Im\u03bb sin(\u2206md\u2206t)) ,\nIm(A\u22a5(\u2206t)A\u2217\n+(\u2206t)) =\n(12.1.9)\nIm(A\u22a5(0)A\u2217\n+(0)) e\u2212|\u2206t|/\u03c4 cos(\u2206md\u2206t)\n\u2212Re(A\u22a5(0)A\u2217\n+(0)) e\u2212|\u2206t|/\u03c4\u03b7Re\u03bb sin(\u2206md\u2206t) .\nIn the case of the B \u2192K\u2217J/\u03c8 decay mode, where\n\u03bb = e2i\u03b2, the \ufb01rst three terms of Eq. (12.1.9) have the\nusual Im\u03bb = sin 2\u03b2 coe\ufb03cient in front of sin(\u2206md\u2206t),\nwhile the last term introduces a Re\u03bb = cos 2\u03b2 coe\ufb03cient,\nallowing one to resolve an ambiguity on the measurement\nof \u03b2 (Aubert, 2005c), as discussed in Section 17.6.\n12.2 List of modes\nThe common decay modes are reviewed here according\nto the type of the particles M0, M1, M2 and, when rel-\nevant, the daughters of M1 and M2. In the title of the\nsubsections, P, V , and T stand for pseudoscalar, vector,\nand tensor mesons, respectively, while l(\u03b3) is for a lepton\n(photon). When two vector mesons with di\ufb00erent decay\ntypes are present, they are labeled V1 and V2.\nFor each mode, the expressions governing the angu-\nlar distributions are given. The procedure to derive the\nformulae can be found elsewhere (Chung, 1971; Richman,\n1984).\n12.2.1 V \u2192P P\nLet us start with the simple case of a vector meson decay-\ning to two pseudoscalar mesons. The distribution of the\nhelicity angle \u03b81 of the vector meson depends upon the\npolarization of the vector meson.\nFor longitudinal polarization, the distribution is given\nby:\n1\n\u0393\nd\u0393\nd cos \u03b81\n= 3\n2 cos2 \u03b81 .\n(12.2.1)\nFor transverse polarization, the expression is the fol-\nlowing:\n1\n\u0393\nd\u0393\nd cos \u03b81\n= 3\n4 sin2 \u03b81 .\n(12.2.2)\nThe latter case applies to the decay \u03a5(4S) \u2192BB,\nas the \u03a5(4S) vector meson produced in e+e\u2212collisions\nthrough a virtual photon is transversely polarized. Hence\nthe angle of the B-meson direction with respect to the\nbeam axis at the B Factories is governed by Eq. (12.2.2).\n12.2.2 P \u2192V P , V \u2192P P\nThe case of a pseudoscalar meson decaying to a pseu-\ndoscalar meson and a vector meson, which then decays\nto two pseudoscalar mesons, is found for example in the\nfollowing modes:\n\u2013 B \u2192\u03c1\u03c0, with \u03c1 \u2192\u03c0\u03c0,\n\u2013 B \u2192D\u2217\u03c0, with D\u2217\u2192D\u03c0,\n\u2013 B \u2192D\u2217D, with D\u2217\u2192D\u03c0.\nThis case was brie\ufb02y mentioned in Section 12.1. Here\nthere is no degree of freedom. As the helicity of the pseu-\ndoscalar meson is 0, the helicity of the vector meson must\nalso be 0: it is then known that the vector meson is longitu-\ndinally polarized. Hence the distribution of the \u03b81 angle is\ndetermined: it follows Eq. (12.2.1). In such modes, where\nthe angular distribution is known, the helicity angle can\nbe used in the selection for background rejection.\n\n144\n12.2.3 P \u2192V \u03b3 , V \u2192P P and P \u2192T \u03b3 , T \u2192P P\nSimilarly, if a pseudoscalar meson decays to a photon and\na vector meson, which then decays to two pseudoscalar\nmesons, as in the mode:\n\u2013 B \u2192K\u2217\u03b3, with K\u2217\u2192K\u03c0,\nthe vector meson can only have an helicity which is allowed\nfor the photon, i.e. \u00b11. So it is transversely polarized.\nConsequently the distribution of the \u03b81 angle is given by\nEq. (12.2.2).\nWhen applying the same argument to a pseudoscalar\nmeson decaying to a photon and a tensor meson, which\nthen decays to two pseudoscalar mesons, such as:\n\u2013 B \u2192K\u2217\n2(1430)\u03b3, with K\u2217\n2(1430) \u2192K\u03c0,\nit is found that the tensor meson can only have helicity\n\u00b11. In this case the \u03b81 angle is distributed according to:\n1\n\u0393\nd\u0393\nd cos \u03b81\n= 15\n4 sin2 \u03b81 cos2 \u03b81 .\n(12.2.3)\n12.2.4 P \u2192V V , V \u2192P P\nThe case of a pseudoscalar meson decaying to two vec-\ntor mesons, each of them decaying to two pseudoscalar\nmesons, can be illustrated by the following decay modes:\n\u2013 B \u2192\u03c1\u03c1, with \u03c1 \u2192\u03c0\u03c0,\n\u2013 B \u2192K\u2217\u03c1, with K\u2217\u2192K\u03c0 and \u03c1 \u2192\u03c0\u03c0,\n\u2013 B \u2192K\u2217\u03c6, with K\u2217\u2192K\u03c0 and \u03c6 \u2192K+K\u2212,\n\u2013 B \u2192D\u2217K\u2217, with D\u2217\u2192D\u03c0 and K\u2217\u2192K\u03c0,\n\u2013 B \u2192D\u2217D\u2217, with D\u2217\u2192D\u03c0.\nBoth bases have been used to analyse this type of de-\ncay. In the helicity basis, the gi functions of Eq. (12.1.1)\nhave the following angular dependence:\ng1 = cos2 \u03b81 cos2 \u03b82 ,\ng2 = 1\n4 sin2 \u03b81 sin2 \u03b82 ,\ng3 = 1\n4 sin2 \u03b81 sin2 \u03b82 cos 2\u03c6 ,\n(12.2.4)\ng4 = \u2212\u03b7 1\n2 sin2 \u03b81 sin2 \u03b82 sin 2\u03c6 ,\ng5 =\n1\n2\n\u221a\n2 sin 2\u03b81 sin 2\u03b82 cos \u03c6 ,\ng6 = \u2212\u03b7\n1\n2\n\u221a\n2 sin 2\u03b81 sin 2\u03b82 sin \u03c6 .\nWhen integrating over the \u03c6 angle, the last four terms\ng3\u2212g6 disappear and the di\ufb00erential decay rate reduces to\nthe following expression, with fL as the single parameter:\n1\n\u0393\nd2\u0393\nd cos \u03b81d cos \u03b82\n=\n(12.2.5)\n9\n4\n\u0012\nfL cos2 \u03b81 cos2 \u03b82 + (1 \u2212fL)1\n4 sin2 \u03b81 sin2 \u03b82\n\u0013\n.\nIn the transversity basis the corresponding gtr\ni\nfunc-\ntions appearing in Eq. (12.1.3) are:\ngtr\n1 = cos2 \u03b81 sin2 \u03b8tr cos2 \u03c6tr ,\ngtr\n2 = 1\n2 sin2 \u03b81 sin2 \u03b8tr sin2 \u03c6tr ,\ngtr\n3 = 1\n2 sin2 \u03b81 cos2 \u03b8tr ,\n(12.2.6)\ngtr\n4 = \u2212\u03b7 1\n2 sin2 \u03b81 sin 2\u03b8tr sin \u03c6tr ,\ngtr\n5 =\n1\n2\n\u221a\n2 sin 2\u03b81 sin2 \u03b8tr sin 2\u03c6tr ,\ngtr\n6 = \u2212\u03b7\n1\n2\n\u221a\n2 sin 2\u03b81 sin 2\u03b8tr cos \u03c6tr .\nAfter integrating over the \u03c6tr angle, the last three\nterms disappear and the di\ufb00erential decay rate simpli\ufb01es\nto:\n1\n\u0393\nd2\u0393\nd cos \u03b81d cos \u03b8tr\n= 9\n8\n\u0012\nfL cos2 \u03b81 sin2 \u03b8tr\n+f\u2225\n1\n2 sin2 \u03b81 sin2 \u03b8tr + f\u22a5sin2 \u03b81 cos2 \u03b8tr\n\u0013\n.\n(12.2.7)\nThis expression allows the extraction of the fraction\nof the three amplitudes. Figure 12.2.1 illustrates, in the\ncase of the B0 \u2192D\u2217+D\u2217\u2212analysis (Miyake, 2005), the\nsine square (cosine square) dependence on \u03b8tr of the AL\nand A\u2225amplitudes (A\u22a5amplitude) and the cosine square\n(sine square) dependence on \u03b81 of the AL amplitude (A\u2225\nand A\u22a5amplitudes).\nThe following expression, depending only on the frac-\ntion f\u22a5of the CP-odd amplitude, is obtained by integrat-\ning also over the \u03b81 angle:\n1\n\u0393\nd\u0393\nd cos \u03b8tr\n=\n(12.2.8)\n3\n4\n\u0012\n(1 \u2212f\u22a5) sin2 \u03b8tr + 2f\u22a5cos2 \u03b8tr\n\u0013\n.\n12.2.5 P \u2192V V , V1 \u2192P \u03b3 , V2 \u2192P P\nVector-vector \ufb01nal states, where one vector meson decays\nto a pseudoscalar meson and a photon and the other one\nto two pseudoscalar mesons, include:\n\u2013 B \u2192D\u2217K\u2217, with D\u2217\u2192D\u03b3 and K\u2217\u2192K\u03c0,\n\u2013 B \u2192D\u2217\ns\u03c1, with D\u2217\ns \u2192Ds\u03b3 and \u03c1 \u2192\u03c0\u03c0,\n\u2013 B \u2192D\u2217\nsD\u2217, with D\u2217\ns \u2192Ds\u03b3 and D\u2217\u2192D\u03c0,\n\u2013 Bs \u2192D\u2217\ns\u03c1, with D\u2217\ns \u2192Ds\u03b3 and \u03c1 \u2192\u03c0\u03c0.\nHere the helicity basis is used and the di\ufb00erential decay\nrate, integrated over the \u03c6 angle, is expressed as:\n1\n\u0393\nd2\u0393\nd cos \u03b81d cos \u03b82\n=\n(12.2.9)\n9\n4\n\u0012\nfL sin2 \u03b81 cos2 \u03b82 + (1 \u2212fL)1\n4(1 + cos2 \u03b81) sin2 \u03b82\n\u0013\n.\n\n145\nFigure 12.2.1. Angular distributions in the transversity frame\nfor (top) cos \u03b8tr and (bottom) cos \u03b81, shown in the example of\nthe B0 \u2192D\u2217+D\u2217\u2212analysis (Miyake, 2005). The points with\nerror bars represent the data. The dot-dashed, dotted, and\ndashed lines correspond to the AL, A\u2225, and A\u22a5amplitudes\nrespectively. The lower solid line is the background (BG), while\nthe upper solid line shows the sum of all contributions. The\nasymmetry in the cos \u03b81 distribution is due to an ine\ufb03ciency\nfor low momentum track reconstruction.\n12.2.6 P \u2192V V , V \u2192P \u03b3\nAn example of a vector-vector \ufb01nal state, where both vec-\ntor mesons decay to a pseudoscalar meson and a photon,\nis:\n\u2013 Bs \u2192D\u2217\nsD\u2217\ns, with D\u2217\ns \u2192Ds\u03b3.\nThe di\ufb00erential decay rate in the helicity basis, inte-\ngrated over the \u03c6 angle, is:\n1\n\u0393\nd2\u0393\nd cos \u03b81d cos \u03b82\n= 9\n4\n\u0012\nfL sin2 \u03b81 sin2 \u03b82\n(12.2.10)\n+ (1 \u2212fL)1\n4(1 + cos2 \u03b81)(1 + cos2 \u03b82)\n\u0013\n.\n12.2.7 P \u2192V V , V1 \u2192P P , V2 \u2192ll\nIn the case of a B-meson decay to two vector mesons,\nwhere M1 decays to two pseudoscalar mesons and M2 de-\ncays to two leptons, the transversity basis is used. An ex-\nample of this is B \u2192K\u2217\u03c8, with K\u2217\u2192K\u03c0 and \u03c8 \u2192e+e\u2212,\nwhere \u03c8 is either J/\u03c8 or \u03c8(2S). The gtr\ni\nfunctions have\nthe following angular dependence:\ngtr\n1 = 1\n2 cos2 \u03b81(1 \u2212sin2 \u03b8tr cos2 \u03c6tr) ,\ngtr\n2 = 1\n4 sin2 \u03b81(1 \u2212sin2 \u03b8tr sin2 \u03c6tr) ,\ngtr\n3 = 1\n4 sin2 \u03b81 sin2 \u03b8tr ,\n(12.2.11)\ngtr\n4 = \u03b7 1\n4 sin2 \u03b81 sin 2\u03b8tr sin \u03c6tr ,\ngtr\n5 = \u22121\n4\n\u221a\n2 sin 2\u03b81 sin2 \u03b8tr sin 2\u03c6tr ,\ngtr\n6 = \u03b7\n1\n4\n\u221a\n2 sin 2\u03b81 sin 2\u03b8tr cos \u03c6tr .\n12.2.8 P \u2192V V , V1 \u2192P P , V2 \u2192V \u03b3\nThe case of a B-meson decay to two vector mesons, where\nM1 decays to two pseudoscalar mesons and M2 decays\nto a vector meson and a photon, is illustrated by the de-\ncay B \u2192K\u2217\u03c7c1, with K\u2217\u2192K\u03c0 and \u03c7c1 \u2192J/\u03c8\u03b3. The\ntransversity basis is used in this case. The gtr\ni\nfunctions\nhave the following angular dependence:\ngtr\n1 = 1\n2 cos2 \u03b81(1 + sin2 \u03b8tr cos2 \u03c6tr) ,\ngtr\n2 = 1\n4 sin2 \u03b81(1 + sin2 \u03b8tr sin2 \u03c6tr) ,\ngtr\n3 = 1\n4 sin2 \u03b81(2 cos2 \u03b8tr + sin2 \u03b8tr) , (12.2.12)\ngtr\n4 = \u2212\u03b7 1\n4 sin2 \u03b81 sin 2\u03b8tr sin \u03c6tr ,\ngtr\n5 = \u22121\n4\n\u221a\n2 sin 2\u03b81 sin2 \u03b8tr sin 2\u03c6tr ,\ngtr\n6 = \u2212\u03b7\n1\n4\n\u221a\n2 sin 2\u03b81 sin 2\u03b8tr cos \u03c6tr .\n\n146\n12.2.9 P \u2192T V , T \u2192P P , V \u2192P P\nThe mode B \u2192K\u2217\n2(1430)\u03c6, with K\u2217\n2(1430) \u2192K\u03c0 and\n\u03c6 \u2192K+K\u2212, is an example of a pseudoscalar meson de-\ncaying to a tensor and a vector meson, each of them de-\ncaying to two pseudoscalar mesons. In the helicity basis\nthe gi functions have the following angular dependence\n(Datta et al., 2008):\ng1 = 5\n12(3 cos2 \u03b81 \u22121)2 cos2 \u03b82 ,\ng2 = 5\n4 cos2 \u03b81 sin2 \u03b81 sin2 \u03b82 ,\ng3 = 5\n4 cos2 \u03b81 sin2 \u03b81 sin2 \u03b82 cos 2\u03c6 ,\n(12.2.13)\ng4 = \u2212\u03b7 5\n2 cos2 \u03b81 sin2 \u03b81 sin2 \u03b82 sin 2\u03c6 ,\ng5 =\n5\n8\n\u221a\n6(3 cos2 \u03b81 \u22121) sin 2\u03b81 sin 2\u03b82 cos \u03c6 ,\ng6 = \u2212\u03b7\n5\n8\n\u221a\n6(3 cos2 \u03b81 \u22121) sin 2\u03b81 sin 2\u03b82 sin \u03c6 .\nAfter integrating over the \u03c6 angle, the four last terms\ndisappear and the di\ufb00erential decay rate depends simply\non the parameter fL:\n1\n\u0393\nd2\u0393\nd cos \u03b81d cos \u03b82\n= 15\n16\n\u0012\nfL(3 cos2 \u03b81 \u22121)2 cos2 \u03b82\n+ 3(1 \u2212fL) cos2 \u03b81 sin2 \u03b81 sin2 \u03b82\n\u0013\n.\n(12.2.14)\n12.3 Analysis details\n12.3.1 Generators\nIn order to perform an angular analysis it is important\nto have simulated data with the correct angular distribu-\ntions. This allows one to calculate, for example, the correct\ne\ufb03ciencies on the signal (see the next subsection) and to\nstudy how well (with how much bias) the angular \ufb01ts de-\nscribed in Section 12.4 can extract the \ufb01tted parameters.\nHere is a brief explanation of how this is achieved in\nthe EvtGen event generator (Lange, 2001) introduced in\nChapter 3. The crucial point is that decay amplitudes,\nand not probabilities, are used for each step in the gen-\neration of a decay chain. This allows one to include all\nangular correlations in the entire decay chain. Each parti-\ncle is described according to the value of its spin and mass\nby an object with the corresponding number of degrees of\nfreedom. Each decay in the decay chain is handled by a\nspeci\ufb01c model taking into account the spin of the initial\nand \ufb01nal state particles. Relevant parameters can be given\nas arguments to the decay model. For example in the case\nof the model describing the decay of a scalar to two vec-\ntor mesons, the six arguments are the magnitude and the\nphase of the three helicity amplitudes.\n12.3.2 Experimental e\ufb00ects\nA large number of angular analyses require cuts on the\nhelicity angles, \u03b8i (i = 1 or 2), as the region at high val-\nues of | cos \u03b8i|, which usually corresponds to soft decay\nproducts, has a rapidly changing e\ufb03ciency and may be\ndominated by background. The cut may be asymmetric\nif the decay products are di\ufb00erent. For example, if one of\nthe decay products is a \u03c1+ vector meson, decaying subse-\nquently into \u03c0+\u03c00, the kinematics of the \u03c1+-meson decay\nare strongly correlated with the value of the relevant he-\nlicity angle \u03b8i. Assuming \u03b8i was de\ufb01ned with respect to\nthe \u03c0+, high (cos \u03b8i \u223c1), medium (cos \u03b8i \u223c0), and low\n(cos \u03b8i \u223c\u22121) values correspond respectively to a decay\nwith a hard \u03c0+ and a soft \u03c00, two pions of similar mo-\nmentum, and a hard \u03c00 and a soft \u03c0+ in the laboratory\nframe. Since there is usually a huge background of low\nmomentum \u03c00s, an upper cut on cos \u03b8i in this case sould\nbe tighter than a lower cut in order to reduce the soft \u03c00\nbackground.\nFor the same reason, the reconstruction e\ufb03ciency de-\npends upon the fraction of longitudinal polarization. De\ufb01n-\ning \u03f5L (\u03f5T ) as the reconstruction e\ufb03ciency obtained if the\nsignal was completely longitudinally (transversely) polar-\nized, i.e. fL = 1 (fL = 0), \u03f5L and \u03f5T would be di\ufb00er-\nent, usually with \u03f5L < \u03f5T . This e\ufb00ect has to be taken\ninto account to correct the measured raw value f meas\nL\nof\nthe fraction of longitudinal polarization to obtain the true\nlongitudinal polarization fraction:\nfL =\nf meas\nL\nf meas\nL\n+ (1 \u2212f meas\nL\n) \u03f5L\n\u03f5T\n.\n(12.3.1)\nSimilarly, the rate of mis-reconstructed signal events de-\npends on the value of the fraction of longitudinal polar-\nization.\nIn the various analyses, the e\ufb03ciency is often modeled\nas a function of cos \u03b8i (i = 1 or 2) with an appropriate\nfunction A(cos \u03b8i). Figure 12.3.1 illustrates the e\ufb03ciency\nfunction in the case of the B0 \u2192\u03c6K\u22170 analysis (Au-\nbert, 2008bf). This otherwise smooth function shows some\nsharp dips due to D meson vetoes (special cuts applied\nin the analysis in order to reject the background coming\nfrom a D meson decay), as seen in Figure 12.3.1(a) near\ncos \u03b81 = 0.8.\n12.3.3 Caveats\nHere is a discussion of some technical points that should\nbe considered in speci\ufb01c angular analyses.\nWhen studying decays with identical particles in the\n\ufb01nal state, the formulae need to be symmetrized. For ex-\nample the B0 \u2192\u03c10\u03c10 \u2192(\u03c0+\u03c0\u2212)(\u03c0+\u03c0\u2212) decay has four\nbosons, identical by pairs, in the \ufb01nal state. In this case the\namplitude A(p+\n1 , p\u2212\n1 , p+\n2 , p\u2212\n2 ), as a function of the four-\nmomenta, p+\n1 , p+\n2 , p\u2212\n1 , and p\u2212\n2 , of the two \u03c0+ and the\ntwo \u03c0\u2212, has to be replaced by the symmetrized amplitude\nunder the permutations p+\n1 \u2192p+\n2 and p\u2212\n1 \u2192p\u2212\n2 .\n\n147\n \n1\nH\n-1\n-0.5\n0\n0.5\n1\nAcceptance Function\n0\n0.01\n(a)\n \n1\nH\n-1\n-0.5\n0\n0.5\nAcceptance Function\n0\n0.01\n(b)\nFigure 12.3.1. Angular e\ufb03ciency functions for H1 = cos \u03b81\n(here \u03b81 is the angle associated with the K\u03c0 system) in the\ncases of (a) B0 \u2192\u03c6K\u00b1\u03c0\u2213and (b) B0 \u2192\u03c6K0\ns\u03c00 (Aubert,\n2008bf). The wiggles in the upper plot are due to the D meson\nvetoes.\nWhen performing a multi-variable maximum likelihood\n\ufb01t, care has to be taken for correlations between variables.\nIn particular, continuum events tend to have correlations\nbetween the masses of the reconstructed Mi (i = 1 or\n2) candidates and the cosine of their helicity angles. A\nsolution is to use a two-dimensional probability density\nfunction in this case.\n12.4 Angular \ufb01ts\nIn this section, the various types of angular \ufb01ts which have\nbeen performed are quickly reviewed.\n12.4.1 Dedicated or global \ufb01ts\nTwo strategies are possible:\n\u2013 The signal yield is \ufb01rst extracted using variables such\nas mES and \u2206E. Second, only the angular variables are\n\ufb01tted to extract the polarization information. Where\nappropriate, time-dependent information can be ob-\ntained in a third step.\n\u2013 A single maximum likelihood \ufb01t is performed using\nthe signal selection variables, as well as the angular\nvariables, and any relevant time-dependence. The po-\nlarization parameters are determined in the \ufb01t at the\nsame time as other parameters such as signal yields.\nThe angular parameters can usually be extracted in\ntime-integrated analyses. Numerous results in various de-\ncay modes are given in this book, in particular in Sec-\ntion 17.4. The time-dependence, when used, is added es-\nsentially to study CP violation, as shown in Sections 17.6\nand 17.7.\nThe angular information is also used in Dalitz analyses,\nthrough either the helicity formalism or Zemach tensors,\nas described in Chapter 13.\n12.4.2 Partial and complete angular analyses\nMost angular analyses integrate over the angle \u03c6, for which\nthe acceptance in the B Factory detectors is uniform, to\ndetermine the fraction of longitudinally polarized events:\nfL. The helicity basis is the natural one to use in this\ncase, as the two daughters are treated symmetrically. The\nformulae to \ufb01t have been given in Section 12.2 for di\ufb00erent\ncases:\n\u2013 Eq. (12.2.5) for P \u2192V V , V \u2192PP,\n\u2013 Eq. (12.2.9) for P \u2192V V , V1 \u2192P\u03b3 , V2 \u2192PP,\n\u2013 Eq. (12.2.10) for P \u2192V V , V \u2192P\u03b3,\n\u2013 Eq. (12.2.14) for P \u2192TV , T \u2192PP, V \u2192PP.\nPartial angular analyses have been performed to mea-\nsure fL in a large number of decay modes, such as B \u2192\u03c1\u03c1,\nB \u2192K\u2217\u03c1, and B \u2192D\u2217K\u2217. In some cases, the angular\nanalysis is performed to disentangle the CP-even and CP-\nodd components. In that case, f\u22a5has to be measured and\nthe transversity basis is more suited for such a partial an-\ngular analysis. If the decay is dominated by the CP-even\nlongitudinal polarization, however, one can e\ufb00ectively use\neither basis and deal with the small transverse component\nwhen addressing systematic uncertainties. If no attempt\nis made to disentangle the CP-even and CP-odd compo-\nnents, the mixture of these two components results in a\ndilution of the CP asymmetry.\nFinally, in a limited number of channels, a complete an-\ngular \ufb01t has been performed to measure not only the frac-\ntions of the three amplitudes, but also the relative phases\nbetween them. Of course, the complete angular analysis\nis more di\ufb03cult than the partial one, as it implies \ufb01t-\nting more free parameters. Consequently it requires su\ufb03-\nciently large data samples. Such an analysis has been per-\nformed in the B-meson decays to \u03c6K\u2217, both in the vector-\nvector modes (B+ \u2192\u03c6K\u2217+ and B0 \u2192\u03c6K\u22170) using either\nEq. (12.2.4) or Eq. (12.2.6), and in the vector-tensor mode\n(B0 \u2192\u03c6K\u22170\n2 (1430)) using Eq. (12.2.13). More details can\nbe found in (Chen, 2005a), (Aubert, 2007c), and (Aubert,\n2008bf). A complete angular analysis was also performed\nin the B-meson decays to charmonium K\u2217, according to\nEq. (12.2.11) when the charmonium decays to two leptons\n(B+ \u2192J/\u03c8K\u2217+, B0 \u2192J/\u03c8K\u22170, and B0 \u2192\u03c8(2S)K\u22170),\nand to Eq. (12.2.12) when the charmonium decays to a\nvector meson and a photon (B0 \u2192\u03c7c1K\u22170). They are\ndocumented in (Aubert, 2005c), (Itoh, 2005b), and (Au-\nbert, 2007x).\n\n148\n12.4.3 Other angular analyses\nNot all the types of angular analyses have been covered\nin this chapter and other kinds of angular analyses have\nalso been performed at B Factories. The goal may be to\ndetermine the unknown spin of a particle by studying the\nangular distribution of its decay products. Examples can\nbe found in charmed meson spectroscopy (Section 19.3)\nand in charmed baryon spectroscopy (Section 19.4). An-\ngular analyses also allow one to study angular asymme-\ntries or correlations, in particular in the case of baryonic\ndecay modes which are presented in Section 17.12, in or-\nder to investigate the underlying dynamics of the decay.\nFinally, in two-photon physics, described in Chapter 22,\nthe angular dependence of the di\ufb00erential cross section for\nvarious processes is studied.\n\n149\nChapter 13\nDalitz-plot analysis\nEditors:\nThomas Latham (BABAR)\nAnton Poluektov (Belle)\nAdditional section writers:\nEli Ben-Haim, Mathew Graham, Fernando Martinez-Vidal\n13.1 Introduction\nDalitz-plot analysis is a powerful technique that involves\nstudying the amplitude for the decay of a parent parti-\ncle into a three-body \ufb01nal state. Compared to two-body\ndecays, the three-body decay possesses intrinsic degrees\nof freedom that permit the determination of the relative\nmagnitudes and phases of interfering amplitudes. The types\nof measurements that can bene\ufb01t from using the Dalitz-\nplot analysis technique include:\n\u2013 Searches for new states;\n\u2013 Measurements of properties of resonances \u2014 masses,\nwidths, quantum numbers;\n\u2013 CP violation searches and measurements of the asso-\nciated parameters;\n\u2013 Studies of \ufb02avor mixing.\nThis chapter starts with a discussion of the kinematics\nof three-body decays (Sections 13.1.1 and 13.1.2) before\ndescribing the formalisms commonly used to model the\nthree-body decay amplitude (Section 13.2). This is fol-\nlowed by an outline of the experimental e\ufb00ects that must\nalso be accounted for in order to successfully describe the\ndistribution of the data over the Dalitz plot (Section 13.3).\nTechnical details of the implementation are presented in\nSection 13.4 before a discussion of the uncertainties arising\nfrom the chosen model (Section 13.5).\n13.1.1 Three-body decay phase space\nIn the case of a two-body decay, the energies of the \ufb01nal\nstate particles in the center-of-mass frame are fully de-\ntermined by the conservation of energy and momentum,\nup to an overall rotation. In contrast, the kinematics of\nthree-body decays are not similarly constrained: after re-\nquiring energy and momentum conservation in the system\nof three \ufb01nal state particles, there are \ufb01ve remaining de-\ngrees of freedom. In the case where the initial and \ufb01nal\nstate particles all have spin zero, after taking into account\narbitrary rotations, two degrees of freedom remain. The\namplitude of the decay can thus be represented as a func-\ntion of two parameters; the scatter plot of this pair of\nparameters is called the Dalitz plot (Dalitz distribution).\nThere is freedom in the choice of which two parameters\none uses to describe the amplitude of a three-body decay.\nIt is often convenient to choose a pair of parameters where\nthe phase-space term is constant within the kinematically\nallowed region in the two-dimensional space spanned by\nthese variables. In this case the structure of the amplitude\nbecomes apparent. This can be achieved by taking either\nthe kinetic energies of two of the \ufb01nal-state particles, or\nthe squares of the invariant masses of two pairs of \ufb01nal-\nstate particles. The former parameterization is convenient\nfor nonrelativistic decays and was originally proposed by\nR. H. Dalitz to study the decay of charged kaons to three\npions (Dalitz, 1953). The corresponding relativistic formu-\nlation was \ufb01rst introduced in Fabri (1954). However, the\nlatter approach is generally more suitable for relativistic\ndecays and has an additional advantage that it allows for\neasy determination of the masses of intermediate states.\nFor a particle of mass M decaying into three particles de-\nnoted as a, b and c, the di\ufb00erential decay probability is\nd\u0393 =\n1\n(2\u03c0)3\n1\n32M 3 |A|2dm2\nabdm2\nbc ,\n(13.1.1)\nwhere mab and mbc are the invariant masses of the pairs of\nparticles ab and bc, respectively. Thus, any nonuniformity\nobserved in the distribution of the variables m2\nab and m2\nbc\nis due to the dynamical structure of the decay amplitude\nA. Most of the analyses performed at the B Factories deal\nwith the Dalitz plot expressed this way; the exception to\nthis will be considered in Section 13.4.1.\n13.1.2 Boundaries, kinematic constraints\nThe invariant masses of pairs of \ufb01nal-state particles are\nrelated by the linear dependence:\nm2\nab + m2\nbc + m2\nac = M 2 + m2\na + m2\nb + m2\nc.\n(13.1.2)\nThe range of invariant masses m2\nbc can be written in terms\nof either one of the other squared invariant masses (e.g.,\nm2\nab):\n(m2\nbc)max = (E\u2217\nb + E\u2217\nc )2 \u2212(p\u2217\nb \u2212p\u2217\nc)2 ,\n(m2\nbc)min = (E\u2217\nb + E\u2217\nc )2 \u2212(p\u2217\nb + p\u2217\nc)2 ,\n(13.1.3)\nwhere\nE\u2217\nb = m2\nab \u2212m2\na + m2\nb\n2mab\n, E\u2217\nc = M 2 \u2212m2\nab \u2212m2\nc\n2mab\n,\n(13.1.4)\nare the energies of particles b and c in the ab rest frame\nand\np\u2217\nb =\nq\nE\u22172\nb \u2212m2\nb , p\u2217\nc =\np\nE\u22172\nc \u2212m2c ,\n(13.1.5)\nare the corresponding momenta.\nThe region of kinematically allowed phase space de-\nscribed by these constraints is shown in Fig. 13.1.1. The\npoints on the boundary of the phase space correspond\nto the con\ufb01gurations where the \ufb01nal state particles are\ncollinear. In particular, three extreme points where m2\nab,\nm2\nbc, or m2\nac are maximal, correspond to the con\ufb01gurations\nwith one of the particles produced at rest (in the frame of\nthe decaying particle).\n\n150\n)\n4\n/c\n2\n (GeV\nab\n2\nm\n0\n5\n10\n15\n20\n25\n30\n)\n4\n/c\n2\n (GeV\nbc\n2\nm\n0\n5\n10\n15\n20\n25\n30\n2)\nb\n+m\na\n(m\n2)\na\n (M-m\n2)\nc\n(M-m\n \n2)\nc\n+m\nb\n(m\nmin\n)\nbc\n2\n (m\nmax\n)\nbc\n2\n (m\na\nc\nb\nb\na\nc\na\nb\nc\na b\nc\nb c\na\na c\nb\na\nc\nb\nFigure 13.1.1. Kinematic boundaries of the three-body decay\nphase space and illustration of various kinematic con\ufb01gurations\nof the \ufb01nal-state particles for characteristic Dalitz plot points.\nIn this example, the B0 \u2192\u03c0\u2212D0K+ phase space is shown;\na = \u03c0\u2212, b = D0, c = K+.\n13.2 Amplitude description\nExperimental data show that nonleptonic three-body B\nand D decays proceed predominantly through resonant\ntwo-body decays. For three-body decays of a spin-zero\nparticle P (e.g., a D or B meson) to pseudoscalar \ufb01nal-\nstate particles abc, the baseline model commonly adopted\nto describe the decay amplitude A(m2\nab, m2\nbc) consists of a\ncoherent sum of two-body amplitudes (subscript r) and\na \u201cnonresonant\u201d (subscript NR) contribution (Beringer\net al., 2012),\nA(m) =\nX\nr\narei\u03c6rAr(m) + aNRei\u03c6NRANR(m) . (13.2.1)\nThe parameters ar (aNR) and \u03c6r (\u03c6NR) are the magni-\ntude and phase of the amplitude for component r (NR).\nThe functions Ar and ANR are Lorentz-invariant expres-\nsions that describe the dynamical properties of the de-\ncay into the multi-body \ufb01nal state as a function of posi-\ntion in the Dalitz plot m \u2261(m2\nab, m2\nbc). When the \ufb01nal\nstate contains identical particles, e.g. D+ \u2192\u03c0+\u03c0+\u03c0\u2212or\nB0 \u2192K0\nSK0\nSK0\nS, it is important that the total amplitude\nA(m) is correctly symmetrized with respect to exchange\nof those particles.\nThe most common ways to parameterize the functions\nAr are reviewed in the following Sections 13.2.1 and 13.2.2.\nThe parameterizations of nonresonant amplitude are dis-\ncussed in Section 13.2.3. Section 13.2.4 discusses a special\ncase of time-dependent amplitude analyses.\n13.2.1 Isobar formalism\nThe isobar formalism (or isobar model) is so-called be-\ncause it was \ufb01rst used to describe pion-nucleon, nucleon-\nnucleon, and antinucleon-nucleon interactions (Stern-\nheimer and Lindenbaum, 1961). In such reactions the in-\ntermediate resonances are isobars of a particular nuclear\nstate. The isobar model was later generalized to any three-\nbody \ufb01nal state (Herndon, Soding, and Cashmore, 1975).\nIn this formalism, the function Ar describes the decay\nthrough a single intermediate resonance r and takes the\nform\nAr = FP \u00d7 Fr \u00d7 Tr \u00d7 Wr,\n(13.2.2)\nwhere Tr \u00d7 Wr is the resonance propagator (Tr is the dy-\nnamical function for the resonance r, while Wr describes\nthe angular distribution of the decay), FP and Fr are the\ntransition form factors of the parent particle and reso-\nnance, respectively. In what follows, we assume that the\nresonance is produced in the ab channel. In that case the\nparticle c will be referred to as the bachelor particle. Nat-\nurally, the full amplitude A may contain contributions of\nresonances in any of the ab, ac, and bc channels.\nThe dynamical function Tr is commonly described\nusing a relativistic Breit-Wigner (BW) parameterization\nwith mass-dependent width (see, e.g., review on Dalitz\nplot analysis formalism on p. 889 in Beringer et al. (2012))\nTr =\n1\nm2r \u2212m2\nab \u2212imr\u0393ab\n.\n(13.2.3)\nHere mr is the mass of the resonance, and the mass-\ndependent width \u0393ab is given by\n\u0393ab = \u0393r\n\u0012qab\nqr\n\u00132J+1 \u0012 mr\nmab\n\u0013\nF 2\nr ,\n(13.2.4)\nwhere \u0393r and J are the width and spin of the resonance,\nqab is the momentum of the daughter particles in the\ncenter-of-mass frame of a and b, and qr is the momen-\ntum the decay products would have in the rest frame of a\nresonance with mass mr.\nStrictly speaking, the Breit-Wigner parameterization\nworks well only in the case of narrow states. The use of\nthe mass-dependent width results in the amplitude Tr be-\ncoming a non-analytic function. An alternative parametri-\nzation proposed by Gounaris and Sakurai (GS) (Gounaris\nand Sakurai, 1968) recovers the analyticity of the ampli-\ntude and provides a better description for broad vector\nresonances such as \u03c1(770) and \u03c1(1450).\nFor resonances such as the f0(980) \u2192\u03c0\u03c0 that lie close\nto the threshold of another channel (f0(980) \u2192KK in\nthis case), the e\ufb00ect of the opening of the second channel\nmust be taken into account, for example, by employing\nthe Flatt\u00b4e coupled-channel form (Flatte, 1976),\nTr =\ng1\nm2r \u2212m2\nab \u2212i(\u03c11g2\n1 + \u03c12g2\n2) ,\n(13.2.5)\nwhere \u03c11, \u03c12 and g1, g2 are the phase-space factors and\ncoupling constants of the \u03c0\u03c0 and KK channels, respec-\ntively.\nValues of the mass and width of resonances are in gen-\neral taken from world averages (Beringer et al., 2012).\n\n151\nSince di\ufb00erent parameterizations of the resonance line-\nshapes, especially for broad resonances, often give di\ufb00erent\nvalues, one has to make sure that the values used in the \ufb01t\nwere extracted using the same parameterization as in the\nmodel. If the resonance is apparent and systematic biases\n(or external errors) of its parameters are expected to be\nlarger than their statistical errors from the \ufb01t, the mass\nand width can be left unconstrained.\nThe angular dependence Wr is described using either\nZemach tensors (Zemach, 1964, 1965), where transversal-\nity is enforced, or the helicity formalism (Bonvicini et al.,\n2008; Jacob and Wick, 1959), which allows for a longitudi-\nnal component in the resonance propagator (see Beringer\net al. (2012) for a comprehensive summary). The expres-\nsions for scalar, vector and tensor states are\nJ = 0 :\nWr = 1 ,\n(13.2.6)\nJ = 1 :\nWr = m2\nac \u2212m2\nbc \u2212(M 2 \u2212m2\nc)(m2\na \u2212m2\nb)\nm2r\n,\nJ = 2 :\nWr =\n\u0014\nm2\nbc \u2212m2\nac + (M 2 \u2212m2\nc)(m2\na \u2212m2\nb)\nm2r\n\u00152\n\u2212\n1\n3\n\u0014\nm2\nab \u22122M 2 \u22122m2\nc + (M 2 \u2212m2\nc)2\nm2r\n\u0015\n\u00d7\n\u0014\nm2\nab \u22122m2\na \u22122m2\nb + (m2\na \u2212m2\nb)2\nm2r\n\u0015\n.\nTransversality is enforced by substituting m2\nab for m2\nr in\nthe denominators of the previous expressions. This leads\nto the alternative expressions\nJ = 0 :\nWr = 1,\n(13.2.7)\nJ = 1 :\nWr = \u22122 (p \u00b7 q) ,\nJ = 2 :\nWr = 4\n3\nh\n3 (p \u00b7 q)2 \u2212(|p| |q|)2i\n,\nwhere q and p are the momenta of one of the resonance\ndaughters and the bachelor particle, respectively, evalu-\nated in the rest frame of the resonance. The decision as to\nwhich daughter to choose is a matter of convention and it\nis very important that this choice be documented since it\na\ufb00ects the interpretation of the relative phases. The an-\ngle between q and p is known as the helicity angle (see\nalso Section 12.1) and p \u00b7 q is proportional to the cosine\nof the helicity angle cos \u03b8H. The Zemach expressions are\nessentially Legendre polynomials of cos \u03b8H multiplied by\ncoe\ufb03cients that contain the momenta of the daughter and\nbachelor particles raised to the power J.\nThe form factors FP and Fr usually use the Blatt-\nWeisskopf parameterization for the decay vertex (Blatt\nand Weisskopf, 1952). The expressions for the Blatt-\nWeisskopf penetration factors depend on the spin J of\nthe intermediate resonance\nJ = 0 :\nF = 1\nJ = 1 :\nF =\ns\n1 + R2q2r\n1 + R2q2\nab\n(13.2.8)\nJ = 2 :\nF =\ns\n9 + 3R2q2r + R4q4r\n9 + 3R2q2\nab + R4q4\nab\n,\nwhere R is the radial parameter of the decaying meson and\ntypically takes values between 1 and 5 (GeV)\u22121. In this\nprescription, F is normalized so that F = 1 for qr = qab.\nWhile the P- and D-waves of the decay amplitude are\nusually well described using a certain number of BW or GS\npropagators, the actual number depending on the speci\ufb01c\ndecay, the S-wave typically contains a number of broad\noverlapping states, for which the isobar model gives a poor\ndescription. In that case, more complex alternatives have\nbeen adopted, which are reviewed in Section 13.2.2.\nFigure 13.2.1 illustrates how various intermediate two-\nbody states appear in the Dalitz plot. Unlike the uniform\ndistribution of the phase-space decay (Fig. 13.2.1(a)), sca-\nlar resonances appear as bands in the Dalitz plot, as shown\nin Fig. 13.2.1(b-d) for resonances in bc, ac, and ab chan-\nnels, respectively. Angular distributions for vector and\ntensor intermediate states introduce characteristic non-\nuniformity of the event density along the resonance bands\n(Fig. 13.2.1(e,f)). Finally, the region where the amplitudes\nof two resonances overlap is sensitive to the phase di\ufb00er-\nence between the two amplitudes (Fig. 13.2.1(g,h)).\n13.2.2 K-matrix formalism\nThe complex S-wave dynamics, which can also include\nthe presence of several broad and overlapping scalar res-\nonances, can alternatively be described through the use\nof a K-matrix formalism (Chung et al., 1995; Wigner,\n1946) with the production vector (P-vector) approxima-\ntion (Aitchison, 1972). Within this formalism, the produc-\ntion process described by the P-vector can be viewed as\nthe initial formation of several states, which are then prop-\nagated by the K-matrix term into the \ufb01nal state that is\nobserved. This approach ensures that the two-body scat-\ntering matrix respects unitarity, which is not guaranteed\nin the case of the isobar model. At the B Factories this\napproach is most commonly used to describe the \u03c0+\u03c0\u2212\nS-wave contribution to the Dalitz-plot amplitude, e.g. in\nthe BABAR analyses (Aubert, 2008l, 2009h; del Amo San-\nchez, 2010a,b) and Belle analysis (Abe, 2007b). In such\ncases the amplitude is given by\nAu(s) =\nX\nv\n[I \u2212iK(s)\u03c1(s)]\u22121\nuv Pv(s) ,\n(13.2.9)\nwhere s \u2261m2\nab is the \u03c0+\u03c0\u2212invariant mass, I is the iden-\ntity matrix, K is the matrix describing the scattering pro-\ncess, \u03c1 is the diagonal phase-space matrix, and P is the\nproduction vector. The indices u and v represent the pro-\nduction and scattering channels, respectively, and take the\nvalues 1 to 5, where 1 = \u03c0\u03c0, 2 = KK, 3 = \u03c0\u03c0\u03c0\u03c0, 4 = \u03b7\u03b7,\n5 = \u03b7\u03b7\u2032. Hence in the case of describing the \u03c0+\u03c0\u2212am-\nplitude u = 1. The propagator can be described using\nscattering data, provided that the two-body system in the\n\ufb01nal state is isolated and does not interact with the rest\nof the \ufb01nal state in the production process.\nThe parameterizations adopted for the K, \u03c1, and P\nterms in Eq. (13.2.9) by the B Factories are the same as\nthose used by previous analyses (Anisovich and Sarantsev,\n\n152\n(a)\nPhase-space decay\n(b)\nScalar in bc channel\n(c)\nScalar in ac channel\n(d)\nScalar in ab channel\n(e)\nVector in ab channel\n(f)\nTensor in ab channel\n(g)\nTwo scalars, \u2206\u03c6 = 0\n(h)\nTwo scalars, \u2206\u03c6 = \u03c0\nFigure 13.2.1. Example Dalitz plots with (a) phase-space\ndecay, (b-d) one scalar resonance appearing in various decay\nchannels, (e, f) vector and tensor resonances, and (g, h) the\ninterference of two scalar resonances with di\ufb00erent values of\nthe relative phase \u2206\u03c6.\n2003; Link et al., 2004a), up to some sign conventions and\nconstant terms. The K-matrix is formulated as\nKuv(s) =\n X\n\u03b1\ng\u03b1\nug\u03b1\nv\nm2\u03b1 \u2212s + f scatt\nuv\n1 \u2212sscatt\n0\ns \u2212sscatt\n0\n!\nfA0(s),\n(13.2.10)\nwhere g\u03b1\nu is the coupling constant of the K-matrix pole at\nm\u03b1 to the uth channel. The parameters f scatt\nuv\nand sscatt\n0\ndescribe the slowly varying part of the K-matrix. The fac-\ntor\nfA0(s) = 1 \u2212sA0\ns \u2212sA0\n\u0012\ns \u2212sA\nm2\n\u03c0\n2\n\u0013\n(13.2.11)\nsuppresses the false kinematic singularity at s = 0 in\nthe physical region near threshold, the Adler zero (Adler,\n1965). For example, the parameter values used in the\nBABAR analysis of D0 \u2192K0\nS\u03c0+\u03c0\u2212(Aubert, 2008l) are\nlisted in Table 13.2.1, and are adapted from a global anal-\nysis of the available \u03c0\u03c0 scattering data from threshold up\nto 1900 MeV/c2 (Anisovich and Sarantsev, 2003). The pa-\nrameters f scatt\nuv\n, for u \u0338= 1, are all set to zero since they\nare not related to the \u03c0\u03c0 scattering process. Similarly, the\nparameterization for the P-vector is\nPv(s) =\nX\n\u03b1\n\u03b2\u03b1g\u03b1\nv\nm2\u03b1 \u2212s + f prod\n1v\n1 \u2212sprod\n0\ns \u2212sprod\n0\n.\n(13.2.12)\nNote that the P-vector has the same poles as the K-matrix,\notherwise the A1 amplitude would vanish (diverge) at the\nK-matrix (P-vector) poles. The parameters \u03b2\u03b1, f prod\n1v\n, and\nsprod\n0\nof the initial P-vector depend on the production\nmechanism and cannot be extrapolated from scattering\ndata. Thus they have to be determined directly from the\nD or B meson decay data sample. They are complex num-\nbers analogous to the arei\u03c6r coe\ufb03cients in Eq. (13.2.1),\nhence they can be \ufb01tted in the same way.\nFor the K\u03c0 S-wave, the B Factories generally have\neither used a simple K\u2217\n0(1430) BW that neglects a possi-\nble nonresonant contribution or a K\u2217\n0(1430) BW together\nwith an e\ufb00ective-range nonresonant component with a\nphase shift derived from scattering data (Aston et al.,\n1988),\nAK\u03c0,L=0(m) = TK\u03c0,L=0(s)/\u03c1(s) .\n(13.2.13)\nHere s \u2261m2\nK\u03c0, \u03c1(s) = 2q/\u221as is the phase-space factor,\nq is the momentum of the kaon and pion in the K\u03c0 rest\nframe, and\nTK\u03c0,L=0(s) = B sin(\u03b4B + \u03c6B)ei(\u03b4B+\u03c6B) +\nR sin \u03b4Rei(\u03b4R+\u03c6R)ei2(\u03b4B+\u03c6B) ,\n(13.2.14)\nwhere the phases \u03b4B and \u03b4R have a dependence on s and\nq given by\ntan \u03b4R = M\u0393(s)/(M 2 \u2212s) ,\ncot \u03b4B = 1/(aq) + rq/2 .\n(13.2.15)\nThe parameters a and r play the role of a scattering length\nand e\ufb00ective interaction length, respectively, and B (\u03c6B)\nand R (\u03c6R) are the magnitudes (phases) for the nonreso-\nnant and resonant terms. M and \u0393(s) are the mass and\nmass-dependent width, see Eq. (13.2.4), of the K\u2217\n0(1430)\nresonance. This parametrization in fact corresponds to a\nK-matrix approach describing a rapid phase shift coming\nfrom the resonant term and a slowly rising phase shift gov-\nerned by the nonresonant term, with relative strengths R\n\n153\nTable 13.2.1.\nK-matrix parameters used in the BABAR analysis of D0 \u2192K0\nS\u03c0+\u03c0\u2212(Aubert, 2008l). They are adapted from\nthe results of a global analysis of the available \u03c0\u03c0 scattering data from threshold up to 1900 MeV/c2 (Anisovich and Sarantsev,\n2003). Masses and coupling constants are given in GeV/c2.\nm\u03b1\ng\u03b1\n\u03c0+\u03c0\u2212\ng\u03b1\nKK\ng\u03b1\n4\u03c0\ng\u03b1\n\u03b7\u03b7\ng\u03b1\n\u03b7\u03b7\u2032\n0.65100\n0.22889\n\u22120.55377\n0.00000\n\u22120.39899\n\u22120.34639\n1.20360\n0.94128\n0.55095\n0.00000\n0.39065\n0.31503\n1.55817\n0.36856\n0.23888\n0.55639\n0.18340\n0.18681\n1.21000\n0.33650\n0.40907\n0.85679\n0.19906\n\u22120.00984\n1.82206\n0.18171\n\u22120.17558\n\u22120.79658\n\u22120.00355\n0.22358\nsscatt\n0\nf scatt\n11\nf scatt\n12\nf scatt\n13\nf scatt\n14\nf scatt\n15\n\u22123.92637\n0.23399\n0.15044\n\u22120.20545\n0.32825\n0.35412\nsA0\nsA\n\u22120.15\n1\nand B. The parameters B, \u03c6B, R, \u03c6R, a, and r can be\ndetermined from the \ufb01t to data as with the P-vector pa-\nrameters and isobar coe\ufb03cients. Or, in the case of limited\ndata sample, they can be taken from \ufb01ts to the LASS scat-\ntering data (Aston et al., 1988). Other recent experimental\ne\ufb00orts to improve the description of the K\u03c0 S-wave using\nK-matrix and model independent parameterizations from\nlarge samples of D+ \u2192K\u2212\u03c0+\u03c0+ decays are described\nin Aitala et al. (2006); Bonvicini et al. (2008); Link et al.\n(2007).\n13.2.3 Nonresonant description\nIn many analyses the nonresonant amplitude is taken to be\na uniform phase-space distribution, i.e. a constant mag-\nnitude and phase. Indeed, such a constant matrix ele-\nment is the most strict de\ufb01nition of a nonresonant am-\nplitude. However, \ufb01nal-state interactions and other e\ufb00ects\nare likely to change this behavior, meaning that a uniform\namplitude is not fully motivated. In addition, it is found\nin many cases not to give a good description of the data.\nThis has been seen both in analyses of charm decays with\nvery large event yields and in analyses of B decays where,\nalthough the event yields are generally much smaller, the\nphase space is considerably larger and so there is greater\nsensitivity to the nonresonant description. This has led\nanalysts either to adopt various empirical forms or to at-\ntempt to use information from scattering data to describe\nthe entire S-wave amplitude. The latter approach is de-\nscribed in the previous Section 13.2.2.\nAn example of one of the empirical forms that has been\nadopted by Garmash (2005) is\nANR = e\u2212\u03b1m2\nab ,\n(13.2.16)\nwhere \u03b1 is a free parameter of the \ufb01t. This modi\ufb01cation\nof the uniform amplitude allows for enhancements of the\nmagnitude at lower m2\nab values while the phase remains\nconstant over the Dalitz plot. In most cases more than\none such term is employed, often for each neutral or singly\ncharged m2\nij combination. The recent BABAR analysis of\nB \u2192KKK decays (Lees, 2012y) uses a model that has\npolynomial dependence on the invariant mass and includes\nan explicit P-wave term.\nIn recent years there has been an increasing amount\nof theoretical work towards an understanding of the dy-\nnamics of nonresonant three-body amplitudes, see for ex-\nample Lesniak et al. (2009) and Kamano, Nakamura, Lee,\nand Sato (2011). In particular, the work focuses on both\nthe e\ufb00ects of \ufb01nal-state interactions and the requirement\nthat two- and three-body prescriptions respect unitarity in\nthe Dalitz-plot model. However, these developments are,\nin general, yet to be put into practice in the analysis of\nexperimental data.\n13.2.4 Time-dependent analyses\nPerforming a time-dependent Dalitz-plot analysis of neu-\ntral B decays allows the extraction of the CP-violating pa-\nrameters along with the parameters of the isobar model.\nA full time- and tag-dependent Dalitz-plot analysis has\nthe following advantages compared to a quasi-two-body\nanalysis:\n\u2013 determines weak and strong phases simultaneously, al-\nleviating ambiguities from di\ufb00erent amplitude contri-\nbutions;\n\u2013 provides sensitivity to cos 2\u03c6 (where \u03c6 is the appro-\npriate weak phase), alleviating the degeneracy of the\ntrigonometric ambiguities;\n\u2013 correctly accounts for contamination between di\ufb00erent\nresonant contributions.\nSee Chapters 8 and 10 for details of the techniques of\n\ufb02avor tagging and time-dependent analyses. Here we will\ngive a brief description of how the time dependence and\nthe Dalitz-plot dependence are combined.\nWith \u2206t \u2261trec \u2212ttag de\ufb01ned as the proper time inter-\nval between the decay of the fully reconstructed Brec and\nthat of the other meson Btag from the \u03a5(4S) decay, the\n\n154\ntime-dependent decay rate |A+(\u2206t)|2 (|A\u2212(\u2206t)|2) when\nthe Btag is a B0 (B0) is given by\n|A\u00b1(\u2206t)|2 = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u0014\n|A|2 + |A|2\n(13.2.17)\n\u2213\n\u0000|A|2 \u2212|A|2\u0001\ncos(\u2206md\u2206t)\n\u00b1 2Im\n\u0014q\npAA\u2217\n\u0015\nsin(\u2206md\u2206t)\n\u0015\n,\nwhere \u03c4B0 is the mean neutral B lifetime and \u2206md is the\nmass di\ufb00erence between BH and BL. The time distribu-\ntion is convolved with the \u2206t resolution function in the\ntypical way. Here, we have assumed that CP is conserved\nin B0B0 mixing (|q/p| = 1) and that the lifetime di\ufb00er-\nence between BH and BL is negligible (\u2206\u0393d = 0). The\ndecay rate, Eq. (13.2.17), is used as a p.d.f. in a maximum-\nlikelihood \ufb01t and must therefore be normalized:\n|A\u00b1(\u2206t)|2 \u2212\u2192\n1\n\u27e8|A|2 + |A|2\u27e9|A\u00b1(\u2206t)|2 ,\n(13.2.18)\nwhere \u27e8...\u27e9denotes the value of the integral over the Dalitz\nplot.\n13.3 Experimental e\ufb00ects\nThe amplitude formalisms outlined above provide a model\nof the underlying physics of the three-body decay. How-\never, these descriptions may have to be modi\ufb01ed or aug-\nmented to account for the imperfections of experimental\nmeasurements. Broadly, these modi\ufb01cations fall into two\ncategories, one accounting for candidates from background\nprocesses (see Section 13.3.1) and the other for e\ufb00ects of\nreconstruction of signal candidates. The latter category\nincorporates two main e\ufb00ects: e\ufb03ciency (Section 13.3.2)\nand misreconstruction (Section 13.3.3).\n13.3.1 Backgrounds\nAt the B Factories, the dominant source of background\nin most three-body analyses is from combinatorics, i.e.\nwhere three random particles in an event happen to fake\nthe signal decay under consideration. This is largely due\nto the cross-section for light quark production being two\nto three times higher than that for charm or bottom. Ad-\nditionally, in searches for rare decays (such as charmless\nB decays) the branching fraction of the decay of interest\nis small, O\n\u000010\u22127 \u221210\u22125\u0001\n. Therefore the relative rate of\nparticles from other B decays combining to fake the sig-\nnal is correspondingly greater. While these types of back-\ngrounds can be greatly suppressed using the multivariate\ntechniques described in Chapter 4, the Dalitz-plot distri-\nbution of the events that remain must still be modeled.\nIn general, such random combinations of particles tend to\npopulate the edges and corners of the Dalitz plot, since\nthey are most frequently formed from collinear and anti-\ncollinear particles in the predominantly jet-like continuum\nevents.\nIn addition to the combinatoric backgrounds, there ex-\nist fully or partially reconstructed backgrounds that origi-\nnate from decays of the same class of parent meson to a \ufb01-\nnal state similar to the one under consideration. For exam-\nple, in an analysis of the decay B0 \u2192K0\nS\u03c0+\u03c0\u2212there are\npotentially large backgrounds from many other B decays\nincluding B0 \u2192\u03b7\u2032(\u2192\u03c10\u03b3)K0\nS, B0 \u2192D\u2212(\u2192K0\nS\u03c0\u2212)K+,\nand B+ \u2192K0\nS\u03c0+. In the \ufb01rst of these examples the de-\ncay has been partially reconstructed but the energy of the\nmissing photon is su\ufb03ciently small that the reconstructed\nB0 candidate passes selection criteria. In the second case\nthe decay is fully reconstructed but a kaon/pion misiden-\nti\ufb01cation occurs. In the third case the decay is again fully\nreconstructed and combined with an additional soft pion\nfrom the rest of the event to form a signal candidate. Each\nof these scenarios can lead to very di\ufb00erent distributions\nof events in the Dalitz plot.\nIn general, the distributions of backgrounds across the\nDalitz plot are rather di\ufb03cult to model with parametric\nfunctions. Additionally, the precise nature of the back-\ngrounds can vary dramatically from one analysis to an-\nother. Thus, the most common approach for modeling the\nDalitz-plot distributions of the backgrounds is to use his-\ntograms obtained from either Monte Carlo simulation or\nsidebands in data. Often some form of smoothing or in-\nterpolation is applied to the histograms in order to limit\nthe e\ufb00ect of statistical \ufb02uctuations in the input data sam-\nple. In B decay analyses, it is found that most back-\ngrounds (particularly the dominant combinatoric back-\ngrounds) preferentially populate the corners and edges of\nthe Dalitz plot. In order to increase the resolution of the\nhistograms in these regions, adaptive binning techniques\ncan be used and/or the histograms can be formed in the\nso-called \u201csquare Dalitz plot\u201d, which is discussed in detail\nin Section 13.4.1.\n13.3.2 E\ufb03ciency\nThe most obvious e\ufb00ect of detector acceptance is a re-\nduction in the number of events detected. In three-body\ndecays this is complicated by the fact that the kinematic\nproperties of the decay products di\ufb00er accross the Dalitz\nplot. Thus, the acceptance as a function of the Dalitz plot\nvariables is, in general, nonuniform.\nThe typical acceptance function drops at the corners of\nthe phase space, which correspond to the kinematic con\ufb01g-\nuration where one of the \ufb01nal state particles is produced at\nrest in the frame of the decaying particle. Reconstruction\ne\ufb03ciency is typically smaller for such particles, especially\nif the decaying particle has a small boost in the laboratory\nframe.\nAt BABAR and Belle, the e\ufb03ciency pro\ufb01le is usually\nwell modeled by the full detector simulation. The pro\ufb01le\nis then modeled either by a parameterized form, such as\na two-dimensional polynomial, or by a histogram. Either\nway, this allows the e\ufb03ciency as a function of the position\nin phase space, \u03b5 (m), to be included in the signal Dalitz-\nplot model, where it multiplies the squared absolute value\nof the amplitude. When histograms are used they often\n\n155\nutilize adaptive binning techniques and/or are formed in\nthe \u201csquare Dalitz plot\u201d (see Section 13.4.1) to improve\nthe resolution in the areas of most rapidly changing ef-\n\ufb01ciency or of greatest importance for the signal model.\nInterpolation or smoothing techniques can be employed\nto reduce the e\ufb00ect of statistical \ufb02uctuations.\nAnother, nonparametric, technique to include the ef-\n\ufb01ciency pro\ufb01le in the Dalitz plot \ufb01t was used in some\nBelle analyses (Abe, 2004f; Kuzmin, 2007). The method\nuses the fact that in the unbinned maximum likelihood \ufb01t\nthe e\ufb03ciency pro\ufb01le enters only the normalization term.\nThe normalization of the p.d.f. over the Dalitz plot is cal-\nculated using the Monte-Carlo integration technique, but\ninstead of a uniformly distributed sample in the phase-\nspace variables, a large number of simulated events is used\nthat pass the same selection as applied to data.\n13.3.3 Misreconstructed signal\nAnother extremely important e\ufb00ect of reconstruction for a\nDalitz-plot analysis is the potential migration of an event\nfrom its true coordinate on the Dalitz plot to its recon-\nstructed position. In reality, these e\ufb00ects of reconstruction\nlie on a continuum, but in order to produce a reasonable\nmodel they are most often classi\ufb01ed into two types. The\n\ufb01rst type consists of so-called \u201ccorrectly reconstructed\u201d\nevents, where the migration is negligible relative to the\nwidths of the resonances under consideration. In this case\nthe amplitude models are used without alteration. In very\nfew cases the migration is not negligible but can be mod-\neled using a simple Gaussian resolution. This class of cor-\nrectly reconstructed signal events will not be discussed\nfurther here. The second type contains events which have\nmore pronounced migration and are sometimes called \u201cself\ncross feed\u201d in BABAR and Belle publications; they form\nthe main topic of this section, and will be referred to as\n\u201cmisreconstructed signal\u201d.\nFor many three-body decay modes, there is a signi\ufb01-\ncant fraction of signal events that are incorrectly recon-\nstructed yet still satisfy the selection criteria. Such events\ntypically occur when one low-energy particle from the sig-\nnal decay is replaced by another in the same event. This\nbehavior is especially prevalent in decays containing neu-\ntral pions, where another photon in the event is incorrectly\nassigned as one of the low-energy photons used to recon-\nstruct the \u03c00.\nIn order to correctly model this behavior, it is neces-\nsary to determine both the frequency of the misreconstruc-\ntion (including the variation of that frequency over the\nDalitz plot) and the precise migration e\ufb00ects that occur.\nThis can only be achieved with full detector simulation,\nwhere both the generated and reconstructed Dalitz-plot\npositions are known.\nConsider an event that is generated with Dalitz-plot\ncoordinate mt. The probability that this event passes the\nselection criteria is given by the e\ufb03ciency as a function of\nthe true position, \u03b5 (mt). If the event is selected then there\nis a further chance that it is misreconstructed. Since such\nmisreconstructions are dependent on the kinematic con\ufb01g-\nuration, this probability is also a function of the true posi-\ntion, fMR (mt). The resulting migration probability from\ntrue coordinate mt to the reconstructed one, mr, can be\ndescribed by the four-dimensional function RMR (mr, mt),\nwhich obeys the unitary condition\nZ Z\nRMR\n\u0000mr, mt\u0001\ndmr = 1 \u2200mt .\n(13.3.1)\nConsequently, for an event reconstructed at mr the\nprobability for it to be a well-reconstructed signal event is\nP WR\nsig\n\u221d[1 \u2212fMR(mr)] \u03b5(mr) |A(mr)|2 ,\n(13.3.2)\nwhile the corresponding probability for a misreconstructed\nsignal event is\nP MR\nsig\n\u221d\nZ Z\nfMR\n\u0000mt\u0001\n\u03b5\n\u0000mt\u0001 \f\fA\n\u0000mt\u0001\f\f2 \u00d7\nRMR\n\u0000mr, mt\u0001\ndmt .\n(13.3.3)\nTypically, this integration is implemented as a summation\nover binned distributions. Therefore, it is essential to in-\nclude factors that account for the amount of phase space\ncontained within each bin in both the generated and re-\nconstructed histograms.\n13.4 Technical details\nThis part of the chapter describes various technical issues\nnot related to the physics processes involved, but aimed\nto improve or simplify analyses or presentation of their re-\nsults. These include the square Dalitz plot transformation\n(Section 13.4.1), various parameterizations of the complex\ncoe\ufb03cients for amplitude components (Section 13.4.2), \ufb01t-\nting techniques (Section 13.4.3), and the concept of \ufb01t\nfractions, which are used in the presentation of \ufb01t results\n(Section 13.4.4).\n13.4.1 Square Dalitz plot\nA common feature of Dalitz-plot analyses of B-meson de-\ncays to charmless \ufb01nal states is that both the signal events\nand the combinatorial e+e\u2212\u2192qq (q = u, d, s, c) contin-\nuum background events populate the kinematic bound-\naries of the Dalitz plot. This is due to the low masses of\nthe \ufb01nal state particles compared with the B mass. Large\nvariations occurring over small areas of the Dalitz plot\nare di\ufb03cult to describe in detail. As a result, the typi-\ncal representation of the Dalitz plot may be inconvenient\nwhen using empirical reference shapes in a maximum-\nlikelihood \ufb01t. The boundaries of the Dalitz plot are par-\nticularly important since it is here that the interference\nbetween light meson resonances occurs. These are the re-\ngions with the greatest sensitivity to relative phases. A\nsolution that was adopted by some analyses is to apply a\ntransformation to the kinematic variables that maps the\n\n156\nDalitz plot into a rectangle: the so-called square Dalitz plot\n(SDP). Such a transformation avoids the curved kinematic\nboundary, which simpli\ufb01es the use of nonparametric p.d.f.s\n(histograms) to model the distribution of events over the\nDalitz plot. Moreover, the transformation is required to\nexpand the regions of interference and simplify parame-\nterization; for instance, the Dalitz plot can be tiled by\nequally sized bins.\nA common de\ufb01nition of the SDP \ufb01rst appeared in the\nanalysis of B+ \u2192\u03c0+\u03c0+\u03c0\u2212by BABAR (Aubert, 2005d),\nwhere the SDP is obtained by the transformation:\ndm2\nab dm2\nbc \u2212\u2192| det J| dm\u2032 d\u03b8\u2032.\n(13.4.1)\nThe new coordinates are\nm\u2032 \u22611\n\u03c0 arccos\n\u0012\n2 mac \u2212mmin\nac\nmmax\nac\n\u2212mmin\nac\n\u22121\n\u0013\n,\n(13.4.2)\n\u03b8\u2032 \u22611\n\u03c0 \u03b8ac ,\n(13.4.3)\nwhere mmax\nac\n= M \u2212mb and mmin\nac\n= ma + mc are the\nkinematic limits of mac, \u03b8ac is the helicity angle of the ac\ncombination, and J is the Jacobian of the transformation.\nBoth new variables range between 0 and 1. The determi-\nnant of the Jacobian is given by\n| det J| = 4 |p\u2217\na||p\u2217\nb| mac \u00b7 \u2202mac\n\u2202m\u2032 \u00b7 \u2202cos \u03b8ac\n\u2202\u03b8\u2032\n,\n(13.4.4)\nwhere |p\u2217\na| =\np\nE\u2217a \u2212m2a, |p\u2217\nb| =\np\nE\u2217\nb \u2212m2\nb, and the en-\nergies are de\ufb01ned in the ac rest frame. Figure 13.4.1 shows\nthe determinant of the Jacobian as a function of the SDP\nparameters m\u2032 and \u03b8\u2032. If the events in the nominal Dalitz\nplot were distributed according to a uniform three-body\nphase space, their distribution in the SDP would match\nthe plot of | det J|.\nThe e\ufb00ect of the transformation, Eq. (13.4.1), is illus-\ntrated in Fig. 13.4.2, which shows the nominal and square\nDalitz plots for Monte Carlo simulated B0 \u2192\u03c0+\u03c0\u2212\u03c00\nsignal events, where the Dalitz-plot model contains only\n\u03c1+\u03c0\u2212, \u03c1\u2212\u03c0+, and \u03c10\u03c00 amplitudes. The bene\ufb01ts of the\nSDP explained above are clearly visible in this \ufb01gure. This\nsimulation does not take into account any detector e\ufb00ects\nand corresponds to a particular choice of the decay ampli-\ntudes for which destructive interferences occur in regions\nwhere the \u03c1 resonances overlap. To simplify the compar-\nison, hatched areas showing the interference regions be-\ntween \u03c1 bands and dashed isocontours mij = 1.5 GeV/c2\nhave been superimposed on both Dalitz plots.\nAnother transformation of the phase space was used in\nthe recent BABAR amplitude analysis of B0 \u2192K0\nSK0\nSK0\nS\ndecays (Lees, 2012c). In this particular case, due to the\npresence of identical particles in the \ufb01nal state, symme-\ntrization of the amplitude under exchange of the identical\nparticles is required. The square Dalitz plot transforma-\ntion described above would result in curved boundaries.\nOn the other hand, mapping the invariant masses to the\nplane de\ufb01ned by two helicity angles results in a rectangle.\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n100\n200\n300\n400\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n100\n200\n300\n400\ne'\nm'\nFigure 13.4.1.\nJacobian determinant, Eq. (13.4.4), of the\ntransformation, Eq. (13.4.1), de\ufb01ning the square Dalitz plot\n(SDP). Such a distribution would be obtained in the SDP if\nevents were uniformly distributed over the nominal Dalitz plot.\n13.4.2 Complex coe\ufb03cients\nThe complex coe\ufb03cients of each contribution to the ampli-\ntude are expressed in Eq. (13.2.1) in terms of a magnitude\nand a phase,\ncr = arei\u03c6r ,\n(13.4.5)\nwhich is arguably the most intuitive formulation. However,\nit is also possible to use the real and imaginary parts as\nthe \ufb01t parameters\ncr = xr + iyr .\n(13.4.6)\nThis latter form has the advantage that the parameters\nare well behaved when the magnitude of the contribution\nis small, while the former expression can exhibit biases\nunder these circumstances. One caveat is that, conversely,\nwhen the magnitude is large the latter form can appear\nto exhibit bias. Since the magnitude of a contribution is,\nin general, better constrained than the phase, the \ufb01tted\nvalues from a group of pseudo experiments tend to lie on\nan arc in the complex plane. When projecting this arc\nonto the real and imaginary axes the distributions can\nappear skewed. This behavior is not generally indicative\nof a true bias in the \ufb01t; indeed the distributions of the\nmagnitudes and phases (calculated from the \ufb01tted xr and\nyr parameters) can be perfectly centered on the true val-\nues. However, care should be taken when interpreting the\nerrors on the \ufb01t parameters due to their large correlation.\nThe choice of formulations is much broader when para-\nmetrizing CP violation. Perhaps the simplest approach is\nto assign the B (or D) one set of parameters and the B\n(or D) another set\ncr = arei\u03c6r\n(13.4.7)\n\u00afcr = \u00afarei \u00af\u03c6r ,\n\n157\n0\n5\n10\n15\n20\n25\n30\n0\n5\n10\n15\n20\n25\n30\nm2(/+/0) (GeV/c2)2\nm2(/\u2013/0) (GeV/c2)2\n0\n1\n2\n3\n4\n5\n22\n23\n24\n25\n26\n27\nB0A /+/\u2013/0 (kin.)\ninterference regs.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nm'\ne'\ninterference regions\nm(l0) = 1.5 GeV/c2\nm(l+) = 1.5 GeV/c2\nm(l\u2013) = 1.5 GeV/c2\nFigure 13.4.2. Nominal (left) and square (right) Dalitz plots for Monte Carlo generated B0 \u2192\u03c0+\u03c0\u2212\u03c00 decays (Aubert, 2007v).\nThe comparison of the two Dalitz plots shows that the transformation, Eq. (13.4.1), indeed homogenizes the distribution of\nevents, which are no longer near the plot boundaries but rather cover a larger fraction of the physical region. The decays\nhave been simulated without any detector e\ufb00ects and the three \u03c1\u03c0 amplitudes have been chosen in order to have destructive\ninterference where the \u03c1 bands overlap. The main overlap regions between the \u03c1 bands are indicated by the hatched areas.\nDashed lines in both plots correspond to mij = 1.5 GeV/c2.\nor\ncr = xr + iyr\n(13.4.8)\n\u00afcr = \u00afxr + i\u00afyr .\nAlternatively, one can use sets of CP-conserving and CP-\nviolating parameters, such as those used in the BABAR\nanalysis of B+ \u2192K+\u03c0+\u03c0\u2212(Aubert, 2008j)\ncr = (xr + \u2206xr) + i(yr + \u2206yr)\n(13.4.9)\n\u00afcr = (xr \u2212\u2206xr) + i(yr \u2212\u2206yr) ,\nor those used in the Belle analysis of the same decay (Gar-\nmash, 2006)\ncr = arei\u03b4r \u00001 + bjei\u03c6j\u0001\n(13.4.10)\n\u00afcr = arei\u03b4r \u00001 \u2212bjei\u03c6j\u0001\n,\nor those used in the CLEO analysis of D0 \u2192K0\nS\u03c0+\u03c0\u2212(As-\nner et al., 2004b)\ncr = arei(\u03b4r+\u03c6r)\n\u0012\n1 + bj\naj\n\u0013\n(13.4.11)\n\u00afcr = arei(\u03b4r\u2212\u03c6r)\n\u0012\n1 \u2212bj\naj\n\u0013\n.\nEach of these formulations has advantages and disadvan-\ntages. For example, there can be ambiguities in the phases\nin the CLEO prescription. While the formulation in terms\nof real and imaginary parts is generally better behaved\nwhen the magnitude of the CP violation is small, it is less\nintuitive in terms of interpretation of the results. Hence it\nis advisable to try several forms and to choose that which\nbest suits the particular measurement being attempted.\n13.4.3 Fitting\nOnce the model of the Dalitz-plot distribution has been\nformed for all event categories (signal and backgrounds)\nit is necessary to \ufb01t the data to determine the values of\nthe parameters of the model. This is generally achieved\nusing the technique of maximum-likelihood \ufb01tting, which\nis discussed in detail in Chapter 11. As such, only the\ndetails speci\ufb01c to Dalitz-plot analyses will be discussed\nhere. Both binned and unbinned \ufb01ts are used, the former\nbeing more common in the analysis of charm decays where\nthe signal yields and purities are greater.\nOne of the key issues is the normalization of the signal\nDalitz-plot p.d.f.. There is, in general, no analytic solu-\ntion to the integral of such a function and so numerical\ntechniques must be employed. The two most commonly\nused approaches are Monte Carlo and Gauss-Legendre es-\ntimation. When a Dalitz-plot model contains narrow reso-\nnances such as \u03c6(1020) or \u03c7c0, it can be useful to perform\nan integration with higher resolution in the region of those\nstructures. This can involve dividing the Dalitz plot into a\nnumber of regions, performing the integration with di\ufb00er-\nent resolutions in each region, and \ufb01nally combining the\nresults.\nSince the calculation of the normalization integrals can\nbe computationally expensive, it is desirable to calculate\nthem only once and to cache the values for later use. From\nEq. (13.2.1), it is clear that while the complex coe\ufb03cients\nfactorize from the integral, the parameters of the reso-\nnance dynamics, e.g., the mass and width, do not. It is\nthus possible to cache the integrals only if the parameters\n\n158\nof the resonances are \ufb01xed in the \ufb01t. Under these circum-\nstances, the integrals of each of the ArA\u22c6\nr\u2032 terms can be\ncalculated prior to the \ufb01t. The p.d.f. normalization can\nthen be calculated by combining these cached terms and\nthe current values of the complex coe\ufb03cients at each iter-\nation of the \ufb01t. Consequently, it is a common procedure to\n\ufb01x the resonance parameters in the \ufb01t. Where necessary,\nlikelihood scans are used to determine the values of any\nless well-known parameters.\nDue to the complexity of the likelihood function and\nthe large numbers of parameters involved in Dalitz-plot\n\ufb01ts it is quite common for several local minima to ap-\npear in the parameter space. This can cause problems for\nthe minimization routine in \ufb01nding the global minimum.\nIn addition, these local minima can be almost degenerate\nwith the global minimum, leading to the need to quote\nmultiple solutions. This can occur, for example, when am-\nbiguities arise from broad overlapping states. The data\ncan often be well described by two or more con\ufb01gurations\nof the magnitudes and phases of these states. The prob-\nlem of \ufb01nding the global minimum is usually overcome\nby performing multiple \ufb01ts to a given data sample, each\nwith di\ufb00erent (often randomized) starting values for the\nvarious parameters. One can then choose the case where\nthe best likelihood was obtained as the global solution.\nThis method also permits the exploration of the other lo-\ncal minima, which allows the results from other solutions\nto be quoted if they are not signi\ufb01cantly separated in like-\nlihood from the global minimum.\n13.4.4 Fit fractions\nThe choice of normalization, phase convention, and am-\nplitude formalism may not always be the same for dif-\nferent experiments or indeed among the di\ufb00erent \ufb01tting\npackages used within a single experiment. Consequently,\nit is extremely important to provide as much convention-\nindependent information as possible to allow a more mean-\ningful comparison of results. Fit fractions are quite com-\nmonly used, both for this purpose and for providing a\nmeans to estimate the branching fractions of the various\ndecay modes involved. The \ufb01t fraction for a component j\nis de\ufb01ned as the integral of the square of the decay am-\nplitude for that component divided by the integral of the\nsquare of the entire matrix element over the Dalitz plot:\nFF j =\nRR\nDP |cjAj(m)|2 dm\nRR\nDP |P\nk ckAk(m)|2 dm\n.\n(13.4.12)\nSimilarly, the \ufb01t fraction for the conjugate process is de-\n\ufb01ned to be:\nFF j =\nRR\nDP\n\f\fcjAj(m)\n\f\f2 dm\nRR\nDP\n\f\fP\nk ckAk(m)\n\f\f2 dm\n.\n(13.4.13)\nFurthermore, the \ufb01t fraction asymmetry is de\ufb01ned to be\nAFF\nj\n= FF j \u2212FF j\nFF j + FF j\n,\n(13.4.14)\nand the CP-conserving (CP-violating) \ufb01t fraction is given\nby the sum (di\ufb00erence) of the numerators of Eq. (13.4.12)\nand Eq. (13.4.13) divided by the sum of the denomina-\ntors of the same equations. These de\ufb01nitions follow those\nin Asner et al. (2004b). Note that the sum of the \ufb01t frac-\ntions is not necessarily unity due to the presence of net\nconstructive or destructive interference.\nWhile the \ufb01t fractions can be very useful in comparing\nresults for a given channel, there is additional information\nin the interference between the contributing decay modes.\nIn order to allow such comparisons one can de\ufb01ne inter-\nference \ufb01t fractions by (del Amo Sanchez, 2010a)\nFF ij =\nRR\nDP 2Re\n\u0002\ncic\u2217\njAi(m)A\u2217\nj(m)\n\u0003\ndm\nRR\nDP |P\nk ckAk(m)|2 dm\n,\n(13.4.15)\nfor i < j only. Note that, with this de\ufb01nition, FF jj =\n2FF j.\n13.5 Model uncertainties\nWhile most of the experimental uncertainties in the mea-\nsurements involving Dalitz-plot analyses can, in princi-\nple, be controlled with Monte Carlo simulation and con-\ntrol samples, there is an essential contribution to the sys-\ntematic error which is usually hard to quantify. This is\nthe uncertainty on the amplitude arising from model as-\nsumptions in its description. This section will describe the\npossible sources of model uncertainties and outline some\nmethods by which they can be estimated (Section 13.5.1),\nbefore discussing the various approaches towards model-\nindependent analysis that have been adopted by the B\nFactories (Sections 13.5.2 and 13.5.3 ).\n13.5.1 Estimation of model uncertainties\nThe sources of model uncertainty and common methods\nto estimate them are listed below.\n\u2013 Isobar description:\nThe isobar formalism is valid only in the case of nar-\nrow and non-overlapping resonances, otherwise the uni-\ntarity of the amplitude is violated. In contrast, most of\nthe Dalitz-plot analyses have to deal with wide states\nthat interfere with each other. If the use of the isobar\nmodel is not implied by the nature of the measurement,\nmore accurate results can be obtained (or at least, the\nuncertainty due to the use of the isobar description can\nbe quanti\ufb01ed) by using an alternative approach, such\nas the K-matrix.\n\u2013 Lineshapes of two-body amplitudes:\nReasonable theoretical description of broad resonances\nrequires corrections to be applied to the Breit-Wigner\nlineshape, discussed in Section 13.2. Those corrections\n(i.e. Blatt-Weisskopf form factors and mass-dependent\nwidths) depend on a number of poorly constrained pa-\nrameters, such as radial parameters of the decaying\nparticle and intermediate resonances. The uncertainty\n\n159\ndue to these parameters can be estimated by variation\nwithin their errors, if known, or otherwise within some\nreasonable range.\n\u2013 Identi\ufb01cation of intermediate states:\nWhile the presence of narrow states is usually appar-\nent, some broad states can be misinterpreted as re-\n\ufb02ections of other two-body channels or as nonresonant\nstructures. In addition, a good description of the am-\nplitude requires that broad states beyond the kinemat-\nically allowed region of phase space are properly ac-\ncounted for. Thus, the model uncertainty estimation\noften involves variation of the list of intermediate res-\nonances.\n\u2013 Parameters of the intermediate states:\nUncertainty due to the \ufb01nite precision on, for example,\nthe masses and widths of resonances, can be evaluated\nin a straightforward way by varying the parameters\nwithin their errors.\n\u2013 Uncertainty of the nonresonant amplitude:\nA range of di\ufb00erent parameterizations of the nonreso-\nnant amplitude is available. Analyses involving D de-\ncays, where the phase space of the decay is reasonably\nsmall, often parameterize the nonresonant amplitude\nwith the constant complex term, while in B decays\nmore complicated parameterizations, discussed in Sec-\ntion 13.2.3, are necessary. Comparison of the \ufb01t results\nwhen using alternative parameterizations can give an\nestimate of the associated uncertainty.\n13.5.2 Model-independent analysis\nSome applications of Dalitz-plot analyses require a model\ndescription of the amplitude, such as searches for interme-\ndiate states and measurements of their parameters. Other\napplications need only that the three-body amplitude (or\npart of it) is described as a certain function of the phase\nspace variables. In the latter case, the model-independent\n(MI) Dalitz-plot analysis is a possible option. Below we\ngive two examples of MI approaches: binned analysis and\nMI partial-wave analysis.\nOne example of the type of analysis that does not re-\nquire a model description of the amplitude is the search for\nCP violation in the three-body decays of B or D mesons.\nWhile the CP asymmetry integrated over the phase space\ncan be small, the local asymmetries in some areas of the\nphase space can be signi\ufb01cant. The understanding of these\nlocal asymmetries requires a Dalitz-plot analysis. On the\nother hand, establishing the existence of CP violation does\nnot require a full amplitude analysis. One can therefore di-\nvide the phase space into a large number of bins and search\nfor asymmetries in the number of events reconstructed in\neach bin (Bediaga et al., 2009). The drawback of such an\napproach is that if CP violation is observed, its interpre-\ntation will require a full amplitude analysis.\nThere is, however, a quantitative measurement that\nuses a model-independent binned Dalitz-plot analysis ap-\nproach \u2014 it is the measurement of the angle \u03c63 in B \u2192\nDK, D \u2192K0\nS\u03c0\u03c0 decays. In this measurement, the Dalitz-\nplot analysis is a tool to obtain the parameters of the\nadmixture of D0 and D0 states: their relative amplitude\nand phase di\ufb00erence. This is possible in the binned ap-\nproach. The average amplitude and D0 \u2212D0 strong phase\ndi\ufb00erence over the bin is described by a few coe\ufb03cients.\nThe analysis of the binned D \u2192K0\nS\u03c0\u03c0 Dalitz plot from\nB \u2192DK allows the extraction of \u03c63 once the amplitude\ncoe\ufb03cients are known. These coe\ufb03cients can be extracted\nfrom other measurements: \ufb02avor-tagged D0 \u2192K0\nS\u03c0\u03c0 de-\ncays, and quantum-correlated decays of pairs of D mesons\nfrom e+e\u2212\u2192\u03c8(3770) \u2192D0D0 processes. This analysis,\nperformed by the Belle collaboration (Aihara, 2012) using\nthe strong phase parameters measured by CLEO (Libby\net al., 2010), is described in detail in Section 17.8.\n13.5.3 Model independent partial wave analysis\nAnother kind of model-independent Dalitz-plot analysis is\npossible in cases when the data sample is large: the (quasi)\nmodel-independent partial wave analysis (MI-PWA). The\nbasic idea behind MI-PWA is that most of the model un-\ncertainty in Dalitz-plot analyses usually comes from the\nscalar component. One can deal with the scalar compo-\nnent in a model-independent way while keeping the model\ndescription for the rest of the amplitude. The scalar com-\nponent can be parameterized as\nA0(s) = f(s)ei\u03c6(s) ,\n(13.5.1)\nwhere the functions f(s) and \u03c6(s) are de\ufb01ned by interpo-\nlation of the values fj and \u03c6j in each bin j. The values fj\nand \u03c6j are treated as free parameters in the amplitude \ufb01t.\nThe interference with the non-scalar (reference) part of\nthe amplitude allows one to obtain not only the absolute\nvalue of the scalar amplitude, but also its phase as a func-\ntion of s. The MI-PWA analysis was proposed in the E791\ncollaboration (Aitala et al., 2006) and used by BABAR for\nthe analysis of the D+\ns \u2192\u03c0+\u03c0\u2212\u03c0+ Dalitz plot (Aubert,\n2009i).\nIn cases where the size of the data sample is insu\ufb03cient\nto use a full MI-PWA, it is still possible to study the con-\ntributions of each partial wave using an angular-moments\nanalysis. This can then inform the choice of model to be\nused. Such an approach can be highly informative when\na number of overlapping contributions are present. A re-\ncent example of this approach is the BABAR analysis of\nB \u2192KKK decays (Lees, 2012y).\n\n160\nChapter 14\nBlind analysis\nEditors:\nAaron Roodman (BABAR)\nAlan Schwartz (Belle)\nIn developing an analysis, it is important not to opti-\nmize the analysis procedure on the data that will be used\nfor the measurement (known colloquially as \u201ctuning on\nthe data\u201d). This point is discussed above in Section 4.\nIn this chapter we discuss the method of a blind analysis,\nwhich aims to exclude the possibility of even unintentional\noptimization based on the data. Blind analyses have be-\ncome widespread in particle physics in recent years, and\nthe blind analysis method has been used extensively at the\nB Factories. Some of the jargon of blind analyses (\u201copen-\ning the box\u201d for a measurement) has also entered into\nwidespread use, even for measurements that are not blind\nanalyses in the strict sense; there has been an increased\nawareness of the general requirement to avoid tuning on\nthe data.\nHere we present the blind analysis method, introduc-\ning its de\ufb01nition and history (Section 14.1), and giving\npedagogical examples for the cases of upper limits (Sec-\ntion 14.2) and precision measurements (Section 14.3). We\nthen provide some examples of the use of the method at\nBelle (Section 14.4) and BABAR (Section 14.5). For an in-\ndepth discussion of the blind analysis method, see the re-\nview article by Klein and Roodman (2005).\n14.1 De\ufb01nition and brief history\nA blind analysis is a measurement such as that of a branch-\ning fraction or upper limit that is performed without look-\ning at the data result until most or all analysis criteria are\n\ufb01nalized. The purpose is to eliminate the possibility of an\nexperimenter biasing the result in a particular direction.\nFor example, if all previous measurements of a parameter\nhad obtained positive values, then one might be tempted\nto keep adjusting analysis criteria until a positive value\nis obtained. This, however, yields a result biased positive.\nAn early example of a blind analysis is the measurement\nof the e/m ratio of the electron performed by Dunnington\n(1933). In this measurement, the e/m value was propor-\ntional to the angle between the electron source and the\ndetector. Dunnington asked his machinist to arbitrarily\nlabel this angle around 340\u25e6; only when the analysis was\ncompleted did Dunnington accurately measure this angle\nto obtain the \ufb01nal result.\nWithin high energy physics, the blind analysis tech-\nnique was motivated by a number of positive results\nthat were later found to be due to faulty analysis meth-\nods (for examples see Harrison (2002)). It was originally\nchampioned by rare kaon decay experiments running at\nBrookhaven National Laboratory (BNL) in the mid-1980s.\nProbably the \ufb01rst experiment to use this technique was\nBNL E791 (Arisaka et al., 1993), which searched for the\nforbidden decay K0\nL \u2192\u00b5\u00b1e\u2213. The experiment de\ufb01ned\na signal region in two kinematic variables, the \u00b5\u00b1e\u2213in-\nvariant mass (M\u00b5e) and the K0\nL candidate\u2019s transverse\nmomentum squared (P 2\nT ). The signal region was subse-\nquently \u201cblinded,\u201d i.e., events falling within this region\nwere not selected for viewing, while all selection criteria\nwere \ufb01nalized. Only after these criteria were \ufb01nalized was\nthis region unblinded and signal events counted. A simi-\nlar technique was used by BNL E787 (Adler et al., 1996),\nwhich searched for the rare decay K+ \u2192\u03c0+\u03bd\u03bd, and by\nBNL E888 (Belz et al., 1996a,b), which searched for a long-\nlived H dibaryon. The method was subsequently adopted\nby the Fermilab KTeV experiment (Alavi-Harati et al.,\n1999), which measured \u03f5\u2032/\u03f5 in the K0-K0 system; Fermi-\nlab E791 (Aitala et al., 1999b, 2001a), which measured\nrare/forbidden D meson decays; and the CERN NOMAD\nexperiment (Astier et al., 1999), which searched for neu-\ntrino oscillations.\nAs mentioned, the principle of a blind analysis is to\nnot look at potential signal events before \ufb01nalizing anal-\nysis criteria in order to avoid biasing the result. There\nare three main types of measurements this applies to: set-\nting an upper limit, in which one wants to avoid selection\ncriteria that bias one against signal events; measuring a\nbranching fraction, in which one wants to avoid selections\nthat bias one against background events (this can \u201csculpt\u201d\na signal peak); and precision measurements such as that\nof measuring mixing or CP-violation parameters, in which\none wants to avoid selections or \ufb01tting procedures that\nbias the result in a preferred direction. Some general exam-\nples of these cases are discussed below, followed by speci\ufb01c\nexamples from Belle and BABAR. Not every measurement\nrequires a blind analysis: usually when one searches for\nnew particles and does not know a priori where to look,\none inspects relevant distributions in an unblind manner.\nHowever, one still must be careful not to adjust selection\ncriteria to increase or decrease the signal yield while look-\ning at the signal events for feedback. A blind analysis is\ntypically more time-consuming than an unblind one and,\nin the case of setting an upper limit, can produce a poor\nresult (see below).\n14.2 Setting upper limits: a quantitative\nexample\nAn upper limit can become biased when one searches for\na decay that is not expected to occur and observes one\nor more signal candidates; one tends to assume they are\nbackground and tighten one or more selection cuts to elim-\ninate them. The problem with this procedure is that one\nmay eliminate a real signal event, in which case the upper\nlimit obtained for the rate of the rare process is biased low\nand has statistical undercoverage.\nTo illustrate this bias quantitatively, consider the fol-\nlowing example. An ensemble of 1000 identical experi-\nments search for the rare decay D \u2192X, which we postu-\nlate to have a branching fraction of 2.5 \u00d7 10\u22125. If the ex-\nperiments have a single-event-sensitivity (S.E.S.) of 1.0 \u00d7\n\n161\n10\u22125, then the expected number of observed events is 2.5\n(The S.E.S. of an experiment is the branching fraction\nthat would produce, given the experiment\u2019s data set and\ne\ufb03ciency, an average over a statistical ensemble of one\ndetected event). From Poisson statistics for \u00b5 = 2.5, we\ncalculate that the ensemble obtains the following results:\n\u2013 about 82 experiments observe no events;\n\u2013 about 205 experiments observe one event;\n\u2013 about 257 experiments observe two events;\n\u2013 the remainder, about 456 experiments, observe \u22653\nevents.\nFor simplicity we assume that the experiments observe no\nbackground (this is typically the case for rare K and \u03c4 de-\ncay searches). This assumption does not change our \ufb01nal\nconclusions. The experiments that observe no events will\nset a 90% C.L. upper limit of 2.30 times the S.E.S. [see\nSection 36.3.2.5 and Table 36.3 of Beringer et al. (2012)]\nor 2.30 \u00d7 10\u22125, which is below the true value. The experi-\nments observing one, two, three, etc., events will set upper\nlimits of 3.89, 5.32, 6.68, etc., times the S.E.S., which are\nabove the true value. In this manner 8.2% of experiments\nobtain \u201cincorrect\u201d upper limits, which is less than 10% of\nthe ensemble and thus consistent with the de\ufb01nition of a\n90% C.L. limit.\nNow suppose that each experiment that observed events\nlooks at their candidate(s) and that some \ufb01nd a kinematic\nor particle identi\ufb01cation variable (for at least one of the\ncandidates) that is more than 2\u03c3 away from the value ex-\npected for a signal event. These experiments then impose\na 2\u03c3 cut on that variable to eliminate the event(s) and ad-\njust the S.E.S. upwards to account for the 4.6% loss in sen-\nsitivity. However, if up to 20 variables are potentially con-\nsidered to be cut on, then the chance of an event surviving\nthis procedure is only (0.9545)20 = 0.394. Therefore, af-\nter experiments observing events adjust a single cut value,\napproximately 82 + (1 \u22120.394)(205) + [1 \u2212(0.394)2](1 \u2212\n0.954)(257) = 216 experiments observe no events and set\nan upper limit of either 2.30 \u00d7 10\u22125 (no events originally\nobserved) or 2.30\u00d7(S.E.S.)/0.954 = 2.41\u00d710\u22125. Both lim-\nits are below the true value. The fraction of experiments is\n22%, which is larger than 10% and thus inconsistent with\nthe de\ufb01nition of a 90% C.L. limit. The bias of the pro-\ncedure has resulted in undercoverage. To avoid such bias,\nthe decision whether to cut on a variable or not must be\nmade before looking at signal candidate events.\nWhile a blind analysis does yield unbiased upper lim-\nits, it has a serious drawback in that it is possible to miss\nan obvious background, observe a large number of events\nin the signal region, and end up setting a poor upper limit.\nThis situation does a disservice to the experiment, as the\nfull \u201cdiscriminating power\u201d of the detector has not been\nutilized. Thus in practice, experiments carefully study sig-\nnal candidates after all cuts have been \ufb01nalized to check\nwhether there are any due to a trivial background or in-\nstrumental problem such as the high voltage having been\ntripped o\ufb00. If such events are found, it usually is prefer-\nable to eliminate them and set a biased but useful upper\nlimit rather than leave them and set an unbiased but not\nuseful limit.\nHere we have discussed only bias introduced in the sig-\nnal acceptance, not bias potentially introduced when esti-\nmating backgrounds. The latter depends upon the back-\nground sample used and the method of estimation. For ex-\nample, if one is estimating background by counting events\nin a sideband and extrapolating, then to avoid bias one\nmust blind that part of the sideband used to estimate\nbackground when \ufb01nalizing cuts, or at least not \u201ctune\u201d\ncuts to explicitly remove events from that sideband re-\ngion.\n14.3 Precision measurements\nFor precision measurements of parameters in which one\ntypically performs a \ufb01t rather than simply counts events,\na di\ufb00erent technique for avoiding bias must be used. In this\ncase hiding the answer is often the appropriate method.\nFor example, the KTeV experiment used this technique\nfor its measurement of \u03f5\u2032/\u03f5. The value of \u03f5\u2032/\u03f5 was obtained\nfrom a \ufb01t to the data, and to avoid bias KTeV inserted\nan unknown o\ufb00set into the \ufb01tting program such that the\n\ufb01t yielded the \u201chidden\u201d value\n\u0012\u03f5\u2032\n\u03f5\n\u0013\nhidden\n\u2261\n\u001a\n+1\n\u22121\n\u001b\n\u00d7\n\u0012\u03f5\u2032\n\u03f5\n\u0013\ntrue\n+ c .\n(14.3.1)\nIn this expression, c is a hidden random constant, and\nthe choice of the factor \u00b11 is also hidden. The values of\nc and \u00b11 were made by a pseudo-random number gener-\nator. Thus KTeV could \ufb01nalize its data samples, analysis\ncuts, Monte-Carlo corrections, and \ufb01tting technique while\nremaining una\ufb00ected by the (hidden) true value of \u03f5\u2032/\u03f5.\nThe use of the factor \u00b11 prevented KTeV from knowing\nthe direction in which the result moved as changes to the\nanalysis were applied.\nWhen performing a blind analysis using the \u201chidden\nanswer\u201d technique, one must consider whether there exists\n\ufb01gures, tables, or other ancillary results that could inad-\nvertently reveal the blinded result. Only if the measure-\nment result is not readily apparent from such information\nshould the \ufb01gure, table, etc. be presented.\n14.4 Examples from Belle\nThe Belle experiment used blind analysis methods exten-\nsively: in measuring branching fractions, CP asymmetries,\nin \ufb01tting Dalitz plots, and in searching for rare and for-\nbidden decays. Only after selection criteria and the \ufb01tting\nprocedure were \ufb01nalized, and the background estimated,\nwere the results unblinded. To unblind a result required\napproval from one\u2019s internal review committee. If a com-\nmittee member felt that more studies were needed before\nunblinding, then the analyzer could not proceed. If an\nanalysis was an update to a previous Belle result, then\nbefore unblinding the analyzer was usually required to\nrun his/her analysis code on the previous data set used\nand compare the result obtained with that obtained pre-\nviously. If there were a discrepancy, it had to be under-\nstood before continuing. After unblinding, the only steps\n\n162\nremaining in the analysis were \ufb01nalizing the systematic er-\nrors and, occasionally, re\ufb01ning the background estimate.\nThis methodology yielded unbiased results but also oc-\ncasional surprises such as:\n\u2013 signi\ufb01cant direct CP violation in B0 \u2192K+\u03c0\u2212de-\ncays (Chao, 2004);\n\u2013 large direct CP violation in B0 \u2192\u03c0+\u03c0\u2212decays, and\nvalues of CP parameters C\u03c0\u03c0 and S\u03c0\u03c0 outside the\nphysical region (Abe, 2004b, 2005b);\n\u2013 the value of sin 2\u03c61 and CP asymmetries measured in\nb \u2192sqq transitions such as B0 \u2192\u03c6K0\nS and B0 \u2192\nf0(980)K0\nS di\ufb00ered substantially from that expected\nbased on measurements of the b \u2192ccs transition B0 \u2192\nJ/\u03c8K0\nS (Chen, 2005b); and\n\u2013 the branching fraction for B+ \u2192\u03c4 +\u03bd measured with\n414 fb\u22121 was much larger than that expected based\non the value of |Vub| determined from B semileptonic\ndecays (Ikado, 2006).\nA typical example of a blind analysis is a search for the\nlepton-number-violating decays \u03c4 \u2212\u2192\u00b5\u2212V 0 and \u03c4 \u2212\u2192\ne\u2212V 0, where V 0 is a neutral vector meson \u03c10, \u03c6, \u03c9, or\nK\u22170 (Miyazaki, 2011). These mesons were reconstructed\nvia \u03c10 \u2192\u03c0+\u03c0\u2212, \u03c6 \u2192K+K\u2212, \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00, and K\u22170 \u2192\nK+\u03c0\u2212. The analysis selected candidate events based on\nthe variables M\u2113V and \u2206E, where M\u2113V is the invariant\nmass of the \u2113\u2212V 0 pair (\u2113= e, \u00b5), and \u2206E is the di\ufb00erence\nin energy between the \u2113\u2212V 0 system and the beam energy\nin the e+e\u2212center-of-mass frame. Events were \ufb01rst se-\nlected by dividing the reconstructed tracks and calorime-\nter hits for each event into two azimuthal hemispheres and\nrequiring that, in one of the hemispheres, there be only a\nsingle track. This topology corresponds to a \u03c4 \u2212\u2192\u2113\u2212\u03bd\u03bd,\n\u03c4 \u2212\u2192\u03c0\u2212\u03bd, or \u03c4 \u2212\u2192\u03c1\u2212(\u2192\u03c0\u2212\u03c00)\u03bd decay; the presence of\nthis \u201ctagging\u201d decay indicates e+e\u2212\u2192\u03c4 +\u03c4 \u2212production.\nFrom this tagged sample, events were selected that\nhave three tracks in the \u201csignal hemisphere\u201d. Two of the\ntracks were required to reconstruct to a \u03c10, \u03c6, \u03c9, or K\u22170\nmeson and satisfy particle identi\ufb01cation criteria. The third\ntrack was required to satisfy muon or electron identi\ufb01ca-\ntion criteria. At this point an elliptical signal region in the\nM\u2113V -\u2206E plane was blinded while topological and kine-\nmatic selection criteria were optimized using MC-simulated\nevents and applied. The blinded signal ellipse was centered\nnear M\u2113V = m\u03c4 and \u2206E = 0 and had semi-major and\nsemi-minor axes equal to 3\u03c3 in resolution.\nAfter the cut optimization procedure, the background\nin the signal region was estimated by extrapolating from\nthe number of events observed in a larger M\u2113V -\u2206E region\nsurrounding the blinded ellipse. The backgrounds ranged\nfrom 0.06 to 1.5 events. After selection criteria were \ufb01-\nnalized and the backgrounds estimated, the signal regions\nwere unblinded and the signal yields obtained. The results\nfor four modes are shown in Fig. 14.4.1. From the observed\nsignal yields along with the background estimates, recon-\nstruction e\ufb03ciencies, and systematic uncertainties, upper\nlimits were calculated using a frequentist approach (Con-\nrad, Botner, Hallgren, and Perez de los Heros, 2003).\nIt should be noted that in performing a blind analysis\none doesn\u2019t have to rely solely on the simulated data. Any\n-0.4\n-0.2\n0\n0.2\n1.7\n1.8\nM\u00b5l (GeV/c2)\n6E (GeV)\n(a) oA\u00b5l\n-0.2\n0\n0.2\n1.75\n1.8\n1.8\nM\u00b5q (GeV/c2)\n6E (GeV)\n(b) oA\u00b5q\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n1.6\n1.8\nMet (GeV/c2)\n6E (GeV)\n(c) oAet\n-0.4\n-0.2\n0\n0.2\n1.7\n1.8\nMeK*0 (GeV/c2)\n6E (GeV)\n(d) oAeK*0\nFigure 14.4.1.\nM\u2113V -\u2206E signal region (see text) for four\ntypical lepton-number-violating decays: (a) \u03c4 \u2212\u2192\u00b5\u2212\u03c10 (b)\n\u03c4 \u2212\u2192\u00b5\u2212\u03c6 (c) \u03c4 \u2212\u2192e\u2212\u03c9, and (d) \u03c4 \u2212\u2192e\u2212K\u22170 from Miyazaki\n(2011). Data points are shown as solid circles, and MC signal\ndistributions are shown as yellow boxes (with arbitrary nor-\nmalization). Red ellipses denote blinded regions, and horizon-\ntal lines denote the regions used for estimating background\nwithin the blinded ellipses.\ndata sample statistically independent from the data used\nfor the evaluation of the measurement result can be used.\nThis includes (real) data samples with decay modes ex-\nhibiting similarities with the studied one, or even samples\nof the studied decay mode on a distinct (typically smaller)\ndata set. For example, in Belle study of D+ \u2192K0\nSK+ and\nD+\ns \u2192K0\nS\u03c0+ decays (Won, 2009) a smaller sample of se-\nlected decays obtained in the o\ufb00-resonance data sample\nwas used to optimize the selection, subsequently applied\nto the larger on-resonance data sample.\n14.5 Examples from BABAR\nThe BABAR collaboration extensively discussed the use\nof the blind analysis method prior to data taking, and\nwrote a document describing possible methods (Ford,\n2000) which recommended their use whenever possible.\nMost BABAR results that could make use of a blind anal-\nysis technique did in fact do so.\nFor certain measurements, hiding the answer is not\nsu\ufb03cient; it may also be necessary to hide the visual as-\npect of the measurement. One example is the CP-violation\nmeasurements performed by BABAR. In this case the ap-\nproximate size and sign of the CP asymmetry can be seen\nby looking at the \u2206t distributions for B0 and B0 decays\n\n163\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n t\n6\n Tags\n0\nB\n Tags\n0\nB\n(a)\n t (Blinded)\n6\n Tags\n0\nB\n Tags\n0\nB\n(b)\nFigure 14.5.1.\nThe \u2206t distributions for B decays into CP\neigenstates, for sin 2\u03c61 = 0.75 with the B0 \ufb02avor tagging and\nvertex resolution that are typical for BABAR. (a) The true num-\nber of B0-tagged (solid line) and B0-tagged (dashed line) de-\ncays into CP eigenstates as a function of \u2206t. (b) The \u2206tBlind\ndistributions for B0-tagged (solid) and B0-tagged (dashed) de-\ncays.\ninto CP eigenstates, as shown in Figure 14.5.1a (see also\nChapter 10). Before CP violation had been established,\nand to avoid any chance of bias, a blind analysis was de-\nveloped to hide both the answer and the visual asymme-\ntry (Roodman, 2000).\nIn BABAR\u2019s initial CP-violation measurement (Aubert,\n2001a), the result (obtained from \ufb01tting the data) was hid-\nden as in Eq. (14.3.1). In addition, the visual asymmetry\nwas hidden by altering the \u2206t distribution used to display\nthe data. This was achieved by using the variable\n\u2206tBlind \u2261\n\u001a\n+1\n\u22121\n\u001b\n\u00d7 stag \u00d7 \u2206t + c .\n(14.5.1)\nThe parameter stag equals +1 or \u22121 for B0 or B0 \ufb02avor\ntags, respectively. Since the asymmetry is nearly equal and\nopposite for the two B \ufb02avors, BABAR hid the asymme-\ntry by \ufb02ipping one of the distributions. In addition, CP-\nviolation can be manifest by the asymmetry about \u2206t = 0\nof an individual B0 or B0 distribution. This feature was\nhidden by the o\ufb00set term c in Eq. (14.5.1), which has the\na\ufb00ect of hiding the \u2206t = 0 point. The result is shown\nin Fig. 14.5.1b, where the amount of CP-violation is no\nlonger visible.\nThis technique allowed BABAR to use the \u2206tBlind dis-\ntribution and blinded \ufb01t results to validate the analysis\nand study systematic e\ufb00ects while remaining blind to the\npresence of any asymmetry. There was one additional re-\nstriction: that the \ufb01t result could not be superimposed on\nthe data, since the smooth \ufb01t curve would show the asym-\nmetry. Instead, to assess the agreement of the \ufb01t curve and\nthe data, a distribution of only the residuals was used. In\npractice, this added only a small complication to the mea-\nsurement. In fact, after the second iteration of the anal-\nysis (Aubert, 2001e), it was realized that the asymmetry\nwould remain blinded if the only \u2206t distribution used was\nthat of the sum of B0 and B0 events. Subsequently, no\nadditional checks were done (or needed) using individual\nB0 and B0 \u2206t distributions.\nBABAR developed other methods for blinding an anal-\nysis, depending on its nature (upper limit, branching frac-\ntion, or precision measurement). For example, \ufb01t results\nwere sometimes blinded directly within the RooFit pack-\nage (Verkerke and Kirkby, 2003), and so Root-based \ufb01ts\nto data could be subjected to a blind analysis methodol-\nogy with relative ease. An alternative to a RooFit-based\nblinding method was to set up an analysis chain whereby\none performs a \ufb01t to data using Minuit (James and Roos,\n1975) and writes the output to a log \ufb01le, removing any ref-\nerence to signal observables while writing the log \ufb01le. In\nthis manner the output of the \ufb01t can be viewed in order to\nstudy issues such as the convergence of the \ufb01t, the values\nof ancillary \ufb01t parameters, and the covariance matrix.\nLastly, BABAR often worked the blind analysis strategy\ninto its internal review process. For many, but not all anal-\nyses, the three-person review committee\u2019s approval was\nrequired before the authors could unblind their analysis\n(as done in Belle).\n\n164\nChapter 15\nSystematic error estimation\nEditors:\nWolfgang Gradl (BABAR)\nPao-Ti Chang (Belle)\nAdditional section writers:\nAdrian Bevan, Chih-hsiang Cheng, Andreas Hafner, Ken-\nkichi Miyabayashi\nFor most measurements at the B Factories, the estima-\ntion of systematic uncertainties is a very important and\nchallenging part of the analysis. There are a number of\ne\ufb00ects which can systematically in\ufb02uence the result. The\nones which are frequently encountered in measurements\nperformed by the B Factories are discussed in the present\nchapter.\nSources of systematic e\ufb00ects include the di\ufb00erence be-\ntween data and simulation, the uncertainty on external\ninput needed to convert a directly measured value (e.g.\nthe number of signal events) to the desired quantity (e.g.\na branching fraction), and the analysis procedure chosen\nto extract the signal (e.g. background model, \ufb01t bias). In\naddition, physics processes can introduce discrepancies be-\ntween the measured value and the parameter of interest.\nThis is often the case because the signal model used is only\nan approximation of the true, underlying process. An ex-\nample of this type of systematic uncertainty is the e\ufb00ect of\ntag-side interference in measurements of time-dependent\nCP asymmetries.\nWhere possible, measured values are corrected for such\nsystematic shifts, and there is a systematic uncertainty as-\nsociated with the correction. Some of the systematic cor-\nrections are derived from control sample studies; their as-\nsociated uncertainty is essentially statistical in nature and\nscales with the size of the corresponding control sample\nand therefore with the data sample available for analysis.\nCareful design of the analysis strategy can help to min-\nimize the e\ufb00ect of systematic errors on the \ufb01nal result. A\nparticular systematic e\ufb00ect might cancel in the ratio of\ntwo observable quantities, such as the total number of\nproduced B mesons in the measurements of rate asym-\nmetries. Similarly, if the branching fraction of a decay is\nmeasured relative to a well-known decay mode with sim-\nilar \ufb01nal state topology, systematic uncertainties due to\nreconstruction or PID e\ufb03ciency cancel to a certain extent.\n15.1 Di\ufb00erences between data and simulation\nMost analyses at the B Factories are designed and op-\ntimized using simulated data (\u2018Monte Carlo\u2019). Collected\ndata are only looked at after the analysis procedure has\nbeen thoroughly tested and validated (see Chapter 14 for\na rationale and methods). Quantities such as the event\nselection e\ufb03ciency and mis-tag or mis-identi\ufb01cation rates\nare needed for measurements of branching fractions or ab-\nsolute cross sections, and they are typically obtained from\nsimulated data. If the simulation does not describe the de-\ntector perfectly, the e\ufb03ciency of the selection as applied\nto real data di\ufb00ers from the e\ufb03ciency derived from sim-\nulated events; this di\ufb00erence needs to be quanti\ufb01ed and\ncorrected. The correction factors to be applied to e\ufb03cien-\ncies obtained from simulation are derived from indepen-\ndent control samples and their simulated counterparts and\nhave their own statistical and systematic uncertainties.\nThe total uncertainty in the correction factor is taken as\na systematic uncertainty for the selection e\ufb03ciency. Corre-\nlations between systematic uncertainties need to be taken\ninto account; for example, for a \ufb01nal state with multiple\n\u03c00, the e\ufb03ciency correction has to be applied for each\n\u03c00 in the \ufb01nal state, and the systematic uncertainties are\nadded linearly.\n15.1.1 Track reconstruction\nMany analyses performed at the B Factories require a\nprecise simulation of the charged track \ufb01nding and recon-\nstruction e\ufb03ciency in order to determine absolute rates or\ncross sections. The way to measure the tracking e\ufb03ciency\nis by predicting the presence of a charged particle un-\nambiguously (e.g. using kinematic constraints on a series\nof particle decays) and checking if a reconstructed track\nmatches the prediction. Once the method is validated, one\ncan study the tracking e\ufb03ciency as a function of the track\nmomentum and polar angle. The same procedure is ap-\nplied to Monte Carlo events to estimate the tracking e\ufb03-\nciency in simulation. From the tracking e\ufb03ciencies in data\nand Monte Carlo, one produces a look-up table of correc-\ntion factors and their uncertainties to correct for the data-\nMC discrepancy in terms of track momentum and polar\nangle. This table is used to correct for the signal e\ufb03ciency\nestimated from Monte Carlo simulation and to calculate\nthe systematic uncertainty from track reconstruction.\n15.1.1.1 Methods at BABAR\nAt BABAR several methods are exploited to study possi-\nble e\ufb03ciency di\ufb00erences between the data and simulation\nover a wide range of particle momenta and production en-\nvironments relevant to most analyses. They are discussed\nin detail in (Allmendinger, 2012).\nThese methods rely on distinct data samples, where\nadditional constraints are applied to select speci\ufb01c event\ntopologies. The primary method to study the charged track\nreconstruction e\ufb03ciency in the data and simulation uses\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212events. Events of interest for the e\ufb03ciency\nstudy involve one leptonic \u03c4 decay \u03c4 \u00b1 \u2192\u00b5\u00b1\u03bd\u00b5\u03bd\u03c4 (\u2018tag\nside\u2019), B(\u03c4 \u00b1 \u2192\u00b5\u00b1\u03bd\u00b5\u03bd\u03c4) = (17.36 \u00b1 0.05)% (Beringer\net al., 2012), back-to-back with a semi-leptonic decay \u03c4 \u2213\u2192\nh\u2213h\u2213h\u00b1\u03bd\u03c4(\u22650n) (\u2018signal side\u2019) with a branching fraction\nof B(\u03c4 \u2213\u2192h\u2213h\u2213h\u00b1\u03bd\u03c4(\u22650n)) = (14.56 \u00b1 0.08)%, (Berin-\nger et al., 2012). Here, h denotes a charged hadron, and\nat least two tracks are required to fail a loose electron\nselection. The presence of one or more neutral particles,\ndenoted by \u22651n, e.g. \u03c00, but excluding K0\nS \u2192\u03c0+\u03c0\u2212, is\n\n165\nallowed in the \ufb01nal state. This data sample is referred to\nas \u2018Tau31\u2019 sample. The primary selection for \u03c4 pair can-\ndidates requires one isolated muon track in combination\nwith at least two tracks consistent with being hadrons.\nThrough charge conservation, the existence of an addi-\ntional track is inferred.\nDue to the presence of multiple neutrinos in the event,\nhowever, the direction of the additional track cannot be\ndetermined exactly. Using the measured trajectories of\nthe muon and the two hadrons, kinematic regions can be\nde\ufb01ned which are correlated with the polar angle \u03b8 and\ntransverse momentum pT of the missing track. The vari-\nation of the agreement between data and simulation as\na function of \u03b8 and pT is conservatively quanti\ufb01ed using\nthese estimator quantities.\nThis variation is the largest uncertainty when apply-\ning the results to a physics analysis, where the events typ-\nically have distributions in \u03b8 and pT di\ufb00erent from the\n\u03c4 pair events. The other main uncertainties include both\n\u03c4 and non-\u03c4 backgrounds: radiative Bhabha events with\na converted photon (i.e., e+e\u2212\u2192e+e\u2212\u03b3, \u03b3 \u2192e+e\u2212), \u03c4\npair events with a converted photon or a K0\nS \u2192\u03c0\u2212\u03c0+, 2-\u03b3\nevents, and continuum events (qq, with q = u, d, s, c). Con-\ntrol samples are used to estimate the levels and/or shapes\nof the most important backgrounds. This study shows no\ndi\ufb00erence in the track \ufb01nding e\ufb03ciency between the data\nand simulation with an uncertainty of (0.13-0.24)% per\ntrack, depending on the exact requirements on the track\nquality. This method is also used to investigate the sta-\nbility of track reconstruction over the diverse BABAR run-\nning periods. No time-dependent e\ufb00ects in the di\ufb00erence\nbetween the data and simulation have been observed.\nInitial-state radiation (ISR) events in the reaction\nchannel e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\u03b3ISR are used to cross-check\nthe systematic uncertainties in track reconstruction deter-\nmined from \u03c4 +\u03c4 \u2212events. The absence of neutrinos in this\nreaction allows to apply a \ufb01t with kinematic constraints\nto events with at least three detected pions. Hereby the\nkinematic parameters of the possibly missing track are de-\ntermined using energy and momentum conservation, and\nthe track reconstruction e\ufb03ciency can be measured as a\nfunction of track momentum and angles. In these events,\nthe high-energy ISR photon is emitted back-to-back to the\ncollimated hadronic system in the center-of-mass frame.\nBecause the analysis only selects events with photon en-\nergy E\u03b3 > 3 GeV, this back-to-back topology is approxi-\nmately preserved in the laboratory frame. This leads to an\nenvironment with a slightly higher track overlap probabil-\nity. In this environment, the track reconstruction e\ufb03ciency\ndi\ufb00erence between the data and simulation is found to be\n(0.7 \u00b1 0.4)% per track, compatible with the result of the\n\u03c4 based study of no signi\ufb01cant bias.\nLow momentum tracks are studied in D\u2217\u00b1 \u2192D0\u03c0\u00b1\ns\ndecays, using inclusively selected D\u2217\u00b1. \u03c0s denotes the low\nmomentum pion (\u201cslow pion\u201d) from the D\u2217decay. The rel-\native reconstruction e\ufb03ciency for the slow pions as a func-\ntion of the pion momentum is measured using their angu-\nlar distribution, following a method developed by CLEO\n(Menary, 1992). This method exploits the fact that in\nthe decay of a vector meson to two pseudoscalar mesons\nthe expected distribution of events is an even function of\nthe cosine of the \u03c0s helicity angle \u03b8\u2217. Furthermore, cos \u03b8\u2217\nis related to the slow pion momentum in the lab frame:\np\u03c0s = \u03b3(p\u2217\n\u03c0s cos \u03b8\u2217\u2212\u03b2E\u2217\n\u03c0s). Any observed asymmetry in\ndN/d cos \u03b8\u2217can be therefore mapped to a relative e\ufb03-\nciency di\ufb00erence as a function of p\u03c0s (see Allmendinger\n(2012) for a more complete discussion). Repeating the\nstudy on data and simulation, a relative di\ufb00erence be-\ntween the slow \u03c0 reconstruction e\ufb03ciencies is extracted,\nwhich is then ascribed as a systematic uncertainty. Using\nthe full BABAR dataset, this study results in a systematic\nuncertainty of 1.5% per track with a transverse momen-\ntum of pT < 180 MeV/c. This systematic uncertainty in-\ncludes the e\ufb00ects from both reconstruction e\ufb03ciency and\ndetector acceptance.\nAn asymmetry in the track reconstruction e\ufb03ciency\nbetween positively and negatively charged tracks can arise\nfrom a charge dependence of the interaction with the de-\ntector material; such a detector-induced asymmetry can\nintroduce a bias when measuring small CP rate asymme-\ntries. The asymmetry in reconstruction e\ufb03ciency has to be\ndetermined directly from data with a precision of O(10\u22123).\nLike the overall tracking e\ufb03ciency, it can also be measured\nusing the above mentioned Tau31 sample by comparing\nthe number of (2+1)-track events (in which one track was\nnot reconstructed) to the number of (3+1)-track events.\nThe asymmetry in the reconstruction e\ufb03ciency is found\nto be (\u03b5(\u03c0+) \u2212\u03b5(\u03c0\u2212))/(\u03b5(\u03c0+) + \u03b5(\u03c0\u2212)) = (0.10 \u00b1 0.26)%,\nthus consistent with zero within its uncertainty. This high-\nstatistics measurement is cross-checked and validated with\na high purity sample of D0 \u2192\u03c0+\u03c0\u2212events tagged by the\ndecay D\u2217+ \u2192D0\u03c0+\ns ; the charge-dependent reconstruction\nasymmetry as measured in this decay is also consistent\nwith zero asymmetry, but has a larger uncertainty.\nVery sensitive measurements of charge asymmetries,\nsuch as ACP in charm meson decays, require a much better\ncontrol of any detector-induced charge asymmetry. These\nanalyses rely on data-driven methods to determine the\ncharge asymmetry in the track reconstruction with a sys-\ntematic uncertainty as small as 0.08% (see Section 19.2.6).\nFinally, the e\ufb00ect of a vertex of the charged tracks\nthat is displaced from the primary event origin is inves-\ntigated in B \u2192h+h\u2212K0\nS (with h = \u03c0, K) decays with\nK0\nS \u2192\u03c0+\u03c0\u2212. Here the \ufb01nite lifetime of the K0\nS leads to\na displacement of the vertex of the two daughter pions.\nFor these tracks a di\ufb00erence of (0.5 \u00b1 0.8)% in the recon-\nstruction e\ufb03ciency between data and simulation has been\nobserved.\nThe results of these studies show that at BABAR the\ntrack \ufb01nding e\ufb03ciency in data agrees within uncertainties\nwith the simulated data. Thus, in a BABAR analysis, simu-\nlated track \ufb01nding e\ufb03ciencies can be applied to data. The\nappropriate systematic errors depending on the number\nof tracks involved need to be propagated, taking into ac-\ncount that the systematic errors are fully correlated i.e.,\nthe systematic uncertainties per track are added linearly.\n\n166\n15.1.1.2 Methods at Belle\nThe track \ufb01nding e\ufb03ciency for charged particles with mo-\nmenta above 200 MeV/c is studied using the decay chain\nD\u2217\u2192D0\u03c0s, D0 \u2192\u03c0+\u03c0\u2212K0\nS and K0\nS \u2192\u03c0+\u03c0\u2212.46 Par-\ntially reconstructed D\u2217decays provide a clean sample with\nsu\ufb03cient statistics to perform the tracking study. The de-\ncay chain can be reconstructed without actually detecting\none of the pions from the K0\nS decay. The four-momentum\nof this pion can be inferred from the kinematic constraints\nof the decay chain.\nFigure 15.1.1. Illustration of the Belle method to determine\nthe e\ufb03ciency of tracking.\nThe method is illustrated in Fig. 15.1.1. The D\u2217me-\nson partial reconstruction starts from the reconstruction\nof the common vertex of the two charged pions from the\nD0 decay (the D0 decay vertex; see Chapter 6 about ver-\ntexing). Following is the determination of possible K0\nS de-\ncay vertex positions, which are constrained to lie on the\ntrajectory of the detected pion and within a certain ra-\ndius (speci\ufb01cally this is chosen to be 3 cm) from the in-\nteraction region to limit the amount of possible points.\nThe segment of the pion track on which the K0\nS vertex\nis searched for is discretely scanned and for each discrete\npart of the track the momentum magnitude and direc-\ntion of the K0\nS is calculated (the latter is determined by\nthe line joining the D0 and K0\nS decay vertices, and the\nformer from the requirement that the K0\nS together with\nthe detected charged pion pair yields the invariant mass\nof the D0). For each possible value of K0\nS four-momentum\n(corresponding to each possible K0\nS decay vertex position)\na corresponding un-detected pion four-momentum can be\ncalculated by subtracting the momentum of the detected\ndaughter pion. The correct K0\nS momentum (i.e. the cor-\nrect position of the K0\nS decay vertex) is then determined\n46 For particles with p < 200 MeV/c a di\ufb00erent method is used\nas described below.\nby requiring that the resulting pion four-momentum mag-\nnitude corresponds to the pion nominal mass. A slow pion\ncandidate is added to the D0 and the signal of partially\nreconstructed D\u2217\u2019s is determined from the D0\u03c0s invariant\nmass distribution (Fig. 15.1.2).\nPractically, several selection requirements are imple-\nmented to improve the signal-to-background ratio. For in-\nstance, the D0 momentum must be larger than 2 GeV/c in\nthe laboratory frame to reduce combinatorial background.\nThe K0\nS vertex should be inside the innermost layer of the\nsilicon vertex detector to ensure silicon hits for the K0\nS\ndaughter tracks, and the missing pions are required to be\nin the tracking \ufb01ducial region. The ratio of the yield of\nfully reconstructed D\u2217\u2019s to those partially reconstructed\nwith one pion from the K0\nS not required is the track re-\nconstruction e\ufb03ciency.\nFinally the ratio of the tracking e\ufb03ciencies of data and\nMC can be obtained as a function of other variables, such\nas track total momentum and polar angle. The e\ufb03ciency\nas a function of particle\u2019s transverse momenta for real and\nsimulated data is shown in Fig. 15.1.3. Since the ratio of\nthe data-MC e\ufb03ciencies is found to be consistent with\nunity the di\ufb00erence and its uncertainties are assigned as\nthe tracking uncertainty. For Belle, the systematic error\nfor charged-track reconstruction is 0.35% on average for\nhigh momentum tracks (p > 200 MeV/c).\n10 3\n10 4\n2.004 2.006 2.008\n2.01\n2.012 2.014 2.016 2.018\n2.02\nRecovered D* Mass (GeV/c2)\nNo of Entries\nFigure 15.1.2. D\u2217mass distribution for partially (circle) and\nfully (triangle) reconstructed candidates in Belle data. A sim-\nilar reconstruction in the simulated data yields the ratio of\ndata-MC simulation tracking e\ufb03ciencies. The solid line repre-\nsents a \ufb01t to the partially reconstructed candidates.\nThe e\ufb03ciency di\ufb00erence of low momentum tracks (p <\n200 MeV/c) is studied using the decay chain, B0 \u2192D\u2217\u2212\u03c0+\nand D\u2217\u2212\u2192D0\u03c0\u2212\ns . The large B0 \u2192D\u2217\u2212\u03c0+ branching\nfraction provides a sample of slow pions large enough to\ninvestigate possible track reconstruction discrepancies be-\n\n167\nFigure 15.1.3. Reconstruction e\ufb03ciency for charged tracks as\na function of the particle\u2019s transverse momentum for simulated\nand real Belle data.\ntween data and simulation. Since the tracking di\ufb00erence\nbetween data and the MC expectation at higher momenta\nis known, the data-MC ratios are normalized according to\nthe data-MC ratio obtained using the D\u2217partial recon-\nstruction method for track momenta above 200 MeV/c.\nFor events with lower \u03c0s momentum, the di\ufb00erence be-\ntween the reconstructed yields in data and MC simulation\nis ascribed to a di\ufb00erence in the low momentum track re-\nconstruction e\ufb03ciency. Experimentally D0 candidates are\nreconstructed using several sub-decay modes. A slow pion\n(\u03c0s) and a high momentum pion with opposite charge are\nincluded to form a B candidate. The sample is divided in\nterms of the momentum of the slow pion, and the number\nof B events in each momentum bin can be extracted using\na \ufb01t to mES and \u2206m (mass di\ufb00erence between D\u2217\u2212and\nD0). The yield ratio of data and MC is thus obtained in\neach \u03c0s momentum bin. The normalized ratios and their\nuncertainties at low momentum are used to correct for\ndata-MC di\ufb00erences and to estimate the corresponding\nuncertainties. In Belle the tracking e\ufb03ciency in simula-\ntion agrees well with that in data for track momenta above\n125 MeV/c and the simulation may over-estimate the re-\nconstruction e\ufb03ciency for tracks with momentum below\n100 MeV/c. On average the systematic uncertainty for low\nmomentum tracks is 1.3% per track.\n15.1.2 K0\nS and \u039b reconstruction\nExperimentally, K0\nS and \u039b usually are reconstructed\nthrough K0\nS \u2192\u03c0+\u03c0\u2212and \u039b \u2192p\u03c0\u2212decays. Both par-\nticles have a long lifetime. They are identi\ufb01ed by the re-\nquirement that their decay vertex is displaced from the in-\nteraction point and that their reconstructed mass is close\nto their corresponding nominal mass. For long-lived par-\nticles systematic uncertainties in addition to the tracking\nuncertainties of their daughter particles need to be taken\ninto account. The tracks may originate far from the inter-\naction point, and also the reconstruction of the secondary\nvertex may show di\ufb00erences between simulation and data.\nSeveral studies are performed to investigate the K0\nS/\u039b re-\nconstruction.\n15.1.2.1 Exclusive D\u2217\u2192D0\u03c0s, D0 \u2192\u03c0+\u03c0\u2212K0\nS\nSimilar to the study of track reconstruction systematics,\nthe K0\nS reconstruction is studied using the exclusive de-\ncays of D\u2217\u2192D0\u03c0s, D0 \u2192\u03c0+\u03c0\u2212K0\nS. One measures the\ne\ufb03ciency of the displaced vertex requirement for the K0\nS\nreconstruction by obtaining the numbers of K0\nS candidates\nwith and without reconstructing a K0\nS vertex. The Belle\nmethod is described as follows. Two oppositely charged\ntracks that are identi\ufb01ed as pions are selected and their\ninvariant mass is computed without applying a vertex con-\nstraint. A pair with invariant mass close to the nominal K0\nS\nmass is selected as a K0\nS candidate. Every K0\nS candidate\nis combined with another \u03c0+\u03c0\u2212pair to form a D0 candi-\ndate, which is required to pair with a slow charged pion\nto form a D\u2217. To reduce the combinatorial background,\na suitable mass range, estimated using simulations, is se-\nlected in the D0 mass and \u2206m\u2032 = mD\u2217\u2212mD \u2212m\u03c0s. The\nuncertainty in \u2206m\u2032 is signi\ufb01cantly reduced with respect\nto mD\u2217because the contribution from the K0\nS candidate\nmomentum largely cancels in the subtraction and hence\na tighter signal window can be applied due to a better\nresolution. Finally, the numbers of all K0\nS particles and of\nthose passing a displaced vertex selection are estimated by\n\ufb01tting the candidate K0\nS mass with and without requiring\na displaced vertex, respectively.\nThe control sample has su\ufb03ciently high statistics so\nthat the study is extended to measure the e\ufb03ciency in\nterms of K0\nS momentum and polar angle similar to the\ncharged track study described in Section 15.1.1. Likewise\nthe e\ufb03ciency of requiring a displaced vertex for Monte\nCarlo events can be estimated. Hence, the data-MC e\ufb03-\nciency ratio can be obtained. The systematic uncertainty\nthat arises from the reconstruction of the two K0\nS daughter\npion tracks has to be added to the e\ufb03ciency uncertainty\nof the displaced vertex for the total K0\nS systematic uncer-\ntainty. Since \u039b and K0\nS decays have a similar topology, the\n\u039b systematic uncertainty can be estimated using the K0\nS\nresults. For the Belle full data sample, the total system-\natic uncertainty of the K0\nS reconstruction is on average\naround 1% including track reconstruction systematic un-\ncertainties.\n15.1.2.2 Ratio of two D decays\nThe performance of the K0\nS reconstruction in data can be\nchecked using the double ratio\n\u03b7(K0\nS) =\nN(D+ \u2192K0\nS\u03c0+)data\nN(D+ \u2192K\u2212\u03c0+\u03c0+)data\n\u001e\nN(D+ \u2192K0\nS\u03c0+)MC\nN(D+ \u2192K\u2212\u03c0+\u03c0+)MC .\n(15.1.1)\nIn order to obtain a higher purity sample one can de-\nmand a high enough momentum of the D+ candidates.\n\n168\nThe disadvantages of this method are: the uncertainty in\nthe D+ \u2192K+\u03c0+\u03c0\u2212branching fraction is large, the res-\nonant substructure in these D+ decays needs to be prop-\nerly implemented in the simulation of K+\u03c0+\u03c0\u2212decays,\nand the systematic uncertainty from particle identi\ufb01ca-\ntion needs to be included.\n15.1.2.3 K0\nS decay length distribution\nAnother method to check the data-MC discrepancy in the\nK0\nS reconstruction is to compare the K0\nS decay length\ndistribution. The D\u2217decay mode D\u2217\u2192D0\u03c0s, D0 \u2192\n\u03c0+\u03c0\u2212K0\nS used for the K0\nS e\ufb03ciency study above provides\na clean sample to measure the K0\nS decay length. Assuming\nthat decays with short decay length are inside the \ufb01ducial\nregion of the silicon vertex detector and are well simu-\nlated based on the tracking study, one can compare the\nfraction of reconstructed K0\nS with longer decay length be-\ntween data and MC events. The K0\nS data-MC e\ufb03ciency\ncorrection and the corresponding systematic uncertainty\nare thus obtained.\n15.1.3 Particle identi\ufb01cation\nThe performance of particle identi\ufb01cation (PID) for\nBABAR and Belle is described in Chapter 5, with the\nrelated systematic uncertainties brie\ufb02y discussed in Sec-\ntions 5.3.2 and 5.4. The PID e\ufb03ciency and its uncertainty\nare studied by choosing low-background samples in which\nthe type of charged particles is identi\ufb01ed without using\nthe PID information. Then one can examine if the PID\ngives the correct identi\ufb01cation. The PID e\ufb03ciency and\nuncertainty can be estimated by counting the number of\nparticles that are correctly identi\ufb01ed. For instance, K0\nS\nand \u039b are relatively long-lived and can \ufb02y a measurable\ndistance before they decay into \u03c0+\u03c0\u2212or p\u03c0\u2212; requiring\na distinct vertex and the appropriate mass range for the\ntwo-track mass provides clean samples of pions and pro-\ntons. As for kaons, the sample of D\u2217+ \u2192D0\u03c0+\ns\nand\nD0 \u2192K\u2212\u03c0+ is used. For electrons and muons, samples\nof e+e\u2212\u2192e+e\u2212l+l\u2212, e+e\u2212\u2192l+l\u2212(\u03b3) and J/\u03c8 \u2192l+l\u2212\n(l = e or \u00b5) are chosen to study the performance of lepton\nidenti\ufb01cation; by positively identifying one of the leptons,\nthe PID e\ufb03ciency for the other can be studied.\nThe correction and systematic uncertainty for the sig-\nnal e\ufb03ciency due to PID can be estimated using the data-\nMC ratios of the PID e\ufb03ciency and their uncertainties\nin di\ufb00erent momentum, polar angle and azimuthal angle\nbins, similar to what is described for tracking systematics\nin Section 15.1.1. An alternative way to obtain the PID\ne\ufb03ciency and its systematic uncertainty is to use signal\nMC events without applying any PID selection and weight\neach event according to the PID e\ufb03ciency obtained in\ndata. For su\ufb03ciently large Monte Carlo samples, the un-\ncertainty due to the size of the sample for understanding\nthe PID performance can be omitted. Typical systematic\nuncertainties per charged track in BABAR and Belle mea-\nsurements are 0.8%-1.0%. The uncertainty due to the PID\ne\ufb03ciency is treated as correlated among several tracks.\n15.1.4 \u03c00 reconstruction\nThe reconstruction e\ufb03ciency of \u03c00\u2019s in the decay channel\n\u03c00 \u2192\u03b3\u03b3 can di\ufb00er between data and simulation mainly\nfor the following reasons (see Section 2.2.4 for the descrip-\ntion of the electromagnetic calorimeters):\n\u2013 Imperfect modeling of the material distribution in the\ndetector. A photon can undergo pair production in the\nmaterial of the detector before reaching the calorime-\nter. If the produced tracks are reconstructed in the\ntracking detectors, the corresponding clusters in the\ncalorimeter, if any, are tagged as being produced by a\ncharged track and the photon candidate is lost. Even if\nthe reconstruction algorithms still \ufb01nd a photon candi-\ndate, the energy resolution might be degraded, leading\nto a \u03c00 candidate with an incorrectly reconstructed en-\nergy or mass.\n\u2013 Imperfect modeling of photon shower shape. In order to\ndiscriminate electromagnetic from hadronic showers,\nshower shape variables such as the lateral moment,47\nthe number of crystals in a shower etc. are used. Show-\ners tend to be somewhat narrower in simulation than\nin data, creating a small e\ufb03ciency di\ufb00erence between\ndata and MC.\n\u2013 Split-o\ufb00s. The particle showers created by hadrons in-\nteracting with the material in the calorimeter contain\na fraction of neutral hadrons. Such secondary hadrons\ncan travel a sizable distance in the calorimeter before\ninteracting with the material and depositing (a part\nof) their energy. These so-called split-o\ufb00s leave the sig-\nnature of a calorimeter cluster without an associated\ntrack pointing to it, which is hard to distinguish from\na real photon. Cluster split-o\ufb00s occur close to tracks,\nand the secondary showers usually have low energies.\nDetailed modeling of hadronic showers is di\ufb03cult, thus\nsplit-o\ufb00s present a further potential source of system-\natic di\ufb00erence between data and simulation.\n\u2013 Additional background in data. Real data events typ-\nically contain more (soft) photon candidates, most of\nwhich originate from beam-related background. This\nbackground consists primarily of electrons and posi-\ntrons from radiative Bhabha scattering which hit ele-\nments of the detector or the beam line, producing neu-\ntrons with energies in the MeV range, which then can\nproduce low energy showers in the calorimeter. These\nadditional photon candidates increase the number of\n\u03b3\u03b3 combinations in data, giving rise to more \u03c00 can-\ndidates, especially at low \u03c00 momentum.\nThe data-MC e\ufb03ciency ratio is \ufb01rst measured in very\nclean events in which the presence of a \u03c00 can be pre-\ndicted with little background. Possible di\ufb00erences between\nthe \u03c00 reconstruction e\ufb03ciency in such events and high-\nmultiplicity events with higher background must then be\n47 The lateral moment of a cluster in the calorimeter is de\ufb01ned\nas LAT \u2261PN\ni=3 r2\n\u22a5iEi/(25(E1 +E2)+PN\ni=3 r2\n\u22a5iEi), where the\nN crystals which belong to a cluster are sorted by their energy\nEi, and r\u22a5i is the (transverse) distance between the cluster\ncentroid and the ith crystal.\n\n169\nalso estimated. The data-MC e\ufb03ciency ratio is measured\nusing \u03c4 (Belle, BABAR) and \u03b7 (Belle) decays and multi-\nhadronic events with a photon radiated from the initial\nstate (BABAR). An important step is the validation of the\ne\ufb03ciency correction which is derived from this class of\nevents and to make sure the correction is applicable to\nB or charm decays, which tend to produce substantially\nmore activity in the detector. In the following, we present\nsome of the methods used to determine the \u03c00 e\ufb03ciency\ncorrection and the associated systematic uncertainty.\n15.1.4.1 Methods using \u03c4 decays\nA clean way to extract the \u03c00 reconstruction e\ufb03ciency\nis provided by comparing the observed rates of \u03c4 \u2212\u2192\n\u03c0\u2212\u03c00\u03bd\u03c4 to \u03c4 \u2212\u2192\u03c0\u2212\u03bd\u03c4 with the respective ratio of the\nbranching fractions. The branching fractions of the two\ndecays are known with sub-percent precision, allowing a\nmeasurement of the \u03c00 reconstruction e\ufb03ciency with an\nuncertainty of the order of 1%.\nIn BABAR, e+e\u2212\u2192\u03c4 +\u03c4 \u2212events are tagged with one \u03c4\ndecaying into e\u00b1\u03bde\u03bd\u03c4 (tag). On the signal side, a charged\ntrack incompatible with either the electron or the muon\nhypothesis is required. \u03c00 candidates are reconstructed\nfrom two photon candidates; events with more than two\nphoton candidates (i.e. those with extra activity in the\ncalorimeter) are removed.\nThe e\ufb03ciency correction \u03b7 \u2261\u03b5data/\u03b5MC is computed\nas a function of the \u03c00 momentum p\u03c00 as the double ratio\n\u03b7(p\u03c00) = N(\u03c4 \u2192\u03c0\u03c00\u03bd)data(p\u03c00)\nN(\u03c4 \u2192\u03c0\u03bd)data\n\u001eN(\u03c4 \u2192\u03c0\u03c00\u03bd)MC(p\u03c00)\nN(\u03c4 \u2192\u03c0\u03bd)MC\n(15.1.2)\n= N(\u03c4 \u2192\u03c0\u03c00\u03bd)data(p\u03c00)\nN(\u03c4 \u2192\u03c0\u03c00\u03bd)MC(p\u03c00)\n\u001eN(\u03c4 \u2192\u03c0\u03bd)data\nN(\u03c4 \u2192\u03c0\u03bd)MC .\n(15.1.3)\nIn this double ratio, the track reconstruction and PID ef-\n\ufb01ciencies (used on the tag side track) largely cancel pro-\nvided there are no correlations between the tag and the\nsignal side of the event:\nN(\u03c4 \u2192\u03c0\u03c00\u03bd)data\nN(\u03c4 \u2192\u03c0\u03bd)data\n= N\u03c4\u03c4 B(\u03c4 \u2192\u03c0\u03c00\u03bd) \u03b5data\ntag \u03b5data\ntrack \u03b5data\n\u03c00\nN\u03c4\u03c4 B(\u03c4 \u2192\u03c0\u03bd) \u03b5data\ntag \u03b5data\ntrack\n\u2248\u03b5data\n\u03c00\nB(\u03c4 \u2192\u03c0\u03c00\u03bd)\nB(\u03c4 \u2192\u03c0\u03bd)\n(15.1.4)\nUsing the well-measured branching fractions (and the\ncorresponding values for simulated data), the double ratio\ndirectly measures the ratio of \u03c00 reconstruction e\ufb03ciencies\nin data and simulation, modulo a few small corrections for\nsplit-o\ufb00s and the mis-modeling of the high-energy tail of\nthe \u03c00\u03c0\u2212mass spectrum. The resulting correction factor\ndepends on the \u03c00 momentum in the laboratory frame. For\na typical \u03c00 momentum spectrum, the correction factor is\naround 0.97 with a statistical uncertainty well below 1%.\nThe result of the \u03c4 based study is combined with the\nresults from \u03c9 production in events with hard initial state\nradiation (see below, Section 15.1.4.2) to obtain an overall\nmomentum dependent \u03c00 e\ufb03ciency correction. A system-\natic uncertainty of about 1.5% is assigned to cover the\nsystematic di\ufb00erences between the two methods.\nBelle also uses \u03c4 +\u03c4 \u2212events where one of the \u03c4 leptons\ndecays leptonically and the other into \u03c0\u00b1\u03c00\u03bd (single \u03c00\nevents), and events where both decay into \u03c0\u00b1\u03c00\u03bd (dou-\nble \u03c00 events). The ratio of data and MC simulation \u03c00\nreconstruction e\ufb03ciencies can be expressed as\n\u03b5data\n\u03c00\n\u03b5MC\n\u03c00\n= 2 \u00b7 N data\n2\nN data\n1\n\u00b7\nB(\u03c4 \u2192\u2113\u03bd\u00af\u03bd)\nB(\u03c4 \u2192\u03c0\u03c00\u03bd) \u00b7 \u03b5MC\n1\n\u03b5MC\n2\n\u00b7 (\u03b5data\n1\u2032\n/\u03b5MC\n1\u2032 )\n(\u03b5data\n2\u2032\n/\u03b5MC\n2\u2032 ),\n(15.1.5)\nwhere N data\n1,2\nare the numbers of reconstructed single and\ndouble \u03c00 events, and \u03b5MC\n1,2 are the e\ufb03ciencies to recon-\nstruct these events in the Monte Carlo; writing \u03b51 = \u03b5\u03c00\u03b51\u2032\nand \u03b52 = \u03b52\n\u03c00\u03b52\u2032, Belle separates the e\ufb03ciency for each\nclass of event into the \u03c00 reconstruction e\ufb03ciency, and\na remainder term. The \ufb01nal double-ratio expression in\nEq. (15.1.5) is assumed to be unity. Such a study reveals\na correction factor of around 0.96 to be applied to the\nsimulated reconstruction e\ufb03ciency, with an uncertainty\nof 2.4%.\nA comparison of \u03b7 \u21923\u03c00 and \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 decays\nalso yields the \u03c00 reconstruction e\ufb03ciency directly from\nthe data, and the systematic uncertainty at Belle is found\nto be 4%.\n15.1.4.2 Methods using \u03c9-ISR and \u03c9\u03c00-ISR events\nAnother approach to measure the di\ufb00erence in the \u03c00 re-\nconstruction e\ufb03ciency between data and Monte Carlo is\nto use the low-background processes e+e\u2212\u2192\u03b3ISR\u03c9 and\ne+e\u2212\u2192\u03b3ISR\u03c9\u03c00, where the \u03c9 decays to \u03c0+\u03c0\u2212\u03c00 and the\ninitial state radiation photon is required to have a labo-\nratory energy above 3 GeV. As in the case of the tracking\ne\ufb03ciency study, one can exploit the fact that the kine-\nmatics of the reaction are fully known: both energy and\nmomentum vector of the \u03c00 are predicted by a kinematic\n\ufb01t, using only the information of the initial state particles,\nthe ISR photon and the two pion tracks. In the reaction\ne+e\u2212\u2192\u03b3ISR\u03c9\u03c00 the directly produced \u03c00 is required to\nbe reconstructed while the e\ufb03ciency study is performed\nwith the \u03c00 from the \u03c9 decay. This method allows to study\nthe \u03c00 e\ufb03ciency as a function of the \u03c00 momentum and\n\ufb02ight direction.\nThis method, in both reaction channels, makes use of\nthe rather narrow width of the \u03c9. Signal events in which\nthe \u03c00 momentum and energy were correctly inferred by\nthe kinematic \ufb01t peak strongly close to the nominal \u03c9\nmass; a \ufb01t to this mass spectrum yields the number of\nproduced events which should contain a \u03c00. The number\nof events with a reconstructed \u03c00 is extracted from test-\ning all \u03c00 candidates in the event with a 5C kinematic\n\ufb01t under the hypothesis e+e\u2212\u2192\u03c9\u03b3 \u2192\u03c0+\u03c0\u2212\u03c00\u03b3. The\nclassi\ufb01cation of events into the categories \u2018\u03c00 found\u2019 or\n\u2018\u03c00 lost\u2019 is quite sensitive to the presence of extra \u03c00 can-\ndidates due to background photons, which is di\ufb00erent in\ndata and simulation.\n\n170\nAt BABAR, the \u03c00 e\ufb03ciency corrections derived from \u03c4\nand \u03c9-ISR events as described above are combined into an\noverall e\ufb03ciency correction with an associated systematic\nuncertainty which also accounts for the remaining di\ufb00er-\nences between the two methods. The \u03c00 e\ufb03ciency correc-\ntion factors as a function of the \u03c00 lab momentum for\nboth analyses as well as the combined correction factor\nwhich is recommended for general analyses are shown as\na function of the \u03c00 lab momentum in Fig. 15.1.4.\n (GeV/c)\n0\n\u03c0\np\n0\n1\n2\n3\n4\n5\n6\n - 1\nMC\n\u03b5/\ndata\n\u03b5\n-0.1\n-0.05\n0\n0.05\n0.1\n\u03c4\nISR\n\u03b3 \n\u03c9\nCombination\nFigure 15.1.4. BABAR \u03c00 e\ufb03ciency correction factors as a\nfunction of the \u03c00 lab momentum. The closed squares show the\ncombination of the two analyses described in the text, with the\nerror bars indicating the total systematic uncertainty associ-\nated with the e\ufb03ciency correction (Aubert, 2013).\n15.1.4.3 Slow \u03c00, and \u03c00 e\ufb03ciency in multi-hadronic decays\nAs described above, the \u03c00 e\ufb03ciency correction is primar-\nily measured in very clean events with few tracks and few\nor no additional neutrals. Typical B decays, however, con-\ntain more tracks and neutral candidates, which can a\ufb00ect\nthe probability to correctly reconstruct a \u03c00. To ensure\nthat the e\ufb03ciency correction is applicable to this class of\nmulti-hadron events, an inclusive measurement of the ratio\nof D0 \u2192K\u03c0\u03c00 to D0 \u2192K\u03c0 decays has been performed\nat BABAR. The \u03c00 e\ufb03ciency correction derived from this\nanalysis su\ufb00ers from a larger statistical uncertainty due to\nbackground subtraction and is less precise than the one de-\nrived from \u03c4 or ISR events. Within the given uncertainties,\nthe \u03c00 e\ufb03ciency corrections agree.\nA dedicated study of low-momentum \u03c00\u2019s has been\nperformed using the decay chain B0 \u2192D\u2217\u2212\u03c0+, D\u2217\u2212\u2192\nD\u2212\u03c00. The method is similar to the one used for low-\nmomentum tracks described in Section 15.1.1.2.\nSimilar to the study for the tracking e\ufb03ciency, the\ndata-MC e\ufb03ciency ratio can also be computed using the\ndouble ratio\n\u03b7(p\u03c00) = N(D0 \u2192K+\u03c0\u2212\u03c00)data\nN(D0 \u2192K+\u03c0\u2212)data\n\u001eN(D0 \u2192K+\u03c0\u2212\u03c00)MC\nN(D0 \u2192K+\u03c0\u2212)MC\n.\n(15.1.6)\nThis \u03c00 e\ufb03ciency correction is thus obtained in ha-\ndronic events, as opposed to the e\ufb03ciency in clean e+e\u2212\u2192\n\u03c4 +\u03c4 \u2212events. To reduce the D0 combinatorial background,\none can demand a soft \u03c0+ that combines with a D0 can-\ndidate to form a D\u2217+ and the reconstruction uncertainty\nfor slow pions cancels in the ratio. The dominant sys-\ntematic error in the correction is the branching fraction\nuncertainty of D0 \u2192K+\u03c0\u2212\u03c00, which results in a com-\nmon scale factor across the full momentum range. If the\ndata-simulation e\ufb03ciency ratio for the \u03c00 reconstruction is\nknown from other studies in a typical momentum range,\none can normalize the double ratio in that momentum\nrange to obtain the correction factors and the correspond-\ning uncertainties in other momentum ranges. For neutral\npions with momenta below 200 MeV/c the data-MC simu-\nlation correction factor at Belle is found to be 1.023\u00b10.024\nfor the data recorded with the SVD2 vertex detector (see\nChapter 2). For BABAR, a similar study results in a cor-\nrection factor for low-momentum \u03c00 of 0.98 \u00b1 0.07.\n15.1.5 High-energy photons\nThe detection e\ufb03ciency of high energy photons (with typ-\nical energies above E\u03b3 \u22482 GeV) is measured using radia-\ntive Bhabha events: e+e\u2212\u2192e+e\u2212\u03b3 (Belle) and e+e\u2212\u2192\n\u00b5+\u00b5\u2212\u03b3 (BABAR). After requiring exactly two tracks in an\nevent that are identi\ufb01ed as an e+e\u2212or \u00b5+\u00b5\u2212pair, the\nmissing energy direction can be computed. The photon ef-\n\ufb01ciency is estimated from the fraction of events that have\na reconstructed photon matching the magnitude and di-\nrection of the missing energy, which is required to point to\nthe electromagnetic calorimeter \ufb01ducial region. The pre-\ncise value of the e\ufb03ciency correction depends on the de-\ntails of the criteria to select photon candidates and the\ndecision whether a photon candidate matches the predic-\ntion from the kinematic \ufb01t.\nFor recent BABAR analyses of ISR events (Lees, 2012h),\nthe di\ufb00erence in the reconstruction e\ufb03ciency of high-\nenergy photons between data and simulation was de-\ntermined to be \u03b5data \u2212\u03b5MC = (\u22121.00 \u00b1 0.02 (stat) \u00b1\n0.55 (syst)) \u00d7 10\u22122.\n15.2 Analysis procedure\nA second, important group of systematic uncertainties is\nrelated to the analysis procedure. This includes the use\nof external parameters as well as the use of speci\ufb01c mod-\nels to separate signal from background and to extract the\nquantity of interest from the data. In a typical analysis at\nthe B Factories, multi-dimensional maximum likelihood\n\ufb01ts are often used to separate signal and background on a\nstatistical basis (see Section 11). This procedure needs to\nbe carefully checked and validated and systematic uncer-\ntainties assigned where appropriate. The most important\nsources of these systematic uncertainties are discussed in\nthis section.\n\n171\n15.2.1 External input\nIn many analyses, the physics observables are extracted\nfrom a \ufb01t with some of the parameters \ufb01xed to values\nbased on external information. Using external information\nis necessary if for example the statistical power of the se-\nlected sample under consideration is not large enough to\ndetermine all relevant parameters with su\ufb03cient accuracy.\nFor instance, in rare B decay searches the peak positions\nand resolutions of mES and \u2206E of signal events are of-\nten \ufb01xed; in Dalitz plot analyses the masses and natural\nwidths of intermediate resonances are \ufb01xed to their PDG\nvalues; the mixing parameter \u2206md and the B0 meson life-\ntime are not allowed to vary in \ufb01ts for time-dependent CP\nasymmetries. The systematic uncertainties that arise from\nusing external input parameters are obtained by checking\nthe deviations in the \ufb01tted values after varying the exter-\nnal parameters according to their uncertainties.\nUnlike the PDG values used as the external parame-\nters, some of the p.d.f. parameters explicitly depend on\nthe detector resolution, and the corresponding uncertain-\nties are determined using data. For instance, the uncer-\ntainty of mES is dominated by the beam energy spread\nand the mES peak position and resolution are determined\nusing high-statistics control samples such as B \u2192D0\u03c0\nand D0 \u2192K+\u03c0\u2212(\u03c00) for decay modes without (with)\nphotons in the \ufb01nal state. The corrections between data\nand simulation and their uncertainties are obtained from\nthese control samples and applied to the decay modes of\ninterest. The same procedure is applied to estimate the\ncorrection and uncertainty for the \u2206E p.d.f. parameters\nobtained in simulation. It is preferred to choose a con-\ntrol decay mode with high statistics that has the same\nnumbers of charged and neutral particles in the \ufb01nal state\nas the mode under study. The same consideration can be\napplied to estimate systematic uncertainties related to \ufb02a-\nvor tagging, vertexing, mass resolutions and other external\nparameters.\nMost analyses also rely on external input to derive the\nquantity of interest from directly measured quantities. Ex-\namples of such external parameters are the integrated lu-\nminosity (or, alternatively, the number of BB pairs pro-\nduced), branching fractions of daughter decays, particle\nmasses and their lifetimes, etc. These quantities and their\nuncertainties are typically taken from averages calculated\nby the Particle Data Group, with the exception of the lu-\nminosities, which are measured by the B Factories (see\nSections 3.2.1 and 3.6.2). At both experiments, the preci-\nsion of the luminosity measurement is limited by system-\natic uncertainties, mainly by uncertainties of the Monte\nCarlo generator(s) used to calculate the cross-sections of\nthe physics processes used to measure luminosity. At Belle,\nthe luminosity is measured using Bhabha scattering to a\nprecision of about 1.4%. BABAR uses both Bhabha scat-\ntering and e+e\u2212\u2192\u00b5+\u00b5\u2212(Lees, 2013i); the systematic\nuncertainty of the luminosity is about 0.5% for the data\ncollected at the \u03a5(4S).\nThe uncertainties from these external parameters are\npropagated to the \ufb01nal result using either Gaussian er-\nror propagation in the simplest cases, or by varying the\nparameters within their uncertainties and repeating the\nanalysis.\n15.2.2 Modeling of background\nBackground distributions are often modeled using events\nfrom simulation or sidebands of e.g. mass distributions. A\ntypical example is modeling the background distributions\nin the Dalitz plot for B or D decays. One can assume\nthat the Dalitz plot distributions for the combinatorial\nbackground are the same as those obtained using events\noutside the mES \u2212\u2206E signal region or in the D mass side-\nband region. The background model can be cross-checked\nby comparing the distributions of simulated background\nevents in the signal and sideband regions or by comparing\nthe data distributions in di\ufb00erent sideband regions. The\nsystematic uncertainty due to the background modeling is\nthen estimated by using the p.d.f.s obtained from di\ufb00er-\nent sideband regions and by varying the p.d.f. parameters\naccording to the uncertainties.\nIn many cases the background is su\ufb03ciently large so\nthat the background p.d.f. parameters can be determined\ndirectly from a \ufb01t to data. This procedure moves the un-\ncertainty originating from the background p.d.f. param-\neters into the overall statistical uncertainty returned by\nthe \ufb01t. However, in many cases the actual shape of the\nbackground distribution is not known from \ufb01rst princi-\nples, and there may be several di\ufb00erent parameterizations\nwhich describe, within the given uncertainties of the data,\nthe background shape equally well. The systematic uncer-\ntainty related to this is determined by choosing di\ufb00erent\nfunctions for the background p.d.f.s and repeating the \ufb01t.\nFor example, B yields in many rare decay searches are ex-\ntracted with an unbinned maximum likelihood \ufb01t to the\ndistributions of mES, \u2206E and other variables (see Chap-\nter 9). The p.d.f.s of the B decay background are usually\nestimated from simulations, while the continuum p.d.f.s\nare modeled as a polynomial function for \u2206E and an AR-\nGUS function (see Eq. 7.1.11) for mES with their parame-\nters allowed to vary in the \ufb01t. Systematic uncertainties of\nthe \ufb01t can be evaluated using other function models that\nprovide an acceptable goodness of the \ufb01t.\n15.2.3 Fit bias\nThe results of multi-dimensional maximum likelihood \ufb01ts\n(see Chapter 11) can be systematically biased when the\ncorrelations between various discriminating variables are\nnot considered or several components have similar p.d.f.s,\nso that the \ufb01t cannot completely distinguish between those\ncomponents. The \ufb01t bias can be examined using large\nensembles of simulated experiments (\u2018toy MC\u2019, see Sec-\ntion 11.5.2); a bias correction is then derived from these\nstudies. There is no unique method of assigning a sys-\ntematic uncertainty to this bias correction, and analyst\ndiscretion is required. As a conservative approach, the sys-\ntematic uncertainty associated with the bias correction is\noften taken to be half or even all of the correction.\n\n172\n15.3 Systematic e\ufb00ects for time-dependent\nanalyses\nA number of systematic e\ufb00ects need to be understood\nin order to verify that one is able to correctly extract\ntime-dependent information from \ufb01ts to data. The general\nmethodology for performing a time-dependent CP asym-\nmetry analysis at the B Factories is outlined in Chap-\nter 10. In addition there are special cases that have been\nconsidered over the course of these experiments including\ntime-dependent analyses of modes requiring a full angu-\nlar analysis (Chapter 12), and time-dependent Dalitz plot\nanalyses (Chapter 13).\nIn the following we discuss systematic uncertainties\narising from detector and reconstruction e\ufb00ects (see Sec-\ntions 15.3.1 through 15.3.3), uncertainties from physics\nparameters (see Section 15.3.4), and uncertainties aris-\ning from approximations made in the analyses (see Sec-\ntions 15.3.5 through 15.3.6). The systematic uncertainties\nquoted on S and C (see Chapter 10) in the remainder of\nthis chapter are typical values obtained by the B Facto-\nries.\n15.3.1 Alignment of the vertex detector\nIn order to precisely reconstruct the decay vertex position\nof both B mesons in an event and the value of the proper\ntime di\ufb00erence \u2206t between the decays of both mesons\n(see Chapter 6 for a detailed discussion on these mat-\nters), accurate information is required on the position of\nthe reconstructed hits that correspond to the signature of\ncharged particles traveling through the tracking volume.\nThe silicon detectors at the B Factories dominate our\nunderstanding of the vertex positions by virtue of their\nproximity to the interaction point, and hence the B decay\nvertices. The \ufb01rst few measurement points of each track\noriginating from a B decay will be recorded in the silicon\ndetector, and hence one must precisely know the posi-\ntion of the strips embedded in the silicon. This position\nchanges slightly with time, and if not corrected for, will\nsmear out the knowledge of each hit position, and hence\n\ufb01tted track and computed vertex. The purpose of the sil-\nicon detector calibration is to correct for variations in the\nalignment as a function of run period, and in the case of\nBelle, the di\ufb00erences between the di\ufb00erent SVDs installed\nduring operation (see Chapter 2).\nWhile the detector calibration is extremely e\ufb00ective at\ncorrecting for variations in detector position as a function\nof time, there is an uncertainty arising from any resid-\nual lack of knowledge in the position and orientation of\neach double-sided silicon sensor module that provides a\nmeasurement of r, \u03c6 and z within the detector. The lo-\ncal alignment procedure adopted by BABAR is described\nin detail in (Brown, Gritsan, Guo, and Roberts, 2009). In\norder to estimate the magnitude of the uncertainty arising\nfrom the alignment of the silicon detector, di\ufb00erent sets\nof alignment constants are applied to simulated Monte\nCarlo data for signal events or equivalently the silicon\ndetector positions are intentionally modi\ufb01ed in a plau-\nsible range in both global displacement and rotation as\nwell as random misalignment for each silicon sensor, and\nthe change in \ufb01tted values of the CP-violating parame-\nters S and C (see Section 10.2) from the nominal value\nis assigned as an uncertainty from this source of system-\natic. The magnitude of this uncertainty on S and C is at\nmost a few per mille. In extreme cases, for example modes\nsuch as B0 \u2192\u03c1+\u03c1\u2212that su\ufb00er from a signi\ufb01cant contri-\nbution from mis-reconstructed signal in the \ufb01nal state,\nthe e\ufb00ect of the silicon detector alignment is somewhat\nlarger: \u223c0.01. The reason for this is that some of the\nmis-reconstructed signal in this \ufb01nal state has a biased\nreconstructed vertex position, resulting from the inclusion\nof low-momentum tracks reconstructed at the extremities\nof the helicity angle distributions (see Chapter 12). Some-\ntimes these low momentum tracks are incorrectly assigned\nfrom the rest of the event to a signal B candidate, rather\nthan including the correct tracks from the signal side. Dif-\nferent alignment sets change the reconstruction rate of this\ncomponent of mis-reconstructed signal, and thus induce a\nbias on the measured observables S and C.\n15.3.2 Beamspot position, z scale and boost\nAs discussed in Chapter 6, the beamspot location can be\nused to improve constraints on vertex reconstruction, and\nis used when reconstructing the tagging B meson vertex.\nThe dominant contribution to the systematic uncertainty\nwhen adding this constraint comes from the limited knowl-\nedge of the vertical position of the beamspot. The knowl-\nedge of the beamspot is included in the vertex \ufb01t via the\naddition of an extra term in the \u03c72 of the track \ufb01t. The\nlimitation in the absolute knowledge of the beamspot lo-\ncation therefore translates into a systematic uncertainty\non the reconstructed value of \u2206t, and hence propagates\nthrough onto the measured observables S and C in a time-\ndependent CP asymmetry analysis. Detailed studies of the\nbeam-spot position calibration were performed at the B\nFactories (see Section 6.4).\nKnowledge of the mean vertical position is the domi-\nnant systematic uncertainty from the use of the beamspot\nin BABAR, while its spread is found to give a much larger\ne\ufb00ect in Belle. The corresponding systematic uncertain-\nties in the measured values of S and C are estimated\nby modifying the position and uncertainty on the verti-\ncal beamspot position according to the variations seen in\ndata. For example, BABAR varies this position by \u00b120\u00b5m,\nas well as increase the uncertainty on this quantity by\n20\u00b5m to evaluate the systematic uncertainty arising from\nthe use of the beamspot in vertex reconstruction. Belle\nchanges the beamspot position uncertainty to a factor of\n2 larger or smaller value than the nominal one, 21\u00b5m.\nThe relative change in S (C) from its nominal value (S \u223c\nsin 2\u03c61, C \u223c0) is found to be 0.13% (0.06%) in BABAR\nand 0.3% (0.08%) in Belle for B decays to c\u00afcs \ufb01nal states.\nOther important factors impacting the measurement\nof S and C are the z scale determined from the vertex\ndetector, and the boost factor. Detailed studies of control\n\n173\nsamples show that the z scale uncertainty is the dominant\nof these two e\ufb00ects, and to account for these uncertainties\n\u2206t and \u03c3\u2206t are scaled by 0.6%. This results in negligible\nsystematic shifts, of the order of 4.7\u00d710\u22124 in S and 2.3\u00d7\n10\u22124 in C, for B decays to ccs \ufb01nal states. These are\ninterpreted as systematic uncertainties from the z scale\nand boost determination.\n15.3.3 Resolution function and \ufb02avor tagging\nparameters\nBoth the \u2206t resolution function parameters and \ufb02avor\ntagging performance parameters are integral inputs to a\ntime-dependent analysis. There are two conceptual ways\nto incorporate systematic uncertainties from these param-\neters into the extracted values of S and C. Firstly one can\nperform a simultaneous \ufb01t to the so-called B\ufb02av sample\nof events (see Section 10.2) and the selected signal can-\ndidates. In this approach the uncertainties on and cor-\nrelations between resolution function and tagging model\nparameters are automatically folded into the statistical\nuncertainty reported for the asymmetry parameters. This\napproach is adopted by BABAR. The second approach is\nto take the results of a reference \ufb01t to the B\ufb02av data sam-\nple, and incorporate the variations of S and C from the\nnominal result when varying the resolution and tagging\nparameters by their uncertainties. This approach results\nin a number of contributions that are added in quadra-\nture ignoring the correlations that exist between them.\nBelle uses the second approach as there are only small\ncorrelations between the parameters describing the reso-\nlution and tagging performance. As a result this second\napproach provides a conservative and still proper estima-\ntion of the systematic uncertainty from the knowledge of\nthese parameters. The typical uncertainty on S and C ob-\ntained for the resolution function and tagging parameters\nusing the second approach is \u22640.01.\n15.3.4 The e\ufb00ect of physics parameters\nTime-dependent CP asymmetry measurements at the B\nFactories follow the method described in Chapter 10. In\nparticular, these analyses assume \u2206\u0393d = 0, unlike the sit-\nuation for time-dependent measurement for Bs (and even-\ntually D) meson decays. No systematic uncertainty is as-\ncribed for the use of this assumption, which is well moti-\nvated by theoretical arguments for the statistics available\nat BABAR and Belle. A non-zero value of \u2206\u0393d = 0 would\ngive rise to hyperbolic sine and cosine terms in the time-\ndependent asymmetries as discussed in Section 17.5.2.6,\nand one can estimate the magnitude of any systematic un-\ncertainty from neglecting these hyperbolic terms by com-\nparing results obtained using an ensemble of simulated\nMonte Carlo experiments with \u2206\u0393d \u0338= 0, and observing\nthe bias introduced on the \ufb01tted values of S and C. If one\nassumes that \u2206\u0393d \u22640.01, the systematic uncertainties in\nS and C would be negligible, if one were to use the exist-\ning experimental limit on the value of \u2206\u0393d the bias on S\nwould be 0.005.\nThe physics parameters \u03c4B0 and \u2206md are required in-\nputs for time-dependent measurements. During the ML\n\ufb01tting procedure used to extract S and C from data, the\nB0 lifetime and mixing frequency are \ufb01xed to their nomi-\nnal values. The uncertainty on the measured values of \u03c4B0\nand \u2206md are propagated through the \ufb01tting procedure,\nassuming that they are uncorrelated, and the resulting\nvariation of S and C from the nominal \ufb01tted values is\nassigned as an uncertainty. This source of uncertainty is\nfound to be at most a few per-mille.\n15.3.5 CP violation in background components\nA subtlety raised in Chapter 10 is the issue of correctly ac-\ncounting for any CP asymmetry (time-dependent or time-\nintegrated) in background modes when performing a time-\ndependent analysis. This issue is not signi\ufb01cant for the\ncase of charmonium decays such as B0 \u2192J/\u03c8K0\nS, where\nthere is very little background, however it should be con-\nsidered when analyzing modes with signi\ufb01cant levels of\nbackground such as B0 \u2192\u03c1+\u03c1\u2212.\nThere are two types of CP violating background that\nmay occur (i.e. direct and mixing-induced CP violation,\nsee Chapter 16) from neutral B mesons, and charged B\nmesons may only violate CP via direct decay. In addition\none may need to consider the BB background, where the\nB signal candidates are formed by combining the daugh-\nter particles of the true Btag and Brec . In general the\nreconstructed |\u2206t| values of these background events are\nsmaller than the true ones as the reconstructed Btag and\nBCP vertices tend to be closer to each other.\nSuch an e\ufb00ect can be taken into account by replacing\nthe B lifetime in the exponential decay of Eq. (10.2.2) with\nan e\ufb00ective lifetime. This is particularly relevant for \ufb01nal\nstates with charm mesons in them as discussed in Chap-\nter 10, but is also manifest at a lower level for B back-\ngrounds without charm decays. Generally one assumes\nthat any bias for the latter class of B decays is negligi-\nble.\nHaving corrected for the above reconstruction e\ufb00ects\none is faced with having to address the issue of a physical\nasymmetry in the background decay channel. In the case\nof a neutral B decay the asymmetry will be of the form of\nEq. (10.2.8). One has to account for tagging and resolution\ne\ufb00ects, and typically it is assumed that it is valid to use\nthe same tagging and resolution parameters for the back-\nground channels as for the correctly reconstructed signal.\nIdeally one should generate samples of Monte Carlo sim-\nulated data for each CP violating background mode with\nthe values of S and C as measured in data. This way any\ndilution from mis-reconstructing a given channel is taken\ninto account when setting the values of the e\ufb00ective S and\nC required to model the CP asymmetry of a given back-\nground mode. In cases where there is no measurement of\nthe asymmetry parameters, but it is reasonable to expect\na non-zero asymmetry, one varies the e\ufb00ective values of S\nand C between +1 and \u22121 to estimate the maximal e\ufb00ect\na given background would have on the signal. CP violation\n\n174\nin charged decay modes can be accounted for in an analo-\ngous way, where one uses the time-integrated asymmetry\nto allow for any possible direct CP violation.\nTypical systematic uncertainties in the values of the\nCP asymmetry parameters measured for the high-back-\nground decay B \u2192\u03c1+\u03c1\u2212arising from possible CP viola-\ntion in the background are \u22640.2% for S and 1 \u22122% for\nC, see Aubert (2007b). This uncertainty is dominated by\ncontributions from B \u2192a1\u03c0 decays, assuming that CP vi-\nolation could be large, as the example discussed predates\nCP asymmetry measurements of B \u2192a\u00b1\n1 \u03c0\u2213.\n15.3.6 Tag-side interference\nIn order for a decay channel to have non-zero CP asymme-\ntry, it must have at least two interfering amplitudes with\ndi\ufb00erent weak phases. This is a necessary condition, but it\nis not su\ufb03cient to guarantee that there will be an observ-\nable CP violation e\ufb00ect in that \ufb01nal state. The discussion\nso far has focused on interfering amplitudes on the Brec\nside of the event leading to a measurable CP violation ef-\nfect. However it was pointed out by Long, Baak, Cahn, and\nKirkby (2003) that in addition to interference on the Brec\nside, one has to consider possible e\ufb00ects of interference on\nthe Btag side, where more than one amplitude contributes\nto the \ufb01nal state. If neglected, interference e\ufb00ects on the\nBtag side of the event could result in an undesired contri-\nbution to the measured CP asymmetry for the Brec. Many\ndi\ufb00erent \ufb01nal states are included in the (inclusive) recon-\nstruction of the Btag with di\ufb00erent contributions to the\nso-called tag-side interference e\ufb00ect.\nAs discussed in Section 8, the dominant contributions\nto the tagging e\ufb03ciency come from semi-leptonic decays\nwith \ufb01nal state leptons, and hadronic decays such as B \u2192\nD(\u2217)\u2212\u03c0+. Since the semi-leptonic decays proceed via a sin-\ngle amplitude in the SM, semi-leptonic tagged decays do\nnot su\ufb00er from tag-side interference. However possible in-\nterference e\ufb00ects need to be considered when performing a\ntime-dependent analysis, where Btag decays to a hadronic\n\ufb01nal state as the decay can proceed by more than one\namplitude.\nIf one considers the decay B \u2192D\u2212\u03c0+, with subse-\nquent D\u2212\u2192K+\u03c0\u2212\u03c0\u2212decay as an example, the \ufb01nal\nstate can be reached via the CKM preferred b \u2192cud tran-\nsition of a B0. The same \ufb01nal state can also be reached\nfrom a B0 through B0 \u2212B0 mixing followed by a doubly-\nCKM suppressed b \u2192ucd transition. The ratio of these\ntwo amplitudes is given approximately by the ratio of\nCKM matrix elements |(V \u2217\nubVcd)/(VcbV \u2217\nud)| \u22430.02.\nThe strength of the amplitude of the doubly-CKM sup-\npressed relative to the allowed decay can be parameterized\nas\nAf\nAf\n= rfe\u2212i\u03c63+i\u03b4f ,\n(15.3.1)\nwhere rf is the ratio of suppressed to favored decays, and\n\u03b4f is the relative strong phase di\ufb00erence between the B0\nand B0 decay proceeding via b \u2192cud and b \u2192ucd tran-\nsitions, respectively. In practice a number of modes are\nsummed over on the tag-side of the event, and we replace\nrf and \u03b4f with primed variants to represent the e\ufb00ective\nratio of amplitudes and phase di\ufb00erence of an ensemble of\nmodes.\nIt is possible to compute a correction on the time-\ndependent asymmetry parameters S and C resulting from\nthe use of hadronic tag modes, either for a given mode, or\nan ensemble of modes. These corrections are a function of\n\u2206t and have the e\ufb00ect of slightly reducing the amplitude\nand broadening the time distribution, or increasing the\namplitude and narrowing the distribution as discussed in\nSection VI and Fig. 3 of Long, Baak, Cahn, and Kirkby\n(2003). The e\ufb00ect depends on the values of r\u2032\nf and \u03b4\u2032\nf.\nThus one can expect the measured values of S and C in a\ntime-dependent analysis to di\ufb00er from the true values for\nhadronically tagged events.\nThe semileptonic decay, B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113is a high pu-\nrity B\ufb02av mode and free from doubly-CKM suppressed\ndiagram as already discussed. Thus applying the proper\n\ufb02avor tagging algorithm on the Btag decay products in\nthis sample gives an estimation of the possible range of\nthe e\ufb00ective ratio of the amplitudes and phase di\ufb00erence\nfor an ensemble of the tag-side modes. This estimation is\nused to see the e\ufb00ects on S and C as described in more\ndetail later.\nIf a time-dependent analysis were limited by system-\natic uncertainties arising from tag-side interference, there\nare two possible approaches that may be considered to\nmitigate this uncertainty: (i) only use semi-leptonic tagged\nevents, thus removing the a\ufb00ected data from the analysis,\nand (ii) given su\ufb03cient data, to measure the ratio of CKM\nallowed to suppressed decays, and the corresponding phase\ndi\ufb00erence between the amplitudes using control samples.\nIn the following discussion the true values of these time-\ndependent asymmetry parameters are represented by S0\nand C0, whereas the measured values of these observables\nare denoted by S\ufb01t and C\ufb01t.\n15.3.6.1 The tree dominated B0 \u2192J/\u03c8K0\nS decay\nThe prime example of a time-dependent measurement\nmade by the B Factories is that of B0 \u2192J/\u03c8K0\nS, which\nis described in Section 17.6. The biases on the true val-\nues of measured time-dependent asymmetries in this decay\narising from tag-side interference can be treated as a per-\nturbation on the measurement, i.e. a systematic shift with\nan associated uncertainty. It is possible to relate the true\nvalues of the CP asymmetry parameters S0 and C0 to the\n\ufb01tted values S\ufb01t and C\ufb01t up to some correction related\nto the additional amplitudes interfering on the tag side of\nthe event. The correction depends on \u03a6 = 2\u03c61 +\u03c63 result-\ning from the phase di\ufb00erence between the doubly CKM\nsuppressed and CKM allowed amplitudes on the tag side\nof the decay and the short distance B0 \u2212B0 mixing box\ncontributions. The corrections to the \ufb01tted CP asymmetry\nparameters are related to the magnitude of the e\ufb00ective\nratio of CKM suppressed to allowed amplitudes for the\ntag-side decay given by r\u2032\nf, as shown in the following\n\n175\nC\ufb01t = C0 + 2C0r\u2032\nf cos \u03b4\u2032\nf{G cos(\u03a6) \u2212S0 sin(\u03a6)}\n\u22122r\u2032\nf sin \u03b4\u2032\nf{S0 cos(\u03a6) + G sin(\u03a6)},\n(15.3.2)\nS\ufb01t = S0 + 2S0r\u2032\nf cos \u03b4\u2032\nfG cos(\u03a6)\n+2r\u2032\nf sin \u03b4\u2032\nfC0 cos(\u03a6).\n(15.3.3)\nHere the factor G is 2Re\u03bbCP /(|\u03bbCP |2 + 1), and \u03bbCP is\nthe quantity given in Eq. (10.1.10) evaluated for the Brec\nreconstructed in a CP eigenstate.\nUsing a Monte Carlo simulation based approach, one\ncan estimate the magnitude of the e\ufb00ect on the value of\nS\ufb01t and C\ufb01t extracted from data, and hence determine S0\nand C0. In order to do this one has to determine r\u2032\nf and\n\u03b4\u2032\nf. The value of r\u2032\nf is given by |(V \u2217\nubVcd)/(VcbV \u2217\nud)| and an\nestimate of the uncertainty on this can be derived from\na comparison of rates for allowed to suppressed D \u2192K\u03c0\ntransitions. This comparison indicates that the error on\nr\u2032\nf is about 25%. As there is no knowledge of the phase\ndi\ufb00erence, one assumes that this parameter is uniformly\ndistributed in the simulated pseudo-experiments. This ap-\nproach of evaluating the e\ufb00ect of tag-side interference for\nB0 \u2192J/\u03c8K0\nS has been broadly applied to b \u2192ccs, ccd,\nand qqs \ufb01nal states. The magnitude of the systematic un-\ncertainty ascribed to the measurement of S (C) in this set\nof channels is typically 0.001 (0.014). The systematic un-\ncertainty is negligible for the extraction of sin 2\u03c61 from the\ngolden b \u2192ccs measurements. However this source of sys-\ntematic uncertainty is signi\ufb01cant for some of the precision\nmeasurements of C, and in fact dominant for the golden\nchannel B0 \u2192J/\u03c8K0\nS discussed in Section 17.6. For the\nmeasurement of \u03c61 from an ensemble of CP-even and odd\nstates (i.e. J/\u03c8K0\nL and ccK0\nS) BABAR ascribes a system-\natic uncertainty as described above. However, Belle note\nthat there may be some cancellation between the even and\nodd states and account for this in their estimation of the\nsystematic uncertainty from this source on the combined\nmeasurements of S and C (Adachi, 2012c).\nThere is no indication of a signi\ufb01cant shift in the mea-\nsured values of S and C found via this Monte Carlo sim-\nulation based approach, hence no corrections are applied\nto the results obtained by the B Factories.\n15.3.6.2 The complication of loop amplitudes in\nB0 \u2192\u03c0+\u03c0\u2212\nAn example of a decay with both tree and loop (penguin)\namplitudes used in a time-dependent analysis is B0 \u2192\n\u03c0+\u03c0\u2212which is discussed further in Section 17.7. The decay\namplitude for the reconstructed B meson depends on \u03c63,\nas does the tag-side. Thus the situation encountered with\nB0 \u2192\u03c0+\u03c0\u2212is therefore much more complicated than the\nprevious case. The uncertainty from tag-side interference\ncan be as large as 2r\u2032\nf. This complication for calculat-\ning tag-side interference applies not only to B0 \u2192\u03c0+\u03c0\u2212\ndecays, but more generally to the set of b \u2192uud tran-\nsitions related to \u03c62 where there are signi\ufb01cant penguin\ncontributions. The least problematic of these decays be-\ning B0 \u2192\u03c1+\u03c1\u2212, which is known to have a small penguin\ncontribution, relative to other b \u2192uud transitions.\nThe magnitude of the systematic uncertainty ascribed\nto the measurement of S (C) in this set of channels is typ-\nically 0.007 \u22120.010 (0.016 \u22120.04) depending on the \ufb01nal\nstate. While small, compared to the overall experimental\nuncertainty, this is the dominant source of systematic un-\ncertainty for the extraction of C from the B0 \u2192\u03c0+\u03c0\u2212\nand \u03c1+\u03c1\u2212channels discussed in Section 17.7. The sys-\ntematic uncertainty is negligible on the extraction of \u03c62\nfor the golden b \u2192uud measurements given the statistics\navailable at the B Factories.\n15.3.6.3 Time-dependent measurement of sin(2\u03c61 + \u03c63)\nThe measurement of sin(2\u03c61 + \u03c63) using B \u2192D\u2217\u00b1\u03c0\u2213\ndecays is discussed in Section 17.8. The manifestation of\ntag-side interference in this time-dependent measurement\ndi\ufb00ers from that discussed for the previous two examples\nas described below. As with the b \u2192uud transition case\nthe reconstructed B meson depends on \u03c63, so it is not\nstraightforward to extract an estimate of tag-side interfer-\nence for B \u2192D\u2217\u00b1\u03c0\u2213decays. Furthermore, the amplitude\nof the sin(\u2206md\u2206t) term in the time-evolution of this de-\ncay is 2r sin(2\u03c61 + \u03c63). Here the parameter r is the ratio\nof doubly-CKM suppressed to allowed decays for the re-\nconstructed B meson (the B \u2192D\u2217\u00b1\u03c0\u2213) and has nothing\nto do with the tag-side of the event.48 The magnitudes\nof both rf and r\u2032\nf are expected to be comparable and of\nthe order of 0.02, thus there is the potential for tag-side\ninterference to obscure the signal measurement. It is pos-\nsible to perform an analysis of the time-dependence of\nB \u2192D\u2217\u00b1\u03c0\u2213explicitly taking into account the e\ufb00ect of\ntag-side interference while doing so. In contrast to the dis-\ncussion of B decays to J/\u03c8K0\nS or \u03c0+\u03c0\u2212\ufb01nal states where\nthe e\ufb00ect of tag-side interference is treated as a pertur-\nbation on a measurement, for sin(2\u03c61 + \u03c63) one attempts\nto formally incorporate the full time-dependence of both\nB mesons decaying in an event, allowing for CP violation\nfor both the signal and tag sides. A scheme for doing this\nis outlined by Long, Baak, Cahn, and Kirkby (2003) and\nthis approach has been adopted by the B Factories.\n15.4 Summary\nIn order to provide for very precise measurements of var-\nious observables the systematic uncertainties of the mea-\nsurements must be kept under control. In an ideal case the\nsystematic uncertainty should not exceed the statistical\none by a large margin. At the B Factories several inge-\nnious methods were developed to estimate the remaining\nsystematic errors as precisely as possible. Whenever pos-\nsible the uncertainties are obtained using real data control\n48 The parameter r should not be confused with either the\nratio rf in Eq. (15.3.1), or the e\ufb00ective parameter r\u2032\nf for an\nensemble of modes on the tag-side of the event.\n\n176\nsamples, thus avoiding systematic e\ufb00ects due to possible\ndiscrepancies between MC simulation and data. For some\nsources of systematic uncertainties encountered in several\nmeasurements performed at the B Factories the estima-\ntion methods and representative values are summarized in\nTable 15.4.1.\n\n177\nTable 15.4.1. Summary of typical BABAR and Belle systematic uncertainties appearing in various measurements. \u2206\u03b5 denotes the di\ufb00erence between the e\ufb03ciency as\nestimated in the MC simulation and in the real data, \u03c3\u03b5 denotes the uncertainty on the e\ufb03ciency. \u03c3S,C denotes the uncertainty of CP violating parameters S, C (see\nChapter 10).\nMeasurement\nBABAR\nBelle\nComment\nMethod\nTypical value\nMethod\nTypical value\nTracking\ne+e\u2212\u2192\u03c4 \u00b1\u03c4 \u2213,\n\u03c3\u03b5/\u03b5 = (0.13 \u22120.24)%\nD\u2217+ \u2192D0(\u2192\u03c0+\u03c0\u2212K0\ns)\u03c0+\n\u03c3\u03b5/\u03b5 = 0.35%\nUncertainty per charged track\n\u03c4 \u00b1 \u2192h\u00b1h\u00b1h\u2213\u03bd, \u03c4 \u2213\u2192\u00b5\u2213\u00af\u03bd\n\u2206\u03b5\u2032/2\u03b5 = (0.10 \u22120.26)%\nAsymmetry for h+/h\u2212\ne+e\u2212\u21922\u03c0+2\u03c0\u2212\u03b3ISR\n\u2206\u03b5/\u03b5 = (0.7 \u22120.4)%\nUncertainty per charged track\nB \u2192h+h\u2212K0\ns(\u2192\u03c0+\u03c0\u2212)\n\u2206\u03b5/\u03b5 = (0.5 \u00b1 0.8)%\nUncertainty for tracks with displaced vertex\nD\u2217+ \u2192D0\u03c0+\ns\n\u03c3\u03b5/\u03b5 = 1.5%\nB0 \u2192D\u2217\u2212(\u2192D0\u03c0\u2212\ns )\u03c0+\n\u03c3\u03b5/\u03b5 = 1.3%\nUncertainty for low momentum\ntracks (p \u2272200 MeV/c)\nD\u2217+ \u2192D0(\u2192\u03c0+\u03c0\u2212K0\ns)\u03c0+\n\u03c3\u03b5/\u03b5 = 1%\nUncertainty for K0\ns reconstruction\n(including tracking uncertainty\nfor \u03c0+\u03c0\u2212)\nPID\nD\u2217+ \u2192D0(\u2192K\u2212\u03c0+)\u03c0+\n\u03c3\u03b5/\u03b5 = (0.8 \u22121.0)%\nD\u2217+ \u2192D0(\u2192K\u2212\u03c0+)\u03c0+\n\u03c3\u03b5/\u03b5 = (0.8 \u22121.0)%\nUncertainty per charged track\ne+e\u2212\u2192e+e\u2212(\u03b3)\ne+e\u2212\u2192e+e\u2212(\u03b3)\ne+e\u2212\u2192e+e\u2212\u2113+\u2113\u2212\ne+e\u2212\u2192e+e\u2212\u2113+\u2113\u2212\nJ/\u03c8 \u2192\u2113+\u2113\u2212\nJ/\u03c8 \u2192\u2113+\u2113\u2212\n\u03c00 reconstruction\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212,\n\u03b5data/\u03b5MC \u223c0.970 \u00b1 0.015\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212,\n\u03b5data/\u03b5MC = 0.960 \u00b1 0.024\nE\ufb03ciency correction per \u03c00 (p \u2265200 MeV/c)\n\u03c4 + \u2192e+\u03bd\u00af\u03bd, \u03c4 \u2212\u2192\u03c0\u2212(\u03c00)\u03bd\n\u03c4 + \u2192\u2113+\u03bd\u00af\u03bd or \u03c0+\u03c00\u00af\u03bd, \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\ne+e\u2212\u2192\u03b3ISR\u03c9(\u2192\u03c0+\u03c0\u2212\u03c00)\n\u03b7 \u21923\u03c00/\u03b7 \u2192\u03c0+\u03c0\u2212\u03c00\n\u03c3\u03b5/\u03b5 = 4%\nB0 \u2192D\u2217\u2212\u03c0+ \u2192D0\u03c00\u03c0+\n\u03b5data/\u03b5MC = 0.98 \u00b1 0.07\nB0 \u2192D\u2217\u2212\u03c0+ \u2192D0\u03c00\u03c0+\n\u03b5data/\u03b5MC = 1.024 \u00b1 0.027\nE\ufb03ciency correction per \u03c00 (p < 200 MeV/c)\nHigh energy photons\ne+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3\n\u2206\u03b5 = (1.00 \u00b1 0.55) \u00b7 10\u22122\nt-dependent\nMC\n\u03c3S,C \u22720.01\nMC\n\u03c3S,C \u22720.01\nvertex detector alignment\nchanging beam spot position\n\u03c3S/S \u223c0.13%\nchanging beam spot position\n\u03c3S/S \u223c0.3%\nbeam spot position\n\u03c3C/C \u223c0.06%\n\u03c3C/C \u223c0.08%\nvarying parameters\n\u03c3S,C \u22720.01\nvarying parameters\n\u03c3S,C \u22720.01\nresolution function, \ufb02avor tag\nfrom Bflav sample\nfrom Bflav sample\nvarying parameters\n\u03c3S,C \u223cO(10\u22123)\nvarying parameters\n\u03c3S,C \u223cO(10\u22123)\nphysics parameters (\u2206\u0393d, \u2206md, ...)\nvarying possible S, C\n\u03c3C/C \u2272(1 \u22122)%\nvarying possible S, C\n\u03c3C/C \u2272(1 \u22122)%\nCP violation in background\nfor background\nfor background\nB0 \u2192D\u2217\u2212\u2113+\u03bd\n\u03c3S,C \u223c(0.1, 1.4) \u00b7 10\u22122\nB0 \u2192D\u2217\u2212\u2113+\u03bd\n\u03c3S,C \u223c(0.1, 0.8) \u00b7 10\u22122\ntag-side interference in B \u2192J/\u03c8K0\ns\n\u03c3S \u223c1.0 \u00b7 10\u22122\n\u03c3S \u223c1.0 \u00b7 10\u22122\n}tag-side interference in b \u2192u\u00afud\n\u03c3C \u223c(1.6 \u22124.0) \u00b7 10\u22122\n\u03c3C \u223c(1.6 \u22124.0) \u00b7 10\u22122\n\n178\nPart C\nThe results and their\ninterpretation\nChapter 16\nThe CKM matrix and the\nKobayashi-Maskawa mechanism\nEditors:\nAdrian Bevan and Soeren Prell (BABAR)\nBo\u02c7stjan Golob and Bruce Yabsley (Belle)\nThomas Mannel (theory)\n16.1 Historical background\nFundamentals\nIn the early twentieth century the \u201celementary\u201d particles\nknown were the proton, the electron and the photon. The\n\ufb01rst extension of this set of particles occurred with the\nneutrino hypothesis, \ufb01rst formulated by W. Pauli in his\nfamous letter to his \u201cradioactive friends\u201d in 1924. From\nthe theoretical side, the formulation of a theory of weak\ninteractions by Fermi in 1934 marked another milestone\nin the development of our understanding. This set up for\nthe \ufb01rst time a framework, in which some of the funda-\nmental questions on the role of hadrons versus leptons and\non the properties of particles and their interactions could\nbe formulated. This also resulted in a clear formulation of\n\u201cweak\u201d versus \u201cstrong\u201d interactions and the understand-\ning of interactions as an exchange of mediating particles.\nIn particular, Yukawa postulated the existence of such a\nparticle and triggered the search for what we now know\nas the pion. At about the same time the muon was dis-\ncovered, and initially called the \u201c\u00b5 meson\u201d, however this\nsoon turned out to be distinct from the pion.\nAlthough the the term \u201c\ufb02avor\u201d came much later, one\nmay mark the beginning of (quark) \ufb02avor physics by the\ndiscovery of strange particles (Rochester and Butler, 1947).\nTheir decays into non-strange particles had lifetimes too\nlong to be classi\ufb01ed as strong decays: this led to the intro-\nduction of the strangeness quantum number (Gell-Mann,\n1953), which is conserved in strong decays but may change\nin a weak decay.\nThe subsequent proliferation of new particles could\nnicely be classi\ufb01ed and ordered by Gell Mann\u2019s \u201ceight-\nfold way\u201d (Gell-Mann, 1962), which was an extension of\nthe isospin symmetry to a symmetry based on the group\nSU(3). However, none of the particles \ufb01tted into the fun-\ndamental representation of this group, although there were\nvarious attempts such as Sakata\u2019s model, in which the pro-\nton, the neutron and the \u039b baryon formed the fundamen-\ntal representation. Eventually this puzzle was resolved by\nthe postulate of quarks as the fundamental building blocks\nof matter.\nStrangeness, parity violation, and charm\nThe decays of the strange particles, in particular of the\nkaons, paved the way for the further development of our\nunderstanding. Before 1954, the three discrete symmetries\nC (charge conjugation), P (parity) and T (time rever-\nsal) were believed to be conserved individually, a conclu-\nsion drawn from the well known electromagnetic interac-\ntion. Based on this assumption, the so called \u03b8-\u03c4 puzzle\nemerged: Two particles (at that time called \u03b8 and \u03c4, where\nthe latter is not to be confused with the third generation\nlepton) were observed, which had identical masses and\nlifetimes. However, they obviously had di\ufb00erent parities,\nsince the \u03b8 particle decayed into two pions (a state with\neven parity), and the \u03c4 particle decays into three pions (a\nstate with odd parity).\nThe resolution was provided by the bold assumption\nby Lee and Yang (1956) that parity is not conserved in\nweak interactions, and \u03b8 and \u03c4 are in fact the same par-\nticle, which we now call the charged kaon. Subsequently\nthe parity violating V \u2212A structure of the weak interac-\ntion was established and, on the experimental side, par-\nity violation was con\ufb01rmed directly in \u03b2 decays (Garwin,\nLederman, and Weinrich, 1957; Wu, Ambler, Hayward,\nHoppes, and Hudson, 1957). However, the combination of\ntwo discrete transformations, namely CP, still seemed to\nbe conserved.\nAnother puzzle related to kaon decays was the relative\ncoupling strength. It tuned out that the coupling strength\nof strangeness-changing processes is much smaller than\nthat of strangeness-conserving transitions. This \ufb01nding\neventually led to the parameterization of quark mixing\nby Cabibbo (1963). In modern language, the up quark u\ncouples to a combination d cos \u03b8C + s sin \u03b8C of the down\nquark d and the strange quark s. The value \u03b8C \u223c13\u25e6\nfor the Cabibbo angle explained the observed pattern of\nbranching ratios in baryon decays.\nExperiments at that time only probed the three light-\nest quarks, and there was no known reason for the extreme\nsuppression of the \ufb02avor changing neutral current (FCNC)\ndecay K+ \u2192\u03c0+\u2113+\u2113\u2212with respect to the charged cur-\nrent decay K+ \u2192\u03c00\u2113+\u03bd, \u0393(K+ \u2192\u03c0+\u2113+\u2113\u2212)/\u0393(K+ \u2192\n\u03c00\u2113+\u03bd) \u223c10\u22126. The resolution of this puzzle was found\nby Glashow, Iliopoulos, and Maiani (1970): one includes\nthe charm quark, with the same quantum numbers as the\nup quark, and coupling to the orthogonal combination\n\u2212d sin \u03b8C + s cos \u03b8C.\nFCNC processes are suppressed by this \u201cGIM mecha-\nnism\u201d. In fact, FCNC\u2019s in the kaon system involve a tran-\nsition of an s quark into a d quark. This can be achieved\nby two successive charged current processes involving (in\nthe two-family picture) either the up or the charm quark\nas an intermediate state. Taking Cabibbo mixing into ac-\n\n179\ncount, these amplitudes are\nA(s \u2192d) = A(s \u2192u \u2192d) + A(s \u2192c \u2192d)\n= sin \u03b8C cos \u03b8C [f(mu) \u2212f(mc)],(16.1.1)\nwhere f(m) is some smooth function of the mass m. Hence,\nif the up and charm quark masses were degenerate, K0 \u2212\nK0 mixing and other kaon FCNC processes would not oc-\ncur.\nHowever, the up and charm masses are not degenerate\nand thus K0 \u2212K0 mixing can occur. Neglecting the small\nup-quark mass, the mixing amplitude turns out to be\nA(K \u2192K) \u221dsin2 \u03b8C cos2 \u03b8C\nm2\nc\nM 2\nW\n.\n(16.1.2)\nThis implies that a mass di\ufb00erence \u2206mK appears in the\nneutral kaon system. From this mass di\ufb00erence (an expres-\nsion analogous to Eq. 10.1.17) Gaillard and Lee (1974b)\ncould extract the prediction that the charm-quark mass\nshould be about mc \u223c1.5 GeV, and it was one of the\ngreat triumphs of particle physics when narrow resonances\nwith masses of about 3 GeV were discovered a few months\nlater (Aubert et al., 1974; Augustin et al., 1974): these\nwere identi\ufb01ed as cc bound states. Around this time the\nterm \u201cparticle family\u201d was coined, and the discovery of\nthe charm quark completed the second particle family; it\nalso introduced a 2 \u00d7 2 quark mixing matrix into the phe-\nnomenology of weak interactions.\nCP violation and the Kobayashi-Maskawa mechanism\nAlmost ten years before the discovery of charm, CP vio-\nlation was observed in the study of rare kaon decays by\nChristenson, Cronin, Fitch, and Turlay (1964). This ef-\nfect is di\ufb03cult to accommodate for two families, but an\nextension to three families allows it to be taken into ac-\ncount naturally. The \u201csix-quark model\u201d was proposed by\nKobayashi and Maskawa (1973), extending Cabibbo\u2019s 2\u00d72\nquark mixing matrix into the 3 \u00d7 3 Cabibbo-Kobayashi-\nMaskawa (CKM) matrix. The GIM mechanism for the six\nquark model is implemented by the unitarity of the CKM\nmatrix.\nWhile the observation of decays K0\nL \u21922\u03c0 meant that\nCP was violated, the data at that time only required\nCP violation in mixing (see Section 16.6 for the classi-\n\ufb01cation of CP-violating e\ufb00ects). The observed strength\nof CP violation in mixing, \u03b5K \u22432.3 \u00d7 10\u22123, was consis-\ntent with the Kobayashi-Maskawa (KM) mechanism (El-\nlis, Gaillard, and Nanopoulos, 1976; Pakvasa and Sug-\nawara, 1976). However, this did not constitute a proof\nthat the KM mechanism was really the origin of the ob-\nserved CP violation; the measurement of the single pa-\nrameter \u03b5K could not be used to test the KM mechanism.\nOne alternative explanation was o\ufb00ered by the super-weak\nmodel of Wolfenstein (1964), where CP violation was due\nto a new, very weak four-fermion interaction that changed\nstrangeness by 2 units (\u2206S = 2). This possibility was\nruled out by the observation of direct CP violation in\nKL \u2192\u03c0\u03c0 decays, Re(\u03b5\u2032\nK/\u03b5K) = (1.65 \u00b1 0.26) \u00d7 10\u22123\n(Alavi-Harati et al., 1999; Burkhardt et al., 1988; Fanti\net al., 1999). Nonetheless, convincing evidence for the KM\nmechanism required the measurement of sin(2\u03c61) at the\nB Factories.\nWith the discovery of the \u03c4 lepton in 1975 (Perl et al.,\n1975) and of the bottom quark in 1977 (Herb et al., 1977)\nit became clear that there is a third generation of quarks\nand leptons. Furthermore, the bottom quark turned out\nto be quite long-lived, indicating a small mixing angle be-\ntween the \ufb01rst and second generation. This fact is the\nexperimental foundation of using B decays to study CP\nviolation, as well as for b tagging in high-pt physics.\nThe third generation remained incomplete for many\ndecades, since the top quark turned out to be quite heavy,\nand a direct discovery had to wait until 1995, when it was\ndiscovered at the Tevatron at Fermilab (Abachi et al.,\n1995a; Abe et al., 1994). However, the \ufb01rst hint of the\nlarge top-quark mass was the discovery of B0 \u2212B0 oscil-\nlations (also known as mixing) by ARGUS (Albrecht et al.,\n1987b). The measured \u2206md implied a heavy top with a\nmass mt above 50 \u221270 GeV, if the standard six quark\nmodel was assumed (Bigi and Sanda, 1987; Ellis, Hagelin,\nand Rudaz, 1987). The phenomenon of neutral meson mix-\ning is discussed in Chapter 10, while Section 17.5 discusses\nresults on B mixing from the B Factories.\nIn fact, if the top mass had been signi\ufb01cantly smaller,\nARGUS could not have observed B0\u2212B0 oscillations. The\nGIM mechanism for down-type quarks leads generally to\nsuppression factors of the form\nCKM Factor \u00d7\n1\n16\u03c02\nm2\nt \u2212m2\nu\nM 2\nW\n(16.1.3)\nand hence the GIM suppression for the bottom quark is\nmuch weaker than in the up-quark sector, where the cor-\nresponding factor is\nCKM Factor \u00d7\n1\n16\u03c02\nm2\nb \u2212m2\nd\nM 2\nW\n.\n(16.1.4)\nHence FCNC decays of B-mesons have branching ratios\nin the measurable region, while FCNC processes for D-\nmesons are heavily suppressed.\nThe third particle family was completed by the dis-\ncovery of the \u03c4 neutrino as a particle distinct from the\nelectron and the muon neutrino by the DONUT collabora-\ntion (Kodama et al., 2001). Although models with a fourth\nparticle generation are frequently considered as bench-\nmark models for physics beyond the Standard Model, there\nis no indication of a fourth family. On the contrary, from\nthe width of the Z boson precisely measured at LEP it\ncan be inferred that there is no further family with a neu-\ntrino lighter than 40 GeV, and the recent discovery of a\nHiggs boson in the mass range of 125 GeV (Aad et al.,\n2012; Chatrchyan et al., 2012b) rules out a large class of\nfourth-generation models.\n\n180\n16.2 CP violation and baryogenesis\nParticle physics experiments of the past thirty years have\ncon\ufb01rmed the Standard Model (SM) even at the quan-\ntum level, including quark mixing and CP violation. How-\never, the observed matter-antimatter asymmetry of the\nuniverse indicates that there must be additional sources\nof CP violation, since the amount of CP violation implied\nby the CKM mechanism is insu\ufb03cient to create the ob-\nserved matter-antimatter asymmetry.\nIn fact, the excess of baryons over antibaryons in the\nuniverse\n\u2206= nB \u2212nB\n(16.2.1)\nis small compared to the number of photons: the ratio is\nmeasured to be \u2206/n\u03b3 \u223c10\u221210. Although it is conceiv-\nable that there might be regions in the universe consisting\nof antimatter, just as our neighborhood consists of mat-\nter, no mechanism is known which could, from the Big\nBang, produce regions of matter (or antimatter) as large\nas we observe today. Furthermore, searches have been per-\nformed for sources of photons indicative of regions of mat-\nter and antimatter colliding. These searches failed to \ufb01nd\nany large regions of antimatter.\nThe conditions under which a non-vanishing \u2206can\nemerge dynamically from the symmetric situation \u2206=\n0 have been discussed by Sakharov (1967). He identi\ufb01ed\nthree ingredients\n1. There must be baryon number violating interactions\nHe\ufb00(\u2206B \u0338= 0) \u0338= 0.\n2. There must be CP violating interactions. If CP were\nunbroken, then we would have for every process i \u2192f\nmediated by He\ufb00(\u2206B \u0338= 0) the CP conjugate one with\nthe same probability\n\u0393(i \u2192f) = \u0393(i \u2192f)\n(16.2.2)\nwhich would erase any matter-antimatter asymmetry.\n3. The universe must have been out of thermal equilib-\nrium. Under the assumption of locality, causality, and\nLorentz invariance, CPT is conserved. Since in an equi-\nlibrium state time becomes irrelevant on the global\nscale, CPT reduces to CP, and the argument of point\n2 applies.\nIn order to illustrate the \ufb01rst two Saharov conditions,\nwe employ a very simplistic example. Assume that in the\nearly universe, there was a particle X that could decay to\nonly two \ufb01nal states |f1\u27e9and |f2\u27e9, with baryon numbers\nN (1)\nB\nand N (2)\nB\nrespectively, and decay rates\n\u0393(X \u2192f1) = \u03930r\nand\n\u0393(X \u2192f2) = \u03930(1 \u2212r) ,\n(16.2.3)\nwhere \u03930 is the total width of X. Taking the CP conjugate,\nthe particle X decays to the state f 1 with baryon number\n\u2212N (1)\nB\nand f 2 with baryon number \u2212N (2)\nB ; the rates are\n\u0393(X \u2192f 1) = \u03930r\nand\n\u0393(X \u2192f 2) = \u03930(1 \u2212r),\n(16.2.4)\nwhere \u03930 is the same as for X due to CPT invariance.\nThe overall change \u2206NB in baryon number induced\nby the decay of an equal number of X and X particles is\n\u2206NB = rN (1)\nB + (1 \u2212r)N (2)\nB \u2212rN (1)\nB \u2212(1 \u2212r)N (2)\nB\n= (r \u2212r)\n\u0010\nN (1)\nB \u2212N (2)\nB\n\u0011\n(16.2.5)\nThus \u2206NB \u0338= 0 means that we have to have CP violation\n(r \u0338= r) and a violation of baryon number (N (1)\nB \u0338= N (2)\nB ),\nillustrating the \ufb01rst two conditions.\nSakharov\u2019s paper remained mostly unnoticed until the\n\ufb01rst formulation of Grand Uni\ufb01ed Theories (GUTs). In\nthese theories, for the \ufb01rst time, all the necessary ingredi-\nents were present. In particular, baryon number violation\nappears naturally since quarks and leptons appear in the\nsame multiplets of the GUT symmetry group. Further-\nmore, there are additional sources of CP violation, and a\nphase transition takes place at the scale MGUT, which has\nto be quite high to prevent proton decay.\nOne may also consider electroweak baryogenesis. The\nelectroweak interaction provides CP violation through the\nCKM mechanism, and the electroweak phase transition\nhas been thoroughly studied. The \ufb01rst ingredient is also\npresent, as the current corresponding to baryon number\nis conserved only at the classical level: electroweak quan-\ntum e\ufb00ects violate baryon number, but still conserve the\ndi\ufb00erence B \u2212L of baryon and lepton number. However,\nalthough all the ingredients are present, this cannot ex-\nplain \u2206. In particular, the CKM CP violation is too small\nby several orders of magnitude.\nGiven the \ufb01rm evidence for non-vanishing neutrino\nmasses, there could be new sources of CP violation in the\nlepton sector, and even (although there is no evidence for\nthis as yet) lepton-number violation. This could lead to\nviolation of baryon number via leptogenesis, with the sur-\nplus of leptons transferred to the baryonic sector through\n(B \u2212L)-conserving interactions.\nIn any case, an additional source(s) of CP violation\nis needed, beyond the phase of the CKM matrix (which\nis explained in the next section), in order to explain the\nmatter-antimatter asymmetry of the universe. The search\nfor this new interaction is one of the main motivations for\n\ufb02avor-physics experiments.\n16.3 CP violation in a Lagrangian \ufb01eld theory\nThe SM is formulated as a quantum \ufb01eld theory based on\na Lagrangian derived from symmetry principles. To this\nend, the (hermitian) Lagrangian of the SM is given in\nterms of scalar operators Oi with couplings ai\nL(x) =\nX\ni\n\u0010\naiOi(x) + a\u2217\ni O\u2020\ni (x)\n\u0011\n,\n(16.3.1)\nwhere the Oi are composed of the SM quark, lepton, and\ngauge \ufb01elds. It is straightforward to verify that CP con-\nservation implies that all couplings ai can be made real\nby suitable phase rede\ufb01nitions of the \ufb01elds composing the\n\n181\nOi. In turn, CP is violated in a Lagrangian \ufb01eld theory if\nthere is no choice of phases that renders all ai real.\nIn the SM there are in principle two sources of CP\nviolation. The so-called \u201cstrong CP violation\u201d originates\nfrom special features of the QCD vacuum, resulting in a\ncontribution of the form\nLstrong CP = \u03b8 \u03b1S\n8\u03c0 G\u00b5\u03bd,a \u02dcGa\n\u00b5\u03bd\n(16.3.2)\nwhere G\u00b5\u03bd ( \u02dcG\u00b5\u03bd) is the (dual) strength of the gluon \ufb01eld.\nThis term is P and CP violating due to its pseudoscalar\nnature. However, a term such as Eq. (16.3.2) will have a\nstrong impact on the electric dipole moment (EDM) of the\nneutron, dN \u223c\u03b8 \u00d7 10\u221215 e cm. In combination with the\ncurrent limit on the neutron EDM of dN < 0.29 \u00d7 10\u221225\ne cm, this yields a stringent limit, \u03b8 \u226410\u221210. However,\nthe theoretical reason for its smallness has not yet been\ndiscovered. This is known as the \u201cstrong CP problem\u201d (see\nfor example Cheng, 1988; Kim and Carosi, 2010); we shall\nignore this in what follows by setting \u03b8 = 0.\nThe second source of CP violation is the CKM matrix.\nIt turns out that all terms in the SM Lagrangian are CP\ninvariant except for the charged current interaction term\nHcc =\ng\n\u221a\n2\n\u0000uL cL tL\n\u0001\nVCKM\u03b3\u00b5\n\uf8eb\n\uf8ed\ndL\nsL\nbL\n\uf8f6\n\uf8f8W +\n\u00b5 .\n(16.3.3)\nUnder a CP transformation we have\n\u0000uL cL tL\n\u0001\nVCKM\u03b3\u00b5\n\uf8eb\n\uf8ed\ndL\nsL\nbL\n\uf8f6\n\uf8f8W +\n\u00b5\n(16.3.4)\nCP\n\u2212\u2192\n\u0000dL sL bL\n\u0001\nV T\nCKM\u03b3\u00b5\n\uf8eb\n\uf8ed\nuL\ncL\ntL\n\uf8f6\n\uf8f8W \u2212\n\u00b5\n(16.3.5)\nand hence the combination Hcc+H\u2020\ncc appearing in the SM\nLagrangian is CP invariant, if\nV T\nCKM = V \u2020\nCKM\nor\nVCKM = V \u2217\nCKM.\n(16.3.6)\nThis statement refers to a speci\ufb01c phase convention for\nthe quark \ufb01elds; in general terms it implies that in the\nCP-invariant case, the CKM matrix can be made real by\nan appropriate phase rede\ufb01nition of the quark \ufb01elds.\n16.4 The CKM matrix\nThe CKM matrix VCKM appearing in Eq. (16.3.3) is ex-\nplicitly written as\nVCKM =\n\uf8eb\n\uf8ed\nVud Vus Vub\nVcd Vcs Vcb\nVtd Vts Vtb\n\uf8f6\n\uf8f8.\n(16.4.1)\nHere the Vij are the couplings of quark mixing transitions\nfrom an up-type quark i = u, c, t to a down-type quark\nj = d, s, b.\nIn the SM the CKM matrix is unitary by construction.\nUsing the freedom of phase rede\ufb01nitions for the quark\n\ufb01elds, the CKM matrix has (n \u22121)2 physical parameters\nfor the case of n families. Out of these, n(n \u22121)/2 are\n(real) rotation angles, and ((n \u22123)n + 2)/2 are phases,\nwhich induce CP violation. For n = 2, no CP violation\nis possible, while for n = 3 a single phase appears. This\nis the unique source of CP violation in the SM, once the\npossibility of strong CP violation is ignored.\nThe CKM matrix for 3 families may be represented by\nthree rotations and a matrix generating the phase\nU12 =\n\uf8ee\n\uf8f0\nc12 s12 0\n\u2212s12 c12 0\n0\n0 1\n\uf8f9\n\uf8fb,\nU13 =\n\uf8ee\n\uf8f0\nc13 0 s13\n0\n1 0\n\u2212s13 0 c13\n\uf8f9\n\uf8fb,\nU23 =\n\uf8ee\n\uf8f0\n1\n0\n0\n0 c23 s23\n0 \u2212s23 c23\n\uf8f9\n\uf8fb,\nU\u03b4 =\n\uf8ee\n\uf8f0\n1 0\n0\n0 1\n0\n0 0 e\u2212i\u03b413\n\uf8f9\n\uf8fb,\n(16.4.2)\nwhere cij = cos \u03b8ij, sij = sin \u03b8ij, and \u03b4 is the complex\nphase responsible for CP violation; by convention the mix-\ning angles \u03b8ij are chosen to lie in the \ufb01rst quadrant so that\nthe sij and cij are positive. Then (Chau and Keung, 1984)\nVCKM = U23U \u2020\n\u03b4 U13U\u03b4U12\n=\n\uf8eb\n\uf8ed\nc12c13\ns12c13\ns13e\u2212i\u03b4\n\u2212s12c23 \u2212c12s23s13ei\u03b4\nc12c23 \u2212s12s23s13ei\u03b4\ns23c13\ns12s23 \u2212c12c23s13ei\u03b4\n\u2212c12s23 \u2212s12c23s13ei\u03b4 c23c13\n\uf8f6\n\uf8f8.\n(16.4.3)\nThis is the representation used by the PDG (Beringer\net al., 2012).\nThe elements of the CKM matrix exhibit a pronounced\nhierarchy. While the diagonal elements are close to unity,\nthe o\ufb00-diagonal elements are small, such that e.g. Vud \u226b\nVus \u226bVub. In terms of the angles \u03b8ij we have \u03b812 \u226b\n\u03b823 \u226b\u03b813. This fact is usually expressed in terms of the\nWolfenstein parameterization (Wolfenstein, 1983), which\ncan be understood as an expansion in \u03bb = |Vus|. It reads\nup to order \u03bb3\nVCKM =\n\uf8eb\n\uf8ed\n1 \u2212\u03bb2/2\n\u03bb\nA\u03bb3(\u03c1 \u2212i\u03b7)\n\u2212\u03bb\n1 \u2212\u03bb2/2\nA\u03bb2\nA\u03bb3(1 \u2212\u03c1 \u2212i\u03b7)\n\u2212A\u03bb2\n1\n\uf8f6\n\uf8f8+ O(\u03bb4).\n(16.4.4)\nThe parameters A, \u03c1 and \u03b7 are assumed to be of order\none. When using this parameterization, one has to keep\nin mind that unitarity is satis\ufb01ed only up to order \u03bb4. As\nit turns out that both \u03c1 and \u03b7 are also of order \u03bb, the\n\n182\nextension to higher orders becomes non-trivial, and one\nhas to consider rede\ufb01ning the parameters accordingly; this\nhas been studied by Ahn, Cheng, and Oh (2011).\nOne can obtain an exact parameterization of the CKM\nmatrix in terms of A, \u03bb, \u03c1, and \u03b7, for example, by following\nthe convention of Buras, Lautenbacher, and Ostermaier\n(1994), where\n\u03bb = s12,\n(16.4.5)\nA = s23/\u03bb2,\n(16.4.6)\nA\u03bb3(\u03c1 \u2212i\u03b7) = s13e\u2212i\u03b4,\n(16.4.7)\nand by substituting Eqs (16.4.5) through (16.4.7) into\nEq. (16.4.3), while noting that sin2 \u03b8 = 1 \u2212cos2 \u03b8. Such a\nparameterization is described in Section 19.2.1.3 to illus-\ntrate CP violation in the charm sector.\nSometimes a slightly di\ufb00erent convention for the Wolfen-\nstein parameters is used, with parameters denoted \u03c1 and\n\u03b7. These parameters were de\ufb01ned at \ufb01xed order by Buras,\nLautenbacher, and Ostermaier (1994); the modern de\ufb01ni-\ntion (Charles et al., 2005),\n\u03c1 + i\u03b7 = \u2212VudV \u2217\nub\nVcdV \u2217\ncb\n,\n(16.4.8)\nholds to all orders. The di\ufb00erence with the parameteriza-\ntion de\ufb01ned above appears only at higher orders in the\nWolfenstein expansion; the relation between this scheme\nand the one de\ufb01ned in (16.4.5\u201316.4.7) is given by\n\u03c1 + i\u03b7 = (\u03c1 + i\u03b7)\n\u221a\n1 \u2212A2\u03bb4\n\u221a\n1 \u2212\u03bb2[1 \u2212A2\u03bb4(\u03c1 + i\u03b7)]\n.\n(16.4.9)\n16.5 The Unitarity Triangle\nThe unitarity relations VCKM \u00b7 V \u2020\nCKM = 1 and V \u2020\nCKM \u00b7\nVCKM = 1 yield six independent relations corresponding\nto the o\ufb00-diagonal zeros in the unit matrix. They can be\nrepresented as triangles in the complex plane; each trian-\ngle has the same area, re\ufb02ecting the fact that (with three\nfamilies) there is only one irreducible phase. A non-trivial\ntriangle \u2014 one with angles other than 0 or \u03c0 \u2014 indicates\nCP violation, proportional to the triangles\u2019 common area.\nBigi and Sanda (2000) provide a detailed discussion of the\nvarious triangles, their interpretation, and the possibilities\nto probe them. Only two triangles have sides of compara-\nble length, which means that they are of the same order in\nthe Wolfenstein parameter \u03bb. The corresponding relations\nare\nVudV \u2217\nub + VcdV \u2217\ncb + VtdV \u2217\ntb = 0\n(16.5.1)\nVudV \u2217\ntd + VusV \u2217\nts + VubV \u2217\ntb = 0.\n(16.5.2)\nInserting the Wolfenstein parameterization, both relations\nturn out to be identical, up to terms of order \u03bb5; the\napex of the Unitarity Triangle is given by the coordi-\nnate (\u03c1, \u03b7). The three sides of this triangle (Fig. 16.5.1) \u2014\nusually referred to as \u201cthe\u201d Unitarity Triangle\u2014 control\nsemi-leptonic and non-leptonic Bd transitions, including\nBd \u2212Bd oscillations. In order to obtain the triangle shown\nin Fig 16.5.1, Eq. (16.5.1) is divided by VcdV \u2217\ncb so that the\nbase of the triangle is of unit length. Due to the sizable\nangles, one expects large CP asymmetries in B decays in\nthe SM; this was actually realized before the discovery of\n\u201clong\u201d B lifetimes. Note that in both unitarity-triangle\nrelations CKM matrix elements related to the top quark\nappear; in particular Vtd and Vts can be accessed only\nindirectly via FCNC decays of bottom quarks.\nV V\nud ub\n*\nV V\ncd cb\n*\nV V\ntd tb\n*\nV V\ncd cb\n*\nq = `\nq = a\nq = _\n 1,0)\n(\n 0,0)\n(\n( l,d)\n1\n2\n_ _\n3\n \nFigure 16.5.1. The Unitarity Triangle.\nThe angles of the Unitarity Triangle are de\ufb01ned as\n\u03c61 = \u03b2 \u2261arg [\u2212VcdV \u2217\ncb/VtdV \u2217\ntb] ,\n(16.5.3)\n\u03c62 = \u03b1 \u2261arg [\u2212VtdV \u2217\ntb/VudV \u2217\nub] ,\n(16.5.4)\n\u03c63 = \u03b3 \u2261arg [\u2212VudV \u2217\nub/VcdV \u2217\ncb] ,\n(16.5.5)\nwhere this de\ufb01nition is independent of the speci\ufb01c phase\nchoice expressed in Eq. (16.4.3). Di\ufb00erent notation con-\nventions have been used in the literature for these angles.\nIn particular the BABAR experiment has used \u03b1, \u03b2, and\n\u03b3, whereas the Belle experiment has reported results in\nterms of \u03c62, \u03c61, and \u03c63, respectively. We use the latter for\nbrevity when discussing results in later sections.\nThe presence of CP violation in the CKM matrix im-\nplies non-trivial values for these angles (\u03c6i \u0338= 0\u25e6, 180\u25e6),\ncorresponding to a non-vanishing area for the Unitarity\nTriangle. In fact, all the triangles that can be formed from\nthe unitarity relation have the same area, which is propor-\ntional to the quantity\n\u2206= Im V \u2217\ncsVusVcdV \u2217\nud\n(16.5.6)\nwhich is independent of the phase convention. Note that\nall other, rephasing invariant fourth order combinations of\nCKM matrix elements, which cannot be reduced to prod-\nucts of second order invariants, can be related to \u2206, which\nis thus unique.\nFurthermore, the phase in the CKM matrix could also\nbe removed, if the masses of either two up-type quarks or\ntwo down-type quarks were degenerate. In summary, the\npresence of CP violation is equivalent to (Jarlskog, 1985)\nJ = det[Mu , Md]\n= 2i\u2206\u00d7 (mu \u2212mc)(mu \u2212mt)(mc \u2212mt)\n\u00d7 (md \u2212ms)(md \u2212mb)(ms \u2212mb)\n(16.5.7)\n\n183\nbeing non-vanishing.\nThe SM allows us to construct \u201cthe\u201d Unitarity Tri-\nangle by measuring its angles or its sides or any combi-\nnations of them. Any discrepancy between the observed\nand predicted values indicates a manifestation of dynam-\nics beyond the SM. Clearly this requires good control of\nexperimental and theoretical uncertainties, both in their\nCP sensitive and insensitive rates.\nMeasurements of the magnitudes of CKM matrix el-\nements Vub and Vcb can be found in Section 17.1, and\nmeasurements of Vtd and Vts in Section 17.2. Measure-\nments of the angles \u03c61, \u03c62, and \u03c63 are discussed in Sec-\ntions 17.6, 17.7, and 17.8 respectively. It is possible to\nperform global \ufb01ts, using data from many decay processes\nto over-constrain our knowledge of the CKM mechanism.\nGiven the lack of knowledge of the determination of the\napex of the Unitarity Triangle, these global \ufb01ts are often\nexpressed in terms of constraints on the (\u03c1, \u03b7) plane. Some\nexperimental results require input from Lattice QCD cal-\nculations in order to be used in a global \ufb01t. These global\n\ufb01ts are discussed in Chapter 25, both in the context of the\nSM (Section 25.1) and allowing for physics beyond the SM\n(Section 25.2).\nIt is exactly some of the measurements described in\nChapter 17 and further in Section 25.1 which were ad-\ndressed in (Nobelprize.org, 2010) among experimental ver-\ni\ufb01cations of the Kobayashi-Maskawa mechanism in the\nscienti\ufb01c background to the 2008 Nobel Prize in Physics\nawarded to M. Kobayashi and T. Maskawa: \u201dThe respec-\ntive collaborations BABAR and BELLE have now mea-\nsured the CP violation in remarkable agreement with the\nmodel ... and all experimental data are now in impressive\nagreement with the model ...\u201d.\n16.6 CP violation phenomenology for B\nmesons\nSince CP violation is due to irreducible phases of coupling\nconstants, it becomes observable through interference ef-\nfects. The simplest example is an amplitude consisting of\ntwo distinct contributions\nAf = \u03bb1\u27e8f|O1|B\u27e9+ \u03bb2\u27e8f|O2|B\u27e9\n(16.6.1)\nwhere \u03bb1,2 are (complex) coupling constants (in our case\ncombinations of CKM matrix elements) and \u27e8f|O1,2|B\u27e9\nare matrix elements of interaction operators between the\ninitial and \ufb01nal state.\nThe CP conjugate is the process B \u2192f, yielding\nAf = \u03bb\u2217\n1\u27e8f|O\u2020\n1|B\u27e9+ \u03bb\u2217\n2\u27e8f|O\u2020\n2|B\u27e9.\n(16.6.2)\nThe matrix elements of O(\u2020)\n1,2 involve only strong interac-\ntions, which we assume to be CP-invariant. Hence we have\n\u27e8f|O\u2020\n1|B\u27e9= \u27e8f|O1|B\u27e9\nand\n\u27e8f|O\u2020\n2|B\u27e9= \u27e8f|O2|B\u27e9.\n(16.6.3)\nThus for the CP asymmetry we \ufb01nd\nACP (B \u2192f) \u2261\u0393(B \u2192f) \u2212\u0393(B \u2192f)\n\u0393(B \u2192f) + \u0393(B \u2192f)\n(16.6.4)\n\u221d2 Im[\u03bb1\u03bb\u2217\n2] Im[\u27e8f|O1|B\u27e9\u27e8f|O2|B\u27e9\u2217].\nConsequently, in order to create CP violation, there has\nto be \u2014 aside from the \u201cweak phase\u201d due to the complex\nphases of the CKM matrix \u2014 also a \u201cstrong phase\u201d, i.e.\na phase di\ufb00erence between the matrix elements \u27e8f|O1|B\u27e9\nand \u27e8f|O2|B\u27e9. In the SM these two contributions corre-\nspond to di\ufb00erent diagram topologies. In many cases, one\ncan identify tree-level contributions which carry di\ufb00erent\nCKM factors compared to loop (penguin) contributions.\nCP violation then emerges from the interference of \u201ctrees\u201d\nand \u201cpenguins\u201d.\nIn the following we are going to consider decays into\nCP eigenstates f in which case we have f = f. For a\nquantum-coherent pair of neutral B-mesons (like the color-\nsinglet B0B0 pair from \u03a5(4S) decay) the time evolution\ngenerates a phase di\ufb00erence \u2206m \u2206t, which acts like the\nstrong phase di\ufb00erence between the amplitudes for B \u2192f\nand for B \u2192B \u2192f. Hence we make use of the time-\ndependent CP asymmetry\nAB\u2192f\nCP\n(\u2206t) \u2261\u0393(B0(\u2206t) \u2192f) \u2212\u0393(B0(\u2206t) \u2192f)\n\u0393(B0(\u2206t) \u2192f) + \u0393(B0(\u2206t) \u2192f)\n= SB\u2192f sin (\u2206md \u2206t) \u2212CB\u2192f cos (\u2206md \u2206t) .\n(16.6.5)\nThe derivation (see the discussion in Chapter 10 leading\nto Eq. 10.2.8) neglects the small lifetime di\ufb00erence \u2206\u0393 in\nthe Bd system; the expressions for S and C can be found\nin Eqs (10.2.4) and (10.2.5).\nWe may distinguish three di\ufb00erent types of CP vi-\nolation according to the various sources from which it\nemerges. CP violation in decays, sometimes referred to as\ndirect CP violation, stems from di\ufb00erent rates for a pro-\ncess and for its CP conjugate: hence we have |Af/Af| \u0338= 1.\nThis contribution leads to CB\u2192f \u0338= 0: it is already present\nat \u2206t = 0, and remains in time-integrated measurements.\nCP violation in the mixing emerges in cases where we\nhave |p/q| \u0338= 1.49 One observable related to this is the\nsemileptonic decay asymmetry aSL, which is the asym-\nmetry between the decay rate of B0 \u2192X\u2212\u2113+\u03bd\u2113and the\nCP conjugate process. Finally, mixing-induced CP viola-\ntion, sometimes also called CP violation in interference\nbetween a decay without mixing and a decay with mixing\noccurs for Im\u03bb \u0338= 0, in which case interference of the am-\nplitudes B \u2192f and B \u2192B \u2192f leads to CP violation.50\n49 For a de\ufb01nition of the quantities p, q, and \u03bb, we refer to\nChapter 10, where time evolution is considered.\n50 In kaon physics sometimes the notion indirect CP viola-\ntion is used for saying that the parameter \u03f5 is non-vanishing.\nComparing this with the de\ufb01nitions given here, non-vanishing\n\u03f5 corresponds to a combination of |q/p| \u0338= 1 and |Af/Af| \u0338= 1.\n\n184\nIn the Bd system we have to a very good approxima-\ntion51\nq\np = exp(\u22122i\u03c61) .\n(16.6.6)\nThis follows from Eq. (10.1.19) and by inspection of the\nbox diagram contributing to the Bd mixing (Fig. 10.1.1),\nfrom which it can be seen that the CKM matrix elements\nappearing in the amplitude yield \u03c6M12 = 2\u03c61. Hence in all\ncases where A = A, we \ufb01nd |\u03bb| = 1 and Im\u03bb = \u2212sin(2\u03c61),\nleading to\nCB\u2192f = 0\nand\nSB\u2192f = \u2212sin(2\u03c61).\n(16.6.7)\nThis holds for the golden mode B \u2192J/\u03c8Ks where there\nis no relative weak phase between A and A. However, if\nthere appears a relative weak phase in the decay ampli-\ntudes, then we may still have |A| = |A| and hence |\u03bb| = 1,\nand thus no direct CP violation. For example, the tree\namplitude in B \u2192\u03c0\u03c0 carries a weak phase e\u2212i\u03c63 which\n(neglecting penguin contributions) would lead to\n\u03bb = exp(\u22122i(\u03c61 + \u03c63)) = exp(+2i\u03c62).\n(16.6.8)\nHowever, the penguin contribution in B \u2192\u03c0\u03c0 cannot be\nneglected; in particular it leads to |\u03bb| \u0338= 1 and to direct\nCP violation in these decays.\nIn general we have the \u201cunitarity relation\u201d between\nthe quantities SB\u2192f and CB\u2192f,\n\u0000CB\u2192f\u00012 +\n\u0000SB\u2192f\u00012 = 1 \u2212\n\u0000DB\u2192f\u00012 \u22641\n(16.6.9)\nwhere\nDB\u2192f =\n2 Re\u03bb\n1 + |\u03bb|2 .\n(16.6.10)\nHowever, in the limit of vanishing lifetime di\ufb00erence the\ntime-dependent CP asymmetry does not depend on DB\u2192f,\nand hence a direct measurement of this quantity in the Bd\nsystem is di\ufb03cult.\n51 This relation depends on the phase conventions used. It\nholds in the convention used in (16.4.3).\n\n185\nChapter 17\nB physics\nThe main objective of the B Factories was to perform mea-\nsurements of the decays and CP asymmetries of B mesons.\nWhile the asymmetric set-up and high luminosities of the\nB Factories allowed us for the \ufb01rst time to perform sta-\ntistically signi\ufb01cant measurements of time-dependent CP\nasymmetries, the symmetric predecessors of the B Fac-\ntories, DORIS and CESR, had already produced some\ndata on B decays. Experiments at LEP and the Tevatron\nhad provided a proof of principle of the time-dependent\nCP asymmetry measurement in the golden mode B0 \u2192\nJ/\u03c8K0\nS, and improved our knowledge of B0\nd mixing.\nMost of the time, the B Factories took data near the\n\u03a5(4S) resonance, which decays almost exclusively into\nB0B0 and B+B\u2212pairs. As a consequence, the overwhelm-\ning majority of B Factory measurements relate to these\nstates: these measurements are described in the follow-\ning sections. However, some data has been taken at the\n\u03a5(5S) resonance, which also decays into B(\u2217)0\ns\nB(\u2217)0\ns\npairs.\nMeasurements of B0\ns decays performed with this data are\ndiscussed in Chapter 23.\nThere are many ways to arrange this vast amount of\nmaterial. The scheme adopted for this book uses the Uni-\ntarity Triangle as an organizing principle. We start from\na discussion of the ways the sides of the triangle are con-\nstrained, including theoretical methods as well as exper-\nimental results in the corresponding sections. Hence we\nstart with the measurements determining the magnitude\nof the CKM matrix elements Vcb, Vub, Vts, and Vtd. This\nis followed by a discussion of the decay rates of charmed\nand charmless non-leptonic processes, including a com-\nparison with theoretical expectations. The reason for this\nis that many charmed and charmless non-leptonic decay\nmodes are used in the measurement of CP asymmetries,\nand therefore should be discussed before moving on to re-\nview work related to the angles of the Unitarity Triangle.\nBefore treating the CP asymmetries related to the an-\ngles of the Unitarity Triangle, we discuss measurements\nof B lifetimes and B0 \u2212B0 mixing, which are needed\nto understand the time-dependent analyses performed for\nthe extraction of the angles. Searches for CPT and other\nsymmetry violations which are based on the lifetime- and\nmixing-measurement techniques are then presented. Fol-\nlowing on from this one will \ufb01nd the description of mea-\nsurements of CP violation, i.e. the extraction of the angles\n\u03c61, \u03c62, and \u03c63.\nThe end of this chapter is devoted to special processes.\nThese are either rare decays related to \ufb02avor changing neu-\ntral current transitions of the b quark, processes involving\n\u03c4 leptons or baryons in the \ufb01nal state, or decays which are\nvery rare or forbidden in the Standard Model.\n\n186\n17.1 Vub and Vcb\nEditors:\nVera Luth (BABAR)\nChristoph Schwanda (Belle)\nPaolo Gambino [Vcb]; Frank Tackmann [Vub] (theory)\nAdditional section writers:\nChristine Davies, Jochen Dingfelder, Alexander Khod-\njamirian, Andreas Kronfeld, Matthias Steinhauser, and\nRuth Van de Water\n17.1.1 Overview of semileptonic B decays\n17.1.1.1 Motivation\nSemileptonic decays of B+ and B0 mesons proceed via\nleading-order weak interactions. In the following, only de-\ncays involving low-mass charged leptons, \u2113= e\u00b1 or \u00b5\u00b1, are\nconsidered. They are expected to be free of non-Standard\nModel contributions, and therefore play a critical role in\nthe determination of the magnitudes of the CKM-matrix\nelements Vcb and Vub. |Vcb| normalizes the Unitarity Trian-\ngle, and the ratio |Vub|/|Vcb| determines the side opposite\nto the angle \u03c61. Thus, their values impact most studies of\n\ufb02avor physics and CP-violation in the quark sector. Lep-\ntonic and semileptonic decays involving \u03c4 \u00b1 leptons are\nsensitive to couplings to the charged Higgs boson and are\ndiscussed in Section 17.10.\nThere are two methods to determine |Vcb| and |Vub|,\none based on the study of exclusive semileptonic B decays\nwhere the hadron in the \ufb01nal state is a D, D\u2217, D\u2217\u2217, \u03c0 or\n\u03c1 meson, the other based on the study of inclusive decays\nof the form B \u2192X\u2113+\u03bd\u2113, where X refers to either Xc or\nXu, i.e., to any hadronic \ufb01nal state with charm or without\ncharm, respectively.\nTo extract |Vcb| or |Vub| from the measured partial de-\ncay rates, both inclusive and exclusive determinations rely\non theoretical descriptions of the QCD contributions to\nthe underlying weak decay process. Since both methods\nrely on di\ufb00erent experimental techniques and involve dif-\nferent theoretical approximations, they complement each\nother and provide largely independent determinations (of\ncomparable accuracy) of |Vcb| and |Vub|. This in turn pro-\nvides a crucial cross check of the methods and our under-\nstanding of semileptonic B decays in general.\n17.1.1.2 Theoretical Overview\nSemileptonic decays of B mesons, B \u2192X\u2113\u03bd, proceed\nthrough the electroweak transitions b \u2192c\u2113\u03bd and b \u2192u\u2113\u03bd,\nas illustrated in Figure 17.1.1. These are governed by the\nCKM-matrix elements Vcb and Vub, and since the inter-\nmediate W boson decays leptonically, do not involve any\nother CKM matrix elements. Hence, measurements of the\nB \u2192X\u2113\u03bd decay rate can be used to directly measure |Vcb|\nand |Vub|.\nVqb\nW \u2212\n\u2113\u2212\n\u00af\u03bd\u2113\nb\n\u00afu\nq\n\u00afu\nFigure 17.1.1.\nIllustration of semileptonic decay B\u2212\u2192\nX\u2113\u2212\u03bd\u2113.\nThe theoretical description of semileptonic B decays\nstarts from the electroweak e\ufb00ective Hamiltonian,\nHe\ufb00= 4GF\n\u221a\n2\nX\nq=u,c\nVqb (q\u03b3\u00b5PLb)(\u2113\u03b3\u00b5PL\u03bd\u2113) ,\n(17.1.1)\nwhere PL = (1 \u2212\u03b35)/2, and GF is the Fermi constant\nas extracted from muon decay. The W boson has been\nintegrated out at tree level using the hierarchy mb \u226amW ,\nand higher-order electroweak corrections are suppressed\nby additional powers of GF and are thus very small. The\ndi\ufb00erential B decay rates take the form\nd\u0393 \u221dG2\nF |Vqb|2 \f\fL\u00b5\u27e8X|q\u03b3\u00b5PLb|B\u27e9\n\f\f2 .\n(17.1.2)\nAn important feature of semileptonic decays is that the\nleptonic part in the e\ufb00ective Hamiltonian and the decay\nmatrix element factorizes from the hadronic part, and that\nQCD corrections can only occur in the b \u2192q current.\nThe latter do not a\ufb00ect Eq. (17.1.1) and are fully con-\ntained in the hadronic matrix element \u27e8X|q\u03b3\u00b5PLb|B\u27e9in\nEq. (17.1.2). This factorization is violated by small elec-\ntromagnetic corrections, for example by photon exchange\nbetween the quarks and leptons, which must be taken into\naccount in situations where high precision is required.\nThe challenge in the extraction of |Vcb| and |Vub| is\nthe determination of the hadronic matrix element of the\nquark current in Eq. (17.1.2). For this purpose, di\ufb00erent\ntheoretical methods have been developed, depending on\nthe speci\ufb01c decay mode under consideration. In almost\nall cases, the large mass of the b-quark, mb \u223c5 GeV is\nexploited.\nIn exclusive semileptonic decays, one considers the de-\ncay of the B meson into a speci\ufb01c \ufb01nal state X = D, D\u2217, \u03c0,\nor \u03c1. In this case, one parameterizes the hadronic ma-\ntrix element in terms of form factors, which are non-\nperturbative functions of the momentum transfer q2. This\nis discussed in Sections 17.1.2 and 17.1.4. The two meth-\nods commonly used to determine the form factors are\nlattice QCD (LQCD) and light-cone sum rules (LCSR).\nIn LQCD, the QCD functional integrals for the matrix\nelements are computed numerically from \ufb01rst principles.\nHeavy quark e\ufb00ective theory (HQET), and non-relativistic\nQCD (NRQCD), were \ufb01rst introduced, at least in part, to\nenable lattice-QCD calculations with heavy quarks. Even\nwhen these formalisms are not explicitly used, heavy-\nquark dynamics are usually used to control discretization\n\n187\ne\ufb00ects. An exception are the most recent determinations\nof mc and mb from lattice QCD, discussed below, which\nuse a \ufb01ne lattice in combination with a highly improved\nlattice action such that heavy quarks with masses almost\nup to mb can be treated with a light-quark formalism.\nA complementary method is based on LCSR which use\nhadronic dispersion relations to approximate the form fac-\ntor in terms of quark-current correlators and can be cal-\nculated in an operator product expansion (OPE).\nIn inclusive semileptonic decays, one considers the sum\nover all possible \ufb01nal states X that are kinematically al-\nlowed. Employing parton-hadron duality one can replace\nthe sum over hadronic \ufb01nal states with a sum over par-\ntonic \ufb01nal states. This eliminates any long-distance sen-\nsitivity to the \ufb01nal state, while the short-distance QCD\ncorrections, which appear at the typical scale \u00b5 \u223cmb\nof the decay, can be computed in perturbation theory in\nterms of the strong coupling constant \u03b1S(mb) \u223c0.2. The\nremaining long-distance corrections related to the initial\nB meson can be expanded in powers of \u039bQCD/mb \u223c0.1,\nwhere \u039bQCD is the hadronic scale of order mB \u2212mb \u223c\n0.5 GeV. This is called heavy quark expansion (HQE), and\nit systematically expresses the decay rate in terms of non-\nperturbative parameters that describe universal proper-\nties of the B meson. This is discussed in Sections 17.1.3\nand 17.1.5.\n17.1.1.3 Experimental Techniques\nAs in other analyses of BB data recorded at B Factories,\nthe two dominant sources of background for the recon-\nstruction of semileptonic B decays are the combinatorial\nBB and the continuum backgrounds (see Chapter 9).\nThe suppression of the continuum processes, e+e\u2212\u2192\n\u2113+\u2113\u2212(\u03b3) with \u2113= e, \u00b5, or \u03c4, and quark-antiquark pair pro-\nduction, e+e\u2212\u2192qq(\u03b3) with q = u, d, s, c, is achieved by\nrequiring at least four charged particles in the event and\nby imposing restrictions on several event shape variables,\neither sequentially on individual variables or by construct-\ning multivariable discriminants. Among these variables are\nthrust, the maximum sum of the longitudinal momenta of\nall particles relative to a chosen axis, \u2206\u03b8thrust, the angle\nbetween the thrust axis of all particles associated with the\nsignal decay and the thrust axis of the rest of the event,\nR2, the ratio of the second to the zeroth Fox-Wolfram mo-\nments, and L0 and L2, the normalized angular moments.\nThe separation of semileptonic B decays from BB\nbackgrounds is very challenging because they result in one\nor more undetected neutrinos. The energy and momentum\nof the missing particles can be inferred from the sum of\nall other particles in the event,\n(Emiss, pmiss) = (E0, p0) \u2212\n X\ni\nEi,\nX\ni\npi\n!\n,\n(17.1.3)\nwhere (E0, p0) is the four-vector of the colliding beams.\nIf the only undetected particle in the event is a single\nneutrino, the missing mass should be close to zero and\nthe missing momentum should be non-zero. Figure 17.1.2\nshows examples of missing mass squared distributions,\nm2\nmiss = E2\nmiss \u2212|pmiss|2, for selected B\u2212\u2192Xc\u2113\u2212\u03bd can-\ndidates. There are narrow peaks at zero for correctly re-\nconstructed decays and in most cases rather small back-\ngrounds from other decays modes. In Figure 17.1.2a there\nis a broad enhancement above the peak due to B\u2212\u2192\nD\u22170\u2113\u2212\u03bd decays, in which the low energy pion or pho-\nton from the decay D\u22170 \u2192D0\u03c00 or D\u22170 \u2192D0\u03b3 es-\ncaped detection. To reduce the impact of the dependence\nof the m2\nmiss resolution on the neutrino energy, the variable\nEmiss \u2212pmiss = m2\nmiss/(Emiss + pmiss) is often preferred.\nA variable \ufb01rst introduced by the CLEO Collabora-\ntion (Bartelt et al., 1999) to select exclusive semileptonic\ndecays B \u2192D\u2113\u03bd is\ncos \u03b8BY = (2EBEY \u2212m2\nB \u2212m2\nY )/2|pB||pY |,\n(17.1.4)\nwhere mY and |pY | refer to the invariant mass and mo-\nmentum sum of the hadron X and the charged lepton \u2113.\nIf the only missing particle is the neutrino, \u03b8BY corre-\nsponds to the angle between the momentum vectors pB\nand pY = pX + p\u2113, and the condition | cos \u03b8BY | \u22641.0\nshould be ful\ufb01lled, while for background events or incom-\npletely reconstructed semileptonic decays the distribution\nextends to values well beyond this range, thus enabling a\nseparation from the signal decays.\nFor the isolation of the exclusive signal decay the kine-\nmatic variables\n\u2206E = E\u2217\nB \u2212E\u2217\nbeam and mES =\nq\nE\u22172\nbeam \u2212p\u22172\nB (17.1.5)\nare used. A comparison of \u2206E and mES distributions for\nselected samples of hadronic and semileptonic B decays is\ngiven in Figure 17.1.3. \u2206E is centered on zero and the mES\ndistribution peaks at the B-meson mass. For hadronic de-\ncays the \u2206E resolution is dominated by the detector reso-\nlution. The resolution in mES is determined by the spread\nin the energy of the colliding beams, typically less than 3\nMeV. For semileptonic decays both variables are a\ufb00ected\nby the measurement of the neutrino momentum and en-\nergy. The size of the continuum and combinatorial BB\nbackground depends on the decay mode and the overall\nevent selection. Backgrounds with kinematics very similar\nto the signal B decays may contribute to the peak region\nde\ufb01ned as |\u2206E| < 0.125 GeV, mES > 5.27 GeV.\nThere are several variables that are commonly used\nto describe the kinematics of semileptonic decays, both\nfor exclusive and inclusive decays: the momentum trans-\nfer squared q2, the momentum of the charged lepton p\u2113,\nand the hadronic mass mX. The last two are of particu-\nlar importance for analyses of inclusive decays, summing\nover all possible hadronic states X. They are used to sepa-\nrate charmless decays from the dominant decays to charm\nhadrons.\nThere are two ways to de\ufb01ne and measure q2, either\nas the invariant mass squared of the four-vector sum of\nthe reconstructed lepton and neutrino, or as the momen-\ntum transfer squared from the B meson to the \ufb01nal state\nhadron X, q2 = (p\u2113+ pmiss)2 = (pB \u2212pX)2. In the \ufb01rst\n\n188\n0\n1\n2\nEvents (0.04 GeV2)\n0\n40\n80\n120\n160\n\u03bd\n Dl\n\u2192\nB \n\u03bd\n D*l\n\u2192\nB \n\u03bd\n D**l\n\u2192\nB \nContinuum + BB\nFake Lepton\n(a)\n-1\n0\nM2miss (GeV2)\n1\n2\n0\n100\n200\n300\n(b)\n(c)\n1-2011\n8809A6\n-1\n0\n1\n0\n20\n40\n60\n80\nFigure 17.1.2. Distributions of the missing mass squared for exclusive B \u2192Xc\u2113\u03bd candidates in BB events tagged by a\nhadronic decay of the second B meson (Aubert, 2008b), a) B\u2212\u2192D0\u2113\u2212\u03bd\u2113, b) B0 \u2192D\n\u2217+\u2113\u2212\u03bd\u2113, and c) B\u2212\u2192D\u2217+\u03c0\u2212\u2113\u2212\u03bd\u2113. The\ncontributions from various exclusive decay modes are marked by color shading.\nFigure 17.1.3. Distributions of mES and \u2206E for (a, b) hadronic B decays above combinatorial continuum and BB background\n(blue) (Mazur, 2007), and (c, d) selected B0 \u2192\u03c0\u2212\u2113+\u03bd decays (Ha, 2011) in the q2 range of 0 \u221216 GeV2, above a variety of\nbackgrounds contributions, speci\ufb01cally B \u2192Xu\u2113\u03bd (red), various B \u2192Xc\u2113\u03bd decays (yellow), and continuum background (blue).\nFor both samples, the distributions are restricted to events in the signal bands, i.e., mES is shown for events in the peak region\nfor \u2206E, |\u2206E| < 0.125 GeV, and \u2206E is restricted to events in the peak region for mES, mES > 5.27 GeV.\ncase, the resolution in q2 is dominated by the measure-\nment of the missing energy which tends to have a poorer\nresolution than the measured missing momentum, because\nthe missing momentum is a vector sum and contributions\nfrom particle losses (or additional tracks and EMC show-\ners) do not add linearly as is the case for Emiss. Thus\nit is advantageous to replace Emiss by |p|miss, the ab-\nsolute value of the measured missing momentum, q2 =\n[(E\u2113, p\u2113) + (pmiss, pmiss)]2.\nIn the second case, the q2 measurement is not a\ufb00ected\nby the measurement of the missing momentum, but the\ndirection of the B meson momentum is not known. There-\nfore the B momentum vector is estimated as the average\nover four or more possible directions of the B meson. The\ntwo methods have di\ufb00erent sensitivity to combinatorial\nbackground: the \ufb01rst has the best resolution at high q2,\nwhereas the second method shows the best resolution at\nlow q2 where the hadron background is smaller. The width\nof the core resolution is in the range (0.18 \u22120.34) GeV2,\nand the tails can be approximated by a second Gaussian\nfunction with widths in the range (0.6 \u22120.8) GeV2. Fig-\nure 17.1.4 shows the resolution for selected B \u2192\u03c0\u2113\u03bd can-\ndidates. The q2 resolution is important for many analyses\nof semileptonic decays.\nWith increasing data samples, more recent analyses\nhave employed BB tagging techniques to substantially re-\nduce continuum and combinatorial BB backgrounds. The\ndetection of the decay of one of the B mesons produced\nat the \u03a5(4S) not only identi\ufb01es the second B decay, but\nit uniquely determines its momentum, mass, charge and\n\ufb02avor. Furthermore, the kinematics of the \ufb01nal state are\nconstrained such that an undetectable neutrino from the\n\n189\n)\n2\n (GeV\ntrue\n2\n-q\ncorr\n2\nq\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\nCandidates\n0\n100\n200\n300\n400\n500\n600\n700\nFit Region\nFigure 17.1.4. q2 resolution for selected B0 \u2192\u03c0\u2212\u2113+\u03bd de-\ncays (del Amo Sanchez, 2011n) for true signal (black, solid\nhistogram) and combinatorial signal (blue, dashed histogram)\nas obtained from simulation. The result of the \ufb01t to the signal\nwith the sum of two Gaussian functions is shown (solid and\ndotted lines).\nsecond decay can be identi\ufb01ed from the missing momen-\ntum and missing energy of the rest of the event.\nThe cleanest samples of BB events are obtained with\nhadronic tags. Tag e\ufb03ciencies and purities vary consid-\nerably, depending on the number of charged and neutral\nparticles in the tag decay and the associated signal decay.\nGiven the low branching fractions for individual hadronic\ndecays and their high \ufb01nal-state particle multiplicity, the\naverage achievable tagging e\ufb03ciency is typically 0.3% for\npurities of \u22430.5. Recently, tag e\ufb03ciencies have been in-\ncreased as much as a factor of three by the addition of\nother hadronic decay modes, and by simultaneous con-\nstraints on the semileptonic signal decay in a given event,\nand by e\ufb00ectively selecting the best of several candidates\nper event (see Chapter 7).\nTag e\ufb03ciencies in the range of 1 \u22123% can be obtained\nusing semileptonic B decays. As for hadronic tags, the\nachievable tag e\ufb03ciencies and purities are strongly depen-\ndent on both the tag decay and the decay of the signal\nB recoiling against the tag. In comparison with fully re-\nconstructed hadronic tags, events tagged by semileptonic\ndecays provide looser kinematic constraints on the recoil-\ning B and result in a less accurate measurement of the\nmissing neutrino and higher combinatorial backgrounds.\n17.1.2 Exclusive decays B \u2192D(\u2217)\u2113\u03bd\n17.1.2.1 Theoretical Overview\nIn the following, we discuss exclusive B decays to a D\nor D\u2217meson. The transition matrix elements of the weak\ncurrent given in Eq. (17.1.2) are decomposed into Lorentz-\ncovariant forms, built from the independent four-vectors\nof the decay and form factors. For a pseudoscalar \ufb01nal\nstate, only the vector current contributes,\n\u27e8P|q\u03b3\u00b5b|B\u27e9= f+(q2)\n\u0012\np\u00b5\nB + p\u00b5\nP \u2212m2\nB \u2212m2\nP\nq2\nq\u00b5\n\u0013\n+ f0(q2) m2\nB \u2212m2\nP\nq2\nq\u00b5,\n(17.1.6)\nwhere pB and pP denote the four-vector momenta of the\nmesons, q = pB \u2212pP is the momentum transfer, and\nf+,0(q2) are two form factors. For a vector \ufb01nal state,\nboth the vector and axial currents contribute:\n\u27e8V |q\u03b3\u00b5b|B\u27e9= V (q2) \u03b5\u00b5\u03c3\n\u03bd\u03c1\u03f5\u2217\n\u03c3\n2p\u03bd\nBp\u03c1\nV\nmB + mV\n,\n(17.1.7)\n\u27e8V |q\u03b3\u00b5\u03b35b|B\u27e9= i\u03f5\u2217\n\u03bd\n\u0014\nA0(q2) 2mV q\u00b5q\u03bd\nq2\n(17.1.8)\n+ A1(q2) (mB + mV )\u03b7\u00b5\u03bd\n\u2212A2(q2) (pB + pV )\u03c3q\u03bd\nmB + mV\n\u03b7\u00b5\u03c3\n\u0015\n,\nwhere \u03f5\u03bd is the polarization vector of the vector meson,\n\u03b7\u00b5\u03bd = g\u00b5\u03bd \u2212q\u00b5q\u03bd/q2, \u03b5\u03b1\u03b2\u03b3\u03b4 is the Levi-Civita tensor,\nand V (q2) and Ai(q2) are form factors. These form-factor\ndecompositions are general: to determine |Vcb|, q = c,\nP = D, and V = D\u2217; to determine |Vub|, q = u, P = \u03c0,\nand V = \u03c1.\nThe key feature of B \u2192D(\u2217) decays is that the masses\nof both the charm and bottom quarks are large compared\nto the energy scale of non-perturbative QCD. Therefore,\nin both cases the heavy quark is nearly static, surrounded\nby a cloud of gluons, the light valence quark, and vir-\ntual quark-antiquark pairs. In particular, the e\ufb00ects of\nspin and \ufb02avor are suppressed by powers of \u039bQCD/mQ\n(Q = c, b). In turn, approximate heavy-quark symmetries\nimpose constraints on the form factors. These constraints\nbecome more transparent with a di\ufb00erent basis of form\nfactors,\n\u27e8D|c\u03b3\u00b5b|B\u27e9\n\u221amBmD\n= h+(w) (vB + vD)\u00b5\n(17.1.9)\n+ h\u2212(w) (vB \u2212vD)\u00b5,\n\u27e8D\u2217|c\u03b3\u00b5b|B\u27e9\n\u221amBmD\u2217\n= hV (w) \u03b5\u00b5\u03bd\u03c1\u03c3vB,\u03bdvD\u2217,\u03c1\u03f5\u2217\n\u03c3,\n(17.1.10)\n\u27e8D\u2217|c\u03b3\u00b5\u03b35b|B\u27e9\n\u221amBmD\u2217\n= ihA1(w) (1 + w)\u03f5\u2217\u00b5\n(17.1.11)\n\u2212i [hA2(w)v\u00b5\nB + hA3(w)v\u00b5\nD\u2217] \u03f5\u2217\u00b7 vB,\nwhere the velocities (for hadrons H = B, D, D\u2217) are vH =\npH/mH, the velocity transfer is w = vB \u00b7 vD(\u2217) = (m2\nB +\nm2\nD(\u2217) \u2212q2)/2mBmD(\u2217). Again, these decompositions are\ncompletely general.\nAt zero recoil w = 1, heavy-quark dynamics requires\n(Isgur and Wise, 1989, 1990b; Shifman and Voloshin, 1987)\nh+(1) = 1 + O(\u03b1S) + O\n\u0000(\u039bQCD/mq)2\u0001\n,(17.1.12)\nh\u2212(1) = 0 + O(\u03b1S) + O(\u039bQCD/mq),\n(17.1.13)\nhA1(1) = 1 + O(\u03b1S) + O\n\u0000(\u039bQCD/mq)2\u0001\n.(17.1.14)\n\n190\nThe other zero-recoil form factors are not crucial to the\nextraction of |Vcb|. The task is to compute the correc-\ntions to heavy-quark symmetry; this is usually done in a\nway that aims to have the error scale with the deviation\nfrom the symmetry limit. The long-distance corrections of\norder (\u039bQCD/mq)n must be obtained non-perturbatively;\nthe short-distance corrections of order \u03b1l\nS may be obtained\nperturbatively or non-perturbatively. It is, however, im-\nportant to ensure that the separation of long- and short-\ndistance e\ufb00ects is done in a consistent way. At nonzero\nrecoil, all form factors receive contributions at \ufb01rst order\nin \u039bQCD/mq. Calculations of the form factors dependence\non w require more e\ufb00ort.\nThe di\ufb00erential decay rates for B\u2212\u2192D0(\u2217)\u2113\u2212\u03bd are\nd\u0393B\u2212\u2192D0\u2113\u2212\u03bd\ndw\n= G2\nF m3\nD\n48\u03c03 (mB + mD)2(w2 \u22121)3/2\n\u00d7 |\u03b7EW|2|Vcb|2|G(w)|2,\n(17.1.15)\nd\u0393B\u2212\u2192D0\u2217\u2113\u2212\u03bd\ndw\n= G2\nF m3\nD\u2217\n4\u03c03\n(mB \u2212mD\u2217)2(w2 \u22121)1/2\n\u00d7 |\u03b7EW|2|Vcb|2\u03c7(w)|F(w)|2,\n(17.1.16)\nwhere \u03b7EW = 1.0066 is the one-loop electroweak correc-\ntion (Sirlin, 1982) de\ufb01ned relative to GF as extracted\nfrom muon decay.52 The form factor G(w) is a function\nof h+(w) and h\u2212(w) and in \u03c7(w)|F(w)|2, F(w) contains\nall four B \u2192D\u2217form factors that enter Eqs (17.1.10)\nand (17.1.11). The full expressions can be found in Sec-\ntion 5.2 of Antonelli et al. (2010a). At zero recoil, G(1) = 1\nand F(1) = hA1(1). For decays of neutral mesons, B0 \u2192\nD+(\u2217)\u2113\u2212\u03bd, Coulomb attraction in the \ufb01nal state leads to\nan additional factor 1 + \u03b1\u03c0 (Atwood and Marciano, 1990;\nGinsberg, 1968) on the right-hand sides of Eqs (17.1.15)\nand (17.1.16).\nFor the determination of |Vcb|, the decay B \u2192D\u2217\u2113\u03bd\nis preferred over B \u2192D\u2113\u03bd for three reasons: First, the-\noretical predictions are simplest at zero recoil, where the\nrates are phase-space suppressed, but less so for the D\u2217\n\ufb01nal state [(w2 \u22121)1/2 versus (w2 \u22121)3/2]. Second, at zero\nrecoil, the form factor G(1) receives corrections of order\n\u039bQCD/mQ, instead of (\u039bQCD/mQ)2 for F(1). On the other\nhand, for B \u2192D\u2113\u03bd only the vector current contributes,\nresulting in a single form factor G(1), for low-mass leptons.\nFinally, and less crucially, the three polarization states of\nD\u2217increase the rate.\nFor these reasons let us \ufb01rst consider F(1) = hA1(1).\nOne can show that the optical theorem and the OPE imply\n|hA1(1)|2+ 1\n2\u03c0\nZ\n0\nd\u03f5 w(\u03f5) = 1\u2212\u22061/m2\nQ\u2212\u22061/m3\nQ, (17.1.17)\nwhere \u03f5 = E \u2212mD\u2217is the excess energy of charmed states\nwith JP C = 1\u2212+, w(\u03f5) is a structure function, and the\n52 This is just the QED running of the semileptonic form\nfermion operator from the W mass to the mb scale. The leading\nbremsstrahlung part of the QED corrections is subtracted by\nexperiments using approximate methods. Structure dependent\ncorrections are still poorly understood (Becirevic and Kosnik,\n2010; Bernlochner and Schonherr, 2010), but are unlikely to\ngive non-negligible corrections.\nupper limit of integration may be considered large for the\nmoment. The contributions \u22061/mn describe corrections to\nthe axial vector current for \ufb01nite-mass quarks. The \u22061/m2\nQ\ncontributions can be conveniently written as\n\u22061/m2\nQ = \u00b52\nG\n3m2c\n+ \u00b52\n\u03c0(\u00b5) \u2212\u00b52\nG\n4\n\u0012 1\nm2c\n+\n2/3\nmcmb\n+ 1\nm2\nb\n\u0013\n,\n(17.1.18)\nwhere \u00b52\nG \u22433(m2\nB\u2217\u2212m2\nB)/4 and \u00b52\n\u03c0(\u00b5) are matrix ele-\nments of the chromomagnetic energy and kinetic energy of\nthe b quark in the B meson. The meaning of the scale \u00b5 in\n\u00b52\n\u03c0(\u00b5) is explained below. The 1/m3\nQ contributions have a\nsimilar expression (see, e.g., Gambino, Mannel, and Uralt-\nsev (2010)) with analogs of \u00b52\nG and \u00b52\n\u03c0 that are related to\nmoments of the inclusive semileptonic distribution.\nFor \u03f5 \u226b\u039bQCD, the hadronic states in the excita-\ntion integral are dual to quark-gluon states. Introducing a\nscale \u00b5 to separate this short-distance part from the long-\ndistance part (which must be treated non-perturbatively),\none writes\n1\n2\u03c0\nZ\n0\nd\u03f5 w(\u03f5) = 1\n2\u03c0\nZ \u00b5\n0\nd\u03f5 w(\u03f5) + [1 \u2212\u03b7A(\u00b5)2]. (17.1.19)\nHere the quantity \u03b7A(\u00b5) combines the short-distance (\u03f5 >\n\u00b5) contributions. It has been calculated to two loops in\nperturbation theory (Czarnecki, Melnikov, and Uraltsev,\n1998); its \u00b5 dependence is compensated by \u00b52\n\u03c0(\u00b5). Re-\narranging Eq. (17.1.17) results in\nhA1(1) \u2243\u03b7A(\u00b5) \u22121\n2\u22061/m2\nQ \u22121\n2\u22061/m3\nQ \u22121\n4\u03c0\nZ \u00b5\n0\nd\u03f5 w(\u03f5).\n(17.1.20)\nThe last term from higher hadronic excitations is not di-\nrectly constrained by data.\nUsing recent data to compute \u22061/m2\nQ + \u22061/m3\nQ, Gam-\nbino, Mannel, and Uraltsev (2010) \ufb01nd\n\u22061/m2\nQ + \u22061/m3\nQ = 0.11 \u00b1 0.03\n(17.1.21)\nin the kinetic scheme with \u00b5 = 0.75 GeV. Combining this\nwith the two-loop result of \u03b7A(0.75 GeV) = 0.985 \u00b1 0.010,\nEq. (17.1.20) implies\nF(1) < 0.93,\n(17.1.22)\nsince the excitation integral is positive. They further es-\ntimate the excitation contribution to be (in the notation\nused here)\n1\n4\u03c0\nZ 0.75 GeV\n0\nd\u03f5 w(\u03f5) \u22480.065,\n(17.1.23)\nleading to\nF(1) = 0.86 \u00b1 0.02.\n(17.1.24)\nOne\nshould\nnote,\nhowever,\nthat\nthe\nestimate\nin\nEq. (17.1.23) entails the application of the OPE at scales\nof 1 GeV or lower, and consequently the error is di\ufb03cult\nto assess.\n\n191\nWith lattice QCD, the QCD action is discretized on\nan Euclidean space-time lattice, and calculations are per-\nformed numerically using Monte Carlo methods and im-\nportance sampling (see, e.g., Bazavov et al., 2010; De-\nGrand and Detar, 2006; Hashimoto and Onogi, 2004; Kro-\nnfeld, 2002). Physical results are recovered in the limit of\nzero lattice spacing. Since lattice results are obtained from\n\ufb01rst principles in QCD, they can be improved to arbitrary\nprecision, given su\ufb03cient computing resources. In recent\nyears, LQCD has made substantial progress, particularly\nin \ufb02avor physics. The most computationally demanding\npart of QCD calculations, namely the treatment of the\nsea of virtual quark-antiquark pairs, has become feasible.\nThe Fermilab-MILC calculations (Bernard et al.,\n2009a) are based on 2 + 1 \ufb02avors of sea quarks, two cor-\nresponding to up and down quarks (Bazavov et al., 2010)\nand one for the strange sea. The former two have masses\nlarger than in nature, ml > 0.1ms, but calculations at a\nsequence of light-quark masses are guided to the physical\nlimit with chiral perturbation theory (Laiho and Van de\nWater, 2006).The uncertainties of these calculations can\nbe reliably estimated, because a HQET analysis of the\nform factor follows through on the lattice (Harada, Hashi-\nmoto, Kronfeld, and Onogi, 2002; Kronfeld, 2000), and in\nthis way, the error scales as 1\u2212F(1), rather than as F(1).\nThe current value (Bailey et al., 2010),\n\u03b7EWF(1) = 0.9077(51)(88)(84)(90)(30)(33),\n(17.1.25)\nincludes the electroweak correction \u03b7EW = 1.0066. The\nstated uncertainties stem, respectively, from Monte-Carlo\nstatistics, the D\u2217\u2192D\u03c0 coupling, the chiral extrapo-\nlation, discretization errors, perturbative matching, and\ntuning the bare quark masses. This result is an update\nof earlier calculations by Bernard et al. (2009a) that were\nbased on a smaller set of LQCD data. Adding the errors\nin quadrature, we obtain\n\u03b7EWF(1) = 0.908 \u00b1 0.017,\n(17.1.26)\nwhich agrees well with the bound in Eq. (17.1.22).\nThe di\ufb00erence between the value in Eq. (17.1.24) and\nthe LQCD result of F(1) = 0.902 \u00b1 0.017 (without \u03b7EW),\nthough not large, might be due to a breakdown of the\nOPE in the estimate the low-energy excitation integral,\nalthough this appears to be unlikely in view of our present\nunderstanding of heavy quark physics. LQCD form-factor\ncalculations have passed several very challenging tests, in-\ncluding predictions of the shapes of D \u2192\u03c0\u2113\u03bd and D \u2192\nK\u2113\u03bd form factors (Aubin et al., 2005; Bernard et al., 2009b)\nand agreement to high precision for the normalization of\nthese form factors with experiment (Na, Davies, Follana,\nLepage, and Shigemitsu, 2010; Na et al., 2011).\nLet us now turn, more brie\ufb02y, to B \u2192D\u2113\u03bd and G(1).\nUnquenched LQCD calculations (Okamoto et al., 2005)\nresult in\nG(1) = 1.074 \u00b1 0.024 ,\n(17.1.27)\nand are compatible with the HQE calculation (Uraltsev,\n2004),\nG(1) = 1.04 \u00b1 0.02 ,\n(17.1.28)\nwithin the stated uncertainties.\n17.1.2.2 Measurements of Branching Fractions and\nDi\ufb00erential Distributions\nThe decay B \u2192D\u2217\u2113\u03bd was measured at Belle (Dun-\ngel, 2010) and BABAR (Aubert, 2008h,v, 2009ab) as-\nsuming the HQET parameterization of the form fac-\ntor \u03b7EWF(w) given by (Caprini, Lellouch, and Neubert,\n1998) in terms of the four quantities: the normalization\n\u03b7EWF(1)|Vcb|, the slope \u03c12\nD\u2217, and the form-factor ratios\nR1(1) = R\u22172V (1)/A1(1) and R2(1) = R\u22172A2(1)/A1(1),\nwhere\nR\u2217= (2\u221amBmD\u2217)/(mB + mD\u2217).\n(17.1.29)\nIn some analyses (Aubert, 2008v, 2009ab) the partial\nwidth d\u0393/dw was measured as a function of the veloc-\nity transfer w = vB \u00b7 vD\u2217to determine the normalization\n\u03b7EWF(1)|Vcb| and the slope \u03c12\nD\u2217, with form-factor ratios\nR1(1) and R2(1) taken as input from other measurements.\nIn the analyses by Dungel (2010) and Aubert (2008h) the\ndi\ufb00erential decay rate of B \u2192D\u2217\u2113\u03bd with D\u2217\u2192D\u03c0 is\nmeasured as a function of four variables, w and the angles\n\u03b8\u2113, \u03b8V and \u03c7 (Figure 17.1.5), where\n\u2013 \u03b8\u2113is the angle between the direction of the lepton and\nthe direction opposite the B meson in the rest frame\nof the virtual W,\n\u2013 \u03b8V is the angle between the direction of the D meson\nand the direction opposite the B meson in the D\u2217rest\nframe, and\n\u2013 \u03c7 is the angle between the decay planes of the D\u2217and\nthe W, de\ufb01ned in the B meson rest frame.\nThe di\ufb00erential rate in terms of these four kinematic vari-\nables gives access to all four HQET parameters of the\nB \u2192D\u2217\u2113\u03bd decay.\nFigure 17.1.5. De\ufb01nition of the angles \u03b8\u2113, \u03b8V and \u03c7 for the\ndecay B0 \u2192D\u2217+\u2113\u2212\u03bd with D\u2217+ \u2192D0\u03c0+ (Dungel, 2010).\nThe Belle measurement (Dungel, 2010) is based on\n711 fb\u22121 of \u03a5(4S) data resulting in about 120,000 recon-\nstructed B0 \u2192D\u2217\u2212\u2113+\u03bd decays. In this analysis the decay\nchain D\u2217\u2212\u2192D0\u03c0\u2212followed by D0 \u2192K+\u03c0\u2212is recon-\nstructed and D\u2217candidates are combined with a charged\n\n192\nlepton \u2113(\u2113= e, \u00b5) with momentum between 0.8 GeV and\n2.4 GeV. As the analysis is untagged, the direction of\nthe neutrino is not precisely known. However, using the\ncos \u03b8BY variable with Y = D\u2217\u2113(see Section 17.1.1.3), the\nB momentum vector is constrained to a cone centered on\nthe D\u2217\u2113direction. By averaging over the possible B direc-\ntions one can approximate the neutrino momentum and\ncalculate the kinematic variables of the decay, w, cos \u03b8\u2113,\ncos \u03b8V and \u03c7. The typical 1\u03c3 resolutions for these vari-\nables are 0.025, 0.049, 0.050 and 13.5\u25e6, respectively. Fig-\nure 17.1.6 shows the result of the simultaneous \ufb01t to the\none-dimensional projections of the four variables for the\nselected B0 \u2192D\u2217\u2212\u2113+\u03bd sample. A feature of this method\nis that the same events enter into the four projections and\nthe resulting correlations are accounted for by combining\nseparate covariance matrices for the data and the simu-\nlated signal and background distributions.\nBABAR performed a similar analysis of the decay B0 \u2192\nD\u2217\u2212\u2113+\u03bd based on a sample of 79 fb\u22121 (Aubert, 2008h).\nSeveral D0 decay modes are analyzed and the selected\nsample contains about 52,800 B0 \u2192D\u2217\u2212\u2113+\u03bd decays. The\nresults extracted from the \ufb01t to the four one-dimensional\ndecay distributions were combined with another BABAR\nanalysis of B0 \u2192D\u2217\u2212\u2113+\u03bd which performed a \ufb01t to\nthe four-dimensional decay rate \u0393(w, \u03b8\u2113, \u03b8V , \u03c7) (Aubert,\n2006af), thereby enhancing the sensitivity to R1(1), R2(1)\nand |Vcb|.\nBABAR also analyzed the isospin conjugated decay mode\nB+ \u2192D\u22170e+\u03bd in a sample of 205 fb\u22121, with the neutral\nD\u2217meson decaying to D\u22170 \u2192D0\u03c00 and D0 \u2192K+\u03c0\u2212\n(Aubert, 2008v). The reconstruction of the neutral D\u2217me-\nson involves a low momentum \u03c00 rather than a charged\npion, thus it is sensitive to di\ufb00erent detection e\ufb03ciencies\nand provides an independent check of the D\u2217reconstruc-\ntion. In this analysis the HQET form-factor ratios R1(1)\nand R2(1), are taken as external parameters from other\nmeasurements.\nThe results of the B \u2192D\u2217\u2113\u03bd form-factor measure-\nments, with common input parameters (mainly B life-\ntimes and D meson branching ratios) rescaled to the val-\nues available by the end of the year 2011 (Beringer et al.,\n2012), are summarized in Table 17.1.1. The B0 \u2192D\u2217\u2212\u2113+\u03bd\nbranching ratios calculated by using these form-factor pa-\nrameters are given in Table 17.1.2.\nThe HQET parameterization of the B \u2192D\u2113\u03bd form\nfactor \u03b7EWG(w) (Caprini, Lellouch, and Neubert, 1998)\nhas only two free parameters: the normalization given\nby \u03b7EWG(1)|Vcb| and the slope \u03c12\nD. These parameters are\nadopted for the Belle (Abe, 2002c) and BABAR (Aubert,\n2009ab, 2010e) measurements of this decay.\nUntagged analyses of B \u2192D\u2113\u03bd are limited by large\nbackgrounds and related large irreducible uncertainties.\nBased on a sample of 417 fb\u22121, BABAR performed a study\nof B \u2192D\u2113\u03bd decays, in which the second B meson in the\nevent is reconstructed in a hadronic decay mode (Aubert,\n2010e). This tagging technique results in a sizable back-\nground reduction and a more precise measurement of w.\nWith a tagging e\ufb03ciency of about 0.5%, 16 D meson decay\nmodes and with a lower limit on the lepton momentum at\nTable 17.1.2. The B0 \u2192D\u2217\u2212\u2113+\u03bd branching ratio, calculated\nusing the HQET parameterization of the form factor \u03b7EWF(w)\n(Caprini, Lellouch, and Neubert, 1998) and the parameter val-\nues in Table 17.1.1. For measurements that do not determine\nR1(1) and R2(1), we assume the average values of these pa-\nrameters (Section 17.1.2.3). The errors quoted correspond to\nthe statistical and systematic uncertainties, respectively.\nAnalysis\nB(B0 \u2192D\u2217\u2212\u2113+\u03bd) (%)\nBelle (Dungel, 2010)\n4.59 \u00b1 0.03 \u00b1 0.26\nBABAR D\u2217\u2212\u2113+\u03bd (Aubert, 2008h)\n4.58 \u00b1 0.04 \u00b1 0.25\nBABAR D\u22170e+\u03bd (Aubert, 2008v)\n4.95 \u00b1 0.07 \u00b1 0.34\nBABAR DXl\u03bd (Aubert, 2009ab)\n4.96 \u00b1 0.02 \u00b1 0.20\nAverage\n4.83 \u00b1 0.01 \u00b1 0.12\n0.6 GeV yields of 2147 \u00b1 69 B+ \u2192D0\u2113+\u03bd and 1108 \u00b1 45\nB0 \u2192D\u2212\u2113+\u03bd decays are obtained. These signal yields\nare determined by a \ufb01t to the missing-mass-squared dis-\ntribution, m2\nmiss = (pB \u2212pD \u2212p\u2113)2 (see Figure 17.1.2).\nThe normalization \u03b7EWG(1)|Vcb| and the slope \u03c12\nD are ex-\ntracted from a \ufb01t to the e\ufb03ciency-corrected signal yields\nin ten bins of w (see Figure 17.1.7).\n(a)\n1.0\n1.2\n1.4\n1.6\n\u03b7EWG(w)|VcbI [10-3]\n0\n20\n40\nw\n(b)\n20\n0\n40\n1.0\n1.2\n1.4\n\u03b7EWF(w)|VcbI [10-3]\n7-2012\n8809A13\nFigure 17.1.7. BABAR measurements, corrected for the recon-\nstruction e\ufb03ciency, of the w dependence of the form factors,\nwith \ufb01t results superimposed (solid line): (a) \u03b7EW G(w)|Vcb|\nfor B \u2192D\u2113\u03bd decays from tagged events (Aubert, 2010e), and\nfor comparison (b) \u03b7EW F(w)|Vcb| for B \u2192D\u2217\u2113\u03bd decays from\nuntagged events (Aubert, 2008h).\nThe results of the B \u2192D\u2113\u03bd form-factor measurements\nat the B Factories, rescaled to common input parameters\n(Beringer et al., 2012), are summarized in Table 17.1.3.\nWe also calculate the B0 \u2192D\u2212\u2113+\u03bd branching fraction\nfrom these values (Table 17.1.4).\nBABAR also published a measurement of B \u2192D\u2217\u2113\u03bd\nand B \u2192D\u2113\u03bd adopting an innovative approach. Using\na sample of 207 fb\u22121, this analysis is based on an in-\nclusive selection of B \u2192DX\u2113\u03bd decays, where only the\nD meson and the charged lepton are reconstructed (Au-\n\n193\nFigure 17.1.6. Belle analysis of B \u2192D\u2217\u2113\u03bd (Dungel, 2010): Result of the simultaneous \ufb01t to four one-dimensional projec-\ntions of selected B0 \u2192D\u2217\u2212\u2113+\u03bd events: w (top-left), cos \u03b8\u2113(top-right), cos \u03b8V (botton-left) and \u03c7 (bottom-right). The data\npoints represent continuum subtracted event yields. The histograms represent the signal component and di\ufb00erent background\ncontributions.\nTable 17.1.1. Summary of the B Factory results for the B \u2192D\u2217\u2113\u03bd form-factor parameters \u03b7EWF(1)|Vcb|, \u03c12\nD\u2217, R1(1) and\nR2(1). The measurements have been rescaled to the end of year 2011 values of the common input parameters (Beringer et al.,\n2012). The errors quoted for each parameter correspond to the statistical and systematic uncertainties, respectively. The average\nis obtained by a four dimensional \ufb01t to these values taking into account correlated systematic uncertainties.\nAnalysis\n\u03b7EWF(1)|Vcb| (10\u22123)\n\u03c12\nD\u2217\nR1(1)\nR2(1)\nBelle (Dungel, 2010)\n34.7 \u00b1 0.2 \u00b1 1.0\n1.21 \u00b1 0.03 \u00b1 0.01\n1.40 \u00b1 0.03 \u00b1 0.02\n0.86 \u00b1 0.02 \u00b1 0.01\nBABAR D\u2217\u2212\u2113+\u03bd (Aubert, 2008h)\n34.1 \u00b1 0.3 \u00b1 1.0\n1.18 \u00b1 0.05 \u00b1 0.03\n1.43 \u00b1 0.06 \u00b1 0.04\n0.83 \u00b1 0.04 \u00b1 0.02\nBABAR D\u22170e+\u03bd (Aubert, 2008v)\n35.1 \u00b1 0.6 \u00b1 1.3\n1.12 \u00b1 0.06 \u00b1 0.06\nBABAR DXl\u03bd (Aubert, 2009ab)\n35.8 \u00b1 0.2 \u00b1 1.1\n1.19 \u00b1 0.02 \u00b1 0.06\nAverage\n35.5 \u00b1 0.1 \u00b1 0.5\n1.20 \u00b1 0.02 \u00b1 0.02\n1.40 \u00b1 0.03 \u00b1 0.01\n0.86 \u00b1 0.02 \u00b1 0.01\nTable 17.1.3. Summary of the B Factory results for the B \u2192D\u2113\u03bd form-factor parameters \u03b7EWG(1)|Vcb| and \u03c12\nD. The mea-\nsurements have been rescaled to the end of year 2011 values of the common input parameters (Beringer et al., 2012). The errors\nquoted for each parameter correspond to the statistical and systematic uncertainties, respectively. The average is obtained by\na two dimensional \ufb01t to these values taking into account correlated systematic uncertainties.\nAnalysis\n\u03b7EWG(1)|Vcb| (10\u22123)\n\u03c12\nD\nBelle (Abe, 2002c)\n40.8 \u00b1 4.4 \u00b1 5.0\n1.12 \u00b1 0.22 \u00b1 0.14\nBABAR DXl\u03bd (Aubert, 2009ab)\n43.4 \u00b1 0.8 \u00b1 2.1\n1.20 \u00b1 0.04 \u00b1 0.06\nBABAR tagged (Aubert, 2010e)\n42.5 \u00b1 1.9 \u00b1 1.1\n1.18 \u00b1 0.09 \u00b1 0.05\nAverage\n42.7 \u00b1 0.7 \u00b1 1.5\n1.19 \u00b1 0.04 \u00b1 0.04\nbert, 2009ab). To reduce background from D\u2217\u2217\u2113\u03bd decays\nand other background sources, the lepton momentum is\nrestricted to p\u2113> 1.2 GeV, and the D mesons are re-\nconstructed only in the two cleanest decay modes, D0 \u2192\nK\u2212\u03c0+ and D+ \u2192K\u2212\u03c0+\u03c0+. The D(\u2217)\u2113\u03bd signal and back-\nground yields, the values of \u03c12\nD, \u03c12\nD\u2217, \u03b7EWG(1)|Vcb| and\n\u03b7EWF(1)|Vcb| are obtained from a binned \u03c72 \ufb01t to the\nthree-dimensional distributions of the lepton momentum\np\u2113, the D momentum pD, and cos \u03b8BY . The results of this\nanalysis are listed in Tables 17.1.1 and 17.1.3. The sta-\ntistical errors are less than those of the tagged analysis\nwhich was based on a larger overall event sample, but the\nsystematic uncertainty of the B \u2192D\u2113\u03bd measurement is\nlarger by a factor of two.\n\n194\nTable 17.1.4. The B0 \u2192D\u2212\u2113+\u03bd branching ratio, calculated\nusing the HQET parameterization of the form factor \u03b7EWG(w)\n(Caprini, Lellouch, and Neubert, 1998) and the parameter val-\nues in Table 17.1.3. The errors quoted correspond to the sta-\ntistical and systematic uncertainties, respectively.\nAnalysis\nB(B0 \u2192D\u2212\u2113+\u03bd) (%)\nBelle (Abe, 2002c)\n2.07 \u00b1 0.12 \u00b1 0.52\nBABAR DXl\u03bd (Aubert, 2009ab)\n2.18 \u00b1 0.03 \u00b1 0.13\nBABAR tagged (Aubert, 2010e)\n2.12 \u00b1 0.10 \u00b1 0.06\nAverage\n2.14 \u00b1 0.03 \u00b1 0.10\n17.1.2.3 Extraction of |Vcb| and the Decay Form Factors\nWe combine the results of four measurements of B \u2192\nD\u2217\u2113\u03bd decays, three obtained by BABAR (Aubert, 2008h,v,\n2009ab) and one by Belle (Dungel, 2010), by performing a\nfour-dimensional \ufb01t to the HQET parameters \u03b7EWF(1)|Vcb|,\n\u03c12\nD\u2217, R1(1) and R2(1) taking into account systematic error\ncorrelations. The results are\n\u03b7EWF(1)|Vcb| = (35.45 \u00b1 0.50) \u00d7 10\u22123 ,\n\u03c12\nD\u2217= 1.199 \u00b1 0.027,\n(17.1.30)\nR1(1) = 1.396 \u00b1 0.033,\nR2(1) = 0.860 \u00b1 0.020.\nThe correlations between the di\ufb00erent \ufb01t parameters are\n\u03c1\u03b7EWF(1)|Vcb|,\u03c12\nD\u2217=\n0.326,\n\u03c1\u03b7EWF(1)|Vcb|,R1(1) = \u22120.084,\n\u03c1\u03b7EWF(1)|Vcb|,R2(1) = \u22120.064,\n(17.1.31)\n\u03c1\u03c12\nD\u2217,R1(1) =\n0.563,\n\u03c1\u03c12\nD\u2217,R2(1) = \u22120.804,\n\u03c1R1(1),R2(1) = \u22120.761.\nThe \u03c72 of the combination is 8.0 for 8 degrees of freedom.\nFor B \u2192D\u2113\u03bd, there are three measurements, one by Belle\n(Abe, 2002c) and two by BABAR (Aubert, 2009ab, 2010e).\nThe results of the \ufb01t to \u03b7EWG(1)|Vcb| and \u03c12\nD are\n\u03b7EWG(1)|Vcb| = (42.68 \u00b1 1.67) \u00d7 10\u22123,\n\u03c12\nD = 1.186 \u00b1 0.057,\n(17.1.32)\nwith a correlation of\n\u03c1\u03b7EWG(1)|Vcb|,\u03c12\nD = 0.839.\n(17.1.33)\nThe \u03c72 of the average is 0.3 for 4 degrees of freedom.\nThe measured values and the averages are shown in Fig-\nure 17.1.8.\nUsing the form-factor normalization from the latest\nLQCD calculation of Eq. (17.1.26), we obtain for |Vcb|\nfrom B \u2192D\u2217\u2113\u03bd decays,\n|Vcb| = (39.04 \u00b1 0.55exp \u00b1 0.73th) \u00d7 10\u22123 .\n(17.1.34)\nBased on an earlier LQCD calculations, Eq. (17.1.27), we\nderive |Vcb| from B \u2192D\u2113\u03bd decays,\n|Vcb| = (39.46 \u00b1 1.54exp \u00b1 0.88th) \u00d7 10\u22123 .\n(17.1.35)\nOn the other hand, we obtain values for |Vcb| that are\nabout 5% larger if we rely on heavy \ufb02avor sum rule calcu-\nlations, Eq. (17.1.24), for B \u2192D\u2217\u2113\u03bd decays\n|Vcb| = (40.93 \u00b1 0.58exp \u00b1 0.95th) \u00d7 10\u22123 ,\n(17.1.36)\nor on HQE calculations, Eq. (17.1.28), for B \u2192D\u2113\u03bd de-\ncays,\n|Vcb| = (40.75 \u00b1 1.59exp \u00b1 0.78th) \u00d7 10\u22123 .\n(17.1.37)\nWhile the results for the two decay modes agree well,\n|Vcb| measured in B \u2192D\u2217\u2113\u03bd decays is more precise and\nwill be considered as the main result.\n17.1.3 Inclusive Cabibbo-favored B decays\n17.1.3.1 Theoretical Overview\nOur understanding of inclusive semileptonic B decays rests\non a simple idea: since inclusive decays include all possible\nhadronic \ufb01nal states, the \ufb01nal state quark hadronizes with\nunit probability and the transition amplitude is sensitive\nonly to the long-distance dynamics of the initial B me-\nson. Thanks to the large hierarchy between the typical en-\nergy release, of O(mb), and the hadronic scale \u039bQCD, and\nto asymptotic freedom, any residual sensitivity to non-\nperturbative e\ufb00ects is suppressed by powers of \u039bQCD/mb.\nAn OPE allows us to express the non-perturbative\nphysics in terms of B meson matrix elements of local oper-\nators of dimension d \u22655, while the Wilson coe\ufb03cients can\nbe expressed as a perturbative series in \u03b1S (Bigi, Shifman,\nUraltsev, and Vainshtein, 1993; Bigi, Uraltsev, and Vain-\nshtein, 1992; Blok, Koyrakh, Shifman, and Vainshtein,\n1994; Manohar and Wise, 1994). The OPE disentangles\nthe physics associated with soft scales of order \u039bQCD (pa-\nrameterized by the matrix elements of the local operators)\nfrom that associated with hard scales \u223cmb (in the Wilson\ncoe\ufb03cients). The total semileptonic width and the mo-\nments of the kinematic distributions are therefore double\nexpansions in \u03b1S and \u039bQCD/mb, with a leading term that\nis given by the free b quark decay. Quite importantly, the\npower corrections start at O(\u039b2\nQCD/m2\nb) and are compar-\natively suppressed. At higher orders in the OPE, terms\nsuppressed by powers of mc also appear, starting with\nO(\u039b3\nQCD/m3\nb \u00d7 \u039b2\nQCD/m2\nc) (Bigi, Mannel, Turczyk, and\nUraltsev, 2010).\nThe relevant parameters in the double series are the\nheavy quark masses mb and mc, the strong coupling \u03b1S,\nand the matrix elements of the local operators. As there\nare only two dimension \ufb01ve operators, two matrix elements\nappear at O(1/m2\nb):\n\u00b52\n\u03c0(\u00b5) =\n1\n2mB\n\u27e8B|b \u03c02 b|B\u27e9\u00b5,\n(17.1.38)\n\u00b52\nG(\u00b5) =\n1\n2mB\n\u27e8B|b i\n2\u03c3\u00b5\u03bdG\u00b5\u03bdb|B\u27e9\u00b5,\n(17.1.39)\n\n195\nD*\n2\n\u03c1\n0.8\n1\n1.2\n1.4\n]\n-3\n| [10\ncb\n F(1) |V\n\u03b7\n32\n34\n36\n38\nBELLE\nBABAR (excl.)\nBABAR (D*0)\nBABAR (Global Fit)\nAVERAGE\n = 1\n2\n\u03c7 \n\u2206\n/dof = 8.0/ 8\n2\n\u03c7\nD\n2\n\u03c1\n0.5\n1\n1.5\n]\n-3\n| [10\ncb\n G(1) |V\n\u03b7\n30\n35\n40\n45\n50\nBELLE\nBABAR global fit\nBABAR tagged\nAVERAGE\n = 1\n2\n\u03c7 \n\u2206\n/dof = 0.3/ 4\n2\n\u03c7\nFigure 17.1.8. One sigma contour plots of the averages of \u03b7EWF(1)|Vcb| and \u03c12\nD\u2217(left), and of \u03b7EWG(1)|Vcb| and \u03c12\nD.\nwhere \u03c0 = \u2212iD with D the space component of the co-\nvariant derivative, \u03c3\u00b5\u03bd = i/2[\u03b3\u00b5, \u03b3\u03bd], and G\u00b5\u03bd the gluon\n\ufb01eld tensor. The matrix element of the kinetic operator,\n\u00b52\n\u03c0, is naturally associated with the average kinetic en-\nergy of the b quark in the B meson, while that of the\nchromomagnetic operator, \u00b52\nG, is related to the B\u2217-B hy-\nper\ufb01ne mass splitting. They generally depend on a cuto\ufb00\n\u00b5 = O(1 GeV) chosen to separate soft and hard physics.\nThe cuto\ufb00can be implemented in di\ufb00erent ways. In the\nkinetic scheme (Bigi et al., 1995, 1997), a Wilson cuto\ufb00\non the gluon momentum is employed in the b quark rest\nframe: all soft gluon contributions are attributed to the\nexpectation values of the higher dimensional operators,\nwhile hard gluons with momentum |k| > \u00b5 contribute to\nthe perturbative corrections to the Wilson coe\ufb03cients. In\nthe HQET a di\ufb00erent notation is usually employed: at\nleading order in 1/mQ one can identify \u00b52\n\u03c0 with \u2212\u03bb1 and\n\u00b52\nG with 3\u03bb2. Most current applications of the OPE in-\nvolve O(1/m3\nb) e\ufb00ects (Gremm and Kapustin, 1997) as\nwell, parameterized in terms of two additional parame-\nters, generally indicated by \u03c13\nD and \u03c13\nLS or by their HQET\ncounterparts \u03c11,2. These OPE parameters describe univer-\nsal properties of the B meson and of the quarks and are\nuseful in several applications.\nThe interesting quantities to be measured are the to-\ntal rate and some global shape parameters, such as the\n\ufb01rst few moments of the lepton energy spectrum or of the\nhadronic invariant mass distribution. The lepton energy\nmoments are de\ufb01ned as\n\u27e8En\n\u2113\u27e9=\n1\n\u0393E>Ecut\nZ\nE>Ecut\ndE\u2113En\n\u2113\nd\u0393\ndE\u2113\n,\n(17.1.40)\nwhere E\u2113is the lepton energy in B \u2192Xc\u2113\u03bd, \u0393E>Ecut is the\nsemileptonic width above the energy threshold Ecut and\nd\u0393/dE\u2113is the di\ufb00erential semileptonic width as a function\nof E\u2113. The hadronic mass moments are similarly de\ufb01ned\nas\n\u27e8m2n\nX \u27e9=\n1\n\u0393E>Ecut\nZ\nE>Ecut\ndm2\nXm2n\nX\nd\u0393\ndm2\nX\n.(17.1.41)\nHere, d\u0393/dm2\nX is the di\ufb00erential width as a function of the\nmass squared of the hadronic system X. For both types,\nn is the order of the moment. For n > 1, the moments can\nalso be de\ufb01ned relative to \u27e8E\u2113\u27e9and \u27e8m2\nX\u27e9, respectively, in\nwhich case they are called central moments.\nThe OPE cannot be expected to converge in regions\nof phase space where the momentum of the \ufb01nal hadronic\nstate is O(\u039bQCD) and where perturbation theory has sin-\ngularities. This is because what actually controls the ex-\npansion is not mb but the energy release, which is O(\u039bQCD)\nin those cases. The OPE is therefore valid only for suf-\n\ufb01ciently inclusive measurements and in general cannot\ndescribe di\ufb00erential distributions. The lepton energy mo-\nments can be measured very precisely, while the hadronic\nmass moments are directly sensitive to higher dimensional\nmatrix elements such as \u00b52\n\u03c0 and \u03c13\nD. In most cases, one\nhas to take into account an experimental lower threshold\non the lepton momentum. The leptonic and hadronic mo-\nments give information on the quark masses and on the\nnon-perturbative OPE matrix elements, while the total\nrate allows for the extraction of |Vcb|.\nThe reliability of the inclusive method rests on our\nability to control the higher order contributions in the dou-\nble series and to constrain quark-hadron duality violation,\ni.e. e\ufb00ects beyond the OPE, which exist but are expected\n\n196\nto be rather suppressed in semileptonic decays. The cal-\nculation of higher order e\ufb00ects allows us to verify the con-\nvergence of the double series and to reduce and properly\nestimate the residual theoretical uncertainty. Duality vio-\nlation e\ufb00ects (see Bigi and Uraltsev, 2001a, for a review)\ncan be constrained a posteriori, by checking whether the\nOPE predictions \ufb01t the experimental data. This in turn\ndepends on precise measurements and precise OPE pre-\ndictions. As the experimental accuracy reached at the B\nFactories is better than the theoretical accuracy for all\nthe measured moments, any e\ufb00ort to improve the latter is\nstrongly motivated.\nThe main ingredients for an accurate analysis of the\nexperimental data on the moments and the subsequent\nextraction of |Vcb| have been known for some time. Two\nimplementations are currently employed in global analy-\nses; they are based on either the kinetic scheme (Benson,\nBigi, Mannel, and Uraltsev, 2003; Gambino and Uralt-\nsev, 2004) or the 1S mass scheme for the b quark (Bauer,\nLigeti, Luke, Manohar, and Trott, 2004). They both in-\nclude terms through O(\u03b12\nS\u03b20) and O(1/m3\nb) (\u03b20 = 11 \u2212\n2nl/3 is the \ufb01rst coe\ufb03cient of the QCD beta function) but\nthey use di\ufb00erent perturbative schemes, include a some-\nwhat di\ufb00erent choice of experimental data under speci\ufb01c\nassumptions, and estimate the theoretical uncertainties in\ntwo distinct ways. Nevertheless, the two methods yield\nsimilar results for |Vcb|.\nAn important component of the OPE calculation are\nthe purely perturbative contributions. Although the O(\u03b1S)\nperturbative corrections to various kinematic distributions\nand to the rate have been computed long ago, the triple\ndi\ufb00erential distribution was \ufb01rst computed at O(\u03b1S) only\nrecently by Aquila, Gambino, Ridol\ufb01, and Uraltsev (2005);\nTrott (2004). The so-called BLM corrections, i.e. those\nof O(\u03b12\nS\u03b20), are usually the dominant source of two-loop\ncorrections in B decays. They can be found in complete\nform in Aquila, Gambino, Ridol\ufb01, and Uraltsev (2005).\nThe complete two-loop perturbative corrections to the\nwidth and moments of the lepton energy and hadronic\nmass distributions have been recently computed (Biswas\nand Melnikov, 2010; Melnikov, 2008; Pak and Czarnecki,\n2008) by both numerical and analytic methods. The ki-\nnetic scheme implementation for actual observables can\nbe found in Gambino (2011). In general, using \u03b1S(mb)\nin the on-shell scheme, the non-BLM corrections amount\nto about \u221220% of the two-loop BLM corrections and give\nsmall contributions to normalized moments. In the kinetic\nscheme with cuto\ufb00\u00b5 = 1 GeV, the perturbative expansion\nof the total width is\n\u0393[B \u2192Xce\u03bd] \u221d1 \u22120.96 \u03b1S(mb)\n\u03c0\n\u22120.48 \u03b20\n\u0010\u03b1S\n\u03c0\n\u00112\n+0.82\n\u0010\u03b1S\n\u03c0\n\u00112\n+ O(\u03b13\nS) \u22480.916.\n(17.1.42)\nHigher order BLM corrections of O(\u03b1n\nS\u03b2n\u22121\n0\n) to the width\nand moments are also known (Aquila, Gambino, Ridol\ufb01,\nand Uraltsev, 2005; Benson, Bigi, Mannel, and Uraltsev,\n2003). The resummed BLM result is numerically very close\nto that from NNLO calculations (Benson, Bigi, Mannel,\nand Uraltsev, 2003). The residual perturbative error in\nthe total width is therefore about 1%.\nThe global \ufb01t to moments can be performed to NNLO\nto extract the OPE parameters and |Vcb|. In the normal-\nized leptonic moments the perturbative corrections cancel\nto a large extent, independently of the mass scheme, be-\ncause hard gluon emission is comparatively suppressed.\nThis pattern of cancellations, crucial for an accurate esti-\nmate of the theoretical uncertainties, is con\ufb01rmed by the\ncomplete O(\u03b12\nS) calculation, although the numerical pre-\ncision of the available results is not su\ufb03cient to improve\nthe overall accuracy for the higher central leptonic mo-\nments (Gambino, 2011). The non-BLM corrections turn\nout to be more important for the hadronic moments. Even\nthough it improves the overall theoretical uncertainty only\nmoderately, the complete NNLO calculation leads to the\nmeaningful inclusion of precise mass constraints, such as\nthose discussed in Section 17.1.3.2, in various perturbative\nschemes (Gambino, 2011).\nSources of signi\ufb01cant residual theoretical uncertainty\nare the perturbative corrections to the Wilson coe\ufb03cients\nof the power-suppressed operators. They induce correc-\ntions of O(\u03b1S\u039b2\nQCD/m2\nb) to the width and to the moments.\nOnly the O(\u03b1S\u00b52\n\u03c0/m2\nb) terms are presently known (Becher,\nBoos, and Lunghi, 2007). A complete calculation of these\ne\ufb00ects has recently been performed for inclusive radiative\ndecays (Ewerth, Gambino, and Nandi, 2010), where the\nO(\u03b1S) corrections increase the coe\ufb03cient of \u00b52\nG in the rate\nby almost 20%. The extension of this calculation to the\nsemileptonic decay rate is in progress. In view of the im-\nportance of O(1/m3\nb) corrections, if a theoretical precision\nof 1% in the decay rate is to be reached, the O(\u03b1S/m3\nb)\ne\ufb00ects may need to be calculated.\nAs to the higher order power corrections, a \ufb01rst anal-\nysis of O(1/m4\nb) and O(1/m5\nQ) e\ufb00ects is given in Man-\nnel, Turczyk, and Uraltsev (2010). The main problem is\nthe proliferation of non-perturbative parameters: e.g. as\nmany as nine new expectation values appear at O(1/m4\nb)\nand more at the next order. Because they cannot all be ex-\ntracted from experiment, they are estimated in the ground\nstate saturation approximation, thus reducing them to the\nknown O(1/m2,3\nb ) parameters. In this approximation, the\ntotal O(1/m4,5\nQ ) correction to the width is about +1.3%.\nThe O(1/m5\nQ) e\ufb00ects are dominated by O(1/m3\nbm2\nc) in-\ntrinsic charm contributions, amounting to +0.7% (Bigi,\nMannel, Turczyk, and Uraltsev, 2010). The net e\ufb00ect on\n|Vcb| also depends on the corrections to the moments.\nMannel, Turczyk, and Uraltsev (2010) estimate that the\noverall e\ufb00ect on |Vcb| is a 0.4% increase. While this sets\nthe scale of higher order power corrections, it is as yet\nunclear how much the result depends on the assumptions\nmade for the expectation values.\nIt is worth stressing that the semileptonic moments\nare sensitive to the values of the heavy quark masses and\nin particular to a speci\ufb01c linear combination of mc and\nmb (Voloshin, 1995), which to a good approximation is\nthe one needed for the extraction of |Vcb| (Gambino and\nSchwanda, 2011). Checking the consistency of the con-\n\n197\nstraints on mc and mb from semileptonic moments with\nthe precise determinations of these quark masses (see Sec-\ntion 17.1.3.2) is an important step in the e\ufb00ort to im-\nprove our theoretical description of inclusive semileptonic\ndecays. The inclusion of these constraints in the semilep-\ntonic \ufb01ts will eventually improve the accuracy of the |Vub|\nand |Vcb| determinations. Indeed, the b quark mass and\nthe OPE expectation values obtained from the moments\nare crucial inputs in the determination of |Vub| from inclu-\nsive semileptonic decays (see Section 17.1.5 and Antonelli\net al., 2010a). The heavy quark masses and the OPE pa-\nrameters are also relevant for a precise calculation of other\ninclusive decay rates such as that of B \u2192Xs\u03b3 (Gambino\nand Giordano, 2008).\nThe \ufb01rst two moments of the photon energy distribu-\ntion in B \u2192Xs\u03b3 are also often included in the semilep-\ntonic \ufb01ts. They are sensitive to mb and \u00b52\n\u03c0 and play the\nsame role as a loose constraint on mb (\u03b4mb \u223c90 MeV).\nHowever, as discussed in Section 17.9, experiments place a\nlower limit on the photon energy, which introduces a sen-\nsitivity to the Fermi motion of the b-quark inside the B\nmeson and tends to disrupt the OPE. One can still re-sum\nthe higher-order terms into a non-local distribution func-\ntion and since the lowest integer moments of this function\nare given in terms of the local OPE parameters, one can\nparameterize it assuming di\ufb00erent functional forms (Ben-\nson, Bigi, and Uraltsev, 2005). Another serious problem is\nthat only the leading operator contributing to inclusive ra-\ndiative decays can be described by an OPE. Therefore, un-\nknown O(\u03b1S\u039bQCD/mb) contributions should be expected\n(Paz, 2010) and radiative moments, though interesting in\ntheir own respect, should be considered with care in the\ncontext of precision moment analyses.\n17.1.3.2 Recent charm and bottom quark mass\ndeterminations (other than from semileptonic B decays)\nIn the following, we discuss recent determinations of mc\nand mb, excluding those from semileptonic B decays, and\nonly including results since 2007 (except for the use of non-\nrelativistic sum rules). All quark mass values are presented\nin the MS scheme where the renormalization scale is set\nto \u00b5 = mb for the bottom and \u00b5 = 3 GeV for the charm\nquark. For convenience we also provide results for mc(mc),\neven though the scale \u00b5 = mc is too small considering the\ncurrent level of precision.\nLow-energy sum rules (LESR)\nThe theoretical prediction of moments of the vector cur-\nrent correlator depend on the heavy quark mass and thus\nthe latter can be extracted from the comparison to mo-\nments evaluated with the help of experimental data for the\ntotal cross section \u03c3(e+e\u2212\u2192hadrons). The method is re-\nstricted to the \ufb01rst few moments which permits using the\n\ufb01xed-order polarization function. In K\u00a8uhn, Steinhauser,\nand Sturm (2007) the charm quark mass has been de-\ntermined with an uncertainty of 13 MeV. The extraction\nof the bottom quark mass has been updated (Chetyrkin\net al., 2009) using new experimental input. More recently,\nLESR have also been used to extract the charm quark\nmass (Dehnadi, Hoang, Mateu, and Zebarjad, 2011).\nNon-relativistic sum rules (NRSR)\nThis method requires the evaluation of the polarization\nfunction in the non-relativistic limit and is therefore not\nrestricted to lower moments. The most advanced analy-\nsis (Pineda and Signer, 2006) uses an almost complete\nnext-to-next-to-leading logarithmic approximation to de-\ntermine the bottom quark mass.\nIn Signer (2009) non-relativistic sum rules have been\nused to extract the charm-quark mass in an approach\nwhich combines \ufb01xed-order and non-relativistic calcula-\ntions.\nFinite-energy sum rules (FESR)\nThe residue theorem can be used to relate the (appro-\npriately weighted) experimental cross section \u03c3(e+e\u2212\u2192\nhadrons) to a contour integral of the vector current cor-\nrelation function. The freedom to choose the integration\nkernel can be used to extract a precise value for the charm\nquark mass. The most recent analysis was published in Bo-\ndenstein, Bordes, Dominguez, Penarrocha, and Schilcher\n(2011).\nLattice QCD (LQCD)\nEach quark mass in the lattice QCD Lagrangian must be\ntuned at each value of the lattice spacing by calibrating\nto the experimentally-measured value of a \u2018gold-plated\u2019\nhadron mass. For mc and mb the best choices are ground-\nstate heavy quarkonium or heavy-strange mesons, because\nthey allow very precise tuning. Direct conversion to the\nMS scheme using mc(\u00b5) = Zmc,latt is possible using lat-\ntice or continuum QCD perturbation theory, but this in-\ntroduces a signi\ufb01cant source of error. The most recent de-\ntermination of mc(mc) using this approach (Blossier et al.,\n2010) gives a value of 1.28(4) GeV. Since the stated un-\ncertainty includes only the impact of working with only u\nand d quarks in the sea, it is omitted from Table 17.1.5.\nFor the b quark, it is also possible to use non-relativistic\nor even static quark methods to determine the binding en-\nergy of a heavy-light meson, and thereby mb. These calcu-\nlations are currently underway with gluon con\ufb01gurations\nthat include the full e\ufb00ect of sea quarks.\nThe most precise results from full lattice QCD in-\nstead use time-moments of charmonium or bottomonium\ncurrent-current correlators, extrapolated to the continuum\nlimit and compared to the high-order continuum QCD\nperturbation theory developed for LESR (Allison et al.,\n2008; McNeile, Davies, Follana, Hornbostel, and Lepage,\n2010). The pseudoscalar current in a highly improved rela-\ntivistic quark formalism with an exact Partially Conserved\n\n198\nAxial Current (PCAC) relation produces the smallest er-\nrors, although reaching bottomonium also requires an ex-\ntrapolation in the heavy quark mass to the b on current\nlattices. This method also allows for a completely non-\nperturbative determination of the ratio of mb(\u00b5)/mc(\u00b5) =\n4.51(4), which can be used to test other determinations.\nIn Tables 17.1.5 and 17.1.6 the results for mc and mb\nmentioned in the text are listed in chronological order.\nOne observes that the method based on NRSR is not (yet)\ncompetitive which is probably due to missing third-order\ncorrections. They are available for the other analyses. For\nboth mb and mc the results from LESR and LQCD are\nvery precise and in excellent agreement. They use similar\nperturbative analyses, but very di\ufb00erent input data, with\ndi\ufb00erent sources of systematic errors. The recent LESR re-\nsult (Dehnadi, Hoang, Mateu, and Zebarjad, 2011) gives\nan error on mc, which is two to four times larger than for\nother analyses. This has sparked a debate on the theoret-\nical uncertainties of LESR, and in particular on the use\nof renormalization scales as low as 1 GeV in their esti-\nmation, and on the uncertainty of the perturbative QCD\nprediction for R(s) = \u03c3(e+e\u2212\u2192hadrons, s)/\u03c3(e+e\u2212\u2192\n\u00b5+\u00b5\u2212, s) above 5 GeV. Tables 17.1.5 and 17.1.6 also in-\nclude the results from Narison (2012), where mc and mb\nhave been extracted together with the gluon condensates.\nIn contrast to other determinations based on LESRs and\nLQCD, a signi\ufb01cant in\ufb02uence of the gluon condensate on\nthe quark masses is observed which is quite surprising.\nFurthermore, the energy region between 3.73 GeV and\n4.6 GeV has been parameterized using \u03c8 resonances in\nthe narrow-width approximation, instead of precise ex-\nperimental data. This might explain the 1.5\u03c3 di\ufb00erence in\nthe central value of mc(mc) compared to, for example, the\nLQCD result. An analogous treatment for bottom quarks\nseems to have a smaller e\ufb00ect.\nWe conclude that mb and mc can be reliably and pre-\ncisely extracted using a variety of methods. The results in\nTables 17.1.5 and 17.1.6 have correlated errors, so we do\nnot average them. They are well encompassed, however,\nby mc(3 GeV) = 0.99(1) GeV and mb(mb) = 4.16(2) GeV.\n17.1.3.3 Moment Measurements\nMoments of inclusive observables in B \u2192Xc\u2113\u03bd decays\nhave been measured by the Belle (Schwanda, 2007; Urquijo,\n2007) and BABAR (Aubert, 2004c,n,r, 2010c) collabora-\ntions.\nThe Belle collaboration has measured spectra of the\nlepton energy E\u2113and the hadronic mass mX in B \u2192Xc\u2113\u03bd\nusing 152 million \u03a5(4S) \u2192BB events (Schwanda, 2007;\nUrquijo, 2007). These analyses proceed as follows: \ufb01rst,\nthe decay of one B meson in the event is fully recon-\nstructed in a hadronic mode (Btag). Next, the semilep-\ntonic decay of the second B meson in the event (Bsig) is\nidenti\ufb01ed by searching for a charged lepton among the re-\nmaining particles in the event. In Urquijo (2007), the elec-\ntron momentum spectrum p\u2217\ne in the B meson rest frame is\nmeasured down to 0.4 GeV (Figure 17.1.9). In Schwanda\n(2007), all remaining particles in the event, excluding the\n (GeV/c)\ne\n*B\np\n0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\n2.2 2.4\nEntries per 0.1 GeV/c\n0\n100\n200\n300\n400\n500\n0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\n2.2 2.4\n0\n100\n200\n300\n400\n500 Belle\n data\n+\nB\n (GeV/c)\ne\n*B\np\n0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\n2.2 2.4\nEntries per 0.1 GeV/c\n0\n100\n200\n300\n400\n500\n600\n0.4 0.6 0.8\n1\n1.2 1.4 1.6 1.8\n2\n2.2 2.4\n0\n100\n200\n300\n400\n500\n600\nBelle\n data\n0\nB\ni\n e \nc\n X\nA\nB \ni\n e \nu\n X\nA\nB \nSecondaries\nCombinatorial\nContinuum\nFigure 17.1.9. Belle analysis of the electron momentum spec-\ntrum for B+ and B0 decays (Urquijo, 2007) before background\nsubtraction, overlaid with the sum of various background con-\ntributions and the signal.\ncharged lepton (electron or muon), are combined to recon-\nstruct the hadronic X system. The mX spectrum is mea-\nsured for di\ufb00erent lepton energy thresholds in the B meson\nrest frame (Figure 17.1.10).\nThe observed spectra are distorted by resolution and\nacceptance e\ufb00ects and cannot be used directly to obtain\nthe moments. In the Belle analyses, acceptance and \ufb01nite\nresolution e\ufb00ects are corrected by unfolding the observed\nspectra using the Singular Value Decomposition (SVD) al-\ngorithm (H\u00a8ocker and Kartvelishvili, 1996). Belle measures\nthe energy moments \u27e8Ek\n\u2113\u27e9for k = 0, 1, 2, 3, 4 and minimum\nlepton energies ranging from 0.4 to 2.0 GeV. Moments of\nthe hadronic mass \u27e8mk\nX\u27e9are measured for k = 2, 4 and\nminimum lepton energies from 0.7 to 1.9 GeV.\nTo determine |Vcb|, Belle performs \ufb01ts to 14 lepton en-\nergy moments, 7 hadronic mass moments and 4 moments\nof the photon energy spectrum in B \u2192Xs\u03b3 (Schwanda,\n2008) based on OPE expressions derived in the kinetic\n(Benson, Bigi, Mannel, and Uraltsev, 2003; Benson, Bigi,\nand Uraltsev, 2005; Gambino and Uraltsev, 2004) and\n\n199\nTable 17.1.5. Recent results for the charm-quark mass. An asterisk indicates that we have obtained this number from the\nvalue of mc quoted as the main result of the paper using four-loop accuracy (together with \u03b1S(mZ) = 0.1184 (Nakamura et al.,\n2010)).\nmc(3 GeV) (GeV)\nmc(mc) (GeV)\nMethod\nReference\n0.986 \u00b1 0.013\n1.275 \u00b1 0.013\u2217\nLESR\nK\u00a8uhn, Steinhauser, and Sturm (2007)\n0.96\n\u00b1 0.04\u2217\n1.25\n\u00b1 0.04\nNRSR\nSigner (2009)\n0.986 \u00b1 0.006\n1.275 \u00b1 0.006\u2217\nLQCD\nMcNeile, Davies, Follana, Hornbostel, and Lepage (2010)\n0.998 \u00b1 0.029\n1.277 \u00b1 0.026\nLESR\nDehnadi, Hoang, Mateu, and Zebarjad (2011)\n0.987 \u00b1 0.009\n1.278 \u00b1 0.009\nFESR\nBodenstein, Bordes, Dominguez, Penarrocha, and Schilcher (2011)\n0.972 \u00b1 0.006\u2217\n1.262 \u00b1 0.006\nFESR\nNarison (2012)\nTable 17.1.6. Recent results for the bottom-quark mass.\nmb(mb) (GeV)\nMethod\nReference\n4.19\n\u00b1 0.06\nNRSR\nPineda and Signer (2006)\n4.163 \u00b1 0.016\nLESR\nChetyrkin et al. (2009)\n4.164 \u00b1 0.023\nLQCD\nMcNeile, Davies, Follana, Hornbostel, and Lepage (2010)\n4.167 \u00b1 0.013\nLESR\nNarison (2012)\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n0\n5\n10\n15\nM2\nX (GeV2/c4)\nentries / 0.333 GeV2/c4\nBelle\nE*\nl > 0.7 GeV\ndata\nfake/secondary\ncombinatorial\nB A Xuli\nB A Xcli\nFigure 17.1.10. Belle analysis of the hadronic mass distribu-\ntion for B \u2192Xc\u2113\u03bd decays (Schwanda, 2007). The data after\ncontinuum subtraction are compared with the sum of simulated\nXc\u2113\u03bd signal and background contributions.\nTable 17.1.7. Results of the OPE \ufb01ts in the kinetic and 1S\nschemes to moments measured by Belle (Schwanda, 2008): |Vcb|\nand the inclusive branching fractions for B \u2192Xc\u2113\u03bd decays,\nplus \u03c72 per degree of freedom.\nKinetic scheme\n1S scheme\n|Vcb| (10\u22123)\n41.58 \u00b1 0.90\n41.56 \u00b1 0.68\nBXc\u2113\u03bd (%)\n10.49 \u00b1 0.23\n10.60 \u00b1 0.28\n\u03c72/ndf.\n4.7/18\n7.3/18\n1S schemes (Bauer, Ligeti, Luke, Manohar, and Trott,\n2004). Both theoretical frameworks are considered inde-\npendently and yield very consistent results (see Table 17.1.7).\nBABAR has measured the hadronic mass spectrum mX\nin B \u2192Xc\u2113\u03bd using a data sample of 232 million \u03a5(4S) \u2192\nBB events (Aubert, 2010c). The experimental method is\nsimilar to the Belle analysis discussed previously, i.e., one\nB meson is fully reconstructed in a hadronic mode and\na charged lepton with momentum above 0.8 GeV in the\nB meson frame identi\ufb01es the semileptonic decays of the\nsecond B. The remaining particles in the event are com-\nbined to reconstruct the hadronic system X. The resolu-\ntion in mX is improved by a kinematic \ufb01t to the whole\nevent, taking into account 4-momentum conservation and\nconstraining the missing mass to zero.\nTo derive the true moments from the reconstructed\nones, BABAR applies a set of linear corrections. These cor-\nrections depend on the charged particle multiplicity of the\nX system, the normalized missing mass, Emiss\u2212pmiss, and\nthe lepton momentum. In this way, BABAR measures the\nmoments of the hadronic mass spectrum up to \u27e8m6\nX\u27e9for\nminimum lepton energies ranging from 0.8 to 1.9 GeV.\nThis study also updates the previous BABAR measure-\nment of the lepton energy moments in B \u2192Xc\u2113\u03bd (Aubert,\n2004n) using new branching fraction measurements for\nbackground decays and improving the evaluation of sys-\ntematic uncertainties. Furthermore, \ufb01rst measurements of\ncombined hadronic mass and energy moments of the form\n\u27e8nk\nX\u27e9with k = 2, 4, 6 are presented. They are de\ufb01ned as\nn2\nX = m2\nX \u22122 e\u039bEX + e\u039b2, where mX and EX are the mass\nand the energy of the X system and the constant e\u039b is\ntaken to be 0.65 GeV.\nBABAR performs a simultaneous \ufb01t to 12 hadronic mass\nmoments (or 12 combined mass-energy moments), 13 lep-\nton energy moments (including partial branching fractions\nas zero order moments), and 3 photon energy moments in\nB \u2192Xs\u03b3 (Aubert, 2005x, 2006t), and based on OPE cal-\nculations in the kinetic scheme (Benson, Bigi, Mannel, and\nUraltsev, 2003; Benson, Bigi, and Uraltsev, 2005; Gam-\nbino and Uraltsev, 2004) extracts |Vcb|, the total branching\n\n200\nTable 17.1.8. Results of the OPE \ufb01ts in the kinetic scheme\nto moments measured by BABAR (Aubert, 2010c). |Vcb| and the\ninclusive branching fractions for B \u2192Xc\u2113\u03bd decays, plus \u03c72 per\ndegree of freedom. The \ufb01rst uncertainty is experimental, the\nsecond theoretical.\nHadronic moment\nMass-energy moment\n|Vcb| (10\u22123)\n42.05 \u00b1 0.45 \u00b1 0.70\n41.91 \u00b1 0.48 \u00b1 0.70\nmb (GeV)\n4.549 \u00b1 0.031 \u00b1 0.038\n4.556 \u00b1 0.034 \u00b1 0.041\nBXc\u2113\u03bd (%)\n10.64 \u00b1 0.17 \u00b1 0.06\n10.64 \u00b1 0.17 \u00b1 0.06\n\u03c72/ndf.\n10.9/28\n8.2/28\nfractions, mb and mc, and OPE parameters. The results\nare given in Table 17.1.8.\n17.1.3.4 Global Fit and Determination of |Vcb|\nWe perform a global analysis of the B Factory measure-\nments using the full O(\u03b12\nS) calculations of the moments in\nthe kinetic scheme (Gambino, 2011). This \ufb01t combines the\n54 moment measurements shown in Table 17.1.9 and de-\ntermines |Vcb|, the b-quark mass mb and the higher order\nparameters in the OPE description of semileptonic decays.\nThe only external input is the average B0 and B+ lifetime,\nassumed to be (1.582 \u00b1 0.007) ps (Beringer et al., 2012).\nFrom the \ufb01ts to moments in B \u2192Xc\u2113\u03bd we obtain a\nlinear combination of the b- and c-quark masses. To en-\nhance the precision on mb, we make two choices to gain\nadditional constraints: we either include photon energy\nmoments from B \u2192Xs\u03b3 decays in the \ufb01t, or use as a pre-\ncise constraint on the c-quark mass mc(3 GeV) = 0.998 \u00b1\n0.029 GeV, as derived with low-energy sum rules (Dehnadi,\nHoang, Mateu, and Zebarjad, 2011). The results for the\nkinetic scheme based on the Belle and BABAR moments\nare shown in Table 17.1.10 and Figure 17.1.11.\nThe same moments are \ufb01t with expressions derived in\nthe 1S scheme (Bauer, Ligeti, Luke, Manohar, and Trott,\n2004). In this framework, we cannot introduce a c-quark\nmass constraint. Results are thus presented for the entire\nset of 54 moment measurements and for the Xc\u2113\u03bd mo-\nments only (Table 17.1.11).\nThe \ufb01t results shown in the \ufb01rst rows of Tables 17.1.10\nand 17.1.11 are based on the same set of measurements\nand can thus be compared directly. For |Vcb|, the result ob-\ntained in the kinetic scheme, (42.09 \u00b1 0.75) \u00d7 10\u22123, agrees\nvery well with the 1S result, (42.01\u00b10.49)\u00d710\u22123. The un-\ncertainty on |Vcb| in the kinetic scheme is 1.8% compared\nto 1.2% is the 1S scheme. Note however that the assump-\ntions on the dominant theory error are signi\ufb01cantly dif-\nferent in the two frameworks. The results for the b-quark\nmass cannot be compared directly due to di\ufb00erent mass\nde\ufb01nitions.\nWe adopt the results of the \ufb01t in the kinetic scheme\nwith the constraint on the c-quark mass as currently the\nmost precise result, based on inclusive B \u2192Xc\u2113\u03bd decays,\n|Vcb|incl = (42.01 \u00b1 0.47exp \u00b1 0.59th) \u00d7 10\u22123.\n(17.1.43)\n (GeV)\nb\nm\n4.5\n4.52\n4.54\n4.56\n4.58\n)\n2\n (GeV\n/\n2\n\u00b5\n0.45\n0.5\n0.55\n constraint\na s\n X\n constraint\nc\n m\n (GeV)\nb\nm\n4.5\n4.52\n4.54\n4.56\n4.58\n|\ncb\n|V\n0.04\n0.041\n0.042\n0.043\n constraint\na s\n X\n constraint\nc\n m\nFigure 17.1.11. \u2206\u03c72 = 1 contours for the global \ufb01t to Belle\nand BABAR moments in the kinetic mass scheme, for details see\nthe text.\n17.1.4 Exclusive decays B \u2192\u03c0\u2113\u03bd\n17.1.4.1 Theoretical Overview\nThe decay rate for B \u2192\u03c0\u2113\u03bd semileptonic decay is given\nby:\nd\u0393\ndq2 = G2\nF |Vub|2\n24\u03c03\n(q2 \u2212m2\n\u2113)2 p\u03c0\nq4m2\nB\n\u00d7\n( \u0012\n1 + m2\n\u2113\n2q2\n\u0013\nm2\nB p2\n\u03c0\n\u0002\nf B\u03c0\n+ (q2)\n\u00032\n+3m2\n\u2113\n8q2 (m2\nB \u2212m2\n\u03c0)2 \u0002\nf B\u03c0\n0\n(q2)\n\u00032\n)\n,(17.1.44)\nwhere q \u2261pB \u2212p\u03c0 is the 4-momentum transferred to the\nlepton-neutrino pair and\np\u03c0 =\n\u0002\n(m2\nB + m2\n\u03c0 \u2212q2)2 \u22124m2\nBm2\n\u03c0\n\u00031/2 /(2mB)\nis the pion 3-momentum in the B rest frame. The form\nfactors f B\u03c0\n+ (q2) and f B\u03c0\n0\n(q2) are de\ufb01ned in Eq. (17.1.6).\n\n201\nTable 17.1.9. Experimental inputs used in the global analysis of B \u2192Xc\u2113\u03bd. n is the order of the moment, c is the threshold\nvalue in GeV. In total, there are 29 measurements from BABAR and 25 from Belle.\nExperiment\nHadron moments \u27e8mn\nX\u27e9\nLepton moments \u27e8En\n\u2113\u27e9\nPhoton moment \u27e8En\n\u03b3 \u27e9\nBABAR\nn = 2, c = 0.9, 1.1, 1.3, 1.5\nn = 0, c = 0.6, 1.2, 1.5\nn = 1, c = 1.9, 2.0\nn = 4, c = 0.8, 1.0, 1.2, 1.4\nn = 1, c = 0.6, 0.8, 1.0, 1.2, 1.5\nn = 2, c = 1.9\nn = 6, c = 0.9, 1.3\nn = 2, c = 0.6, 1.0, 1.5\n(Aubert, 2005x, 2006t)\n(Aubert, 2010c)\nn = 3, c = 0.8, 1.2\n(Aubert, 2004n, 2010c)\nBelle\nn = 2, c = 0.7, 1.1, 1.3, 1.5\nn = 0, c = 0.6, 1.0, 1.4\nn = 1, c = 1.8, 1.9\nn = 4, c = 0.7, 0.9, 1.3\nn = 1, c = 0.6, 0.8, 1.0, 1.2, 1.4\nn = 2, c = 1.8, 2.0\n(Schwanda, 2007)\nn = 2, c = 0.6, 1.0, 1.4\n(Limosani, 2009)\nn = 3, c = 0.8, 1.0, 1.2\n(Urquijo, 2007)\nTable 17.1.10. Results of the OPE global \ufb01t to B \u2192Xc\u2113\u03bd moments in the kinetic scheme: the \ufb01rst row refers to the \ufb01t\nincluding B \u2192Xs\u03b3 moments, the second row gives the results obtained with the charm-quark mass constraint. In all cases, the\n\ufb01rst error is the uncertainty of the global \ufb01t. For |Vcb| the second error is an additional theoretical uncertainty arising from the\ncalculation of |Vcb|. The \u03c72/ndf. is 17.1/(54 \u22127) for the B \u2192Xs\u03b3 and 23.3/(44 \u22127) for the mc constrained \ufb01t.\nConstraint\n|Vcb| (10\u22123)\nmkin\nb\n(GeV)\n\u00b52\n\u03c0 (GeV2)\n\u03c13\nD (GeV3)\n\u00b52\nG (GeV2)\n\u03c13\nLS (GeV3)\nB \u2192Xs\u03b3\n42.09 \u00b1 0.46 \u00b1 0.59\n4.538 \u00b1 0.038\n0.515 \u00b1 0.045\n0.209 \u00b1 0.021\n0.263 \u00b1 0.047\n\u22120.121 \u00b1 0.090\nmc(3 GeV)\n42.01 \u00b1 0.47 \u00b1 0.59\n4.551 \u00b1 0.025\n0.499 \u00b1 0.044\n0.177 \u00b1 0.021\n0.227 \u00b1 0.048\n\u22120.081 \u00b1 0.092\nTable 17.1.11. Results of the OPE global \ufb01t to B \u2192Xc\u2113\u03bd moments in the 1S scheme: the \ufb01rst row refers to the \ufb01t including\nB \u2192Xs\u03b3 moments, the second row gives the results obtained with B \u2192Xc\u2113\u03bd moments only.\nInput\n|Vcb| (10\u22123)\nm1S\nb\n(GeV)\n\u03bb1 (GeV2)\n\u03c11 (GeV3)\n\u03c41 (GeV3)\n\u03c42 (GeV3)\n\u03c43 (GeV3)\nall moments\n42.01 \u00b1 0.49\n4.696 \u00b1 0.043\n\u22120.354 \u00b1 0.072\n0.057 \u00b1 0.060\n0.154 \u00b1 0.122\n\u22120.039 \u00b1 0.078\n0.194 \u00b1 0.105\nXc\u2113\u03bd only\n42.58 \u00b1 0.78\n4.595 \u00b1 0.110\n\u22120.428 \u00b1 0.099\n0.080 \u00b1 0.062\n0.150 \u00b1 0.124\n\u22120.023 \u00b1 0.086\n0.204 \u00b1 0.112\nIn the limit of zero momentum-transfer the form factors\nmust satisfy the kinematic constraint f B\u03c0\n+ (0) = f B\u03c0\n0\n(0).\nFurthermore, in the limit m\u2113\u21920, which is a good ap-\nproximation for \u2113= e, \u00b5, the scalar form factor f B\u03c0\n0\n(q2)\nbecomes negligible:\nd\u0393\ndq2 = G2\nF |Vub|2\n24\u03c03\np3\n\u03c0|f B\u03c0\n+ (q2)|2.\n(17.1.45)\nHence precise experimental measurements of the B \u2192\u03c0\u2113\u03bd\nbranching fraction along with reliable theoretical calcula-\ntions of the form factor f B\u03c0\n+ (q2) enable a clean determi-\nnation of the CKM matrix element |Vub|.53\nThe form factors encode the non-perturbative dynam-\nics of binding quarks into hadrons and therefore they can-\nnot be calculated perturbatively. In practice, two meth-\nods are available for computing QCD form factors with\n53 In principle, the exclusive semileptonic decay channel B \u2192\n\u03c1\u2113\u03bd can also be used to determine |Vub| (see, e.g., Flynn, Naka-\ngawa, Nieves, and Toki, 2009). In practice, however, systematic\nuncertainties are not under control in current lattice QCD cal-\nculations of the \u03c1 meson because the \u03c1 is unstable and is not\ndescribed within the framework of chiral perturbation theory;\nthese concerns will be addressed in future LQCD calculations\nwhen more computing resources are available. Light-cone sum\nrule determinations of the B \u2192\u03c1\u2113\u03bd form factor are available,\nsuch as in Ball and Zwicky (2005b), but there has not been\nany recent work on this channel.\ncontrolled uncertainties: lattice QCD and light-cone sum\nrules. As discussed in Section 17.1.2, LQCD is a \ufb01rst-\nprinciples approach providing results with steadily im-\nprovable errors. LCSR is derived from the correlator of\nquark currents calculated in terms of the OPE. Matching\nthe result of this calculation to the hadronic dispersion re-\nlation yields an analytical expression for the form factor.\nThe precision of LCSR is limited by the accuracy of OPE\nand by the quark-hadron duality approximation used in\nthe dispersion relation. Lattice QCD and light-cone sum\nrule form-factor calculations are complementary in that\nthey work in di\ufb00erent kinematical regions: LQCD is best\nat high q2 while LCSR are applicable at low q2-values.\nHeavy-to-light form-factor parameterizations\nIt is useful for comparing di\ufb00erent theoretical calcula-\ntions or theory with experiment to parameterize the form\nfactor f B\u03c0\n+ (q2) as a function of q2. Many parameteriza-\ntions are available in the literature, but here we focus on\nthe model-independent parameterization of Boyd, Grin-\nstein, and Lebed (1995), hereafter \u201cBGL\u201d, and its vari-\nants, which is based on the general properties of ana-\nlyticity, unitarity and crossing-symmetry. All form fac-\ntors are analytic functions of q2, except at physical poles\nand threshold branch points. Hence, given an appropriate\n\n202\nchange of variables, they can be expressed in a particularly\nuseful manner as a convergent power series (see, e.g., Ar-\nnesen, Grinstein, Rothstein, and Stewart, 2005; Bourrely,\nMachet, and de Rafael, 1981; Boyd and Savage, 1997; Lel-\nlouch, 1996).\nConsider the following change of variables:\nz(q2, t0) =\np\n1 \u2212q2/t+ \u2212\np\n1 \u2212t0/t+\np\n1 \u2212q2/t+ +\np\n1 \u2212t0/t+\n,\n(17.1.46)\nwhere t+\u2261(mB +m\u03c0)2, and t0 < t+ is an arbitrary param-\neter to be discussed later. This transformation maps the\nsemileptonic region of q2 onto a unit circle in the complex\nz plane. In terms of the new variable z, the B \u2192\u03c0 form\nfactor takes a simple form:\nP+(q2)\u03c6+(q2, t0)f+(q2) =\n\u221e\nX\nk=0\nak(t0)z(q2, t0)k. (17.1.47)\n(A similar function can be derived for the scalar form fac-\ntor f0(q2).) The function P+(q2) must be chosen to vanish\nat the B\u2217pole in order to preserve the correct analytic\nstructure of f+(q2):\nP B\u03c0\n+ (q2) = z(q2, m\u2217\nB) ,\n(17.1.48)\nwhile the function \u03c6+(q2, t0) can be any analytic function.\nIt is helpful, however, to choose \u03c6+(q2, t0) so that the uni-\ntarity constraint on the series coe\ufb03cients (ak\u2019s) obeys a\nsimple form. The choice for \u03c6+(q2, t0) corresponding to\nthe BGL parameterization is given in Arnesen, Grinstein,\nRothstein, and Stewart (2005):\n\u03c6+(q2, t0) =\ns\n3\n96\u03c0\u03c7(0)\nJ\n\u0010p\nt+ \u2212q2 +\np\nt+ \u2212t0\n\u0011\n\u00d7\n\u0010p\nt+ \u2212q2 +\np\nt+ \u2212t\u2212\n\u00113/2\n\u00d7\n\u0010p\nt+ \u2212q2 +\np\nt+\n\u0011\u22125\n(t+ \u2212q2)\n(t+ \u2212t0)1/4 ,\n(17.1.49)\nwhere the numerical factor \u03c7(0)\nJ\ncan be calculated using\nperturbation theory and the OPE.\nUnitarity constrains the size of the BGL series coe\ufb03-\ncients:\nN\nX\nk=0\na2\nk \u223c< 1,\n(17.1.50)\nwhere this holds for any value of N. In the case of the\nB \u2192\u03c0 form factor, Becher and Hill (2006) use the heavy-\nquark power-counting to argue that the sizes of the series\ncoe\ufb03cients should in fact be much less than one:\nN\nX\nk=0\na2\nk \u2264\n\u0012 \u039b\nmQ\n\u00133\n\u226a1,\n(17.1.51)\nwhere \u039b is a typical hadronic scale; this is consistent with\nlattice calculations by Bailey et al. (2009) and experimen-\ntal measurements by BABAR in del Amo Sanchez (2011n)\nand Belle in Ha (2011). The free parameter t0 appearing\nin Eq. (17.1.46) determines the range of |z| in the semilep-\ntonic region, and hence can be chosen to accelerate the se-\nries convergence. For example, Arnesen, Grinstein, Roth-\nstein, and Stewart (2005) use the value t0 = 0.65t\u2212such\nthat \u22120.34 < z < 0.22 for B \u2192\u03c0l\u03bd decay. The small mag-\nnitude of |z|, in conjunction with the tight heavy-quark\nbound on the size of the series coe\ufb03cients, ensures that\nonly the \ufb01rst few terms in the series are needed to describe\nthe B \u2192\u03c0 form factor to sub-percent accuracy.\nBourrely, Caprini, and Lellouch (2009) (BCL) use the\nsame series expansion of Eq. (17.1.47), but without an\nouter function \u03c6+ and with a di\ufb00erent Blashke factor P+:\nf+(q2) =\n1\n1 \u2212q2/m2\nB\u2217\nK\nX\nk=0\nbk(t0)z(q2, t0)k.\n(17.1.52)\nTheir choice avoids unphysical singularities which are gen-\nerated at q2 = t+ by the outer function in a truncated\nBGL parameterization. Further, Bourrely, Caprini, and\nLellouch (2009) optimize the parameter t0 such that the\nsemileptonic domain is mapped onto a symmetric interval\nin z. With the choice t0 = (mB + m\u03c0)(\u221amB \u2212\u221am\u03c0)2,\nthe value of |z| < 0.279. Although the BCL parameteriza-\ntion has a simpler functional form, the constraint on the\nseries is more complicated than Eq. (17.1.50) in that it is\nno longer diagonal in the series index k. We use the BCL\nparameterization to obtain |Vub| in Section 17.1.4.3.\nA di\ufb00erent approach suggested by Flynn and Nieves\n(2007a,b) uses the Omn`es parameterization, allowing one\nto express the form-factor shape in terms of the elastic B-\n\u03c0 scattering phase shift and the value of f+(q2) at a few\nsubtraction points below the B\u03c0 production threshold.\nLattice QCD form-factor calculations\nState-of-the-art LQCD computations now regularly in-\nclude the e\ufb00ects of three light dynamical quarks. Often\ncalculations are done in the isospin limit with two lighter\ndegenerate quarks and one heavier quark with a mass close\nto the physical strange quark; these are referred to as\n\u201c2+1\u201d \ufb02avor simulations.\nIn practice, limited computational resources prohibit\ncalculations with simulated values of the u- and d-quark\nas light as those in the real world. LQCD calculations\nmust also be done at \ufb01xed, nonzero values of the lat-\ntice spacing. Hence one generates data with a sequence\nof light-quark masses (down to \u223cmstrange/10 for current\nB \u2192\u03c0 calculations) and a sequence of lattice spacings\n(down to a \u223c0.09 fm for current B \u2192\u03c0 calculations)\nand extrapolates the remainder of the way to the physical\nmasses and zero lattice spacing. Because these limits are\ninterrelated, it is now standard to use model-independent\nfunctional forms derived in Chiral Perturbation Theory\n(\u03c7PT) for the speci\ufb01c lattice quark formulation being used\n(i.e. including discretization corrections) to guide the ex-\ntrapolation (see, e.g., Aubin and Bernard, 2007, for the\ncase of B \u2192\u03c0). This procedure leaves a remaining sys-\ntematic uncertainty in the physical matrix element due\n\n203\nto truncation of the chiral expansion that is typically in-\ncluded in error budgets as a \u201cchiral extrapolation error.\u201d\nThis, in combination with statistical errors, is currently\nthe largest source of uncertainty in lattice calculations of\nthe B \u2192\u03c0 form factor. Fortunately, increasing computa-\ntional resources are allowing this error to be reduced in a\nstraightforward manner.\nThe next-largest uncertainty in current lattice B \u2192\n\u03c0 form-factor calculations is due to perturbative opera-\ntor matching. Numerical lattice simulations evaluate the\nhadronic matrix element of the vector current V\u00b5 = iu\u03b3\u00b5b\nwritten in terms of the discretized versions of the heavy-\nquark (b) and light anti-quark (u) \ufb01elds that appear in\nthe lattice actions. Hence one must compute matching\nfactors to relate the continuum vector current to its lat-\ntice counterpart. Current B \u2192\u03c0 form-factor calculations\nrely on either a combination of perturbative and non-\nperturbative methods or on one-loop lattice perturbation\ntheory; the residual uncertainties from neglected 2-loop\nand higher-order terms in the perturbative series can be\napproximately as large as the chiral-continuum extrapo-\nlation error. Hence new methods are being developed and\nnew actions are being used in order to reduce the renor-\nmalization error in the future.\nCurrently there are two realistic \u201c2+1\u201d \ufb02avor LQCD\ncalculations of the B \u2192\u03c0 form factor \u2013 one by the HPQCD\nCollaboration (Dalgic et al., 2006) and one by the Fermi-\nlab Lattice and MILC collaborations (Bailey et al., 2009).\nThese calculations were both performed on gauge con\ufb01g-\nurations made publicly available by the MILC Collabo-\nration (see Aubin et al., 2004) and include the e\ufb00ects of\nthree \ufb02avors of dynamical staggered light quarks; hence\nthe statistical errors are somewhat correlated among the\ntwo results. The two calculations use di\ufb00erent heavy-quark\nformalisms, however, for the b quark. The Fermilab and\nMILC collaborations use the Fermilab formalism devel-\noped by El-Khadra, Kronfeld, and Mackenzie (1997) in\nwhich one uses knowledge of the heavy-quark limit of QCD\nto systematically remove heavy-quark discretization errors\norder-by-order in 1/mb. The HPQCD Collaboration uses\nthe formulation of the NRQCD action from Lepage, Mag-\nnea, Nakhleh, Magnea, and Hornbostel (1992), in which\nthe b-quark is a non-relativistic \ufb01eld and the action is ex-\npanded in powers of vb/c, where vb is the spatial velocity\nof the b quark. Both heavy-quark formulations work well\nfor b quarks at currently available values of the lattice\nspacing. The Fermilab formalism, however, has two ad-\nvantages in that it possesses a continuum limit and that\nit can also be used for c quarks, thereby providing a cross\ncheck of the method. Future calculations using other lat-\ntice formulations for the light and heavy quarks, such the\nrelativistic heavy-quark action developed by Christ, Li,\nand Lin (2007) and used by the RBC and UKQCD Col-\nlaborations for B-meson leptonic decays and mixing (see\nVan de Water and Witzel, 2010), will provide valuable in-\ndependent cross checks of the B \u2192\u03c0 form factor in the\nnext few years.\nThe Fermilab Lattice and MILC Collaborations present\ntheir form-factor results in terms of the BGL series coef-\nTable 17.1.12. Coe\ufb03cients ak and correlation matrix \u03c1kl of a\n3-parameter BGL series expansion of f B\u03c0\n+\nfrom Bernard et al.\n(2009b). Statistical and systematic errors are added in quadra-\nture.\nFit:\n0.0216(27)\n\u22120.0378(191)\n\u22120.113(27)\n\u03c1\na0\na1\na2\na0\n1.000\n0.640\n0.475\na1\n0.640\n1.000\n0.964\na2\n0.474\n0.964\n1.000\n\ufb01cients and the correlation matrix; these are given in Ta-\nble 17.1.12. The series coe\ufb03cients can be used to obtain\nthe form factor over the entire q2 range, and are therefore a\nuseful way to present the data, as pointed out by Bernard\net al. (2009b). This is particularly helpful for state-of-the\nart extractions of |Vub| that rely on simultaneous BGL \ufb01ts\nof the lattice and experimental data including correlations\n(see del Amo Sanchez, 2011n; Ha, 2011). Alternatively\none can present the integrated decay rate over a q2 range\nfor which the lattice calculation is most reliable, typically\nfrom q2 = 16 GeV2 to q2\nmax = (mB \u2212m\u03c0)2:\n\u2206\u03b6 \u2261G2\nF\n24\u03c03\nq2\nf\nZ\nq2\ni\ndq2p3\n\u03c0|f B\u03c0\n+ (q2)|2 .\n(17.1.53)\nThe quantity \u2206\u03b6 is given for both the Fermilab/MILC\nand HPQCD calculations in Table 17.1.13.\nThe 2006 HPQCD B \u2192\u03c0 form-factor calculation re-\nlies on the parameterization of Ball and Zwicky (2005a)\n(BZ) during an intermediate step to interpolate their data\nto \ufb01ducial values of the pion energy before performing\nthe chiral extrapolation. Use of models such as the one\nin Becirevic and Kaidalov (2000), hereafter \u201cBK\u201d; or the\nBZ parameterization can lead to an underestimation in\nthe quoted form-factor errors, particularly at low values\nof q2 where the lattice data are poor or nonexistent and\nthe shape is constrained primarily by the model function.\nMoreover, any comparisons between di\ufb00erent theoretical\nor experimental determinations of the BK or BZ \ufb01t param-\neters are not necessarily meaningful, since any observed\ndiscrepancies could simply be due to limitations of the\nmodel. Hence only lattice QCD form factor determina-\ntions based on BGL-like series (such as also the BCL pa-\nrameterization) should be considered model-independent.\nLight-cone sum rule form-factor calculations\nThe method of QCD light-cone sum rules allows one to\ncalculate the B \u2192\u03c0 form factors at small and interme-\ndiate q2 (see, e.g., Bagan, Ball, and Braun, 1998; Ball\nand Zwicky, 2005c; Belyaev, Khodjamirian, and Ruckl,\n1993; Duplancic, Khodjamirian, Mannel, Melic, and Of-\nfen, 2008; Khodjamirian, Ruckl, Weinzierl, and Yakovlev,\n1997). The key element of the calculational procedure is\n\n204\nTable 17.1.13. Results for the integrated decay rate \u2206\u03b6 = \u2206\u0393 B\u2192\u03c0l\u03bd/|Vub|2 from lattice QCD and light-cone sum rules.\nStatistical and systematic errors are added in quadrature.\nq2 (GeV2)\n\u2206\u03b6 (ps\u22121)\nHPQCD (Dalgic et al., 2006)\n> 16\n2.02 \u00b1 0.55\nFermilab/MILC (Bailey et al., 2009)\n> 16\n2.21+0.47\n\u22120.42\nLCSR (Khodjamirian, Mannel, O\ufb00en, and Wang, 2011)\n< 12\n4.59+1.00\n\u22120.85\nthe correlator of the two heavy-light quark currents:\ni\nZ\nd4xeiqx\u27e8\u03c0+(p)| T{u\u03b3\u00b5b(x), mbbi\u03b35d(0)} |0\u27e9\n\u2261F((p + q)2, q2)p\u00b5 + eF((p + q)2, q2)q\u00b5 ,\n(17.1.54)\nF((p + q)2, q2) = 2m2\nBfBf B\u03c0\n+ (q2)\nm2\nB \u2212(p + q)2 + ... ,\n(17.1.55)\nwhere Eq. (17.1.55) represents the hadronic dispersion\nrelation for the amplitude F, with the ground-state B-\nmeson contribution containing the vector B \u2192\u03c0 form\nfactor multiplied by the B decay constant. The remaining\nhadronic sum in Eq. (17.1.55) is indicated by ellipses. The\namplitude eF is used to calculate the scalar form factor\nf B\u03c0\n0\n(q2). At (p + q)2 \u226am2\nb and q2 \u226am2\nb, the T-product\nin Eq. (17.1.54) is expanded near the light-cone x2 \u223c0,\nyielding process-independent nonlocal vacuum-pion ma-\ntrix elements, such as \u27e8\u03c0(p)|u\u03b1(x)d\u03b2(0)|0\u27e9. The light-cone\nOPE yields\nF((p + q)2, q2) =\n(17.1.56)\nX\nt=2,3,4,...\nZ\nDui\nX\nk=0,1,...\n\u0010\u03b1S\n\u03c0\n\u0011k\nT (t)\nk ((p + q)2, q2, ui, mb, \u00b5)\u03d5(t)\n\u03c0 (ui, \u00b5) ,\na convolution (at the factorization scale \u00b5) of calcula-\nble short-distance coe\ufb03cient functions T (t)\nk\nand universal\npion light-cone distribution amplitudes (DA\u2019s) \u03d5(t)\n\u03c0 (ui, \u00b5)\nof growing twist t \u22652. The integration goes over the\nmomentum fractions ui = u1, u2, ... of quarks and gluons\nin the pion. The terms in Eq. (17.1.56) corresponding to\nhigher-twist pion DA\u2019s are suppressed by inverse powers of\nthe b-quark virtuality ((p + q)2 \u2212m2\nb) \u223c\u039bmb, where \u039b \u226b\n\u039bQCD does not scale with mb. Currently Eq. (17.1.54) in-\ncludes all LO contributions of the twist 2, 3, 4 quark-\nantiquark and quark-antiquark-gluon DA\u2019s of the pion and\nthe NLO, O(\u03b1S) corrections to the twist-2 and twist-3 two-\nparticle coe\ufb03cient functions.\nFurthermore, one uses quark-hadron duality and ap-\nproximates the sum over excited B-states in the hadronic\ndispersion relation by the quark-gluon spectral density\nIm F (OPE)(s, q2) calculated from the OPE, Eq. (17.1.56),\nintroducing the e\ufb00ective threshold parameter sB\n0 . The \ufb01-\nnal step involves a Borel transformation (p + q)2 \u2192m2 \u223c\n\u039bmb. The resulting LCSR for the B \u2192\u03c0 form factor has\nthe following form\nf B\u03c0\n+ (q2) =\n \nem2\nB/m2\n2m2\nBfB\n!\n1\n\u03c0\nZ sB\n0\nm2\nb\nds Im F (OPE)(s, q2) e\u2212s/m2.\n(17.1.57)\nThe uncertainty introduced by the quark-hadron duality\napproximation is minimized by calculating the B meson\nmass from the derivative of the same LCSR, thereby \ufb01x-\ning sB\n0 . Details of the method can be found in Duplancic,\nKhodjamirian, Mannel, Melic, and O\ufb00en (2008); an intro-\nductory review is in Colangelo and Khodjamirian (2000).\nThe LCSR method and input was also successfully tested\nfor D \u2192\u03c0, K form factors by Khodjamirian, Klein, Man-\nnel, and O\ufb00en (2009). The input includes \u03b1S and the\nb quark mass (in the MS scheme), as well as the non-\nperturbative parameters of the pion DA\u2019s, e.g., f\u03c0 and the\nshape parameters (Gegenbauer moments) for the twist-2\npion DA \u03d5(2)\n\u03c0 . For the decay constant fB the QCD sum\nrule for the two-point correlator of bi\u03b35q currents is em-\nployed. More details on the numerical results and their\nuncertainties can be found in the most recent LCSR anal-\nysis by Khodjamirian, Mannel, O\ufb00en, and Wang (2011),\npredicting f B\u03c0\n+ (q2) at 0 \u2264q2 < 12 GeV2, in particu-\nlar, f B\u03c0\n+ (0) = 0.28 \u00b1 0.03. Extrapolation to larger q2 re-\nveals a reasonable agreement with the lattice QCD re-\nsults (see Figure 17.1.12). The most convenient quantity\nfor the |Vub| determination is the integrated decay rate\n\u2206\u03b6 de\ufb01ned in Eq. (17.1.53); the most recent LCSR re-\nsult from Khodjamirian, Mannel, O\ufb00en, and Wang (2011)\nis given in Table 17.1.13. The estimated error corresponds\nto the quadratic sum of the uncertainties due to variations\nof the input parameters in LCSR. The largest individual\nerrors originate from the uncertainties of the MS quark\nmasses (mu,d and mb) and of the shape parameters in the\npion twist-2 DA, as well as from the renormalization scale\nuncertainty. There is still room for improvement of the\nOPE in the future, e.g., if one calculates the O(\u03b12\nS) and\ntwist-5, 6 corrections and gains a better control over the\npion DA\u2019s. On the other hand, the systematic error due to\nthe quark-hadron duality approximation cannot be com-\npletely eliminated from the LCSR calculation. Hence, with\nthis method it seems not feasible to reach a precision at a\nfew percent level foreseeable with the future improvements\nof the lattice QCD calculations.\n\n205\n\u009f \u009f \u009f \u009f \u009f\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\n\u00f2\nf +\nB \u00ae \u03a0 Hq2L\n0\n5\n10\n15\n20\n25\n0\n2\n4\n6\n8\n10\nq2 HGeV2L\nFigure 17.1.12. The vector form factor f B\u03c0\n+ (q2) (in arbi-\ntrary units) calculated from LCSR (Khodjamirian, Mannel, Of-\nfen, and Wang, 2011) and \ufb01tted to the BCL parameterization\nfrom Bourrely, Caprini, and Lellouch (2009) (solid line) with\nuncertainties (dashed lines), compared to the LQCD results by\nHPQCD (Dalgic et al., 2006) (squares) and by FNAL/MILC\n(Bailey et al., 2009) (triangles with error bars).\n17.1.4.2 Measurements of Branching Fractions and q2\nDistributions\nThe semileptonic decay B \u2192\u03c0\u2113\u03bd has been studied with\ndi\ufb00erent experimental approaches at the B Factories. The\ngoal is a precise measurement of the branching fraction\nand the spectrum of the squared momentum transfer, q2,\nto allow for a determination of the q2 dependence of the\nB \u2192\u03c0 form factor. The main experimental challenge is\nthe reduction of the much more abundant background\nfrom B \u2192Xc\u2113\u03bd decays, where Xc is any hadronic \ufb01nal\nstate with a charm quark. It is also di\ufb03cult to separate\nB \u2192\u03c0\u2113\u03bd decays from the other B \u2192Xu\u2113\u03bd decays, where\nXu is a charmless hadronic \ufb01nal state, due to very sim-\nilar decay kinematics. The B \u2192\u03c0\u2113\u03bd analyses are based\non event samples with a tagged B meson or on untagged\nevent samples. In the tagged analyses, one of the two B\nmesons in the BB event is either fully reconstructed in a\nhadronic decay mode or partially reconstructed in a semi-\nleptonic decay mode. While the tagged analyses provide a\nvery clean environment, they are statistically limited for\nthe B Factory data samples. At present, untagged analy-\nses, which were \ufb01rst performed by the CLEO collaboration\n(Athar et al., 2003), still provide the most precise results\nfor B \u2192\u03c0\u2113\u03bd.\nIn untagged analyses, the four-momentum of the un-\ndetected neutrino is inferred from the missing energy and\nmomentum in the whole event. The reconstructed neu-\ntrino is combined with a charged lepton (\u2113= e, \u00b5) and a\npion to form a B \u2192\u03c0\u2113\u03bd candidate. The dominant back-\nground at low q2 is due to e+e\u2212\u2192qq (q = u, d, s, c)\ncontinuum events, where the charged lepton originates\nfrom a semileptonic decay of a produced hadron (mostly\nfrom e+e\u2212\u2192cc events) or the misidenti\ufb01cation of a\ncharged hadron as a lepton. Continuum events produce\njet-like event topologies and can thus be e\ufb03ciently sep-\narated from the more isotropic BB events with selection\ncriteria on event shape variables (e.g. R2, L2, cos \u2206\u03b8thrust,\nsee Chapter 9). The overall largest background comes from\nB \u2192Xc\u2113\u03bd decays. It is reduced by selection criteria on\nvariables that are related to the neutrino reconstruction,\ne.g. the missing mass squared in the event or the polar an-\ngle of the missing momentum vector, or on kinematic vari-\nables, e.g. the helicity angle of the lepton. These variables\nalso help to partially suppress the B \u2192Xu\u2113\u03bd background,\nwhich has a large uncertainty and limits the measurement\nat high q2.\nThree untagged analyses have been performed by the\nBABAR (del Amo Sanchez, 2011d,n) and Belle collabo-\nrations (Ha, 2011). The background suppression based\non event shape, neutrino reconstruction and kinematical\nvariables is optimized as a function of q2 to allow for a\nprecise measurement over the full q2 range. While the\nBelle (Ha, 2011) and one of the BABAR (del Amo San-\nchez, 2011d) analyses use one-dimensional selection cri-\nteria, the other BABAR measurement (del Amo Sanchez,\n2011n) makes use of neural-network discriminators, which\nhave been trained individually for each background class\nand q2 interval, yielding an improved background sup-\npression. In contrast to the other two analyses that focus\non B0 \u2192\u03c0\u2212\u2113+\u03bd decays, this analysis includes a simul-\ntaneous measurement of B0 \u2192\u03c0\u2212\u2113+\u03bd, B+ \u2192\u03c00\u2113+\u03bd,\nB0 \u2192\u03c1\u2212\u2113+\u03bd and B+ \u2192\u03c10\u2113+\u03bd decays. By measuring\nthese four decay modes, the uncertainties due to cross\nfeed between these modes and various background con-\ntributions are reduced. In all three analyses the signal is\nextracted from a \ufb01t to the two-dimensional \u2206E-mES dis-\ntribution. The \ufb01t is performed in several intervals of q2 to\nmeasure the shape of the q2 spectrum. The Belle analysis\nuses 13 q2 intervals (Ha, 2011), the BABAR analyses 6 (del\nAmo Sanchez, 2011n) or 12 (del Amo Sanchez, 2011d) q2\nintervals. The shapes of the signal and background con-\ntributions are taken from simulation whereas the yields\nfor the signal and the dominant background contributions\nare obtained from the \ufb01t. Figures 17.1.3 and 17.1.13 show\nthe mES and \u2206E projections from BABAR and Belle for a\nspeci\ufb01c q2 range, indicating the signal above the sum of\nbackgrounds from several sources.\nA number of tagged measurements have been per-\nformed by BABAR (Aubert, 2006r, 2008y) and Belle\n(Adachi, 2008a; Hokuue, 2007). They have led to a simpler\nand more precise reconstruction of the neutrino momen-\ntum and have low backgrounds and a uniform acceptance\nin q2. This is achieved at the expense of much smaller\nsignal samples which limit the statistical precision of the\nform-factor measurement. The semileptonic-tag measure-\nments from BABAR and Belle use B \u2192D(\u2217)\u2113\u03bd decays to\npartially reconstruct one of the two B mesons. They have\na signal-to-background ratio of \u223c2 and yield \u223c0.5 signal\ndecays per fb\u22121. The signal is extracted from the distri-\nbution of the variable cos2 \u03c6B, where \u03c6B is the angle be-\ntween the direction of either B meson and the plane con-\ntaining the momentum vectors of the tag-side D\u2217\u2113system\n\n206\nE (GeV)\n6\n-1\n-0.5\n0\n0.5\n1\nCandidates\n0\n100\n200\n300\n400\nE (GeV)\n6\n-1\n-0.5\n0\n0.5\n1\nCandidates\n0\n100\n200\n300\n400\n (GeV)\nES\nm\n5.1\n5.15\n5.2\n5.25\nCandidates\n0\n100\n200\n300\n400\n (GeV)\nES\nm\n5.1\n5.15\n5.2\n5.25\nCandidates\n0\n100\n200\n300\n400\n2\n < 8 GeV\n2\n4 < q\nData (on-resonance)\nSignal\nCombinatorial signal\ni\n l \nl\n \nA\nB \n incl.\ni\n l \nu\n X\nA\nB \ni\n D* l \nA\nB \ni\n) l \n/\n (n\n)*\n(\n D/D\nA\nB \nOther BB\nqq\nFigure 17.1.13. mES and \u2206E distributions for the q2 interval 4 < q2 < 8 GeV2 from the BABAR untagged B \u2192\u03c0\u2113\u03bd measurement\n(del Amo Sanchez, 2011n).\nand the signal-side \u03c0\u2113system (Aubert, 2008y; Hokuue,\n2007). The hadronic-tag measurements yield fewer signal\nevents, \u223c0.1 signal decays per fb\u22121, but reach signal-to-\nbackground ratios of up to \u223c10. The signal is extracted\nfrom the missing mass squared distribution, where the sig-\nnal is expected to be located in a narrow peak near zero,\nas shown in Figure 17.1.14.\nTable 17.1.14 summarizes the signal yields, approxi-\nmate signal-to-background ratios and integrated luminosi-\nties of the various measurements.\nThe leading experimental systematic uncertainties are\nassociated with the reconstruction of charged and neutral\nparticles, which a\ufb00ect the reconstruction of the missing\nmomentum, with backgrounds from continuum events at\nlow q2 and from B \u2192Xu\u2113\u03bd decays at high q2. Due to\nthe feed-down from B \u2192\u03c1\u2113\u03bd decays, the uncertainties\non the branching fraction and form factors for this de-\ncay mode also contribute to the systematic uncertainty.\nFor the tagged measurements, the systematic uncertain-\nties are about a factor of two smaller. They contribute to\nthe knowledge of the total branching fraction, but their\nstatistical precision is not yet su\ufb03cient to provide signi\ufb01-\ncant information on the shape of the q2 spectrum.\nTable 17.1.15 summarizes all B \u2192\u03c0\u2113\u03bd branching frac-\ntion measurements. Shown are the total branching fraction\nas well as the partial branching fractions for q2 < 12 GeV2\nand q2 > 16 GeV2. Overall the individual measurements\nare in a good agreement, though for the tagged measure-\nments the partial branching fractions at intermediate q2\nare somewhat smaller. A combination of all untagged B \u2192\n\u03c0\u2113\u03bd measurements from the B Factories results in an aver-\nage total branching fraction of (1.44\u00b10.03\u00b10.05)\u00d710\u22124,\nwith a precision of 3 \u22124% (2% statistical and 3% system-\natic).\nFigure 17.1.15 shows a \ufb01t of the z-expansion intro-\nduced in Section 17.1.4.1 to the measured q2 spectra\nfrom all untagged B \u2192\u03c0\u2113\u03bd analyses, using the BCL pa-\nrameterization with three parameters (b0, b1, b2). The re-\nsults are summarized in Table 17.1.16. The \u03c72 probabil-\nity of this \ufb01t is 1.1%. An inclusion of the tagged mea-\nsurements would decrease the probability to 0.02%. This\nlow probability is mostly due to the lower branching frac-\ntions from the tagged measurements. The BABAR measure-\nment in 12 q2 bins prefers a larger (negative) quadratic\nterm and a smaller linear term in the z expansion com-\npared to the other two untagged analyses. The \ufb01tted func-\ntion also determines the product f+(0)|Vub|, which for a\ngiven value of |Vub| can be compared with LCSR predic-\ntions of f+(0), the B \u2192\u03c0 form factor at q2 = 0. The\nlargest value of f+(0)|Vub| from the individual measure-\nments comes from the untagged BABAR measurement in\n6 q2 bins. For the combination of all untagged measure-\nments, a value of f+(0)|Vub| = (0.940 \u00b1 0.029) \u00d7 10\u22123\nis obtained. Combining this value with the |Vub| result\nobtained using the LCSR calculation (see Table 17.1.17)\ngives f+(0) = (0.27 \u00b1 0.03), in good agreement with the\nLCSR result, f+(0) = (0.28 \u00b1 0.02). A comparison of the\n\ufb01tted BCL parameterization with the shapes predicted\nby form-factor calculations from LQCD, LCSR or quark\nmodels like ISGW2. is presented in Figure 17.1.15 (right).\nIt agrees best with the recent LCSR calculation (Khod-\njamirian, Mannel, O\ufb00en, and Wang, 2011) and deviates\nsigni\ufb01cantly from the ISGW2 quark model prediction.\n17.1.4.3 Determination of |Vub|\nTwo di\ufb00erent methods have been used to determine |Vub|\nfrom the measured B \u2192\u03c0\u2113\u03bd di\ufb00erential decay rates.\nThe more traditional approach relates the measured par-\ntial branching fractions, \u2206B(q2\nmin, q2\nmax), with the nor-\nmalized partial decay rate, \u2206\u03b6(q2\nmin, q2\nmax), predicted by\nform-factor calculations integrated over a certain q2 range.\nFor LQCD calculations (Bailey et al., 2009; Dalgic et al.,\n2006), the range q2 > 16 GeV2 is used, and for the recent\nLCSR (Khodjamirian, Mannel, O\ufb00en, and Wang, 2011)\ncalculation the range is q2 < 12 GeV2 . |Vub| is obtained\nfrom the relation\n|Vub| =\ns\n\u2206B(q2\nmin, q2max)\n\u03c40\u2206\u03b6(q2\nmin, q2max),\n(17.1.58)\nwhere \u03c40 = (1.519 \u00b1 0.007) ps is the B0 lifetime (Be-\nringer et al., 2012). Table 17.1.17 shows the values of\n\u2206B(q2\nmin, q2\nmax), \u2206\u03b6(q2\nmin, q2\nmax) and the |Vub| results for\n\n207\n)\n2\nMissing mass squared (GeV\n-1\n0\n1\n2\n3\n4\n5\n2\nEvents / 0.2 GeV\n0\n5\n10\n15\n20\n25\n30\n35\n40\n)\n2\nMissing mass squared (GeV\n-1\n0\n1\n2\n3\n4\n5\n2\nEvents / 0.2 GeV\n0\n5\n10\n15\n20\n25\n30\n35\n40\nData\n+\n/\n crossfeed\ni\nul\nOther backgrounds\n)\n2\nMissing mass squared (GeV\n-1\n0\n1\n2\n3\n4\n5\n2\nEvents / 0.2 GeV\n0\n10\n20\n30\n40\n50\n)\n2\nMissing mass squared (GeV\n-1\n0\n1\n2\n3\n4\n5\n2\nEvents / 0.2 GeV\n0\n10\n20\n30\n40\n50\nData\n0\n/\n crossfeed\ni\nul\nOther backgrounds\nB\nq\n2\ncos\n0\n2\n4\n6\n8\n10 12 14 16 18 20\nevents / 0.5\n0\n20\n40\n60\n80\n100\nB\nq\n2\ncos\n0\n2\n4\n6\n8\n10 12 14 16 18 20\nevents / 0.5\n0\n20\n40\n60\n80\n100\n \nFigure 17.1.14. Missing mass squared distributions from the Belle tagged B0 \u2192\u03c0\u2212\u2113+\u03bd (left) and B+ \u2192\u03c00\u2113+\u03bd (center)\nmeasurements (Adachi, 2008a) and cos2 \u03c6B distribution from the BABAR semileptonic-tag B0 \u2192\u03c0\u2212\u2113+\u03bd measurement (Aubert,\n2008y) (right). In the right \ufb01gure, the solid line represents the signal and the dotted and dashed lines represent the backgrounds\nwith combinatorial and with correctly reconstructed D mesons in the semileptonic tag, respectively.\nTable 17.1.14. Integrated luminosity, signal yield and approximate signal-to-background ratio, S/B, for the B \u2192\u03c0\u2113\u03bd mea-\nsurements.\nMeasurement\nInt. lumi. (fb\u22121)\nNsig(B0 \u2192\u03c0\u2212\u2113+\u03bd)\nNsig(B+ \u2192\u03c00\u2113+\u03bd)\nS/B\nBABAR untagged (6 bins) (del Amo Sanchez, 2011n)\n349\n7181\n3446\n\u223c0.2\nBABAR untagged (12 bins) (del Amo Sanchez, 2011d)\n423\n11778\n\u2013\n\u223c0.1\nBelle untagged (Ha, 2011)\n605\n21486\n\u2013\n\u223c0.1\nBABAR semileptonic tag (Aubert, 2008y)\n348\n150\n134\n\u223c2\nBelle semileptonic tag (Hokuue, 2007)\n253\n156\n69\n\u223c2\nBABAR hadronic tag (Aubert, 2006r)\n211\n31\n26\n\u223c10\nBelle hadronic tag (Adachi, 2008a)\n605\n59\n49\n\u223c10\nTable 17.1.15. Branching fractions for B0 \u2192\u03c0\u2212\u2113+\u03bd. The two untagged BABAR measurements are assumed to be statistically\nindependent since the selected data samples have less than 1% of the events in common (del Amo Sanchez, 2011d).\nMeasurement\nBtot (10\u22124)\n\u2206B(q2 < 12 GeV2) (10\u22124)\n\u2206B(q2 > 16 GeV2) (10\u22124)\nBABAR untagged (6 bins)\n1.41 \u00b1 0.05 \u00b1 0.07\n0.88 \u00b1 0.03 \u00b1 0.05\n0.32 \u00b1 0.02 \u00b1 0.02\nBABAR untagged (12 bins)\n1.42 \u00b1 0.05 \u00b1 0.07\n0.84 \u00b1 0.03 \u00b1 0.04\n0.33 \u00b1 0.02 \u00b1 0.03\nBelle untagged\n1.49 \u00b1 0.04 \u00b1 0.07\n0.83 \u00b1 0.02 \u00b1 0.04\n0.40 \u00b1 0.02 \u00b1 0.02\nAverage untagged\n1.44 \u00b1 0.03 \u00b1 0.05\n0.84 \u00b1 0.02 \u00b1 0.03\n0.36 \u00b1 0.01 \u00b1 0.02\nAverage tagged\n1.31 \u00b1 0.08 \u00b1 0.06\n0.67 \u00b1 0.06 \u00b1 0.03\n0.37 \u00b1 0.04 \u00b1 0.02\nAverage\n1.42 \u00b1 0.03 \u00b1 0.05\n0.81 \u00b1 0.02 \u00b1 0.03\n0.36 \u00b1 0.01 \u00b1 0.02\nTable 17.1.16. Results of the \ufb01ts of the BCL parameterization with 3 parameters to the measured \u2206B/\u2206q2 distribution.\nMeasurement\n\u03c72/ndf\nProb(\u03c72/ndf)\nFit parameters\nf+(0)|Vub| (10\u22123)\nBABAR (6 bins)\n6.0/3\n11.2%\nb1/b0 = \u22120.90 \u00b1 0.45\n1.090 \u00b1 0.055\nb2/b0 = +0.47 \u00b1 1.49\nBABAR (12 bins)\n4.1/9\n90.5%\nb1/b0 = +0.09 \u00b1 0.53\n0.863 \u00b1 0.044\nb2/b0 = \u22124.65 \u00b1 1.55\nBelle\n11.9/10\n29.4%\nb1/b0 = \u22121.31 \u00b1 0.27\n0.914 \u00b1 0.040\nb2/b0 = \u22120.79 \u00b1 0.91\nBABAR +Belle\n48.0/28\n1.1%\nb1/b0 = \u22120.75 \u00b1 0.22\n0.940 \u00b1 0.029\nb2/b0 = \u22121.84 \u00b1 0.69\n\n208\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n\u2206\nB/\n\u2206\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n\u00d7\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n\u2206\nB/\n\u2206\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n\u00d7\nBelle\nBaBar (12 bins)\nBaBar (6 bins)\nBCL fit (3 par.)\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n!\nB/\n!\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n!\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n!\nB/\n!\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n!\nLCSR\nHPQCD\nISGW2\nBGL (3 par.)\n!\"#\nFigure 17.1.15. Left: Fit of the BCL parameterization with 3 parameters to the measured B \u2192\u03c0\u2113\u03bd q2 distribution. The\nuncertainty of the \ufb01t is shown as shaded error band. Right: Comparison of the \ufb01t result with form-factor predictions from\nHPQCD (Dalgic et al., 2006), LCSR (Khodjamirian, Mannel, O\ufb00en, and Wang, 2011) and ISGW2 (Scora and Isgur, 1995). The\nextrapolations of the predictions to the full q2 range are shown as dashed lines.\nthe three untagged B \u2192\u03c0\u2113\u03bd measurements and the av-\nerages of the untagged and tagged measurements, and for\nthree form-factor calculations. The uncertainty on |Vub| is\ndominated by the theoretical form-factor uncertainty.\nThe more recent method is based on a simultaneous\n\ufb01t to the measured q2 spectra and the LQCD predictions.\nThe BCL parameterization is used as parameterization\nfor f+(q2) over the whole q2 range to minimize the model\ndependence of the form factor. This method makes use\nof the full shape information from data and the shape\nand normalization from theory, which results in a reduced\nuncertainty on |Vub|.\nThe combined \ufb01t to the FNAL/MILC lattice calcu-\nlations and the data from the three untagged measure-\nments yields |Vub| = (3.23 \u00b1 0.30) \u00d7 10\u22123. Figure 17.1.16\nand Table 17.1.17 show the results of the \ufb01t. Only four\nof the twelve FNAL/MILC points have been included in\nthe \ufb01t, avoiding LQCD points with a correlation higher\nthan 80%. This reduction of the theoretical input does\nnot change the |Vub| result but leads to a better agree-\nment of the \ufb01tted curve with the lattice points. The \ufb01t\nresults for the parameters in the BCL parameterization\nare b1/b0 = \u22120.82 \u00b1 0.20 and b2/b0 = \u22121.63 \u00b1 0.62, and\na value of f+(0)|Vub| = 0.945 \u00b1 0.028 is obtained. The \u03c72\nprobability of the \ufb01t is 2.2% (\u03c72/ndf = 58.9/31). The |Vub|\nvalues obtained from \ufb01ts to the individual untagged mea-\nsurements agree with each other within about one stan-\ndard deviation. The total uncertainty of |Vub| is about 9%.\nThe contributions to this uncertainty have been estimated\nto be 3% from the branching fraction measurements, 4%\nfrom the shapes of the q2 spectra determined from data,\nand 8% from the form-factor normalization obtained from\ntheory. Using the HPQCD lattice calculation gives simi-\nlar \ufb01t results. However, at present no information on the\ncorrelation of the HPQCD points is available and there-\nfore only one point can be used in the \ufb01t to determine the\nnormalization of the decay rate, which results in larger\nuncertainties.\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n\u2206\nB/\n\u2206\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n\u00d7\n)\n2\n (GeV\n2\nq\n0\n5\n10\n15\n20\n25\n)\n-2\n (GeV\n2\n q\n\u2206\nB/\n\u2206\n0\n2\n4\n6\n8\n10\n12\n-6\n10\n\u00d7\nBelle\nBaBar (12 bins)\nBaBar (6 bins)\nBCL fit (3+1 par.)\nFNAL/MILC\nFigure 17.1.16. Simultaneous \ufb01t of the BCL parameteriza-\ntion to the measured q2 spectra and to four of the twelve points\nof the FNAL/MILC calculation (magenta, closed triangles).\nThe FNAL/MILC prediction has been rescaled to the data\naccording to the |Vub| value obtained in the \ufb01t.\nAs a \ufb01nal result for |Vub| from B \u2192\u03c0\u2113\u03bd decays we\nquote the value obtained from the simultaneous \ufb01t to\nthe three untagged measurements from BABAR and Belle,\ncombined with the FNAL/MILC calculation:\n|Vub|excl = (3.23 \u00b1 0.30) \u00d7 10\u22123.\n(17.1.59)\nFuture improvements for |Vub| will rely on progress in\nform-factor calculations based on LQCD or LCSR and\n\n209\nTable 17.1.17. |Vub| derived from B \u2192\u03c0\u2113\u03bd decays for various q2 regions and form-factor calculations: LCSR (Khodjamirian,\nMannel, O\ufb00en, and Wang, 2011), HPQCD (Dalgic et al., 2006), FNAL/MILC (Bailey et al., 2009). The quoted errors on\n|Vub| are due to experimental uncertainties and theoretical uncertainties on \u2206\u03b6. The last column shows the |Vub| results of the\nsimultaneous \ufb01ts to data and the FNAL/MILC prediction. Here the stated error represents the combined experimental and\ntheoretical uncertainty.\nLCSR\nHPQCD\nFNAL/MILC\nFNAL/MILC \ufb01t\n\u2206\u03b6 (ps\u22121)\n4.59+1.00\n\u22120.85\n2.02\u00b10.55\n2.21+0.47\n\u22120.42\n2.21+0.47\n\u22120.42\nq2 range ( GeV2)\n0 \u221212\n16 \u221226.4\n16 \u221226.4\n16 \u221226.4\nExperiment\n|Vub| (10\u22123)\nBABAR (6 bins)\n3.54 \u00b1 0.12+0.38\n\u22120.33\n3.22 \u00b1 0.15+0.55\n\u22120.37\n3.08 \u00b1 0.14+0.34\n\u22120.28\n2.98 \u00b1 0.31\nBABAR (12 bins)\n3.46 \u00b1 0.10+0.37\n\u22120.32\n3.26 \u00b1 0.19+0.56\n\u22120.37\n3.12 \u00b1 0.18+0.35\n\u22120.29\n3.22 \u00b1 0.31\nBelle\n3.44 \u00b1 0.10+0.37\n\u22120.32\n3.60 \u00b1 0.13+0.61\n\u22120.41\n3.44 \u00b1 0.13+0.38\n\u22120.32\n3.52 \u00b1 0.34\nBABAR +Belle\n3.47 \u00b1 0.06+0.37\n\u22120.32\n3.43 \u00b1 0.09+0.59\n\u22120.39\n3.27 \u00b1 0.09+0.36\n\u22120.30\n3.23 \u00b1 0.30\nTagged\n3.10 \u00b1 0.16+0.33\n\u22120.29\n3.47 \u00b1 0.23+0.60\n\u22120.39\n3.32 \u00b1 0.22+0.37\n\u22120.31\n3.33 \u00b1 0.39\non more precise experimental determinations of the q2\nspectrum in B \u2192\u03c0\u2113\u03bd decays. In particular an improved\nprecision in the high q2 region, where LQCD predictions\nexist, would be important. This will require a better un-\nderstanding of the composition and dynamics of the B \u2192\nXu\u2113\u03bd background and signi\ufb01cantly larger data samples for\ntagged event samples expected at the next generation of\nB Factories.\n17.1.5 Inclusive Cabibbo-suppressed B decays\n17.1.5.1 Theoretical Overview\nThe theoretical description of inclusive B \u2192Xu\u2113\u03bd de-\ncays rests on the same basic principles as that of inclusive\nB \u2192Xc\u2113\u03bd decays described in Section 17.1.3.1. Due to\nthe inclusive nature of the process, the only sensitivity\nto long-distance dynamics comes from the B meson in the\ninitial state. The total B \u2192Xu\u2113\u03bd rate is given by an OPE\nin terms of local operators, which has a similar structure\nas that for the B \u2192Xc\u2113\u03bd rate, with non-perturbative\ncorrections \ufb01rst appearing at O(1/m2\nb).\nIn practice, the experimental sensitivity to B \u2192Xu\u2113\u03bd\nand |Vub| is highest in the region of phase space that is less\nimpacted by the dominant B \u2192Xc\u2113\u03bd background, namely\nthe region where the hadronic Xu system has invariant\nmass mX below the mass of the lightest charm meson,\nmX \u2272mD. In this phase-space region non-perturbative\ncorrections are kinematically enhanced, and as a result\nthe non-perturbative dynamics of the decaying b quark\ninside the B meson becomes an O(1) e\ufb00ect.\nIn addition to the lepton energy, E\u2113, convenient vari-\nables to describe the decay kinematics are the hadronic\nvariables\np+\nX = EX \u2212|pX| ,\np\u2212\nX = EX + |pX| ,\n(17.1.60)\nwhere EX and pX are the energy and momentum of the\nhadronic system in the B-meson rest frame. In terms of\nthese variables, the total hadronic and leptonic invariant\nmasses are given by\nm2\nX = p+\nXp\u2212\nX ,\nq2 = (mB \u2212p+\nX)(mB \u2212p\u2212\nX) .\n(17.1.61)\nThe fully di\ufb00erential decay rate is given by\nd3\u0393\ndp+\nX dp\u2212\nX dE\u2113\n= G2\nF |Vub|2\n192\u03c03\nZ\ndk C(E\u2113, p\u2212\nX, p+\nX, k) F(k)\n+ O\n\u0010\u039bQCD\nmb\n\u0011\n.\n(17.1.62)\nThe coe\ufb03cient C(E\u2113, p\u2212\nX, p+\nX, k) describes the quark de-\ncay b \u2192u\u2113\u03bd and can be computed in QCD perturbation\ntheory. The \u201cshape-function\u201d F(k) is a non-perturbative\nfunction. It describes the momentum distribution of the b\nquark in the B meson (Bigi, Shifman, Uraltsev, and Vain-\nshtein, 1994; Neubert, 1994a). For p+\nX \u223ck \u223c\u039bQCD, which\nincludes a large portion of the small mX region, the full\nnon-perturbative shape of F(k) is necessary to obtain an\naccurate description of the di\ufb00erential decay rate. On the\nother hand, in the limit p+\nX \u226bk \u223c\u039bQCD, only the \ufb01rst\nfew moments of F(k) are needed. Typically, the experi-\nmental measurements can lie anywhere between these two\nkinematic regimes.\nThere are several sources of uncertainties in the the-\noretical predictions that must be considered. First, there\nare perturbative uncertainties in the calculation of C due\nto unknown higher-order corrections. Second, there are\nparametric uncertainties due to the imprecise knowledge\nof inputs, in particular the b-quark mass and F(k). The to-\ntal decay rate scales like m5\nb, while partial rates restricted\nto the small mX region typically exhibit an even stronger\ndependence on mb. The \ufb01rst few moments of F(k) are de-\ntermined by mb and the expectation values of local oper-\nators that are constrained by \ufb01ts to B \u2192Xc\u2113\u03bd moments.\nA substantial part of the mb dependence enters indirectly\nvia the \ufb01rst moment of F(k). Depending on the kinematic\ncuts, the shape of F(k) (beyond what is encoded in its \ufb01rst\nfew moments) can also have a signi\ufb01cant in\ufb02uence on the\n\n210\npredictions. An important consistency check for the over-\nall shape of F(k) is to give a reasonable description of the\nmeasured shape of the photon-energy spectrum in inclu-\nsive B \u2192Xs\u03b3 decays (see Section 17.9), which at leading\norder in 1/mb is given in terms of the same function F(k)\nvia an expression analogous to Eq. (17.1.62).\nIn addition to the leading shape function F(k), sev-\neral additional shape functions appear at O(\u039bQCD/mb)\n(Bauer, Luke, and Mannel, 2003). Apart from their \ufb01rst\nfew moments, very little is known about the form of these\nsubleading shape functions. They thus introduce an uncer-\ntainty in the theoretical predictions that is hard to quan-\ntify in a systematic fashion. An even larger number of un-\nknown shape functions appears at O(\u03b1S\u039bQCD/mb) (Lee\nand Stewart, 2005).\nWeak annihilation contributions could have a large im-\npact at large q2 and might be another source of theoret-\nical uncertainties. However, recent analyses (Bigi, Man-\nnel, Turczyk, and Uraltsev, 2010; Gambino and Kamenik,\n2010; Ligeti, Luke, and Manohar, 2010) have used CLEO-\nc data to constrain contributions from weak annihilation,\nresulting in a rather small impact. The corresponding un-\ncertainty is below 2% for the total rate, translating into an\nuncertainty of less than 1% on |Vub| for the most inclusive\nanalyses.\nFor the determination of |Vub| theoretical predictions\nby di\ufb00erent groups are in use. A more detailed summary\nand comparison can be found elsewhere (Antonelli et al.,\n2010a). At their core, the di\ufb00erent calculations are all\nbased on Eq. (17.1.62), but they di\ufb00er in the treatment of\nthe perturbative and non-perturbative contributions.\nThe BLNP approach (Bosch, Lange, Neubert, and Paz,\n2004; Lange, Neubert, and Paz, 2005) preferentially treats\nthe kinematic region p+\nX \u226ap\u2212\nX where the p+\nX and p\u2212\nX de-\npendences of C factorize. This allows for the resummation\nof Sudakov double logarithms of p+\nX/p\u2212\nX and p+\nX/mB to\nNNLL. They also include the full O(\u03b1S) corrections, for\nwhich the perturbative expansions are performed using\nthe so-called shape-function scheme for mb, and a sub-\nset of the perturbative corrections in C are absorbed into\nF(k). The subleading shape functions are separately mod-\neled and included in the predictions.\nThe GGOU approach (Gambino, Giordano, Ossola,\nand Uraltsev, 2007) treats the p+\nX \u226ap\u2212\nX and p+\nX \u223cp\u2212\nX re-\ngions on the same footing. The coe\ufb03cient C is computed\nat \ufb01xed order to O(\u03b1S) and O(\u03b12\nS\u03b20) (Gambino, Gardi,\nand Ridol\ufb01, 2006), where the perturbative expansion is\nperformed using the kinetic scheme for mb. In this case no\nresummation e\ufb00ects at small p+\nX are included. The e\ufb00ect\nof resummation as well as all contributions from sublead-\ning shape functions are absorbed into F(k). This results in\nthree non-universal distribution functions Fi(k, q2), which\nhave subleading dependence on q2.\nIn the dressed-gluon exponentiation (DGE) approach\n(Andersen and Gardi, 2006; Gardi, 2008) the perturba-\ntive expansion includes the NNLL resummation in mo-\nment space as well as the full O(\u03b1S) and O(\u03b12\nS\u03b20) correc-\ntions. It also incorporates an internal resummation of run-\nning coupling corrections in the Sudakov exponent. This\napproach e\ufb00ectively corresponds to a perturbative model\nfor the leading shape function, with non-perturbative cor-\nrections only included via its moments. Therefore, it tends\nto be more predictive than the other approaches, resulting\nin smaller theoretical uncertainties within the framework.\nHowever, the intrinsic uncertainties due the assumptions\ninherent in the framework are not estimated. Another ap-\nproach based on Sudakov resummation has been proposed\nin (Aglietti, Di Lodovico, Ferrera, and Ricciardi, 2009). It\nemploys the so-called analytic coupling in the infrared.\nThe full O(\u03b12\nS) corrections to the b \u2192u\u2113\u03bd spectrum\nare only known in the limit p+\nX \u226ap\u2212\nX (Greub, Neubert,\nand Pecjak, 2010), and are currently not included in the\ndetermination of |Vub|. In case of BLNP, their e\ufb00ect turns\nout to be much larger than expected from the pertur-\nbative uncertainties at O(\u03b1S), resulting in an increase of\n|Vub| by 8%. On the other hand, the O(\u03b12\nS\u03b20) terms of-\nten dominate the O(\u03b12\nS) corrections, and their inclusion\nin the GGOU and DGE approaches does not lead to sim-\nilarly large corrections. A resolution of this apparent dis-\ncrepancy will probably have to await a calculation of the\ncomplete O(\u03b12\nS) corrections.\nAll the above approaches choose speci\ufb01c model pa-\nrameterizations of the shape function(s), and it is un-\nclear to what extent the model variations used to estimate\nthe shape function uncertainties re\ufb02ect the actual limited\nknowledge of their form, particularly at subleading order\nin 1/mb. Also, the theoretical uncertainties do not include\nexplicit estimates of the possible size of O(\u03b1S\u039bQCD/mb)\ncorrections.\nGiven all the above, it is possible that the theoreti-\ncal uncertainties currently quoted for |Vub| might be un-\nderestimated. On the other hand, the di\ufb00erent theoreti-\ncal frameworks yield values of |Vub| that are compatible\nwithin uncertainties with each other and across a variety\nof di\ufb00erent experimental cuts.\nImposing an additional lower cut on q2 restricts the de-\ncay kinematics to the part of the small mX region where\np+\nX \u223cp\u2212\nX. Formally, this allows the application of the OPE\nin terms of local operators (Bauer, Ligeti, and Luke, 2001).\nIn practice, the resulting OPE still has rather large 1/m2\nb\nand higher order corrections, and some residual shape-\nfunction e\ufb00ects must be included. Nevertheless, this ap-\nproach provides an important cross check on the extracted\nvalue of |Vub|.\nIn some recent experimental analyses the phase-space\nrestrictions have been relaxed and up to 90% of the to-\ntal inclusive B \u2192Xu\u2113\u03bd rate is measured. In principle,\nthis makes it possible to use a simpler theoretical descrip-\ntion based on the local OPE only. Consequently, the main\ntheoretical uncertainties are due to mb and higher-order\nperturbative corrections. In practice, these analyses still\nmake explicit use of the theoretical description of the sig-\nnal shape in the shape-function region to determine the ex-\nperimental reconstruction e\ufb03ciencies, and the associated\ntheoretical uncertainties contribute via the experimental\nsystematic uncertainties. Nevertheless, the fact that the\nresulting values of |Vub| are consistent with the other anal-\n\n211\nyses enhances the con\ufb01dence in our current understanding\nof inclusive B \u2192Xu\u2113\u03bd decays.\nRecently, an improved treatment of the shape func-\ntion has been developed (Ligeti, Stewart, and Tackmann,\n2008), which combines the advantages of the BLNP and\nGGOU approaches and uses appropriate basis functions\nto approximate the shape function. It is expected that\nthis procedure will allow for a combined global \ufb01t to all\navailable inclusive B \u2192Xs\u03b3 and B \u2192Xu\u2113\u03bd measure-\nments (Bernlochner et al., 2011). As in the determination\nof |Vcb| from inclusive B \u2192Xc\u2113\u03bd decays, a global \ufb01t has\nthe advantage that the input parameters, such as F(k) and\nmb, are directly constrained by data and are determined\ntogether with |Vub|.\n17.1.5.2 Measurements of Partial Branching Fractions\nThe observation of charged leptons with momenta exceed-\ning the kinematic limit for B \u2192Xc\u2113\u03bd decays by the CLEO\nCollaboration (Bartelt et al., 1993) was the \ufb01rst evidence\nfor charmless semileptonic decays. Since then, a series of\nmeasurements near the kinematic limit have been per-\nformed (Bornheim et al., 2002; Limosani, 2005; Aubert,\n2006x); they di\ufb00er in the kinematic selection and the size\nof the data sample. At lower lepton momenta, the back-\nground from B \u2192Xc\u2113\u03bd increases sharply to more than\n10 times the signal and the dominant uncertainty arises\nfrom the subtraction of the sum of lepton spectra from\nexclusive B \u2192Xc\u2113\u03bd decays, for which the branching frac-\ntions and form factors are known to di\ufb00erent degrees. The\nsignal-to-background ratio can be substantially improved\nby combining the high energy lepton with a measurement\nof the missing neutrino in the event, but this can only\nbe achieved with a substantial reduction in the selection\ne\ufb03ciency (Aubert, 2005h).\nExperimenters simulate the charmless semileptonic\nB \u2192Xu\u2113\u03bd decays as a hybrid, i.e., a combination of\ntwo components: three-body decays involving a single low-\nmass charmless meson, \u03c0, \u03c1, \u03b7, \u03b7\u2032, or \u03c9, and decays to non-\nresonant multi-body hadronic \ufb01nal states. The three-body\ndecays make up about the 20% of the charmless semilep-\ntonic decay rate, and their simulation is based on OPE\ncalculations and form-factor measurements and measured\nbranching fractions (Beringer et al., 2012). The generated\nmass distribution and kinematics of multi-body hadronic\nstates Xu are based on the prescription by De Fazio and\nNeubert (De Fazio and Neubert, 1999). The fragmenta-\ntion of Xu into \ufb01nal state hadrons are simulated by using\nJetset (Sj\u00a8ostrand, 1994). The two components are com-\nbined so that the cumulative distributions of the hadronic\nmass, the momentum transfer squared, and the lepton mo-\nmentum reproduce OPE predictions. The generated dis-\ntributions are often reweighted to accommodate speci\ufb01c\nchoices of the parameters for the inclusive and exclusive\ndecays. The overall normalization is adjusted to reproduce\nthe measured inclusive charmless branching fraction (Be-\nringer et al., 2012).\nAn example of the extraction of the signal yield is il-\nlustrated in Figure 17.1.17 (Aubert, 2006x), showing the\n10 5\n(a)\n10\n10 4\n10 5\n(b)\n0\n5000\n1.1\n1.5\n1.9\n2.3\n2.7\n3.1\n3.5\n(c)\nElectron Momentum (GeV/c)\n Number of Electrons / (50 MeV/c)\nFigure 17.1.17. BABAR analysis of the electron momentum\nspectra in the \u03a5(4S) rest frame (Aubert, 2006x): (a) on-\nresonance data (open circles - blue), scaled o\ufb00-resonance data\n(solid circles - green); the solid line shows the result of the \ufb01t\nto the non-BB events using both on- and o\ufb00-resonance data;\n(b) on-resonance data after subtraction of the \ufb01tted non-BB\nbackground (triangles - blue) compared to simulated BB back-\nground (histogram) that is adjusted by a combined \ufb01t to the\non- and o\ufb00-resonance data; (c) on-resonance data after sub-\ntraction of all backgrounds (data point - red), compared to the\nsimulated B \u2192Xue\u03bd signal spectrum (histogram); the error\nbars indicate errors from the \ufb01t, which include the uncertain-\nties in the \ufb01tted yields for continuum and Xce\u03bd backgrounds.\nThe shaded area indicates the momentum interval for which\nthe on-resonance data are combined into a single bin for the\npurpose of reducing the sensitivity of the \ufb01t to the simulated\nshape of the signal spectrum in this region.\nobserved spectra of the highest momentum electron in\nevents recorded on and below the \u03a5(4S) resonance. The\ndata collected on the \u03a5(4S) resonance include contribu-\ntions from BB events and continuum events. The latter\nis subtracted using o\ufb00-resonance data, collected below the\nBB production threshold, and on-resonance data with lep-\nton momenta above 2.8 GeV, i.e., well above the endpoint\nfor semileptonic B decays. The principal challenge is the\nsubtraction of the electron spectrum from B-meson de-\ncays which is dominated by various B \u2192Xc\u2113\u03bd decays.\nHadronic B decays contribute mostly via hadron misiden-\nti\ufb01cation and secondary electrons from decays of D, J/\u03c8,\nand \u03c8(2S) mesons. The signal contribution is determined\nfrom a \u03c72 \ufb01t of the observed inclusive electron spectrum\nto the sum of Monte Carlo (MC) simulated signal and in-\ndividual background contributions. The relative normal-\nization factors for signal and background distributions are\nfree parameters of the \ufb01t.\n\n212\nIn this analysis, a potential bias of the \ufb01tted yield from\nthe assumed shape of the signal spectrum is reduced by\ncombining the on-resonance data for the interval from 2.1\nto 2.8 GeV in a single bin. The lower limit of this bin\nis chosen so as to retain the sensitivity to the steeply\nfalling BB background distributions, while containing a\nlarge fraction of the signal events in a region where the\nbackground is low.\nIn total, the selected sample includes 610 \u00d7 103 elec-\ntrons, from which roughly 6.5% have been extracted as\nthe signal yield in the momentum interval 2.0 \u22122.6 GeV.\nThis translates to a partial branching fraction of \u2206B(B \u2192\nXue\u03bd) = (0.572\u00b10.041\u00b10.051)\u00d710\u22123. Here the \ufb01rst error\nis statistical and the second is the total systematic error.\nThe systematic error includes the uncertainty in the as-\nsumed shape of the signal spectrum. The gain in precision\ncompared to earlier analyses of the lepton spectrum near\nthe kinematic endpoint can be attributed to higher statis-\ntics, and to improved background estimates. While earlier\nmeasurements were restricted to lepton energies close to\nthe kinematic endpoint for B \u2192Xc\u2113\u03bd decays at 2.3 GeV\nand covered only 10% of the B \u2192Xu\u2113\u03bd spectrum, this\nand other more recent measurements have been extended\nto lower momenta, thus covering about 25% to 35% of the\nspectrum (see Table 17.1.18).\nMore recently, the large data samples accumulated at\nthe B Factories have enabled studies of BB event sam-\nples tagged by the full reconstruction of the hadronic de-\ncays of one of the B mesons. An electron or muon with\nmomentum p\u2217\n\u2113> 1 GeV in the CM system is taken as a\nsignature for a semileptonic decay of the second B meson.\nThe overall event rate is low due to the low tag e\ufb03ciency,\nbut the combinatorial backgrounds are substantially re-\nduced allowing the extension of the acceptance for sig-\nnal events to 90% of the remaining phase space. The tag\ndecay determines the CM momentum and charge of the\nrecoiling signal B decay, and permits the reconstruction\nof hadronic observables with good resolution. Of partic-\nular relevance are q2 and mX, the mass of the hadronic\nstate X. The systematic uncertainties related to the tag\ne\ufb03ciency largely cancel in the measurement of the ratio\nof event yields for selected charmless semileptonic decays\nrelative to all B \u2192X\u2113\u03bd decays. Corrections to the sig-\nnal yield account for a possible di\ufb00erence in the tagging\ne\ufb03ciency in the presence of a signal B \u2192Xu\u2113\u03bd decay or\ngeneric semileptonic decay. The combinatorial background\nof the tag decay is subtracted by \ufb01ts to the mES dis-\ntributions. Other backgrounds originate from secondary\nB \u2192X \u2192\u2113decays and hadron misidenti\ufb01ed as leptons,\nprimarily muons. The dominant B \u2192Xc\u2113\u03bd background\nis reduced by vetoing kaons from charm particle decays\nand low-momentum pions from D\u2217\u2192D\u03c0 decays. Events\nwith additional missing particles result in large values of\nthe missing mass squared m2\nmiss and are rejected. This not\nonly reduces the backgrounds, but also improves the reso-\nlution of the reconstructed variables describing the signal\ndecays. In particular, the hadronic variable P+ = p+\nX is\nsensitive to detector resolution and the background model-\ning. The normalization of the remaining B \u2192Xc\u2113\u03bd back-\nground is determined from \ufb01ts to the observed inclusive\nspectra of di\ufb00erent kinematic variables.\nUsing the hadron-tagged BB events, Belle (Bizjak,\n2005; Urquijo, 2010) and BABAR (Aubert, 2008ac; Lees,\n2012x) have measured partial decay rates. The BABAR\nmeasurements are based on the full dataset of 467 million\nproduced BB events, whereas the Belle results are based\non 275 million (Bizjak, 2005) and 657 million (Urquijo,\n2010) produced BB pairs, respectively. Figure 17.1.18 shows\nBABAR data and results of \ufb01ts (Lees, 2012x) to four dif-\nferent kinematic distributions of B \u2192Xu\u2113\u03bd decays, per-\nformed to extract the partial branching fractions. These\nbranching fractions are listed in Table 17.1.19 for tagged\ndata samples from BABAR and Belle. Unless stated oth-\nerwise, the minimum lepton momentum is 1 GeV. The\nlisted branching fractions and extraction of |Vub| are based\non \ufb01ts to the distributions of the variables listed in the\n\ufb01rst column with the speci\ufb01c restrictions imposed. For\nthe BABAR and Belle results listed in the last line, no ad-\nditional restriction is imposed, and the results agree very\nwell within the stated errors.\nThese most recent analyses by Belle (Urquijo, 2010)\nand BABAR (Lees, 2012x), based on their full data sam-\nples, use a two-dimensional \ufb01t to mX versus q2 to extract\nthe branching fraction. Figures 17.1.19 and 17.1.20 show\nthe Belle and BABAR data and \ufb01t results. The BABAR se-\nlection of the signal candidates is cut-based, whereas Belle\nemploys a nonlinear multivariate discriminator, a boosted\ndecision tree. For the two analyses, the statistical and sys-\ntematic errors on the branching fractions are comparable\nin size (\u22437\u22129%). The systematic uncertainties are domi-\nnated by the simulation of the signal decays; in particular,\nthey are sensitive to the shape function and the b-quark\nmass. The average of these two branching fraction mea-\nsurements, assuming full correlation of the uncertainty\nin the predicted signal spectrum, is \u2206B(p\u2217\n\u2113> 1 GeV) =\n(1.87 \u00b1 0.10 \u00b1 0.11) \u00d7 10\u22123.\n)\n2\n (GeV/c\nX\nM\n0\n1\n2\n3\n4\nEvents\n0\n500\n1000\n1500\n2000\n0\n1\n2\n3\n4\n0\n500\n1000\n1500\n2000\n)\n2\n/c\n2\n (GeV\n2\nq\n0\n10\n20\n30\nEvents\n0\n1000\n2000\n0\n10\n20\n30\n0\n1000\n2000\n data\n0/+\nB\ni\n l \nu\n X\nA\nB \ni\n l \nc\n X\nA\nB \nSecondaries\nCombinatorial\nContinuum\nFigure 17.1.19. Belle (Urquijo, 2010): Projections of mea-\nsured distributions (data points) of (a) mX and (b) q2 with\nvarying bin size, compared to results of a two-dimensional\nmX \u2212q2 distribution for the sum of scaled MC contributions.\nThe data are not e\ufb03ciency corrected.\n\n213\nTable 17.1.18. Overview of partial branching fraction measurements with statistical and systematic errors, based on mea-\nsurements of the inclusive lepton spectrum for B \u2192Xu\u2113\u03bd decays using untagged data samples. smax\nh\nrefers to the maximum\nkinematically allowed hadronic mass squared for a given electron energy and q2.\nExperiment\nSelection\n\u2206B (10\u22123)\nCLEO (Bornheim et al., 2002)\np\u2217\n\u2113> 2.1 GeV\n0.328 \u00b1 0.023 \u00b1 0.073\nBelle (Limosani, 2005)\np\u2217\n\u2113> 1.9 GeV\n0.847 \u00b1 0.037 \u00b1 0.153\nBABAR (Aubert, 2006x)\np\u2217\n\u2113> 2.0 GeV\n0.572 \u00b1 0.041 \u00b1 0.051\nBABAR (Aubert, 2005h)\np\u2217\n\u2113> 2.0 GeV, smax\nh\n> 3.5 GeV2\n0.441 \u00b1 0.042 \u00b1 0.042\n-100\n0\n0\n2\n4\n100\n200\n300\n0\n1000\n2000\n3000\n(a)\nMX(GeV)\nEntries/0.31 GeV\nEntries/bin\n0\n200\n1000\n2000\n3000\n0\n4\n2\n0\nP+(GeV)\nEntries/0.22 GeV\nEntries/bin\n(b)\n0\n100\n200\n0\n200\n400\n600\n0\n10\n20\nq2(GeV2)\nEntries/2 GeV2\nEntries/bin\n(c)\nMX<1.7 GeV\nMX<1.7 GeV\n0\n100\n200\n0\n500\n1000\n(d)\n1\n1.5\n2\n2.5\np* (GeV)\nEntries/0.1 GeV\nEntries/0.1 GeV\nFigure 17.1.18. BABAR (Lees, 2012x): Extraction of |Vub| from selected samples of inclusive B \u2192Xu\u2113\u03bd decays: (a) hadronic\nmass mX, (b) P+, (c) q2 with restriction mX \u22641.7 GeV, and (d) lepton momentum p\u2217\n\u2113. upper row: comparison of data (points\nwith statistical errors) with results of \u03c72 \ufb01t with varying bin size for the sum of scaled MC distributions (histograms) of\nsignal inside (white) and outside (blue) the selected kinematic region and background (gray); lower row: background subtracted\ndistributions, compared to the results of the \ufb01t with \ufb01ner binning. The data are not e\ufb03ciency corrected.\nTable 17.1.19. Partial B \u2192Xu\u2113\u03bd branching fractions (Bizjak, 2005; Urquijo, 2010; Lees, 2012x) and values of |Vub| (Lees,\n2012x) based on BLNP calculations for di\ufb00erent kinematic regions in tagged BB events. The stated errors are statistical and\nsystematic, and for |Vub| the third error refers to the theoretical uncertainty.\nSelection\nBelle: \u2206B (10\u22123)\nBABAR: \u2206B (10\u22123)\nBABAR: |Vub| (10\u22123)\nmX \u22641.55 GeV\n\u2014\n1.08 \u00b1 0.08 \u00b1 0.06\n4.17 \u00b1 0.15 \u00b1 0.12+0.24\n\u22120.24\nmX \u22641.70 GeV\n1.24 \u00b1 0.11 \u00b1 0.12\n1.15 \u00b1 0.06 \u00b1 0.08\n3.97 \u00b1 0.17 \u00b1 0.14+0.20\n\u22120.20\nP+ \u22640.66 GeV\n1.11 \u00b1 0.10 \u00b1 0.16\n0.98 \u00b1 0.09 \u00b1 0.08\n4.02 \u00b1 0.18 \u00b1 0.16+0.24\n\u22120.23\nmX \u22641.70 GeV, q2 \u22658 GeV2\n0.84 \u00b1 0.08 \u00b1 0.10\n0.68 \u00b1 0.06 \u00b1 0.04\n4.25 \u00b1 0.19 \u00b1 0.13+0.23\n\u22120.25\np\u2217\n\u2113> 1.3 GeV\n\u2014\n1.52 \u00b1 0.16 \u00b1 0.14\n4.29 \u00b1 0.22 \u00b1 0.20+0.19\n\u22120.20\np\u2217\n\u2113> 1.0 GeV, mX \u2212q2\n1.96 \u00b1 0.17 \u00b1 0.16\n1.80 \u00b1 0.13 \u00b1 0.15\n4.28 \u00b1 0.15 \u00b1 0.18+0.18\n\u22120.20\n17.1.5.3 Determination of |Vub|\nThe measured partial branching fractions \u2206B can be re-\nlated to |Vub| in the following way,\n|Vub| =\nq\n\u2206B/(\u03c4B \u2206\u0393theory),\n(17.1.63)\nwhere \u2206\u0393theory is the theoretically predicted partial rate\n(in units of ps\u22121) for a selected phase space region.\nThe extracted values of |Vub| are presented in Table\n17.1.20 for both untagged and tagged BB samples. The\n|Vub| results have been adjusted by HFAG to include up-\ndates of input parameters and re\ufb02ect the latest under-\nstanding of the theoretical uncertainties. The averages of\nthe various available measurements have been obtained\nby taking correlations into account. In particular, all the-\noretical uncertainties are considered to be correlated, as\nare the uncertainties on the modeling of B \u2192Xc\u2113\u03bd and\nB \u2192Xu\u2113\u03bd decays. Experimental uncertainties due to\nparticle identi\ufb01cation and reconstruction e\ufb03ciencies are\nfully correlated for measurements from the same experi-\n\n214\nTable 17.1.20. Overview of |Vub| measurements based on inclusive B \u2192Xu\u2113\u03bd decays. The critical input parameters mb and\n\u00b52\n\u03c0 depend on the di\ufb00erent mass schemes and have been obtained from the OPE \ufb01ts to B \u2192Xc\u2113\u03bd hadronic mass and lepton\nenergy moments in the kinetic mass scheme. For the BLNP and the DGE calculations, they have been subsequently translated\nfrom the kinetic to the shape function and MS schemes, respectively. The additional uncertainties mb and \u00b52\n\u03c0 are due to these\nscheme translations. The \ufb01rst error is experimental and the second re\ufb02ects the uncertainties of the QCD calculations and the\nHQE parameters (Asner et al., 2011).\nBLNP\nGGOU\nDGE\nmb scheme\nSF scheme\nKinetic scheme\nMS scheme\nmb (GeV)\n4.588 \u00b1 0.023 \u00b1 0.011\n4.560 \u00b1 0.023\n4.194 \u00b1 0.043\n\u00b52\n\u03c0 (GeV2)\n0.189+0.041\n\u22120.040 \u00b1 0.020\n0.453 \u00b1 0.036\n\u2014\nExperiment\n|Vub| (10\u22123)\nCLEO (Bornheim et al., 2002)\n4.19 \u00b1 0.49+0.26\n\u22120.34\n3.93 \u00b1 0.46+0.22\n\u22120.29\n3.82 \u00b1 0.43+0.23\n\u22120.26\nBelle (Limosani, 2005)\n4.88 \u00b1 0.45+0.24\n\u22120.27\n4.75 \u00b1 0.44+0.17\n\u22120.22\n4.79 \u00b1 0.44+0.21\n\u22120.24\nBABAR (Aubert, 2006x)\n4.48 \u00b1 0.25+0.27\n\u22120.28\n4.29 \u00b1 0.24+0.18\n\u22120.24\n4.28 \u00b1 0.24+0.22\n\u22120.24\nBABAR (Aubert, 2005h)\n4.66 \u00b1 0.31+0.31\n\u22120.36\n\u2014\n4.32 \u00b1 0.29+0.24\n\u22120.29\nAverage untagged\n4.65 \u00b1 0.22+0.26\n\u22120.29\n4.39 \u00b1 0.22+0.18\n\u22120.24\n4.44 \u00b1 0.21+0.21\n\u22120.25\nBelle (Urquijo, 2010)\n4.47 \u00b1 0.27+0.19\n\u22120.21\n4.54 \u00b1 0.27+0.10\n\u22120.11\n4.60 \u00b1 0.27+0.11\n\u22120.13\nBABAR (Lees, 2012x)\n4.28 \u00b1 0.24+0.18\n\u22120.20\n4.35 \u00b1 0.24+0.09\n\u22120.11\n4.40 \u00b1 0.24+0.12\n\u22120.13\nAverage tagged\n4.35 \u00b1 0.19+0.19\n\u22120.20\n4.43 \u00b1 0.21+0.09\n\u22120.11\n4.49 \u00b1 0.21+0.13\n\u22120.13\nAverage all\n4.40 \u00b1 0.15+0.19\n\u22120.21\n4.39 \u00b1 0.15+0.12\n\u22120.14\n4.45 \u00b1 0.15+0.15\n\u22120.16\n0\n100\n200\n300\n0\n500\n1000\n1500\n(a)\n0\n10\n20\nq2(GeV2)\nEntries/bin\nEntries/2 GeV2\n-100\n0\n100\n200\n300\n0\n1000\n2000\n3000\n4000\n(b)\n0\n2\n4\nMx(GeV)\nEntries/bin\nEntries/0.33 GeV\nFigure 17.1.20. BABAR (Lees, 2012x): Projection of measured\ndistributions (data points) of (a) q2 and (b) mX with varying\nbin size. Upper row: comparison with the result of the \u03c72 \ufb01t\nto the two-dimensional mX \u2212q2 distribution for the sum of\ntwo scaled MC contributions. Lower row: corresponding spec-\ntra with equal bin size after background subtraction based on\nthe \ufb01t. The data are not e\ufb03ciency corrected.\nment, and uncorrelated for di\ufb00erent experiments. Statis-\ntical correlations are also taken into account, whenever\navailable. The averaging procedure used is documented\nby the HFAG Collaboration (Asner et al., 2010). The ear-\nlier measurements near the kinematic limit of the lepton\nspectrum covered limited fractions of the total phase space\nand had sizable experimental and theoretical uncertain-\nties. The more recent measurements based on the tagged\nBB samples of the full BABAR and Belle data sets have\nreduced backgrounds and cover a much larger fraction of\nthe phase space.\nThe extracted values of |Vub| based on the di\ufb00erent\nQCD calculations agree well. The estimated theoretical er-\nrors are dominated by the uncertainty on mb, and by other\nnon-perturbative corrections. For BLNP there are sizable\ncontributions from the leading and subleading shape func-\ntions and the matching scales. For GGOU the uncertain-\nties in the parameterization of the di\ufb00erent shape func-\ntions are important. For the DGE calculation, the main\nuncertainty comes from \u03b1S and mb for which the MS\nrenormalization scheme is used. The uncertainty in the\nweak annihilation process is included. It contributes asym-\nmetrically to the error for the three QCD calculations.\nValues of |Vub| based on partial branching fractions\n(Lees, 2012x) for di\ufb00erent regions of phase space are pre-\nsented in Table 17.1.19 for the BLNP calculation. The\nresulting uncertainties are highly correlated. For the dif-\nferent kinematic regions, the variations of |Vub| are consis-\ntent within the experimental uncertainties. Similar results\nwere also obtained for other QCD calculations. The analy-\nsis based on the restricted region mX < 1.7 GeV combined\nwith q2 > 8 GeV2, is expected to be less a\ufb00ected by non-\nperturbative contributions to the shape functions. There-\nfore, the use of a more HQE inspired approach (Bauer,\nLigeti, and Luke, 2001) is appropriate. It results in a value\nof |Vub| that is in good agreement with the results based on\nthe three QCD calculations presented here. As discussed\nin Section 17.1.5, NNLO e\ufb00ects in the BLNP calculation\nwould lead to an increase of about 8% in |Vub| in some\nof the BLNP values reported above, but not in those re-\nlated to tagged measurements with looser signal selection\ncriteria. Further investigation is necessary to clarify this\nunexpected indication.\nThere is a high degree of consistency among the mea-\nsurements and results for di\ufb00erent QCD calculations show\n\n215\nlittle variation. Based on results in Table 17.1.20, we quote\nthe unweighted arithmetic average of the results and un-\ncertainties from the tagged data analyses as the overall\nresult,\n|Vub|incl = (4.42 \u00b1 0.20exp \u00b1 0.15th) \u00d7 10\u22123.\n(17.1.64)\n17.1.6 Evaluation of the results\nAs a result of joint e\ufb00orts by theorists and experimen-\ntalists our understanding of semileptonic B-meson decays\nhas substantially advanced over the last decade. Here we\nsummarize the present situation.\n17.1.6.1 Summary on |Vcb|\nSubstantial progress has been made in the application of\nHQE calculations to extract |Vcb| and mb from \ufb01ts to mea-\nsured moments from B \u2192Xc\u2113\u03bd decays. The total error\nquoted on |Vcb| is 1.8% and the introduction of a c-quark\nmass constraint, mc(3 GeV) = (0.998 \u00b1 0.029) GeV, has\nreduced the overall uncertainty on mb to only 25 MeV.\nThe measurement of |Vcb| based on the exclusive decay\nB \u2192D\u2217\u2113\u03bd\u2113now has a combined experimental and theo-\nretical uncertainty of 2.3%, still dominated by the form-\nfactor normalization. The measurement based on B \u2192\nD\u2113\u03bd\u2113has substantially improved and now provides a very\nuseful cross check on the more precise B \u2192D\u2217\u2113\u03bd\u2113deter-\nmination. However, the values of |Vcb| based on the latter\ndi\ufb00er by about 5%, depending on the choice of the QCD\ncalculation for the normalization of the form factors; lat-\ntice calculations lead to lower values of |Vcb| than heavy\n\ufb02avor sum rules.\nConsequently the comparison of the inclusive and ex-\nclusive determinations of |Vcb| depends on the choice of\nthe normalization of the form factors. For the LQCD cal-\nculations, the values of the inclusive and exclusive deter-\nmination of |Vcb| di\ufb00er at the level of 2.5\u03c3,\n|Vcb|excl = [39.04 (1 \u00b1 0.014exp \u00b1 0.019th)] \u00d7 10\u22123\n|Vcb|incl = [42.01 (1 \u00b1 0.011exp \u00b1 0.014th)] \u00d7 10\u22123 .\n(17.1.65)\nThe average has a probability of P(\u03c72) = 0.015. We there-\nfore scale the errors by\np\n\u03c72 = 2.51 and arrive at\n|Vcb| = [40.81 (1 \u00b1 0.022exp \u00b1 0.028th)] \u00d7 10\u22123 . (17.1.66)\nFor the heavy \ufb02avor sum rule calculations, the value is\n|Vcb|excl = [40.93 (1 \u00b1 0.014exp \u00b1 0.023th)] \u00d7 10\u22123\n(17.1.67)\nand agrees very well with the inclusive measurement. The\naverage value with unscaled uncertainties is\n|Vcb| = [41.67 (1 \u00b1 0.009exp \u00b1 0.012th)] \u00d7 10\u22123 . (17.1.68)\n17.1.6.2 Summary on |Vub|\nFor inclusive measurements of |Vub| experimental and the-\noretical errors are comparable in size. The dominant ex-\nperimental uncertainties are related to the limited size of\nthe tagged samples, the signal simulation, and background\nsubtraction. The theoretical uncertainties are dominated\nby the error on the b-quark mass; a 20-30 MeV uncertainty\nin mb impacts |Vub| by 2-3%.\nMeasurements of the di\ufb00erential decay rate as a func-\ntion of q2 for B0 \u2192\u03c0\u2212\u2113+\u03bd\u2113provide valuable information\non the shape of the form factor, though with sizable errors\ndue to large backgrounds. Results based on di\ufb00erent QCD\ncalculations agree within the stated theoretical uncertain-\nties. While the traditional method of normalizing to QCD\ncalculations in di\ufb00erent ranges of q2 results in uncertain-\nties of +17%\n\u221210%, combined \ufb01ts to LQCD predictions and the\nmeasured spectrum using a theoretically motivated ansatz\n(Becher and Hill, 2006; Bourrely, Caprini, and Lellouch,\n2009; Boyd, Grinstein, and Lebed, 1995) have resulted in\na reduction of the theoretical uncertainties to about 8%.\nThe values of the inclusive and exclusive determina-\ntions of |Vub| are only marginally consistent, they di\ufb00er at\na level of 3\u03c3,\n|Vub|excl = [3.23 (1 \u00b1 0.05exp \u00b1 0.08th)] \u00d7 10\u22123\n|Vub|incl = [4.42 (1 \u00b1 0.045exp \u00b1 0.034th)] \u00d7 10\u22123.\n(17.1.69)\nThis average has a probability of P(\u03c72) = 0.003. Thus we\nscale the error by\np\n\u03c72 = 3.0 and arrive at\n|Vub| = [3.95 (1 \u00b1 0.096exp \u00b1 0.099th)] \u00d7 10\u22123. (17.1.70)\n17.1.6.3 Conclusions and Outlook\nWhile there has been tremendous progress, we have not\nachieved the precision of 1% for |Vcb| or 5% on |Vub|, goals\nmany of us had hoped to reach by now, based on the \ufb01-\nnal results of the Belle and BABAR experiments. The puz-\nzling di\ufb00erences in the results of exclusive and inclusive\nmeasurements of |Vub|, and to a lesser extent of |Vcb| if\nwe rely on non-lattice calculations, challenge our current\nunderstanding of the experimental and theoretical tech-\nniques. To resolve this puzzle a major e\ufb00ort will be re-\nquired. It will take much larger tagged data samples and\na more detailed assessment of the detector performance\nand the background composition to reduce experimental\nerrors. It will also require further progress in QCD cal-\nculations, based on lattice or heavy \ufb02avor sum rules or\nother methods, to reduce the uncertainties of form-factor\npredictions for exclusive decays, to adopt precision deter-\nminations of the heavy quark masses, and to improve the\ndetailed predictions of inclusive processes.\n\n216\n17.2 Vtd and Vts\nEditors:\nKevin Flood (BABAR)\nTobias Hurth (theory)\nThe CKM matrix elements |Vtd| and |Vts| are funda-\nmental parameters of the Standard Model that can only\nbe determined experimentally using rare radiative B or\nK decays (Fig. 17.2.1), or B0 and B0 oscillations involv-\ning top quarks through a box diagram (Fig. 17.2.2). A\ndiscussion of kaon decays is beyond the scope of this ar-\nticle; see, e.g., (Donoghue, Golowich, and Holstein, 1982;\nGaillard and Lee, 1974b; Gilman and Wise, 1983). Mea-\nsurement of the single top quark production cross-section\nallows for a model-independent direct determination of\n|Vtb|, but the magnitudes of |Vtd| and |Vts| cannot be sim-\nilarly extracted from tree-level decays. However, a recent\npaper (Ali, Barreiro, and Lagouri, 2010) speculates that\n\u223c10% precision for the signal t \u2192Ws can be achieved\nat the LHC with an integrated luminosity of 10fb\u22121, de-\nspite the presence of a nearly three orders of magnitude\nlarger background from single top production of t \u2192Wb.\nDerivation of |Vtd| and |Vts| from the experimental ob-\nservables necessarily assumes the SM although the FCNC\nobservables used, e.g. from Bd,s mixing, B \u2192X(s, d)\u03b3,\nor \u03f5 in the kaon sector, may receive new physics contribu-\ntions from unrelated sources (with the term new physics\n- NP - one addresses experimentally yet uncon\ufb01rmed pro-\ncesses and particles beyond those included in the Standard\nModel). Independent determination of the magnitudes of\n|Vtd| and |Vts| from several di\ufb00erent sources, along with\nVtb from single top measurements, can provide a robust\nmodel-independent check of the unitarity of the CKM ma-\ntrix or, conversely, o\ufb00er a sensitive probe for the possible\npresence of physics beyond the SM.\nV \u2217\ntb\nW \u2212\n\u00afq\nd, s\nVtd,s\nb\n\u00afq\n\u03b3\nt\nFigure 17.2.1. Lowest order SM Feynman diagram for a loop-\nmediated radiative B decay.\nIn the past few years, the experimental and lattice\nQCD inputs necessary to calculate |Vtd| and |Vts| to good\nprecision have become available. The B Factories have\ncontributed measurements of \u2206md, the mass di\ufb00erence\nbetween the neutral Bd mass eigenstates, and branching\nV \u2217\ntb\nW\nW\n\u00afb\nd, s\nVtd,s\nVtd,s\nb\nV \u2217\ntb\n\u00afd, \u00afs\nt\n\u00aft\n\u00afB0\nd,s\nB0\nd,s\nFigure 17.2.2. Lowest order SM Feynman diagram describing\nB0 and B0 oscillations.\nfractions from the inclusive and exclusive one-loop radia-\ntive penguin processes B \u2192X(s, d)\u03b3, while the CDF, D\u00d8\nand LHCb collaborations have measured \u2206ms, the mass\ndi\ufb00erence between the neutral Bs mass eigenstates, to sub-\npercent precision. These results have been matched by\nprogress in lattice QCD calculations leading to increased\nprecision in the additional parameters required to extract\n|Vtd| and |Vts| from the experimental results.\n17.2.1 Bd,s mixing\nEquation (17.2.1) relates \u2206md to |Vtd| (Bigi and Sanda,\n2000):\n\u2206md = G2\nF\n6\u03c02 f 2\nBmBM 2\nW \u03b7BS0|V \u2217\ntbVtd|2 bBB ,\n(17.2.1)\nwhere we have inserted\n\u27e8B0|(bd)(bd)|B0\u27e9= 4\n3f 2\nBm2\nBd bBB\n(17.2.2)\nfor the hadronic matrix element in Eq. (10.1.17). Here, mB\nand MW are respectively the B0 and W masses; GF is the\nFermi constant; \u03b7B is a QCD correction (Buras, Jamin,\nand Weisz, 1990); S0 is a function of m2\nt/m2\nW (Buras,\n1981; Inami and Lim, 1981); fB is the B-meson decay con-\nstant; and bBB is the B-meson bag parameter (Donoghue,\nGolowich, and Holstein, 1992). A discussion of the exper-\nimental techniques used at the B Factories to measure\n\u2206md is given in Section 17.5.\nIn order to extract |Vtd| using Eq. (17.2.1), we adopt\nthe latest combination of lattice QCD results avail-\nable from \u201cwww.latticeaverages.org\u201d (Laiho, Lunghi, and\nVan de Water, 2010), who report fb\nq\nbBB = 227\u00b119 MeV.\nThis result is obtained by combining the average decay\nconstant fb obtained from the MILC and HPQCD collab-\norations, along with the HPQCD determination of the bag\nparameter bBB, which reduces the total uncertainty with\nrespect to taking the two parameters separately. Other\nrequired inputs are taken from Tables 25.1.2 and 25.1.3,\nas well as the PDG (Beringer et al., 2012). We addi-\ntionally assume that |Vtb| = 1. Using the B Factory re-\nsults given in Table 17.5.2, which are averaged by the\n\n217\nHeavy Flavor Averaging Group (HFAG) to obtain a \ufb01-\nnal value of \u2206md = 0.508 \u00b1 0.003 \u00b1 0.003 ps\u22121, we \ufb01nd\nVtd = (9.5 \u00b1 0.7) \u00d7 10\u22123.\nThe uncertainty in |Vtd| induced by the uncertainty\nin fb\nq\nbBB can be reduced by rewriting this factor as\nfb\nq\nbBB = fs\nq\nbBBs/\u03be, where \u03be = fs\nq\nbBBs/fb\nq\nbBB. The\nfactor \u03be can be more accurately determined in lattice QCD\ncalculations than its individual terms because of the in-\nclusion of fs\nq\nbBBs, which is obtained directly at the phys-\nical strange quark mass rather than by extrapolation to\nthe down quark mass, and approximate cancellation of\nsome uncertainties in the ratio. Using the values \u03be =\n1.237\u00b10.032 and fs\nq\nbBBs = 279\u00b115 MeV, we \ufb01nd Vtd =\n(9.6 \u00b1 0.5) \u00d7 10\u22123, with a reduction in the uncertainty of\n\u223c30% relative to the result based solely on fb\nq\nbBB. The\nlattice parameter uncertainties can be further controlled\nby taking the ratio |Vtd/Vts|, which directly uses \u03be\u22121, and\nincorporating the PDG combination of the B0\nsB0\ns oscilla-\ntion frequency results from CDF (Abulencia et al., 2006b)\nand LHCb (Aaij et al., 2012f), \u2206ms = 17.69 \u00b1 0.08 ps\u22121.\nUsing an expression for |Vts| analogous to Eq. (17.2.1), we\nobtain |Vtd/Vts| = 0.208 \u00b1 0.005.\n17.2.2 B \u2192X(s, d)\u03b3\nLoop-mediated radiative decays provide a set of processes\ncomplementary to B0 and B0 oscillations from which\nthe value of |Vtd/Vts| can be derived using experimen-\ntal branching fraction results together with inputs from\nlattice QCD. Since new physics may enter each type of\nprocess di\ufb00erently, a comparison of |Vtd/Vts| extracted\nfrom both mixing and radiative decays provides a ro-\nbust test of the consistency of the SM CKM paradigm\nor, conversely, o\ufb00ers a powerful probe for the presence\nof new physics (Descotes-Genon, Ghosh, Matias, and Ra-\nmon, 2011; Lenz et al., 2011). Amplitudes for the rare\n\u2206F = 1 decays b \u2192d\u03b3 and b \u2192s\u03b3, essentially pro-\nportional to Vtd and Vts respectively, have been measured\nusing both inclusive and exclusive \ufb01nal states at the B\nFactories. These provide the experimental inputs neces-\nsary to calculate the ratio of CKM elements |Vtd/Vts|.\nThe details of the various experimental techniques used\nto measure the branching fractions for the radiative pen-\nguin B \u2192X(s, d)\u03b3 processes are addressed in Section 17.9.\nHere, we discuss the calculation of the ratio |Vtd/Vts| us-\ning a combination of the latest branching fraction results\nfrom BABAR (Aubert, 2008z, 2009r) and Belle (Nakao,\n2004; Taniguchi, 2008) in the exclusive B \u2192(\u03c1, \u03c9, K\u2217)\u03b3\nmodes, followed by calculation of the ratio using BABAR\u2019s\nlatest B \u2192Xd\u03b3 semi-inclusive results (del Amo Sanchez,\n2010q). Belle has no comparable semi-inclusive analysis\nas of the time of publication of this review. The exclusive\nand inclusive BABAR results use the same BABAR dataset\nas well as a similar event selection, and are thus highly\ncorrelated; they cannot be averaged easily. Since there are\ncorrelated inputs to both the inclusive and exclusive cal-\nculations, as well as non-trivial correlations in the the-\nory assumptions, we forego any attempt here to make any\ncombination of the exclusive and inclusive results.\nIn their measurements of combinations of the exclusive\nmode branching fractions, both BABAR (Aubert, 2008z)\nand Belle (Taniguchi, 2008) assume an exact isospin sym-\nmetry, i.e. \u0393(B\u00b1 \u2192\u03c1\u00b1\u03b3) \u22612\u0393(B0 \u2192\u03c10\u03b3), as well\nas 2\u0393(B0 \u2192\u03c10\u03b3) \u22612\u0393(B0 \u2192\u03c9\u03b3) However, these re-\nlations are not exact and symmetry-breaking corrections\nhave been calculated (Ball, Jones, and Zwicky, 2007; Ball\nand Zwicky, 2006b). The asymmetry expected between \u03c10\nand \u03c9 predominantly arises from the di\ufb00erent form factors\nfor these decays, while the principal contribution to sym-\nmetry breaking between neutral and charged \u03c1 mesons is\nthe presence of a weak annihilation diagram with photon\nemission from the spectator quark. Both collaborations re-\nport CP- and isospin-averaged results for B \u2192(\u03c1, \u03c9)\u03b3 and\nB \u2192\u03c1\u03b3, as well as branching fractions for contributing in-\ndividual modes. BABAR and Belle have searched for isospin\nasymmetries in these modes, and no statistically signi\ufb01-\ncant asymmetry is observed in either the \u03c1\u03b3 or (\u03c1, \u03c9)\u03b3\nmodes. A discussion of the experimental measurements\nthemselves, as well as related theoretical background, can\nbe found below in Section 17.9.\nBelle (Taniguchi, 2008) calculates the ratio of branch-\ning fractions from products of likelihoods for each of the\nindividual B \u2192(\u03c1, \u03c9)\u03b3 and B \u2192K\u2217\u03b3 \ufb01nal states, which\nare convolved with residual systematics that do not cancel\nin the ratio of branching fractions, and \ufb01nds\nR\u03c10 =\nB(B0 \u2192\u03c10\u03b3)\nB(B0 \u2192K\u22170\u03b3)\n= 0.0206+0.0045+0.0014\n\u22120.0043\u22120.0016,\n(17.2.3)\nR\u03c1 =\nB(B \u2192\u03c1\u03b3)\nB(B \u2192K\u2217\u03b3)\n= 0.0302+0.0060+0.0026\n\u22120.0055\u22120.0028,\n(17.2.4)\nR\u03c1/\u03c9 = B(B \u2192(\u03c1, \u03c9)\u03b3)\nB(B \u2192K\u2217\u03b3)\n= 0.0284 \u00b1 0.0050+0.0027\n\u22120.0029,\n(17.2.5)\nwhere the \ufb01rst and second errors are statistical and sys-\ntematic, respectively.\nThe BABAR result for the exclusive modes (Aubert,\n2008z) employs a di\ufb00erent strategy, \ufb01rst concatenating\nall B \u2192(\u03c1, \u03c9)\u03b3 \ufb01nal states into a single dataset which\nis then simultaneously \ufb01t over all modes with an isospin\nconstraint applied in order to extract the isospin-averaged\nB \u2192(\u03c1, \u03c9)\u03b3 branching fraction. A similar procedure omit-\nting the \u03c9\u03b3 \ufb01nal state is used to produce the B \u2192\u03c1\u03b3\nbranching fraction. The B \u2192K\u2217\u03b3 branching fraction used\nin BABAR\u2019s calculation of the ratio is taken from HFAG,\nand thus it is not possible to account for systematic exper-\nimental e\ufb00ects which may be common to both numerator\nand denominator in the ratio of branching fractions, and\nthey quote only a total uncertainty for the branching frac-\n\n218\ntion ratio results,\nR\u03c1+ =\nB(B+ \u2192\u03c1+\u03b3)\nB(B+ \u2192K\u2217+\u03b3) = 0.030+0.012\n\u22120.011,\n(17.2.6)\nR\u03c10 =\nB(B0 \u2192\u03c10\u03b3)\nB(B0 \u2192K\u22170\u03b3) = 0.024 \u00b1 0.006, (17.2.7)\nR\u03c9 =\nB(B0 \u2192\u03c9\u03b3)\nB(B0 \u2192K\u22170\u03b3) = 0.012+0.007\n\u22120.006,\n(17.2.8)\nR\u03c1 =\nB(B \u2192\u03c1\u03b3)\nB(B \u2192K\u2217\u03b3) = 0.042 \u00b1 0.009,\n(17.2.9)\nR\u03c1/\u03c9 = B[B \u2192(\u03c1/\u03c9)\u03b3]\nB(B \u2192K\u2217\u03b3)\n= 0.039 \u00b1 0.008.(17.2.10)\nWe use a weighted average of the common central val-\nues reported by each collaboration, given the total uncer-\ntainty for each measurement and symmetrizing uncertain-\nties where applicable, to arrive at averaged values subse-\nquently used in the calculation of |Vtd/Vts|,\nR\u03c10 =\nB(B0 \u2192\u03c10\u03b3)\nB(B0 \u2192K\u22170\u03b3) = 0.0219 \u00b1 0.0037,\nR\u03c1 =\nB(B \u2192\u03c1\u03b3)\nB(B \u2192K\u2217\u03b3) = 0.0341 \u00b1 0.0052,\nR\u03c1/\u03c9 = B(B \u2192(\u03c1, \u03c9)\u03b3)\nB(B \u2192K\u2217\u03b3)\n= 0.0320 \u00b1 0.0047.\n(17.2.11)\nBoth collaborations adopt similar formalisms to derive\nthe ratio of CKM elements from the underlying experi-\nmental results, with the ratio Rth(\u03c1\u03b3/K\u2217\u03b3) (and similarly\nRth(\u03c9\u03b3/K\u2217\u03b3)) given by (Ali, Lunghi, and Parkhomenko,\n2004; Ball, Jones, and Zwicky, 2007; Beneke, Feldmann,\nand Seidel, 2005; Bosch and Buchalla, 2005):\nRth(\u03c1\u03b3/K\u2217\u03b3) =\nBth(B \u2192\u03c1\u03b3)\nBth(B \u2192K\u2217\u03b3)\n(17.2.12)\n\u2261S\u03c1\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n2 (M 2\nB \u2212m2\n\u03c1)3\n(M 2\nB \u2212m2\nK\u2217)3\n\u03b62 [1 + \u2206R(\u03c1/K\u2217)] ,\n(17.2.13)\nwhere m\u03c1 is the mass of the \u03c1 meson, \u03b6 is the ratio of the\ntransition form factors, \u03b6 = T\n\u03c1\n1(0)/T\nK\u2217\n1 (0) and S\u03c1 = 1\nand 1/2 for the \u03c1\u00b1 and \u03c10 mesons, respectively. A similar\nexpression applies for B \u2192(\u03c1, \u03c9)\u03b3 with the substitution\n\u03c1 \u2192(\u03c1, \u03c9) based on the symmetries de\ufb01ned above. These\ntheoretical relations are based on the method of QCD fac-\ntorization; the application of this method to radiative de-\ncays is discussed in Section 17.9. Within such factorization\nformulae, process-independent non-perturbative functions\nlike form factors are separated from perturbatively calcu-\nlable functions. Here, the main sources of theoretical un-\ncertainties are the form factors and the \u039b/mb corrections.\nThe former is expected to be reduced by taking ratios of\nthe observables. The \u03b1S corrections to the hard kernels\nand the power corrections, both included in the ratio in\nEq. (17.2.13) via the factor (1 + \u2206R), introduce further\ndependences on the CKM matrix elements, namely \u03c62 as\ngiven in Eq. (16.5.4) and Rut = |VudV \u2217\nub/VtdV \u2217\ntb|, and one\n\ufb01nds numerically (Beneke, Feldmann, and Seidel, 2005):\n\u2206R(\u03c1\u00b1/K\u2217\u00b1) =\n\b\n1 \u22122Rut cos \u03c62 [0.24+0.18\n\u22120.18]\n+R2\nut [0.07+0.12\n\u22120.07]\n\t\n,\n(17.2.14)\n\u2206R(\u03c10/K\u22170) =\n\b\n1 \u22122Rut cos \u03c62 [\u22120.06+0.06\n\u22120.06]\n+R2\nut [0.02+0.02\n\u22120.01]\n\t\n.\n(17.2.15)\nThese results are consistent with the predictions given\nin the literature (Ali, Lunghi, and Parkhomenko, 2004;\nBall, Jones, and Zwicky, 2007; Bosch and Buchalla, 2005).\nThe neutral mode is better suited for the determination\nof |Vtd/Vts| than the charged mode, in which the function\n\u2206R is dominated by the weak annihilation contribution,\nwhich leads to a larger error. The most recent determi-\nnation of the ratio \u03b6 within the light-cone QCD sum rule\napproach (Ball and Zwicky, 2006b), 1/\u03b6 = 1.17 \u00b1 0.09,\nleads to the determination of |Vtd/Vts| via Eq. (17.2.13).\nHowever, the experimental data on the branching frac-\ntions of B \u2192K\u2217\u03b3 and B \u2192\u03c1\u03b3 calls for a larger error on\n\u03b6, if one assumes no large power corrections beyond the\nknown annihilation terms (Beneke, Feldmann, and Seidel,\n2005) (see also Section 17.9.4.1).\nUsing the combined results from both experiments, we\nobtain\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n\u03c10 = 0.26 \u00b1 0.02 \u00b1 0.03,\n(17.2.16)\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n\u03c1\n= 0.22 \u00b1 0.02 \u00b1 0.02,\n(17.2.17)\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n\u03c1,\u03c9\n= 0.21 \u00b1 0.02 \u00b1 0.02,\n(17.2.18)\nwhere the \ufb01rst error is the total experimental uncertainty\nand the second is the theory uncertainty. BABAR addi-\ntionally reports the ratio for the two exclusive modes not\nmeasured by Belle:\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n\u03c1+ = 0.198+0.039\n\u22120.035 \u00b1 0.016,\n(17.2.19)\n\f\f\f\f\nVtd\nVts\n\f\f\f\f\n\u03c9\n= 0.202+0.058\n\u22120.050 \u00b1 0.016.\n(17.2.20)\nAlthough experimental uncertainties on the exclusive\nbranching fractions may be substantially reduced in the\nfuture, irreducible theory uncertainties can complicate in-\nterpretation of any observed discrepancy in |Vtd/Vts| with\nvalues from other processes. Such uncertainties are gen-\nerally under better control for inclusive radiative penguin\ndecays, where |Vtd/Vts| has been calculated to next-to-\nleading-log (NLL) precision (Ali, Asatrian, and Greub,\n1998). Following this formalism, the ratio of the inclu-\nsive branching fractions can be written as a function of\n\n219\nthe Wolfenstein parameters \u03bb, \u03c1, \u03b7\nR(d\u03b3/s\u03b3) =\n\u03bb2[1 + \u03bb2(1 \u22122\u03c1)] [(1 \u2212\u03c1)2 + \u03b72 +\nDu\nDt\n(\u03c12 + \u03b72) + Dr\nDt\n(\u03c1(1 \u2212\u03c1) \u2212\u03b72)] ,\n\u22430.046 [for (\u03c1, \u03b7) = (0.11, 0.33),\nor (\u03c1, \u03b7) = (0.107, 0.322)] , (17.2.21)\nwhere the quantities Di, which depend on several input\nparameters such as mt, mb, mc, must be calculated numer-\nically. As with the exclusive decays, care must be taken to\nuse a set of input parameters determined independently\nfrom |Vtd| and |Vts|. For the BABAR result, this was done\nby re-expressing the Unitarity Triangle apex (\u03c1, \u03b7) as a\nfunction of \u03c61 and using the HFAG world-average for \u03c61.\nGiven the current HFAG world-average values of the CKM\ninputs, the theory uncertainty on the ratio R(d\u03b3/s\u03b3) is ex-\npected to be < 0.2%, an order of magnitude smaller than\nthe uncertainty for the exclusive modes prediction.\nThe BABAR analysis (del Amo Sanchez, 2010q) of the\nb \u2192d\u03b3 and b \u2192s\u03b3 inclusive rates used in the calculation\nof |Vtd/Vts| are extrapolated from measurements of the\npartial decay rates to seven exclusive hadronic \ufb01nal states,\nshown in Table 17.9.6, in the mass ranges 0.5 < M(Xd) <\n1.0 GeV/c2 and 1.0 < M(Xd) < 2.0 GeV/c2. The low-mass\nregion contains contributions that are highly correlated\nwith the dataset used for the BABAR exclusive modes anal-\nysis and, in the inclusive analysis, it is assumed that there\nis no non-resonant signal component in this mass range.\nTo obtain the inclusive rates, the experimentally de-\ntermined partial rates must be corrected for the fraction\nof missing \ufb01nal states, as well as for hadronic systems\nwith M(X) > 2.0 GeV/c2. Well-characterized corrections\nfor \ufb01nal states with neutral kaons and non-reconstructed\n\u03c9 \ufb01nal states are made in the low-mass region. In the\nhigh-mass region, the missing fractions depend on the de-\ntails of the fragmentation of the hadronic system, which\nis modeled using Jetset (Sj\u00a8ostrand, 1995) and expected\nto be di\ufb00erent for Xd and Xs. The Kagan-Neubert pho-\nton spectrum model (Kagan and Neubert, 1998) is used to\ncorrect for the mass region above 2.0 GeV/c2 that is not\nmeasured. The photon spectra for b \u2192d\u03b3 and b \u2192s\u03b3\nare expected to be nearly identical, and the uncertainty\nin the extrapolation is mainly from lack of knowledge of\nthe details of the underlying fragmentation process. In the\nhigh-mass region, this is the largest contribution to the to-\ntal systematic uncertainty. BABAR \ufb01nds\nB(b \u2192d\u03b3)\nB(b \u2192s\u03b3) = 0.040 \u00b1 0.009 \u00b1 0.010 ,\n(17.2.22)\nand determines\n\f\f\f\f\nVtd\nVts\n\f\f\f\f = 0.199 \u00b1 0.022 \u00b1 0.024 \u00b1 0.002 ,\n(17.2.23)\nwhere the \ufb01rst error is purely statistical, the second ac-\ncounts for systematic e\ufb00ects including the uncertainty in\nthe extrapolation for the missing mass and \ufb01nal states,\nand the third uncertainty is purely from theory consider-\nations.\nThere is good agreement among the values of |Vtd/Vts|\nobtained from exclusive and inclusive analyses of radia-\ntive penguin processes. The farthest outlier from the cen-\ntral value of |Vtd/Vts| is obtained from the average of the\n\u03c10 mode. However, all results are in reasonable agreement\nwith each other. While the total uncertainty in the cur-\nrent results for the exclusive and inclusive approaches is\ncomparable, the relatively very small inclusive theory un-\ncertainty will make it a more sensitive observable at future\n\ufb02avor facilities that plan to integrate much larger datasets\nthan available at Belle or BABAR. Comparing these results\nwith the |Vtd/Vts| value from mixing, there is also good\nagreement, albeit with substantially larger uncertainties\nfor the radiative decays results. For any future Belle in-\nclusive analysis, it seems reasonable to assume that the\nuncertainty will be similar to that for their exclusive anal-\nysis, just as at BABAR. This would allow for more precise\ncomparisons between |Vtd/Vts| from rare radiative decays\nand from mixing.\n17.2.3 Summary\nA direct determination of |Vts| and |Vtd| from a measure-\nment of the decays t \u2192s and t \u2192d at LHC is di\ufb03-\ncult, and will likely remain so at least in the near future.\nIndirect methods involving virtual top quarks are there-\nfore required to measure these CKM matrix elements. At\nthe B Factories, the FCNC transitions b \u2192s and b \u2192d\nin radiative penguin processes have been used to obtain\nmeasurements of the ratio |Vtd/Vts|, while the value of\n|Vtd| has been obtained from measurements of Bd mixing.\nExtracting the values of the CKM elements from these\nprocesses necessarily assumes there are no contributions\nfrom physics beyond the SM and it is di\ufb03cult to distin-\nguish possible NP contributions, which may enter at the\nsame order as the lowest order SM processes.\nThe major uncertainties in the existing measurements\noriginate from ignorance of the hadronic matrix elements.\nThe current method for extracting |Vtd| and |Vts| from\n\u2206B = \u00b12 processes relies heavily on lattice calculations,\nand any further experimental improvements in \u2206ms/d\nmeasurements will need to be matched by correspond-\ning improvements in the lattice calculations. Likewise, for\nimprovement in the precision of |Vtd| and |Vts| extracted\nfrom radiative penguin processes, signi\ufb01cant advances in\nthe theoretical methods will be necessary.\nExperimentally, it may be possible at future super \ufb02a-\nvor factories to make a fully inclusive branching fraction\nmeasurement of b \u2192d\u03b3, as well as b \u2192s\u2113+\u2113\u2212and b \u2192\nd\u2113+\u2113\u2212, which will help to reduce theory and model depen-\ndences. In b \u2192s\u2113+\u2113\u2212and b \u2192d\u2113+\u2113\u2212decays, additional\namplitudes arise from diagrams similar to Fig. 17.2.1 but\nwith a Z boson replacing the photon (see Section 17.9\nfor a discussion of these modes). Because the contribu-\ntion of these additional electroweak amplitudes becomes\ngreater, and the contribution from the photon pole de-\ncreases, with increasing invariant mass of the di-lepton\n\n220\n\ufb01nal state, extracting |Vtd/Vts| as a function of dilepton\nmass using these decays may allow one to disentangle any\nunderlying new physics contributions from those of the\nSM CKM matrix elements. Finally, if such future facili-\nties obtain enough data at the \u03a5(5S), it may also be pos-\nsible to very cleanly determine |Vtd/Vts| from the ratio of\nbranching fractions for the annihilation penguin processes\nBd \u2192\u03b3\u03b3 and Bs \u2192\u03b3\u03b3 (Bosch and Buchalla, 2002a).\nThese di-photon modes are further discussed below in Sec-\ntion 17.11.\n\n221\n17.3 Hadronic B to charm decays\nEditors:\nRichard Kass (BABAR)\nMartin Beneke (theory)\nAdditional section writers:\nJustin Albert, Vincent Poireau, Stephen Schrenk\n17.3.1 Introduction\nB meson decays into all hadronic \ufb01nal states containing\nopen charm or charmonium account for almost three quar-\nters of all B decays. Despite constituting the majority of\n\ufb01nal states, these decays pose a challenge to both exper-\niment and theory. The large available phase space in a B\nmeson decay means that there are hundreds of possible\n\ufb01nal states all with rather small branching fractions, typi-\ncally a few tenths of a percent. Therefore to study in detail\nany particular \ufb01nal state a very large sample of B mesons\nis necessary as well as a detector capable of measuring\nthe energy, momentum, and identity of the \ufb01nal state\nparticles to high precision. Since these are all hadronic\n\ufb01nal states, decay rate calculations must be done using\nnon-perturbative QCD. For the majority of \ufb01nal states, a\nquantitative prediction with controlled theoretical uncer-\ntainties remains out of reach. Only the decay rates of the\nsimplest hadronic decays to charm, such as B0 \u2192D+\u03c0\u2212,\ncan be calculated from \ufb01rst principles using QCD.\nIn spite of the above drawbacks, hadronic B decays\nto charm play an important role in the more glamorous\naspects of B physics, i.e. the determination of the CKM\nparameters, measurements of CP violation, and search for\nphysics beyond the Standard Model. If for no other reason\nthese decay modes must be measured in order to under-\nstand the possible backgrounds involved in a measurement\nof a CKM parameter. Although the branching fractions\nhere are small, it is still possible to collect very clean sam-\nples of B events using modes such as B \u2192D\u03c0, B \u2192D\u2217\u03c0,\netc. Two-body decays such as D0\u03c0+ and D\u2212\u03c0+ provide\nimportant detector calibration tools for determining mo-\nmentum resolution (\u03c0\u00b1, K\u00b1; see Sections 2.2.2, 6.2), elec-\ntromagnetic energy resolution (\u03c00, \u03b7; see Section 2.2.4),\nmass resolution (D, B; see Chapter 7), secondary ver-\ntex location (D, K0\ns; see Chapter 6), and particle iden-\nti\ufb01cation e\ufb03ciency and rejection (\u03c0/K; see Chapter 5).\nFinally, precision measurements of modes such as B \u2192\nD(\u2217)\u03c0, D(\u2217)\u03c0\u03c0 may serve as standard candles for QCD\ncalculations.\nIn this section we are mainly concerned with decay\nrates and not the speci\ufb01cs of how the \ufb01nal states are recon-\nstructed and the techniques involved. These techniques are\ndescribed in detail in Chapters 7 (B reconstruction), 12\n(angular analysis), and 13 (Dalitz analysis).\n17.3.2 Theory overview\nA \ufb01rst principles calculation of the decay rate of the full set\nof B decays to charm, and even the two-body \ufb01nal states\nonly, is still beyond our capabilities. Instead a variety of\napproaches to these calculations have been tried with var-\nious levels of success. An excellent and still relevant dis-\ncussion of these techniques can be found in Chapters 2\nand 10 of (Harrison and Quinn, 1998). In the following\noverview we cover the generalized factorization approach\nof Bauer, Stech, and Wirbel (1987) (BSW) and Neubert\nand Stech (1998) (NS), and the QCD factorization ap-\nproach (Beneke, Buchalla, Neubert, and Sachrajda, 2000),\nwhich provides a \ufb01rst principles calculation for a limited\nclass of \ufb01nal states.\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afc\n\u00afd\nu\n\u03c0+\n\u00afD0\n|Vcb|\n|Vud|\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afc\n\u00afs\nu\nK+\n\u00afD0\n|Vcb|\n|Vus|\nFigure 17.3.1. Dominant Feynman diagrams contributing to\nthe decays B+ \u2192D0\u03c0+ (top) and B+ \u2192D0K+ (bottom).\nWe begin our discussion with b \u2192c\u00afud transitions. The\ncase of b \u2192c\u00afus is completely analogous. Examples for\nthese transitions are shown in Fig. 17.3.1. A popular and\nuseful approach to calculate decay rates (especially for\ntwo-body B decays) is the factorization ansatz. To under-\nstand this technique, consider the decays that are shown\nin Fig. 17.3.2. In this \ufb01gure only the electroweak contribu-\ntions to the decay amplitudes are shown. A na\u00a8\u0131ve attempt\nto calculate the decay rate would write the matrix ele-\nment in terms of the usual currents, e.g., c\u03b3u(1 \u2212\u03b35)b.\nHowever, this is clearly a drastic approximation as it ne-\nglects the all important role of gluons in the production\nof the \ufb01nal state hadrons. Nevertheless, at this early stage\nof calculation an important distinction becomes apparent.\nThe decay B+ \u2192D0\u03c0+ can proceed through two ampli-\ntudes as shown in Figs 17.3.2a) and b). Since all \ufb01nal state\nparticles must be color singlets, diagram b) will be sup-\npressed due to color matching relative to a) by 1/Nc, with\nNc the number of colors. Amplitudes such as Fig. 17.3.2 a)\nare known as \u201ccolor-allowed\u201d while an amplitude such as\nFig. 17.3.2 b) is often called \u201ccolor-suppressed\u201d. The decay\n\n222\nB0 \u2192D\u2212\u03c0+ shown in Fig. 17.3.2 c) is color-allowed, while\nB0 \u2192D0\u03c00, Fig. 17.3.2 d), is color-suppressed. Although\nnot suitable for a quantitative prediction, the notion of\ncolor suppression provides a useful guide to the hierar-\nchies in the branching fractions of B to charm decays, in\naddition to the hierarchies caused by the CKM elements.\na)\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afc\n\u00afd\nu\n\u03c0+\n\u00afD0\n|Vcb|\n|Vud|\nc)\nB0\n\u0001\nW +\nd\n\u00afb\nd\n\u00afc\n\u00afd\nu\n\u03c0+\nD\u2212\n|Vcb|\n|Vud|\nb)\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afd\nu\n\u00afc\n\u00afD0\n\u03c0+\n|Vud|\n|Vcb|\nd)\nB0\n\u0001\nW +\nd\n\u00afb\nd\n\u00afd\nu\n\u00afc\n\u00afD0\n\u03c00\n|Vud|\n|Vcb|\nFigure 17.3.2. Two-body Feynman diagrams contributing to\nthe B+ \u2192D0\u03c0+ (a, b) and B0 \u2192D\u03c0 (c, d) decays.\nFor a more detailed discussion we recall the e\ufb00ective\nHamiltonian\nHe\ufb00= GF\n\u221a\n2 VcbV \u2217\nud\n( \u0012\nC1 + C2\nNc\n\u0013\n[cibi]V\u2212A[dkuk]V\u2212A\n+ 2C2 [ciT a\nijbj]V\u2212A[dkT a\nklul]V\u2212A\n)\n(17.3.1)\nfor the b \u2192cud transition. Here C1 and C2 are Wilson\ncoe\ufb03cients that account for short-distance QCD e\ufb00ects\nand Eq. (17.3.1) includes the color indices i, j, k, l. In the\nna\u00a8\u0131ve factorization approach the \u27e8D+\u03c0\u2212|He\ufb00|B0\u27e9matrix\nelement is separated into currents by inserting the QCD\nvacuum state, which ignores all long-distance QCD inter-\nactions between the currents. Applied to B0 \u2192D+\u03c0\u2212\n(B0 \u2192D\u2212\u03c0+ in Fig. 17.3.2c) the \u201cfactorized\u201d matrix el-\nement is now:\nGF\n\u221a\n2 VcbV \u2217\nud a1 \u27e8D+|c\u03b3\u00b5(1 \u2212\u03b35)b|B0\u27e9\u27e8\u03c0\u2212|d\u03b3\u00b5(1 \u2212\u03b35)u|0\u27e9\n(17.3.2)\nwith a1 = C1 + C2/Nc. The matrix element of the color-\noctet operator is set to zero in the factorization approxi-\nmation. Decays which involve this combination of Wilson\ncoe\ufb03cients are often called color-allowed or Type I transi-\ntions. In addition there are also color-suppressed (or Type\nII) transitions. As an example B0 \u2192D0\u03c00 is illustrated\nin Fig. 17.3.2 d). Here one \ufb01rst uses a so-called Fierz iden-\ntity [\u03c81\u03c82]V\u2212A[\u03c83\u03c84]V\u2212A = [\u03c83\u03c82]V\u2212A[\u03c81\u03c84]V\u2212A to re-\narrange the four-fermion operators in He\ufb00into the form\n[db]V\u2212A[cu]V\u2212A. Then the factorized amplitude similar to\nEq. (17.3.2) for this process is\nGF\n\u221a\n2 VcbV \u2217\nud a2 \u27e8\u03c00|d\u03b3\u00b5(1 \u2212\u03b35)b|B0\u27e9\u27e8D0|c\u03b3\u00b5(1 \u2212\u03b35)u|0\u27e9,\n(17.3.3)\nwhere now a2 = C2 + C1/Nc. Finally there are decay\nmodes such as B+ \u2192D0\u03c0+ (Fig. 17.3.2 a) and b)) which\nare a combination of color-allowed and color-suppressed\namplitudes. These decays are called \u201cType III\u201d processes.\nIn the absence of any QCD e\ufb00ects, C1 = 1 and C2 =\n0, and we recover the estimate based on color-matching.\nShort-distance QCD e\ufb00ects renormalize the Wilson coef-\n\ufb01cients, such that at the mass scale \u00b5 = mb = 4.8 GeV\nwe have a1 \u22481 and a2 \u22480.2. The value of a2 is strongly\nscale-dependent. The uncanceled scale-dependence of the\nphysical amplitude is a clear manifestation of the short-\ncomings of the na\u00a8\u0131ve factorization approach. As we discuss\nbelow, factorization is expected to work more reliably for\nthe color-allowed amplitude.\nIn applying Eqs (17.3.2) and (17.3.3) the matrix ele-\nments with the quarks are usually written in the familiar\nforms:\n\u27e8\u03c0|d\u03b3\u00b5\u03b35u|0\u27e9= \u2212if\u03c0q\u00b5\n(17.3.4)\n\u27e8D|c\u03b3\u00b5b|B\u27e9= f+(q2)(pB + pD)\u00b5 + f\u2212(q2)q\u00b5.\n(17.3.5)\nHere q = pB \u2212pD where pD and pB are the D and B\n4-momentum respectively and q2 = m2\n\u03c0. The parameter-\nization of the matrix elements in terms of the pion de-\ncay constant f\u03c0 and two B \u2192D transition form factors\nfollows from the spin and parity transformations of the\nmeson states and current operators, and Lorentz invari-\nance. Thus using the factorization approach, the ampli-\ntude Eq. (17.3.2) for B0 \u2192D+\u03c0\u2212can now be written\nconveniently as:\n\u2212iGF\n\u221a\n2 VcbV \u2217\nuda1f\u03c0f+(m2\n\u03c0)(m2\nB \u2212m2\nD).\n(17.3.6)\nThe pion decay constant and B \u2192D form factor must be\ndetermined by other methods or from data (for the latter\nsee Section 17.1.2).\na)\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afc\n\u00afs\nc\nD+\ns\n\u00afD0\n|Vcb|\n|Vcs|\nb)\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afc\nc\n\u00afs\nD+\ns\n\u00afD0\nFigure 17.3.3. Spectator a) and penguin b) diagrams con-\ntributing to B+ \u2192D+\ns D.\nThis formalism can also be applied to b \u2192ccs (and\nthe Cabibbo-suppressed b \u2192ccd) transitions. The color-\nallowed amplitude leads to \ufb01nal states such as B \u2192DD\n\n223\nand B \u2192DDs with two charmed mesons. The color-\nsuppressed amplitude produces a charmonium. The mo-\nmentum transfer q2 is now large, approximately m2\nD, and\ntherefore both form factors (f+, f\u2212) appear in the decay\namplitude, which, e.g., for B+ \u2192D0D+\ns is now given by:\nAtree = \u2212iGF\n\u221a\n2 VcbV \u2217\ncsa1 fDsf+(m2\nDs)(m2\nB \u2212m2\nD) F\nwith\nF = 1 +\nf\u2212(m2\nDs)m2\nDs\n(m2\nB \u2212m2\nD)f+(m2\nDs) .\n(17.3.7)\nAs shown in Fig. 17.3.3, these decays include contributions\nfrom penguin diagrams, since they contain two quarks\nwith identical \ufb02avor. However, the penguin operator coef-\n\ufb01cients (C3, C4, C5, C6) in the e\ufb00ective Hamiltonian are\nall small, of the order of a few percent. The amplitude can\nbe written as the sum of two pieces, Atree and Apeng:\nA(B \u2192DD) = Atree + Apeng,\n(17.3.8)\nwith an estimate |Apeng| < 0.1|Atree|. It is important to\nnote that while the decay rate is hardly changed by in-\ncluding the penguin contributions they are essential for\nthe observation of direct CP-violating asymmetries (see\nSection 16.6).\nA phenomenological approach to predict the branching\nfractions of hadronic B decays that incorporates factoriza-\ntion is followed in Bauer, Stech, and Wirbel (1987) (BSW)\nand Neubert and Stech (1998) (NS). In this approach the\nQCD e\ufb00ects and Wilson coe\ufb03cients are captured by two\nphenomenological parameters, a1 and a2. Here a1 repre-\nsents the factor for decay modes that proceed via Type I\n(color-favored) amplitudes while a2 is the corresponding\nfactor for Type II (color-suppressed) amplitudes. Decay\namplitudes that have contributions from both Type I and\nII amplitudes (Type III) contain a linear combination of\na1 and a2. The values of a1 and a2 are determined from\n\ufb01ts to measured B decay rates. For B meson decays the\nrelative phase between a1 and a2 turns out to be positive,\nwhich implies constructive interference in the Type III\ndecays. These constants, once determined, are assumed to\napply universally to all two-body hadronic B \ufb01nal states.\nTable 17.3.1 gives predictions from this model for sev-\neral Type I, II, and III B decay modes as well as the\ncurrent PDG (Beringer et al., 2012) values (dominated by\nBABAR and Belle results) for the corresponding branching\nfractions. The model reproduces well the Type I (color-\nfavored) measurements as well as the Type III where the\na1 term dominates the amplitude. Not surprisingly, the\nType II predictions di\ufb00er considerably for some of the de-\ncay modes. In particular, the NS model predictions for\nthe K(\u2217)\u03c8\u2032 di\ufb00er by a factor of two from the experimental\nmeasurements. For the K\u03c8\u2032 modes, the prediction is half\nthe measurement while for the K\u2217\u03c8\u2032 modes the prediction\nis twice the measurement.\nA generalization of factorization can indeed be rig-\norously derived from the \ufb01rst principles of QCD for the\ncolor-allowed amplitude of \ufb01nal states with one charmed\nmeson (Beneke, Buchalla, Neubert, and Sachrajda, 2000).\nThe physical picture is that of color transparency (Bjorken,\n1989): in the heavy-quark mass limit, the light meson (e.g.\nthe pion) is emitted as a compact color-singlet object with\nlarge momentum from the B \u2192D transition region. In the\nQCD factorization approach of BBNS (Beneke, Buchalla,\nNeubert, and Sachrajda, 2000) the coe\ufb03cient a1 is written\nas\na1(M) =\nX\ni=1,2\nCi\nZ 1\n0\ndu Ti(u)\u03a6M(u),\n(17.3.9)\nup to 1/mb corrections, where \u03a6M denotes the light-cone\ndistribution amplitude of the light meson, which, roughly\nspeaking, describe how the longitudinal momentum of the\nenergetic meson M is shared between the quark and an-\ntiquark in the meson, and Ti(u) is a function that can be\ncalculated order by order in the strong coupling \u03b1S(mb).\nAt tree level, the QCD factorization result reproduces\nna\u00a8\u0131ve factorization. At the one-loop order, the previously\nneglected matrix element of the color-octet operator in\nEq. (17.3.1) is now non-zero, and leads to a consistent\ncancellation of the renormalization scale dependence. A\nconsequence of this is that a1 is non-universal, and de-\npends on the light \ufb01nal state meson M. However, the non-\nuniversality is small, a few percent, as is the correction to\nna\u00a8\u0131ve factorization. In Table 17.3.1, the decay modes la-\nbeled \u201cType I\u201d receive small corrections to factorization,\nsee (Beneke, Buchalla, Neubert, and Sachrajda, 2000).\nUnfortunately, the color-suppressed amplitude a2 in\nheavy-light \ufb01nal states and the color-allowed amplitude\nin all \ufb01nal states with two charmed mesons, are not ac-\ncessible to a rigorous factorization treatment. Counting\npowers of the small quantity \u039bQCD/mb shows that the\ncolor-suppressed amplitude in B \u2192D\u03c0 and related de-\ncays is 1/mb suppressed, but the parametric suppression\nfrom the form factors and decay constants is not opera-\ntive in practice. This implies that contrary to the Type I\ndecays, there are no \ufb01rst-principles calculations of Type\nII and III modes. The same statement applies to the cal-\nculation of CP-violating charge asymmetries in decays to\ntwo charmed mesons.\nIt is instructive to compare the Type I, II, and III\namplitudes for the B \u2192D\u03c0 \ufb01nal states. In complete gen-\nerality, we may write\nA(B0 \u2192D+\u03c0\u2212) = T + A,\n(17.3.10)\n\u221a\n2 A(B0 \u2192D0\u03c00) = C \u2212A,\n(17.3.11)\nA(B\u2212\u2192D0\u03c0\u2212) = T + C,\n(17.3.12)\nwhere T stands for the \u201ccolor-allowed tree topology\u201d, C\nfor \u201ccolor-suppressed tree topology\u201d, and A for \u201cannihi-\nlation topology\u201d. Since the three \ufb01nal states are related\nby exchanges of up and down quark, and since the cor-\nresponding SU(2) isospin symmetry is a very good ap-\nproximate symmetry of the QCD Lagrangian, only two of\nthe three amplitudes are independent. The isospin rela-\ntion A(B0 \u2192D+\u03c0\u2212) +\n\u221a\n2 A(B0 \u2192D0\u03c00) + A(B\u2212\u2192\nD0\u03c0\u2212) = 0 allows one to regard (T + A) and (C \u2212A)\n\n224\nTable 17.3.1. Predictions of branching fractions of the Neubert & Stech (NS) model (Neubert and Stech, 1998) using a1 = 0.98\nand a2 = 0.29 and comparisons with the PDG (Beringer et al., 2012) values.\nDecay mode\nNS Model\nBtheo(\u00d710\u22123)\nPDG B(\u00d710\u22123)\nType I\nD\u2212\u03c0+\n0.318a2\n1\n3.0\n2.68\u00b10.13\nD\u2212K+\n0.025a2\n1\n0.2\n0.197\u00b10.021\nD\u2212\u03c1+\n0.778a2\n1\n7.5\n7.8\u00b11.3\nD\u2212K\u2217+\n0.041a2\n1\n0.4\n0.45\u00b10.07\nD\u2212a+\n1\n0.844a2\n1\n8.1\n6.0\u00b12.2\u00b12.4\nD\u2217\u2212\u03c0+\n0.296a2\n1\n2.8\n2.76\u00b10.13\nD\u2217\u2212K+\n0.022a2\n1\n0.2\n0.214\u00b10.016\nD\u2217\u2212\u03c1+\n0.870a2\n1\n8.4\n6.8\u00b10.9\nD\u2217\u2212K\u2217+\n0.049a2\n1\n0.5\n0.33\u00b10.06\nD\u2217\u2212a+\n1\n12.17a2\n1\n11.6\n13.0\u00b12.7\nType II\nD0\u03c00\n0.084a2\n2\n0.07\n0.263\u00b10.014\nK0J/\u03c8\n0.800a2\n2\n0.7\n0.871\u00b10.032\nK+J/\u03c8\n0.852a2\n2\n0.7\n1.013\u00b10.034\nK0\u03c8\u2032\n0.326a2\n2\n0.3\n0.62\u00b10.05\nK+\u03c8\u2032\n0.347a2\n2\n0.3\n0.639\u00b10.033\nK\u22170J/\u03c8\n2.518a2\n2\n2.1\n1.33\u00b10.06\nK\u2217+J/\u03c8\n2.680a2\n2\n2.3\n1.43\u00b10.08\nK\u22170\u03c8\u2032\n1.424a2\n2\n1.2\n0.61\u00b10.05\nK\u2217+\u03c8\u2032\n1.516a2\n2\n1.3\n0.67\u00b10.14\n\u03c00J/\u03c8\n0.018a2\n2\n0.02\n0.0176\u00b10.0016\n\u03c0+J/\u03c8\n0.038a2\n2\n0.03\n0.049\u00b10.004\n\u03c10J/\u03c8\n0.050a2\n2\n0.04\n0.027\u00b10.004\n\u03c1+J/\u03c8\n0.107a2\n2\n0.09\n0.050\u00b10.008\nType III\nD0\u03c0+\n0.338(a1 + 0.729a2(fD/200 MeV))2\n4.8\n4.84\u00b10.15\nD0\u03c1+\n0.828(a1 + 0.450a2(fD/200 MeV))2\n10.2\n13.4\u00b11.8\nD\u22170\u03c0+\n0.315(a1 + 0.886a2(fD\u2217/230 MeV))2\n4.8\n5.19\u00b10.26\nD\u22170\u03c1+\n0.926(a2\n1 + 0.456a2\n2(fD\u2217/230 MeV)2 + 1.291a1a2(fD\u2217/230 MeV))\n12.6\n9.8\u00b11.7\nD\u22170a+\n1\n1.296(a2\n1 + 0.128a2\n2(fD\u2217/230 MeV)2 + 0.269a1a2(fD\u2217/230 MeV))\n13.6\n19\u00b15\nas the two independent amplitudes. These amplitudes are\ncomplex due to strong-interaction phases from \ufb01nal-state\ninteractions. Only the relative phase of the two indepen-\ndent amplitudes is an observable. We de\ufb01ne \u03b4T C to be the\nrelative phase of (T + A) and (C \u2212A). The QCD factor-\nization formula implies that (Beneke, Buchalla, Neubert,\nand Sachrajda, 2000)\n\f\f\f\f\nC \u2212A\nT + A\n\f\f\f\f = O(\u039bQCD/mb),\n\u03b4T C = O(1).\n(17.3.13)\nTreating the charm meson as a light meson compared to\nthe scale mb, one \ufb01nds that it is not di\ufb03cult to accom-\nmodate |C \u2212A|/|T + A| \u223c0.2 \u22120.3 and a large phase\n\u03b4T C \u223c40\u25e6, which is in qualitative agreement with ex-\nperimental results. The large phase shows that large cor-\nrections to na\u00a8\u0131ve factorization must be expected for the\ncolor-suppressed amplitude in heavy-light decays.\nThe situation for B decays to charmonium is ambigu-\nous. QCD factorization formally holds for these decays de-\nspite their color suppression, since the \u201cemitted\u201d charmo-\nnium is a compact object (Beneke, Buchalla, Neubert, and\nSachrajda, 2000). However, various corrections from soft\ngluon reconnections (Melic, 2004) and color-octet contri-\nbutions (Beneke and Vernazza, 2009) turn out to be very\nlarge relative to the formally dominant color-suppressed\namplitude, and prevent a reliable prediction. One should\ntherefore expect large corrections to the na\u00a8\u0131ve factoriza-\ntion and generalized factorization (BSW) estimates of\nthese decay modes, as is indeed observed. Again, these\nuncertainties prevent a reliable calculation of the (small)\nCP-violating charge asymmetries for \ufb01nal states such as\nK\u03c8.\n\n225\nWhile the BSW/NS approach to factorization and the\nQCD factorization approach (where applicable) provides\nestimates in agreement with many measured branching\nfractions, extending this technique to decays with more\nthan two particles in the \ufb01nal state (e.g. B \u2192D\u03c0\u03c0 or\nB0 \u2192D\u2217\u2212\u03c0+\u03c0+\u03c0\u2212\u03c00) is not nearly as successful. A fun-\ndamental problem here is that some of the \ufb01nal state par-\nticles are the result of gluons and therefore the role of\nQCD can not be ignored. In (Reader and Isgur, 1993) the\nproblem of multi-body decays with D\u2019s and \u03c0\u2019s in the \ufb01-\nnal state is discussed using results from heavy-quark sym-\nmetry and factorization. Here the decay process proceeds\nthrough intermediate states such as D\u03c1 or D\u2217\n2\u03c0 and the\ncontributions are summed to obtain the total branching\nfraction. Unfortunately, for many of the modes mentioned\nin (Reader and Isgur, 1993) and Table 17.3.2, precision\nmeasurements are lacking, making a detailed comparison\nnot possible. In Table 17.3.2 the entries with a \u201c>\u201d indi-\ncate modes where only an intermediate state and not the\nexplicit \ufb01nal state has been measured. In these cases the\nmeasured branching fraction of the intermediate state is\ntaken as the lower limit of the branching fraction of the\nmode of interest. An example of such a mode is D0\u03c0+\u03c00\nwhere only the intermediate state D0\u03c1+ has been mea-\nsured. For this mode we note that their model\u2019s prediction\nfor B+ \u2192D0\u03c0+\u03c00 of 0.59% is signi\ufb01cantly lower than the\nmeasured 1.34 \u00b1 0.18% for D0\u03c1+.\nTable 17.3.2. Branching fraction predictions of the RI model\n(Reader and Isgur, 1993) and comparisons with the PDG (Be-\nringer et al., 2012) values. The entries with a \u201c>\u201d indicate\nmodes where only an intermediate state and not the explicit\n\ufb01nal state has been measured. The measured branching frac-\ntion of the intermediate state is taken as the lower limit of the\nbranching fraction of the mode of interest.\nDecay mode\nRI Model\nPDG\nB (\u00d710\u22123)\nB (\u00d710\u22123)\nD\u2212\u03c0+\u03c00\n5.9\n> 7.8\u00b10.13\nD\u2212\u03c0+\u03c0\u2212\n0.7\n0.84\u00b10.09\nD0\u03c0+\u03c00\n5.9\n> 13.4\u00b11.8\nD\u2212\u03c0+\u03c0+\n0.7\n1.07\u00b10.05\nD\u2217\u2212\u03c0+\u03c00\n7.5\n15\u00b15\nD\u22170\u03c0+\u03c0\u2212\n1.1\n0.62\u00b10.22\nD\u22170\u03c0+\u03c00\n7.5\n> 9.8\u00b11.7\nD\u2217\u2212\u03c0+\u03c0+\n1.1\n1.35\u00b10.22\nD\u2212\u03c0+\u03c0+\u03c0\u2212\n2.1\n8.0\u00b12.5\nD0\u03c0+\u03c0+\u03c0\u2212\n2.1\n11\u00b14\nD\u2217\u2212\u03c0+\u03c0+\u03c0\u2212\n2.9\n> 13\u00b13\nD\u2217\u2212\u03c0+\u03c0+\u03c00\n2.2\n15\u00b17\n17.3.3 Decays with a single D decay (D, D\u2217, Ds)\nDue to the experiments at the B Factories there has been\nan enormous increase in both the number of single charm\nmodes reconstructed and the precision of their branching\nfractions. As shown in Tables 17.3.3 and 17.3.4 the typi-\ncal branching fractions for decay modes in this category\nare in the few tenths of a percent for the modes with a\nW \u2192ud transition and an order of magnitude smaller\nfor modes with a W \u2192us transition. In Fig. 17.3.1 the\nsimplest diagrams for B+ \u2192D0\u03c0+ and B+ \u2192D0K+ are\nshown. Including the CKM factors Vud and Vus at the rel-\nevant vertices explains the dominance of the pion modes\nover the kaon modes. Other mechanisms such as color-\nsuppression can play an important role in simple two-body\n\ufb01nal states such as D0\u03c00 (Fig. 17.3.2 d). It is important\nto note that although these diagrams contain only pseu-\ndoscalars in the \ufb01nal state it is also likely that the quarks\nwill hadronize into vector particles. Thus the D\u2019s can be\nreplaced with D\u2217\u2019s, \u03c0\u2019s with \u03c1\u2019s, K\u2019s with K\u2217\u2019s, etc. Fi-\nnally, the hadronization process also allows for more com-\nplicated \ufb01nal states such as D0K+K\u2217, D\u2217\u22123\u03c0+\u03c0\u2212, etc.\n17.3.3.1 Two body \ufb01nal states\nIn this section we do not consider the kaon \ufb01nal states (e.g.\nD0K+) as they are discussed in detail in Section 17.8 due\nto their important role in determining \u03c63.\nColor-favored\ntwo-body\ndecay\nmodes,\nD(\u2217)\u2212\u03c0+,\nD(\u2217)0\u03c0+, were studied in (Aubert, 2007g) using approx-\nimately one quarter of the \ufb01nal BABAR \u03a5(4S) data sam-\nple. These \ufb01nal states are such that even with relatively\nsimple selection criteria (e.g. only using D0 \u2192K+\u03c0\u2212and\nD\u2212\u2192K+\u03c0\u2212\u03c0\u2212), high purity samples are obtained. To il-\nlustrate the quality (i.e. very large signal to background)\npossible in hadronic B decays into charm we show the\nbeam-energy-substituted mass plots (mES) from (Aubert,\n2007g) in Fig. 17.3.4. In all modes the systematic errors\nare at least a factor of two larger than the statistical\nerrors. In general, there is good agreement between the\nmodel predictions in Table 17.3.1 and the branching frac-\ntion measurements from this study.\nColor-suppressed two-body decay modes have been ex-\ntensively studied in (Lees, 2011b; Blyth, 2006; Kuzmin,\n2007; Schumann, 2005). In the most comprehensive study\n(Lees, 2011b) eight modes (D(\u2217)0X, X = \u03c00, \u03b7, \u03c9, \u03b7\u2032) are\nanalyzed and their branching fractions measured. The re-\nsults of this study are in agreement with previous BABAR\nand Belle measurements, although with higher precision.\nThe improved precision in the branching fractions allows\nfor a detailed comparison with predictions from factor-\nization models (Chua, Hou, and Yang, 2002; Deandrea\nand Polosa, 2002; Eeg, Hiorth, and Polosa, 2002; Neubert\nand Stech, 1998) and perturbative QCD (pQCD) (Keum,\nKurimoto, Li, Lu, and Sanda, 2004; Lu, 2003). There is\npoor agreement with the factorization predictions; in most\ncases the measurements are signi\ufb01cantly larger than the\nexpectation. In contrast, with the exception of D0\u03c9 where\nthe measurement is signi\ufb01cantly lower than the prediction,\n\n226\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n100\n200\n300\n400\n500\n600\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n100\n200\n300\n400\n500\n600\n(a)\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n50\n100\n150\n200\n250\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n50\n100\n150\n200\n250\n(b)\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n(c)\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n)\n2\n (GeV/c\nES\nm\n5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3\n)\n2\nEvents/(MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n(d)\nFigure 17.3.4. The mES distributions for (a) B0 \u2192D\u2212\u03c0+,\n(b) B0 \u2192D\u2217\u2212\u03c0+, (c) B+ \u2192D0\u03c0+, and (d) B+ \u2192D\u22170\u03c0+\n(from Aubert, 2007g). In the \ufb01gures the solid line is the \ufb01t to\nthe data while the background component (including peaking\nbackground) is shown as a dashed line.\nexperiment and pQCD are close. These di\ufb00erences should\nnot come as a surprise since there is no rigorous QCD\napproach to the color-suppressed amplitude, as discussed\nin the theory overview of this chapter. The experimen-\ntal results along with the model predictions are given in\nTable VII of Lees (2011b).\nB meson decay provides a convenient laboratory to\nstudy orbitally excited states of the D meson. For the case\nwhere a light quark is bound to a c quark, heavy quark\ne\ufb00ective theory (HQET) suggests that j = L + sl with\nsl the total angular momentum of the light quark and L\nthe orbital angular momentum of the cq system will be a\ngood quantum number. As a result, four L = 1 states are\nexpected with total angular momentum and parity (JP ),\nand j values of 0+ (j = 1/2), 1+ (j = 1/2), 1+ (j = 3/2),\nand 2+ (j = 3/2). These states are known as the D\u2217\n0, D\u2032\n1,\nD1, and D\u2217\n2 respectively. The states in the mass range\nof 2.2-2.8 GeV/c2 are often collectively referred to as the\nD\u2217\u2217. Both BABAR and Belle have studied these states in\ndetail using both speci\ufb01c decay channels (Aubert, 2006p;\nAbe, 2005i) and Dalitz plot analyses of B+ \u2192D\u2212\u03c0+\u03c0+\nand B0 \u2192D0\u03c0+\u03c0\u2212(Abe, 2004f; Kuzmin, 2007; Aubert,\n2009g). In addition to branching fraction measurements\nthese studies have also determined the masses and widths\nof these states. The results are in good agreement with\nthe expectations of HQET. More details on those mea-\nsurements can be found in Section 19.3.\nA variety of \ufb01nal states with a Ds or D\u2217\ns in addi-\ntion to a scalar or vector meson were the subject of sev-\neral studies by BABAR (Aubert, 2007l, 2008u) and Belle\n(Das, 2010; Joshi, 2010). These decays are of interest as\nthey can proceed via color-suppressed W exchange (e.g.\nB0 \u2192D(\u2217)\u2212\ns\nK(\u2217)+), and assuming SU(3) \ufb02avor symmetry\ncan be used to calculate the amplitude ratio r(D(\u2217)\u03c0) =\n|A(B0 \u2192D(\u2217)+\u03c0\u2212)|/|A(B0 \u2192D(\u2217)\u2212\u03c0+)|, an important\nparameter for the determination of sin(2\u03c61 + \u03c63) using\nB0 \u2192D\u2213\u03c0\u00b1. As shown in Tables 17.3.3 and 17.3.4 the\nbranching fractions into D(\u2217)\ns X states are small, a few\ntimes 10\u22125, as expected from CKM factors and the ev-\nident lack of rescattering in the W exchange modes. As\npredicted in Mantry, Pirjol, and Stewart (2003) the ra-\ntios B(B0 \u2192D\u2212\ns K+)/B(B0 \u2192D\u2217\u2212\ns K+) and B(B0 \u2192\nD\u2212\ns K\u2217+)/B(B0 \u2192D\u2217\u2212\ns K\u2217+) are consistent with one\nwithin the experimental uncertainties.\n17.3.3.2 Three or more body \ufb01nal states\nGiven the large phase space available and mean charged\nmultiplicity of almost six in B meson decay, \ufb01nal states\nwith three or more particles make up a sizable amount\nof hadronic B decays. The branching fractions for many\nof the modes of the form B \u2192D(\u2217)(n\u03c0), n = 2 \u22125\ncharged pions have been measured in (Aubert, 2009g)\nand (Abe, 2005i; Majumder, 2004). The analysis in (Ma-\njumder, 2004) illustrates a di\ufb03culty with \ufb01nal states in-\nvolving a large number of particles, i.e. systematic errors\nfrom track \ufb01nding dominate in such high multiplicity de-\ncays. It is also interesting to note the absence of branching\nfraction measurements with multiple \u03c00s (i.e. not a decay\nproduct of a D(\u2217)) in the \ufb01nal state.\nThe three-body decay, B0 \u2192D\u2217\u2212\u03c9\u03c0+, has been used\nto study factorization in Aubert (2006ay). As discussed\nin Reader and Isgur (1993) and Ligeti, Luke, and Wise\n(2001) the factorization approach allows data from \u03c4 \u2192\nX\u03bd to be used to predict the properties of decays such as\nB \u2192D\u2217X, where X is the same hadronic system in both\ndecays. The invariant mass spectrum of the \u03c9\u03c0 system\nwas found to be in good agreement with the theoretical\nexpectations based on factorization and \u03c4 decay data. In\naddition, a Dalitz plot analysis shows a non uniform dis-\ntribution with a preference for \u03c9\u03c0 at low mass. A broad\nenhancement in the D\u2217\u03c0 system at about 2.5 GeV/c2 may\nindicate the presence of B0 \u2192D\u2032\n1\u03c9. Finally, the longitu-\ndinal polarization of the D\u2217was found to be in agreement\nwith expectations of HQET.\nThree-body decays with charged and neutral kaons as\nwell as K\u2217s in the \ufb01nal state were studied in (Drutskoy,\n2002). Even though only 29.4 fb\u22121 of data was used here\n(a small fraction of Belle\u2019s \ufb01nal data sample) \ufb01ve modes\nof the form B \u2192D(0)KK(\u2217)0 were observed for the \ufb01rst\ntime. An angular analysis of the KK\u2217system is consistent\nwith the assignment JP = 1+ and that the decay mainly\nproceeds through an a1(1260) intermediate state.\nThe branching fraction and resonant substructure of\nthe CKM-favored mode B0 \u2192D0K+\u03c0\u2212(not including\nthe D\u2217) was determined in (Aubert, 2006n). A motiva-\ntion for studying this decay was to gain access to \u03c63\nthrough the interference of the b \u2192cus and b \u2192ucs\namplitudes and use the Dalitz plot to reduce the ambi-\nguity in the strong phase. Unfortunately, the branching\nfraction turned out to be too small to be of practical use\n\n227\nin determining \u03c63 with the \ufb01nal BABAR and Belle data\nsamples.\nDecays of the type B \u2192D(\u2217)\ns K\u03c0 can proceed through\nthe production of an ss pair \u201cpopping\u201d out of the vacuum.\nThree such modes (D\u2212\ns K+\u03c0+, D\u2217\u2212\ns K+\u03c0+, and D\u2212\ns K0\ns\u03c0+)\nas well as the CKM suppressed D\u2212\ns K+K+ mode were ob-\nserved in (Aubert, 2008ai). The \ufb01rst two modes were also\nstudied by Belle (Wiechczynski, 2009). Both groups \ufb01nd\nthat the invariant mass distributions of the D(\u2217)\ns K+ sub-\nsystem are incompatible with three-body phase space and\nwith enhancements near 2.7 GeV/c2, suggestive of charm\nresonances below the D(\u2217)\ns K+ threshold.\n17.3.4 Decays with 2 D\u2019s\n17.3.4.1 W \u2192c \u00afd\nIn the neutral B \u2192D(\u2217)+D(\u2217)\u2212decays, the interference\nof the dominant tree diagram (see Fig. 17.3.5 a) with the\nB0B0 mixing diagram is sensitive to the CKM phase \u03c61 .\nHowever, the theoretically uncertain contributions of pen-\nguin diagrams (Fig. 17.3.5 b) with di\ufb00erent weak phases\nare potentially signi\ufb01cant and may shift both the observed\nCP asymmetries and the branching fractions by amounts\nthat depend on the ratios of the penguin to tree contribu-\ntions and their relative phases.\nThe penguin-tree interference in neutral and charged\nB \u2192D(\u2217)D(\u2217) decays can also provide some sensitivity to\nthe angle \u03c63, with additional information on the branching\nfractions of B \u2192D(\u2217)\ns D(\u2217) decays, assuming SU(3) \ufb02avor\nsymmetry between B \u2192D(\u2217)D(\u2217) and B \u2192D(\u2217)\ns D(\u2217).\nThe color-suppressed decay modes B0 \u2192D(\u2217)0D(\u2217)0,\nif observed, would provide evidence of W-exchange or an-\nnihilation contributions (see Fig. 17.3.5 c, 17.3.5 d). In\nprinciple, these decays could also provide sensitivity to\nthe CKM phase \u03c61, if su\ufb03cient data were available.\nThe most precise published results on D(\u2217)D(\u2217) de-\ncays from the B Factories use exclusive reconstruction\nof these decays: all tracks and neutral energy from each\nof the decay chain products is reconstructed, and the\nreconstructed B meson is ultimately composed from\nthese charged tracks and clusters. The D mesons are re-\nconstructed in their decays to some or all of the fol-\nlowing: D0 \u2192K\u2212\u03c0+, K\u2212\u03c0+\u03c00, K\u2212\u03c0+\u03c0+\u03c0\u2212, K+K\u2212,\nK0\nS\u03c0+\u03c0\u2212, K0\nS\u03c0+\u03c0\u2212\u03c00; and D+\n\u2192\nK0\nS\u03c0+, K0\nS\u03c0+\u03c00,\nK0\nSK+, K\u2212\u03c0+\u03c0+, K\u2212K+\u03c0+. The D\u2217+ mesons are then\nreconstructed in their decays to D0\u03c0+ or D+\u03c00. Charge\nconjugate decays are of course implied throughout. As\nthe product branching fractions of these decays are small\n(O(10\u22127 \u221210\u22126)) particular attention must be paid to\nparticle identi\ufb01cation as well as background rejection, de-\ntails of which can be found in Chapters 5 (charged particle\nidenti\ufb01cation) and 9 (background suppression). An exam-\nple of an mES distribution with good signal-to-background\nis shown in Fig. 17.3.6.\nBoth BABAR and Belle have several results for these\ndecays. The branching fraction results, as well as corre-\na)\nB0,B+\nW\nd, u\n\u00afb\nd, u\n\u00afc\nc\n\u00afd\nD(\u2217)+\nD(\u2217)\u2212or\nD(\u2217)0\nb)\nB0,B+\nW\n\u00aft\nd, u\n\u00afb\nd, u\n\u00afc\nc\n\u00afd\nD(\u2217)+\nD(\u2217)\u2212or\nD(\u2217)0\nc)\nB0\nW\nd\n\u00afb\nc\n\u00afu, \u00afd\nu, d\n\u00afc\nD(\u2217)0 or D(\u2217)\u2212\nD(\u2217)0 or D(\u2217)+\nd)\nB0\nW\nd\n\u00afb\nc\n\u00afu, \u00afd\nu, d\n\u00afc\nD(\u2217)0 or D(\u2217)\u2212\nD(\u2217)0 or D(\u2217)+\nFigure 17.3.5.\nFeynman graphs for B \u2192D(\u2217)D(\u2217) decays:\nthe tree (a) and penguin (b) diagrams are the leading terms\nfor both B0 \u2192D(\u2217)+D(\u2217)\u2212and B+ \u2192D(\u2217)+D(\u2217)0 decays,\nwhereas the exchange (c) and annihilation (d) diagrams (the\nlatter of which is OZI-suppressed) are the lowest-order terms\nfor B0 \u2192D(\u2217)0D(\u2217)0 decays.\nsponding theoretical predictions, are summarized in Ta-\nble 17.3.5.\nIn addition to the branching fractions (and to the time-\ndependent CP asymmetries, detailed in Section 17.6), CP-\nviolating charge asymmetries can be measured in the four\ncharged B \u2192D(\u2217)D(\u2217) decays as well as in B0 \u2192D\u2217\u00b1D\u2213,\nand also polarization can be measured in the vector-vector\ndecays B0 \u2192D\u2217+D\u2217\u2212and B+ \u2192D\u2217+D\u22170. Those results\nare summarized in Tables 17.3.6 and 17.3.7 respectively.\nThe Cabibbo-favored D(\u2217)\ns D(\u2217) decays (which can oc-\ncur via tree and penguin diagrams analogous to those\nin Fig. 17.3.5a and b, each with the upper d replaced\nwith an s) typically have branching fractions an order of\nmagnitude higher than their D(\u2217)D(\u2217) analogues, i.e. in\nthe O(10\u22123 \u221210\u22122) range rather than O(10\u22124 \u221210\u22123).\nThe measured and predicted branching fractions for these\nmodes can be found in Table 17.3.8, and measured and\npredicted polarizations can be found in Table 17.3.9.\n\n228\nTable 17.3.3. Measured single charm B+ branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al., 2012)\n(average). The PDG value may use measurements from other experiments when calculating the average.\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nD0\u03c0+\n4.90 \u00b1 0.07 \u00b1 0.22\n(Aubert, 2007g)\n4.84 \u00b1 0.15\nD0K+/B(D0\u03c0+)\n83.1 \u00b1 3.5 \u00b1 2.0\n(Aubert, 2004l)\n67.7 \u00b1 2.3 \u00b1 3.0\n(Horii, 2008)\n76 \u00b1 6\nD0K\u2217(892)+\n0.529 \u00b1 0.030 \u00b1 0.034\n(Aubert, 2006q)\n0.53 \u00b1 0.04\nD0K+K0\n0.55 \u00b1 0.14 \u00b1 0.08\n(Drutskoy, 2002)\n0.55 \u00b1 0.14 \u00b1 0.08\nD0K+K\u2217(892)0\n0.75 \u00b1 0.13 \u00b1 0.11\n(Drutskoy, 2002)\n0.75 \u00b1 0.13 \u00b1 0.11\nD\u2217(2010)\u2212\u03c0+\u03c0+\n1.25 \u00b1 0.08 \u00b1 0.22\n(Abe, 2004f)\n1.35 \u00b1 0.22\nD\u2212\u03c0+\u03c0+\n1.08 \u00b1 0.03 \u00b1 0.05\n(Aubert, 2009g)\n1.02 \u00b1 0.04 \u00b1 0.15\n(Abe, 2004f)\n1.07 \u00b1 0.05\nD\u2217(2007)0\u03c0+\n5.52 \u00b1 0.17 \u00b1 0.42\n(Aubert, 2007g)\n5.18 \u00b1 0.26\nD\u2217(2007)0K+\n0.421+0.030\n\u22120.026 \u00b1 0.021\n(Aubert, 2005t)\n0.40 \u00b1 0.11 \u00b1 0.02\n(Abe, 2001f)\n0.420 \u00b1 0.034\nD\u2217(2007)0K\u2217(892)+\n0.83 \u00b1 0.11 \u00b1 0.10\n(Aubert, 2004k)\n0.81 \u00b1 0.14\nD\u2217(2007)0K+K\u2217(892)0\n1.53 \u00b1 0.31 \u00b1 0.29\n(Drutskoy, 2002)\n1.53 \u00b1 0.31 \u00b1 0.29\nD\u2217(2007)0\u03c0+\u03c0+\u03c0\u2212\n10.55 \u00b1 0.47 \u00b1 1.29\n(Majumder, 2004)\n10.3 \u00b1 1.2\nD\u221703\u03c0+2\u03c0\u2212\n5.67 \u00b1 0.91 \u00b1 0.85\n(Majumder, 2004)\n5.67 \u00b1 0.91 \u00b1 0.85\nD\u2217(2010)\u22123\u03c0+\u03c0\u2212\n2.56 \u00b1 0.26 \u00b1 0.33\n(Majumder, 2004)\n2.56 \u00b1 0.26 \u00b1 0.33\nD\u2217\u22170\u03c0+\n5.9 \u00b1 1.3 \u00b1 0.2\n(Aubert, 2006p)\n5.9 \u00b1 1.3 \u00b1 0.2\nD1(2420)0\u03c0+ \u00d7 B(D0\n1 \u2192D0\u03c0+\u03c0\u2212)\n0.185 \u00b1 0.029+0.035\n\u22120.055\n(Abe, 2005i)\n0.185 \u00b1 0.029+0.035\n\u22120.055\nD1(2421)0\u03c0+ \u00d7 B(D0\n1 \u2192D\u2217\u2212\u03c0+)\n0.68 \u00b1 0.07 \u00b1 0.13\n(Abe, 2004f)\n0.68 \u00b1 0.07 \u00b1 0.13\nD\u2217\n2(2462)0\u03c0+ \u00d7 B(D\u22170\n2 \u2192D\u2212\u03c0+)\n0.35 \u00b1 0.02 \u00b1 0.04\n(Aubert, 2009g)\n0.34 \u00b1 0.03 \u00b1 0.072\n(Abe, 2004f)\n0.35 \u00b1 0.04\nD\u2217\n2(2462)0\u03c0+ \u00d7 B(D\u22170\n2 \u2192D\u2217\u2212\u03c0+)\n0.18 \u00b1 0.03 \u00b1 0.04\n(Abe, 2004f)\n0.18 \u00b1 0.03 \u00b1 0.04\nD\u2217\n0(2400)0\u03c0+ \u00d7 B(D\u22170\n0 \u2192D\u2212\u03c0+)\n0.68 \u00b1 0.03 \u00b1 0.2\n(Aubert, 2009g)\n0.61 \u00b1 0.06 \u00b1 0.18\n(Abe, 2004f)\n0.64 \u00b1 0.14\nD\u2032\n1(2427)0\u03c0+ \u00d7 B(D\u20320\n1 \u2192D\u2217\u2212\u03c0+)\n0.50 \u00b1 0.04 \u00b1 0.11\n(Abe, 2004f)\n0.50 \u00b1 0.04 \u00b1 0.11\nD+\ns \u03c00\n0.016+0.006\n\u22120.005 \u00b1 0.001\n(Aubert, 2007l)\n0.016+0.006\n\u22120.005 \u00b1 0.001\nD\u2212\ns \u03c0+K+\n0.202 \u00b1 0.013 \u00b1 0.038\n(Aubert, 2008ai)\n0.171+0.008\n\u22120.007 \u00b1 0.025\n(Wiechczynski, 2009)\n0.180 \u00b1 0.022\nD\u2217\u2212\ns \u03c0+K+\n0.167 \u00b1 0.016 \u00b1 0.035\n(Aubert, 2008ai)\n0.131+0.013\n\u22120.012 \u00b1 0.028\n(Wiechczynski, 2009)\n0.145 \u00b1 0.024\nD\u2212\ns K+K+\n0.011 \u00b1 0.004 \u00b1 0.002\n(Aubert, 2008ai)\n0.011 \u00b1 0.004 \u00b1 0.002\nFigure 17.3.6. The mES distribution for D\u2217+D\u2217\u2212candidates\nfrom (Aubert, 2006m).\nB mesons can also decay to D(\u2217)\nsJ D(\u2217) states, with\nthe multiple D(\u2217)\nsJ states having been discovered at the B\nFactories since the original observation of D\u2217\nsJ(2317)+ at\nBABAR in 2002. These decays are described in Section 19.3\nof this Book, and speci\ufb01cally B decays to D(\u2217)\nsJ D(\u2217) are de-\nscribed in Section 19.3.4.\n17.3.4.2 W \u2192c\u00afs\nDiagrams similar to Fig. 17.3.2 with W \u2192c\u00afs and u\u00afu/d \u00afd\npopping lead to B \u2192D(\u2217)D(\u2217)K \ufb01nal states. These \ufb01nal\nstates play a substantial role in the B decays since they\naccount for about 4% of their total branching fraction.\nHere, D(\u2217) is either a D0, D\u22170, D+ or D\u2217+, D(\u2217) is the\ncharge conjugate of D(\u2217) and K is either a K+ or a K0.\nTwenty-two decay modes are possible with this con\ufb01gu-\nration. The decays of B mesons to D(\u2217)D(\u2217)K \ufb01nal states\nare interesting for many di\ufb00erent reasons. For example, in\nthe past (i.e. early 1990\u2019s), the hadronic decays of the B\nmeson were in theoretical con\ufb02ict with the B semileptonic\nbranching fraction due to the inconsistency originating\nfrom the number of charmed hadrons per B decay (Bigi,\nBlok, Shifman, and Vainshtein, 1994). At the time, the\nmeasured semileptonic branching fraction, \u224810%, was in\n\n229\nTable 17.3.4. Measured single charm B0 branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al., 2012)\n(average). The PDG value may use measurements from other experiments when calculating the average.\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nD\u2212\u03c0+\n2.55 \u00b1 0.05 \u00b1 0.16\n(Aubert, 2007g)\n2.68 \u00b1 0.13\nD\u2212K0\u03c0+\n0.49 \u00b1 0.07 \u00b1 0.05\n(Aubert, 2005aa)\n0.49 \u00b1 0.07 \u00b1 0.05\nD\u2212K\u2217(892)+\n0.46 \u00b1 0.06 \u00b1 0.05\n(Aubert, 2005aa)\n0.45 \u00b1 0.07\nD\u2212K+\n0.18 \u00b1 0.04 \u00b1 0.01\n(Abe, 2001f)\n0.197 \u00b1 0.021\nD\u2212K+K\u2217(892)0\n0.88 \u00b1 0.11 \u00b1 0.15\n(Drutskoy, 2002)\n0.88 \u00b1 0.11 \u00b1 0.15\nD0\u03c0+\u03c0\u2212\n0.84 \u00b1 0.04 \u00b1 0.08\n(Kuzmin, 2007)\n0.84 \u00b1 0.04 \u00b1 0.08\nD\u2217(2010)\u2212\u03c0+\n2.79 \u00b1 0.08 \u00b1 0.17\n(Aubert, 2007g)\n2.76 \u00b1 0.13\nD\u2217(2010)\u2212K+\n0.214 \u00b1 0.012 \u00b1 0.010\n(Aubert, 2006n)\n0.20 \u00b1 0.04 \u00b1 0.01\n(Abe, 2001f)\n0.214 \u00b1 0.016\nD\u2217(2010)\u2212K0\u03c0+\n0.30 \u00b1 0.07 \u00b1 0.03\n(Aubert, 2005aa)\n0.30 \u00b1 0.07 \u00b1 0.03\nD\u2217(2010)\u2212K\u2217(892)+\n0.32 \u00b1 0.06 \u00b1 0.03\n(Aubert, 2005aa)\n0.33 \u00b1 0.06\nD\u2217(2010)\u2212K+K\u2217(892)0\n1.29 \u00b1 0.22 \u00b1 0.25\n(Drutskoy, 2002)\n1.29 \u00b1 0.22 \u00b1 0.25\nD\u2217(2010)\u2212\u03c0+\u03c0+\u03c0\u2212\n6.81 \u00b1 0.23 \u00b1 0.72\n(Majumder, 2004)\n7.0 \u00b1 0.8\nD\u2217\u22123\u03c0+2\u03c0\u2212\n4.72 \u00b1 0.59 \u00b1 0.71\n(Majumder, 2004)\n4.72 \u00b1 0.59 \u00b1 0.71\nD\u2217(2010)\u2212\u03c9\u03c0+\n2.88 \u00b1 0.21 \u00b1 0.31\n(Aubert, 2006k)\n2.89 \u00b1 0.30\nD1(2430)0\u03c9\n0.41 \u00b1 0.12 \u00b1 0.11\n(Aubert, 2006k)\n0.41 \u00b1 0.12 \u00b1 0.11\n\u00d7B(D1(2430)0 \u2192D\u2217+\u03c0+)\nD\u2217\u2217\u2212\u03c0+\n2.1 \u00b1 1.0 \u00b1 0.1\n(Aubert, 2006p)\n2.1 \u00b1 1.0 \u00b1 0.1\nD1(2420)\u2212\u03c0+\n0.089 \u00b1 0.015+0.017\n\u22120.032\n(Abe, 2005i)\n0.100+0.021\n\u22120.025\n\u00d7B(D\u2212\n1 \u2192D\u2212\u03c0+\u03c0\u2212)\nD\u2217\n2(2460)\u2212\u03c0+\n0.215 \u00b1 0.017 \u00b1 0.031\n(Kuzmin, 2007)\n0.215 \u00b1 0.017 \u00b1 0.031\n\u00d7B(D\u2217\n2(2460) \u2192D0\u03c0\u2212)\nD\u2217\n0(2400)\u2212\u03c0+\n0.060 \u00b1 0.013 \u00b1 0.027\n(Kuzmin, 2007)\n0.060 \u00b1 0.013 \u00b1 0.027\n\u00d7B(D\u2217\n0(2400) \u2192D0\u03c0\u2212)\nDs0(2317)\u2212K+\n0.042+0.014\n\u22120.013 \u00b1 0.004\n(Drutskoy, 2005)\n0.042+0.014\n\u22120.013 \u00b1 0.004\n\u00d7B(Ds0(2317) \u2192Ds\u03c00)\nD+\u03c0\u2212\n(7.8 \u00b1 1.3 \u00b1 0.4) \u00d7 10\u22124\n(Das, 2010)\n(7.8 \u00b1 1.3 \u00b1 0.4) \u00d7 10\u22124\nD+\ns \u03c0\u2212\n0.025 \u00b1 0.004 \u00b1 0.002\n(Aubert, 2008u)\n0.0199 \u00b1 0.0026 \u00b1 0.0018\n(Das, 2010)\n0.0216 \u00b1 0.0026\nD\u2217+\ns \u03c0\u2212\n0.026+0.005\n\u22120.004 \u00b1 0.002\n(Aubert, 2008u)\n0.0175 \u00b1 0.0034 \u00b1 0.0020\n(Joshi, 2010)\n0.021 \u00b1 0.004\nD\u2217+\ns \u03c1\u2212\n0.041+0.013\n\u22120.012 \u00b1 0.004\n(Aubert, 2008u)\n0.041+0.013\n\u22120.012 \u00b1 0.004\nD\u2212\ns K+\n0.029 \u00b1 0.004 \u00b1 0.002\n(Aubert, 2008u)\n0.0191 \u00b1 0.0024 \u00b1 0.0017\n(Das, 2010)\n0.022 \u00b1 0.005\nD\u2217\u2212\ns K+\n0.024 \u00b1 0.004 \u00b1 0.002\n(Aubert, 2008u)\n0.0202 \u00b1 0.0033 \u00b1 0.0022\n(Joshi, 2010)\n0.0219 \u00b1 0.0030\nD\u2212\ns K\u2217(892)+\n0.035+0.01\n\u22120.009 \u00b1 0.004\n(Aubert, 2008u)\n0.035+0.01\n\u22120.009 \u00b1 0.004\nD\u2217\u2212\ns K\u2217(892)+\n0.032+0.014\n\u22120.012 \u00b1 0.004\n(Aubert, 2008u)\n0.032+0.014\n\u22120.012 \u00b1 0.004\nD\u2212\ns \u03c0+K0\n0.110 \u00b1 0.026 \u00b1 0.020\n(Aubert, 2008ai)\n0.110 \u00b1 0.026 \u00b1 0.020\nD0K0\n0.053 \u00b1 0.007 \u00b1 0.003\n(Aubert, 2006k)\n0.050+0.013\n\u22120.012 \u00b1 0.006\n(Krokovny, 2003a)\n0.052 \u00b1 0.007\nD0K+\u03c0\u2212\n0.088 \u00b1 0.015 \u00b1 0.009\n(Aubert, 2006n)\n0.088 \u00b1 0.015 \u00b1 0.009\nD0K\u2217(892)0\n0.040 \u00b1 0.007 \u00b1 0.003\n(Aubert, 2006k)\n0.048+0.013\n\u22120.010 \u00b1 0.005\n(Krokovny, 2003a)\n0.042 \u00b1 0.006\nD\u2217\n2(2460)\u2212K+\n0.0183 \u00b1 0.0040 \u00b1 0.0031\n(Aubert, 2006n)\n0.0183 \u00b1 0.0040 \u00b1 0.0031\n\u00d7B(D\u2217\n2(2460)\u2212\u2192D0\u03c0\u2212)\nD0\u03c00\n0.269 \u00b1 0.009 \u00b1 0.013\n(Lees, 2011b)\n0.225 \u00b1 0.014 \u00b1 0.035\n(Blyth, 2006)\n0.263 \u00b1 0.014\nD0\u03c10\n0.319 \u00b1 0.020 \u00b1 0.045\n(Kuzmin, 2007)\n0.319 \u00b1 0.020 \u00b1 0.045\nD0f2\n0.120 \u00b1 0.018 \u00b1 0.038\n(Kuzmin, 2007)\n0.120 \u00b1 0.018 \u00b1 0.038\nD0\u03b7\n0.253 \u00b1 0.009 \u00b1 0.011\n(Lees, 2011b)\n0.177 \u00b1 0.016 \u00b1 0.021\n(Blyth, 2006)\n0.236 \u00b1 0.032\nD0\u03b7\u2032\n0.148 \u00b1 0.013 \u00b1 0.007\n(Lees, 2011b)\n0.114 \u00b1 0.020+0.010\n\u22120.013\n(Schumann, 2005)\n0.138 \u00b1 0.016\nD0\u03c9\n0.257 \u00b1 0.011 \u00b1 0.014\n(Lees, 2011b)\n0.237 \u00b1 0.023 \u00b1 0.028\n(Blyth, 2006)\n0.253 \u00b1 0.016\nD\u2217(2007)0\u03c00\n0.305 \u00b1 0.014 \u00b1 0.028\n(Lees, 2011b)\n0.139 \u00b1 0.018 \u00b1 0.026\n(Blyth, 2006)\n0.22 \u00b1 0.06\nD\u2217(2007)0\u03b7\n0.269 \u00b1 0.014 \u00b1 0.023\n(Lees, 2011b)\n0.140 \u00b1 0.028 \u00b1 0.026\n(Blyth, 2006)\n0.23 \u00b1 0.06\nD\u2217(2007)0\u03b7\u2032\n0.148 \u00b1 0.022 \u00b1 0.013\n(Lees, 2011b)\n0.121 \u00b1 0.034 \u00b1 0.022\n(Schumann, 2005)\n0.140 \u00b1 0.022\nD\u2217(2007)0\u03c0+\u03c0\u2212\n0.62 \u00b1 0.012 \u00b1 0.018\n(Satpathy, 2003)\n0.62 \u00b1 0.012 \u00b1 0.018\nD\u2217(2007)0K0\n0.036 \u00b1 0.012 \u00b1 0.003\n(Aubert, 2006k)\n0.036 \u00b1 0.012 \u00b1 0.003\nD\u2217(2007)0\u03c0+\u03c0+\u03c0\u2212\u03c0\u2212\n2.60 \u00b1 0.47 \u00b1 0.37\n(Majumder, 2004)\n2.7 \u00b1 0.5\nD\u2217(2007)0\u03c9\n0.455 \u00b1 0.024 \u00b1 0.0039\n(Lees, 2011b)\n0.229 \u00b1 0.039 \u00b1 0.040\n(Blyth, 2006)\n0.36 \u00b1 0.11\n\n230\nTable 17.3.5. Results of the measured branching fractions for the ten B \u2192D(\u2217)D(\u2217) decay modes from BABAR and Belle: the\nnumber of events for \ufb01tted signal N sig, the branching fractions B (and where appropriate 90% C.L. upper limits on branching\nfractions), as compared with theoretical predictions. All BABAR measurements are from (Aubert, 2006m). (Empty entries indicate\nno measurement from the given experiment, or no prediction.)\nMode\nNsig\nBABAR\nNsig\nBelle\nBBABAR\n(10\u22124)\nBBelle\n(10\u22124)\nBtheory\npredict\n(10\u22124)\nB0 \u2192D\u2217+D\u2217\u2212\n270\u00b119\n1225\u00b159\n8.1 \u00b10.6\u00b1 1.0\n7.82 \u00b10.38\u00b1 0.63 (Kronenbitter, 2012)\n6.0 (Rosner, 1990)\nB0 \u2192D\u2217\u00b1D\u2213\n156\u00b117\n887\u00b139\n5.7 \u00b10.7\u00b1 0.7\n6.14 \u00b10.29\u00b1 0.50 (Rohrken, 2012)\nB0 \u2192D+D\u2212\n63\u00b19\n221\u00b119\n2.8 \u00b10.4\u00b1 0.5\n2.12 \u00b10.16\u00b1 0.18 (Rohrken, 2012)\nB0 \u2192D\u22170D\u22170\n0\u00b16\n\u22121.3 \u00b11.1\u00b1 0.4 (< 0.9)\nB0 \u2192D\u22170D0\n10\u00b18\n1.0 \u00b11.1\u00b1 0.4 (< 2.9)\nB0 \u2192D0D0\n\u221211\u00b112\n0\u00b125\n\u22120.1 \u00b10.5\u00b1 0.2 (< 0.6)\n< 0.43 (Adachi, 2008b)\nB+ \u2192D\u2217+D\u22170\n185\u00b120\n8.1 \u00b11.2\u00b1 1.2\n7.1 (Sanda and Xing, 1997)\nB+ \u2192D\u2217+D0\n115\u00b116\n74\u00b112\n3.6 \u00b10.5\u00b1 0.4\n4.57 \u00b10.71\u00b1 0.56 (Majumder, 2005)\n3.7 (Sanda and Xing, 1997)\nB+ \u2192D+D\u22170\n63\u00b111\n6.3 \u00b11.4\u00b1 1.0\n3.1 (Sanda and Xing, 1997)\nB+ \u2192D+D0\n129\u00b120\n370\u00b129\n3.8 \u00b10.6\u00b1 0.5\n3.85 \u00b10.31\u00b1 0.38 (Adachi, 2008b)\n5.3 (Sanda and Xing, 1997)\nTable 17.3.6.\nResults of measured CP-violating charge asymmetries ACP for D\u2217\u00b1D\u2213and the four charged B modes, as\ncompared with theoretical predictions (where ACP is de\ufb01ned as (\u0393 \u2212\u2212\u0393 +)/(\u0393 \u2212+ \u0393 +), where the superscript refers to the sign\nof the B\u00b1 meson in the case of the charged B decays, and for D\u2217\u00b1D\u2213, \u0393 + refers to D\u2217\u2212D+ and \u0393 \u2212to D\u2217+D\u2212. Empty entries\nindicate no measurement from the given experiment, or no prediction.)\nMode\nABABAR\nCP\nABelle\nCP\nTheoretical\npredictions\nB0 \u2192D\u2217\u00b1D\u2213\n0.008 \u00b1 0.048 \u00b1 0.013 (Aubert, 2009ad)\n0.06 \u00b1 0.05 \u00b1 0.02 (Rohrken, 2012)\nB+ \u2192D\u2217+D\u22170\n\u22120.15 \u00b1 0.11 \u00b1 0.02 (Aubert, 2006m)\n0.012 (Xing, 2000)\nB+ \u2192D\u2217+D0\n\u22120.06 \u00b1 0.13 \u00b1 0.02 (Aubert, 2006m)\n0.012 (Xing, 2000)\nB+ \u2192D+D\u22170\n0.13 \u00b1 0.18 \u00b1 0.04 (Aubert, 2006m)\n0.002 (Xing, 2000)\nB+ \u2192D+D0\n\u22120.13 \u00b1 0.14 \u00b1 0.02 (Aubert, 2006m)\n0.00 \u00b1 0.08 \u00b1 0.02 (Adachi, 2008b)\n0.030 (Xing, 2000)\nTable 17.3.7. Results of measured polarization parameters for the two D\u2217D\u2217vector-vector decays, as compared with theoretical\npredictions. Here RL is the fraction of longitudinal polarization and R\u22a5is the CP-odd fraction. (Empty entries indicate no\nmeasurement from the given experiment, or no prediction. There are presently no published measurements of, or predictions\nfor, polarization in the D\u2217+D\u22170 mode.)\nMode\n \nR\u22a5\nRL\n!BABAR\n \nR\u22a5\nRL\n!Belle\nTheoretical\npredictions\nB0 \u2192D\u2217+D\u2217\u2212\n0.158 \u00b1 0.028 \u00b1 0.006 (Aubert, 2009ad)\n0.138 \u00b1 0.024 \u00b1 0.006 (Kronenbitter, 2012)\n0.624 \u00b1 0.029 \u00b1 0.011 (Kronenbitter, 2012)\n0.06 (Rosner, 1990)\n0.55 (Rosner, 1990)\ncon\ufb02ict with expectations from parton model calculations,\n15 \u221216%. It was realized (Buchalla, Dunietz, and Ya-\nmamoto, 1995) that an enhancement in the b \u2192c\u00afcs tran-\nsition was needed to resolve the theoretical discrepancy\nwith the B semileptonic branching fraction. Buchalla et\nal. predicted sizable branching fractions for decays of the\nform B \u2192D(\u2217)D(\u2217)K (X). Furthermore, the D(\u2217)D(\u2217)K\nevents have been used to investigate isospin relations and\nto extract a measurement of the ratio of \u03a5(4S) \u2192B+B\u2212\nand \u03a5(4S) \u2192B0B0 decays (Poireau and Zito, 2011). Like-\nwise, the mode B0 \u2192D\u2217\u2212D\u2217+K0\nS has been used to per-\nform a time-dependent CP asymmetry measurement to\ndetermine the sign of cos 2\u03c61 (see Section 17.6). It is also\nworth recalling that many D(\u2217)K and D(\u2217)D(\u2217) resonant\nprocesses are at play in the studied decay channels. Using\nB \u2192D(\u2217)D(\u2217)K \ufb01nal states, BABAR and Belle observed\nand measured properties of the resonances D+\ns1(2536) (see\nSection 19.3), DsJ(2700) (see also Section 19.3), \u03c8(3770)\n(see Section 18.2), and X(3872) (see Section 18.3).\nBABAR reconstructs the B0 and B+ mesons in the\n22 D(\u2217)D(\u2217)K modes using 429 fb\u22121 (del Amo San-\nchez, 2011e), while Belle studies only the modes B0 \u2192\nD\u2217\u2212D\u2217+K0 and B+ \u2192D0D0K+ with 414 fb\u22121 (Brodz-\nicka, 2008; Dalseno, 2007). The collaborations use the\ndecays of particles into K0\nS \u2192\u03c0+\u03c0\u2212, D0 \u2192K\u2212\u03c0+,\nK\u2212\u03c0+\u03c00, and K\u2212\u03c0+\u03c0\u2212\u03c0+, D+ \u2192K\u2212\u03c0+\u03c0+, D\u2217+ \u2192\nD0\u03c0+, and D+\u03c00, D\u22170 \u2192D0\u03c00, and D0\u03b3 \ufb01nal states.\nAdditionally, Belle uses the decays D0 \u2192K0\nS\u03c0+\u03c0\u2212and\nD0 \u2192K\u2212K+. The selection of these particles is based\non mass cuts, energies of the decay products, vertexing\nand particle identi\ufb01cation to name a few. The B candi-\ndates are reconstructed by combining a D(\u2217), a D(\u2217) and\na K candidate in a subset of the 22 modes. To suppress\nthe background, topological variables are used which dis-\n\n231\nTable 17.3.8.\nResults of the measured branching fractions for the eight B \u2192D(\u2217)\ns D(\u2217) decay modes from BABAR and Belle:\nthe number of events for \ufb01tted signal N sig, and the branching fractions B, as compared with theoretical predictions. (Empty\nentries indicate no measurement from the given experiment, or no prediction.)\nMode\nAnalysis\ntechnique\nBBABAR\n(10\u22123)\nBBelle\n(10\u22123)\nBtheory\npredict\n(10\u22123)\nB0 \u2192D\u2217+\ns D\u2217\u2212\nSemi-exclusive tag\nD\u2217\ns partial reco.\nD\u2217partial reco.\n17.3\n18.8\n15.8\n\u00b11.8\u00b1\n\u00b10.9\u00b1\n\u00b11.7\u00b1\n1.5 (Aubert, 2006aw)\n1.7 (Aubert, 2005q)\n1.4 (Aubert, 2003d)\n24.0 \u00b1 6.7 (Luo and Rosner, 2001)\nB0 \u2192D\u2217+\ns D\u2212\nSemi-exclusive tag\n7.1 \u00b11.6\u00b1 0.6 (Aubert, 2006aw)\n10.0 \u00b1 2.8 (Luo and Rosner, 2001)\nB0 \u2192D+\ns D\u2217\u2212\nSemi-exclusive tag\nD\u2217partial reco.\n7.3\n8.3\n\u00b11.3\u00b1\n\u00b11.5\u00b1\n0.7 (Aubert, 2006aw)\n0.7 (Aubert, 2003d)\n8.6 \u00b1 2.4 (Luo and Rosner, 2001)\nB0 \u2192D+\ns D\u2212\nSemi-exclusive tag\nFull reconstruction\n6.6 \u00b11.4\u00b1 0.6 (Aubert, 2006aw)\n7.3 \u00b10.4\u00b1 0.7 (Zupanc, 2007)\n14.9 \u00b1 4.1 (Luo and Rosner, 2001)\nB+ \u2192D\u2217+\ns D\u22170\nSemi-exclusive tag\n16.7 \u00b11.9\u00b1 1.5 (Aubert, 2006aw)\nB+ \u2192D\u2217+\ns D0\nSemi-exclusive tag\n7.9 \u00b11.7\u00b1 0.7 (Aubert, 2006aw)\nB+ \u2192D+\ns D\u22170\nSemi-exclusive tag\n7.8 \u00b11.8\u00b1 0.7 (Aubert, 2006aw)\nB+ \u2192D+\ns D0\nSemi-exclusive tag\n9.5 \u00b12.0\u00b1 0.8 (Aubert, 2006aw)\nTable 17.3.9. Results of measured polarization parameters for the D\u2217\nsD\u2217vector-vector decays, as compared with theoretical\npredictions. Here RL is the fraction of longitudinal polarization and R\u22a5is the CP-odd fraction. (Empty entries indicate no\nmeasurement from the given experiment, or no prediction. There are presently no published measurements of, or predictions\nfor, polarization in the D\u2217+\ns D\u22170 mode.)\nMode\n\uf8eb\n\uf8edR\u22a5\nRL\n\uf8f6\n\uf8f8\nBABAR\nTheoretical\nPredictions\nB0 \u2192D\u2217+\ns D\u2217\u2212\n0.519 \u00b1 0.050 \u00b1 0.028 (Aubert, 2003d)\n0.06 (Rosner, 1990)\n0.55 (Rosner, 1990)\ncriminate against continuum background (see Chapter 4).\nSignal events have mES compatible with the known B me-\nson mass, and a di\ufb00erence between the candidate energy\nand the beam energy in the center-of-mass, \u2206E (see Chap-\nter 9), compatible with zero.\nFor each mode, BABAR \ufb01ts the mES distribution to get\nthe signal yield. According to their physical origin, four\ncategories of events with di\ufb00erently shaped mES distribu-\ntions are separately considered: D(\u2217)D(\u2217)K signal events,\n\u201ccross-feed\u201d events, combinatorial background events, and\npeaking background events. To determine the yields and\nthe branching fractions, the shape of each of these con-\ntributions are determined. The cross-feed events are from\nall the D(\u2217)D(\u2217)K modes, except the one we reconstruct,\nthat pass the complete selection, and which are recon-\nstructed in the signal mode; the peaking background is\nthe part of the combinatorial background that is peaking\nin the signal region. BABAR observes from the analysis of\nsimulated samples that most of the cross-feed originates\nfrom the combination of an unrelated soft \u03c00 or \u03b3 with\nthe D0 from a D\u2217+ decay to form a wrong D\u22170 candidate.\nA part of the combinatorial BB background is peaking\nin the signal region, and is \ufb01tted separately from generic\nMC samples e+e\u2212\u2192qq (q = u, d, s, c, b) satisfying the\nD(\u2217)D(\u2217)K selection. For the modes B+ \u2192D\u22170D\u22170K+\nand B+ \u2192D0D0K+, the cross-feed events and the peak-\ning background are negligible, and Belle performs a two\ndimensional \ufb01t on mES and \u2206E to obtain the signal yield.\nDue to the presence of cross-feed events, the \ufb01t for\nthe branching fraction for any one channel uses as inputs\nthe branching fractions from the other channels. Since\nthese branching fractions are not a priori known, BABAR\nemploys an iterative procedure to obtain the 22 branch-\ning fractions. It has been shown that D(\u2217)D(\u2217)K events\ncontain resonant contributions (Aubert, 2008bd). In or-\nder to measure the branching fractions inclusively without\nany assumptions on the resonance structure of the signal,\nBABAR estimates the e\ufb03ciency as a function of location in\nthe Dalitz plane of the data. BABAR uses this e\ufb03ciency at\nthe event position in the Dalitz plane to reweight the sig-\nnal contribution. To isolate the signal contribution event-\nper-event, BABAR uses the sPlots technique (Pivk and\nLe Diberder, 2005) (see Chapter 11). The sPlots technique\nexploits the result of the mES \ufb01t (yield and covariance\nmatrix) and the p.d.f.s of this \ufb01t to compute an event-\nper-event weight for the signal category and background\ncategory.\n\n232\nBoth experiments consider several sources of system-\natic uncertainties on the branching fraction measure-\nments: signal shape, cross-feed determination, peaking\nbackground, combinatorial background, \ufb01t bias, iterative\nprocedure, limited MC statistics, e\ufb03ciency mapping, dif-\nference between data and MC, number of B mesons in the\ndata sample, and secondary branching fractions.\nThe combination from the BABAR and Belle results\ncan be found in Table 17.3.10. Summing the 10 neutral\nmodes and the 12 charged modes, the D(\u2217)D(\u2217)K events\nrepresent (3.65\u00b10.10\u00b10.24)% of the B0 decays and (4.06\u00b1\n0.11 \u00b1 0.28)% of the B+ decays.\n17.3.5 Decays to charmonium\nDecays of B mesons to charmonium modes are color sup-\npressed. In all they consist of a few percent of B decays.\nDespite their small branching fractions, these decays play\na major role in CP studies due to the ability to reconstruct\nmany charmonium modes cleanly with little background\nas well as the simplicity in interpreting the results theoret-\nically. B0 meson decays to charmonium are used to mea-\nsure the CP violation parameter sin 2\u03c61 as well as cos 2\u03c61\n(see Sections 17.6.3 and 17.6.8). The relevant decay dia-\ngrams for charmonium modes are shown in Fig. 17.3.7.\na)\nB+\n\u0001\nW +\nu\n\u00afb\nu\n\u00afs, \u00afd\nc\n\u00afc\nb)\nB0\n\u0001\nW +\nd\n\u00afb\nd\n\u00afs, \u00afd\nc\n\u00afc\nFigure 17.3.7. Color-suppressed Feynman diagrams for B\nmeson decays to charmonium.\nThe easiest way to reconstruct decays to charmonium\nis via the dileptonic decays of J/\u03c8 or \u03c8(2S) to electrons\nor muons. The relatively high energy and topology of the\nleptons allows a clean sample of charmonium to be re-\nconstructed (which helped in earning the decay to the\nCP state B0 \u2192J/\u03c8K0\nS the title of \u201cGolden Mode\u201d). The\n\u03c7c1 and \u03c7c2 states can be reconstructed through their ra-\ndiative decays to J/\u03c8\u03b3. \u03c8(2S) can also be reconstructed\nthrough the decay \u03c8(2S) \u2192J/\u03c8\u03c0\u03c0. The lower mass states\n\u03b7c and \u03c7c0 do not decay to two leptons and the \u03c7c0 branch-\ning fraction to J/\u03c8\u03b3 is small thus these states must be\nreconstructed through their decay to hadrons. The higher\nmass \u201cexotic\u201d charmonium-like X states are reconstructed\nthrough decays to J/\u03c8\u03c0\u03c0, radiative decays to J/\u03c8 or \u03c8(2S),\nor through decays that include two D mesons. They are\ncovered in Section 18.3. Inclusive decays of B mesons to\ncharmonium are covered in Section 18.2.4.1.\n17.3.5.1 Reconstruction of charmonium via dileptons\nThere are several factors that must be taken into account\nwhen reconstructing B decays to charmonium where the\ncharmonium are reconstructed via dileptons. The \ufb01rst is\nthat the invariant mass of the two leptons is often signi\ufb01-\ncantly below the nominal J/\u03c8 or \u03c8(2S) mass. This is the\nresult of both \ufb01nal state radiation and energy loss in the\ndetector via bremsstrahlung. This is particularly true for\nthe dielectron mode. Analyses often correct for this en-\nergy loss by adding in the energy of photon showers that\nare within a small angle (typically 50 mrad) of the ini-\ntial electron direction (e.g. Aubert, 2009m; Guler, 2011)\nto the invariant mass calculation.\nThe second is that for fully reconstructed B mesons, it\nis important to perform a mass-constrained \ufb01t of the J/\u03c8\nor \u03c8(2S). This improves the energy resolution of the re-\nconstructed B signi\ufb01cantly as most of the energy of a char-\nmonium meson coming from a B decay is in its mass.54\nThis \ufb01t or a global \ufb01t for the B meson usually includes\nthe well-measured dilepton vertex.\nFor charmonium states with radiative decay to J/\u03c8 or\n\u03c8(2S), radiative \u03b3 candidates must pass a minimum en-\nergy cut, typically 30 MeV. A common additional require-\nment is that the \u03b3 candidate not be a part of a \u03c00 \u2192\u03b3\u03b3\ncandidate.\n17.3.5.2 Reconstruction of charmonium via hadrons\nThe \u03b7c is reconstructed via KK\u03c0 modes (Fang, 2003; Au-\nbert, 2008ba) in addition to the pp mode (Fang, 2003; Au-\nbert, 2007k). The \u03b7c(2S) is reconstructed via KK\u03c0 (Vi-\nnokurova, 2011; Aubert, 2008ba), as well as via \u03b7c\u03b3.\n17.3.5.3 Reconstruction of B candidates\nB mesons are reconstructed by combining charmonium\ncandidates with the appropriate other particle candidates.\nTypically a vertex-constrained \ufb01t is done at this point.\nBoth Belle and BABAR use kinematic variables to discrim-\ninate signal candidates from background. These variables\nare discussed in Section 7.1.\n17.3.5.4 W \u2192cd\nDecays of B mesons to charmonium cd are Cabibbo sup-\npressed and thus are expected to have decay rates of about\n5% of the equivalent Cabibbo-allowed cs modes. In these\nmodes, the tree and penguin contributions have di\ufb00erent\nphases (unlike the Cabibbo-allowed modes where they are\nthe same) and thus charge asymmetries of a few percent\nmay occur. See Section 17.6.4 for more details.\n54 A key variable for B reconstruction is \u2206E = E\u2217\nB \u2212E\u2217\nbeam\nwhere * refers to the center-of-mass system, EB is the B can-\ndidate\u2019s energy, and E\u2217\nbeam is the beam energy.\n\n233\nTable 17.3.10. Branching fractions of B \u2192D(\u2217)D(\u2217)K decays in units of 10\u22124. The \ufb01rst uncertainties are statistical and the\nsecond are systematic. The results from the modes B0 \u2192D\u2217\u2212D\u2217+K0 and B+ \u2192D0D0K+ are a combination between the\nBABAR (del Amo Sanchez, 2011e) and Belle (Brodzicka, 2008; Dalseno, 2007) measurements.\nMode\nB (10\u22124)\nMode\nB (10\u22124)\nB decays through external W-emission amplitudes\nB0 \u2192D\u2212D0K+\n10.7 \u00b1 0.7 \u00b1 0.9\nB+ \u2192D0D+K0\n15.5 \u00b1 1.7 \u00b1 1.3\nB0 \u2192D\u2212D\u22170K+\n34.6 \u00b1 1.8 \u00b1 3.7\nB+ \u2192D0D\u2217+K0\n38.1 \u00b1 3.1 \u00b1 2.3\nB0 \u2192D\u2217\u2212D0K+\n24.7 \u00b1 1.0 \u00b1 1.8\nB+ \u2192D\u22170D+K0\n20.6 \u00b1 3.8 \u00b1 3.0\nB0 \u2192D\u2217\u2212D\u22170K+\n106.0 \u00b1 3.3 \u00b1 8.6\nB+ \u2192D\u22170D\u2217+K0\n91.7 \u00b1 8.3 \u00b1 9.0\nB decays through external+internal W-emission amplitudes\nB0 \u2192D\u2212D+K0\n7.5 \u00b1 1.2 \u00b1 1.2\nB+ \u2192D0D0K+\n14.0 \u00b1 0.7 \u00b1 1.2\nB0 \u2192D\u2217\u2212D+K0\n64.1 \u00b1 3.6 \u00b1 3.9\nB+ \u2192D0D\u22170K+\n63.2 \u00b1 1.9 \u00b1 4.5\n+D\u2212D\u2217+K0\nB+ \u2192D\u22170D0K+\n22.6 \u00b1 1.6 \u00b1 1.7\nB0 \u2192D\u2217\u2212D\u2217+K0\n79.3 \u00b1 3.8 \u00b1 6.7\nB+ \u2192D\u22170D\u22170K+\n112.3 \u00b1 3.6 \u00b1 12.6\nB decays through internal W-emission amplitudes\nB0 \u2192D0D0K0\n2.7 \u00b1 1.0 \u00b1 0.5\nB+ \u2192D\u2212D+K+\n2.2 \u00b1 0.5 \u00b1 0.5\nB0 \u2192D0D\u22170K0\n10.8 \u00b1 3.2 \u00b1 3.6\nB+ \u2192D\u2212D\u2217+K+\n6.3 \u00b1 0.9 \u00b1 0.6\n+D\u22170D0K0\nB+ \u2192D\u2217\u2212D+K+\n6.0 \u00b1 1.0 \u00b1 0.8\nB0 \u2192D\u22170D\u22170K0\n24.0 \u00b1 5.5 \u00b1 6.7\nB+ \u2192D\u2217\u2212D\u2217+K+\n13.2 \u00b1 1.3 \u00b1 1.2\nTable 17.3.11. Measured B0 to charmonium cd branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al.,\n2012) (average). The PDG value may use measurements from other experiments when calculating the average.\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22126)\nRef.\nB (\u00d710\u22126)\nRef.\nB (\u00d710\u22126)\nJ/\u03c8 \u03c00\n16.9 \u00b1 1.4 \u00b1 0.7\n(Aubert, 2008i)\n23 \u00b1 5 \u00b1 2\n(Abe, 2003c)\n17.6 \u00b1 1.6\nJ/\u03c8 \u03b7\n12.3+1.8\n\u22121.7 \u00b1 0.7\n(Chang, 2012)\n12.3 \u00b1 1.9\nJ/\u03c8 \u03c0+\u03c0\u2212\n46 \u00b1 7 \u00b1 6\n(Aubert, 2003a)\n46 \u00b1 9\nJ/\u03c8 \u03c10\n27 \u00b1 3 \u00b1 2\n(Aubert, 2007e)\n27 \u00b1 4\n\u03c7c1\u03c00\n11.2 \u00b1 2.5 \u00b1 1.2\n(Kumar, 2008)\n11.2 \u00b1 2.8\nTable 17.3.12. Measured B+ to charmonium cd branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al.,\n2012) (average). The PDG value may use measurements from other experiments when calculating the average. Note: in (Aubert,\n2004ae) BABAR measures the ratio B(J/\u03c8\u03c0+)/B(J/\u03c8K+).\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22126)\nRef.\nB (\u00d710\u22126)\nRef.\nB (\u00d710\u22126)\nJ/\u03c8 \u03c0+\n38 \u00b1 6 \u00b1 3\n(Abe, 2003c)\n49 \u00b1 4\nJ/\u03c8 \u03c1+\n50 \u00b1 7 \u00b1 3\n(Aubert, 2007e)\n50 \u00b1 8\n\u03c8(2S)\u03c0+\n24.4 \u00b1 2.2 \u00b1 2.0\n(Bhardwaj, 2008)\n24.4 \u00b1 3.0\n\u03c7c1\u03c0+\n22 \u00b1 4 \u00b1 3\n(Kumar, 2006)\n22 \u00b1 5\nMeasured branching fractions for these modes are given\nin Tables 17.3.11 and 17.3.12. In Table 17.3.1 the mea-\nsured branching fractions of the J/\u03c8\u03c0 and J/\u03c8\u03c1 modes\nare compared with the predictions from the NS model.\nAmong the four measured modes only the J/\u03c8\u03c00 is con-\nsistent with the model\u2019s prediction. Both of the \u03c1 modes\nare overestimated by the model while the J/\u03c8\u03c0+ is un-\nderestimated.\n17.3.5.5 W \u2192cs\nMeasured branching fractions for these modes are given\nin Tables 17.3.13 and 17.3.14.\nThe measured branching fractions of the J/\u03c8K and\nJ/\u03c8K\u2217modes are compared in Table 17.3.1 with the pre-\ndictions from the NS model. All of the J/\u03c8K measure-\nments are higher than the predictions from the model\nwhile for the K\u2217modes the situation is reversed. The mea-\n\n234\nTable 17.3.13. Measured B0 to charmonium cs branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al.,\n2012) (average). The PDG value may use measurements from other experiments when calculating the average.\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\n\u03b7cK0\n0.64+0.22\n\u22120.20 \u00b1 0.20\n(Aubert, 2007k)\n1.23 \u00b1 0.23+0.40\n\u22120.41\n(Fang, 2003)\n0.83 \u00b1 0.12\n\u03b7cK\u22170\n0.57 \u00b1 0.07 \u00b1 0.8\n(Aubert, 2007k)\n1.62 \u00b1 0.32+0.55\n\u22120.60\n(Fang, 2003)\n0.64 \u00b1 0.09\nJ/\u03c8 K0\n0.869 \u00b1 0.022 \u00b1 0.030\n(Aubert, 2007k)\n0.79 \u00b1 0.04 \u00b1 0.09\n(Abe, 2003c)\n0.874 \u00b1 0.032\nJ/\u03c8 K\u22170\n1.309 \u00b1 0.026 \u00b1 0.077\n(Aubert, 2005k)\n1.29 \u00b1 0.05 \u00b1 0.013\n(Abe, 2002d)\n1.34 \u00b1 0.06\nJ/\u03c8 K1(1270)0\n1.30 \u00b1 0.34 \u00b1 0.32\n(Abe, 2001e)\n1.30 \u00b1 0.5\nJ/\u03c8 \u03b7K0\nS\n0.084 \u00b1 0.026 \u00b1 0.027\n(Aubert, 2004v)\n0.08 \u00b1 0.04\nJ/\u03c8 \u03c6K0\n0.102 \u00b1 0.038 \u00b1 0.010\n(Aubert, 2003l)\n0.094 \u00b1 0.026\nJ/\u03c8 \u03c9K0\n0.23 \u00b1 0.03 \u00b1 0.03\n(del Amo Sanchez, 2010c)\n0.23 \u00b1 0.04\n\u03c8(2S)K0\n0.646 \u00b1 0.065 \u00b1 0.051\n(Aubert, 2005k)\n0.67 \u00b1 0.011\n(Abe, 2003c)\n0.62 \u00b1 0.05\n\u03c8(2S)K\u22170\n0.592 \u00b1 0.085 \u00b1 0.089\n(Aubert, 2005k)\n0.552+0.035+0.053\n\u22120.032\u22120.058\n(Mizuk, 2009)\n0.61 \u00b1 0.05\n\u03c7c0K0\n0.142+0.055\n\u22120.044 \u00b1 0.022\n(Aubert, 2009av)\n0.14+0.06\n\u22120.04\n\u03c7c0K\u22170\n0.17 \u00b1 0.03 \u00b1 0.02\n(Aubert, 2008ag)\n0.17 \u00b1 0.04\n\u03c7c1K0\n0.42 \u00b1 0.03 \u00b1 0.03\n(Aubert, 2009m)\n0.351 \u00b1 0.033 \u00b1 0.045\n(Soni, 2006)\n0.393 \u00b1 0.027\n\u03c7c1K\u22170\n0.25 \u00b1 0.02 \u00b1 0.02\n(Aubert, 2009m)\n0.173+0.015+0.034\n\u22120.012\u22120.022\n(Mizuk, 2008)\n0.222+0.040\n\u22120.031\n\u03c7c2 K\u22170\n0.066 \u00b1 0.018 \u00b1 0.005\n(Aubert, 2009m)\n0.066 \u00b1 0.019\nTable 17.3.14. Measured B+ to charmonium cs branching fractions (B) from BABAR, Belle, and the PDG (Beringer et al.,\n2012) (average). The PDG value may use measurements from other experiments when calculating the average.\nBABAR results\nBelle results\nPDG Averages\nFinal state\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\nRef.\nB (\u00d710\u22123)\n\u03b7cK+\n0.87 \u00b1 0.15\n(Aubert, 2006ae)\n1.25 \u00b1 0.14+0.39\n\u22120.40\n(Fang, 2003)\n0.96 \u00b1 0.12\n\u03b7cK\u2217+\n1.1+0.5\n\u22120.4 \u00b1 0.1\n(Aubert, 2007k)\n1.1+0.5\n\u22120.4\n\u03b7c(2S)K+\n0.34 \u00b1 0.18 \u00b1 0.03\n(Aubert, 2007k)\n0.34 \u00b1 0.18\nJ/\u03c8 K+\n1.061 \u00b1 0.015 \u00b1 0.048\n(Aubert, 2007k)\n1.01 \u00b1 0.02 \u00b1 0.07\n(Abe, 2003c)\n1.016 \u00b1 0.033\nJ/\u03c8 K+\u03c0+\u03c0\u2212\n1.16 \u00b1 0.07 \u00b1 0.09\n(Aubert, 2008d)\n0.716 \u00b1 0.010 \u00b1 0.060\n(Guler, 2011)\n0.81 \u00b1 0.013\nJ/\u03c8 K\u2217+\n1.454 \u00b1 0.047 \u00b1 0.097\n(Aubert, 2005k)\n1.28 \u00b1 0.07 \u00b1 0.014\n(Abe, 2002d)\n1.43 \u00b1 0.08\nJ/\u03c8 K1(1270)+\n1.80 \u00b1 0.34 \u00b1 0.39\n(Abe, 2001e)\n1.80 \u00b1 0.5\nJ/\u03c8 \u03b7K+\n0.108 \u00b1 0.023 \u00b1 0.024\n(Aubert, 2004v)\n0.108 \u00b1 0.033\nJ/\u03c8 \u03c6K+\n0.044 \u00b1 0.014 \u00b1 0.005\n(Aubert, 2003l)\n0.052 \u00b1 0.017\nJ/\u03c8 \u03c9K+\n0.32 \u00b1 0.01+0.06\n\u22120.03\n(del Amo Sanchez, 2010c)\n0.320+0.060\n\u22120.032\n\u03c8(2S)K+\n0.617 \u00b1 0.032 \u00b1 0.044\n(Aubert, 2005k)\n0.665 \u00b1 0.017 \u00b1 0.055\n(Guler, 2011)\n0.639 \u00b1 0.033\n\u03c8(2S)K\u2217+\n0.592 \u00b1 0.085 \u00b1 0.089\n(Aubert, 2005k)\n0.67 \u00b1 0.14\n\u03c8(2S)K+\u03c0+\u03c0\u2212\n0.431 \u00b1 0.020 \u00b1 0.050\n(Guler, 2011)\n0.43 \u00b1 0.05\n\u03c8(3370)K+\n3.5 \u00b1 2.5 \u00b1 0.3\n(Aubert, 2006ae)\n0.48 \u00b1 0.11 \u00b1 0.07\n(Chistov, 2004)\n0.49 \u00b1 0.13\n\u03c7c0K+\n0.123+0.027\n\u22120.025 \u00b1 0.006\n(Aubert, 2008l)\n0.112 \u00b1 0.012+0.030\n\u22120.020\n(Garmash, 2006)\n0.134+0.019\n\u22120.016\n\u03c7c1K+\n0.45 \u00b1 0.01 \u00b1 0.03\n(Aubert, 2009m)\n0.449 \u00b1 0.019 \u00b1 0.053\n(Garmash, 2006)\n0.479 \u00b1 0.023\n\u03c7c1K\u2217+\n0.26 \u00b1 0.05 \u00b1 0.04\n(Aubert, 2009m)\n0.405 \u00b1 0.059 \u00b1 0.095\n(Soni, 2006)\n0.30 \u00b1 0.06\n\u03c7c2K+\n0.0111+0.0036\n\u22120.0034 \u00b1 0.0009\n(Bhardwaj, 2011)\n0.011 \u00b1 0.004\nsurements are all lower than the predictions. The level of\ndisagreement is typically about a factor of two.\nAs discussed in Colangelo, De Fazio, and Pham (2002)\nna\u00a8\u0131ve factorization would predict a zero branching frac-\ntion for decays such as B \u2192\u03c7c0K(\u2217) and B \u2192\u03c7c2K(\u2217)\n55. However, as seen in Tables 17.3.13 and 17.3.14 this is\n55 Note that in the amplitude for B \u2192\u03c7c0(2)K decays one\nencounters the \u27e8\u03c7c0(2)|(cc)V\u2212A|0\u27e9matrix element, as can be\nseen following the examples given in Eqs 17.3.2 and 17.3.3. This\nmatrix element includes the (axial-)vector operator between\nstates with spin 0 and 0 (2) and hence equals to zero.\nnot the case. There are non-zero branching fraction mea-\nsurements for \ufb01ve of the eight possible \ufb01nal states. In fact,\nthe B \u2192\u03c7c0K(\u2217) branching fractions are the same order\nof magnitude as the factorization allowed B \u2192\u03c7c1K(\u2217)\ndecays. In Beneke and Vernazza (2009) it is shown that\nincluding color-octet contributions leads to a \u201ccorrection\u201d\nto na\u00a8\u0131ve factorization that may even dominate the entire\ndecay amplitude. The calculation is, however, highly un-\ncertain and formally valid only, when the charmonium is\na truly non-relativistic bound state. It qualitatively de-\nscribes correctly the hierarchies of charmonium branching\nfractions with a sizable \u03c7c0K one, and a suppression of\n\n235\n\u03c7c2K and hcK, although the suppression of the latter two\nis not as strong as seen in the data.\n17.3.6 Summary\nHadronic decays of B mesons into charm make up the\nlargest category of \ufb01nal states. From the point of view of\nan experimentalist many of these \ufb01nal states are easy to\nreconstruct as the hardware and software capabilities of\nboth Belle and BABAR are well matched to the demands\nmade by \ufb01nal states such as D\u03c0, D\u2217\u03c0, and DDK to name\na few. A glance at the PDG (Beringer et al., 2012) reveals\nthe enormous progress made by BABAR and Belle in the\nnumber of \ufb01nal states observed and the precision of the\nmeasurement of their branching fractions. However there\nare still some challenges left for experimentalists in this\narea. To date, no radiative B decays have been observed,\nthere is only an upper limit for B0 \u2192D\u22170\u03b3 (Aubert,\n2005ad). There is also much work to be done reconstruct-\ning \ufb01nal states with multiple \u03c00s.\nSince all of these \ufb01nal states rely on QCD to turn\nquarks into hadrons, gluons play an important role in the\ndynamics of the decay. At the moment a comprehensive\ntheoretical picture capable of \ufb01rst principle calculations of\ndecay rates is still an elusive goal. The precision data now\navailable on a large number of decay modes will make it\neasier to achieve this goal. It is also important to keep\nin mind that the glory in B physics lies not with the\nQCD component of these decay modes but with the elec-\ntroweak role in the transition to the \ufb01nal state. Much of\nwhat we have learned about CP violation in the b sector of\nthe CKM model has come from hadronic \ufb01nal states with\ncharm such as \u03c8K0\nS (\u03c61) and DK\u2212(\u03c63). Looking to the\nupcoming era of super \ufb02avor factories it is clear that this\ncategory of \ufb01nal state will continue to play an important\nrole in many aspects of the physics program.\n\n236\n17.4 Charmless B decays\nEditors:\nFergus Wilson (BABAR)\nPeter Krizan (Belle)\nMartin Beneke (theory)\n17.4.1 Introduction\nIn 1964, indirect CP violation was discovered in the mixing\nof the neutral kaon system (Christenson, Cronin, Fitch,\nand Turlay, 1964) with a value that is currently |\u03f5| =\n(2.228 \u00b1 0.011) \u00d7 10\u22123 (Beringer et al., 2012). It took an-\nother 30 years before direct CP violation was fully es-\ntablished in the kaon system. The absence of direct CP\nviolation in the meantime led to the super-weak theory\nthat suggested that CP violation would only occur in mix-\ning with a change of two units of \ufb02avor (\u2206S = 2) and\nthat CP violation in the B system would be negligible.\nAt the same time, the discovery of neutral currents in\nthe 1970s and the suggestion that there were six quarks\nmeant that a CP violating phase could be introduced into\nwhat became the CKM matrix. This would allow \ufb02avor to\nchange by one unit (\u2206S = 1) and lead to direct CP vio-\nlation in decays. It wasn\u2019t until 1999, six years after the\nstart of the construction of the B Factories, that direct\nCP in the kaon system was \ufb01nally found to be non-zero,\nRe(\u03f5\u2032/\u03f5) = (1.65 \u00b1 0.26) \u00d7 10\u22123 (Fanti et al. (1999)). This\nresult appeared just as the B Factories hoped to establish\nCP violation in the B meson sector. This was achieved\nthrough the observation of the angle \u03c61 in B0 \u2192J/\u03c8K0\nS\nin 2001 (see Section 17.6).\nAlthough CP violation was initially measured in a b \u2192\nccs quark transition, the decays of B mesons to \ufb01nal states\nwithout a charm quark are equally as important for the\nthorough understanding of CP violation. The study of the\nbranching fractions and angular distributions (see Chap-\nter 12) probes the dynamics of both weak and strong in-\nteractions. In many cases, the measurement of the weak\nphases can be directly related to the CKM angles (\u03c61, \u03c62,\n\u03c63). Since the CKM element |Vub| is much smaller than\n|Vcb|, the branching fractions for these charmless modes\nare typically less than 10\u22125, and so are only feasible in\nthe era of large integrated luminosities. The accumulated\ndatasets has made it possible to measure branching frac-\ntions, direct and indirect CP asymmetries, G-parity con-\nservation, longitudinal polarization fL, weak and strong\nphases. This has enabled comprehensive comparison with\ntheoretical predictions and models.\nFigure 17.4.1 shows six of the main amplitudes that\ncontribute to the hadronic B meson decays (there are\na number of other less important diagrams that are not\nshown). The color-allowed tree diagram (T) dominates in\nb \u2192c decays but the color-suppressed diagram (C) can\nalso contribute. If the c quark is replaced by a u quark,\nthe tree diagrams are suppressed and the one-loop \ufb02avor-\nchanging neutral current (FCNC) penguin diagrams (P)\nbecome more or equally important. For example, decays\nT\nC\nE\nV\nP\nA\nFigure 17.4.1. The dominant amplitudes contributing to\ncharmless B meson decays: T) color-allowed external W-\nemission\ntree\ndiagram;\nC)\ncolor-suppressed\ninternal\nW-\nemission tree diagram; E) W-exchange diagram; A) W-\nannihilation diagram; P) penguin diagram with gluon ex-\nchange; and V) W-loop diagram.\nsuch as B \u2192\u03c0\u03c0, \u03c0\u03c1, \u03c1\u03c1, proceed through b \u2192u tree dia-\ngram but also have a non-negligible b \u2192d penguin loop\ncontribution. Transitions of b \u2192s can only occur through\nthe penguin diagrams (P) and CKM suppressed tree de-\ncays (b \u2192u\u00afus). The former have approximately the same\nweak phase \u03c61 as the b \u2192ccs modes (see Chapter 17.6).\nPenguin diagrams in B meson decays can be relatively\nlarge as they involve the CKM elements |Vtb| and |Vts|.\nThis is in contrast to D meson decays which require |Vcb|\nand |Vub|. As a result D meson decays are a good place\nto study tree-level, SM-dominated CP violation (such as\n\u03c63) while B meson charmless decays have the potential to\nreveal non-SM physics through heavy virtual particles in\nthe penguin loops.\nIn B meson decays with an odd number of kaons, the\npenguin loop (P) will dominate as the b \u2192u tree dia-\ngram is suppressed by the |Vub| coupling. If there are an\neven number of kaons, the b \u2192u color-allowed tree dia-\ngram (T) again becomes possible and start to contribute\na noticeable level.\nIn the search for indirect CP violation, any decay with\na b \u2192duu transition is useful as it provides a possible\nsource of measurement of \u03c62, through interference between\nthe decay and the B meson mixing. Examples include\nB \u2192\u03c0\u03c0, \u03c0\u03c1, \u03c1\u03c1 as discussed in Chapter 17.7. However\nthe presence of the penguin loop as an alternative decay\nchannel complicates the interpretation. Similarly, transi-\ntions b \u2192qqs (where q is not a charm quark) provide\na precise measurement of \u03c61 but in this case there is one\ndominant penguin decay. Since penguin loops are sensitive\nto new virtual heavy particles, discrepancies in the value\nof \u03c61 measured in di\ufb00erent decay modes could be a sign\nof new physics. This chapter does not explicitly discuss\nthe CKM angles and more information on the extraction\nof \u03c61 (e.g. B \u2192\u03b7\u2032K0\nS), \u03c62 (e.g. B \u2192\u03c1\u03c1), and \u03c63 (e.g.\nB \u2192K\u03c0\u03c0) from charmless decays can be found in Chap-\nters 17.6, 17.7, and 17.8, respectively. For information on\ncharmless baryonic decays, please see Chapter 17.12.\n\n237\nDirect CP violation is observed as an asymmetry in\nthe yields between a decay and its CP conjugate when at\nleast two contributing decay amplitudes Ai carry di\ufb00erent\nweak \u03c6i and strong phases \u03b4i as explained in detail in\nChapter 16:\nACP =\n2 sin(\u03c6i \u2212\u03c6j) sin(\u03b4i \u2212\u03b4j)\nR + R\u22121 + cos(\u03c6i \u2212\u03c6j) cos(\u03b4i \u2212\u03b4j), R \u2261\n\f\f\f\f\nAi\nAj\n\f\f\f\f\n(17.4.1)\nNeutral and charged B meson decays involving both\ntree and penguin amplitudes are a natural place to look\nfor this e\ufb00ect and charmless meson decays have provided\nevidence for direct CP violation in B0 \u2192K+\u03c0\u2212, B0 \u2192\n\u03c0+\u03c0\u2212, B0 \u2192\u03b7K\u22170, and B+ \u2192\u03c10K+ (see below).\nThe diagrams in Fig. 17.4.1 give a simplistic view of\nthe decays. The weak decays of the B meson are subject to\nboth short and long distance QCD e\ufb00ects. The calculation\nof these properties is challenging as it involves both short-\ndistance perturbative and long-distance non-perturbative\nQCD. The various models, techniques and successes are\nthe subject of the next section.\n17.4.2 Theoretical overview\nTheoretical calculations of charmless decays of B mesons\nare based on an e\ufb00ective description of the weak interac-\ntion valid at scales below the scale MW . Extracting the\nCKM elements \u03bb(D)\np\n\u2261VpbV \u2217\npD (p = u, c, D = d, s), the\ne\ufb00ective Hamiltonian for \u2206B = 1 transitions is\nHe\ufb00= GF\n\u221a\n2\nX\np=u,c\n\u03bb(D)\np\nX\ni\nCi Qp\ni ,\n(17.4.2)\nwhere Qp\ni denotes the so-called tree, QCD and electroweak\npenguin, and dipole operators. The Wilson coe\ufb03cients Ci\ninclude the physics from the highest scales, including MW ,\ndown to the scale mb, and their calculation is under com-\nplete theoretical control, provided the underlying short-\ndistance physics is known. Eq. 17.4.2 assumes the Stan-\ndard Model, and the convention that \u03bb(D)\nt\nis eliminated by\nthe unitarity relation \u03bb(D)\nu\n+\u03bb(D)\nc\n+\u03bb(D)\nt\n= 0. The structure\nof the operators Qi, the values of their Wilson coe\ufb03cients,\nand the \ufb02avor structures can be modi\ufb01ed in extensions of\nthe SM.\nIt is su\ufb03cient to work to \ufb01rst order in the weak inter-\naction. The decay amplitude A( \u00afB \u2192f) = \u27e8f|He\ufb00| \u00afB\u27e9can\nbe written as\nA( \u00afB \u2192f) = \u03bb(D)\nu\nAu\nf + \u03bb(D)\nc\nAc\nf .\n(17.4.3)\nThe larger of the two partial amplitudes determines the\nbranching fraction, while the interference with the sub-\nleading one causes the direct CP asymmetry, provided\nthere is a relative strong phase between the hadronic am-\nplitudes Au\nf and Ac\nf. For a \ufb01rst estimate, the size of an\namplitude is governed by three factors:\n\u2013 the size of the Wilson coe\ufb03cients, which divides the\namplitudes into tree (Ci \u223c1) and penguin (Ci \u223c\n0.1) which are loop-suppressed. Tree amplitudes can\nbe color-allowed or color-suppressed (see the introduc-\ntion to the section on B decays to charm, 17.3).\n\u2013 the size of the CKM factors is \u03bb(d)\nu\n\u223c\u03bb(d)\nc\n\u223c\u03bb3 for\nb \u2192d transitions. For these transitions the penguin\namplitude Ac\nf is typically sub-leading on account of its\nsmaller Wilson coe\ufb03cient. For b \u2192s transitions \u03bb(s)\nc\n\u223c\n\u03bb2 \u226b\u03bb(s)\nu\n\u223c\u03bb4, hence these transitions are dominated\nby the loop-induced penguin amplitude despite their\nsmaller Wilson coe\ufb03cient.\n\u2013 the size of the hadronic matrix elements \u27e8f|Qp\ni | \u00afB\u27e9,\nwhich can vary substantially depending on the spin\nand parity of the \ufb01nal state particles, and whether the\n\ufb01nal state can only be reached by annihilation of the\nB meson constituents. The direct CP asymmetry de-\npends crucially on the phases of these matrix elements.\nThe three factors in combination lead to a fascinating va-\nriety of decay patterns, which are summarized in this sec-\ntion.\nFrom the theoretical point of view, the basic problem\nfor the quantitative prediction of charmless B decays is the\ncomputation of the hadronic matrix elements \u27e8f|Qp\ni | \u00afB\u27e9.\nThe di\ufb03culty resides in the strong interaction, which can-\nnot be treated perturbatively at the hadronic scale \u039b \u2248\n0.5 GeV relevant to the formation of the hadronic \ufb01nal\nstate f, and to the initial bound state. An extreme point of\nview (\u201cnon-perturbative anarchy\u201d) would declare the ma-\ntrix elements to be non-perturbative and unpredictable.\nIn this case, large phases and large direct CP asymme-\ntries in charmless B decays would be expected. The other\nextreme is the assumption of na\u00a8\u0131ve factorization. The op-\nerators Qi can mostly be written as local products of two\nbilinear quark currents Ja\ni Jb\ni . In the decay of a B meson\nto two light mesons M, na\u00a8\u0131ve factorization sets\n\u27e8M1M2|Qi| \u00afB\u27e9\u2248\u27e8M1|Ja\ni | \u00afB\u27e9\u27e8M2|Jb\ni |0\u27e9\n(17.4.4)\n(with M1 \u2194M2 added where appropriate). With this\nassumption all direct CP asymmetries vanish.\nA direct computation of the matrix elements \u27e8f|Qp\ni | \u00afB\u27e9\nwith numerical simulations of QCD is neither conceptu-\nally nor practically within reach. The available theoreti-\ncal methods therefore exploit (approximate) \ufb02avor sym-\nmetries of QCD, or the existence of several scales, which\nallows for an expansion in \u039b/mb. The two methods are\ncomplementary to a large extent. While the SU(3) ap-\nproach does not allow the computation of any individual\ndecay from \ufb01rst principles of QCD, its virtue lies in re-\nlating groups of decays by expressing them in terms of\nonly a few reduced matrix elements. The second method,\nthe factorization approach, begins with the identi\ufb01cation\nof mb, \u221amb\u039b, and \u039b as relevant scales in \u27e8f|Qp\ni | \u00afB\u27e9. Only\nthe scale \u039b requires a non-perturbative treatment of the\nstrong interaction. By computing the strong interaction\ne\ufb00ects at the other two scales perturbatively, a great deal\nof simpli\ufb01cation of the matrix elements can be achieved.\nMost of the analytical progress in the theory of hadronic B\n\n238\ndecays achieved over the past few years can be attributed\nto a systematic implementation of factorization and the\nheavy-quark expansion. The conclusion is that the truth\nfor B decays lies in between the two above extremes, but\ncloser to na\u00a8\u0131ve factorization than non-perturbative anar-\nchy. In the remainder of this section we provide a brief\noverview of the di\ufb00erent methods and some generic re-\nsults.\n17.4.2.1 SU(3) approach\nThe SU(3) approach is based on an approximation to\nQCD, where the up, down, and strange quark masses\nare equal. In practice, this amounts to an expansion in\nms/\u039b, or, since only the \ufb01rst term is kept, to the ap-\nproximation ms \u22430. In this approximation, QCD ac-\nquires an SU(3) \ufb02avor symmetry. The quark \ufb01elds, me-\nson states and the weak interaction Hamiltonian are de-\ncomposed into SU(3) representations, and the matrix ele-\nments \u27e8f|He\ufb00| \u00afB\u27e9are expressed in terms of reduced matrix\nelements and SU(3) Clebsch-Gordan coe\ufb03cients (Zeppen-\nfeld, 1981). The generic accuracy of this approach is de-\ntermined by the size of SU(3)-breaking corrections, which\ncannot be calculated. A typical estimate for the ratio of\nK and \u03c0 decay constants fK/f\u03c0 \u22121 \u224325% at the am-\nplitude level, though it appears that the non-factorizable\nSU(3)-breaking e\ufb00ects may be smaller than those in decay\nconstants and form factors.\nFor applications it is more intuitive to work with topo-\nlogical or \ufb02avor amplitudes rather than the abstract re-\nduced matrix elements, and hence this notation is widely\nused. These amplitudes arise naturally in factorization-\nbased calculations of \u27e8f|He\ufb00| \u00afB\u27e9as well. The \u201ccolor-allowed\ntree amplitude\u201d T stands for an amplitude \u27e8M1M2| \u00afB\u27e9\nwith quark \ufb02avors \u27e8[\u00afqsu][\u00afuD]|[\u00afqsb]\u27e9(qs = u, d, s the spec-\ntator quark, D = d, s); the \u201ccolor-suppressed tree am-\nplitude\u201d C is related to \u27e8[\u00afqsD][\u00afuu]|[\u00afqsb]\u27e9. The terminology\ncomes from the structure of the e\ufb00ective Hamiltonian He\ufb00\nand the na\u00a8\u0131ve factorization approximation, where T (C)\ncontains a large (small) combination of Wilson coe\ufb03cients,\ngiving rise to the na\u00a8\u0131ve expectation that C/T \u22430.2. The\n\u201ctree\u201d amplitudes are distinguished from the QCD and\nelectroweak \u201cpenguin\u201d amplitudes, in which u\u00afu is replaced\nby P\nq q\u00afq (q = u, d, s) and P\nq eqq\u00afq, respectively .\nThe amplitudes for a given set of B decays are written\nin terms of the independent SU(3) (or topological) ampli-\ntudes and CKM parameters, all of which are then \ufb01tted to\nthe relevant data. There are often too many amplitude pa-\nrameters to carry out this program to completion. Possible\nways to proceed consist of marginalizing over the phases\nof amplitudes, resulting in \u201cSU(3) bounds\u201d for the other\nparameters, or of making further simplifying assumptions\nbeyond the SU(3) limit. The most common additional\nassumptions are a particular implementation of meson-\nmixing for \u03b7, \u03b7\u2032 (\u03c9, \u03c6), and neglecting weak annihilation\namplitudes.\nFor instance, with the latter assumption, the B \u2192\u03c0\u03c0\nand B \u2192\u03c0K decay amplitudes are parameterized as fol-\nlows\n\u221a\n2 AB\u2212\u2192\u03c0\u2212\u03c00 = \u03bb(d)\nu [T + C + P EW\nu\n+ P C,EW\nu\n]\n+ \u03bb(d)\nc [P EW\nc\n+ P C,EW\nc\n]\nA \u00af\nB0\u2192\u03c0+\u03c0\u2212= \u03bb(d)\nu [T + Pu + 2\n3P C,EW\nu\n]\n+ \u03bb(d)\nc [Pc + 2\n3P C,EW\nc\n]\n\u2212A \u00af\nB0\u2192\u03c00\u03c00 = \u03bb(d)\nu [C \u2212Pu + P EW\nu\n+ 1\n3P C,EW\nc\n]\n+ \u03bb(d)\nc [\u2212Pc + P EW\nc\n\u22121\n3P C,EW\nc\n],\nAB\u2212\u2192\u03c0\u2212\u00af\nK0 = \u03bb(s)\nc [Pc \u22121\n3P C,EW\nc\n]\n+ \u03bb(s)\nu [Pu \u22121\n3P C,EW\nu\n]\n\u221a\n2 AB\u2212\u2192\u03c00K\u2212= \u03bb(s)\nc [Pc + P EW\nc\n+ 2\n3P C,EW\nc\n]\n+ \u03bb(s)\nu [T + C + Pu + P EW\nu\n+ 2\n3P C,EW\nu\n]\nA \u00af\nB0\u2192\u03c0+K\u2212= \u03bb(s)\nc [Pc + 2\n3P C,EW\nc\n]\n+ \u03bb(s)\nu [T + Pu + 2\n3P C,EW\nu\n]\n\u221a\n2 A \u00af\nB0\u2192\u03c00 \u00af\nK0 = \u03bb(s)\nc [\u2212Pc + P EW\nc\n+ 1\n3P C,EW\nc\n]\n+ \u03bb(s)\nu [C \u2212Pu + P EW\nu\n+ 1\n3P C,EW\nu\n],\n(17.4.5)\nin terms of T, C, the two penguin amplitudes Pp, and\nfour electroweak (EW) penguin amplitudes (the super-\nscript \u201cC\u201d indicates color-suppressed). Since T, C, Pu,\nP EW\nu\nand P C,EW\nu\nappear only as T + P C,EW\nu\n, C + P EW\nu\n,\nand Pu\u2212P C,EW\nu\n/3 the parameterization contains six com-\nplex strong interaction amplitudes. Assuming only SU(2)\nisospin symmetry, the most general parameterization of\nthe \u03c0\u03c0 (\u03c0K) amplitudes requires four (six) complex num-\nbers, so SU(3) symmetry has eliminated four of the 10\nindependent amplitudes. The full power of SU(3) symme-\ntry becomes apparent, when one adds the analogous de-\ncomposition of the B \u2192KK decays and all the Bs \u2192\n\u03c0\u03c0, \u03c0K, KK decays. The parameterization can be ex-\ntended to include \u03b7 and \u03b7\u2032 (requiring two singlet penguin\namplitudes Sp and an assumption on meson-mixing), and\nto \ufb01nal states including vector mesons (requiring a larger\nnumber of new parameters).\nThe SU(3) approach is primarily data-driven. No at-\ntempt is undertaken to predict the decay amplitudes from\nQCD dynamics. Where enough experimental information\nis available, SU(3) relations can give direct access to CKM\nangles. In particular, if only the more accurate relations\nof SU(2) isospin are required, this leads to strategies to\ndetermine angles almost free of theoretical uncertainties,\nas discussed elsewhere in this book. SU(3) \ufb01ts of large\nsets of \ufb01nal states have been performed (Chiang, Gronau,\nLuo, Rosner, and Suprun, 2004; Chiang, Gronau, Rosner,\n\n239\nand Suprun, 2004; Chiang and Zhou, 2006, 2009; Soni and\nSuprun, 2007).\n17.4.2.2 QCD-based factorization\nThe factorization approach is more ambitious than the\nSU(3) approach as it attempts the calculation of indi-\nvidual decays directly from the Lagrangian of the theory\nin terms of only a few remaining hadronic parameters.\nIn the following, we outline the factorization structure of\nthe matrix elements of hadronic two-body decays, and dis-\ncuss some general results. The discussion applies to (quasi)\ntwo-body \ufb01nal states of mesons. A theoretical description\nof multi-body \ufb01nal states with similar rigour is not yet\navailable.\nThe concept of factorization has a long history in B\nphysics as an approximation of \u27e8f|He\ufb00| \u00afB\u27e9as a product\nof a decay constant, form factor and a Wilson coe\ufb03cient\n(Bauer, Stech, and Wirbel, 1987; Wirbel, Stech, and Bauer,\n1985). The term \u201cQCD factorization\u201d refers to a system-\natic separation of scales in \u27e8f|He\ufb00| \u00afB\u27e9. Contrary to the\n(useful but ad-hoc) approximation of \u201cna\u00a8\u0131ve\u201d factoriza-\ntion, QCD factorization implies an expansion of the ma-\ntrix element in the small parameters \u03b1S(\u00b5) and \u039b/mb,\nwith \u00b5 = mb or \u221amb\u039b one of the perturbative scales.\nSince the \u03b1S series can be calculated (with some e\ufb00ort),\nbut only the leading term in the 1/mb expansion assumes\na simple form, the generic accuracy of this approach is lim-\nited by power corrections \u039b/mb \u224320% at the amplitude\nlevel.\nThe QCD factorization approach developed in (Be-\nneke, Buchalla, Neubert, and Sachrajda, 1999, 2000, 2001)\nreplaces the na\u00a8\u0131ve factorization ansatz by a factorization\nformula that includes radiative corrections and spectator-\nscattering e\ufb00ects. Where it can be justi\ufb01ed, the na\u00a8\u0131ve fac-\ntorization ansatz emerges in the simultaneous limit, when\nmb becomes large and when radiative corrections are ne-\nglected. The basic formula for the hadronic matrix ele-\nments is\n\u27e8M1M2|Qi| \u00afB\u27e9= F BM1(0)\nZ 1\n0\ndu T I\ni (u)\u03a6M2(u)\n+\nZ 1\n0\nd\u03bedudv T II\ni (\u03be, u, v) \u03a6B(\u03be)\u03a6M1(v)\u03a6M2(u)\n= F BM1 T I\ni \u22c6\u03a6M2 + \u03a6B \u22c6[HII\ni \u22c6JII] \u22c6\u03a6M1 \u22c6\u03a6M2 ,\n(17.4.6)\nwhere F BM1(0) is a (non-perturbative) B to light-meson\ntransition form factor, \u03a6Mi and \u03a6B are light-cone distri-\nbution amplitudes, and T I,II\ni\nare perturbatively calculable\nhard-scattering kernels. M1 is the meson that picks up\nthe spectator quark from the B meson, as illustrated in\nFig. 17.4.2. The third line uses a short-hand notation \u22c6for\nconvolutions and indicates that the spectator-scattering\ne\ufb00ect in the second line is a convolution of physics at the\nhard scale mb, encoded in HII\ni , and the hard-collinear scale\n\u221amb\u039b, encoded in the jet function JII. Eq. 17.4.6 shows\n\u0000\u0001\u0003\u0002\n\u0004\n\u0005\u0007\u0006\n\u0002\n\b\n\t\f\u000b\n\r\u0003\u000e\n\r\u0003\u000f\n\u0010\n\u0004\n\u0005\n\u0005\n\u0006\n\b\u0011\t\u0013\u0012\n\b\n\t\n\u000b\n\b\u0011\u0014\n\u0000\r\u0003\u000e\n\r\u0015\u000f\n\u03c0\n\u03c0\n\u03c0\n\u03c0\nFigure 17.4.2. Graphical representation of the factorization\nformula given Eq. 17.4.6 (Beneke, Buchalla, Neubert, and\nSachrajda, 2000).\nthat there is no long-distance interaction between the con-\nstituents of the meson M2 and the (BM1) system at lead-\ning order in 1/mb. This is the precise meaning of factoriza-\ntion. Strong interaction scattering phases are generated at\nleading order in the heavy-quark expansion only by per-\nturbative loop diagrams contributing to the kernels T I\ni and\nHII\ni . Thus the phases are of order \u03b4 \u223cO(\u03b1S(mb), \u039b/mb).\nFactorization as embodied by Eq. 17.4.6 is not ex-\npected to hold at sub-leading order in 1/mb. Some power\ncorrections related to scalar currents are enhanced by fac-\ntors such as m2\n\u03c0/((mu + md)\u039b). Some corrections of this\ntype, in particular those related to scalar penguin ampli-\ntudes, nevertheless appear to be calculable and turn out to\nbe numerically important. On the other hand, attempts to\ncompute sub-leading power corrections to hard spectator-\nscattering in perturbation theory usually result in infrared\ndivergences, which signal the breakdown of factorization.\nThese e\ufb00ects are usually estimated and included into the\nerror budget. All weak annihilation contributions belong\nto this class of e\ufb00ects and often constitute the dominant\nsource of theoretical error, in particular for the direct\nCP asymmetries. Factorization as above applies to pseu-\ndoscalar \ufb02avor-non-singlet \ufb01nal states and to the longi-\ntudinal polarization amplitudes for vector mesons. Final\nstates with \u03b7 and \u03b7\u2032 require additional considerations, but\ncan be included (Beneke and Neubert, 2003a). The trans-\nverse helicity amplitudes for vector mesons are formally\npower-suppressed but can be sizeable, and do not factor-\nize in a simple form (Beneke, Rohrer, and Yang, 2007;\nKagan, 2004). The description of polarization is therefore\nmore model-dependent than branching fractions and CP\nasymmetries. QCD factorization results are available for a\nvariety of complete sets of \ufb01nal states. (Beneke and Neu-\nbert, 2003b; Beneke, Rohrer, and Yang, 2007) contain the\ntheoretical predictions for pseudoscalar and vector meson\n\ufb01nal states (PP, PV, VV). A similar analysis has been per-\nformed for \ufb01nal states with a scalar meson (Cheng, Chua,\nand Yang, 2008), axial-vector mesons (Cheng and Yang,\n2007, 2008), and a tensor meson (Cheng and Yang, 2011).\nSeveral variations of factorization have been consid-\nered in the literature and applied to the calculation of\nbranching fractions, CP asymmetries and polarization\nobservables. The perturbative QCD (PQCD) framework\n(Keum, Li, and Sanda, 2001; Lu, Ukai, and Yang, 2001)\nmakes the stronger (and controversial) additional assump-\ntion that the B meson transition form factors F B\u2192M1(0)\n\n240\nare also dominated by short-distance physics and factor-\nize into light-cone distribution amplitudes. Both terms in\nEq. 17.4.6 can then be combined to\n\u27e8M1M2|Qi| \u00afB\u27e9= \u03c6B \u22c6[T PQCD \u22c6JPQCD] \u22c6\u03c6M1 \u22c6\u03c6M2.\n(17.4.7)\nPQCD needs fewer non-perturbative input parameters,\nbut there is a larger dependence on unknown light-cone\ndistribution amplitudes. Since the approach relies on reg-\nularizing the infrared sensitivity by intrinsic transverse\nmomentum, there is a larger sensitivity to perturbative\ncorrections at low scales, where the strong coupling is\nlarge and perturbation theory is potentially unreliable.\nFrom a phenomenological perspective, the principal dif-\nference between the PQCD and all other approaches is\nthe relative importance of the weak annihilation mecha-\nnism. In QCD factorization the strong interaction phases\narise at the scale mb from loop diagrams, that have yet to\nbe included in the PQCD approach, and from the model\nfor weak annihilation. In the most widely used implemen-\ntation of PQCD, the strong phases originate only from\na weak annihilation tree diagram. As a consequence, the\npredicted direct CP asymmetries can be rather di\ufb00erent\nin the two approaches. There is a large literature cover-\ning individual or few decay modes in PQCD. Large sets\nof \ufb01nal states were analyzed in (Ali et al., 2007; Li and\nMishima, 2006). We note that the PQCD factorization for-\nmula Eq. 17.4.7 was recently revised due to infrared diver-\ngences in loop e\ufb00ects (Li and Mishima, 2011), which weak-\nens its predictive power. Most phenomenological analyses\npredate this revision.\nAlternative to the diagrammatic arguments put for-\nward in the BBNS approach in (Beneke, Buchalla, Neu-\nbert, and Sachrajda, 1999, 2000, 2001), factorization of\ncharmless B decays can be elegantly derived in the frame-\nwork of soft-collinear e\ufb00ective theory (SCET) (Bauer, Pir-\njol, Rothstein, and Stewart, 2004; Beneke and Feldmann,\n2004; Chay and Kim, 2004). It is important to stress that\nthe theoretical basis of QCD factorization and SCET is\nexactly the same. However, the phenomenological imple-\nmentation of factorization put forward in (Bauer, Pirjol,\nRothstein, and Stewart, 2004) di\ufb00ers in two respects from\nthe BBNS approach. First, perturbation theory at the in-\ntermediate scale \u221amb\u039b is avoided by not factorizing the\nspectator-scattering term into a hard and jet function.\nEq. 17.4.6 then takes the form\n\u27e8M1M2|Qi| \u00afB\u27e9= F BM1 T I\ni \u22c6\u03a6M2 + \u039eBM1 \u22c6HII\ni \u22c6\u03a6M2 ,\n(17.4.8)\nwhere \u039eBM1 is a generalized, non-local B meson form fac-\ntor related to the matrix element \u27e8M1|\u00afqA\u22a5b| \u00afB\u27e9(Beneke\nand Feldmann, 2004), which depends on momentum trans-\nfer q2 and an additional convolution variable. Second, pen-\nguin diagrams with charm loops (Ciuchini, Franco, Mar-\ntinelli, Pierini, and Silvestrini, 2001) are supposed to be\nnon-factorizable, hence non-perturbative. From the phe-\nnomenological perspective, the principal di\ufb00erence to the\nBBNS approach concerns again the generation of strong\ninteraction phases. Since the non-local form factor is un-\nknown, Eq. 17.4.8 can be used only at the tree level, hence\nthe amplitudes, including the color-suppressed tree ampli-\ntude C, have no phases. The only exception is the charm\npenguin amplitude Pc, which is considered as an unknown\ncomplex number and is therefore the only source of direct\nCP violation. The approach proposed in (Bauer, Pirjol,\nRothstein, and Stewart, 2004) assumes that scalar pen-\nguin and weak annihilation power corrections are zero,\nbut since Pc is a phenomenological parameter, this has no\ne\ufb00ect on the analysis. Because of the need to \ufb01t the dom-\ninant penguin amplitudes to data, the \u201cSCET\u201d approach,\nunlike the QCD factorization or PQCD approach, shares\nmany features of other data-driven approaches such as the\nSU(3) amplitude approach. It uses the fewest theoretical\nassumptions of the three factorization-based methods, at\nthe price of having less predictive power. Large sets of \ufb01-\nnal states have been analyzed with this method in (Bauer,\nRothstein, and Stewart, 2006; Wang, Wang, Yang, and Lu,\n2008; Williamson and Zupan, 2006). We mention that the\nquestion whether the penguin loops with charm factorize\nor not, which for some time has been a point of contro-\nversy, has meanwhile been resolved in favor of factoriza-\ntion (Beneke, Buchalla, Neubert, and Sachrajda, 2009).\nFor a more detailed comparison of the various QCD-\nbased factorization approaches we refer to the short re-\nview in (Artuso et al., 2008). This review also provides an\noverview of the status of the calculation of radiative cor-\nrections, which up to now are computed at next-to-leading\norder (NLO), and partly even at next-to-next-to-leading\norder (NNLO) (Bell, 2008, 2009; Beneke, Huber, and Li,\n2010; Beneke and Jager, 2006, 2007), only in the QCD\nfactorization (BBNS) approach.\n17.4.2.3 Generic results\nTo conclude this overview we summarize a few general\nresults that emerged from comparing theoretical calcu-\nlations to data. The remainder of this section contains\na more speci\ufb01c mode-by-mode analysis. The comparison\nstill su\ufb00ers from a lack of precise knowledge of quantities\nsuch as |Vub|, B meson form factors, and light-cone distri-\nbutions amplitudes, which cause a signi\ufb01cant theoretical\nuncertainty.\n1. The color-allowed tree amplitude T that governs the\nbranching fractions of decays to \ufb01nal states such as\n\u03c0+\u03c0\u2212and its vector-meson relatives is well described\nby factorization, and even close to its na\u00a8\u0131ve factoriza-\ntion value. The main uncertainty in color-allowed tree-\ndominated decays comes from F BM1(0), the B meson\nform factor.\n2. The color-suppressed tree amplitude C that governs\nbranching fractions of decays to \ufb01nal states such as\n\u03c00\u03c00 and its vector-meson relatives is often underesti-\nmated. Its value depends strongly on the precise mag-\nnitude of the spectator-scattering e\ufb00ect. This can be\nseen from the numerical representation (Beneke, Hu-\nber, and Li, 2010) of the NNLO color-suppressed tree\namplitude:\n\u03b12(\u03c0\u03c0) = 0.220 \u2212[0.179 + 0.077 i]NLO\n\n241\n\u2212[0.031 + 0.050 i]NNLO\n+\nh rsp\n0.445\ni \u001a\n[0.114]LOsp\n+ [0.049 + 0.051i ]NLOsp + [0.067]tw3\n\u001b\n= 0.240+0.217\n\u22120.125 + (\u22120.077+0.115\n\u22120.078)i .\n(17.4.9)\nHere 0.220 represents the na\u00a8\u0131ve factorization value.\nLoop corrections to the form-factor-like term in the\n\ufb01rst line of Eq. 17.4.6 and the \ufb01rst two lines of Eq. 17.4.9\nalmost cancel this number, but generate a sizable imag-\ninary part, i.e. scattering phase. The real part of the\namplitude is regenerated by spectator-scattering in the\nsecond line of Eq. 17.4.6 and the third and fourth line\nof Eq. 17.4.9. It is evident that the strong interaction\ndynamics of the color-suppressed tree amplitude is far\nfrom the na\u00a8\u0131ve factorization picture, and is governed\nby quantum e\ufb00ects. The theoretical uncertainty is cor-\nrespondingly large.\n3. The QCD penguin amplitude P that governs branch-\ning fractions of decays to \ufb01nal states such as \u03c0K and\nits vector-meson relatives is certainly underestimated\nin leading order in the heavy-quark expansion. The\npower-suppressed but chirally-enhanced scalar penguin\namplitude, and perhaps a (di\ufb03cult to disentangle) weak\nannihilation contribution, is required to explain the\npenguin-dominated PP \ufb01nal states. While the scalar\npenguin amplitude is calculable, some uncertainty re-\nmains. An important observation is the smaller size\nof the PV, VP and VV penguin amplitudes as com-\npared to PP \ufb01nal states, which can be inferred from\nthe measured branching fractions of hadronic b \u2192s\ntransitions. This is a clear indication of the relevance\nof factorization, which predicts this pattern as a conse-\nquence of the quantum numbers of the operators Qi. If\nthe penguin amplitude were entirely non-perturbative,\nno pattern of this form would be expected. A similar\nstatement applies to the \u03b7(\u2032)K(\u2217) \ufb01nal states, where\nfactorization explains naturally the strikingly large dif-\nferences in branching fractions, including the large \u03b7\u2032K\nbranching fraction, through the interference of penguin\namplitudes, although sizeable theoretical uncertainties\nremain. A \ufb02avor-singlet penguin amplitude seems to\nplay a sub-ordinate role in these decays.\n4. The situation is much less clear for the strong phases\nand direct CP asymmetries. A generic qualitative pre-\ndiction is that the strong phases are small, since they\narise through either loop e\ufb00ects (\u03b1S(mb)) or power cor-\nrections (\u039b/mb). Enhancements may arise, when the\nleading-order term is suppressed, for instance by small\nWilson coe\ufb03cients. This pattern is indeed observed.\nQuantitative predictions have met only partial suc-\ncess. The observed direct CP asymmetry in the de-\ncay to \u03c0+\u03c0\u2212, and the asymmetry di\ufb00erence in the de-\ncays to \u03c00K+ and \u03c0\u2212K+ are prominently larger than\npredicted. A comparison of all CP asymmetry results\nshows a pattern of quantitative agreements and dis-\nagreements that are not presently understood. Since\n\u03b1S(mb) and \u039b/mb are roughly of the same order, it is\nquite possible that power corrections are O(1) e\ufb00ects\nrelative to the perturbative calculation, preventing a\nreliable quantitative estimate. However, the direct CP\nasymmetry calculations are still LO calculations, con-\ntrary to the branching fractions, so the \ufb01nal verdict\nmust await the completion of the NLO asymmetry cal-\nculation. Contrary to direct CP asymmetries, the S pa-\nrameter that appears in time-dependent CP asymme-\ntries is predicted more reliably, since it does not require\nthe computation of a strong phase. This is exploited\nin computations of the di\ufb00erence between sin 2\u03c61 from\nb \u2192s penguin dominated and b \u2192ccs tree decays (Be-\nneke, 2005; Cheng, Chua, and Soni, 2005b).\n5. Polarization in B \u2192V V decays was expected to be\npredominantly longitudinal, since the transverse helic-\nity amplitudes are \u039b/mb suppressed due to the V-A\nstructure of the weak interaction and helicity conser-\nvation in short-distance QCD. While this is paramet-\nrically true (with one exception (Beneke, Rohrer, and\nYang, 2006)), a closer inspection shows that the para-\nmetric suppression is hardly realized in practice for the\npenguin amplitudes (Beneke, Rohrer, and Yang, 2007;\nKagan, 2004). This leads to the qualitative prediction\n(or rather, in this case, postdiction) that the longi-\ntudinal polarization fraction should be close to 1 in\ntree-dominated decays, but can be much less, even less\nthan 0.5, in penguin-dominated decays, as is indeed\nobserved. However, quantitative predictions of polar-\nization fractions for penguin-dominated decays must\nbe taken with a grain of salt, since they rely on model-\ndependent or universality-inspired assumptions of the\nnon-factorizing transverse helicity amplitudes.\nThe remainder of this chapter is devoted to an overview\nof experimental techniques of importance to charmless B\ndecay measurements and provides a summary of two-body\nand three-body \ufb01nal state data collected by the BABAR\nand Belle experiments. A detailed comparison and inter-\npretation of the data in the light of theoretical approaches\nas discussed above is beyond the scope of this review. For\nthis reason we will generally refrain from making reference\nto speci\ufb01c theoretical papers in the following.\n17.4.3 Experimental techniques\nThe decays of B mesons to \ufb01nal states with two or three\nhadrons without a charm quark are loosely broken down\ninto \u201ctwo-body\u201d, \u201cquasi-two-body\u201d and \u201cthree-body\u201d de-\ncays. The \u201ctwo-body\u201d analyses concentrate on long-lived\n\ufb01nal states such as \u03c0\u03c0, K\u03c0, KK, etc. As these modes can\nbe used to access the CKM angle \u03c62, they are covered\nin Chapter 17.7; only the observation of direct CP viola-\ntion is discussed here. The \u201cquasi-two-body\u201d category in-\ncludes decays where one or both of the decay products is a\nresonance. Final state particles that have been measured\ninclude scalar (S) particles (a0 (980), f0(980), f0(1370),\nf0(1500), K\u2217\n0(1430)); pseudoscalar (P) particles (K\u00b1, K0,\n\u03c0\u00b1,\u03c00, \u03b7, \u03b7\u2032); vector (V) particles (\u03c1, \u03c6, \u03c9, K\u2217); tensor\n(T) particles (K\u2217\n2(1430), f2(1270)); and axial-vector (A)\n\n242\nmesons, which can be classi\ufb01ed into two groups as the 3P1\nnonet (a1(1260), f1(1285), f1(1420), K1A) and the 1P1\nnonet (b1, b1(1170), b1(1380), K1B).56 Three-body charm-\nless decays concentrate on \ufb01nal states with \u03c0 or K but can\nsometimes branch out to include protons and resonances\nsuch as K\u2217e.g. B+ \u2192ppK+ (see Chapter 17.12) and\nB+ \u2192K\u22170K\u22170K+.\nThe \u201cquasi-two-body\u201d decays are traditionally recon-\nstructed assuming that the resonances decaying to the\nsame \ufb01nal state (such as \u03c1 and f0(980) decaying to \u03c0\u03c0) do\nnot interfere. This has the advantage that branching frac-\ntions can be compared to measurements from earlier ex-\nperiments but the e\ufb00ect of interference is then considered\nas a systematic. The main di\ufb00erences between the ways\nthat decays are analysed are usually dictated by the extent\nand nature of the background, as the B meson charmless\ndecays have a low signal-to-background ratio. This can be\ncompared to D meson decays which are typically selected\nwith very high purity.\nWhatever the \ufb01nal state, the candidate selection pro-\ncess follows a broadly similar path (see Chapter 7 for more\ndetails on B meson reconstruction). The B meson candi-\ndates are reconstructed through their decays. The inter-\nmediate resonance will be formed \ufb01rst and then combined\nwith a third particle to form the B meson. The recon-\nstructed mass will usually be required to be less than \u223c3\ntimes the width from the nominal central value. If the\nnatural widths of the resonances are smaller than the de-\ntector resolution, the resonance masses (including \u03c00\u2019s)\nare constrained to their nominal PDG values in the \ufb01t for\nthe B meson candidate (Beringer et al., 2012); this im-\nproves the precision of the parameters obtained in the \ufb01t.\nQuality criteria are applied to the tracks before \ufb01tting,\nsuch as demanding the tracks are well-measured, have a\nminimum pT , and originate from close to the beam spot.\nThe momenta of the charged tracks will usually be ex-\ntracted assuming a particular mass hypothesis determined\nby the particle type (e.g. pion versus kaon, see Chapter 5).\nHowever, in some analyses, such as B0 \u2192h+h\u2212(with\nh = K, \u03c0), the B meson will be \ufb01tted under one mass hy-\npothesis (usually a pion), and any shift in the value of \u2206E\nis used to di\ufb00erentiate between decays with one or more\nkaons. The shift is of the order of \u223c50 MeV per kaon.\nThe vertexing will apply various constraints to improve\nthe resolution (see Chapter 6) and to take into account\nthe \ufb02ight distance of long lived particles such as the K0\nS\nmeson. These constraints become more important as the\nnumber of neutral particles in the decay increases. A fur-\nther criterion that is sometimes applied is to require that\nthere is at least one additional charged track from the\nbeam spot region; this is a crude indicator that there has\nbeen at least one other decay in the event, which is as-\nsumed to be the other B meson.\nTwo kinematic variables, mES and \u2206E, are used to\nselect the events (see Eqs 7.1.8 and 7.1.5 for de\ufb01nitions).\nAny linear correlation between these variables can be re-\nmoved by rotating them in the (mES, \u2206E) plane or a two\ndimensional p.d.f. can be used in the maximum likelihood\n56 K1(1270) and K1(1400) are admixtures of K1A and K1B\n(ML) \ufb01t. Events with |\u2206E| < 300 MeV are typically ac-\ncepted, although an asymmetric acceptance region is used\nif there is a chance of energy loss from photon emission\nor \u03c00 reconstruction. The minimum value of mES is set to\nallow a good \ufb01t to the mES background distribution and is\nrarely set less than 5.220 GeV/c2 (below this value, other\nselection criteria start to distort the selection e\ufb03ciency).\nThe (mES, \u2206E) plane is divided into regions to aid\nanalysis. A signal region is de\ufb01ned around the point mES =\nmB, \u2206E = 0 with a width roughly 3 times the resolution\non mES (\u223c3 MeV/c2) and \u2206E (\u223c20\u221250 MeV, depending\non the number of neutral particles). Although the signal\nregion is usually rectangular in shape, elliptical signal re-\ngions have been used e.g. Fig. 3 in (Garmash, 2005). Two\nsidebands are de\ufb01ned above and below the \u2206E signal re-\ngion, the upper region allowing for the study of two-body\ndecays that have been combined with a random track and\nthe lower region to study four-body decays that have lost\na track. A further sideband below the signal region in mES\ncan be used to study the continuum background, although\ncare must be taken to account for any decays from B\nmesons.\nIn the center-of-mass (CM) frame, the continuum back-\nground is characterized by a jet-like, back-to-back struc-\nture while the BB events have a more spherical distri-\nbution since they are produced close to rest (see Chap-\nter 9 for details). Therefore, event shape variables are used\nto separate signal from this background. Many di\ufb00erent\ncriteria have been used over the years including spheric-\nity, spherocity, planarity, acoplanarity and thrust (see the\nGlossary and Chapter 9). In addition, angles are often\nmeasured between the direction of the B meson decay and\na reference axis, such as the beam line or the direction of\nthe rest of the event (ROE). An important example is the\nthrust angle in the CM frame, de\ufb01ned as the angle \u03b8T be-\ntween the thrust axis of the B meson candidate and that\nof the rest of the particles in an event. Signal events are\nuniformly distributed in cos \u03b8T , while continuum events\nare peaked near cos \u03b8T = \u00b11. A requirement on cos \u03b8T or\n| cos \u03b8T | of less than 0.7 \u22120.9 is usually applied.\nAny remaining event shape variables are combined into\na multivariate discriminant that can either be used as\nselection criteria or as a p.d.f. observable in a ML \ufb01t.\nFisher discriminants and neural networks are popular but\nBoosted Decision Trees (or Forests) have also been ap-\nplied (see Chapter 4 for details). The number of variables\nis typically about six. Although discriminants with many\nmore variables have been tried, they rarely bring any ad-\nditional discrimination. The choice of variables depends\non the mode under consideration, consistency with pre-\nviously used discriminants, and ultimately on the prej-\nudice of the analyst. It is important to check for corre-\nlations between the input variables and any other vari-\nables used in the ML \ufb01t. Variables that have been used\nover the years include (see Chapter 9 for many de\ufb01ni-\ntions): CLEO cones (momentum distribution in nine angu-\nlar cones about the thrust vector); modi\ufb01ed Fox-Wolfram\nmoments (Abe, 2001c); the variable ST , the scalar sum\nof the transverse momenta, calculated with respect to the\n\n243\nthrust axis, of particles outside a 45\n\u25e6cone around the\nB thrust axis, divided by the scalar sum of their mo-\nmenta (Jen, 2006); the polar angles of the B meson mo-\nmentum vector and the B meson thrust axis with respect\nto the beam axis; the angle between the B meson thrust\naxis and the thrust axis of the rest of the event; and the\nratio of the second- and zeroth-order momentum-weighted\npolynomial moments of the energy \ufb02ow around the B me-\nson thrust axis (Aubert, 2004a). Although not strictly\nevent shape variables, some success has been achieved\nby using two additional inputs to the neural network:\nthe \ufb02avor of the other B meson as reported by a multi-\nvariate tagging algorithm (Aubert, 2005i); and the boost-\ncorrected proper-time di\ufb00erence between the decay ver-\ntices of the two B mesons divided by its error. The mul-\ntivariate discriminant can be trained with Monte Carlo\n(MC) simulation for the signal, and qq continuum MC,\no\ufb00-resonance data or sideband data for the background.\nThe discriminant can sometimes be used as a selection cri-\nterion as well as a p.d.f. as a simple cut on the output can\neliminate a substantial part of the background (of the or-\nder of 20%-40%) with little signal loss. Instead of using the\ntagging information in the event-shape, Belle have some-\ntimes used the B meson \ufb02avor tagging output (Kakuno,\n2004) to calculate a \ufb01gure of merit; signal retention of\ngreater than 60% with background rejection greater than\n90% has been achieved (Jen, 2006).\nB meson decays to charm have large branching frac-\ntions and \ufb01nal states that are either the same as the\nmode under consideration or easily mis-reconstructed.\nThese charm backgrounds can be suppressed by recon-\nstructing the charm candidate from combinations of tracks\nand applying a veto around the nominal mass (typically\n\u223c40 MeV/c2 for the D meson).\nThe helicity distribution is an important variable that\ncan be used to identify particles of a particular spin, ex-\ntract the longitudinal polarization fL, or simply as a se-\nlection criterion. The helicity angle \u03b8H of the resonance\nis de\ufb01ned as the angle between the momentum vector of\none of the resonance\u2019s daughter particles and the direction\nopposite to the B meson momentum in the resonance rest\nframe (Kramer and Palmer (1992)). The choice of daugh-\nter must be consistent from event to event (either based\non charge or \ufb02avor) and care must be taken to avoid any\nunexpected ordering in momentum or azimuthal angle in-\ntroduced by the track \ufb01nding algorithms.\nIt is often necessary to limit the range of the helicity\nangle. At values of | cos \u03b8H| > 0.9 the signal reconstruc-\ntion e\ufb03ciency starts to fall o\ufb00, as one of the daughter\ntracks of the resonance has a low momentum. At the same\ntime, backgrounds created from combinations of tracks\nstart to increase. If the resonance decays to particles of\ndi\ufb00ering mass, then the momentum selection criteria on\nthe daughter particles will cause the cos \u03b8H distribution to\nbe skewed, requiring careful compensation for the change\nin e\ufb03ciency. The allowed range of cos \u03b8H is mode depen-\ndent but typically events are rejected if cos \u03b8H is greater\nthan 0.7 \u22120.9, with di\ufb00erent ranges for negative and pos-\nitive cos \u03b8H. In Vector-Vector (VV) decays, the longitudi-\nnal component is typically dominant and causes the helic-\nity angle distribution to be enhanced near \u00b11. For these\ndecays, careful consideration of the cos \u03b8H rejection cri-\nterion is required to optimize the signal and background\nratio. The value of the longitudinal component is an im-\nportant measurement (see Section 17.4.5.3) so care must\nbe taken to limit any bias in the acceptance.\nThere can be multiple B meson candidates in an event.\nThe average number of candidates per accepted event\nranges up to \u223c1.5, with more mis-reconstructed can-\ndidates expected in decays with more neutrals (such as\n\u03c00) due to low-energy photons or noise in the electromag-\nnetic calorimeter. Resonances with large widths (such as\n\u03c10) also have more mis-reconstructed candidates due in-\ncreased combinatorics. One approach to dealing with mul-\ntiple candidates is to accept all N candidates in an event\nwith a weight 1/N applied to each, but usually a crite-\nrion is used to select the best one. This is sometimes a\nrandom choice but more common methods rely on a \u03c72\nbased on the pull of the \ufb01tted resonance mass from the\nnominal value or the B meson vertex probability. The ac-\ncuracy of the selection depends on the mass width of the\nresonance and the number of neutral particles in the \ufb01t.\nThe true candidate is selected with an accuracy that is\nrarely below 75% and often greater than 95%, based on\nMC simulation. If the number of mis-reconstructed can-\ndidates is large then these \u201cself-crossfeed\u201d candidates are\nsometimes included as a separate hypothesis category in\nthe ML \ufb01t. There is no agreed point at which this happens\nbut it is typically considered as an option when the true\ncandidate selection accuracy falls below \u223c85%.\nAfter the application of all the selection criteria, there\nwill still be a number of backgrounds from B meson de-\ncays either from decays via a charm particle that have\nnot been rejected by the D meson mass requirement or\nB meson decays that have been mis-reconstructed. Un-\nlike the continuum background, these BB backgrounds\nare likely to have a peaking distribution in one or more of\nthe observables used in a ML \ufb01t. The contribution to the\nbackground from BB decays is identi\ufb01ed by running the\nselection on generic BB background MC decays, where\nall the known decay channels have been included. Decays\nthat have not been observed are often included assuming\nsome estimated branching fraction (10\u22126 \u221210\u22125) that al-\nlows a small number to be selected and characterized. If\na decay is observed to pass the selection, the analysis is\nrerun on the exclusive MC events to extract an estimate of\nthe number of events expected in the \ufb01nal sample. If there\nare many modes (\u223c20 are not uncommon) an attempt is\noften made to group them into a smaller number based\non similarities in the distributions of the observables. The\ncombined sample must be correctly weighted by the ex-\npected branching fractions and reconstruction e\ufb03ciencies\nfor each individual mode. This is a problem for decays\nthat have not been measured yet and in these cases it is\ntypical to assume a branching fraction that is about half\nthe reported branching fraction upper limit. If no upper\nlimit has been reported, a branching fraction is chosen\n\n244\nsuch that only a few events can be expected to appear in\nthe data.\nHigher mass resonances that peak outside the invari-\nant mass selection region can still feed-down to the sig-\nnal region because: they have a large width, such as\nf0(1370); through re\ufb02ection, where a daughter particle is\nmis-identi\ufb01ed, such as in B \u2192\u03c9\u03c0+; or where a resonance\nhas a long range component e.g. the S-wave component of\nthe K\u2217\n0(1430). These backgrounds are often treated in a\nseparate analysis that looks in the mass region above the\nresonance under consideration (since this is still blinded)\nand performs a ML \ufb01t to the higher mass region using\nmES, \u2206E, the multivariate discriminant, and the recon-\nstructed mass. Once the yield is extracted, the number of\nevents in the resonance signal region is estimated by ex-\ntrapolating the \ufb01tted mass p.d.f. (or a \ufb01t to the extracted\nsWeights, see Chapter 4) down to the low mass region\nand integrating.\nA further category of background occurs when the\nB meson decays to the same \ufb01nal state without passing\nthrough a resonance, such as B+ \u2192\u03c0+ \u03c0\u2212\u03c0+ when look-\ning for B+ \u2192\u03c10 \u03c0+ or B0 \u2192\u03c0+ \u03c0\u2212\u03c10 when looking for\nB0 \u2192\u03c10 \u03c10. These backgrounds also become important\nwhen D mesons are used as calibration channels as these\n\u201cnon-resonant\u201d decays can be responsible for a signi\ufb01cant\nnumber of the events underneath the calibration chan-\nnel of interest. Strictly speaking, \u201cnon-resonant\u201d means\na decay in a Dalitz Plot that is uniformly distributed in\nphase space (see later and Chapter 13). However, this dis-\ntinction is generally ignored and any \ufb01nal state which\ncannot be represented by a peaking structure is usually\ncategorized as non-resonant. This has practical bene\ufb01ts\nwhen performing a \ufb01t as it is often di\ufb03cult to identify\nthe source of smoothly varying distributions. A \ufb01t which\nuses more than one such distribution is likely to \ufb01nd that\nthe background events \ufb02ow between the di\ufb00erent distri-\nbutions without a\ufb00ecting the signi\ufb01cance of the signal. As\na result, some papers will report a non-resonant measure-\nment while others will simply consider it as part of the\nbackground.\nThe signal modes, mis-reconstructed signal modes (if\nused), continuum background and BB backgrounds dis-\ntributions are used in a ML \ufb01t to extract the signal yield,\nbranching fraction, ACP , and longitudinal polarization fL.\nThe observables used are usually mES, \u2206E, the multivari-\nate discriminant and the intermediate resonance masses.\nIf an angular analysis is required, the helicity cos \u03b8H of the\nresonances is also used. In this later case, the reconstruc-\ntion e\ufb03ciency as a function of cos \u03b8H must be taken into\naccount, often by multiplying the expected true distribu-\ntion by a polynomial of a suitable order. The e\ufb03ciency for\nthe other variables is usually treated as uniform.\nThe observables used in the p.d.f.s are usually assumed\nto be uncorrelated and the total p.d.f. is taken to be the\nproduct of the separate individual p.d.f.s. However, in\nsome cases this assumption is invalid and the correlations\nneed to be taken into account explicitly. If the correlation\nonly exists between two observables and is reasonably lin-\near, then the correlation can be reduced by using rotated\nvariables derived from the observables in the p.d.f.s. Some-\ntimes, a two-dimensional p.d.f. is used. A third option is to\ncreate a p.d.f. based on one of the observables, where the\np.d.f. parameters (e.g. means and widths) are dependent\non the other observable.\nA standard set of cross-checks on the \ufb01t is performed.\nThe p.d.f.s are used to generate a series of simulated data\nsamples that are then \ufb01tted with the ML method. This\nreveals any problems with minimization, pulls and biases.\nThe tests are repeated with data samples generated from\nthe full MC simulated data; this can reveal problems with\ncorrelations between observables. The ML \ufb01t is sometimes\nperformed on a calibration channel taken from the data,\nsuch as a charm decay to the same or similar \ufb01nal state as\nthe B meson decay under consideration. In this case, the\nML model is simpli\ufb01ed (e.g. no angular observables are\nused), any charm vetoes are removed, and all the model\nparameters are \ufb02oated, if possible. This can reveal any dif-\nferences between the MC simulation and data in the mES\nand \u2206E signal distributions, which can then be corrected\nfor in the \ufb01nal \ufb01t.\nThe systematic uncertainties for the result are often\nseparated into two categories and will depend on the mea-\nsurement under consideration. Additive systematics a\ufb00ect\nthe \ufb01t yield and hence the signi\ufb01cance of a branching frac-\ntion measurement. Multiplicative systematics a\ufb00ect the\ncentral value of the result but not the signi\ufb01cance. In the\nadditive category, we place uncertainties on the accuracy\nof the \ufb01xed parameters in the p.d.f.s, any ML \ufb01t biases in\nextracting the yields, model-dependent parameters (such\nas the mean and width of poorly known resonances), the\npresence or absence of uncertain resonances (such as the\n\u03c3(600)), interference, BB background yields, and uncer-\ntainty on the longitudinal polarization fL. In a large num-\nber of modes, the uncertainty on the \ufb01xed parameters ex-\ntracted from the MC simulation is the dominant system-\natic (see Chapter 15 for more details on systematic error\nestimation). In the multiplicative category falls the recon-\nstruction e\ufb03ciency uncertainties arising from di\ufb00erences\nbetween data and MC simulation from tracking, uncer-\ntainties in the branching fractions of any intermediate de-\ncays, charged particle identi\ufb01cation, neutral particle (\u03c00)\nidenti\ufb01cation, and long-lived particle (K0\nS) identi\ufb01cation.\nAlso, the accuracy of the known BB cross-section, lumi-\nnosity and limited MC statistics can contribute. If various\nsub-decays are combined (e.g. K\u2217+\u2192K0\nS \u03c0+ or K+ \u03c00)\nto form an overall measurement, the multiplicative sys-\ntematics are correlated and must be added linearly.\nMany of the systematic errors associated with fL and\nACP cancel since these two measurements are based on\nratios of signal yields. The systematic uncertainty on ACP\ncaused by the detector responding di\ufb00erently to positive\nand negative tracks or the presence of s and s in K\u2212\nand K+ respectively is generally considered to be 0.5% at\nmost.\nOnce calculated, the systematic error is convolved with\nthe likelihood function with a Gaussian distribution with\na variance equal to the total systematic error (see Chap-\nter 15). The signal signi\ufb01cance is then de\ufb01ned as\n\u221a\n2\u2206ln L,\n\n245\n0.0 \n12.5 \n25.0 \nHFAG\nAug 2012\nBranching Ratio x 106 \nB(B \u2192K\u03c0, \u03c0\u03c0, KK )\nBABA R \nBelle \nCLE O \nNew Avg.\nCDF \nLHCb\nK0\u03c0+\nK+\u03c0\u2212\nK+\u03c00\nK0\u03c00\n\u03c0+\u03c00\n\u03c0+\u03c0\u2212\n\u03c00\u03c00\nK+K0\nK+K\u2212\nK0K0\nFigure 17.4.3. Summary of branching fraction measurements\n(\u00d710\u22126) and HFAG averages for two-body decays to K\u03c0,\u03c0\u03c0\nand KK (Amhis et al. (2012)).\nwhere \u2206ln L is the change in log-likelihood ln L from the\nmaximum value to the value when the number of signal\nevents is set to zero. If multiple signal resonances are ex-\ntracted in the same \ufb01t it is often helpful to state the linear\ncorrelation coe\ufb03cient between the results.\n17.4.4 Two-body decays\nIn this section, we just report on branching fractions and\nACP measurements; further details are covered in Chap-\nter 17.7. Table 17.4.1 summarises the branching fraction\nand direct CP measurements made for charmless two-\nbody decays, while Figure 17.4.3 illustrates the branching\nfraction measurements made so far.\nThe \ufb01nal state particles in B meson decays to two\nlong-lived particles bene\ufb01t from having relatively larger\nmomenta than most B decays, leading to a cleaner anal-\nysis environment. Decays such as B \u2192K\u03c0 and B \u2192\u03c0\u03c0\nare therefore good places to look for new physics and\nCP violation, both direct and indirect. The \ufb01rst obser-\nvations of QCD penguin b \u2192d transitions were made in\nB+ \u2192K0K+ (Aubert, 2006ai) and B0 \u2192K0K0 (Abe,\n2005e).\nThe decay B0 \u2192K+\u03c0\u2212proceeds via both b \u2192u\ntree and b \u2192s transitions, which can interfere, leading\nto a direct CP violating asymmetry (Lin, 2008). The two\ndominant decay diagrams are shown in Fig. 17.4.4. The\nworld average is now ACP (K+\u03c0\u2212) = \u22120.098 \u00b1 0.013. The\nfour K\u03c0 asymmetries can be related through sum rules.\nFrom Eq. 17.4.5 it follows that\nAB\u2212\u2192\u03c0\u2212\u00af\nK0 \u2212\n\u221a\n2 AB\u2212\u2192\u03c00K\u2212+ A \u00af\nB0\u2192\u03c0+K\u2212\n+\n\u221a\n2 A \u00af\nB0\u2192\u03c00 \u00af\nK0 = 0\n(17.4.10)\na\nb\nB+, B0\nu\np0, p\u2013\nu\nK+, p+\nb\nu\nu\nB+, B0\nu, d\nu, d\nb\ns, d\nu, d\nu, d p0, p\u2013\nW\nW\nK+, p+\ns, d\ng\nFigure 17.4.4. The dominant Tree-level (a) and Penguin-loop\n(b) Feynman diagrams in the two-body decays B \u2192K\u03c0 and\nB \u2192\u03c0\u03c0 (Lin, 2008).\nThis, together with the fact that penguin decays domi-\nnate, leads to the prediction (Gronau, 2005)\n\u2206(K+\u03c0\u2212) + \u2206(K0\u03c0+) =\n2 (\u2206(K+\u03c00) + \u2206(K0\u03c00)) \u00d7 (1 + O(5%))\n(17.4.11)\nwhere \u2206(K\u03c0) = \u0393(B \u2192\u00afK\u00af\u03c0) \u2212\u0393(B \u2192K\u03c0). Conse-\nquently, it is expected that:\nACP (K+\u03c0\u2212) + ACP (K0\u03c0+) \u2248ACP (K+\u03c00) + ACP (K0\u03c00)\n(17.4.12)\nThe sum rule prediction for the width agrees quite well\nwith experimental results. If ACP (K0 \u03c0+) and ACP (K0\n\u03c00) are small then the predicted values for ACP (K+ \u03c00)\nand ACP (K+ \u03c0\u2212) are very similar. However the measured\nvalues for ACP (K+ \u03c00) and ACP (K+ \u03c0\u2212) di\ufb00er by about\n\ufb01ve standard deviations. This is shown in Fig. 17.4.5 where\nthe di\ufb00erence in the number of events is clearly visible and\nthe sign of the di\ufb00erence between the number of events in\nB0 \u2192K+\u03c0\u2212is opposite to that of B+ \u2192K+\u03c00. This\ncould be a sign of new physics but other e\ufb00ects, including\nenhancements in sub-dominant decay diagrams or strong\ninteraction e\ufb00ects, have also been suggested as an expla-\nnation.\n\n246\n0\n250\n500\n750\na K\u2013p+\nb K+p\u2013\nMbc (GeV/c2)\nEntries per 2 MeV/c2\n0\n100\n200\n300\n5.2 5.25\nc K\u2212p0\n5.2 5.25\nd K+p0\nFigure 17.4.5. The direct CP violation in B \u2192K\u2213\u03c0\u00b1 (top)\nand B\u00b1 \u2192K\u00b1\u03c00 (bottom) can be seen in the di\ufb00erence be-\ntween the heights of signal distributions (red/points) in the left\nand right plots (Lin, 2008).\n\n247\nTable 17.4.1. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for decays B \u2192KK, K\u03c0, \u03c0\u03c0. The averages come from HFAG\nand may include measurements from other experiments such as CLEO and CDF (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK+K\u2212\n0.04 \u00b1 0.15 \u00b1 0.08\n(Aubert, 2007o)\n0.09+0.18\n\u22120.13 \u00b1 0.01\n(Abe, 2007g)\n0.15+0.11\n\u22120.10\nK+K\n0\n1.61 \u00b1 0.44 \u00b1 0.09\n0.10 \u00b1 0.26 \u00b1 0.03\n(Aubert, 2006ai)\n1.11+0.19\n\u22120.18 \u00b1 0.05\n0.017 \u00b1 0.168 \u00b1 0.002\n(Chang, 2011)\n1.19 \u00b1 0.18\n0.041 \u00b1 0.141\nK+\u03c0\u2212\n19.1 \u00b1 0.6 \u00b1 0.6\n\u22120.107 \u00b1 0.016+0.006\n\u22120.004\n(Aubert, 2007o)\n20.0 \u00b1 0.34 \u00b1 0.63\n\u22120.069 \u00b1 0.014 \u00b1 0.007\n(Chang, 2011)\n19.55+0.54\n\u22120.53\n\u22120.086 \u00b1 0.007\nK+\u03c00\n13.6 \u00b1 0.6 \u00b1 0.7\n0.030 \u00b1 0.039 \u00b1 0.010\n(Aubert, 2007ay)\n12.62 \u00b1 0.31 \u00b1 0.56\n0.043 \u00b1 0.024 \u00b1 0.002\n(Chang, 2011)\n12.94+0.52\n\u22120.51\n0.037 \u00b1 0.021\nK0K\n0\n1.08 \u00b1 0.28 \u00b1 0.11\n(Aubert, 2006ai)\n1.26+0.19\n\u22120.18 \u00b1 0.06\n(Chang, 2011)\n1.21 \u00b1 0.16\nK0\u03c0+\n23.9 \u00b1 1.1 \u00b1 1.0\n\u22120.029 \u00b1 0.039 \u00b1 0.010\n(Aubert, 2006ai)\n23.97+0.53\n\u22120.52 \u00b1 0.69\n\u22120.014 \u00b1 0.012 \u00b1 0.006\n(Chang, 2011)\n23.80 \u00b1 0.74\n\u22120.015 \u00b1 0.012\nK0\u03c00\n10.1 \u00b1 0.6 \u00b1 0.4\n(Aubert, 2008m)\n9.66 \u00b1 0.46 \u00b1 0.49\n(Chang, 2011)\n9.92+0.49\n\u22120.48\n\u03c0+\u03c0\u2212\n5.5 \u00b1 0.4 \u00b1 0.3\n(Aubert, 2007o)\n5.04 \u00b1 0.21 \u00b1 0.19\n(Chang, 2011)\n5.11 \u00b1 0.22\n\u03c0+\u03c00\n5.02 \u00b1 0.46 \u00b1 0.29\n0.03 \u00b1 0.08 \u00b1 0.01\n(Aubert, 2007ay)\n5.86 \u00b1 0.26 \u00b1 0.38\n0.025 \u00b1 0.043 \u00b1 0.007\n(Chang, 2011)\n5.48+0.35\n\u22120.34\n0.026 \u00b1 0.039\n\u03c00\u03c00\n1.83 \u00b1 0.21 \u00b1 0.13\n0.43 \u00b1 0.26 \u00b1 0.05\n(Aubert, 2008m)\n2.3+0.4+0.2\n\u22120.5\u22120.3\n0.44+0.53\n\u22120.52 \u00b1 0.17\n(Abe, 2005h)\n1.91+0.22\n\u22120.23\n0.43 \u00b1 0.24\n\n248\nThe branching fractions of two-body decays to \u03c0\u03c0 \ufb01nal\nstates are of interest to understand the so-called penguin\npollution in B0 \u2192\u03c0+\u03c0\u2212(discussed in Section 17.7). It\nwas observed that in the \u03c0+\u03c0\u2212\ufb01nal state there appeared\nto be evidence for a signi\ufb01cant tail in the \u2206E distribution\nfor selected events that was not apparent in the Monte\nCarlo simulation used at that time. After some investiga-\ntion it was realised that the tail in \u2206E was the result of\n\ufb01nal state radiation (FSR) which needed to be accounted\nfor properly in the simulation in order to continue to im-\nprove the precision of branching fraction measurements\nin an un-biased way. The \ufb01rst B0 \u2192\u03c0+\u03c0\u2212branching\nfraction measurement that attempted to account for this\nFSR e\ufb00ect appropriately was performed by BABAR (Au-\nbert, 2007o). Subsequent results account for this e\ufb00ect.\nInitial expectations for the decay B0 \u2192\u03c00\u03c00 were that\nthe branching fraction would be small, led in part by the-\noretical calculations indicating that this process would be\ndominated by a color suppressed tree. In the summer of\n2002, preliminary results from the B Factories started to\nshow hints of a relatively large signal with a branching\nfraction central value of a few 10\u22126. Subsequent results\npublished by BABAR and Belle led to the observation of\nthis channel. The world average branching fraction is cur-\nrently (1.91+0.22\n\u22120.23) \u00d7 10\u22126.\n17.4.5 Quasi-two-body decays\nIn the sections that follow, the quasi-two-body decays have\nbeen grouped according to the spins of their \ufb01nal state\nparticles. For each grouping of spin, the results for the\nbranching fractions are itemized in tables and are shown\nin the plots to enable convenient comparison.\n17.4.5.1 B \u2192two Pseudoscalars, Pseudoscalar Vector,\nPseudoscalar Scalar, Pseudoscalar Tensor with \u03b7(\u2032)\nA number of searches have been performed with a Pseu-\ndoscalar \u03b7 or \u03b7\u2032 in the \ufb01nal state together with one other\nparticle. For Pseudoscalar-Pseudoscalar (PP) modes, the\nother particle is an \u03b7(\u2032), K, or \u03c0; for Pseudoscalar-Vector\n(PV) modes, a K\u2217, \u03c1, \u03c9, or \u03c6; for Pseudoscalar-Scalar (PS)\nmodes, an f0(980) or K\u2217\n0(1430); for Pseudoscalar-Tensor\n(PT), K\u2217\n2(1430). The branching fractions and asymme-\ntries reported by Belle and BABAR, and their HFAG av-\nerages, are given in Table 17.4.2. Figure 17.4.6 shows the\nbranching fractions. The HFAG averages represent a snap-\nshot of the \ufb01eld in late 2012 (Amhis et al. (2012)) but are\nbeing annually updated on the website (see Asner et al.\n(2011)).\n0.0 \n50.0 \n100.0 \nBranching Ratio x 106 \nB(B \u2192(\u03b7, \u03b7\u2032) (K(\u2217), \u03c0, \u03c1))\nHFAG\nAug 2012\nCLEO \nBelle \nBABAR \nNew Avg. \n \n \n\u03b7 \u03b7 K0\n\u03b7 \u03b7 K+\n\u03b7 K\u22170(1430)0\n\u03b7 K\u22170(1430)+\n\u03b7 K\u22172(1430)0\n\u03b7 K\u22172(1430)+\n\u03b7 K+\n\u03b7 K0\n\u03b7 K\u2217+\n\u03b7 K\u22170\n\u03b7 \u03c1+\n\u03b7 \u03c10\n\u03b7 \u03c0+\n\u03b7 \u03c00\nKSKS\u03b7\n\u03c9\u03b7\n\u03c6\u03b7\n\u03b7 \u03b7\n\u03b7 \u03b7\n\u03b7K\u22170(1430)+\n\u03b7K\u22170(1430)0\n\u03b7K\u22172(1430)+\n\u03b7K\u22172(1430)0\n\u03b7K\u2217+\n\u03b7K\u22170\n\u03b7\u03c1+\n\u03b7\u03c10\n\u03b7K+\n\u03b7K0\n\u03b7\u03c0+\n\u03b7\u03c00\nf0(980)\u03b7 \u2020\nKSKS\u03b7\n\u03c9\u03b7\n\u03c6\u03b7\n\u03b7\u03b7\n\u03b7(1475)K+\u2020\n\u03b7(1405)K+\u2020\n\u03b7(1295)K+\u2020\nFigure 17.4.6. Summary of branching fraction measurements\n(\u00d710\u22126) and HFAG averages for decays with an \u03b7 or \u03b7\u2032 meson\ncombined with a pseudoscalar, vector, scalar or tensor particle\n(Amhis et al. (2012)).\n\n249\nTable 17.4.2. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for decays with an \u03b7 or \u03b7\u2032 in the \ufb01nal state. The averages come\nfrom HFAG. The decays are arranged from top to bottom, as Pseudoscalar-Pseudoscalar (PP), Pseudoscalar-Vector (PV), Pseudoscalar-Scalar (PS), Pseudoscalar-Tensor\n(PT), and three-body decays (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\n\u03b7K+\n2.94+0.39\n\u22120.34 \u00b1 0.21\n\u22120.36 \u00b1 0.11 \u00b1 0.03\n(Aubert, 2009d)\n2.12 \u00b1 0.23 \u00b1 0.11\n\u22120.38 \u00b1 0.11 \u00b1 0.01\n(Hoi, 2012)\n2.36+0.22\n\u22120.21\n\u22120.37 \u00b1 0.09\n\u03b7K0\n1.15+0.43\n\u22120.38 \u00b1 0.09\n(Aubert, 2009d)\n1.27+0.33\n\u22120.29 \u00b1 0.08\n(Hoi, 2012)\n1.23+0.27\n\u22120.24\n\u03b7\u03b7\n< 1.0\n(Aubert, 2009d)\n< 2.0\n(Chang, 2005)\n< 1.0\n\u03b7\u03c0+\n4.00 \u00b1 0.40 \u00b1 0.24\n\u22120.03 \u00b1 0.09 \u00b1 0.03\n(Aubert, 2009d)\n4.07 \u00b1 0.26 \u00b1 0.21\n\u22120.19 \u00b1 0.06 \u00b1 0.01\n(Hoi, 2012)\n4.02 \u00b1 0.27\n\u22120.13 \u00b1 0.10\n\u03b7\u03c00\n< 1.5\n(Aubert, 2008af)\n< 2.5\n(Chang, 2005)\n< 1.5\n\u03b7(1295)K+\n< 4.0\n(Aubert, 2008bb)\n< 4.0\n\u03b7(1405)K+\n< 1.2\n(Aubert, 2008bb)\n< 1.2\n\u03b7(1475)K+\n13.8+1.8+1.0\n\u22121.7\u22120.6\n(Aubert, 2008bb)\n13.8+2.1\n\u22121.8\n\u03b7\u2032K+\n71.5 \u00b1 1.3 \u00b1 3.2\n0.008+0.017\n\u22120.018 \u00b1 0.009\n(Aubert, 2009d)\n69.2 \u00b1 2.2 \u00b1 3.7\n0.028 \u00b1 0.028 \u00b1 0.021\n(Schumann, 2006)\n71.1 \u00b1 2.6\n0.013 \u00b1 0.017\n\u03b7\u2032K0\n68.5 \u00b1 2.2 \u00b1 3.1\n(Aubert, 2009d)\n58.9+3.6\n\u22123.5 \u00b1 4.3\n(Schumann, 2006)\n66.1 \u00b1 3.1\n\u03b7\u2032\u03b7\n< 1.2\n(Aubert, 2008af)\n< 4.5\n(Schumann, 2007)\n< 1.2\n\u03b7\u2032\u03b7\u2032\n< 1.7\n(Aubert, 2009d)\n< 6.5\n(Schumann, 2007)\n< 1.7\n\u03b7\u2032\u03c0+\n3.5 \u00b1 0.6 \u00b1 0.2\n0.03 \u00b1 0.17 \u00b1 0.02\n(Aubert, 2009d)\n1.8+0.7\n\u22120.6 \u00b1 0.1\n0.20+0.37\n\u22120.36 \u00b1 0.04\n(Schumann, 2006)\n2.7+0.5\n\u22120.4\n0.06 \u00b1 0.16\n\u03b7\u2032\u03c00\n0.9 \u00b1 0.4 \u00b1 0.1\n(Aubert, 2008af)\n2.8 \u00b1 1.0 \u00b1 0.3\n(Schumann, 2006)\n1.2 \u00b1 0.4\n\u03b7K\u2217+\n18.9 \u00b1 1.8 \u00b1 1.3\n0.01 \u00b1 0.08 \u00b1 0.02\n(Aubert, 2006l)\n19.3+2.0\n\u22121.9 \u00b1 1.5\n0.03 \u00b1 0.10 \u00b1 0.01\n(Wang, 2007a)\n19.3 \u00b1 1.6\n0.02 \u00b1 0.06\n\u03b7K\u22170\n16.5 \u00b1 1.1 \u00b1 0.8\n0.21 \u00b1 0.06 \u00b1 0.02\n(Aubert, 2006l)\n15.2 \u00b1 1.2 \u00b1 1.0\n0.17 \u00b1 0.08 \u00b1 0.01\n(Wang, 2007a)\n15.9 \u00b1 1.0\n0.19 \u00b1 0.05\n\u03b7\u03c1+\n9.9 \u00b1 1.2 \u00b1 0.8\n0.13 \u00b1 0.11 \u00b1 0.02\n(Aubert, 2008af)\n4.1+1.4\n\u22121.3 \u00b1 0.4\n\u22120.04+0.34\n\u22120.32 \u00b1 0.01\n(Wang, 2007a)\n6.9 \u00b1 1.0\n0.11 \u00b1 0.11\n\u03b7\u03c10\n< 1.5\n(Aubert, 2007as)\n< 1.9\n(Wang, 2007a)\n< 1.5\n\u03b7\u2032K\u2217+\n4.8+1.6\n\u22121.4 \u00b1 0.8\n\u22120.26 \u00b1 0.27 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n< 2.9\n(Schumann, 2007)\n5.0+1.8\n\u22121.6\n\u22120.30+0.33\n\u22120.37 \u00b1 0.02\n\u03b7\u2032K\u22170\n3.1+0.9\n\u22120.8 \u00b1 0.3\n0.02 \u00b1 0.23 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n< 2.6\n(Schumann, 2007)\n3.1 \u00b1 0.9\n0.08 \u00b1 0.25 \u00b1 0.02\n\u03b7\u2032\u03c1+\n9.7+1.9\n\u22121.8 \u00b1 1.1\n0.26 \u00b1 0.17 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n< 5.8\n(Schumann, 2007)\n9.8+2.1\n\u22122.0\n0.04 \u00b1 0.28 \u00b1 0.02\n\u03b7\u2032\u03c10\n< 2.8\n(del Amo Sanchez, 2010h)\n< 1.3\n(Schumann, 2007)\n< 1.3\n\u03c9\u03b7\n< 1.4\n(Aubert, 2009d)\n< 1.4\n\u03c9\u03b7\u2032\n< 1.8\n(Aubert, 2009d)\n< 2.2\n(Schumann, 2007)\n< 1.8\n\u03c6\u03b7\n< 0.5\n(Aubert, 2009d)\n< 0.5\n\u03c6\u03b7\u2032\n< 1.1\n(Aubert, 2009d)\n< 0.5\n(Schumann, 2007)\n< 0.5\nf0(980)\u03b7\n< 0.4\n(Aubert, 2007as)\n< 0.4\nf0(980)\u03b7\u2032\n< 0.9\n(del Amo Sanchez, 2010h)\n< 0.9\n\u03b7K\u2217\n0 (1430)+\n15.8 \u00b1 2.2 \u00b1 2.2\n0.05 \u00b1 0.13 \u00b1 0.02\n(Aubert, 2006l)\n15.8 \u00b1 3.1\n0.05 \u00b1 0.13 \u00b1 0.02\n\u03b7K\u2217\n0 (1430)0\n9.6 \u00b1 1.4 \u00b1 1.3\n0.06 \u00b1 0.13 \u00b1 0.02\n(Aubert, 2006l)\n9.6 \u00b1 1.9\n0.06 \u00b1 0.13 \u00b1 0.02\n\u03b7\u2032K\u2217\n0 (1430)+\n5.2 \u00b1 1.9 \u00b1 1.0\n0.06 \u00b1 0.20 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n5.2 \u00b1 2.1\n\u03b7\u2032K\u2217\n0 (1430)0\n6.3 \u00b1 1.3 \u00b1 0.9\n\u22120.19 \u00b1 0.17 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n6.3 \u00b1 1.6\n\u03b7K\u2217\n2 (1430)+\n9.1 \u00b1 2.7 \u00b1 1.4\n\u22120.45 \u00b1 0.30 \u00b1 0.02\n(Aubert, 2006l)\n9.1 \u00b1 3.0\n\u22120.45 \u00b1 0.30 \u00b1 0.02\n\u03b7K\u2217\n2 (1430)0\n9.6 \u00b1 1.8 \u00b1 1.1\n\u22120.07 \u00b1 0.19 \u00b1 0.02\n(Aubert, 2006l)\n9.6 \u00b1 2.1\n\u22120.07 \u00b1 0.19 \u00b1 0.02\n\u03b7\u2032K\u2217\n2 (1430)+\n28.0+4.6\n\u22124.3 \u00b1 2.6\n0.15 \u00b1 0.13 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n28.0+5.3\n\u22125.0\n\u03b7\u2032K\u2217\n2 (1430)0\n13.7+3.0\n\u22121.9 \u00b1 1.2\n0.14 \u00b1 0.18 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n13.7+3.2\n\u22122.2\nK0\nSK0\nS\u03b7\n< 1.0\n(Aubert, 2009am)\n< 1.0\nK0\nSK0\nS\u03b7\u2032\n< 2.0\n(Aubert, 2009am)\n< 2.0\n\u03b7\u2032\u03b7\u2032K+\n< 25\n(Aubert, 2006al)\n< 25\n\u03b7\u2032\u03b7\u2032K0\n< 31\n(Aubert, 2006al)\n< 31\n\n250\nTheory predictions for PP and PV branching frac-\ntions are typically in the low parts per million. In lead-\ning order SM calculations, the time dependent CP viola-\ntion asymmetry parameter S = sin 2\u03c61 in decays such as\nB0 \u2192\u03b7\u2032K0\nS, B0 \u2192KKK0\nS and B0 \u2192\u03c6K0\nS is expected\nto be the same as in the golden mode B0 \u2192J/\u03c8K0\nS and\nprovide a useful comparison between decays mediated by\nb \u2192ssu, b \u2192suu, b \u2192sdd and b \u2192ccs (see Section 17.6\nfor details), provided the decays are dominated by a single\nweak phase. Within the standard model (SM), the decay\nB \u2192\u03b7\u2032K proceeds through b \u2192s penguin loops with only\na small contribution from b \u2192u tree diagrams (Chen,\n2002). Corrections can be estimated in QCD factorization\nand turn out to be small. Therefore a signi\ufb01cant deviation\nwould be a sign of new physics (Abe, 2003e). The decay\nrates of \u03b7\u03b7, \u03b7\u2032\u03b7\u2032, \u03b7\u03c6 and \u03b7\u2032\u03c6 can be related to any devia-\ntion in \u2206S from the charmonium measured \u03c61 via SU(3)\n\ufb02avor symmetry (Aubert, 2006av, 2007am).\nIn charged decays such as B+ \u2192\u03b7\u2032K+ and B+ \u2192\n\u03b7\u2032\u03c0+ (Abe, 2001d; Schumann, 2006), the CP charge asym-\nmetry ACP is expected to be small in \u03b7\u2032K+. A large di-\nrect CP asymmetry is expected in B+ \u2192\u03b7K+ but not\nin B+ \u2192\u03b7\u2032K+ because the overall penguin amplitudes\nin B+ \u2192\u03b7K+ are of the same order as the tree ampli-\ntude, while in B+ \u2192\u03b7\u2032K+ the penguin dominates. This\nis con\ufb01rmed by the experiments, which measure ACP =\n\u22120.37\u00b10.09 for B+ \u2192\u03b7K+ but only ACP = 0.013\u00b10.017\nfor B+ \u2192\u03b7\u2032K+. In \u03b7\u03c1+, \u03b7\u03c0+ and \u03b7\u2032\u03c0+, the b \u2192u and\nb \u2192s amplitudes are of similar size possibly leading to\nlarge direct CP violation (Aubert, 2005l).\nAny sub-leading terms in B0 \u2192\u03b7\u2032K0\nS can be con-\nstrained by measuring the decays \u03b7\u2032\u03b7, \u03b7\u03c00 and \u03b7\u2032\u03c00. B0 \u2192\n\u03b7\u03c00 and B0 \u2192\u03b7\u2032\u03c00 may also constrain isospin break-\ning e\ufb00ects on the value of sin 2\u03c62 in B0 \u2192\u03c0+\u03c0\u2212decays.\nThe branching fractions are a useful test of predictions\nfrom QCD factorization, perturbative QCD (for \u03b7\u2032\u03c00) and\n\ufb02avor-SU(3) symmetry (Aubert, 2006g). These limit the\ndeviation \u2206S of the measured S from the value seen in\ncharmonium decays, with bounds on |\u2206S| < 0.05.\nMixing-induced CP violation has been observed in B0 \u2192\n\u03b7\u2032K0 (Aubert, 2007am) and (Chen, 2007a). The \u03b7\u2032K\u2217and\n\u03b7K branching fractions are suppressed while \u03b7\u2032K and \u03b7K\u2217\nare enhanced, since the two b \u2192s penguins that con-\ntribute interfere constructively in \u03b7\u2032K decays and destruc-\ntively in \u03b7K, while the situation is reversed for \u03b7\u2032K\u2217and\n\u03b7K\u2217(Beneke and Neubert, 2003a; Lipkin, 1991) as is ob-\nserved (Abe, 2007a; Chang, 2005). Searches for \u03b7\u2032h can\nimprove the understanding of \ufb02avor-singlet penguin am-\nplitudes with intermediate up-type (u,c,t) quarks (Schu-\nmann, 2007).\nSearches for excited \u03b7 and \u03b7\u2032 mesons (e.g. the JP = 0\u2212\nstates \u03b7(1295), \u03b7(1405), \u03b7(1475)) with a kaon have also\nbeen performed (Aubert, 2008bb). They decay strongly to\nat least three pseudoscalar mesons but their exact nature\nis uncertain and they could be gluonium admixtures (i.e. a\nstate with additional gg components). Partial wave analy-\nsis suggests that the meson spectrum is a linear combina-\ntion of the resonant state and a non-resonant phase-space\ncontribution. The JP = 1+ states f1(1285) and f1(1420),\nand the JP = 1\u2212state \u03c6(1680) have a similar mass and\n\ufb01nal decay states as the JP = 0\u2212states so have to be\nincluded in any search for excited \u03b7 and \u03b7\u2032 mesons.\nPenguin (tree) diagrams dominate in the B decay to\n\u03b7K\u2217(\u03b7\u03c1) (Wang, 2007a). The decays \u03b7\u2032\u03c1 are suppressed\ndue to the small value of the CKM matrix element, even\nthough they proceed via tree diagrams (Aubert, 2007ak).\nThe expected branching fraction for B0 \u2192\u03b7\u2032\u03c10 is of the\norder 10\u22128 \u221210\u22127 and a few times 10\u22126 for B+ \u2192\u03b7\u2032\u03c1+.\nThe measured values for B (B+ \u2192\u03b7(\u2032)\u03c1+) are \u223c10\u00d710\u22126\nwhile only upper limits (UL) of < (1.5 \u22122.8) \u00d7 10\u22126 have\nbeen placed on B0 \u2192\u03b7(\u2032)\u03c10 decays.\nUpper limits of 0.4 \u00d7 10\u22126 and 0.9 \u00d7 10\u22126 have been\nfound for B0 \u2192f0(980)\u03b7 and B0 \u2192f0(980)\u03b7\u2032, respec-\ntively (Aubert, 2007as; del Amo Sanchez, 2010h). Mea-\nsurements also exist for B \u2192\u03b7(\u2032)K\u2217\n0(1430) and B \u2192\n\u03b7(\u2032)K\u2217\n2(1430); the measured values of ACP are compati-\nble with zero.\nDecays involving two identical neutral spin zero parti-\ncles and another spin zero particle can be used to add im-\nportant information on time-dependent CP violation and\nhadronic B decays (Aubert, 2006al). Examples of such de-\ncays include B \u2192\u03b7\u2032\u03b7\u2032K and B0 \u2192K0\nSK0\nS\u03b7(\u2032). There are\nno theoretical predictions for the branching fractions for\nthese SM-suppressed modes.\n17.4.5.2 B \u2192PV excluding \u03b7(\u2032)\nThe branching fractions and asymmetries for the remain-\ning PV modes without an \u03b7 or \u03b7\u2032 are given in Table 17.4.3\nand the hierarchy of the branching fraction values are\nshown in Fig. 17.4.7. The decays B \u2192\u03c9\u03c0\u2212and B \u2192\u03c9K\u2212\nare dominated by b \u2192u tree and b \u2192s QCD penguin dia-\ngrams. They can therefore give an insight into gluonic pen-\nguin diagrams (Lu, 2002; Wang, 2004a), (Aubert, 2006ad)\nand direct CP (Lu, 2002).\nCharmless B meson decays to \ufb01nal states with an odd\nnumber of kaons are usually expected to be dominated\nby b \u2192s penguin loops while b \u2192u tree amplitudes are\ntypically large for \ufb01nal states with \u03c0 and \u03c1 but \u03b7K decays\nare suppressed relative to the abundant \u03b7\u2032K.\nThe B \u2192\u03c9K0 decay is a b \u2192uus process dominated\nby a single penguin loop amplitude with the same weak\nphase \u03c61 as \u03c6K0, K+K\u2212K0, \u03b7\u2032K0, \u03c00K0, and f0(980)K0,\nbut additional amplitudes and multiple particles in the\nloop complicate the situation by introducing non-negligible\nweak phases. B meson decays to CP eigenstates \u03c9K0\nS (to-\ngether with \u03b7\u2032K0\nS, \u03b7\u2032K0\nL and \u03c00K0\nS) can be used to extract\nS and C (Aubert, 2009aa). The maximum deviation \u2206S\nfrom the value of S = sin 2\u03c61 measured in charmonium\nK0\nS decays is \u223c0.1. The charged decay modes are ex-\npected to have a direct CP violation value consistent with\nzero (Aubert, 2006ad).\nIn the Standard Model, B \u2192K\u2217K decays are dom-\ninated by b \u2192dss gluonic penguin diagrams; for the\ncharged B\u00b1 decay, the spectator d is replaced with u. Such\ntransitions provide a valuable tool with which to test the\nquark-\ufb02avor sector of the SM. The mode B+ \u2192K\u22170K+ is\n\n251\nTable 17.4.3. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for Pseudoscalar-Vector (PV) \ufb01nal states. The averages come\nfrom HFAG and may include measurements from other experiments such as CLEO and CDF (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK\u2217(1410)+\u03c0\u2212\n< 86\n(Garmash, 2007)\n< 86\nK\u2217(1410)0\u03c0+\n< 45\n(Garmash, 2005)\n< 45\nK\u2217(1680)+\u03c0\u2212\n< 25\n(Aubert, 2008g)\n< 10.1\n(Garmash, 2007)\n< 10.1\nK\u2217(1680)0\u03c0+\n< 15\n(Aubert, 2005g)\n< 12\n(Garmash, 2005)\n< 12\nK\u2217(1680)0\u03c00\n< 7.5\n(Aubert, 2008g)\n< 7.5\nK\u2217+\u03c0\u2212\n8.3+0.9\n\u22120.8 \u00b1 0.8\n\u22120.24 \u00b1 0.07 \u00b1 0.02\n(Aubert, 2009av)\n8.4 \u00b1 1.1+1.0\n\u22120.9\n\u22120.21 \u00b1 0.11 \u00b1 0.07\n(Garmash, 2007)\n8.6 \u00b1 0.9\n-0.19 \u00b1 0.07\nK\u2217+\u03c00\n8.2 \u00b1 1.5 \u00b1 1.1\n\u22120.06 \u00b1 0.24 \u00b1 0.04\n(Lees, 2011g)\n8.2 \u00b1 1.8\n0.04 \u00b1 0.29 \u00b1 0.05\nK\u22170K\n0\n< 1.9\n(Aubert, 2006au)\n< 1.9\nK\u22170\u03c0+\n10.8 \u00b1 0.6+1.2\n\u22121.4\n0.032 \u00b1 0.052+0.016\n\u22120.013\n(Aubert, 2008j)\n9.7 \u00b1 0.6+0.8\n\u22120.9\n\u22120.149 \u00b1 0.064 \u00b1 0.022\n(Garmash, 2006)\n9.9+0.8\n\u22120.9\n\u22120.04 \u00b1 0.09\nK\u22170\u03c00\n3.3 \u00b1 0.5 \u00b1 0.4\n\u22120.15 \u00b1 0.12 \u00b1 0.04\n(Lees, 2011a)\n0.4+1.9\n\u22121.7 \u00b1 0.1\n(Chang, 2004)\n2.5 \u00b1 0.6\n\u22120.09+0.23\n\u22120.26\n\u03c9K+\n6.3 \u00b1 0.5 \u00b1 0.3\n\u22120.01 \u00b1 0.07 \u00b1 0.01\n(Aubert, 2007f)\n8.1 \u00b1 0.6 \u00b1 0.6\n0.05+0.08\n\u22120.07 \u00b1 0.01\n(Jen, 2006)\n6.7 \u00b1 0.5\n0.02 \u00b1 0.05\n\u03c9K0\n5.4 \u00b1 0.8 \u00b1 0.3\n(Aubert, 2007f)\n4.4+0.8\n\u22120.7 \u00b1 0.4\n(Jen, 2006)\n5.0 \u00b1 0.6\n\u03c9\u03c0+\n6.7 \u00b1 0.5 \u00b1 0.4\n\u22120.02 \u00b1 0.08 \u00b1 0.01\n(Aubert, 2007f)\n6.9 \u00b1 0.6 \u00b1 0.5\n\u22120.02 \u00b1 0.09 \u00b1 0.01\n(Jen, 2006)\n6.9 \u00b1 0.5\n\u22120.04 \u00b1 0.06\n\u03c9\u03c00\n< 0.5\n(Aubert, 2008af)\n< 2.0\n(Jen, 2006)\n< 0.5\nK\n\u22170K+\n< 1.1\n(Aubert, 2007av)\n< 1.1\n\u03c6K+\n9.2 \u00b1 0.4+0.7\n\u22120.5\n0.128 \u00b1 0.044 \u00b1 0.013\n(Lees, 2012y)\n9.60 \u00b1 0.92+1.05\n\u22120.84\n0.01 \u00b1 0.12 \u00b1 0.05\n(Garmash, 2005)\n8.8 \u00b1 0.5\n\u22120.01 \u00b1 0.06\n\u03c6K0\n7.1 \u00b1 0.6+0.4\n\u22120.3\n\u22120.05 \u00b1 0.18 \u00b1 0.05\n(Lees, 2012y)\n9.0+2.2\n\u22121.8 \u00b1 0.7\n(Chen, 2003)\n7.3+0.7\n\u22120.6\n\u03c6\u03c0+\n< 0.24\n(Aubert, 2006am)\n< 0.33\n(Kim, 2012)\n< 0.24\n\u03c6\u03c00\n< 0.28\n(Aubert, 2006am)\n< 0.28\n\u03c6(1680)K+\n< 0.8\n(Garmash, 2005)\n< 0.8\n\u03c1(1450)\u2212K+\n2.4 \u00b1 1.0 \u00b1 0.6\n(Lees, 2011a)\n2.4 \u00b1 1.2\n\u03c1(1450)0\u03c0+\n1.4 \u00b1 0.4+0.5\n\u22120.8\n\u22120.06 \u00b1 0.28+0.23\n\u22120.32\n(Aubert, 2009h)\n1.4+0.6\n\u22120.9\n\u22120.06+0.36\n\u22120.42\n\u03c1(1700)\u2212K+\n0.6 \u00b1 0.6 \u00b1 0.4\n(Lees, 2011a)\n0.6 \u00b1 0.7\n\u03c1+K0\n8.0+1.4\n\u22121.3 \u00b1 0.6\n\u22120.12 \u00b1 0.17 \u00b1 0.02\n(Aubert, 2007al)\n8.0+1.5\n\u22121.4\n\u22120.12 \u00b1 0.17 \u00b1 0.02\n\u03c1+\u03c00\n10.2 \u00b1 1.4 \u00b1 0.9\n\u22120.01 \u00b1 0.13 \u00b1 0.02\n(Aubert, 2007y)\n13.2 \u00b1 2.3+1.4\n\u22121.9\n0.06 \u00b1 0.17+0.04\n\u22120.05\n(Zhang, 2005)\n10.9+1.4\n\u22121.5\n0.02 \u00b1 0.11\n\u03c1\u2212K+\n6.6 \u00b1 0.5 \u00b1 0.8\n0.20 \u00b1 0.09 \u00b1 0.08\n(Lees, 2011a)\n15.1+3.4+2.4\n\u22123.3\u22122.6\n0.22+0.22+0.06\n\u22120.23\u22120.02\n(Chang, 2004)\n7.2 \u00b1 0.9\n0.15 \u00b1 0.13\n\u03c10K+\n3.56 \u00b1 0.45+0.57\n\u22120.46\n0.44 \u00b1 0.10+0.06\n\u22120.14\n(Aubert, 2008j)\n3.89 \u00b1 0.47+0.43\n\u22120.41\n0.30 \u00b1 0.11+0.11\n\u22120.05\n(Garmash, 2006)\n3.81+0.48\n\u22120.46\n0.37 \u00b1 0.10\n\u03c10K0\n4.4 \u00b1 0.7 \u00b1 0.3\n(Aubert, 2009av)\n6.1 \u00b1 1.0+1.1\n\u22121.2\n(Garmash, 2007)\n4.7 \u00b1 0.7\n\u03c10\u03c0+\n8.1 \u00b1 0.7+1.3\n\u22121.6\n0.18 \u00b1 0.07+0.05\n\u22120.15\n(Aubert, 2009h)\n8.0+2.3\n\u22122.0 \u00b1 0.7\n(Gordon, 2002)\n8.3+1.2\n\u22121.3\n0.18+0.09\n\u22120.17\n\u03c10\u03c00\n1.4 \u00b1 0.6 \u00b1 0.3\n(Aubert, 2004g)\n3.0 \u00b1 0.5 \u00b1 0.7\n(Kusaka, 2008)\n2.0 \u00b1 0.5\n\u03c10(1450)K+\n< 11.7\n(Aubert, 2005g)\n< 11.7\n\u03c1\u2213\u03c0\u00b1\n22.6 \u00b1 1.8 \u00b1 2.2\n(Aubert, 2002g)\n22.6 \u00b1 1.1 \u00b1 4.4\n(Kusaka, 2008)\n23.0 \u00b1 2.3\n\n252\n0.0 \n25.0 \nHFAG\nAug 2012\nBranching Ratio x 106 \nB(B \u2192(K\u2217, \u03c1, \u03c9, \u03c6)(\u03c0, K ))\nBABA R \nBelle \nCLE O \nNe w A vg . \nCDF \n\u03c1+K0\n\u03c10K0\n\u03c1\u2212K+\n\u03c10K+\n\u03c10(1450)K+\n\u03c1(1450)\u2212K+\n\u03c1(1450)0\u03c0+ \u2020\n\u03c1(1700)\u2212K+\n\u03c1\u2213\u03c0\u00b1\n\u03c1+\u03c00\n\u03c10\u03c0+\n\u03c10\u03c00\nK\u2217+\u03c00\nK\u22170\u03c0+\nK\u2217+\u03c0\u2212\nK\u22170\u03c00\nK\u2217(1410)0\u03c0+\nK\u2217(1410)+\u03c0\u2212\u2020\nK\u2217(1680)0\u03c0+\nK\u2217(1680)0\u03c00\nK\u2217(1680)+\u03c0\u2212\n\u03c9K+\n\u03c9K0\n\u03c9\u03c0+\n\u03c9\u03c00\n\u03c6K+\n\u03c6K0\n\u03c6\u03c0+\n\u03c6\u03c00\n\u03c6(1680)K+\u2020\nK\u22170K0\nK\u22170K+\nFigure 17.4.7. Summary of branching fraction measurements\n(\u00d710\u22126) and HFAG averages for Pseudovector-Vector (PV) de-\ncays (Amhis et al. (2012)).\nalso relevant for the interpretation of the time dependent\nCP asymmetry obtained with the B0 \u2192\u03c6K0\nS mode. To\nleading order, the CP asymmetry equals sin 2\u03c61 for this\nmode. However, sub-dominant amplitudes proportional to\nV \u2217\nubVus could produce a deviation \u2206S\u03c6K0\nS from sin 2\u03c61.\nBounds can be placed on \u2206S\u03c6K0\nS by exploiting SU(3)\n\ufb02avor symmetry and combining measured rates for rel-\nevant b \u2192s and b \u2192d processes (including B+ \u2192\nK\u22170K+). Measurements yielding a signi\ufb01cant deviation in\nexcess of such a bound would be a strong indication of\nphysics beyond the SM. Furthermore, B+ \u2192K\u22170K+ is\none of several charmless decays that can be used, together\nwith U-spin symmetry, to extract the angle \u03c63 (Aubert,\n2007av). Only upper limits exist on B0 \u2192K\u22170K0 (Au-\nbert, 2006au), which can be used to constrain certain ex-\ntensions of the Standard Model.\nPolarizations of Charmless Decays \nLongitudinal Polarization Fraction (fL) \n0.2 \n 0.4 \n 1.0 \n 1.2\n 0.6 \n 0.8 \nHFAG\nAug 2012\nBABAR \n \nBelle \nNe w A vg . \n\u03c1+\u03c1\u2212\n\u03c1+\u03c10\n\u03c10\u03c10\n\u03c9\u03c1+\na\u00b1\n1 a\u2213\n1\nK\u22170K\u22170\nK\u2217+K\u22170\nK\u2217+\u03c1\u2212\nK\u2217+\u03c10\nK\u22170\u03c10\nK\u22170\u03c1+\n\u03c9K\u22170\n\u03c9K\u2217+\n\u03c9K\u22172(1430)+\n\u03c9K\u22172(1430)0\n\u03c6K\u22170\n\u03c6K\u2217+\n\u03c6K1(1270)+\n\u03c6K\u22172(1430)0\n\u03c6K\u22172(1430)+\nFigure 17.4.8. The longitudinal polarization fractions fL for\ncharmless B decays at BABAR and Belle. The average is from\nthe HFAG group (Amhis et al. (2012)).\n17.4.5.3 B \u2192VV\nDecays to a Vector-Vector (VV) \ufb01nal state with pairs\nformed from \u03c9, K\u2217, \u03c1, and \u03c6 can, in principle, be used to\ndetermine the helicity amplitudes of the decay. However,\nthis requires a complete angular analysis and in general\nthe number of reconstructed events currently restricts any\nanalysis to integrating over two of the helicity angles and\nsimply reporting the longitudinal polarization fL. A full\nangular analysis has been done for low-background decays\nsuch as B0 \u2192\u03c6K\u22170. Further details of the angular analy-\nsis process can be found in Chapter 12, where the angular\ndistributions for the VV \ufb01nal states is given in Eq. 12.2.5.\nAs discussed in Section 17.4.2, the B \u2192V V decays\nare na\u00a8\u0131vely predicted to be dominated by the longitudinal\npolarization since fL \u22481 \u22124mV /mB \u223c0.9, but the na\u00a8\u0131ve\nfactorization expectation is not born out by the QCD fac-\ntorization analysis for the penguin-dominated decays.\nThe measured fL from a number of VV decays are\ngiven in Table 17.4.4. Figure 17.4.8 shows the reported\nresults from Belle and BABAR and their HFAG averages.\nThere is an apparent hierarchy with \u03c1\u03c1 modes near fL = 1,\nK\u2217K\u2217and \u03c6K\u2217\n2(1430) near 0.75, and \u03c6K\u2217, \u03c9K\u2217, and\na\u00b1\n1 (1260)a\u2213\n1 (1260) near 0.5. Modes dominated by tree de-\ncays have fL \u223c1 while penguin-dominated decays are\ncloser to 0.5. There is also a hierarchy based on the masses\nof the vector mesons, with larger masses having smaller\nvalues of fL. However, this is more evident when compar-\ning decays with a D\u2217as one or both of the daughter vector\nmesons.\n\n253\nTable 17.4.4. Longitudinal Polarization fractions fL for BABAR and Belle. The average is from the HFAG group (Amhis et al.\n(2012)).\nBABAR results\nBelle results\nAverage\nFinal state\nfL\nRef.\nfL\nRef.\nfL\nK\u2217+K\n\u22170\n0.75+0.16\n\u22120.26 \u00b1 0.03\n(Aubert, 2009k)\n0.75+0.16\n\u22120.26 \u00b1 0.03\nK\u22170K\n\u22170\n0.80+0.10\n\u22120.12 \u00b1 0.06\n(Aubert, 2008ah)\n0.80+0.10\n\u22120.12 \u00b1 0.06\nK\u2217+\u03c1\u2212\n0.38 \u00b1 0.13 \u00b1 0.03\n(Lees, 2012l)\n0.38 \u00b1 0.13 \u00b1 0.03\nK\u2217+\u03c10\n0.78 \u00b1 0.12 \u00b1 0.03\n(del Amo Sanchez, 2011g)\n0.78 \u00b1 0.12 \u00b1 0.03\nK\u22170\u03c1+\n0.52 \u00b1 0.10 \u00b1 0.04\n(Aubert, 2006ab)\n0.43 \u00b1 0.11+0.05\n\u22120.02\n(Abe, 2005f)\n0.48 \u00b1 0.08\nK\u22170\u03c10\n0.40 \u00b1 0.08 \u00b1 0.11\n(Lees, 2012l)\n0.40 \u00b1 0.08 \u00b1 0.11\n\u03c9K\u2217+\n0.41 \u00b1 0.18 \u00b1 0.05\n(Aubert, 2009af)\n0.41 \u00b1 0.18 \u00b1 0.05\n\u03c9K\u22170\n0.72 \u00b1 0.14 \u00b1 0.02\n(Aubert, 2009af)\n0.56 \u00b1 0.29+0.18\n\u22120.08\n(Goldenzweig, 2008)\n0.69 \u00b1 0.13\n\u03c9K\u2217\n2(1430)+\n0.56 \u00b1 0.10 \u00b1 0.04\n(Aubert, 2009af)\n0.56 \u00b1 0.10 \u00b1 0.04\n\u03c9K\u2217\n2(1430)0\n0.45 \u00b1 0.12 \u00b1 0.02\n(Aubert, 2009af)\n0.45 \u00b1 0.12 \u00b1 0.02\n\u03c9\u03c1+\n0.90 \u00b1 0.05 \u00b1 0.03\n(Aubert, 2009af)\n0.90 \u00b1 0.06\n\u03c6K\u2217+\n0.49 \u00b1 0.05 \u00b1 0.03\n(Aubert, 2007c)\n0.52 \u00b1 0.08 \u00b1 0.03\n(Chen, 2005a)\n0.50 \u00b1 0.05\n\u03c6K\u22170\n0.494 \u00b1 0.034 \u00b1 0.013\n(Aubert, 2008bf)\n0.45 \u00b1 0.05 \u00b1 0.02\n(Chen, 2005a)\n0.480 \u00b1 0.030\n\u03c6K1(1270)+\n0.46+0.12+0.06\n\u22120.13\u22120.07\n(Aubert, 2008ad)\n0.46+0.12+0.06\n\u22120.13\u22120.07\n\u03c6K\u2217\n2(1430)+\n0.80+0.09\n\u22120.10 \u00b1 0.03\n(Aubert, 2008ad)\n0.80+0.09\n\u22120.10 \u00b1 0.03\n\u03c6K\u2217\n2(1430)0\n0.901+0.046\n\u22120.058 \u00b1 0.037\n(Aubert, 2008bf)\n0.901+0.046\n\u22120.058 \u00b1 0.037\n\u03c1+\u03c1\u2212\n0.992 \u00b1 0.024+0.026\n\u22120.013\n(Aubert, 2007b)\n0.941+0.034\n\u22120.040 \u00b1 0.030\n(Somov, 2006)\n0.977+0.028\n\u22120.024\n\u03c1+\u03c10\n0.950 \u00b1 0.015 \u00b1 0.006\n(Aubert, 2009p)\n0.95 \u00b1 0.11 \u00b1 0.02\n(Zhang, 2003)\n0.950 \u00b1 0.016\n\u03c10\u03c10\n0.75+0.11\n\u22120.14 \u00b1 0.04\n(Aubert, 2008r)\n0.75+0.11\n\u22120.14 \u00b1 0.04\na\u00b1\n1 a\u2213\n1\n0.31 \u00b1 0.22 \u00b1 0.10\n(Aubert, 2009ae)\n0.31 \u00b1 0.22 \u00b1 0.10\nThe branching fractions and asymmetries are given in\nTable 17.4.5 and the hierarchy of measured branching frac-\ntions is shown in Fig. 17.4.9.\nThe decay to \u03c9K\u2217is penguin dominated but the tree\ndiagrams are more important for the other decays (Au-\nbert (2006f) and Goldenzweig (2008)). The branching frac-\ntion hierarchy of the decays to \u03c9K\u2217and \u03c9\u03c6 is a useful\ndetermination of the contribution of electro-weak pen-\nguins and so potentially helpful for the understanding\nof \u03c62. The \u03c9K\u2217\ufb01nal state can also be used to look at\nbranching fractions and fL in Vector-Tensor (VT) decays\n(B \u2192\u03c9K\u2217\n2(1430)) and Scalar-Vector (SV) decays (B \u2192\n\u03c9K\u22170(1430)) and compared to other VT decays such as\nB \u2192\u03c6K\u2217\n2(1430) (Aubert, 2009af).\nDecays proceeding via electro-weak and gluonic b \u2192d\npenguin diagrams have been measured in the decays B \u2192\n\u03c1\u03b3 and B0 \u2192K0K0. The charmless decay B0 \u2192K\u22170K\u22170\nproceeds through both electro-weak and gluonic b \u2192d\npenguin loops to two vector particles (VV). The standard\nmodel suppressed decay B0 \u2192K\u22170K\u22170 could appear via\nan intermediate heavy boson (Aubert (2008ah,ao, 2009k)\nand Chiang (2010)).\n17.4.5.4 B \u2192SP, SV, SS\nThe modes involving a B meson decay to Pseudoscalar-\nScalar (PS), Vector-Scalar (VS) and Scalar-Scalar (SS)\nare summarized in Table 17.4.6 with branching fractions\nplotted in Fig. 17.4.10.\n\n254\nTable 17.4.5. Charmless B decays branching fractions B and CP Asymmetries ACP for BABAR and Belle for mode Vector-Vector (VV) \ufb01nal states. The averages come\nfrom HFAG and may include measurements from other experiments such as CLEO (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK\u2217+K\u2217\u2212\n< 2.0\n(Aubert, 2008ao)\n< 2.0\nK\u2217+K\n\u22170\n1.2 \u00b1 0.5 \u00b1 0.1\n(Aubert, 2009k)\n1.2 \u00b1 0.5\nK\u22170K\u22170\n< 0.41\n(Aubert, 2008y)\n< 0.2\n(Chiang, 2010)\n< 0.2\nK\u22170K\n\u22170\n1.28+0.35\n\u22120.30 \u00b1 0.11\n(Aubert, 2008y)\n0.26+0.33+0.10\n\u22120.29\u22120.08\n(Chiang, 2010)\n0.81 \u00b1 0.23\nK\u2217+\u03c1\u2212\n10.3 \u00b1 2.3 \u00b1 1.3\n0.21 \u00b1 0.15 \u00b1 0.02\n(Lees, 2012l)\n10.3 \u00b1 2.6\nK\u22170\u03c1+\n9.6 \u00b1 1.7 \u00b1 1.5\n\u22120.01 \u00b1 0.16 \u00b1 0.02\n(Aubert, 2006ab)\n8.9 \u00b1 1.7 \u00b1 1.2\n(Abe, 2005f)\n9.2 \u00b1 1.5\n\u22120.01 \u00b1 0.16\nK\u22170\u03c10\n5.1 \u00b1 0.6+0.6\n\u22120.8\n\u22120.06 \u00b1 0.09 \u00b1 0.02\n(Lees, 2012l)\n2.1+0.8+0.9\n\u22120.7\u22120.5\n(Kyeong, 2009)\n3.9 \u00b1 0.8\n\u22120.06 \u00b1 0.09\nK\u2217+\u03c10\n4.6 \u00b1 1.1 \u00b1 0.4\n0.31 \u00b1 0.13 \u00b1 0.03\n(del Amo Sanchez, 2011g)\n4.6 \u00b1 1.1\n0.31 \u00b1 0.13\n\u03c9K\u2217+\n< 7.4\n0.29 \u00b1 0.35 \u00b1 0.02\n(Aubert, 2009af)\n< 7.4\n0.29 \u00b1 0.35\n\u03c9K\u22170\n2.2 \u00b1 0.6 \u00b1 0.2\n0.45 \u00b1 0.25 \u00b1 0.02\n(Aubert, 2009af)\n1.8 \u00b1 0.7+0.3\n\u22120.2\n(Goldenzweig, 2008)\n2.0 \u00b1 0.5\n0.45 \u00b1 0.25\n\u03c9\u03c9\n< 4.0\n(Aubert, 2006f)\n< 4.0\n\u03c9\u03c6\n< 1.2\n(Aubert, 2006f)\n< 1.2\n\u03c9\u03c1+\n15.9 \u00b1 1.6 \u00b1 1.4\n\u22120.20 \u00b1 0.09 \u00b1 0.02\n(Aubert, 2009af)\n15.9 \u00b1 2.1\n\u22120.20 \u00b1 0.09\n\u03c9\u03c10\n< 1.6\n(Aubert, 2009af)\n< 1.6\n\u03c6K\u2217(1410)+\n< 4.3\n(Aubert, 2008ad)\n< 4.3\n\u03c6K\u2217(1680)0\n< 3.5\n(Aubert, 2007ap)\n< 3.5\n\u03c6K\u2217+\n11.2 \u00b1 1.0 \u00b1 0.9\n0.00 \u00b1 0.09 \u00b1 0.04\n(Aubert, 2007c)\n6.7+2.1+0.7\n\u22121.9\u22121.0\n\u22120.02 \u00b1 0.14 \u00b1 0.03\n(Chen, 2003)\n10.0 \u00b1 1.1\n\u22120.01 \u00b1 0.08\n\u03c6K\u22170\n9.7 \u00b1 0.5 \u00b1 0.6\n0.01 \u00b1 0.06 \u00b1 0.03\n(Aubert, 2008bf)\n10.0+1.6+0.7\n\u22121.5\u22120.8\n0.02 \u00b1 0.09 \u00b1 0.02\n(Chen, 2003)\n9.8 \u00b1 0.7\n0.01 \u00b1 0.05\n\u03c6\u03c6\n< 0.2\n(Aubert, 2008ay)\n< 0.2\n\u03c6\u03c1+\n< 3.0\n(Aubert, 2008ay)\n< 3.0\n\u03c6\u03c10\n< 0.33\n(Aubert, 2008ay)\n< 0.33\n\u03c1+\u03c1\u2212\n25.5 \u00b1 2.1+3.6\n\u22123.9\n(Aubert, 2007b)\n22.8 \u00b1 3.8+2.3\n\u22122.6\n(Somov, 2006)\n24.2+3.1\n\u22123.2\n\u03c1+\u03c10\n23.7 \u00b1 1.4 \u00b1 1.4\n\u22120.054 \u00b1 0.055 \u00b1 0.010\n(Aubert, 2009p)\n31.7 \u00b1 7.1+3.8\n\u22126.7\n0.00 \u00b1 0.22 \u00b1 0.03\n(Zhang, 2003)\n24.0+1.9\n\u22122.0\n\u22120.05 \u00b1 0.05\n\u03c10\u03c10\n0.92 \u00b1 0.32 \u00b1 0.14\n(Aubert, 2008r)\n0.4 \u00b1 0.4+0.2\n\u22120.3\n(Chiang, 2008)\n0.73+0.27\n\u22120.28\n\n255\nB(B \u2192V V )\nBABA R \nBelle \nCLE O \nNe w A vg . \nBranching Ratio x 106 \n0.0 \n25.0 \n50.0 \nHFAG\nAug 2012\n\u03c1+\u03c1\u2212\n\u03c1+\u03c10\n\u03c10\u03c10\n\u03c6K\u22170\n\u03c6K\u2217+\n\u03c6\u03c1+\n\u03c6\u03c10\n\u03c6K\u2217(1410)+\n\u03c6K\u2217(1680)0\n\u03c6\u03c6\nK\u2217+\u03c10\nK\u22170\u03c10\nK\u22170\u03c1+\nK\u2217+\u03c1\u2212\n\u03c9\u03c6\n\u03c9\u03c9\n\u03c9\u03c10\n\u03c9\u03c1+\n\u03c9K\u2217+\n\u03c9K\u22170\nK\u2217+K\u2217\u2212\nK\u2217+K\u22170\nK\u22170K\u22170\nK\u22170K\u22170\nFigure 17.4.9. Summary of branching fraction measurements\n(\u00d710\u22126) and HFAG averages for Vector-Vector (VV) decays\n(Amhis et al. (2012)).\n\n256\n0.0 \n30.0 \n60.0 \nBABA R \nBelle \nNe w A vg . \nHFAG\nAug 2012\nBranching Ratio x 106 \nCharmless B Decays to JP = 0+ mesons \n\u03b7K\u2217\n0 (1430)0\n\u03b7K\u2217\n0 (1430)+\n\u03b7 K\u2217\n0 (1430)0\n\u03b7 K\u2217\n0 (1430)+\nK\u2217\n0(1430)0K+\nK\u2217\n0 (1430)0\u03c0+\nK\u2217\n0 (1430)+\u03c0\u2212\nK\u2217\n0 (1430)0K\u2217\n0(1430)0\nK\u2217\n0 (1430)0K\u22170\nK\u2217\n0 (1430)0\u03c0+K\u2212\nK\u2217\n0 (1430)0K\u2217\n0 (1430)0\nK\u2217\n0 (1430)0K\u22170\n\u03c9K\u2217\n0 (1430)+\n\u03c9K\u2217\n0 (1430)0\n\u03c6K\u2217\n0 (1430)0\n\u03c6K\u2217\n0 (1430)+\nf0(2010)KS \u2020\nf0(1710)K+\u2020\nf0(1710)K0\u2020\nf0(1710)KS \u2020\nf0(1500)K+ \u2020\nf0(1500)K0 \u2020\nf0(1370)0K+ \u2020\nf0(1370)\u03c0+ \u2020\nf0(980)K0 \u2020\nf0(980)K+ \u2020\nf0(980)K\u2217+ \u2020\nf0(980)K\u22170 \u2020\nf0(980)K\u2217\n2 (1430)0 \u2020\nf0(980)\u03c9 \u2020\nf0(980)\u03b7\n\u2020\nf0(980)\u03b7 \u2020\nf0(980)\u03c10 \u2020\nf0(980)\u03c1+ \u2020\nf0(980)\u03c6 \u2020\nf0(980)f0(980) \u2020\nf0(980)\u03c0+ \u2020\na\u2213\n0 (1450)\u03c0\u00b1 \u2020\na0(1450)\u2212K+ \u2020\na0(980)0K0 \u2020\na0(980)0\u03c0+ \u2020\na\u2213\n0 (980)\u03c0\u00b1 \u2020\na0(980)0K0 \u2020\na0(980)+K0 \u2020\na0(980)\u2212K+ \u2020\na0(980)0K+ \u2020\na\u2213\n0 (980)\u03c0\u00b1 \u2020\na0(980)+\u03c00 \u2020\na0(980)0\u03c0+ \u2020\nFigure 17.4.10. Summary of branching fraction measurements (\u00d710\u22126) and HFAG averages for JP = 0+ \ufb01nal states, including\nScalar-Pseudoscalar (SP), Scalar-Vector (SV) and Scalar-Scalar (SS) decays (Amhis et al. (2012)).\n\n257\nTable 17.4.6. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for JP = 0+ \ufb01nal states, including Scalar-Pseudoscalar (SP),\nScalar-Vector (SV) and Scalar-Scalar (SS) decays. The averages come from HFAG (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK\n\u2217\n0(1430)0K+\n< 2.2\n(Aubert, 2007av)\n< 2.2\nK\u2217\n0 (1430)+\u03c0\u2212\n29.9+2.3\n\u22121.7 \u00b1 3.6\n0.07 \u00b1 0.14 \u00b1 0.01\n(Aubert, 2009av)\n49.7 \u00b1 3.8+6.8\n\u22128.2\n(Garmash, 2007)\n33.5+3.9\n\u22123.8\n0.10 \u00b1 0.07\nK\u2217\n0 (1430)0\u03c0+K\u2212\n< 31.8\n(Chiang, 2010)\n< 31.8\nK\u2217\n0 (1430)0\u03c0+\n32.0 \u00b1 1.2+10.8\n\u22126.0\n0.032 \u00b1 0.035+0.034\n\u22120.028\n(Aubert, 2008j)\n51.6 \u00b1 1.7+7.0\n\u22127.5\n0.076 \u00b1 0.038+0.028\n\u22120.022\n(Garmash, 2006)\n45.1 \u00b1 6.3\n0.55 \u00b1 0.33\n\u03b7K\u2217\n0 (1430)+\n15.8 \u00b1 2.2 \u00b1 2.2\n0.05 \u00b1 0.13 \u00b1 0.02\n(Aubert, 2006l)\n15.8 \u00b1 3.1\n0.05 \u00b1 0.13\n\u03b7K\u2217\n0 (1430)0\n9.6 \u00b1 1.4 \u00b1 1.3\n0.06 \u00b1 0.13 \u00b1 0.02\n(Aubert, 2006l)\n9.6 \u00b1 1.9\n0.06 \u00b1 0.13\n\u03b7\u2032K\u2217\n0 (1430)+\n5.2 \u00b1 1.9 \u00b1 1.0\n0.06 \u00b1 0.20 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n5.2 \u00b1 2.1\n\u03b7\u2032K\u2217\n0 (1430)0\n6.3 \u00b1 1.3 \u00b1 0.9\n\u22120.19 \u00b1 0.17 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n6.3 \u00b1 1.6\na0(1450)\u2212K+\n< 3.1\n(Aubert, 2007as)\n< 3.1\na0(980)+K0\n< 3.9\n(Aubert, 2004x)\n< 3.9\na0(980)+\u03c00\n< 1.4\n(Aubert, 2008ax)\n< 1.4\na0(980)\u2212K+\n< 1.9\n(Aubert, 2007as)\n< 1.9\na0(980)0K+\n< 2.5\n(Aubert, 2004x)\n< 2.5\na0(980)0K0\n< 7.8\n(Aubert, 2004x)\n< 7.8\na0(980)0\u03c0+\n< 5.8\n(Aubert, 2004x)\n< 5.8\na\u2213\n0 (1450)\u03c0\u00b1\n< 2.3\n(Aubert, 2007as)\n< 2.3\na\u2213\n0 (980)\u03c0\u00b1\n< 3.1\n(Aubert, 2007as)\n< 3.1\nf0(1370)\u03c0+\n< 4.0\n(Aubert, 2009h)\n< 4.0\nf0(1370)0K+\n< 10.7\n(Aubert, 2005g)\n< 10.7\nf0(1500)K+\n0.74 \u00b1 0.18 \u00b1 0.52\n(Lees, 2012y)\n0.74 \u00b1 0.55\nf0(1500)K0\n13.3+5.8\n\u22124.4 \u00b1 3.2\n(Lees, 2012y)\n13.3+6.6\n\u22125.4\nf0(1710)K0\nS\n0.50+0.46\n\u22120.24 \u00b1 0.11\n(Lees, 2012c)\n0.5+0.5\n\u22120.3\nf0(1710)K+\n1.12 \u00b1 0.25 \u00b1 0.50\n(Lees, 2012y)\n1.12 \u00b1 0.56\nf0(2010)K0\nS\n0.54+0.21\n\u22120.20 \u00b1 0.52\n(Lees, 2012c)\n0.54 \u00b1 0.56\nf0(980)K+\n10.3 \u00b1 0.5+2.0\n\u22121.4\n\u22120.106 \u00b1 0.050+0.036\n\u22120.015\n(Aubert, 2008j)\n8.8 \u00b1 0.8+0.9\n\u22121.8\n\u22120.077 \u00b1 0.065+0.046\n\u22120.026\n(Garmash, 2006)\n9.4+0.9\n\u22121.0\n\u22120.10+0.05\n\u22120.04\nf0(980)K0\n6.9 \u00b1 0.8 \u00b1 0.6\n\u22120.28 \u00b1 0.24 \u00b1 0.09\n(Lees, 2012y)\n7.6 \u00b1 1.7+0.9\n\u22121.3\n(Garmash, 2007)\n7.0 \u00b1 0.9\nf0(980)K\u2217+\n4.2 \u00b1 0.6 \u00b1 0.3\n\u22120.15 \u00b1 0.12 \u00b1 0.03\n(del Amo Sanchez, 2011g)\n4.2 \u00b1 0.7\n\u22120.15 \u00b1 0.12\nf0(980)K\u22170\n5.7 \u00b1 0.6 \u00b1 0.4\n0.07 \u00b1 0.10 \u00b1 0.02\n(Lees, 2012l)\n< 2.2\n(Kyeong, 2009)\n5.7 \u00b1 0.7\n0.07 \u00b1 0.10\nf0(980)\u03b7\n< 0.4\n(Aubert, 2007as)\n< 0.4\nf0(980)\u03b7\u2032\n< 0.9\n(del Amo Sanchez, 2010h)\n< 0.9\nf0(980)\u03c9\n< 1.5\n(Aubert, 2009af)\n< 1.5\nf0(980)\u03c6\n< 0.38\n(Aubert, 2008ay)\n< 0.38\nf0(980)\u03c0+\n< 1.5\n(Aubert, 2009h)\n< 1.5\nK\u2217\n0 (1430)0K\u22170\n< 1.7\n(Chiang, 2010)\n< 1.7\nK\u2217\n0 (1430)0K\n\u22170\n< 3.3\n(Chiang, 2010)\n< 3.3\nK\u2217\n0 (1430)0\u03c10\n27 \u00b1 4 \u00b1 2 \u00b1 3\n(Lees, 2012l)\nK\u2217\n0 (1430)+\u03c1\u2212\n28 \u00b1 10 \u00b1 5 \u00b1 3\n(Lees, 2012l)\nK\u2217\n0 (1430)+\u03c9\n24.0 \u00b1 2.6 \u00b1 4.4\n\u22120.10 \u00b1 0.09 \u00b1 0.02\n(Aubert, 2009af)\n24.0 \u00b1 5.1\n\u22120.10 \u00b1 0.09\nK\u2217\n0 (1430)0\u03c9\n16.0 \u00b1 1.6 \u00b1 3.0\n\u22120.07 \u00b1 0.09 \u00b1 0.02\n(Aubert, 2009af)\n16.0 \u00b1 3.4\n\u22120.07 \u00b1 0.09\nK\u2217\n0 (1430)+\u03c6\n7.0 \u00b1 1.3 \u00b1 0.9\n0.04 \u00b1 0.15 \u00b1 0.04\n(Aubert, 2008ad)\n7.0 \u00b1 1.6\n0.04 \u00b1 0.15\nK\u2217\n0 (1430)0\u03c6\n3.9 \u00b1 0.5 \u00b1 0.6\n0.20 \u00b1 0.14 \u00b1 0.06\n(Aubert, 2008bf)\n3.9 \u00b1 0.8\n0.20 \u00b1 0.15\nf0(980)\u03c1+\n< 2.0\n(Aubert, 2009p)\n< 2.0\nf0(980)\u03c10\n< 0.40\n(Aubert, 2008r)\n< 0.3\n(Chiang, 2008)\n< 0.3\nf0(980)f0(980)\n< 0.19\n(Aubert, 2008r)\n< 0.1\n(Chiang, 2008)\n< 0.1\nf0(980)K\u2217\n2 (1430)0\n8.6 \u00b1 1.7 \u00b1 1.0\n(Lees, 2012l)\n(Kyeong, 2009)\n8.6 \u00b1 2.0\nK\u2217\n0 (1430)0K\u2217\n0 (1430)0\n< 4.7\n(Chiang, 2010)\n< 4.7\nK\u2217\n0 (1430)0K\n\u2217\n0(1430)0\n< 8.4\n(Chiang, 2010)\n< 8.4\n\n258\nThe exact structure of scalar mesons is not clear with\nvarious models proposed such as two-quark and four-quark\nstates with potential contributions from glueballs and mo-\nlecules (compare with the search for exotic states in Chap-\nter 18.3). The experimental measurement of scalars is also\ncomplicated as they are often quite broad, decay to pions\n(and so can be faked by combining the relatively large\nnumber of unrelated pions), and have an angular decay\nstructure that is very similar to the non-resonant back-\nground. The a0(980) (along with the a1(1260) and b1) is\nan ideal candidate for a four-quark structure as it lies near\nthe K \u00afK threshold and so could be a qq state with a K \u00afK\nadmixture. As an example, the decay B+ \u2192a+\n0 \u03c00 can\ndi\ufb00erentiate between two- and four-quark models as the\ntwo-body branching fraction could be as high as 2 \u00d7 10\u22127\nwhile the four-quark model is an order of magnitude lower.\nThe branching fraction however is only measured to a pre-\ncision of B(B+ \u2192a+\n0 \u03c00) < 1.4 \u00d7 10\u22126 (Aubert, 2008ax).\nThe current experimental upper limits on B(B0 \u2192a\u00b1\n0 \u03c0\u2213)\nand B(B0 \u2192a\u2212\n0 K+) are 3.1\u00d710\u22126 and 1.9\u00d710\u22126, respec-\ntively (Aubert, 2007as). Vector-current considerations and\nG-parity conservation suppress the color-allowed electro-\nweak tree decay, leading to the small predicted branching\nfractions. G-parity G = Cei\u03c0I2 is a product of charge con-\njugation C and a rotation about the second Isospin axis\nI2; it is expected to be conserved by strong interactions\n(as the strong force conserves both C and Isospin) but not\nin electro-weak interactions.\nThe a0, including the a0(980) and a0(1450), decays to\n\u03b7\u03c0 but the exact branching fraction is not well known\n(roughly 85%). The decay B\u00b1 \u2192a0\u03c0\u00b1 has the bene\ufb01t\nof being self-tagging as the pion charge identi\ufb01es the B\nmeson \ufb02avor (Aubert, 2004x).\nThe averaged decay rates for B+ \u2192f0(980)K+ and\nB0 \u2192f0(980)K0 have been measured to be 9.4\u00d710\u22126 (Au-\nbert, 2008j), (Garmash, 2006) and 7.0 \u00d7 10\u22126 (Aubert,\n2009av) (Garmash, 2007), respectively. These are compat-\nible with expectations that the b \u2192sss penguin domi-\nnates over the b \u2192suu penguin.\nThe SV mode \u03c6K\u2217\n0(1430)0 has been measured as part\nof a time-dependent and time-integrated analysis of B \u2192\n\u03c6K0\nS\u03c00 and B \u2192\u03c6K\u00b1\u03c0\u2213decays (Aubert, 2008bf), which\nalso include VV and VT decays (see Tables 17.4.5 and 17.4.8).\nThe decay B \u2192\u03c9f0(980) naturally forms part of a search\nfor \u03c9\u03c1.\n17.4.5.5 B \u2192AP, AV, AA\nFigure 17.4.11 and Table 17.4.7 show the reported re-\nsults from Belle and BABAR, and their HFAG averages, for\nmodes involving Axial-Pseudovector (AP), Axial-Vector\n(AV) and Axial-Axial (AA) decays.\n0.0 \n30.0 \n60.0 \nBABA R \nBelle \nNe w A vg . \nHFAG\nAug 2012\nBranching Ratio x 106 \nCharmless B Decays to JP = 1+ mesons \na\u00b1\n1 a\u2213\n1\nK1(1400)0\u03c0+\nK1(1400)+\u03c0\u2212\n\u03c6K1(1400)+\nK1(1270)0\u03c0+\nK1(1270)+\u03c0\u2212\n\u03c6K1(1270)+\na\u00b1\n1 \u03c1\u2213\na\u2212\n1 K+\na+\n1 K0\na\u2213\n1 \u03c0\u00b1\na+\n1 \u03c00\na01\u03c0+\na+\n1 K\u22170\nb+\n1 K\u22170 \u2020\nb01K\u22170 \u2020\nb01K\u2217+ \u2020\nb\u2212\n1 K\u2217+ \u2020\nb+\n1 \u03c10 \u2020\nb01\u03c1+ \u2020\nb01\u03c10 \u2020\nb\u00b1\n1 \u03c1\u2213\u2020\nb01K+ \u2020\nb+\n1 K0 \u2020\nb\u2212\n1 K+ \u2020\nb01K0 \u2020\nb01\u03c0+ \u2020\nb\u2213\n1 \u03c0\u00b1 \u2020\nb+\n1 \u03c00 \u2020\nb01\u03c00 \u2020\nf1(1420)K+\u2020\nf1(1285)K+\nFigure 17.4.11. Summary of branching fraction measure-\nments (\u00d710\u22126) and HFAG averages for JP = 1+ \ufb01nal states,\nincluding Axial-Pseudovector (AP), Axial-Vector (AV) and\nAxial-Axial (AA) decays (Amhis et al. (2012)).\n\n259\nTable 17.4.7. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for JP = 1+ \ufb01nal states, including Axial-Pseudovector (AP),\nAxial-Vector (AV) and Axial-Axial (AA) decays. The averages come from HFAG (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK1(1270)+\u03c0\u2212\n17+8\n\u221211\n(Aubert, 2010d)\n17+8\n\u221211\nK1(1270)0\u03c0+\n< 40\n(Aubert, 2010d)\n< 40\nK1(1400)+\u03c0\u2212\n17+7\n\u22129\n(Aubert, 2010d)\n17+7\n\u22129\nK1(1400)0\u03c0+\n< 39\n(Aubert, 2010d)\n< 39\na+\n1 K0\n34.9 \u00b1 5.0 \u00b1 4.4\n0.12 \u00b1 0.11 \u00b1 0.02\n(Aubert, 2008ae)\n34.9 \u00b1 6.7\n0.12 \u00b1 0.11 \u00b1 0.02\na+\n1 \u03c00\n26.4 \u00b1 5.4 \u00b1 4.1\n(Aubert, 2007i)\n26.4 \u00b1 6.8\na\u2212\n1 K+\n16.3 \u00b1 2.9 \u00b1 2.3\n\u22120.16 \u00b1 0.12 \u00b1 0.01\n(Aubert, 2008ae)\n16.3 \u00b1 3.7\n\u22120.16 \u00b1 0.12 \u00b1 0.01\na0\n1\u03c0+\n20.4 \u00b1 4.7 \u00b1 3.4\n(Aubert, 2007i)\n20.4 \u00b1 5.8\na\u2213\n1 \u03c0\u00b1\n33.2 \u00b1 3.8 \u00b1 3.0\n(Aubert, 2006aj)\n33.2 \u00b1 4.8\nb+\n1 K0\n9.6 \u00b1 1.7 \u00b1 0.9\n\u22120.03 \u00b1 0.15 \u00b1 0.02\n(Aubert, 2008aj)\n9.6 \u00b1 1.9\n\u22120.03 \u00b1 0.15\nb+\n1 \u03c00\n< 3.3\n(Aubert, 2008aj)\n< 3.3\nb\u2212\n1 K+\n7.4 \u00b1 1.0 \u00b1 1.0\n0.07 \u00b1 0.12 \u00b1 0.02\n(Aubert, 2007aj)\n7.4 \u00b1 1.4\n0.07 \u00b1 0.12 \u00b1 0.02\nb0\n1K+\n9.1 \u00b1 1.7 \u00b1 1.0\n\u22120.46 \u00b1 0.20 \u00b1 0.02\n(Aubert, 2007aj)\n9.1 \u00b1 2.0\n\u22120.46 \u00b1 0.20 \u00b1 0.02\nb0\n1K0\n< 7.8\n(Aubert, 2008aj)\n< 7.8\nb0\n1\u03c0+\n6.7 \u00b1 1.7 \u00b1 1.0\n0.05 \u00b1 0.16 \u00b1 0.02\n(Aubert, 2007aj)\n6.7 \u00b1 2.0\n0.05 \u00b1 0.16 \u00b1 0.02\nb0\n1\u03c00\n< 1.9\n(Aubert, 2008aj)\n< 1.9\nb\u2213\n1 \u03c0\u00b1\n10.9 \u00b1 1.2 \u00b1 0.9\n\u22120.05 \u00b1 0.10 \u00b1 0.02\n(Aubert, 2007aj)\n10.9 \u00b1 1.5\n\u22120.05 \u00b1 0.10 \u00b1 0.02\nb\u00b1\n1 \u03c1\u2213\n< 1.4\n(Aubert, 2009ak)\n< 1.4\nf1(1285)K+\n< 2.0\n(Aubert, 2008bb)\n< 2.0\nf1(1420)K+\n< 2.9\n(Aubert, 2008bb)\n< 2.9\n\u03c6K1(1270)+\n6.1 \u00b1 1.6 \u00b1 1.1\n0.15 \u00b1 0.19 \u00b1 0.05\n(Aubert, 2008ad)\n6.1 \u00b1 1.9\n0.15 \u00b1 0.20\n\u03c6K1(1400)+\n< 3.2\n(Aubert, 2008ad)\n< 3.2\na+\n1 K\u22170\n< 3.6\n(del Amo Sanchez, 2010l)\n< 3.6\na\u00b1\n1 \u03c1\u2213\n< 61\n(Aubert, 2006as)\n< 61\nb+\n1 K\u22170\n< 5.9\n(Aubert, 2009ak)\n< 5.9\nb\u2212\n1 K\u2217+\n< 5.0\n(Aubert, 2009ak)\n< 5.0\nb0\n1K\u2217+\n< 6.7\n(Aubert, 2009ak)\n< 6.7\nb0\n1K\u22170\n< 8.0\n(Aubert, 2009ak)\n< 8.0\nb0\n1\u03c1+\n< 3.3\n(Aubert, 2009ak)\n< 3.3\nb0\n1\u03c10\n< 3.4\n(Aubert, 2009ak)\n< 3.4\nb+\n1 \u03c10\n< 5.2\n(Aubert, 2009ak)\n< 5.2\na\u00b1\n1 a\u2213\n1\n47.3 \u00b1 10.5 \u00b1 6.3\n(Aubert, 2009ae)\n47.3 \u00b1 12.2\n\n260\nThe b1 is the IG = 1+ member of the JP C = 1+\u2212,\n1P1 nonet while the a1(1260) is the IG = I\u2212state in\nthe JP C = 1++, 3P1 nonet. The decays that happen via a\ntree diagram favor \ufb01nal states with a pion due to Cabibbo-\nfavored coupling (B+ \u2192b0\n1\u03c0+, B0 \u2192b\u2212\n1 \u03c0+) while pen-\nguin loop decays favor the kaon \ufb01nal states (B+ \u2192b0\n1K+,\nB0 \u2192b\u2212\n1 K+). The even G-parity of the b1 means only am-\nplitudes in which the b1 contains the spectator quark from\nthe B meson are allowed (apart from isospin-breaking and\nradiative correction e\ufb00ects). This is because the weak cur-\nrent has a G-parity even vector part and a G-parity odd\naxial-vector part. Neither part can produce a G-parity\nodd scalar meson such as the a0\n1(1260). The W + is con-\nstrained to decay to states of even G-parity. As a re-\nsult, the decay B0 \u2192b+\n1 \u03c0\u2212is suppressed with respect\nto B0 \u2192b\u2212\n1 \u03c0+. The B0 \u2192b\u2212\n1 K+ decays can be used\nto measure ACP while B0 \u2192b1\u03c0\u00b1\u03c0\u2213can also measure\nC and CP-conserving \u2206C (Aubert, 2007aj, 2008aj). The\ndominant decay of the b1 is through \u03c9\u03c0.\nB decays involving an a1(1260) are similarly of inter-\nest to the b1 but with the added distinction that decays\nto a1(1260) with a \u03c0+ proceed via a b \u2192uud transi-\ntion and the angle \u03c62 can be measured through the time-\ndependent decay rate asymmetry caused by interference\nbetween the direct decay and the decay after BB mixing.\nThe branching fraction, when combined together with de-\ncays of the a1(1260) and K1 can be used to di\ufb00erentiate\nbetween QCD and na\u00a8\u0131ve factorization model predictions\nfor branching fractions and branching fraction ratios, as\nwell as B \u2192a1(1260) transition form factors calculations.\nThese decays can also be an important background to\nother \u03c62 measurements, such as \u03c1\u03c0 and \u03c1\u03c1. The measure-\nments can be combined with SU(3) symmetry arguments\nto place bounds on the deviation \u2206\u03c62 of the measured \u03c62\nfrom the true value. The a1(1260) decays predominantly\nto \u03c0\u03c0\u03c0 via intermediate states involving a vector P-wave\n\u03c1 or scalar S-wave \u03c3 but most analyses assume a pure \u03c1\u03c0\nintermediate decay.\nThe branching fractions B(B0 \u2192b\u2212\n1 \u03c0+) are expected\nto be much greater than B(B0 \u2192b+\n1 \u03c0\u2212) and that of\nB(B0 \u2192a+\n1 (1260)\u03c0\u2212) to be much greater than B(B0 \u2192\na\u2212\n1 (1260)\u03c0+) and this has been con\ufb01rmed (Aubert, 2006aj,\n2007aj). The branching fractions for charged and neutral\ndecays B \u2192b1K and B \u2192b1\u03c0 are also in line with expec-\ntations (Aubert, 2006am, 2007aj, 2008aj). ACP has also\nbeen successfully measured in B+ \u2192b+\n1 K0, B0 \u2192b\u2212\n1 K+,\nB+ \u2192b0\n1K+, B+ \u2192b0\n1\u03c0+, B0 \u2192b\u00b1\n1 \u03c0\u2213and is compatible\nwith zero (see Table 17.4.11).\nFor the B \u2192a1(1260)K and B \u2192a1(1260)\u03c0 de-\ncays, both the neutral B0 decays (Aubert, 2006aj, 2008ae)\nand the charged B+ modes (Aubert, 2007i, 2008ae) have\nbeen measured as well as the asymmetries ACP and S in\nB+ \u2192a+\n1 (1260) K0\nS and B0 \u2192a\u2212\n1 (1260) K+ (Aubert,\n2008ae). There is strong evidence for B+ \u2192a\u00b1\n1 (1260)\u03c00\nand B+ \u2192a0\n1(1260)\u03c0\u00b1 (Aubert, 2007i). The neutral decay\nB0 \u2192a\u00b1\n1 (1260)\u03c0\u2213has been observed (Aubert, 2006aj)\nand a separate paper later measured ACP , the mixing in-\nduced CP asymmetry, and the direct CP asymmetry (Au-\nbert, 2007ae); as a result the angle \u03c62 was extracted (see\nChapter 17.7). Belle have recently published their results\nand report the \ufb01rst evidence for mixing-induced CP vio-\nlation in B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213(Dalseno, 2012).\nThe B meson decay B \u2192K1\u03c0, which changes the\nstrangeness by one unit \u2206S = 1, is sensitive to the pres-\nence of penguin amplitudes because its CKM couplings\nare larger than the corresponding \u2206S = 0 penguin am-\nplitudes. Therefore, measurements of the decay rate for\n\u2206S = 1 transitions sharing the same SU(3) \ufb02avor multi-\nplet as a1(1260) can be used to put constraints on \u03c62 (Au-\nbert, 2010d). This is similar to the SU(3)-based approach\nto measuring \u03c62 in \u03c0+\u03c0\u2212, \u03c1\u00b1\u03c0\u2213and \u03c1+\u03c1\u2212channels. The\ndecay rate to K1A\u03c0 (where K1A is the SU(3) partner of\nthe a1(1260) and a nearly equal admixture of K1(1270)\nand K1(1400) with the quantum numbers IJP = 1/21+)\ncan be derived from the decay rates to K1(1270)\u03c0 and\nK1(1400)\u03c0. The K1 is reconstructed through its predom-\ninant decay to K\u03c0\u03c0 \ufb01nal states.\nThere are a number of results for the branching frac-\ntions of B meson decays to Axial-Vector (AV) and Axial-\nAxial (AA) \ufb01nal states. Decays to a b1 and a vector meson\n(\u03c1 or K\u2217) have been searched for as a possible measure-\nment of longitudinal polarization fL, but only upper lim-\nits on the branching fractions B(B \u2192b1K\u2217) \u22648 \u00d7 10\u22126\nand B(B \u2192b1\u03c1) \u2264\n(3.3 \u22125.2) \u00d7 10\u22126 have been mea-\nsured (Aubert, 2009ak). B0 \u2192a\u00b1\n1 (1260)\u03c1\u2213has also been\nsearched for as it is both a background to \u03c62 measurements\nin B \u2192\u03c1\u03c1 and a possible place to measure \u03c62 itself. An\nupper limit of < 61 \u00d7 10\u22126 has been obtained (Aubert,\n2006as). However this was only performed with 100 fb\u22121.\nThe B+ \u2192\u03c6K1(1270)+, B+ \u2192\u03c6K1(1400)+, and\nB+ \u2192a+\n1 (1260)K\u22170 modes have been searched for (Au-\nbert, 2008ad; del Amo Sanchez, 2010l) and fL in B+ \u2192\n\u03c6K1(1270)+ has been measured.\nAA modes such as a+\n1 (1260) a\u2212\n1 (1260), a+\n1 (1260)\na0\n1(1260), a+\n1 (1260) b\u2212\n1 , and a+\n1 (1260) b0\n1 should have\nbranching fractions in the range (20\u221240)\u00d710\u22126. Although\nall the branching fractions have been measured, only\nB(B0 \u2192a+\n1 (1260)a\u2212\n1 (1260)) = (47.3 \u00b1 10.5 \u00b1 6.3) \u00d7 10\u22126\nhas been observed (Aubert, 2009ae).\n17.4.5.6 B \u2192VT, TP\nTable 17.4.8 summarizes the reported branching fractions\nB and ACP asymmetries from Belle and BABAR and their\nHFAG averages for Tensor-Pseudoscalar (TP) and Vector-\nTensor (VT) states. The hierarchy of branching fractions\nis shown in Figure 17.4.12. There are as yet very few pre-\ndictions for these modes.\n\n261\n0.0 \n20.0 \n40.0 \nBABA R \nBelle \nNe w A vg . \nHFAG\nAug 2012\nBranching Ratio x 106 \nCharmless B Decays to JP = 2+ mesons \n\u03c6K2(1770)+\n\u03c6K2(1820)+\n\u03b7 K\u22172(1430)+\n\u03b7 K\u2217\n2(1430)0\n\u03b7K\u22172(1430)+\n\u03b7K\u2217\n2(1430)0\nK\u2217\n2(1430)0\u03c0+\nK\u2217\n2(1430)+\u03c0\u2212\nK\u22172(1430)0\u03c00\n\u03c9K\u22172(1430)+\n\u03c9K\u22172(1430)0\n\u03c6K\u2217\n2(1430)0\n\u03c6K\u22172(1430)+\nf2(1525)K+\nf2(1525)K0\nf2(1270)0K+\nf2(1270)0K0\nf2(1270)\u03c0+\na2(1320)K+ \u2020\na\u2213\n2 \u03c0\u00b1\nFigure 17.4.12. Summary of branching fraction measure-\nments (\u00d710\u22126) and HFAG averages for JP = 2+ \ufb01nal states,\nincluding Tensor-Pseudoscalar (TP) and Tensor-Vector (TV)\nstates (Amhis et al. (2012)).\n\n262\nTable 17.4.8. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for JP = 2+ \ufb01nal states, including Tensor-Pseudoscalar (TP)\nand Tensor-Vector (TV) states. The averages come from HFAG (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK\u2217\n2 (1430)+\u03c0\u2212\n< 16.2\n(Aubert, 2008g)\n< 6.3\n(Garmash, 2007)\n< 6.3\nK\u2217\n2 (1430)0\u03c0+\n5.6 \u00b1 1.2+1.8\n\u22120.8\n0.05 \u00b1 0.23+0.18\n\u22120.08\n(Aubert, 2008j)\n< 6.9\n(Garmash, 2005)\n5.6+2.2\n\u22121.4\n0.05+0.29\n\u22120.24\nK\u2217\n2 (1430)0\u03c00\n< 4.0\n(Aubert, 2008g)\n< 4.0\n\u03b7K\u2217\n2 (1430)+\n9.1 \u00b1 2.7 \u00b1 1.4\n\u22120.45 \u00b1 0.30 \u00b1 0.02\n(Aubert, 2006l)\n9.1 \u00b1 3.0\n\u22120.45 \u00b1 0.30\n\u03b7K\u2217\n2 (1430)0\n9.6 \u00b1 1.8 \u00b1 1.1\n\u22120.07 \u00b1 0.19 \u00b1 0.02\n(Aubert, 2006l)\n9.6 \u00b1 2.1\n\u22120.07 \u00b1 0.19\n\u03b7\u2032K\u2217\n2 (1430)+\n28.0+4.6\n\u22124.3 \u00b1 2.6\n0.15 \u00b1 0.13 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n28.0+5.3\n\u22125.0\n\u03b7\u2032K\u2217\n2 (1430)0\n13.7+3.0\n\u22121.9 \u00b1 1.2\n0.14 \u00b1 0.18 \u00b1 0.02\n(del Amo Sanchez, 2010h)\n13.7+3.2\n\u22122.2\na2(1320)K+\n< 1.1\n(Garmash, 2005)\n< 1.1\nf2(1270)\u03c0+\n1.57 \u00b1 0.42+0.55\n\u22120.25\n0.41 \u00b1 0.25+0.18\n\u22120.15\n(Aubert, 2009h)\n1.57+0.69\n\u22120.49\n0.41+0.31\n\u22120.29\nf2(1270)0K+\n0.88 \u00b1 0.26+0.26\n\u22120.21\n(Aubert, 2008j)\n1.33 \u00b1 0.30+0.23\n\u22120.34\n(Garmash, 2006)\n1.06+0.28\n\u22120.29\nf2(1270)0K0\n2.7+1.0\n\u22120.8 \u00b1 0.9\n(Aubert, 2009av)\n< 2.5\n(Garmash, 2007)\n2.7+1.3\n\u22121.2\nf \u2032\n2(1525)K+\n1.56 \u00b1 0.36 \u00b1 0.30\n0.14 \u00b1 0.10 \u00b1 0.04\n(Lees, 2012y)\n< 4.9\n(Garmash, 2005)\n1.56 \u00b1 0.47\n0.14 \u00b1 0.11\nf \u2032\n2(1525)K0\n0.29+0.27\n\u22120.18 \u00b1 0.36\n(Lees, 2012y)\n0.29+0.45\n\u22120.40\n\u03c9K\u2217\n2 (1430)+\n21.5 \u00b1 3.6 \u00b1 2.4\n0.14 \u00b1 0.15 \u00b1 0.02\n(Aubert, 2009af)\n21.5 \u00b1 4.3\n0.14 \u00b1 0.15\n\u03c9K\u2217\n2 (1430)0\n10.1 \u00b1 2.0 \u00b1 1.1\n0.37 \u00b1 0.17 \u00b1 0.02\n(Aubert, 2009af)\n10.1 \u00b1 2.3\n0.37 \u00b1 0.17\n\u03c6K2(1770)+\n< 15\n(Aubert, 2008ad)\n< 15\n\u03c6K2(1820)+\n< 16\n(Aubert, 2008ad)\n< 16\n\u03c6K\u2217\n2 (1430)+\n8.4 \u00b1 1.8 \u00b1 1.0\n\u22120.23 \u00b1 0.19 \u00b1 0.06\n(Aubert, 2008ad)\n8.4 \u00b1 2.1\n\u22120.23 \u00b1 0.20\n\u03c6K\u2217\n2 (1430)0\n7.5 \u00b1 0.9 \u00b1 0.5\n\u22120.08 \u00b1 0.12 \u00b1 0.05\n(Aubert, 2008bf)\n7.5 \u00b1 1.0\n\u22120.08 \u00b1 0.13\n\n263\nThe angular distributions for the VT \ufb01nal states is\ngiven in Eq. 12.2.14. The longitudinal polarization fL for\nthe VT mode \u03c6K\u2217\n2(1430) is close to 0.8 \u22120.9 (Aubert,\n2008ad,bf) but there is a large transverse component in the\nVA mode \u03c6K1(1270)+ with fL \u223c0.46 (Aubert, 2008ad).\nThis lower value of fL is also seen in \u03c9K\u2217\n2(1430) (Aubert,\n2009af).\nTable 17.4.9 itemizes a few measurements that have\nbeen a by-product of the analyses described above. In a\nnumber of cases, the non-resonant component of B me-\nson decays has been measured, primarily by Belle (Chi-\nang, 2008, 2010; Kyeong, 2009). BABAR has extended\ntheir analysis of B \u2192\u03c6K\u2217to include the higher mass\nand higher spin resonances K\u2217(1680)0, K\u2217\n3(1780)0, and\nK\u2217\n4(2045)0\n(Aubert, 2007ap). Rather than look at indi-\nvidual modes, the partial branching fractions of the in-\nclusive charmless decays B \u2192K+ X, B \u2192K0 X, and\nB \u2192\u03c0+ X have been measured. The inclusive branch-\ning fraction of B mesons to charmless \ufb01nal states is about\n2%. Here X represents any accessible \ufb01nal state above the\nendpoint for B meson decays to charmed mesons and the\nbranching fractions and ACP are reported for a restricted\nrange of K and \u03c0 momentum range.\n17.4.5.7 ACP summary\nA subset of the most precise ACP measurements cur-\nrently available are shown graphically in Fig. 17.4.13. Fig-\nures 17.4.14, 17.4.15, and 17.4.16 show the ACP CP asym-\nmetries for kaonic modes, separated into \ufb01nal states with\na kaon or pion (both quasi-two-body and three-body), \ufb01-\nnal states with an \u03b7 or \u03c6, and \ufb01nal states with an \u03c1, \u03c9, f,\na1, or b1, respectively.\n17.4.6 Dalitz experimental techniques\nA quasi-two-body approach to extracting CKM parame-\nters is not ideal as these modes often interfere with other\nresonances as well as non-resonant decays to the same \ufb01-\nnal state. As a result, quasi-two-body measurements have\nan unknown uncertainty in their reported results that re-\nquires careful consideration. In principle, these e\ufb00ects can\nbe taken into account by a Dalitz Plot (also known as a\nDalitz Plane) analysis. The major advantage to the Dalitz\nPlot is that it gives access to the phases as well as the mag-\nnitudes of the resonances. Since the weak phase changes\nsign under CP but the strong phase does not, the weak\nand strong phase components can be extracted by sub-\ntracting or adding together the B meson \ufb02avor-tagged\nDalitz Plots. In some Dalitz Plots, the weak phase can\noften be directly interpreted as one of the Wolfenstein an-\ngles e.g. Dalseno (2009). The mathematical formalism for\na Dalitz Plot analysis is given in Chapter 13. In this section\nwe consider the experimental problems in its implementa-\ntion.\nThe extension of quasi-two-body charmless decays to\nthree-body charmless decays brings with it greater com-\nplexity but provides a deeper understanding of the decays\nHFAG\nAug 2012\nCDF\nBABAR\nBelle\nLHCb\nNew Avg.\nACP\nCP Asymmetry\n-0.5\n 0\n 0.5\n\u03c9\u03c0+\nK+\u03c0\u2212\u03c00\n\u03c0+\u03c0\u2212\u03c0+\nK0\u03c0+\u03c0\u2212\n\u03c1+\u03c10\nK\u22170K+K\u2212\n\u03c6K\u22170\n\u03c9K+\n\u03b7\u03c0+\nK\u22170\u03c0+\u03c0\u2212\n\u03b7K\u22170\nf0(980)K+\nppK+\n\u03c6K+\nK\u22170\u03c0+\n\u03c0+\u03c00\nK\u2217\n0(1430)0\u03c0+\ns\u03b3\nK+\u03c00\n\u03b7 K+\nK\u2217\u03b3\nK0\u03c0+\nK+K\u2212K+\nK+\u03c0+\u03c0\u2212\nK+\u03c0\u2212\nFigure 17.4.13. Summary of the most precise ACP measure-\nments (Amhis et al. (2012)).\nand their CP properties. As the integrated luminosity in-\ncreases, the analyses have started with inclusive measure-\nments of branching fractions and charge asymmetries, in-\ntegrated over the three-body phase space (e.g. B \u2192\u03c0\u03c0\u03c0).\nThis has been followed by exploring intermediate states ig-\nnoring interference (e.g. B \u2192\u03c1\u03c0) before \ufb01nally perform-\ning a full Dalitz Plot analysis taking into account inter-\nference between all intermediate resonance states. And \ufb01-\nnally, time-dependent asymmetries can be extracted from\nindividual resonances. The choice is dictated by the lu-\nminosity, expected signal and background, and the un-\nderstanding of the intermediate resonances (such as the\npresence or absence of poorly known states such as \u03c3/\u03ba,\nand higher mass f0 and K\u2217).\nThe Dalitz Plots of B meson decays are usually in-\nterpreted in the scattering matrix (S-matrix) or isobar\nmodel (see Section 13.2.1). If a more detailed understand-\n\n264\nTable 17.4.9. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for non-resonant\ndecays and other unclassi\ufb01ed modes. The averages come from HFAG and may include measurements from other experiments\nsuch as CLEO, CDF and D\u00d8 (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK+X\n< 187\n0.57 \u00b1 0.24 \u00b1 0.05\n(del Amo Sanchez, 2011c)\nK0X\n195+51\n\u221245 \u00b1 50\n(del Amo Sanchez, 2011c)\n\u03c0+X\n372+50\n\u221247 \u00b1 59\n0.10 \u00b1 0.16 \u00b1 0.05\n(del Amo Sanchez, 2011c)\nK+X(1812)\n< 0.32\n(Liu, 2009)\n< 0.32\n\u03c6K\u2217\n3(1780)0\n< 2.7\n(Aubert, 2007ap)\n< 2.7\n\u03c6K\u2217\n4(2045)0\n< 15.3\n(Aubert, 2007ap)\n< 15.3\nK+\u03c0\u2212K+\u03c0\u2212\n< 6.0\n(Chiang, 2010)\n< 6.0\nK+\u03c0\u2212\u03c0+K\u2212\n< 72\n(Chiang, 2010)\n< 72\nK+\u03c0\u2212\u03c0+\u03c0\u2212\n< 2.1\n(Kyeong, 2009)\n< 2.1\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\n< 23.1\n(Aubert, 2008r)\n< 19.3\n(Chiang, 2008)\n< 19.3\ning of the amplitude properties is required, for instance the\nspin, the scattering amplitude can be expressed in terms\nof partial-wave amplitudes. The drawback of the S-matrix\nformalism is that it is not unitary and as a result the sum\nof the amplitudes of the resonances in the Dalitz Plot can\nbe greater or less than the inclusive Dalitz Plot amplitude\ndepending on whether the overall interference is construc-\ntive or destructive. The individual branching fractions are\ntherefore often reported as \ufb01t fractions (FF), de\ufb01ned as\nthe integral of a single amplitude squared divided by the\ncoherent matrix element squared for the whole Dalitz Plot\n(Section 13.4.1). An alternative parameterization uses the\nK-matrix formalism which is unitary by construction but\nhas a drawback that the masses and widths can be dif-\nferent to the S-matrix results. The K-matrix formalism is\nmore commonly used in Dalitz Plot analyses of D meson\ndecays (section 13.2.2). This is because many of the res-\nonances in the D meson Dalitz Plot contain a large num-\nber of events and the S-matrix approximation of a Breit-\nWigner or similar shape for the decay of the resonance is\nno longer adequate, especially when the resonances over-\nlap in the Dalitz Plot.\nThe selection criteria for three-body decays are very\nsimilar to that employed for quasi-two-body analyses. An\nobvious exception is that the B meson decay is treated as\na decay to the three \ufb01nal state particles and no interme-\ndiate resonance vertex is formed when reconstructing the\nB meson. As the number of neutral \ufb01nal state particles\nincreases the importance of any constraint from the beam\nspot on the B meson vertex position also increases.\nIn quasi-two-body analyses, event shape variables and\nmultivariate discriminants can be used to extract the sig-\nnal yield because the reconstruction e\ufb03ciency is \ufb02at in the\nsmall volume of phase space under consideration. In Dalitz\nPlot analyses, this is no longer true and variables that de-\npend on momentum vectors are correlated with position\nin phase space. Even variables like mES and \u2206E need to\nbe treated carefully. Some analyses deal with the problem\nusing an elliptical selection region in (mES, \u2206E). Others\nrotate (mES, \u2206E) about a point to eliminate the linear\ncorrelation component. If the event-by-event resolution on\n\u2206E changes signi\ufb01cantly, this can be compensated for by\nusing a derived observable such as \u2206E/\u03c3(\u2206E). For sim-\nilar reasons, multivariate discriminants need to be care-\nfully constructed from variables that are as independent\nas possible from the position of the event in the Dalitz\nPlot.\nAs in quasi-two-body analyses, care must be taken\nwith charm mesons that either decay to the same \ufb01nal\nstate or are mis-reconstructed e.g. where a lepton is mis-\ntaken for a pion or kaon. This is particularly important\nin searches for highly suppressed modes such as B\u2212\u2192\nK+\u03c0\u2212\u03c0\u2212Aubert (2008aw). The charm background can\nusually be much reduced by applying mass range crite-\nria about known resonances such as D mesons, J/\u03c8 and\n\u03c8(2S). This will result in empty bands in the Dalitz Plot\nthat must be carefully considered when calculating e\ufb03-\nciencies and migrations. Alternatively, some charm decays\nare deliberately kept in the Dalitz Plot. A motivation for\nthis comes from resonances such as the \u03c7c0 that have no\nweak phase and so can be used in an interference analysis\nto extract the weak phase from the Dalitz Plot. Unfortu-\nnately, the branching fraction for B \u2192\u03c7c0h is too small\nto be useful currently.\nWhen the Dalitz Plot is represented as a Cartesian co-\nordinate system, with the square of the mass of pairs of\n\ufb01nal state particles as the x and y axes, the phase space\nis roughly triangular in shape. Figure 17.4.17 illustrates\nthe distribution of events extracted from data in the de-\ncay of B0 \u2192K0\nS\u03c0+\u03c0\u2212. The distribution of events on the\nDalitz Plot is plotted after applying a constraint on the\nB meson mass (mES = mB). This improves the resolu-\ntion and ensures that all events fall within the kinematic\nboundaries of the Dalitz Plot. An alternative often used\nis a \u201csquare\u201d Dalitz Plot where one of the axes is trans-\nformed into a \u201chelicity-like\u201d variable e.g. (Aubert, 2007v)\nor see Chapter 13. Although this transforms the distribu-\ntion of resonances from simple bands parallel to the axes to\nmore complex hyperboloids, the \u2018square\u201d Dalitz Plot has\na number of bene\ufb01ts. It can expand the region near areas\nwhere large variations are occurring such as in narrow res-\nonances like the \u03c6. Bands near the Dalitz Plot edges also\n\n265\nHFAG \nAug 2012\nCDF \nBABAR \nBelle \nLHCb \n \n \n \nNe w A vg . \nACP\nCP Asymmetry\n -1 \n 0 \n 1 \nK\u2217+K+K\u2212\nK\u22170K+K\u2212\nK\u22170\u03c0+K\u2212\nK+\u03c00\u03c00\nK\u2217+\u03c0+\u03c0\u2212\nK\u22170\u03c0+\u03c0\u2212\nK+KSKS\nK+K\u2212K+\nK+K\u2212\u03c0+\nK+\u03c0\u2212\u03c00(NR)\nK+\u03c0\u2212\u03c00\nK0\u03c0+\u03c0\u2212\nK+\u03c0+\u03c0\u2212\nK\u2217\n2(1430)0\u03c0+\nK\u2217\n0(1430)+\u03c0\u2212\nK\u2217\n0(1430)0\u03c0+\nK\u2217\n0(1430)0\u03c00\nK+K\n0\nK+\u03c00\nK0\u03c0+\nK+\u03c0\u2212\nK\u2217+\u03c0\u2212\nK\u2217+\u03c00\nK\u22170\u03c00\nK\u22170\u03c0+\nFigure 17.4.14. ACP measurements for kaonic modes with\nkaons or pions (Amhis et al. (2012)).\nget expanded, enabling \ufb01ner control over regions where the\ne\ufb03ciency is changing (such as the \u03c1 meson in B \u2192\u03c0\u03c0\u03c0).\nHowever attention must be paid to the Jacobian as equal\nareas in the \u201csquare\u201d Dalitz Plot no longer correspond to\nequal areas of phase-space.\nWhatever the choice of Dalitz Plot, care must be taken\nin plotting the candidates, especially in three-body states\nwhich have two or more \ufb01nal state identical particles of\nthe same mass and sign (e.g. B+ \u2192\u03c0+ \u03c0+ \u03c0\u2212). Typical\nchoices are to randomly select one of the pair, to fold the\nDalitz Plot about the diagonal, or to consistently plot the\nhigher mass pair on one of the axes. Even so, arti\ufb01cial or-\ndering of the candidates must be eliminated or controlled.\nSuch e\ufb00ects can be introduced by, for example, reconstruc-\nHFAG \nAug 2012\nCDF\nBABAR\nBelle\nNew Avg.\nACP\nCP Asymmetry\n -1 \n 0 \n 1 \n\u03b7K+\nK+\u03b7\u03b3\n\u03b7K\u22170\n\u03b7K\u2217+\n\u03b7K\u2217\n2(1430)+\n\u03b7K\u2217\n2(1430)0\n\u03b7K\u2217\n0(1430)0\n\u03b7K\u2217\n0(1430)+\ns\u03b7\n\u03b7 K+\n\u03b7 K\u2217+\n\u03b7 K\u22170\n\u03b7 K\u2217\n0(1430)0\n\u03b7 K\u2217\n0(1430)+\n\u03b7 K\u2217\n2(1430)0\n\u03b7 K\u2217\n2(1430)+\n\u03c6\u03c6K+\n\u03c6K\u2217\n2(1430)0\n\u03c6K\u2217\n2(1430)+\n\u03c6K1(1270)+\n\u03c6K\u2217\n0(1430)0\n\u03c6K\u2217\n0(1430)+\n\u03c6K\u22170\n\u03c6K\u2217+\nK+\u03c6\u03b3\n\u03c6K+\nFigure 17.4.15. ACP measurements for kaonic modes with \u03b7\nor \u03c6 (Amhis et al. (2012)).\ntion tracking software that, through its track-\ufb01nding al-\ngorithm, can result in momentum ordering.\nThe reconstruction e\ufb03ciency over the Dalitz Plot can\nbe modeled with a two-dimensional histogram, a technique\nthat bene\ufb01ts from the \u201csquare\u201d Dalitz Plot. All selection\ncriteria are applied apart from any mass vetoes. A ratio\nis taken between the histogram of reconstructed events\nand a histogram of the true Dalitz Plot distribution of all\ngenerated MC simulated events. The reconstructed events\nare re-weighted to take into account any known di\ufb00erences\nbetween MC simulation and data such as particle identi-\n\ufb01cation and tracking e\ufb03ciencies. The ratio can be used to\nprovide event-by-event weighting, with linear interpola-\ntion between histogram bins where needed. The e\ufb03ciency\n\n266\nBABAR\nBelle\nNew Avg.\nHFAG \nAug 2012\nACP\nCP Asymmetry\n -1 \n 0 \n 1 \nb0\n1K+\nb+\n1 K0\nb\u2212\n1 K+\na+\n1 K0\na\u2212\n1 K+\n\u03c1\u2212K+\n\u03c10K+\n\u03c1+K0\nK\u22170\u03c10\nK\u22170\u03c1+\nK\u2217+\u03c10\nK\u2217+\u03c1\u2212\n\u03c1(1450)\u2212K+\n\u03c1(1700)\u2212K+\n\u03c9K+\n\u03c9K\u22170\n\u03c9K\u2217+\n\u03c9K\u2217\n0(1430)0\n\u03c9K\u2217\n0(1430)+\n\u03c9K\u2217\n2(1430)0\n\u03c9K\u2217\n2(1430)+\nf0(980)K+\nf0(980)K\u2217+\nf0(980)K\u22170\nf2(1270)K+\nf0(1500)K+\u2020\nf2(1525)K+\nFigure 17.4.16. ACP measurements for kaonic modes with \u03c1,\n\u03c9, f, a1, or b1 (Amhis et al. (2012)).\ncan be calculated from phase-space generated MC sim-\nulated events, but this will result in poor accuracy for\nnarrow resonances such as the \u03c6. Better accuracy can be\nobtained by generating the MC with a model that con-\ntains the expected resonances in the Dalitz distribution,\nperhaps guided by previous quasi-two-body measurements\nor theory. Interference is a secondary e\ufb00ect but full Dalitz\nPlot MC simulation models which include interference ef-\nfects can be used to achieve a more uniform accuracy on\nthe e\ufb03ciency. Narrow resonances pose an additional prob-\nlem since their reconstructed width is dominated by the\ndetector resolution.\nIf the reconstruction resolution is poor compared to\nthe size of the histogram bin then it is necessary to take\ninto account migrations from the true Dalitz Plot position\nto the reconstructed position. This becomes more impor-\ntant as the number of neutral particles in the \ufb01nal state\nincreases. Care needs to be taken near the Dalitz Plot\n)\n4\n/c\n2\n(GeV\n+\n\u03c0\nS\n0\nK\n2\nm\n0\n5\n10\n15\n20\n25\n)\n4\n/c\n2\n(GeV\n-\u03c0\nS\n0\nK\n2\nm\n0\n5\n10\n15\n20\n25\nFigure 17.4.17. Dalitz Plot of data selected from B0 \u2192\nK0\nS\u03c0+\u03c0\u2212decays (Aubert, 2009av). The narrow bands corre-\nspond to D\u00b1\u03c0\u2213, J/\u03c8 K0\nS, and \u03c8(2S)K0\nS background events. As\nin many charmless B meson decay Dalitz Plots, the events of\ninterest are often at the edges of the allowed kinematic region.\nedges where migrations can be systematically in one di-\nrection, and also near mass regions that are close to any\nregion that is excluded by the selection criteria e.g. D\nmeson mass vetoes.\nThe identi\ufb01cation of the BB backgrounds is an in-\ntensive task. These backgrounds arise from combinations\nof unrelated tracks; three- and four-body decays involv-\ning intermediate D mesons; charmless two- and four-body\ndecays with an extra or missing track; and three-body\ndecays with one or more particles misidenti\ufb01ed. The num-\nber of such decays can be large (\u223c50). For \ufb01tting pur-\nposes, modes are combined that have similar behavior in\nthe discriminating variables such as mES and \u2206E. The\nrelative contributions are estimated from the reconstruc-\ntion e\ufb03ciency and estimates of the branching fractions\neither from measurement or theory. In some cases, the\nBB backgrounds are included in the maximum likelihood\n(ML) \ufb01t through the use of two-dimensional histograms\nrather than p.d.f.s.\nThe term \u201cnon-resonant\u201d is used quite loosely by ex-\nperimentalists and is often used as a short-hand for contin-\nuum background. In Dalitz Plot analyses, it should strictly\nrefer to decays that are uniformly distributed in phase-\nspace. In principle, this allows phenomenological predic-\ntions of the distribution to be used in the \ufb01ts. These\ntypically involve decaying exponential distributions as a\nfunction of the invariant mass-squared of the pairs of\nparticles (e.g. Ae\u2212c1m2). These functions attempt to de-\nscribe the increase in the number of background events\nnear the borders and corners of the Dalitz Plot. This in-\ncrease originates from the jet-like structure of the contin-\nuum background (Garmash, 2007). However, these distri-\n\n267\nbutions have turned out not to be very satisfactory and\nother more complex functions are called upon. This can\npartly be explained as the in\ufb02uence of poorly understood\nresonances (such as the \u03c3/\u03ba or the higher mass resonances\nmentioned above). As a result \u201cnon-resonant\u201d has come\nto mean anything that is not modeled by a resonance. In\npractical terms, this means the distributions often have to\ncome from MC simulations, o\ufb00-resonance data or sideband\ndata, or a combination of all three. In the case of sideband\ndata, MC samples must be used to remove events from\nB meson decays that are also present and to determine\npossible di\ufb00erences in the background shape between the\nsideband and signal regions. Linear interpolation between\nbins can be used where needed.\nThe backgrounds are constructed separately for both\nthe B0 and B0 events and a p.d.f. or histogram is formed\ntaking into account any asymmetry that might be present\nin the background distributions (see, for example Eq. 20\nin Aubert (2009h)).\nThe observables that are used in the ML depend on the\nanalysis under consideration. Typically, a combination of\n\u2206E, mES, multivariate discriminant, position in the Dalitz\nPlot and charge (\ufb02avor) of the B meson candidate is used.\nSometimes a cut is applied to the observable \ufb01rst (e.g. on\nthe multivariate discriminant) and then this observable is\nexcluded from the \ufb01t. This usually happens for observables\nthat are correlated with position in the Dalitz Plot.\nAs in two-body and quasi-two-body decays, certain D\nmeson decays to the same or similar \ufb01nal state can be\nused as a calibration channel and allow for correction to\n\ufb01tted parameters derived just from MC simulation.\nAlthough many of the resonances in the Dalitz Plot\ncan be predicted from previous quasi-two-body measure-\nments, there is still a large uncertainty in the number\nand type of resonances that should be included in any\nparticular model. Examples include the exact parameter-\nization of the non-resonant three-body decay component,\nthe \u03c3/\u03ba with masses in the region 400 \u2212600 MeV/c2 and\nwidths that are large and uncertain, the \u03c9(782), the \u03c7c0\nand \u03c7c2, and the higher mass partners of the \u03c1, f0(980),\nand K\u2217. The addition of a resonance to the model that\nis not present in the data can be just as problematic as\nany exclusion of a resonance that is present. The prob-\nlem is exacerbated if a blind \ufb01t is being performed. One\ntechnique is to use the log-likelihood reported by a partic-\nular model \ufb01tted to the data or to calculate a \u03c72 statistic\nbased on the number of events predicted from a \ufb01t and\nthe number of real events in a bin in the Dalitz Plot. The\nstatistical signi\ufb01cance of the presence of a component can\nbe estimated by evaluating the di\ufb00erence \u2206ln L between\nthe negative log-likelihood of the nominal \ufb01t and that of\na \ufb01t where the amplitude and ACP is set to zero. This is\nthen used to evaluate a p value which is the integral from\n2\u2206ln L to in\ufb01nity of the p.d.f. of the \u03c72 distribution.\nAn important goal of the Dalitz Plot analysis is the ex-\ntraction of CP asymmetries either from a time-integrated\nor time-dependent analysis. Consequently, the resonances\nare parameterized not just in terms of their widths and\nmasses but as functions of the decay dynamics, angular\ndistributions, and the transition form factors for the B\nmeson and the resonances (see Chapter 13.2.1). As ex-\nplained in more detail in Chapter 13.4.2, complex coe\ufb03-\ncients are used to parameterize the B and B meson decay.\nThe same parameterization is not consistently used be-\ntween papers or experiments, although they are all math-\nematically related. As a speci\ufb01c example from (Dalseno,\n2009), the intermediate resonances i in B and B meson\ndecay are parameterized respectively as:\na\u2032\ni = ai(1 + ci)ei(bi+di)\n\u00afa\u2032\ni = ai(1 \u2212ci)ei(bi\u2212di)\n(17.4.13)\nwhere bi and di represent the strong and weak phase re-\nspectively (notice the strong phase does not change sign).\nConsequently, the CP asymmetry for each resonance i can\nbe written as:\nACP (i) = |\u00afa\u2032\ni|2 \u2212|a\u2032\ni|2\n|\u00afa\u2032\ni|2 + |a\u2032\ni|2 = \u22122ci\n1 + c2\ni\n(17.4.14)\nIn the case of time-dependent Dalitz plot analyses, the\nresonance parameterizations above are combined with the\nequation describing the time-dependent decay properties\nof the B and B meson as given in Equation 13.2.17. In\nthis case, a great deal of attention has to be given to the\ntagging and resolution functions.\nCharmless B decays, especially those without access to\ntree decay diagrams, may have a large non-resonant con-\ntribution. This can be as high as 90% for B \u2192KKK. The\ncontribution is not uniform across the Dalitz diagram and\nso a parameterization must be adopted that depends on\nposition in the Dalitz Plot. In some analyses, BABAR and\nBelle have adopted the same non-resonant parameteriza-\ntion but in most cases they di\ufb00er, which can complicate\ncomparisons.\nThe statistical errors on the measured \ufb01t fractions\nand CP parameters are often derived from \ufb01ts to a large\nnumber of MC experiments generated with the \ufb01tted pa-\nrameters obtained from the data. These MC experiments\nare also vital for understanding the minimization process.\nWith a large number of \ufb02oating parameters, the \ufb01t can\nsometimes have more than one local minimum. There can\nbe systematic shifts in the \ufb01t caused by the starting values\nof the \ufb02oating parameters. A number of techniques for in-\nvestigating this e\ufb00ect have been applied, including using\ndi\ufb00erent minimizers, scanning through a set of starting\nvalues, randomly initializing the starting values, and the\nuse of genetic algorithms. Each has its bene\ufb01ts and draw-\nbacks but there is no one method that works better than\nthe others in all circumstances.\nThe systematic uncertainties that a\ufb00ect the \ufb01nal result\nare very similar to those seen in other charmless B decays.\nHowever their e\ufb00ects can be modi\ufb01ed since there are more\nopportunities for correlations between parameters and the\n\ufb01tted results are often reported as ratios rather than ab-\nsolute numbers. Although the magnitude and phase of\nthe complex coe\ufb03cients of the amplitude are sometimes\ntransformed to a more orthogonal set of parameters, this\n\n268\ndoes not wholly eliminate the correlations. Systematic un-\ncertainties that are unique to the Dalitz Plot are: the\nasymmetries in the background; limited statistics from the\nsidebands used to form the continuum histograms (if his-\ntograms are used); the mass rejection regions; di\ufb00erences\nin the continuum shape between the sideband and the sig-\nnal region; and charge bias introduced either by the detec-\ntor response or the selection criteria. A model dependent\nerror derived from performing \ufb01ts with an alternative set\nof resonances is sometimes quoted either in quadrature\nwith the systematic error or its own. As with quasi-two-\nbody modes, an important systematic is associated with\nuncertainty on the parameters that are \ufb01xed in the \ufb01t.\nIf a resonance is deemed to be signi\ufb01cant, the mass and\nwidth may still not be well known. Rather than \ufb02oat the\nmass and width, a series of \ufb01ts can be performed with the\nmass and width \ufb01xed at di\ufb00erent values and the change in\nthe likelihood used as a guide to the best values. Even so,\nit may be necessary to modify a model after unblinding,\nparticularly to remove resonances that are not signi\ufb01cant.\n17.4.7 Three-body and Dalitz decays\nApproximately seven B0 and eleven B\u00b1 Dalitz Plots have\nbeen investigated by BABAR and Belle. It is impossible to\ndo justice to the wealth of information available. Decays\ninvolving three pions, particularly B \u2192\u03c1\u03c0, are important\nfor the measurement of \u03c62 and are considered in Chap-\nter 17.6. Decays with an \u03b7, \u03b7\u2032, \u03c9, f0(980), or K\u2217in the\n\ufb01nal three-body state are itemized in the tables and \ufb01g-\nures of this section but are not described in detail. Instead,\nthis section concentrates on modes with one or more kaons\nin the \ufb01nal state.\nB meson decays to three-body \ufb01nal states B \u2192Khh\nproceed predominantly via b \u2192u tree-level diagrams (T\nand C diagrams in Fig. 17.4.1) and b \u2192s(d) penguin\ndiagrams (P in Fig. 17.4.1). The other diagrams can con-\ntribute but are expected to be much smaller. Final states\nwith an odd number of kaons (s-quarks) are expected\nto proceed dominantly via b \u2192s penguin transitions as\nthe b \u2192u transition is color-suppressed. If there are two\nkaons, the decay proceeds through the color-allowed b \u2192u\ntree diagram and the b \u2192d penguin decay with no b \u2192s\npenguin contribution. As a result, these Dalitz decays pro-\nvide an excellent opportunity to understand the relative\ncontribution of tree and penguin amplitudes in charmless\ndecays. This is shown in Fig. 17.4.18 where the extracted\nvalues of sin 2\u03c61 in b \u2192s penguin transitions are com-\npared to b \u2192ccs decays.\nTable 17.4.10 summarizes the reported branching frac-\ntions and asymmetries. In many cases, no resonances have\nbeen found in a Dalitz Plot and so consequently it has\nonly been possible to give a branching fraction (or up-\nper limit) and a CP asymmetry for the whole Dalitz Plot.\nFigure 17.4.19 shows the relative values of the reported\nbranching fractions so far measured.\nFigure 17.4.18. Comparison between the value of sin 2\u03c61\nfrom b \u2192ccs decays such as B0 \u2192J/\u03c8 K0 (indicated by\n\u201cWorld Average\u201d) and strange charmless b \u2192uus decays\n(Amhis et al. (2012)).\n\n269\n0.0 \n50.0 \n100.0 \nBranching Ratio x 106\nB(B \u2192(3 body modes))\nCLEO\nBelle\nBABAR\nLHCb\nNew Avg.\n \nHFAG\nAug 2012\n\u03b7 \u03b7 K0\n\u03b7 \u03b7 K+\nK\u2217\n0(1430)0\u03c0+K\u2212\nK\u22170\u03c0+\u03c0\u2212\nK\u2217+\u03c0+\u03c0\u2212\nK\u22170\u03c0+K\u2212\nK\u2217+\u03c0+K\u2212\nK\u22170K+\u03c0\u2212\nK\u2217+K+\u03c0\u2212\nK\u22170K+K\u2212\nK\u2217+K+K\u2212\nK+\u03c0+\u03c0\u2212(NR)\nK+\u03c0+\u03c0\u2212\nK0\u03c0+\u03c00\nK0\u03c0+\u03c0\u2212(NR)\nK0\u03c0+\u03c0\u2212\nK+\u03c0\u2212\u03c00(NR)\nK+\u03c0\u2212\u03c00\nK+\u03c00\u03c00\nK+K\u2212K+\nK+K\u2212K0\nK+KSKS\nKSKSKL\nKSKSKS\n\u03c9K+\u03c0\u2212(NR)1\n\u03c0+\u03c0\u2212\u03c0+(NR)\n\u03c0+\u03c0+\u03c0\u2212\n\u03c10\u03c0+\u03c0\u2212(NR)\n\u03c10K+\u03c0\u2212\nf0(980)K+\u03c0\u2212\nf0(980)\u03c0+\u03c0\u2212(NR)\n\u03c6\u03c6K0 \u00a7\n\u03c6\u03c6K+ \u00a7\nK0K+\u03c00\nK+K\u2212\u03c00\nK0K\u2212\u03c0+\nK+K\u2212\u03c0+\nKSKS\u03b7\nKSKS\u03b7\nKSKS\u03c00\nKSKS\u03c0+\nK+K+\u03c0\u2212\nK\u2212\u03c0+\u03c0+\nK+\u03c9\u03c6\nFigure 17.4.19. Summary of branching fraction measurements (\u00d710\u22126) and HFAG averages for decays with three mesons in\nthe \ufb01nal state (Amhis et al. (2012)).\n\n270\nTable 17.4.10. Charmless B decays branching fractions B and CP asymmetries ACP for BABAR and Belle for decays with three mesons in the \ufb01nal state. The averages\ncome from HFAG and may include measurements from other experiments such as CLEO and LHCb (Amhis et al. (2012)).\nBABAR results\nBelle results\nAverages\nFinal state\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nRef.\nB (\u00d710\u22126)\nACP\nK+K+\u03c0\u2212\n< 0.16\n(Aubert, 2008aw)\n< 2.4\n(Garmash, 2004)\n< 0.16\nK+K\u2212K+\n34.6 \u00b1 0.6 \u00b1 0.9\n\u22120.017+0.019\n\u22120.014 \u00b1 0.014\n(Lees, 2012y)\n30.6 \u00b1 1.2 \u00b1 2.3\n(Garmash, 2005)\n34.0 \u00b1 1.0\n\u22120.017 \u00b1 0.026\nK+K\u2212K0\n26.5 \u00b1 0.9 \u00b1 0.8\n(Lees, 2012y)\n28.3 \u00b1 3.3 \u00b1 4.0\n(Garmash, 2004)\n26.6 \u00b1 1.1\nK+K\u2212\u03c0+\n5.0 \u00b1 0.5 \u00b1 0.5\n0.00 \u00b1 0.10 \u00b1 0.03\n(Aubert, 2007an)\n< 13\n(Garmash, 2004)\n5.0 \u00b1 0.7\n0.00 \u00b1 0.10\nK+K\u2212\u03c00\n< 19\nK+K0\nSK0\nS\n10.6 \u00b1 0.5 \u00b1 0.3\n0.04 \u00b1 0.05 \u00b1 0.02\n(Lees, 2012y)\n13.4 \u00b1 1.9 \u00b1 1.5\n(Garmash, 2004)\n10.8 \u00b1 0.6\n0.04 \u00b1 0.05\nK+\u03c0+\u03c0\u2212(NR)\n9.3 \u00b1 1.0+6.9\n\u22121.7\n(Aubert, 2008j)\n16.9 \u00b1 1.3+1.7\n\u22121.6\n(Garmash, 2006)\n16.3 \u00b1 2.0\nK+\u03c0+\u03c0\u2212\n54.4 \u00b1 1.1 \u00b1 4.6\n0.028 \u00b1 0.020 \u00b1 0.023\n(Aubert, 2008j)\n48.8 \u00b1 1.1 \u00b1 3.6\n0.049 \u00b1 0.026 \u00b1 0.020\n(Garmash, 2006)\n51.0 \u00b1 3.0\n0.038 \u00b1 0.022\nK+\u03c0\u2212\u03c00(NR)\n2.8 \u00b1 0.5 \u00b1 0.4\n0.10 \u00b1 0.16 \u00b1 0.08\n(Lees, 2011a)\n< 9.4\n(Chang, 2004)\n2.8 \u00b1 0.6\n0.23+0.22\n\u22120.28\nK+\u03c0\u2212\u03c00\n38.5 \u00b1 1.0 \u00b1 3.9\n\u22120.030+0.045\n\u22120.051 \u00b1 0.055\n(Lees, 2011a)\n36.6+4.2\n\u22124.3 \u00b1 3.0\n0.07 \u00b1 0.11 \u00b1 0.01\n(Chang, 2004)\n37.8 \u00b1 3.2\n0.00 \u00b1 0.06\nK+\u03c00\u03c00\n16.2 \u00b1 1.2 \u00b1 1.5\n\u22120.006 \u00b1 0.006 \u00b1 0.004\n(Lees, 2011g)\n16.2 \u00b1 1.9\nK+\u03c9\u03c6\n< 1.9\n(Liu, 2009)\n< 1.9\nK\u2212\u03c0+\u03c0+\n< 0.95\n(Aubert, 2008aw)\n< 4.5\n(Garmash, 2004)\n< 0.95\nK0K\u2212\u03c0+\n6.4 \u00b1 1.0 \u00b1 0.6\n(del Amo Sanchez, 2010j)\n< 18\n(Garmash, 2004)\n6.4 \u00b1 1.2\nK0\u03c0+\u03c0\u2212(NR)\n11.1+2.5\n\u22121.0 \u00b1 0.9\n(Aubert, 2009av)\n19.9 \u00b1 2.5+1.7\n\u22122.0\n(Garmash, 2007)\n14.7 \u00b1 2.0\nK0\u03c0+\u03c0\u2212\n50.2 \u00b1 1.5 \u00b1 1.8\n\u22120.01 \u00b1 0.05 \u00b1 0.01\n(Aubert, 2009av)\n47.5 \u00b1 2.4 \u00b1 3.7\n(Garmash, 2007)\n49.6 \u00b1 2.0\n\u22120.01 \u00b1 0.05\nK0\u03c0+\u03c00\n< 66\nK\u2217+K+K\u2212\n36.2 \u00b1 3.3 \u00b1 3.6\n0.11 \u00b1 0.08 \u00b1 0.03\n(Aubert, 2006h)\n36.2 \u00b1 4.9\n0.11 \u00b1 0.09\nK\u2217+K+\u03c0\u2212\n< 6.1\n(Aubert, 2006h)\n< 6.1\nK\u2217+\u03c0+K\u2212\n< 11.8\n(Aubert, 2006h)\n< 11.8\nK\u2217+\u03c0+\u03c0\u2212\n75.3 \u00b1 6.0 \u00b1 8.1\n0.07 \u00b1 0.07 \u00b1 0.04\n(Aubert, 2006h)\n75.3 \u00b1 10.1\n0.07 \u00b1 0.08\nK\u22170K+K\u2212\n27.5 \u00b1 1.3 \u00b1 2.2\n0.01 \u00b1 0.05 \u00b1 0.02\n(Aubert, 2007ah)\n27.5 \u00b1 2.6\n0.01 \u00b1 0.05\nK\u22170K+\u03c0\u2212\n< 2.2\n(Aubert, 2007ah)\n< 7.6\n< 2.2\nK\u22170\u03c0+K\u2212\n4.6 \u00b1 1.1 \u00b1 0.8\n0.22 \u00b1 0.33 \u00b1 0.20\n(Aubert, 2007ah)\n< 13.9\n4.6 \u00b1 1.4\n0.22 \u00b1 0.39\nK\u22170\u03c0+\u03c0\u2212\n54.5 \u00b1 2.9 \u00b1 4.3\n0.07 \u00b1 0.04 \u00b1 0.03\n(Aubert, 2007ah)\n4.5+1.1+0.9\n\u22121.0\u22121.6\n54.5 \u00b1 5.2\n0.07 \u00b1 0.05\nK\u2217\n0 (1430)0\u03c0+K\u2212\n< 31.8\n(Chiang, 2010)\n< 31.8\nK0\nSK0\nSKL\n< 16\n(Aubert, 2006at)\n< 16\nK0\nSK0\nSK0\nS\n6.19 \u00b1 0.48 \u00b1 0.19\n(Aubert, 2005e)\n4.2+1.6\n\u22121.3 \u00b1 0.8\n(Garmash, 2004)\n6.2 \u00b1 0.9\nK0\nSK0\nS\u03b7\n< 1.0\n(Aubert, 2009am)\n< 1.0\nK0\nSK0\nS\u03b7\u2032\n< 2.0\n(Aubert, 2009am)\n< 2.0\nK0\nSK0\nS\u03c0+\n< 0.51\n(Aubert, 2009ar)\n< 3.2\n(Garmash, 2004)\n< 0.51\nK0\nSK0\nS\u03c00\n< 0.9\n(Aubert, 2009am)\n< 0.9\n\u03b7\u2032\u03b7\u2032K+\n< 25\n(Aubert, 2006al)\n< 25\n\u03b7\u2032\u03b7\u2032K0\n< 31\n(Aubert, 2006al)\n< 31\n\u03c9K+\u03c0\u2212(NR)1\n5.1 \u00b1 0.7 \u00b1 0.7\n(Goldenzweig, 2008)\n5.1 \u00b1 1.0\nK\n0K+\u03c00\n< 24\n\u03c6\u03c6K+\n5.6 \u00b1 0.5 \u00b1 0.3\n\u22120.10 \u00b1 0.08 \u00b1 0.02\n(Lees, 2011e)\n3.2+0.6\n\u22120.5 \u00b1 0.3\n0.01+0.19\n\u22120.16 \u00b1 0.02\n(Abe, 2008b)\n4.6 \u00b1 0.4\n\u22120.08 \u00b1 0.07\n\u03c6\u03c6K0\n4.5 \u00b1 0.8 \u00b1 0.3\n(Lees, 2011e)\n2.3+1.0\n\u22120.7 \u00b1 0.2\n(Abe, 2008b)\n3.6 \u00b1 0.7\n\u03c0+\u03c0+\u03c0\u2212\n15.2 \u00b1 0.6 \u00b1 1.3\n(Aubert, 2009h)\n15.2 \u00b1 1.4\n\u03c0+\u03c0\u2212\u03c0+(NR)\n5.3 \u00b1 0.7+1.3\n\u22120.8\n\u22120.14 \u00b1 0.14+0.18\n\u22120.08\n(Aubert, 2009h)\n5.3+1.5\n\u22121.1\n\u22120.14+0.23\n\u22120.16\n\u03c10K+\u03c0\u2212\n2.8 \u00b1 0.5 \u00b1 0.5\n(Kyeong, 2009)\n2.8 \u00b1 0.7\n\u03c10\u03c0+\u03c0\u2212(NR)\n< 8.8\n(Aubert, 2008r)\n< 12\n(Chiang, 2008)\n< 8.8\nf0(980)K+\u03c0\u2212\n1.4 \u00b1 0.4+0.3\n\u22120.4\n(Kyeong, 2009)\n1.4+0.5\n\u22120.6\nf0(980)\u03c0+\u03c0\u2212(NR)\n< 3.8\n(Chiang, 2008)\n< 3.8\n\n271\nCP asymmetries are expected in b \u2192sss decays con-\nsistent with asymmetries measured in b \u2192ccs. The tree\ncontributions are small and the amplitude is dominated by\nloop contributions, where new virtual particles can con-\ntribute. In B0 \u2192K+K\u2212K0, both the direct CP asymme-\ntry ACP and \u03c6eff\n1\n(\u03c61 = arg(\u2212VcdV \u2217\ncb/VtdV \u2217\ntb)) have been\nmeasured for the whole Dalitz Plot and the dominant indi-\nvidual resonances. BABAR \ufb01nd two equally likely solutions\nfor B0 \u2192\u03c6K0 and B0 \u2192f0(980)K0, the \ufb01rst consistent\nwith the SM and the second with a signi\ufb01cantly di\ufb00er-\nent phase \u03c6eff\n1\nfor B0 \u2192f0(980)K0. In the high mass\nregion, the CP-conserving case \u03c6eff\n1\n= 0 is excluded at\nthe 5.1 standard deviations level. Across the whole Dalitz\nPlot the CP asymmetry is ACP = \u22120.015 \u00b1 0.077 \u00b1 0.053\nand \u03c6eff\n1\n= 0.352 \u00b1 0.076 \u00b1 0.026 (Aubert, 2007af). Belle,\nwith approximately twice the data size, \ufb01nd four solu-\ntions for \u03c6eff\n1\nbut solution 1 is preferred when external\nconstraints, such as known branching fraction ratios, are\nincluded (Nakahama, 2010). Belle see no evidence for ACP\nin B0 \u2192\u03c6K0\nS nor in B0 \u2192f0(980)K0\nS and measure\n\u03c6eff\n1\nto be (33.2 \u00b1 9.0 \u00b1 2.6 \u00b1 1.4)\n\u25e6for B0 \u2192\u03c6K0\nS and\n(31.3 \u00b1 9.0 \u00b1 3.4 \u00b1 4.0)\n\u25e6for B0 \u2192f0(980)K0\nS (solution 1).\nThese are consistent with \u03c6eff\n1\nmeasurements from other\nb \u2192ccs transitions, such as B0 \u2192J/\u03c8K0.\nBABAR performed a binned \ufb01t to the B+ \u2192K+K+K\u2212\nDalitz Plot and found no evidence for CP violation, nei-\nther for the whole plane (ACP = \u22120.017 \u00b1 0.026 \u00b1 0.015)\nnor for any resonance (Aubert, 2006i). Belle in their anal-\nysis (Garmash, 2005) do not report asymmetries but their\nresults for branching and \ufb01t fractions do not agree well\nwith BABAR. This is primarily due to the fact that BABAR\nreport a broad scalar resonance, which they label X0(1550),\nwhile Belle include only the f0(980) in their model.\nThe Dalitz Plot structure of B0 \u2192K0\nSK0\nSK0\nS has\nbeen investigated and the inclusive branching fractions\nmeasured. The product branching fractions of f0(980)K0\nS,\nf0(1270)K0\nS and f2(2010)K0\nS have been measured and\nthere are hints of f \u2032\n2(1525) and f0(1500) (Lees, 2012c).\nThe mixing-induced CP-violation parameters for B0 \u2192\nK0K0K0 are measured to be S = \u22120.94+0.24\n\u22120.21 \u00b1 0.06\nand C = \u22120.17 \u00b1 0.18 \u00b1 0.04. These are compatible\nwithin 2 standard deviations with those measured in tree-\ndominated B0 \u2192J/\u03c8K0\nS decays. As a result CP conserva-\ntion is excluded at the 3.8 standard deviation level. Belle\nhave looked at B0 \u2192K0\nSK0\nSK0\nS and intermediate reso-\nnances that decay to the \ufb01nal state K+K\u2212K0\nS (Chen,\n2007a).\nBelle measure sin 2\u03c61 in B0 \u2192\u03b7\u2032K0 to be 0.64\u00b10.10\u00b1\n0.04 with a signi\ufb01cance of 5.6 standard deviations and \ufb01nd\nno evidence for direct CP violation. BABAR also measure\na signi\ufb01cant value of sin 2\u03c61 = 0.58 \u00b1 0.10 \u00b1 0.03 (5.5\nstandard deviations signi\ufb01cance) in B0 \u2192\u03b7\u2032K0 (Aubert,\n2007am). However, in this case, the direct CP result Af =\n\u22120.16 \u00b1 0.07 \u00b1 0.03 is 2.1 standard deviation from zero.\nFor B+ \u2192K0K0K+, Belle report branching frac-\ntions (Garmash, 2004), while BABAR has also extracted\nthe CP charge asymmetry ACP = \u22120.04 \u00b1 0.1 \u00b1 0.02 (Au-\nbert, 2004b).\nFigure 17.4.20. Example of the SM suppressed decay dia-\ngram for the decay B\u2212\u2192K+\u03c0\u2212\u03c0\u2212.\nModes with just two kaons in the \ufb01nal state are im-\nportant as they proceed through b \u2192d penguin loops and\nare suppressed. Consequently, small branching fractions\nare expected and the opportunities for measuring asym-\nmetries are few.\nThere have been no measurements of the decay B0 \u2192\nK+K\u2212\u03c00 by BABAR or Belle. The decay B+ \u2192K+K\u2212\u03c0+\nhas been observed by BABAR (Aubert, 2007an) with B =\n(5.0\u00b10.5\u00b10.5)\u00d710\u22126 and ACP = 0.00\u00b10.10\u00b10.03; Belle\nhave placed upper limits (UL) on the branching fraction\n< 13\u00d710\u22126 (Garmash, 2004). The mode B+ \u2192K+K+\u03c0\u2212\nis additionally suppressed by a factor |VtdV \u2217\nts| \u223c3 \u00d7 10\u22124\nbut could be enhanced in SM extensions with extra Z\u2032\nbosons. BABAR \ufb01nds for this decay a branching fraction\nUL of 0.16 \u00d7 10\u22126 (Aubert, 2008aw). The decay B0 \u2192\nK0\nSK\u00b1\u03c0\u2213has been observed by BABAR with branching\nfraction (3.2 \u00b1 0.5 \u00b1 0.3) \u00d7 10\u22126 at 5.2 standard deviation\nsigni\ufb01cance (del Amo Sanchez, 2010j).\nBoth Belle and BABAR have made signi\ufb01cant progress\nin measuring B \u2192K0\nSK0\nSh where h includes mesons such\nas \u03c0+, \u03c00, \u03b7, and \u03b7\u2032. The b \u2192d transition has been mea-\nsured in B0 \u2192\u03c0+\u03c0\u2212\u03c00 where the beauty \ufb02avor changes\nby \u2206F = 2 (due to mixing) but in B+ \u2192K0\nSK0\nS\u03c0+ by\n\u2206F = 1 (due to decay). Both BABAR and Belle have\nplaced upper limits of B(B+ \u2192K0\nSK0\nS\u03c0+) < 0.51 \u00d7\n10\u22126 (Aubert, 2009ar) and < 3.2\u00d710\u22126 (Garmash, 2004),\nrespectively. BABAR \ufb01nd ULs on B(B0 \u2192K0\nSK0\nS\u03c00),\nB(B0 \u2192K0\nSK0\nS\u03b7), and B(B0 \u2192K0\nSK0\nS\u03b7\u2032) of 2 \u00d7 10\u22126\nand below (Aubert, 2009am).\nLarge CP asymmetries are expected in B+ \u2192\u03c10K+.\nBABAR \ufb01nd evidence of direct CP violation in B+ \u2192\n\u03c10K+, \u03c10 \u2192\u03c0+\u03c0\u2212with ACP = (0.44\u00b10.10\u00b10.04+0.06\n\u22120.13) (Au-\nbert, 2008j) at the 3.7\u03c3 level and Belle report very similar\nresults, with ACP = (0.30\u00b10.11\u00b10.02+0.11\n\u22120.04) with 3.9\u03c3 sig-\nni\ufb01cance (Garmash, 2006) A Dalitz analysis is essential\ndue to the possibility of interference of the wide \u03c10 width\nwith neighboring resonances. CP asymmetries in B+ \u2192\nK\u22170\u03c0+, B+ \u2192K\u22170\n0 (1430)\u03c0+, and B+ \u2192K\u22170\n2 (1430)\u03c0+,\non the other hand, are small. The SM-suppressed mode\nB\u2212\u2192K+\u03c0\u2212\u03c0\u2212has also been investigated by both ex-\nperiments and the decay diagram is shown in Fig. 17.4.20.\nBABAR and Belle place UL on the branching fraction of\n0.95\u00d710\u22126 (Aubert, 2008aw) and < 4.5\u00d710\u22126 (Garmash,\n2004), respectively.\n\n272\nThe decay B+ \u2192K+\u03c0\u2212\u03c0+ is important for search-\ning for direct CP violation in B \u2192K\u2217\u03c0 decays. BABAR\n\ufb01nd four compatible solutions of the Dalitz Plot (Lees,\n2011a). When combined with the time-dependent analy-\nsis of B0 \u2192K0\nS\u03c0\u2212\u03c0+\n(Aubert, 2009av), BABAR report\nACP = \u22120.24 \u00b1 0.07 \u00b1 0.02 with a signi\ufb01cance of 3.1\u03c3 for\nB \u2192K\u2217+\u03c0\u2212decays. A similar Belle analysis has half the\nnumber of events and is restricted to branching fraction\nmeasurements and ranges for ACP (Chang, 2004).\nIn B0 \u2192\u03c0+\u03c0\u2212K0\nS, the decay B0 \u2192f0(980)K0\nS is ex-\npected to be dominated by b \u2192s transitions. The f0(980)\ncan overlap with nearby resonances, requiring a Dalitz\nanalysis to extract a robust estimate of sin 2\u03c61, taking\ninterference into account. Belle \ufb01nd no evidence for direct\nCP violation in B0 \u2192\u03c10K0\nS, B0 \u2192f0(980)K0\nS, and B0 \u2192\nK\u2217+\u03c0\u2212and measure ACP (K\u2217+\u03c0\u2212) = \u22120.21\u00b10.11\u00b10.05\u00b1\n0.05 (Dalseno, 2009; Garmash, 2007). The sin 2\u03c61 mea-\nsurements for B0 \u2192\u03c10K0\nS and B0 \u2192f0(980)K0\nS are\nconsistent with sin 2\u03c61 from b \u2192ccs decays. The phase\ndi\ufb00erence between B0 \u2192K\u2217+\u03c0\u2212and B0 \u2192K\u2217\u2212\u03c0+,\nwhich could lead to a measurement of \u03c63, is reported as\n\u2206\u03c6(K\u2217+\u03c0\u2212) = (\u22120.7+23.5\n\u221222.8 \u00b1 11.0 \u00b1 17.6)\u25e6. BABAR has\nalso looked at this mode but only report ranges for \u03c61\nin B0 \u2192\u03c10K0\nS and B0 \u2192f0(980)K0\nS but they measure\nACP (K\u2217+\u03c0\u2212) consistent with Belle (Aubert, 2009av).\nThe B Factories have started to look at Dalitz Plots\ninvolving short-lived particles such as the K\u2217. The branch-\ning fractions of the decays B0 \u2192K\u22170\u03c0+K\u2212and B+ \u2192\nK\u2217+\u03c0+K\u2212are sensitive to the CKM matrix elements Vtd\nand Vub. Additionally, a branching fraction of the Stan-\ndard Model suppressed decay B0 \u2192K\u22170K+\u03c0\u2212compara-\nble or larger than that of B0 \u2192K\u22170\u03c0+K\u2212would be an\nindication of new physics (Aubert, 2006h, 2007ah). There\nis no evidence for this in the current data with branching\nfraction measurements of B(B0 \u2192K\u22170K+\u03c0\u2212) = (4.6 \u00b1\n1.1 \u00b1 0.8) \u00d7 10\u22126 and B(B0 \u2192K\u22170\u03c0+K\u2212) < 2.2 \u00d7 10\u22126.\nAs an example of the detail of information that can\nbe extracted from a Dalitz Plot analysis, Table 17.4.11\nshows the branching fractions, charged asymmetries, \ufb01t\nfractions, and phases for the decay B+ \u2192K+K+K\u2212.\nSimilar results exist for a number of the Dalitz Plots listed\nin Table 17.4.10.\n17.4.8 Summary\nTogether BABAR and Belle have collected well over 1 ab\u22121\nof B meson decays. Even with low branching fractions,\nthe study of charmless hadronic B decays have enabled\nthe measurement of: the CKM angles \u03c61, \u03c62, \u03c63; the dis-\ncovery of many new decay modes with a measured branch-\ning fraction; new branching fraction upper limits placed\non many rare decays; direct and indirect CP asymmetries;\nG-parity conservation tests; longitudinal polarization; in-\nterference e\ufb00ects; and weak and strong phases. This has\nenabled a comprehensive comparison with theoretical pre-\ndictions and models. These theoretical models continue to\nprogress, with more precise calculations over a wider range\nof observables. Yet despite this, the study of charmless\nhadronic decays is still only partially complete. Work is\nstill on-going in understanding the hierarchy of the longi-\ntudinal polarization. Some measured branching fractions\ndo not agree with predictions. The prediction, understand-\ning and interpretation of the phases and amplitudes in\nthree-body Dalitz Plots are still in their infancy.\n\n273\nTable 17.4.11. An illustration of the results that can be extracted from a full Dalitz Plot analysis of B+ \u2192K+K+K\u2212for\nBABAR (Aubert, 2006i) and Belle (Garmash, 2005). The extracted parameters are: the branching fraction B or product branching\nfraction B \u00d7 Bf (\u00d710\u22126); the charged CP asymmetry ACP (%); the \ufb01t fraction FF (%); the phase \u03b4 (\u25e6) relative to the reference\ndecay; mass M and width \u0393 (GeV/c2); NR is the non-resonant component and some errors have been rounded.\nDecay\nParam.\nBABAR\nBelle\nK+ K+ K\u2212\nB\n33.5 \u00b1 0.9 \u00b1 1.6\n30.6 \u00b1 1.2 \u00b1 2.3\nACP\n\u22120.02 \u00b1 0.03 \u00b1 0.02\n\u03c6K+\nB\n8.4 \u00b1 0.7 \u00b1 0.7\n9.60 \u00b1 0.92 \u00b1 0.71\nACP\n0 \u00b1 8 \u00b1 2\nFF\n11.8 \u00b1 0.9 \u00b1 0.8\n14.7 \u00b1 1.3\n\u03b4\n\u22127 \u00b1 0.11 \u00b1 3\n\u2212123 \u00b1 10\n\u03c6(1680)K+\nB \u00d7 Bf\n< 0.8\nf0(980)K+\nB \u00d7 Bf\n6.5 \u00b1 2.5 \u00b1 1.6\n< 2.9\nACP\n\u221231 \u00b1 25 \u00b1 8\nFF\n19 \u00b1 7 \u00b1 4\n\u03b4\n28 \u00b1 9 \u00b1 5\nfX(1500)K+\nB \u00d7 Bf\n43 \u00b1 6 \u00b1 3\nACP\n\u22124 \u00b1 7 \u00b1 2\nFF\n121 \u00b1 19 \u00b1 6\n63.4 \u00b1 6.9\n\u03b4\n74 \u00b1 5 \u00b1 2\n0 (\ufb01xed)\nM\n1.539 \u00b1 0.020\n1.524 \u00b1 0.014\n\u0393\n0.257 \u00b1 0.033\n0.136 \u00b1 0.023\nf0(1710)K+\nB \u00d7 Bf\n1.7 \u00b1 1.0 \u00b1 0.3\nf \u2032(1525)K+\nB \u00d7 Bf\n< 4.9\na2(1320)K+\nB \u00d7 Bf\n< 1.1\nNR\nB\n50 \u00b1 6 \u00b1 4\n24.0 \u00b1 1.5 \u00b1 1.8\nFF\n141 \u00b1 16 \u00b1 9\n74.8 \u00b1 3.6\n\u03b4\n0 (\ufb01xed)\n\u221268 \u00b1 9\n\n274\n17.5 B-meson lifetimes, B0 \u2212B0 mixing,\nand symmetry violation searches\nEditors:\nSoeren Prell (BABAR)\nBruce Yabsley (Belle)\nAdditional section writers:\nThomas Mannel\nThe charged and neutral B meson lifetimes, \u03c4B+ and\n\u03c4B0, and the B0 \u2212B0 oscillation frequency \u2206md, are fun-\ndamental parameters of B meson decays. They provide\nimportant input for the determination of the CKM ma-\ntrix elements |Vcb| and |Vtd| (discussed in Sections 17.1\nand 17.2). In addition, precise knowledge of \u03c4B0 and \u2206md\nis necessary for the extraction of CP asymmetries from\nthe neutral B decay-time distributions. Here we describe\nprecision measurements of \u03c4B+, \u03c4B0 (Section 17.5.1), and\n\u2206md (Section 17.5.2); measurements of \u2206\u0393d are also dis-\ncussed (Section 17.5.2.6). By relaxing the assumptions be-\nhind standard mixing analyses, it is also possible to test\nthe quantum-mechanical nature of B0 \u2212B0 oscillations\n(Section 17.5.3), search for violations of CP, T, or even\nCPT symmetry in mixing (Section 17.5.4), and search for\nviolations of Lorentz symmetry (Section 17.5.5).\n17.5.1 B-meson lifetimes\nIn 1983 the MAC and MARK II Collaborations (Fernan-\ndez et al., 1983; Lockyer et al., 1983) discovered, in 29 GeV\ncenter-of-mass energy e+e\u2212collisions recorded at the PEP\nstorage ring at SLAC, that the impact parameters of high-\nmomentum leptons in hadronic \ufb01nal states were largely\npositive. From the measured impact parameter distribu-\ntions and assuming these leptons originated mostly from\nb hadron decays, the collaborations estimated a b hadron\nlifetime of the order of one picosecond. Such a long life-\ntime was unexpected. At the time, the phenomenological\nguidance on the strength of weak b hadron decays was\nthe mixing between the \ufb01rst and second quark genera-\ntion, characterized by the Cabibbo angle \u03b8C (Section 16).\nIf quark mixing between the second and the third genera-\ntion was similar, the expected b lifetime would be around\n0.1 ps (Barger, Long, and Pakvasa, 1979). The long life-\ntime of b hadrons was the \ufb01rst evidence that the mag-\nnitude of the CKM matrix element Vcb is much smaller\nthan sin \u03b8C. Along with \ufb01rst limits on the branching frac-\ntions of semileptonic b \u2192u transitions, and thus |Vub/Vcb|,\nfrom experiments at Cornell around the same time (Chen\net al., 1984; Klopfenstein et al., 1983) and unitarity con-\nstraints, the measurement of |Vcb| led to the \ufb01rst com-\nplete picture of the magnitudes of all the CKM matrix\nelements (Ginsparg and Wise, 1983). Soon after, it was\nrealized that due to its long lifetime the B0 can oscillate\ninto a B0 before it decays, allowing for measurements of\nB0 \u2212B0 mixing and time-dependent CP asymmetries.\nAt the time when the B Factories started to record\ntheir \ufb01rst data, the Particle Data Group listed in their\n2000 Review of Particle Physics (Groom et al., 2000) the\naverages of the B0 and B+ lifetimes and their ratio as:\n\u03c4B0 = (1.548 \u00b1 0.032) ps, \u03c4B+ = (1.653 \u00b1 0.028) ps, and\n\u03c4B+/\u03c4B0 = 1.062 \u00b1 0.029, with relative uncertainties of\n2.1%, 1.7%, and 2.7%, respectively.\nWhile the \ufb01rst measurements of the magnitude of the\nCKM matrix element Vcb were provided by the initial b\nhadron lifetime measurements, the most precise determi-\nnation of |Vcb|, based on advances in the theoretical de-\nscriptions of B-meson decays, now comes from semilep-\ntonic branching ratios (see Section 17.1).\nIn the following, we brie\ufb02y discuss the theory of B me-\nson lifetimes (Section 17.5.1.1), and the motivation and\nprinciples of lifetime measurements (Section 17.5.1.2), be-\nfore reviewing lifetime measurements at the B Factories\nusing fully-reconstructed (Section 17.5.1.3) and partially-\nreconstructed \ufb01nal states (Section 17.5.1.4). Averages of\nthe B lifetimes and their ratio are presented in Sec-\ntion 17.5.1.5.\n17.5.1.1 Theory of B meson lifetimes\nFrom the theoretical side the lifetime (or equivalently the\ntotal decay rate \u0393) of a heavy quark hadron is a fully inclu-\nsive quantity for which a systematic expansion in powers\nof \u039bQCD/mQ can be performed (Bigi, 1996; Neubert and\nSachrajda, 1997). Schematically one obtains an expression\nof the form\n\u0393 = \u03930 + \u03931\n\u0012\u039bQCD\nmQ\n\u0013\n(17.5.1)\n+ \u03932\n\u0012\u039bQCD\nmQ\n\u00132\n+ \u03933\n\u0012\u039bQCD\nmQ\n\u00133\n+ \u00b7 \u00b7 \u00b7\nThe leading term in the decay rate\nIt turns out that the leading term of this expansion does\nnot depend on any hadronic matrix element and is simply\nthe decay of a free quark. This is illustrated in Fig. 17.5.1:\nIt depicts the square of the amplitude of a heavy quark\ndecaying via a four quark operator into three \ufb01nal state\nfermions, i.e. the internal lines should not be interpreted\nas propagators, but rather as the corresponding phase\nspace integration. Since only the heavy quark is involved,\nto this level of the expansion, the lifetime of all charm and\nFigure 17.5.1. Illustration of the leading term of the heavy\nquark expansion for the total rate.\n\n275\nbottom hadrons, respectively, are predicted to be iden-\ntical. Neglecting CKM suppressed contributions and the\nmasses of the electron, the muon, the up and the down\nquark, the leading term for charm hadrons (i.e. without\nQCD corrections) can be written as,\n\u0393c = |Vcs|2 [Nc\u0393(c \u2192sud) + 2\u0393(c \u2192s\u2113\u03bd\u2113)] ,\n(17.5.2)\nwhere Nc is the number of colors, \u2113= e, \u00b5, and\n\u0393(c \u2192sff \u2032) = G2\nF m5\nc\n192\u03c03 fPS,\n(17.5.3)\nwhere fPS is a phase space factor depending on the mass\nof the charm and the strange quarks.\nFor bottom hadrons this expression is slightly more\ncomplicated since more \ufb01nal states are involved. For the\nleading term, neglecting again CKM suppressed contribu-\ntions, setting |Vcs| = |Vud| \u22481, and neglecting the e, \u00b5, u,\nand d masses, one obtains\n\u0393b = |Vcb|2\n\u0014\nNc[\u0393(b \u2192ccs) + \u0393(b \u2192cud)]\n+2\u0393(b \u2192c\u2113\u03bd\u2113) + \u0393(b \u2192c\u03c4\u03bd\u03c4)\n\u0015\n,\n(17.5.4)\nwhere now\n\u0393(b \u2192cff \u2032) = G2\nF m5\nb\n192\u03c03 f(ff \u2032),\n(17.5.5)\nand f(ff \u2032) is a phase space function depending on the bot-\ntom and the charm mass as well as on the masses of the\ntwo additional fermions f and f \u2032.\nAlthough the analytic expression for the phase space\nfunctions are not complicated, we give here only a sim-\nple numerical consideration. Putting in the phase space\nfunctions, one obtains\n\u0393c \u22483.5 \u00d7 G2\nF m5\nc\n192\u03c03 |Vcs|2 = [1.1 \u00d7 10\u221212 s]\u22121, (17.5.6)\n\u0393b \u22482.9 \u00d7 G2\nF m5\nb\n192\u03c03 |Vcb|2 = [1.2 \u00d7 10\u221212 s]\u22121. (17.5.7)\nBeing the \ufb01rst term of a systematic expansion, it is reas-\nsuring that these numbers are in the right ballpark. Note\nthat the rates have to be proportional to m5\nQ to compen-\nsate the dimension of the Fermi coupling GF ; however the\nfull dependence on the heavy quark mass is not as strong\ndue to the phase space factors. The fact that the bottom\nand charm lifetimes are still comparable is due to the small\nmagnitude of the CKM element |Vcb| relative to |Vcs|.\nThe prediction that the heavy-hadron lifetimes are\nidentical was considered a problem in the early days of\nthe heavy quark expansion. In fact, we have for example\n\u03c4(D+)/\u03c4(D0) = 2.52 \u00b1 0.09, indicating large corrections\nfrom higher-order terms in the expansion. Furthermore,\nthe leading term depends on a high power of mQ, such\nthat any uncertainty in mQ would be ampli\ufb01ed so much\nthat it was originally believed that no precise predictions\ncould be made. However, including QCD corrections in\ncombination with suitable mass de\ufb01nitions, this could be\nremedied.\nWe note in passing that the na\u00a8\u0131ve spectator model also\npredicts the semileptonic branching ratios. Taking into ac-\ncount only the Cabibbo-allowed contributions and neglect-\ning the masses of the \ufb01nal state fermions we obtain\nB(D \u2192X\u2113\u03bd) =\n\u0393(c \u2192s\u2113\u03bd)\nNc\u0393(c \u2192sdu) + Nlept\u0393(c \u2192s\u2113\u03bd),\n(17.5.8)\nwhere \u2113= e or \u00b5, Nc = 3 is the number of colors, and\nNlept = 2 is for the two leptons that can appear as a\n\ufb01nal state in a D decay. With the approximation |Vcs| =\n|Vud| \u223c1, and \ufb01nal state masses neglected, the partial\nwidths are equal,\n\u0393(c \u2192sdu) = \u0393(c \u2192s\u2113\u03bd) = G2\nF m5\nc\n192\u03c03 ,\n(17.5.9)\nso we \ufb01nd\nB(D \u2192X\u2113\u03bd) =\n1\n3 + 2 = 0.2.\n(17.5.10)\nFor bottom we can perform the same calculation, however\nhere one has to take into account phase space factors, since\nthe phase space for e.g. b \u2192ccs is signi\ufb01cantly di\ufb00erent\nfrom that for b \u2192cud. Taking this e\ufb00ect into account one\narrives at\nB(B \u2192X\u2113\u03bd) = 0.17 .\n(17.5.11)\nAgain these predictions are in the right ballpark, but de-\npend strongly on the quark masses and the de\ufb01nitions\nused for these masses. Including the higher order terms\nin \u03b1S as well as in the heavy quark expansion improves\nthe precision of the predictions dramatically. In particu-\nlar, the determination of |Vcb| is performed on the basis\nof the total semileptonic rate, which is computed at the\npercent level of precision.\nHigher-order terms\nThe higher order terms in the heavy quark expansion have\nbeen investigated in detail. The term of order \u039bQCD/mQ\nvanishes due to heavy quark symmetries, so the \ufb01rst non-\nperturbative input to the lifetimes appears at the second\norder of the expansion. To this order, the kinetic energy\nparameter \u00b52\n\u03c0 and the chromo-magnetic moment \u00b52\nG ap-\npear as non-perturbative input (for the precise de\ufb01nition\nof these parameters see Section 17.1). However, assum-\ning light-quark \ufb02avor symmetry, one obtains \u00b52\n\u03c0(B0) =\n\u00b52\n\u03c0(B\u00b1) = \u00b52\n\u03c0(B0\ns) and hence the second order in the ex-\npansion still does not induce a lifetime di\ufb00erence between\nB0, B\u00b1, and B0\ns.\nA lifetime di\ufb00erence between the bottom mesons needs\nto involve the spectator quark. Contributions of this kind\nare illustrated in Fig. 17.5.2. However, such contributions\nare induced only at order (\u039bQCD/mQ)3, which was taken\nas an embarrassment at the time this was derived, since\nthe lifetimes in the D meson system di\ufb00er by a factor\n\n276\nFigure 17.5.2. Spectator contributions.\nas large as 2.5. However, subsequently it has been found\nthat the coe\ufb03cient \u03933 can be enhanced by a loop factor\n16\u03c02, which at least qualitatively explains this large ef-\nfect. This can actually be seen by comparing Figs 17.5.1\nand 17.5.2: the leading term shown in Fig 17.5.1 is a two-\nloop diagram, leading to a factor (1/(16\u03c02))2, whereas the\nspectator contributions shown in Fig 17.5.2 are one-loop\ndiagrams with only a single power of 1/(16\u03c02) (Neubert\nand Sachrajda, 1997).\nOver the past ten years lifetime calculations have been\nre\ufb01ned by adding higher order terms in the 1/mb expan-\nsion as well as QCD corrections. A recent review can be\nfound in Lenz (2008).\n17.5.1.2 Motivation and principles of lifetime measurements\nThere were both theoretical and experimental reasons for\nthe B Factories to measure the B-meson lifetimes more\nprecisely:\n\u2013 Predictions for lifetime ratios based on a na\u00a8\u0131ve\nestimate of the hadronic matrix elements yielded\n\u03c4B+/\u03c4B0 = 1.067 \u00b1 0.027 (Becirevic, 2001). While in\nagreement with this prediction, the pre-B Factory data\nwere not conclusive on whether the charged or neutral\nB lifetime was longer, motivating a more precise mea-\nsurement of \u03c4B+/\u03c4B0 to provide a stronger test of these\ncalculations.\n\u2013 The B0 meson lifetime provides an essential input to\nthe measurements of the B0 \u2212B0 oscillation frequency\n(see Section 17.5.2) and time-dependent CP asymme-\ntries including the angles \u03c61 and \u03c62 of the Unitarity\nTriangle (see Sections 17.6 and 17.7). Accurate values\nof \u03c4B0 and \u2206md reduce the systematic uncertainties in\nthese analyses of time-dependent CP asymmetries.\nThe most precise measurements of the B-meson life-\ntimes before the \ufb01rst B Factory results became available\nwere from experiments at the Z0 resonance and CDF.\nThese experiments measured the distance l the B me-\nson travels from its production point to its decay ver-\ntex. The production point is, respectively, the e+e\u2212or\npp interaction point and the decay vertex is determined\nfrom the B decay products. From this decay distance l,\nthe measured B momentum pB, and the known B mass\nmB, they determined the proper time of the B-meson de-\ncay t = l/c(\u03b2\u03b3)B = mBl/(pBc). The proper-time dis-\ntribution of the B-meson candidates is given by \u0393(t) =\n1\n\u03c4B exp(\u2212t/\u03c4B) before accounting for detector resolution\nand backgrounds. The experiments extracted the B-meson\nlifetimes from \ufb01ts to the measured proper-time spectra.\nWhile the ARGUS and CLEO experiments had collected\nlarge samples of B mesons at the \u03a5(4S) resonance, their\nB mesons were essentially produced at rest in the lab-\noratory frame, rendering a proper-time method through\ndecay-length measurements impossible.\nThese earlier B-lifetime measurements are character-\nized by high-precision measurements of the relative de-\ncay length of the B mesons (\u03c3l/\u27e8l\u27e9\u224810%), but typi-\ncally su\ufb00ered from a combination of relatively small signal\nsamples, large backgrounds, and in the case of partially-\nreconstructed B mesons, a poor measurement of the B\nmomentum. In contrast, the measurements from BABAR\nand Belle have worse \u03c3l/\u27e8l\u27e9resolution, but their high-\nstatistics B samples have little background and excellent\nknowledge of the B momentum.\nA principal di\ufb00erence between the B-meson lifetime\nmeasurements at previous experiments and at the asym-\nmetric-energy B Factories is the knowledge of the B pro-\nduction point. At all experiments the B mesons are pro-\nduced in the luminous region of the particle beams (beam\nspot). The coordinates of the beam spot are well known.\nThe beam spot size is much smaller in the plane trans-\nverse to the beam direction than along the beam direction.\nAt the LEP and Tevatron experiments and at SLD most\nB mesons travel a measurable distance in the transverse\nplane before they decay, and the B meson proper time\nis derived from this distance. In \ufb01ts to the proper-time\ndistributions, events with measured t < 0 provide valu-\nable information about the proper-time resolution func-\ntion. Since there are no true negative proper times, all\nevents with measured t < 0 are due to resolution e\ufb00ects.\nIn contrast, at the B Factories the B mesons are barely\nmoving in the center-of-mass frame. Thus their transverse\nmomentum and transverse \ufb02ight distance are close to zero\nand cannot be used for a precise proper-time measure-\nment. The length of the beam spot in the z direction is\nabout a centimeter in BABAR and Belle and there are no\nfragmentation tracks coming from the B production point\n(as only a BB-pair is produced in the decay of the \u03a5(4S)).\nTherefore the z coordinate of the B production vertex can-\nnot be reconstructed with good precision. Instead, at the\nB Factories the distance \u2206z between the decay vertices of\nthe two B mesons is measured. The proper-time di\ufb00erence\nis then given to good approximation by\n\u2206t \u2248\u2206z/(c(\u03b2\u03b3)B),\n(17.5.12)\n\n277\nwhere (\u03b2\u03b3)B is the Lorentz boost factor of the B meson\nin the lab frame (see Section 6.5). The \u2206t distribution is\ngiven by\n\u0393(\u2206t) =\n1\n2\u03c4B\nexp (\u2212|\u2206t|/\u03c4B).\n(17.5.13)\nIt is symmetric around \u2206t = 0. Detector resolution e\ufb00ects\nwill smear this distribution, but there is no region in \u2206t\nthat allows a similarly clean access to the \u2206t resolution\nfunction as in the experiments at the Z0 and CDF and D\u00d8\n(see Fig. 17.5.3). One of the challenges of the B-lifetime\nmeasurements at the B Factories is to disentangle the un-\nderlying true \u2206t distribution from the resolution function.\nBoth BABAR and Belle use multiple samples of B me-\nsons to determine the B0 and B+ lifetimes and their ratio.\nOne of the B mesons, Brec, is typically reconstructed in an\nexclusive \ufb01nal state. The various samples di\ufb00er in their B\nmeson yield per inverse femtobarn and in their signal pu-\nrity.57 More exclusive samples have less background, but\nalso a smaller yield. In the lifetime analyses, the z position\nof the Brec decay vertex zrec is determined from its decay\nproducts. The z position zoth of the decay vertex of the\nother B meson, Both, is reconstructed from the tracks not\nbelonging to Brec. The proper-time di\ufb00erence \u2206t is then\ncalculated from \u2206z = zrec \u2212zoth using Eq. (17.5.12). It\nturns out that the uncertainty in \u2206t is dominated by the\nuncertainty in zoth and is almost the same for all lifetime\nanalyses at the B Factories. The B lifetimes are extracted\nfrom a \ufb01t to the \u2206t distributions of the selected candi-\ndates after accounting for detector resolution e\ufb00ects and\nbackground. In the following, we will brie\ufb02y describe the\nvarious measurements of the B-meson lifetimes by the B\nFactories. The results of these analyses are summarized in\nTable 17.5.1; averages are discussed in Section 17.5.1.5.\n17.5.1.3 Fully-reconstructed \ufb01nal states\nB lifetime measurements with samples in which one B\ndecays to an exclusive hadronic \ufb01nal state have the\nlowest background. BABAR measures the B0 and B+\nlifetimes with the hadronic decays B0\n\u2192\nD(\u2217)\u2212\u03c0+,\nD(\u2217)\u2212\u03c1+, D(\u2217)\u2212a+\n1 , J/\u03c8K\u22170 and B+ \u2192D(\u2217)0\u03c0+, J/\u03c8K+,\n\u03c8(2S)K+ in a data sample of 20.6 fb\u22121 (Aubert, 2001c).\nBelle\nperforms\nan\nanalysis\ncombining\nthe\nexclusive\nhadronic \ufb01nal states B0 \u2192D(\u2217)\u2212\u03c0+, D\u2217\u2212\u03c1+, J/\u03c8K0\nS,\nJ/\u03c8K\u22170 to measure the B0 lifetime and the modes B+ \u2192\nD0\u03c0+, J/\u03c8K+ to measure the B+ lifetime in a sample\nof 29.1 fb\u22121 (Abe, 2002m). The decay channels K+\u03c0\u2212,\nK+\u03c0\u2212\u03c00, K+\u03c0\u2212\u03c0+\u03c0\u2212, and K0\nS\u03c0+\u03c0\u2212are used to recon-\nstruct D0 candidates, while the modes K+\u03c0\u2212\u03c0+ and\nK0\nS\u03c0\u2212are used for D\u2212candidates (Belle does not use\nthe D decay modes involving a K0\nS). Charged D\u2217\u2212can-\ndidates are formed by combining a D0 with a soft \u03c0\u2212.\n57 The signal purity is the fraction of signal events in the\nselected candidates (see also Section 4.3). It is often de\ufb01ned\nfor a region of about \u00b12 standard deviations around the signal\npeak (for example, in mES or \u2206E).\n\u2206t (ps)\nentries / 0.8ps\n1\n10\n10 2\n10 3\nB\n\uf8e70\n1\n10\n10 2\n10 3\n\u221220 \u221215 \u221210\n\u22125\n0\n5\n10\n15\n20\nB\u2212\nFigure 17.5.3. The \u2206t distributions of B0 (top) and B\u2212(bot-\ntom) candidates (plus c.c.) for fully-reconstructed B decays to\nhadronic \ufb01nal states. The dashed lines represent the sum of\nthe background and outlier components, and the dotted lines\nrepresent the outlier component (Abe, 2002m).\nThe B0 candidates are formed by combining a D\u2217\u2212or\nD\u2212with a \u03c0+, \u03c1+ (\u03c1+ \u2192\u03c0+\u03c00) or a+\n1 (a+\n1 \u2192\u03c0+\u03c0\u2212\u03c0+).\nThe B0 \u2192J/\u03c8K\u22170 and B0 \u2192\u03c8(2S)K\u22170 candidates are\nreconstructed from combinations of a J/\u03c8 or a \u03c8(2S) can-\ndidate, in the decay modes e+e\u2212and \u00b5+\u00b5\u2212, with a K\u22170\n(K\u22170 \u2192K+\u03c0\u2212). The \u03c8(2S) candidates are reconstructed\nin their decays to J/\u03c8\u03c0+\u03c0\u2212. In these measurements, the\ncollaborations impose constraints on the B candidates re-\nquiring them to be compatible with one of the \ufb01nal states\nmentioned above. The corresponding branching fractions\nfor the B and D decays to these \ufb01nal states are at most\na few percent. Therefore, the selected signal samples have\nrelatively small B0 and B+ yields (for example, 291 B0\nand 304 B+ per inverse femtobarn of data for the BABAR\nanalysis). Due to the tight selection criteria, a main back-\nground present in other analyses that arises from incor-\nrect combinations of tracks is highly suppressed, leading\nto event samples with high signal purities of 80%\u201390%.\nThe z position of the decay vertex, zrec, of the fully-\nreconstructed B meson, Brec , is measured with high preci-\nsion, typically of the order of \u03c3(zrec) \u223c50 \u00b5m. The decay\nvertex position of the other B, zoth, is determined from\nall tracks not belonging to Brec as described in Chapter 6.\nFor these samples, the zrec resolution is 100\u2013200 \u00b5m with\nan RMS value of about 170 \u00b5m. Thus, the \u2206z resolution\n\n278\nTable 17.5.1. B Factory measurements of \u03c4B0, \u03c4B+, and \u03c4B0/\u03c4B+ along with the journal paper, selected \ufb01nal state, signal\npurity fsignal, B meson signal yield, and integrated luminosity for each measurement. The purity and yield values marked with\nan asterisk \u2217are approximate.\nExperiment\nMethod\nfsignal\nYield\nR\nL dt\n[B/fb\u22121]\n[fb\u22121]\nNeutral B meson lifetime \u03c4B0:\n\u03c4B0 [ps]\nBABAR (Aubert, 2001c)\nExcl. hadronic modes\n90%\n291\n21\n1.546 \u00b1 0.032 \u00b1 0.022\nBABAR (Aubert, 2003e)\nIncl. D\u2217\u03c0, D\u2217\u03c1\n55%\n603\n21\n1.533 \u00b1 0.034 \u00b1 0.038\nBABAR (Aubert, 2003m) Excl. D\u2217l\u03bd\n76%\n680\n21\n1.523+0.024\n\u22120.023 \u00b1 0.022\nBABAR (Aubert, 2002f)\nIncl. D\u2217l\u03bd\n53%\n4430\n21\n1.529 \u00b1 0.012 \u00b1 0.029\nBABAR (Aubert, 2006s)\nIncl. D\u2217l\u03bd\n64%\n605\n81\n1.504 \u00b1 0.013+0.018\n\u22120.013\nBelle (Abe, 2002m)\nExcl. hadronic modes\n82%\u2217\n220\u2217\n29\n1.554 \u00b1 0.030 \u00b1 0.019\nBelle (Abe, 2005c)\nExcl. had. modes + D\u2217l\u03bd 81%\n707\n140\n1.534 \u00b1 0.008 \u00b1 0.010\nBABAR-Belle average\n1.530 \u00b1 0.005 \u00b1 0.009\nCharged B meson lifetime \u03c4B+:\n\u03c4B+ [ps]\nBABAR (Aubert, 2001c)\nExcl. hadronic modes\n93%\n304\n21\n1.673 \u00b1 0.032 \u00b1 0.023\nBelle (Abe, 2002m)\nExcl. hadronic modes\n75%\u2217\n310\u2217\n29\n1.695 \u00b1 0.026 \u00b1 0.015\nBelle (Abe, 2005c)\nExcl. hadronic modes\n81%\n319\n140\n1.635 \u00b1 0.011 \u00b1 0.011\nBABAR-Belle average\n1.640 \u00b1 0.010 \u00b1 0.010\n\u03c4B+/\u03c4B0:\n\u03c4B+/\u03c4B0\nBABAR (Aubert, 2001c)\nExcl. hadronic modes\n93%, 90%\n304, 291\n21\n1.082 \u00b1 0.026 \u00b1 0.012\nBelle (Abe, 2002m)\nExcl. hadronic modes\n75%, 82%\u2217\n310, 220\u2217\n29\n1.091 \u00b1 0.023 \u00b1 0.014\nBelle (Abe, 2005c)\nExcl. had. modes + D\u2217l\u03bd 81%, 81%\n319, 707\n140\n1.066 \u00b1 0.008 \u00b1 0.008\nBABAR-Belle average\n1.068 \u00b1 0.009 \u00b1 0.007\nis dominated by the resolution of zoth. It is similar for all\ndecay modes (\u03c3(\u2206z) = 180 \u2212190 \u00b5m). Belle converts the\nmeasured \u2206z into a \u2206t value according to Eq. (17.5.12),\nwhereas in fully-reconstructed decays BABAR uses a more\nprecise approximation by exploiting the precise knowledge\nof the B \ufb02ight direction to correct for the B momentum\nin the \u03a5(4S) frame (Eq. 6.5.5). The \u2206t distributions of\nthe selected B0 and B+ candidates are then \ufb01t to a like-\nlihood function that describes the true \u2206t distribution\nof the signal events (Eq. 17.5.13), convoluted with a \u2206t\nsignal resolution function Rsig to account for the uncer-\ntainty in the \u2206t measurements; and to an empirical \u2206t\ndistribution describing background events. BABAR uses a\nsignal \u2206t resolution function Rsig consisting of the sum\nof a Gaussian distribution with zero mean and its convo-\nlution with an exponential decay that models the bias of\nzoth due to tracks originating from a displaced decay ver-\ntex of a charm meson. Charged and neutral B decays are\ndescribed with the same \u2206t resolution function. Belle\u2019s\nsignal \u2206t resolution function Rsig is formed by the con-\nvolution of four components: the detector resolutions for\nzrec and zoth, the bias in zoth due to tracks originating\nfrom the decay of a charm meson, and the kinematic ap-\nproximation that the B mesons are at rest in the center-\nof-mass frame (Tajima, 2004). Both resolution functions\nhave a term accounting for a small number of poorly recon-\nstructed vertices, so-called \u2206t outliers. Both experiments\ndescribe the background \u2206t distribution with a prompt\nterm (i.e. zero lifetime) and a term with an e\ufb00ective back-\nground lifetime. The background \u2206t resolution functions\nfor the component with e\ufb00ective lifetime is of the same\nform as the signal resolution functions, but with separate\nparameters in order to minimize correlations with the sig-\nnal resolution parameters. The \u2206t resolution function is\ndiscussed further in Chapter 10.\nBABAR and Belle determine the values of \u03c4B0 and \u03c4B+\nfrom a simultaneous \ufb01t to the samples of B0 and B+ can-\ndidates. BABAR measures \u03c4B0 = (1.546\u00b10.032\u00b10.022) ps\nand \u03c4B+ = (1.673 \u00b1 0.032 \u00b1 0.023) ps, while Belle mea-\nsures \u03c4B0 = (1.554\u00b10.030\u00b10.019) ps and \u03c4B+ = (1.695\u00b1\n0.026 \u00b1 0.015) ps. The measurements of the B0 and the\nB+ lifetimes share the same sources of systematic uncer-\ntainty. Some of these uncertainties cancel in the ratio of\nthe lifetimes r\u03c4 \u2261\u03c4B+/\u03c4B0. In a separate \ufb01t the param-\neter \u03c4B+ is replaced with r\u03c4 \u00b7 \u03c4B0 to estimate the statis-\ntical error of the lifetime ratio. BABAR and Belle mea-\nsure, respectively, \u03c4B+/\u03c4B0 = 1.082 \u00b1 0.026 \u00b1 0.012 and\n\u03c4B+/\u03c4B0 = 1.091 \u00b1 0.023 \u00b1 0.014. The largest contribu-\n\n279\ntions to the systematic uncertainties in the measured life-\ntimes come from the modeling of the signal \u2206t resolution\nfunction (0.009 \u2013 0.014 ps) and the background \u2206t dis-\ntribution (0.005 \u2013 0.012 ps), the alignment of the vertex\ndetector (0.008 ps), the knowledge of the z scale of the\ndetector (0.008 ps), and limited statistics of the MC sim-\nulation (0.007 \u2013 0.009 ps). The dominant contributions to\nthe systematic error in r\u03c4 come from limited MC statis-\ntics (0.005 \u2013 0.006), uncertainties in the background \u2206t\ndistributions (0.005 \u2013 0.011), and the signal \u2206t resolution\nfunction (0.006 \u2013 0.008).\nIn another analysis BABAR uses events in which Brec\nis reconstructed in the semileptonic decay B0 \u2192D\u2217\u2212l+\u03bd\n(l = e, \u00b5) to determine the B0 lifetime (Aubert, 2003m).\nThe B yield is larger than for the hadronic \ufb01nal state\nanalysis due to the large B semileptonic branching frac-\ntion. They reconstruct 680 B/ fb\u22121. Due to the missing\nneutrino the background level is higher than in the sam-\nple of fully-reconstructed hadronic B decays. The com-\nbinatorial D\u2217\u2212background is about 18% and the sum\nof the backgrounds from events where the D\u2217\u2212and the\nlepton come from di\ufb00erent B decays, events with a fake\nlepton candidate and events from continuum cc \u2192D\u2217\u2212X\nprocesses add up to 5 \u22128% depending on the lepton \ufb02a-\nvor. In this analysis, BABAR simultaneously \ufb01ts for \u03c4B0\nand the B0 \u2212B0 mixing frequency \u2206md (see also Sec-\ntion 17.5.2). Because of the di\ufb00erent \u2206t distributions for\nmixed (B0B0 or B0B0) and unmixed (B0B0) events, sepa-\nrately \ufb01tting the two \u2206t distributions enhances the sensi-\ntivity to the common signal \u2206t resolution function. As\na result the uncertainty of \u03c4B0 is reduced by approxi-\nmately 15%. BABAR measures the B0 lifetime to be \u03c4B0 =\n(1.523+0.024\n\u22120.023 \u00b1 0.022) ps. The dominant systematic error\nsources are the same as for the analyses of the hadronic\n\ufb01nal states and similar in size. A large additional sys-\ntematic uncertainty in the \u03c4B0 measurement comes from\nthe limited statistical precision in determining the bias\ndue to the background modeling. By comparing the \ufb01t-\nted \u03c4B0 in simulated events, BABAR observes a shift of\n(0.022 \u00b1 0.009) ps between a signal-only sample and a\nsignal-plus-background sample. The measured B0 lifetime\nis corrected for the observed bias from the \ufb01t to the MC\nsample with background; the full statistical uncertainty\nin \u03c4B0 from this \ufb01t (\u00b10.018 ps) is assigned as systematic\nuncertainty.\nBelle also performs a measurement of the B lifetimes\nand their ratio in a larger sample of 140 fb\u22121 (Abe, 2005c).\nIn this analysis they reconstruct B0 and B+ candidates in\nthe same hadronic decay modes as in their previous anal-\nysis. In addition they reconstruct B0 candidates in the\nsemileptonic decay B0 \u2192D\u2217\u2212l+\u03bd. Using a \ufb01t to the \u2206t\ndistributions of the signal candidates, they determine the\nB0 and B+ lifetimes and the B0 \u2212B0 mixing frequency\n\u2206md simultaneously. The analysis of the neutral B decays\nis described in more detail in Section 17.5.2. Belle mea-\nsures \u03c4B0 = (1.534 \u00b1 0.008 \u00b1 0.010) ps, \u03c4B+ = (1.635 \u00b1\n0.011 \u00b1 0.011) ps and \u03c4B+/\u03c4B0 = 1.066 \u00b1 0.008 \u00b1 0.008.\nThe largest contributions to the systematic uncertainties\nin the measured lifetimes come from uncertainties in the\nvertex reconstruction (0.005 \u2013 0.007 ps) and the modeling\nof the background (0.007 ps). The dominant contributions\nto the systematic error in r\u03c4 come from uncertainties in\nthe background \u2206t distributions (0.005) and the signal \u2206t\nresolution function (0.004).\n17.5.1.4 Partially-reconstructed \ufb01nal states\nBABAR also measures the B0 meson lifetime in a sample\nof 21 fb\u22121 using the decay modes B0 \u2192D\u2217\u2212l+\u03bd (Au-\nbert, 2002f) and B0 \u2192D\u2217\u2212\u03c0+, B0 \u2192D\u2217\u2212\u03c1+ (Aubert,\n2003e) with a partially-reconstructed D\u2217\u2212in the \ufb01nal\nstate. These measurements also serve as a proof-of-principle\nfor the analyses of the time-dependent CP asymmetries in\nB \u2192D(\u2217)\u2213\u03c0\u00b1 to extract sin(2\u03c61+\u03c63) (see Section 17.8.5).\nIn the measurement of \u03c4B0 with B0 \u2192D\u2217\u2212l+\u03bd de-\ncays, BABAR requires a high-momentum lepton (1.4 <\np\u2217\nl < 2.3 GeV/c) and an opposite-charge soft pion (\u03c0s)\nconsistent with coming from the decay D\u2217\u2212\u2192D0\u03c0\u2212\ns\n(p\u2217\n\u03c0s < 0.19 GeV/c). The D\u2217\u2212momentum is inferred from\nthe \u03c0s momentum without reconstructing the D0 (see\nEq. 7.3.6). The analysis of this inclusive \ufb01nal state does\nnot su\ufb00er from the small D0 branching fractions to exclu-\nsive \ufb01nal states and consequently has a large B yield (4430\nB/ fb\u22121). However, without the additional constraints from\nthe D0 reconstruction the signal purity of the selected B\ncandidates is only 53%. The Brec decay vertex is calcu-\nlated from the lepton and \u03c0s tracks, and the beam spot.\nThe decay point of the Both is determined from the re-\nmaining tracks in the event. In events that have another\nhigh-momentum lepton (p\u2217\nl > 1.1 GeV/c), the B vertex is\ncalculated from this lepton track constrained to the beam\nspot in the transverse plane. Otherwise, all tracks with\na center-of-mass angle greater than 90\u25e6with respect to\nthe \u03c0s direction are considered. This requirement removes\nmost of the tracks from the decay of the D0 daughter\nof the D\u2217\u2212, which would otherwise bias the reconstruc-\ntion of the Both vertex position. Tracks are also removed\nif they contribute more than 6 to the vertex \u03c72. BABAR\nmeasures the B0 lifetime with a binned maximum likeli-\nhood \ufb01t to the \u2206t and \u03c3\u2206t distributions of the selected\nB candidates to be \u03c4B0 = (1.529 \u00b1 0.012 \u00b1 0.029) ps. For\nthis result, the \ufb01tted B0 lifetime is multiplied by a cor-\nrection factor RD0 = 1.032 \u00b1 0.007 \u00b1 0.007 to account for\ndaughter tracks of the D0 included in the calculation of\nthe Both decay vertex. The largest systematic uncertain-\nties in \u03c4B0 are due to the knowledge of the fractions and\nparameterizations of the background types (0.015 ps), the\n\u2206t resolution model (0.017 ps) and RD0 (0.015 ps).\nIn a more recent analysis with 81 fb\u22121, BABAR uses\nB0 \u2192D\u2217\u2212l+\u03bd decays with a partially-reconstructed D\u2217\u2212\nto measure \u03c4B0 and the B0 \u2212B0 oscillation frequency\n\u2206md (Aubert, 2006s). They require the other B0 in the\nevent Both also to decay semileptonically and determine\nits decay vertex by constraining the high-energy lepton to\nthe beam spot. After correcting for a small bias (\u22120.006 ps)\nobserved in MC-simulated events they measure \u03c4B0 =\n(1.504 \u00b1 0.013+0.018\n\u22120.013) ps. The dominant contributions to\n\n280\nthe systematic error in \u03c4B0 come from uncertainties in the\nalignment (+0.013\n\u22120.004 ps) and z scale (0.007 ps) of the SVT,\nand from MC statistics (0.007 ps).\nBABAR also measures the B0 lifetime with a partially-\nreconstructed D\u2217\u2212in the decays B0 \u2192D\u2217\u2212h+, where h+\nis either a \u03c0+ or a \u03c1+ (Aubert, 2003e). Similarly to the\npartial reconstruction of the semi-leptonic \ufb01nal state, they\nreconstruct only the soft pion \u03c0s from the decay D\u2217\u2212\u2192\nD0\u03c0\u2212\ns\nand the D\u2217\u2212momentum is inferred from the \u03c0s\nmomentum. The main variable to suppress background in\nthis analysis is the missing D0 mass mmiss, which peaks\nat the nominal D0 mass with a spread of 3 MeV/c2 for\nB0 \u2192D\u2217\u2212\u03c0+ and 3.5 MeV/c2 for B0 \u2192D\u2217\u2212\u03c1+. Addi-\ntional variables to suppress backgrounds include the angle\nbetween h and the B0, the D\u2217\u2212and \u03c1+ helicity angles,\nand event shape variables. After all selection requirements\nare applied, the signal purity is approximately 55%. The\ndominant background comes from continuum events. The\nremaining background from BB events is due to random\nh and \u03c0s combinations and feed-down from B \u2192D\u2217\u2217\u03c0,\nB0 \u2192D\u2217\u2212\u03c1+ (for B0 \u2192D\u2217\u2212\u03c0+), and B0 \u2192D\u2217\u2212a+\n1\n(for B0 \u2192D\u2217\u2212\u03c1+). The z position of the B0 decay ver-\ntex is determined from the h and \u03c0s tracks constrained\nto the nominal beam spot. The decay vertex of Both is\ndetermined in the same way as in BABAR\u2019s early analysis\nof B0 \u2192D\u2217\u2212l+\u03bd (Aubert, 2002f). For the mode B0 \u2192\nD\u2217\u2212\u03c0+ they calculate an event-by-event \u2206z correction to\naccount for tracks from the D0 included in the vertex of\nBoth. In both modes a small additional correction to the\n\ufb01tted B0 lifetime is applied. BABAR uses several data con-\ntrol samples to determine the di\ufb00erent background frac-\ntions in the signal sample and their p.d.f. parameters.\nThese parameters are \ufb01xed in the \ufb01t to the signal sample.\nThe \ufb01tted lifetimes are \u03c4B0 = (1.510 \u00b1 0.040 \u00b1 0.041) ps\nin B0 \u2192D\u2217\u2212\u03c0+ and \u03c4B0 = (1.616 \u00b1 0.064 \u00b1 0.075) ps\nin B0 \u2192D\u2217\u2212\u03c1+. The combined result accounting for\ncorrelated errors is \u03c4B0 = (1.533 \u00b1 0.034 \u00b1 0.038) ps.\nThe dominant uncertainties in the measurements with the\nmodes B0 \u2192D\u2217\u2212\u03c0+ and B0 \u2192D\u2217\u2212\u03c1+ come from the\nknowledge of the composition of the background and its\np.d.f. parameters (0.024 ps, 0.050 ps), limited MC statis-\ntics (0.021 ps, 0.042 ps), and the D0 track bias (0.017 ps,\n0.026 ps).\n17.5.1.5 Averages of \u03c4B0, \u03c4B+ and \u03c4B+/\u03c4B0\nThe world averages of the B0 and B+ lifetimes and\ntheir ratio are calculated by HFAG from the BABAR\nmeasurements in Aubert (2001c, 2002f, 2003e,m, 2006s),\nthe Belle measurements in Abe (2005c) and measure-\nments from CDF, D\u00d8, ALEPH, DELPHI, L3, OPAL, SLD\nand ATLAS (Beringer et al., 2012) to be, respectively,\n\u03c4B0 = (1.519 \u00b1 0.007) ps, \u03c4B+ = (1.641 \u00b1 0.008) ps and\n\u03c4B+/\u03c4B0 = (1.079 \u00b1 0.007) ps. The most precise measure-\nments contributing to these averages come from the B Fac-\ntories and a recent set of measurements from CDF using\nfully-reconstructed B \u2192J/\u03c8K(\u2217) events (Aaltonen et al.,\n2011a). D\u00d8 provides a precise measurement of \u03c4B+/\u03c4B0\nfrom samples of B \u2192D\u2217+\u00b5\u03bdX and B \u2192D0\u00b5\u03bdX (Abazov\net al., 2005). By using only the B Factories measure-\nments, one obtains the averages \u03c4B0 = (1.530 \u00b1 0.010) ps,\n\u03c4B+ = (1.640\u00b10.014) ps and \u03c4B+/\u03c4B0 = (1.068\u00b10.011) ps.\nThe measurements of the charged and neutral B life-\ntimes and their ratio now have errors of about half a per-\ncent, and the B+ lifetime is now measured to be larger\nthan the B0 lifetime by many standard deviations. The\nprecision in these measurements exceeds that of existing\ntheoretical calculations. Thus, with the original motiva-\ntions fully addressed by the current set of measurements\nand the multitude of relevant systematic error sources that\ncome with sub-percent precision measurements, it is un-\nlikely that there will be improved measurements using the\nfull data set of the B Factories or the even larger data sets\nof future super \ufb02avor factories.\n17.5.2 B0 \u2212B0 mixing\nNeutral meson-antimeson oscillations were predicted by\nGell-Mann and Pais (1955) and \ufb01rst observed in 1956\nin the K0 \u2212K0 system (Lande, Booth, Impeduglia, Le-\nderman, and Chinowsky, 1956). Mixing in the B0 \u2212B0\nsystem was discovered in 1987 by the ARGUS collabora-\ntion (Albrecht et al., 1987b). It was clear from the \ufb01rst B0\ns\nmeasurements that mixing was an important e\ufb00ect in the\nB0\ns \u2212B0\ns system (see for example the review of Danilov,\n1993), although the mixing frequency was not resolved un-\ntil much later by the CDF collaboration (Abulencia et al.,\n2006b) as previous results established only lower limits\non xs = \u2206ms/\u0393s. Finally, D0 \u2212D0 mixing was \ufb01rst ob-\nserved by the B Factories and is described in detail in\nSection 19.2.\nMeson-antimeson\noscillations\nproceed\nin\ngeneral\nthrough both long distance e\ufb00ects (common decay modes)\nand second order weak interactions as described by box di-\nagrams containing virtual quarks (Figure 10.1.1). B0 \u2212B0\nmixing is predominantly a short-distance phenomenon;\namong the various box diagrams, those containing the top\nquark dominate due to the large top mass. The observa-\ntion of mixing, in fact, provided the \ufb01rst indication that\nthe top quark was very heavy: see the discussion in Sec-\ntion 16.1. The mixing frequency \u2206md is sensitive to the\nCKM matrix element Vtd (see Section 17.2). In the neutral\nK, D (see Section 19.2), and B0\ns meson systems, mixing\nalso has contributions from real intermediate states acces-\nsible to both the meson and the antimeson. Real interme-\ndiate states lead to a di\ufb00erence in the decay rate for the\ntwo mass eigenstates of the neutral meson system. How-\never, for the B0\nd system, the decay rate di\ufb00erence \u2206\u0393 is\nexpected to be of O(10\u22122 \u221210\u22123) times smaller than the\naverage decay rate and the mixing frequency (Lenz and\nNierste, 2011), and is typically ignored in the measure-\nments of \u2206md.\nIn the following, we brie\ufb02y review the principles of\n\u2206md measurements (Section 17.5.2.1), and then summa-\nrize the techniques and results of the B Factory mea-\nsurements using dilepton (Section 17.5.2.2), partially-\nreconstructed (Section 17.5.2.3), and fully-reconstructed\n\n281\n\ufb01nal states (Section 17.5.2.4). The average of these re-\nsults is discussed in Section 17.5.2.5. Throughout, we set\n\u2206\u0393\n= 0; the specialized analyses allowing \u2206\u0393\n\u0338= 0,\nand setting constraints on its value, are discussed in Sec-\ntion 17.5.2.6 below.\n17.5.2.1 Principles of \u2206md measurements\nThe time-evolution of the B0 \u2212B0 system is given by a\nphenomenology-based 2 \u00d7 2 Hamiltonian matrix (for de-\ntails see Chapter 10). Solving this system of equations\ngives the time-dependent probabilities for B0 \u2212B0 os-\ncillations. For a B0 decay to a \ufb02avor eigenstate that is\nnot accessible from a B0 decay (e.g. the semileptonic de-\ncay B0 \u2192D\u2217+l\u2212\u03bdl), the parameter \u03bb in Eqs (10.1.10\u2013\n10.1.15) and (10.2.2\u201310.2.5) is zero. Neglecting CP viola-\ntion in mixing, the probability that a B0 produced at time\nt = 0 decays as B0 at time t is given by\nPB0\u2192B0(t) = e\u2212t/\u03c4B0\n2\u03c4B0\n\u00d7 [1 \u2212cos(\u2206mdt)],\n(17.5.14)\nwhere \u2206md is the B0 \u2212B0 oscillation frequency and \u03c4B0\nis the neutral B lifetime. Similarly, the probability that\na produced B0 decays as B0 (for example through B0 \u2192\nD\u2217\u2212l+\u03bdl) is given by\nPB0\u2192B0(t) = e\u2212t/\u03c4B0\n2\u03c4B0\n\u00d7 [1 + cos(\u2206mdt)].\n(17.5.15)\nLikewise the probabilities for a produced B0 to decay as\na B0 or a B0 are given, respectively, by\nPB0\u2192B0(t) = e\u2212t/\u03c4B0\n2\u03c4B0\n\u00d7 [1 \u2212cos(\u2206mdt)],\n(17.5.16)\nand\nPB0\u2192B0(t) = e\u2212t/\u03c4B0\n2\u03c4B0\n\u00d7 [1 + cos(\u2206mdt)].\n(17.5.17)\nThe \ufb01rst measurements of B0 \u2212B0 oscillations were\ntime-integrated measurements by ARGUS (Albrecht et al.,\n1987b) and CLEO (Artuso et al., 1989). They measured\nthe time-integrated probability \u03c7d that a B0 (B0) pro-\nduced in \u03a5(4S) \u2192B0B0 decays as a B0 (B0),\n\u03c7d =\nx2\nd\n2 (1 + x2\nd),\n(17.5.18)\nwhere xd = \u2206md/\u0393d = \u2206md\u03c4B0. In 1993 the LEP exper-\niments started to provide the \ufb01rst time-dependent mea-\nsurements of \u2206md, made possible through their precision\nvertex detectors and highly-boosted B0 mesons from Z0\ndecays (Abreu et al., 1994; Acciarri et al., 1996; Akers\net al., 1994b; Buskulic et al., 1993b). The CDF collabora-\ntion published their \ufb01rst \u2206md measurement in 1998 (Abe\net al., 1998). In the 2000 Review of Particle Physics (Groom\net al., 2000) the PDG calculated an average B0 \u2212B0\noscillation frequency from time-dependent measurements\nby the LEP experiments and CDF of \u2206md = (0.478 \u00b1\n0.018) ps\u22121. Including the measurements of the time-in-\ntegrated mixing probability \u03c7d = 0.156 \u00b1 0.024 by CLEO\nand ARGUS, they obtained \u2206md = (0.472 \u00b1 0.017) ps\u22121.\nThe experimental strengths and weaknesses in \u2206md\nmeasurements, when comparing these older experiments\nto the B Factories, are the same as for measurements of\nthe B lifetimes. The former bene\ufb01t from high-precision\nproper-time measurements, whereas the latter have the\nadvantage of low-background, high-statistics B samples,\nand excellent B-momentum resolution.\nThe experimental methods of the \u2206md analyses are\nvery similar to those used in the measurement of time-\ndependent CP asymmetries in B decays to CP eigenstates\n(see the measurement of sin 2\u03c61 in Section 17.6). In par-\nticular, fully-reconstructed B decays to \ufb02avor \ufb01nal states\nB\ufb02av, such as B0 \u2192D(\u2217)+\u03c0\u2212, have the same B vertex\nresolutions and thus \u2206t resolution function as B decays\nto (cc)s CP eigenstates, BCP (see Chapter 6 and Sec-\ntion 17.6). The same B \ufb02avor-tagging algorithms are used\nto determine the \ufb02avors of B\ufb02av and BCP at the time of\ntheir production (see Chapter 8). In both cases, maxi-\nmum likelihood \ufb01ts are used to extract the parameters of\nthe time-dependent asymmetries from the measured \u2206t\ndistributions. By-products of the \u2206md measurement with\nfully-reconstructed \ufb01nal states are the B \ufb02avor-tagging\nmistag rates, which cannot be determined with CP eigen-\nstates. In addition, a con\ufb01rmation of the \u2206md results\nof previous experiments served as a convincing proof-of-\nprinciple of this novel technique for measuring time-depen-\ndent CP asymmetries at the asymmetric beam-energy B\nFactories. So, it is no coincidence that one of the \ufb01rst\nmeasurements from the B Factories was the precise time-\ndependent measurement of \u2206md. On the other hand, im-\nproving the knowledge of \u2206md has been and still is inter-\nesting in its own right. The oscillation frequency \u2206md is\nproportional to |Vtd|2 (Eq. 17.2.1). Thus, a precise \u2206md\nmeasurement along with a measurement of the B0\ns \u2212B0\ns os-\ncillation frequency \u2206ms from hadron colliders, combined\nwith lattice QCD calculations of the decay constants and\nQCD bag parameters of B0 and B0\ns mesons (for details see\nSection 17.2) provide strong constraints on the Unitarity\nTriangle (see Section 25.1).\nThe time-dependent \u2206md measurements by the B Fac-\ntories all follow the same basic idea. In the \u03a5(4S) \u2192B0B0\ndecay the two neutral B mesons are produced in a coher-\nent P-wave state. If one of the B mesons, referred to as\nBtag, can be ascertained to decay to a state of known \ufb02a-\nvor (i.e. B0 or B0) at a certain time ttag, the other B,\nreferred to as Brec, at that time must be of the opposite\n\ufb02avor as a consequence of Bose symmetry. Consequently,\nthe probabilities to observe unmixed (+) B0B0, or mixed\n(\u2212) B0B0/B0B0 events, are functions of the proper-time\ndi\ufb00erence \u2206t = trec \u2212ttag and of \u2206md:\nPB0B0\u2192B0B0(\u2206t) \u2261P+(\u2206t)\n= e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u00d7 [1 + cos(\u2206md\u2206t)] ,\n\n282\nPB0B0\u2192B0B0/B0B0(\u2206t) \u2261P\u2212(\u2206t)\n= e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u00d7 [1 \u2212cos(\u2206md\u2206t)] .\n(17.5.19)\nFrom these two equations one can de\ufb01ne the so-called\nB0B0 mixing asymmetry as\nAmix(\u2206t) \u2261P+(\u2206t) \u2212P\u2212(\u2206t)\nP+(\u2206t) + P\u2212(\u2206t) = cos(\u2206md\u2206t).\n(17.5.20)\nThe functions P\u00b1(\u2206t) are illustrated in Fig. 17.5.4. The\nmixed event function (P\u2212) rises slowly from zero at \u2206t = 0\nuntil it reaches a maximum at around \u2206t = 2.6 ps.\nThe B Factories have measured the B0\u2212B0 oscillation\nfrequency with various \ufb01nal states and B-reconstruction\ntechniques. In the analyses of dilepton inclusive \ufb01nal states,\nthe \ufb02avors of both B mesons are identi\ufb01ed only through\nhigh-momentum leptons from semileptonic decays. In all\nother \u2206md measurements one B is reconstructed through\nits decay to an exclusive \ufb02avor \ufb01nal state, Brec, while\nthe remaining charged particles in the event are used to\nidentify (or \u201ctag\u201d) the \ufb02avor of the other B (referred\nto as Btag), as a B0 or B0. The proper-time di\ufb00erence\n\u2206t = \u2206z/\u27e8\u03b2\u03b3\u27e9c is determined from the z positions of the\nB decay vertices \u2206z = zrec \u2212ztag and the average boost\nof the \u03a5(4S) frame in the lab frame \u27e8\u03b2\u03b3\u27e9. The boost is\nknown to good precision from the e+ and e\u2212beam en-\nergies, so that the \u2206z measurement dominates the \u2206t\nresolution (see Chapter 6). The value of \u2206md is then ex-\ntracted from a simultaneous \ufb01t to the \u2206t distributions of\nthe unmixed and mixed events. There are two principal ex-\nperimental complications to the probability distributions\nin Eq. (17.5.19). First, the \ufb02avor tagging algorithm some-\ntimes incorrectly identi\ufb01es the Btag \ufb02avor. The probability\nto incorrectly identify the \ufb02avor of Btag, w, reduces the\nobserved amplitude for the oscillation by a factor (1\u22122w).\nSecond, the resolution of \u2206t is comparable to the oscilla-\ntion period and must be accounted for. The p.d.f.s for the\nunmixed and mixed signal events H\u00b1,sig can be expressed\nas the convolution of the underlying \u2206t distribution,\nh\u00b1,sig(\u2206t; \u2206md, w) = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n[1 \u00b1 (1 \u22122w) cos(\u2206md\u2206t)] ,\n(17.5.21)\nwith a signal \u2206t resolution function Rsig containing pa-\nrameters \u02c6aj:\nH\u00b1,sig(\u2206t; \u2206md, w, \u02c6aj) = h\u00b1,sig(\u2206t; \u2206md, w) \u2297Rsig(\u2206t; \u02c6aj).\n(17.5.22)\nThe functions H\u00b1,sig are shown in Fig. 17.5.4. The im-\npact of typical mistag and \u2206t resolution e\ufb00ects is clearly\nvisible in the comparison with the functions P\u00b1(\u2206t) that\nrepresent ideal detector performance.\nA \ufb01t is then performed to simultaneously extract the\nmistag rates w, the resolution function parameters \u02c6aj,\nand the mixing frequency \u2206md. In the following sections\nwe give brief descriptions of the various \u2206md measure-\nments by the B Factories, in dilepton (Section 17.5.2.2),\npartially-reconstructed (17.5.2.3), and fully-reconstructed\n(17.5.2.4) \ufb01nal states. The results are summarized in Ta-\nble 17.5.2; their average is discussed in Section 17.5.2.5.\nUnmixed\nMixed\narbitrary scale\na)\nUnmixed\nMixed\nb)\n6t (ps)\n-5\n0\n5\nFigure 17.5.4. The \u2206t distributions of mixed and unmixed\nevents (a) with perfect tagging and \u2206t resolution (P\u00b1(\u2206t)) (b)\nwith mistag rates and \u2206t resolution typical at the B Factories\n(H\u00b1,sig(\u2206t)). From Aubert (2002a).\n17.5.2.2 Dilepton \ufb01nal states\nBelle published their \ufb01rst measurement of \u2206md using\ndilepton events in a sample of 5.9 fb\u22121 (Abe, 2001b). In a\nlater analysis of the same \ufb01nal state, they used a sample\nof 29 fb\u22121 (Hastings, 2003). BABAR published one mea-\nsurement of \u2206md with dilepton events using a sample of\n21 fb\u22121 (Aubert, 2002e).\nThe inclusive nature of the dilepton \ufb01nal state pro-\nvides large event samples. The measurements are based\non the identi\ufb01cation of events containing pairs of high-\nmomentum leptons (ee, \u00b5\u00b5 and e\u00b5) from semileptonic de-\ncays of B mesons. The \ufb02avors of the B mesons at the\ntime of their decay are determined by the charges of the\nleptons in the \ufb01nal state. For \u03a5(4S) resonance decays\ninto B0B0 pairs, opposite-sign charge (OS) and same-sign\ncharge (SS) lepton pairs correspond to unmixed and mixed\nevents, respectively. Both experiments apply selection re-\nquirements on the lepton momenta, overall event shape,\nand track quality to ensure a well-measured \u2206t and to sup-\npress backgrounds from fake leptons, continuum events,\nJ/\u03c8 decays, and so-called B cascade decays. In the lat-\nter, one lepton originates from the semileptonic decay of\na charm meson, which can come from the same or the op-\nposite B as the other lepton. An irreducible background\ncomes from semileptonic decays of B+B\u2212pairs.\nBelle determines the z coordinates of the B decay\nvertices from the intersections of the lepton tracks with\nthe pro\ufb01le of the beam interaction point (IP) convoluted\nwith the average B0 \ufb02ight length (\u223c20 \u00b5m in the \u03a5(4S)\nrest frame). The mean position and width of the IP are\ndetermined on a run-by-run basis using hadronic events\n(see Chapter 6). The proper-time di\ufb00erence \u2206t is calcu-\nlated from the z positions of the two lepton vertices using\nEq. (17.5.12), where \u2206z = z1 \u2212z2 is the distance along\nthe beam axis between the two vertices. For OS events, the\n\n283\nTable 17.5.2. B Factory measurements of \u2206md along with the journal paper, selected \ufb01nal state, signal purity fsignal, B meson\nsignal yield, and integrated luminosity for each measurement. The \u2206md measurements in Hara (2002) and Tomura (2002b)\nhave been superseded by Abe (2005c), and those in Abe (2001b) by Hastings (2003); the superseded measurements are not\nseparately included in the B Factories average (Asner et al., 2010).\nExperiment\nMethod\nfsignal\nYield [B/ fb\u22121]\nR\nL dt\n\u2206md [ps\u22121]\nBABAR (Aubert, 2002a,b) Excl. hadronic modes\n86%\n214\n30 fb\u22121\n0.516 \u00b1 0.016 \u00b1 0.010\nBABAR (Aubert, 2002e)\nIncl. dilepton\n21 fb\u22121\n0.493 \u00b1 0.012 \u00b1 0.009\nBABAR (Aubert, 2006s)\nD\u2217l\u03bd (partial)\n64%\n605\n81 fb\u22121\n0.511 \u00b1 0.007 \u00b1 0.007\nBABAR (Aubert, 2003m)\nExcl. D\u2217l\u03bd\n76%\n680\n21 fb\u22121\n0.492 \u00b1 0.018 \u00b1 0.014\nBelle (Abe, 2001b)\nIncl. dilepton\n6 fb\u22121\n0.463 \u00b1 0.008 \u00b1 0.016\nBelle (Hastings, 2003)\nIncl. dilepton\n29 fb\u22121\n0.503 \u00b1 0.008 \u00b1 0.010\nBelle (Zheng, 2003)\nD\u2217\u03c0 (partial)\n70%\n118\n29 fb\u22121\n0.509 \u00b1 0.017 \u00b1 0.020\nBelle (Hara, 2002)\nExcl. D\u2217l\u03bd\n80%\n453\n29 fb\u22121\n0.494 \u00b1 0.012 \u00b1 0.015\nBelle (Tomura, 2002b)\nExcl. hadronic modes\n80%\n229\n29 fb\u22121\n0.528 \u00b1 0.017 \u00b1 0.011\nBelle (Abe, 2005c)\nExcl. hadronic modes, D\u2217l\u03bd 81%\n707\n140 fb\u22121\n0.511 \u00b1 0.005 \u00b1 0.006\nBABAR-Belle average\n0.508 \u00b1 0.003 \u00b1 0.003\npositively charged lepton is taken as the \ufb01rst lepton (z1).\nFor SS events Belle uses the absolute value of \u2206z. BABAR\napplies a beam spot constraint to the two lepton tracks\nto \ufb01nd the primary vertex of the event in the transverse\nplane. The positions of closest approach of the two tracks\nto this vertex in the transverse plane are computed and\ntheir z coordinates are denoted z1 and z2, where the sub-\nscripts refer to the highest and second highest momentum\nleptons in the \u03a5(4S) rest frame. The vertex \ufb01t constrains\nthe lepton tracks to originate from the same point in the\ntransverse plane, thereby neglecting the nonzero trans-\nverse \ufb02ight length for B0 mesons. As a consequence, the\n\u2206t resolution function is \u2206z dependent, becoming worse\nat higher |\u2206z|. Neglecting this dependence introduces a\nsmall bias that BABAR accounts for in the systematic un-\ncertainty.\nBABAR and Belle use binned maximum likelihood \ufb01ts\nto the \u2206t and \u2206z distributions, respectively, of the se-\nlected dilepton candidates to extract \u2206md. BABAR \ufb01ts\nthe shapes of the \u2206t distributions with the p.d.f.s for OS\nand SS dilepton events as given in Eq. (17.5.22). Belle \ufb01ts\nthe \u2206z distributions and constrains the integrated mixing\nprobability to \u03c7d. Their \u2206z distributions are described by\nconverting the constrained signal \u2206t distributions P\u00b1(\u2206t)\nto \u2206z distributions using Eq. (17.5.12) and convolving\nthem with the \u2206z resolution function. The constrained\nsignal \u2206t distributions are given by\nP\u00b1(\u2206t) = N\u03a5 (4S)f0b2\n0\u03f5\u00b1\nll\ne\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n[1 \u00b1 cos(\u2206md\u2206t)] ,\nPch(\u2206t) = N\u03a5 (4S)fchb2\nch\u03f5ch\nll\ne\u2212|\u2206t|/\u03c4B+\n2\u03c4B+\n,\n(17.5.23)\nwhere N\u03a5 (4S) is the total number of \u03a5(4S) events, f0 and\nfch are the branching fractions of the \u03a5(4S) to neutral and\ncharged B pairs (assuming f0+fch = 1), b0 and bch are the\nsemileptonic branching fractions for neutral and charged\nB mesons, and \u03f5\u00b1\nll are the e\ufb03ciencies for selecting dilepton\nevents of unmixed and mixed origins. Belle determines the\nratio \u03f5+\nll : \u03f5\u2212\nll from MC simulation and \ufb01xes it in the \ufb01t to\nthe data assuming detector e\ufb00ects that are not simulated\ncorrectly equally a\ufb00ect events with these origins. The \u2206z\ndistributions are obtained for these distributions by con-\nversion from \u2206t and convolution with the \u2206z resolution\nfunction.\nBABAR describes the \u2206t resolution function for dilep-\nton events as the sum of three Gaussian distributions.\nThe resolution function parameters are free parameters in\nthe \ufb01t. Belle determines the signal \u2206z resolution function\nfrom J/\u03c8 decays in data. For these decays the true \u2206z\nis equal to zero and the measured \u2206z distribution, after\nthe contributions of backgrounds are subtracted, yields\nthe \u2206z resolution function. A comparison between data\nand MC simulation shows that after convolving the MC\n\u2206z distribution of J/\u03c8 decays with a Gaussian of width\n\u03c3 = (50 \u00b1 18) \u00b5m, the MC distribution agrees with data.\nThe \u2206t and \u2206z distributions of background events are\ndetermined from MC-simulated events and data control\nsamples. The large background from semileptonic B+B\u2212\nevents has the same resolution function as the signal events.\nThe numbers of selected OS and SS dilepton pairs along\nwith the corresponding mixing asymmetry as a function of\n\u2206t from the BABAR analysis are shown in Fig. 17.5.5. Due\nto the small mixing frequency, OS signal events are much\nmore abundant than SS events. Most of the background\nevents are also OS (for example from B+B\u2212events). There-\nfore, even a small mistag probability will blur the charac-\nteristic features of the SS \u2206t distribution. This is partic-\nularly evident at \u2206t = 0 where the OS P+ distribution\nhas its maximum and the SS \u2206t distribution P\u2212is zero:\nthe measured \u2206t distribution of selected SS events does\nnot have a dip at zero. However, the mixing asymmetry\n\n284\nEvents / 0.24 ps\n0\n2000\n4000\n0\n200\n400\n600\n-10\n-5\n0\n5\n10\n0\n0.2\n0.4\n0.6\n0.8\nt (ps)\n(b)\n(c)\n(a)\nEvents / 0.24 ps\nAsymmetry / 0.24 ps\n\u2206\nFigure 17.5.5. The \u2206t distributions for (a) opposite-sign\nand (b) same-sign charge dilepton events; (c) mixing asym-\nmetry between opposite-sign and same-sign dilepton events.\nThe points are the data and lines correspond to the projection\nof the likelihood \ufb01t (Aubert, 2002e).\nstill shows the expected cosine shape as mis-tagging and\nnon-oscillating backgrounds, respectively, only reduce the\namplitude and shift the baseline of the asymmetry curve.\nFrom dilepton events BABAR measures \u2206md = (0.493\u00b1\n0.012\u00b10.009) ps\u22121 in a sample of 21 fb\u22121 (Aubert, 2002e)\nwhile Belle measures \u2206md = (0.503\u00b10.008\u00b10.010) ps\u22121 in\na sample of 29 fb\u22121 (Hastings, 2003), where the \ufb01rst errors\nare statistical and the second are systematic. The largest\ncontributions to the systematic errors come from the un-\ncertainties in the B0 and B+ lifetimes (\u223c0.006 ps\u22121) and\nin the \u2206z and \u2206t resolution functions (\u223c0.006 ps\u22121).\n17.5.2.3 Partially-reconstructed \ufb01nal states\nBABAR measures \u2206md with a sample of partially-recon-\nstructed B0 \u2192D\u2217+l\u2212\u03bdl events in 81 fb\u22121 (Aubert, 2006s).\nThey select B0 \u2192D\u2217+l\u2212\u03bdl (l = e or \u00b5) events with par-\ntial reconstruction of the decay D\u2217+ \u2192D0\u03c0+\ns , using only\nthe charged lepton from the neutral B decay (lrec) and the\nsoft pion (\u03c0+\ns ) from the D\u2217+ decay. This decay mode has\na large selection e\ufb03ciency since the D0 decay is not recon-\nstructed and the branching fraction of B0 \u2192D\u2217+l\u2212\u03bdl is\nabout half of the semileptonic branching ratio of the B0.\nThe other B in the event is identi\ufb01ed through a second\nhigh-momentum lepton (ltag).\nEvents are required to have at least four charged\ntracks. The normalized second Fox-Wolfram moment R2\n(see Chapter 9) must be less than 0.5 to reduce back-\nground from light quark production in continuum events.\nThe lepton from the B decay must have a momentum\nin the range 1.3\u20132.4 GeV/c, and the soft pion momentum\nmust be between 60 and 200 MeV/c. By approximating\nthe D\u2217+ momentum from the \u03c0+\ns momentum, they calcu-\nlate the square of the missing neutrino mass (m\u03bd\nmiss)2. The\n(m\u03bd\nmiss)2 distribution peaks at zero for signal events, while\nit is spread over a wide range of mostly negative values\nfor background events.\nBABAR determines the Brec decay vertex from a ver-\ntex \ufb01t of the lrec and \u03c0s tracks, constrained to the beam\nspot position in the transverse plane, but accounting for\nthe average B0 \ufb02ight distance. The decay point of Btag is\ndetermined from ltag and the beam spot following a pro-\ncedure similar to that of the Brec decay vertex. The \ufb02avor\nof Brec is determined from the lrec and soft pion charges.\nThe \ufb02avor of the other B in the event is determined from\nthe charge of ltag.\nAfter all selection criteria BABAR \ufb01nds 49,000 signal\nevents over a background of 28,000 events in the region\n(m\u03bd\nmiss)2 > \u22122.5 GeV2/c4. Background studies are done\nwith events in the region (m\u03bd\nmiss)2 < \u22122.5 GeV2/c4 if no\nsignal candidate is found in the event.\nBABAR simultaneously \ufb01ts the distributions of (m\u03bd\nmiss)2,\n\u2206t, and its uncertainty \u03c3\u2206t, for mixed and unmixed events,\nwith a binned maximum-likelihood method. Probabilities\nfor a given event to belong to any of the identi\ufb01ed back-\nground sources (e+e\u2212\u2192qq continuum, BB combinato-\nrial, and B+ peaking background) are calculated based\non the background (m\u03bd\nmiss)2 distributions. Signal is con-\nsidered to be any combination of a lepton and a charged\nD\u2217+ produced in the decay of a single B0 meson. They\nfurther divide their signal events according to the origin of\nthe tag lepton into primary, cascade, and decay-side lep-\nton tags. A primary lepton tag is produced in the direct\ndecay B0 \u2192Xl+\u03bdl, a cascade lepton tag is produced in\nthe process B0 \u2192DX, D \u2192l\u2212Y , and a decay-side tag\nis produced by the semi-leptonic decay of the unrecon-\nstructed D0. The relative normalization between mixed\nand unmixed signal events is constrained based on the\ntime-integrated mixing rate \u03c7d. The \u2206t signal p.d.f. for\nboth unmixed and mixed events consists of the sum of\np.d.f.s for primary, cascade, and decay-side tags each con-\nvoluted with its own resolution function. They use the\nstandard three Gaussian resolution function with event-\nby-event \u2206t uncertainties.\nFrom\nthe\n\ufb01t\nBABAR\nobtains\n\u03c4B0\n=\n(1.504 \u00b1\n0.013+0.018\n\u22120.013) ps and \u2206md = (0.511 \u00b1 0.007+0.007\n\u22120.006) ps\u22121,\nwhere the \ufb01rst errors are statistical and the second are\nsystematic. The statistical correlation between \u03c4B0 and\n\u2206md is 0.7%. The results include corrections of \u22120.006 ps\non \u03c4B0 and +0.007 ps\u22121 on \u2206md due to biases from event\nselection, boost approximation, B\u2212peaking background,\nand combinatorial BB background based on MC stud-\nies. The systematic error in \u2206md is dominated by un-\ncertainties in the SVT alignment (+0.0038\n\u22120.0033 ps\u22121), the se-\nlected range of \u2206t and \u03c3\u2206t (0.0033 ps\u22121), and analysis\nbias (0.0035 ps\u22121), whereas the largest systematic error\nsources in the \u03c4B0 measurement are the SVT alignment\n\n285\n(+0.0132\n\u22120.0038 ps), the z scale of the detector (0.0070 ps), and\nanalysis bias (0.0070 ps).\nBelle measures \u2206md with a sample of partially-recon-\nstructed B0 \u2192D\u2217+\u03c0\u2212events in 29.1 fb\u22121 (Zheng, 2003).\nThey select B0 \u2192D\u2217+\u03c0\u2212\nh events with partial reconstruc-\ntion of the decay D\u2217+ \u2192D0\u03c0+\ns , using only the hard\npion (\u03c0\u2212\nh ) from the B0 decay and the soft pion (\u03c0+\ns ) from\nthe D\u2217+ decay. Using this partial reconstruction method,\nBelle obtains an order of magnitude more events com-\npared to the full reconstruction of the D\u2217+. The \ufb02avor\nof the other B in the event is identi\ufb01ed through a high-\nmomentum lepton ltag from semileptonic decay.\nHadronic events are selected by applying requirements\non track multiplicity and total energy variables. The hard\npion from the B decay must have a momentum in the\nrange 2.05\u20132.45 GeV/c and the soft pion momentum must\nbe below 450 MeV/c. Belle applies impact parameter re-\nquirements on \u03c0\u2212\nh and \u03c0+\ns to suppress backgrounds from\ninteractions of beam particles with residual gas in the\nbeam pipe or the beam pipe wall. They require both tracks\nto have SVD information and to not be identi\ufb01ed as lep-\ntons.\nThe event kinematics are fully constrained by four-\nmomentum conservation in the decays B0 \u2192D\u2217+\u03c0\u2212\nh and\nD\u2217+ \u2192D0\u03c0+\ns , the masses of all particles in these decays,\nthe B0 energy, and the \u03c0\u2212\nh and \u03c0+\ns momenta. Belle uses\ntwo variables, the missing D0 mass, MDmiss, and the cosine\nof the angle between the soft pion in the D\u2217+ rest frame\nand the momentum of the D\u2217+ in the center-of-mass frame\ncos \u03b8\u2217\n\u03c0s. The MDmiss distribution for signal events peaks\nsharply at the nominal D0 mass, while background events\nspread towards smaller values. Signal events are required\nto have MDmiss > 1.85 GeV/c and 0.3 < | cos \u03b8\u2217\n\u03c0s| < 1.05.\nThe \ufb02avor of Brec is determined from the \u03c0h charge.\nThe \ufb02avor of the other B in the event is determined from\nthe charge of ltag. The tag lepton is required to have mo-\nmentum greater than 1.1 GeV/c and to pass similar re-\nquirements on SVD hits and impact parameter as the Brec\npions. Tag leptons are rejected if when combined with any\nother lepton in the event the pair has an invariant mass\nconsistent with a J/\u03c8. Belle determines the Brec (Btag) de-\ncay vertex from the intersection of the \u03c0h (ltag) track with\nthe beam spot accounting for the B meson \ufb02ight distance.\nAfter all selection criteria Belle \ufb01nds 3433 signal events\nover a background of 1466 events which are used in the\n\u2206md measurement. Studies of MC-simulated events show\nthat a signi\ufb01cant fraction of the selected events come from\nB0 \u2192D\u2217+\u03c1\u2212decays.\nBelle simultaneously \ufb01ts the \u2206t distributions of the\nmixed and unmixed events with an unbinned maximum-\nlikelihood method. The B0B0 mixing frequency \u2206md is\nthe only free parameter in the \ufb01t. The B0 lifetime is\n\ufb01xed to the world average. The signal \u2206t resolution func-\ntion uses a triple-Gaussian p.d.f. (see Eq. 10.4.2) in the\n\u2206t residuals. The resolution function parameters are de-\ntermined from decays of J/\u03c8 to e+e\u2212and \u00b5+\u00b5\u2212. Back-\ngrounds are divided into peaking and non-peaking cate-\ngories. Non-peaking background is dominated by random\ncombinations of \u03c0\u2212\nh and \u03c0+\ns with primary leptons from\nB0 and B\u00b1 decays, and combinatorial background from\ncontinuum. Peaking background is dominated by the fol-\nlowing sources: B0 \u2192D\u2217+\u03c0\u2212and B0 \u2192D\u2217+\u03c1\u2212with\nsecondary-lepton or fake lepton tags; B0 \u2192D\u2217\u2217\u2212\u03c0+,\nB+\n\u2192\nD\u2217\u22170\u03c0+, and B0\n\u2192\nD\u2217\u2212\u03c0+\u03c00 decays with\nprimary-lepton, secondary-lepton, or fake lepton tags.\nPeaking and non-peaking background p.d.f.s are convolved\nwith their own resolution functions.\nFrom the \ufb01t Belle obtains \u2206md = (0.509 \u00b1 0.017 \u00b1\n0.020) ps\u22121, where the \ufb01rst error is statistical and the\nsecond is systematic. The systematic error in \u2206md\nis dominated by uncertainties in the background frac-\ntions (0.014 ps\u22121) and the signal \u2206t resolution function\n(0.012 ps\u22121).\n17.5.2.4 Fully-reconstructed \ufb01nal states\nHadronic decay modes\nBABAR reconstructs neutral B mesons in the decay modes\nB0 \u2192D(\u2217)\u2212\u03c0+, D(\u2217)\u2212\u03c1+, D(\u2217)\u2212a+\n1 , J/\u03c8K\u22170 using a data\nsample of 29.7 fb\u22121 (Aubert, 2002a,b). Belle uses the B\ndecays to the hadronic \ufb01nal states D\u2212\u03c0+, D\u2217\u2212\u03c0+, and\nD\u2217\u2212\u03c1+ in a data sample of 29.1 fb\u22121 (Tomura, 2002b).\nThe B0B0 mixing analyses with fully-reconstructed \ufb01-\nnal states reconstruct the same decay modes of the B0\ndaughters as in the B0 lifetime measurements described\nin Section 17.5.1.3 (Aubert, 2001c; Abe, 2002m). Both\nexperiments reduce background from continuum events\nby applying requirements on the normalized second Fox-\nWolfram moment R2 and the angle between the thrust\naxis of the particles that form the reconstructed B can-\ndidate and the thrust axis of the remaining tracks and\nunmatched calorimeter clusters in the event, computed\nin the \u03a5(4S) frame. Neutral B candidates are identi-\n\ufb01ed by their \u2206E and mES values. BABAR selects events\nwith mES > 5.2 GeV/c2 and |\u2206E| within \u00b12.5\u03c3 of zero.\nThey use the events in the background-dominated region\nmES < 5.27 GeV/c2 to determine the parameters of the\nbackground \u2206t distributions. Belle requires mES and \u2206E\nto be within \u00b13\u03c3 around their expected means. They use\ncandidates from a sideband region in the mES \u2212\u2206E plane\nto determine the background parameters.\nEvents with a reconstructed B0 are then analyzed to\ndetermine the \ufb02avor of the other B using the B \ufb02avor\ntagging algorithms described in detail in Chapter 8. Belle\nassigns 99.5% of the events to a \ufb02avor tag category, while\nBABAR rejects the 30% of events with marginal \ufb02avor dis-\ncrimination.\nThe decay time di\ufb00erence \u2206t between B decays is\ndetermined from the measured separation \u2206z = zrec \u2212\nztag along the z axis between the vertices of the recon-\nstructed Brec and the \ufb02avor-tagging Btag according to\nEq. (17.5.13). BABAR applies an event-by-event correction\nfor the directions of the B meson momenta with respect\nto the z direction in the \u03a5(4S) frame. A description of this\ncorrection and details of the calculation of zrec and ztag\nand their respective resolutions for fully-reconstructed B\ndecays are given in Chapter 6. In its paper, BABAR notes\n\n286\na correlation between the \u2206t residual \u03b4\u2206t = \u2206t \u2212\u2206ttrue\nand \u03c3\u2206t (see Fig. 6.5.4). It is due to the fact that, in B\ndecays, the vertex error ellipse for the D decay products is\noriented with its major axis along the D \ufb02ight direction,\nleading to a correlation between the D \ufb02ight direction and\nthe calculated uncertainty on the vertex position in z of\nthe Btag. In addition, the \ufb02ight length of the D in the z di-\nrection is correlated with its \ufb02ight direction. Therefore, the\nbias in the measured Btag vertex position due to including\nthe D decay products is correlated with the D \ufb02ight direc-\ntion. Taking into account these two correlations, BABAR\nconcludes that D mesons that have a \ufb02ight direction per-\npendicular to the z axis in the laboratory frame will have\nthe best z resolution and will introduce the least bias in\na measurement of the z position of the Btag vertex, while\nD mesons that travel forward in the laboratory will have\npoorer z resolution and will introduce a larger bias in the\nmeasurement of the Btag vertex.\nAfter all selection criteria are applied, BABAR (Belle)\n\ufb01nds 6300 (5300) signal events with an average purity of\n86% (80%). Both experiments use an unbinned maximum\nlikelihood \ufb01t to extract \u2206md from the \u2206t distributions of\nthe selected candidates. The p.d.f. describing the data ac-\ncounts for the presence of backgrounds with terms added\nto the signal description of Eq. (17.5.22):\nH\u00b1,i = fsig,iH\u00b1,sig,i +\nX\nj=bkgd\nfi,jB\u00b1,i,j(\u2206t,\u02c6b\u00b1,i,j).\n(17.5.24)\nThe background \u2206t p.d.f.s B\u00b1,i,j(\u2206t,\u02c6b\u00b1,i,j) provide an\nempirical description for the \u2206t behavior of background\nevents in each tagging category i. The background \u2206t\ntypes considered are a prompt component and an expo-\nnentially decaying component with an e\ufb00ective lifetime.\nThe prompt term is modeled with a delta function \u03b4(\u2206t).\nBoth experiments describe the background resolution p.d.f.\nwith the same function as the signal resolution p.d.f., but\nwith separate parameters to minimize correlations. Both\nexperiments determine the signal probability fsig,i for each\nB candidate i from its mES and \u2206E values (BABAR only\nuses mES) based on separate \ufb01ts to the mES and \u2206E dis-\ntributions.\nIn the likelihood \ufb01t BABAR approximates the signal\n\u2206t resolution function by a sum of three Gaussian distri-\nbutions (core, tail, and outlier) with di\ufb00erent means and\ndi\ufb00erent widths (see Chapter 10). The resolution is de-\ntermined separately for each signal candidate depending\non the uncertainty of its \u2206t value. BABAR uses separate\nresolution function parameters for each tagging category,\nwhile Belle uses a common parameterization.\nIn the \ufb01nal \ufb01t Belle lets only \u2206md and the mistag\nrates wi (i = 1\u20136) vary. BABAR\u2019s likelihood \ufb01t has 44\nfree parameters: \u2206md, average mistag rate and di\ufb00erence\nbetween B0 and B0 for each tagging category (8), signal\nresolution function parameters (16), and parameters for\nbackground time dependence (5), \u2206t resolution (6), and\ne\ufb00ective mistag rates (8).\nIn fully-reconstructed B decays to hadronic \ufb01nal states\nBABAR measures in a sample of 29.7 fb\u22121 \u2206md = (0.516\u00b1\n0.016 \u00b1 0.010) ps\u22121, where the \ufb01rst error is statistical and\nthe second is systematic. The central value has been cor-\nrected by (\u22120.002\u00b10.002) ps\u22121 to account for a small vari-\nation of the background composition as a function of mES.\nAn additional correction of (\u22120.007\u00b10.003) ps\u22121 has been\napplied to account for a bias observed in fully-simulated\nMC events due to correlations between the mistag rate\nand the \u2206t resolution that are not explicitly included in\nthe likelihood function. Belle measures \u2206md = (0.528 \u00b1\n0.017 \u00b1 0.011) ps\u22121 in a sample of 29.1 fb\u22121.\nThe largest contributions to the systematic uncertainty\nin the Belle measurement come from the uncertainties in\nthe signal \u2206t resolution function parameters (0.008 ps\u22121)\nand limited MC statistics (0.005 ps\u22121). In the BABAR \ufb01t\nthe parameters of the signal and background \u2206t resolu-\ntions functions are allowed to vary, and their contribution\nto the uncertainty on \u2206md is included as part of the statis-\ntical error. The largest remaining systematic uncertainties\ncome from uncertainties in the B0 lifetime (0.006 ps\u22121)\nand in the alignment of the SVT (0.005 ps\u22121).\nSemileptonic decays B0 \u2192D\u2217\u2212l+\u03bdl\nBABAR performs a simultaneous measurement of the B0\nlifetime and \u2206md with a sample of semileptonic B0 \u2192\nD\u2217\u2212l+\u03bdl decays using 21 fb\u22121 of data (Aubert, 2003m).\nThe D\u2217\u2212candidates are selected in the decay mode D\u2217\u2212\u2192\nD0\u03c0\u2212, and the D0 candidates are reconstructed in the\nmodes K+\u03c0\u2212, K+\u03c0\u2212\u03c0+\u03c0\u2212, K+\u03c0\u2212\u03c00, and K0\nS\u03c0+\u03c0\u2212. Can-\ndidate B0 \u2192D\u2217\u2212l+\u03bdl events are rejected if they fail selec-\ntion criteria required to suppress backgrounds and ensure\na well-measured \u2206t. These requirements include lepton\nand kaon identi\ufb01cation, momenta of the lepton and the\nD\u2217\u2212and D0 daughter tracks and \u03c00, the D0 invariant\nmass, the D\u2217\u2212\u2212D0 mass di\ufb00erence, vertex probabilities,\ncos \u03b8\u2217\nthrust, the absolute value of \u2206z, and the calculated\nerror on \u2206t. Furthermore they use two angular variables.\nThe \ufb01rst angle is \u03b8D\u2217,l, the angle between the D\u2217\u2212and\nthe lepton candidate in the \u03a5(4S) frame. The second is\n\u03b8B,D\u2217l, the inferred angle between the direction of the B0\nand the vector sum of the D\u2217\u2212and the lepton candidate\nmomenta, calculated in the \u03a5(4S) frame.\nThe B yield is larger than for the hadronic \ufb01nal state\nanalysis due to the large B semileptonic branching frac-\ntion. They reconstruct 680 B/ fb\u22121. Due to the missing\nneutrino the background level is higher than in the sample\nof fully-reconstructed hadronic B decays. The combinato-\nrial D\u2217\u2212background is about 18%, and the sum of the\nbackgrounds from events where the D\u2217\u2212and the lepton\ncome from di\ufb00erent B decays, events with a fake lepton\ncandidate, and events from continuum cc \u2192D\u2217\u2212X pro-\ncesses add up to 5\u20138%, depending on the lepton \ufb02avor.\nThe measurements of the decay vertex of the B0 \u2192\nD\u2217\u2212l+\u03bdl candidate and that of the other B in the event\nin this analysis is similar to BABAR\u2019s \u2206md analysis of fully-\nreconstructed hadronic \ufb01nal states. The decay time di\ufb00er-\nence is determined from the z positions of these vertices\naccording to Eq. (17.5.12). The \ufb02avor of Btag is deter-\nmined from the charged tracks in the event that do not\n\n287\nbelong to the B0 \u2192D\u2217\u2212l+\u03bdl candidate using the algo-\nrithms described in Chapter 8. About 30% of the selected\nsignal candidates have a mistag rate close to 50%. These\nevents are not sensitive to \u2206md, but they increase the\nsensitivity to the B0 lifetime. In this paper, BABAR de-\nscribes an interesting correlation between the mistag rate\nand the \u2206t resolution for the tagging category based on\nidenti\ufb01ed charged kaons.58 Both the mistag rate for kaon\ntags and the calculated \u03c3\u2206t depend inversely on\npP p2\nt,\nwhere pt is the transverse momentum with respect to the\nz axis of tracks from the Btag decay. The mistag rate de-\npendence originates from the kinematics of the physical\nsources for wrong-charge kaons. The three major sources\nof mis-tagged events in the kaon tag category are wrong-\nsign D0 mesons from B decays to double charm (b \u2192ccs),\nwrong-sign kaons from D+ decays, and kaons produced di-\nrectly in B decays. All these sources produce a spectrum of\ntracks that have smaller\npP p2\nt than B decays that pro-\nduce a correct tag. The \u03c3\u2206t dependence originates from\nthe 1/p2\nt dependence of \u03c3z for the individual contributing\ntracks due to multiple scattering in the SVT and the beam\npipe.\nAfter all selection requirements are applied, the B0 \u2192\nD\u2217\u2212l+\u03bdl selected event sample contains contributions from\nthe following types of background: events with a misre-\nconstructed D\u2217\u2212candidate, events from continuum cc \u2192\nD\u2217\u2212X processes, events with a fake lepton candidate,\nevents with a charged B, and events in which the lepton\ndoes not come from the primary B decay. They model the\n\u2206t distributions of each background with combinations of\nprompt, exponential, and oscillatory functions convolved\nwith background resolution functions. The parameters of\nbackground p.d.f.s are obtained from \ufb01ts to control sam-\nples and simulated events. BABAR split their data into\ntwo signal samples and ten control samples depending on\nwhether the data was taken on or o\ufb00the \u03a5(4S) resonance,\nwhether the lepton candidate was on the same side or op-\nposite side to the D\u2217\u2212candidate, and whether the lep-\nton candidate was an electron, muon, or fake lepton. Fur-\nthermore they split each of these samples into subsamples\naccording to the reconstruction of the soft pion, the D0\ndecay mode, and the B \ufb02avor-tagging category for a total\nof 360 subsamples.\nThey extract the B0 lifetime and \u2206md from a simul-\ntaneous \ufb01t to the \u2206t and \u03c3\u2206t values of the events of the\n360 event samples. The \ufb01t has 70 additional free param-\neters to describe the signal and background \u2206t resolu-\ntion functions and mistag rates, and the background \u2206t\nshapes. From the \ufb01t they determine \u03c4B0 = (1.523+0.024\n\u22120.023 \u00b1\n0.022) ps and \u2206md = (0.492 \u00b1 0.018 \u00b1 0.013) ps\u22121. The\nstatistical correlation coe\ufb03cient between \u03c4B0 and \u2206md\nis \u22120.22. Dominant systematic error sources in the \u2206md\nmeasurement are the SVT alignment and the signal and\nbackground probabilities. An additional systematic un-\ncertainty in the \u2206md measurement comes from the lim-\nited statistical precision in determining the bias due to\n58 This correlation is already observed and accounted for in\nAubert (2002b), but is not described in that paper.\nthe background modeling. By comparing the \ufb01tted \u2206md\nin simulated events, BABAR observes a shift of (0.020 \u00b1\n0.005) ps\u22121 between a signal-only sample and a signal-\nplus-background sample. The measured \u2206md is corrected\nfor the observed bias from the \ufb01t to the MC sample with\nbackground, and the full statistical uncertainty in \u2206md of\n\u00b10.012 ps\u22121 is assigned as a systematic uncertainty.\nBelle also measures \u2206md with a sample of semilep-\ntonic B0 \u2192D\u2217\u2212l+\u03bdl decays corresponding to 29.1 fb\u22121 of\ndata (Hara, 2002). They select D\u2217\u2212candidates in the de-\ncay mode D\u2217\u2212\u2192D0\u03c0\u2212and the D0 candidates are recon-\nstructed in the modes K+\u03c0\u2212, K+\u03c0\u2212\u03c0+\u03c0\u2212, and K+\u03c0\u2212\u03c00.\nCandidate events are rejected if they fail selection crite-\nria required to suppress backgrounds and ensure a well-\nmeasured \u2206t. The applied requirements are similar to\nthose in the BABAR \u2206md measurement described above.\nBelle uses its standard algorithms for the \u2206t measure-\nments and B \ufb02avor tagging in this analysis, which are\nthe same as in its measurement of sin \u03c61 (Abe, 2002k).\nThe algorithms are described in more detail in Chapters 6\nand 8. After all selection criteria, including \ufb02avor tagging\nand vertex reconstruction, are applied, Belle reconstructs\n453 B0/ fb\u22121 with a signal purity of 80.4%. The back-\nground consists of misreconstructed D\u2217mesons (7.8%),\nB \u2192D\u2217\u2217l\u03bd events (7.4%), random combinations of D\u2217\nmesons with leptons with no angular correlation (2.6%),\nand continuum events (1.8%).\nBelle measures \u2206md from a simultaneous \ufb01t to the\n\u2206t and \u03c3\u2206t distributions of the mixed and unmixed\nevents. The \ufb01t has a total of ten free parameters in-\ncluding \u2206md, six \ufb02avor mistag rates, the fraction of the\nD\u2217\u2217background coming from charged B decays, its ef-\nfective lifetime, and the fraction of charged B decays.\nAll other parameters are determined from MC simula-\ntion and data control samples. The likelihood \ufb01t gives\n\u2206md = (0.494\u00b10.012\u00b10.015) ps\u22121. Dominant systematic\nerror sources in the \u2206md measurement are due to uncer-\ntainties in the D\u2217\u2217branching fractions (0.007 ps\u22121), the\nselected |\u2206t| range (0.007 ps\u22121), the background \u2206t p.d.f.\nparameters (0.006 ps\u22121), the signal \u2206t resolution function\n(0.006 ps\u22121), and the B0 lifetime (0.005 ps\u22121).\nBelle hadronic and semileptonic combination\nBelle\u2019s most recent measurement of \u2206md comes from a si-\nmultaneous analysis of B decays to the exclusive hadronic\n\ufb01nal states B0 \u2192D(\u2217)\u2212\u03c0+, D\u2217\u03c1+, J/\u03c8K0\nS, J/\u03c8K\u22170,\nand the semileptonic decay B0 \u2192D\u2217\u2212l\u03bd in a sample of\n140 fb\u22121 (Abe, 2005c). In the same analysis, they also de-\ntermine the B0 lifetime and, using the decays B+ \u2192D0\u03c0+\nand J/\u03c8K+, the B+ lifetime.\nThe signal modes and selection criteria of the hadronic\n\ufb01nal states are similar to the ones used in Tomura (2002b),\nwhile the B0 \u2192D\u2217\u2212l+\u03bd selection follows that described\nin Zheng (2003). The \u2206t reconstruction uses the algorithm\ndescribed in Tajima (2004). The B \ufb02avor tagging algo-\nrithm is similar to the one used in Belle\u2019s previous anal-\nyses of fully-reconstructed \ufb01nal states, but they allow for\nseparate mistag rates for B0 and B0 tagged events. The\n\n288\noverall B0 signal purity after all selection criteria are ap-\nplied is 80.9%, and the B0 signal yield is 707 B/ fb\u22121.\nBelle performs an unbinned maximum likelihood \ufb01t to\nthe \u2206t distributions of the selected B0 and B+ candi-\ndates to simultaneously obtain values of the B0 and B+\nlifetimes (2), \u2206md (1), the mistag fractions (12), the sig-\nnal \u2206t resolution function parameters (14), and param-\neters to describe the B+ background in B0 decays (3).\nThe signal resolution function has two parameters added\nto the ones described in Tajima (2004) to better describe\nthe e\ufb00ect of charmed particle decays on the Btag vertex.\nThe same \u2206t resolution function is used for B0 and B+\nsignal candidates. The background for the hadronic B de-\ncay modes is described by the convolution of the sum of\na prompt term and a term with an e\ufb00ective background\nlifetime with a background \u2206t resolution function. The\nbackground for the B0 \u2192D\u2217\u2212l+\u03bd decays is the same as\nin the earlier study of this mode (Hara, 2002) described\nabove. The \u2206t behavior of the backgrounds is modeled\nwith prompt and lifetime terms. The backgrounds due to\nD\u2217\u2217and misreconstructed D\u2217candidates also have an os-\ncillatory component.\nBelle extracts the B0 lifetime and \u2206md to be, re-\nspectively, \u03c4B0 = (1.534 \u00b1 0.008 \u00b1 0.010) ps and \u2206md =\n(0.511 \u00b1 0.005 \u00b1 0.006) ps\u22121. Dominant systematic error\nsources in the \u2206md measurement are the B vertex recon-\nstruction (0.004 ps\u22121) and the D\u2217\u2217background parame-\nters (0.003 ps\u22121).\n17.5.2.5 Average of \u2206md\nThe various measurements of \u2206md by the B Factories\nlisted in Table 17.5.2 have been averaged by the Heavy\nFlavor Averaging Group (HFAG; Asner et al., 2010), where\nresults superseded by more recent ones have been omit-\nted from the average. Before being combined, the \u2206md\nmeasurements have been adjusted to a common set of\ninput values, including the B meson lifetimes. The to-\ntal systematic uncertainty in \u2206md is of the same size\nas the statistical uncertainty, although only a small frac-\ntion of the total B Factories\u2019 data sets have been used\nin the measurements. Systematic correlations arise from\ncommon physics sources (e.g. B lifetimes and branching\nfractions) and common experimental techniques and algo-\nrithms (e.g. \ufb02avor tagging, \u2206t resolution, and background\ndescription). Combining the B Factories \u2206md measure-\nments and accounting for all identi\ufb01ed correlations, HFAG\nquotes\n\u2206md = (0.508 \u00b1 0.003 \u00b1 0.003) ps\u22121,\n(17.5.25)\nwhere the \ufb01rst error is statistical and the second is system-\natic (Asner et al., 2010). Combining the B Factories \u2206md\naverage with time-dependent measurements from the LEP\nand Tevatron experiments, and time-integrated measure-\nments from CLEO and ARGUS, gives the same value. The\nvalues of \u2206md as measured by di\ufb00erent experiments along\nwith the time-dependent and time-integrated averages are\nshown in Fig. 17.5.6. Two recent measurements by the\n0.4\n0.45\n0.5\n0.55\n\u2206md (ps-1)\nWorld average\nEnd 2009\n 0.508 \u00b1 0.004 ps-1\nCLEO+ARGUS\n(\u03c7d measurements)\n 0.498 \u00b1 0.032 ps-1\nAverage of above\nafter adjustments\n 0.508 \u00b1 0.004 ps-1\nBELLE *\n(3 analyses)\n 0.509 \u00b1 0.004 \u00b1 0.005 ps-1\nBABAR *\n(4 analyses)\n 0.506 \u00b1 0.006 \u00b1 0.004 ps-1\nD0 \n(1 analysis)\n 0.506 \u00b1 0.020 \u00b1 0.016 ps-1\nCDF2 *\n(2 prel. analyses)\n 0.517 \u00b1 0.009 \u00b1 0.013 ps-1\nCDF1 *\n(4 analyses)\n 0.495 \u00b1 0.033 \u00b1 0.027 ps-1\nOPAL \n(5 analyses)\n 0.479 \u00b1 0.018 \u00b1 0.015 ps-1\nL3 \n(3 analyses)\n 0.444 \u00b1 0.028 \u00b1 0.028 ps-1\nDELPHI *\n(5 analyses)\n 0.519 \u00b1 0.018 \u00b1 0.011 ps-1\nALEPH \n(3 analyses)\n 0.446 \u00b1 0.026 \u00b1 0.019 ps-1\n * HFAG average\n without adjustments\nFigure 17.5.6. The B0B0 oscillation frequency \u2206md as mea-\nsured by the di\ufb00erent experiments along with their average.\nAverages are also given separately for the time-dependent mea-\nsurements by the B Factories and the LEP and Tevatron ex-\nperiments, and the time-integrated measurements by CLEO\nand ARGUS (Asner et al., 2010).\nLHCb Collaboration, \u2206md = (0.516 \u00b1 0.005 \u00b1 0.003) ps\u22121\n(Aaij et al., 2013b) and \u2206md = (0.499\u00b10.032\u00b10.003) ps\u22121\n(Aaij et al., 2012f), are not included in the HFAG average\nand the \ufb01gure. The 2013 PDG world average including\nthese results is \u2206md = (0.510 \u00b1 0.004) ps\u22121\n(Beringer\net al., 2012). The world average of the B0B0 oscillation\nfrequency \u2206md is an input to the calculation of the mag-\nnitude of the CKM matrix element Vtd. Along with \u2206ms,\nthe B0\nsB0\ns oscillation frequency as measured by CDF and\nD\u00d8, \u2206md is used to calculate the ratio of CKM matrix\nelements |Vtd/Vts| (see Section 17.2).\n17.5.2.6 Measurements of \u2206\u0393d\nTransitions between a B0 state and a B0 state can be me-\ndiated by a box diagram involving virtual top quarks (see\nFig. 10.1.1) or by real intermediate states accessible to\nboth B0 and B0. The former process determines the mag-\nnitude of \u2206md, while the latter gives rise to a di\ufb00erence in\ndecay width of the neutral B mass eigenstates. The decay\nwidth di\ufb00erence is de\ufb01ned as \u2206\u0393d \u2261\u0393H,d \u2212\u0393L,d,59 where\nH and L refer to the heavy and light B0 states, respec-\ntively. In the B0\ns system the corresponding relative decay\nwidth di\ufb00erence is large, \u2206\u0393s/\u0393s = (15 \u00b1 2)% (Beringer\net al., 2012), due to the signi\ufb01cant branching fractions of\nB0\ns and B0\ns to D(\u2217)+\ns\nD(\u2217)\u2212\ns\n. Since the decays of B0 and\n59 Note, the Particle Data Group (Beringer et al., 2012) uses\nthe de\ufb01nition \u2206\u0393d = \u0393L,d \u2212\u0393H,d.\n\n289\nB0 to common \ufb01nal states are strongly suppressed, \u2206\u0393d\nis expected to be much smaller than \u2206\u0393s. A recent SM\ncalculation predicts \u2206\u0393d/\u0393d = (\u22124.2 \u00b1 0.8) \u00d7 10\u22123 (Lenz\nand Nierste, 2011). The best limit prior to the B Facto-\nries measured by DELPHI was \u2206\u0393d/\u0393d < 0.18 at 95%\nC.L. (Abdallah et al., 2003). The small value of \u2206\u0393d in\nthe SM makes it a sensitive parameter in the search for\nnew physics (Dighe, Hurth, Kim, and Yoshikawa, 2002).\nIn the derivation of the time-dependent decay rates in\nChapter 10 we have neglected the case of non-zero \u2206\u0393d.\nThis is justi\ufb01ed because of the small values of \u2206\u0393d/\u0393d and\n\u2206\u0393d/\u2206md predicted by the SM. The decay rates given in\nEqs (10.2.2) and (10.2.3) are su\ufb03cient for all measure-\nments of \u2206md (Section 17.5.2) and mixing-induced CP\nasymmetries in B decays (Sections 17.6\u201317.8). However,\nphysics from processes beyond the SM can lead to a sizable\n\u2206\u0393d. BABAR (Aubert, 2004e,f) and Belle (Higuchi, 2012)\nhave both measured \u2206\u0393d as part of analyses that search\nfor CP, T, and CPT violation in B0B0 mixing. The analy-\nses are described in detail below (see Section 17.5.4). Here\nwe describe the sensitivity to \u2206\u0393d and the results from\nthe B Factories.\nThe time-dependence of the decay rates for B decays\nto CP eigenstates and \ufb02avor-speci\ufb01c \ufb01nal states in the\nabsence of CP and CPT violation in B0B0 mixing, but\nincluding additional terms due to \u2206\u0393d, are given by\nf \u2206\u0393d\n\u00b1\n(\u2206t)\u221de\u2212|\u2206t|/\u03c4B0\n\"\ncosh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n\u2213C cos(\u2206md\u2206t)\n+A\u2206\u0393d sinh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n\u00b1S sin(\u2206md\u2206t)\n#\n,\n(17.5.26)\nwith\nC = 1 \u2212|\u03bb|2\n1 + |\u03bb|2 , S = 2 Im\u03bb\n1 + |\u03bb|2 , A\u2206\u0393d = 2 Re\u03bb\n1 + |\u03bb|2 . (17.5.27)\nThe parameter \u03bb =\nq\np\nAf\nAf has been introduced in Chap-\nter 10, where Af (Af) represents the amplitude for the\ndecay of a B0 (B0) to the \ufb01nal state f, and q/p is the weak\nphase in B0B0 mixing. Note that (S)2+(C)2+\n\u0000A\u2206\u0393d\u00012 =\n1 by de\ufb01nition. The time-dependence for a B0 (B0) tagged\nevent is given by f \u2206\u0393d\n+\n(f \u2206\u0393d\n\u2212\n).\nFor B decays to CP eigenstates that proceed through a\nsingle weak amplitude, |\u03bb| = 1 and thus C = 0, S = Im\u03bb,\nand A\u2206\u0393d = Re\u03bb. For example, the time-dependence for\nthe golden CP mode B \u2192J/\u03c8K0\nS (see Chapter 10 and\nSection 17.6) simpli\ufb01es to\nf J/\u03c8 K0\nS,\u2206\u0393d\n\u00b1\n(\u2206t) \u221de\u2212|\u2206t|/\u03c4B0\n\"\ncosh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n+ cos(2\u03c61) sinh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n\u00b1 sin(2\u03c61) sin(\u2206md\u2206t)\n#\n,\n(17.5.28)\nwhere \u03c61 is one of the angles of the Unitarity Triangle.\nFor B decays to \ufb02avor-eigenstates which are only ac-\ncessible from either a B0 or a B0, |\u03bb| is zero or in\ufb01nite\nand thus C = 1, S = A\u2206\u0393d = 0. The corresponding time-\ndependence is given by\nh\u2206\u0393d\n\u00b1\n(\u2206t) \u221de\u2212|\u2206t|/\u03c4B0\n\"\ncosh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n\u00b1 cos(\u2206md\u2206t)\n#\n,\n(17.5.29)\nwhere h\u2206\u0393d\n+\nand h\u2206\u0393d\n\u2212\nrefer to unmixed and mixed events,\nrespectively.\nBABAR and Belle both use samples of B decays to CP\neigenstates and \ufb02avor-speci\ufb01c \ufb01nal states in their measure-\nment of \u2206\u0393d. The BABAR analysis is performed with 88 \u00d7\n106 BB pairs and uses the B\ufb02av decays to D(\u2217)\u2212\u03c0+(\u03c1+, a+\n1 ),\nJ/\u03c8K\u22170(\u2192K+\u03c0\u2212) and BCP decays to J/\u03c8K0\nS, \u03c8(2S)K0\nS,\n\u03c7c1K0\nS, and J/\u03c8K0\nL. The Belle analysis is performed with\n535\u00d7106 BB pairs and uses the B\ufb02av decays to D(\u2217)\u2212\u03c0+,\nD\u2217\u2212\u03c1+, and D\u2217\u2212\u2113+\u03bdl and BCP decays to J/\u03c8K0\nS and\nJ/\u03c8K0\nL. The cosh and sinh terms in Eqs (17.5.28) and\n(17.5.29) do not change sign with the \ufb02avor of Btag. This\nallows the experiments to also use events without a \ufb02avor-\ntagged B in their analyses. The time-dependence of the\nBCP samples include a sinh\n\u0000 \u2206\u0393d\u2206t\n2\n\u0001\nterm, which is prac-\ntically linear in \u2206\u0393d. The B\ufb02av sample is only sensitive to\n\u2206\u0393d through a cosh\n\u0000 \u2206\u0393d\u2206t\n2\n\u0001\nterm and thus e\ufb00ectively to\nO(\u2206\u0393 2\nd ). Therefore, even though the BCP events represent\nonly 8% (4%) of the selected signal events in the BABAR\n(Belle) analysis, they dominate the \u2206\u0393d measurement.\nThe experiments perform unbinned likelihood \ufb01ts to\nthe \u2206t distributions of the \ufb02avor-tagged and untagged\nBCP and B\ufb02av samples (after accounting for experimental\ne\ufb00ects such as the \u2206t resolution and B \ufb02avor-tagging) to\nextract parameters that violate CP, T, or CPT symme-\ntries and \u2206\u0393d. In the \ufb01t the sign of A\u2206\u0393d is \ufb01xed to the\nvalue obtained from global CKM \ufb01ts (see Section 25.1).\nBABAR measures \u2206\u0393d/\u0393d = \u22120.008 \u00b1 0.037 \u00b1 0.018 and\nBelle measures \u2206\u0393d/\u0393d = \u22120.017 \u00b1 0.018 \u00b1 0.011. The\ndominant systematic error contributions arise from un-\ncertainties in the reconstruction of the B vertices and the\n\u2206t resolution function. The results are consistent with\neach other. The B Factories average value is \u2206\u0393d/\u0393d =\n\u22120.015\u00b10.019 (Beringer et al., 2012), consistent with the\nsmall predicted value. Larger B samples at LHCb and fu-\nture super \ufb02avor factories should allow the measurement\nof \u2206\u0393d at the SM value or \ufb01nd discrepancies as evidence\nof new physics (Gershon, 2011), if the systematic uncer-\ntainties can be kept under control.\n17.5.3 Tests of quantum entanglement\nThe B-lifetime and B0 \u2212B0 mixing results of the previ-\nous sections rely on certain assumptions about the physics\nof B-meson production and decay (see the discussion in\nChapter 10). Some of these assumptions can be tested\nby performing an extended analysis including symmetry-\nbreaking parameter(s) in the \ufb01nal \ufb01t. This approach is\n\n290\nused to test discrete symmetries, including CPT (Sec-\ntions 17.5.4 and 17.5.5 below); if the assumption of Lorentz\ninvariance is also relaxed, qualitatively new phenomena\nare expected and the B0 \u2212B0 mixing analysis method of\nSection 17.5.2 must be heavily modi\ufb01ed (Section 17.5.5),\neven when a standard mixing event selection is retained.\nQuantum mechanical principles governing the entan-\ngled B0B0 state may also be tested. The careful concep-\ntual treatment required in this case is reviewed in Sec-\ntion 17.5.3.1. One such analysis has been performed by\nBelle (Go, 2007): the event selection and background treat-\nment are both straightforward modi\ufb01cations of those in\nthe D\u2217\u2113\u03bd mixing analysis of Abe (2005c), as discussed in\nSection 17.5.3.2. The \ufb01nal analysis is presented in Sec-\ntion 17.5.3.3.\n17.5.3.1 B0 \u2212B0 mixing and entanglement tests\nAs discussed in Section 10.2, \u03a5(4S) decay prepares a neu-\ntral B meson pair in the coherent state\n\u03a8 =\n1\n\u221a\n2\n\u0002\n|B0(p)\u27e9|B0(\u2212p)\u27e9\u2212|B0(p)\u27e9|B0(\u2212p)\u27e9\n\u0003\n(17.5.30)\ngiven there in a more compact notation as Eq. (10.2.1).\nThe formulae for the time-dependent evolution of the B\npair in the remainder of that section follow from this ex-\npression. Such a state is entangled: it cannot be repre-\nsented as a product of states of the \ufb01rst B (with momen-\ntum p) and the second B (with momentum \u2212p); it is a\n\ufb02avor analog of the spin-singlet state for a photon pair,\n\u03a8 =\n1\n\u221a\n2 (|\u21d1\u27e91|\u21d3\u27e92 \u2212|\u21d3\u27e91|\u21d1\u27e92) ,\n(17.5.31)\nfamiliar from Bohm\u2019s version of the thought experiment\non \u201cEPR correlations\u201d (Bohm, 1951; Einstein, Podolsky,\nand Rosen, 1935). Powerful tests of such correlations are\npossible (Bell, 1964), and have been carried out on pho-\nton pairs by Aspect, Grangier, and Roger (1982) and many\nsubsequent investigators. Subject to certain experimental\n\u201cloopholes\u201d, such tests exclude the hypothesis that the in-\ndividual photons have de\ufb01nite physical states at all times\n(a feature of so-called \u201clocal realistic\u201d models). Quantum\nentanglement thus appears to be an experimental fact,\nwhich would persist even if quantum mechanics (QM) it-\nself were replaced by future developments.\nBell tests using photons rely on experimental choice\nof the orientation (polarization axis) of analyzers, in ex-\nperiments of the Aspect type; or on \ufb01xed analyzers, and\nexperimental choice of phase shifts imposed on the pho-\ntons in \ufb02ight (following Franson, 1989); see Fig. 17.5.7(a)\nand (b) for schematics of both arrangements. B0 \u2212B0\nmixing is analogous to the latter case, as a \ufb02avor-tagging\ndecay projects a neutral B meson onto one of two \ufb01xed\naxes: B0, equivalent to spin-up for a fermion or vertical\npolarization for a photon; or B0, equivalent to spin-down\nor to horizontal polarization. For discussion of this quasi-\nspin analogy, see Lee and Wu (1966), Lipkin (1968), and\n(a) Aspect: freely-chosen analyzer orientations a, b.\nL1\nD2\nM2\nt2\nF2\nL2\nL1\nF1\nM1 ~+\nS1\n/\nD1\nD2\n(b) Franson: freely-chosen phase shifts \u03c61, \u03c62.\nD\nD\nD\nD\n!1\n!2\nS\n(c) Go: \ufb01xed analyzers; variable phase shifts \u03c61, \u03c62.\nFigure 17.5.7. Schematics of the Bell inequality tests with\nphotons by (a) Aspect, Grangier, and Roger (1982); (b) the\nposition-time test proposed by Franson (1989); and (c) an op-\ntical analog of the Go (2007) analysis of B0B0 pairs (from Yab-\nsley, 2008). To perform a Bell test, projective measurements\nmust be performed onto axes determined outside the system\nunder study. In (a), the analyzer orientations can be freely\nchosen; in (b) the projections recorded by the detectors Di are\n\ufb01xed, but phase shifts imposed on the photons can be chosen;\nin (c), neither the projection axes (\u2195\u2261B0 or \u2194\u2261B0) nor\nphase shifts (\u03c6i = \u2206mdti) are subject to experimental control.\nBertlmann and Hiesmayr (2001); the assignment of spin\nand polarization states to \ufb02avors is arbitrary. If we ignore\nB-meson decay, the state |B0\u27e9at production evolves to\nthe state\n1\n2\n\u0002\n{1 + cos(\u2206mdt)}|B0\u27e9+ {1 \u2212cos(\u2206mdt)}|B0\u27e9\n\u0003\n(17.5.32)\nat a later time t, from Eqs (10.1.6) and (10.1.7); cf.\nEqs (17.5.14)\u2013(17.5.17) above. For a B0B0 pair undergoing\ntwo \ufb02avor-tagging decays, the product \u2206md\u2206t therefore\ncorresponds to the di\ufb00erence in phase shifts \u2206\u03c6 imposed\nin a Franson-type experiment, or the angle between po-\nlarization analyzers chosen in an Aspect-type experiment\n(see Fig. 17.5.7(c)).\nAn early attempt to re-interpret B Factory mixing re-\nsults as Bell inequality tests was presented by Go (2004).\nIn fact, no such test is possible using B Factory mea-\nsurements of the B0 \u2212B0 system (Bertlmann, Bramon,\nGarbarino, and Hiesmayr, 2004):\n1. Flavor measurements at the B Factories are passive,\nrelying on spontaneous decay of the B mesons rather\n\n291\nthan (say) interactions with converters placed in the\npath of each B. It is therefore not possible to ex-\nclude local models where EPR-like decays of the two B\nmesons have been determined in advance, as \u2206md\u2206t\nis not subject to experimental control. Schematic di-\nagrams comparing this case and entangled-photon ex-\nperiments are shown in Fig. 17.5.7; note that in pho-\nton experiments, control of analyzer orientations has\nbeen demonstrated for spacelike-separated measure-\nments (for example Weihs, Jennewein, Simon, Wein-\nfurter, and Zeilinger, 1998).\n2. The rate of B0\nd-mixing is too low, relative to the rate\nof decay, to construct a Bell test even in the case of\nactive measurements. The crucial value of x = \u2206m/\u0393\nis found to be 2.0; cf. xd = \u2206md/\u0393d = (0.775\u00b10.007).\nNote that as xs = \u2206ms/\u0393s = (26.82 \u00b1 0.23) \u226b2.0,\na Bell test using active measurements of the B0\ns \u2212B0\ns\nsystem is possible in principle, although not practical\nwith foreseeable technology. Values are taken from the\n2013 update of Beringer et al., 2012.\nArti\ufb01cial local models which reproduce QM predic-\ntions for B Factory results have been constructed by Bertl-\nmann, Bramon, Garbarino, and Hiesmayr (2004), follow-\ning Kasday (1971); and by Santos (2007), to further demon-\nstrate that such models cannot be excluded as a class.\nIt is however possible to compare B Factory results\nwith the predictions of both quantum mechanics and var-\nious local models. The Belle analysis (Go, 2007) tested\nboth decoherence models (following Bertlmann, Grimus,\nand Hiesmayr, 1999), and a broad class of models that\nreproduce the QM predictions for uncorrelated B decays\n(Pompili and Selleri, 2000). Predictions for the B0B0 mix-\ning asymmetry Amix(\u2206t) of Eq. (17.5.20) are shown in\nFig. 17.5.8 for QM and for spontaneous disentanglement\n(SD), an extreme form of decoherence corresponding to\n\u03b6 = 1 in the {B0, B0} basis in Bertlmann et al., or the\nhypothesis of Furry (1936); asymmetries for models in the\nPompili and Selleri class must lie between the two curves\nPSmax and PSmin. With su\ufb03cient resolution, Amix(\u2206t)\nmeasurements can discriminate between these models; with\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\n0\n2\n4\n6\n8\n10\n12\n6t [ps]\nAsymmetry\nFigure 17.5.8. Time dependent asymmetry predictions for\n(QM) quantum mechanics, (SD) spontaneous disentanglement,\nand (PSmax to PSmin) the allowed range for models in the class\ndescribed by Pompili and Selleri (2000). See the discussion in\nthe text. From Go (2007).\nreconstruction of individual decay times (not just \u2206t),\nmuch stronger discrimination would be possible at a next-\ngeneration \ufb02avor factory (see Eqs (2)\u2013(5) of Go, 2007, and\nFigure 4 of Yabsley, 2008).\n17.5.3.2 Event selection and background treatment\nThe Belle analysis (Go, 2007) uses a sample of B0B0 events\nwhere one B is reconstructed as B0 \u2192D\u2217\u2212\u2113+\u03bd (or charge\nconjugate), and the remaining tracks are subjected to the\nBelle \ufb02avor-tagging algorithm (Section 8.6.4). Taken from\n140 fb\u22121 of data, the sample is a subset of the D\u2217\u2113\u03bd sample\nof Abe (2005c) discussed in Sections 17.5.1.3 and 17.5.2.4\nabove. To perform the entanglement analysis, the event\nselection and background treatment of Abe (2005c) are\nmodi\ufb01ed in the following ways:\n1. Only events with the highest-purity \ufb02avor tag are used\n(i.e. 0.875 < r < 1.000; see Section 8.6.4), with the\nfurther restriction that the tag is based on a recon-\nstructed lepton. This reduces the sample from 84823\nto 8565 events.\n2. The data are binned, separately for opposite-\ufb02avor (OF)\nand same-\ufb02avor (SF) events, into 11 variable-width\nbins in \u2206t.\n3. Backgrounds are subtracted, in both OF and SF sam-\nples, using the same background categorization as Abe\n(2005c): e+e\u2212\u2192qq continuum (found to be negligi-\nble), non-D\u2217events, wrong D\u2217-lepton combinations,\nand B+ \u2192D\u2217\u22170\u2113+\u03bd events; B0 \u2192D\u2217\u2217\u2212\u2113+\u03bd events,\nwhich undergo mixing, are retained.\n4. Remaining reconstruction e\ufb00ects are unfolded using\ndeconvolution with single value decomposition (H\u00a8ocker\nand Kartvelishvili, 1996) separately on the OF and SF\nsamples, based on 11\u00d711 response matrices built from\nMC D\u2217\u2113\u03bd events; see Go (2007) for the details.\nTo avoid potential bias due to the MC events underly-\ning the response matrices, the deconvolution procedure is\nvalidated on Monte Carlo samples generated according to\neach of the QM, SD, and PS models. Di\ufb00erences between\nresults and inputs are averaged over the three models, and\nsubtracted from the measured asymmetry; the largest re-\nmaining deviation in each \u2206t bin, over all three models, is\nthen assigned as a contribution to the systematic uncer-\ntainty.\nThe resulting asymmetry Amix = (NOF\u2212NSF)/(NOF+\nNSF) in bins of the time di\ufb00erence \u2206t, with statistical and\nfour categories of systematic uncertainties, is given in Ta-\nble 1 of Go (2007); systematics become comparable to\nstatistical uncertainties for \u2206t > 4.0 ps, with the uncer-\ntainties due to background subtraction and deconvolution\ndominant in the \ufb01nal [13.0, 20.0] ps bin. These results can\nbe directly compared with theoretical models that lie out-\nside the analysis discussed in the following section.\n17.5.3.3 Analysis and interpretation\nFor each model, a weighted least-squares \ufb01t is performed,\nto the asymmetries Amix and their total uncertainties as\n\n292\n-3\n0\n3\n6\n6!mtot\n-3\n0\n3\n6\n6!mtot\n-3\n0\n3\n6\n6!mtot\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\n0\n10\n20\n6t \"ps#\nAsymmetry\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\n0\n10\n20\n6t \"ps#\nAsymmetry\n-1\n-0.75\n-0.5\n-0.25\n0\n0.25\n0.5\n0.75\n1\n0\n10\n20\n6t \"ps#\nAsymmetry\nFigure 17.5.9. Asymmetry Amix and its total uncertainty (crosses) in bins of \u2206t, and the results of \ufb01ts to predictions from\n(left: QM) quantum mechanics, (middle: SD) spontaneous decomposition, and (right: PS) the Pompili and Selleri (2000) class\nof models. The shaded boxes show the variation in the predictions as the \ufb01tted value of \u2206md is allowed to vary by \u00b11\u03c3; see the\ntext, in particular for handling of the PS case. The upper panels show normalized residuals in each bin. From Go (2007).\ndata, and the function shown in Fig. 17.5.8 as the pre-\ndiction. The mass di\ufb00erence \u2206md appears as a param-\neter in each model, however the world-average value of\n\u2206md is dominated by B Factory measurements, which\nassume time evolution according to QM in their analysis\n(see Section 17.5.2.1). An average of results then avail-\nable (Barberio et al., 2006), excluding B Factory mea-\nsurements, was therefore performed, yielding \u27e8\u2206md\u27e9=\n(0.496 \u00b1 0.014) ps\u22121. The uncertainty was treated by in-\ncluding \u2206md as a parameter in the \ufb01t, and adding an addi-\ntional term [(\u2206md \u2212\u27e8\u2206md\u27e9)/\u03c3\u2206md]2 to the least-squares\nstatistic; this technique is now in common use for treating\nsystematic uncertainties e.g. at LHC experiments).\nThe results of the \ufb01ts are shown in Fig. 17.5.9. The\npredictions of quantum mechanics are favored over spon-\ntaneous disentanglement at 13\u03c3; more general decoher-\nence models are treated by \ufb01tting the data with a func-\ntion (1 \u2212\u03b6)AQM + \u03b6ASD, equivalent to modifying the in-\nterference term in the {B0, B0} basis, or assuming dis-\nentanglement into B0 and B0 of a fraction of neutral B\npairs (Bertlmann, Grimus, and Hiesmayr, 1999). The re-\nsult, \u03b6 = 0.029 \u00b1 0.057, is consistent with no decoherence.\nThe analysis of Pompili and Selleri (2000) constrains\nthe relevant models to have an asymmetry within a range\n(PSmax to PSmin; see Fig. 17.5.8 and Section 17.5.3.1). If\nthe data fall within this range, a null deviation is assigned;\notherwise, the nearest boundary is treated as the PS pre-\ndiction. Even with this conservative treatment, this class\nof models is disfavored at 5.1\u03c3. The discrepancy with data\nis concentrated at \u2206t < 4.0 ps, where statistical uncer-\ntainty dominates. In summary the Belle results are consis-\ntent with a QM description of entangled neutral B meson\npairs created via \u03a5(4S) decay.\n17.5.4 Violation of CP , T , and CP T symmetries in\nB0 \u2212B0 mixing\nThe phenomenological description introduced in Sec-\ntion 10.1 of B0 \u2212B0 mixing with a 2 \u00d7 2 matrix e\ufb00ective\nHamiltonian already allows for the possibility of CP, T,\nand CPT symmetry violations. Section 17.5.4.1 discusses\nthe parameterization of the Hamiltonian including new\nvariables that represent the magnitudes of the symmetry\nviolations. In Section 17.5.4.2 we summarize the B Fac-\ntory measurements of these variables. In the case of CPT\nviolation, one would expect on general grounds that viola-\ntion of Lorentz invariance would also occur; an extended\nformalism is required to treat this consistently. Such an\napproach, and the B Factory analysis taking this into ac-\ncount, are presented in Section 17.5.5.\nThe CP symmetry violations discussed in this section\npertain to CP violation in mixing.60 These di\ufb00er from\nasymmetries due to mixing-induced CP violation that re-\nsult from non-trivial values of the angles of the Unitarity\nTriangle, \u03c61, \u03c62, and \u03c63, discussed in Sections 17.6\u201317.8.\nThe recent observation of T violation by BABAR (Lees,\n2012m) is discussed in Section 17.6. The large observed T\nasymmetry is expected in the Standard Model and can be\nunderstood as a consequence of the CKM phase. If CPT\nsymmetry is conserved, there is a direct correspondence\nbetween the T asymmetry resulting from the CKM phase\nand the magnitude of the corresponding CP asymmetry\n(here sin 2\u03c61). As such one could call this violation of T\nsymmetry mixing-induced T violation. In this section we\ndiscuss searches for T violation in mixing.\n17.5.4.1 Parameterization of mixing with CP, T, CPT\nviolation\nThe e\ufb00ective Hamiltonian of B0 \u2212B0 mixing, He\ufb00= M\u2212\ni\u0393/2, de\ufb01ned in Eq. (10.1.1), is completely described by\nonly eight independent real quantities. Four of them are\nthe masses and decay rates of the eigenstates. These four\nquantities are su\ufb03cient to describe the B0\u2212B0 oscillations\nexpected in the Standard Model accurately enough for the\nsensitivity of the B Factories.\nTo allow for CP, T and CPT-violating e\ufb00ects in mix-\ning, it is necessary to extend the treatment presented in\n60 For a brief overview of the types of CP violation relevant\nfor B mesons see Section 16.6.\n\n293\nSection 10.1; there are many di\ufb00erent conventions in the\nliterature. For consistency with B Factory papers we fol-\nlow the notation of Aubert (2004f).\nThe quantity q/p (Eq. 10.1.3) is given by\nq\np \u2261\ns\nM \u2217\n12 \u2212i\n2\u0393 \u2217\n12\nM12 \u2212i\n2\u039312\n.\n(17.5.33)\nIts magnitude is expected to be very close to unity:\n\f\f\f\f\nq\np\n\f\f\f\f\n2\n\u22481 \u2212Im\n\u0012 \u039312\nM12\n\u0013\n.\n(17.5.34)\nIf |q/p| \u22121 di\ufb00ers from zero, CP and T symmetries are\nbroken, but CPT symmetry can still hold. In the Stan-\ndard Model, |q/p| \u22121 is small because |\u039312| \u226a|M12|\nand because Im(\u039312/M12) is suppressed with respect to\n|\u039312/M12|. The size of this suppression is (m2\nc \u2212m2\nu)/m2\nb \u2248\n0.1. The suppression re\ufb02ects the fact that CP violation is\nnot possible if two of the quark masses are identical. In\nthat case one could rede\ufb01ne the quark states such that\none of them does not mix with the other two, and mixing\nbetween two quark generations is insu\ufb03cient to allow for\nCP violation. The phase of q/p is convention-dependent\nand unobservable.61 Therefore, the physics of He\ufb00is de-\ntermined by only seven real parameters.\nTo allow for CPT-violating e\ufb00ects in mixing, we intro-\nduce the complex parameter\nz \u2261\u03b4m \u2212i\n2\u03b4\u0393\n\u2206m \u2212i\n2\u2206\u0393 ,\n(17.5.35)\nwhere \u03b4m \u2261M11 \u2212M22 and \u03b4\u0393 \u2261\u039311 \u2212\u039322 are the\ndi\ufb00erences of the diagonal terms of He\ufb00. If z \u0338= 0 CP\nand CPT symmetries are broken, but T symmetry can be\nconserved. In the Standard Model, z is zero.62\nWith\nthese\nde\ufb01nitions,\nthe\nmass\neigenstates\nof\nEq. (10.1.2) are replaced by\n|B1,2\u27e9= p\n\u221a\n1 \u2213z\n\f\fB0\u000b\n\u00b1 q\n\u221a\n1 \u00b1 z\n\f\fB0\u000b\n,\n(17.5.36)\n61 In addition, di\ufb00erent conventions for the sign of the phase\nof q/p are used in the literature. Here we set the phase of q/p\nusing Eqs (10.1.3) and (17.5.33). The convention in Aubert\n(2004f) di\ufb00ers by ei\u03c0 = \u22121. As a result their Eqs (9) and (10)\nhave a negative sign in front of the\n\u221a\n1 \u2212z2 term relative to our\nEq. (17.5.37). The same comment applies to Eq. (12.30) of the\n2013 PDG review on CP violation in meson decays (Beringer\net al., 2012), where the phase of q/p is not explicitly stated.\nOur expressions otherwise agree with those of Aubert (2004f).\n62 In Hastings (2003), Belle uses a di\ufb00erent parameteriza-\ntion, following Mohapatra, Satpathy, Abe, and Sakai (1998),\nbased on complex parameters \u03b8 and \u03c6. The relationship be-\ntween these and several other notations is discussed by Kost-\neleck\u00b4y (2001): in particular, cos \u03b8 = \u2212z = \u03be, and | exp(i\u03c6)| =\n|q/p| = w, where \u03be (complex) and w (real) are the param-\neters preferred by Kosteleck\u00b4y. While we rely heavily on this\nand related references in the Lorentz-violation discussion below\n(Section 17.5.5), we use the notation of Eq. (17.5.35) through-\nout. In neutral kaon mixing, CPT violation is described by\n\u03b4K = \u2212z/2.\nand the time-evolved states given in Eq. (10.1.6) are re-\nplaced by\n|B0(t)\u27e9= [f+(t) + zf\u2212(t)]\n\f\fB0\u000b\n+\np\n1 \u2212z2 q\npf\u2212(t)\n\f\fB0\u000b\n,\n|B0(t)\u27e9= [f+(t) \u2212zf\u2212(t)]\n\f\fB0\u000b\n+\np\n1 \u2212z2 p\nq f\u2212(t)\n\f\fB0\u000b\n,\n(17.5.37)\nwhere the functions f\u00b1(t) are de\ufb01ned in Eq. (10.1.7). In\nSection 17.5.2.6, Eq. (17.5.26), we have already introduced\na non-zero \u2206\u0393d in the time-dependent decay rate of B me-\nson pairs from \u03a5(4S) decays. We extend this expression to\ninclude the CP, T, and CPT-violating parameters de\ufb01ned\nabove:\nN(\u2206t) \u221de\u2212\u0393 |\u2206t| \u00d7\n\u001a1\n2c+ cosh(\u2206\u0393d\u2206t/2) + 1\n2c\u2212cos(\u2206md\u2206t)\n\u2212Re(s) sinh(\u2206\u0393d\u2206t/2) + Im(s) sin(\u2206md\u2206t)\n\u001b\n,\n(17.5.38)\nwhere\nc\u00b1 = |a+|2 \u00b1 |a\u2212|2,\ns = a\u2217\n+a\u2212.\n(17.5.39)\nThe complex expressions a\u00b1 depend on the decay ampli-\ntudes for a set of speci\ufb01c \ufb01nal states of Btag and Brec and\non the symmetry-violating parameters q/p and z:\na+ = \u2212AtagArec + AtagArec,\na\u2212=\np\n1 \u2212z2\n\u0014p\nq AtagArec \u2212q\npAtagArec\n\u0015\n+z\n\u0002\nAtagArec + AtagArec\n\u0003\n.\n(17.5.40)\nThe amplitudes Atag (Arec) and Atag (Arec) represent the\ncases where Btag (Brec) is reconstructed, respectively, as\na B0 or a B0.\nWe can write Eq. (17.5.38) explicitly for the cases\nwhere the \ufb02avors of the two B mesons from a \u03a5(4S) decay\nare reconstructed as B0B0, B0B0, or B0B0:63\nN BB \u221de\u2212|\u2206t|/\u03c4\n2\n\f\f\f\f\np\nq\n\f\f\f\f\n2 (\ncosh\n\u0012\u2206\u0393\u2206t\n2\n\u0013\n\u2212cos(\u2206md\u2206t)\n)\nN BB \u221de\u2212|\u2206t|/\u03c4\n2\n\f\f\f\f\nq\np\n\f\f\f\f\n2 (\ncosh\n\u0012\u2206\u0393\u2206t\n2\n\u0013\n\u2212cos(\u2206md\u2206t)\n)\nN BB \u221de\u2212|\u2206t|/\u03c4\n2\n(\ncosh\n\u0012\u2206\u0393\u2206t\n2\n\u0013\n+ 2Re(z) sinh\n\u0012\u2206\u0393\u2206t\n2\n\u0013\n63 In Eqs (17.5.41)\u2013(17.5.43) we assume that the B transition\nto a \ufb02avor eigenstate f has a single weak amplitude Af and\nthat the B decay does not violate CPT symmetry, i.e. Af =\nAf. We also assume that the amplitude for the B decay to the\nCP conjugate \ufb01nal state is zero, i.e. Af = Af = 0.\n\n294\n+ cos(\u2206md\u2206t) \u22122Im(z) sin(\u2206md\u2206t)\n)\n;\n(17.5.41)\nhere we have ignored terms quadratic in z. The \ufb01rst (sec-\nond) B in the superscript denotes the \ufb02avor of Btag (Brec).\nIf one of the B mesons decays through a b \u2192(cc)s\ntransition to a CP eigenstate BCP such as J/\u03c8K0\nS or J/\u03c8K0\nL,\nand the other B meson decays to a \ufb02avor state (B0 or B0),\nthe time-dependent decay rates are given by\nN BBCP \u221de\u2212|\u2206t|/\u03c4\n2\n\u00d7\n(\n[1 \u2213Re(z) cos 2\u03c61 \u2213Im(z) sin 2\u03c61] cosh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n+ [\u00b1Re(z) cos 2\u03c61 \u00b1 Im(z) sin 2\u03c61] cos(\u2206md\u2206t)\n+ [\u2213cos 2\u03c61 + Re(z)] sinh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n+ [\u00b1 sin 2\u03c61 \u2212Im(z)] sin(\u2206md\u2206t)\n)\n,\n(17.5.42)\nN BBCP \u221de\u2212|\u2206t|/\u03c4\n2\n\u00d7\n(\n[1 \u00b1 Re(z) cos 2\u03c61 \u2213Im(z) sin 2\u03c61] cosh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n+ [\u2213Re(z) cos 2\u03c61 \u00b1 Im(z) sin 2\u03c61] cos(\u2206md\u2206t)\n+ [\u2213cos 2\u03c61 \u2212Re(z)] sinh\n\u0012\u2206\u0393d\u2206t\n2\n\u0013\n+ [\u2213sin 2\u03c61 + Im(z)] sin(\u2206md\u2206t)\n)\n,\n(17.5.43)\nwhere the upper (lower) sign in front of terms with cos 2\u03c61\nor sin 2\u03c61 represents \ufb01nal states with \u03b7CP = \u22121 (+1). In\nEqs (17.5.42) and (17.5.43), we assume |q/p| = 1.\nThe decay rates de\ufb01ned in Eqs (17.5.41)\u2013(17.5.43) can\nbe used to construct asymmetries sensitive to T, CP, and\nCPT violation. The same-\ufb02avor asymmetry AT/CP be-\ntween the two oscillation probabilities P(B0 \u2192B0) and\nP(B0 \u2192B0) depends on |q/p| and probes both T and CP\nsymmetries:\nAT/CP = P(B0 \u2192B0) \u2212P(B0 \u2192B0)\nP(B0 \u2192B0) + P(B0 \u2192B0)\n= N BB \u2212N BB\nN BB + N BB\n= 1 \u2212|q/p|4\n1 + |q/p|4 .\n(17.5.44)\nThe opposite-\ufb02avor asymmetry, ACP T/CP , depends on\nz and probes both CP and CPT symmetries. De\ufb01ning the\ndecay-time di\ufb00erence for such events as \u2206t = t+ \u2212t\u2212,\nwhere t+ (t\u2212) corresponds to B0 (B0), the asymmetry\nACP T/CP (\u2206t; \u2206t > 0)\n= P(B0 \u2192B0) \u2212P(B0 \u2192B0)\nP(B0 \u2192B0) + P(B0 \u2192B0)\n= N BB(\u2206t) \u2212N BB(\u2212\u2206t)\nN BB(\u2206t) + N BB(\u2212\u2206t)\n\u22432Im(z) sin(\u2206md\u2206t) \u2212Re(z) sinh(\u2206\u0393d\u2206t/2)\ncos(\u2206md\u2206t) + cosh(\u2206\u0393d\u2206t/2)\n\u22432Im(z) sin(\u2206md\u2206t) \u2212Re(z)\u2206\u0393d\u2206t\ncos(\u2206md\u2206t) + cosh(\u2206\u0393d\u2206t/2)\n,\n(17.5.45)\nwhere the approximation in the third line is the neglect of\nterms of higher order in z; in the fourth line, as |\u2206\u0393d/\u0393| \u226a\n1, we take sinh(\u2206\u0393d\u2206t/2) \u2243\u2206\u0393d\u2206t/2.\nBy comparing the rates of a B versus a B decaying to\na CP eigenstate, we can de\ufb01ne another asymmetry that is\nsensitive to z using Equations (17.5.42) and (17.5.43):\nA\u2032\nCP T/CP (\u2206t) = P(B0 \u2192BCP ) \u2212P(B0 \u2192BCP )\nP(B0 \u2192BCP ) + P(B0 \u2192BCP )\n= N BBCP (\u2206t) \u2212N BBCP (\u2206t)\nN BBCP (\u2206t) + N BBCP (\u2206t)\n\u2243{\u00b1Re(z) cos 2\u03c61[\u22121 + cos(\u2206md\u2206t)]\n+[\u00b1 sin 2\u03c61 \u22122Im(z)] sin(\u2206md\u2206t)}/\n{1 \u00b1 Im(z) sin 2\u03c61[\u22121 + cos(\u2206md\u2206t)]\n\u2213cos 2\u03c61\u2206\u0393d\u2206t/2}.\n(17.5.46)\nIn the last step we have again neglected terms of higher\nthan linear order in z and \u2206\u0393d, and the upper (lower)\nsign in front of terms with cos 2\u03c61 or sin 2\u03c61 refers to \ufb01nal\nstates with \u03b7CP = \u22121 (+1).\nIn the expressions of the decay rates (Eqs 17.5.41\u2013\n17.5.43) and associated asymmetries (Eqs 17.5.44\u201317.5.46)\nwe have assumed that a B \ufb02avor state can unambigu-\nously be identi\ufb01ed by its decay products. In the quark\nmodel, this is true for semi-leptonic decays. For hadronic\nB decays to \ufb02avor \ufb01nal states, however, the presence of\ndoubly-CKM-suppressed decays (DCS) makes it impossi-\nble to determine the original \ufb02avor of the B meson with-\nout ambiguity. Accounting for DCS decays leads to more\ncomplicated expressions for c\u00b1, s, and the resulting decay\nrates and asymmetries. A complete list of general expres-\nsions of c\u00b1 and s can be found in Aubert (2004f).\nIn the SM the asymmetry AT/CP is expected to be\nvery small (Beneke, Buchalla, Lenz, and Nierste, 2003;\nCiuchini, Franco, Lubicz, Mescia, and Tarantino, 2003). A\nrecent calculation predicts AT/CP = (\u22120.40\u00b10.06)\u00d710\u22123\nor correspondingly |q/p| \u22121 = (0.20 \u00b1 0.03) \u00d7 10\u22123 (Nier-\nste, 2012). A measurement signi\ufb01cantly di\ufb00erent from\nzero with the data samples of the B Factories would\nbe evidence for new physics. In the Standard Model\nCPT symmetry is conserved and Re(z) and Im(z) as\nwell as ACP T/CP are expected to be zero. The asym-\nmetry A\u2032\nCP T/CP reduces to the CP-violating, but CPT-\nconserving asymmetry, \u2212\u03b7CP sin 2\u03c61 sin(\u2206md\u2206t). It is a\nmeasurement of mixing-induced CP violation.\n\n295\n17.5.4.2 Results on CP, T and CPT violation in B0 \u2212B0\nmixing\nBABAR and Belle published several papers on searches for\nviolation of T, CP, and CPT symmetries in B0 \u2212B0 mix-\ning. The analyses are performed with inclusive dilepton\n\ufb01nal states or fully-reconstructed hadronic and semilep-\ntonic \ufb01nal states. Here we review the measurements of\n|q/p| \u22121, Re(z), and Im(z).\nMeasurements of |q/p| \u22121\nEarlier measurements of the asymmetry AT/CP have been\nperformed by CLEO (Behrens et al., 2000; Ja\ufb00e et al.,\n2001), ALEPH (Barate et al., 2001), and OPAL (Abbi-\nendi et al., 2000b; Ackersta\ufb00et al., 1997a) before the B\nFactories took their data. In the 2002 Review of Particle\nPhysics (Hagiwara et al., 2002) the PDG calculated an\naverage64 of AT/CP = (0 \u00b1 16) \u00d7 10\u22123 corresponding to a\nvalue of |q/p| \u22121 = (0 \u00b1 8) \u00d7 10\u22123.\nBABAR and Belle both measure |q/p| \u22121 with inclu-\nsive samples of semileptonic B0 decays. In these events\nonly the two leptons from semileptonic decays B \u2192Xl\u03bd\n(l = e, \u00b5) are reconstructed. The charge of the lepton\nl+ (l\u2212) unambiguously identi\ufb01es the \ufb02avor of the par-\nent B meson to be a B0 (B0). The asymmetry between\nthe numbers of same-sign dilepton pairs, N BB = N(l+l+)\nand N BB = N(l\u2212l\u2212), is related to the two oscillation\nprobabilities P(B0 \u2192B0) and P(B0 \u2192B0) as given\nin Eq. (17.5.44). Although AT/CP is a time-independent\nasymmetry, both experiments use the decay time di\ufb00er-\nence \u2206t between the two B decays to discriminate signal\nevents from background.\nBABAR and Belle measure |q/p|\u22121 in samples of 211 fb\u22121\n(Aubert, 2006aq) and 78 fb\u22121 (Nakano, 2006), respectively.\nThe BABAR result supersedes an earlier measurement with\n21 fb\u22121 (Aubert, 2002i). The event selections in these anal-\nyses are similar to the ones for measurements of \u2206md with\ndilepton events described above (see Section 17.5.2.2), but\nwith attention to keeping charge-dependent asymmetries\nin reconstruction and PID e\ufb03ciencies small and under\ncontrol. Events with two identi\ufb01ed leptons in a momen-\ntum range (0.8 GeV/c (BABAR) or 1.2 GeV/c (Belle) <\np\u2217< 2.3 GeV/c) and with topology consistent with that\nof semileptonic B decays are selected. Leptons that orig-\ninate from photon conversions in the detector or from\nJ/\u03c8 and \u03c8(2S) decays are explicitly vetoed. Both experi-\nments carefully determine detector-induced charge asym-\nmetries in their lepton identi\ufb01cation (Chapter 5). BABAR\nuses a control sample of radiative Bhabha events and Belle\nuses two photon production of e+e\u2212to study electron\nID asymmetries. The charge asymmetry in muon ID is\ndetermined with e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3 events by BABAR and\n64 The PDG quotes Re(\u03f5B)/(1+|\u03f5B|2) = (0\u00b14)\u00d710\u22123, where\n\u03f5B = (p\u2212q)/(p+q) corresponds to the parameter \u03f5K describing\nthe corresponding asymmetry in the neutral kaon system and\nAT/CP \u22484Re(\u03f5B)/(1 + |\u03f5B|2) for small AT/CP .\nT/CP\nA\n-0.04\n-0.02\n0\n0.02\n0.04\n(a)\n t| (ps)\n\u2206\n |\n0\n2\n4\n6\n8\n10\n12\n14\nCPT/CP\nA\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n(b)\nFigure 17.5.10. The measured asymmetries (a) AT/CP and\n(b) ACP T/CP from inclusive dilepton events, as functions of\n|\u2206t| (Aubert, 2006aq). The deviation from zero in AT/CP is a\nresult of background from cascade muons that is dominant at\nsmall |\u2206t|.\nwith events in which a simulated muon track is embed-\nded in a hadronic event by Belle. Hadron fake rates are\ndetermined with pions from K0\nS \u2192\u03c0+\u03c0\u2212, kaons from\nD\u2217+ \u2192D0\u03c0+\ns\n\u2192(K\u2212\u03c0+)\u03c0+\ns (BABAR) and from \u03c6 \u2192\nK+K\u2212(Belle), and protons from \u039b \u2192p\u03c0\u2212. The dis-\ntance between the two B decay vertices \u2206z is measured\nas described in Section 17.5.2.2. BABAR \ufb01ts the \u2206t dis-\ntributions of the l+l+ and l\u2212l\u2212events and randomly as-\nsigns the sign of \u2206t for each event. Belle \ufb01ts the \u2206z =\nz1 \u2212z2 distribution, where z1 (z2) is the z coordinate of\nthe higher- (lower-) momentum lepton. The majority of\nthe events are events where both leptons originate from\na B decay. BABAR distinguishes background from events\nin which one lepton is a primary lepton from a B decay\nand the other lepton comes from a secondary charm de-\ncay (b \u2192c \u2192l), events with one direct lepton and one\nlepton from a tau (b \u2192\u03c4 \u2192l) or charmonium (b \u2192\n(cc) \u2192l) cascade decay, and events from the light quark\ne+e\u2212\u2192qq continuum. Belle subtracts the contribution\nfrom light quark continuum candidates to their dilepton\nsample. The background events from BB decays are sep-\narated into correctly tagged and wrongly tagged events.\nThe wrongly tagged sample is dominated by events where\none lepton is from a primary B decay and the other one\nfrom a cascade charm decay. The correctly tagged back-\nground sample consists mainly of events in which both lep-\ntons come from secondary charm decays. BABAR extracts\n|q/p|\u22121 from a binned likelihood \ufb01t to the \u2206t distribution\nof the selected dilepton sample.65 The likelihood function\n65 In the same analysis BABAR measures the CP- and CPT-\nviolating parameter z (see below). They employ a simultaneous\n\n296\ncombines detector-related charge asymmetries and time-\ndependent p.d.f.s for signal and background events. The\nmeasured asymmetry AT/CP as a function of |\u2206t| is shown\nin Fig. 17.5.10. Belle determines a raw dilepton asymme-\ntry from their selected events as a function of \u2206z, applies\na bin-wise background correction, and calculates an aver-\nage AT/CP in a range 0.15 mm < |\u2206z| < 2 mm. BABAR\nmeasures |q/p| \u22121 = (\u22120.8 \u00b1 2.7 \u00b1 1.9) \u00d7 10\u22123 and Belle\nmeasures AT/CP = (\u22121.1 \u00b1 7.9 \u00b1 8.5) \u00d7 10\u22123, which cor-\nresponds to |q/p| \u22121 = (0.5 \u00b1 4.0 \u00b1 4.3) \u00d7 10\u22123. The\nlargest contributions to the systematic error in the BABAR\nmeasurement come from potential charge asymmetries in\ntrack reconstruction (1.0 \u00d7 10\u22123) and electron identi\ufb01ca-\ntion (1.0 \u00d7 10\u22123). Belle\u2019s systematic error in |q/p| \u22121 is\ndominated by potential charge asymmetries in the track\n\ufb01nding e\ufb03ciency (2.6\u00d710\u22123) and uncertainties in the con-\ntinuum background subtraction (2.4 \u00d7 10\u22123).\nBABAR also measures |q/p| \u22121 in an analysis of fully-\nreconstructed B decays to hadronic \ufb01nal states in a sample\nof 88 \u00d7 106 BB pairs (Aubert, 2004e,f). One B is recon-\nstructed either in a \ufb02avor state or a CP eigenstate. In the\nsame analysis BABAR measures \u2206\u0393d (Section 17.5.2.6) and\nthe CP and CPT-violating parameters Re(z) and Im(z)\n(Section 17.5.4.2) from the \u2206t distributions of the selected\nevents. The sensitivity to |q/p| \u22121 comes from events in\nwhich both B mesons have the same \ufb02avor. Because the\nbranching fractions to exclusive \ufb02avor states are much\nsmaller than the inclusive semileptonic branching frac-\ntion, the signal sample is comparatively small compared to\nevent samples in the dilepton analyses. From the analysis\nof fully-reconstructed hadronic \ufb01nal states BABAR quotes\n|q/p| \u22121 = (29 \u00b1 13 \u00b1 11) \u00d7 10\u22123.\nThe average of the measurements of |q/p| \u22121 pub-\nlished by the B Factories is (0.3 \u00b1 2.8) \u00d7 10\u22123 (see Ta-\nble 17.5.3). While we were \ufb01nishing the writing of this\nBook, BABAR submitted another measurement of |q/p|\u22121\nfor publication (Lees, 2013g). In that analysis one B me-\nson is reconstructed as B0 \u2192D\u2217\u2212l+\u03bdl (and the D\u2217\u2212is\npartially-reconstructed using only the slow pion) and the\n\ufb02avor of the other is tagged with a charged kaon. The\nvalue of |q/p| \u22121 = (0.29 \u00b1 0.84+1.88\n\u22121.61) \u00d7 10\u22123 measured\nin this analysis represents the most precise single mea-\nsurement of |q/p| \u22121 by the B Factories. However, due\nto the overlap of events used in this analysis with those\nused for the |q/p| \u22121 measurement in Aubert (2006aq),\na simple average could not be calculated for this Book.\nThe PDG in their 2013 partial update of the Review of\nParticle Physics quotes a world average of Re(\u03f50\nB)/(1 +\n|\u03f50\nB|2 = (0.6 \u00b1 0.7) \u00d7 10\u22123 corresponding to |q/p| \u22121 =\n(\u22121.2 \u00b1 1.4) \u00d7 10\u22123 (Beringer et al., 2012), which in-\ncludes two recent measurements from D\u00d8 corresponding\nto |q/p| \u22121 = (0.6 \u00b1 2.6) \u00d7 10\u22123 (Abazov et al., 2011) and\n|q/p|\u22121 = (\u22123.4\u00b12.2\u00b10.8)\u00d710\u22123 (Abazov et al., 2012).\nThere has been signi\ufb01cant interest in the measurement\nof |q/p| or the corresponding asymmetry AT/CP since D\u00d8\nannounced evidence for an anomalous like-sign dimuon\n\ufb01t to both same-sign and opposite-sign dilepton pairs to deter-\nmine the \u2206t resolution in addition to the symmetry-violating\nparameters.\nTable 17.5.3. B Factory measurements of |q/p| \u22121 along\nwith the journal paper and selected \ufb01nal state for each mea-\nsurement. The measurement in Aubert (2002i) has been su-\nperseded by Aubert (2006aq) and is not included in the B\nFactories average.\nExperiment\nMethod\n|q/p| \u22121 [10\u22123]\nBABAR (Aubert, 2006aq) Incl. dilepton \u22120.8 \u00b1 2.7 \u00b1 1.9\nBABAR (Aubert, 2002i)\nIncl. dilepton\n\u22122 \u00b1 6 \u00b1 7\nBABAR (Aubert, 2004e,f) Hadr. modes\n29 \u00b1 13 \u00b1 11\nBelle (Nakano, 2006)\nIncl. dilepton\n0.5 \u00b1 4.0 \u00b1 4.3\nBABAR-Belle average\n0.3 \u00b1 2.8\ncharge asymmetry in pp collisions (Abazov et al., 2010a,b).\nThe asymmetry Ab\nsl is de\ufb01ned similarly to Eq. (17.5.44),\nbut has contributions from the charge asymmetries of B0\nd\nmesons (AT/CP ) and B0\ns mesons (As\nT/CP ):\nAb\nsl = CdAT/CP + CsAs\nT/CP\n(17.5.47)\nwith Cd = 0.594 \u00b1 0.022, Cs = 0.406 \u00b1 0.022 (Abazov\net al., 2011). With their latest measurement of Ab\nsl =\n(\u22127.87 \u00b1 1.72 \u00b1 0.93) \u00d7 10\u22123 D\u00d8 claims a 3.9\u03c3 discrep-\nancy with the Standard Model prediction of Ab\nsl(SM) =\n(\u22120.28+0.05\n\u22120.06) \u00d7 10\u22123 (Abazov et al., 2011). However, no\nsigni\ufb01cant measurement has yet been observed in either\nAT/CP or As\nT/CP . The world average for |q/p| \u22121 corre-\nsponds to AT/CP = (2.4 \u00b1 2.8) \u00d7 10\u22123. Based on two D\u00d8\nmeasurements HFAG calculates the corresponding average\nfor B0\ns mesons of As\nT/CP = (\u221211\u00b16)\u00d710\u22123 (Amhis et al.,\n2012). It is important to improve the measurements of\nAT/CP or As\nT/CP to understand if there is CP and T viola-\ntion in the mixing of B0\nd or B0\ns mesons or both. LHCb is ex-\npected to improve the measurement of As\nT/CP in the near\nfuture. The B Factories have only analyzed fractions of\ntheir full datasets for |q/p|. Some improvement in AT/CP\nwill be possible by using more data, but systematic un-\ncertainties are already of comparable size to the statistical\nerrors. LHCb may be able to reduce the error in AT/CP us-\ning fully-reconstructed semileptonic B0 decays similar to\nthe D\u00d8 analysis described in (Abazov et al., 2012). The\nlarge data set of a future super \ufb02avor factory paired with\nanalyses of fully-reconstructed semi-leptonic decays could\nsubstantially reduce the overall uncertainty in AT/CP .\nMeasurements of Re(z) and Im(z)\nPrior to the B Factories a search for CPT violation in\nB0 \u2212B0 mixing was performed by the OPAL collabora-\ntion (Ackersta\ufb00et al., 1997a). They quote their result in\nterms of the CPT parameter \u03b4B, a variable with a de\ufb01ni-\ntion equivalent to \u03b4K, which is used to characterize CPT\nviolation in kaon mixing (Beringer et al., 2012). OPAL\u2019s\nresult Im(\u03b4B) = \u22120.020 \u00b1 0.016 \u00b1 0.006 corresponds to\n\n297\nRe(z) = +0.28\nNominal fit\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\n\u2206t [ps]\nDeviation of asymmetries\n0.2\n0\n\u22120.2\n\u22120.4\n0.4\n(a) B\n0\n0\nJ/\u03c8KS decay\nRe(z) = +0.28\nNominal fit\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\n\u2206t [ps]\n0.2\n0\n\u22120.2\n\u22120.4\n0.4\nDeviation of asymmetries\n(b) B\n0\n0\nJ/\u03c8KL decay\n\u22126\n\u22124\n\u22122\n0\n2\n4\n6\n\u2206t [ps]\n0.2\n0.1\n0\n\u22120.1\n\u22120.2\nIm(z) = \u22120.03\nNominal fit\nDeviation of asymmetries\n(c)\nB decays\nFlavor-specific\nFigure 17.5.11. Deviations of the asymmetries from the reference asymmetry [Re(z) = Im(z) = \u2206\u0393d/\u0393d = 0] in fully-\nreconstructed hadronic and semileptonic \ufb01nal states (Higuchi, 2012). Shown are raw asymmetries uncorrected for backgrounds,\n\ufb02avor mis-tagging, and \u2206t resolution. The underlying asymmetries for (a) and (b) corresponding to \u03b7CP = \u22121 and +1, respec-\ntively, are given by Eq. (17.5.46). The asymmetry tested in (c) is given in Eq. (17.5.45). The crosses with error bars are data.\nThe solid curves are deviations for the nominal \ufb01ts. The dashed curves are for illustration only: they represent scenarios where\neither Re(z) = +0.28 or Im(z) = \u22120.03. These values are equal to approximately 5\u00d7 the total uncertainty of the corresponding\nparameter.\nIm(z) = 0.040 \u00b1 0.032 \u00b1 0.012. The world averages for the\nreal and imaginary parts of \u03b4K determined from kaon ex-\nperiments are Re(\u03b4K) = (2.5 \u00b1 2.3) \u00d7 10\u22124 and Im(\u03b4K) =\n(\u22121.5\u00b11.6)\u00d710\u22125 (Beringer et al., 2012). The correspond-\ning limit on the mass di\ufb00erence between K0 and K0 nor-\nmalized to the mass average is |mK0 \u2212mK0|/maverage <\n6 \u00d7 10\u221219, assuming \u0393K0 = \u0393K0.\nBABAR and Belle have studied samples of inclusive\ndilepton events and fully-reconstructed hadronic and se-\nmileptonic events to measure Re(z) and Im(z) in B0 \u2212B0\nmixing. In dilepton events the \u2206t distribution of opposite-\nsign dilepton pairs has been used to search for violation of\nCP and CPT asymmetry. The asymmetry ACP/CP T be-\ntween events with positive and negative true \u2206t is re-\nlated to the two oscillation probabilities P(B0 \u2192B0) and\nP(B0 \u2192B0) as given in Eq. (17.5.45). Here the decay-\ntime di\ufb00erence is de\ufb01ned as \u2206t = t+ \u2212t\u2212, where t+ (t\u2212)\ncorresponds to l+ (l\u2212).\nBABAR measures the CP- and CPT-violating param-\neters Re(z) and Im(z) with opposite-sign dilepton pairs\nin a sample of 211 fb\u22121 (Aubert, 2006aq). The selection\ncriteria are the same as for the measurement of |q/p| \u2212\n1 with same-sign dilepton pairs in the same paper (see\nabove). The parameter Im(z) appears as coe\ufb03cient to the\nsin(\u2206md\u2206t) term in the \u2206t distribution of opposite-sign\ndilepton pairs N BB given by Eq. (17.5.41) and the cor-\nresponding asymmetry ACP T/CP of Eq. (17.5.45). Thus a\nmeasurement of the shape of the \u2206t distribution is sensi-\ntive to Im(z). On the other hand, sensitivity to Re(z) only\ncomes from the sinh(\u2206\u0393d\u2206t/2) term. Since \u2206\u0393d is a small\nquantity and has not been measured, BABAR substitutes\nsinh(\u2206\u0393d\u2206t/2) \u2243\u2206\u0393d\u2206t/2 and quotes only the product\n\u2206\u0393d \u00d7 Re(z) in their paper. In the cosh(\u2206\u0393d\u2206t/2) term\nthey use |\u2206\u0393d| = (5 \u00b1 3) \u00d7 10\u22123 ps\u22121. Although BABAR\n\ufb01ts the \u2206t distributions of the same-sign and opposite-\nsign dilepton pairs in a single \ufb01t, they do not constrain\nthe ratio between the numbers of events of the two types.\nBABAR quotes Im(z) = (\u221213.9 \u00b1 7.3 \u00b1 3.2) \u00d7 10\u22123 and\n\u2206\u0393d \u00d7Re(z) = (\u22127.1\u00b13.9\u00b12.0)\u00d710\u22123 ps\u22121. The statis-\ntical correlation between the measurements of Im(z) and\n\u2206\u0393d \u00d7 Re(z) is 76%. The systematic errors in Im(z) and\n\u2206\u0393d \u00d7 Re(z) are dominated by uncertainties in the p.d.f.\nmodeling (2.5\u00d7 and 1.2 \u00d7 10\u22123), the external parameters\n\u03c4B0, \u03c4B\u2212, \u2206md, and \u2206\u0393d (1.9\u00d7 and 1.1 \u00d7 10\u22123) and SVT\nalignment (0.6\u00d7 and 1.2 \u00d7 10\u22123). Assuming \u2206\u0393d = 0,\nBABAR obtains Im(z) = (\u22123.7 \u00b1 4.6 \u00b1 2.9) \u00d7 10\u22123. The\nmeasured asymmetry AT/CP as a function of |\u2206t| is shown\nin Fig. 17.5.10.\nBelle\u2019s results on Re(z) and Im(z) with 29.4 fb\u22121 of\ndata are published in Hastings (2003). The analysis uses\nthe same selection criteria as in their measurement of \u2206md\nwith dilepton pairs (see Section 17.5.2.2) that is described\nin the same paper. A major di\ufb00erence to the BABAR anal-\nysis is that Belle constrains the time-integrated fractions\nof same-sign and opposite sign events to\n\u03c7d =\n|1 \u2212z2|x2\nd\n|1 \u2212z2|x2\nd + 2 + x2\nd + |z|2x2\nd\n,\n(17.5.48)\nwhere xd = \u03c4B0\u2206md. N BB (N BB, N BB) is proportional\nto opposite-sign (same-sign) dilepton e\ufb03ciency. Belle de-\ntermines the ratio of the e\ufb03ciencies from MC simulation.\nThey quote Re(z) = (0\u00b112\u00b11)\u00d710\u22122 and Im(z) = (\u22123\u00b1\n1 \u00b1 3) \u00d7 10\u22122. These measurements supersede the results\nfrom an earlier Belle paper (Abe, 2001b). The dominant\nsystematic uncertainties in Im(z) come from data/MC\nagreement of the \u2206t p.d.f. and the requirement that the\npolar angle of the lepton tracks be in the \ufb01ducial volume.\nThe largest contribution to the systematic error in Re(z)\ncomes from the MC-modeling of the \u2206t resolution.\n\n298\nTable 17.5.4. Measurements of Re(z) and Im(z) and, if given in the paper, the corresponding limits (at 90% C.L.) on the\nmass di\ufb00erence and width di\ufb00erence between B0 and B0. In Aubert (2006aq), BABAR measures \u2206\u0393d \u00d7 Re(z) = (\u22120.71 \u00b1 0.39 \u00b1\n0.20) \u00d7 10\u22122 ps\u22121, but does not quote a value for Re(z).\nExperiment\nMethod\nRe(z)\nIm(z)\n|\u03b4m/m|\n\u03b4\u0393/\u0393\n[10\u22122]\n[10\u22122]\n[10\u221214]\nBABAR (Aubert, 2006aq) Incl. dilepton\n\u2014\n\u22121.39 \u00b1 0.73 \u00b1 0.32\n\u2014\n\u2014\nBelle (Hastings, 2003)\nIncl. dilepton\n0.0 \u00b1 12 \u00b1 1\n\u22123 \u00b1 1 \u00b1 3\n< 1.16\n|\u03b4\u0393/\u0393| < 0.11\nBelle (Abe, 2001b)\nIncl. dilepton\n0 \u00b1 15 \u00b1 6\n\u22123.5 \u00b1 2.9 \u00b1 5.1\n< 1.6\n|\u03b4\u0393/\u0393| < 0.161\nBABAR (Aubert, 2004e,f) Hadronic\n2.0 \u00b1 5.1 \u00b1 4.9\n3.8 \u00b1 2.9 \u00b1 2.5\n< 1.0\n\u22120.156 < \u03b4\u0393/\u0393 < 0.042\nBelle (Higuchi, 2012)\nHadr. + semilep. 1.9 \u00b1 3.7 \u00b1 3.3 \u22120.57 \u00b1 0.33 \u00b1 0.33\n\u2014\n\u2014\nBABAR and Belle also measure Im(z) and Re(z) in\nsamples of fully-reconstructed hadronic and semi-leptonic\n\ufb01nal states. BABAR reconstructs B0 decays to the \ufb02a-\nvor \ufb01nal states D(\u2217)\u2212\u03c0+/\u03c1+/a+\n1 and J/\u03c8K\u22170 and CP-\neigenstates J/\u03c8K0\nS, \u03c8(2S)K0\nS, \u03c7c1K0\nS, and J/\u03c8K0\nL in 88\nmillion BB events (Aubert, 2004e,f). Belle reconstructs\nsignal events in the decays B0 \u2192D(\u2217)\u2212\u03c0+, D\u2217\u2212\u03c1+,\nD\u2217\u2212l\u03bd, J/\u03c8K0\nS, and J/\u03c8K0\nL in a sample of 535 million\nBB events (Higuchi, 2012). Raw asymmetries as function\nof \u2206t for J/\u03c8K0\nS, J/\u03c8K0\nL and \ufb02avor-speci\ufb01c \ufb01nal states\noverlaid with curves representing the nominal \ufb01t result\nand scenarios with signi\ufb01cant CPT violation are shown\nin Fig. 17.5.11. In addition to z both analyses also mea-\nsure \u2206\u0393d and |q/p|\u22121. These results are described above.\nThe measurements use the \u2206t reconstruction and \ufb02avor\ntagging methods of the standard time-dependent analy-\nses of the B Factories described in earlier Chapters (6, 8,\n10). The time-dependent p.d.f.s for events to \ufb01nal states\nthat contain a fully-reconstructed Brec identi\ufb01ed either\nas B0, B0, or BCP , and a Btag with identi\ufb01ed \ufb02avor as\nB0 or B0 are given in Eqs (17.5.42) and (17.5.43). How-\never, interference e\ufb00ects between the amplitudes for dom-\ninant decays of \ufb02avor-eigenstates (e.g. B0 \u2192D\u2212\u03c0+) and\nfor doubly-CKM-suppressed decays (e.g. B0 \u2192D+\u03c0\u2212)\nlead to more complicated p.d.f.s (Aubert, 2004f). These\ninterference e\ufb00ects are present when either Brec or Btag\nis reconstructed in a \ufb02avor state. In principle, the ratio of\nfavored and DCS decay amplitudes is di\ufb00erent for each\nmode. BABAR shows that an e\ufb00ective ratio can be de-\n\ufb01ned for ensembles of \ufb01nal states as long as terms lin-\near in |z|, |q/p| \u22121, and in the amplitude ratios of the\ncontributing modes can be neglected. Belle treats the ef-\nfects of DCS decays as part of the systematic error. The\ndominant contribution of Im(z) to the time-dependence\nis through the coe\ufb03cient of sin(\u2206md\u2206t) for \ufb02avor \ufb01-\nnal states, while Re(z) contributes primarily to the co-\ne\ufb03cients of the cosh(\u2206\u0393d\u2206t/2) \u22481 and cos(\u2206md\u2206t)\nterms for CP eigenstates. The main physics parameters\nextracted in BABAR\u2019s analysis are sgn(Re\u03bbCP ), \u2206\u0393d/\u0393d,\n|q/p|, Im(z), and (Re\u03bbCP /|\u03bbCP |)\u00d7Re(z). The parameters\n(Im\u03bbCP /|\u03bbCP |) and \u2206md are determined together with\nthe main parameters as cross checks against earlier mea-\nsurements. BABAR measures (Re\u03bbCP /|\u03bbCP |) \u00d7 Re(z) =\n0.014\u00b10.035\u00b10.034 and Im(z) = (3.8\u00b12.9\u00b12.5)\u00d710\u22122.\nUsing BABAR\u2019s measurement of sin 2\u03c61 (Im\u03bbCP ) on the\nsame data set (Aubert, 2005i) and assuming |\u03bbCP | = 1,\nwe calculate a value of Re(z) = (+2.0 \u00b1 5.1 \u00b1 4.9) \u00d7 10\u22122.\nBelle quotes the physics parameters Re(z) = (+1.9\u00b13.7\u00b1\n3.3)\u00d710\u22122 and Im(z) = (\u22125.7\u00b13.3\u00b13.3)\u00d710\u22123. The \ufb01t\nhas a twofold ambiguity in the sign of Re\u03bbCP . The sign of\nRe(z) has been determined assuming Re\u03bbCP > 0, which is\na result of global \ufb01ts of the Unitarity Triangle (see Section\n25.1). The largest systematic uncertainty in Re(z) comes\nfrom the knowledge of tag-side interference (0.028). The\nerror in Im(z) is dominated by uncertainties in vertex re-\nconstruction (0.0028).\nThe results of all Re(z) and Im(z) measurements by\nthe B Factories are summarized in Table 17.5.4. The mea-\nsurements are still mostly statistically limited and many of\nthe systematic uncertainties are statistical in nature. Us-\ning the full data sets will allow one to further improve the\nconstraints on these CP and CPT-violating parameters.\nFuture super \ufb02avor factories should be able to improve\ncurrent limits even further. How much they can improve\nwill depend on how well the systematic uncertainties can\nbe controlled.\n17.5.5 Lorentz invariance violation in B0 \u2212B0 mixing\nIf we go beyond a purely phenomenological treatment of\nCPT-violating e\ufb00ects, Lorentz violation should also be\nconsidered. CPT invariance follows from assumptions that\nare currently understood to hold in the low-energy (Stan-\ndard Model-like) domain: point particles, the applicability\nof quantum \ufb01eld theory, and in particular, Lorentz invari-\nance (Jost, 1957; Luders, 1954; Pauli, 1955; Streater and\nWightman, 2000). If CPT symmetry is broken, then one\nor more of these conditions must be violated.\nIn particle physics, Lorentz violation is usually studied\nin the framework of the Standard Model Extension. This\ntheory and its application to B mixing is brie\ufb02y reviewed\nin Section 17.5.5.1. We then describe the analysis carried\nout within this framework by BABAR (Section 17.5.5.2),\nand discuss the implications for work at future facilities\n(Section 17.5.5.3).\n\n299\n17.5.5.1 The Standard Model Extension and mixing\nSimplifying assumptions are required to make an e\ufb00ec-\ntive search for Lorentz violation in data. If we posit a\nfundamental theory whose dynamics are both CPT- and\nPoincar\u00b4e-invariant,66 and a low-energy e\ufb00ective theory that\nexhibits spontaneous CPT- and Lorentz-symmetry break-\ning, we obtain the so-called Standard Model Extension\n(SME) of Colladay and Kosteleck\u00b4y (1997, 1998); see also\nKosteleck\u00b4y (2004). In this theory nature remains invari-\nant under translations, and is covariant under changes\nin the inertial frame of the observer: the usual kinematic\nexpressions may consistently be used to analyse particle\nmotion, reconstruct invariant masses, and so on. How-\never under boosts of individual particles, CPT is broken\nand certain Lorentz-violating terms appear, due to the\n(constant) expectation values of one or more Lorentz ten-\nsors (cf. the mass terms due to particles coupling to the\n[scalar] Higgs \ufb01eld in the Standard Model). The Lorentz-\nviolating coe\ufb03cients due to these background \ufb01elds vary\nfrom particle to particle in general; the resulting param-\neters are similar in number to the supersymmetric cou-\nplings, and have been exhaustively tabulated, together\nwith current bounds from experimental and observational\ntests, by Kosteleck\u00b4y and Russell (2011). As neutral-meson\noscillation is \ufb02avor-changing, CPT-violation measurements\nin mixing provide access to couplings that are not con-\nstrained by other experimental tests (Kosteleck\u00b4y, 1998).\nFor a neutral meson, the Lorentz-violating parameters\nare given by the four-vector \u2206a\u00b5 \u2261rq1aq1\n\u00b5 \u2212rq2aq2\n\u00b5 , the dif-\nference in the couplings of the two valence quarks qi (Kost-\neleck\u00b4y, 2001; Kosteleck\u00b4y and Potting, 1995).67 These pa-\nrameters are constant in any inertial frame. We then \ufb01nd,\nfor the CPT-violating parameter de\ufb01ned in Eq. (17.5.35),\nz \u2261\n\u03b4m \u2212i\n2\u03b4\u0393\n\u2206md \u2212i\n2\u2206\u0393 \u2243\n\u03b2\u00b5\u2206a\u00b5\n\u2206md \u2212i\n2\u2206\u0393 ,\n(17.5.49)\nwhere \u03b2\u00b5 = \u03b3(1, \u03b2) is the meson four-velocity. The ap-\nproximation in Eq. (17.5.49) is due to the neglect of higher-\norder e\ufb00ects in the SME, and does not otherwise rely on\nthe size of z (Kosteleck\u00b4y, 2001; Kosteleck\u00b4y and Potting,\n1995).68 Note that the relative values of the imaginary\nand real parts of z are \ufb01xed by the B-mixing parame-\nters (Kosteleck\u00b4y and Potting, 1995),69\nIm z\nRe z =\n\u2206\u0393\n2\u2206md\n,\n(17.5.50)\n66 That is, invariant under translations, as well as rotations\nand boosts.\n67 The factors rqi, which represent the e\ufb00ect of binding the\nquarks qi within the meson, are not used consistently in the\nliterature, disappearing (for example) in Kosteleck\u00b4y (1998).\n68 BABAR (Aubert, 2008ar) cites Kosteleck\u00b4y (1998), where a\nfurther approximation exists due to the use of another parame-\nter, \u03b4 \u2248\u2212z/2 in the case of small T- and CPT-violating e\ufb00ects.\n69 The BABAR analysis (Aubert, 2008ar) derives this condition\nfrom Eq. (17.5.49) using \u2206\u0393 \u226a\u2206md, but it is derived from\nfundamental considerations by Kosteleck\u00b4y and Potting (1995),\nassuming only that T- and CPT-violating e\ufb00ects are small.\nFigure 17.5.12. Transformation between non-rotating and\nlaboratory (rotating) reference frames for the Lorentz-violation\nanalysis: from Kosteleck\u00b4y and Lane (1999).\nproviding a distinctive signature for CPT-violating e\ufb00ects\nwithin this scheme.\nThe motion of the laboratory must be taken into ac-\ncount: the (non-relativistic) velocity may be neglected, but\nthe earth\u2019s rotation changes the relative orientation of the\ndetector coordinate system and the spatial components\n\u2206a. BABAR (Aubert, 2008ar) chooses a non-rotating frame\n( \u02c6X, \u02c6Y , \u02c6Z) following Kosteleck\u00b4y and Lane (1999), with \u02c6Z\nparallel to the earth\u2019s rotation axis, and \u02c6X ( \u02c6Y ) at right\nascension 0\u25e6(90\u25e6). With the further choices that the lab-\noratory coordinate \u02c6z lies along \u2212\u03b2, and \u02c6y lies in the equa-\ntorial plane (declination 0\u25e6), it follows from Eq. (14) of\nKosteleck\u00b4y (2001) that\n\u03b2\u00b5\u2206a\u00b5 = \u03b3 [\u2206a0 \u2212\u03b2\u2206aZ cos \u03c7\n\u2212\u03b2 sin \u03c7 (\u2206aY sin \u2126tsid\n+ \u2206aX cos \u2126tsid)] ,\n(17.5.51)\nwhere cos \u03c7 \u2261\u02c6z \u00b7 \u02c6Z = 0.628 for BABAR, tsid is the\nsidereal time, and \u2126= 2\u03c0/dsid the sidereal frequency;\ndsid \u22430.99727 solar days. The transformation between\nlaboratory and non-rotating coordinates is illustrated in\nFig. 17.5.12. The sidereal time tsid is given by the right\nascension of \u02c6z; this will become important when compar-\ning results from di\ufb00erent experiments (Section 17.5.5.3 be-\nlow).\nFrom Eqs (17.5.49) and (17.5.51) it is clear that in\nthe general case, the measured CPT-violating parameter\nz will vary with a period of one sidereal day (dsid); a value\nz obtained from data without time-binning will depend\non the latitude of the experiment and the distribution of\nmeson momenta in the laboratory frame.\n17.5.5.2 The BABAR analysis\nThe Lorentz violation study in Aubert (2008ar) is an ex-\ntension of the CPT-violation search of Aubert (2006aq),\n\n300\nTable 17.5.5. Parameters from \ufb01ts to the asymmetry ACP T\nas a function of sidereal time, assuming constant (z0) and si-\nnusoidal (z1) contributions according to the Standard Model\nExtension. Statistical and total systematic uncertainties are\nshown; a breakdown of systematic contributions is given in\nTable I of Aubert (2008ar). Results are shown without (cen-\nter) and with (right) the SME constraint of Eq. (17.5.50) on\nthe real and imaginary parts of z.\nACP T parameter\nunconstrained\nSME constraint\nIm z0\n[10\u22123]\n\u221214.2 \u00b1 7.3 \u00b1 2.2\n\u22125.2 \u00b1 3.6 \u00b1 1.9\nRe z0 \u2206\u0393 [10\u22123/ps]\n\u22127.3 \u00b1 4.1 \u00b1 1.8\nIm z1\n[10\u22123]\n\u221224\n\u00b1 11\n\u00b1 3.3\n\u221217.0 \u00b1 5.8 \u00b1 1.9\nRe z1 \u2206\u0393 [10\u22123/ps]\n\u221218.5 \u00b1 5.6 \u00b1 1.7\n\u03c6\n[rad]\n2.63 \u00b1 0.31 \u00b1 0.21\n2.56 \u00b1 0.36 \u00b1 0.15\ndiscussed in Section 17.5.4.2 above, using the same sam-\nple of opposite-sign dilepton events to measure the CP-\nand CPT-violating asymmetry between B0 \u2192B0 and\nB0 \u2192B0 rates,\nACP T/CP (\u2206t) = 2Im z sin(\u2206md\u2206t) \u2212Re z\u2206\u0393\u2206t\ncos(\u2206md\u2206t) + cosh(\u2206\u0393\u2206t/2) ;\n(17.5.52)\nsee Eq. (17.5.45) for the full expression. As in Aubert\n(2006aq), same-sign dilepton events are used to provide\nadditional information on the fractions of the various sig-\nnal and background components.\nThe analysis is extended to include the sidereal time\ntsid, allowing for variations in z of the form\nz = z0 + z1 cos(\u2126tsid + \u03c6);\n(17.5.53)\nthe discrete ambiguity (z1 \u2192\u2212z1, \u03c6 \u2192\u03c6 + \u03c0) does\nnot a\ufb00ect the physical parameters \u2206a\u00b5 of Eq. (17.5.51).\nA two-dimensional maximum likelihood \ufb01t is performed,\nwith opposite- and same-sign events separately binned in\n(\u2206t, tsid); 24 sidereal-time bins are used. The values ob-\ntained for the parameters z0,1 and \u03c6 are shown in Ta-\nble 17.5.5. Individual systematic uncertainties are item-\nized in Table I of Aubert (2008ar): the dominant terms\nare due to alignment of the BABAR SVT and the absolute\nz scale (especially for \u03c6), and modeling of the resolution.\nDeviations from zero are seen for both the con-\nstant and sidereal-time-dependent CPT-violating terms in\nEq. (17.5.53). The constant terms Re z0 \u2206\u0393 and Im z0 are\nalmost identical to those in the time-independent analysis\n(Aubert, 2006aq), where a \u03c72 of 3.25 for 2 degrees of free-\ndom is quoted (the results have a correlation coe\ufb03cient of\n0.76 in both analyses): consistent with CPT invariance at\n19.7% con\ufb01dence. The sidereal-time dependence of ACP T\nis shown in Figure 17.5.13; events at small time di\ufb00erences\n|\u2206t| < 3, while included in the \ufb01t, are suppressed in the\n\ufb01gure as their predicted asymmetry is small.\nResults are consistent with the SME condition of Eq.\n(17.5.50), so a further \ufb01t is performed with this expres-\nsion used as a constraint, to improve the precision of the\nmeasurement: these results are also shown in the table.\nConsistent results are found if second-order terms |z|2 =\n (sidereal-hours)\nt\n Time \n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\n \nmeas\nCPT\nA\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\nFigure 17.5.13. Measured asymmetry ACP T for opposite-sign\ndilepton events with 3 ps < |\u2206t| < 15 ps, as a function of\nsidereal time \u02c6t = tsid. The curve shows a projection of the full\ntwo-dimensional |\u2206t| < 15 ps \ufb01t, also requiring 3 ps < |\u2206t|.\nFrom Aubert (2008ar).\n\u03c12 cos2(\u2126tsid + \u03c6) are added to the \ufb01t (cf. the derivation\nof Eq. (17.5.41) above).\nTwo kinds of signi\ufb01cance estimates are quoted for the\nsidereal-time-dependent results. Based on the likelihood\n\ufb01t, (Re z1 \u2206\u0393, Im z1) di\ufb00er from zero at 2.8\u03c3, with or\nwithout the SME constraint. Based on the periodogram\nmethod (Lomb, 1976; Scargle, 1982) measuring the spec-\ntral power P(\u03bd) for variations in z at test frequencies \u03bd, a\nvalue P(1/dsid) = 5.28 is found; the probability to exceed\nthis value in the absence of an oscillatory signal is\nP [P(\u03bd) > S] = e\u2212S\n(17.5.54)\n= 5.1 \u00d7 10\u22123 for S = 5.28,\nalso corresponding to 2.8\u03c3. This is signi\ufb01cantly stronger\nthan the result at the solar-day frequency, where ef-\nfects due to diurnal variations in detector response would\noccur: P(1/dsolar) = 1.47. The largest spectral power\namong the M = 9500 independent frequencies tested is\nP(0.46312/dsid) = 8.78; the probability of \ufb01nding a larger\nspectral power than this is\nP [P(\u03bd)|max > S; M] = 1 \u2212\n\u00001 \u2212e\u2212S\u0001M\n(17.5.55)\n= 76% for S = 8.78.\nHowever we note that the frequency expected within the\nSME is unambiguous: \u03bd = 1/dsid.\nFinal results are quoted for the SME quantities:\n\u2206a0 \u22120.30\u2206aZ = (\u22123.0 \u00b1 2.4)(\u2206md/\u2206\u0393) \u00d7 10\u221215 GeV,\n\u2206aX = (\u221222 \u00b1 7)(\u2206md/\u2206\u0393) \u00d7 10\u221215 GeV,\n\u2206aY = (\u221214+10\n\u221213)(\u2206md/\u2206\u0393) \u00d7 10\u221215 GeV.\n(17.5.56)\n17.5.5.3 Implications for future measurements\nA study of Lorentz covariance violation has not been per-\nformed by Belle, nor has the full available BABAR dataset\n\n301\nbeen used to update the Aubert (2008ar) analysis. The re-\nsults of that analysis thus remain untested. If con\ufb01rmed,\na non-zero measurement would be a result of the utmost\nimportance; the burden of proof for such a measurement\nis correspondingly high.\nAt face value, the Aubert (2008ar) analysis provides\nweak evidence for CPT violation together with depar-\ntures from Lorentz covariance, consistent with the Stan-\ndard Model Extension. Combining the con\ufb01dence levels\nof the time-independent (\u03b11 = 0.197) and sidereal-time-\ndependent results (\u03b12 = 5.1\u00d710\u22123) discussed above, using\nEq. (11.35) of James (2006), we \ufb01nd an overall result com-\npatible with zero at \u03b1 = \u03b11\u03b12[1\u2212ln(\u03b11\u03b12)] = 7.9\u00d710\u22123: a\n2.66\u03c3 e\ufb00ect. While there is greater spectral power at some\nfrequencies \u03bd \u0338= 1/dsid, and even the largest such signal\nis within expectations in the absence of oscillation, this\nadds little new information beyond the relative weakness\nof the sidereal-time dependence; within the SME, the pre-\ndicted signal is not at some undetermined frequency but\nat \u03bd = 1/dsid \u2014 there is no \u201clook-elsewhere e\ufb00ect\u201d.\nThe current results are statistically limited. While\nmuch larger datasets are foreseen at super \ufb02avor factories,\neven the \ufb01nal BABAR and Belle samples exceed those used\nby Aubert (2008ar) by factors of 2.0 and 3.3 respectively,\nallowing for both a repetition of the analysis on indepen-\ndent data, and a test on di\ufb00erent equipment with statisti-\ncal errors reduced by a factor\n\u221a\n3.3 = 1.82. Assuming no\nchange in central value, systematics, or intrinsic power,\na hypothetical Belle result with statistical uncertainty of\n3.2 \u00d7 10\u22123 and systematic uncertainty of 1.9 \u00d7 10\u22123 (cf.\nTable 17.5.5) would have 4.6\u03c3 signi\ufb01cance for the sidereal-\ntime-dependent measurement alone; the probability to ex-\nceed the corresponding spectral power, at any frequency,\nwould be 5% (from Eqs (17.5.54) and (17.5.55), assuming\nthe same number of frequencies tested by Aubert, 2008ar).\nThe latitude of Belle is similar to that of BABAR, and\nby chance the compass orientations of the \u03a5(4S) boost\nare also similar for the two experiments. The longitudes\nare substantially di\ufb00erent at the two sites: this leads to a\ndi\ufb00erence in the right ascension of \u02c6z, and thus an o\ufb00set\nin tsid in Eq. (17.5.51) at a given clock time. The phase\n\u03c6 of sidereal-time dependence in Eq. (17.5.53) predicted\nin the SME for Belle therefore di\ufb00ers from that at BABAR\nby a \ufb01xed amount, whereas for results due to statistical\n\ufb02uctuation, the phase would be arbitrary.\nThe dominant systematic uncertainties \u2014 alignment,\nthe z-scale, and the modeling of resolution \u2014 are\namenable to improvement at a redesigned experiment, al-\nthough the underlying time-dependent analysis techniques\n(Chapter 10) would need to be mature. Even without a\nsigni\ufb01cant reduction in systematics, a super \ufb02avor factory\ncould perform a measurement of overwhelming statistical\npower.\n\n302\n17.6 \u03c61, or \u03b2\nEditors:\nChih-hsiang Cheng (BABAR)\nYoshihide Sakai (Belle)\nIkaros Bigi (theory)\nAdditional section writers:\nTagir Aushev, Eli Ben-Haim, Adrian Bevan, Bob Cahn,\nChunhui Chen, Ryosuke Itoh, Al\ufb01o Lazzaro, Owen Long,\nFernando Martinez-Vidal, Vincent Poireau, Klaus Schu-\nbert\nPrecision measurement of the CP asymmetries in B \u2192\nJ/\u03c8K0\nS decays was the principal motivation for building\nthe B Factories. With the accumulation of data samples\nlarger than anticipated, the BABAR and Belle experiments\nat the B Factories are able to study CP asymmetries in a\nwide range of related channels. This section describes mea-\nsurements of the Unitarity Triangle angle \u03c61, also known\nas \u03b2 in the literature. An overview of \u03c61 measurements and\ntheir motivation is presented in Section 17.6.1, followed by\na review of the quark transitions and the formalism of \u03c61\nmeasurements in Section 17.6.2. The various channels for\n\u03c61 measurement, and the B Factories results, are then\ndescribed in Sections 17.6.3\u201317.6.7. Resolution of discrete\nambiguities is discussed in Section 17.6.8, and a summary\nof \u03c61 results is presented in Section 17.6.10.\nIn the Standard Model, non-zero asymmetries mea-\nsured in these analyses re\ufb02ect violation of both the CP\nand T symmetries. Performing the measurement in a way\nthat directly demonstrates T violation, without assuming\n(for example) CPT symmetry, requires special care. Such\nan analysis has been performed at BABAR, and is presented\nin Section 17.6.9. Tests of CPT symmetry are presented\nin Section 17.5.\n17.6.1 Overview of \u03c61 measurement at the B\nFactories\nInitially, CP violation seemed isolated from the mainstream\nof particle physics. Since it was seen only in the K0\nS-K0\nL\nsystem, it was possible to imagine that it was due entirely\nto a \u2206S = 2 operator as postulated in the superweak\ntheory (Wolfenstein, 1964). Two developments put CP vi-\nolation at center stage. The \ufb01rst was A. D. Sakharov\u2019s\ndemonstration (Sakharov, 1967) that CP violation was\none of the three requirements for the existence of the\nbaryon anti-baryon asymmetry of the universe (see Sec-\ntion 16.2). The second was Kobayashi\u2019s and Maskawa\u2019s\ndemonstration that CP violation was natural if there were\nthree generations of quarks (see Chapter 16). With the\nsubsequent discovery of the last three quarks, testing the\nCKM model became urgent.\nThe K0\nS-K0\nL system was not su\ufb03cient by itself to test\nthe CKM picture. The measured parameters, \u2206mK, \u03f5K\nand \u03f5\u2032\nK, depended not just on the fundamentals of the\nweak interactions, but on non-perturbative hadronic ma-\ntrix elements. Moreover, CP violation in the kaon system\nwas feeble. Since \u03f5K was measured in 1964, it took until\n1973 before Kobayashi and Maskawa provided a real the-\nory for CP violation. It needed many years to demonstrate\nthat the parameter \u03f5\u2032 was non-zero. Even before the unex-\npected \u2018long\u2019 lifetime of B mesons was discovered, the B\nmeson system was recognized as the ideal testing ground\nfor CP violation (Bigi and Sanda, 1981) and the decay\nB \u2192J/\u03c8K0\nS as ideal for the purpose. Detection of the\n\ufb01nal state is especially clean because the J/\u03c8 decays to\nlepton pairs and the K0\nS is su\ufb03ciently long-lived to de-\ncay into pairs of oppositely charged pions at a secondary\nvertex displaced from the interaction region.\nUnlike neutral kaons, the neutral B mesons start oscil-\nlating just after their production, since their mixing rate\n\u2206md is comparable to their natural widths \u0393 (see Sec-\ntion 17.5). If we begin with a B0, at a later time the state\nwill be a superposition of B0 and B0. The decay to J/\u03c8K0\nS\nwill occur through both components and the interference\npattern will depend on the relative phases between the\nB0 and B0 components, which is directly calculable in\nthe CKM model. The interference pattern depends on the\ntwo decay amplitudes to the \ufb01nal state. Because the \ufb01-\nnal state is a CP eigenstate and because there is only one\nsigni\ufb01cant pathway to it from B0 or B0, the two decay\namplitudes are identical, up to another calculable phase.\nAs a result, the oscillation pattern can be predicted simply\nin terms of the phases due to the CKM matrix without\nany dependence on hadronic physics. The time-dependent\nformalism required for the measurement of sin 2\u03c61 can be\nfound in Chapter 10.\nIn order to test the CKM paradigm we need to know\nif we are starting with a B0 or with a B0. The \u03a5(4S) is\nvery near the threshold for BB so if one B is observed, the\nremaining particles must come from another B. Moreover,\nby Bose symmetry, if a B0 is observed the other particle\nmust be a B0 at that instant, since the two mesons must be\nin an antisymmetric state to produce the unit of angular\nmomentum carried by the \u03a5(4S). Thus \u201ctagging\u201d one B\nmeson tells us both, when to start the clock and the type\nof B at that time (see Chapter 8).\nThe decay B0 \u2192J/\u03c8K0\nS is just one of a large family of\nrelated decays due to a b \u2192c\u00afcs transition. Of particular\ninterest is the decay to J/\u03c8K0\nL because the \ufb01nal state has\nthe opposite CP eigenvalue, and we expect exactly the\nopposite oscillation. Other charmonia can take the place\nof J/\u03c8, including \u03c8(2S), \u03b7c, and \u03c7c1. The decay B0 \u2192\nJ/\u03c8K\u22170 is more complex because the spins of the \ufb01nal\nstate particles can be combined to produce an overall spin\nequal to 0, 1, or 2, and correspondingly the orbital angular\nmomentum will be 0, 1, or 2. This complexity has the\nadvantage that it can help resolve the ambiguity inherent\nin determining the angle \u03c61 when only sin 2\u03c61 is known.\nAt \ufb01rst, the B Factories concentrated on measuring\ntime-dependent asymmetries in the so-called charmonium\n\u201cgolden modes\u201d concentrating on B0 \u2192J/\u03c8K0\nS, \u03c8(2S)K0\nS,\n\u03c7c1K0\nS, J/\u03c8K0\nL, and J/\u03c8\u03c00. However, it was understood\nthat there were other ways to measure \u03c61. Once an un-\nderstanding of how to do these measurements started to\ndevelop, the experiments branched out to study similar\n\n303\n\ufb01nal states that were more di\ufb03cult to isolate from the\ndata. These states either had smaller branching fractions,\nor were experimentally more challenging to isolate. Stud-\nies performed in the BABAR physics book (Harrison and\nQuinn, 1998), prior to the commencement of data taking,\nassumed that a data sample of 30 fb\u22121 would be available\nto use for testing the SM. In reality this data sample was\nquickly attained on both sides of the Paci\ufb01c Ocean and\nthe B Factories program of measuring \u03c61 expanded, both\nin terms of the number of measurements and in terms of\nthe complexity of analysis used, to accommodate the rich\nharvest of B meson pairs. The \ufb01rst results on the mea-\nsurement of sin 2\u03c61 were shown at the International Con-\nference on High Energy Physics in 2000, which became\nknown colloquially within BABAR and Belle as \u2018the Osaka\nconference\u2019. The B Factories presented values of sin 2\u03c61 of\n0.12 \u00b1 0.37 \u00b1 0.09 (Aubert, 2000) and 0.45+0.43\n\u22120.44\n+0.07\n\u22120.09 (Ai-\nhara, 2000a) at this conference. A year later Belle and\nBABAR established large CP asymmetry in this \ufb01nal state.\nSince then both B Factories have accumulated much larger\ndata samples, and the \ufb01nal results obtained by BABAR and\nBelle are signi\ufb01cantly more precise than these \ufb01rst mea-\nsurements (see Section 17.6.3).\nWhile the charmonium decays were the primary focus\nof the \u03c61 program, \ufb01nal states mediated by other transi-\ntions were also studied in subsequent waves of measure-\nments that quickly followed the \ufb01rst results. In particular\nthe modes B \u2192\u03c6K0\nS, B \u2192\u03b7\u2032K0\nS, and D(\u2217)+D(\u2217)\u2212were\nhighlighted. The expectation was that these would pro-\nvide alternative ways of constraining \u03c61, and would com-\nplement the constraint on the Unitarity Triangle given by\nthe golden mode measurements. Any measurement of \u03c61\nthat di\ufb00ered signi\ufb01cantly from expectations, or any two\nmeasurements that disagreed with each other, could re-\nveal physics beyond the Standard Model.\nThe \ufb01rst few measurements of S \u2243sin(2\u03c61) in a quasi-\ntwo-body analysis of B \u2192\u03c6K0\nS decays in 2003 were far\nfrom the SM expectation. While these were low statistics\nstudies, with only a handful of high purity events (well\ntagged events with a low mistag probability, see Chap-\nter 8), the community was tantalized by the possibility\nthat this could herald a new age in modern physics. As\na result, the interest in alternative measurements of \u03c61\nblossomed, and this remains a vibrant area a decade later.\nAlas, the early deviations from the SM turned out to be\nstatistical \ufb02uctuations, and the most recent measured val-\nues of \u03c61 obtained from the B Factories are compatible\nwith SM expectations within experimental and theoreti-\ncal uncertainties.\nThe early \ufb02uctuation had several consequences. First,\na large number of neutral B meson decays to CP eigen-\nstate or admixture \ufb01nal states have been studied in the\nhope that one or more of them might yield a result in-\ncompatible with the SM. Second, both the theoretical\nand experimental communities started to take possible\nhadronic uncertainties more seriously in both golden and\nalternative measurements of \u03c61. Today the constraints on\nhadronic uncertainties in these modes are a mixture of the-\noretical calculations and data-driven constraints obtained\nvia a more phenomenological approach. The golden chan-\nnels are theoretically clean, up to the extent that anal-\nysis at the B Factories would be concerned about. This\nhas been determined via theoretical calculation, and via a\ndata-driven interpretation of results. However other \ufb01nal\nstates, in particular those dominated by penguin loop am-\nplitudes, have non-negligible uncertainties. The cleanest\nmodes are B \u2192\u03b7\u2032K0\nS, which is the most precisely mea-\nsured charmless \ufb01nal state, and B \u2192\u03c6K0\nS. These have\nhadronic uncertainties of a few percent on the measured\nvalue of S. In the case of B \u2192f0K0\nS there are only partial\ncalculations where, for example, long distance e\ufb00ects are\nignored, and the estimated hadronic uncertainties for this\nmode provide a lower bound. More details on this part of\nthe B Factory program can be found in Section 17.6.6.\nEarly time-dependent studies of B decays to charmless\n\ufb01nal states relied on a simpli\ufb01ed analysis paradigm by im-\nposing the quasi-two-body assumption that resonances are\nparticles of de\ufb01nite mass, so that interference between am-\nplitudes could be neglected. As the recorded data samples\nof the two experiments increased, more sophisticated tech-\nniques were incorporated. Just as the measurements of \u03c62\nultimately required that the B Factories pioneer the use\nof time-dependent Dalitz plot techniques, so eventually\none had to perform similar analyses in order to constrain\n\u03c61. The ability to study amplitudes in a Dalitz plot leads\nto the possibility of resolving the four-fold ambiguity in\nthe value of \u03c61 obtained from the golden mode measure-\nment, and complements other approaches such as the full\nangular analysis of the B0 \u2192J/\u03c8K\u2217\ufb01nal state. Results\nfrom three-body charmless decays on \u03c61 are discussed in\nSection 17.6.7, and resolution of discrete ambiguities on\nthe value of this angle using other modes is considered in\nSection 17.6.8.\nThe large amounts of data accumulated by the B\nFactories also required an improvement in understanding\nthe systematic uncertainties involved in the measurements\nthemselves. In particular the concept of \ufb02avor tagging as\noriginally conceived, while good enough to describe semi-\nleptonic tagged events, turned out to be an approximation\nfor hadronically tagged \ufb01nal states. It is possible to have\na small level of CP violation manifest on the tag side of\nthe event that would need to be considered as a systematic\nuncertainty in order to ensure that one reports the correct\nlevel of CP violation obtained for a given result. In some\ncases with small expected CP violating asymmetries, such\nas the measurement of sin(2\u03c61 + \u03c63), this so-called tag-\nside interference needs to be incorporated into the mea-\nsurement technique. The main systematic uncertainties for\ntime-dependent measurements at the B Factories, includ-\ning tag-side interference, are discussed in Chapter 15.\nThe \ufb01nal measurement of sin 2\u03c61 \u2261sin 2\u03b2 obtained by\nthe B Factories has a combined precision of 3%. This can\nbe compared with the estimated relative statistical preci-\nsion for this measurement estimated in the BABAR physics\nbook, 12%, using a foreseen data sample of 30 fb\u22121 (Har-\nrison and Quinn, 1998). The achieved precision is a nice\nexample of exceeding the initial expectations put forward\nbefore the startup of the B Factories. The \ufb01nal result of\n\n304\nthe B Factories is not systematically limited and may be\nimproved upon by the next generation of experiments.\n17.6.2 Transitions and formalism\nThe Unitarity Triangle angle \u03c61 = \u03b2 is de\ufb01ned as\n\u03c61 \u2261\u03b2 \u2261arg[\u2212(VcdV \u2217\ncb)/(VtdV \u2217\ntb)].\n(17.6.1)\nIt describes CP violation in the interference between de-\ncays with and without B0-B0 mixing and is best measured\nin B0 \u2192J/\u03c8(\u03c8(2S))K0\nS transitions, which have CP-odd\n\ufb01nal states (ignoring the small CP violation in K0-K0\nmixing). As discussed in Section 10.1, \u2206B = 2 transitions\nin the SM are produced by quark box diagrams Obox in-\ncluding QCD radiative corrections for \u2206md.\nThe most precise technique for measuring \u03c61 uses B0\ndecays to CP eigenstates with quark transitions of the\ntype b \u2192c\u00afcs (Fig. 17.6.1). Since the \ufb01nal state f is ac-\ncessible to both B0 and B0, the amplitudes for B0 \u2192f\n(direct decay) and B0 \u2192B0 \u2192f (decay preceded by\nneutral meson oscillation) will interfere. As described in\nSection 10.2,70 the resulting time-dependent CP asymme-\ntry is given as\nA(\u2206t) = S sin(\u2206md\u2206t) \u2212C cos(\u2206md\u2206t),\n(17.6.2)\nwhere S = 2Im\u03bb/(1 + |\u03bb|2), C = (1 \u2212|\u03bb|2)/(1 + |\u03bb|2),\nand \u03bb = (q/p)(Af/Af). In the SM, q/p = VtdV \u2217\ntb/V \u2217\ntdVtb\nto a good approximation. For the \ufb01nal state f = J/\u03c8K0\nS,\nthe B decay is dominated by a tree b \u2192c\u00afcs (or its CP\nconjugate) amplitude71 followed by K0-K0 mixing.72 The\nresult is \u03bb = \u03b7f\nVtdV \u2217\ntb\nVtbV \u2217\ntd\nVcbV \u2217\ncd\nVcdV \u2217\ncb , which leads to C = 0 and\nS = \u2212\u03b7f sin 2\u03c61, where \u03b7f = \u03b7J/\u03c8 K0\nS = \u22121 is the CP\neigenvalue. B0 \u2192J/\u03c8K0\nL has \u03b7f = \u03b7J/\u03c8 K0\nL = +1 and has\nthe opposite sign for S. The same magnitude is expected\nfor the CP-even and -odd modes up to a small correction\nfor CP violation in K0-K0 oscillations.\nTo understand the penguin amplitude contributions,\none can group tree (T) and penguin (P q) amplitudes ac-\ncording to their CKM factors, remove the VtbV \u2217\nts term us-\ning the unitarity condition\nX\nq=u,c,t\nVqbV \u2217\nqs = 0,\n(17.6.3)\nand express the b \u2192c\u00afcs decay amplitude as\nAc\u00afcs = VcbV \u2217\ncs(T + P c \u2212P t) + VubV \u2217\nus(P u \u2212P t), (17.6.4)\nwhere the superscripts indicate the quark in the loop. The\nsecond term has a di\ufb00erent phase but the magnitude is\nsuppressed by |VubV \u2217\nus/VcbV \u2217\ncs| \u223cO(\u03bb2\nCabibbo). Therefore,\nthe e\ufb00ect of the penguin amplitude on \u03c61 is expected to\nbe very small.\n70 See in particular Eqs (10.2.2, 10.2.4, 10.2.4, and 10.1.10).\n71 B decay amplitude ratio provides a factor \u03b7f\nVcbV \u2217\ncs\nV \u2217\ncbVcs .\n72 K0-K0 mixing provides a factor V \u2217\ncdVcs/VcdV \u2217\ncs.\nWithin the SM the level of CP violation in decay\n(|Af/ \u00afA \u00af\nf| \u0338= 1) is expected to be inaccessible to exist-\ning experiments, and new physics (NP) beyond the SM\nis unlikely to generate large e\ufb00ects due to the dominance\nof the tree amplitude in decay. However, NP could modify\nthe time-dependent CP asymmetry across di\ufb00erent modes\nby a\ufb00ecting the phase in q/p and lead to inconsistencies\nbetween \u03c61 and other observables that determine the Uni-\ntarity Triangle.\nb\nc\nc\ns\nb\ns\nc\nc\nFigure 17.6.1. Tree and penguin diagrams of b \u2192ccs.\nIn b \u2192c\u00afcd (Fig. 17.6.2) decays, the di\ufb00erence be-\ntween the CKM phase of the tree diagram and that of\nb \u2192c\u00afcs is negligible. This allows the measurements of\nsin 2\u03c61 through decays to CP eigenstates of b \u2192c\u00afcd (such\nas B0 \u2192J/\u03c8\u03c00 and D+D\u2212) in the same way as b \u2192c\u00afcs.\nUnlike b \u2192c\u00afcs, however, the CKM factors of the pen-\nguin diagrams here are of the same order (O(\u03bb3\nCabibbo)) as\nthe tree diagram. The possible contribution of the b \u2192c\u00afcd\npenguin diagrams, which have a di\ufb00erent CKM phase, can\nalter the measured value of sin 2\u03c61. Any such deviation\nwould be due to the e\ufb00ect of penguin contributions or due\nto NP.\nb\nc\nc\nd\nb\nd\nc\nc\nFigure 17.6.2. Tree and penguin diagrams of b \u2192ccd.\nThe b \u2192c\u00afud transition (Fig. 17.6.3) proceeds through\na tree diagram, and has no penguin contribution. It can\nagain be used to probe sin 2\u03c61 if the \ufb01nal state is accessible\nto both B0 and B0 (e.g., in the case of intermediate D0\nand D0 decays to the same \ufb01nal state). However, in this\ncase, the process b \u2192u\u00afcd also contributes. The relative\nCKM factor of these two tree diagrams, VubV \u2217\ncd/VcbV \u2217\nud,\nhas a large phase and the magnitude is approximately\n0.02. Therefore, the deviation from the b \u2192c\u00afcs value for\nsin 2\u03c61 obtained in these decays is expected to be small.\nb\nc\nu\nd\nb\nu\nc\nd\nFigure 17.6.3. Tree diagrams of b \u2192c\u00afud and b \u2192u\u00afcd.\n\n305\nThe decays to CP eigenstates dominated by b \u2192s\u00afqq\npenguin transitions (Fig. 17.6.4) also can be used for sin 2\u03c61\nmeasurements in the SM. Similar to Eq. (17.6.4), the dom-\ninant penguin contribution has the same phase as that in\nthe b \u2192c\u00afcs tree diagram, and the sub-dominant term is\nsuppressed. Any deviation of S from the b \u2192c\u00afcs decay\n(beyond theoretical uncertainty) is a clear indication of\nthe e\ufb00ect of NP. The decays proceeding via b \u2192s\u00afss pen-\nguin diagrams, such as B0 \u2192\u03c6K0, K0\nSK0\nSK0\nS, and \u03b7\u2032K0,\nhave a small theoretical uncertainty on S due to the lack\nof a tree amplitude contribution. These decays are partic-\nularly promising for future new physics searches.\nb\ns\nq\nq\nFigure 17.6.4. Penguin diagram of b \u2192qqs.\nMeasurements of sin 2\u03c61 have a four-fold ambiguity in\n\u03c61: \u03c61 \u2194\u03c0/2 \u2212\u03c61, \u03c61 + \u03c0 and 3\u03c0/2 \u2212\u03c61 (all these four\nvalues result in the same sin 2\u03c61). The \u03c61 \u2194\u03c0/2 \u2212\u03c61\nand 3\u03c0/2 \u2212\u03c61 ambiguity can be resolved in one of several\nways: the full time-dependent angular analysis of vector-\nvector \ufb01nal states such as B0 \u2192J/\u03c8K\u22170[K0\nS\u03c00]; time-\ndependent Dalitz analysis of three-body decays; time-\ndependent Dalitz analysis of D0 \u2192K0\nS\u03c0+\u03c0\u2212in B0 \u2192\nD(\u2217)0h0; and time-dependent measurements in two sepa-\nrate Dalitz regions in B0 \u2192D\u2217+D\u2217\u2212K0. Using these mea-\nsurements the ambiguity is partially resolved and only the\ntwo fold ambiguity \u03c61 \u2192\u03c61 +\u03c0 remains, which cannot be\nresolved by a single measurement. When combining with\nother CKM measurements, one can clearly see which of\nthe two remaining solutions is ruled out. See Chapter 25\nfor details.\nThe following sections describe the di\ufb00erent measure-\nments of \u03c61 made at the B Factories.\n17.6.3 \u03c61 from b \u2192c\u00afcs decays\nThe decays to CP eigenstates via a b \u2192c\u00afcs transition\ninclude B0 decays to charmonium (c\u00afc) and a K0\nS or K0\nL.\nThese modes have experimentally clean signals, and large\nsignal yields are expected due to relatively large branch-\ning fractions (they are CKM favored, though color sup-\npressed73). These decays are also theoretically very clean\nfor \u03c61 determination, i.e., the deviation due to the contri-\nbution of penguin diagrams with a di\ufb00erent CKM phase\nis expected to be at the \u22641% level (H. Boos and Reuter,\n73 Each of the two quarks (\u00afcs) from the virtual W is paired\nwith the quark originating from the initial state (b \u00afd) to form a\nhadron. Since hadrons have to stay color-neutral, the color of\n\u00afc and s must match that of b and \u00afd. Therefore the overall am-\nplitude is 1/number-of-colors smaller than the decays in which\nW \u2217\u2192\u00afqq\u2032 hadronize by themselves.\n2004, 2007). As a result the B0 \u2192J/\u03c8K0\nS decay is called\na \u201cGolden mode\u201d.\nSince the observation of CP violation in B decays\nand the precise measurements of sin 2\u03c61 are the primary\ngoals of the asymmetric B Factories, the measurements\nmade using b \u2192c\u00afcs modes were performed shortly after\ndata taking commenced, and have been updated several\ntimes during the course of data taking. Both B Facto-\nries have updated their measurements using the whole\ndata sample collected by each experiment. BABAR (Au-\nbert, 2009z) uses 465 \u00d7 106 BB, while Belle (Adachi,\n2012c) uses 772\u00d7106 BB pairs. For \u03c61 measurements with\nb \u2192c\u00afcs decays, the B0 decays to the \ufb01nal states J/\u03c8K0\nS,\nJ/\u03c8K0\nL, \u03c8(2S)K0\nS, \u03c7c1K0\nS, \u03b7cK0\nS, and J/\u03c8K\u2217(890)0[K0\nS\u03c00]\nare used. The J/\u03c8K0\nL state is CP-even, and J/\u03c8K\u2217(890)0\nis an admixture of two CP states. All the others are CP-\nodd states.\nThe J/\u03c8 and \u03c8(2S) mesons are reconstructed via their\ndecays to \u2113+\u2113\u2212(\u2113= e, \u00b5). For decays to an e+e\u2212\ufb01nal\nstate, photons near the direction of the e\u00b1 are added to\nrecover the energy lost by radiated bremsstrahlung. The\n\u03c8(2S) mesons are also reconstructed in the J/\u03c8\u03c0+\u03c0\u2212\ufb01-\nnal state. The \u03c7c1 mesons are reconstructed in the J/\u03c8\u03b3\n\ufb01nal state, and these photons must not be consistent with\nphotons from \u03c00 decays. The \u03b7c mesons are reconstructed\nin the K0\nSK+\u03c0\u2212\ufb01nal states, and the regions that con-\ntain the dominant intermediate resonant states in K+\u03c0\u2212\nand K0\nSK+ are selected. Candidate K0\nS mesons are recon-\nstructed via decays to the \u03c0+\u03c0\u2212\ufb01nal state. For the B0 \u2192\nJ/\u03c8K0\nS decay mode, K0\nS mesons are also reconstructed in\nthe \u03c00\u03c00 \ufb01nal state. Inclusion of the K0\nS \u2192\u03c00\u03c00 channel\nincreases a signal yield by about 20% of the K0\nS \u2192\u03c0+\u03c0\u2212\nchannel. The masses of J/\u03c8, \u03c8(2S), \u03c7c1, and K0\nS candi-\ndates are constrained to their respective nominal values\nto improve their momentum resolutions. Candidate K0\nL\nmesons are identi\ufb01ed using information from the electro-\nmagnetic calorimeter and IFR/KLM detectors (see Chap-\nter 2), requiring that the signals in these detectors are not\nassociated with any charged tracks. Since the energy of a\nK0\nL cannot be measured precisely, only the \ufb02ight direction\nis used when reconstructing B0 \u2192J/\u03c8K0\nL decay candi-\ndates. The K\u22170 candidates are selected by combining K0\nS\nand \u03c00 mesons. BABAR uses all of the aforementioned \ufb01nal\nstates for their analysis. While Belle (Abe, 2001g) used the\nsame set of modes for earlier iterations of their analysis,\nmore recent updates do not include the J/\u03c8K0\nS(\u2192\u03c00\u03c00),\n\u03b7cK0\nS, and J/\u03c8K\u22170 \ufb01nal states.\nCandidate B0 mesons are reconstructed by combin-\ning charmonium and K0\nS, K0\nL, or K\u22170 candidates. Two\nkinematic variables \u2206E and mES (see Section 7.1.1) are\nused to select signal candidates, with the exception of the\nB0 \u2192J/\u03c8K0\nL channel. For the latter case a kinematic con-\nstraint is applied assuming a two-body decay of the B0,\nand both BABAR and Belle use \u2206E and the momentum of\nthe reconstructed B0 in the center-of-mass (CM) system\n(p\u2217\nB) to isolate signal candidates. Figure 17.6.5 shows the\nmES and \u2206E distributions for candidates satisfying the\n\ufb02avor tagging and vertex reconstructions in the BABAR\n\n306\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n1000\n2000\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n1000\n2000\nS\n0\nK\n\u03c8\n J/\n\u2192\n0\nB\nS\n0\n(2S)K\n\u03c8\n \n\u2192\n0\nB\nS\n0\nK\nc1\n\u03c7 \n\u2192\n0\nB\nS\n0\nK\nc\n\u03b7\n \n\u2192\n0\nB\na)\nE (MeV)\n\u2206\n0\n20\n40\n60\n80\nEvents / 2 MeV\n0\n500\n1000\nE (MeV)\n\u2206\n0\n20\n40\n60\n80\nEvents / 2 MeV\n0\n500\n1000\nL\n0\nK\n\u03c8\n J/\n\u2192\n0\nB\nb)\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n100\n200\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n100\n200\n*0\nK\n\u03c8\n J/\n\u2192\n0\nB\nc)\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n10\n20\n30\n40\n3\n10\n\u00d7\n)\n2\n (GeV/c\nES\nm\n5.2\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 2 MeV/c\n0\n10\n20\n30\n40\n3\n10\n\u00d7\n modes\nflav\nB\nd)\nFigure 17.6.5. Distributions of mES or \u2206E for (a) B0 \u2192\n(c\u00afc)K0\nS, (b) B0 \u2192J/\u03c8K0\nL, (c) B0 \u2192J/\u03c8K\u22170, and (d) B0\ndecays to \ufb02avor-speci\ufb01c \ufb01nal states for the samples used in the\nBABAR measurement (Aubert, 2009z) of \u03c61. The shaded regions\nrepresent the estimated background, and the solid lines are the\nprojections of the \ufb01ts to the data.\nanalysis. Figure 17.6.6 shows the mES and p\u2217\nB distribu-\ntions for the Belle analysis.\nVertex reconstruction and B meson \ufb02avor tagging al-\ngorithms (described in Chapters 6 and 8) are applied to\nthe selected signal candidates. Time-dependent CP asym-\nmetry parameters are extracted from \ufb01ts to the distribu-\ntions of proper decay time di\ufb00erence between signal and\ntagged B mesons as described in Chapter 10. BABAR ex-\ntracts the time-dependent asymmetry parameters (S and\nC) from a simultaneous \ufb01t to both the BCP and B\ufb02av\n(see Section 10.2) samples with 69 additional free param-\neters, where tagging and resolution parameters are trans-\nparently propagated into the CP analysis as part of the\n\ufb01nal statistical error. Belle takes a multi-step approach:\nthe \ufb01nal \ufb01t includes only S and C as free parameters, and\nall the \ufb01t model parameters, which include signal frac-\ntions, \ufb02avor tagging performance parameters, and proper\ntime di\ufb00erence resolution function parameters are \ufb01xed\nto the values determined from separate \ufb01ts to the B\ufb02av\nand BCP samples. E\ufb00ects arising from the uncertainties\nof these parameters are included in the \ufb01nal result as sys-\ntematic errors.\nThe results of the time-dependent CP asymmetry mea-\nsurements are summarized in Table 17.6.1 for each decay\nmode, and for the combined set of modes. As described\nin Section 17.6.8, the time-dependent full angular analy-\nsis of the B0 \u2192J/\u03c8K\u22170 decay can provide a value for\ncos 2\u03c61 in addition to sin 2\u03c61. The angular information\npresented in the table has been averaged over, resulting\nin a dilution of the measured CP asymmetry by a fac-\n* (GeV/c)\nB\np\n0\n0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6 1.8\n2\ncounts / 50 MeV/c\n0\n1000\n2000\n3000\n4000\n5000\nFigure 17.6.6. Distributions of mES (= Mbc) for B0 \u2192\n(c\u00afc)K0\nS (top) and p\u2217\nB for B0 \u2192J/\u03c8 K0\nL (bottom) obtained with\nthe samples used for the Belle measurement (Adachi, 2012c)\nof \u03c61. The shaded regions in the bottom plot represent the\nestimated background components: (from top to bottom) real\nJ/\u03c8 and real K0\nL (yellow), real J/\u03c8 and fake K0\nL (green), and\nfake J/\u03c8 (blue).\ntor of 1 \u22122R\u22a5, where R\u22a5is the fraction of the CP-odd\ncomponent. BABAR uses the previously measured value\n0.233 \u00b1 0.010 \u00b1 0.005 (Aubert, 2007x). Systematic errors\non the time-dependent asymmetry parameters are sum-\nmarized in Table 17.6.2. The dominant sources for S are\ndue to the uncertainties in vertex reconstruction and \u2206t\nresolutions, \ufb02avor tagging, and background in the J/\u03c8K0\nL\nmode. The systematic error on C is dominated by tag-\nside interference. For this source, Belle takes into account\na cancellation between CP-even and CP-odd states, while\nBABAR does not. Chapter 15 discusses the main sources of\nsystematic uncertainty on time-dependent CP asymmetry\nparameter measurements in detail.\nThe \u2206t distributions and asymmetries obtained from\nthe data for all modes combined are shown in Fig. 17.6.7.\nThe values of C obtained are consistent with zero in ac-\ncordance with SM expectations, and hence \u2212\u03b7fS gives\nessentially sin 2\u03c61. The average of the two experiments\n\n307\nTable 17.6.1. Summary of the time-dependent CP-asymmetry measurements using B0 decays to charmonium + K0 \ufb01nal states, for each decay mode and for all\nmodes combined. Ntag and P are the number of candidates and signal purity (in %), respectively, in the signal region after \ufb02avor tagging and vertex reconstruction\nrequirements have been applied. S and C are the CP asymmetry parameters for the \ufb01nal state with the CP eigenvalue \u03b7f.\nBABAR (Aubert, 2009z)\nBelle (Adachi, 2012c)\nMode\nNtag\nP\n\u2212\u03b7fS\nC\nNtag\nP\n\u2212\u03b7fS\nC\nJ/\u03c8 K0\nS\n6750\n95\n0.657 \u00b1 0.036 \u00b1 0.012\n0.026 \u00b1 0.025 \u00b1 0.016\n13040\n97\n0.670 \u00b1 0.029 \u00b1 0.013\n0.015 \u00b1 0.021 +0.023\n\u22120.045\nJ/\u03c8K0\nL\n5813\n56\n0.694 \u00b1 0.061 \u00b1 0.031\n\u22120.033 \u00b1 0.050 \u00b1 0.027\n15937\n63\n0.642 \u00b1 0.047 \u00b1 0.021\n\u22120.019 \u00b1 0.026 +0.041\n\u22120.017\n\u03c8(2S)K0\nS\n861\n87\n0.897 \u00b1 0.100 \u00b1 0.036\n0.089 \u00b1 0.076 \u00b1 0.020\n2169\n91\n0.738 \u00b1 0.079 \u00b1 0.036\n\u22120.104 \u00b1 0.055 +0.027\n\u22120.047\n\u03c7c1K0\nS\n385\n88\n0.614 \u00b1 0.160 \u00b1 0.040\n0.129 \u00b1 0.109 \u00b1 0.025\n1093\n86\n0.640 \u00b1 0.117 \u00b1 0.040\n0.017 \u00b1 0.083 +0.026\n\u22120.046\n\u03b7cK0\nS\n381\n79\n0.925 \u00b1 0.160 \u00b1 0.057\n0.080 \u00b1 0.124 \u00b1 0.029\nJ/\u03c8 K\u22170\n1291\n67\n0.601 \u00b1 0.239 \u00b1 0.087\n0.025 \u00b1 0.083 \u00b1 0.054\nAll\n15481\n76\n0.687 \u00b1 0.028 \u00b1 0.012\n0.024 \u00b1 0.020 \u00b1 0.016\n32239\n79\n0.667 \u00b1 0.023 \u00b1 0.012\n\u22120.006 \u00b1 0.016 \u00b1 0.012\n\n308\nTable 17.6.2. Summary of systematic errors on the time-\ndependent CP asymmetry parameters measured in B0 decays\nto charmonium + K0 for all modes combined.\nBABAR\nBelle\nSource\nS\nC\nS\nC\nVertex and \u2206t\n0.007\n0.003\n0.010\n0.007\nFlavor tagging\n0.006\n0.002\n0.004\n0.003\nJ/\u03c8K0\nL background\n0.006\n0.001\n0.004\n0.002\nOther signal/background\n0.005\n0.003\n0.002\n0.001\nPhysics parameters\n0.003\n0.001\n0.001\n0.000\nTag-side interference\n0.001\n0.014\n0.001\n0.008\nPossible \ufb01t bias\n0.002\n0.003\n0.004\n0.005\nTotal\n0.012\n0.016\n0.012\n0.012\n(Amhis et al., 2012) gives\nsin 2\u03c61 = 0.677\u00b10.020 and C = 0.006\u00b10.017. (17.6.5)\nThis corresponds to \u03c61 = (21.30 \u00b1 0.78)\u25e6(up to the four-\nfold ambiguity mentioned above). An accuracy of 3% on\nsin 2\u03c61 (0.8\u25e6on \u03c61) is achieved.\nThe evolution of the measured value of sin 2\u03c61 can be\nseen in Fig. 17.6.8. Central values for the initial measure-\nments from both experiments were slightly lower than the\ncurrent world average. A signi\ufb01cant milestone in the mea-\nsurement of sin 2\u03c61 was achieved in the summer of 2001\nwhen both BABAR and Belle observed CP violation in B0\nmeson decay.74 The data samples used for these measure-\nments each consists of about 30 \u00d7 106 BB pairs. Since\nthat time, improved measurements have proved to be sta-\nble, and the results reported by BABAR and Belle have\nremained consistent with each other.\n17.6.4 \u03c61 from b \u2192c\u00afcd decays\n17.6.4.1 B0 \u2192J/\u03c8\u03c00\nThe decay B0 \u2192J/\u03c8\u03c00 is a b \u2192ccd transition into\na CP-even \ufb01nal state. The \ufb01nal state has contributions\nfrom both a color- and Cabibbo-suppressed tree ampli-\ntude, and penguin amplitudes with di\ufb00erent weak phases.\nIn the absence of penguin contributions one can measure\nthe Unitarity Triangle angle \u03c61 using this decay. If there\nare signi\ufb01cant penguin contributions, the measured value\nof \u03c61, called the \u201ce\ufb00ective phase\u201d \u03c6e\ufb00\n1 , may di\ufb00er from\nthat obtained from the tree-dominated B \u2192J/\u03c8K0 de-\ncays. There are two motivations for such a measurement;\n\ufb01rstly it is possible to constrain theoretical uncertainties in\nB \u2192J/\u03c8K0 decays using B0 \u2192J/\u03c8\u03c00 (Ciuchini, Pierini,\nand Silvestrini, 2005), and secondly one may be able to\nprobe, or constrain, possible new physics contributions to\nb \u2192ccd transitions manifesting via loop diagrams.\n74 A commonly accepted de\ufb01nition of \u201cobservation\u201d is a result\nwith a statistical signi\ufb01cance of at least \ufb01ve standard devia-\ntions if the uncertainties are treated as Gaussian.\n1\n\u03c6\nsin 2\n0\n0.5\n1\nBABAR (2000)\n(9.0/fb)\n0.09 (a)\n\u00b1\n0.37 \n\u00b1\n0.12 \nBelle (2000)\n(6.2/fb)\n (b)\n -0.44 -0.09\n +0.43 +0.07\n0.45\nBelle (2001)\n)\nB\n(11 M B\n (c)\n -0.34 -0.10\n +0.32 +0.09\n0.58\nBABAR (2001)\n)\nB\n(23 M B\n0.05 (d)\n\u00b1\n0.20 \n\u00b1\n0.34 \nBABAR (2001)\n)\nB\n(32 M B\n0.05 (e)\n\u00b1\n0.14 \n\u00b1\n0.59 \nBelle (2001)\n)\nB\n(31 M B\n0.06 (f)\n\u00b1\n0.14 \n\u00b1\n0.99 \nBABAR (2002)\n)\nB\n(88 M B\n0.034 (g)\n\u00b1\n0.067 \n\u00b1\n0.741 \nBelle (2002)\n)\nB\n(85 M B\n0.035 (h)\n\u00b1\n0.074 \n\u00b1\n0.719 \nBelle (2003)\n)\nB\n(152 M B\n0.023 (i)\n\u00b1\n0.056 \n\u00b1\n0.728 \nBABAR (2004)\n)\nB\n(227 M B\n0.023 (j)\n\u00b1\n0.040 \n\u00b1\n0.722 \nBelle (2005)\n)\nB\n(386 M B\n0.020 (k)\n\u00b1\n0.039 \n\u00b1\n0.652 \nBABAR (2006)\n)\nB\n(348 M B\n0.019 (l)\n\u00b1\n0.034 \n\u00b1\n0.710 \nBelle (2006)\n)\nB\n(535 M B\n0.017 (m)\n\u00b1\n0.031 \n\u00b1\n0.642 \nBABAR (2008)\n)\nB\n(465 M B\n0.012 (n)\n\u00b1\n0.028 \n\u00b1\n0.687 \nBelle (2011)\n)\nB\n(772 M B\n0.012 (o)\n\u00b1\n0.023 \n\u00b1\n0.667 \nCurrent Average\n0.020\n\u00b1\n0.677 \nFigure 17.6.8. History of the sin 2\u03c61 measurements with b \u2192\nc\u00afcs decays, ordered by the dates they appeared in public. Refer-\nences: (a) (Aubert, 2000), (b) (Aihara, 2000a), (c) (Abashian,\n2001), (d) (Aubert, 2001a), (e) (Aubert, 2001e), (f) (Abe,\n2001g), (g) (Aubert, 2002g), (h) (Abe, 2002b), (i) (Abe, 2005c),\n(j) (Aubert, 2005i), (k) (Abe, 2005j), (l) (Aubert, 2006j),\n(m) (Chen, 2007a), (n) (Aubert, 2009z), (o) (Adachi, 2012c).\nUnlike b \u2192ccs decays, which are experimentally clean,\none has to consider signi\ufb01cant background contributions\nwhen trying to extract information from B0 \u2192J/\u03c8\u03c00 sig-\nnal events. These background contributions include events\nfrom B decays to J/\u03c8\u03c10, J/\u03c8K0\nS, J/\u03c8K\u22170, J/\u03c8K\u2217\u00b1, and\nJ/\u03c8\u03c1\u00b1 \ufb01nal states as well as smaller contributions from\nother B decays to \ufb01nal states including a J/\u03c8. The afore-\nmentioned backgrounds populate the negative \u2206E region\n(peak \u223c\u22120.2 GeV) and have a tail in the signal region\naround \u2206E \u223c0 (see Fig. 17.6.9). Since these modes are\nwell measured, the B Factories have relied on existing\nbranching fraction measurements from the Particle Data\nGroup (Yao et al., 2006) in order to \ufb01x the normalization\nof background contributions while extracting signal yields\nand CP asymmetry parameters. The normalization of the\ncombinatorial background is allowed to vary in the \ufb01t.\nBoth experiments perform an unbinned maximum like-\nlihood \ufb01t to data using discriminating variables: mES, \u2206E,\nand \u2206t. In order to suppress background from light-quark\ncontinuum events, BABAR also includes a Fisher discrim-\ninant as one of the discriminating variables in their \ufb01t\nto data. This is computed using three variables: L0, L2\n\n309\nEvents / ( 0.4 ps )\n200\n400\nEvents / ( 0.4 ps )\n200\n400\n tags\n0\nB \n tags\n0 \nB\n\u03b7f=-1\n(a)\nRaw Asymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\nRaw Asymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\n(b)\nEvents / ( 0.4 ps )\n100\n200\n300\nEvents / ( 0.4 ps )\n100\n200\n300\n tags\n0\nB \n tags\n0 \nB\n\u03b7f=+1\n(c)\nt (ps)\n\u2206\n-5\n0\n5\nRaw Asymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\n-5\n0\n5\nRaw Asymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\n(d)\nEvents / (0.5 ps)\n100\n200\n300\n400\n = -1\nf\u03b7\n tags\n0\nB\n tags\n0\nB\nAsymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / (0.5 ps)\n100\n200\n = +1\nf\u03b7\n tags\n0\nB\n tags\n0\nB\nt (ps)\n\u2206\n-5\n0\n5\nAsymmetry\n-0.4\n-0.2\n0\n0.2\n0.4\nFigure 17.6.7. Flavor-tagged \u2206t distributions (a,c) and raw CP asymmetries (b,d) for the BABAR (left, (Aubert, 2009z)) and\nBelle (right, (Adachi, 2012c)) measurements of sin 2\u03c61. The top two plots show the B \u2192(c\u00afc)K0\nS (\u03b7f = \u22121) samples, and the\nbottom two show the B \u2192J/\u03c8K0\nL (\u03b7f = +1) sample. The shaded regions for BABAR represent the \ufb01tted background, while the\nBelle distributions are background subtracted. The two experiments adopt the opposite color code in \u2206t distribution plots.\nE (GeV)\n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nEvents / ( 0.01 GeV )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nE (GeV)\n\u2206\n-0.2\n-0.15\n-0.1\n-0.05\n-0\n0.05\n0.1\n0.15\n0.2\nEvents / ( 0.01 GeV )\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nFigure 17.6.9. Distributions of \u2206E for B0 \u2192J/\u03c8\u03c00 samples\nused in the Belle measurement (Lee, 2008) of \u03c61. The super-\nimposed curves show the signal (solid line), B \u2192J/\u03c8 X back-\nground (dot-dashed line), combinatorial background (dashed\nline) and the sum of all the contributions (thick solid line).\n(Eq. (9.4.1)), and cos \u03b8H, where \u03b8H is the angle between\nthe positively charged lepton and the B candidate mo-\nmenta in the J/\u03c8 rest frame. In contrast, Belle achieves\ncontinuum background rejection by applying a cut on the\nratio of zeroth to second Fox-Wolfram moments, R2 < 0.4.\nDetails on these background suppression techniques can\nbe found in Chapter 9.\nThe most recent results obtained by BABAR (Aubert,\n2008i) and Belle (Lee, 2008) use 465 \u00d7106 and 535 \u00d7106\nBB pairs, respectively, and are summarized in Table 17.6.3.\nBABAR \ufb01nds CP violation with 4.0\u03c3 signi\ufb01cance, and Belle\n\ufb01nds 2.4\u03c3 signi\ufb01cance. Both results, and their average, are\nconsistent with the value of S measured in b \u2192ccs decays.\nThe obtained value of C is consistent with zero.\nTable 17.6.3. The time-dependent CP asymmetry parameters\n\u2212\u03b7fS and C for the decay B0 \u2192J/\u03c8 \u03c00. The \ufb01rst quoted\nuncertainty is statistical, and the second is systematic. The\naverages are obtained by HFAG (Amhis et al., 2012).\nExperiment\n\u2212\u03b7fS\nC\nBABAR\n1.23 \u00b1 0.21 \u00b1 0.04\n\u22120.20 \u00b1 0.19 \u00b1 0.03\nBelle\n0.65 \u00b1 0.21 \u00b1 0.05\n\u22120.08 \u00b1 0.16 \u00b1 0.05\nAverage\n0.93 \u00b1 0.15\n\u22120.10 \u00b1 0.13\n17.6.4.2 B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213\nThe decay B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213is dominated by a color-\nfavored tree-diagram in the SM. When neglecting the pen-\nguin (loop) diagram, the mixing induced CP asymmetry\nof B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213is also determined by sin 2\u03c61. The\n\n310\ne\ufb00ect of neglecting the penguin amplitude has been esti-\nmated in models based on factorization and heavy quark\nsymmetry, and the corrections are expected to be a few\npercent (Xing, 1998, 2000). Signi\ufb01cant deviation of S in\nB0 \u2192D(\u2217)\u00b1D(\u2217)\u2213decays with respect to sin 2\u03c61 deter-\nmined from b \u2192ccs transitions, or a large non-zero value\nof C, could indicate physics beyond the SM (Grossman\nand Worah, 1997; M. Gronau and Pirjol, 2008; Zwicky,\n2007).\nThe B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213candidates are formed from op-\npositely charged D(\u2217) mesons reconstructed in the follow-\ning channels: D\u2217+ \u2192D0\u03c0+, D\u2217+ \u2192D+\u03c00, D0 \u2192K\u2212\u03c0+,\nD0 \u2192K\u2212\u03c0+\u03c00, D0 \u2192K\u2212\u03c0+\u03c0\u2212\u03c0+, D0 \u2192K0\nS\u03c0+\u03c0\u2212, and\nD+ \u2192K\u2212\u03c0+\u03c0+. Belle also uses the D0 \u2192K+K\u2212, D+ \u2192\nK0\nS\u03c0+ and K0\nS\u03c0+\u03c00 channels. In the B0 \u2192D\u2217+D\u2217\u2212mode,\nB0 candidates where both D\u2217mesons decay to D\u03c00 are ex-\ncluded because of its smaller branching fraction and larger\nbackgrounds. At least one D meson is required to decay\nvia D+ \u2192K\u2212\u03c0+\u03c0+ for the B0 \u2192D+D\u2212decay.\nBoth BABAR and Belle also analyze these decays using\npartially reconstructed events. However, while Belle in-\ncludes these events in their analysis of fully reconstructed\nevents, BABAR performs a separate B0 \u2192D\u2217+D\u2217\u2212anal-\nysis of partially reconstructed events. For the partial re-\nconstruction method one D\u2217\u2212(or a D\u2212\u2192K+\u03c0\u2212\u03c0\u2212)\nis fully reconstructed as described in the previous para-\ngraph. For the other D\u2217+, only a slow pion \u03c0+\nslow from\nthe decay D\u2217+ \u2192D0\u03c0+\nslow, is reconstructed. The details\nof the partial reconstruction technique are described in\nSection 7.3. Due to low B meson CM momentum and\nsmall energy release in the D\u2217+ decay, the momenta of\n\u03c0+\nslow and D(\u2217)\u2212are almost back-to-back. This signature\nis used as a discriminator in Belle\u2019s analysis. BABAR on the\nother hand exploits the kinematics of the event and calcu-\nlates the B four-momentum up to an unknown azimuthal\nangle around the direction of the fully reconstructed D\u2217.\nBABAR uses the median value for this angle based on simu-\nlation to calculate the recoil mass of the unreconstructed\nD0 and uses this recoil mass as a \ufb01t variable to sepa-\nrate signal and background. Belle requires the CM mo-\nmenta of the reconstructed mesons in the D\u2217+D\u2212mode\nto satisfy 1.63 GeV/c < p\u2217\nD(\u2217)\u2212< 1.97 GeV/c and p\u2217\n\u03c0+\nslow <\n0.18 GeV/c. BABAR selects events with 1.3 GeV/c < p\u2217\nD\u2217\u2212<\n2.1 GeV/c and p\u2217\n\u03c0+\nslow < 0.6 GeV/c.\nIn the partial reconstruction technique used by both\nexperiments, a lepton \u2113tag is used to provide \ufb02avor tagging,\nsuppress continuum background to a negligible level, and\nreduce combinatorial BB background. In addition to lep-\ntons BABAR also uses kaons for \ufb02avor tagging. The vertex\nof the reconstructed B (Brec ) is determined by a \ufb01t with\nthe fully reconstructed D0 or D\u2212mesons to the interac-\ntion region. On the tagging side, the \u2113tag is \ufb01tted to the\ninteraction region to provide the Btag vertex information.\nFor the kaon-tagged events (BABAR), all tracks that do\nnot belong to Brec and are outside of a cone of cos \u03b8 = 0.5\naround the missing D0 direction are used for Btag vertex-\ning. A kinematic cut is applied to remove a large fraction\nof the background events from B \u2192D(\u2217)\u2212\u2113+X decays or\nother sources where the tagging track originates from the\nsame B as the fully reconstructed D\u2217or D\u2212. In Belle\u2019s\nanalysis, the calculated angle between the B and D(\u2217)\u2113tag\ncombination is required to be outside the physical region\nof B \u2192D(\u2217)\u2212\u2113+X, i.e.,\ncos \u03b8B,D\u2113= (Ebeam \u2212E\u2217\nD\u2113)2 \u2212p\u22172\nB \u2212p\u22172\nD\u2113\n2p\u2217\nBp\u2217\nD\u2113\n< \u22121.1.\n(17.6.6)\nIn BABAR\u2019s analysis, the angle between the tagging lepton\n(kaon) and the missing D0 is required to be larger than\narccos 0.75 (arccos 0.5). This kind of background (tag-\nging and reconstructed particles originating from the same\nB) cannot be completely eliminated, and care is taken to\nevaluate the mistag e\ufb00ects.\nFor each B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213candidate, BABAR con-\nstructs a likelihood function Lmass from the masses and\nmass uncertainties of the D and D\u2217candidates. The val-\nues of Lmass and \u2206E are used to reduce the combinatorial\nbackground. From the simulated events, the minimum al-\nlowed values of \u2212ln Lmass and |\u2206E| for each individual\n\ufb01nal state are optimized to obtain the highest expected\nsignal signi\ufb01cance.\nThe technique used to \ufb01t the \u2206t distribution is anal-\nogous to the one used in b \u2192ccs decays. Since the\nB0 \u2192D\u2217+D\u2217\u2212\ufb01nal state contains two vector mesons, it\nis an admixture of CP-even and CP-odd states depending\non the orbital angular momentum of the decay products\n(Chapter 12). In the partial reconstruction approach, the\nhelicity angles are calculated ignoring the B meson mo-\nmentum. In the \ufb01t to data, two scenarios are considered.\nIn the \ufb01rst scenario, the CP-even amplitude is allowed\nto have di\ufb00erent CP-violating parameters (C+ and S+)\nfrom those of the CP-odd amplitude (C\u22a5and S\u22a5). In the\nsecond scenario, we assume that C+ = C\u22a5= CD\u2217+D\u2217\u2212\nand S+ = \u2212S\u22a5= SD\u2217+D\u2217\u2212.75 In the absence of pen-\nguin contributions, SD+D\u2212= S+ = \u2212S\u22a5= \u2212sin 2\u03c61 and\nCD+D\u2212= C+ = C\u22a5= 0.\nAs B0 \u2192D\u2217\u00b1D\u2213is not a CP eigenstate, the expres-\nsions for the di\ufb00erent S and C parameters are related,\nSD\u2217\u00b1D\u2213= \u2212\nq\n1 \u2212C2\nD\u2217\u00b1D\u2213sin(2\u03c6e\ufb00\n1 \u00b1\u03b4) (see Eq. 10.2.6) ,\nwhere \u03b4 is the strong phase di\ufb00erence between the D\u2217+D\u2212\nand D\u2217\u2212D+ amplitudes. Neglecting the penguin contribu-\ntions, \u03c6e\ufb00\n1\n= \u03c61 and CD\u2217+D\u2212= \u2212CD\u2217\u2212D+. It is convenient\nto express the CP asymmetry parameters as\nSD\u2217D = 1\n2(SD\u2217+D\u2212+ SD+D\u2217\u2212),\nCD\u2217D = 1\n2(CD\u2217+D\u2212+ CD+D\u2217\u2212),\n\u2206SD\u2217D = 1\n2(SD\u2217+D\u2212\u2212SD+D\u2217\u2212),\n(17.6.7)\n\u2206CD\u2217D = 1\n2(CD\u2217+D\u2212\u2212CD+D\u2217\u2212).\n75 In some literature, the opposite sign convention of S\u22a5is\nused, i.e., S+ = +S\u22a5= SD\u2217+D\u2217\u2212.\n\n311\nTable 17.6.4. Summary of CP asymmetry parameter mea-\nsurements for B0 \u2192D(\u2217)\u00b1D(\u2217)\u2213decays. Signal yields quoted\nhere include tagged and untagged events. Reference: (a) (Au-\nbert, 2009ad); (b) Lees (2012k); (c) (Kronenbitter, 2012);\n(d) (Rohrken, 2012).\nBABAR\nBelle\nB0 \u2192D\u2217+D\u2217\u2212\n934 \u00b1 40 (a)\n1225 \u00b1 59 (c)\nS+\n\u22120.76 \u00b1 0.16 \u00b1 0.04\n\u22120.81 \u00b1 0.13 \u00b1 0.03\nC+\n+0.00 \u00b1 0.12 \u00b1 0.02\n\u22120.18 \u00b1 0.10 \u00b1 0.05\n\u2212S\u22a5\n\u22121.80 \u00b1 0.70 \u00b1 0.16\n\u22121.52 \u00b1 0.62 \u00b1 0.12\nC\u22a5\n+0.41 \u00b1 0.49 \u00b1 0.08\n+0.05 \u00b1 0.39 \u00b1 0.08\nSD\u2217+D\u2217\u2212\n\u22120.70 \u00b1 0.16 \u00b1 0.03\n\u22120.79 \u00b1 0.13 \u00b1 0.03\nCD\u2217+D\u2217\u2212\n+0.05 \u00b1 0.09 \u00b1 0.02\n\u22120.15 \u00b1 0.08 \u00b1 0.04\nB0 \u2192D\u2217+D\u2217\u2212\n4972 \u00b1 453 (b)\n-\n(partial rec.)\nSD\u2217+D\u2217\u2212\n\u22120.49 \u00b1 0.18 \u00b1 0.08\n-\nCD\u2217+D\u2217\u2212\n+0.15 \u00b1 0.09 \u00b1 0.04\n-\nB0 \u2192D\u2217D\n724 \u00b1 37 (a)\n887 \u00b1 39 (d)\nSD\u2217D\n\u22120.68 \u00b1 0.15 \u00b1 0.04\n\u22120.78 \u00b1 0.15 \u00b1 0.05\nCD\u2217D\n+0.04 \u00b1 0.12 \u00b1 0.03\n\u22120.01 \u00b1 0.11 \u00b1 0.04\n\u2206SD\u2217D\n+0.05 \u00b1 0.15 \u00b1 0.02\n\u22120.13 \u00b1 0.15 \u00b1 0.04\n\u2206CD\u2217D\n+0.04 \u00b1 0.12 \u00b1 0.03\n\u22120.12 \u00b1 0.11 \u00b1 0.03\nB0 \u2192D+D\u2212\n152 \u00b1 17 (a)\n269 \u00b1 21 (d)\nSD+D\u2212\n\u22120.63 \u00b1 0.36 \u00b1 0.05\n\u22121.06 +0.21\n\u22120.14 \u00b1 0.08\nCD+D\u2212\n\u22120.07 \u00b1 0.23 \u00b1 0.03\n\u22120.43 \u00b1 0.16 \u00b1 0.05\nThe parameters SD\u2217D and CD\u2217D characterize mixing in-\nduced CP violation and \ufb02avor-dependent direct CP vio-\nlation, respectively. \u2206SD\u2217D and \u2206CD\u2217D are insensitive\nto CP violation. In the case of BABAR\u2019s B0 \u2192D\u2217+D\u2217\u2212\npartial reconstruction method, the \ufb01t parameter S is (1 \u2212\n2R\u22a5)SD\u2217+D\u2217\u2212, where R\u22a5is the CP-odd fraction measured\nfrom fully reconstructed D\u2217+D\u2217\u2212events.\nThe most recent measurements of the CP violation in\nB0 \u2192D(\u2217)\u00b1D(\u2217)\u2213decays by BABAR are based on the\nfull data sample, 467 \u00d7 106 BB pairs (Aubert, 2009ad),\nwhile Belle measurements are based on 772 \u00d7 106 BB\npairs (Kronenbitter, 2012; Rohrken, 2012). The results are\nsummarized in Table 17.6.4. These supersede the previous\nBABAR (Aubert, 2003g, 2005u, 2007n,u) and Belle (Au-\nshev, 2004; Fratina, 2007; Miyake, 2005; Vervink, 2009)\nmeasurements, except for the Belle result based on the\nB0 \u2192D\u2217D partial reconstruction (Aushev, 2004).\nThe averages of BABAR and Belle results (Amhis et al.,\n2012) are SD\u2217+D\u2217\u2212= \u22120.77 \u00b1 0.10, SD\u2217D = \u22120.73 \u00b1 0.11,\nand SD+D\u2212= \u22120.98 \u00b1 0.17, and other parameters are\nconsistent with zero within uncertainties. All three modes\nhave signi\ufb01cant CP violation asymmetries (> 5\u03c3), which\nare consistent with the SM expectation with small penguin\namplitude contributions (S parameters are consistent with\nthe sin 2\u03c61 value from b \u2192c\u00afcs decays).\n17.6.5 \u03c61 from b \u2192c\u00afud decays\n17.6.5.1 B0 \u2192D(\u2217)h0\nThe decay B0 \u2192D(\u2217)h0, where h0 is a light, un\ufb02avored\nneutral meson, is dominated by a b \u2192c\u00afud color-suppressed\ntree diagram in the SM. The \ufb01nal state D(\u2217)h0 is a CP\neigenstate if the neutral D meson decays to a CP eigen-\nstate as well. In this case, the time-dependent asymme-\ntry in B0 decays is similar to that of b \u2192c\u00afcs decays\nbut with a small correction from the b \u2192u\u00afcd amplitude.\nThis amplitude is suppressed by VubV \u2217\ncd/VcbV \u2217\nud \u22430.02,\nand therefore the deviation is expected to be small in the\nSM (Fleischer, 2003a,b; Grossman and Worah, 1997). R-\nparity violating (\u0338Rp) supersymmetric processes (Grossman\nand Worah, 1997) could enter at the tree level in these de-\ncays, leading to a deviation from the SM prediction.\nIn BABAR\u2019s analysis (Aubert, 2007ad) with 383 \u00d7 106\nBB pairs, the B0 meson is fully reconstructed in the fol-\nlowing channels: D(\u2217)\u03c00 (D \u2192K+K\u2212, K0\nS\u03c9) and D(\u2217)\u03b7\n(D \u2192K+K\u2212), where D\u22170 \u2192D0\u03c00, and D\u03c9 (D \u2192\nK+K\u2212, K0\nS\u03c9, K0\nS\u03c00). The \u03b7 mesons are reconstructed via\n\u03b3\u03b3 and \u03c0+\u03c0\u2212\u03c00 \ufb01nal states, and the \u03c9 candidates are\nreconstructed from the \u03c0+\u03c0\u2212\u03c00 decay mode. The event\nselection criteria are determined by maximizing the ex-\npected signal signi\ufb01cance using Monte Carlo simulated\nsignal events and simulated samples of generic BB and\ne+e\u2212\u2192qq (q = u, d, s, c) continuum events.\nAngular distributions of the D \u2192K0\nS\u03c9 decay mode\nare exploited to take advantage of the polarization in the\ndecay. The background from continuum qq production is\nsuppressed by a Fisher discriminant constructed using sev-\neral event shape variables and angular distributions (see\nChapter 9).\nThe signal and combinatorial background yields are\ndetermined by a \ufb01t to the mES distribution using a Gaus-\nsian and a threshold function (ARGUS, see Eq. (7.1.11))\nfor the signal and combinatorial background components,\nrespectively. The contribution from each mode is shown in\nTable 17.6.5. Peaking background contributions are stud-\nied using both simulation and D0 sideband data. The con-\ntributions to CP-even and CP-odd modes are (0.8\u00b12.6)%\nand (11 \u00b1 6)%, respectively.\nThe \ufb01t technique adopted to extract the CP violating\nparameters S and C is similar to that used in b \u2192c\u00afcs\ndecays. The mistag parameters and the resolution func-\ntion are determined from a large data control sample of\nB0 \u2192D(\u2217)\u2212h+ decays, where h+ is a \u03c0+, \u03c1+, or a+\n1 me-\nson. An exponential decay is used to model the \u2206t p.d.f.\nof the peaking background and accounts for possible CP\nasymmetries in the systematic uncertainty. In addition to\nthe \ufb01t to the entire sample, \ufb01ts to CP-even and CP-odd\nsubsamples are performed to check consistency. As the SM\ncorrections due to the sub-leading-order b \u2192u\u00afcd diagram\nare di\ufb00erent for DCP + and DCP \u2212(Fleischer, 2003a,b), a\n\ufb01t is also performed allowing di\ufb00erent CP asymmetries\nfor DCP + and DCP \u2212. The results are summarized in Ta-\nble 17.6.5, and the \u2206t distribution projections and the\nasymmetry of the events in the signal region are shown\nin Fig. 17.6.10. The result is consistent with the world\n\n312\nTable 17.6.5. Summary of the B0 \u2192D(\u2217)0\nCP h0 analysis from\nBABAR (Aubert, 2007ad). The CP eigenvalue of the D0 \ufb01nal\nstate is indicated in the column \u2018DCP \u2019.\n\u03b7f = +1 (CP even)\n\u03b7f = \u22121 (CP odd)\nMode\nDCP\nNsignal\nMode\nDCP\nNsignal\nD0\nK0\nS\u03c9\u03c00\n\u2212\n26.2 \u00b1 6.3\nD0\nKK\u03c00\n+\n104 \u00b1 17\nD0\nK0\nS\u03c00\u03c9\n\u2212\n40.0 \u00b1 8.0\nD0\nKK\u03b7\u03b3\u03b3\n+\n28.9 \u00b1 6.5\nD0\nK0\nS\u03c9\u03c9\n\u2212\n23.2 \u00b1 6.8\nD0\nKK\u03b73\u03c0\n+\n14.2 \u00b1 4.7\nD\u22170\nKK\u03c00\n+\n23.2 \u00b1 6.3\nD0\nKK\u03c9\n+\n51.2 \u00b1 8.5\nD\u22170\nKK\u03b7\u03b3\u03b3\n+\n9.8 \u00b1 3.5\nD\u22170\nK0\nS\u03c9\u03c00\n\u2212\n5.5 \u00b1 3.3\nD\u22170\nKK\u03b73\u03c0\n+\n6.8 \u00b1 2.9\nCombined\n131 \u00b1 16\n209 \u00b1 23\n\u03b7fS\n\u22120.17 \u00b1 0.37\n\u22120.82 \u00b1 0.28\nC\n\u22120.21 \u00b1 0.25\n\u22120.21 \u00b1 0.21\n\u03b7fS (combined)\n\u22120.56 \u00b1 0.23 \u00b1 0.05\nC (combined)\n\u22120.23 \u00b1 0.16 \u00b1 0.04\nDCP +\nDCP \u2212\n\u03b7fS\n\u22120.65 \u00b1 0.26 \u00b1 0.06\n\u22120.46 \u00b1 0.45 \u00b1 0.13\nC\n\u22120.33 \u00b1 0.19 \u00b1 0.04\n\u22120.03 \u00b1 0.28 \u00b1 0.07\naverage of \u2212sin 2\u03c61, and is 2.3\u03c3 from the CP-conserving\nhypothesis S = C = 0.\nFigure 17.6.10. \u2206t distributions and asymmetries of B0 \u2192\nD(\u2217)0\nCP h0 candidates from BABAR (Aubert, 2007ad) for (a, b)\nCP-even and (c, d) CP-odd candidates in the signal region\n(mES > 5.27 GeV/c2). In (a) and (c), the solid points and curve\n(open circles and dashed curve) are B0-tagged (B0-tagged)\ncandidates and \u2206t projection curves. Shaded areas (dotted\nlines) are background distributions for the B0-tagged (B0-\ntagged) candidates. In (b) and (d), the solid curve represents\nthe combined \ufb01t result, and the dashed curve represents the\nresult of the \ufb01ts to CP-even and CP-odd modes separately.\n17.6.6 \u03c61 from charmless quasi-two-body B decays\nThe time-dependent CP asymmetry parameter S mea-\nsured in charmless decays to CP eigenstates via b \u2192s\u00afqq\npenguin transitions is also equal to S = \u2212\u03b7f sin 2\u03c61 in\nthe SM. These decays are particularly sensitive to new\nphysics because any unobserved heavy particle could con-\ntribute an additional penguin loop and alter the value of\nthe measured weak phase. If the measured S in one or\na group of charmless decays deviates signi\ufb01cantly from\nthat in tree-dominated processes, it could be a signature\nof new physics e\ufb00ects. The comparison between loop and\ntree-dominated decays, however, must to be made with\ncareful estimates of the SM corrections from higher order\ntopologies. The key issue in the theoretical understanding\nof these CP asymmetries is the tree-to-penguin ratio, both\nin short- and long-distance interactions. The typical devi-\nations in theoretical calculations are below a few percent,\nand the corresponding uncertainty can be as small as one\nor two percent. The modes that bene\ufb01t from the least the-\noretical uncertainties are \u03b7\u2032K0\nS, \u03c6K0\nS, and K0\nSK0\nSK0\nS (Be-\nneke, 2005; Cheng, Chua, and Soni, 2005a,b).\nOf the charmless decays of interest, two-body and quasi-\ntwo-body \ufb01nal states are the simplest states to study ex-\nperimentally. The term \u201cquasi-two-body\u201d refers to a \ufb01nal\nstate that includes a resonance whose interference with\nany other amplitude is ignored (details in Section 17.4.5).\nThe experiments at the B Factories have studied the CP-\nodd states B0 \u2192\u03b7\u2032K0\nS, \u03c9K0\nS, \u03c00K0\nS and the CP-even\nstates B0 \u2192\u03b7\u2032K0\nL and \u03c00K0\nL. Measurements of time-\ndependent asymmetries in three-body decays are discussed\nin Section 17.6.7.\nDue to the similarity between the experimental tech-\nniques used to reconstruct the B0 \u2192\u03c00K0\nS and B0 \u2192\nK0\nSK0\nS decays, the latter measurement is included in this\nsection. The 2K0\nS mode is dominated by a b \u2192d\u00afss penguin\ntransition. Assuming top-quark dominance in the virtual\nloop, the time-dependent CP asymmetry parameters in\nthis decay are expected to vanish, i.e. SK0\nSK0\nS = CK0\nSK0\nS =\n0 (Fleischer, 1994). If a signi\ufb01cant discrepancy is observed,\nthis would be a clear signature of new physics (Giri and\nMohanta, 2004).\nMeasurements of time-dependent asymmetry param-\neters of B mesons decaying into \u03b7\u2032K0, \u03c9K0\nS, \u03c00K0, and\nK0\nSK0\nS are described in the following.\n17.6.6.1 B0 \u2192\u03b7\u2032K0\nThe branching fraction of the B0 \u2192\u03b7\u2032K0 decay was \ufb01rst\nmeasured by CLEO (Behrens et al., 1998) and was sur-\nprisingly large compared to na\u00a8\u0131ve expectations. This result\nis con\ufb01rmed by both Belle (Abe, 2001d) and BABAR (Au-\nbert, 2001d). Because of the large branching fraction, this\nmode provides the most precise time-dependent CP asym-\nmetry parameter measurement of any b \u2192s\u00afqq decay mode.\nThe \ufb01rst measurements were made in 2002 by Belle (Chen,\n2002) and in 2003 by BABAR (Aubert, 2003i). For these\nmeasurements, the \u03b7\u2032 candidates were reconstructed via\n\u03b7\u2032 \u2192\u03b7\u03c0+\u03c0\u2212and \u03b7\u2032 \u2192\u03c10\u03b3 decays, with \u03b7 \u2192\u03b3\u03b3 and \u03c10 \u2192\n\n313\n\u03c0+\u03c0\u2212. Only the B0 \u2192\u03b7\u2032K0\nS mode was considered, using\nK0\nS \u2192\u03c0+\u03c0\u2212. The measured values of S were consistent\nbetween the two experiments but the uncertainties were\nlarge. Over the years both experiments have improved the\nmeasurements method and increased the available data\nsample. The decays \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 and K0\nS \u2192\u03c00\u03c00 are\nadded to the reconstructed sub-decays listed above. All\nthe combinations of the sub-decays are used except for\nthe \u03b7\u2032 \u2192\u03c0+\u03c0\u2212\u03c00, K0\nS \u2192\u03c00\u03c00 combination. Belle also\nexcludes the \u03b7\u2032 \u2192\u03c10\u03b3, K0\nS \u2192\u03c00\u03c00 combination. A ten-\nsion between these results and the SM expectation at\na level of 3\u03c3 was reported by BABAR in 2005 (Aubert,\n2005w), but was not con\ufb01rmed by Belle (Chen, 2005b). In\nthe 2007 update of the measurements (Aubert (2007am);\nChen (2007a)), the decay B0 \u2192\u03b7\u2032K0\nL with \u03b7\u2032 \u2192\u03b7\u03c0+\u03c0\u2212\n(both sub-decays of the \u03b7 considered) is also added. With\nthese measurements, both experiments are able to estab-\nlish the existence of CP violation in the B0 \u2192\u03b7\u2032K0 mode,\nobtained from the combination of the B0 \u2192\u03b7\u2032K0\nS and\nB0 \u2192\u03b7\u2032K0\nL decays. This is the \ufb01rst observation of CP\nviolation (with a signi\ufb01cance greater than 5\u03c3) in b \u2192s\u00afqq\ntransitions. These measurements are consistent with the\nSM expectation.\nIn the most recent measurements, BABAR and Belle use\ndata samples of 467 \u00d7 106 and 535 \u00d7 106 BB pairs (Au-\nbert (2009aa); Chen (2007a)), respectively. The kinematic\nvariables used to identify B0 candidates are mES and\n\u2206E for \u03b7\u2032K0\nS; \u2206E (BABAR) or p\u2217\nB (Belle) for \u03b7\u2032K0\nL. As\nwith other charmless B decays, the dominant background\ncomes from e+e\u2212\u2192q\u00afq (q = u, d, s, c) continuum events.\nLoose cuts are applied to continuum suppression variables.\nThese variables are also used together with the aforemen-\ntioned kinematic variables in the \ufb01t to extract signals.\nBABAR uses a Fisher discriminant formed from shape vari-\nables, while Belle uses a likelihood ratio formed from a\nFisher discriminant with modi\ufb01ed Fox-Wolfram moments\n(see Chapter 9). The \ufb02avor tagging, vertex reconstruction,\nand \ufb01t procedures used to extract the CP asymmetry pa-\nrameters are essentially the same as for b \u2192c\u00afcs decays.\nThe results obtained are shown in Table 17.6.6. The time-\ndependent event yields and asymmetry from Belle are\nshown in Fig. 17.6.11. Both experiments measure asym-\nmetry parameters consistent with results from b \u2192c\u00afcs\ndecays. These measurements are limited by statistical un-\ncertainties. Most of the systematic uncertainties are in\ncommon with the b \u2192c\u00afcs modes, and summarized in\nSection 15.3. The main contributions to the systematic\nuncertainty arise from the CP content of the BB back-\nground and the likelihood \ufb01t model used.\nIn the course of the book preparation the \ufb01nal Belle\nresult in this mode became available, using the integrated\nluminosity of 711 fb\u22121 (Santelj, 2013). The measurement\nmainly pro\ufb01ts from the increased statistical power of the\nsample due to both, the increase in the luminosity as well\nas the reprocessing of data (see Section 3.3). The result\nincluding K0\nS and K0\nL \ufb01nal states is in agreement with the\nSM prediction,\nS = 0.68 \u00b1 0.07 \u00b1 0.03\nC = 0.03 \u00b1 0.05 \u00b1 0.03 .\n(17.6.8)\n(a) B0 \u2192\u03b7\u2032K0\n0\n50\n100\n150\nq=+1\nq=\u22121\nEntries / 1.5 ps\n-0.5\n0\n0.5\n-7.5\n-5\n-2.5\n0\n2.5\n5\n7.5\n-\u03bef\u2206t(ps)\nAsymmetry\nFigure 17.6.11. Background subtracted \u2206t distributions and\ntime-dependent asymmetry for B0 \u2192\u03b7\u2032K0 events with a good\n\ufb02avor tag from Belle (Chen, 2007a).\n17.6.6.2 B0 \u2192\u03c9K0\nS\nB0 \u2192\u03c9K0\nS candidates are reconstructed via \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00\nand K0\nS \u2192\u03c0+\u03c0\u2212sub-decay channels. The \u03c9 candidates\nare selected by requiring the \u03c0+\u03c0\u2212\u03c00 invariant mass to\nbe within a window around the nominal mass. As for\nB0 \u2192\u03b7\u2032K0\nS, mES, \u2206E, and continuum suppression vari-\nables are used to extract signals from background. BABAR\nalso includes the invariant mass of \u03c0+\u03c0\u2212\u03c00 and H in the\n\ufb01t to data to improve signal to background discrimination.\nThe variable H is the cosine of the angle between the op-\nposite direction of the B meson and the normal to the\ndecay plane in the \u03c9 rest frame. BABAR (Aubert, 2009aa)\nand Belle (Abe, 2007e) analyze data samples of 467 \u00d7 106\nand 535\u00d7106 BB pairs, respectively. Results are shown in\nTable 17.6.6, where the number of signal events obtained\nis small (\u223c100) and the uncertainties on S and C are\nlarge.\n17.6.6.3 B0 \u2192\u03c00K0\nSince the B0 \u2192\u03c00K0\nS decay does not produce charged\ntracks at the B0 decay vertex, it is experimentally chal-\nlenging to perform a time-dependent analysis. The decay\nposition is determined from the intersection of the K0\nS tra-\njectory, which is determined from the \u03c0+ and \u03c0\u2212tracks\nand the pro\ufb01le of the interaction point. BABAR imposes\nthe constraint that the sum of the two B decay times\n(tCP +ttag) is equal to 2\u03c4B0 with an uncertainty\n\u221a\n2\u03c4B0 in\norder to further improve the accuracy of the reconstructed\nvalue of \u2206t. The \u03c0+ and \u03c0\u2212tracks are required to be well\nmeasured in the silicon vertex detector. Since c\u03c4 of a K0\nS\nis 2.84 cm, about 60% and 30% of K0\nS candidates satisfy\nthis condition at BABAR and Belle, respectively. Flavor\ntagged signal events can contribute to the precision ob-\ntained on C. Events that fail to satisfy the requirement\nare also used in the \ufb01t with a p.d.f which is obtained by\n\n314\nTable 17.6.6. Summary of time-dependent asymmetry parameter measurements for charmless two-body and quasi-two-body\ndecays. Signal yields quoted here are for tagged and untagged events for BABAR and only tagged events for Belle. The B0 \u2192K0\nSK0\nS\nmode is expected to have S = C = 0 in the SM, and S = \u2212\u03b7f sin 2\u03c61 and C = 0 for the other modes.\nBABAR\nBelle\nAverage (Amhis et al., 2012)\n\u03b7\u2032K0\nRef.\nAubert (2009aa)\n(Chen, 2007a)\nYield\n2515 \u00b1 69\n1875 \u00b1 60\n\u2212\u03b7fS\n0.57 \u00b1 0.08 \u00b1 0.02\n0.64 \u00b1 0.10 \u00b1 0.04\n0.59 \u00b1 0.07\nC\n\u22120.08 \u00b1 0.06 \u00b1 0.02\n0.01 \u00b1 0.07 \u00b1 0.05\n\u22120.05 \u00b1 0.05\n\u03c9K0\nS\nRef.\n(Aubert, 2009aa)\n(Abe, 2007e)\nYield\n163 \u00b1 18\n118 \u00b1 18\n\u2212\u03b7fS\n0.55+0.26\n\u22120.29 \u00b1 0.02\n0.11 \u00b1 0.46 \u00b1 0.07\n0.45 \u00b1 0.24\nC\n\u22120.52+0.22\n\u22120.20 \u00b1 0.03\n0.09 \u00b1 0.29 \u00b1 0.06\n\u22120.32 \u00b1 0.17\n\u03c00K0\nS\n\u03c00K0\nRef.\n(Aubert, 2009aa)\n(Fujikawa, 2010)\nYield\n556 \u00b1 32\n919 \u00b1 62\n\u2212\u03b7fS\n0.55 \u00b1 0.20 \u00b1 0.03\n0.67 \u00b1 0.31 \u00b1 0.08\n0.57 \u00b1 0.17\nC\n0.13 \u00b1 0.13 \u00b1 0.03\n\u22120.14 \u00b1 0.13 \u00b1 0.06\n0.01 \u00b1 0.10\nK0\nSK0\nS\nRef.\n(Aubert, 2006ai)\n(Nakahama, 2008)\nYield\n32 \u00b1 9\n58 \u00b1 11\nS\n\u22121.28+0.80+0.11\n\u22120.73\u22120.16\n\u22120.38+0.69\n\u22120.77 \u00b1 0.09\n\u22121.08 \u00b1 0.49\nC\n\u22120.40 \u00b1 0.41 \u00b1 0.06\n0.38 \u00b1 0.38 \u00b1 0.05\n\u22120.06 \u00b1 0.26\nintegrating the time-dependent p.d.f. with respect to \u2206t.\nBABAR (Aubert, 2009aa) and Belle (Fujikawa, 2010) ana-\nlyze 467 \u00d7 106 and 657 \u00d7 106 BB pairs, respectively. The\ncontinuum background suppression method adopted by\nthe two experiments is discussed in more detail in Chap-\nter 9.\nBelle also includes B0 \u2192\u03c00K0\nL decays. Here mES is\ncalculated using the direction of the K0\nL meson assuming\nthat the parent B0 is at rest in the CM system. The signal\nis extracted using mES and a likelihood ratio variable for\ncontinuum suppression. Since the vertex position cannot\nbe calculated, B0 \u2192\u03c00K0\nL only contributes to the deter-\nmination of C. The signal yield obtained for the K0\nL mode\nis 285 \u00b1 52 events compared to 634 \u00b1 34 for the K0\nS mode.\nThe CP asymmetry parameters S and C are obtained\nby \ufb01tting the events with and without the vertex position\ninformation. The results are shown in Table 17.6.6. While\nthe C values measured by BABAR and Belle have opposite\nsigns, they are consistent at the level of \u223c1.5\u03c3.\n17.6.6.4 B0 \u2192K0\nSK0\nS\nAs with the B0 \u2192\u03c00K0\nS case, prompt charged tracks from\nthe B vertex are absent in B0 \u2192K0\nSK0\nS decays. Therefore,\nthe study of time-dependent CP asymmetry parameters\nuses the same technique developed for B0 \u2192\u03c00K0\nS. In this\ncase both charged pions from at least one of the K0\nS mesons\nare required to have been well reconstructed using hits in\nthe silicon vertex detector. The e\ufb03ciency is approximately\n82% and 61% for BABAR and Belle, respectively. Events\nin which both K0\nS mesons decay outside the silicon vertex\ndetector do not have a well reconstructed B vertex; they\nare only used to determine C.\nData samples of 348 \u00d7 106 and 657 \u00d7 106 BB pairs\nare used for the BABAR (Aubert, 2006ai) and Belle (Naka-\nhama, 2008) measurements, respectively. The suppression\nof the continuum background is achieved in the same way\nas for the B0 \u2192\u03c00K0\nS measurement. The results obtained\nfor the time-dependent asymmetry parameters are shown\nin Table 17.6.6. The dominant sources of systematic un-\ncertainty are due to the \ufb01t model parameterization. These\nresults are consistent with the SM prediction of no CP\nasymmetry in b \u2192d\u00afss penguin modes.\n17.6.7 \u03c61 from charmless three-body decays\nCharmless three-body decays through b \u2192s\u00afqq penguin\ntransitions also provide measurements of \u03c61. In general,\nthree-body decays are not CP eigenstates and also often\ninclude intermediate resonances. These resonances com-\nplicate the extraction of useful CP violation parameters.\nHowever, for B0 \u2192P 0P 0X0 decays, where P 0 and X0\nare any spin-0 neutral particles, the \ufb01nal state has a de\ufb01-\nnite CP eigenvalue, that of the X0 (Gershon and Hazumi,\n2004), regardless of intermediate states. The decay B0 \u2192\nK0\nSK0\nSK0\nS is of particular interest since it proceeds only\n\n315\nthrough a b \u2192s penguin transition and is free from any\nb \u2192u contribution. The \u03c00\u03c00K0\nS \ufb01nal state also has a\nde\ufb01nite CP (even) eigenvalue but has a b \u2192u tree contri-\nbution, similar to B0 \u2192K0\nS\u03c00, discussed in Section 17.6.6.\nAs with similar loop-dominated transitions, the deviations\nof measured CP asymmetry parameters from those found\nin b \u2192c\u00afcs decays are expected to be quite small in the\nSM. If a large deviation were to be measured, then this\ncould indicate the presence of new physics.\nIn general, analysis of the Dalitz plane for three-body\ndecays can be used to extract the amplitude of each con-\ntribution. Time-dependent Dalitz plot analysis, therefore,\ncan be used to extract CP asymmetry parameters of each\nintermediate two-body CP eigenstate and also those of\nany non-resonant CP eigenstate components (see Chap-\nter 13). This method is applied to B0 \u2192K+K\u2212K0 and\nB0 \u2192\u03c0+\u03c0\u2212K0 decays.\n17.6.7.1 B0 \u2192K0\nSK0\nSK0\nS\nThe \ufb01rst measurement of CP asymmetry parameters for\nB0 \u2192K0\nSK0\nSK0\nS decays is made by Belle (Sumisawa, 2005)\nwith 275 \u00d7 106 BB pairs. The latest measurements re-\nported by BABAR (Lees, 2012c) and Belle (Chen, 2007a)\nuse 468 \u00d7 106 and 535 \u00d7 106 BB pairs, respectively.\nThe K0\nS candidates are reconstructed in the K0\nS \u2192\n\u03c0+\u03c0\u2212and K0\nS \u2192\u03c00\u03c00 modes. B0 \u2192K0\nSK0\nSK0\nS decays are\nreconstructed with all K0\nS mesons decaying into a \u03c0+\u03c0\u2212\n\ufb01nal state (B3K0\nS(+\u2212)) and also with one of the K0\nS mesons\ndecaying into a \u03c00\u03c00 \ufb01nal state (B3K0\nS(00)). Signal is ex-\ntracted by \ufb01tting the distributions of kinematic variables\n(mES and \u2206E) and a continuum suppression variable.\nSince B0 \u2192\u03c7c0,2K0\nS (\u03c7c0,2 \u2192K0\nSK0\nS) decays give the\nsame \ufb01nal states but proceed through a b \u2192c\u00afcs transition,\nvetoes are applied for candidates with a K0\nSK0\nS mass com-\nbination within a window around the nominal \u03c7c0 mass.\nThe contribution from \u03c7c2 is found to be negligible. Belle\nalso applies a veto based on the measured D0 mass to re-\nmove the decays B0 \u2192D0K0\nS (D0 \u2192K0\nSK0\nS). In case of\nmultiple candidates in an event, a single candidate is se-\nlected based on the reconstructed K0\nS mass or the quality\nof a \ufb01t with a constraint on the D0 mass.\nThe decay vertex position of the reconstructed B is\nobtained using the trajectories of the K0\nS mesons in the\n\u03c0+\u03c0\u2212channels constraining the reconstructed K0\nS mesons\nto come from the beam spot. As is the case for \u03c00K0\nS and\nK0\nSK0\nS decays, these measurements use K0\nS \u2192\u03c0+\u03c0\u2212can-\ndidates reconstructed from tracks that are well measured\nin the silicon vertex detectors.\nThe usual \ufb02avor tagging and \ufb01tting procedure are ap-\nplied to extract the CP asymmetry parameters. The re-\nsults obtained are summarized in Table 17.6.7. The \u2206t dis-\ntribution and the time-dependent asymmetry from BABAR\nis shown in Fig. 17.6.12.\nt [ps]\n\u2206\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\nWeight/(2 ps)\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nFigure 17.6.12. (Top) \u2206t distribution and (bottom) CP\nasymmetry as a function of \u2206t, for the B0 \u2192K0\nSK0\nSK0\nS sig-\nnal (points) obtained by BABAR (Lees, 2012c) using the sPlot\ntechnique (see Section 11.2.3), superimposed on the \ufb01t results\n(histograms). The data points marked with crosses (circles)\nand solid (dashed) histograms correspond to B0 (B0) tagged\nevents.\nTable 17.6.7. Summary of CP asymmetry measurements for\ncharmless B0 \u2192K0\nSK0\nSK0\nS decays, (Lees, 2012c) and (Chen,\n2007a). The signal yield includes both tagged and untagged\nevents.\nBABAR\nBelle\nAverage\nSignal\n263 +21\n\u221219\n185 \u00b1 17\nS\n0.94 +0.24\n\u22120.21 \u00b1 0.06\n0.30 \u00b1 0.32 \u00b1 0.08\n0.74 \u00b1 0.17\nC\n\u22120.17 \u00b1 0.18 \u00b1 0.04\n\u22120.31 \u00b1 0.20 \u00b1 0.07\n\u22120.23 \u00b1 0.13\n17.6.7.2 B0 \u2192\u03c00\u03c00K0\nS\nThe event reconstruction of B0 \u2192\u03c00\u03c00K0\nS is similar to\nthat of B0 \u2192K0\nS\u03c00 (Section 17.6.6) with an additional\n\u03c00. Even though no charged tracks come directly from\nthe interaction point, the intersection of the K0\nS trajec-\ntory and the beamspot provide adequate measurement of\nthe B0 decay vertex. Approximately 70% of the candi-\ndates at BABAR have well measured K0\nS \u2192\u03c0+\u03c0\u2212tracks\nin the silicon vertex detector. This is higher than that\nin B0 \u2192K0\nS\u03c00 because the K0\nS momentum spectrum is\nsofter in B0 \u2192\u03c00\u03c00K0\nS decays. BABAR uses a neural net-\nwork (Section 4.4.4) with event shape variables to dis-\ncriminate against continuum background. Events consis-\ntent with B0 \u2192K0\nS\u03c00, D0\u03c00, \u03b7(\u2032)K0\nS, and \u03c7c0,2K0\nS decays\nare vetoed. In case of multiple candidates in an event, the\ncandidate with the smallest value of P2\ni=1(m(i)\n\u03b3\u03b3 \u2212m\u03c00)2\n\n316\nis selected, where m(1)\n\u03b3\u03b3 and m(2)\n\u03b3\u03b3 are the invariant masses\nof the two \u03c00 \u2192\u03b3\u03b3 candidates.\nThe \ufb01t uses mES, \u2206E/\u03c3(\u2206E), the neural-network out-\nput, \u2206t, \u03c3(\u2206t), and \ufb02avor tagging as variables. Using a\nsample of 227 \u00d7 106 BB pairs, BABAR (Aubert, 2007t)\n\ufb01nds 117 \u00b1 27 signal events, and S = 0.72 \u00b1 0.71 \u00b1 0.08\nand C = 0.23 \u00b1 0.52 \u00b1 0.13. Belle has not measured this\nchannel.\n17.6.7.3 B0 \u2192K+K\u2212K0 time-dependent Dalitz plot\nanalysis\nB0 \u2192\u03c6K0 decays proceed almost purely through a b \u2192\ns\u00afss penguin transition. This is one of the most promising\nmodes to search for new physics. In general, the decays\nB0 \u2192K+K\u2212K0 have a contribution from the b \u2192u\u00afus\ntree transition. Therefore, its theoretical uncertainty must\nbe taken into account when comparing asymmetry param-\neter results with those obtained from charmonium decays.\nThe measurements were originally made treating this\ndecay in terms of the quasi-two-body process B0 \u2192\u03c6K0,\nwhere \u03c6 \u2192K+K\u2212(Abe (2003e,f); Chen (2007a); Aubert\n(2004o, 2005m)). Other analyses measuring CP asymme-\ntry parameters in B0 \u2192K+K\u2212K0\nS decays excluded the \u03c6\nmass region in the K+K\u2212invariant mass spectrum (Abe,\n2003e,f, 2007e) (Aubert, 2005m), where they found the\nphase space was dominantly CP-even.\nThere can be nonresonant B0 \u2192K+K\u2212K0 contribu-\ntions and also B0 \u2192f0(980)K0 that may interfere with\nthe B0 \u2192\u03c6K0 decay. Therefore, the measurement of\nB0 \u2192\u03c6K0 as a quasi-two-body decay would ultimately\nhave limited precision. This problem can be resolved via\nthe use of a time-dependent amplitude analysis of the\nthree-body \ufb01nal state. The amplitudes and time-dependent\nasymmetry parameters can be extracted for each interme-\ndiate state (including any nonresonant component) while\nsimultaneously accounting for interference between ampli-\ntudes as discussed in Chapter 13. With increasingly large\ndata samples this became feasible, and such a measure-\nment was \ufb01rst made by BABAR (Aubert, 2007af) using\n383 \u00d7 106 BB pairs. The latest measurements are made\nusing 470 \u00d7 106 BB pairs by BABAR (Lees, 2012y) and\n657 \u00d7 106 BB pairs by Belle (Nakahama, 2010).\nThe B0 \u2192K+K\u2212K0 decays are reconstructed in\nK0\nS \u2192\u03c0+\u03c0\u2212and K0\nS \u2192\u03c00\u03c00 channels (in the \ufb01rst BABAR\nmeasurement, the K+K\u2212K0\nL channel was also used). Belle\nuses only K0\nS \u2192\u03c0+\u03c0\u2212decay. Signal components are\nextracted using kinematic variables (mES, \u2206E) and an\ne+e\u2212\u2192q\u00afq continuum suppression variable (a Fisher dis-\ncriminant, a neural network, or a \ufb02avor-tagging quality,\nsee Chapter 9).\nIn the Dalitz plot analysis, each amplitude of an inter-\nmediate resonant or nonresonant state r (called \u201cisobar\u201d)\nis parameterized as\nar = cr(1 + br)ei(\u03c6r+\u03b4r),\n\u00afar = cr(1 \u2212br)ei(\u03c6r\u2212\u03b4r),\n(17.6.9)\nfor B0 and B0 decays respectively, where cr is the mag-\nnitude of the amplitude. Only weak phase of the two am-\nplitudes is written in the above equation, and the CP vio-\nlating weak phase di\ufb00erence is 2\u03b4r. The magnitudes of B0\nand B0 decay amplitudes are also allowed to be di\ufb00erent,\nparameterized by br. With this parameterization and fol-\nlowing Eqs (10.2.4 and 10.2.5), the direct CP asymmetry,\ne\ufb00ective phase \u03c6e\ufb00\n1 , and time-dependent CP coe\ufb03cient are\ngiven, respectively, as\nCr \u2248\u2212Ar\nCP = \u2212|\u00afar|2 \u2212|ar|2\n|\u00afar|2 + |ar|2 =\n2br\n1 + b2r\n, (17.6.10)\n\u03c6e\ufb00,r\n1\n= \u03c61 + \u03b4r,\n(17.6.11)\n\u2212\u03b7rSr \u22481 \u2212b2\nr\n1 + b2r\nsin[2\u03c6e\ufb00,r\n1\n].\n(17.6.12)\nThe measured phase is referred to as \u201ce\ufb00ective\u201d because\none measures \u03c61 up to theoretical uncertainties related to\nhigher order contributions, which can be signi\ufb01cant.\nBelle vetoes events consistent with a B0 decaying\ninto the following \ufb01nal states using appropriate mass\nwindows: D0K0\nS, D\u2212\n(s)K+, and J/\u03c8K0\nS, where D0\n\u2192\nK+K\u2212, K+\u03c0\u2212, D\u2212\u2192K0\nSK\u2212, K0\nS\u03c0\u2212, D\u2212\ns\n\u2192K0\nSK\u2212,\nand J/\u03c8 \u2192K+K\u2212. The B0 \u2192\u03c7c0K0\nS amplitude is in-\ncluded in the \ufb01t. On the other hand, BABAR includes\nB0 \u2192J/\u03c8K0\nS, D\u2212K+, D\u2212\ns K+, and D0K0\nS as background\ncomponents in the \ufb01t. The latest BABAR analysis \ufb01nds\n1419 \u00b1 43 K+K\u2212K0\nS[\u03c0+\u03c0\u2212] signal events and 160 \u00b1 17\nK+K\u2212K0\nS[\u03c00\u03c00] signal events. Belle obtains 1176\u00b151 sig-\nnal events.\nBoth experiments perform a time-dependent \ufb01t to the\nwhole Dalitz plane, using three sets of \u03c6e\ufb00\n1\nand ACP pa-\nrameters; the \ufb01rst two are for \u03c6(1020)K0\nS and f0(980)K0\nS,\nand the third is shared by all the other charmless isobars.\nDue to the possible presence of multiple solutions, the\nsame \ufb01t is performed many times with di\ufb00erent starting\nparameter values to ensure the global minimum of the like-\nlihood is reached. Scans of log-likelihood values are done\nto study the behavior of the p.d.f. near the minimum and\nthe statistical uncertainties. The latest BABAR analysis\n\ufb01nds \ufb01ve local minima within 9 units in \u22122 ln L; the sec-\nond solution is 3.9 larger than the global minimum. Belle\n\ufb01nds four solutions, separated by approximately 10 units\nin \u22122 ln L; Solution 1 is taken as the preferred one based\non external information though it has the second lowest\n\u22122 ln L value, which is 3.1 units larger than the lowest one\n(Solution 2). The results are summarized in Table 17.6.8.\nIt should be noted that the discrete ambiguities on\nthe value of \u03c61 can be resolved using the time-dependent\nDalitz plot \ufb01t method because the log-likelihood values\ncan be compared for multiple solutions. In both B0 \u2192\n\u03c6K0\nS and f0(980)K0\nS decays the \u03c6e\ufb00\n1\n< \u03c0/2 solution is\nclearly preferred. BABAR excludes the \u03c0/2 \u2212\u03c6e\ufb00\n1\nvalue at\n4.8 standard deviations.\n17.6.7.4 B0 \u2192\u03c0+\u03c0\u2212K0\nS time-dependent Dalitz plot\nanalysis\nThe decay B0 \u2192\u03c0+\u03c0\u2212K0\nS includes transitions via B0 \u2192\n\u03c10K0\nS, B0 \u2192f0(980)K0\nS, and B0 \u2192K\u2217+\u03c0\u2212. The mea-\nsurements of time-dependent asymmetry parameters for\n\n317\nTable 17.6.8. Results for time-dependent asymmetry parameters for B0 \u2192K+K\u2212K0 decays. The three uncertainties are\nstatistical, systematic and Dalitz plot model uncertainty (for BABAR the latter is included in the systematic uncertainty). The\nsolutions with the (three) smallest \u22122 ln L value(s) are shown for BABAR (Belle).\nBABAR (Lees, 2012y)\nBelle (Nakahama, 2010)\nSolution 1\nSolution 1\nSolution 2\nSolution 3\nACP (\u03c6K0\nS)\n\u22120.05 \u00b1 0.18 \u00b1 0.05\n+0.04 \u00b1 0.20 \u00b1 0.10 \u00b1 0.02\n+0.08 \u00b1 0.18 \u00b1 0.10 \u00b1 0.03\n\u22120.01 \u00b1 0.20 \u00b1 0.11 \u00b1 0.02\n\u03c6eff\n1 (\u03c6K0\nS)\n(21 \u00b1 6 \u00b1 2)\u25e6\n(32.2 \u00b1 9.0 \u00b1 2.6 \u00b1 1.4)\u25e6\n(26.2 \u00b1 8.8 \u00b1 2.7 \u00b1 1.2)\u25e6\n(27.3 \u00b1 8.6 \u00b1 2.8 \u00b1 1.3)\u25e6\nACP (f0(980)K0\nS)\n\u22120.28 \u00b1 0.24 \u00b1 0.9\n\u22120.30 \u00b1 0.29 \u00b1 0.11 \u00b1 0.09\n\u22120.20 \u00b1 0.15 \u00b1 0.08 \u00b1 0.05\n+0.02 \u00b1 0.21 \u00b1 0.09 \u00b1 0.09\n\u03c6eff\n1 (f0(980)K0\nS)\n(18 \u00b1 6 \u00b1 4)\u25e6\n(31.3 \u00b1 9.0 \u00b1 3.4 \u00b1 4.0)\u25e6\n(26.1 \u00b1 7.0 \u00b1 2.4 \u00b1 2.5)\u25e6\n(25.6 \u00b1 7.6 \u00b1 2.9 \u00b1 0.8)\u25e6\nACP (others)\n\u22120.02 \u00b1 0.09 \u00b1 0.03\n\u22120.14 \u00b1 0.11 \u00b1 0.08 \u00b1 0.03\n\u22120.06 \u00b1 0.15 \u00b1 0.08 \u00b1 0.04\n\u22120.03 \u00b1 0.09 \u00b1 0.08 \u00b1 0.03\n\u03c6eff\n1 (others)\n(20.3 \u00b1 4.3 \u00b1 1.2)\u25e6\n(24.9 \u00b1 6.4 \u00b1 2.1 \u00b1 2.5)\u25e6\n(29.8 \u00b1 6.6 \u00b1 2.1 \u00b1 1.1)\u25e6\n(26.2 \u00b1 5.9 \u00b1 2.3 \u00b1 1.5)\u25e6\nthe \ufb01rst two of these decays were initially made using a\nquasi-two-body approach (Aubert (2007aa); Abe (2007e)),\nsimilar to the B0 \u2192K+K\u2212K0\nS (\u03c6K0) case above. Ob-\nservation of direct CP asymmetry in B0 \u2192K+\u03c0\u2212and\nevidence of CP asymmetry in resonances in other similar\nthree-body decays such as B+ \u2192K+\u03c0+\u03c0\u2212(see Chap-\nter 17.4) suggest possible large CP asymmetry in reso-\nnances in B0 \u2192K0\nS\u03c0+\u03c0\u2212decays. Time-dependent CP\nasymmetry measurements of B0 \u2192\u03c0+\u03c0\u2212K0\nS may shed\nlight on the ACP (K\u03c0) puzzle together with the CP asym-\nmetry of other B \u2192K\u2217\u03c0 decays (see for example (Li and\nMishima, 2011)). In addition, the phase di\ufb00erence between\nB0 \u2192K\u2217+\u03c0\u2212and B0 \u2192K\u2217\u2212\u03c0+ decays can be used\nto determine \u03c63 (Ciuchini, Pierini, and Silvestrini, 2006;\nDeshpande, Sinha, and Sinha, 2003; Gronau, Pirjol, Soni,\nand Zupan, 2007). Time-dependent Dalitz plot analysis\nof B0 \u2192\u03c0+\u03c0\u2212K0\nS decays can provide all these measure-\nments simultaneously.\nBABAR (Aubert, 2009av) analyzes a sample of 383\u00d7106\nBB pairs and Belle (Dalseno, 2009) analyzes 657\u00d7106 BB\npairs. The B0 \u2192\u03c0+\u03c0\u2212K0\nS candidates are identi\ufb01ed us-\ning the kinematic variables mES and \u2206E. The e+e\u2212\u2192\nq\u00afq continuum background is suppressed by a loose re-\nquirement on the continuum suppression variable. This\nrequirement retains about 90% of the signal. BABAR uses\nthe neural-network output from various shape parameters\nwhile Belle uses a likelihood ratio. Belle applies vetoes\nfor B0 \u2192D\u2212\u03c0+ decays and B0 \u2192(c\u00afc)K0\nS decays, while\nBABAR includes them as a background in the \ufb01t. Belle\n\ufb01nds that 20\u201330% of events have multiple candidates in\nquasi-two-body modes. By selecting the B candidate with\nmES closest to the nominal B mass, the fraction of misre-\nconstructed events is reduced to the level of a few percent.\nThe signal yield is found to be 1944 \u00b1 98 events using the\n\u2206E distribution. BABAR \ufb01nds that 1\u20138% of the events\nhave multiple candidates and selects single events ran-\ndomly The fraction of misreconstructed candidates is 4\u2013\n8% depending on the intermediate states. The signal yield\nis extracted using mES, \u2206E, and neural-network output\ninformation; 2182 \u00b1 64 signal events are obtained.\nBoth groups use square Dalitz plot variables (Sec-\ntion 13.4.1) in the \ufb01t. The phase di\ufb00erence for \ufb02avor spe-\nci\ufb01c decays is given as\n\u2206\u03c6r = 2\u03b4r.\n(17.6.13)\nAs in B0 \u2192K+K\u2212K0\nS decays, the \ufb01ts lead to multiple\nsolutions: two for BABAR and four for Belle. Table 17.6.9\nshows the two most likely solutions in each experiment.\nCP violation parameters for the B0 \u2192f0(980)K0\nS and\n\u03c10(770)K0\nS decays are similar for two solutions in the Belle\nresult, while they di\ufb00er in the BABAR measurement (note\nthat the statistical uncertainties between di\ufb00erent solu-\ntions are correlated). In both cases, the \u03c6e\ufb00\n1\nvalues are\nconsistent with the value of \u03c61 measured in b \u2192c\u00afcs de-\ncays.\n17.6.7.5 Summary of \u03c61 from charmless decays\nFigure 17.6.13 (17.6.14) shows a summary of measure-\nments of sin 2\u03c6e\ufb00\n1\n(vs. C) from charmless decays includ-\ning both quasi-two-body and three-body decays. The fa-\nvored solutions are shown for B0 \u2192K+K\u2212K0 and B0 \u2192\n\u03c0+\u03c0\u2212K0 decays.\nThe measured sin 2\u03c6e\ufb00\n1\nvalues for all of the individual\nmodes are consistent with the sin 2\u03c61 value measured in\nb \u2192c\u00afcs decays within statistical and theoretical uncer-\ntainties. However, the current statistical precision is not\nenough to draw de\ufb01nite conclusions about the presence of\nnew physics; a much larger data sample is necessary.\n17.6.8 Resolving discrete ambiguities in \u03c61\nSince the time-dependent CP asymmetry parameter mea-\nsurements described so far usually provide a value for\nsin 2\u03c61, there is a four-fold ambiguity on the angle, \u03c61 \u2192\n\u03c0/2 \u2212\u03c61, \u03c61 + \u03c0 and 3\u03c0/2 \u2212\u03c61. As mentioned in Sec-\ntion 17.6.7, time-dependent Dalitz plot analyses of charm-\nless three-body decays measure (e\ufb00ective) values of 2\u03c61,\nrather than sin 2\u03c61, and can resolve the \u03c61 \u2192\u03c0/2 \u2212\u03c61\nambiguity. However, charmless decays are dominated by\npenguin transitions, which can be a\ufb00ected by NP entering\nin loops. Resolving the ambiguity using decays dominated\nby a b \u2192c tree transition can avoid such complication\nSeveral tree level b \u2192c measurements are possible, and\nthose performed at the B Factories are described in the\nfollowing.\n\n318\nTable 17.6.9. Results of CP asymmetry parameters for B0 \u2192\u03c0+\u03c0\u2212K0 decays. The \ufb01rst uncertainty is statistical, the second\nis systematic, and the third represents the Dalitz plot signal model dependence.\nBABAR (Aubert, 2009av)\nBelle (Dalseno, 2009)\nSolution 1\nSolution 2\nSolution 1\nSolution 2\nACP (f0(980)K0\nS)\n\u22120.08 \u00b1 0.19 \u00b1 0.03 \u00b1 0.04\n\u22120.23 \u00b1 0.19 \u00b1 0.03 \u00b1 0.04\n\u22120.06 \u00b1 0.17 \u00b1 0.07 \u00b1 0.09\n+0.00 \u00b1 0.17 \u00b1 0.06 \u00b1 0.09\n\u03c6eff\n1 (f0(980)K0\nS)[\u25e6]\n36.0 \u00b1 9.8 \u00b1 2.1 \u00b1 2.1\n56.2 \u00b1 10.4 \u00b1 2.1 \u00b1 2.1\n12.7 +6.9\n\u22126.5 \u00b1 2.8 \u00b1 3.3\n14.8 +7.3\n\u22126.7 \u00b1 2.7 \u00b1 3.3\nFraction [%]\n13.8 +1.5\n\u22121.4 \u00b1 0.8 \u00b1 0.6\n13.5 \u22121.4\n\u22121.3 \u00b1 0.8 \u00b1 0.6\n14.3 \u00b1 2.7\n14.9 \u00b1 3.3\nACP (\u03c10(770)K0\nS)\n0.05 \u00b1 0.26 \u00b1 0.10 \u00b1 0.03\n0.14 \u00b1 0.26 \u00b1 0.10 \u00b1 0 : 03\n+0.03 +0.23\n\u22120.24 \u00b1 0.11 \u00b1 0.10\n\u22120.16 \u00b1 0.24 \u00b1 0.12 \u00b1 0.10\n\u03c6eff\n1 (\u03c10(770)K0\nS)[\u25e6]\n10.2 \u00b1 8.9 \u00b1 3.0 \u00b1 1.9\n33.4 \u00b1 10.4 \u00b1 3.0 \u00b1 1.9\n+20.0 +8.6\n\u22128.5 \u00b1 3.2 \u00b1 3.5\n+22.8 \u00b1 7.5 \u00b1 3.3 \u00b1 3.5\nFraction [%]\n8.6 +1.4\n\u22121.3 \u00b1 0.5 \u00b1 0.2\n8.5 +1.3\n\u22121.2 \u00b1 0.5 \u00b1 0.2\n6.1 \u00b1 1.5\n8.5 \u00b1 2.6\nACP (K\u2217\u2212\u03c0+)\n\u22120.21 \u00b1 0.10 \u00b1 0.01 \u00b1 0.02\n\u22120.19 +0.10\n\u22120.11 \u00b1 0.01 \u00b1 0.02\n\u22120.21 \u00b1 0.11 \u00b1 0.05 \u00b1 0.05\n\u22120.20 \u00b1 0.11 \u00b1 0.05 \u00b1 0.05\n\u2206\u03c6(K\u2217\u2212\u03c0+)[\u25e6]\n72.2 \u00b1 24.6 \u00b1 4.1 \u00b1 4.4\n\u2212175.1 \u00b1 22.6 \u00b1 4.1 \u00b1 4.4\n\u22120.7 +23.5\n\u221222.8 \u00b1 11.0 \u00b1 17.6\n+14.6 +19.4\n\u221220.3 \u00b1 11.0 \u00b1 17.6\nFraction [%]\n45.2 \u00b1 2.3 \u00b1 1.9 \u00b1 0.9\n46.1 \u00b1 2.4 \u00b1 1.9 \u00b1 0.9\n9.3 \u00b1 0.8\n9.0 \u00b1 1.3\nsin(2\u03b2eff) \u2261 sin(2\u03c6e\n1\nff)\nb\u2192ccs\n\u03c6 K0\n\u03b7\u2032 K0\nKS KS KS\n\u03c00 K0\n\u03c10 KS\n\u03c9 KS\nf0 KS\nf2 KS\nfX KS\n\u03c00 \u03c00 KS\n\u03c6 \u03c00 KS\n\u03c0+ \u03c0- KS NR\nK+ K- K0\nb\u2192qqs\n-2\n-1\n0\n1\n2\nWorld Average\n0.68 \u00b1 0.02\nBaBar\n0.66 \u00b1 0.17 \u00b1 0.07\nBelle\n0.90 +\n-\n0\n0\n.\n.\n0\n1\n9\n9\nBaBar\n0.57 \u00b1 0.08 \u00b1 0.02\nBelle\n0.64 \u00b1 0.10 \u00b1 0.04\nBaBar\n0.94 +\n-\n0\n0\n.\n.\n2\n2\n1\n4 \u00b1 0.06\nBelle\n0.30 \u00b1 0.32 \u00b1 0.08\nBaBar\n0.55 \u00b1 0.20 \u00b1 0.03\nBelle\n0.67 \u00b1 0.31 \u00b1 0.08\nBaBar\n0.35 +\n-\n0\n0\n.\n.\n2\n3\n6\n1 \u00b1 0.06 \u00b1 0.03\nBelle\n0.64 +\n-\n0\n0\n.\n.\n1\n2\n9\n5 \u00b1 0.09 \u00b1 0.10\nBaBar\n0.55 +\n-\n0\n0\n.\n.\n2\n2\n6\n9 \u00b1 0.02\nBelle\n0.11 \u00b1 0.46 \u00b1 0.07\nBaBar\n0.74 +\n-\n0\n0\n.\n.\n1\n1\n2\n5\nBelle\n0.63 +\n-\n0\n0\n.\n.\n1\n1\n6\n9\nBaBar\n0.48 \u00b1 0.52 \u00b1 0.06 \u00b1 0.10\nBaBar\n0.20 \u00b1 0.52 \u00b1 0.07 \u00b1 0.07\nBaBar\n-0.72 \u00b1 0.71 \u00b1 0.08\nBaBar\n0.97 +\n-\n0\n0\n.\n.\n0\n5\n3\n2\nBaBar\n0.01 \u00b1 0.31 \u00b1 0.05 \u00b1 0.09\nBaBar\n0.65 \u00b1 0.12 \u00b1 0.03\nBelle\n0.76 +\n-\n0\n0\n.\n.\n1\n1\n4\n8\nNa\u00efve average\n0.64 \u00b1 0.03\nH F AG\nH F A G\nMoriond 2012\nPRELIMINARY\nFigure 17.6.13. Summary of sin 2\u03c6e\ufb00\n1\nmeasurements from\ncharmless B0 decays (Amhis et al., 2012).\n17.6.8.1 Time-dependent angular analysis in B0 \u2192J/\u03c8K\u22170\nThere are two classes of parameters obtained through the\nangular analysis of the B meson decay to the two vector\nmesons J/\u03c8 and K\u22170. The \ufb01rst is the measurement of the\ndecay amplitudes of the three angular states. These can\nbe obtained using a time-integrated angular analysis to\n\ufb02avor-speci\ufb01c decays (see Chapter 12). The second class\ncomprises the CP parameters (sin 2\u03c61 and cos 2\u03c61) that\nare measured through a time-dependent angular analysis.\nIn particular, the measurement of cos 2\u03c61, which appears\nsin(2\u03b2eff) \u2261 sin(2\u03c6e\n1\nff) vs CCP \u2261 -ACP\nContours give -2\u2206(ln L) = \u2206\u03c72 = 1, corresponding to 60.7% CL for 2 dof\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\nsin(2\u03b2eff) \u2261 sin(2\u03c6e\n1\nff)\nCCP \u2261 -ACP\nb\u2192ccs\n\u03c6 K0\n\u03b7\u2032 K0\nKS KS KS\n\u03c00 KS\n\u03c10 KS\n\u03c9 KS\nf0 K0\nf2 KS\nfX KS\n\u03c00 \u03c00 KS\n\u03c0+ \u03c0- KS NR\nK+ K- K0\nH F AG\nH F A G\nMoriond 2012\nPRELIMINARY\nFigure 17.6.14. Summary of C vs. sin 2\u03c6e\ufb00\n1\nmeasurements\nfrom charmless B0 decays (Amhis et al., 2012).\nin the time-dependent interference terms (Eq. (12.1.9)),\nis important both to solve the two-fold ambiguity in 2\u03c61\nand to test the consistency of this determination with the\nmore precise value from other b \u2192ccs decays.\nThe decay of a pseudo-scalar to vector-vector \ufb01nal\nstate can be described with three angles de\ufb01ned in the\ntransversity basis (Dunietz, Quinn, Snyder, Toki, and Lip-\nkin, 1991), where the three amplitudes, A0, A\u2225, and A\u22a5\nhave well-de\ufb01ned CP eigenvalues. The amplitudes are de-\ntermined by a time-integrated angular analysis of B0 \u2192\n\n319\nTable\n17.6.10.\nMeasured decay amplitudes for B0\n\u2192\nJ/\u03c8K\u22170. The \ufb01rst uncertainty is statistical, and the second\nis systematic.\nBABAR (Aubert, 2007x)\nBelle (Itoh, 2005b)\n|A0|2\n0.556 \u00b1 0.009 \u00b1 0.010\n0.574 \u00b1 0.012 \u00b1 0.009\n|A\u2225|2\n0.211 \u00b1 0.010 \u00b1 0.006\n0.231 \u00b1 0.012 \u00b1 0.008\n|A\u22a5|2\n0.233 \u00b1 0.010 \u00b1 0.005\n0.195 \u00b1 0.012 \u00b1 0.008\narg(A\u2225)\n\u22122.93 \u00b1 0.08 \u00b1 0.04\n\u22122.89 \u00b1 0.09 \u00b1 0.01\narg(A\u22a5)\n2.91 \u00b1 0.05 \u00b1 0.03\n2.94 \u00b1 0.06 \u00b1 0.01\nJ/\u03c8K\u22170[K+\u03c0\u2212] and B+ \u2192J/\u03c8K\u2217+[K0\nS\u03c0+, K+\u03c00] de-\ncays. Belle (Itoh, 2005b) and BABAR (Aubert, 2007x) an-\nalyze the data samples of 275 and 232 \u00d7 106 BB pairs,\nrespectively.\nFigure 17.6.15 shows the projected angular distribu-\ntions for B0 \u2192J/\u03c8K\u22170 decays, where K\u22170 \u2192K+\u03c0\u2212,\nfrom Belle. The decay amplitudes determined from the \ufb01t\nare summarized in Table 17.6.10.\ncos etr\n0\n100\n200\n300\n400\n500\n-1\n-0.5\n0\n0.5\n1\nqtr\n0\n100\n200\n300\n400\n500\n-2\n0\n2\ncos eK*\n0\n100\n200\n300\n400\n500\n600\n700\n-1\n-0.5\n0\n0.5\n1\nFigure\n17.6.15.\nAngular\ndistributions\nof\nB0\n\u2192\nJ/\u03c8K\u22170(K+\u03c0\u2212), as obtained by Belle (Itoh, 2005b). The\nangles are de\ufb01ned in Eq. (12.2.6), where \u03b81 = \u03b8K\u2217. The curves\nshow the \ufb01t results.\nThere is a two-fold ambiguity in the choice of the\nphases. BABAR resolves this ambiguity by extending the\nformalism to include a K\u03c0 S-wave amplitude and then\nmeasuring the K\u03c0 invariant mass dependence of its phase\ndi\ufb00erence with respect to the dominant K\u2217(892) P-wave\naround its mass peak (Aubert, 2005c). The result agrees\nwith the prediction where the s-quark helicity is conserved\nas predicted by Suzuki (Suzuki, 2001). Belle adopts this\nchoice in their analysis as well. The phases shown in Ta-\nble 17.6.10 are given for this choice.\nThe values of sin 2\u03c61 and cos 2\u03c61 are determined by\nthe time-dependent angular analysis of the decays to the\nCP eigenstate B0 \u2192J/\u03c8K\u22170, where K\u22170 \u2192K0\nS\u03c00, from\nthe same data set of 275 \u00d7 106 BB pairs by Belle (Itoh,\n2005b), and a sample of 88\u00d7106 BB pairs by BABAR (Au-\nbert, 2005c). The P-wave amplitudes are \ufb01xed to the re-\nsults obtained from the time-independent analysis of the\n\ufb02avor-de\ufb01nite \ufb01nal states described above. Figure 17.6.16\nshows the \u2206t distributions for B0 and B0 tags and the\nraw asymmetry between them by BABAR. Since sin 2\u03c61\nand cos 2\u03c61 are independent parameters in the analysis,\nthey can be obtained simultaneously using a \ufb01t. However,\nsince the precision of the sin 2\u03c61 measurement using only\nB0 \u2192J/\u03c8K\u22170 decays is limited by statistics, the value\nof cos 2\u03c61 is also obtained by \ufb01xing sin 2\u03c61 to the world\naverage at that time, 0.726 (Belle) or 0.731 (BABAR). The\nresults are summarized in Table 17.6.11.\n0\n10\n20\n30\nB0 tag\n(a)\nEntries / 2 ps\n0\n10\n20\n30\nB0 tag\n\u2013\n(b)\nEntries / 2 ps\n-1\n-0.5\n0\n0.5\n1\n-10\n-8\n-6\n-4\n-2\n0\n2\n4\n6\n8\n10\n(c)\n6t (ps)\nAsymmetry\nFigure 17.6.16. \u2206t distributions for (a) B0 and (b) B0 tagged\nB0 \u2192J/\u03c8 K\u22170 events, and (c) raw asymmetry between them\nby BABAR (Aubert, 2005c).\nThe sign of cos 2\u03c61 is positive in both measurements,\nwhich is consistent with the value of \u03c61 predicted by global\nCKM \ufb01ts obtained using other measurements (see Sec-\ntion 25.1).\n17.6.8.2 Time-dependent Dalitz analysis in\nB0 \u2192D(\u2217)0[K0\nS\u03c0+\u03c0\u2212]h0\nAnother method to resolve discrete ambiguities uses a\ntime-dependent Dalitz plot analysis with B0 \u2192D(\u2217)0h0,\nD0 \u2192K0\nS\u03c0+\u03c0\u2212decays, where h0 is a light neutral meson,\nsuch as \u03c00, \u03b7, \u03b7\u2032, and \u03c9 (Bondar, Gershon, and Krokovny,\n2005). As described in Section 17.6.5, the B0 \u2192D(\u2217)0h0\ndecay is dominated by a color-suppressed b \u2192cud tree\namplitude. Neglecting a small contribution from b \u2192ucd,\nthe decay amplitude for B0 \u2192D\n0[K0\nS\u03c0+\u03c0\u2212]h0 can be\nfactorized as Af = ABAD0 and for B0 as Af = ABAD0,\n\n320\nTable 17.6.11. sin 2\u03c61 and cos 2\u03c61 determined for B0 \u2192J/\u03c8 K\u22170, K\u22170 \u2192K0\nS\u03c00. The \ufb01rst two numbers show the result of the\nsimultaneous \ufb01t with both sin 2\u03c61 and cos 2\u03c61 treated as free parameters. The \ufb01nal set of values for cos 2\u03c61 are obtained with\nsin 2\u03c61 \ufb01xed at the world average at the time of the analysis.\nBABAR (Aubert, 2005c)\nBelle (Itoh, 2005b)\nsin 2\u03c61\n\u22120.10 \u00b1 0.57 \u00b1 0.14\n+0.24 \u00b1 0.31 \u00b1 0.05\ncos 2\u03c61\n+3.32+0.76\n\u22120.96 \u00b1 0.27\n+0.56 \u00b1 0.79 \u00b1 0.11\ncos 2\u03c61 (\ufb01xed value of sin 2\u03c61)\n+2.72+0.50\n\u22120.79 \u00b1 0.27 (0.731)\n+0.87 \u00b1 0.74 \u00b1 0.12 (0.726)\nwhere AD0 = f(m2\n+, m2\n\u2212) and AD\n0 = f(m2\n\u2212, m2\n+) with\nm2\n\u00b1 = M 2\nK0\nS\u03c0\u00b1. The \u2206t distribution is given as\nf\u00b1(\u2206t) \u221de\u2212|\u2206t|/\u03c4B0\n2\n|AB|2[(|AD0|2 + |\u03bb|2|AD0|2) (17.6.14)\n\u2213(|AD0|2 \u2212|\u03bb|2|AD0|2) cos(\u2206md\u2206t)\n\u00b12|\u03bb|\u03beh0(\u22121)LIm(e\u22122\u03c61AD0A\u2217\nD0) sin(\u2206md\u2206t)],\nwhere \u03beh0 is the CP eigenvalue of h0 and L is the orbital\nangular momentum of the Dh0 system. One notices that if\nAD0 = AD0 (e.g., if the \ufb01nal state is a CP eigenstate), this\nequation reduces to Eq. (10.2.2). An additional factor of\n\u22121 is required in the sin(\u2206md\u2206t) term for the D\u22170[D0\u03c00]\nmode to take into account the CP eigenvalue of the \u03c00.\nThe sin(\u2206md\u2206t) term can be written as\nIm(e\u22122\u03c61AD0A\u2217\nD0) = Im(AD0A\u2217\nD0) cos 2\u03c61\n(17.6.15)\n\u2212Re(AD0A\u2217\nD0) sin 2\u03c61.\nTherefore, cos 2\u03c61 and sin 2\u03c61 can be independently de-\ntermined by \ufb01tting the time-dependent Dalitz plot distri-\nbution.\nBelle (Krokovny, 2006) and BABAR (Aubert, 2007s)\nperform the measurements using 386 \u00d7 106 and 383 \u00d7 106\nBB pairs, respectively. They use D\u03c00, D\u03b7, D\u03c9, D\u2217\u03c00,\nand D\u2217\u03b7 decay modes. BABAR also uses D\u03b7\u2032. The recon-\nstruction includes the decay chains D\u22170 \u2192D0\u03c00, D0 \u2192\nK0\nS\u03c0+\u03c0\u2212, K0\nS \u2192\u03c0+\u03c0\u2212, \u03b7 \u2192\u03b3\u03b3 and \u03c0+\u03c0\u2212\u03c00, \u03b7\u2032 \u2192\n\u03b7\u03c0+\u03c0\u2212, and \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00. The B0 signal candidates\nare identi\ufb01ed by mES and \u2206E. The reconstruction of the\ntag-side B meson and \ufb02avor tagging are performed in the\nsame way as other time-dependent CP asymmetry mea-\nsurements.\nThe parameters sin 2\u03c61 and cos 2\u03c61 are obtained by\n\ufb01tting the Dalitz plot (m2\n+, m2\n\u2212) and \u2206t distributions for\nthe events in the signal region in mES and \u2206E. The iso-\nbar model described in Chapter 13 is used for the D0 \u2192\nK0\nS\u03c0+\u03c0\u2212decay amplitude. The results are summarized\nin Table 17.6.12. Belle \ufb01xes |\u03bb| to unity as expected in\nthe SM, while BABAR measures |\u03bb| = 1.01 \u00b1 0.08(stat.) \u00b1\n0.02(syst.). Belle and BABAR determine the sign of cos 2\u03c61\nto be positive at 98.3% and 86% C.L., respectively.\n17.6.8.3 Time-dependent CP asymmetry in\nB0 \u2192D\u2217+D\u2217\u2212K0\nS\nAnother way to resolve the \u03c61 \u2192\u03c0/2 \u2212\u03c61 ambiguity\nis to study the decay channel B0 \u2192D\u2217+D\u2217\u2212K0\nS. No\ndirect CP violation is expected in this mode since the\npenguin contributions are negligible. It is shown (Brow-\nder, Datta, O\u2019Donnell, and Pakvasa, 2000) that a time-\ndependent analysis can be performed in this channel, where\nin principle the values of sin 2\u03c61 and cos 2\u03c61 can be ex-\ntracted. The time-dependent \u2206t distribution, consider-\ning the mistag probability w and the di\ufb00erence \u2206w =\nw(B0) \u2212w(B0), is given by\nf\u00b1(\u2206t) \u2261e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u001a\n(1 \u2213\u2206w) \u00b1 (1 \u22122w).\n\u00d7\n\u0014\n\u03b7y\nJc\nJ0\ncos (\u2206md\u2206t) \u2212\n\u00122Js1\nJ0\nsin 2\u03c61\n+\u03b7y\n2Js2\nJ0\ncos 2\u03c61\n\u0013\nsin (\u2206md\u2206t)\n\u0015\u001b\n,\n(17.6.16)\nwhere f+ and f\u2212correspond respectively to a B0 and\nB0 tag. This equation is de\ufb01ned in the half Dalitz plane\ns+ < s\u2212or s+ > s\u2212, where s+ \u2261m2(D\u2217+K0\nS) and\ns\u2212\u2261m2(D\u2217\u2212K0\nS). The parameter \u03b7y is equal to +1 or\n\u22121 for s\u2212< s+ or s\u2212> s+, respectively. The parameters\nJ0, Jc, Js1, and Js2 are the integrals over the half Dalitz\nphase space with s+ < s\u2212of the functions |A|2 + |A|2,\n|A|2\u2212|A|2, Re(AA\u2217), and Im(AA\u2217), where A and A are the\namplitudes of B0 \u2192D\u2217+D\u2217\u2212K0\nS and B0 \u2192D\u2217+D\u2217\u2212K0\nS\ndecays, respectively. The values of these parameters de-\npend strongly on the intermediate resonances present in\nthis \ufb01nal state. The presence of the Ds1(2536) resonance\nis well established (Section 19.3) in this decay mode, but\nthis meson is narrow and does not contribute much to Js2.\nAlthough it had not been studied speci\ufb01cally in B0 \u2192\nD\u2217+D\u2217\u2212K0\nS decays, the D\u2217\ns1(2700) meson (Section 19.3)\nis expected to have a large contribution due to its large\nwidth. D\u2217\ns1(2700) decays to D\u2217K and has a large width,\n125 \u00b1 30 MeV. This implies that Js2 is nonzero and that\nJc may be large.\nBABAR (Aubert, 2006u) and Belle (Dalseno, 2007)\nstudy this decay mode using 230 \u00d7 106 and 449 \u00d7 106\nBB pairs, respectively. The mode B0 \u2192D\u2217+D\u2217\u2212K0\nS is\nreconstructed from D\u2217+ \u2192D0\u03c0+ and D\u2217+ \u2192D+\u03c00, re-\nquiring at least one D0\u03c0+ decay. Candidate D mesons\nare reconstructed in the modes D0 \u2192K\u2212\u03c0+, K\u2212\u03c0+\u03c00,\nK\u2212\u03c0+\u03c0\u2212\u03c0+, and D+ \u2192K\u2212\u03c0+\u03c0+. Belle also includes the\nmodes D0 \u2192K0\nS\u03c0+\u03c0\u2212, K\u2212K+, and D+ \u2192K\u2212K+\u03c0+,\nrejecting cases with two D0 \u2192K0\nS\u03c0+\u03c0\u2212decays. When\nmultiple B mesons are reconstructed in an event, BABAR\n\n321\nTable 17.6.12. Results of the time-dependent Dalitz plot analysis for B0 \u2192D(\u2217)0[K0\nS\u03c0+\u03c0\u2212]h0 decays. Nsig is a signal yield\nobtained from the \ufb01t to data. The uncertainties are statistical, systematic, and those due to the Dalitz model, respectively. The\nuncertainties in the averages include all sources.\nBABAR (Aubert, 2007s)\nBelle (Krokovny, 2006)\nAverage\nNsig\n335 \u00b1 32\n325 \u00b1 31\nsin 2\u03c61\n0.29 \u00b1 0.34 \u00b1 0.03 \u00b1 0.05\n0.78 \u00b1 0.44 \u00b1 0.20 \u00b1 0.1\n0.45 \u00b1 0.28\ncos 2\u03c61\n0.42 \u00b1 0.49 \u00b1 0.09 \u00b1 0.13\n1.87\n+0.40\n+0.20\n\u22120.53\n\u22120.30 \u00b1 0.1\n1.01 \u00b1 0.40\nselects the one with the smallest |\u2206E| value; Belle chooses\nthe best candidate by using a \u03c72 test based on the mass\ndi\ufb00erences from the world averages of the particles present\nin the \ufb01nal state.\nIn BABAR, the signal yield is extracted from a \ufb01t to\nthe mES distribution with an additional peaking compo-\nnent to account for misreconstructed events from B+ \u2192\nD\u22170D\u2217+K0\nS decays (\u223c1.4% of the signal yield). The un-\nbinned maximum likelihood \ufb01t yields 201\u00b117 signal events.\nIn Belle, the signal yield is extracted from a simultaneous\n\ufb01t to the mES and \u2206E distributions. The \ufb01t result from\nBelle, shown in Fig. 17.6.17, has a signal yield of 131 \u00b1 15\nevents.\n)\n2\n (GeV/c\nbc\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n )\n2\nEvents / ( 0.002 GeV/c\n0\n10\n20\n30\n40\n50\n60\n)\n2\n (GeV/c\nbc\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n )\n2\nEvents / ( 0.002 GeV/c\n0\n10\n20\n30\n40\n50\n60\n E (GeV)\n\u2206\n-0.2\n-0.12\n-0.04\n0.04\n0.12\n0.2\nEvents / ( 0.008 GeV )\n0\n10\n20\n30\n40\n50\n60\n E (GeV)\n\u2206\n-0.2\n-0.12\n-0.04\n0.04\n0.12\n0.2\nEvents / ( 0.008 GeV )\n0\n10\n20\n30\n40\n50\n60\nFigure 17.6.17. The (left) mES and (right) \u2206E distributions\nof B0 \u2192D\u2217+D\u2217\u2212K0\nS candidates in Belle (Dalseno, 2007). The\ncurves show the \ufb01t projections.\nA time-dependent analysis is performed using the\nevent samples described previously. BABAR rejects events\nin which the invariant mass of the D\u2217\u00b1K0\nS pair is less\nthan 2.55 GeV/c2 in order to exclude the Ds1(2536) me-\nson, while Belle accounts for this resonance in the sys-\ntematic uncertainties. Table 17.6.13 shows the results of\nboth experiments and their averages using the half Dalitz\nplane to \ufb01t the coe\ufb03cients as described in Eq. (17.6.16).\nFigure 17.6.18 shows the projections in \u2206t of the \ufb01ts in\nBABAR\u2019s analysis. Belle also uses the whole Dalitz plane\nto determine the CP asymmetry parameters to be:\nC = +0.01+0.28\n\u22120.28 (stat) \u00b1 0.09 (syst)\n(17.6.17)\nD sin 2\u03c61 = +0.06+0.45\n\u22120.44 (stat) \u00b1 0.06 (syst),\n(17.6.18)\nwhere D is the dilution factor de\ufb01ned by D = 1 \u22122w. No\nevidence for either mixing-induced or direct CP violation\nis found.\ndt\n-5\n0\n5\nEvents / 1.0ps\n0\n5\n10\ndt\n-5\n0\n5\nEvents / 1.0ps\n0\n5\n10\n tags\n0\nB\n tags\n0\nB\n(a)\n t [ps]\n\u2206\n-5\n0\n5\nRaw asymmetry\n-1\n-0.5\n0\n0.5\n1\n t [ps]\n\u2206\n-5\n0\n5\nRaw asymmetry\n-1\n-0.5\n0\n0.5\n1\n(b)\ndt\n-5\n0\n5\nEvents / 1.0ps\n0\n5\n10\n15\ndt\n-5\n0\n5\nEvents / 1.0ps\n0\n5\n10\n15\n tags\n0\nB\n tags\n0\nB\n(c)\n t [ps]\n\u2206\n-5\n0\n5\nRaw asymmetry\n-1\n-0.5\n0\n0.5\n1\n t [ps]\n\u2206\n-5\n0\n5\nRaw asymmetry\n-1\n-0.5\n0\n0.5\n1\n(d)\nFigure\n17.6.18.\nFit\nresults\nfrom\nBABAR\nfor\nB0\n\u2192\nD\u2217+D\u2217\u2212K0\nS (Aubert, 2006u). (a) Distribution of \u2206t in the re-\ngion mES > 5.27 GeV/c2 for B0 (B0) tag candidates in the\nhalf Dalitz space s+ < s\u2212(\u03b7y = \u22121). The solid (dashed)\ncurve represents the \ufb01t projections in \u2206t for B0 (B0) tags.\n(b) Raw asymmetry (NB0 \u2212NB0)/(NB0 + NB0), as a function\nof \u2206t, where NB0 (NB0) is the number of candidates with a\nB0 (B0) tag. (c) and (d) contain the corresponding information\nfor the B0 candidates in the other half Dalitz space s+ > s\u2212\n(\u03b7y = +1).\n\n322\nThe main sources of systematic uncertainties, listed\nhere in decreasing order of magnitude, consist of non-\nuniform acceptance over the Dalitz plane, vertex resolu-\ntion, mistag fraction, \u2206t resolution function, \ufb01t bias, mis-\nreconstructed signal events, limited MC statistics, knowl-\nedge of the background, and tag-side interference.\nThe ratio Jc/J0 is found to be signi\ufb01cantly di\ufb00er-\nent from zero, which con\ufb01rms a sizable contribution of\na broad resonance in the decay B0 \u2192D\u2217+D\u2217\u2212K0\nS. Since\n(2Js2)/J0 is predicted to be positive when a wide reso-\nnance is present (Browder, Datta, O\u2019Donnell, and Pak-\nvasa, 2000), the sign of cos 2\u03c61 can be deduced, in princi-\nple, from the measurements presented here. These results\nare not precise enough to allow one to conclusively de-\ntermine the sign of cos 2\u03c61. However, the BABAR data do\nprefer a value of cos 2\u03c61 that is positive at the 94% con\ufb01-\ndence level.\nAs described above, all of the three independent mea-\nsurement methods, which use di\ufb00erent decay modes and\nrather di\ufb00erent techniques, indicate that con\ufb01dence lev-\nels for cos 2\u03c61 > 0 are around 90% or higher. Therefore,\ncos 2\u03c61 is experimentally proved to be positive with rela-\ntively high con\ufb01dence. Furthermore, the global \ufb01t results\ndiscussed in Section 25.1 prove that cos 2\u03c61 > 0 with a\nlarge con\ufb01dence.\n17.6.9 Time-reversal violation in b \u2192ccs decays\nEntangled pairs of neutral B mesons from \u03a5(4S) decays\nhave been used for establishing CP violation in the in-\nterference between amplitudes with and without B0 \u2212B0\nmixing in decays into ccs states (as discussed above, see\nSections 17.6.1-17.6.3), and also for demonstrating time-\nreversal violation in this interference. Just as one B meson\nin a pair is prepared in the B0 state at the time when the\nother B is identi\ufb01ed as a B0 by a decay into a \ufb02avor-\nspeci\ufb01c decay such as e+\u03bdeX, the decay of one B into\nccK0\nS prepares the other B in the well de\ufb01ned state B+,\nwhich does not decay into ccK0\nS. Similarly, when the \ufb01rst\nB decays into ccK0\nL, the second B is prepared in the state\nB\u2212, which does not decay into ccK0\nL.\nViolation of CP symmetry has been established by\nobserving the di\ufb00erence between the transition rates of\nB0 \u2192ccK0\nS and B0 \u2192ccK0\nS. In the same way, as pro-\nposed by Ba\u02dcnuls and Bernabeu (1999), the di\ufb00erence be-\ntween the rates of the transitions B0 \u2192B\u2212and B\u2212\u2192B0\nprobes time-reversal symmetry. Such an analysis has been\nperformed by BABAR (Lees, 2012m). In the following we\nde\ufb01ne the states B+ and B\u2212as linear combinations of B0\nand B0 and show their relevance for time reversal. We then\ndescribe the analysis and its results, which are indepen-\ndent of Standard Model or other model assumptions and\nare only based on quantum mechanics and entanglement.\nThe time-reversal transformation, usually called T, con-\nsists of changing the sign of the time coordinate t in the\nequations of motion. In quantum mechanics, this trans-\nformation involves changing the sign of all odd variables\nunder t \u2192\u2212t in the Hamiltonian H, such as velocities,\nmomenta and spins (called bT in the following), and the\nexchange of \ufb01nal and initial states (Branco, Lavoura, and\nSilva, 1999; Sachs, 1987). Since it is di\ufb03cult to prepare\nthe time-reversed process, methods based on bT-odd ob-\nservables for non-degenerate stationary states (e.g. elec-\ntric dipole moments for particles), or for \ufb01nal states after\nweak decay, have been used. The latter, however, require\ndetailed understanding of \ufb01nal-state interactions (FSI),\nsince they may lead to bT symmetry violation without the\noccurrence of T violation (Wolfenstein, 1999).\nFor T-symmetric processes, the probability of an initial\nstate i being transformed into a \ufb01nal state f is the same\nas the probability that an initial state identical to f, but\nwith all momenta and spins reversed, transforms into the\nstate i with all momenta and spins reversed,\n|\u27e8f|S|i\u27e9|2 = |\u27e8iT |ST |fT \u27e9|2,\n(17.6.19)\nwhere S is the transition matrix given by the Hamiltonian\nH. This is referred to as detailed balance (Sachs, 1987).\nIn Eq. (17.6.19), |i\u27e9\u2261|pi, si\u27e9and \u27e8f| \u2261\u27e8pf, sf| are the\ninitial and \ufb01nal states, \u27e8iT | and |fT \u27e9are the T-transformed\nstates of |i\u27e9and \u27e8f|, respectively, \u27e8iT | \u2261T|i\u27e9= \u27e8\u2212pi, \u2212si|\nand |fT \u27e9\u2261T\u27e8f| = | \u2212pf, \u2212sf\u27e9, and ST = S\u2020 = TST \u22121.\nIt should be noted that T invariance is a su\ufb03cient, but\nnot necessary, condition for detailed balance. Therefore,\ndetailed-balance breaking is an unambiguous signal for\nT violation. If S is Hermitian, |\u27e8f|S|i\u27e9| = |\u27e8iT |S|fT \u27e9| =\n|\u27e8fT |S|iT \u27e9|; in this case, T invariance implies bT invariance,\nand vice versa. This occurs, for instance, to \ufb01rst order in\nthe weak interactions when FSI may be neglected (Branco,\nLavoura, and Silva, 1999; Sachs, 1987).\nWithin the framework of the Wigner-Weisskopf ap-\nproximation (Weisskopf and Wigner, 1930a,b), the two\ncontributions to CP violation in K0 \u2194K0 transitions are\ndescribed by the parameters Re\u03f5 (violation of CP and T\nsymmetry) and Re\u03b4+iIm\u03b4 (violation of CP and CPT sym-\nmetry). Here, CP and T symmetry is known to be violated\nsince 1970, when a Bell-Steinberger unitarity analysis de-\ntermined Re\u03f5 \u0338= 0 (|qK/pK| \u0338= 1) with a signi\ufb01cance of\nabout 5\u03c3 (Schubert et al., 1970). Direct evidence for the\nviolation of CP and T, however, has been found only 28\nyears later (Angelopoulos et al., 1998), through the mea-\nsurement of detailed-balance breaking in K0 \u2194K0 transi-\ntions with a signi\ufb01cance of about 4\u03c3, leading to a value of\nRe\u03f5 consistent with that obtained using Bell-Steinberger\nunitarity.\nCP violation in B \u2192ccK0 decays is described by\nthe parameter \u03bb = qA/pA, where A = \u27e8ccK0|D|B0\u27e9,\nA = \u27e8ccK0|D|B0\u27e9, and the operator D is the B decay\ncontribution to S (Section 10.2). Assuming that the ampli-\ntude A can be described by a single weak phase with only\none FSI phase shift, the two parts of \u03bb (CP with T viola-\ntion, and CP with CPT violation) are easily identi\ufb01ed by\nseparating it into its modulus and phase: \u03bb = |\u03bb| exp (i\u03c6).\nCPT invariance in the decay requires |A/A| = 1 (Lee,\nOehme, and Yang, 1957). With |q/p| = 1, which is ob-\nserved to be well ful\ufb01lled (see Section 17.5.4), it follows\nthat |\u03bb| = 1. T invariance of S requires \u03c6 = 0 or \u03c0, i.e.\nIm\u03bb = 0 (Enz and Lewis, 1965). Conversely, if A is the\n\n323\nTable 17.6.13. Time-dependent CP parameters obtained from BABAR (Aubert, 2006u) and Belle (Dalseno, 2007) for the decay\nB0 \u2192D\u2217+D\u2217\u2212K0\nS. The \ufb01rst uncertainty is statistical and the second is systematic. The averages of the two experiments and\ntheir total uncertainty are also shown.\nBABAR\nBelle\nAverage\nJc\nJ0\n0.76 \u00b1 0.18 \u00b1 0.07\n0.60+0.25\n\u22120.28 \u00b1 0.08\n0.71 \u00b1 0.16\n2Js1\nJ0\nsin 2\u03c61\n0.10 \u00b1 0.24 \u00b1 0.06\n\u22120.17 \u00b1 0.42 \u00b1 0.09\n0.03 \u00b1 0.21\n2Js2\nJ0\ncos 2\u03c61\n0.38 \u00b1 0.24 \u00b1 0.05\n\u22120.23+0.43\n\u22120.41 \u00b1 0.13\n0.24 \u00b1 0.22\nsum of two (or more) amplitudes, |A/A| \u0338= 1 when both\nthe strong and weak phase di\ufb00erences between the two\ndecay amplitudes do not vanish, even if D is CPT sym-\nmetric (direct CP violation, see Section 16.6). Therefore,\nif |A/A| = 1 then we either have both CPT symmetry in\ndecay and a single amplitude, or an unlikely \u201caccidental\u201d\ncancellation of T and CPT violation in the decay.\nThe \ufb01rst signi\ufb01cant observations of large CP violation\nin B \u2192ccK0 decays (Aubert, 2001e; Abe, 2001g) (see\nSections 17.6.2 and 17.6.3) found C = (1\u2212|\u03bb|2)/(1+|\u03bb|2)\nto be consistent with zero (|\u03bb| = 1) and S = 2Im\u03bb/(1 +\n|\u03bb|2) \u0338= 0. These results are obtained from the \u2206t = t\u03b2\u2212t\u03b1\ndistributions of events \u03a5(4S) \u2192B0B0 \u2192(ccK0\nS or ccK0\nL)\nand (e+\u03bdeX or e\u2212\u03bdeX) at times t\u03b2 and t\u03b1, respectively,\nparameterized according to Eq. (10.2.2) in Section 10.2.\nThis expression assumes a negligible di\ufb00erence between\nthe decay rates of the mass eigenstates (i.e. \u2206\u0393d = 0),\n|q/p| = 1 and Rez +iImz = 0 (see Section 17.5.4); i.e. CP\nsymmetry in B0 \u2212B0 mixing. However, it is valid for both\nsigns of \u2206t and neither requires T nor CPT symmetry\nin decay. Within the framework of the Wigner-Weisskopf\napproximation, the results are compatible with CP and\nCPT symmetry in decay, and violate CP and T symmetry\nin the interference between decay and mixing (Fidecaro,\nGerber, and Ruf, 2013). 11 years later, time-reversal vio-\nlation has been directly observed in the measurement of\ndetailed-balance breaking (Lees, 2012m), as described in\nthe following.\nExperimentally we know to a su\ufb03ciently good approx-\nimation that K0\nS and K0\nL are orthogonal states. Adopting\nan arbitrary sign convention, we have\nK0\nS =\n\u0000K0 \u2212K0\u0001\n/\n\u221a\n2,\nK0\nL =\n\u0000K0 + K0\u0001\n/\n\u221a\n2,\n(17.6.20)\nwithin O(10\u22123) due to CP violation in K0 \u2212K0 mixing.76\nFurthermore, assuming the absence of wrong strangeness\nB decays, i.e. the B0 does not decay into ccK0 and the B0\ndoes not decay into ccK0, \u27e8ccK0|D|B0\u27e9= \u27e8ccK0|D|B0\u27e9=\n76 In general K0\nS(L) \u221dK0(1 + \u03f5) \u2212(+)K0(1 \u2212\u03f5), where |\u03f5| =\n(2.228 \u00b1 0.011) \u00d7 10\u22123(Beringer et al., 2012).\n0, we have\n\u03bbS = qAS/pAS = \u2212\u03bb,\n\u03bbL = qAL/pAL = \u03bb,\n(17.6.21)\nwhere\nAS,L = \u27e8ccK0\nS, ccK0\nL|D|B0\u27e9,\nAS,L = \u27e8ccK0\nS, ccK0\nL|D|B0\u27e9.\n(17.6.22)\nWith the aforementioned approximations, the normalized\nstates\nB+ = N\n\u0012\nB0 + A\nAB0\n\u0013\n,\nB\u2212= N\n\u0012\nB0 \u2212A\nAB0\n\u0013\n,\n(17.6.23)\nwith N = |A|/\nq\n|A|2 + |A|2, have the property that the\nformer decays into ccK0\nL, but not into ccK0\nS, and the lat-\nter into ccK0\nS, but not into ccK0\nL (Alvarez and Szynkman,\n2008; Bernabeu, Martinez-Vidal, and Villanueva-Perez,\n2012). Like the two mixing eigenstates BH and BL,\nthe two states B+ and B\u2212are well de\ufb01ned and phase-\nconvention-free physical states, but all four are not CP\neigenstates. In contrast to the K0, D0 and B0\ns systems,\nwhere the mass eigenstates are approximate CP eigen-\nstates, none of the linear combinations of B0 and B0\nhas this approximate property because of large CP vio-\nlation in the system. The states B+ and B\u2212are orthog-\nonal, i.e. \u27e8B+|B\u2212\u27e9= 0, if |A/A| = 1. An extended dis-\ncussion, including wrong strangeness and wrong sign (i.e.\n\u27e8e+\u03bdeXD|B0\u27e9\u0338= 0, \u27e8e\u2212\u00af\u03bdeXD|B0\u27e9\u0338= 0) B decays has been\nvery recently presented by Applebaum, Efrati, Grossman,\nNir, and Soreq (2013).\nPreparing the four initial states B0, B0, B+ and B\u2212\nby entanglement, the BABAR analysis (Lees, 2012m) de-\ntermines the four di\ufb00erences\n|\u27e8ccK0\nS|S|B0\u27e9|2 \u2212|\u27e8e+\u03bdeX|S|B\u2212\u27e9|2,\n|\u27e8ccK0\nL|S|B0\u27e9|2 \u2212|\u27e8e+\u03bdeX|S|B+\u27e9|2,\n|\u27e8ccK0\nS|S|B0\u27e9|2 \u2212|\u27e8e\u2212\u03bdeXS|B\u2212\u27e9|2,\n\n324\n|\u27e8ccK0\nL|S|B0\u27e9|2 \u2212|\u27e8e\u2212\u03bdeX|S|B+\u27e9|2,\n(17.6.24)\nwhere S = DU(t) and U(t) describes the time evolution of\nB0 \u2194B0 transitions, given by M and \u0393, the two-by-two\nmass and decay Hermitian matrices of the e\ufb00ective Hamil-\ntonian, as introduced in Section 10.1, and t > 0 is the\nelapsed time between the \ufb01rst and second B decay of the\nentangled pair. If |A/A| = 1 (Schubert, Gioi, Bevan, and\nDi Domenico, 2014), the four di\ufb00erences in Eq. (17.6.24)\nare equal to the di\ufb00erences\n|\u27e8B\u2212|U(t)|B0\u27e9|2 \u2212|\u27e8B0|U(t)|B\u2212\u27e9|2,\n|\u27e8B+|U(t)|B0\u27e9|2 \u2212|\u27e8B0|U(t)|B+\u27e9|2,\n|\u27e8B\u2212|U(t)|B0\u27e9|2 \u2212|\u27e8B0|U(t)|B\u2212\u27e9|2,\n|\u27e8B+|U(t)|B0\u27e9|2 \u2212|\u27e8B0|U(t)|B+\u27e9|2,\n(17.6.25)\nrespectively. The observation that these di\ufb00erences are\nnon-zero, with a sin \u2206mdt time dependence, is a clear\ndemonstration of detailed-balance breaking.\nWithin the same approximation, di\ufb00erences like\n|\u27e8ccK0\nS|S|B0\u27e9|2 \u2212|\u27e8e\u2212\u03bdeX|S|B\u2212\u27e9|2,\n(17.6.26)\ndemonstrate CPT symmetry.\nThe experimental analysis (Lees, 2012m) uses the same\ndata sample as the most recent CP-violation study in\nB \u2192ccK0, consisting of 426 fb\u22121 of integrated luminos-\nity (Aubert, 2009z) (see Section 17.6.3). The analysis relies\non identical reconstruction algorithms, selection criteria\nand calibration techniques. Events are selected in which\none B candidate is reconstructed in a ccK0\nS or ccK0\nL state,\nand the other B in a \ufb02avor eigenstate. We denote gener-\nally as \u2113\u2212X (\u2113+X) \ufb01nal states that identify the \ufb02avor of\nthe B as B0 (B0), which can be either semileptonic decays\nsuch as B0 \u2192e+\u03bdeX or \ufb02avor-speci\ufb01c hadronic decays.\nThe selection leads to event classes (f1, f2) where the \ufb01nal\nstate f1 is reconstructed at time t1, and the \ufb01nal state f2\nis reconstructed at time t2 > t1. Thus, only the eight event\nclasses given in Table 17.6.14 are used for further analy-\nsis. Within the same approximations and if |A/A| = 1 can\nexperimentally be proven, these eight classes correspond\nto the transitions reported on the right column of the ta-\nble. For example, the event class (\u2113+X, ccK0\nL) involves the\ndecay of one B meson at time t1 into a \u2113+X \ufb01nal state,\nthus at this time the B is in a B0 state. It then follows\nthat the still living (second) B meson is, at that time, in\na B0 state. If this same B meson decays and is recon-\nstructed at time t2 > t1 as ccK0\nL, it is a B+ state at t2.\nHence, it undergoes a transition B0 \u2192B+ in the elapsed\ntime t = t2 \u2212t1. Each of the four time-reversal symmetry\ndi\ufb00erences in Eq. (17.6.24) uses a pair of event classes in-\nvolving four di\ufb00erent \ufb01nal states, \u2113+X and \u2113\u2212X at times\nt1 (or t2) and t2 (or t1), and ccK0\nS and ccK0\nL at times t2\n(or t1) and t1 (or t2), respectively.\nAssuming \u2206\u0393d = 0, each of the eight transitions has a\ntime-dependent rate g\u00b1\n\u03b1,\u03b2(t) given by\ne\u2212\u0393 t[1 + S\u00b1\n\u03b1,\u03b2 sin(\u2206mdt) + C\u00b1\n\u03b1,\u03b2 cos(\u2206mdt)],\n(17.6.27)\nTable 17.6.14. Event classes (f1, f2) and their corresponding\ntransitions between B meson states, assuming that K0\nS and K0\nL\nare orthogonal states, the B0 (B0) does not decay into ccK0\n(ccK0), and |A/A| = 1. The e\ufb00ect of the \ufb01rst two assumptions\nis well below the statistical sensitivity, whereas the third is\ndirectly demonstrated in the same analysis (see text).\nEvent class\nTransition\n(\u2113+X, ccK0\nL)\nB0 \u2192B+\n(\u2113+X, ccK0\nS)\nB0 \u2192B\u2212\n(\u2113\u2212X, ccK0\nL)\nB0 \u2192B+\n(\u2113\u2212X, ccK0\nS)\nB0 \u2192B\u2212\n(ccK0\nL, \u2113+X)\nB\u2212\u2192B0\n(ccK0\nS, \u2113+X)\nB+ \u2192B0\n(ccK0\nL, \u2113\u2212X)\nB\u2212\u2192B0\n(ccK0\nS, \u2113\u2212X)\nB+ \u2192B0\nwhere the lower indices \u03b1 = \u2113+, \u2113\u2212and \u03b2 = K0\nS, K0\nL\nstand for the \ufb01nal reconstructed states \u2113+X, \u2113\u2212X and\nccK0\nS, ccK0\nL, respectively, and the upper indices indicate if\nthe \ufb02avor eigenstate (+) or the CP eigenstate (\u2212) is recon-\nstructed \ufb01rst. The coe\ufb03cients S\u00b1\n\u03b1,\u03b2 and C\u00b1\n\u03b1,\u03b2 are model-\nindependent; the eight pairs of S and C coe\ufb03cients can\nbe written in terms of eight complex \u03bb parameters, as\n2Im\u03bb/(1+|\u03bb|2) and (1\u2212|\u03bb|2)/(1+|\u03bb|2), respectively. The\nstate ccK0\nS is identi\ufb01ed by the \ufb01nal states with cc = J/\u03c8,\n\u03c8(2S) or \u03c7c1, while ccK0\nL only by J/\u03c8K0\nL. As in Au-\nbert (2009z), the \ufb02avor eigenstates labeled \u2113+X and \u2113\u2212X\nare identi\ufb01ed by prompt leptons, kaons, pions from D\u2217\nmesons, and high-momentum charged particles, combined\nin a neural network. The \ufb01nal sample contains 7796 ccK0\nS\nevents, with purities ranging between 87% and 96%, and\n5813 J/\u03c8K0\nL events with a purity of 56%.\nThe coe\ufb03cients S\u00b1\n\u03b1,\u03b2 and C\u00b1\n\u03b1,\u03b2 are determined by a si-\nmultaneous, unbinned maximum likelihood \ufb01t to the four\nmeasured \u2206t = t\u03b2 \u2212t\u03b1 distributions. The time di\ufb00er-\nence \u2206t is determined as described in Section 6.5 and\nused in the CP-violation studies based on the same de-\ncay modes (see Section 17.6.3). Neglecting time resolu-\ntion, the elapsed time between the \ufb01rst and second decay\nis t = \u2206t if the \ufb01rst B decays into a \ufb02avor eigenstate,\nand t = \u2212\u2206t if it decays into a CP eigenstate. Time\nresolution mixes events with positive and negative true\n\u2206t, i.e., a true event class (\u2113+X, ccK0\nL), corresponding\nto a B0 \u2192B+ transition, could appear reconstructed as\n(ccK0\nL, \u2113+X), corresponding to a B\u2212\u2192B0 transition, and\nvice versa. Therefore, the \ufb01t cannot be performed with\neight event classes but only with four. The separate de-\ntermination of the coe\ufb03cients for the event classes with\n\ufb02avor before CP eigenstates and those with CP before \ufb02a-\nvor eigenstates, i.e., the unfolding of time ordering and\n\u2206t resolution, is accomplished by using a signal p.d.f. for\nthe four distributions of the form\nH\u03b1,\u03b2(\u2206t) = g+\n\u03b1,\u03b2(\u2206ttrue)H(\u2206ttrue) \u2297R(\u03b4t; \u03c3\u2206t) +\n\n325\ng\u2212\n\u03b1,\u03b2(\u2212\u2206ttrue)H(\u2212\u2206ttrue) \u2297R(\u03b4t; \u03c3\u2206t),\n(17.6.28)\nwhere \u2206ttrue \u2261\u00b1t is the signed di\ufb00erence of proper time\nbetween the two B decays in the limit of perfect \u2206t res-\nolution, H is the Heaviside step function, R(\u03b4t; \u03c3\u2206t) is\nthe resolution function with \u03b4t = \u2206t \u2212\u2206ttrue, and \u03c3\u2206t\nis the estimate of the \u2206t uncertainty obtained by the re-\nconstruction algorithms (Bernabeu, Martinez-Vidal, and\nVillanueva-Perez, 2012). A total of 27 parameters are var-\nied in the likelihood \ufb01t: eight pairs (S\u00b1\n\u03b1,\u03b2, C\u00b1\n\u03b1,\u03b2) of signal\ncoe\ufb03cients and 11 for describing possible CP and T vio-\nlation in the background. All remaining signal and back-\nground parameters are treated in an identical manner as\ndone in the CP violation analysis (see Section 17.6.3).\nFrom the 16 signal coe\ufb03cients, reported in Table 17.6.15,\nwe construct six pairs of independent asymmetry parame-\nters (\u2206S\u00b1\nT , \u2206C\u00b1\nT ), (\u2206S\u00b1\nCP , \u2206C\u00b1\nCP ), and (\u2206S\u00b1\nCP T , \u2206C\u00b1\nCP T ),\nas shown in Table 17.6.16. The asymmetry parameters\nhave the advantage that the breaking of time-reversal sym-\nmetry would directly manifest itself through any nonzero\nvalue of \u2206S\u00b1\nT or \u2206C\u00b1\nT , or any di\ufb00erence between \u2206S\u00b1\nCP\nand \u2206S\u00b1\nCP T , or between \u2206C\u00b1\nCP and \u2206C\u00b1\nCP T .\nTable 17.6.15. Measured values of the S\u00b1\n\u03b1,\u03b2 and C\u00b1\n\u03b1,\u03b2 coef-\n\ufb01cients (Lees, 2012m). The \ufb01rst uncertainty is statistical and\nthe second systematic. The indices \u2113\u2212, \u2113+, K0\nS, and K0\nL stand\nfor reconstructed \ufb01nal states that identify the B meson state\nas B0, B0 and B\u2212, B+, respectively.\nTransition\nParameter\nResult\nB0 \u2192B+\nS+\n\u2113+,K0\nL\n\u22120.69 \u00b1 0.11 \u00b1 0.04\nC+\n\u2113+,K0\nL\n\u22120.02 \u00b1 0.11 \u00b1 0.08\nB0 \u2192B\u2212\nS+\n\u2113+,K0\nS\n0.55 \u00b1 0.09 \u00b1 0.06\nC+\n\u2113+,K0\nS\n0.01 \u00b1 0.07 \u00b1 0.05\nB0 \u2192B+\nS+\n\u2113\u2212,K0\nL\n0.51 \u00b1 0.17 \u00b1 0.11\nC+\n\u2113\u2212,K0\nL\n\u22120.01 \u00b1 0.13 \u00b1 0.08\nB0 \u2192B\u2212\nS+\n\u2113\u2212,K0\nS\n\u22120.76 \u00b1 0.06 \u00b1 0.04\nC+\n\u2113\u2212,K0\nS\n0.08 \u00b1 0.06 \u00b1 0.06\nB\u2212\u2192B0\nS\u2212\n\u2113+,K0\nL\n0.70 \u00b1 0.19 \u00b1 0.12\nC\u2212\n\u2113+,K0\nL\n0.16 \u00b1 0.13 \u00b1 0.06\nB+ \u2192B0\nS\u2212\n\u2113+,K0\nS\n\u22120.66 \u00b1 0.06 \u00b1 0.04\nC\u2212\n\u2113+,K0\nS\n\u22120.05 \u00b1 0.06 \u00b1 0.03\nB\u2212\u2192B0\nS\u2212\n\u2113\u2212,K0\nL\n\u22120.83 \u00b1 0.11 \u00b1 0.06\nC\u2212\n\u2113\u2212,K0\nL\n0.11 \u00b1 0.12 \u00b1 0.08\nB+ \u2192B0\nS\u2212\n\u2113\u2212,K0\nS\n0.67 \u00b1 0.10 \u00b1 0.08\nC\u2212\n\u2113\u2212,K0\nS\n0.03 \u00b1 0.07 \u00b1 0.04\nTable 17.6.16. Measured values of the asymmetry param-\neters, de\ufb01ned as the di\ufb00erences in S\u00b1\n\u03b1,\u03b2 and C\u00b1\n\u03b1,\u03b2 between\nsymmetry-transformed transitions (Lees, 2012m). The param-\neters \u2206S\u00b1\nT , \u2206C\u00b1\nT and the di\ufb00erences \u2206S\u00b1\nCP \u2212\u2206S\u00b1\nCP T , \u2206C\u00b1\nCP \u2212\n\u2206C\u00b1\nCP T are all T violating. The \ufb01rst uncertainty is statistical\nand the second systematic.\nParameter\nResult\n\u2206S+\nT = S\u2212\n\u2113\u2212,K0\nL \u2212S+\n\u2113+,K0\nS\n\u22121.37 \u00b1 0.14 \u00b1 0.06\n\u2206S\u2212\nT = S+\n\u2113\u2212,K0\nL \u2212S\u2212\n\u2113+,K0\nS\n1.17 \u00b1 0.18 \u00b1 0.11\n\u2206C+\nT = C\u2212\n\u2113\u2212,K0\nL \u2212C+\n\u2113+,K0\nS\n0.10 \u00b1 0.14 \u00b1 0.08\n\u2206C\u2212\nT = C+\n\u2113\u2212,K0\nL \u2212C\u2212\n\u2113+,K0\nS\n0.04 \u00b1 0.14 \u00b1 0.08\n\u2206S+\nCP = S+\n\u2113\u2212,K0\nS \u2212S+\n\u2113+,K0\nS\n\u22121.30 \u00b1 0.11 \u00b1 0.07\n\u2206S\u2212\nCP = S\u2212\n\u2113\u2212,K0\nS \u2212S\u2212\n\u2113+,K0\nS\n1.33 \u00b1 0.12 \u00b1 0.06\n\u2206C+\nCP = C+\n\u2113\u2212,K0\nS \u2212C+\n\u2113+,K0\nS\n0.07 \u00b1 0.09 \u00b1 0.03\n\u2206C\u2212\nCP = C\u2212\n\u2113\u2212,K0\nS \u2212C\u2212\n\u2113+,K0\nS\n0.08 \u00b1 0.10 \u00b1 0.04\n\u2206S+\nCP T = S\u2212\n\u2113+,K0\nL \u2212S+\n\u2113+,K0\nS\n0.16 \u00b1 0.21 \u00b1 0.09\n\u2206S\u2212\nCP T = S+\n\u2113+,K0\nL \u2212S\u2212\n\u2113+,K0\nS\n\u22120.03 \u00b1 0.13 \u00b1 0.06\n\u2206C+\nCP T = C\u2212\n\u2113+,K0\nL \u2212C+\n\u2113+,K0\nS\n0.14 \u00b1 0.15 \u00b1 0.07\n\u2206C\u2212\nCP T = C+\n\u2113+,K0\nL \u2212C\u2212\n\u2113+,K0\nS\n0.03 \u00b1 0.12 \u00b1 0.08\nAll eight C\u00b1\n\u03b1,\u03b2 coe\ufb03cients are compatible with zero.\nSince C = (1 \u2212|\u03bb|2)/(1 + |\u03bb|2), \u03bb = qA/pA and |q/p| \u22481,\nC = 0 implies |A/A| = 1. Therefore, the time dependence\nwith only a sin \u2206mdt function proves experimentally the\napproximation |A/A| = 1 required for the demonstration\nof time-reversal violation. With this observation (i.e. the\nabsence of all eight cos \u2206mdt terms) the two states B+ and\nB\u2212are orthogonal; we have the association between event\nclasses and B meson transitions given in Table 17.6.14,\nand the di\ufb00erences in Eqs (17.6.24) and (17.6.25) become\nidentical.\nFor visualizing the T-violating di\ufb00erences of the tran-\nsition rates, the \ufb01t results are shown in Fig. 17.6.19 in the\nform of asymmetries such as (for the transition B0 \u2192B\u2212)\nAT (\u2206t) =\nH\u2212\n\u2113\u2212,K0\nL(\u2206t) \u2212H+\n\u2113+,K0\nS(\u2206t)\nH\u2212\n\u2113\u2212,K0\nL(\u2206t) + H+\n\u2113+,K0\nS(\u2206t), (17.6.29)\nwhere H\u00b1\n\u03b1,\u03b2(\u2206t) = H\u03b1,\u03b2(\u00b1\u2206t)H(\u2206t). With this construc-\ntion, AT (\u2206t) is de\ufb01ned only for positive \u2206t values. Ne-\nglecting reconstruction e\ufb00ects,\nAT (t) \u2248\u2206S+\nT\n2\nsin(\u2206mdt) + \u2206C+\nT\n2\ncos(\u2206mdt).\n(17.6.30)\nThe three other asymmetries in Fig. 17.6.19 are constructed\nin an analogous way and have the same time dependence,\nwith \u2206S+\nT replaced by \u2206S\u2212\nT , \u2206S\u2212\nCP \u2212\u2206S\u2212\nCP T , and \u2206S+\nCP\n\u2212\u2206S+\nCP T , respectively, and equally for \u2206C+\nT .\n\n326\nt (ps)\n\u2206\n0\n2\n4\n6\n8\n \nT\nA\n-0.5\n0\n0.5\na)\nt (ps)\n\u2206\n0\n2\n4\n6\n8\n \nT\nA\n-0.5\n0\n0.5\nb)\nt (ps)\n\u2206\n0\n2\n4\n6\n8\n \nT\nA\n-0.5\n0\n0.5\nc)\nt (ps)\n\u2206\n0\n2\n4\n6\n8\n \nT\nA\n-0.5\n0\n0.5\nd)\nFigure 17.6.19. The four independent time-reversal violat-\ning asymmetries (Lees, 2012m) for transition a) B0 \u2192B\u2212\n(\u2113+X, ccK0\nS), b) B+\n\u2192\nB0 (ccK0\nS, \u2113+X), c) B0\n\u2192\nB+\n(\u2113+X, J/\u03c8 K0\nL), d) B\u2212\u2192B0 (J/\u03c8K0\nL, \u2113+X), for combined \ufb02a-\nvor categories with low misidenti\ufb01cation (leptons and kaons),\nin the signal region (5.27 < mES < 5.29 GeV/c2 for ccK0\nS\nmodes and |\u2206E| < 10 MeV for J/\u03c8K0\nL). The points with error\nbars represent the data, the red solid and dashed blue curves\nrepresent the projections of the best \ufb01t results with and with-\nout time-reversal violation, respectively.\nThe evaluation of systematic uncertainties, reported in\nTable 17.6.16, follows closely that of the CP analysis based\non the same \ufb01nal states, discussed in Section 17.6.3. A pos-\nsible CP violation in right- and wrong-sign \ufb02avor-speci\ufb01c\nB decays (denoted \u2113\u00b1X) is found to have an impact on\nthe measurement well below the statistical uncertainty.\nAs seen in Fig. 17.6.19, time-reversal symmetry is\nclearly violated in all four transition comparisons. The\nsigni\ufb01cance of the observed T violation is obtained from\nthe log-likelihood value ln L. The di\ufb00erence 2\u2206ln L be-\ntween the best \ufb01t and the \ufb01t without T violation, includ-\ning systematic errors, is 226 with 8 d.o.f., which corre-\nsponds, assuming Gaussian errors, to 14\u03c3. Using the same\nprocedure for the CPT-symmetry di\ufb00erences such as in\nEq. (17.6.26), no CPT violation is observed. The di\ufb00er-\nence 2\u2206ln L between the values for the best \ufb01t and the\n\ufb01t with CPT symmetry is 5, equivalent to 0.3\u03c3. The anal-\nysis also determines four CP asymmetries; the results are\ncompatible with those obtained from the standard CP vio-\nlation analysis based on the same CP \ufb01nal states (Aubert,\n2009z); the observed signi\ufb01cance of CP violation is equiv-\nalent to 17\u03c3. This is larger than 14\u03c3 for T violation since\nthe comparison between two (\u2113\u00b1, ccKS) rates has a higher\nstatistical and systematic signi\ufb01cance than the compari-\nson of the rates (\u2113\u00b1, ccKS) and (\u2113\u00b1, ccKL).\nIn the Standard Model, the eight coe\ufb03cients S\u00b1\n\u03b1,\u03b2 are\nmeasurements of sin 2\u03c61. Hence the four measured T-\nviolating asymmetries, \u2206S\u00b1\nT and \u2206S\u00b1\nCP \u2212\u2206S\u00b1\nCP T , can be\nseen as four measurements of 2 sin 2\u03c61. The results in Ta-\nble 17.6.16 lead to a mean value \u03c61 = (21.8 \u00b1 2.0)\u25e6, which\nis of course completely correlated with the \u03c61 value ob-\ntained from the CP-asymmetry measurements discussed\nin Sections 17.6.3 and 17.6.10.\nIn conclusion, the BABAR experiment (Lees, 2012m)\nhas demonstrated with a large signi\ufb01cance of 14\u03c3 that de-\ntailed balance and therefore time-reversal symmetry are\nviolated. In b \u2192ccs decays, T and CP symmetry break-\nings are seen in two di\ufb00erent observations, are time de-\npendent with only a sin \u2206mt term, are of order O(10\u22121),\nand are induced by the interference between qA and pA,\ni.e. the interference between decay and mixing. All these\nproperties are di\ufb00erent from those of the earlier observed\n\ufb02avor mixing asymmetry in K0 \u2212K0 transitions, where\nCP and T transformations lead to the same observation,\nthe asymmetry is time independent, is of order O(10\u22123),\nand is produced by the interference of absorptive (\u039312)\nand dispersive (M12) contributions to mixing.\n17.6.10 \u03c61 summary\nEstablishing CP violation in B0 meson decays by mea-\nsuring sin 2\u03c61 was the most important initial goal of the\nB Factories. Both experiments achieved this goal after\ntwo years of operation through time-dependent analyses\nof b \u2192c\u00afcs transitions. This represents the \ufb01rst obser-\nvation of CP violation outside of the neutral kaon sys-\ntem (Christenson, Cronin, Fitch, and Turlay, 1964). With\na combined \ufb01nal data set of 1.2 billion BB pairs, the\nachieved precision on sin 2\u03c61 is 0.020. BABAR have also\ndemonstrated T violation in b \u2192c\u00afcs transitions which\nprovides an additional test of the CKM matrix (this is\nstatistically completely correlated with the CP violation\nresult). The ambiguity between \u03c61 and \u03c0/2 \u2212\u03c61 is re-\nsolved by several measurements. They all use interference\nwith known or measured strong phases (transversity states\n\n327\nand K\u2217\u2192K\u03c0 phases for B0 \u2192J/\u03c8K\u2217, and Dalitz plot\nphases for B0 \u2192D(\u2217)0[K0\nS\u03c0+\u03c0\u2212]h0 and D\u2217D\u2217K0\nS and\nother three-body decays). The result in terms of angle\nis \u03c61 \u2261\u03b2 = (21.30 \u00b1 0.78)\u25e6. The direct CP asymme-\ntry parameter C is found to be consistent with zero in\nthese channels, as expected in the SM. The consistency\nbetween \u03c61 and other CKM angles and sides of the Uni-\ntarity Triangle demonstrates that the KM mechanism is\nthe dominant source of CP violation in the SM. Kobayashi\nand Maskawa shared the 2008 Nobel Prize in physics for\ntheir work on the KM mechanism presented in (Kobayashi\nand Maskawa, 1973). The test of the CKM matrix by ex-\namining the agreement between di\ufb00erent measurements is\ndiscussed in Section 25.1.\nA number of other channels have been studied by the\nexperiments at the B Factories. These are suppressed to\nvarious degrees in the SM compared to b \u2192c\u00afcs transi-\ntions. They are either tree dominated modes with a pen-\nguin (or another tree) contribution that has a di\ufb00erent\nweak phase (J/\u03c8\u03c00, D(\u2217)D(\u2217) or D(\u2217)h0), or\ncharmless\nmodes (b \u2192sq\u00afq). The penguin-dominated modes are par-\nticularly sensitive to the presence of any postulated new\nheavy particles that could contribute to such a loop tran-\nsition.\nThe most precisely determined time-dependent asym-\nmetry parameters from a loop dominated b \u2192sq\u00afq channel\ncome from B0 \u2192\u03b7\u2032K0 and K+K\u2212K0 with a precision of\n0.07 on sin 2\u03c61. The uncertainties of other modes range\nfrom around 0.2 to 0.7. The sin 2\u03c61 results obtained from\nthese measurements are consistent with the value mea-\nsured in the b \u2192c\u00afcs golden channels. The na\u00a8\u0131ve average\nof charmless decays is within one sigma of b \u2192c\u00afcs re-\nsults. However, it should be noted that the na\u00a8\u0131ve average\nis not a good observable to use when searching for NP, as\nthe hadronic uncertainties vary from mode to mode. The\nmost recent measurements of these decays are consistent\nwith the SM.\nNo signi\ufb01cant direct CP asymmetry is found in the\nchannels discussed in this section. However some of these\nchannels exhibit central values that are more than 2\u03c3 from\nC = 0 (e.g., D+D\u2212for Belle and \u03c9K0\nS for BABAR). The\nglobal \u03c72 among the di\ufb00erent channels studied is consis-\ntent with the interpretation that these measurements are\nthe result of a statistical \ufb02uctuation.\n\n328\n17.7 \u03c62, or \u03b1\nEditors:\nYury Kolomensky (BABAR)\nTagir Aushev (Belle)\nIkaros Bigi (theory)\nAdditional section writers:\nAdrian Bevan, Cheng-Chin Chiang, Jeremy Dalseno,\nJ. William Gary, Mathew Graham, Akito Kusaka, Fer-\nnando Palombo, Kolja Prothmann, Aaron Roodman,\nAbner\nSo\ufb00er,\nAlexander\nSomov,\nAlexandre\nTelnov,\nKarim Trabelsi, Pit Vanhoefer, Georges Vasseur, Fergus\nWilson\nIn the Standard Model of particle physics the CKM\nmatrix results in a set of nine unitary relationships, six\nof which are triangles in a complex plane (Chapter 16).\nThe imaginary components of these triangles are manifes-\ntations of a single complex phase that dictates the amount\nof CP violation in the theory. The measurement of \u03c61 de-\nscribed in Chapter 17.6 establishes one of the angles of the\nUnitarity Triangle associated with Bd decays, introduced\nin Section 16.5. To check the self-consistency of the trian-\ngle one has to measure its other two angles and the sides.\nThe second angle of the Unitarity Triangle to be measured\nis \u03c62, which is the subject of this chapter. Together the\nmeasurements of \u03c61 and \u03c62 are su\ufb03cient to test the pre-\ndictions of the SM. Constraints on the third angle, \u03c63 ,\nare discussed in Chapter 17.8 and how one typically inter-\nprets these results in the context of the SM is reviewed in\nChapter 25.1.\nA probe that can be used to determine \u03c62 is the mea-\nsurement of the time-dependent CP asymmetry in B0 \u2192\n\u03c0+\u03c0\u2212transitions. This CP violation is produced by the\ninterference of the dominant box diagram for B0\u2212B0 mix-\ning with the tree diagram bd \u2192uudd. If these were the\nonly contributing diagrams, the resulting CP asymmetry\nparameters would be S = sin 2\u03c62 and C = 0. However the\nsituation is not so simple: this \ufb01nal state is also produced\nby higher order weak transitions, and of particular rele-\nvance is the one-loop diagram usually called the \u2018penguin\u2019\ndiagram (Shifman, Vainshtein, and Zakharov, 1977). The\npresence of penguin contributions with weak phases that\ndi\ufb00er from the leading order tree results in theoretical un-\ncertainties on \u03c62 that are sometimes referred to as \u2018pen-\nguin pollution\u2019 in the literature. The penguin contribu-\ntion a\ufb00ects B(B0 \u2192\u03c0+\u03c0\u2212) and its CP asymmetry (Bigi,\nKhoze, Uraltsev, and Sanda, 1989). Gronau and London\n(1990) suggested using isospin symmetry to correct for the\ne\ufb00ect of penguin contributions when extracting \u03c62. At \ufb01rst\nit was thought that penguin contributions are very small\nin the SM for B0 \u2192\u03c0\u03c0, since the amplitude b \u2192dqq is\nsuppressed by a factor of |\u03bb| = |Vus| relative to b \u2192sqq.\nHowever, data showed that the B0 \u2192\u03c00\u03c00 rate is larger\nthan had been initially expected, and this is explained by\nthe presence of a sizable penguin contribution; therefore\npenguin amplitudes can signi\ufb01cantly a\ufb00ect the extraction\nof \u03c62. Thus the measurement of \u03c62 with B \u2192\u03c0\u03c0 requires\na more complicated approach than the measurement of\n\u03c61 with B \u2192J/\u03c8K0\nS. The theoretical issues associated\nwith this approach are described in Section 17.7.1.1, and\nthe corresponding experimental treatment is summarized\nin Section 17.7.3.1. It is worth noting that new physics\n(NP) could enhance penguin contributions signi\ufb01cantly.\nExperimentally one could identify such contributions by\nobserving a signi\ufb01cant di\ufb00erence between values of \u03c62 ob-\ntained using di\ufb00erent decay modes.\nThe impact of penguin amplitudes in general is di\ufb00er-\nent for di\ufb00erent \ufb01nal states, and as bd \u2192uudd decays can\nbe used to measure \u03c62, it became necessary to explore ex-\nperimentally and theoretically more di\ufb03cult scenarios in\nthe hope that nature was kind enough to permit measure-\nment of this angle in one or another way. Having deter-\nmined that the measurement of \u03c62 via B0 \u2192\u03c0\u03c0 would be\nless sensitive than anticipated, the B Factories approached\nthe problem using a rather di\ufb00erent technique: a time-\ndependent analysis of the Dalitz plot of B0 \u2192\u03c0+\u03c0\u2212\u03c00.\nThe theoretical issues related to this measurement are in-\ntroduced in Section 17.7.1.2, while the corresponding ex-\nperimental discussion can be found in Section 17.7.4. The\nresulting constraints obtained from BABAR and Belle data\ndo not add a signi\ufb01cant amount of information to im-\nprove the accuracy of the SM solution for \u03c62, however\nthey suppress the discrete ambiguities arising from the in-\nterpretation of other measurements. For the future higher\nstatistics experiments, the decay B0 \u2192\u03c0+\u03c0\u2212\u03c00 is ex-\npected to dominate the experimental determination of \u03c62\nand to provide a sensitive probe for the impact of NP and\nits features as a non-leading source of CP violation.\nAfter several years of data taking it became apparent\nthat extraction of \u03c62 from the B Factories is a di\ufb03cult\nenterprise. Thus it was realized that one has to think\nabout other \ufb01nal states and BABAR started to investi-\ngate other related options such as B \u2192\u03c1\u03c1 decays. They\nwere previously dismissed by the community as experi-\nmentally and theoretically too challenging to be a viable\nalternative compared with the already ambitious attempts\nto study B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c0. When the experimen-\ntal work commenced, the outcome of this endeavor was\nnot entirely clear; however, there were hints that indi-\ncated these modes could be more promising than originally\nthought. The presence of two vector particles in the \ufb01nal\nstate meant that one would have to perform a full angular\nanalysis of the \ufb01nal state (see Chapter 12) in addition to\nconstraining penguin contributions. However, it was pos-\nsible to piece together su\ufb03cient information from various\nsources in order to motivate attempting the measurement\nof \u03c62 with B \u2192\u03c1\u03c1 decays. Ultimately a full angular anal-\nysis was not required to constrain \u03c62 as the fraction of\nlongitudinal polarization in B \u2192\u03c1\u03c1 decays was found to\nalmost completely dominate (Section 17.7.3.2). The result\nof this approach turned out to provide the most stringent\nconstraint on \u03c62, where the e\ufb00orts of BABAR and Belle\nare summarized in Section 17.7.3.2. The time-dependent\nanalysis of B0 \u2192\u03c10\u03c10 promises to help resolve some of the\ndiscrete ambiguities inherent in the isospin analysis and\nis discussed in Section 17.7.3.3. An additional cross-check\n\n329\nusing SU(3) for B \u2192\u03c1\u03c1 and K\u2217\u03c1 decays is discussed in\nSection 17.7.6.\nAs a further development one constrains \u03c62 using \ufb01-\nnal states including vector and axial-vectors particles, in\nparticular using B \u2192a1(1260)\u03c0 decays, where one can\ndetermine the impact of penguin contributions with the\naid of SU(3) \ufb02avor symmetry. This theoretical approach\nis discussed in Section 17.7.1.3. Time-dependent measure-\nments of B \u2192a1(1260)\u03c0 and the complementary studies\nof B \u2192K1\u03c0 decays are used to control penguin pollution\nas discussed in Section 17.7.5.\nIn contrast to the initial expectations of the B Facto-\nries where it was anticipated that \u03c0\u03c0 \ufb01nal states would\nprovide a measurement of \u03c62 and \u03c1\u03c0 would be used to\nresolve ambiguities, \u2018reality\u2019 told a di\ufb00erent story. Mea-\nsurements of B \u2192\u03c1\u03c1 decays dominate the determination\nof the angle \u03c62 and B \u2192a1(1260)\u03c0 decays provide addi-\ntional precision on the overall measurement of this angle.\nThe study of \u03c1\u03c0 \ufb01nal states provides additional discrim-\nination: the power to resolve some of the discrete ambi-\nguities, as originally expected. The B Factories have been\nable to make an accurate measurement of \u03c62, using B de-\ncays to \u03c0\u03c0, \u03c1\u03c0, \u03c1\u03c1, and a1\u03c0 \ufb01nal states, as discussed in\nSection 17.7.7.\n17.7.1 Introduction\nThe angle \u03c62 can be inferred from time-dependent CP\nasymmetries in charmless b \u2192u transitions. Feynman di-\nagrams describing these decays, such as B0 \u2192\u03c0\u03c0 and\nB0 \u2192\u03c1\u03c1, are shown in Fig. 17.7.1. Interference between\nthe leading tree amplitude and the amplitude of B0 \u2212B0\nmixing (Fig. 10.1.1) provides access to the observable \u03c62.\nAs explained above, if the tree amplitude was the only\ndecay amplitude (as is the case for B0 \u2192J/\u03c8K0\nS), the S\nparameter in B0 \u2192\u03c0+\u03c0\u2212would be equal to sin 2\u03c62 and\nC zero (see Eq. 16.6.8). However, the penguin contribu-\ntions to charmless B decays cannot be ignored. In general\nS measures sin 2\u03c6e\ufb00\n2\ninstead sin 2\u03c62, where \u03c6e\ufb00\n2\nis related\nto \u03c62 up to a shift \u2206\u03c62 resulting from penguin ampli-\ntudes with a di\ufb00erent weak phase to that of the leading\norder tree contribution, i.e. \u2206\u03c62 = \u03c6e\ufb00\n2 \u2212\u03c62. We have to\nunderstand how to control the penguin contributions and\ndetermine the di\ufb00erence between \u03c6e\ufb00\n2\nand \u03c62.\nIn the following, we discuss four complementary tech-\nniques to extract the angle \u03c62 from time-dependent CP\nasymmetry measurements in B \u21922\u03c0, 3\u03c0 and 4\u03c0 decays.\n\u2013 Isospin analysis in B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c1;\n\u2013 Dalitz analysis in B \u2192\u03c1\u03c0;\n\u2013 SU(3) analysis of B \u2192a1(1260)\u03c0(K);\n\u2013 SU(3) constraints in charmless B decays to two vector\nmeson \ufb01nal states.\nThe analysis methodology outlined in the remainder\nof this chapter in terms of the study of four body \ufb01nal\nstates relies on the quasi-two-body approximation (see\nSection 17.4.3), which is su\ufb03cient for work at the B Fac-\ntories. However, it should be borne in mind that in the\nfuture one will want to probe the impact of NP in 4\u03c0\n(a) T\n(b) C\n(c) P\nFigure 17.7.1. Feynman diagrams contributing to the charm-\nless B decays B0 \u2192\u03c0\u03c0 or B0 \u2192\u03c1\u03c1: (a) external tree (T), (b)\ninternal (or color suppressed) tree (C), and (c) gluonic penguin\n(P). Nearby quarks are implied to be grouped into mesons.\nand 2\u03c0KK \ufb01nal states to search for possible non-leading\nsources of CP violation. Amplitude analyses, introduced\nin Section 13, will be required for such searches and fu-\nture super \ufb02avor factory will have to adopt a more general\napproach for such analyses.\nThe combined accuracy on \u03c62 obtained by the B Fac-\ntories is discussed in Section 17.7.7. Some time-integrated\nmeasurements are required to constrain penguin contribu-\ntions in various decays; those are discussed in Section 17.4.\n17.7.1.1 Isospin analysis of B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c1\nThe CP asymmetry in B0 \u2192\u03c0+\u03c0\u2212depends on \u03c62. How-\never (unlike B0 \u2192J/\u03c8K0\nS), because of the two contribut-\ning amplitudes (tree and penguin, see Section 16.6) in\nthe SM one expects direct CP violation to be manifest\nin B0 \u2192\u03c0+\u03c0\u2212, hence:\n\u0393(B \u2192\u03c0+\u03c0\u2212) \u2212\u0393(B \u2192\u03c0+\u03c0\u2212)\n\u0393(B \u2192\u03c0+\u03c0\u2212) + \u0393(B \u2192\u03c0+\u03c0\u2212)\n(17.7.1)\n= C cos \u2206md\u2206t \u2212S sin \u2206md\u2206t\nwith\nC = 1 \u2212|\u03bb|2\n1 + |\u03bb|2 ,\nS =\n2 Im\u03bb\n1 + |\u03bb|2 ,\n(17.7.2)\nwhere \u03bb = (q/p)A/A as noted in Chapter 10, and from\nChapter 16 we recall that\n0 \u2264C2 + S2 \u22641.\n(17.7.3)\n\n330\nCP violation is manifest if 0 < C2 + S2, i.e. if either\nof the asymmetry parameters are non-zero. Here \u03bb =\n(q/p)R(\u03c0+\u03c0\u2212) where R(\u03c0+\u03c0\u2212) refers to the amplitude\nof the B0 decay to the \ufb01nal state normalized by the B0\ndecay to the same one (Eq. 17.7.4):\nR(\u03c0+\u03c0\u2212) \u2261A(B0 \u2192\u03c0+\u03c0\u2212)\nA(B0 \u2192\u03c0+\u03c0\u2212) .\n(17.7.4)\nWithout penguin contributions one predicts in the SM (Bigi,\nKhoze, Uraltsev, and Sanda, 1989)\n\f\f\f\f\nq\npR(\u03c0+\u03c0\u2212)\n\f\f\f\f \u22431,\nIm\n\u0014q\npR(\u03c0+\u03c0\u2212)\n\u0015\n\u2243sin 2\u03c62.\n(17.7.5)\nHowever, penguin amplitudes do contribute. In this case\none \ufb01nds | q\npR(\u03c0+\u03c0\u2212)| \u0338= 1 and therefore C2 \u0338= 0. Our\nknowledge of the quantitative impact of penguin ampli-\ntudes and in general non-perturbative QCD is rather lim-\nited.\nOne technique for measuring \u03c62 is to study time-de-\npendent CP asymmetries in B0 \u2192\u03c0+\u03c0\u2212decays (Aubert\n(2002h); Abe (2003b)). The data show (see Section 17.7.3.1)\nthat:\nS = \u22120.66 \u00b1 0.07,\nC = \u22120.30 \u00b1 0.05,\n(17.7.6)\nwhich are consistent with expectation from the SM. The\nnon-zero value of C, indicating direct CP violation in this\nmode, arises from the interference of tree and penguin am-\nplitudes with di\ufb00erent weak and strong phases. It is not\npossible to determine if the penguin amplitudes are con-\nsistent with the SM expectation, or include contributions\nfrom physics beyond the SM. The SM level of contribution\nto these decays can be determined using the isospin anal-\nysis described below, the results of which can be found\nin Section 17.7.7. Therefore one cannot directly obtain \u03c62\nfrom the time-dependent analysis and use this with the\nvalue of \u03c61 from B0 \u2192J/\u03c8K0\nS, discussed in Section 17.6,\nto construct the SM Unitarity Triangle. A complemen-\ntary study in B0 \u2192\u03c1+\u03c1\u2212was pioneered by BABAR (Au-\nbert, 2004ag) with the hope of being able to contribute\nto the measurement of \u03c62. However once again the ex-\ntraction of this angle is complicated by the presence of\nboth tree and penguin amplitudes, with di\ufb00erent weak\nphases. An isospin analysis of the \u03c0\u03c0 or \u03c1\u03c1 system is nec-\nessary (Gronau and London, 1990) to disentangle the tree\ncontribution, and hence determine \u03c62 as explained in the\nfollowing.\nThe all-charged modes (B0 \u2192\u03c0+\u03c0\u2212and B0 \u2192\u03c1+\u03c1\u2212)\nare dominated by the external tree (T) and gluonic pen-\nguin (P) amplitudes, while the all-neutral modes (B0 \u2192\n\u03c00\u03c00 and B0 \u2192\u03c10\u03c10) are very sensitive to the P con-\ntribution, since the internal tree diagram (C) is color-\nsuppressed. The amplitudes A00 \u2261A(B0 \u2192h0h0), A+\u2212\u2261\nA(B0 \u2192h+h\u2212), and A+0 \u2261A(B+ \u2192h+h0), where\nh = \u03c0, \u03c1, and their complex conjugates, obey the Gronau-\nLondon isospin relation (Gronau and London, 1990). Here\nwe note that I = 1/2 for u and d quarks only and as a re-\nsult the isospin decomposition of B \u2192\u03c0\u03c0 decays follows\nthe corresponding K \u2192\u03c0\u03c0 case. Bose statistics forbids\nI = 1 \u03c0\u03c0 \ufb01nal states, which simpli\ufb01es the isospin con-\nstruction of these decays. The tree topologies shown in\nFig 17.7.1 come from operators that describe \u2206I = 1/2 or\n\u2206I = 3/2 transitions, and so as a B meson has I = 1/2,\nthe corresponding \ufb01nal states can either be I = 0 or 2. In\ncontrast the gluonic penguin contributions come from a\n\u2206I = 1/2 operator, hence these can only be I = 0. Both\nh+h\u2212and h0h0 \ufb01nal states can be I = 0 or 2, and so in\ngeneral these decays may proceed via both tree and pen-\nguin transitions. In contrast, the h+h0 \ufb01nal state is I = 2\nand therefore can only have tree contributions. The re-\nsulting isospin relations obtained by Gronau and London\nare:\nA+\u2212/\n\u221a\n2 + A00 = A+0,\nA\n+\u2212/\n\u221a\n2 + A\n00 = A\n\u22120,\n(17.7.7)\neach of which can be represented by a triangle in a com-\nplex plane (Fig. 17.7.2). The CP conjugate relation is usu-\nally shown with a tilde replacing the bar to denote that\nthe bases of the two isospin triangles have been aligned\nsuch that A+0 = eA+0, which explicitly neglects any ef-\nfect coming from electroweak (EW) penguins.77 The rela-\ntive sizes and phases of each amplitude can be extracted\nfrom the complete isospin analysis of the three decay rates\nand corresponding CP asymmetries (Gronau and London,\n1990). The angle between the sides of lengths A+\u2212/\n\u221a\n2\nand eA+\u2212/\n\u221a\n2 is 2\u2206\u03c62.\nExperimentally, the complete isospin analysis of the\nB \u2192\u03c0\u03c0 system is complicated by the need to measure\ntime-dependent CP asymmetry of the all-neutral \ufb01nal state\ndecay of B0 mesons to \u03c00\u03c00. This is not possible at the\npresent level of statistics, although high luminosity super\n\ufb02avor factory may be able to constrain the decay vertex\nof the B0 \u2192\u03c00\u03c00 candidate using Dalitz decays of one or\nboth \u03c00 mesons, or events where one or more photons con-\nvert in the detector material. The situation is further exac-\nerbated by the relatively large observed branching fraction\nof B0 \u2192\u03c00\u03c00 decays (Aubert (2003k); Abe (2003a)); this\nimplies a large penguin contribution, which results in a\nsigni\ufb01cant uncertainty in the extraction of \u03c62. The branch-\ning fraction measurements of the decays B0 \u2192\u03c00\u03c00 and\nB+ \u2192\u03c0+\u03c00 are described in Section 17.4.\nThe isospin analysis of the vector-vector modes B \u2192\n\u03c1\u03c1 is more complicated than that for B \u2192\u03c0\u03c0. The \u03c1\u03c1\n\ufb01nal states include three contributions: one longitudinal\nand two transverse amplitudes following the discussion\n77 Electroweak penguins have the same topology as the glu-\nonic penguin shown in Fig 17.7.1, but are mediated by a pho-\nton or Z0 boson. It is expected that EW penguins are small\nand can be neglected. This assumption can be tested by con-\nstraining the level of direct CP violation found in B+ \u2192h+h0\ndecays, which is predicted to be zero in the absence of any EW\npenguin contribution.\n\n331\n2\n / \n+-\nA\n-0\n, A\n+0\nA\n00\nA\n2\n / \n+-\nA~\n~\n00\nA~\n2\n\u03c6 \n\u2206\n2 \nFigure 17.7.2. Gronau-London isospin triangles for B0 \u2192hh\n(solid lines) and B0 \u2192hh (dashed lines), drawn for illustration\npurposes (not to scale). The B0 amplitudes are denoted with\na tilde to highlight that the two triangles have been rotated\nrelative to each other so that the h+h0 and h\u2212h0 amplitudes\nare aligned.\nin Chapter 12. As a result there are three isospin anal-\nyses that can be performed, one for each of the transver-\nsity amplitudes. Na\u00a8\u0131ve factorization expectations (Suzuki,\n2002) indicated that one would expect the longitudinal\npolarization (CP-even) to dominate over the transverse\none (a CP admixture), which had the implication that\nanalysis of these decays could be simpli\ufb01ed from a full\nangular treatment to a partial angular one where only\nthe fraction of longitudinally polarized events needed to\nbe extracted from data (see Chapter 12). However, the\npolarization measurements of charmless B decays avail-\nable at the time were not straightforward and did not\nall support the expectation of nearly a 100% longitudinal\npolarization contribution (see Section 17.4). It had also\nbeen noted in (Aleksan et al., 1995) that using na\u00a8\u0131ve fac-\ntorization calculations one obtains a de\ufb01nite hierarchy of\npenguin contributions in B \u2192\u03c0\u03c0, \u03c1\u03c0 and \u03c1\u03c1 \ufb01nal states.\nThe results of these calculations implied that the pen-\nguin contributions would be largest for B \u2192\u03c0\u03c0 decays\nand smallest for B \u2192\u03c1\u03c1. However at the time the B\nFactories started taking data this message had not been\nwidely appreciated by the community. Given that one ex-\npects the ratio of amplitudes of \u03c1\u03c1 to \u03c0\u03c0 decays to be\nO(f 2\n\u03c1/f 2\n\u03c0) \u223c2.5, one could piece together a credible the-\noretically motivated scenario that indicated the \u03c1\u03c1 \ufb01nal\nstates might be an attractive alternative way to measure\n\u03c62, if one could overcome the experimental challenges. For-\ntunately, the longitudinal polarization in B0 \u2192\u03c1+\u03c1\u2212\ufb01nal\nstate has been found to be consistent with unity (Aubert\n(2004w); Somov (2006)). Moreover, the neutral branching\nfraction B0 \u2192\u03c10\u03c10 was found to be relatively small (Au-\nbert (2007h, 2008r); Chiang (2008)), which constrains the\npenguin uncertainty in the B \u2192\u03c1\u03c1 system signi\ufb01cantly\n(see Section 17.4 for the details of the branching fraction\nmeasurements of the decays B0 \u2192\u03c1+\u03c1\u2212, B0 \u2192\u03c10\u03c10\nand B+ \u2192\u03c1+\u03c10). Shortly after the observation of B0 \u2192\n\u03c1+\u03c1\u2212, BABAR performed a time-dependent CP asymmetry\nmeasurement as a proof of principle that one could indeed\nconstrain \u03c62 (Aubert, 2004ag) using larger data samples.\nIt has been noted by Falk et al. (2004) that there could\nbe a small I = 1 component to B \u2192\u03c1\u03c1, which could\nbe tested by measuring S as a function of the di\ufb00erence\nbetween the mass of the two \u03c1\u2019s. Any departure from uni-\nformity would indicate that there is an I = 1 component,\nin which case the isospin construct required to correct for\npenguins would require some modi\ufb01cation.\n17.7.1.2 Dalitz analysis of B \u2192\u03c1\u03c0\nThe B Factories have performed analyses of the quasi-two-\nbody \ufb01nal states B \u2192\u03c1\u03c0 to check our theoretical control\nover extracting \u03c62.\nA proposed analysis of quasi-two-body \ufb01nal states (Lip-\nkin, Nir, Quinn, and Snyder, 1991; Snyder and Quinn,\n1993) relies on the isospin symmetry of the rates of all\nB \u2192\u03c1\u03c0 modes. The decay channels B+ \u2192\u03c10\u03c0+ and\nB0 \u2192\u03c1\u00b1\u03c0\u2213have been observed \ufb01rst by Belle (Gordon,\n2002) and then by BABAR (Aubert, 2003h). Evidence for\nthe B0 \u2192\u03c10\u03c00 mode, which was expected to be small, has\nbeen reported by Belle (Dragic, 2004) with a rate higher\nthan an upper bound obtained by BABAR (Aubert, 2004g).\nHowever, these two results are in agreement at the level\nof 1.5\u03c3. The remaining mode B+ \u2192\u03c1+\u03c00 has two neu-\ntral pions in the \ufb01nal state that makes it a challenging\nmeasurement. BABAR has reported the observation of this\nmode (Aubert, 2004g). These analyses are described in\ndetail in Section 17.4.\nA better approach uses a Dalitz-plot analysis of B \u2192\n3\u03c0 \ufb01nal states, which relaxes the quasi-two-body approx-\nimation and uses information from the interference be-\ntween resonances in the corners of the Dalitz plot. Sny-\nder and Quinn (1993) pointed out that a time-dependent\nDalitz-plot analysis (TDPA) of B0 \u2192\u03c1\u03c0 \u2192\u03c0+\u03c0\u2212\u03c00\no\ufb00ers a unique way to determine the angle \u03c62 without\ndiscrete ambiguities. The TDPA uses isospin symmetry\nand takes into account contamination from b \u2192d pen-\nguin transitions. Additional information to constrain \u03c62\ncan be provided by the measurements of B+ \u2192\u03c1+\u03c00\nand \u03c10\u03c0+ (Gronau, 1991; Lipkin, Nir, Quinn, and Snyder,\n1991). Technicalities required to perform a TDPA can be\nfound in Chapter 13.\nA preliminary TDPA was reported by BABAR at ICHEP\nin 2004 using a data sample of 213 million BB pairs. Sub-\nsequent analyses have been published by both Belle (Ku-\nsaka, 2007) and BABAR (Aubert, 2007v; Lees, 2013c) using\nlarger data samples.\nFuture Flavor Factories should study the Dalitz plots\nfor B \u21923\u03c0 states beyond intermediate \u03c1\u03c0 contributions\nand also explore B \u2192KK\u03c0 to search for possible signs of\nNP as a non-leading source of CP violation.\n17.7.1.3 B \u2192a1(1260)\u03c0, B0 \u2192a1(1260)K constraints\nThe last set of decay modes considered at the B Factory\nexperiments for the extraction of \u03c62 is B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213,\n\n332\nwith a\u00b1\n1 (1260) \u2192\u03c0\u2213\u03c0\u00b1\u03c0\u00b1. As with the previous exam-\nples these decays proceed mainly via b \u2192uud tree ampli-\ntudes which can be used to measure time-dependent CP\nasymmetries and allow one to extract the angle \u03c62. As\nwith the other modes discussed in this section the exis-\ntence of non-trivial penguin amplitudes complicates the\nextraction of \u03c62.\nSimilar to B\n\u2192\n\u03c1\u03c0 decays, B meson decays to\na\u00b1\n1 (1260)\u03c0\u2213\ufb01nal states are not CP eigenstate decays, so\nto extract \u03c62 from these channels one needs to simulta-\nneously consider B0(B0) \u2192a+\n1 (1260)\u03c0\u2212and B0(B0) \u2192\na\u2212\n1 (1260)\u03c0+ transitions (Aleksan, Dunietz, Kayser, and\nLe Diberder, 1991). One might cope with the di\ufb03culty\ndue to the contribution of penguin amplitudes by using\nisospin symmetry (Gardner, 1999; Gronau, 1991; Gronau\nand London, 1990; Gronau and Zupan, 2004; Lipkin, Nir,\nQuinn, and Snyder, 1991) or a TDPA (Quinn and Silva,\n2000; Snyder and Quinn, 1993) or approximate SU(3) \ufb02a-\nvor symmetry (Charles, 1999; Gronau, London, Sinha, and\nSinha, 2001; Grossman and Quinn, 1998).\nA full isospin analysis requires the precise measure-\nment of the branching fractions and time-dependent asym-\nmetries in the \ufb01ve modes (and their CP conjugates) B0 \u2192\na+\n1 (1260)\u03c0\u2212, a\u2212\n1 (1260)\u03c0+, a0\n1(1260)\u03c00, B+ \u2192a+\n1 (1260)\u03c00,\na0\n1(1260)\u03c0+. Currently the poor precision of most of these\nmeasurements (Aubert, 2007i,ae) does not permit the ap-\nplication of this method.\nAs pointed out in the references (Quinn and Silva,\n2000; Snyder and Quinn, 1993) the angle \u03c62 may be ex-\ntracted without ambiguities from a TDPA. This method\nhas been successfully applied to the decay B0 \u2192\u03c0+\u03c0\u2212\u03c00\nby both experiments. This approach could also be applied\nto the decay B0 \u2192\u03c0+\u03c0\u2212\u03c00\u03c00 with contributions from\na+\n1 (1260)\u03c0\u2212, a\u2212\n1 (1260)\u03c0\u2212, a0\n1(1260)\u03c00, and \u03c1+\u03c1\u2212ampli-\ntudes or to the decay B0 \u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212with contri-\nbutions from a+\n1 (1260)\u03c0\u2212, a\u2212\n1 (1260)\u03c0+, and \u03c10\u03c10 ampli-\ntudes. Such analyses would be di\ufb03cult because of the four\nparticles in the \ufb01nal state, the small overlapping region\nof the phase space of the pions from the a\u00b1\n1 (1260) and\na0\n1(1260) mesons, uncertainties in the a1(1260) meson pa-\nrameters and line shape, the small number of signal events\nand the large expected background.\nGronau and Zupan (2006) proposed an SU(3)-based\nprocedure for extracting \u03c62 in the presence of penguin\ncontributions that the B Factories have followed. This pro-\ncedure requires measurements of B meson decays into the\naxial-vector plus pseudoscalar \ufb01nal states a1\u03c0, a1K, and\nK1\u03c0.\nBABAR (Aubert, 2006aj) and Belle (Dalseno, 2012)\nmeasure the branching fraction of the B0 meson decay\nto a\u00b1\n1 (1260) \u03c0\u2213to be relatively large (\u223c3 \u00d7 10\u22125, see\nSection 17.4). Following on from the observation of this\ndecay mode BABAR performed a set of measurements of\na1\u03c0 and a1K decays to extract the angle \u03c62. This includes\nthe time-dependent asymmetry measurement of B decays\nto a\u00b1\n1 (1260)\u03c0\u2213(Aubert, 2007ae), and observation of both\nB+ \u2192a+\n1 (1260)K0 and B0 \u2192a\u2212\n1 (1260)K+ decays (Au-\nbert, 2008ae). The \ufb01nal piece of information required to\nconstrain \u03c62 using this approach is the branching frac-\ntion of B decays to K1\u03c0, which was also measured by\nBABAR (Aubert, 2010d), where K1 denotes the axial vec-\ntor excited K meson states.\nThe method chosen by BABAR for the study of B0 \u2192\na\u00b1\n1 (1260)\u03c0\u2213decays follows the quasi-two-body approxi-\nmation. The decays B0(B0) \u2192a\u00b1\n1 (1260)\u03c0\u2213have been\nreconstructed with a\u00b1\n1 (1260) \u2192\u03c0\u2213\u03c0\u00b1\u03c0\u00b1. The other sub-\ndecay modes with a\u00b1\n1 (1260) \u2192\u03c0\u00b1\u03c00\u03c00 could be used to\nenhance statistics, however these are ignored as they have\nlow reconstruction e\ufb03ciency and large background. From\na time-dependent CP analysis one extracts an e\ufb00ective an-\ngle \u03c6e\ufb00\n2\nwhich, in analogy with the approaches described\nabove, is an approximate measure of the angle \u03c62. Details\non this approach for the decays B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213are\ndiscussed by Gronau and Zupan (2006). Applying \ufb02avor\nSU(3) symmetry one can determine an upper bound on\n\u2206\u03c62 = |\u03c62 \u2212\u03c6e\ufb00\n2 | by relating the B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213decay\nrates with those of the \u2206S = 1 transitions involving the\nsame SU(3) multiplet of a1(1260), B \u2192a1(1260)K and\nB \u2192K1A\u03c0. The K1A meson is a nearly equal admixture\nof the K1(1270) and K1(1400) resonances (Amsler et al.,\n2008). The rates of B \u2192K1A\u03c0 decays can be derived from\nthe decay rates of B \u2192K1(1270)\u03c0 and B \u2192K1(1400)\u03c0.\nMotivated by the B \u2192a1\u03c0 study BABAR performed\na search for the related decay B \u2192a\u00b1\n1 \u03c1\u2213using a data\nsample of 100 fb\u22121, but were unable to establish the pres-\nence of a signi\ufb01cant signal (Aubert, 2006as). Future exper-\niments may have su\ufb03cient data to isolate a clean sample\nof a\u00b1\n1 \u03c1\u2213and augment the list of channels used in the de-\ntermination of \u03c62.\n17.7.1.4 SU(3) constraints on \u03c62 using B0 \u2192\u03c1+\u03c1\u2212and\nB+ \u2192K\u22170\u03c1+ decays\nA way to constrain penguin contributions to B0 \u2192\u03c1+\u03c1\u2212\ndecays using SU(3) \ufb02avor symmetry was proposed by Be-\nneke, Gronau, Rohrer, and Spranger (2006), and is re-\nferred to here as the BGRS method. The amplitude of\nthis decay has SM contributions from both tree and pen-\nguin topologies, so may be written as\nA(B0 \u2192\u03c1+\u03c1\u2212) = Tei\u03c63 + Pei\u03b4P T ,\n(17.7.8)\nwhere T and P are the magnitudes of the tree and pen-\nguin contributions to the decay, \u03c63 is the Unitarity Trian-\ngle angle introduced in Chapter 16, and \u03b4P T is the strong\nphase di\ufb00erence between the tree and penguin contribu-\ntions. Interference between the amplitudes in Eq. (17.7.8)\nand those responsible for B0 \u2212B0 mixing results in the\ntime-dependent asymmetry of this decay being sensitive\nto \u03c62 as discussed above. The SU(3) related decay B+ \u2192\nK\u22170\u03c1+ only proceeds via a penguin transition, so one can\nuse knowledge of the branching fraction and longitudinal\npolarization fraction of this decay to constrain the cor-\nresponding penguin contribution in \u03c1+\u03c1\u2212up to SU(3)\nbreaking corrections.78\n78 As the fraction of longitudinally polarized events is near\none it is possible to neglect information contained in the CP\n\n333\nIn practice in order to constrain \u03c62 using this approach\none needs to have seven experimental inputs in total: the\nbranching fractions and fraction of longitudinally polar-\nized events for the two decays, as well as S and C mea-\nsured for \u03c1+\u03c1\u2212, and \ufb01nally the value of \u03c61 obtained from\nb \u2192ccs transitions (see Section 17.6). These experimental\ninputs can be used to constrain the three unknowns: \u03c62,\n\u03b4P T , and rP T = |P/T| using\nC =\n2rP T sin \u03b4P T sin(\u03c61 + \u03c62)\n1 \u22122rP T cos \u03b4P T cos(\u03c61 + \u03c62) + r2\nP T\n,\n(17.7.9)\nS = sin 2\u03c62 + 2rP T cos \u03b4P T sin(\u03c61 \u2212\u03c62) \u2212r2\nP T sin 2\u03c61\n1 \u22122rP T cos \u03b4P T cos(\u03c61 + \u03c62) + r2\nP T\n,\n(17.7.10)\nand\n\u0012 |Vcd|f\u03c1\n|Vcs|fK\u2217\n\u00132 \u0393L(B+ \u2192K\u22170\u03c1+)\n\u0393L(B0 \u2192\u03c1+\u03c1\u2212)\n(17.7.11)\n=\nFr2\nP T\n1 \u22122rP T cos \u03b4P T cos(\u03c61 + \u03c62) + r2\nP T\n,\nwhere the coe\ufb03cient F is not equal to one in case of\nSU(3) breaking, and f\u03c1 (fK\u2217) is the \u03c1 (K\u2217) decay con-\nstant. The factor F is estimated to be 0.9 \u00b1 0.6 (Beneke,\nGronau, Rohrer, and Spranger, 2006). In fact it turns\nout that SU(3) breaking has little e\ufb00ect on the overall\nconstraint obtained for \u03c62, and one can obtain a pre-\ncision comparable to the isospin analysis approach even\nwith 100% SU(3) breaking uncertainty. The decay widths\n\u0393L in Eq. (17.7.11) can be replaced by the corresponding\nbranching fractions multiplied by the ratio of B0 to B\u00b1\nlifetimes. This approach provides a stringent constraint\non \u03c62 that can be used as a cross-check of the traditional\nSU(2) isospin analysis. Results of using this approach can\nbe found in Section 17.7.6, but given that the same in-\nputs are used for this approach and the isospin analysis\n(Section 17.7.7), one should take care not to combine the\nresults obtained from the two methods when computing a\nglobal average for \u03c62.\n17.7.2 Event reconstruction\nThe reconstruction of the charmless B decays and event\nselection follows a similar sequence in both BABAR and\nBelle. First, a sample of charged tracks and photons is\nselected. Typically, charged tracks are required to origi-\nnate from the interaction region and to be identi\ufb01ed as\npions (Chapter 5). In most of the cases an electron veto\nis applied. After an initial \u03c00 selection based on two-\nphoton candidates, the \u03c00 candidates are kinematically\nconstrained to the nominal \u03c00 mass. Tracks and \u03c00 can-\ndidates are combined to produce composite candidates\n(e.g. \u03c1, a1(1260)), and \ufb01nally, signal B candidates are\nadmixture of the transverse polarization without signi\ufb01cantly\na\ufb00ecting the overall precision on the constraint obtained for \u03c62\ngiven the data samples available at the B Factories.\nformed. The beam energy substituted mass mES and the\nenergy di\ufb00erence \u2206E are calculated for these candidates\n(see Chapter 7).\nFor time-dependent CP analyses, the \ufb02avor of the B\ncandidates is determined using a \ufb02avor-tagging algorithm\n(Chapter 8) and the proper time di\ufb00erence \u2206t between\nthe signal B and the accompanying B meson (Btag), is\nmeasured (Chapter 6). Finally, the signal yields and other\ndecay properties (polarization, CP asymmetries) are de-\ntermined in a multi-variate maximum likelihood \ufb01t.\nThe continuum process e+e\u2212\u2192qq (q = u, d, s, c) is\nthe main source of background for the charmless B decays.\nIn order to suppress this background, charmless analyses\nemploy multi-variate discriminants based on event topol-\nogy, which tends to be isotropic for BB events and jet-like\nfor qq events. A detailed description of these methods is\ngiven in Chapter 9.\nAdditional discrimination against the continuum back-\nground is provided by the output of the B-\ufb02avor tagging\nalgorithms (Chapter 8). In Belle, the tag parameter r\nranges from 0 to 1 and is a measure of the likelihood that\nthe b \ufb02avor of the accompanying B meson is correctly as-\nsigned by the Belle \ufb02avor-tagging algorithm. Events with\nhigh values of r are well-tagged and are less likely to orig-\ninate from continuum production. It is found that there\nis no strong correlation between r and any of the topo-\nlogical variables used above to separate signal from con-\ntinuum. In BABAR, the background discrimination power\narises from the di\ufb00erence between the tag e\ufb03ciencies for\nsignal and continuum background in seven tag categories\n(ctag = 1 . . . 7) which is manifest in terms of a di\ufb00erent\nsignal purity in each tag category (Section 9.5.3).\nAfter the signal candidates are identi\ufb01ed, the proper\ntime di\ufb00erence \u2206t between the signal B and Btag can be\ndetermined from the spatial separation between their de-\ncay vertices. The Btag vertex is reconstructed from the\nremaining charged tracks in the event and its uncertainty\ndominates the \u2206t resolution \u03c3\u2206t. The typical proper time\nresolution is \u27e8\u03c3\u2206t\u27e9\u22480.7 ps. The distribution of the proper\ntimes provides further discrimination against the contin-\nuum backgrounds, which are characterized by smaller val-\nues of |\u2206t| (Section 9.5.3). The parameters of the proper-\ntime distributions for signal modes, as well as the tagging\ne\ufb03ciencies and mistag fractions, are obtained in dedicated\n\ufb01ts to events with identi\ufb01ed exclusive B decays as dis-\ncussed in Section 10.6.\n17.7.3 B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c1\nAn isospin analysis needs as ingredients the measurements\nof branching fractions, given in Section 17.4, and CP vio-\nlation parameters, described in this section.\n17.7.3.1 B0 \u2192\u03c0+\u03c0\u2212\nThe B Factories started performing time-dependent anal-\nyses of B0 \u2192\u03c0+\u03c0\u2212early in their lifetime, and these re-\nsults were updated on a number of occasions. The follow-\ning describes only the most recent publications by BABAR\n\n334\n(Lees, 2013b) and Belle (Adachi, 2013), which use data\nsamples of 467\u00d7106 and 772\u00d7106 BB pairs, respectively.\nThe candidates for the CP-eigenstate decay B0 \u2192\n\u03c0+\u03c0\u2212are constructed from two oppositely charged tracks\noriginating from a common vertex. A good quality of the\nvertex \ufb01t is required (Chapter 6). The mES and \u2206E re-\nquirements are loose relative to the signal resolution (mES\n> 5.24 GeV/c2 and \u22120.2 GeV < \u2206E < 0.15 GeV at Belle,\nand mES > 5.2 GeV/c2 and |\u2206E| < 0.15 GeV at BABAR),\nleaving sidebands for accurate determination of the back-\nground level.\nThe dominant background for this decay mode is\ncontinuum. To discriminate between signal and contin-\nuum background, multivariate discriminants composed of\nevent-shape variables are used. The de\ufb01nitions of these\nvariables appear in Chapter 9. Belle applies a loose re-\nquirement | cos \u03b8T | < 0.9, rejecting 50% of the con-\ntinuum background while keeping 90% of the signal\nevents, and uses a Fisher discriminant FB \u00af\nB composed of\ncos \u03b8T, cos \u03b8B, cos \u03b8T,B, P p\u2217\nt and moments L0 and L2.\nBABAR requires | cos \u03b8S| < 0.91 and R2 < 0.7, rejecting\n65% of the continuum background while keeping 90% of\nthe signal events, and then constructs a Fisher discrimi-\nnant from the L0 and L2 moments.\nThe selected samples contain not only B0 \u2192\u03c0+\u03c0\u2212\nsignal events but also B \u2192K\u00b1\u03c0\u2213, qq, and background\nfrom higher multiplicity B decays. The signal and back-\nground yields and the CP parameters are determined from\nunbinned extended maximum likelihood \ufb01ts.\nThe Belle \ufb01t is performed using the variables \u2206E, mES,\nL(\u03c0\u00b1), FB \u00af\nB, the Btag \ufb02avor q (q = +1 for Btag = B0 and\nq = \u22121 for Btag = B0) and \u2206t, where L(\u03c0\u00b1) are the\nidenti\ufb01cation likelihoods for each of the pions from the\n\u03c0\u03c0 candidate. BABAR uses the \ufb01t variables \u2206E, mES, and\nFisher discriminant composed of L0 and L2, the DIRC\nCherenkov angles and dE/dx values for each track, q and\n\u2206t. The decay rate as a function of \u2206t of the signal events\nis described by\nFq(\u2206t) =\n1\n4\u03c4B0 e\u2212|\u2206t|/\u03c4B0 \u00b7 (1 \u2212qC cos \u2206md\u2206t\n+qS sin \u2206md\u2206t),(17.7.12)\nup to vertex position resolution and \ufb02avor mistag e\ufb00ects,\nwhich are included in the \ufb01t p.d.f.s.79 The \u2206t p.d.f.s for\nall other event types in the sample are CP conserving.\nThe two collaborations use di\ufb00erent methods for pre-\nsenting the event distributions and \ufb01t functions. Belle ap-\nplies cuts on discriminating variables and plots the distri-\nbutions of signal and background of the remaining events,\nwhile BABAR uses\nsPlots (Section 11.2.3). As an exam-\nple, Fig. 17.7.3 shows the \u2206E distributions of the BABAR\ndata overlaid with components of the \ufb01t functions. The\n\u2206t distributions and time-dependent CP asymmetries are\nshown in Fig. 17.7.4 for the Belle results.\n79 Note the similarity with Eq. (10.2.2), the sign di\ufb00erences\nresulting from the fact that the CP eigenvalue of the decay is\nopposite that of B0 \u2192J/\u03c8K0\nS.\nE (GeV)\n\u2206\n-0.1\n0\n0.1\nEvents / (10 MeV)\n0\n50\n100\n150\n200\nE (GeV)\n\u2206\n-0.1\n0\n0.1\nEvents / (10 MeV)\n0\n50\n100\n150\n200\nE (GeV)\n\u2206\n-0.1\n0\n0.1\nEvents / (6 MeV)\n0\n100\n200\n300\n400\nE (GeV)\n\u2206\n-0.1\n0\n0.1\nEvents / (6 MeV)\n0\n100\n200\n300\n400\nFigure 17.7.3. sPlots of \u2206E for the BABAR B \u2192\u03c0+\u03c0\u2212anal-\nysis, showing the data distributions (data points with errors)\nand overlaid \ufb01t functions (curves) for the \u03c0+\u03c0\u2212(top) and\nbackground K+\u03c0\u2212(bottom) components, from Lees (2013b).\nSchematically, the\nsPlots use the information mainly from\nmES and the Fisher discriminant to separate the hh (both\n\u03c0+\u03c0\u2212and K\u03c0) signal from the continuum background and the\ninformation from the Cherenkov angles to separate the \u03c0+\u03c0\u2212\nsignal from the K\u03c0 signal.\nThe \ufb01t to the Belle data yields 2964 \u00b1 88 B0 \u2192\u03c0+\u03c0\u2212\nevents, 9205\u00b1124 B0 \u2192K\u00b1\u03c0\u2213events, and 23\u00b135 B0 \u2192\nK+K\u2212events. In both analyses, most of the selected can-\ndidates (almost 98%) are from continuum background.\nThe BABAR \ufb01t \ufb01nds 1394 \u00b1 54 \u03c0+\u03c0\u2212events, 5410 \u00b1 90\nK\u00b1\u03c0\u2213events, and 7 \u00b1 17 K+K\u2212events. The CP viola-\ntion parameters obtained by Belle are\nS = \u22120.64 \u00b1 0.08 \u00b1 0.03,\nC = \u22120.33 \u00b1 0.06 \u00b1 0.03,\n(17.7.13)\nand those obtained by BABAR are\nS = \u22120.68 \u00b1 0.10 \u00b1 0.03,\nC = \u22120.25 \u00b1 0.08 \u00b1 0.02,\n(17.7.14)\nwhere the \ufb01rst error is statistical and the second is sys-\ntematic.\nThe systematic uncertainties account for a variety of\nsystematic e\ufb00ects. These include biases in \u2206t due to de-\ntector misalignment and beam pro\ufb01le; uncertainties on\nparameters that are \ufb01xed in the \ufb01t; uncertainties on the\nparameterization of the detector \u2206t resolution function\n(main one for S), particle-identi\ufb01cation performance, and\n\ufb02avor tagging performance and CP violation in the Btag\n\n335\nEvents / (1.5 ps)\n50\n100\n150\n200\n250\n300\nq = +1\nq = -1\nt (ps)\n6\n-7.5\n-5\n-2.5\n0\n2.5\n5\n7.5\n0\nB\n+N\n0\nB\nN\n0\nB\n-N\n0\nB\nN\n-0.5\n0\n0.5\nFigure 17.7.4. Background subtracted time-dependent \ufb01t re-\nsult for B0 (B0)\u2192\u03c0+ \u03c0\u2212. The top plot shows the time-\ndependent decay rate for each Btag \ufb02avor q, where q = +1(\u22121)\nrefers to a B0 (B0) tag. The bottom plot shows the asym-\nmetry between the plots above, (NB0 \u2212NB0)/(NB0 + NB0).\nNB0(NB0) is the measured signal yield in each bin of \u2206t for\nB0 (B0) tagged events, from (Adachi, 2013).\ndecay (main one for C). Since S and C are extracted from\nan asymmetry, the procedure is insensitive to many e\ufb00ects\nand the systematic uncertainties are quite small.\nHistorically there was indication of some level of dis-\nagreement between the two experiments on the measure-\nments of S and C in this decay mode. While this di\ufb00erence\nwas never large enough to claim a signi\ufb01cant discrepancy\nbetween the results, the evolution of the parameters from\none conference season to the next remained of wide in-\nterest to the community. Over time these measurements\nslowly regressed toward a common mean, and as one can\nsee from the results presented here \u2212results from the two\nexperiments agree with each other within uncertainties.\nThe B Factory average of these results is\nS = \u22120.66 \u00b1 0.07,\nC = \u22120.30 \u00b1 0.05,\n(17.7.15)\nwhere the resulting correlation between S and C for the\naverage is \u22128.1%.\n17.7.3.2 B0 \u2192\u03c1+\u03c1\u2212\nThe B0 \u2192\u03c1+\u03c1\u2212candidates are reconstructed by com-\nbining pairs of oppositely charged \u03c1 mesons, which in\nturn are selected using \u03c0\u00b1 candidates and \u03c00 candidates.\nAs the \u03c1 meson is a wide resonance, when reconstruct-\ning the signal \ufb01nal state some events contain multiple re-\nconstructed B candidates. Most of these candidates arise\nfrom combinations of fake \u03c00 mesons with tracks from\nthe signal side. In such events the B candidate with the\nsmallest sum P\n\u03c00\n1,2(m\u03b3\u03b3 \u2212m0\n\u03c0)2 is selected. Other in-\ncorrectly reconstructed B candidates appear from events\nwith mis-reconstructed \u03c0\u00b1 tracks. These events contain\nmis-reconstructed vertices and may bias time-dependent\nCP measurements if not accounted for appropriately. The\nfraction of signal decays in data samples selected for the\ntime-dependent measurements of BABAR and Belle that\nhave at least one \u03c0\u00b1 track incorrectly identi\ufb01ed but pass\nall selection criteria is 13.8 % and 6.5 %, respectively. Sig-\nnal decays that have at least one \u03c0 meson incorrectly iden-\nti\ufb01ed are referred to as mis-reconstructed signal. The two\ntypes of mis-reconstructed signals described above, where\nthe fake pion is either neutral or charged, are dealt with\nseparately.\nSimilarly to other charmless B decays the dominant\nbackground for the B0 \u2192\u03c1+\u03c1\u2212channel originates from\ne+e\u2212\u2192qq (q = u, d, s, c) continuum events. The proce-\ndures adopted for background suppression are described\nbrie\ufb02y in the following paragraphs.\nThe Belle analysis uses a Fisher discriminant formed\nfrom modi\ufb01ed Fox-Wolfram moments and \u03b8B, the polar\nangle in the CM frame between the B direction and the\nbeam axis. These two variables are combined into a signal\nto background likelihood ratio, R. The p.d.f.s for signal\nand qq components are obtained from MC simulation and\nthe data mES sideband, respectively, and used to \ufb01t the\nselected B \u2192\u03c1+\u03c1\u2212candidates.\nIn the BABAR analysis qq background is reduced by re-\nquiring | cos \u03b8T | < 0.8, where \u03b8T is the angle between the\nthrust axis of the candidate and that of the remaining de-\ntected particles in the event. Further signal to background\nseparation is performed by using a multi-layer perceptron\n(neural network, NN, see Chapter 4), which is trained\nand validated using o\ufb00-resonance data (background) and\nMC simulated events (signal). Eight topological variables,\nsee Aubert (2007b), are included into this neural network,\nand the output is transformed by a 1 : 1 mapping that\nbroadens the peaking contribution for the signal target\ntype (NN \u223c1) to facilitate p.d.f. parameterization so that\nthe neural network output can be used in a maximum like-\nlihood \ufb01t to data.\nThe following components are distinguished in both\nBelle and BABAR analyses: signal and \u03c1\u03c0\u03c0 non-resonant\ndecays, signal events with a mis-reconstructed \u03c00, sig-\nnal events with a mis-reconstructed \u03c0\u00b1, continuum back-\nground (q\u00afq), charm B background (b \u2192c), and charmless\n(b \u2192u) background. The \ufb01tted yield for the non-resonant\n4\u03c0 component was found to be consistent with zero by\nboth experiments. The (b \u2192u) background is dominated\nby B \u2192(\u03c1\u03c0, a1\u03c0, a1\u03c1, \u03c1\u00b1\u03c10) decays.\nThe latest BABAR analysis is based on a data sam-\nple of 383.6 million BB pairs (Aubert, 2007b) and su-\npersedes two previous BABAR analyses (Aubert, 2004ag,\n2005j). The signal yield, longitudinal polarization frac-\ntion fL, and CP asymmetry parameters C and S are ob-\ntained simultaneously from an unbinned extended ML \ufb01t\nto 37424 events. The background discriminating variables\n\n336\nare mES, \u2206E, \u2206t, m\u03c0\u00b1\u03c00, cos \u03b8\u00b1, and NN. Part of the\nb \u2192u background has distributions similar to the signal\nfor one or more of the discriminating variables. There-\nfore, even if it is smaller than the b \u2192c background, it is\nimportant to account for it correctly. A total of 165 dif-\nferent possible background contributions are considered\nfor the b \u2192u background. However, only components\nwhere more than one event is expected to contribute to\nthe selected data sample are modeled individually. Those\nmodes where less than one event is expected are collected\ntogether and modeled using an inclusive component (split\ninto neutral and charged contributions). As a result the\nBABAR analysis incorporates 22 components for di\ufb00erent\nbackground types explicitly, whose yields are \ufb01xed to ex-\npectations, except for the non-resonant \u03c1\u03c0\u03c0 \ufb01nal state\nyield left free in the \ufb01t as a secondary signal. The \ufb01t results\nare N\u03c1\u03c1 = 729 \u00b1 60+94\n\u2212102 events, fL = 0.992 \u00b1 0.024+0.026\n\u22120.013,\nC = 0.01 \u00b1 0.15 \u00b1 0.06, and S = \u22120.17 \u00b1 0.20+0.05\n\u22120.06. Dis-\ntributions of mES, \u2206E, cos \u03b8\u00b1, and m\u03c0\u00b1\u03c00, for the high-\nest purity tagged events are shown in Fig. 17.7.5. The\n\u2206t distribution for B0 and B0 tagged events and the\ntime-dependent decay-rate asymmetry are presented in\nFig. 17.7.6.\n)\n2\n (GeV/c\nES\nm\n5.25\n5.26\n5.27\n5.28\n5.29\n)\n2\nEvents / (5 MeV/c\n0\n100\n(a)\n E (GeV)\n\u2206\n-0.1\n0\n0.1\nEvents / (30 MeV)\n0\n50\n(b)\n)i\u03b8\ncos(\n-0.5\n0\n0.5\nEvents / (0.188)\n0\n100\n200\n(c)\n)\n2\n (GeV/c\n0\n\u03c0\n\u00b1\n\u03c0\nm\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEvents / (50 MeV)\n0\n50\n100\n(d)\nFigure 17.7.5. (a) mES, (b) \u2206E, (c) cosine of the \u03c1 helicity\nangle, and (d) m\u03c0\u00b1\u03c00 for the highest purity tagged B \u2192\u03c1+\u03c1\u2212\nevents. For the plots (b), (c) and (d), mES is required to be\nlarger than 5.27 GeV/c2. The dashed lines are the sum of back-\ngrounds and the solid lines are the total p.d.f. (from Aubert\n(2007b)).\nMeasurements of the polarization fraction and the frac-\ntion of \u03c1\u03c0\u03c0 non-resonant events were performed by Belle\nin (Somov, 2006) and found to be 0.941+0.034\n\u22120.040 \u00b1 0.030 and\n(6.3 \u00b1 6.7)%, respectively. The latest Belle measurements\nof the CP asymmetry parameters are based on a data sam-\nple of 535 million BB pairs (Somov, 2007). The analysis is\norganized into two steps. During the \ufb01rst step the yields\nof signal and background components are obtained us-\ning an unbinned extended ML \ufb01t to the three-dimensional\n(mES, \u2206E, R) distribution. A total of 176843 events are\nselected for the analysis. The \ufb01t yields N\u03c1\u03c1+\u03c1\u03c0\u03c0 = 576 \u00b1\n53 events. During the second step the CP asymmetry\nEvents / 2 ps\n10\n20\n30\nEvents / 2 ps\n10\n20\n30\n(a)\nEvents / 2 ps\n10\n20\n30\nEvents / 2 ps\n10\n20\n30\n(b)\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nAsymmetry\n-1\n-0.5\n0\n0.5\n1\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nAsymmetry\n-1\n-0.5\n0\n0.5\n1\n(c)\nFigure 17.7.6. The \u2206t distributions of events enriched in sig-\nnal for (a) B0 and (b) B0 tagged B \u2192\u03c1+\u03c1\u2212events. The solid\nlines are the sum of signal and backgrounds and the dashed\nlines are the sum of backgrounds. The time-dependent CP\nasymmetry is presented in (c). (As there is no entry in the\nsecond bin from the left in (b), the corresponding point is at\n1 in (c).) The curve corresponds to the measured asymmetry\n(from Aubert (2007b)).\nparameters S and C are determined from a \ufb01t to the\n\u2206t distributions. The signal region used for the \u2206t \ufb01t is\n5.27 GeV/c2 < mES < 5.29 GeV/c2, \u22120.12 GeV < \u2206E <\n0.08 GeV, and R > 0.15, a soft requirement, which elim-\ninates the background dominated events. The fractions\nof mis-reconstructed signal events are \ufb01xed to the expec-\ntation from MC simulation, the fraction of non-resonant\nB \u2192\u03c1\u03c0\u03c0 decays is \ufb01xed from the result obtained in So-\nmov (2006), and the fractions of correctly reconstructed\nsignal, b \u2192c background, qq background and b \u2192u\nbackground are normalized to the event fractions obtained\nfrom the (mES, \u2206E, R) \ufb01t and are \ufb01xed in the \u2206t \ufb01t. The\nevent fractions and \u2206t p.d.f.s depend on the \ufb02avor tag cat-\negory assigned to an event. A \ufb01t to the 18016 events in the\n(mES, \u2206E, R) signal region gives C = \u22120.16\u00b10.21\u00b10.08\nand S = 0.19 \u00b1 0.30 \u00b1 0.08.\nThe B Factory combined values for fL, C and S are\nS = \u22120.05 \u00b1 0.17,\nC = \u22120.06 \u00b1 0.13,\nfL = 0.978 \u00b1 0.023,\n(17.7.16)\nwhere the correlation between S and C is small. The mea-\nsured B0 \u2192\u03c1+\u03c1\u2212branching fraction is given in Sec-\ntion 17.4.\n17.7.3.3 B0 \u2192\u03c10\u03c10\nThe analyses reported here are based on the full data\nsample of both experiments, containing respectively 465\u00d7\n106 BB pairs recorded with the BABAR detector (Aubert,\n2008r) and 772 \u00d7 106 BB pairs collected with the Belle\ndetector (Adachi, 2014). Two other analyses on a par-\ntial data sample were also published by BABAR (Aubert,\n2007h) and Belle (Chiang, 2008).\n\n337\nB0 meson candidates are reconstructed from two\n\u03c10 candidates, each reconstructed from two oppositely\ncharged pions. The analyses use six kinematic variables\nto reconstruct the signal: mES, \u2206E, the invariant \u03c0+\u03c0\u2212\nmasses m(\u03c0+\u03c0\u2212)1,2, and the helicity angles \u03b81,2, de\ufb01ned\nas the angles between the \u03c0+ and the B \ufb02ight direction\nin each \u03c10 rest frame. The BABAR analysis applies the fol-\nlowing kinematic selection: 5.245 < mES < 5.290 GeV/c2,\n|\u2206E| < 85 MeV, 0.55 < m(\u03c0+\u03c0\u2212)1,2 < 1.05 GeV/c2,\nand | cos \u03b81,2| < 0.98. The Belle analysis requires that\nthe invariant \u03c0+\u03c0\u2212masses lie within the signal window\nm(\u03c0+\u03c0\u2212)1,2 \u2208[0.52, 1.15] GeV/c2, |\u2206E| < 0.1 GeV, and\nmES > 5.27 GeV/c2. In both cases, the \u03c0+\u03c0\u2212mass win-\ndow is chosen to accept \u03c10 \u2192\u03c0+\u03c0\u2212, f0(980) \u2192\u03c0+\u03c0\u2212,\nand non-resonant modes, and to exclude K0\nS \u2192\u03c0+\u03c0\u2212and\ncharm meson decays such as D0 \u2192\u03c0+\u03c0\u2212. Furthermore,\nto remove the peaking backgrounds from the D+ (espe-\ncially D+ \u2192K\u2212\u03c0+\u03c0+), D+\ns , D0, J/\u03c8, and K0\nS decays,\ncorresponding mass vetoes are applied to any combina-\ntions of the two or three \ufb01nal state particles. To remove\nevents from the decay J/\u03c8 \u2192\u00b5+\u00b5\u2212, the muon mass hy-\npothesis is assigned to the selected pion candidates and\nthe mass veto is applied.\nTo distinguish BB events from the dominant jet-like\ncontinuum background BABAR uses a neural network-based\ndiscriminant, NN, which combines the same eight topolog-\nical variables used in the B0 \u2192\u03c1+\u03c1\u2212analysis, while Belle\nuses a Fisher discriminant, F, constructed from seven vari-\nables (Chapter 4). These discriminants are used as inputs\nto the ML \ufb01ts described below. In addition Belle places a\nloose requirement on F, which removes about 60% of the\ncontinuum background and 10% of the signal.\nThe B meson can decay to \u03c10\u03c10 via two polarizations,\nlongitudinal or transverse. These polarizations have dif-\nferent angular distributions and therefore, as described in\nSection 12.3, signi\ufb01cantly di\ufb00erent kinematics and aver-\nage multiplicities of reconstructed candidates per event.\nFor simulated signal events Belle (BABAR) \ufb01nds 1.17 and\n1.03 (1.15 and 1.03) B candidates per event for the longi-\ntudinal and transverse polarization, respectively. In case\nof multiple B candidates, the one whose mES is closest to\nthe nominal B mass is chosen for Belle, and the one that\nhas the smallest \u03c72 for the four-pion vertex is selected for\nBABAR. The reconstruction e\ufb03ciency for the signal is cal-\nculated from MC to be 21.1% (26.5%) for Belle and 22.3%\n(26.1%) for BABAR for the longitudinal (transverse) polar-\nization.\nThe branching ratio, B(B0 \u2192\u03c10\u03c10), as well as the frac-\ntion of longitudinal polarization, fL, are extracted in Belle\nfrom an unbinned extended ML \ufb01t, using six discriminat-\ning variables (\u2206E, m(\u03c0+\u03c0\u2212)1, m(\u03c0+\u03c0\u2212)2, cos \u03b81, cos \u03b82,\nF), where \u03b81,2 allows one to measure the polarization ac-\ncording to Eq. (12.2.5). In BABAR the extended ML \ufb01t is\nused to extract not only B(B0 \u2192\u03c10\u03c10) and fL, but also\nthe coe\ufb03cients of the time-dependent CP asymmetry for\nthe longitudinal signal, C\u03c10\u03c10\nL\nand S\u03c10\u03c10\nL\n. Hence it uses ten\nvariables: mES, \u2206E, m(\u03c0+\u03c0\u2212)1, m(\u03c0+\u03c0\u2212)2, cos \u03b81, cos \u03b82,\nNN, ctag, \u2206t, and \u03c3\u2206t, where the tagging category ctag of\nthe B-\ufb02avor tagging algorithm, introduced in Chapter 8,\nprovides additional background discrimination power, and\n\u2206t and its error \u03c3\u2206t are added in order to include the\ntime-dependent information.\nFour categories of signal are distinguished in the \ufb01ts:\nthe longitudinally and transversely polarized signals and\ntheir respective mis-reconstructed components.80 The frac-\ntions of the mis-reconstructed signal are \ufb01xed according\nto MC expectations. Several kinds of background, includ-\ning a variety of four pion \ufb01nal states, have to be dealt\nwith. While \u2206E and mES are powerful in discriminat-\ning B decays into four charged pions from other decays,\nm(\u03c0+\u03c0\u2212) helps to distinguish signal from non-resonant\n\ufb01nal states with four charged pions. Belle considers 17\ndi\ufb00erent event types in its \ufb01t. In addition to the four sig-\nnal types, these are continuum, neutral or charged B\u2019s\ndecaying into charm or charmless \ufb01nal states and eight\npeaking background modes (a\u00b1\n1 (1260)\u03c0\u2213, a\u00b1\n2 \u03c0\u2213, b\u00b1\n1 \u03c0\u2213,\n\u03c10\u03c0+\u03c0\u2212, non-resonant 4\u03c0\u00b1, \u03c10f0, f0f0 and f0\u03c0+\u03c0\u2212). The\nbranching fraction of B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213is \ufb01xed to the\npublished value (33.2\u00b13.0\u00b13.8)\u00d710\u22126 (Aubert, 2006aj)\nand the ones of B0 \u2192a\u00b1\n2 \u03c0\u2213and B0 \u2192b\u00b1\n1 \u03c0\u2213to val-\nues based on measured upper limits and theoretical ex-\npectation. All other branching fractions, yields, and the\ncontinuum shape are allowed to vary in the \ufb01t. In the\n\ufb01t from BABAR, the following background categories are\nconsidered: continuum, B decays into \ufb01nal states con-\ntaining at least one charm meson, B decays into charm-\nless \ufb01nal states, \u03c10f0, f0f0, \u03c10\u03c0+\u03c0\u2212, non-resonant 4\u03c0\u00b1,\na\u00b1\n1 (1260)\u03c0\u2213, \u03c10K\u22170, and f0K\u22170. All yields are allowed\nto vary in the \ufb01t, except the last two which are \ufb01xed to\nthe expected values. Belle and BABAR use slightly di\ufb00er-\nent sets of decay modes considered in the \ufb01t. The modes\nwhich are di\ufb00erent have quite small contributions to the\n\ufb01nal sample.\nThe p.d.f.s are obtained from MC for all B decay com-\nponents. For the mES, \u2206E, and F or NN p.d.f.s, pos-\nsible di\ufb00erences between real data and the MC model-\ning are calibrated using a large control sample of B0 \u2192\nD\u2212(K+\u03c0\u2212\u03c0\u2212)\u03c0+ decays. To obtain the continuum p.d.f.,\nBelle uses o\ufb00-resonance data and BABAR on-resonance side-\nband data (mES < 5.27 GeV/c2), with parameters of most\np.d.f.s left free in the \ufb01nal \ufb01t. When possible, the p.d.f.\nfor each component is taken to be the product of analyt-\nical one-dimensional functions, but correlations as small\nas 2% between the \ufb01t variables are also accounted for us-\ning di\ufb00erent techniques such as multidimensional p.d.f.s\nor di\ufb00erent p.d.f.s for di\ufb00erent slices of another discrimi-\nnating variable. For example in Belle, since the shape of\nF depends on the \ufb02avor tagging quality r, it is described\nin seven bins of the variable r.\nFigure 17.7.7 shows the projections of the \ufb01t results\nonto mES and m\u03c0+\u03c0\u2212(where the peaks of the \u03c10 and f0\ncan be seen). Table 17.7.1 summarizes the measurements\nof the branching fraction, fL, and the time-dependent\nasymmetries for B0 \u2192\u03c10\u03c10. The results obtained by the\ntwo experiments are in agreement with each other. This\n80 At least one track from the signal decay is replaced by one\nfrom the accompanying tag B meson in the event for a signal\nevent to be mis-reconstructed.\n\n338\nmode is seen with a signi\ufb01cance of 3.1 \u03c3 by BABAR and\n3.4 \u03c3 by Belle, taking into account systematic uncertain-\nties.\n)\n2\n (GeV/c\nES\nm\n5.25\n5.26\n5.27\n5.28\n5.29\n )\n2\nEvents / ( 0.0018 GeV/c\n0\n10\n20\n30\n40\n50\n(a)\n)\n2\n (GeV/c\n/\n/\nm\n0.6\n0.7\n0.8\n0.9\n1\n )\n2\nEvents / ( 0.02 GeV/c\n0\n10\n20\n30\n40\n50\n(b)\nFigure 17.7.7. Projections of the multidimensional \ufb01t of the\nBABAR \u03c10\u03c10 analysis (Aubert, 2008r) onto the (a) mES, and\n(b) di-pion invariant mass (combining the m(\u03c0\u03c0)1 and m(\u03c0\u03c0)2\ndistributions), after a requirement on the signal-to-background\nprobability ratio calculated using all discriminating variables\nexcluding the one plotted, which enhances the fraction of signal\nevents in the sample. This selection has 40% (60%) e\ufb03ciency\nfor signal for the mES (m\u03c0\u03c0) projection. The data points are\noverlaid by the full p.d.f. projection (solid black line). Also\nshown are the B0 \u2192\u03c10\u03c10 p.d.f. component (dotted line) and\nthe sum of all other p.d.f.s (dashed line).\nTable 17.7.1. Branching fraction, fraction of longitudinal\npolarization, branching fraction to the longitudinal polarized\nstate, and coe\ufb03cients of the time-dependent CP asymmetry in\nB0 \u2192\u03c10\u03c10.\nBABAR\nBelle\n(Aubert, 2008r)\n(Adachi, 2014)\nB\u03c10\u03c10[10\u22126]\n0.92 \u00b1 0.32 \u00b1 0.14\n1.02 \u00b1 0.30 \u00b1 0.15\nf \u03c10\u03c10\nL\n0.75 +0.11\n\u22120.14 \u00b1 0.05\n0.21 +0.18\n\u22120.22 \u00b1 0.15\nBL\n\u03c10\u03c10[10\u22126]\n0.69 \u00b1 0.25 \u00b1 0.11\n0.2 \u00b1 0.2 \u00b1 0.1\nS\u03c10\u03c10\nL\n0.3 \u00b1 0.7 \u00b1 0.2\nC\u03c10\u03c10\nL\n0.2 \u00b1 0.8 \u00b1 0.3\nThe branching fraction of longitudinally polarized B0 \u2192\n\u03c10\u03c10 is an input to the isospin analysis in B \u2192\u03c1\u03c1. As\npointed out in Section 17.7.1.1, the small branching frac-\ntion B(B0 \u2192\u03c10\u03c10) \u224810\u22126 in comparison with the rela-\ntively large branching fraction B(B0 \u2192\u03c1+\u03c1\u2212) = (24.2+3.1\n\u22123.2)\n\u00d710\u22126 signi\ufb01cantly constrains the penguin uncertainty.\nThe results of the constraint on \u03c62 are presented in Sec-\ntion 17.7.7. The time-dependent analysis performed by\nBABAR is a proof of principle of this technique which, with\nsigni\ufb01cantly larger data sets, would help determine \u03c62\nwith high precision. The e\ufb00ect of using the measured val-\nues of S and C from the BABAR analysis in the \u03c1\u03c1 isospin\nanalysis is evident as the shoulder above \u03c62 = \u03b1 \u223c100\u25e6\nin Fig. 17.7.12. With larger statistics this input will help\nto resolve some of the discrete ambiguities inherent in the\ndetermination of \u03c62 using an isospin analysis.\n17.7.4 B0 \u2192(\u03c1\u03c0)0\nThe decays B \u2192\u03c1\u03c0 are similar to B \u2192\u03c0\u03c0 and B \u2192\u03c1\u03c1 in\nthat they are also dominated by the b \u2192u tree amplitude\nand contain b \u2192d penguin pollution. The CP-violation in\nthe \u03c1\u03c0 \ufb01nal state is related to the Unitarity Triangle an-\ngle \u03c62. The main complicating factor for measuring \u03c62 in\nB \u2192\u03c1\u03c0 is that it is not a CP-eigenstate; one can still mea-\nsure CP-violation in B0 \u2192\u03c1\u00b1\u03c0\u2213but it is more challeng-\ning than the case for B0 \u2192\u03c0+\u03c0\u2212decays. A measurement\nof \u03c62 is possible in \u03c1\u03c0 but instead of a triangular isospin\nrelationship between the amplitudes it is pentagonal, re-\nquiring measurements of all of the rate and CP-violation\nparameters of the decays B0 \u2192\u03c1+\u03c0\u2212, B0 \u2192\u03c1\u2212\u03c0+,\nB0 \u2192\u03c10\u03c00, B+ \u2192\u03c1+\u03c00, and B+ \u2192\u03c10\u03c0+. Early at-\ntempts to constrain \u03c62 using these decays in an isospin\npentagon analysis were based on a quasi-two-body analy-\nsis methodology, measuring decay rates and CP asymme-\ntry parameters sensitive to CP violating and CP conserv-\ning observables S, C, \u2206S, \u2206C and ACP (c.f. the B \u2192a1\u03c0\ntime-dependent analysis discussed in Section 17.7.5). Due\nto the number of parameters involved, extracting \u03c62 from\n\u03c1\u03c0 via the pentagon relationship yields poor results with\nmany discrete ambiguities.\nHowever, the B0 \u2192\u03c1+\u03c0\u2212, B0 \u2192\u03c1\u2212\u03c0+, and B0 \u2192\n\u03c10\u03c00 all decay to the same \ufb01nal state, \u03c0+\u03c0\u2212\u03c00 and there\nare regions in the 3-body phase space where there is in-\nterference between decay amplitudes. Because of this in-\nterference, it is possible to perform an amplitude analysis\nof the Dalitz plot to extract the complex decay ampli-\ntudes. Snyder and Quinn (1993) pointed out that there\nare enough observables in a full time- and tag-dependent\namplitude analysis of the B0 \u2192\u03c0+\u03c0\u2212\u03c00 Dalitz plot to\nsimultaneously extract the tree and penguin amplitudes\nalong with the weak phase, \u03c62.\nThe time-dependent rate for B0 (B0) decays, |A+\n3\u03c0(\u2206t)|2\n(|A\u2212\n3\u03c0(\u2206t)|2), is given by:\n|A\u00b1\n3\u03c0(\u2206t)|2 = e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u0014\n|A3\u03c0|2 + |A3\u03c0|2 \u2213\n\u0000|A3\u03c0|2 \u2212|A3\u03c0|2\u0001\ncos(\u2206md\u2206t)\n\u00b1 2Im\n\u0014q\npA3\u03c0A\u2217\n3\u03c0\n\u0015\nsin(\u2206md\u2206t)\n\u0015\n.(17.7.17)\nThe B0 \u2192\u03c0+\u03c0\u2212\u03c00 Dalitz plot is dominated by the\n\u03c1 resonances; it was checked that other contributions\n(f0(980), non-resonant, etc.) can safely be neglected at\nthe size of the current data samples. The amplitudes can\nbe written as a sum of terms:\nA3\u03c0 = f+A+ + f\u2212A\u2212+ f0A0 ,\n(17.7.18)\nA3\u03c0 = f+A+ + f\u2212A\u2212+ f0A0 ,\n(17.7.19)\n\n339\nwhere the f\u03ba are the Dalitz-plot position-dependent \u03c1 line-\nshapes and the A+,\u2212,0 are Dalitz-plot independent com-\nplex amplitudes for the \u03c1+\u03c0\u2212, \u03c1\u2212\u03c0+, and \u03c10\u03c00 \ufb01nal states\nrespectively, which contain information on the strong and\nweak phases. They are indeed related to \u03c62 through an\nisospin relation:\ne2i\u03c62 = A+ + A\u2212+ 2A0\nA+ + A\u2212+ 2A0 .\n(17.7.20)\nInserting the amplitudes of Eqs (17.7.18) and (17.7.19)\nand assuming no CP violation in B0 \u2212B0 mixing (|q/p| =\n1), one obtains the following for the terms appearing in\nEq. (17.7.17)\n|A3\u03c0|2 \u00b1 |A3\u03c0|2 =\nX\n\u03ba\u2208{+,\u2212,0}\n|f\u03ba|2U \u00b1\n\u03ba +\nX\n\u03ba<\u03c3\u2208{+,\u2212,0}\n2\n\u0000Re [f\u03baf \u2217\n\u03c3] U \u00b1,Re\n\u03ba\u03c3\n\u2212Im [f\u03baf \u2217\n\u03c3] U \u00b1,Im\n\u03ba\u03c3\n\u0001\n,\nIm\n\u0012q\npA3\u03c0A\u2217\n3\u03c0\n\u0013\n=\nX\n\u03ba\u2208{+,\u2212,0}\n|f\u03ba|2I\u03ba\n+\nX\n\u03ba<\u03c3\u2208{+,\u2212,0}\n\u0000Re [f\u03baf \u2217\n\u03c3] IIm\n\u03ba\u03c3 + Im [f\u03baf \u2217\n\u03c3] IRe\n\u03ba\u03c3\n\u0001\n,\n(17.7.21)\nwhere the coe\ufb03cients of the bi-linear terms (\u201cthe U\u2019s and\nI\u2019s\u201d) are related to the amplitudes by:\nU \u00b1\n\u03ba = |A\u03ba|2 \u00b1 |A\u03ba|2 ,\nU \u00b1,Re\n\u03ba\u03c3\n= Re\n\u0002\nA\u03baA\u03c3\u2217\u00b1 A\u03baA\u03c3\u2217\u0003\n,\nU \u00b1,Im\n\u03ba\u03c3\n= Im\n\u0002\nA\u03baA\u03c3\u2217\u00b1 A\u03baA\u03c3\u2217\u0003\n,\nI\u03ba = Im\n\u0002\nA\u03baA\u03ba\u2217\u0003\n,\nIRe\n\u03ba\u03c3 = Re\n\u0002\nA\u03baA\u03c3\u2217\u2212A\u03c3A\u03ba\u2217\u0003\n,\nIIm\n\u03ba\u03c3 = Im\n\u0002\nA\u03baA\u03c3\u2217+ A\u03c3A\u03ba\u2217\u0003\n.\n(17.7.22)\nThe above coe\ufb03cients are used as the \ufb01t parameters in\nthe time-dependent maximum likelihood \ufb01t to the B0 \u2192\n\u03c0+\u03c0\u2212\u03c00 Dalitz plot. In order to extract the amplitude-\nlevel information (e.g. the phase \u03c62) from the bi-linear\ncoe\ufb03cients, one can construct a \u03c72 quantity using the 27\nmeasured U\u2019s and I\u2019s and the full correlation matrix and\nminimize it to \ufb01nd the 12 best \ufb01t amplitude parameters.\nBoth BABAR (Lees, 2013c) and Belle (Kusaka, 2008)\nhave performed the time-dependent analysis to the B0 \u2192\n\u03c0+\u03c0\u2212\u03c00 Dalitz plot using the above method. The result-\ning values, including correlation matrices, for the bi-linear\ncoe\ufb03cients can be found in the references. The resulting\n\u03c62 contour, with systematic uncertainties taken into ac-\ncount, is shown in Figure 17.7.13 where one can see that\nthe individual measurements are not able to constrain \u03c62\nsigni\ufb01cantly. The combined power of the B Factory re-\nsults is su\ufb03cient to start providing important information\nin terms of our knowledge on \u03c62. Solutions appear with\nvalues of \u223c50\u25e6and \u223c120\u25e6that can be used to suppress\nnon-SM solutions when combined with the results from \u03c0\u03c0\nand \u03c1\u03c1 isospin analyses. A discussion on the extraction of\n\u03c62 using these decays can be found in (Lees, 2013c), where\nBABAR conclude that while the the U and I parameters\n(and derived quasi-two-body parameters) can be reliably\nextracted from data, the 1\u2212C.L. scan for \u03c62 is not robust\nusing the full BABAR data set.\nA signi\ufb01cant increase in the available statistics for this\nmode, which is expected from the next generation of Fla-\nvor Factories, will result in the B0 \u2192\u03c0+\u03c0\u2212\u03c00 time-de-\npendent Dalitz-plot analysis playing a more prominent\nrole in the determination of \u03c62. Given the available level of\nprecision it is not possible to make concrete predictions on\nthe possible sensitivity that one might be able to achieve\nin the future as there are too many parameters that feed\ninto the determination of \u03c62, and many of these are only\nweakly constrained by the current data.\n17.7.5 B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213\nThe following describes analyses of B0(B0) \u2192a+\n1 (1260)\u03c0\u2212\nand B0(B0) \u2192a\u2212\n1 (1260)\u03c0+ performed using the quasi-\ntwo-body approximation (which is directly analogous to\nthe corresponding early analyses of B \u2192\u03c1\u03c0 decays). The\n\u2206t distributions81 are given by (Gronau and Zupan, 2006)\nF\na\u00b1\n1 \u03c0\u2213\nq\n(\u2206t) = (1 \u00b1 ACP )e\u2212|\u2206t|/\u03c4B0\n4\u03c4B0\n\u001a\n1 \u2212q\u2206w+\nq \u00b7 (1 \u22122w)\n\u0014\n(S \u00b1 \u2206S) sin(\u2206md\u2206t) \u2212\n(C \u00b1 \u2206C) cos(\u2206md\u2206t)\n\u0015\u001b\n,\n(17.7.23)\nwhere q = +1(\u22121) when the tagging meson B0\ntag is a\nB0(B0). The time- and \ufb02avor-integrated charge asymme-\ntry ACP is the rate asymmetry between a+\n1 (1260)\u03c0\u2212and\na\u2212\n1 (1260)\u03c0+ \ufb01nal states including contributions from both\nB0 and B0 decays. The quantities S and C parameterize\nmixing-induced CP violation related to the angle \u03c62, and\n\ufb02avor-dependent direct CP violation, respectively. The pa-\nrameter \u2206C describes the di\ufb00erence in B0 \u2212B0 asym-\nmetries between the a+\n1 (1260)\u03c0\u2212and a\u2212\n1 (1260)\u03c0+ \ufb01nal\nstates, while \u2206S is related to the strong phase di\ufb00erence\nbetween the amplitudes contributing to B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213\ndecays. The parameters \u2206C and \u2206S are insensitive to CP\nviolation. De\ufb01ning the CP-averaged rate into a \ufb01nal state\nf as B(f) = (B(B0 \u2192f) + B(B0 \u2192f))/2, the asymme-\ntry between the CP-averaged rates B(a+\n1 (1260)\u03c0\u2212) and\nB(a\u2212\n1 (1260)\u03c0+) is \u2206C + ACP C.\nThe following e\ufb00ective value \u03c6e\ufb00\n2 of the weak phase \u03c62\nis obtained (Gronau and Zupan, 2006)\n\u03c6e\ufb00\n2 = 1\n4\n\u0014\narcsin\n\u0012\nS + \u2206S\np\n1 \u2212(C + \u2206C)2\n\u0013\n+\n81 Note that the form of the \u2206t distributions involves more\nparameters than the example described in Eq. 10.2.2. The rea-\nson for this is that the a\u00b1\n1 (1260)\u03c0\u2213\ufb01nal state is not a CP\neigenstate.\n\n340\narcsin\n\u0012\nS \u2212\u2206S\np\n1 \u2212(C \u2212\u2206C)2\n\u0013\u0015\n.\n(17.7.24)\nA bound on |\u2206\u03c62| is derived (Gronau and Zupan, 2006)\nfrom the CP asymmetry parameters and from the ratios\nR0\n\u00b1 and R+\n\u00b1 of CP-averaged rates:\nR0\n+ \u2261\u03bb\n2f 2\na1B(K+\n1 \u03c0\u2212)\nf 2\nK1B(a+\n1 \u03c0\u2212) ,\nR0\n\u2212\u2261\u03bb\n2f 2\n\u03c0B(a\u2212\n1 K+)\nf 2\nKB(a\u2212\n1 \u03c0+) ,\nR+\n+ \u2261\u03bb\n2f 2\na1B(K0\n1\u03c0+)\nf 2\nK1B(a+\n1 \u03c0\u2212) ,\nR+\n\u2212\u2261\u03bb\n2f 2\n\u03c0B(a+\n1 K0)\nf 2\nKB(a\u2212\n1 \u03c0+) .\n(17.7.25)\nThe constant \u03bb is |Vus|/|Vud| = |Vcd|/|Vcs| while fK, f\u03c0,\nfa1(1260), and fK1 are the decay constants of K, \u03c0, a1(1260),\nand K1 mesons, respectively. The branching fraction mea-\nsurements are described in detail in Section 17.4.5.5.\nThe a1(1260) \u21923\u03c0 decay proceeds mainly through\nthe intermediate states (\u03c0\u03c0)\u03c1\u03c0 and (\u03c0\u03c0)\u03c3\u03c0 (Amsler et al.,\n2008). Because of the limited number of signal events,\nBABAR and Belle made no attempt to separate the con-\ntributions of the dominant P-wave (\u03c0\u03c0)\u03c1 and the S-wave\n(\u03c0\u03c0)\u03c3. The a1(1260) meson is reconstructed in its \u03c1\u03c0 de-\ncay. A systematic uncertainty is then estimated due to the\ndi\ufb00erence in the selection e\ufb03ciency. The B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213\ncandidates are reconstructed by combining an a1(1260)\ncandidate and a charged pion.\nBoth experiments use the same selection strategy. As\nfor other charmless B decays studied at the B Factories,\nfor this decay mode the dominant background is contin-\nuum. To suppress it, the angle \u03b8T between the thrust axis\nof the B candidate and that of the rest of the tracks and\nneutral clusters in the event, calculated in the CM frame\nis used. To suppress further combinatorial background in\nthe modes containing an a1(1260) meson, it is required\nthat the absolute value of the cosine of the angle between\nthe direction of the \u03c0 meson from a1(1260) \u2192\u03c1\u03c0 with re-\nspect to the \ufb02ight direction of the B in the a1(1260) meson\nrest frame is less than 0.85. Peaking backgrounds from B\ndecays to \ufb01nal states involving D+(\u2192K\u2212\u03c0+\u03c0+, K0\nS\u03c0+),\nD0(\u2192K\u2212\u03c0+, K\u2212\u03c0+\u03c00), J/\u03c8(\u2192\u00b5+\u00b5\u2212) and K0\nS(\u2192\u03c0+\u03c0\u2212)\nmesons are removed by applying the corresponding mass\nvetoes.\nThe CP asymmetry parameters are measured at BABAR\nusing an unbinned extended ML \ufb01t using the selected sam-\nple of B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213with the input observables \u2206E,\nmES, a Fisher discriminant F (described in Chapter 9),\nma1(1260), a helicity angle H, and \u2206t (Aubert, 2007ae).\nAt Belle a two step procedure is used. Firstly the sig-\nnal yield (thus the branching fraction measurement) in\na1(1260)\u03c0 decay mode is obtained from an extended ML\n\ufb01t to the selected sample B \u2192a\u00b1\n1 (1260)\u03c0\u2213with the in-\nput observables \u2206E, ma1(1260), H, and F. The mES dis-\ntribution is not included in the \ufb01t, as it is used to select\nthe best B candidate in cases of multiple candidates per\nevent. After that a one-dimensional unbinned maximum\nlikelihood \ufb01t is performed to the \u2206t distribution of events\nin the signal region |\u2206E| < 0.04 GeV, using the branch-\ning fraction measurement from the \ufb01rst step to provide\nE (GeV)\n\u2206\n-0.1 -0.05\n0\n0.05 0.1\nEvents / 8 MeV\n20\n40\n60\nE (GeV)\n\u2206\n-0.1 -0.05\n0\n0.05 0.1\nEvents / 8 MeV\n20\n40\n60\n (GeV)\nES\nm\n5.25 5.26 5.27 5.28 5.29\nEvents / 1.6 MeV \n0\n20\n40\n60\n (GeV)\nES\nm\n5.25 5.26 5.27 5.28 5.29\nEvents / 1.6 MeV \n0\n20\n40\n60\n(a)\n(b)\nFigure 17.7.8. Signal enhanced projections of a) \u2206E, b)\nmES from the BABAR B \u2192a1\u03c0 analysis. Points represent on-\nresonance data, dotted lines the sum of all backgrounds, and\nsolid lines the full \ufb01t function. These plots are made with a\ncut on the signal-to-continuum likelihood ratios excluding the\nvariable being plotted (from Aubert (2007ae)).\nthe event-dependent signal probability for each compo-\nnent (Dalseno, 2012).\nIn both experiments the p.d.f.s for signal and BB back-\ngrounds are determined from MC distributions in each\nobservable. For the continuum background the functional\nforms and initial parameter values of the p.d.f.s are estab-\nlished with o\ufb00-resonance data. The p.d.f. of the a1(1260)\nmeson invariant mass distribution of signal events is pa-\nrameterized as a relativistic Breit-Wigner line-shape with\na mass-dependent width (Armstrong et al., 1990).\nAt BABAR, the maximum likelihood \ufb01t to a sample of\n29300 events results in a signal yield of 608 \u00b1 53, of which\n461\u00b146 have their \ufb02avor identi\ufb01ed. Fig. 17.7.8 shows dis-\ntributions of mES and \u2206E, enhanced in signal content by\nrequirements on the signal-to-continuum likelihood ratios\nusing all discriminating variables other than the one plot-\nted.\nWith a data sample of 304 \u00d7 106 BB pairs, the follow-\ning results for the CP asymmetries are obtained (Aubert,\n2007ae)\nS =\n0.37 \u00b1 0.21 \u00b1 0.07,\nC = \u22120.10 \u00b1 0.15 \u00b1 0.09,\nACP = \u22120.07 \u00b1 0.07 \u00b1 0.02,\n(17.7.26)\nwhere the errors are statistical and systematic in nature,\nrespectively. For the CP conserving parameters one ob-\ntains\n\u2206S = \u22120.14 \u00b1 0.21 \u00b1 0.06,\n\u2206C =\n0.26 \u00b1 0.15 \u00b1 0.07.\n(17.7.27)\nAt Belle (Dalseno, 2012), the \ufb01t to 83799 a\u00b1\n1 (1260)\u03c0\u2213\ncandidates in the signal region results in\nS = \u22120.51 \u00b1 0.14 \u00b1 0.08,\nC = \u22120.01 \u00b1 0.11 \u00b1 0.09,\nACP = \u22120.06 \u00b1 0.05 \u00b1 0.07,\n(17.7.28)\nand the CP conserving parameters obtained are\n\u2206S = \u22120.09 \u00b1 0.14 \u00b1 0.06,\n\n341\n\u2206C =\n0.54 \u00b1 0.11 \u00b1 0.07.\n(17.7.29)\nFigure 17.7.9 shows the \u2206t and CP asymmetry distribu-\ntions obtained for the Belle analysis. From a likelihood\nscan, the signi\ufb01cance of mixing-induced CP violation is\nfound by Belle to be 3.1\u03c3 including systematic uncertain-\nties. There is a discrepancy at the level of 3.2 \u03c3 between\nthe BABAR and Belle values of S, which requires more data\nto resolve.\nt (ps)\n6\n-6\n-4\n-2\n0\n2\n4\n6\nEvents / (2.5 ps)\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nq = +1\nq = -1\nt (ps)\n6\n-6\n-4\n-2\n0\n2\n4\n6\nEvents / (2.5 ps)\n0\n100\n200\n300\n400\n500\nqc = +1\nqc = -1\nt (ps)\n6\n-6\n-4\n-2\n0\n2\n4\n6\n-\nFit\n+N\n+\nFit\n/N\n-\nFit\n-N\n+\nFit\nN\n-0.5\n-0.4\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nt (ps)\n6\n-6\n-4\n-2\n0\n2\n4\n6\n-\nFit\n+N\n+\nFit\n/N\n-\nFit\n-N\n+\nFit\nN\n-0.5\n-0.4\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nFigure 17.7.9. Background subtracted time-dependent \ufb01t re-\nsults for B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213(Dalseno, 2012). (a) and (b) show\nthe \u2206t distributions for the B0\ntag \ufb02avor q and the product of\nthe B0\ntag \ufb02avor and a1 charge qc, respectively. The left plot\nshows the e\ufb00ect of \ufb02avor-dependent CP violation while the\nplot on the right shows the e\ufb00ects of the CP conserving pa-\nrameters. The solid blue and dashed red curves represent the\n\u2206t distributions for q = +1 and q = \u22121, respectively. (c) and\n(d) show the asymmetry of the plots immediately above them,\n(N Fit\n+ \u2212N Fit\n\u2212)/(N Fit\n+ +N Fit\n\u2212), where N Fit\n+\n(N Fit\n\u2212) is the measured\nsignal yield of positive (negative) quantities in bins of \u2206t. All\ncurves are the expected ones for the values in Eqs (17.7.28)\nand (17.7.29).\nThe main contributions to the systematic error on the\nsignal parameters come from the p.d.f. parameterization,\nuncertainty due to CP violation present in the BB back-\nground and uncertainty due to the interference between\nB0 \u2192a\u00b1\n1 (1260)\u03c0\u2213and other 4\u03c0 \ufb01nal states.\n\u03c6e\ufb00\n2 can be determined from Eq. (17.7.24) up to a four-\nfold discrete ambiguity in the range [0\u25e6, 180\u25e6]. This can\nbe reduced to a two-fold ambiguity with the assumption\nthat the relative strong phase of the tree amplitudes of\nthe B0 decays to a\u2212\n1 (1260)\u03c0+ and a+\n1 (1260)\u03c0\u2212is much\nsmaller than 90\u25e6(Gronau and Zupan, 2006), as predicted\nby QCD factorization (Beneke and Neubert, 2003b). This\nassumption is valid to leading order in 1/mb (Bauer and\nPirjol, 2004; Bauer, Pirjol, Rothstein, and Stewart, 2004).\nUnder this assumption, the two solutions at BABAR are\n(78.6 \u00b1 7.3)\u25e6and (11.4 \u00b1 7.3)\u25e6. At Belle the four obtained\nsolutions for \u03c6e\ufb00\n2 are (\u221217.3\u00b16.6\u00b14.8)\u25e6, (41.6\u00b16.2\u00b13.4)\u25e6,\n(48.4 \u00b1 6.2 \u00b1 3.4)\u25e6, and (107.3 \u00b1 6.6 \u00b1 4.8)\u25e6. Multiple so-\nlutions appear in the \ufb01ts for reasons analogous to the \u03c0\u03c0\nand \u03c1\u03c1 constraints on \u03c62. The \ufb01rst of the two solutions\nquoted for BABAR is compatible with the results of Stan-\ndard Model based \ufb01ts to the Unitarity Triangle to be pre-\nsented in Section 25.1. In Belle the solution most compat-\nible with the results of Standard Model based \ufb01ts is the\nlast quoted one.\nIn BABAR a MC technique is used to estimate a prob-\nability region for the bound on |\u2206\u03c62|. The CP-averaged\nrates and CP asymmetry parameters used in estimating\nthe bounds are generated according to the experimental\ndistributions. The input values of branching fractions are\nthose presented in Section 17.4.5.5 while CP asymme-\ntry parameters are from this section (Eq. 17.7.26). For\nthe decay constants the following values are used: f\u03c0 =\n(130.4 \u00b1 0.2) MeV (Amsler et al., 2008), fK = (155.5 \u00b1\n0.9) MeV (Amsler et al., 2008), fa1 = (203 \u00b1 18) MeV\n(Cheng and Yang, 2007), and fK1 = 207 MeV (Bloch,\nKalinovsky, Roberts, and Schmidt, 1999). For fK1 an un-\ncertainty of 20 MeV is assumed. For the constant \u03bb the\nvalue 0.23 (Amsler et al., 2008) is used.\nFor each set of generated values, the bound on |\u2206\u03c62| is\nevaluated. The limits on |\u2206\u03c62| are obtained by counting\nthe fraction of bounds within a given value and the results\nare |\u2206\u03c62| < 11\u25e6(13\u25e6) at 68% (90%) probability (Aubert,\n2010d). Combining the solution near 90\u25e6, consistent with\nthe results of global CKM \ufb01ts, with the bound on |\u03c62\u2212\u03c6e\ufb00\n2 |\nwe measure the weak phase \u03c62 = (79 \u00b1 7 \u00b1 11)\u25e6.\nThis solution is in agreement with the value of \u03c62 found\nin the analyses of B \u2192\u03c0\u03c0, B \u2192\u03c1\u03c1, and B \u2192\u03c1\u03c0 decays.\nThis measurement is currently limited by statistics and a\nsubstantial improvement of its precision may come from a\nfuture super \ufb02avor factory.\n17.7.6 SU(3) constraint using B0 \u2192\u03c1+\u03c1\u2212, and\nB+ \u2192K\u22170\u03c1+\nTable 17.7.2 summarizes the measurements of the time-\ndependent asymmetries with their correlation coe\ufb03cient\n\u03c1S,C, branching fractions, and fL for the B Factory re-\nsults on B0 \u2192\u03c1+\u03c1\u2212and B+ \u2192K\u22170\u03c1+. The e\ufb00ect of cor-\nrelated systematic uncertainties on the ratio of branching\nfractions of these two decay channels is negligible. The\nconstraint obtained from the B Factory data on \u03c62 fol-\nlowing the BGRS procedure outlined in Section 17.7.1.4\nis shown in Figure 17.7.10. There are two overlapping so-\nlutions consistent with the SM. These two solutions di\ufb00er\nby the magnitude of \u03b4P T , where values of \u03b4P T \u223c0 cor-\nrespond to the left of the two central peaks in the \ufb01gure.\nThe determination of \u03c62 using this approach only weakly\nconstrains this phase di\ufb00erence given the data from the B\nFactories, however QCD factorization calculations favor\na small phase di\ufb00erence and the solution with |\u03b4P T | \u223c0\nis preferred (Beneke, Buchalla, Neubert, and Sachrajda,\n1999, 2000, 2001). This favored solution is summarized in\nTable 17.7.2 for the individual and combined B Factory\nresults where the requirement that |\u03b4P T | < 90\u25e6is im-\nposed. While the BABAR data give a more precise value of\n\n342\n\u03c62 with this method, the Belle data provide a more strin-\ngent constraint on \u03b4P T than BABAR. This can be seen in\nFigure 17.7.10 as the mirror solution at \u03c62\n\u223c5\u25e6is less\nprobable than the other possible solutions. The ratio of\npenguin to tree amplitudes (see Section 17.7.1.4) obtained\nfrom the data is rP T = 0.10 \u00b1 0.04.\n\u03b1\n = \n2\n\u03c6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n1 - C.L.\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 17.7.10. The 1 \u2212C.L. function obtained on \u03c62 = \u03b1\nfrom the B Factories (solid blue) using B0 \u2192\u03c1+\u03c1\u2212, and B+ \u2192\nK\u22170\u03c1+ decays and the BGRS method discussed in the text.\nThe constraints from BABAR (dashed black) and Belle (dotted\nred) are also shown. The curves shown include solutions for all\npossible values of \u03b4P T .\n17.7.7 Summary\nFirst we discuss the constraints on \u03c62 obtained by the\nB Factories mode-by-mode and then on the \u2018average\u2019 of\nthe B \u2192\u03c0\u03c0/\u03c1\u03c1 and the B \u2192\u03c1\u03c0 \u21923\u03c0 Dalitz results.\nThe mode B \u2192a1(1260)\u03c0 can play an important role in\nconstraining \u03c62; however, at the time of writing this book\nthe SU(3) constraint from B \u2192a1(1260)\u03c0 is typically not\nincluded in global averages together with the SU(2) con-\nstraints, as it is believed that the former measurements\nhave to account for SU(3) breaking e\ufb00ects which may not\nbe straight forward to compute, whereas the latter are\nagreed to have small theoretical uncertainties. A \u2018na\u00a8\u0131ve\u2019\nweighted average of the two sets of measurements is given\nat the end. The SU(3) constraint from B0 \u2192\u03c1+\u03c1\u2212and\nB+ \u2192K\u22170\u03c1+ discussed in Section 17.7.6 is completely\ncorrelated with inputs for the isospin analysis and this re-\nsult is used only as a cross check of the underlying theoret-\nical interpretation of S and C. The averaging procedure\nadopted here is to combine the \u03c72(\u03c62) distributions ob-\ntained from each individual constraint (B \u2192\u03c0\u03c0, \u03c0+\u03c0\u2212\u03c00\nand \u03c1\u03c1), and from this determine the value of 1 \u2212C.L.\nas a function of \u03c62. The value of \u03c62 obtained near 90\u25e6is\nreported as the SM value of this angle. The na\u00a8\u0131ve average\nincluding B \u2192a1(1260)\u03c0 is simply the weighted average\nobtained from the \u03c72(\u03c62) combination described in this\nsection with the result of the SU(3) constraint from Sec-\ntion 17.7.5.\nThe constraint on \u03c62 obtained from B \u2192\u03c0\u03c0 decays\nfrom Belle and BABAR is shown in Figure 17.7.11. The\neight solutions corresponding to the eight-fold ambiguity\ninherent in the isospin analysis are visible. The solution\nnear the zero value is suppressed by physical constraints\non possible magnitudes of penguin contributions within\nthe SM (Bona et al., 2007a). Furthermore one can exclude\nallowed values around \u03c62 \u223c40 \u221250\u25e6as can be seen from\nthe \ufb01gure.\n\u03b1\n = \n2\n\u03c6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n1 - C.L.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 17.7.11. The solid (blue) curve shows the 1 \u2212C.L.\nfunction obtained on \u03c62 = \u03b1 from the B Factories using\nthe Gronau-London isospin analysis for B \u2192\u03c0\u03c0 decays. The\ndashed (black) curve shows the BABAR only constraint, the dot-\nted (red) curve shows the Belle only constraint. As discussed\nin the text, the solutions near \u03c62 = 0 are unphysical and can\nbe removed by extending the isospin analysis.\nThe constraint on \u03c62 obtained from the BABAR and\nBelle analyses of B \u2192\u03c1\u03c1 is shown in Figure 17.7.12.\nOne gets two values, one near zero and the other near\n90\u25e6. The underlying eight-fold ambiguity expected for the\nisospin analysis is not visible, since the isospin triangles,\nillustrated in Figure 17.7.2, are essentially \ufb02at as a re-\nsult of the equally large branching fractions of the \u03c1+\u03c1\u2212\nand \u03c1+\u03c10 modes, and the small value of \u03c10\u03c10. The value\nobtained for the solution consistent with the SM expec-\ntation is \u03c62 = (89.9+5.4\n\u22125.6)\u25e6. The accurate value obtained\nusing isospin symmetry with \u03c1\u03c1 decays is similar to that\nattained using the BGRS SU(3) \ufb02avor based approach dis-\ncussed in Section 17.7.6. The individual BABAR and Belle\nresults are (92.7\u00b16.3)\u25e6and (84.3+12.4\n\u221212.8)\u25e6, respectively. The\nbetter accuracy of BABAR with respect to Belle is partly\ndue to the time-dependent CP asymmetry measurement of\n\u03c10\u03c10 \ufb01nal state, the more accurate measurement of \u03c1+\u03c1\u2212,\nand partly due to the accuracy on the \u03c1\u00b1\u03c10 branching\nfraction from BABAR. One can see from the \ufb01gure that the\n\u03c1\u03c1 modes exclude values of \u03c62 around \u223c50\u25e6and \u223c140\u25e6.\nThese decays help to discard unphysical solutions result-\ning from the B \u2192\u03c0\u03c0 isospin analysis.\n\n343\nTable 17.7.2. A summary of experimental inputs used for the BGRS method, along with the constraints on \u03c62 derived using\nthis method. \u2021The solution given for \u03c62 is the one in agreement with the SM with the additional requirement that |\u03b4P T | < 90\u25e6\n(consistent with theoretical expectations (Beneke, Buchalla, Neubert, and Sachrajda, 1999, 2000, 2001)).\nBABAR\nBelle\nAverage\nS (\u03c1+\u03c1\u2212)\n\u22120.17 \u00b1 0.20+0.05\n\u22120.06\n+0.19 \u00b1 0.30 \u00b1 0.08\n\u22120.05 \u00b1 0.17\nC (\u03c1+\u03c1\u2212)\n+0.01 \u00b1 0.15 \u00b1 0.06\n\u22120.16 \u00b1 0.21 \u00b1 0.08\n\u22120.06 \u00b1 0.13\n\u03c1S,C\n\u22120.035\n0.10\n0.009\nB(\u03c1+\u03c1\u2212)\n[10\u22126]\n25.5 \u00b1 2.1+3.6\n\u22123.9\n22.8 \u00b1 3.8 +2.3\n\u22122.6\n24.2 \u00b1 3.1\nB(K\u22170\u03c1+)\n[10\u22126]\n9.6 \u00b1 1.7 \u00b1 1.5\n8.9 \u00b1 1.7 \u00b1 1.2\n9.2 \u00b1 1.5\nfL (\u03c1+\u03c1\u2212)\n0.992 \u00b1 0.024+0.026\n\u22120.013\n0.941 +0.034\n\u22120.040 \u00b1 0.030\n0.978 \u00b1 0.023\nfL (K\u22170\u03c1+)\n0.52 \u00b1 0.10 \u00b1 0.04\n0.43 \u00b1 0.11+0.05\n\u22120.02\n0.48 \u00b1 0.08\n\u03c62 = \u03b1 (SM solution\u2021) (\u25e6)\n89.5+6.7\n\u22126.5\n81.7+11.4\n\u221211.3\n86.5+7.3\n\u22125.4\n\u03b1\n = \n2\n\u03c6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n1 - C.L.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 17.7.12. The solid (blue) curve shows the 1 \u2212C.L.\nfunction obtained on \u03c62 = \u03b1 from the B Factories using\nthe Gronau-London isospin analysis for B \u2192\u03c1\u03c1 decays. The\ndashed (black) curve shows the BABAR only constraint, the dot-\nted (red) curve shows the Belle only constraint.\nThe constraint on \u03c62 from B0 \u2192\u03c0+\u03c0\u2212\u03c00 decays ob-\ntained by the B Factories is shown in Figure 17.7.13.\nWhile these results do not completely exclude any interval,\nthey do strongly suppress unphysical values. It is the abil-\nity of these results to resolve ambiguities that makes the\nanalysis of B0 \u2192\u03c0+\u03c0\u2212\u03c00 very important. In the longer\nterm it is expected that the measurement of \u03c62 with the\ntime-dependent Dalitz-plot method will provide the most\nprecise value of this angle, however it is not yet possible to\nmake estimates of how much more data will be required\nfor the precision on \u03c62 from these decays to surpass the\ntheoretical uncertainty limits of \u223c1\u25e6found in the other\nmodes. At the time of compiling this book, it was not\nstraightforward to perform the joint isospin and Dalitz-\nplot analysis as originally published by Belle. As a result\nwe resorted to using Dalitz-plot results from each experi-\nment to compute an average of \u03c62 from B0 \u2192\u03c0+\u03c0\u2212\u03c00 de-\ncays. Looking to the future, it will be important to probe\nthe Dalitz plot beyond \u03c1\u03c0 intermediate states in order to\nmaximize our sensitivity to possible second order NP ef-\nfects that may be manifest in nature. Theoretical work on\nhow one might identify underlying non-SM contributions\nfrom three body \ufb01nal states is ongoing.\n\u03b1\n = \n2\n\u03c6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n1 - C.L.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 17.7.13. The solid (blue) curve shows 1\u2212C.L. function\nobtained on \u03c62 = \u03b1 from the B Factories using the Dalitz-plot\nanalysis of B \u2192\u03c0+\u03c0\u2212\u03c00 decays. The dashed (black) curve\nshows the BABAR only constraint, the dotted curve (red) shows\nthe Belle only constraint.\nThe B Factories results for \u03c62 from B \u2192\u03c0\u03c0, \u03c1\u03c1, and\n\u03c0+\u03c0\u2212\u03c00 decays are summarized in Figure 17.7.14. Initial\nmeasurements from B \u2192\u03c0\u03c0 decays excluded the range\nof 40 \u221250\u25e6while at the same time highlighted the issue\nof understanding penguin contributions in detail. As can\nbe seen from the combined B Factories result (the dashed\nline in the \ufb01gure), it was not possible to measure the an-\ngle precisely with this channel alone even with full data\nsample obtained by both experiments. The measurement\nof \u03c62 using B \u2192\u03c1\u03c1 decays (the dashed-dotted line in\nthe \ufb01gure) provides the most accurate value; it also sup-\npresses the unphysical solution near \u223c140\u25e6as well as\n\n344\nthose in the range 40\u25e6\u221250\u25e6. Early quasi-two-body anal-\nyses of B \u2192\u03c1\u03c0 \u2192\u03c0+\u03c0\u2212\u03c00 provided an interesting third\nalternative to constrain this angle. However, as the data\nsets of B Factories increased, it became apparent that a\ntime-dependent Dalitz analysis was required. The value\nof \u03c62 from \u03c0+\u03c0\u2212\u03c00 is also shown (the dotted line). This\nresult plays an important role in suppressing those val-\nues inconsistent with the SM solution for the Unitarity\nTriangle. Noting that physical penguin contributions to\nB \u2192\u03c0\u03c0 suppress \u03c62 \u223c0 leaves\n\u03c62 = \u03b1 = (88 \u00b1 5)\u25e6,\n(17.7.30)\nwhich is consistent with the SM expectations as discussed\nin Section 25.1. While B \u2192\u03c1\u03c1 dominates the measured\nvalue of the angle, there is a theoretical uncertainty from\nisospin breaking currently of the order of \u223c1\u25e6. It is worth\nnoting that B \u2192\u03c0\u03c0 decays also have a theoretical limit\nfrom isospin breaking at a similar level. A high statistics\nstudy of B \u21924\u03c0 will require an amplitude analysis in\norder to fully utilize interference between the various in-\ntermediate states and remove experimental limitations of\nthe quasi-two-body approximation.\n\u03b1\n = \n2\n\u03c6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n1 - C.L.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nFigure 17.7.14. The 1 \u2212C.L. function obtained on \u03c62 =\n\u03b1 from the B Factories (solid thick red curve). Constraints\nobtained using the Gronau-London isospin analysis for (dashed\nblue) B \u2192\u03c0\u03c0 and (dash-dotted black) \u03c1\u03c1 decays as well as the\nDalitz analysis for (dotted red) \u03c0+\u03c0\u2212\u03c00 decays are shown.\nIt is interesting to note that the most probable value\nfrom the B0 \u2192\u03c0+\u03c0\u2212\u03c00 Dalitz-plot analysis peaks around\n55\u25e6which is somewhat smaller than the SM expectation.\nThe di\ufb00erence is not signi\ufb01cant, however a higher statis-\ntics study is called for in order to improve the precision of\nthe B0 \u2192\u03c0+\u03c0\u2212\u03c00 Dalitz result.\nThe last constraint on \u03c62 comes from time-dependent\nmeasurements of B \u2192a1(1260)\u03c0 decays with input from\nSU(3) related modes in order to constrain penguins. The\naccuracy obtained using this method on \u03c6e\ufb00\n2\nis \u00b17\u25e6for\neach experiment, with an additional \u00b111\u25e6uncertainty from\npenguin contributions. Usually the community does not\ninclude a1(1260)\u03c0 results in the global average of \u03c62 to\navoid the complexity of the SU(3) analysis. On the other\nhand one can compute a \u2018na\u00a8\u0131ve\u2019 weighted average for \u03c62\nfrom the combination of B \u2192\u03c0\u03c0, \u03c1\u03c1, \u03c0+\u03c0\u2212\u03c00 decays with\nthe B \u2192a1(1260)\u03c0 SU(3) value of (79 \u00b1 7 \u00b1 11)\u25e6(from\nBABAR). This gives an average of\n\u03c62 = \u03b1 = (87 \u00b1 5)\u25e6.\n(17.7.31)\nThe measurement of this angle of the Unitarity Triangle is\na direct constraint to test the CKM matrix description of\nquark mixing and thus the KM description of CP violation\nin the SM. The use of \u03c62 in this context is discussed in\nChapter 25. The presence of penguin contributions, while\na nuisance in terms of the determination of \u03c62, means that\nthese decays are also sensitive to NP e\ufb00ects manifest in\nloops. High precision measurements of \u03c62 in the di\ufb00erent\nmodes can be compared in order to search for NP in anal-\nogy with the ongoing searches via penguin measurements\nof \u03c61 discussed in Section 17.6.\nOne of the great successes of the BABAR and Belle B\nFactories has been the con\ufb01rmation that the CKM matrix\nprovides the leading order description of CP violation in\nthe quark sector. The next generation of experiments will\nfocus on searches for possible second order CP violation\ne\ufb00ects beyond the SM. This will require detailed studies of\nthe interference patterns manifest in three and four body\n\ufb01nal states.\nIn the future it may be possible to include constraints\non \u03c62 obtained using additional modes such as B0 \u2192\nKK\u03c0\u03c0 and B \u2192a1\u03c1. The precision of the next genera-\ntion super \ufb02avor factory will approach theoretical limits on\nisospin breaking for B \u2192\u03c0\u03c0 and \u03c1\u03c1, so it will be impor-\ntant for experimentalists and theorists alike to continue\nto explore all possible avenues to improve the precision on\nthis weak angle.\n\n345\n17.8 \u03c63, or \u03b3\nEditors:\nFernando Martinez-Vidal (BABAR)\nKarim Trabelsi (Belle)\nIkaros Bigi (theory)\nAdditional section writers:\nGiovanni Marchiori, Gagan Mohanty, Anton Poluektov,\nMatteo Rama, Abner So\ufb00er\n17.8.1 Introduction\nWhile \u03c61 and \u03c62 have been determined to a good level\nof precision, knowledge of \u03c63 = \u03b3 \u2261arg [\u2212VudV \u2217\nub/VcdV \u2217\ncb]\n(see Section 16.4) is still limited by the small branching\nfractions of the processes used in its measurement. The\nmost powerful methods for measuring this angle in a the-\noretically clean way are based on the interference between\nb \u2192cus and b \u2192ucs tree amplitudes in the charged-B\nmeson decays to open-charm \ufb01nal states, B\u2212\u2192D(\u2217)K(\u2217)\u2212\n(charge-conjugate modes are implied here and through-\nout the text unless otherwise speci\ufb01ed). The interference\nis between B\u2212\u2192DK\u2212followed by a D \u2192f decay and\nB\u2212\u2192DK\u2212followed by a D \u2192f decay, where f is any\ncommon \ufb01nal state of D and D mesons (Fig. 17.8.1).\nW \u2212\nW \u2212\n\u00afu\nB\u2212\nK\u2212\n\u00afu\nu\n\u00afc\ns\nb\n\u00afD0\nB\u2212\n\u00afu\nb\n\u00afu\nc\n\u00afu\ns\nK\u2212\nD0\nFigure 17.8.1. Dominant Feynman diagrams contributing\nto the B\u2212\u2192DK\u2212decay. The top diagram proceeds via a\nb \u2192ucs transition, and is suppressed by both the small value\nof |Vub|, and color considerations; the bottom diagram pro-\nceeds via a b \u2192cus transition, and is only singly Cabibbo-\nsuppressed.\nSince there is no penguin contribution for these decays\nand consequently no theoretical uncertainty involved, all\nthe hadronic unknowns are obtainable from experiment.\nThey are rB, the magnitude of the ratio of the amplitudes\nfor the processes B\u2212\u2192D0K\u2212and B\u2212\u2192D0K\u2212, and \u03b4B,\nthe relative strong phase between these two amplitudes.\nFor charged B decays, rB \u223ccf|VcsV \u2217\nub/VusV \u2217\ncb| \u223c0.1,\nwhere cf is a color suppression factor (\u223c0.3). There is no\ntheoretical guidance for the strong phase di\ufb00erence \u03b4B.\nTypically, e\ufb00ects due to neutral D mixing and CP vio-\nlation are neglected, since these are expected (and mea-\nsured) to be small (see the text on D-mixing and CP\nviolation in Section 19.2). In general however, such ef-\nfects can also be taken into account (Grossman, So\ufb00er,\nand Zupan, 2005). There is also an irreducible error com-\ning from electroweak corrections estimated to be \u03b4\u03c63/\u03c63\n\u223c10\u22126 (Zupan, 2011).\nThe possibility of observing direct CP violation in\nB\u2212\u2192DK\u2212was \ufb01rst discussed by Bigi, Carter, and\nSanda (Bigi and Sanda, 1988; Carter and Sanda, 1980). It\nwas suggested to use charged B decays to \ufb01nal states with\nD0/D0 \u2192K0\nS plus pion(s), where the presence of the K0\nS\ngenerated by K0 \u2212K0 mixing was the essential element\nfor making the interference. Since then, several methods\nhave been proposed which can be grouped according to\nthe choice of the \ufb01nal state: the \u201cGLW\u201d method (Gronau\nand London, 1991; Gronau and Wyler, 1991), based on\nCabibbo-suppressed D decays to CP eigenstates, such as\nK+K\u2212or K0\nS\u03c00 (Section 17.8.2); the \u201cADS\u201d method (At-\nwood, Dunietz, and Soni, 1997, 2001), where the neu-\ntral D is reconstructed in Cabibbo-favored (CF) and dou-\nbly Cabibbo-suppressed (DCS) \ufb01nal states such as K\u00b1\u03c0\u2213\n(Section 17.8.3); and the \u201cGGSZ\u201d method (Giri, Gross-\nman, So\ufb00er, and Zupan, 2003b), which uses the Dalitz-\nplot distribution of the products of D decays to multi-\nbody self-conjugate \ufb01nal states, such as K0\nS\u03c0+\u03c0\u2212(Sec-\ntion 17.8.4). The main issue with these methods is the\nsmall overall branching fractions of the decays involved,\nwhich range from 5\u00d710\u22126 to 5\u00d710\u22129. Therefore a precise\ndetermination of \u03c63 requires a very large data sample. The\nvarious methods are combined in Section 17.8.6 to provide\na determination of \u03c63 from B Factory data. The study of\nthe time-dependent decay rates of B \u2192D(\u2217)\u2213h\u00b1, provid-\ning a measure of sin(2\u03c61 + \u03c63), is discussed separately in\nSection 17.8.5.\n17.8.2 GLW method\nIn the method proposed by Gronau and London (1991)\nand Gronau and Wyler (1991), the neutral D meson is\nreconstructed in decays to CP-even eigenstates such as\nK+K\u2212(denoted as DCP +) or CP-odd eigenstates such as\nK0\nS\u03c00 (DCP \u2212). Although a B0 may decay weakly to either\na D0 or to a D0, when looking for a CP-even decay product\none is actually selecting the CP-even superposition (D0 +\nD0)/\n\u221a\n2. The measurements are of the ratio\nRCP \u00b1 = 2\u0393(B\u2212\u2192DCP \u00b1K\u2212) + \u0393(B+\u2192DCP \u00b1K+)\n\u0393(B\u2212\u2192DfavK\u2212) + \u0393(B+\u2192DfavK+) ,\n(17.8.1)\nwhere Dfav indicates that the neutral D meson is re-\nconstructed in a favored hadronic decay mode such as\n\n346\nTable 17.8.1. Compilation of RCP and ACP results for CP-even and CP-odd D decay modes. The three horizontal blocks refer\nto B\u00b1 \u2192DK\u00b1 (top), B\u00b1 \u2192D\u2217K\u00b1 (center), and B\u00b1 \u2192DK\u2217\u00b1 (bottom).\nB decay\nBABAR\nBelle\nAverage\nB\u00b1 \u2192DK\u00b1\n(del Amo Sanchez, 2010e)\n(Trabelsi, 2013)\nRCP +\n1.18 \u00b1 0.09 \u00b1 0.05\n1.03 \u00b1 0.07 \u00b1 0.03\n1.08 \u00b1 0.06\nRCP \u2212\n1.03 \u00b1 0.09 \u00b1 0.04\n1.13 \u00b1 0.09 \u00b1 0.05\n1.08 \u00b1 0.07\nACP +\n+0.25 \u00b1 0.06 \u00b1 0.02\n+0.29 \u00b1 0.06 \u00b1 0.02 +0.27 \u00b1 0.04\nACP \u2212\n\u22120.08 \u00b1 0.07 \u00b1 0.02\n\u22120.12 \u00b1 0.06 \u00b1 0.01 \u22120.10 \u00b1 0.05\nB\u00b1 \u2192D\u2217K\u00b1\n(Aubert, 2008o)\n(Trabelsi, 2013)\nRCP +\n1.31 \u00b1 0.13 \u00b1 0.04\n1.19 \u00b1 0.13 \u00b1 0.03\n1.25 \u00b1 0.09\nRCP \u2212\n1.10 \u00b1 0.12 \u00b1 0.04\n1.03 \u00b1 0.13 \u00b1 0.03\n1.06 \u00b1 0.09\nACP +\n\u22120.11 \u00b1 0.09 \u00b1 0.01\n\u22120.14 \u00b1 0.10 \u00b1 0.01 \u22120.12 \u00b1 0.07\nACP \u2212\n+0.06 \u00b1 0.10 \u00b1 0.02\n+0.22 \u00b1 0.11 \u00b1 0.01 +0.13 \u00b1 0.07\nB\u00b1 \u2192DK\u2217\u00b1\n(Aubert, 2009t)\nRCP +\n2.17 \u00b1 0.35 \u00b1 0.09\n\u2212\n\u2212\nRCP \u2212\n1.03 \u00b1 0.27 \u00b1 0.13\n\u2212\n\u2212\nACP +\n+0.09 \u00b1 0.13 \u00b1 0.06\n\u2212\n\u2212\nACP \u2212\n\u22120.23 \u00b1 0.21 \u00b1 0.07\n\u2212\n\u2212\nD0 \u2192K\u2212\u03c0+, and ACP \u00b1, de\ufb01ned as\nACP \u00b1 = \u0393(B\u2212\u2192DCP \u00b1K\u2212) \u2212\u0393(B+\u2192DCP \u00b1K+)\n\u0393(B\u2212\u2192DCP \u00b1K\u2212) + \u0393(B+\u2192DCP \u00b1K+).\n(17.8.2)\nThese four observables can be expressed in terms of the\nphysics parameters \u03c63, \u03b4B, and rB,\nRCP \u00b1 =\n1 + r2\nB \u00b1 2rB cos \u03b4B cos \u03c63,\nACP \u00b1 =\n\u00b12rB sin \u03b4B sin \u03c63/RCP \u00b1.\n(17.8.3)\nE\ufb00ects due to interference would result in RCP \u00b1 \u0338= 1, while\nCP violation would show up as ACP \u00b1 \u0338= 0.\nBoth BABAR (Aubert, 2008o; del Amo Sanchez, 2010e)\nand Belle (Trabelsi, 2013) have reconstructed B\u2212\u2192DK\u2212\nand B\u2212\u2192D\u2217K\u2212decays with D\u2217\u2192D\u03c00 and D\u2217\u2192D\u03b3.\nThe data samples used by BABAR and Belle consist of 467\nand 772 \u00d7 106 BB pairs respectively for the B\u2212\u2192DK\u2212\ndecay, whereas 383 and 772 \u00d7 106 BB pairs are used re-\nspectively for the B\u2212\u2192D\u2217K\u2212decays. BABAR has also\nincluded the decay B\u2212\u2192DK\u2217\u2212with K\u2217\u2212\u2192K0\nS\u03c0\u2212(Au-\nbert, 2009t). For both experiments, the reconstructed CP-\neven \ufb01nal states are K+K\u2212and \u03c0+\u03c0\u2212, whereas the CP-\nodd eigenstates used by BABAR are K0\nS\u03c00, K0\nS\u03c9 (\u03c9 \u2192\n\u03c0+\u03c0\u2212\u03c00) and K0\nS\u03c6 (\u03c6 \u2192K+K\u2212); Belle uses K0\nS\u03c00 and\nK0\nS\u03b7. The K0\nS candidates are reconstructed through their\ndecays to charged pion pairs, while \u03b7 and \u03c00 mesons are\nidenti\ufb01ed through their decays to photon pairs.\nThe B decay \ufb01nal states are fully reconstructed,\nwith e\ufb03ciencies between 40% (for low-multiplicity, low-\nbackground decay modes, e.g. D \u2192K+K\u2212) and 5% (for\nhigh-multiplicity decays, e.g. D \u2192K0\nS\u03c9). The selection is\noptimized to maximize the \ufb01gure of merit S/\n\u221a\nS + B (an\nestimator of the statistical precision; Section 4.3), where\nthe numbers of expected signal (S) and background (B)\nevents are estimated from simulated and data control sam-\nples respectively. Signal B decays are distinguished from\nBB and continuum qq background by means of maximum\nlikelihood \ufb01ts to the energy-substituted invariant mass\nmES and/or the energy di\ufb00erence \u2206E, as described in Sec-\ntion 7.1.1. Additional continuum background discrimina-\ntion is in some cases achieved by including in the likelihood\na Fisher discriminant F for BABAR, or a non-linear neural\nnetwork NB for Belle, based on several event-shape quan-\ntities that distinguish nearly isotropic BB events from\nmore jet-like qq events and exploit the di\ufb00erent angu-\nlar correlations in the two event categories (Section 9.3).\nB\u2212\u2192D(\u2217)\u03c0\u2212decays, which are 12 times more abundant\nthan B\u2212\u2192D(\u2217)K\u2212and are expected to show negligible\nCP-violating e\ufb00ects (rB \u22480.01 in such decays), are distin-\nguished using charged hadron identi\ufb01cation variables and\n\u2206E, and are used as control samples.\nThe results are summarized in Table 17.8.1. The B\u00b1 \u2192\nDK\u00b1, D \u2192K0\nS\u03c6 results of BABAR are omitted here, as\nthey are included in the Dalitz B\u00b1 \u2192DK\u00b1, D \u2192K0\nSKK\nresult (Section 17.8.4). BABAR and Belle results are in\ngood agreement. The results are also compatible with ex-\npectations from Eqs (17.8.1) and (17.8.2) using the values\nof rB, \u03b4B, and \u03c63 measured with the Dalitz method (Sec-\ntion 17.8.4). Both experiments \ufb01nd evidence (> 3\u03c3 and\n> 4\u03c3, respectively) of direct CP violation in the B\u2212\u2192\nDCP +K\u2212decay (Figs 17.8.2 and 17.8.3). The combined\nresult has a signi\ufb01cance larger than 6\u03c3.\n\n347\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents / ( 0.01 GeV )\n0\n10\n20\n30\n40\n50\n60\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents / ( 0.01 GeV )\n0\n10\n20\n30\n40\n50\n60\n-\n DK\n\u2192\n -\nB\n,-\nK\n+\n K\n\u2192\nD \n-\u03c0\n+\n\u03c0 \n\u2192\nD \na)\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents / ( 0.01 GeV )\n0\n10\n20\n30\n40\n50\n60\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents / ( 0.01 GeV )\n0\n10\n20\n30\n40\n50\n60\n+\n DK\n\u2192\n \n+\nB\n,-\nK\n+\n K\n\u2192\nD \n-\u03c0\n+\n\u03c0 \n\u2192\nD \nb)\nFigure 17.8.2. \u2206E projections of the \ufb01ts to the B\u00b1 \u2192DCP +K\u00b1 candidates selected in the full BABAR data sample (Aubert,\n2008o), split into subsets of de\ufb01nite charge of the B candidate: a) B\u2212\u2192DCP +K\u2212, and b) B+ \u2192DCP +K+. The curves are\nthe full probability density function (solid, blue), and B\u00b1 \u2192D\u03c0\u00b1 (dash-dotted, green) stacked on the remaining backgrounds\n(dotted, purple). The region between the solid and the dash-dotted lines represents the B\u00b1 \u2192DK\u00b1 contribution. We show the\nsubset of the data sample in which the track from the B decay is identi\ufb01ed as a kaon and a signal-enriching selection is applied\nto the other variables used in the \ufb01t (mES and F).\n E (GeV)\n\u2206\n-0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3\nEvents / ( 0.008 GeV )\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n E (GeV)\n\u2206\n-0.1-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3\nEvents / ( 0.008 GeV )\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nFigure 17.8.3. \u2206E projections of the \ufb01ts to the B\u00b1 \u2192DCP +K\u00b1 candidates selected in the full Belle data sample (Trabelsi,\n2013), split into subsets of de\ufb01nite charge of the B candidate: (left) B\u2212\u2192DCP +K\u2212, and (right) B+ \u2192DCP +K+. The\ncurves are the full p.d.f. (solid, blue), B\u00b1 \u2192DK\u00b1 (dashed, red), B\u00b1 \u2192D\u03c0\u00b1 (dash-dotted, light blue), the charmless peaking\nbackground (dash-dot-dotted, magenta), the BB background (dash-dotted, green) and the remaining combinatorial background\n(dotted, blue).\n17.8.3 ADS method\nThis idea was extended further by Atwood, Dunietz, and\nSoni (1997, 2001), who showed that additional neutral D\ndecay modes, in particular DCS D decays, could also be\nused to measure \u03c63. For example, B\u2212\u2192[K+\u03c0\u2212]DK\u2212\ncan be reached via favored B\u2212\u2192D0K\u2212followed by DCS\nD0 \u2192K+\u03c0\u2212decay, or via suppressed B\u2212\u2192D0K\u2212fol-\nlowed by favored D0 \u2192K+\u03c0\u2212decay. In the case that the\nneutral D meson decays to a non-CP eigenstate, one also\nhas to consider the ratio of the magnitudes of the sup-\npressed and favored decays to the particular \ufb01nal state\n(rD) as well as the strong phase di\ufb00erence between them\n(\u03b4D). This information on the hadronic parameters of the\nD meson can be obtained from a charm factory (CLEO-c\nand BES III). Large CP violation e\ufb00ects are possible when\nthe overall ratio of magnitudes of amplitudes is close to\nunity (rD \u223crB). There is an e\ufb00ective strong phase shift of\n180\u25e6between the cases where a D\u2217is reconstructed in the\nD\u03c00 and D\u03b3 \ufb01nal states, which in principle allows \u03c63 to\nbe measured using the ADS technique with B\u00b1 \u2192D\u2217K\u00b1\nalone (Bondar and Gershon, 2004).\n17.8.3.1 B\u00b1 \u2192D(\u2217)K(\u2217)\u00b1, D \u2192K+\u03c0\u2212decays\nThe observables in this method are the charge-averaged\npartial decay width ratio\nRADS = \u0393(B\u2212\u2192[K+\u03c0\u2212]K\u2212) + \u0393(B+\u2192[K\u2212\u03c0+]K+)\n\u0393(B\u2212\u2192[K\u2212\u03c0+]K\u2212) + \u0393(B+\u2192[K+\u03c0\u2212]K+),\n(17.8.4)\nand the CP asymmetry\nAADS = \u0393(B\u2212\u2192[K+\u03c0\u2212]K\u2212) \u2212\u0393(B+\u2192[K\u2212\u03c0+]K+)\n\u0393(B\u2212\u2192[K+\u03c0\u2212]K\u2212) + \u0393(B+\u2192[K\u2212\u03c0+]K+).\n\n348\nTable 17.8.2. Compilation of RADS and AADS results for (from top to bottom) B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192D\u2217K\u00b1 with D\u2217\u2192D\u03c00\nand D\u03b3, and B\u00b1 \u2192DK\u2217\u00b1.\nB decay\nBABAR\nBelle\nAverage\nB\u00b1 \u2192DK\u00b1\n(del Amo Sanchez, 2010m)\n(Horii, 2011)\nRADS\n0.011 \u00b1 0.006 \u00b1 0.002\n0.0163+0.0044\n\u22120.0041\n+0.0007\n\u22120.0013 0.015 \u00b1 0.004\nAADS\n\u22120.86 \u00b1 0.47+0.12\n\u22120.16\n\u22120.39+0.26\n\u22120.28\n+0.04\n\u22120.03\n\u22120.51 \u00b1 0.25\nB\u00b1 \u2192D\u2217[D\u03c00]K\u00b1\n(del Amo Sanchez, 2010m)\n(Trabelsi, 2013)\nRADS\n0.018 \u00b1 0.009 \u00b1 0.004\n0.010+0.008\n\u22120.007\n+0.001\n\u22120.002\n0.013 \u00b1 0.006\nAADS\n+0.77 \u00b1 0.35 \u00b1 0.12\n+0.4+1.1\n\u22120.7\n+0.2\n\u22120.1\n+0.72 \u00b1 0.34\nB\u00b1 \u2192D\u2217[D\u03b3]K\u00b1\n(del Amo Sanchez, 2010m)\n(Trabelsi, 2013)\nRADS\n0.013 \u00b1 0.014 \u00b1 0.008\n0.036+0.014\n\u22120.012 \u00b1 0.002\n0.027 \u00b1 0.010\nAADS\n+0.36 \u00b1 0.94+0.25\n\u22120.41\n\u22120.51+0.33\n\u22120.29 \u00b1 0.08\n\u22120.43 \u00b1 0.31\nB\u00b1 \u2192DK\u2217\u00b1\n(Aubert, 2009t)\nRADS\n0.066 \u00b1 0.031 \u00b1 0.010\n\u2212\n\u2212\nAADS\n\u22120.34 \u00b1 0.43 \u00b1 0.16\n\u2212\n\u2212\n(17.8.5)\nIn terms of physics parameters, these can be written as\nRADS = r2\nB + r2\nD + 2rBrD cos(\u03b4B + \u03b4D) cos \u03c63,\nAADS = 2rBrD sin(\u03b4B + \u03b4D) sin \u03c63/RADS.\n(17.8.6)\nThe original and \ufb01rst objective for these analyses was to\nobserve RADS \u0338= 0.\nBoth\nBABAR\n(del\nAmo\nSanchez,\n2010m)\nand\nBelle (Horii, 2011) have reconstructed the decays B\u2212\u2192\nDK\u2212and B\u2212\u2192D\u2217K\u2212with D\u2217\u2192D\u03c00 and D\u2217\u2192\nD\u03b3 (del Amo Sanchez, 2010m; Trabelsi, 2013) followed\nby D \u2192K+\u03c0\u2212on datasets of 467 and 772 \u00d7 106 BB\npairs respectively. BABAR (Aubert, 2009t) has also se-\nlected B\u2212\u2192DK\u2217\u2212with K\u2217\u2212\u2192K0\nS\u03c0\u2212using 379 \u00d7 106\nBB pairs. As in the GLW analysis, the B decay \ufb01nal states\nare fully reconstructed. The selection criteria are usually\ntighter in order to achieve a higher signal purity, given\nthat the signal rate is typically O(10\u22122) weaker than in\nthe case of D decaying to CP eigenstates. Particular care\nis taken over the suppression of \u201cpeaking\u201d backgrounds\nfrom misidenti\ufb01ed B\u2212\u2192D(\u2217)\u03c0\u2212or B\u2212\u2192D(\u2217)K\u2212de-\ncays. After the selection, the main background is due to qq\nevents. In order to achieve a better continuum background\nsuppression, a non-linear neural network (Section 4.4.4),\nNN (BABAR) or NB (Belle), of several event-shape quan-\ntities (Section 9.3) is used. The \ufb01nal yields are extracted\nfrom maximum likelihood \ufb01ts to mES and NN (BABAR)\nor \u2206E and NB (Belle) for B\u2212\u2192D(\u2217)K\u2212, and to mES\n(after a tight selection criteria on NN) for B\u2212\u2192DK\u2217\u2212\n(BABAR).\nThese results are summarized in Table 17.8.2. The\nstrongest evidence for suppressed signals have been re-\nported by Belle with a signi\ufb01cance (including systematic\nuncertainties) of 4.1\u03c3 for the B\u2212\u2192DK\u2212mode and of\n3.5\u03c3 for the B\u2212\u2192D\u2217[D\u03b3]K\u2212decay (Fig. 17.8.4).\nThe observables R+ and R\u2212, de\ufb01ned as\nR+ = \u0393(B+\u2192[K\u2212\u03c0+]K+)/\u0393(B+\u2192[K+\u03c0\u2212]K+),\nR\u2212= \u0393(B\u2212\u2192[K+\u03c0\u2212]K\u2212)/\u0393(B\u2212\u2192[K\u2212\u03c0+]K\u2212),\n(17.8.7)\nhave been noted recently as more suitable to use than\nRADS and AADS, since the former are better behaved.\nThey are statistically independent observables, while the\nuncertainty on AADS depends on the central value of RADS.\nR+ and R\u2212are related to RADS and AADS by\nRADS = (R+ + R\u2212)/2,\nAADS = (R\u2212\u2212R+)/(R\u2212+ R+).\n(17.8.8)\nRecent BABAR B\u2212\u2192D(\u2217)K\u2212measurements have been\nreported in terms of R+ and R\u2212(Table 17.8.3), as well as\nRADS, AADS (Table 17.8.2).\nTable 17.8.3. Compilation of R+ and R\u2212results reported by\nBABAR for B\u00b1 \u2192DK\u00b1 and B\u00b1 \u2192D\u2217K\u00b1, with D\u2217\u2192D\u03c00\nand D\u03b3 (del Amo Sanchez, 2010m).\nR+ (10\u22122)\nR\u2212(10\u22122)\nB\u00b1 \u2192DK\u00b1\n2.2 \u00b1 0.9 \u00b1 0.3 0.2 \u00b1 0.6 \u00b1 0.2\nB\u00b1 \u2192D\u2217[D\u03c00]K\u00b1 0.5 \u00b1 0.8 \u00b1 0.3 3.7 \u00b1 1.8 \u00b1 0.9\nB\u00b1 \u2192D\u2217[D\u03b3]K\u00b1\n0.9 \u00b1 1.6 \u00b1 0.7 1.9 \u00b1 2.3 \u00b1 1.2\n17.8.3.2 B\u00b1 \u2192DK\u00b1, D \u2192K+\u03c0\u2212\u03c00 decay\nBABAR has also presented ADS results for the D \u2192\nK+\u03c0\u2212\u03c00 decay, quoting a measurement of R+ and R\u2212\n\n349\nE (GeV)\n6\n-0.1\n0\n0.1\n0.2\n0.3\nEvents / 10 MeV\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nE (GeV)\n6\n-0.1\n0\n0.1\n0.2\n0.3\nEvents / 10 MeV\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nNB\n-0.5\n0\n0.5\n1\nEvents / 0.04\n0\n10\n20\n30\n40\n50\nNB\n-0.5\n0\n0.5\n1\nEvents / 0.04\n0\n10\n20\n30\n40\n50\n(a) B\u2212\u2192DK\u2212, D \u2192K+\u03c0\u2212\nE (GeV)\n6\n-0.1\n0\n0.1\n0.2\n0.3\nEvents / 20 MeV\n0\n5\n10\n15\n20\nE (GeV)\n6\n-0.1\n0\n0.1\n0.2\n0.3\nEvents / 20 MeV\n0\n5\n10\n15\n20\nNB\u2019\n-10\n-5\n0\n5\n10\n15\nEvents / 1\n0\n5\n10\n15\n20\n25\n30\n35\nNB\u2019\n-10\n-5\n0\n5\n10\n15\nEvents / 1\n0\n5\n10\n15\n20\n25\n30\n35\n(b) B\u2212\u2192D\u2217K\u2212, D\u2217\u2192D\u03b3, and D \u2192K+\u03c0\u2212\nFigure 17.8.4. \u2206E and neural-network NB (or NB\u2032, a modi\ufb01ed NB variable) distributions in a signal-enriched region for\nB\u2212\u2192DK\u2212where D \u2192K+\u03c0\u2212(top; Horii, 2011) and for B\u2212\u2192D\u2217K\u2212where D\u2217\u2192D\u03b3 and D \u2192K+\u03c0\u2212(bottom;\nTrabelsi, 2013) from the Belle collaboration. In these plots, DK\u2212components are shown by thicker dashed curves (red), and\nD\u03c0\u2212components are shown by thinner curves (magenta). BB backgrounds are shown by dash-dotted curves (green) while qq\nbackgrounds are shown by dotted curves (blue). The sum of all components are shown by solid curves (black).\non a data sample of 474 \u00d7 106 BB pairs (Lees, 2011h).\nThe relation between R\u00b1 and the physics parameters is\nsimilar to the two-body case:\nR+ = r2\nB + r2\nD + 2rBrDkD cos(\u03b4B + \u03b4D + \u03c63),\nR\u2212= r2\nB + r2\nD + 2rBrDkD cos(\u03b4B + \u03b4D \u2212\u03c63),\n(17.8.9)\nwith\nr2\nD = \u0393(D0 \u2192f)\n\u0393\n\u0000D0 \u2192f\n\u0001 =\nR\ndmA2\nDCS(m)\nR\ndmA2\nCF (m) ,\nkDei\u03b4D =\nR\ndmADCS(m)ACF (m)ei\u03b4(m)\nqR\ndmA2\nDCS(m)A2\nCF (m)\n,\n(17.8.10)\nwhere ACF (m) and ADCS(m) are the magnitude of the\nCF and the DCS D \u2192K\u2213\u03c0\u00b1\u03c00 amplitudes, respectively,\n\u03b4(m) is the relative strong phase, and m indicates the\nposition in the D decay Dalitz plot of squared invariant\nmasses (m2\nK\u03c0, m2\nK\u03c00) (Atwood and A. Soni, 2003). The\nparameter kD is called the coherence factor and takes a\nvalue in the interval [0,1] depending on the Dalitz struc-\nture of the decay. Both kD and \u03b4D have been measured\nby the CLEO-c collaboration, who \ufb01nd kD = 0.84 \u00b1 0.07\nand \u03b4D = (47+14\n\u221217)\u25e6(Lowrey et al., 2009). The ratio rD\nhas been measured in di\ufb00erent experiments with an aver-\nage value r2\nD = (2.2 \u00b1 0.1) \u00d7 10\u22123 (Beringer et al., 2012).\nBABAR found\nR+ =\n\u00005+12 +1\n\u221210 \u22124\n\u0001\n\u00d7 10\u22123 ,\nR\u2212=\n\u000012+12 +2\n\u221210 \u22124\n\u0001\n\u00d7 10\u22123 .\n(17.8.11)\nFrom these measurements a limit of rB < 0.13 at the 90%\ncon\ufb01dence level (C.L.) is obtained.\n17.8.3.3 B0 \u2192DK\u22170, D \u2192K+\u03c0\u2212decay\nBABAR and Belle have also performed an ADS analysis\nof neutral B0 \u2192DK\u22170, with K\u22170 \u2192K+\u03c0\u2212decays. In\nthese modes, the \ufb02avor of the K\u2217unambiguously deter-\nmines the \ufb02avor of the neutral B so no time-dependent\nmeasurement is needed. Here rB is expected to be ap-\nproximately 0.3, due to CKM factors only, since both\n\n350\nthe interfering amplitudes are color-suppressed. The CF\ncharge-conjugate \ufb01nal states are used as normalization\nand control samples. BABAR (Aubert, 2009al) uses a sam-\nple of 465 \u00d7 106 BB pairs and reconstructs the neutral\nD mesons in the following DCS D0 \ufb01nal states: K+\u03c0\u2212,\nK+\u03c0\u2212\u03c00, and K+\u03c0\u2212\u03c0\u2212\u03c0+. Signal yields are extracted\nfrom \ufb01ts to the mES distribution of the selected candi-\ndates. Due to the small size of the \ufb01nal sample after the\nselection (24 signal candidates in total for all D0 \ufb01nal\nstates), the CP asymmetries AADS have not been mea-\nsured. Instead, 95% C.L. limits on RADS have been set:\nRK\u03c0\nADS < 0.244; RK\u03c0\u03c00\nADS < 0.181; RK\u03c0\u03c0\u03c0\nADS < 0.391. From the\ncombination of these three results the ratio between the\nb \u2192u and the b \u2192c mediated decay amplitudes has been\nestimated to be 0.07 < rB < 0.41 at the 95% con\ufb01dence\nlevel. Belle (Negishi, 2012), with a sample of 772\u00d7106 BB\npairs, reconstructs only the neutral D mesons in the DCS\nD0 \ufb01nal state K+\u03c0\u2212. No signal is found and the most\nstringent limit to date is set, RK\u03c0\nADS < 0.16 at the 95%\ncon\ufb01dence level.\n17.8.4 Dalitz plot (GGSZ) method\nThe measurement of \u03c63 using Dalitz plot analysis of three-\nbody decays of the D meson from the B\u00b1 \u2192DK\u00b1 pro-\ncess was proposed by Giri, Grossman, So\ufb00er, and Zupan\n(2003a) (and is therefore often referred to as the GGSZ\nmethod) and independently by Bondar (2002). The basic\nidea behind this method is to use \ufb01nal states accessible to\nboth D0 and D0 and to measure the phase of the inter-\nference between them in the decay of D mesons produced\nin B\u00b1 \u2192DK\u00b1 transitions.\nThe most convenient decay for this kind of measure-\nment is D \u2192K0\nS\u03c0+\u03c0\u2212. This mode has a unique combina-\ntion of three advantages:\n1. Large branching fraction.\n2. Signi\ufb01cant overlap between D0 \u2192K0\nS\u03c0+\u03c0\u2212and D0 \u2192\nK0\nS\u03c0+\u03c0\u2212amplitudes which gives a large interference\nterm sensitive to \u03c63.\n3. Rich resonant structure which provides large variations\nof the strong phase in D decay and results in sensitivity\nto \u03c63 that is only weakly dependent on the values of\n\u03c63 and strong phase \u03b4B.\nHowever, other decay modes can also be used. D0 \u2192\nK0\nSK+K\u2212is another convenient mode which has a smaller\nbranching ratio than D0 \u2192K0\nS\u03c0+\u03c0\u2212, but is generally\ncleaner due to the presence of two kaons. The mode D0 \u2192\n\u03c0+\u03c0\u2212\u03c00 has a comparable rate, but is more a\ufb00ected by\nthe background. Modes that are not self-conjugate, such\nas K+\u03c0\u2212\u03c00, can also be used: this requires two ampli-\ntudes, D0 \u2192K+\u03c0\u2212\u03c00 and D0 \u2192K+\u03c0\u2212\u03c00, to be studied\nseparately. However, given the large coherence factor in\nthis mode (Lowrey et al., 2009), there would be little to\ngain from a GGSZ-like approach. The description of the\ntechnique below uses the mode D \u2192K0\nS\u03c0+\u03c0\u2212as an ex-\nample.\nThe amplitude of the B+ \u2192DK+ decay as a func-\ntion of the two D Dalitz plot variables m2\n+ \u2261m2\nK0\nS\u03c0+ and\nm2\n\u2212\u2261m2\nK0\nS\u03c0\u2212is\nAB+(m2\n+, m2\n\u2212) = AD + rBei(\u03b4B+\u03c63)AD ,\n(17.8.12)\nwhere AD = AD(m2\n+, m2\n\u2212) is the complex amplitude of\nD0 \u2192K0\nS\u03c0+\u03c0\u2212decay, and AD = AD(m2\n+, m2\n\u2212) is the\namplitude of D0 \u2192K0\nS\u03c0+\u03c0\u2212decay. Similarly, for B\u2212\u2192\nDK\u2212decay, the amplitude is\nAB\u2212(m2\n+, m2\n\u2212) = AD + rBei(\u03b4B\u2212\u03c63)AD .\n(17.8.13)\nIn the case of CP conservation in D0 decay and neglecting\nD0 \u2212D0 mixing (as the mixing parameters x, y are 1%\nor less; see the text on D-mixing and CP violation in Sec-\ntion 19.2), AD(m2\n+, m2\n\u2212) = AD(m2\n\u2212, m2\n+). The unknown\nquantities \u03c63, rB, and \u03b4B can be obtained from a \ufb01t to\nthe D-decay Dalitz distributions for B\u00b1 \u2192DK\u00b1 decays\nonce the complex amplitude AD is known.\nAlthough the original proposal of Giri et al. was to use\na binned analysis, in the case of limited statistics an un-\nbinned \ufb01t is used in order to optimally extract information\nfrom the data, at the price of introducing model depen-\ndence. Section 17.8.4.1 describes the unbinned analyses\nusing D0 \u2192K0\nS\u03c0+\u03c0\u2212performed by Belle and BABAR.\nOther decay modes studied by BABAR are presented in\nSection 17.8.4.2. A binned approach used by Belle has its\nown advantages, and is discussed in Section 17.8.4.3.\n17.8.4.1 Model-dependent technique\nMeasurements of \u03c63 using the model-dependent unbinned\nDalitz plot analysis technique have been performed by\nBelle (Poluektov, 2004, 2006, 2010) and BABAR (Aubert,\n2005o, 2008l; del Amo Sanchez, 2010b), their latest anal-\nyses using 657 and 468\u00d7106 BB pairs, respectively. Both\nexperiments use B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192D\u2217K\u00b1 (with D\u2217\u2192\nD\u03c00 and D\u2217\u2192D\u03b3) and B\u00b1 \u2192DK\u2217\u00b1 with K\u2217\u00b1 \u2192\nK0\nS\u03c0\u00b1 decays. While Belle reconstructs the neutral D in\nthe K0\nS\u03c0+\u03c0\u2212\ufb01nal state, BABAR uses both the K0\nS\u03c0+\u03c0\u2212\nand K0\nSK+K\u2212\ufb01nal states.\nThis method requires a model to describe the am-\nplitude as a function of the Dalitz plot variables. Both\ncollaborations use D\u2217+ \u2192D0\u03c0+ and D\u2217\u2212\u2192D0\u03c0\u2212de-\ncays to \ufb02avor-tag D0 and D0 mesons, and \ufb01t the neutral\nD decay amplitude in the resulting sample. The Dalitz\nplots obtained by BABAR for D0 \u2192K0\nS\u03c0+\u03c0\u2212and D0 \u2192\nK0\nSK+K\u2212decays are shown in Fig. 17.8.5 (del Amo San-\nchez, 2010b,f).\nD decay amplitudes\nThe description of amplitudes di\ufb00ers in the Belle and\nBABAR analyses. Belle uses an isobar model for S-, P-,\nand D-waves in their D0 \u2192K0\nS\u03c0+\u03c0\u2212analysis in each of\nthe K0\nS\u03c0+, K0\nS\u03c0\u2212, and \u03c0+\u03c0\u2212channels, and a \ufb02at non-\nresonant term. The isobar model involves describing am-\nplitudes with relativistic Breit-Wigner (BW) propagators,\n\n351\n) \n4\n/c\n2\n (GeV\n-s\n1\n2\n3\n) \n4\n/c\n2\n (GeV\n+\ns\n1\n2\n3\n1\n10\n2\n10\n3\n10\na)\n) \n4\n/c\n2\n (GeV\n+\ns\n1\n1.2\n1.4\n1.6\n1.8\n) \n4\n/c\n2\n (GeV\n0\ns\n1\n1.2\n1.4\n1.6\n1.8\n1\n10\n2\n10\nb)\nFigure 17.8.5. BABAR Dalitz plots of (a) D0 \u2192K0\nS\u03c0+\u03c0\u2212and (b) D0 \u2192K0\nSK+K\u2212decays (del Amo Sanchez, 2010b,f), where\ns\u00b1 \u2261m2\n\u00b1 \u2261m2\nK0\nSh\u00b1 and s0 \u2261m2\nh+h\u2212, with h = \u03c0, K.\nTable 17.8.4. Belle \ufb01t results for the D0 \u2192K0\nS\u03c0+\u03c0\u2212decay (Poluektov, 2010). Errors are statistical only. The phases are given\nin the interval [0, 360]\u25e6. The \ufb01t fraction for each mode is de\ufb01ned as the ratio of the integrals of the square absolute value of\nthe amplitude for that mode and the squared absolute value of the total amplitude. The \ufb01t fractions do not sum to one due to\ninterference e\ufb00ects.\nIntermediate state\nAmplitude\nPhase (\u25e6)\nFit fraction (%)\nK0\nS\u03c31\n1.56 \u00b1 0.06\n214 \u00b1 3\n11.0 \u00b1 0.7\nK0\nSf0(980)\n0.385 \u00b1 0.006\n207.3 \u00b1 2.3\n4.72 \u00b1 0.05\nK0\nS\u03c32\n0.20 \u00b1 0.02\n212 \u00b1 12\n0.54 \u00b1 0.10\nK0\nSf0(1370)\n1.56 \u00b1 0.12\n110 \u00b1 4\n1.9 \u00b1 0.3\nK0\nS\u03c1(770)0\n1.0 (\ufb01xed)\n0 (\ufb01xed)\n21.2 \u00b1 0.5\nK0\nS\u03c9(782)\n0.0343 \u00b1 0.0008\n112.0 \u00b1 1.3\n0.526 \u00b1 0.014\nK0\nSf2(1270)\n1.44 \u00b1 0.04\n342.9 \u00b1 1.7\n1.82 \u00b1 0.05\nK0\nS\u03c10(1450)\n0.49 \u00b1 0.08\n64 \u00b1 11\n0.11 \u00b1 0.04\nK\u2217\n0(1430)\u2212\u03c0+\n2.21 \u00b1 0.04\n358.9 \u00b1 1.1\n7.93 \u00b1 0.09\nK\u2217\n0(1430)+\u03c0\u2212\n0.36 \u00b1 0.03\n87 \u00b1 4\n0.22 \u00b1 0.04\nK\u2217(892)\u2212\u03c0+\n1.638 \u00b1 0.010\n133.2 \u00b1 0.4\n62.9 \u00b1 0.8\nK\u2217(892)+\u03c0\u2212\n0.149 \u00b1 0.004\n325.4 \u00b1 1.3\n0.526 \u00b1 0.016\nK\u2217(1410)\u2212\u03c0+\n0.65 \u00b1 0.05\n120 \u00b1 4\n0.49 \u00b1 0.07\nK\u2217(1410)+\u03c0\u2212\n0.42 \u00b1 0.04\n253 \u00b1 5\n0.21 \u00b1 0.03\nK\u2217\n2(1430)\u2212\u03c0+\n0.89 \u00b1 0.03\n314.8 \u00b1 1.1\n1.40 \u00b1 0.06\nK\u2217\n2(1430)+\u03c0\u2212\n0.23 \u00b1 0.02\n275 \u00b1 6\n0.093 \u00b1 0.014\nK\u2217(1680)\u2212\u03c0+\n0.88 \u00b1 0.27\n82 \u00b1 17\n0.06 \u00b1 0.04\nK\u2217(1680)+\u03c0\u2212\n2.1 \u00b1 0.2\n130 \u00b1 6\n0.30 \u00b1 0.07\nnon-resonant\n2.7 \u00b1 0.3\n160 \u00b1 5\n5.0 \u00b1 1.0\nor Gounaris-Sakurai in the case of \u03c10 \u2192\u03c0+\u03c0\u2212, with Blatt-\nWeisskopf centrifugal factors and angular terms (see the\nIsobar formalism text in Section 13.2.1). The resonance\ncomposition measured by Belle is shown in Table 17.8.4.\nNote that \u03c31 and \u03c32 states, with masses and widths al-\nlowed to vary in the \ufb01t, are introduced as an e\ufb00ective\ndescription of structure in the \u03c0\u03c0 S-wave.\nBABAR, in contrast, uses the K-matrix formalism with\nthe P-vector approximation to describe the \u03c0+\u03c0\u2212S-wave,\nwhile the K\u03c0 S-wave description uses a BW for the\nK\u2217\n0(1430)\u00b1 state and a non-resonant contribution param-\neterized by a scattering length and e\ufb00ective range, as de-\nscribed in Section 13.2.2. The resonance composition, P-\nvector, and K\u03c0 S-wave parameters measured by BABAR\nare shown in Table 17.8.5.\n\n352\nTable 17.8.5. BABAR \ufb01t results for the D0 \u2192K0\nS\u03c0+\u03c0\u2212decay (del Amo Sanchez, 2010b,f). Errors are statistical only. The phases\nare given in the interval [\u2212\u03c0, +\u03c0] rad. The description of the \u03c0\u03c0 and K\u03c0 S-wave parameters can be found in Section 13.2.2;\nwe follow the notation of that section. The \u03c0\u03c0 S-wave parameters \u03b25, f prod\n14\n, and f prod\n15\nare \ufb01xed to zero due to the lack of\nsensitivity. We report the mass and the width of the K\u2217(892)\u00b1 resonance, which are also determined.\nIntermediate state or component\nParameter value\nFit fraction (%)\nAmplitude\nPhase (rad)\n\u03c0\u03c0 S-wave\n15.4\n\u03b21\n5.54 \u00b1 0.06\n\u22120.054 \u00b1 0.007\n\u03b22\n15.64 \u00b1 0.06\n\u22123.125 \u00b1 0.005\n\u03b23\n44.6 \u00b1 1.2\n+2.731 \u00b1 0.015\n\u03b24\n9.3 \u00b1 0.2\n+2.30 \u00b1 0.02\nf prod\n11\n11.43 \u00b1 0.11\n\u22120.005 \u00b1 0.009\nf prod\n12\n15.5 \u00b1 0.4\n\u22121.13 \u00b1 0.02\nf prod\n13\n7.0 \u00b1 0.7\n+0.99 \u00b1 0.11\nsprod\n0\n\u22123.92637\nK0\nS modes\nK0\nS\u03c1(770)0\n1\n0\n21.1\nK0\nS\u03c9(782)\n0.0420 \u00b1 0.0006\n+2.046 \u00b1 0.014\n0.6\nK0\nSf2(1270)\n0.410 \u00b1 0.013\n+2.88 \u00b1 0.03\n0.3\nK\u03c0 S-wave\nK\u2217\n0(1430)\u2212\u03c0+\n2.650 \u00b1 0.015\n+1.497 \u00b1 0.007\n6.1\nK\u2217\n0(1430)+\u03c0\u2212\n0.145 \u00b1 0.014\n+1.78 \u00b1 0.10\n< 0.1\nMK\u2217\n0 (1430) (MeV/c2)\n1421.5 \u00b1 1.6\n\u0393K\u2217\n0 (1430) (MeV/c2)\n247 \u00b1 3\nB\n0.62 \u00b1 0.04\n\u03c6B (rad)\n\u22120.100 \u00b1 0.010\nR\n1\n\u03c6R (rad)\n+ 1.10 \u00b1 0.02\na ([GeV/c]\u22121)\n0.224 \u00b1 0.003\nr ([GeV/c]\u22121)\n\u221215.01 \u00b1 0.13\nK\u2217modes\nK\u2217(892)\u2212\u03c0+\n1.735 \u00b1 0.005\n+2.331 \u00b1 0.004\n57.0\nK\u2217(892)+\u03c0\u2212\n0.164 \u00b1 0.003\n\u22120.768 \u00b1 0.019\n0.6\nK\u2217\n2(1430)\u2212\u03c0+\n1.303 \u00b1 0.013\n+2.498 \u00b1 0.012\n1.9\nK\u2217\n2(1430)+\u03c0\u2212\n0.115 \u00b1 0.013\n+2.69 \u00b1 0.11\n< 0.1\nK\u2217(1680)\u2212\u03c0+\n0.90 \u00b1 0.03\n\u22122.97 \u00b1 0.04\n0.3\nK\u2217(892) parameters\nMK\u2217(892) (MeV/c2)\n893.70 \u00b1 0.07\n\u0393K\u2217(892) (MeV/c2)\n46.74 \u00b1 0.15\nThe description of the D0 \u2192K0\nSK+K\u2212decay am-\nplitude adopted by BABAR is based on an isobar model\ncontaining \ufb01ve distinct resonances leading to 8 two-body\ndecays (see Table 17.8.6). The \u03c6(1020) resonance is de-\nscribed using a relativistic BW, with mass and width al-\nlowed to vary in the \ufb01t in order to account for mass res-\nolution e\ufb00ects. The use of this approach, rather than the\ntechnically challenging convolution of the relativistic BW\nwith a Gaussian-like resolution function, has been stud-\nied with simulated data and shown to have a negligible\nsystematic e\ufb00ect. Since the a0(980) resonance has a mass\nvery close to the KK threshold and decays mostly to \u03b7\u03c0,\nit is described using a coupled channel BW, as described\nin Section 13.2.1, where the pole mass and coupling con-\nstant to \u03b7\u03c0 are taken from Abele et al. (1998), and the\ncoupling constant to KK, gKK, is directly obtained from\nthe \ufb01t.\nBoth experiments estimate the quality of their am-\nplitude models using \u03c72 tests. BABAR employs a two-\ndimensional adaptive binning that requires at least 30 ob-\nserved events per bin, obtaining \u03c72/ndof = 1.21 for 8585\ndegrees of freedom (dof) for D0 \u2192K0\nS\u03c0+\u03c0\u2212, and 1.28 for\n1178 dof for D0 \u2192K0\nSK+K\u2212. Belle divides the region\nbounded by m2\n\u00b1 = 0.3 and 3.0 GeV2/c4 into 54 \u00d7 54 bins;\nbins with an expected population of less than 50 events are\nthen combined with adjacent ones, \ufb01nding \u03c72/ndof = 2.35\n\n353\nTable 17.8.6.\nBABAR \ufb01t results for the D0 \u2192K0\nSK+K\u2212decay (del Amo Sanchez, 2010b,f). Errors are statistical only. The\nphases are given in the interval [\u2212\u03c0, +\u03c0] rad. We also report the mass and the width of the \u03c6(1020) resonance, and the a0(980)\ncoupling constant to KK introduced in Section 13.2.2, as determined from the \ufb01t.\nIntermediate state or component\nParameter value\nFit fraction (%)\nAmplitude\nPhase (rad)\nK0\nSa0(980)0\n1\n0\n51.8\na0(980)+K\u2212\n0.635 \u00b1 0.006\n\u22122.91 \u00b1 0.02\n19.5\na0(980)\u2212K+\n0.125 \u00b1 0.008\n+2.47 \u00b1 0.04\n0.7\nK0\nSf0(1370)\n0.16 \u00b1 0.05\n+0.2 \u00b1 0.2\n1.7\nK0\nSa0(1450)0\n0.83 \u00b1 0.10\n\u22121.93 \u00b1 0.12\n19.3\na0(1450)+K\u2212\n0.93 \u00b1 0.03\n+1.66 \u00b1 0.07\n25.6\nK0\nS\u03c6(1020)\n0.2313 \u00b1 0.0011\n\u22120.977 \u00b1 0.008\n44.1\nK0\nSf2(1270)\n0.385 \u00b1 0.015\n+0.06 \u00b1 0.04\n0.7\n\u03c6(1020) and a0(980) parameters\nM\u03c6(1020) (MeV/c2)\n1019.55 \u00b1 0.02\n\u0393\u03c6(1020) (MeV/c2)\n4.60 \u00b1 0.04\ngKK (MeV/c2)\n537 \u00b1 9\nfor 1065 dof. The values are large, but both experiments\n\ufb01nd that the main features of the Dalitz plot are well\nreproduced, with some signi\ufb01cant but numerically small\ndiscrepancies at the peaks and dips of the distribution,\nwhich are used later to assign systematic uncertainties.\nBABAR has estimated that most of their excess in \u03c72/ndof,\n\u2206\u03c72/ndof \u22480.16, arises from imperfections in modeling\nexperimental e\ufb00ects \u2014 mostly e\ufb03ciency variations at the\nboundaries of the Dalitz plot, and invariant mass resolu-\ntion \u2014 rather than the amplitude model (Aubert, 2008l).\nSelection of B decays\nEvent selection for B\u00b1 \u2192D(\u2217)K(\u2217)\u00b1 decays is performed\nusing the mES and \u2206E variables. Additional suppression\nof background from e+e\u2212\u2192qq (q = u, d, s, c) events is\nprovided by using cos \u03b8T, where \u03b8T is the angle between\nthe thrust axes of the B signal candidate and the rest of\nthe event, and a Fisher discriminant F combining 11 pa-\nrameters that describe the momentum \ufb02ow in the event\nrelative to the B thrust axis (Belle; see Section 9.3) or\ncombining the monomials L0, L2, and the variables cos \u03b8S\nand cos \u03b8B (BABAR; see Sections 9.3 and 9.4). All topolog-\nical variables are optimized to separate continuum events\nfrom signal.\nThe \ufb01t of the event distributions di\ufb00ers for the two\ncollaborations. In the Belle approach, the \ufb01t is performed\nin two stages. At the \ufb01rst stage, the distributions of the\nevent selection variables (mES, \u2206E, cos \u03b8T, and F, shown\nin Fig. 17.8.6, top row, for B\u00b1 \u2192DK\u00b1 decays) are \ufb01tted\nto obtain the relative fractions of signal and backgrounds.\nIn the second stage, the Dalitz plot \ufb01t is performed (sepa-\nrately for B+ and B\u2212data) with the event-by-event back-\nground fractions based on the information obtained at\nthe \ufb01rst stage. BABAR uses a simultaneous combined \ufb01t\nto mES, \u2206E, F, shown in Fig. 17.8.6 (bottom row) for\nB\u00b1 \u2192DK\u00b1, D \u2192K0\nSK+K\u2212decays, and to the Dalitz\nplot variables. The signal event yields and purities ob-\ntained by the two experiments, in signal-enriched regions,\nare given in Table 17.8.7. While Belle has a larger sam-\nple of BB pairs, the \ufb01nal signal yields from BABAR are\nlarger. This di\ufb00erence in D0 \u2192K0\nS\u03c0+\u03c0\u2212reconstruction\ne\ufb03ciencies between the two experiments is mostly due to\nthe enhanced tracking performance of BABAR for high-\nmultiplicity (low pT ) events, re\ufb02ecting di\ufb00erences in their\nlow momentum pattern recognition and the silicon detec-\ntor. As discussed in Section 2.2.1, the BABAR SVT per-\nforms stand-alone e\ufb03cient low-momentum tracking, while\nthe Belle SVD is employed to extrapolate tracks recon-\nstructed in the CDC to the interaction region.\nFit results\nInstead of directly using the physical observables, both\nanalyses use Cartesian variables\nz\u00b1 = x\u00b1 + iy\u00b1,\n(17.8.14)\n\ufb01rst proposed in Aubert (2005o), which are expressed in\nterms of the physical observables as\nz\u00b1 = rB exp[i(\u03b4B \u00b1 \u03c63)].\n(17.8.15)\nThese observables have better statistical behavior (small\ncorrelation, minimal dependence of their uncertainties on\nthe actual values) and allow for easier combination of sev-\neral measurements into a single result. The obvious disad-\nvantage is the necessary conversion required to obtain the\nvalues of \u03c63 and other related quantities. The strong phase\nin the D\u2217\u2192D\u03c00 and D\u2217\u2192D\u03b3 modes di\ufb00ers by 180\u25e6,\nthus the observables x\u2217\n\u00b1 and y\u2217\n\u00b1 for B\u00b1 \u2192D\u2217K\u00b1 have\nopposite sign (Bondar and Gershon, 2004). For B\u00b1 \u2192\nDK\u2217\u00b1 decays, following the suggestion in Gronau (2003),\n\n354\n0\n25\n50\n75\n100\n125\n150\n175\n200\n5.22\n5.24\n5.26\n5.28\n5.3\nMbc (GeV/c2)\nEntries/2 MeV/c2\nSignal\nuds\ncharm\nBBbar\nB\u2192D\u03c0\n0\n20\n40\n60\n80\n100\n120\n-0.1\n0\n0.1\n\u2206E (GeV)\nEntries/5 MeV\n0\n50\n100\n150\n200\n250\n-5\n0\n5\nFisher discr.\nEntries/0.3\nSignal\nBBbar\nCharm\nuds\n)\n2\n (GeV/c\nES\nm\n5.2\n5.25\n2\nEvents/2.25 MeV/c\n0\n20\n40\n60\n)\n2\n (GeV/c\nES\nm\n5.2\n5.25\n2\nEvents/2.25 MeV/c\n0\n20\n40\n60\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents/5 MeV\n0\n10\n20\nE (GeV)\n\u2206\n-0.05\n0\n0.05\n0.1\nEvents/5 MeV\n0\n10\n20\nFisher\n-1\n0\n1\nEvents/0.007\n0\n10\n20\n30\nFisher\n-1\n0\n1\nEvents/0.007\n0\n10\n20\n30\nFigure 17.8.6. The mES, or Mbc (left column), \u2206E (middle column), and F (right column) distributions for B\u00b1 \u2192DK\u00b1,\nD \u2192K0\nS\u03c0+\u03c0\u2212decays from Belle (Poluektov, 2010; top row) and for B\u00b1 \u2192DK\u00b1, D \u2192K0\nSK+K\u2212decays from BABAR (del\nAmo Sanchez, 2010b; bottom row). Points with error bars are the data. In the top row the histograms are \ufb01tted contributions\ndue to signal, misidenti\ufb01ed B\u00b1 \u2192D\u03c0\u00b1 events, and BB, charm, and continuum background. In the bottom row the curves\nsuperimposed represent the projections of the BABAR \ufb01t: signal plus background (solid black lines), the continuum plus BB\nbackground contributions (dotted red lines), and the sum of the continuum, BB, and misidenti\ufb01ed B\u00b1 \u2192D\u03c0\u00b1 events (dashed\nblue lines). The distributions are for events in the signal region de\ufb01ned through the requirements mES > 5.272 GeV/c2, |\u2206E| <\n30 MeV (common to the two experiments), | cos \u03b8T| < 0.8 and F > \u22120.7 by Belle, and F > \u22120.1 by BABAR, except the one on\nthe plotted variable.\nTable 17.8.7. Event yields in modes used for Dalitz plot analyses. The numbers in parenthesis indicate the signal purity in\nthe signal region. This region is de\ufb01ned through the requirements mES > 5.272 GeV/c2, |\u2206E| < 30 MeV (common to the two\nexperiments), | cos \u03b8T| < 0.8 and F > \u22120.7 by Belle, and F > \u22120.1 by BABAR.\nMode\nBelle, D0 \u2192K0\nS\u03c0+\u03c0\u2212\nBABAR, D0 \u2192K0\nS\u03c0+\u03c0\u2212\nBABAR, D0 \u2192K0\nSK+K\u2212\n(Poluektov, 2010)\n(del Amo Sanchez, 2010b)\n(del Amo Sanchez, 2010b)\nB\u00b1 \u2192DK\u00b1\n756 (71%)\n896 \u00b1 35 (68%)\n154 \u00b1 14 (82%)\nB\u00b1 \u2192D\u2217K\u00b1, D\u2217\u2192D\u03c00\n149 (78%)\n255 \u00b1 21 (81%)\n56 \u00b1 11 (87%)\nB\u00b1 \u2192D\u2217K\u00b1, D\u2217\u2192D\u03b3\n141 (42%)\n193 \u00b1 19 (55%)\n30 \u00b1 7 (78%)\nB\u00b1 \u2192DK\u2217\u00b1\n54 \u00b1 8 (65%) (Poluektov, 2006)\n163 \u00b1 18 (58%)\n28 \u00b1 6 (81%)\nBABAR measures the e\ufb00ective Cartesian parameters zs\n\u00b1 =\nxs\n\u00b1 + iys\n\u00b1 = \u03bars\nB exp[i(\u03b4s\nB \u00b1 \u03c63)], where 0 < \u03ba < 1 is an\ne\ufb00ective hadronic parameter that accounts for the inter-\nference between B\u00b1 \u2192DK\u2217\u00b1 and other B\u00b1 \u2192DK0\nS\u03c0\u00b1\ndecays, as a consequence of the K\u2217\u00b1 natural width. This\ne\ufb00ective parameterization also accounts for e\ufb03ciency vari-\nations as a function of the kinematics of the B decay. Belle\nmeasures zs\n\u00b1 assuming \u03ba = 1. Both experiments \ufb01nally as-\nsign an additional source of systematic uncertainty due to\nnon-resonant decays.\nResults for z\u00b1, z\u2217\n\u00b1, and zs\n\u00b1 for B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192\nD\u2217K\u00b1, and B\u00b1 \u2192DK\u2217\u00b1 decays, respectively, are pre-\n\n355\n\u00b1\nx\n-0.5\n0\n\u00b1\ny\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nBaBar\nBelle\nCombined\n+\nB\n-\nB\n*\n\u00b1\nx\n-0.5\n0\n*\n\u00b1\ny\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\ns\n\u00b1\nx\n-0.5\n0\ns\n\u00b1\ny\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nFigure 17.8.7.\nContours at the 60.7% con\ufb01dence level for 2 degrees of freedom (corresponding to \u22122\u2206ln L = \u2206\u03c72 = 1,\ni.e., one standard deviation in two dimensions assuming Gaussian errors, solid lines), and two- and three-standard deviation\ncontours (dashed lines) in the (left) z\u00b1, (center) z\u2217\n\u00b1, and (right) zs\n\u00b1 planes, for BABAR and Belle separately (including all errors\nother than model uncertainties), and their HFAG combination (Asner et al., 2011).\nTable 17.8.8. Fit results for B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192D\u2217K\u00b1, and B\u00b1 \u2192DK\u2217\u00b1 modes using the Dalitz analysis technique\nin Cartesian variables z\u00b1, z\u2217\n\u00b1, and zs\n\u00b1, respectively. The \ufb01rst error is statistical, the second is the experimental systematic\nuncertainty, and the third re\ufb02ects the uncertainty in the description of the neutral D decay amplitudes.\nReal part (%)\nImaginary part (%)\nReal part (%)\nImaginary part (%)\nBABAR (del Amo Sanchez, 2010b)\nBelle (Poluektov, 2010)\nz\u2212\n+ 6.0 \u00b1 3.9 \u00b1 0.7 \u00b1 0.6\n+ 6.2 \u00b1 4.5 \u00b1 0.4 \u00b1 0.6\n+10.5 \u00b1 4.7 \u00b1 1.1 \u00b1 6.4\n+17.7 \u00b1 6.0 \u00b1 1.8 \u00b1 5.4\nz+\n\u221210.3 \u00b1 3.7 \u00b1 0.6 \u00b1 0.7\n\u22122.1 \u00b1 4.8 \u00b1 0.4 \u00b1 0.9\n\u221210.7 \u00b1 4.3 \u00b1 1.1 \u00b1 5.5\n\u22126.7 \u00b1 5.9 \u00b1 1.8 \u00b1 6.3\nz\u2217\n\u2212[D\u03c00]\n\u221210.4 \u00b1 5.1 \u00b1 1.9 \u00b1 0.2\n\u22125.2 \u00b1 6.3 \u00b1 0.9 \u00b1 0.7\n+2.4 \u00b1 14.0 \u00b1 1.8 \u00b1 9.0\n\u221224.3 \u00b1 13.7 \u00b1 2.2 \u00b1 4.9\nz\u2217\n+ [D\u03c00]\n+14.7 \u00b1 5.3 \u00b1 1.7 \u00b1 0.3\n\u22123.2 \u00b1 7.7 \u00b1 0.8 \u00b1 0.6\n+13.3 \u00b1 8.3 \u00b1 1.8 \u00b1 8.1\n+13.0 \u00b1 12.0 \u00b1 2.2 \u00b1 6.3\nz\u2217\n\u2212[D\u03b3]\nIncluded in z\u2217\n\u2212(D\u03c00)\n+14.4 \u00b1 20.8 \u00b1 2.5 \u00b1 9.0\n+19.6 \u00b1 21.5 \u00b1 3.7 \u00b1 4.9\nz\u2217\n+ [D\u03b3]\nIncluded in z\u2217\n+ (D\u03c00)\n\u22120.6 \u00b1 14.7 \u00b1 2.5 \u00b1 8.1\n\u221219.0 \u00b1 17.7 \u00b1 3.7 \u00b1 6.3\nBABAR (del Amo Sanchez, 2010b)\nBelle (Poluektov, 2006)\nzs\n\u2212\n+ 7.5 \u00b1 9.6 \u00b1 2.9 \u00b1 0.7\n+12.7 \u00b1 9.5 \u00b1 2.7 \u00b1 0.6\n\u221278.4+24.9\n\u221229.5 \u00b1 2.9 \u00b1 9.7\n\u221228.1+44.0\n\u221233.5 \u00b1 4.6 \u00b1 8.6\nzs\n+\n\u221215.1 \u00b1 8.3 \u00b1 2.9 \u00b1 0.6\n+ 4.5 \u00b1 10.6 \u00b1 3.6 \u00b1 0.8\n\u221210.5+17.7\n\u221216.7 \u00b1 0.6 \u00b1 8.8\n\u22120.4+16.4\n\u221215.6 \u00b1 1.3 \u00b1 9.5\nsented in Table 17.8.8. Belle reports z\u2217\n\u00b1 values separately\nfor D\u2217\u2192D\u03c00 and D\u2217\u2192D\u03b3 modes and combines them\nin the \u03c63 \ufb01t (Poluektov, 2010), while BABAR reports D\u2217\u2192\nD\u03c00 and D\u2217\u2192D\u03b3 combined values inverting the sign\nfor the latter (del Amo Sanchez, 2010b). Belle results\nfor B\u00b1 \u2192DK\u2217\u00b1 are reported in Poluektov (2006). The\nmodel uncertainties in the case of the Belle analysis are\nreported for the physics parameters \u03c63, rB, and \u03b4B; the\nuncertainties on z\u00b1, z\u2217\n\u00b1, and zs\n\u00b1 quoted in Table 17.8.8\nare based on information provided by Belle and published\nin Asner et al. (2011). Figure 17.8.7 shows the correspond-\ning one-, two-, and three-standard deviation contours in\ntwo dimensions in the z\u00b1, z\u2217\n\u00b1, and zs\n\u00b1 planes, together\nwith the HFAG combination (Asner et al., 2011). These\naverages take into account the e\ufb00ect of correlations within\neach experiment\u2019s set of measurements, both statistical\nand systematic (excluding e\ufb00ects of the amplitude model),\nand are performed assuming that both experiments use\nthe same decay amplitude model and that the model un-\ncertainty is fully correlated between the two experiments\n(thus this source of error is not used in the averaging pro-\ncedure). It is also assumed that the selection of B\u00b1 \u2192\nDK\u2217\u00b1 decays is the same in both experiments, neglecting\nthe Belle model uncertainty due to possible non-resonant\ndecays.\nInterpretation of \ufb01t results\nThe \ufb01t results expressed in terms of the z\u00b1 variables are\nthen converted into physical parameters \u03c63, rB, and \u03b4B.\n\u03c63 is constrained to be the same in all modes used, while\nrB and \u03b4B are allowed to be di\ufb00erent for di\ufb00erent B\ndecay modes. Note that, due to this constraint and the\nfact that rB is expected to be the same for B+ and B\u2212,\nthe number of physical parameters is smaller than the\nnumber of experimental observables. Thus, the statisti-\ncal treatment has to take into account the mathematical\n\n356\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0\n50 100 150 200 250 300 350\n\u03c63 (degrees)\nr\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0\n50 100 150 200 250 300 350\n\u03c63 (degrees)\nr\nFigure 17.8.8. Belle projections of the con\ufb01dence regions for B\u00b1 \u2192DK\u00b1 (left) and B\u00b1 \u2192D\u2217K\u00b1 (right) decays onto\nthe (\u03c63, rB) and (\u03c63, r\u2217\nB, ) planes (Poluektov, 2010). Contours indicate projections of one-, two-, and three-standard deviation\nregions.\nmismatch between the experimental results z\u00b1 and the\nset of physical observables (\u03c63, rB, \u03b4B) due to statistical\n\ufb02uctuations (Yabsley, 2006). Both collaborations use a fre-\nquentist approach to obtain \u03c63, although the details of the\ntreatment di\ufb00er. In both cases the method requires knowl-\nedge of the probability density function (p.d.f.) p(z|\u00b5) of\nthe vector z of measured parameters z\u00b1, z\u2217\n\u00b1, and zs\n\u00b1 as\na function of the true parameters \u00afz, which can easily be\nexpressed in terms of the vector \u00b5 = (\u03c63, rB, \u03b4B, r\u2217\nB, \u03b4\u2217\nB,\n\u03bars\nB, \u03b4s\nB).\nTo obtain this p.d.f., Belle uses a simpli\ufb01ed Monte\nCarlo (MC) simulation of the experiment which incorpo-\nrates the same e\ufb03ciencies, resolution, and backgrounds as\nused in the \ufb01t to the experimental data. Belle constructs\nthree-dimensional regions in the \u00b5 space, using the uni\ufb01ed\napproach of Feldman and Cousins (1998). The con\ufb01dence\nlevel \u03b1 is calculated as \u03b1(\u00b5) =\nR\nD(\u00b5) p(z|\u00b5)dz, where the\nintegration domain D is given by the likelihood ratio or-\ndering\np(z|\u00b5)\np(z|\u00b5best(z)) >\np(z0|\u00b5)\np(z0|\u00b5best(z0)),\n(17.8.16)\nwhere \u00b5best(z) stands for the best parameters \u00b5 such that\np(z|\u00b5) is maximized for the given measurement z, and z0\nis the measurement from the \ufb01t to the experimental data.\nBABAR instead constructs directly one-dimensional in-\ntervals calculating the con\ufb01dence level as a function of\nthe true value of a given parameter \u00b5 from \u00b5 \u2261{\u00b5, q} as\n\u03b1(\u00b5) = 1\u2212F[\u2206\u03c72(\u00b5)], where F[\u2206\u03c72(\u00b5)] is the cumulative\nexpected distribution of \u2206\u03c72(\u00b5), with\n\u2206\u03c72(\u00b5) = \u22122 ln p(z0|\u00b5, q(\u00b5))\np(z0|\u00b5best(z0)).\n(17.8.17)\nHere q(\u00b5) stands for the parameters q that maximize\np(z0|\u00b5) for the given \u00b5, and \u00b5best(z0) is as de\ufb01ned above.\nThe p(z|\u00b5) p.d.f. is approximated by a correlated, multidi-\nmensional Gaussian in the vector z of measurements, pre-\nviously validated using a simpli\ufb01ed MC simulation, similar\nto that performed by Belle. The distribution F[\u2206\u03c72(\u00b5)] is\nobtained using a large number of MC simulated samples,\nby counting of the number of experiments generated with\ntrue values \u00b5 = {\u00b5, q(\u00b5)} that have better \u2206\u03c72(\u00b5) than\nthe actual experiment.\nFigure 17.8.8 shows the Belle projection of the three-\ndimensional region onto the (rB, \u03c63) plane, for each of\nthe B\u00b1 \u2192DK\u00b1 and B\u00b1 \u2192D\u2217K\u00b1 modes, for 20%,\n74%, and 97% con\ufb01dence level regions, which correspond\nto one-, two-, and three-standard deviations for a three-\ndimensional Gaussian distribution. Similarly, Fig. 17.8.9\nshows the BABAR con\ufb01dence level as a function of \u03c63 and\nrB for each of the three B decay channels, as well as their\ncombination for the case of the weak phase. Table 17.8.9\nreports the corresponding central values with their one-\nand two-standard deviation intervals. Using these frequen-\ntist procedures, each of the experiments obtains a de-\nparture from \u03c63 = 0 equivalent to 3.5 standard devia-\ntions, providing evidence for direct CP violation in B\u00b1 \u2192\nD(\u2217)K(\u2217)\u00b1 decays.\nModel uncertainty\nWhile the experimental systematic uncertainties in the\nGGSZ measurements with the model-dependent technique\ncan be understood using control samples and Monte Carlo\nsimulation, the uncertainty arising from the description of\nthe amplitude model is more di\ufb03cult to quantify. Both\nexperiments follow the general guidelines discussed in Sec-\ntion 13.5, although with di\ufb00erences in the details. BABAR\nuses alternative models that give similar D0 \u2192K0\nS\u03c0+\u03c0\u2212\n\ufb01t quality to that of the default model, where BW pa-\nrameters are varied according to their uncertainties, the\nreference K-matrix solution is replaced by other solu-\ntions (Anisovich and Sarantsev, 2003), and the standard\n\n357\n (deg)\na\n-150 -100 -50\n0\n50\n100 150\n1 - CL\n0\n0.2\n0.4\n0.6\n0.8\n1\nm\n1\nm\n2\n<+\n DK\nA\n \n<+\nB\n<+\n D*K\nA\n \n<+\nB\n<+\n DK*\nA\n \n<+\nB\nCombined\nsr\ng,\n(*)\nB\nr\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n1 - CL\n0\n0.2\n0.4\n0.6\n0.8\n1\nm\n1\nm\n2\n<+\n DK\nA\n \n<+\nB\n<+\n D*K\nA\n \n<+\nB\n<+\n DK*\nA\n \n<+\nB\nFigure 17.8.9. The BABAR 1 \u2212C.L. distributions as a function of \u03b3 = \u03c63 (left) and rB (right) for B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192D\u2217K\u00b1,\nand B\u00b1 \u2192DK\u2217\u00b1 decays separately, and their combination, including statistical and systematic uncertainties (del Amo Sanchez,\n2010b). The dashed (upper) and dotted (lower) horizontal lines correspond to the one- and two-standard deviation intervals,\nrespectively.\nTable 17.8.9.\nThe 68.3% and 95.4% one-dimensional C.L. regions, equivalent to one- and two-standard deviation intervals,\nfor \u03c63, \u03b4B, rB, \u03b4s\nB, and \u03bars\nB, including all sources of uncertainty. The 68.3% C.L. regions show separate contributions from\nstatistical, experimental systematic, and model uncertainties. The 95.4% regions include statistical and systematic uncertainties\nfor BABAR, but only statistical for Belle. B\u00b1 \u2192DK\u2217\u00b1 results from Belle (Poluektov, 2006), shown in the bottom panel of the\ntable, are obtained assuming the e\ufb00ective hadronic parameter \u03ba = 1, and are not included in the combined value for \u03c63.\nParameter\n68.3% C.L.\n95.4% C.L.\n68.3% C.L.\n95.4% C.L.\nBABAR (del Amo Sanchez, 2010b)\nBelle (Poluektov, 2010)\n\u03c63 (\u25e6)\n68+15\n\u221214 \u00b1 4 \u00b1 3\n[39, 98]\n78.4+10.8\n\u221211.6 \u00b1 3.6 \u00b1 8.9\n[54.2, 100.5]\nrB (%)\n9.6 \u00b1 2.9 \u00b1 0.5 \u00b1 0.4\n[3.7, 15.5]\n16.0+4.0\n\u22123.8 \u00b1 1.1+5.0\n\u22121.0\n[8.4, 23.9]\nr\u2217\nB (%)\n13.3+4.2\n\u22123.9 \u00b1 1.3 \u00b1 0.3\n[4.9, 21.5]\n19.6+7.2\n\u22126.9 \u00b1 1.2+6.2\n\u22121.2\n[6.1, 27.1]\n\u03bars\nB (%)\n14.9+6.6\n\u22126.2 \u00b1 2.6 \u00b1 0.6\n< 28.0\n\u2212\n\u2212\n\u03b4B (\u25e6)\n119+19\n\u221220 \u00b1 3 \u00b1 3\n[75, 157]\n136.7+13.0\n\u221215.8 \u00b1 4.0 \u00b1 22.9\n[102.2, 162.3]\n\u03b4\u2217\nB (\u25e6)\n\u221282 \u00b1 21 \u00b1 5 \u00b1 3\n[\u2212124, \u221238]\n341.9+18.0\n\u221219.6 \u00b1 3.0 \u00b1 22.9\n[296.5, 382.7]\n\u03b4s\nB (\u25e6)\n111 \u00b1 32 \u00b1 11 \u00b1 3\n[42, 178]\n\u2212\n\u2212\nBelle (Poluektov, 2006)\n\u03bars\nB (%)\n56.4+21.6\n\u221215.5 \u00b1 4.1 \u00b1 8.4\n[23.1, 1.106]\n\u03b4s\nB (\u25e6)\n242.6+20.2\n\u221223.2 \u00b1 2.5 \u00b1 49.3\n[186.0, 300.2]\nparameterizations are replaced by other related choices,\nfor example, replacing the Gounaris-Sakurai and K\u03c0 S-\nwave parameterizations by BWs, removing the mass de-\npendence in the P vector, changing form factors, and\nadopting the helicity formalism instead of Zeemach ten-\nsors to describe the angular dependence. Other models are\nbuilt by removing or adding resonances with small or neg-\nligible fractions, or accounting explicitly for D0 \u2212D0 mix-\ning e\ufb00ects. Belle performs model variations that employ a\nreduced number of resonances while keeping the absolute\nvalue of the amplitude the same as in the default model.\nModels excluding the \u03c31 and \u03c32 states; or using only\nthe largest Cabibbo-favored term D0 \u2192K\u2217(892)\u2212\u03c0+,\nthe narrow resonances, D0 \u2192K0\nSf0(980), and D0 \u2192\nK\u2217\n0(1430)\u2212\u03c0+, and a large \ufb02at non-resonant term; or the\nmodel used by CLEO (Muramatsu et al., 2002), are more\nconservative model variations than those performed by\nBABAR, where these extreme models have been discarded\non the basis of their signi\ufb01cantly poorer \ufb01t quality. Other\nvariations used by Belle include removal of the form fac-\ntors for the D meson and intermediate resonances, and of\nthe momentum dependence of the resonance width.\n17.8.4.2 Model-dependent technique with other \ufb01nal states\nBABAR has carried out similar analyses using the decay\nB\u00b1 \u2192DK\u00b1 with the D \u2192\u03c0+\u03c0\u2212\u03c00 \ufb01nal state (Aubert,\n2007w), and the neutral B decay B0 \u2192DK\u22170, K\u22170 \u2192\nK+\u03c0\u2212, with D \u2192K0\nS\u03c0+\u03c0\u2212(Aubert, 2009f).\n\n358\nIn the study of the B\u00b1 \u2192DK\u00b1, D \u2192\u03c0+\u03c0\u2212\u03c00 decay,\nBABAR measures from 324 \u00d7 106 BB pairs \u03c1\u2212= 0.815 \u00b1\n0.034, \u03b8\u2212= (186 \u00b1 7)\u25e6, \u03c1+ = 0.854 \u00b1 0.035, \u03b8+ = (192 \u00b1\n7)\u25e6, where the polar parameterization \u03c1\u00b1 \u2261|z\u00b1 \u2212x0|,\n\u03b8\u00b1 = tan\u22121 y\u00b1/(x\u00b1 \u2212x0) (with x0 = 0.850) is chosen\nto re\ufb02ect the symmetry properties of the measurement:\nstudies show that this removes nonlinear correlations (and\nconsequent bias) in the \ufb01t, and improves the sensitivity\nof the result. These results are consistent with \u03c1\u00b1 = x0,\n\u03b8\u00b1 = 180\u25e6, which corresponds to z\u00b1 = 0.\nFor the neutral B decay B0 \u2192DK\u22170, K\u22170 \u2192K+\u03c0\u2212,\nD \u2192K0\nS\u03c0+\u03c0\u2212, rB is na\u00a8\u0131vely expected to be larger, \u223c0.3\n(Section 17.8.3), although the overall rate of events is sig-\nni\ufb01cantly smaller than for B\u00b1 \u2192DK\u2217\u00b1 decays. The \ufb02a-\nvor of the neutral B meson is tagged by the charge of the\nkaon produced in the K\u2217(892)0 decay (K+\u03c0\u2212or K\u2212\u03c0+).\nThe analysis \ufb01nds 39 \u00b1 9 signal events from 371 \u00d7 106\nBB pairs, and using a Bayesian analysis with external in-\nputs yields \u03c63 = (162 \u00b1 56)\u25e6and rB < 0.55 at the 90%\ncon\ufb01dence level.\nNevertheless, in both cases the errors on the experi-\nmental measurements are too large for a meaningful de-\ntermination of \u03c63, or \u03b3, and have not been included in the\ncombined determination of \u03c63.\n17.8.4.3 Binned model-independent technique\nIn the binned \ufb01t approach to \u03c63 determination using B\u00b1 \u2192\nDK\u00b1, D0 \u2192K0\nS\u03c0+\u03c0\u2212decays, it is possible to avoid de-\npendence on a detailed model of the D0 amplitude across\nthe Dalitz plot. Instead, if the plot is divided into bins,\nthe amplitude in each bin can be described by quanti-\nties averaged over that bin. These quantities can be ex-\ntracted from analyses of charm data, thus allowing for a\ncompletely model-independent measurement of \u03c63. This\napproach is particularly attractive for precision measure-\nment at a super \ufb02avor factory where the model uncertainty\nwould otherwise dominate the precision. The approach\nwas \ufb01rst proposed in Giri, Grossman, So\ufb00er, and Zupan\n(2003a), and further developed by Bondar and Poluek-\ntov (2006, 2008), where the experimental feasibility of the\nmethod was shown and an optimization procedure for the\nanalysis was proposed. The analysis has been performed\nby Belle as a proof of principle using the \ufb01nal data sam-\nple of 772 \u00d7 106 BB pairs (Aihara, 2012) and based on\nresults of the measurement of strong phase parameters by\nthe CLEO collaboration (Briere et al., 2009; Libby et al.,\n2010).\nProcedure\nIn the model-independent approach, the Dalitz plot is di-\nvided into 2N bins symmetric under the exchange m2\n\u2212\u2194\nm2\n+. The bin index \u201ci\u201d ranges from \u2212N to N (excluding\nzero); the exchange m2\n+ \u2194m2\n\u2212corresponds to the ex-\nchange i \u2194\u2212i. The expected number of events in the bin\n\u201ci\u201d of the Dalitz plot of the D from a B+ \u2192DK+ decay\nis\nN +\ni = hB\nh\nKi + r2\nBK\u2212i + 2\np\nKiK\u2212i(x+ci + y+si)\ni\n,\n(17.8.18)\nwhere hB is a normalization constant and Ki is the num-\nber of events in the ith bin of the Dalitz plot of the D\nmeson decaying into a \ufb02avor eigenstate (obtained using a\nD\u2217\u00b1 \u2192D\u03c0\u00b1 sample). The terms ci and si include infor-\nmation about the cosine and sine of the phase di\ufb00erence\n\u03b4D(m2\n+, m\u2212) between D0 and D0 averaged over the bin\nregion:\nci =\nR\nDi\n|AD||AD| cos \u03b4D dD\nrR\nDi\n|AD|2dD\nR\nDi\n|AD|2dD\n.\n(17.8.19)\nHere D represents the Dalitz plot phase space and Di is\nthe bin region over which the integration is performed.\nThe terms si are de\ufb01ned similarly with sine substituted\nfor cosine.\nNeglecting e\ufb00ects due to neutral D mixing and CP\nviolation (which are measured or constrained at the 1%\nlevel or less; see the text on D-mixing and CP violation\nin Section 19.2), the strong phase di\ufb00erence \u03b4D is anti-\nsymmetric (\u03b4D(m2\n+, m2\u2212) = \u2212\u03b4D(m\u2212, m+)) and thus the\nrelations ci = c\u2212i and si = \u2212s\u2212i hold. The values of the ci\nand si terms can be measured using quantum correlated\npairs of D mesons created at charm-factory experiments\noperated at the threshold of DD pair production. The\nwave function of the two mesons is antisymmetric,\nAcorr = A(1)\nD A(2)\nD \u2212A(2)\nD A(1)\nD ,\n(17.8.20)\nwhere the indices \u201c(1)\u201d and \u201c(2)\u201d correspond to the two\ndecaying D mesons. The four-dimensional probability den-\nsity for the two correlated D \u2192K0\nS\u03c0+\u03c0\u2212Dalitz plots is\nsensitive to the strong phase di\ufb00erence. In the case of the\nbinned analysis, the number of events where one D me-\nson lies in the i-th bin of the Dalitz plot and the other D\nmeson in the j-th bin is\nMij =KiK\u2212j + K\u2212iKj\n\u22122\np\nKiK\u2212iKjK\u2212j(cicj + sisj).\n(17.8.21)\nIn addition to the process where both D mesons decay\ninto K0\nS\u03c0+\u03c0\u2212, CLEO (Briere et al., 2009; Libby et al.,\n2010) use decays (K0\nL\u03c0+\u03c0\u2212)D(K0\nS\u03c0+\u03c0\u2212)D to increase the\navailable data sample, although weak model assumptions\nare made to constrain the ci and si values in this case,\nsince the amplitudes with K0\nL and K0\nS di\ufb00er.\nAdditional information about the values of ci is ob-\ntained from the process where one D meson decays in a\nCP eigenstate, and the second \u2014 in the CP eigenstate\nof opposite sign \u2014 decays to K0\nS\u03c0+\u03c0\u2212. The amplitude of\nthis decay is\nA\u00b1 = AD \u00b1 AD,\n(17.8.22)\nand the number of events in bins of the DCP \u2192K0\nS\u03c0+\u03c0\u2212\ndecay is\nMi = Ki + K\u2212i \u00b1 2\np\nKiK\u2212ici.\n(17.8.23)\n\n359\n)\n4\n/c\n2\n (GeV\n\u2212\n2\nm\n0.5\n1\n1.5\n2\n2.5\n3\n)\n4\n/c\n2\n (GeV\n+\n2\nm\n0.5\n1\n1.5\n2\n2.5\n3\n|Bin index i|\n1\n2\n3\n4\n5\n6\n7\n8\ni>0\ni<0\ni\nC\n-1\n0\n1\ni\nS\n-1.5\n-1\n-0.5\n0\n0.5\n1\n1.5\n1\n1\n2\n2\n3\n3\n4\n4\n5\n5\n6\n6\n7\n7\n8\n8\nCLEO\nBelle\nmodel\nFigure 17.8.10. (a) Optimal binning of the D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz plot and (b) comparison of phase terms ci, si for the optimal\nbinning measured by CLEO, and calculated from the Belle D0 \u2192K0\nS\u03c0+\u03c0\u2212amplitude model, taken from Aihara (2012).\nNote that the use of a CP eigenstate allows one to re-\nsolve an ambiguity in the measurement of ci and si from\ncorrelated K0\nS\u03c0+\u03c0\u2212decays, as Eq. (17.8.21) is invariant\nunder the simultaneous change of the signs of all ci or si,\nwhile Eq. (17.8.23) provides the signs of ci. The ambiguity\nunder the simultaneous change of signs of si remains (cor-\nresponding to complex conjugation of the amplitude AD),\nhowever this can be resolved with a weak model assump-\ntion. The solution that best \ufb01ts the isobar model with\nBW amplitudes is preferred, since the other one, corre-\nsponding to the complex-conjugated parameterization, is\nunphysical: the complex-conjugated BW amplitude corre-\nsponds to the converging spherical wave in the quantum-\nmechanical scattering problem, and violates causality.\nOptimal binning\nThe statistical precision of the binned procedure depends\nstrongly on the chosen binning. If the amplitude varies\nsigni\ufb01cantly across the bin area, the integral over the bin\naverages over the interference term, discarding informa-\ntion and reducing the sensitivity of the analysis. An op-\ntimal binning of the Dalitz plot, that takes into account\nboth the variations of the strong phase di\ufb00erence and the\nabsolute value of the D0 \u2192K0\nS\u03c0+\u03c0\u2212amplitude, was pro-\nposed by Bondar and Poluektov (2008). The optimization\nuses the amplitude of D0 \u2192K0\nS\u03c0+\u03c0\u2212decay from the\nmodel-dependent analysis. However, although the choice\nof binning is model-dependent, a bad choice of model re-\nsults only in poorer statistical precision of the measure-\nment, and not in systematic bias. It has been shown that\nas few as 16 bins are su\ufb03cient to reach statistical precision\ncomparable to that of the unbinned \ufb01t.\nMeasurements of the phase terms ci and si have been\nperformed by CLEO (Briere et al., 2009; Libby et al.,\n2010), with various binnings of the Dalitz plot. The Belle\nanalysis uses the binning shown in Fig. 17.8.10(a) op-\ntimized for the best statistical accuracy under the as-\nsumption that the background in B\u00b1 \u2192DK\u00b1 decays\nis small. This optimization uses the BABAR amplitude\nmeasurement (Aubert, 2008l). The results of the CLEO\nmeasurement of ci and si for this binning are presented\nin Fig. 17.8.10(b). Comparison with ci and si calculated\nfrom the Belle model (Poluektov, 2010) shows reason-\nable agreement between the model and measurement:\n\u03c72/ndof = 18.6/16.\nOnce the values of the terms ci and si are known, the\nsystem of equations (17.8.18) contains only three free pa-\nrameters (x, y, and hB) for each B charge, and can be\nsolved using the maximum likelihood method to extract\nthe values of rB, \u03c63, and \u03b4B. The numbers of events Ki and\nNi are extracted from D\u2217\u00b1 \u2192D\u03c0\u00b1 and B\u00b1 \u2192DK\u00b1 sam-\nples respectively. To minimize the systematic error coming\nfrom the di\ufb00erence in reconstruction e\ufb03ciency across the\nphase space for the two samples, the \ufb02avor-tagged results\nKi are obtained by choosing D mesons in the momen-\ntum range 1.8 GeV/c < pD < 2.8 GeV/c, i.e., with the\nsame average momentum pD as for B\u00b1 \u2192DK\u00b1 decays.\nMomentum resolution is taken into account by using a\nmigration matrix to describe the cross-feed between bins.\nFit results and interpretation\nThe parameters x\u00b1 and y\u00b1 are determined by a simulta-\nneous \ufb01t over the 16 bins, using signal selection variables\nto determine the yield Ni in each bin: \u2206M and MD for the\nD\u2217\u00b1 \u2192D\u03c0\u00b1 sample, and mES, \u2206E, cos \u03b8T, and the same\nFisher discriminant F as used in Belle\u2019s model-dependent\nanalysis (Section 17.8.4) for the B\u00b1 \u2192DK\u00b1 sample. Fig-\nure 17.8.11 shows the binned signal yield separately for\nB+ and B\u2212data, its charge asymmetry, and the results\nof the \ufb01t using Eq. (17.8.18) for each bin in the Dalitz\nplot. Di\ufb00erent binned yields for positive and negative B\ncharges in Figs 17.8.11(a,b) suggest signi\ufb01cant CP asym-\nmetry, while the pattern in Figs 17.8.11(c,d) shows that\nthis CP asymmetry is well described by the model involv-\ning a nonzero value of \u03c63 (Eq. 17.8.18).\n\n360\nBin\n-8 -6 -4\n-2\n0\n2\n4\n6\n8\nNumber of events\n0\n20\n40\n60\n80\n100\n-\nB\n+\nB\nBin\n-8 -6 -4\n-2\n0\n2\n4\n6\n8\n)\n-\n)-N(B\n+\nN(B\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n30\n40\n50\n / ndf \n2\n\u03c7\n 33.31 / 15\nProb \n 0.004247\nBin\n-8 -6 -4 -2\n0\n2\n4\n6\n8\n)-N(flavor)\n-\nN(B\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n30\n40\n50\n/ndf(fit)=13.1/13 P=0.44\n2\n\u03c7\n/ndf(flavor)=27.1/15 P=0.03\n2\n\u03c7\nBin\n-8 -6 -4\n-2\n0\n2\n4\n6\n8\n)-N(flavor)\n+\nN(B\n-50\n-40\n-30\n-20\n-10\n0\n10\n20\n30\n40\n50\n/ndf(fit)=7.9/13 P=0.85\n2\n\u03c7\n/ndf(flavor)=19.0/15 P=0.21\n2\n\u03c7\n(a)\n(b)\n(c)\n(d)\nFigure 17.8.11. Results of the model-independent binned \ufb01t of the B\u00b1 \u2192DK\u00b1 sample (Aihara, 2012). (a) Numbers of events\nin bins of the D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz plot: from B\u2212\u2192DK\u2212(blue triangle downwards), B+ \u2192DK+ (red triangle upwards)\nand the \ufb02avor-tagged sample (histogram). (b) Di\ufb00erence of the number of events from B+ \u2192DK+ and B\u2212\u2192DK\u2212decays. (c)\nDi\ufb00erence of the number of events from B\u2212\u2192DK\u2212and \ufb02avor-tagged sample (normalized to the total number of B\u2212\u2192DK\u2212\ndecays): data (points with vertical and horizontal error bars), and as a result of the (x, y) \ufb01t (horizontal bars). (d) Same as (c)\nfor B+ \u2192DK+ data.\nThe values of the z\u00b1 parameters obtained from the\nbinned \ufb01t to the B\u00b1 \u2192DK\u00b1 sample are\nx\u2212= +0.095 \u00b1 0.045 \u00b1 0.014 \u00b1 0.010,\ny\u2212= +0.137+0.053\n\u22120.057 \u00b1 0.015 \u00b1 0.023,\nx+ = \u22120.110 \u00b1 0.043 \u00b1 0.014 \u00b1 0.007,\ny+ = \u22120.050+0.052\n\u22120.055 \u00b1 0.011 \u00b1 0.017.\n(17.8.24)\nHere the \ufb01rst error is statistical, the second error is the\nsystematic uncertainty, and the third error is the uncer-\ntainty due to the errors on ci and si terms coming from\nthe CLEO analysis. This translates to\n\u03c63 = (77.3+15.1\n\u221214.9 \u00b1 4.1 \u00b1 4.3)\u25e6,\nrB = 0.145 \u00b1 0.030 \u00b1 0.010 \u00b1 0.011,\n\u03b4B = (129.9 \u00b1 15.0 \u00b1 3.8 \u00b1 4.7)\u25e6.\n(17.8.25)\nThese results are consistent with the CP-conservation hy-\npothesis at the 99.35% C.L., which corresponds to a 2.7\nstandard deviation discrepancy. They are also in good\nagreement with those obtained with the model-dependent\napproach, given in Tables 17.8.8 and 17.8.9.\nIt is important to note that, unlike the model uncer-\ntainty of the unbinned analysis, which is di\ufb03cult to quan-\ntify, the error due to ci and si is statistical in nature, since\nthe measurements of these quantities are largely domi-\nnated by statistical uncertainties. It is expected that a\nprecision measurement of \u03c63 at the 1\u25e6level (or better)\nwith the binned model-independent Dalitz plot analysis\nwill be possible at a super \ufb02avor factory, using data from\nthe BES III experiment. There are no other critical sys-\ntematic uncertainties in this analysis that would dominate\nthe measurement at the 1\u25e6level \u2014 the most signi\ufb01cant un-\ncertainties are determined by the \ufb01nite size of the auxiliary\nsamples (\ufb02avor-tagged D0 \u2192K0\nS\u03c0+\u03c0\u2212and B\u00b1 \u2192D\u03c0\u00b1),\nwhich will also increase in future analyses.\n17.8.5 sin(2\u03c61 + \u03c63)\n17.8.5.1 Method involving B \u2192D(\u2217)h (h = \u03c0, \u03c1) decays\nThe study of the time-dependent decay rates of B \u2192\nD(\u2217)\u2213h\u00b1 provides a measure of sin(2\u03c61 + \u03c63), where h\ndenotes a pion, a \u03c1, or an a1 meson (Dunietz, 1998).\nAs shown in Fig. 17.8.12, these decays proceed through\nCF and DCS transitions, whose amplitudes are propor-\ntional to the CKM matrix element products V \u2217\ncbVud and\nV \u2217\nubVcd, respectively. Thus, the weak phase di\ufb00erence be-\ntween these amplitudes in the usual Wolfenstein (1983)\nconvention is \u03c63 (see Eq. 16.4.4 and Fig. 16.5.1). Interfer-\nence between the two contributing diagrams also involves\nB0B0 mixing (see Eq. 16.6.6), hence resulting in a total\nweak phase di\ufb00erence 2\u03c61 + \u03c63.\n\n361\nB 0\nD \u2212\n+\nb\nd\nc\nd\nu\nd\nW +\nB 0 b\nd\nu\nd\nd\nc\nD +\n\u2212\nW +\nFigure 17.8.12. Typical leading order Feynman diagrams for\nthe CF decay B0 \u2192D\u2212h+ (left) and the DCS decay B0 \u2192\nD+h\u2212(right).\nIn \u03a5(4S) \u2192BB decays, the observed decay rate dis-\ntribution of B \u2192D(\u2217)\u2213h\u00b1 is (see Section 10.2)\nf\u00b1(\u2206t) = e\u2212|\u2206t|/\u03c4B\n4\u03c4B\n\u00d7[1 \u2213S\u03be sin(\u2206md\u2206t) \u2213\u03b7 C cos(\u2206md\u2206t)],\n(17.8.26)\nwhere \u03c4B is the neutral B meson lifetime averaged over\nthe two mass eigenstates, \u2206md is the B0B0 mixing fre-\nquency, \u2206t is the proper time di\ufb00erence between the B \u2192\nD(\u2217)\u2213h\u00b1 decay (Brec) and the decay of the other B in the\nevent (Btag), the upper (lower) sign on \u00b1 or \u2213indicates\nthe \ufb02avor of the Btag as a B0 (B0), and the parameters \u03be\nand \u03b7 have the values \u03be = +(\u2212) and \u03b7 = +1(\u22121) for the\nBrec \ufb01nal state D(\u2217)\u2212h+ (D(\u2217)+h\u2212). The coe\ufb03cients S\u00b1\nand C are\nS\u00b1 =\n2R\n1 + R2 sin(2\u03c61 + \u03c63 \u00b1 \u03b4),\nC = 1 \u2212R2\n1 + R2 ,\n(17.8.27)\nwhere R is the ratio of the magnitudes of the DCS and CF\namplitudes (in the SM, their magnitudes are the same for\nB0 and B0 decays), and \u03b4 is the strong phase di\ufb00erence\nbetween the two amplitudes. The values of R and \u03b4 are\nnot necessarily the same for di\ufb00erent D(\u2217)h \ufb01nal states,\nmaking S\u00b1 and C mode dependent. For instance,\nRD(\u2217)h = |A(B0 \u2192D(\u2217)+h\u2212)|\n|A(B0 \u2192D(\u2217)\u2212h+)| =\n\f\f\f\f\nV \u2217\nubVcd\nV \u2217\ncbVud\n\f\f\f\f r,\n(17.8.28)\ncould be di\ufb00erent owing to possible distinct values for r,\nwhere r is the ratio of decay constants and form factors\ninvolved with the two diagrams shown in Fig. 17.8.12. As-\nsuming r \u22481 in the above equation, we can estimate R\npurely in terms of the CKM matrix elements to be 2%.\nIt follows from Eq. (17.8.27) that the value of RD(\u2217)h\ndictates the sensitivity of CP violation measurement in\nB \u2192D(\u2217)\u2213h\u00b1, as the sine term containing weak phases\nis essentially weighted by the factor R. Now because R\nis predicted to be small, the experimental precision on\n2\u03c61 + \u03c63 expected from these measurements is poor. Fur-\nthermore, these measurements are susceptible to poten-\ntial model uncertainties caused by the assumptions used\nin the calculation of R. However, when the decay pro-\nceeds through several interfering amplitudes such as the\nthree helicity amplitudes in B \u2192D\u2217\u2213\u03c1\u00b1, it is possible\nto extract R directly from the data (London, Sinha, and\nSinha, 2000; Sinha, Sinha, and So\ufb00er, 2005), eliminating\nthese uncertainties.\n17.8.5.2 Determination of RD(\u2217)h\nUnfortunately, we cannot directly measure the R values\nwith the current B Factory dataset as the DCS decay\nB0 \u2192D(\u2217)+h\u2212is overwhelmed by the copious background\nfrom B0 \u2192D(\u2217)+h\u2212. They can be, however, indirectly\nobtained from self-tagging neutral B decays involving a\ncharmed-strange meson such as B0 \u2192D+\ns \u03c0\u2212, assuming\nSU(3) \ufb02avor symmetry, or from suppressed charged B\ndecays (e.g., B+ \u2192D+\u03c00) with an isospin relation. In\nthe former case, R is extracted using the following re-\nlation (Dunietz, 1998; Dunietz and Sachs, 1988; Suprun,\nChiang, and Rosner, 2002),\nRD(\u2217)h = |Vcd|\n|Vcs|\nfD(\u2217)\nfD(\u2217)\ns\ns\nB(B0 \u2192D(\u2217)+\ns\nh\u2212)\nB(B0 \u2192D(\u2217)\u2212h+),\n(17.8.29)\nwhere fx denotes the decay constant of the meson x, and\nB denotes the branching fraction of the mode shown. This\nrelation can be inferred from the DCS decay diagram of\nFig. 17.8.12, where by replacing the d quark with an s\nquark one can get B0 \u2192D(\u2217)+\ns\nh\u2212. In the \ufb01rst case the\nvirtual W + boson hadronizes into a D(\u2217)+ meson, with\nthe decay constant fD(\u2217) and CKM matrix element Vcd,\nand in the second it forms a D(\u2217)+\ns\nmeson, with the decay\nconstant fD(\u2217)\ns\nand CKM matrix element Vcs. The theory\nerrors on R due to possible SU(3) breaking e\ufb00ects are\ndi\ufb03cult to quantify, but are estimated to be in the range\n10\u201315% (Baak, 2007). Furthermore, the above relation as-\nsumes that internal W-exchange amplitudes contribute\nmuch less than tree amplitudes to the B0 \u2192D(\u2217)\u2213h\u00b1\ndecays. We can verify this assumption by measuring the\nbranching fraction for B0 \u2192D(\u2217)\u2212\ns\nK(\u2217)+, because in the\nabsence of re-scattering the exchange diagram is the lone\ncontributor to these decays. Therefore, their branching\nfractions can provide a measure of the W-exchange con-\ntribution to B0 \u2192D(\u2217)\u2213h\u00b1.\n17.8.5.3 Results from B \u2192D(\u2217)h (h = \u03c0, \u03c1) decays\nBoth BABAR (Aubert, 2005v, 2006aa) and Belle (Bahini-\npati, 2011; Ronga, 2006) have performed these measure-\nments using both full as well as partial reconstruction\nof D(\u2217)\u2213\u03c0\u00b1. In the case of partial reconstruction, signal\nD\u2217\u2213\u03c0\u00b1 decay candidates are identi\ufb01ed using information\nsolely from the high momentum pion originating from the\nB decay, and the low momentum pion from the subsequent\ndecay of the D\u2217meson, without reconstructing the neu-\ntral D. This results in increased e\ufb03ciency at the cost of a\nlarger background. BABAR (Aubert, 2006aa) has extended\nthe study to include the B \u2192D\u2213\u03c1\u00b1 decays.\n\n362\nz(cm)\n\u2206\n-0.1\n-0.05\n0\n0.05\n0.1\nSF events CP asmmetry\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nz(cm)\n\u2206\n-0.1\n-0.05\n0\n0.05\n0.1\nOF events CP asymmetry\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nFigure 17.8.13. Belle\u2019s measurement of the distance between Brec and Btag vertices along the z axis for lepton-tagged events,\nwhere the lepton has either the (left) same or (right) opposite charge as the low-momentum pion. The \ufb01t results (solid curves)\nare superimposed on the data (points with error bars). CP violation is characterized by a nonzero amplitude of the sinusoidal\noscillation. These plots show the central regions of those presented in Bahinipati (2011), with an expanded vertical scale.\nTable 17.8.10. Time-dependent CP violation parameters measured by Belle and BABAR in B \u2192D(\u2217)\u2213h\u00b1 decays.\nBABAR\nBelle\nPartial reconstruction\nFull reconstruction\nPartial reconstruction\nFull reconstruction\n(Aubert, 2005v)\n(Aubert, 2006aa)\n(Bahinipati, 2011)\n(Ronga, 2006)\nN(BB) = 232 \u00d7 106\nN(BB) = 232 \u00d7 106\nN(BB) = 657 \u00d7 106\nN(BB) = 386 \u00d7 106\naD\u2217\u03c0\n\u22120.034 \u00b1 0.014 \u00b1 0.009\n\u22120.040 \u00b1 0.023 \u00b1 0.010\n\u22120.046 \u00b1 0.013 \u00b1 0.015\n\u22120.039 \u00b1 0.020 \u00b1 0.013\ncD\u2217\u03c0\n\u22120.019 \u00b1 0.022 \u00b1 0.013\n+0.049 \u00b1 0.042 \u00b1 0.015\n\u22120.015 \u00b1 0.013 \u00b1 0.015\n\u22120.011 \u00b1 0.020 \u00b1 0.013\naD\u03c0\n\u2212\n\u22120.010 \u00b1 0.023 \u00b1 0.007\n\u2212\n\u22120.050 \u00b1 0.021 \u00b1 0.012\ncD\u03c0\n\u2212\n\u22120.033 \u00b1 0.042 \u00b1 0.012\n\u2212\n\u22120.019 \u00b1 0.021 \u00b1 0.012\naD\u03c1\n\u2212\n\u22120.024 \u00b1 0.031 \u00b1 0.009\n\u2212\n\u2212\ncD\u03c1\n\u2212\n\u22120.098 \u00b1 0.055 \u00b1 0.018\n\u2212\n\u2212\nIn Table 17.8.10 we summarize results on CP viola-\ntion parameters sensitive to 2\u03c61 + \u03c63 obtained with B \u2192\nD(\u2217)\u00b1\u03c0\u2213by the two experiments. Results are given in\nterms of two parameters a and c, de\ufb01ned as\na = (S+ + S\u2212)/2,\nc = (S+ \u2212S\u2212)/2.\n(17.8.30)\nThese parameters were introduced by BABAR (Aubert,\n2005v, 2006aa) in both partial and full reconstruction anal-\nyses in an attempt to disentangle the results from possi-\nble CP violation e\ufb00ects on the Btag side. The parameter a\nis always independent of tag-side CP violation; the same\nalso holds true for c in the case of semileptonic Btag decays\nsince those decays are dominated by a single amplitude.\nIn the partial reconstruction analysis, Belle (Bahinipati,\n2011) uses only lepton tags for Btag, while BABAR em-\nploys kaon- and lepton-tagged events. Both experiments\nuse the a and c notation in the partial reconstruction anal-\nyses, whereas full-reconstruction results of Belle (Ronga,\n2006) are presented in terms of S+ and S\u2212. To compare\nresults from the two experiments, we convert S+ and S\u2212\ninto a and c after taking into account the relative factor\n(\u22121)L between Belle and BABAR in the de\ufb01nition of S\u00b1,\nwhere the orbital angular momentum L equals 0 (1) for\nthe D\u03c0 (D\u2217\u03c0) \ufb01nal state. The search for CP violation in\nthese decays has provided results with signi\ufb01cance at the\nlevel of 2.5 (2.0) standard deviations from Belle (BABAR).\nFigure 17.8.13, for instance, provides an illustration of\nCP violation results obtained in the partial reconstruc-\ntion analysis of Belle.\n17.8.5.4 Results from B \u2192D(\u2217)\ns h (h = \u03c0, K) decays\nAmong charmed-strange meson \ufb01nal states, BABAR (Au-\nbert, 2008u) and Belle (Das, 2010; Joshi, 2010) have\nstudied B0 \u2192D(\u2217)+\ns\n\u03c0\u2212and B0 \u2192D(\u2217)\u2212\ns\nK+ (see Sec-\ntion 17.3.3). As mentioned earlier, the former decay consti-\ntutes an independent measurement of the small parameter\nR and the latter provides a measure of the W-exchange\ncontribution in B \u2192D(\u2217)\u00b1\u03c0\u2213.\nIn Table 17.8.11 we present the branching fraction\nmeasurement of B0 \u2192D(\u2217)+\ns\nh\u2212, where h = \u03c0 or \u03c1, from\nthe two experiments. By substituting these numbers along\nwith world-average values for |Vcd|, |Vcs| and B(B0 \u2192\nD(\u2217)\u2212h+) (Beringer et al., 2012) as well as for lattice\nQCD estimates of the decay constants of the D(\u2217) and\n\n363\nTable 17.8.11. Measured branching fractions for B0 \u2192D(\u2217)+\ns\nh\u2212(h = \u03c0, \u03c1) and B0 \u2192D(\u2217)\u2212\ns\nK(\u2217)+ with the corresponding\naverage values. All are in units of 10\u22125.\nBABAR (Aubert, 2008u)\nBelle (Das, 2010; Joshi, 2010)\nAverage\nN(BB) = 381 \u00d7 106\nN(BB) = 657 \u00d7 106\nB(B0 \u2192D+\ns \u03c0\u2212)\n2.5 \u00b1 0.4 \u00b1 0.2\n1.99 \u00b1 0.26 \u00b1 0.18\n2.16 \u00b1 0.26\nB(B0 \u2192D\u2217+\ns \u03c0\u2212)\n2.6+0.5\n\u22120.4 \u00b1 0.3\n1.75 \u00b1 0.34 \u00b1 0.20\n2.02 \u00b1 0.33\nB(B0 \u2192D+\ns \u03c1\u2212)\n1.1+0.9\n\u22120.8 \u00b1 0.3\n\u2212\n1.10 \u00b1 0.95\nB(B0 \u2192D\u2217+\ns \u03c1\u2212)\n4.1+1.3\n\u22121.2 \u00b1 0.8\n\u2212\n4.10 \u00b1 1.53\nB(B0 \u2192D\u2212\ns K+)\n2.9 \u00b1 0.4 \u00b1 0.2\n1.91 \u00b1 0.24 \u00b1 0.17\n2.21 \u00b1 0.25\nB(B0 \u2192D\u2217\u2212\ns K+)\n2.4 \u00b1 0.4 \u00b1 0.2\n2.02 \u00b1 0.33 \u00b1 0.22\n2.19 \u00b1 0.30\nB(B0 \u2192D\u2212\ns K\u2217+)\n3.5+1.0\n\u22120.9 \u00b1 0.4\n\u2212\n3.50 \u00b1 1.08\nB(B0 \u2192D\u2217\u2212\ns K\u2217+)\n3.2+1.4\n\u22121.2 \u00b1 0.4\n\u2212\n3.20 \u00b1 1.46\nD(\u2217)\ns\nmesons (Laiho, Lunghi, and Van de Water, 2010) in\nEq. (17.8.29), we determine\nRD\u03c0 = (1.73 \u00b1 0.15 \u00b1 0.04)%,\nRD\u2217\u03c0 = (1.65 \u00b1 0.18 \u00b1 0.04)%,\nRD\u03c1 = (0.74 \u00b1 0.33 \u00b1 0.02)%,\nRD\u2217\u03c1 = (1.50 \u00b1 0.31 \u00b1 0.04)%,\n(17.8.31)\nwhere the second errors are due to those on fD(\u2217)/fD(\u2217)\ns .\nNote that here we have assumed the ratio fD\u2217/fD\u2217s to be\nthe same as fD/fDs. The R values obtained are somewhat\nsmaller than the na\u00a8\u0131ve expectations of 2%: in particular,\nRD\u03c1 is signi\ufb01cantly below 2%. Table 17.8.11 also summa-\nrizes the branching fractions for B0 \u2192D(\u2217)\u2212\ns\nK(\u2217)+ mea-\nsured by the two experiments. These branching fractions\nare two orders of magnitude smaller than those of the\nCF decays B0 \u2192D(\u2217)\u2212\u03c0+, implying insigni\ufb01cant contri-\nbutions from the internal W exchange diagram (or a CF\nB0 \u2192D0dd diagram followed by dd \u2192ss re-scattering).\nThis justi\ufb01es neglecting contributions from similar dia-\ngrams in the determination of R (Eq. 17.8.29).\n17.8.5.5 Results from the decay B+ \u2192D\u2217+\u03c00\nBelle (Iwabuchi, 2008) has performed a search for the DCS\ndecay B+ \u2192D\u2217+\u03c00. No signi\ufb01cant signal is found, and a\n90% con\ufb01dence-level upper limit is set on the branching\nfraction, B(B+ \u2192D\u2217+\u03c00) < 3.6 \u00d7 10\u22126. This limit is\nused to constrain RD\u2217\u03c0 to be less than 5.1% at the 90%\ncon\ufb01dence level. The upper limit on R is consistent with\nthe values obtained from B \u2192D(\u2217)\ns h.\n17.8.5.6 Constraint on 2\u03c61 + \u03c63 from B \u2192D(\u2217)h\nOne can derive a combined constraint on 2\u03c61 + \u03c63 using\nrelevant observables measured in the B \u2192D(\u2217)\u2213h\u00b1 de-\ncays. There are two measurements, a and c (or S+ and\nS\u2212), and three unknown quantities, R, \u03b4, and 2\u03c61 + \u03c63,\nof which the \ufb01rst two are di\ufb00erent for each decay chan-\nnel. To \ufb01nd a solution, we can use the RD(\u2217)h values ex-\ntracted with the SU(3) relation of Eq. (17.8.29) as an ad-\nditional input. Combining results on a and c with RD(\u2217)h\n(see Table 17.8.10 and Eq. 17.8.31) using a frequentist\nmethod described in Charles et al. (2005), we obtain a\nconstraint on 2\u03c61 + \u03c63. The con\ufb01dence level as a func-\ntion of | sin(2\u03c61 + \u03c63)| is shown in Fig. 17.8.14. We set\na lower limit | sin(2\u03c61 + \u03c63)| > 0.74 (0.51) at 68% (90%)\ncon\ufb01dence level.\n17.8.5.7 Constraint on 2\u03c61 + \u03c63 from B \u2192DK\u03c0\nBABAR (Aubert, 2008bg) has performed a time-dependent\nDalitz plot analysis of B0 \u2192D\u2213K0\u03c0\u00b1. Since both b \u2192c\nand b \u2192u diagrams involved in these decays are color\nsuppressed, the R value is expected to be larger than that\nfound in B \u2192D(\u2217)\u2213h\u00b1. Assuming R is 30% and constant\nacross the Dalitz plot, BABAR \ufb01nds 2\u03c61 + \u03c63 = (83 \u00b1 53 \u00b1\n20)\u25e6along with an equivalent solution at a value 180\u25e6\nlarger than this, where the \ufb01rst error is statistical and the\nsecond is systematic.\n17.8.6 Determination of \u03c63 and discussion\nWe combine the available BABAR (B\u00b1 \u2192DK\u00b1, B\u00b1 \u2192\nD\u2217K\u00b1, and B\u00b1 \u2192DK\u2217\u00b1) and Belle (B\u00b1 \u2192DK\u00b1,\nB\u00b1 \u2192D\u2217K\u00b1) observables obtained for the GLW method\n(Table 17.8.1), the ADS method (Table 17.8.2), and the\nGGSZ method (model-dependent results as shown in\nTable 17.8.8) using the frequentist procedure (plug-in\nmethod) exploited in Charles et al. (2005). The p-value\n(1 \u2212C.L.) curves for the angle \u03c63 as well as the hadronic\nparameters (\u03b4B and rB) of the B \u2192DK mode are shown\nin Fig. 17.8.15 and the 68% C.L. intervals are summarized\nin Table 17.8.12. The results obtained are in very good\nagreement with individual constraints available for each\nexperiment (Lees, 2013e and Trabelsi, 2013): the combined\nB Factory \u03c63 average is (67 \u00b1 11)\u25e6.\n\n364\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.2\n0.4\n0.6\n0.8\n1\n| sin 2 \u03c61 + \u03c63 |\n 1-CL\nFigure 17.8.14. Combined constraint on 2\u03c61 + \u03c63 using relevant observables measured in the B \u2192D(\u2217)h decays. The dashed\n(dotted) line indicates the 68% (90%) con\ufb01dence-level lower limit.\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n\u03c63 (degree)\n1-CL\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2\nrB (DK)\n1-CL\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n\u03b4B (degree)\n1-CL\nFigure 17.8.15. Combined constraint (red curve) on \u03c63 (left), rB(DK) (middle) and \u03b4B(DK) (right) using relevant BABAR\nand Belle observables measured in the B \u2192D(\u2217)K(\u2217) decays. The green (blue) curve represents the results using only the BABAR\n(Belle) observables, the dashed (dotted) line indicates the 68% (90%) con\ufb01dence-level lower limit.\nTable 17.8.12. Con\ufb01dence intervals for \u03c63, rB(DK) and\n\u03b4B(DK) obtained from the combination of the relevant BABAR\nand Belle observables measured in the B \u2192D(\u2217)K(\u2217) decays.\n\u03c63 (\u25e6)\nrB(DK)\n\u03b4B(DK) (\u25e6)\nBABAR\n69 \u00b1 17\n0.090+0.016\n\u22120.017\n105 \u00b1 19\nBelle\n68 \u00b1 14\n0.112 \u00b1 0.015\n116+19\n\u221221\nB Factories\n67 \u00b1 11\n0.102 \u00b1 0.011\n111+13\n\u221214\n\n365\n17.9 Radiative and electroweak penguin\ndecays\nEditors:\nAl Eisner, Stephen Playfer (BABAR)\nMikihiko Nakao (Belle)\nTobias Hurth (theory)\nAdditional section writers:\nJohn Walsh\nThis section discusses radiative penguin B meson decays\nwith b \u2192s\u03b3 and b \u2192d\u03b3 transitions, and electroweak pen-\nguin82 B meson decays with b \u2192s\u2113+\u2113\u2212, b \u2192d\u2113+\u2113\u2212and\nb \u2192s\u03bd\u00af\u03bd transitions. These B decay modes are considered\nto be among the most sensitive probes for physics beyond\nthe SM, because they occur at loop level, and their rates\ncan be accurately predicted. In the SM the decays proceed\nat lowest order through penguin loop and box diagrams in-\nvolving heavy virtual top quarks and weak W or Z bosons\nas shown in Figure 17.9.1. Beyond the SM these could also\ncontain hypothetical heavy particles, e.g. supersymmetric\npartners of quarks and bosons, or charged Higgs bosons.\nAt the B Factories many of these decays have been\nstudied. Inclusive and exclusive branching fractions have\nbeen accurately determined for b \u2192s\u03b3, and measured for\nthe \ufb01rst time for b \u2192d\u03b3 and b \u2192s\u2113+\u2113\u2212. Here, an in-\nclusive decay is denoted for example as B \u2192Xs\u03b3, where\nXs is the sum of the hadronic \ufb01nal states formed by the\nrecoiling s quark from b \u2192s\u03b3 and the spectator u or d\nquark, whereas an exclusive decay speci\ufb01es the \ufb01nal state\nhadron(s), for example, B \u2192K\u2217(892)\u03b3. Time-integrated\nand time-dependent CP asymmetries have also been mea-\nsured. For b \u2192s\u2113+\u2113\u2212, the decay amplitude depends on q2,\nwhich is the invariant mass squared of the di-lepton sys-\ntem, or the virtual momentum squared of the electroweak\nboson in the case of the lowest order penguin diagram.\nIn addition, angular analyses, which are sensitive to the\ninterference between di\ufb00erent terms in the decay ampli-\ntudes, have been performed as functions of q2.\nTheoretically, the SM predictions are at a similar level\nof accuracy to the experimental precision for the inclusive\nbranching fractions. This is due to the presence of leptons\nand photons in the \ufb01nal state which reduces the size of\nnon-perturbative QCD corrections.\nThis section (17.9) is organized into a short review\nof the theoretical aspects (17.9.1), then discussions of in-\nclusive and exclusive b \u2192s\u03b3 (17.9.2 and 17.9.3) and\nb \u2192d\u03b3 (17.9.4) decays, separate subsections on rate\nasymmetries (17.9.5) and time-dependent CP asymme-\ntry measurements (17.9.6), followed by subsections on\nb \u2192s(d)\u2113+\u2113\u2212(17.9.7) and b \u2192s\u03bd\u00af\u03bd (17.9.8) decays.\n82 In the literature these decays are also called semileptonic\nrare decays. We do not adopt this term here to avoid confusion\nwith semileptonic B meson decays with b \u2192c\u2113\u03bd and b \u2192u\u2113\u03bd.\nW \u2212\nt\nu, d\nb\nu, d\ns\n\u03b3\nW \u2212\nt\n\u03b3, Z\nu, d\nb\nu, d\ns\n\u2113+\n\u2113\u2212\nt\nW \u2212\nW +\n\u03bd\nu, d\nb\nu, d\ns\n\u2113+\n\u2113\u2212\nFigure 17.9.1. Examples of penguin loop diagram for b \u2192s\u03b3\n(top), and loop and box diagrams for b \u2192s\u2113+\u2113\u2212(bottom).\n17.9.1 Theoretical framework\n17.9.1.1 E\ufb00ective electroweak Hamiltonian\nRare B decays are governed by an interplay between the\nweak and strong interactions. This is especially the case\nfor inclusive B decay modes, where short-distance QCD\ne\ufb00ects are very important. In the decay B \u2192Xs\u03b3 these ef-\nfects lead to a rate enhancement by a factor of greater than\ntwo. Such e\ufb00ects are induced by hard-gluon exchanges\nbetween the quark lines of the one-loop electroweak di-\nagrams.\nThe perturbative QCD corrections that arise from hard\ngluon exchange bring in large logarithms of the form\n\u03b1n\nS(mb) logm(mb/M),\n(17.9.1)\nwhere m \u2264n (with n = 0, 1, 2, ...). M is the top or W\nmass and mb the b quark mass. These large logarithms\nare a natural feature in any process in which two di\ufb00erent\nmass scales are present. To obtain a reasonable result,\none must re-sum at least all the leading-log (LL) terms\nwith m = n, or \u03b1n\nS(mb) logn(mb/M), with the help of\nrenormalization group techniques (Grinstein, Savage, and\nWise, 1989; Grinstein, Springer, and Wise, 1988, 1990).\nWorking to next-to-leading-log (NLL) or next-to-next-to-\nleading-log (NNLL) precision means that one re-sums all\nthe terms with m = n \u22121 or m = n \u22122, too (Buchalla,\nBuras, and Lautenbacher, 1996; Misiak, 1993).\nA suitable framework in which to achieve the nec-\nessary re-summations of the large logarithms is an ef-\nfective low-energy theory with \ufb01ve quarks; this frame-\nwork is obtained by integrating out the heavy particles\ni.e. by removing them from the theory as dynamical \ufb01elds\n(Buchalla, Buras, and Lautenbacher, 1996). These are the\nelectroweak bosons and the top quark in the SM. This ef-\nfective \ufb01eld theory approach serves as a theoretical frame-\nwork for both inclusive and exclusive modes. The standard\nmethod of the operator product expansion (OPE) (Wil-\nson and Zimmermann, 1972) allows for a separation of\nthe B meson decay amplitude into two distinct parts, the\nlong-distance contributions contained in the operator ma-\ntrix elements and the short-distance physics described by\n\n366\nthe Wilson coe\ufb03cients. The electroweak e\ufb00ective Hamilto-\nnian can schematically be written as (Altarelli and Maiani,\n1974; Gaillard and Lee, 1974a; Witten, 1977)\nHe\ufb00= 4GF\n\u221a\n2\nX\ni\n\u03bbCKMCi(\u00b5, M) Oi(\u00b5),\n(17.9.2)\nwhere Oi(\u00b5) are operators of dimension six, Ci(\u00b5, M) are\nthe corresponding Wilson coe\ufb03cients, \u03bbCKM are products\nof CKM matrix elements, and \u00b5 denotes the factorization\nscale. As the heavy \ufb01elds are integrated out, the complete\ntop and W mass dependence is contained in the Wilson\ncoe\ufb03cients. Within the observable He\ufb00the scale depen-\ndence (\u00b5) should cancel out.\nThe e\ufb00ective electroweak Hamiltonian relevant to b \u2192\ns(d) \u03b3 and b \u2192s(d) \u2113+\u2113\u2212transitions in the SM reads\nHe\ufb00= \u22124GF\n\u221a\n2\n\"\n\u03bbt\nq\n10\nX\ni=1\nCiOi + \u03bbu\nq\n2\nX\ni=1\nCi(Oi \u2212Ou\ni )\n#\n,\n(17.9.3)\nwhere the explicit CKM factors are \u03bbt\nq = VtbV \u2217\ntq and \u03bbu\nq =\nVubV \u2217\nuq (q = s, d). The unitarity relations \u03bbc\nq = \u2212\u03bbt\nq \u2212\n\u03bbu\nq have already been used. The numerically signi\ufb01cant\ndimension-six operators are:83\nO1 = (sL\u03b3\u00b5T acL)(cL\u03b3\u00b5T abL) ,\n(17.9.4)\nO2 = (sL\u03b3\u00b5cL)(cL\u03b3\u00b5bL) ,\nOu\n1 = (sL\u03b3\u00b5T auL)(uL\u03b3\u00b5T abL) ,\nOu\n2 = (sL\u03b3\u00b5uL)(uL\u03b3\u00b5bL) ,\nO7 =\ne\n16\u03c02 mb(sL\u03c3\u00b5\u03bdbR)F\u00b5\u03bd ,\nO8 =\ngs\n16\u03c02 mb(sL\u03c3\u00b5\u03bdT abR)Ga\n\u00b5\u03bd ,\nO9 =\ne2\n16\u03c02 (sL\u03b3\u00b5bL)\nX\n\u2113\n(\u00af\u2113\u03b3\u00b5\u2113) ,\nO10 =\ne2\n16\u03c02 (sL\u03b3\u00b5bL)\nX\n\u2113\n(\u00af\u2113\u03b3\u00b5\u03b35\u2113) ,\nwhere T a are SU(3) color generators, F\u00b5\u03bd and G\u00b5\u03bd are\nelectromagnetic and chromomagnetic \ufb01elds, and the sub-\nscripts L and R refer to the left- and right-handed com-\nponents of the fermion \ufb01elds. In b \u2192s transitions the\ncontributions proportional to \u03bbu\ns are rather small, while in\nb \u2192d decays, where \u03bbu\nd is of the same order as \u03bbt\nd, these\ncontributions play an important role in CP and isospin\nasymmetries. The operators O9 and O10 only occur in the\nb \u2192s(d)\u2113+\u2113\u2212and b \u2192s\u03bd\u03bd modes.\nIt is worth noting that among the four-quark opera-\ntors, only the e\ufb00ective couplings for i = 1, 2 are large at\n83 There are also operators O\u2032\n7 and O\u2032\n8 where mb is replaced\nby ms (or md, respectively), and here these are suppressed by\nfactors ms/d/mb and are usually omitted.\nthe low scale \u00b5 = mb where C1,2(mb) \u22481. The so-called\nQCD penguin operators\nO3 = (sL\u03b3\u00b5bL)\nX\nq=u,d,c,s,b\n(qL\u03b3\u00b5qL) ,\n(17.9.5)\nO4 = (sL\u03b3\u00b5T abL)\nX\nq=u,d,c,s,b\n(qL\u03b3\u00b5T aqL) , (17.9.6)\nO5 = (sL\u03b3\u00b5bL)\nX\nq=u,d,c,s,b\n(qR\u03b3\u00b5qR) ,\n(17.9.7)\nO6 = (sL\u03b3\u00b5T abL)\nX\nq=u,d,c,s,b\n(qR\u03b3\u00b5T aqR) , (17.9.8)\nhave very small coe\ufb03cients C3, . . . , C6 and hence can safely\nbe neglected. The electromagnetic penguin with C7(mb) \u2248\n\u22120.3, and the chromomagnetic penguin with C8(mb) \u2248\n\u22120.15, play a signi\ufb01cant role in both b \u2192s(d)\u03b3 and b \u2192\ns(d)\u2113+\u2113\u2212. Finally the vector and axial-vector contribu-\ntions to b \u2192s(d)\u2113+\u2113\u2212have C9(mb) \u22484, C10(mb) \u2248\u22124.\nThere are three principal calculational steps that lead\nto the LL (NNLL) result within the e\ufb00ective \ufb01eld theory\napproach:\n1. At the scale \u00b5 = mW the full SM theory is matched\nwith the e\ufb00ective theory. This means that the calcu-\nlation of the amplitude in the full SM is expanded\nin inverse powers of the large masses (mW , mZ, mt)\nand the result is compared to the corresponding am-\nplitude in the e\ufb00ective theory. In this way the Wil-\nson coe\ufb03cients Ci(mW ) are extracted by comparison.\nAt the high scale \u00b5 = mW the Ci pick up only small\nQCD corrections, which can be calculated within \ufb01xed-\norder perturbation theory. In the LL (NNLL) calcula-\ntion, the matching has to be worked out at the O(\u03b10\nS)\n[O(\u03b12\nS)] level.\n2. The evolution of these Wilson coe\ufb03cients from \u00b5 =\nmW down to \u00b5 \u2248mb must then be performed with the\nhelp of the renormalization group. In this way the large\nlogarithms (Eq. 17.9.1) are shifted from the matrix\nelements of the operators into the Wilson coe\ufb03cients,\nand the matrix elements of the operators evaluated at\nthe low scale mb are free of these large logarithms. For\nthe LL (NNLL) calculation, this renormalization step\nhas to be performed up to order \u03b11\nS (\u03b13\nS).\n3. To LL (NNLL) precision, the corrections to the matrix\nelements of the operators \u27e8s\u03b3|Oi(\u00b5)|b\u27e9at the scale \u00b5 \u2248\nmb must be calculated to order \u03b10\nS (\u03b12\nS) precision.\nWhile the Wilson coe\ufb03cients Ci enter both inclusive\nand exclusive processes and can be calculated with pertur-\nbative methods, the calculational approaches to the ma-\ntrix elements of the operators di\ufb00er in the two cases. In\ninclusive modes, one can use quark-hadron duality in or-\nder to derive a well-de\ufb01ned heavy mass expansion of the\ndecay rates in powers of \u039bQCD/mb (Heavy Quark Expan-\nsion, HQE)84 (Bigi, Blok, Shifman, Uraltsev, and Vain-\nshtein, 1992; Bigi, Uraltsev, and Vainshtein, 1992; Chay,\nGeorgi, and Grinstein, 1990; Manohar and Wise, 1994). In\n84 In the following text the symbol \u039b/mb is also used to denote\n\u039bQCD/mb.\n\n367\nparticular, it turns out that the decay width of B \u2192Xs\u03b3\nis well approximated by the partonic decay rate, which can\nbe calculated in renormalization group improved pertur-\nbation theory (Ali, Hiller, Handoko, and Morozumi, 1997;\nFalk, Luke, and Savage, 1994):\n\u0393(B \u2192Xs\u03b3) = \u0393(b \u2192Xparton\ns\n\u03b3) + O(\u039b/mb)\n(17.9.9)\nIn exclusive processes one cannot rely on quark-hadron\nduality, and face the di\ufb03cult task of estimating matrix ele-\nments between meson states. A promising approach is the\nmethod of QCD-improved factorization (QCDF) which\nhas been systematically formalized for non-leptonic de-\ncays in the heavy quark limit mb \u2192\u221e(Beneke, Buchalla,\nNeubert, and Sachrajda, 1999, 2000, 2001). This method\nallows for a perturbative calculation of QCD corrections\nto na\u00a8\u0131ve factorization, and is the basis for the up-to-date\npredictions for exclusive rare B decays. However, within\nthis approach, a general, quantitative method to estimate\nthe important 1/mb corrections to the heavy quark limit\nis missing.\n17.9.1.2 Power corrections to inclusive decays\nThe inclusive decay rate is de\ufb01ned as (see also Section 17.1)\n\u0393 =\n1\n2mHb\nX\nX\n(2\u03c0)4\u03b44(pi \u2212pf) | \u27e8X | He\ufb00| Hb\u27e9|2 ,\n(17.9.10)\nwhere the sum runs over all possible states X. In order to\nset up a systematic approach, we use the optical theorem\nwhich relates the inclusive decay rate of a hadron Hb to\nthe imaginary part of the forward scattering amplitude\n\u0393(Hb \u2192X) =\n1\n2mHb\nIm \u27e8Hb | T | Hb\u27e9,\n(17.9.11)\nwhere T is the time-ordered product of two e\ufb00ective Hamil-\ntonians T = i\nR\nd4x T[He\ufb00(x)He\ufb00(0)].\nFrom this it is possible to construct an OPE of the op-\nerator T, which is expressed as a series of local operators\nthat are suppressed by powers of the b quark mass and\nwritten in terms of the b quark \ufb01eld (Bigi, Blok, Shifman,\nUraltsev, and Vainshtein, 1992; Bigi, Uraltsev, and Vain-\nshtein, 1992; Chay, Georgi, and Grinstein, 1990; Manohar\nand Wise, 1994):\nT[He\ufb00He\ufb00]\nOPE\n=\n1\nmb\n\u0000 X\ni\nc(0)\ni P(0)\ni\n+ 1\nmb\nX\ni\nc(1)\ni P(1)\ni\n+ 1\nm2\nb\nX\ni\nc(2)\ni P(2)\ni\n+ ...\n\u0001\n,\n(17.9.12)\nwhere P (n)\ni\nare local operators of dimension n+3 and c(n)\ni\nare the Wilson coe\ufb03cient of the OPE.\nTaking the forward matrix element (Eq. 17.9.11) gen-\nerates an expansion in inverse powers of the heavy quark\nmass. Note that the matrix elements \u27e8Hb | P(n)\ni\n| Hb\u27e9\nare of the order \u039bQCD to some appropriate power, and\nhence this expansion is expected to converge su\ufb03ciently\nwell as long as the energy release in the decay is large\nwith respect to the QCD scale, \u039bQCD \u226amb. With the\nhelp of heavy quark e\ufb00ective theory (HQET), where new\nheavy quark spin-\ufb02avor symmetries arise in the heavy\nquark limit mb \u2192\u221e(Isgur and Wise, 1992; Shifman\nand Voloshin, 1988), the hadronic matrix elements within\nthe OPE, \u27e8Hb | P(n)\ni\n| Hb\u27e9, can be further simpli\ufb01ed.\nIn this well-de\ufb01ned expansion, the free quark model is the\n\ufb01rst term in the constructed expansion in powers of 1/mb,\nand therefore the dominant contribution. In inclusive rare\nB decays, one \ufb01nds no correction of order \u039b/mb to the\nfree quark model approximation. The corrections to the\npartonic decay rate begin with 1/m2\nb only, which implies\na rather small numerical impact of the non-perturbative\ncorrections on the decay rate of inclusive modes. How-\never, there are more subtleties to consider if other than\nthe leading operators are taken into account (see below).\nOne can directly apply these methods to the inclusive\ndecay mode B \u2192Xs\u03b3. If one neglects perturbative QCD\ncorrections and assumes that the decay B \u2192Xs\u03b3 is due\nto the leading electromagnetic dipole operator O7 alone,\nthen the photon would always be emitted directly from the\nhard process of the b quark decay. One has to consider the\ntime-ordered product T[O+\n7 (x) O7(0)]. Using the OPE for\nT[O+\n7 (x) O7(0)] and HQET methods, as discussed above,\nthe decay width \u0393(B \u2192Xs\u03b3) reads (up to and including\nterms of order 1/m2\nb):\n\u0393 (O7,O7)\nB\u2192Xs\u03b3 = \u03b1EMG2\nF m5\nb\n32\u03c04\n|VtbVts|2 C2\n7(mb) (17.9.13)\n\u00d7\n\u0012\n1 \u22121\nm2\nb\n\u00141\n2\u00b52\n\u03c0 + 3\n2\u00b52\nG\n\u0015\u0013\n,\nwhere \u00b52\n\u03c0 and \u00b52\nG are the HQE parameters for the kinetic\nenergy and the chromomagnetic energy, respectively (see\nEqs 17.1.38 and 17.1.39 in Section 17.1). If the B \u2192Xs\u03b3\ndecay width is normalized to the charmless semileptonic\ndecays, the non-perturbative corrections of order 1/m2\nb\ncancel out within the ratio B(B \u2192Xs\u03b3)/B(B \u2192Xu\u2113\u03bd).\nHowever, in practice the branching fraction of inclusive\nrare decays are often normalized to the well measured\nB \u2192Xc\u2113\u03bd semileptonic branching fraction with which\nthe m5\nb dependence in Eq. (17.9.13) cancels.\nThe OPE for the inclusive decay B \u2192Xs\u03b3 breaks\ndown if one considers operators beyond the leading elec-\ntromagnetic dipole operator O7 (Buchalla, Isidori, and\nRey, 1998; Ligeti, Randall, and Wise, 1997; Voloshin, 1997).\nFor example, one \ufb01nds a contribution to the total decay\nrate due to the interference between the electromagnetic\ndipole operator O7 and the charming penguin amplitude\ndue to the current-current operator O2. This is an example\nof a so-called resolved photon contribution. These contri-\nbutions contain subprocesses in which the photon couples\nto light partons instead of connecting directly to the ef-\nfective weak interaction vertex. A systematic analysis of\nall resolved photon contributions related to other opera-\ntors in the weak Hamiltonian establishes this breakdown\nof the local OPE within the hadronic power corrections\n\n368\nas a generic result (Benzke, Lee, Neubert, and Paz, 2010).\nEstimating such nonlocal matrix elements is very di\ufb03-\ncult, and leads to an irreducible theoretical uncertainty of\n\u00b1(4 \u22125)% for the total CP averaged decay rate, de\ufb01ned\nwith a photon-energy cuto\ufb00E\u03b3 = 1.6 GeV (Benzke, Lee,\nNeubert, and Paz, 2011). This result indicates that the\ntheoretical e\ufb00orts for the B \u2192Xs\u03b3 mode have reached\nthe non-perturbative boundaries.\nThe non-perturbative contributions in the decay B \u2192\nXd\u03b3 can be treated analogously to those in the decay\nB \u2192Xs\u03b3. The local corrections that scale as 1/m2\nb are\nthe same for the two modes (up to CKM factors). Also,\nthe analysis of resolved contributions can be applied to\nthis case. On the other hand, the long-distance contribu-\ntions from the intermediate u quark in the penguin loops\nare critical. While they are suppressed in the B \u2192Xs\u03b3\nmode by the CKM matrix elements, there is no such CKM\nsuppression in B \u2192Xd\u03b3, and one must account for the\nnon-perturbative contributions that arise from the oper-\nator Ou\n1 . However, this interference contribution vanishes\nin the total CP-averaged rate of B \u2192Xd\u03b3 at order \u039b/mb.\nOther interference terms from the double resolved contri-\nbutions, involving Ou\n1 and O8, or Ou\n1 and Ou\n1 , arise \ufb01rst\nat order 1/m2\nb. Thus, there is no power correction due to\nthe operator Ou\n1 in the total rate of B \u2192Xd\u03b3 at order\n\u039b/mb, which implies that the CP-averaged decay rate of\nB \u2192Xd\u03b3 is as theoretically clean as the decay rate of\nB \u2192Xs\u03b3 (Benzke, Lee, Neubert, and Paz, 2010).\nLocal hadronic power corrections due to the leading\noperator O9 in the decay B \u2192Xs\u2113+\u2113\u2212that scale with\n1/m2\nb, 1/m3\nb, and 1/m2\nc have also been considered. They\ncan be calculated analogously to those in the decay B \u2192\nXs\u03b3. However, a systematic analysis of hadronic power\ncorrections including all relevant operators has yet to be\nperformed. Thus, an additional uncertainty of \u00b15% should\nbe added to all theoretical predictions for this mode on the\nbasis of a simple dimensional estimate.\nIn the high-q2 region of the decay b \u2192s\u2113+\u2113\u2212, one en-\ncounters a breakdown of the heavy quark expansion at\nthe end point of the di-lepton mass spectrum. Whereas\nthe partonic contribution vanishes, the 1/m2\nb and 1/m3\nb\ncorrections tend towards non-zero values. In contrast to\nthe end point region of the photon energy spectrum in\nthe B \u2192Xs\u03b3 decay (see below), no partial all-order re-\nsummation into a shape function is possible. However, for\nan integrated high-q2 spectrum an e\ufb00ective expansion is\nfound in inverse powers of me\ufb00\nb\n= mb \u00d7(1\u2212\u221asmin) rather\nthan mb. The expansion converges less rapidly, depend-\ning on the lower dilepton-mass cut smin = q2\nmin. The large\ntheoretical uncertainties could be signi\ufb01cantly reduced by\nnormalizing the B \u2192Xs\u2113+\u2113\u2212decay rate to the semilep-\ntonic B \u2192Xu\u2113\u03bd decay rate with the same q2 cut:\nR(s0) =\nZ 1\ns0\nds d\u0393(B \u2192Xs\u2113+\u2113\u2212)\nds\nZ 1\ns0\nds d\u0393(B \u2192Xu\u2113\u03bd)\nds\n.\n(17.9.14)\nIn this way, the relative uncertainty in this ratio due to the\ndominating 1/m3\nb term would be reduced to 9%, whereas\nthe relative uncertainty in the numerator alone is about\n19%.\n17.9.1.3 Shape functions and kinematical cuts\nIn the measurements of the inclusive mode B \u2192Xs\u03b3 one\nneeds cuts in the photon energy spectrum to suppress the\nbackground from other B decays. A threshold of 1.6 GeV\nis also required for theoretical predictions to remove cc\nbound states.\nIn order to deal with these cuts, one needs a theoret-\nical description of the photon energy spectrum. In prin-\nciple, this can be computed along the same lines as the\ntotal rates by using the heavy quark expansion. However,\nat leading order in \u03b1S and 1/mb, the spectrum is simply\na \u03b4-function expressing the fact that the photon recoils\nagainst a single quark and hence E\u03b3 = mb/2 (for a mass-\nless s quark). Without \u03b1S corrections, the spectrum re-\nmains concentrated at this single energy and the heavy\nquark expansion takes the form\nd\u0393\ndx = G2\nF \u03b1m5\nb\n32\u03c04\n|VtsV \u2217\ntb|2|C7|2\n\u0012\n\u03b4(1 \u2212x)\n(17.9.15)\n+\u00b52\n\u03c0 \u2212\u00b52\nG\n2m2\nb\n\u03b4\u2032(1 \u2212x) + \u00b52\n\u03c0\n6m2\nb\n\u03b4\u2032\u2032(1 \u2212x) + \u00b7 \u00b7 \u00b7\n\u0013\nwith x = 2E\u03b3/mb.\nIt has been shown in (Bigi, Shifman, Uraltsev, and\nVainshtein, 1994; Mannel and Neubert, 1994; Neubert,\n1994a) that the leading terms can be resummed into a\nshape function de\ufb01ned as\n2MBf(k+) = \u27e8B(v)|\u00afbv\u03b4(k+ \u2212iD+)bv|B(v)\u27e9,\n(17.9.16)\nwhich has a moment expansion according to\nf(\u03c9) = \u03b4(\u03c9) + \u00b52\n\u03c0\n6 \u03b4\u2032\u2032(\u03c9) \u2212\u03c13\nD\n18 \u03b4\u2032\u2032\u2032(\u03c9) + \u00b7 \u00b7 \u00b7 .\n(17.9.17)\nIn terms of the shape function, the spectrum takes the\nform\nd\u0393\ndx = G2\nF \u03b1m6\nb\n32\u03c04\n|VtsV \u2217\ntb|2|C7|2f(mb(1 \u2212x)) .\n(17.9.18)\nThe shape function is a non-perturbative quantity, which\nis universal for all heavy-to-light transitions. It either needs\nto be modeled or it can be extracted from other heavy-to-\nlight decays such as b \u2192u\u2113\u03bd. However, at the sub-leading\nlevel, several new shape functions need to be de\ufb01ned, spoil-\ning the simple relation between B \u2192Xs\u03b3 and B \u2192Xu\u2113\u03bd\n(Bauer, Luke, and Mannel, 2002, 2003).\nThe fact that the shape function is not well known\ninduces uncertainties in experimental branching fraction\nresults in two ways. First, the form (as well as the scheme)\nchosen for the shape function a\ufb00ects e\ufb03ciencies, and hence\na\ufb00ects the measured integrated branching fractions above\nE\u03b3 thresholds of 1.7 to 2.0 GeV. Second, the need for such\nthresholds in the measurements leads to further shape-\nfunction e\ufb00ects which are taken into account when the\n\n369\nbranching fractions are extrapolated down to an E\u03b3 thresh-\nold of 1.6 GeV, in order to compare to theoretical predic-\ntions. Both stages result in \u201cmodel-dependence\u201d uncer-\ntainties in the experimental results.\nThe shape functions have been represented using three\ndi\ufb00erent theoretical approaches: the \u201ckinetic\u201d scheme, the\n\u201cshape function\u201d scheme and \u201cdressed gluon exponentia-\ntion\u201d (DGE).\n\u2013 The kinetic scheme is frequently used in the context\nof the determination of Vcb and Vub from inclusive se-\nmileptonic decays and is described in some detail in\nSection 17.1.3.1.\n\u2013 In the shape function scheme (Neubert, 2005) a multi-\nscale OPE with three short-distance scales mb, \u221amb\u2206,\nand \u2206= mb \u22122E\u03b3 has been proposed to connect the\nshape function and the local OPE region (Becher and\nNeubert, 2007). Additional perturbative e\ufb00ects related\nto the kinematic cuto\ufb00have been calculated to NNLL\nprecision by the use of SCET methods. Further work\nis needed to clarify the applicability of these numerical\nresults (Misiak, 2008).\n\u2013 An alternative approach to the e\ufb00ects of the cuto\ufb00in\nthe photon energy spectrum is based on DGE, which\nincorporates Sudakov and renormalon re-summations\n(Andersen and Gardi, 2005). The greater predictive\npower of this approach is related in part to the as-\nsumption that non-perturbative power corrections as-\nsociated with the shape function follow the pattern of\nambiguities present in the perturbative calculation.\nIn the inclusive decay B \u2192Xs\u2113+\u2113\u2212, the hadronic and\ndi-lepton invariant masses are independent kinematical\nquantities. An upper hadronic invariant-mass cut is im-\nposed by the experiments to reduce backgrounds. The high\ndi-lepton mass region is not a\ufb00ected by this cut, since at\nhigh di-lepton mass the hadronic invariant mass is con-\nstrained to small values due to kinematics. In the low\ndi-lepton mass region the kinematics with a jet-like Xs\nand m2\nX \u2264mb\u039b implies the need to include the e\ufb00ects\nof a shape function. A recent SCET analysis shows that\nto leading order, using the universality of the shape func-\ntion, the form of the di-lepton mass spectrum at small\ndi-lepton masses remains unchanged, but the di\ufb00erential\nrate becomes smaller by an overall factor of 0.7\u22120.9. Nev-\nertheless, the e\ufb00ects of sub-leading shape functions lead to\nan additional uncertainty of 5% (Lee, Ligeti, Stewart, and\nTackmann, 2006; Lee and Stewart, 2006). Another anal-\nysis estimates the uncertainties due to sub-leading shape\nfunctions more conservatively. By scanning over a range of\nmodels of these functions, one \ufb01nds corrections in the rates\nrelative to the leading-order result to be between \u221210%\nto +10% with equally large uncertainties (Lee and Tack-\nmann, 2009). In the future it may be possible to decrease\nsuch uncertainties signi\ufb01cantly by constraining both the\nleading and sub-leading shape functions using the com-\nbined data from B \u2192Xs\u03b3, B \u2192Xu\u2113\u03bd and B \u2192Xs\u2113+\u2113\u2212\n(Lee and Tackmann, 2009).\n17.9.1.4 Soft Collinear E\ufb00ective Theory (SCET)\nThe Wilson coe\ufb03cients of the weak e\ufb00ective Hamilto-\nnian are process independent and can be used for both\ninclusive and exclusive modes. However, exclusive \ufb01nal\nstates require the computation of hadronic matrix ele-\nments between meson states, which is di\ufb03cult and limits\nthe theoretical precision. The na\u00a8\u0131ve approach is to write\nthe amplitude A \u2243Ci(\u00b5b)\u27e8Oi(\u00b5b)\u27e9and parameterizing\n\u27e8Oi(\u00b5b)\u27e9in terms of form factors. A substantial improve-\nment can be obtained by using the QCDF method (Be-\nneke, Buchalla, Neubert, and Sachrajda, 1999, 2000, 2001)\nand its \ufb01eld-theoretical formulation, SCET (Bauer, Flem-\ning, and Luke, 2000; Bauer, Fleming, Pirjol, and Stewart,\n2001; Bauer, Pirjol, and Stewart, 2002; Bauer and Stew-\nart, 2001; Beneke, Chapovsky, Diehl, and Feldmann, 2002;\nHill and Neubert, 2003). These methods form the basis of\nthe up-to-date predictions of exclusive B decays. Within\nthis framework one can show that, even if the form fac-\ntors were known with in\ufb01nite precision, the description of\nexclusive decays would be incomplete due to the existence\nof non-factorizable strong interaction e\ufb00ects that cannot\nbe represented by form factors.\nThe QCDF and SCET methods were \ufb01rst systematized\nfor exclusive non-leptonic decays in the heavy quark limit.\nIn contrast to the HQET, SCET does not correspond to\na local operator expansion. Whereas HQET is applica-\nble to B decays if the energy transfer to light hadrons is\nsmall, e.g. in B \u2192D transitions at small recoil, HQET\nis not applicable to rare decays where light particles have\nmomenta of order mb. One faces a multi-scale problem\nthat can be tackled within SCET. There are three rele-\nvant scales: (a) \u039b = few \u00d7 \u039bQCD, the soft scale set by\nthe typical energies and momenta of the light degrees of\nfreedom in the hadronic bound states; (b) mb, the hard\nscale set by both the heavy b quark mass and the energy\nof the \ufb01nal state hadrons in the B meson rest frame; and\n(c) the hard-collinear scale \u00b5hc = \u221amb\u039b, which appears\nthrough interactions between the soft and energetic modes\nin the initial and \ufb01nal states. The dynamics of the hard\nand hard-collinear parts can be described perturbatively\nin the heavy quark limit mb \u2192\u221e. In this limit SCET\ndescribes B decays to light hadrons with energies much\nlarger than their masses, assuming that their constituents\nhave momenta collinear to the hadron momenta.\n17.9.1.5 Application to the modes B \u2192K\u2217\u03b3 and B \u2192\u03c1\u03b3\nThe QCDF formalism can be applied to exclusive radiative\nand electroweak penguin decays (Beneke and Feldmann,\n2001). For B \u2192K\u2217\u03b3, or more generally for B \u2192V \u03b3,\nwhere V is a light vector meson, the QCDF formula for the\nhadronic matrix element of each operator of the e\ufb00ective\nHamiltonian in the heavy quark limit and to all orders in\n\u03b1S reads\n\u27e8V \u03b3| Oi |B\u27e9= T I\ni F B\u2192V\u22a5\n(17.9.19)\n+\nZ \u221e\n0\nd\u03c9\n\u03c9 \u03c6B(\u03c9)\nZ 1\n0\ndu \u03c6V\u22a5(u) T II\ni (\u03c9, u).\n\n370\nThis formula separates out the process independent non-\nperturbative quantities into F B\u2192V\u22a5, a form factor evalu-\nated at maximum recoil (q2 = 0), and the light-cone dis-\ntribution amplitudes (LCDA), \u03c6B and \u03c6V\u22a5, for the heavy\nand light mesons. This leaves the quantities T I and T II,\nknown as hard-scattering kernels, which can be calculated\nperturbatively. These correspond to vertex and specta-\ntor corrections, respectively, and have been calculated to\nO(\u03b11\nS) (Ali and Parkhomenko, 2002; Beneke, Feldmann,\nand Seidel, 2001; Bosch and Buchalla, 2002b; Descotes-\nGenon and Sachrajda, 2004), and recently in some cases\nto O(\u03b12\nS) (Ali, Pecjak, and Greub, 2008).\nThe LCDA of light pseudoscalar and vector mesons\nthat enter the factorization formula have been studied in\ndetail through the use of light-cone QCD sum rules (Ball\nand Braun, 1999; Ball, Braun, Koike, and Tanaka, 1998;\nBraun and Filyanov, 1989, 1990). However, not much is\nknown about the B meson LCDA, whose \ufb01rst moment\nenters the factorized amplitude at O(\u03b1S). Because this\nmoment also enters the factorized expression for the B \u2192\n\u03b3 form factor, it might be possible to extract its value\nfrom measurements of decays such as B \u2192\u03b3e\u03bd, if the\npower corrections are under control.\nThe QCDF formula introduces an important simpli\ufb01-\ncation in the form factor description. The B \u2192V\u22a5form\nfactors at large recoil have been analyzed in SCET and\nare independent of the Dirac structure of the current in\nthe heavy quark limit (Charles, Le Yaouanc, Oliver, P`ene,\nand Raynal, 1999). As a consequence of this, all the form\nfactors reduce to a single form factor up to factorizable\ncorrections in the heavy quark and large energy limits.\nField-theoretical methods such as SCET make it pos-\nsible to reach a deeper understanding of the QCDF ap-\nproach. The various momentum regions are represented\nby di\ufb00erent \ufb01elds, and the hard-scattering kernels T I and\nT II can be shown to be Wilson coe\ufb03cients of e\ufb00ective\n\ufb01eld operators. Using SCET one can prove the factoriza-\ntion formula to all orders in \u03b1S and to leading order in\n\u039b/mb (Becher, Hill, and Neubert, 2005). QCD is matched\non SCET in a two-step procedure that separates the hard\nscale \u00b5 \u223cmb and then the hard-collinear scale \u00b5 \u223c\u221a\u039bmb\nfrom the hadronic scale \u039b. The vertex correction term T I\ninvolves the hard scales, whereas the spectator scattering\nterm T II involves both the hard and the hard-collinear\nscales. This is why large logarithms have to be resummed,\nwhich can be done most e\ufb03ciently in SCET.\nIn principle, the \ufb01eld-theoretical framework of SCET\nallows one to go beyond the leading-order result in \u039b/mb.\nHowever, a breakdown of factorization is expected at that\norder. For example, in the analysis of B \u2192K\u2217\u03b3 de-\ncays at sub-leading order, an infrared divergence is en-\ncountered in the matrix element of O8 (Kagan and Neu-\nbert, 2002). In general, power corrections involve convo-\nlutions, which turn out to be divergent. Currently, no\nsolution to this well-analyzed problem of end-point di-\nvergences within power corrections is available (Arne-\nsen, Ligeti, Rothstein, and Stewart, 2008; Becher, Hill,\nand Neubert, 2004; Beneke and Feldmann, 2004). Thus,\nwithin the QCDF/SCET approach, a general, quantita-\ntive method to estimate the important \u039b/mb corrections\nto the heavy quark limit is missing, which signi\ufb01cantly\nlimits the precision in phenomenological applications.\nNevertheless, some very speci\ufb01c power corrections are\nstill computable and are often numerically important. In-\ndeed, this is the case for the annihilation and weak ex-\nchange amplitudes in B \u2192\u03c1\u03b3, where the annihilation\ndiagram represents the leading contribution to the isospin\nasymmetry (Kagan and Neubert, 2002). These corrections\nare included in recent theoretical predictions of these de-\ncays. The method of light-cone QCD sum rules can also\nhelp to provide estimates of such unknown sub-leading\nterms. For example, power corrections to the indirect CP\nasymmetries in B \u2192V \u03b3 decays have been analyzed in\nthis manner (Ball, Jones, and Zwicky, 2007).\n17.9.1.6 Application to the mode B \u2192K\u2217\u2113+\u2113\u2212\nThere is a similar factorization formula for the exclusive\nelectroweak penguin B decays, such as B \u2192K\u2217\u2113+\u2113\u2212, but\nthe simpli\ufb01cation due to form factor relations is even more\ndrastic. The hadronic form factors can be expanded in the\nsmall ratios \u039b/mb and \u039b/E, where E is the energy of the\nlight meson. If corrections of order 1/mb and \u03b1S are ne-\nglected, the seven a priori independent B \u2192K\u2217form\nfactors reduce to two universal form factors \u03be\u22a5and \u03be\u2225\n(Charles, Le Yaouanc, Oliver, P`ene, and Raynal, 1999).\nThis reduction makes it possible to design interesting ra-\ntios of observables in which any soft form factor depen-\ndence cancels out for all di-lepton masses q2 at leading or-\nder in \u03b1S and \u039b/mb (Bobeth, Hiller, van Dyk, and Wacker,\n2012; Egede, Hurth, Matias, Ramon, and Reece, 2008,\n2010).\nThe theoretical simpli\ufb01cations of the QCDF/SCET\napproach are restricted to the kinematic region in which\nthe energy of the K\u2217is of the order of the heavy quark\nmass, q2 \u226am2\nB. However, in the limit q2 \u21920 the longitu-\ndinal amplitude in the QCDF/SCET approach generates\na logarithmic divergence, which indicates problems in the\ntheoretical description. The presence of light resonances\nbelow 1 GeV/c2 may also call into question the QCDF re-\nsults in this region. Thus, the factorization formula only\napplies well in the di-lepton mass range 1 GeV2/c2 < q2 <\n6 GeV2/c2.\nThe QCDF and SCET methods are also applicable to\nother phenomenologically important electroweak penguin\ndecays such as B \u2192K\u2113+\u2113\u2212(Bobeth, Hiller, and Piran-\nishvili, 2007), B \u2192\u03c1\u2113+\u2113\u2212(Beneke, Feldmann, and Seidel,\n2005), and Bs \u2192\u03c6\u2113+\u2113\u2212. Note that the decay into a pseu-\ndoscalar meson is analogous to the decay into a longitu-\ndinally polarized vector meson.\n17.9.2 Inclusive b \u2192s\u03b3\nThe transition b \u2192s\u03b3 was \ufb01rst observed by CLEO II\nthrough the exclusive decay B \u2192K\u2217\u03b3 (Ammar et al.,\n1993). This was followed by the \ufb01rst measurement of the\ninclusive rate for b \u2192s\u03b3 using a combination of a fully\n\n371\ninclusive photon spectrum, and a \u201cpseudoreconstruction\u201d\n(see Section 17.9.2.4) of a sum of exclusive \ufb01nal states in\nB \u2192Xs\u03b3 (Alam et al., 1995).\nThe detailed computation described in Sections 17.9.1.1\nand 17.9.1.2 results in the NNLL prediction for a photon-\nenergy (E\u03b3) threshold of E\u03b3 > 1.6 GeV (Misiak et al.,\n2007)\nB(B \u2192Xs\u03b3)NNLL = (3.15 \u00b1 0.23) \u00d7 10\u22124.\n(17.9.20)\nThe overall uncertainty is the quadratic sum of non-per-\nturbative (5%), parametric (3%), perturbative scale (3%)\nand mc interpolation ambiguity (3%) uncertainties. An\nadditional scheme dependence has since been found (Gam-\nbino and Giordano, 2008), but it is within the perturbative\nuncertainty of 3% (Misiak, 2008).\nHowever, in experimental measurements, a large back-\nground from non-signal BB events at low values of photon\nenergy limits the minimum useful E\u03b3. The \ufb01nal B \u2192Xs\u03b3\nCLEO publication (Chen et al., 2001b) reports results for\nE\u03b3 above 2.0 GeV using 9 fb\u22121 of \u03a5(4S) data and 4.4 fb\u22121\nof o\ufb00-resonance data. They made an extrapolation down\nto the full energy range, and quoted an inclusive branch-\ning fraction of (3.21 \u00b1 0.43 \u00b1 0.27+0.18\n\u22120.10) \u00d7 10\u22124, where the\nerrors are statistical, systematic and model-dependence,\nrespectively.\nThe much larger data samples of the B Factories and\nto some extent their improved detectors have allowed for a\nnumber of signi\ufb01cant advances in the analysis techniques,\nleading to large reductions in the systematic uncertain-\nties as well as the statistical uncertainties of measured\nbranching fractions. They have also made it possible to\nreduce the photon energy threshold, in one case down to\n1.7 GeV, and detailed studies of the E\u03b3 spectrum are used\nto help constrain the model-dependent extrapolation. The\nworld-average extrapolated branching fraction now has an\nuncertainty comparable to that on the theoretical predic-\ntion.\nIn the following, four measurements of the inclusive\nB \u2192Xs\u03b3 branching fraction are described. Three of these\nare fully inclusive, while the fourth builds up the branch-\ning fraction as a sum of exclusive \ufb01nal states. The hall-\nmark of a fully inclusive measurement is that for a signal\nB it requires only the detection of a high-energy photon\nwith E\u03b3 close to half the b-quark mass. Because of this the\nprocesses B \u2192Xs\u03b3 and B \u2192Xd\u03b3 are not separated. For\nbranching fractions, the B \u2192Xd\u03b3 contribution is easily\nsubtracted using\nB(B \u2192Xd\u03b3)\nB(B \u2192Xs\u03b3) = (|Vtd|/|Vts|)2 = 0.044\u00b10.003 . (17.9.21)\nAs the measurement is based on the photon, the result is\nnot much a\ufb00ected by uncertainties in the hadronization\nprocess of the s quark. However, the measured value of\nE\u03b3 is subject to electromagnetic-calorimeter resolution.\nAlso, because (for two of the three measurements) the\nB rest frame is not known, there is Doppler smearing\ndue to the motion of the B in the \u03a5(4S) center-of-mass\nframe. Inclusiveness is not compromised by imposing re-\nquirements on the non-signal B (B) meson in the event.\nSuch requirements can signi\ufb01cantly reduce the large back-\nground from continuum processes (i.e., e+e\u2212\u2192qq or\n\u03c4 +\u03c4 \u2212, with q = u, d, s, c), which dominates the statisti-\ncal uncertainty on the extracted signal. One such require-\nment is lepton tagging: for BB events a high-momentum\nelectron or muon can arise from the semileptonic decay\nof the non-signal B. The Belle analysis described in Sec-\ntion 17.9.2.1 combines separate samples of untagged and\nlepton-tagged events, while the BABAR analysis in Sec-\ntion 17.9.2.2 relies on lepton tagging. The BABAR analysis\nin Section 17.9.2.3 fully reconstructs the non-signal B in\nhadronic decay modes. This has the advantage that the\nsignal-B frame is known, but at a great cost in statistics.\nThe sum-of-exclusive-modes method in Section 17.9.2.4\nspeci\ufb01cally reconstructs Xs \ufb01nal states, and determines\nthe photon energy in the B rest frame, using\nE\u03b3 = m2\nB \u2212m2\nXs\n2mB\n,\n(17.9.22)\nwith a resolution that is much better than that of the\ndirect photon energy measurement with the calorimeter.\nOn the other hand, there are substantial systematic un-\ncertainties from the hadronization model and unmeasured\nmodes, and signal e\ufb03ciency decreases signi\ufb01cantly with\nincreasing mXs.\nThe branching-fraction results from all the methods\nare summarized at the end in Table 17.9.3. The \ufb01rst two\nfully-inclusive approaches provide by far the best preci-\nsion on the branching fraction above any given energy\nthreshold. (The sum-of-exclusive-modes approach is sys-\ntematically limited by uncertainties in the Xs hadroniza-\ntion, which a\ufb00ect both the e\ufb03ciency for the selected decay\nmodes and the contribution of the unmeasured modes.)\nResults are also presented for the photon energy spectrum\n(Section 17.9.2.5) and, later, for direct CP asymmetries\n(Section 17.9.5.3). Extrapolating the branching fraction\nmeasurements down to a 1.6 GeV threshold, for which the\ntheoretical SM prediction is made, can provide useful con-\nstraints on new physics (Section 17.9.2.7).\n17.9.2.1 Belle fully inclusive (untagged and lepton-tagged)\nThe untagged inclusive method was \ufb01rst applied by Belle\nwith 140 fb\u22121 of \u03a5(4S) data (Koppenburg, 2004). High-\nenergy photons leave a clear signal in the CsI (Tl) electro-\nmagnetic calorimeter, with good energy resolution. The\nmain challenge for this method is the subtraction of\nthe large background from other sources of photons and\nphoton-like signals.\nThat initial analysis is superseded by the latest mea-\nsurement (Limosani, 2009), with 605 fb\u22121 of \u03a5(4S) data\n(657M BB) and 68 fb\u22121 of data collected 60 MeV below\nthe \u03a5(4S). In the updated analysis, a separate measure-\nment with the lepton tag method (Section 17.9.2.2) is also\nperformed on the same sample. The sizes of the statistical\nerrors are comparable between the two methods. Since the\nevents that pass the selection criteria are not fully over-\nlapping between the two methods, the photon spectra are\n\n372\nseparately measured and then combined (taking correla-\ntions into account) to increase the sensitivity.\nThe photons need to be isolated from other clusters\nin the calorimeter. They are then matched to other low\nenergy photons to see if they form either a \u03c00 or \u03b7 meson.\nIf they do they are rejected from further analysis (\u201c\u03c00/\u03b7\nveto\u201d). There is a systematic error of 3% from the photon\nselection e\ufb03ciency, which mainly comes from the isolation\nrequirement and the understanding of the \u03c00 and \u03b7 veto.\nEvent shape information is used to suppress a large\nfraction of the background from continuum events. Then\nthe remainder, which for the untagged sample is still huge,\nas illustrated in Figure 17.9.2, is subtracted by using a\nsample of o\ufb00-resonance data, which is free from B-meson\ndecays. The B Factories took o\ufb00-resonance data at a frac-\ntion of \u223c10% to 11% of their \u03a5(4S) data (much lower\nthan CLEO\u2019s 50%). The subtraction of the continuum\nbackground is the largest statistical error source in this\nmethod. There is also a systematic error of up to 7.5%\n(depending on the photon energy threshold) of the sub-\ntracted value,85 originating from the anti-correlated small\nuncertainties in the scaling factor for the continuum sub-\ntraction (0.3%) and in the number of BB for the B back-\nground subtraction (1.4%). The continuum scaling factor\nis the luminosity ratio corrected for the change in cross-\nsection and photon energy spectrum as a function of the\ncenter-of-mass energy.\nOnce the non-B backgrounds are subtracted, the dom-\ninant background source are the B decay modes that pro-\nduce photons through secondary meson decays, with the\nmain contribution coming through \u03c00 \u2192\u03b3\u03b3 decays, and\nthe next largest through \u03b7 \u2192\u03b3\u03b3 as shown in Figure 17.9.3.\nThese photons are on average lower in energy, but follow\na steeply rising spectrum as the photon energy threshold\nis reduced. This background is simulated by a generic BB\nMonte Carlo sample, in which the \u03c00 and \u03b7 momentum\nspectra are calibrated using their distributions from B de-\ncays measured in the data. Other sources of photons in B\ndecays then dominate the uncertainty on the background,\ngiving a systematic error of 2\u20137% (depending on the pho-\nton energy threshold). These include real photons from\n\u03c9, \u03b7\u2032 and charmonia decays, and fake photons from elec-\ntrons, anti-neutrons and K0\nL. An artifact due to remnant\nenergy clusters of out-of-time electrons from QED pro-\ncesses, which is not fully subtracted by the o\ufb00-resonance\nsample as its rate depends on the instantaneous luminos-\nity, is also subtracted. These contributions are evaluated\nusing data as much as possible.\nThe combined (untagged and lepton-tagged) photon\nenergy spectrum is shown in Figure 17.9.4, after back-\nground subtraction, e\ufb03ciency correction and unfolding of\nthe calorimeter resolution. The B \u2192Xd\u03b3 contribution is\nthen subtracted, using Eq. (17.9.21), to give the B \u2192Xs\u03b3\nbranching fraction. The photon energy spectrum and the\nreconstruction e\ufb03ciency are considered to be the same for\nB \u2192Xs\u03b3 and B \u2192Xd\u03b3.\n85 The quoted systematic errors in this section are for the\ncombined untagged and lepton-tag results for the integrated\nbranching fraction.\n [GeV]\n\u03b3\nc.m.s\nE\n1.5\n2\n2.5\n3\n3.5\n4\nPhoton candidates/(0.05 GeV)\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\nON resonance\nscaled OFF resonance\n\u03b3\n X \n\u2192\n \nB\n B\n\u2192\n(4S) \n\u03a5\nFigure 17.9.2. Photon energy spectrum before background\nsubtraction, continuum background estimated from the o\ufb00-\nresonance events, and the continuum-subtracted spectrum, all\nfor the untagged selection in Belle\u2019s 657M BB data.\n [GeV]\n\u03b3\nc.m.s\nE\n1.5\n2\n2.5\n3\n3.5\nPhoton Candidates/(0.05 GeV)\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n7\n10\n\u03b3\n\u03b3\n\u2192\n0\n\u03c0\n\u03b3\n\u03b3\n\u2192\n\u03b7\nOther decays\nBeam bkgd\nMis-ID e\nMis-ID hadron\nSignal\nFigure 17.9.3. Expected B \u2192Xs\u03b3 signal and background\ncontributions as functions of the center-of-mass photon energy\nfrom Belle\u2019s Monte Carlo simulation for 657M BB. This illus-\ntration is for the untagged selection.\nUsing a photon energy threshold E\u03b3 > 1.7 GeV, where\nthe photon energy is de\ufb01ned in the B-meson rest frame,\nthe B \u2192Xs\u03b3 branching fraction is measured to be\n(3.45 \u00b1 0.15 \u00b1 0.40) \u00d7 10\u22124 (Belle, E\u03b3 > 1.7 GeV),\n(17.9.23)\nwhere the errors are statistical and systematic. The small\ncorrection due to the boost of the B meson in the center-\nof-mass system is calculated using a Monte Carlo simula-\ntion. Results for higher energy thresholds are tabulated in\nTable 17.9.3 of Section 17.9.2.6.\n\n373\n [GeV]\n\u03b3\nc.m.s\nE\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\nPhotons / 50 MeV\n-30000\n-20000\n-10000\n0\n10000\n20000\n30000\n \nFigure 17.9.4. From Limosani (2009). Combined untagged\nand lepton-tagged inclusive photon spectrum from Belle in the\nrest frame of the \u03a5(4S) after background subtraction, e\ufb03ciency\ncorrection and unfolding of calorimeter resolution.\n17.9.2.2 BABAR fully inclusive with lepton tagging\nThe lepton tag method was \ufb01rst used by the BABAR col-\nlaboration (Aubert, 2006t). That initial measurement has\nbeen superseded by an analysis based on an integrated\nluminosity of 347 fb\u22121 (383M BB pairs) collected on the\n\u03a5(4S) resonance, plus 36 fb\u22121 collected 40 MeV below the\nresonance (Lees, 2012j,o). For the signal it relies on the\ndetection of high energy photons \u2014 with photon-quality\nrequirements analogous to those used by Belle including\nisolation, and a veto if the high-energy photon is part of a\nreconstructed \u03c00 or \u03b7 \u2192\u03b3\u03b3 decay \u2014 in association with\na lepton tag from a semileptonic decay of the other B.\nThe lepton momentum threshold is p\u2217> 1.05 GeV/c for\nboth electrons and muons, where p\u2217is measured in the\ncenter-of-mass frame. There are additional requirements\non the angle between the photon and the lepton (near\nback-to-back con\ufb01gurations are rejected) and on the miss-\ning energy in the event (since a semileptonic decay entails\na missing neutrino).\nThese preliminary lepton-tag requirements remove 98%\nof the continuum events, at a cost of retaining only 12%\nof signal events. The tag variables are then combined with\ntopological (event-shape) information in a multivariate\nselector to further suppress continuum background. The\nsubtraction of the remaining continuum background using\nthe o\ufb00-resonance data still dominates the statistical un-\ncertainty, but at a lower level than for an untagged analy-\nsis. Lepton tagging introduces an additional small system-\natic error of up to 2.4% (decreasing as the photon energy\nthreshold increases) due to lepton identi\ufb01cation and un-\ncertainties in b \u2192c\u2113\u03bd branching fractions.\nThe largest background is now from other B decays,\nwhich have a lepton-tag e\ufb03ciency slightly below that for\nsignal events. The composition of the B background is\nsimilar to that for Belle. It consists of high-energy photons\nfrom unvetoed \u03b3\u03b3 decays of \u03c00\u2019s (by far the largest compo-\nnent) and \u03b7\u2019s, radiative decays of other mesons, electrons\nwhich are misidenti\ufb01ed as photons (due to tracking in-\ne\ufb03ciency or bremsstrahlung), antineutrons which annihi-\nlate in the detector, \ufb01nal-state radiation, and other small\ne\ufb00ects. Each signi\ufb01cant component of the MC-predicted\nB background is corrected by comparisons of data and\nMC control samples. The uncertainties on these correc-\ntions give the main contribution to the systematic error\non the branching fraction for lower E\u03b3 thresholds (7.8%\nfor 1.8 GeV, decreasing as the threshold rises). The largest\nuncertainties arise from unvetoed \u03c00\u2019s and from electrons\nwithout reconstructed tracks. The signal e\ufb03ciency uncer-\ntainty is 3.0%, independent of the threshold; its largest\ncomponent is from the photon isolation requirement. Cor-\nrelations between common sources of signal-e\ufb03ciency and\nBB-background uncertainties are additionally taken into\naccount.\nThe measured photon energy spectrum in the center-\nof-mass frame, after subtracting both continuum and cor-\nrected BB backgrounds, is shown in the top plot of\nFig. 17.9.5. After correcting for e\ufb03ciency, adjusting the re-\nsult to the B rest frame (both of which steps have a small\ndependence on the spectral shape, i.e. model-dependence,\nas noted in Section 17.9.1.3), and removing the small\nB \u2192Xd\u03b3 contribution (using Eq. 17.9.21), the resulting\nB(B \u2192Xs\u03b3) is\n(3.21 \u00b1 0.15 \u00b1 0.29 \u00b1 0.08) \u00d7 10\u22124\n(BABAR, E\u03b3 > 1.8 GeV),(17.9.24)\nwhere the errors are statistical, systematic and model-\ndependence, respectively. Results for higher energy thresh-\nolds are tabulated in Table 17.9.3 of Section 17.9.2.6.\nThe photon energy spectrum in the top plot of Fig.\n17.9.5 is also corrected bin by bin for e\ufb03ciency, and the\ne\ufb00ects of calorimeter resolution and Doppler smearing are\nunfolded using a technique adapted from (Malaescu, 2009).\nFor a binned energy spectrum, the method starts from\nan assumed model (for the unfolded spectrum) and com-\nputes the bin-by-bin di\ufb00erence between the initial (not-\nyet-unfolded) data and the predictions of this model. A\nregularization function is then de\ufb01ned to ascribe a frac-\ntion of the di\ufb00erence in each bin to \ufb02uctuations, with the\nremainder applied as a correction to the model. The func-\ntion is optimized using Monte Carlo studies with di\ufb00erent\nstarting models. The entire procedure is then iterated, and\nconverges quickly. The resulting spectrum in terms of true\nphoton energy in the B rest frame is shown in the lower\nplot of Fig. 17.9.5.\nAn advantage of the lepton tag is that it provides a\nCP-\ufb02avor tag for the combined B \u2192Xs+d\u03b3 decays and\ncan be used to determine the direct CP asymmetry. The\nmeasurement is described in Section 17.9.5.3.\n\n374\n1.5\n2\n2.5\n3\n3.5\n0\n500\n1000\n1500\n* (GeV)\n\u03b3\nE\nEvents/0.1 GeV\nB\nB\ncontrol\nContinuum\ncontrol\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n0\n0.5\n1\n (GeV)\n\u03b3\nE\n per 100 MeV\n-4\n)/10\n\u03b3\ns+d\n X\n\u2192\n(B \nB\n\u2206\nFigure 17.9.5. From (Lees, 2012j,o). Photon spectra in the\nBABAR lepton-tagged fully-inclusive measurement: (top) in the\ncenter-of-mass frame after background subtraction, uncor-\nrected for e\ufb03ciency and resolution smearing, and (bottom) in\nthe B rest frame, after correcting for e\ufb03ciency and unfolding\nthe e\ufb00ects of both calorimeter resolution and Doppler smear-\ning. The control regions (delineated by vertical red lines) were\nused to check the backgrounds; all BB background corrections\nwere determined and applied before unblinding the signal re-\ngion (1.8 to 2.9 GeV). The curve in the lower plot is based on\nthe kinetic-scheme computation of (Benson, Bigi, and Uralt-\nsev, 2005), using the HFAG world-average determination of\nHQE parameters (see Section 17.9.2.5).\n17.9.2.3 BABAR fully inclusive with reconstructed-B tagging\nAs an alternative to the lepton-tag approach, BABAR (Au-\nbert, 2008q) has also used the recoil-B technique (Sec-\ntion 7.4), in which the signal (\u201crecoil\u201d) B meson is tagged\nby fully reconstructing the non-signal B meson in a hadronic\ndecay mode. This technique (along with reconstruction in\nsemileptonic decay modes) has been widely used at the\nB Factories to study rare decays with multiple neutrinos,\ne.g., B \u2192\u03c4\u03bd and B \u2192K\u03bd\u03bd.\nIn BABAR\u2019s reconstructed-B-tag analysis, based on\n210 fb\u22121 of \u03a5(4S) data, more than 1000 di\ufb00erent hadronic\n\ufb01nal states are reconstructed, representing 5% of the de-\ncay width of the B meson. This large number of \ufb01nal\nstates is essential in order to reach a maximal signal ef-\n\ufb01ciency for B \u2192Xs\u03b3, although it is still only 0.3%. A\nhigh-energy photon is required among the remaining par-\nticles in the event. After applying a \u03c00 veto, suppressing\ncontinuum background using event-topology criteria, and\nselecting events with \u2206E of the hadronic B candidates in\na \u00b160 MeV window, \ufb01ts are made to the mES distribution\nof those candidates in bins of photon energy. These \ufb01ts re-\nmove all the continuum and combinatorial B backgrounds,\nleaving only signal events and those B decays with a sim-\nilar topology. These mostly contain photons from \u03c00 de-\ncays which have survived the \u03c00 veto. The remaining B\nbackgrounds are estimated using similar techniques to the\nuntagged and lepton-tagged B \u2192Xs\u03b3 analyses.\nThe hadronic tag has the advantage that it measures\nthe momentum of the tag B, which makes it possible to\ncalculate the photon energy in the recoiling signal-B rest\nframe. It also identi\ufb01es both the \ufb02avor and the charge of\nthe B in the B \u2192Xs\u03b3 decay (apart from B0\u2212B0 mixing).\nResulting asymmetries are presented in Section 17.9.5. Fi-\nnally, the rest of the event that has not been used to form\nthe tagging B can be used to study the hadronic Xs sys-\ntem associated with the b \u2192s\u03b3 decay. It may eventually\nbe possible to separate out the 4% of B \u2192Xd\u03b3 decays\nusing this information.\nThe BABAR analysis (Aubert, 2008q) obtains a B \u2192\nXs\u03b3 branching fraction\n(3.66 \u00b1 0.85 \u00b1 0.60) \u00d7 10\u22124 (BABAR, E\u03b3 > 1.9 GeV),\n(17.9.25)\nwhere the errors are statistical and systematic (including\nsome small model-dependence). Although this analysis is\ncurrently statistically limited, it is a promising method\nfor the future, i.e., at a high-luminosity B Factory. The\ndominant systematic uncertainties (e.g., from BB back-\ngrounds) may also be reduced signi\ufb01cantly with a larger\ndata sample. (This is equally true for the untagged and\nlepton-tag methods, despite the use in those cases of o\ufb00-\nresonance data.) An improvement might also be possible\nby including semileptonic tags.\n17.9.2.4 Sum of exclusive modes\nAn alternative technique to measure the inclusive branch-\ning fraction is to reconstruct the B \u2192Xs\u03b3 decay chain\nwith the Xs \ufb01nal state as the sum of as many exclu-\nsive modes as possible. This method is a development\nof the \u201cpseudoreconstruction\u201d method used by CLEO for\nthe continuum background suppression, a \u03c72 technique in\nwhich an Xs candidate is required to have mES and \u2206E\nwithin broad ranges around expected values.\nAn early analysis by Belle (Abe, 2001a) has used 6 fb\u22121,\nand explicitly reconstructed a set of 16 \ufb01nal states with\none kaon and 1 to 4 pions of which only one is allowed to be\na \u03c00. The Xs mass is restricted to be below 2.05 GeV/c2,\nwhich corresponds to an E\u03b3 threshold of 2.24 GeV. The\nquoted branching fraction:\n(3.36 \u00b1 0.53 \u00b1 0.42 +0.50\n\u22120.54) \u00d7 10\u22124 (Belle, E\u03b3 > 2.24 GeV)\n(17.9.26)\nis for the full energy range, where the errors are statisti-\ncal, systematic and model-dependence, respectively. This\nmethod has not been used by Belle with a larger dataset\n\n375\nfor the branching fraction measurement, but it was used\nto measure the direct CP asymmetry with a 152M BB\nsample as discussed in Section 17.9.5.\nIn an improved version of this method adopted by\nBABAR (Aubert, 2005x; Lees, 2012f), a set of 38 exclusive\n\ufb01nal states is explicitly reconstructed. Multiple candidates\nin an event are resolved using a signal-selecting classi\ufb01er\nbased on \u2206E, and a \ufb01t is made to the mES distributions\nfor the sum of the \ufb01nal states in bins of photon energy. All\nof the continuum and almost all the B backgrounds are\nthereby subtracted, apart from a small component which\npeaks in mES, primarily due to \u03c00\u2019s that survive the veto.\nThe photon energy in the B rest frame is precisely deduced\nfrom the measured Xs mass (Eq. 17.9.22).\nThe main limitation of this analysis is the understand-\ning of the hadronization of the s quark into di\ufb00erent Xs\n\ufb01nal states, and the estimation of the fraction of missing\n\ufb01nal states that have not been included in the analysis.\nThe most prominent exclusive signal is from B \u2192K\u2217\u03b3,\nbut it covers only 12% of the total B \u2192Xs\u03b3 branch-\ning fraction. The rest of the decay width is covered by\nmodes with higher mass Xs \ufb01nal states. Of the 38 \ufb01-\nnal states considered by BABAR, most of them are of the\nform B \u2192Kn(\u03c0)\u03b3, where K stands for K+ or K0\nS, and\nn(\u03c0) stands for 1 to 4 pions of which up to two can\nbe a \u03c00. In addition they include B \u2192Kn(\u03c0)\u03b7\u03b3 modes\nwith 0 to 2 pions of which up to one can be a \u03c00, and\nB \u2192KK+K\u2212(\u03c0)\u03b3 with 0 or 1 pion. This set of 38 \ufb01-\nnal states accounts for approximately half of the rate for\nB \u2192Xs\u03b3. A further quarter of the rate is due to modes\nwith a K0\nL; this contribution can be accurately estimated\nusing the observed K0\nS modes. The remaining 25% of the\ntotal rate is mostly in high multiplicity \ufb01nal states, and\nis associated with lower photon energies and higher Xs\nmass. The largest Xs mass considered in the analysis is\n2.8 GeV, which corresponds to a minimum photon energy\nof 1.9 GeV. At this mass the missing fraction is 70%, or\njust over 50% if the K0\nL part is accounted for.\nTo evaluate the systematic errors associated with\nthe Xs hadronization and the missing fractions, BABAR\ncompares the distribution of \ufb01nal states observed in\ndata with a prediction from a MC simulation using\nJetset (Sj\u00a8ostrand, 1994). Within the often-large uncer-\ntainties, they \ufb01nd agreement except for the low multiplic-\nity K\u03c0 \ufb01nal states where the data are only about 30%\nof the MC prediction. These modes are dominated by the\nK\u2217(892) and K\u2217\n2(1430) resonances. Since Jetset performs\na non-resonant hadronization, this disagreement is not\nsurprising. For higher multiplicity \ufb01nal states the agree-\nment is better, but the statistical accuracy of the compar-\nisons is limited. With larger data samples it is desirable\nto add more \ufb01nal states, and make more detailed compar-\nisons with the simulation to understand the hadronization\nmore accurately.\nBABAR\u2019s \ufb01rst analysis (Aubert, 2005x) used 82 fb\u22121\n(89M BB), and was updated to 429 fb\u22121 (471M BB)\n(Lees, 2012f). The latest branching fraction is\n(3.29 \u00b1 0.19 \u00b1 0.48) \u00d7 10\u22124 (BABAR, E\u03b3 > 1.9 GeV),\n(17.9.27)\n (GeV)\n\u03b3\nE\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n6\n) x10\ns\nX\n in m\nPBF/(100 MeV/c\n-20\n-10\n0\n10\n20\n30\n40\n50\n(b)\nFigure 17.9.6. From (Lees, 2012f). Photon spectrum in the B\nrest frame from BABAR\u2019s sum of exclusive \ufb01nal states analysis\n(blue solid lines), compared to the results from the older (su-\nperseded) similar BABAR analysis (red dashed lines). The bin\nwidths are de\ufb01ned in terms of the Xs mass, and converted to\nE\u03b3 using Eq. (17.9.22). The peak at 2.56 GeV is from exclusive\nB \u2192K\u2217\u03b3 decays.\nwhere the errors are statistical and systematic, respec-\ntively. The photon spectrum is shown in Figure 17.9.6.\nThe systematic error from hadronization already dom-\ninated with only 82 fb\u22121, and adding statistics did not\nreduce the overall error in the branching fraction with\n\ufb01ve times more data. However, this analysis is an impor-\ntant cross-check of the other inclusive analyses, where the\nsystematic error is dominated by a di\ufb00erent source, the\nbackground from other B decays. And as can be seen in\nFigure 17.9.6, the spectrum measurement has been signif-\nicantly improved with more data.\nA key point to note about this method is that it is the\nonly one that distinguishes b \u2192s\u03b3 from b \u2192d\u03b3, and hence\nis the only method used to measure inclusive b \u2192d\u03b3 (see\nSection 17.9.4). The method also determines the \ufb02avor\nand charge of the b \u2192s\u03b3 decay, allowing measurements\nof direct CP and isospin asymmetries in inclusive b \u2192s\u03b3\ndecays. These asymmetry measurements are not expected\nto be sensitive to the hadronization of the Xs.\n17.9.2.5 Photon energy spectrum and moments\nThe photon energy spectrum in B \u2192X\u03b3 is insensitive\nto NP (Kagan and Neubert, 1998); rather, it re\ufb02ects the\nmotion of the b quark inside the B meson, as detailed in\nSection 17.9.1.3. However, uncertainties in the true spec-\ntrum result in a small model-dependence in fully-inclusive\nmeasurements of the branching fraction, a quantity which\nis sensitive to NP. Such uncertainties also enter when ex-\ntrapolating the measured branching fraction down to an\nE\u03b3 threshold of 1.6 GeV, where the theoretical prediction\nis made.\nA general way to quantify the E\u03b3 spectrum is to ex-\ntract the moments of the spectrum, where the \ufb01rst two\nmoments are equivalent to the mean and width. These\nquantities depend on the minimum photon energy; or put\nanother way, moments with di\ufb00erent minimum photon en-\nergies can be treated as additional information about the\n\n376\nTable 17.9.1. Measured \ufb01rst moments \u27e8E\u03b3\u27e9(in GeV) of the B \u2192Xs\u03b3 photon energy spectrum in the B rest frame, for several\ndi\ufb00erent photon energy thresholds. The methods are in the order they are described in the text. The errors are statistical and\nsystematic (including model-dependence). SoE refers to sum-of-exclusive modes.\nMeasurement\nE\u03b3 > 1.7 GeV\nE\u03b3 > 1.8 GeV\nE\u03b3 > 1.9 GeV\nE\u03b3 > 2.0 GeV\nBelle\n2.282 \u00b1 0.015 \u00b1 0.051\n2.294 \u00b1 0.011 \u00b1 0.028\n2.311 \u00b1 0.009 \u00b1 0.015\n2.334 \u00b1 0.007 \u00b1 0.009\nBABAR lepton tag\n2.267 \u00b1 0.019 \u00b1 0.032\n2.304 \u00b1 0.014 \u00b1 0.017\n2.342 \u00b1 0.010 \u00b1 0.009\nBABAR reco.-B tag\n2.289 \u00b1 0.058 \u00b1 0.027\n2.315 \u00b1 0.036 \u00b1 0.019\nBABAR SoE\n2.346 \u00b1 0.018 +0.027\n\u22120.022\n2.338 \u00b1 0.010 +0.020\n\u22120.017\nTable 17.9.2. Measured second moments \u27e8(E2\n\u03b3 \u2212\u27e8E\u03b3\u27e92)\u27e9(in GeV2) of the B \u2192Xs\u03b3 photon energy spectrum in the B rest\nframe, for several di\ufb00erent photon energy thresholds. The methods are in the order they are described in the text. The errors\nare statistical and systematic (including model-dependence). SoE refers to sum-of-exclusive modes.\nMeasurement\nE\u03b3 > 1.7 GeV\nE\u03b3 > 1.8 GeV\nE\u03b3 > 1.9 GeV\nE\u03b3 > 2.0 GeV\nBelle\n0.043 \u00b1 0.005 \u00b1 0.020\n0.037 \u00b1 0.003 \u00b1 0.008\n0.030 \u00b1 0.002 \u00b1 0.003\n0.023 \u00b1 0.001 \u00b1 0.002\nBABAR lep. tag\n0.0484 \u00b1 0.0053 \u00b1 0.0077\n0.0362 \u00b1 0.0033 \u00b1 0.0033\n0.0251 \u00b1 0.0021 \u00b1 0.0016\nBABAR B tag\n0.033 \u00b1 0.012 \u00b1 0.006\n0.027 \u00b1 0.006 \u00b1 0.002\nBABAR SoE\n0.0211 \u00b1 0.0057 +0.0055\n\u22120.0069\n0.0239 \u00b1 0.0018 +0.0023\n\u22120.0030\nTable 17.9.3. Measured B \u2192Xs\u03b3 inclusive branching fractions (in 10\u22126) for several photon energy (E\u03b3) thresholds, 1.7 GeV and\nlarger. Errors are statistical, systematic and model-dependence (if applicable); if there is no third error, the model dependence\nis included in the systematic error. The column with E\u03b3 > 1.6 GeV contains HFAG\u2019s extrapolations (see text) from the\nlowest measured threshold (HFAG\u2019s reciprocal factors are shown in the bottom row.) and their computed world average. The\nmeasurements are in the order they are described in the text. The CLEO result is taken from HFAG, who corrected CLEO\u2019s\npublished value for the entire spectrum to the value at the listed threshold. The Belle sum-of-exclusive result, which is obtained\nwith E\u03b3 > 2.24 GeV and is corrected by HFAG, is listed only for the sake of the HFAG extrapolated value and average. All\naverages above measured threasholds assume errors are uncorrelated. For the HFAG world average of extrapolated values the\n\ufb01rst error combines statistics and systematics (assumed uncorrelated between experiments), while the second error is from shape\nfunction systematics (assumed fully correlated).\nMeasurement\n(E\u03b3 > 1.6 GeV)\nE\u03b3 > 1.7 GeV\nE\u03b3 > 1.8 GeV\nE\u03b3 > 1.9 GeV\nE\u03b3 > 2.0 GeV\nCLEO\n328 \u00b1 44 \u00b1 28 \u00b1 6\n306 \u00b1 41 \u00b1 26\nBelle un- & lepton tag\n350 \u00b1 15 \u00b1 41 \u00b1 1\n345 \u00b1 15 \u00b1 40\n336 \u00b1 13 \u00b1 25\n321 \u00b1 11 \u00b1 16\n302 \u00b1 10 \u00b1 11\nBABAR lepton tag\n332 \u00b1 16 \u00b1 31 \u00b1 2\n321 \u00b1 15 \u00b1 29 \u00b1 8\n300 \u00b1 14 \u00b1 19 \u00b1 6\n280 \u00b1 12 \u00b1 14 \u00b1 4\nBABAR reco.-B tag\n390 \u00b1 91 \u00b1 64 \u00b1 4\n366 \u00b1 85 \u00b1 60\nBelle sum-of-excl.\n369 \u00b1 58 \u00b1 46 \u00b1 60\nBABAR sum-of-excl.\n352 \u00b1 20 \u00b1 51 \u00b1 4\n329 \u00b1 19 \u00b1 48\nAverage\n343 \u00b1 21 \u00b1 7\n345 \u00b1 15 \u00b1 40\n330 \u00b1 10 \u00b1 19\n315 \u00b1 8 \u00b1 12\n294 \u00b1 9 \u00b1 11\n(Extrapolation factor)\n(0.985 \u00b1 0.004)\n(0.967 \u00b1 0.006)\n(0.936 \u00b1 0.010)\n(0.894 \u00b1 0.016)\nspectrum, although they are strongly correlated. The re-\nsults are given in Tables 17.9.1 and 17.9.2. BABAR (Lees,\n2012j) has also measured third moments, which are sev-\neral standard deviations away from zero. For all four mea-\nsurements detailed above, correlation matrices between all\nmeasured moments are provided in the published papers\nor in EPAPS material cited therein.\nWith su\ufb03cient experimental precision, the universal\nshape function could be extracted from the photon energy\nspectrum. Fits to the photon spectrum are also relevant\nto the extraction of Vub from inclusive B \u2192Xu\u2113\u03bd decays\n(Section 17.1.5). Global \ufb01ts to spectra from both processes\nare the goal of the SIMBA collaboration; recent progress\non their \ufb01ts to the B \u2192Xs\u03b3 spectrum can be found, for\nexample, in (Bernlochner et al., 2013).\nMoments of the photon energy spectrum are related\nto the parameters of the heavy quark expansion (HQE),\nsuch as mb, \u00b52\n\u03c0 and \u03c1D. Thus these parameters could be\nextracted from the spectrum. Note that the precise mean-\nings and values of such parameters di\ufb00er somewhat be-\ntween di\ufb00erent schemes. Parameterized computations of\nthe E\u03b3 moments (and spectrum) are described for the ki-\nnetic scheme in (Benson, Bigi, and Uraltsev, 2005) and for\nthe shape function scheme in (Lange, Neubert, and Paz,\n2005). To date, HFAG has found that the HQE parameters\nare not adequately constrained from \ufb01ts to B \u2192Xs\u03b3 mo-\nments alone, but that spectral moments from B \u2192Xc\u2113\u03bd\nmust be included. Such a \ufb01t to both sets of moments was\n\ufb01rst carried out in the kinetic scheme by (Buchm\u00a8uller\nand Fl\u00a8acher, 2006). Recent HFAG results can be found\nin (Amhis et al., 2012). The \ufb01t values of mb and \u00b52\n\u03c0 are\n\n377\n(4.57 \u00b1 0.03) GeV/c2 and (0.46 \u00b1 0.04) GeV2/c2, respec-\ntively. (This \ufb01t predates inclusion of the BABAR lepton-\ntagged B \u2192Xs\u03b3 results described in Section 17.9.2.2.)\nA di\ufb00erent approach is DGE (Andersen and Gardi,\n2007), in which the moments are predicted as functions of\nthe energy threshold. As pointed out in Section 17.9.1.3,\nthere are additional assumptions in this approach concern-\ning the structure of the non-perturbative contributions.\nMeasurements of moments including energy cuts thus al-\nlow for testing these assumptions.\n17.9.2.6 Branching fraction summary and extrapolation\nAll measured results for the inclusive B \u2192Xs\u03b3 branching\nfraction are summarized in Table 17.9.3. For each of the\nfour measurements detailed above, correlations between\nresults at di\ufb00erent thresholds are provided in the pub-\nlished papers or in EPAPS material cited therein. The\nmeasurements have E\u03b3 thresholds ranging from 1.7 to over\n2.0 GeV, while theoretical predictions are usually made\nwith a minimum E\u03b3 of 1.6 GeV. The approach adopted\nby HFAG and the PDG to produce a world average has\nbeen to extrapolate the experimental results down to the\n1.6 GeV threshold from the lowest measured experimental\nthreshold in each case. The extrapolation factors are taken\nfrom the initial HQE analysis of B \u2192Xc\u2113\u03bd and B \u2192Xs\u03b3\ndecays by (Buchm\u00a8uller and Fl\u00a8acher, 2006) (rather than\nfrom the latest HFAG HQE \ufb01ts). A current HFAG sum-\nmary can be found at (HFAG, 2013). The extrapolation\nfactors and extrapolated branching fractions are included\nin Table 17.9.3. The quoted world average of extrapolated\nvalues is\nB(B \u2192Xs\u03b3) = (3.43 \u00b1 0.21 \u00b1 0.07) \u00d7 10\u22124 (E\u03b3 > 1.6),\n(17.9.28)\nwhere the \ufb01rst error is the combined statistical and sys-\ntematic error, and the second is from the model depen-\ndence of the extrapolations.\nWe note that because experimental systematic uncer-\ntainties decrease strongly with increasing E\u03b3 threshold (a\nconsequence of the large BB backgrounds at lower E\u03b3 val-\nues), the uncertainty on an extrapolated branching frac-\ntion decreases if one starts with a measurement at a higher\nthreshold. This seems contrary to the theoretical preju-\ndice that the result should be most reliable if one begins\nat the lowest possible measured threshold, so there may\nbe more unaccounted uncertainties in the extrapolation\nfactors. (For example, the systematic uncertainty of the\nextrapolated CLEO result seems to be arti\ufb01cially low, a\nconsequence of the high photon energy threshold used.)\nHFAG\u2019s chosen method minimizes the overall dependence\non the extrapolation factors when the branching fracion\nis evaluated at 1.6 GeV.\nEventually, perhaps moments from the di\ufb00erent thresh-\nold could be combined, taking into account their correla-\ntions, to provide a better extrapolation. This is related to\nspectrum-\ufb01tting goals described in Section 17.9.2.5.\n17.9.2.7 Constraints on new physics from B(B \u2192Xs\u03b3)\nThe SM prediction for the extrapolated branching frac-\ntion (Eq. 17.9.20) and the latest experimental average now\nhave similar levels of uncertainty, and are consistent at the\n1\u03c3 level. This \ufb01nding implies very stringent constraints on\nNP models (Section 25.2). As examples we quote\n\u2013 In the type-II two-Higgs doublet model (THDM)\nthe bound on the charged Higgs mass is MH+ >\n380 GeV/c2 at 95% C.L. See (Misiak et al., 2007)\nand the improved computation in (Hermann, Misiak,\nand Steinhauser, 2012). [Note a slightly older world-\naverage branching fraction was used in the latter work.]\n\u2013 In\nthe\nminimal\nuniversal\nextra-dimension\nmodel (Haisch and Weiler, 2007), the bound on\nthe inverse compacti\ufb01cation radius is 1/R > 600 GeV\nat 95% C.L. [This limit should be recomputed to\nre\ufb02ect improvements in the world-average branching\nfraction since 2007.]\nIn both cases, the bounds are much stronger than those\npreviously derived from other measurements \u2014 but see\nSection 17.10.2.2 regarding an even stronger constraint\non the THDM. Constraints on various supersymmetric\nmodels have been reviewed in (Altmannshofer, Buras,\nGori, Paradisi, and Straub, 2010; Hurth, 2003). Bounds on\nthe little Higgs model with T-parity have also been pre-\nsented (Blanke, Buras, Duling, Recksiegel, and Tarantino,\n2010). Finally, model-independent analyses in the e\ufb00ec-\ntive \ufb01eld theory approach with the assumption of minimal\n\ufb02avor violation (D\u2019Ambrosio, Giudice, Isidori, and Stru-\nmia, 2002; Hurth, Isidori, Kamenik, and Mescia, 2009)\nalso show the strong constraining power of the B \u2192Xs\u03b3\nbranching fraction.\n17.9.3 Exclusive b \u2192s\u03b3\nAs already discussed, B \u2192K\u2217\u03b3 was the \ufb01rst b \u2192s\u03b3 decay\nto be observed, and the K\u2217(892) resonance is the only\none clearly visible in the Xs mass spectrum of B \u2192Xs\u03b3\n(Fig. 17.9.6). Contributions to B \u2192Xs\u03b3 with Xs heavier\nthan K\u2217have also been studied in detail. Some of the\nheavier Xs \ufb01nal states are from resonances, but these are\nharder to disentangle, and non-resonant contributions also\nseem to be large, as the sum of the measured resonant\ncontributions is far from saturating the total B \u2192Xs\u03b3\ndecay width.\n17.9.3.1 B \u2192K\u2217\u03b3\nThe B \u2192K\u2217\u03b3 signal is reconstructed in the four K\u2217\n\ufb01nal states, K+\u03c0\u2212, K0\nS\u03c00, K+\u03c00, K0\nS\u03c0+, and their charge\nconjugate modes; K0\nS\u03c00 is a CP eigenstate that can be\nused to study time-dependent CP violation.\nThe signal is identi\ufb01ed by the kinematic variables mES\nand \u2206E. There is a combinatorial background that is sup-\npressed by event shape variables, and then has to be sub-\ntracted. There are also small \u201cpeaking\u201d backgrounds from\n\n378\n)\n2\n (GeV/c\nES\nM\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 4 MeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n-\u03c0\n+\nK\n)\n2\n (GeV/c\nES\nM\n5.22\n5.24\n5.26\n5.28\n2\nEvents / 4 MeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n E (GeV)\n\u2206\n-0.3 -0.2 -0.1\n0\n0.1\n0.2\n0.3\nEvents / 30 MeV\n0\n100\n200\n300\n400\n500\n600\n700\n-\u03c0\n+\nK\n E (GeV)\n\u2206\n-0.3 -0.2 -0.1\n0\n0.1\n0.2\n0.3\nEvents / 30 MeV\n0\n100\n200\n300\n400\n500\n600\n700\nFigure 17.9.7. From (Aubert, 2009r). Signals from BABAR for\nB \u2192K\u2217\u03b3 with K\u22170 \u2192K+\u03c0\u2212in mES (top) and \u2206E (bottom).\nShort-dashed (magenta) line is for peaking background, dot-\ndashed (red) for continuum, long-dashed (green) for the total\nbackground, solid (blue) for the total, overlaid on (black) data\npoints.\nB \u2192K\u03c0\u03c0\u03b3 and B \u2192K\u03c00 which are separated in \u2206E\nfrom the signal (see Figure 17.9.7).\nAs a two-body decay of a quite narrow resonance, the\nphoton energy is almost monochromatic in the B rest\nframe, and ranges between 2.40 and 2.74 GeV in the center-\nof-mass frame. The energy resolution for this high energy\nphoton as well as the \u2206E resolution is determined by the\nCsI calorimeter system, and shows a low energy tail due\nto the energy leakage from the crystals and energy loss in\nthe material of the particle identi\ufb01cation device in front\nof it. The mES resolution is not much a\ufb00ected because the\nphoton energy is rescaled by using a \u2206E = 0 constraint.\nThe \ufb01nal state is a vector-vector state, but as the photon\nis massless, the K\u2217is always transversely polarized, and\nthe helicity angle \u03b8K, the angle of the kaon with respect\nto the B meson in the K\u2217rest frame, follows a 1\u2212cos2 \u03b8K\ndistribution.\nThe branching fraction is now measured to a precision\nof a few %. This is much more accurate than the theo-\nretical predictions, which are limited by knowledge of the\nB \u2192K\u2217form factor at q2 = 0 (see Section 17.9.3.3).\nFor rate asymmetries, the form factor uncertainties partly\ncancel, and the theoretical predictions are rather precise.\nMeasurements of CP and isospin asymmetries are dis-\ncussed later in Section 17.9.5.\nThe results for the branching fractions are summa-\nrized in Table 17.9.4. There is also a CLEO measure-\nment (Coan et al., 2000) which is included in the world\naverage. The BABAR measurement is based on 347 fb\u22121\nof data (Aubert, 2009r), and the Belle measurement on\nTable 17.9.4. Summary of measurements of exclusive b \u2192s\u03b3\nbranching fractions (in 10\u22126). For the K\u03c0\u03c0\u03b3 \ufb01nal states, Belle\n(BABAR) integrates over masses up to 2.0 (1.8) GeV/c2. Several\nslightly asymmetric errors are symmetrized. The averages for\nK\u2217(892)\u03b3 are recalculated (see text) also including CLEO re-\nsults. Otherwise the averages are only from Belle and BABAR\nand are identical to PDG values. Averages assume that sys-\ntematics are uncorrelated between Belle and BABAR.\nMode\nBelle\nBABAR\nAverage\nK\u2217(892)0\u03b3\n40.1 \u00b1 2.1 \u00b1 1.7 43.3 \u00b1 1.0 \u00b1 1.6\n42.4 \u00b1 1.5\nK\u2217(892)+\u03b3\n42.5 \u00b1 3.1 \u00b1 2.4 43.6 \u00b1 1.4 \u00b1 1.6\n43.1 \u00b1 1.8\nK\u2217\n2(1430)0\u03b3\n13.0 \u00b1 5.0 \u00b1 1.0 12.2 \u00b1 2.5 \u00b1 1.0\n12.4 \u00b1 2.4\nK\u2217\n2(1430)+\u03b3\n14.5 \u00b1 4.0 \u00b1 1.5\n14.5 \u00b1 4.3\nK1(1270)+\u03b3 43.0 \u00b1 9.0 \u00b1 9.0\n43.0 \u00b1 13.0\nK+\u03c0\u2212\u03c0+\u03b3\n25.0 \u00b1 1.8 \u00b1 2.2 29.5 \u00b1 1.3 \u00b1 1.9\n27.6 \u00b1 2.2\nK0\u03c0+\u03c0\u2212\u03b3\n24.0 \u00b1 4.0 \u00b1 3.0 18.5 \u00b1 2.1 \u00b1 1.2\n19.5 \u00b1 2.2\nK+\u03c0\u2212\u03c00\u03b3\n40.7 \u00b1 2.2 \u00b1 3.1\n40.7 \u00b1 3.9\nK0\u03c0+\u03c00\u03b3\n45.6 \u00b1 4.2 \u00b1 3.0\n45.6 \u00b1 5.1\nK+\u03c6\u03b3\n2.5 \u00b1 0.3 \u00b1 0.2\n3.5 \u00b1 0.6 \u00b1 0.4\n2.8 \u00b1 0.3\nK0\u03c6\u03b3\n2.7 \u00b1 0.6 \u00b1 0.3\n2.7 \u00b1 0.7\nK+\u03b7\u03b3\n8.4 \u00b1 1.5 \u00b1 1.1\n7.7 \u00b1 1.0 \u00b1 0.4\n7.9 \u00b1 0.9\nK0\u03b7\u03b3\n8.7 \u00b1 2.9 \u00b1 1.8\n7.1 \u00b1 2.1 \u00b1 0.4\n7.6 \u00b1 1.8\nK+\u03b7\u2032\u03b3\n3.6 \u00b1 1.2 \u00b1 0.4\n1.9 \u00b1 1.4 \u00b1 0.1\n2.9 \u00b1 1.0\n\u039bp\u03b3\n2.5 \u00b1 0.4 \u00b1 0.2\n2.5 \u00b1 0.5\nB0\ns \u2192\u03c6\u03b3\n57 \u00b1 17 \u00b1 12\n57 \u00b1 21\n78 fb\u22121 (Nakao, 2004). Instead of assuming equal B+B\u2212\nand B0B0 production, BABAR used the measured pro-\nduction rates B(\u03a5(4S) \u2192B0B0) = 0.484 \u00b1 0.006 and\nB(\u03a5(4S) \u2192B+B\u2212) = 0.516 \u00b1 0.006 (the 2008 PDG val-\nues (Amsler et al., 2008)).86 With these values the quoted\nbranching fractions are\nB(B0 \u2192K\u22170\u03b3) = (44.7 \u00b1 1.0 \u00b1 1.6) \u00d7 10\u22126,\nB(B+ \u2192K\u2217+\u03b3) = (42.2 \u00b1 1.4 \u00b1 1.6) \u00d7 10\u22126.\n(17.9.29)\nIn Table 17.9.4 the published BABAR results have been\nadjusted so that all the results are based on the same as-\nsumption of equal B+ and B0 production at the \u03a5(4S).\nThis also leads to an adjustment of the world averages\ncompared to those given by the Particle Data Group (Be-\nringer et al., 2012).\n17.9.3.2 Other exclusive b \u2192s\u03b3 modes\nMany other b \u2192s\u03b3 decay modes have been searched for\nby Belle and BABAR. The branching fractions for the ob-\nserved decays are summarized in Table 17.9.4. The higher\nK\u03c0 mass region is dominated by the K\u2217\n2(1430) resonance,\nseen \ufb01rst by CLEO (Coan et al., 2000) and con\ufb01rmed by\n86 The 2012 PDG value for B0B0 is 0.487 \u00b1 0.006. See Sec-\ntion 18.4.6.8 for a detailed discussion.\n\n379\nboth Belle (Nishida, 2002) and BABAR (Aubert, 2004i)\nwith relatively small datasets. Non-resonant B \u2192K\u03c0\u03b3\ncontributions seem to be small and have not been observed\nso far. Note that an S-wave K\u03c0 system is forbidden by an-\ngular momentum conservation.\nThe decays B \u2192K\u03c0\u03c0\u03b3 have been suggested as place\nto measure the photon polarization (Gronau, Grossman,\nPirjol, and Ryd, 2002). In the SM the photon in b \u2192s\u03b3 de-\ncays is left-handed up to small corrections of order ms/mb.\nIn the K\u03c0\u03c0 hadronic system Belle (Yang, 2005) reports a\nsignal for B+ \u2192K1(1270)+\u03b3 where K1(1270)+ \u2192K+\u03c10.\nThere is no branching fraction measurement for B0 \u2192\nK1(1270)0\u03b3, but this mode is clearly visible and is the\ndominant contribution in the time-dependent CP viola-\ntion study of B0 \u2192K0\nS\u03c10\u03b3 by Belle (Li, 2008), as illus-\ntrated in Fig. 17.9.10 below. Both Belle (Nishida, 2002)\nand BABAR (Aubert, 2007r) measure inclusive rates for\nthe K\u03c0\u03c0 \ufb01nal states without restricting the \ufb01nal state to\na resonance. Belle separates out the K\u2217\u03c0 and K\u03c1 con-\ntributions, but neither experiment has performed a full\nDalitz plot analysis of the K\u03c0\u03c0 system.\nIn addition, Belle has reported upper limits for radia-\ntive branching fractions to other resonant states, such as\nK\u2217(1410), K1(1400), and K\u2217\n3(1780). These were searched\nfor in K\u03c0, K\u03c0\u03c0 and K\u03b7 \ufb01nal states but no signi\ufb01cant sig-\nnals were found. A summary of these upper limits is given\nby the Particle Data Group (Beringer et al., 2012).\nThe Xs \ufb01nal states K\u03b7, K\u03b7\u2032 and K\u03c6 have all been\nmeasured for the \ufb01rst time at the B Factories. They are\nprimarily of interest because the neutral decay modes can\nbe used to measure time-dependent CP violation (dis-\ncussed later in Section 17.9.5). The decays B \u2192\u03c6K\u03b3\nhave clear signals seen by Belle (Drutskoy, 2004; Sahoo,\n2011) and BABAR (Aubert, 2007q). Observations of the\ndecays B \u2192K\u03b7\u03b3 are also reported by BABAR (Aubert,\n2009e) and Belle (Nishida, 2005). Only Belle has reported\nevidence for B+ \u2192K+\u03b7\u2032\u03b3 (Wedd, 2010), and neither ex-\nperiment has seen the neutral counterpart B0 \u2192K0\u03b7\u2032\u03b3\nwith upper limits on its branching fraction of 6.4 \u00d7 10\u22126\nfrom Belle (Wedd, 2010) and 6.6\u00d710\u22126 from BABAR (Au-\nbert, 2006o).\nThe baryonic radiative decay B+ \u2192\u039bp\u03b3 has been\nmeasured by Belle (Wang, 2007b) with 449M BB. One\nwould expect similar branching fractions for other bary-\nonic radiative decays. B+ \u2192\u03a30p\u03b3 was searched for as a\nby-product, where the signal would show up at a shifted\n\u2206E compared to \u039bp\u03b3. An upper limit of 5\u00d710\u22126 has been\nobtained by Belle (Wang, 2007b).\nFinally, the \ufb01rst radiative B0\ns decay B0\ns \u2192\u03c6\u03b3 was\nobserved by Belle using a data sample of 23 fb\u22121 taken at\nthe \u03a5(5S) resonance (Wicht, 2008). The analysis is almost\nidentical to the study of B \u2192K\u2217\u03b3 at the \u03a5(4S), except\nthat there are three possible mES-\u2206E peaks because of\nproduction through B0\ns-B0\ns, B0\ns-B\u22170\ns\nand B\u22170\ns -B\u22170\ns\nat the\n\u03a5(5S). The measured branching fraction is similar to B \u2192\nK\u2217\u03b3 as would be expected if exchange diagrams are small.\nThis decay mode has now also been seen by LHCb (Aaij\net al., 2012j), and is going to be useful in the search for\ntime-dependent CP asymmetry due to new physics in the\nB0\ns system. Although such a measurement looks similar\nto those in the B0 system (see Section 17.9.6), it has a\ndi\ufb00erent implication due to the di\ufb00erent CKM parameters\nand the non-negligible value of \u2206\u0393s (Muheim, Xie, and\nZwicky, 2008).\n17.9.3.3 Theoretical predictions for exclusive b \u2192s\u03b3 modes\nUp-to-date theoretical predictions for exclusive radia-\ntive decays are based on the method of QCD factoriza-\ntion. Large hadronic uncertainties are due to the non-\nperturbative input of the QCDF approach, namely light-\ncone wave functions and form factors, and our limited\nknowledge of power corrections. These uncertainties do\nnot allow precise predictions of the branching fractions of\nexclusive modes. For example the branching fraction of\nB \u2192K\u2217\u03b3 is directly proportional to the soft form factor\nat q2 = 0, which can only be determined by QCD sum\nrules with an uncertainty of about 20%. The decay rate is\ngiven by (Ali and Parkhomenko, 2002)\n\u0393(B \u2192K\u2217\u03b3) = G2\nF \u03b1|VtbV \u2217\nts|2\n32\u03c04\nm2\nbM 3\nB|\u03be\u22a5(0)|2\n\u0012\n1 \u2212m2\nK\u2217\nM 2\nB\n\u0013 \u0002\nCe\ufb00\n7\n+ A\n\u00032 ,(17.9.30)\nwhere \u03be\u22a5(0) is the soft form factor at q2 = 0 and A is\nthe contribution of NLO terms such as spectator interac-\ntions. Using the value of the form factor from a QCD sum\nrule calculation, the branching fraction becomes (Ali and\nParkhomenko, 2002)\nB(B \u2192K\u2217\u03b3) = (7.3 \u00b1 2.7) \u00d7 10\u22125.\n(17.9.31)\nThis prediction is consistent with the experimental mea-\nsurements, but, because the form factor input results in\nby far the largest error, Eq. (17.9.30) is often used to de-\ntermine the form factor via the experimental data.\nHowever, within ratios of branching fractions of exclu-\nsive modes such as CP asymmetries, parts of the uncer-\ntainties cancel out. This way, exclusive modes also provide\nvaluable constraints, for example on the ratio of CKM el-\nements |Vtd/Vts| (see Section 17.2).\n17.9.4 Exclusive and inclusive b \u2192d\u03b3\nThe b \u2192d\u03b3 transition from the third generation to the\n\ufb01rst, proceeds through a penguin loop diagram very sim-\nilar to b \u2192s\u03b3, except that the transition rate is sup-\npressed by the ratio of the CKM matrix elements squared,\n|Vtd/Vts|2 (see Eq. 17.9.21). It is thus one of the possible\nmeans to extract |Vtd/Vts| (see Section 17.2). If |Vts| is\nidentical to |Vcb| from unitarity to the required precision.\nthis in turn allows a determination of |Vtd|, the length of\nthe least-known side of the Unitarity Triangle.\nThere are some di\ufb00erences with respect to b \u2192s\u03b3,\nbecause the suppression of the penguin transition ampli-\ntude increases the relative importance of other contribu-\ntions, as indicated in the detailed theoretical discussion\n\n380\nof Sections 17.9.1.1 and 17.9.1.2. The contribution to the\npenguin diagram from the u quark is no longer small com-\npared to the t quark, since it now involves Vud rather than\nVus. This is also true for the contributions from the four-\nquark operators containing u quarks. Finally, the annihi-\nlation diagram for charged B and the exchange diagram\nfor neutral B become signi\ufb01cant, leading to isospin asym-\nmetries and potentially large CP asymmetries. All these\ncorrections have to be taken into account in the extraction\nof |Vtd|.\nExperimentally, b \u2192s\u03b3 processes are large back-\ngrounds to similar b \u2192d\u03b3 processes, so the former have\nto be suppressed using the particle identi\ufb01cation capabil-\nities of the detectors. The b \u2192s\u03b3 decays provide a good\ncontrol sample, and many systematic uncertainties cancel\nin the ratios of b \u2192d\u03b3 to b \u2192s\u03b3.\n17.9.4.1 Exclusive modes B \u2192\u03c1\u03b3 and B \u2192\u03c9\u03b3\nAs was the case in the early days of b \u2192s\u03b3, it was the ex-\nclusive modes that were used to make the \ufb01rst observation\nof the b \u2192d\u03b3 process at the B Factories. The three decay\nmodes B+ \u2192\u03c1+\u03b3, B0 \u2192\u03c10\u03b3, and B0 \u2192\u03c9\u03b3 have all been\nseen, although the B0 \u2192\u03c9\u03b3 signals are only 2\u03c3 signi\ufb01-\ncant in each experiment. Based on na\u00a8\u0131ve quark counting,\nB+ \u2192\u03c1+\u03b3 should have twice the decay width (hence ap-\nproximately twice the branching fraction) of the other two\nmodes, whose branching fractions should be the same:\nB(B+ \u2192\u03c1+\u03b3) = 2 \u03c4B+\n\u03c4B0 B(B0 \u2192\u03c10\u03b3) = 2 \u03c4B+\n\u03c4B0 B(B0 \u2192\u03c9\u03b3).\n(17.9.32)\nDue to the wide \u03c1 mass window, the B \u2192\u03c1\u03b3 modes\nhave large backgrounds from similar B \u2192K\u2217\u03b3 modes.\nThese are separated using K/\u03c0 particle identi\ufb01cation and\n\u2206E. Both BABAR and Belle use a K/\u03c0 likelihood ratio se-\nlection, with similar pion e\ufb03ciencies of 85%, but with sig-\nni\ufb01cantly di\ufb00erent probabilities of misidentifying a kaon as\na pion, 1% and 8.5%, respectively (for relevant momenta),\ndue to di\ufb00erences in the particle identi\ufb01cation systems.\nThe K\u2217\u03b3 background is more pronounced in B0 \u2192\u03c10\u03b3\nthan in B+ \u2192\u03c1+\u03b3 because Eq. (17.9.32) predicts about\ntwice the rate for \u03c1+\u03b3 than \u03c10\u03b3, while the (K+\u03c00)\u03b3 rate\nis only about 3/8 of that for (K+\u03c0\u2212)\u03b3. Also, there are\ntwo charged pions that could be misidenti\ufb01ed kaons in\n\u03c10\u03b3 while there is only one in \u03c1+\u03b3. To constrain the back-\nground from K\u22170\u03b3 Belle additionally uses the K\u03c0 mass in\ntheir \ufb01t to \u03c10\u03b3. Both experiments also take into account\nanother peaking background at lower \u2206E from B \u2192\u03c1\u03c00\nevents, which survive a \u03c00 veto on the high energy photon.\nThe Belle signal for \u03c10\u03b3 is shown in Figure 17.9.8, in which\nit is seen that \u2206E and M(K\u03c0) are used to separate the\nsignal from K\u22170\u03b3 and other peaking backgrounds, while\nmES is essential to \ufb01x the size of the continuum back-\nground.\nThe backgrounds from other B decays are lower in\nthe B \u2192\u03c9\u03b3 mode because the \u03c9 resonance is narrower,\nB \u2192\u03c9\u03c00 is color-suppressed and has not been observed,\nand there is very little K\u03c0\u03c0\u03b3 background at low Xs mass.\nThe branching fractions are summarized in Table 17.9.5,\n)\n2\n (GeV/c\nbc\nM\n5.2\n5.25\n5.3\n)\n2\nEntries/(2.5 MeV/c\n0\n20\n40\n60\n)\n2\n (GeV/c\nbc\nM\n5.2\n5.25\n5.3\n)\n2\nEntries/(2.5 MeV/c\n0\n20\n40\n60\n\u03b3\n0\n\u03c1\n \n\u2192\n B \nE (GeV)\n\u2206\n-0.5\n0\n0.5\nEntries/(25 MeV)\n0\n20\n40\nE (GeV)\n\u2206\n-0.5\n0\n0.5\nEntries/(25 MeV)\n0\n20\n40\n\u03b3\n0\n\u03c1\n \n\u2192\n B \n)\n2\n (GeV/c\n\u03c0\nK\nM\n0.8\n0.92\n1.04\n1.16\n)\n2\nEntries/(10 MeV/c\n0\n10\n20\n30\n)\n2\n (GeV/c\n\u03c0\nK\nM\n0.8\n0.92\n1.04\n1.16\n)\n2\nEntries/(10 MeV/c\n0\n10\n20\n30\n\u03b3\n0\n\u03c1\n \n\u2192\n B \nFigure 17.9.8. From (Taniguchi, 2008). Signal for B0 \u2192\u03c10\u03b3\nfrom Belle in mES (=Mbc), \u2206E and M(K\u03c0) (dashed, red)\nand backgrounds from B0 \u2192K\u22170\u03b3 (dotted, magenta), other\nB decays (dot-dashed, green) and continuum (dot-dot-dashed,\ncyan). Each spectrum is made with signal-region cuts on the\nother plotted quantities.\nTable 17.9.5. Summary of measurements of exclusive B \u2192\nXd\u03b3 branching fractions (in 10\u22126). The combined results in the\nlast two lines assume na\u00a8\u0131ve quark counting, quoting values of\nB(B+ \u2192\u03c1+\u03b3) from constrained \ufb01ts to the two \u03c1\u03b3 modes or all\nthree modes. Errors are statistical and systematic, respectively.\nMode\nBelle\nBABAR\nAverage\n\u03c1+\u03b3\n0.87 \u00b1 0.28 \u00b1 0.10 1.20 \u00b1 0.40 \u00b1 0.20 0.98 \u00b1 0.25\n\u03c10\u03b3\n0.78 \u00b1 0.17 \u00b1 0.10 0.97 \u00b1 0.23 \u00b1 0.06 0.86 \u00b1 0.15\n\u03c9\u03b3\n0.40 \u00b1 0.18 \u00b1 0.13 0.50 \u00b1 0.25 \u00b1 0.09 0.44 \u00b1 0.17\n\u03c1\u03b3\n1.21 \u00b1 0.33 \u00b1 0.17 1.73 \u00b1 0.33 \u00b1 0.17 1.39 \u00b1 0.25\n\u03c1/\u03c9\u03b3\n1.14 \u00b1 0.20 \u00b1 0.11 1.63 \u00b1 0.29 \u00b1 0.16 1.30 \u00b1 0.23\nwhere the BABAR measurements (Aubert, 2008z) are from\n465M BB, and the Belle measurements (Taniguchi, 2008)\nare from 657M BB.\nNa\u00a8\u0131ve quark counting breaks down due to the isospin\nasymmetries from the additional diagrams mentioned\nabove, and due to di\ufb00erences in the hadronic form factors.\nIt can be seen from the branching fractions in Table 17.9.5\nthat the na\u00a8\u0131ve isospin factor of two between \u03c1+ and \u03c10\nis not very consistent with the experimental results (the\nisospin asymmetry will be discussed in Section 17.9.5 in\nmore detail). Nevertheless each experiment has combined\nits measurements by using Eq. (17.9.32) to do constrained\n\ufb01ts to B(B+ \u2192\u03c1+\u03b3) using either just the two \u03c1 modes\nor all three modes. These combined results are quoted in\nTable 17.9.5 for completeness. The ratios of the measured\nbranching fractions to those for corresponding K\u2217\u03b3 \ufb01nal\nstates are consistent with the SM predictions, with the\nvalue of |Vtd|/|Vts| extracted from measurements of \u2206md\nin B0 \u2212B0 mixing using precise lattice calculations. Nu-\n\n381\nTable 17.9.6. Final states used to measure the ratio of branch-\ning fractions of inclusive B \u2192Xd\u03b3 to inclusive B \u2192Xs\u03b3\ndecays.\nB \u2192Xd\u03b3\nB \u2192Xs\u03b3\nB0 \u2192\u03c0+\u03c0\u2212\u03b3\nB0 \u2192K\u00b1\u03c0\u2213\u03b3\nB\u00b1 \u2192\u03c0\u00b1\u03c00\u03b3\nB\u00b1 \u2192K\u00b1\u03c00\u03b3\nB\u00b1 \u2192\u03c0\u00b1\u03c0+\u03c0\u2212\u03b3\nB\u00b1 \u2192K\u00b1\u03c0+\u03c0\u2212\u03b3\nB0 \u2192\u03c0+\u03c0\u2212\u03c00\u03b3\nB0 \u2192K\u00b1\u03c0\u2213\u03c00\u03b3\nB0 \u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\u03b3 B0 \u2192K\u00b1\u03c0\u2213\u03c0+\u03c0\u2212\u03b3\nB\u00b1 \u2192\u03c0\u00b1\u03c0+\u03c0\u2212\u03c00\u03b3 B\u00b1 \u2192K\u00b1\u03c0+\u03c0\u2212\u03c00\u03b3\nB\u00b1 \u2192\u03c0\u00b1\u03b7\u03b3\nB\u00b1 \u2192K\u00b1\u03b7\u03b3\nmerical results and detailed discussion can be found in\nSection 17.2.2.\n17.9.4.2 Inclusive b \u2192d\u03b3\nAn inclusive B \u2192Xd\u03b3 measurement could provide a bet-\nter sensitivity to extract |Vtd|/|Vts|, as it is free from the\ntheoretical uncertainty of the form factors that appear in\nthe exclusive modes B \u2192\u03c1\u03b3 and B \u2192K\u2217\u03b3. As discussed\nearlier, the fully inclusive approaches cannot separate Xs\nand Xd, and hence cannot be used to measure B \u2192Xd\u03b3.\nWith the sum-of-exclusive modes approach it is possible to\ndiscriminate between B \u2192Xd\u03b3 and B \u2192Xs\u03b3 \ufb01nal states\nusing particle identi\ufb01cation requirements on the charged\npions and kaons. A comparison of the ratio |Vtd|/|Vts| to\nthat extracted from B mixing studies is a test of the SM,\nbecause di\ufb00erent diagrams are involved.\nThe \ufb01rst inclusive B \u2192Xd\u03b3 measurement was re-\nported by BABAR in (Aubert, 2009q). This analysis has\nbeen updated to include the full dataset with 471M BB\npairs (del Amo Sanchez, 2010q). The Xd and Xs are each\nreconstructed as the sum of seven \ufb01nal states (Table 17.9.6).\nThe pion identi\ufb01cation algorithm in this analysis has an\ne\ufb03ciency of 95%, but also accepts kaons with a probability\nof 4%. Hence, because of the considerably larger B \u2192Xs\u03b3\nbranching fraction, there is signi\ufb01cant misidenti\ufb01cation of\nB \u2192Xs\u03b3 as B \u2192Xd\u03b3. This B \u2192Xs\u03b3 background is\nincluded as an additional component in the B \u2192Xd\u03b3 \ufb01ts\nto distributions of the kinematic variables mES and \u2206E;\nsuch misidenti\ufb01ed events have a displaced and broader \u2206E\ndistribution.\nSeparate results are quoted for a low mass range 0.5 <\nmXd,s < 1.0 GeV/c2, which is dominated by the \u03c1, \u03c9 and\nK\u2217resonances, and for a high mass range 1.0 < mXd,s <\n2.0 GeV/c2. In the low-mass region, missing \ufb01nal states are\nreadily accounted for by the known resonant decays. How-\never, in the high-mass region there are signi\ufb01cant uncer-\ntainties due to missing \ufb01nal states. The seven \ufb01nal states\ngiven in Table 17.9.6 account for only 43% of b \u2192d\u03b3 and\n36% of b \u2192s\u03b3 in the high mass range. A further 37% of\nb \u2192s\u03b3 is accounted for using isospin to relate neutral and\ncharged kaon modes. The hadronization of a non-resonant\nXd,s is modeled using Jetset, and constrained using the\nobserved distribution among the Xs \ufb01nal states. Two al-\nternative hadronization models are considered: replacing\n50% of the inclusive hadronization by known resonances,\nand setting the b \u2192d\u03b3 hadronization fractions to be the\nsame as for the corresponding b \u2192s\u03b3 states, instead of\nallowing for the di\ufb00erences predicted by Jetset . The re-\nsulting missing fractions in B \u2192Xd\u03b3 vary by up to 40%\ncompared to the nominal model. There is a partial can-\ncellation of this uncertainty in the ratio of B \u2192Xd\u03b3 to\nB \u2192Xs\u03b3, but it remains the dominant systematic error.\nBABAR quotes inclusive branching fractions for the low\nmass range 0.5 < mXd,s < 1.0 GeV/c2:\nB(B \u2192Xd\u03b3) = (1.3 \u00b1 0.3 \u00b1 0.1) \u00d7 10\u22126,\nB(B \u2192Xs\u03b3) = (38 \u00b1 2 \u00b1 2) \u00d7 10\u22126,\n(17.9.33)\nwhich are consistent with the measurements of exclusive\nB \u2192\u03c1(\u03c9)\u03b3 and B \u2192K\u2217\u03b3 decays. In the high mass range\n1.0 < mXd,s < 2.0 GeV/c2 they measure:\nB(B \u2192Xd\u03b3) = (7.9 \u00b1 2.0 \u00b1 2.2) \u00d7 10\u22126,\nB(B \u2192Xs\u03b3) = (192 \u00b1 9 \u00b1 29) \u00d7 10\u22126.\n(17.9.34)\nThe results in these two mass ranges do not combine to\ngive fully inclusive branching fractions, because they have\nnot been extrapolated to include higher Xd,s masses (lower\nE\u03b3). The ratio of the inclusive decays over the combined\nmass range 0.5 < mXd,s < 2.0 GeV/c2 is\nB(B \u2192Xd\u03b3)\nB(B \u2192Xs\u03b3) = 0.040 \u00b1 0.009 \u00b1 0.010.\n(17.9.35)\nThis ratio can be regarded as fully inclusive, because the\nphoton energy spectra for b \u2192d\u03b3 and b \u2192s\u03b3 are expected\nto be almost identical at higher Xd,s mass. The measured\nratio of 4% is completely consistent with the SM predic-\ntions with |Vtd|/|Vts| derived from B0 \u2212B0 mixing (see\nSection 17.2).\n17.9.4.3 Theoretical predictions for b \u2192d\u03b3\nThe theoretical prediction for the branching fraction\nB(B \u2192Xd\u03b3) for photon energies E\u03b3 > 1.6 GeV is (Hurth,\nLunghi, and Porod, 2005)\nB(B \u2192Xd\u03b3) \u00d7 105\n=\n\u0012\n1.38 +0.14\n\u22120.21\n\f\f mc\nmb\n\u00b1 0.15CKM \u00b1 0.09param. \u00b1 0.05scale\n\u0013\n,\n(17.9.36)\nand when normalized to B(B \u2192Xs\u03b3) it is\nB(B \u2192Xd\u03b3)\nB(B \u2192Xs\u03b3) \u00d7 102\n=\n\u0012\n3.82 +0.11\n\u22120.18\n\f\f mc\nmb\n\u00b1 0.42CKM \u00b1 0.08param. \u00b1 0.15scale\n\u0013\n.\n(17.9.37)\n\n382\nScaling by the ratio of |Vtd/Vts|2 between the current PDG\nvalue (Beringer et al., 2012) and that used by (Hurth,\nLunghi, and Porod, 2005),87 the ratio in Eq. (17.9.37) in-\ncreases to 3.98\u00d710\u22122, and the CKM uncertainty contribu-\ntion decreases to 0.22\u00d710\u22122. That reduced uncertainty is\nbased in part on lattice QCD calculations of \u2206md/\u2206ms.\nThese predictions are of NLL order. They are fully con-\nsistent with previous results presented in (Ali, Asatrian,\nand Greub, 1998). Due to the fact that a good part of\nthe uncertainties cancel out in the ratio, the CKM uncer-\ntainties are an important component. In principle, mea-\nsurements of B(B \u2192Xd\u03b3) could be used to constrain the\nCKM parameters, and thus crosscheck their PDG ratio,\nbut present experimental precision is far from adequate\nfor that task. Such measurements are also of interest with\nrespect to new physics, because the CKM suppression by\nthe factor |Vtd/Vts|2 in the SM may not hold in extended\nmodels. As discussed in the general theory section (Sec-\ntion 17.9.1) the CP-averaged decay rate of B \u2192Xd\u03b3 is,\nin principle, as theoretically clean as the decay rate of\nB \u2192Xs\u03b3, but the analogous NNLL QCD calculation is\nstill missing.\n17.9.5 Rate asymmetries in b \u2192s(d)\u03b3\nIn many cases, signal events can be divided into two halves\nbased on the \ufb02avor or charge, and the asymmetry in their\ndecay rate provides information in addition to the branch-\ning fractions. In this section, we discuss the isospin asym-\nmetry and direct CP asymmetry for b \u2192s\u03b3 and b \u2192d\u03b3\nprocesses.\nThe isospin asymmetry in B decays into a \ufb01nal state X\n(asymmetry between B0 \u2192X0 and B\u2212\u2192X\u2212) is usually\nde\ufb01ned as\n\u22060\u2212= \u0393(B0 \u2192X0) \u2212\u0393(B\u2212\u2192X\u2212)\n\u0393(B0 \u2192X0) + \u0393(B\u2212\u2192X\u2212).\n(17.9.38)\nA related quantity often used for B \u2192\u03c1\u03b3 is\n\u2206\u03c1 = \u0393(B\u2212\u2192\u03c1\u2212\u03b3)\n2\u0393(B0 \u2192\u03c10\u03b3) \u22121.\n(17.9.39)\nThe direct CP asymmetry in the time-integrated rates is\nde\ufb01ned as\nACP = \u0393(B \u2192X) \u2212\u0393(B \u2192X)\n\u0393(B \u2192X) + \u0393(B \u2192X),\n(17.9.40)\nWe \ufb01rst summarize theoretical predictions in the SM for\nthese asymmetries.\n17.9.5.1 Theoretical predictions for rate asymmetries\nThe theoretical prediction for the isospin breaking ratio\n\u22060\u2212(B \u2192K\u2217\u03b3) based on the QCDF/SCET approach is\n87 The published version of (Hurth, Lunghi, and Porod, 2005)\ndoes not present the numerical CKM values used, but they can\nbe found in the arXiv version 2.\ngiven by (Beneke, Feldmann, and Seidel, 2005):\n\u22060\u2212(B \u2192K\u2217\u03b3) = (0.28/T K\u2217\n1 (0)) (5.8 +3.3\n\u22122.9) \u00d7 10\u22122\n(17.9.41)\nwhere 0.28/T K\u2217\n1 (0) is a quantity of O(1), and the par-\ntial decay rates are CP-averaged. In the SM, spectator-\ndependent e\ufb00ects enter only at order \u039b/mb while isospin-\nbreaking in the form factors is expected to be a negligible\ne\ufb00ect, and the SM prediction is O(5%) (Ali, Lunghi, and\nParkhomenko, 2004; Ball, Jones, and Zwicky, 2007; Be-\nneke, Feldmann, and Seidel, 2005; Bosch and Buchalla,\n2005; Kagan and Neubert, 2002). The ratio is especially\nsensitive to new physics e\ufb00ects in the penguin sector, name-\nly to the ratio of the two e\ufb00ective couplings C6/C7. The\nisospin ratio in the \u03c1\u03b3 decay strongly depends on CKM\nparameters (again an average over CP-conjugate decay\nmodes is made), and predicted for example (Beneke, Feld-\nmann, and Seidel, 2005) to be:\n\u2206\u03c1 = (\u22124.6 +5.4\n\u22124.2\n\f\f\nCKM\n+5.8\n\u22125.6\n\f\f\nhad) \u00d7 10\u22122\n(17.9.42)\nThe hadronic error is mainly due the weak annihilation\ncontribution to which a 50% error is assigned. Other pre-\ndictions (Ali and Lunghi, 2002; Ball, Jones, and Zwicky,\n2007; Lu, Matsumori, Sanda, and Yang, 2005) are simi-\nlarly small.\nFor direct CP asymmetries, in exclusive decays, the\nuncertainties due to form factors cancel out to a large\nextent. But both the scale dependence and the depen-\ndence on the charm quark mass of the NLO predictions are\nrather large because the CP asymmetries arise at O(\u03b1S).\nWhile the direct CP asymmetry in B \u2192K\u2217\u03b3 is dou-\nbly Cabibbo suppressed and expected to be very small,\nwith QCDF and SCET one \ufb01nds \u221210% predictions for\nthe direct CP asymmetries in B \u2192\u03c1\u03b3 (Ali, Lunghi, and\nParkhomenko, 2004; Beneke, Feldmann, and Seidel, 2005;\nBosch and Buchalla, 2002b). Since the weak annihilation\ncontribution does not contribute signi\ufb01cantly here, the\nneutral and charged mode are of similar size (Beneke,\nFeldmann, and Seidel, 2005):\nACP (B0 \u2192\u03c10\u03b3) =\n\u0010\n\u221210.4 +1.6\n\u22122.4\n\f\f\nCKM\n+3.0\n\u22123.6\n\f\f\nhad\n\u0011\n\u00d7 10\u22122,\n(17.9.43)\nACP (B\u2212\u2192\u03c1\u2212\u03b3) =\n\u0010\n\u221210.7 +1.5\n\u22122.0\n\f\f\nCKM\n+2.6\n\u22123.7\n\f\f\nhad\n\u0011\n\u00d7 10\u22122.\n(17.9.44)\nFinally, one should emphasize again that all predictions of\nexclusive observables with QCDF and SCET may receive\nfurther uncertainties due to the unknown power correc-\ntions. This might be speci\ufb01cally important in the case of\nCP asymmetries.\nThe theoretical situation is signi\ufb01cantly better for di-\nrect CP asymmetries in the inclusive modes, as \ufb01rst noted\nin (Kagan and Neubert, 1998). (There are apparently no\ntheoretical predictions for isospin asymmetries in the in-\nclusive radiative processes ) The NP sensitivities of direct\nCP asymmetries in these modes have been analyzed in\nKagan and Neubert (1998), Hurth, Lunghi, and Porod\n(2005), and Benzke, Lee, Neubert, and Paz (2011).\n\n383\nA SM computation (Hurth, Lunghi, and Porod, 2005)\nyielded (for E\u03b3 > 1.6 GeV)\nACP (B \u2192Xs\u03b3)\n=\n\u0010\n0.44 +0.15\n\u22120.10\n\f\f mc\nmb\n\u00b1 0.03CKM\n+0.19\n\u22120.09\n\f\f\nscale\n\u0011\n\u00d7 10\u22122,\n(17.9.45)\nACP (B \u2192Xd\u03b3)\n=\n\u0010\n\u221210.2 +2.4\n\u22123.7\n\f\f mc\nmb\n\u00b1 1.0CKM\n+2.1\n\u22124.4\n\f\f\nscale\n\u0011\n\u00d7 10\u22122.\n(17.9.46)\nNote the very small uncertainty on ACP (B \u2192Xs\u03b3).\nHowever, recent theoretical work (Benzke, Lee, Neu-\nbert, and Paz, 2011) has shown that previously unac-\ncounted long-distance (resolved-photon) e\ufb00ects shift the\npredicted central values of ACP in the SM to 0.011 for\nB \u2192Xs\u03b3 and \u22120.24 for B \u2192Xd\u03b3. The new contribu-\ntions greatly increase the uncertainties, and the resulting\nACP predictions have what the authors term \u201cirreducible\u201d\nranges\n\u22120.006 < ACP (B \u2192Xs\u03b3) < +0.028 ,\n(17.9.47)\n\u22120.62 < ACP (B \u2192Xd\u03b3) < +0.14 .\n(17.9.48)\nThese ranges were computed for an E\u03b3 threshold of\n1.9 GeV, but might be larger for higher thresholds. The im-\nplication is that ACP (B \u2192Xs\u03b3) is not as sensitive a probe\nfor new physics as had once been thought. (The authors\nnote that the long-distance e\ufb00ects are essentially isospin-\nindependent, so that the di\ufb00erence between ACP for B0\nand B+ decays has much better sensitivity.)\nThe two inclusive CP asymmetries are connected by\nthe relative CKM factor \u03bb2 ((1 \u2212\u03c1)2 + \u03b72). The small SM\nprediction for the CP asymmetry in the decay B \u2192Xs\u03b3 is\na result of three factors: (a) a strong phase can only appear\nthrough QCD radiative corrections, so the CP asymmetry\nis O(\u03b1s(mb)); (b) there is a CKM suppression of order\n\u03bb2; (c) there is a GIM suppression, leading to a factor\n(mc/mb)2, which re\ufb02ects the fact that in the limit mc =\nmu any CP asymmetry in the SM would vanish.\nUsing CKM unitarity one can derive the following U-\nspin relation between the un-normalized CP asymmetries\n(Soares, 1991):\n\u2206\u0393(B \u2192Xs\u03b3) + \u2206\u0393(B \u2192Xd\u03b3) = 0,\n(17.9.49)\nwhere \u2206\u0393(B \u2192Xq\u03b3) = \u0393(B \u2192Xq\u03b3) \u2212\u0393(B \u2192Xq\u03b3)\nand q = s, d. U-spin breaking e\ufb00ects can be estimated\nwithin the heavy mass expansion (even beyond the par-\ntonic level) and one \ufb01nds that the total ACP (B \u2192Xs+d\u03b3)\nis zero to order 10\u22126 (Hurth and Mannel, 2001a,b). This\nprecision is preserved even in the presence of the long-\ndistance e\ufb00ects (Benzke, Lee, Neubert, and Paz, 2011).\nSince the prediction is based on CKM unitarity, this null\ntest is a clear probe for new CP phases beyond the CKM\nphase.\n17.9.5.2 Measurements of Isospin asymmetries\nIn order to measure isospin asymmetries, the decay widths\n\u0393 in Eq. (17.9.38) are evaluated as the ratios of branch-\ning fractions and B lifetimes, B/\u03c4, where \u03c4B0 = (1.519 \u00b1\n0.007) ps and \u03c4B\u2212= (1.641 \u00b1 0.008) ps, and the ratio\n\u03c4B\u2212/\u03c4B0 = 1.071 \u00b1 0.009 from Particle Data Group (Be-\nringer et al., 2012).\nThere is an inclusive measurement of \u22060\u2212(B \u2192Xs\u03b3),\nbut only from the sum of exclusive modes (Aubert, 2005x).\nThe recoil-B tag method (Aubert, 2008q) has measured\n\u22060\u2212(B \u2192Xs+d\u03b3), albeit with limited precision. Other\ninclusive methods do not distinguish between B0 and B\u2212.\nBoth results use a minimum photon E\u03b3 of 2.2 GeV, and\nare given in Table 17.9.7.\nThe most precise measurement of an isospin asymme-\ntry comes from B \u2192K\u2217\u03b3. Indeed it is so precise that\nit is important to take into account a possible produc-\ntion asymmetry between B+B\u2212and B0B0 at the \u03a5(4S).\nBABAR chooses to use the measured production fractions\nB+B\u2212= 0.516 \u00b1 0.006 and B0B0 = 0.484 \u00b1 0.006, and\nobtains an isospin asymmetry:\n\u22060\u2212(B \u2192K\u2217\u03b3) = 0.066 \u00b1 0.021 \u00b1 0.022.\n(17.9.50)\nBelle has a measurement based on a smaller data sample,\nand assumes equal production fractions. For consistency in\naveraging, and with other decay modes, the BABAR result\nis adjusted to assume equal production fractions in Ta-\nble 17.9.7. This gives an average isospin asymmetry con-\nsistent with zero and with the inclusive isospin asymmetry.\nIf instead the Belle result is changed to use the measured\nproduction fractions, the world average becomes\n\u22060\u2212(B \u2192K\u2217\u03b3) = 0.058 \u00b1 0.025.\n(17.9.51)\nThe e\ufb00ect of the measured production fractions is a change\nfrom no isospin asymmetry to about 2\u03c3 positive asym-\nmetry. The same shift towards a positive asymmetry is\nexpected for the inclusive result, although here it is not\nsigni\ufb01cant due to the larger error. A small positive isospin\nasymmetry is in accordance with SM predictions (Kagan\nand Neubert, 2002; Keum, Matsumori, and Sanda, 2005)\n\u2014 see Eq. (17.9.41).\nThe isospin asymmetry for B \u2192\u03c1\u03b3 reported by BABAR\nand Belle is reported in terms of \u2206\u03c1 (Eq. 17.9.39). To be\nmore consistent with the de\ufb01nition in Eq. (17.9.38), we\nrede\ufb01ne the isospin asymmetry for B \u2192\u03c1\u03b3 as\n\u22060\u2212(B \u2192\u03c1\u03b3) = 2\u0393(B0 \u2192\u03c10\u03b3) \u2212\u0393(B\u2212\u2192\u03c1\u2212\u03b3)\n2\u0393(B0 \u2192\u03c10\u03b3) + \u0393(B\u2212\u2192\u03c1\u2212\u03b3).\n(17.9.52)\nIt is straightforward to convert between these di\ufb00erent\nforms. Here in the text the published numbers are given\nin their original form, since this is what is used by HFAG\nand many theory papers. In Table 17.9.7 both results are\nconverted to the form of \u22060\u2212.\nThe published Belle result (Taniguchi, 2008) is \u2206\u03c1 =\n\u22120.48 \u00b1 0.20 \u00b1 0.09, which converts to \u22060\u2212(B \u2192\u03c1\u03b3) =\n+0.32\u00b10.12\u00b10.05. The published BABAR result (Aubert,\n2008z) is \u2206\u03c1 = \u22120.43 \u00b1 0.24 \u00b1 0.10, which converts to\n\u22060\u2212(B \u2192\u03c1\u03b3) = +0.27 \u00b1 0.13 \u00b1 0.05. The world average\nprovided by HFAG is\n\u2206\u03c1 = \u22120.46 \u00b1 0.17\n(17.9.53)\n\n384\nTable 17.9.7. Summary of measurements of isospin asymme-\ntries \u22060\u2212in b \u2192s(d)\u03b3 decays (in 10\u22122). The BABAR Xs\u03b3 result\nassumed an older value for the lifetime ratio, 1.086\u00b10.017. The\n\u03c1\u03b3 asymmetry is de\ufb01ned in a consistent fashion with s\u03b3, which\nis di\ufb00erent from the de\ufb01nition \u2206\u03c1 found in the literature (see\ntext for discussion). This table assumes equal production of\nB+B\u2212and B0B0 at the \u03a5(4S) (see Eq. (17.9.50) for the pub-\nlished b result for K\u2217\u03b3, which uses the measured production\nfractions). The e\ufb00ect of these on the isospin asymmetry is dis-\ncussed in the text.\nMode\nBABAR\nBelle\nAverage\nXs\u03b3\n\u22120.6 \u00b1 5.8 \u00b1 2.6\n\u22120.6 \u00b1 6.3\nXs+d\u03b3\n\u22126 \u00b1 15 \u00b1 7\n\u22126 \u00b1 17\nK\u2217\u03b3\n3.4 \u00b1 2.1 \u00b1 2.2 \u22121.5 \u00b1 4.4 \u00b1 1.2\n2 \u00b1 3\n\u03c1\u03b3\n27 \u00b1 13 \u00b1 5\n32 \u00b1 12 \u00b1 5\n30 \u00b1 10\nwhich converts to:\n\u22060\u2212(B \u2192\u03c1\u03b3) = +0.30 \u00b1 0.10.\n(17.9.54)\nIn either form, there is 3\u03c3 evidence for an isospin asym-\nmetry in B \u2192\u03c1\u03b3, which is much larger than the SM\nexpectation (Eq. 17.9.42); and therefore a larger dataset\nis needed to clarify the situation.\n17.9.5.3 Measurements of Direct CP asymmetries\nThe direct CP asymmetry of Eq. (17.9.40) has been\nmeasured in inclusive b \u2192s\u03b3 decays using the sum-\nof-exclusive-states method. The BABAR result (Aubert,\n2008a) is based on 383M BB, and the Belle result (Ni-\nshida, 2004) on 152M BB. The \ufb01nal states are divided\ninto b modes (B0 and B+) and b modes (B0 and B\u2212) us-\ning the kaon charge or total charge. CP eigenstates with\na K0\nS and an even number of charged pions are excluded\nfrom the analysis. Dilution of the asymmetry due to events\nmisreconstructed in the wrong \ufb01nal state is very small and\nis corrected for. BABAR measures the CP asymmetry for\nXs mass below 2.8 GeV/c2 (but note that there are rela-\ntively few selected events above \u223c2 GeV/c2):\nACP (B \u2192Xs\u03b3) = \u22120.011 \u00b1 0.030 \u00b1 0.014\n(17.9.55)\nwhile Belle measures for Xs mass below 2.1 GeV/c2:\nACP (B \u2192Xs\u03b3) = 0.002 \u00b1 0.050 \u00b1 0.030.\n(17.9.56)\nBoth measurements are consistent with zero, and are sta-\ntistically limited. In the SM the direct CP asymmetry in\nB \u2192Xs\u03b3 is expected to be small, as explained in Sec-\ntion 17.9.5.1.\nIn the lepton-tagged fully-inclusive analysis, the lep-\nton charge can be used to \ufb02avor-tag the signal-B decay,\nalthough there is some dilution due primarily to B0 \u2212B0\nmixing. Because this measurement does not separate B \u2192\nXs\u03b3 from B \u2192Xd\u03b3 decays, the resulting CP asymmetry\nTable 17.9.8. Summary of measurements of direct CP asym-\nmetries ACP in b \u2192s(d)\u03b3 decays (in 10\u22122). The two values\nlisted for BABAR B \u2192Xs+d\u03b3 are from the lepton-tag and\nreconstructed-B-tag methods, respectively (kept separate be-\ncause of di\ufb00erent E\u03b3 thresholds). Uncertainties are statistical\nand systematic, respectively, combined for the BABAR plus Belle\naverage in the last column.\nMode\nBABAR\nBelle\nAverage\nXs\u03b3\n\u22121.1 \u00b1 3.0 \u00b1 1.4 0.2 \u00b1 5.0 \u00b1 3.0\n\u22121 \u00b1 3\nXs+d\u03b3\n+5.7 \u00b1 6.0 \u00b1 1.8\n+6 \u00b1 6\n+10 \u00b1 18 \u00b1 5\n+10 \u00b1 19\nK\u2217\u03b3\n\u22120.3 \u00b1 1.7 \u00b1 0.7 1.2 \u00b1 4.4 \u00b1 2.6\n0 \u00b1 2\nK+\u03b7\u03b3\n\u22129.0 +10.2\n\u22129.8 \u00b1 1.4\n\u221216 \u00b1 9 \u00b1 6\n\u221212 \u00b1 7\nK+\u03c6\u03b3\n26 \u00b1 14 \u00b1 5\n\u22123 \u00b1 11 \u00b1 8\n\u221213 \u00b1 10\nK\u2217\n2(1430)0\u03b3\n\u22128 \u00b1 15 \u00b1 1\n\u22128 \u00b1 15\n\u03c1+\u03b3\n\u221211 \u00b1 32 \u00b1 9\n\u221211 \u00b1 33\nis for a sum of B \u2192Xs+d\u03b3 events. (In the corresponding\nbranching fraction analysis of Section 17.9.2.2, the small\nB \u2192Xd\u03b3 contribution could be removed using a ratio of\nCKM matrix elements, but this procedure is not applica-\nble to the CP asymmetries.) In the SM this asymmetry\nis predicted to be zero, to a precision of order 10\u22126, with\nthe larger Xd\u03b3 asymmetry (Eq. 17.9.46) exactly compen-\nsated by the smaller Xd\u03b3 branching fraction. BABAR has\nmeasured this combined asymmetry based on a 383M BB\nsample (Lees, 2012j,o). The photon energy threshold of 2.1\nGeV suppresses BB background, while being adequately\ninclusive to preserve the SM prediction. The \ufb02avor-mistag\nfraction (primarily from mixing, with contributions from\ncascade decays and misidenti\ufb01ed leptons) is 0.133\u00b10.006.\nThe measured asymmetry is\nACP (B \u2192Xs+d\u03b3) = +0.057 \u00b1 0.060 \u00b1 0.018 , (17.9.57)\nwhere the errors are statistical and systematic.\nAnother measurement of the combined ACP (B \u2192\nXs+d\u03b3) comes from BABAR\u2019s use of reconstructed-B tags\n(Section 17.9.2.3). In this case (Aubert, 2008q) ACP is\nmeasured by splitting the reconstructed tags into known B\nand B states. The \ufb02avor-mistag fraction, due to B0 \u2212B0\nmixing, is 0.188 times the fraction of B0 events in the\nsample, and the measured asymmetry for E\u03b3 > 2.2 GeV is\nACP (B \u2192Xs+d\u03b3) = +0.10 \u00b1 0.18 \u00b1 0.05 .\n(17.9.58)\nUsing the \ufb02avor-speci\ufb01c B \u2192K\u2217\u03b3 \ufb01nal states, pre-\ncise measurements of direct CP violation have been made\nby both BABAR and Belle. The results are given in Ta-\nble 17.9.8. The world average is consistent with zero with\nan error of only 2%:\nACP (B \u2192K\u2217\u03b3) = \u22120.003 \u00b1 0.017 .\n(17.9.59)\nThere are also measurements of direct CP asymmetries in\nB0 \u2192K\u2217\n2(1430)0\u03b3 by BABAR (Aubert, 2004i), in B+ \u2192\n\u03c1+\u03b3 by Belle (Taniguchi, 2008), and in B+ \u2192K+\u03b7\u03b3\n(Nishida (2005) and Aubert (2009e)) and B+ \u2192K+\u03c6\u03b3\n\n385\n(Sahoo (2011) and Aubert (2007q)) by Belle and BABAR,\nrespectively. Direct CP asymmetry is also measured for\nneutral B decay modes with no self-\ufb02avor-tagging in time\ndependent CP asymmetry measurements as discussed in\nSection 17.9.6. All the measurements of direct CP asym-\nmetries in b \u2192s(d)\u03b3 are consistent with zero.\n17.9.6 Time-dependent CP asymmetries\nExclusive decay modes that have a common \ufb01nal state\nbetween B0 and B0 are candidates to measure the time-\ndependent CP asymmetry due to interference between\nmixing and decay amplitudes. The distribution of the\nproper time di\ufb00erence \u2206t between the decay of a tag-\nging B0 or B0 and the decay of the signal B is given\nby Eq. (10.2.2). The coe\ufb03cients of the sine and cosine\nterms are represented as parameters S and C, respec-\ntively. The time-dependent asymmetry is then de\ufb01ned by\nEq. (10.2.7), which results in\nACP (B \u2192f; \u2206t) = S sin(\u2206md\u2206t) \u2212C cos(\u2206md\u2206t) .\n(17.9.60)\nFor a measurement, \u2206t-resolution must be convoluted with\nthe underlying \u2206t distributions, and incorrect B-\ufb02avor\ntagging results in a dilution factor multiplying the S and\nC terms. The full e\ufb00ects of this \ufb02avor mistagging on the\ntime distributions are given in Eq. (10.3.3). Note that \u2212C\nrepresents the size of the direct CP asymmetry discussed\nabove.88 In contrast to most rare hadronic B decays, the\nuniquely time-dependent S term is strongly suppressed in\nradiative decays because of the left-handedness of the \ufb01-\nnal state photon, as discussed below in Section 17.9.6.1.\nStudies of these asymmetries are thus considered to be\none of the most promising methods to search for non-SM\nright-handed currents.\n17.9.6.1 Theoretical predictions for time-dependent CP\nasymmetries\nIn the hadronic decay mode B \u2192J/\u03c8K0\nS, a large value of\nS has been measured, its size a consequence of the value of\nthe angle \u03c61 \u2261\u03b2 = \u2212arg(VtdV \u2217\ntb/VudV \u2217\nub) of the Unitarity\nTriangle. Similar large CP asymmetries are expected for\nhadronic penguin decays. However, this asymmetry is sup-\npressed in radiative penguin decays because the photon\nhelicity is opposite between B0 and B0 decays as a result\nof the left-handed current of SM weak decays. In the limit\nof massless quarks there is no CP violation due to interfer-\nence between mixing and decay amplitudes. This implies a\nsuppression factor of 2ms/mb in the leading contribution\nto S induced by the electromagnetic dipole operator O7:\nSSM = \u2212sin 2\u03c61\nms\nmb\n[2 + O(\u03b1S)] + SSM,s\u03b3g\n(17.9.61)\nAs noted in Grinstein, Grossman, Ligeti, and Pirjol (2005)\nand Grinstein and Pirjol (2006), there are additional\n88 The symbol A = \u2212C is also often used.\nTable 17.9.9. Summary of measurements of time-dependent\nCP asymmetries in b \u2192s(d)\u03b3 decays. S refers to coe\ufb03cients of\nsin(\u2206md\u2206t), and C to coe\ufb03cients of cos(\u2206md\u2206t). The entries\nfor B \u2192K0\nS\u03c00\u03b3 are for the high K0\nS\u03c00 mass region excluding\nthe K\u22170 resonance.\nBABAR\nBelle\nAverage\nS(K\u22170\u03b3)\n\u22120.03 \u00b1 0.29 \u00b1 0.03 \u22120.32 \u00b1 0.35 \u00b1 0.05 \u22120.17 \u00b1 0.20\nC(K\u22170\u03b3)\n\u22120.14 \u00b1 0.16 \u00b1 0.03\n0.20 \u00b1 0.24 \u00b1 0.05\n0.00 \u00b1 0.13\nS(K0\nS\u03c00\u03b3) \u22120.78 \u00b1 0.59 \u00b1 0.09 \u22120.10 \u00b1 0.31 \u00b1 0.07 \u22120.40 \u00b1 0.25\nC(K0\nS\u03c00\u03b3) \u22120.36 \u00b1 0.33 \u00b1 0.04\n0.20 \u00b1 0.20 \u00b1 0.06\n0.00 \u00b1 0.16\nS(K0\nS\u03b7\u03b3)\n\u22120.18 \u00b1 0.48 \u00b1 0.12\n\u22120.18 \u00b1 0.50\nC(K0\nS\u03b7\u03b3)\n\u22120.32 \u00b1 0.40 \u00b1 0.07\n\u22120.32 \u00b1 0.41\nS(K0\nS\u03c6\u03b3)\n0.74 \u00b1 0.90 \u00b1 0.20\n0.74 \u00b1 0.91\nC(K0\nS\u03c6\u03b3)\n\u22120.35 \u00b1 0.58 \u00b1 0.20 \u22120.35 \u00b1 0.61\nS(K0\nS\u03c10\u03b3)\n0.11 \u00b1 0.33 \u00b1 0.07\n0.11 \u00b1 0.35\nC(K0\nS\u03c0+\u03c0\u2212\u03b3)\u2020\n0.05 \u00b1 0.18 \u00b1 0.06\n0.05 \u00b1 0.20\nS(\u03c10\u03b3)\n\u22120.83 \u00b1 0.65 \u00b1 0.18 \u22120.83 \u00b1 0.68\nC(\u03c10\u03b3)\n0.44 \u00b1 0.49 \u00b1 0.14\n0.44 \u00b1 0.53\n\u2020For mK\u03c0\u03c0 < 1.8 GeV/c2 and m\u03c0\u03c0 \u2208[0.6, 0.9] GeV/c2.\ncontributions, SSM,s\u03b3g induced by the process b \u2192s\u03b3g via\nother operators than O7. One example is a contribution of\nthe operator O2 \u223c(bs)(cc) where the charm quark forms\na loop from which a (right-handed) photon and a gluon is\nemitted. These corrections are power-suppressed but not\nhelicity-suppressed. A conservative estimate of this con-\ntribution in B \u2192K\u2217\u03b3 due to a non-local SCET oper-\nator series leads to |SSM,s\u03b3g| \u22480.06 (Grinstein, Gross-\nman, Ligeti, and Pirjol, 2005; Grinstein and Pirjol, 2006),\nwhile within a QCD sum rule calculation the contribution\ndue to soft gluon emission is estimated to be SSM,s\u03b3g =\n\u22120.005 \u00b1 0.01 (Ball, Jones, and Zwicky, 2007; Ball and\nZwicky, 2006a) which leads to SSM = \u22120.022\u00b10.015+0\n\u22120.01\nfor the process B \u2192K\u2217\u03b3. The QCD sum rule estimates of\npower corrections, due to long-distance contributions with\nphoton and soft-gluon emission from quark loops (Ball,\nJones, and Zwicky, 2007), lead to analogous results for\nthe other radiative decay modes such as B \u2192\u03c1\u03b3 (Ball,\nJones, and Zwicky, 2007). If a large value of S beyond the\nSM prediction is observed, this will be a clear signal of a\nnew right-handed current beyond the SM.\nIt was pointed out by (Atwood, Gershon, Hazumi, and\nSoni, 2007) that, due to the left-handed photon coupling,\nCP asymmetries in the SM are equally small for any de-\ncay of the form B \u2192P 0Q0\u03b3, where P 0 is a neutral pseu-\ndoscalar and Q0 is another neutral pseudoscalar or a neu-\ntral vector meson. In the case of the pseudoscalar-vector-\nphoton \ufb01nal states there is also information in the angular\ndistribution of the \ufb01nal state.\n17.9.6.2 Measurements of time-dependent CP asymmetries\nThe decay mode B0 \u2192K\u22170\u03b3 with K\u22170 \u2192K0\nS\u03c00 has the\nlargest branching fraction and hence has the largest po-\ntential for a time-dependent CP asymmetry search. How-\never, to measure the time-dependent CP asymmetry for\n\n386\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nnts per 2 ps\n0\n20\n40\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nnts per 2 ps\n0\n20\n40\n Tags\n0\nB\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nWeighted Eve\n0\n20\n40\n t (ps)\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nWeighted Eve\n0\n20\n40\n Tags\n0\nB\nt [ps]\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nAsymmetry\n-1\n0\n1\nt [ps]\n\u2206\n-6\n-4\n-2\n0\n2\n4\n6\nAsymmetry\n-1\n0\n1\nFigure 17.9.9. Results of BABAR time-dependent CP asym-\nmetry \ufb01t to B \u2192K\u2217\u03b3 events with K\u2217\u2192K0\nS\u03c00, from (Au-\nbert, 2008x). The underlying \u2206t distributions (before includ-\ning resolution e\ufb00ects) are given by Eq. (10.3.3). Shown are\nbackground-subtracted distributions for B0 tags (top) B0 tags\n(middle) and their asymmetry (bottom).\nB0 \u2192K0\nS\u03c00\u03b3, one has to measure the B meson decay ver-\ntex by extrapolating the displaced K0\nS \u2192\u03c0+\u03c0\u2212vertex.\nIt is only possible to do this accurately when the K0\nS de-\ncays inside the vertex detector volume. This requirement\nreduces the acceptance by a factor of 0.68 for BABAR and\n0.55 for Belle. Note that the K0\nS momentum in this decay\nis lower than in the charmless hadronic decay B0 \u2192K0\nS\u03c00,\nso the acceptance is somewhat larger. A control sample of\nB \u2192J/\u03c8K0\nS events is used to demonstrate that it is feasi-\nble to make a time-dependent measurement using the ver-\ntex reconstruction from the K0\nS extrapolation alone (Ushi-\nroda, 2005).\nBABAR (Aubert, 2008x) and Belle (Ushiroda, 2006)\nhave both made measurements of the amplitudes S and\nC of the sin(\u2206md\u2206t) and cos(\u2206md\u2206t) terms in the\ntime-dependent asymmetry. The results are given in Ta-\nble 17.9.9. Although they use large data samples of 467M\nand 535M BB respectively, their results are statistically\nlimited, because only 1/9 of B0 \u2192K\u22170\u03b3 events decay into\nK0\nS(\u2192\u03c0+\u03c0\u2212)\u03c00\u03b3. The \ufb01t results from BABAR is shown in\nFig. 17.9.9.\nBoth experiments have also looked at a higher K0\nS\u03c00\nmass region in B \u2192K0\nS\u03c00\u03b3 in a range up to 2 GeV. In this\nregion the \ufb01nal state is no longer dominated by a single\nresonance, with the largest contribution coming from the\nK\u2217\n2(1430).\nA few other exclusive b \u2192s\u03b3 \ufb01nal states have been\ninvestigated experimentally (see Table 17.9.9). For B \u2192\nK0\nS\u03b7\u03b3, the vertex can be reconstructed from charged pions\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n1.6\n1.7\n1.8\n0\n20\n40\n60\n80\n100\n120\nmK\u03c0\u03c0(GeV/c2)\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n1.6\n1.7\n1.8\nEvents / ( 0.025 GeV/c )\n2\n0\n20\n40\n60\n80\n100\n120\ntotal\nsignal (1 )\n+\nsignal (1 )\n-\nsignal (2 )\n+\nSCF\ncontinuum\nother BG\nFigure 17.9.10. K+\u03c0+\u03c0\u2212mass distribution for a K\u2217enriched\nB+ \u2192K+\u03c0+\u03c0\u2212\u03b3 sample for Belle\u2019s B0 \u2192K0\nS\u03c10\u03b3 analysis.\nSignal components (1+, 1\u2212and 2+) are based on known reso-\nnances (K1(1270) and K1(1400), K\u2217(1680) and K\u2217\n2(1430)), of\nwhich the K\u2217\n2(1430) component is \ufb01xed. Dashed curves are for\nself-crossfeed (SCF), continuum and other backgrounds.\n)\n2\n (GeV/c\n\u03c0\n\u03c0\nm\n0.4\n0.6\n0.8\n1\n1.2\n0\n5\n10\n15\n20\n25\n30\n35\n)\n2\n (GeV/c\n\u03c0\n\u03c0\nm\n0.4\n0.6\n0.8\n1\n1.2\n0\n5\n10\n15\n20\n25\n30\n35\n(b)\n )\n2\nEvents / ( 0.015 GeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n )\n2\nEvents / ( 0.015 GeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n(a)\nFigure 17.9.11. Belle measurements of \u03c0+\u03c0\u2212mass distribu-\ntions (with no K\u2217mass restriction) for (a) B+ \u2192K+\u03c0+\u03c0\u2212\u03b3\nand (b) B0 \u2192K0\nS\u03c0+\u03c0\u2212\u03b3, from (Li, 2008). The thin solid\n(dashed) line corresponds to the K\u03c10\u03b3 (K1(1270)\u03b3 subset) sig-\nnal, and dot-dashed (dashed) line to the total (continuum)\nbackground.\nfor the \ufb01nal state with \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00, but for \u03b7 \u2192\u03b3\u03b3 it is\nstill necessary to reconstruct the vertex from the K0\nS. The\ntime-dependent CP asymmetry for B \u2192K0\nS\u03b7\u03b3 has been\nmeasured by BABAR (Aubert, 2009e) with 465M BB. A\nsimilar mode, B \u2192K0\u03b7\u2032\u03b3, has not been observed yet.\nThe B \u2192K0\nS\u03c6\u03b3 mode has recently been measured by\nBelle (Sahoo, 2011) with 772M BB, in which the vertex\nis determined from \u03c6 \u2192K+K\u2212.\nThe B \u2192K0\nS\u03c10\u03b3 mode was measured by Belle with\n657M BB (Li, 2008). Unlike the other decays discussed\nhere, the CP purity of this \ufb01nal state is diluted by the\n\ufb02avor speci\ufb01c B0 \u2192K\u2217+\u03c0\u2212\u03b3 mode. (This dilution is in\naddition to the usual e\ufb00ect of \ufb02avor mistags.) In order\nto \ufb01x the contribution of each resonant state, assuming\n\n387\nisospin symmetry, the K+\u03c0+\u03c0\u2212mass distribution of the\nK\u2217\u03c0 enriched sample of more abundant charged mode\nB+ \u2192K+\u03c0+\u03c0\u2212\u03b3 is \ufb01tted with known states: those with\n1+ spin-parity of which K1(1270) is the dominant res-\nonance with a small K1(1400) contribution, those with\n1\u2212from K\u2217(1680), and those with 2+ from K\u2217\n2(1430) as\nshown in Figure 17.9.10. As a part of the systematic er-\nror study, contributions from other possible modes were\ntested, and it was found that the inclusion of B \u2192K0\nS\u03c3\u03b3\ncauses the largest shift, where \u03c3 is a controversial scalar\nstate also listed as f0(500) by the Particle Data Group (Be-\nringer et al., 2012). The absolute values of the amplitudes\nto the K\u2217\u03c0 and K\u03c10 modes are deduced from the results of\nthe K\u2217\u03c0 enriched sample and known branching fractions.\nThe relative phase between K\u2217\u03c0 and K\u03c1 for K1(1270) is\ndetermined from a \ufb01t to the K\u03c0 and \u03c0\u03c0 mass distributions\nafter integrating out the K\u03c0\u03c0 mass, in which the corre-\nsponding phases for K\u2217(1680) and K\u2217\n2(1430) are \ufb01xed to\nknown values and that for K1(1400) is determined from a\nscan to give the smallest \u03c72.\nThe dilution factor is calculated by integrating the sum\nof decay amplitudes for B0 decays, using the parameters\nobtained for B+ decays. It can be seen in Figure 17.9.11\nthat the K\u03c10\u03b3 is the dominant contribution in the \u03c0+\u03c0\u2212\nmass range [0.6, 0.9] GeV/c2. The dilution factor in this\nrange is found to be 0.83 +0.19\n\u22120.03, which is used as a correc-\ntion factor to the measured CP asymmetry in the same\nmass range. Despite this complication, the K0\nS\u03c10\u03b3 mode\nis statistically competitive to the K\u22170\u03b3 mode as listed\nin Table 17.9.9 because the vertex is determined from\n\u03c10 \u2192\u03c0+\u03c0\u2212. The dilution e\ufb00ect is corrected for in the\nS measurement, but the C coe\ufb03cient is not corrected as\ndirect CP asymmetry does not necessarily originate only\nfrom CP eigenstates.\nTime dependent CP asymmetries can also be measured\nin b \u2192d\u03b3 decay modes. The weak phases due to Vtd that\nappear in the B0B0 mixing and b \u2192d penguin diagrams\ncancel each other, so a time dependent CP asymmetry re-\nquires a new contribution to the phase beyond the SM that\nenters di\ufb00erently in mixing and penguin diagrams. As with\nthe b \u2192s\u03b3 decays, this new contribution also has to have\na signi\ufb01cant right-handed amplitude. Although the rate\nfor b \u2192d\u03b3 is only 4% of b \u2192s\u03b3, in the case of B \u2192\u03c10\u03b3\na large fraction of this suppression is compensated with\nrespect to B \u2192K\u22170\u03b3, because of the 1/9 factor for the\nK0\nS\u03c00 fraction and the K0\nS vertex requirement in the ver-\ntex detector volume. Belle has measured time-dependent\nCP asymmetries in B \u2192\u03c10\u03b3 with 657M BB (Ushiroda,\n2008). The results are given in Table 17.9.9.\nAt present all the measurements of time-dependent CP\nviolation are consistent with zero, and dominated by sta-\ntistical errors that are 0.16 or greater. This is an area\nwhere larger samples at a super \ufb02avor factory would make\na signi\ufb01cant improvement.\n17.9.7 Electroweak penguin decays b \u2192s(d)\u2113+\u2113\u2212\nThe b \u2192s\u2113+\u2113\u2212transition, where \u2113+\u2113\u2212is an electron or\na muon pair, provides a number of additional probes of\nthe SM and possible new physics contributions. In the\nlanguage of the e\ufb00ective electroweak Hamiltonian (Sec-\ntion 17.9.1.1), the contributions present for the radiative\nb \u2192s\u03b3 transitions (most importantly the O7 term) are\nsupplemented by the lepton-current terms, O9 and O10.\nThe lepton pair can be generated from a virtual photon\nwith the same penguin diagram as b \u2192s\u03b3, or the pho-\nton can be replaced by a virtual Z boson. There is also\na contribution from a box diagram that is formed by vir-\ntual W bosons and a neutrino (Figure 17.9.1). The decays\nb \u2192s\u2113+\u2113\u2212are suppressed relative to b \u2192s\u03b3 by an addi-\ntional factor of \u03b1, which results in branching fractions of\nO(10\u22126). For this reason they had not been observed at\nexperiments prior to the B Factories. The b \u2192d\u2113+\u2113\u2212tran-\nsition has similar properties, but it is further suppressed\nby |Vtd/Vts|2 and thus has been beyond the reach of the\nB Factories.\nThe theoretical methods to describe the observables in\nb \u2192s(d)\u2113+\u2113\u2212are discussed in Section 17.9.1. The exclu-\nsive channel B \u2192K\u2217\u2113+\u2113\u2212is of particular interest experi-\nmentally, but is theoretically more di\ufb03cult than inclusive\nchannels, since it depends on a set of form factors. A de-\nscription of the necessary theoretical tools can be found\nin Section 17.9.1.6.\nThe b \u2192s\u2113+\u2113\u2212decays have additional degrees of free-\ndom as compared to b \u2192s\u03b3 decays. First, the ampli-\ntudes of the di\ufb00erent contributions vary as a function of\nthe invariant mass squared q2 of the di-lepton system.89\nThe lower end of the q2 distribution has a large contri-\nbution from the virtual photon, whereas the higher end\nis dominated by weak boson transitions. Second, the two\n\ufb01nal-state leptons provide several additional angular vari-\nables (see Section 17.9.7.3 for the speci\ufb01cs in the case of\nB \u2192K\u2217\u2113+\u2113\u2212). In particular, the interference between the\ncontributions generates a forward-backward asymmetry in\nthe di-lepton decay angle. The pattern of this asymmetry\nas a function of q2 is expected to provide a sensitive test\nof the SM (Ali, Giudice, and Mannel, 1995), especially via\nthe presence in the SM of a zero-crossing point at q2 \u22483\nto 4 GeV2/c2 (Ali, Ball, Handoko, and Hiller, 2000).\n17.9.7.1 The exclusive modes B \u2192K(\u2217)\u2113+\u2113\u2212\nThe exclusive modes B \u2192K\u2113+\u2113\u2212and B \u2192K\u2217\u2113+\u2113\u2212have\ncommon \ufb01nal states with B \u2192\u03c8K and B \u2192\u03c8K\u2217. These\n\ufb01nal states are a source of calibration events for optimizing\nthe search for the b \u2192s\u2113+\u2113\u2212modes, but they are also a\nlarge background in the di-lepton mass ranges around the\nJ/\u03c8 and \u03c8\u2032. There is interference between the electroweak\npenguin and charmonium amplitudes which is di\ufb03cult to\nhandle theoretically, although it could eventually provide\nuseful information about relative phases. For both exper-\nimental and theoretical reasons the regions around the\nJ/\u03c8 and \u03c8\u2032 are vetoed in the BABAR and Belle analy-\nses. For e+e\u2212pairs there is a long and large radiative\n89 Although here we de\ufb01ne the q2 in terms of mass, the origi-\nnal meaning is in terms of momentum of the virtual boson and\nhence we quote the values in the unit of GeV2/c2.\n\n388\ntail on the lower q2 side of the charmonium peaks due to\nbremsstrahlung from the \ufb01nal state electrons, which also\nshifts the measured kinematic variables mES (slightly) and\n\u2206E. These o\ufb00sets are partially removed by adding pho-\ntons to the electron momentum if they are found near the\nelectron direction. Details of this bremsstrahlung recovery\nprocedure can be found in (Ishikawa, 2003) and (Aubert,\n2006ac). Note that Belle uses wider J/\u03c8 and \u03c8\u2032 veto win-\ndows for electron modes than for the muon modes.\nAnother region that is usually vetoed in B \u2192K(\u2217)e+e\u2212\nis the very low q2 region where there is a large peak from\nthe virtual photon diagram. Removing the region below\nthe threshold \u00b5+\u00b5\u2212mass squared from analysis results\nin similar SM expectations for the inclusive decay rates of\nB \u2192K\u2217e+e\u2212and B \u2192K\u2217\u00b5+\u00b5\u2212. There is no virtual pho-\nton peak in B \u2192Ke+e\u2212due to angular momentum sup-\npression of the photons, but there are other background\ncontributions in this region. They arise from charmless\nhadronic B decays followed by a Dalitz decay of a \u03c00, and\nfrom pair conversions of photons in the detector, and it is\ndesirable to remove them.\nObservation of the decay B \u2192K\u2113+\u2113\u2212was already re-\nported by Belle with only 31M BB data (Abe, 2002l). This\nwas followed by the \ufb01rst observation of B \u2192K\u2217\u2113+\u2113\u2212by\nBelle in 2003 with a data sample of 152M BB (Ishikawa,\n2003). Both results were supported by BABAR with a data\nsample of 123M BB (Aubert, 2003c). There have been\nfrequent updates from BABAR using 229M BB (Aubert,\n2006ac), 384M BB (Aubert, 2009c,j), and 471M BB (Lees,\n2012i), and the latest result from Belle uses 657M BB (Wei,\n2009).\nWe also compare in this section the B Factories results\non B \u2192K(\u2217)\u2113+\u2113\u2212modes with recent results from the\nCDF experiment at the Tevatron (Aaltonen et al., 2011c),\nand from the LHCb experiment at CERN (Aaij et al.,\n2012a,b,g,i). CDF has been very competitive with the B\nFactories in these exclusive modes, and LHCb has recently\nsurpassed the precision of the B Factories in \u00b5+\u00b5\u2212modes.\n17.9.7.2 Branching fractions and rate asymmetries in\nB \u2192K(\u2217)\u2113+\u2113\u2212\nGiven the limited statistics in these exclusive decay modes,\ncombined branching fractions are determined using all\nmeasured \ufb01nal states. In the case of B \u2192K\u2113+\u2113\u2212there\nare four \ufb01nal states, with K+ or K0\nS and \u00b5+\u00b5\u2212or e+e\u2212.\nIn the case of B \u2192K\u2217\u2113+\u2113\u2212there are eight \ufb01nal states\nwith K\u2217+ \u2192K0\nS\u03c0+ or K+\u03c00, K\u22170 \u2192K+\u03c0\u2212or K0\nS\u03c00 and\n\u00b5+\u00b5\u2212or e+e\u2212. At the hadron colliders the modes with\n\u03c00 or electrons have not been used thus far. The com-\nbined branching fractions assume CP and isospin sym-\nmetries, and lepton universality, all of which are satis-\n\ufb01ed to good accuracy in the SM, to sum over K\u2217de-\ncay modes and average over lepton \ufb02avor and B charge.\nRegarding lepton \ufb02avor, the BABAR measurements (Lees,\n2012i) are for q2 \u22650.1 GeV2/c2, where the e+e\u2212and\n\u00b5+\u00b5\u2212branching fractions are expected to be very close.\nBelle (Wei, 2009), on the other hand, measures in e\ufb00ect\nTable 17.9.10. Measurements of exclusive b \u2192s\u2113+\u2113\u2212branch-\ning fractions in 10\u22128, integrated over all di-lepton q2 (including\nthe vetoed regions \u2014 see text). BABAR and Belle results are\nbased on both e+e\u2212and \u00b5+\u00b5\u2212modes, while CDF and LHCb\nresults are based on \u00b5+\u00b5\u2212modes only. In their papers, BABAR\ndoes not quote separate results for B+ and B0 decays, while\nCDF and LHCb do not quote combined results. LHCb does\nnot report the total branching fraction for B0 \u2192K\u22170\u00b5+\u00b5\u2212, al-\nthough precise dB/dq2 results are given in (Aaij et al., 2012b).\nUncertainties are statistical and systematic, respectively; these\nerrors are combined in some of the LHCb results.\nModel\nBABAR\nBelle\nCDF\nLHCb\nK+\u2113+\u2113\u2212\n53 +6\n\u22125 \u00b1 3\n46 \u00b1 4 \u00b1 2\n43.6 \u00b1 1.5 \u00b1 1.8\nK0\u2113+\u2113\u2212\n34 +9\n\u22128 \u00b1 2\n32 \u00b1 10 \u00b1 2\n31 +7\n\u22126\nK\u2113+\u2113\u2212\n47 \u00b1 6 \u00b1 2\n48 +5\n\u22124 \u00b1 3\nK\u2217+\u2113+\u2113\u2212\n124 +23\n\u221221 \u00b1 13\n95 \u00b1 32 \u00b1 8\n116 \u00b1 19\nK\u22170\u2113+\u2113\u2212\n97 +13\n\u221211 \u00b1 7\n102 \u00b1 10 \u00b1 6\nK\u2217\u2113+\u2113\u2212\n102 +14\n\u221213 \u00b1 5\n107 +11\n\u221210 \u00b1 9\nto the minimum possible q2 values, hence including the\ne\ufb00ects of the virtual photon peak in the B \u2192K\u2217e+e\u2212\nmode. Then for B \u2192K\u2217\u2113+\u2113\u2212, Belle averages the lepton\n\ufb02avors using an SM-based constraint of 1.33 on the ratio\nof B(B \u2192K\u2217e+e\u2212) to B(B \u2192K\u2217\u00b5+\u00b5\u2212), and quotes the\nlatter value for its results.\nIt has been customary to divide the branching fraction\nresults into a set of six bins in q2, three below the J/\u03c8\nmass, two above the \u03c8\u2032 mass, and one in the gap between\nthe two charmonium veto regions. The distributions of\ndB/dq2 are in good agreement between experiments and\nwith the SM as shown in Figure 17.9.12 for BABAR, Belle\nand CDF.\nThe branching fractions integrated over all q2 from\nBABAR (Lees, 2012i), Belle (Wei, 2009), CDF (Aaltonen\net al., 2011c) and LHCb (Aaij et al., 2012a,i) are given\nin Table 17.9.10. For these integrals, the veto regions are\n\ufb01lled in by interpolation, using SM-based predictions of\nthe spectral shape vs. q2. Figure 17.9.13 compares the\nisospin-averaged total branching fractions for these three\nexperiments to two SM predictions. The results are con-\nsistent with the predicted branching fractions.\nLepton universality is tested by looking at the ratios:\nR\u2113(K(\u2217)) = B(B \u2192K(\u2217)e+e\u2212)\nB(B \u2192K(\u2217)\u00b5+\u00b5\u2212),\n(17.9.62)\nwhich should be equal to one if the region q2 < (2m\u00b5)2 is\nremoved, and about 30% greater than one for K\u2217\u2113+\u2113\u2212if\nthe low-q2 virtual photon region is included for e+e\u2212. De-\nviations from these predictions could be due to enhance-\nments from new physics, e.g. a SUSY Higgs. The results\nfrom Belle (Wei, 2009) with 657M BB, and BABAR (Au-\nbert, 2009j) with 384M BB are given in Table 17.9.11.\n(The Belle paper de\ufb01nes R\u2113with the \u00b5+\u00b5\u2212and e\u2212e\u2212\nswapped, as compared to Eq. (17.9.62), so reciprocals have\nbeen taken for presentation here.) The measured R\u2113are\nconsistent with SM expectations (1.00, except 1.33 for the\n\n389\n)\n4\n/c\n2\n/GeV\n-7\ndBF/ds (10\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nB\nBABAR, 471 M B\n-1\nCDF, 6.8 fb\nB\nBelle, 657 M B\n(a)\n)\n2\n/c\n2\ns (GeV\n0\n5\n10\n15\n20\n)\n4\n/c\n2\n/GeV\n-7\ndBF/ds (10\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n(b)\nFigure 17.9.12. From (Lees, 2012i). Branching fractions\ndB/dq2 for (a) B \u2192K\u2113+\u2113\u2212and (b) B \u2192K\u2217\u2113+\u2113\u2212from Belle,\nCDF and BABAR vs. s \u2261q2. The yellow bands correspond to\nthe J/\u03c8 and \u03c8\u2032 veto windows used by BABAR. The magenta\ncurves show the range of the SM predictions from (Ali, Lunghi,\nGreub, and Hiller, 2002).\n0\n0.5\n1\n1.5\n2\n2.5\nBranching Fraction\n-l\n+\nKl\n-l\n+l\n*\nK\nB\nBABAR, 471 M B\n-1\nCDF, 6.8 fb\nB\nBelle, 657 M B\nAli \u201902\nZhong \u201902\n-6\n 10\n\u00d7\nFigure 17.9.13. From (Lees, 2012i). Total branching fractions\ndB/dq2 for B \u2192K\u2113+\u2113\u2212and B \u2192K\u2217\u2113+\u2113\u2212from BABAR, CDF\nand Belle, compared to SM predictions from the models of (Ali,\nLunghi, Greub, and Hiller, 2002) and (Zhong, Wu, and Wang,\n2003).\nBelle measurement of R\u2113(K\u2217)), but with quite large un-\ncertainties.\nDirect CP asymmetries, de\ufb01ned as per Eq. (17.9.40),\nhave also been searched for, with results given in Ta-\nble 17.9.11. They are consistent with zero.\nThe\nresults\nfor\nthe\nisospin\nasymmetries\ndrew\nmore attention. Isospin asymmetry AI (called \u22060\u2212in\nEq. (17.9.38), which de\ufb01nes its sign) is evaluated as per\nSection 17.9.5.2. The isospin asymmetry in the mode B \u2192\nK\u2217\u2113+\u2113\u2212is a subleading \u039bQCD/mb e\ufb00ect as in the radiative\nmode, but again the dominant isospin-breaking e\ufb00ects can\nbe calculated perturbatively, while other \u039bQCD/mb correc-\ntions are just estimated. The exact uncertainty is di\ufb03cult\nto estimate due to unknown power corrections, but the ob-\nservable may still be useful in the NP search because of the\nTable 17.9.11. Summary of measurements of lepton univer-\nsality R\u2113, direct CP asymmetries ACP , and isospin asymmetries\nAI in B \u2192K(\u2217)\u2113+\u2113\u2212decays. For AI, \u201clow q2\u201d means below\nm2\nJ/\u03c8 . Uncertainties are statistical and systematic, respectively,\nfor the separate measurements, combined for the weighted av-\nerages. Because the Belle measurements of R\u2113extend to lower\nq2 than do the BABAR measurement, the two R\u2113(K\u2217) values\nhave di\ufb00erent SM expectations, (see text); hence no average is\nquoted for that quantity.\nBABAR\nBelle\nAverage\nR\u2113(K)\n1.00 +0.31\n\u22120.25 \u00b1 0.07\n0.97 \u00b1 0.18 \u00b1 0.06\n0.98 \u00b1 0.16\nR\u2113(K\u2217)\n1.13 +0.34\n\u22120.26 \u00b1 0.10\n1.20 \u00b1 0.25 \u00b1 0.12\nACP (K)\n\u22120.03 \u00b1 0.14 \u00b1 0.01 +0.04 \u00b1 0.10 \u00b1 0.02 +0.02 \u00b1 0.08\nACP (K\u2217)\n+0.03 \u00b1 0.13 \u00b1 0.01 \u22120.10 \u00b1 0.10 \u00b1 0.01 \u22120.05 \u00b1 0.08\nAlow q2\nI\n(K)\n\u22120.58 +0.29\n\u22120.37 \u00b1 0.02\n\u22120.31 +0.17\n\u22120.14 \u00b1 0.08\n\u22120.37 \u00b1 0.15\nAlow q2\nI\n(K\u2217)\n\u22120.25 +0.20\n\u22120.17 \u00b1 0.03\n\u22120.29 \u00b1 0.16 \u00b1 0.09 \u22120.27 \u00b1 0.13\nhigh sensitivity to speci\ufb01c Wilson coe\ufb03cients (Feldmann\nand Matias, 2003). These authors predict only a rather\nsmall isospin asymmetry in the SM, with a positive sign\nat low q2.\nIn (Aubert, 2009j) BABAR reported evidence for a large\nnegative isospin asymmetry in the q2 range below the\nJ/\u03c8, with about 3\u03c3 signi\ufb01cance in both B \u2192K\u2113+\u2113\u2212and\nB \u2192K\u2217\u2113+\u2113\u2212. However, the latest BABAR results (Lees,\n2012i) are more consistent with null asymmetry, as listed\nin Table 17.9.11. Belle\u2019s results (Wei, 2009) with higher\nstatistics are compatible with BABAR and also with null\nasymmetry. Note that the average AI values are still nega-\ntive, and about 2\u03c3 from zero, so higher-precision measure-\nments are desirable. Neither experiment sees a signi\ufb01cant\nasymmetry in the high-q2 region. See the cited papers for\nmeasured isospin asymmetries in all q2 bins. These are\nillustrated for Belle in Fig. 17.9.14.\n17.9.7.3 Angular distributions in B \u2192K\u2217\u2113+\u2113\u2212: formalism\nand theory\nIn the B \u2192K\u2217\u2113+\u2113\u2212decay mode the angular distribu-\ntion contains useful information about the di\ufb00erent am-\nplitudes. This is in contrast to B \u2192K\u2113+\u2113\u2212or B \u2192K\u2217\u03b3,\nwhere the angular distributions are fully constrained by\nangular momentum conservation. The decay B \u2192K\u2217\u2113+\u2113\u2212\n(K\u2217\u2192K\u03c0) is completely described by four indepen-\ndent kinematic variables:90 the lepton-pair invariant mass\nsquared, q2, the angle \u03b8K of the K+ relative to the B in\nthe K\u2217rest frame, the angle \u03b8\u2113of the \u2113+ relative to the\nB in the di-lepton rest frame, and the angle \u03c6 between\nthe K\u2217decay plane and the di-lepton plane. Summing\nover the spins of the \ufb01nal particles, the di\ufb00erential decay\ndistribution can be written as (Kruger and Matias, 2005;\nKruger, Sehgal, Sinha, and Sinha, 2000)\nd4\u0393\ndq2 d\u03b8\u2113d\u03b8K d\u03c6 =\n9\n32\u03c0 I(q2, \u03b8\u2113, \u03b8K, \u03c6) .\n(17.9.63)\n90 This discussion assumes a P-wave K\u2217\ufb01nal state with no\nS-wave K\u03c0 background.\n\n390\nA full expression for I contains twelve angular coe\ufb03cients,\nI(s,c)\n1\u22129 , which are functions of q2, and may be di\ufb00erent for\nB and B decays91 (Altmannshofer et al., 2009):\nI(q2, \u03b8\u2113, \u03b8K, \u03c6) = Is\n1 sin2 \u03b8K + Ic\n1 cos2 \u03b8K\n+ (Is\n2 sin2 \u03b8K + Ic\n2 cos2 \u03b8K) cos 2\u03b8\u2113\n+ I3 sin2 \u03b8K sin2 \u03b8\u2113cos 2\u03c6\n+ I4 sin 2\u03b8K sin 2\u03b8\u2113cos \u03c6\n+ I5 sin 2\u03b8K sin \u03b8\u2113cos \u03c6\n+ (Is\n6 sin2 \u03b8K + Ic\n6 cos2 \u03b8K) cos \u03b8\u2113\n+ I7 sin 2\u03b8K sin \u03b8\u2113sin \u03c6\n+ I8 sin 2\u03b8K sin 2\u03b8\u2113sin \u03c6\n+ I9 sin2 \u03b8K sin2 \u03b8\u2113sin 2\u03c6.\n(17.9.64)\nThe coe\ufb03cients I(s,c)\n1\u22129\ncan be expressed in terms of ei-\nther helicity amplitudes H0,+,\u2212, or transversity ampli-\ntudes A\u22a5,||,0. These amplitudes contain left and right-\nhanded contributions which can be written in terms of\nthe Wilson coe\ufb03cients C7,9,10 and form-factors. The co-\ne\ufb03cients I(s,c)\n1\u22123 are sensitive to amplitudes squared, while\nI(s,c)\n4\u22129 are sensitive to interference terms.\nIn practice a full angular analysis has not yet been\ndone, because it requires a few thousand B \u2192K\u2217\u2113+\u2113\u2212sig-\nnal events. BABAR (Aubert, 2009c) and Belle (Wei, 2009)\nhave performed angular \ufb01ts, in bins of q2, to the \u03b8K and \u03b8\u2113\ndistributions, in each case after integrating over the other\ntwo angles. The \u03b8K distribution\n1\n\u0393\nd\u0393\nd cos \u03b8K\n= 3\n2FL cos2 \u03b8K + 3\n4(1 \u2212FL)(1 \u2212cos2 \u03b8K)\n(17.9.65)\nis sensitive to the fraction of longitudinal polarization,\nFL = |A0|2. In the SM this varies as a function of q2,\ngoing to zero as q2 \u21920, increasing to a maximum of 0.8\nat q2 \u22483 GeV2/c2, and falling gradually towards higher\nq2.\nThe \u03b8\u2113distribution\n1\n\u0393\nd\u0393\nd cos \u03b8\u2113\n= 3\n4FL(1 \u2212cos2 \u03b8\u2113) + 3\n8(1 \u2212FL)(1 + cos2 \u03b8\u2113)\n+ AFB cos \u03b8\u2113\n(17.9.66)\nis sensitive to the forward-backward asymmetry:\nAFB =\nR\nd\u03b8\u2113sgn(\u03b8\u2113)B(B \u2192K\u2217\u2113+\u2113\u2212; \u03b8\u2113)\nR\nd\u03b8\u2113B(B \u2192K\u2217\u2113+\u2113\u2212; \u03b8\u2113)\n.\n(17.9.67)\nIn the SM, AFB is a strong function of q2. It goes to zero\nas q2 \u21920, is small and negative at low q2, with a zero-\ncrossing point at q2\n0 \u22484 GeV2/c2, then it gradually in-\ncreases to about 0.4 at high q2, where the electroweak\nV \u2212A contributions dominate; e.g., (Ali, Ball, Handoko,\nand Hiller, 2000).\nAngular \ufb01ts to the projected distributions of \u03b8K and \u03b8\u2113\nare used to measure the observables FL and AFB in bins of\n91 Note that I5,6,8,9 change sign between B and B.\nq2. The hadronic uncertainties on these two observables in\nthe SM are large. However, the value of the di-lepton in-\nvariant mass q2\n0, for which the forward-backward asymme-\ntry vanishes, can be predicted in quite a clean way. In the\nQCD factorization approach at leading order in \u039bQCD/mb,\nthe value of q2\n0 is free from hadronic uncertainties at order\n\u03b10\nS. A dependence on the soft form factor and on the light\ncone wave functions of the B and K\u2217mesons appears only\nat order \u03b11\nS. At NLO one \ufb01nds (Beneke, Feldmann, and\nSeidel, 2005):\nq2\n0[K\u22170\u2113+\u2113\u2212] = (4.36 +0.33\n\u22120.31) GeV2/c2,\nq2\n0[K\u2217+\u2113+\u2113\u2212] = (4.15 +0.27\n\u22120.27) GeV2/c2.\n(17.9.68)\nFor all observables from the angular analysis the unknown\n\u039bQCD/mb power corrections are the source of the largest\ntheoretical uncertainty. The small di\ufb00erence between the\ntwo modes is due to isospin-breaking power corrections.\nThe value of q2\n0 is highly sensitive to the ratio of the\ntwo Wilson coe\ufb03cients C7 and C9, and the region near this\nSM-predicted zero-crossing point is particularly sensitive\nto the interplay between the terms proportional to C7 and\nto C9. Using the magnitude of C7 constrained from B \u2192\nXs\u03b3, this angular distribution can be used to determine\nthe sign of C7, and to constrain the two other Wilson\ncoe\ufb03cients C9 and C10. If the sign of C7 is \ufb02ipped, there\nis no zero-crossing point at q2\n0 (Ali, Giudice, and Mannel,\n1995).\nThe position of q2\n0 can also be moved by new physics\ncontributions (Altmannshofer et al., 2009). Detailed NP\nanalyses of the angular observables have been presented\nin Bobeth, Hiller, and Piranishvili (2008), Altmannshofer\net al. (2009), and Egede, Hurth, Matias, Ramon, and Reece\n(2008, 2010). They provide sensitivity to various Wilson\ncoe\ufb03cients, but the sensitivity to new weak phases turns\nout to be restricted (Egede, Hurth, Matias, Ramon, and\nReece, 2010).\n17.9.7.4 B \u2192K\u2217\u2113+\u2113\u2212angular analysis\nBABAR (Aubert, 2009c) and Belle (Wei, 2009) have ex-\ntracted FL and AFB values for B \u2192K\u2217\u2113+\u2113\u2212by \ufb01rst\n\ufb01tting their measured \u03b8K distributions in bins of q2 to\nEq. (17.9.65), and then \ufb01tting each corresponding \u03b8\u2113dis-\ntribution to Eq. (17.9.66) with FL \ufb01xed from the result\nof the \u03b8K \ufb01t. Belle measures AFB in six bins in q2 using\na data set of 657M BB, while BABAR measures AFB in\ntwo bins in q2, below and above the J/\u03c8 (with the \u03c8(2S)\nwindow excluded in the higher mass region), using a data\nset of 384M BB.\nThe results for FL are listed in Table 17.9.12 along with\nmore recent results from CDF (Aaltonen et al., 2011b) and\nLHCb (Aaij et al., 2012b), with results in good agreement\nwith the SM. Figure 17.9.14 shows the Belle results.\nThe Belle and BABAR results for AFB are listed in Ta-\nble 17.9.13, along with the recent results from CDF and\nLHCb. Figure 17.9.14 illustrates the Belle results. Given\nthe current level of precision, all results are compatible\nwith the SM predictions.\n\n391\nTable 17.9.12. Measurements of longitudinal polarization fraction FL in B \u2192K\u2217\u2113+\u2113\u2212as a function of di-lepton q2. (BABAR\nmeasures this in only two q2 bins, the other experiments in six bins). Errors are statistical and systematic, respectively.\nq2 (GeV2/c2)\nBelle\nBABAR\nCDF\nLHCb\n0.00 \u22122.00\n0.29 \u00b1 0.20 \u00b1 0.02\n0.30 \u00b1 0.16 \u00b1 0.02\n0.00 +0.13\n\u22120.00 \u00b1 0.02\n2.00 \u22124.30\n0.71 \u00b1 0.24 \u00b1 0.05\n(0.35 \u00b1 0.16 \u00b1 0.04)\n0.37 +0.25\n\u22120.24 \u00b1 0.10\n0.77 \u00b1 0.15 \u00b1 0.03\n4.30 \u22128.68\n0.64 \u00b1 0.24 \u00b1 0.07\n0.68 +0.15\n\u22120.17 \u00b1 0.09\n0.60 +0.06\n\u22120.07 \u00b1 0.01\n10.09 \u221212.86\n0.17 \u00b1 0.16 \u00b1 0.03\n0.47 \u00b1 0.14 \u00b1 0.03\n0.41 \u00b1 0.11 \u00b1 0.03\n14.18 \u221216.00\n\u22120.15 \u00b1 0.25 \u00b1 0.07\n(0.71 \u00b1 0.21 \u00b1 0.04)\n0.29 +0.14\n\u22120.13 \u00b1 0.05\n0.37 \u00b1 0.09 \u00b1 0.05\n16.00 \u221219.30\n0.12 \u00b1 0.14 \u00b1 0.02\n0.20 +0.19\n\u22120.17 \u00b1 0.05\n0.26 +0.10\n\u22120.08 \u00b1 0.03\nTable 17.9.13. Measurements of di-lepton forward-backward asymmetry AFB in B \u2192K\u2217\u2113+\u2113\u2212as a function of di-lepton q2.\n(BABAR measures this in only two q2 bins, the other experiments in six bins). Errors are statistical and systematic, respectively.\nq2 (GeV2/c2)\nBelle\nBABAR\nCDF\nLHCb\n0.00 \u22122.00\n+0.47 +0.26\n\u22120.32 \u00b1 0.03\n\u22120.35 +0.26\n\u22120.23 \u00b1 0.10\n\u22120.15 \u00b1 0.20 \u00b1 0.06\n2.00 \u22124.30\n+0.11 +0.31\n\u22120.36 \u00b1 0, 07\n(+0.24 +0.18\n\u22120.23 \u00b1 0.05)\n+0.29 +0.32\n\u22120.35 \u00b1 0.15\n+0.05 +0.16\n\u22120.20 \u00b1 0.04\n4.30 \u22128.68\n+0.45 +0.15\n\u22120.21 \u00b1 0.15\n+0.01 \u00b1 0.20 \u00b1 0.09\n+0.27 +0.06\n\u22120.08 \u00b1 0.02\n10.09 \u221212.86\n+0.43 \u00b1 0.19 \u00b1 0.03\n+0.38 +0.16\n\u22120.19 \u00b1 0.09\n+0.27 +0.11\n\u22120.13 \u00b1 0.02\n14.18 \u221216.00\n+0.40 +0.16\n\u22120.22 \u00b1 0.10\n(+0.76 +0.52\n\u22120.32 \u00b1 0.07)\n+0.44 +0.18\n\u22120.21 \u00b1 0.10\n+0.47 +0.06\n\u22120.08 \u00b1 0.03\n16.00 \u221219.30\n+0.66 +0.11\n\u22120.16 \u00b1 0.04\n+0.65 +0.17\n\u22120.18 \u00b1 0.16\n+0.16 +0.11\n\u22120.13 \u00b1 0.06\n0\n0.5\n1\n0\n0.5\n1\nFL\nAFB\nq2(GeV2/c2)\nAI\n-1\n0\n1\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nFigure 17.9.14. From (Wei, 2009). Measurements of longitu-\ndinal polarization fraction FL, and di-lepton forward-backward\nasymmetry AFB for B \u2192K\u2217\u2113+\u2113\u2212from Belle. The solid (red)\ncurves show the SM predictions. The dotted (blue) curves show\nthe e\ufb00ect of reversing the sign of the Wilson coe\ufb03cient C7. The\nbottom plot shows the isospin asymmetries for B \u2192K\u2217\u2113+\u2113\u2212\n(\ufb01lled circles) and B \u2192K\u2113+\u2113\u2212(open circles).\nBelle (Ishikawa, 2006) earlier provided constraints on\nC9 and C10 using 386M BB events, from a \ufb01t to the \u03b8\u2113\ndistribution under the assumption that FL follows the SM\ndistribution.\n17.9.7.5 Theoretical predictions for inclusive B \u2192Xs\u2113+\u2113\u2212\nAn inclusive measurement of b \u2192s\u2113+\u2113\u2212is expected to\nhave reduced theoretical uncertainties in comparison with\nthe exclusive decays B \u2192K(\u2217)\u2113+\u2113\u2212. The situation is sim-\nilar to b \u2192s\u03b3, where understanding of exclusive decays is\nlimited by knowledge of hadronic form factors. In the case\nof b \u2192s\u2113+\u2113\u2212these reduced theoretical uncertainties ap-\nply not only to the inclusive branching fraction, but also\nto the angular information, e.g. the zero crossing point in\nthe di-lepton forward-backward asymmetry AFB.\nThe angular decomposition of the inclusive decay\nB \u2192Xs\u2113+\u2113\u2212provides three independent observables,\nHT , HA and HL, from which one can extract the short-\ndistance electroweak Wilson coe\ufb03cients that test for new\nphysics (Lee, Ligeti, Stewart, and Tackmann, 2007).\nd3\u0393\ndq2 dz = 3\n8\n\u0002\n(1+z2)HT (q2)+2(1\u2212z2)HL(q2)+2zHA(q2)\n\u0003\n.\n(17.9.69)\nHere, z = cos \u03b8\u2113, HA is equivalent to the forward-\nbackward asymmetry in the exclusive decays, and the di-\nlepton mass spectrum is given by HT + HL. The observ-\nables depend on the Wilson coe\ufb03cients C7, C9 and C10\nin the SM. The present measurements of B \u2192Xs\u2113+\u2113\u2212\nalready favor the SM sign of the coe\ufb03cient C7, which is\nundetermined by the B \u2192Xs\u03b3 mode (Gambino, Haisch,\nand Misiak, 2005).\nThe observables in inclusive B \u2192Xs\u2113+\u2113\u2212are dom-\ninated by perturbative contributions in a low-q2 region,\n1 < q2 < 6 GeV2/c2, and in the high-q2 region above\nthe cc resonances, q2 > 14.4 GeV2/c2. The present predic-\ntions are based on the perturbative calculations to NNLL\n\n392\nprecision in QCD and to NLL precision in QED (Sec-\ntion 17.9.1). The branching fraction in the low-q2 region\nis (Huber, Lunghi, Misiak, and Wyler, 2006):\nB(B \u2192Xs\u2113+\u2113\u2212)low =\n(\n(1.59 \u00b1 0.11) \u00d7 10\u22126\n(\u2113= \u00b5)\n(1.64 \u00b1 0.11) \u00d7 10\u22126\n(\u2113= e)\n(17.9.70)\nand in the high-q2 region (Huber, Hurth, and Lunghi,\n2008a):\nB(B \u2192Xs\u2113+\u2113\u2212)high =\n(\n2.40 \u00d7 10\u22127 \u00d7 (1+0.29\n\u22120.26)\n(\u2113= \u00b5)\n2.09 \u00d7 10\u22127 \u00d7 (1+0.32\n\u22120.30)\n(\u2113= e)\n(17.9.71)\nThe value of q2\n0 for which the inclusive forward-backward\nasymmetry vanishes,\n(q2\n0)[Xs\u2113+\u2113\u2212] =\n(\n(3.50 \u00b1 0.12) GeV2/c2\n(\u2113= \u00b5)\n(3.38 \u00b1 0.11) GeV2/c2\n(\u2113= e) ,\n(17.9.72)\nis one of the most precise predictions in \ufb02avor physics.\nIt determines the relative sign and magnitude of the co-\ne\ufb03cients C7 and C9 (Huber, Hurth, and Lunghi, 2008a).\nUnknown subleading non-perturbative corrections of or-\nder O(\u03b1S\u039bQCD/mb) are estimated to give an additional\nuncertainty of order 5%, which has to be added to all\nB \u2192Xs\u2113+\u2113\u2212observables. In all predictions it is assumed\nthat there is no cut on the hadronic mass region.\nAfter including the NLL QED matrix elements, the\nelectron and muon channels receive di\ufb00erent contribu-\ntions. This is due to the fact, that the leptons can emit\ncollinear photons, which generate large logarithms of the\nform ln(m2\nb/m2\n\u2113). This generates a di\ufb00erences between\nthese two channels. We note that in theoretical calcu-\nlations all collinear photons are assumed to be included\nin the Xs system. The di-lepton invariant mass does not\ncontain any additional photon, i.e. q2 = (p\u2113+ + p\u2113\u2212)2.\nThis di\ufb00ers from the experimental analyses which recover\nbremsstrahlung photons and add them to the di-lepton\nsystem, and therefore small modi\ufb01cations to the theo-\nretical predictions are needed \u2013 see (Huber, Hurth, and\nLunghi, 2008b).\n17.9.7.6 Measurements of inclusive B \u2192Xs\u2113+\u2113\u2212\nThe fully inclusive approach has not been used for b \u2192\ns\u2113+\u2113\u2212because the presence of large backgrounds from se-\nmileptonic B decays. In these background events the ini-\ntial BB produces two oppositely charged leptons either\ndirectly from the two B mesons, or as a cascade from\nthe b \u2192c \u2192s decay chain. These backgrounds cannot\nbe removed without further kinematic constraints. The\nreconstructed-B-tag approach (also not yet attempted)\nshould remove the direct two-B-decay background com-\nponent, leaving only the cascade decays, which can then\nbe removed using missing energy variables. The di\ufb03culty\nhere is the need for millions of B tags in order to mea-\nsure an inclusive branching fraction of a few \u00d710\u22126. This\nTable 17.9.14. Measurements of inclusive B \u2192Xs\u2113+\u2113\u2212\nbranching fractions (in 10\u22126), with m\u2113+\u2113\u2212> 0.2 GeV/c2, while\nthe excluded regions around the J/\u03c8 and \u03c8\u2032 are interpolated\nassuming the SM with no interference. Uncertainties are sta-\ntistical and systematic, respectively.\nMode\nBABAR\nBelle\nAverage\nXse+e\u2212\n6.0 \u00b1 1.7 \u00b1 1.3 4.0 \u00b1 1.3 \u00b1 0.9 4.7 \u00b1 1.3\nXs\u00b5+\u00b5\u22125.0 \u00b1 2.8 \u00b1 1.2 4.1 \u00b1 1.1 \u00b1 0.8 4.3 \u00b1 1.3\nXs\u2113+\u2113\u2212\n5.6 \u00b1 1.5 \u00b1 1.3 4.1 \u00b1 0.8 \u00b1 0.8 4.5 \u00b1 1.0\nis a challenging measurement even with the anticipated\nultimate dataset of a super \ufb02avor factory.\nThe sum-of-exclusive method does provide su\ufb03cient\nconstraints to discriminate against the semileptonic back-\ngrounds using the mES and \u2206E kinematic variables. In\na similar fashion to the B \u2192Xs\u03b3 analysis, the Xs state\nis reconstructed as one kaon and multiple pions (but in-\ncluding the zero pion case, which corresponds to B \u2192\nK\u2113+\u2113\u2212). Belle (Iwasaki, 2005) uses up to 4 pions of which\none can be a \u03c00, and includes the Xs mass range below\n2.0 GeV/c2, while BABAR (Aubert, 2004h) uses up to 2 pi-\nons of which one can be a \u03c00, and includes the Xs mass\nbelow 1.8 GeV/c2. After assuming that modes containing\na K0\nL have equal branching fractions to corresponding K0\nS\nmodes, both experiments account for \u223c70% of B decays\nin their measured Xs ranges. In order to reduce the se-\nmileptonic decay backgrounds, the analyses exploit the\nfact that energy is carried away by two or more neutri-\nnos. Belle uses the total visible energy and missing mass,\nwhile BABAR uses the missing energy in the rest of the\nevent (ROE) excluding the Xs\u2113+\u2113\u2212candidate, as well as\nthe mES of the ROE. If the two leptons originate from se-\nmileptonic background, they may have displaced vertices,\nwhich is used for further discrimination.\nAs with the exclusive B \u2192K(\u2217)\u2113+\u2113\u2212analysis, it is\nnecessary to remove the di-lepton mass ranges around the\nJ/\u03c8 and \u03c8\u2032. In both analyses e+e\u2212pairs with masses be-\nlow 0.2 GeV/c2 are removed. This makes the di-muon and\ndi-electron samples consistent, and removes the theoreti-\ncally less interesting region dominated by the virtual pho-\nton contribution.\nBelle measures 31.8 \u00b1 10.2 Xse+e\u2212and 36.3 \u00b1 9.3\nXs\u00b5+\u00b5\u2212signal events with a sample of 152M BB, while\nBABAR measures 29.2\u00b18.4 Xse+e\u2212and 11.2\u00b16.3 Xs\u00b5+\u00b5\u2212\nevents with the smaller sample of 89M BB. There are ex-\nperimental systematic uncertainties associated with the\nbackground subtraction and the reconstruction e\ufb03ciency,\nwhich total about 10%. However the dominant system-\natic uncertainties come from the modeling of the Xs sys-\ntem (as they did in B \u2192Xs\u03b3). The fractions of exclusive\nB \u2192K\u2113+\u2113\u2212and B \u2192K\u2217\u2113+\u2113\u2212are varied, as well as the\nmissing fractions of \ufb01nal states in the mass range above\n1.1 GeV/c2. Finally there is an extrapolation to the full\nXs mass range, which uses a spectral shape of a Fermi-\nmotion model (Ali, Hiller, Handoko, and Morozumi, 1997)\nwith parameters determined from analyses of inclusive\nB \u2192Xs\u03b3 and B \u2192Xc\u2113\u03bd. The q2 distribution is mod-\n\n393\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n10\n-7\n10\n-6\nq2 (GeV/c)2\nMxs (GeV/c2)\n(b)\n(a)\ndB/dMxs(10-5(GeV/c2)-1)\ndB/dq2((GeV/c)-2)\n5\n10\n15\n25\n20\nFigure 17.9.15. From (Iwasaki, 2005). Belle\u2019s results on the\ndi\ufb00erential branching fractions for B \u2192Xs\u2113+\u2113\u2212as functions\nof (a) MXs and (b) q2. All branching fractions have been inter-\npolated through the vetoed J/\u03c8 and \u03c8(2S) regions. The MXs\nresults correspond to all q2 > 0.04 GeV2/c2, while the q2 results\nfollow an extrapolation to all values of MXs. Inner (outer) er-\nror bars are statistical (total) errors. Histograms represent the\nSM-based predictions described in the text.\neled based on (Ali, Hiller, Handoko, and Morozumi, 1997;\nAli, Lunghi, Greub, and Hiller, 2002; Kruger and Sehgal,\n1996) in which the J/\u03c8 and \u03c8(2S) regions are interpo-\nlated as if these contributions do not exist. The model-\ndependent e\ufb00ects give a total systematic error of 20%, still\nslightly smaller than the statistical error. The resulting in-\nclusive branching fractions are given in Table 17.9.14. In\nFigure 17.9.15 Belle\u2019s results on the di\ufb00erential branch-\ning fractions for B \u2192Xs\u2113+\u2113\u2212as functions of MXs and\nq2 are shown. With more events the measurements could\nbe broken into bins of di-lepton mass squared, and the\nforward-backward asymmetry AFB could be studied.\nThe results for the inclusive b \u2192s\u2113+\u2113\u2212branching frac-\ntion are consistent with the SM prediction (e.g., B(B \u2192\nXs\u00b5+\u00b5\u2212) = (4.20 \u00b1 0.70) \u00d7 10\u22126 assuming interpolation\nover the veto region (Ali, Lunghi, Greub, and Hiller, 2002)).92\nThey can be interpreted as giving a preference to a neg-\native sign for Wilson coe\ufb03cient C7, where the inclusive\nb \u2192s\u03b3 branching fraction only determines the magnitude\nof C7 and not the sign.\nBelle has reported an unpublished preliminary result\nwith 657M BB, with several improvements in the anal-\nysis (Iijima, 2010). The largest improvement is that the\nXs mass range is divided into the K, K\u2217and high mass\nrange, and the high mass range alone has been measured\nwith 3\u03c3 signi\ufb01cance. In addition, several new background\nsources have been identi\ufb01ed. They include a semileptonic\nB decay background that peaks in the mES distribution\ndue to one additional misidenti\ufb01ed lepton that compen-\nsates the missing neutrino, and contributions from higher\ncc resonances that were disregarded in the previous anal-\nyses. Although the preliminary results have been used in\nthe HFAG averages and also in some literature, we do not\ninclude them in Table 17.9.14.\nIn addition, BABAR has submitted for publication an\nupdated measurement of B \u2192Xs\u2113+\u2113\u2212based on 471M\nBB events (Lees, 2014). Along with the results in the\n92 The more recent theory publications used for Eqs 17.9.70\nand 17.9.71 do not quote values for the full q2 range.\nusual q2 bins, results are provided for the 1 < q2 <\n6 GeV2/c2 range suitable for comparison to the most pre-\ncise SM prediction.\n17.9.7.7 B \u2192\u03c0\u2113+\u2113\u2212\nThe B \u2192\u03c0\u2113+\u2113\u2212decay mode has been the \ufb01rst exclu-\nsive decay mode utilized in the search for the b \u2192d\u2113+\u2113\u2212\ntransition. The analysis for B \u2192\u03c0\u2113+\u2113\u2212is almost iden-\ntical to that for B \u2192K\u2113+\u2113\u2212(Section 17.9.7.1). Tight\ncharged-pion identi\ufb01cation, similar to that used for the\nmeasurement of B \u2192\u03c1\u03b3 (Section 17.9.4.1), is applied to\nthe pion in B+ \u2192\u03c0+\u2113+\u2113\u2212. It is necessary to account for\nmisidenti\ufb01ed B+ \u2192K+\u2113+\u2113\u2212events, which give a peaking\nbackground in mES, but are shifted to lower \u2206E. Both B\nFactories also include B0 \u2192\u03c00\u2113+\u2113\u2212in their searches.\nBABAR (Aubert, 2007ax) has analyzed 230M BB and\n\ufb01nds one candidate in the (mES, \u2206E) signal region in each\nof \u03c0+e+e\u2212, \u03c0+\u00b5+\u00b5\u2212and \u03c00e+e\u2212. This is consistent with\nthe expectations from background. De\ufb01ning the isospin-\nconstrained branching fraction\nB(B \u2192\u03c0\u2113+\u2113\u2212) \u2261B(B+ \u2192\u03c0+\u2113+\u2113\u2212)\n(17.9.73)\n= 2\u03c4B+\n\u03c4B0 B(B0 \u2192\u03c00\u2113+\u2113\u2212) ,\nthey set an upper limit of:\nB(B \u2192\u03c0\u2113+\u2113\u2212) < 9.1 \u00d7 10\u22128 .\n(17.9.74)\nBelle (Wei, 2008a) has analyzed 657M BB and also \ufb01nds\na few candidate events. A \ufb01t gives a small excess with a\nsigni\ufb01cance of 1.2\u03c3. They set an upper limit of:\nB(B \u2192\u03c0\u2113+\u2113\u2212) < 6.2 \u00d7 10\u22128 .\n(17.9.75)\nThe SM prediction of 2\u00d710\u22128 is not far below these limits,\nand the backgrounds are quite manageable, and in fact the\n\ufb01rst observation for the charged mode B+ \u2192\u03c0+\u00b5+\u00b5\u2212has\nbeen recently reported by LHCb (Aaij et al., 2012e) with\na branching fraction consistent with the SM.\n17.9.8 Electroweak penguin decays b \u2192s(d)\u03bd\u03bd\nThe b \u2192s\u03bd\u03bd decays are described by an electroweak pen-\nguin diagram including a Z0 boson or a W +W \u2212box di-\nagram, with Wilson coe\ufb03cients for the vector and axial-\nvector parts C9 and C10. Unlike b \u2192s\u2113+\u2113\u2212, there is no\ncontribution from a virtual photon penguin diagram (C7).\nThere is also no contribution from cc resonances. Measur-\ning the branching fractions of these decays provides a pow-\nerful test of new physics complementary to other rare B\ndecays (Altmannshofer, Buras, Straub, and Wick, 2009).\nThe experimental challenge is to identify a B decay to\nan Xs system and two missing neutrinos. This is similar\nto B\u2212\u2192\u03c4 \u2212\u03bd decays, which have been \ufb01rst observed at\nthe B Factories. All that has to be done is to replace the\nobservable \u03c4 decay products (\u03c0, \u03c1, e, \u00b5), with a K or\nK\u2217meson. However, the SM predictions for B \u2192K\u03bd\u03bd or\n\n394\nBDT Output\n0.96 0.965 0.97 0.975 0.98 0.985 0.99 0.995\n1\nAverage Number of Events\n0\n2\n4\n6\n8\n10\n12\nData\nBackground MC\nSignal MC\nFigure 17.9.16. From (del Amo Sanchez, 2010p). Boosted\nDecision Tree output from the BABAR search for B+ \u2192K+\u03bd\u03bd,\nalong with expected SM-signal and background contributions.\nErrors on the data are statistical, while those on the expected\nnumbers include systematics.\nB \u2192K\u2217\u03bd\u03bd branching fractions are rather small, 4 \u00d7 10\u22126\nand 13\u00d710\u22126, respectively. This makes suppression of the\nbackground from semileptonic B decays more di\ufb03cult.\nThe recoil-B method is used, in which either fully-\nreconstructed hadronic B decays, or semileptonic B \u2192\nD(\u2217)\u2113\u03bd decays, are used as the tag (Section 7.4). The re-\nmaining charged tracks and neutral clusters then have to\nbe consistent with the Xs system being searched for. The\nmost powerful variables for suppressing background are\nassociated with the missing energy carried by the neutri-\nnos, and the lack of extra energy in the detector. Informa-\ntion on the momentum, charge and \ufb02avor of the recoil tag\ncan be correlated with the Xs system to further reduce\nthe backgrounds.\nBelle (Chen, 2007b) uses hadronic B tags to search for\nB \u2192h(\u2217)\u03bd\u03bd where h(\u2217) includes charged and neutral K,\nK\u2217, \u03c0, \u03c1 and \u03c6. They reconstruct 788k charged B and\n491k neutral B decays from a sample of 535M BB events,\nwith an overall tag e\ufb03ciency of 2.5 \u00d7 10\u22123. They observe\nbetween 1 and 30 candidate events in the di\ufb00erent h(\u2217)\n\ufb01nal states. These yields are consistent with the expecta-\ntions from backgrounds, so they set upper limits at 90%\nC.L. between 4.4\u00d710\u22124 for \u03c10\u03bd\u03bd and 1.4\u00d710\u22125 for K+\u03bd\u03bd.\nThe best limit on K\u03bd\u03bd comes from BABAR (del\nAmo Sanchez, 2010p), also using the hadronic B tag\nmethod. This analysis uses bagged decision trees with\n26 (38) inputs to separate signal and background in\nthe K+ (K0) modes as illustrated in Figure 17.9.16.\nThe K+ search is separated into high and low-q2 re-\ngions, corresponding to low and high kaon momenta. The\nbackgrounds are very large at high-q2, so the sensitiv-\nity mainly comes from the low-q2 region. This introduces\nsome model-dependence into the extraction of the upper\nlimit. The quoted upper limits at 90% C.L. are 5.6\u00d710\u22125\nfor K0\u03bd\u03bd and 1.3 \u00d7 10\u22125 for K+\u03bd\u03bd. BABAR also reports a\nsearch using semileptonic B tags (Aubert, 2009aq).\nThe BABAR search for K\u2217\u03bd\u03bd uses a combination of\nhadronic and semileptonic tags (Aubert, 2008an). The ef-\n\ufb01ciency is slightly lower with hadronic tags, but the back-\nground with the semileptonic tags is signi\ufb01cantly higher.\nA \ufb01t to the distribution of extra energy in the events leads\nto comparable upper limits from the two types of tags, and\nyields combined upper limits at 90% C.L. of 12\u00d710\u22125 for\nK\u22170\u03bd\u03bd and 8 \u00d7 10\u22125 for K\u2217+\u03bd\u03bd. These limits are lower\nthan those reported by Belle (Chen, 2007b).\nThe experimental limits are already about 3 and 6\ntimes the SM predictions for K\u03bd\u03bd and K\u2217\u03bd\u03bd, respectively,\nbut the backgrounds are severe. Initial studies of what\ncould be done at a super \ufb02avor factory suggest that a\ndata sample of about 50 ab\u22121 will be needed to observe\neither of these decays.\n\n395\n17.10 B+ \u2192\u2113+\u03bd(\u03b3) and B \u2192D(\u2217)\u03c4\u03bd\nEditors:\nSteven Robertson (BABAR)\nToru Iijima (Belle)\nAdditional section writers:\nDana Lindemann\n17.10.1 Overview\nIn this section, we review the measurements of purely lep-\ntonic decays, B+ \u2192\u2113+\u03bd (\u2113= e, \u00b5, \u03c4), and the semileptonic\nB decays B \u2192D(\u2217)\u03c4\u03bd. As b \u2192u and b \u2192c quark tran-\nsitions, these processes depend on the magnitudes of the\nCKM matrix elements Vub and Vcb, respectively, however\nboth have potential sensitivity to physics beyond the SM.\nIn extensions of the SM which include an expanded Higgs\nsector, in particular the type-II two Higgs doublet model\n(2HDM) such as in the minimal supersymmetric exten-\nsion of the Standard Model (MSSM), these processes are\npotentially sensitive to a charged Higgs boson (H\u00b1). A\nnumber of benchmark new physics models, such as 2HDM\nand MSSM, are discussed in Section 25.2. The presence of\nthe H\u00b1 can impact the experimentally observed branch-\ning fractions for these decay modes and, in the case of\nB \u2192D(\u2217)\u03c4\u03bd, also the kinematic distributions of \ufb01nal\nstate particles. Figure 17.10.1 shows Feynman diagrams\nfor these tree level processes.\nH +\nu\nW +\nb\n+\n \nB\n+\nH +\nb\nu\nW +\n+\nB\n+\nu\nc D\n \n\u03c4\n(\u2217)\n\u03c4\nFigure 17.10.1. Feynman diagrams of B+ \u2192\u2113+\u03bd\u2113(top) and\nB+ \u2192D(\u2217)\u03c4 +\u03bd\u03c4 (bottom).\nSince B+ \u2192\u2113+\u03bd proceeds via a quark annihilation\nprocess with no hadrons in the \ufb01nal state, all hadronic\ne\ufb00ects are encapsulated in the B decay constant fB,\n\u27e80|b(0)\u03b3\u00b5\u03b35q(0)|B(p)\u27e9= ip\u00b5fB ,\n(17.10.1)\nwhich can be interpreted as the wave function of the light\nquark at the location of the b quark. In contrast, in se-\nmileptonic B \u2192D(\u2217)\u03c4\u03bd decays the hadronic transition is\ndescribed by form factors, which are functions of the mo-\nmentum transfer squared, q2, resulting in larger theoret-\nical uncertainties in the decay kinematics and branching\nfractions.\nThe e\ufb00ective Hamiltonian describing B \u2192D(\u2217)\u03c4\u03bd and\nB \u2192\u03c4\u03bd transitions mediated by W \u00b1 or H\u00b1 can be writ-\nten as,\nHeff = GF\n\u221a\n2 Vqb{[q\u03b3\u00b5(1 \u2212\u03b35)b][\u03c4\u03b3\u00b5(1 \u2212\u03b35)\u03bd\u03c4]\n\u2212MbM\u03c4\nM 2\nB\nq[gS + gP \u03b35]b[\u03c4(1 \u2212\u03b35)\u03bd\u03c4]}\n+ h.c. ,\n(17.10.2)\nwhere GF is the Fermi coupling constant, Vqb is the CKM\nmatrix element and MB is the B meson mass. The \ufb01rst\nterm corresponds to the SM W \u00b1 couplings. The second\nterm, which can occur in beyond-SM models, represents\nscalar couplings to H\u00b1. Since these couplings are propor-\ntional to the fermion masses, which are relatively large for\nB mesons and tau leptons, it is natural to look for new\nphysics in leptonic or semileptonic B decays involving tau\nleptons.\nIn the MSSM, the couplings gS,P in Eq. (17.10.2) are\nwritten as\ngS = gP = M 2\nBtan2\u03b2\nM 2\nH\n1\n(1 + \u03f50tan\u03b2)(1 \u2212\u03f5\u03c4tan\u03b2) ,\n(17.10.3)\nwhere tan \u03b2 is the ratio of the two Higgs vacuum expecta-\ntion values and MH is the charged Higgs boson mass. The\nparameters \u03f50,\u03c4 arise from sparticle loop contributions and\ntheir values depend on other MSSM parameters. These are\ntypically expected to be of O(10\u22122). Since these contribu-\ntions to gS,P are relatively small for moderate values of\ntan \u03b2, and in the absence of other experimental evidence\nfor SUSY, studies of B \u2192\u03c4\u03bd and B \u2192D(\u2217)\u03c4\u03bd are usu-\nally interpreted in the context of the simpler extension of\nthe SM with only the addition of a second Higgs doublet\n(that is, with only the Type-II 2HDM and no other heavy\nnew physics contributions). In this case, \u03f50 = \u03f5\u03c4 = 0, and\nmeasurements of B \u2192(D(\u2217))\u03c4\u03bd provide information on\ntan \u03b2/MH.\nExperimentally, it is challenging to study these pro-\ncesses due to the presence of neutrinos in the \ufb01nal state.\nThe decays B+ \u2192\u03c4 +\u03bd and B \u2192D(\u2217)\u03c4\u03bd involve two\nor more neutrinos and hence cannot be fully constrained\nkinematically. Although the B+ \u2192e+\u03bd and B+ \u2192\u00b5+\u03bd\nmodes have only a single neutrino in the \ufb01nal state, they\nhave very small branching fractions compared with B+ \u2192\n\u03c4 +\u03bd, due to helicity suppression. However, the B+ \u2192\u03c4 +\u03bd\nbranching fraction is roughly two orders of magnitude\nsmaller than the semileptonic B \u2192D(\u2217)\u03c4\u03bd modes due to\nthe relative sizes of |Vub| and |Vcb|, and the contribution\nof fB.\nAt B Factories, one can fully reconstruct one of the\nB mesons produced in an \u03a5(4S) \u2192BB event, referred\nto as the \u201ctag B\u201d (Btag), and examine the properties of\nthe remaining particles in the event, which are collectively\n\n396\nreferred to as the \u201csignal B\u201d (Bsig), to look for evidence\nof a signal decay (see Chapter 7). This method strongly\nsuppresses the combinatorial background and provides a\nunique identi\ufb01cation of the decay daughters of the signal\nB decay. The disadvantage of this method is the low ef-\n\ufb01ciency of the Btag reconstruction, which is at the level\nof O(0.1)%. In spite of this, the high luminosity B Facto-\nries have provided a su\ufb03ciently large number of events to\nenable measurements of these decays for the \ufb01rst time.\nIn this section we describe the theoretical and exper-\nimental status of B+ \u2192\u2113+\u03bd and B \u2192D(\u2217)\u03c4\u03bd studies.\nA theoretical introduction to leptonic decays is presented\nin Section 17.10.2.1. The experimental status of B+ \u2192\n\u03c4 +\u03bd and B+ \u2192\u2113+\u03bd (with \u2113= e, \u00b5) is described in Sec-\ntions 17.10.2.2 and 17.10.2.3, respectively. Searches for ra-\ndiative leptonic decays are discussed in Section 17.10.2.4.\nB \u2192D(\u2217)\u03c4\u03bd are likewise presented in the remaining sec-\ntions, with a brief theory introduction in Section 17.10.3\nfollowed by a description of experimental measurements\nin Section 17.10.3.1 and interpretation of these results in\nSection 17.10.3.2. Some comments on the current status\nand future prospects for studies of these decays conclude\nthis section, while additional interpretation is provided\nin the context of global \ufb01ts to the Unitarity Triangle in\nChapter 25.\n17.10.2 B+ \u2192\u2113+\u03bd(\u03b3)\n17.10.2.1 Theory of leptonic decays\nIn the SM, the purely leptonic decay B+ \u2192\u2113+\u03bd proceeds\nvia the annihilation of b and u quarks to a W + boson (see\nFigure 17.10.1). The branching fraction is given by\nB(B+ \u2192\u2113+\u03bd)SM = G2\nF MBM 2\n\u2113\n8\u03c0\n\u0012\n1 \u2212M 2\n\u2113\nM 2\nB\n\u00132\n\u00d7 f 2\nB|Vub|2\u03c4B ,\n(17.10.4)\nwhere the M\u2113is is the mass of the lepton, and \u03c4B is the\nB meson lifetime. The B meson decay constant fB =\n0.191\u00b10.009 GeV is obtained from the most recent lattice\nQCD calculations (Na et al., 2012). The helicity suppres-\nsion of the leptonic decays can be seen in the lepton mass\ndependence in Eq. (17.10.4). The expected branching frac-\ntion for the \u03c4 mode is\nBSM(B+ \u2192\u03c4 +\u03bd) = (1.01 \u00b1 0.29) \u00d7 10\u22124 ,\n(17.10.5)\nusing |Vub| = (3.95 \u00b1 0.38exp \u00b1 0.39th) \u00d7 10\u22123, which is\nan average of |Vub| values determined using charmless se-\nmileptonic B decay data, see Eq. (17.1.70). Due to the\nrelatively small mass of the e and \u00b5 compared with the \u03c4,\nthese modes are suppressed by factors of 1.05 \u00d7 10\u22127 and\n4.49 \u00d7 10\u22123, respectively, relative to the \u03c4 mode.\nWithin the Type-II 2HDM, the addition of the charged\nHiggs boson in Eq. (17.10.2) and Eq. (17.10.3) modi\ufb01es\nthe B+ \u2192\u2113+\u03bd branching fraction (Hou, 1993),\nB(B+ \u2192\u2113+\u03bd)2HDM = B(B+ \u2192\u2113+\u03bd)SM \u00d7 rH , (17.10.6)\nwhere the ratio rH is given by\nrH = (1 \u2212M 2\nBtan2\u03b2/M 2\nH)2 .\n(17.10.7)\nThe interference between the SM W \u00b1 and H\u00b1 contri-\nbutions is destructive. Consequently, the charged Higgs\ncontribution suppresses the branching fraction relative to\nthe SM expectation, resulting in rH < 1, unless the H\u00b1 is\nsu\ufb03ciently large that it dominates the SM W \u00b1 contribu-\ntion. The case where M 2\nBtan2\u03b2/M 2\nH = 2 is indistinguish-\nable from the SM. It is notable that Eq. (17.10.7) applies\nequally to the other leptonic decay modes, B+ \u2192\u00b5+\u03bd and\nB+ \u2192e+\u03bd. As the H\u00b1 is expected to decrease the ob-\nserved branching fraction, much of the present constraint\non charged Higgs bosons results from the lower bound\non the experimental value of the B+ \u2192\u03c4 +\u03bd branching\nfractions rather than the upper bound on the branch-\ning fraction. A much weaker bound is currently obtained\nfrom B+ \u2192\u00b5+\u03bd decays because only upper limits on its\nbranching fraction have been reported.\nThe radiative decays B+ \u2192\u2113+\u03bd\u2113\u03b3 are also of inter-\nest since the presence of the radiated photon can remove\nthe helicity suppression of the purely leptonic modes, pos-\nsibly by coupling the spin-0 B meson to the spin-1 W \u00b1\nboson through an intermediate o\ufb00-shell state (Burdman,\nGoldman, and Wyler, 1995). Consequently, the predicted\nbranching fractions of B+ \u2192e+\u03bd\u2113\u03b3 and B+ \u2192\u00b5+\u03bd\u2113\u03b3 are\nconsiderably larger than the corresponding non-radiative\nmodes, in spite of an additional suppression by the fac-\ntor \u03b1EM. The branching fractions for B+ \u2192\u2113+\u03bd\u2113\u03b3 (with\n\u2113= e, \u00b5, \u03c4) are predicted to be of order 10\u22126 indepen-\ndent of the lepton type, making these modes potentially\naccessible at the B Factories. They potentially provide an\nadditional method to access |Vub|, and they are also a po-\ntential background to the non-radiative mode searches.\nThe decay rate for B+ \u2192\u2113+\u03bd\u2113\u03b3 is given by\ndB\ndE\u03b3\n= \u03b1EMG2\nF |Vub|2\n48\u03c02\nM 5\nB\u03c4B\n\u0002\nf 2\nA(E\u03b3) + f 2\nV (E\u03b3)\n\u0003\n(1 \u2212y)y3\n(17.10.8)\nwhere y = 2E\u03b3/MB. The axial-vector and vector B \u2192\n\u03b3X form factors, fA and fV , respectively, are assumed to\nbe equal in most models. The branching fraction can be\napproximated as (Korchemsky, Pirjol, and Yan, 2000)\nB(B+ \u2192\u2113+\u03bd\u2113\u03b3) \u2248\u03b1EMG2\nF |Vub|2\n288\u03c02\nf 2\nBM 5\nB\u03c4B\n\u0012Qu\n\u03bbB\n\u2212Qb\nMb\n\u00132\n,\n(17.10.9)\nwhere Qi is the quark charge, and \u03bbB is the \ufb01rst in-\nverse moment of the B-meson wave function. This last\nparameter plays an important role in QCD factorization\n(Descotes-Genon and Sachrajda, 2003; Lunghi, Pirjol, and\nWyler, 2003). It also enters into calculations of the B \u2192\u03c0X\nform factor at zero momentum transfer and the branching\nfractions of two-body hadronic B-meson decays such as\nB \u2192\u03c0\u03c0, a benchmark channel for measuring the CKM\nangle \u03c62 (Le Yaouanc, Oliver, and Raynal, 2008). How-\never, \u03bbB has a large theoretical uncertainty, so B+ \u2192\n\u2113+\u03bd\u2113\u03b3 is a useful decay for obtaining a clean measurement\nof \u03bbB.\n\n397\n17.10.2.2 B+ \u2192\u03c4 +\u03bd measurements\nMethodology common to Belle and BABAR\nAmong the leptonic B decays, B+ \u2192\u03c4 +\u03bd has the largest\nbranching fraction and, in spite of the di\ufb03culties associ-\nated with multiple neutrinos in the \ufb01nal state, was the \ufb01rst\nof these modes to be successfully measured at the B Facto-\nries. Both Belle and BABAR use a similar analysis method\nin which they fully reconstruct the accompanying B meson\n(Btag) using either hadronic or semileptonic decays, and\nexamine the rest of the event to search for a B+ \u2192\u03c4 +\u03bd\ndecay. In both experiments, analyses employing hadronic-\nand semileptonic-tag methods were performed and pub-\nlished as separate measurements. Since there is essentially\nno overlap between the tag samples, the analyses are sta-\ntistically independent B+ \u2192\u03c4 +\u03bd and the two results from\neach collaboration can be combined into a single branch-\ning fraction measurement.\nDetails of Btag reconstruction are described in Sec-\ntion 7. Analyses using semileptonic tags have higher e\ufb03-\nciency than the hadronic tag searches, but su\ufb00er from a\nlower signal-to-background ratio. This is a consequence of\nthe less stringent kinematic constraints associated with\nthe presence of the undetectable tag-B neutrino. As a\nresult, searches using the hadronic and semileptonic tag\nmethods employ somewhat di\ufb00erent optimizations.\nOnce a Btag has been reconstructed, using either the\nhadronic or semileptonic tag method, the selection of B+ \u2192\n\u03c4 +\u03bd candidates exploits the low multiplicity and missing\nenergy signatures of the signal mode. Since the \u03c4 + decays\ninto \ufb01nal states in which one or two neutrinos accompany\neither hadrons or a charged lepton, it is not possible to re-\nconstruct the two-body kinematics of B+ \u2192\u03c4 +\u03bd from the\n\ufb01nal state particles. Tau decays to leptons, \u03c4 + \u2192\u2113+\u03bd\u03bd\n(\u2113= e, \u00b5) comprise approximately 35% of the branch-\ning fraction, while decays to \u03c0+\u03bd, \u03c0+\u03c00\u03bd, \u03c0+\u03c00\u03c00\u03bd and\n\u03c0+\u03c0\u2212\u03c0+\u03bd contribute approximately 11%, 25%, 9% and\n10%, respectively. The \u03c0+\u03c00\u03bd and 3\u03c0\u03bd modes proceed\nprimarily through the \u03c1(770) and a1(1260) resonances,\nhence mass constraints can be imposed on the pions to\nprovide background rejection. However, these states are\nbroad and so the suppression is modest. Since modes de-\ncaying to kaons (charged or neutral) make up only \u223c1%\nof \u03c4 decays, a kaon veto is usually applied to suppress\nlarge BB backgrounds involving charm mesons. The lep-\ntonic modes have a clean signature, but because the lep-\nton has relatively low momentum, e\ufb03cient and high-purity\nparticle identi\ufb01cation is needed. In tau decay modes with\ncharged hadrons the pions are usually e\ufb03ciently identi\ufb01ed\nbut large backgrounds must be overcome. Modes with one\nor more neutral pions have both low reconstruction e\ufb03-\nciency and high backgrounds. The entire B+ \u2192\u03c4 +\u03bd signal\nselection is optimized on a mode-by-mode basis so as to\nmaximize the overall sensitivity. Due to di\ufb00erences in de-\ntectors and data samples, BABAR and Belle do not utilize\nexactly the same set of tau decay modes in their respective\nsearches.\nCharged particles from tau decays are selected as tracks\nthat are not identi\ufb01ed as the daughters of the reconstructed\nBtag. It is required that exactly three such tracks are\npresent in the case of the \u03c0+\u03c0\u2212\u03c0+\u03bd \ufb01nal state and exactly\none track otherwise. The summed charge of these tracks\nis required to be consistent with that expected based on\nthe reconstructed Btag. Particle identi\ufb01cation criteria are\napplied to the track(s) to distinguish leptons and pions,\nand to veto kaons. In the case of a single identi\ufb01ed charged\npion, \u03c00 candidates are reconstructed from \u03b3\u03b3 combina-\ntions which do not overlap with Btag daughters. These\nare combined with the \u03c0+ and constraints are applied to\nidentify \u03c1(770) or a1(1260) candidates. Events containing\nidenti\ufb01ed leptons are vetoed if a \u03c00 is also reconstructed\nin the event. Once each event has been uniquely clas-\nsi\ufb01ed as one of the candidate tau decay modes and \u03c00\ncandidates have been associated to the tau mode when\napplicable, there should be no additional energy deposi-\ntion in the electromagnetic calorimeter in signal events.\nIn practice, a small amount of energy is usually present\ndue to accelerator beam backgrounds and reconstruction\ne\ufb00ects. In particular, hadronic shower fragments (\u201csplit-\no\ufb00s\u201d) from pions or kaons interacting in the calorimeter\nare sometimes reconstructed as separate calorimeter clus-\nters rather than being associated with the originating par-\nticle. The most powerful variable for separating signal and\nbackground is the sum of the energies of neutral clusters\nthat are not associated with decays of the Btag or the tau.\nThis quantity is denoted as EECL in Belle and Eextra in\nBABAR (and hereafter referred to as Eextra). The speci\ufb01c\nde\ufb01nition of Eextra depends of the low energy threshold ap-\nplied to calorimeter clusters and di\ufb00ers between analyses.\nIn BABAR analyses, cluster thresholds range from 30\u2212100\nMeV, while in Belle they are chosen to be 50 MeV for\nthe barrel and 100 (150) MeV for the forward (backward)\nend-cap ECL. Signal events are expected to peak at or\nnear Eextra = 0. In contrast, many background events con-\ntain one or more additional neutral clusters from unrecon-\nstructed \u03c00 mesons or other particles. Consequently, for\nbackgrounds Eextra extends to higher values. The Eextra\ndistributions are estimated based on MC simulations. In\norder to reproduce the e\ufb00ects of beam backgrounds, data\nrecorded with random triggers are overlaid on simulated\nevents in both BABAR and Belle analyses. Furthermore,\nto take into account the possible di\ufb00erence between MC\nand data description of split-o\ufb00showers, the signal Eextra\ndistribution is calibrated, both for hadronic and semilep-\ntonic Btag analyses, using \u201cdouble tagged\u201d event samples.\nIn these events, a Btag is reconstructed as described above,\nbut a second hadronic or semileptonic B decay is also ex-\nclusively reconstructed in the same event using tracks and\ncalorimeter clusters not already assigned to the Btag.\nBackground from e+e\u2212\u2192\u03c4 +\u03c4 \u2212and other continuum\nprocesses are suppressed using signal-mode-speci\ufb01c crite-\nria relating to event shapes, in particular the ratio of the\nsecond and zeroth Fox-Wolfram moments (R2, see Chap-\nter 9), and the angle between the thrust axis computed\nusing the daughters of the Btag and the thrust axis com-\nputed using all other track and clusters in the event. BB\nbackgrounds in which the Btag has been correctly recon-\nstructed are suppressed by using kinematic variables of\n\n398\nthe signal track (and \u03c00 in the case of \u03c4 + \u2192\u03c1+\u03bd) and\nany additional calorimeter clusters. These include the CM\nframe momentum of the signal track (p\u2217\ntrk) and the angle\n(cos \u03b8miss) of the missing momentum vector of the event\nwith respect to the beam axis, computed using the Btag\nfour-vector, the signal track, and any additional calorime-\nter clusters.\nA blind analysis (Chapter 14) procedure was adopted\nand the signal selection was optimized to obtain the small-\nest uncertainty on the measured branching fraction. The\nsignal yield is extracted using an extended unbinned max-\nimum likelihood \ufb01t to the Eextra distribution for the var-\nious tau decay signal modes. In the \ufb01t, the background\nyields are allowed to vary independently, while the signal\nyields in all of the tau modes are constrained to a common\nB+ \u2192\u03c4 +\u03bd branching fraction.\nBelle results\nThe Belle collaboration reported the \ufb01rst evidence of the\nB+ \u2192\u03c4 +\u03bd decay by applying the hadronic tagging method\non a sample of 449 \u00d7 106 BB pairs. The extracted signal\nyield is NS = 24.1+7.6\n\u22126.6(stat)+5.5\n\u22126.3(syst) events, correspond-\ning to 3.5 \u03c3 signi\ufb01cance. The branching fraction is mea-\nsured to be B(B+ \u2192\u03c4 +\u03bd) = (1.79+0.56\n\u22120.49(stat)+0.46\n\u22120.51(syst))\u00d7\n10\u22124 (Ikado, 2006).\nMore recently, Belle has reported an updated result\nusing a similar method on the full \u03a5(4S) data sample con-\ntaining 772\u00d7106 BB pairs (Adachi, 2012b). This analysis\nhas a number of signi\ufb01cant improvements compared to the\nprevious one, improved hadronic tagging e\ufb03ciency (a fac-\ntor of 2.2 times larger), and improved signal e\ufb03ciency due\nto less restrictive selection criteria (a factor of 1.8 times\nlarger). The \u03c4 lepton is identi\ufb01ed in the \u03c4 + \u2192e+\u03bde\u03bd\u03c4,\n\u00b5+\u03bd\u00b5\u03bd\u03c4, \u03c0+\u03bd\u03c4, and \u03c0+\u03c00\u03bd\u03c4 decay channels. Multiple neu-\ntrinos in the \ufb01nal state are distinguished using the miss-\ning mass squared M 2\nmiss = (ECM \u2212EBtag \u2212EBsig)2/c4 \u2212\n|pBtag + pBsig|2/c2, where EBsig and pBsig are the energy\nand the momentum, respectively of the Bsig candidate in\nthe CM frame. For the Bsig selection, the event is required\nto have no extra \u03c00 or K0\nL candidates (\u201cK0\nL veto\u201d). The\nsignal yield is extracted from a two-dimensional extended\nmaximum likelihood \ufb01t to Eextra and M 2\nmiss. By combin-\ning the four \u03c4 decay modes, the extracted signal yield is\n62+23\n\u221222(stat) \u00b1 6(syst) events, corresponding to a signi\ufb01-\ncance of 3.0 \u03c3. The branching fraction is measured to be\nB(B+ \u2192\u03c4 +\u03bd) = (0.72+0.27\n\u22120.25(stat) \u00b1 0.11(syst)) \u00d7 10\u22124.\nFigure 17.10.2 (a) shows the Eextra distribution overlaid\nwith the \ufb01t results for the sum of the individual \u03c4 decay\nmodes.\nBelle has also reported a result using the semileptonic\ntagging method, based on a sample of 657\u00d7106 BB events\n(Hara, 2010). In this analysis, Btag candidates were re-\nconstructed via B\u2212\u2192D\u22170\u2113\u2212\u03bd and B\u2212\u2192D0\u2113\u2212\u03bd de-\ncays, where \u2113is an electron or muon. D0 mesons were\nreconstructed in the K\u2212\u03c0+, K\u2212\u03c0+\u03c00, and K\u2212\u03c0+\u03c0\u2212\u03c0+\nmodes. For the Bsig, Belle considered \u03c4 + decays to one\ncharged particle and neutrinos, i.e. \u03c4 + \u2192\u2113+\u03bd\u2113\u03bd\u03c4 and\n\u03c4 + \u2192\u03c0+\u03bd\u03c4. Figure 17.10.2 (b) shows the Eextra distri-\nbution overlaid with the \ufb01t results for the sum of the \u03c4\ndecay modes. Belle reported a clear excess of signal events\nin the region near zero and obtained a signal yield of\n143+36\n\u221235 events, corresponding to a signi\ufb01cance of 3.6\u03c3. The\nbranching fraction was determined to be B(B+ \u2192\u03c4 +\u03bd) =\n(1.54+0.38\n\u22120.37(stat)+0.29\n\u22120.31(syst)) \u00d7 10\u22124.\n0\n50\n100\n150\n200\n250\n300\n350\n400\n0 0.25 0.5 0.75 1\nEECL (GeV)\nEvents / 0.05 GeV\n (GeV)\nECL\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents / 0.05 GeV\n0\n20\n40\n60\n80\n100\n120\n (GeV)\nECL\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents / 0.05 GeV\n0\n20\n40\n60\n80\n100\n120\na)\nb)\nFigure 17.10.2. (a) Distribution of residual energy EECL (re-\nferred to as Eextra in the text) reported by Belle using hadronic\ntags (Adachi, 2012b). The solid circles with error bars are data.\nThe solid histograms show the projection of the \ufb01t. The dashed\nand dotted histograms show the signal and background compo-\nnents, respectively. (b) The same distribution obtained using\nsemileptonic tagged events (Hara, 2010). The points with error\nbars are data. The hatched histogram and solid open histogram\nare the background and the total signal plus background con-\ntributions, respectively.\n\n399\nBABAR results\nBABAR has published searches for B+ \u2192\u03c4 +\u03bd using both\nthe hadronic and semileptonic tag reconstruction meth-\nods. The most recent hadronic tag search is based on the\nfull BABAR dataset of 467.8\u00d7106 BB events (Lees, 2013a).\nThis search utilized the four tau decay channels \u03c4 + \u2192\ne+\u03bd\u03bd, \u03c4 + \u2192\u00b5+\u03bd\u03bd, \u03c4 + \u2192\u03c0+\u03bd, and \u03c4 + \u2192\u03c1+(\u2192\u03c0+\u03c00)\u03bd,\ntotaling approximately 70% of the total branching frac-\ntion. This search utilizes an expanded set of hadronic\ntag reconstruction modes (see Chapter 7) that includes\nB\u2212\u2192J/\u03c8X\u2212along with lower purity modes to increase\nthe overall tag reconstruction e\ufb03ciency by almost a factor\nof two compared to previous searches by BABAR.\nExactly one charged track is required in addition to the\nreconstructed tag B daughter particles. Events are classi-\n\ufb01ed into \u03c4 decay modes according to electron, muon and\npion particle identi\ufb01cation criteria applied to the track.\nIf the signal track is identi\ufb01ed as a \u03c0+, the event is con-\nsidered to be a \u03c4 + \u2192\u03c1+\u03bd candidate if a \u03c00 candidate\nsatis\ufb01es the condition 115 < M\u03b3\u03b3 < 155 MeV/c2. Other-\nwise it is considered to be a \u03c4 + \u2192\u03c0+\u03bd candidate. Mul-\ntivariate likelihood ratios are constructed, for each sig-\nnal mode, for signal and background hypotheses. For the\n\u03c4 + \u2192e+\u03bd\u03bd, \u03c4 + \u2192\u00b5+\u03bd\u03bd and \u03c4 + \u2192\u03c0+\u03bd modes, the\nlikelihoods are constructed from the products of p.d.f.s\nfor p\u2217\ntrk and cos \u03b8miss. For the \u03c4 + \u2192\u03c1+\u03bd mode, the re-\nconstructed invariant mass of the \u03b3\u03b3 combination and of\nthe \u03c0+\u03c00 combination are also used as inputs. The signal\nyield is extracted using an unbinned maximum likelihood\n\ufb01t to the Eextra distribution for the four signal modes. The\ncombinatorial background p.d.f. is obtained from data in\nthe mES sideband region and combined with a B+B\u2212\n\u201cpeaking\u201d component from MC to de\ufb01ne an overall back-\nground p.d.f. to use in the \ufb01t. The \ufb01t yields a positive\nsignal with a signi\ufb01cance of approximately 3.8\u03c3 and a\nbranching fraction of B(B+ \u2192\u03c4 +\u03bd) = (1.83+0.53\n\u22120.49(stat) \u00b1\n0.24(syst))\u00d710\u22124. Figure 17.10.3 (a) shows the Eextra dis-\ntribution obtained from this analysis. An earlier version of\nthis search based on 383\u00d7106 BB events (Aubert, 2008c)\nand utilizing the same four tau decay modes reported a\nsimilar branching fraction central value B(B+ \u2192\u03c4 +\u03bd) =\n1.8+0.9\n\u22120.8(stat)\u00b10.4\u00b10.2(syst). However, the statistical sig-\nni\ufb01cance (2.2\u03c3) was not su\ufb03cient to provide compelling\nevidence for the signal decay.\nBABAR has also performed searches for B+ \u2192\u03c4 +\u03bd us-\ning semileptonic tag reconstruction (Aubert, 2006a, 2007a,\n2010a). The most recent BABAR study (Aubert, 2010a)\nwas based on 458.9\u00d7106 BB events and analyzed the four\ntau decay modes \u03c4 + \u2192e+\u03bd\u03bd, \u03c4 + \u2192\u00b5+\u03bd\u03bd, \u03c4 + \u2192\u03c0+\u03bd,\nand \u03c4 + \u2192\u03c1+(\u2192\u03c0+\u03c00)\u03bd. Two likelihood ratios are con-\nstructed from kinematic and event shape variables de-\nsigned, respectively, for suppression of continuum back-\ngrounds and non-signal BB backgrounds. Signal and back-\nground p.d.f.s are obtained from MC for each of the four\nsignal channels and likelihood ratios are constructed from\nthe product of the p.d.f.s. The selection is optimized to\nmaximize the expected signal signi\ufb01cance for each of the\nsignal modes. Three variables are optimized: the outputs\nof the continuum and BB likelihood ratio selectors and\nEextra. In the optimized selection the cut on Eextra ranges\nfrom 200 MeV to 350 MeV and predicted background\nyields range from approximately 60 to 230 events, depend-\ning on the signal mode. The overall selection e\ufb03ciency,\nincluding both Btag reconstruction and signal selection,\nis at the level of \u223c10\u22123. Figure 17.10.3 (b) shows the\nEextra distribution obtained. A slight excess of events in\ndata compared with the predicted background is found\nin each of the four signal modes resulting in a combined\nbranching fraction central value of B(B+ \u2192\u03c4 +\u03bd) = (1.7\u00b1\n0.8(stat) \u00b1 0.2(syst)) \u00d7 10\u22124 with an overall signal signif-\nicance of approximately 2.3\u03c3.\n [GeV]\nextra\nE\n0\n0.2\n0.4\n0.6\n0.8\n/100 MeV\nevt\nN\n0\n50\n100\n150\n200\n250\n300\na)\n (GeV)\nExtra\nE\n0\n0.5\n1\nEvents/0.125 GeV\n0\n100\n200\n300\n400\n\u03bd \n+\n\u03c4 \n\u2192\n \n+\nB\nb)\nFigure 17.10.3. (a) Distribution of Eextra reported by BABAR\nusing hadronic tags (Lees, 2013a). The points with error bars\nrepresent data. The solid histogram shows the background and\nthe dashed component is the best-\ufb01t signal excess distribution.\n(b) The same distribution obtained using semileptonic tagged\nevents (Aubert, 2010a). The points with error bars are data.\nThe gray shaded boxes represent MC simulated backgrounds\nand the dotted histogram is the signal MC simulation normal-\nized to 10 times the expected branching fraction.\n\n400\nSummary of B+ \u2192\u03c4 +\u03bd measurements\nThe branching fractions reported by Belle and BABAR us-\ning the hadronic and semileptonic tagged samples are sum-\nmarized in Table 17.10.1 and graphically compared in Fig-\nure 17.10.4. The errors for Nsig are statistical only. For the\nsemileptonic-tag analysis at BABAR, we obtain Nsig by tak-\ning a di\ufb00erence between the total yield of 583 events and\nthe expected background yield of 509 \u00b1 30 events, where\nthe error is obtained by taking a quadratic sum of the er-\nrors for the above two yields assuming a Poisson error for\nthe total yield. The signi\ufb01cance \u03a3sig includes systematic\nuncertainties. The e\ufb03ciency \u03f5sig includes the branching\nratios of the tau decay modes. The \ufb01rst and second er-\nrors for B are the statistical and systematic uncertainties,\nrespectively.\nThe four results are consistent within the errors. Both\nBelle and BABAR quote average branching fractions from\nthe combination of their own hadronic and semileptonic\ntag results. Taking the simple weighted average of these\ntwo values one obtains\nB(B+ \u2192\u03c4 +\u03bd)AVG = (1.15 \u00b1 0.23) \u00d7 10\u22124.\n(17.10.10)\n ]\n-4\n ) [ 10\ni o \nA\nB ( B \n0\n0.5\n1\n1.5\n2\n2.5\n3\n0.11\n\u00b1 \n -0.25\n+0.27\nBelle, hadronic tag: 0.72 \n -0.37 -0.31\n+0.38 +0.29\nBelle, semileptonic tag: 1.54 \n 0.26\n\u00b1\nBelle, combined: 0.96 \n 0.24\n\u00b1 \n -0.49\n+0.53\nBaBar, hadronic tag: 1.83 \n 0.2\n\u00b1\n 0.8 \n\u00b1\nBaBar, semileptonic tag: 1.7 \n 0.48\n\u00b1\nBaBar, combined: 1.79 \n 0.23\n\u00b1\nWorld average: 1.15 \nFigure 17.10.4. Comparison of the branching fractions re-\nported by Belle and BABAR\nusing the hadronic and semi-\nleptonic tagged samples of data. The error bars indicate the\nquadratic sums of the statistical and systematic uncertainties.\nInterpretation of results\nThe experimental average for the B+ \u2192\u03c4 +\u03bd branching\nfraction is consistent with the SM prediction from Equa-\ntion (17.10.5). In turn, using the average B+ \u2192\u03c4 +\u03bd\nbranching fraction, the product of |Vub| and the B me-\nson decay constant fB is calculated to be,\nfB|Vub| = (8.06 \u00b1 0.81) \u00d7 10\u22124 GeV.\n(17.10.11)\nUsing the value of fB above (Section 17.10.2.1), |Vub| is\ndeduced to be,\n|Vub| = (4.22 \u00b1 0.47) \u00d7 10\u22123.\n(17.10.12)\nThis is consistent, within errors, with the average values of\n|Vub| obtained from inclusive and exclusive B semileptonic\ndecay data in Eq. (17.1.70). This result is also consistent\nwith the value from inclusive B semileptonic decay data\nalone, but higher than the value from exclusive B semi-\nleptonic decay data by 2.1 \u03c3.\nThe obtained branching fraction can also be used to\nconstrain the charged Higgs. The ratio rH, as de\ufb01ned in\nEq. (17.10.7), is found to be rH = 1.14 \u00b1 0.40. Based\non this result and Eq. (17.10.6), the charged Higgs can\nbe constrained in the (tan\u03b2, MH) plane, as shown in Fig-\nure 17.10.5.\n)\n2\n Mass (GeV/c\n\u00b1\nH\n0\n200\n400\n600\n800\n1000\n`\ntan \n0\n20\n40\n60\n80\n100\nFigure 17.10.5. Constraint on the ratio of the two vacuum\nexpectation values tan \u03b2 and the charged Higgs mass in the\ntype II of two Higgs doublet model. The green regions indicate\nthe excluded regions at a con\ufb01dence level of 95%.\n17.10.2.3 B+ \u2192\u2113+\u03bd (\u2113= e, \u00b5)\nAlthough the B+ \u2192e+\u03bd and B+ \u2192\u00b5+\u03bd branching\nfractions are substantially suppressed compared to the \u03c4\nmode, these modes are still of considerable interest at the\nB Factories. While the electron mode, within the SM, is\nwell beyond reach, the \u00b5 mode has a predicted branch-\ning fraction of \u223c5 \u00d7 10\u22127, which is potentially detectable\nby BABAR and Belle. It is also notable that the relative\n\n401\nTable 17.10.1. Summary table for the B+ \u2192\u03c4 +\u03bd analyses. The number of BB pairs in the data sample (NBB), the signal\nyield (Nsig), the signi\ufb01cance (\u03a3sig), the detection e\ufb03ciency (\u03f5sig), and the branching ratio (B) are shown for each of the hadronic-\ntag and semileptonic-tag analyses. The combined results reported by Belle and BABAR for B are also shown, where the errors\nare the sum in quadrature of the statistical and systematic uncertainties.\nExperiment\nTagging\nNBB (106)\nNsig\n\u03a3sig\n\u03f5sig (10\u22124)\nB (10\u22124)\nReference\nHadronic\n772\n62+23\n\u221222\n3.0\u03c3\n11.2\n0.72+0.27\n\u22120.25 \u00b1 0.11\n(Adachi, 2012b)\nBelle\nSemileptonic\n657\n143+36\n\u221235\n3.6\u03c3\n14.3\n1.54+0.38+0.29\n\u22120.37\u22120.31\n(Hara, 2010)\nCombined\n0.96 \u00b1 0.26\n(Adachi, 2012b)\nHadronic\n468\n62 \u00b1 17\n3.8\u03c3\n7.3\n1.83+0.53\n\u22120.49 \u00b1 0.24\n(Lees, 2013a)\nBABAR\nSemileptonic\n459\n74 \u00b1 39\n2.3\u03c3\n9.6\n1.7 \u00b1 0.8 \u00b1 0.2\n(Aubert, 2010a)\nCombined\n1.79 \u00b1 0.48\n(Lees, 2013a)\nenhancement (or suppression) of the leptonic branching\nfractions due to the existence of a charged Higgs boson is\nindependent of the \ufb01nal state lepton mass as can be seen\nfrom Eq. (17.10.7). Consequently, equally precise determi-\nnations of experimental branching fractions in any of the\nthree leptonic modes would yield identical constraints on a\npostulated charged Higgs boson. Additionally, because the\nB+ \u2192\u00b5+\u03bd \ufb01nal state contains only a single neutrino and\na high momentum \u00b5, there exist su\ufb03cient constraints that\nthe search can be performed without the need for exclusive\nBtag reconstruction and hence with substantially higher\nsignal e\ufb03ciency than in the case of B+ \u2192\u03c4 +\u03bd. The higher\ne\ufb03ciency and cleaner signature compensates to some de-\ngree for the smaller SM branching fraction, however cur-\nrent measurements of B+ \u2192\u00b5+\u03bd are not yet su\ufb03ciently\nsensitive to provide evidence of a non-zero signal. Both\nBABAR (Aubert, 2004ac, 2009as) and Belle (Satoyama,\n2007) have published the results of searches for B+ \u2192\u00b5+\u03bd\nand B+ \u2192e+\u03bd using this \u201cinclusive\u201d (i.e. un-tagged) ap-\nproach. These inclusive searches have resulted in branch-\ning fraction upper limits that are within about a factor of\ntwo of the SM expectation, and that are limited by the\n\ufb01nite size of the background event samples. BABAR has\nalso performed a search using hadronic Btag reconstruc-\ntion (Aubert, 2008az) and a search using semileptonic tag\nreconstruction (Aubert, 2010a).\nInclusive searches\nThe most stringent limits on B+ \u2192\u00b5+\u03bd and B+ \u2192e+\u03bd\nare obtained from \u201cinclusive\u201d searches from BABAR (Au-\nbert, 2009as) and Belle (Satoyama, 2007). These analyses\nrely on the distinctive signature of the high-momentum\nlepton (e or \u00b5) resulting from the two-body B decay. The\nlepton momentum lies well above the kinematic limit for\nb \u2192c\u2113\u03bd and close to the endpoint for b \u2192u\u2113\u03bd. Con-\nsequently, backgrounds from B decays with real leptons\nare relatively limited, but continuum background can be\nlarge.\nTight particle identi\ufb01cation requirements are imposed\nin order to cleanly identify the signal candidate electron\nor muon. Although the lepton is expected to be mono-\nenergetic in the signal B rest frame, the \u03a5(4S) rest frame\n(i.e. the e+e\u2212CM frame) is initially used as an approxi-\nmation since the rest frame of the parent B is not known.\nBecause the two B mesons have momenta of \u223c320 MeV/c\nin this frame, the signal lepton momentum is smeared out\nand ranges from 2.4 GeV/c to about 3.2 GeV/c.\nSince the only other daughter of the signal B is an\nundetected neutrino, it is expected that all other particles\ndetected in the \u03a5(4S) \u2192B+B\u2212event originate from the\nnon-signal B. Consequently, for signal events, the combi-\nnation of all particles should yield a four-vector consistent\nwith a B meson, and a total charge that is opposite that of\nthe signal lepton. In order to obtain the best possible reso-\nlution for this four-vector, tracks used in this combination\nare assigned mass hypotheses based on particle identi\ufb01ca-\ntion criteria. Events with any additional identi\ufb01ed leptons\nare vetoed since their presence often implies either addi-\ntional missing energy from unobserved neutrinos, or that\nthe event is continuum background. Missing energy can\nalso arise due to particles lost outside the detector \ufb01du-\ncial acceptance; in particular this can occur for continuum\nbackgrounds, which tend to produce particles in the for-\nward and backward regions of the detector. Belle requires\nthe transverse component of the missing momentum to be\ngreater than 1.75 GeV/c and the cosine of the angle with\nrespect to the beam axis to be less than 0.84 (0.82) for the\nmuon (electron) mode. Continuum background is further\nsuppressed by exploiting the di\ufb00erences in event shapes\ncompared with BB events. To this end both BABAR and\nBelle use a Fisher discriminant (see Chapter 4) combining\nkinematic and angular variables describing the distribu-\ntion and energies of reconstructed particles in the event.\nThe four-vector of the non-signal B is obtained by\nsumming the four-vectors of all tracks and clusters in the\nevent other than the signal lepton. The kinematic vari-\nables \u2206E and mES are used to characterize the B can-\ndidate. Events in which all non-signal B decay daugh-\nters, and no additional particles, are correctly identi\ufb01ed\nand included in the four-vector sum are expected to have\n\u2206E \u22480 and mES close to the nominal B mass. Due to the\n\u201cinclusive\u201d nature of the method, the resolution of both\nof these quantities is relatively poor compared to what is\ntypically obtained for exclusively reconstructed B decays.\nThe signal B four-vector can be inferred from the non-\nsignal B four-vector and used to re\ufb01ne the estimate of the\n\n402\nB rest frame momentum of the signal lepton. This results\nin a modest improvement in the resolution of the lepton\nmomentum (see e.g. Figure 17.10.6 upper plot), compared\nwith the e+e\u2212CM frame.\nThe signal yield is extracted based on the distribu-\ntions of the corrected lepton momentum (pB\n\u2113) and the non-\nsignal B mES and \u2206E distributions. BABAR and Belle use\ndi\ufb00erent methods. Belle requires 2.6 < pB\n\u00b5(e) < 2.84 (2.80)\nGeV/c and \u22120.8 (\u22121.0) < \u2206E < 0.4 GeV for the muon\n(electron) mode (see Figure 17.10.6 upper plot), then de-\n\ufb01nes a \ufb01t region, 5.10 < mES < 5.29 GeV/c2, and a more\nconstrained signal region, 5.26 < mES < 5.29 GeV/c2,\nwhich are used for background and signal estimation, re-\nspectively. The signal is extracted using an unbinned max-\nimum likelihood \ufb01t to mES in the signal region. The over-\nall signal e\ufb03ciency is estimated to be \u03f5\u00b5 = (2.18 \u00b1 0.06)%\nand \u03f5e = (2.39 \u00b1 0.06)% for the muon and electron chan-\nnels, respectively. Belle observes a total of 12 (15) events\nwith an expected background of 7.4\u00b11.0 (13.4\u00b11.4) events\nin the muon (electron) channel, yielding branching frac-\ntion upper limits of 1.7 \u00d7 10\u22126 (0.98 \u00d7 10\u22126) at a 90%\ncon\ufb01dence level (see Table 17.10.2). The SM expectation\nfor the signal yield in the B+ \u2192\u00b5+\u03bd channel is 2 \u2013 3\nevents in this analysis.\nIn the BABAR analysis, \u2206E is required to satisfy\n\u22122.25 < \u2206E < 0 GeV. A Fisher discriminant is then con-\nstructed from the two variables, pCM\n\u2113\nand pB\n\u2113, representing\nthe signal lepton momentum in the CM frame and the in-\nferred signal B rest frame, respectively. The signal yield is\nthen determined using an extended maximum likelihood\n\ufb01t to the Fisher discriminant output and mES. The total\nsignal e\ufb03ciencies are estimated to be \u03f5\u00b5 = (6.1 \u00b1 0.2)%\nand \u03f5e = (4.7 \u00b1 0.3)% in the muon and electron channel,\nrespectively. The \ufb01t yields 1 \u00b1 15 (18 \u00b1 14) events in the\nmuon (electron) channel. In the absence of signi\ufb01cant evi-\ndence for signal, BABAR obtains branching fraction upper\nlimits of 1.0 \u00d7 10\u22126 (1.9 \u00d7 10\u22126) at the 90% con\ufb01dence\nlevel (see Table 17.10.2). In a previous inclusive search for\nB+ \u2192\u00b5+\u03bd by BABAR (Aubert, 2004ac), a simpler signal\nextraction method was used in which the signal yield was\nobtained using a so-called cut-and-count (or rectangular\ncut) method based on a rectangular signal region de\ufb01ned\nin the (mES, \u2206E) plane. The signal e\ufb03ciency was esti-\nmated to be \u03f5\u00b5 = (2.09 \u00b1 0.06(stat) \u00b1 0.13(syst))% with a\ntotal background of 5.2 \u00b1 0.5 events in a data sample of\n88 \u00d7 106 BB pairs.\nSearches using tag reconstruction\nBABAR has also performed searches for B+ \u2192\u00b5+\u03bd and\nB+ \u2192e+\u03bd using methods based on hadronic (Aubert,\n2008az) and semileptonic (Aubert, 2010a) tag B recon-\nstruction, similar to the methods used for B+ \u2192\u03c4 +\u03bd and\ndescribed in Section 17.10.2.2 above. The semileptonic tag\nsearch is performed simultaneously with the correspond-\ning B+ \u2192\u03c4 +\u03bd study, essentially representing a special\ncase of the \u03c4 + \u2192\u2113+\u03bd\u03bd (\u2113= e, \u00b5) signal channels in which\nthe \ufb01nal state lepton has a high momentum.\nWhile the signal e\ufb03ciency in the \u201ctagged\u201d searches\nis substantially reduced compared with inclusive searches\ndue to the tag reconstruction procedure, an advantage\nis gained (particularly in the case of hadronic tags) due\nto increased continuum background suppression and im-\nproved knowledge of the signal event kinematics. In par-\nticular, the hadronic Btag four-vector permits the signal\nB four-vector to be precisely determined, with the conse-\nquence that the lepton momentum can be precisely deter-\nmined in the B rest frame. The improved pB\n\u00b5 resolution\nis illustrated in the lower plot of Figure 17.10.6, which\ncan be compared with the \u201cinclusive\u201d distribution from\nBelle shown in the upper plot. The improved resolution\nallows for a signi\ufb01cantly improved separation between sig-\nnal events and backgrounds from semileptonic B decays,\nin particular b \u2192u\u2113\u03bd events. In the BABAR study (Aubert,\n2008az), the hadronic tag search is essentially background\nfree in the signal region. However, with the number of\nevents available with the BABAR and Belle data samples,\nthe tagged approach is statistically limited and the in-\nclusive approach results in a signi\ufb01cantly more stringent\nbranching fraction limit than the tagged analyses. How-\never, both the hadronic tag and inclusive methods yield\nsimilar sensitivities for a 5\u03c3 signal observation, with the\nevent samples available at the current B Factories, due\nto the large statistical uncertainty in the background in\nthe inclusive method. It is anticipated that the two meth-\nods will provide complementary and precise B+ \u2192\u00b5+\u03bd\nbranching fraction measurements with the data expected\nat future high luminosity B Factories.\n17.10.2.4 Radiative decays B+ \u2192\u2113+\u03bd\u03b3\nTo date, only a single search for B(B+ \u2192\u2113+\u03bd\u2113\u03b3) has been\npublished (Aubert, 2009a) by the asymmetric B Facto-\nries, although CLEO had previously published results us-\ning an un-tagged search method (Browder et al., 1997).\nThe BABAR result, which is based on a data sample of\n465 million BB pairs, uses a method based on hadronic-\ntag reconstruction (see Chapter 7). However, Belle (Abe,\n2004d) and BABAR (Aubert, 2007aw) have both reported\nunpublished results using an \u201cinclusive\u201d method similar\nto that used by CLEO. Although the hadronic-tag tech-\nnique results in a low signal e\ufb03ciency (0.3% for signal\nmodes), it compensates by providing a high purity sample\nof B mesons with comparatively little non-BB (contin-\nuum) background. This background is very problematic\nfor the inclusive analyses. In addition, by reconstructing\nthe Btag using only detectable hadronic decay modes, the\nmissing four-vector of the signal neutrino is fully deter-\nmined. Thus the BABAR hadronic tag analysis was able\nto avoid the model-dependent kinematic constraints in\nthe signal selection which had complicated the interpreta-\ntion of the earlier analyses. However, the inclusive analy-\nses bene\ufb01t from signi\ufb01cantly higher statistical sensitivity.\nWith the available BABAR or Belle data it is expected that\nthe inclusive measurements, if they had been published,\nwould have yielded more stringent experimental limits or\npossibly observation of these decay modes.\n\n403\nTable 17.10.2. B+ \u2192\u2113+\u03bd and B+ \u2192\u2113+\u03bd\u03b3 branching fraction measurements by BABAR and Belle.\nExperiment\nDecay Mode\nMethod\nNBB\nB upper limit\nReference\n(106)\n90% C.L.\nBelle\nB+ \u2192\u00b5+\u03bd\ninclusive\n253 fb\u22121\n1.7 \u00d7 10\u22126\nSatoyama (2007)\nB+ \u2192e+\u03bd\n0.98 \u00d7 10\u22126\nBABAR\nB+ \u2192\u00b5+\u03bd\ninclusive\n268\n1.0 \u00d7 10\u22126\nAubert (2009as)\nB+ \u2192e+\u03bd\n1.9 \u00d7 10\u22126\nBABAR\nB+ \u2192\u00b5+\u03bd\nhadronic\n378\n5.6 \u00d7 10\u22126\nAubert (2008az)\nB+ \u2192e+\u03bd\n5.2 \u00d7 10\u22126\nBABAR\nB+ \u2192\u00b5+\u03bd\nsemileptonic\n459\n11 \u00d7 10\u22126\nAubert (2010a)\nB+ \u2192e+\u03bd\n8 \u00d7 10\u22126\nBABAR\nB+ \u2192\u00b5+\u03bd\u03b3\nhadronic\n465\n24 \u00d7 10\u22126\nAubert (2009a)\nB+ \u2192e+\u03bd\u03b3\n16 \u00d7 10\u22126\nB+ \u2192\u2113+\u03bd\u03b3\n15.6 \u00d7 10\u22126\n [GeV/c]\nB\nlp\n2.3\n2.4\n2.5\n2.6\n2.7\n2.8\n2.9\nEntries/0.05 GeV/c\n0\n20\n40\n60\n80\n100\n120\n140\nOn resonance\nOff resonance\nB\nB\ni\n l \nu\nX\nSignal x 10\n-1\n 253fb\ni \n\u00b5\n \nA\nB \nLepton momentum (GeV/c)\n2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3\nEntries / 0.025 GeV/c\n0\n5\n10\n15\n20\n25\n30\n35\nLepton momentum (GeV/c)\n2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3\nEntries / 0.025 GeV/c\n0\n5\n10\n15\n20\n25\n30\n35\nBABAR\ni\n+\n\u00b5\n \nA\n+\nB\nFigure 17.10.6. (Top) Momentum of the reconstructed B+ \u2192\n\u00b5+\u03bd signal muon in the Belle \u201cinclusive\u201d search (Satoyama,\n2007) and (bottom) in the BABAR \u201chadronic tag\u201d search (Au-\nbert, 2008az).\nThe hadronic-tag analysis proceeds as follows. After\nreconstructing a Btag, remaining continuum background\nis suppressed using a multivariate selector incorporating\nseveral event shape variables. From this sample, signal\ncandidate events are required to possess only one \u201csignal-\nside\u201d track, in addition to those used to reconstruct the\nBtag. This track is required to satisfy either electron or\nmuon particle identi\ufb01cation. In the case of electrons, can-\ndidate Bremsstrahlung clusters in the calorimeter are used\nto correct the momentum of the electron track. The high-\nest energy remaining calorimeter cluster, not associated\nwith the reconstructed Btag, is assumed to be the radiated\nsignal photon. The energy spectrum of radiated photons\nin signal candidates is expected to peak at \u223c1 GeV. The\nenergies of any remaining calorimeter clusters are summed\nto obtain Eextra. A loose requirement of Eextra < 0.8 GeV\nis imposed to reject B backgrounds. To ensure that the\nsignal candidates are consistent with a three-body de-\ncay, the lepton momentum and the total missing momen-\ntum in the event were required to be back-to-back in the\nframe recoiling against the photon. As the signal B four-\nvector can be inferred from the Btag four-vector, the 3-\nbody kinematics can be uniquely determined by combin-\ning this information with the signal lepton and photon\ncandidate four-vectors. The most discriminating variable\nis the reconstructed invariant mass of the neutrino, given\nas m2\n\u03bd \u2261|p\u03a5 (4S) \u2212pBtag \u2212p\u2113\u2212p\u03b3|2 where pi is the four-\nmomentum of particle i. Figure 17.10.7 shows that the\nsignal peaks at zero, while the background rises with m2\n\u03bd.\nThe dominant backgrounds arise from B+ \u2192X0\nu\u2113+\u03bd\u2113\nevents, where Xu is a neutral meson containing a u-quark.\nEvents in which the signal photon candidate could be com-\nbined with another calorimeter cluster to form an invari-\nant mass consistent with the \u03c00 or \u03b7 mass, or combined\nwith a \u03c00 candidate to form an \u03c9, were rejected. However,\nB+ \u2192X0\nu\u2113+\u03bd\u2113events can mimic the signal decay kinemat-\nics. This can occur especially if only one high-energy pho-\nton daughter from the Xu decay is present in the signal-\nside clusters, or if the two photons from a B+ \u2192\u03c00\u2113+\u03bd\u2113\ndecay are merged into a single calorimeter cluster contain-\ning the full energy of the \u03c00. Consequently, the combina-\ntion of this \u201cphoton\u201d cluster with the signal lepton results\nin an m2\n\u03bd distribution that peaks at zero, mimicking sig-\nnal. These backgrounds are suppressed by examining the\nshape of the calorimeter cluster and limiting the lateral\nmoment of the cluster energy deposit.\nA cut-and-count method is used to determine the sig-\nnal yield. The background is divided into two compo-\nnents: events that peak in the mES signal region are es-\n\n404\n)\n4\n/c\n2\n (GeV\ne\n! 2\nm\n\u22121\n\u22120.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n)\n4\n/c\n2\nEntries/(0.2 GeV\n0\n1\n2\n3\n4\n5\n6\n7\n)\n4\n/c\n2\n (GeV\n\u00b5\n! 2\nm\n\u22120.5\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n)\n4\n/c\n2\nEntries/(0.2 GeV\n0\n1\n2\n3\n4\n5\n6\n7\nFigure 17.10.7. m2\n\u03bd distribution in B+ \u2192\u2113+\u03bd\u03b3, from Aubert\n(2009a), after all selection criteria are applied, in the electron\n(top) and muon (bottom) modes. The mES-peaking (shaded)\nand non-peaking (solid) background contributions are shown\nstacked, along with signal MC (dashed) normalized to B =\n40 \u00d7 10\u22126, and data (points). Events to the left of the vertical\nlines are selected.\ntimated from various dedicated B+ \u2192X0\nu\u2113+\u03bd\u2113MC sam-\nples, while non-peaking events are extrapolated directly\nfrom the data events in the mES sideband region in or-\nder to reduce the dependence on MC simulations. The\nlargest background uncertainties stem, respectively, from\nthe branching fractions and form factors of the various\nB+ \u2192X0\nu\u2113+\u03bd\u2113decays, and from the limited number of\nsideband data events.\nA measurement of B(B+ \u2192\u2113+\u03bd\u2113\u03b3) = (6.5+7.6 +2.8\n\u22124.7 \u22120.8) \u00d7\n10\u22126 was obtained with a signi\ufb01cance of 2.1\u03c3, along with\nan upper limit of B(B+ \u2192\u2113+\u03bd\u2113\u03b3) < 15.6 \u00d7 10\u22126 at 90%\ncon\ufb01dence level. These results are the most stringent pub-\nlished limits, and are close to the theoretical predictions\nfor these modes. E\ufb00ectively no requirements are applied\nto the lepton or photon kinematics, thus this analysis is\nessentially independent of the B \u2192\u03b3 form factor models\nand valid over the full kinematic range.\nHowever, the extraction of \u03bbB (see Eq. 17.10.9) can\nbe improved by including a minimum energy requirement\non the signal photon (Ball and Kou, 2003; Beneke and\nRohrwild, 2011). Therefore, additional branching fraction\nresults were reported in speci\ufb01c kinematic regions. A re-\nquirement that the signal photon candidate energy is >\n1 GeV results in a partial branching fraction of \u2206B(B+ \u2192\n\u2113+\u03bd\u2113\u03b3) < 14 \u00d7 10\u22126 at a C.L. of 90%. More stringent\nbranching fraction limits were determined by introducing\na kinematic requirement on the angles between the three\ndaughter particles of the signal decay. In a model in which\nthe two B \u2192\u03b3 form-factors, fV and fA, are equal, the re-\nsult B(B+ \u2192\u2113+\u03bd\u2113\u03b3) < 3.0 \u00d7 10\u22126 is obtained. In a model\nwith fA = 0, B(B+ \u2192\u2113+\u03bd\u2113\u03b3) < 18 \u00d7 10\u22126 is obtained.\nAlthough a signi\ufb01cant B+ \u2192\u2113+\u03bd\u2113\u03b3 signal has not yet\nbeen observed, the sensitivity of the this method is such\nthat it is likely that these decays will be accessible at\nfuture high-luminosity B Factories.\n17.10.3 B \u2192D(\u2217)\u03c4\u03bd\nIn the SM the branching fractions for the semileptonic\ndecays B \u2192D(\u2217)\u03c4\u03bd\u03c4, which proceed via a tree-level pro-\ncess with an intermediate W \u00b1, are predicted to be (0.69\u00b1\n0.04)% and (1.41 \u00b1 0.07)% for B0 \u2192D\u2212\u03c4 +\u03bd\u03c4 and B0 \u2192\nD\u2217\u2212\u03c4 +\u03bd\u03c4, respectively (Chen and Geng, 2006). However,\nif a charged Higgs boson exists, the branching fraction\nmay di\ufb00er signi\ufb01cantly due to interference from a tree-\nlevel H\u00b1 exchange contribution similar to that for B+ \u2192\n\u03c4 +\u03bd (see Figure 17.10.1). E\ufb00ects of the charged Higgs on\nB \u2192D(\u2217)\u03c4\u03bd decays are discussed in a number of the-\noretical papers\n(Fajfer, Kamenik, and Nisandzic, 2012;\nGrzadkowski and Hou, 1992; Itoh, Komine, and Okada,\n2005; Kiers and Soni, 1997; Nierste, Trine, and Westho\ufb00,\n2008; Tanaka, 1995). From a theoretical point of view, the\nB \u2192D(\u2217)\u03c4\u03bd\u03c4 decay has a similar sensitivity to H\u00b1 as\nthe B+ \u2192\u03c4 +\u03bd decay, but with di\ufb00erent theoretical and\nparametric uncertainties. While the purely leptonic decay\ndepends only on the relatively well known B meson decay\nconstant fB, the semileptonic decays depend on form fac-\ntors. The formulae for the semileptonic rates can be found\nin Section 17.1. However, for \u2113= e, \u00b5 the lepton mass is\nusually neglected in which case the rates are not sensitive\nto the \u201clongitudinal\u201d form factors, which are proportional\nto the momentum transfer q = (p \u2212p\u2032)\n\u27e8D(p\u2032)|c\u03b3\u00b5b|B(p)\u27e9= (p\u00b5 \u2212p\u2032\n\u00b5)F0(q2) + \u00b7 \u00b7 \u00b7\n(17.10.13)\nand similarly for the transition B \u2192D\u2217. These form fac-\ntors become relevant for B \u2192D(\u2217)\u03c4\u03bd, since their contribu-\ntions to the di\ufb00erential rates are proportional to M 2\n\u2113/M 2\nB\nwhich is sizable for \u2113= \u03c4. Detailed results for the di\ufb00er-\nential rates including lepton mass e\ufb00ects can be found, for\nexample, in (Fajfer, Kamenik, and Nisandzic, 2012; Nier-\nste, Trine, and Westho\ufb00, 2008).\nThe longitudinal form factors for B \u2192D(\u2217)\u03c4\u03bd are not\nas well known as the ones appearing in the decays with\nan e or a \u00b5. Nevertheless, one can apply the heavy quark\nlimit for both the bottom and the charm quark in which\ncase all form factors of the B \u2192D(\u2217) transitions may\nbe related to a single form factor, the Isgur-Wise function\n(see Section 17.1). This limit is expected to be valid at the\nlevel of (20-30)%, however, in combination with the factor\nM 2\n\u2113/M 2\nB one still arrives at fairly precise predictions for\nratios of branching fractions. The ratio\nRD(\u2217) = B(B \u2192D(\u2217)\u03c4\u03bd)\nB(B \u2192D(\u2217)\u2113\u03bd) ,\n(17.10.14)\n\n405\ncan provide sensitivity to H\u00b1. Measurement of this quan-\ntity has the additional advantage of using two decay modes\nwith very similar experimental signatures, if only the lep-\ntonic decay modes of the tau are considered. This method\ntherefore permits the cancellation of form factor uncer-\ntainties as well as many experimental systematic uncer-\ntainties.\nIn contrast, sensitivity to H\u00b1 in B+ \u2192\u03c4 +\u03bd\u03c4 requires\nmeasurement of the absolute branching fraction and com-\nparison with the expected SM prediction, which in turn\nrequires knowledge of the CKM matrix element Vub. Given\nthe current discrepancy between inclusive and exclusive\nVub measurements (see Section 17.1), the B \u2192D(\u2217)\u03c4\u03bd\u03c4\nmodes currently provide a cleaner interpretation of possi-\nble H\u00b1 contributions. These modes therefore provide com-\nplementary approaches to searching for H\u00b1 signatures in\nB decays.\nThe three-body kinematics of the B \u2192D(\u2217)\u03c4\u03bd\u03c4 decay\nalso potentially permit the study of the \u03c4 polarization via\nthe decay distributions of \ufb01nal state particles. These mea-\nsurements can in principle discriminate between H\u00b1 and\nW \u00b1 exchange, however studies performed to date have\nnot been sensitive to these distributions.\n17.10.3.1 Experimental methodology and results\nLike B+ \u2192\u03c4 +\u03bd, the B \u2192D(\u2217)\u03c4\u03bd decay has two or more\nneutrinos in the \ufb01nal state and so cannot be fully recon-\nstructed using only the observable particles. It therefore\nrelies on exclusive reconstruction of the accompanying B\n(\u201cBtag\u201d) to provide the necessary level of background sup-\npression (see Chapter 7). BABAR has reported B \u2192D(\u2217)\u03c4\u03bd\nresults using the method of hadronic B tag reconstruc-\ntion (Aubert, 2008al; Lees, 2012e) while Belle has pub-\nlished results based on another method, referred to as \u201cin-\nclusive tags\u201d (Bozek, 2010; Matyja, 2007), in which Btag\u2019s\nare reconstructed by calculating the four-vector sum of\nthe tracks inclusively without reconstructing the interme-\ndiate mesons. This method is similar to the \u201cinclusive\u201d\nmethod used in B+ \u2192\u2113+\u03bd (\u2113= e, \u00b5) described in Sec-\ntion 17.10.2.3 above. Belle has also produced a prelimi-\nnary measurement of B \u2192D(\u2217)\u03c4\u03bd based on hadronic tag\nreconstruction (Adachi, 2009).\nThe Belle Collaboration reported the \ufb01rst observation\n(5.2\u03c3) of a B0 \u2192D\u2217\u2212\u03c4 +\u03bd using the inclusive tag method\nwith a data sample of 535 M BB pairs (Matyja, 2007). The\n\u03c4 + \u2192e+\u03bde\u03bd\u03c4 and \u03c4 + \u2192\u03c0+\u03bd\u03c4 decays were used to recon-\nstruct \u03c4 lepton candidates. A follow-up to this analysis\nfor B+ \u2192D(\u2217)0\u03c4\u03bd\u03c4 was performed using 657 M BB pairs\n(Bozek, 2010). In this analysis, the signal and combinato-\nrial background yields were extracted using an extended\nunbinned maximum likelihood \ufb01t to the distributions of\nthe Btag mES (referred to as Mtag) and the CM frame mo-\nmentum of the reconstructed D0, pD0. The \u03c4 + \u2192e+\u03bde\u03bd\u03c4,\n\u03c4 + \u2192\u00b5+\u03bd\u00b5\u03bd\u03c4 and \u03c4 + \u2192\u03c0+\u03bd\u03c4 decay modes were used to\nreconstruct the \u03c4 + lepton candidates. In total, 13 di\ufb00er-\nent decay channels, 8 for D\u22170 and 5 for D0, were consid-\nered. The \ufb01ts were performed simultaneously to all data\nsubsets. In each of the sub-channels, the data were de-\nscribed as the sum of four components; signal, cross-feed\nbetween D\u22170\u03c4 +\u03bd\u03c4 and D0\u03c4 +\u03bd\u03c4, combinatorial and peak-\ning backgrounds. Figure 17.10.8 shows the Mtag and pD0\ndistributions and \ufb01t results for the two decay modes. The\nextracted signal yields (signi\ufb01cances) are 446+58\n\u221256 (8.1 \u03c3)\nfor B+ \u2192D\u22170\u03c4 +\u03bd\u03c4 and 146+42\n\u221241 (3.5 \u03c3) for B+ \u2192D0\u03c4 +\u03bd\u03c4.\nThis was the \ufb01rst evidence for the B+ \u2192D0\u03c4 +\u03bd\u03c4 decay.\nBranching fraction results are given in Table 17.10.3.\n]\n2\n [GeV/c\ntag\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n2\nN / 4 MeV/c\n0\n50\n100\n]\n2\n [GeV/c\ntag\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n2\nN / 4 MeV/c\n0\n50\n100\na)\n [GeV/c]\nD0\nP\n0\n0.5\n1\n1.5\n2\nN / 80 MeV/c\n0\n20\n40\n [GeV/c]\nD0\nP\n0\n0.5\n1\n1.5\n2\nN / 80 MeV/c\n0\n20\n40\nb)\n]\n2\n [GeV/c\ntag\nM\n5.2\n5.25\n5.3\n2\nN / 4 MeV/c\n0\n50\n100\n150\n]\n2\n [GeV/c\ntag\nM\n5.2\n5.25\n5.3\n2\nN / 4 MeV/c\n0\n50\n100\n150\nc)\n [GeV/c]\nD0\nP\n0\n0.5\n1\n1.5\n2\nN / 80 MeV/c\n0\n50\n100\n [GeV/c]\nD0\nP\n0\n0.5\n1\n1.5\n2\nN / 80 MeV/c\n0\n50\n100\nd)\nFigure 17.10.8. The \ufb01t projection to Mtag and pD0 for\nMtag > 5.26 GeV/c2 (a, b) for D\u22170\u03c4 +\u03bd\u03c4 and (c, d) for D0\u03c4 +\u03bd\u03c4,\nfrom (Bozek, 2010).\nBABAR reported an observation of B \u2192D\u2217\u03c4\u03bd as well\nas \ufb01rst evidence of B \u2192D\u03c4\u03bd in Aubert (2008al) using\na method based on exclusive hadronic Btag reconstruc-\ntion and a data sample of 232M BB events. This analysis\nreports measurements of the four modes B+ \u2192D0\u03c4 +\u03bd,\nB+ \u2192D\u22170\u03c4 +\u03bd, B0 \u2192D\u2212\u03c4 +\u03bd and B0 \u2192D\u2217\u2212\u03c4 +\u03bd, as well\nas the combined modes B \u2192D\u03c4\u03bd and B \u2192D\u2217\u03c4\u03bd. A fol-\nlow up to this paper, based on the full BABAR data sample\nof 471M BB events (Lees, 2012e) uses similar methodol-\nogy. This more recent analysis reports the \ufb01rst observation\nof B \u2192D\u03c4\u03bd and measures the ratios, R(D(\u2217)) in a simul-\ntaneous measurement of B \u2192D(\u2217)\u03c4\u03bd and B \u2192D(\u2217)\u2113\u03bd\n(\u2113= e, \u00b5), reporting an excess over SM predictions for\nboth R(D) and R(D\u2217). Several improvements are incor-\nporated into the Btag reconstruction and signal selection,\nwhich result in a factor of three improvement of the signal\ne\ufb03ciency compared to the earlier analysis.\nSince only leptonic decay modes of the tau are consid-\nered in this analysis, \u201csignal\u201d B \u2192D(\u2217)\u03c4\u03bd decays have\nidentical \ufb01nal states as the \u201cnormalization\u201d B \u2192D(\u2217)\u2113\u03bd\nmodes, di\ufb00ering only in the kinematics of the observed\n\ufb01nal state. Consequently, many uncertainties associated\n\n406\nwith the signal reconstruction, including charged particle\ntracking, particle identi\ufb01cation and calorimeter-related re-\nconstruction issues, cancel in the ratio. As \u03c4 + \u2192\u2113+\u03bd\u03bd re-\nsults in two additional undetected neutrinos, the missing\nmass, Mmiss, computed from the signal B (inferred from\nthe Btag), the reconstructed D(\u2217) and lepton four-vectors,\npeaks at zero for the normalization modes but not for sig-\nnal decays. The \ufb01nal state e or \u00b5 in the B \u2192D(\u2217)\u03c4\u03bd\nchannel also has a softer momentum distribution than the\nmeasured primary lepton in the normalization mode. The\ntwo quantities Mmiss and |p\u2217\n\u2113|, the magnitude of the lepton\nmomentum in signal B rest frame, are used to extract the\nsignal and normalization mode yields, as described below.\nSignal events are further distinguished from normal-\nization events and other backgrounds by requiring that\nthe missing momentum magnitude, |pmiss| and the square\nof the magnitude of the exchanged four-momentum in\nB \u2192D(\u2217)\u03c4\u03bd, q2 satisfy |pmiss| > 200 MeV and q2 > 4\nGeV2.\nThe signal D(\u2217) and lepton candidates are reconstructed\nfrom tracks and clusters that are not already associated\nwith the Btag. Signal and normalization mode electrons\n(muons) are required to have laboratory frame momenta\ngreater than 300 MeV (200 MeV) and satisfy particle\nidenti\ufb01cation criteria. The D or D\u2217mesons that are com-\nbined with this lepton to form the signal or normalization-\nmode candidates are reconstructed in the D0 modes K\u2212\u03c0+,\nK\u2212K+, K\u2212\u03c0+\u03c00, K\u2212\u03c0+\u03c0\u2212\u03c0+, K0\ns\u03c0+\u03c0\u2212and the charged\nmodes D+ \u2192K\u2212\u03c0+\u03c0+, K\u2212\u03c0+\u03c0+\u03c00, K0\ns\u03c0+, K0\ns\u03c0+\u03c0\u2212\u03c0+,\nK0\ns\u03c0+\u03c00, K0\nsK+, where K0\ns \u2192\u03c0+\u03c0\u2212. D\u2217mesons are iden-\nti\ufb01ed by combining reconstructed D candidates with pho-\ntons or charged or neutral pions to obtain D\u2217+ \u2192D0\u03c0+,\nD+\u03c00 and D\u22170 \u2192D0\u03c00, D0\u03b3 candidates. No additional\ntracks are permitted in the event after reconstruction of\nthe D(\u2217) and lepton, but additional photons are permit-\nted. If multiple candidates are reconstructed in a single\nevent, the candidate with the lowest Eextra is selected,\nwhere Eextra is the sum of the CM energies of any remain-\ning photons in the event.\nFour signal channels are analyzed, corresponding to\nthe \ufb01nal states D0\u2113, D\u22170\u2113, D+\u2113and D\u2217+\u2113. Control sam-\nples are constructed by requiring the presence of an addi-\ntional \u03c00 in each mode, i.e. D(\u2217)\u03c00\u2113. These control sam-\nples are used to estimate background contributions from\ndecays to higher-mass charm states, such as B \u2192D\u2217\u2217\u2113\u03bd,\nwhich are relatively poorly understood and not reliably\nmodeled in the MC. Additional event shape requirements\nare imposed on the control samples to suppress large con-\ntinuum backgrounds in these samples.\nAdditional background suppression is obtained by us-\ning a set of boosted decision tree multivariate selectors\n(see Chapter 4) trained and optimized for each of the\nfour signal modes to select signal and normalization modes\nwhile rejecting backgrounds including D\u2217\u2217contributions\nand cross-feed from other signal and normalization modes.\nEight kinematic variables are used as inputs, including\nEextra, the invariant masses of the signal and Btag daugh-\nter D mesons, the D\u2217\u2212D mass di\ufb00erence (when a D\u2217is\npresent), as well as other quantities related to the quality\nof the Btag reconstruction and the overall event shape.\nThe level of agreement between data and MC sim-\nulation is veri\ufb01ed, and the MC description is improved\nthrough use of additional data sideband control samples\nobtained by requiring Eextra > 0.5 GeV, mES < 5.26, or\nq2 < 4 GeV2. Conservative systematic uncertainties on\nsignal e\ufb03ciencies and background estimates are based on\nthese comparisons.\nThe signal and normalization mode yields are obtained\nsimultaneously for each of the four signal channels us-\ning an unbinned extended maximum likelihood \ufb01t to the\nMmiss - |p\u2217\n\u2113| distribution for the signal and D(\u2217)\u03c00\u2113sam-\nples. The \ufb01t consists of eight components including signal\n(D\u03c4\u03bd, D\u2217\u03c4\u03bd), normalization modes (D\u2113\u03bd, D\u2217\u2113\u03bd), D\u2217\u2217\u2113\u03bd,\ncharge cross-feed, other BB background and continuum\nbackground. The \ufb01rst \ufb01ve of these are allowed to vary in\nthe \ufb01t, while the last three are \ufb01xed to the values deter-\nmined from MC and sideband studies. The D\u2217\u2217\u2113\u03bd contri-\nbutions in the signal sample \ufb01t are constrained by the \ufb01t to\nthe D(\u2217)\u03c00\u2113samples. Even with this method to control the\nD\u2217\u2217\u2113\u03bd contributions, this background imposes the domi-\nnant systematic uncertainty on the signal yield extraction.\nThe branching fraction ratios R(D(\u2217)) are determined\nfrom the signal and normalization mode yields and selec-\ntion e\ufb03ciencies. Fit projections are shown in Fig. 17.10.9\nfor the four signal modes. Since most of the uncertainties\nin the signal and normalization mode e\ufb03ciencies cancel\nin the ratio of modes, the dominant uncertainty in the\ne\ufb03ciency ratio comes from the form factor model uncer-\ntainties for B \u2192D(\u2217)\u03c4\u03bd and B \u2192D(\u2217)\u2113\u03bd. The results are\npresented in Table 17.10.3. In addition to results for the\nfour individual signal channels, two additional results are\nobtained by combining charged and neutral B results by\nimposing isospin constraints.\n17.10.3.2 Interpretation of results\nTable 17.10.3 summarizes the results of the B \u2192D(\u2217)\u03c4\u03bd\nbranching fraction measurements and R(D(\u2217)) results from\nBelle and BABAR. All results are somewhat high com-\npared with the SM expectations, with averages dominated\nby the 2012 BABAR measurements. BABAR (Lees, 2012e)\nhas interpreted the results in the context of the SM and\nthe type-II 2HDM, estimating R(D)SM = 0.297 \u00b1 0.017\nand R(D\u2217)SM = 0.252 \u00b1 0.003 based on Fajfer, Kamenik,\nand Nisandzic (2012); Kamenik and Mescia (2008) with\nupdated form factor measurements. The combination of\nR(D) and R(D\u2217) measurements, including the experimen-\ntal correlation between the B \u2192D\u03c4\u03bd and B \u2192D\u2217\u03c4\u03bd\nmeasurements, is determined to be inconsistent with the\nSM at the level of 3.4\u03c3. Interpretation within the con-\ntext of the 2HDM is shown in Figure 17.10.10. The decay\nkinematics are sensitive to the presence of a H\u00b1 contri-\nbution, impacting both the momentum spectrum of the\n\ufb01nal state leptons and the missing mass distribution. This\ncauses the signal e\ufb03ciency to depend on tan \u03b2/MH, with\nthe consequence that the measured value of R(D(\u2217)) also\n\n407\nTable 17.10.3. Summary of measurements of B \u2192D(\u2217)\u03c4\u03bd. NBB: number of BB pairs in the data sample used for the analysis,\nB: branching fraction (the \ufb01rst error is statistical, the second systematic, and the third due to the branching fraction uncertainty\nin the normalization mode), \u03a3: signi\ufb01cance of the signal including systematic, R(D(\u2217)): the ratio B(B \u2192D(\u2217)\u03c4\u03bd)/B(B \u2192\nD(\u2217)\u2113\u03bd).\nExperiment\nTag\nNBB (106)\nB (10\u22124)\n\u03a3\nR(D(\u2217))\nReference\nB0 \u2192D\u2217\u2212\u03c4 +\u03bd\u03c4\nBelle\ninclusive\n535\n2.02+0.40\n\u22120.37 \u00b1 0.37\n5.2\nMatyja (2007)\nBABAR\nhadronic\n471\n1.74 \u00b1 0.19 \u00b1 0.12\n10.4\n0.355 \u00b1 0.039 \u00b1 0.021\nLees (2012e)\nB+ \u2192D\u22170\u03c4 +\u03bd\u03c4\nBelle\ninclusive\n657\n2.12+0.28\n\u22120.27 \u00b1 0.29\n8.1\nBozek (2010)\nBABAR\nhadronic\n471\n1.71 \u00b1 0.17 \u00b1 0.13\n9.4\n0.322 \u00b1 0.032 \u00b1 0.022\nLees (2012e)\nB0 \u2192D\u2212\u03c4 +\u03bd\u03c4\nBABAR\nhadronic\n471\n1.01 \u00b1 0.18 \u00b1 0.12\n5.2\n0.469 \u00b1 0.084 \u00b1 0.053\nLees (2012e)\nB+ \u2192D0\u03c4 +\u03bd\u03c4\nBelle\ninclusive\n657\n0.77 \u00b1 0.22 \u00b1 0.12\n3.5\nBozek (2010)\nBABAR\nhadronic\n471\n0.99 \u00b1 0.19 \u00b1 0.13\n4.7\n0.429 \u00b1 0.082 \u00b1 0.052\nLees (2012e)\nB \u2192D\u03c4 +\u03bd\u03c4 (isospin constrained)\nBABAR\nhadronic\n471\n1.02 \u00b1 0.13 \u00b1 0.11\n6.8\n0.440 \u00b1 0.058 \u00b1 0.042\nLees (2012e)\nB \u2192D\u2217\u03c4 +\u03bd\u03c4 (isospin constrained)\nBABAR\nhadronic\n471\n1.76 \u00b1 0.13 \u00b1 0.12\n13.2\n0.332 \u00b1 0.024 \u00b1 0.018\nLees (2012e)\ndepends on this quantity, as shown in the Figure. In or-\nder to correctly estimate the e\ufb03ciency, BABAR re-weights\nthe kinematics of simulated signal events to correspond\nto representative tan \u03b2/MH values in the range shown in\nthe Figure and repeats the full \ufb01t to arrive at measure-\nments of R(D(\u2217)) as a function of tan \u03b2/MH. It should be\nnoted that this has implications for averaging the results\nof the BABAR and Belle analyses, since the e\ufb03ciency de-\npendence of the Belle analysis is not available, a simple\naverage can only be correctly interpreted in the context\nof the SM. Within the context of the 2HDM, the BABAR\nR(D(\u2217)) measurements imply speci\ufb01c values of tan \u03b2/MH\nthat are incompatible with each other, and hence with the\n2HDM type II, at a C.L. of 99.8%.\n17.10.4 Discussion and future prospects\nSearching for leptonic decays of charged B mesons at the\npresent generation of B Factories has proven to be very\nchallenging, with the light lepton modes B+ \u2192e+\u03bd and\nB+ \u2192\u00b5+\u03bd remaining beyond the experimental sensitivi-\nties and the B+ \u2192\u03c4 +\u03bd mode observed, but not yet pre-\ncisely measured. Prior to the most recent Belle hadronic-\ntag search (Adachi, 2012b), all B+ \u2192\u03c4 +\u03bd measurements,\nincluding previous Belle hadronic-tag studies, had reported\nbranching fractions which were consistently high compared\nwith SM expectations. The most recent BABAR hadronic-\ntag measurement (Lees, 2013a) determines a branching\nfraction which is approximately a factor of two higher\nthan the corresponding Belle result, although the discrep-\nancy between the two is only about 2\u03c3. Other possible\npoints of concern are the modeling of the experimentally\ncrucial Eextra variable, which has shown indications of\ndiscrepancies in previous measurements, and the inter-\nnal consistency of B+ \u2192\u03c4 +\u03bd branching fraction values\nobtained with di\ufb00erent tau decay modes, see for exam-\nple Lees (2013a). Leptonic and hadronic tau decay signa-\ntures have vastly di\ufb00erent background sources and rates,\nhence inconsistencies in signal yields between tau decay\nmodes is a potential red-\ufb02ag of experimental problems.\nAs both BABAR and Belle have published B+ \u2192\u03c4 +\u03bd re-\nsults based on their full data samples, it is unlikely that\nthis situation will be clari\ufb01ed without additional mea-\nsurements from future B Factory experiments with very\nlarge data samples. However, the experimental challenges\nposed by this decay, in particular low momentum lep-\nton particle identi\ufb01cation and modeling of hadronic back-\ngrounds and extra calorimeter energy, will likely be sim-\nilar (or worse) at high luminosity experiments. Conse-\nquently, it is not clear how precisely B+ \u2192\u03c4 +\u03bd will ul-\ntimately be measured. It is notable that precise measure-\nments of B(B+ \u2192\u00b5+\u03bd) at the SM rate will be possible\nwith data samples of O(50\u2212100) ab\u22121, using both tagged\nand un-tagged approaches. As the B+ \u2192\u00b5+\u03bd searches\nutilize a cleanly identi\ufb01able high momentum muon and\ndo not rely on Eextra, they will provide an independent\ntest of possible new physics in leptonic B decays. If new\nphysics were present in the form of a Type II 2HDM, then\nB(B+ \u2192\u00b5+\u03bd) would potentially be sensitive to it. This\n\n408\n0\n50\n100\n150\n200\n0\n0.5\n1\n1.5\n0\n100\n200\n0\n0.5\n1\n1.5\n0\n100\n200\n0\n50\n100\n150\n200\n0\n50\n100\n0\n0.5\n1\n1.5\n0\n50\n100\n0\n0.5\n1\n1.5\n0\n50\n100\n0\n50\n100\n0\n50\n100\n0\n0.5\n1\n1.5\n0\n50\n100\n0\n0.5\n1\n1.5\n0\n50\n100\n0\n50\n100\n-2\n0\n2\n4\n6\n8\n0\n20\n40\n60\n0\n0.5\n1\n1.5\n0\n20\n40\n0\n0.5\n1\n1.5\n0\n20\n40\n-2\n0\n2\n4\n6\n8\n0\n20\n40\n60\n) [Events/(100 MeV) in insets]\n2\nEvents/(0.25 GeV\n0\n0\n0\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\n|p\u2217\n\u2113| (GeV)\nm2\nmiss (GeV2)\nD0\u2113\nD\u22170\u2113\nD+\u2113\nD\u2217+\u2113\nB \u2192D\u03c4 \u2212\u03bd\u03c4\nB \u2192D\u2217\u03c4 \u2212\u03bd\u03c4\nBackground\nB \u2192D\u2217\u2217(\u2113\u2212/\u03c4 \u2212)\u03bd\nB \u2192D\u2113\u2212\u03bd\u2113\nB \u2192D\u2217\u2113\u2212\u03bd\u2113\nFigure 17.10.9. Projections of the BABAR (Lees, 2012e) B \u2192\nD(\u2217)\u03c4\u03bd \ufb01t for the four signal modes (a) D0\u2113, (b) D\u22170\u2113, (c)\nD+\u2113and (d) D\u2217+\u2113in M 2\nmiss. Inset \ufb01gures show the corre-\nsponding projection in |p\u2217\n\u2113| for M 2\nmiss > 1 GeV2 in order to\nexclude the B \u2192D(\u2217)\u2113\u03bd normalization component. Stacked\nin order from the bottom the components are: continuum and\nBB background (below dashed line), charge cross-feed (white\nabove dashed line), B \u2192D\u2217\u2113+\u03bd (blue hatched), B \u2192D\u2113+\u03bd\n(yellow hatched), B \u2192D\u2217\u2217\u2113+\u03bd (black), B \u2192D\u2217\u03c4 +\u03bd (green),\nB \u2192D\u03c4 +\u03bd (red).\nscenario is, however, disfavored by B \u2192D(\u2217)\u03c4\u03bd measure-\nments discussed above, so it is not clear what the implica-\ntions might be for the purely leptonic B decay modes. It\nis, however, likely that these modes will play an important\n0\n0.2\n0.4\n0.6\n0.8\n1\nR(D)\n0.2\n0.4\n0.6\n0.8\ntan /m (GeV )\n`\n\u00ef1\nH+\n0\n0.2\n0.4\n0.6\n0.8\n1\nR(D*)\n0.2\n0.3\n0.4\nFigure 17.10.10. Comparison of the BABAR measurements\nof R(D) (top) and R(D\u2217) (bottom) with the prediction of\nthe Type-II 2HDM (red curves). The tan \u03b2/MH dependence of\nthe BABAR R(D(\u2217)) results (blue shaded bands) arises due to\nchanges to the signal kinematics in the case that the process is\nmediated by a H\u00b1 rather than a W \u00b1. The SM case corresponds\nto the case tan \u03b2/MH = 0, and the favored values for tan \u03b2/MH\ndi\ufb00er for R(D) and R(D\u2217). Plot is taken from Lees (2012e).\nrole in elucidating any new physics that might be present\nin B \u2192D(\u2217)\u03c4\u03bd.\nMeasurement of the radiative decay B+ \u2192\u2113+\u03bd\u03b3 has\nproven to be problematic at the current generation of B\nFactories, but the method using hadronic tag B recon-\nstruction (Aubert, 2009a) appears to o\ufb00er a solution that\ncan permit observation and measurement of this branch-\ning fraction at future high-luminosity B Factories. Al-\nthough these modes do not provide interesting new physics\nsensitivity, they may be relevant for the interpretation of\nprecision measurements of B+ \u2192\u2113+\u03bd and of B \u2192\u03c0+\u03c0\u2212\ndecays.\nFuture measurements of B \u2192D(\u2217)\u03c4\u03bd will greatly im-\nprove our understanding of this process. The recent BABAR\nstudy of R(D(\u2217)) (Lees, 2012e) provides a conceptually ro-\nbust experimental method for measuring these decays us-\ning the ratio R(D(\u2217)), but this analysis yields results that\nare incompatible both with the SM and the \u201cpreferred\u201d\n2HDM scenario that underlies the MSSM. These results\nhave not as of yet been independently con\ufb01rmed by Belle,\nbut may provide a tantalizing glimpse of new physics cou-\npling to third-generation leptons. In addition to deter-\nmining R(D(\u2217)), future measurements of B \u2192D(\u2217)\u03c4\u03bd at\nhigh luminosity B Factories also have the potential to pre-\ncisely study the q2 distributions or angular properties of\nthese decays, providing an additional handle on possible\nbeyond-SM contributions. However, these studies will be\nconfronted with the same experimental challenges as the\nBABAR measurement, in particular the modeling of the\nmissing mass, lepton momentum and Eextra distributions,\nand the understanding of background contributions from\nsemileptonic decays with higher mass open-charm states.\nAll of these issues will need to be addressed with increased\nprecision in order to make substantial improvements to the\n\n409\nexisting R(D(\u2217)) measurements at future high luminosity\nexperiments.\n\n410\n17.11 Rare and forbidden B decays\nEditors:\nSteve Robertson (BABAR)\nYoungjoon Kwon (Belle)\nAdditional section writers:\nMatthew Bellis, Fergus Wilson\nWhile many B decay modes are \u201crare\u201d in the sense\nthat they have small branching fractions, the term usually\nrefers speci\ufb01cally to modes which are suppressed within\nthe SM due to some property of the decay, often related to\na symmetry or conserved quantum number. The interest\nin these modes arises from the possibility that contribu-\ntions from physics beyond the SM may not be similarly\nsuppressed. In this sense, many of the modes discussed in\nSections 17.9 and 17.10 would be considered rare decays\nas well, since for example the tree-level process B+ \u2192\u2113+\u03bd\nis suppressed by helicity conservation when the decay is\nmediated by a SM W + boson. New-physics models permit\npossible contributions to this process which are mediated\nby a scalar charged Higgs boson and lead to potentially\nobservable deviations from the SM expectations for the\nbranching fractions. Similarly, the \ufb02avor changing neu-\ntral current modes in Section 17.9 are suppressed due to\nthe absence of tree-level FCNCs in the SM. Possible new-\nphysics contributions, which also enter at one-loop level,\ncan therefore be comparable in size to the suppressed SM\ncontributions. The decays B0 \u2192\u2113+\u2113\u2212and B0 \u2192\u03bd\u00af\u03bd, dis-\ncussed below in Sections 17.11.1 and 17.11.2, are in fact\nexactly such processes: highly suppressed SM electroweak\npenguin FCNC processes which can be strongly enhanced\nin beyond-SM models by neutral Higgs boson contribu-\ntions or other new physics. The distinction as to which\nmodes are considered \u201crare\u201d is obviously somewhat arbi-\ntrary.\nIn contrast, \u201cforbidden\u201d modes are those which are\nexpected to proceed primarily through processes beyond\nthe SM, which typically violate quantum numbers that\nare conserved within the SM such as charged lepton \ufb02a-\nvor and number, and baryon number. These decays are\nforbidden in the SM in the absence of neutrino masses.\nHowever, lepton \ufb02avor is not associated with a fundamen-\ntal conservation law in the SM and in fact the existence\nof neutrino mixing explicitly requires that lepton \ufb02avor\nis not conserved in the neutrino sector. This in turn im-\nplies lepton \ufb02avor violation (LFV) in the charged lepton\nsector as well, via loop processes which contain neutrinos.\nHowever, the expected rate for such processes is many\norders of magnitude below current or foreseen future ex-\nperimental sensitivity to these decay modes. Observation\nof LFV in B decays would therefore be unambiguous evi-\ndence for a new source of LFV beyond the SM. Similarly,\nlepton number is not protected by any fundamental con-\nservation law and in fact is explicitly violated if neutrinos\nare of Majorana type, i.e. if they are their own antipar-\nticles. Consequently, searches for lepton number violation\n(LNV), discussed in 17.11.5, can provide insight into the\nnature of neutrinos.\nWe discuss B0 \u2192\u2113+\u2113\u2212along with the radiative mode\nB0 \u2192\u2113+\u2113\u2212\u03b3 in Section 17.11.1 and the neutrino coun-\nterparts to these modes, B0 \u2192\u03bd\u00af\u03bd(\u03b3), in Section 17.11.2.\nWe describe B0\n(s) \u2192\u03b3\u03b3 in Section 17.11.3. Lepton \ufb02a-\nvor and lepton number violating modes are presented in\nSections 17.11.4 and 17.11.5, respectively, and searches\nfor baryon number violating modes are discussed in Sec-\ntion 17.11.6.\n17.11.1 B0 \u2192\u2113+\u2113\u2212(\u03b3)\nB0 \u2192\u2113+\u2113\u2212decays are expected to proceed through the\ndiagrams shown in Figure 17.11.1 within the SM (SM).\nThe branching fraction for the B0 \u2192\u2113+\u2113\u2212decays can be\nwritten to good accuracy as\nB(B0 \u2192\u2113+\u2113\u2212) =\nG2\nF \u03b12\n64\u03c03 sin4 \u03b8W\n\u00d7\n|V \u2217\ntbVtd|2\u03c4BM 3\nBf 2\nB\ns\n1 \u22124m2\n\u2113\nM 2\nB\n\u00b7 4m2\n\u2113\nM 2\nB\nY 2(m2\nt/M 2\nW ) .\n(17.11.1)\nThe equation reveals a high suppression of the decays due\nto the internal quark annihilation within the B meson\ninvolving a b \u2192d transition (CKM element |Vtd| and\nthe B meson decay constant fB) and helicity consider-\nations (helicity suppression factor m2\n\u2113/M 2\nB).93 The SM\nexpected branching fractions are of the order of 10\u221215\nand 10\u221210 for the e+e\u2212and \u00b5+\u00b5\u2212modes, respectively. In\nsome new-physics models, including those with two Higgs\ndoublets and Z-mediated FCNC, the branching fractions\ncould be enhanced by two orders of magnitude (Babu\nand Kolda, 2000; Bobeth, Ewerth, Kruger, and Urban,\n2001; Chankowski and Slawianowska, 2001; Choudhury\nand Gaur, 1999; Hewett, Nandi, and Rizzo, 1989).\nB0 \u2192\u03c4 +\u03c4 \u2212is much less helicity suppressed than\nB0 \u2192e+e\u2212and B0 \u2192\u00b5+\u00b5\u2212due to the large tau mass,\nwith a predicted branching fraction of order 10\u22127 (Harri-\nson and Quinn, 1998; Grossman, Ligeti, and Nardi, 1997).\nThe large masses of the tau leptons also provide the poten-\ntial for substantial enhancements due to Higgs couplings in\ntwo-Higgs-doublet models (Babu and Kolda, 2000; Logan\nand Nierste, 2000). However, due to the presence of multi-\nple neutrinos in the experimental \ufb01nal state (between two\nand four depending on the tau decay modes), the \u03c4 +\u03c4 \u2212\n\ufb01nal state is considerably more di\ufb03cult to access experi-\nmentally than the e+e\u2212and \u00b5+\u00b5\u2212modes. The e+e\u2212and\n\u00b5+\u00b5\u2212searches are described in 17.11.1.1, and the \u03c4 +\u03c4 \u2212\ndecay in 17.11.1.2.\nAlthough B0 \u2192\u2113+\u2113\u2212\u03b3 (\u2113= e or \u00b5) decays can oc-\ncur by emitting a photon from any of the initial or \ufb01nal-\nstate fermions of B0 \u2192\u2113+\u2113\u2212, the dominant contribu-\ntion is due to photon emission from one of the initial-\nstate quarks, since this process is free from the helic-\nity suppression associated with B0 \u2192\u2113+\u2113\u2212. In the SM,\n93 The function Y (m2\nt/M 2\nW ) is known with good accuracy at\nNLO.\n\n411\nFigure 17.11.1. SM diagrams for B0 \u2192\u2113+\u2113\u2212.\nthe expected B0 \u2192\u2113+\u2113\u2212\u03b3 branching fractions are about\n10\u221210 (Aliev, Ozpineci, and Savci, 1997; Eilam, Halperin,\nand Mendel, 1995). Observation of such signals with cur-\nrent sensitivities of BABAR and Belle would provide clear\nevidence for new physics. B0 \u2192\u2113+\u2113\u2212\u03b3 is discussed in\nSection 17.11.1.3.\n17.11.1.1 B0 \u2192\u2113\u00b1\u2113\u2032\u2213(\u2113, \u2113\u2032 = e, \u00b5)\nSearches for B0 decays to pairs of light leptons, \u2113= e, \u00b5,\nhave been performed at both B Factories and at hadron\ncolliders; the latter are able to probe not only B0 but also\nB0\ns decays. Searches for B0 \u2192e+e\u2212and B0 \u2192\u00b5+\u00b5\u2212as\nwell as the LFV mode B0 \u2192e\u00b1\u00b5\u2213by BABAR and Belle\nprovided the most stringent limits on new physics in these\nmodes until around 2008, when they were superseded by\nresults from Run-II at the Tevatron. LHC experiments\nhave now pushed the experimental results considerably\nbeyond the current B Factory sensitivities. The BABAR\nand Belle analyses are described in the following.\nBABAR has searched for these decays in a data sample\nof 384\u00d7106 BB pairs (Aubert, 2008as). The signal candi-\ndates are reconstructed by pairing oppositely charged lep-\ntons. Leptons are identi\ufb01ed with stringent requirements\nwhich retain \u223c93% (\u223c73%) of e\u00b1 (\u00b5\u00b1), while less than\n\u223c0.1% (\u223c3%) of pions are misidenti\ufb01ed as electrons\n(muons). The signal candidates are required to satisfy\nmES > 5.2 GeV/c2 and |\u2206E| < 0.15 GeV. To partially\nrecover the energy lost by electrons due to \ufb01nal-state ra-\ndiation or bremsstrahlung, photons consistent with orig-\ninating from the e+ or e\u2212track have their 4-momentum\nadded to the track. Using MC simulations, peaking back-\nground contributions from B0 \u2192h+h\u2032\u2212(h, h\u2032 = \u03c0 or K)\ndecays are estimated to be of the order of 10\u22124 or less. Af-\nter applying the lepton ID requirements, other BB back-\nground is found to be negligible. The backgrounds from\nnon-BB events, such as q\u00afq (q = u, d, s, c) continuum and\n\u03c4 +\u03c4 \u2212production, are reduced by using event shape vari-\nables which are combined into a single Fisher discrimi-\nnant F. The signal yields for e+e\u2212, \u00b5+\u00b5\u2212and e\u00b1\u00b5\u2213(see\nSection 17.11.4 for further discussion of LFV modes) are\nindependently obtained by maximum likelihood (ML) \ufb01ts\nto mES, \u2206E and F, where the p.d.f.s used in the like-\nlihood function is composed of an uncorrelated product\nof the p.d.f.s of the individual discriminating variables.\nAs an example the distribution of \u2206E in the search for\nB0 \u2192\u00b5+\u00b5\u2212is shown in Fig. 17.11.2. No signi\ufb01cant ex-\ncesses of signal were seen in any modes, and the 90% C.L.\nupper limits on the corresponding branching fractions are\ncalculated utilizing a Bayesian approach assuming a \ufb02at\npositive prior and including systematic uncertainties. The\nobtained upper limit is, at 90% C.L., 11.3 (5.2)\u00d710\u22128 for\nthe e+e\u2212(\u00b5+\u00b5\u2212) mode (see Table 17.11.1).\n]\n\u00b5\n\u00b5\n0\n (GeV) [B\nE\n\u2206\n\u22120.15\n0\n0.15\nEvents /0.02 MeV\n0\n10\n20\n]\n\u00b5\n\u00b5\n\u2192\n (GeV) [B\nE\n\u2206\n\u22120.15\n0\n0.15\nEvents /0.02 MeV\n0\n10\n20\n \nFigure 17.11.2. \u2206E distribution of selected B0 \u2192\u00b5+\u00b5\u2212\ncandidates (Aubert, 2008as). The solid curve is the background\nsPlot (see Section 11.2.3) and the dashed curve is the expected\ndistribution of signal with an arbitrary normalization.\nUsing a data sample of 85 million BB pairs, Belle has\nalso searched for these modes (Chang, 2003) and obtained\n90% C.L. upper limits of 1.9 (1.6) \u00d7 10\u22127 for the e+e\u2212\n(\u00b5+\u00b5\u2212) mode. These upper limits are calculated based on\nthe likelihood ratio ordering (Feldman and Cousins, 1998)\nand including systematic uncertainties using the POLE\nprogram\n(Conrad, Botner, Hallgren, and Perez de los\nHeros, 2003). 94\nThe Belle analysis included missing-momentum-based\nquantities in its Fisher discriminant, which signi\ufb01cantly\nreduced the important class of background due to double\nsemileptonic charm decays from the continuum. Using the\nPati-Salam model (Kuznetsov and Mikheev, 1994), which\npredicts a vector leptoquark at a mass associated with the\nscale of the breaking of an SU(4) gauge group to the usual\ncolor SU(3) group, along with the assumption that there\nare no other colored particles between the t-quark mass\nand the mass, MLQ, of the Pati-Salam leptoquark, Belle\nhas obtained MLQ > 46 TeV/c2 at the 90% C.L..\n17.11.1.2 B0 \u2192\u03c4 +\u03c4 \u2212\nBABAR published a search for B0 \u2192\u03c4 +\u03c4 \u2212(Aubert, 2006b)\nbased on a data sample of (232 \u00b1 3) \u00d7 106 BB events\n(210 fb\u22121) and using the method of exclusive hadronic\n94 The POLE program calculates an upper limit with an\nextension of the Feldman Cousins method\n(Feldman and\nCousins, 1998) by incorporating systematic uncertainties on\nthe background yields and signal reconstruction e\ufb03ciency.\nThese uncertainties are incorporated in the calculation by in-\ntegrating the p.d.f.s that parameterize them.\n\n412\ntag reconstruction of the accompanying B meson as de-\nscribed in Section 7.4.1. Evidence for a B0 \u2192\u03c4 +\u03c4 \u2212de-\ncay is sought by considering all charged tracks and clus-\nters which are not associated with a B candidate, \u201cBtag\u201d,\nwhich has been exclusively reconstructed in one of a large\nnumber of hadronic decay modes, as illustrated in Fig-\nure 17.11.3. Only events with \u201cone-prong\u201d decays of both\ntaus are considered, so signal events are required to con-\ntain exactly two charged tracks on the signal side, each\nof which is identi\ufb01ed as an electron, muon or pion. Each\nof the two tau leptons can potentially decay to \u03c4 \u2192e\u03bd\u00af\u03bd,\n\u03c4 \u2192\u00b5\u03bd\u00af\u03bd, \u03c4 \u2192\u03c0\u03bd or \u03c4 \u2192\u03c1(770)\u03bd. Signal topologies\nare therefore de\ufb01ned corresponding to each combination\nof \u03c4 +\u03c4 \u2212decay modes. Charged pion tracks are considered\nto be \u03c1(770) candidates if a \u03c00 candidate, reconstructed\nfrom a pair of photon clusters, can be combined with the\n\u03c0 track to give 0.6 < m\u03c0\u03c00 < 1.0 GeV/c2. Events with\nany additional \u03c00 candidates are rejected, and the sum of\nany remaining calorimeter energy (Eextra) is required to\nbe less than 110 MeV (summing all clusters with energy\nexceeding 30 MeV).\nFigure 17.11.3. Illustration of a B0 \u2192\u03c4 +\u03c4 \u2212event in which\nthe associated B0 is reconstructed as a hadronic Btag. The\ntau decay modes are depicted as \u03c4 \u2212\u2192e\u2212\u03bd\u00af\u03bd and \u03c4 + \u2192\u03c0+\u00af\u03bd.\nSince the B0 4-vector is determined by the tag reconstruction,\nthe signal B0 4-vector can be obtained using the known CM\nenergy, and the event missing energy can be fully attributed\nto the neutrinos.\nBackgrounds from B decays to open charm, which sub-\nsequently decay to \ufb01nal states containing a strange quark,\nare suppressed by vetoing events in which any signal can-\ndidate track is identi\ufb01ed as a K+, or if the combination\nof the two tracks is consistent with originating from a\nK0\nS \u2192\u03c0+\u03c0\u2212decay. Note that this background is large\ndue to the Cabibbo favored b \u2192c \u2192s transitions. Simi-\nlarly, events possessing a calorimeter cluster which is iden-\nti\ufb01ed as a K0\nL candidate, based on cluster energy and event\nshape information, are rejected.\nAdditional background suppression is obtained by ex-\nploiting correlations between the momenta and angular\ndistributions of the tau decay daughters in the signal B\nrest frame, which is estimated from the 4-vector of the\nreconstructed tag B. A set of neural networks, one for\neach of the \u03c4 +\u03c4 \u2212decay topologies, are trained to dis-\ncriminate signal from background based on four inputs:\nthe B rest frame momenta of the positively and nega-\ntively charged tau daughters, p+ and p\u2212, respectively,\ncos \u03b8 \u2261p+ \u00b7 p\u2212/p+p\u2212, and Eextra.\nSubstantial backgrounds remain following this selec-\ntion, primarily arising from b \u2192c \u2192s processes with sig-\nni\ufb01cant missing energy and no identi\ufb01ed kaon. Typically\nthese are B decays with an undetected K0\nL, with one or\nmore particles passing outside of the detector acceptance\nand/or semileptonic B or charm decays. A total of 281\u00b148\nbackground events are expected and 263 \u00b1 19 events are\nobserved in data, distributed across all modes. A 90% C.L.\nbranching fraction limit of B(B0 \u2192\u03c4 +\u03c4 \u2212) < 4.1 \u00d7 10\u22123\nis obtained. Because of the limited sensitivity imposed by\nthe high backgrounds, this analysis has not been repeated,\neither by BABAR with a larger data sample or by Belle.\n17.11.1.3 B0 \u2192\u2113+\u2113\u2212\u03b3 (\u2113= e, \u00b5)\nBABAR has searched for the radiative decays B0 \u2192\u2113+\u2113\u2212\u03b3\nin the \u2113= e, \u00b5 modes in an event sample of 320 \u00d7 106 BB\npairs (Aubert, 2008av). Signal MC events are simulated\nusing a leading-order calculation of the Wilson coe\ufb03cients\nC7, C9, and C10 (Dincer and Sehgal, 2001; see also the\ndiscussion in Section 17.9.1 of this book). Events are se-\nlected by combining a pair of oppositely-charged leptons\nand an energetic photon yielding B candidates within the\nregion |\u2206E| \u22640.5 GeV and 5.0 \u2264mES \u22645.3 GeV/c2.\nSignal candidates are required to lie in the smaller sig-\nnal region de\ufb01ned by \u22120.146(\u22120.112) \u2264\u2206E \u22640.082 GeV\nand 5.270 \u2264mES \u22645.289 GeV/c2 for the e+e\u2212\u03b3 (\u00b5+\u00b5\u2212\u03b3)\nmode, while the remainder of the larger region is used for\nbackground studies. The dominant backgrounds include:\n(1) un-modelled higher-order QED and two-photon pro-\ncesses for the e+e\u2212\u03b3 mode, (2) B decays where a \u03c00 pro-\nduces the photon or a J/\u03c8 (or \u03c8(2S)) produces one or\nboth of the leptons, and (3) continuum processes. Back-\ngrounds of type (1) are suppressed by imposing \ufb01ducial\nconstraints on the electrons, cutting on event shape vari-\nables, requiring that the photon energy exceeds 0.3 GeV\nand requiring that there are at least 5 charged tracks and\n10 calorimeter clusters in the event. The B decay back-\ngrounds are suppressed by \u03c00 and J/\u03c8 (or \u03c8(2S)) vetoes.\nContinuum backgrounds are rejected by using a combina-\ntion of event shape variables (see Chapter 9). A neural net-\nwork is constructed using event shape, angular and kine-\nmatic variables and trained using MC to discriminate be-\ntween signal events and remaining background events. Af-\nter applying all selection requirements, the expected num-\nber of background events is estimated from data sideband\nregions to be 1.75\u00b11.38\u00b10.36 and 2.66\u00b11.40\u00b11.58 events\nfor e+e\u2212\u03b3 and \u00b5+\u00b5\u2212\u03b3, respectively, where the quoted\nerrors are statistical and systematic. The background is\ndominated by non-B backgrounds and so is estimated by\nextrapolation from the signal sideband regions. One event\nis found in the signal region in data for each mode, con-\nsistent with the size of the expected backgrounds. The\n90% C.L. upper limits on the corresponding branching\nfractions are determined using a frequentist method (Bar-\nlow, 2002): B(B0 \u2192e+e\u2212\u03b3) < 1.2 \u00d7 10\u22127 and B(B0 \u2192\n\n413\n\u00b5+\u00b5\u2212\u03b3) < 1.6 \u00d7 10\u22127. Belle has not reported any results\nfor these decay modes.\nAll the results described in this subsection are summa-\nrized in Table 17.11.1.\n17.11.2 B0 \u2192invisible\nThe decay of a B meson into \u03bd\u00af\u03bd pairs is similar from a the-\noretical point of view to the leptonic decays B0 \u2192\u2113+\u2113\u2212\ndescribed in Section 17.11.1. It is extremely suppressed\nin the SM due to helicity considerations, and is only per-\nmitted, albeit at a rate orders of magnitude below experi-\nmental sensitivity, due to the miniscule but non-zero neu-\ntrino mass. As is the case with other radiative decays, for\nexample B0 \u2192\u2113+\u2113\u2212\u03b3 (Section 17.11.1) and B+ \u2192\u2113+\u03bd\u03b3\n(Section 17.10.2), the radiation of a photon from an initial-\nstate quark can remove this helicity suppression, resulting\nin a larger branching fraction than the non-radiative pro-\ncess. SM branching fractions for B0 \u2192\u03bd\u00af\u03bd and B0 \u2192\u03bd\u00af\u03bd\u03b3\nhave been computed to be \u223c1 \u00d7 10\u221225 and 2 \u00d7 10\u22129,\nrespectively (Badin and Petrov, 2010). In practice, exper-\nimental searches for these modes cannot directly detect\nthe neutrinos, and so are more correctly considered to be\nsearches for B \u2192Emiss(+\u03b3), where Emiss represents miss-\ning energy from all sources including not only neutrinos,\nbut also possible new-physics particles which do not inter-\nact in the detector. As such, they are frequently referred\nto as \u201cB0 \u2192invisible(+\u03b3)\u201d.\nNew stable particles which do not interact in the de-\ntector are potential dark matter candidates. Consequently,\nthese decay modes are interesting probes of new physics.\nDecays to pairs of such particles, B0 \u2192\u03c70\u03c70(\u03b3) where\n\u03c70 are massive scalars, are not helicity suppressed and\nhence can occur at rates substantially above the SM rate\nfor B \u2192invisible decays. A phenomenological model for\nB0 \u2192\u00af\u03bd\u03c70\n1, where \u03c70\n1 is a neutralino, predicts a branch-\ning fraction in the range 10\u22127\u201310\u22126 (Dedes, Dreiner, and\nRichardson, 2001). Since both decay products would be\nundetected, the experimental signature would be B \u2192\ninvisible. Models with large extra dimensions (Agashe,\nDeshpande, and Wu, 2000; Agashe and Wu, 2001; Davoudi-\nasl, Langacker, and Perelstein, 2002) can also result in\nsigni\ufb01cant enhancements to the invisible decay rate.\nBecause the signature for B0 \u2192invisible(\u03b3) decays is\nthe absence of detector activity (i.e. charged tracks and\nneutral calorimeter clusters) associated with an identi\ufb01ed\nB meson decay, the analysis strategy relies on exclusive\ntag-B reconstruction (see Section 7.4). Tag reconstruc-\ntion serves the dual purpose of identifying the event as\nan \u03a5(4S) \u2192B0B0 transition, and uniquely associating\nall detector activity with either the tag B or the signal\nB candidate. Unlike other modes which use this method,\nfor example B0 \u2192\u03c4 \u00b1\u2113\u2213and B+ \u2192h+\u03c4 \u00b1\u2113\u2213discussed\nin Section 17.11.4, there is no kinematic advantage to be\ngained from knowledge of the signal B candidate 4-vector\n(estimated from the tag B 4-vector). Consequently, tag B\nreconstruction based on semileptonic B decays, which pos-\nsess additional missing energy due to the un-reconstructed\nneutrino, is equally viable to hadronic B tagging for these\nsearches, although signal e\ufb03ciencies and background rates\ndi\ufb00er signi\ufb01cantly between the two methods.\nTo date, only Belle has published limits on B0 \u2192\ninvisible using hadronic tag reconstruction (Hsu, 2012),\nwhile BABAR has only published results based on semi-\nleptonic tag reconstruction. A recent BABAR paper (Lees,\n2012g) updated the results of an earlier analysis (Aubert,\n2004y) to include the full BABAR data sample. BABAR also\nreports limits on the B0 \u2192\u03bd\u00af\u03bd\u03b3 branching fraction for\nE\u03b3 > 1.2 GeV and assuming decay kinematics based on a\nconstituent quark model (Lu and Zhang, 1996).\nIn the BABAR analysis, semileptonic Btag candidates\nare reconstructed in the modes B0 \u2192D(\u2217)\u2212\u2113+\u03bd. Details of\nthe BABAR semileptonic tag reconstruction procedure can\nbe found in Section 7.4.2. The D(\u2217)\u2212candidates are com-\nbined with identi\ufb01ed electrons or muons having lab-frame\nmomentum greater than 800 MeV, and the \u2113+ \u2013 D(\u2217)\u2212\ncombination is required to be consistent with a common\ndecay vertex. B0 candidates are then selected by requir-\ning the \u2113+ \u2013 D(\u2217)\u2212combination to be kinematically con-\nsistent with a B0 \u2192D(\u2217)\u2212\u2113+\u03bd event, i.e. that the only\nmissing particle is the unobserved neutrino. The quantity\ncos \u03b8B,D(\u2217)\u2212\u2113+ is computed as\ncos \u03b8B,D(\u2217)\u2212\u2113+ = 2EBED(\u2217)\u2212\u2113+ \u2212m2\nB \u2212m2\nD(\u2217)\u2212\u2113+\n2|pB||pD(\u2217)\u2212\u2113+|\n,\n(17.11.2)\nwhere ED(\u2217)\u2212\u2113+, pD(\u2217)\u2212\u2113+ and mD(\u2217)\u2212\u2113+ are the CM frame\nenergy, momentum 3-vector and the invariant mass of the\n\u2113+-D(\u2217)\u2212combination. The quantity mB is the nominal B\nmeson mass, while EB and |pB| are the expected B energy\nand momentum magnitude computed from the known CM\nenergy. The quantity cos \u03b8B,D(\u2217)\u2212\u2113+ represents the cosine\nof a physical angle only in the case of a correctly recon-\nstructed B0 \u2192D(\u2217)\u2212\u2113+\u03bd decay. For background events,\nhowever, it does not relate to a physical angle, and so\ncos \u03b8B,D(\u2217)\u2212\u2113+ can assume values outside of the mathemat-\nically allowed region [\u22121, 1]. Lees (2012g) accepts events\nin the region \u22125.5 < cos \u03b8B,D(\u2217)\u2212\u2113+ < 1.5 in order to re-\ntain high signal e\ufb03ciency while accounting for detector\nresolution e\ufb00ects which produce values slightly outside of\nthe allowed region. The larger range for negative values\nwas chosen to implicitly include contributions from higher-\nmass open charm states in which some of the decay prod-\nucts have not been explicitly reconstructed.\nAfter identifying a well-reconstructed B0 \u2192D(\u2217)\u2212\u2113+\u03bd\ncandidate (and an energetic photon in the case of B0 \u2192\n\u03bd\u00af\u03bd\u03b3), signal events should have little or no additional de-\ntector activity. Consequently, the signal selection requires\nthat no additional tracks are present in the event, there is\nonly limited activity in the calorimeter, and the missing\nmomentum vector of the event is required to point within\nthe detector \ufb01ducial acceptance.\nAdditional background suppression is obtained by us-\ning a neural network which includes as inputs the CM-\nframe lepton momentum, cos \u03b8B,D(\u2217)\u2212\u2113+, and the angle\nbetween the event thrust axis and the D(\u2217)\u2212\u2113+ momen-\ntum direction. A number of additional inputs are included\nwhich are speci\ufb01c to the B0 \u2192\u03bd\u00af\u03bd and B0 \u2192\u03bd\u00af\u03bd\u03b3 searches.\n\n414\nTable 17.11.1. Summary of the results for B0 \u2192\u2113+\u2113\u2212(\u03b3), B0 \u2192\u03bd\u00af\u03bd(\u03b3) and B0\n(s,d) \u2192\u03b3\u03b3 modes.\nExperiment\nDecay Mode\nMethod\nNBB\nB upper limit\nReference\n(106)\n(90% C.L.)\nBelle\nB0 \u2192e+e\u2212\nsignal recon. only\n85\n1.9 \u00d7 10\u22127\nChang (2003)\nBABAR\nB0 \u2192e+e\u2212\nsignal recon. only\n384\n1.1 \u00d7 10\u22127\nAubert (2008as)\nBABAR\nB0 \u2192e+e\u2212\u03b3\nsignal recon. only\n320\n1.2 \u00d7 10\u22127\nAubert (2008av)\nBelle\nB0 \u2192\u00b5+\u00b5\u2212\nsignal recon. only\n85\n1.6 \u00d7 10\u22127\nChang (2003)\nBABAR\nB0 \u2192\u00b5+\u00b5\u2212\nsignal recon. only\n384\n0.52 \u00d7 10\u22127\nAubert (2008as)\nBABAR\nB0 \u2192\u00b5+\u00b5\u2212\u03b3\nsignal recon. only\n320\n1.6 \u00d7 10\u22127\nAubert (2008av)\nBABAR\nB0 \u2192\u03c4 +\u03c4 \u2212\nhadronic tag\n232\n4.1 \u00d7 10\u22123\nAubert (2006b)\nBelle\nB0 \u2192\u03bd\u00af\u03bd\nhadronic tag\n657\n13 \u00d7 10\u22125\nHsu (2012)\nBABAR\nB0 \u2192\u03bd\u00af\u03bd\nsemileptonic tag\n471\n2.4 \u00d7 10\u22125\nLees (2012g)\nBABAR\nB0 \u2192\u03bd\u00af\u03bd\u03b3\nsemileptonic tag\n471\n1.7 \u00d7 10\u22125\nLees (2012g)\nBelle\nB0 \u2192\u03b3\u03b3\nsignal recon. only\n111\n6.2 \u00d7 10\u22127\nVilla (2006)\nBABAR\nB0 \u2192\u03b3\u03b3\nsignal recon. only\n226\n3.2 \u00d7 10\u22127\ndel Amo Sanchez (2011k)\nBelle\nB0\ns \u2192\u03b3\u03b3\nsignal recon. at \u03a5(5S)\n23 fb\u22121\n8.7 \u00d7 10\u22126\nWicht (2008)\nThe quantity Eextra is constructed by summing the CM-\nframe energies of any remaining calorimeter clusters with\na laboratory-frame energy greater than 30MeV. Signal and\nbackground p.d.f.s are constructed from MC simulation\nfor Eextra, and an extended ML \ufb01t is performed on data to\nextract the signal and background yields. No evidence of\nsignal is seen in either the B0 \u2192\u03bd\u00af\u03bd or B0 \u2192\u03bd\u00af\u03bd\u03b3 search.\nBranching fraction upper limits at are obtained using a\nBayesian method which assumes a positive prior distri-\nbution (i.e. the observed negative signal yield does not\nresult in a more stringent branching fraction limit than\nif zero signal yield had been obtained). Upper limits of\nB(B0 \u2192\u03bd\u00af\u03bd) < 2.4\u00d710\u22125 and B(B0 \u2192\u03bd\u00af\u03bd\u03b3) < 1.7\u00d710\u22125\nare obtained at 90% C.L..\nThe Belle search (Hsu, 2012) utilizes hadronic B tag\nreconstruction based on B0 \u2192D(\u2217)\u2212h+ decays, where\nh+ can be \u03c0+, \u03c1(770)+, a1(1260)+, or D(\u2217)+\ns\n. Details\nof the reconstruction procedure can be found in Sec-\ntion 7.4.1. Compared with the semileptonic tag recon-\nstruction method used in the BABAR analysis, the hadronic\ntag method yields a somewhat lower reconstruction e\ufb03-\nciency, but, since it does not have to deal with an unob-\nserved neutrino, it also provides more stringent kinematic\nconstraints on the reconstructed Btag. As a consequence,\nbackgrounds arising from Btag misreconstruction are in-\nherently lower and a simpler signal selection procedure can\nbe used. In the Belle analysis, after hadronic Btag events\nare selected, B0 \u2192invisible candidate events are required\nto have no additional tracks and no \u03c00 or K0\nL candidates\nin the rest of the event. Continuum backgrounds are sup-\npressed by considering two quantities: the cosine of the\nangle of the Btag \ufb02ight direction (in the CM frame) rela-\ntive to the beam axis, cos \u03b8B, and the cosine of the angle\nof the Btag thrust axis relative to the beam axis, cos \u03b8T .\nSignal decays peak at zero in both of these variables.\nEvents are retained in the region \u22120.9 < cos \u03b8B < 0.9\nand \u22120.6 < cos \u03b8T < 0.6. Belle de\ufb01nes the variable EECL\nanalogously to Eextra for BABAR by summing the ener-\ngies of remaining calorimeter clusters. However, di\ufb00erent\ncluster energy thresholds are applied in di\ufb00erent regions\nof the calorimeter: 50 MeV in the barrel region, 100 MeV\nin the forward endcap and 150MeV in the backward end-\ncap. MC modeling of e\ufb03ciencies and kinematic distribu-\ntions is veri\ufb01ed by studying B0 \u2192D(\u2217)\u2212\u2113+\u03bd decays in\nevents with a hadronic Btag. The signal yield is extracted\nusing a two-dimensional, unbinned ML \ufb01t to the EECL\nand cos \u03b8B distributions, where the p.d.f.s for the two dis-\ntributions are treated as uncorrelated. A slight excess of\nsignal events is obtained in the \ufb01t, with a signi\ufb01cance of\napproximately 1.5\u03c3. A branching fraction upper limit of\nB(B0 \u2192invisible) < 1.3 \u00d7 10\u22124 at 90% C.L. is obtained,\nwhich is slightly worse than the expected sensitivity of\n1.1\u00d710\u22124. The di\ufb00erence in sensitivity between the BABAR\nand Belle analyses (2.4\u00d710\u22125 and 13\u00d710\u22125, respectively),\nroughly a factor of \ufb01ve, is thought to be primarily due to\nthe di\ufb00erence in tag e\ufb03ciencies between the hadronic and\nsemileptonic methods, but also re\ufb02ects di\ufb00erent optimiza-\ntions of the level of background between the two experi-\nments.95 The observed distributions of Eextra (EECL) are\nshown in Fig.\n17.11.4 for both measurements. It is not\nclear at this point how the sensitivities of the two tag\nmethods compare for B0 \u2192invisible, since neither exper-\niment has performed these searches using both methods.\nThe details of the signal selection, in particular the detec-\ntor acceptance and extra energy environment, di\ufb00er su\ufb03-\nciently between BABAR and Belle that it is di\ufb03cult to draw\n\ufb01rm conclusions regarding future B Factory sensitivities.\n17.11.3 B0 \u2192\u03b3\u03b3 and B0\ns \u2192\u03b3\u03b3\nThe B0 \u2192\u03b3\u03b3 mode is related to the b \u2192d\u03b3 process,\nas the \u00afb and d quarks in the initial state B0 annihilate\n95 The BABAR measurement optimizes the selection in order\nto achieve the most stringent upper limit, assuming no signal\nevents to be found.\n\n415\n (GeV)\nextra\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents/(0.03 GeV)\n-10\n-5\n0\n5\n10\n15\n20\n25\n30\n35\n40\n (GeV)\nextra\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents/(0.03 GeV)\n-10\n-5\n0\n5\n10\n15\n20\n25\n30\n35\n40\nBABAR\nTotal\nBackground\nSignal\nData\n (GeV)\nECL\nE\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nEvents/0.05 GeV\n-2\n0\n2\n4\n6\n8\n10\n12\n14\nFigure 17.11.4. Distribution of Eextra in the BABAR search for\nB0 \u2192invisible using semileptonic tagged events (Lees, 2012g).\nLines represent the result of the \ufb01t. Distribution of a similar\nquantity (bottom, called EECL at Belle) for the search in the\nsame decay mode using hadronic tagged events (Hsu, 2012).\nLines are the result of the \ufb01t (lightly hatched yellow region is\nthe background contribution and the solid red line the total).\nthrough a penguin loop. Moreover, it involves radiation\nof one additional photon. Therefore this mode is highly\nsuppressed in the SM, with a branching fraction which\nis estimated to be (3.1+6.4\n\u22121.6) \u00d7 10\u22128(Bosch and Buchalla,\n2002a).\nBABAR (del Amo Sanchez, 2011k) used 226M B0B0\n(426 fb\u22121) to search for B0 \u2192\u03b3\u03b3. Two photons with\nCM energies within 1.15 \u2264E\u2217\n\u03b3 \u22643.50 GeV are selected\nand required to satisfy mES > 5.1 GeV/c2 and |\u2206E| \u2264\n0.50 GeV. Background from e+e\u2212\u2192q\u00afq continuum and\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212events, respectively, are suppressed by us-\ning the Fox-Wolfram moment ratio, R2 (see Section 9.3),\nand by requiring the number of reconstructed charged\ntracks to be larger than two. The dominant sources of\nbackground, at this stage, are \u03c00 and \u03b7 decays to \u03b3\u03b3.\nDiscrimination against these backgrounds is obtained by\ncombining each of the candidate photons (\u03b3) with other\nphotons in the event (\u03b3\u2032), and using the \u03b3\u03b3\u2032 invariant mass\nand the energy E\u03b3\u2032 of the other photon as input variables\nto a likelihood ratio.\nBackgrounds due to merged photons from \u03c00 decays\nare suppressed by the energy distribution shape of the\nphoton candidate in the calorimeter. Further suppression\nof the remaining continuum events is performed with a\nneural network (see Chapter 4). After all selections are\napplied, the peaking background contribution from rare\nB decays is estimated to be 1.18 \u00b1 0.22 events. Using an\nunbinned extended ML \ufb01t to mES and \u2206E, the signal yield\nNsig is determined to be Nsig = 21.3+12.8\n\u221211.8 events, with\nstatistical signi\ufb01cance of 1.8\u03c3. The systematic error on\nthe branching fraction, 12.1%, is dominated by the \ufb01tting\nuncertainty (9.9%), and is included by convolution with\nthe likelihood function. A branching fraction upper limit\nB(B0 \u2192\u03b3\u03b3) < 3.2 \u00d7 10\u22127 (at the 90% C.L.) is obtained.\nIn an earlier analysis (Villa, 2006) based on data col-\nlected prior to 2004, Belle used a limited data sample of\n111M BB events to search for B \u2192\u03b3\u03b3. This search set a\nbranching fraction upper limit B(B \u2192\u03b3\u03b3) < 6.2 \u00d7 10\u22127\nat the 90% C.L., but the analysis was notable for the\nfact that it su\ufb00ered due to calorimeter backgrounds aris-\ning from out-of-time signals from previous bunch cross-\nings. As a result of the relatively long decay time of the\nscintillation light from the CsI(Tl) crystals in the Belle\ncalorimeter, there is a non-negligible probability that a\nresidual calorimeter signal from a previous QED event,\ntypically e+e\u2212\u2192e+e\u2212, can persist long enough to pro-\nduce a \u201cfake\u201d photon cluster in a later \u03a5(4S) \u2192BB event.\nIf two back-to-back clusters from such a Bhabha event are\npresent, and the reduced energy of the pair happens to\nmatch the B mass, then it resembles the B signal in the\nmES distribution. This background can be mostly removed\nusing the timing information of the calorimeter signals,\nhowever, this information was not available in the reduced\ndata format for data processed before summer 2004, and\nin particular for the sample used for the Villa (2006) anal-\nysis. In subsequent reprocessings of this data sample (see\nSection 3.3), this information was made available however,\nat the time of writing, the analysis has not been updated.\nIn the existing measurement the background composed of\nphotons from the continuum events (mainly decays of \u03c00\nand \u03b7 mesons) is suppressed by the selection based on\nthe polar angle of the more energetic photon. The issue\nof out-of-time calorimeter clusters has also been studied\nby BABAR, as a potential background for other B decay\nmodes which rely on neutral clusters, in particular b \u2192s\u03b3\n(Section 17.9) and B0 \u2192\u03c00\u03c00. While this background\nwas not an issue for the BABAR B0 \u2192\u03b3\u03b3 study, it is po-\ntentially a concern for future high-luminosity experiments\nin which the Bhabha rate is much higher than the present\ngeneration of experiments.\n\n416\nIn comparison to B0 \u2192\u03b3\u03b3, the B0\ns \u2192\u03b3\u03b3 decay is\nfavored by \u223c|Vts/Vtd|2, with the SM prediction B(B0\ns \u2192\n\u03b3\u03b3) \u223c(0.5\u22121.0)\u00d710\u22126. Production of Bs mesons does not\noccur at the \u03a5(4S), hence a large sample of \u03a5(5S) events\nis required. BABAR did not collect signi\ufb01cant data at this\nenergy. However, Belle obtained a substantial sample (see\nTable 3.2.1). Using 23.6 fb\u22121 of such data, Belle (Wicht,\n2008) performed a search for B0\ns \u2192\u03b3\u03b3 decays. Details of\nthe measurement can be found in Section 23.3.6, only the\nmain results are presented at this place. The signal yield\nis determined by an unbinned extended ML \ufb01t to mES\nand \u2206E. Figure 17.11.5 shows the projections to the \ufb01t\nvariables, mES and \u2206E. No signal is observed. Including\nthe systematic error of +21\n\u221219% which is dominated by the\nuncertainties in the number of B0\ns events in the \u03a5(5S) \u2192\nb\u00afb process (+16\n\u221213%), the 90% C.L. branching fraction upper\nlimit is determined to be B(B0\ns \u2192\u03b3\u03b3) < 8.7 \u00d7 10\u22126. This\nlimit is about an order of magnitude larger than the SM\nprediction.\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n-4\n-2\n0\n2\n4\n6\n8\n10\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n-4\n-2\n0\n2\n4\n6\n8\n10\nE (GeV)\n\u2206\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.11 GeV )\n-2\n0\n2\n4\n6\n8\n10\nE (GeV)\n\u2206\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.11 GeV )\n-2\n0\n2\n4\n6\n8\n10\nFigure 17.11.5. mES (left; called Mbc on the plot) and \u2206E\n(right) data yield (points) and \ufb01t results for B0\ns \u2192\u03b3\u03b3 in the\nBelle analysis (Wicht, 2008). The solid black curve represents\nthe overall \ufb01t, while the dashed red and solid blue curves repre-\nsent the continuum/combinatorial background and signal com-\nponents of the \ufb01t, respectively. See Chapter 23 for an expla-\nnation of the structure of the mES distribution. On the \u2206E\nprojection, mES > 5.4 GeV/c2 is required to select only the\nB\u2217\nsB\u2217\ns contributions from \u03a5(5S). The \ufb01t returns a slight nega-\ntive yield, consistent with zero within the data statistical un-\ncertainties.\n17.11.4 Lepton \ufb02avor violating modes\nLepton \ufb02avor violation is permitted within the SM if non-\nzero neutrino masses are included, since mixing of neu-\ntrino generations can then occur. LFV in the charged lep-\nton sector can then occur in processes which contain one\nor more neutrinos as internal lines in any contributing\nFeynman diagram. However, the expected rates for LFV\nB decays via this mechanism are far beyond current or\nexpected future experimental sensitivity. Potentially mea-\nsurable rates can however result from non-SM contribu-\ntions, since most models do not explicitly conserve lepton\n\ufb02avor. In models with Higgs-mediated LFV, modes with\nheavier leptons generally are expected to exhibit larger\nLFV than modes with lighter leptons. However, experi-\nmental searches for modes containing tau leptons in the\n\ufb01nal state tend to be more di\ufb03cult due to the multiple\ndecay modes of the tau and missing energy resulting from\nthe presence of one or more neutrinos. Consequently, ex-\nperimental limits on \u00b5 - e LFV modes tend to be more\nstringent than \u03c4 - e or \u03c4 - \u00b5. As many of the proposed\nmechanisms for LFV tend to have couplings which favor\nheavier-generation leptons, the experimental limits from\nLFV modes with tau leptons can still provide interesting\nconstraints on the parameters of these models.\nMany lepton \ufb02avor violation searches, particularly\nthose containing only \ufb01rst and second generation lep-\ntons, are performed as \u201cincidental\u201d studies along with\nrelated non-LFV modes. This is the case, for example,\nfor B0 \u2192\u00b5\u00b1e\u2213and B \u2192K(\u2217)\u00b5\u00b1e\u2213, which have been\npublished by both BABAR and Belle along with the corre-\nsponding B0 \u2192\u2113+\u2113\u2212modes (discussed in Section 17.11.1)\nand B \u2192K(\u2217)\u2113+\u2113\u2212modes (see Section 17.9), respec-\ntively, as well as for D0 \u2192e\u00b1\u00b5\u2213searched for together\nwith D0 \u2192\u2113\u00b1\u2113\u2213decays (Section 19.1.8). In general, these\nanalyses have few unique features which distinguish them\nfrom the related non-LFV modes, hence we do not discuss\nthem further in this section. For completeness, we tabulate\nthe results in Table 17.11.2. In several instances however,\nBABAR and Belle have published dedicated searches for\nspeci\ufb01c lepton \ufb02avor or lepton number violating decays.\nSearches involving \ufb01nal state tau leptons generally re-\nquire special techniques to overcome the challenges pre-\nsented by the missing neutrinos and lack of a distinc-\ntive tau signature. In particular, tau decays to leptonic\n\ufb01nal states, \u03c4 \u2192\u2113\u03bd\u00af\u03bd, are three-body \ufb01nal states with\ntwo unobserved neutrinos, providing essentially no kine-\nmatic constraints that can be exploited experimentally.\nTau decays to hadronic \ufb01nal states are largely indistin-\nguishable from B and continuum backgrounds containing\ncharged and neutral pions. To overcome these limitations,\nhadronic tag reconstruction (see Section 7.4.1) has been\nused in BABAR searches for B+ \u2192h+\u03c4 \u00b1\u2113\u2213(17.11.4.1) and\nB0 \u2192\u03c4 \u00b1\u2113\u2213(17.11.4.2). As is the case with other studies\nwhich use this method, the resulting sensitivity is limited\nprimarily by the very low signal e\ufb03ciency. Hadronic tag\nreconstruction provides a number of kinematic advantages\nfor these particular searches, since knowledge of the sig-\nnal B 4-vector (inferred from the Btag 4-vector) allows\nthe 2-body kinematics of B0 \u2192\u03c4 \u00b1\u2113\u2213to be exploited and,\nin both B0 \u2192\u03c4 \u00b1\u2113\u2213and B+ \u2192h+\u03c4 \u00b1\u2113\u2213, permits the 4-\nvector of the daughter tau to be uniquely determined from\nthe observed non-tau decay daughters.\nBecause they can potentially proceed via a \u201cCKM-\nfavored\u201d b - s FCNC process (see Section 17.9) rather\nthan a b - d FCNC process in which the quarks anni-\nhilate, B+ \u2192K+\u03c4 \u00b1\u2113\u2213are generally predicted to have\nlarger branching fractions in potential new-physics mod-\nels than B0 \u2192\u03c4 \u00b1\u2113\u2213. The primary di\ufb00erence from the ex-\nperimental point of view is the presence of the additional\ncharged kaon in B+ \u2192K+\u03c4 \u00b1\u2113\u2213. This has two conse-\nquences: that the signal has 3-body (rather than 2-body)\ndynamics, and that the \ufb01nal states all topologically resem-\n\n417\nble various b \u2192c\u2113\u03bd modes, resulting in potentially very\nlarge backgrounds from these high-branching-fraction pro-\ncesses.\n17.11.4.1 B+ \u2192h+\u03c4 \u00b1\u2113\u2213(h = K, \u03c0, \u2113= e, \u00b5)\nSearches for B+ \u2192h+\u03c4 \u00b1\u2113\u2213(Aubert, 2007au; Lees, 2012b)\nuse a methodology which exploits hadronic tag reconstruc-\ntion (Section 7.4.1) to enhance the available kinematic\nconstraints and to suppress continuum and combinatorial\nBB backgrounds. Searches for the corresponding neutral\nmodes B0 \u2192h0\u03c4 \u00b1\u2113\u2213were not performed due to the lower\ne\ufb03ciency for K0 reconstruction via K0\ns \u2192\u03c0+\u03c0\u2212and the\nfact that the tag reconstruction yield is somewhat higher\nfor charged B mesons than for neutral B0 mesons due\nto the branching fractions of the available tag modes. In\nthe more recent study, h = K, \u03c0, \u2113= e, \u00b5 and the decays\nB+ \u2192h+\u03c4 +\u2113\u2212and B+ \u2192h+\u03c4 \u2212\u2113+ are considered sep-\narately, for a total of eight distinct decay modes (charge\nconjugate modes are implied, but are not treated as dis-\ntinct decay modes).\nSince details of the speci\ufb01c new physics which could\nresult in a signal for B+ \u2192h+\u03c4 \u00b1\u2113\u2213are not known a\npriori, a 3-body phase space model is assumed for the\nsignal modes. This is in contrast to studies of the SM\nB \u2192K+\u2113+\u2113\u2212channels described in Section 17.9.\nSignal events are required to contain exactly three\ntracks, with total charge opposite that of the tag B. The\nprimary hadron, h, is required to be one of the two tracks\nhaving charge opposite the tag B and can be identi\ufb01ed\neither as a kaon or pion. The two remaining tracks are\nthen inferred to be the primary lepton \u2113and a charged\ntau decay daughter, which is identi\ufb01ed as e, \u00b5 or \u03c0.\nThe tau decay 4-vector is uniquely speci\ufb01ed using the\ntag B, primary lepton and primary hadron 4-vectors, in-\ndependent of the tau decay daughters. The tau invariant\nmass, m\u03c4,\nm2\n\u03c4 =\n\u0002\n(ECMS, 0)\u2212(E\u2217\nBtag, p\u2217\nBtag)\u2212(E\u2217\n\u2113, p\u2217\n\u2113)\u2212(E\u2217\nh, p\u2217\nh)\n\u00032 ,\n(17.11.3)\nis obtained from this 4-vector and is used to extract the\n\ufb01nal signal yield as it peaks strongly for signal and is non-\npeaking for background. In the cases where the primary\nlepton and the tau daughter are identi\ufb01ed as leptons of\nthe same type, vetoes are imposed on the di-lepton in-\nvariant mass to reject J/\u03c8 and \u03c8(2S) decays to \u2113+\u2113\u2212:\n3.03 < m\u2113+\u2113\u2212< 3.14 GeV/c2 and 3.60 < m\u2113+\u2113\u2212< 3.75\nGeV/c2. In the di-electron case, a photon conversion veto\nof me+e\u2212> 0.1 GeV/c2 is also applied.\nThe dominant background sources depend on the rela-\ntive charge of the primary lepton and the primary hadron\nin the signal mode. In the case of B+ \u2192h+\u03c4 \u2212\u2113+, the dom-\ninant background is from semileptonic B decays, B+ \u2192\nD(\u2217)0\u2113+\u03bd with D0 \u2192K+X\u2212(where X is a hadronic sys-\ntem), in which some or all of the X\u2212system is incorrectly\nreconstructed as the signal tau decay daughters.\nIn the case of B+ \u2192h+\u03c4 +\u2113\u2212however, the dominant\nbackground is from B+ \u2192D(\u2217)0X+ with the charm sys-\ntem decaying semileptonically. In both cases, the primary\nhadron and the track of opposite charge originate from\nthe D(\u2217)0. The quantity m(K\u03c0), the invariant mass of the\ncombination of these two tracks computed assuming ap-\npropriate kaon and pion mass hypotheses, is required to\nbe greater than 1.95 GeV/c2, i.e. to exceed the D0 mass,\ne\ufb00ectively suppressing these decays although with a sig-\nni\ufb01cant loss of signal e\ufb03ciency (see Figure 17.11.6). The\nremaining background is mainly from continuum q\u00afq pro-\nduction and is further suppressed by using a multivariate\nlikelihood selector based on event shape and PID quality\ncriteria, and the scalar sum of any remaining energy in\nthe calorimeter.\nSignal branching fractions are determined relative to\nhigh-branching fraction decays with similar topologies,\nspeci\ufb01cally B+ \u2192D(\u2217)0\u2113+\u03bd with D0 \u2192K+\u03c0\u2212. Signal\nyields in each of eight signal modes are determined within\na mass window of \u00b160 MeV/c2 in m\u03c4, centered around the\nnominal tau mass. For each signal mode, a likelihood func-\ntion is obtained from the products of the Poisson p.d.f.s\nrepresenting the yields in the e, \u00b5 and \u03c0 decay channels.\nSince models of LFV can produce signatures in which\nthe charge of the tau is either correlated or uncorrelated\nwith that of the charged hadron, BABAR reports results\non both the signed (e.g. B+ \u2192h+\u03c4 \u2212\u00b5+) and unsigned\n(e.g. B+ \u2192h+\u03c4 \u2213\u00b5\u00b1) branching fractions. No signi\ufb01cant\nsignals were found in any modes and upper limits (see\nTable 17.11.2) were obtained at the level of a few times\n10\u22125.\n)\n2\n) (GeV/c\n\u03c0\nm(K\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 50 MeV/c\n0\n500\n1000\n1500\n2000\n2500\n3000\nall backgrounds\n+\n\u00b5\n-\u03c4\n+\n K\n\u2192\n+\nB\n\u03c4\n\u03bd -\u03c0\n) \n0\n\u03c0\n (n\n\u2192\n-\u03c4\n)\n2\n) (GeV/c\n\u03c0\nm(K\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 50 MeV/c\n0\n20\n40\n60\n80\n100\n120\nsignal MC\nFigure 17.11.6. The reconstructed invariant mass, m(K\u03c0),\nfor the B+ \u2192K+\u03c4 \u2212\u00b5+ and \u03c4 \u2212\u2192(n\u03c00)\u03c0\u2212\u03bd\u03c4 (Lees, 2012b).\nThe upper plot shows the full data distribution and the bot-\ntom the simulated expectation for the signal. The vertical line\ndenotes the selection requirement just above the D0 peak at\napproximately 1.86 GeV/c2.\n\n418\n17.11.4.2 B0 \u2192\u03c4 \u00b1\u2113\u2213(\u2113= e, \u00b5)\nBABAR performed a search (Aubert, 2008az) for B0 \u2192\n\u03c4 \u00b1\u2113\u2213(with \u2113= e, \u00b5) based on a data sample of 378 \u00d7 106\nBB pairs using methodology similar to B+ \u2192K+\u03c4 \u00b1\u2113\u2213\n(Section 17.11.4.1). Due to the 2-body kinematics and the\nlarge tau mass, the light lepton is expected to possess a\nmomentum (in the signal B rest frame) of \u223c2.34 GeV/c,\nnear the kinematic endpoint for leptons from B decays.\nSince the B rest frame is inferred from the Btag, the reso-\nlution of the signal peak is dictated primarily by the reso-\nlution of the Btag 4-vector. This 2-body decay is somewhat\nsimilar kinematically to the charged B decay B+ \u2192\u2113+\u03bd\n(\u2113= e, \u00b5) and hence a search is performed simultaneously\n(see Section 17.10.2).\nThe signal and background distribution of the elec-\ntron momentum in B0 \u2192\u03c4 \u00b1e\u2213, from Aubert (2008az),\nis shown in Figure 17.11.7. After reconstructing the Btag\nand high-momentum lepton, all remaining particles in the\nevent are then assumed to be the decay daughters of the\ntau lepton. Hence there should be either one or three addi-\ntional tracks with total charge opposite that of the high-p\nlepton. Six tau decay modes are considered: e\u2212\u03bd\u00af\u03bd, \u00b5\u2212\u03bd\u00af\u03bd,\n\u03c0\u2212\u03bd, \u03c1(770)\u2212(\u2192\u03c0\u2212\u03c00)\u03bd, a1(1260)\u2212(\u2192\u03c0\u2212\u03c00\u03c00)\u03bd and\na1(1260)\u2212(\u2192\u03c0\u2212\u03c0+\u03c0\u2212)\u03bd, where \u03c1(770) or a1(1260) mass\nconstraints are imposed in the latter three cases. In the\nhadronic tau decay modes only a single neutrino is present.\nConsequently, the neutrino 4-vector can be uniquely deter-\nmined from the combination of the reconstructed tag B,\nthe high-p lepton and the hadronic tau daughter 4-vectors.\nThe neutrino mass therefore provides an additional kine-\nmatic constraint on these modes. Aubert (2008az) exploits\nthis by de\ufb01ning the quantity \u2206E\u03c4, representing the dif-\nference between the expected tau energy and the total\nenergy of the hadronic tau daughters combined with the\nneutrino (assuming zero mass). Computed in the tau rest\nframe, this quantity should peak at zero if the missing en-\nergy vector is consistent with a single massless neutrino.\n\u2206E\u03c4 is used to select a \u201cbest\u201d tau candidate from possi-\nble \u03c0\u00b1, \u03c1(770)\u00b1 and a1(1260)\u00b1 candidates in the case that\none or more \u03c00 \u2192\u03b3\u03b3 candidates have been reconstructed.\nIn signal events, the combination of the high-p lepton\nwith the tau decays daughter(s) should account for all\nparticles in the event which are not associated with the\nreconstructed tag B, while in background events other\nparticles may be present. A loose Eextra (de\ufb01ned as the\nscalar sum of energies of any remaining tracks or clus-\nters with energy > 50 MeV) requirement is imposed of\nEextra < 1.0 GeV. Signal yields are extracted from un-\nbinned ML \ufb01ts to the the high-p lepton momentum spec-\ntrum in the signal B rest frame, as shown for B0 \u2192\u03c4 \u00b1e\u2213\nin Figure 17.11.7. No signi\ufb01cant signal is seen in either\nmode and limits of B(B0 \u2192\u03c4 \u00b1e\u2213) < 2.8 \u00d7 10\u22125 and\nB(B0 \u2192\u03c4 \u00b1\u00b5\u2213) < 2.2 \u00d7 10\u22125 are obtained. Due to the\nvery low backgrounds, this search is statistically limited.\nInterpretation of these results in a new-physics context\nis model-dependent. However as an example we can con-\nsider a SUSY seesaw model with degenerate right-handed\nneutrino masses MN = 1014 GeV (Babu and Kolda, 2002;\nDedes, Ellis, and Raidal, 2002). In such a model B0 \u2192\n\u03c4 \u00b1\u00b5\u2213is mediated by a SUSY neutral Higgs with e\ufb00ective\nLFV couplings, which would also lead to a potentially ob-\nservable signal in \u03c4 \u2212\u2192\u00b5\u2212\u00b5+\u00b5\u2212(see Section 20.4). In\nthis model B(B0 \u2192\u03c4 \u00b1\u00b5\u2213) \u221d(tan2 \u03b2/MA)4, leading to\na lower bound on the A0 mass (MA) of \u223c30 GeV for\ntan \u03b2 = 100. Although not currently very stringent, im-\nproved experimental limits on these modes from future\nexperiments could place signi\ufb01cant constraints on new-\nphysics models.\nLepton Momentum (GeV/c)\n1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7\nEntries / 0.025 GeV/c\n0\n10\n20\n30\n40\nLepton Momentum (GeV/c)\n1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7\nEntries / 0.025 GeV/c\n0\n10\n20\n30\n40\n-!\n+\n e\n\"\n0\nB\nBABAR\nFigure 17.11.7. Signal electron candidate momentum in the\nsignal B rest frame for B0 \u2192\u03c4 \u00b1e\u2213(Aubert, 2008az). The\npoints with errors are BABAR data, the solid blue curve is the\n\ufb01tted background p.d.f. and the dashed green curve shows the\nexpected signal shape.\n17.11.5 Lepton number violating modes\nLNV processes are possible if neutrinos are of the Ma-\njorana type. As for the case of neutrino-less double beta\ndecay, lepton number must change by \u2206L = 2. Two possi-\nble diagrams for such decays are shown in Figure 17.11.8.\nFor a heavy sterile Majorana neutrino with a mass of a\nfew GeV/c2, the s-channel process (Figure 17.11.8(b)) is\nexpected to give the dominant contribution.\nBABAR reports a measurement of the LNV decays\nB+ \u2192h\u2212\u2113+\u2113+ (where h = K, \u03c0 based on 471 \u00d7 106 BB\ndecays (Lees, 2012r). The experimental technique is very\nsimilar to that used for studies of B+ \u2192h+\u2113+\u2113\u2212described\nin Section 17.9, and the analysis sensitivity is similar. A\nthree-body phase space model is assumed for the signal\nsimulation. Events are required to possess at least four\ncharged tracks, including two same-sign charged leptons\neach with momentum greater than 0.3 GeV/c. The leptons\nare required to originate from a common vertex and to sat-\nisfy m\u2113+\u2113+ < 5.0 GeV/c2. Leptons from identi\ufb01ed photon\nconversions are not permitted, and a bremsstrahlung re-\ncovery procedure is applied to electron and positron tracks\nto provide the best possible 4-vector for these particles.\nFor consistency with the B+ \u2192h+\u2113+\u2113\u2212studies, mass\nvetoes are imposed on the J/\u03c8 and \u03c8(2S) mass regions,\nrejecting events with 2.85 < m\u2113+\u2113\u2212< 3.15 GeV/c2 and\n\n419\nFigure 17.11.8. Diagrams for a LNV B decay B+ \u2192D\u2212\u2113+\u2113+\nin (a) t-channel and (b) s-channel processes.\n3.59 < m\u2113+\u2113\u2212< 3.77 GeV/c2, respectively, although no\nactual peaking contribution is expected in this case. In\nthe B+ \u2192\u03c0\u2212\u00b5+\u00b5+ mode, an additional veto is imposed\non the combination of the \u03c0\u2212with each of the two op-\npositely charged muons in order to reject J/\u03c8 events in\nwhich a muon has been misidenti\ufb01ed as a pion. Events\nare rejected if the \u03c0\u2212\u00b5+ combination is within the range\n3.05 < m\u03c0\u2212\u00b5+ < 3.13 GeV/c2.\nThe di-lepton pair is then combined with an identi\ufb01ed\ncharged kaon or pion track of sign opposite that of the\nleptons, requiring the combined B candidate to lie within\n5.200 < mES < 5.289 GeV/c2 and \u22120.10 < \u2206E < 0.05\nGeV. Backgrounds from q\u00afq and BB are suppressed using\na set of Boosted Decision Trees based on 18 inputs repre-\nsenting event shape and kinematic variables and trained\non MC signal and background samples (see Chapter 4 for\na description of Boosted Decision Tree classi\ufb01ers). A likeli-\nhood ratio, LR, is de\ufb01ned using the Boosted Decision Tree\noutputs as input p.d.f.s. The signal yield in each mode is\nextracted from an unbinned ML \ufb01t to mES and LR. No\nsigni\ufb01cant signals are observed, and branching fraction up-\nper limits are determined in the range [2, 11]\u00d710\u22128 at the\n90% C.L. as shown in Table 17.11.2.\nIf B+ \u2192h\u2212\u2113+\u2113+ is the result of the exchange of a\nMajorana neutrino, then the reconstructed invariant mass\nof the hadron h with the opposite-sign lepton, m\u2113+h\u2212, can\nbe related to the Majorana neutrino mass m\u03bd (Atre, Han,\nPascoli, and Zhang, 2009; Han and Zhang, 2006; Zhang\nand Wang, 2011). The BABAR results are presented as a\nfunction of m\u2113+h\u2212in Figure 17.11.9.\nSince b \u2192c decays are in general favored over charm-\nless B decays, it is interesting to extend the search for\nLNV processes to B+ \u2192X\u2212\nc \u2113+\u2113+ decays, where X\u2212\nc\nis\nany charmed hadron that has the opposite charge to the\nleptons. Using a sample of 772 \u00d7 106 BB pairs, Belle re-\nFigure 17.11.9. Branching fraction upper limits (UL) as a\nfunction of the mass m\u2113+h\u2212for the BABAR (Lees, 2012r) search\nmodes B+ \u2192\u03c0\u2212\u00b5+\u00b5+ (dotted magenta line), B+ \u2192K\u2212\u00b5+\u00b5+\n(dash-dotted red line), B+ \u2192K\u2212e+e+ (dashed black line) and\nB+ \u2192\u03c0\u2212e+e+ (solid blue line).\nports a measurement of the B+ \u2192D\u2212\u2113+\u2113\u2032+ decays (Seon,\n2011), where \u2113, \u2113\u2032 = e or \u00b5 in any combination. Since we\nhave no prior knowledge nor widely accepted model for\nthese decays, a 3-body phase-space model is assumed for\nthe signal simulation. To \ufb01nd signal candidates, \ufb01rst an\nenergetic same-sign lepton pair is chosen. The lepton mo-\nmentum in the lab frame is required to be greater than\n0.5(0.8) GeV/c for electrons (muons). Particle identi\ufb01ca-\ntion requirements select electrons (muons) with an e\ufb03-\nciency of approximately 90% and a misidenti\ufb01cation rate\nof 0.1% (1%) for pions in the kinematic region of inter-\nest. The energy sum of the dilepton system in the CM\nframe is required to exceed 1.3 GeV: this has minimal\ne\ufb00ect on the signal e\ufb03ciency in the phase-space model.\nThe lepton pair is then combined with a D\u2212\u2192K+\u03c0\u2212\u03c0\u2212\ndecay candidate. Kaons (pions) are discriminated from pi-\nons (kaons) with an e\ufb03ciency of approximately 91% (95%)\nand a misidenti\ufb01cation rate below 4% (6%) in the kine-\nmatic region of interest. The K+\u03c0\u2212\u03c0\u2212invariant mass\n(MK\u03c0\u03c0) is required to be within \u00b110 MeV/c2 from the\nnominal D\u2212mass. The B candidates are further required\nto lie within mES > 5.2 GeV/c2 and |\u2206E| < 0.3 GeV\n(the \u2018analysis region\u2019). The major background sources are\nfrom continuum processes and to a lesser degree from se-\nmileptonic B decays such as B \u2192D\u2212\u2113+\u03bd\u2113X, in which\na same-sign lepton from the decay products of the other\nB is combined with the signal B. These backgrounds are\nsuppressed by a single likelihood ratio R using the four\nvariables: the Fisher discriminant F of the modi\ufb01ed Fox-\nWolfram moments (see Section 9.3), the cosine of the po-\nlar angle of the B candidate \ufb02ight direction in the CM\nframe, cos \u03b8B, the missing energy Emiss of the event, and\nthe di\ufb00erence \u03b4z between the impact parameters of the\ntwo leptons in the beam direction. The requirement on\nR, determined mode-by-mode by a MC study, eliminates\n\n420\nmore than 99% of the background while retaining 11\u201326%\nof the signal, depending on the mode. Signal yield is esti-\nmated in the \u2018signal region\u2019, 5.27 < mES < 5.29 GeV/c2\nand \u22120.055(\u22120.035) < \u2206E < 0.035 GeV for the e+e+\nand e+\u00b5+ modes (\u00b5+\u00b5+ mode). The background region\nis de\ufb01ned as the complement of the analysis region ex-\ncluding the signal region. The amount of background is\ndetermined by \ufb01tting the 2-dimensional (\u2206E, mES) p.d.f.\nto the data in the background region and then integrat-\ning the \ufb01tted p.d.f. over the signal region. There was no\nevent observed in the signal region of any mode. Figure\n17.11.10 shows the (\u2206E, mES) distribution of selected\nB+ \u2192D\u2212\u00b5+\u00b5+ candidates. Upper limits (at the 90%\nC.L.) are calculated based on a frequentist approach (Feld-\nman and Cousins, 1998) including systematic uncertain-\nties using the POLE program, (Conrad, Botner, Hallgren,\nand Perez de los Heros, 2003). The results are summarized\nin Table 17.11.2, and are in the range [1.1, 2.6] \u00d7 10\u22126.\n)\n2\n (GeV/c\nbc\nM\n5.2\n5.22\n5.24\n5.26\n5.28\nE (GeV)\n\u2206\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\nFigure 17.11.10. (\u2206E, mES) distribution of B+ \u2192D\u2212\u00b5+\u00b5+\ncandidates from (Seon, 2011). The solid red line denotes the\nsignal region.\n17.11.6 Lepton/baryon number violating modes\nAlthough baryon number is approximately conserved\nwithin the SM, it is predicted to be violated in many mod-\nels of grand uni\ufb01cation (Fritzsch and Minkowski, 1975;\nGeorgi and Glashow, 1974), and indeed baryon number\nviolation is one of Sakharov\u2019s conditions for cosmologi-\ncal baryogenesis (see Section 16.2). Most GUT models\nhowever conserve B \u2212L, the di\ufb00erence of baryon and\nlepton number, implying that lepton number is also vi-\nolated. In these models the proton is predicted to be un-\nstable, albeit with a very long lifetime, decaying for ex-\nample into a positron and \u03c00. However, the proton decay\nrates predicted by many of these models have not been ob-\nserved and very stringent experimental limits have been\nplaced on the proton lifetime (Nakamura et al., 2010).\nThese limits, based on measurements of \ufb01rst-generation\nquarks, have been used to estimate the potential for bar-\nyon number violation in decays involving second- and\nTable 17.11.2. Summary of the results for lepton \ufb02avor, lep-\nton number and baryon number violating modes.\nDecay Mode\nNBB\nB upper limit\nReference\n(106)\n(90% C.L.)\nLepton \ufb02avor violating modes (light \ufb02avors):\nB0 \u2192\u00b5\u00b1e\u2213\n85\n17\n\u00d7 10\u22128\nChang (2003)\nB0 \u2192\u00b5\u00b1e\u2213\n384\n9.2 \u00d7 10\u22128\nAubert (2008as)\nB+ \u2192\u03c0+\u00b5\u00b1e\u2213\n230\n17\n\u00d7 10\u22128\nAubert (2007ax)\nB0 \u2192\u03c00\u00b5\u00b1e\u2213\n14\n\u00d7 10\u22128\nB\n\u2192\u03c0\u00b5\u00b1e\u2213\n9.2 \u00d7 10\u22128\nB+ \u2192K+\u00b5\u2212e+\n229\n9.1 \u00d7 10\u22128\nAubert (2006ac)\nB+ \u2192K+\u00b5+e\u2212\n13\n\u00d7 10\u22128\nB+ \u2192K+\u00b5\u2213e\u00b1\n9.1 \u00d7 10\u22128\nB0 \u2192K0\u00b5\u2213e\u00b1\n27\n\u00d7 10\u22128\nB\n\u2192K\u00b5\u2213e\u00b1\n3.8 \u00d7 10\u22128\nB+ \u2192K\u22170\u00b5\u2212e+\n53\n\u00d7 10\u22128\nB+ \u2192K\u22170\u00b5+e\u2212\n34\n\u00d7 10\u22128\nB+ \u2192K\u22170\u00b5\u2213e\u00b1\n58\n\u00d7 10\u22128\nB+ \u2192K\u2217+\u00b5\u2212e+\n130\n\u00d7 10\u22128\nB+ \u2192K\u2217+\u00b5+e\u2212\n99\n\u00d7 10\u22128\nB+ \u2192K\u2217+\u00b5\u2213e\u00b1\n140\n\u00d7 10\u22128\nB\n\u2192K\u2217\u00b5\u2213e\u00b1\n51\n\u00d7 10\u22128\nLepton \ufb02avor violating modes (including \u03c4):\nB0 \u2192\u03c4 \u00b1e\u2213\n378\n2.8 \u00d7 10\u22125\nAubert (2008az)\nB0 \u2192\u03c4 \u00b1\u00b5\u2213\n2.2 \u00d7 10\u22125\nB+ \u2192K+\u03c4 \u2212\u00b5+\n472\n4.5 \u00d7 10\u22125\nLees (2012b)\nB+ \u2192K+\u03c4 +\u00b5\u2212\n2.8 \u00d7 10\u22125\nB+ \u2192K+\u03c4 \u2213\u00b5\u00b1\n4.8 \u00d7 10\u22125\nB+ \u2192K+\u03c4 \u2212e+\n4.3 \u00d7 10\u22125\nB+ \u2192K+\u03c4 +e\u2212\n1.5 \u00d7 10\u22125\nB+ \u2192K+\u03c4 \u2213e\u00b1\n3.0 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 \u2212\u00b5+\n6.2 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 +\u00b5\u2212\n4.5 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 \u2213\u00b5\u00b1\n7.2 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 \u2212e+\n7.4 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 +e\u2212\n2.0 \u00d7 10\u22125\nB+ \u2192\u03c0+\u03c4 \u2213e\u00b1\n7.5 \u00d7 10\u22125\nLepton number violating modes:\nB+ \u2192\u03c0\u2212e+e+\n471\n2.3 \u00d7 10\u22128\nLees (2012r)\nB+ \u2192K\u2212e+e+\n3.0 \u00d7 10\u22128\nB+ \u2192\u03c0\u2212\u00b5+\u00b5+\n10.7 \u00d7 10\u22128\nB+ \u2192K\u2212\u00b5+\u00b5+\n6.7 \u00d7 10\u22128\nB+ \u2192D\u2212e+e+\n772\n2.6 \u00d7 10\u22126\nSeon (2011)\nB+ \u2192D\u2212\u00b5+e+\n1.8 \u00d7 10\u22126\nB+ \u2192D\u2212\u00b5+\u00b5+\n1.1 \u00d7 10\u22126\nBaryon and lepton number violating modes:\nB0 \u2192\u039b+\nc \u00b5\u2212\n471\n1.8 \u00d7 10\u22126\ndel Amo Sanchez\u2020\nB0 \u2192\u039b+\nc e\u2212\n5.2 \u00d7 10\u22126\nB\u2212\u2192\u039b\u00b5\u2212\n6.2 \u00d7 10\u22128\nB\u2212\u2192\u039be\u2212\n8.1 \u00d7 10\u22128\nB\u2212\u2192\u039b\u00b5\u2212\n6.1 \u00d7 10\u22128\nB\u2212\u2192\u039be\u2212\n3.2 \u00d7 10\u22128\n\u2020\ndel Amo Sanchez (2011l)\n\n421\nthird-generation quarks (Hou, Nagashima, and Soddu,\n2005). In particular for B0 \u2192\u039b+\nc \u2113\u2212, which violates both\nlepton number and baryon number, the branching fraction\nis estimated to be less than 4 \u00d7 10\u221229. Although this is\nfar beyond any expected experimental sensitivity, searches\nhave still been performed to the precision permitted by\ncurrent data samples.\nBABAR has performed a search for the decays B0 \u2192\n\u039b+\nc \u2113\u2212, B\u2212\u2192\u039b\u2113\u2212, and the B \u2212L violating mode B\u2212\u2192\n\u039b\u2113\u2212, where the lepton is a muon or an electron (del\nAmo Sanchez, 2011l). This is the \ufb01rst experimental search\nfor these decays, and any positive signal would be evidence\nof new physics.\nB-meson candidates are formed by combining a \u039b+\nc , \u039b\nor \u039b candidate with an identi\ufb01ed muon or electron. The\n\u039b+\nc candidates are reconstructed in the decay mode \u039b+\nc \u2192\npK\u2212\u03c0+, which has a branching fraction of about 5%. The\n\u039b candidates are reconstructed in the decay \u039b \u2192p\u03c0\u2212,\nwhich has a branching fraction of about 64%.\nThe \ufb01nal state hadron (p, K, \u03c0) and lepton (\u00b5, e)\ncandidates are all required to be consistent with the\ncandidate particle hypothesis according to PID crite-\nria based on dE/dx , DIRC, EMC and IFR informa-\ntion. The 4-momenta of photons that are consistent with\nbremsstrahlung radiation from the electron candidate are\nadded to that of the electron.\n\u039b+\nc\ncandidates are required to have pK\u2212\u03c0+ invari-\nant mass within \u00b115 MeV/c2 of the nominal \u039b+\nc mass.\nSimilarly, \u039b candidates must have p\u03c0\u2212mass within \u00b14\nMeV/c2 of the nominal \u039b mass. The \ufb01nal state tracks\nwhich form the decay daughters of the the \u039b+\nc (\u039b) are\nconstrained to a common spatial vertex, and their invari-\nant mass is constrained to the \u039b+\nc (\u039b) mass. This has the\ne\ufb00ect of improving the 4-momentum resolution for true\nB \u2192\u039b(c)\u2113candidates. The baryon and lepton candidates\nare also constrained to originate from a common vertex.\nAs the \u039b has c\u03c4 = 7.89 cm, the purity of the \u039b-\ncandidate sample is further improved by selecting can-\ndidates for which the reconstructed decay point of the \u039b\ncandidate is at least 0.2 cm from the reconstructed de-\ncay point of the B candidate in the plane perpendicu-\nlar to the e+e\u2212beams. Particle mis-ID backgrounds from\ne+e\u2212\u2192e+e\u2212\u03b3 events in which the photon converts to an\ne+e\u2212pair are eliminated by requiring that there are more\nthan four tracks in the events.\nB-meson candidates are selected within the kinematic\nregion |\u2206E| < 0.2 GeV and 5.2 < mES < 5.3 GeV/c2\nare \ufb01tted to extract the signal yield. The signal yield is\nextracted using an unbinned extended ML \ufb01t in which the\ntotal p.d.f. is a sum of p.d.f.s for signal and background.\nThe signal and background p.d.f.s are each a product of\np.d.f.s describing the dependence on mES and \u2206E. For the\n\u039b+\nc \u2113\u2212modes, additional discriminating power is gained\nfrom a three dimensional p.d.f., where the output from a\nneural network discriminator is used as the third variable.\nNo signi\ufb01cant signal is observed for any of the de-\ncay modes, and branching fraction upper limits are de-\ntermined, ranging from 5.2 \u00d7 10\u22126 to 3.2 \u00d7 10\u22128 at the\n90% C.L. (see Table 17.11.2). Less stringent limits are ob-\ntained for the B0 \u2192\u039b+\nc \u2113\u2212modes than the \u039b modes due\nto the relatively low branching fraction for the studied \u039b+\nc\ndecay and a higher level of background compared with the\n\u039b modes.\n17.11.7 Summary\nAlthough there is currently no evidence for any of the rare\nor forbidden decay modes described in this section, they\nremain useful as probes for physics beyond the SM. In the\ncase of B(s) \u2192\u2113+\u2113\u2212and B \u2192h\u2113+\u2113+ (with \u2113= e, \u00b5),\nexperimental results from hadron colliders have already\nexceeded the current sensitivity from B Factories and it is\nunlikely that future e+e\u2212facilities will change this situa-\ntion. In other modes, particularly those with tau leptons\nor neutrinos, hadron colliders are at a signi\ufb01cant disad-\nvantage. It is notable that in some cases, either due to\nexperimental challenges or due to the small size of the\nexpected new-physics e\ufb00ects, current experimental limits\non these modes do not yet reach the ranges predicted by\nmost reasonable new-physics models. Consequently, these\nsearches are essentially of the \u201cshot-in-the-dark\u201d variety:\nessentially probing dark corners of the SM to verify that\nwe see nothing in places where we expect to see noth-\ning. As a rule of thumb one can summarize the achieved\nsensitivity of B Factories to O(10\u22125) for B \u2192invisible\nand LFV decays with \u03c4\u2019s, O(10\u22126) for B(s) \u2192\u03b3\u03b3, and\nO(10\u22127) for B \u2192\u2113+\u2113\u2212, LFV decays with light leptons\nand baryon and/or lepton number violating modes. Im-\nprovements in experimental sensitivity with large datasets\nat the future generation of B Factories could change this\npicture, with experimental results in some cases directly\nconfronting realistic new-physics models.\n\n422\n17.12 B decays to baryons\nEditors:\nRoland Waldi (BABAR)\nMin-Zu Wang (Belle)\nHai-Yang Cheng (theory)\nAdditional section writers:\nThomas Hartmann\nBaryons and antibaryons have to be produced in pairs\nin the Standard Model, therefore most mesons cannot de-\ncay to baryons for lack of energy. The only baryonic D\ndecay is D+\ns \u2192pn, which has only just enough energy to\nproceed. But the phase space of the two or four quarks in\na purely hadronic weak decay of a B meson is much larger\nthan that of charmed or light mesons, and leaves ample\nfreedom for high multiplicities and for the production of\nbaryon-antibaryon pairs.\nThat B decays to baryons play an important role be-\ncame evident by the large proton multiplicities found by\nARGUS and CLEO at the \u03a5(4S) (Albrecht et al., 1989b;\nCrawford et al., 1992).\nThe interest in decays to baryons was increased when\nARGUS claimed the observation of B decays to pp\u03c0\u00b1 and\npp\u03c0+\u03c0\u2212(Albrecht et al., 1988b). Subsequently, baryonic\nB decays were studied extensively by theorists around the\nearly 1990s with the focus on the tree-dominated two-\nbody decay modes. Experimental studies were \ufb01rst led by\nCLEO, but with the accumulating data at the B Factories,\nBABAR and Belle came to dominate the \ufb01eld.\nThe features of B decays to baryons re\ufb02ect the prop-\nerties of both the weak interaction, and the hadronization\nof quarks. One or two qq pairs have to be produced out of\nthe vacuum to produce a baryon-antibaryon pair, similar\nto jet fragmentation.\nThis section presents the inclusive production of bar-\nyons in B meson decays (Section 17.12.1), then exclusive\ntwo-body decays (Section 17.12.2), followed by the more\nfrequent multibody \ufb01nal states with a baryon-antibaryon\npair plus one or more mesons (Section 17.12.3). Com-\nplex phenomena are seen in multibody decays, and our\ntreatment includes dedicated discussions of threshold en-\nhancement (Section 17.12.3.3), multiplicity e\ufb00ects (Sec-\ntion 17.12.3.4), and angular correlations (Section 17.12.3.5).\nFinally, radiative and semileptonic decays with baryons in\nthe \ufb01nal state are discussed (Sections 17.12.4 and 17.12.5\nrespectively). Theoretical interpretations and model pre-\ndictions for each of these topics are discussed within the\nthe corresponding section. Baryon number violating de-\ncays have been presented in the previous section, 17.11.6.\n17.12.1 Inclusive decays into baryons\nThe inclusive production of protons and antiprotons from\n\u03a5(4S) decays, i.e., an admixture of B+, B\u2212, B0, and B0,\nhas been measured by ARGUS and CLEO (Albrecht et al.,\n1993a; Crawford et al., 1992). The combined multiplicity\nFigure 17.12.1. Di\ufb00erential B \u2192\u039b+\nc X production rate per\n\u03a5(4S) from BABAR (Aubert, 2007p), Belle (Seuster, 2006), and\nCLEO (Crawford et al., 1992) versus the momentum fraction\nxp = p/pmax in the \u03a5(4S) rest frame. Also shown is the di\ufb00er-\nential \u039e0\nc production rate normalized to match the peak of the\n\u039b+\nc rate.\nof protons and antiprotons in an average B decay is\n\u27e8np + np\u27e9= 0.080 \u00b1 0.004.\n(17.12.1)\nSome of these protons come from \u039b decays; the multi-\nplicity of \u039b baryon production has been determined to be\n\u27e8n\u039b + n\u039b\u27e9= 0.040 \u00b1 0.005 (Albrecht et al., 1989b; Craw-\nford et al., 1992).\nInclusive particle spectra in (scaled) momentum are\nobtained from data at the \u03a5(4S) energy by subtracting\nthe spectra obtained o\ufb00resonance, scaled to the on reso-\nnance luminosity and cross section. The scaled momentum\nof a particle of mass m is given by xp = p/pmax with the\nmaximum center-of-mass momentum pmax =\np\ns/4 \u2212m2.\nIntegration over the extrapolated spectra yields the par-\nticle multiplicity.\nIf protons were the only stable baryons, any bary-\nonic event would have one proton and one antiproton.\nThis would imply a 4% branching fraction into baryon an-\ntibaryon + X (ignoring decays with two pairs). But since\nthere are also neutrons, a more sophisticated analysis is\nrequired to obtain the total baryonic branching fraction.\nSuch an analysis has been performed by the ARGUS col-\nlaboration (Albrecht et al., 1992c) using in addition to the\nproton and \u039b multiplicities the fractions of events at the\n\u03a5(4S) with baryon-antibaryon pairs, baryon \u2113+ pairs, and\nbaryon \u2113\u2212pairs (where \u2113is an electron or muon). The\nbaryon-antibaryon fraction allows for the elimination of\nthe unknown contribution of neutrons to the \ufb01nal state,\nwhile the remaining fractions help to establish baryon-\n\ufb02avor correlations. The result is\nB(B \u2192B1B2X) = (6.8 \u00b1 0.5 \u00b1 0.3)%\n(17.12.2)\nwhere B represents a generic baryon.\n\n423\nSince the dominant weak process in B decays is b \u2192\ncX, most \ufb01nal states with baryons contain either a meson\nwith charm quarks (like B+ \u2192J/\u03c8p\u039b or B0 \u2192D0pp)\nor a charmed baryon. While there are a few charmed bar-\nyon decays to charmed mesons and non-charmed bary-\nons (such as \u039bc(2880)+ \u2192D0p), most decays are to \u039b+\nc ,\n\u039e0\nc , \u039e+\nc , or \u21260\nc. Inclusive production rates for all of these\nstates, except \u21260\nc, have been determined by ARGUS (Al-\nbrecht et al., 1988a) and CLEO (Crawford et al., 1992).\nInclusive \u039bc production has also been measured at the B\nFactories (Aubert, 2004m, 2007p,ba; Seuster, 2006): the\nmost precise average multiplicity per B meson has been\ndetermined by BABAR (Aubert, 2007p),\n\u27e8n\u039b+\nc + n\u039b\u2212\nc \u27e9= 0.0456 \u00b1 0.0009 \u00b1 0.0031 \u00b1 0.0118\u039bc.\n(17.12.3)\nThe scaled momentum spectrum in the \u03a5(4S) rest frame\nis shown in Fig. 17.12.1. As in most measurements where\na \u039b+\nc baryon is reconstructed, the decay \u039b+\nc \u2192pK\u2212\u03c0+\nis used in this analysis. All channels with the \u039bc baryon\nin the \ufb01nal state su\ufb00er from a large systematic uncer-\ntainty of 26% since the branching fractions are only poorly\nknown, with B(\u039b+\nc \u2192pK\u2212\u03c0+) = 0.050 \u00b1 0.013 (Beringer\net al., 2012). This value is also used to normalize other \u039bc\nbranching fractions: it is the source of the dominant third\nuncertainty on the multiplicity in Eq. (17.12.3). A further\ndiscussion of this problem is found in Section 19.4.2.3.96\nThe situation is even worse for \u039ec baryons, where no abso-\nlute branching fraction measurement is available. For our\nmultiplicity estimate and also for exclusive branching frac-\ntions (e.g., Table 17.12.1) we use B(\u039e0\nc \u2192\u039e\u2212\u03c0+) \u22481.2%,\nassuming a 50% error. This value is based on the range of\ntheoretical predictions for the partial width (Cheng and\nTseng, 1993) and the lifetime of the \u039e0\nc baryon (Berin-\nger et al., 2012). In the same spirit, we use B(\u039e\u2212\nc\n\u2192\n\u039e+\u03c0\u2212\u03c0\u2212) \u22486.4%, assuming a 50% error. This value is ob-\ntained from the theoretical prediction \u0393(\u039e\u2212\nc \u2192\u039e0\u03c0\u2212) \u2248\n0.8\u00d71011 s\u22121 derived from Cheng and Tseng (1993), the\nexperimental ratio \u0393(\u039e\u2212\nc \u2192\u039e0\u03c0\u2212)/\u0393(\u039e\u2212\nc \u2192\u039e+\u03c0\u2212\u03c0\u2212) =\n0.55\u00b10.16, and the lifetime \u03c4(\u039e\u2212\nc ) = (4.42\u00b10.26)\u00d710\u221213 s\n(Beringer et al., 2012).\nThe multiplicity of charged \u039ec baryons has only been\nmeasured at CLEO (Barish et al., 1997), corresponding\nto \u27e8n\u039e+\nc + n\u039e\u2212\nc \u27e9\u223c0.007. For neutral \u039ec baryons the av-\nerage from the CLEO (Crawford et al., 1992) and BABAR\n(Aubert, 2005z) measurements is \u27e8n\u039e0c + n\u039e0c\u27e9\u223c0.016.\nProduction of \u21260\nc baryons in B decays is even more\nrare, and has been observed by BABAR (Aubert, 2007ao),\nwith an average multiplicity of the order 0.0005 assuming\nB(\u2126c \u2192\u2126\u2212\u03c0+) \u223c1%.\n96 While we were \ufb01nalising this book Belle submitted an ab-\nsolute branching fraction measurement for publication, with\nsigni\ufb01cantly improved precision: B(\u039b+\nc \u2192pK\u2212\u03c0+) = (6.84 \u00b1\n0.24+0.21\n\u22120.27)% (Zupanc, 2013a). See the discussion in Section\n19.4.2.3.\n-0.2\n-0.1\n0\n0.1\n0.2\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nMbc (GeV/c2)\n\u2206E (GeV)\n(a)\n0\n1\n2\n3\n4\n5\n6\n-0.2\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\n\u2206E (GeV)\nEvents/(5 MeV)\n(b)\n0\n1\n2\n3\n4\n5\n6\n7\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nMbc (GeV/c2)\nEvents/(1 MeV/c2)\n(c)\nFigure 17.12.2. Candidate events for the decay B0 \u2192\u039b+\nc p\nfrom Belle (Gabyshev, 2003): (a) scatter plot of \u2206E versus\nmES = Mbc, (b) \u2206E distribution for mES > 5.270 GeV/c2, and\n(c) mES distribution for |\u2206E| < 0.030 GeV. The curves indicate\nthe result of a two-dimensional \ufb01t.\n17.12.2 Two-body decays\nOne might expect a large fraction of baryonic decays to\nproceed via two-body decay channels, since the phase space\nfor heavy particles is rather small. However, from the spec-\ntrum in Fig. 17.12.1 it is evident that two-body decays are\nrare, since they would show up as a peak around xp = 0.4.\nIndeed, it has been found experimentally that decays of\nB mesons to just a baryon and an antibaryon have very\nsmall branching fractions. First measurements of B de-\ncays to baryons were made by CLEO, but no two-body\ndecay could be established, and upper limits of those de-\ncays were reported (Bornheim et al., 2003; Dytman et al.,\n2002; Procario et al., 1994).\n\n424\nTable 17.12.1. Branching fractions of observed two-body decays of B mesons to baryons. Upper limits are at the 90% C.L.\nChannels with the \u039b+\nc baryon in the \ufb01nal state have an additional \u00b126% relative error (not included) from the assumption\nB(\u039b+\nc \u2192pK\u2212\u03c0+) = 0.050\u00b10.013 and are marked with \u2020. The same holds for B(\u039e0\nc \u2192\u039e\u2212\u03c0+) = 0.012 and B(\u039e+\nc \u2192\u039e\u2212\u03c0+\u03c0+) =\n0.064, both with an additional \u00b150% taken from the range of theoretical predictions (Cheng and Tseng, 1993). Two daggers\nindicate that two such errors have to be added (linearly due to correlation).\nDecay\nBABAR\nBelle\nAverage\nBcBc \ufb01nal states (B: 10\u22123)\nB+ \u2192\u039e0\nc\u039b+\nc\n1.73 \u00b1 0.54 \u00b1 0.24\u2020\u2020 (Aubert, 2008e)\n4.00 \u00b1 0.83 \u00b1 0.92\u2020\u2020 (Chistov, 2006a)\n2.16 \u00b1 0.54\u2020\u2020\nB0 \u2192\u039e\u2212\nc \u039b+\nc\n0.23 \u00b1 0.17 \u00b1 0.03\u2020\u2020 (Aubert, 2008e)\n1.5 \u00b1 0.5 \u00b1 0.3\u2020\u2020\n(Chistov, 2006a)\n\u223c0.3\nB0 \u2192\u039b\u2212\nc \u039b+\nc\n< 0.062\n(Uchida, 2008)\n< 0.062\nsingly-charmed \ufb01nal states (B: 10\u22126)\nB0 \u2192\u039b\u2212\nc p\n18.9 \u00b1 2.1 \u00b1 0.6\u2020\n(Aubert, 2008aa)\n21.9+5.6\n\u22124.9 \u00b1 3.2\u2020\n(Gabyshev, 2003)\n19 \u00b1 2\u2020\nB+ \u2192\u039b\u2212\nc \u2206++\n< 19\n(Gabyshev, 2006)\n< 19\nB+ \u2192\u039b\u2212\nc \u2206++(1600)\n59 \u00b1 10 \u00b1 6\u2020\n(Gabyshev, 2006)\n59 \u00b1 12\u2020\nB+ \u2192\u039b\u2212\nc \u2206++(2420)\n47 \u00b1 10 \u00b1 4\u2020\n(Gabyshev, 2006)\n47 \u00b1 11\u2020\nB0 \u2192\u03a3c(2455)\u2212p\n< 30\n(Aubert, 2010h)\n< 30\nB+ \u2192\u03a3c(2455)0p\n42 \u00b1 4 \u00b1 3\u2020\n(Aubert, 2008aa)\n37 \u00b1 7 \u00b1 4\u2020\n(Gabyshev, 2006)\n40 \u00b1 4\u2020\nB+ \u2192\u03a3c(2520)0p\n< 3\n(Aubert, 2008aa)\n< 27\n(Gabyshev, 2006)\n< 3\nB+ \u2192\u03a3c(2800)0p\n40 \u00b1 8 \u00b1 8\u2020\n(Aubert, 2008aa)\n40 \u00b1 11\u2020\nun\ufb02avored \ufb01nal states (B: 10\u22126)\nB0 \u2192pp\n< 0.27\n(Aubert, 2004ab)\n< 0.11\n(Tsai, 2007)\n< 0.11\nB+ \u2192p\u22060\n< 1.4\n(Wei, 2008b)\n< 1.4\nB+ \u2192\u2206++p\n< 0.14\n(Wei, 2008b)\n< 0.14\nB0 \u2192\u039b\u039b\n< 0.32\n(Tsai, 2007)\n< 0.32\nstrange \ufb01nal states (B: 10\u22126)\nB+ \u2192p\u039b\n< 0.32\n(Tsai, 2007)\n< 0.32\nB+ \u2192p\u039b(1520)\n< 1.5\n(Aubert, 2005p)\n< 1.5\nB+ \u2192p\u03a3(1385)0\n< 0.47\n(Wang, 2007b)\n< 0.47\nB0 \u2192p\u03a3(1385)\u2212\n< 0.26\n(Wang, 2007b)\n< 0.26\nB+ \u2192\u2206+\u039b\n< 0.82\n(Wang, 2007b)\n< 0.82\nB0 \u2192\u22060\u039b\n< 0.93\n(Wang, 2007b)\n< 0.93\n17.12.2.1 Results from B Factories\nAn overview of the results from the B Factories for two-\nbody decays is given in Table 17.12.1.\nFirst observation\nThe \ufb01rst two-body baryonic B decay observed was B0 \u2192\n\u039b+\nc p with \u039b+\nc \u2192pK\u2212\u03c0+ (Gabyshev, 2003) using a 78.2 fb\u22121\ndata sample at Belle.\nThe mass resolution of reconstructed \u039bc is very good.\nOne can just select \u039bc and apply simple continuum sup-\npression (see Chapter 9) to reject most of the background\nevents. Exclusive reconstruction is described in Section\n7.1. Fig. 17.12.2 shows the scatter plot of \u2206E versus mES\nand their projections for selected events. The \u2206E projec-\ntion is shown for mES > 5.270 GeV/c2 and the mES pro-\njection for |\u2206E| < 0.030 GeV. A two-dimensional binned\nmaximum likelihood \ufb01t is performed to determine the sig-\nnal yield. For this \ufb01t, the \u2206E distribution is represented\nby a double Gaussian for the signal plus a \ufb01rst order poly-\nnomial for the background. The mES distribution is rep-\nresented by a single Gaussian for the signal plus the AR-\nGUS function for the background. The signal shapes de-\ntermined from MC simulation are \ufb01xed in the \ufb01t. The re-\ngion \u2206E < \u22120.1 GeV is excluded from the \ufb01t to avoid feed-\ndown from modes including extra pions. The measured\nbranching fraction is (2.19+0.56\n\u22120.49\u00b10.32\u00b10.57)\u00d710\u22125 where\nthe last error comes from the uncertainty on the sub-\ndecay branching fraction of \u039b+\nc \u2192pK\u2212\u03c0+. The branch-\ning fraction is thusan order-of-magnitude smaller than\nthat of the three-body decay B\u2212\u2192\u039b+\nc p\u03c0\u2212(see Ta-\nble 17.12.6). This suppression is a unique feature of two-\nbody baryonic decays and will be addressed further in\nSections 17.12.2.2 and 17.12.3.4. In contrast, the two- and\nthree-body mesonic B decays are comparable.\n\n425\nEvents/(5 MeV/c2)\nM(\u039bc\n+\u03c0-) (GeV/c2)\n0\n5\n10\n15\n20\n25\n2.4\n2.45\n2.5\n2.55\n2.6\n2.65\n2.7\n2.75\n2.8\n(a) Belle: B signal region (open histogram), \ufb01t\nresults (curve) and background from sidebands\n(hatched).\n)\n2\n (GeV/c\n\u03c0\nc\n\u039b\nm\n2.48\n2.50 2.52\n2.54 2.56\n2.58 2.60\n2.62 2.64\n )\n2\nEvents / ( 0.005 GeV/c\n-20\n0\n20\n40\n60\n80\n100\n)\n2\n (GeV/c\n\u03c0\nc\n\u039b\nm\n2.48\n2.50 2.52\n2.54 2.56\n2.58 2.60\n2.62 2.64\n )\n2\nEvents / ( 0.005 GeV/c\n-20\n0\n20\n40\n60\n80\n100\n(b) BABAR: sPlot projections of the\n\u03a3c(2520)0p signal (data points) and\n\ufb01ts (curves).\n)\n2\n (GeV/c\n\u03c0\nc\n\u039b\nm\n2.5\n2.6\n2.7\n2.8\n2.9\n3.0\n3.1\n3.2\n3.3\n3.4\n )\n2\nEvents / ( 0.015 GeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n)\n2\n (GeV/c\n\u03c0\nc\n\u039b\nm\n2.5\n2.6\n2.7\n2.8\n2.9\n3.0\n3.1\n3.2\n3.3\n3.4\n )\n2\nEvents / ( 0.015 GeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n(c) BABAR: sPlot projections of the\n\u03a3c(2800)0p signal (data points) and\n\ufb01ts (curves).\nFigure 17.12.3. m(\u039b+\nc \u03c0\u2212) distributions from (a) Belle (Gabyshev, 2006), and (b,c) BABAR (Aubert, 2008aa); for the\nsPlot\ntechnique, see Section 11.2.3. Three \u03a30\nc resonances are visible at 2.455 GeV/c2 (a), 2.52 GeV/c2 (a and b, not signi\ufb01cant) and\n2.80 GeV/c2 (c).\nQuasi-two-body decays\nFollowing the study of B\u2212\u2192\u039b+\nc p\u03c0\u2212at CLEO (Dytman\net al., 2002) and at Belle (Gabyshev, 2002), an analy-\nsis of this \ufb01nal state has been performed using a much\nlarger data sample (containing \u223c152 \u00d7 106 BB pairs)\nand extending the \u039b+\nc reconstruction to the following \ufb01ve\ndecay modes: \u039b+\nc \u2192pK\u2212\u03c0+, pK0, \u039b\u03c0+, pK0\u03c0+\u03c0\u2212, and\n\u039b\u03c0+\u03c0+\u03c0\u2212(Gabyshev, 2006). A clear signal peak is seen\nfrom the intermediate two-body B\u2212\u2192\u03a3c(2455)0p de-\ncay, together with a hint of B\u2212\u2192\u03a3c(2520)0p, shown\nin Fig. 17.12.3a. The open histogram is the distribution\nfrom the B signal region (|\u2206E| < 0.03 GeV and mES >\n5.27 GeV/c2). The hatched histogram is the distribution\nfrom sideband regions (\u22120.10 GeV < \u2206E < \u22120.04 GeV or\n0.04 GeV < \u2206E < 0.20 GeV) normalized to the B signal\nregion. The curve shows the result of the \ufb01t which includes\nthe contributions from \u03a3c(2455)0 and \u03a3c(2520)0 \u2192\u039b+\nc \u03c0\u2212\ndecays and the background parameterized with a linear\nfunction. The \u03a3c(2455/2520)0 signal shapes are \ufb01xed from\nMC assuming a Breit-Wigner function convolved with the\nresolution function.\nA subsequent BABAR analysis (Aubert, 2008aa) using\n\u223c383\u00d7106 BB pairs con\ufb01rms the \u03a3c(2455)0, but with an\neven weaker signal from \u03a3c(2520)0 shown in Fig. 17.12.3b.\nA broad structure \u03a3c(2800)0, however, is clearly seen (Fig.\n17.12.3c). The \u03a3c(2455)0 is a spin- 1\n2 baryon, while the\n\u03a3c(2520)0 has spin 3\n2. A decay of the spin-0 B meson to\na spin- 1\n2 antiproton and a spin- 3\n2 \u03a3c requires one or two\nunits of orbital angular momentum, and hence its sup-\npression is reasonable.\nFinal states from weak B meson decays b \u2192cud have\nthree light quarks, therefore the isospin can be I = 1\n2 or\nI = 3\n2, while the W exchange bd \u2192cu has only one and\ntherefore I =\n1\n2 (see Fig. 17.12.5a and c below). Since\nhadronization is a strong interaction process, isospin is\nconserved and we can classify \ufb01nal states according to\ntheir isospin. The average branching fraction B(B\u2212\u2192\n\u03a3c(2455)0p) = (4.0 \u00b1 0.4 \u00b1 1.0\u039bc) \u00d7 10\u22125 (pure isospin\nI = 3\n2) is about twice that of B0 \u2192\u039b+\nc p (pure isospin I =\n1\n2). Using Clebsch-Gordan coe\ufb03cients, one would expect\nB(B0 \u2192\u03a3c(2455)+p) < 2.5\u00d710\u22125, compatible with the\npresent limit (Table 17.12.1).\nDecays to two charmed baryons\nAn unexpectedly large rate is found for B mesons decaying\nto two charmed baryons, speci\ufb01cally B+ \u2192\u039e0\nc\u039b+\nc (Chis-\ntov, 2006a). In this analysis, the following sub-decays are\nreconstructed: \u039e0\nc \u2192\u039e\u2212\u03c0+ and \u039bK\u2212\u03c0+, \u039b+\nc \u2192pK\u2212\u03c0+,\n\u039e\u2212\u2192\u039b\u03c0\u2212, and \u039b \u2192p\u03c0\u2212. For \u039e\u2212\u2192\u039b\u03c0\u2212, one can\n\ufb01t the p and \u03c0\u2212tracks to a common vertex in order\nto get the \u039b 4-momenta. Then one can \ufb01t the \u039b trajec-\ntory and the \u03c0\u2212track to a common vertex to reconstruct\nthe long lived \u039e\u2212. Fig. 17.12.4 shows the projection plots\nof selected candidate events; the maximum likelihood \ufb01t\nresults are overlaid. The product of branching fractions\nB(B+ \u2192\u039e0\nc\u039b+\nc ) \u00d7 B(\u039e0\nc \u2192\u039e+\u03c0\u2212) is measured to be\n(4.8+1.0\n\u22120.9 \u00b1 1.1 \u00b1 1.2) \u00d7 10\u22125. BABAR found a somewhat\nsmaller branching fraction (Aubert, 2008e), but still about\ntwo orders of magnitude larger than that of B0 \u2192\u039b+\nc p.\nUsing our estimate B(\u039e0\nc \u2192\u039e\u2212\u03c0+) \u22481.2% described\nin Section 17.12.1, the average translates to B(B+ \u2192\n\u039e0\nc\u039b+\nc ) \u22480.22%. This is quite intriguing and o\ufb00ers an im-\nportant clue to understand the underlying dynamics for\nbaryonic B decays.\nThe decay of the neutral B meson B0 \u2192\u039e\u2212\nc \u039b+\nc (with\n\u039e\u2212\nc\n\u2192\u039e+\u03c0\u2212\u03c0\u2212) has not yet been observed with high\nsigni\ufb01cance, however we have averaged the results of Belle\nand BABAR, using the theoretical estimate (described in\nSection 17.12.1) B(\u039e\u2212\nc \u2192\u039e+\u03c0\u2212\u03c0\u2212) \u22486.4%, assuming a\n50% uncertainty.\nCharmless decays\nSo far, no charmless two-body baryonic B decays have\nbeen observed. The 90% con\ufb01dence level upper limits have\nbeen pushed below the 10\u22126 level and are listed in Ta-\nble 17.12.1. The method to determine upper limit yields\n\n426\n0\n2\n4\n6\n8\n10\n12\n-0.2\n-0.1\n0\n0.1\n0.2\n0\n2\n4\n6\n8\n10\n12\n14\n16\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\n0\n2\n4\n6\n8\n10\n2.42\n2.44\n2.46\n2.48\n2.5\n2.52\n\u2206E (GeV)\nEvents/10 MeV\na)\nMbc (GeV/c2)\nEvents/2 MeV/c2\nb)\nM(\u039e\n\u2013\nc\n0) (GeV/c2)\nEvents/4 MeV/c2\nc)\nM(\u039bc\n+) (GeV/c2)\nEvents/4 MeV/c2\nd)\n0\n2\n4\n6\n8\n10\n12\n2.24 2.26 2.28 2.3 2.32 2.34\nFigure 17.12.4. The \u2206E (a) and mES = Mbc (b) distri-\nbutions for the B+ \u2192\u039e0\nc\u039b+\nc candidates from Belle (Chistov,\n2006a). The hatched histograms show the combined \u039e0\nc and \u039b+\nc\nmass sidebands normalized to the signal region. Also shown are\nthe \u039e0\nc (c) and \u039b+\nc (d) mass distributions for the B+ \u2192\u039e0\nc\u039b+\nc\ncandidates taken from the B signal region of |\u2206E| < 0.025 GeV\nand mES > 5.272 GeV/c2. For the \u039e0\nc (\u039b+\nc ) distribution \u039b+\nc\n(\u039e0\nc) is required to be within \u00b115 MeV/c2 of the nominal mass.\nThe overlaid curves are the \ufb01t results.\nis either based on the Feldman-Cousins approach (Conrad,\nBotner, Hallgren, and Perez de los Heros, 2003; Feldman\nand Cousins, 1998) or by integration of the likelihood \ufb01t\nfunction convolved with a Gaussian error function. Since\nthere is no sign of observation, it will be interesting to\nknow the order of magnitude of the branching fractions of\nthese rare decays, and hopefully they can be determined\nby the LHCb experiment or future super \ufb02avor factories.\n17.12.2.2 Theory and interpretation\nSince baryonic B decays involve two baryons in the \ufb01-\nnal state, the underlying mechanism is complicated. The\nquark diagrams for two-body baryonic B decays are shown\nin Fig. 17.12.5: internal W-emission for b \u2192c(u) (a), the\nb \u2192s(d) penguin transition (b), W-exchange for the neu-\ntral B meson (c), and W-annihilation for the charged\nB (d). As for mesonic B decays, W-exchange and W-\nannihilation are expected to be helicity suppressed (Chau,\n1983) which can be understood in the same way as for lep-\ntonic decays (see Eq. 17.10.4 and the accompanying dis-\ncussion). Therefore, the main contributions to two-body\nbaryonic B decay B \u2192B1B2 are due to either the in-\nternal W-emission diagram or the penguin diagram. It\nshould be stressed that, unlike the case of mesonic B de-\ncays, internal W emission in baryonic B decays is not\n(a)\n(b)\n(c)\n(d)\nFigure 17.12.5. Quark diagrams for two-body baryonic B\ndecay B \u2192B1B2. The waveline represents a W, while gluon\nlines are omitted. Quark antiquark pairs from the vacuum are\ndenoted as x, y and determine the \ufb02avor of the two \ufb01nal bar-\nyons. In this and subsequent \ufb01gures, the colors of the quark\nlines are signi\ufb01cant: see the discussion in Section 17.12.2.2.\nnecessarily color suppressed. This is because the baryon\nwave function is totally antisymmetric in the color indices.\nOne component of this wave function is illustrated in Fig.\n17.12.5, where the internal W-emission (a) needs either of\ntwo matching colors (blue or green) to produce a baryon,\nwhile exactly one matching color (red) would be required\nto produce a meson. The black quark lines in (d) indicate\nthat any color will do.\nIn short, the two-body decay proceeds mainly through\nthe nonfactorizable internal W-emission or the b \u2192s(d)\npenguin transition. This is why it is di\ufb03cult to determine\ntheoretical estimates for the rates of two-body decays.\nThere exist several theoretical models for describing\nB decays into two baryons: the pole model of Jar\ufb01et al.\n(1990) and Cheng and Yang (2002a), the diquark model\nof Ball and Dosch (1991) and the QCD sum rule analy-\nsis by Chernyak and Zhitnitsky (1990). The predictions of\nthese models for some selected charmless, singly-charmed\nand doubly-charmed baryonic B decays are listed in Ta-\nbles 17.12.2\u201317.12.4. Evidently, many of the earlier model\npredictions are either too large compared to or marginally\ncomparable to experiment.\nExperimentally, two-body baryonic B decays follow\nthe pattern\nB(B \u2192B1cB2c) \u223c10\u22123\n\u226bB(B \u2192BcB)\n\u223c10\u22125\n\u226bB(B \u2192B1B2)\n<\n\u223c10\u22126 .\n(17.12.4)\nwhere no c subscript indicates a non-charmed baryon.\nSince the doubly-charmed baryonic decay B \u2192\u039ec\u039bc\nproceeds via b \u2192csc, while B \u2192\u039bcp proceeds via a\nb \u2192cdu quark transition, the CKM matrix elements for\nthe two decays are the same in magnitude but opposite in\nsign. One may therefore wonder why the \u039ec\u039bc mode has a\n\n427\nTable 17.12.2. Branching fractions (in units of 10\u22127) for\nsome charmless two-body baryonic B decays classi\ufb01ed into two\ncategories: tree-dominated (upper) and penguin-dominated\n(lower). Branching fractions denoted by \u201c\u2020\u201d are calculated only\nfor the parity-conserving part. Experimental limits are taken\nfrom Table 17.12.1. Theoretical predictions are taken from the\nfollowing references \u2014 \u201cCZ\u201d: Chernyak and Zhitnitsky (1990);\n\u201cJar\ufb01\u201d: Jar\ufb01et al. (1990); and \u201cCY\u201d: Cheng and Yang (2002a).\nDecay\nCZ\nJar\ufb01\nCY\nExperiment\nB0 \u2192pp\n12\n70\n1.1\u2020\n< 1.1\nB0 \u2192nn\n3.5\n70\n1.2\u2020\nB0 \u2192np\n6.9\n170\n5.0\nB0 \u2192\u039b\u039b\n2\n0\u2020\n< 3.2\nB\u2212\u2192p\u2206\u2212\u2212\n2.9\n3200\n14\n< 1.4\nB0 \u2192p\u2206\u2212\n0.7\n1000\n1.4\nB\u2212\u2192n\u2206\u2212\n1\n4.6\nB0 \u2192n\u22060\n1000\n4.3\nB\u2212\u2192\u039bp\n<\n\u223c30\n2.2\u2020\n< 3.2\nB0 \u2192\u039bn\n2.1\u2020\nB0 \u2192\u03a3+p\n60\n0.18\u2020\n< 2.6\nB\u2212\u2192\u03a30p\n30\n0.58\n< 4.7\nB\u2212\u2192\u03a3+\u2206\u2212\u2212\n60\n2.0\nB0 \u2192\u03a3+\u2206\u2212\n60\n0.63\nB\u2212\u2192\u03a3\u2212\u22060\n20\n0.87\nTable 17.12.3. Predictions (in units of 10\u22125) of singly\ncharmed two-body baryonic B decays in various models. Theo-\nretical references are as in Table 17.12.2. Experimental results\nare taken from Table 17.12.1.\nDecay\nCZ\nJar\ufb01\nCY\nExperiment\nB0 \u2192\u039b+\nc p\n190\n110\n1.1\n1.9 \u00b1 0.2\nB\u2212\u2192\u03a30\ncp\n300\n1500\n6.0\n4.0 \u00b1 0.4\nB0 \u2192\u03a30\ncn\n580\n0.06\nB\u2212\u2192\u039b+\nc \u2206\u2212\u2212\n20\n3600\n1.9\n5.9 \u00b1 1.2\nrate two orders of magnitude larger than \u039bcp. Indeed, ear-\nlier calculations based on QCD sum rules (Chernyak and\nZhitnitsky, 1990) or the diquark model (Ball and Dosch,\n1991) all predict that B(B \u2192\u039ec\u039bc) \u2248B(B \u2192BcN) (see\nTable 17.12.3), which is in violent disagreement with ex-\nperiment. The decay pattern (17.12.4) can be understood\nas follows. In an energetic heavy baryon, the momentum is\nmostly carried by the constituent heavy quark. Therefore,\nin b \u2192ccs decays, the energetic c quark will fragment\ninto B1c, and c into B2c. Consequently, no hard gluon is\nneeded to produce the energetic \u039ec\u039bc pair in B decays\n(see Fig. 17.12.6a). In B \u2192\u039bcp decay, the three quarks of\nthe energetic proton share the same momentum fraction\nTable 17.12.4. Predicted branching fractions (in units of\n10\u22124) of doubly-charmed two-body baryonic B decays (Cheng,\nChua, and Hsiao, 2009). Experimental results are taken from\nTable 17.12.1.\nDecay\nTheory\nExperiment\nB\u2212\u2192\u039e0\nc \u039b\u2212\nc\n10.4+5.7\n\u22125.5\n\u223c21.6 \u00b1 5.4\nB0 \u2192\u039e+\nc \u039b\u2212\nc\n9.4+6.3\n\u22124.1\n\u223c3\nB0 \u2192\u039b+\nc \u039b\u2212\nc\n0.52+0.35\n\u22120.19\n< 0.62\nB\nb\nc\n\u039b+\nc\n\u00afp\nB\nb\nc\n\u039ec\n\u00af\u039bc\n\u00afc\ns\n(a)\n(b)\nFigure 17.12.6. Quark diagrams for two-body baryonic B\ndecays B \u2192\u039ec\u039bc and B \u2192\u039b+\nc p. At least two hard gluons are\nneeded for \u039b+\nc p production.\n\u223c1/3. Hence, two hard gluons are needed to produce an\nenergetic p: one hard gluon to kick the spectator quark of\nthe B meson to make it energetic and the other to produce\nthe hard qq pair (see Fig. 17.12.6b). Therefore, the decay\nrate of B \u2192\u039bcp is suppressed with respect to B \u2192\u039ec\u039bc\ndue to a dynamical factor O(\u03b14\nS) \u223c10\u22122. These qualita-\ntive statements have been supported by realistic calcula-\ntions of the decay rates for B \u2192\u039ec\u039bc (Cheng, Chua, and\nHsiao, 2009) and B0 \u2192\u039b+\nc p (He, Li, Li, and Wang, 2007).\nThe charmless decay B0 \u2192pp is suppressed relative\nto B \u2192\u039bcp by the CKM matrix elements |Vub/Vcb|2 and\nis also subject to a possible dynamical suppression:\nB(B \u2192pp) = B(B \u2192\u039b+\nc p)\n\f\f\f\f\nVub\nVcb\n\f\f\f\f\n2\n\u00d7 fdyn\n\u22482\u00d710\u22127 \u00d7 fdyn .\n(17.12.5)\nIn the absence of dynamical suppression fdyn, the pre-\ndicted rate for two-body charmless decays is on the verge\nof the experimental upper limit.\nIf the dynamical suppression is of order 10\u22122 as in the\ncase of B \u2192\u039bcp, then the branching fraction for charm-\nless two-body decays will be of order 10\u22129 and thus be-\nyond the reach even of super \ufb02avor factories. In reality, the\nbranching fraction is most likely of order 10\u22128, between\nthe extreme cases of 10\u22127 and 10\u22129. Thus far, there is no\nclear theoretical prediction for charmless two-body decays.\nPresumably a reliable prediction based on pQCD can be\nmade as the energy release in charmless two-body decay is\nvery large, justifying the use of pQCD (Cheng and Yang,\n2002a).\nMost of the previous theoretical predictions are not\ntrustworthy: for example, predictions based on the QCD\nsum rule, the pole model and the diquark model are too\nlarge compared to experiment. The most reliable predic-\ntions are based on pQCD, which has been successfully\napplied to B \u2192\u039bcp (He, Li, Li, and Wang, 2007). The\n\n428\nTable 17.12.5. Branching fractions of observed decays of B mesons to charmless baryons plus charmed mesons. Contributing\nquark diagrams are given in square brackets following each mode: annihilation type A (Fig. 17.12.5c with an extra qq pair),\nexternal W-emission type 1 (Fig. 17.12.7), and internal W-emission type 2 (Fig. 17.12.8).\nDecay\nBABAR\nBelle\nother\nAverage\n(B : 10\u22124)\n(del Amo Sanchez, 2012)\n(Abe, 2002g)\n(Anderson et al., 2001)\nB0 \u2192D0pp\n[2c, 2e, A]\n1.02 \u00b1 0.04 \u00b1 0.06\n1.18 \u00b1 0.15 \u00b1 0.16\n1.04 \u00b1 0.07\nB0 \u2192D\u22170pp\n[2c, 2e, A]\n0.97 \u00b1 0.07 \u00b1 0.09\n1.20+0.33\n\u22120.29 \u00b1 0.21\n1.00 \u00b1 0.11\nB0 \u2192D\u2217+np\n[2c, 2e, A]\n14.5+3.4\n\u22123.0 \u00b1 2.7\nB0 \u2192D+pp\u03c0\u2212\n3.32 \u00b1 0.10 \u00b1 0.29\nB0 \u2192D\u2217+pp\u03c0\u2212\n4.55 \u00b1 0.16 \u00b1 0.39\n6.5+1.3\n\u22121.2 \u00b1 1.0\n4.67 \u00b1 0.40\nB\u2212\u2192D0pp\u03c0\u2212\n3.72 \u00b1 0.11 \u00b1 0.25\nB\u2212\u2192D\u22170pp\u03c0\u2212\n3.73 \u00b1 0.17 \u00b1 0.27\nB0 \u2192D0pp\u03c0\u2212\u03c0+\n2.99 \u00b1 0.21 \u00b1 0.45\nB0 \u2192D\u22170pp\u03c0\u2212\u03c0+\n1.91 \u00b1 0.36 \u00b1 0.29\nB\u2212\u2192D+pp\u03c0\u2212\u03c0\u2212\n1.66 \u00b1 0.13 \u00b1 0.27\nB\u2212\u2192D\u2217+pp\u03c0\u2212\u03c0\u2212\n1.86 \u00b1 0.16 \u00b1 0.19\n(B : 10\u22125)\n(Chang, 2009)\nB0 \u2192D0\u039b\u039b\n[2c, 2e, A]\n1.05+0.57\n\u22120.44 \u00b1 0.14\n(B : 10\u22125)\n(Medvedeva, 2007)\nB0 \u2192D+\ns \u039bp\n[2c]\n2.9 \u00b1 0.7 \u00b1 0.5 \u00b1 0.4Ds\n(B : 10\u22125)\n(Chen, 2011)\nB\u2212\u2192D0\u039bp\n[1b, 2e]\n1.43+0.28\n\u22120.25 \u00b1 0.18\nB\u2212\u2192D\u22170\u039bp\n[1b, 2e]\n< 4.8\n(B : 10\u22126)\n(Aubert, 2003b)\n(Xie, 2005)\nB\u2212\u2192J/\u03c8 \u039bp\n[2e]\n12+9\n\u22126\n11.6 \u00b1 2.8+1.8\n\u22122.3\n11.7 \u00b1 3.1\nB\u2212\u2192J/\u03c8 \u03a30p\n[2e]\n< 11\nB0 \u2192J/\u03c8 pp\n[2e]\n< 1.9\n< 0.83\n< 0.83\npQCD calculation for charmless modes such as \u039bp and pp\nis much more involved and has not yet been carried out.\n17.12.3 Decays to baryon antibaryon plus mesons\nBefore Belle and BABAR investigated baryonic B decays,\nthere were already observations by CLEO of B+ \u2192\u039bcp\u03c0+\n(Fu et al., 1997) and B0 \u2192D\u2217\u2212pp\u03c0+, D\u2217\u2212pn (Anderson\net al., 2001). These are all generic b \u2192c transitions, and\nmany more have since been investigated by the B Facto-\nries. Their branching fractions are shown in Table 17.12.5\nfor cases where a c quark hadronizes into a charmed me-\nson, and in Table 17.12.6 where a c quark hadronizes into\na charmed baryon. In the following subsections we con-\nsider in turn theoretical issues (Section 17.12.3.1), rare de-\ncays (Section 17.12.3.2), the threshold enhancement seen\nin many multibody baryonic decays (Section 17.12.3.3),\nthe role of \ufb01nal state multiplicity (Section 17.12.3.4),\nand angular correlations of the \ufb01nal state particles (Sec-\ntion 17.12.3.5); we conclude with brief discussions of the\nrole of Cabibbo suppression (Section 17.12.3.6), isospin re-\nlations (Section 17.12.3.7), and the suppression of ss pairs\n(Section 17.12.3.8).\n17.12.3.1 Theoretical models and Feynman diagrams\nThe complexity of quark diagrams increases with the \ufb01nal\nstate multiplicity. For three-body decays of a B meson to\nthe baryonic \ufb01nal state B1B2M there are many distinct\nquark diagrams: two type-1 or external W-diagrams (Figs\n17.12.7a and b), and eight type-2 or internal W-emission\n\n429\nTable 17.12.6. Branching fractions of observed decays of B mesons to \ufb01nal states with a charmed baryon including three\nor more \ufb01nal state particles. Channels with a \u039b+\nc baryon in the \ufb01nal state have an additional \u00b126% relative uncertainty (not\nincluded) from the assumption B(\u039b+\nc \u2192pK\u2212\u03c0+) = 0.050 \u00b1 0.013 and are marked with \u2020. Two daggers indicate that two such\nterms have to be added (linearly due to correlation). Decays via intermediate resonances are marked with \u2022. Contributing quark\ndiagrams are given in square brackets following each three-body mode: annihilation type A (Fig. 17.12.5c with an extra qq pair),\nexternal W-emission type 1 (Fig. 17.12.7), and internal W-emission type 2 (Fig. 17.12.8).\nDecay\nBABAR\nBelle\nother\nAverage\n(B : 10\u22124)\n(Aubert, 2010h)\nB0 \u2192\u039b+\nc p\u03c00\n[2abdfg, A]\n1.94 \u00b1 0.17 \u00b1 0.14\u2020\n\u2022 see Table 17.12.1\n(B : 10\u22124)\n(Aubert, 2008aa)\n(Gabyshev, 2006)\n(Dytman et al., 2002)\nB\u2212\u2192\u039b+\nc p\u03c0\u2212\n[1a, 2abdfg]\n3.38 \u00b1 0.12 \u00b1 0.12\u2020\n2.01 \u00b1 0.15 \u00b1 0.20\u2020\n2.4 \u00b1 0.6+0.19\n\u22120.17\n\u2020\n2.92 \u00b1 0.14\n\u2022 see Table 17.12.1\n(B : 10\u22124)\n(Aubert, 2008e)\n(Abe, 2006b)\nB\u2212\u2192\u039b+\nc \u039b\u2212\nc K\u2212\n[2d]\n11.4 \u00b1 1.5 \u00b1 1.7\u2020\u2020\n6.5+1.0\n\u22120.9 \u00b1 1.1\u2020\u2020\n8.0 \u00b1 1.3\nB0 \u2192\u039b+\nc \u039b\u2212\nc K0\n[2dg]\n3.8 \u00b1 3.1 \u00b1 0.5\u2020\u2020\n7.9+2.9\n\u22122.3 \u00b1 1.2\u2020\u2020\n6.2 \u00b1 2.0\n(B : 10\u22125)\n(Lees, 2011f)\nB0 \u2192\u039b+\nc \u039bK\u2212\n[2abf, A]\n3.8 \u00b1 0.8 \u00b1 0.2\u2020\n(B : 10\u22124)\n(Lees, 2013h)\n(Park, 2007)\n(Dytman et al., 2002)\nB0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212\ntotal\n12.3 \u00b1 0.5 \u00b1 0.7\u2020\n11.2 \u00b1 0.5 \u00b1 1.4\u2020\n16.7 \u00b1 1.9+1.9\n\u22121.6\n\u2020\n12.35 \u00b1 0.72\n\u2022 B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212\nnonresonant\n7.9 \u00b1 0.4 \u00b1 0.4\u2020\n6.4 \u00b1 0.4 \u00b1 0.9\u2020\n6.66 \u00b1 0.89\n\u2022 B0 \u2192\u03a3++\nc\n(2455)p\u03c0\u2212\n[1a, 2g, A]\n2.13 \u00b1 0.10 \u00b1 0.10\u2020\n2.1 \u00b1 0.2 \u00b1 0.3\u2020\n3.7 \u00b1 0.8 \u00b1 0.7\u2020\n2.15 \u00b1 0.13\n\u2022 B0 \u2192\u03a3++\nc\n(2520)p\u03c0\u2212\n[1a, 2g, A]\n1.15 \u00b1 0.10 \u00b1 0.05\u2020\n1.2 \u00b1 0.1 \u00b1 0.2\u2020\n1.20 \u00b1 0.10\n\u2022 B0 \u2192\u03a30\nc(2455)p\u03c0+\n[2ab, A]\n0.91 \u00b1 0.07 \u00b1 0.04\u2020\n1.4 \u00b1 0.2 \u00b1 0.2\u2020\n2.2 \u00b1 0.6 \u00b1 0.4\u2020\n0.94 \u00b1 0.08\n\u2022 B0 \u2192\u03a30\nc(2520)p\u03c0+\n[2ab, A]\n0.22 \u00b1 0.07 \u00b1 0.01\u2020\n< 0.38\nB\u2212\u2192\u039b+\nc p\u03c0\u2212\u03c00\n18.1 \u00b1 2.9+2.2\n\u22121.6\n\u2020\n\u2022 B\u2212\u2192\u03a30\ncp\u03c00\n[2abfg]\n4.2 \u00b1 1.3 \u00b1 0.4\u2020\n(B : 10\u22124)\n(Aubert, 2009ag)\nB0 \u2192\u039b+\nc p\u03c0+K\u2212\ntotal\n0.433 \u00b1 0.082 \u00b1 0.033\u2020\n\u2022 B0 \u2192\u03a3++\nc\n(2455)pK\u2212\n[1a, 2g]\n0.111 \u00b1 0.030 \u00b1 0.009\u2020\n\u2022 B0 \u2192\u039b+\nc pK\u22170\n[2dg]\n0.160 \u00b1 0.061 \u00b1 0.012\u2020\n(B : 10\u22126)\n(Gr\u00a8unberg, 2012)\nB\u2212\u2192\u039b+\nc ppp\n< 6.2\n(B : 10\u22124)\n(Lees, 2012aa)\n(Dytman et al., 2002)\nB\u2212\u2192\u039b+\nc p\u03c0\u2212\u03c0+\u03c0\u2212\n22.5 \u00b1 2.5+2.4\n\u22121.9\n\u2020\n\u2022 B\u2212\u2192\u03a30\ncp\u03c0\u2212\u03c0\n4.4 \u00b1 1.2 \u00b1 0.5\u2020\n\u2022 B\u2212\u2192\u03a3++\nc\np\u03c0\u2212\u03c0\u2212\n2.98 \u00b1 0.16 \u00b1 0.15\u2020\n2.8 \u00b1 0.9 \u00b1 0.5\u2020\n2.97 \u00b1 0.21\ndiagrams (Figs 17.12.8a\u2013h); W-exchange diagrams (basi-\ncally Fig. 17.12.5c, inserting another qq pair) for the neu-\ntral B meson; and W-annihilation (Fig. 17.12.5d with an-\nother qq pair) for the charged B. The various possibilities\nfor inserting the extra qq pair are only illustrated for the\ntype-2 decay in Fig. 17.12.8, as the same modi\ufb01cation to\n\n430\n(a)\n(b)\nFigure 17.12.7. Quark diagrams for three-body baryonic B\ndecay B \u2192B1B2M corresponding to type 1, factorizable ex-\nternal W-emission contributions.\nthe annihilation diagrams is straightforward. Penguin di-\nagrams can also contribute: these can be obtained from\nFig. 17.12.5b by adding the extra qq pair in the same way\nas for W exchange.\nIn the Feynman diagrams presented in the \ufb01gures, the\nqq pairs are shown detached; they can be produced by\nsoft or hard gluons attached to any other quark line in\nthe diagram, and usually involve more than one gluon to\naccomplish color matching for color neutral mesons and\nbaryons.\nIt should be stressed that among the internal W-\nemission diagrams, Figs 17.12.8d and e (where a red qq\npair is created by the W) are color suppressed while the\nremaining diagrams in Fig. 17.12.8 are not, since the bar-\nyon wave function is antisymmetric in color indices (Cheng\nand Yang, 2002a). For example, B\u2212\u2192J/\u03c8\u039bp proceeds\nvia Fig. 17.12.8e, while B0 \u2192\u03a30\ncp\u03c0+ receives contribu-\ntions predominantly from Figs 17.12.8a and b. The ex-\nperimental observation that J/\u03c8\u039bp is suppressed by one\norder of magnitude is due to the color suppression for\nFig. 17.12.8e and non-suppression for Figs 17.12.8a and b.\nThe decay to \u03a3++\nc\np\u03c0\u2212can also proceed through the (non-\nsuppressed) external W-emission Fig. 17.12.7a, and has a\nhigher branching fraction than the internal W-emission\nprocesses for \u03a30\ncp\u03c0+. This may be explained by simple\ncolor counting: all three colors are possible in color-allowed\nprocesses (type 1), only one color in fully color-suppressed\nprocesses (type 2d,e) and two colors in the unsuppressed\nprocesses (type 2a\u2013c,f\u2013h).\nNeglecting the factorizable annihilation contributions,\nwhich are helicity suppressed, the factorizable contribu-\ntions to three-body decays consist of two parts: (i) the\ntransition process with meson emission, \u27e8M|(q3q2)|0\u27e9\u00d7\n\u27e8B1B2|(q1b)|B\u27e9where (\u00afqiqj)\n\u2261\nqi\u03b3\u00b5(1 \u2212\u03b35)qj\nand\nM denotes a meson, and (ii) the current-induced pro-\ncess in association with a B\nto meson transition,\n\u27e8B1B2|(q1q2)|0\u27e9\u00d7 \u27e8M|(q3b)|B\u27e9. The two-body matrix el-\nement \u27e8B1B2|(q1q2)|0\u27e9in the latter process can be either\nrelated to some measurable quantities, or calculated using\nthe quark model. Note that while the form factors in the\nmatrix elements \u27e8B1B2|(q1q2)|0\u27e9and \u27e8M|(q3b)|B\u27e9depend\non the dibaryon invariant mass squared t = (p1 + p2)2,\nform factors in \u27e8B1(p1)B2(p2)|(q1b)|B(pB)\u27e9are functions\nnot only of t but also of one of the other Mandelstam\n(a)\n(b)\n(c)\n(d)\n(e)\n(f)\n(g)\n(h)\nFigure 17.12.8. Spectator diagrams of type 2, factorizable\n(d,e) and non-factorizable (a\u2013c,f\u2013h) internal W-emission, for\nthree-body baryonic B decays B \u2192B1B2M.\nvariables s = (pB \u2212p1)2 or u = (pB \u2212p2)2. The current-\ninduced contribution to three-body baryonic B decays has\nbeen discussed in various publications, e.g. Chua, Hou,\nand Tsai (2002a). By contrast, it is di\ufb03cult to evaluate\nthe three-body matrix element in the transition process\nand in this case one can appeal to the pole model (Cheng\nand Yang, 2002b). Instead of showing various model pre-\ndictions for three-body decays, we summarize in Table\n17.12.7 the references related to the study of doubly-\ncharmed, singly-charmed, and charmless three-body bary-\nonic B decays. The interested reader is referred to the\noriginal work for more details.\n\n431\nTable 17.12.7. References for the theoretical studies of\ndoubly-charmed, singly-charmed, and charmless three-body\nbaryonic B decays.\nModes\nReference\nDoubly charmed:\n\u039bc\u039bcK0, \u039bc\u039bcK\u2212\nCheng, Chua, and\nHsiao (2009)\nSingly charmed:\nnpD(\u2217)+,0, \u039bpD(\u2217)+,0, \u03a30pD(\u2217)+,0\nChua, Hou, and Tsai\n(2002b)\n\u03a3\u2212nD(\u2217)+,0, nnD(\u2217)0, \u039bnD(\u2217)0\nChen, Cheng, Geng,\nand Hsiao (2008)\n\u03a3+pD(\u2217)0, \u039e\u2212\u03a3\u2212D(\u2217)0, \u039e\u2212\u03a30D(\u2217)0\n\u039e\u2212\u039bD(\u2217)0, \u039e0\u03a3+D(\u2217)0\nnpJ/\u03c8 , \u039bpJ/\u03c8 , \u039e\u2212\u03a30J/\u03c8, \u039e0\u03a3+J/\u03c8\nnnJ/\u03c8 , \u039bnJ/\u03c8 , \u039e0\u03a30J/\u03c8, \u039e\u2212\u03a3+J/\u03c8\n\u039b+\nc p\u03c0\u2212, \u03a3++\nc\np\u03c0\u2212, \u03a30\ncp\u03c0+(\u03c00)\nCheng and Yang\n(2003)\nCharmless (tree):\nnp\u03c0+, np\u03c1+, pn\u03c0\u2212, pn\u03c1\u2212\nCheng and Yang\n(2002a)\n\u03a3\u2212\u039b\u03c0+, \u039e\u2212\u039e0\u03c0+, \u03a30\u03a3\u2212\u03c0+, pp\u03c0\u2212\nChua and Hou\n(2003)\nCharmless (penguin):\nppK\u2212, ppK\u2217\u2212, pnK\u2212, pnK\u2217\u2212\nCheng and Yang\n(2002a)\nppK0, ppK\u22170, nnK\u2212, nnK\u2217\u2212\n\u039bp\u03c0+, \u039bp\u03c1+, \u03a30p\u03c0+, \u03a30p\u03c1+\n\u03a3\u2212n\u03c0+, \u03a3\u2212n\u03c1+, \u039bp\u03b7\u2032\n17.12.3.2 Rare decays\nThe \ufb01rst charmless baryonic B decay observed was B+ \u2192\nppK+, in an analysis of a 29.4 fb\u22121 data sample (Abe,\n2002f). One unexpected feature of this rare decay pro-\ncess is that the observed mass distribution of the baryon-\nantibaryon pair is peaked near threshold as shown in Fig.\n17.12.9. To ensure that the measured events are gen-\nuine non-b \u2192c signals, the regions 2.850 < M(pp) <\n3.128 GeV/c2 and 3.315 < M(pp) < 3.735 GeV/c2 are ex-\ncluded to remove background from modes with \u03b7c and J/\u03c8\nmesons, and \u03c8\u2032, \u03c7c0, and \u03c7c1 mesons, respectively. The\nmass distribution of vetoed events can be found in the in-\nset plot of Fig. 17.12.9, where a J/\u03c8 peak can be clearly\nidenti\ufb01ed. Since the e\ufb03ciency of particle identi\ufb01cation\nvaries with respect to the particle\u2019s momentum, the over-\nall reconstruction e\ufb03ciency is dependent on the mass of\nthe baryon-antibaryon system. The partial branching frac-\ntions in bins of baryon-antibaryon mass are then summed\nto obtain the total branching fraction.\n0\n20\n40\n60\n80\n100\n120\n2\n2.5\n3\n3.5\n4\n4.5\nMpp\n_ (GeV/c2)\ndN / dMpp\n_ (Events / (GeV/c2))\nEvents / (5 MeV/c2)\n0\n5\n10\n3\n3.05\n3.1\n3.15\nFigure 17.12.9. The \ufb01tted yield from Belle (Abe, 2002f) di-\nvided by the bin size for B+ \u2192ppK+ as a function of pp\nmass. A charmonium veto is applied. The distribution from\nnon-resonant B+ \u2192ppK+ MC simulation is superimposed\n(shaded). The inset shows the pp mass distribution for the\nJ/\u03c8 K+ signal region.\nThe measured B+ \u2192ppK+ branching fraction is \u223c\n4\u00d710\u22126. The decay is di\ufb03cult to observe due to the large\nbackground from continuum events. A good particle iden-\nti\ufb01cation system is a key for this analysis since both p\nand K+ should be positively identi\ufb01ed in order to reject\nthe background. Another important point is that a more\nsophisticated pattern recognition method based on event\nshape information was adopted to discriminate the more\nisotropic B events from the jet-like continuum events.\nFollowing this \ufb01rst observation, many other three-body\ncharmless baryonic B decays have been found: p\u039b\u03c0\u2212, p\u039b\u03c00,\npp\u03c0+, ppK0, ppK\u22170, ppK\u2217+, \u039b\u039bK+, \u039b\u039bK0, and \u039b\u039bK\u22170.\nExcept for B+ \u2192p\u039b\u03c00, all these modes are reconstructed\nentirely from charged particles in the \ufb01nal state, i.e. \u039b \u2192\np\u03c0\u2212, K0\nS \u2192\u03c0+\u03c0\u2212, K\u22170 \u2192K+\u03c0\u2212, and K\u2217+ \u2192K0\nS\u03c0+.\nThe signal shape can be well described by a single Gaus-\nsian in mES and a sum of two Gaussians in \u2206E. In the \ufb01t\nto determine signal yield with the \u2206E spectrum, there are\nfeed-across events between similar B decays. For example,\nB+ \u2192ppK+ events can form a bump at \u22120.05 GeV in\n\u2206E in the study of B+ \u2192pp\u03c0+ when the K+ is misiden-\nti\ufb01ed as a \u03c0+. There are also feed-down events from sim-\nilar decays with higher multiplicity, e.g. B0 \u2192ppK\u22170 can\nform a bump below \u22120.01 GeV in \u2206E in the study of\nB+ \u2192ppK+. These structures are useful as a sanity check\nfor the measured branching fractions of related modes.\nThe measured branching fractions of the above modes are\nall \u223c10\u22126, and are summarized in Table 17.12.8.\n17.12.3.3 Threshold enhancement\nMany of the abovementioned channels also have the\nspecial feature that the measured mass spectrum of\n\n432\nTable 17.12.8. Branching fractions of observed decays of B mesons to charmless baryons plus charmless mesons. Decays via\nintermediate resonances are marked with \u2022.\nDecay\nBABAR\nBelle\nAverage\n(B : 10\u22126)\n(Aubert, 2009w)\n(Wang, 2003)\nB0 \u2192\u039bp\u03c0\u2212\n3.07 \u00b1 0.31 \u00b1 0.23\n3.97+1.00\n\u22120.80 \u00b1 0.56\n3.18 \u00b1 0.36\nB0 \u2192\u039bpK\u2212\n< 0.82\nB0 \u2192\u03a30p\u03c0\u2212\n< 0.38\n(B : 10\u22126)\n(Aubert, 2007k)\n(Chen, 2008a)\nB0 \u2192ppK0\n3.0 \u00b1 0.5 \u00b1 0.3\n2.51+0.35\n\u22120.29 \u00b1 0.21\n2.66 \u00b1 0.32\nB0 \u2192ppK\u22170\n1.5 \u00b1 0.5 \u00b1 0.4\n1.18+0.29\n\u22120.25 \u00b1 0.11\n1.23 \u00b1 0.27\nB+ \u2192ppK\u2217+\n5.3 \u00b1 1.5 \u00b1 1.3\n3.38+0.73\n\u22120.60\n3.57 \u00b1 0.63\n(B : 10\u22126)\n(Aubert, 2005p)\n(Wei, 2008b)\nB+ \u2192ppK+\n6.7 \u00b1 0.5 \u00b1 0.4\n5.00+0.24\n\u22120.22 \u00b1 0.32\n5.47 \u00b1 0.34\n(B : 10\u22126)\n(Aubert, 2007k)\n(Wei, 2008b)\nB+ \u2192pp\u03c0+\n1.7 \u00b1 0.3 \u00b1 0.3\n1.57+0.17\n\u22120.15 \u00b1 0.12\n1.59 \u00b1 0.15\n(B : 10\u22126)\n(Chang, 2009)\nB+ \u2192\u039b\u039b\u03c0+\n< 0.94\nB0 \u2192\u039b\u039bK0\n4.76+0.84\n\u22120.65 \u00b1 0.61\nB0 \u2192\u039b\u039bK\u22170\n2.46+0.87\n\u22120.72 \u00b1 0.34\nB+ \u2192\u039b\u039bK+\n3.38+0.36\n\u22120.41 \u00b1 0.41\nB+ \u2192\u039b\u039bK\u2217+\n2.19+1.13\n\u22120.88 \u00b1 0.33\n(B : 10\u22126)\n(Chen, 2009)\nB+ \u2192\u039bp\u03c0\u2212\u03c0+\n5.92+0.88\n\u22120.84 \u00b1 0.69\n\u2022 B+ \u2192\u039bp\u03c10\n4.78+0.67\n\u22120.64 \u00b1 0.60\n\u2022 B+ \u2192\u039bpf2(1270)\n2.03+0.77\n\u22120.72 \u00b1 0.27\nthe baryon-antibaryon pair peaks near threshold. Fig-\nure 17.12.10 shows the di\ufb00erential branching fractions in\nbins of the baryon-antibaryon invariant mass for some rep-\nresentative decays: B+ \u2192pp\u03c0+, presumed to proceed via\nthe b \u2192u tree process, and B+ \u2192ppK+ and B0 \u2192p\u039b\u03c0\u2212,\npresumably b \u2192s strong penguin modes. They will be\nfurther discussed below in Section 17.12.3.5 on angular\ncorrelations.\nThreshold enhancement has also been found in the\nb \u2192c process, although the e\ufb00ect is not as pronounced\nor dominant as in the charmless case. When the available\nenergy is limited to a small amount, say \u223c200 MeV, there\nis no visible peaking feature. Figure 17.12.11 shows the\nbaryon-antibaryon mass for B0 \u2192ppD0, B+ \u2192J/\u03c8p\u039b,\nB+ \u2192p\u039bc\u03c0+, B+ \u2192\u039bc\u039bcK+, B0 \u2192\u039bc\u039bK\u2212, and\nB0 \u2192\u03a30\ncp\u03c0+. There are clear threshold enhancement\npeaks in B0 \u2192ppD0, B+ \u2192p\u039bc\u03c0+, and B0 \u2192\u039bc\u039bK\u2212\nalong with non-negligible phase space components. But\nnot all three-body decays show the threshold behavior. For\nB+ \u2192J/\u03c8p\u039b and B+ \u2192\u039bc\u039bcK+ (Fig. 17.12.11b and d),\nwhere the available phase space is small, there is no clear\nthreshold peak visible, but still a slight enhancement can\nbe detected. The threshold peaking e\ufb00ect is totally absent\nin B0 \u2192\u03a30\ncp\u03c0+ (Fig. 17.12.11f).\nThe same threshold behavior has also been observed in\nthe baryonic J/\u03c8 decays J/\u03c8 \u2192\u03b3pp (Bai et al., 2003) and\nJ/\u03c8 \u2192K\u2212p\u039b (Ablikim et al., 2004b). However, it is often\nargued in the literature (see references in Table 17.12.9\nunder the item \u201cFinal-state interactions\u201d) that threshold\nenhancement in J/\u03c8 \u2192\u03b3pp can be explained in terms\n\n433\nMpp\n_ (GeV/c2)\ndBF / dMpp\n_ ( 10\u22126 / (GeV/c2))\n0\n2\n4\n6\n8\n10\n12\n14\n16\n2\n2.5\n3\n3.5\n4\n4.5\n5\n(a) B+ \u2192ppK+ (Wei, 2008b)\nMpp\n_ (GeV/c2)\ndBF / dMpp\n_ ( 10\u22126 / (GeV/c2))\n0\n1\n2\n3\n4\n5\n6\n2\n2.5\n3\n3.5\n4\n4.5\n5\n(b) B+ \u2192pp\u03c0+ (Wei, 2008b)\nMp\u039b\n_ (GeV/c2)\ndBr / dMp\u039b\n_ ( 10\u22126 / (GeV/c2))\n0\n1\n2\n3\n4\n5\n6\n7\n2\n2.5\n3\n3.5\n4\n4.5\n5\n(c) B0 \u2192p\u039b\u03c0\u2212(Wang, 2007b)\nFigure 17.12.10. Di\ufb00erential branching fractions in bins of the baryon-antibaryon mass for three representative modes. The\ntwo charm veto regions are shown shaded in (a) and (b); in (c), the shaded histogram shows the phase space distribution, which\nis distinctly di\ufb00erent from the measured distribution. The curves indicate the theoretical predictions (Geng and Hsiao, 2006)\nnormalized to the measured charmless branching fractions.\n0\n5\n10\n15\n20\n25\n30\n35\n40\n2\n2.2\n2.4\n2.6\n2.8\n3\n3.2\nM(pp\n_) (GeV/c2)\nEvents/(0.25 GeV/c2)\n(a) B0 \u2192ppD0 (Abe, 2002g)\nEntries/10 MeV/c2\n0\n1\n2\n3\n4\n5\n6\n7\n8\n2\n2.1\n2.2\n M (\u039b,p\n\u2013)\nmass(GeV/c2)\n(b) B+ \u2192J/\u03c8 p\u039b (Xie, 2005)\n(c) B+ \u2192p\u039bc\u03c0+ (Gabyshev, 2006)\n(d) B+ \u2192\u039bc\u039bcK+ (Abe, 2006b)\n)\n2\n) (GeV/c\n\u039b\n \nc\n\u039b\nm(\n3.4\n3.6\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n)\n2\nEvents/ (140 MeV/c\n-5\n0\n5\n10\n15\n20\n(e) B0 \u2192\u039b+\nc \u039bK\u2212(Lees, 2011f)\n2\nGeV/c\n) \np\n(2455)\n0\nc\n\u03a3\nm(\n3.4 3.6 3.8\n4\n4.2 4.4 4.6 4.8\n5\n5.2\n2\n100 MeV/c\n1\n )\np\n0\nc\n\u03a3\ndm(\ndn\n0\n10\n20\n30\n40\n50\n60\n(f) B0 \u2192\u03a30\ncp\u03c0+ (Lees, 2013h)\nFigure 17.12.11. Signal yields (points with error bars) as a function of the baryon antibaryon mass for various modes.\n\n434\nTable 17.12.9. Various interpretations of threshold e\ufb00ects in baryonic B decays.\nModel\nDescription\n1. Pole model\nThe absence of 1/m2\nb suppression of the propagator in pole diagrams and the presence of\na \u039bb or \u039eb intermediate state lead to threshold enhancement (Cheng and Yang, 2002a;\nHou and Soni, 2001).\n2. B1B2 bound state\nThe pp pair forms a bound state such as baryonium or X(1835) (Datta and O\u2019Donnell,\n2003a; Rosner, 2003).\n3. Glueball\nAn isoscalar pp pair forms a gluonic state (Chua, Hou, and Tsai, 2002a; Rosner, 2003).\n4. Final-state interactions\nEnhancement due to \ufb01nal-state interactions between the baryon pair (Haidenbauer, Meiss-\nner, and Sibirtsev, 2006; Kerbikov, Stavinsky, and Fedotov, 2004; Laporta, 2007; Sibirtsev,\nHaidenbauer, Krewald, Meissner, and Thomas, 2005).\n5. Baryon form factors\nIn some approaches such as factorization, fragmentation, etc., the amplitude is governed\nby dibaryon form factors which fall o\ufb00rapidly with dibaryon invariant mass as suggested\nby QCD counting rules (Chua and Hou, 2003; Chua, Hou, and Tsai, 2002a).\nof \ufb01nal-state interactions between the baryon pair, while\nthe same threshold e\ufb00ect in baryonic B decays can be\nunderstood in terms of the simple short-distance picture\ndepicted in Fig. 17.12.12.\nThe so-called \u201cthreshold e\ufb00ect\u201d indicates that the B\nmeson prefers to decay into a baryon-antibaryon pair with\nlow invariant mass accompanied by a fast recoil meson.\nThis peaking behavior was quite unexpected, and has lead\nto various speculations about possible mechanisms, such\nas a glueball bound state formed by gluons, a baryonium\nbound state of the baryon-antibaryon pair, etc. Threshold\nenhancement was \ufb01rst proposed by Hou and Soni (2001),\nmotivated by the CLEO measurement of B \u2192D\u2217pn and\nD\u2217pp\u03c0 (Anderson et al., 2001). They argued that in order\nto enhance baryonic B decay, one has to reduce the energy\nrelease and at the same time allow for baryonic ingredi-\nents to be present in the \ufb01nal state. In other words, they\nconjectured that enhanced baryon production is favored\nby reduced energy release on the baryon side. This is in-\ndeed the near threshold e\ufb00ect mentioned above. Hence,\nthe smallness of the two-body baryonic decay B \u2192B1B2\nhas to do with its large energy release.\nA heuristic approach to understanding the threshold\nenhancement in three-body decays can be obtained by\nlooking at the Feynman diagrams in Fig. 17.12.8. In all\nthese diagrams, the weak decay of a B meson produces\ntwo quarks and two antiquarks including the spectator.\nBaryons are formed with additional qq pairs produced by\nstrong interaction from the vacuum. The initial arrange-\nment of the primary four quarks determines whether the\nbaryon-antibaryon pair is close in phase space (i.e., at\nmass threshold) or distant. If the diagram can be con-\nverted into a B \u2192MM diagram by omitting the extra qq\npairs from the vacuum (as in Figs 17.12.8d and e, the fac-\ntorizable color-suppressed diagrams) we observe enhance-\nment, while diagrams where the same process leaves a\ndiquark-antidiquark pair would produce no enhancement\nat threshold. The latter class includes B0 \u2192\u03a30\ncp\u03c0+ (see\nFig. 17.12.11f) proceeding through diagrams Fig. 17.12.8a\nand b.\nq\nq\nq\n\u00afq\n\u00afq\n\u00afqs\nq\n\u00afq\nq\nq\nq\n\u00afq\n\u00afq\n\u00afqs\nbaryon\nmeson\nantibaryon\nbaryon\nantibaryon\n(a)\n(b)\nFigure 17.12.12. Short-distance picture in terms of quarks\nand antiquarks for (a) two-body baryonic decay and (b) three-\nbody baryonic decay. The slow spectator antiquark is denoted\nby the short line qs.\nThis idea is illustrated in Fig. 17.12.13. The diagram\n(a) would produce two mesons; with the extra qq pairs in\n(b) one meson transforms into a B1B2 pair (\u039b+\nc p) with\npreferentially low invariant mass. This may be related to a\nmeson pole, as described below. The diagram (c), however,\nproduces a diquark-antidiquark pair, which is transformed\nby the extra qq pairs into a B1MB2 state \u03a30\ncp\u03c0+. Here,\nno meson pole is possible, and no threshold enhancement\nis observed.\nOf course, one has to understand the underlying origin\nof the threshold peaking e\ufb00ect. Threshold enhancement\nis closely linked to the behavior of baryon form factors\nwhich fall o\ufb00sharply with t, the invariant mass squared\nof the dibaryon. While various theoretical ideas, summa-\nrized in Table 17.12.9, have been put forward to explain\nthe low mass threshold enhancement, this e\ufb00ect can be\nunderstood in terms of a simple short-distance picture il-\nlustrated in Fig. 17.12.12 (Suzuki, 2007). To produce a\nbaryon and an antibaryon in the two-body decay, one en-\nergetic qq pair must be emitted at high invariant mass,\ni.e., by a hard gluon (high q2). This hard gluon is far\no\ufb00mass shell and hence the two-body decay amplitude\nis suppressed by a factor of order \u03b1S/q2. In three-body\nbaryonic B decays, a possible con\ufb01guration is that the\nB1B2 pair is emitted collinearly against the meson. The\n\n435\n(a)\n(b)\n(c)\n(d)\nFigure 17.12.13. Spectator diagrams of type 2, illustrating\nthe basic picture for a B1B2 threshold enhancement: (b) shows\none diagram for B\u2212\u2192\u039b+\nc p\u03c0\u2212with preferentially low B1B2\nmass related to the meson pair diagram (a), and (d) shows\nB0 \u2192\u03a30\ncp\u03c0+ with preferentially high B1B2 mass related to\nthe diquark pair diagram (c).\nquark-antiquark pair emitted from a gluon is moving in\nnearly the same direction. Since this gluon is close to mass\nshell, the corresponding con\ufb01guration is not subject to the\nshort-distance suppression. This implies that the dibaryon\npair tends to have a small invariant mass.\nAll present explanations for the baryon antibaryon\nthreshold enhancement have in common that the partial\nrate increases at low values of the baryon-antibaryon in-\nvariant mass, while other regions of phase space are poorly\npopulated. Decay channels which have a small phase space\nwould be naturally suppressed through the phase space\nfactor, but this is counteracted by the property of the\nmatrix element to cluster in a small phase space volume\nanyway, resulting in no or a much smaller suppression\nof those channels. A \ufb01rst test of this idea has been per-\nformed by BABAR (Gr\u00a8unberg, 2012), looking for the decay\nB0 \u2192\u039b+\nc ppp, where two baryon-antibaryon pairs are pro-\nduced within a small overall phase space region. However,\nno event of this type has been found, yielding the upper\nlimit shown in Table 17.12.6.\n17.12.3.4 Multiplicity\nThere is a noticeable hierarchy in decay rates: three-body\ndecays have substantially larger rates than their two-body\ncounterparts. Likewise, four-body decays are usually more\nfrequent than the three-body ones. For example,\nB(B\u2212\u2192pp\u03c0\u2212) \u226bB(B0 \u2192pp),\nB(B0 \u2192\u039bp\u03c0\u2212) \u226bB(B\u2212\u2192\u039bp),\nB(B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212) \u226bB(B0 \u2192\u039b+\nc p\u03c00)\n\u226bB(B0 \u2192\u039b+\nc p),\nB(B0 \u2192D\u2217+pp\u03c0\u2212) \u226bB(B0 \u2192D\u22170pp),\n(17.12.6)\n#Mesons\nn \n0\n1\n2\n3\n4\nBranching Ratio\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n\u03c0\n + n \np\n \n+\nc\n\u039b\n \n\u2192\n \n0\nB\n\u03c0\n + n \np\n \n+\nc\n\u039b\n \n\u2192\n \n-\nB\n\u03c0\n + (n-1) \np\n p \n0/+\n D\n\u2192\n \n0\nB\n\u03c0\n + (n-1) \np\n p \n0/+\n D\n\u2192\n \n-\nB\n\u03c0\n + (n-1) \np\n p \n* 0/+\n D\n\u2192\n \n0\nB\n\u03c0\n + (n-1) \np\n p \n* 0/+\n D\n\u2192\n \n-\nB\nFigure 17.12.14. Multiplicities for decays B \u2192B1B2 + nM.\nas shown in Fig. 17.12.14. This phenomenon can be under-\nstood in terms of the aforementioned threshold e\ufb00ect, that\nis, the preference for the invariant mass of the dibaryon\nto be close to threshold. The con\ufb01guration of the two-\nbody decay B \u2192B1B2 is not favorable since its invariant\nmass is mB. In B \u2192B1B2M decays, the e\ufb00ective mass\nof the baryon pair is reduced as the emitted meson can\ncarry away energy. This explains why B(B \u2192B1B2M) \u226b\nB(B \u2192B1B2). The same reasoning applies to decays with\ntwo or more mesons.\nHowever, it is not always true that a larger rate for\nthree-body decays can be ascribed to threshold enhance-\nment. As an example, consider the three-body doubly-\ncharmed baryonic decay B \u2192\u039bc\u039bcK which has been ob-\nserved at the B Factories with a branching fraction of\norder 10\u22123 (see Table 17.12.6). Since this mode is color-\nsuppressed and has a very small phase space, the estimate\nis B(B \u2192\u039bc\u039bcK) \u223c10\u22126 in na\u00a8\u0131ve factorization. This is\ntoo small by two to three orders of magnitude compared\nto experiment. Possibilities for the enhancement of \u039bc\u039bcK\nrates include \ufb01nal-state interactions and some resonances.\nThere are two possible resonant states: a hidden-charm\nbound state Xc\u00afc with a mass near the \u039bc\u039bc threshold,\n4.6 \u223c4.7 GeV, and a \u039bcK resonance. Indeed, Belle has re-\nported a peak, called the X(4630), in the e+e\u2212\u2192\u039b+\nc \u039b\u2212\nc\nexclusive cross section (Pakhlova, 2008b; see also the dis-\ncussion in Sections 21.4.6 and 18.3.5), while BABAR has\nfound a resonance in the \u039bcK invariant mass distribu-\ntion with mass \u223c2930 MeV (Aubert, 2008e; see also Sec-\ntion 19.4.1.3). It is therefore plausible that it is the res-\nonant contribution rather than the threshold e\ufb00ect that\nrenders B(B \u2192\u039b+\nc \u039b\u2212\nc K) > B(B \u2192\u039b+\nc \u039b\u2212\nc ).\nAlso, as has already been pointed out, double charmed\ntwo-body decays are enhanced over single charm or charm-\nless decays by the same mechanism: the baryon-antibaryon\npair is closer to threshold in the former case. Much softer\ngluons are employed in double charmed decays. At least\ntwo hard gluons are needed for single charm or charmless\ntwo-body decays, and they are suppressed by factors of\n\u03b14\nS relative to double-charm two-body decays as explained\nabove in Section 17.12.2.2.\n\n436\ncos\u03b8p\ndBF/dcos\u03b8p ( 10\u22126 / 0.25 )\n0\n1\n2\n3\n4\n5\n6\n7\n8\n-1\n-0.75 -0.5 -0.25\n0\n0.25\n0.5\n0.75\n1\n(a) B+ \u2192ppK+ (Wei, 2008b)\ncos\u03b8p\ndBF/dcos\u03b8p ( 10\u22126 / 0.25)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\n-0.75 -0.5 -0.25\n0\n0.25\n0.5\n0.75\n1\n(b) B+ \u2192pp\u03c0+ (Wei, 2008b)\ncos\u03b8p\nd BF/d cos\u03b8p (10-6)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n-1\n-0.75 -0.5 -0.25\n0\n0.25\n0.5\n0.75\n1\n(c) B0 \u2192p\u039b\u03c0\u2212(Wang, 2007b)\nFigure 17.12.15. Di\ufb00erential branching fractions as a function of cos \u03b8p. The curves show the model of Geng and Hsiao (2006),\nbased on a preliminary version of the B+ \u2192ppK+ results.\n17.12.3.5 Baryon-meson angular correlations in three-body\ndecays\nThe measurement of angular correlations of the outgo-\ning meson in the dibaryon rest frame can provide further\ninsight into the underlying mechanism for three-body de-\ncays. From the theoretical point of view, within pQCD\nit is expected that the meson in B \u2192B1B2M decays\nhas a stronger correlation with the antibaryon than with\nthe baryon in the dibaryon rest frame. Hence, the oppo-\nsite correlation e\ufb00ect seen in B\u2212\u2192ppK\u2212and \u039bp\u03c0\u2212is\nastonishing and entirely unexpected.\nExperimental results\nAfter su\ufb03cient data was accumulated at the B Facto-\nries, there was an e\ufb00ort to study the threshold region\nby investigating the angular distribution in the baryon-\nantibaryon rest frame (Chang, 2009; Wang, 2005, 2007b;\nWei, 2008b). In these analyses, \u03b8p is de\ufb01ned as the an-\ngle between the (anti)proton direction and the oppositely\ncharged meson direction in the baryon antibaryon rest\nframe for B+ \u2192ppK+, B+ \u2192pp\u03c0+, and B0 \u2192p\u039b\u03c0\u2212.\nFigure 17.12.15 shows the di\ufb00erential branching fractions\nas a function of cos \u03b8p for these representative modes with\nbaryon-antibaryon mass < 2.85 GeV/c2. These distribu-\ntions are not symmetric and have some puzzling features.\nSince the proton and the antiproton move almost collinearly\nin the B rest frame due to the threshold constraint, the\npeaking toward cos \u03b8p = 1 for B+ \u2192ppK+ indicates that\nthe baryon containing the spectator quark of the B me-\nson moves faster in the B rest frame. This is opposite to\nthe pQCD expectation for b \u2192sg\u2217decays (see below).\nSimilarly, most of the time the protons in B0 \u2192p\u039b\u03c0\u2212\ndecays move faster in the p\u039b system. An early attempt to\naccount for the B+ \u2192ppK+ data within pQCD, based\non the preliminary result shown at the International Con-\nference on High Energy Physics held in Beijing in 2004,\npredicted a similar correlation for B+ \u2192pp\u03c0+ (Geng and\nHsiao, 2006; see the curve in Fig. 17.12.15b). Instead, the\nopposite e\ufb00ect is seen. The di\ufb00erence between these modes\nmay indicate a crucial di\ufb00erence between the b \u2192s strong\npenguin and the b \u2192u tree processes.\nMpp\n_ (GeV/c2)\nA\u03b8p\n0\n0.25\n0.5\n0.75\n1\n2\n2.25\n2.5\n2.75\nFigure 17.12.16. Measured angular asymmetries (A\u03b8p) as a\nfunction of pp mass near threshold for B+ \u2192ppK+ from Belle\n(Wei, 2008b).\nUsing 449\u00d7106 BB pairs (Wei, 2008b), enough data is\navailable for a detailed study of B+ \u2192ppK+ signal events\nnear threshold. The angular asymmetry\nA\u03b8p = N+ \u2212N\u2212\nN+ + N\u2212\n,\n(17.12.7)\nwhere N+ and N\u2212are the e\ufb03ciency-corrected B yields\nwith cos \u03b8p > 0 and cos \u03b8p < 0 respectively, is shown as a\nfunction of mpp in Fig. 17.12.16. The distribution is not\n\ufb02at, indicating that the relative contributions from di\ufb00er-\n\n437\nent decay amplitudes are changing in this near-threshold\nmass range.\nb \u2192sg\u2217and other models\nIn the short-distance b \u2192sg\u2217picture, it is expected\nthat the antibaryon produced in penguin-dominated B \u2192\nB1B2M decays tends to emerge parallel to the outgoing\nmeson, while the baryon moves antiparallel to the me-\nson in the B1B2 rest frame. This is also true for tree-\ndominated three-body decays. Intuitively, this can be un-\nderstood in the following manner. Since in the B rest\nframe\nm2\n12 = m2\n1 + m2\n2 + 2(E1E2 \u2212|p1||p2| cos \u03b812), (17.12.8)\nthreshold enhancement implies that the baryon pair B1\nand B2 tends to move collinearly in this frame, i.e.\n\u03b812 \u21920. See Fig. 17.12.5(b) for a comparable penguin\ndiagram, and Fig. 17.12.7a for a comparable three-body\ndecay. From Fig. 17.12.7a we see that the B1 is moving\nfaster than B2 as the former picks up an energetic quark\nfrom the b decay. When the system is boosted to the B1B2\nrest frame, B2 and M are moving collinearly away from\nthe B1.\nThis picture has been tested and con\ufb01rmed by the\nmeasurements of angular correlations in B\u2212\u2192pp\u03c0\u2212(see\nFig. 17.12.15b) and \u039b+\nc p\u03c0\u2212decays. (For the related B\u2212\u2192\n\u039bp\u03b3 decay, see Section 17.12.4 and Fig. 17.12.21.) How-\never, from the study of the polar angle distribution of the\nproton in the pp system of B\u2212\u2192ppK\u2212, it was found\nby both BABAR (Aubert, 2005p) and Belle (Wang, 2004b)\nthat there is a preference for K\u2212to be collinear with the\nproton in the pp rest frame (see Fig. 17.12.15a, recall-\ning that \u03b8p is the angle between K+ and p or K\u2212and\np). This is against the theoretical prediction based on a\nshort-distance b \u2192sg\u2217picture. The fragmentation model\nby Rosner (2003) implies a large correlation between K\u2212\nand p from the penguin annihilation diagram. However,\nthis diagram is suppressed by a factor 1/mb relative to the\ndominant diagram that leads to the opposite correlation.\nFor a detailed discussion of this model on B\u2212\u2192ppK\u2212,\nsee Cheng (2006). This puzzle may indicate that (i) some\nlong-distance e\ufb00ect enters and reverses the angular depen-\ndence, or (ii) the pp pair is produced from some interme-\ndiate states such as a baryonium, a pp bound state, or a\nglueball. For example, the angular puzzle for ppK\u2212can\nbe resolved if pp is produced via a 1S0 or 3S1 baryonium\nstate. However, the same \ufb02ip mechanism will modify the\ncorrect (1\u2212cos \u03b8p)2 distribution for pp\u03c0\u2212to a wrong one,\nunless one assumes D- and P-waves for pp\u03c0\u2212(Suzuki,\n2007). This is the \ufb01rst big surprise.\nThe second big surprise arises from the experimental\n\ufb01ndings by Belle (Wang, 2007b) that the \u039b particle is\nmoving slower than the p in the decay of B0 \u2192\u039bp\u03c0+ (see\nFig. 17.12.15c which shows that \u039b moves collinearly with\n\u03c0+ in the \u039bp rest frame, which in turn implies that \u039b is\nmoving slower than p in the B rest frame). This violates\nthe common idea for b \u2192sg\u2217decay since the \u039b particle\n0\n10\n20\n30\n40\n50\n60\n-1\n-0.5\n0\n0.5\n1\ncos\u03b8K\nSignal Yields\nFigure 17.12.17. B yield distributions from Belle (Chen,\n2008a) as a function of cos \u03b8K with a \ufb01t curve overlaid for\nB0 \u2192ppK\u22170. The fraction of the signal in the helicity zero\nstate is the \ufb01t parameter and is denoted by H0. The asymme-\ntry in the \ufb01t curve is due to detection e\ufb03ciency: the underlying\ntheoretical distribution is symmetric.\ncosep\nSignal Yields / Efficiency\n0\n50\n100\n150\n200\n250\n300\n350\n-1\n-0.5\n0\n0.5\n1\n(a) B0 \u2192ppK\u22170\ncosep\nSignal Yields / Efficiency\n0\n200\n400\n600\n800\n1000\n-1\n-0.5\n0\n0.5\n1\n(b) B+ \u2192ppK\u2217+\nFigure 17.12.18. Distributions of e\ufb03ciency corrected signal\nyields vs cos \u03b8p in the proton-antiproton system with M(pp) <\n2.85 GeV/c2 from Belle (Chen, 2008a).\ninherits the energetic s quark from b decay directly. It is\nna\u00a8\u0131vely expected that the pion has no preference for its\ncorrelation with \u039b or p. The aforementioned baryonium\nmechanism does not work for this case.\nFurther measurements, including B \u2192ppK\u2217\nThe abovementioned correlation enigmas are great chal-\nlenges to theorists. It appears that these puzzles occur\nonly in the penguin-dominated decays B\u2212\u2192ppK\u2212and\nB0 \u2192\u039bp\u03c0\u2212. Experimental studies of the angular distribu-\ntions in charmed decays such as B0 \u2192\u039bpD\u2217+ may help\nsolve the angular correlation puzzle in B0 \u2192\u039bp\u03c0+, as\nthe same vacuum to \u039bp transition form factors appear in\nboth cases (Chen, Cheng, Geng, and Hsiao, 2008). It is\nalso very important to study the angular distributions of\nthe baryon for ppX with X = K\u2217+, K0, K\u22170, \u03c0\u2212, and the\n\u039b\u039bK\u2212modes.\nBoth the pp threshold enhancement and baryon-meson\ncorrelations have been studied for the the isospin-related\n\n438\ndecays B+ \u2192ppK\u2217+ and B0 \u2192ppK\u22170 (Chen, 2008a);\nthe analysis relies on a measurement of the helicity of\nthe K\u2217in the decays. Large MC samples with di\ufb00erent\nhelicity states, 0 or \u00b11, of K\u2217mesons are generated in\norder to obtain the corresponding angular p.d.f.s in cos \u03b8K,\nwhere \u03b8K is the polar angle of the K meson in the K\u2217\nhelicity frame. For events with mpp < 2.85 GeV/c2, the B\nyield distribution in bins of cos \u03b8K is used to determine the\nhelicity zero fraction: the result is shown in Fig. 17.12.17\nfor B0 \u2192ppK\u22170. It is interesting to note that the K\u22170\nmeson is likely to be fully polarized in the helicity zero\nstate, whereas the K\u2217+ produced in B+ \u2192ppK\u2217+ has\nonly a (32\u00b117\u00b19)% fraction in this state (Chen, 2008a). If\nmore than one decay amplitude is important, interference\nbetween them could lead to sizeable direct CP violation. A\ntheoretical conjecture based on the factorization approach\npredicts that the CP violation in B\u00b1 \u2192ppK\u2217\u00b1 could be as\nlarge as \u223c22% (Geng, Hsiao, and Ng, 2007). This should\nbe checked experimentally in the future.\nWith \ufb01xed K\u2217polarization, the ppK\u2217detection ef-\n\ufb01ciency is determined as a function of M(pp), and the\ndi\ufb00erential cross section is then measured in M(pp) bins.\nThreshold enhancements similar to those of B+ \u2192ppK+\nor pp\u03c0+ (Fig. 17.12.10) are seen. Distributions of the\ne\ufb03ciency-corrected signal yield as a function of cos \u03b8p are\nshown in Fig. 17.12.18. For B0 \u2192ppK\u22170, consistent with\na pure helicity state (and presumably dominated by the\nb \u2192s penguin transition), the distribution is featureless;\nfor B+ \u2192ppK\u2217+, where the polarization is lower (and\nboth b \u2192s penguin and external W-emission transitions\ncan contribute) an angular correlation comparable to that\nin B\u2212\u2192ppK\u2212or B0 \u2192\u039bp\u03c0\u2212is seen. The statistical\npower is limited in both cases.\n17.12.3.6 Cabibbo suppression\nBABAR measured the Cabibbo suppressed decay B0 \u2192\n\u039b+\nc p\u03c0+K\u2212(Aubert, 2009ag) which can be compared to\nthe Cabibbo favored decay B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212(Park, 2007).\nFrom a na\u00a8\u0131ve comparison of the matrix elements one would\nexpect a ratio of |Vus/Vud|2 = 0.054 \u00b1 0.002 if the decay\nmechanisms would be dominated solely by the CKM ma-\ntrix elements. Comparing the branching ratios, as given\nin Table 17.12.6, the ratio is\nB\n\u0000B0 \u2192\u039b+\nc pK\u2212\u03c0+\u0001\nB\n\u0000B0 \u2192\u039b+\nc p\u03c0\u2212\u03c0+\u0001 = 0.038 \u00b1 0.009,\n(17.12.9)\nwhich implies that additional decay amplitudes (similar\nto 2b and 2h in Fig. 17.12.8) are only present in B0 \u2192\n\u039b+\nc p\u03c0+\u03c0\u2212and their contribution cannot be neglected.\nThe resonant subchannels have a ratio\nB\n\u0000B0 \u2192\u03a3++\nc\n(2455)pK\u2212\u0001\nB\n\u0000B0 \u2192\u03a3++\nc\n(2455)p\u03c0\u2212\u0001 = 0.048 \u00b1 0.016, (17.12.10)\nwhich is in better agreement with the expectation from\nCabibbo suppression. This may be understood by the fact\nthat the spectator amplitudes are the same (1a, 2g, see\nTable 17.12.6) for these decays.\n17.12.3.7 Isospin relations\nIsospin relations between two-body decays have already\nbeen used in Section 17.12.2 for the ratios of \u03a30\ncp, \u039b+\nc p,\nand \u03a3+\nc p. Similar considerations can be applied to three-\nbody states. The isospin restrictions on the \ufb01nal states in\nB0 \u2192\u039b+\nc p\u03c00 (Aubert, 2010h) and B\u2212\u2192\u039b+\nc p\u03c0\u2212(Au-\nbert, 2008aa; Gabyshev, 2006) are di\ufb00erent: while B\u2212\u2192\n\u039b+\nc p\u03c0\u2212can have only a \ufb01nal isospin of IX\u03c0\u2212= 3/2 (where\nX = \u039b+\nc p) the neutral decay B0 \u2192\u039b+\nc p\u03c00 can have\nIX\u03c00 = 1/2, 3/2. If the decay mechanisms were equiv-\nalent in both decays one would expect a ratio of the decay\nrates B0 \u2192\u039b+\nc p\u03c00 : B\u2212\u2192\u039b+\nc p\u03c0\u2212of 2 : 3 for IX\u03c0\u2212=\nIX\u03c00 = 3/2. A signi\ufb01cant di\ufb00erence would suggest contri-\nbution from amplitudes speci\ufb01c to one of the decays, e.g.\namplitudes where the \u03c0\u2212originates from the W in B\u2212\u2192\n\u039b+\nc p\u03c0\u2212or B0 \u2192\u039b+\nc p\u03c00 contributions with IX\u03c00 =\n1\n2.\nBABAR \ufb01nds the ratio of partial decay widths for all de-\ncays to the \ufb01nal state particles\n\u0393\n\u0000B0 \u2192\u039b+\nc p\u03c00\u0001\n\u0393\n\u0000B\u2212\u2192\u039b+\nc p\u03c0\u2212\u0001 = 0.61 \u00b1 0.09\n(17.12.11)\nto be consistent with the expectation of 2/3. When we\nremove the \u03a3c resonant states that are only visible in the\ncharged B decay, the ratio\n\u0393\n\u0000B0 \u2192\u039b+\nc p\u03c00\u0001\n\u0393\n\u0000B\u2212\u2192\u039b+\nc p\u03c0\u2212\u0001\nnonresonant\n= 0.80 \u00b1 0.11\n(17.12.12)\nis found to be in agreement with the assumption of similar\nprocesses in both decays.\nThere are, however, penguin decays for which the iso-\nspin relations are violated. Using the average of the results\nreported in Table 17.12.8, and correcting for the di\ufb00erent\nlifetimes \u03c4+/\u03c40 = 1.071 \u00b1 0.009 and the di\ufb00erent \u03a5(4S)\nbranching fraction B+\u2212/B00 = 1.066 \u00b1 0.024 (Beringer\net al., 2012) we obtain\n\u0393(B+ \u2192ppK+)\n\u0393(B0 \u2192ppK0) = 1.91 \u00b1 0.27\nand\n\u0393(B+ \u2192ppK\u2217+)\n\u0393(B0 \u2192ppK\u22170) = 2.7 \u00b1 0.3\n(17.12.13)\nwhile a ratio of 1 is expected. Note that the helicities of the\nK\u2217+ and K\u22170 mesons in the latter pair di\ufb00er, as discussed\nat the end of Section 17.12.3.5 above.\n17.12.3.8 ss suppression\nIn fragmentation, ss-production is suppressed by a factor\nof three compared to uu or dd. This is attributed to the\ntunnelling process leading to additional qq-pairs from the\nvacuum. In B meson decays, a similar process occurs in\nhadronization. This can be investigated using pairs of de-\ncays such as B0 \u2192D0\u039b\u039b (Chang, 2009) and B0 \u2192D0pp\n\n439\nB\u2212\nB\u2212\n\u00afp\n\u039b(\u2217)\nb , \u03a30(\u2217)\nb\n\u03b3\n\u039b\n\u03b3\nK\u2217\u2212\n\u039b\n\u00afp\nFigure 17.12.19. Pole diagrams for B\u2212\u2192\u039bp\u03b3.\n(Abe, 2002g), where both decays can have contributions\nfrom the same diagram types (see Table 17.12.5). The ra-\ntio\nB\n\u0000B0 \u2192D0\u039b\u039b\n\u0001\nB\n\u0000B0 \u2192D0pp\n\u0001 = 0.103+0.056\n\u22120.043 \u00b1 0.014\n(17.12.14)\ndoes not include the additional possible \ufb01nal states\nD0\u03a30\u039b, D0\u039b\u03a30, and D0\u03a30\u03a30 for the ss diagrams. As-\nsuming branching fractions of the same order for each of\nthose, the resulting ratio \u223c0.4 is compatible with the\nfragmentation picture.\nOne would expect a similar ratio between the penguin\ndecays B0 \u2192K0\u039b\u039b (Chang, 2009) and B0 \u2192K0pp (Wei,\n2008b), however more diagrams can contribute to B0 \u2192\nK0\u039b\u039b due to the combinatoric rearrangements of b \u2192\ns + ss compared to b \u2192s + uu in B0 \u2192K0pp. The\nexperimental ratio of\nB\n\u0000B0 \u2192K0\u039b\u039b\n\u0001\nB\n\u0000B0 \u2192K0pp\n\u0001 = 1.89+0.37\n\u22120.40 \u00b1 0.29\n(17.12.15)\nis larger by a factor of \u223c10 than that for the D0B1B2\nchannels.\nAn ss suppression may also be expected between B0 \u2192\n\u039b+\nc p\u03c0+\u03c0\u2212and B0 \u2192\u039b+\nc pK+K\u2212. However, di\ufb00erences\nare not attributable to ss suppression alone since possible\ncontributing diagrams di\ufb00er: Only B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212can\nhave contributions from diagrams of type 1 (Fig. 17.12.7).\nIn decays of type 2 (Fig. 17.12.8) di\ufb00erent intermediate\nresonant states are contributing, and the number of dia-\ngrams for B0 \u2192\u039b+\nc pK+K\u2212is smaller.\n17.12.4 Radiative decays into baryons\nIt would be very di\ufb03cult to detect the radiative bary-\nonic B decay B \u2192B1B2\u03b3 if it proceeded only via\nbremsstrahlung. Fortunately, there is an important short-\ndistance electromagnetic penguin transition b \u2192s\u03b3 which\nis neither Cabibbo suppressed nor (due to the large top\nquark mass) loop suppressed. Moreover, it is considerably\nenhanced by QCD corrections. At the mesonic level, it is\nwell known that the electromagnetic penguin transition\nb \u2192s\u03b3 is represented by the radiative decays B \u2192K\u2217\u03b3.\nThe measurement of B\u2212\u2192\u039bp\u03b3 using a 449 \u00d7 106 BB\nsample in 2005 by Belle (Lee, 2005) provided the \ufb01rst ob-\nservation of b \u2192s\u03b3 in baryonic B decays.\nMp\u039b\n_ (GeV/c2)\ndBr / dMp\u039b\n_ ( 10\u22126/ (GeV/c2))\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n2\n2.5\n3\n3.5\n4\n4.5\n5\nFigure 17.12.20. Di\ufb00erential branching fractions for B\u2212\u2192\n\u039bp\u03b3 as a function of baryon-antibaryon pair mass from Belle\n(Wang, 2007b). The shaded distribution shows the expecta-\ntion from a phase-space MC simulation. The theoretical pre-\ndiction from Geng and Hsiao (2005) is overlaid as a solid line\nfor comparison. The area of the shaded distributions and areas\nunder the theoretical curves are scaled to match the measured\nbranching fractions from data. The uncertainties are statistical\nonly.\ncos\u03b8p\nd BF/d cos\u03b8p (10-6)\n0\n0.25\n0.5\n0.75\n1\n1.25\n1.5\n1.75\n2\n-1\n-0.75 -0.5 -0.25\n0\n0.25\n0.5\n0.75\n1\nFigure 17.12.21. Di\ufb00erential branching fractions vs cos \u03b8p for\nB\u2212\u2192\u039bp\u03b3 in the region near threshold (baryon-antibaryon\nmass < 2.8 GeV/c2) from Belle (Wang, 2007b). The uncertain-\nties are statistical only.\nTheoretically, radiative baryonic B decays have been\nstudied in the pole model, in which the dominant contri-\nbutions are assumed to arise from low-lying baryon and\nmeson intermediate states (Cheng and Yang, 2002b). For\nexample, the relevant intermediate states for B\u2212\u2192\u039bp\u03b3\nare K\u2217, \u039b(\u2217)\nb\nand \u03a3(\u2217)0\nb\n(see Fig. 17.12.19). Predictions\nfor some radiative decay modes are summarized in Ta-\nble 17.12.10. The model prediction for B(B\u2212\u2192\u039bp\u03b3) =\n\n440\nTable 17.12.10. Predicted branching fractions for radiative\nbaryonic B decays where A\u03b8 is the angular asymmetry de\ufb01ned\nin Eq. (17.12.7) and \u201cB(tot)\u201d denotes the sum of the baryon\nand meson pole contributions (Cheng and Yang, 2006).\nMode\nBaryon\nMeson\nB(tot)\nA\u03b8\nB\u2212\u2192\u039bp\u03b3\n7.9\u00d710\u22127\n9.5 \u00d7 10\u22127 2.6\u00d710\u22126 0.25\nB\u2212\u2192\u03a30p\u03b3\n4.6\u00d710\u22129\n2.5\u00d710\u22127\n2.9\u00d710\u22127 0.07\nB\u2212\u2192\u039e0\u03a3\u2212\u03b3\n7.5\u00d710\u22127\n1.6 \u00d7 10\u22127 5.6\u00d710\u22127 0.43\nB\u2212\u2192\u039e\u2212\u039b\u03b3\n1.6\u00d710\u22127\n2.4 \u00d7 10\u22127 2.2\u00d710\u22127 0.13\n2.6\u00d710\u22126 is in good agreement with the latest measure-\nment (Wang, 2007b)\nB(B\u2212\u2192\u039bp\u03b3) = (2.45+0.44\n\u22120.38 \u00b1 0.22)\u00d710\u22126 .\n(17.12.16)\nThe measured di\ufb00erential branching fraction as a func-\ntion of baryon-antibaryon mass for B\u2212\u2192\u039bp\u03b3 is shown\nin Fig. 17.12.20. This distribution is sharply peaked near\nthreshold and is quite similar to those observed in B\u2212\u2192\n\u039bp\u03c00 and B0 \u2192\u039bp\u03c0+ (Wang, 2007b; see the discussion\nin Section 17.12.3.3 above).\nExperimentally, the angular correlation in B\u2212\u2192\u039bp\u03b3\nis measured by considering the angular asymmetry A\u03b8 de-\n\ufb01ned in Eq. (17.12.7). Figure 17.12.21 shows the di\ufb00eren-\ntial branching fraction as a function of cos \u03b8p near the \u039bp\nmass threshold, where \u03b8p is the angle between the pho-\nton and the antiproton in the \u039b\u00afp rest frame. From Fig.\n17.12.20, we know that \u039b and p tend to move in paral-\nlel. Since the energetic s quark from the b \u2192s\u03b3 pro-\ncess will hadronize into \u039b, it is expected that \u039b will move\nfaster than p in the B rest frame. Indeed, after boosting to\nthe baryon-antibaryon rest frame, the antiproton prefers\nleaning to the photon direction as shown in Fig. 17.12.21.\nAgain, the predicted angular asymmetry A\u03b8 = 0.25 agrees\nwith the measured value of 0.29 \u00b1 0.14 \u00b1 0.03 (Wang,\n2007b). We see from Table 17.12.10 that the decay B\u2212\u2192\n\u039e0\u03a3\u2212\u03b3, with an estimated branching fraction of order\n6\u00d710\u22127, should be accessible at the B Factories. Penguin-\ninduced radiative baryonic B decays should be further ex-\nplored both experimentally and theoretically.\n17.12.5 Semileptonic decays with a baryon-antibaryon\npair\nSemileptonic decays would proceed only through the type 1\n(external) diagram shown in Fig. 17.12.7a, when the W\ndecays into a \u2113\u2212\u03bd\u2113pair instead of a quark antiquark pair.\nThe observation of such decays could therefore establish\nthe relevance of this diagram compared to the type 2\n(internal) ones. Unfortunately, no semileptonic decay to\nbaryons has been observed so far. The upper limit from\nBABAR (Lees, 2012p) is\nB(B \u2192\u039b+\nc X\u2113\u2212\u03bd\u2113)\nB(B/B \u2192\u039b+\nc X) < 0.025 at 90% CL\n(17.12.17)\nwhich, using the inclusive \u039b\u00b1\nc\nmultiplicity in B decays\nfrom Section 17.12.1, translates into an approximate up-\nper limit B(B \u2192\u039b+\nc X\u2113\u2212\u03bd\u2113) < 1.2\u00d710\u22123.\n17.12.6 Summary\nThe observed pattern in two-body baryonic B decays,\nnamely, B(B \u2192B1cB2c) \u226bB(B \u2192BcB) \u226bB(B \u2192\nB1B2), can be understood in pQCD, though there is still\nno clear theoretical prediction for charmless two-body de-\ncays. Given the large energy release in such decays, an\nestimate based on the pQCD approach should be reliable.\nThe enhancement of the baryon-antibaryon invariant\nmass near threshold observed in multi-body baryonic B\ndecays indicates that the B meson preferentially decays\ninto a baryon-antibaryon pair with low invariant mass\naccompanied by a fast recoil meson. Theoretically, the\nthreshold peaking e\ufb00ect is closely linked to the behav-\nior of baryon form factors which fall o\ufb00sharply with t,\nthe invariant mass squared of the dibaryon. There are two\nunsolved puzzles in the study of baryon-antibaryon an-\ngular correlations. First, the anomalous correlation e\ufb00ect\nmeasured in B\u2212\u2192ppK\u2212decay is against the theoretical\nprediction based on the short-distance b \u2192sg\u2217picture.\nSecond, the \u039b particle in the decay of B0 \u2192\u039bp\u03c0\u2212moves\ncollinearly with \u03c0\u2212in the \u039bp rest frame, whereas it is\nna\u00a8\u0131vely expected that the pion has no preference for its\ncorrelation with \u039b or the antiproton. These correlation\nenigmas are great challenges to theorists.\nThe measured branching fraction and the angular cor-\nrelation in B\u2212\u2192\u039bp\u03b3 are consistent with the theoretical\nmodel based on the weak penguin process b \u2192s\u03b3. Hence,\nthis radiative baryonic B decay is induced by the elec-\ntroweak penguin transition. It is important to further ex-\nplore penguin-mediated radiative baryonic B decays both\nexperimentally and theoretically.\n\n441\nChapter 18\nQuarkonium physics\n18.1 Introduction to quarkonium\nEditors:\nNora Brambilla, Thomas Mannel (theory)\nHeavy quarkonia are systems composed of a heavy\nquark and antiquark of the same \ufb02avor (charm, bottom,\nor top97), with mass m much larger than the \u201cQCD con-\n\ufb01nement scale\u201d \u039bQCD, so that \u03b1S(m) \u226a1 holds. Within\nboth the c\u00afc and b\u00afb quarkonium spectra, it is evident that\nthe di\ufb00erence in energy levels is much smaller than the\nquark mass: quarkonia are non-relativistic systems.\nDue to the large quark mass and small (relative) quark\nvelocity |v| = v in quarkonia, these states are a\ufb00ected by\nphysical processes at a range of energy scales. They probe\nall the regimes of QCD, from high energies where an ex-\npansion in the coupling constant is possible, to low en-\nergies where non-perturbative e\ufb00ects dominate; they also\nprobe intermediate scales. Quarkonium is thus a labora-\ntory where our understanding of non-perturbative QCD\nand its interplay with perturbative QCD may be tested\nin a controlled framework. The large mass and the clean\nand known decay modes also make quarkonia an ideal\nprobes of new physics in some well de\ufb01ned window of be-\nyond Standard Model (BSM) parameters, in particular\nfor some searches for dark matter candidates (Brambilla\net al., 2004, 2011; Dermisek, Gunion, and McElrath, 2007;\nMcElrath, 2005; Sanchis-Lozano, 2010).\nBelle and BABAR have collected a wide range of quarko-\nnium data, including clean samples of charmonia produced\nin B decays, two-photon fusion, initial state radiation, and\ne+e\u2212annihilation, including the unexpected observation\nof large associated (cc)(cc) production. The \ufb01nal years of\ndatataking have also seen extensive studies of bb states.\nEven if quarkonium studies were not a priority at the start\nof the running of the B Factories, these facilities have come\nto function as heavy meson factories, producing many new\nstates and new data on quarkonia, and accumulating large\ndata samples on spectra and decays. In the same period,\nquarkonia have been studied at BES and BESIII at BEPC\nand BEPC2, KEDR at VEPP-4M, CLEO-III and CLEO-c\nat CESR, CDF and D\u00d8 at Fermilab, and the PHENIX and\nSTAR experiments at RHIC. New states and exotics, new\nproduction mechanisms, new transitions and unexpected\nstates of an exotic nature have been observed. Large new\ndata samples are now being collected at the LHC experi-\nments and new facilities will become operational (PANDA\nat GSI, a much higher luminosity B Factory at KEK)\nadding challenges and opportunities to this research \ufb01eld.\nIn the following, we describe the possible quantum\nnumbers and some features of the spectrum of quarko-\n97 The top quark does not form a proper bound state since it\ndecays weakly on a time scale shorter than that typical of the\nwould-be bound state. However, to calculate the t\u00aft production\ncross section, bound state e\ufb00ects have to be taken into account.\nnium states (Section 18.1.1), and brie\ufb02y review the po-\ntential model approach (Section 18.1.2). The hierarchy\nof scales required to describe quarkonia, and its implica-\ntions, are then discussed (Section 18.1.3), followed by an\nextended review of e\ufb00ective \ufb01eld theory (EFT) methods\n(Section 18.1.4) and a brief discussion of lattice calcula-\ntions (Section 18.1.5). We conclude this introduction with\nexamples of results obtained from theoretical studies of\nquarkonia. In the remainder of this chapter, we describe\nin turn the B Factory results on conventional charmo-\nnium states (Section 18.2), the exotic charmonium-like\nor \u201cXYZ\u201d states (Section 18.3), and bottomonium states\n(Section 18.4).\n18.1.1 Quantum numbers and spectroscopy\nThe term \u201cquarkonium\u201d was coined because of the simi-\nlarity of heavy quark-antiquark bound states to those of\npositronium: the bound states of an e+ and an e\u2212. These\nsystems share similar spectroscopy and decays. For exam-\nple, the parapositronium decays into two photons, while\nits charmonium analogue \u03b7c decays into two gluons; the\northopositronium decays into three photons, while the \u201cor-\nthocharmonium\u201d (J/\u03c8) decays into and gluons, as these\ndecays are \ufb01xed by quantum numbers and related parity\nand charge conjugation conservation.\nIn Fig. 18.1.1 our present knowledge of the bottomo-\nnium and charmonium energy levels is illustrated: our cur-\nrent understanding has changed dramatically after the B\nFactory era and we have acquired information about many\nnew energy levels, both below and above threshold, and\namong several new decays and transitions.\nThe spectroscopic notation n 2s+1\u2113J (with the JP C\nnumber often given in parenthesis) is conventionally used\nfor quarkonium levels, where n is the radial quantum num-\nber (equal to the number of nodes in the wavefunction)\nplus 1, \u2113is the orbital angular momentum between quarks\n(designated by letters as S, P, D, etc.), s = 0, 1 is the\ntotal spin of the quarks, and J is the quarkonium spin\n(|\u2113\u2212s| \u2264J \u2264\u2113+ s). We note, that among the above four\nquantum numbers, only the spin of a state can be mea-\nsured; the others are merely assigned based on the mea-\nsured parity P, and charge-conjugation C. The behavior\nof a state under parity is dictated by the symmetry of the\nangular momentum eigenfunctions, the spherical harmon-\nics Y m\nl , for which P = (\u22121)\u2113,, and by the opposite parity\nof the antifermion with respect to the fermion, which \ufb01-\nnally yields for the quarkonium parity\nP = (\u22121)\u2113+1.\n(18.1.1)\nCharge conjugation exchanges the two constituents. Be-\ncause of Fermi-Dirac statistics, the exchange of two iden-\ntical fermions gives a minus sign. On the other hand, this\nexchange is performed applying the charge conjugation\noperator (which gives a factor C), exchanging the coordi-\nnates (which gives (\u22121)\u2113) and exchanging the spin (which\ngives a factor (\u22121)s+1). Therefore C(\u22121)\u2113(\u22121)s+1 = \u22121\nand\nC = (\u22121)\u2113+s.\n(18.1.2)\n\n442\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n)\n2\nMass (MeV/c\n9200\n9400\n9600\n9800\n10000\n10200\n10400\n10600\n10800\n11000\nOpen bottom threshold\nTheory\nEstablished\nNew States\n-+\n0\n--\n1\n++\n2\n++\n1\n++\n0\n+-\n1\n--\n3\n--\n2\n--\n1\n-+\n2\n?\n?\nPC\nJ\n0\nS\n1\n1\nS\n3\n2\nP\n3\n1\nP\n3\n0\nP\n3\n1\nP\n1\n3\nD\n3\n2\nD\n3\n1\nD\n3\n2\nD\n1\n?\n?\n?\nJ\nL\n(2S+1)\n(1S)\nb\n\u03b7\n(2S)\nb\n\u03b7\n(1S)\n\u03d2\n(2S)\n\u03d2\n(3S)\n\u03d2\n(4S)\n\u03d2\nb\n(5S)/Y\n\u03d2\n(1P)\nb2\n\u03c7\n(1P)\nb1\n\u03c7\n(1P)\nb0\n\u03c7\n(2P)\nb2\n\u03c7\n(2P)\nb1\n\u03c7\n(2P)\nb0\n\u03c7\n(3P)\nbJ\n\u03c7\n(10610)\n+\nb\nZ\n(10650)\n+\nb\nZ\n(1P)\nb\nh\n(2P)\nb\nh\n)\n2\n(1D\n\u03d2\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n)\n2\nMass (MeV/c\n2500\n2750\n3000\n3250\n3500\n3750\n4000\n4250\n4500\n4750\n5000\nOpen charm threshold\nTheory\nNew States\nEstablished\n-+\n0\n--\n1\n++\n2\n++\n1\n++\n0\n+-\n1\n--\n3\n--\n2\n--\n1\n-+\n2\n?\n?\nPC\nJ\n0\nS\n1\n1\nS\n3\n2\nP\n3\n1\nP\n3\n0\nP\n3\n1\nP\n1\n3\nD\n3\n2\nD\n3\n1\nD\n3\n2\nD\n1\n?\n?\n?\nJ\nL\n(2S+1)\n(1S)\nc\n\u03b7\n(2S)\nc\n\u03b7\n\u03c8\nJ/\n(2S)\n\u03c8\n(4040)\n\u03c8\n(4415)\n\u03c8\nc2\n\u03c7\nc1\n\u03c7\nc0\n\u03c7\nc\nh\n(3770)\n\u03c8\n(4160)\n\u03c8\n(2P)\nc2\n\u03c7\nX(3872)\nX(3940)\nX(4160)\nY(3915)\nY(4260)\nY(4350)\nY(4660)\n(4430)\n+\nZ\n1\n+\nZ\n2\n+\nZ\n(3900)\n+\nZ\n(4020)\n+\nZ\nX(4350)\nY(4140)\nFigure 18.1.1. Energy levels of bottomonium (upper plot)\nand charmonium (lower plot) as known at the end of the B\nFactory era. \u201cEstablished\u201d states are those predicted in the\ntheory and whose measured properties are in agreement with\npredictions. \u201cNew states\u201d are unpredicted and/or their mea-\nsured properties are di\ufb03cult to accommodate in the theory. In\nthe last column we list states with unknown quantum numbers,\nand the charged quarkonium-like resonances.\nSpin, P or C are often determined from the selection rules\nboth of the production and the decay mechanism. When\nthis is not the case, or if they cannot unambiguously \ufb01x \u2113\nand s, a quarkonium state assignment can be tried rely-\ning on theoretical predictions for the mass, width, decay\nchannels, or production mechanisms.\nFrom its non-relativistic nature some speci\ufb01c features\nof the quarkonium spectrum can be derived. The sepa-\nration between levels of di\ufb00erent n and same l typically\nscales like mv2; the spin separation between pseudoscalar\nmesons n 1S0(0\u2212+) and vector mesons n 3S1(1\u2212\u2212), called\nhyper\ufb01ne splitting, scales like mv4; the spin separation\nbetween states within the same \u2113\u0338= 0 and S multiplets\n(e.g. the splittings in the 1 3Pj multiplet \u03c7c(1P) in char-\nmonium), called \ufb01ne splitting, scales like mv4; and the hy-\nper\ufb01ne separation between the spin-singlet state 1P1 and\nthe spin-averaged triplet state \u27e83Pj\u27e9, which again scales\nlike mv4.\nThe fact that all splittings are much smaller than the\nmasses implies that all the dynamical scales of the bound\nstate, such as the kinetic energy or the momentum of\nthe heavy quarks, are small compared to the quark mass.\nTherefore, the heavy quarkonia are to a good approxima-\ntion non-relativistic systems. For further discussion of the\nvarious energy scales relevant for quarkonium system, see\nSection 18.1.3.\nAnother important feature of the spectrum is the\npresence of an \u201copen \ufb02avor threshold\u201d (open charm, or\nopen bottom), where a quarkonium state can undergo\nstrong decay to a pair of mesons carrying the correspond-\ning quark \ufb02avor. States above threshold are considerably\nwider than states below. Excited states below threshold\ndecay either by strong interactions or electromagnetically\ninto lower-lying states; the ground states \ufb01nally decay by\nan annihilation process of the heavy quark-antiquark pair.\nThis annihilation is controlled by powers of the strong cou-\npling constant evaluated at the quark mass, which gives a\nlarge suppression factor, resulting in a small width.\n18.1.2 Potential models\nTo make quantitative predictions of masses and for the\nthe full and partial widths of charmonium states, one has\nto resort to theory. For many years a phenomenological\napproach, based on both non-relativistic and relativistic\npotential model, has been used. Non-relativistic potential\nmodels are justi\ufb01ed by the fact that the bottom and, to\na lesser extent, the charm masses are large in comparison\nto \u039bQCD, the typical hadronic scale. Hence a quantum\nmechanical description of the system based on two heavy\nquarks interacting through a suitable potential appears\nreasonable. In this approach, the quarks are located in\na potential V (r) and the charmonium wave function can\nbe found as a solution of the stationary non-relativistic\nSchr\u00a8odinger equation. The potential is usually chosen such\nthat at short distances it coincides with the QCD one-\ngluon exchange Coulomb potential \u22124\n3\u03b1S/r, and at long\ndistances it incorporates con\ufb01nement by for example in-\ncluding a linearly rising term. Since relativistic e\ufb00ects ap-\npear to be sizable for some states, di\ufb00erent models in-\ncorporate relativistic kinematics appropriately matched\nto their con\ufb01nement features. Di\ufb00erent models of quark\ncon\ufb01nement may result in di\ufb00erent classes of relativis-\ntic corrections. For states close to and beyond the two\nheavy-light meson threshold, potential models have to be\ncomplemented with extra degrees of freedom in order to\naccount for possible mixing e\ufb00ects. Hybrid states which\nare expected from QCD are also incorporated by hand.\n\n443\nExamples of results obtained for the charmonia in such\nphenomenological approaches are listed in Table 18.2.1:\nthe states below open \ufb02avor threshold are well described.\nThe problem with this approach is that it is purely phe-\nnomenological, with no way to link the model parameters\nto QCD. In this approach on can neither use the quarko-\nnia to improve our understanding of strong interactions,\nnor as a tool to extract precise information on the Stan-\ndard Model and beyond. The modern approach to charmo-\nnium physics relies on non-relativistic e\ufb00ective \ufb01eld the-\nories (NRQCD, pNRQCD), discussed in Section 18.1.4,\nand lattice calculations, discussed in Section 18.1.5 below.\nThese methods are conditioned by the importance of a\nrange of di\ufb00erent energy scales in quarkonium physics, to\nwhich we now turn.\n18.1.3 Quarkonium as a multiscale system\nAs non-relativistic systems, quarkonia are characterized\nby the heavy-quark velocity v (v2 \u223c0.1 for the b\u00afb, and \u223c\n0.3 for the c\u00afc systems) and by a hierarchy of energy scales:\nthe mass m of the heavy quark (hard scale), the typical\nrelative momentum p \u223cmv (in the meson rest frame)\ncorresponding to the inverse Bohr radius r \u223c1/(mv) (soft\nscale), and the typical binding (or kinetic) energy E \u223c\nmv2 (ultrasoft scale). This is similar to the energy scales\nfor the hydrogen atom, in which case v \u223c\u03b1EM.\nThe hierarchy of non-relativistic scales makes the\nheavy quarkonia qualitatively di\ufb00erent from the heavy-\nlight mesons, which are characterized by just two scales:\nm and \u039bQCD. This makes the theoretical description of\nquarkonium physics more complicated. There are e\ufb00ects\nat each of these scales in a typical amplitude involving a\nquarkonium observable. In particular, quarkonium annihi-\nlation and production take place at the scale m, quarko-\nnium binding takes place at the scale mv, which is the typ-\nical momentum exchanged inside the bound state, while\nvery low-energy gluons and light quarks (also called ul-\ntrasoft degrees of freedom) live long enough that a bound\nstate has time to form and, therefore, are sensitive to the\nscale mv2. Ultrasoft gluons are responsible for phenomena\nsimilar to the Lamb shift in QCD.\nThe appearance of a hierarchy of scales calls for the\napplication of e\ufb00ective \ufb01eld theory (EFT) methods. How-\never, \u201cheavy quark e\ufb00ective theory\u201d (HQET), where only\nan ultraviolet mass scale m and an infrared mass scale\n\u039bQCD appear, is not suitable for the description of heavy\nquarkonia, since HQET is unable to describe the dynam-\nics of binding. The appropriate e\ufb00ective \ufb01eld theories\nare \u201cnon-relativistic QCD\u201d (NRQCD; Section 18.1.4.1)\nand \u201cpotential non-relativistic QCD\u201d (pNRQCD; Sec-\ntion 18.1.4.2) which are far more complicated, since the\nscales mv and mv2 are generated by the dynamics of the\nsystem which determines the velocity of the quarks in the\nbound state.\nThe description of the heavy quark-antiquark sys-\ntems depends on the relation of \u039bQCD to the above-\nmentioned scales. Clearly for energy scales close to \u039bQCD\nthere is no perturbative description and one has to rely\n\u00b5\nmv\n\u00b5\nperturbative matching\nperturbative matching\nperturbative matching\nSHORT\u2212RANGE\nQUARKONIUM\nnon\u2212perturbative\nmatching\nLONG\u2212RANGE\nmv 2\n QCD\n NRQCD\n pNRQCD\nQUARKONIUM\nm\nFigure 18.1.2. Energy scales and corresponding e\ufb00ective \ufb01eld\ntheories for quarkonium. The scale \u00b5 separates QCD from\nNRQCD, while \u00b5\u2032 separates NRQCD from pNRQCD.\non non-perturbative methods. Regardless of this, the non-\nrelativistic hierarchy m \u226bmv \u226bmv2 persists below the\n\u039bQCD threshold, as long as v is small. While the hard\nscale m is always larger than \u039bQCD, di\ufb00erent situations\nmay arise for the other two scales.\nIn a case with \u039bQCD \u226amv2 both scales are still per-\nturbative and the system is similar to a Coulombic system:\nfor such a quarkonium we would have \u2014 as for the hydro-\ngen atom \u2014 v \u223c\u03b1S(mv). However, none of the b\u00afb or c\u00afc\nstates satisfy this condition. In all realistic quarkonia (b\u00afb\nand c\u00afc) the ultrasoft scale is non-perturbative. Only for t\u00aft\nthreshold states may the ultrasoft scale be considered to\nlie in the perturbative regime.\nThe soft scale, proportional to the inverse quarkonium\nradius r, may be either perturbative (mv \u226b\u039bQCD) or\nnon-perturbative (mv \u223c\u039bQCD) depending on the physi-\ncal system under consideration. Unfortunately, we do not\nhave any direct information on the radius of the quarko-\nnia, and thus the assignment of some of the lowest bot-\ntomonium and charmonium states to the perturbative or\nthe non-perturbative soft regime is at the moment still\nambiguous, but it is likely that the lowest bottomonium\nand possibly also the lowest charmonium states have small\nenough radii that the scale mv is in fact still perturbative.\nIn Fig. 18.1.2 we schematically show the various scales.\nThe short-range quarkonia are small enough to allow for\na perturbative treatment of the scale mv, while for the\nlong range quarkonia already this scale requires a non-\nperturbative treatment.\nThe implications of the hierarchy of scales for lattice\ncalculations of quarkonium are outlined in Section 18.1.5\nbelow; e\ufb00ective \ufb01eld theory methods are described in the\nfollowing section.\n\n444\n18.1.4 E\ufb00ective Field Theories\nE\ufb00ective \ufb01eld theories for the description of quarkonium\nprocesses have recently been developed, providing a unify-\ning description as well as a solid and versatile tool giving\nwell-de\ufb01ned, model-independent and precise predictions.\nThey rely on the one hand on high-order perturbative\ncalculations and on the other hand on lattice simulations,\nthe recent progress in both \ufb01elds having added signi\ufb01-\ncantly to the reach of theory. The progress in our under-\nstanding of EFTs has made it possible to move beyond\nphenomenological models (at least for states below open-\n\ufb02avor threshold) and to provide a systematic description,\ninside QCD, of heavy-quarkonium physics. On the other\nhand, the recent progress in the measurement of several\nheavy-quarkonium observables makes it meaningful to ad-\ndress the problem of their precise theoretical determina-\ntion. Here we will give a brief introduction to EFTs for\nheavy quarkonium. For a general introduction to the \ufb01eld\nof quarkonium, a detailed review of quarkonium theory\nand experiments and a comparison of theory predictions\nto experiments with a discussion of the most important\nopen problems, see Brambilla et al. (2004, 2011).\nThe idea of non-relativistic E\ufb00ective Field Theories\n(NR EFTs) was pioneered by Caswell and Lepage (1986)\nand was later re\ufb01ned and cast into the NRQCD e\ufb00ective\ntheory language by Bodwin, Braaten, and Lepage (1995);\nsubsequently, the EFT at the lowest possible energy scale\n(the ultrasoft scale), potential NRQCD (pNRQCD), was\nobtained (Brambilla, Pineda, Soto, and Vairo, 2000; Pineda\nand Soto, 1998). A recent review can be found in Bram-\nbilla, Pineda, Soto, and Vairo (2005). The point is to take\nadvantage of the existence of the di\ufb00erent energy scales to\nsubstitute QCD with simpler but equivalent NR EFTs. A\nhierarchy of NR EFTs may be constructed by systemat-\nically integrating out modes associated with high-energy\nscales not relevant for the quarkonium system. Such in-\ntegration is performed in a matching procedure that en-\nforces the equivalence between QCD and the EFT at a\ngiven order of the expansion in v. The EFT Lagrangian\nis factorized in matching coe\ufb03cients, encoding the high-\nenergy degrees of freedom and low-energy operators; rel-\nativistic invariance is realized via exact relations among\nthese coe\ufb03cients (Brambilla, Gromes, and Vairo, 2001,\n2003; Manohar, 1997). The EFT displays power counting\nin the small parameter v, i.e. we are able to attach a def-\ninite power of v to the contribution of each of the EFT\noperators to the physical observables.\n18.1.4.1 Physics at the scale m: NRQCD\nQuarkonium annihilation and production take place at the\nscale m. The suitable EFT is non-relativistic QCD (Bod-\nwin, Braaten, and Lepage, 1995; Caswell and Lepage,\n1986), which follows from QCD after integrating out the\nscale m. As a consequence, the e\ufb00ective Lagrangian is or-\nganized as an expansion in 1/m and \u03b1S(m):\nLNRQCD =\nX\nn\ncn(\u03b1S(m), \u00b5)\nmn\n\u00d7 On(\u00b5, mv, mv2, ...),\n(18.1.3)\nwhere cn are Wilson coe\ufb03cients that contain the contri-\nbutions from the scale m; they can be perturbatively cal-\nculated by matching the full QCD result to the e\ufb00ective\ntheory. The On are the local operators of NRQCD; the\nmatrix elements of these operators contain the physics of\nscales below m, in particular of the scales mv and mv2\nand also of the non-perturbative scale \u039bQCD. Finally, the\nparameter \u00b5 is the NRQCD factorization scale, which sep-\narates the contributions to be described in QCD from\nthe ones to be described in NRQCD. Matrix elements\nof On depend on the scales \u00b5, mv, mv2 and \u039bQCD and\nthe power counting is performed in powers of v. The low-\nenergy operators On are constructed out of two or four\nheavy quark/antiquark \ufb01elds plus gluons. The operators\nwith a fermion and an antifermion \ufb01eld are the same ones\nobtained from the non-relativistic reduction of the QCD\nLagrangian. This part of the Lagrangian is equal, in the\nmeson rest frame, to the Lagrangian of Heavy Quark Ef-\nfective Theory (HQET) which is used to treat heavy-light\nmesons. The power counting is, however, di\ufb00erent: while\nin HQET there is a strict counting in inverse powers of m,\nin NRQCD the power counting is in powers of v, because\nthe energy scales of heavy-light mesons and quarkonia are\ndi\ufb00erent. In particular, in a heavy-light meson, the three-\nmomentum and the energy of the heavy quark are both\nof order \u039bQCD, in contrast with the situation in a heavy\nquarkonium, in which the three-momentum is of order mv\nand the energy is of order mv2.\nAnnihilation decays\nTo describe the annihilation decays of heavy quarkonia\ninto light hadrons, we have to consider four-fermion op-\nerators with four heavy quark/antiquark \ufb01elds in the ef-\nfective interaction. Considering operators up to dimension\nsix we have the following contributions\nc1(1S0)\nm2\nO1(1S0) + c1(3S1)\nm2\nO1(3S1)\n+c8(1S0)\nm2\nO8(1S0) + c8(3S1)\nm2\nO8(3S1),\n(18.1.4)\nwhere cj are the matching coe\ufb03cients: they are calculated\nas a series in \u03b1S and in this case they acquire also imagi-\nnary parts. The dimension-6 operators (i.e. the operators\ncontaining two quark and two antiquark operators) are\nO1(1S0) = \u03c8\u2020\u03c7 \u03c7\u2020\u03c8,\nO1(3S1) = \u03c8\u2020\u03c3\u03c7 \u03c7\u2020\u03c3\u03c8,\nO8(1S0) = \u03c8\u2020Ta\u03c7 \u03c7\u2020Ta\u03c8,\nO8(3S1) = \u03c8\u2020Ta\u03c3\u03c7 \u03c7\u2020Ta\u03c3\u03c8,\n(18.1.5)\nwhere \u03c8 and \u03c7 are the Pauli \ufb01elds for the quark and the\nantiquark, \u03c3 are the three spin Pauli matrices and T a are\n\n445\nthe SU(3) color matrices. The subscript 1 or 8 indicates\nthe color structure: since we consider states made by a\nquark and an antiquark, from the point of view of color\nSU(3) these are 3 \u00d7 \u00af3 states, 3 being the fundamental\ncolor representation of SU(3) and \u00af3 the antifundamental.\nTherefore, since in SU(3) 3 \u00d7 \u00af3 = 1 \u22958, q\u00afq states behave\nunder color transformation as color singlets or color octets.\nThe arguments 2S+1LJ indicate the angular-momentum\nstate of the QQ pair which is annihilated or created by the\noperator. Then, the annihilation rate can be calculated\nby recalling that the decay rate is minus two times the\nimaginary part of the energy of the state, so that we obtain\nthat the inclusive decays of a heavy quarkonium state |H\u27e9\ninduced through annihilation of the heavy quarks can be\ncalculated in NRQCD as (Bodwin, Braaten, and Lepage,\n1995)\n\u0393(H \u2192light hadrons) =\nX\nn\n2Im cn\nmdn\u22124 \u27e8H|O4fermions\nn\n|H\u27e9,\n(18.1.6)\ndn being the dimension of the operator On. This formula\nrealizes a factorization between the physics at the hard\nscale contained in the imaginary parts of the matching\ncoe\ufb03cients and the low-energy physics contained in the\nnon-perturbative matrix elements of four-fermion opera-\ntors. The sum, over operators of increasing dimension, has\nto be truncated at the desired accuracy counting the con-\ntribution of each matrix element in powers of v and the\nsuppression factor in \u03b1S coming from the matching coe\ufb03-\ncient. Electromagnetic annihilation is treated in a similar\nway.\nColor octet contributions\nA quarkonium state |H\u27e9in NRQCD is expanded in the\nnumber of partons\n|H\u27e9= |QQ\u27e9+ |QQg\u27e9+ |QQ\u00afqq\u27e9+ \u00b7 \u00b7 \u00b7\n(18.1.7)\nwhere the states including one or more light parton are\nshown to be suppressed by powers of v. In |QQg\u27e9for ex-\nample the quark-antiquark are in a color octet state, since\nthe in total the state may not carry any color, and thus\nthe two quarks have to compensate the color of the gluon.\nThen both color singlet and color octet operators con-\ntribute in Eq. (18.1.6).\nIf one instead assumes that only heavy-quarkonium\nstates with quark-antiquark in a color-singlet con\ufb01gura-\ntion can exist, then only color-singlet four-fermion oper-\nators can contribute and the matrix elements reduce to\nheavy-quarkonium wave functions (or derivatives of them)\ncalculated at the origin. This assumption is known as the\n\u201ccolor-singlet model\u201d.\nExplicit calculations show that at higher order the\ncolor-singlet matching coe\ufb03cients cn develop infrared di-\nvergences, e.g. for P-waves this takes place at order \u03b1s. In\nthe color-singlet model, these singularities do not cancel\nin the expression of the decay widths. The \ufb01rst success\nof NRQCD (Bodwin, Braaten, and Lepage, 1995) was to\nshow that the Fock space of a heavy-quarkonium state\nmay contain a small component of quark-antiquark in a\ncolor-octet con\ufb01guration, bound with some gluonic de-\ngrees of freedom. Due to this component, matrix elements\nof color-octet four-fermion operators contribute, and it is\nexactly these contributions that absorb the infrared di-\nvergences of the color-singlet matching coe\ufb03cients in the\ndecay widths, giving rise to \ufb01nite results.\nQuarkonium production\nThe relevant scale for direct quarkonium production is\nalso the hard scale m, so this process can be described\nby a local interaction in NRQCD, as we have done for\ninclusive decays. As a result, the inclusive cross section\nfor the direct production of a quarkonium state H at large\nmomentum in the center-of-mass frame can be written as\na sum of products of NRQCD matrix elements and short-\ndistance coe\ufb03cients:\n\u03c3[H] =\nX\nn\n\u03c3n\u27e8K4fermions\nn\n\u27e9\n(18.1.8)\nwhere the \u03c3n are short-distance coe\ufb03cients, and the ma-\ntrix elements \u27e8K4fermions\nn\n\u27e9are vacuum-expectation values\nof objects similar to the four-fermion operators in decays,\ncontaining both color singlet and color octet contribu-\ntions. This factorization formula for production however\nhas been proven only at next-to-next-to-leading order in\n\u03b1S (Nayak, Qiu, and Sterman, 2005). Interesting new de-\nvelopments are coming from de\ufb01ning fragmentation func-\ntions in the NRQCD formalism (Kang, Qiu, and Sterman,\n2012) and using soft collinear theory (Fleming, Leibovich,\nMehen, and Rothstein, 2012). The short-distance coe\ufb03-\ncients \u03c3n(\u039b) are essentially the process-dependent par-\ntonic cross sections to make a QQ pair (convoluted with\nparton distributions if there are hadrons in the initial\nstate). The QQ pair can be produced in a color-singlet\nstate or in a color-octet state. Its spin state can be singlet\nor triplet, and it can also have orbital angular momen-\ntum. The matrix elements \u27e8K4fermions\nn\n\u27e9contain all of the\nnon-perturbative physics associated with the evolution of\nthe QQ pair into a quarkonium state. An important prop-\nerty of these matrix elements, which greatly increases the\npredictive power of NRQCD, is the fact that they should\nbe universal, i.e., process independent. However, this is\nstill an object of study. Again, NRQCD power-counting\nrules allow one to organize the sum over operators as an\nexpansion in powers of v so that through a given order in\nv, only a \ufb01nite set of matrix elements contributes.\nAside from NRQCD, which is a QCD-based approach,\nmodels have also been used to study quarkonium produc-\ntion. One is the color singlet model, which can be related\nto NRQCD by retaining in Eq. (18.1.8) only the color sin-\nglet contributions at leading order in v. Another is the\ncolor evaporation model, where the QQ pair only has to\nhave a certain invariant mass close to the quarkonium\nmass, but the color of the QQ state is assumed to \u201cevap-\norate\u201d. However, both models lead to inconsistencies: see\nBrambilla et al. (2004, 2011) for a detailed review.\n\n446\nFor a review of applications of NRQCD to quarkonium\nproduction at the B Factories see Bodwin (2010, 2012)\nand Brambilla et al. (2004, 2011); for original calculations\nsee Bodwin, Braaten, Lee, and Yu (2006); Bodwin, Kang,\nand Lee (2006); Bodwin, Lee, and Yu (2008); He, Fan,\nand Chao (2010); Li, He, and Chao (2009); Wang, Ma,\nand Chao (2011).\nIt is important to relate quarkonium production at B\nFactories and at hadron colliders. For example, recently\nNLO order NRQCD calculations for the process e+e\u2212\u2192\nJ/\u03c8 + X(non\u2212c\u00afc) have been carried out by Zhang, Ma,\nWang, and Chao (2010) and by Butenschoen and Kniehl\n(2011); the latter authors rely on the extraction of the\nNRQCD production matrix elements obtained from a global\n\ufb01t to all production data. For a note on intepretation of\nB Factory measurements of such cross sections, see Sec-\ntion 18.2.4.3.\nRecently, factorization theorems have been obtained\nin two exclusive heavy-quarkonium production processes:\nproduction of two quarkonia in e+e\u2212annihilation and pro-\nduction of a quarkonium and a light meson in B-meson\ndecays (Bodwin, Garcia i Tormo, and Lee, 2010).\n18.1.4.2 Physics at the scales mv, mv2: pNRQCD\nQuarkonium formation takes place at the scale mv. The\nsuitable EFT is potential non-relativistic QCD, pNRQCD\n(Brambilla, Pineda, Soto, and Vairo, 2000, 2005; Pineda\nand Soto, 1998), which follows from NRQCD by integrat-\ning out the scale mv \u223cr\u22121. The soft scale mv may be\neither larger or smaller than the con\ufb01nement scale \u039bQCD\ndepending on the radius of the quarkonium system. When\nmv \u226b\u039bQCD, we speak about weakly-coupled pNRQCD\nbecause the soft scale is perturbative and the matching\nfrom NRQCD to pNRQCD may be performed in per-\nturbation theory. When mv \u223c\u039bQCD, we speak about\nstrongly-coupled pNRQCD because the soft scale is non-\nperturbative and the matching from NRQCD to pNRQCD\nis non-perturbative and cannot be calculated with an ex-\npansion in \u03b1S.\nIt is generally assumed that the lowest levels of quarko-\nnium, like J/\u03c8 and \u03a5(1S), may be described by weakly\ncoupled pNRQCD, while the radii of the excited states are\nlarger and presumably need to be described by strongly\ncoupled pNRQCD. All this is valid for states away from\nopen charm (bottom) threshold.\nClose to threshold, many additional degrees of freedom\nbecome relevant and many more scales, which do not have\na clear hierarchy, appear. Hence it will be di\ufb03cult to de-\nvise an e\ufb00ective theory for this situation and thus one has\npresently to refer to models.\nFrom pNRQCD one can also derive the QQ QCD in-\nteraction potentials which may be used as an input for\ncalculations of spectra on the basis of the Schr\u00a8odinger\nEquation. In this way one can obtain QCD-based infor-\nmation on the spectra of heavy quarkonium systems.\nThe case mv \u226b\u039bQCD: weakly-coupled pNRQCD\nThe e\ufb00ective Lagrangian is organized as an expansion in\n1/m and \u03b1S(m), inherited from NRQCD, and an expan-\nsion in r (Brambilla, Pineda, Soto, and Vairo, 2000):\nLpNRQCD =\nZ\nd3r\nX\nn\nX\nk\ncn(\u03b1S(m), \u00b5)\nmn\n\u00d7Vn,k(r, \u00b5\u2032, \u00b5) rk \u00d7 Ok(\u00b5\u2032, mv2, ...),\n(18.1.9)\nwhere Ok are the operators of pNRQCD. The matrix el-\nements of these operators depend on the low-energy scale\nmv2 and \u00b5\u2032, where \u00b5\u2032 is the pNRQCD factorization scale.\nThe Vn,k are the Wilson coe\ufb03cients of pNRQCD that\nencode the contributions from the scale r and are non-\nanalytic in r. The cn are the NRQCD matching coe\ufb03cients\nas given in Eq. (18.1.3).\nThe degrees of freedom, which are relevant below the\nsoft scale, and which appear in the operators Ok, are QQ\nstates (a color-singlet S and a color-octet O = OaT a\nstate) and (ultrasoft) gluon \ufb01elds, which are expanded\nin r as well (multipole expanded). Looking at the equa-\ntions of motion of pNRQCD, we may identify Vn,0 = Vn\nwith the 1/mn potentials that enter the Schr\u00a8odinger equa-\ntion and Vn,k\u0338=0 with the couplings of the ultrasoft degrees\nof freedom, which provide corrections to the Schr\u00a8odinger\nequation. Since the degrees of freedom that enter the\nSchr\u00a8odinger description are in this case both QQ color\nsinglet and QQ color octets, both singlet and octet po-\ntentials exist. Nonpotential interactions, associated with\nthe propagation of low-energy degrees of freedom are, in\ngeneral, present as well, and start to contribute at NLO\nin the multipole expansion. They are typically related to\nnon-perturbative e\ufb00ects.\nIf the quarkonium system is small (r \u226a\u039bQCD), the\nsoft scale is perturbative and the potentials can be cal-\nculated in perturbation theory, i.e. no non-perturbative\nquantities enter the potential (Brambilla, Pineda, Soto,\nand Vairo, 2005). Being matching coe\ufb03cients of the e\ufb00ec-\ntive \ufb01eld theory, the potentials undergo renormalization,\ndevelop a scale dependence and satisfy renormalization\ngroup equations, which allow the resummation of large\nlogarithms having as arguments ratios of physical scales,\nsuch as log( mv2\nmv ) = log(v).\nThe case mv \u223c\u039bQCD: strongly-coupled pNRQCD\nWhen mv \u223c\u039bQCD the soft scale is non-perturbative, and\nmatching cannot be performed in perturbation theory any\nmore. Rather the potential matching coe\ufb03cients Vn,k are\nobtained as non-perturbative quantities in the form of ex-\npectation values of gauge invariant Wilson-loop operators.\nIn this case, under certain assumptions, the quarkonium\nsinglet \ufb01eld S = QQ is the only low-energy dynamical de-\ngree of freedom in the pNRQCD Lagrangian which reads\n(Brambilla, Pineda, Soto, and Vairo, 2001, 2005; Pineda\n\n447\nand Vairo, 2001):\nLpNRQCD =\nZ\nd3r S\u2020\n\u0012\ni\u22020 \u2212p2\n2m \u2212VS(r)\n\u0013\nS .\n(18.1.10)\nThe singlet potential VS(r) is a series in the expansion\nin the inverse of the quark masses; the terms up to 1/m2\nhave been calculated long ago (Brambilla, Pineda, Soto,\nand Vairo, 2001; Pineda and Vairo, 2001). They involve\nNRQCD matching coe\ufb03cients (containing the contribu-\ntion from the hard scale) and low-energy non-perturbative\nparts given in terms of static Wilson loops and \ufb01eld\nstrength insertions in the static Wilson loop (containing\nthe contribution from the soft scale).\nIn this regime, from pNRQCD we recover the quark\npotential singlet model. However, here the potentials are\nobtained from QCD by non-perturbative matching and\nthey often appear to have a di\ufb00erent form with respect\nto phenomenological potential models. Their evaluation\nrequires calculations on the lattice or in QCD vacuum\nmodels. Recent progress includes new precise lattice cal-\nculations of these potentials (Koma, Koma, and Wittig,\n2008; Koma and Koma, 2010). Using these potentials, all\nthe masses for heavy quarkonia away from threshold can\nbe obtained by the solution of the Schr\u00a8odinger equation.\nA trivial example of application of this method is the\nmass of the hc. The lattice data show a vanishing long-\nrange component of the spin-spin potential so that the\npotential appears to be entirely dominated by its short-\nrange, delta-like part. This suggests that the 1P1 state\nshould be close to the center-of-gravity of the 3PJ system.\nIndeed, the measurements show consistency between data\nand this expected value (see experimental results in Ta-\nble 18.2.1).\n18.1.5 Lattice calculations\nLattice calculations play a key role for quarkonium physics.\nFor an introduction to the lattice treatment of quarkonia\nsee Brambilla et al. (2004) and for recent results see Bram-\nbilla et al. (2011). We already mentioned that the recent\nprogress in this \ufb01eld relies both on high order perturbative\ncalculations and on lattice simulations, the results of the\ntwo being often combined inside the EFT framework.\nIn fact it is di\ufb03cult to put a multiscale system on the\nlattice as the lattice step should be smaller than the small-\nest scale (m\u22121) and the lattice size should be bigger than\nthe biggest scale of the system \u039b\u22121\nQCD, putting prohibitive\nrequirements on the lattice dimensions. This is true in par-\nticular for bottomonium, due to its larger mass. In this\ncase one could use direct anisotropic lattice simulations\nor EFTs. The Lagrangian of NRQCD can be put on the\nlattice and used to obtain quarkonium energy levels. Re-\ncent results can be found in Daldrop, Davies, and Dowdall\n(2012), Dowdall et al. (2012), Gregory et al. (2011), and\nDonald et al. (2012). Charmonium spectra may also be\ncalculated on the lattice with relativistic actions. Very re-\ncently new lattice techiques have been introduced that will\neventually allow the excited charmonium spectroscopy to\nbe obtained from the lattice (Bali, Collins, and Ehmann,\n2011; Liu et al., 2012). Another possibility is to evaluate\non the lattice the potentials of strongly coupled pNRQCD\nand use them inside a Schr\u00a8odinger equation to obtain\nall the quarkonium energy levels. New precise quenched\nlattice calculations of these potentials obtained using the\nL\u00a8uscher multilevel algorithm have recently become avail-\nable (Koma, Koma, and Wittig, 2008; Koma and Koma,\n2010).\n18.1.6 Applications\nA large set of phenomenological applications of the EFT\nframework outlined above to quarkonium spectra, decays,\nand production has been presented elsewhere (Brambilla,\nPineda, Soto, and Vairo, 2005; Brambilla et al., 2004,\n2011), and discussed in relation to experimental data. Here\nwe brie\ufb02y recall some selected results.\nIn the regime in which the soft scale mv is perturba-\ntive the energy levels of quarkonium have been calculated\nat order m\u03b15\nS (Brambilla, Pineda, Soto, and Vairo, 1999;\nKniehl, Penin, Smirnov, and Steinhauser, 2002).\nDecay amplitudes (Brambilla, Pineda, Soto, and Vairo,\n2005; Brambilla et al., 2011; Kiyo, Pineda, and Signer,\n2010) and production and annihilation (Beneke, Kiyo, and\nPenin, 2007) have been calculated in perturbation theory\nat high order. Since for systems with a small radius the\nnon-perturbative contributions are power suppressed, it is\npossible to obtain a good determinations of the masses\nof the lowest quarkonium resonances with purely pertur-\nbative calculations in the cases in which the perturba-\ntive series is convergent (after the appropriate subtrac-\ntions of renormalons have been performed) and large log-\narithms in the scale ratios are resummed. For example, in\nBrambilla and Vairo (2000) a prediction of the Bc mass98\nhas been obtained: (6326 +29\n\u22129 ) MeV/c2, to be compared\nto the experimental value of (6277 \u00b1 6) MeV/c2 (Berin-\nger et al., 2012). An NNLO calculation with \ufb01nite charm\nmass e\ufb00ects (Brambilla, Sumino, and Vairo, 2002) pre-\ndicts a mass that well matches the Fermilab measure-\nment (Brambilla et al., 2011) and the lattice determi-\nnation (Allison et al., 2005). The same procedure has\nbeen applied at NNLO even for higher states (Brambilla,\nSumino, and Vairo, 2002). An NLO calculation repro-\nduces in part the 1P \ufb01ne splitting (Brambilla and Vairo,\n2005). Including log resummation at NLL, it is possi-\nble to obtain a prediction for the Bc hyper\ufb01ne separa-\ntion \u2206= 50 \u00b1 17(th)+15\n\u221212(\u03b4\u03b1S) MeV/c2 (Penin, Pineda,\nSmirnov, and Steinhauser, 2004) and for the hyper\ufb01ne\nseparation between the \u03a5(1S) and the \u03b7b the value of\n41\u00b111(th)+9\n\u22128(\u03b4\u03b1S) MeV/c2 (where the second error comes\nfrom the uncertainty in \u03b1S; Kniehl, Penin, Pineda, Smirnov,\n98 The Bc states constitute a separate class of heavy mesons,\ndistinct both from the quarkonia (e.g. in lacking electromag-\nnetic and strong decays) and from the simpler heavy mesons\n(in lacking light valence quarks). Because of their masses they\nlie outside the scope of research at the B Factories.\n\n448\nand Steinhauser, 2004). This last value turned out to con-\nsiderably undershoot the measurements of BABAR (Au-\nbert, 2008ak, 2009l) and Belle (Mizuk, 2012).\nNRQCD lattice calculations (Gray et al., 2005) ob-\ntained a value close to the experimental one but did not\ninclude the calculation of the matching coe\ufb03cient at one\nloop. Recent lattice calculations (Hammant, Hart, von\nHippel, Horgan, and Monahan, 2011) aim at including\nthe NRQCD matching coe\ufb03cients in the NRQCD lattice\ncalculation and will help to settle this issue, see for exam-\nple the result contained on the \u03b7b mass in Dowdall et al.\n(2012). See also the result contained in Meinel (2010). The\nhyper\ufb01ne separation of Bc has been calculated on the lat-\ntice to be MB\u2217\nc \u2212MBc = 54(3) MeV/c2 in Dowdall, Davies,\nHammant, and Horgan (2012). In the same paper values\nfor the excited energy levels of Bc have been presented.\nAn EFT of the magnetic dipole transition has been\ngiven in Brambilla, Jia, and Vairo (2006), allowing mag-\nnetic dipole transitions between c\u00afc and b\u00afb ground states to\nbeen considered in pNRQCD at NNLO. The results are:\n\u0393(J/\u03c8 \u2192\u03b3 \u03b7c) = (1.5 \u00b1 1.0) keV and \u0393(\u03a5(1S) \u2192\u03b3 \u03b7b)\n= (k\u03b3/71 MeV)3 (15.1 \u00b1 1.5) eV, where the errors ac-\ncount for uncertainties coming from higher-order correc-\ntions. The width \u0393(J/\u03c8 \u2192\u03b3 \u03b7c) is consistent with the\nworld-average value (Beringer et al., 2012) but bears a\nlarge error. Working in the same formalism but exactly in-\ncorporating the perturbative static potential in the leading\norder Hamiltonian and resumming large logarithms in the\nmass scale in Pineda and Segovia (2013) a number of M1\ntransitions have been calculated. In particular, the values\n\u0393(J/\u03c8 \u2192\u03b3\u03b7c) = 2.12(40) keV has been obtained, which\nis in agreement with the experimental determination with\na smaller error, and \u0393(\u03a5(1S \u2192\u03b3\u03b7b) = 15.18(51) eV and\n\u0393(\u03a5(2S \u2192\u03b3\u03b7b) = 0.668(60) eV has been obtained. The\ntransition \u0393(J/\u03c8 \u2192\u03b3\u03b7c) and the J/\u03c8 annihilation con-\nstant have been evaluated on the lattice in Becirevic and\nSan\ufb01lippo (2013) and in Davies et al. (2012). The quarko-\nnium magnetic moment is explicitly calculated in Bram-\nbilla, Jia, and Vairo (2006) and turns out to be very small\nin agreement with a recent lattice calculation (Dudek,\nEdwards, and Richards, 2006); the M1 transition of the\nlowest quarkonium states at relative order v2 turn out to\nbe completely accessible in perturbation theory (Bram-\nbilla, Jia, and Vairo, 2006). A theory of electric dipole\ntransitions has been given in Brambilla, Pietrulewicz, and\nVairo (2012) and Pietrulewicz (2012), reproducing some\nof the results of the phenomenological potential models\nwith some important di\ufb00erences.\nA description of the \u03b7c line shape has been given in\nBrambilla, Roig, and Vairo (2011). Using pNRCD and Soft\nCollinear EFT (SCET) a good description of the \u03a5(1S)\nradiative decay has been obtained (Garcia i Tormo and\nSoto, 2007).\nConcerning decays, substantial progress has recently\nbeen made in the evaluation of the NRQCD factoriza-\ntion formula for inclusive decays at order v7 (Brambilla,\nMereghetti, and Vairo, 2006, 2009), in the lattice evalua-\ntion of the NRQCD matrix elements (Bodwin, Lee, and\nSinclair, 2005), and in the higher order perturbative cal-\nculation of some NRQCD matching coe\ufb03cients (Guo, Ma,\nand Chao, 2011; Jia, Yang, Sang, and Xu, 2011; Li, Ma,\nand Chao, 2013). The data are clearly sensitive to NLO\ncorrections in the Wilson coe\ufb03cients and presumably also\nto relativistic corrections. Improved theory predictabil-\nity would entail the lattice calculation or data extrac-\ntion of the NRQCD matrix elements and perturbative re-\nsummation of large contribution in the NRQCD match-\ning coe\ufb03cients. The J/\u03c8 \u21923\u03b3 decay has been studied\nin NRQCD in Feng, Jia, and Sang (2012). Inclusive de-\ncay amplitudes have been calculated in pNRQCD (Bram-\nbilla, Eiras, Pineda, Soto, and Vairo, 2003) and the num-\nber of non-perturbative correlators appears to be size-\nably reduced with respect to NRQCD so that new model-\nindependent predictions have been made possible (Bram-\nbilla, Eiras, Pineda, Soto, and Vairo, 2002). Still, the new\ndata on hadronic transitions and hadronic decays pose in-\nteresting challenges to the theory. Exclusive decay modes\nare more di\ufb03cult to address in theory (He, Lu, Soto, and\nZheng, 2011; Soto, 2011; Vairo, 2004).\nFor excited states with masses away from threshold,\nphenomenological applications of the QCD potentials ob-\ntained in Brambilla, Pineda, Soto, and Vairo (2001) and\nPineda and Vairo (2001) are ongoing (Laschka, Kaiser,\nand Weise, 2011). For a full phenomenological description\nof the spectra and decays it would be helpful to have up-\ndated, more precise and unquenched lattice calculation of\nthe Wilson loop \ufb01eld strength insertion expectation values\nand of the local and nonlocal gluon correlators (Brambilla,\nPineda, Soto, and Vairo, 2005). For recent lattice results\non the spectroscopy see Gregory et al. (2011).\nIn the most interesting region, the region close to thresh-\nold where many new (possibly exotic) states have recently\nbeen discovered, a full EFT description has not yet been\nconstructed nor the appropriate degrees of freedom clearly\nidenti\ufb01ed (Brambilla, Vairo, Polosa, and Soto, 2008; Bram-\nbilla et al., 2011). An exception is the X(3872), which dis-\nplays universal characteristics related to its being so close\nto threshold, allowing a beautiful EFT description to be\nobtained (Braaten, 2009; Braaten and Kusunoki, 2004).\nThe light quark mass dependence in quarkonium has been\nstudied in Guo and Meissner (2012).\nThe threshold region remains troublesome also for the\nlattice, although several excited state calculations have\nrecently been pionereed.\n\n449\n18.2 Conventional charmonium\nEditors:\nRiccardo Faccini (BABAR)\nPasha Pakhlov (Belle)\nNora Brambilla (theory)\nAdditional section writers:\nPietro Biassoni, Galina Pakhlova, Antimo Palano, Torsten\nSchroeder, Korneliy Todyshev, Timofey Uglov, Anna Vi-\nnokurova, Bruce Yabsley\nSince its discovery in 1974 the charmonium family has\nserved as a laboratory to test strong interactions.\nAfter the discovery of the \ufb01rst charmonium state, the\nJ/\u03c8, its radial excitation, the \u03c8(2S), was found just two\nweeks later, and another eight states were discovered with-\nin the subsequent \ufb01ve years. More than half of the char-\nmonium states known by 1980 were observed in e+e\u2212an-\nnihilation, while the others were found in the decays of\nJ/\u03c8 or \u03c8(2S). Next, the decays of the ten known char-\nmonia were studied in detail; theoretical frameworks used\nto compute the masses and widths for charmonium states\nevolved over the years from purely phenomenological ap-\nproaches to the e\ufb00ective \ufb01eld and lattice gauge theories\nthat are the current state of the art.\nThe known conventional charmonium states are listed\nin Table 18.2.1, together with predictions for their masses\nfrom the potential models described in Section 18.1.2 above.\nFor accounts of e\ufb00ective \ufb01eld theory (NRQCD) and lattice\napproaches to charmonium, see Sections 18.1.4 and 18.1.5\nrespectively. In the following material, we present the ex-\nperimental results on charmonia from the B Factories: the\nobservation of four new states (Section 18.2.1), and new\ndecay modes of well known states (Section 18.2.2); more\nprecise determinations of the parameters of some char-\nmonium states (Section 18.2.3); and the various mecha-\nnisms of charmonium production at the B Factories (Sec-\ntion 18.2.4). Some concluding remarks are provided in Sec-\ntion 18.2.5.\n18.2.1 New conventional charmonium states\n18.2.1.1 \u03b7c(2S)\nIn the heavy quark potential model the \u03b7c(2S), the \ufb01rst\nradial excitation of the charmonium ground state \u03b7c, is\npredicted to lie below the DD threshold (Buchm\u00a8uller and\nTye, 1981; Ebert, Faustov, and Galkin, 2000; Eichten and\nFeinberg, 1981; Eichten and Quigg, 1994; Godfrey and Is-\ngur, 1985). Calculations within this model predict a mass\nsplitting m\u03c8(2S) \u2212m\u03b7c(2S) in the range (42\u2212103) MeV/c2.\nIn 1982 the Crystal Ball Collaboration reported evi-\ndence of a signal in \u03c8(2S) radiative decay attributed to\nthe \u03b7c(2S) with a mass of (3594 \u00b1 5) MeV/c2 (Edwards\net al., 1982). This claim remained uncon\ufb01rmed and unre-\nfuted for about 20 years until the observation of the \u03b7c(2S)\nat the B Factories.\nExclusive observation in B decays\nThe \ufb01rst modern evidence for the \u03b7c(2S) was the obser-\nvation of a signi\ufb01cant peak in the K0\nSK\u00b1\u03c0\u2213mass spec-\ntrum, near the mass 3.65 GeV/c2, in B \u2192K0\nSK\u00b1\u03c0\u2213K\ndecays at Belle (Choi, 2002). In this analysis the B can-\ndidates are exclusively reconstructed, and B meson signal\nevents are distinguished from continuum qq background\nby using a likelihood ratio combining event-shape vari-\nables (see Chapter 9). To suppress potential backgrounds\nfrom B \u2192D(s)X decays, combinations with any K\u03c0\n(K0\nSK) pairs lying near the D (D+\ns ) nominal masses are\nvetoed. To extract the number of signal B \u2192K0\nSK\u00b1\u03c0\u2213K\ndecays as a function of MK0\nSK\u00b1\u03c0\u2213, Belle performs \ufb01ts to\nthe mES and \u2206E distributions in bins of MK0\nSK\u00b1\u03c0\u2213with\n40 MeV/c2 width. The signal yields obtained from these\n\ufb01ts are plotted in Fig. 18.2.1, where in addition to a promi-\nnent \u03b7c signal, another signi\ufb01cant peak is evident at higher\nmass. This spectrum is \ufb01tted to a sum of \u03b7c and \u03b7c(2S)\nBreit-Wigner signal components and a polynomial back-\nground. The signal functions are convolved with a Gaus-\nsian representing the detector resolution function. The \ufb01t-\nted \u03b7c(2S) parameters are reported in Table 18.2.2.\n2900\n3100\n3300\n3500\n3700\nMKsK/ (MeV/c2)\n0\n40\n80\nEvents/40 MeV/c2\nFigure 18.2.1. K0\nSK\u00b1\u03c0\u2213invariant mass distribution for B \u2192\nK0\nSK\u00b1\u03c0\u2213K signal events with the \u03b7c and \u03b7c(2S) mass peaks\nvisible (Choi, 2002). The solid line represents the \ufb01t function.\nBABAR follows a similar approach in the analysis of B\ndecays to KK\u03c0K(0) \ufb01nal states (Aubert, 2008ba). The\nKK\u03c0 system is reconstructed in K0\nSK\u00b1\u03c0\u2213and K+K\u2212\u03c00\n\ufb01nal states, and the sum over these two modes is reported\nin the results. Signal B mesons are selected by applying\na tight \u2206E requirement. The KK\u03c0 invariant mass dis-\ntribution from continuum-background events is extrap-\nolated from the mES sidebands. In the \ufb01t to the KK\u03c0\nbackground-subtracted distribution the \u03b7c(2S) mass and\nwidth are \ufb01xed to world-average values, 3637 MeV and\n14 MeV respectively (Yao et al., 2006). The measured B+ \u2192\n\u03b7c(2S)K+ yield is 59\u00b112. By using B(B+ \u2192\u03b7c(2S)K+) =\n(3.4 \u00b1 1.8) \u00d7 10\u22124 (Aubert, 2006ae; see the details of this\nanalysis under \u201cInclusive B decays at BABAR\u201d below),\nBABAR measures the absolute branching ratio for \u03b7c(2S) \u2192\nKK\u03c0 to be B(\u03b7c(2S) \u2192KK\u03c0) = (1.9\u00b10.4\u00b10.5\u00b11.0)%,\nwhere the \ufb01rst error is statistical, the second systematic\n\n450\nTable 18.2.1. Charmonium masses (MeV/c2) according to potential models, compared with the observed values (Beringer\net al., 2012). The states observed by the B Factories and the CLEO collaboration after 2002 are marked with \u2217: see Sections\n18.2.1.1 (\u03b7c(2S)), 18.2.1.2 (\u03c7c2(2P)), and 18.2.1.3 (\u03b7c(3S) and \u03b7c(4S)). The model names are built from the \ufb01rst letters of the\nauthors and the year: GI85 (Godfrey and Isgur, 1985); EG94 (Eichten and Quigg, 1994); F91 (Fulcher, 1991); GJ95 (Gupta and\nJohnson, 1996); EFG02 (Ebert, Faustov, and Galkin, 2003); ZVR94 (Zeng, Van Orden, and Roberts, 1995); BGS05 (Barnes\net al., 2005).\nState\nJP C\nExperiment\nGI85\nEG94\nF91\nGJ95\nEFG02\nZVR94\nBGS05\n1 1S0\n\u03b7c\n0\u2212+\n2981.0 \u00b1 1.1\n2975\n2980\n2987\n2979\n2979\n3000\n2982\n1 3S1\nJ/\u03c8\n1\u2212\u2212\n3096.9\n3098\n3097\n3104\n3097\n3096\n3100\n3090\n1 1P1\nhc\n1+\u2212\n3525.41 \u00b1 0.16\n3517\n3493\n3529\n3526\n3526\n3510\n3516\n1 3P0\n\u03c7c0\n0++\n3414.75 \u00b1 0.31\n3445\n3436\n3404\n3415\n3424\n3440\n3424\n1 3P1\n\u03c7c1\n1++\n3510.66 \u00b1 0.07\n3510\n3486\n3513\n3511\n3510\n3500\n3505\n1 3P2\n\u03c7c2\n2++\n3556.20 \u00b1 0.09\n3550\n3507\n3557\n3557\n3556\n3540\n3556\n2 1S0\n\u03b7c(2S)\n0\u2212+\n3637 \u00b1 4 \u2217\n3623\n3608\n3584\n3618\n3588\n3670\n3630\n2 3S1\n\u03c8(2S)\n1\u2212\u2212\n3686.09 \u00b1 0.04\n3676\n3686\n3670\n3686\n3686\n3730\n3672\n1 1D2\n\u03b7c2\n2\u2212+\n3837\n3872\n3811\n3820\n3799\n1 3D1\n\u03c8(3770)\n1\u2212\u2212\n3772.92 \u00b1 0.35\n3819\n3840\n3798\n3800\n3785\n1 3D2\n\u03c82\n2\u2212\u2212\n3838\n3871\n3813\n3820\n3800\n1 3D3\n\u03c83\n3\u2212\u2212\n3849\n3884\n3815\n3830\n3806\n2 1P1\nhc(2P)\n1+\u2212\n3956\n3945\n3990\n3934\n2 3P0\n\u03c7c0(2P)\n0++\n3916\n3854\n3940\n3852\n2 3P1\n\u03c7c1(2P)\n1++\n3953\n3929\n3990\n3925\n2 3P2\n\u03c7c2(2P)\n2++\n3927.2 \u00b1 2.6 \u2217\n3979\n3972\n4020\n3972\n3 1S0\n\u03b7c(3S)\n0\u2212+\n3942 \u00b1 9 \u2217\n4064\n4130\n3991\n4043\n3 3S1\n\u03c8(3S)\n1\u2212\u2212\n4039 \u00b1 1\n4100\n4180\n4088\n4072\n2 3D1\n\u03c8(2D)\n1\u2212\u2212\n4153 \u00b1 3\n4194\n4142\n4 1S0\n\u03b7c(4S)\n0\u2212+\n4156 +29\n\u221225\n\u2217\n4425\n4384\n4 3S1\n\u03c8(3S)\n1\u2212\u2212\n4421 \u00b1 4\n4450\n4406\nand the third is due to the uncertainty of the branching\nfractions used in the calculation.\nRecently, Belle has updated the \u03b7c(2S) measurement\nin the decays B+ \u2192(K0\nSK\u00b1\u03c0\u2213)K+ by using a much\nlarger data sample (Vinokurova, 2011). Besides improving\nthe statistical accuracy, this analysis accounts for \u03b7c(2S)\ninterference with the non-resonant continuum for the \ufb01rst\ntime in a model-independent way, thus providing more re-\nliable measurements of the \u03b7c(2S) mass and width, and\nthe branching ratio for the B+ \u2192\u03b7c(2S)K+ decay. In-\ndeed the decays B+ \u2192K0\nSK\u00b1\u03c0\u2213K+ can occur without\nproceeding via a charmonium state; the amplitude for such\ndecays can interfere with the \u03b7c(2S) signal, which has a\nnon-vanishing width. Di\ufb00erent values of the interference\nphase can result in di\ufb00erent \u03b7c(2S) resonance line shapes,\nand can lead to signi\ufb01cant variations in the number of\n\u03b7c(2S) events while the total number of observed events\nin the \u03b7c(2S) peak remains the same. In this study Belle\njointly analyzes the MK0\nSK\u00b1\u03c0\u2213spectrum and the distri-\nbution of the angle \u03b8 between the K0\nS and K+ in the rest\nframe of the K0\nSK\u00b1\u03c0\u2213system. The angular analysis pro-\nvides discrimination between the component of the non-\nresonant amplitudes that interfere with the signal and the\none that does not. As can be seen from Fig. 18.2.2, the\ninterference deforms the Breit-Wigner, making it asym-\nmetric and lengthening its tail; the angular distribution in\nthe \u03b7c(2S) signal region is dominated by S-wave,99 while\nin the \u03b7c(2S) sidebands a sum of S-, P-, and D-waves\nis visible. The \ufb01tted \u03b7c(2S) mass and width are listed\nin Table 18.2.2. Taking interference into account has a\ndramatic e\ufb00ect on the measured \u03b7c(2S) parameters: if in-\nterference is ignored, Belle \ufb01nds a \u223c10 MeV/c2 upward\nmass shift, while the \u03b7c(2S) width increases by more than\na factor 6. The measured product of branching fractions\nB(B\u00b1 \u2192K\u00b1\u03b7c(2S)) \u00d7 B(\u03b7c(2S) \u2192K0\nSK\u00b1\u03c0\u2213) is equal to\n(3.4 +2.2\n\u22121.5\n+0.5\n\u22120.4) \u00d7 10\u22126.\n99 Since the \u03b7c(2S) is a pseudoscalar, one expects a uniform\ndistribution in cos \u03b8 for pure \u03b7c(2S) decay (pure S-wave). The\nsignal region also contains non-resonant background, but the\n\u03b7c(2S) component is much larger, so the S-wave contribution\nhere is dominant.\n\n451\n0\n25\n50\n75\n100\n3.25\n3.5\n3.75\n4\nM(KSK\u03c0), GeV/c2\nN/16 MeV/c2\n0\n50\n100\n150\n-1\n-0.5\n0\n0.5\n1\ncos\u03b8\nN/0.2\n0\n50\n100\n150\n-1\n-0.5\n0\n0.5\n1\ncos\u03b8\nN/0.2\nFigure 18.2.2. From the Belle B \u2192K0\nSK\u00b1\u03c0\u2213K analysis Vinokurova (2011): Projections of a 2D-\ufb01t onto the MK0\nSK\u00b1\u03c0\u2213\naxis (left) and onto the cos \u03b8 axis in the \u03b7c(2S) signal (center) and sideband (right) regions. The combinatorial background\nis subtracted. In the mass plot, the change in binning between the signal (16 MeV/c2) and sideband regions (130 MeV/c2) is\nevident; the gap near 3.5 GeV/c2 is due to a veto of the \u03c7c1 region, MK0\nSK\u00b1\u03c0\u2213\u2208[3.48, 3.54] GeV/c2.\nExclusive observation in two-photon fusion\nThe \u03b7c(2S) decay into the K0\nSK\u00b1\u03c0\u2213\ufb01nal state has also\nbeen studied by BABAR in the two-photon production pro-\ncess (Aubert, 2004s; del Amo Sanchez, 2011h). In the lat-\nter analysis the \u03b7c(2S) signal has also been observed in\nthe K+K\u2212\u03c0+\u03c0\u2212\u03c00 \ufb01nal state. Events produced via two-\nphoton fusion (see Chapter 22) are selected with require-\nments on the total number of charged and neutral particles\nin the event, and transverse momentum pT of the recon-\nstructed hadronic \ufb01nal state. In addition, to suppress ISR\nbackground the missing mass squared is required to be\ngreater than 2 GeV2/c4 ISR events are expected to show\na peak at m2\nmiss \u223c0 GeV2/c4, while in two-photon events\nthe missing mass should be large due to the large mo-\nmentum taken away by the outgoing e+e\u2212. The invariant\nmass distributions are \ufb01tted to a sum of non-relativistic\nBreit-Wigner functions to model \u03b7c, \u03c7c0, \u03c7c2, and \u03b7c(2S)\nsignals plus a polynomial shape to describe combinatorial\nbackground. In the K0\nSK\u00b1\u03c0\u2213\ufb01t a \u03c7c0 component is not\nincluded, since a JP = 0+ resonance cannot decay to this\n\ufb01nal state, due to angular momentum and parity conser-\nvation.100 The signal shapes are convolved with the de-\ntector resolution function obtained from MC simulation.\nThe width of the \u03b7c(2S) in the \ufb01t to the K+K\u2212\u03c0+\u03c0\u2212\u03c00\ninvariant mass distribution is \ufb01xed to the value found\nin the K0\nSK\u00b1\u03c0\u2213decay mode. Results of the \ufb01t are re-\nported in Table 18.2.2 and shown in Fig. 18.2.3. Although\nthe interference of the \u03b7c(2S) state with the non-resonant\n\u03b3\u03b3 \u2192K0\nSK\u00b1\u03c0\u2213(K+K\u2212\u03c0+\u03c0\u2212\u03c00) continuum may shift\nthe measured parameters, this e\ufb00ect can not be deter-\nmined in this analysis due to the small signal to back-\n100 The decay proceeds via the strong interaction, so P is con-\nserved. In the K0\nSK\u00b1\u03c0\u2213system, let l1 be the angular mo-\nmentum between K0\nS and K\u00b1, and l2 the angular momen-\ntum between \u03c0\u2213and the K0\nSK\u00b1 system. The \ufb01nal state has\nP = (\u22121)1+l1+l2. Since the \ufb01nal state spin is equal to 0,\nJ = l1 + l2. Thus J = 0 implies l1 = l2 and P = \u22121.\nground ratio. The pT distribution is found to be consistent\nwith that expected for two-photon production.\n)\n2\n) (GeV/c\n+\u2212\n\u03c0\n\u00b1\nK\nS\n0\nm(K\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\n4\n )\n2\nEvents / ( 0.004 GeV/c\n0\n200\n400\n600\n800\n1000\n(a)\n3.3\n3.4\n3.5\n3.6\n3.7\n-50\n0\n50 (b)\n)\n2\n) (GeV/c\n0\n\u03c0\n-\u03c0\n+\n\u03c0\n-\nK\n+\nm(K\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\n4\n )\n2\nEvents / ( 0.004 GeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n(c)\n3.3\n3.4\n3.5\n3.6\n3.7\n-50\n0\n50\n100\n150 (d)\nFigure\n18.2.3.\nFit to (a) the K0\nSK\u00b1\u03c0\u2213\nand (c) the\nK+K\u2212\u03c0+\u03c0\u2212\u03c00 mass spectra in two-photon fusion events (del\nAmo Sanchez, 2011h). The solid curves represent the total\n\ufb01t functions and the dashed curves show the combinatorial\nbackground contributions. The background-subtracted distri-\nbutions are shown in (b) and (d), where the solid curves in-\ndicate the signal components. The prominent peak is the \u03b7c,\nwhile the small peak above 3 GeV/c2 is due to residual ISR J/\u03c8\nproduction. The peaks in the insets are (left to right) \u03c7c0, \u03c7c2,\nand \u03b7c(2S). The \u03c7c0 peak is not present in (a) and (b), since\nthe decay to K0\nSK\u00b1\u03c0\u2213is not allowed for this state.\n\n452\nAngular analysis of the \u03b7c(2S) \u2192K0\nSK\u00b1\u03c0\u2213decay\n(Aubert, 2004s) con\ufb01rms that the observed events are con-\nsistent with the two-photon production mechanism and\ninconsistent with production via ISR. This analysis also\nrestricts the allowed JP C values for the \ufb01nal state (Yang,\n1950) to be 0\u2212+ or J \u22652. The measured mass and the\nprobable JP C = 0\u2212+ assignment support the interpreta-\ntion of the observed signal as the \u03b7c(2S) resonance. These\nresults are consistent with those previously obtained by\nCLEO with a similar analysis of the \u03b3\u03b3 \u2192K0\nSK\u00b1\u03c0\u2213\nprocess (Asner et al., 2004a). BABAR has also measured\nthe product of the two-photon coupling, \u0393\u03b3\u03b3, and the \ufb01-\nnal state branching fractions, B. This quantity is related\nto the ratio of the resonance signal yield and the de-\ntection e\ufb03ciency. In order to reduce the systematic un-\ncertainty due to the unknown resonant substructure of\nthe decays, a weighted \ufb01t to the e\ufb03ciency-corrected mass\ndistribution is performed, taking into account the depen-\ndence of the e\ufb03ciency on the K0\nSK\u00b1\u03c0\u2213(K+K\u2212\u03c0+\u03c0\u2212\u03c00)\ndecay kinematics. The values \u0393\u03b3\u03b3(\u03b7c(2S)) \u00d7 B(\u03b7c(2S) \u2192\nKK\u03c0) = (41 \u00b1 4 \u00b1 6) eV and \u0393\u03b3\u03b3(\u03b7c(2S)) \u00d7 B(\u03b7c(2S) \u2192\nK+K\u2212\u03c0+\u03c0\u2212\u03c00) = (30 \u00b1 6 \u00b1 5) eV, and the ratio be-\ntween the \u03b7c(2S) branching fractions to the \ufb01nal states\nB(\u03b7c(2S)\u2192K+K\u2212\u03c0+\u03c0\u2212\u03c00)\nB(\u03b7c(2S)\u2192K0\nSK\u00b1\u03c0\u2213)\n= 2.2 \u00b1 0.5 \u00b1 0.5 are found (del\nAmo Sanchez, 2011h).\nBABAR has also searched for the \u03b7c(2S) in the process\n\u03b3\u03b3 \u2192\u03b7c\u03c0+\u03c0\u2212, with the \u03b7c decaying to K0\nSK\u00b1\u03c0\u2213(Lees,\n2012t). The analysis uses a two-dimensional \ufb01t in the vari-\nables m(K0\nSK\u00b1\u03c0\u2213) and m(K0\nSK\u00b1\u03c0\u2213\u03c0+\u03c0\u2212). Signal events\npeak in both of these quantities. The combinatorial back-\nground is expected to be distributed smoothly, with sig-\nni\ufb01cant correlation between the distributions over these\ntwo variables. The correlation, studied with \u03b7c sidebands,\nis found to be consistent with being due to phase space.\nUtilizing this enables precise determination of the com-\nbinatorial background shape from the data. The anal-\nysis also accounts for backgrounds that peak in either\nm(K0\nSK\u00b1\u03c0\u2213) or m(K0\nSK\u00b1\u03c0\u2213\u03c0+\u03c0\u2212). The \ufb01t yields the ra-\ntio\nB(\u03b7c(2S)\u2192\u03b7c\u03c0+\u03c0\u2212)\nB(\u03b7c(2S)\u2192K0\nSK\u00b1\u03c0\u2213) = 4.9\u00b13.5(stat)\u00b11.3(syst)\u00b10.8(B),\nwhere the third error is due to the uncertainty on B(\u03b7c \u2192\nK0\nSK\u00b1\u03c0\u2213) (Beringer et al., 2012). No signi\ufb01cant signal is\nfound, and an upper limit of 10.0 is set on this ratio of\nbranching fractions at the 90% con\ufb01dence level.\nInclusive observation in double charmonium production\nThe \u03b7c(2S) has also been observed in the process e+e\u2212\u2192\nJ/\u03c8\u03b7c(2S) by both Belle (Abe, 2002j, 2004g, 2007f) and\nBABAR (Aubert, 2005n): see Section 18.2.4.2. The \u03b7c(2S)\nis not reconstructed in these analyses, but inferred from\nthe reconstructed J/\u03c8 by using energy-momentum con-\nservation. The \u03b7c(2S) signal is identi\ufb01ed as a peak in the\nmass spectrum of the system recoiling against the recon-\nstructed J/\u03c8; Mrecoil(J/\u03c8) is de\ufb01ned in Eq. (18.2.3), and\nthe technique is discussed in the surrounding text. We il-\nlustrate these measurements using the BABAR analysis as\na representative. The recoil mass spectrum is \ufb01tted with\n)\n2\n (GeV/c\nrec\nM\n2\n2.5\n3\n3.5\n \n2\nN / 20 MeV/c\n0\n10\n20\n30\n2\n2.5\n3\n3.5\n0\n10\n20\n30\n(2S)\n\u03c8\n+ ISR \n(2S) feeddown\n\u03c8\n+ \n sidebands\n\u03c8\nJ/\n)\n2\n (GeV/c\nrec\nM\n2\n2.5\n3\n3.5\n \n2\nN / 20 MeV/c\n0\n10\n20\n30\nFigure 18.2.4. The Mrecoil(J/\u03c8) distribution for the e+e\u2212\u2192\nJ/\u03c8 X process (Aubert, 2005n). The solid line represents the\ntotal \ufb01t function and the dashed line is the background con-\ntribution. The histograms represent di\ufb00erent sources of back-\ngrounds. Signals from \u03b7c, \u03c7c0, and \u03b7c(2S) are visible.\nsignal line shapes determined from MC simulation, tak-\ning into account phase space suppression due to the varia-\ntion of the virtual photon energy in ISR (Fig. 18.2.4). The\nJ/\u03c8\u03b7c(2S) system is assumed to be produced in P-wave as\nrequired by parity conservation. The combinatorial back-\nground contribution is estimated from J/\u03c8 sidebands. The\n\u03c8(2S) ISR background is estimated by using MC simula-\ntions; the other feed-down from \u03c8(2S) \u2192J/\u03c8 X is esti-\nmated by using \u03c8(2S) events reconstructed in the data.\nThe Mrecoil distributions for such backgrounds are struc-\ntureless and are described by a smooth function in the \ufb01t.\nThe main sources of systematic uncertainty in the mass\nmeasurement are the uncertainty on the signal lineshape,\nselection procedure, and mass scale calibration. BABAR\nand Belle results are summarized in Table 18.2.2.\nInclusive B decays at BABAR\nA search for \u03b7c(2S) has also been performed by BABAR\nin inclusive B-meson decays to XccK\u00b1 (Aubert, 2006ae).\nThe analysis is carried out by fully reconstructing one B\nmeson (Btag), so the signal B-meson (Bsig) momentum is\nknown from the Btag and beam momenta. In events with\none charged kaon not associated with Btag, its momentum\nis calculated in the Bsig rest frame. The mass of Xcc is\nmX =\np\nm2\nB + m2\nK \u22122EKmB, where mB and mK are\nthe B\u00b1 and K\u00b1 masses and EK is the K\u00b1 energy in the\nB rest frame. The resulting mX spectrum is \ufb01tted with a\nsum of signal and combinatorial background components,\nto obtain the \u03b7c(2S) signal yield. An excess of events with\na statistical signi\ufb01cance of 1.8\u03c3 is observed at the expected\nposition for the \u03b7c(2S) peak. Results of the \ufb01t are reported\nin Table 18.2.2.\nSummary\nIn conclusion, the \u03b7c(2S) has been measured in several\nproduction processes and \ufb01nal states at the B Factories.\nThe mass values measured in di\ufb00erent processes show quite\n\n453\nTable 18.2.2. \u03b7c(2S) mass and width as measured by BABAR and Belle. The \ufb01rst three rows refer to measurements performed by\nusing B meson decays, the fourth and \ufb01fth rows to two-photon collisions, and the last rows to double charmonium production.\nThese results are discussed in the summary at the end of Section 18.2.1.1. Limits are at 90% C.L.\nExperiment\nProcess\nLuminosity\nMass\nWidth\nReference\n(fb\u22121)\n(MeV/c2)\n(MeV)\nBelle\nB \u2192(K0\nSK\u00b1\u03c0\u2213)K\n42\n3654 \u00b1 6 \u00b1 8\n< 55\nChoi (2002)\nBABAR\nB\u00b1 \u2192XccK\u00b1\n211\n3639 \u00b1 7\n< 23\nAubert (2006ae)\nBelle\nB\u00b1 \u2192(K0\nSK\u00b1\u03c0\u2213)K\u00b1\n492\n3636.1 +3.9\n\u22124.2\n+0.7\n\u22122.0\n6.6 +8.4\n\u22125.1\n+2.6\n\u22120.9\nVinokurova (2011)\nBABAR\n\u03b3\u03b3 \u2192K0\nSK\u00b1\u03c0\u2213\n520\n3638.5 \u00b1 1.5 \u00b1 0.8\n13.4 \u00b1 4.6 \u00b1 3.2\ndel Amo Sanchez (2011h)\nBABAR\n\u03b3\u03b3 \u2192K+K\u2212\u03c0+\u03c0\u2212\u03c00\n520\n3640.5 \u00b1 3.2 \u00b1 2.5\n\u2013\ndel Amo Sanchez (2011h)\nBABAR\ne+e\u2212\u2192J/\u03c8\u03b7c(2S)\n112\n3645.0 \u00b1 5.5 +4.9\n\u22127.8\n22 \u00b1 14\nAubert (2005n)\nBelle\ne+e\u2212\u2192J/\u03c8\u03b7c(2S)\n357\n3626 \u00b1 5 \u00b1 6\n\u2013\nAbe (2007f)\na large spread ranging from 3626 to 3654 MeV/c2. The\nlarge spread among the mass values measured in various\nprocesses does not indicate an actual discrepancy: its size\nis marginally consistent with the experimental uncertain-\nties, and the interference of the \u03b7c(2S) resonance with the\nunderlying background is neglected in all but one mea-\nsurement (Vinokurova, 2011). In that analysis a 10 MeV\nmass shift due to this e\ufb00ect is estimated. Similar shifts\nwith di\ufb00erent values or signs are expected for the vari-\nous \u03b7c(2S) production processes (B decays, two-photon\nfusion, and double charmonium production). Nonetheless,\nall the B Factory measurements are in contradiction with\nthe previous result reported by the Crystal Ball Collabo-\nration (Edwards et al., 1982).\nHadronic branching fractions of the \u03b7c(2S) are ex-\npected to be similar to those of \u03b7c (Chao, Gu, and\nTuan, 1996). However, the measured branching fraction\nB(\u03b7c(2S) \u2192KK\u03c0) = (1.9 \u00b1 1.2)% (Aubert, 2008ba)\nis signi\ufb01cantly smaller than the corresponding B(\u03b7c \u2192\nKK\u03c0) = (7.0 \u00b1 1.2)% (Beringer et al., 2012). Further-\nmore, the \u03b7c is observed to decay into h+h\u2212h\u2032+h\u2032\u2212(with\nh(\u2032) = K, \u03c0) with a branching fraction \u223c1.6% (Beringer\net al., 2012), while the corresponding decays for \u03b7c(2S)\nwere searched for, but not observed (e.g. B(\u03b7c(2S) \u2192\n4\u03c0) < 4.5 \u00d7 10\u22123 at 90% C.L.; Uehara, 2008b). The only\nexclusive \u03b7c(2S) decays observed to date are to KK\u03c0 and\nK+K\u2212\u03c0+\u03c0\u2212\u03c00.\n18.2.1.2 \u03c7c2(2P)\nAlthough the lowest 3PJ charmonium states (the \u03c7cJ)\nare well established, no experimental information existed\nabout their radial excitations \u03c7cJ(2P) before the B Fac-\ntory era. Theory predicts that the masses of these states\nlie in the region 3.9 \u22124.0 GeV/c2 (Godfrey and Isgur,\n1985), which places them well above the DD threshold.\nThe \u03c7c0(2P) and \u03c7c2(2P) mesons would then decay pri-\nmarily into DD; the decay \u03c7c1(2P) \u2192DD is forbidden\nby parity conservation, but the \u03c7c1(2P) could decay into\nDD\u2217, if energetically allowed.\nIn 2006, the Belle Collaboration reported the obser-\nvation of a new resonance, provisionally called Z(3930),\nbased on analysis of a data sample of 395 fb\u22121 (Ue-\nhara, 2006). The resonance is observed in two-photon\nproduction, a mechanism providing a clean environment\nfor studying resonances in direct formation (see Chap-\nter 22 for the details), both in \u03b3\u03b3 \u2192D0D0 and \u03b3\u03b3 \u2192\nD+D\u2212(see Fig. 18.2.5 (a) and (b), respectively). The \ufb01-\nnal state charmed mesons are fully reconstructed. Two-\nphoton events are separated from e+e\u2212annihilation and\nISR events by requiring that the transverse momentum\nof the DD system be small, as expected for two-photon\nevents in the no-tag mode (i.e., where neither the outgo-\ning electron nor the positron are detected). The result-\ning combined invariant mass distribution is \ufb01tted with a\nrelativistic Breit-Wigner signal function (taking the mass\nresolution and reconstruction e\ufb03ciency into account) and\na background component (Fig. 18.2.5 (c)). The statistical\nsigni\ufb01cance of the Z(3930) peak is 5.3 \u03c3. The measured\nmass and total width of the resonance are listed in Ta-\nble 18.2.3. The systematic uncertainties are dominated by\nuncertainties in the D mass and the choice of the signal\nfunction lineshape.\nBelle performs an angular analysis to identify the spin\nof the observed resonance. If one de\ufb01nes \u03b8 as the an-\ngle of a D meson relative to the beam axis in the \u03b3\u03b3\nframe (equivalent to the DD frame), the cos \u03b8 distribution\nfor a scalar particle will be \ufb02at, while for a spin-2 reso-\nnance produced with helicity 2 along the incident axis, a\ndistribution proportional to sin4 \u03b8 is expected. Spin-1 is\nlargely suppressed in two-photon events with quasi-real\nphotons (Yang, 1950), thus this assignment is not consid-\nered. The Belle data signi\ufb01cantly favor spin-2 over spin-0\nassignment, while the production and decay mechanisms\nrequire positive parity and C-parity. The resulting quan-\ntum numbers, JP C = 2++, suggest identifying this parti-\ncle with the previously unobserved \u03c7c2(2P) charmonium\nstate. Assuming production of a spin-2 state, Belle calcu-\nlated the product of its two-photon width and the branch-\ning fraction into DD (Table 18.2.3). The systematic errors\nare primarily due to uncertainties in tracking and particle\nidenti\ufb01cation e\ufb03ciencies, the choice of \ufb01t lineshapes and\nthe errors of D branching fractions.\n\n454\nM(DD)\n(GeV/c\n2\n)\n(a) D\n0\nD\n0\n(b) D\n+\nD\n-\n(c) combined\nEvents/10 MeV/c\n2\nEvents/10 MeV/c\n2\nFigure 18.2.5. (a) D0D0, (b) D+D\u2212, and (c) combined DD\ninvariant mass distributions in two-photon fusion events (Ue-\nhara, 2006). The open histogram shows the combinatorial back-\nground distribution estimated from D sidebands. The solid line\nrepresents the total \ufb01t function, the dashed line the \ufb01t without\nany resonant structure.\nSimilar results have been obtained by BABAR, using\na 384 fb\u22121 data sample (Aubert, 2010g). The D0D0 and\nD+D\u2212\ufb01nal states are fully reconstructed, selecting two-\nphoton events (in the no-tag mode) by requiring a large\nmissing mass (\np\n(pe+e\u2212\u2212pDD)2) and a small transverse\nmomentum of the DD system. Additionally, the energy\ndeposited in the calorimeter unmatched to any charged-\nparticle track should not exceed 400 MeV. A peak in the\nDD invariant mass distribution near 3.93 GeV/c2 is also\nclearly seen in BABAR data. The combined e\ufb03ciency-\ncorrected DD invariant mass spectrum is \ufb01tted with a\nrelativistic Breit-Wigner signal function convolved with a\nmass-dependent Gaussian resolution function and a back-\nground lineshape taking the DD threshold into account.\n|\u03b8\n|cos\n0\n0.2\n0.4\n0.6\n0.8\n1\nEntries / 0.1\n-5\n0\n5\n10\n15\n20\nFigure 18.2.6. The cos \u03b8 distribution (see the text) for\n\u03c7c2(2P) signal candidates in DD events produced in two-\nphoton fusion at BABAR (Aubert, 2010g). The results of a \ufb01t\nto the J = 2 hypothesis are shown with the solid curve; the\ndashed curve corresponds to the J = 0 hypothesis.\nThe signi\ufb01cance of the \u03c7c2(2P) observation is 5.8 \u03c3; the \ufb01t-\nted mass and width are listed in Table 18.2.3. The angular\ndistribution for signal entries is obtained from \ufb01ts to data\nin 10 bins of cos \u03b8, with \u03b8 being the angle of a D in the DD\nsystem relative to the DD lab momentum (Fig. 18.2.6).\nAs in the Belle study, the expected distribution for spin-2\nis signi\ufb01cantly favored over spin-0; taking the production\nand decay processes into account, JP C = 2++ is therefore\npreferred. The calculated product of the two-photon width\nand the branching fraction into the DD \ufb01nal state is in\ngood agreement with the Belle value (Table 18.2.3). Sys-\ntematic errors in this analysis address the choice of signal\nand background lineshapes, tracking and particle identi\ufb01-\ncation issues, and uncertainties in D mass and branching\nfractions.\nIn summary, the \u03c7c2(2P) has been observed in two-\nphoton production at both B Factory experiments, de-\ncaying into D0D0 and D+D\u2212. The parameters reported\nby BABAR and Belle are in good agreement. The mea-\nsured \u03c7c2(2P) mass is 50 MeV/c2 lower than potential\nmodel predictions (Table 18.2.1); other parameters includ-\ning the two-photon width are consistent with the model\nexpectations for the \u03c7c2(2P) state. This state has so far\nnot been seen in any other production mechanism or de-\ncay mode. For example, BABAR has obtained a 90% C.L.\nupper limit \u0393\u03b3\u03b3(\u03c7c2(2P)) \u00d7 B(\u03c7c2(2P) \u2192\u03b7c\u03c0+\u03c0\u2212) <\n18 eV (del Amo Sanchez, 2011h). Only two other reported\ncharmonium-like states in the predicted mass region are\nobserved to decay into DD or DD\u2217: the X(3872), the\nstructure of which is controversial (see Section 18.3.2), and\nthe X(3940), which is likely an excitation of the \u03b7c (see\n\n455\nTable 18.2.3. Summary of \u03c7c2(2P) mass and width measurements obtained by Belle and BABAR in \u03b3\u03b3 \u2192DD.\nExperiment\nLuminosity\nMass\nWidth\nSpin\n\u0393\u03b3\u03b3(\u03c7c2(2P))\u00d7\nReference\n(fb\u22121)\n(MeV/c2)\n(MeV)\nJP C\nB(\u03c7c2(2P) \u2192DD) (keV)\nBelle\n395\n3929 \u00b1 5 \u00b1 2\n29 \u00b1 10 \u00b1 2\n2++\n0.18 \u00b1 0.05 \u00b1 0.03\nUehara (2006)\nBABAR\n384\n3926.7 \u00b1 2.7 \u00b1 1.1\n21.3 \u00b1 6.8 \u00b1 3.6\n2++\n0.24 \u00b1 0.05 \u00b1 0.04\nAubert (2010g)\nSections 18.2.1.3 and 18.3.3). The \u03c7c2(2P) remains the\nonly con\ufb01rmed radial excitation of the 3PJ charmonium\nstates.\n18.2.1.3 X(3940) and X(4160) as candidates for higher\nradial excitations of \u03b7c\nDouble charmonium production in e+e\u2212annihilation, \ufb01rst\nobserved in 2002 by Belle (Abe, 2002j) and con\ufb01rmed by\nBABAR (Aubert, 2005n), can be regarded as a mini-factory\nof charmonium production. This process, described in de-\ntail in Section 18.2.4.2, provides opportunities both to\nsearch for new charmonia, and to study the decays of\nknown states. Using two-body kinematics, exclusive \ufb01nal\nstates can be identi\ufb01ed by reconstructing a state such as\nthe J/\u03c8, and then studying the spectrum of the recoil mass\n(Mrecoil(J/\u03c8), as de\ufb01ned in Eq. 18.2.3, Section 18.2.4.2).\nBoth known and new states produced in association with\nJ/\u03c8 appear as peaks in this spectrum.101 Studies of var-\nious double charmonium \ufb01nal states have demonstrated\nthat scalar and pseudoscalar charmonia are copiously pro-\nduced in recoil against J/\u03c8 or \u03c8(2S), and there is no sig-\nni\ufb01cant suppression of the production of radially excited\nstates (Abe, 2004g; Aubert, 2005n).\nIn the study by Abe (2007f) of the Mrecoil(J/\u03c8) dis-\ntribution, in addition to previously reported peaks at the\n\u03b7c, \u03c7c0, and \u03b7c(2S) masses, a fourth enhancement around\n3940 MeV/c2 was found (Fig. 18.2.7). The new state was\ncalled X(3940). A \ufb01t to this spectrum that includes the\nthree previously seen charmonium states plus a fourth\nstate \ufb01nds the signi\ufb01cance of the new state to be 5.0\u03c3 in-\ncluding systematics. However, in this study it is not pos-\nsible to prove that the observed peak is due to a single\nresonance.\nThe X(3940) mass is above both the DD and DD\u2217\nthresholds, so it is natural to search for X(3940) decays\ninto these \ufb01nal states. Because of the small product of\nD(\u2217) reconstruction e\ufb03ciencies and branching fractions,\nit is not feasible to reconstruct fully the chain e+e\u2212\u2192\nJ/\u03c8X(3940), X(3940) \u2192DD(\u2217). To increase the e\ufb03ciency,\nonly the J/\u03c8 and one D meson are reconstructed, detect-\ning the other D(\u2217) as a peak in the Mrecoil(J/\u03c8D) spec-\ntrum. The instrumental resolution allows the D and D\u2217\npeaks to be clearly resolved, thus e\ufb00ectively tagging the\nprocesses e+e\u2212\u2192J/\u03c8 DD and e+e\u2212\u2192J/\u03c8 DD\u2217. A clear\n101 Only states with charge conjugation C = +1 can be pro-\nduced in association with the J/\u03c8, due to the conservation of\nthis quantum number in e+e\u2212\u2192\u03b3\u2217\u2192J/\u03c8 X and to the fact\nthat both the \u03b3\u2217and the J/\u03c8 have C = \u22121.\n\u03b7c\n\u03c7c0\n\u03b7c(2S) X(3940)\nMrecoil(J/\u03c8) GeV/c2\nN/20 MeV/c2\n0\n50\n100\n150\n2\n2.5\n3\n3.5\n4\n4.5\nFigure 18.2.7. From the Abe (2007f) analysis: The distribu-\ntion of Mrecoil(J/\u03c8) in inclusive e+e\u2212\u2192J/\u03c8 X events (points\nwith error bars). The cross-hatched histogram shows the scaled\nJ/\u03c8 sideband distribution; the open histogram corresponds to\nthe feed-down from \u03c8(2S) decay. The solid curve is the \ufb01t re-\nsult; the dashed curve shows the background and non-resonant\ncontribution.\nX(3940) signal is seen only in the latter process, with 5.0\u03c3\nsigni\ufb01cance. We illustrate the method, and present the\nmeasured parameters of both the X(3940) and another\nnew state, using the results of the latest Belle study.\nUsing a dataset twice as large, Pakhlov (2008) per-\nformed a detailed study of the processes e+e\u2212\u2192J/\u03c8 DD,\nJ/\u03c8 DD\u2217, and J/\u03c8 D\u2217D\u2217. After reconstruction of a J/\u03c8D\ncombination, signals for all three processes are evident in\nthe spectrum of recoil mass Mrecoil(J/\u03c8D) (Fig. 18.2.8\n(a)), at the D mass, the D\u2217mass, and at \u223c2.2 GeV/c2\nrespectively. The latter peak is shifted and widened due\nto the missing pion or photon from D\u2217decay. The pro-\ncesses e+e\u2212\u2192J/\u03c8 DD\u2217and J/\u03c8 D\u2217D\u2217are also clearly\nseen following J/\u03c8D\u2217reconstruction, in the spectrum\nof recoil mass Mrecoil(J/\u03c8D\u2217) (Fig. 18.2.8 (b)), as dis-\ntinct peaks around the D and D\u2217masses. Selecting\nJ/\u03c8D or J/\u03c8D\u2217combinations from the proper interval\nof Mrecoil(J/\u03c8D(\u2217)), events can be e\ufb00ectively divided into\nnon-overlapping samples corresponding to each of the\nstudied processes. In particular, only the process e+e\u2212\u2192\nDD (and combinatorial background) contributes in the\ninterval |Mrecoil(J/\u03c8D) \u2212MD| < 70 MeV/c2. Events from\nthe adjacent interval |Mrecoil(J/\u03c8D) \u2212MD\u2217| < 70 MeV/c2\nare dominated by the process e+e\u2212\u2192J/\u03c8DD\u2217; a small\nfeed-down from the process e+e\u2212\u2192J/\u03c8DD appears in\nthis interval due to initial state radiation. J/\u03c8D\u2217com-\nbinations from the interval |Mrecoil(J/\u03c8D\u2217) \u2212MD| <\n70 MeV/c2 provide a very clean sample of the same pro-\n\n456\n0\n20\n40\n60\na) J/\u03c8 D\nN/20 MeV/c2\nb) J/\u03c8 D*\nMrecoil(J/\u03c8 D(*)) GeV/c2\n0\n5\n10\n15\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\nFigure 18.2.8. From Pakhlov (2008): The distribution of (a)\nMrecoil(J/\u03c8 D) and (b) Mrecoil(J/\u03c8D\u2217) in e+e\u2212\u2192J/\u03c8 D(\u2217)X\nevents (points with error bars). The histograms show the scaled\nD(\u2217) sideband distribution. The solid curve is the \ufb01t result; the\ndashed curve shows the background contribution.\ncess e+e\u2212\u2192J/\u03c8DD\u2217, with very small background and\nfree of feed-down. However, as this sample is a small\nsubsample of the previous case, it is used only as a\ncross check. Finally, J/\u03c8D\u2217combinations from the inter-\nval |Mrecoil(J/\u03c8D\u2217) \u2212MD\u2217| < 70 MeV/c2 tag the process\ne+e\u2212\u2192J/\u03c8D\u2217D\u2217.\nThe spectra of M(D(\u2217)D(\u2217)) \u2261Mrecoil(J/\u03c8) are shown\nin Figs 18.2.9 (a), (b), (c), and (d) for the four selected\ncases in turn. Enhancements near threshold are evident in\neach distribution. A \ufb01t to the M(DD) distribution \ufb01nds\na broad resonance-like structure near the threshold, ten-\ntatively denoted X(3880). However the signi\ufb01cance of the\nbroad peak is low (3.8 \u03c3), and the \ufb01t is not stable under\nvariation of the background parameterization. Therefore,\nwith the existing sample the resonant structure in this\nprocess cannot be reliably determined. The signi\ufb01cance of\nthe X(3940) signal found by the \ufb01t to the M(DD\u2217) spec-\ntrum is 5.7 \u03c3 (including systematic uncertainties). The\nX(3940) mass and width are M = (3942 + 7\n\u22126 \u00b1 6) MeV/c2\nand \u0393 = (37 + 26\n\u221215 \u00b1 8) MeV. The insets in Figs 18.2.9 (a)\nand (b) show the background subtracted spectra with the\nsignal functions superimposed.\nThe M(D\u2217D\u2217) spectrum has a clear broad enhance-\nment near threshold, which is seen above the small com-\nbinatorial background and the X(3940) re\ufb02ection. The\nobserved enhancement, which has a signi\ufb01cance of 5.1 \u03c3\n(including systematics), was interpreted as a new reso-\nnance and denoted X(4160). The X(4160) parameters\nare M = (4156 + 25\n\u221220 \u00b1 15) MeV/c2 and \u0393 = (139 + 111\n\u221261 \u00b1\n21) MeV. Although the masses and widths of the X(4160)\nand \u03c8(4160) are not inconsistent, the latter cannot be pro-\nduced in e+e\u2212annihilation via a single virtual photon due\nto C-parity conservation, as explained above; annihilation\na) Drec Dassoc\n--\nN/50 MeV/c2\nb) Drec Dassoc\n*\n--\nN/25 MeV/c2\nc) Drec Dassoc\n*\n--\nN/25 MeV/c2\nd) Drec Dassoc\n*\n-- *\n M(D(*) D(*)\n--\n) GeV/c2\nN/50 MeV/c2\n0\n20\n0\n20\n0\n2\n0\n5\n4\n4.5\n5\n0\n10\n4\n5\n0\n20\n4\n5\nFigure\n18.2.9.\nFrom\nPakhlov\n(2008):\nThe\nspectra\nof\nM(D(\u2217)D(\u2217)) \u2261Mrecoil(J/\u03c8) for events tagged and constrained\nas (a) e+e\u2212\u2192J/\u03c8 DD, (b,c) e+e\u2212\u2192J/\u03c8 DD\u2217, and (d)\ne+e\u2212\u2192J/\u03c8 D\u2217D\u2217in the data (points with error bars).\nHatched histograms show the combinatorial background distri-\nbutions and open histograms show the feed-down contribution\n(see text). The solid lines represent the \ufb01t results; the dashed\nlines are background functions.\nvia two virtual photons is strongly suppressed, as demon-\nstrated by the non-observation of e+e\u2212\u2192J/\u03c8J/\u03c8 (Abe,\n2004g).\nIf the X(3940) has spin equal to 0, like other states pro-\nduced together with the J/\u03c8, the absence of a DD decay\nmode strongly favors JP = 0\u2212, for which the most likely\ncharmonium assignment is the \u03b7c(3S) (see Table 18.2.1).102\nThe fact that the lower-mass \u03b7c and \u03b7c(2S) are also pro-\nduced in double charmonium production supports this as-\nsignment. However, there is the problem that the mea-\nsured X(3940) mass is below potential model estimates\nfor the \u03b7c(3S) mass of \u223c4050 MeV/c2 or higher (Barnes\net al., 2005). A further complication is the observation of\nthe X(4160), which could also be attributed to the 1S0\nstate, using similar arguments. But the X(4160) mass\nis well above expectations for the \u03b7c(3S) and well be-\n102 The decay of the pseudoscalar state, 0\u2212, into two pseu-\ndoscalar mesons is forbidden by parity conservation, as only\nS-wave is allowed. On the contrary, for the scalar state, 0+,\nthis decay is allowed and should be dominant.\n\n457\nlow those for the \u03b7c(4S), which is predicted to be near\n4400 MeV/c2 (Barnes et al., 2005). Although either the\nX(3940) or the X(4160) or both might conceivably \ufb01t a\ncharmonium assignment, the \ufb01nal identi\ufb01cation of these\nstates will be possible only after angular analysis of the\ne+e\u2212\u2192J/\u03c8 D\u2217D(\u2217) processes has been performed, allow-\ning quantum numbers to be \ufb01xed. Such a study requires\nmuch larger samples than those collected by the B Facto-\nries.\n18.2.2 New decay modes of known charmonia\nIt is di\ufb03cult for the B Factories to compete with the\ncharm factories (BES and CLEO-c) in searching for new\ndecay modes of the charmonium states below DD thresh-\nold, as the charm factories have collected large datasets at\nthe J/\u03c8 and \u03c8(2S) peaks. Automatically, large samples of\ntagged \u03b7c, \u03c7cJ, and hc events are also collected through\nradiative or hadronic transitions. Nonetheless, one new \u03b7c\ndecay mode was observed by the B Factories.\nFor the states above DD threshold the B Factories\nare competitive: for a study of wide \u03c8 resonances charm\nfactories need to perform an energy scan, with relatively\nlow luminosity at each point, whereas the B Factories can\nsee the whole energy region in many open charm exclusive\n\ufb01nal states. Here we present the observed new decay mode\nof the \u03b7c (Section 18.2.2.1) and \ufb01rst measurements of the\nexclusive decays of \u03c8 states above open charm threshold\n(Section 18.2.2.2).\n18.2.2.1 \u03b7c \u2192\u039b\u039b\nBelle has studied decays of \u03b7c and J/\u03c8 to both pp and \u039b\u039b,\nusing two-body B decays B \u2192\u03b7cK and J/\u03c8K (Wu, 2006).\nThe primary goal was to study anisotropy parameters in\nthe decays of J/\u03c8 to baryon-antibaryon pairs (Murgia and\nMelis, 1995). In addition to a clear \u03b7c \u2192pp signal, a\nsigni\ufb01cant excess has also been observed in \u03b7c \u2192\u039b\u039b for\nthe \ufb01rst time.\nIn this analysis B mesons are reconstructed using\nthe standard procedure, with \u2206E and mES as discrim-\ninating variables (see Section 7.1). The dominant back-\nground, continuum events, is suppressed using a Fisher\ndiscriminant that combines seven event shape variables\n(Section 9.3). The \u039b\u039b mass spectrum from the B me-\nson signal window is presented in Fig. 18.2.10. An un-\nbinned maximum likelihood \ufb01t to this spectrum is per-\nformed using a relativistic Breit-Wigner function for the\n\u03b7c peak, a Gaussian for the J/\u03c8 peak, and a linear func-\ntion for the non-resonant background. The Breit-Wigner\nfunction is convolved with the detector resolution func-\ntion, which is taken from the Gaussian width of the J/\u03c8\npeak. The \ufb01t result is shown in the Fig. 18.2.10 inset. The\nmeasured \u03b7c mass and width are (2974 \u00b1 7 +2\n\u22121) MeV/c2\nand (40 \u00b1 19 \u00b1 5) MeV, respectively. The signal yield is\n(18.2 \u00b1 4.8) \u03b7c events.\nA \ufb01t to the mES spectrum from the \u03b7c signal window\nyields (19.5 +5.1\n\u22124.4) events, consistent with the result of the\n0\n5\n10\n15\n20\n25\n30\n2.5\n3\n3.5\n4\n4.5\nEvents / 10 MeV/c2\nM\u039b\u039b\n_ (GeV/c2)\n0\n25\n2.9\n3\n3.1\nFigure 18.2.10. From Wu (2006): The \u039b\u039b mass spectrum in\nB \u2192\u039b\u039bK events from the B meson signal window. The \u03b7c\nand J/\u03c8 region is shown inset, with the \ufb01t results as a solid\nline. No signi\ufb01cant signal is visible in the \u03b7c(2S) region.\nformer \ufb01t. The statistical signi\ufb01cance of the observation\nof the new \u03b7c decay mode is estimated to be 7.9 standard\ndeviations. Taking into account reconstruction e\ufb03ciency,\nthe branching fraction of the \u03b7c \u2192\u039b\u039b decay is calculated\nto be B = (0.87+0.24\n\u22120.21(stat) +0.09\n\u22120.14(syst) \u00b1 0.27 (B)) \u00d7 10\u22123,\nwhere the third uncertainty term is due to the poorly\nknown absolute branching fractions of \u03b7c. This term can-\ncels in the ratio B(\u03b7c \u2192\u039b\u039b)/B(\u03b7c \u2192p\u00afp), measured to be\n0.67 +0.19\n\u22120.16 \u00b1 0.12, consistent with the theoretical expecta-\ntions.\n18.2.2.2 Open charm decays of JCP = 1\u2212\u2212charmonium\nstates\nThe process with a photon radiated from the initial state\n(ISR), e+e\u2212\u2192\u03b3ISR V (see Fig. 21.2.2 for the Feynman di-\nagram), generates a state V coupled to the virtual photon,\nand therefore with the same quantum numbers, JP C =\n1\u2212\u2212. Such events represent an excellent laboratory to study\nexclusive decays of the vector V , with very clean signals\nobserved in most studied \ufb01nal states (see Chapter 21 for\na detailed description of the process). The ISR method\nhas been successfully used to measure charmonium de-\ncays into open charm \ufb01nal states: their high multiplicity\nallows for e\ufb03cient reconstruction with the ISR method,\nwhile the small branching fractions of charmed mesons to\nmodes convenient for reconstruction make them di\ufb03cult\nto detect in exclusive B decays. The B Factories have pro-\nvided measurements of the branching fractions of various\nvector charmonium states for the \ufb01rst time. Here we de-\nscribe only the procedure that was used to extract the\nbranching fractions, and summarize the results.\nBoth BABAR (Aubert, 2009n) and Belle (Abe, 2007d;\nPakhlova, 2008a) have studied the processes e+e\u2212\u2192\n\n458\n0\n50\n100\n0\n50\n100\n0\n25\n50\n0\n25\n50\n0\n10\n20\n4\n4.5\n5\n5.5\n0\n10\n20\n4\n4.5\n5\n5.5\nFigure 18.2.11. From Aubert (2009n): The (a) DD, (b) DD\u2217,\nand (c) D\u2217D\u2217mass spectra in the e+e\u2212\u2192\u03b3ISR D(\u2217)D(\u2217) pro-\ncess. The curves represent the \ufb01tted functions as described in\nthe text. The shaded histogram corresponds to the smoothed\nincoherent background. The second smooth solid line repre-\nsents the non-resonant contribution.\n\u03b3ISR D(\u2217)D(\u2217); their results are in good agreement. The\nmeasured cross-sections for these processes around thresh-\nold exhibit many structures, which could be attributed\nto the various \u03c8 states. BABAR has performed \ufb01ts to the\nmeasured mass spectra including interference between the\nresonant terms (ciWi(m)ei\u03c6i, where Wi(m) is a P-wave\nrelativistic Breit-Wigner) and the non-resonant contribu-\ntion. The \ufb01tting functions for each channel are computed\nwith their own thresholds, e\ufb03ciencies, purities, and back-\ngrounds. The \ufb01ts, summed over the charged and neutral\n\ufb01nal states, provide a good description of all the data\n(Fig. 18.2.11). The fraction for each resonant contribution\ni is de\ufb01ned by\nfi =\n|ci|2 R\n|Wi(m)|2dm\nP\nj,k cjc\u2217\nk\nR\nWj(m)W \u2217\nk (m)dm;\n(18.2.1)\nthe fractions fi do not necessarily add up to 1 because of\ninterference between amplitudes. The error for each frac-\ntion has been evaluated by propagating the full covariance\nFigure 18.2.12. From del Amo Sanchez (2010d): The ob-\nserved (a) D+\ns D\u2212\ns , (b) D\u2217+\ns D\u2212\ns , and (c) D\u2217+\ns D\u2217\u2212\ns\nmass spec-\ntra in the processes e+e\u2212\u2192\u03b3ISRD(\u2217)\ns D(\u2217)\ns\n(del Amo Sanchez,\n2010d). The shaded areas show the background contribution.\nThe dashed lines indicate the sum of this background and the\ncoherent background. The solid lines are the results from the\n\ufb01t as described in the text.\nmatrix obtained by the \ufb01t. The resulting relative branch-\ning fractions are listed in Table 18.2.4, and compared with\nthe predictions of theoretical models.\nA similar \ufb01t was performed by BABAR to the D+\ns D\u2212\ns ,\nD\u2217+\ns D\u2212\ns , and D\u2217+\ns D\u2217\u2212\ns\nmass spectra (del Amo Sanchez,\n2010d). In the \ufb01t the mass and width of the \u03c8(4040),\n\u03c8(4160), \u03c8(4415), and the exotic state Y (4260) (see Sec-\ntion 18.3) are \ufb01xed to the PDG values (Amsler et al.,\n2008); interference with the coherent non-resonant contri-\nbution is taken into account. The \ufb01t results are shown in\nFig. 18.2.12 and measured \ufb01t fractions are given in Ta-\nble 18.2.5.\n\n459\nTable 18.2.4. From Aubert (2009n): Ratios of branching fractions for the three \u03c8 resonances. The \ufb01rst error is statistical, the\nsecond systematic. Theoretical expectations are from the 3P0 model (Barnes et al., 2005), C3 model (Eichten, Lane, and Quigg,\n2006), and \u03c1K\u03c1 model (Swanson, 2006).\nRatio\nMeasurement\n3P0\nC3\n\u03c1K\u03c1\nB(\u03c8(4040) \u2192DD)/B(\u03c8(4040) \u2192D\u2217D)\n0.24 \u00b1 0.05 \u00b1 0.12\n0.003\n0.14\nB(\u03c8(4040) \u2192D\u2217D\u2217)/B(\u03c8(4040) \u2192D\u2217D)\n0.18 \u00b1 0.14 \u00b1 0.03\n1.0\n0.29\nB(\u03c8(4160) \u2192DD)/B(\u03c8(4160) \u2192D\u2217D\u2217)\n0.02 \u00b1 0.03 \u00b1 0.02\n0.46\n0.08\nB(\u03c8(4160) \u2192D\u2217D)/B(\u03c8(4160) \u2192D\u2217D\u2217)\n0.34 \u00b1 0.14 \u00b1 0.05\n0.011\n0.16\nB(\u03c8(4415) \u2192DD)/B(\u03c8(4415) \u2192D\u2217D\u2217)\n0.14 \u00b1 0.12 \u00b1 0.03\n0.025\nB(\u03c8(4415) \u2192D\u2217D)/B(\u03c8(4415) \u2192D\u2217D\u2217)\n0.17 \u00b1 0.25 \u00b1 0.03\n0.14\nTable\n18.2.5.\nFrom del Amo Sanchez (2010d): D+\ns D\u2212\ns ,\nD\u2217+\ns D\u2212\ns , and D\u2217+\ns D\u2217\u2212\ns\n\ufb01t fractions (in %). Errors are statistical\nonly.\nResonance\nFraction\nD+\ns D\u2212\ns\nD\u2217+\ns D\u2212\ns\nD\u2217+\ns D\u2217\u2212\ns\n\u03c8(4040)\n62\n\u00b1 21\n\u03c8(4160)\n23\n\u00b1 26\n53 \u00b1 8\n\u03c8(4415)\n6\n\u00b1 11\n4 \u00b1 2\n5 \u00b1 12\nY (4260)\n0.5 \u00b1 3.0\n18 \u00b1 24\n11 \u00b1 16\nnon-resonant\n11\n\u00b1 5\n27 \u00b1 5\n71 \u00b1 20\nSum\n103\n\u00b1 36\n102 \u00b1 26\n87 \u00b1 28\nIn similar studies of two-body charmed mesons states\nproduced via ISR, Belle does not perform \ufb01ts to the ob-\ntained cross-sections, motivating their choice by the di\ufb03-\nculty of taking coupled channel e\ufb00ects into account. How-\never, a \ufb01t is performed to the prominent \u03c8(4415) peak\nfound in the process e+e\u2212\u2192\u03b3ISR D0D\u2212\u03c0+ (Pakhlova,\n2008c). As this peak is observed far from other \u03c8 states,\nand \u03c8(4415) decay to this \ufb01nal state turns out to be large,\na na\u00a8\u0131ve one-resonance \ufb01t is justi\ufb01ed in this case. A study\nof invariant masses of the D\u2212\u03c0+ and D0\u03c0+ combinations\ndemonstrates that the decay \u03c8(4415) \u2192D0D\u2212\u03c0+ is dom-\ninated by the D0D\u2217\n2(2460)0 and D\u2212D\u2217\n2(2460)+ interme-\ndiate states. Because of their positive interference (due to\nC = \u22121 of the \u03c8(4415)) Belle does not study them sepa-\nrately, but divides the selected sample into DD\u2217\n2(2460) +\nc.c. and non-resonant D0D\u2212\u03c0+ regions. A \u03c8(4415) peak\nis seen only in the former region; no sign of \u03c8(4415) is seen\nin the second case (Fig. 18.2.13). A \ufb01t to the MD0D\u2212\u03c0+\nspectrum in the DD\u2217\n2(2460) + c.c. regions yields 109 \u00b1\n25(stat) signal events, and the signi\ufb01cance for the \u03c8(4415)\nsignal is \u223c10\u03c3. The measured peak mass M\u03c8(4415) =\n(4.411 \u00b1 0.007(stat)) GeV/c2 and total width \u0393tot = (77 \u00b1\n20(stat)) MeV are in good agreement with the BES re-\nsults (Ablikim et al., 2007). Belle measures B(\u03c8(4415) \u2192\nDD\u2217\n2(2460))\u00d7B(D\u2217\n2(2460) \u2192D\u03c0+) = (10.5\u00b12.4\u00b13.8)%\nand sets an upper limit on the ratio of the branching frac-\ntions of \u03c8(4415) decays to non-resonant D0D\u2212\u03c0+ and\nDD\u2217\n2(2460) + c.c. to be 0.22 at the 90% C.L.\n0\n20\n40\nN/40 MeV/c2\n (a)\n M(D0D-\u03c0+), GeV/c2\n (b)\n0\n20\n4\n4.2\n4.4\n4.6\n4.8\n5\nFigure 18.2.13. From Pakhlova (2008c): Mass distributions\nfor D0D\u2212\u03c0+ in e+e\u2212\u2192\u03b3ISRD0D\u2212\u03c0+ events. Fit results are\nshown by the solid curve. (a) The MD0D\u2212\u03c0+ spectrum for the\nDD\u2217\n2(2460) signal region; the dashed curve corresponds to the\nnon-\u03c8(4415) contribution. (b) The MD0D\u2212\u03c0+ spectrum out-\nside the DD\u2217\n2(2460) signal region; the dashed curve shows the\nupper limit on the \u03c8(4415) yield at the 90% C.L. In both\nplots, shaded histograms show the normalized contributions\nfrom MD0 and MD\u2212sidebands.\nIn the study of the process e+e\u2212\u2192D0D\u2217\u2212\u03c0+ Belle\nfound only a hint for the \u03c8(4415) signal with statistical\nsigni\ufb01cance 3.1\u03c3 (Pakhlova, 2009) and set an upper limit\non the branching fraction B(\u03c8(4415) \u2192D0D\u2217\u2212\u03c0+) <\n10.6% at the 90% C.L.\n18.2.3 Measurements of parameters\nB Factory analyses have contributed to the precision with\nwhich various charmonium parameters are known: studies\nhave been performed for the \u03b7c (Section 18.2.3.1), J/\u03c8\n(Section 18.2.3.2), \u03c7c0 and \u03c7c2 (Section 18.2.3.3), and\n\u03c8(3770) (Section 18.2.3.4). The treatment of interference\ne\ufb00ects is important in a number of these analyses, as dis-\ncussed below.\n\n460\nTable 18.2.6. Summary of \u03b7c mass and width measurements obtained by BABAR and Belle in di\ufb00erent production processes as\nmarked in the second column.\nExperiment\nProcess\nDecay\nMass (MeV/c2)\nWidth (MeV)\nReference\nBelle\nB \u2192K\u03b7c\nhadrons\n2979.6 \u00b1 2.3 \u00b1 1.6\n29 \u00b1 8 \u00b1 6\nFang (2003)\nBABAR\nB \u2192K\u03b7c\ninclusive\n2982 \u00b1 5\n\u2014\nAubert (2006ae)\nBelle\nB \u2192K\u03b7c\npp\n2971 \u00b1 3+2\n\u22121\n48+8\n\u22127 \u00b1 5\nWu (2006)\nBelle\nB \u2192K\u03b7c\n\u039b\u039b\n2974 \u00b1 7+2\n\u22121\n40 \u00b1 19 \u00b1 5\nWu (2006)\nBABAR\nB \u2192K(\u2217)\u03b7c\nKK\u03c0\n2985.8 \u00b1 1.5 \u00b1 3.1\n36.3+3.7\n\u22123.6 \u00b1 4.4\nAubert (2008ba)\nBelle\nB \u2192K\u03b7c\nK0\nSK\u03c0\n2985.4 \u00b1 1.5+0.5\n\u22122.0\n35.1 \u00b1 3.1+1.0\n\u22121.6\nVinokurova (2011)\nBABAR\n\u03b3\u03b3 \u2192\u03b7c\nKK\u03c0\n2982.5 \u00b1 1.1 \u00b1 0.9\n34.3 \u00b1 2.3 \u00b1 0.9\nAubert (2004s)\nBelle\n\u03b3\u03b3 \u2192\u03b7c\nhadrons\n2986.1 \u00b1 1.0 \u00b1 2.5\n28.1 \u00b1 3.2 \u00b1 2.2\nUehara (2008b)\nBABAR\n\u03b3\u03b3 \u2192\u03b7c\nK0\nSK\u03c0\n2982.2 \u00b1 0.4 \u00b1 1.6\n31.7 \u00b1 1.2 \u00b1 0.8\nLees (2010b)\nBelle\n\u03b3\u03b3 \u2192\u03b7c\n\u03b7\u2032\u03c0+\u03c0\u2212\n2982.7 \u00b1 1.8 \u00b1 2.2 \u00b1 0.3\n37.8 +5.8\n\u22125.3 \u00b1 2.8 \u00b1 1.4\nZhang (2012)\nBelle\ne+e\u2212\u2192J/\u03c8\u03b7c\ninclusive\n2970 \u00b1 5 \u00b1 6\n\u2014\nAbe (2007f)\n18.2.3.1 \u03b7c mass, width, and transition form factor\nThe \u03b7c is the lightest S-wave spin-singlet charmonium\nstate. In spite of a long history of studies, the \u03b7c parame-\nters are still not well de\ufb01ned. As detailed in Section 18.1,\nthe \u03b7c mass and total width are of particular importance\nfor QCD tests in the charmonium sector, where a set of\nQCD complications are partially removed due to the large\nquark mass. While the spin-independent part of the cc po-\ntential is well-\ufb01xed by experimental data, for the study of\nthe spin-dependent part exact knowledge of the \u03b7c mass\nplays an important role. There is a relatively large spread\nin the \u03b7c mass and total width values obtained in di\ufb00erent\nexperiments (in Beringer et al., 2012, the fourteen mea-\nsurements have \u03c72 = 36), and no de\ufb01nitive explanation\nfor the discrepancy between the \u03b7c parameters measured\nin J/\u03c8 and \u03c8(2S) radiative decays, in \u03b3\u03b3 and p\u00afp produc-\ntion, and in B decays has been suggested to date.\nOne of the critical issues for the correct measurement\nof \u03b7c parameters in the decays J/\u03c8(\u03c8(2S)) \u2192\u03b7c\u03b3 may\nbe the theoretical understanding of the \u03b7c line shape in\nM1 radiative transitions. For example, the e\ufb00ect of a dis-\ntorted \u03b7c line shape in these decays was discussed by\nCLEO (Mitchell et al., 2009b). In other processes where \u03b7c\nparameters are measured, there is another source of sys-\ntematic uncertainty which was only recently recognized\nas of possible signi\ufb01cance: interference of the \u03b7c, which is\ncommonly exclusively reconstructed in a multihadron \ufb01-\nnal state, with a non-resonant (continuum) substrate. It is\nnot an easy task to take the e\ufb00ect of interference into ac-\ncount. If the \ufb01nal state contains more than two particles,\nthe resonant structure and the orbital angular momentum\nbetween \ufb01nal state hadrons may di\ufb00er for \u03b7c decay and the\ncontinuum. Hence the interference may be partial or even\nabsent, and simply adding a coherent continuum ampli-\ntude to the \u03b7c Breit-Wigner amplitude in the \ufb01t does not\nguarantee results more correct than those obtained when\ninterference is ignored. Over the past decade, both BABAR\nand Belle have carried out many measurements of \u03b7c pa-\nrameters, as summarized in Table 18.2.6. Below we brie\ufb02y\nreview some recent analyses where the e\ufb00ect of interfer-\nence has been considered.\nIn a study of \u03b7c production in \u03b3\u03b3 fusion BABAR es-\ntimates the uncertainty on the \u03b7c mass and width due\nto interference e\ufb00ects (Lees, 2010b). In the baseline \ufb01t\nto the measured K0\nSK\u03c0 mass spectra for the selected \u03b3\u03b3\nevents the interference term is ignored. To estimate the\npossible mass shift a \ufb01t assuming the maximum (full) in-\nterference with the continuum \u03b3\u03b3 \u2192K0\nSK\u03c0 background\nis performed. The \u03b7c mass value changes by 1.5 MeV/c2,\nwhich is the dominant contribution to the systematic un-\ncertainty. Belle observes a clear \u03b7c signal in the mass spec-\ntrum of \u03b7\u2032\u03c0+\u03c0\u2212combinations produced in two-photon col-\nlisions (Zhang, 2012), and measures its mass and width.\nAs in the BABAR analysis above, the e\ufb00ect of interference\ncan only be estimated: the di\ufb00erences in the \u03b7c parame-\nters with and without interference, \u2206M = 0.3 MeV/c2 and\n\u2206\u0393 = 1.4 MeV, are taken as model-dependent uncertain-\nties of the measurement. In the Belle study of B \u2192K\u03b7c\nfollowed by \u03b7c \u2192K0\nSK\u03c0 (Vinokurova, 2011) an angular\nanalysis is used to distinguish the contributions from the\ncoherent and noncoherent K0\nSK\u03c0 continuum amplitudes\nfrom B \u2192K(K0\nSK\u03c0) decays, mediated by the penguin di-\nagram. This analysis takes interference into account with\nno assumptions on its phase or absolute value. If interfer-\nence is turned o\ufb00, the \ufb01tted mass and width do not vary\nsigni\ufb01cantly. Finally, a recent BES paper (Ablikim et al.,\n2012a) has presented a high statistics measurement of the\ninterference: considering such results in future measure-\nments would help to reduce systematic uncertainties.\nAnother important \u03b7c property, the transition form\nfactor, has been measured by BABAR (Lees, 2010b). Such\na measurement allows the shape of the charmonium wave\nfunction to be probed, and provides a test of the predic-\ntions of pQCD as well as calculations that use the lat-\ntice QCD approach. BABAR studies the process e+e\u2212\u2192\ne+e\u2212\u03b3\u03b3\u2217\u2192e+e\u2212\u03b7c for the momentum transfer range\nfrom 2 to 50 GeV2. To ensure high virtuality of one of\nthe photons, either the electron or positron is required to\nbe detected, while the other is scattered at a small an-\n\n461\nQ2 (GeV2)\n|F(Q2)/F(0)|\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n10\n20\n30\n40\n50\nFigure 18.2.14. From Lees (2010b): The F(Q2)/F(0) dis-\ntribution for the \u03b7c (points with error bars). The solid curve\nshows the \ufb01t to the simple monopole shape. The dotted curve\nshows the leading order pQCD prediction from Feldmann and\nKroll (1997).\ngle and hence escapes detection. The transition form fac-\ntor F(Q2) (Fig. 18.2.14) is extracted from the measured\ndi\ufb00erential cross section d\u03c3/dQ2, where the squared mo-\nmentum transfer is calculated from the measured (p\u2032) and\nknown (p) four-momenta of the \ufb01nal and initial state elec-\ntrons respectively: Q2 = \u2212(p\u2032 \u2212p)2. The obtained distri-\nbution is well described by the simple monopole form\n\f\f\f\f\nF(Q2)\nF(0)\n\f\f\f\f=\n1\n1+Q2/\u039b, \u039b=(8.5\u00b10.6\u00b10.7) GeV2, (18.2.2)\nand in fair agreement with the QCD prediction (Feldmann\nand Kroll, 1997).\n18.2.3.2 Electronic and total width of the J/\u03c8\nThe electronic width of 1\u2212\u2212charmonium resonances is\nan important characteristic that measures the charmo-\nnium wavefunction \u03c8(0) and helps to \ufb01x potential model\nparameters. Lattice QCD calculations of \u0393ee, which are\ngradually approaching experimental results in precision,\nwill also soon be put to the test.\nExperimentally \u0393ee can be derived from the resonance\npeak cross section. This either requires a dedicated en-\nergy scan of the resonance at a charm factory, or can\nbe achieved at B Factories via ISR. The latter process\nprovides signi\ufb01cant cancellation of systematic uncertain-\nties, as an energy range including both the resonance and\nnearby regions is simultaneously available. BABAR pio-\nneered this method for determination of the J/\u03c8 electronic\nand total widths (Aubert, 2004d). In this analysis the J/\u03c8\nis reconstructed in the dimuon channel only, because the\ne+e\u2212\ufb01nal state has much larger backgrounds from ra-\ndiative Bhabha events. The directly measured quantity\nis \u0393ee \u00d7 B(J/\u03c8 \u2192\u00b5+\u00b5\u2212),103 which is found to be equal\nto (0.3301 \u00b1 0.0077 \u00b1 0.0073) keV. Then using the known\nleptonic branching fractions it is possible to derive both\nthe electronic width \u0393ee = (5.61 \u00b1 0.20) keV, and the to-\ntal width \u0393tot = \u0393ee/B(J/\u03c8 \u2192e+e\u2212) = (94.7 \u00b1 4.4) keV.\nThe statistical and systematic uncertainties are combined\nin quadrature. The BABAR \u0393ee \u00d7 B(J/\u03c8 \u2192\u00b5+\u00b5\u2212) result\nis one of three measurements contributing to the current\nworld average, which is (0.334\u00b10.005) keV (Beringer et al.,\n2012).\n18.2.3.3 \u03c7c0 and \u03c7c2\nThe B Factories have also made a moderate contribution\nto the precision measurement of the P-wave charmonium\nmasses and widths. Belle has measured charmonium pro-\nduction in two-photon collisions (Uehara, 2008b), observ-\ning signals for the three C-even charmonia \u03b7c, \u03c7c0, and \u03c7c2\nin the \u03c0+\u03c0\u2212\u03c0+\u03c0\u2212, K+K\u2212\u03c0+\u03c0\u2212, and K+K\u2212K+K\u2212de-\ncay modes. The invariant mass distributions in the vicinity\nof each charmonium peak are \ufb01tted to the sum of charmo-\nnium and background components. The combined results\nfor the three decay modes yield a \u03c7c0 mass of (3414.2 \u00b1\n0.5 \u00b1 2.3) MeV/c2 and a width of (10.6 \u00b1 1.9 \u00b1 2.6) MeV.\nThe measured \u03c7c2 mass is (3555.3 \u00b1 0.6 \u00b1 2.2) MeV/c2.\nBABAR has also searched for resonances decaying to\n\u03b7c\u03c0+\u03c0\u2212in two-photon collisions (Lees, 2012t). In this\nanalysis \u03b7c is reconstructed in the K0\nSK\u03c0 decay mode,\nand searches for several known charmonium states, includ-\ning the \u03c7c2, are performed in the reconstructed \u03b7c\u03c0+\u03c0\u2212\nmass spectrum. The \ufb01t in the \u03c7c2 region yields a central\nvalue for the ratio of branching fractions B(\u03c7c2\u2192\u03b7c\u03c0+\u03c0\u2212)\nB(\u03c7c2\u2192K0\nSK\u03c0) =\n14.5\u00b19.8(stat)\u00b17.3(syst)\u00b12.5 (B), where the last uncer-\ntainty is due to the uncertainty on B(\u03b7c \u2192K0\nSK\u03c0). No\nsigni\ufb01cant signal is found, and an upper limit of 31.4 is\nset on this ratio of branching fractions at the 90% C.L.\n18.2.3.4 \u03c8(3770) mass and width\nThe \u03c8(3770) is thought to be a D-wave state with a small\nadmixture of S-wave, and as it is above DD threshold,\nit is expected to decay mostly to DD. The \u03c8(3770) has\nbeen investigated in direct formation in e+e\u2212annihila-\ntion by numerous experiments since its observation by\nMARK I (Rapidis et al., 1977). Precise measurements\nof its mass and width have been obtained from energy\nscans near the resonance. However, as the accuracy of\nmeasurements has increased, an anomalous deviation of\n103 The peak Born cross section, which can be extracted\nfrom the \ufb01t to the data spectrum, is equal to \u03c3peak\nBorn\n=\n12\u03c02\nms \u0393eeB(J/\u03c8 \u2192\u00b5+\u00b5\u2212)\n\n462\nthe \u03c8(3770) peak lineshape from the Breit-Wigner func-\ntion has appeared (Ablikim et al., 2008a), and remained\npuzzling until recently.\nAt the B Factories one can use the process with ini-\ntial state radiation to study \u03c8(3770) formation, and both\nBABAR and Belle have observed the \u03c8(3770) in their anal-\nysis of e+e\u2212\u2192\u03b3ISRDD (Pakhlova, 2008a and Aubert,\n2009n; see Section 21.4.2). Only BABAR has \ufb01tted its DD\nmass spectrum to measure M = (3778.8\u00b11.9\u00b10.9) MeV/c2\nand \u0393 = (23.5\u00b13.7\u00b10.9) MeV. Although the electromag-\nnetic suppression of ISR processes results in small data\nsamples104 and does not allow the study of the \u03c8(3770)\npeak in detail, the access to the large energy range pro-\nvided by ISR turns out to be extremely important for\nunderstanding the \u03c8(3770) lineshape. Both BABAR and\nBelle observe a structure in the ISR cross section at\n\u223c3.9 GeV/c2 (Fig. 21.4.3), known as G(3900),105 which\nmust be taken into account to describe the cross section\nin the region below 4 GeV. This observation suggests that\nresonance-continuum interference is essential for determi-\nnation of the \u03c8(3770) parameters. A recent KEDR anal-\nysis of e+e\u2212scan data (Anashin et al., 2012), which in-\ncludes interference with the tail of the \u03c8(2S) resonance,\nconcludes that the interference causes a signi\ufb01cant shift\nin the \ufb01tted \u03c8(3770) peak and can explain the nontriv-\nial \u03c8(3770) lineshape. The Particle Data Group (Beringer\net al., 2012), when determining the \u03c8(3770) mass, now\nuses only those analyses which take interference into ac-\ncount.\nThe B Factories have also observed the \u03c8(3770) in B\ndecays (Brodzicka, 2008; Chistov, 2004; Aubert, 2008bd).\nThe measured mass and width are in good agreement with\nthe parameters obtained from the direct formation analy-\nsis that accounts for interference.\n18.2.4 Production\nThe B Factories also provide useful information on char-\nmonium production mechanisms. Measurement of the char-\nmonium production rates in di\ufb00erent processes, as well\nas kinematic characteristics of produced charmonia, help\nto test models numerically and to determine charmonium\nproperties. At the B Factories charmonia are produced\nin \u03b3\u03b3 fusion, via resonant direct production in e+e\u2212an-\nnihilation with initial state radiation, in the decays of B\nmesons, and in the fragmentation of cc pairs produced in\ne+e\u2212annihilation.\nThe former two processes provide a direct measure-\nment of important charmonium parameters, namely the\ntwo-photon and dielectron widths. Both are related to the\ncharmonium wave function, and are used to \ufb01x the param-\neters of the potential models that describe charmonium\n104 Note that the emission of the ISR photon is suppressed by\nthe electromagnetic coupling constant \u03b1EM.\n105 The G(3900) is not considered to be a real resonance, as\nthe appearance of a bump in this region is qualitatively consis-\ntent with predictions of the coupled-channel model of Eichten,\nGottfried, Kinoshita, Lane, and Yan (1980).\nspectroscopy. Chapters 21 and 22 describe in detail the\nnumerous experimental results obtained at the B Facto-\nries, in ISR and two-photon physics respectively.\nWhen describing charmonium formation from cc pairs\nproduced either in B decays or in e+e\u2212annihilation, e\ufb00ec-\ntive \ufb01eld theories are used. The EFT most often exploited\nis non-relativistic QCD (NRQCD), which assumes factor-\nization of the production of charmonium partons (e.g. a\ncc pair) in the given process, and the formation of char-\nmonium from those partons (Bodwin, Braaten, and Lep-\nage, 1995; Caswell and Lepage, 1986; Thacker and Lepage,\n1991). The former part contains a partonic level cross sec-\ntion generally calculated in perturbative QCD, in which\nthe cc pair may be produced in a color singlet or color octet\nstate (Braaten and Fleming, 1995; Cho and Leibovich,\n1996a). The latter part, which describes the evolution of\nthe cc pair with the quantum numbers of the \ufb01nal charmo-\nnium state, cannot be calculated in perturbation theory,\nand the relevant parameters are usually extracted from\nthe data. A signature of the NRQCD approach is the uni-\nversality of the long distance production matrix elements,\nwhich are assumed to be independent of the hard pro-\ncess of parton production. For a more extensive account\nof EFTs and quarkonia, see Section 18.1.4.\nBefore presenting the experimental results it is worth\nemphasizing that the B Factories provide the cleanest pro-\ncesses for calculation of charmonium production, as cc-\npairs in B decays (Section 18.2.4.1) and e+e\u2212annihilation\n(Section 18.2.4.2) are produced via weak and electromag-\nnetic processes, which can be calculated exactly. However\nin some cases, the test of such predictions requires a care-\nful treatment of the details of the experimental measure-\nments (Section 18.2.4.3).\n18.2.4.1 B decays\nB mesons can decay into almost all possible charmonium\nstates, with typical inclusive branching fractions \u223c1%, al-\nthough some states are dynamically suppressed. The \ufb01rst\nexample of charmonium production in B decays, B \u2192\nJ/\u03c8X, was discovered in 1985 by the ARGUS and CLEO\ncollaborations (Albrecht et al., 1985b; Haas et al., 1985).\nAt present, the Particle Data Group lists branching ratios\nfor 31 charmonium modes, while upper limits are set for\na further 26 modes. Although the B Factories have made\na formidable contribution to the majority of these mea-\nsurements, in this section we limit ourselves to the \ufb01rst\nobservations of inclusive and exclusive B to charmonium\ndecays that are interesting for the theory of charmonium\nproduction.\nInclusive decays\nTwo-body B-decays\nInclusive B decays to charmonia provide a very good op-\nportunity to test charmonium production models. The\n\n463\n0.20\n0.30\n0.40\n0.50\n0.60\n0\n500\n1000\n1500\n2000\nMl+l-\u03b3 - Ml+l- (GeV/c2)\nEvents/(5 MeV/c2)\n\u03c7c1 Yield: 2529. \u00b1 127.\n\u03c7c1 Mean: 411.5 \u00b1 0.4 MeV/c2\n\u03c7c1 Width: 10.0 \u00b1 0.6 MeV/c2\n\u03c7c2 Yield: 611. \u00b1 76.\n\u03c7c2 Mean: 457.2 MeV/c2 (Constrained)\n\u03c7c2 Width: 11.0 MeV/c2 (Constrained)\nFigure 18.2.15. Mass di\ufb00erence between J/\u03c8\u03b3 and J/\u03c8 can-\ndidates in B decays (Abe, 2002i).\nwell measured inclusive J/\u03c8 production rate (after sub-\ntraction of the contribution from cascade decays \u03c8(2S)\nand \u03c7c \u2192J/\u03c8 X) is a factor 5 \u221210 larger than the pre-\ndicted color singlet contribution: inclusion of the color\noctet mechanism to resolve this discrepancy therefore\nmakes the octet the dominant contribution. One of the\ncleanest ways to check whether this conclusion is correct\nis to measure the \u03c7c2-to-\u03c7c1 production ratio in B decays:\nthe only contribution to \u03c7c2 production comes from the\ncolor octet model, which favors \u03c7c2 over \u03c7c1 production,\nthe rate being proportional to 2J + 1, the number of spin\nstates.106 Experimentally, B \u2192\u03c7c1 X was measured many\nyears ago by ARGUS (Albrecht et al., 1992b), while only\nan upper limit had been set on \u03c7c2 production before the\nB Factories began operation (Chen et al., 2001c).\nInclusive B \u2192\u03c7c2X decays were \ufb01rst observed by\nBelle in 2002 using 29.4 fb\u22121 of data (Abe, 2002i). \u03c7c can-\ndidates are reconstructed in the J/\u03c8\u03b3 mode. In addition\nto the prominent \u03c7c1 peak, a \u03c7c2 signal is clearly seen in\nthe J/\u03c8\u03b3 \u2212J/\u03c8 mass di\ufb00erence spectrum (Fig. 18.2.15).\nSignal yields are extracted by \ufb01tting the distribution with\nthe sum of two Crystal Ball functions representing the \u03c7c1\nand \u03c7c2 contributions, and a third-order Chebyshev poly-\nnomial parameterizing the background. After subtraction\nof the \u03c8(2S) \u2192\u03c7cJ\u03b3 feed-down the direct branching frac-\ntions are found to be B(B \u2192\u03c7c1X) = (3.32 \u00b1 0.22 \u00b1\n0.34) \u00d7 10\u22123 and B(B \u2192\u03c7c2X) = (1.80+0.23\n\u22120.28 \u00b1 0.26) \u00d7\n10\u22123. A similar analysis was performed by BABAR (Au-\n106 If the cc pair is produced in the singlet state, it can directly\nform a meson, but this one can only have J = 0, 1. In order\nto be able to produce the \u03c7c2 state, which has J = 2, a gluon\nneeds to be emitted; gluon emission is also necessary when the\ncc is produced in a color octet state. Note also that in the na\u00a8\u0131ve\nfactorization approach \u0393(B \u2192\u03c7c0(2)P) is expected to vanish\nas explained in Section 17.3.5.4.\nbert, 2003n), with results in good agreement with those\nof Belle: B(B \u2192\u03c7c1X) = (3.41 \u00b1 0.35 \u00b1 0.42) \u00d7 10\u22123 and\nB(B \u2192\u03c7c2X) = (1.90 \u00b1 0.45 \u00b1 0.29) \u00d7 10\u22123. As can be\nseen, the ratio of production rates of \u03c7c2 and \u03c7c1 is roughly\n1 : 2, between the pure color singlet and pure color octet\npredictions (0 : 1 and 5 : 3 respectively).\nTwo-body decays of the type B \u2192(cc)resK(\u2217) have\nbeen extensively studied, because of their extremely clean\nexperimental environment and their importance for CP-\nviolation measurements. Theoretical calculations for these\ndecays are more di\ufb03cult than those for inclusive charmo-\nnium production, as they have to include the fragmenta-\ntion of light quarks into K(\u2217) mesons, introducing an addi-\ntional uncertainty. However, for such decays it is justi\ufb01ed\nto use the factorization hypothesis, since a charmonium\nstate (which does not pick up the spectator quark from\nthe B meson) is an object of small size and escapes the\ndecay region; only the kaon partner is a\ufb00ected by soft-\ngluon exchange. The factorization approach predicts large\nsuppression in the production of \u03c7c0, hc, and \u03c7c2 in com-\nparison with \u03c7c1 in B \u2192(cc)resK decays (Beneke and\nVernazza, 2009). By the start of B Factory data taking,\nonly the B \u2192\u03c7c1K decay had been observed.\nThe decay B \u2192\u03c7c0K was seen for the \ufb01rst time at the\nB Factories; this process was di\ufb03cult to observe, due to\nthe small \u03c7c0 branching fractions to modes suitable for re-\nconstruction. In 2001 Belle (Abe, 2002e) observed a B+ \u2192\n\u03c7c0K+ signal in two \u03c7c0 decay modes: \u03c0+\u03c0\u2212and K+K\u2212.\nA more substantial study of this decay, that takes into ac-\ncount interference of the \u03c7c0 resonance with a large variety\nof possible intermediate hadron resonances in the K+\u03c0\u2212,\n\u03c0+\u03c0\u2212, and K+K\u2212systems, was performed by Belle (Gar-\nmash, 2005) with a larger data set using the Dalitz anal-\nysis technique (see Chapter 13). In this analysis, signal\nevents are selected from an ellipse around the nominal \u2206E\nand mES values in the \u2206E \u2212mES plane. The regions with\ndipion mass around the J/\u03c8 or \u03c8(2S) nominal masses con-\ntain a large background from B+ \u2192J/\u03c8(\u03c8(2S))K+ de-\ncays followed by J/\u03c8(\u03c8(2S)) \u2192\u00b5+\u00b5\u2212, where both muons\nare misidenti\ufb01ed as pions. Similarly, the region in the\nK+\u03c0\u2212mass corresponding to D0 \u2192K+\u03c0\u2212decay is con-\ntaminated by the B+ \u2192D0K+ process. These three re-\ngions are excluded from further analysis. The Dalitz plot\nfor the signal region is shown in Fig. 18.2.16 (a) and (b)\nfor B+ \u2192\u03c0+\u03c0\u2212K+ and K+K\u2212K+ decays respectively.\nThe B+ \u2192\u03c7c0K+ signal can be seen as a horizontal band\nat M 2(\u03c0+\u03c0\u2212) and M 2(K+K+) \u223c11.6 GeV2/c4. The \u03c7c0\nsignal yield in B+ \u2192\u03c0+\u03c0\u2212K+ is extracted by an un-\nbinned maximum-likelihood \ufb01t to the Dalitz distribution\nwith a coherent sum of all known intermediate quasi-\ntwo-body processes (\u03c7c0K+, K\u2217(892)0\u03c0+, K\u2217\n0(1430)0\u03c0+,\n\u03c1(770)0K+, f0(980)K+, f(1300)K+, \u03ba\u03c0+), a non-resonant\nthree-body K+\u03c0+\u03c0\u2212contribution, and a background shape\n\ufb01xed from sideband studies. A similar procedure is used\nfor the K+K\u2212K+ \ufb01nal state. Signi\ufb01cant signals for \u03c7c0\nare observed in both modes, and the combined branch-\ning fraction is found to be B(B+ \u2192\u03c7c0K+) = (1.96 \u00b1\n0.35\u00b10.33+1.97\n\u22120.26)\u00d710\u22124, where the \ufb01rst error is statistical,\nthe second is systematic, and the third is the model error\n\n464\n0\n5\n10\n15\n20\n25\n0\n5\n10\n15\n20\n25\n30\nM2(K+\u03c0-) (GeV2/c4)\nM2(\u03c0+\u03c0-) (GeV2/c4)\n(a)\n0\n5\n10\n15\n20\n25\n0\n2\n4\n6\n8\n10\n12\n14\nM2(K+K-)min (GeV2/c4)\nM2(K+K-)max (GeV2/c4)\n(b)\nFigure 18.2.16. From Garmash (2005): Dalitz plot for events in the signal region for the (a) B+ \u2192\u03c0+\u03c0\u2212K+ and (b)\nB+ \u2192K+K\u2212K+ processes.\ndue to Dalitz plot parameterization. Subsequent, similar\nmeasurements based on larger samples by Belle (B(B+ \u2192\n\u03c7c0K+) = (1.12 \u00b1 0.12 +0.30\n\u22120.20) \u00d7 10\u22124; Garmash, 2006) and\nBABAR (B(B+ \u2192\u03c7c0K+) = (1.23 +0.27\n\u22120.25 \u00b1 0.06) \u00d7 10\u22124;\nAubert, 2008j) are in good agreement.\nTwo-body B decay into \u03c7c2 (such as B \u2192\u03c7c2K(\u2217)) has\nnot yet been observed with high statistical signi\ufb01cance.\nThe upper limit obtained by BABAR is B(B+ \u2192\u03c7c2K+) <\n1.8 \u00d7 10\u22125 at 90% C.L. (Aubert, 2009m). Belle has found\n3.6\u03c3 evidence for the B+ \u2192\u03c7c2K+ decay, with B(B+ \u2192\n\u03c7c2K+) = (1.11 +0.36\n\u22120.34 \u00b1 0.09) \u00d7 10\u22125 (Bhardwaj, 2011),\ni.e. almost 40 times smaller than the branching fraction\nfor the B+ \u2192\u03c7c1K+ decay. There is also an upper limit\nfrom Belle B(B+ \u2192hcK+) < 3.8 \u00d7 10\u22125 (Fang, 2006).\nSuch a large suppression of production of \u03c7c2 and hc with\nrespect to \u03c7c1 in two-body B decays is anticipated by\ntheory, as discussed above.\n18.2.4.2 e+e\u2212annihilation\nPrompt charmonium production in e+e\u2212annihilation was\n\ufb01rst observed in 1990 by the CLEO collaboration (Alexan-\nder et al., 1990), which found 15.2 \u00b1 4.9 events with re-\nconstructed J/\u03c8 above the kinematical limit for B-decays\n(pJ/\u03c8 > 2 GeV/c) in the \u03a5(4S) data. In the \ufb01rst analysis\nthis observation was misinterpreted as non-BB decays of\n\u03a5(4S), but later a J/\u03c8 signal was also seen in the CLEO\ncontinuum data.\nFor more than ten years after this observation, there\nwere attempts by theoreticians to explain the estimated\ncross section (\u03c3 \u223c2 pb) without new experimental in-\nputs. Due to the lack of experimental information, all pos-\nsible production mechanisms had to be considered. The\ndominant contribution to prompt J/\u03c8 production was ex-\npected to be due to color singlet and color octet diagrams\ne+e\u2212\u2192cc g(g). In the color singlet e+e\u2212\u2192cc gg pro-\ncess, two hard gluons are emitted, pushing the mass of\nthe cc pair into the charmonium region. Although the ra-\ndiation of two gluons is suppressed by \u03b12\nS, the contribution\nof this diagram is comparable with single gluon produc-\ntion because it provides a colorless cc pair, which can be\ndirectly projected into a physical charmonium state, e.g.\nJ/\u03c8 (Fig. 18.2.17 (a)). NRQCD, based on leading-order\nperturbative QCD calculations, predicted that the cross\nsection of the color singlet process e+e\u2212\u2192ccgg \u2192J/\u03c8 X\nmight be as high as 0.8 pb (Cho and Leibovich, 1996b;\nYuan, Qiao, and Chao, 1997b). The color octet e+e\u2212\u2192\nccg diagram leads to the formation of a color (cc)8 state,\nwhich is required to be \u201cdecolorized\u201d by emission of an-\nother soft gluon before it can be transformed into a phys-\nical charmonium state (Fig. 18.2.17 (b)). Due to the large\nvalue of \u03b1S at low energy, such emission is both large and\nimpossible to compute perturbatively. According to theo-\nretical estimates, the color singlet and color octet contri-\nbutions may be of the same order (Schuler, 1999; Yuan,\nQiao, and Chao, 1997a,b), although the uncertainty of this\nestimate is large due to poorly-constrained color octet ma-\ntrix elements. Another color singlet diagram e+e\u2212\u2192cc cc\n(Fig. 18.2.17 (c)) that can contribute to prompt charmo-\nnium production was estimated to be so small (\u223c0.05 pb;\nKiselev, Likhoded, and Shevlyagin, 1994), that detection\nof this process was considered hardly possible.\nInitial cross section measurements\nIn 2001 both BABAR and Belle performed much more pre-\ncise measurements of the e+e\u2212\u2192J/\u03c8 X cross section\n\n465\ne\n\u2013\ne+\n\u03b3 *\ng\ng\nc\nc\u2013\nJ/\u03c8\na)\ne\n\u2013\ne+\n\u03b3 *\ng\ngsoft\nc\nc\u2013\n(cc)8\n\u2013\nJ/\u03c8\nb)\ne\u2013\ne+\n\u03b3 *\ng\nc\nc\u2013\ncc\u2013\nJ/\u03c8\nD\nc)\ne\u2013\ne+\n\u03b3 *\ng\nc\nc\u2013\nc\nc\u2013\nJ/\u03c8\n\u03b7c\nd)\nFigure 18.2.17. Feynman diagrams describing J/\u03c8 produc-\ntion in e+e\u2212annihilation: see the text for details.\nusing the data sets obtained in the \ufb01rst year of their op-\neration (L \u223c20 fb\u22121). In both collaborations the J/\u03c8\nproduction was studied in the full momentum interval:\nthe region below 2 GeV/c was studied using continuum\ndata. BABAR obtained (2.52 \u00b1 0.21 \u00b1 0.21) pb (Aubert,\n2001b), while Belle obtained (1.47 \u00b1 0.10 \u00b1 0.13) pb (Abe,\n2002n). The discrepancies between the two measurements\nare likely due to di\ufb00erences in the selection criteria for\nJ/\u03c8 events that were used to suppress contributions from\nthe huge QED background. Corrections for the selection\ne\ufb03ciency are model dependent and may result in poorly\ncontrolled systematic uncertainty. (See also the discussion\nin Section 18.2.4.3 below.) While the measured cross sec-\ntion is not in contradiction with the NRQCD predictions\n(color singlet + color octet) of 1.1\u20131.6 pb (Yuan, Qiao,\nand Chao, 1997a,b), the expected sole color singlet con-\ntribution is too small to describe the data. On the other\nhand, the J/\u03c8 momentum spectrum measured by Belle\nand BABAR does not show any indication of the sizable\ncolor octet contribution, that was expected to result in an\nenhancement at the maximum momentum value. BABAR\nand Belle also measured the J/\u03c8 production and helic-\nity angle distributions, which roughly agree with NRQCD\nexpectations.\nBelle and BABAR performed searches for other char-\nmonium states produced in e+e\u2212annihilation. In addi-\ntion to the J/\u03c8 production study, Belle also measured\n\u03c3(e+e\u2212\u2192\u03c8(2S) X) = (0.67\u00b10.09+0.09\n\u22120.11) pb (Abe, 2002n)\nand set upper limits on the production of \u03c7c1 and \u03c7c2.\nLater BABAR, using a much larger data sample, improved\nthese limits: \u03c3prompt\nNch\u22653 (e+e\u2212\u2192\u03c7c1(2) X) < 77(79) fb at the\n90% con\ufb01dence level (Aubert, 2007at). Upper limits were\nset for events where the charmonium momentum exceeds\n2.0 GeV/c and there are at least three additional charged\ntracks. These limits are consistent with NRQCD predic-\ntions.\nThe recoil mass analyses\nIn 2002, contrary to NRQCD expectations, Belle ob-\nserved that most of the prompt J/\u03c8\u2019s are accompanied\nMrecoil(J/\u03c8) (GeV/c2)\nN/20 MeV/c2\n0\n10\n20\n30\n40\n50\n2.2\n2.6\n3\n3.4\n3.8\nMrecoil(\u03c8(2S)) (GeV/c2)\nN/20 MeV/c2\n0\n5\n10\n2.2\n2.6\n3\n3.4\n3.8\nFigure 18.2.18. From Abe (2004g): the mass of the system\nrecoiling against the reconstructed (top) J/\u03c8 and (bottom)\n\u03c8(2S) in inclusive e+e\u2212\u2192J/\u03c8(\u03c8(2S)) X events. The solid\ncurve is the result of a \ufb01t that includes \u03b7c, \u03c7c0, and \u03b7c(2S);\nthe dashed curve is the background contribution.\nby charmed hadrons (Abe, 2002j). The J/\u03c8 is recon-\nstructed in its \u2113+\u2113\u2212(\u2113= e, \u00b5) decays, with its mass\nconstrained to the nominal value to improve the momen-\ntum resolution. BB background is suppressed by requir-\ning p\u2217\nJ/\u03c8 > 2 GeV/c, where p\u2217\nJ/\u03c8 is the J/\u03c8 momentum in\nthe CM system. Backgrounds from QED e+e\u2212\u2192\u2113+\u2113\u2212(\u03b3)\nprocesses are suppressed by requiring the number of tracks\nin each event to be larger than 4. Unexpectedly, Belle\nfound that a signi\ufb01cant fraction of J/\u03c8\u2019s are produced\ntogether with another charmonium state in two-body re-\nactions of the type e+e\u2212\u2192J/\u03c8\u03b7c (Fig. 18.2.17 (d)). More\noften, charmed mesons are found in the events with recon-\nstructed J/\u03c8 (Fig. 18.2.17 (c)). To identify the \ufb01rst type\nof process (with the double charmonium \ufb01nal state) it\nis not necessary to reconstruct both mesons, which in-\nevitably leads to substantial e\ufb03ciency loss. Relying on\nfour-momentum conservation, the mass of the system pro-\nduced together with J/\u03c8 can be calculated using only the\nmeasured J/\u03c8 momentum. The mass of the system re-\ncoiling against the J/\u03c8 candidate\u2014the \u201crecoil mass\u201d\u2014 is\nde\ufb01ned as\nMrecoil(J/\u03c8) =\nh\n(\u221as \u2212E\u2217\nJ/\u03c8 )2 \u2212p\u22172\nJ/\u03c8\ni1/2\n,\n(18.2.3)\nwhere E\u2217\nJ/\u03c8 is the J/\u03c8 energy in the CM system. A\nclear peak was observed around the \u03b7c mass; two more\npeaks were seen around the masses of \u03c7c0 and \u03b7c(2S).\n\n466\nTable 18.2.7. Comparison of experimental cross sections (\u03c3 \u00d7 B>2 in fb, see text for symbol de\ufb01nition) with theoretical\nexpectations that do not include the B>2 factor.\nJ/\u03c8 cc\n\u03b7c\n\u03c7c0\n\u03b7c(2S)\nReference\nBelle\n25.6 \u00b1 2.8 \u00b1 3.4\n6.4 \u00b1 1.7 \u00b1 1.0\n16.5 \u00b1 3.0 \u00b1 2.4\nAbe (2004g)\nBABAR\n17.6 \u00b1 2.8+1.5\n\u22122.1\n10.3 \u00b1 2.5+1.4\n\u22121.8\n16.4 \u00b1 3.7+2.4\n\u22123.0\nAubert (2005n)\nNRQCD\n3.78 \u00b1 1.26\n2.40 \u00b1 1.02\n1.57 \u00b1 0.52\nBraaten and Lee (2003)\nNRQCD\n5.5\n6.9\n3.7\nLiu, He, and Chao (2003)\nLight cone\n14.4 +11.2\n\u22129.8\n\u2212\n13.0 +12.2\n\u221211.0\nBraguta (2009)\nNLO NRQCD\n17.6 +10.7\n\u22128.3\n\u2212\n\u2212\nBodwin, Lee, and Yu (2008)\nThis observation was later con\ufb01rmed by subsequent\nBelle (Fig. 18.2.18; Abe, 2004g) and BABAR analyses\n(Fig. 18.2.4; Aubert, 2005n) using larger samples. The\nmost recent results are summarized in Table 18.2.7. Be-\ncause of the selection criteria applied by both collabora-\ntions the results are given in terms of the product of the\ncross section and the branching fraction of the recoil char-\nmonium state into more than 2 charged tracks, \u03c3 \u00d7 B>2.\nThe similar process involving \u03c8(2S) was also observed by\nBelle (Fig. 18.2.18; Abe, 2004g). Surprisingly, the cross\nsections of double charmonium production with \u03c8(2S) are\nclose to those with J/\u03c8.\nFollowing the observation of double charmonium pro-\nduction, the corresponding cross sections were calculated\nusing NRQCD to be an order of magnitude smaller than\nexperimental values (Braaten and Lee, 2003; Liu, He, and\nChao, 2003). Later the importance of relativistic correc-\ntions was recognized by Ma and Si (2004) and Bondar\nand Chernyak (2005); the relative momentum of the heavy\nquarks in the charmonium was taken into account using\nthe light cone approximation. As a result, the calculated\ncross sections are now close to the experimental values\nthough within a large uncertainty (Braguta, 2009). Alter-\nnatively, other authors (Bodwin, Lee, and Yu, 2008; He,\nFan, and Chao, 2007) suggested to resolve the discrep-\nancy within the NRQCD approach by the resummation\nof the corrections of next-to-leading order (NLO) in \u03b1S,\nrelativistic corrections, and contributions from pure QED\ndiagrams. The theoretical expectations (not including the\nB>2 factor) are summarized in comparison with the Belle\nand BABAR measurements in Table 18.2.7.\nMeasuring the large double-cc fraction\nIn 2002 Belle also observed that J/\u03c8\u2019s are often accompa-\nnied by D\u2217+ and D0-mesons (Abe, 2002j). Scatter plots\nof the invariant mass of J/\u03c8 candidates versus masses of\nD\u2217+ and D0 candidates are shown in Fig. 18.2.19 (a), (c).\nThe charmed meson mass projections for the J/\u03c8 signal\nand sideband regions are shown in Fig. 18.2.19 (b), (d). A\nsigni\ufb01cant excess of D\u2217+ (ND\u2217+J/\u03c8 = 10.1 +3.6\n\u22123.0, with sig-\nni\ufb01cance 5.3 \u03c3), and D0 mesons (ND0J/\u03c8 = 14.9 +5.4\n\u22124.8, with\nsigni\ufb01cance 3.7 \u03c3) in the events with J/\u03c8\u2019s above the kine-\nmatical limit for \u03a5(4S) decays demonstrates that another\ncc pair is present. To calculate the e+e\u2212\u2192J/\u03c8cc cross\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n2.01\n2.02\n2.03\n0\n1\n2\n3\n4\n5\n6\n7\n2.01\n2.02\n2.03\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n1.81\n1.86\n1.91\na)\nM(D0\u03c0+) GeV/c2\nM(l+l-) GeV/c2\nb)\nM(D0\u03c0+) GeV/c2\nN/1 MeV/c2\nc)\nM(K-\u03c0+) GeV/c2\nM(l+l-) GeV/c2\nd)\nM(K-\u03c0+) GeV/c2\nN/4 MeV/c2\n0\n2\n4\n6\n8\n10\n1.81\n1.86\n1.91\nFigure 18.2.19. Results of a search for associated produc-\ntion of J/\u03c8 and charm mesons (Abe, 2002j): (a) the scatter\nplot M(\u2113+\u2113\u2212) vs M(D0\u03c0+); (b) projection onto the M(D0\u03c0+)\naxis; (c) the scatter plot M(\u2113+\u2113\u2212) vs M(K\u2212\u03c0+(K+K\u2212)); (d)\nprojection onto the M(K\u2212\u03c0+(K+K\u2212)) axis. Points with error\nbars show the J/\u03c8 signal region and the hatched histograms\nshow the scaled sidebands.\nsection, one needs to know how often the second cc-pair\nfragments into D\u2217+ or D0-mesons. Using the Lund frag-\nmentation model (Sj\u00a8ostrand, 1994) Belle calculated the\nratio of the J/\u03c8 cc and inclusive J/\u03c8 X production cross\nsections to be equal to 0.59 +0.15\n\u22120.13\u00b10.12. This result clearly\ndemonstrates that, contrary to NRQCD predictions, the\ndominant diagram for J/\u03c8 production is e+e\u2212\u2192J/\u03c8 cc.\nIn 2009, using an order of magnitude larger data\nsample (673 fb\u22121) Belle measured the cross sections for\nthe processes e+e\u2212\u2192J/\u03c8 cc in a model-independent\nway (Pakhlov, 2009). In the study of associated produc-\ntion of a J/\u03c8 with charmed hadrons, all the ground state\ncharmed mesons (D0, D+, D+\ns ) and the \u039bc-baryon were\nused. As two charmed hadrons are produced in cc frag-\nmentation, the e+e\u2212\u2192J/\u03c8 cc cross section is given by\nthe sum of double-charmonium e+e\u2212\u2192J/\u03c8 (cc)res cross\n\n467\nd\u03c3(e+e\u2013 \u2192 J/\u03c8 X)/dp*\na)\np*\nJ/\u03c8 GeV/c\n0\n50\n100\n150\n0\n1\n2\n3\n4\n5\n0\n5\n10\n15\nb)\n\u00d710 4\nNJ/\u03c8 /0.2\nc)\n|cos(\u03b8)|\n0\n5\n10\n15\n20\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 18.2.20. From Pakhlov (2009): (a) Di\ufb00erential cross\nsection for the e+e\u2212\u2192J/\u03c8 cc (open squares) and e+e\u2212\u2192\nJ/\u03c8 non-cc processes (\ufb01lled triangles). The curves represent a\n\ufb01t to the Peterson fragmentation function (Peterson, Schlat-\nter, Schmitt, and Zerwas, 1983). Angular distributions (b)\n| cos \u03b8helicity| and (c) | cos \u03b8production| for inclusive (open circles),\ne+e\u2212\u2192J/\u03c8 cc (open squares), and e+e\u2212\u2192J/\u03c8 non-cc pro-\ncesses (\ufb01lled triangles).\nsections (for (cc)res states below open-charm threshold)\nplus half the sum of the cross sections for production of\nJ/\u03c8 with any of ground state charmed hadrons. Produc-\ntion of the J/\u03c8 via mechanisms other than e+e\u2212\u2192J/\u03c8 cc\nwas also studied: the e+e\u2212\u2192J/\u03c8 non-cc cross section was\ncalculated as the di\ufb00erence between inclusive e+e\u2212\u2192\nJ/\u03c8 X and e+e\u2212\u2192J/\u03c8 cc cross sections. Belle found\n\u03c3(e+e\u2212\u2192J/\u03c8 cc) = (0.74 \u00b1 0.08 +0.09\n\u22120.08) pb and \u03c3(e+e\u2212\u2192\nJ/\u03c8 non-cc) = (0.43 \u00b1 0.09 \u00b1 0.09) pb, respectively, thus\ncon\ufb01rming the dominance of the e+e\u2212\u2192J/\u03c8 cc produc-\ntion mechanism. It should be noted that in this analysis\n(unlike that of Abe, 2002n) no correction for the charged\ntrack multiplicity (Nch > 4) requirement was applied for\nany of the processes. For e+e\u2212\u2192J/\u03c8 non-cc, such cor-\nrections are only possible by relying on a model, while\nfor e+e\u2212\u2192J/\u03c8 cc they are close to unity. A note on the\ninterpretation of these results follows in Section 18.2.4.3.\nWith the same technique Belle measured the J/\u03c8 mo-\nmentum (Fig. 18.2.20 (a)) and J/\u03c8 helicity and production\nangle distributions (Fig. 18.2.20 (b) and (c), respectively)\nfor both e+e\u2212\u2192J/\u03c8 cc (open squares) and e+e\u2212\u2192\nJ/\u03c8 non-cc (\ufb01lled triangle) processes. For the e+e\u2212\u2192\nJ/\u03c8 non-cc process, the J/\u03c8 momentum spectrum is sig-\nni\ufb01cantly softer than that for e+e\u2212\u2192J/\u03c8 cc, and the\nproduction angle distribution peaks along the beam axis.\nRecently, both e+e\u2212\n\u2192\nJ/\u03c8 gg and J/\u03c8 cc cross\nsections have been recalculated including NLO correc-\ntions (Gong, Wang, and Zhang, 2011; He, Fan, and Chao,\n2010; Li, Song, Zhang, and Ma, 2011) and are in bet-\nter agreement with the experimental data than the \ufb01rst\nleading-order calculations. A complete discussion can be\nfound in Brambilla et al. (2011).\n18.2.4.3 Special note: the e+e\u2212\u2192J/\u03c8 X cross section\nIt is both important and di\ufb03cult to compare measure-\nments of the e+e\u2212\u2192J/\u03c8 X cross section with theory.\nThis is especially true in the case where the recoil sys-\ntem X does not include open or hidden charm (\u201ce+e\u2212\u2192\nJ/\u03c8 non-cc\u201d), as this allows the NRQCD framework\u2014\nwith universal matrix elements describing production in\ne+e\u2212, pp, and other environments\u2014to be tested (Sec-\ntion 18.1.4.1). The measurements are described in detail in\nSection 18.2.4.2; here we treat problems of interpretation.\nThe main pitfall is the selection requiring more than\nfour reconstructed tracks. As described above, B Factory\ne+e\u2212\u2192J/\u03c8 X analyses impose such a requirement to\nsuppress low-multiplicity events of QED origin, which are\nnumerous and poorly understood. While the physics of\nQED events is straightforward, practical measurement re-\nquires control of cases where tracks are missed or misre-\nconstructed, and where beam-background tracks are added\nto the event, together with photon conversions and brems-\nstrahlung. The lack of coverage close to the beamlines, and\nthe trigger conditions, are key limitations: see Chapter 2\nfor the design of the experiments; for the forward-peaked\ncross-section of QED processes, in a simple case (initial\nstate radiation), see the discussion in Section 21.2.1.\nThe requirement of more than four reconstructed tracks\nmust be taken into account when comparing measure-\nments with theoretical predictions:\n1. For double charmonium production, e+e\u2212\u2192J/\u03c8 cc,\nthis is straightforward: both collaborations quote re-\nsults for \u03c3 \u00d7 B>2 (Table 18.2.7), where the factor B>2\ndescribes the fraction of cc decays to \ufb01nal states with\nmore than two charged particles. (J/\u03c8 is reconstructed\nonly in the decay to a lepton pair \u2113+\u2113\u2212.)\n2. The \ufb01rst B Factory measurements of e+e\u2212\u2192J/\u03c8 X\nquoted the cross section directly, attempting to cor-\nrect for the e\ufb00ect of track requirements. The initial\nBABAR analysis (Aubert, 2001b) required more than\nfour tracks in the J/\u03c8\n\u2192e+e\u2212case (i.e. not for\nJ/\u03c8 \u2192\u00b5+\u00b5\u2212), with additional selections to suppress\ne+e\u2212\u2192\u03b3ISRJ/\u03c8 and \u03b3ISR\u03c8(2S). The initial Belle\nanalysis (Abe, 2002n) required more than four tracks\nin all events (the same condition used by more re-\ncent analyses), with additional selections to suppress\ne+e\u2212\u2192\u03b3\u03c8(2S)(\u2192\u03c0+\u03c0\u2212J/\u03c8). Both experiments in-\ncorporated these requirements into their e\ufb03ciency cal-\nculations, making assumptions about the angular dis-\ntribution and polarization of these events, the fraction\nof recoil systems X containing charm, and the mix of\nhadronic \ufb01nal states within the system X in the light-\nquark case. All of these were poorly known at the time;\n\n468\nin the case of the fraction containing charm, prevailing\nassumptions were incorrect. These early measurements\nare thus subject to a signi\ufb01cant and poorly-controlled\nmodel dependence.\n3. The latest Belle measurement (Pakhlov, 2009) seeks\nto minimize such problems, reconstructing a list of\nstates that exhausts most of the possibilities for X\nsystems containing charm: the omissions are systems\nincluding the \u039ec, \u2126c, and their excitations. There is\nthus only weak dependence on modelling of the system\nX. Because the intrinsic reliance on models is so low,\nBelle quotes cross-sections without correcting for the\nnumber-of-tracks cut. As noted above, this has little\nimpact on the e+e\u2212\u2192J/\u03c8 cc measurement: the cor-\nrection approaches unity. For the important e+e\u2212\u2192\nJ/\u03c8 non-cc cross-section, however, the Belle result is\nan underestimate of the true value.\nThe remaining issue is the comparison of Belle and\nBABAR results. The disagreement between the initial mea-\nsurements was much larger than their reported uncertain-\nties (Aubert, 2001b; Abe, 2002n); while the Belle result\nhas been superseded by Pakhlov (2009), there has been no\nupdate of the BABAR cross section. (The successor analy-\nsis Aubert, 2005n concentrated on the then-controversial\nproduction of double cc \ufb01nal states.) The systematic limi-\ntations of the early measurements have been listed at point\n2 above: while the two collaborations\u2019 results formally dis-\nagree, experimentalists do not interpret Aubert (2001b) as\ncasting doubt on the Pakhlov (2009) cross sections.\n18.2.5 Concluding remarks\nThe last decade saw both an experimental and a theoreti-\ncal revival in charmonium physics due to the B Factories,\nwith their large enriched charm sample, playing a lead-\ning role with the observation and study of dozens new\ncharmonium-like states. For most of them a charmonium\nassignment has not been found so far: these states are re-\nviewed in Section 18.3. Only a few of the new states match\nthe conventional charmonium level scheme and have been\ndiscussed in this section. However even this selection of\nnew states reveals problems in the quantitative description\nof the charmonium spectrum, since potential models can\nnot accurately predict masses above the DD threshold.\nThis suggests that the coupling between the charmonium\nand two-charmed-meson sectors is not well described, and\nB Factory measurements provide a stimulating input for\nthe development of theoretical models. In a complemen-\ntary development, rigorous work at the B Factories on\naccurate description of broad charmonium states in their\ninterference with non-resonant background has helped to\nmeasure properly their masses and widths, which are also\nof great importance for theory.\nThe majority of the results presented in this section\nare illustrated by Fig. 18.2.21, which shows with colors the\nsigni\ufb01cant contribution of the B Factories to the study of\nthe charmonium spectrum.\nCharmonium production is another case where the B\nFactories managed to obtain surprising results. Observa-\nJPC\nM(GeV/c2)\n\u03b7c\nhadrons\n\u039b\u039b\u2013\nJ/\u03c8\n\u03b3*\nhadrons\nradiative\n\u03b3\nhc\nhadrons\n\u03b3\n\u03c7c0\nhadrons\n\u03c7c1\nhadrons\n\u03c7c2\nhadrons\n\u03b7c(2S)\nKK\u03c0\n\u2013\nKK\u03c0\u03c0\u03c0\n\u2013\n\u03c8(2S)\n\u03b3*\nhadrons\n\u03b3\n\u03b3\n\u03c0\u03c0,\n\u03c0,\u03b7\n\u03c0\n\u03b3\n\u03b3\n\u03b3\nhc(2P)\nDD\u2013\n\u03c7c0(2P)\nDD\u2013\n\u03c7c1(2P)\nDD\u2013\n\u03c7c2(2P)\nDD\u2013\n\u03c8(3770)\nDD\u2013\n\u03c8(4040)\nD(*)D(*)\n\u2013\n(s)\n(s)\n\u03c8(4160)\nD(*)D(*)\n\u2013\n(s)\n(s)\n\u03c8(4415)\nD(*)D(*)\n\u2013\n(s)\n(s)\nDD2\n\u2013\nX(3940)\nDD*\n\u2013\nX(4160)\nD*D*\n\u2013\n3.00\n3.25\n3.50\n3.75\n4.00\n4.25\n4.50\n0\u2013 +\n1\u2013 \u2013\n1+ \u2013\n0+ +\n1+ +\n2+ +\nFigure 18.2.21. The charmonium spectrum and scheme of\ncharmonium transitions and decays. The red bands correspond\nto states newly observed at the B Factories, blue bands show\nstates where the B Factories have made a substantial contri-\nbution to the accurate measurement of parameters, while the\nwhite bands represent yet unobserved states. The arrows show\ncharmonium transitions and decays: decay modes newly ob-\nserved at the B Factories are shown in red.\ntion of unexpectedly large double cc continuum produc-\ntion stimulated new methods to calculate charmonium\nproduction. The importance of relativistic corrections and\nlarge NLO contributions were recognized in attempts to\nresolve this puzzling discrepancy.\nIn conclusion, the numerous results obtained by the B\nFactories in the charmonium sector have triggered theo-\nretical developments for better descriptions of the spec-\ntroscopy, decay and production of charmonium states.\n\n469\n18.3 Exotic charmonium-like states\nEditors:\nRiccardo Faccini (BABAR)\nStephen Lars Olsen (Belle)\nEric Swanson (theory)\nAdditional section writers:\nBryan Fulsom, Arafat Gabareen Mokhtar, Alessandro Pil-\nloni, Bruce Yabsley, Shuwei Ye\nAs discussed in Section 18.1, the theory of bound states\nof heavy quarks, such as charmonium, provides quanti-\ntative predictions for masses and other properties of the\nphysically observable states with minimal ambiguity, pri-\nmarily because the velocities of the heavy quarks in these\nbound states are low enough for relativistic e\ufb00ects to be\ntreated as small perturbations to non-relativistic calcula-\ntions. The quantum numbers that are most appropriate\nto characterize a realizable state are, in decreasing order\nof the energy-splitting among eigenstates: the radial exci-\ntation n, the orbital angular momentum \u2113, the spin s, and\nthe total angular momentum J. Given this set of quantum\nnumbers, the parity and charge conjugation of c\u00afc states107\nare given by P = (\u22121)\u2113+1 and C = (\u22121)\u2113+s. States are\ndesignated by the usual spectroscopic notation: n 2s+1\u2113J.\nFigure 18.1.1 shows the mass and quantum number assign-\nments of the experimentally well established charmonium\nstates (see also Table 18.2.1).\nAll of the predicted c\u00afc states with mass below the\nopen-charm threshold (i.e., M < 2mD) have been ob-\nserved with measured masses and other properties that\nare in good agreement with theoretical predictions. This\nsuggests that the charmonium system is a good environ-\nment to search for \u201cexotic\u201d states, i.e. states containing a\nc\u00afc quark pair, as evidenced from its decay products, but\nwith properties that deviate from theoretical expectations\nfor c\u00afc spectroscopy. Before the advent of the B Factories\nno evidence for deviations from standard charmonium ex-\npectations was found.\nIn this section, we \ufb01rst summarize the existing mod-\nels that describe possible exotic states, then review the\nexperimental observations, reporting both the \ufb01nal states\nwhere the states have been observed and those where they\nhave not. Since the easiest quantum number to assign is\nthe charge-conjugation parity C, which is uniquely deter-\nmined either by the production method or decay \ufb01nal state\n(see Section 18.2), we \ufb01rst examine the C = +1 states\n(Sections 18.3.2, 18.3.3, and 18.3.4) and then discuss the\nJP C = 1\u2212\u2212states (Section 18.3.5). In addition, we dis-\ncuss the evidence for candidates for states with non-zero\nelectric charge that contain a c\u00afc pair among their con-\nstituents. These play a crucial role since they can by no\nmeans be regular charmonium states, which, by de\ufb01nition,\ncontain only a c\u00afc pair and are, therefore, electrically neu-\ntral. We conclude by summarizing the observations and\nthe remaining open issues (Section 18.3.7).\n107 A complete discussion of quantum numbers can be found\nin Section 18.1.1.\n18.3.1 Theoretical models\nAlthough the Standard Model is well established, QCD,\nthe fundamental theory of strong interactions, is only\namenable to analytic computation at very high energy\nscales, where perturbation theory is e\ufb00ective due to\nasymptotic freedom. Lattice gauge theory has recently\nreached the level where it is able to provide precision pre-\ndictions of simple hadronic properties (Durr et al., 2008;\nsee also the discussion in Section 18.1.5). Nevertheless, a\ncomprehensive understanding of low energy phenomena\nremains elusive.\nSystems that include heavy quark-antiquark pairs\n(quarkonia) are a unique and, in fact, ideal laboratory\nfor probing both the high energy regime of QCD and the\nlow energy regime, where non-perturbative e\ufb00ects domi-\nnate. For this reason, quarkonia have been the subject of\ndetailed experimental study for several decades. The accu-\nracy of current models of quarkonia is such that a particle\nwhich mimics quarkonia but does not \ufb01t in the model spec-\ntrum is a likely candidate for a nonconventional, \u201cexotic\u201d\nstate.\nIndeed, in the past years the B Factories and the Teva-\ntron have provided evidence for states that do not admit\na conventional mesonic interpretation and that instead\ncould be made of a larger number of constituents. While\nthis possibility has been considered since the beginning of\nthe quark model (Gell-Mann, 1964), the actual identi\ufb01ca-\ntion of such states would represent a major revolution in\nour understanding of elementary particles. It would also\nimply the existence of a possibly large number of addi-\ntional states that have not yet been observed.\nFinally, the study of strong bound states could be of\nrelevance to understanding the Higgs boson. It could tran-\nspire, for example, that the Higgs is a bound state, as\npredicted by several technicolor models, with or without\nextra dimensions (Contino, Kramer, Son, and Sundrum,\n2007; Dietrich, Sannino, and Tuominen, 2005).\nA short list of possible \u201cexotic\u201d bound states is:\nhybrids: bound states of a quark-antiquark pair and a\nnumber of constituent gluons. A signature of such\nstates is that they can have quantum numbers that\ncannot be assumed by quarkonium states (e.g. JP C =\n0+\u2212or 1\u2212+). Model and lattice computations indi-\ncate that the 1\u2212+ states are the lightest hybrid states\nand thus should be easy to distinguish from conven-\ntional quarkonia. Additional signatures are the pre-\ndicted preference for decays to either a pair of open-\ncharm mesons, one S- and one P-wave (Kokoski and\nIsgur, 1987) or to quarkonium plus pions; see e.g. Kou\nand Pene (2005) and Close and Page (2005).\nmolecules: bound states of two mesons, usually repre-\nsented as [Qq][q\u2032Q], where Q is the heavy quark. The\nsystem would be stable if the binding energy were suf-\n\ufb01cient to place the mass below all meson-meson con-\ntinua that couple to the molecule. It is expected that\nthis can happen readily when Q = b. For Q = c model\ncomputations indicate that resonant states are possi-\nble in certain channels. These states can decay strongly\n\n470\nvia con\ufb01guration mixing (Braaten and Kusunoki, 2004;\nBraaten and Lu, 2009; Close and Page, 2004; Flem-\ning, Kusunoki, Mehen, and van Kolck, 2007; Swanson,\n2006; Tornqvist, 2004; Voloshin, 2006).\ntetraquarks: a bound quark pair, neutralizing its color\nwith a bound antiquark pair, usually represented as\n[Qq][q\u2032Q]. A full nonet of states is predicted for each\nspin-parity, i.e. a large number of states are expected.\nThere is no need for these states to be close to any\nthreshold (Maiani, Piccinini, Polosa, and Riquer, 2006).\nIn addition, before the panorama of states is fully clar-\ni\ufb01ed, there is always the lurking possibility that some of\nthe observed states are misinterpretations of threshold ef-\nfects: a given amplitude might be enhanced when new\nhadronic \ufb01nal states become energetically possible, even\nin the absence of resonances.\n18.3.2 The X(3872)\nThe X(3872) was the \ufb01rst exotic charmonium-like state\ndiscovered. As shown in Fig. 18.3.1, it was initially ob-\nserved decaying into J/\u03c8\u03c0+\u03c0\u2212by the Belle experiment\nin B \u2192XK decays (Choi, 2003), and subsequently con-\n\ufb01rmed both in B decays (Aubert, 2005af) and in inclusive\np\u00afp production (Abazov et al., 2004; Acosta et al., 2004).\nFar more information is available on the X(3872) than on\nany other state; this information will be reviewed here by\ntopic: quantum numbers, mass and width, and production\nand decay.\n18.3.2.1 Quantum numbers\nThe exotic nature of this state was initially signalled by\nthe narrowness of its width, \u0393X(3872) < 2.3 MeV/c2 at\n90% con\ufb01dence (Choi, 2003), despite being above thresh-\nold for decay to a pair of charmed mesons. Furthermore,\nthe \u03c0+\u03c0\u2212invariant mass distribution \ufb01rst (Choi, 2003;\nAbulencia et al., 2006a), and a detailed angular analysis\nnext (Abulencia et al., 2007), showed that the dominant\ndecay is X(3872) \u2192J/\u03c8\u03c1, which would be isospin vi-\nolating if the X(3872) were a conventional charmonium\nstate.108\nThe above-mentioned angular analysis from the CDF\nexperiment (Abulencia et al., 2007) was able to discrim-\ninate among the possible JP C assignments, excluding all\nexcept JP C = 1++ and 2\u2212+. Positive intrinsic charge con-\njugation had already been established, with the evidence\nfor the decay X \u2192J/\u03c8\u03b3 (Abe, 2005a; Aubert, 2006an)\nand an upper limit on the branching fraction of the decay\nX \u2192\u03c7c1\u03b3 (Choi, 2003), thus con\ufb01rming positive intrinsic\ncharge conjugation.109\n108 In this case, an isosinglet particle (the X(3872)) would be\ndecaying into an isovector state: the combination of an isosin-\nglet (J/\u03c8) and an isovector (\u03c1) particle.\n109 The \u03c7c1 has C = +1, while the \u03b3 has C = \u22121: the \ufb01nal\nstate therefore has C = \u22121. If the X has positive charge con-\njugation it cannot decay via electromagnetic interactions into\na C = \u22121 \ufb01nal state.\n) (GeV)\n/\n/\n \ns\nM(J/\n3.82\n3.84\n3.86\n3.88\n3.9\n3.92\nEvents / ( 0.005 GeV )\n0\n5\n10\n15\n20\n25\n30\n35\n)\n2\n Invariant Mass (GeV/c\n0\nD\n*0\nD\n3.88\n3.9\n3.92\n3.94\n3.96\n3.98\n4\n2\nEvents/2 MeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n16\n)\n2\n Invariant Mass (GeV/c\n0\nD\n*0\nD\n3.88\n3.9\n3.92\n3.94\n3.96\n3.98\n4\n2\nEvents/2 MeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n16\n modes\n0\nD\n*0\nD\nAll \n(e)\nX(3872)\nFigure 18.3.1. Invariant mass spectrum of the J/\u03c8\u03c0+\u03c0\u2212sys-\ntem in B \u2192J/\u03c8\u03c0\u03c0K decays as observed by Belle (Choi, 2003;\nupper plot) and of the D\u22170D0 system in B \u2192D\u2217DK decays\nas published by BABAR (Aubert, 2008bd; lower plot).\nFor years the most favored option has been to assume\nthat the X has JP C = 1++; a D\u22170D molecule with L = 0\nwould have these quantum numbers. Such a deuteron-like\nstate, bound by pion exchange, was discussed by Tornqvist\n(1994), and proposed as a model of the X(3872) structure\nby Swanson (2004b), and many subsequent investigators.\nHowever, de\ufb01nitive arguments against the 2\u2212+ assignment\nhave been lacking.\nThe spin-2 hypothesis has been considered implausi-\nble from early studies onwards: the 2\u2212+ decay to \u03b3J/\u03c8\nis not an electric dipole transition, and so should be sup-\npressed;110 for the charmonium state with these quantum\nnumbers, the 1 1D2 or \u03b7c2, the isospin-violating transi-\ntion \u03b7c2 \u2192\u03c0+\u03c0\u2212J/\u03c8 would be expected to have a small\nrate, relative to isospin-conserving \u03b7c2 \u2192\u03c0+\u03c0\u2212\u03b7c (Olsen,\n2005). However the BABAR study of X(3872) \u2192J/\u03c8\u03c9 (del\nAmo Sanchez, 2010c) reported a (relatively weak) prefer-\nence for JP C = 2\u2212+, and there has since been a renewed\ndiscussion of this possibility (e.g. Burns, Piccinini, Polosa,\nand Sabelli, 2010; Faccini, Pilloni, and Polosa, 2012; Han-\nhart, Kalashnikova, Kudryavtsev, and Nefediev, 2012). If\nthe X(3872) has quantum numbers JP C = 2\u2212+, it should\nbe produced by two-photon fusion (see Chapter 22).\n110 This straightforward point is part of the commonly-\naccepted wisdom about the X(3872). We are not aware of who\n\ufb01rst brought it to general attention.\n\n471\nBABAR has searched for \u03b3\u03b3 \u2192X(3872) \u2192\u03b7c(1S)\u03c0+\u03c0\u2212\nwith the \u03b7c(1S) decaying to K0\nSK\u00b1\u03c0\u2213(Lees, 2012t). No\nsignal events were found, and a 90% con\ufb01dence-level upper\nlimit \u03c3(\u03b3\u03b3 \u2192X(3872)) \u00d7 B(X(3872) \u2192\u03b7c(1S)\u03c0+\u03c0\u2212) <\n48 fb was set on the product of the \u03b3\u03b3 \u2192X(3872) cross\nsection and X(3872) \u2192\u03b7c(1S)\u03c0+\u03c0\u2212branching fraction.\nCLEO has searched for \u03b3\u03b3 \u2192X(3872) \u2192J/\u03c8\u03c0+\u03c0\u2212and\nhas found no signi\ufb01cant signal (Dobbs et al., 2005).\nThe updated Belle analysis of X(3872) \u2192\u03c0+\u03c0\u2212J/\u03c8,\nusing the full 711 fb\u22121 \u03a5(4S) \u2192BB data sample (Choi,\n2011), con\ufb01rmed two key CDF results: the M(\u03c0+\u03c0\u2212) spec-\ntrum is consistent with X(3872) \u2192\u03c10J/\u03c8 with either\nL = 0 or L = 1, consistent with JP C = 1++ and 2\u2212+\nrespectively (cf. Abulencia et al., 2006a); and the angu-\nlar distribution of the decay allows both 1++ and 2\u2212+\ninterpretations (cf. Abulencia et al., 2007). Decays B \u2192\nKX(3872)[\u2192\u03c0+\u03c0\u2212J/\u03c8{\u2192\u2113+\u2113\u2212}] are described in gen-\neral by a \ufb01ve-dimensional angular distribution; under cer-\ntain assumptions, the 1++ distribution is \ufb01xed, while there\nare two free parameters for 2\u2212+: the relative magnitude\nand phase of two complex amplitudes.111 Due to this ex-\ntra freedom for 2\u2212+, and complementary limitations of\nthe Belle and CDF analyses, it is not possible to exclude\n2\u2212+. The Belle analysis, due to the limited size of the sam-\nple, considers three di\ufb00erent one-dimensional projections\nof the full distribution; CDF works with a binned three-\ndimensional distribution, as the other two quantities are\nunmeasurable on the sample used (inclusive X(3872) pro-\nduction from pp, without requiring B \u2192KX).\nWhile we were preparing this book, LHCb published\nan analysis of a large and clean B+ \u2192K+X(3872) sample\n(313 \u00b1 26 events), based on an event-by-event likelihood\nratio test of 1++ and 2\u2212+ hypotheses on the full \ufb01ve-\ndimensional angular distribution (Aaij et al., 2013a). This\nstudy favored 1++ over 2\u2212+ by more than eight standard\ndeviations; the complex ratio of amplitudes for the 2\u2212+\nhypothesis, which is treated as a nuisance parameter, is\nfound to be consistent with both the Belle result (Choi,\n2011) and with the expectation for decays of a 1++ state.\nIt therefore appears that the JP C = 1++ assignment has\n\ufb01nally been established.\n18.3.2.2 Mass, width, and hypothetical partner states\nMeasurements of the mass and width of the X(3872) have\nbeen complicated by discussion of two further questions:\nis the X a single particle, or a pair of neutral states; and,\neven in the case of a single state, what lineshape do we\nexpect to observe in any given decay mode? These ques-\ntions have been particularly important for the analysis\nand interpretation of the decays X(3872) \u2192\u03c00D0D0 and\n111 A publicly available LHC note (Mangiafave, Dickens, and\nGibson, 2010), cited by Belle (Choi, 2011), lists the various\nangular distributions but incorrectly represents the normalized\nratio of amplitudes for the 2\u2212+ hypothesis, \u03b1 = B11/(B11 +\nB12), as a real number with 0 \u2264\u03b1 \u22641. The corresponding\nLHCb thesis (Mangiafave, 2011) notes that \u03b1 is complex in\ngeneral.\n\u03b3D0D0; at the time of writing, the default approach is\nto exclude results of these decays from averages of mass\nand width measurements (see for example Beringer et al.,\n2012). In the following, we will brie\ufb02y sketch the history,\nbefore presenting a summary of the results from the B\nFactories and other experiments.\nPartner states, and nontrivial lineshape\nModels in which the X(3872) is a compact four-quark\nstate (a \u201ctetraquark\u201d; see Section 18.3.1) predict part-\nner states, in particular an additional neutral state. The\ndiscovery process B+ \u2192K+X(3872) and the isospin-\nrelated decay B0 \u2192K0\nSX(3872) in general produce both\nstates with di\ufb00erent branching ratios, see for example\nMaiani, Piccinini, Polosa, and Riquer (2005). However,\nit could happen that each B decays into a di\ufb00erent X\nmass eigenstate. Both BABAR (Aubert, 2006ax, 2008d)\nand Belle (Adachi, 2008c; Choi, 2011) have performed\nanalyses that distinguish the two samples, in order to\ntest this idea. The most recent results (Aubert, 2008d and\nChoi, 2011; see Fig. 18.3.2) set the mass di\ufb00erence of the\nstates produced in B+ and B0 decay at\n\u03b4M \u2261M(X | B+ \u2192K+X) \u2212M(X | B0 \u2192K0X)\n= (+2.7 \u00b1 1.6 \u00b1 0.4) MeV/c2 (BABAR),\n= (\u22120.7 \u00b1 1.0 \u00b1 0.2) MeV/c2 (Belle),\n= (+0.2 \u00b1 0.8) MeV/c2\n(mean).\n(18.3.1)\nA complementary analysis by CDF (Aaltonen et al.,\n2009c), \ufb01tting the inclusive \u03c0+\u03c0\u2212J/\u03c8 spectrum, yields no\nevidence for any other neutral state and sets a limit on\nthe mass di\ufb00erence of 3.6 MeV/c2 at the 95% C.L., to be\ncompared to the expectation\n\u03b4M = (7 \u00b1 2)/ cos(2\u03b8) MeV/c2\n(18.3.2)\nfrom Maiani, Piccinini, Polosa, and Riquer (2005), where\n\u03b8 is a (small) angle describing mixing between \ufb02avor eigen-\nstates.\nThe same analyses provide measurements of the ratio\nof product branching fractions,\nR \u2261B(B0 \u2192K0X) \u00d7 B(X \u2192\u03c0+\u03c0\u2212J/\u03c8)\nB(B+ \u2192K+X) \u00d7 B(X \u2192\u03c0+\u03c0\u2212J/\u03c8),\n\ufb01nding\nR = 0.41 \u00b1 0.24 \u00b1 0.05 (BABAR),\n= 0.50 \u00b1 0.14 \u00b1 0.04 (Belle).\n(18.3.3)\nThe expectation in the case of molecular models of the X\nhas been a source of confusion: an extensively-cited study\nby Braaten and Kusunoki (2005) predicted R < 0.1, and\ntogether with \u03b4M measurements prior to Choi (2011), this\nled to a widespread interpretation that B Factory B+-\nversus-B0 production results favored the tetraquark pic-\nture. Other estimates of R for D\u22170D0 molecules exist: for\n\n472\n (GeV)\nbc\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nEvents / ( 0.002 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\n (GeV)\nbc\nM\n5.2\n5.22\n5.24\n5.26\n5.28\n5.3\nEvents / ( 0.002 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\n) (GeV)\n/\n/\n \ns\nM(J/\n3.8\n3.85\n3.9\n3.95\nEvents / ( 0.004 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\n) (GeV)\n/\n/\n \ns\nM(J/\n3.8\n3.85\n3.9\n3.95\nEvents / ( 0.004 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\n16\nE (GeV)\n6\n-0.15 -0.1 -0.05\n0\n0.05\n0.1\n0.15\n0.2\nEvents / ( 0.007 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nE (GeV)\n6\n-0.15 -0.1 -0.05\n0\n0.05\n0.1\n0.15\n0.2\nEvents / ( 0.007 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nFigure 18.3.2. Events from the B0 \u2192K0\nS\u03c0+\u03c0\u2212J/\u03c8 analysis of Belle (Choi, 2011), with the results of a three-dimensional \ufb01t\nto Mbc \u2261mES, M(J/\u03c8\u03c0+\u03c0\u2212), and \u2206E shown (blue solid curve); the \ufb01tted contributions of combinatorial background (red\ndotted), and combinatorial plus peaking background (green dashed) are also shown.\nexample, Swanson (2006) found 0.06\u20130.29. Braaten and\nLu (2008) subsequently described the R < 0.1 prediction\nas the result of a \u201cconceptual error\u201d and found that in the\nmolecular model R could be studied only together with\nthe lineshapes of X(3872) decays.\nAs no signi\ufb01cant separation is seen between the masses\nof the peaks in the K+\u03c0+\u03c0\u2212J/\u03c8 and K0\nS\u03c0+\u03c0\u2212J/\u03c8 \ufb01nal\nstates, we assume in what follows that both are due to\nthe decay of a single X(3872) state. In the mass and\nwidth measurements presented below, the results from\nK+\u03c0+\u03c0\u2212J/\u03c8 dominate.\nBelle observed the decay X(3872) \u2192D\u22170D0 in the\n\u03c00D0D0 \ufb01nal state at the higher mass M = (3875.2 \u00b1\n0.7+0.3\n\u22121.6 \u00b1 0.8) MeV/c2 (Gokhroo, 2006; the \ufb01nal error re-\n\ufb02ects the then-current uncertainty in the D0 mass). Subse-\nquent analyses by both BABAR (Aubert, 2008bd) and Belle\n(Aushev, 2010) con\ufb01rmed the observation, also adding the\n\u03b3D0D0 \ufb01nal state, and \ufb01nding a mass of M = (3873.8 \u00b1\n0.5) MeV/c2 if the two results are averaged. As this is sig-\nni\ufb01cantly larger than the value observed in the discovery\nmode \u03c0+\u03c0\u2212J/\u03c8 (see below) there has been some specula-\ntion that D\u22170D0 and \u03c0+\u03c0\u2212J/\u03c8 are produced by the decay\nof two distinct parent particles (see for example the dis-\ncussion in Aubert, 2008bd). While this is possible a priori,\nthere are two related problems with using this model to\ninterpret the data:\n\u2013 Expected lineshape: In a decay X(3872) \u2192D\u22170D0 the\nD\u22170 will in general be o\ufb00-shell, because of the proxim-\nity of the D\u22170D0 threshold. The e\ufb00ect on the decays is\npronounced if the X is below threshold, and study of\nthe \u03c00D0D0 and \u03b3D0D0 lineshapes (which can have\na complicated structure in general) is required to dis-\ntinguish between an X state which is below threshold\nand an above-threshold \u201cvirtual state\u201d (see for exam-\nple the discussions by Artoisenet, Braaten, and Kang,\n2010, and Hanhart, Kalashnikova, and Nefediev, 2010,\n2011).\n\u2013 Analysis technique: The mature analyses of both col-\nlaborations impose a D\u2217mass constraint on one of the\n\u03c00D0 (or \u03b3D0) combinations, to improve the resolu-\ntion of the resulting B \u2192KX candidates, and hence\nthe suppression of the background. This yields a re-\nconstructed X(3872) mass that is above threshold by\nconstruction, and complicates the task of extracting\nthe \u03c00D0D0 (or \u03b3D0D0) lineshape.\nWithin a model where a state above threshold is decay-\ning to on-shell D\u22170 and D0, both collaborations resolve\na nonzero width for that state, with an average of \u0393 =\n(3.4\u00b11.5) MeV/c2. Some care is taken with the simulation\nand \ufb01tting in both measurements, including (in the Au-\nbert, 2008bd analysis for example) simulations of X(3872)\nwith a range of masses and widths, rather than relying\non parameterization of the reconstructed mass. Aubert\n(2008bd) also \ufb01nds \u03b4M = (0.7 \u00b1 1.9 \u00b1 0.3) MeV/c2 for the\ndi\ufb00erence between masses observed in B+ and B0 decays\nto D\u22170D0.\nFor the reasons quoted above, and in common with\nother recent reviews (e.g. Beringer et al., 2012), we exclude\nthese D\u22170D0 results from averages of the X(3872) mass\nand width below.\nSearches for charged partner states have also been con-\nducted by both BABAR (Aubert, 2005aa) and Belle (Choi,\n2011). No evidence for such a state is seen, with limits\nfrom Belle (BABAR) on the product branching fractions of\nB(B0 \u2192K\u2212X+) \u00d7 B(X+ \u2192\u03c1+J/\u03c8) < 4.2(5.4) \u00d7 10\u22126,\nB(B+ \u2192K0X+) \u00d7 B(X+ \u2192\u03c1+J/\u03c8) < 6.1(22) \u00d7 10\u22126,\n(18.3.4)\n\n473\nto be compared with\nB(B+ \u2192K+X) \u00d7 B(X \u2192\u03c10J/\u03c8)\n= (8.4 \u00b1 1.5 \u00b1 0.7) \u00d7 10\u22126 (BABAR),\n= (8.6 \u00b1 0.8 \u00b1 0.5) \u00d7 10\u22126 (Belle)\n(18.3.5)\nfor the discovery mode, from Aubert (2008d) and Choi\n(2011) respectively. This excludes models in which the\nX(3872) is the neutral member of an isospin triplet, where\ndecays to the charged states would be favored by a factor\nof two. However, the tetraquark model of Maiani, Pic-\ncinini, Polosa, and Riquer (2005) provides lower limits for\nthe rates in Eq. (18.3.4) which are still allowed by the\nX(3872) rate in Eq. (18.3.5).\nMass measurements in J/\u03c8 \ufb01nal states\nA summary of all available mass measurements is shown\nin Fig. 18.3.3. The current world average, considering only\nX(3872) decays to \ufb01nal states including the J/\u03c8, is M =\n(3871.68 \u00b1 0.17) MeV/c2 (Beringer et al., 2012). The most\nprecise measurements are those of CDF (Aaltonen et al.,\n2009c), Belle (Choi, 2011), the new measurement from\nLHCb (Aaij et al., 2012k), and BABAR (Aubert, 2008d),\nall e\ufb00ectively \u03c0+\u03c0\u2212J/\u03c8 measurements; the hadron ma-\nchines measure inclusive production in pp and pp respec-\ntively, while the B Factory measurements are dominated\nby B+ \u2192K+\u03c0+\u03c0\u2212J/\u03c8.\nThe D\u22170D0 threshold is at (3871.84 \u00b1 0.27) MeV/c2\n(using the D0 mass and mD\u22170 \u2212mD0 di\ufb00erence values\nfrom Beringer et al., 2012). If the X(3872) is interpreted\nas a D\u22170D0 \u201cmolecule\u201d (see Section 18.3.1), bound by\npion exchange, then the binding is exceptionally weak,\nmX \u2212mD\u22170 \u2212mD0 = (0.16 \u00b1 0.31) MeV, to be compared\nto 2.2 MeV for the deuteron. Although the B Factory (and\n3867.0 3869.5 3872.0 3874.5 3877.0\nBelle KJ/\u03c8\u03c0+\u03c0\u2212\nBABAR KJ/\u03c8\u03c9\nBABAR K+J/\u03c8\u03c0+\u03c0\u2212\nBABAR K0\nSJ/\u03c8\u03c0+\u03c0\u2212\nLHCb J/\u03c8\u03c0+\u03c0\u2212X\nCDF J/\u03c8\u03c0+\u03c0\u2212X\nD\u00d8 J/\u03c8\u03c0+\u03c0\u2212X\nAverage\n3871.85 \u00b1 0.27 \u00b1 0.19\n3873+1.8\n\u22121.6 \u00b1 1.3\n3871.4 \u00b1 0.6 \u00b1 0.1\n3868.7 \u00b1 1.5 \u00b1 0.4\n3871.95 \u00b1 0.48 \u00b1 0.12\n3871.61 \u00b1 0.16 \u00b1 0.19\n3871.8 \u00b1 3.1 \u00b1 3.0\n3871.68 \u00b1 0.17\nb\nb\nb\nb\nb\nb\nb\nb\nFigure 18.3.3. Measured mass of the X(3872). We show\nthe measurements which contribute to the average in Berin-\nger et al. (2012).\nLHCb) mass measurements for the X(3872) are statisti-\ncally limited, the precision of the comparison with D\u22170D0\nthreshold will only signi\ufb01cantly improve with better mea-\nsurements of the D0 mass, the D\u22170 mass (or mD\u22170 \u2212mD0\ndi\ufb00erence), or the use of some new techniques.\nWidth measurements in J/\u03c8 \ufb01nal states\nThe X(3872) was known to be relatively narrow from the\ndiscovery analysis, with a limit \u0393 < 2.3 MeV/c2 at 90%\nC.L. (Choi, 2003). The con\ufb01rmations by BABAR (Aubert,\n2005af), CDF (Acosta et al., 2004), and D\u00d8 (Abazov et al.,\n2004) each found a peak width consistent with the mea-\nsurement resolution, but did not present explicit width\nmeasurements; subsequent analyses by BABAR (Aubert,\n2006ax, 2008d) set upper limits on the width (4.1 MeV/c2\nand 3.3 MeV/c2 respectively). The CDF analysis that set\nlimits on the two-neutral-state hypothesis, and provides\nthe best single measurement of the mass, used an X(3872)\nintrinsic width of \u0393 = 1.34 MeV/c2 (Aaltonen et al., 2009c),\nbased on an average of the central values of the (not statis-\ntically signi\ufb01cant) width measurements from Belle (Choi,\n2003) and BABAR (Aubert, 2008d); no independent deter-\nmination of the width was performed.\nThe best current estimate of the width comes from\nthe recent Belle analysis (Choi, 2011), which \ufb01nds \u0393 <\n1.2 MeV/c2 at 90% C.L. based on a three-dimensional \ufb01t\nto mES, \u2206E, and M(\u03c0+\u03c0\u2212J/\u03c8). This is below the exper-\nimental resolution. Simulation studies show that natural\nwidths in this range can be recovered; Belle attributes this\nto constraints on the area of the peak in M(\u03c0+\u03c0\u2212J/\u03c8)\nprovided by the distributions in mES and \u2206E, which make\nthe peak height in M(\u03c0+\u03c0\u2212J/\u03c8) sensitive to the natural\nwidth. Improved precision will presumably be possible if\nthis technique is applied in the future.\n18.3.2.3 Production and decay\nThe X(3872) has been sought in a range of possible decays\nB \u2192KX, X \u2192f: these are listed, together with the\nmeasured product branching fractions (or upper limits)\nin Table 18.3.1. Plots from a number of important decay\nmodes have been shown above in Figs 18.3.1 and 18.3.2;\nresults in two modes where no signal is seen are shown in\nFig. 18.3.4\nThe most important unresolved case is X(3872) \u2192\n\u03b3\u03c8(2S), shown in Fig. 18.3.5, where BABAR (Aubert,\n2009m) \ufb01nds a signal with\nB(B+ \u2192K+X) \u00d7 B(X \u2192\u03b3\u03c8(2S))\n= (9.5 \u00b1 2.7 \u00b1 0.6) \u00d7 10\u22126,\n(18.3.6)\nwhile Belle (Bhardwaj, 2011) sees no signi\ufb01cant signal and\n\ufb01nds\n= (0.8+2.0\n\u22121.8 \u00b1 0.4) \u00d7 10\u22126.\n(18.3.7)\n\n474\n (GeV)\n)\nc1\nr\na\nM(\n3.78\n3.8\n3.82\n3.84\n3.86\n3.88\n3.9\n3.92\n3.94\n3.96\nEvents / ( 0.01 GeV )\n0\n2\n4\n6\n8\n10\n12\n \n(a) \u03b3\u03c7c1(1P) at Belle (Choi, 2003).\n0\n2\n4\n6\n3.75\n4\n4.25\n4.5\n4.75\nJ/sd Mass(GeV/c2)\nEvents/6.25 MeV/c2\nBABAR\n(b) \u03b7J/\u03c8 at BABAR (Aubert, 2004v).\nFigure\n18.3.4.\nInvariant\nmass\nplots\nfor\nrepresentative\nX(3872) searches where no signal is seen.\nThis is in contrast to the X(3872) \u2192\u03b3J/\u03c8 decay, where\nthe same two analyses both \ufb01nd a signal, with consistent\nproduct branching fractions\nB(B+ \u2192K+X) \u00d7 B(X \u2192\u03b3J/\u03c8)\n= (2.8 \u00b1 0.8 \u00b1 0.1) \u00d7 10\u22126 (BABAR),\n= (1.8+0.5\n\u22120.4 \u00b1 0.1) \u00d7 10\u22126 (Belle).\n(18.3.8)\nThe radiative decays are crucial for understanding the\nstructure of the X(3872): while the \u03b3J/\u03c8 decay is ex-\npected, the \u03b3\u03c8(2S) decay should be heavily suppressed for\na molecular state; by contrast, decays of the 2 3P1 char-\nmonium state (\u03c7\u2032\nc1) to \u03b3\u03c8(2S) should be enhanced over\nthose to \u03b3J/\u03c8 (Barnes and Godfrey, 2004; Suzuki, 2005;\nSwanson, 2004a, 2006). And unlike other disputed exotic\ncharmonium measurements, where the two experiments\ndisagree on the signi\ufb01cance of a signal but make statisti-\ncally compatible measurements of the rate, the measure-\nments in Eqs (18.3.6) and (18.3.7) are in apparent con-\ntradiction. During the \ufb01nal editing of this book, LHCb\nfound evidence for this decay (Aaij et al., 2014a), with\nB(X \u2192\u03b3\u03c8(2S))/B(X \u2192\u03b3J/\u03c8) = 2.46 \u00b1 0.64 \u00b1 0.29.\nCritical study of the radiative decay modes will therefore\nbe an urgent priority for a super \ufb02avor factory.\nMeasured product branching fractions can be trans-\nlated into absolute branching fractions of the X(3872)\nby exploiting the upper limit on B \u2192KX(3872) mea-\nsured by BABAR from the spectrum of the kaons recoiling\nagainst fully reconstructed B mesons (Aubert, 2006ae),\nB(B\u00b1 \u2192K\u00b1X(3872)) < 3.2 \u00d7 10\u22124 at 90% C.L.. Such\nan analysis has been performed by Drenska et al. (2010),\nwho combine likelihoods for the various product branch-\ning fractions (using results available up to mid-2010), the\nB \u2192KX(3872) upper limit, and the X width measure-\n)\n2\n (GeV/c\nX\nm\n3.8\n3.85\n3.9\n3.95\n)\n2\nEvents / (5 MeV/c\n-5\n0\n5\n10\n)\n2\n (GeV/c\nX\nm\n3.8\n3.85\n3.9\n3.95\n)\n2\nEvents / (5 MeV/c\n-5\n0\n5\n10\n \n(a) \u03b3J/\u03c8 at BABAR\n)\n2\n (GeV/c\nX\nm\n3.8\n3.85\n3.9\n3.95\n)\n2\nEvents / (5 MeV/c\n-5\n0\n5\n10\n15\n)\n2\n (GeV/c\nX\nm\n3.8\n3.85\n3.9\n3.95\n)\n2\nEvents / (5 MeV/c\n-5\n0\n5\n10\n15\n \n(b) \u03b3\u03c8(2S) at BABAR\n)\n2\n (GeV/c\na \ns\nJ/\nM\n3.75\n3.8\n3.85\n3.9\n3.95\n4\n)\n2\nEvents/ (9.5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n)\n2\n (GeV/c\na \ns\nJ/\nM\n3.75\n3.8\n3.85\n3.9\n3.95\n4\n)\n2\nEvents/ (9.5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n \n(c) \u03b3J/\u03c8 at Belle\n)\n2\n (GeV/c\na\n(2S) \ns\nM\n3.75\n3.8\n3.85\n3.9\n3.95\n4\n)\n2\nEvents/ (9.5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n35\n40\n)\n2\n (GeV/c\na\n(2S) \ns\nM\n3.75\n3.8\n3.85\n3.9\n3.95\n4\n)\n2\nEvents/ (9.5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n35\n40\n \n(d) \u03b3\u03c8(2S) at Belle\nFigure 18.3.5. Invariant mass plots for radiative decays of\nthe X(3872): (a,c) B+ \u2192K+X[\u2192\u03b3J/\u03c8] and (b,d) B+ \u2192\nK+X[\u2192\u03b3\u03c8(2S)], at (a,b) BABAR (Aubert, 2009m) and (c,d)\nBelle (Bhardwaj, 2011). See the discussion in the text. The\nBABAR analyses in (a,b) use the\nsPlot technique (Pivk and\nLe Diberder, 2005) to extract the number of signal events.\nThe curves in the Belle plots show: in (c,d) the \ufb01t to data\n(blue solid) and \ufb01tted yields for the signal (red dashed); in (c)\nthe background component (blue dotted); and in (d) the com-\nbinatorial background (black dotted), and background from\nB \u2192K\u2217\u03c8(2S) and B \u2192K\u03c8(2S) (pink dot-dashed).\nment in the D\u22170D0 channel of Aubert (2008bd) using a\nBayesian procedure. The resulting 68% con\ufb01dence inter-\nvals are summarized in Table 18.3.1 for each of the decay\nmodes. The same analysis \ufb01nds a B \u2192KX(3872) branch-\ning fraction in the range (0.1\u20130.2)\u00d710\u22123, to be compared\nto the corresponding branching fractions for conventional\ncharmonium states, which are at least 5 \u00d7 10\u22123 .\nAs far as other production mechanisms are concerned,\nB0 \u2192K+\u03c0\u2212X(3872) decays have also been studied.\nSuch decays are seen, but with a smooth distribution in\nK+\u03c0\u2212invariant mass; an upper limit is set on B(B0 \u2192\nK\u2217(892)0X(3872)) (Adachi, 2008c; see the results in Ta-\nble 18.3.1). This is in contrast to other charmonium states,\nwhere B \u2192K\u2217cc and Kcc branching fractions are com-\nparable, and K\u2217dominates over nonresonant K\u03c0.\n18.3.2.4 Summary\nIn summary, the X(3872) is the most studied of the exotic\nhidden-charm states, and the only one observed in several\n\n475\nTable 18.3.1. Measured X(3872) product branching fractions, separated by production and decay mechanism. The combined\nresults and \ufb01tted values are taken from Drenska et al. (2010); see the text. When more than one publication is present, the\ncombination is performed assuming Gaussian uncorrelated errors. The last two columns report the results in terms of absolute\nX(3872) branching fraction (Bfit) and in terms of the branching fraction normalized to J/\u03c8\u03c0\u03c0 (Rfit) as obtained from the\nglobal likelihood \ufb01t described in the text. Ranges and limits are provided at 68% and 90% C.L., respectively. Averages marked\nwith a dagger\u2020 include Belle results that have been superseded by subsequent publications: those from Adachi (2008c) by Choi\n(2011); those from Gokhroo (2006) by Aushev (2010); and those from Abe (2005a) by Bhardwaj (2011). The \u03b3\u03c8(2S) results in\nparticular are controversial: see the text. Concerning \u03c0\u03c0\u03c00 results (marked with a double dagger\u2021): the B Factories \ufb01nd that\nthe X(3872) \u2192\u03c0\u03c0\u03c00J/\u03c8 process is dominated by \u03c9J/\u03c8, but set no limits on the nonresonant \u03c0\u03c0\u03c00J/\u03c8 rate; the unpublished\nBelle result Abe (2005a) quotes only the ratio of \u03c0\u03c0\u03c00J/\u03c8 and \u03c0\u03c0J/\u03c8 branching fractions.\nB Decay mode\nX decay mode\nproduct branching fraction (\u00d7105)\nBfit\nRfit\nK\u00b1X\nX \u2192\u03c0\u03c0J/\u03c8\n0.82 \u00b1 0.09\u2020\n(Aubert, 2008d; Adachi, 2008c)\n[0.035, 0.075]\nN/A\n0.84 \u00b1 0.15 \u00b1 0.07\n(Aubert, 2008d)\n0.86 \u00b1 0.08 \u00b1 0.05\n(Choi, 2011)\nK0X\nX \u2192\u03c0\u03c0J/\u03c8\n0.53 \u00b1 0.13\u2020\n(Aubert, 2008d; Adachi, 2008c)\n0.35 \u00b1 0.19 \u00b1 0.04\n(Aubert, 2008d)\n0.43 \u00b1 0.12 \u00b1 0.04\n(Choi, 2011)\n(K+\u03c0+)NRX\nX \u2192\u03c0\u03c0J/\u03c8\n0.81 \u00b1 0.20+0.11\n\u22120.14\n(Adachi, 2008c)\nK\u22170X\nX \u2192\u03c0\u03c0J/\u03c8\n< 0.34, 90% C.L.\n(Adachi, 2008c)\nKX\nX \u2192\u03c0\u03c0\u03c00J/\u03c8\n{R = 1.0 \u00b1 0.4 \u00b1 0.3}\u2021\n(Abe, 2005a)\n[0.015, 0.075]\n[0.42, 1.38]\nK+X\nX \u2192\u03c9J/\u03c8\n0.6 \u00b1 0.2 \u00b1 0.1\u2021\n(del Amo Sanchez, 2010c)\nK0X\n0.6 \u00b1 0.3 \u00b1 0.1\u2021\n(del Amo Sanchez, 2010c)\nK\u00b1X\nX \u2192D\u22170D0\n13 \u00b1 3\u2020\n(Aubert, 2008bd; Gokhroo, 2006)\n[0.54, 0.8]\n[7.2, 16.2]\n16.7 \u00b1 3.6 \u00b1 4.7\n(Aubert, 2008bd)\n7.7 \u00b1 1.6 \u00b1 1.0\n(Aushev, 2010)\nK0X\nX \u2192D\u22170D0\n19 \u00b1 6\u2020\n(Aubert, 2008bd; Gokhroo, 2006)\n22 \u00b1 10 \u00b1 4\n(Aubert, 2008bd)\n9.7 \u00b1 4.6 \u00b1 1.3\n(Aushev, 2010)\nKX\nX \u2192\u03b3J/\u03c8\n0.22 \u00b1 0.05\u2020\n(Aubert, 2009m; Abe, 2005a)\n[0.0075, 0.0195]\n[0.19, 0.33]\nK+X\n0.28 \u00b1 0.08 \u00b1 0.01\n(Aubert, 2009m)\n0.18+0.05\n\u22120.04 \u00b1 0.01\n(Bhardwaj, 2011)\nK0X\n0.26 \u00b1 0.18 \u00b1 0.02\n(Aubert, 2009m)\n0.12+0.08\n\u22120.06 \u00b1 0.01\n(Bhardwaj, 2011)\nKX\nX \u2192\u03b3\u03c8(2S)\n1.0 \u00b1 0.3\u2020\n(Aubert, 2009m)\n[0.03, 0.09]\n[0.75, 1.55]\nK+X\n0.95 \u00b1 0.27 \u00b1 0.06\n(Aubert, 2009m)\n0.08+0.20\n\u22120.18 \u00b1 0.04\n(Bhardwaj, 2011)\nK0X\n1.14 \u00b1 0.55 \u00b1 0.10\n(Aubert, 2009m)\n0.11+0.36\n\u22120.29 \u00b1 0.06\n(Bhardwaj, 2011)\nK+X\nX \u2192\u03b3\u03c7c1\n< 0.19\n(Bhardwaj, 2013)\nK+X\nX \u2192\u03b3\u03c7c2\n< 0.67\n(Bhardwaj, 2013)\nKX\nX \u2192\u03b3\u03b3\n< 0.024\n(Abe, 2008a)\n< 0.0004\n< 0.0078\nKX\nX \u2192\u03b7J/\u03c8\n< 0.77\n(Aubert, 2004v)\n< 0.098\n< 1.9\ndecay modes; estimates of its width and absolute branch-\ning fractions are also available. Some of the early ques-\ntions about the state \u2014 such as its quantum numbers, and\nwhether charged or neutral partners exist \u2014 seem to have\nbeen resolved. However the structure of the X(3872) is still\nnot fully understood. Outstanding experimental questions\nare whether the disputed decay X(3872) \u2192\u03b3\u03c8(2S) takes\nplace (and if so at what rate), and whether the X(3872)\nlies above or below the D\u22170D0 threshold. For the latter,\nlarge and clean B+ \u2192K+\u03c00D0D0 and K+\u03b3D0D0 sam-\nples will be required; a super \ufb02avor factory provides some\nhope of performing these measurements.\n\n476\nTable 18.3.2. Measured JP C, masses, and widths of the \u201c3940 family\u201d of states. The \ufb01rst error is statistical, the second\nsystematic.\nState\nReference\nJP C\nMass (MeV)\nWidth (MeV)\nconventional\nassignment\nX(3940)\n(Pakhlov, 2008)\n0\u00b1+\n3942+7\n\u22126 \u00b1 6\n37+26\n\u221215 \u00b1 8\n\u03b7c(3S)\nY (3940)\n(Abe, 2005g)\n[0,1,2]\u00b1+\n3943 \u00b1 11 \u00b1 13\n87 \u00b1 22 \u00b1 26\n\u03c7c0(2P)?\nY (3940)\n(Aubert, 2008am)\n[0,1,2]\u00b1+\n3914.6+3.8\n\u22123.4 \u00b1 1.9\n33+12\n\u22128 \u00b1 5\n\u03c7c0(2P)?\nY (3915)\n(Uehara, 2010b)\n[0,1,2]\u00b1+\n3915 \u00b1 3 \u00b1 2\n17 \u00b1 10 \u00b1 3\n\u03c7c0(2P)?\nY (3915)\n(Lees, 2012ad)\n0++\n3919 \u00b1 2 \u00b1 2\n13 \u00b1 6 \u00b1 3\n\u03c7c0(2P)?\nZ(3930)\n(Uehara, 2006)\n2++\n3929 \u00b1 5 \u00b1 2\n29 \u00b1 10 \u00b1 2\n\u03c7c2(2P)\nZ(3930)\n(Aubert, 2010g)\n2++\n3926 \u00b1 2.7 \u00b1 1.1\n21.3 \u00b1 6.8 \u00b1 3.6\n\u03c7c2(2P)\n18.3.3 The 3940 family\nA number of resonances have been reported by the Belle\nCollaboration with masses near 3940 MeV/c2: the X(3940),\nY (3940), Z(3930), and Y (3915). These states have some\npossible, albeit not certain, interpretations as regular char-\nmonium states and are discussed in Section 18.2. We con-\ncentrate here on aspects related to possible exotic assign-\nments. The measured masses and widths of these states\nare summarized in Table 18.3.2 and Fig. 18.3.6.\n3900\n3910\n3920\n3930\n3940\n3950\n3960\n3970\n0\n160\n0\n20\n40\n60\n80\n100\n120\n140\n160\n\u0393 ( MeV/c2)\nM ( MeV/c2)\nY (3915)\nY (3940) BABAR\nZ(3930)\nX(3940)\nY (3940)\nBelle\nFigure 18.3.6. Measured masses and widths of the \u201c3940 fam-\nily\u201d of states; the boxes represent \u00b11\u03c3 ranges of the measure-\nments.\n18.3.3.1 The X(3940)\nThe X(3940) state was observed in association with a\nJ/\u03c8 meson in double-charmonium production events (i.e.\nnot in \u03a5(4S) decays) (Abe, 2007f; Pakhlov, 2008). Sub-\nsequently, by applying a partial reconstruction technique\nto the same production channel, Belle measured the ab-\nsolute production rate and established that X(3940) \u2192\nD\u2217D is a prominent decay mode; searches were made for\nX(3940) \u2192DD and J/\u03c8\u03c9 without evidence for any sig-\nnals. The lower and upper limits on the branching frac-\ntions for these modes set in Abe (2007f) were withdrawn\nby Belle in Pakhlov (2008), as the inclusive peak in the ear-\nlier analysis, used to provide the denominator of the frac-\ntion, may have contributions from more than one state.\nSince the X(3940) is a candidate for a conventional char-\nmonium state, it is also discussed in Section 18.2.1.3.\nThe production mechanism constrains it to have positive\ncharge conjugation since this is an electromagnetic pro-\ncess and the initial state virtual photon and the accom-\npanying J/\u03c8 have the same C. Furthermore, all of the\nknown states that are observed via this production mech-\nanism have J = 0. Although the reason for this is not\nunderstood, it is plausible that this state also has J = 0.\nThus, the most likely quantum numbers of the X(3940)\nare JP C = 0++ or 0\u2212+; the apparent absence of the DD\ndecay channel favors 0\u2212+.\n18.3.3.2 The Y (3940) and Y (3915)\nA second state, named Y (3940), was observed as a near-\nthreshold peak in the J/\u03c8\u03c9 invariant mass spectrum in\nB \u2192J/\u03c8\u03c9K decays (Abe, 2005g). The Y (3940) state is\nnot seen in B \u2192D\u2217DK decays and a lower limit has\nbeen set on the ratio B(Y (3940) \u2192J/\u03c8\u03c9)/B(Y (3940) \u2192\nD\u2217D) > 0.71 at 90% C.L. (Aushev, 2010); as the X(3940)\n(discussed above) is seen in D\u2217D but not in J/\u03c8\u03c9, this\nstrongly suggests that these two states are not the same.\nThe Y (3940) must have positive charge conjugation, while\nJ\n= 0, 1, 2 with either sign parity are possible. The\nBABAR Collaboration con\ufb01rmed the Y (3940) \u2192J/\u03c8\u03c9\nobservation in B \u2192J/\u03c8\u03c9K decays (Aubert, 2008am),\nbut measure a lower mass and narrower width, which are\nonly marginally consistent with the Belle results (see Ta-\nble 18.3.2); there are various di\ufb00erences between the two\nanalyses, e.g. in the assumptions made about the shape\nof the background. A Belle study of the \u03b3\u03b3 \u2192J/\u03c8\u03c9\nreaction (Uehara, 2010b) observed a state, named the\n\n477\nW (GeV)\nEvents/10 MeV\nFigure 18.3.7. The J/\u03c8\u03c9 distribution in \u03b3\u03b3 events as mea-\nsured by Belle (Uehara, 2010b). The black curve is the result\nof a \ufb01t to the data to determine the Y (3915) mass and width.\nThe dot-dashed curve (brown) represents the result of the \ufb01t\nwithout the resonant contribution.\nY (3915), with mass and width values consistent with those\nfor the Y (3940) measured by BABAR (see Fig. 18.3.7).\nThis observation was con\ufb01rmed by a BABAR analysis of\n\u03b3\u03b3 \u2192J/\u03c8\u03c9 events in which a peak with similar mass and\nwidth is seen and an angular correlation study favors a\nJP C = 0++ assignment (Lees, 2012ad).\nA likely hypothesis is that the Y (3940) and Y (3915)\nstates coincide, in which case this is the only candidate for\nan exotic state other than the X(3872) to be seen in two\ndi\ufb00erent production mechanisms. The weighted averages\nof the mass and width measurements listed for Y (3940)\nand Y (3915) in Table 18.3.2 are MY (3915) = (3918.4 \u00b1\n1.9) MeV/c2 and \u0393Y (3915) = (20 \u00b1 5) MeV/c2. A BABAR\nsearch for \u03b3\u03b3 \u2192Y (3915) \u2192\u03b7c\u03c0+\u03c0\u2212with \u03b7c \u2192K0\nSK\u00b1\u03c0\u2213\nfound no signal events and established an upper limit of\n\u0393\u03b3\u03b3(Y (3915)) \u00d7 B(Y (3915) \u2192\u03b7c\u03c0+\u03c0\u2212) < 91 eV (Lees,\n2012t).\n18.3.3.3 The Z(3930)\nAnother state, named Z(3930), was seen by Belle in \u03b3\u03b3\nfusion into DD (Uehara, 2006). This state has been con-\n\ufb01rmed by the BABAR Collaboration (Aubert, 2010g), which\nhas also performed an angular analysis of the decay prod-\nucts that favors a JP C = 2++ assignment. This state\nis generally accepted as the \u03c7\u2032\nc2, the 2 3P2 charmonium\nstate. Details of the relevant analyses can be found in Sec-\ntion 18.2.1.2.\n18.3.3.4 Charmonium assignments for the X(3940),\nY (3915) and Z(3930)?\nThe X(3940)\u2019s prominent decay to D\u2217D taken together\nwith the lack of any evidence for DD is strongly sug-\ngestive of JP C = 0\u2212+ quantum numbers, which implies\nthat the most likely charmonium assignment is the 3 1S0,\ncommonly known as the \u03b7c(3S). This assignment is some-\nwhat problematic because the hyper\ufb01ne partner state, the\n3 3S1, or \u03c8(4040), has already been established with a mea-\nsured mass of (4040 \u00b1 4) MeV/c2 (Ablikim et al., 2007);\nthis would imply an n = 3 hyper\ufb01ne splitting of (98 \u00b1\n8) MeV/c2, almost twice as large as the n = 2 splitting of\n(47 \u00b1 1) MeV/c2.\nThe BABAR study of the Y (3915) state favors a 0++\nquantum number assignment, for which the closest char-\nmonium level is the 2 3P0 state, the so-called \u03c7\u2032\nc0. In this\ncase, its 2 3P2 multiplet partner is likely the Z(3930) with\na measured mass of (3927\u00b13) MeV/c2, implying an anoma-\nlously small 3P2-3P0 \ufb01ne splitting of only \u224310 MeV/c2 for\nthe n = 2 triplet P-wave multiplet (an order of magnitude\nsmaller than the corresponding n = 1 splitting). More-\nover, the \u03c7\u2032\nc0 is expected to have a partial decay width to\nDD of order 30 MeV/c2 (Barnes et al., 2005), which, by it-\nself, is substantially wider than the measured total width\nof the Y (3915). Even though no experimental limits on\nB(Y (3915) \u2192DD) have been reported to date, no signs\nof a signal for Y (3915) \u2192DD are evident in the measured\nDD invariant mass distributions for B \u2192DDK decays\npublished by BABAR (Aubert, 2008bd) or Belle (Brodz-\nicka, 2008), even though both studies see prominent sig-\nnals for B \u2192\u03c8(3770)K, \u03c8(3770) \u2192DD.\nThe Z(3930) has measured properties that match well\nto the expectations for the 2 3P2 charmonium state and\nhas no need for an exotic interpretation.\n18.3.4 Other C = +1 states\nWe review now the remaining C = +1 resonances. The\n\ufb01rst is called X(4160), and was discovered by Belle in\ndouble charmonium events. It is produced in association\nwith a J/\u03c8 meson and decays into D\u2217+D\u2217\u2212(Pakhlov,\n2008; see top panel of Fig. 18.3.8). The \ufb01tted mass and\nwidth are M = (4156+25\n\u221220\u00b115) MeV/c2 and \u0393 = (139+111\n\u221261 \u00b1\n21) MeV/c2. The charge conjugation C = +1 is constrained\nby the production mechanism, which favors also J = 0.\nHence, this state is a good candidate for a radial excita-\ntion of the pseudoscalar charmonium, a \u03b7c(nS) state. The\nidenti\ufb01cation is discussed in Section 18.2.1.3.\nThe CDF experiment announced a resonance close to\nthreshold in J/\u03c8\u03c6 invariant mass, in the channel B \u2192\nJ/\u03c8\u03c6K (Aaltonen et al., 2009a). This state is called\nY (4140), and has mass and width M = (4143.0 \u00b1 2.9 \u00b1\n1.2) MeV/c2 and \u0393 = (11.7+8.3\n\u22125.0 \u00b13.7) MeV/c2. The natural\nquantum number would be JP C = 0++, but the exotic as-\nsignment JP C = 1\u2212+ is not excluded. If the latter hypoth-\nesis were con\ufb01rmed, this could be the hybrid ground state.\nThe measured mass is indeed close to lattice calculations\nfor the lightest hybrid meson (for instance, see Bernard\net al., 1997). The search for states in this production mech-\nanism at the B Factories su\ufb00ers from poor acceptance, and\nthus does not have su\ufb03cient statistical power to be con-\nclusive. Some models (Branz, Gutsche, and Lyubovitskij,\n2009) predict a copious production of such state in \u03b3\u03b3\nfusion. Belle searched in this channel, but found no evi-\ndence for a Y (4140). A limit \u0393\u03b3\u03b3\u00d7B(\u03c6J/\u03c8) < 41 (6) eV for\nJP = 0+ (2+) was set at 90% C.L. for the Y (4140) (Shen,\n2010a).\n\n478\n \n \n \n M(D(*) D(*)\n--\n) GeV/c2\nN/50 MeV/c2\n \n0\n5\n4\n4.5\n5\n(a) X(4160) \u2192D\u2217+D\u2217\u2212from Belle (Pakhlov, 2008)\n0\n2\n4\n6\n8\n4.2\n4.4\n4.6\n4.8\n5\nM(qJ/s) (GeV/c2)\nEntries/25 MeV/c2\n(b) X(4350) \u2192J/\u03c8\u03c6 from Belle (Shen, 2010a).\nFigure 18.3.8. Invariant mass distributions of the most sig-\nni\ufb01cant observations of states with C = +1 and mass above 4\nGeV.\nDuring the search for \u03b3\u03b3 \u2192X \u2192J/\u03c8\u03c6, Belle found\ninstead a 3.2\u03c3 peak with M = (4350.6+4.6\n\u22125.1 \u00b1 0.7) MeV/c2\nand \u0393 = (13+18\n\u22129 \u00b14) MeV/c2 (see Fig. 18.3.8, bottom plot).\nThis is possibly another state called X(4350), with C =\n+1 and close in mass to one of the vector states we will\ndiscuss in Section 18.3.5.\n18.3.5 The 1\u2212\u2212family\nThe most unambiguous way to assign JP C quantum num-\nbers a particle is when it is produced in e+e\u2212annihilation,\nso that its quantum numbers must be the same as the\nphoton ones: JP C = 1\u2212\u2212. The B Factories can investi-\ngate a large range of masses for such particles by looking\nfor events where the emission of an energetic photon by\nthe initial state reduces the e+e\u2212center-of-mass energy\ndown to the particle\u2019s mass (so-called \u201cISR\u201d events). Such\nanalyses are discussed in more detail in Chapter 21. Alter-\nnatively, dedicated e+e\u2212machines, like CESR and BEPC\nscan directly the center-of-mass energies of interest.\nThe \ufb01rst new state to be observed via these pro-\ncesses was the Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212resonance seen\nby BABAR (Aubert, 2005y) and promptly con\ufb01rmed by\nCLEO both in ISR events (He et al., 2006) and in direct\nproduction (Coan et al., 2006). The latter paper also re-\nported evidence for Y (4260) \u2192J/\u03c8\u03c00\u03c00 and some events\nof Y (4260) \u2192J/\u03c8K+K\u2212.\nA BABAR search for the Y (4260) in the \u03c8(2S)\u03c0+\u03c0\u2212de-\ncay channel found no evidence of a signal (Aubert, 2007m),\nbut, instead, saw a peak at a di\ufb00erent mass, the Y (4350).\nWhile the absence of Y (4260) \u2192\u03c8(2S)\u03c0+\u03c0\u2212decays might\nbe understood if the pion pair in the J/\u03c8\u03c0+\u03c0\u2212decay were\nconcentrated in an intermediate state (such as f0(980) \u2192\n\u03c0\u03c0) that is too massive to be produced with a \u03c8(2S),\nthe absence of any sign of the Y (4350) \u2192J/\u03c8\u03c0+\u03c0\u2212is\nnot so easily understood. Cotugno, Faccini, Polosa, and\nSabelli (2010) have shown this absence to be signi\ufb01cant:\nB(Y (4350) \u2192J/\u03c8\u03c0+\u03c0\u2212)/B(Y (4350) \u2192\u03c8(2S)\u03c0+\u03c0\u2212) <\n3.4 \u00d7 10\u22123 at the 90% C.L..\nBelle subsequently con\ufb01rmed both of these 1\u2212\u2212\nstates (Wang, 2007c; Yuan, 2007), and observed another\nstate in the \u03c8(2S)\u03c0+\u03c0\u2212channel that was not visible\nin BABAR data due to the size of the data sample: the\nY (4660). Figure 18.3.9 shows Belle\u2019s published invariant\nmass spectra for both the J/\u03c8\u03c0+\u03c0\u2212and the \u03c8(2S)\u03c0+\u03c0\u2212\nchannels.\nAn important question is whether or not the pion pair\ncomes from one or more resonant states. Figure 18.3.10\nshows the di-pion invariant mass spectra from Belle for\nevents in the J/\u03c8\u03c0+\u03c0\u2212and \u03c8(2S)\u03c0+\u03c0\u2212invariant mass\npeaks that correspond to each of the three resonances.\nAlthough a subtraction of the continuum background has\nnot been performed, there is some indication that only\nthe Y (4660) has a well de\ufb01ned intermediate state (most\nlikely the f0(980)); the other two peaks have a more com-\nplex structure. In addition, the BABAR analysis of the\nJ/\u03c8\u03c0+\u03c0\u2212channel (Lees, 2012ab) \ufb01nds some evidence\nof a J/\u03c8f0(980) component. The observation of decays\ninvolving an f0 is particularly interesting because the\nscalar mesons have long been considered tetraquark can-\ndidates (Ja\ufb00e, 1977a).\nThe relative decay rate of these new states into lower-\nmass charmonium states and into two charm mesons can\nbe used to distinguish between identi\ufb01cations as regular\ncharmonium states and other possibilities. Searches for\nY \u2192D(\u2217)D(\u2217) decay channels carried out by Belle (Abe,\n2007d; Pakhlova, 2008a) and BABAR (Aubert, 2007u) found\nno evidence for a signal; 90% C.L. limits from BABAR are:\nB(Y (4260) \u2192DD)/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 1.0,\nB(Y (4260) \u2192D\u2217D)/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 34,\nB(Y (4260) \u2192D\u2217D\u2217)/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 40.\n(18.3.9)\nBABAR also set 90% C.L. limits for the Y \u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\ndecay channels (del Amo Sanchez, 2010d):\nB(Y (4260) \u2192D+\ns D\u2212\ns )/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 0.7,\nB(Y (4260) \u2192D\u2212\ns D\u2217\u2212\ns )/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 44,\nB(Y (4260) \u2192D\u2217+\ns D\u2217\u2212\ns )/B(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) < 30.\n(18.3.10)\nAnalogously, Belle studied Y \u2192D0D\u2217\u2212\u03c0+ decays in\nISR events as described in Section 21.4.5. The signi\ufb01cances\nfor the Y (4260), Y (4350), Y (4660), and X(4630) signals\nare 0.9\u03c3, 1.4\u03c3, 0.1\u03c3, and 1.8\u03c3, respectively, and the cor-\nresponding upper limits on the peak cross sections for\n\n479\n0\n20\n40\n60\n80\n4\n4.5\n5\n5.5\nM(!+!-J/\") (GeV/c2)\nEntries/20 MeV/c2\nSolution I\nSolution II\n0\n5\n10\n15\n4\n4.5\n5\n5.5\nM(!+!-\"(2S)) (GeV/c2)\nEntries/25 MeV/c2\nFigure 18.3.9. Distributions of J/\u03c8\u03c0+\u03c0\u2212(left; Yuan, 2007) and \u03c8(2S)\u03c0+\u03c0\u2212(right; Wang, 2007c) invariant masses in ISR\nproduction. The data points (left) and open histogram (right) show the data while the green histograms show the normalized\nsidebands of the charmonium candidates. The curves show the best \ufb01t with two coherent resonances together with a background\nterm; the dashed curve shows the contribution from each component. The interference between the two resonances is not shown.\nIn both cases the likelihood \ufb01ts to the spectra return two solutions of equally good quality as indicated by the two dashed\ncurves.\n0\n10\n20\n30\n40\n0.5\n1\nM(/+/-) (GeV/c2)\n \n0\n2\n4\n6\n0.4\n0.6\n0.8\nM(/+/-) (GeV/c2)\nEntries/20 MeV/c2\n \n0\n2\n4\n6\n8\n10\n12\n0.4 0.6 0.8\n1\nM(/+/-) (GeV/c2)\nEntries/20 MeV/c2\n \nFigure 18.3.10. The di-pion invariant mass distribution in Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212(left; Yuan, 2007), Y (4350) \u2192\u03c8(2S)\u03c0+\u03c0\u2212\n(center; Wang, 2007c), and Y (4660) \u2192\u03c8(2S)\u03c0+\u03c0\u2212decays (right; Wang, 2007c). Points are pure signal events, histograms are\nMC simulations of phase space distributions.\ne+e\u2212\u2192X(Y ) \u2192DD\u2217\u2212\u03c0+ processes are presented in\nTable 18.3.3. The upper limits presented in the Table are\nat the 90% C.L. and include systematic uncertainties.\nA distinctive signature of tetraquarks would be the\nobservation of 1\u2212\u2212states decaying into two baryons since\nit is easier to form two baryons starting from four con-\nstituent quarks than from two (see Cotugno, Faccini,\nPolosa, and Sabelli, 2010 for details). This motivated a\nBelle search for the ISR production of resonant structures\ndecaying into \u039bc\u039bc (Pakhlova, 2008b). A structure is seen\nnear threshold (see Fig. 18.3.11) that, when \ufb01tted with\na Breit-Wigner line shape, has M = (4634+8+5\n\u22127\u22128) MeV/c2\nand \u0393tot = (92+40+10\n\u221224\u221212) MeV/c2, values that are close to\nthose of the Y (4660). An analysis performed by using the\nsame model for the line-shape of the two measured spec-\ntra concluded that the two structures are consistent with\nthe hypothesis that they are the same state with a strong\npreference for the baryonic decay mode: B(Y (4660) \u2192\n\u039bc\u039bc)/B(Y (4660) \u2192\u03c8(2S)\u03c0\u03c0) = 25 \u00b1 7 (Cotugno, Fac-\ncini, Polosa, and Sabelli, 2010).\n18.3.5.1 Charmonium assignments for the Y (4260),\nY (4350) and Y (4660)?\nThe reasons that at least some of the Y (4260), Y (4350),\nand Y (4660) are considered as exotic candidates are\nthe lack of unassigned 1\u2212\u2212charmonium levels below\n4500 MeV/c2, and the large apparent partial widths of\nthese states in \u03c0+\u03c0\u2212transitions to the J/\u03c8 or \u03c8(2S).\nA comparison of the measured cross section for e+e\u2212\u2192\nY (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212with limits on resonance produc-\ntion in the hadron cross section at the same mass leads\nto the 90% C.L. lower limit \u0393(Y (4260) \u2192J/\u03c8\u03c0+\u03c0\u2212) > 1\nMeV/c2 (Mo et al., 2006). This is much larger than the\ntypical for 1\u2212\u2212charmonium states: for instance, the cor-\nresponding partial width for the \u03c8(3770) is 52 \u00b1 8 keV/c2.\n\n480\nTable 18.3.3. Upper limits on the peak cross section for the processes e+e\u2212\u2192Y \u2192D0D\u2217\u2212\u03c0+, Bee \u00d7 B(Y \u2192D0D\u2217\u2212\u03c0+)\nand B(Y \u2192D0D\u2217\u2212\u03c0+)/B(Y \u2192\u03c0+\u03c0\u2212J/\u03c8(\u03c8(2S))) at the 90% C.L., where Y = Y (4260), Y (4350), Y (4660), X(4630). From\nPakhlova (2009); this analysis is also brie\ufb02y discussed in Section 21.4.5 (especially Fig. 21.4.9) and Section 18.2.2.2.\nY (4260)\nY (4350)\nY (4660)\nX(4630)\n\u03c3(e+e\u2212\u2192Y ) \u00d7 B(Y \u2192D0D\u2217\u2212\u03c0+))\n[nb]\n0.36\n0.55\n0.25\n0.45\nBee \u00d7 B(Y \u2192D0D\u2217\u2212\u03c0+))\n[\u00d710\u22126]\n0.42\n0.72\n0.37\n0.66\nB(Y \u2192D0D\u2217\u2212\u03c0+)/B(Y \u2192\u03c0+\u03c0\u2212J/\u03c8)\n9\nB(Y \u2192D0D\u2217\u2212\u03c0+)/B(Y \u2192\u03c0+\u03c0\u2212\u03c8(2S))\n8\n10\n0\n10\n20\n30\n40\nN/20 MeV/c2\n(a)\n(b)\nGeV/c2\nM(R+\nc R\u2013\nc)\n0\n5\n10\n4.5\n4.6\n4.7\n4.8\n4.9\n5\n5.1\n5.2\n5.3\n5.4\nFigure 18.3.11. \u039bc\u039bc invariant mass distribution in ISR\nevents from Belle (Pakhlova, 2008b): (a) using partial recon-\nstruction plus proton tags, and (b) background events with\nwrong-sign proton tags. The histograms in each case show nor-\nmalized contributions from \u039bc sidebands. The superimposed\ncurve is the result of the \ufb01t reported in the text.\n18.3.6 Charged charmonium-like States\nA signi\ufb01cant turning point in the quest for states beyond\nthe standard charmonium model would be the observation\nof charged states decaying into charmonium plus accom-\npanying charged hadrons. There is no way to explain such\nan observation without at least four bound quarks (e.g.\nc\u00afcd\u00afu). There is evidence for three such charged states,\nseen by Belle but not by BABAR: the Z(4430)+ state de-\ncaying into \u03c8(2S)\u03c0+ (Choi, 2008; see Section 18.3.6.1),\nand the Z1(4050)+ and Z2(4250)+ states decaying into\n\u03c7c1\u03c0+ (Mizuk, 2008; see Section 18.3.6.2).\nThese states have been observed in B decays in as-\nsociation with a charged kaon, i.e. in three-body B \u2192\nXcc \u03c0K decays, where Xcc = \u03c8(2S) or \u03c7c1. Three-body\ndecays su\ufb00er from interference terms between strong am-\nplitudes mediated by di\ufb00erent resonances. In these partic-\nular cases the K\u03c0 system has several known resonances\nthat could cause signi\ufb01cant re\ufb02ection e\ufb00ects. Namely, the\ndecays B \u2192XccK\u2217(892), B \u2192XccK\u2217(1410), and, in\nparticular, their mutual interference constitute irreducible\nsources of background which are di\ufb03cult to estimate.\nFurther developments on charged states (as this book\nwas being \ufb01nalised), and some possible future studies, are\nbrie\ufb02y discussed in Section 18.3.6.3\n18.3.6.1 Z(4430+) \u2192\u03c8(2S)\u03c0+\nIn the original Belle paper on the observation of the\nZ(4430)+ \u2192\u03c8(2S)\u03c0+ resonance in B \u2192\u03c8(2S)\u03c0+K\ndecays (Choi, 2008), they report the distinct peak\nin the M(\u03c8(2S)\u03c0+) invariant mass distribution near\n4430 MeV/c2\nthat\nis\nshown\nin\nthe\nupper\npanel\nof\nFig. 18.3.12. Belle argued that this peak could not be\ndue to interference e\ufb00ects in the K\u03c0 channel because in\nB \u2192\u03c8(2S)\u03c0+K decays, events with M(\u03c8(2S)\u03c0+) near\n4430 MeV/c2 correspond to K\u03c0 systems with a decay an-\ngle \u03b8K\u03c0 in the region cos \u03b8K\u03c0 \u22430.25, an angular region\nwhere interfering S-, P- and D-waves cannot create a peak\nwithout other, much larger structures elsewhere.\nThe Belle analysis was the subject of scrutiny by the\nBABAR Collaboration, which investigated the same \ufb01nal\nstate by studying in detail the e\ufb03ciency corrections and\nthe shape of the background, relying for the latter on the\ndata as much as possible (Aubert, 2009at). The search\nresulted in hints of a structure close to Belle\u2019s reported\npeak, but after estimates of the background they reported\nan 95% C.L. upper limit on the product branching frac-\ntion:\nB(B \u2192Z+K\u2212) \u00d7 B(Z+ \u2192\u03c8(2S)\u03c0+) < 3.1 \u00d7 10\u22125,\n(18.3.11)\nto be compared with Belle\u2019s non-zero value (Choi, 2008)\nB(B \u2192Z+K\u2212) \u00d7 B(Z+ \u2192\u03c8(2S)\u03c0+) = (4.1+1.0\n\u22121.4) \u00d7 10\u22125.\n(18.3.12)\nSubsequent to the BABAR analysis, Belle made a de-\ntailed Dalitz-plot analyses of B \u2192\u03c8(2S)\u03c0+K events that\nincluded interfering amplitudes for all known resonances\nin the K\u03c0 channel, both with and without a coherent am-\nplitude for a resonance in the \u03c8(2S)\u03c0+ channel (Mizuk,\n2009). The results of this Belle analysis con\ufb01rm those from\nthe original report of a signi\ufb01cant resonant structure in\n\n481\n3.8\n4.05\n4.3\n4.55\n4.8\nM(/+sf) (GeV)\n0\n10\n20\n30\nEvents/0.01 GeV\nM (rc1/+), GeV/c2\nEvents / 0.024 GeV/c2\n0\n5\n10\n15\n20\n25\n30\n35\n40\n3.6\n3.8\n4\n4.2\n4.4\n4.6\n4.8\nFigure 18.3.12. Invariant mass distributions from (top)\n\u03c8(2S)\u03c0\u00b1 (Choi, 2008), and (bottom) \u03c7c1\u03c0\u00b1 (Mizuk, 2008), su-\nperimposed with \ufb01t result showing the charged resonances. In\nboth \ufb01gures, events with M(K\u03c0) in the region of the K\u2217(890)\nand K\u2217(1410) peaks are removed. The solid red histogram in\nthe lower \ufb01gure shows the results of the \ufb01t that includes coher-\nent Z1 and Z2 amplitudes; the dashed blue curve is the result\nof the \ufb01t using K\u03c0 amplitudes only.\nthe \u03c8(2S)\u03c0+ channel near 4430 MeV/c2. Although both\nstatistical and systematic uncertainties on the Z(4430)+\nresonance parameters increased, the signi\ufb01cance of the ob-\nserved resonance signal remained the same; for the default\nDalitz distribution model it was found to be 6.4\u03c3; the \ufb01t-\nted mass and width of the Z(4430)+ \u2192\u03c8(2S)\u03c0+ from the\nDalitz analysis are MZ(4430)+ = (4443+15\n\u221212\n+19\n\u221213) MeV/c2 and\n\u0393Z(4430)+ = (109+86\n\u221243\n+74\n\u221256) MeV/c2.\nWhile we were preparing this book, LHCb performed\na four-dimensional \ufb01t of the decay amplitude (Aaij et al.,\n2014b). The Z(4430)+ is con\ufb01rmed with a signi\ufb01cance of\n13.9 \u03c3 at least; the \ufb01tted mass and width are MZ(4430)+ =\n(4475\u00b17+15\n\u221225) MeV/c2 and \u0393Z(4430)+ = (172\u00b113+37\n\u221234) MeV/c2,\nconsistent with Belle measurements. Moreover, an analy-\nsis of the Argand diagram con\ufb01rms the resonant character\nof the Z(4430)+.\n18.3.6.2 States decaying to \u03c7c1\u03c0+\nIn a Dalitz-plot analysis of three-body B \u2192\u03c7c1\u03c0+K de-\ncays, Belle was unable to get an acceptable \ufb01t using only\nresonances in the K\u03c0 channel (Mizuk, 2008). The inclu-\nsion of a single \u03c7c1\u03c0+ resonance improved the \ufb01t sub-\nstantially, but still did not reproduce the observed fea-\ntures very accurately. Belle \ufb01nally settled on a \ufb01t that in-\ncluded two resonances in the \u03c7c1\u03c0 channel: the Z1(4050)+\nand Z2(4250)+. The \u03c7c1\u03c0+ invariant-mass distribution for\nevents in the Dalitz-plot region between the K\u2217(980) and\nK\u2217(1410) bands is shown as data points with the pro-\njected \ufb01nal \ufb01t shown as a red histogram in the lower\npanel of Fig. 18.3.12. The \ufb01tted masses and widths of the\ntwo \u03c7c1\u03c0+ resonances are MZ+\n1 = (4051 \u00b1 14+20\n\u221241) MeV/c2,\nMZ+\n2 = (4248+44+180\n\u221229\u221235 ) MeV/c2, \u0393Z+\n1 = (82+21+47\n\u221217\u221222) MeV/c2\nand \u0393Z+\n2 = (177+54+316\n\u221239\u221261 ) MeV/c2, respectively.\nBABAR investigated B \u2192\u03c7c1\u03c0+K decays using an\nanalysis that carefully studied the e\ufb00ects of interference\nbetween resonances in the K\u03c0 system (Lees, 2012w). They\nreport adequate \ufb01ts to the data using interfering reso-\nnances only in the K\u03c0 channel. They set 95% C.L. upper\nlimits on the product branching fractions to the Z+\n1 and\nZ+\n2\nstates by studying the e\ufb00ects of adding incoherent\nresonant amplitudes for these two states to their \ufb01tting\nmodel:\nB(B \u2192Z+\n1 K\u2212) \u00d7 B(Z+\n1 \u2192\u03c7c1\u03c0+) < 1.8 \u00d7 10\u22125,\nB(B \u2192Z+\n2 K\u2212) \u00d7 B(Z+\n2 \u2192\u03c7c1\u03c0+) < 4.0 \u00d7 10\u22125.\n(18.3.13)\nFor comparison, the non-zero values from Belle for the\nsame quantities are\nB(B \u2192Z+\n1 K\u2212) \u00d7 B(Z+\n1 \u2192\u03c7c1\u03c0+) = (3.0+1.2+3.7\n\u22120.8\u22121.6) \u00d7 10\u22125,\nB(B \u2192Z+\n2 K\u2212) \u00d7 B(Z+\n2 \u2192\u03c7c1\u03c0+) = (4.0+2.3+19.7\n\u22120.9\u22120.5 ) \u00d7 10\u22125.\n(18.3.14)\nPart of the discrepancy between the two experiments may\nbe due to the fact that in the Belle analysis, the Z+\n1 , Z+\n2\nand K\u03c0 amplitudes are all coherent and mutually inter-\nfere, while in the BABAR analysis the Z+\n1 and Z+\n2 terms are\nadded incoherently and do not interfere with the K\u03c0 am-\nplitudes. In the Belle results shown in Fig. 18.3.12 (lower),\nsigni\ufb01cant constructive and destructive interference be-\ntween the Z+\n1 and Z+\n2 amplitudes with the K\u03c0 terms is\nevident (see the dips and peaks of the solid red curve, rel-\native to the dashed blue curve showing the K\u03c0 amplitude\n\ufb01t result).\n\n482\n18.3.6.3 Other candidates for charged charmonium-like\nstates\nBoth Belle (Liu, 2013) and BESIII (Ablikim et al., 2013a)\nhave claimed the observation of another charged reso-\nnance, Z(3900)+, as a peak in the J/\u03c8\u03c0+ invariant mass\ndistribution in Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8 decay; the Belle\npeak has Breit-Wigner parameters M = (3894.5 \u00b1 6.6 \u00b1\n4.5) MeV/c2 and \u0393 = (63 \u00b1 24 \u00b1 26) MeV/c2. A structure\nwith similar parameters has also been seen by BESIII in\ne+e\u2212\u2192(DD\u2217)+\u03c0\u2212(Ablikim et al., 2014b). As this book\nwas being \ufb01nalised, BESIII also presented evidence for a\nstructure Z(4020)+ in the hc\u03c0+ invariant mass distribu-\ntion in e+e\u2212\u2192\u03c0+\u03c0\u2212hc (Ablikim et al., 2013b), with\nparameters similar to those of a structure Z(4025)+ seen\nin e+e\u2212\u2192(D\u2217D\u2217)\u00b1\u03c0\u2213(Ablikim et al., 2014a). Note\nthat charged states Zb(10610)+ and Zb(10650)+ \u2192hb\u03c0+\nhave been seen by Belle in \u03a5(5S) \u2192hb\u03c0+\u03c0\u2212(see Sec-\ntion 18.4.5).\n0\n5\n10\n15\n20\n25\n4\n4.25\n4.5\n4.75\n m(D*-D*0) (GeV/c2)\nEntries/20 MeV/c2\nFigure 18.3.13. The D\u22170D\u2217\u2212invariant mass spectrum from\nB \u2192D\u22170D\u2217\u2212K decays from BABAR (Aubert, 2003f). The\nhatched histograms show the contribution expected from the\ncombinatorial background. The open histograms show the con-\ntribution expected for the three-body decay generated with a\nphase-space model.\nA further step in the study of the currently-claimed\ncharged states would be to search for these, or other sim-\nilar states, in D(\u2217)D(\u2217) systems produced in three-body\nB \u2192D(\u2217)D(\u2217)K decays. For these the experimental e\ufb03-\nciencies are lower and detailed three-body amplitude anal-\nyses are of limited use with the currently available BABAR\nand Belle data samples. Nevertheless, results based on ex-\nisting data samples are intriguing, as can be seen, for ex-\nample, in the M(D\u22170D\u2217\u2212) invariant-mass distribution for\nB \u2192D\u22170D\u2217\u2212K decays in BABAR (shown in Fig. 18.3.13).\nHere signs of structure can be seen, but with limited statis-\ntical signi\ufb01cance. This will be a promising area of research\nat future \ufb02avor factories.\n18.3.7 Summary and outlook\nThe status of experimental studies of exotic charmonium-\nlike states is shown below in tabular form, for the vari-\nous production mechanisms: B decay (Table 18.3.4), ini-\ntial state radiation in e+e\u2212annihilation (so-called radia-\ntive return events; Table 18.3.5), double charmonium pro-\nduction (Table 18.3.6), and two-photon production (Ta-\nble 18.3.7); studies of charged states are summarized in\nTable 18.3.8.\nAs can be seen from the tables, our knowledge is quite\nfragmentary, despite the large B Factory datasets. Apart\nfrom the X(3872) (by far the best-studied state) and the\nY (3915), all of the candidate exotic mesons have been ob-\nserved in only one production mechanism. Most have been\nobserved in only one \ufb01nal state, and none has been the ob-\nject of a systematic study in a range of \ufb01nal states. Anal-\nyses of particular combinations of production mechanism\nand \ufb01nal state are variously missing, or not performed in\nthe relevant range of invariant mass (\u201cN\u201d in the tables),\nor lacking a \ufb01t to the data to test for the presence of ex-\notic states (\u201cMF\u201d). To give some examples: the M(J/\u03c8 \u03b3)\nspectra in Fig. 18.3.5 are focussed on the X(3872) region\nand no information is provided for other masses; the J/\u03c8\u03b7\ninvariant mass spectrum in Fig. 18.3.4(b) is published,\nbut not \ufb01tted for all the candidate new states. To obtain\na more complete picture for any candidate would require\neither an observation or a limit in many \ufb01nal states, allow-\ning quantitative tests of di\ufb00erent models to be performed.\nFor a number of particles where the current data is sta-\ntistically limited, new decay modes would also add to the\nevidence for the existence of a new state, as opposed to\n(say) a \ufb01nal state interaction e\ufb00ect.\nStates produced in B decays (Table 18.3.4) have been\nthe most studied, although many \ufb01ts are missing, espe-\ncially of the baryonic \ufb01nal states pp and \u039b\u039b which are\npredicted to be important for tetraquark states. Among\nthe decays that have never been studied, B \u2192\u03c8(2S)\u03c0\u03c0K\nshould be relatively clean, whereas D(\u2217)+\ns\nD(\u2217)\u2212\ns\nmodes suf-\nfer from the low branching fractions of the usable decays\nof the \ufb01nal-state Ds mesons.\nAnalysis of states produced in conjunction with an ini-\ntial state radiation (ISR) photon (Table 18.3.5) is rela-\ntively straightforward, due to the unambigous JP C = 1\u2212\u2212\nassignment, although the original exotic candidate of this\nkind, the Y (4260), is still by far the best studied. A com-\nplementary set of states, exclusively C = +1, is accessible\nin recoil from a J/\u03c8 in e+e\u2212annihilation (Table 18.3.6)\nan in production via \u03b3\u03b3 fusion (Table 18.3.7). Many of\nthese analyses are challenging, however, due to large back-\ngrounds and (in the case of \u03b3\u03b3 decays) large missing mo-\nmentum; as a result, the C = +1 states seen only through\nthese production mechanisms are relatively poorly stud-\nied. Concerning the recoil analyses, production in recoil\nagainst particles other than the J/\u03c8 has not been system-\natically investigated: the available samples in B Factory\ndata are small. Studies of the system recoiling against the\n\u03c7c0 and/or the \u03c7c2 would be particularly interesting, given\nthe selection rules.\n\n483\nTable 18.3.4. Status of searches for the new states in the process B \u2192XK, X \u2192f, for several \ufb01nal states f, adapted from\nDrenska et al. (2010). Following the discussion in Section 18.3.3.2 we treat the state Y (3940) seen in B decay as a di\ufb00erent\nstate to the X(3940) seen in e+e\u2212\u2192X J/\u03c8 (see Table 18.3.6 below). Final states where each exotic states were observed (S:\n\u201cseen\u201d) or excluded (NS: \u201cnot seen\u201d) are indicated. A \ufb01nal state is marked as N (\u201cnot performed\u201d) if the analysis has not been\nperformed in a given mass range and with MF (\u201cmissing \ufb01t\u201d) if the spectra are published but a \ufb01t to a given state has not been\nperformed. Finally \u201c\u2014\u201d indicates that, although no search has been performed in this mode, the known quantum numbers or\navailable energy forbid the decay; and \u201chard\u201d that an analysis is experimentally too challenging.The same labels are used in\nsubsequent tables (18.3.5\u201318.3.8). In the headings, \u03c8 denotes the J/\u03c8; \u03c8\u2032 = \u03c8(2S), 2D\u2217= D\u2217D\u2217, and 2D(\u2217)\ns\n= D(\u2217)+\ns\nD(\u2217)\u2212\ns\n.\nState\nJP C\n\u03c8\u03c0\u03c0\n\u03c8\u03c9\n\u03c8\u03b3\n\u03c8\u03c6\n\u03c8\u03b7\n\u03c8\u2032\u03c0\u03c0 \u03c8\u2032\u03c9\n\u03c8\u2032\u03b3\n\u03c7c\u03b3\npp\n\u039b\u039b\n\u039bc\u039bc\nDD\nDD\u22172D\u2217\n2D(\u2217)\ns\n\u03b3\u03b3\nX(3872)\n1++\nS\nS\nS\n\u2014\nNS\n\u2014\n\u2014\nS\nNS\nMF\nMF\n\u2014\n\u2014\nS\n\u2014\n\u2014\nNS\nY(3940)\nJP +\nMF\nS\nNS\n\u2014\n\u2014\n\u2014\n\u2014\nMF\n\u2014\nMF\nMF\n\u2014\nMF\nNS\n\u2014\nN\nN\nZ(3930)\n2++\nMF\nMF\nNS\n\u2014\n\u2014\n\u2014\n\u2014\nMF\n\u2014\nMF\nMF\n\u2014\nMF\nMF\n\u2014\nN\nN\nY(4140)\nJP +\nMF\nMF\nN\nS\n\u2014\nN\n\u2014\nN\n\u2014\nMF\nMF\n\u2014\nMF\nN\nN\nN\nN\nX(4160)\n0P +\nMF\nMF\nN\nMF\n\u2014\nN\n\u2014\nN\n\u2014\nMF\nMF\n\u2014\nMF\nN\nN\nN\nN\nY(4260)\n1\u2212\u2212\nNS\n\u2014\n\u2014\n\u2014\nMF\nN\n\u2014\n\u2014\nN\nMF\nMF\n\u2014\nN\nN\nN\nN\n\u2014\nX(4350)\nJP +\nMF\nMF\nN\nMF\n\u2014\nN\nN\nN\n\u2014\nMF\nMF\n\u2014\nN\nN\nN\nN\nN\nY(4350)\n1\u2212\u2212\nMF\n\u2014\n\u2014\n\u2014\nMF\nN\n\u2014\n\u2014\nN\nMF\nMF\n\u2014\nN\nN\nN\nN\n\u2014\nY(4660)\n1\u2212\u2212\nN\n\u2014\n\u2014\n\u2014\nMF\nN\n\u2014\n\u2014\nN\nMF\nMF\nMF\nN\nN\nN\nN\n\u2014\nTable 18.3.5. Status of searches for the new states in the process e+e\u2212\u2192\u03b3ISRX, X \u2192f, for several \ufb01nal states f, adapted\nfrom Drenska et al. (2010). The meaning of the symbols is explained in the caption of Table 18.3.4.\nState\nJP C\n\u03c8\u03c0\u03c0\n\u03c8\u2032\u03c0\u03c0\n\u03c8\u03b7\n\u03c7c\u03b3\npp\n\u039b\u039b\n\u039bc\u039bc\nDD\nDD\u2217\n2D\u2217\n2D(\u2217)\ns\nY(4260)\n1\u2212\u2212\nS\nNS\nNS\nNS\nNS\nMF\n\u2014\nNS\nNS\nNS\nNS\nY(4350)\n1\u2212\u2212\nNS\nS\nMF\nMF\nMF\nMF\n\u2014\nMF\nMF\nMF\nMF\nY(4660)\n1\u2212\u2212\nNS\nS\nMF\nMF\nMF\nMF\nS\nMF\nMF\nMF\nMF\nTable 18.3.6. Status of searches for the new states in the process e+e\u2212\u2192XJ/\u03c8, X \u2192f, for several \ufb01nal states f, adapted\nfrom Drenska et al. (2010). The meaning of the symbols is explained in the caption of Table 18.3.4; as stated there, we treat\nthe X(3940) and Y (3940) as di\ufb00erent states.\nState\nJP C\n\u03c8\u03c0\u03c0\n\u03c8\u03c9\n\u03c8\u03b3\n\u03c8\u03c6\n\u03c8\u2032\u03c0\u03c0 \u03c8\u2032\u03c9\n\u03c8\u2032\u03b3\n\u03c7c\u03b3\npp\n\u039b\u039b\n\u039bc\u039bc DD\nDD\u22172D\u2217\nX(3872)\n1++\nhard\nN\nhard\n\u2014\nhard\n\u2014\nhard\nhard\nhard\nhard\n\u2014\nMF\nMF\n\u2014\nX(3940)\n0\u2212+\nhard\nN\nhard\n\u2014\nhard\n\u2014\nhard\nhard\nhard\nhard\n\u2014\nNS\nS\n\u2014\nZ(3930)\n2++\nhard\nN\nhard\n\u2014\nhard\n\u2014\nhard\nhard\nhard\nhard\n\u2014\nMF\nMF\n\u2014\nY(4140)\nJP +\nhard\nN\nhard\nN\nhard\n\u2014\nhard\nhard\nhard\nhard\n\u2014\nMF\nMF\nMF\nX(4160)\n0P +\nhard\nN\nhard\nN\nhard\n\u2014\nhard\nhard\nhard\nhard\n\u2014\nMF\nS\nMF\nX(4350)\nJP +\nhard\nN\nhard\nN\nhard\nN\nhard\nhard\nhard\nhard\nhard\nMF\nMF\nMF\nTable 18.3.7. Status of searches for the new states in the process \u03b3\u03b3 \u2192X, X \u2192f, for several \ufb01nal states f, adapted from\nDrenska et al. (2010). The meaning of the symbols is explained in the caption of Table 18.3.4. The identi\ufb01cation of the Y (3915)\nwith the \u03c7c0(2P) is problematic, for the reasons discussed in Section 18.3.3.4, so we retain the former notation. As discussed in\nSection 18.3.3.2, the Y (3915) and the Y (3940) may be the same state.\nState\nJP C\n\u03c8\u03c0\u03c0\n\u03c8\u03c9\n\u03c8\u03b3\n\u03c8\u03c6\n\u03c8\u2032\u03c0\u03c0 \u03c8\u2032\u03c9\n\u03c8\u2032\u03b3\npp\n\u039b\u039b\n\u039bc\u039bc DD\nDD\u22172D\u2217\n2D(\u2217)\ns\nX(3872)\n1++\nN\nhard\nhard\n\u2014\n\u2014\n\u2014\nhard\nMF\nMF\n\u2014\nMF\nN\n\u2014\n\u2014\nY(3915)\n0++\nN\nS\nhard\n\u2014\n\u2014\n\u2014\nhard\nMF\nMF\n\u2014\nMF\nN\n\u2014\nN\nZ(3930)\n2++\nN\nMF\nhard\n\u2014\n\u2014\n\u2014\nhard\nMF\nMF\n\u2014\nS\nN\n\u2014\nN\nY(4140)\nJP +\nN\nMF\nhard\nNS\nN\n\u2014\nhard\nN\nN\n\u2014\nMF\nN\nN\nN\nX(4160)\n0P +\nN\nMF\nhard\nNS\nN\n\u2014\nhard\nN\nN\n\u2014\nMF\nN\nN\nN\nX(4350)\nJP +\nN\nN\nhard\nS\nN\nN\nhard\nN\nN\nN\nN\nN\nN\nN\n\n484\nTable 18.3.8. Status of searches for the new charged states in several \ufb01nal states, adapted from Drenska et al. (2010). The\nmeaning of the symbols is explained in the caption of Table 18.3.4.\nState\n\u03c8\u03c0\n\u03c8\u03c0\u03c00\n\u03c8\u2032\u03c0\n\u03c8\u2032\u03c0\u03c00\n\u03c7c1\u03c0\nhc\u03c0\nDD\nDD\u2217\n2D\u2217\nX(3872)+\nMF\nNS\nMF\nN\nMF\nMF\nN\nMF\n\u2014\nZ(3900)+\nS\nMF\nMF\nN\nMF\nNS\nN\nS\n\u2014\nZ(3930)+\nMF\nN\nMF\nN\nMF\nMF\nN\nN\n\u2014\nZ(4020)+\nNS\nN\nMF\nN\nMF\nS\nN\nN\nS\nZ(4050)+\nMF\nN\nMF\nN\nS\nMF\nN\nN\nMF\nY (4140)+\nMF\nN\nMF\nN\nMF\nN\nN\nN\nMF\nZ(4250)+\nMF\nN\nMF\nN\nS\nN\nN\nN\nMF\nX(4350)+\nMF\nN\nMF\nN\nMF\nN\nN\nN\nMF\nZ(4430)+\nNS\nN\nS\nN\nMF\nN\nN\nN\nMF\nZ(4660)+\nMF\nN\nMF\nN\nMF\nN\nN\nN\nMF\nRelatively few searches for charged exotic states \u2014 the\nmost striking signature of states made of more than two\nquarks \u2014 have been conducted in B decays; as shown in\nTable 18.3.8, searches have been accomplished for only \ufb01ve\ncombinations of \ufb01nal states and exotic candidates. Ideally,\na search for charged partner states should be performed\nfor each neutral exotic meson. A general spectrum of four-\nquark bound states would also include mesons containing\na single s quark, with distinctive strong decays to charmo-\nnium plus a charged kaon. Searches for such states could\nbe conducted in B decays in association with an s\u00afs state,\nor inclusively at a hadron collider.\nIn conclusion, a systematic study of the exotic spec-\ntrum is required to form a global and de\ufb01nite picture of\nthese states and their structure. As well as \ufb01nalizing stud-\nies with existing B Factory and Tevatron data, results\nfrom newer, even higher luminosity machines such as the\nLHC and the super \ufb02avor factories are needed. The appar-\nent con\ufb01rmation of the Z(4430)+ by LHCb, just as this\nbook was being completed (Aaij et al., 2014b), is both\na welcome clari\ufb01cation of the experimental picture, and\na reminder that the exotic charmonium-like states \u2014 an\nunexpected product of the bounty of data from the B\nFactories\u2014 must be studied in larger data samples if they\nare to be more fully understood.\n\n485\n18.4 Bottomonium\nEditors:\nStephen Sekula (BABAR)\nRoberto Mussa (Belle)\nNora Brambilla (theory)\nAdditional section writers:\nBryan Fulsom, Romulus Godang, Christopher Hearty, Todd\nPedlar, Cheng Ping Shen\n18.4.1 Introduction\nAt the advent of the B-factory experiments, measurements\nof the spectrum of the bottomonium system were lim-\nited to only a few states \u2014 the \u03a5(nS) and \u03c7b(nP) reso-\nnances. However, the theoretical predictions for this spec-\ntrum were abundant and the bottomonium system o\ufb00ered\nopen territory for scienti\ufb01c exploration. The spectrum of\nthe bottomonium system is illustrated in Fig. 18.4.1. Of\nparticular interest were the bottomonium ground state,\nthe \u03b7b(1S), and its excitations (the S-wave singlet states,\ne.g. \u03b7b(2S)), the discovery of the hb(nP) P-wave singlet\nstates, measurements of their properties and of transitions\nbetween bottomonium states as tests of various theoretical\nframeworks (Lattice QCD, NRQCD, pNRQCD, QCD po-\ntential models, etc.). In addition, these measurements al-\nlowed for searches for physics beyond the Standard Model\n(such as violation of universal couplings to leptons, dark\nmatter, and low-mass Higgs bosons).\nThe bottomonium programs at BABAR and Belle yielded\na rich assortment of both discoveries and measurements.\nThe ground state of the bottomonium system was \ufb01rst dis-\ncovered by BABAR and later con\ufb01rmed by Belle, yielding\nmultiple independent mass and branching fraction mea-\nsurements (Section 18.4.4.2). In addition, Belle discovered\nthe \u03b7b(2S) and measured its mass. The BABAR Collabora-\ntion was the \ufb01rst to show evidence of the existence of the\nP-wave singlet state, hb(1P), and the Belle Collaboration\ndemonstrated clear discovery of this state and also of its\npartner, the hb(2P) (Section 18.4.4.3). Discovery of these\nstates required in parallel the measurement of transitions\nbetween states, and these are detailed in the aforemen-\ntioned sections. Independent measurements (unconnected\nwith searches for new resonances) of transitions between\nbottomonium states, as well as decays to hadronic \ufb01nal\nstates, are detailed in Section 18.4.6.\nThe bottomonium system yielded many surprises, how-\never, when compared to the expectations from theoretical\npredictions. The Belle con\ufb01rmation of the \u03b7b(1S) and dis-\ncoveries of the \u03b7b(2S) and hb(1P, 2P) were all made possi-\nble in part by apparently large and anomalous \u03c0+\u03c0\u2212tran-\nsition rates from the \u03a5(5S) resonance. This is discussed in\nSection 18.4.4.3. In addition, as a result of their investiga-\ntions of these anomalous transition rates, two new states\nwere discovered by the Belle Collaboration just above the\nopen-bottom threshold (Fig. 18.4.1) - the charged Zb states\n(Section 18.4.5).\n\u0000\u0001\u0002\n\u0001\u0002\u0003\u0004\u0005\u0006\n\u0001\u0002\u0003\u0000\u0005\u0006\n\u0003\u0000\u0005\u0006\n\u0007\u0002\n\u0007\u0003\u0004\u0005\u0006\n\u0002\n\b\t\n\n\u0004\n\n\n\n\u0004\n\u000b\n\n\u0004\n\u000b\n\n\u0004\n\f\n\n\u0004\n\t\n\n\u0004\n\u0000\n\n\b\f\n\n\b\u000b\n\n\r\u0003\u0004\u000e\u0006\n\u000f\u0010\u0010\u000f\u0011\u0001\u0012\u0013\u0014\u0001\u0001\u0015\u0016\u0017\n\r\u0003\u0000\u000e\u0006\n\r\u0003\u0018\u000e\u0006\n\r\u0003\u0019\u000e\u0006\n\r\u0003\t\u000e\u0006\n\r\u0003\u0004\u001a\u0006\n\u001b\u001c\u0014\u0014\u0003\u001b\u0013\u001d\u001e\u001f\u000f\u000f\u0006\n\u0003\u0004\u000e\u0006\n\u0003\u0000\u000e\u0006\n \n \n \u0002\n\u0002\n\u0002\n\u0003\u0018\u0005\u0006\n\u0007\u0002\n\u0003\u0018\u0005\u0006\n\u001a\n\u0018\n!\n\u000e\n\u0004\n\u000e\n\u0018\n\u0005\n\u0004\n\u0005\n\u0018\n!\n\u0004\n\u0004\n\n\u0003\u0018\u000e\u0006\n\"#\u001e$ \"\n\n\u0002\n\u0002\nFigure 18.4.1. The bottomonium spectrum. Solid lines cor-\nrespond to observed states while dashed lines indicate the lo-\ncation of predicted ones. See also the upper plot of Fig. 18.1.1,\nand the accompanying discussion.\nBoth collaborations pursued physics beyond the Stan-\ndard Model using their bottomonium samples. The Belle\nCollaboration, followed by the BABAR Collaboration, both\nsearched for invisible decays of the \u03a5(1S) meson; these\nsearches, and the theoretical work that motivated them,\nare discussed in Section 18.4.7.2. The BABAR Collabora-\ntion also searched for evidence of a low-mass Higgs boson\n(Section 18.4.7.1), as well as lepton-\ufb02avor-violating decays\n(Section 18.4.7.3) and violation of the universality of cou-\nplings to leptons (Section 18.4.7.4).\n18.4.2 Common techniques\n18.4.2.1 Transition Recoil Method\nThe use of transition particles between two resonances to\n\u201ctag\u201d the presence of one of the resonances is a common\ntechnique in the bottomonium analyses. Here, we describe\nthe method and its application.\nConsider two resonances with masses M1 and M2,\nand a transition between them involving the emission of\none or more transition particles, M1 \u2192(trans) + M2.\nIf the transition particles can be reconstructed, and the\nmass of either the parent or daughter resonance is known,\nthen the remaining mass, which may be said to \u201crecoil\u201d\nagainst the transition particles, can be determined from\nfour-momentum conservation:\nP(M1) = P(tr) + P(M2)\n(18.4.1)\n\n486\nwhere P(tr) is the four-vector describing the entire\ntransition-particle energy and momentum. The mass re-\ncoiling against the transition particles, de\ufb01ned here as \u201dre-\ncoil mass\u201d (though sometimes the term \u201dmissing mass\u201d is\nalso used for the same quantity) is then determined by\nM 2\nrecoil \u2261(P(M1) \u2212P(tr))2 = P(M2)2 = M 2\n2\n(18.4.2)\nwhere Mrecoil is de\ufb01ned as the \u201crecoil mass.\u201d This expres-\nsion is valid in any reference frame. It is usually convenient\nto then choose a reference frame that simpli\ufb01es the com-\nputation while still giving access to the invariant quantity\nin question.\nThe most common use of this technique is to deter-\nmine the mass of a daughter resonance using the four-\nmomentum of the reconstructed transition particles and\nthat of the parent resonance, in the rest frame of the par-\nent resonance. In this case, the equation simpli\ufb01es to:\nM 2\nrecoil = M 2\n1 + m2\ntr \u22122M1Etr\n(18.4.3)\nwhere Etr is the total energy of the transition particles\nin the parent resonance rest frame and m2\ntr is the total\ninvariant mass-squared of the transition particles.\nIn many instances, the parent resonance is produced\nat rest in the center-of-mass (CM) frame of the collider,\nand when this is true, the above calculation holds ex-\nactly. When this is not true, the calculated recoil mass\nusing the transition particles\u2019 four-momentum in the CM\nframe will be shifted due to the presence, for instance,\nof another intermediate resonance before the transition\nparticles are produced. For instance, if the transition par-\nticles are produced in the second of two transitions, e.g.\nM1 \u2192(undetected)+M2 followed by M2 \u2192(trans)+M3,\nthen Lorentz boosting into the CM frame - the frame of\nthe original parent resonance - will yield a shifted recoil\nmass.\nMost often, sequential transitions in which a shifted re-\ncoil mass is observed are transitions in which each of states\n1, 2 and 3 is a bottomonium state, and as such the emit-\nted transition particles have small masses and momenta.\nIn such cases transition particle energies and momenta are\nsmall compared to the masses M1, M2, and M3. In these\ncases the amount of the shift is nearly equal to M1 \u2212M2.\nWhen one calculates the recoil mass assuming the transi-\ntion particles, which were emitted in the second transition,\nwere emitted from the initial state, then the shifted recoil\nmass obtained is given by\nM 2\nshifted = (P(M1) \u2212P(tr))2.\n(18.4.4)\nThis is not equal to M 2\n3 , which is properly calculated\nas (P(M2) \u2212P(tr))2, assuming both four-momenta are\nboosted into the CM frame. In our approximation, then,\nwe \ufb01nd (Ei and pi are the energies and the spatial com-\nponents of the four momenta P(Mi) and P(tr))\nMshifted =\np\n(E1 \u2212Etr)2 \u2212(p1 \u2212ptr)2)\n=\np\n(M1 \u2212Etr)2 \u2212(ptr)2)\n= (M1 \u2212Etr)\np\n1 \u2212(ptr)2/(M1 \u2212Etr)2\n\u2248(M1 \u2212Etr) \u2212p2\ntr/2(M1 \u2212Etr)\n(18.4.5)\nand\nM3 =\np\n(E2 \u2212Etr)2 \u2212(p2 \u2212ptr)2)\n= (E2 \u2212Etr)\nq\n1 \u2212(p2\n2 \u2212ptr)2/(E2 \u2212Etr)2\n\u2248(E2 \u2212Etr) \u2212(p2\n2 \u2212ptr)2/2(E2 \u2212Etr).(18.4.6)\nWe then calculate the shift, \u2206M = Mshifted \u2212M3,\n\u2206M = (M1 \u2212E2) + (p2 \u2212p2\ntr)/2(M1 \u2212Etr)\n\u2212p2\ntr/2(E2 \u2212Etr)\n\u2248(M1 \u2212M2),\n(18.4.7)\nsince in the cases we are discussing, E2 \u2248M2 and p2, E2,\nand ptr are all much smaller than either M1 or M2. Shifted\nrecoil masses of this kind will be observed in the plot of\nthe Mrecoil(\u03c0+\u03c0\u2212) distribution in Figure 18.4.9.\n18.4.3 e+e\u2212energy scans\nAs is discussed in Section 18.3, the discovery of non-\nbaryonic charmonium states that behave in ways not pre-\ndicted by two-quark-system models has yielded a renais-\nsance of experimental and theoretical interplay in quarko-\nnium. The observation of such exotic charmonium states\nsuggests that a similar search for exotic bottomonium\nstates is experimentally warranted. Such searches can be\nconducted in at least a couple of ways: energy scans of\nthe accelerator across a range of center-of-mass energies,\nor searches at speci\ufb01c center-of-mass energies. The former\nwill be discussed here, while a discussion of the latter ap-\nproach can be found in Section 18.4.5.\nAn energy scan can be used to look for anomalous\nfeatures in the ratio of the bb(\u03b3) and \u00b5+\u00b5\u2212production\ncross-sections. Exotic charmonium states with quantum\nnumbers JP C = 1\u2212\u2212have been observed and named\nthe Y (4260), Y (4350), and Y (4660). One can make na\u00a8\u0131ve\npredictions for the bottomonium system by taking their\nmasses and scaling them up by the mass di\ufb00erence be-\ntween the J/\u03c8 and the \u03a5(1S), yielding predicted masses\nabove the \u03a5(4S) mass and below 11.2 GeV/c2.\nDuring the \ufb01nal two weeks of data taking by the BABAR\nexperiment, March 28 \u2013 April 7, 2008, the experiment col-\nlected 3.9 fb\u22121 of data at more than 300 di\ufb00erent center-\nof-mass energies above the \u03a5(4S) resonance, with typical\nspacing of 5 MeV. This is a factor of 30 more data than\nearlier scans (Besson et al., 1985; Lovelock et al., 1985;\nAubert, 2009x). An additional 7.8 fb\u22121 sample recorded\nat 10.54 GeV was used to study continuum background.\nThe quantity of interest is Rb(s) \u2261\u03c3b(s)/\u03c30\n\u00b5\u00b5(s), the\nratio of the total cross section for e+e\u2212\u2192b\u00afb(\u03b3) divided\nby the lowest order cross section for e+e\u2212\u2192\u00b5+\u00b5\u2212. Note\nthat \u03c3b includes Initial State Radiation (ISR) production\nof \u03a5 states.\nThe experimental quantities used to calculate Rb(s)\nare the number of hadronic events and muon pairs at\n\n487\n [GeV]\ns\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\nb\nR\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nB\nB\nB\n B*\n*\nB\n B*\ns\nB\ns\nB\n*\ns\nB\ns\n B\n*\ns\nB\n*\ns\n B\nFigure 18.4.2. Measured Rb as a function of \u221as with the\nposition of the opening thresholds of the e+e\u2212\u2192B(\u2217)\n(s) \u00afB(\u2217)\n(s)\nprocesses indicated by dotted lines (Aubert, 2009x).\ncenter-of-mass energy \u221as and in the continuum sample.\nHadronic events are selected using criteria that preferen-\ntially select events with open bottom (B) mesons. Muon\npairs are cleanly and e\ufb03ciently selected using the track-\ning system and calorimeter only; the muon identi\ufb01cation\nsystem is not required.\nThe 10.54 GeV data includes all event types that sat-\nisfy the hadronic selection, other than open bottom: con-\ntinuum e+e\u2212\u2192q\u00afq (the dominant background), ISR pro-\nduction of \u03a5, and two photon events. The ISR contribution\nis calculated using simulated events. The two-photon com-\nponent, 2% of the continuum sample, is estimated from\nthe direction of the missing-momentum vector. The con-\ntinuum component is obtained from the 10.54 GeV data\nby subtracting the other two components.\nThe e\ufb03ciency for open bottom events to satisfy the cri-\nteria is obtained from simulation. It is taken to be the av-\nerage of all possible two-body \ufb01nal states. Half the spread\nis taken as a systematic error.\nThe resulting values of Rb(s) are shown in Fig. 18.4.2.\nNote that radiative corrections have not been applied. Not\nshown in the \ufb01gure are correlated systematic errors total-\ning 2.6%, with equal contributions from hadronic event\nand muon pair e\ufb03ciencies and \u00b5+\u00b5\u2212radiative corrections.\nThe region 10.80\u201311.20 GeV is \ufb01t with a model con-\ntaining two interfering relativistic Breit Wigner resonances\nrepresenting the \u03a5(10860) and the \u03a5(11020), a \ufb02at inter-\nfering component, plus an addition \ufb02at component repre-\nsenting b\u00afb continuum not interfering with the resonances\n(Fig. 18.4.3). The resulting mass and widths are 10.876 \u00b1\n0.002 GeV/c2 and 43\u00b14 MeV for the \u03a5(10860) and 10.996\u00b1\n0.002 GeV/c2 and 37 \u00b1 3 MeV for the \u03a5(11020) (Aubert,\n2009x). These widths are considerably narrower than the\nprevious PDG values.\nThe results are sensitive to the details of the \ufb01t model.\nFor example, using a threshold function instead of the \ufb02at\nnon-resonant component gives a slightly di\ufb00erent mass\nand a signi\ufb01cantly larger width (74 \u00b1 4 MeV) for the\n\u03a5(10860). A proper coupled channel approach including\n [GeV]\ns\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\nb\nR\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nFigure 18.4.3. A zoom of Fig. 18.4.2 with the result of the\n\ufb01t superimposed (Aubert, 2009x). The errors on the data rep-\nresent the statistical and uncorrelated systematic errors added\nin quadrature.\nthe e\ufb00ects of the various thresholds would undoubtedly\nmodify the results.\nFinally it is noted that no evidence for exotic states\nhas been found in the scans.\nThe Belle Collaboration also conducted a scan above\nthe \u03a5(4S) resonance, in part in order to investigate possi-\nble causes for the anomalously large rates for the processes\n\u03a5(10860) \u2192\u03a5(nS)\u03c0+\u03c0\u2212) with (n = 1, 2, 3) that they had\nobserved (Chen, 2008b). These rates, if the \u03a5(10860) is in-\nterpreted as the fourth radial excitation of the 1\u2212\u2212\u03a5(1S)\nstate, were up to two orders of magnitude larger than ex-\npectations.\nBelle undertook a scan similar to that conducted by\nthe BABAR Collaboration of the cross section for e+e\u2212\u2192\n\u03a5(nS)\u03c0+\u03c0\u2212(n = 1, 2, 3) in the vicinity of the known mass\nof the \u03a5(10860), taking data at center-of-mass energies\nbetween 10.83 and 11.02 GeV (Chen, 2010). In this study,\nthey observed a peak in \u03c3(e+e\u2212\u2192\u03a5(nS)\u03c0+\u03c0\u2212) (n =\n1, 2, 3) at an energy of (10888+2.7\n\u22122.6\u00b11.2) MeV with a width\nof (30.7+8.3\n\u22127.0 \u00b1 3.1) MeV. The measured cross section with\nthe result of the \ufb01t using the Breit Wigner function for\nthe signal is shown in Figure 18.4.4 (top).\nThe important thing to note is that this peak di\ufb00ers\nsubstantially in mass from the observed maximum in the\noverall hadronic cross section (shown in the lower pannel\nof Fig. 18.4.4) , and led to the suggestion that the peak\nin the \u03a5(nS)\u03c0+\u03c0\u2212) (n = 1, 2, 3) cross section may not, in\nfact, be due to the \u03a5(10860) but rather some exotic state\n(Liu and Ding, 2012).\n18.4.4 Spectroscopy\n18.4.4.1 Introduction to Bottomonium Spectroscopy\nAs discussed in Section 18.4.1, the BABAR and Belle Col-\nlaborations advanced signi\ufb01cantly the experimental mea-\nsurements of states within the predicted bottomonium\n\n488\n (GeV)\ns\n10.75\n10.8\n10.85\n10.9\n10.95\n11\n11.05\n]\n\u00b5\n\u00b5\n[\n0\n\u03c3\n] / \n\u03c0\n\u03c0\n(nS)\n\u03a5\n[\n\u03c3\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\n\u03c0\n\u03c0\n(1S)\n\u03a5\n\u03c0\n\u03c0\n(2S)\n\u03a5\n\u03c0\n\u03c0\n(3S)\n\u03a5\n (GeV)\ns\n10.75\n10.8\n10.85\n10.9\n10.95\n11\n11.05\n]\n\u00b5\n\u00b5\n[\n0\n\u03c3\n] / \nb\n[b\n\u03c3\n = \nb\nR\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n(a)\nFigure 18.4.4. Top: The energy dependence of the cross sec-\ntion for e+e\u2212\u2192\u03a5(nS)\u03c0+\u03c0\u2212(n = 1, 2, 3) normalized to the\nleading order e+e\u2212\u2192\u00b5+\u00b5\u2212cross section (Chen, 2010). The\ndashed line shows the energy at which the hadronic cross sec-\ntion is maximal. Bottom: Rb as a function of the energy.\nspectrum. At the time that the \ufb01rst \u03a5(3S) data sam-\nples were collected by the Belle and then the BABAR Col-\nlaborations, predictions of the mass splitting between the\nlowest-mass S-wave pseudoscalar spin-singlet, \u03b7b(1S), and\nthe lowest-mass S-wave vector spin-triplet, \u03a5(1S), ranged\nfrom 36 MeV/c2 to 100 MeV/c2 (Godfrey and Rosner, 2001).\nA measurement of this splitting was clearly critical in es-\ntablishing which theoretical frameworks more accurately\npredicted the properties of the bottomonium spectrum\nand to help inform further developments in those frame-\nworks; a discussion on the theoretical framework of quarko-\nnium physics can be found in Section 18.1. For instance, a\nmeasurement of the hyper\ufb01ne mass splitting would further\nour understanding of non-relativistic QCD bound states\nand shed light on the contribution of spin-spin interac-\ntions in models of the bottomonium system (Burch and\nEhmann, 2007; Gray et al., 2005)\nThis line of argument also extended to the P-wave\nspin-singlet states, the hb(nP), and their properties as\npredicted in various theoretical frameworks. Prior to their\ndiscovery, it was recognized that measuring the hyper-\n\ufb01ne splitting for the P-wave states was similarly impor-\ntant for assessing the role of spin-spin interactions in po-\ntential models for heavy quarks. Treating the bottomo-\nnium system non-relativistically, the splitting can be de-\ntermined from the square of the wave function for the\nsystem at the origin. This is expected to be a non-zero\nquantity for states with L = 0; for the P-wave states\n(L = 1), the splitting between the hb(1P) and the spin-\naveraged triplet state \u27e8\u03c7bJ(1P)\u27e9is expected to be approx-\nimately zero; therefore, one can approximate the mass of\nthe hb(1P) as the spin-weighted center-of-gravity of the\n\u03c7bJ(1P) system: M(hb(1P)) = (9899.87 \u00b1 0.27) MeV/c2\n(Beringer et al., 2012). If one takes into account higher-\norder corrections to this approximation, one would expect\nto observe deviations from this prediction; however, mea-\nsured deviations from the prediction that correspond to\na hyper\ufb01ne splitting larger than a few MeV/c2 would in-\ndicate a vector component to the con\ufb01nement potential\n(Rosner et al., 2005).\nIn addition to measuring the masses of these states,\nmeasuring the branching fractions for the correspond-\ning transitions to and from these states is important\nfor testing theoretical frameworks of heavy quarkonium.\nThe branching fraction for the isospin-violating transi-\ntion \u03a5(3S) \u2192\u03c00hb(1P) was expected to be about 0.1%\n(Godfrey, 2005a; Voloshin, 1986). The branching fraction\nfor the transition \u03a5(3S) \u2192\u03c0+\u03c0\u2212hb(1P) was expected\nto range between \u223c10\u22124 (Godfrey, 2005a) and \u223c10\u22123\n(Kuang, Tuan, and Yan, 1988; Kuang and Yan, 1981, 1990;\nTuan, 1992). The branching fraction for the favored E1\ntransition hb(1P) \u2192\u03b3\u03b7b(1S) was expected to be large,\n41.4% (Godfrey and Rosner, 2002).\n18.4.4.2 Observation of the \u03b7b(1S) and \u03b7b(2S)\nIn the thirty years following the \ufb01rst discovery of the\n\u03a5(nS) bottomonium states (Herb et al., 1977), no evi-\ndence for the spin-singlet \u03b7b(nS) states had been found.\nThe previous best limits for the decays \u03a5(3, 2S) \u2192\u03b3\u03b7b\nwere set by the CLEO experiment (Artuso et al., 2005b).\nBABAR \ufb01rst observed the \u03b7b in 2008 via the \u03a5(3S) \u2192\u03b3\u03b7b\ndecay channel (Aubert, 2008ak). The discovery was con-\n\ufb01rmed in 2009 in the BABAR \u03a5(2S) data in decays of\n\u03a5(2S) \u2192\u03b3\u03b7b (Aubert, 2009l). The CLEO experiment sub-\nsequently veri\ufb01ed the discovery in a re-analysis of its own\n\u03a5(3S) data sample (Bonvicini et al., 2010).\nThese analyses performed \ufb01ts to the inclusive photon\nCM energy (E\u2217\n\u03b3) spectrum, searching above the smooth,\nnon-peaking background for evidence of a monochromatic\nphoton associated with a radiative transition to the \u03b7b.\nTwo other peaking components were expected in the en-\nergy region close to this signal: one from photons from\n\u03a5(1S) production in ISR (e+e\u2212\u2192\u03b3ISR\u03a5(1S)), and a\nmerged triplet from the decays \u03a5(nS) \u2192\u03b3\u03c7bJ(mP),\n\u03c7bJ(mP) \u2192\u03b3\u03a5(1S), where m = n \u22121. The photons that\nresult from the decay \u03c7bJ(mP) \u2192\u03b3\u03a5(1S) have energies\nin the range of the searches and thus serve to contribute\nbackground photon energy peaks.\nThe data samples used in the BABAR analyses included\n28 (14) fb\u22121 collected the \u03a5(3S) (\u03a5(2S)) resonance, with\napproximately 9 (7)% of this data (refered to here as the\n\u201ctest sample\u201d) used for preliminary studies and later dis-\ncarded. A total number of (109 \u00b1 1) \u00d7 106 \u03a5(3S) events\nand (91.6 \u00b1 0.9) \u00d7 106 \u03a5(2S) events were used in the \ufb01-\nnal analysis. Additionally, \u201co\ufb00-resonance\u201d samples of 43.9\n(2.4) fb\u22121 were taken approximately 40 (30) MeV below\n\n489\nTable 18.4.1. Summary of the optimized variables used in the\n\u03b7b analyses (Aubert, 2008ak, 2009l).\nVariable\n\u03a5(3S)\n\u03a5(2S)\n\u03b3LAT\n< 0.55\ncos(\u03b8\u03b3,LAB)\n\u22120.762 < cos(\u03b8\u03b3,LAB) < 0.890\nNT RK\n> 3\n| cos \u03b8T |\n< 0.7\n< 0.8\n|m\u03b3\u03b32 \u2212m\u03c00|\n> 15 MeV\nE\u03b32\n> 50 MeV\n> 40 MeV\nE\ufb03ciency\n37%\n35.8%\nthe \u03a5(4S) (\u03a5(3S)) resonance energies for studies of ISR\nproduction.\nCandidate\nphotons\nwere\nsingle\nelectromagnetic\ncalorimeter (EMC) bumps not matched to any track,\nwith a minimum lab energy of 30 MeV and a lateral\nmoment (Section 15.1.4) less than 0.8. The selection\ncriteria for this analysis were optimized by maximizing\nthe \ufb01gure of merit S/\n\u221a\nB, where S represents the number\nof signal events from \u03a5(nS) \u2192\u03b3\u03b7b Monte Carlo (MC),\nand B represents the number of background events\ntaken from the test sample. For optimization purposes,\nthe signal region was restricted to 850 < E\u2217\n\u03b3 < 950\n(500 < E\u2217\n\u03b3 < 700) MeV for \u03a5(3S) (\u03a5(2S)). A summary\nof the optimized selection criteria is given in Table 18.4.1,\nwith the individual variables described below.\nTo improve photon candidate quality, \u03b3LAT < 0.55 was\nrequired, where \u201cLAT\u201d refers to the lateral moment of the\nelectromagnetic energy deposit. Furthermore, by requir-\ning the photon angle in the lab frame to satisfy \u22120.762 <\ncos(\u03b8\u03b3,LAB) < 0.890, only photon candidates with fully-\ncontained electromagnetic showers detected within the bar-\nrel of the EMC were used in this analysis. To select hadronic\ndecays of the \u03b7b, the number of charged tracks (NT RK) in\nthe event was required to be greater than or equal to 4, and\nthe ratio of the second to zeroth Fox-Wolfram moments\nto be less than 0.98. This is typical of the way in which\nhigh-multiplicity hadronic \ufb01nal states of B meson decay\nare selected in the B factories, c.f. Section 9. Background\nfrom continuum events was rejected by imposing require-\nments on | cos \u03b8T |, the cosine of the angle in the CM frame\nbetween the photon momentum and the thrust axis of the\nrest of the event. The optimal requirement was found to\nbe | cos \u03b8T | < 0.7 (0.8). The dominant background to this\nanalysis, \u03c00 \u2192\u03b3\u03b3 decays, was reduced by vetoing photon\ncandidates that, when paired with another photon in the\nevent with a lab energy (E\u03b32) greater than 50 (40) MeV,\nformed an invariant mass (m\u03b3\u03b32) within 15 MeV/c2 of the\nnominal \u03c00 mass (Beringer et al., 2012). The values for the\nthrust angle and \u03c00 veto were optimized simultaneously.\nThe signal e\ufb03ciency resulting from these selection criteria\nwas 37% (35.8%). The e\ufb03ciency and selection criteria val-\nues were independently veri\ufb01ed using the signal yield of\nthe nearby \u03c7bJ \u2192\u03b3\u03a5(1S) signal peaks as a cross-check.\nTo extract the \u03b7b signal, a binned maximum likelihood\n\ufb01t of the E\u2217\n\u03b3 spectrum was performed over the range 0.5 <\nE\u2217\n\u03b3 < 1.1 (0.27 < E\u2217\n\u03b3 < 0.80) GeV for the \u03a5(3S) (\u03a5(2S))\ndataset. The \ufb01t contained four components: non-peaking\nbackground, \u03c7bJ \u2192\u03b3\u03a5(1S), \u03b3ISR\u03a5(1S), and the \u03b7b signal.\nFor the \u03a5(3S) analysis, the non-peaking background\nwas parameterized with a smooth lineshape de\ufb01ned as\nf(E\u2217\n\u03b3) = A(C + exp[\u2212\u03b1E\u2217\n\u03b3 \u2212\u03b2E\u22172\n\u03b3 ]), where A, C, \u03b1, and\n\u03b2 were empirically-determined variables. The probability\ndensity functions (p.d.f.s) for the \u03c7bJ(2P) \u2192\u03b3\u03a5(1S) tran-\nsitions were parameterized using the Crystal Ball (CB)\nfunction (Gaiser, 1982), a Gaussian distribution with an\nextended, power-law tail on the low side. The relative\nrates and peak positions for these three decays were \ufb01xed\nto their PDG values (Beringer et al., 2012). The values\nof the CB parameters were determined from a \ufb01t to the\nbackground-subtracted data in 840 < E\u2217\n\u03b3 < 960 MeV, and\nare common to all three peaks. Based on MC-simulated\nevents, the ISR p.d.f. was parameterized by a CB func-\ntion. The \u03a5(1S) production yield from ISR was measured\nin the o\ufb00-resonance \u03a5(4S) sample, con\ufb01rmed in \u03a5(3S)\no\ufb00-resonance data, and extrapolated to \ufb01x the size of the\ncontribution in the \u03a5(3S) on-resonance sample. The \u03b7b\nsignal p.d.f. was a non-relativistic Breit-Wigner function\nconvolved with a CB function to account for the experi-\nmental E\u2217\n\u03b3 resolution. The CB parameters were \ufb01xed from\nMC events generated with a width of zero, but a natural\nwidth of 10 MeV (within the range of theoretical predic-\ntions based on expectations for two-photon widths was\nassumed for the \ufb01nal \ufb01t to the data. In the \ufb01t, the free\nparameters were the \u03b7b peak position and yield, the total\n\u03c7bJ(2P) yield and peak position, and values of the non-\npeaking background p.d.f. parameters.\nA similar approach was taken for the analysis of the\n\u03a5(2S) decay modes. In this case, the non-peaking back-\nground was parameterized using the function g(E\u2217\n\u03b3) =\nD exp\n\u0000\u03a34\ni=1ciE\u2217i\n\u03b3\n\u0001\n, where D and ci were determined in\nthe \ufb01t. A more sophisticated parameterization was used\nfor the \u03c7bJ(1P) transition peaks. A CB function was an-\nalytically convolved with a rectangular function with a\nwidth accounting for the Doppler broadening due to the\nmotion of the \u03c7bJ(1P) relative to the CM frame. The val-\nues of the half-width of the rectangular functions were 6.6,\n5.5, and 4.9 MeV for the J = 0, 1, 2 states, respectively.\nThe CB tail parameters, taken as a free parameter in the\n\ufb01nal \ufb01t, were common to all three peaks, and relative peak\npositions were \ufb01xed to the nominal values (Beringer et al.,\n2012). The relative yields were \ufb01xed to values determined\nfrom a control sample of exclusive \u03c7bJ(1P) \u2192\u03b3\u03a5(1S),\n\u03a5(1S) \u2192\u00b5+\u00b5\u2212decays. The ISR p.d.f. was determined\nfrom MC-simulated events, with the extrapolated yield\nfrom the \u03a5(4S) o\ufb00-resonance data used only as a cross-\ncheck. The \u03b7b signal p.d.f. was parameterized in a fashion\nidentical to \u03a5(3S) analysis. For the \ufb01nal \ufb01t, the free pa-\nrameters were the \u03b7b peak position and yield, the ISR\nyield, the total \u03c7bJ(1P) yield, the \u03c7b1,2(1P) CB resolu-\ntions, the \u03c7bJ(1P) CB transition point value, an overall\nenergy scale o\ufb00set based on the \u03c7bJ(1P) and ISR peak po-\nsitions, and the power law components for the non-peaking\nbackground. The \ufb01ts to the E\u2217\n\u03b3 spectrum for both datasets\nare shown in Fig. 18.4.5 and 18.4.6.\n\n490\n (GeV)\n\u03b3\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nEntries / ( 0.005 GeV )\n0\n100\n200\n300\n400\n500\n3\n10\n\u00d7\n (GeV)\n\u03b3\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nEntries / ( 0.005 GeV )\n0\n100\n200\n300\n400\n500\n3\n10\n\u00d7\n(a)\n (GeV)\n\u03b3\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nEntries/ (0.005 GeV) \n-2000\n0\n2000\n4000\n6000\n8000\n10000\n (GeV)\n\u03b3\nE\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nEntries/ (0.005 GeV) \n-2000\n0\n2000\n4000\n6000\n8000\n10000\n(b)\nFigure 18.4.5. (a) Inclusive photon spectrum from \u03a5(3S) de-\ncays in the region 0.50 < E\u2217\n\u03b3 < 1.1 GeV (Aubert, 2008ak). The\nsolid line indicates the total \ufb01t to the data; the dotted line in-\ndicates the non-peaking background component. (b) The same\nspectrum after the non-peaking background component has\nbeen subtracted, with the \u03c7bJ(2P), ISR, and \u03b7b signal compo-\nnents of the \ufb01t indicated from left to right on the plot.\nIn the \u03a5(3S) dataset, systematic uncertainties on the\nyield due to varying the assumed \u03b7b Breit-Wigner width,\nthe extrapolated ISR yield, and varying the p.d.f. param-\neters were estimated to produce an 11% e\ufb00ect. By far\nthe largest uncertainty (10%) was due to the \u03b7b width\nassumption. In the \u03a5(2S) dataset, the largest systematic\nuncertainties on the yield arise from varying the assumed\n\u03b7b width and the background shape (\u224817% total).\nThe total systematic uncertainty due to assumptions\nmade on the e\ufb03ciency calculation was estimated to be\n5.5%(6.7%) at the \u03a5(3S) (\u03a5(2S)).\nCombining the two BABAR results gave a ratio of branch-\ning fractions\nB(\u03a5(2S) \u2192\u03b3\u03b7b)\nB(\u03a5(3S) \u2192\u03b3\u03b7b) = 0.89+0.25+0.12\n\u22120.23\u22120.16.\n(18.4.8)\nA new, unpredicted pathway to access the \u03b7b(1S) and\n\u03b7b(2S) states from \u03a5(5S) energies allowed Belle to improve\nsubstantially the \u03b7b(1S) mass measurement, perform the\n\ufb01rst measurement of its width, and discover the \u03b7b(2S).\n (GeV)\n\u03b3\nE\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nEntries / ( 0.005 GeV )\n0\n100\n200\n300\n400\n500\n600\n700\n800\n3\n10\n\u00d7\n (GeV)\n\u03b3\nE\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nEntries / ( 0.005 GeV )\n0\n100\n200\n300\n400\n500\n600\n700\n800\n3\n10\n\u00d7\n(a)\n (GeV)\n\u03b3\nE\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nEntries / ( 0.005 GeV )\n-2000\n0\n2000\n4000\n6000\n8000\n10000\n(b)\nFigure 18.4.6. (a) Inclusive photon spectrum from \u03a5(2S) de-\ncays in the region 0.27 < E\u2217\n\u03b3 < 0.80 GeV (Aubert, 2009l). The\nsolid line indicates the total \ufb01t to the data. (b) The same spec-\ntrum after the non-peaking background component has been\nsubtracted, with the \u03c7bJ(1P) (cyan), ISR (red), and \u03b7b (blue)\nsignal components from the \ufb01t indicated from left to right on\nthe plot.\nThis progress followed the discovery of the hb(nP) and\nZb states, which will be described in the following sec-\ntions, and allowed Belle to access the \u03b7b(1S) and \u03b7b(2S)\nstates via E1 transitions from the hb(nP) states. One\nkey development in Belle\u2019s ability to study these tran-\nsitions was the discovery that the hb(nP) production in\ne\u2212e\u2212collisions at the \u03a5(5S) resonance is essentially sat-\nurated by charged pion cascades through the Zb states,\nBy requiring that the single charged pion missing mass\nbe consistent with the mass of the Zb states, signi\ufb01cant\nimprovement in the signal to background ratio for the in-\nclusive Mmiss(\u03c0+\u03c0\u2212) \u2261Mrecoil(\u03c0+\u03c0\u2212) spectrum was re-\nalizable. Using the resulting cleaner hb(nP) signals and\nadding the observation of a photon, Belle was able to\nreport the \ufb01rst evidence for the \u03b7b(2S) produced in the\nhb(2P) \u2192\u03b7b(2S)\u03b3 transition and the \ufb01rst observation of\nthe hb(1P) \u2192\u03b7b(1S)\u03b3 and hb(2P) \u2192\u03b7b(1S)\u03b3 transitions\n(Mizuk, 2012). The \u03b7b(1S) samples obtained via this tran-\nsition chain enabled to improve the mass measurement\nwith respect to the one obtained via M1 transitions, and\nenabled the \u03b7b(1S) width to be measured for the \ufb01rst time.\nIn this analysis, Belle used a slightly larger data sam-\nple than was used in the two analyses which led to the\n\n491\n0\n2.5\n5\n7.5\n10\n0\n1\n2\n3\n8.8\n9\n9.2\n9.4\n9.6\n9.8\n0\n10\n20\n30\n9.7\n9.8\n9.9\n10\n10.1\n(a)\nhb(1P) yield, 103 / 10 MeV/c2\n(b)\nhb(2P) yield, 103 / 10 MeV/c2\n(c)\nM(n)\nmiss (\u03c0+\u03c0-\u03b3), GeV/c2\nhb(2P) yield, 103 / 10 MeV/c2\nFigure 18.4.7. The hb(1P) yield vs. M (1)\nmiss(\u03c0+\u03c0\u2212\u03b3) (a), and\nhb(2P) yield vs. M (2)\nmiss(\u03c0+\u03c0\u2212\u03b3) in the \u03b7b(1S) region (b) and in\nthe \u03b7b(2S) region (c). The solid (dashed) histogram presents\nthe \ufb01t result (background component of the \ufb01t function). From\n(Mizuk, 2012).\ndiscovery of the hb(nP) and of the Zb states, described in\nthe next sections: 121.4 fb\u22121 at the \u03a5(5S) resonance and\n12.0 fb\u22121 of energy-scan data collected nearby. A pair of\ncharged pions, selected according to the same criteria as\ndescribed by Adachi (2012a), and then subject to the re-\nquirement that the single charged pion missing mass sat-\nis\ufb01es the relation:\n10.59 GeV/c2 < Mrecoil(\u03c0\u00b1) < 10.67 GeV/c2.\n(18.4.9)\nThis cut resulted in a reduction of the combinatorial back-\nground by a factor of 5 [1.6] for the hb(1P) [hb(2P)] with-\nout any signi\ufb01cant loss of the signal.\nClusters in the electromagnetic calorimeter unassoci-\nated with any charged track and which could not be paired\nwith another photon in the event to form a \u03c00 were iden-\nti\ufb01ed as photon candidates. The missing mass against\n\u03c0+\u03c0\u2212\u03b3 was then used to form the variable M (n)\nmiss(\u03c0+\u03c0\u2212\u03b3) \u2261\nTable 18.4.2. Summary of the results on hb(1, 2P) \u2192\u03b7b\n(Mizuk, 2012).\nTransition\nhb(1P) \u2192\u03b7b(1S)\nhb(2P) \u2192\u03b7b(1S)\nYield\u00d710\u22123\n23.5 \u00b1 2.0\n10.3 \u00b1 1.3\nB \u00d7 102\n49.2 \u00b1 5.7 +5.6\n\u22123.3\n22.3 \u00b1 3.8 +3.1\n\u22123.3\nSigni\ufb01cance\n15\u03c3\n9\u03c3\nm\u03b7b(1S)(MeV/c2)\n9402.4 \u00b1 1.5 \u00b1 1.8\n(joint \ufb01t)\n\u2206mhf (MeV/c2)\n57.9 \u00b1 2.3\n(joint \ufb01t)\n\u0393(\u03b7b(1S)) (MeV)\n11+6\n\u22124\n(joint \ufb01t)\nTable 18.4.3. Summary of the results on hb(2P) \u2192\u03b7b(2S)\n(Mizuk, 2012).\nTransition\nhb(2P) \u2192\u03b7b(2S)\nYield\u00d710\u22123\n25.8 \u00b1 4.9\nB \u00d7 102\n49.2 \u00b1 5.7 +5.6\n\u22123.3\nSigni\ufb01cance\n4.2\u03c3\nm\u03b7b(2S)(MeV/c2)\n9999.0 \u00b1 3.5 +2.8\n\u22121.9\n\u2206mhf (MeV/c2)\n24.3+4.0\n\u22124.5\nMrecoil(\u03c0+\u03c0\u2212\u03b3)\u2212Mrecoil(\u03c0+\u03c0\u2212)+mhb(nP ), and the yield\nof hb(nP) radiative decays to \u03b7b(mS) was obtained by de-\ntermining the yield of hb(nP) as a function of M (n)\nmiss(\u03c0+\u03c0\u2212\u03b3).\nFits\nto\nthe\nMmiss(\u03c0+\u03c0\u2212)\nspectra\nfor\neach\nM (n)\nmiss(\u03c0+\u03c0\u2212\u03b3) bin were done using peak shapes for\nthe transitions observed in the inclusive study, keeping\nthe masses of the peaking components \ufb01xed at the values\ngiven in Table 18.4.5. The combinatorial background was\n\ufb01tted using a polynomial with parameters \ufb01xed to the\nvalues found in the overall \ufb01t, multiplied by a lower-order\npolynomial\nwith\n\ufb02oating\ncoe\ufb03cients.\nThe\nresulting\nhb(1P) and hb(2P) yields as a function of M (n)\nmiss(\u03c0+\u03c0\u2212\u03b3)\nare presented in Fig. 18.4.7. Clear peaks in M (n)\nmiss(\u03c0+\u03c0\u2212\u03b3)\nat 9.4 GeV/c2 and 10.0 GeV/c2 were identi\ufb01ed as signals\nfor the \u03b7b(1S) and \u03b7b(2S), respectively.\nThe branching fraction for these radiative transitions\nwas obtained by \ufb01tting the hb(nP) yield as a function of\nM (n)\nmiss(\u03c0+\u03c0\u2212\u03b3) to the sum of the \u03b7b(nS) signal compo-\nnents described by the convolution of a non-relativistic\nBreit-Wigner function with the resolution function and a\nbackground parameterized as ef(x), where f(x) is a \ufb01rst-\n[second-] order polynomial, in the \u03b7b(1S) [\u03b7b(2S)] region.\nThe two M (n)\nmiss(\u03c0+\u03c0\u2212\u03b3) spectra [from the hb(1P) and\nhb(2P)] with \u03b7b(1S) signals were \ufb01tted simultaneously. In\nthis \ufb01t, the width of the \u03b7b(1S) Breit-Wigner function was\na variable parameter; the width of the \u03b7b(2S) was \ufb01xed\nto a value obtained in perturbative calculations (Kwong,\nMackenzie, Rosenfeld, and Rosner, 1988):\n\u0393\u03b7b(2S) = \u0393\u03b7b(1S)\n\u0393 \u03a5 (2S)\nee\n\u0393 \u03a5 (1S)\nee\n= (4.9+2.7\n\u22121.9) MeV,\n(18.4.10)\n\n492\nwhere the uncertainty is due to the experimental un-\ncertainty in \u0393\u03b7b(1S). If the \u03b7b(2S) width was allowed to\n\ufb02oat in the \ufb01t, a value of \u0393\u03b7b(2S) = (4+12\n\u221220) MeV or\n\u0393\u03b7b(2S) < 24 MeV at 90% C.L. using the Feldman-Cousins\napproach (Feldman and Cousins, 1998) was obtained. Re-\nsults are given in Tables 18.4.2 and 18.4.3.\nSystematic uncertainties in the \u03b7b(nS) parameters were\nevaluated due to the background \ufb01t function choice, \ufb01t\nrange and binning choice, as well as signal shape and con-\ntributions from the experimental hb(nP) mass uncertain-\nties and photon energy resolution. The various contribu-\ntions in quadrature to estimate the total systematic un-\ncertainty.\nThe e\ufb03ciencies used to normalize the above radiative\ntransition yields were determined using a combination of\nMonte Carlo and data-driven studies (Mizuk, 2012)\n18.4.4.3 Observation of the hb(1P, 2P)\nBoth the BABAR and Belle Collaborations pursued searches\nfor the lowest P-wave spin-singlet state, the hb(1P) (Lees,\n2011c) (Adachi, 2012a). These searches and their results\nare described below.\nThe BABAR Collaboration searched for this state using\nthe experimentally favored transition, \u03a5(3S) \u2192\u03c00hb(1P),\nwith subsequent decay hb(1P) \u2192\u03b3\u03b7b(1S). This search\nleveraged the measurement of the \u03b7b mass to constrain the\nexpected energy of the photon. The invariant mass of the\nsystem recoiling against the \u03c00, Mrecoil(\u03c00) was then used\nto search for evidence of a resonance consistent with the\nhb. The distribution of Mrecoil(\u03c00) was binned, and in each\nbin a \ufb01t was performed to the \u03c00 mass spectrum to deter-\nmine the yield.This resulted in a Mrecoil(\u03c00) spectrum due\nonly to the recoil against real \u03c00 mesons. This distribution\nwas then modeled using a combination of a smooth com-\nbinatoric background and a peaking distribution resulting\nfrom resonance like the hb (Fig. 18.4.8). The \ufb01t to the\ndata determined that there was 3.3\u03c3 evidence for a reso-\nnance recoiling against the \u03c00. The mass of this resonance\nwas determined to be (9902\u00b14\u00b12) MeV/c2, which is con-\nsistent with the prediction of the hb mass from the spin-\nweighted average of the \u03c7bJ(1P) states. The product of the\nbranching fractions B(\u03a5(3S) \u2192\u03c00hb(1P)) \u00d7 B(hb(1P) \u2192\n\u03b3\u03b7b(1S)) was determined to be (4.3\u00b11.1(stat)\u00b10.9(syst))\u00d7\n10\u22124. This measurement established the \ufb01rst evidence for\nthe existence of the hb(1P) (Lees, 2011c).\nSoon thereafter, the Belle Collaboration announced\n\ufb01rst observations of both hb(1P) and its radial excita-\ntion hb(2P) in the reaction e+e\u2212\u2192hb(nP)\u03c0+\u03c0\u2212using\ntheir 121.4 fb\u22121 data sample collected at energies near the\n\u03a5(5S) resonance (Adachi, 2012a). Among the observations\nthat prompted this search in \u03a5(5S) data were two anoma-\nlous results in data taken above open \ufb02avor threshold in\nboth charmonium and bottomonium. First was the ob-\nservation by CLEO of the process e+e\u2212\u2192hc\u03c0+\u03c0\u2212at a\nrate comparable to that for e+e\u2212\u2192J/\u03c8\u03c0+\u03c0\u2212in data\ntaken above open charm threshold (Pedlar et al. (2011)).\nSuch a large rate was unexpected because the production\n2\n) GeV/c\n0\n\u03c0\n(\nrecoil\nm\n9.75\n9.8\n9.85\n9.9\n9.95\n10\n2\nEntries/6 MeV/c\n-2000\n-1000\n0\n1000\n2000\n3000\n4000\n2\n) GeV/c\n0\n\u03c0\n(\nrecoil\nm\n9.75\n9.8\n9.85\n9.9\n9.95\n10\n2\nEntries/6 MeV/c\n-2000\n-1000\n0\n1000\n2000\n3000\n4000\n(b)\nFigure 18.4.8. The \u03c00 recoil mass spectrum used by the\nBABAR Collaboration (Lees, 2011c) to search for \u03a5(3S) \u2192\n\u03c00hb(1P), shown after subtracting the smooth combinatoric\nbackground (black points). The green histogram represents the\nbest-\ufb01t value from modeling the data with a signal component.\nThe red-colored square points represent the hb signal region,\nand the blue-shaded area indicates the uncertainty in that re-\ngion due to the background.\nof hc requires a c-quark spin-\ufb02ip, while production of J/\u03c8\ndoes not. Secondly, Belle had previously observed anoma-\nlously high rates for e+e\u2212\u2192\u03a5(nS)\u03c0+\u03c0\u2212(n = 1, 2, 3) at\nenergies near the \u03a5(5S) mass (Chen, 2008b). These ob-\nservations motivated Belle to undertake a search for the\nhb(nP) states in data taken above open-bottom threshold\nat and near the \u03a5(5S) resonance.\nBelle undertook an inclusive search for the hb(nP)\nstates using the distribution of the mass recoiling against\n\u03c0+\u03c0\u2212, denoted Mmiss(\u03c0+\u03c0\u2212) in what follows. Rather than\nrelying upon Monte Carlo simulations to determine the\nshape of the Mmiss(\u03c0+\u03c0\u2212) spectrum for signal events,\nBelle used the \u03c0+\u03c0\u2212transitions between \u03a5(nS) states,\nreconstructed using \u00b5+\u00b5\u2212\u03c0+\u03c0\u2212combinations from well-\nreconstructed four-track events having positively identi-\n\ufb01ed \u00b5+\u00b5\u2212and \u03c0+\u03c0\u2212pairs. These \u00b5+\u00b5\u2212\u03c0+\u03c0\u2212events re-\nvealed peaks corresponding to transitions to (and among)\nthe three \u03a5(nS) states below open-\ufb02avor threshold, and\nmasses obtained for each of the \u03a5(nS) states were consis-\ntent within \u00b11 MeV/c2 with the world averages for those\nstates.\nThe search for the hb(nP) states was performed inclu-\nsively on hadronic events, wherein only \u03c0+\u03c0\u2212candidate\npairs were considered. The inclusive Mmiss(\u03c0+\u03c0\u2212) spec-\ntrum is dominated by combinatoric \u03c0+\u03c0\u2212pairs and also,\nin the region near Mmiss(\u03c0+\u03c0\u2212) = M(\u03a5(3S)) a step in-\ncrease in the \u03c0+\u03c0\u2212spectrum which occurs because of the\nopening up of the threshold for K0\nS production. This sec-\nond background shape was obtained by \ufb01tting the \u03c0+\u03c0\u2212\ninvariant mass corresponding to bins of Mmiss(\u03c0+\u03c0\u2212). The\n\ufb01t to the inclusive Mmiss(\u03c0+\u03c0\u2212) spectrum included a poly-\nnomial term for the combinatoric background, the K0\nS\nshape as just described, and signal shapes for each of\n\n493\nEvents / 5 MeV/c2\n0\n10000\n20000\n30000\n40000\n9.4\n9.6\n9.8\n10\n10.2\n10.4\n2\nMmiss (GeV/c ) \n\u03d2(3S)\u2192\u03d2(1S)\n\u03d2(2S)\u2192\u03d2(1S)\n\u03d2(1S)\n\u03d2(2S)\n\u03d2(3S)\n\u03d2(1D)\nh (2P)\nb\nh (1P)\nb\nFigure 18.4.9. The spectrum of recoil mass Mmiss \u2261Mrecoil(\u03c0+\u03c0\u2212), used by the Belle Collaboration (Adachi, 2012a) to search\nfor \u03a5(5S) \u2192\u03c0+\u03c0\u2212hb(nP), shown after subtracting the smooth combinatoric background (black points).\nthe peaks seen in the \u00b5+\u00b5\u2212\u03c0+\u03c0\u2212data as well as those\narising from \u03c0+\u03c0\u2212transitions to hb(nP) and \u03a5(1D). The\nMmiss(\u03c0+\u03c0\u2212) spectrum, after subtraction of both the com-\nbinatoric and K0\nS \u2192\u03c0+\u03c0\u2212contributions is shown with the\n\ufb01tted signal functions overlaid in Fig. 18.4.9. The yields\nand masses obtained in the \ufb01ts are listed in Table 18.4.4.\nTable 18.4.4. Yield and mass obtained in the \ufb01t (Adachi,\n2012a) to the inclusive Mmiss(\u03c0+\u03c0\u2212) distribution displayed in\nFig. 18.4.9. The \ufb01rst uncertainty is statistical, while the second,\nif present, is the sum of all systematic uncertainties.\nYield, 103\nMass, MeV/c2\n\u03a5(1S)\n105.0 \u00b1 5.8 \u00b1 3.0\n9459.4 \u00b1 0.5 \u00b1 1.0\nhb(1P)\n50.0 \u00b1 7.8+4.5\n\u22129.1\n9898.2+1.1\n\u22121.0\n+1.0\n\u22121.1\n3S \u21921S\n55 \u00b1 19\n9973.01\n\u03a5(2S)\n143.8 \u00b1 8.7 \u00b1 6.8\n10022.2 \u00b1 0.4 \u00b1 1.0\n\u03a5(1D)\n22.4 \u00b1 7.8\n10166.1 \u00b1 2.6\nhb(2P)\n84.0 \u00b1 6.8+23.\n\u221210.\n10259.8 \u00b1 0.6+1.4\n\u22121.0\n2S \u21921S\n151.3 \u00b1 9.7+9.0\n\u221220.\n10304.6 \u00b1 0.6 \u00b1 1.0\n\u03a5(3S)\n45.5 \u00b1 5.2 \u00b1 5.1\n10356.7 \u00b1 0.9 \u00b1 1.1\nSystematic uncertainties on the mass and yield of the\nhb(nP) states included contributions from the background\n\ufb01t polynomial order, range and bin size used in the \ufb01t,\nvariation of selection criteria, and the signal shapes used.\nBy far the most signi\ufb01cant source of uncertainty on the\nyield arose from the choice of signal shape - a relative un-\ncertainty of +9.0%\n\u221218.2% and +27%\n\u221212% on the hb(1P) and hb(2P)\nyields, respectively. The most signi\ufb01cant source of system-\natic uncertainty on the hb(nP) masses (\u00b11.0 MeV) is es-\ntimated from the di\ufb00erences between the \ufb01tted masses of\nthe known \u03a5(nS) states and the world average values. The\nsignal for the \u03a5(1D) is marginal (\u223c2.4\u03c3 statistical signif-\nicance) and therefore systematic uncertainties on its yield\nand mass were not evaluated.\nThe identity of the observed peaks as the hb(nP)\nstates is established as follows. The observed masses for\nthe hb(nP) are more than 3\u03c3 from the \u03c7b1(nP) states,\nand the JP C for the hb(nP) candidates can be inferred\nfrom two observations. The observation by Belle of the\nhb(nP) \u2192\u03b7b(1S)\u03b3 decays (Section 18.4.4.2) establishes\nthe C\u2212parity of the states as odd, while the \u03c7b1(nP)\nstates have even C\u2212parity. Similarly, angular analysis of\nthe \u03a5(5S) \u2192hb(1P)\u03c0+\u03c0\u2212transition (Adachi, 2011) is\nconsistent with the hb(1P) candidate having JP = 1+, as\nrequired for hb(1P) states.\nThe signi\ufb01cances of the hb(1P) and hb(2P) sig-\nnals,\nwith\nsystematic\nuncertainties\naccounted\nfor,\nwere, in this measurement, 5.5\u03c3 and 11.2\u03c3, respec-\ntively. The measured masses of hb(1P) and hb(2P),\nM\n= (9898.2+1.1\n\u22121.0\n+1.0\n\u22121.1) MeV/c2 and M\n= (10259.8 \u00b1\n0.6+1.4\n\u22121.0) MeV/c2, respectively, correspond to hyper\ufb01ne\nsplittings\nof\n\u2206MHF\n=\n(+1.7 \u00b1 1.5) MeV/c2\nand\n(+0.5+1.6\n\u22121.2) MeV/c2, respectively, where statistical and sys-\ntematic uncertainties are combined in quadrature. As ex-\npected, then, the hyper\ufb01ne splittings for both the 1P and\n2P levels are consistent with zero.\nThe ratios R \u2261\u03c3(hb(nP )\u03c0+\u03c0\u2212)\n\u03c3(\u03a5 (2S)\u03c0+\u03c0\u2212) were determined to be\nR = 0.45 \u00b1 0.08+0.07\n\u22120.12 for the hb(1P) and R = 0.77 \u00b1\n0.08+0.22\n\u22120.17 for the hb(2P). Thus \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212and\n\u03a5(5S) \u2192\u03a5(2S)\u03c0+\u03c0\u2212proceed at similar rates, despite the\nfact that the production of hb(nP) requires a spin-\ufb02ip of\na b quark. The measured rates for \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212\nare much larger than the upper limit for that of \u03a5(3S) \u2192\nhb(nP)\u03c0+\u03c0\u2212obtained by the BABAR Collaboration (Lees,\n2011l). This is consistent with the similarly anomalously\nhigh rates for \u03a5(5S) \u2192\u03a5(mS)\u03c0+\u03c0\u2212with m = 1, 2, 3.\n\n494\n1000\n1250\n1500\n1750\n2000\n2250\n0\n5\n10\n15\n20\n9.8\n9.9\n10\n10.1\n(a)\nEvents, 103 / 5 MeV/c2\n(b)\nMmiss(\u03c0+\u03c0-), GeV/c2\nEvents, 103 / 5 MeV/c2\n2400\n2600\n2800\n3000\n3200\n0\n10\n20\n10.1\n10.2\n10.3\n10.4\n(a)\nEvents, 103 / 5 MeV/c2\n(b)\nMmiss(\u03c0+\u03c0-), GeV/c2\nEvents, 103 / 5 MeV/c2\nFigure 18.4.10. The Mmiss(\u03c0+\u03c0\u2212) spectrum with the com-\nbinatorial background and K0\nS contribution subtracted (points\nwith errors) and signal component of the \ufb01t function over-\nlaid (smooth curve) in the hb(1P) (a) and hb(2P) (b) regions\n(Mizuk, 2012).\nSubsequent studies on this anomaly lead to the discovery\nof the charged Zb states, which will be described later\nin this chapter, and which mediate 100% of the \u03c0+\u03c0\u2212\ntransitions to the hb(nP) states. This observation allowed\na further reduction of the combinatorial background by a\nfactor of 5 [1.6] for the hb(1P) [hb(2P)], by imposing the\nrequirement:\n10.59 GeV/c2 < Mrecoil(\u03c0+\u03c0\u2212) < 10.67 GeV/c2\n(18.4.11)\non the mass recoiling against the single pion.\nThe\nMmiss(\u03c0+\u03c0\u2212)\nspectra\nin\nthe\nhb(1P)\nand\nhb(2P) regions, de\ufb01ned as 9.8 GeV/c2 \u221210.1 GeV/c2 and\n10.1 GeV/c2 \u221210.4 GeV/c2, are shown in Fig. 18.4.10. The\n\ufb01t procedure was essentially identical to that described\nbefore, using a \ufb01t function that is the sum of peaking\nTable 18.4.5. The yield and mass of peaking components from\nthe \ufb01ts to the Mmiss(\u03c0+\u03c0\u2212) (Mizuk, 2012). The \ufb01rst quoted\nuncertainty is statistical (unless stated otherwise) and the sec-\nond (if present) is systematic. Parameters without uncertain-\nties were \ufb01xed in the \ufb01t.\nN, 103\nMass, MeV/c2\n\u03a5(5S) \u2192hb(1P)\n70.3 \u00b1 3.3+1.9\n\u22120.7\n9899.1 \u00b1 0.4 \u00b1 1.0\n\u03a5(3S) \u2192\u03a5(1S)\n13 \u00b1 7\n9973.0\n\u03a5(5S) \u2192\u03a5(2S)\n61.3 \u00b1 4.1\n10021.3 \u00b1 0.5\n\u03a5(5S) \u2192\u03a5(1D)\n14 \u00b1 7\n10169 \u00b1 3\n\u03a5(5S) \u2192hb(2P)\n89.5 \u00b1 6.1+0.0\n\u22125.8\n10259.8 \u00b1 0.5 \u00b1 1.1\n\u03a5(2S) \u2192\u03a5(1S)\n97 \u00b1 12\n10305.6 \u00b1 1.2\n\u03a5(5S) \u2192\u03a5(3S)\n58 \u00b1 8\n10357.7 \u00b1 1.0\ncomponents, a background shape due to the threshold for\nK0\nS production, and a combinatorial background. The re-\nsulting masses and yields are listed in Table 18.4.5.\nSystematic uncertainties in the hb(nP) parameters\narise from the \ufb01tting procedure, including polynomial\norder,\n\ufb01t\ninterval\nand\nsignal\nshape.\nAn\nadditional\n\u00b11 MeV/c2 uncertainty in the mass measurements is\nadded, based on the observed deviations of the masses ob-\ntained for previously known vector bottomonium states,\nas in Adachi (2012a).\nThese updated mass measurements correspond to hy-\nper\ufb01ne splittings of \u2206MHF(1P) = (+0.8 \u00b1 1.1) MeV/c2\nand \u2206MHF(2P) = (+0.5 \u00b1 1.2) MeV/c2, where statistical\nand systematic uncertainties in mass are added in quadra-\nture.\n18.4.4.4 \u03a5(1D)\nThe existence of the bottomonium D-wave states has been\nestablished. The CLEO Collaboration reported observa-\ntion of the D-wave triplet bottomonium state, \u03a5(1 3DJ),\nwhere J = 1, 2, 3 (Bonvicini et al., 2004). They report\nobservation of a single member of the triplet, \u03a5(1 3D2),\nusing the decay \u03a5(1 3D2) \u2192\u03b3\u03b3\u03a5(1S). They identify the\nstate in their analysis as corresponding to the \u03a5(1 3D2)\nbased on the fact that the mass and branching fractions\nin question correspond well to the theoretical preductions;\nhowever, they were not able to experimentally verify the\nassignment of quantum numbers L and J.\nThe BABAR Collaboration reported in 2010 the ob-\nservation of the J = 2 state of the \u03a5(1 3DJ) triplet us-\ning instead the hadronic decay transition \u03a5(1 3D2) \u2192\n\u03c0+\u03c0\u2212\u03a5(1S), with subsequent leptonic decay of the \u03a5(1S)\nstate, \u03a5(1S) \u2192\u2113+\u2113\u2212(where \u2113= e, \u00b5) (del Amo San-\nchez, 2010k). The analysis was performed using a sample\nof (121.8 \u00b1 1.2) \u00d7 106 \u03a5(3S) mesons. The parent \u03a5(3S)\nwas then subsequently observed to decay to the D-wave\nstate via a two-photon radiative transition, \u03a5(3S) \u2192\n\u03b3\u03b3\u03a5(1 3DJ). An intermediate \u03c7bJ\u2032(2P) state is produced\nbetween the radiation of the \ufb01rst and second photon,\nwhere J\u2032 = 0, 1, 2. The presence of these intermediate res-\nonances implies a pattern of energies that one can use in\n\n495\n)\n2\n mass (GeV/c\n-l\n+l-\u03c0\n+\n\u03c0\n10.15\n10.2\n10.25\n )\n2\nEvents / ( 0.0025 GeV/c\n0\n10\n20\n)\n2\n mass (GeV/c\n-l\n+l-\u03c0\n+\n\u03c0\n10.15\n10.2\n10.25\n )\n2\nEvents / ( 0.0025 GeV/c\n0\n10\n20\nData\nFit\n)\nJ\n(13D\n\u03d2\nSignal \n(1S)\n\u03d2\n\u03c9\n\u03b3\n\u2192\n(2P )\nb\nJ'\n\u03c7\n\u03b3\n(1S)\n\u03d2\n-\u03c0\n+\n\u03c0\n(1S)\n\u03d2\n\u03b7\n(2S)\n\u03d2\n)\n0\n\u03c0\n0\n\u03c0\n(\u03b3\n\u03b3\nFigure 18.4.11. The mass spectrum of the \u03a5(1 3DJ) candi-\ndates, and the unbinned maximum likelihood \ufb01t to the spec-\ntrum. Background peaks from several sources are evident in\nthe spectrum and modeled in the \ufb01t. A clear signal from the\nD-wave triplet is also evident (del Amo Sanchez, 2010k).\nthe search to reject background and identify candidates\nfor the signal processes in question.\nEvents are required to contain exactly four good\ncharged tracks. Two of the tracks must be identi\ufb01ed as\nsame-\ufb02avor, opposite-charge leptons. The pion candidates\nare taken to be the remaining two tracks and must fail an\nelectron requirement. Radiative Bhabha events, a back-\nground to this event topology, are rejected by requiring\nthat the electron satisfy a laboratory polar angle require-\nment, cos(\u03b8) < 0.8.\nThe \u03a5(1S) candidate is selected by making \ufb02avor-\ndependent mass requirements on the lepton pairs: \u22120.35 <\nme+e\u2212\u2212m\u03a5 (1S)) < 0.2 GeV/c2 or |m\u00b5+\u00b5\u2212\u2212m\u03a5 (1S))| <\n0.2 GeV/c2. The mass of the dilepton pair is then con-\nstrained to the nominal \u03a5(1S) mass. The pions can be\nfaked by a photon conversion in material. To reject this\nbackground, the opening angle between the pions must\nsatisfy cos \u03b8\u03c0+\u03c0\u2212< 0.95 if m\u03c0+\u03c0\u2212< 0.050 GeV/c2; for any\ndipion mass, the angle between the dipion system and ei-\nther of the leptons must satisfy cos \u03b8\u03c0+\u03c0\u2212,\u2113\u00b1 < 0.98.\nThe events are also required to contain at least two\nphotons, with minimum energy requirements (one with\nCM energy > 0.070 GeV and the other with CM energy\n> 0.060 GeV) consistent with the typical energies expected\nfrom the transition photons. Final-state radiation photons\nare rejected by requiring that cos \u03b8\u03b3,\u2113< 0.98. If there is\nmore than one photon pair combination that satis\ufb01es these\nrequirements, the pair whose energies minimize a \u03c72 con-\nstructed from the measured and expected photon energies\nis chosen as the best pair.\nThe \u03a5(1 3DJ) candidate is combined with the photon\npair to form the \u03a5(3S) candidate, whose momentum must\nbe < 0.3 GeV/c. The \u03a5(3S) candidate mass is then con-\nstrained to the nominal mass value.\nAn extended unbinned maximum likelihood \ufb01t is then\nperformed on the mass of the \u03c0+\u03c0\u2212\u2113+\u2113\u2212system (Fig.\n18.4.11). The \ufb01t includes components for several expected\nbackgrounds, which were studied using MC simulation:\n\u03a5(3S) decays to \u03b3\u03c7b(2PJ\u2032) \u2192\u03b3\u03c9\u03a5(1S), \u03c0+\u03c0\u2212\u03a5(1S),\n)\n2\n masss (GeV/c\n-\u03c0\n+\n\u03c0\n0.4\n0.6\n)\n2\nEvents / (60 MeV/c\n0\n20\n40\nData\n(a)\nD state\nS state\n state\n1\n1P\nFigure\n18.4.12.\nThe\ndipion\nmass\nspectrum\nfor\nthe\nbackground-subtracted\ndata\nin\nthe\nregion\n10.155\n<\nm\u03c0+\u03c0\u2212\u2113+\u2113\u2212< 10.68 GeV/c2. The shapes expected from S-\nwave, D-wave, and 1P1 states are shown (del Amo Sanchez,\n2010k).\n\u03b7\u03a5(1S), and \u03b3\u03b3(\u03c00\u03c00)\u03a5(2S). The models for these and\nsignal are obtained from MC simulation. A clear excess\nexists in the region where \u03a5(1 3DJ), and is \ufb01tted with the\nsignal model.\nLarge data control samples of dipion transitions to\n\u03a5(1S) and \u03a5(2S) \ufb01nal states, directly from the parent\n\u03a5(3S), are used to validate the p.d.f.s used in the \ufb01t to\nthe spectrum. Where shifts are present between the p.d.f.\nparameters determined from MC or data, the shifts are\napplied as corrections. Only a small shift in the recon-\nstructed mass of the \u03a5(2S) is observed.\nThe yield of D-wave triplet states is as follows (deter-\nmined from the \ufb01t to the data): 10.6+5.7\n\u22124.9 \u03a5(1 3D1), 33.9+8.2\n\u22127.5\n\u03a5(1 3D2), and 9.4+6.2\n\u22125.2 \u03a5(1 3D1). Fit biases for the yield of\nsignal events are determined by applying the data model\nto 2000 data-sized MC samples with events randomly drawn\nfrom the simulation subsamples. The biases are found to\ntypically be at the level of 1-2 events in the signal region,\nand these biases are subtracted from the signal yields.\nMultiplicative systematic uncertainties arise from var-\nious sources, with the largest of them being the photon\nreconstruction e\ufb03ciency (3.0%) and particle identi\ufb01cation\n(2.0%). Additive systematic uncertainties arise from the\np.d.f. shapes, and total 1.5-2.0 events in the signal yields.\nThe statistical signi\ufb01cance of the signal yield for the\nJ = 2 D-wave triplet state is 6.5\u03c3 (5.8\u03c3) including statis-\ntical (statistical and systematic) uncertainties.\nThe quantum numbers of the state are determined by\nstudying the \u03c0+\u03c0\u2212mass distribution after subtracting\nthe backgrounds in the region 10.155 < m\u03c0+\u03c0\u2212\u2113+\u2113\u2212<\n10.68 GeV/c2. The dipion mass distribution is shown in\nFig. 18.4.12, compared to the shapes expected from an S-\n\n496\nwave, D-wave, and 1P1 state. The data are observed to be\nmost consistent with the D-wave hypothesis.\n18.4.5 Discovery of charged Zb states\nIn an e\ufb00ort to explain the large rate of dipion transitions\nto \u03a5(nS) and hb(nP) states in e+e\u2212annihilation at en-\nergies near \u03a5(5S), which suggest that exotic mechanisms\ncontribute to \u03a5(5S) decays, Belle searched for evidence\nof resonant substructures in these decays (Bondar, 2012).\nFor the analysis of \u03c0+\u03c0\u2212transitions to \u03a5(nS) states, the\n\u03a5(nS) states were observed in their \u00b5+\u00b5\u2212decays, which\nled to a relatively background-free sample for investiga-\ntion. Transitions to hb(nP) states were investigated inclu-\nsively by examining only the \u03c0+\u03c0\u2212transition pairs.\n\u03a5(nS) samples were obtained using four-track events,\npositively identi\ufb01ed as a \u03c0+\u03c0\u2212and \u00b5+\u00b5\u2212pair, subject\nto the requirement that |Mmiss(\u03c0+\u03c0\u2212) \u2212M(\u00b5+\u00b5\u2212)| <\n0.2 GeV/c2, where Mmiss(\u03c0+\u03c0\u2212) is the missing mass recoil-\ning against the \u03c0+\u03c0\u2212system, and that |Mmiss(\u03c0+\u03c0\u2212) \u2212\nm\u03a5 (nS)| < 0.05 GeV/c2. Sideband regions for the study of\nbackground were de\ufb01ned as 0.05 GeV/c2 < |Mmiss(\u03c0+\u03c0\u2212)\u2212\nm\u03a5 (nS)| < 0.10 GeV/c2. The hb(nP) samples utilized events\nin which only the \u03c0+\u03c0\u2212system was selected.\nAmplitude analysis of the three-body \u03a5(5S)\n\u2192\n\u03a5(nS)\u03c0+\u03c0\u2212employed unbinned maximum likelihood \ufb01ts\nto the two-dimensional M 2[\u03a5(nS)\u03c0+] vs. M 2[\u03a5(nS)\u03c0\u2212]\nDalitz distributions. Signal events were found to make up\nmore than 90% of the events in the signal region, and\nthe e\ufb03ciency-corrected distribution of background events\n(from \u03a5(nS) sidebands) was found to be featureless across\nthe Dalitz plot. As an example, the Dalitz distributions\nof events in the \u03a5(2S) sidebands and signal regions are\nshown in Fig. 18.4.13 where, for ease of visualization, the\nsquare of the larger of the two \u03a5(nS)\u03c0 masses is plotted vs.\nthe square of the dipion invariant mass. One-dimensional\ninvariant mass projections for events in each \u03a5(nS) sig-\nnal region are shown in Fig. 18.4.14, where two peaks\nare observed in the \u03a5(nS)\u03c0 system near 10.61 GeV/c2\nand 10.65 GeV/c2, and are subsequently referred to as\nZb(10610) and Zb(10650), respectively.\nThe parameterization of the \u03a5(5S) \u2192\u03a5(nS)\u03c0+\u03c0\u2212\nthree-body decay amplitude includes terms correspond-\ning to the Zb states as well as f0(980), f2(1270) and a\nnon-resonant contribution:\nM = AZ1 + AZ2 + Af0 + Af2 + Anr.\n(18.4.12)\nIn performing the \ufb01t, it was assumed that the dominant\ncontributions come from amplitudes that preserve the ori-\nentation of the spin of the heavy quarkonium state and,\nthus, both pions in the cascade decay \u03a5(5S) \u2192Zb\u03c0 \u2192\n\u03a5(nS)\u03c0+\u03c0\u2212are emitted in an S-wave with respect to the\nheavy quarkonium system. Subsequent angular studies, as\noutlined in Bondar (2012), support this assumption.\nThe Zb(10610) and Zb(10650) peaks were parameter-\nized with an S-wave Breit-Wigner function, and, to allow\nfor the \u03a5(5S) decay to both Z+\nb \u03c0\u2212and Z\u2212\nb \u03c0+, the ampli-\ntudes AZ1 and AZ2 were symmetrized with respect to \u03c0+\n108\n110\n112\n114\n116\n0\n0.2\n0.4\n0.6\n0.8\nM2(\u03c0+\u03c0-), GeV2/c4\nM2(Y(2S)\u03c0)max, GeV2/c4\n(b)\n108\n110\n112\n114\n116\n0\n0.2\n0.4\n0.6\n0.8\nM2(\u03c0+\u03c0-), GeV2/c4\nM2(Y(2S)\u03c0)max, GeV2/c4\n(b)\nFigure 18.4.13. Dalitz plots for \u03a5(2S)\u03c0+\u03c0\u2212events in the\n\u03a5(2S) sidebands (upper); \u03a5(2S) signal region (lower). Events\nto the left of the vertical line are excluded. From (Bondar,\n2012).\nand \u03c0\u2212transposition:\nAZk = aZkei\u03b4Zk (BW(s1, Mk, \u0393k) + BW(s2, Mk, \u0393k)),\n(18.4.13)\nwhere s1 = M 2[\u03a5(nS)\u03c0+], s2 = M 2[\u03a5(nS)\u03c0\u2212]. Results of\nthe \ufb01ts to \u03a5(5S) \u2192\u03a5(nS)\u03c0+\u03c0\u2212signal events are shown\nin Fig. 18.4.14, and numerical results are summarized in\nTable 18.4.6, where the relative normalization is de\ufb01ned as\nthe ratio of amplitudes aZ2/aZ1 and the relative phase as\n\u03b4Z2 \u2212\u03b4Z1. The systematic uncertainties on the parameters\nin Table 18.4.6 includes all evaluated sources - the greatest\nof which is related to the parameterization of the decay\namplitude, and was studied by \ufb01tting the data with several\nmodi\ufb01cations of the nominal model (Eq. 18.4.12).\nFor the study of \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212resonant sub-\nstructure (which is naturally a much more background-\ndominated study given the inclusive nature of the \u03c0+\u03c0\u2212\n\n497\n0\n20\n40\n60\n80\n10.1\n10.2\n10.3\n10.4\n10.5\n10.6\n10.7\n10.8\nM(Y(1S)\u03c0)max, (GeV/c2)\n(Events/10 MeV)\n(a)\n0\n20\n40\n60\n80\n100\n0.3\n0.5\n0.7\n0.9\n1.1\n1.3\n1.5\nM(\u03c0+\u03c0-), (GeV/c2)\n(Events/20 MeV)\n(b)\n0\n20\n40\n60\n80\n10.4\n10.45\n10.5\n10.55\n10.6\n10.65\n10.7\n10.75\nM(Y(2S)\u03c0)max, (GeV)\n(Events/5 MeV)\n0\n20\n40\n60\n80\n100\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\nM(\u03c0+\u03c0-), (GeV)\n(Events/5 MeV)\n0\n20\n40\n60\n80\n100\n120\n10.58 10.6 10.62 10.64 10.66 10.68 10.7 10.72 10.74\nM(Y(3S)\u03c0)max, (GeV/c2)\n(Events/4 MeV/c2)\n(a)\n0\n10\n20\n30\n40\n50\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\nM(\u03c0+\u03c0-), (GeV/c2)\n(Events/5 MeV/c2)\n(b)\nFigure 18.4.14. Comparison of \ufb01t results (open histogram)\nwith experimental data (points with error bars) for events in\nthe \u03a5(1S) (upper), \u03a5(2S) (middle), and \u03a5(3S) (lower) signal\nregions. The hatched histogram shows the background compo-\nnent. From (Bondar, 2012).\ndetection) the yield of Zb states contributing to hb(nP)\nproduction is measured as a function of the hb(1P)\u03c0\u00b1 in-\nvariant mass by \ufb01tting the Mmiss(\u03c0+\u03c0\u2212) spectra in bins\nof Mmiss(\u03c0\u2213), the mass recoiling against \u03c0\u2213(which is\nequivalent to the hb(1P)\u03c0\u00b1 invariant mass). The yields\nof \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212(n = 1, 2) decays as a func-\ntion of the Mrecoil(\u03c0) (both signs of \u03c0 are included) are\nshown in Fig. 18.4.15. The distributions for the hb(nP)\nexhibit a clear two-peak structure without a signi\ufb01cant\nnon-resonant contribution. To \ufb01t the Mrecoil(\u03c0) distribu-\ntions for Zb yields, a combination of P-wave Breit-Wigner\namplitudes is used:\n|BW1(s, M1, \u03931) + aei\u03c6BW1(s, M2, \u03932) + bei\u03c8|2 qp\n\u221as.\n(18.4.14)\nwhere \u221as \u2261Mrecoil(\u03c0); the variables Mk, \u0393k (k = 1, 2),\na, \u03c6, b and \u03c8 are free parameters;\nqp\n\u221as is a phase-space\nfactor, where p (q) is the momentum of the pion origi-\nnating from the \u03a5(5S) (Zb) decay measured in the rest\nframe of the corresponding mother particle. The P-wave\nBreit-Wigner amplitude is expressed as BW1(s, M, \u0393) =\n\u221a\nM \u0393 F (q/q0)\nM 2\u2212s\u2212iM \u0393 . Here F- is the P-wave Blatt-Weisskopf form\nfactor F =\nq\n1+(q0R)2\n1+(qR)2 , q0 is a daughter momentum cal-\nculated with pole mass of its mother, R = 1.6 GeV\u22121.\nMM(\u03c0), GeV/c2\nEvents / 10 MeV/c2\n-2000\n0\n2000\n4000\n6000\n8000\n10000\n12000\n10.4\n10.5\n10.6\n10.7\nMM(\u03c0), GeV/c2\nEvents / 10 MeV/c2\n0\n2500\n5000\n7500\n10000\n12500\n15000\n17500\n10.4\n10.5\n10.6\n10.7\nFigure 18.4.15. The (a) hb(1P) and (b) hb(2P) yields as a\nfunction of Mrecoil(\u03c0) (points with error bars) and results of\nthe \ufb01t (histogram). From (Bondar, 2012).\nThe function (Eq. 18.4.14) is convolved with the detec-\ntor resolution function (\u03c3 = 5.2 MeV/c2), integrated over\nthe 10 MeV/c2 histogram bin and corrected for the recon-\nstruction e\ufb03ciency. The \ufb01t results are shown as solid his-\ntograms in Fig. 18.4.15 and the numerical results are sum-\nmarized in Table 18.4.6. The non-resonant contribution to\nhb(nP) production is consistent with zero [signi\ufb01cance is\n0.3 \u03c3 both for the hb(1P) and hb(2P)], while the default \ufb01t\nhypothesis is favored over the phase-space \ufb01t hypothesis\nat the 18 \u03c3 [6.7 \u03c3] level for the hb(1P) [hb(2P)].\nSystematic uncertainies were studied by evaluating con-\ntributions from the background function used in \ufb01ts to\nthe Mmiss(\u03c0+\u03c0\u2212) spectra, e\ufb00ects of \ufb01nite bin size in the\n\ufb01ts, model uncertainties, and data-MC comparisons. An\nadditional 1 MeV/c2 uncertainty in mass measurements\nwas applied, as in the previous analysis, based on the dif-\nference between the observed \u03a5(nS) peak positions and\ntheir world averages (Adachi, 2012a). The total system-\natic uncertainty presented in Table 18.4.6 is the sum in\nquadrature of contributions from all sources. After inclu-\nsion of systematic uncertainties, the signi\ufb01cance of the\nZb(10610) and Zb(10650) including systematic uncertain-\nties was 16.0 \u03c3 [5.6 \u03c3] for the hb(1P) [hb(2P)].\nThe\ntwo\ncharged\nbottomonium-like\nresonances\nZb(10610)\nand\nZb(10650)\nare\nhence\n\ufb01rmly\nestab-\nlished with signals in \ufb01ve di\ufb00erent decay channels,\n\u03a5(nS)\u03c0\u00b1 (n\n=\n1, 2, 3) and hb(nP)\u03c0\u00b1 (m\n=\n1, 2).\nThe\nweighted\naverages\nover\nall\n\ufb01ve\nchannels\ngive\nM\n=\n10607.2 \u00b1 2.0 MeV/c2, \u0393\n=\n18.4 \u00b1 2.4 MeV\nfor the Zb(10610) and M\n=\n10652.2 \u00b1 1.5 MeV/c2,\n\u0393 = 11.5 \u00b1 2.2 MeV for the Zb(10650), where statistical\nand systematic errors are added in quadrature. The\nZb(10610) production rate is similar to that of the\nZb(10650) for each of the \ufb01ve decay channels. Their\nrelative phase is consistent with zero for the \ufb01nal states\nwith the \u03a5(nS) and consistent with 180 degrees for the\n\ufb01nal states with hb(nP). Production of the Zb\u2019s saturates\nthe \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212transitions and accounts for\nthe high inclusive hb(mS) production rate reported in\nAdachi (2012a). Analyses of charged pion angular distri-\nbutions (Bondar, 2012) favor the JP = 1+ spin-parity\nassignment for both the Zb(10610) and Zb(10650). Since\nthe \u03a5(5S) has negative G-parity, the Zb states have\npositive G-parity due to the emission of the pion.\n\n498\nTable 18.4.6. Comparison of results on Zb(10610) and Zb(10650) parameters obtained from \u03a5(5S) \u2192\u03a5(nS)\u03c0+\u03c0\u2212(n = 1, 2, 3)\nand \u03a5(5S) \u2192hb(nP)\u03c0+\u03c0\u2212(m = 1, 2) analyses (Bondar, 2012).\nFinal state\n\u03a5(1S)\u03c0+\u03c0\u2212\n\u03a5(2S)\u03c0+\u03c0\u2212\n\u03a5(3S)\u03c0+\u03c0\u2212\nhb(1P)\u03c0+\u03c0\u2212\nhb(2P)\u03c0+\u03c0\u2212\nM[Zb(10610)], MeV/c2\n10611 \u00b1 4 \u00b1 3\n10609 \u00b1 2 \u00b1 3\n10608 \u00b1 2 \u00b1 3\n10605 \u00b1 2+3\n\u22121\n10599+6+5\n\u22123\u22124\n\u0393[Zb(10610)], MeV\n22.3 \u00b1 7.7+3.0\n\u22124.0\n24.2 \u00b1 3.1+2.0\n\u22123.0\n17.6 \u00b1 3.0 \u00b1 3.0\n11.4 +4.5+2.1\n\u22123.9\u22121.2\n13 +10+9\n\u22128\u22127\nM[Zb(10650)], MeV/c2\n10657 \u00b1 6 \u00b1 3\n10651 \u00b1 2 \u00b1 3\n10652 \u00b1 1 \u00b1 2\n10654 \u00b1 3 +1\n\u22122\n10651+2+3\n\u22123\u22122\n\u0393[Zb(10650)], MeV\n16.3 \u00b1 9.8+6.0\n\u22122.0\n13.3 \u00b1 3.3+4.0\n\u22123.0\n8.4 \u00b1 2.0 \u00b1 2.0\n20.9 +5.4+2.1\n\u22124.7\u22125.7\n19 \u00b1 7 +11\n\u22127\nRel. normalization\n0.57 \u00b1 0.21+0.19\n\u22120.04\n0.86 \u00b1 0.11+0.04\n\u22120.10\n0.96 \u00b1 0.14+0.08\n\u22120.05\n1.39 \u00b1 0.37+0.05\n\u22120.15\n1.6+0.6+0.4\n\u22120.4\u22120.6\nRel. phase, degrees\n58 \u00b1 43+4\n\u22129\n\u221213 \u00b1 13+17\n\u22128\n\u22129 \u00b1 19+11\n\u221226\n187+44+3\n\u221257\u221212\n181+65+74\n\u2212105\u2212109\nThe minimal quark content of the Zb(10610) and\nZb(10650) is a four-quark combination. The masses of\nthese new states are a few MeV/c2 above the thresholds\nfor the open beauty channels B\u2217B (10604.6 MeV/c2) and\nB\u2217B\n\u2217\n(10650.2 MeV/c2), which suggests a \u201cmolecular\u201d nature of\nthese new states, which might explain most of their ob-\nserved properties (Bondar, Garmash, Milstein, Mizuk, and\nVoloshin, 2011), although other possible interpretations\nhave also been o\ufb00ered (Bugg, 2011; Cui, Liu, and Huang,\n2012; Danilkin, Orlovsky, and Simonov, 2012; Guo, Cao,\nZhou, and Chen, 2011).\n18.4.6 Transitions and decays\n18.4.6.1 Introduction to transitions and decays\nMeasuring the transitions between bottomonium states,\nindependent of trying to discover new states, also pro-\nvides important information for theoretical predictions of\nheavy quarkonium systems. These transitions can be pre-\ndicted by e\ufb00ective potential models, and for existing mea-\nsurements of transitions in the bottomonium system the\ndata appeared well described (cf. Brambilla et al., 2004;\nEichten, Godfrey, Mahlke, and Rosner, 2008). At lead-\ning order, the dominant radiative decays (those involving\nemission of a photon) are expected to be electric (E1) or\nmagnetic (M1) transitions. If the bottomonium system is\ntreated as a non-relativistic bound state, the predictions\nare relatively straight-forward and well-characterized. The\npicture is complicated, however, in transitions such as\n\u03a5(nS) \u2192\u03b3\u03b7b(mS), where n > m, which are referred to as\n\u201chindered\u201d M1 transitions between the S-wave bottomo-\nnium states. In the case of \u03a5(3S) \u2192\u03b3\u03c7bJ(1P), there is\nan overlap between the wave functions of the initial state\nand the \ufb01nal state; this makes the calculation of such tran-\nsitions more complex. One experimental goal in measur-\ning such transitions is to improve our understanding of\nthe non-relativistic e\ufb00ects in heavy quarkonium systems,\nwhich should in turn inform and improve the theoretical\ncalculations.\nCharmonium spectroscopy is a \ufb01eld revived after the\noperation of the two B Factories. States with JP C = 1\u2212\u2212\nmay be studied using ISR in the large \u03a5(4S) data samples.\nFor a study of charge-parity-even charmonium states, ra-\ndiative decays of the \u03a5 states below open-bottom thresh-\nold may be used.\nThe production rates of the lowest-lying P-wave spin-\ntriplet (\u03c7cJ, J=0, 1, or 2) and S-wave spin-singlet (\u03b7c)\nstates in \u03a5(1S) radiative decays are calculated (Gao, Zhang,\nand Chao, 2007), where the former is at the part per mil-\nlion level, and the latter is about 5 \u00d7 10\u22125. The rates in\n\u03a5(2S) decays are estimated to be at the same level.\nWe know that the OZI-suppressed decays of J/\u03c8 and\n\u03c8(2S) to hadrons occur by annihilation of the charm\nquarks into three gluons or a photon. In either case, pQCD\npredicts (Appelquist and Politzer, 1975; De Rujula and\nGlashow, 1975)\nQ\u03c8 = B\u03c8(2S)\u2192h\nBJ/\u03c8\u2192h\n= B\u03c8(2S)\u2192e+e\u2212\nBJ/\u03c8\u2192e+e\u2212\n\u224812% .(18.4.15)\nThis relation is referred to as the \u201c12% rule\u201d which is\nexpected to hold to a reasonably good degree for both\ninclusive and exclusive decays. But the measured exper-\nimental data do not follow this rule. The prediction by\nEq. 18.4.15 is severely violated in the \u03c1\u03c0 and several other\ndecay channels. This is the so-called \u201c\u03c1\u03c0 puzzle\u201d. It was\n\ufb01rst observed by Mark-II Collaboration in 1983 (Franklin\net al., 1983). From then on many experimental studies and\ntheoretical explanations have been put forth to decipher\nthis puzzle (Mo, Yuan, and Wang, 2006).\nAs this so-called \u201c12% rule\u201d in \u03c8 decays is derived\nfrom the pQCD and potential models, it is expected to be\nvalid for the bottomonium family, namely, the \u03a5s. Since\nthere are three narrow \u03a5 states below the bottom meson\nthreshold, we expect, using PDG average values of the\nbranching fractions:\nQ21 = B\u03a5 (2S)\u2192h\nB\u03a5 (1S)\u2192h\n= B\u03a5 (2S)\u2192e+e\u2212\nB\u03a5 (1S)\u2192e+e\u2212= 0.77 \u00b1 0.07,\nQ31 = B\u03a5 (3S)\u2192h\nB\u03a5 (1S)\u2192h\n= B\u03a5 (3S)\u2192e+e\u2212\nB\u03a5 (1S)\u2192e+e\u2212= 0.88 \u00b1 0.09,\nQ32 = B\u03a5 (3S)\u2192h\nB\u03a5 (2S)\u2192h\n= B\u03a5 (3S)\u2192e+e\u2212\nB\u03a5 (2S)\u2192e+e\u2212= 1.14 \u00b1 0.15.\n(18.4.16)\nThese \u201cpQCD rules\u201d should hold better than the 12% rule\nin \u03c8 decays, since the bottomonium states have higher\n\n499\n (GeV)\n*\n\u03b3\nE\n0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8\nEvents / (2 MeV)\n0\n500\n1000\n1500\n2000\n(b)\n(1P)\nb0\n\u03c7\n(1P)\nb1\n\u03c7\n(1P)\nb2\n\u03c7\nISR\n(1S)\nb\n\u03b7\n (GeV)\n*\n\u03b3\nE\n0.5\n0.55\n0.6\n0.65\n0.7\nEvents/(4 MeV)\n-300\n-200\n-100\n0\n100\n200\n300\nISR\n(1S)\nb\n\u03b7\nFigure 18.4.16. The converted-photon energy spectrum, after\nsubtracting the smooth background (Lees, 2011m). These data\nwere taken at the \u03a5(2S) resonance.\nmasses, and pQCD and the potential models should work\nbetter, as has been the case for calculations of the bot-\ntomonium spectrum.\n18.4.6.2 Radiative transitions between bottomonium states\nThe radiative transitions between \u03a5 and \u03c7bJ states were a\nbackground to the discovery of the bottomonium ground\nstate (c.f. Section 18.4.4.2). These transition rates are gen-\nerally precisely predicted (Section 18.1); however, more\nprecise experimental measurements were needed to deter-\nmine the accuracy of the methods used to make those\npredictions. The method used to discover the \u03b7b used pho-\ntons reconstructed using only the BABAR electromagnetic\ncalorimeter. The resolution of the \u03c7bJ transitions is lim-\nited by the energy resolution of the calorimeter, which was\ninsu\ufb03cient to convincingly separate the transitions to and\nfrom the three \u03c7bJ states.\nFor the BABAR Collaboration measurement discussed\nin this section, photon transitions were reconstructed us-\ning photons that had converted in material. This results\nin a much-improved photon energy resolution, reducing\nit from 25 MeV using calorimeter-only photons to 5 MeV\nusing converted photons. The improved resolution allows\nfor the separation of many radiative transitions. The pho-\nton energy spectrum was analyzed (Lees, 2011m) using\ndata taken at the \u03a5(3S) in three di\ufb00erent energy regions:\nE\u2217= [180, 300] MeV, [300, 600] MeV, and [600, 1100] MeV.\nThis was done so that regions expected to contain di\ufb00er-\nent kinds of transitions could be separately studied. The\ndata taken at the \u03a5(2S) resonance was analyzed in a sin-\ngle bin, E\u2217= [300, 800] MeV. Besides studying prominent\ntransitions, a goal of this approach was to \u201cre-discover\u201d\nthe \u03b7b and make an additional measurement of its using\nan independent technique.\nThe primary background in these measurements arises\ndue to using a randomly chosen converted photon as the\ncandidate photon from a bottomonium transition. This\n (GeV)\n*\n\u03b3\nE\n0.18\n0.2\n0.22\n0.24\n0.26\n0.28\n0.3\nEvents / (2 MeV)\n-200\n0\n200\n400\n600\n800\n1000\n1200\n(b)\n(2P)\nb0\n\u03c7\n(2P)\nb1\n\u03c7\n(2P)\nb2\n\u03c7\n)\nJ\n(1D\n\u03a5\n (GeV)\n*\n\u03b3\nE\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\nEvents / (3 MeV)\n0\n1000\n2000\n3000\n4000 (b)\n(1P)\nb0\n\u03c7\n(1P)\nb1\n\u03c7\n(1P)\nb2\n\u03c7\n(1P)\nb0\n\u03c7\n(1P)\nb1\n\u03c7\n(1P)\nb2\n\u03c7\n(1P)\nb\nh\n (GeV)\n*\n\u03b3\nE\n0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95\n1\n1.05 1.1\nEvents / (2 MeV)\n0\n500\n1000\n1500\n2000\n(2P)\nb0\n\u03c7\n(2P)\nb1\n\u03c7\n(2P)\nb2\n\u03c7\nISR\n(1S)\nb\n\u03b7\n (GeV)\n*\n\u03b3\nE\n0.8\n0.82 0.84 0.86 0.88\n0.9\n0.92 0.94 0.96 0.98\n1\nEvents/(4 MeV)\n-200\n-150\n-100\n-50\n0\n50\n100\n150\n200\n250\n300\nISR\n(1S)\nb\n\u03b7\n(b)\nFigure 18.4.17. The converted-photon energy spectrum, after\nsubtracting the smooth background (Lees, 2011m). These data\nwere taken at the \u03a5(3S) resonance. In the lower plot, \u03c7 denotes\n\u03c7b2(2P).\nbackground is again modeled using a smooth function,\nand is subtracted (as in Fig. 18.4.16 and 18.4.17). The\ncontributions from monochromatic photons are modeled\nusing functions that describe both their peak location and\ndetector resolution e\ufb00ects.\n\n500\nThe \u03a5(3S) data in the range [180, 300] MeV were ex-\npected to contain three monochromatic peaks due to the\ntransitions \u03c7bJ(2P) \u2192\u03b3\u03a5(2S) and six monochromatic\npeaks due to the transitions \u03a5(1DJ) \u2192\u03b3\u03c7bJ(1P). Due to\nthe very low rates for these latter transitions, the prop-\nerties of the models describing these transitions are \ufb01xed\nfrom existing measurements of the masses of the involved\nstates. The branching fractions for the \u03c7bJ(2P) \u2192\u03b3\u03a5(2S)\ntransitions are determined from the data and shown in Ta-\nble 18.4.7.\nThe \u03a5(3S) data in the range [300, 600] MeV were ex-\npected to contain photons from the six transitions \u03a5(3S) \u2192\n\u03b3\u03c7bJ(1P) and \u03c7bJ(1P) \u2192\u03b3\u03a5(1S). The photons from\nthese transitions are all comparable in energy and were ex-\npected to overlap. In addition, this region could also con-\ntain photons from the hb(1P) \u2192\u03b3\u03b7b(1S) transition. No\nevidence was seen for this latter transition, and the mea-\nsured rates for the transition \u03a5(3S) \u2192\u03b3\u03c7bJ(1P) are given\nin Table 18.4.7. The pattern of these transitions is unusual\nfor quarkonium, with the pattern for the relative rates to\nthe di\ufb00erent J = 0, 1, 2 \u03c7bJ states being J = 2 > 0 > 1.\nA comment on the non-observation of hb(1P) \u2192\n\u03b3\u03b7b(1S) in this search may be helpful, since in Sec-\ntion 18.4.4.3 a discussion was made of the discovery by the\nBelle Collaboration of the transition hb(1P) \u2192\u03b3\u03b7b(1S).\nFrom Table 18.4.7, we can see that the smallest branching\nfraction to which this search method had sensivity at the\n\u03a5(3S) resonance was at the level of 0.03 \u22120.04% (limited\nby the statistical uncertainty of the sample). The favored\ntransition for \u03a5(3S) \u2192hb(1P) is via radiation of a \u03c00,\nand the branching fraction for that process is expected to\nbe at the level of 0.1%, while the branching fraction for\nhb(1P) \u2192\u03b3\u03b7b(1S) was measured by the Belle Collabo-\nration to be about 49%, (Mizuk, 2012) as mentioned in\nSection 18.4.4.1.\nThe product of these two branching fractions, mark-\ning the rate at which hb(1P) is expected to be produced\nfrom the \u03a5(3S) in the BABAR data sample, is therefore\nabout 0.05%, comparable to the statistical uncertainty of\nthis technique. This product of branching fractions is con-\n\ufb01rmed by the evidence from the BABAR Collaboration for\n\u03a5(3S) \u2192\u03c00hb(1P), hb(1P) \u2192\u03b3\u03b7b(1S), discussed in Sec-\ntion 18.4.4.3.\nAnother predicted leading process from the \u03a5(3S) that\ncan produce the hb(1P) is \u03a5(3S) \u2192\u03c0+\u03c0\u2212hb(1P), but\nthis has been found by the BABAR Collaboration to occur\nwith a branching fractiom < 2.5\u00d710\u22124 at 90% con\ufb01dence\nlevel (Lees, 2011l). In addition, the contribution of these\nprocesses to the photon spectrum overlaps with the much\nmore signi\ufb01cant \u03c7b0(1P) spectral line. Therefore, the non-\nobservation of this photon spectral line in the data from\nthis photon-conversion technique is consistent with inde-\npendent evidence that the rate is below or comparable\nto the statistical sensitivity of this technique. In fact, in\nthis study the contribution from these two sources was a\n\ufb01xed component of the \ufb01t, and found to be comparable to\nstatistical uncertainties in the region where such a signal\nwould be expected.\nTable 18.4.7. Measured radiative transition rates, where the\n\ufb01rst uncertainty is statistical, the second is due to systematic\ne\ufb00ects, and the third (where present) is due to uncertainties\non secondary branching fractions (Lees, 2011m). Numbers in\nparentheses are the 90% con\ufb01dence level upper limits.\nTransition\nBranching Fraction in %\n\u03a5(3S) \u2192\u03b3\u03c7b0(1P)\n0.27 \u00b1 0.04 \u00b1 0.02\n\u03a5(3S) \u2192\u03b3\u03c7b1(1P)\n0.05 \u00b1 0.03+0.02\n\u22120.01 (< 0.10)\n\u03a5(3S) \u2192\u03b3\u03c7b2(1P)\n1.06 \u00b1 0.03+0.07\n\u22120.06\n\u03c7b0(1P) \u2192\u03b3\u03a5(1S)\n2.2 \u00b1 1.5+1.0\n\u22120.7 \u00b1 0.2 (< 4.6)\n\u03c7b1(1P) \u2192\u03b3\u03a5(1S)\n34.9 \u00b1 0.8 \u00b1 2.2 \u00b1 2.0\n\u03c7b2(1P) \u2192\u03b3\u03a5(1S)\n19.5 \u00b1 0.7+1.3\n1.5\n\u00b1 1.0\n\u03c7b0(2P) \u2192\u03b3\u03a5(2S)\n\u22124.7 \u00b1 2.8+0.7\n\u22120.8 \u00b1 0.5(< 2.8)\n\u03c7b1(2P) \u2192\u03b3\u03a5(2S)\n18.9 \u00b1 1.1 \u00b1 1.2 \u00b1 1.8\n\u03c7b2(2P) \u2192\u03b3\u03a5(2S)\n8.3 \u00b1 0.8 \u00b1 0.6 \u00b1 1.0\n\u03c7b0(2P) \u2192\u03b3\u03a5(1S)\n0.7 \u00b1 0.4+0.2\n\u22120.1 \u00b1 0.1 (< 1.2)\n\u03c7b1(2P) \u2192\u03b3\u03a5(1S)\n9.9 \u00b1 0.3+0.5\n0.4\n\u00b1 0.9\n\u03c7b2(2P) \u2192\u03b3\u03a5(1S)\n7.0 \u00b1 0.2 \u00b1 0.3 \u00b1 0.9\nFinally, the \u03a5(3S) data in the range [600, 1100] MeV\nwere expected to contain photons due to the transitions\n\u03c7bJ(2P) \u2192\u03b3\u03a5(1S) and \u03a5(3S) \u2192\u03b3\u03b7b(1S). The latter\ntransition was seen, but only with a signi\ufb01cance of 2.7\u03c3\nand so no independent measurement of the \u03b7b(1S) mass\nwas possible from this sample; more data is needed to\nfully utilize this technique for measuring that transition.\nHowever, the rates for the transitions \u03c7bJ(2P) \u2192\u03b3\u03a5(1S)\nwere measured and are reported in Table 18.4.7.\nThe \u03a5(2S) data in the range [300, 800] MeV were\nexpected to contain photons due to the transitions\n\u03c7bJ(1P) \u2192\u03b3\u03a5(1S) and \u03a5(2S) \u2192\u03b3\u03b7b(1S). No evidence\nwas seen for the latter transitions, and the rates of the\ntransitions \u03c7bJ(1P) \u2192\u03b3\u03a5(1S) are reported in Table\n18.4.7.\n18.4.6.3 Searches for \u03a5(1S) and \u03a5(2S) radiative transitions\nto charmonium states\nThe Belle Collaboration searched for radiative transitions\nfrom \u03a5(2S) (Shen, 2010b) and \u03a5(1S) (Wang, 2011) to\ncharmonium states using the following data samples : on-\nresonance samples of 5.7 fb\u22121 at the \u03a5(1S) (102 million\n\u03a5(1S) events) and a 24.7 fb\u22121 at the \u03a5(2S) (158 million\n\u03a5(2S) events), and continuum samples of 1.8 fb\u22121 at \u221as =\n9.43 GeV and 1.7 fb\u22121 collected at \u221as = 9.993 GeV.\nThe search for the \u03c7cJ was conducted using the \u03b3J/\u03c8\nmode, where J/\u03c8 was observed in both \u00b5+\u00b5\u2212and e+e\u2212\ndecay modes. The \u00b5+\u00b5\u2212mode shows a clear J/\u03c8 signal,\nwhile the e+e\u2212mode has some residual radiative Bhabha\nbackground. No clear \u03c7cJ signal is observed in both \u03a5(1S)\nand \u03a5(2S) data samples, as shown in Fig. 18.4.18.\nThe search for \u03b7c was done using full hadronic recon-\nstruction of the \u03b7c in the modes: KSK\u00b1\u03c0\u2213, \u03c0+\u03c0\u2212K+K\u2212,\n2(K+K\u2212), 2(\u03c0+\u03c0\u2212), and 3(\u03c0+\u03c0\u2212). The combined mass\n\n501\n)\n2\n) (GeV/c\n\u03c8\n J/\n\u03b3\nM(\n3.3\n3.35\n3.4\n3.45\n3.5\n3.55 3.6\n3.65\n3.7\n2\nEvents/8 MeV/c\n0\n1\n2\n3\n4\n5\n6\n7\n8\n)\n2\n) (GeV/c\n\u03c8\n J/\n\u03b3\nM(\n3.3\n3.35\n3.4\n3.45\n3.5\n3.55 3.6\n3.65\n3.7\n2\nEvents/8 MeV/c\n0\n1\n2\n3\n4\n5\n6\n7\n8\n)\n2\n) (GeV/c\n\u03c8\nJ/\n\u03b3\nM(\n3.3\n3.4\n3.5\n3.6\n3.7\n3.8\n3.9\n4\n4.1\n2\nEvents/8 MeV/c\n0\n2\n4\n6\n8\n10\n)\n2\n) (GeV/c\n\u03c8\nJ/\n\u03b3\nM(\n3.3\n3.4\n3.5\n3.6\n3.7\n3.8\n3.9\n4\n4.1\n2\nEvents/8 MeV/c\n0\n2\n4\n6\n8\n10\nFigure 18.4.18. The \u03b3J/\u03c8 invariant mass distributions in\n(top) the \u03a5(1S) (Shen, 2010b) and (bottom) \u03a5(2S) (Wang,\n2011) data samples. No clear \u03c7cJ signal is observed. The solid\ncurve is the best \ufb01t, the dashed curve is the background, and\nthe shaded histogram is from the normalized J/\u03c8 mass side-\nbands.\ndistributions of the hadronic \ufb01nal states are shown in\nFig. 18.4.19 for the \ufb01ve \u03b7c decay modes from \u03a5(1S) and\n\u03a5(2S) data, respectively. The large J/\u03c8 signal is due to\nthe ISR process e+e\u2212\u2192\u03b3ISRJ/\u03c8, while the accumulation\nof events within the \u03b7c mass region is small.\n18.4.6.4 Searches for \u03a5(1S) and \u03a5(2S) radiative transitions\nto charmonium-like states\nIn addition to many conventional charmonium states, a\nnumber of charmonium-like states (the so-called \u201cXY Z\nparticles\u201d) have been discovered with unusual properties.\nThese may include exotic states, such as quark-gluon hy-\nbrids, meson molecules, and multi-quark states (Brambilla\net al., 2011). Many of these new states are established in\na single production mechanism or in a single decay mode\nonly. To better understand them, it is necessary to search\nfor such states in more production processes and/or decay\nmodes. For charge-parity-even charmonium-like states, ra-\ndiative decays of the narrow \u03a5 states below the open bot-\ntom threshold can be examined. There are no calculations\nfor radiative decays for \u201cXY Z particles\u201d due to the lim-\nited knowledge of their nature.\nThe Belle Collaboration searched for four of these XY Z\nstates, the X(3872), X(3915), Y (4140) and X(4350), us-\n)\n2\nM(hadrons) (GeV/c\n2.5\n2.6\n2.7\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n2\nEvents/10 MeV/c\n0\n10\n20\n30\n40\n50\n60\n70\n80\n)\n2\nM(hadrons) (GeV/c\n2.5\n2.6\n2.7\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n2\nEvents/10 MeV/c\n0\n10\n20\n30\n40\n50\n60\n70\n80\n)\n2\nM(hadrons) (GeV/c\n2.5\n2.6\n2.7\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n2\nEvents/10 MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n)\n2\nM(hadrons) (GeV/c\n2.5\n2.6\n2.7\n2.8\n2.9\n3\n3.1\n3.2\n3.3\n3.4\n2\nEvents/10 MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nFigure 18.4.19. The mass distributions for a sum of the \ufb01ve\n\u03b7c decay modes (top) from \u03a5(1S) (Shen, 2010b) and (bottom)\n\u03a5(2S) (Wang, 2011) data, respectively. The solid curve is a sum\nof the corresponding functions obtained from a simultaneous\n\ufb01t to all the \u03b7c decay modes, and the dashed curve is a sum of\nthe background functions from the \ufb01t. The shaded histogram\nis a sum of the continuum events (not normalized in \u03a5(2S)\ndata). The J/\u03c8 signal is produced via ISR rather than from a\nradiative decay of an \u03a5(nS) resonance.\ning the \u03a5(1S)(Shen, 2010b) and \u03a5(2S) (Wang, 2011) data\nsamples described in the previous section.\nThe X(3872) signal was searched for via X(3872) \u2192\n\u03c0+\u03c0\u2212J/\u03c8 and \u03c0+\u03c0\u2212\u03c00J/\u03c8. Except for a few residual ISR\nproduced \u03c8(2S) signal events, only a small number of\nevents appear in the \u03c0+\u03c0\u2212J/\u03c8 invariant mass distribu-\ntions for both \u03a5(1S) and \u03a5(2S) decays. Belle observed\ntwo events in the \u03a5(1S) data with masses of 3.67 GeV/c2\nand 4.23 GeV/c2; only a few events were observed in the\n\u03a5(2S) data.\nThe search for X(3915) was undertaken in the \u03c9J/\u03c8\nmode. No events were observed within the X(3915) mass\nregion in \u03a5(1S) data. One event was observed with\nm(\u03c0+\u03c0\u2212\u03c00J/\u03c8) at 3.923 GeV/c2\nand m(\u03c0+\u03c0\u2212\u03c00) at\n0.790 GeV/c2 from \u03a5(2S) data.\nFinally, the Y (4140) in both \u03a5(1S) and \u03a5(2S) data,\nand X(4350) in \u03a5(2S) data only were searched for using\nthe \u03c6J/\u03c8 mode. No candidates were observed in either in\nthe Y (4140) or X(4350) mass regions.\nSince\nthere\nis\nno\nevidence\nfor\ncharmonium\nor\ncharmonium-like states signals in the modes studied, Belle\nplaced upper limits on the branching fractions of \u03a5(1S)\n\n502\nTable 18.4.8. Summary of the limits on \u03a5(1S) and \u03a5(2S)\nradiative decays to charmonium and charmonium-like states\nR. Here BR is the upper limit at the 90% C.L. on the decay\nbranching fraction in the charmonium state case, and on the\nproduct branching fraction in the case of a charmonium-like\nstate.\nState (R)\nBR (\u03a5(1S))\nBR (\u03a5(2S))\n\u03c7c0\n6.5 \u00d7 10\u22124\n1.0 \u00d7 10\u22124\n\u03c7c1\n2.3 \u00d7 10\u22125\n3.6 \u00d7 10\u22126\n\u03c7c2\n7.6 \u00d7 10\u22126\n1.5 \u00d7 10\u22125\n\u03b7c\n5.7 \u00d7 10\u22125\n2.7 \u00d7 10\u22125\nX(3872) \u2192\u03c0+\u03c0\u2212J/\u03c8\n1.6 \u00d7 10\u22126\n0.8 \u00d7 10\u22126\nX(3872) \u2192\u03c0+\u03c0\u2212\u03c00J/\u03c8\n2.8 \u00d7 10\u22126\n2.4 \u00d7 10\u22126\nX(3915) \u2192\u03c9J/\u03c8\n3.0 \u00d7 10\u22126\n2.8 \u00d7 10\u22126\nY (4140) \u2192\u03c6J/\u03c8\n2.2 \u00d7 10\u22126\n1.2 \u00d7 10\u22126\nX(4350) \u2192\u03c6J/\u03c8\n\u00b7 \u00b7 \u00b7\n1.3 \u00d7 10\u22126\nand \u03a5(2S) radiative decays. Table 18.4.8 lists \ufb01nal results\nfor the upper limits on the branching fractions. The results\nobtained on the \u03c7cJ and \u03b7c production rates are consis-\ntent with the theoretical predictions of Gao, Zhang, and\nChao (2007). With much larger \u03a5(1S) and \u03a5(2S) data\nsamples in the future at super \ufb02avor factories, we can ob-\ntain better results for charmonium \ufb01nal states which can\ntell us if experimental results support or disfavor theoret-\nical predictions. If any one of charmonium-like states can\nbe observed, it will do much help to understand its nature.\n18.4.6.5 Search for \u03c7b(1P) exclusive decays to double\ncharmonium\nThe cross sections of the double-charmonium produc-\ntion processes e+e\u2212\u2192J/\u03c8\u03b7c, J/\u03c8\u03b7\u2032\nc, \u03c8(2S)\u03b7c, \u03c8(2S)\u03b7\u2032\nc,\nJ/\u03c8\u03c7c0, and \u03c8(2S)\u03c7c0 measured at the Belle (Abe, 2002j,\n2004g) and BABAR\n(Aubert, 2005n) experiments were\napproximately an order of magnitude larger than the\nleading order non-relativistic QCD (NRQCD) predic-\ntions (Braaten and Lee, 2003; Liu, He, and Chao, 2003,\n2008). It was shown that the calculations are very sensi-\ntive to the choices of the values of some parameters (Bod-\nwin, Lee, and Braaten, 2003; Bodwin, Lee, and Yu, 2008;\nBraaten and Lee, 2003; He, Fan, and Chao, 2007; Zhang,\nGao, and Chao, 2006) and the agreement between theory\nand experiment can be achieved if one takes into account\nradiative and relativistic corrections.\nSimilar to the production in e+e\u2212annihilation, double\ncharmonium \ufb01nal states can also be produced in bottomo-\nnium decays, which supplied a new test of the dynamics of\nhard exclusive processes and the structure of the charmo-\nnia. While \u03b7b \u2192J/\u03c8J/\u03c8 has been calculated (Sun, Hao,\nand Qiao, 2011), the P-wave spin-triplet bottomonium\nstates \u03c7bJ (J=0, 1, 2) decays into double charmonium\nstates were calculated using di\ufb00erent theoretical models.\nUnder the NRQCD factorization approach, Zhang,\nDong, and Feng (2011) calculated \u03c7bJ \u2192J/\u03c8J/\u03c8 to a\nrelativistic correction of the order v2\nc and considered a\nsmall pure QED contribution. The branching fraction is\npredicted to be of order 10\u22125 for \u03c7b0 or \u03c7b2 \u2192J/\u03c8J/\u03c8,\nand 10\u221211 for \u03c7b1 \u2192J/\u03c8J/\u03c8; Sang, Rashidin, Kim, and\nLee (2011) considered the corrections to all orders in the\ncharm-quark velocity vc in the charmonium rest frame,\nand found decay partial widths that are about a factor of\nthree larger than those determined by Zhang, Dong, and\nFeng (2011). In the light cone (LC) formalism, however,\nmuch larger production rates (with also large uncertain-\nties) are obtained by Braguta, Likhoded, and Luchinsky\n(2009): B(\u03c7bJ \u2192J/\u03c8J/\u03c8) = 9.6 \u00d7 10\u22125 or 1.1 \u00d7 10\u22123,\nB(\u03c7bJ \u2192J/\u03c8\u03c8(2S)) = 1.6 \u00d7 10\u22124 or 1.6 \u00d7 10\u22123, and\nB(\u03c7bJ \u2192\u03c8(2S)\u03c8(2S)) = 6.6\u00d710\u22125 or 5.9\u00d710\u22124 for J=0\nor 2, respectively. It is therefore very important to pin\ndown the source of such signi\ufb01cant discrepancies between\nthe NRQCD factorization and LC formalisms.\nIn perturbative QCD theory, the branching fraction of\nB(\u03c7b0 \u2192J/\u03c8J/\u03c8) \u22483\u00d710\u22125 and for \u03c7b1 decays, it is even\nlarger (Kartvelishvili and Likhoded, 1984). It has been\nargued (Braguta, Likhoded, and Luchinsky, 2005) that\ntaking into account the relative motion of quarks in the\namplitude of the decay of \u03c7b meson to c-quarks increases\nthe branching fractions of the decays of \u03c7b0 (0++) and \u03c7b2\n(2++) into a pair of J/\u03c8 mesons by an order of magnitude.\nBased on a 24.7 fb\u22121 \u03a5(2S) data sample collected by\nthe Belle Collaboration, no signi\ufb01cant signals are found for\nthe \u03c7bJ \u2192J/\u03c8J/\u03c8, J/\u03c8\u03c8(2S), or \u03c8(2S)\u03c8(2S) \ufb01nal states\n(Shen, Yuan, Iijima, 2012). The upper limits on the \u03c7bJ\ndecay branching fractions are lower than the theoretical\npredictions using LC formalism, while are not in contra-\ndiction with other calculations(Zhang, Dong, and Feng,\n2011) using NRQCD factorization approach.\n18.4.6.6 Two-body Hadronic Transitions: \u03c00, \u03b7\nIn the charmonium system, single-meson transitions be-\ntween states have been well-established; the transition\n\u03c8\u2032 \u2192\u03b7J/\u03c8 has a branching ratio of 3.3%, one tenth of\nthe dominant \u03c0+\u03c0\u2212transition (Beringer et al., 2012). In\ncontrast, the \ufb01rst such transition in the bottomonium sys-\ntem, \u03c7b(2P) \u2192\u03c9\u03a5(1S), was observed by the CLEO Col-\nlaboration in 2002 (Severini et al., 2004).\nGenerally, the hadronic transitions between heavy\nquarkonia are described by the QCD multipole expansion\nmodel (QCDME) (Kuang, 2006). In this framework the\n\u03c0\u03c0 transitions are mediated by the emission of two gluons\nin the E1 state, while the \u03b7 transitions proceed either via\nE1M2 or M1M1 terms. Such terms should be suppressed\nby a factor which is inversely proportional to the mass of\nthe heavy quark. The suppression should be even larger\nwhen the \u03b7 is replaced by \u03c00, and the transition violates\nisospin. In the case of charmonium, the suppression fac-\ntor is about 1/25. In the proximity of thresholds, coupled\nchannel e\ufb00ects can provide di\ufb00erent mechanisms to evade\nthe spin \ufb02ip suppression.\n\n503\nFigure 18.4.20. The distribution of M3\u03c0 vs \u2206M\u03b7 = M3\u03c0ll \u2212\nMll for \u03b7\u03a5(1S) candidate events, demonstrating the observed\nsignal (Aubert, 2008bc). Solid lines delimit the signal region,\nwhile dashed lines delimit the sideband regions used for the\nbackground estimate. Crosses represent the data from the\n\u03a5(1S) \u2192e+e\u2212sample and dots the data from the \u03a5(1S) \u2192\n\u00b5+\u00b5\u2212sample.\nThe BABAR Collaboration observed the transition\n\u03a5(4S) \u2192\u03b7\u03a5(1S) (Aubert, 2008bc) using 347.5 fb\u22121 of\ndata taken at the \u03a5(4S) resonance. The observed rate was\n2.5 times larger than that of the \u03a5(4S) \u2192\u03c0+\u03c0\u2212\u03a5(1S)\ntransition, which is the dominant hadronic transition in\nboth charmonium and bottomonium. The BABAR Col-\nlaboration performed the search for the hadronic transi-\ntions \u03c0+\u03c0\u2212\u03a5(1, 2S) and \u03b7\u03a5(1S) using the \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00\nmode, where the \u03a5 is decaying either to e+e\u2212or to \u00b5+\u00b5\u2212.\nCandidate events were selected requiring at least four\ncharged tracks in acceptance; the lepton candidates are\nrequired to have center-of-mass momentum between 4.20\nand 5.25 GeV/c, and the dilepton pair is required to have\ninvariant mass within \u00b1200 MeV (+200\n\u2212350 MeV) of the nomi-\nnal \u03a5(1S) (\u03a5(2S)) mass. The dipion and dilepton candi-\ndates are constrained to have a common vertex.\nThe dominant background is due to e+e\u2212\u03b3 and \u00b5+\u00b5\u2212\u03b3,\nwhere a photon converts in material and creates an e+e\u2212\npair that is misidenti\ufb01ed as a pion pair. This background\nis rejected by requiring the pion pair to have an open-\ning angle above 18\u25e6in the laboratory frame; in addition,\nthe invariant mass of the low momentum pair, calculated\nassuming the e\u00b1 mass hypothesis, is required to satisfy\nme+e\u2212> 100 MeV/c2.\nThe two photons used in \u03c00 reconstruction are required\nto have E\u03b3 > 50 MeV and an invariant mass, m\u03b3\u03b3, in the\nrange [110, 150] MeV/c2. The residual background, from\n\u03a5(mS) \u2192\u03c0\u03c0\u03a5(nS) transitions, is reduced by requiring\n\u2206M = M\u03c0\u03c0ll \u2212Mll to be at least 20 MeV/c2 away from\nFigure 18.4.21. Signal of \u03a5(2S) \u2192\u03b7\u03a5(1S) from the Belle\nCollaboration result (Tamponi, 2013).\nknown transitions. The distribution of M3\u03c0 vs \u2206M\u03b7 =\nM3\u03c0ll \u2212Mll for \u03b7\u03a5(1S) candidate events is shown in Fig.\n18.4.20. Solid lines delimit the signal region, while dashed\nlines delimit the sideband regions used for the background\nestimate. The signal observed by BABAR has a signi\ufb01cance\nof 11(6.2)\u03c3 in the \u00b5\u00b5(ee) channel.\nShortly after the observation of the \u03a5(4S) \u2192\u03b7\u03a5(1S)\ntransition, the CLEO Collaboration reported the \ufb01rst ob-\nservation of \u03a5(2S) \u2192\u03b7\u03a5(1S), with a signi\ufb01cance of 5.3 \u03c3\n(He et al., 2008). The observed branching ratio was about\ntwo times smaller than the theoretical prediction. Using\ntheir samples of \u03a5(2, 3S) decays, the BABAR (Lees, 2011n)\nand Belle Collaborations (Tamponi, 2013) have studied\nthe \u03b7 and \u03c00 transitions between narrow bottomonium\nstates.\nThe dominant peaking backgrounds are due to the\nfavored neutral and charged dipion and diphoton (via\n\u03c7b) transitions, and the continuum e+e\u2212\u2192e+e\u2212(n\u03b3),\n\u00b5+\u00b5\u2212(n\u03b3) processes. The dominant transition \u03a5(2S) \u2192\n\u03c0\u2212\u03c0+\u03a5(1S), which is expected to yield about O(103)\nmore events, can be used as normalization sample. By nor-\nmalizing the rate of \u03b7 and \u03c00 transitions to the rate of the\n\u03c0+\u03c0\u2212transition, the systematic error of the measurement\nis reduced by cancellation of common uncertainties.\nBoth experiments detect the \u03b7 meson in the \u03b3\u03b3 and\nthe \u03c0+\u03c0\u2212\u03c00 \ufb01nal states. Due to the tighter requirements\nimposed by the Bhabha veto at trigger level, the BABAR\nCollaboration was only able to use the \u03a5 \u2192\u00b5+\u00b5\u2212\ufb01nal\nstate, while the Belle Collaboration uses both leptonic \ufb01-\nnal states.\nCharged tracks with momenta in the collider center-of-\nmass frame are required to have be greater than 4 GeV/c;\nsuch tracks are selected as candidate leptons from \u03a5(1S)\ndecay. Particle identi\ufb01cation is applied to categorize events\nas having electrons or muons in the \ufb01nal state.\nThe momentum of all photons detected in the ECL in\nthe proximity of each leptonic track is added to its mo-\nmentum, to reduce the e\ufb00ect of \ufb01nal state radiation (FSR)\nand bremsstrahlung. In order to suppress the contribution\nfrom continuum QED processes, a single-constraint kine-\n\n504\nTable 18.4.9. Branching ratios (in units of 10\u22124 ) and upper limits (at 90% C.L.) for \u03b7 and \u03c00 transitions from BABAR (Aubert,\n2008bc; Lees, 2011n) and Belle (Tamponi, 2013), compared to previous results from CLEO (He et al., 2008).\ntransition\nBABAR\nBelle\nCLEO\n\u03a5(2S) \u2192\u03b7\u03a5(1S)\n2.39 \u00b1 0.31 \u00b1 0.14 3.57 \u00b1 0.25 \u00b1 0.21 2.10.7\n0.6 \u00b1 0.3\n\u03a5(2S) \u2192\u03c00\u03a5(1S)\n\u2212\n< 0.41\n< 1.8\n\u03a5(3S) \u2192\u03b7\u03a5(1S)\n< 1.0\n\u2212\n< 1.8\n\u03a5(3S) \u2192\u03c00hb(1P)\n7.4 \u00b1 2.2 \u00b1 1.4\n\u2212\n\u2212\n\u03a5(4S) \u2192\u03b7\u03a5(1S)\n1.96 \u00b1 0.06 \u00b1 0.09\n\u2212\n\u2212\nmatic \ufb01t with a constraint on the \u03a5(1S) mass is then\napplied on the two lepton candidate momenta, corrected\nfor nearby photons, as described above. The threshold on\nthe con\ufb01dence level of this \ufb01t has been optimized using\nthe Monte Carlo simulation for each speci\ufb01c channel.\nA requirement on the polar angle of the e\u2212track\nwith respect to the beam direction, cos(\u03b8\u2217\ne\u2212) < 0.5, is\nimposed to further suppress singly or doubly radiative\nBhabha events, which represent the dominant QED back-\nground. The Bhabha requirement is not included in the\n\u03a5(2S) \u2192\u03c00\u03a5(1S) analysis, since the \u03a5(1S) mass con-\nstraint provides already a good suppression of the QED\nprocesses.\nThe \u03c0+\u03c0\u2212candidate for the \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 decay (and\nalso for the \u03a5(2S) \u2192\u03c0+\u03c0\u2212\u03a5(1S) transition used by the\nBelle Collaboration) is selected requiring the two tracks to\nbe oppositely charged, to originate from the primary in-\nteraction point, and to have a large opening angle in the\ne+e\u2212CM frame (e.g. cos(\u03b8\u2217\nch+,ch\u2212) < 0.6 in the Belle Col-\nlaboraton result), in order to reject the e+e\u2212pairs com-\ning from photon conversions in the inner detector. In the\nsearch for the \u03a5(3S) \u2192\u03b7\u03a5(1S) transition, an additional\nrequirement on \u2206M\u03c0\u03c0 = M\u03c0\u03c0ll \u2212Mll is imposed, to avoid\ncontamination from the \u03a5(2, 3S) \u2192\u03c0+\u03c0\u2212\u03a5(1, 2S) transi-\ntions.\nA second kinematic \ufb01t is then performed after the \u03b7 or\n\u03c00 selection, constraining all \ufb01nal state particles (i.e. the\ndilepton, the dipion and/or the best photon pair) to have\nan invariant mass equal to the \u03a5(2, 3S) mass, to generate\nfrom the same vertex, and to have a total energy equal to\nthe sum of the beam energies.\nAn unbinned maximum-likelihood \ufb01t to the measured\ndistribution of one (Belle, Fig. 18.4.21) or two (BABAR)\nobservables is then performed to extract the signal yields.\nEach observed distribution is \ufb01t to a sum of signal and\nbackground components, with functional forms determined\nfrom the simulations. The value of the branching fraction\nfor each mode is then extracted. The results of all analyses\nare summarized in Table 18.4.9.\nThe branching ratio for the \u03a5(3S) \u2192\u03c00hb(1P) tran-\nsition is obtained by combining the product of branch-\ning ratio measured by BABAR in the study of the reac-\ntion \u03a5(3S) \u2192\u03c00hb(1P); hb \u2192\u03b3\u03b7b(1S), with B(hb(1P) \u2192\n\u03b7b(1S)), measured by Belle. The evidence of an isospin\nviolating transition at least one order of magnitude larger\nthan yet unobserved \u03b7 transition from \u03a5(3S) is even more\nsurprising than the enhanced \u03b7\u03a5(1S) rate from \u03a5(4S).\n18.4.6.7 Exclusive \u03a5(1S) and \u03a5(2S) decays into light\nhadrons\nA number of channels in \u03c8 decays have been studied,\nmost of which satisfy predictions about their properties\nto within experimental errors. One example of a property\nwhich does not conform to expectation arises from the\ncomparison of \u03c8 decays into vector-pseudoscalar (VP) and\nvector-tensor (VT) \ufb01nal states: \u03c1\u03c0, K\u2217\u00afK, \u03c1a2(1320) and\n\u03c9f2(1270). The rates of decay to these \ufb01nal states devi-\nate from expectations, such as those implies by the \u201c12%\nrule\u201d (Section 18.4.6.1). It is interesting, therefore, to see\nif similar patterns of deviation occur in the bottomonium\nsystem by studying similar \ufb01nal states of \u03a5 decay.\nAlthough 82% of the \u03a5(1S) and 59% of the \u03a5(2S) de-\ncays are expected to be light-hadron \ufb01nal states, little ex-\nperimental information exists on exclusive decays of the \u03a5\nresonances below the BB threshold. This situation is very\ndi\ufb00erent in charmonium sector, where numerous channels\nhave been measured and used to perform model tests.\nThe Belle Collaboration published \ufb01rst observations of\nexclusive, light-hadron \ufb01nal states of the \u03a5(1S) and \u03a5(2S)\n(Shen, 2012). A large number of \ufb01nal states were studied\nand the key results are summarized in Table 18.4.10.\nThe measurements are mostly consistent with the pre-\ndiction from pQCD (Section 18.4.6.1), Q21 = 0.77 \u00b1 0.07.\nThe one measured mode that demonstrates a deviation\nfrom the prediction is \u03c9\u03c0+\u03c0\u2212, which is consistent with\nthe prediction at the level of 2.6\u03c3. For the \ufb01nal states\nmeasured so far, the predictions from pQCD appear to be\nreliable within the experimental uncertainties.\n18.4.6.8 \u03a5(4S) decays to B \u00afB\nThe \u03a5(4S)(10580) is a resonance state that has a mass\nslightly above the BB threshold. It decays mostly into\nB0B0 and B+B\u2212pairs which are not available to the\nlighter resonances due to the phase space.\nGiven the similar masses of B+ and B0, it is expected\nthat the branching fractions f00 \u2261B(\u03a5(4S) \u2192B0B0)\n\n505\nTable 18.4.10. Results from the Belle Collaboration (Shen, 2012) in the measurement of exclusive hadronic decays of the\n\u03a5(1S) and \u03a5(2S) mesons. Here, B is the measured branching fraction (in units of 10\u22126), and where the sign\ufb01cance of the result\nis low BUP (the 90% con\ufb01dence level upper limit on the branching fraction) is also reported. Q21 is the computed ratio of\nthe \u03a5(2S) and \u03a5(1S) branching fractions. Where the signi\ufb01cance is small, QUP\n21 (the upper limit on the value of Q21) is also\nreported. The \ufb01rst error in B and Q21 is statistical, and the second systematic.\nChannel\n\u03a5(1S)\n\u03a5(2S)\nB\nBUP\nB\nBUP\nQ21\nQUP\n21\n\u03c6K+K\u2212\n2.36 \u00b1 0.37 \u00b1 0.29\n1.58 \u00b1 0.33 \u00b1 0.18\n0.67 \u00b1 0.18 \u00b1 0.11\n\u03c9\u03c0+\u03c0\u2212\n4.46 \u00b1 0.67 \u00b1 0.72\n1.32 \u00b1 0.54 \u00b1 0.45\n2.58\n0.30 \u00b1 0.13 \u00b1 0.11\n0.55\nK\u22170K\u2212\u03c0+\n4.42 \u00b1 0.50 \u00b1 0.58\n2.32 \u00b1 0.40 \u00b1 0.54\n0.52 \u00b1 0.11 \u00b1 0.14\n\u03c6f \u2032\n2\n0.64 \u00b1 0.37 \u00b1 0.14\n1.63\n0.50 \u00b1 0.36 \u00b1 0.19\n1.33\n0.77 \u00b1 0.70 \u00b1 0.33\n2.54\n\u03c9f2\n0.57 \u00b1 0.44 \u00b1 0.13\n1.79\n\u22120.03 \u00b1 0.24 \u00b1 0.01\n0.57\n\u22120.06 \u00b1 0.42 \u00b1 0.02\n1.22\n\u03c1a2\n1.15 \u00b1 0.47 \u00b1 0.18\n2.24\n0.27 \u00b1 0.28 \u00b1 0.14\n0.88\n0.23 \u00b1 0.26 \u00b1 0.12\n0.82\nK\u22170 \u00afK\u22170\n2\n3.02 \u00b1 0.68 \u00b1 0.34\n1.53 \u00b1 0.52 \u00b1 0.19\n0.50 \u00b1 0.21 \u00b1 0.07\nK1(1270)+K\u2212\n0.54 \u00b1 0.72 \u00b1 0.21\n2.41\n1.06 \u00b1 0.42 \u00b1 0.32\n3.22\n1.96 \u00b1 2.71 \u00b1 0.84\n4.73\nK1(1400)+K\u2212\n1.02 \u00b1 0.35 \u00b1 0.22\n0.26 \u00b1 0.23 \u00b1 0.09\n0.83\n0.26 \u00b1 0.25 \u00b1 0.10\n0.77\nb1(1235)+\u03c0\u2212\n0.47 \u00b1 0.22 \u00b1 0.13\n1.25\n0.02 \u00b1 0.07 \u00b1 0.01\n0.40\n0.05 \u00b1 0.16 \u00b1 0.03\n0.35\nand f+\u2212\u2261B(\u03a5(4S) \u2192B+B\u2212) are around 0.5. How-\never, predictions for the ratio R+/0 \u2261f+\u2212/f00 range from\n1.03 to 1.25 (Aubert, 2005r). This is due to the e\ufb00ect of\nthe Coulomb force in the decays of \u03a5(4S) into B0 \u00af\nB0 and\nB+B\u2212pairs. The kinematic aspects of the \u03a5(4S) decays\nare treated as non-relativistic. The B meson velocity in\nthe \u03a5(4S) rest frame is relatively small,\n\u03b2 = v/c =\ns\n1 \u2212\n4m 2\nB\nm 2\n\u03a5 (4S)\n\u22480.065,\n(18.4.17)\nwhere mB and m\u03a5 (4S) are the masses of the B meson and\nthe \u03a5(4S) resonance, respectively.\nTable 18.4.11 shows the experimental results on R+/0.\nAll measurements assumed the isospin invariance in\n\u0393(B+ \u2192x+) = \u0393(B0 \u2192x0), where x+ and x0 are the\ncharged and neutral \ufb01nal particles.\nThe only measurement that did not follow the above\nassumption is the measurement from the Belle experi-\nment, Hastings, 2003. This measurement used dilepton\nevents, but assumed that there is isospin invariance,\n\u0393(B+ \u2192\u2113+X) = \u0393(B0 \u2192\u2113+X). Therefore, this result is\ntreated slightly di\ufb00erently, described as follows:\n\u2013 Using the corresponding lifetime ratio (Table 18.4.11),\neach measurement from CLEO and BABAR is converted\ninto its original measurement of R+/0 \u00d7 \u03c4(B+)/\u03c4(B0)\n\u2013 No statistical and systematic correlation between the\nmeasurements from CLEO and BABAR is assumed, and\na simple weighted average of R+/0 \u00d7 \u03c4(B+)/\u03c4(B0) is\ncomputed.\n\u2013 This weighted average is converted into an average\nvalue of R+/0 by dividing it by the latest average of\nthe lifetime ratio, \u03c4(B+)/\u03c4(B0) = 1.079 \u00b1 0.007.\n\u2013 The measurement of R+/0 from the Belle experiment\nis adjusted using the current values of \u03c4(B+)/\u03c4(B0) =\n1.079 \u00b1 0.007 and \u03c4(B0) = 1.519 \u00b1 0.007 ps.\n\u2013 The weighted-average value of R+/0 from CLEO and\nBABAR is then averaged with the adjusted value of the\nR+/0 from Belle, assuming there is 100% correlation of\nthe systematic uncertainty due to the limited knowl-\nedge of the lifetime ratio of \u03c4(B+)/\u03c4(B0).\nMost measurements of the R+/0 have been made as-\nsuming isospin symmetry in speci\ufb01c decay rates and re-\nsulting in an average value of R+/0,\nR+/0 = 1.056 \u00b1 0.028 (total).\n(18.4.18)\nThis global average of R+/0 is in good agreement with\nisospin invariance in the decay of \u03a5(4S) \u2192B \u00afB pairs at\nthe level of 2\u03c3.\nIn 2005, the BABAR collaboration reported (Aubert,\n2005r) the \ufb01rst measurement of the branching fraction of\nB(\u03a5(4S) \u2192B0B0), f00, using a novel technique: the par-\ntial reconstruction method (Section 17.5.1.4). This is a\ndirect measurement of the f00 that does not depend on\nthe isospin invariance nor requires the knowledge of the B\nlifetime ratio, \u03c4(B+)/\u03c4(B0). The measurement is based on\nthe comparison between the number of events of a single-\nand double-tag sample using the decay of \u00afB0 \u2192D\u2217+\u2113\u2212\u00af\u03bd\u2113,\nand yields\nf00 = 0.487 \u00b1 0.010(stat) \u00b1 0.008(syst) (18.4.19)\nThe two results in Equations 18.4.18 and 18.4.19 re-\nsult from very di\ufb00erent approaches and are completely\nindependent. Combining the two results leads to f+\u2212=\n0.514 \u00b1 0.019 and the sum of f00 and f+\u2212is equal to\n1.001 \u00b1 0.030 which is consistent with unity.\n\n506\nTable 18.4.11. Published measurements of R+/0 = f+\u2212/f00 values in the decay of \u03a5(4S) resonance to B \u00afB pairs. The assumed\nlifetime ratio for each measurement is included.\nExperiment\nMode B \u2192\nR+/0 Result\n\u03c4(B+)/\u03c4(B0)\nCLEO (Alexander et al. (2001))\nJ/\u03c8K\u2217\n1.04 \u00b1 0.07 \u00b1 0.04\n1.066 \u00b1 0.024\nBABAR (Aubert, 2002c)\n(c\u00afc)K\u2217\n1.10 \u00b1 0.06 \u00b1 0.05\n1.062 \u00b1 0.029\nCLEO (Athar et al. (2002))\nD\u2217\u2113\u03bd\n1.058 \u00b1 0.084 \u00b1 0.136 1.074 \u00b1 0.028\nBelle (Hastings, 2003)\ndilepton events\n1.01 \u00b1 0.03 \u00b1 0.09\n1.083 \u00b1 0.017\nBABAR (Aubert, 2004j)\nJ/\u03c8K\n1.006 \u00b1 0.036 \u00b1 0.031 1.083 \u00b1 0.017\nBABAR (Aubert, 2005k)\n(c\u00afc)K\u2217\n1.06 \u00b1 0.02 \u00b1 0.03\n1.086 \u00b1 0.017\nAverage\n1.056 \u00b1 0.028 (total)\n1.079 \u00b1 0.007\nAssuming f00 + f+\u2212= 1, the two results in Equa-\ntions 18.4.18 and 18.4.19 lead to the most precise average\nvalues of f00 and f+\u2212,\nf00 = 0.487 \u00b1 0.006,\n(18.4.20)\nf+\u2212= 0.513 \u00b1 0.006\n(18.4.21)\nand R+/0,\nR+/0 = 1.055 \u00b1 0.025\n(18.4.22)\nwhere the R+/0 ratio di\ufb00ers from unity by 2.2\u03c3.\n18.4.7 Physics beyond the Standard Model\n18.4.7.1 Light Higgs Searches\nMotivation - low-mass, CP-odd Higgs boson\nThe existence of a low-mass Higgs boson (mA0 < mbb) be-\ncame one of the beyond-the-Standard Model search topics\nfor the bottomonium data sample of the BABAR Collab-\noration. This was motivated by extensions of the Stan-\ndard Model, such as the next-to-minimal supersymmetric\nStandard Model, or NMSSM, that was developed to solve\nproblems in the MSSM (cf. Dermisek and Gunion, 2005).\nWhile the MSSM requires two Higgs \ufb01eld doublets in order\nto provide mass to all particles in the theory, the NMSSM\nadds one more Higgs singlet \ufb01eld for a total of seven phys-\nical Higgs bosons. One of these is a CP-odd state, and is\nthe lightest of the seven Higgs bosons (henceforth denoted\nas A0). The purpose of this additional Higgs \ufb01eld singlet is\nto solve the \u201cnaturalness\u201d problem in the MSSM (e.g. the\napparently \ufb01ne-tuned value of the \u00b5 parameter). Depend-\ning on the couplings and mass of this A0, it was possible\nthat the branching fraction for \u03a5 \u2192\u03b3A0 could have been\nas high as 10\u22124 and thus easily accessible to the B Factory\nexperiments (Dermisek, Gunion, and McElrath, 2007).\nExperimental searches\nThe BABAR collaboration has searched for low-mass Higgs\nbosons produced in bottomonium decay using two decay\nmodes: A0 \u2192\u00b5+\u00b5\u2212, \u03c4 +\u03c4 \u2212(Aubert, 2009ai,an). All of\nthese searches assume that the parent Upsilon meson de-\ncays to the low-mass Higgs boson by radiating a photon,\n\u03a5 \u2192\u03b3A0.\n(18.4.23)\nPrior to the publication of the BABAR searches described\nin this section, the CLEO Collaboration published searches\nfor the same \ufb01nal states (Love et al., 2008) using 21.5\u00d7106\n\u03a5(1S) decays. They obtained 90% con\ufb01dence level limits\non the branching fraction for A0 \u2192\u03c4 +\u03c4 \u2212decay covering\nthe range 2m\u03c4 < mA0 < 9.5 GeV/c2 (where m\u03c4 is the tau\nlepton mass) that ranged between and (1 \u221248) \u00d7 10\u22125.\nThey obtained 90% con\ufb01dence level limits on the branch-\ning fraction for A0 \u2192\u00b5+\u00b5\u2212decay covering the range\nmA0 < 3.6 GeV/c2 that ranged between (1 \u221220) \u00d7 10\u22126.\nThe BABAR searches use a data sample taken at a\ncollider energy corresponding in the CM frame to the\n\u03a5(3S) mass. The sample contains (121.8\u00b11.2)\u00d7106 \u03a5(3S)\nmesons.\nThe BABAR searches proceed by selecting events con-\ntaining a good photon candidate and two opposite electric\ncharge tracks. The selection of these \ufb01nal states diverge\nafter the de\ufb01ntion of the topology due to the di\ufb00ering\nkinematics of the two di-lepton \ufb01nal states.\nA0\u2192\u00b5+\u00b5\u2212\nThe A0 \u2192\u00b5+\u00b5\u2212\ufb01nal state is selected by requiring that\nthe photon have a CM energy E\u03b3 \u22650.5 GeV. Other pho-\ntons can be present in an event only if their individual\nenergies are below this threshold. The charged tracks are\nassigned a muon mass hypothesis and are henceforth re-\nferred to as \u201cmuon candidates\u201d independent of whether\nadditional particle identi\ufb01cation is required. The muon\ncandidates must original from a common point in space,\nand the vertex of the two charged tracks must have a\n\n507\n\u03c72 < 20 (for 1 degree of freedom) and be displaced by no\nmore than 2 cm from the nominal e+e\u2212interaction region\nin a plane transverse to the beams.\nThe dimuon system is combined with the highest-\nenergy photon candidate to build an \u03a5(3S) candidate. A\nkinematic \ufb01t is performed to the three particles, constrain-\ning the total energy of the three particles to be within the\nbeam-energy spread of the e+e\u2212collision that should have\nproduced the \u03a5(3S), and the constraint that the particles\noriginate from the primary interaction region. The \ufb01t is re-\nquired to satisfy \u03c72 < 36 (for 6 degrees of freedom), which\ncorresponds to a probability of rejecting good kinematic\n\ufb01ts that is less than 10\u22126.\nParticle identi\ufb01cation is used in certain regions of pho-\nton energy in order to reject speci\ufb01c backgrounds. After\nthe above kinematic selection, the primary background is\ndetermined from MC simulation to be e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3.\nIn a photon-energy region corresponding to mA0\n<\n1.05 GeV/c2, contributions from \u03c6\n\u2192\nK+K\u2212(where\nK+ \u2192\u00b5+\u03bd) and \u03c1 \u2192\u03c0+\u03c0\u2212are suppressed by requiring\nthat both tracks be positively identi\ufb01ed as muons using\nparticle identi\ufb01cation. In an mA0 region corresponding to\nthe location of the \u03b7b mass, events are required to have no\nadditional photons with E\u03b3 > 0.08 GeV; this suppresses\nradiative transitions of the \u03a5(3S) to the \u03a5(2S) through a\n\u03c7b state.\nThe e\ufb03ciency of the above selection of A0 \u2192\u00b5+\u00b5\u2212is\nstudied using a signal MC simulation and varies between\n24-44%, depending on mA0. The signal yield is extracted\nfrom the data in the range 0.212 \u2264mA0 \u22649.3 GeV/c2\nusing a maximum-likelihood \ufb01t to the variable,\nmR =\nq\nm2\u00b5\u00b5 \u22124m2\u00b5.\n(18.4.24)\nThis equation represents twice the momentum of the\nmuons in the rest frame of the parent particle. This is\nused instead of just m\u00b5\u00b5 because it is a smooth function\nof m\u00b5\u00b5 across the entire dimuon mass range, including\nclose to the threshold for dimuon production (m\u00b5\u00b5 \u22482m\u00b5\ncorresponds to mR \u22480). The background distribution of\nm\u00b5\u00b5 turns on sharply near threshold, whereas mR has\na more gradual rise and can be more easily empirically\nmodeled with a simple analytic function. Two functions\nare developed for use in the maximum likelihood \ufb01t: a\nsignal function (determined from signal MC simulation)\nand a background function (determined from data taken\nat \u221as = M\u03a5 (4S)). The signal model is constructed from\na sum of two Crystal Ball functions; the parameters of\nthis model are determined from many independent sim-\nulations of an A0 whose mass varies across the range of\ninterest, and these parameters are cross-checked using a\nsample of J/\u03c8 mesons obtained from initial-state radia-\ntion, e+e\u2212\u2192\u03b3ISRJ/\u03c8. The background model has al-\nternative parameterizations in di\ufb00erent regions of mR; for\nmR < 0.23 GeV/c2, a threshold (hyperbolic) function is\nused, while elsewhere the background is described by a\n\ufb01rst-order (mR < 9.3 GeV/c2) or second-order (mR >\n9.3 GeV/c2) polynomial.\nThe \ufb01t for signal and background is performed in steps\nwhose size varies by region. In addition to continuum back-\n (GeV)\nA0\nm\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n ) \n-6\n UL (10\n\u00b5\n\u00b5\n B\n 2\n\u03a5\nf\n1\n10\n(c)\n ) \n-6\nBF UL (10\n1\n2\n3\n4\n5\n(b)\n ) \n-6\nBF UL (10\n0\n1\n2\n3\n4\n5\n6\n7\n8\n(a)\n0\n0\nFigure 18.4.22. Upper limits on the product of branching\nfractions (at 90% C.L.) for \u03a5(nS) \u2192\u03b3A0 and A0 \u2192\u00b5+\u00b5\u2212\nfor (a) \u03a5(3S) and (b) \u03a5(2S). The upper limit on the e\ufb00ective\ncoupling, f 2\nY B\u00b5\u00b5, is shown in (c). From (Aubert, 2009an).\nground, speci\ufb01c backgrounds that contribute peaks to the\nmass spectrum are accounted using the same model as\nfor signal. The J/\u03c8 and \u03c8(2S) regions are excluded from\nthe \ufb01t since those contributions overwhelm any possible\nsignals in those regions.\nThe BABAR Collaboration reports no evidence for de-\ncay of a low-mass Higgs boson using these data and com-\nputes upper limits on the branching fraction for \u03a5(3S) \u2192\n\u03b3A0 \u2192\u03b3(\u00b5+\u00b5\u2212), shown in Fig. 18.4.22. These upper\nlimits, including systematic uncertainties, range between\n(0.25 \u22125.2) \u00d7 10\u22126 depending on the value of mR (at the\n90% con\ufb01dence level). These results constrain the branch-\ning fraction for \u03b7b \u2192\u00b5+\u00b5\u2212to be < 0.8% at the 90%\ncon\ufb01dence level.\nA0\u2192\u03c4 + \u03c4 \u2212\nThe search for A0 \u2192\u03c4 +\u03c4 \u2212proceeds similarly to the\ndimuon search. Events must contain a photon satisfying\nE\u03b3 > 0.1 GeV; any additional photons (up to nine are\nallowed) must each satisfy E < 0.1 GeV. The dominant\nbackground processes in this search are due to e+e\u2212\u2192\n\u03b3\u03c4 +\u03c4 \u2212, e+e\u2212\u2192e+e\u2212e+e\u2212, e+e\u2212\u2192e+e\u2212\u00b5+\u00b5\u2212, and\ne+e\u2212\u2192qq. These are rejected by using eight discriminat-\ning variables: the total CM energy calculated from the two\nleptons and the most energetic photon; the squared miss-\ning mass obtained from the missing four-momentum; the\naplanarity of the photon and A0 candidate, which is the\ncosine of the angle between the photon and the plane of\n\n508\nthe leptons; the largest cosine between the photon and one\nof the tracks; the cosine of the polar angle of the highest-\nmomentum track; the transverse momentum of the event\ncalculated in the CM frame; the cosine of the polar an-\ngle of the missing momentum vector; and the cosine of\nthe opening angle between the tracks in the photon recoil\nframe. The selection on these variables is optimized si-\nmultaneously in order to achieve the best value of S/\n\u221a\nB,\nwhere S is the number of expected signal and B is the\nnumber of expected background. The backgrounds vary\ndepending on the photon energy, so this optimization is\nperformed as a function of photon energy in \ufb01ve regions\nwhich slightly overlap in order to reduce discontinuities in\nperformance between the regions.\nThe energy of the photon in the \u03a5(3S) rest frame is\nused to de\ufb01ne a range of A0 masses studied in this search,\nusing the relationship\nm2\nA0 = m2\n\u03a5 (3S) \u22122m\u03a5 (3S)E\u03b3\n(18.4.25)\nwhere m\u03a5 (3S) is the nominal \u03a5(3S) mass. The range\nof photon energies studied corresponds to mA0\n=\n[4.03, 10.10] GeV/c2,\nexcluding\nthe\nregion\nmA0\n=\n[9.52, 9.61] GeV/c2 due to an irreducible background from\nphotons produced in the process \u03a5(3S) \u2192\u03b3\u03c7bJ(2P),\n\u03c7bJ(2P) \u2192\u03b3\u03a5(1S), where J = 0, 1, 2. The photon energy\nresolution varies over the range in this search, increasing\nfrom 8 MeV at E\u03b3 \u22480.2 GeV to 55 MeV at E\u03b3 \u22484.5 GeV.\nThe e\ufb03ciency of event selection also varies with photon\nenergy, ranging as follows: 10-14% for the \u03c4\u03c4 \u2192ee \ufb01nal\nstate; 12-20% for \u03c4\u03c4 \u2192e\u00b5; and 22-26% for \u03c4\u03c4 \u2192\u00b5\u00b5\n(neutrinos are not explicitly written in the \ufb01nal states).\nThe photon energy spectrum is modeled using the com-\nbination of a peaking function for signal and a predomi-\nnantly smooth function for background. The data are \ufb01rst\ntreated as purely background and \ufb01t with only the latter\nfunction. This allows the parameters of the background to\nbe determined as initial values for the next stage of the \ufb01t\nto the data.\nBackgrounds causing real peaks in the photon spec-\ntrum are expected from radiative decays from the \u03a5(3S)\nresonance to lower-mass bottomonium states, speci\ufb01cally\n\u03a5(3S) \u2192\u03b3\u03c7bJ(2P), \u03c7bJ(2P) \u2192\u03b3\u03a5(nS), and \u03a5(nS) \u2192\n\u03c4 +\u03c4 \u2212(J = 0, 1, 2; n = 1, 2). Peaks arise in the pho-\nton spectrum when the photon from the \u03c7bJ(2P) decay is\nused as the photon radiated by the \u03a5(3S) when it decays\nto an A0. Each of the peaks is described using a Crystal\nBall function whose means are \ufb01xed by the photon en-\nergies expected from the PDG values of the bottomonia\nmasses (Beringer et al., 2012) and whose widths are \ufb01xed\nfrom the MC predictions of the reconstructed widths of\nthe photon peaks. The other parameters of the Crystal\nBall functions are also \ufb01xed from the MC simulation of\nthese decays.\nThe results of a \ufb01t of the background model to the\nphoton energy spectrum in each \ufb01nal state are shown in\nFig. 18.4.23. A complete \ufb01t of the data including the sig-\nnal model is performed by scanning the photon energy\nin 307 steps and \ufb01tting for signal and background yields\nat each step. This procedure \ufb01nds no signi\ufb01cant yield of\nEvents/10 MeV \n1\n10\n100\n1000\n ee\n\u2192\n\u03c4\n\u03c4\n(a)\nPull\n-5\n0\n5\n(b)\nEvents/10 MeV \n1\n10\n100\n1000\ne\n\u00b5\n \n\u2192\n\u03c4\n\u03c4\n(c)\nPull\n-5\n0\n5\n(d)\nEvents/10 MeV \n1\n10\n100\n1000\n\u00b5\n\u00b5\n \n\u2192\n\u03c4\n\u03c4\n(e)\n (GeV)\n\u03b3\n E\n0.5\n1\n1.5\n2\nPull\n-5\n0\n5\n(f)\nFigure 18.4.23. (a), (c), (e): Photon energy distributions\nfor the di\ufb00erent \u03c4\u03c4-decay modes (Aubert, 2009ai). Filled cir-\ncles show the data; dotted lines represent contributions from\n\u03a5(3S) \u2192\u03b3\u03c7bJ(2P), \u03c7bJ(2P) \u2192\u03b3\u03a5(2S); dotted-dashed lines\nshow contributions from \u03a5(3S) \u2192\u03b3\u03c7bJ(2P), \u03c7bJ(2P) \u2192\n\u03b3\u03a5(1S); and solid lines show the total background function. For\neach \u03c4\u03c4-decay mode, the di\ufb00erence between the background\nfunction and the data divided by the uncertainty in the data\nis shown in (b), (d) and (f).\nsignal events anywhere in the spectrum. The branching\nfraction product B(\u03a5(3S) \u2192\u03b3A0)B(A0 \u2192\u03c4 +\u03c4 \u2212) is cal-\nculated, along with the upper limit at the 90% C.L., both\nas a function of Higgs mass, as shown in Fig. 18.4.24. The\nupper limits on the product branching fraction range be-\ntween (1.5 \u221216) \u00d7 10\u22125 at 90% C.L. for a mass range of\n4.03 < mA0 < 10.10 GeV/c2, excluding 9.52 < mA0 < 9.61\nGeV/c2 to veto the \u03c7bJ(2P) with \u03c7bJ(2P) \u2192\u03b3\u03a5(1S).\nImpact of the results\nThe low-mass Higgs boson models discussed earlier in this\nsection predicted that the branching fraction for \u03a5(1S) \u2192\n\u03b3A0 could range as high as \u223c10\u22123 (the range of possible\nbranching fractions is dependent on the speci\ufb01c NMSSM\nmodel used). The measurements from the BABAR collab-\noration put strong constraints on the upper range of this\nkind of decay down to the level of 10\u22126, removing a few\norders of magnitude of possible range from the top level\nof predicted branching fractions.\n\n509\n-3\n 10\n\u00d7\n) \n\u03c4\n\u03c4\n\u2192\n0\n(A\nB\n \n\u00d7\n) \n0\n A\n\u03b3 \n\u2192\n(3S)\n\u03d2\n(\nB\n-0.1\n0\n0.1\n(a)\n)\n2\n (GeV/c\n0\nA\nm\n4\n6\n8\n10\n90% C.L. Upper Limit\n-6\n10\n-5\n10\n-4\n10\nTotal uncertainty\nStatistical uncertainty only\n(b)\nFigure 18.4.24. (a) Product branching fractions as a function of the Higgs mass (Aubert, 2009ai). For each point, both the\nstatistical uncertainty (from the central value to the horizontal bar) and the total uncertainty (statistical and systematic added\nin quadrature) are shown (from the central value to the end of the error bar). In (b), the corresponding 90% C.L. upper limits\non the product of the branching fractions versus the Higgs mass values are shown, with total uncertainty (solid line) and\nstatistical uncertainty only (dashed line). The shaded vertical region represents the excluded mass range corresponding to the\n\u03c7bJ(2P) \u2192\u03b3\u03a5(1S) states.\n18.4.7.2 Invisible Final States of the \u03a5(1S)\nMotivation - low-mass dark matter\nThe nature of dark matter is one of the great modern\nphysics puzzles. Assuming dark matter is composed of at\nleast one species of particle, the properties of this parti-\ncle have not been measured (e.g. mass). If the mass of\ndark matter is small (< mbb), then there is the possibility\nof detecting it using rare processes involving undetectable\n(invisible) \ufb01nal states. One of these, \u03a5 \u2192invisible, was\nmotived by work by McElrath (2005), where it was sug-\ngested that a new interaction that couples Standard Model\nparticles to dark matter particles could mediate the decay\nof the \u03a5. Based on the interaction cross-section required\nto achieve the \u201cfreeze-out\u201d of dark matter annihilations\nin the early universe (a process that is required to ex-\nplain the signi\ufb01cant remnant of dark matter in today\u2019s\nuniverse), it was estimated that the branching fractions for\n\u03a5 \u2192(\u03b3+) invisible (the dominant decay mechanism de-\npended on the spin of the dark matter constituent) could\nbe as high as 0.41% \u2014 easily measured at the B-factories\nwith even a modest sample of \u03a5 mesons.\nThe BABAR and Belle collaborations have both searched\nfor invisible \ufb01nal states of \u03a5(1S) decay (Tajima, 2007;\nAubert, 2009b; del Amo Sanchez, 2011j). Both collabo-\nrations produced results in the search for purely invisible\n\ufb01nal states, \u03a5 \u2192invisible while the BABAR collaboration\nalso produced results for radiative invisible \ufb01nal states,\n\u03a5 \u2192\u03b3 +invisible. These searches are sensitive to di\ufb00erent\npossible angular momentum con\ufb01gurations of unknown in-\nvisible \ufb01nal states.\nSearches for \u03a5 \u2192invisible\nThe BABAR and Belle searches for purely invisible \ufb01nal\nstates proceed similarly. The Belle search appeared \ufb01rst\nand used a sample of 11 \u00d7 106 \u03a5(3S) mesons (Tajima,\n2007), while the BABAR search appeared later and used a\nsample of 91.4\u00d7106 \u03a5(3S) mesons (Aubert, 2009b). Both\nsearches used the transition\n\u03a5(3S) \u2192\u03c0+\u03c0\u2212\u03a5(1S)\n(18.4.26)\nto \u201ctag\u201d the presence of the \u03a5(1S) meson without recon-\nstructing it by using the kinematics of the dipion sys-\ntem. Speci\ufb01cally, if the pions are both produced recoiling\nagainst the \u03a5(1S) state then from four-momentum conser-\nvation the mass of the system recoiling against the dipion\nis given by\nM 2\nrecoil(\u03c0+\u03c0\u2212) = s + M 2\n\u03c0+\u03c0\u2212\u22122\u221asE\u2217\n\u03c0+\u03c0\u2212\n(18.4.27)\nwhere s is the square of the collider CM energy and\nM\u03c0+\u03c0\u2212(E\u03c0+\u03c0\u2212) is the mass (energy) of the dipion sys-\ntem. For a real dipion transition \u03a5(3S) \u2192\u03c0+\u03c0\u2212\u03a5(1S),\nM 2\nrecoil(\u03c0+\u03c0\u2212) = M 2\n\u03a5 (1S).\n\n510\nThe major challenges in this search are the trigger ef-\n\ufb01ciency for signal events and the large background from\npions that come from non-transition decays and from real\ntransition decays where the \ufb01nal-state products of the\n\u03a5(1S) are simply undetected due to detector e\ufb00ects. The\ntrigger e\ufb03ciency is a challenge due to the low transverse\nmomentum possessed by the pions; the energy from the\ntransition is shared between the two pions, typically lead-\ning to one low-momentum pion and one higher-momentum\npion.\nBoth the Belle and BABAR trigger systems require that\nlow-multiplicity events be triggered only when at least one\nof the tracks has a su\ufb03cient pT to distinguish it from back-\nground, and that the opening-angle between the tracks in\nthe plane transverse to the beams satisfy a minimum re-\nquirement. The Belle collaboration evaluated their trigger\ne\ufb03ciency by studying the e\ufb03ciency with which events are\nselected by a single-track trigger and then subsequently by\ndi\ufb00erent requirements on a second track in those events.\nThe BABAR collaboration evaluated their trigger e\ufb03ciency\nby explicitly reconstructing a control sample of events\nwhere \u03a5(3S) \u2192\u03c0+\u03c0\u2212\u03a5(1S) and the \u03a5(1S) then decays\nto a pair of leptons (either electrons or muons). The pi-\nons in this sample have identical kinematics to those in\nan equivalent \u03a5(1S) \u2192invisible decay, except that these\nevents are triggered by the high-momentum leptons and\nnot the lower-momentum pions. A selection similar to the\none applied by the BABAR trigger was then used on the pi-\nons to evaluate the e\ufb03ciency with which the dipion system\nis selected.\nThe backgrounds to this search come from the two\nsources mentioned above: events with pions that come\nfrom sources other than the \u03a5(3S) \u2192\u03a5(1S) dipion tran-\nsition (combinatorial) and events with pions that come\nfrom a real transition but where the \u03a5(1S) decay prod-\nucts are simply unreconstructed due to detector e\ufb00ects\n(peaking). The pions from combinatorial sources have no\npeak at Mrecoil(\u03c0+\u03c0\u2212) = M\u03a5 (1S) but dominate the data\nsamples prior to any rejection after selection the pions.\nBoth collaboration use combinations of kinematic infor-\nmation (Belle uses a Fisher discriminant while BABAR uses\na Random Forest of Decision Trees - see Chapter 4 for a\ndescription of these tools) to reject this source of back-\nground. Any remaining background has a smooth distri-\nbution through the signal region around the \u03a5(1S) mass\nand is easily modeled using a polynomial function whose\nparameters are determined by \ufb01tting the data directly.\nThe peaking background from real dipion transitions\nis studied using Monte Carlo simulations and the control\nsample described above, where \u03a5(1S) \u2192\u2113+\u2113\u2212is explicitly\nreconstructed using electron and muon \ufb01nal states. Both\ncollaborations compare the rate at which both \ufb01nal-state\nleptons, or just one \ufb01nal-state lepton, are reconstructed\nas a function of polar angle in the detector. This allows\nthem to correct the MC simulation of these backgrounds\nusing data measurements of the detector acceptance for\nthe \u03a5(1S) \ufb01nal-state products. In addition to this tech-\nnique, the BABAR collaboration studied the non-leptonic\n\u03a5(1S) decay backgrounds by using a control sample where\n)\n2\n (GeV/c\nrecoil\n-\u03c0\n+\n\u03c0\nM\n9.4\n9.42\n9.44\n9.46\n9.48\n9.5\n9.52\n)\n2\nEvents / (0.004GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n)\n2\n (GeV/c\nrec\nM\n9.42\n9.44\n9.46\n9.48\n9.5\n9.52\n )\n2\nEvents / ( 0.001 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n)\n2\n (GeV/c\nrec\nM\n9.42\n9.44\n9.46\n9.48\n9.5\n9.52\n )\n2\nEvents / ( 0.001 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\nFigure 18.4.25. The \ufb01ts to the recoil mass spectra. (top) The\nBelle \ufb01t, where the solid curve shows the result of the \ufb01t to\nsignal plus background distributions, the shaded area shows\nthe total background contribution, the dashed line shows the\ncombinatorial background contribution, and the dot-dashed\nline shows the expected signal for B(\u03a5(1S) \u2192invisible) =\n6 \u00d7 10\u22123 (Tajima, 2007). (bottom) The BABAR \ufb01t to Mrec \u2261\nMrecoil(\u03c0+\u03c0\u2212), where the solid line shows the \ufb01t including both\ncombinatorial and peaking contributions and the dash-dotted\nline indicates the contribution only from combinatorial back-\nground (Aubert, 2009b).\na photon of energy E\u03b3 > 0.250 GeV is present in addition\nto the pions; this selection is orthogonal to the nominal\nsignal selection. This sample is enriched in hadronic \u03a5(1S)\ndecays and was used to correct the modeling of acceptance\nfor such decays in the nominal selection.\nThe shape of the real transition background will be\nidentical to that of the signal because in both cases a real\n\u03a5(1S) is recoiling against the dipion system. Thus the re-\ncoil mass shape of this background (and that of the signal)\ncan be determined from the \u03a5(1S) \u2192\u2113+\u2113\u2212control sample\nbut the yield of the real transition backgrounds must be\ndetermined from the aforementioned studies and \ufb01xed in\nthe \ufb01nal \ufb01t to the data. The Belle collaboration estimated\ntheir real transition background to be 133.2+19.7\n\u221214.69 events,\nwhile the BABAR collaboration measured their peaking\nbackground to be 2444 \u00b1 123 events, with the dominant\ncontribution coming from \u03a5(1S) \u2192\u2113+\u2113\u2212decays where\nthe \ufb01nal-state leptons are undetected.\n\n511\nThe \ufb01ts to the recoil mass spectra from both experi-\nments are shown in Fig. 18.4.25. Neither experiment ob-\nserved a signi\ufb01cant deviation from their expected yield\nof peaking events due to background sources. Both ex-\nperiments set upper limits on the branching fraction for\n\u03a5(1S) \u2192invisible. Folding in the measured value for\n\u03a5(3S) \u2192\u03c0+\u03c0\u2212\u03a5(1S), the Belle collaboration determined\nthat\nB(\u03a5(1S) \u2192invisible < 2.5 \u00d7 10\u22123\n(18.4.28)\nat 90% C.L. and the BABAR collaboration determined that\nB(\u03a5(1S) \u2192invisible < 3.0 \u00d7 10\u22124\n(18.4.29)\nat 90% C.L.\nImpact of the results\nThe measurements described here for \u03a5(1S) \u2192invisible\nleave only about an order-of-magnitude of branching frac-\ntion space left before encountering the Standard Model\npredicted rate for \u03a5(1S) \u2192\u03bd\u03bd. This has closed much of\nthe space for low-mass dark matter, with m\u03c7 < m\u03a5 (1S)/2,\nto be produced in this way.\nSearch for \u03a5 \u2192\u03b3 + invisible\nThe search for radiative invisible \ufb01nal states, \u03a5(1S) \u2192\n\u03b3 + invisible also proceeds from a dipion transition sam-\nple but uses a sample of 98.3 \u00d7 106 \u03a5(2S) mesons and\nthe transition \u03a5(2S) \u2192\u03c0+\u03c0\u2212\u03a5(1S) to tag the presence\nof the \u03a5(1S) meson. Such a search has been performed\nby BABAR (del Amo Sanchez, 2011j). The presence of a\nphoton in addition to the dipion system is then used the\ntag the decay of the \u03a5(1S) via \u03a5(1S) \u2192\u03b3 + invisible.\nThe analysis assumes that the invisible system recoiling\nagainst the photon is a resonance (e.g. a low-mass Higgs),\ndenoted A0, that subsequently decays into a two-body in-\nvisible \ufb01nal state, A0 \u2192\u03c7\u00af\u03c7, where \u03c7 denotes an unde-\ntectable long-lived particle.\nThe signal events have a low multiplicity and are trig-\ngered in two ways: either by the presence of a pair of tracks\neach with pT > 0.25 GeV/c or by the presence of a single\nphoton with energy in the CM frame E\u2217> 0.8 GeV. Be-\ncause of the trigger selection depends on the energy of the\nphoton, the analysis is performed in regions corresponding\nto the mass of the recoiling resonance. The two regions are\na high-mass region, 7.5 \u2264mA0 \u22649.2 GeV/c2 (correspond-\ning to 3.5 \u2264m\u03c7 \u22644.5 GeV/c2) and a low-mass region\nmA0 \u22648.0 GeV/c2 (m\u03c7 \u22644 GeV/c2). The low-mass re-\ngion relies entirely on the single-photon trigger, while the\nhigh-mass region relies entirely on the track trigger.\nThe reconstructed dipion system is required to contain\ntwo positively identi\ufb01ed pion candidates (to reject electron\nand muon contamination) and have pT < 0.5 GeV/c. Nei-\nther pion can have momentum p > 1.0 GeV/c. The pho-\nton must have a CM energy satisfying E\u2217> 0.15 GeV\nand lie well within the central part of the electromagnetic\ncalorimeter. Additional photons can be present as long\nas their individual energies are less than that of the sig-\nnal photon and their total energy in the laboratory frame\ndoes not exceed 0.14 GeV. A multilayer perceptron neural\nnetwork is then used to combine kinematic variables from\nthe dipion system into a single discriminant that can re-\nject background. The neural network is trained on data\ntaken at a collider CM energy below the \u03a5(2S) resonance,\nand on signal MC simulation. In the low-mass region, this\napproach retains 87% of simulated signal events while re-\njecting 96% of events from non-\u03a5(2S) (continuum) events.\nIn the high-mass region, this approach retains 73% of sig-\nnal while rejecting 98% of continuum background.\nIn addition to backgrounds from sources other than\nthe \u03a5(2S), there could be backgrounds from real \u03a5(1S)\nradiative decays where the \ufb01nal-state products are di\ufb03-\ncult to detect reliably. For instance, \u03a5(2S) \u2192\u03c0+\u03c0\u2212\u03a5(1S),\nwhere the \u03a5(1S) then decays to either \u03a5(1S) \u2192\u03b3n\u00afn or\n\u03a5(1S) \u2192\u03b3K0\nLK0\nL, are allowed decays where the \ufb01nal-state\nhadrons are not e\ufb03ciently reconstructed in the BABAR de-\ntector. To reject these backgrounds, events are rejected\nwhere there is activity in the BABAR instrumented \ufb02ux\nreturn within a 20\u25e6window opposite the reconstructed\nsignal photon. This requirement is only applied in the\nlow-mass region for mA0 < 4 GeV/c2. In the high-mass\nregion there is a potential contamination from the process\ne+e\u2212\u2192e+e\u2212\u03b3\u2217\u03b3\u2217where \u03b3\u2217\u03b3\u2217\u2192\u03b7\u2032 and \u03b7\u2032 \u2192\u03b3\u03c0+\u03c0\u2212\nwhile the electron and positron escape detection at low-\nangles to the beams. This is largely rejected by requiring\nthe opening angle between the photon and the dipion sys-\ntem be no more than 160\u25e6.\nThe signal is extracted from a maximum likelihood \ufb01t\nto two variables: the dipion recoil mass Mrecoil(\u03c0+\u03c0\u2212) and\nthe \u201cmissing mass\u201d, i.e. the mass of the system recoiling\nagainst the reconstructed dipion and photon,\nM 2\nrecoil(\u03c0+\u03c0\u2212\u03b3) = (Pe+e\u2212\u2212P\u03c0+\u03c0\u2212\u2212P\u03b3)2.\n(18.4.30)\nThe \ufb01t is performed in steps of M 2\nrecoil(\u03c0+\u03c0\u2212\u03b3). The mod-\nels contain contributions from multiple sources, including\nsignal (whose shape is determined from MC simulation),\ncontinuum background, radiative \u03a5(1S) decays, and back-\nground from real \u03a5(3S) \u2192\u03a5(1S) transitions. Projections\nof the \ufb01ts in each of the two dimensions are shown in\nFig. 18.4.26. No signi\ufb01cant yield of signal events is ob-\ntained from any of the scan points in the \ufb01ts. The 90%\nC.L. upper limits on the product of branching fraction\nB(\u03a5(1S) \u2192\u03b3A0) \u00d7 B(A0 \u2192invisible) are shown in Fig.\n18.4.27 and ranges (1.9 \u22124.5) \u00d7 10\u22126 for the low-mass\nregion and (2.7 \u221237) \u00d7 10\u22126 in the high-mass region, as-\nsuming a scalar A0.\nThe low-mass dark matter models cited earlier in this\nsection predicted that the branching fraction for the ra-\ndiative \ufb01nal state could be as high as 10\u22125 \u221210\u22124. The\nexperimental results discussed here cover well that upper\nrange of the predicted branching fractions and exclude the\nlargest possible rates predicted by these models.\n\n512\nEvents / ( 0.001 GeV ) \n0\n2\n4\n6\n8\n10\n(a)\n ) \n2\nEvents / ( 1 GeV\n0\n2\n4\n6\n8\n(b)\n9.44\n9.45\n9.46\n9.47\n9.48\n0\n5\n10\n15\n(c)\n0\n20\n40\n60\n0\n2\n4\n6\n8\n10\n(d)\n (GeV)\nrecoil\nM\n9.44\n9.45\n9.46\n9.47\n9.48\n0\n5\n10\n15\n20\n25\n30\n(e)\n)\n2\n (GeV\n2\nX\nM\n40\n50\n60\n70\n80\n-1\n10\n1\n10\n2\n10\n(f)\n0\n0\nFigure 18.4.26. Projection plots from the \ufb01t with Nsig = 0\nonto (a,c,e) recoil mass Mrecoil \u2261Mrecoil(\u03c0+\u03c0\u2212) and (b,d,f)\nmissing mass-squared M 2\nX \u2261M 2\nrecoil(\u03c0+\u03c0\u2212\u03b3) (del Amo San-\nchez, 2011j). (a,b): low-mass region with a veto on activity\nin the BABAR instrumented \ufb02ux return (IFR); (c,d): low-mass\nregion without IFR veto; (e,f): high-mass region. Overlaid is\nthe \ufb01t with Nsig = 0 (solid blue line), continuum background\n(black dashed line), radiative leptonic \u03a5(1S) decays (green\ndash-dotted line), and (c,d) radiative hadronic \u03a5(1S) decays\nor (e,f) \u03b7\u2032 background (magenta dotted line).\n (GeV)\nA0\nm\n0\n2\n4\n6\n8\n)\n-6\nBF UL \u001d@ 90% C.L. (10\n1\n10\nFigure 18.4.27. 90% C.L. upper limits for B(\u03a5(1S) \u2192\u03b3A0)\u00d7\nB(A0 \u2192invisible) (del Amo Sanchez, 2011j).\n18.4.7.3 Search for Lepton Flavor Violation\nMotivation: new interactions\nLepton \ufb02avor is an accidentally conserved quantum num-\nber in the original formulation of the Standard Model;\nhowever, the observation of neutrino mixing implies that\ncharged lepton \ufb02avor violation should occur, albeit at a\nscale that is suppressed by a factor of (\u2206m2\n\u03bd/M 2\nW )2 \u2264\n10\u221248, as discussed by Feinberg (1958), Bilenky and Pon-\ntecorvo (1976), Strumia and Vissani (2006). An exper-\nimental observation of such violation at present exper-\nimental capabilities would be unambiguous evidence of\nphysics beyond the Standard Model, as discussed by El-\nlis, Gomez, Leontaris, Lola, and Nanopoulos (2000), El-\nlis, Raidal, and Yanagida (2004), Pati and Salam (1974),\nGeorgi and Glashow (1974). For instance, supersymmetry\nincludes mechanisms by which such violation naturally oc-\ncurs.\nExperimental measurement\nThe BABAR Collaboration performed a search for lepton\n\ufb02avor violation using the decays \u03a5(nS) \u2192(e\u00b1/\u00b5\u00b1)\u03c4 \u2213,\nwhere n = 2, 3. The searches were performed using (98.6\u00b1\n0.9)\u00d7106 \u03a5(2S) decays and (116.7\u00b11.2)\u00d7106 \u03a5(3S) de-\ncays (Lees, 2010c). In addition, data from other resonances\nand from runs taken away from Upsilon resonances were\nused to characterize and study the backgrounds.\nThe search uses the fact that the collider is producing\nthe parent Upsilon resonance at rest in the CM frame; the\nelectron or muon that results directly from the Upsilon\ndecay (the \u201cprimary lepton\u201d) will have energy very close\nto the single-beam energy in the Upsilon rest frame, EB =\n\u221as/2. The primary tau lepton will decay, and a second\nlepton, or a charged pion, consistent with tau decay is\nthen searched for. If a second lepton is found, it is required\nto have a di\ufb00erent \ufb02avor from the primary lepton. If a\npion is found, one or two additional neutral pions must\nalso be reconstructed in the same event. These measures\nare required in order to suppress Bhabha events or \u00b5-pair\nbackgrounds.\nThe main source of background in this search is from\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212events. The four individual search channels\neach have other sources of background, arising primarily\nfrom lepton and hadron misidenti\ufb01cation. Bhabha events\nare further suppressed by requiring that the visible mass\nin each candidate event has less than 95% of the collider\nCM energy (indicating the presence of neutrinos, which\nare not present in Bhabha events). In addition, the miss-\ning momentum in each event must not point close to the\nbeamline. Higher-order QED backgrounds, as from two-\nphoton fusion, are suppressed by requiring that the trans-\nverse momentum component of the charge particles\u2019 vec-\ntor sum is more than 20% of the quantity \u221as\u2212|p1|\u2212|p2|,\nwhere pi is the three-momentum of charged particle i.\nThe primary lepton momentum is de\ufb01ned by the re-\nquirement that x \u2261|p1|/EB > 0.75. For the hadronic tau\ndecays, the momentum of the tau daughter charged parti-\ncle is required to satisfy |p2|/EB < 0.8, and the invariant\nmasses of the track and neutral pion(s) system must be\nconsistent with the mass of either the \u03c1\u00b1 or the a\u00b1\n1 . The\n\u00b5-pair background in the \u00b5\u03c4 channel is suppressed by re-\nquiring that the opening angle between the charged tracks\nin the plane transverse to the beams is less than 172\u25e6.\nAfter all selection criteria are applied, the selection\ne\ufb03ciency determined from a signal MC simulation range\n\n513\nTable 18.4.12. Branching fractions and 90% CL ULs for\nlepton-\ufb02avor violating \u03a5(nS) \u2192\u2113\u00b1\u03c4 \u2213decays (Lees, 2010c).\nThe \ufb01rst error is statistical and the second is systematic.\nB (10\u22126)\nUL (10\u22126)\nB(\u03a5(2S) \u2192e+\u03c4 \u2212)\n0.6+1.5+0.5\n\u22121.4\u22120.6\n< 3.2\nB(\u03a5(2S) \u2192\u00b5+\u03c4 \u2212)\n0.2+1.5+1.0\n\u22121.3\u22121.2\n< 3.3\nB(\u03a5(3S) \u2192e+\u03c4 \u2212)\n1.8+1.7+0.8\n\u22121.4\u22120.7\n< 4.2\nB(\u03a5(3S) \u2192\u00b5+\u03c4 \u2212)\n\u22120.8+1.5+1.4\n\u22121.5\u22121.3\n< 3.1\nbetween (4\u22126)%, depending on the signal mode, including\nthe tau decay branching fractions.\nThe signal yield in the data is determined by an un-\nbinned extended maximum likelihood \ufb01t to the distri-\nbution of x, de\ufb01ned earlier. Signal events are expected\nto peak at x \u22480.97, while \u03c4-pair background exhibits\na smoothly falling shape that cuts o\ufb00at the kinematic\nendpoint of x = 0.97 (the lepton kinematic endpoint for\ncharged leptons produced in tau decay). Bhabha and \u00b5-\npair background exhibit a peak at x = 1, which is about\n(2.5 \u22123)\u03c3x above the signal, where \u03c3x \u22480.01 is the de-\ntector resolution on x.\nProbability density functions are obtained for each of\nthese components. The signal and Bhabha/\u00b5-pair p.d.f.s\nare obtained from MC simulation. Signal events are de-\nscribed using a Crystal Ball function, while the Bhabha/\u00b5-\npair backgrounds have a smooth component modeled us-\ning and ARGUS function and a peaking component mod-\neled using a Gaussian. The \u03c4-pair background is modeled\nusing a polynomial convoluted with a detector resolution\nfunction. The \ufb01t procedure is validated by using \u03a5(4S)\nand o\ufb00-resonance data that are separated into samples\nwith comparable numbers of events to those expected at\nthe \u03a5(3S) and \u03a5(2S). No signi\ufb01cant signal yield is ob-\ntained in these control tests.\nThe results of the \ufb01ts to the \u03a5(3S) and \u03a5(2S) data\nare given in Table 18.4.12. No signi\ufb01cant signal yields\nare obtained. These results are then used to place con-\nstraints on physics beyond the Standard Model. For exam-\nple, Domingo and Ellwanger (2011) use this measurement\nto put limits on the decay of a Higgs boson to a pair of\nlow-mass CP-odd Higgs bosons, interpreting this result as\na limit on the mixing of the \u03b7b meson with such a CP-odd\nHiggs boson.\n18.4.7.4 Test of Lepton Universality\nMotivation - mass-dependent couplings\nThe Standard Model expresses no preference for the par-\ntial width \u0393\u03a5 (1S)\u2192\u2113\u2113that depends on lepton \ufb02avor, up to\ncorrections due to phase space (where \u2113= e, \u00b5, \u03c4). This\nis referred to as \u201clepton universality\u201d in the decay of the\n\u03a5(1S) meson. One can compute the ratio of partial widths\nto di\ufb00erent \ufb01nal states and measure those ratios in data to\nsee whether the Standard Model prediction is correct. For\ninstance, the ratio of the \u03c4-to-\u00b5 partial widths is predicted\nto be R\u03c4\u00b5(\u03a5(1S)) \u22480.992 in the Standard Model.\nExperimental measurement\nThe BABAR Collaboration has searched for violation of\nlepton universality in \u03a5 decay using the \u03a5(3S) and \u03a5(2S)\ndata samples (del Amo Sanchez, 2010r). The analysis de-\ntermines the ratio of branching fractions,\nB(\u03a5(1S) \u2192\u00b5+\u00b5\u2212)\nB(\u03a5(1S) \u2192\u03c4 +\u03c4 \u2212)\n(18.4.31)\nwhose value is de\ufb01nitively predicted in the Standard\nModel. For instance, work by Sanchis-Lozano (2004), Ful-\nlana and Sanchis-Lozano (2007), and Domingo, Ellwanger,\nFullana, Hugonie, and Sanchis-Lozano (2009) calculate\nthe Standard Model rate and then discuss the implica-\ntions of beyond-the-Standard Model physics on altering\nthis value. Deviation from the SM prediction would indi-\ncate the presence of an interaction that couples di\ufb00erently\nto the two lepton \ufb02avors, such as the presence of a low-\nmass CP-odd Higgs Boson like the one searched for in\n18.4.7.1. The analysis uses the recoil method to tag the\npresence of the \u03a5(1S) in the \ufb01nal state and the presence\nof leptons to indicate the \ufb01nal-state decay of the \u03a5(1S).\nThe BABAR Collaboration has measured the above ra-\ntio as a test of lepton universality (del Amo Sanchez,\n2010r). The measurement uses a sample of (121.8\u00b11.2)\u00d7\n106 \u03a5(3S) mesons; 10% of the sample is used to tune the\nanalysis and the remaining 90% is used to obtain the \ufb01nal\nresults. A previous measurement of R\u03c4\u00b5(\u03a5(1S)) was per-\nformed by the CLEO Collaboration (Besson et al., 2007)\nand found R\u03c4\u00b5(\u03a5(1S)) = 1.02 \u00b1 0.02 (stat.) \u00b1 0.05 (syst.).\nThe BABAR measurement uses the transition \u03a5(3S) \u2192\n\u03c0+\u03c0\u2212\u03a5(1S) to tag the existence of the \u03a5(1S) meson, fol-\nlowed by \u03a5(1S) \u2192\u2113+\u2113\u2212. Only \u03c4 decays to a single charged\nparticle and neutrinos are considered. Event selection is\noptimized using MC simulations.\nEvents are required to contain exactly four charged\ntracks, each with transverse momentum satisfying 0.1 <\npT < 10.0 GeV/c. The four tracks are geometrically con-\nstrained to come from the same spatial location, and the\ndistance of closest approach of each track must lie within\n10 cm of the interaction region along the beam axis and\nwithin 1.5 cm in the plane transverse to the beam axis.\nThe ratio of the second-to-zeroth Fox-Wolfram moments\nfor the events must be < 0.97 in order to reject events like\nradiative Bhabha scatters and \u00b5+\u00b5\u2212\u03b3, where the photon\nconverts to a pair of tracks. In addition, the absolute value\nof the cosine of the polar angle of the event thrust axis\nmust be less than 0.96.\nAs in previous measurements using this topology, the\n\u03a5(1S) candidate is formed from an opposite-charge lepton\npair which are constrained to arise from a common spa-\ntial point. The \u03a5(1S) \u2192\u00b5+\u00b5\u2212and \u03a5(1S) \u2192\u03c4 +\u03c4 \u2212\ufb01nal\nstates have di\ufb00erent background contributions. Due to the\npresence of neutrinos in the tau \ufb01nal states, backgrounds\nfrom e+e\u2212\u2192\u03c4 +\u03c4 \u2212and non-leptonic \u03a5(1S) decays are\npossible.\n\n514\nFigure 18.4.28. The recoil mass distribution for the dimuon (left) and di-tau (center) \ufb01nal states, and the dilepton mass for\nthe dimuon \ufb01nal state (right) (del Amo Sanchez, 2010r).\nThe \u03a5(1S) \u2192\u00b5+\u00b5\u2212\ufb01nal state (denoted D\u00b5) is re-\nquired to contain same-\ufb02avor identi\ufb01ed muons. The dif-\nference between the intial-state and \ufb01nal-state energies is\nrequired to be less than 0.5 GeV, to select events where the\nfour tracks represent all of the \ufb01nal-state particles (e.g. no\nsigni\ufb01cant missing energy from neutrinos). The magnitude\nof the dipion momentum in the CM frame is required to\nsatisfy < 0.875 GeV/c, and the cosine of the angle between\nthe two lepton candidates is required to satisfy < \u22120.96.\nFor the \u03a5(1S) \u2192\u03c4 +\u03c4 \u2212candidates (denoted D\u03c4),\na tighter set of restrictions are required to reject back-\ngrounds mentioned above. The di\ufb00erence between the\nintial-state and \ufb01nal-state energies is required to be\ngreater than 5.0 GeV, to select events with signi\ufb01cant\nmissing energy due to neutrinos. The magnitude of the\ndipion momentum in the CM frame is required to sat-\nisfy < 0.825 GeV/c and each pion must have a CM mo-\nmentum satisfying < 0.725 GeV/c. The measured di\ufb00er-\nence in the energy of the \u03a5(3S) and \u03a5(1S) must satisfy\n0.835 < \u2206E\u2217< 0.925 GeV. A boosted decision tree (see\nChapter 4 for a description of this tool) is used to further\nreject background, employing event-shape and kinematic\nvariables. The performance of the classi\ufb01er is assessed us-\ning data taken at a CM energy below the \u03a5(3S) mass.\nIn order to select events resulting from the dipion tran-\nsition, a requirement is placed on the di\ufb00erence in the in-\nvariant mass of the \u03a5(3S) and \u03a5(1S) states; as determined\nfrom the \ufb01nal-state tracks, \u2206M < 2.5 GeV/c2. In addition,\nthe dipion mass is required to satisfy 0.28 < M\u03c0+\u03c0\u2212<\n0.90 GeV/c2. For events with multiple track combinations\nsatisfying these cuts, the combination with the \u2206M clos-\nest to the nominal value is chosen.\nAn unbinned extended maximum likelihood \ufb01t is used\nto extract the signal yields. The \ufb01t employs two variables:\nfor the \u03a5(1S) \u2192\u00b5+\u00b5\u2212\ufb01nal state, the \ufb01t used the mass\nrecoiling against the dipion system (Equation 18.4.3) and\nthe invariant mass of the lepton pair. Monte Carlo simu-\nlations are used to verify these variables are uncorrelated,\nand the total likelihood is the product of the likelihoods in\neach dimension. For the \u03a5(1S) \u2192\u03c4 +\u03c4 \u2212\ufb01nal state, only\nthe dipion recoil mass is used.\nThe use of a ratio of branching fraction to the two\npossible \ufb01nal states allows for the cancellation of common\nsystematic uncertainties. The two \ufb01nal-state samples are\nsimultaneously \ufb01tted using the likelihood functions, and\nthe result of the \ufb01t is R\u03c4\u00b5 = 1.006 \u00b1 0.013 (statistical\nuncertainty only). The projections of the \ufb01ts to the data\nin the di\ufb00erent variables are shown in Fig. 18.4.28.\nResidual systematic uncertainties that do not cancel in\nthe ratio are due to the trigger selection e\ufb03ciency, event\nselection, and muon selection. The event selection e\ufb03-\nciency systematic uncertainty is determined by comparing\nthe shape of each variable in data and MC; the di\ufb00erence\nin e\ufb03ciency due to shape di\ufb00erences is determined to be\n1.2%. The muon identi\ufb01cation systematic uncertainty is\ndetermined in situ by comparison the data and MC rates\nat which only one, or both, tracks are identi\ufb01ed as muons.\nThis uncertainty is determined to be 1.2%, and a correc-\ntion factor of 1.023 on the e\ufb03ciency is also determined. A\ncorrection to the di-tau \ufb01nal-state trigger e\ufb03ciency is de-\ntermined to be 1.020; the systematic uncertainty on the ef-\n\ufb01ciency is determined to be 0.10%. For the di-muon mode,\nthe systematic uncertainty on the trigger e\ufb03ciency is de-\ntermined to be 0.18%.\nThe p.d.f. shape uncertainty for the signal components\nis determined by varying the parameters; the model pa-\nrameters were determined from the 10% of data used for\ndeveloping the analysis. This uncertainty on the p.d.f.\nshapes is determined to be 0.22%. The recoil mass shape\nis assumed to be the same for the two \ufb01nal states; shape\ne\ufb00ects due to trigger e\ufb03ciency are assumed to be ne-\nglectable, and this assumption incurs a systematic uncer-\ntainty of 0.6%.\nTaking into account correction factors and systematic\nuncertainties, the \ufb01nal measured ratio of branching frac-\ntions is determined to be:\nR\u03c4\u00b5 = 1.005 \u00b1 0.013 (stat.) \u00b1 0.022 (syst.).\n(18.4.32)\nNo signi\ufb01cant deviation from the Standard Model expec-\ntation of one is observed.\n\n515\nChapter 19\nCharm physics\nIn this chapter we proceed to the studies of open charm.\nIt is fair to say that charm physics \u2014 more precisely the\nstudies of hadrons containing a charm quark \u2014 under-\nwent a revival of interest, both experimentally and theo-\nretically, during the time of the B Factories. The main\nreasons for this are threefold; the \ufb01rst reason may be\ncalled experimental, the second electroweak, and the third\nstrong. The experimental reason is the awareness of the\ncommunity that B Factories are an abundant source of\ncharm hadrons as well as B mesons. The cross-section for\ne+e\u2212\u2192\u03a5(4S) production at \u221as \u224810.58 GeV is around\n1.1 nb, while that for the so-called continuum produc-\ntion of charm quark pairs, e+e\u2212\u2192\u03b3\u2217\u2192c\u00afc, is around\n1.3 nb. For an integrated luminosity of 1 ab\u22121 this corre-\nsponds to about 600\u00d7106 D\u2217+ mesons produced together\nwith another charmed hadron, available for study. The\nelectroweak reason is due to the \ufb01rst experimental evi-\ndence for mixing phenomena in the system of neutral D\nmesons, which became available in 2007. At about that\ntime it became obvious that \u2014 on using the world av-\nerages of the measured quantities including results from\nhadron colliders \u2014 the mixing parameters can and will be\nmeasured to sub-percent accuracy. Such measurements per\nse represent a possible way to search for processes beyond\nthe SM. When it became clear that with the experimen-\ntally determined values of parameters it would be di\ufb03cult\nto make speci\ufb01c statements about the presence of New\nPhysics phenomena, experimental as well as theoretical ef-\nforts turned to studies of CP violation in the charm sector.\nThis remains the focus of charm physics measurements to-\nday. Last but certainly not least there has been a third,\nstrong-sector reason for the increased interest in charm\nphysics. The discovery of the X(3872) particle in 2003\n(the observation of this particle has been con\ufb01rmed and\nits properties studied by many experiments) with some\nof its properties similar to the conventional charmonia,\nbut some in obvious disagreement with those, provides\nstrong evidence that QCD has a rich spectrum of states\nbeyond conventional mesons and baryons. Most of these\nso-called exotic states (although not all of them) bear a\nresemblance to hadrons composed of charm quarks. Sur-\nprises in the spectroscopy of charm hadrons continued also\nin the open charm sector with the discovery of D\u2217\ns0(2317)+\nand Ds1(2460)+ in 2003 and 2004, with their properties\nsigni\ufb01cantly di\ufb00erent than expected from the na\u00a8\u0131ve quark\nmodel.\nThe topic of conventional and exotic charmonium-like\nstates is addressed in Chapter 18. This chapter focuses\non the studies of open charm: mesons and baryons with\na single charm quark. These states yield a number of in-\nteresting results which are, in many ways, complementary\nto results from B mesons. For any study of charm mesons\ntheir decay modes must be known. The latter are the sub-\nject of the \ufb01rst section in the chapter. The following sec-\ntion discusses the electroweak aspect of the charm physics\nwith the results on mixing and CP violation parameters.\nThe strong-sector is in more details illuminated in the last\ntwo sections on the charm meson and charm baryon spec-\ntroscopy.\n\n516\n19.1 Charmed meson decays\nEditors:\nAntimo Palano (BABAR)\nJolanta Brodzicka (Belle)\nAdditional section writers:\nChunhui Chen, Patrick Roudeau, An\u02c7ze Zupanc\n19.1.1 Introduction\nThe \ufb01rst discovered weak decays of the charm hadrons\nwere D0 \u2192K\u2212\u03c0+, K\u2212\u03c0+\u03c0+\u03c0\u2212(Goldhaber et al., 1976)\nand D+ \u2192K\u2212\u03c0+\u03c0+\n(Peruzzi et al., 1976) observed\nby MARK III at the SPEAR e+e\u2212collider operating at\ncharm threshold. They allowed D mass measurements and\nestablished the Glashow-Iliopoulos-Maiani (GIM) mecha-\nnism (Glashow, Iliopoulos, and Maiani, 1970), which re-\nquired existence of a charm quark to explain absence of\n\ufb02avor-changing neutral currents (FCNC) at tree level, re-\nsulting in large suppression of the strangeness-changing\nkaon decays like K0 \u2192\u00b5+\u00b5\u2212. Later on, the D+\ns \u2192\u03c6\u03c0+\ndecay was discovered by CLEO at CESR (Chen et al.,\n1983), and followed by the color-suppressed D+\ns \u2192\u00afK\u22170K+\nobserved by ARGUS at DORIS-II (Albrecht et al., 1986).\nSince then, charm decay measurements have been thor-\noughly performed, and triggered o\ufb00by searches for non-\nstandard weak interactions, as well as need for under-\nstanding of non-perturbative features in strong interac-\ntions. Both aspects are signi\ufb01cantly di\ufb00erent from the b-\nquark sector, making the measurements in general more\ndi\ufb03cult. Charm sector o\ufb00ers however an unique way to\ntest the \ufb02avor physics of up-type quarks,112 complemen-\ntary to down-type quarks being investigated through mea-\nsurements of strange and bottom decays.\nShort distance contributions to \ufb02avor changing neutral\ncurrent processes of the charm quark are highly GIM sup-\npressed in the Standard Model, since the mass di\ufb00erences\nof the down-type quarks are small compared to the weak\nboson mass. A perturbative calculation of c \u2192u FCNC\nprocesses yield a suppression factor (m2\nb \u2212m2\nd)/m2\nW ,\nwhereas FCNC in B and K decays are relatively strong\ndue to the factor (m2\nt \u2212m2\nu)/m2\nW ; thus the heavy top quark\nweakened the GIM suppression mechanism. However, due\nto the fact that in D decays no particular suppression hap-\npens due to CKM factors, there are in general large long\ndistance contributions, making an analysis of the short-\ndistance dynamics di\ufb03cult. As an example, the short dis-\ntance contribution to D0 \u2212\u00afD0 oscillation is very small, by\nfar exceeded by long distance contributions that are hard\nto compute.\nConsequently, long-distance dynamics, like \ufb01nal state\ninteractions (FSI), play an important role, since they are\nin general much larger in charm meson decays than for\nB(s) decays. In many cases they exceed the short-distance\n112 Top quarks due to their short lifetime do not hadronize,\nthus many phenomena cannot be studied.\ncontributions even by a few order of magnitudes. Com-\npared to B decays there is a smaller energy release in D(s)\ndecays, resulting in production of slower daughter parti-\ncles, which thus are more likely to in\ufb02uence each other\nbefore they leave interaction region. Any precision elec-\ntroweak predictions require then theoretical improvement\nin calculating long-distance QCD e\ufb00ects to remove sub-\nstantial hadronic uncertainties. Strategies for NP searches\nand interpretation of measurements highly depend on quan-\ntitative information on hadronic e\ufb00ects. Such e\ufb00ects are\nnon-perturbative and their theoretical calculations are still\nchallenging for any approach/method. As charm quark\nlies inbetween the light \ufb02avours (mu,d,s \u2264\u039bQCD) de-\nscribed by chiral perturbation theory (ChPT) and heavy\nquarks (mb \u226b\u039bQCD) treated by heavy-quark e\ufb00ective\ntheory (HQET), charm decays can bring new insight into\nnon-perturbative QCD. Since heavy-quark mass expan-\nsion does not work as well for charm decays, thus compu-\ntation of hadronic e\ufb00ects is more di\ufb03cult than for corre-\nsponding B decays. Despite of this, charm decays can still\nhelp to establish theoretical tools and allow their callibra-\ntion for calculations inevitable for B(s) decays.\n19.1.1.1 Quark diagrams for weak decays of charm mesons\nQuark diagrams underlying hadronic, semileptonic and\nleptonic decays of charm mesons are shown in Fig. 19.1.1.\nTaking into account topology of these quark graphs, they\nare either simple tree-level diagrams (Fig. 19.1.1(a-d,g,h))\nor pengiun diagrams (Fig. 19.1.1(e,f)) representing higher-\norder, loop-level processes.\nTree-level hadronic decays (Fig. 19.1.1(a-c)) and semi-\nleptonic ones (Fig. 19.1.1(f)) proceed through c \u2192W +s\ncurrent and thus have amplitudes governed by the CKM\nmatrix element |Vcs| \u22430.97. These decays are Cabibbo-\nfavored (CF) processes, while the corresponding Cabibbo-\nsuppressed (CS) decays proceed via c \u2192W +d and involve\n|Vcd| \u22430.22. Unless W + materializes into either l+\u03bdl lep-\ntons (Fig. 19.1.1(g,h)) or u \u00afd pair (Fig. 19.1.1(a,b,d)) in-\nducing the CKM factor of |Vud|, Cabibbo suppression may\narise from the light-quark u\u00afs vertex involving |Vus|. Thus\nthe CF modes at the tree level proceed through c \u2192\ns \u00afdu, singly Cabibbo-suppressed (SCS) ones through ei-\nther c \u2192d \u00afdu or c \u2192s\u00afsu, while doubly Cabibbo-suppresed\n(DCS) modes via c \u2192d\u00afsu.\nFigures 19.1.1(a,b,e,g) represent spectator decays, in\nwhich a light constituent antiquark does not participate\nin the weak interaction, contrary to non-spectator decays\nshown in Fig. 19.1.1(c,d,f,h).\nDecays of ground charmed mesons to \ufb01nal states in-\nvolving leptons (Fig. 19.1.1(g,h)) are the simplest and the\ncleanest channels and, as such, enable tests of the SM\npredictions or the Lattice-QCD calculations in the charm\nsector.\nSemileptonic D(s) \u2192Xl+\u03bdl decays (where l = e or\n\u00b5), comprise signi\ufb01cant fractions of D(s) total widths (see\nSection 19.1.5); up to about for 6% D0, 16% for D+ and\n6% for D+\ns mesons. In the underlying CF decay diagram\n(Fig. 19.1.1(g)), a virtual W + boson decays to the l+\u03bdl\n\n517\nFigure 19.1.1. Quark diagrams for charm meson decays:\nhadronic (a-f), semileptonic (g), leptonic (h). Diagrams un-\nderlying hadronic decays: external W emission (a), internal\nW emission (b), W exchange (c), W annihilation (d), W-loop\npenguin (e) and W-loop penguin annihilation (f).\nsystem, while the s\u00afq pair hadronizes into a strange meson\nindependently of the leptonic current. This hadronization\nis described by related form factors; single one for spin-0\nhadron and three form factors for vector meson. The form\nfactors increase with momentum transfer q2 \u2261M 2(l+\u03bdl),\nas for maximal q2 value the \ufb01nal state hadron is at rest in\nthe initial D rest frame and an overlap of wave functions\nof initial and \ufb01nal states is largest. Measurements of shape\nof the form factor and its value at maximal q2 allow one to\ntest theoretical calculations performed with either HQET\nbased models or with LQCD. Since semileptonic decays\noften serve as a reference for hadronic decays, it is impor-\ntant to check whether the D+\ns semileptonic decays mirror\nthe D ones. Precision of D+\ns decays like D+\ns \u2192\u03b7(\u2032)l+\u03bdl\nand D+\ns \u2192\u03c6l+\u03bdl (with uncertainties of \u00b16%-\u00b120%), is\nstill lower than for CF D \u2192\u00afK(\u2217)l+\u03bdl and CS D \u2192\u03c0l+\u03bdl\nor D \u2192\u03c1l+\u03bdl decays (with uncertainties of \u00b12%-\u00b13%).\nHadronic analogue of the semileptonic process is\nshown in Fig. 19.1.1(a) where an externally-emitted vir-\ntual W + materializes into quark pair forming the \ufb01nal-\nstate hadron. The corresponding process with an inter-\nnal W emission (Fig. 19.1.1(b)) has di\ufb00erent quark pair-\nings. Such a diagram represents a color-suppressed de-\ncay, as it requires a color matching between the quarks\noriginating from di\ufb00erent decay vertices. In the simplest\napproach based on analogy to semileptonic decays, pre-\nsented hadronic decays are expressed as a product of two\nhadronic currents describing formation of mesons out of\nquark-antiquark pairs. In this approach, called na\u00a8\u0131ve fac-\ntorization, the hadronic currents for a two body decay\nare expressed by the decay constants of the respective\nmeson and the form factors for the D \u2192meson transi-\ntion (see Section 19.1.1.3). Non-perturbative strong inter-\nactions, like soft-gluon e\ufb00ects and rescattering of the \ufb01nal-\nstate particles, complicates the simple picture represented\nby the quark diagrams, and thus renders factorization in-\nvalid. Measurements performed so far suggest that na\u00a8\u0131ve\nfactorization for D decays does not work as well as for\nB decays, where a QCD based factorization has been for-\nmulated using a 1/mb expansion. Overall it is fair to say\nthat there is no satisfactory theoretical framework for the\ndescription of exclusive non-leptonic charm decays.\nLeptonic D+\n(s) \u2192l+\u03bdl decays (see Section 19.1.6),\nproceed through W-annihilation diagram (Fig. 19.1.1(h)).\nDue to helicity suppression which results in the m2\nl lepton-\nmass dependence of the decay width, rate for light charged\nleptons is small. Since D+\ns \u2192l+\u03bdl decays involve Vcs, with\nrespect to Vcd underlying D+ \u2192l+\u03bdl, leptonic D+\ns de-\ncay rates are signi\ufb01cantly larger than those for D+. All\nthe strong interaction e\ufb00ects, namely hadronic dynam-\nics of the initial meson, are factorized into its decay con-\nstant fD+\n(s), which is related to an overlap of wave func-\ntions of the constituent quark and antiquark. Measure-\nment of D+\n(s) \u2192l+\u03bdl allows ones to determine the product\nfD+\n(s)|Vcd(cs)|, thus to extract fD+\n(s) one needs the |Vcd(cs)|\nvalue from other than leptonic decays.\nDecay constants are fundamental parameters, and can\nserve as a test how well we are able to model dynamics of,\nin general, non-perturbative e\ufb00ects of hadronic dynamics.\nBy measuring fD+\n(s) one can verify the Lattice-QCD cal-\nculations used for calculation of B decay constants, which\nare di\ufb03cult to measure as their leptonic decays are addi-\ntionally suppressed by the tiny value of Vub. Also, having\nboth fD+ and fD+\ns measured one can directly estimate\nSU(3)-\ufb02avor symmetry breaking and compare it with the-\nory prediction. Such a test would help to estimate reliably\ne\ufb00ects of violation of the SU(3)-symmetry based fBs = fB\nrelation, as fBs cannot be directly measured and must rely\non fB measurement.\nThe\nW-annihilation\nhadronic\ndecays\n(Fig. 19.1.1(d)), although the helicity suppression is\n\n518\nhere mitigated by strong interactions, are still strongly\nsuppressed\nwith\nrespect\nto\nthe\ntree-level\nspectator\nprocesses; similar applies to W-exchange processes\n(Fig. 19.1.1(c)). First signal for W-exchange decay was\nD0 \u2192\n\u00afK0\u03c6 (Albrecht et al., 1985a) owing to the fact\nthat helicity suppression does not apply to spin-0 meson\ndecays with vector particle in \ufb01nal state. Though its large\nbranching ratio of 10\u22122 suggests that some QCD e\ufb00ects,\nlike rescattering, are involved in the decay dynamics.\nThe CKM elements parameterizing the mixing of the\n\ufb01rst two families into the third are all at least of order\n\u03bb2 in the Wolfenstein parameterization, and hence charm\nphysics can be described to a good approximation by tak-\ning into account only the \ufb01rst two families. To this end, we\nhave approximatively VusV \u2217\ncs \u2248\u2212VudV \u2217\ncd which has the in-\nteresting implication that the e\ufb00ective interaction for SCS\nc \u2192u transitions takes the form\nHe\ufb00= GF\n\u221a\n2 VusV \u2217\ncs(\u00afcu)V\u2212A[(\u00afss)V\u2212A \u2212( \u00afdd)V\u2212A] (19.1.1)\nwhich vanishes in the SU(3) limit, i.e. once the strange\nand the down quark have the same mass. However, SU(3)\nis severely broken and hence this suppression due to the\nSU(3) \ufb02avor symmetry is not very e\ufb00ective.\n19.1.1.2 Hadronic decays; application of symmetries\nD mesons decay dominantly (84%) into hadronic \ufb01nal\nstates and, as a charm-quark mass is quite sizable, number\nof hadronic D(s) decays is quite large. About 63% of the\ntotal width are two-body modes, as multibody processes\nare in fact quasi-two-body ones if intermediate resonances\nare considered as a single particle. Study of dynamics of\nmultibody D(s) decays via either Dalitz plot or partial-\nwave analysis (PWA), can bring important information\non light-\ufb02avor hadron spectroscopy (see Section 19.1.4).\nAll the two-body hadronic decays of charm mesons\ncan be classi\ufb01ed according to the six diagrams shown in\nFig. 19.1.1(a-f). Measurements of two-body exclusive D(s)\ndecays allow a quark-diagram analysis in which one de-\ntermines magnitudes and signs of the amplitudes corre-\nsponding to the individual diagrams (Chau and Cheng,\n1986) (Cheng and Chiang, 2010)\n(Bhattacharya and\nRosner, 2010) (Bhattacharya and Rosner, 2009) (Bhat-\ntacharya, Gronau, and Rosner, 2012). Such decomposi-\ntion allowed to understand important properties of charm\nmesons. As an example, external and internal diagrams in\nFig. 19.1.1 (a,b) give rise to respectively the D0 \u2192K\u2212\u03c0+\nand D0 \u2192\n\u00afK0\u03c00 decays, while they both can lead to\nthe D+ \u2192\u00afK0\u03c0+ \ufb01nal state. Destructive interference be-\ntween CF external and internal amplitudes in D+ decays,\nalong with fewer CF D+ channels, increases signi\ufb01cantly\nthe D+ lifetime. Somewhat enhanced contribution from\nthe exchange diagram (Fig. 19.1.1(c)) to the D0 width\ncould also reduce the D0 lifetime. A pattern similar to\nthe one for the D \u2192\u00afK\u03c0 decays is also preferred by the\ndata for the decays with vector meson in the \ufb01nal state,\nD+ \u2192\u00afK\u22170\u03c0+ and D+ \u2192\u00afK0\u03c1+. On the other hand,\n\u03c4(D0) < \u03c4(D+\ns ) lifetime di\ufb00erence can be explained with\nW-annihilation contribution to the Ds decay width, via\nfor example D+\ns \u2192\u03c1\u03c0, as all the spectator diagrams con-\ntribute similarly into D+\ns and D0 decays.\nThese analyses also show that the measured rates of\nthe D \u2192\u00afK\u03c0 decays, and many other channels with ei-\nther two pseudoscalars or pseudoscalar and vector in \ufb01nal\nstate, hardly can be \ufb01tted if the contributing quark ampli-\ntudes are real. This suggests that strong interactions mod-\nify the weak decay amplitudes, so that they carry phases\ninduced by, for example, rescattering e\ufb00ects.\nUsing the \ufb01tted amplitudes one can make predictions\nfor not yet measured decays based on their quark-diagram\nstructure. Precision measurements of certain D(s) chan-\nnels, especially those involving vector mesons, can help\nto determine better or/and ambiguously the suppressed\namplitudes: exchange amplitudes (D0 \u2192\u00afK\u22170K0, \u00afK0K\u22170,\nD0 \u2192\u00afK\u22170\u03b7(\u2032)), annihilation amplitudes (D+\ns \u2192\u03b7(\u2032)\u03c0+,\nD+\ns \u2192\u03c1+\u03c00, D+\ns \u2192\u03c9\u03c0+) and penguin amplitudes (D0 \u2192\n\u03c00\u03c00, D0 \u2192\u00afK0K0).\nA powerful method of studying rescattering is an isospin\nanalysis as isospin invariance holds to a very high accu-\nracy. The isospin analysis requires an isospin decomposi-\ntion of decay amplitudes for all possible charge states in\nisospin-related \ufb01nal states. For D \u2192K\u03c0 decays, the de-\ncay amplitudes (A) for D0 \u2192K\u2212\u03c0+, D0 \u2192K0\u03c00 and\nD+ \u2192\u00afK0\u03c0+ are linear combinations of the partial-wave\nisospin amplitudes (AI) with I = 1/2 and I = 3/2:\nA(D0 \u2192K\u2212\u03c0+) =\np\n1/3A3/2 +\np\n2/3A1/2\nA(D0 \u2192K\n0\u03c00) =\np\n2/3A3/2 \u2212\np\n1/3A1/2\nA(D+ \u2192K\n0\u03c0+) =\n\u221a\n3A3/2,\n(19.1.2)\ndecomposition of the D0 \u2192\u03c0+\u03c0\u2212, D0 \u2192\u03c00\u03c00 and D+ \u2192\n\u03c0+\u03c00 amplitudes into the I = 0 and I = 2 isospin ampli-\ntudes gives:\nA(D0 \u2192\u03c0+\u03c0\u2212) =\np\n1/3A2 +\np\n2/3A0\nA(D0 \u2192\u03c00\u03c00) =\np\n2/3A2 \u2212\np\n1/3A0\nA(D+ \u2192\u03c0+\u03c00) =\np\n3/2A2,\n(19.1.3)\nwhile the D0 \u2192KK \ufb01nal states form the isospin ampli-\ntudes of I = 0 and I = 1 as:\nA(D0 \u2192K\u2212K+) =\np\n1/2A1 +\np\n1/2A\u2032\n0\nA(D0 \u2192K\n0K0) =\np\n1/2A1 \u2212\np\n1/2A\u2032\n0\nA(D+ \u2192K\n0K+) =\n\u221a\n2A1.\n(19.1.4)\nThe amplitudes A(\u2032)\ni\nare in general complex numbers;\nhowever, only their relative phase is observable. This al-\nlows us to introduces relative \ufb01nal-state phase between\nthe isospin amplitudes in Eqs (19.1.2)\u2013(19.1.4), de\ufb01ned as\n\u03b4K\u03c0 = arg(A3/2/A1/2), \u03b4\u03c0\u03c0 = arg(A2/A0) and \u03b4KK =\narg(A1/A0).\nHaving measured partial widths for all three \ufb01nal states\nin each of Eqs (19.1.2)\u2013(19.1.4), one can obtain magni-\ntudes of isospin amplitudes and their relative phase. Old\n\n519\nCLEO analyses (Bishai et al., 1997) (Selen et al., 1993)\nshowed that the isospin-amplitude relative phases for both,\nD \u2192K\u03c0 and D \u2192\u03c0\u03c0 decays were almost 90\u25e6, implying\nlarge FSI. Adding the isospin amplitudes with no phase\nallowed estimation of the decay rates without rescattering:\nB(D0 \u2192K\u2212\u03c0+)no FSI \u22481.3 B(D0 \u2192K\u2212\u03c0+), B(D0 \u2192\n\u03c0+\u03c0\u2212)no FSI \u22481.6 B(D0 \u2192\u03c0+\u03c0\u2212). An isospin phase\nshift for D \u2192KK decays was however found to be con-\nsistent with zero. Thus elastic FSI explains neither en-\nhanced B(D0 \u2192K\u2212K+), nor the decay rate of about\n10\u22124 for D0 \u2192K\n0K0 which, if one neglects W-exchange\namplitude, should be in the SM forbidden. Therefore ei-\nther inelastic FSI or large W-exchange contribution could\nexplain the latter. Another issue emerging from the isospin\nanalyses is related to a large I = 2 amplitude for D \u2192\u03c0\u03c0\ndecays, |A2|/|A0| = 0.72 \u00b1 0.17. This indicates that there\nis no \u2206I = 1/2 for the D decays into two pions, while it\nis well known that for K \u2192\u03c0\u03c0 decays A2 is very small.\nEach of the Equations 19.1.2-19.1.4 leads to a trian-\ngle relation among the decay amplitudes. Nonzero area\nfor the formed triangle would be an evidence for either a\ndi\ufb00erence in phases between the isospin amplitudes or con-\ntributions from quark-diagram amplitudes with di\ufb00erent\nweak (CKM) phases. The latter would be a sign of isospin\nviolation, possibly originating form a NP contribution.\nUnlike the isospin symmetry, the SU(3)-\ufb02avor symme-\ntry is heavily broken, and its long-standing indication in\ncharm decays comes from the D0 \u2192K\u2212K+ and D0 \u2192\n\u03c0+\u03c0\u2212widths, which, without SU(3) violation and with\nphase-space related factor removed, are expected to be\nequal. The measured ratio is \u0393(D0 \u2192K\u2212K+)/\u0393(D0 \u2192\n\u03c0+\u03c0\u2212) \u22433, although a phase-space allowed in a numer-\nator is smaller. An SU(3)-breaking e\ufb00ect in a dominant,\nexternal W-emission amplitude itself may arise from a dif-\nference in decay constants of pion and kaon, fK > f\u03c0. It\nimplies a larger external amplitude for D0 \u2192K\u2212K+, but\nis insu\ufb03cient to explain the measured ratio. Due to in-\nelastic FSI the \u03c0\u03c0 mode can be converted into \u00afKK via\nfor example scalar resonances coupling to both these \ufb01nal\nstates. To con\ufb01rm this scenario one needs quantitative es-\ntimation of inelastic rescattering.\nPenguin diagram contributes to D0 \u2192K\u2212K+ and\nD0 \u2192\u03c0+\u03c0\u2212with opposite relative signs, and for the KK\nmode is destructive with respect to the tree amplitude, re-\nducing the expected width ratio and thus making the sit-\nuation even worse. The penguin contribution is expected\nto be small, however, similarly to the exchange amplitude,\nthe long-distance QCD e\ufb00ects can enhance it signi\ufb01cantly\nand make the theoretical calculations very di\ufb03cult. On\nthe other hand, knowledge of a size of the penguin am-\nplitude is of great importance for estimation of the CP\nviolation expected in the charm sector within the SM (see\nSection 19.2). Measurement of a width for D0 \u2192\u03c00\u03c00,\ncontaining the same penguin pollution as D0 \u2192K\u2212K+\nand \u03c0+\u03c0\u2212, will allow an estimation of the penguin contri-\nbution.\n19.1.1.3 Methods for estimating matrix elements\nTheoretical description of charm-changing decay, D \u2192f,\nexploits an (low-energy) e\ufb00ective Hamiltonian constructed\nwith the help of an Operator Product Expansion (OPE)\n(framework) in terms of local operators Oi and the (cou-\nplings) Wilson coe\ufb03cients ci. Following the same line of\nargument as for B decays, one obtains an e\ufb00ective Hamil-\ntonian of the form:\n\u27e8f|Heff|D\u27e9= GF\n\u221a\n2 VCKM\u27e8f|\nX\ni\nci(\u00b5)Oi(\u00b5)|D\u27e9, (19.1.5)\nwhere GF is Fermi constant and VCKM is a factor re-\nlated to the CKM matrix elements involved in the de-\ncay. The renormalization scale \u00b5 separates contributions\nfrom long-distance dynamics (with length scales above\n1/\u00b5) and short-distance interactions (with length scales\nbelow 1/\u00b5). All degrees of freedom with masses above \u00b5\ngive rise to e\ufb00ectively point-like interactions and are inte-\ngrated out into the coe\ufb03cents ci using perturbation the-\nory. Degrees of freedom having mass scales below \u00b5 remain\ndynamical and are included in the operators Oi. Their\nhadronic matrix elements (hadronic expectation values),\n\u27e8f| P\ni ci(\u00b5)Oi(\u00b5)|D\u27e9, involve non-perturbative dynamics.\nTypically \u00b5 \u2248mc is used as it assures that \u00b5 \u226b\u039bQCD\nand thus ci, which depends on the strong coupling con-\nstant, can be treated perturbatively. Also such a choice\nprovides a resonable momentum cut-o\ufb00for hadron wave\nfunctions used to calculate the hadronic matrix elements.\nThese calculations, especially for nonleptonic transitions,\nare still challenging.\nThe e\ufb00ective Hamiltonian for the \u2206C = 1 weak decay\nis (Buchalla, Buras, and Lautenbacher, 1996):\nH\u2206C=1\neff\n= GF\n\u221a\n2 [\nX\nq=d,s\nVuqV \u2217\ncq(c1O1 + c2O2)\n\u2212VubV \u2217\ncb\n6\nX\ni=3\nciOi + c8gO8g] + h.c.,\n(19.1.6)\nwhere O1 and O2 are the tree-level operators expressed as\nthe current products:\nO1 = (\u00afqc)V \u2212A(\u00afuq)V \u2212A, O2 = (\u00afuc)V \u2212A(\u00afqq)V \u2212A. (19.1.7)\nAlthough the weak decays are mainly driven by the opera-\ntor O1, QCD e\ufb00ects also induce other operators such as O2\nand, in general, both terms contribute to the amplitudes\nin Fig 19.1.1(a-d). The remaining operators correspond to\nthe penguin contributions in Fig 19.1.1(e-f):\nO3,5 = (\u00afuc)V \u2212A\nX\nq\u2032=u,d,s\n(\u00afq\u2032q\u2032)V \u2213A,\nO4,6 =\nX\nq\u2032=u,d,s\n(\u00afuq\u2032)V \u2212A\nX\nq\u2032=u,d,s\n(\u00afq\u2032c)V \u2213A,\nO8g = \u2212gs\n8\u03c02 mc\u00afu\u03c3\u00b5\u03bd(1 + \u03b35)G\u00b5\u03bdc,\n(19.1.8)\n\n520\nwhere gs is the strong decay constant, G\u00b5\u03bd denotes the\nQCD \ufb01eld strength tensor, while the (\u00afqq)V \u2213A current struc-\nture in Eq. (19.1.7)-(19.1.8) corresponds to (\u00afq\u03b3(1 \u2213\u03b35)q).\nThe Wilson coe\ufb03cients evaluated at \u00b5 \u2248mc are c1 \u22431.21,\nc2 = \u22120.41, c3 = 0.02, c4 = \u22120.04, c5 = 0.01, c6 = \u22120.05\nand c8g = \u22120.06 (Buchalla, Buras, and Lautenbacher,\n1996).\nThe remaining task, namely the calculation if the ma-\ntrix elements of the e\ufb00ective operators, is di\ufb03cult for charm\ndecays, since charm is neither heavy enough for a reliable\n1/mc expansion, nor light enough to be described in terms\nof chiral perturbation theory. Motivated by the form of\nthe e\ufb00ective Hamiltonian, a pragmatic approach has been\nsuggested some decades ago (Bauer, Stech, and Wirbel,\n1987) by introducing two parameters a1 and a2 according\nto\nA(D \u2192f) \u223ca1\u27e8f|(\u00afqc)H(\u00afuq)H|D\u27e9+ a2\u27e8f|(\u00afuc)H(\u00afqq)H|D\u27e9,\n(19.1.9)\nwhere the subscripts H mean that the matrix element is\ncalculated in na\u00a8\u0131ve factorization:\n\u27e8f1f2|(\u00afqc)H(\u00afuq)H|D\u27e9\u2243\u27e8f1|(\u00afqc)|0\u27e9\u27e8f2|(\u00afuq)|D\u27e9,\n\u27e8f1f2|(\u00afuc)H(\u00afqq)H|D\u27e9\u2243\u27e8f1|(\u00afuc)|0\u27e9\u27e8f2|(\u00afqq)|D\u27e9.\n(19.1.10)\nThe quantities a1 and a2 are scale-invariant, phe-\nnomenological parameters, which are assumed to be uni-\nversal for all the decays. Comparing with the QCD calcu-\nlation of the e\ufb00ective Hamiltonian, we write\na1 = c1 + \u03bec2, a2 = c2 + \u03bec1\n(19.1.11)\nwhere \u03be parameterizes the long distance e\ufb00ects that are\nnot correctly treated by na\u00a8\u0131ve factorization.\nThe matrix elements appearing in the na\u00a8\u0131ve factoriza-\ntion (19.1.10) correspond to the meson decay constants\nand form factors and can be taken from measurements of\nthe (semi)leptonic D(s) decays. The a1,2 can then be \ufb01t-\nted from the experimental data and \ufb01rst such a analysis,\nthe Bauer-Stech-Wirbel (BSW) analysis, was performed\nfor the D \u2192K\u03c0 decays (Bauer, Stech, and Wirbel, 1987)\nand yielded a1 = 1.3\u00b10.1 and a2 = \u22120.5\u00b10.1. Once com-\npared with the theoretical expectations, a1 = 1.25\u22120.48\u03be\nand a2 = \u22120.48 + 1.25\u03be, suggested \u03be \u22430.\nThe non-spectator, exchange and annihilation diagrams\n(Fig. 19.1.1(c-d)) are within the factorization described\nusing a vacuum insertion:\n\u27e8f1f2|(\u00afqc)H(\u00afuq)H|D\u27e9\u2243\u27e8f1f2|(\u00afqc)H|0\u27e9\u27e80|(\u00afuq)H|D\u27e9,\n(19.1.12)\nand are in general a small correction with respect to the\ndecays determined by the a1 or/and a2. An impact of\nthe non-spectator diagrams on the two-body charm de-\ncays was also studied in the BSW analysis (Bauer, Stech,\nand Wirbel, 1987).\nNa\u00a8\u0131ve factorization as de\ufb01ned by BSW approach is\nvery simply and allows us to parameterize most of the\nhadronic decays with just two parameters. However, this\nsimple ansatz is not satisfactory for the improved measure-\nments, and thus more sophisticated theoretical approaches\nneed to be developed.\n19.1.2 Branching ratio measurements\nThe large statistics accumulated at B Factories and clean\nenvironment of the e+e\u2212experiment allowed precision\nmeasurements of absolute branching fraction of favored\nweak D(s) decays, previously obtained using sometimes\nonly a few hundred signal events. Such measurements re-\nquire a knowledge of a total number of produced D(s)\nmesons to normalize the D(s) signal reconstructed in the\ndecay mode of interest. That can be achieved either via\nan exclusive reconstruction of e+e\u2212\u2192c\u00afc events for mea-\nsurement of directly produced D(s) (Belle technique), or\nthrough tagging selected B decays as a source of charmed\nmesons (BABAR technique). The measured decays serve as\na reference for measurements of the branching fractions of\nthe D(s) to any other \ufb01nal state, improve our knowledge of\nmost of the decays of the B(s) mesons, and of fundamental\nparameters of the Standard Model.\nThe suppressed D(s) decays are measured with re-\nspect to the favored processes having a similar topology.\nRelative branching ratio measurements allow cancelation\nof numerous systematic uncertainties. Precision measure-\nments of the suppressed charm decays give insight into\ndecay dynamics and allow tests of the various symmetries\nassumed in the theoretical calculations.\n19.1.2.1 Absolute Branching Fraction of D0 \u2192K\u2212\u03c0+\nThe D0 \u2192K\u2212\u03c0+ is a reference mode for many measure-\nments of the D decays. CLEO-c (He et al., 2005) published\nits result on this branching fraction, the most precise at\nthe time, which was widely used (Yao et al., 2006). BABAR\nusing 210 fb\u22121 data, has produced even more precise mea-\nsurement based on a di\ufb00erent technique (Aubert, 2008p).\nThe D0 \u2192K\u2212\u03c0+ decays are identi\ufb01ed in a sample of\nD0 mesons produced in D\u2217+ \u2192D0\u03c0+ decays and ob-\ntained with partial reconstruction of B0 \u2192D\u2217+(X)\u2113\u2212\u00af\u03bd\u2113\n(see also Section 7.3.2). Such B candidates are selected\nby retaining events containing a charged lepton (\u2113= e, \u00b5)\nand a low momentum (soft) pion (\u03c0+\ns ) which may arise\nfrom the decay D\u2217+ \u2192D0\u03c0+\ns . Momenta of the lepton\nand the soft pion must respectively satisfy the 1.4 < p\u2113\u2212<\n2.3 GeV/c and 60 < p\u03c0+\ns < 190 MeV/c. The minimum p\u2113\u2212\nand p\u03c0+\ns are optimized to minimize uncertainties due to\ncharm production in B decays and tracking errors, respec-\ntively, while the maximum momenta are determined by\nthe available phase space. The two tracks must be consis-\ntent with originating from a common vertex, constrained\nto the beam-spot in the plane transverse to the beam axis.\nThen they combine p\u2113\u2212, p\u03c0+\ns and the probability from the\nvertex \ufb01t into a likelihood ratio variable, optimized to re-\nject BB background. Using conservation of momentum\nand energy, the invariant mass squared of the undetected\nneutrino is calculated as:\nM2\n\u03bd \u2261(Ebeam \u2212ED\u2217\u2212E\u2113)2 \u2212(pD\u2217+ p\u2113)2,\n(19.1.13)\nwhere Ebeam is half the total center-of-mass (c.m.) energy\nand E\u2113(ED\u2217) and p\u2113(pD\u2217) are the energy and momentum\n\n521\nof the lepton (the D\u2217meson) in the c.m. system. Since the\nmagnitude of the B meson momentum in the c.m. system\n|pB| \u226a|p\u2113|, |pD\u2217|, they set pB = 0 in the above equation.\nAs a consequence of the limited phase space available in\nthe D\u2217+ decay, the soft pion is emitted nearly at rest in the\nD\u2217+ rest frame. The D\u2217+ four-momentum can therefore\nbe computed by approximating its direction as that of the\nsoft pion, and parameterizing its momentum as a linear\nfunction of the soft-pion momentum.\nAll events where D\u2217+ and \u2113\u2212originate from the same\nB meson, producing a peak near zero in the M2\n\u03bd distri-\nbution, are considered as signal candidates. This sample\nof events is referred to as the inclusive sample. Sample of\nevents with the same charge of \u03c0s and lepton is also se-\nlected for background studies and is referred to as wrong-\ncharge sample. Number of the inclusive signal events is\nobtained from a minimum \u03c72 \ufb01t to the M2\n\u03bd distribution\nin the interval \u221210 < M2\n\u03bd < 2.5 GeV2/c4. Figure 19.1.2(a)\nshows the \ufb01t result in the M2\n\u03bd projection, with signal\nand background shapes obtained with the MC simula-\ntions, while the M2\n\u03bd distribution of the wrong-charge sam-\nple that contains background candidates only is shown in\nFig. 19.1.2(b). The inclusive yield for M2\n\u03bd > \u22122 GeV2/c4\nis N incl = (2171 \u00b1 3 \u00b1 18) \u00d7 103.\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\nx 10 2\n0\n400\n800\n1200\n1600\n-10\n-8\n-6\n-4\n-2\n0\n2\nEntries / 0.2 (GeV2 /c4)\n(a)\nB0 \u2192 D*l\u03bd\nB \u2192 D**l\u03bd\nBB combinatorial\ncontinuum\nOther Peaking\nM2 \u03bd (GeV2/c4)\n(b)\nFigure 19.1.2. From (Aubert, 2008p). The M 2\n\u03bd distribution\nof the inclusive sample, for right-charge (a) and wrong-charge\n(b) samples. The data are represented by solid points with\nuncertainty. The MC \ufb01t results are overlaid on the data, as\nexplained in the \ufb01gure.\nTo obtain the exclusive signal sample, D0 \u2192K\u2212\u03c0+\ndecays are reconstructed using all tracks in the event,\naside from the \u2113\u2212and \u03c0+\ns , with momenta in the direction\ntransverse to the beam axis exceeding 0.2 GeV/c. They\ncombine pairs of tracks with opposite charge and com-\npute the invariant mass m(K\u03c0) assigning the kaon mass\nto the track with charge opposite the \u03c0s charge. D0 candi-\ndates from the mass range 1.82 < m(K\u03c0) < 1.91 GeV/c2\nare combined with the \u03c0+\ns . Events having the mass dif-\nference, \u2206M = m(K\u2212\u03c0+\u03c0+\ns ) \u2212m(K\u2212\u03c0+), in the range\nof 142.4 < \u2206M < 149.9 MeV/c2 are selected as the signal\ncandidates (see Fig. 19.1.3). The exclusive selection yields\nN excl = (33.8 \u00b1 0.3) \u00d7 103 signal events. The branching\n0.140\n0.145\n0.150\n0.155\n0.160\n0.165\n \u2206M (GeV/c2)\n0.\n1000.\n2000.\n3000.\n4000.\n5000.\n6000.\n Entries/(0.3 MeV/c2)\nExclusive sample\ndata\npeaking\nCabibbo-suppressed\ncombinatorial BB\n\u2212\nFigure 19.1.3. From (Aubert, 2008p). Continuum subtracted\n\u2206M distribution for data (points with error bars) and back-\ngrounds overlaid as explained in the \ufb01gure.\nfraction is computed as:\nB(D0 \u2192K\u2212\u03c0+) = N excl/(N incl\u03b6\u03b5(K\u2212\u03c0+)),\n(19.1.14)\nwhere \u03b5(K\u2212\u03c0+) = (36.96\u00b10.09)% is the D0 reconstruction\ne\ufb03ciency from MC simulation, and \u03b6 = 1.033 \u00b1 0.002 is\nthe selection bias introduced by the partial reconstruction.\nThe measured result is:\nB(D0 \u2192K\u2212\u03c0+) = (4.007 \u00b1 0.037 \u00b1 0.072)%,\n(19.1.15)\nwhere the \ufb01rst uncertainty is statistical and the second\nuncertainty is systematic. This result is comparable in\nprecision with the so far the most precise measurement\nby Cleo-c (Dobbs et al., 2007b) and is consistent with it\nwithin one standard deviation.\n19.1.2.2 Absolute Branching Fractions of D+\ns decays\nBelle has measured absolute branching fractions of D+\ns \u2192\nK+K\u2212\u03c0+, D+\ns \u2192\u00afK0K+ and D+\ns \u2192\u03b7\u03c0+ (Zupanc, 2013b)\nbeing reference modes for the leptonic D+\ns decays (see Sec-\ntion 19.1.6). The analysis is based on the 913 fb\u22121 and the\nstudied Ds mesons are produced in the following reaction:\ne+e\u2212\u2192c\u00afc \u2192DtagKXfragD\u2217\u2212\ns , D\u2217\u2212\ns\n\u2192D\u2212\ns \u03b3,\n(19.1.16)\n\n522\nwhere one of the charm quarks hadronizes into the Ds,\nwhile the other into tagging charm hadron Dtag, which is\nreconstructed as D(\u2217)+, D(\u2217)0 or \u039b+\nc . The ground charmed\nhadrons, D+, D0 and \u039b+\nc , are reconstructed in 18 hadronic\ndecay modes in total, with up to one \u03c00 in the \ufb01nal state to\nkeep low background level. In order to reject background\nfrom e+e\u2212\u2192BB events and combinatorial background\nthe e+e\u2212center-of-mass Dtag momentum is required to be\ngreater than 2.3 GeV/c2 (or 2.5 GeV/c2 for less clean Dtag\nmodes). To further clean up the reconstructed sample of\nthe ground Dtag hadrons several variables being either\ntopological (the Dtag decay vertex quality, distance be-\ntween production and decay vertices, angle between Dtag\nmomentum vector and production-to-decay vector), re-\nlated to the dynamics (Dtag decay angle) or quality of the\ndecay products (charged hadron identi\ufb01cation, \u03c00 qual-\nity) are combined into a single neural network output\nvariable (NBout), being a probability that a given Dtag\ncandidate is a correctly reconstructed signal. The NBout\nselection is optimized using NeuroBayes neural network\n(see Section B) trained on a small data sample; the opti-\nmization procedure maximizes the signal signi\ufb01cance mea-\nsured from the Dtag invariant-mass distribution. Within\nthe selected Dtag sample, D+ and D0 mesons originat-\ning from D\u2217+ \u2192D0\u03c0+, D+\u03c00 and D\u22170 \u2192D0\u03c00, D0\u03b3\ndecays are identi\ufb01ed using the invariant-mass di\ufb00erence\n\u2206M(D\u2217) \u2261M(D\u03c0/\u03b3) \u2212M(D).\nAn additional K in Eq. (19.1.16), detected as either\nK+ or K0\nS, assures strangeness conservation in the event,113\nwhile Xfrag is a fragmentation system denoting additional\nparticles that can be created in the hadronization. The\nXfrag is formed from the remaining charged pions (up\nto three) and up to one \u03c00 candidate. The DtagKXfrag\ncombinations are required to have a common vertex, to-\ntal electric charge of \u00b11 (giving inclusively reconstructed\nD\u2217\u2213\ns ) and right sign of their charm and strangeness quan-\ntum numbers relative to their total charge (charm in the\nDtag and strangeness of the primary K, if speci\ufb01ed, are\nrequired to be opposite to the charge of the D\u2217\ns).\nThe method uses only D+\ns mesons produced through\nparent D\u2217+\ns , so one requires a photon consistent with\nD\u2217+\ns\n\u2192D+\ns \u03b3. This provides a powerful constraint on the\nD+\ns signal and improves a resolution of the missing mass\nused to identify D+\ns signal and de\ufb01ned as:\nMmiss(DtagKXfrag\u03b3) \u2261\nq\np2\nmiss(DtagKXfrag\u03b3),\n(19.1.17)\nwhere pmiss is the missing four-momentum in the event\npmiss(DtagKXfrag\u03b3)=pe++pe\u2212\u2212pDtag\u2212pK \u2212pXfrag\u2212p\u03b3\n(19.1.18)\nFor correctly reconstructed events described by Eq.\n(19.1.16), the Mmiss(DtagKXfrag\u03b3) peaks at the nominal\nDs mass, while the corresponding Mmiss(DtagKXfrag)\nat the nominal D\u2217\ns\nmass. To improve the Ds\nsig-\nnal resolution, the D\u2217\ns candidates within the 2.0\n<\n113 In the case of tagging \u039b+\nc an antiproton is also required to\nbalance the baryon number in the event.\nMmiss(DtagKXfrag) < 2.25 GeV/c2 region are selected\nand re\ufb01tted with a D\u2217\ns mass constraint.\nTo obtain a fully inclusive D+\ns sample used for normal-\nization in the branching fraction calculation, there are no\nrequirements on the D+\ns decay products. The inclusive D+\ns\nsignal\nyield\nis\nobtained\nfrom\nthe\n\ufb01t\nto\nthe\nMmiss(DtagKXfrag\u03b3) spectrum for each Xfrag mode sep-\narately. Figs 19.1.4 show the \ufb01tted spectra for Xfrag modes\ngiving the largest yields, Xfrag = nothing, \u03c0\u00b1, and \u03c0+\u03c0\u2212.\nSignal component is modeled with histogram from the MC\nsimulations and is convolved with a Gaussian resolution\n(of about 2 MeV/c2) measured from real data using fully\nreconstructed Ds \u2192\u03c6\u03c0 decays. Background contributions\nare: mis-reconstructed signal (K or Xfrag pion originating\nfrom Ds decays), re\ufb02ections from D\u22170 \u2192D0\u03b3 or D\u2217\n(s) \u2192\nD(s) \u2192D0\u03c00 (being sources of the signal photon), wrong\n\u03b3 (wrongly reconstructed in the calorimeter) and \u03b3 com-\ning from \u03c00 decays not originating from D\u2217\n(s). Their shapes\nare histograms obtained from the generic MC, while nor-\nmalizations are mostly kept free in the \ufb01t. Total inclusive\nD+\ns yield is measured to be (94.4 \u00b1 1.3 \u00b1 1.4) \u00d7 103.\nTo obtain exclusive D+\ns sample within the inclusive\nsample, all the tracks of D+\ns\n\u2192K+K\u2212\u03c0+ decays are\nfully reconstructed using the events with exactly three\nsuch charged tracks remaining. The exclusively recon-\nstructed D+\ns \u2192K+K\u2212\u03c0+ events are identi\ufb01ed as a peak\nat D\u2217+\ns\nnominal mass in the M(K+K\u2212\u03c0+\u03b3) mass distri-\nbution (Fig. 19.1.5). To increase reconstruction e\ufb03ciency\nfor D+\ns \u2192\u00afK0K+ and D+\ns \u2192\u03b7\u03c0+, only the charged kaon\nand pion, respectively, are explicitely reconstructed. The\nD+\ns\n\u2192\n\u00afK0K+ signal is identi\ufb01ed in the missing mass\nsquared distribution M 2\nmiss(DtagKXfrag\u03b3K) (Fig. 19.1.6)\nand expected at mass squared of K0 nominal mass,\nwhile the D+\ns\n\u2192\u03b7\u03c0+ in the M 2\nmiss(DtagKXfrag\u03b3\u03c0)\n(Fig. 19.1.7) at \u03b7 nominal mass squared. All these spectra\nare \ufb01tted with signals parameterized using MC simula-\ntions with data-based resolution taken into account. In the\nbackground part, in addition to a smooth combinatorial\nbackground, there are also peaking re\ufb02ections, modeled\nin the \ufb01ts with MC simulations and included in the \ufb01ts\n(see Figs 19.1.5-19.1.7 for details). In the D+\ns \u2192\u03b7\u03c0+ case\ncontribution from D+\ns \u2192\u03c4 +\u03bd\u03c4 \u2192\u03c0+\u00af\u03bd\u03c4\u03bd\u03c4 is suppressed\nby requiring that extra neutral energy in the electromag-\nnetic calorimeter (not associated to the particles used in\nthe inclusive or exclusive D+\ns reconstruction) to be larger\nthan 1 GeV, as signi\ufb01cant energy deposit is expected from\nthe \u03b7 decay products while none from the tauonic decays.\nThe absolute B of D+\ns to given f \ufb01nal state recon-\nstructed in the exclusive sample is:\nB(Ds \u2192f) =\nN excl(D+\ns \u2192f)\nN incl(D+\ns ) \u00b7 fbias \u00b7 \u03b5(D+\ns \u2192f|incl D+\ns ),\n(19.1.19)\nwhere N incl(Ds) is a number of inclusively reconstructed\nDs mesons, N excl(Ds \u2192f) is the number of exclusively\nreconstructed Ds \u2192f decays, while \u03b5(Ds \u2192f|incl Ds)\nis the e\ufb03ciency of exclusive Ds \u2192f reconstruction given\ninclusively reconstructed Ds and is determined from MC\nsimulations of the events containing the signal decays. The\n\n523\n1 85\n1 9\n1 95\n2\n2 05\n )\n2\nEvents / ( 0.002 GeV/c\n0\n2\n4\n6\n3\n10\n\u00d7\n = nothing\nfrag\n(a) X\n)\n2\n) (GeV/c\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\nmiss\nM\n1.85\n1.9\n1.95\n2\n2.05\nPull\n-5\n0\n5\n1 85\n1 9\n1 95\n2\n2 05\n )\n2\nEvents / ( 0.002 GeV/c\n0\n2\n4\n6\n8\n3\n10\n\u00d7\n\u00b1\u03c0\n = \nfrag\n(b) X\n)\n2\n) (GeV/c\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\nmiss\nM\n1.85\n1.9\n1.95\n2\n2.05\nPull\n-5\n0\n5\n1 85\n1 9\n1 95\n2\n2 05\n )\n2\nEvents / ( 0.002 GeV/c\n0\n5\n10\n3\n10\n\u00d7\n-\u03c0\n+\u03c0\n = \nfrag\n(e) X\n)\n2\n) (GeV/c\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\nmiss\nM\n1.85\n1.9\n1.95\n2\n2.05\nPull\n-5\n0\n5\nFigure 19.1.4.\nFrom (Zupanc, 2013b). Inclusive Ds in Mmiss(DtagKXfrag\u03b3) for three out of seven possible Xfrag modes.\nThe solid blue (red) line shows the contribution of signal and background (background only) candidiates. The cumulative\ncontributions of candidates originating from di\ufb00erent background sources as described in the text are shown with di\ufb00erent gray\ndashed lines. Dashed vertical lines indicate the signal region considered in further analysis.\n2\n2 05\n2 1\n2 15\n2 2\n )\n2\nEvents / ( 0.002 GeV/c\n0\n200\n400\n600\n)\n2\n) (GeV/c\n\u03b3\n+\n\u03c0\n+\nK\n-\nM(K\n2\n2.05\n2.1\n2.15\n2.2\nPull\n-5\n0\n5\nFigure 19.1.5. From (Zupanc, 2013b). M(K+K\u2212\u03c0+\u03b3) mass\ndistribution of exclusively reconstructed D+\ns \u2192K+K\u2212\u03c0+ de-\ncays within the inclusive Ds sample, with the \ufb01t result super-\nimposed and including \ufb01tted signal contribution (solid green\nline), re\ufb02ection from D\u2217\ns \u2192Ds\u03c00 \u2192K+K\u2212\u03c0+\u03b3\u03b3 with one of\nthe photons missing (full dark gray histogram) and combina-\ntorial background (dashed red line).\ne\ufb03ciency of inclusive Ds reconstruction depends on the\nDs-decay mode and drops with increasing multiplicity of\nthe f \ufb01nal state. It is accounted for by introducing a fac-\ntor fbias which is a ratio of e\ufb03ciency of inclusive Ds re-\nconstruction for Ds \u2192f and for Ds decaying generically\ni.e. to all known decay modes. This number is further cor-\nrected to account for a di\ufb00erent multiplicities of \ufb01nal state\nparticles in Ds decays in MC and real data. Fitted exclu-\nsive yields of the hadronic Ds decays and measured abso-\nlute branching fractions are summarized in Table 19.1.1.\nPrecision of these measurements is approximately equal\nto the precission of the curent world average values.\nAll the measured decays are Cabibbo-favored pro-\ncesses. However, since the \ufb02avor of neutral kaon in D+\ns \u2192\n\u00afK0K+ is not determined, the doubly Cabibbo suppressed\ndecays, D+\ns\n\u2192K0K+, also contribute to the signal in\nFig. 19.1.6. Its expected contribution is at the level of\n10\u22124, thus, much below the statistical uncertainty of the\nmeasured B. The D+\ns \u2192K+K\u2212\u03c0+ decays entirely pro-\n0 2\n0\n0 2\n0 4\n0 6\n )\n4\n/c\n2\nEvents / ( 0.01 GeV\n0\n100\n200\n300\n400\n)\n4\n/c\n2\nK) (GeV\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\n2\nmiss\nM\n-0.2\n0\n0.2\n0.4\n0.6\nPull\n-5\n0\n5\nFigure\n19.1.6.\nFrom\n(Zupanc,\n2013b).\nM 2\nmiss(DtagKXfrag\u03b3K)\ndistribution\nof\npartially\nrecon-\nstructed D+\ns \u2192\u00afK0K+ decays within the inclusive Ds sample.\nThe \ufb01t result is superimposed and includes \ufb01tted signal\ncontribution (solid green line), re\ufb02ections from charged kaon\noriginating from D+\ns\n\u2192\u03b7K+ and D+\ns\n\u2192\u03c00K+ (full grey\nhistograms) and other true Ds decays (for example D+\ns \u2192\u03b7\u03c0+\nwith pion being misidenti\ufb01ed as kaon) (full blue histogram),\nand combinatorial background (dashed red line).\nTable 19.1.1. Absolute B of D+\ns from (Zupanc, 2013b)\nDecay mode\nExclusive yield\nB [%]\nD+\ns \u2192K+K\u2212\u03c0+\n4094 \u00b1 123\n5.06 \u00b1 0.15 \u00b1 0.21\nD+\ns \u2192\u00afK0K+\n2018 \u00b1 75\n2.95 \u00b1 0.11 \u00b1 0.09\nD+\ns \u2192\u03b7\u03c0+\n788 \u00b1 59\n1.82 \u00b1 0.14 \u00b1 0.07\nceed through resonances contributing to either the KK\nor K\u03c0 systems (see Section 19.1.4.9), which correspond\nrespectively to color-allowed and color-suppressed contri-\nbutions. A corresponding decay model is assumed in the\nD+\ns \u2192K+K\u2212\u03c0+ MC simulations used for estimation the\ne\ufb03ciency for Eq. (19.1.19).\n\n524\n0\n0 2\n0 4\n0 6\n0 8\n )\n4\n/c\n2\nEvents / ( 0.01 GeV\n0\n100\n200\n)\n4\n/c\n2\n) (GeV\n\u03c0\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\n2\nmiss\nM\n0\n0.2\n0.4\n0.6\n0.8\nPull\n-5\n0\n5\nFigure\n19.1.7.\nFrom\n(Zupanc,\n2013b).\nM 2\nmiss(DtagKXfrag\u03b3\u03c0)\ndistribution\nof\npartially\nrecon-\nstructed D+\ns \u2192\u03b7\u03c0+ decays within the inclusive Ds sample.\nThe \ufb01t result is superimposed and includes \ufb01tted signal\ncontribution (solid green line), re\ufb02ections from charged pion\noriginating from D+\ns \u2192K0\u03c0+ (full grey histograms) and other\ntrue Ds decays (D+\ns \u2192\u03c1K+ \u2192\u03c0+\u03c0\u2212K+ and D+\ns \u2192\u00afK0K+\ndue to K-\u03c0 mis-reconstruction) (full blue histogram), and\ncombinatorial background (dashed red line).\n19.1.2.3 The D\u2217+\ns\nand D\u22170 Branching Ratios\nThe decay of any excited c\u00afs meson into D+\ns \u03c00 violates\nisospin conservation,114 thus guaranteeing a small partial\nwidth. The amount of suppression is a matter of large the-\noretical uncertainty according to most models of charm-\nmeson radiative decay (Goity and Roberts, 2001). One\nsuch a model (Cho and Wise, 1994) suggests that the de-\ncay D\u2217+\ns\n\u2192D+\ns \u03c00 may proceed via \u03c00-\u03b7 mixing. Even\nincluding such considerations, the radiative decay D\u2217+\ns\n\u2192\nD+\ns \u03b3 is still expected to dominate. An existence of isospin-\nviolating decay modes, such as D\u2217+\ns\n\u2192D+\ns \u03c00, is partic-\nularly relevant given the observations of the new narrow\nD+\nsJ states decaying dominantly into D(\u2217)+\ns\n\u03c00 (see Section\n19.3). In particular, in contrast to the D\u2217+\ns\nmeson, there is\nno experimental evidence for the electromagnetic decay of\nthe DsJ(2317)+. Besides the D+\ns \u03c00 and D+\ns \u03b3 \ufb01nal states,\nno other decay modes of the D\u2217+\ns\nhave been observed and\nnone are expected to occur at a signi\ufb01cant level.\nThe decay D\u22170 \u2192D0\u03c00, in contrast to D\u2217+\ns\n\u2192D+\ns \u03c00,\ndoes not violate isospin conservation.115 As for the D\u2217+\ns ,\nthe D0\u03c00 and D0\u03b3 decay modes are expected to saturate\nthe D\u22170 decay width.\nThe BABAR analysis of the D\u2217\n(s) decays is based on\n90.4 fb\u22121 (Aubert, 2005s). D+\ns mesons are reconstructed\nvia the decay sequence D+\ns \u2192\u03c6\u03c0+, \u03c6 \u2192K+K\u2212, and the\nscaled momentum must satisfy xp(D+\ns ) > 0.6. The D+\ns\nsignal sample is of (73.5 \u00b1 0.3) \u00d7 103 events. In a search\nfor the D\u2217+\ns\n\u2192D+\ns \u03c00, the D+\ns and \u03c00 are combined and\na \ufb01t is applied to the distribution of the mass di\ufb00erence\n\u2206m(D+\ns \u03c00) = m(K+K\u2212\u03c0+\u03c00) \u2212m(K+K\u2212\u03c0+). The re-\n114 The D(\u2217)\ns\nhas I = 0, while in the \ufb01nal state there is I = 1\ndue to the pion.\n115 The D(\u2217)0 has I = 1/2, so the \ufb01nal state pion (I = 1) can\nbe combined with the D0 to a total of I = 1/2.\n]\n2\nm [GeV/c\n\u2206\n0.14\n0.15\n0.16\n)\n2\nEntries/(0.5 MeV/c\n0\n50\n100\n150\n]\n2\nm [GeV/c\n\u2206\n0\n0.1\n0.2\n)\n2\nEntries/(2.5 MeV/c\n0\n1\n2\n3\n3\n10\n\u00d7\n(a)\n(b)\nFigure 19.1.8. From (Aubert, 2005s). The D\u2217+\ns\nsignals in:\n(a) \u2206m(D+\ns \u03c00) and (b) \u2206m(D+\ns \u03b3). The dots represent data\npoints, the solid curve shows the \ufb01tted function, the dashed\ncurve indicates the \ufb01tted background.\nsult of this \ufb01t is shown in Fig. 19.1.8(a), and the obtained\nsignal yield is 560 \u00b1 40. To obtain the D\u2217+\ns\n\u2192D+\ns \u03b3 signal\nevent yield, a \ufb01t is applied to the distribution of the mass\ndi\ufb00erence \u2206m(D+\ns \u03b3) = m(K+K\u2212\u03c0+\u03b3) \u2212m(K+K\u2212\u03c0+),\nas shown in Fig. 19.1.8(b). The \ufb01t function is a sum of\na third-order polynomial to model the background plus a\nCrystal Ball function for the signal.\nAfter correcting for e\ufb03ciency, the measured branching\nratio is:\n\u0393(D\u2217+\ns\n\u2192D+\ns \u03c00)\n\u0393(D\u2217+\ns\n\u2192D+\ns \u03b3) = 0.062 \u00b1 0.005 \u00b1 0.006 ,\n(19.1.20)\nand is consistent with the previous measurement (Gron-\nberg et al., 1995), but has higher precision.\nThe ratio \u0393(D\u22170 \u2192D0\u03c00)/\u0393(D\u22170 \u2192D0\u03b3), where\nD0 \u2192K\u2212\u03c0+, is measured using the same selection cri-\nteria for the \u03c00 and photon candidates as in the D\u2217+\ns\nre-\nconstruction. The D0 \u2192K\u2212\u03c0+ signal sample consists\nof (996.0 \u00b1 1.5) \u00d7 103 events. These D0 candidates com-\nbined with the \u03c00 candidates result in the mass di\ufb00er-\nence \u2206m(D0\u03c00) = m(K\u2212\u03c0+\u03c00) \u2212m(K\u2212\u03c0+) shown in\nFig. 19.1.9(a). A \ufb01t, using a double Gaussian for the sig-\nnal, yields (69.0 \u00b1 0.5) \u00d7 103 signal events. The D0 candi-\ndates combined with photons produce the distribution of\nthe mass di\ufb00erence \u2206m(D0\u03b3) = m(K\u2212\u03c0+\u03b3) \u2212m(K\u2212\u03c0+)\nshown in Fig. 19.1.9(b). In this case, a peak correspond-\ning to the D\u22170 \u2192D0\u03b3 signal is close to a large re\ufb02ection\nfrom D\u22170 \u2192D0\u03c00 with one photon from \u03c00 decay missing\n(such a re\ufb02ection appears also in D\u2217+\ns\ndecay, but with a\nlower rate and less distinctive shape). The D\u22170 \u2192D0\u03b3\nsignal is modeled by the Crystal Ball function and the \ufb01t-\nted signal yield is (67.9 \u00b1 0.7) \u00d7 103 events. The resulting\nbranching ratio, corrected for e\ufb03ciency, is:\n\u0393(D\u22170 \u2192D0\u03c00)\n\u0393(D\u22170 \u2192D0\u03b3) = 1.74 \u00b1 0.02 \u00b1 0.13.\n(19.1.21)\n19.1.3 Cabibbo-suppressed decays\nCabibbo-suppressed (CS) charm decays o\ufb00er a good lab-\noratory for studying weak interactions. Branching ratio\n\n525\n]\n2\nm [GeV/c\n\u2206\n0.14\n0.15\n0.16\n)\n2\nEntries/(0.5 MeV/c\n0\n5\n10\n3\n10\n\u00d7\n]\n2\nm [GeV/c\n\u2206\n0\n0.1\n0.2\n)\n2\nEntries/(2.5 MeV/c\n0\n5\n10\n15\n3\n10\n\u00d7\n(a)\n(b)\nFigure 19.1.9. From (Aubert, 2005s). The D\u22170 signals in:\n(a) \u2206m(D0\u03c00) and (b) \u2206m(D0\u03b3). The dots represent data\npoints, the solid curve shows the \ufb01tted function, the dashed\ncurve indicates the \ufb01tted background.\nmeasurements provide insight into charm decay dynamics\nand sources of SU(3) \ufb02avor symmetry breaking, as well\nas allow to investigate beyond SM e\ufb00ects a\ufb00ecting decay\nrates. The CS charm decays are very sensitive probes of\nthe CP violation and D0\u2212\u00afD0 mixing, as described in Sec-\ntion 19.2. Understanding the size of the SU(3)-violating\ne\ufb00ects in D(s) decays can help to disantangle New Physics\ne\ufb00ects from ones having origins in long-distance QCD ef-\nfects.\nWhile Cabibbo-favored (CF) modes at the tree level\nproceed through c \u2192s \u00afdu, the singly Cabibbo-suppressed\n(SCS) decays are mediated by c \u2192d \u00afdu or c \u2192s\u00afsu,\nand the underlying process for doubly Cabibbo-suppresed\n(DCS) modes is c \u2192d\u00afsu. The SCS decay rates are\nna\u00a8\u0131vely expected to be suppressed relative to CF decay\nrate by tan2 \u03b8C, where tan \u03b8C = |Vcd|\n|Vcs| \u22480.23 and \u03b8C is the\nCabibbo angle. Correspondingly, the ratio of DCS and\nCF decay rates is expected to be of tan4 \u03b8C. The SU(3)\nsymmetry can be however broken by strong \ufb01nal-state in-\nteractions, interference between di\ufb00erent contributing am-\nplitudes and leading to the same \ufb01nal states. In particular,\nthe two-body SCS decays of D0 meson have anomalous\nrates. The D0 \u2192\u03c0\u2212\u03c0+ branching fraction is observed\nto be suppressed relative to the D0 \u2192K\u2212K+ by a fac-\ntor of almost three (Yao et al., 2006), even though the\nphase space for the former is larger. On the other hand,\nthree-body decay rates have larger uncertainties but do\nnot exhibit such a suppression. Number of analyses of the\nCS charm decays were previously performed mainly by\nMARK III, Argus, CLEO and FOCUS.\n19.1.3.1 The D+ \u2192\u03c0+\u03c00 and D+ \u2192K+\u03c00 Branching\nFractions\nBABAR has measured branching fractions of the SCS\nD+ \u2192\u03c0+\u03c00 and the DCS D+ \u2192K+\u03c00 decays with\nrespect to the well-measured D+ \u2192K\u2212\u03c0+\u03c0+ decay\nmode, with a data sample of 124.3 fb\u22121 (Aubert, 2006v).\nIn order to reduce a large combinatorial background in\nthe D+ signal modes, only D+ mesons that originate\nfrom D\u2217+ \u2192D+\u03c00 decays are considered. D+ candi-\ndates for the signal modes are obtained by combining a\n)\n2\n invariant mass (GeV/c\n0\n\u03c0\n+\n\u03c0\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.01 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n)\n2\n invariant mass (GeV/c\n0\n\u03c0\n+\n\u03c0\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.01 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n)\n2\n invariant mass (GeV/c\n0\n\u03c0\n+\nK\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.01 GeV/c\n0\n100\n200\n300\n400\n500\n)\n2\n invariant mass (GeV/c\n0\n\u03c0\n+\nK\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.01 GeV/c\n0\n100\n200\n300\n400\n500\nFigure 19.1.10.\nFrom (Aubert, 2006v). M(\u03c0+\u03c00) and\nM(K+\u03c00) with the likelihood \ufb01t results. The dashed lines show\nthe projected backgrounds in the D+ signal region.\ncharged track, identi\ufb01ed either as a pion or kaon, with\na reconstructed \u03c00 candidate and requiring xp(D\u2217) >\n0.6. The scaled momentum of the D\u2217+, xp(D\u2217), is de-\n\ufb01ned as xp(D\u2217) \u2261p\u2217(D\u2217+)/p\u2217\nmax(D\u2217+), where p\u2217(D\u2217+)\nis the momentum of the D\u2217in the e+e\u2212c.m. frame\nand p\u2217\nmax(D\u2217+) \u2261\np\ns/4 \u2212m2\nD\u2217is the maximal D\u2217c.m.\nmomentum allowed, with s being the square of the en-\nergy of the initial e+e\u2212system. The energy of the \u03c00\nin the laboratory frame (lab) is required to be greater\nthan 0.2 GeV. Requirements on the D+ helicity angle \u03b8h,\n\u22120.9 < cos \u03b8h < 0.8 for the D+ \u2192\u03c0+\u03c00 and \u22120.9 <\ncos \u03b8h < 0.7 for the D+ \u2192K+\u03c00, are motivated by uni-\nformly distributed cos \u03b8C expected for signal events and\npeaking at \u00b11 for background. The \u03b8h is de\ufb01ned as the\nangle between the direction of the D+ charged daughter\nand the direction of the D\u2217+ meson evaluated in the D+\nrest frame. Figure 19.1.10 shows the measured invariant-\nmass spectra, M(\u03c0+\u03c00) and M(K+\u03c00), with the \ufb01t re-\nsults superimposed. The signal yields for D+ \u2192\u03c0+\u03c00 and\nD+ \u2192K+\u03c00 are respectively 1229\u00b198 and 189\u00b135, while\nfor the D+ \u2192K\u2212\u03c0+\u03c0+ reference mode is 101380 \u00b1 415.\nThe branching ratio of the signal and reference modes is\nobtained as a ratio of the measured yields (N) corrected\nfor the reconstruction e\ufb03ciencies (\u03b5):\nB(D \u2192signal)\nB(D \u2192reference) =\nN(signal)\nN(reference) \u00d7 \u03b5(reference)\n\u03b5(signal) .\n(19.1.22)\nThe measured branching ratios:\nB(D+ \u2192\u03c0+\u03c00)\nB(D+ \u2192K\u2212\u03c0+\u03c0+) = (1.33 \u00b1 0.11 \u00b1 0.09) \u00d7 10\u22122,\nB(D+ \u2192K+\u03c00)\nB(D+ \u2192K\u2212\u03c0+\u03c0+) = (2.68 \u00b1 0.50 \u00b1 0.26) \u00d7 10\u22123,\n(19.1.23)\ncombined with the world-average value of B(D+\n\u2192\nK\u2212\u03c0+\u03c0+) = (9.4\u00b10.3)% yield in the following branching\nfractions for the CS decays:\nB(D+ \u2192\u03c0+\u03c00) = (1.25 \u00b1 0.10 \u00b1 0.09 \u00b1 0.04) \u00d7 10\u22123,\nB(D+ \u2192K+\u03c00) = (2.52 \u00b1 0.47 \u00b1 0.25 \u00b1 0.08) \u00d7 10\u22124,\n(19.1.24)\n\n526\nwhere the last error is due to the uncertainty in the ref-\nerence mode branching fraction. This represents the \ufb01rst\nobservation of the DCS D+ \u2192K+\u03c00 decays and an im-\nproved measurement of the SCS D+ \u2192\u03c0+\u03c00 branching\nfraction.\n19.1.3.2 The D+ \u2192K0\nSK+ and D+\ns \u2192K0\nS\u03c0+ Branching\nFractions\nBoth D+ \u2192\u00afK0K+ and D+\ns \u2192\u00afK0\u03c0+ are DCS decays\ninvolving the color-favored tree, penguin and annihilation\ndiagrams, while the related CF modes are D+ \u2192\u00afK0\u03c0+\nand D+\ns \u2192\u00afK0K+.\nBelle has measured branching fractions of the corre-\nsponding D+\n(s) decays including K0\nS in the \ufb01nal states,\nnamely D+ \u2192K0\nSK+ and D+\ns\n\u2192K0\nS\u03c0+ with respect\nto the D+ \u2192K0\nS\u03c0+ and D+\ns\n\u2192K0\nSK+ decays, using\n605 fb\u22121 data collected at the \u03a5(4S) resonance (Won,\n2009). An additional 60 fb\u22121 of the o\ufb00-resonance data col-\nlected below the \u03a5(4S) have been used for the optimiza-\ntion procedures. They select the K0\nS \u2192\u03c0+\u03c0\u2212candidates\nhaving daughter-pion tracks separated from the interac-\ntion point (IP) in the plane perpendicular to the beam axis\nand \u03c0+\u03c0\u2212vertex displaced from the IP, whereas the direc-\ntion of the K0\nS momentum must agree with the direction\nof the decay vertex point from the IP. Selection criteria\non the related distances and angle are optimized, sepa-\nrately for high-momentum (above 1.5 GeV/c) and the re-\nmaining K0\nS candidates, to maximize a signi\ufb01cance of the\nK0\nS signal identi\ufb01ed in the M(\u03c0+\u03c0\u2212) invariant-mass spec-\ntrum. The reconstructed D+\n(s) \u2192K0\nSh+ candidates, where\nh+ = K+, \u03c0+, are required to have a good quality decay\nvertex and the c.m. momentum greater than 2.6 GeV/c to\nremove the D+\n(s) produced in B meson decays. Removing\nthe K0\nSh+ pairs with an invariant mass close to the nom-\ninal D+\n(s) mass but having in the laboratory frame (lab)\nhighly asymmetrical momenta, has signi\ufb01cantly improved\nsigni\ufb01cance of the CS D+\n(s) signals.\nThe M(K0\nSK+) and M(K0\nS\u03c0+) invariant mass distri-\nbutions after the \ufb01nal selections, shown in Fig 19.1.11,\nexhibit clear signals for both CF and DCS decays in the\nboth decay channels. All the signals are parameterized\nusing double Gaussians with a common mean value. In\nthe maximum-likelihood \ufb01ts performed to the mass spec-\ntra, all the signal parameters are kept free, except for\nthe broad Gaussian fraction and width for the D+\ns\n\u2192\nK0\nS\u03c0+; those are \ufb01xed to the values obtained for the D+ \u2192\nK0\nS\u03c0+ mode. In addition to the smooth combinatorial\nbackground, there is a peaking background due to parti-\ncle misidenti\ufb01cation. It appears in the D+\ns \u2192K0\nSK+ mass\nregion, when \u03c0+ from D+ \u2192K0\nS\u03c0+ decays is misidenti-\n\ufb01ed as K+. Similarly, when K+ is misidenti\ufb01ed as \u03c0+ in\nD+\ns \u2192K0\nSK+ decays, a peaking structure appears under\nthe D+ \u2192K0\nS\u03c0+. The shapes and yields of these peak-\ning backgrounds are obtained from the MC simulations in\nwhich hadron momentum scale and resolution are tuned\nwith the data.\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\ndata\nsignal\n+\n\u03c0\n0\nS\n K\n\u2192\n+\nD\nrandom\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n)\n2\nc\n) (GeV/\n+\nK\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\n16000\n18000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\ndata\nsignal\n+\nK\n0\nS\n K\n\u2192\ns\n+\nD\nrandom\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.94\n1.96\n1.98\n2\n)\n2\nc\nEvents/(1 MeV/\n0\n1000\n2000\n3000\n4000\n5000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\n)\n2\nc\n) (GeV/\n+\n\u03c0\n0\nS\nM(K\n1.85\n1.9\n1.95\n2\n)\n2c\nEvents/(1 MeV/\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\nFigure 19.1.11.\nFrom (Won, 2009). M(K0\nSK+) (top) and\nM(K0\nS\u03c0+) (bottom) for the selected candidates. Points with\nerror bars show the data, the histograms represent the \ufb01t re-\nsults. Signals for D+\n(s) \u2192K0\nSK+ (top) and D+\n(s) \u2192K0\nS\u03c0+\n(bottom), peaking backgrounds originating from misidenti\ufb01ed\nD+ \u2192K0\nS\u03c0+ (top) and D+\ns \u2192K0\nSK+ (bottom) decays, and\nrandom combinatorial backgrounds are also shown. The inset\nin the bottom plot is enlarged view of the D+\ns region.\nBased on the \ufb01tted signal yields and reconstruction\ne\ufb03ciencies (of about 12 \u221215%) obtained with the tuned\nMC, the measured branching ratios are:\nB(D+ \u2192K0\nSK+)\nB(D+ \u2192K0\nS\u03c0+) = (18.99 \u00b1 0.11 \u00b1 0.22)%\nB(D+\ns \u2192K0\nS\u03c0+)\nB(D+\ns \u2192K0\nSK+) = (8.03 \u00b1 0.24 \u00b1 0.19)%.\n(19.1.25)\nThese are the most precise measurements to date and\nagree with the present WA values of respectively (20.6 \u00b1\n1.4)% and (8.4 \u00b1 0.9)%.\nThe ratio for D+ is larger than na\u00a8\u0131ve expectation\nof tan2 \u03b8C due to destructive interference between color-\nfavored and color-suppressed tree diagrams contributing\nto the CF D+ \u2192\n\u00afK0\u03c0+ decay. Increase of the ratio\nmesured for D+\ns over the tan2 \u03b8C can be due to the color\nsuppression in the tree amplitude in the D+\ns \u2192\u00afK0K+.\nUsing the WA values for CF modes, the branching frac-\ntions for CS decays are:\n\n527\nB(D+ \u2192K0\nSK+) = (2.75 \u00b1 0.08) \u00d7 10\u22123\nB(D+\ns \u2192K0\nS\u03c0+) = (1.20 \u00b1 0.09) \u00d7 10\u22123,\n(19.1.26)\nwith statistical and systematic uncertainties summed in\nquadrature. However, experimentaly measured are D(s)\ndecays including K0\nS and converting them to the B involv-\ning K0 or \u00afK0 is not straightforward, as the corresponding\nDCS and CF modes can interfere with the unknown in-\nterference phase.\n19.1.3.3 D+ \u2192K+\u03b7(\u2032) and D+ \u2192\u03c0+\u03b7(\u2032)\nD+ decays into two-body \ufb01nal states with \u03b7(\u2032) are all\nthe CS decays with poorly studied SU(3) \ufb02avor sym-\nmetry structure. Such DCS decays, D+ \u2192K+\u03b7(\u2032), have\nnot been observed before, while their SCS counterparts,\nD+ \u2192\u03c0+\u03b7(\u2032), are quite well measured by CLEO.\nBelle analysis of the D+ \u2192h+\u03b7(\u2032) decays (Won, 2011),\nwith h+ = K+, \u03c0+, is based on the data sample of 791 fb\u22121\nand exploits the decays \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 and \u03b7\n\u2032 \u2192\u03b7\u03c0+\u03c0\u2212\nwith \u03b7 \u2192\u03b3\u03b3. This allows reconstruction of the D+ de-\ncay vertex formed using only charged tracks. The \u03c00 and\n\u03b7(\u2032) candidates are selected based on the invariant masses\nof their decay products. For the \ufb01nal selection the au-\nthors optimize criteria to maximize signi\ufb01cance of the\nD+ \u2192K+\u03b7(\u2032) signal studied with the MC simulations.\nThe following variables are considered in the optimiza-\ntion: the D+ c.m. momentum, the \u03b7(\u2032) lab momentum, as\nwell as variables related to the decay topology: an angle\nbetween momentum vector of the reconstructed D+ and\nthe vector joining its production and decay vertices, and\n\u03c72 of the hypothesis that the candidate tracks forming\nthe D+ are isolated from the primary vertex, de\ufb01ned as\na point of intersection of the D+ momentum vector with\nthe IP. Such an isolation is expected due to the \ufb01nite D+\nlifetime. The optimized selection cuts are also applied to\nthe normalization modes, D+ \u2192\u03c0+\u03b7(\u2032).\nThe measured M(\u03c0+\u03b7(\u2032)) and M(K+\u03b7(\u2032)) distributions\nare shown in Fig. 19.1.12. The signal function is modelled\nwith a sum of Gaussian and bifurcated Gaussian. In the\n\ufb01ts for the DCS decays, widths of both Gaussians and\nbifurcated Gaussian fraction are \ufb01xed to the values ob-\ntained for the SCS decays and scaled according to the\ndi\ufb00erence obtained with the MC simulations. Observed\nbackground is purely combinatorial and smooth, no peak-\ning background has been detected. The signal yields of the\nDCS modes amount to 166 \u00b1 23 for the D+ \u2192K+\u03b7 and\n188 \u00b1 19 for the D+ \u2192K+\u03b7\n\u2032, while reconstruction e\ufb03-\nciencies are at the level of 1.5%. The measured branching\nratios are:\nB(D+ \u2192K+\u03b7)\nB(D+ \u2192\u03c0+\u03b7) = (3.06 \u00b1 0.43 \u00b1 0.14) \u00d7 10\u22122\nB(D+ \u2192K+\u03b7\n\u2032)\nB(D+ \u2192\u03c0+\u03b7\n\u2032) = (3.77 \u00b1 0.39 \u00b1 0.10) \u00d7 10\u22122.\n(19.1.27)\nThe D+ \u2192K+\u03b7(\u2032) decays are observed for the \ufb01rst\ntime and have completed a class of the DCS D+ decays\nto pairs of light pseudoscalar mesons. The measured ratios\nare within errors in agreement with SU(3) based expec-\ntations. Using the measurements of the B(D+ \u2192\u03c0+\u03b7(\u2032))\nfrom (Mendez et al., 2010), the absolute branching frac-\ntions for the DCS modes are B(D+ \u2192K+\u03b7) = (1.08 \u00b1\n0.17 \u00b1 0.08) \u00d7 10\u22124 and B(D+ \u2192K+\u03b7\n\u2032) = (1.76 \u00b1 0.22 \u00b1\n0.12) \u00d7 10\u22124.\nUsing relations from (Chiang and Rosner, 2002), the\nmeasured B(D+ \u2192K+\u03b7(\u2032)) toghether with the WA value\nB(D+ \u2192K+\u03c00) = (1.72\u00b10.20)\u00d710\u22124 (Chiang and Ros-\nner, 2002) are used to calculate a relative phase di\ufb00er-\nence between the contributing tree and annihilation am-\nplitudes, \u03b4T A, to be (72\u00b19)\u25e6or (288\u00b19)\u25e6. It is an impor-\ntant information for \ufb01nal-state interactions in D decays.\nSimilar measurement for penguin amplitudes is impossi-\nble, as they contribute to DCS decays involving K0, while\nthese are overwhelmed by CF decays involving \u00afK0 in the\ndetected K0\nS.\n19.1.3.4 Branching Ratios of the Decays D0 \u2192\u03c0\u2212\u03c0+\u03c00\nand D0 \u2192K\u2212K+\u03c00\nThe BABAR experiment has measuread the rates of three-\nbody CS decays D0 \u2192\u03c0\u2212\u03c0+\u03c00 and D0 \u2192K\u2212K+\u03c00 rela-\ntive to the CF decay D0 \u2192K\u2212\u03c0+\u03c00, using 232 fb\u22121 (Au-\nbert, 2006ak). To reduce combinatorial backgrounds, the\nD0 candidates are reconstructed in decays D\u2217+ \u2192D0\u03c0+\ns .\nThe number of D0 signal events in each decay mode is\nobtained by \ufb01tting the observed D0 candidate mass dis-\ntributions (Fig. 19.1.13) to the sum of signal and back-\nground components, where the latter has combinatorial\ncontributions and re\ufb02ection contributions from real three-\nbody D0 decays where a kaon (pion) is misidentifed as a\npion (kaon). The reconstruction e\ufb03ciency for each event\nis calculated as a function of its position in the D0 Dalitz\nplot. The resulting branching ratios,\nB(D0 \u2192\u03c0\u2212\u03c0+\u03c00)\nB(D0 \u2192K\u2212\u03c0+\u03c00) = (10.59 \u00b1 0.06 \u00b1 0.13) \u00d7 10\u22122\nB(D0 \u2192K\u2212K+\u03c00)\nB(D0 \u2192K\u2212\u03c0+\u03c00) = (2.37 \u00b1 0.03 \u00b1 0.04) \u00d7 10\u22122,\n(19.1.28)\ncombined with B(D0 \u2192K\u2212\u03c0+\u03c00) = (14.1 \u00b1 0.5) \u00d7\n10\u22122 (Yao et al., 2006), give:\nB(D0 \u2192\u03c0\u2212\u03c0+\u03c00) = (1.493 \u00b1 0.008 \u00b1 0.018 \u00b1 0.053) \u00d7 10\u22122,\nB(D0 \u2192K\u2212K+\u03c00) = (0.334 \u00b1 0.004 \u00b1 0.006 \u00b1 0.012) \u00d7 10\u22122.\n(19.1.29)\nThe measured branching ratios contain the phase space\nfactor which enters decay rate as116 \u0393 =\nR\nd\u03a6|M|2 =\n116 Branching fraction and decay width for given process D \u2192\nf are related through B(D \u2192f) = \u0393(D \u2192f) \u00d7 \u03c4D, where\n\u03c4D \u22611/\u0393total is D lifetime\n\n528\n)\n2\nc\n) (GeV/\n\u03b7\n+\n\u03c0\nM(\n1.82 1.84 1.86 1.88\n1.9\n1.92\n)\n2\nc\nEvents/(4 MeV/\n0\n500\n1000\n1500\n)\n2\nc\n\u2019) (GeV/\n\u03b7\n+\n\u03c0\nM(\n1.82 1.84 1.86 1.88\n1.9\n1.92\n)\n2\nc\nEvents/(4 MeV/\n0\n500\n1000\n1500\n)\n2\nc\n) (GeV/\n\u03b7\n+\nM(K\n1.82 1.84 1.86 1.88\n1.9\n1.92\n)\n2\nc\nEvents/(4 MeV/\n0\n20\n40\n60\n80\n)\n2\nc\n\u2019) (GeV/\n\u03b7\n+\nM(K\n1.82 1.84 1.86 1.88\n1.9\n1.92\n)\n2\nc\nEvents/(4 MeV/\n0\n20\n40\n60\n80\nFigure 19.1.12. From (Won, 2011). Invariant mass ditributions for the \u03c0+\u03b7, \u03c0+\u03b7\n\u2032, K+\u03b7 and K+\u03b7\n\u2032 \ufb01nal states. Points with\nerror bars and histograms correspond respectively to the data and \ufb01t result.\n]\n2\n) [GeV/c\n0\n\u03c0\n+\n\u03c0\n-\n\u03c0\nm (\n1.75\n1.8\n1.85\n1.9\n1.95\n 2\nEvents / 2.5 MeV/c\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\n]\n2\n) [GeV/c\n0\n\u03c0\n+\n\u03c0\n-\n\u03c0\nm (\n1.75\n1.8\n1.85\n1.9\n1.95\n 2\nEvents / 2.5 MeV/c\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n4500\n] \n2\n) [GeV/c\n0\n\u03c0\n+\nK\n-\nm (K\n1.75\n1.8\n1.85\n1.9\n1.95\n2\nEvents / 5 MeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n] \n2\n) [GeV/c\n0\n\u03c0\n+\nK\n-\nm (K\n1.75\n1.8\n1.85\n1.9\n1.95\n2\nEvents / 5 MeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nFigure 19.1.13. From (Aubert, 2006ak). Fitted mass for the\n\u03c0\u2212\u03c0+\u03c00, and K\u2212K+\u03c00 data samples. Dots are data points,\nthe solid curves are the \ufb01t. The dot-dashed lines show the level\nof combinatorial background, the shaded region represents the\ntotal background.\n\u03a6 \u00d7 \u27e8|M|2\u27e9, where \u03a6 is the phase space of a particular\n\ufb01nal state, M is the decay matrix element, and \u27e8|M|2\u27e9\nis average |M|2 value over the Dalitz plot and the three-\nbody phase space. The relative \u03a6 for the studied decays is\n\u03c0\u2212\u03c0+\u03c00 : K\u2212\u03c0+\u03c00 : K+K+\u03c0\u2212= 5.0 : 3.2 : 1.7, which\ngives:\n\u27e8|M|2\u27e9(D0 \u2192\u03c0\u2212\u03c0+\u03c00)\n\u27e8|M|2\u27e9(D0 \u2192K\u2212\u03c0+\u03c00) = (6.68 \u00b1 0.04 \u00b1 0.08) \u00d7 10\u22122\n(19.1.30)\n\u27e8|M|2\u27e9(D0 \u2192K\u2212K+\u03c00)\n\u27e8|M|2\u27e9(D0 \u2192K\u2212\u03c0+\u03c00) = (4.53 \u00b1 0.06 \u00b1 0.08) \u00d7 10\u22122\n(19.1.31)\n\u27e8|M|2\u27e9(D0 \u2192K\u2212K+\u03c00)\n\u27e8|M|2\u27e9(D0 \u2192\u03c0\u2212\u03c0+\u03c00) = (6.78 \u00b1 0.14 \u00b1 0.21) \u00d7 10\u22121.\n(19.1.32)\nThe deviations from the na\u00a8\u0131ve picture, in which the\nratios 19.1.30 and 19.1.31 are of the order tan2 \u03b8C,\nwhile 19.1.32 is of order unity, are less than 35% for\nthese three-body \ufb01nal states. In contrast, the correspond-\ning ratios may be calculated for the two-body decays\nD0 \u2192\u03c0\u2212\u03c0+, D0 \u2192K\u2212\u03c0+, and D0 \u2192K\u2212K+. Using\nthe WA values for these two-body branching ratios (Yao\net al., 2006), the ratios corresponding to Eqs (19.1.30)\u2013\n(19.1.32), are, respectively, 0.034\u00b10.001, 0.111\u00b10.002, and\n3.53 \u00b1 0.12. Thus the na\u00a8\u0131ve Cabibbo-suppression model\nworks well for three-body \ufb01nal states, but not so good for\ntwo-body decays.\n19.1.3.5 Doubly-Cabibbo Suppressed D+\ns \u2192K+K+\u03c0\u2212and\nD+ \u2192K+\u03c0+\u03c0\u2212Decays\nThe expected branching ratio for the DCS D+\ns\n\u2192\nK+K+\u03c0\u2212with respect to its CF counterpart D+\ns\n\u2192\nK+K\u2212\u03c0+ is about 1\n2 tan4 \u03b8C. A factor modi\ufb01ng the SU(3)\nbased expectation arises from the phase space suppresion\nfor the D+\ns \u2192K+K+\u03c0\u2212due to the two identical kaons\nin the \ufb01nal state. For a similar reason, the ratio of de-\ncays rates for corresponding DCS and CF D+ decays,\nD+ \u2192K+\u03c0+\u03c0\u2212and D+ \u2192K\u2212\u03c0+\u03c0+, should be about\n2 tan4 \u03b8C. Thus within SU(3) symmetry one expects\nB(D+\ns \u2192K+K+\u03c0\u2212)\nB(D+\ns \u2192K+K\u2212\u03c0+)\nB(D+ \u2192K+\u03c0+\u03c0\u2212)\nB(D+ \u2192K\u2212\u03c0+\u03c0+) = tan8 \u03b8C,\n(19.1.33)\nas the phase-space related factors cancel out (Lipkin, 2003).\nIn order to test this prediction, Belle has searched for the\nDCS D+\ns \u2192K+K+\u03c0\u2212decays and studied the other de-\ncays entering Eq. (19.1.33) with 605 fb\u22121 data (Ko, 2009).\nAll the D+\n(s) candidates are required to have the scaled\nmomentum xp greater than 0.5 and a good quality decay\nvertex. In addition, track isolation and consistency of the\nD+\n(s) momentum vector with its production-to-decay vec-\ntor (see Section 19.1.3.3) are required, with related vari-\nables optimized for the CF decays using a small part of\nthe data further discarded from the measurement.\n\n529\n)\n2\n) (GeV/c\n+\n\u03c0\n+\n\u03c0\n\u2212\nM(K\n1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89\n1.9\n1.91 1.92\n)\n2\nEvents/(2 MeV/c\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\n)\n2\n) (GeV/c\n+\n\u03c0\n+\n\u03c0\n\u2212\nM(K\n1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89\n1.9\n1.91 1.92\n)\n2\nEvents/(2 MeV/c\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\n10\ndata\nsignal\n+\n\u03c0\n\u2212\nK\n+\n K\n\u2192\ns\n+\nD\nrandom\n)\n2\n) (GeV/c\n\u2212\n\u03c0\n+\n\u03c0\n+\nM(K\n1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89\n1.9\n1.91 1.92\n)\n2\nEvents/(2 MeV/c\n100\n200\n300\n400\n500\n600\n700\n1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89\n1.9\n1.91 1.92\n100\n200\n300\n400\n500\n600\n700\nFigure 19.1.14.\nFrom (Ko, 2009). Invariant mass ditribu-\ntions for the K+\u03c0+\u03c0\u2212and K\u2212\u03c0+\u03c0+ \ufb01nal states. Points with\nerror bars correspond to the data, histogram is \ufb01t result and in-\nclude signal, random (combinatorial) background and peaking\nbackground from D+\ns \u2192K+K\u2212\u03c0+.\nThe measured M(K+\u03c0+\u03c0\u2212) and M(K\u2212\u03c0+\u03c0+), shown\nin Fig. 19.1.14, exibit the D+ signals, while M(K+K+\u03c0\u2212)\nand M(K+K\u2212\u03c0+) in Fig. 19.1.15 the D+\ns signals. The\nsignals are parameterized with double Gaussians, with\nthe parameters for the DCS modes \ufb01xed to the val-\nues \ufb01tted for the CF decays. There are peaking back-\ngrounds detected coming from the K-\u03c0 misidenti\ufb01cation:\nD+\ns\n\u2192K+K\u2212\u03c0+ re\ufb02ecting in D+ \u2192K+\u03c0+\u03c0\u2212and\nD+ \u2192K\u2212\u03c0+\u03c0+, and D+ \u2192K\u2212\u03c0+\u03c0+ contributing to\nD+\ns\n\u2192K+K\u2212\u03c0+. Shapes of the re\ufb02ections are deter-\nmined from the real data by assigning a nominal kaon\n(pion) mass to pion (kaon) track, and their yields are kept\nfree in the \ufb01ts. The measured branching ratios are:\nB(D+ \u2192K+\u03c0+\u03c0\u2212)\nB(D+ \u2192K\u2212\u03c0+\u03c0+) = (0.569 \u00b1 0.018 \u00b1 0.014) \u00d7 10\u22122\nB(D+\ns \u2192K+K+\u03c0\u2212)\nB(D+\ns \u2192K+K\u2212\u03c0+) = (0.229 \u00b1 0.028 \u00b1 0.012) \u00d7 10\u22122.\n(19.1.34)\nReconstruction e\ufb03ciencies used for these B calculations\nare based on the MC simulations which include interme-\ndiate resonances contributing to the D+ \u2192K\u2212\u03c0+\u03c0+,\nD+ \u2192K+\u03c0+\u03c0\u2212and D+\ns \u2192K+K\u2212\u03c0+ decays (Amsler\net al., 2008; Anjos et al., 1993). As the Dalitz-plot model\nfor the D+\ns \u2192K+K+\u03c0\u2212is not known, it is generated ac-\ncording to the phase space model, while the largest relative\ndi\ufb00erences obtained with various decay models assumed\nare included in the sytematic uncertainty.\nThe double branching ratio in Eq. (19.1.33) is mea-\nsured to be (1.57 \u00b1 0.21) tan8 \u03b8C, with the error being the\n)\n2\n) (GeV/c\n+\n\u03c0\n\u2212\nK\n+\nM(K\n1.93\n1.94\n1.95\n1.96\n1.97\n1.98\n1.99\n2\n2.01\n2.02\n2.03\n)\n2\nEvents/(2 MeV/c\n0\n5000\n10000\n15000\n20000\n)\n2\n) (GeV/c\n+\n\u03c0\n\u2212\nK\n+\nM(K\n1.93\n1.94\n1.95\n1.96\n1.97\n1.98\n1.99\n2\n2.01\n2.02\n2.03\n)\n2\nEvents/(2 MeV/c\n0\n5000\n10000\n15000\n20000\ndata\nsignal\n\u2212\nK\n+\n K\n\u2192\n0\n, D\n+\n\u03c0\n0\n D\n\u2192\n*+\nD\n+\n\u03c0\n+\n\u03c0\n\u2212\n K\n\u2192\n+\nD\nrandom\n)\n2\n) (GeV/c\n\u2212\n\u03c0\n+\nK\n+\nM(K\n1.93\n1.94\n1.95\n1.96\n1.97\n1.98\n1.99\n2\n2.01\n2.02\n2.03\n)\n2\nEvents/(2 MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n1.93\n1.94\n1.95\n1.96\n1.97\n1.98\n1.99\n2\n2.01\n2.02\n2.03\n0\n20\n40\n60\n80\n100\n120\n140\nFigure 19.1.15.\nFrom (Ko, 2009). Invariant mass ditribu-\ntions for the K+K+\u03c0\u2212and K+K\u2212\u03c0+ \ufb01nal states. Points with\nerror bars correspond to the data, histogram is \ufb01t result and\nincludes signal, random (combinatorial) background and peak-\ning background from D+ \u2192K\u2212\u03c0+\u03c0+ and D\u2217+ \u2192D0\u03c0+ with\nD0 \u2192K+K\u2212.\ntotal uncertainty. Its slight deviation from the expected\nvalue can be the e\ufb00ect of di\ufb00erent resonant intermediate\nstate, which are not taken into account in the prediction\n(Lipkin, 2003). Using the world average values for the CF\nbranching fractions (Amsler et al., 2008), the absolute B\nfor the DCS decays are:\nB(D+ \u2192K+\u03c0+\u03c0\u2212) = (5.2 \u00b1 0.2 \u00b1 0.1) \u00d7 10\u22124,\nB(D+\ns \u2192K+K+\u03c0\u2212) = (1.3 \u00b1 0.2 \u00b1 0.1) \u00d7 10\u22124.\n(19.1.35)\nThe former is an improvement of the existing measure-\nment, the latter comprises the \ufb01rst signi\ufb01cant measure-\nment.\n19.1.3.6 Wrong-Sign Decays D0 \u2192K\u03c0, D0 \u2192K\u03c0\u03c00,\nD0 \u2192K\u03c0\u03c0\u03c0\nSome DCS D0 decays are measured for the sake of the\nD0\u2212\u00afD0 mixing phenomenon appearing in so called wrong-\nsign (WS) decays (see Section 19.2), like D0 \u2192K+\u03c0\u2212,\nD0 \u2192K+\u03c0\u2212\u03c00 or D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212, named after a\ncharge of the \ufb01nal state kaon being opposite to the one\nproduced in counterpart CF processes: D0 \u2192K\u2212\u03c0+,\nD0 \u2192K\u2212\u03c0+\u03c00 or D0 \u2192K\u2212\u03c0+\u03c0\u2212\u03c0\u2212, and being called\nright-sign (RS) decays. The WS process proceeds either\nthrough direct DCS decay (for example D0 \u2192K+\u03c0\u2212)\nor through D0 \u2212\u00afD0 mixing followed by RS CF decays\n(i.e. D0 \u2212\u00afD0 \u2192K+\u03c0\u2212). These two decays can be distin-\nguished by the D0 decay-time distribution (Eq. 19.2.22),\n\n530\nTable 19.1.2. RW S measurements from (Tian, 2005; Zhang,\n2006) [10\u22123].\nDecay mode\nBranching Ratio\nD0\u2192K+\u03c0\u2212\nD0\u2192K\u2212\u03c0+\n3.77 \u00b1 0.08 \u00b1 0.05\nD0\u2192K+\u03c0\u2212\u03c00\nD0\u2192K\u2212\u03c0+\u03c00\n2.29 \u00b1 0.15+0.13\n\u22120.09\nD0\u2192K+\u03c0\u2212\u03c0+\u03c0\u2212\nD0\u2192K\u2212\u03c0+\u03c0+\u03c0\u2212\n3.20 \u00b1 0.18+0.18\n\u22120.13\nand the RD entering this formula is the ratio of the DCS\nand CF decays.\nIn the Belle studies of the D0 \u2192K+\u03c0\u2212(Zhang, 2006)\nand of the D0 \u2192K+\u03c0\u2212\u03c00 and D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212(Tian,\n2005) the D0 mesons originating from D\u2217+ \u2192D0\u03c0+ de-\ncays are studied, and both RS and WS signals are ob-\ntained from the two-dimensional \ufb01t to invariant mass of\nthe D0 decay products, M(D0), and an energy release\nin D\u2217+ decays, Q \u2261M(D\u2217+) \u2212M(D0) \u2212m\u03c0. Measured\nratios of the WS to the RS signals are summarized in\nTable 19.1.2. E\ufb03ciencies for both multi-body D0 decays\ntake into account that they are dominated by various in-\ntermediate resonances, that can be di\ufb00erent for the RS\nand WS decays. The event yields are corrected for ac-\nceptance in multi-dimensional space comprised of the in-\nvariant mass squared for various K\u03c0 and \u03c0\u03c0 subsystems.\nGiven that the mixing is small, RW S \u2248RD. Fit to distri-\nbution of the WS D0 \u2192K+\u03c0\u2212proper decay time yields\nRD = (3.64 \u00b1 0.17) \u00d7 10\u22123, in agreement with the RW S.\nThus the RW S gives a good estimate of the branching ra-\ntio of the DCS to CF rates. In terms of consistency with\nthe SU(3) symmetery based prediction, all the results in\nTable 19.1.2 are consistent with the expected tan4 \u03b8C.\n19.1.3.7 Summary of the CS decays\nThe measured ratios of CS to CF branching ratios are\nsummarized in Table 19.1.3, while branching fractions of\nCS decays, extracted from measurements relative to ref-\nerence modes are listed in Table 19.1.4.\n19.1.4 Dalitz analysis of three-body charmed meson\ndecays\n19.1.4.1 Introduction\nDalitz plot analyses of three-body charm decays can pro-\nvide new information on the resonances that contribute to\nobserved three-body \ufb01nal states. In addition, since the in-\ntermediate quasi-two-body modes are dominated by light\nquark meson resonances, new information on light me-\nson spectroscopy can be obtained. Comparison between\nthe production of resonances in decays of di\ufb00erently \ufb02a-\nvored charmed mesons D0(c\u00afu), D+(c \u00afd) and D+\ns (c\u00afs) can\nyield new information on their possible quark composi-\ntion. Another bene\ufb01t of studying charm decays is that, in\nsome cases, partial wave analyses are able to isolate the\nTable 19.1.3. Branching ratios measured by Belle and BABAR.\nRatio\ntype\nB [10\u22122]\nD+\u2192\u03c0+\u03c00\nD+\u2192K\u2212\u03c0+\u03c0+\nSCS\nCF\n1.33 \u00b1 0.11 \u00b1 0.09\nD+\u2192K+\u03c00\nD+\u2192K\u2212\u03c0+\u03c0+\nDCS\nCF\n0.268 \u00b1 0.05 \u00b1 0.026\nD+\u2192K0\nSK+\nD+\u2192K0\nS\u03c0+\nDCS\nCF\n18.99 \u00b1 0.11 \u00b1 0.22\nD+\ns \u2192K0\nS\u03c0+\nD+\ns \u2192K0\nSK+\nDCS\nCF\n8.03 \u00b1 0.24 \u00b1 0.19\nD+\u2192K+\u03b7\nD+\u2192\u03c0+\u03b7\nDCS\nSCS\n3.06 \u00b1 0.43 \u00b1 0.14\nD+\u2192K+\u03b7\n\u2032\nD+\u2192\u03c0+\u03b7\u2032\nDCS\nSCS\n3.77 \u00b1 0.39 \u00b1 0.10\nD0\u2192\u03c0\u2212\u03c0+\u03c00\nD0\u2192K\u2212\u03c0+\u03c00\nSCS\nCF\n6.68 \u00b1 0.04 \u00b1 0.08\nD0\u2192K\u2212K+\u03c00\nD0\u2192K\u2212\u03c0+\u03c00\nSCS\nCF\n4.53 \u00b1 0.06 \u00b1 0.08\nD+\u2192K+\u03c0+\u03c0\u2212\nD+\u2192K\u2212\u03c0+\u03c0+\nDCS\nCF\n0.569 \u00b1 0.018 \u00b1 0.014\nD+\ns \u2192K+K+\u03c0\u2212\nD+\ns \u2192K+K\u2212\u03c0+\nDCS\nCF\n0.229 \u00b1 0.028 \u00b1 0.012\nTable 19.1.4.\nBranching fractions of CS decays, extracted\nfrom measurements relative to reference modes. Errors are re-\nspectively statistical, systematic and due to the uncertainty in\nthe reference mode branching fraction. If single error is quoted\nit includes all these contributions.\nDecay mode\nBranching Fraction\nD+ \u2192\u03c0+\u03c00\n(1.25 \u00b1 0.10 \u00b1 0.09 \u00b1 0.04) \u00d7 10\u22123\nD+ \u2192K+\u03c00\n(2.52 \u00b1 0.47 \u00b1 0.25 \u00b1 0.08) \u00d7 10\u22124\nD+ \u2192K0\nSK+\n(2.75 \u00b1 0.08) \u00d7 10\u22123\nD+\ns \u2192K0\nS\u03c0+\n(1.20 \u00b1 0.09) \u00d7 10\u22123\nD+ \u2192K+\u03b7\n(1.08 \u00b1 0.17 \u00b1 0.08) \u00d7 10\u22124\nD+ \u2192K+\u03b7\n\u2032\n(1.76 \u00b1 0.22 \u00b1 0.12) \u00d7 10\u22124\nD+ \u2192K+\u03c0+\u03c0\u2212\n(5.2 \u00b1 0.2 \u00b1 0.1) \u00d7 10\u22124\nD+\ns \u2192K+K+\u03c0\u2212\n(1.3 \u00b1 0.2 \u00b1 0.1) \u00d7 10\u22124\nD0 \u2192\u03c0\u2212\u03c0+\u03c00\n(1.493 \u00b1 0.008 \u00b1 0.018 \u00b1 0.053) \u00d7 10\u22122\nD0 \u2192K\u2212K+\u03c00\n(0.334 \u00b1 0.004 \u00b1 0.006 \u00b1 0.012) \u00d7 10\u22122\nscalar contribution almost background free. A dedicated\ndescription of the Dalitz analysis methods can be found\nin Chapter 13. Table 19.1.5 gives a list of various three-\nbody charm Dalitz analyses performed by the B Factories\ntogether with references and corresponding sections with\na detailed description.\n19.1.4.2 Dalitz Plot Analysis of D0 \u2192K0K+K\u2212\nThe paper from BABAR (Aubert, 2005f) focuses on the\nstudy of the three-body D0 meson decay\nD0 \u2192K0K+K\u2212,\nwhere the K0 is detected via the decay K0\nS \u2192\u03c0+\u03c0\u2212. The\nD0 is tagged with a D\u2217. In a \ufb01rst analysis BABAR made use\n\n531\nTable 19.1.5. Dalitz analyses of three-body charm decays performed by the B Factories.\nDecay\nReference\nSection with description\nD0 \u2192K0K+K\u2212\n(Aubert, 2005f, 2008l)\n19.1.4.2\nD0 \u2192K0\nS\u03c0+\u03c0\u2212\n(Aubert, 2008l; Zhang, 2006)\n19.1.4.4\nD0 \u2192K+\u03c0\u2212\u03c00\n(Aubert, 2009u)\n19.1.4.5\nD0 \u2192\u03c0\u2212\u03c0\u2212\u03c00\n(Aubert, 2007w)\n19.1.4.7\nD+\ns \u2192\u03c0\u2212\u03c0+\u03c0+\n(Aubert, 2009i)\n19.1.4.8\nD+\ns \u2192K\u2212K+\u03c0+\n(del Amo Sanchez, 2011b)\n19.1.4.9\nFigure 19.1.16. From (Aubert, 2005f). Dalitz plot of D0 \u2192\nK0K+K\u2212.\nof 91.5 fb\u22121 collecting N=13536 \u00b1 116 events with a 97.3%\npurity. An additional analysis, with increased statistics (\u2248\n69000 candidates) has been performed in with the aim of\nmeasuring \u03c63. We \ufb01rst describe the lower statistics anal-\nysis and in particular the partial wave analysis of the\nK+K\u2212threshold region.\nThe Dalitz plot for these D0 \u2192K0K+K\u2212candidates\nis shown in Fig. 19.1.16.\nIn the K+K\u2212threshold region, a strong \u03c6(1020) sig-\nnal is observed, together with a rather broad structure.\nA large asymmetry with respect to the K0K+ axis can\nalso be seen in the vicinity of the \u03c6(1020) signal, which\nis the result of interference between S- and P-wave am-\nplitude contributions to the K+K\u2212system. The f0(980)\nand a0(980) S-wave resonances are, in fact, just below the\nK+K\u2212threshold, and might be expected to contribute\nin the vicinity of \u03c6(1020). An accumulation of events due\nto a charged a0(980)+ can be observed on the lower right\nedge of the Dalitz plot. This contribution, however, does\nnot overlap with the \u03c6(1020) region and this allows the\nK+K\u2212scalar and vector components to be separated us-\ning a partial wave analysis in the low mass K+K\u2212region.\n19.1.4.3 Partial Wave Analysis of D0 \u2192K0K+K\u2212.\nIt is assumed that near threshold the production of the\nK+K\u2212system can be described in terms of the diagram\nshown in Fig. 19.1.17. The helicity angle, \u03b8K, is then de-\n\ufb01ned as the angle between the K+ for D0 (or K\u2212for\nD0) in the K+K\u2212rest frame and the K+K\u2212direction\nin the D0 (or K0) rest frame. The K+K\u2212mass distribu-\ntion has been modi\ufb01ed by weighting each D0 candidate\nby the spherical harmonic Y 0\nL(cos \u03b8K), L = 0 \u22124, divided\nby its (Dalitz-plot-dependent) \ufb01tted e\ufb03ciency. The result-\ning distributions\n\nY 0\nL\n\u000b\nare shown in Fig. 19.1.18 and are\nproportional to the K+K\u2212mass-dependent harmonic mo-\nments. It is found that all the\n\nY 0\nL\n\u000b\nmoments are small or\nconsistent with zero, except for\n\nY 0\n0\n\u000b\n,\n\nY 0\n1\n\u000b\nand\n\nY 0\n2\n\u000b\n.\nFigure 19.1.17. The kinematics describing the production of\nthe K+K\u2212system in the threshold region of the decay D0 \u2192\nK0K+K\u2212.\nIn order to interpret these distributions a simple par-\ntial wave analysis has been performed, involving only S-\nand P-wave amplitudes. This results in the following set\nof equations (Chung, 1997):\n\u221a\n4\u03c0\n\nY 0\n0\n\u000b\n= S2 + P 2\n\u221a\n4\u03c0\n\nY 0\n1\n\u000b\n= 2 | S || P | cos \u03c6SP\n\u221a\n4\u03c0\n\nY 0\n2\n\u000b\n=\n2\n\u221a\n5P 2,\n(19.1.36)\nwhere S and P are proportional to the size of the S- and\nP-wave contributions and \u03c6SP is their relative phase. Un-\nder these assumptions, the\n\nY 0\n2\n\u000b\nmoment is proportional\nto P 2 so that it is natural that the \u03c6(1020) appears free\nof background, as is observed.\n\n532\nFigure 19.1.18. From (Aubert, 2005f). The unnormalized\nspherical harmonic moments\n\nY 0\nL\n\u000b\nas functions of K+K\u2212in-\nvariant mass. The histograms represent the result of the full\nDalitz plot analysis.\nFigure 19.1.19. From (Aubert, 2005f). Results from the\nK+K\u2212Partial Wave Analysis corrected for phase space. (a)\nP-wave strength, (b) S-wave strength. (c) m(K0K+) distribu-\ntion, (d) cos \u03c6SP in the \u03c6(1020) region. (e) \u03c6SP in the threshold\nregion after having subtracted the \ufb01tted \u03c6(1020) phase motion\nshown in (d).\nA strong S \u2212P interference is evidenced by the rapid\nmotion of the\n\nY 0\n1\n\u000b\nmoment in Fig. 19.1.18 in the \u03c6(1020)\nmass region.\nFigure 19.1.20. (Aubert, 2005f). Comparison between the\nphase-space-corrected K+K\u2212and K0K+ normalised to the\nsame area in the mass region between 0.992 and 1.05 GeV/c2.\nThe above system of equations 19.1.36 can be solved\ndirectly for S2, P 2 and cos \u03c6SP . However, since these am-\nplitudes are de\ufb01ned in a D0 decay, it is necessary to cor-\nrect for phase space. The corrected spectra are shown in\nFig. 19.1.19.\nThe distributions have been \ufb01tted using the following\nmodel:\n\u2013 The P-wave is entirely due to the \u03c6(1020) meson\n(Fig.19.1.19(a)).\n\u2013 The scalar contribution in the K+K\u2212mass projection\nis entirely due to the a0(980)0 (Fig. 19.1.19(b)).\n\u2013 The K0K+ mass distribution is entirely due to a0(980)+\n(Fig. 19.1.19(c)).\n\u2013 The angle \u03c6SP (Fig. 19.1.19(d)) is obtained \ufb01tting the\nS, P waves and cos \u03c6SP with ca0BWa0 + c\u03c6BW\u03c6ei\u03b1.\nHere BWa0 and BW\u03c6 are the Breit-Wigner functions\n(BW) describing the a0(980) and \u03c6(1020) resonances.\nThe a0(980) scalar resonance has a mass very close to\nthe KK threshold and decays mostly to \u03b7\u03c0. It has been\ndescribed by a coupled channel Breit-Wigner shape of the\nform:\nBWch(a0)(m) =\ngKK\nm2\n0 \u2212m2 \u2212i(\u03c1\u03b7\u03c0g2\u03b7\u03c0 + \u03c1KKg2\nKK)\n(19.1.37)\nwhere \u03c1(m) = 2q/m while g\u03b7\u03c0 and gKK describe the\na0(980) couplings to the \u03b7\u03c0 and KK systems respectively.\nFixing m0 and g\u03b7\u03c0 to the Crystal Barrel measurements\n(Abele et al., 1998) it is possible to measure:\ngKK = (464 \u00b1 29) MeV)1/2.\n(19.1.38)\nFigure 19.1.19(e) shows the residual a0(980) phase, ob-\ntained by \ufb01rst computing \u03c6SP in the range (0,\u03c0) and then\n\n533\nTable 19.1.6. From (Aubert, 2008l). Complex amplitudes arei\u03c6r and \ufb01t fractions, obtained from the \ufb01t of the D0 \u2192K0\nSK+K\u2212\nDalitz plot distribution. The mass and width of the \u03c6(1020), and the gKK coupling constant are simultaneously determined in\nthe \ufb01t, yielding M\u03c6(1020) = 1.01943 \u00b1 0.00002 GeV/c2, \u0393\u03c6(1020) = 4.59319 \u00b1 0.00004 MeV/c2, and gKK = 0.550 \u00b1 0.010 GeV/c2.\nErrors for amplitudes are statistical only. Uncertainties (largely dominated by systematic contributions) are not estimated for\nthe \ufb01t fractions.\nComponent\nar\n\u03c6r (deg)\nFraction (%)\nK0\nSa0(980)0\n1\n0\n55.8\nK0\nS\u03c6(1020)\n0.227 \u00b1 0.005\n\u221256.2 \u00b1 1.0\n44.9\nK0\nSf0(1370)\n0.04 \u00b1 0.06\n\u22122 \u00b1 80\n0.1\nK0\nSf2(1270)\n0.261 \u00b1 0.020\n\u22129 \u00b1 6\n0.3\nK0\nSa0(1450)0\n0.65 \u00b1 0.09\n\u221295 \u00b1 10\n12.6\nK\u2212a0(980)+\n0.562 \u00b1 0.015\n179 \u00b1 3\n16.0\nK\u2212a0(1450)+\n0.84 \u00b1 0.04\n97 \u00b1 4\n21.8\nK+a0(980)\u2212\n0.118 \u00b1 0.015\n138 \u00b1 7\n0.7\n)\n4\n/c\n2\n (GeV\n2\n-\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n500\n1000\n1500\n2000\n)\n4\n/c\n2\n (GeV\n2\n-\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n500\n1000\n1500\n2000 d)\n)\n4\n/c\n2\n (GeV\n2+\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n500\n1000\n1500\n2000\n)\n4\n/c\n2\n (GeV\n2+\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n500\n1000\n1500\n2000 e)\n)\n4\n/c\n2\n (GeV\n2\n0\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n5000\n10000\n)\n4\n/c\n2\n (GeV\n2\n0\nm\n1\n1.2\n1.4\n1.6\n1.8\n0\n5000\n10000\nf)\nFigure 19.1.21.\nFrom (Aubert, 2008l). D0 \u2192K0\nSK+K\u2212Dalitz plot projections from D\u2217+ \u2192D0\u03c0+ events on (d) m2\n\u2212, (e)\nm2\n+, and (f) m2\n0. The curves are the reference model \ufb01t projections.\nsubtracting the known phase motion due to the \u03c6(1020)\nresonance.\nIn this \ufb01t the possible presence of an f0(980) contri-\nbution has not been considered. This assumption can be\ntested by comparing the K+K\u2212and K0K+ phase space\ncorrected mass distributions. Since the f0(980) has isospin\n0, it cannot decay to K0K+. Therefore an excess in the\nK+K\u2212mass spectrum with respect to K0K+ would in-\ndicate the presence of an f0(980) contribution.\nFigure 19.1.20 compares the K+K\u2212and K0K+ mass\ndistributions, normalised to the same area between 0.992\nand 1.05 GeV/c2 and corrected for phase space. It is pos-\nsible to observe that the two distributions show a good\nagreement, supporting the argument that the f0(980) con-\ntribution is small.\nWe now refer to the higher statistics Dalitz plot anal-\nysis from BABAR (Aubert, 2008l). The description of the\nD0 \u2192K0\nSK+K\u2212decay amplitude consists of \ufb01ve distinct\nresonances leading to 8 two-body decays: K0\nSa0(980)0,\nK0\nS\u03c6(1020),\nK\u2212a0(980)+,\nK0\nSf0(1370),\nK+a0(980)\u2212,\nK0\nSf2(1270)0, K0\nSa0(1450)0, and K\u2212a0(1450)+. This iso-\nbar model is essentially identical to that used in the pre-\nvious analysis, but for the addition of the a0(1450) scalar,\nwhose contribution is strongly supported by the much\nlarger data sample, as well as of a D-wave contribution\nparameterized with the f2(1270) tensor. Attempts to im-\nprove the model quality by adding other contributions (in-\ncluding the non-resonant term) did not give better results.\nTable 19.1.6 summarizes the values obtained for all\nfree parameters of the D0 \u2192K0\nSK+K\u2212Dalitz model,\nthe complex amplitudes arei\u03c6r, the mass and width of the\n\u03c6(1020) and the coupling constant gKK, together with\nthe \ufb01t fractions. The value of gKK is consistent with the\nprevious result, and di\ufb00ers signi\ufb01cantly from the mea-\nsurement reported in (Abele et al., 1998). All amplitudes\nare measured with respect to D0 \u2192K0\nSa0(980)0, which\ngives the largest contribution. The sum of \ufb01t fractions is\n152.3%, and the reduced \u03c72 is 1.09 (with statistical er-\nrors only) for 6856 degrees of freedom, estimated from\na binning of the Dalitz plot into square regions of size\n0.045 GeV2/c4. Figure 19.1.21(d,e,f) shows the \ufb01t pro-\njections overlaid with the data distributions. The Dalitz\nplot distributions are well reproduced, with some small\ndiscrepancies at the peaks of the m2\n\u2212and m2\n+ projections.\n\n534\n19.1.4.4 D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz model\nThis analysis from BABAR is related to the measurement of\n\u03c63 (Section 17.8) and makes use of 487 000 D0 \u2192K0\nS\u03c0+\u03c0\u2212\nevents tagged with a D\u2217+ with 97.7% purity (Aubert,\n2008l). The P- and D-waves of the D0 \u2192K0\nS\u03c0+\u03c0\u2212decay\namplitude are described using a total of 6 resonances lead-\ning to 8 two-body decay amplitudes: the Cabibbo allowed\n(CA) K\u2217(892)\u2212, K\u2217(1680)\u2212, K\u2217\n2(1430)\u2212, the doubly-\nCabibbo suppressed (DCS) K\u2217(892)+, K\u2217\n2(1430)+, and\nthe CP eigenstates \u03c1(770)0, \u03c9(782), and f2(1270). Since\nthe K\u03c0 P-wave is largely dominated by the K\u2217(892)\u2213, the\nmass and width of this resonance are simultaneously deter-\nmined from the \ufb01t to the tagged D0 sample, MK\u2217(892)\u2213=\n893.61\u00b10.08 MeV/c2 and \u0393K\u2217(892)\u2213= 46.34\u00b10.16 MeV/c2\n(errors are statistical only). The mass and width values of\nthe K\u2217(1680)\u2212are taken from (Aston et al., 1988), where\nthe interference between the K\u03c0 S- and P-waves is prop-\nerly accounted for.\nThey adopt the same parameterizations for K, \u03c1, and\nP as in Yao et al. (2006), Anisovich and Sarantsev (2003),\nand Link et al. (2004a). The K matrix is written as\nKuv(s) =\n X\n\u03b1\ng\u03b1\nug\u03b1\nv\nm2\u03b1 \u2212s + f scatt\nuv\n1 \u2212sscatt\n0\ns \u2212sscatt\n0\n!\nfA0(s),\n(19.1.39)\nwhere g\u03b1\nu is the coupling constant of the K-matrix pole\nm\u03b1 to the uth channel. The parameters f scatt\nuv\nand sscatt\n0\ndescribe the slowly-varying part of the K-matrix. The fac-\ntor\nfA0(s) = 1 \u2212sA0\ns \u2212sA0\n\u0012\ns \u2212sA\nm2\n\u03c0\n2\n\u0013\n,\n(19.1.40)\nsuppresses the false kinematical singularity at s = 0\nin the physical region near the \u03c0\u03c0 threshold (the Adler\nzero (Adler, 1965)). The parameter values used in this\nanalysis are listed in Section 13, and are obtained from\na global analysis of the available \u03c0\u03c0 scattering data from\nthreshold up to 1900 MeV/c2 (Anisovich and Sarantsev,\n2003). The parameters f scatt\nuv\n, for u \u0338= 1, are all set to zero\nsince they are not related to the \u03c0\u03c0 scattering process.\nSimilarly, for the P vector we have\nPv(s) =\nX\n\u03b1\n\u03b2\u03b1g\u03b1\nv\nm2\u03b1 \u2212s + f prod\n1v\n1 \u2212sprod\n0\ns \u2212sprod\n0\n.\n(19.1.41)\nNote that the P-vector has the same poles as the K-matrix,\notherwise the F1 vector would vanish (diverge) at the K-\nmatrix (P-vector) poles. The parameters \u03b2\u03b1, f prod\n1v\nand\nsprod\n0\nof the initial P-vector are obtained from the \ufb01t to\nthe tagged D0 \u2192K0\nS\u03c0+\u03c0\u2212data sample.\nFor the K\u03c0 S-wave contribution to Eq. (19.1.39)\nthey use a parameterization extracted from scattering\ndata (Aston et al., 1988) which consists of a K\u2217\n0(1430)\u2212\nor K\u2217\n0(1430)+ BW (for CA or DCS contribution, respec-\ntively) together with an e\ufb00ective range non-resonant com-\nponent with a phase shift,\nAK\u03c0 L=0(m) = F sin \u03b4F ei\u03b4F + R sin \u03b4Rei\u03b4Rei2\u03b4F ,\n(19.1.42)\nwith\n\u03b4R = \u03c6R + tan\u22121\n\u0014 M\u0393(m2\nK\u03c0)\nM 2 \u2212m2\nK\u03c0\n\u0015\n,\n\u03b4F = \u03c6F + cot\u22121\n\u0014 1\naq + rq\n2\n\u0015\n.\n(19.1.43)\nThe parameters a and r play the role of a scattering length\nand e\ufb00ective interaction length, respectively, F (\u03c6F ) and\nR (\u03c6R) are the amplitudes (phases) for the non-resonant\nand resonant terms, and q is the momentum of the spec-\ntator particle in the K\u03c0 system rest frame. Note that the\nphases \u03b4F and \u03b4R depend on m2\nK\u03c0. M and \u0393(m2\nK\u03c0) are the\nmass and running width of the resonant term. This param-\neterization corresponds to a K-matrix approach describing\na rapid phase shift coming from the resonant term and a\nslow rising phase shift governed by the non-resonant term,\nwith relative strengths R and F. The parameters M, \u0393,\nF, \u03c6F , R, \u03c6R, a and r are determined from the \ufb01t to the\ntagged D0 sample, along with the other parameters of the\nmodel. Other recent experimental e\ufb00orts to improve the\ndescription of the K\u03c0 S-wave using K-matrix and model\nindependent parameterizations from high-statistics sam-\nples of D+ \u2192K\u2212\u03c0+\u03c0+ decays are described in Aitala\net al. (2006), Link et al. (2007), and Bonvicini et al. (2008).\nTable 19.1.7 summarizes the values obtained for all free\nparameters of the D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz model: CA, DCS,\nand CP eigenstates complex amplitudes arei\u03c6r, \u03c0+\u03c0\u2212S-\nwave P-vector parameters, and K\u03c0 S-wave parameters,\nalong with the \ufb01t fractions. The non-resonant term of\nEq. (19.1.42) has not been included since the \u03c0\u03c0 and\nK\u03c0 S-wave parameterizations naturally account for their\nrespective non-resonant contributions. The \ufb01fth P-vector\nchannel and pole have also been excluded since the \u03b7\u03b7\u2032\nthreshold and the pole mass m5 are both far beyond our\n\u03c0\u03c0 kinematic range, and thus there is little sensitivity to\nthe associated parameters, f prod\n15\nand \u03b25, respectively. The\namplitudes are measured with respect to D0 \u2192K0\nS\u03c1(770)0\nwhich gives the second largest contribution.\nThe K\u03c0 and \u03c0\u03c0 P-waves dominate the decay, but sig-\nni\ufb01cant contributions from the corresponding S-waves are\nalso observed (above 6 and 4 standard deviations, respec-\ntively). They obtain a sum of \ufb01t fractions of (103.6 \u00b1\n5.2)%, and the goodness-of-\ufb01t is estimated through a two-\ndimensional \u03c72 test performed binning the Dalitz plot into\nsquare regions of size 0.015 GeV2/c4, yielding a reduced\n\u03c72 of 1.11 (including statistical errors only) for 19274 de-\ngrees of freedom. The variation of the contribution to the\n\u03c72 as a function of the Dalitz plot position is approx-\nimately uniform. Figure 19.1.22(a,b,c) shows the Dalitz\n\ufb01t projections overlaid with the data distributions. The\nDalitz plot distributions are well reproduced, with some\n\n535\nTable 19.1.7. From (Aubert, 2008l). CA, DCS, and CP eigenstates complex amplitudes arei\u03c6r, \u03c0\u03c0 S-wave P-vector parameters,\nK\u03c0 S-wave parameters, and \ufb01t fractions, as obtained from the \ufb01t of the D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz plot distribution from D\u2217+ \u2192\nD0\u03c0+. P-vector parameters f\n\u2032prod\n1v\n, for v \u0338= 1, are de\ufb01ned as f prod\n1v\n/f prod\n11\n. Errors for amplitudes are statistical only, while for\n\ufb01t fractions include statistical and systematic uncertainties, largely dominated by the latter. Upper limits on \ufb01t fractions are\nquoted at 95% con\ufb01dence level.\nComponent\nar\n\u03c6r (deg)\nFraction (%)\nK\u2217(892)\u2212\n1.740 \u00b1 0.010\n139.0 \u00b1 0.3\n55.7 \u00b1 2.8\nK\u2217\n0(1430)\u2212\n8.2 \u00b1 0.7\n153 \u00b1 8\n10.2 \u00b1 1.5\nK\u2217\n2(1430)\u2212\n1.410 \u00b1 0.022\n138.4 \u00b1 1.0\n2.2 \u00b1 1.6\nK\u2217(1680)\u2212\n1.46 \u00b1 0.10\n\u2212174 \u00b1 4\n0.7 \u00b1 1.9\nK\u2217(892)+\n0.158 \u00b1 0.003\n\u221242.7 \u00b1 1.2\n0.46 \u00b1 0.23\nK\u2217\n0(1430)+\n0.32 \u00b1 0.06\n143 \u00b1 11\n< 0.05\nK\u2217\n2(1430)+\n0.091 \u00b1 0.016\n85 \u00b1 11\n< 0.12\n\u03c1(770)0\n1\n0\n21.0 \u00b1 1.6\n\u03c9(782)\n0.0527 \u00b1 0.0007\n126.5 \u00b1 0.9\n0.9 \u00b1 1.0\nf2(1270)\n0.606 \u00b1 0.026\n157.4 \u00b1 2.2\n0.6 \u00b1 0.7\n\u03b21\n9.3 \u00b1 0.4\n\u221278.7 \u00b1 1.6\n\u03b22\n10.89 \u00b1 0.26\n\u2212159.1 \u00b1 2.6\n\u03b23\n24.2 \u00b1 2.0\n168 \u00b1 4\n\u03b24\n9.16 \u00b1 0.24\n90.5 \u00b1 2.6\nf prod\n11\n7.94 \u00b1 0.26\n73.9 \u00b1 1.1\nf\n\u2032prod\n12\n2.0 \u00b1 0.3\n\u221218 \u00b1 9\nf\n\u2032prod\n13\n5.1 \u00b1 0.3\n33 \u00b1 3\nf\n\u2032prod\n14\n3.23 \u00b1 0.18\n4.8 \u00b1 2.5\nsprod\n0\n\u22120.07 \u00b1 0.03\n\u03c0\u03c0 S-wave\n11.9 \u00b1 2.6\nM (GeV/c2)\n1.463 \u00b1 0.002\n\u0393 (GeV/c2)\n0.233 \u00b1 0.005\nF\n0.80 \u00b1 0.09\n\u03c6F\n2.33 \u00b1 0.13\nR\n1\n\u03c6R\n\u22125.31 \u00b1 0.04\na\n1.07 \u00b1 0.11\nr\n\u22121.8 \u00b1 0.3\n)\n4\n/c\n2\n (GeV\n2\n-\nm\n1\n2\n3\n0\n10000\n20000\n30000\n)\n4\n/c\n2\n (GeV\n2\n-\nm\n1\n2\n3\n0\n10000\n20000\n30000\na)\n)\n4\n/c\n2\n (GeV\n2+\nm\n1\n2\n3\n0\n2000\n4000\n6000\n)\n4\n/c\n2\n (GeV\n2+\nm\n1\n2\n3\n0\n2000\n4000\n6000 b)\n)\n4\n/c\n2\n (GeV\n2\n0\nm\n0\n0.5\n1\n1.5\n2\n0\n2000\n4000\n6000\n)\n4\n/c\n2\n (GeV\n2\n0\nm\n0\n0.5\n1\n1.5\n2\n0\n2000\n4000\n6000\nc)\nFigure 19.1.22. From (Aubert, 2008l). D0 \u2192K0\nS\u03c0+\u03c0\u2212Dalitz plot projections from D\u2217+ \u2192D0\u03c0+ events on (a) m2\n\u2212, (b) m2\n+,\nand (c) m2\n0. The curves are the reference model \ufb01t projections.\n\n536\n1\n2\n3\n1\n2\n3\nm-\n2 (GeV2/c4)\nm+\n2 (GeV\n2/c\n4)\n0\n2500\n5000\n7500\n10000\n1\n2\n3\nm+\n2 (GeV2/c4)\nEvents /0.02 GeV\n2/c\n4\n0\n20000\n40000\n1\n2\n3\nm-\n2 (GeV2/c4)\nEvents /0.02 GeV\n2/c\n4\n0\n5000\n10000\n0\n0.5\n1\n1.5\n2\nm\u03c0\u03c0\n2 (GeV2/c4)\nEvents /0.02 GeV\n2/c\n4\nFigure 19.1.23.\nFrom (Zhang, 2006). Dalitz plot distribution of D0 \u2192K0\nS\u03c0+\u03c0\u2212) and the projections for data (points with\nerror bars) and the \ufb01t result (curve). Here, m2\n\u00b1 corresponds to m2(K0\nS\u03c0\u00b1) for D0 decays and to m2(K0\nS\u03c0\u2213) for \u00afD0 decays.\nsmall discrepancies in low and high mass regions of the\nm2\n0 projection, and in the \u03c1(770)0 \u2212\u03c9(782) interference\nregion.\nAs a cross-check, they alternatively parameterize the\n\u03c0\u03c0 and K\u03c0 S-waves using the isobar approximation with\nthe following BW amplitudes (plus the non-resonant con-\ntribution): the CA K\u2217\n0(1430)\u2212, the DCS K\u2217\n0(1430)+, and\nthe CP eigenstates f0(980), f0(1370), \u03c3 and an ad hoc \u03c3\u2032.\nMasses and widths of the \u03c3 and \u03c3\u2032 scalars are obtained\nfrom the \ufb01t, M\u03c3 = 528\u00b15, \u0393\u03c3 = 512\u00b19, M\u03c3\u2032 = 1033\u00b14,\nand \u0393\u03c3\u2032 = 99 \u00b1 6, given in MeV/c2. Mass and width val-\nues for the K\u2217\n0(1430)\u2213, f0(980), and f0(1370) are taken\nfrom (Aitala et al., 2001b, 2002). They obtain a sum of \ufb01t\nfractions of 122.5%, and a reduced \u03c72 of 1.20 (with sta-\ntistical errors only) for 19274 degrees of freedom, which\nstrongly disfavors the isobar approach in comparison to\nthe K-matrix formalism.\nBelle study of the D0 \u2192K0\nS\u03c0+\u03c0\u2212decays, based on\n540 fb\u22121 of the data, has been performed for the D0 \u2212D0\nmixing measurement (Zhang, 2006). The reconstructed\nsignal yield of D0 mesons, tagged with D\u2217+ \u2192D0\u03c0+\ndecays, is of (534.4 \u00b1 0.8) \u00d7 103 events and the signal pu-\nrity amounts to about 95%. The Dalitz distribution for\nthe D0 \u2192K0\nS\u03c0+\u03c0\u2212candidiates is modeled assuming an\nisobar model in which the total D0 \u2192K0\nS\u03c0+\u03c0\u2212amplitude\nis a sum of 18 quasi-two-body amplitudes, described with\nrelativistic Breit-Wigner functions, and a constant non-\nresonant term. The amplitudes and their relative phases,\nobtained from an unbinned maximum likelihood \ufb01t per-\nformed to the Dalitz distribution, are summarized in Ta-\nTable 19.1.8. From (Zhang, 2006). Fit results for Dalitz plot\nparameters for D0 \u2192K0\nS\u03c0+\u03c0\u2212. The errors are statistical only.\nResonance\nAmplitude\nPhase (\u25e6)\nFraction\nK\u2217(892)\u2212\n1.629 \u00b1 0.006\n134.3 \u00b1 0.3\n0.6227\nK\u2217\n0(1430)\u2212\n2.12 \u00b1 0.02\n\u22120.9 \u00b1 0.8\n0.0724\nK\u2217\n2(1430)\u2212\n0.87 \u00b1 0.02\n\u221247.3 \u00b1 1.2\n0.0133\nK\u2217(1410)\u2212\n0.65 \u00b1 0.03\n111 \u00b1 4\n0.0048\nK\u2217(1680)\u2212\n0.60 \u00b1 0.25\n147 \u00b1 29\n0.0002\nK\u2217(892)+\n0.152 \u00b1 0.003\n\u221237.5 \u00b1 1.3\n0.0054\nK\u2217\n0(1430)+\n0.541 \u00b1 0.019\n91.8 \u00b1 2.1\n0.0047\nK\u2217\n2(1430)+\n0.276 \u00b1 0.013\n\u2212106 \u00b1 3\n0.0013\nK\u2217(1410)+\n0.33 \u00b1 0.02\n\u2212102 \u00b1 4\n0.0013\nK\u2217(1680)+\n0.73 \u00b1 0.16\n103 \u00b1 11\n0.0004\n\u03c1(770)\n1 (\ufb01xed)\n0 (\ufb01xed)\n0.2111\n\u03c9(782)\n0.0380 \u00b1 0.0007\n115.1 \u00b1 1.1\n0.0063\nf0(980)\n0.380 \u00b1 0.004\n\u2212147.1 \u00b1 1.1\n0.0452\nf0(1370)\n1.46 \u00b1 0.05\n98.6 \u00b1 1.8\n0.0162\nf2(1270)\n1.43 \u00b1 0.02\n\u221213.6 \u00b1 1.2\n0.0180\n\u03c1(1450)\n0.72 \u00b1 0.04\n41 \u00b1 7\n0.0024\n\u03c31\n1.39 \u00b1 0.02\n\u2212146.6 \u00b1 0.9\n0.0914\n\u03c32\n0.267 \u00b1 0.013\n\u2212157 \u00b1 3\n0.0088\nNR\n2.36 \u00b1 0.07\n155 \u00b1 2\n0.0615\nble 19.1.8. The main features of the Dalitz plot are well\nreproduced as can be seen from the Dalitz plot and its\n\n537\n0\n20\n40\n60\n80\n100\n120\n140\n160\n]\n4\n/c\n2\n [GeV\n+\n\u03c0\n-\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n-\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n(a)\n0\n5\n10\n15\n20\n25\n30\n]\n4\n/c\n2\n [GeV\n-\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n(b)\n]\n4\n/c\n2\n [GeV\n-\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n4\n/c\n2\nEvents/0.05 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n]\n4\n/c\n2\n [GeV\n-\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n4\n/c\n2\nEvents/0.05 GeV\n0\n20\n40\n60\n80\n100\n120\n140\n160\n(c)\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n4\n/c\n2\nEvents/0.05 GeV\n0\n50\n100\n150\n200\n250\n300\n350\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n4\n/c\n2\nEvents/0.05 GeV\n0\n50\n100\n150\n200\n250\n300\n350\n(d)\nFigure 19.1.24. From (Aubert, 2009u). Dalitz plots for the\n(a) RS D0 \u2192K\u2212\u03c0+\u03c00 and (b) WS D0 \u2192K+\u03c0\u2212\u03c00 samples.\n(c, d) m2\nK+\u03c0\u2212and m2\nK+\u03c00 projections with superimposed \ufb01t\nresults (line). The light histogram represents the mistag back-\nground, while the dark histogram shows the combinatoric back-\nground;\nprojections shown, along with projections of the \ufb01t result,\nin Fig. 19.1.23. The goodness-of-\ufb01t of the Dalitz plot is\nestimated to be \u03c72/ndf = 2.1 for 3653 \u221240 degrees of\nfreedom (ndf). The K-matrix formalism was used in ad-\ndition to the above mentioned isobar model in estimation\nof systematic uncertanties for the D0 \u2212D0 mixing mea-\nsurement.\n19.1.4.5 Dalitz Plot Analysis of three-body (wrong-sign)\nD0 \u2192K+\u03c0\u2212\u03c00 decays.\nThis analysis from BABAR (Aubert, 2009u) has been per-\nformed on a data sample of 384 fb\u22121. The Dalitz analysis\nis performed on the wrong-sign (WS) dataset only consist-\ning of D\u2217+ \u2192D0(\u2192K+\u03c0\u2212\u03c00)\u03c0+ events. The right sign\n(RS) sample (D\u2217+ \u2192D0(\u2192K\u2212\u03c0+\u03c00)\u03c0+) is composed\nof 658, 986 events with a purity of 99%, the WS by 3009\nevents with a purity of 50%. The e\ufb03ciency of the signal\nregion selection is 54.6%. In the Dalitz plot analysis, the\n\ufb01t fraction of the non-resonant contribution to the K-\u03c0\nS-wave is absorbed into the K\u2217+\n0 (1430) and K\u22170\n0 (1430)\n\ufb01t fractions. Projections of the \ufb01t results are shown in\nFig. 19.1.24(b-d), amplitudes, phases, and fractions are\ngiven in Table 19.1.9.\n19.1.4.6 Dalitz Plot Analysis of D0 \u2192K\u2212K+\u03c00 decay.\nUsing 385 fb\u22121 of e+e\u2212collisions, BABAR has performed\na Dalitz analysis of the singly Cabibbo-suppressed decay\nD0 \u2192K\u2212K+\u03c00 (Aubert, 2007d). Fig. 19.1.25 shows the\nTable 19.1.9. From (Aubert, 2009u). Fit results for the WS\nD0 \u2192K+\u03c0\u2212\u03c00 data sample. The total \ufb01t fraction is 102% and\nthe \u03c72/ndof is 188/215.\nResonance\naDCS\nj\n\u03b4DCS\nj\n(degrees)\nfj (%)\n\u03c1(770)\n1 (\ufb01xed)\n0 (\ufb01xed)\n39.8 \u00b1 6.5\nK\u22170\n2 (1430)\n0.088 \u00b1 0.017\n\u221217.2 \u00b1 12.9\n2.0 \u00b1 0.7\nK\u2217+\n0 (1430)\n6.78 \u00b1 1.00\n69.1 \u00b1 10.9\n13.1 \u00b1 3.3\nK\u2217+(892)\n0.899 \u00b1 0.005\n\u2212171.0 \u00b1 5.9\n35.6 \u00b1 5.5\nK\u22170\n0 (1430)\n1.65 \u00b1 0.59\n\u221244.4 \u00b1 18.5\n2.8 \u00b1 1.5\nK\u22170(892)\n0.398 \u00b1 0.038\n24.1 \u00b1 9.8\n6.5 \u00b1 1.4\n\u03c1(1700)\n5.4 \u00b1 1.6\n157.4 \u00b1 20.3\n2.0 \u00b1 1.1\nD0 \u2192K\u2212K+\u03c00 Dalitz plot and mass projections, to-\ngether with results from the Dalitz plot analysis. The\nLASS K\u03c0 S-wave amplitude gives the best agreement\nwith data and they use it in the nominal \ufb01ts. The K\u03c0\nS-wave modeled by the combination of \u03ba(800) (with pa-\nrameters taken from Aitala et al., 2002), a nonresonant\nterm and K\u2217\n0(1430) has a smaller \ufb01t probability (\u03c72 prob-\nability < 5%). The best \ufb01t with this model (\u03c72 probabil-\nity 13%) yields a charged \u03ba of mass (870 \u00b1 30) MeV/c2,\nand width (150 \u00b1 20) MeV/c2, signi\ufb01cantly di\ufb00erent from\nthose reported in Aitala et al. (2002) for the neutral state.\nThis does not support the hypothesis that production of\na charged, scalar \u03ba is being observed. The E-791 ampli-\ntude Aitala et al. (2006) describes the data well, except\nnear threshold (\u03c72 probability 23%).\n] \n4\n/c\n2\n) [GeV\n0\n\u03c0\n-\n(K\n2\nm\n1\n2\n]\n4\n/c\n2\n) [GeV\n0\n\u03c0\n+\n(K\n2\nm\n1\n2\n(a)\n]\n4\n/c\n2\n) [GeV\n0\n\u03c0\n+\n(K\n2\nm\n0\n1\n2\n4\n/c\n2\nEvents / 0.05 GeV\n0\n1000\n2000\n]\n4\n/c\n2\n) [GeV\n0\n\u03c0\n+\n(K\n2\nm\n0\n1\n2\n4\n/c\n2\nEvents / 0.05 GeV\n0\n1000\n2000\n(b)\n]\n4\n/c\n2\n) [GeV\n0\n\u03c0\n-\n(K\n2\nm\n0\n1\n2\n4\n/c\n2\nEvents / 0.05 GeV\n0\n200\n400\n600\n800\n]\n4\n/c\n2\n) [GeV\n0\n\u03c0\n-\n(K\n2\nm\n0\n1\n2\n4\n/c\n2\nEvents / 0.05 GeV\n0\n200\n400\n600\n800\n(c)\n]\n4\n/c\n2\n) [GeV\n+\nK\n-\n(K\n2\nm\n1\n2\n3\n4\n/c\n2\nEvents / 0.05 GeV\n10\n2\n10\n3\n10\n4\n10\n]\n4\n/c\n2\n) [GeV\n+\nK\n-\n(K\n2\nm\n1\n2\n3\n4\n/c\n2\nEvents / 0.05 GeV\n10\n2\n10\n3\n10\n4\n10\n(d)\nFigure 19.1.25. From (Aubert, 2007d). Dalitz plot for D0 \u2192\nK\u2212K+\u03c00 data (a), and the corresponding squared invariant\nmass projections (b\u2013d). The three-body invariant mass of the\nD0 candidate is constrained to the nominal value. In plots (b\u2013\nd), the dots (with error bars, black) are data points and the\nsolid lines (blue) correspond to the best isobar \ufb01t models.\n\n538\nTable 19.1.10. From (Aubert, 2007d). The results obtained from the D0 \u2192K\u2212K+\u03c00 Dalitz plot \ufb01t. The amplitude coe\ufb03cients,\nar and \u03c6r, are computed relatively to those of the K\u2217(892)+. The a0(980) contribution, when it is included in place of the\nf0(980), is given in square brackets. The K\u03c0 S-wave states are incicated as K\u00b1\u03c00(S). The LASS amplitude is used to describe\nthe K\u03c0 S-wave states in both the isobar models (I and II).\nModel I\nModel II\nState\nAmplitude, ar\nPhase, \u03c6r (\u25e6)\nFraction, fr (%)\nAmplitude, ar\nPhase, \u03c6r (\u25e6)\nFraction, fr (%)\nK\u2217(892)+\n1.0 (\ufb01xed)\n0.0 (\ufb01xed)\n45.2\u00b10.8\u00b10.6\n1.0 (\ufb01xed)\n0.0 (\ufb01xed)\n44.4\u00b10.8\u00b10.6\nK\u2217(1410)+\n2.29\u00b10.37\u00b10.20\n86.7\u00b112.0\u00b19.6\n3.7\u00b11.1\u00b11.1\nK+\u03c00(S)\n1.76\u00b10.36\u00b10.18\n-179.8\u00b121.3\u00b112.3\n16.3\u00b13.4\u00b12.1\n3.66\u00b10.11\u00b10.09\n-148.0\u00b12.0\u00b12.8\n71.1\u00b13.7\u00b11.9\n\u03c6(1020)\n0.69\u00b10.01\u00b10.02\n-20.7\u00b113.6\u00b19.3\n19.3\u00b10.6\u00b10.4\n0.70\u00b10.01\u00b10.02\n18.0\u00b13.7\u00b13.6\n19.4\u00b10.6\u00b10.5\nf0(980)\n0.51\u00b10.07\u00b10.04\n-177.5\u00b113.7\u00b18.6\n6.7\u00b11.4\u00b11.2\n0.64\u00b10.04\u00b10.03\n-60.8\u00b12.5\u00b13.0\n10.5\u00b11.1\u00b11.2\n\u0002\na0(980)0\u0003\n[0.48\u00b10.08\u00b10.04]\n[-154.0\u00b114.1\u00b18.6]\n[6.0\u00b11.8\u00b11.2]\n[0.68\u00b10.06\u00b10.03]\n[-38.5\u00b14.3\u00b13.0]\n[11.0\u00b11.5\u00b11.2]\nf \u2032\n2(1525)\n1.11\u00b10.38\u00b10.28\n-18.7\u00b119.3\u00b113.6\n0.08\u00b10.04\u00b10.05\nK\u2217(892)\u2212\n0.601\u00b10.011\u00b10.011\n-37.0\u00b11.9\u00b12.2\n16.0\u00b10.8\u00b10.6\n0.597\u00b10.013\u00b10.009\n-34.1\u00b11.9\u00b12.2\n15.9\u00b10.7\u00b10.6\nK\u2217(1410)\u2212\n2.63\u00b10.51\u00b10.47\n-172.0\u00b16.6\u00b16.2\n4.8\u00b11.8\u00b11.2\nK\u2212\u03c00(S)\n0.70\u00b10.27\u00b10.24\n133.2\u00b122.5\u00b125.2\n2.7\u00b11.4\u00b10.8\n0.85\u00b10.09\u00b10.11\n108.4\u00b17.8\u00b18.9\n3.9\u00b10.9\u00b11.0\nTwo di\ufb00erent isobar models describe the data well.\nBoth yield almost identical behavior in invariant mass\n(Fig. 19.1.25b\u201319.1.25d). The results of the best \ufb01ts (Model\nI: \u03c72/\u03bd = 702.08/714, probability 61.9%; Model II: \u03c72/\u03bd =\n718.89/717, probability 47.3%) are summarized in Table\n19.1.10. They \ufb01nd that the K\u03c0 S-wave is not in phase with\nthe P-wave at threshold as it was in the LASS scattering\ndata. Both \ufb01tting models include signi\ufb01cant contributions\nfrom K\u2217(892), and each indicates that D0 \u2192K\u2217+K\u2212\ndominates over D0 \u2192K\u2217\u2212K+. This suggests that, in tree-\nlevel diagrams, the form factor for D0 coupling to K\u2217\u2212is\nsuppressed compared to the corresponding K\u2212coupling.\nWhile the measured \ufb01t fraction for D0 \u2192K\u2217+K\u2212agrees\nwell with a phenomenological prediction (Buccella, Lusig-\nnoli, Miele, Pugliese, and Santorelli, 1995) based on a large\nSU(3) symmetry breaking, the corresponding results for\nD0 \u2192K\u2217\u2212K+ and the color-suppressed D0 \u2192\u03c6\u03c00 de-\ncays di\ufb00er signi\ufb01cantly from the predicted values.\nIn a limited mass range, from threshold up to\n1.02 GeV/c2, they also measure the scalar amplitude us-\ning a model-independent partial-wave analysis. Agreement\nwith similar measurements from D0 \u2192K\u2212K+ \u00af\nK0 de-\ncay (Aubert, 2005f), and with the isobar models consid-\nered here, is excellent.\n19.1.4.7 D0 \u2192\u03c0+\u03c0\u2212\u03c00\nThis analysis from BABAR makes use of NS = 44780\u00b1250\nsignal and NB = 830 \u00b1 70 background events (Aubert,\n2007w). Table 19.1.11 summarizes the results of the Dalitz\nplot analysis. The Dalitz plot distribution of the data is\nshown in Fig. 19.1.26(a-c). The distribution is marked by\nthree destructively interfering \u03c1\u03c0 amplitudes, suggesting\nan I = 0-dominated \ufb01nal state (Zemach, 1964).\n19.1.4.8 D+\ns \u2192\u03c0+\u03c0\u2212\u03c0+\nBABAR has performed a Dalitz plot analysis of D+\ns\n\u2192\n\u03c0+\u03c0\u2212\u03c0+ (Aubert, 2009i) and D+\ns\n\u2192K+K\u2212\u03c0+ (del\nAmo Sanchez, 2011b) using 380 fb\u22121. The selection of\nthe two channels is similar and it will be described only\nonce.\nThe three tracks are \ufb01tted to a common vertex, and\nthe \u03c72 \ufb01t probability (labeled P1) must be greater than\n0.1 %. A separate kinematic \ufb01t which makes use of the\nD+\ns mass constraint, to be used in the Dalitz plot anal-\nysis, is also performed. To help discriminate signal from\nbackground, an additional \ufb01t which uses the constraint\nthat the three tracks originate from the e+e\u2212luminous\nregion (beam spot) is performed. The \u03c72 probability of\nthis \ufb01t is labeled as P2, and it is expected to be large\nfor background and small for D+\ns signal events, since in\ngeneral the latter will have a measurable \ufb02ight distance.\nThe combinatorial background is reduced by requiring\nthe D+\ns to originate from the decay\nD\u2217+\ns\n\u2192D+\ns \u03b3\n(19.1.44)\nusing the mass di\ufb00erence \u2206m = m(\u03c0+\u03c0\u2212\u03c0+\u03b3) \u2212\nm(\u03c0+\u03c0\u2212\u03c0+). Each D+\ns candidate is characterized by three\nvariables: the center-of-mass momentum p\u2217, the di\ufb00erence\nin probability P1 \u2212P2, and the signed decay distance dxy\nbetween the D+\ns\ndecay vertex and the beam spot pro-\njected in the plane normal to the beam collision axis.\nThe distributions for these variables for background are\ninferred from the D+\ns\n\u2192\u03c0+\u03c0\u2212\u03c0+ invariant mass side-\nbands. Since these variables are (to a good approxima-\ntion) independent of the decay mode, the distributions\nfor the three-pion invariant mass signal, are inferred from\nthe D+\ns \u2192K+K\u2212\u03c0+ decay. These normalized distribu-\ntions are then combined in a likelihood ratio test. The cut\non the likelihood ratio has been chosen in order to ob-\ntain the largest statistics with background small enough\nto perform a Dalitz plot analysis.\nThe distributions of these variables for the D+\ns\n\u2192\nK+K\u2212\u03c0+ decay for signal and background are shown in\nFig. 19.1.27.\nThe resulting D+\ns signal region contains 13179 events\nwith a purity of 80%. The resulting Dalitz plot, sym-\nmetrized along the two axes, is shown in Fig. 19.1.28. We\nobserve a clear f0(980) signal, evidenced by the two nar-\nrow crossing bands. We also observe a broad accumulation\nof events in the 1.9 GeV2/c4 region. The e\ufb03ciency is found\nto be almost uniform as a function of the \u03c0+\u03c0\u2212invariant\nmass with an average value of \u22481.6 %.\nIn the Dalitz plot analysis spin-1 and spin-2 resonances\nare described by relativistic Breit-Wigner function. For\n\n539\n) \n4\n/c\n2\n (GeV\n+s\n0\n1\n2\n3\n4\n/c\n2\nEvents / 0.1 GeV\n0\n2000\n4000\n6000\n8000\n) \n4\n/c\n2\n (GeV\n+s\n0\n1\n2\n3\n4\n/c\n2\nEvents / 0.1 GeV\n0\n2000\n4000\n6000\n8000\n (a)\n) \n4\n/c\n2\n (GeV\n-s\n0\n1\n2\n3\n4\n/c\n2\nEvents / 0.1 GeV\n0\n1000\n2000\n3000\n4000\n) \n4\n/c\n2\n (GeV\n--s\n0\n1\n2\n3\n4\n/c\n2\nEvents / 0.1 GeV\n0\n1000\n2000\n3000\n4000\n (b)\n) \n4\n/c\n2\n (GeV\n--s\n0\n1\n2\n3\n) \n4\n/c\n2\n (GeV\n+s\n0\n1\n2\n3\n (c)\nFigure 19.1.26. From (Aubert, 2007w). (a,b) Projections of the D\u2217+ \u2192D0(\u2192\u03c0+\u03c0\u2212\u03c00)\u03c0+ data events and p.d.f. onto the\nDalitz plot variables s+= m2(\u03c0+\u03c00) and s\u2212= m2(\u03c0\u2212\u03c00). (c) The 2-dimensional (s+, s\u2212) distribution of the D\u2217+ \u2192D0\u03c0+ data.\nTable 19.1.11. From (Aubert, 2007w). Result of the \ufb01t to the D0 \u2192\u03c0+\u03c0\u2212\u03c00 sample, showing the amplitudes ratios Rr \u2261\nar/a\u03c1+(770), phase di\ufb00erences \u2206\u03c6r \u2261\u03c6r \u2212\u03c6\u03c1+(770), and \ufb01t fractions fr \u2261\nR\n|arAr(s+, s\u2212)|2ds\u2212ds+ (see 13.4.4). The \ufb01rst\n(second) errors are statistical (systematic). The mass (width) of the \u03c3 meson is taken as 400 (600) MeV/c2.\nState\nRr (%)\n\u2206\u03c6r (\u25e6)\nfr(%)\n\u03c1+(770)\n100\n0\n67.8\u00b10.0\u00b10.6\n\u03c10(770)\n58.8\u00b10.6\u00b10.2\n16.2\u00b10.6\u00b10.4\n26.2\u00b10.5\u00b11.1\n\u03c1\u2212(770)\n71.4\u00b10.8\u00b10.3\n\u22122.0\u00b10.6\u00b10.6\n34.6\u00b10.8\u00b10.3\n\u03c1+(1450)\n21\u00b16\u00b113\n\u2212146\u00b118\u00b124\n0.11\u00b10.07\u00b10.12\n\u03c10(1450)\n33\u00b16\u00b14\n10\u00b18\u00b113\n0.30\u00b10.11\u00b10.07\n\u03c1\u2212(1450)\n82\u00b15\u00b14\n16\u00b13\u00b13\n1.79\u00b10.22\u00b10.12\n\u03c1+(1700)\n225\u00b118\u00b114\n\u221217\u00b12\u00b13\n4.1\u00b10.7\u00b10.7\n\u03c10(1700)\n251\u00b115\u00b113\n\u221217\u00b12\u00b12\n5.0\u00b10.6\u00b11.0\n\u03c1\u2212(1700)\n200\u00b111\u00b17\n\u221250\u00b13\u00b13\n3.2\u00b10.4\u00b10.6\nf0(980)\n1.50\u00b10.12\u00b10.17\n\u221259\u00b15\u00b14\n0.25\u00b10.04\u00b10.04\nf0(1370)\n6.3\u00b10.9\u00b10.9\n156\u00b19\u00b16\n0.37\u00b10.11\u00b10.09\nf0(1500)\n5.8\u00b10.6\u00b10.6\n12\u00b19\u00b14\n0.39\u00b10.08\u00b10.07\nf0(1710)\n11.2\u00b11.4\u00b11.7\n51\u00b18\u00b17\n0.31\u00b10.07\u00b10.08\nf2(1270)\n104\u00b13\u00b121\n\u2212171\u00b13\u00b14\n1.32\u00b10.08\u00b10.10\n\u03c3(400)\n6.9\u00b10.6\u00b11.2\n8\u00b14\u00b18\n0.82\u00b10.10\u00b10.10\nNon-Res\n57\u00b17\u00b18\n\u221211\u00b14\u00b12\n0.84\u00b10.21\u00b10.12\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n3\n4\n5\np* (GeV/c)\nProbability\n(a)\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n-0.1\n0\n0.1\n0.2\n0.3\ndxy (cm)\n(b)\n0\n0.02\n0.04\n0.06\n0.08\n0\n0.5\n1\nP1 - P2\n(c)\nFigure 19.1.27. From (del Amo Sanchez, 2011b). Normalized probability distribution functions for signal (solid) and back-\nground events (hatched) used in a likelihood-ratio test for the event selection of D+\ns\n\u2192K+K\u2212\u03c0+: (a) the center-of-mass\nmomentum p\u2217, (b) the signed decay distance dxy and (c) the di\ufb00erence in probability P1 \u2212P2.\n\n540\n0\n1\n2\n3\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nm2(!+ !-) (GeV2/c4)\nm2(!+!-) (GeV2/c4)\n(b)\nFigure 19.1.28. From (Aubert, 2009i). Symmetrized D+\ns \u2192\n\u03c0+\u03c0\u2212\u03c0+ Dalitz plot (two entries per event).\nthe \u03c0+\u03c0\u2212S-wave amplitude, a di\ufb00erent approach is used\nbecause:\n\u2013 Scalar resonances have large uncertainties. In addition,\nthe existence of some states needs con\ufb01rmation.\n\u2013 Modelling the S-wave as a superposition of Breit-\nWigner functions is unphysical since it leads to a vio-\nlation of unitarity when broad resonances overlap.\nTo overcome these problems, the Model-Independent\nPartial Wave Analysis introduced by the Fermilab E791\nCollaboration (Aitala et al., 2006) has been used. Instead\nof including the S-wave amplitude as a superposition of\nrelativistic Breit-Wigner functions, the \u03c0+\u03c0\u2212mass spec-\ntrum is divided into 29 slices and the S-wave is param-\neterized by an interpolation between the 30 endpoints in\nthe complex plane:\nAS\u2212wave(m\u03c0\u03c0) = Interp(ck(m\u03c0\u03c0)ei\u03c6k(m\u03c0\u03c0))k=1,..,30.\n(19.1.45)\nThe amplitude and phase of each endpoint are free param-\neters. The width of each slice is tuned to get approximately\nthe same number of \u03c0+\u03c0\u2212combinations (\u224313179\u00d72/29).\nInterpolation is implemented by a Relaxed Cubic Spline.\nThe phase is not constrained in a speci\ufb01c range in order\nto allow the spline to be a continuous function.\nThe background shape is obtained by \ufb01tting the D+\ns\nsidebands. In this \ufb01t, resonances are assumed to be in-\ncoherent, i.e. are represented by Breit-Wigner intensity\nterms only. A good representation of the background in-\ncludes contributions from K0\nS, \u03c10(770) and three ad-hoc\nscalar resonances with free parameters.\nThe resulting S-wave \u03c0+\u03c0\u2212amplitude and phase is\nshown in Fig. 19.1.29(a),(b). The results from the Dalitz\nanalysis are summarized in Table 19.1.12.\nThe Dalitz-plot projections together with the \ufb01t re-\nsults are shown in Fig. 19.1.30. The labels m2(\u03c0+\u03c0\u2212)low\nand m2(\u03c0+\u03c0\u2212)high refer to the lower and higher values of\nthe two \u03c0+\u03c0\u2212mass combinations.\n0\n10\n20\n30\n0\n0.5\n1\n1.5\n2\n(a)\nm(\u03c0+ \u03c0-) (GeV/c2)\nAmplitude\n-5\n-3\n-1\n1\n3\n5\n7\n0\n0.5\n1\n1.5\n2\n(b)\nm(\u03c0+ \u03c0-) (GeV/c2)\nPhase (rad)\nFigure 19.1.29. (a) S-wave amplitude extracted from the\nD+\ns \u2192\u03c0+\u03c0\u2212\u03c0+ Dalitz plot analysis. (b) corresponding S-wave\nphase.\nTable 19.1.12. From (Aubert, 2009i). Results from the D+\ns \u2192\n\u03c0+\u03c0\u2212\u03c0+ Dalitz plot analysis. The table reports the \ufb01t frac-\ntions, amplitudes and phases. Errors are statistical and sys-\ntematic respectively.\nDecay mode\nFraction(%)\nAmplitude\nPhase(rad)\nf2(1270)\u03c0+\n10.1\u00b11.5\u00b11.1\n1.(Fixed)\n0.(Fixed)\n\u03c1(770)\u03c0+\n1.8\u00b10.5\u00b11.0 0.19\u00b10.02\u00b10.12\n1.1\u00b10.1\u00b10.2\n\u03c1(1450)\u03c0+\n2.3\u00b10.8\u00b11.7\n1.2\u00b10.3\u00b11.0\n4.1\u00b10.2\u00b10.5\nS-wave\n83.0\u00b10.9\u00b11.9\nTotal\n97.2\u00b13.7\u00b13.8\n\u03c72/NDF\n437\n422\u221264 = 1.2\n0\n200\n400\n600\n800\n1000\n1200\n0\n0.5\n1\n1.5\n2\n(a)\nm2(\u03c0+\u03c0-)low (GeV2/c4)\nevents/0.05 GeV2/c4\n0\n200\n400\n600\n800\n1000\n1200\n0\n1\n2\n3\n(b)\nm2(\u03c0+\u03c0-)high (GeV2/c4)\nevents/0.0875 GeV2/c4\n0\n500\n1000\n1500\n2000\n2500\n0\n1\n2\n3\n(c)\nm2(\u03c0+ \u03c0-) (GeV2/c4)\nevents/0.0875 GeV2/c4\n0\n200\n400\n600\n800\n1000\n1200\n0\n1\n2\n3\n(d)\nm2(\u03c0+\u03c0+) (GeV2/c4)\nevents/0.0875 GeV2/c4\nFigure 19.1.30. From (Aubert, 2009i). Dalitz plot projec-\ntions (points with error bars) and \ufb01t results (solid histogram)\nfrom D+\ns \u2192\u03c0+\u03c0\u2212\u03c0+ Dalitz plot analysis. (a) m2(\u03c0+\u03c0\u2212)low,\n(b) m2(\u03c0+\u03c0\u2212)high, (c) total m2(\u03c0+\u03c0\u2212), (d) m2(\u03c0+\u03c0+). The\nhatched histograms show the background distribution.\nThe \ufb01t \u03c72 is computed by dividing the Dalitz plot into\n30\u00d730 cells with 422 cells having entries.\n\n541\n19.1.4.9 Dalitz plot analysis of D+\ns \u2192K+K\u2212\u03c0+\nThe Dalitz analysis of D+\ns \u2192K+K\u2212\u03c0+ is described in (del\nAmo Sanchez, 2011b). The selection of the channel is sim-\nilar to that of the D+\ns\n\u2192\u03c0+\u03c0\u2212\u03c0+ channel (see Sec-\ntion 19.1.4.8). The resulting K+K\u2212\u03c0+ mass distribution\ncontains 96307 \u00b1 369 events with 95% purity. The D+\ns \u2192\nK+K\u2212\u03c0+ Dalitz plot is shown in Fig. 19.1.31.\n0.5\n1\n1.5\n2\n1\n1.5\n2\n2.5\n3\n3.5\nm2(K+K-) GeV2/c4\nm2(K-\u03c0+) GeV2/c4\n(b)\nFigure 19.1.31. From (del Amo Sanchez, 2011b). D+\ns\n\u2192\nK+K\u2212\u03c0+ Dalitz plot.\nPartial Wave Analysis of the K+K\u2212threshold region for\nD+\ns \u2192K+K\u2212\u03c0+.\nIn the K+K\u2212threshold region both a0(980) and f0(980)\ncan be present, and both resonances have very similar pa-\nrameters which su\ufb00er from large uncertainties. In this sec-\ntion a model-independent information on the K+K\u2212S-\nwave is obtained by a performing a partial wave analysis\nin the K+K\u2212threshold region. The procedure is similar\nto that reported in the analysis of the D0 \u2192K0K+K\u2212\ndecay (Section 19.1.4.2).\nFigure 19.1.32 shows the K+K\u2212mass spectrum up to\n1.5 GeV/c2 weighted by the spherical harmonics moments.\nThese distributions are corrected for e\ufb03ciency and phase\nspace, and background is subtracted using the D+\ns side-\nbands.\nThe results from the Partial Wave Analysis are shown\nin Fig. 19.1.33. We observe a threshold enhancement in\nthe S-wave (Fig. 19.1.33(a)), and the expected \u03c6(1020)\nBreit-Wigner (BW) in the P-wave (Fig. 19.1.33(b)). We\nalso observe the expected S-P relative phase motion in\nthe \u03c6(1020) region (Fig. 19.1.33(c)). In Fig. 19.1.33(c),\nthe S-P phase di\ufb00erence is plotted twice because of the\nsign ambiguity associated with the value of \u03c6SP extracted\n0\n20000\n40000\n60000\n80000\n100000\n120000\n0.95\n1\n1.05\n1.1\n1.15\nm(K+K-) (GeV/c2)\nEvents/4 MeV\n(a) \u2329Y0\n0\u232a\n0\n5000\n10000\n15000\n20000\n25000\n0.95\n1\n1.05\n1.1\n1.15\nm(K+K-) (GeV/c2)\n(b) \u2329Y0\n1\u232a\n0\n20000\n40000\n60000\n80000\n0.95\n1\n1.05\n1.1\n1.15\n(c) \u2329Y0\n2\u232a\nm(K+K-) (GeV/c2)\nFigure 19.1.32. From (del Amo Sanchez, 2011b). K+K\u2212\nmass spectrum from D+\ns \u2192K+K\u2212\u03c0+ in the threshold region\nweighted by (a) Y 0\n0 , (b) Y 0\n1 , and (c) Y 0\n2 , corrected for e\ufb03ciency\nand phase space, and background-subtracted.\n0\n10000\n20000\nEvents/4 MeV/c2\n(a) |S|2\n0\n20000\n40000\n60000\n(b) |P|2\nEvents/0.5 MeV/c2\n-100\n0\n100\nPhase difference (degree)\n(c) \u03c6SP\n50\n100\n150\n0.95\n1\n1.05\n1.1\n1.15\nm(K+K-) (GeV/c2)\nS-wave phase (degree)\n(d) \u03c6S\nFigure 19.1.33. From (del Amo Sanchez, 2011b). Squared (a)\nS- and (b) P-wave amplitudes; (c) the phase di\ufb00erence \u03c6SP ;\n(d) \u03c6S obtained as explained in the text. The curves result\nfrom the \ufb01t described in the text.\n\n542\n0\n200\n400\n600\n800\n0.95\n1\n1.05\n1.1\n1.15\nIntensity(arbitrary units)\nG K+K-(Ds\n+\u2192K+K-\u03c0+)\nK K\n\u2013 0K+(D0\u2192K\n\u2013 0K+K-)\nL K+K-(D0\u2192K\n\u2013 0K+K-)\n# K+K-(D0\u2192K+K-\u03c00)\nm(KK\n\u2013 ) (GeV/c2)\n(a)\n0\n250\n500\n750\n1000\n0.95\n1\n1.05\n1.1\n1.15\nG K+K-(Ds\n+\u2192K+K-\u03c0+)\nH \u03c0+\u03c0-(D+\ns\u2192\u03c0+\u03c0-\u03c0+)\nm(GeV/c2)\n(b)\nFigure 19.1.34. From (del Amo Sanchez, 2011b). (a) Com-\nparison between KK S-wave intensities from di\ufb00erent charmed\nmeson Dalitz plot analyses. (b) Comparison of the KK S-wave\nintensity from D+\ns \u2192K+K\u2212\u03c0+ with the \u03c0+\u03c0\u2212S-wave inten-\nsity from D+\ns \u2192\u03c0+\u03c0\u2212\u03c0+.\nfrom cos(\u03c6SP). The lines represent the result from the \ufb01t\nperformed using S-P interfering amplitudes.\nThe mass-dependent f0(980) phase is extracted by\nadding the mass-dependent \u03c6(1020) Breit-Wigner phase\nto the \u03c6SP distributions of Fig. 19.1.33(c). The phase am-\nbiguity of Fig. 19.1.33(c) is resolved by choosing as the\nphysical solution the one which decreases rapidly in the\n\u03c6(1020) peak region, since this re\ufb02ects the rapid forward\nBreit-Wigner-phase motion associated with a narrow res-\nonance. The result is shown in Fig. 19.1.33(d), where we\nsee that the S-wave phase is roughly constant, as would\nbe expected for the tail of a resonance.\nIn Fig. 19.1.34(a) the S-wave pro\ufb01le from this analysis\nis compared with the S-wave intensity values extracted\nfor Dalitz plot analyses of D0 \u2192K0K+K\u2212(Aubert,\n2005f) and D0 \u2192K+K\u2212\u03c00 (Aubert, 2007d). The four\ndistributions are normalized in the region from thresh-\nold up to 1.05 GeV/c2 and show a substantial agreement.\nAs the a0(980) and f0(980) mesons couple mainly to the\nu\u00afu/d \u00afd and s\u00afs systems respectively, the former is favored in\nD0 \u2192K0K+K\u2212and the latter in D+\ns \u2192K+K\u2212\u03c0+. Both\nresonances can contribute in D0 \u2192K+K\u2212\u03c00. We con-\nclude that the S-wave projections in the KK system for\nboth resonances are consistent in shape. It has been sug-\ngested that this feature supports the hypothesis that the\na0(980) and f0(980) are 4-quark states (Maiani, Polosa,\nand Riquer, 2007). Figure 19.1.34(b)) also compares the S-\nwave pro\ufb01le from this analysis with the \u03c0+\u03c0\u2212S-wave pro-\n\ufb01le extracted from BABAR data in a Dalitz plot analysis of\nD+\ns \u2192\u03c0+\u03c0\u2212\u03c0+ Aubert (2009i). The observed agreement\nsupports the argument that only the f0(980) is present in\nthis limited mass region.\nDalitz plot analysis of D+\ns \u2192K+K\u2212\u03c0+\nIn the full Dalitz plot analysis, the K\u2217(892)0 amplitude\nis chosen as reference. The decay fractions, amplitudes,\nand relative phase values are summarized in Table 19.1.13\nwhere the \ufb01rst error is statistical, and the second is sys-\ntematic. We observe that the decay is dominated by the\n0\n5000\n10000\n15000\n20000\n25000\n1\n1.5\n2\n2.5\n3\n3.5\nm2(K+K-) (GeV2/c4)\nevents/0.027 GeV2/c4\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n1\n1.05\n1.1\nm2(K+K-) (GeV2/c4)\nevents/0.0024 GeV2/c4\n0\n2000\n4000\n6000\n8000\n0.5\n1\n1.5\n2\nm2(K-\u03c0+) (GeV2/c4)\nevents/0.02 GeV2/c4\n0\n1000\n2000\n3000\n4000\n0.5\n1\n1.5\n2\nm2(K+\u03c0+) (GeV2/c4)\nevents/0.02 GeV2/c4\nPull\n0\n3\n-3\nPull\n0\n3\n-3\nPull\n0\n3\n-3\nPull\n0\n3\n-3\nFigure 19.1.35. From (del Amo Sanchez, 2011b). D+\ns\n\u2192\nK+K\u2212\u03c0+: Dalitz plot projections. The data are represented\nby points with error bars, the \ufb01t results by the histograms.\nThe upper right plot shows zoom of the m2(K+K\u2212) in the \u03c6\nmass region.\nK\u2217(892)0K+ and \u03c6(1020)\u03c0+ amplitudes and that the \ufb01t\nquality is substantially improved by leaving the K\u2217(892)0\nparameters free in the \ufb01t. The \ufb01tted parameters are:\nmK\u2217(892)0 = (895.6 \u00b1 0.2stat \u00b1 0.3sys) MeV/c2\n\u0393K\u2217(892)0 = (45.1 \u00b1 0.4stat \u00b1 0.4sys) MeV\n(19.1.46)\nWe notice that the width is about 5 MeV lower than\nthat in Amsler et al. (2008). However this measurement\nis consistent with results from other Dalitz plot analy-\nses (Mitchell et al., 2009a) and measurements with semi-\nleptonic D+ \u2192K\n\u2217(892)0e+\u03bde decays (see Section 19.1.5.6).\nThe f0(1370) contribution is also left free in the \ufb01t,\nand we obtain the following parameter values:\nmf0(1370) = (1.22 \u00b1 0.01stat \u00b1 0.04sys) GeV/c2\n\u0393f0(1370) = (0.21 \u00b1 0.01stat \u00b1 0.03sys) GeV\n(19.1.47)\nThese values are within the broad range of values mea-\nsured by other experiments (Amsler et al., 2008).\nThe nonresonant contribution is consistent with zero.\nThe results of the best \ufb01t are superimposed on the\nDalitz plot projections in Fig. 19.1.35. The normalized \ufb01t\nresiduals shown under each distribution (Fig. 19.1.35) are\nde\ufb01ned as (Ndata \u2212N\ufb01t)/\u221aNdata.\n\n543\nTable 19.1.13. From (del Amo Sanchez, 2011b). Results from the D+\ns \u2192K+K\u2212\u03c0+ Dalitz plot analysis. The table gives \ufb01t\nfractions, amplitudes and phases from the best \ufb01t. Quoted uncertainties are statistical and systematic, respectively.\nDecay Mode\nDecay fraction (%)\nAmplitude\nPhase (radians)\nK\u2217(892)0K+\n47.9 \u00b1 0.5 \u00b1 0.5\n1.(Fixed)\n0.(Fixed)\n\u03c6(1020) \u03c0+\n41.4 \u00b1 0.8 \u00b1 0.5\n1.15 \u00b1 0.01 \u00b1 0.26\n2.89 \u00b1 0.02 \u00b1 0.04\nf0(980) \u03c0+\n16.4 \u00b1 0.7 \u00b1 2.0\n2.67 \u00b1 0.05 \u00b1 0.20\n1.56 \u00b1 0.02 \u00b1 0.09\nK\u2217\n0(1430)0K+\n2.4 \u00b1 0.3 \u00b1 1.0\n1.14 \u00b1 0.06 \u00b1 0.36\n2.55 \u00b1 0.05 \u00b1 0.22\nf0(1710) \u03c0+\n1.1 \u00b1 0.1 \u00b1 0.1\n0.65 \u00b1 0.02 \u00b1 0.06\n1.36 \u00b1 0.05 \u00b1 0.20\nf0(1370) \u03c0+\n1.1 \u00b1 0.1 \u00b1 0.2\n0.46 \u00b1 0.03 \u00b1 0.09\n\u22120.45 \u00b1 0.11 \u00b1 0.52\nSum\n110.2 \u00b1 0.6 \u00b1 2.0\n\u03c72/NDF\n2843/(2305 \u221214) = 1.24\nP-wave/S-wave ratio in the \u03c6(1020) region\nThe decay mode D+\ns \u2192\u03c6(1020)\u03c0+ is used often as the\nnormalizing mode for D+\ns decay branching fractions, typ-\nically by selecting a K+K\u2212invariant mass region around\nthe \u03c6(1020) peak. The observation of a signi\ufb01cant S-wave\ncontribution in the threshold region means that this con-\ntribution must be taken into account in such a procedure.\nBABAR has estimated the P-wave/S-wave ratio in an\nalmost model-independent way. Integrating the distribu-\ntions of\n\u221a\n4\u03c0pq\u2032 \nY 0\n0\n\u000b\nand\n\u221a\n5\u03c0pq\u2032 \nY 0\n2\n\u000b\n(Fig. 19.1.32),\nwhere p is the K+ momentum in the K+K\u2212rest frame,\nand q\u2032 is the momentum of the bachelor \u03c0+ in the D+\ns\nrest frame, in a region around the \u03c6(1020) peak yields\nR\n(|S|2 + |P|2)pq\u2032dmK+K\u2212and\nR\n|P|2pq\u2032dmK+K\u2212respec-\ntively.\nThe S-P interference contribution integrates to zero,\nand the P-wave and S-wave fractions are de\ufb01ned as\nfP \u2212wave =\nR\n|P|2pq\u2032dmK+K\u2212\nR\n(|S|2 + |P|2)pq\u2032dmK+K\u2212(19.1.48)\nfS\u2212wave =\nR\n|S|2pq\u2032dmK+K\u2212\nR\n(|S|2 + |P|2)pq\u2032dmK+K\u2212\n= 1 \u2212fP \u2212wave .\n(19.1.49)\nThe experimental mass resolution is estimated to be\n\u22430.5 MeV/c2 at the \u03c6 mass peak. Table 19.1.14 gives\nthe resulting S-wave and P-wave fractions computed\nfor three K+K\u2212mass regions. The last column of Ta-\nble 19.1.14 shows the measurements of the relative over-\nall rate (N/Ntot) de\ufb01ned as the number of events in the\nTable 19.1.14. From (del Amo Sanchez, 2011b). S-wave\nand P-wave fractions computed in three K+K\u2212mass ranges\naround the \u03c6(1020) peak. Errors are statistical only.\nmK+K\u2212\nfS\u2212wave\nfP \u2212wave\nN\nNtot\n(MeV/c2)\n(%)\n(%)\n(%)\n1019.456 \u00b1\n5\n3.5 \u00b1 1.0\n96.5 \u00b1 1.0\n29.4 \u00b1 0.2\n1019.456 \u00b1 10\n5.6 \u00b1 0.9\n94.4 \u00b1 0.9\n35.1 \u00b1 0.2\n1019.456 \u00b1 15\n7.9 \u00b1 0.9\n92.1 \u00b1 0.9\n37.8 \u00b1 0.2\nK+K\u2212mass interval over the number of events in the en-\ntire Dalitz plot after e\ufb03ciency correction and background\nsubtraction.\n19.1.5 Semileptonic charm decays\n19.1.5.1 Introduction\nExclusive semileptonic decays of B and D mesons are a\nfavored means of determining the weak interaction cou-\nplings of quarks within the Standard Model because of\ntheir relative abundance; in addition, the hadronic uncer-\ntainties in their theoretical description are by far better\nunder control than in hadronic decays. Our knowledge of\nthe form factors parameterizing the hadronic current is\nlimiting the precision on extractions of the couplings |Vcb|\nand |Vub|. Form factors from B and D meson semileptonic\ndecays have been calculated using lattice QCD techniques\nwhilst heavy quark symmetry relates the two form factors.\nMeasurements of D \u2192K/\u03c0\u2113+\u03bd\u2113are required to confront\nthe theoretical predictions.117\nCharm meson semileptonic decays with two pseudo\nscalar mesons (P1, P2) emitted in the \ufb01nal state allow\nalso to study the strong interaction of the two pseudo-\nscalar mesons in systems with well de\ufb01ned values of isospin\nand angular momentum, without parasitic e\ufb00ects from the\npresence of a third hadron as in Dalitz plot analyses. In\nparticular S-wave systems can be isolated and properties\nof P-wave resonances can be accurately measured. Large\nstatistics are analyzed, exceeding previous analyses by two\norders of magnitude, in particular for the D+\ns meson.\n19.1.5.2 D \u2192K/\u03c0\u2113+\u03bd\u2113decays\nTo measure D meson semileptonic decays with a pseudo\nscalar particle emitted in the \ufb01nal state (D\u21133 decays), Belle\nand BABAR have used completely di\ufb00erent techniques. In\nBelle, events with all particles reconstructed are selected.\nThis allows to isolate signal events over a low background\n117 Inclusion of charge-conjugate states is implied throughout\nthis section.\n\n544\nlevel and a high resolution in q2 = (p\u2113+ p\u03bd\u2113)2, at the\nprice of a low e\ufb03ciency. In BABAR, a more inclusive ap-\nproach allows to have larger statistics at the price of a\nhigher background level and poorer q2 resolution. In this\ncase, additional measurements allow to control distribu-\ntions from background events.\n19.1.5.3 Belle measurement\nTo achieve good resolution in the neutrino momentum\nand q2, the D0 is tagged by fully reconstructing the re-\nmainder of the event (Widhalm, 2006). Events of the\ntype e+e\u2212\n\u2192D(\u2217)\ntagD\u2217\u2212\nsig X with D\u2217\u2212\nsig\n\u2192D0\nsig\u03c0\u2212\ns\nare\nseeked, where X may include additional \u03c0\u00b1, \u03c00, or K\u00b1\nmesons. Each candidate is assembled from a fully re-\nconstructed \u201ctag-side\u201d charm meson (D(\u2217)\ntag) which can\nbe D\u2217+ \u2192D0\u03c0+, D+\u03c00 or D\u22170 \u2192D0\u03c00, D0\u03b3 with\nD+/0 \u2192K\u2212(n\u03c0)++/+, n = 1, 2, 3. To the (D(\u2217)\ntag) is\nadded a charged pion, that is kinematically consistent with\nthe \u03c0\u2212\ns from D\u2217\u2212\nsig decay, and the candidate X is formed\nfrom combinations of unassigned \u03c0 and K+K\u2212pairs, con-\nserving total event electric charge. The 4-momentum of\nD\u2217\u2212\nsig is found by energy-momentum conservation, assum-\ning a D(\u2217)\ntagD\u2217\u2212\nsig X event. The candidate D0\nsig 4-momentum\nis calculated from that of the D\u2217\u2212\nsig and \u03c0\u2212\ns . The corre-\nsponding D0\nsig invariant mass distribution, obtained after\nanalyzing an integrated luminosity of 282 fb\u22121, contains\n56461 \u00b1 309 \u00b1 830 signal over 39789 \u00b1 830 background\nevents, the latter beeing estimated using wrong sign com-\nbinations in data and few corrections from the simulation.\nWithin this sample of D0\nsig tags, the semileptonic decay\nD0\nsig \u2192K+/\u03c0+\u2113\u2212\u03bd\u2113is reconstructed with K+/\u03c0+ and \u2113\u2212\ncandidates from among the remaining tracks. The neu-\ntrino 4-momentum is reconstructed by energy-momentum\nconservation, its invariant mass squared, m2\n\u03bd, is required\nto satisfy\n\f\fm2\n\u03bd\n\f\f < 0.05 GeV2/c4. About 1300 and 150 se-\nmileptonic decays are isolated for each lepton \ufb02avor (e\nand \u00b5) in Cabibbo-allowed and Cabibbo-suppressed de-\ncays respectively. These numbers have to be corrected for\nremaining background contributions from other semilep-\ntonic and hadronic decays where a hadron is mis-identi\ufb01ed\nas a lepton. Corrections amount typically to 2% and 20%\nrespectively in Cabibbo-allowed and Cabibbo-suppressed\ndecays. The accuracy on branching fraction measurements\nis limited by systematic uncertainties for Cabibbo-allowed\ndecays whereas systematic and statistical uncertainties are\nsimilar in Cabibbo-suppressed events. The main contribu-\ntion to systematic uncertainties comes from the evaluation\nof fake D0\nsig tags. The resolution in q2 = (p\u2113+p\u03bd\u2113)2 is found\nto be 0.0145\u00b10.0007stat GeV2/c2 in MC signal events. This\nis much smaller than statistically reasonable bin widths,\nwhich have been chosen as 0.067 (0.3) GeV2/c2 for kaon\n(pion) modes, and hence no unfolding is necessary.\nMeasured hadronic form factors obtained by Belle are\ngiven in Figure 19.1.36 where they are compared with sev-\neral theoretical expectations.\n0\n0.25\n0.5\n0.75\n1\n1.25\n1.5\n1.75\n2\n2.25\n2.5\n0.5\n1\n1.5\nf+(q2)\n0\n0.25\n0.5\n0.75\n1\n1.25\n1.5\n1.75\n2\n2.25\n0\n1\n2\n3\nq2 (GeV2/c2)\nf+(q2)\nFigure 19.1.36. From (Widhalm, 2006). Form factors for (a)\nD0 \u2192K\u2212\u2113+\u03bd\u2113, in q2 bins of 0.067 GeV2/c2 and (b) D0 \u2192\n\u03c0\u2212\u2113+\u03bd\u2113, in q2 bins of 0.3 GeV2/c2. Overlaid are the predictions\nof the simple pole model using the physical pole mass (dashed)\n(Amoros, Noguera, and Portoles, 2003) and a quenched (light\ngrey) (Abada et al., 2003) and unquenched (dark grey) LQCD\ncalculation (Aubin et al., 2005). The shaded band re\ufb02ects the\ntheoretical uncertainty.\n19.1.5.4 BABAR measurement\nD0 \u2192K\u2212e+\u03bde(\u03b3) decays are reconstructed in e+e\u2212\u2192\ncc events from the continuum where the D0 originates\nfrom D\u2217+ \u2192D0\u03c0+ (Aubert, 2007ab). The analyzed in-\ntegrated luminosity is 75 fb\u22121 and semileptonic decays\nwith a muon are not selected. In each event, the direc-\ntion of the thrust axis is used to de\ufb01ne two hemispheres.\nIn each hemisphere, pairs of oppositely charged leptons\nand kaons are searched. Since the \u03bde momentum is un-\nmeasured, a kinematic \ufb01t is performed, constraining the\ninvariant mass of the candidate K\u2212e+\u03bde system to the D0\nmass. In this \ufb01t, the D0 momentum and the neutrino en-\nergy are estimated from the other particles measured in\nthe event. Each D0 candidate is retained if the \u03c72 proba-\nbility of the kinematic \ufb01t exceeds 10\u22123 and it is combined\nwith a charged pion, with the same charge as the lepton,\nand situated in the same hemisphere. The mass di\ufb00erence\n\u03b4(m) = m(D0\u03c0+) \u2212m(D0) is evaluated and signal events\naccumulate at low values of this variable. Only events with\n\u03b4(m) < 0.16 GeV/c2 are used in the analysis. Background\nevents are rejected by applying cuts on Fisher discriminant\nvariables against BB, other cc, and light quark events.\nTo improve the accuracy of the reconstructed D0 mo-\nmentum, the nominal D\u2217+ mass is added as a constraint\nin the previous \ufb01t and only events with a \u03c72 probabil-\nity higher than 1% are kept. There are 85260 selected\nD0 candidates containing an estimated number of 11280\n\n545\n1\n1.5\n2\n0\n0.5\n1\n1.5\n2\nq2(GeV2)\nf+(q2) / f+(0)\nBABAR\nFOCUS\nLattice-QCD (\u03b1pole = 0.50(4))\nFigure 19.1.37. From (Aubert, 2007ab). Comparison of the\nmeasured variation of f K\n+ (q2)/f K\n+ (0) obtained in BABAR and in\nthe FOCUS experiment (Link et al., 2005). The band corre-\nsponds to an estimate from LQCD (Aubin et al., 2005).\nbackground events. The 4-momentum squared of the lep-\ntonic system is obtained using the \ufb01tted D0 and kaon\n4-momenta: q2\nr = (pD0 \u2212pK)2. The resolution on the re-\nconstructed q2 obtained from the simulation is found to\nbe around 0.16 GeV/c2. To obtain the true q2 distribution,\nthe measured one is corrected for selection e\ufb03ciency, de-\ntector resolution and radiative e\ufb00ects. This is done using\nan unfolding algorithm based on MC simulation of these\ne\ufb00ects. Other data samples are used to validate the MC\nsimulation. Events with D\u2217+ \u2192D0\u03c0+, D0 \u2192K\u2212\u03c0+ al-\nlows to control the charm quark hadronization mechanism\nand the reconstruction accuracy of the D0 4-momentum\nfrom other particles in the event. A sample of D\u2217+ \u2192\nD0\u03c0+, D0 \u2192K\u2212\u03c0+\u03c00 decays is used also to verify the\nreconstruction accuracy on q2\nr and to de\ufb01ne corrections.\nTo reduce systematic uncertainties on the semileptonic\ndecay branching fraction determination, this quantity is\nmeasured relative to the D\u2217+ \u2192D0\u03c0+, D0 \u2192K\u2212\u03c0+ de-\ncay channel which is isolated in data and in the simulation\nusing, as much as possible, similar selection criteria. This\nhas also the advantage that future improvements in the\nB(D0 \u2192K\u2212\u03c0+) determination can be incorporated (this\nwas indeed the case since results have been published).\nThe uncertainty on the branching fraction measurement is\ndominated by systematic uncertainties which have di\ufb00er-\nent origins (reconstruction algorithm, electron identi\ufb01ca-\ntion, background subtraction, control of the discriminant\nFisher variable distribution and, counting of D\u2217+ events\nin the normalization channel) of similar importance.\nFigure 19.1.37 gives the measured variation versus q2\nof the ratio f K\n+ (q2)/f K\n+ (0) obtained in BABAR.\n19.1.5.5 Comparison with theory and with other\nexperiments\nIn D0 \u2192K\u2212/\u03c0\u2212e+\u03bde decays, neglecting the electron mass,\nthe di\ufb00erential decay rate depends on only one form fac-\ntor, f K/\u03c0\n+\n(q2):\nd\u0393\ndq2 = G2\nF\n24\u03c03 |Vcq|2 \f\fpP (q2)\n\f\f3 \f\ff P\n+ (q2)\n\f\f2 ,\n(19.1.50)\nwhere GF is the Fermi constant, |Vcq| with q = s or d, re-\nspectively for P = K or \u03c0, is the absolute value of the cor-\nresponding CKM element, and pP (q2) is the pseudoscalar\n(P) three-momentum in the D0 rest frame.\nThe unitarity of the \ufb01rst line of the CKM matrix is\nveri\ufb01ed with high accuracy using beta decays of nuclei,\nK\u21133, and K\u21132 decays (Antonelli et al., 2010b):\n|Vud| = 0.97425(22), |Vus| = 0.2253(9),\n(19.1.51)\ngiving:\n|Vud|2 + |Vus|2 \u22121 = \u22120.0001(8).\n(19.1.52)\nNote the the contribution from |Vub|2 is completely negli-\ngible. The unitarity condition for the \ufb01rst column reads:\n|Vud|2 + |Vcd|2 + |Vtd|2 = 1.\n(19.1.53)\nThere could be large e\ufb00ects from new physics in the present\nvalue of |Vtd| but they will have essentially no contribu-\ntion in the unitarity constraint as |Vtd| \u223c|Vub|. So, inde-\npendently of e\ufb00ects from new physics in B0B0 oscillations,\none can use |Vcd| = |Vus| = 0.2253(9). Using this, together\nwith the unitarity condition of the second line of the CKM\nmatrix, one gets:\n|Vcs| = |Vud| \u2212|Vcb|2\n2\n= 0.97343 \u00b1 0.00023,\n(19.1.54)\nusing the value |Vcb| = (40.6 \u00b1 1.3) \u00d7 10\u22123 (Nakamura\net al., 2010). D\u21133 decays depend on the product |Vcq|\n\f\ff P\n+ (q2)\n\f\f\nand, as the CKM elements |Vcq| are precisely determined,\ncharm semileptonic decays allow to measure the absolute\nvalues of the corresponding hadronic form factors and\ntheir variation versus q2.\nThe most general expressions of the form factor f P\n+ (q2)\nare analytic functions satisfying the dispersion relation:\nf P\n+ (q2) =\nRes(f P\n+ )q2=m2\nD\u2217q\nm2\nD\u2217q \u2212q2\n+ 1\n\u03c0\nZ \u221e\nt+\ndt Imf P\n+ (t)\nt \u2212q2 \u2212i\u03f5.\n(19.1.55)\nThe singularities in the complex t \u2261q2 plane originate\nfrom the interaction of the charm and light s or d quarks\n(for P = K and \u03c0, respectively) forming charmed hadron\nvector states. They represent a pole, situated at the D\u2217\nq =\nD\u2217+\ns\nor D\u2217+ mass squared and a cut, along the positive\nreal axis, starting at threshold (t+ = (mD + mP )2) for\nD0P production.\n\n546\nThis cut t-plane can be mapped onto the open unit\ndisk with center at t = t0 using the variable:\nz(t, t0) =\n\u221at+ \u2212t \u2212\u221at+ \u2212t0\n\u221at+ \u2212t + \u221at+ \u2212t0\n.\n(19.1.56)\nIn this variable, the physical region for the semileptonic\ndecay (0 < t < t\u2212= q2\nmax = (mD\u2212mP )2) corresponds to a\nreal segment extending between \u00b1zmax = \u00b10.051 for D \u2192\nK and \u00b10.17 for D \u2192\u03c0. This value of zmax is obtained for\nt0 = t+\n\u0010\n1 \u2212\np\n1 \u2212t\u2212/t+\n\u0011\n, where t+ = (mD +mP )2. The\nz expansion of f P\n+ is thus expected to converge quickly.\nThe most general parameterization (Hill, 2006), consistent\nwith constraints from QCD,\nf+(t) =\n1\nP(t)\u03a6(t, t0)\n\u221e\nX\nk=0\nak(t0) zk(t, t0),\n(19.1.57)\nis based on earlier considerations by (Boyd and Savage,\n1997) and other references quoted therein. For D0 \u2192\nK\u2212e+\u03bde, the function P(t) = z(t, m2\nD\u2217s ) has a zero at the\nD\u2217\ns pole mass and |P| = 1 along the unit circle. For D0 \u2192\n\u03c0\u2212e+\u03bde, as the D\u2217+ mass is higher than (mD0 + m\u03c0+),\nP(t) = 1. The expression for \u03a6 can be found in (Boyd and\nSavage, 1997).\nThe choice of P and \u03a6 is such that:\n\u221e\nX\nk=0\na2\nk(t0) \u22641.\n(19.1.58)\nHaving measured the \ufb01rst coe\ufb03cients of this expan-\nsion, Eq. (19.1.58) can constrain the others. This con-\nstraint is used in B meson semileptonic decays and found\nto be quite e\ufb00ective. For charm, this approach is not really\njusti\ufb01ed because the charm quark mass is rather light ren-\ndering the perturbative QCD determination of the func-\ntion \u03a6 questionable and because the z physical range is\nquite limited. Numerically it appears that the \ufb01rst mea-\nsured coe\ufb03cients are quite small and no useful constraint\ncan be placed on higher order coe\ufb03cients (ak with k \u22653).\nIt seems preferable to consider phenomenological mod-\nels to describe the q2 variation of f P\n+ (q2) because they have\na simple physical interpretation. In the simple pole model,\nf+(q2)simple pole =\nf+(0)\n1 \u2212\nq2\nm2\npole\n.\n(19.1.59)\nThe pole mass value mpole = mD\u2217s (mD\u2217+) respectively\nfor D0 \u2192K\u2212(\u03c0\u2212)\u2113+\u03bd\u2113. When \ufb01tting data, mpole is taken\nas a free parameter and its value can be compared with\nthese expectations.\nThe\nq2\ndependence\nof\nthe\nform\nfactor\nis\nnon-\nperturbative and the only \ufb01rst-principles approaches\nare lattice QCD calculations. Nevertheless, a vector-\ndominance assumption would lead to a single pole form\nwith the pole located at q2 = m2\nD\u2217s for the D \u2192K vec-\ntor form factor. However, this does not take into account\ncontributions from other states, and so also double-pole\nTable 19.1.15. Values of \ufb01tted parameters for di\ufb00erent mod-\nels of the hadronic form factor q2 dependence in D \u2192K\u2113+\u03bd\u2113\ndecays. The di\ufb00erent labels given in the \ufb01rst column cor-\nrespond to the following references: Belle (Widhalm, 2006),\nBABAR (Aubert, 2007ab), and CLEO-c (Besson et al., 2009).\nThe simple pole and ISGW2 models, with nominal values of\nthe parameters, are excluded.\nSource\nSimple pole\nBK\nISGW2\nmpole (GeV/c2)\n\u03b1BK\n\u03b1I (GeV\u22122)\nBelle(2006)\n1.82(4)(3)\n0.52(8)(6)\n0.51(3)(3)\nBABAR(2007)\n1.884(12)(15)\n0.38(2)(3)\n0.226(5)(6)\nCLEOc(2009)\n1.93(2)(1)\n0.30(3)(1)\n0.211(5)(3)\nExpectation\n2.112\n\u223c0.5\n0.104\nstructures have been suggested. The Isgur Scora Grinstein\nWise (ISGW2) quark model (Isgur, Scora, Grinstein, and\nWise, 1989; Scora and Isgur, 1995) belongs to this cate-\ngory:\nf+(q2)ISGW2 =\nf+(q2\nmax)\n(1 + \u03b1I(q2max \u2212q2))2 , \u03b1I = 1\n12r2.\n(19.1.60)\nThis expression is normalized at q2 = q2\nmax = (mD0 \u2212\nmP )2. For D \u2192K, the predicted values of the parameters\nare f+(q2\nmax) = 1.23 and r = 1.12 GeV\u22121.\nThe modi\ufb01ed pole model of (Becirevic and Kaidalov,\n2000) (BK model) has also two poles. The \ufb01rst pole is at\nthe vector meson mass and the second accounts for higher\nmass vector states:\nf+(q2)BK =\nf+(0)\n\u0012\n1 \u2212\nq2\nm2\nD\u2217s\n\u0013 \u0012\n1 \u2212\u03b1BK\nq2\nm2\nD\u2217s\n\u0013.\n(19.1.61)\nThe authors predict \u03b1BK \u223c0.5.\nAll proposed ansatze \ufb01t well the measured distribu-\ntions. However, apart for the BK model (which doesn\u2019t\nhave precisely determined expectations), predicted values\nof the parameters di\ufb00er markedly from the measurements\nas indicated in Table 19.1.15. E\ufb00ects from hadronic singu-\nlarities, in addition to the pole at the D\u2217\ns(d) mass, are thus\nmeasurable. The simple pole and ISGW2 models, with\nnominal values of the parameters, are excluded.\nQCD based form-factor calculations can also be per-\nformed in the framework of QCD sum rules. In particular,\nlight-cone QCD sum rules are well suited for the calcu-\nlation of form factors especially for heavy-to-light tran-\nsitions. The input into these sum rules is the light-cone\ndistribution of the quarks in the pion or kaon; a more\ndetailed description of this can be found in Section 17.1\nwhere this is applied to the B \u2192\u03c0 form factor. A recent\ndiscussion of the form factors for semileptonic charm de-\ncays can be found in (Khodjamirian, Klein, Mannel, and\nO\ufb00en, 2009). It turns out that the QCD sum rule calcula-\ntion yields a form factor which is compatible with lattice\n\n547\ndeterminations as well as with the BK parameterization;\nit can be used to perform an independent and competitive\nextraction of Vcs and Vcd from semileptonic charm decays.\nTo compare absolute determinations of the form fac-\ntors, obtained by several experiments and from LQCD,\nresults are evaluated at q2 = 0 in Table 19.1.16. Measure-\nments at B factories are \ufb01ve times more accurate than pre-\nvious determinations. Corresponding results from CLEO-\nc were published later with similar accuracy and central\nvalues. The measurement accuracy on f K/\u03c0\n+\n(0) combined\nresults reaches 1 and 3% respectively. They are in agree-\nment with LQCD recent expectations (Na, Davies, Fol-\nlana, Lepage, and Shigemitsu, 2010; Na et al., 2011). In\nspite of spectacular progress from lattice QCD, present\ncomputations are still a factor three (two) less accurate\nthan actual measurements for D \u2192K (D \u2192\u03c0). In fu-\nture, detailed comparisons of the measured and expected\nvariations of the hadronic form factors versus q2 are ex-\npected. Combining experimental and theoretical uncer-\ntainties, one can say also that, at present, the values of\n|Vcs| and |Vcd| obtained from the measurements of Dl3 de-\ncays and using the values of the corresponding hadronic\nform factors from lattice QCD, agree with expectations\nfrom unitarity with a relative uncertainty of 2.7% and 5%\nrespectively.\n19.1.5.6 The D+ \u2192K\u2212\u03c0+e+\u03bde decay\nDetailed study of the D+ \u2192K\u2212\u03c0+e+\u03bde decay channel\n(del Amo Sanchez, 2011a) is of interest for three main\nreasons:\n\u2013 it allows measurements of the di\ufb00erent K\u03c0 resonant\nand non-resonant amplitudes that contribute to this\ndecay. In this respect, BABAR has measured the S-wave\ncontribution and searched for radially excited P-wave\nand for D-wave components.\n\u2013 high statistics allows accurate measurements of the\nproperties of the K\n\u2217(892)0 meson, the main contri-\nbution to the decay. Both resonance parameters and\nhadronic transition form factors are precisely measured.\nThe latter can be compared with hadronic model ex-\npectations and lattice QCD computations.\n\u2013 variation of the K\u03c0 S-wave phase versus the K\u03c0 mass\ncan be determined, and compared with other experi-\nmental determinations.\nThe approach used to reconstruct D+ mesons decaying\ninto K\u2212\u03c0+e+\u03bde is similar to that already explained in Sec-\ntion 19.1.5.2. Charged and neutral particles are boosted\nto the center-of-mass system and the event thrust axis is\ndetermined. A plane perpendicular to this axis is used to\nde\ufb01ne two hemispheres.\nA candidate D+ is represented by a positron, a charged\nkaon, and a charged pion present in the same hemisphere.\nA vertex is formed using these three tracks, and events\nwith the corresponding \u03c72 probability larger than 10\u22127\nare kept. The value of this probability is used with other\nTable 19.1.16. Summary of hadronic form factor measure-\nments at q2 = 0. Measurements from CLEOc(2009) supercede\nthose from CLEOc(2008). Results at B factories have an ac-\ncuracy similar to CLEOc and results are compatible. All pub-\nlished results have been corrected for normalization branching\nfractions, lifetimes, and assumed values for CKM matrix el-\nements if needed, using values quoted in (Nakamura et al.,\n2010). The di\ufb00erent labels quoted in the \ufb01rst column corre-\nspond to the following references : E691 (Anjos et al., 1989),\nCLEO (Crawford et al., 1991), CLEOII (Bean et al., 1993),\nE687(1995) (Frabetti et al., 1995), E687(1996) (Frabetti et al.,\n1996a), BES II (Ablikim et al., 2004a), CLEO III (Huang et al.,\n2005), Belle\n(Widhalm, 2006), BABAR\n(Aubert, 2007ab),\nCLEO-c (2008) (Dobbs et al., 2008), CLEO-c (2009) (Besson\net al., 2009), and HPQCD (Na, Davies, Follana, Lepage, and\nShigemitsu, 2010; Na et al., 2011). Combining measurements\nfrom Belle , BABAR and CLEO-c, and assuming that uncertain-\nties are uncorrelated, the corresponding averaged values are ob-\ntained. LQCD results obtained by the HPQCD collaboration\nare given in the last line. They agree with the measurements.\nExperiment (date)\nf K\n+ (0)\nf \u03c0\n+(0)\nE691(1989)\n0.70(5)(5)\nCLEO(1991)\n0.78(3)(3)\nCLEOII(1993)\n0.77(1)(4)\n0.72(13)(5)\nE687(1995)\n0.70(3)(3)\nE687(1996)\n0.71(7)(2)\nBESII(2004)\n0.80(4)(3)\nCLEOIII(2005)\n0.62(6)(4)\nBelle(2006)\n0.695(7)(22)\n0.624(20)(30)\nBABAR(2007)\n0.734(7)(7)\nCLEOc(2008)\n0.763(7)(6)\n0.629(22)(7)(3)\nCLEOc(2009)\n0.739(7)(5)\n0.666(19)(4)(3)\nOur avg.(2012)\n0.734(6)\n0.657(17)(3)\nHPQCD(2010 \u221211)\n0.747(19)\n0.666(29)\ninformations combined in two Fisher discriminant vari-\nables to reject, respectively, \u03a5(4S) decays and continuum\nbackground events.\nTo estimate the neutrino momentum, the (K\u2212\u03c0+e+\u03bde)\nsystem is constrained to the D+ mass. In this \ufb01t, esti-\nmates of the D+ direction and of the neutrino energy are\nincluded from measurements obtained from all tracks reg-\nistered in the event. The D+ direction estimate is taken\nas the direction of the vector opposite to the momentum\nsum of all reconstructed particles but the kaon, the pion,\nand the positron. The neutrino energy is evaluated by sub-\ntracting from the hemisphere energy the energy of recon-\nstructed particles contained in that hemisphere.\nAnalyzing an integrated luminosity of 347 fb\u22121, about\n244 \u00d7 103 signal events are selected with a ratio Signal /\nBackground= 2.3.\nAs there are four particles in the \ufb01nal state, the di\ufb00er-\nential decay rate has \ufb01ve degrees of freedom that can be\n\n548\nexpressed in the following variables (Cabibbo and Maksy-\nmowicz, 1965; Pais and Treiman, 1968):\n\u2013 m2, the mass squared of the K\u03c0 system;\n\u2013 q2, the mass squared of the e+\u03bde system;\n\u2013 cos (\u03b8K), where \u03b8K is the angle between the K three-\nmomentum in the K\u03c0 rest frame and the line of \ufb02ight\nof the K\u03c0 in the D rest frame;\n\u2013 cos (\u03b8e), where \u03b8e is the angle between the charged\nlepton three-momentum in the e\u03bde rest frame and the\nline of \ufb02ight of the e\u03bde in the D rest frame;\n\u2013 \u03c7, the angle between the normals to the planes de\ufb01ned\nin the D rest frame by the K\u03c0 pair and the e\u03bde pair.\n\u03c7 is de\ufb01ned between \u2212\u03c0 and +\u03c0.\nFor the di\ufb00erential decay partial width, we use the\nformalism given in (Lee, Lu, and Wise, 1992). Apart for\nthe S-wave for which there is one hadronic form factor,\neach higher spin component has three form factors associ-\nated. Using the conclusions of the D0 \u2192K\u2212e+\u03bde analysis,\nwhere we \ufb01nd that all usual ansatze give a good param-\neterization of data, and noting that the q2 range is even\nmore limited, we use the simple pole model to describe\nthe q2 dependence of these form factors. As an example,\nfor the K\n\u2217(892)0 meson, we use:\nV (q2) =\nV (0)\n1 \u2212\nq2\nm2\nV\n,\nA1(q2) =\nA1(0)\n1 \u2212\nq2\nm2\nA\n,\n(19.1.62)\nA2(q2) =\nA2(0)\n1 \u2212\nq2\nm2\nA\n.\nHadronic resonances are parameterized using relativis-\ntic Breit-Wigner distributions with mass dependent widths\nand a Blatt-Weisskopf damping factor. For the S-wave\ncomponent we \ufb01t the amplitude and measure the phase in\nseveral mass intervals.\nA binned distribution of data events is analyzed. The\nexpected number of events in each bin depends on signal\nand background estimates and the former is a function of\nthe values of the \ufb01tted parameters. We perform a min-\nimization of a negative log-likelihood distribution. This\ndistribution has two parts. One corresponds to the com-\nparison between measured and expected number of events\nin bins which span the \ufb01ve dimensional space of the dif-\nferential decay rate. The other part is used to measure\nthe fraction of background events and corresponds to the\ndistribution of the values of one of the Fisher discriminant\nvariables. There are 2800 bins in total.\n19.1.5.7 Measured components\nThe K\u2212\u03c0+ \ufb01nal state is dominated by the K\n\u2217(892)0 me-\nson (94.1%) and the S-wave component (5.8%). There\nis marginal evidence for the \ufb01rst radial excitation of\nthe P-wave (0.3%) and a stringent limit is placed on a\nTable\n19.1.17.\nComparison\nbetween\nBABAR\n(del\nAmo\nSanchez,\n2011a)\nmeasurements\nand\npresent\nworld\naverages\n(Nakamura\net\nal.,\n2010).\nValues\nfor\nB(D+\n\u2192\nK\n\u2217(1410)0/K\n\u2217\n2(1430)0e+\u03bde)\nare\ncorrected\nfor\ntheir respective branching fractions into K\u2212\u03c0+.\nBranching fraction\nBABAR\nPDG 2010\nB(D+ \u2192K\u2212\u03c0+e+\u03bde)(%)\n4.00(3)(4)(9)\n4.1 \u00b1 0.6\nB(D+ \u2192K\u2212\u03c0+e+\u03bde)K\u2217(892)0(%)\n3.77(4)(5)(9)\n3.68 \u00b1 0.21\nB(D+ \u2192K\u2212\u03c0+e+\u03bde)S\u2212wave(%)\n0.232(7)(7)(5)\n0.21 \u00b1 0.06\nB(D+ \u2192K\n\u2217(1410)0e+\u03bde)(%)\n< 0.6 at 90% C.L.\nB(D+ \u2192K\n\u2217\n2(1430)0e+\u03bde)(%)\n< 0.05 at 90% C.L.\nD-wave contribution. The small K\n\u2217(1410)0 contribution\nagrees with the na\u00a8\u0131ve expectation based on correspond-\ning measurements in \u03c4 decays and its phase relative to\nthe K\n\u2217(892)0 is compatible with zero. Branching frac-\ntions for these components are obtained by reference to\nthe D+ \u2192K\u2212\u03c0+\u03c0+ channel which is measured using a\nsimilar analysis, and are reported in Table 19.1.17.\nThe S-wave contribution is dominated by events with\na mass below the K\n\u2217\n0(1430) resonance pole and, for the\n\ufb01rst time, the S-wave phase is measured at several values\nof the K\u2212\u03c0+ mass. The K\u03c0 hadronic system can have\ntwo isospin components (I = 1/2, 3/2) however, in charm\nsemileptonic decays, the c \u2192s transition corresponds to\n\u2206I = 0 and only the I = 1/2 component is produced.\nThe K\u03c0 scattering S-wave, with isospin I = 1/2, remains\nelastic up to the K\u03b7 threshold, but since the coupling to\nthis channel is weak, it is considered in practice to be\nelastic up to the K\u03b7\u2032 threshold. In this elastic regime,\nthe Watson theorem (Watson, 1954) implies that, phases\nmeasured in K\u03c0 elastic scattering and in a decay channel\nin which the K\u03c0 system has no strong interaction with\nother hadrons are equal modulo \u03c0 radians for the same\nvalues of isospin and angular momentum. The ambiguity\nis solved by determining the sign of the S-wave amplitude\nfrom data. This theorem does not provide any constraint\non the corresponding amplitude moduli. In particular, it is\nnot legitimate (though nonetheless frequently done) to as-\nsume that the S-wave amplitude in a decay is proportional\nto the elastic amplitude. In Figure 19.1.38 the K\u2212\u03c0+ S-\nwave phase with I = 1/2 measured in the elastic channel\n(Aston et al., 1988; Estabrooks et al., 1978) and in D+\nsemileptonic decays, are compared. We measure that the\ntwo amplitudes di\ufb00er by a negative sign and that phases\nare compatible within uncertainties, in agreement with the\nWatson theorem. Similar analyses of the D+ \u2192K\u2212\u03c0+\u03c0+\nDalitz plot (Aitala et al., 2006; Bonvicini et al., 2008; Link\net al., 2007, 2009) measure a signi\ufb01cant di\ufb00erence between\nthe variation of the K\u03c0 S-wave and of the elastic phases\nversus the K\u03c0 mass. This di\ufb00erence has thus to be at-\ntributed to \ufb01nal state interactions with the third hadron.\n\n549\n)\n2\n (GeV/c\n\u03c0\nK\nm\n0.8\n1\n1.2\n1.4\n1.6\n (degrees)\nS\n\u03b4\n0\n50\n100\n0\n(1410)\n*\nK\n+\n0\n(892)\n*\nK\nMod. Ind. S+\n0\n(1410)\n*\nK\n+\n0\n(892)\n*\nK\nS+\nLASS\nEstabrooks et al\nFigure 19.1.38. From (del Amo Sanchez, 2011a). Points (red\ncrosses) give the S-wave phase variation assuming a signal con-\ntaining S-wave, K\n\u2217(892)0 and K\n\u2217(1410)0 components. The\nS-wave phase is assumed to be constant within each consid-\nered mass interval. Error bars include systematic uncertain-\nties. The full line corresponds to the \ufb01tted parameterized S-\nwave phase variation expected from elastic scattering experi-\nments. The phase variation measured in K\u03c0 scattering by (Es-\ntabrooks et al., 1978) (triangles) and LASS (Aston et al., 1988)\n(squares), after correcting for the I = 3/2 isospin component,\nare given.\n19.1.5.8 Detailed measurements of the K\n\u2217(892)0\nUsing a model for signal which includes S-wave, K\n\u2217(892)0\nand K\n\u2217(1410)0 contributions, and the simple pole ansatz\nfor the q2 variation of hadronic form factors, parameters\nof the K\n\u2217(892)0 component are obtained from a \ufb01t to\nthe \ufb01ve-dimensional decay distribution. These parame-\nters, listed in Table 19.1.18, de\ufb01ne the K\n\u2217(892)0 lineshape\nand the relative contributions of the di\ufb00erent form factors:\nr2 = A2(0)/A1(0) and rV = V (0)/A1(0). The analysis is\nnot sensitive to the q2 dependence of the vector form fac-\ntor (V (q2)) but we measure, for the \ufb01rst time the e\ufb00ective\npole mass of the axial vector form factors (A1,2(q2)) and\n\ufb01nd a value compatible with expectations mpole \u223cmDs1.\nThe branching fraction of D+ \u2192K\n\u2217(892)0e+\u03bde is\ndetermined by normalizing the signal yield of D+ \u2192\nK\u2212\u03c0+e+\u03bde to the reconstructed yield of D+ \u2192K\u2212\u03c0+\u03c0+\n(with the branching fraction as measured in (Dobbs et al.,\n2007a)), after subtracting the S-wave and K\n\u2217(1410)0 con-\ntributions, and after correcting for the e\ufb03ciency di\ufb00er-\nence. The decay rate depends only on the value of A1(0).\nIn the zero-width approximation for the K\n\u2217(892)0 reso-\nnance the measured decay rate corresponds to:\nA1(0) = 0.6200 \u00b1 0.0056 \u00b1 0.0065 \u00b1 0.0071.\n(19.1.63)\nThe last uncertainty includes the uncertianty of Br(D+ \u2192\nK\u2212\u03c0+\u03c0+) as well as the systematic uncertainty due to ex-\nternal parameters used in the extraction of A1(0) (values\nof |Vcs| and \u03c4 +\nD).\nTable\n19.1.18.\nMeasured properties (del Amo Sanchez,\n2011a) of the D+ \u2192K\n\u2217(892)0e+\u03bde decay channel and of the\nK\n\u2217(892)0 resonance are compared with corresponding world\naverages (Nakamura et al., 2010). rBW is the Blatt-Weisskopf\ndamping parameter. mA is the pole mass of the axial vector\nform factors.\nMeasured quantity\nBABAR\nPDG 2010\nmK\u2217(892)0(MeV/c2)\n895.4 \u00b1 0.2 \u00b1 0.2\n895.94 \u00b1 0.22\n\u0393 0\nK\u2217(892)0(MeV/c2)\n46.5 \u00b1 0.3 \u00b1 0.2\n48.7 \u00b1 0.8\nrBW (GeV/c)\u22121\n2.1 \u00b1 0.5 \u00b1 0.5\n2.72 \u00b1 0.55\nrV\n1.463 \u00b1 0.017 \u00b1 0.031\n1.62 \u00b1 0.08\nr2\n0.801 \u00b1 0.020 \u00b1 0.020\n0.83 \u00b1 0.05\nmA(GeV/c2)\n2.63 \u00b1 0.10 \u00b1 0.13\nno result\nIn the present analysis, the measured distribution in\n\ufb01ve dimensions is not unfolded and the experimental res-\nolution expected from the simulation is controlled using\ndata. Because angular distributions are completely deter-\nmined by the kinematics for each helicity component, mea-\nsurements are giving the decay rate variation versus the\nremaining two variables, q2 and m2. The q2 dependence\nof hadronic form factors is smooth and can be parame-\nterized in a simple way as explained in Section 19.1.5.2.\nFor the mass measurement, the experimental resolution\nis high. It results that the distribution, for which statisti-\ncal and systematic error matrices on the \ufb01tted parameters\nare provided, can be compared with di\ufb00erent theoretical\nexpressions when they will be available.\n19.1.5.9 Measured and expected values of the hadronic\nform factors\nThe normalization and speci\ufb01c q2 behavior of the hadronic\nform factors are obtained in some speci\ufb01c limits for which\nintermediate scales are identi\ufb01ed. When a heavy hadron\ndecays semileptonically into another heavy hadron a new\nsymmetry emerges which gives constraints on the behaviour\nof the form factors. This symmetry is exact in the limit of\nin\ufb01nite quark mass values, which can be formulated as an\ne\ufb00ective \ufb01eld theory, the Heavy Quark E\ufb00ective Theory\n(HQET) (Isgur and Wise, 1989; Shifman and Voloshin,\n1988). For \ufb01nite values of quark masses, and depending\non the form factors, corrections start at order 1/mQ or\n1/m2\nQ. These properties are used to determine the value\nof Vcb from measurements of B \u2192D\u2217\u2113\u03bd\u2113as corrections are\nexpected to be at order 1/m2\nQ for q2 \u223cq2\nmax. For charm,\nthe value of the charm-quark mass is of the order of 2 \u22123\ntimes \u039bQCD and the strange quark cannot be described as\na heavy quark. Considerations based on HQET are thus\nexpected not to hold for charm semileptonic decays; still\nthey may serve as a starting point, and hence we consider\nit of interest to review the constraints on form factors, im-\nplied by HQET, and to indicate how they are violated in\ncharm to eventually get insights for B decays. For in\ufb01nite\n\n550\nTable 19.1.19. Comparison between measured and expected\nvalues of the form factors in D+ \u2192K\n\u2217(892)0e+\u03bde decays,\nevaluated at q2 = 0. Only measurements from BABAR\n(del\nAmo Sanchez, 2011a) and FOCUS (Link et al., 2002) which\nare corrected for the S-wave contribution are listed. Results\nfrom PDG 2010 (Nakamura et al., 2010) include those from\nFOCUS and all previous measurements. Expected values are\ncoming from the HM\u03c7T model (Fajfer and Kamenik, 2005)\nand LQCD (Gill, 2002) computations.\nFOCUS 2002\nBABAR\nPDG 2010 HM\u03c7T\nLQCD\nrV\n1.504(57)(39)\n1.493(14)(21)\n1.62(8)\n1.6\n1.23(10)\nr2\n0.875(49)(64)\n0.775(11)(11)\n0.83(5)\n0.50\n0.94(12)\nA1(0)\n0.6200(56)(65)(71)\n0.62\n0.65(3)\nA2(0)\n0.480(8)(10)\n0.31\n0.61(7)\nV (0)\n0.926(12)(19)\n0.99\n0.80(5)\nquark masses one has the following equalities (Neubert,\n1994b):\nf+(q2) = V (q2) = A2(q2) =\nA1(q2)\n1 \u2212\nq2\n(mH+mV )2\n= R\u22121\u03be(q2)\n(19.1.64)\nThe Isgur-Wise function \u03be(q2) satis\ufb01es \u03be(q2\nmax) = 1. The\nparameter R = 2\u221amH mP (V )/(mH +mP (V )) is equal to \u223c\n0.9(0.8) for B(D) semileptonic favored decays. MH is the\nheavy hadron mass whereas mP (V ) are the pseudo scalar\nand vector meson masses. In this limit, the ratio of form\nfactors are equal for q2 = q2\nmax: rV (q2\nmax) = r2(q2\nmax) =\nR\u22122. For other values of q2 they read:\nrV (2)(q2) =\n1\n1 \u2212\nq2\n(mH+mV )2\nR1(2)(q2)\n(19.1.65)\nwith R1(2)(q2\nmax) = 1. Corrections to these expressions\ncorrespond to expansions in 1/m, where m can take the\nvalues of the masses of the two quarks involved in the\nweak transition, and in the strong coupling constant, from\nperturbative QCD. It is an unambiguous prediction of\nHQET that R1(q2) > 1 as both the QCD and 1/m correc-\ntions are positive. For R2(q2), QCD corrections are small\nand 1/m corrections seem to decrease the value of the\nratio. HQET relates the form factors in semileptonic de-\ncays to pseudoscalar and vector particles as expressed in\nEquation (19.1.64). According to (Amundson and Ros-\nner, 1993), QCD corrections alone cannot explain the ra-\ntio B(D \u2192K\u2217e+\u03bde)/B(D \u2192K\u2212e+\u03bde) = 0.62 \u00b1 0.02 as\nthey have rather similar e\ufb00ects on all form factors.\nIn previous considerations it is assumed that the charm\nand also the strange quark behave as a heavy quark in\nc \u2192s\u2113+\u03bd\u2113decays. It is also possible to relate form factors\nin B and D semileptonic decays to light hadrons (Isgur\nand Wise, 1990a).\nResults on absolute values and on ratios of hadronic\nform factors evaluated at q2 = 0 are compared in Ta-\nble 19.1.19. In this table, BABAR measurements are quoted\nfor \ufb01xed values of the pole masses mV = 2.1 GeV/c2 and\nmV = 2.5 GeV/c2, and only experimental results cor-\nrected for the S-wave contribution are kept.\nThe HM\u03c7T model proposed by (Fajfer and Kamenik,\n2005, 2006) generalizes the approach of Becirevic and\nKaidalov and satis\ufb01es the scaling laws of obtained in\nthe in\ufb01nite mass limit as well as the known scaling at\nlarge energy of the outgoing kaon. Values from lattice\nQCD (Abada et al., 2003; Gill, 2002) are obtained us-\ning the quenched approximation. The relative accuracy\nof experimental measurements is typically 2% whereas it\nis around 10% for lattice QCD. Theoretical expectations\nagree with the general picture (A2(0) \u2264A1(0) < V (0))\nbut signi\ufb01cant di\ufb00erences are observed.\n19.1.5.10 The D+\ns \u2192K+K\u2212e+\u03bde decay\nUsing 214 fb\u22121 of data collected at the \u03a5(4S) resonance,\nBABAR measure the D+\ns\n\u2192K+K\u2212e+\u03bde channel decay\ncharacteristics, for events produced in the continuum (Au-\nbert, 2008be), in a similar manner as described above for\nD+ \u2192K\u2212\u03c0+e+\u03bde (Section 19.1.5.6).\nThe K+K\u2212mass distribution is displayed in Figure\n19.1.39(a). It contains about 25\u00d7103 signal events whereas\n0.98 0.99\n1\n1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08\n2\nEntries/2 MeV/c\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\n0.98 0.99\n1\n1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\ndata\nsignal\nB\nB\n \nc\nc\nuds\na)\n)\n2\n(GeV/c\n-\nK\n+\nK\nm\n0.98 0.99\n1\n1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08\n)\nK\ne\n cos(\n\u00d7\nEntries \n-50\n0\n50\n100\n150\n200\n250\n0.98 0.99\n1\n1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08\n-50\n0\n50\n100\n150\n200\n250\ndata\nMC \nb)\nFigure 19.1.39. From (Aubert, 2008be). a) K+K\u2212invariant\nmass distribution from D+\ns \u2192K+K\u2212e+\u03bde data and simulated\nevents. MC events have been normalized to the data luminosity\naccording to the di\ufb00erent cross sections. The arrows indicate\nthe selected K+K\u2212mass interval. In b), each event is weighted\nby the measured value of cos \u03b8K. Negative entries are produced\nby the c\u00afc background asymmetry in cos \u03b8K.\n\n551\nTable 19.1.20. Comparison between measured and expected\nvalues of the form factors in D+\ns\n\u2192\u03c6e+\u03bde decays, evalu-\nated at q2 = 0. The di\ufb00erent labels listed in the \ufb01rst col-\numn correspond to the following references: E653 (Kodama\net al., 1993), E687 (Frabetti et al., 1994b), CLEO II (Av-\nery et al., 1994a), E791 (Aitala et al., 1999a), FOCUS (Link\net al., 2004b), BABAR\n(Aubert, 2008be), HM\u03c7T (Fajfer and\nKamenik, 2005), UKQCD (Gill, 2002), and HPQCD (Donald,\nDavies, and Koponen, 2011). Results for K\u2217e+\u03bde correspond\nto the BABAR\nmeasurement (del Amo Sanchez, 2011a).\nA1(0)\nrV\nr2\nE653(1993)\n2.3+1.1\n\u22120.9 \u00b1 0.4\n2.1+0.6\n\u22120.5 \u00b1 0.2\nE687(1994)\n1.8 \u00b1 0.9 \u00b1 0.2 1.1 \u00b1 0.8 \u00b1 0.1\nCLEOII(1994)\n0.9 \u00b1 0.6 \u00b1 0.3 1.4 \u00b1 0.5 \u00b1 0.3\nE791(1999)\n2.27(35)(22)\n1.57(25)(19)\nFOCUS(2004)\n1.55(25)(15)\n0.71(20)(28)\nBABAR (2008)\n0.607(11)(19)(18)\n1.807(46)(65)\n0.816(36)(30)\nK\u2217e+\u03bde\n0.6200(56)(65)(71)\n1.493(14)(21)\n0.775(11)(11)\nHM\u03c7T\n0.61\n1.80\n0.52\nUKQCD(2001)\n0.63(2)\n1.35(7)\n0.98(8)\nHPQCD(2011)\n0.603(20)\n1.52(12)\n0.62(12)\nprevious experiments and CLEO-c have collected few hun-\ndred events only. The analysis focuses on the \u03c6e+\u03bde \ufb01nal\nstate in the K+K\u2212mass range between 1.01 and 1.03\nGeV/c2 for which accurate hadronic form factors normal-\nization and q2 dependence are measured. These results\nare given in Table 19.1.20 where they are compared with\nprevious measurements and those obtained for D+ \u2192\nK\n\u2217(892)0e+\u03bde.\nThe accuracy of experimental measurements compared\nto previous ones is improved by a factor \ufb01ve. The form\nfactors are de\ufb01ned in an analogous way as for the D+ \u2192\nK\n\u2217(892)0e+\u03bde decays in Section 19.1.5.6. Also the angular\nvariables are analogous, with a di\ufb00erence that \u03b8K is the\nangle between the K+ meson direction in the K+K\u2212rest\nframe and the K+K\u2212direction in the D+\ns rest frame. The\ncomparison between the values of the form factors mea-\nsured in the two channels D+ \u2192K\n\u2217(892)0e+\u03bde and D+\ns \u2192\n\u03c6e+\u03bde shows that they are compatible within uncertain-\nties, apart for the parameter V (0). This indicates that\nSU(3) violations are small. Recent unquenched LQCD\ncomputations (Donald, Davies, and Koponen, 2011) are\nin better agreement with data than previous unquenched\nresults (Gill, 2002).\nThe \u03c6 resonance is dominant in this K+K\u2212mass re-\ngion although a small S-wave component is measured, for\nthe \ufb01rst time, through its interference with the \u03c6 (see Fig-\nure 19.1.39(b). After integration over the \u03b8e and \u03c7 angular\nvariables, the di\ufb00erential decay rate is proportional to:\n|F1|2 + sin2 \u03b8K\n\u0010\n|F2|2 + |F3|2\u0011\n.\n(19.1.66)\nThe form factors Fi are function of q2, m2 and, \u03b8K. Con-\nsidering contributions from S\u2212and P\u2212wave of the K+K\u2212\nsystem, only the form factor F1 depends on \u03b8K:\nF1 = F10 + cos \u03b8KF11.\n(19.1.67)\nForm factors F10 and F11 correspond respectively to S\u2212\nand P-wave contributions. Using this last expression, the\n\ufb01rst term in Eq. (19.1.66) generates an interference be-\ntween the two wave components. The value of the pa-\nrameter which quanti\ufb01es this interference, r0 = (15.1 \u00b1\n2.6 \u00b1 1.0) GeV\u22121, is obtained with more than 5\u03c3 signi\ufb01-\ncance.118 This is the only experimental result on the con-\ntribution from the S-wave component, precisely in the\nK+K\u2212mass region of the \u03c6 meson. D+\ns decays can be\nused in B0\ns \u2192J/\u03c8\u03c6 analyses determining the CP violat-\ning phase \u03b2s. They can provide for an evaluation of the\nS-wave contribution in the \u03c6 resonance region, as pro-\nposed in (Stone and Zhang, 2009). Using measurements\nfrom CLEO-c of D+\ns \u2192f0e+\u03bde, f0 \u2192\u03c0+\u03c0\u2212, they con-\nclude that there could be, in the \u03c6 mass region, about\n10% contribution from the f0 in the K+K\u2212\ufb01nal state.\nSuch a large S-wave component can add uncertainties in\nthe measurement of \u03b2s. The direct measurement done in\nBABAR\ncontradicts these expectations because they ob-\ntain, within a range of \u00b110 MeV/c2 centered on the nom-\ninal \u03c6 meson mass, a relative contribution of the S-wave\nequal to (0.22+0.12\n\u22120.08 \u00b1 0.03)%. The S-wave decay rate in\nB0\ns \u2192J/\u03c8K+K\u2212channel, within the same K+K\u2212mass\ninterval is thus expected to be below 1%, in agreement\nwith the limit of 6% at 95%C.L. obtained by CDF (Aal-\ntonen et al., 2012c). The recent measurement by LHCb\n((4.2 \u00b1 1.5 \u00b1 1.8)% (Aaij et al., 2012h)) is less than 2\u03c3\naway form this limit.\n19.1.6 D+\ns leptonic decays\n19.1.6.1 Introduction\nThe cleanest transitions where a partial decay width can\nshow the manifestation of NP are D+\n(s) \u2192\u2113+\u03bd\u2113(\u2113= \u00b5, \u03c4).\nThe decay partial widths depend on a single hadronic pa-\nrameter, namely the decay constants fD(s):\n\u0393(D+\n(s) \u2192\u2113+\u03bd\u2113)\n(19.1.68)\n= G2\nF\n8\u03c0 f 2\nD(s)m2\n\u2113mD(s)\n \n1 \u2212\nm2\n\u2113\nm2\nD(s)\n!2 \f\fVcd(s)\n\f\f2 ,\nwhere GF is the Fermi coupling constant, m\u2113and mD(s)\nare the masses of the charged lepton and of the D meson,\nrespectively. Vcd(s) is the corresponding CKM matrix ele-\nment. As these decay channels are suppressed by helicity\nconservation, corresponding decay rates are proportional\nto the square of the lepton mass. Decays into electrons are\nnot observable whereas decays into \u03c4 leptons are favored\nin spite of the reduced phase-space.\n118 The precise de\ufb01nition of the r0 parameter arises from\nthe parameterization of F10 assuming f0 production: F10 =\nr0[pKKmDs/(1 \u2212\nq2\nm2\nA )][mf0g\u03c0/(m2\nf0 \u2212m2 \u2212imf0\u0393f0)], where\npKK is the momentum of the K+K\u2212system in the D+\ns rest\nframe.\n\n552\nD+ leptonic decays are Cabibbo suppressed and dif-\n\ufb01cult to measure at B factories meanwhile D+\ns leptonic\ndecays are measured in the muon and tau channels.\n19.1.6.2 BABAR and Belle measurements\nThe approach pioneered by Belle (Widhalm, 2006) for\nsemileptonic decays of D0 mesons is used by the two\nB-factory experiments to measure absolute leptonic de-\ncay branching fractions of Ds mesons. As an example, in\nthe BABAR analysis, the Ds meson production is tagged\nby considering events from the reaction e+e\u2212\u2192cc \u2192\nHcKXD\u2212\ns \u03b3; Hc is D0, D+, D\u2217or \u039bc exclusively recon-\nstructed, K a K+ or K0\nS and X a system of at most\nthree pions, including at most one \u03c00 with a total elec-\ntric charge appropriate to ensure the neutrality of the\noverall \ufb01nal state. The number of produced Ds mesons\nis obtained by considering the distribution in the recoil\nmass Mrecoil(HcKX\u03b3) which has a peak at the Ds mass\nfor signal events. The hadron Hc is reconstructed using\n15 modes. In addition to the size of the mass window,\nseveral other properties of the Hc candidate are used.\nThe center-of-mass (CM) momentum of the Hc must be\nat least 2.35 GeV/c in order to remove B meson back-\ngrounds. Particle identi\ufb01cation requirements are used on\nthe tracks, a cut is applied on the probability of the Hc\nvertex \ufb01t, and a minimum lab energy of \u03c00 photons is re-\nquested. Only HcKX\u03b3 candidates with a total charge, a\ncharm, and a strange quark content consistent with recoil-\ning from a D\u2212\ns , are selected from which the signal yield\nis extracted. A kinematic \ufb01t to each HcKX candidate is\nperformed and the Hc mass is constrained to its nominal\nvalue. The 4-momentum of the signal D\u2217\u2212\ns\nis extracted\nas the missing 4-momentum in the event. It is required\nthat the D\u2217\u2212\ns\ncandidate mass be within 2.5\u03c3 of the signal\npeak. A similar kinematic \ufb01t is performed with the signal\n\u03b3 included and with the mass recoiling against the HcKX\nconstrained to the nominal D\u2217\u2212\ns\nmass in order to deter-\nmine the D\u2212\ns 4-momentum. It is required that the D\u2212\ns\nmomentum exceeds 3 GeV/c and that its mass be greater\nthan 1.82 GeV/c2. Having reconstructed the inclusive D\u2212\ns\nsample one proceeds to the selection of D\u2212\ns\n\u2192\u00b5\u2212\u03bd\u00b5\nevents within that sample. The HcKX\u03b3 mass range be-\ntween 1.934 and 2.012 GeV/c2 is used and it is required\nthat there be exactly one more charged particle in the re-\nmainder of the event, and that it be identi\ufb01ed as a \u00b5\u2212.\nIn addition it is required that the extra neutral energy\nin the event, Eextra, be less than 1 GeV. Eextra is de-\n\ufb01ned as the total energy of clusters in the electromag-\nnetic calorimeter with individual energy greater than 30\nMeV and not overlapping with the HcKX\u03b3 candidate.\nSince the only missing particle in the event should be the\nneutrino, the distribution of Eextra is expected to peak\nat zero for signal events. To extract the signal yield, the\ndistribution of the mass squared of the system recoiling\nagainst the HcKX\u03b3\u00b5\u2212combination, M 2\nrecoil(HcKX\u03b3\u00b5\u2212)\nis used. The method is slightly modi\ufb01ed in the updated\nmeasurement by Belle (Zupanc, 2013b), as described in\nSection 19.1.2.2. The result is shown in Fig. 19.1.40. To\n0 2\n0\n0 2\n0 4\n0 6\n )\n4\n/c\n2\nEvents / ( 0.01 GeV\n0\n20\n40\n60\n)\n4\n/c\n2\n) (GeV\n\u00b5\n\u03b3\nfrag\nX\nfrag\nK\ntag\n(D\n2\nmiss\nM\n-0.2\n0\n0.2\n0.4\n0.6\nPull\n-5\n0\n5\nFigure 19.1.40. From (Zupanc, 2013b). M 2\nrecoil(HcKX\u03b3\u00b5\u2212)\nspectrum for D+\ns\n\u2192\u00b5+\u03bd\u00b5 candidates for the selected data\n(points with error bars). The solid green line shows the contri-\nbution of signal, the red dashed line the contribution of com-\nbinatorial background, while the contributions of D+\ns \u2192\u03c4 +\u03bd\u03c4\nand D+\ns \u2192K0K+ or \u03b7\u03c0+ are indicated by the full blue and\ndark gray histograms, respectively.\n (GeV) \nextra\nE\n0\n1\n2\n3\nEvents / 0.05 GeV\n50\n100\n0\n1\n2\n3\nEvents / ( 0.05 GeV )\n0\n50\n100\n150\n200\n(c) pion mode\n (GeV)\nECL\nE\n0\n1\n2\n3\nPull\n-5\n0\n5\nFigure 19.1.41. Eextra (EECL in case of Belle) distribution\nfor D\u2212\ns\n\u2192\u03c4 \u2212\u03bd\u03c4, \u03c4 \u2212\u2192e\u2212\u03bd\u03c4\u03bde (del Amo Sanchez, 2010g)\n(top) and for D\u2212\ns \u2192\u03c4 \u2212\u03bd\u03c4, \u03c4 \u2212\u2192\u03c0\u2212\u03bd\u03c4 (Zupanc, 2013b). The\npoints represent the data with statistical error bars. In the top\nplot the open histogram is from the \ufb01t, and the solid histogram\nis the background component from the \ufb01t. For the bottom plot\nthe lines represent di\ufb00erent components of the \ufb01t.\n\ufb01nd D\u2212\ns\n\u2192\u03c4 \u2212\u03bd\u03c4, \u03c4 \u2212\u2192\u00b5\u2212(e\u2212)\u03bd\u03c4\u03bd\u00b5(e) decays, events\n\n553\nTable 19.1.21. Statistics of D\u2217\u2212\ns\ntag and signal events mea-\nsured by Belle (Zupanc, 2013b) and BABAR (del Amo Sanchez,\n2010g).\nBelle\nBABAR\nintegrated lumi.\n913 fb\u22121\n521 fb\u22121\nD\u2217\u2212\ns\ntag\n(94.4 \u00b1 1.3 \u00b1 1.4) \u00d7 103 (67.2 \u00b1 1.5) \u00d7 103\nD\u2212\ns \u2192\u00b5\u2212\u03bd\u00b5\n492 \u00b1 26\n275 \u00b1 17\nD\u2212\ns \u2192\u03c4 \u2212\ne\u03bd\u03bd\u03bd\u03c4\n952 \u00b1 59\n408 \u00b1 42\nD\u2212\ns \u2192\u03c4 \u2212\n\u00b5\u03bd\u03bd\u03bd\u03c4\n758 \u00b1 48\n340 \u00b1 32\nD\u2212\ns \u2192\u03c4 \u2212\n\u03c0\u03bd\u03bd\u03c4\n496 \u00b1 35\nTable 19.1.22. Measured branching fractions of D+\ns \u2192\u2113+\u03bd\u2113\ndecays by Belle (Zupanc, 2013b) and BABAR (del Amo Sanchez,\n2010g).\nBelle\nBABAR\nB(D+\ns \u2192\u00b5+\u03bd\u00b5)[10\u22123] 5.31 \u00b1 0.28 \u00b1 0.20 6.02 \u00b1 0.38 \u00b1 0.34\nB(D+\ns \u2192\u03c4 +\u03bd\u03c4)[10\u22122]\n5.70 \u00b1 0.21+0.31\n\u22120.30\n5.00 \u00b1 0.35 \u00b1 0.49\nassociated with D\u2212\ns \u2192\u00b5\u2212\u03bd\u00b5 decays are removed by re-\nquiring m2\nr > 0.5 GeV2/c4. The Eextra distribution is used\nto extract the yield of signal events as illustrated in Fig-\nure 19.1.41 for the BABAR (del Amo Sanchez, 2010g) and\nBelle (Zupanc, 2013b) analysis.\nThese analyses have a 100 times lower tagging e\ufb03-\nciency than CLEO-c data collected at threshold. Yet this\nsmall e\ufb03ciency is compensated by the much higher reg-\nistered integrated luminosity. Measured statistics for the\nD\u2217\u2212\ns\ntag and the signals are given in Table 19.1.21. From\nthe obtained Ds \u2192\u2113\u03bd\u2113signal yields the branching frac-\ntions for individual modes are calculated and are given in\nTable 19.1.22.\n19.1.6.3 Measured and Expected fDs Values\nUsing Eq. (19.1.69), measured branching fractions of Ds\nleptonic decays are used to extract the value of the de-\ncay constant f expt.,SM\nDs\n. Results obtained by the di\ufb00erent\nexperiments are compared in Table 19.1.23. While mea-\nsurements at CLEO-c are statistically limited, systematic\nuncertainties related to the background control dominate\nthe methods developed at B factories which have a total\ncombined accuracy similar to CLEO-c. Having two results\nwith di\ufb00erent systematics and similar uncertainty is im-\nportant to have con\ufb01dence in the \ufb01nal result as it was al-\nready illustrated for the measurement of f +\nK(0) in charm\nsemileptonic decays. The averaged value of all measure-\nments is fDs = (257.5 \u00b1 4.6) MeV.\nNew physics can change Eq. (19.1.69) and the value\nof f expt.,SM\nDs\nextracted previously from data, in the Stan-\ndard Model framework, may di\ufb00er from QCD expecta-\ntions. Several LQCD collaborations using an unquenched\nformulation of QCD have computed the value of f QCD\nDs\n(see Table 19.1.24). These are in agreement with the mea-\nsured values within the uncertainties.\nAmong new physics models which can change the lep-\ntonic charm meson decay rate, there are the Two Higgs\nDoublet Model (2HDM) and the Minimal Supersymmet-\nric Model. (MSSM) In these models it is expected that the\nleptonic decay partial width, given in Equation (19.1.69)\nis modi\ufb01ed according to expressions given in (Akeroyd and\nMahmoudi, 2009) where references to previous studies can\nbe found. For the D+, the correction is negligible, whereas\nfor the D+\ns the relative variation on fDs is expected to be\nequal to:\nks = \u03b4(fDs)\nfDs\n= \u2212ms\nmc\n\u0012mDs tan \u03b2\nmH\n\u00132\n(19.1.69)\nfor tan \u03b2 >\np\nmc/ms \u22433. In this expression ms and mc\nare respectively the strange and the charm quark mass,\nmH is the charged Higgs boson mass and tan \u03b2 is the\nratio between the vacuum expectations of the two Higgs\ndoublets.\nBecause ks is negative, it is expected that f expt.,SM\nDs\n<\nf QCD\nDs\nin these models. First measurements from CLEO-\nc (f expt.,SM\nDs\n= 274(11) MeV) (Ecklund et al., 2008) and\nevaluations from the HPQCD collaboration (f QCD\nDs\n=\n241(3) MeV) (Follana, Davies, Lepage, and Shigemitsu,\n2008) were in the opposite direction. These circumstances\nprovide rather stringent limits on the parameters (mH and\ntan \u03b2) of the previous models. At present, measured and\nexpected values of fDs are more accurate and agree within\n1.5 standard deviation. Derived limits on model parame-\nters are thus less impressive. To have evidence (3\u03c3) for\nTable 19.1.23. Measured averaged values of the Ds decay\nconstant (averaging \u00b5\u03bd and \u03c4\u03bd \ufb01nal states) assuming that\ncorresponding decay rates are given by the Standard Model\n(f expt.,SM\nDs\n). References for the measurements are the follow-\ning: Belle (Zupanc, 2013b), BABAR (del Amo Sanchez, 2010g),\nand CLEO-c (Naik et al., 2009).\nBelle\nBABAR\nCLEOc\n255.5(4.2)(5.1) 258.6(6.4)(7.5) 259.0(6.2)(3.0)\nTable 19.1.24. Expected values of the Ds decay constant from\nunquenched LQCD (f QCD\nDs\n). The di\ufb00erent labels correspond to\nthe following references: HPQCD (Davies et al., 2010), PACS-\nCS (Namekawa et al., 2011), ETMC (Dimopoulos et al., 2012),\nand Fermilab MILC (Bazavov et al., 2011). Results obtained\nusing QCD sum rules correspond to SR1 (Bordes, Penarrocha,\nand Schilcher, 2005) and SR2 (Lucha, Melikhov, and Simula,\n2011).\nHPQCD\nPACS \u2212CS ETMC Fermilab MILC\nSR1\nSR2\n248.0(2.5)\n257(5)\n248(6)\n260.1(10.8)\n205(22) 245.3(16.3)\n\n554\nnew physics from these models, the following condition\nmust be satis\ufb01ed:\nmH\ntan \u03b2 < mDs\nr\nms\nmc\n1\n3\u03c3 .\n(19.1.70)\nThe parameter \u03c3 is the total relative uncertainty on fDs\ncoming from theory and measurements. At present \u03c3 \u223c\n3% and evidence for new physics can be obtained if\nmH\ntan \u03b2 <\n2.1 GeV/c2. In future, when precision of \u223c1% can be\nreached, this condition becomes:\nmH\ntan \u03b2 < 3.6 GeV/c2. Un-\nless the charged Higgs boson mass is rather low or the\nvalue of tan \u03b2 quite large, no new physics contributions\nare expected and measurements of leptonic charm decays\ntherefore provide stringent tests of lattice QCD calcula-\ntions.\nIt should be noted also that relative uncertainties com-\ning from external parameters as the \u03c4 mass, the D+\ns mass,\nthe value of |Vcs|, and the D+\ns lifetime have a total con-\ntribution of 0.7%. The largest contribution is from the\nD+\ns lifetime which needs therefore to be more accurately\nmeasured.\n19.1.7 Rare or forbidden charmed meson decays\n19.1.7.1 Measurement of the Branching Fractions of the\nRadiative Charm Decays D0 \u2192\u00afK\u22170\u03b3 and D0 \u2192\u03c6\u03b3\nIn the b-quark sector, radiative decay processes have pro-\nvided a rich \ufb01eld to study the Standard Model of particle\nphysics. These decays are dominated by short-range elec-\ntroweak processes, whereas long-range contributions are\nsuppressed. The situation is reversed in the charm sec-\ntor, where radiative decays are expected to be dominated\nlargely by non-perturbative processes, examples of which\nare shown schematically in Fig. 19.1.42. Long-range con-\ntributions to radiative charm decays are expected to in-\ncrease the branching fractions for these modes to values\nof the order of 10\u22125, whereas short-range interactions are\npredicted to yield rates at the 10\u22128 level. Given the ex-\npected dominance of long-range processes, radiative charm\ndecays provide a laboratory in which these QCD-based\ncalculations can be tested.\nNumerous theoretical models have been developed to\ndescribe these radiative charm decays. The two most com-\nprehensive studies (Burdman, Golowich, Hewett, and Pak-\nvasa, 1995; Fajfer, Prelovsek, and Singer, 1999) predict\nvery similar amplitudes for the dominant diagrams shown\nin Fig. 19.1.42.\nThe \ufb01rst observation of \ufb02avor changing radiative de-\ncay of charm mesons, D0 \u2192\u03c6\u03b3, was accomplished by\nBelle using 78 fb\u22121 (Abe, 2004c). To reduce the combi-\nnatorial background the measurement is performed using\nD\u2217+ \u2192D0\u03c0+ decays, and the \u03c6 meson is reconstructed\nin decays to K+K\u2212. The photons are required to have\nan energy in excess of 450 MeV/c2 (and not yielding a\n\u03c00 mass with any additional photon in the event - the\n\u03c00 veto). Furthermore, the | cos \u03b8hel| < 0.4 requirement,\nwhere \u03b8hel is the angle between the D0 and the K+ mesons\nu\nu\nD0\nc\nW +\n\u03c6\na)\ns\ns\nD0\n\u00afK\nP\nc)\nD0\n\u00afK\nD\n(d)\n*0\n0\nc\nu\n(b)\nW +\nd\nu\nK *0\ns \u00af\n\u03b3\n\u03b3\n\u03b3\n\u03b3\n*0\n*\n\u00af\n\u00af\nD0\n\u00af\n\u00af\nFigure 19.1.42. Feynman diagrams for the long-range elec-\ntromagnetic contributions to D0 \u2192V \u03b3, V = \u00afK\u22170, \u03c6. Figures\n(a) and (b) show sample vector dominance processes, while (c)\nand (d) are examples of pole diagrams, where the circles signify\nthe weak transition and P represents a pseudoscalar meson.\nin the \u03c6 meson rest frame, strongly suppresses contribu-\ntion of D0 \u2192\u03c00\u03b3/\u03b7\u03b3 decays to the \u03c6\u03b3 \ufb01nal state (for\nthe former, due to angular momentum conservation, the\ndistribution in cos \u03b8hel is proportional to cos2 \u03b8hel while\nin the latter it is proportional to 1 \u2212cos2 \u03b8hel). The yield\nof D0 \u2192\u03c6\u03b3 decays, as extracted from the \u03c6\u03b3 invariant\nmass distribution, is 27.6 \u00b1 7.4\n6.5 \u00b1 0.5\n1.0 with a signi\ufb01cance of\n5.4 standard deviations. The branching fraction is deter-\nmined using D0 \u2192K+K\u2212for normalization and is found\nto be B(D0 \u2192\u03c6\u03b3) = (2.60 \u00b1 0.70\n0.61 \u00b1 0.15\n0.17) \u00d7 10\u22125. The\nlargest contribution to the systematic uncertainty is due\nto the uncertainty of the B(D0 \u2192K+K\u2212) (\u00b13.40%) and\nthe choice of the \ufb01tting model and background estimation\n(+2.46% -3.99%).\nBABAR has performed a measurement of the branching\nfractions for the Cabibbo-favored radiative decay, D0 \u2192\n\u00afK\u22170\u03b3, and the Cabibbo-suppressed radiative decay, D0 \u2192\n\u03c6\u03b3 (Aubert, 2008t).\nThe analysis is based on 387.1 fb\u22121 of data. They re-\nconstruct radiative D0 \u2192V \u03b3, V = \u00afK\u22170, \u03c6 decays using\nthe charged decay modes of the vector meson, \u00afK\u22170 \u2192\nK\u2212\u03c0+ (\u03c6 \u2192K\u2212K+). They form \u00afK\u22170 (\u03c6) candidates\nfrom pairs of oppositely charged tracks identi\ufb01ed as K\u2212\u03c0+\n(K\u2212K+) and accept any K\u2212\u03c0+ (K\u2212K+) candidates with\ninvariant mass in the range 0.848 to 0.951 GeV/c2 (1.01\nto 1.03 GeV/c2). The signi\ufb01cant background from \u03c00 \u2192\n\u03b3\u03b3 decays is suppressed by rejecting a photon candidate\nwhich, when paired with another photon in the event, re-\nsults in an invariant mass consistent with the \u03c00 mass,\n(0.115 < M(\u03b3\u03b3) < 0.150) GeV/c2. Background from ran-\ndom D0 \u2192V \u03b3 candidates is reduced by requiring that the\nD0 candidate be a product of the decay D\u2217+ \u2192D0\u03c0+\ns .\nThe mass di\ufb00erence, \u2206M = M(V \u03b3\u03c0+\ns ) \u2212M(V \u03b3) is re-\nquired to be in the range (0.1435 < \u2206M < 0.1475) GeV/c2.\nCombinatoric background from B \u00afB events is reduced to\na negligible level by requiring that the CM momentum of\nthe D\u2217+ candidate be greater than 2.62 GeV/c.\nThe dominant background in the sample of D0 \u2192\u00afK\u22170\u03b3\ncandidates results from D0 \u2192K\u2212\u03c0+\u03c00 decays, where one\nof the photons from the \u03c00 decay is paired with the kaon\nand pion from the D0 decay to closely mimic the signal\nmode. As described above, the \u03c00 veto suppresses such\n\n555\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n)\n2\n) (GeV/c\n\u03b3\n\u03c6\nM(\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.005 GeV/c\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nGeneric Background (BG)\n Background\n0\n\u03c0\n \n\u03c6 \n\u2192\n \n0\nD\n Background\n\u03b7\n \n\u03c6 \n\u2192\n \n0\nD\nBG Fit\n+BG Fit\n0\n\u03c0\n \n\u03c6 \n\u2192\n \n0\nD\nTotal Fit\nData\n(a) The \u03c6\u03b3 invariant mass distribution.\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n0\n50\n100\n150\n200\n250\n300\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n0\n50\n100\n150\n200\n250\n300\n)\n2\n) (GeV/c\n\u03b3\n*0\nK\nM(\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.002 GeV/c\n0\n50\n100\n150\n200\n250\n300\nGeneric Background (BG)\n Background\n0\n\u03c0 \n*0\nK\n \n\u2192\n \n0\nD\n Background\n\u03b7\n \n*0\nK\n \n\u2192\n \n0\nD\nBG Fit\n+BG Fit\n0\n\u03c0 \n*0\nK\n \n\u2192\n \n0\nDTotal Fit\nData\n(b) The \u00afK\u22170\u03b3 invariant mass distribution.\nFigure 19.1.43. From (Aubert, 2008t). Invariant mass distri-\nbutions for data (points) and simulated events (histograms).\nThe curves show the \ufb01t results and the individual signal and\nbackground contributions. BG refers to the combinatoric back-\nground.\nevents but, given the large branching fraction of this mode,\nB(D0 \u2192K\u2212\u03c0+\u03c00) = (13.5\u00b10.6)% (Beringer et al., 2012),\na signi\ufb01cant number of such candidates survives. It is pos-\nsible to separate this background from signal on a statis-\ntical basis because of di\ufb00erences in the K\u2212\u03c0+\u03b3 invariant\nmass distribution. An additional background arises from\nD0 \u2192\u00afK\u22170\u03b7 events where the \u03b7 decays to two photons.\nThis contribution peaks well below the nominal D0 mass.\nThe impact of both D0 \u2192\u00afK\u22170\u03c00 and D0 \u2192\u00afK\u22170\u03b7 is\nfurther reduced by using the \u00afK\u22170 helicity angle \u03b8H. The\nhelicity angle is de\ufb01ned as the angle between the momen-\ntum of the \u00afK\u22170 meson parent particle (D0) and the mo-\nmentum of the \u00afK\u22170 daughter kaon as measured in the\n\u00afK\u22170 rest frame. Based on a Monte Carlo study an asym-\nmetric selection of \u22120.30 < cos \u03b8H < 0.65 is chosen to\nmaximize the signal signi\ufb01cance. Similarly, but to a lesser\nextent, the signal of the Cabibbo-suppressed radiative de-\ncay D0 \u2192\u03c6\u03b3 is obscured by backgrounds from D0 \u2192\u03c6\u03c00\nand D0 \u2192\u03c6\u03b7 decays. The D0 \u2192\u00afK\u22170\u03b3 yield is extracted\nusing an unbinned extended maximum likelihood method\n(E-MLM) 11 to \ufb01t the M( \u00afK\u22170\u03b3) invariant mass spectrum.\nThe yield of D0 \u2192\u03c6\u03b3 events is extracted using an E-MLM\nto \ufb01t the two dimensional distribution of invariant mass,\nM(\u03c6\u03b3), and helicity, cos \u03b8H.\nA Crystal Ball line shape (see Chapter 7) is used to\nmodel the invariant mass distributions for D0 \u2192\u00afK\u22170\u03b3\n(D0 \u2192\u03c6\u03b3) signal events, and background re\ufb02ections\nfrom D0 \u2192K\u2212\u03c0+\u03c00 (D0 \u2192\u03c6\u03c00) decays. The \ufb01t re-\nsults from data and expected signal and background con-\ntributions from MC are shown in Fig. 19.1.43. The result-\ning branching fractions relative to the well-studied decay\nD0 \u2192K\u2212\u03c0+ are B(D0 \u2192\u00afK\u22170\u03b3)/B(D0 \u2192K\u2212\u03c0+) =\n(8.43 \u00b1 0.51 \u00b1 0.70) \u00d7 10\u22123 and B(D0 \u2192\u03c6\u03b3)/B(D0 \u2192\nK\u2212\u03c0+) = (7.15 \u00b1 0.78 \u00b1 0.69) \u00d7 10\u22124.\nThis is the \ufb01rst measurement of B(D0 \u2192\u00afK\u22170\u03b3). In the\ncontext of the vector meson dominance (VMD) model the\nlargest contribution to radiative D0 decays is expected to\ncome from a virtual \u03c10 coupling directly to a single pho-\nton, leading to the prediction that the branching ratios\nB(D0 \u2192\u03c6\u03b3)/B(D0 \u2192\u00afK\u22170\u03b3) and B(D0 \u2192\u03c6\u03c10)/B(D0 \u2192\n\u00afK\u22170\u03c10) should be equal (Burdman, Golowich, Hewett, and\nPakvasa, 1995). Comparing these measurements of the ra-\ndiative D0 decays with the current world averages they\n\ufb01nd a good agreement with the prediction. Assuming all\ncontributions are from VMD type processes and under the\nassumption that the \u03c10 meson is transversely polarized,\nas has been con\ufb01rmed experimentally for D0 \u2192\u00afK\u22170\u03c10,\none expects B(D0 \u2192V \u03b3) \u2248\u03b1EMB(D0 \u2192V \u03c10) where\n\u03b1EM = 1/137 is the \ufb01ne structure constant (Burdman,\nGolowich, Hewett, and Pakvasa, 1995). However they \ufb01nd,\nfor this branching fraction, about a factor of three larger\nthan the VMD prediction. This indicates that enhance-\nments from processes other than VMD are observed, which\nmight be explained by incomplete cancellation between\npole diagrams.\n19.1.8 D0 \u2192\u2113+\u2113\u2212\nIn the Standard Model, the \ufb02avor-changing neutral cur-\nrent (FCNC) decays D0 \u2192e+e\u2212and D0 \u2192\u00b5+\u00b5\u2212\nare highly suppressed by the Glashow-Iliopoulos-Maiani\n(GIM) mechanism (Glashow, Iliopoulos, and Maiani,\n1970) (Chapter 16). Their decay branching fractions have\nbeen estimated to be less than 10\u221213 even with long-\ndistance processes included. This prediction is orders of\nmagnitude beyond the reach of current experiments. Fur-\nthermore, the lepton-\ufb02avor-violating (LFV) decay D0 \u2192\ne\u00b1\u00b5\u2213is forbidden in the SM in the limit of vanishing neu-\ntrino masses. These decays are in principle allowed due to\na non-zero neutrino mass, but branching fractions are ex-\npected to be even much smaller than those of D0 \u2192\u2113+\u2113\u2212.\nSome extensions to the Standard Model can enhance\nthe FCNC processes by many orders of magnitude. For ex-\nample, R-parity violating supersymmetry can increase the\nbranching fractions of D0 \u2192e+e\u2212and D0 \u2192\u00b5+\u00b5\u2212to as\nhigh as 10\u221210 and 10\u22126, respectively (Burdman, Golowich,\nHewett, and Pakvasa, 2002). The same model also predicts\nthe D0 \u2192e\u00b1\u00b5\u2213branching fraction to be of the order of\n10\u22126. The upper bounds on the predicted branching frac-\ntions of D0 \u2192\u00b5+\u00b5\u2212and D0 \u2192e\u00b1\u00b5\u2213are close to the\n\n556\ncurrent experimental sensitivities. As a result, searching\nfor the FCNC and LFV decays in the charm sector is a\npotential way to test the SM and explore new physics.\nSimilar arguments hold for rare K and B decays, but the\ncharm decay is unique since it is sensitive to new physics\ncoupling to the up-quark sector (similar as the D0 mixing,\nsee Section 19.2).\nBoth BABAR and Belle performed a search for the de-\ncay of D0 \u2192e+e\u2212, D0 \u2192\u00b5+\u00b5\u2212, and D0 \u2192e\u00b1\u00b5\u2213. A \ufb01rst\nanalysis by BABAR was based on 122 fb\u22121 of data (Aubert,\n2004z). Recently, a new anaysis has been performed using\n468 fb\u22121 of data (Lees, 2012v). The measurement by Belle\nuses 660 fb\u22121 of data (Petric, 2010).\nThe D0 \u2192\u2113+\u2113\u2212(\u2113= e, \u00b5) branching ratio is deter-\nmined by\nB(D0 \u2192\u2113+\u2113\u2212) = S(Nobs \u2212Nbg),\n(19.1.71)\nwhere Nobs is the number of D0 \u2192\u2113+\u2113\u2212candidates ob-\nserved, Nbg is the expected background and S is the sen-\nsitivity factor, de\ufb01ned as:\nS \u2261B(D0 \u2192\u03c0+\u03c0\u2212) 1\nN\u03c0\u03c0\n\u03f5\u03c0\u03c0\n\u03f5\u2113\u2113\n.\n(19.1.72)\nHere B(D0 \u2192\u03c0+\u03c0\u2212) is the D0 \u2192\u03c0+\u03c0\u2212branching frac-\ntion, N\u03c0\u03c0 is the number of reconstructed D0 \u2192\u03c0+\u03c0\u2212\ndecays, \u03f5\u2113\u2113and \u03f5\u03c0\u03c0 are the e\ufb03ciencies for the correspond-\ning decay mode. They choose D0 \u2192\u03c0+\u03c0\u2212as the nor-\nmalization mode because it is kinematically similar to\nD0 \u2192\u2113+\u2113\u2212and therefore many common systematic un-\ncertainties cancel in the calculation of the e\ufb03ciency ratio\n\u03f5\u03c0\u03c0/\u03f5\u2113\u2113.\nA pair of oppositely charged tracks is selected to form\na D0 \u2192\u2113+\u2113\u2212or D0 \u2192\u03c0+\u03c0\u2212candidate with parti-\ncle identi\ufb01cation applied 5. In BABAR, the average elec-\ntron and muon e\ufb03ciencies are about 95 % and 60 %, and\ntheir hadron misidenti\ufb01cation probabilities are measured\nfrom \u03c4 decay control samples to be around 0.2 % and\n2.0 %. The corresponding single pion identi\ufb01cation e\ufb03-\nciency is around 90 %. At Belle, the average muon and\nelectron identi\ufb01cation e\ufb03ciencies are around 90 % with\nless than 1.5 % and 0.3 % pion misidenti\ufb01cation, respec-\ntively, whereas the pion identi\ufb01cation e\ufb03ciency is around\n83 %. In the analysis, only D0 mesons originating from the\nfragmentation of charm quark in the continuum e+e\u2212\u2192\ncc are considered. The inclusion of D0 mesons from B\nmeson decays o\ufb00ers no advantage because of their higher\ncombinatorial background. As a result, Belle (BABAR) re-\nquires the momentum of each D0 (D\u2217+) candidate in the\ncenter-of-mass frame of the collision to be larger than\n2.5 GeV/c (2.4 GeV/c). In order to further reduce the back-\nground, the D0 candidate is required to originate from a\nD\u2217+ \u2192D0\u03c0+ decay.\nCandidate D0 mesons are selected using two kinematic\nobservables: the invariant mass of the D0 decay product,\nm\u2113\u2113, and the energy released in the D\u2217+ decay, \u03b4m =\nmD\u2217+ \u2212m\u2113\u2113\u2212m\u03c0, where mD\u2217+ is the invariant mass of\nthe D0\u03c0+ combination and m\u03c0 is the \u03c0+ mass. Additional\nexperimental observables are exploited in order to increase\nthe search sensitivities. The BABAR analysis makes use a\nlinear combination (Fisher discriminant 9) of the following\n\ufb01ve variables to reduce the combinatorial BB background:\n\u2013 The measured D0 \ufb02ight length divided by its uncer-\ntainty.\n\u2013 The value of cos \u03b8hel, where \u03b8hel is de\ufb01ned as the angle\nbetween the momentum of the positively-charged D0\ndaughter and the boost direction from the lab frame\nto the D0 rest frame, all in the D0 rest frame.\n\u2013 The missing transverse momentum with respect to the\nbeam axis.\n\u2013 The ratio of the 2nd and 0th Fox-Wolfram moments.\n\u2013 The D0 momentum in the CM frame.\nThe Belle analysis uses the maximum allowed missing en-\nergy Emiss in the event. MC study shows that the semi-\nleptonic B decay, which represent one of the dominant\nbackgrounds, typically have large Emiss due to undetected\nneutrino.\nIn order to avoid biases, a blind analysis techniques\n(see Section 14) has been adopted. All events inside the D0\nsignal region are blinded until the \ufb01nal event selection cri-\nteria are established. The estimate of the number of combi-\nnatorial background in the signal window is done using the\nobserved event distribution in the control region. In the\nBABAR analysis they use a sideband region above the sig-\nnal region in the D0 mass ([1.90, 2.05] GeV) in a wide \u2206m\nwindow ([0.141, 0.149] GeV) while the Belle measurement\nmakes use of the region de\ufb01ned by \u2206m > 1 MeV/c2. The\npeaking background in the signal region due to misidenti\ufb01-\ncation of D0 \u2192\u03c0+\u03c0\u2212decay is calculated by using the lep-\nton misidenti\ufb01cation rates measured from a control data\nsample. Finally, they determine the optimal selection cri-\nteria by maximizing the value \u03f5\u2113\u2113/Nsens, where Nsens is the\naveraged 90 % con\ufb01dence level upper limit on the number\nof observed signal events that would be obtained by an en-\nsemble of experiments with the expected background and\nno real signal (Feldman and Cousins, 1998).\nThe number of D0 \u2192\u03c0+\u03c0\u2212candidates in the data,\nN\u03c0\u03c0, is extracted by \ufb01tting their invariant mass distri-\nbution with a binned maximum likelihood \ufb01t. The signal\nTable 19.1.25. From Lees (2012v) and Petric (2010). Sum-\nmary of the number of expected background events (Nbg), the\nsensitivity factor (S), number of observed events (Nobs), and\nthe branching fraction upper limits at the 90 % C.L. for each\ndecay mode. The errors quoted include statistical and system-\natic uncertainties.\nD0 \u2192e+e\u2212\nD0 \u2192\u00b5+\u00b5\u2212\nD0 \u2192e\u00b1\u00b5\u2213\nBABAR\nNbg\n1.01 \u00b1 0.39\n3.88 \u00b1 0.35\n1.42 \u00b1 0.26\nNobs\n1\n8\n2\nS [10\u22129]\n53.4 \u00b1 0.22\n80.6 \u00b1 0.44\n73.9 \u00b1 0.4\nUL\n1.7 \u00d7 10\u22127\n[0.6, 8.1] \u00d7 10\u22127\n3.3 \u00d7 10\u22127\nBelle\nNbg\n1.7 \u00b1 0.2\n3.1 \u00b1 0.1\n2.6 \u00b1 0.2\nNobs\n0\n2\n3\nS [10\u22129]\n64.7(1 \u00b1 6.4%)\n48.4(1 \u00b1 5.3%)\n54.8(1 \u00b1 4.8%)\nUL\n7.9 \u00d7 10\u22128\n1.4 \u00d7 10\u22127\n2.6 \u00d7 10\u22127\n\n557\ne\ufb03ciencies of D0 \u2192\u2113+\u2113\u2212and D0 \u2192\u03c0+\u03c0\u2212are evaluated\nusing a Monte Carlo simulation.\nThe branching fraction upper limits (UL) have been\ncalculated including all uncertainties using an extended\nversion (Conrad, Botner, Hallgren, and Perez de los Heros,\n2003) of the Feldman-Cousins method (Feldman and\nCousins, 1998). Systematic uncertainties are found to have\na negligible e\ufb00ect on the limits. The results are listed in\nTable 19.1.25.\n19.1.8.1 Search for the decay D0 \u2192\u03b3\u03b3 and Measurement\nof the branching fraction for D0 \u2192\u03c00\u03c00\nIn the Standard Model \ufb02avor-changing neutral currents\n(FCNC) are forbidden at tree level (Glashow, Iliopoulos,\nand Maiani, 1970). These decays are allowed at higher or-\nder (Hurth, 2003) and have been measured in the K and\nB meson systems. In the charm sector, however, the small\nmass di\ufb00erence between down-type quarks of the \ufb01rst two\nfamilies translates to a large suppression at the loop level\nfrom the GIM mechanism. To date, measurements of ra-\ndiative decays of charm mesons are consistent with results\nof theoretical calculations that include both short-distance\nand long-distance contributions and predict decay rates\nseveral orders of magnitude below the sensitivity of cur-\nrent experiments. While these rates are small, it has been\npredicted that new physics (NP) processes can lead to sig-\nni\ufb01cant enhancements (Prelovsek and Wyler, 2001).\nBABAR has searched for the rare decay of the D0 meson\nto two photons, D0 \u2192\u03b3\u03b3, and measured the branching\nfraction for a D0 meson decaying to two neutral pions,\nB(D0 \u2192\u03c00\u03c00) (Lees, 2012u). The data sample analyzed\ncorresponds to an integrated luminosity of 470.5 fb\u22121.\nThe D0 \u2192K0\nS\u03c00 decay is chosen for this purpose due to its\nlarge branching fraction of (1.22\u00b10.05)% (Beringer et al.,\n2012) and partial cancellation of systematic uncertainties.\nThe invariant \u03b3\u03b3 mass distribution obtained from the\nD0 \u2192\u03b3\u03b3 analysis is shown in Fig. 19.1.44 together with\nprojections of the likelihood \ufb01t and the individual signal\nand background contributions. The signal yield is \u22126 \u00b1\n15, consistent with no D0 \u2192\u03b3\u03b3 events. This result is\nconverted to a branching fraction for D0 \u2192\u03b3\u03b3 relative to\nthe D0 \u2192K0\nS\u03c00 reference mode using\nB(D0 \u2192\u03b3\u03b3) =\n1\n\u03b5\u03b3\u03b3 N(D0 \u2192\u03b3\u03b3)\n1\n\u03b5D0\u2192K0\nS \u03c00 N(D0 \u2192K0\nS\u03c00)\n\u00d7B(D0 \u2192K0\nS\u03c00), (19.1.73)\nwhere N and \u03b5 are the yield and e\ufb03ciency of the respec-\ntive modes and B(D0 \u2192K0\nS\u03c00) is the known D0 \u2192K0\nS\u03c00\nbranching fraction. In this analysis the D0 \u2192K0\nS\u03c00 signal\nyield is 126599 \u00b1 568 events. They \ufb01nd B(D0 \u2192\u03b3\u03b3) =\n(\u22120.49 \u00b1 1.23 \u00b1 0.02) \u00d7 10\u22126 where the errors are the\nstatistical uncertainty and the uncertainty in the refer-\nence mode branching fraction, respectively. Therefore they\nplace an upper limit on the branching fraction for the\ndecay of a D0 meson to two photons, B(D0 \u2192\u03b3\u03b3) <\n2.2 \u00d7 10\u22126, at 90% con\ufb01dence level.\n)\n2\n) (GeV/c\n\u03b3\n\u03b3\nm(\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n )\n2\nEvents / ( 0.01 GeV/c\n0\n5\n10\n15\n20\n25\n30\n35\n/27 = 1.53\n2\n\u03c7\nFit Pull\n-5\n0\n5\nFigure 19.1.44. From (Lees, 2012u). The \u03b3\u03b3 mass distribu-\ntion for D0 \u2192\u03b3\u03b3 candidates in data (data points). The curves\nshow the result of an unbinned maximum likelihood \ufb01t to the\nmeasured mass distribution. The solid (blue) line shows the re-\nsult of the \ufb01t, indicating a slightly negative signal yield (consis-\ntent with no signal). The long-dashed (red) curve corresponds\nto combinatoric background component, and the small-dash\npink curve corresponds to the combinatoric background plus\nD0 \u2192\u03c00\u03c00 background shape. The \u03c72 value is determined\nfrom binned data and is provided as a goodness-of-\ufb01t measure.\nThe pull distribution shows di\ufb00erences between the data and\nthe solid blue curve with values and errors normalized to the\nPoisson error.\nThe invariant mass distribution for events in the D0 \u2192\n\u03c00\u03c00 analysis is shown in Fig. 19.1.45. The signal yield for\nD0 \u2192\u03c00\u03c00 is 26010 \u00b1 304 events. For D0 \u2192K0\nS\u03c00 the\nsignal yield is 103859 \u00b1 392 events. Adjusting Eq. (19.1.73)\nfor the D0 \u2192\u03c00\u03c00 case this yield can be converted to a\nbranching fraction and obtain B(D0 \u2192\u03c00\u03c00) = (8.4 \u00b1\n0.1 \u00b1 0.3) \u00d7 10\u22124. The \ufb01rst error denotes the statistical\nuncertainty and the second error re\ufb02ects the uncertainties\nin the reference mode branching fraction.\n)\n2\n) (GeV/c\n0\n\u03c0\n0\n\u03c0\nm(\n1.65\n1.7\n1.75\n1.8\n1.85\n1.9\n1.95\n2\n2.05\n )\n2\nEvents / ( 0.008 GeV/c\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\n/47 = 0.94\n2\n\u03c7\nFit Pull\n-5\n0\n5\nFigure 19.1.45. From (Lees, 2012u). The \u03c00\u03c00 mass distri-\nbution for D0 \u2192\u03c00\u03c00 candidates in data (data points). The\ncurves show the result of the unbinned maximum likelihood \ufb01t\nto the measured mass distribution. The solid (blue) line shows\nthe result of the \ufb01t. The long-dashed (red) curve corresponds\nto the combinatoric background component. The \u03c72 value is\ndetermined from binned data and is provided as a goodness-\nof-\ufb01t measure. The pull distribution shows di\ufb00erences between\nthe data and the solid blue curve with values and errors nor-\nmalized to the Poisson error.\n\n558\nTable 19.1.26. From (Lees, 2012u). Summary of predictions and measured values or limits for branching fractions for D0 \u2192\u03b3\u03b3\nand D0 \u2192\u03c00\u03c00.\nTheoretical predictions\nMode\nValue\nReference\nD0 \u2192\u03b3\u03b3 (SM,VMD)\n\u2248(3.5 +4.0\n\u22122.6) \u00d7 10\u22128\n(Burdman, Golowich, Hewett, and Pakvasa, 2002)\nD0 \u2192\u03b3\u03b3 (SM,HQ\u03c7PT)\n(1.0 \u00b1 0.5) \u00d7 10\u22128\n(Fajfer, Singer, and Zupan, 2001)\nD0 \u2192\u03b3\u03b3 (MSSM)\n6 \u00d7 10\u22126\n(Prelovsek and Wyler, 2001)\nExperimental results\nMode\nValue\nReference\nD0 \u2192\u03b3\u03b3 (2002)\n< 2.9 \u00d7 10\u22125\n(Coan et al., 2003)\nD0 \u2192\u03b3\u03b3 (2012)\n< 2.2 \u00d7 10\u22126\n(Lees, 2012u)\nD0 \u2192\u03c00\u03c00 (2006)\n(7.9 \u00b1 0.8) \u00d7 10\u22124\n(Rubin et al., 2006)\nD0 \u2192\u03c00\u03c00 (2010)\n(8.1 \u00b1 0.5) \u00d7 10\u22124\n(Mendez et al., 2010)\nD0 \u2192\u03c00\u03c00 (2012)\n(8.4 \u00b1 0.1) \u00d7 10\u22124\n(Lees, 2012u)\nA summary of the relevant branching fractions is shown\nin Table 19.1.26.\n19.1.9 Search for rare or forbidden semileptonic charm\ndecays\nBABAR has performed a search for charm semileptonic de-\ncays that are either forbidden or heavily suppressed in the\nStandard Model (Lees, 2011k). The decays are of the form\nX+\nc \u2192h\u00b1\u2113\u2213\u2113(\u2032)+, where X+\nc is a charm hadron (D+, D+\ns ,\nor \u039b+\nc ), and \u2113(\u2032)\u00b1 is an electron or muon. For D+ and D+\ns\nmodes, h\u00b1 can be a pion or kaon, while for \u039b+\nc modes it\nis a proton. Decay modes with oppositely charged leptons\nof the same lepton \ufb02avor are examples of \ufb02avor-changing\nneutral current (FCNC) processes, which are expected to\nbe very rare because they cannot occur at tree level in\nthe SM. Decay modes with two oppositely charged lep-\ntons of di\ufb00erent \ufb02avor correspond to lepton-\ufb02avor violat-\ning (LFV) decays and are essentially forbidden in the SM\nbecause they can occur only through lepton mixing. De-\ncay modes with two leptons of the same charge are lepton-\nnumber violating (LNV) decays and are forbidden in the\nSM. Hence, decays of the form X+\nc\n\u2192h\u00b1\u2113\u2213\u2113(\u2032)+ pro-\nvide sensitive tools to investigate physics beyond the SM.\nThe most stringent existing upper limits on the branch-\ning fractions for X+\nc \u2192h\u00b1\u2113\u2213\u2113(\u2032)+ decays range from 1 to\n700 \u00d7 10\u22126 and do not exist for most of the \u039b+\nc decays.\nCharm hadron candidates are formed from one track\nidenti\ufb01ed as either a pion, kaon, or proton (h) and two\ntracks, each of which is identi\ufb01ed as an electron or a muon\n(\u2113\u2113(\u2032)). The total charge of the three tracks is required to\nbe \u00b11. For three-track combinations with a pion or kaon\ntrack, the h\u2113\u2113(\u2032) invariant mass is required to lie between\n1.7 and 2.1 GeV/c2; for combinations with a proton, the in-\nvariant mass is required to lie between 2.2 and 2.4 GeV/c2.\nThe combinatorial background at low p\u2217is very large\nand they therefore select charm hadron candidates with\np\u2217greater than 2.5 GeV/c. The main backgrounds remain-\ning after this selection are QED events and semileptonic\nB and charm decays, particularly events with two semi-\nleptonic decays.\nThe QED events are mainly radiative Bhabha, initial-\nstate radiation, and two-photon events, which are all rich\nin electrons. These events are easily identi\ufb01ed by their low\nmultiplicity and/or highly jet-like topology. They strongly\nsuppress this background by requiring at least \ufb01ve tracks\nin the event and that the hadron candidate be inconsis-\ntent with the electron hypothesis. The background from\nsemileptonic B and charm decays is also suppressed by\nrequiring the two leptons to be consistent with a common\norigin.\nFor low e+e\u2212invariant mass there is a signi\ufb01cant\nbackground contribution from photon conversions and \u03c00\ndecays to e+e\u2212\u03b3. These are both removed by requiring\nm(e+e\u2212) > 200 MeV/c2.\nFor the D+\n(s) \u2192\u03c0+\u2113+\u2113\u2212decay modes, they exclude\nevents with 0.95 < m(e+e\u2212) < 1.05 GeV/c2 and 0.99 <\nm(\u00b5+\u00b5\u2212) < 1.05 GeV/c2 to reject decays through the \u03c6\nresonance.\nAfter the initial event selection, signi\ufb01cant combinato-\nrial background contributions remain from semileptonic B\ndecays and other sources. The \ufb01nal candidate selection is\nperformed by forming a likelihood ratio RL and requiring\nthe ratio to be greater than a minimum value Rmin\nL\n4.\nThe following three discriminating variables are used\nin the likelihood ratio: charm hadron candidate p\u2217, total\nreconstructed energy in the event and \ufb02ight length signif-\nicance.\nExtended, unbinned, maximum-likelihood \ufb01ts are ap-\nplied to the invariant-mass distributions for the h\u00b1\u2113\u2213\u2113(\u2032)+\ncandidates. The measured signal yields are converted into\nbranching ratios by normalizing them to the yields of\nknown charm decays. For the D+ and D+\ns mesons, they\nuse decays to \u03c0+\u03c6 as normalization modes. For the \u039b+\nc ,\nthey use \u039b+\nc \u2192pK\u2212\u03c0+ as the normalization mode. The\nupper limits are set using a Bayesian approach with a \ufb02at\nprior for the event yield in the physical region. The upper\nlimit on the signal yield is de\ufb01ned as the number of signal\nevents for which the integral of the likelihood from zero\nevents to that number of events is 90% of the integral from\nzero to in\ufb01nity. The systematic uncertainties are included\nin the likelihood as additional nuisance parameters. Exam-\nples of h\u2113\u2113(\u2032) invariant-mass distributions for signal can-\ndidates are in Figs 19.1.46 and 19.1.47. The signal yields\n\n559\n]\n2\n) [GeV/c\n-e\n+\nM(pe\n2.25\n2.3\n2.35\n \n2\nEntries per 10 MeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n-e\n+\npe\n\u2192\nc\n\u039b\n]\n2\n) [GeV/c\n-\n\u00b5\n+\n\u00b5\nM(p\n2.25\n2.3\n2.35\n-\n\u00b5\n+\n\u00b5\np\n\u2192\nc\n\u039b\n]\n2\n) [GeV/c\n-e\n+\n\u00b5\nM(p\n2.25\n2.3\n2.35\n-e\n+\n\u00b5\np\n\u2192\nc\n\u039b\n]\n2\n) [GeV/c\n-\n\u00b5\n+\nM(pe\n2.25\n2.3\n2.35\n-\u00b5\n+\npe\n\u2192\nc\n\u039b\nFigure 19.1.46. From (Lees, 2011k). Invariant-mass distributions for \u039b+\nc \u2192p\u2113+\u2113(\u2032)\u2212candidates. The solid lines are the results\nof the \ufb01ts. The background component for the dimuon mode in which muon candidates arise from hadrons misidenti\ufb01ed is shown\nas a dashed curve.\nTable 19.1.27. From (Lees, 2011k). Signal yields for the \ufb01ts to the 35 X+\nc \u2192h\u00b1\u2113\u2213\u2113(\u2032)+ event samples. The \ufb01rst error is the\nstatistical uncertainty and the second is the systematic uncertainty. The third column lists the estimated signal e\ufb03ciency. The\nfourth column gives for each signal mode the 90% C.L. upper limit (UL) on the ratio of the branching fraction of the signal\nmode to that of the normalization mode (BR). The last column shows the 90% C.L. upper limit on the branching fraction for\neach signal mode (BF). The upper limits include all systematic uncertainties.\nBR UL\nBF UL\nYield\nE\ufb00.\n90% C.L.\n90% C.L.\nDecay mode\n(events)\n(%)\n(10\u22124)\n(10\u22126)\nD+ \u2192\u03c0+e+e\u2212\n\u22123.9 \u00b1 1.6 \u00b1 1.7\n1.56\n3.9\n1.1\nD+ \u2192\u03c0+\u00b5+\u00b5\u2212\n\u22120.2 \u00b1 2.8 \u00b1 0.9\n0.46\n24\n6.5\nD+ \u2192\u03c0+e+\u00b5\u2212\n\u22122.9 \u00b1 3.4 \u00b1 2.4\n1.21\n11\n2.9\nD+ \u2192\u03c0+\u00b5+e\u2212\n3.6 \u00b1 4.3 \u00b1 1.3\n1.54\n13\n3.6\nD+\ns \u2192\u03c0+e+e\u2212\n8 \u00b1 34 \u00b1 8\n6.36\n5.4\n13\nD+\ns \u2192\u03c0+\u00b5+\u00b5\u2212\n20 \u00b1 15 \u00b1 4\n1.21\n18\n43\nD+\ns \u2192\u03c0+e+\u00b5\u2212\n\u22123 \u00b1 11 \u00b1 3\n2.16\n4.9\n12\nD+\ns \u2192\u03c0+\u00b5+e\u2212\n9.3 \u00b1 7.3 \u00b1 2.8\n1.50\n8.4\n20\nD+ \u2192K+e+e\u2212\n\u22123.7 \u00b1 2.9 \u00b1 3.3\n2.88\n3.7\n1.0\nD+ \u2192K+\u00b5+\u00b5\u2212\n\u22121.3 \u00b1 2.8 \u00b1 1.1\n0.65\n16\n4.3\nD+ \u2192K+e+\u00b5\u2212\n\u22124.3 \u00b1 1.8 \u00b1 0.6\n1.44\n4.3\n1.2\nD+ \u2192K+\u00b5+e\u2212\n3.2 \u00b1 3.8 \u00b1 1.2\n1.74\n9.9\n2.8\nD+\ns \u2192K+e+e\u2212\n\u22125.7 \u00b1 5.8 \u00b1 2.0\n3.20\n1.6\n3.7\nD+\ns \u2192K+\u00b5+\u00b5\u2212\n4.8 \u00b1 5.9 \u00b1 1.2\n0.85\n9.1\n21\nD+\ns \u2192K+e+\u00b5\u2212\n9.1 \u00b1 6.0 \u00b1 2.8\n1.74\n5.7\n14\nD+\ns \u2192K+\u00b5+e\u2212\n3.4 \u00b1 6.4 \u00b1 3.5\n2.08\n4.2\n9.7\n\u039b+\nc \u2192pe+e\u2212\n4.0 \u00b1 6.5 \u00b1 2.8\n5.52\n0.8\n5.5\n\u039b+\nc \u2192p\u00b5+\u00b5\u2212\n11.1 \u00b1 5.0 \u00b1 2.5\n0.86\n6.4\n44\n\u039b+\nc \u2192pe+\u00b5\u2212\n\u22120.7 \u00b1 2.9 \u00b1 0.9\n1.10\n1.6\n9.9\n\u039b+\nc \u2192p\u00b5+e\u2212\n6.2 \u00b1 4.6 \u00b1 1.8\n1.37\n2.9\n19\nD+ \u2192\u03c0\u2212e+e+\n4.7 \u00b1 4.7 \u00b1 0.5\n3.16\n6.8\n1.9\nD+ \u2192\u03c0\u2212\u00b5+\u00b5+\n\u22123.1 \u00b1 1.2 \u00b1 0.5\n0.70\n7.5\n2.0\nD+ \u2192\u03c0\u2212\u00b5+e+\n\u22125.1 \u00b1 4.2 \u00b1 2.0\n1.72\n7.4\n2.0\nD+\ns \u2192\u03c0\u2212e+e+\n\u22125.7 \u00b1 14. \u00b1 3.4\n6.84\n1.8\n4.1\nD+\ns \u2192\u03c0\u2212\u00b5+\u00b5+\n0.6 \u00b1 5.1 \u00b1 2.7\n1.05\n6.2\n14\nD+\ns \u2192\u03c0\u2212\u00b5+e+\n\u22120.2 \u00b1 7.9 \u00b1 0.6\n2.23\n3.6\n8.4\nD+ \u2192K\u2212e+e+\n\u22122.8 \u00b1 2.4 \u00b1 0.2\n2.67\n3.1\n0.9\nD+ \u2192K\u2212\u00b5+\u00b5+\n7.2 \u00b1 5.4 \u00b1 1.6\n0.80\n37\n10\nD+ \u2192K\u2212\u00b5+e+\n\u221211.6 \u00b1 4.0 \u00b1 3.1\n1.52\n6.8\n1.9\nD+\ns \u2192K\u2212e+e+\n2.3 \u00b1 7.9 \u00b1 3.3\n4.10\n2.1\n5.2\nD+\ns \u2192K\u2212\u00b5+\u00b5+\n\u22122.3 \u00b1 5.0 \u00b1 2.8\n0.98\n5.3\n13\nD+\ns \u2192K\u2212\u00b5+e+\n\u221214.0 \u00b1 8.4 \u00b1 2.0\n2.26\n2.4\n6.1\n\u039b+\nc \u2192pe+e+\n\u22121.5 \u00b1 4.2 \u00b1 1.5\n5.14\n0.4\n2.7\n\u039b+\nc \u2192p\u00b5+\u00b5+\n\u22120.0 \u00b1 2.1 \u00b1 0.6\n0.94\n1.4\n9.4\n\u039b+\nc \u2192p\u00b5+e+\n10.1 \u00b1 5.8 \u00b1 3.5\n2.50\n2.3\n16\n\n560\n \n2\nEntries per 10 MeV/c\n0\n10\n20\n30\n40\n50\n+\ne\n+\ne\n-\nK\n\u2192\n+\nD\n]\n2\n) [GeV/c\n+\ne\n+\ne\n-\nM(K\n1.8\n1.9\n2\n \n2\nEntries per 10 MeV/c\n0\n10\n20\n30\n40\n50\n60\n70\n+\ne\n+\ne\n-\nK\n\u2192\n+\ns\nD\n+\n\u00b5\n+\n\u00b5\n-\nK\n\u2192\n+\nD\n]\n2\n) [GeV/c\n+\n\u00b5\n+\n\u00b5\n-\nM(K\n1.8\n1.9\n2\n+\n\u00b5\n+\n\u00b5\n-\nK\n\u2192\n+\ns\nD\n+\ne\n+\n\u00b5\n-\nK\n\u2192\n+\nD\n]\n2\n) [GeV/c\n+\ne\n+\n\u00b5\n-\nM(K\n1.8\n1.9\n2\n+\ne\n+\n\u00b5\n-\nK\n\u2192\n+\ns\nD\nFigure 19.1.47. From (Lees, 2011k). Invariant-mass distributions for D+ \u2192K\u2212\u2113+\u2113(\u2032)+ (top) and D+\ns \u2192K\u2212\u2113+\u2113(\u2032)+ (bottom)\ncandidates. The solid lines are the results of the \ufb01ts. The background components for the dimuon modes and D+\n(s) \u2192K\u2212\u00b5+e+\nin which candidates arise from misidenti\ufb01ed hadrons are shown as dashed curves.\nobtained from the unbinned likelihood \ufb01ts are listed in Ta-\nble 19.1.27 with statistical and systematic uncertainties.\nOnly systematic uncertainties associated with the signal\nand background p.d.f.s are included in the systematic un-\ncertainty for the yields. The curves representing the \ufb01ts\nare overlaid in the \ufb01gures. The most signi\ufb01cant signal is\nseen in the distribution for \u039b+\nc \u2192p\u00b5+\u00b5\u2212; the signal yield\nhas a statistical-only signi\ufb01cance of 2.6\u03c3 as determined\nfrom the change in log-likelihood with respect to zero as-\nsumed signal events. With 35 di\ufb00erent measurements, a\n2.6\u03c3 deviation is expected with about 25% probability.\n19.1.10 Summary of charmed meson decays\nCharm decays open the road to investigate the \ufb02avor\nphysics of up-type quarks, which is complementary to the\nweak interactions of the (bottom and strange) down type\nquarks. Since the B decays are dominated by the b \u2192c\ntransitions, and the e+e\u2212\u2192cc cross section is compara-\ntively high, the B factories also generated plenty of charm\nwhich allowed detailed measurements with highly compet-\nitive precision.\nFCNC processes of up-type quarks are predicted to be\nheavily GIM suppressed, which motivated measurements\nand searches of rare and even forbidden decays of charm\nat the B factories. Although for many FCNC processes it\nis di\ufb03cult to make a precise theoretical prediction, the B\nfactories added a lot of new information on these decays,\nconstraining signi\ufb01cantly the limits on physics beyond the\nSM.\nAside from the weak interactions also many studies\nof QCD related issues have been performed. The charm\nquark is neither heavy enough to be cleanly treated within\nthe heavy quark expansion, nor is it light enough to be sen-\nsibly included into chiral Lagrangians, and thus it nicely\ncovers the intermediate region between the two limits. For\nthis reason there has been a lot of e\ufb00ort to measure multi-\nbody decays, where a lot of information on QCD has been\nextracted from e.g. Dalitz analyses.\n\n561\n19.2 D-mixing and CP violation\nEditors:\nBrian Meadows (BABAR)\nBo\u02c7stjan Golob (Belle)\nIkaros Bigi (theory)\nAdditional section writers:\nRay Cowan, Kevin Flood, Maurizio Martinelli, Alan\nSchwartz, Marko Stari\u02c7c, Eunil Won, An\u02c7ze Zupanc\n19.2.1 Introduction\n19.2.1.1 Brief overview\nThe mixing phenomenon in B, D and K neutral meson\nsystem is an example of the \ufb02avor changing neutral cur-\nrent (FCNC) process. Within the SM, FCNC\u2019s are ab-\nsent at the tree level (\ufb01rst order). However, mixing can\noccur through box diagrams (second order), as shown in\nFig. 19.2.1.\ncj\nc\nd,s,b\nu\nu\nd,s,b\nc\nD0\nD0\nW\nW\n+\n\u2212\nVci Vuj*\nVui* V\nFigure 19.2.1. Box diagram leading to D0 \u2212D0 mixing.\nThe strong suppression of FCNC\u2019s is a consequence\nof the GIM mechanism (Glashow, Iliopoulos, and Maiani,\n1970) (see Chapter 16). In the past, measurements of mix-\ning provided a basis for important discoveries. The dis-\ncoveries of K0 \u2212K0 and B0\nd \u2212B0\nd mixing, for example,\nenabled predictions of the masses of the charm and top\nquarks, respectively, before the quarks were \ufb01rst observed\nat Brookhaven and SLAC (Aubert et al., 1974; Augustin\net al., 1974), and at Fermilab (Abachi et al., 1995b; Abe\net al., 1995). The probability for any of the above men-\ntioned neutral mesons to transform into its anti-particle\nin the course of its lifetime is described by the mixing\nparameters x and y. The mixing parameters are de\ufb01ned\nas\n\u0393 = \u03931 + \u03932\n2\nx = m1 \u2212m2\n\u0393\ny = \u03931 \u2212\u03932\n2\u0393\n,\n(19.2.1)\nwhere \u03931,2 are the widths of the two mass eigenstates. The\ntime integrated probability for a neutral meson initially\nproduced as P 0 to decay at a later time as P\n0 is given by\n(x2 + y2)/2(x2 + 1). By inspection of approximate values\nfor x and y in Table 19.2.1 it is clear that this probability\nis by far the smallest for the system of neutral D mesons.\nTable 19.2.1. Discoveries of neutral mesons and their mixing\nApproximate values of the mixing parameters are listed as well.\nMeson\nDiscovery year and place\nMixing parameter\nK0\n1950 Caltech\nMixing\n1956 Columbia\nx \u22481,\ny \u22481\nB0\nd\n1983 CESR\nMixing\n1987 DESY\nx \u22480.8,\ny \u223c0\nB0\ns\n1992 LEP\nMixing\n2006 Fermilab\nx \u224826,\ny \u223c0.05\nD0\n1976 SLAC\nMixing\n2007 KEK, SLAC\nx \u223c0.01,\ny \u223c0.01\nThe reason for the small rate of mixing of D0 mesons\nlies in the fact that they are the only \ufb02avored neutral\nmesons composed of up-type quarks. The GIM mecha-\nnism, as explained below, is even more e\ufb03cient for the case\nof up-type quark FCNC\u2019s. For the same reason measure-\nments of mixing in the D0 system yield complementary\nconstraints on possible contributions from new physics\n(NP) processes beyond the SM to those arising from the\nmeasurements of FCNC\u2019s of down-type quarks (B or K\nmesons). In 2007 the B Factories established evidence for\nmixing in the neutral charm mesons system, and those\nresults were published back-to-back in Phys. Rev. Lett.\nas (Aubert, 2007j) and (Staric, 2007). These results are\ndiscussed in Sections 19.2.2 and 19.2.3, respectively.\n19.2.1.2 Mixing\nA general description of oscillations of pseudoscalar neu-\ntral mesons is given in Section 10.1. In the following we\nemphasize some of the speci\ufb01cs of the D0 system. The\nmixing parameters are de\ufb01ned in Eq. (19.2.1).\nIn the absence of CP violation (q = p = 1/\n\u221a\n2 in Eq.\n10.1.2), D1(2) is the CP-even (odd) state if one adopts the\nphase convention CP|D0\u27e9= |D0\u27e9and CP|D0\u27e9= |D0\u27e9.119\nThe amplitude for the process of Fig. 19.2.1,\n\u27e8D0|H\u2206C=2|D0\u27e9, can be schematically written as\nX\ni,j=d,s,b\nV \u2217\nuiVciVcjV \u2217\nujF(m2\nW , m2\ni , m2\nj),\n(19.2.2)\n119 For the mixing parameter x (y) one subtracts the mass\n(width) of the CP-odd state (or in case of CP violation of the\nstate which has a larger CP-odd component) from that of the\nCP-even state (or in case of CP violation of the state which\nhas a larger CP-even component).\n\n562\nwhere the kinematic function F arises from the integration\nover the momenta of particles exchanged in the loop. The\nformulation above nicely re\ufb02ects the GIM mechanism: if\nmasses of all (down-type) quarks exchanged in the loop\nwere equal, i.e. mi = mj, the function F would be a factor\ncommon to all terms in the sum which would make the\namplitude zero due to the unitarity of the CKM matrix.\nBased on dimensional arguments (Nachtmann, 1990)\nthe form of F is\nF(m2\nW , m2\ni , m2\nj) \u221df0m2\nW\n(19.2.3)\n+f1m2\ni + f2m2\nj + f3mimj + O(m\u22122\nW ) .\nDue to the unitarity of the CKM matrix, only the mimj\nterms survives in the sum (19.2.2), and hence\n\u27e8D0|H\u2206C=2|D0\u27e9\u221d\nX\ni,j=d,s,b\nV \u2217\nuiVciVcjV \u2217\nujmimj . (19.2.4)\nFurthermore, due to the small magnitude of the Vub cou-\npling, the b quark contribution is negligible. The ampli-\ntude is proportional to V \u2217\nusVcsVcdV \u2217\nud, and vanishes in the\nlimit md \u223cms. The D0 mixing thus arises only as a con-\nsequence of the SU(3)\ufb02avor symmetry breaking resulting\nfrom the small di\ufb00erences between the masses of down-\ntype quarks.\nThe short distance contribution calculated from the\nbox diagrams (like the one in Fig. 19.2.1) is proportional\nto the local \u2206C = 2 operator u\u03b3\u00b5(1\u2212\u03b35)cu\u03b3\u00b5(1\u2212\u03b35)c and\nreads (Bigi and Uraltsev, 2001b; Burdman and Shipsey,\n2003; Georgi, 1992)\n\u27e8D0|H\u2206C=2|D0\u27e9= G2\nF m2\nc\n4\u03c02 V \u2217\ncsV \u2217\ncdVudVus\n(m2\ns \u2212m2\nd)2\nm4c\n\u00d7\n\u27e8D0|u\u03b3\u00b5(1 \u2212\u03b35)cu\u03b3\u00b5(1 \u2212\u03b35)c|D0\u27e9.\n(19.2.5)\nEquation (19.2.5) shows that this amplitude is doubly-\nCabibbo suppressed. Furthermore, the factor (m2\ns \u2212\nm2\nd)2/m4\nc shows explicitly that D0 mixing vanishes in the\nlimit of exact SU(3)\ufb02avor symmetry limit, when ms = md.\nIt has been discussed (Bigi and Uraltsev, 2001b; Georgi,\n1992) that the contribution shown in Eq. (19.2.5) is the\n\ufb01rst term of systematic expansion in 1/mc. The peculiar\nfeature of this leading term is the strong suppression by\nthe factor (m2\ns \u2212m2\nd)2/m4\nc, which is not present any more\nin the subleading terms of the expansion. In fact, already\nthe \ufb01rst subleading terms exhibits only a factor m2\ns/m2\nc.\nThis indicates that the leading term cannot properly de-\nscribe D0 mixing, and that large long-distance contribu-\ntions are present.\nTaking into account the long-distance contributions by\nadding the second order terms from H\u2206C=1 involving in-\ntermediate hadronic states |n\u27e9one obtains\n(M \u2212i\n2\u0393)ij = mD\u03b4ij +\n(19.2.6)\n1\n2mD\n\u27e8D0|H\u2206C=2|D0\u27e9+\n1\n2mD\nX\nn\n\u27e8D0|H\u2206C=1|n\u27e9\u27e8n|H\u2206C=1|D0\u27e9\nmD \u2212En + i\u03f5\n.\nNeglecting, for the moment, the last term in the equa-\ntion above and evaluating Mij, \u0393ij from the box diagram\n(\u27e8D0|H\u2206C=2|D0\u27e9), and taking into account the relations\nfor the eigenvalues of the e\ufb00ective Hamiltonian Eq. (10.1.15),\nit is possible to estimate the expected magnitude of the\nmixing parameter, |x| \u223cO(10\u22125). Mixing with this rate\nwould be unobservable with the present experimental fa-\ncilities.\nHowever, the last term in Eq. (19.2.6) also contributes,\nand represents the long distance contribution to the e\ufb00ec-\ntive Hamiltonian. The contribution arises from on- and o\ufb00-\nshell intermediate states |n\u27e9accessible to both D0 and D0\n(see for example Fig. 19.2.2). Due to the non-perturbative\nD0\nK+\nK\u2212\nD0\n \nFigure 19.2.2. K+K\u2212as an example of an intermediate state\naccessible to both D0 and D0, contributing to D0\u2212D0 mixing.\nBlack circles represent quark processes for D0 \u2192K+K\u2212and\nits charge conjugate, similar to the process shown in Fig. 19.2.4.\nquantum chromodynamic nature of these e\ufb00ects, their con-\ntribution is much more di\ufb03cult to evaluate than the short\ndistance contribution illustrated in Fig. 19.2.1. In general,\ntwo methods have been exploited to estimate the mag-\nnitude of the mixing parameters that consider these long\ndistance contributions: the exclusive approach (Donoghue,\nGolowich, Holstein, and Trampetic, 1986; Falk, Grossman,\nLigeti, Nir, and Petrov, 2004), considering various possi-\nble exclusive intermediate states, and the Operator Prod-\nuct Expansion (OPE) method (Bigi and Uraltsev, 2001b;\nGeorgi, 1992).\nThe former method is conceptually straightforward. If\nwe consider only the possible two-body pseudoscalar inter-\nmediate states, K\u2212\u03c0+, K\u2212K+, \u03c0\u2212\u03c0+ and K+\u03c0\u2212, their\ncontributions are summarized in Table 19.2.2.\nThe second and third columns of the table show the\nCKM elements for various states entering the expressions\n|\u27e8D0|H\u2206C=1|n\u27e9|2 and \u27e8D0|H\u2206C=1|n\u27e9\u27e8n|H\u2206C=1|D0\u27e9, ac-\ncording to the Wolfenstein parameterization (see Chap-\nter 16). The minus signs in the third column are a conse-\nquence of a relative sign between the Vus and Vcd elements\nof the CKM matrix. Na\u00a8\u0131vely one expects the contribution\nto the mixing, when summed over the considered states,\nto vanish, i.e.\nX\nn\n\u27e8D0|H\u2206C=1|n\u27e9\u27e8n|H\u2206C=1|D0\u27e9= 0.\n(19.2.7)\n\n563\nTable 19.2.2. Pairs of pseudoscalar mesons accessible to D0 and D0. The CKM suppression factors entering two expressions\nin Eq. (19.2.6) are listed in the second and the third column. Due to the SU(3)\ufb02avor symmetry breaking the ratios of branching\nfractions (B) di\ufb00er from the na\u00a8\u0131ve CKM expectation (fourth column). From these one can estimate the contributions important\nfor the mixing amplitude, listed in the \ufb01fth column.\nState\n|\u27e8D0|H\u2206C=1|n\u27e9|2 \u221d\n\u27e8D0|H\u2206C=1|n\u27e9\u27e8n|H\u2206C=1|D0\u27e9\u221d\nMeasured B/B0\nContribution to mixing\nK+\u03c0\u2212\n1\n\u2212\u03bb2\nr1\n\u2212\u221ar1r4\u03bb2\nK\u2212K+\n\u03bb2\n\u03bb2\nr2\u03bb2\nr2\u03bb2\n\u03c0\u2212\u03c0+\n\u03bb2\n\u03bb2\nr3\u03bb2\nr3\u03bb2\nK\u2212\u03c0+\n\u03bb4\n\u2212\u03bb2\nr4\u03bb4\n\u2212\u221ar1r4\u03bb2\n\u03a3 = 0\n\u03a3 = \u03bb2\u0000r2 + r3 \u22122\u221ar1r4\n\u0001\nHowever, SU(3)\ufb02avor symmetry breaking causes di\ufb00er-\nences beyond those in the CKM factors contributing to the\nvarious states. These can be estimated from the measured\nbranching fractions as given schematically in the fourth\ncolumn of the table. If one denotes the expected B for a\n\ufb01nal state i by \u03bbnBi\n0, the measured B is ri\u03bbnBi\n0. The fac-\ntors ri \u0338= 1 point to SU(3) symmetry breaking. The con-\ntributions to the mixing amplitude as evaluated using the\nmeasured branching fractions is given in the last column.\nThe sum over all the states yields \u03bb2(r2 + r3 \u22122\u221ar1r4)\nwhich is in general di\ufb00erent from zero. In order to precisely\ncalculate the mixing parameters, one would of course need\nto take into account other possible intermediate states for\nsome of which the branching fractions are not well known.\nNevertheless it is possible to estimate the magnitude of the\nmixing parameters to be |x| <\n\u223cO(10\u22123) and |y| <\n\u223cO(10\u22122)\n(Falk, Grossman, Ligeti, Nir, and Petrov, 2004). These\nare in rough agreement with the expectation of the OPE\nmethod, |x|, |y| <\n\u223cO(10\u22123) (Bigi and Uraltsev, 2001b).\nIn summary, theoretical expectations based on the SM\nare that the mixing rate in the D0 system is small, aris-\ning mainly from long distance contributions that are dif-\n\ufb01cult to estimate. Despite this di\ufb03culty, the measure-\nment of mixing in this system over a wide range of decay\nmodes and with su\ufb03cient precision can provide important\nconstraints on possible NP parameters. Importantly and\nuniquely, such constraints will be complementary to those\nfrom down-type FCNC processes.\nOn the experimental side, observations of D0 mixing\ncome predominantly from measurements of the time evo-\nlution of neutral D meson decays to \ufb01nal states f that are\naccessible to both D0 and D0. In such cases, as illustrated\nin Fig. 19.2.3, direct decay and decay preceded by mix-\ning interfere. Mixing can, in principle, also be observed\nin semi-leptonic decays of D0 mesons where the leptons\nhave the wrong sign. The only way, in the SM, for such\ndecays to occur is through D0-D0 mixing, with a tiny rate\n\u221d(x2 + y2)/2 \u223c5 \u00d7 10\u22125.\nAt the B Factories, cc pairs are produced in the\nelectroweak annihilation of electrons and positrons. In\nthe fragmentation of primary quarks various species of\ncharmed hadrons together with lighter hadrons are pro-\nduced. In general, pairs of D0 and D0 mesons are not\nf \nD 0\nA f\nD 0\nA f\nFigure 19.2.3. Illustration of interference between direct D\nmeson decays and decays through mixing into the \ufb01nal state\nf, accessible to either D0 or D0.\nin a quantum correlated state.120 The time evolution of\nthe mass eigenstates D1,2 (i.e. of the eigenstates of the\ne\ufb00ective Hamiltonian, see Section 10.1) follows a simple\nexponential form\n|D1,2(t)\u27e9= e\u2212i(m1,2\u2212i\u03931,2/2)t|D1,2(t = 0)\u27e9,\n(19.2.8)\nand the form of the experimentally accessible \ufb02avor states\nis\n|D0(t)\u27e9= 1\n2p [|D1(t)\u27e9+ |D2(t)\u27e9]\n|D0(t)\u27e9= 1\n2q [|D1(t)\u27e9\u2212|D2(t)\u27e9]\n.\n(19.2.9)\nWriting out the time evolution of the mass eigenstates we\narrive at\n|D0(t)\u27e9=\n\"\n|D0\u27e9cosh\n\u0012ix + y\n2\n\u0393t\n\u0013\n\u2212\n(19.2.10)\n\u2212q\np|D0\u27e9sinh\n\u0012ix + y\n2\n\u0393t\n\u0013 #\ne(\u2212im\u2212\u0393/2)t\n|D0(t)\u27e9=\n\"\n|D0\u27e9cosh\n\u0012ix + y\n2\n\u0393t\n\u0013\n\u2212\n\u2212p\nq |D0\u27e9sinh\n\u0012ix + y\n2\n\u0393t\n\u0013 #\ne(\u2212im\u2212\u0393/2)t .\n120 This is di\ufb00erent from D0D0 production at the charm\nthreshold. There, the pair of D mesons from the decay of a\n\u03c8(3770) is in a quantum correlated state similar to a pair of B\nmesons produced in the decay of an \u03a5(4S).\n\n564\nIn the above equations we use the notation |D0\u27e9and |D0\u27e9\nfor the two \ufb02avor eigenstates.121 The time evolutions can\nbe simpli\ufb01ed. Since |x|, |y| \u226a1, the time dependent decay\nrate of an initially produced D0 meson to a \ufb01nal state f\ncan be written as\nd\u0393(D0 \u2192f)\ndt\n\u221d\n\f\f\fAf \u2212q\np\nix + y\n2\nAf\u0393t\n\f\f\f\n2\ne\u2212\u0393 t . (19.2.11)\nAf and Af denote the instantaneous decay amplitudes\n\u27e8f|D0\u27e9and \u27e8f|D0\u27e9, respectively. Analogously, for an ini-\ntially produced D0 one \ufb01nds\nd\u0393(D0 \u2192f)\ndt\n\u221d\n\f\f\fAf \u2212p\nq\nix + y\n2\nAf\u0393t\n\f\f\f\n2\ne\u2212\u0393 t . (19.2.12)\nFurther simpli\ufb01cation arises if we ignore CP violation\nin mixing and mixing-induced CP violation (see further\ndiscussion in Section 19.2.1.3), i.e. assume that p = q =\n1/\n\u221a\n2:\nd\u0393(D0 \u2192f)\ndt\n\u221d\n\u0002\n|Af|2 \u2212|Af||Af|(x sin \u03b4f + y cos \u03b4f)(\u0393t)\n+|Af|2 x2 + y2\n4\n(\u0393t)2\u0003\ne\u2212\u0393 t ,\nd\u0393(D0 \u2192f)\ndt\n\u221d\n\u0002\n|Af|2 + |Af||Af|(x sin \u03b4f \u2212y cos \u03b4f)(\u0393t)\n+|Af|2 x2 + y2\n4\n(\u0393t)2\u0003\ne\u2212\u0393 t,\n(19.2.13)\nwhere \u03b4f is arg(Af/Af). In Eqs (19.2.13), the \ufb01rst terms\nrepresent direct decay and the third terms describe decay\npreceded by mixing. The middle terms, linear in t, encode\nthe interference between the two processes. They are also\nlinear in the small parameters x and y, and it is those\nterms that make the time dependent decay rates sensitive\nto the values of the mixing parameters.\nThe speci\ufb01c dependence on these quantities di\ufb00ers for\nvarious \ufb01nal states f. When the amplitude for direct decay\nis Cabibbo-favored (CF), the \ufb01rst term dominates and\nthe decays are, e\ufb00ectively, exponential and mixing can be\nneglected. When, however, the direct decay amplitude is\ndoubly Cabibbo-suppressed (DCS), all three terms are of\nthe same order of magnitude and such \ufb01nal states o\ufb00er\nthe maximum sensitivity to the mixing parameters.\n19.2.1.3 CP violation\nFor most BABAR and Belle measurements of D0 \u2212D0 me-\nson mixing, results on the mixing parameters are extracted\n\ufb01rst assuming that CP violation can be neglected, using\nEq. (19.2.13). In some measurements a second \ufb01t to the\ndata distributions is performed examining the possibility\n121 The experimental identi\ufb01cation of these states is possible\nthrough decays into \ufb02avor speci\ufb01c \ufb01nal states, for example\n\u27e8D0|K\u2212\u2113+\u03bd\u2113\u27e9\u0338= 0 while \u27e8D0|K\u2212\u2113+\u03bd\u2113\u27e9= 0.\nfor di\ufb00erences between D0 and D0, and CP asymmetries\nare measured.\nThe decay rates in Eqs (19.2.11) and (19.2.12) depend\nalso on the CP violating parameter q/p (cf. Chapter 10).\nIn general, CP violation in the SM for processes involving\ncharmed hadrons is expected to be tiny. This is conve-\nniently seen in the parameterization of the CKM matrix\ngiven in Eq. (16.4.4). CP violation arises from the phase\nin the CKM matrix, and the elements of the matrix re-\nlated to the \ufb01rst two generations of quarks, which appear\nin the charmed hadron processes, are almost real. Hence\nthe magnitude of the CP violating e\ufb00ect is expected to be\nsmall. As an example, consider the Cabibbo suppressed\ndecay D0 \u2192\u03c0+\u03c0\u2212, shown in Fig. 19.2.4. The relevant\nCKM phase entering the ratio of amplitudes for this de-\ncay and its charge conjugate is\narg \u27e8\u03c0+\u03c0\u2212|D0\u27e9\n\u27e8\u03c0+\u03c0\u2212|D0\u27e9= 2 arg(V \u2217\ncdVud) .\n(19.2.14)\nTo see the expected magnitude of the CP violation due to\nthis weak phase one needs to consider the parameteriza-\ntion of the CKM matrix at least up to the order \u03bb5. The\nusually adopted Wolfenstein parameterization to order \u03bb3\nis given in Eq. (16.4.4) in Section 16. The parameteri-\nzation including the order of \u03bb5 reads (see for example\nreview \u201cCP violation in meson decays\u201d in Beringer et al.\n(2012))\n\uf8eb\n\uf8ed\n1\u2212\u03bb2/2\u2212\u03bb4/8\n\u03bb\nA\u03bb3(\u03c1\u2212i\u03b7)\n\u2212\u03bb+A2\u03bb5[1\u22122(\u03c1+i\u03b7)]/2\n1\u2212\u03bb2/2\u2212\u03bb4(1+4A2)/8\nA\u03bb2\nA\u03bb3[1\u2212(1\u2212\u03bb2/2)(\u03c1+i\u03b7)] \u2212A\u03bb2+A\u03bb4[1\u22122(\u03c1+i\u03b7)]/2 1\u2212A2\u03bb4/2\n\uf8f6\n\uf8f8\n+O(\u03bb6).\n(19.2.15)\nEvaluating Equation (19.2.14) yields\n2 arg(V \u2217\ncdVud) \u22482A2\u03bb4\u03b7 = 1.2 \u00d7 10\u22123 ,\n(19.2.16)\nwhere in the last line we use values of parameters from\nCharles et al. (2005). CP violation e\ufb00ects in the charm\nsector are thus of the order of 10\u22123. Recently some au-\nthors have argued that the CP asymmetries in Cabibbo-\nsuppressed decays can be larger by some factor (Brod,\nKagan, and Zupan, 2011).\n0\nu\nu\n+\nW\nu\nD\nc\n*\nV\nV\n \n \n+\n\u03c0\n\u2212\n\u03c0\nd\nud\ncd\nd\nFigure 19.2.4. D0 \u2192\u03c0+\u03c0\u2212decay with the corresponding\nCKM elements.\n\n565\nIn measurements of various observables sensitive to CP\nviolation, the parameterization\n\f\f\f\f\nq\np\n\f\f\f\f\n2\n\u22611 + AM\n(19.2.17)\nis often used. Three types of CP violating e\ufb00ects can\nbe distinguished, as in any other neutral mesons system\n(see Section 16.6). First, CP violation in mixing occurs\nif AM \u0338= 0 (alternatively, |q/p| \u0338= 1). CP violation in de-\ncay is present if |Af/Af| \u0338= 1. This e\ufb00ect is sometimes\nparameterized in terms of\n\f\f\f\f\f\nAf\nAf\n\f\f\f\f\f\n2\n\u22611 + Af\nD .\n(19.2.18)\nIt should be noted that while the parameter AM is univer-\nsal for all D0 decays, the parameter Af\nD depends on the\n\ufb01nal state f. This type of CP violation can only occur in\ndecays to which at least two processes with di\ufb00erent weak\nand strong phases contribute (see Eq. (16.6.5) in Chap-\nter 16). For D mesons this is only possible in Cabibbo\nsuppressed decays, where both tree (e.g. see Fig. 19.2.4)\nand penguin (Fig. 19.2.5) diagrams are possible. Finally,\nu\nq\nd,s,b\nW\nu\nc\nq\ng\nFigure 19.2.5. Penguin diagram contributing to Cabibbo sup-\npressed decays of D mesons.\nthere is a possibility of mixing-induced CP violation. This\nis characterized by\nIm\n\u0014q\np\nAf\nAf\n\u0015\n\u2261Im[\u03bbf] \u0338= 0 .\n(19.2.19)\nUsing previous parameterizations (and keeping only linear\nterms in small quantities AM and Af\nD), \u03bbf is sometimes\nexpressed as\n\u03bbf =\nq\nRf\nD(1 + AM/2)(1 \u2212Af\nD/2)e\u2212i(\u03b4f \u2212\u03c6) . (19.2.20)\nIn the above expression, the parameter Rf\nD is not related\nto CP violation, but to the possible Cabibbo suppression,\nRf\nD = |Af/Af|2 = |Af/Af|2. The phase \u03b4f includes a\npossible strong phase as well as the weak phase di\ufb00erence\nbetween the two amplitudes. For decays to CP eigenstates\n(such as K+K\u2212) Rf\nD = 1 and the strong phase di\ufb00erence\nis zero. If we neglect the weak phase di\ufb00erences of the\norder of 10\u22123 then the only source of this type of CP\nviolation in decays to CP eigenstates is \u03c6 \u2261arg(q/p) \u0338= 0\nwhich can arise due to some unknown NP processes.\nIn the following sections we neglect CP violation in\nthe neutral D meson system and address this important\nphenomenon separately in Sections 19.2.6 and 19.2.7.\n19.2.1.4 D0 Mixing in New Physics Models\nValues of the mixing parameters for the D0 meson system\ncan di\ufb00er signi\ufb01cantly from SM estimates in several NP\nmodels. In Golowich, Hewett, Pakvasa, and Petrov (2007)\nthe authors examined a large number of such models and\ncalculated the contributions of new particles and processes\nto the mixing parameters x and y. Due to the large un-\ncertainties in SM calculations, the values are obtained for\nspeci\ufb01c NP contributions alone.122 In this approach the\nparameters of a large majority of the models considered\nare additionally constrained by the measured values of the\nD0 mixing parameters. An example of the sensitivity of\nthe value of x to the mass and CKM elements of a possible\nfourth generation b\u2032 quark is shown in Fig. 19.2.6.123\nNot only x but also y can be sensitive to some of the\nNP models considered. As pointed out in Eq. (19.2.5),\nthe mixing parameters in the SM vanish in the exact\nSU(3)\ufb02avor limit. Moreover, the contribution to the mix-\ning parameters enters only as a second order e\ufb00ect in the\nSU(3)\ufb02avor breaking. Hence the NP contributions to y\ncould be signi\ufb01cant for the models in which the contri-\nbutions do not vanish in the SU(3)\ufb02avor symmetry limit\n(Golowich, Pakvasa, and Petrov, 2007). An example is the\nR-parity violating SUSY model, where the slepton medi-\nated interaction is not suppressed in the SU(3)\ufb02avor sym-\nmetry limit and could lead to values as high as |y| \u22483.7%\nfor M\u02dc\u2113= 100 GeV/c2. Section 25.2 is a more general dis-\ncussion on how one can constrain benchmark NP models\nusing constraints from the B Factories.\n19.2.1.5 General experimental remarks\nTwo experimental ingredients are necessary to exploit the\ndecay time distributions of Eqs (19.2.11) and (19.2.12) for\n122 The neglection of the SM contribution leads to less restric-\ntive limits in most cases. If there is also the SM contribution\nto the magnitudes of the mixing parameters, then the contri-\nbution from NP is smaller and hence the constraint gets more\nsevere.\n123 Note that severe lower limits on the b\u2032 mass arise also\nfrom direct searches at the LHC. For example, the CMS col-\nlaboration \ufb01nds m(b\u2032) > 611 GeV at 95% C.L., assuming\nB(b\u2032 \u2192Wt) = 100% and hence |Vub\u2032Vcb\u2032| = 0 (Chatrchyan\net al., 2012c). The ATLAS collaboration provides lower mass\nlimits as a function of B(b\u2032 \u2192Wt) (Gauthier, 2013); for values\nof the latter between 0.8 and 1.0 the limit is m(b\u2032) > 700 GeV\nat 95% C.L. This is complementary to the limit arising from\nD0 \u2212D0 mixing, which provides an upper limit on the b\u2032 mass\nfor a given value of |Vub\u2032Vcb\u2032|.\n\n566\nFigure 19.2.6. Contours of x in the fourth generation b\u2032 quark\nmass and CKM elements (|Vub\u2032Vcb\u2032|) plane (see text for expla-\nnation). Contours are shown for x = [15.0, 11.7, 8.0, 5.0, 3.0] \u00d7\n10\u22123 (from right to left). From (Golowich, Hewett, Pakvasa,\nand Petrov, 2007).\nmeasuring the mixing parameters. The \ufb01rst one is the de-\ntermination of the initial neutral D meson \ufb02avor (\u201c\ufb02avor\ntagging\u201d), that is used to determine whether a D0 or a\nD0 was produced at t = 0. The second ingredient is the\ndetermination of the decay time of a the neutral D meson,\nbased on the measurement of its decay length between the\nproduction and decay point.\nThe initial \ufb02avor tagging is based on the decay chain\nD\u2217+ \u2192D0\u03c0+ \u2192f\u03c0+, and its charge conjugate D\u2217\u2212\u2192\nD0\u03c0\u2212\u2192f\u03c0\u2212. The charge of the pion produced in the de-\ncay of a D\u2217determines the \ufb02avor of the neutral daughter\nD meson. It should be noted that the average laboratory\nmomentum of such pions is low, around 400 MeV/c, and\nhence they are usually denoted as \u201cslow pions\u201d, \u03c0s. The\nuse of D\u2019s from D\u2217\u2019s also reduces the amount of back-\nground in the event samples selected. The di\ufb00erence be-\ntween the invariant masses of the D\u2217+ and the D0 meson,\n\u2206m = m(f\u03c0+) \u2212m(f), is a powerful selection variable\nthat restricts the amount of combinatorial background\nconsiderably. The e\ufb00ectiveness is further enhanced by the\nexcellent experimental resolution in \u2206m arising from the\ncancellation of experimental uncertainty in the determi-\nnation of the momenta of particles comprising the D0. In\nsome measurements an equivalent variable Q = \u2206m\u2212m\u03c0\nis used instead of \u2206m.124\nThe determination of the D meson decay length is il-\nlustrated in Fig. 19.2.7 with typical dimensions indicated.\nThe accuracy depends critically on the silicon detectors\nof the experiments, described in Chapter 2. The decay\npoint is obtained from \ufb01tting the D meson decay products\nto a single vertex. The D0 production point is obtained\nby intersecting the D0 \ufb02ight direction, determined by its\nmomentum vector and decay vertex, with the e+e\u2212in-\nteraction region. The charged (\u201cslow\u201d) pion from the D\u2217\ndecay can be \ufb01tted to a common space point together with\n124 Sometimes in the literature the same variable is denoted as\nq, not to be confused with q from Eq. (19.2.9), for example.\ne+\n100\nbeam spot\ns\nK\ne\u2212\n\u03c0\n\u03c0\n\u00b5m\n\u00b5m\nD0\nD decay vertex\n0\nD extrapolated production point\n200\n0\nFigure 19.2.7. Illustration of D meson decay length determi-\nnation with some typical dimensions.\nthe D momentum and spatial constraints from the inter-\naction region. This improves the momentum accuracy of\nthe slow pion and, thereby, the experimental resolution\nin \u2206m. The average D0 decay length at the B Factories\nis about 200 \u00b5m. The precision by which the interaction\nregion is known is given in Chapter 6. The resulting res-\nolution on the decay length is approximately 100 \u00b5m, de-\npending on the \ufb01nal state considered. The proper decay\ntime is obtained from the decay length l, momentum p\nand nominal mass of the D mesons mD as mDl \u00b7 p/p2.\nIn the measurement of the D0 decay times, it is as-\nsumed that the D0\u2019s are produced at the primary e+e\u2212\nproduction vertex. For D0\u2019s from B meson decays, this\nassumptions results in a biased measurement due to the\n\ufb01nite decay time of the B mesons and the correspond-\ning D0 decay time distribution cannot be described by\nEq. (19.2.13). This complication (and the related system-\natic uncertainties that would result from it) is avoided by\nrequiring the CM momentum of the tagging D\u2217mesons to\nexceed the kinematic limit for B \u2192D\u2217X decays.125 The\ntypical minimal value required for the D\u2217momentum is\n2.5 GeV/c.\nTo measure the mixing parameters from the decay time\ndistributions one needs an accurate description of the res-\nolution, to be convolved with the expected distributions\nof Eqs (19.2.11) and (19.2.12). The simplest way of de-\nscribing the resolution is to use a Gaussian function with\nan appropriate width, but this rarely turns out to be ac-\ncurate enough. In general, the resolution function is more\ncomplicated since the resolution in an individual D meson\ndecay time measurement depends on the speci\ufb01c kinemat-\nics of the decay. In most cases the resolution function can\nbe successfully parameterized with two or three Gaussian\nfunctions of di\ufb00erent widths. In an unbinned \ufb01t to the\ndecay time distribution the width of the resolution func-\ntion can be implemented on an event-by-event basis by\nmultiplying the estimated accuracy of the decay time as\nobtained from the vertex \ufb01ts by a factor which is either a\nfree parameter in the \ufb01t or determined from some control\nsample of decays, if one exists. For a two Gaussian reso-\n125 The largest momentum of a D\u2217, in a two body B \u2192D\u2217\u03c0\ndecay in the CM system, where the B meson is approximately\nat rest, is about 2.3 GeV/c.\n\n567\nlution parameterization, the likelihood value for the i-th\nsignal event is written as\nLi(x, y) =\nZ \u221e\n0\ndt\u2032 d\u0393\ndt\u2032 (t\u2032; x, y)\n\"\nfe(ti\u2212t\u2032)2/2S1\u03c32\ni +\n(1 \u2212f)e(ti\u2212t\u2032)2/2S2\u03c32\ni\n#\n.\n(19.2.21)\nin which \u03c3i is the uncertainty reported by the vertex re-\nconstruction code for this event, and where S1,2 are the\nscale factors mentioned above.\nIn constructing the resolution function special care\nshould be devoted to possible biases in decay length mea-\nsurements. These can occur due to a combination of the\nkinematic properties of decays (mainly arising from de-\npendence on the opening angle of the \ufb01nal state tracks in\nthe laboratory frame) and small residual misalignments of\nindividual detector modules.126 Such e\ufb00ects could result\nin a biased measurement of the mixing parameters. These\ne\ufb00ects can be included in the resolution function through\nvarious more sophisticated parameterizations, for exam-\nple by allowing the mean value of the Gaussian function\nto deviate from zero. In some cases a further dependence\nof the mean value on the kinematic properties of the decay\nis required: for example, the bias can depend on the open-\ning angle of the two tracks in the case of D0 \u2192K\u00b1\u03c0\u2213\ndecays; the opening angle is in turn strongly correlated\nwith the invariant mass and hence the bias can vary as\nthe invariant mass changes across the width of the sig-\nnal peak, as shown in the example below in Fig. 19.2.18.\nIn multi-body decays the bias and hence the mean value\nof the resolution function can also vary depending on the\nposition of the decay in the Dalitz plane.\nThe parameterization of the resolution function must\nbe studied to understand what e\ufb00ect such biases have on\nthe determination of the mixing parameters. For this, a\nnumber of special simulated samples of events are pro-\nduced with non-zero values for x and y and then sub-\njected to the same selection, reconstruction and \ufb01tting\nprocedures as the data to check for possible bias in these\nmixing parameters. Another test is to \ufb01t the Cabibbo-\nfavored decays (e.g. D0 \u2192K\u2212\u03c0+) where the e\ufb00ects of\nmixing are negligible to obtain the average decay lifetime.\nThe resulting values are compared to the current world\naverage of (410.1 \u00b1 1.5) fs (Beringer et al., 2012) to check\nfor possible biases arising from the parameterization of the\nresolution function.\n19.2.2 Hadronic wrong-sign decays\nThe earliest attempts to \ufb01nd evidence for D0 \u2212D0 mixing\nat the B Factories have used limited samples of \u201cwrong\nsign\u201d (WS) hadronic decays. The term WS decays is used\nfor decays to \ufb02avor speci\ufb01c \ufb01nal states which are either\nDCS or can proceed through the mixing process. Both\n126 For example, misalignment between the silicon vertex de-\nvice and the central tracking chamber.\nBABAR and Belle have carefully studied the time depen-\ndence of the D0 \u2192K+\u03c0\u2212+ c.c. decays. These stud-\nies initially set limits on the mixing parameters and ul-\ntimately provided evidence for charm mixing at the 3.9\u03c3\nlevel, as well as setting limits on CP violation (Zhang,\n2006; Aubert, 2007j). These decays, expected to be par-\nticularly sensitive to mixing (Bigi and Uraltsev, 2001b;\nBlaylock, Seiden, and Nir, 1995), were \ufb01rst used to search\nfor this phenomenon by the E791 collaboration (Aitala\net al., 1998). This search resulted in the upper limit for the\nratio of decays with and without mixing of rmix < 0.85%\nat 90% C.L. The CLEO experiment provided limits on\nthe mixing parameters using the same decay mode (see\nbelow for the de\ufb01nitions of x\u20322 and y\u2032), x\u20322 < 0.082% and\n\u22125.5% < y\u2032 < 1.0% at 95% C.L. (Godang et al., 2000).\nAnother type of WS decays that played important role\nin D0\u2212D0 mixing measurements is the D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212\n(K3\u03c0) decay mode. It has been used to search for charm\nmixing since the earliest days of charm physics. In 1977,\nthe SLAC/LBL magnetic detector at SPEAR was used\nto search for \u201csame-sign\u201d K3\u03c0 events where the kaon in\nthe D0 decay had the same charge as the kaon in the re-\ncoil products opposite the D0 (Goldhaber et al., 1977).\nThe result was that less than 18% (at 90% C.L.) of the\nobserved D0 decays exhibited the same-sign signature,\nwhich was consistent with the amount of charged particle\nmis-identi\ufb01cation expected from their time-of-\ufb02ight sys-\ntem. Other searches for wrong-sign decays also saw no\nsignal but did set limits on the wrong-sign rate. In 1995,\nE791 (Aitala et al., 1998) reported a wrong-sign measure-\nment of D0 \u2192K3\u03c0 showing that the mixing rate is less\nthan 0.85% at 90% C.L. This result was soon followed\nby evidence for the wrong-sign K3\u03c0 decay from CLEO\nwith a relative rate with respect to the RS decays of\nRK3\u03c0\nWS\n= [0.41+0.12\n\u22120.11 \u00b1 0.04 \u00b1 0.10]%, where the \ufb01rst er-\nror is statistical, the second is systematic, and the third\nis due to phase space (Dytman et al., 2001). The result\nis consistent with the WS decays arising solely from DCS\ndecays.\n19.2.2.1 Method\nThe time-dependence of mixing in the decays of neutral\nmesons has been discussed in detail in Section 10.1 and,\nfor charm mesons, in Section 19.2.1. The term WS decays\nis related to Eq. (19.2.13). If we select f = K\u2212\u03c0+ the\nD0 decays are CF and the second and third term in the\nexpression for d\u0393(D0 \u2192K\u2212\u03c0+)/dt are negligible. On the\nother hand, the D0 decays are DCS. Hence the contribu-\ntion of direct decay (\ufb01rst term of d\u0393(D0 \u2192K\u2212\u03c0+)/dt)\nis not much larger than the decay preceded by mixing\n(D0 \u2192D0 \u2192K\u2212\u03c0+, last term) and the interference\nbetween the two (second term). Hence the decays of an\ninitially produced D0 to K\u2212\u03c0+ (and analogously of an\ninitially produced D0 to K+\u03c0\u2212), which are either DCS or\ncan proceed through the mixing process, are called WS de-\ncays (as opposed to right sign (RS) decays, D0 \u2192K+\u03c0\u2212\nand D0 \u2192K\u2212\u03c0+). Experimentally, the WS and RS de-\ncays are selected based on the correlation between the\n\n568\ncharge of the slow pion from the tagging D\u2217\u00b1 decay and\nthe charge of the kaon from the D meson decay.\nEvaluating the expressions in Eqs (19.2.13), we get the\ntime dependence of the D0 \u2192K\u03c0 WS decays for small\nvalues of the mixing parameters x and y, as de\ufb01ned in\nEq. (19.2.1), and assuming that CP is conserved:\n\u0393ws\ne\u2212\u0393t \u221dRD +\np\nRDy\u2032 \u0393t + x\u20322 + y\u20322\n4\n(\u0393t)2 ,\n(19.2.22)\nwhere we used a short hand notation RD = RK\u03c0\nD . The\nparameters x\u2032 and y\u2032 are the parameters x and y rotated\nby a strong phase di\ufb00erence \u03b4K\u03c0 between the CF and DCS\ndecays:\nx\u2032 = x cos \u03b4K\u03c0 + y sin \u03b4K\u03c0\ny\u2032 = y cos \u03b4K\u03c0 \u2212x sin \u03b4K\u03c0 ;\n(19.2.23)\n\u03b4K\u03c0 is de\ufb01ned through AK\u2212\u03c0+/AK\u2212\u03c0+ = \u2212\nq\nRK\u03c0\nD e\u2212i\u03b4K\u03c0,\nc.f. Eq. (19.2.20). In the following, often the shorter no-\ntation \u03b4 for \u03b4K\u03c0 is also used. Equation (19.2.22) reveals an\nexponential decay modulated by terms linear and quadratic\nin t. The di\ufb00ering time development of the three terms \u2014\nconstant, linear, and quadratic \u2014 can be used to separate\nthe contributions from DCS decays and decays with mix-\ning. In this approximation, the time-integrated rate, RWS,\nis then\nRWS = RD + y\u2032p\nRD + x2 + y2\n2\n.\n(19.2.24)\nThe mixing rate RM is de\ufb01ned as RM = (x2 + y2)/2 =\n(x\u20322 + y\u20322)/2. A mixing-only search (not allowing for CP\nviolation) combines D0 and D0 decays together. To in-\nclude possible e\ufb00ects from CP violation, both BABAR and\nBelle apply Eq. (19.2.22) to D0 and D0 decays separately,\nas discussed further in Section 19.2.7.\n19.2.2.2 Measurements of D0 \u2192K+\u03c0\u2212decays\nBelle and BABAR used 400 fb\u22121 and 384 fb\u22121, respec-\ntively, in their 2006 and 2007 studies of K\u03c0 WS mixing\n(Zhang, 2006; Aubert, 2007j). Both experiments used the\ndecay chain D\u2217+ \u2192\u03c0+\ns D0, D0 \u2192K\u00b1\u03c0\u2213, using the large\nstatistics, RS decay D0 \u2192K\u2212\u03c0+ + c.c. to determine\nmost of the parameters in the p.d.f.s used to describe the\ndecay structure in four independent variables: the D0 can-\ndidate mass mK\u03c0, the mass di\ufb00erence \u2206m (or q), the re-\nconstructed decay time t, and the event-by-event decay\ntime error, \u03c3t. Both, BABAR and Belle perform a \u201cblind\u201d\nanalysis (see Chapter 14), where the analysis procedure is\n\ufb01nalized before examining the mixing results.\nIn both measurements particle identi\ufb01cation criteria\non charged kaon and pion candidates are imposed, as well\nas requirements on the quality of selected tracks and/or\nmomentum of slow pions. Belle requires the momentum\nof the D0 candidate in the center-of-mass frame to be\n> 2.7 GeV/c, which reduces the number of candidates\noriginating in combinatoric background and BB events.\nBABAR uses a requirement of 2.5 GeV/c for the same pur-\npose.\nBoth experiments reconstruct the D\u2217decay chain by\nperforming a vertex \ufb01t of the K and \u03c0 candidate tracks,\nand extrapolating the \ufb02ight direction of the resulting D0\ncandidate back to the interaction region; the resulting in-\ntersection is taken as the D\u2217decay vertex (see Fig. 19.2.3).\nThe \u03c0s candidate is constrained to originate from the D\u2217\nvertex. Requirements on the \u03c72 of all vertex \ufb01ts are im-\nposed. The resulting decay time t along with its associated\nuncertainty \u03c3t is calculated from the \ufb01tted vertex posi-\ntions and their uncertainties, and from the reconstructed\nD0 momentum. A typical value of \u03c3t is (130-160) fs.\nSome events have multiple D\u2217candidates (about\n5%).127 At Belle, the events in which at least two D\u2217can-\ndidates with the opposite charge are found are rejected,\nwhich reduces the random \u03c0s background (see below) by\nabout 30% and the signal by 1%. In the case of same-sign\nD\u2217candidates, the one with the best vertex \ufb01t \u03c72 was\nretained. At BABAR, if the D\u2217candidate shared daughter\ntracks with other D\u2217candidates, only the one with the\nlargest P(\u03c72) was used.\nThere are several background components required in\norder to correctly describe the two-dimensional RS and\nWS (mK\u03c0, \u2206m) or (mK\u03c0, q) distributions in addition to\nthe signal components. BABAR de\ufb01nes three background\ntypes: \u201crandom \u03c0s\u201d background, where an unassociated\n\u03c0s candidate is paired with a good D0 candidate; \u201cmis-\nreconstructed D0\u201d background, where a \u03c0s candidate is\npaired with a D0 that was reconstructed incorrectly, either\nwith an incorrect particle hypothesis for one of the daugh-\nter tracks, or a multi-body decay reconstructed as a two-\nbody decay; and combinatoric background. In RS events,\nmisreconstructed D0 candidates are primarily from semi-\nleptonic decays; in WS events, from \u201cswapped D0\u201d candi-\ndates which are RS D0 \u2192K\u03c0 decays with the K and \u03c0\nparticle identi\ufb01cations interchanged.\nBelle de\ufb01nes four background types: random \u03c0s (rnd)\nas above; those with a correct \u03c0s but with a misrecon-\nstructed D0 decaying to (\u22653)-body \ufb01nal states (d3b);\ncharged D+ and D+\ns decays (ds3); and combinatoric back-\nground (cmb).\nBoth Belle and BABAR determine the shape of the\nbackground p.d.f.s from MC simulation and only their am-\nplitudes are allowed to vary in the \ufb01ts. Signal events peak\nin both mK\u03c0 and \u2206m (or q). Random \u03c0s events peak in\nmK\u03c0 but not \u2206m (or q). Misreconstructed D0 decays peak\nin \u2206m (or q) but not mK\u03c0. Combinatoric events do not\npeak in either mK\u03c0 or \u2206m (or q).\nFrom the \ufb01ts to the (mK\u03c0, \u2206m) or (mK\u03c0, q) distribu-\ntions Belle \ufb01nds 1, 073, 993 \u00b1 1108 RS signal events and\n4024 \u00b1 88 WS signal events. Fig. 19.2.8 shows mK\u03c0 and q\ndistributions from the Belle analysis for RS and WS data.\nBABAR \ufb01ts the RS and WS (mK\u03c0,\u2206m) plane simultane-\nously using shared parameters that describe the signal and\n127 The largest fraction of multiple D\u2217candidates results from\ncombinations of a single D0 candidate paired with multiple \u03c0s\ncandidates.\n\n569\nrandom \u03c0s background. They \ufb01nd 1, 141, 500 \u00b1 1200 RS\nsignal events and 4030 \u00b1 90 WS signal from the \ufb01ts. Pro-\njections of the WS \ufb01t to data are shown in Fig. 19.2.9.\nFigure 19.2.8. mK\u03c0 and q distributions (Zhang, 2006):\n(a) RS mK\u03c0 for 0 MeV < q < 20 MeV; (b) RS q for\n1.81\nGeV/c2\n< mK\u03c0\n< 1.91\nGeV/c2; (c) WS mK\u03c0 for\n5.3 MeV < q < 6.5 MeV; and (d) WS q for 1.845 MeV/c2 <\nmK\u03c0 < 1.885 GeV/c2. Points with error bars represent the\ndata and the histograms di\ufb00erent components of the \ufb01t.\nFigure 19.2.9. mK\u03c0 and \u2206m distributions (Aubert, 2007j):\n(a) mK\u03c0 for WS candidates in a signal-enhanced region\n(0.1445 GeV/c2 < \u2206m < 0.1465 GeV/c2); (b) \u2206m for WS can-\ndidates in a signal-enhanced region (0.1843 GeV/c2 < mK\u03c0 <\n1.883 GeV/c2). Projections of the \ufb01tted signal and background\np.d.f.s are shown.\nThe DCS decay parameter RD and the mixing parame-\nters x\u20322 and y\u2032 are determined using unbinned, maximum-\nlikelihood \ufb01ts to the WS proper decay-time distribution.\nThe \ufb01t is done in several stages in order to \ufb01x some of\nthe parameters entering the \ufb01nal \ufb01t. The RS distribution\nis \ufb01tted \ufb01rst providing the parameters of the resolution\nfunctions to be used in the \ufb01t to the WS decay-time dis-\ntribution.\nFigure 19.2.10. Belle (top, from Zhang, 2006) and BABAR\n(bottom, from Aubert, 2007j) WS decay-time distributions\noverlaid with projections of \ufb01ts assuming no CP violation.\nBelle: Data distribution (points with error bars) for WS events\nin the signal enhanced region |mK\u03c0 \u2212mD0| < 22 MeV/c2 and\n|q \u22125.9 MeV| < 1.5 MeV. BABAR: (a) Data distribution and\n\ufb01t projections for combined D0 and D0 candidates in the sig-\nnal enhanced region 1.843 GeV/c2 < mK\u03c0 < 1.883 GeV/c2\nand 0.1445 GeV/c2 < \u2206m < 0.1465 GeV/c2. The \ufb01t result\nallowing (not allowing) mixing is shown as a solid (dashed)\nline. (b) Points indicate the di\ufb00erence between the data and\nthe no-mixing \ufb01t. The solid curve shows the di\ufb00erence between\n\ufb01ts with and without mixing.\nThe Belle decay-time \ufb01t uses a likelihood which is a\nfunction of the DCS and mixing parameters RD, x\u20322, and\ny\u2032. For event i, it is given by\ndPi\ndt\u2032 =\nh\nf i\nsigPsig(t\u2032; RD, x\u20322, y\u2032) + f i\nrndPrnd(t\u2032)\ni\n\u2297Rsig(ti \u2212t\u2032)\n\n570\nFigure 19.2.11. Belle (Zhang, 2006) and BABAR (Aubert,\n2007j) con\ufb01dence-level contours from the mixing \ufb01ts. Belle\n(top): (x\u20322, y\u2032) 95% con\ufb01dence-level regions showing the best\n\ufb01t result (point) assuming CP conservation. The statistical-\nonly (statistical plus systematic) contour for no CP violation\nis shown as a dotted (dashed) line. The solid line is the statis-\ntical plus systematic contour for the CP-allowed case. BABAR\n(bottom): Con\ufb01dence-level contours and \ufb01t result (point) for\n1 \u2212C.L. = 0.317(1\u03c3), 4.55 \u00d7 10\u22122(2\u03c3), 2.70 \u00d7 10\u22123(3\u03c3),\n6.33 \u00d7 10\u22125(4\u03c3), and 5.73 \u00d7 10\u22127(5\u03c3). The no-mixing point\nis shown as a \u201c+\u201d sign.\n+f i\nd3bPd3b(t\u2032) \u2297Rd3b(ti \u2212t\u2032)\n+f i\nds3Pds3(t\u2032) \u2297Rds3(ti \u2212t\u2032)\n+f i\ncmb\u03b4(t\u2032) \u2297Rcmb(ti \u2212t\u2032).\n(19.2.25)\nThe f i fractions are functions of mK\u03c0, q, and \u03c3t, and are\ndetermined on an event-by-event basis. Pj is the expected\ndecay-time distribution for event category j; it is given,\nfor example, by Eq. (19.2.22) for j = sig. Rj is the resolu-\ntion function for the corresponding events and \u2297denotes\nthe convolution. Signal and random \u03c0s background events\nhave the same resolution function since the slow pion is\nnot used in the vertex \ufb01t. BABAR models the WS decay-\nFigure 19.2.12. BABAR (Aubert, 2007j) WS branching frac-\ntions RWS for disjoint regions of measured proper time from \ufb01ts\nto the (mK\u03c0, \u2206m) plane (points with error bars). The dashed\nline shows the expected values of RWS for each slice in proper\ntime assuming the nominal mixing \ufb01t results. The \u03c72 with\nrespect to the mixing \ufb01t expectation is 1.5; assuming the no-\nmixing hypotheses (a constant RWS for all time slices), the \u03c72\nis 24.\ntime behavior as given by Eq. (19.2.22) convolved with\nthe signal resolution function as determined in the RS\ndecay-time \ufb01t. The background distribution is modeled in\na similar way as in the Belle case. The WS decay time dis-\ntributions overlaid with the \ufb01t projections for both Belle\nand BABAR are shown in Fig. 19.2.10.\nBoth Belle and BABAR present results from \ufb01ts un-\nder three di\ufb00erent assumptions: (1) that no mixing or CP\nviolation is present; (2) that mixing may be present, but\nthat there is no CP violation; and (3) that mixing and\nCP violation may be present. The \ufb01rst two sets of results\nare shown in Table 19.2.3, while the last is discussed in\nSection 19.2.7. A large correlation between x\u20322 and y\u2032 is\nseen in both experiments: \u22120.909 (Belle), \u22120.95 (BABAR).\nBABAR \ufb01nds the maximum-likelihood point to be\nin the non-physical region x\u20322 < 0. Two-dimensional\ncon\ufb01dence-level contours (see Fig. 19.2.11) in x\u20322 and\ny\u2032 are calculated based on the change in negative log-\nlikelihood values with respect to the no-mixing point for\nBABAR and using the Feldman-Cousins likelihood ratio or-\ndering (Feldman and Cousins, 1998) for Belle.\nSystematic uncertainties are included in the contour\nevaluation as discussed below.\nBABAR \ufb01nds that the \ufb01t allowing mixing provides a\nsubstantially better result than the one without mixing,\nas seen in Fig. 19.2.11. The likelihood maximum is at an\nunphysical value (x\u20322 = \u22122.2\u00d710\u22124, y\u2032 = 9.7\u00d710\u22123). The\ndi\ufb00erence in the \u03c72 between the most likely point in the\nphysically allowed region and the no-mixing point (x\u20322 =\n0, y\u2032 = 0) corresponds to a signi\ufb01cance for mixing of 3.9\u03c3\n(1 \u2212C.L. = 10\u22124) and provides evidence for mixing.128\n128 Here evidence is regarded as a result with a signi\ufb01cance\nof more than three standard deviations. For the explanation\nabout the signi\ufb01cance see Chapter 11.\n\n571\nAs a cross-check of the results, BABAR performs the\nno-mixing \ufb01t in slices in reconstructed decay time with\napproximately equal numbers of events. The resulting val-\nues of RD increase with increasing decay time as seen in\nFig. 19.2.12. The rate of increase is consistent with the\nmeasured mixing parameters and inconsistent with the\nno-mixing hypothesis.\nTable 19.2.3. D0 \u2212D0 mixing results using D0 \u2192K\u03c0 WS\ndecays. When two uncertainties are given, the \ufb01rst is statistical\nand the second systematic. Results with a single uncertainty\nhave both statistical and systematic components combined.\nParameter\nFit Results (\u00d710\u22123)\nBABAR\nBelle\n(Aubert, 2007j)\n(Zhang, 2006)\nAssuming no mixing or CP violation\nRD\n3.53 \u00b1 0.08 \u00b1 0.04\n3.77 \u00b1 0.08 \u00b1 0.05\nAssuming mixing but no CP violation\nRD\n3.03 \u00b1 0.16 \u00b1 0.10\n3.64 \u00b1 0.17\nx\u20322\n\u22120.22 \u00b1 0.30 \u00b1 0.21\n0.18+0.21\n\u22120.23\ny\u2032\n9.7 \u00b1 4.4 \u00b1 3.1\n0.6+4.0\n\u22123.9\nSigni\ufb01cance\n3.9\n2.0\nSome of the sources of systematic uncertainties investi-\ngated are event yields, background modeling, and decay-\ntime p.d.f. models. Belle also investigated the e\ufb00ects of\nchanging selection criteria such as particle-identi\ufb01cation\ncriteria, vertex \ufb01t \u03c72 requirement, and D\u2217momentum\nselection, which cause the signal-to-background rates to\nchange.\nThe e\ufb00ect of each individual systematic variation was\ncalculated from the change in \u22122\u2206ln L evaluated in the\n(x\u20322, y\u2032) plane between the nominal \ufb01t point and the new\n\ufb01t point of the variation under test. This value was scaled\nby a factor of 2.3, \u03c72\u2032 \u2261\u22122\u2206ln L/2.3, to yield the 68%\ncon\ufb01dence level for a single variable. The largest Belle sys-\ntematic is from the D\u2217momentum requirement with \u03c72\u2032 =\n0.083. When shifts from all systematic checks are added in\nquadrature, the overall scale factor is\np\n1 + P \u03c72\u2032\ni = 1.12\nwhich is used to scale the 95% C.L. contours as shown in\nFig. 19.2.11. As a cross-check, Belle \ufb01nds the results for\nthe two SVD subsamples to be within 0.6\u03c3 of each other.\nBABAR estimated systematic uncertainties and included\nthem in the evaluation of contours in a manner simi-\nlar to that of Belle, \ufb01nding the largest contribution to\np\n1 + P \u03c72\u2032\ni\n= 1.3 to be 0.06 from the modeling of the\nlong decay-time component of background D decays in\nthe signal region. A non-zero mean value of 3.6 fs for the\ndecay-time was found and is attributed to detector mis-\nalignments; this contributes 0.05 to the systematic uncer-\ntainty.\nBABAR validated the \ufb01tting procedure on MC data us-\ning both the full detector simulation and on ensembles of\nlarge parameterized (simulated MC) samples. The \ufb01t was\nfound to be unbiased in all cases. A \ufb01t allowing for mixing\nin the RS sample was performed and no signi\ufb01cant mixing\nwas observed, as expected. The staged \ufb01tting procedure\nwas cross-checked by performing a single simultaneous \ufb01t\nin which all parameters were allowed to vary; results were\nconsistent with the nominal \ufb01tting procedure.\n19.2.2.3 Measurements of the D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212\nThe advantages of the K3\u03c0 mode relative to K\u03c0 are its\nlarger branching fraction (about 8.1% compared to 3.9%\nfor K\u03c0) (Nakamura et al., 2010) and the improvement ob-\ntained in decay vertex resolution with four charged tracks\ninstead of two (0.15\u20130.16 ps compared to 0.17\u20130.18 ps for\nK\u03c0 and KK).129 On the other hand, the strong phase dif-\nference of the decay varies over its four-body phase space,\nmaking a simple interpretation of an average mixing rate\nmeasured over all of the phase space problematic. Possible\napproaches to this problem include limiting the measure-\nment to speci\ufb01c regions of interest in phase space or per-\nforming a four-body, time-dependent \ufb01t to the decay using\namplitude models. As with mixing studies using the K\u03c0\ndecay, CP violation can also be searched for by analyzing\nthe di\ufb00erence between D0 and D0 decays.\nBABAR has reported preliminary results from a time-\ndependent\nanalysis\nof\nthe\nfour-body\ndecay\nD0\n\u2192\nK+\u03c0\u2212\u03c0+\u03c0\u2212using a 230\nfb\u22121 data sample (Aubert,\n2006ap). The analysis is very similar to time-dependent\nanalyses of D0 \u2192K\u03c0. \u201cTagged\u201d events (where the decay\nchain D\u2217+ \u2192\u03c0sD0 is reconstructed) are used to deter-\nmine the production \ufb02avor of the D0 candidate via the\ncharge of the slow pion \u03c0s. The variables of interest are\nthe reconstructed D0 candidate mass mK\u03c0\u03c0\u03c0, the mass\ndi\ufb00erence \u2206m between the reconstructed D\u2217+ and the\nD0 candidate, and the decay time t and its uncertainty\n\u03c3t.\nThe D\u2217+ and D0 candidate masses and vertices are\nobtained from a vertex \ufb01t to the decay chain using a\nbeam spot constraint. The \ufb01t to the entire chain is re-\nquired to have large enough probability calculated from\nthe \ufb01t \u03c72, P(\u03c72) > 0.01. The D0 proper decay time t is\nobtained from the vertex \ufb01t along with its uncertainty \u03c3t.\nA requirement is imposed on the decay time uncertainty\nof \u03c3t < 0.5 ps. Unbinned extended maximum-likelihood\n\ufb01ts are performed to both right-sign and wrong-sign can-\ndidates. Two-dimensional distributions in (mK\u03c0\u03c0\u03c0, \u2206m)\nare \ufb01tted to a combination of p.d.f.s that describe the\nsignal shapes and background contributions. The large\namount of right-sign signal is used to determine the sig-\nnal shape parameters for the wrong-sign signal. Approxi-\nmately 3.5\u00d7105 right-sign signal candidates are found are\nfound in each, D0 and D0 sample, and about 1100 wrong-\nsign signal candidates for each. Backgrounds include \u201cbad\nslow pion\u201d events, where a properly-reconstructed D0 has\nbeen paired with an unassociated pion; this background\n129 The improvement w.r.t. two body decays is less than a\nfactor of 1/\n\u221a\n2 because of the lower momentum of the 4 tracks\nand thus increased multiple scattering.\n\n572\nsource peaks in mK\u03c0\u03c0\u03c0 but not in \u2206m. Another back-\nground comes from D0\u2019s where the kaon and one of the\npions are interchanged, but the D\u2217+ is otherwise correctly\nreconstructed. This source peaks in \u2206m only. The remain-\ning background component is combinatoric, which has no\npeaking behavior.\nFits to the decay time distributions are performed.\nAnalogously\nto\nEq.\n(19.2.22)\nthe\nwrong-sign\ntime-\ndependence is \ufb01tted to\n\u0393WS(t)\n\u0393RS(t) = eRD+\u03b1ey\u2032\nq\neRD(\u0393t)+(x2 + y2)\n4\n(\u0393t2). (19.2.26)\nQuantities that are integrated over all or part of phase\nspace are indicated by a tilde. \u03b1 is a factor describing the\nsuppression due to the strong phase variation over the\nphase space. Both a CP-conserving \ufb01t which considers\nD0 and D0 candidates together and a \ufb01t that is poten-\ntially sensitive to CP violation which treats them sepa-\nrately are performed. A description of the latter is given\nin Section 19.2.7.\nSystematics are evaluated by changing various parts of\nthe analysis, including the \u03c3t selection, the p.d.f. param-\neterization of the decay time resolution function, back-\nground p.d.f. shapes, and the measured D0 lifetime value.\nIn the latter, the \ufb01tted lifetime value is \ufb01xed in the \ufb01t to\nthe PDG value. Combined systematics are smaller than\nthe statistical errors on the measured quantities by about\na factor of \ufb01ve.\nAssuming CP conservation, the BABAR preliminary\nanalysis (Aubert, 2006ap) yields a measurement of RM\nand the interference term \u03b1ey\u2032 of\nRM = [0.019+0.016\n\u22120.015(stat) \u00b1 0.002(syst)]%\n\u03b1ey\u2032 = \u22120.006 \u00b1 0.005(stat) \u00b1 0.001(syst) (19.2.27)\nwhich are consistent with the no-mixing hypothesis at the\n4.3% con\ufb01dence level. Results of the \ufb01t allowing for CP\nviolation are given in Section 19.2.7.\nTwo-dimensional coverage probabilities of 68.3% and\n95.0% (\u2206log L = 1.15, 3.0, respectively) are shown in\nFig. 19.2.13 for the doubly Cabibbo-suppressed rate eRD\nvs. the mixing rate RM, and for the interference term\n\u03b1ey\u2032/\np\nx2 + y2 vs. RM.\n19.2.2.4 Summary on hadronic wrong-sign decays\nThe measurements of decay time distributions in D0 \u2192\nK+\u03c0\u2212decays played an important role in the initial\nsearches and \ufb01nally in the experimental discovery of the\nmixing phenomena in the neutral D meson system. It\nshould be noted that neither of the B Factory experi-\nments have performed measurements using their full data\nset, this remains a task for the future. The uncertainties\nof determinations of x\u20322 and y\u2032 on measurements made\nwith larger data sets will be, most probably, dominated\n\u02dcRD [%]\n0\n0.02\n0.04\n0.06\n0.3\n0.4\n0.5\nMax. Likelihood (CP Cons.)\n68.3% Cont. (CP Cons.)\n95.0% Cont. (CP Cons.)\n0\n0.02\n0.04\n0.06\n0.3\n0.4\n0.5\n(x2 + y2)/2 [%]\nBABAR\n230 fb\u22121 preliminary\n\u03b1y\u2032/\u221ax2 + y2\n0\n0.02\n0.04\n0.06\n-1\n-0.5\n0\n0.5\n1\nMax. Likelihood (CP Cons.)\n68.3% Cont. (CP Cons.)\n95.0% Cont. (CP Cons.)\n0\n0.02\n0.04\n0.06\n-1\n-0.5\n0\n0.5\n1\n\u0010\nx2 + y2\u0011\n/2 [%]\nFigure 19.2.13. Likelihood contours for the CP conserving \ufb01t\nfor eRD (top, from (Aubert, 2006ap)) and for the interference\nterm (bottom, BABAR internal, from the (Aubert, 2006ap) anal-\nysis) vs. the mixing rate RM. Solid line: \u2206ln L = 1.15; dotted\nline: \u2206ln L = 3.0.\nby experimental systematic uncertainties. The same mea-\nsurements provide important insights into a possible CP\nviolation in the D0 \u2212D0 system as discussed further in\nSection 19.2.7.\nIt should be noted that an analysis of wrong-sign de-\ncays D0 \u2192K+\u03c0\u2212\u03c00 has also been made by the BABAR\ncollaboration and is described in the section on decay time\ndependent Dalitz analyses, Section 19.2.4.1.\n\n573\n19.2.3 Decays to CP eigenstates\n19.2.3.1 Method\nIf CP is conserved, q = p \u2261\n1\n\u221a\n2, and the mass eigenstates\n|D1,2\u27e9=\n1\n\u221a\n2(|D0\u27e9\u00b1 |D0\u27e9) are CP-even and CP-odd; they\ndecay with the lifetimes \u03c41 = 1/\u03931 and \u03c42 = 1/\u03932, re-\nspectively, into CP-even and CP-odd \ufb01nal states, obey-\ning a simple exponential law, see Eq. (19.2.8). On the\nother hand the time evolution of decays to \ufb02avor spe-\nci\ufb01c \ufb01nal states is approximately exponential only for the\nCabibbo-favored decays, like D0 \u2192K\u2212\u03c0+. In this case\nEqs (19.2.13) simplify due to the fact that |Af/Af| \u226a1\n(and |Af/Af| \u226a1). Because of typically strong Cabibbo\nsuppression one can neglect the \u0393t and (\u0393t)2 terms in\nEqs (19.2.13).130 Hence the decay time distribution is ap-\nproximately exponential with a lifetime of \u03c4FS = 1/\u0393,\nwhere \u03c4FS denotes the lifetime for decays into \ufb02avor spe-\nci\ufb01c \ufb01nal state.\nThe quantity which represents the relative lifetime dif-\nference between decays to CP and \ufb02avor speci\ufb01c \ufb01nal\nstates is obtained experimentally as:\nyCP = \u03b7CP\n\u0012 \u03c4FS\n\u03c4CP\n\u22121\n\u0013\n,\n(19.2.28)\nwhere \u03b7CP = +1 (\u22121) for CP-even (CP-odd) \ufb01nal state,\nand \u03c4CP is the lifetime of decays to a CP \ufb01nal state. In\nthe limit of CP conservation \u03c4CP equals the lifetime of the\ncorresponding mass eigenstate, \u03c41 if \u03b7CP = +1 or \u03c42 if\n\u03b7CP = \u22121, and hence yCP equals the mixing parameter y.\nIf CP is violated yCP obtains a contribution from x:\nyCP = y cos \u03c6 \u22121\n2\n\u0010\nAM \u2212Af\nD\n\u0011\nx sin \u03c6,\n(19.2.29)\nwith AM and Af\nD de\ufb01ned in Eqs (19.2.17) and (19.2.18)\nand \u03c6 = arg(q/p). We assume here that CP violation is\nsmall, i.e. AM, Af\nD \u226a1, so that the time evolution is still\nwell described by an exponential law.\nTo derive equation (19.2.29) one starts with Eqs\n(19.2.11) and (19.2.12); after squaring the modulus we ob-\ntain:\nd\u0393D0\u2192f\ndt\n\u221d(1 \u2212Re [\u03bbf(ix + y)] \u0393t) e\u2212\u0393t\n(19.2.30)\nand\nd\u0393D0\u2192f\ndt\n\u221d\n\u0010\n1 \u2212Re\nh\n\u03bb\u22121\nf (ix + y)\ni\n\u0393t\n\u0011\ne\u2212\u0393t,\n(19.2.31)\nwhere\n\u03bbf = q\np\nAf\nAf\n\u2248\u03b7CP\n\u0012\n1 + 1\n2\nh\nAM \u2212Af\nD\ni\u0013\nei\u03c6.\n(19.2.32)\n130 For example, in D0 \u2192K\u2212\u03c0+ decays |AK\u2212\u03c0+/AK\u2212\u03c0+| =\n(5.75 \u00b1 0.07) \u00d7 10\u22122\n(Amhis\net\nal.,\n2012).\nThe\nde-\ncay\ntime\ndistribution\n[d\u0393(D0\n\u2192\nK\u2212\u03c0+) + d\u0393(D0\n\u2192\nK+\u03c0\u2212)]/dt \u221d[1 \u2212|AK\u2212\u03c0+/AK\u2212\u03c0+| y cos \u03b4K\u03c0 \u0393t]e\u2212\u0393t, where\n|AK\u2212\u03c0+/AK\u2212\u03c0+| y cos \u03b4K\u03c0+ = 2.3\u00d710\u22125 (Amhis et al., 2012).\nThen, Eqs (19.2.30) and (19.2.31) are added together,\nsince in this particular measurement no distinction is made\nbetween two possible initial D0 \ufb02avors (for measurements\nof CP violation in such decays, where one tags the \ufb02avor\nof the initial D0, see Section 19.2.7). We obtain:\nd\u0393\ndt \u221d\n\u0012\n1 \u2212\u03b7CP\n\u0014\ny cos \u03c6 \u22121\n2\n\u0010\nAM \u2212Af\nD\n\u0011\nx sin \u03c6\n\u0015\n\u0393t\n\u0013\ne\u2212\u0393t.\n(19.2.33)\nThe expression in front of e\u2212\u0393t can be regarded as a linear\nexpansion of another exponential function, since x, y \u226a1.\nDenoting the expression in the square brackets by yCP one\nobtains\nd\u0393\ndt \u221de\u2212\u03b7CP yCP \u0393te\u2212\u0393t = e\u2212(1+\u03b7CP yCP )\u0393t .\n(19.2.34)\nComparison of the decay time for decays into CP eigen-\nstates from the above equation, \u03c4CP = 1/[\u0393(1 + \u03b7CP yCP )],\nto the average decay time for decays to \ufb02avor speci\ufb01c \ufb01nal\nstates \u03c4FS = 1/\u0393 yields Eq. (19.2.28).\nThe measured proper decay time distribution can be\nwritten as:\ndN\ndt = N\n\u03c4\nZ \u221e\n0\nR(t \u2212t\u2032)e\u2212t\u2032/\u03c4dt\u2032 + B(t),\n(19.2.35)\nwhere R is a resolution function and B(t) is a background\ndistribution.\nThe most suitable decays to measure yCP are the CP-\neven decays D0 \u2192K+K\u2212and D0 \u2192\u03c0+\u03c0\u2212, because of\ntheir relatively large branching fractions and since the \ufb02a-\nvor speci\ufb01c decay D0 \u2192K\u2212\u03c0+ is kinematically similar.\nThe latter is important in reducing the systematic uncer-\ntainty due to resolution function parameterization. Both\nBABAR and Belle have found that up to an overall scale\nfactor in the width, the resolution function has the same\nshape for all three modes, including its o\ufb00set t0.\nAmong the CP-odd decays, D0 \u2192K0\ns\u03c9 with \u03c9 \u2192\n\u03c0+\u03c0\u2212\u03c00 and D0 \u2192K0\ns\u03c6 with \u03c6 \u2192K+K\u2212have the\nlargest branching fractions. Both resonances are also nar-\nrow. The drawbacks of these decays are smaller recon-\nstruction e\ufb03ciency due to K0\ns and \u03c00 reconstruction, a\ncontribution of other resonances which interfere with the\n\u03c9 or \u03c6, and large di\ufb00erences in the kinematics compared\nto D0 \u2192K\u2212\u03c0+. Up to now only the measurement of\nD0 \u2192K0\ns\u03c6 has been reported (see Section 19.2.3.3).\n19.2.3.2 Results for the D0 \u2192KK/\u03c0\u03c0\nDuring the search for CP violation in charm decays, the\nobservable yCP has been measured by a number of exper-\niments. In 2000 the interest of the scienti\ufb01c community\nwas triggered by the result of the FOCUS collaboration,\nwhich observed a high value of the parameter, albeit with\na rather large statistical uncertainty (Link et al., 2000).\nThe excitement subsided in 2002 following the measure-\nments from CLEO (Csorna et al., 2002) and Belle (Abe,\n2002a) providing more precise values consistent with zero.\nThe latter measurement was performed on an untagged\n\n574\nsample of D meson decays, the method is explained in\nmore detail below. The year 2007 marks the start of the\nera of sub-percent accuracy measurements of yCP using\nthe large B Factories data samples resulting in a number\nof statistically signi\ufb01cant results.\nThe Belle collaboration measured yCP (Staric, 2007)\nusing tagged samples. The D\u2217+ \u2192D0\u03c0+\ns decays are re-\nconstructed with a slow pion \u03c0s, and D0 \u2192K+K\u2212,\nK\u2212\u03c0+, and \u03c0+\u03c0\u2212.\nThe proper decay time of the D0 candidate is calcu-\nlated as described in Section 19.2.1.5. Selection based on\nthe the D(\u2217) momentum in the CM system as described\nthere is also applied. The decay time uncertainty \u03c3t is\nevaluated event-by-event from the covariance matrices of\nthe production and decay vertices, as explained in Sec-\ntion 6. Candidate D0 mesons are selected using the in-\nvariant mass of the D0 decay products, M, and the energy\nreleased in the D\u2217+ decay, q.\nAccording to Monte Carlo simulated distributions of\nt, M, and q, background events fall into four categories:\n(1) combinatorial, with zero apparent lifetime; (2) true\nD0 mesons combined with random slow pions (this has\nthe same apparent lifetime as the signal) (3) D0 decays\nto three or more particles, and (4) other charm hadron\ndecays. The apparent lifetime of the latter two categories\nis 10\u201330% larger than \u03c4D0.\nThe sample of events for the lifetime measurements\nis selected using |\u2206M|/\u03c3M, where \u2206M \u2261M \u2212mD0;\n|\u2206q| \u2261q \u2212(mD\u2217+ \u2212mD0 \u2212m\u03c0)c2; and \u03c3t. The invariant\nmass resolution \u03c3M varies from 5.5\u20136.8 MeV/c2, depend-\ning on the decay channel. Selection criteria are chosen to\nminimize the expected statistical error on yCP , using the\nMC: Belle requires |\u2206M|/\u03c3M < 2.3, |\u2206q| < 0.80 MeV, and\n\u03c3t < 370 fs. Using 540 fb\u22121 of data, they \ufb01nd 111 \u00d7 103\nK+K\u2212, 1.22 \u00d7 106 K\u2212\u03c0+, and 49 \u00d7 103 \u03c0+\u03c0\u2212signal\nevents, with purities of 98%, 99%, and 92% respectively.\nThe mixing parameter yCP is determined from the\nbinned maximum likelihood \ufb01t performed simultaneously\nto decay time distributions of all three decay modes. The\nresolution function of a single event is determined from the\nestimated accuracy of proper decay time \u03c3t as obtained\nfrom the covariance matrices of the vertex \ufb01ts. Ideally, it\nis described by a normalized Gaussian distribution with\na zero mean and with width equal to \u03c3t. However, such\na description is not su\ufb03cient because of multiple scatter-\ning of \ufb01nal state particles in the detector material, which\ncauses the tails of the distribution to increase. To param-\neterize the tails, one or two additional Gaussian terms are\nneeded, which share a common mean t0 and have widths\nproportional to \u03c3t. The common mean can be o\ufb00set from\nzero due to detector misalignment. The parameterization\nfor a single event thus reads:\nR(t) =\nng\nX\nk=1\nwkG(t; t0, \u03c3k),\n(19.2.36)\nwhere G(t; t0, \u03c3k) =\n1\n\u221a\n2\u03c0\u03c3k e\u2212(t\u2212t0)2/2\u03c32\nk are the normal-\nized Gaussian distributions, \u03c3k = sk\u03c3t are the widths,\nwk are their fractions and ng is the number of Gaus-\n\u03c3t /\u03c4PDG\nfi\n\u03c3i\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0\n0.2\n0.4\n0.6\n0.8\nFigure 19.2.14. Normalized distribution of errors \u03c3t on the\ndecay time t showing the construction of the resolution func-\ntion using the fraction fi in the bin with \u03c3t = \u03c3i. Belle internal,\nfrom the Staric (2012a) analysis.\nsian terms (usually ng = 3). This parameterization has\nthe following free parameters: t0, sk, k = 1, ..., ng and\nwk, k = 1, ..., ng \u22121. Parameters sk and wk are highly cor-\nrelated, causing the \ufb01t to sometimes have problems con-\nverging. In order to ensure stable \ufb01tting the fractions wk\ncan be \ufb01xed, using MC simulation, from a \ufb01t to the distri-\nbution of pulls, i.e. the normalized residuals (t \u2212tgen)/\u03c3t,\nwhere tgen is the generated proper decay time of an event.\nThe form Eq. (19.2.36) is suitable for use in an un-\nbinned maximum likelihood \ufb01t (see Chapter 11). The equiv-\nalent parameterization can be derived for a binned max-\nimum likelihood \ufb01t. In this case we \ufb01rst construct the\nnormalized distribution of \u03c3t by binning the events in a\nhistogram. Such a distribution is shown in Fig. 19.2.14: a\nbin i corresponds to a fraction fi of events with a time\nresolution \u03c3t = \u03c3i. The resolution function for the binned\n\ufb01t is thus:\nR(t) =\nn\nX\ni=1\nfi\nng\nX\nk=1\nwkG(t; t0, \u03c3ki),\n(19.2.37)\nwhere \u03c3ki = sk\u03c3i and the \ufb01rst sum runs over bins i of the\n\u03c3t distribution. Note, that Eq. (19.2.37) has the same free\nparameters as Eq. (19.2.36).\nThe resolution function shape including the o\ufb00set t0\nis found to be the same for all three considered decay\nmodes. To account for small di\ufb00erences in the widths of\nresolution functions among various decay modes, two pa-\nrameters SKK and S\u03c0\u03c0 are introduced to scale the overall\nwidth of the KK and \u03c0\u03c0 resolution functions relative to\nthe width of the K\u03c0 resolution function. All other param-\neters can be shared among the di\ufb00erent modes and can be\ndetermined by a simultaneous \ufb01t to all modes together.\nThe background term in Eq. (19.2.35) is parameterized\nassuming two lifetime components: an exponential and a\n\u03b4 function, each convolved with corresponding resolution\nfunctions as parameterized by Eq. (19.2.37). Separate B(t)\n\n575\nt (fs)\nEvents per 61.5 fs\n(a) KK\nt (fs)\nEvents per 61.5 fs\n(b) K\u03c0\nt (fs)\nEvents per 61.5 fs\n(c) \u03c0\u03c0\nt (fs)\n(NKK+N\u03c0\u03c0)/NK\u03c0\n(d)\n1\n10\n10 2\n10 3\n10 4\n-2000\n0\n2000\n4000\n10\n10 2\n10 3\n10 4\n10 5\n-2000\n0\n2000\n4000\n1\n10\n10 2\n10 3\n-2000\n0\n2000\n4000\n0.1\n0.11\n0.12\n0.13\n0.14\n0.15\n0.16\n0\n2000\n4000\nFigure 19.2.15. From (Staric, 2007). Belle results of the si-\nmultaneous \ufb01t to decay time distributions of (a) D0 \u2192K+K\u2212,\n(b) D0 \u2192K\u2212\u03c0+ and (c) D0 \u2192\u03c0+\u03c0\u2212decays. The cross-\nhatched area represents background contributions, the shape\nof which was \ufb01tted using M sideband events. (d) Ratio of\ndecay time distributions between D0 \u2192K+K\u2212, \u03c0+\u03c0\u2212and\nD0 \u2192K\u2212\u03c0+ decays. The solid line is a \ufb01t to the data points\nand the dashed line represents the no-mixing hypothesis.\nparameters for each \ufb01nal state are determined by \ufb01ts to\nthe t distributions of events in M sidebands. The MC is\nused to select the sideband region that best reproduces\nthe timing distribution of background events in the signal\nregion.\nThe results of a simultaneous \ufb01t are shown in\nFig. 19.2.15. The \ufb01tted lifetime of D0 \u2192K\u2212\u03c0+, \u03c4 =\n(408.7\u00b10.6(stat)) fs, is consistent with the world average\nof (410.1 \u00b1 1.5) fs. The value of yCP is determined to be\nyCP = (1.31 \u00b1 0.32(stat) \u00b1 0.25(syst))%.\nThis result and the BABAR result in the D0 \u2192K+\u03c0\u2212\ndecays, described in Section 19.2.2 represent the \ufb01rst ex-\nperimental evidence for D0 \u2212D0 mixing.\nBelle performed an updated measurement of D0 \u2192\nKK/\u03c0\u03c0 decay modes using the full available data sam-\nple\n(Staric, 2012a). Using a larger data sample a small\nbias on the measured lifetime depending on the D me-\nson polar angle in the CM system, \u03b8\u2217, is observed. It is a\nconsequence of small residual misalignments between the\nBelle tracking detectors. To reduce the systematic uncer-\ntainty due to such e\ufb00ects the measurement is performed\nin bins of cos \u03b8\u2217and the \ufb01nal value of yCP is obtained as\na weighted average of the values in individual bins. The\n\ufb01nal result is\nyCP = (1.11 \u00b1 0.22(stat) \u00b1 0.11(syst))%,\n(19.2.38)\nthe signi\ufb01cance of which is above \ufb01ve standard deviations\nconsidering the statistical uncertainty alone, and 4.5 \u03c3\nincluding systematic uncertainties.\nt (ps)\n-2\n-1\n0\n1\n2\n3\n4\nResiduals\nNormalized\n-2\n2\nEvents/0.05 ps\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nEvents/0.05 ps\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\nData\nSignal\nComb.\nCharm\nt (ps)\n-2\n-1\n0\n1\n2\n3\n4\nResiduals\nNormalized\n-2\n2\nEvents/0.05 ps\n1\n10\n2\n10\n3\n10\n4\n10\nEvents/0.05 ps\n1\n10\n2\n10\n3\n10\n4\n10\n1\n10\n2\n10\n3\n10\n4\n10\nData\nSignal\nComb.\nCharm\nFigure 19.2.16. From (Aubert, 2009v). BABAR results of the\nsimultaneous \ufb01t to decay time distributions of untagged sam-\nples: D0 \u2192K\u2212\u03c0+ (left) and D0 \u2192K+K\u2212(right).\nThe BABAR analysis of the tagged samples (Aubert,\n2008n) is similar to the Belle analysis. BABAR has used\n384 fb\u22121 of data and an unbinned maximum likelihood\n\ufb01t performed simultaneously to the K+K\u2212, K\u2212\u03c0+ and\n\u03c0+\u03c0\u2212decay modes. The main di\ufb00erence with respect to\nthe Belle analysis is the form of the resolution function\nused, Eq. (19.2.36). The result obtained is\nyCP = (1.24 \u00b1 0.39(stat) \u00b1 0.13(syst))%,\n(19.2.39)\nwhich is also evidence for D0 \u2212D0 mixing.\nBABAR has also performed an additional method: here\nyCP is measured using the untagged samples of D0 \u2192\nK+K\u2212and D0 \u2192K\u2212\u03c0+ (Aubert, 2009v). The event se-\nlection is similar to the tagged analysis except that the\nD\u2217+ is not reconstructed. The background is much higher\ncompared to the tagged analysis, as can be seen by com-\nparing Fig. 19.2.15 and Fig. 19.2.16 for the corresponding\ndecay modes. However, the signal yields compared to the\ntagged analysis are about \ufb01ve times higher. BABAR uses\nthe same \ufb01tting procedure as in the tagged analysis; the\n\ufb01t is shown in Fig. 19.2.16. The result on 384 fb\u22121 of\ndata is consistent with previous measurements, but with\nsmaller statistical and higher systematic errors: yCP =\n(1.12 \u00b1 0.26(stat) \u00b1 0.22(syst))%. The signi\ufb01cance of the\nresult is 3.3 \u03c3.\nThe above result is superseded by a similar analysis\nusing 468 fb\u22121 (Lees, 2013d) which uses both untagged\n(for the yCP measurement) and tagged (for A\u0393; see Section\n19.2.7) D0 decays:\nyCP = (0.72 \u00b1 0.18(stat) \u00b1 0.12(syst))%.\n(19.2.40)\n19.2.3.3 Results for the D0 \u2192K0\nS\u03c6\nA large fraction of D0 \u2192K0\nSK+K\u2212decays proceed via\nintermediate CP-odd K0\nS\u03c6 and CP-even K0\nSa0 resonant\nstates. Measurement of the apparent lifetimes \u03c4K0\nS\u03c6 and\n\u03c4K0\nSa0 of candidates populating the \u03c6 and a0 regions in\nthe Dalitz plot, respectively, allows for the extraction of\n\n576\n1.00\n1.05\n1.10\n1.15\n1.20\naribtrary units\ns0 [GeV2]\nFigure 19.2.17. From (Zupanc, 2009). Projections of time\nintegrated Dalitz distribution (solid black line) to s0 and con-\ntributions of CP-even and CP-odd amplitudes, |A1|2 (dotted\nblue line) and |A2|2 (dashed red line), respectively.\nthe mixing parameter yCP as\nyCP \u2261\u0393CP \u2212even \u2212\u0393CP \u2212odd\n\u0393CP \u2212even + \u0393CP \u2212odd\n=\n\u03c4K0\nS\u03c6 \u2212\u03c4K0\nSa0\n\u03c4K0\nS\u03c6 + \u03c4K0\nSa0\n.\n(19.2.41)\nThe above equation follows directly from the de\ufb01nition of\nEq. (19.2.28), noting that \u03c4CP =\u00b11 = \u03c4/(1 \u00b1 yCP ).\nHowever, as shown in Fig. 19.2.17, it is impossible to\nidentify the CP value of the \ufb01nal state of an individual\nD0 \u2192K0\nSK+K\u2212decay, since the a0 contribution also\npopulates the region s0 \u2261M 2\nK+K\u2212below the \u03c6 peak and\nvice versa. In order to extract the yCP parameter correctly\nthe CP content of each region needs to be estimated.\nThe time-dependent decay amplitudes of three-body\ndecays of D0 and D0 mesons to self-conjugated \ufb01nal states\nare described in detail in Section 19.2.4 and are given by\nd\u0393(D0)\nds0ds+dt = e\u2212t/\u03c4\n\"\n|A1(s0, s+)|2 e(1+y)\n(19.2.42)\n+ |A2(s0, s+)|2 e(1\u2212y)\n+2Re [A1(s0, s+)A\u2217\n2(s0, s+)] cos\n\u0012xt\n\u03c4\n\u0013\n+2Im [A1(s0, s+)A\u2217\n2(s0, s+)] sin\n\u0012xt\n\u03c4\n\u0013 #\nd\u0393(D0)\nds0ds+dt = e\u2212t/\u03c4\n\"\n\f\fA1(s0, s+)\n\f\f2 e(1+y)\n(19.2.43)\n+\n\f\fA2(s0, s+)\n\f\f2 e(1\u2212y)\n+2Re\nh\nA1(s0, s+)A\n\u2217\n2(s0, s+)\ni\ncos\n\u0012xt\n\u03c4\n\u0013\n+2Im\nh\nA1(s0, s+)A\n\u2217\n2(s0, s+)\ni\nsin\n\u0012xt\n\u03c4\n\u0013 #\n,\nwhere \u03c4 = 1/\u0393 is the D0 lifetime, s0 and s+ are\nthe invariant masses squared of K+K\u2212and KSK+\npairs, respectively. The decay amplitudes A1 and A2\ncan be expressed with D0 and D0 decay amplitudes A\nand A as A1(s0, s+) = [A(s0, s+) + A(s0, s+)]/2 and\nA2(s0, s+) = [A(s0, s+) \u2212A(s0, s+)]/2. In the isobar\nmodel (see Chapter 13) the amplitudes A and A are\nwritten as the sum of intermediate decay channel ampli-\ntudes (denoted by the subscript r) with the same \ufb01nal\nstate, A(s0, s+) = P\nr arei\u03c6rAr(s0, s+) and A(s0, s+) =\nP\nr arei\u03c6rAr(s0, s+) = P\nr arei\u03c6rAr(s0, s\u2212), where CP\nconservation in decay has been assumed in the \ufb01nal step.\nIf r is a CP eigenstate, then Ar(s0, s\u2212) = \u00b1Ar(s0, s+),\nwhere the sign +(\u2212) holds for a CP-even(-odd) eigen-\nstate. Hence the amplitude A1 is CP-even, and the am-\nplitude A2 is CP-odd. According to our current knowl-\nedge of the decay dynamics of D0 \u2192K0\nSK+K\u2212decays,\ntheir Dalitz model includes \ufb01ve CP-even intermediate\nstates: K0\nSa0\n0(980), K0\nSf0(1370), K0\nSf2(1270), K0\nSa0\n0(1450),\nK0\nSf0(980)); one CP-odd intermediate state (K0\nS\u03c6(1020));\nand three \ufb02avor-speci\ufb01c intermediate states (K\u2212a+\n0 (980),\nK\u2212a+\n0 (1450), K+a\u2212\n0 (980) (Aubert, 2008l).\nUpon squaring Eqs (19.2.42) and (19.2.43) and inte-\ngrating over s+, we obtain for the time-dependent decay\nrates of initially produced D0 and D0 (e.g. untagged sam-\nple):\nd\u0393\ndtds0\n\u221da1(s0)e\u2212t\n\u03c4 (1+y) + a2(s0)e\u2212t\n\u03c4 (1\u2212y),(19.2.44)\nwhere a1,2(s0)\n=\nR\n|A1,2(s0, s+)|2ds+. When in-\ntegrating the time-dependent decay rate over s+, all\nterms\ndepending\non\nthe\nmixing\nparameter\nx\n(e.g.\nRe [A1A\u2217\n2] cos(xt/\u03c4)) drop out (see the Appendix in Zu-\npanc, 2009). The two terms in Eq. (19.2.44) have a dif-\nferent time dependence as well as a di\ufb00erent s0 depen-\ndence (see Fig. 19.2.17). In any given s0 interval, R, and\nassuming y \u226a1, the e\ufb00ective D0 lifetime is\n\u03c4R = \u03c4 [1 + (1 \u22122fR)yCP ] ,\n(19.2.45)\nwhere fR =\nR\nR a1(s0)ds0/\nR\nR(a1(s0) + a2(s0))ds0, which\nrepresents the e\ufb00ective fraction of the events in the in-\nterval R due to the A1 amplitude. In Eq. (19.2.45) we\nintroduced the usual notation yCP for the mixing param-\neter y to indicate that we assumed CP conservation in\nderiving Eq. (19.2.44).\nThe mixing parameter yCP can thus be determined\nfrom the relative di\ufb00erence in the e\ufb00ective lifetimes of the\ntwo s0 intervals, one around the \u03c6(1020) peak (interval\nON) and the other in the sideband (interval OFF). Using\nEq. (19.2.45) and taking into account the fact that [1 \u2212\n(fON + fOFF)]yCP \u226a1, we obtain\nyCP =\n1\nfON \u2212fOFF\n\u0012\u03c4OFF \u2212\u03c4ON\n\u03c4OFF + \u03c4ON\n\u0013\n.\n(19.2.46)\nAccording to the Dalitz model of D0 \u2192K0\nSK+K\u2212decays\ngiven in (Aubert, 2008l), the di\ufb00erence in fON \u2212fOFF is\n\u22120.753 \u00b1 0.004 for the ON region given by MK+K\u2212\u2208\n\n577\n[1.015, 1.025] GeV/c2 and the OFF region given by the\nunion of intervals MK+K\u2212\u2208[2mK\u00b1, 1.010] GeV/c2 and\nMK+K\u2212\u2208[1.033, 1.100] GeV/c2.\nThe advantage of this method over the time-dependent\nDalitz analysis (described in Section 19.2.4) is that it can\nbe performed on the much larger untagged sample of D0\ndecays providing better sensitivity on the mixing-related\nparameter yCP . The disadvantage is that the sensitivity\nto the mixing parameter x is lost.\nBelle performed a measurement of yCP using this\nmethod on a data sample corresponding to 673 fb\u22121 (Zu-\npanc, 2009). They \ufb01nd (72.3 \u00b1 0.4) \u00d7 103 untagged signal\nD0 candidates in the ON region and (62.3 \u00b1 0.7) \u00d7 103\nevents in the OFF region. The proper decay time of the D0\ncandidate is reconstructed as described in Section 19.2.1.5.\nHowever it is worth noting, that Belle determines the D0\ndecay position by \ufb01tting only one of the charged kaons\nwith the neutral kaon to a common vertex. The reason\nfor using only K0\nSK\u00b1 pairs for the D0 decay vertex re-\nconstruction, despite the worse resolution, is the strong\ncorrelation between the K+K\u2212invariant mass MK+K\u2212\nand the mean proper decay time t of D0 mesons that\nhas been observed around m\u03c6 in simulations if the ver-\ntex was reconstructed from K0\nSK+K\u2212or from K+K\u2212\npairs (see Fig. 19.2.18). If not accounted for, this corre-\nlation could have biased the measurement of yCP , and it\nmay be explained as follows. Consider a K+K\u2212pair from\nthe decay of a \u03c6 resonance. The reconstructed invariant\nmass MK+K\u2212of the pair is determined from the relation\nM 2\nK+K\u2212= 2m2\nK\u00b1 +2EK+EK\u2212\u22122pK\u2212pK+ cos \u03b1rec, where\npK\u00b1 and EK\u00b1 are the momenta and energies of K\u00b1, and\n\u03b1rec is the reconstructed opening angle between K+ and\nK\u2212. If \u03b1rec is bigger (smaller) than the true opening angle\n\u03b1 because of, for example, the Coulomb multiple scatter-\ning of K\u00b1 in the detector material, MK+K\u2212is shifted to\nhigher (lower) values. Conversely, because of the narrow \u03c6\nresonance, m(K+K\u2212) \u2276m\u03c6 implies \u03b1rec \u2276\u03b1 for the ma-\njority of K+K\u2212pairs from \u03c6(1020). In addition, \u03b1rec \u2276\u03b1\nalso implies Lrec \u2276L and thus trec \u2276t, which then ex-\nplains the correlation between MK+K\u2212and t.\n1\n1.02\n1.04\n1.06\n1.08\n1.1\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\nMK+K\u2212[GeV]\ntn [\u03c4D0]\nK0\nSK+K\u2212Vertex\nON\n1\n1.02\n1.04\n1.06\n1.08\n1.1\n0.8\n0.85\n0.9\n0.95\n1\n1.05\n1.1\n1.15\n1.2\nON\nMK+K\u2212[GeV]\ntn [\u03c4D0]\nK0\nSK\u00b1 Vertex\n(a)\n(b)\nFigure 19.2.18. The mean proper decay time dependence\non MK+K\u2212, where the D0 decay point is determined with a\n(a) K0\nSK+K\u2212and (b) K0\nSK\u00b1 vertex constrained \ufb01t for signal\nD0 \u2192K0\nSK+K\u2212decays. The two vertical red dashed lines\nindicate the borders of the ON m(K+K\u2212) interval. Belle in-\nternal, from the (Zupanc, 2009) analysis.\nThe uncertainties on the vertices of the production and\ndecay of D0 mesons are re\ufb02ected in the uncertainties on\nthe reconstructed decay time trec. The widths (RMS) of\nthe resolution function are 1.35\u03c4D0 and 1.65\u03c4D0 when us-\ning the K0\nSK+K\u2212vertex and the K0\nSK\u00b1 vertex, respec-\ntively.\nIn Section 19.2.1.5 a typical p.d.f. used in a likelihood\n\ufb01t to the decay time distribution in charm mixing mea-\nsurements is given (see Eq. 19.2.21). There exists a sim-\npler and more robust method adopted in the analysis by\nBelle which has similar statistical sensitivity but does not\nrequire detailed knowledge of the resolution function or\nthe time distribution of backgrounds. The average of the\nconvolution is the sum of the averages of the convolved\nfunctions. The mean of the proper decay time distribu-\ntion of a sample consisting of signal decays with lifetime\n\u03c4s and signal fraction p and of background is thus given\nby\n\u27e8t\u27e9= p(\u03c4s + t0) + (1 \u2212p)\u27e8t\u27e9b,\n(19.2.47)\nwhere \u27e8t\u27e9and \u27e8t\u27e9b are the mean decay times of all and of\nbackground events, respectively. The latter was estimated\nusing the events in the sideband regions in the plane of\nD0 and K0\nS invariant masses. The parameter t0 represents\na possible non-zero mean of the signal resolution function.\nAny e\ufb00ect that may cause bias in the lifetime extraction\n(t0 \u0338= 0) such as misalignment of the vertex detector is\ncanceled by the use of kinematically equal decays \u2013 those\nin the ON and OFF region.\nBelle measured \u03c4ON+tON\n0\n= (413.4\u00b12.5) fs and \u03c4OFF+\ntOFF\n0\n= (412.7 \u00b1 3.0) fs (Zupanc, 2009). The measured\nvalues for \u03c4 + t0 are close to the world average for \u03c4D0,\nand, since yCP \u226a1, this implies t0/\u03c4 is \u223c1% or less.\nSince the topology of events in the ON and OFF intervals\nis almost identical, Belle assumes tON\n0\n= tOFF\n0\nand includes\na systematic error to account for this assumption. Using\nEq. (19.2.46) Belle \ufb01nds yCP = (+0.11 \u00b1 0.61 \u00b1 0.52)%,\nwhere the \ufb01rst uncertainty is statistical and the second\nsystematic. This is so far the only measurement of the\nmixing parameter yCP using a CP-odd \ufb01nal state in D0\ndecays. The value agrees with the measurements using\nCP-even \ufb01nal states described in Section 19.2.3.2.\n19.2.3.4 Summary on yCP\nMeasurements of yCP have been at the forefront of the\nsearches and subsequently precise measurements of D0 \u2212\nD0 mixing. Recent individual measurements exhibit signif-\nicances between three and \ufb01ve standard deviations. Fur-\nthermore, they still exhibit larger statistical than system-\natic uncertainties. However, a good control of the system-\natic e\ufb00ects will be needed in future measurements at su-\nper \ufb02avor factories to signi\ufb01cantly improve the accuracy\nof results. Main sources of systematic errors have been\nidenti\ufb01ed in the measurements performed at the B Fac-\ntories and several methods used to reduce the errors were\nsuccessfully exploited.\nSince the main systematic uncertainties are experimen-\ntal, and method dependent, one can calculate the average\n\n578\nvalue of the parameter yCP performed by the B Factories\nassuming uncorrelated errors. The result is\nyCP = (0.86 \u00b1 0.16)% .\n(19.2.48)\nIn the limit of CP conservation yCP = y, and hence the\nresult points to a signi\ufb01cant decay width di\ufb00erence for the\ntwo D meson mass eigenstates.\n19.2.4 t-dependent Dalitz analyses\n19.2.4.1 K+\u03c0\u2212\u03c00 \ufb01nal state\nFor WS decays D0 \u2192K+\u03c0\u2212\u03c00, with an additional \u03c00,\nthe phase space of possible \ufb01nal states is greatly in-\ncreased. Each state can be represented as a point in a\nDalitz plot with coordinates (s+, s0), where s+,0 are the\nsquared invariant masses for the K\u03c0+,0 systems. Ignor-\ning CP violation, each point is populated by decays with\na time evolution described by Eq. (19.2.13) with values\nfor \u03b4f and the ratio of |Af/Af| that are unique to that\npoint (i.e. they depend on s+,0). The interference term\nin Eq. (19.2.13), linear in xt and yt, provides the great-\nest sensitivity to x and y. As for all WS decay chan-\nnels, the measurement pro\ufb01ts from the interference of the\ndoubly-Cabibbo-suppressed (DCS) decay amplitude and\nthe Cabibbo-favored (CF) one preceded by mixing. The\ninterference term is, therefore, comparable in magnitude\nto each of the other two terms. Furthermore, a model for\nthe Dalitz plane point-to-point variations in \u03b4 can be used\nthat allows, in principle, both x and y to be determined.\nFor the two-body WS decays discussed in Section 19.2.2.1,\nthere is just a single value for \u03b4 that allows a determina-\ntion only of the combination y\u2032 = y cos \u03b4 \u2212x sin \u03b4 (and of\nx\u20322).\nUnfortunately, while a model can be found for the vari-\nations in \u03b4 across the separate Dalitz planes of D0 and D0\ndecays, no model exists for the unknown relative strong\nphase (\u03b4K\u03c0\u03c0) between one point in the D0 and another\nin the D0 Dalitz plane. Therefore, only values for x\u2032 =\nx cos \u03b4K\u03c0\u03c0 + y sin \u03b4K\u03c0\u03c0 and y\u2032 = y cos \u03b4K\u03c0\u03c0 \u2212x sin \u03b4K\u03c0\u03c0,\nrotated by this unknown phase, can be measured.\nTo date only BABAR has carried out a mixing analy-\nsis of this channel (Aubert, 2009u). The models for the\ncomplex decay amplitudes ADCS and ACF , respectively\nfor DCS and CF decays, are based on the isobar model\nconstructed from relativistic Breit-Wigner functions. The\nK\u03c0 S-wave components are described in a way suggested\nby K\u03c0 scattering in (Aston et al., 1988). This features\na Breit-Wigner phase variation for the scalar K\u2217\n0(1430)\nadded to a slowly varying background phase. Parameters\n(for the K\u03c0 S-wave and the complex coe\ufb03cients for the\nisobars K\u2217\u03c0, K\u03c1, etc.) are determined from \ufb01ts to the RS\nand WS samples. For ACF a \ufb01t to the time-integrated\nDalitz plot for RS decays D0 \u2192K+\u03c0\u2212\u03c00 (dominated by\nthis amplitude) is used.\nFor ADCS, a full time-dependent \ufb01t to the WS sam-\nple is made. The p.d.f. for this has the form given in\nEq. (19.2.13) with \u03bbf taken as\n\u03bb(s+, s0) = r0ei\u03b4K\u03c0\u03c0 ACF (s+, s0)\nADCS(s+, s0).\n(19.2.49)\nIn this \ufb01t, the mixing parameters are de\ufb01ned in the form\n(x\u2032/r0 and y\u2032/r0), where r0 is the ratio between the CF\nand DCS amplitudes de\ufb01ned above. These are allowed to\nvary in the \ufb01t.\nThe time-dependent p.d.f. for this \ufb01t is convolved with\na decay time resolution function derived from a \ufb01t to the\nRS events. The D0 lifetime is also determined from RS\nevents, and is found to agree with the world average (Be-\nringer et al., 2012).\nSignal samples consisting of 658, 986 RS (purity 99%)\nand 3, 009 WS (purity 50%) candidates are selected. Ma-\njor sources of background come from a variety of wrongly\nreconstructed D0 decays, wrongly associated slow pions\nor from a combination of both. In the WS sample, a small\nbackground also comes from events in which both K+\nand \u03c0\u2212are mis-identi\ufb01ed in the PID detectors. Simulated\nsamples of these categories are used to determine the con-\ntributions of each in the data. The shape of background\nevents in the RS and WS Dalitz plots are determined from\nM and \u2206m sideband regions in the data.\nFor both the RS and WS \ufb01ts, e\ufb03ciency variations over\nthe Dalitz plot are estimated from MC samples generated\nuniformly over the phase space.\nThe Dalitz plots for the RS and WS samples, together\nwith the distributions of M and \u2206m for the WS sample are\nshown in Fig. 19.2.19. In each of the Dalitz plots, bands\ndue to charged and neutral states for K\u2217(890) and for\ncharged \u03c1 are easily seen. CF modes preferentially decay\nvia K\u2217\u03c0 while DCS modes preferentially decay via K\u03c1\namplitudes.\nValues for x\u2032 and y\u2032 are obtained for the combined\nD0 and D0 samples. Separate values are also obtained\nfrom \ufb01ts to each of the two subsamples (for the latter see\nmore details in Section 19.2.7). In all cases, a value for\nr0 is required. This is derived from the ratio NWS/NRS,\nwhere NWS (NRS) is the number of wrong-sign (right-sign)\nsignal events observed and their respective time-integrated\np.d.f.s.\nThis procedure introduces a correlation between the\nx\u2032 and y\u2032 values obtained from the \ufb01t. Uncertainties in\nthese mixing parameters are, therefore derived from the\nvalues obtained in a similar way for 106 pairs of values\nfor (x\u2032/r0, y\u2032/r0) randomly generated in accordance with\nthe \ufb01t covariance matrix (assuming Gaussian errors and\nincluding systematic uncertainties).\nThe major systematic uncertainties arise from uncer-\ntainties in resonance masses and widths, and K\u03c0 S-wave\nparameters in the decay amplitude models, variations in\nthe estimates for the numbers of WS and RS signal events\nand in parameters describing the time resolution.\nThe mixing parameter results obtained are\nx\u2032 = (+2.61+0.57\n\u22120.68 \u00b1 0.39)%\n(19.2.50)\ny\u2032 = (\u22120.06+0.55\n\u22120.64 \u00b1 0.34)%\n(19.2.51)\n\n579\n0\n20\n40\n60\n80\n100\n120\n140\n160\n]\n4\n/c\n2\n [GeV\n+\n\u03c0\n-\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n-\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n(a)\n0\n5\n10\n15\n20\n25\n30\n]\n4\n/c\n2\n [GeV\n-\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n]\n4\n/c\n2\n [GeV\n0\n\u03c0\n+\nK\n2\nm\n0.5\n1\n1.5\n2\n2.5\n(b)\n]\n2\n [GeV/c\n0\n\u03c0\n-\u03c0\n+\nK\nm\n1.75\n1.8\n1.85\n1.9\n1.95\n2\nEvents/3.4 MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n]\n2\n [GeV/c\n0\n\u03c0\n-\u03c0\n+\nK\nm\n1.75\n1.8\n1.85\n1.9\n1.95\n2\nEvents/3.4 MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n(c)\n]\n2\n m [GeV/c\n\u2206\n0.14\n0.142\n0.144\n0.146\n0.148\n0.15\n2\nEvents/0.12 MeV/c\n0\n100\n200\n300\n400\n500\n]\n2\n m [GeV/c\n\u2206\n0.14\n0.142\n0.144\n0.146\n0.148\n0.15\n2\nEvents/0.12 MeV/c\n0\n100\n200\n300\n400\n500\n(d)\nFigure 19.2.19. From (Aubert, 2009u). Dalitz plots for (a) RS\ndecays D0 \u2192K+\u03c0\u2212\u03c00 and (b) WS decays D0 \u2192K+\u03c0\u2212\u03c00.\nInvariant mass distributions for (c) M (D0 decay products)\nand (d) \u2206m = (D\u2217\u2212D0) mass di\ufb00erence for selected WS\nevent candidates are also shown. Arrows indicate the M \u2212\u2206m\nregion selected for making the Dalitz plot \ufb01ts described in the\ntext.\nwhere the \ufb01rst uncertainties are statistical and the second\nare systematic. A Bayesian approach is used to estimate\nthe signi\ufb01cance of these values. The data from the D0 and\nD0 samples are consistent with a hypothesis of no mixing\n(x\u2032 = y\u2032 = 0) at the 3.2\u03c3 level. This constitutes evidence\nfor mixing.\n19.2.4.2 K0\nSh+h\u2212\ufb01nal state\nAnalyses of these channels are important because the \ufb01-\nnal states are CP self-conjugate. This implies a vanishing\nphase between two equal points in the Dalitz planes of D0\nand D0 decays (analogous to \u03b4K\u03c0\u03c0 for D0 \u2192K+\u03c0\u2212\u03c00 de-\ncays, \u03b4K0\nSh+h\u2212= 0). This allows a determination (modulo\nsign) of both x and y, and of their relative sign, with no\nunknown strong phase.\nAs for WS decays to D0 \u2192K+\u03c0\u2212\u03c00, the phase space\nof possible \ufb01nal states is represented by points in a Dalitz\nplot, with coordinates chosen as (s+, s\u2212), where s+,\u2212are\nthe squared invariant masses for the K0\nSh+,\u2212systems, re-\nspectively. Ignoring CP violation, each point is populated\nby decays with a time evolution described by Eq. (19.2.13)\nwith values for \u03b4K0\nSh+h\u2212and |\u03bb| = |AK0\nSh+h\u2212/AK0\nSh+h\u2212|\nthat are unique to that point. The largest sensitivity to\nx and y arises from the interference term in Eq. (19.2.13)\nwhich is linear in the two parameters. Unlike the WS decay\nchannel, however, these decays proceed either by a DCS\namplitude after mixing or by a CF one with no mixing\nat all. They are therefore dominated by the latter process\nand the interference term is very much smaller. The decay\namplitudes for a decay of D0 and D0 tagged at t = 0 are\nwritten as\nM(s+, s\u2212, t) = 1\n2p\n\u0002\np\n\u0000e1(t) + e2(t)\n\u0001\nA(s+, s\u2212)\n+q\n\u0000e1(t) \u2212e2(t)\n\u0001\nA(s\u2212, s+)\n\u0003\nM(s+, s\u2212, t) = 1\n2q\n\u0002\np\n\u0000e1(t) \u2212e2(t)\n\u0001\nA(s+, s\u2212)\n+q\n\u0000e1(t) + e2(t)\n\u0001\nA(s\u2212, s+)\n\u0003\n,(19.2.52)\nwhere e1,2(t) = e\u2212i(m1,2\u2212(i\u03931,2/2))t. Both BABAR (using\n486.5 fb\u22121, (del Amo Sanchez, 2010f)) and Belle (using\n540 fb\u22121, (Abe, 2007b)) have analyzed these channels.\nThe model for the complex decay amplitude A(s+, s\u2212),\ncontains CF and DCS terms. As before, these are based\non the isobar model constructed from relativistic Breit-\nWigner functions. The BABAR collaboration also used a\nK\u03c0 S-wave prescription similar to that outlined for the\nWS channel, and also used a K-matrix parameterization\nfor the \u03c0\u03c0 S-wave. In the Belle analysis the latter was used\nto estimate systematic uncertainties due to the assumed\nDalitz model. Details of these amplitudes are described in\nChapter 13. In calculating \u03bb(s+, s\u2212) in the standard \ufb01t,\nit is assumed that direct CP violation can be ignored so\nthat the amplitude A(s+, s\u2212) can be taken as A(s\u2212, s+).\nBelle also performs a \ufb01t, in which direct CP violation is\npermitted, where separate isobar coe\ufb03cients are allowed\nfor the de\ufb01nition of A(s+, s\u2212). They \ufb01nd, however, no\nsigni\ufb01cant di\ufb00erences in these coe\ufb03cients.\nAs in the WS K+\u03c0\u2212\u03c00 mode, the time-dependent p.d.f.\nis convolved with a decay time resolution function derived\nfrom the combined D0 and D0 event samples. This \ufb01t is\nperformed for both of these samples, each tagged by the\ncharge of the slow pion from D\u2217decays.\nBelle\nand\nBABAR\neach\nuse\napproximately\n540k\nK0\nS\u03c0+\u03c0\u2212candidates, and BABAR also uses 80k K0\nSK+K\u2212\nevents. Event purities for these samples range from 95-\n99%. Major sources of the small backgrounds come from\na variety of wrongly reconstructed D0 decays, wrongly\nassociated slow pions or from a combination of both. In\nthe K0\nS\u03c0\u03c0 mode, there is also a small, but signi\ufb01cant\nbackground from D0 \u2192K0\nSK0\nS decays and another from\nD0 \u21924\u03c0. Simulated samples of these backgrounds are\nused to determine the contributions of each in the data.\nE\ufb03ciency variations over the Dalitz plot are estimated\nfrom MC samples generated uniformly in phase space.\nThe decay time distributions are shown in Fig. 19.2.20.\nResults for the mixing parameters obtained are summa-\nrized in Table 19.2.4. They are obtained from \ufb01ts neglect-\ning CP violation, i.e. setting q = p = 1/\n\u221a\n2 in Eq. (19.2.52).\nSeparate \ufb01ts are performed taking into account the possi-\nbility of CP violation, as discussed further in Section 19.2.7.\nThe BABAR values are the most precise at present. Neither\nBelle nor BABAR show results more than 3\u03c3 from the \u201cno\nmixing\u201d point x = y = 0. The 95% C.L. contour for (x, y)\nparameters obtained by Belle is shown in Fig. 19.2.21.\nSystematic uncertainties in the measurement can be\ndivided into two groups: uncertainties related to experi-\n\n580\nFigure 19.2.20. From (del Amo Sanchez, 2010f). Decay time\ndistributions for (a) D0 \u2192K0\nS\u03c0\u2212\u03c0+, (b) D0 \u2192K0\nSK+K\u2212\ndecays with the time-dependent Dalitz plot \ufb01ts described in\nthe text.\nTable 19.2.4. Results of \ufb01ts to K0\nSh+h\u2212CP self-conjugate\nstates (del Amo Sanchez, 2010f; Abe, 2007b). The \ufb01rst un-\ncertainties are statistical and the second are systematic. The\nthird uncertainties arise from uncertainties in the model for\nA(s+, s\u2212).\nExperiment\nSample\nResults [\u00d7103]\nBABAR\n486.5 fb\u22121\nx = 1.6 \u00b1 2.3 \u00b1 1.2 \u00b1 0.8\nNo CP\nSignal: 540 \u00d7 103\ny = 5.7 \u00b1 2.0 \u00b1 1.3 \u00b1 0.7\nviolation\nPurity: 98.5%\nBelle\n540 fb\u22121\nx = 8.0 \u00b1 2.9+0.0+1.0\n\u22120.7\u22121.4\nNo CP\nSignal: 534 \u00d7 103\ny = 3.3 \u00b1 2.4+0.8+0.6\n\u22121.2\u22120.8\nviolation\nPurity: 98.5%\nx (%)\ny (%)\nno CPV (stat. only)\nno CPV\nCPV (stat. only)\nCPV\n-1\n0\n1\n2\n-1\n0\n1\n2\nFigure 19.2.21. 95% C.L. contour for the mixing parameters\n(x, y) as obtained from decay-time dependent analysis of Dalitz\ndistribution of D \u2192K0\nS\u03c0+\u03c0\u2212. From (Abe, 2007b).\nmental e\ufb00ects and those related to modeling the Dalitz\ndistribution. The contributions to the systematic error\nrelated to the former group are related to the e\ufb03ciency\nvariations across the DP, modeling of the DP and proper-\ntime distributions for background events, and the selec-\ntion criteria. The misidenti\ufb01cation of the D0 \ufb02avor from\nincorrectly assigned slow pions and variations of the time\nresolution function, including alternative ways to describe\nthe correlation between time and DP position also con-\ntribute to this group of uncertainties. An important source\nof the experimental systematic uncertainty is also the lim-\nited statistics of full detector simulations required to study\nbiases from event selection and instrumental e\ufb00ects arising\nfrom the small misalignment of the detector.\nThe second group of systematic uncertainties is esti-\nmated using alternative models for the decay amplitudes\nA(s+, s\u2212). This introduces one of the largest systematic\nuncertainties that would ultimately limit the precision of\nthese results. Further improvements should be possible,\nhowever, using a model-independent method to analyze\nthe Dalitz distribution. The method is based on the mea-\nsurements of the strong phase variation over the Dalitz\nplane as measured from the charm threshold data (Libby\net al., 2010) and does not require modelling of the Dalitz\ndistribution.\n19.2.4.3 Summary\nStudy of the decay-time dependence of Dalitz distribu-\ntions in multibody D0 decays provides an essential tool\nin studying the charm mesons mixing properties. It is the\nonly method which is sensitive to linear order in both mix-\ning parameters, x and y. Especially the time-dependent\nDalitz analysis of self-conjugated states (K0\nSh+h\u2212) en-\nables the determination of the parameters not rotated by\nan unknown phase. On the other hand such measurements\ncarry a systematic uncertainty arising from modeling the\nDalitz distribution. With the increasing statistical power\nof the data samples the models have been gaining in so-\nphistication. Nevertheless in the future the most accurate\nmeasurements of the mixing parameters can be expected\nusing a model independent approach (similar to the mea-\nsurement of \u03c63, see Section 17.8.4.3), which has not yet\nbeen used by the B Factories.\n19.2.5 Semileptonic decays\nIn the case of semileptonic decays, there are no Dou-\nbly Cabibbo Suppressed (DCS) modes as with wrong-sign\nhadronic decays, and only a pure mixing term modulates\nthe exponential lifetime. In the absence of CP violation,\nfrom Eqs (19.2.13) one obtains 131\nd\u0393(D0 \u2192X\u2113+\u03bd\u2113)\ndt\n\u223c|AX\u2113+\u03bd\u2113|2e\u2212\u0393t ,\nd\u0393(D0 \u2192X\u2113+\u03bd\u2113)\ndt\n\u223c|AX\u2113+\u03bd\u2113|2\n\u0014x2 + y2\n4\n(\u0393t)2\n\u0015\ne\u2212\u0393t .\n(19.2.53)\n131 By taking f = X\u2113+\u03bd\u2113, Af = Af = 0, Af = Af.\n\n581\nIntegrating d\u0393(D0 \u2192X\u2113+\u03bd\u2113)/dt over all times t > 0\nand normalizing to the integrated value of d\u0393(D0 \u2192\nX\u2113+\u03bd\u2113)/dt, one \ufb01nds that the relative time-integrated\nmixing rate is\nRM = \u0393(D0 \u2192X\u2113+\u03bd\u2113)\n\u0393(D0 \u2192X\u2113+\u03bd\u2113) = x2 + y2\n2\n.\n(19.2.54)\nBoth BABAR and Belle have searched for neutral D\nmixing in semileptonic K(\u2217)\u2113\u03bd\u2113\ufb01nal states, setting up-\nper limits with two conceptually di\ufb00erent analyses using\nan integrated luminosity of 344 fb\u22121 in the 2007 BABAR\nanalysis (Aubert, 2007aq) and 492 fb\u22121 for the 2008 Belle\nanalysis (Bitenc, 2008). The BABAR analysis uses the \ufb02a-\nvor of fully reconstructed hadronic charm decays in the\nhemisphere opposite the semileptonic signal to provide an\nadditional tag of the production \ufb02avor of signal decays\n(supplemental to the information from the slow pion in\nthe D\u2217signal decay). This double \ufb02avor tag very substan-\ntially reduces the rate of incorrectly tagged signal candi-\ndates, but it also greatly reduces the overall signal e\ufb03-\nciency. Belle\u2019s analysis does not use any additional \ufb02avor\ntagging information from the opposite hemisphere, relying\ninstead on a maximum likelihood \ufb01t to search for mixed\nsignal events. In both analyses the e\ufb03ciency corrected ra-\ntio of mixed D0 \u2192X\u2113\u2212\u03bd\u2113+ D0 \u2192X\u2113+\u03bd\u2113to un-mixed\nD0 \u2192X\u2113+\u03bd\u2113+ D0 \u2192X\u2113\u2212\u03bd\u2113events is used to determine\nthe constraints on x2 + y2.\n19.2.5.1 Belle\nBelle reconstructs the decay chain D\u2217+ \u2192D0\u03c0+\ns , D0 \u2192\nK\u2212l+\u03bdl, where l+ can be either an electron or a muon.\nThe charge of the slow pion \u03c0+\ns tags the production \ufb02avor\nof the neutral D, with unmixed decays having a lepton and\nsoft pion with identical charge (RS) and mixed decays hav-\ning a lepton and soft pion with opposite-sign charge (WS).\nAlthough the neutrino is not directly detected, the uncer-\ntainty due to the missing neutrino four-momentum can be\nminimized by calculating the mass di\ufb00erence between the\nD0 and its D\u2217+ parent\n\u2206M \u2261M(K\u2113\u03bd\u03c0s) \u2212M(K\u2113\u03bd).\n(19.2.55)\nSince the Belle detector covers nearly the entire solid\nangle surrounding the interaction point, the signal neu-\ntrino four-momentum can be estimated as\nP\u03bd = PCM \u2212PK\u2113\u2212PROE,\n(19.2.56)\nwhere PCM denotes the CM four-momentum of the initial\ne+e\u2212frame of reference and ROE stands for the \u201crest of\nthe event\u201d, i.e. the sum of the CM system four-momenta of\nall detected neutral and charged candidates in an event ex-\ncept for the signal kaon and lepton. Neutrals with energy\nless than 70 MeV/c2 and charged tracks with an impact pa-\nrameter larger than 5 cm (2 cm) in z (xy) are not used in\nthis context, although they are used in the computation\nof event-shape variables. Two kinematic constraints are\nused to improve the resolution of the neutrino momentum.\nThe invariant mass squared M 2(K\u2113\u03bd) \u2261(P\u03bd +PK\u2113)2/c2 is\ncomputed, and only candidates with \u221225 < M 2(K\u2113\u03bd) <\n64 GeV2/c4 are kept. For these events, PROE is rescaled by\na correction factor \u03be requiring that\nM 2(K\u2113\u03bd) = (PCM \u2212\u03bePROE)2/c2 \u2261M 2\nD0.\n(19.2.57)\nHaving thus determined \u03be, the neutrino four-momentum\nis then recalculated as P\u03bd = PCM \u2212PK\u2113\u2212\u03bePROE, and this\nnew neutrino momentum is used in the calculation of \u2206M.\nThe most probable value for \u03be is close to 1.0, although\nthere is a long tail in the distribution, which leads to an\naverage value of \u223c1.3.\nThe square of the missing mass M 2\n\u03bd \u2261P 2\n\u03bd = 0 is used as\nan additional kinematic constraint, where P 2\n\u03bd now includes\nthe \u03be correction factor. The squared missing mass can be\nexpressed in terms of the energies and magnitudes of the\nthree-momenta of the \ufb01nal state particles, along with the\ncosine of the angle between the vector momenta of the K\u2113\nsystem and \u03bePROE. This angle is corrected by rotating\nthe vector PROE in the plane de\ufb01ned by the vectors PROE\nand pK\u2113so that the null mass condition is enforced. The\n\ufb01nal neutrino four-momentum is then calculated using the\noriginal expression in Eq. (19.2.56) with a corrected PROE\nterm on the right-hand side, and this neutrino momentum\nis used to compute the value of \u2206M which is subsequently\nused in the \ufb01t to the data. The e\ufb00ect of the kinematic\nconstraints on the \u2206M distribution of the simulated WS\nsignal events is shown in Fig. 19.2.22.\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n0.14\n0.16\n0.18\n0.2\nMC signal, electron mode\nboth constr.\nM2(Kl\u03bd) constr.\nno constraints\n\u2206M [GeV/c2]\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nx 102\n0.14 0.15 0.16 0.17\nmuon mode, MC\nsignal\nassociated\nsignal\n\u2206M [GeV/c2]\nFigure 19.2.22. Left: The e\ufb00ect of the kinematic constraints\non the \u2206M distribution of the simulated D0 \u2192K\u2212e+\u03bde de-\ncays. Right: \u2206M distribution for simulated associated signal\nevents (see text for the explanation). From (Bitenc, 2008).\nThe ratio of WS to RS events NWS/NRS = (x2 +y2)/2\nis small (n.b. x2 + y2 \u223cO(10\u22124), see Section 19.2.1), or\nequivalently NWS \u226aNRS. Hence the central value and the\nstatistical uncertainty of the ratio is mainly determined by\nthe number of WS events.132 The selection criteria for the\n132 Note that in the ratio RM = NWS/NRS the statistical error\nis given by \u03c3R = RM\np\n(\u03c3WS/NWS)2 + (\u03c3RS/NWS)2; in case\nNRS and NWS are simply Poissonian distributed numbers of\nevents \u03c3R = RM\np\n(1/NWS) + (1/NRS) and the smaller of the\ntwo numbers determines the uncertainty.\n\n582\nWS events can thus be determined using a much larger\nsample of kinematically equal RS decays in accordance\nwith blind analysis principles described in Chapter 14.\nThe selection criteria include the requirements on min-\nimum invariant mass and momentum of the kaon and lep-\nton system, which suppress the backgrounds from various\nB meson decays. Two important sources of background\nare D0 \u2192K+K\u2212and \u03c0+\u03c0\u2212decays, which in case of\nmisidenti\ufb01cation of one or both \ufb01nal state mesons pro-\nduce a peak in the \u2206M distribution. These are e\ufb00ectively\nsuppressed by calculating the invariant mass of the K\u2113\nsystem, assigning an appropriate mass to the kaon and\nlepton candidate,133 and requiring that the resulting value\nis not consistent with the nominal D0 mass. The require-\nment on the magnitude of the CM momentum of the K\u2113\nsystem, p\u2217(K\u2113) > 2.0 GeV/c2, improves the resolution on\n\u2206M and rejects a majority of D0 mesons produced in B\nmeson decays. Events with \u03b3 \u2192e+e\u2212conversions are also\na source of background for electron and slow pion candi-\ndates. These are suppressed by calculating the invariant\nmass of the electron and the pion candidate, assigning the\nelectron mass to both tracks, and requiring the result to\nbe larger than 140 MeV/c2.\nApart from the aforementioned backgrounds and gen-\nuine signal there are other D meson decays with \u2206M in\nthe signal region. Despite the fact that the measurement\nmethod is not speci\ufb01cally aiming to reconstruct those de-\ncays the charge correlation between the lepton and the \u03c0s\nis the same as in the signal decays and hence they carry\nsimilar information on the possible mixing parameters. For\nthis reason they are referred to as the associated signal:\n\u2013 D0 \u2192K\u2212\u03c00\u2113+\u03bd,\n\u2013 D0 \u2192K\u2217\u2212\u2113+\u03bd\u2113, followed by K\u2217\u2212\u2192K\u2212\u03c00,\n\u2013 D0 \u2192\u03c0\u2212\u2113+\u03bd\u2113,\n\u2013 D0 \u2192\u03c1\u2212\u2113+\u03bd\u2113, followed by \u03c1\u2212\u2192\u03c0\u2212\u03c00,\n\u2013 D0 \u2192K\u2217\u2212\u2113+\u03bd\u2113, followed by K\u2217\u2212\u2192K0\u03c0\u2212.\nThe mass di\ufb00erence distribution of simulated associated\nsignal events is shown in Fig. 19.2.22.\nThe mixed events have on average a larger decay time\nthan the background WS events. Hence requiring a larger\nvalue of the decay time for selected events can improve\nthe sensitivity. This is illustrated in Fig. 19.2.23 showing\nthe decay time distribution of WS (signal) events.\nThe proper decay time scaled in units of the nominal\nPDG D0 lifetime (Yao et al., 2006) is calculated from the\nD0 momentum pD0 and \ufb02ight distance l:\ntD0 =\nmD0l\n\u03c4D0pD0 .\n(19.2.58)\nThe D0 \ufb02ight distance is the distance between the D0 pro-\nduction and decay vertices, respectively rprod and rdec.\n133 Speci\ufb01cally, the invariant mass is calculated assuming the\npion mass for the kaon candidate and the pion mass for the\nlepton candidate, as well as with the kaon mass for the lepton\ncandidate.\nThe D0 momentum is calculated by summing the mo-\nmenta of the daughter particles. The decay vertex is ob-\ntained by \ufb01tting the kaon and lepton tracks to a com-\nmon vertex. The production vertex is obtained by extrap-\nolating the D0 momentum vector to the e+e\u2212interaction\nregion. Given the relatively large longitudinal extent of\nthe interaction region as explained in Chapter 6, only the\ntransverse components (x, y) are used. The radial \ufb02ight\ndistance lxy is calculated as\nlxy =\n(rx\ndec \u2212rx\nprod, ry\ndec \u2212ry\nprod) \u00b7 (px\nD0, py\nD0)\nq\n(px\nD0)2 + (py\nD0)2\n.\n(19.2.59)\nThe dimensionless proper decay time is then calculated as\ntxy =\nmD0lxy\n\u03c4D0\nq\n(px\nD0)2 + (py\nD0)2\n.\n(19.2.60)\nBecause of data recorded by two di\ufb00erent Belle SVD de-\ntector con\ufb01gurations (Chapter 2) the selected sample is\ndivided into two subsamples. The subsamples are denoted\nas \u2113\u2212i, where \u2113= e, \u00b5 determines the type of the lepton\nand i = 1, 2 the SVD con\ufb01guration.\n \n \n \n102\n+\n0\n5\n10\n15\n20\n25\n\u221210\n\u22125\n0\n5\n1\nDATA, electron SVD\u22122, W\ntxy [\u03c4D]\nEvents / 0.1\n0\n50\n100\n0.14\n0.16\n0.\nWS, electron mode\nSVD-2\n2.5 < txy < 3.1\n\u03c72/d.o.f. = 47.5/40\n\u2206M [GeV/c2]\nEvents / MeV/c2\n2\nFigure 19.2.23. Left: The distribution of the decay time in\nthe transverse plane for selected WS events (dots). The solid\nline shows the simulated distribution of signal events and the\nvertical arrows the interval selected for the signal. Right: An\nexample of the \ufb01t to the \u2206M data distribution (points) in a\nsingle txy bin for the WS e\u22122 data subsample. The histogram\nis the \ufb01t to the distribution, with the contribution of signal\nshown along the horizontal axis. From (Bitenc, 2008).\nThe relative rate of mixed events N i\nWS/N i\nRS is deter-\nmined separately for i = 1, 6 in six intervals of txy for\ndecay times 1.6 < txy < 9.0. An example of the \ufb01t to the\n\u2206M distribution of WS events in a single txy bin is shown\nin Fig. 19.2.23. The shape of the signal is obtained from\nthe simulation. The background is divided into two cate-\ngories: the correlated and the un-correlated background.\nThe former is de\ufb01ned as a combination in which either\nthe lepton or the kaon candidate or both originate from\nthe same decay chain as the slow pion. The shape of this\nbackground is obtained from MC simulation as well. The\n\n583\nmajority of events in the WS sample belong to the un-\ncorrelated background. The shape of the \u2206M distribution\nfor these events is obtained from real data by embedding a\nslow pion candidate track into another event and following\nthe same analysis procedure as described above.\nAveraging the (N i\nWS/N i\nRS)(\u03f5i\nRS/\u03f5i\nWS) values over the\ntxy bins, where \u03f5i\nRS,WS are the relative acceptances for the\nRS and WS events in the corresponding bins, one obtains\nRM \u2261(x2+y2)/2 values for \u2113\u2212i subsamples. Those values\nare shown in Fig. 19.2.24.\n-10\n-5\n0\n5\n10\n15\ne-1\ne-2\n\u00b5-1\n\u00b5-2\nstat. and total uncert.\n RM [ 10-4 ]\nFigure 19.2.24. Values of RM \u2261(x2 + y2)/2 in subsamples\nof selected D0 \u2192K\u2212\u2113+\u03bd\u2113events (dots with error bars repre-\nsenting the statistical and systematic uncertainty). The dashed\nand dotted lines represent the average value and its \u00b11\u03c3 in-\nterval. The solid line corresponds to no mixing. From (Bitenc,\n2008).\nThe average value of the measurement is\nRM = (1.3 \u00b1 2.2 \u00b1 2.0) \u00d7 10\u22124 ,\n(19.2.61)\nincluding the statistical and systematic uncertainty. The\nvalue is consistent with no-mixing and is close to the\nboundary of the physical region (RM > 0). In order\nto obtain the upper limit in the vicinity of the physi-\ncal boundary a Feldman-Cousins (Feldman and Cousins,\n1998) method is used. The 90% C.L. upper limit is found\nto be RM < 6.1 \u00d7 10\u22124.\nOne of the largest sources of systematic uncertainty\nis the \ufb01nite statistical signi\ufb01cance of the samples used to\nobtain the shapes of the signal and background \u2206M distri-\nbution. The uncertainty is estimated by variation of those\nshapes within their statistical uncertainties. Another im-\nportant source of systematic error is the amount of the\ncorrelated background in the WS sample. It is estimated\nby conservatively varying the branching fractions of the\nmain decay mode contributions to this type of the back-\nground.\n19.2.5.2 BABAR\nIn the BABAR analysis (Aubert, 2007aq), the initial \ufb02a-\nvor of the neutral D meson is tagged twice, once using\nthe slow pion from a charged D\u2217decay whose neutral D\ndaughter decays semileptonically, and once using the \ufb02a-\nvor of a high-momentum D fully reconstructed in the CM\nhemisphere opposite the semileptonic candidate. Tagging\nthe \ufb02avor at production twice, rather than once, highly\nsuppresses the background from false WS slow pions, but\nit also reduces the signal by an order of magnitude. Ad-\nditional signal candidate selection criteria similar to that\nemployed above by Belle are used to minimize the remain-\ning sources of background.\nFive hadronic tagging samples are used, where three\nsamples explicitly require a reconstructed D\u2217+: D\u2217+ \u2192\nD0\u03c0+ with D0 \u2192K\u2212\u03c0+, D0 \u2192K\u2212\u03c0+\u03c00, and D0 \u2192\nK\u2212\u03c0+\u03c0+\u03c0\u2212, and the other two samples are CF decays\nwith no D\u2217+ requirement: D0 \u2192K\u2212\u03c0+ and D+ \u2192\nK\u2212\u03c0+\u03c0+. Candidates from the D\u2217+ sample are explic-\nitly excluded from the inclusive D0 \u2192K\u2212\u03c0+ sample to\nensure that the tagging samples are disjoint.\nThe selection criteria for the tagging samples, such as\nthe \u2206M ranges for the D\u2217modes or the use of production\nand decay vertex separation for the D+ mode, vary from\nchannel to channel to balance high purity against high\nstatistical signi\ufb01cance. To eliminate candidates from BB\nevents, the CM momentum of the tag-side D must be at\nleast 2.5 GeV/c.\nUsing a method similar to that employed above by\nBelle, the optimal proper decay time range in which to\nsearch for mixed decays was similarly found to be \u223c1.5\u2212\n9.5 nominal D0 lifetimes. The BABAR \ufb01t to the \u2206M distri-\nbution for double-\ufb02avor-tagged RS data events uses a \ufb01t\nmodel similar to Belle\u2019s, which is shown in Figure 19.2.25\nbefore and after additional kinematic selection exploiting\ncorrelations between tag and signal hemispheres are ap-\nplied. The \ufb01nal RS signal yield is 4780 \u00b1 94 events after\nall event selections are imposed.\n]\n2\n M [GeV/c\n\u2206\n0.15\n0.2\n0.25\n0.3\n0.35\n2\nEntries/3.5 MeV/c\n0\n200\n400\n600\n800\n1000\n]\n2\n M [GeV/c\n\u2206\n0.15\n0.2\n0.25\n0.3\n0.35\n2\nEnties/3.5 MeV/c\n0\n200\n400\n600\n800\nFigure 19.2.25. From (Aubert, 2007aq). RS data \u2206M dis-\ntribution. The main plot shows the RS data (points) before\nimposing the double-tag kinematic selection, and the projec-\ntions of the total \ufb01t p.d.f. (solid line) and the background p.d.f.\n(dashed line). The inset plot shows the RS \u2206M distribution\nafter the double-tag kinematic selection criteria are applied.\n\n584\nThree regions of \u2206M are considered to determine the\nnumber of WS mixed events: the signal region, \u2206M \u2264\n0.20 GeV/c2; the near background region, 0.20 < \u2206M \u2264\n0.25 GeV/c2; and the far background region, 0.25 < \u2206M \u2264\n0.35 GeV/c2. These \u2206M ranges are shown in Fig. 19.2.26,\nand are respectively labeled \u201c1\u201d, \u201c2\u201d and \u201c3\u201d in the plot.\nA blind analysis was performed where the signal region\nwas not examined until after all details of event selection,\n\ufb01t methodology and statistical procedures for setting up-\nper limits were \ufb01nalized. An estimated 2.85 background\nevents was expected in the signal region and, as shown\nin Fig. 19.2.26, three events were found there, yielding a\nnet WS signal of 0.15 events. Note the di\ufb00erence in the\nyields and purities of the selected samples using the Belle\nsingle tag method (Fig. 19.2.23) and the BABAR double\ntag method (Fig. 19.2.26).\n]\n2\nM [GeV/c\n\u2206\n0.15\n0.2\n0.25\n0.3\n0.35\n2\nEntries / 3.5 MeV/c\n0\n0.5\n1\n1.5\n2\n1\n2\n3\nFigure 19.2.26. From (Aubert, 2007aq). WS data \u2206M dis-\ntribution. The dark histogram shows WS events in the data\npassing all event selections. The light histogram shows WS\nevents passing all selections except the double-tag kinematic\nselection. Region \u201c1\u201d is the signal region, \u201c2\u201d is the near side-\nband, and \u201c3\u201d is the far sideband.\nTo calculate con\ufb01dence intervals for the number of\nmixed events observed, a systematic uncertainty associ-\nated with the WS background estimate is determined us-\ning ten data/MC background control samples. The largest\ndiscrepancy between the data and MC rates, 50%, is as-\nsigned as the systematic uncertainty associated with the\nratio between the MC estimate of the background rate\nand its true value. To quantify con\ufb01dence intervals for\nthe number of WS mixed events, a likelihood function is\nused, L(n, nb; s, b), for the number of events observed in\nthe signal region of the WS data sample, n, and the cor-\nresponding number observed in the MC sample, nb. The\nlikelihood L(n, nb; s, b) depends upon the true signal rate\ns and the true background rate b in the signal region, and\nalso accounts for the systematic uncertainty in the ratio of\nthe true background rate in data to that estimated from\nMC. The value of (s, b) which maximizes the likelihood\nfunction, Lmax, is denoted by (bs,bb). As one might na\u00a8\u0131vely\nexpect, bb is equal to nb times the ratio of data and MC\nluminosities, while bs = n \u2212bb. A scan is made for the val-\nues of s where \u2212lnL(s) changes by 0.50 [1.35]; here L(s)\ndenotes the likelihood at s maximized with respect to b.\nThe lower and upper values of s which satisfy this con-\ndition de\ufb01ne the nominal 68% [90%] con\ufb01dence interval\nfor s, assuming Gaussian uncertainties. The con\ufb01dence in-\ntervals produced using this procedure provide frequentist\ncoverage accurate to within a few percent. A central value\nof RM = 0.4 \u00d7 10\u22124 is found, with 68% and 90% con-\n\ufb01dence intervals [\u22125.6, 7.4] \u00d7 10\u22124 and [\u221213, 12] \u00d7 10\u22124,\nrespectively.\n19.2.5.3 Summary\nIn summary, semileptonic decays of D0 mesons can be\nexploited to determine the time integrated mixing rate.\nBy determining the yield of WS decays D0 \u2192X\u2113\u2212\u03bd\u2113\nrelative to the RS decays D0 \u2192X\u2113+\u03bd\u2113one determines\nRM = NWS/NRS = (x2 + y2)/2. Both single and double\ntagged event selections, thereby isolating samples di\ufb00er-\ning in their statistical power and purity, have been used\nby Belle and BABAR. Averaging the two measurements\ndescribed results in\nRM = (0.011 \u00b1 0.027)%\n(19.2.62)\nwhere the error contains statistical and systematic uncer-\ntainties (all individual errors are assumed to be uncorre-\nlated).\nThough wrong-sign semileptonic decays are a sure sign\nof mixing, the low mixing rate (\u224310\u22125) and the need\nto apply strong background suppression requirements will\ncontinue to limit the use of these decays in the mixing\nmeasurements for some time to come.\n19.2.6 t-integrated CP violation measurements\nIn studies of CP violation in the decays of D mesons one\nusually measures time-integrated asymmetries of partial\ndecay rates, de\ufb01ned as\nAf\nCP \u2261\u0393(D \u2192f) \u2212\u0393(D \u2192f)\n\u0393(D \u2192f) + \u0393(D \u2192f) .\n(19.2.63)\nThe underlying CP violating parameters, see Eqs (19.2.17,\n19.2.18, and 19.2.19) upon which such asymmetries de-\npend are determined by the speci\ufb01c \ufb01nal state f and by\nthe type of D meson. For charged D mesons, for example,\nonly mode speci\ufb01c CP violation in the decays is possible.\n\n585\nOn the other hand, for neutral D mesons, these asymme-\ntries can include direct (af\ndir) and indirect (aind) asymme-\ntry contributions (see Section 19.2.1.3):\nAf\nCP = af\ndir + aind.\n(19.2.64)\nThe direct asymmetry term corresponds to the CP\nviolation in decays. The indirect asymmetry in decays to\nCP eigenstates (like K+K\u2212or \u03c0+\u03c0\u2212) consists of the term\ndue to the CP violation in mixing, \u2212\u03b7f(y/2)AM cos \u03c6,\nand of the term due to the mixing induced CP violation,\n\u03b7fx sin \u03c6. \u03b7f denotes the CP eigenvalue of the \ufb01nal state\n(\u03b7f = +1 for CP-even and \u03b7f = \u22121 for CP odd states).\nHence\nAf\nCP = af\ndir \u2212\u03b7f(y/2)AM cos \u03c6 + \u03b7fx sin \u03c6.\n(19.2.65)\nAs a result of D0 \u2212D0 mixing, CP asymmetries for\nD0 mesons depend upon the interval of decay time, t,\nover which the asymmetry is integrated. At the B Facto-\nries, time resolution is comparable with the D0 lifetime,\n\u03c4D0. Therefore, no D0 decay vertex separation require-\nment is imposed on the samples used in any of the anal-\nyses and integration times include t = 0. In contrast,\nhadron collider experiments (CDF, LHCb, etc.) impose\ndecay length based selections to reduce large combinato-\nrial backgrounds. There, the integration times begin at\nt = tmin > 0. In all cases, the upper end of the range,\ntmax is large and can be taken as in\ufb01nite. To \ufb01rst order in\nthe small parameter y, the values for Af\nCP measured can\nbe approximated (see, for example Gersabeck, Alexander,\nBorghi, Gligorov, and Parkes, 2012) as combinations of\naf\ndir and aind that are linear in tmin, thereby allowing sep-\narate values for af\ndir and aind to be estimated.134\nThe feasibility of using measurements of CP asymme-\ntries as a function of time (as distinct from values ACP\nintegrated over \ufb01nite time periods) has also been stud-\nied (Bevan, Inguglia, and Meadows, 2011). Many decay\nmodes can be used to study weak phases in D0 meson de-\ncays in much the same way that such measurements were\nused in the B Factory measurements of the CKM phases\n\u03c61\u22123. Such measurements will be feasible using samples\nabout 100 times larger than those of the B Factory\u2019s.\n19.2.6.1 Using data to measure detector induced\nasymmetries\nIn the experimental determination of the physics param-\neter Af\nCP other asymmetries not originating from the CP\nviolation may enter and have to be corrected for. These in-\nclude detector induced asymmetries, for example an asym-\nmetry in the reconstruction e\ufb03ciencies of positively and\nnegatively charged tracks, as well as the forward-backward\n(FB) asymmetry due to the \u03b3\u2217\u2212Z0 interference in e+e\u2212\u2192\ncc. The former may be induced by di\ufb00erent cross-sections\nfor the interaction of particles and anti-particles in the\n134 For the \ufb01nal states that are CP eigenstates aind does not\ndepend on decay mode f while af\ndir does.\nmaterial of the detector.135 Such subtle e\ufb00ects are not\ndescribed to a su\ufb03cient accuracy in the simulated data\nsamples \u2014 note that as explained in Section 19.2.1.3 in\nthe search for the CP violation in the charm sector one\nis interested in e\ufb00ects of the order of 10\u22123 \u2014 and hence\nthey must be estimated using data control samples.\nTo explain ideas used in the corrections for the non-CP\nviolating asymmetries mentioned above let us \ufb01rst con-\nsider an example of a charged D meson decay, D\u00b1 \u2192\nXh\u00b1, where X denotes a neutral hadronic system which is\nself-conjugated (and hence the same for the D+ and D\u2212)\nand h\u00b1 represents a charged hadron. The experimentally\ndetermined asymmetry is\nArec = N(D+ \u2192Xh+) \u2212N(D\u2212\u2192Xh\u2212)\nN(D+ \u2192Xh+) + N(D\u2212\u2192Xh\u2212) ,\n(19.2.66)\nwhere N denotes the number of observed decays. Taking\ninto account small magnitudes of all CP and non-CP vi-\nolating asymmetries (i.e. neglecting quadratic and higher\nterms) the measured asymmetry can be expressed as the\nsum of various contributions\nArec = ACP + AFB + Ah+\n\u03f5\n,\n(19.2.67)\nwhere AFB and Ah+\n\u03f5\nare the forward-backward asymmetry\nand the detection e\ufb03ciency asymmetry between positively\nand negatively charged tracks.\nIn order to correct for these one has to use real data\nas much as possible to minimize systematic uncertainty\nassociated with the correction. The control samples and\nthe technique used vary from mode to mode. For exam-\nple, if two appropriate control samples can be found, for\nwhich CP violation is negligible and the asymmetry due to\nAFB is equal between the two (both assumptions must be\nsatis\ufb01ed at least to the level below the ACP measurement\nsensitivity), then\nAcont1\nrec\n= Acont1\nFB\n+ Ah+\n\u03f5\n,\nAcont2\nrec\n= Acont2\nFB\n(19.2.68)\nThe above equation assumes that the second control sam-\nple does not receive a contribution from the detection e\ufb03-\nciency asymmetry (for example the control sample con-\nsists of neutral D meson decays). Hence from the dif-\nference Acont1\nrec\n\u2212Acont2\nrec\none can determine the detection\ne\ufb03ciency asymmetry Ah+\n\u03f5\n(with some additional compli-\ncations as explained below).\nAfter correcting for Ah+\n\u03f5\nusing an appropriate control\ndata samples, one arrives at\nAcorr\nrec = ACP + AFB ,\n(19.2.69)\nwhere the superscript corr denotes that the measured asym-\nmetry has already been corrected for Ah+\n\u03f5 . The remaining\n135 Note, for example, that the cross-section for \u03c0\u2212p interac-\ntion through the \u22060 resonance at p\u03c0 \u22481 GeV/c is three times\nsmaller than the cross-section for the \u03c0+p interaction through\nthe \u2206++, as can be easily seen using the isospin decomposition.\n\n586\ntwo contributions can be separated using the fact that\nAFB is antisymmetric with respect to the cosine of the\nD meson production polar angle in CM system (cos \u03b8\u2217),\nwhile the intrinsic CP asymmetry ACP is independent of\nthis angle. At tree level the asymmetry in the number of\nproduced fermions (c quarks) and anti-fermions (c quarks)\nas a function of the angle between the fermion and the in-\ncoming electron in the CM system, \u03b8c, is 136\nNc(cos \u03b8c) \u2212Nc(cos \u03b8c)\nNc(cos \u03b8c) + Nc(cos \u03b8c) =\n8A0\nFB cos \u03b8c\n3(1 + cos2 \u03b8c) .\n(19.2.70)\nA0\nFB is the forward-backward asymmetry parameter, de-\npending on the axial and vector weak couplings of the elec-\ntrons and charm quarks (Eidelman et al., 2004). Assum-\ning the fragmentation of the primary quark into a charmed\nmeson does not signi\ufb01cantly a\ufb00ect the angular distribution\n(i.e. that \u03b8\u2217\u2248\u03b8c) the quark asymmetry above is just the\nasymmetry AFB of Eq. (19.2.69) induced by the forward\nbackward asymmetry:\nAcorr\nrec (cos \u03b8\u2217) = ACP + 8A0\nFB cos \u03b8\u2217\n3(1 + cos2 \u03b8\u2217) .\n(19.2.71)\nHence one can determine AFB and ACP separately from\nACP = [Acorr\nrec (cos \u03b8\u2217) + Acorr\nrec (\u2212cos \u03b8\u2217)]/2\nAFB = [Acorr\nrec (cos \u03b8\u2217) \u2212Acorr\nrec (\u2212cos \u03b8\u2217)]/2.\n(19.2.72)\nThe method of correction for the AFB assumes \u03b8\u2217= \u03b8c\nand Acont\nFB = AFB. The expressions can, however, be modi-\n\ufb01ed when instead of the quark direction one measures the\nexperimentally accessible polar angle of a D meson (in\nother words, the assumption \u03b8\u2217= \u03b8c may not be com-\npletely justi\ufb01ed). Also, the control data samples often in-\nvolve decays of di\ufb00erent charmed mesons from the ones\nfor which ACP is being measured. Hence another assump-\ntion is that AFB is the same for all charmed mesons. Due\nto slightly di\ufb00erent fragmentation when an initial c quark\nhadronizes into various types of D mesons, the asymme-\ntry can also di\ufb00er slightly for di\ufb00erent D mesons. These\nassumptions have been tested. The di\ufb00erences between\nAFB\u2019s for di\ufb00erent D mesons are small (Staric, 2012b) jus-\ntifying the method used to correct for the residual asym-\nmetry arising from AFB.\nFor measurements of ACP in D0 \u2192K+K\u2212, \u03c0+\u03c0\u2212\ndecays, the \ufb02avor of neutral D mesons at production is\ntagged by reconstructing D+\u2217\u2192D0\u03c0+\ns decays. The mea-\nsured asymmetry can be written as\nArec = ACP + AFB + A\u03c0s\n\u03f5 .\n(19.2.73)\nTo determine A\u03c0s\n\u03f5\n(Staric, 2008; Aubert, 2008aq), one re-\nconstructs two D0 \u2192K\u2212\u03c0+ samples: one consisting of\nD mesons with tagged initial \ufb02avor, and one consisting of\n136 The asymmetry follows from the angular distribution of\nproduced fermions in the e+e\u2212collisions, d\u03c3/d cos \u03b8f \u221d1 +\ncos2 \u03b8f + (8/3)A0\nFB cos \u03b8f\n(Eidelman et al., 2004).\nuntagged candidates. The measured asymmetries for these\nmodes can be written as\nAtag\nrec = AK\u03c0\nCP + AFB + AK\u03c0\n\u03f5\n+ A\u03c0s\n\u03f5 ,\nAuntag\nrec\n= AK\u03c0\nCP + AFB + AK\u03c0\n\u03f5\n.\n(19.2.74)\nOne \ufb01rst uses the di\ufb00erence of the two measurements in\nEq. (19.2.74) to determine A\u03c0s\n\u03f5 .\nAfter correcting for A\u03c0s\n\u03f5 , one corrects for AFB from\nEq. (19.2.73) as explained above. An additional complica-\ntion arises due to the fact that A\u03c0s\n\u03f5 , which at least partially\narises from the di\ufb00erence of charged particle interactions\nin the detector material, depends on the momentum and\nthe laboratory polar angle of the pion. Hence A\u03c0s\n\u03f5\nis ex-\namined as a function of (p\u03c0s, cos \u03b8\u03c0) which denote the\nmagnitude of the momentum and the cosine of the polar\nangle of the slow pion, respectively. The asymmetry val-\nues for various decays are thus calculated in bins of (p\u03c0s,\ncos \u03b8\u03c0), as well as in bins of the D meson polar angle, as\nexplained below.\nGraphically the method of correction is illustrated in\nFig. 19.2.27. A similar method has been used in the anal-\nysis of D0 \u2192K0\nSP 0 (P 0 = \u03c00, \u03b7, or \u03b7\u2032) decays (Ko, 2011).\nAn attentive reader may wonder why the treatment of the\ncos\u03b8\u03c0\np\u03c0\ncos\u03b8*\nA tag\nrec\ncos\u03b8\u03c0\np\u03c0\ncos\u03b8*\nA untag\nrec\nA (\n\u03b8\n)\n\u03c0\na)\nb)\ns\ns\ns\ns\ns\nA (cos\u03b8\u03c0 , p\u03c0 )\n\u03c0\n\u03b5\ncos\u03b8\u03c0\np\u03c0\ncos\u03b8*\nA rec\np\u03c0\ncos\u03b8*\nACP + AFB(cos\u03b8*)\nc)\nd)\ncos\u03b8\u03c0\ns\ns\ns\ns\ns\ns\ns\nFigure 19.2.27. Graphical presentation of the method to cor-\nrect the measurement of the CP asymmetry in D meson de-\ncays. In the case of D0 \u2192h+h\u2212the di\ufb00erence between the\nmeasured asymmetries for D\u2217+ \u2192D0(\u2192K\u2212\u03c0+)\u03c0+\ns (a) and\nD0 \u2192K\u2212\u03c0+ (b) decays in a given bin of \u03c0s momentum, its\npolar angle \u03b8\u03c0s and the D meson polar angle in the CM sys-\ntem \u03b8\u2217, yields the detector induced asymmetry A\u03c0s\n\u03f5 . This can\nbe used to correct the measured asymmetry for the decays\nD\u2217+ \u2192D0(\u2192h\u2212h+)\u03c0+\ns (c) resulting in the sum ACP + AFB\n(d). The latter can be distinguished according to their cos \u03b8\u2217\ndependence.\nasymmetries as a function of the D meson polar angle in\nthe CM system, cos \u03b8\u2217, is needed. The forward-backward\n\n587\nasymmetry would vanish when integrated over this vari-\nable. A subtle reason lies in the fact that the pion polar\nangle in the laboratory frame, \u03b8\u03c0, on which the detector\ninduced asymmetries depend upon 137 is correlated with\n\u03b8\u2217. Hence in a given bin of cos \u03b8\u03c0 the integration over\ncos \u03b8\u2217does not assure a vanishing AFB contribution.\nIn D+\n(s) \u2192K0\nSh+ decays (h+=\u03c0+ or K+), the recon-\nstructed asymmetries can be written as\nA\nD+\n(s)\u2192K0\nSh+\nrec\n= A\nD+\n(s)\u2192K0\nSh+\nCP\n+ A\nD+\n(s)\nFB\n+ Ah+\n\u03f5 . (19.2.75)\nTo correct for A\nD+\n(s)\nFB\nand Ah+\n\u03f5 , Belle (Ko, 2010) uses re-\nconstructed samples of D+\ns\n\u2192\u03c6\u03c0+ and D0 \u2192K\u2212\u03c0+\ndecays, assuming that ACP in Cabibbo favored decays\nis negligibly small at the current experimental sensitiv-\nity (note that within the SM CP violation in charm de-\ncays is expected only for Cabibbo suppressed decays, see\nSection 19.2.1.3). Another assumption is that AFB is the\nsame for all charmed mesons.\nThe measured asymmetry for D+\ns \u2192\u03c6\u03c0+ is the sum\nof AD+\ns\nFB and A\u03c0+\n\u03f5 . Hence one can extract the ACP value for\nthe K0\nS\u03c0+ \ufb01nal states by subtracting the measured asym-\nmetry for D+\ns \u2192\u03c6\u03c0+ from that for D+\n(s) \u2192K0\nS\u03c0+. The\nsubtraction is performed in bins of \u03c0+ momentum, p\u03c0,\nand polar angle in the laboratory system, cos \u03b8\u03c0 and the\ncharmed meson\u2019s polar angle in the center-of-mass sys-\ntem, cos \u03b8\u2217\nD+\n(s). The three-dimensional (3D) binning is de-\ntermined in such a way to avoid large statistical \ufb02uctua-\ntions in each bin. The statistical precision of the D+\ns \u2192\nK0\nS\u03c0+ sample is too low to allow for a 3D correction to\nAD+\ns \u2192K0\nS\u03c0+\nrec\nat present. For this mode one corrects for\nthe forward backward and detection e\ufb03ciency asymme-\ntries with an inclusive correction obtained by subtracting\nAD+\u2192K0\nS\u03c0+\nrec\nfrom AD+\u2192K0\nS\u03c0+\nCP\nafter integrating over the\nentire (p\u03c0, cos \u03b8\u03c0, cos \u03b8\u2217\nD+) space. This technique yields\na systematic uncertainty of 0.18%, which originates from\nthe statistical uncertainty of the selected D+\ns \u2192\u03c6\u03c0+ sam-\nple. Similar methods have been used in the analysis of\nD+ \u2192\u03c0+\u03b7(\u2032) decays (Won, 2011).\nRecently, the BABAR collaboration has developed an-\nother data-driven method (del Amo Sanchez, 2011i) to\ndetermine the charge asymmetry in the track reconstruc-\ntion as a function of the magnitude of the track momen-\ntum and its polar angle, in the analysis of D+ \u2192K0\nS\u03c0+\ndecays. B mesons are produced in the process e+e\u2212\u2192\n\u03a5(4S) \u2192BB. This production mechanism is free of any\nphysics-induced charge or \ufb02avor asymmetry. The CP vi-\nolation in the later decays of B mesons must vanish if\none takes a completely inclusive sample of B meson de-\ncay products. Hence the inclusive \u03a5(4S) \u2192BB events\nprovide a very large control sample in which any asym-\nmetry is detector induced. However, data recorded at\nthe \u03a5(4S) resonance also include continuum production\ne+e\u2212\u2192qq (q = u, d, s, c), where there is a non-negligible\n137 More precisely, the amount of the material traversed by the\npion depends on this angle.\nFB asymmetry due to the interference between the single\nvirtual photon process and other production processes, as\ndescribed above. The continuum contribution is estimated\nusing the o\ufb00-resonance data rescaled to the same luminos-\nity as the on-resonance data sample. Subtracting the num-\nber of reconstructed tracks in the rescaled o\ufb00-resonance\nsample from the number of tracks in the on-resonance one,\nBABAR obtains the number of tracks corresponding to the\nB meson decays only. Therefore, the relative detection and\nidenti\ufb01cation e\ufb03ciencies of the positively and negatively\ncharged particles for given selection criteria can be de-\ntermined using the numbers of positively and negatively\nreconstructed tracks directly from data. This technique\nyields a smaller systematic uncertainty of 0.08%. The ob-\ntained \u03c0+/\u03c0\u2212asymmetry map as a function of the pion\nmomentum and polar angle is shown in Fig. 19.2.28. De-\nviations from unity are largest at low polar angles (due to\nthe amount of the material traversed by the pions) and at\nrelatively low momenta (where the di\ufb00erence between the\n\u03c0+ and \u03c0\u2212cross-sections for interactions with nucleons is\nthe largest).\nFigure 19.2.28. Charged pion reconstruction e\ufb03ciency ratio\n\u03f5(\u03c0+)/\u03f5(\u03c0\u2212) (top) obtained using the method of (del Amo San-\nchez, 2011i) as described in the text, and the corresponding\nstatistical errors (bottom).\nThe method for the measurement of ACP in the K0\nSK+\n\ufb01nal state is di\ufb00erent from that for the K0\nS\u03c0+ \ufb01nal state.\nThe A\nD+\n(s)\nFB\nand A\u03c0+\n\u03f5\ncomponents in A\nD+\n(s)\u2192K0\nS\u03c0+\nrec\nare ob-\ntained directly from the D+\ns\n\u2192\u03c6\u03c0+ sample, but there\nis no corresponding large statistics decay mode that can\nbe used to directly measure the A\nD+\n(s)\nFB\nand AK+\n\u03f5\ncompo-\nnents in A\nD+\n(s)\u2192K0\nSK+\nrec\n. Thus, to correct the reconstructed\nasymmetry in the K0\nSK+ \ufb01nal states, one uses samples of\nD0 \u2192K\u2212\u03c0+ and D+\ns \u2192\u03c6\u03c0+ decays.\n\n588\nThe measured asymmetry for D0 \u2192K\u2212\u03c0+ is a sum\nof AD0\nFB, AK\u2212\n\u03f5\n, and A\u03c0+\n\u03f5 . Thus, one can extract AK\u2212\n\u03f5\nby\nsubtracting the measured asymmetry for D+\ns \u2192\u03c6\u03c0+ from\nthat for D0 \u2192K\u2212\u03c0+. An AK\u2212\n\u03f5\ncorrection map is obtained\nas follows; N D0\u2192K\u2212\u03c0+\nrec\nand N D0\u2192K+\u03c0\u2212\nrec\nare corrected ac-\ncording to the reconstructed asymmetry for D+\ns \u2192\u03c6\u03c0+\nin bins of (p\u03c0, cos \u03b8\u03c0, cos \u03b8\u2217\nD(s)). Subsequently, corrected\nN D0\u2192K\u2212\u03c0+\nrec\nand N D0\u2192K+\u03c0\u2212\nrec\nvalues are determined in bins\nof K\u2213momentum and polar angle in the laboratory frame,\n(pK\u2213, cos \u03b8K\u2213). From the corrected values of N D0\u2192K\u2212\u03c0+\nrec\nand N D0\u2192K+\u03c0\u2212\nrec\none obtains an AK\u2212\n\u03f5\nmap that is used\nto correct for AK+\n\u03f5\nin the K0\nSK+ \ufb01nal state. By subtract-\ning AK+\n\u03f5\nfrom the reconstructed asymmetry of D+\n(s) \u2192\nK0\nSK+, one obtains the corrected reconstruction asym-\nmetry A\nD+\n(s)\u2192K0\nSK+\nrec,corr\nfor D+\n(s) \u2192K0\nSK+:\nA\nD+\n(s)\u2192K0\nSK+\nrec,corr\n= A\nD+\n(s)\u2192K0\nSK+\nrec\n\u2212AK+\n\u03f5\n= A\nD+\n(s)\nFB\n+ A\nD+\n(s)\u2192K0\nSK+\nCP\n.\n(19.2.76)\nAs shown in Eq. (19.2.76), A\nD+\n(s)\u2192K0\nSK+\ncorr\nrec\nincludes not\nonly an ACP component but also the AFB component.\nSince ACP is independent of all kinematic variables, while\nAFB is an odd function of cos \u03b8\u2217\nD+\n(s), as explained above,\none extracts the two components from A\nD+\n(s)\u2192K0\nSK+\ncorr\nrec\nas\na function of cos \u03b8\u2217\nD+\n(s) through Eq. (19.2.72).\nIn the most recent measurement of ACP (D+ \u2192K0\nS\u03c0+)\nBelle (Ko, 2012) uses two di\ufb00erent control samples instead\nof D+\ns\n\u2192\u03c6\u03c0+, composed of selected D+ \u2192K\u2212\u03c0+\u03c0+\nand D0 \u2192K\u2212\u03c0+\u03c00 decays. These decays have larger\nbranching fractions and hence the systematic uncertainty\narising from the correction due to the charged pion e\ufb03-\nciency asymmetry is reduced. The two aforementioned de-\ncay modes are Cabibbo favored and hence one does not ex-\npect any observable CP violation (see Section 19.2.1.3).138\nWriting out the detector and forward-backward induced\ncontributions to the measured asymmetries in D+ \u2192\nK\u2212\u03c0+\u03c0+ and D0 \u2192K\u2212\u03c0+\u03c00 (and assuming the latter\nis the same for the two modes) it\u2019s easy to see that the\ncomparison of the two yields the A\u03c0+\n\u03f5\nnecessary to correct\nthe measured asymmetry in D+ \u2192K0\nS\u03c0+:\nAD+\u2192K\u2212\u03c0+\u03c0+\nrec\n= AD+\nFB + A\u03c0+\n\u03f51 + A\u03c0+\n\u03f52 + AK\u2212\n\u03f5\n138 The CP violation in decay is expected only in singly\nCabibbo suppressed decays, and this is the only possible type\nof violation appearing in D+ decays. On the other hand for\nD0 decays there\u2019s also a possibility of CP violation in mix-\ning and mixing induced CP violation, as explained in Sec-\ntion 16.6. Comparison of the decay-time integrated rates of\nD0 \u2192K\u2212\u03c0+\u03c00 and D0 \u2192K+\u03c0\u2212\u03c00 shows that the contribu-\ntion of this type of CP violation to the ACP measurement is\n\u2212y\nq\nRK\u03c0\u03c00\nD\nsin \u03b4K\u03c0\u03c00 sin \u03c6. This small quantity is included as\none of the systematic uncertainties for this result.\nAD0\u2192K\u2212\u03c0+\u03c00\nrec\n= AD0\nFB + A\u03c0+\n\u03f51 + AK\u2212\n\u03f5\n(19.2.77)\nA\u03c0+\n\u03f52\n= AD+\u2192K\u2212\u03c0+\u03c0+\nrec\n\u2212AD0\u2192K\u2212\u03c0+\u03c00\nrec\n,\nassuming AD+\nFB = AD0\nFB.\nAnother correction must be applied to the measured\nasymmetries with a K0\nS in the \ufb01nal state. In speci\ufb01c de-\ncays of charm hadrons either K0 or K0 mesons are pro-\nduced which propagate in time and are at some later time\nreconstructed as a K0\nS decaying to \u03c0+\u03c0\u2212. The K0 and\nK0 have, however, very di\ufb00erent cross-sections for inter-\nactions with nucleons in the material of the detector that\nthey traverse (mainly the beam pipe and the material of\nthe silicon vertex detector, see Chapter 2 for the descrip-\ntion of the detectors and (Beringer et al., 2012) for the\ndi\ufb00erences in the cross-sections). If a neutral kaon inter-\nacts in the material, it normally cannot be reconstructed.\nHence the e\ufb03ciency for the reconstruction of a K0\nS arising\nin, for example, a D \u2192K0X decay may di\ufb00er from the\ne\ufb03ciency of the K0\nS reconstruction arising in a D \u2192K0X\ndecay. This asymmetry is not related to the CP violation\nin charm meson decays and must be corrected for. The\nasymmetry depends on the amount of material traversed\nby the neutral kaon as well as (due to the energy depen-\ndence of the cross-section) on its momentum. The e\ufb00ect\nis not included in the simulation packages used by Belle\nand BABAR (Agostinelli et al., 2003) and hence a dedicated\nstudy has been performed (Ko, Won, Golob, and Pakhlov,\n2011) for various detector geometries. The additional con-\ntribution to the asymmetry due to this source is found to\nbe of the order of 0.1% and is included in the measure-\nments with K0\nS in the \ufb01nal state either as an additional\ncorrection or a systematic uncertainty.\nFurthermore, Grossman and Nir (2012) have pointed\nout a non negligible e\ufb00ect of the K0\nS \u2212K0\nL interference in\ndecays with neutral kaons in the \ufb01nal state. It depends\non the acceptance dependence on the neutral kaon decay\ntime. For the analysis in (Ko, 2012) this e\ufb00ect results in a\ncorrection factor of 1.022 \u00b1 0.007 for ACP (D+ \u2192K0\nS\u03c0+).\n19.2.6.2 Results\nAll results of t-integrated CP violation measurements for\ncharm mesons together with the control data samples used\nfor various corrections are listed in Table 19.2.5. In the\nfollowing some speci\ufb01cs of selected measurements are de-\nscribed.\nD+ \u2192K0\nS\u03c0+, D0 \u2192K0\nSP 0\nA time-integrated CP violation search in D+ \u2192K0\nS\u03c0+\nis carried out by both the Belle and BABAR collabora-\ntions (Ko, 2012; del Amo Sanchez, 2011i). In both exper-\niments corrections for non-CP violating asymmetries are\nperformed as explained in the previous section. Speci\ufb01-\ncally, one expects a non-vanishing asymmetry due to the\npresence of neutral kaons in the \ufb01nal state. The asymme-\ntry measured by Belle is ACP (D+ \u2192K0\nS\u03c0+) =(\u22120.363 \u00b1\n\n589\n0.094 \u00b1 0.067)% where the main systematic uncertainty\n(0.062%) is due to the statistical uncertainty of the con-\ntrol samples used for the A\u03c0+\n\u03f5\ncorrection. In contrast,\nBABAR uses inclusive on- and o\ufb00-resonance data for the\ncorrection and this enables them to achieve a systematic\nuncertainty of 0.08% despite the signi\ufb01cantly lower to-\ntal integrated luminosity of the sample used for the mea-\nsurement. The corrected asymmetry value from BABAR\nis ACP (D+ \u2192K0\nS\u03c0+) = (\u22120.44 \u00b1 0.13 \u00b1 0.10)%. The\nCP asymmetry from BABAR is shown in Fig. 19.2.29 as a\nfunction of | cos \u03b8\u2217\nD|.\nIf results from the two experiments are combined as-\nsuming uncorrelated systematic uncertainties, one obtains\nACP (D+ \u2192K0\nS\u03c0+) = (\u22120.389 \u00b1 0.094)% (where the last\nerror is combined statistical and systematic uncertainty)\nand this is one of the \ufb01rst hints of CP violation in charm\ndecays. It should be noted, however, that this is consis-\ntent with CP violation due to neutral kaon mixing in the\n\ufb01nal state. Namely D+ \u2192K0\nS\u03c0+ decays receive a con-\ntribution from the CF process D+ \u2192K0\u03c0+ as well as\nfrom the DCS process D+ \u2192K0\u03c0+. Either K0 or K0\nat a later time decays as a K0\nS reconstructed through the\nK0\nS \u2192\u03c0+\u03c0\u2212decay. Hence, even in the absence of any\nCP violation in D meson decays, there is an additional\ncontribution to the measured asymmetry due to the CP\nviolation in the neutral kaon system. One expects\nAK0 =\n\f\f\f\f\n\u27e8\u03c0+\u03c0\u2212|K0\u27e9|2 \u2212|\u27e8\u03c0+\u03c0\u2212|K0\u27e9|2\n\u27e8\u03c0+\u03c0\u2212|K0\u27e9|2 + |\u27e8\u03c0+\u03c0\u2212|K0\u27e9|2\n\f\f\f\f\n2\n\u2243\u22121 \u2212|(p/q)K0|2\n1 + |(p/q)K0|2 = \u22122Re(\u03f5)\n1 + |\u03f5|2 .\n(19.2.78)\nThe expected asymmetry in this decay mode due to the\nCP violation in the neutral kaon system is (\u22120.332 \u00b1\n0.006)% (Beringer et al., 2012). The average result for\nACP (D+ \u2192K0\nS\u03c0+) is in good agreement with this expec-\ntation, implying no signi\ufb01cant CP violation in the charged\nD meson sector. The results from both collaborations also\nshow a remarkable precision achieved despite the need for\nsigni\ufb01cant corrections (several corrections of the order of\n0.1% to measure the \ufb01nal central value of the same order)\nin evaluating the intrinsic CP asymmetry.\nACP (D0 \u2192K0\nSP 0), where P 0 is \u03c00 or \u03b7(\u2032) is measured\nby the Belle experiment (Ko, 2011). Assuming no CP vi-\nolation in decay for the K0\nS\u03c00 mode (a mixture of CF and\nDCS decays) it can be used to test the universality of in-\ndirect CP violation, as explained further in Section 19.2.7.\nD0 \u2192KK/\u03c0\u03c0\nSearches for time-integrated CP-violating asymmetries in\ndecays D0 \u2192K+K\u2212and D0 \u2192\u03c0+\u03c0\u2212are carried out\nby the BABAR and Belle collaborations (Aubert, 2008aq;\n(Staric, 2008)) using 386 fb\u22121 and 540 fb\u22121 of data, re-\nspectively. The analysis is similar in both cases, except\nthat the BABAR collaboration extracts the signal yields\nby \ufb01tting the mass distributions, while the Belle collabo-\nration uses the method of sideband-subtraction.\n*D\n\u03b8\n|cos |\n0\n0.2\n0.4\n0.6\n0.8\n1\nCP\nA\n-0.005\n0\n0.005\nFigure 19.2.29. CP asymmetries for D+ \u2192K0\nS\u03c0+ candi-\ndates as a function of | cos \u03b8\u2217\nD|. The solid line represents the\ncentral value of ACP and the hatched region is the \u00b11\u03c3 inter-\nval, obtained from a minimization assuming no dependence on\n| cos \u03b8\u2217\nD| (del Amo Sanchez, 2011i).\nAs already discussed in Section 19.2.6.1 the measured\n(or raw) asymmetry can be expressed with a sum of three\ncontributions Arec = ACP +AFB +A\u03c0s\n\u03f5 , where the \ufb01rst one\nis constant, the second one is an odd function of cos \u03b8\u2217\nand the last one depends on the slow pion phase space\n(p\u03c0s, cos \u03b8\u03c0s), since this asymmetry is due to detector ef-\nfects. In Section 19.2.6.1 we also discussed that the term\nA\u03c0s\n\u03f5\ncan be obtained from data by using tagged and un-\ntagged D0 \u2192K\u2212\u03c0+ decays. Both experiments use this\nmethod; BABAR has determined the slow pion detection\nasymmetry A\u03c0s\n\u03f5\nin 3 \u00d7 3 bins, while Belle uses a 5 \u00d7 5\nbinning in the same momentum range (0.1\u20130.6 GeV/c).\nThe slow pion asymmetry map is used to correct the\nraw asymmetry. This is done by weighting the D0/D0 can-\ndidates with the following weights:\nwD0 = 1 \u2212A\u03c0s\n\u03f5 (p\u03c0s, cos \u03b8\u03c0s) ,\nwD0 = 1 + A\u03c0s\n\u03f5 (p\u03c0s, cos \u03b8\u03c0s) .\n(19.2.79)\nNote that only candidates in bins with valid A\u03c0s\n\u03f5\nmea-\nsurements are taken into account. This procedure results\nin a corrected asymmetry Acor\nrec, which is free of the con-\ntribution due to the slow pion detection asymmetry. It is\ncalculated as,\nAcor\nrec(cos \u03b8\u2217) = m(cos \u03b8\u2217) \u2212m(cos \u03b8\u2217)\nm(cos \u03b8\u2217) + m(cos \u03b8\u2217) ,\n(19.2.80)\nwhere m(m) represent the sum of weights of the D0(D0)\ncandidates in each bin of cos \u03b8\u2217.\nFinally, taking into account their speci\ufb01c dependence\non cos \u03b8\u2217, the asymmetries ACP and AFB are extracted by\nadding or subtracting bins at \u00b1 cos \u03b8\u2217, see Eq. (19.2.72).\nThe systematic uncertainties arise from the signal\ncounting method (BABAR: choice of p.d.f., Belle: non-\nlinear background shape), from slow pion corrections\n\n590\n|cos \u03b8*|\nACP\na) K+K-\n|cos \u03b8*|\nACP\nb) \u03c0+\u03c0-\n|cos \u03b8*|\nAFB\nc) K+K-\n|cos \u03b8*|\nAFB\nd) \u03c0+\u03c0-\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n0.04\n0\n0.2\n0.4\n0.6\n0.8\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n0.04\n0\n0.2\n0.4\n0.6\n0.8\n-0.05\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0\n0.2\n0.4\n0.6\n0.8\n-0.05\n-0.04\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0\n0.2\n0.4\n0.6\n0.8\nFigure 19.2.30. From\n(Staric, 2008). Measurement of CP-\nviolating asymmetries in (a) KK and (b) \u03c0\u03c0 \ufb01nal states, and\nforward-backward asymmetries in (c) KK and (d) \u03c0\u03c0 \ufb01nal\nstates. The solid curves represent the central values obtained\nfrom the least square minimizations; the dashed curves in (c)\nand (d) show the leading order expectation.\n(statistics of K\u2212\u03c0+ samples, binning) and from the ACP\nextraction procedure (binning, cos \u03b8\u2217range).\nThe results of both measurements are presented in Ta-\nble 19.2.5. Figure 19.2.30 is a graphical representation of\nthe Belle results. For individual decay modes the results\nagree within the uncertainties. The BABAR-Belle averages\n(assuming uncorrelated systematic uncertainties) are\nACP (\u03c0\u03c0) = (+0.11 \u00b1 0.39)%\nACP (KK) = (\u22120.24 \u00b1 0.24)% .\n(19.2.81)\nThe measured values are consistent with no CP violation\nat the level of \u223c0.3%.\nBoth experiments obtain forward-backward asymme-\ntries that are consistent with each other (see Fig. 19.2.30),\nbut do not agree well with the leading order calculations.\nSimilar is true for measurements of other decay modes.\nUnfortunately due to lack of reliable predictions at ECM \u2248\n10 GeV it is di\ufb03cult to quantify the level of disagreement\nin the AF B measurements.\nMultibody decays\nDirect CP violation is expected to depend on f, the \ufb01nal\nstate for each decay. For multibody decays, therefore, the\nphenomenon will depend on sub modes. BABAR, in per-\nforming t-integrated measurements of D0 \u2192K+K\u2212\u03c00\nand D0 \u2192\u03c0+\u03c0\u2212\u03c00 decays (Aubert, 2008ap) also ex-\nploited the possibility of normalizing D0 and D0 rates\nseparately to their total 3-body systems, thereby elimi-\nnating the most signi\ufb01cant experimental uncertainty (the\ncharge asymmetry in e\ufb03ciency).\nThey adopt four di\ufb00erent methods, three of which are\nindependent of any decay model. The model-dependent\nmethod, introduced by the CLEO collaboration in a study\nof D+ \u2192K+K\u2212\u03c0+ decays (Rubin et al., 2008) com-\npares results of \ufb01ts to the Dalitz plot distributions of D0\nand D0 decays to a model based upon the isobar (quasi\ntwo-body) approximation with Breit-Wigner parameteri-\nzations for the various intermediate resonances (see Chap-\nter 13). Neither magnitude nor phase of any intermediate\n2-body mode shows a signi\ufb01cant di\ufb00erence between the\ncharge conjugated modes. As an illustration, the interme-\ndiate state with the largest contribution to the \u03c0+\u03c0\u2212\u03c00\n\ufb01nal state, \u03c1\u00b1(770)\u03c0\u2213, exhibits a relative di\ufb00erence of am-\nplitude magnitudes of (\u22123.2 \u00b1 1.7 \u00b1 0.8)% and of phases\n(\u22120.8 \u00b1 1.0 \u00b1 1.0)\u25e6.\nThe \ufb01rst model-independent method is, perhaps, the\nmost obvious. Bin by bin di\ufb00erences between e\ufb03ciency\ncorrected, background subtracted yields of D0 and D0\nDalitz plot distributions (see Chapter 13) are examined.\nThe yields are normalized so that there are equal numbers\nof D0 and D0 events. A \u03c72 is de\ufb01ned as\n\u03c72 =\nX\ni\n\u03c72\ni =\nX\ni\n(nD0\ni\n\u2212RnD0\ni\n)2\n(\u03c3D0\ni\n)2 + R2(\u03c3D0\ni\n)2 ,\n(19.2.82)\nwhere \u03c3D0\ni\nand \u03c3D0\ni\nare the uncertainties of the corre-\nsponding yields nD0\ni\nand nD0\ni\nin the i-th bin of the Dalitz\nplot distribution. The renormalization factor R is intro-\nduced to remove the possible overall asymmetry in the\ntotal number of reconstructed D0 and D0 events. The\nmethod is sensitive to possible di\ufb00erences in the shapes of\nDalitz distributions but not in the total populations. Us-\ning an ensemble of simulated experiments it is found that\nthe value of \u03c72/\u03bd, where \u03bd is the number of the Dalitz\nplot bins, is consistent with no CP violation at the con\ufb01-\ndence levels of 33% and 17% for the D0 \u2192\u03c0+\u03c0\u2212\u03c00 and\nD0 \u2192K+K\u2212\u03c00 decays, respectively. The normalized dif-\nferences in yields for the D0 \u2192\u03c0+\u03c0\u2212\u03c00 decays are shown\nin Fig. 19.2.31.139\nIn the second model independent method the angu-\nlar distributions for the same, normalized, e\ufb03ciency cor-\nrected, background subtracted yields are studied to ex-\ntract information on the partial wave content of any di\ufb00er-\nences between D0 and D0 decays. The di\ufb00erences (nD0\ni\n\u2212\nRnD0\ni\n) are weighted by Legendre polynomial functions\nP\u2113(cos \u03b8) normalized over the range \u22121 < cos \u03b8 \u22641. For\nthe AB \u201cchannel\u201d (quasi two-body mode D0 \u2192r+C, r \u2192\nA + B) \u03b8 is the angle between the momenta of B and C\nin the r rest frame. The resulting \u201cLegendre di\ufb00erence\nmoments\u201d,\nX\u2113=\n(P \u2113\u2212R \u00b7 P\u2113)\nq\n\u03c32\nP \u2113+ R2 \u00b7 \u03c32\nP\u2113\n,\n(19.2.83)\n(where the \u03c32\u2019s are variances for the indicated quantities)\nare highly correlated. This is because any partial wave\n139 An almost identical method is discussed in a later paper\n(Bediaga et al., 2009) and is commonly referred to as the \u201cMi-\nranda method\u201d.\n\n591\nTable 19.2.5. Summary of results of time-integrated CP violation measurements for charm mesons. The decay modes are\ngrouped to singly Cabibbo suppressed (SCS), Cabibbo favored (CF) and doubly Cabibbo suppressed (DCS) modes. The third\ncolumn lists the control data samples used to correct for non-CP asymmetries appearing in the measurements.\nDecay mode\nReference\nControl\nACP [%]\ncomment\nSCS decays\nD0 \u2192K+K\u2212\n(Staric, 2008)\nD\u2217+ \u2192D0(\u2192K\u2212\u03c0+)\u03c0+,\n\u22120.43 \u00b1 0.30 \u00b1 0.11\nD0 \u2192K\u2212\u03c0+\n(Aubert, 2008aq)\nsame as above\n0.00 \u00b1 0.34 \u00b1 0.13\nD0 \u2192\u03c0+\u03c0\u2212\n(Staric, 2008)\nsame as above\n0.43 \u00b1 0.52 \u00b1 0.12\n(Aubert, 2008aq)\nsame as above\n\u22120.24 \u00b1 0.52 \u00b1 0.22\nD0 \u2192K+K\u2212\u03c00\n(Aubert, 2008ap)\nsame as above\n1.00 \u00b1 1.67 \u00b1 0.25\nD0 \u2192\u03c0+\u03c0\u2212\u03c00\n(Aubert, 2008ap)\nsame as above\n\u22120.31 \u00b1 0.41 \u00b1 0.17\n(Arinstein, 2008)\npartially reconstructed\n0.43 \u00b1 0.41 \u00b1 1.23\nD\u2217+ \u2192D0(\u2192K0\ns\u03c0+\u03c0\u2212)\u03c0+\nD+ \u2192K0\nSK+\n(Ko, 2013)\nD+\ns \u2192\u03c6\u03c0+ , D0 \u2192K\u2212\u03c0+\n0.25 \u00b1 0.28 \u00b1 0.14\nD+\ns \u2192K0\nS\u03c0+\n(Ko, 2010)\nD+\ns \u2192\u03c6\u03c0+\n5.45 \u00b1 2.50 \u00b1 0.33\nCF decays\nD+ \u2192K0\nS\u03c0+\n(del Amo Sanchez, 2011i)\ninclusive on- and\n\u22120.44 \u00b1 0.13 \u00b1 0.10\nsigni\ufb01cant asymmetry due to\no\ufb00-resonance data\nCP violation in the K0 system\n(Ko, 2012)\nD+ \u2192K\u2212\u03c0+\u03c0+,\n\u22120.363 \u00b1 0.094 \u00b1 0.067\nsame as above\nD0 \u2192K\u2212\u03c0+\u03c00\nD+\ns \u2192K0\nSK+\n(Ko, 2010)\nD+\ns \u2192\u03c6\u03c0+ , D0 \u2192K\u2212\u03c0+\n0.12 \u00b1 0.36 \u00b1 0.22\nD0 \u2192K0\nS\u03c00\n(Ko, 2011)\nD\u2217+ \u2192D0(\u2192K\u2212\u03c0+)\u03c0+,\n\u22120.28 \u00b1 0.19 \u00b1 0.10\nD0 \u2192K\u2212\u03c0+\nD0 \u2192K0\nS\u03b7\n(Ko, 2011)\nsame as above\n0.54 \u00b1 0.51 \u00b1 0.16\nD0 \u2192K0\nS\u03b7\u2032\n(Ko, 2011)\nsame as above\n0.98 \u00b1 0.67 \u00b1 0.14\nDCS decays\nD0 \u2192K+\u03c0\u2212\u03c00\n(Tian, 2005)\n\u22120.6 \u00b1 5.3\nsyst. uncertainty negligible\nD0 \u2192K+\u03c0\u2212\u03c0\u2212\u03c0+\n(Tian, 2005)\n\u22121.8 \u00b1 4.4\nsame as above\narising from CP violation in D decay to any of the reso-\nnances in any of the three channels would stimulate non-\nzero moments in several related values of \u2113.\nA statistical test for CP violation estimates the prob-\nability for any moment (which is chosen to be within the\nrange 0 \u22127) to be inconsistent with no CP violation. For\nthis, the quantity\n\u03c72/\u03bd =\nk\nX\n0\n7\nX\n\u2113=0\n7\nX\nm=0\n(X\u2113\u03c1\u2113mXm)/\u03bd\n(19.2.84)\nsummed over each of the k invariant mass ranges in various\nchannels is de\ufb01ned. The number of degrees of freedom\n\u03bd = 8k.\nFive hundred Dalitz plots consistent with no CP\nviolation are simulated from actual BABAR data in which\neach event is taken randomly as either D0 or D0. The\nresulting moments X\u2113and their correlations \u03c1\u2113m are com-\nputed for each sample. The \u03c72/\u03bd for the actual BABAR\nsample, with D\u2217-tagged assignments as D0 or D0 is then\ncompared with the distribution of 500 simulated samples\nto obtain a one-sided Gaussian C.L. for no CP violation.\nThe C.L.\u2019s obtained are 28.2% for the \u03c0+\u03c0\u2212channel,\n28.4% for \u03c0+\u03c00, 63.1% for K+K\u2212, and 23.8% for the\nK+\u03c00 channels, each consistent with no CP violation.\nThe \ufb01nal method, also model independent, consists of\ncomparison of the total number of D0 and D0 decays in\nthe quoted modes and was also used by Belle for D0 \u2192\n\u03c0+\u03c0\u2212\u03c00 (Arinstein, 2008). The correction for A\u03c0s\n\u03f5\nis, in\nthe BABAR case, made as described in Section 19.2.6.1\nwhile Belle uses partially reconstructed D\u2217+ \u2192D0(\u2192\nK0\ns\u03c0+\u03c0\u2212)\u03c0+ decays to estimate the tracking e\ufb03ciency\nsystematics (see Chapter 15), but separately for the neg-\native and positive pions. The values of ACP obtained by\nthis method are quoted in Table 19.2.5.\nFigure 19.2.31. From\n(Aubert, 2008ap). \u03c72\ni\nde\ufb01ned in\nEq. (19.2.82) calculated from e\ufb03ciency corrected and back-\nground subtracted D0 \u2192\u03c0+\u03c0\u2212\u03c00 and D0 \u2192\u03c0+\u03c0\u2212\u03c00 yields\nacross the Dalitz plane.\n\n592\n19.2.6.3 T-odd correlations\nThe study of T-odd correlations provides a powerful tool\nto indirectly search for CP violation. It is straight forward\nto show that any triple product of momenta (TP), given by\nv1\u00b7(v2\u00d7v3), is odd under the time-reversal symmetry op-\nerator T. It is clearly also odd under the spatial inversion\n(parity operator P). The kinematics of a four-body decay\ncan be described by a TP, and so in the usual way one can\nconstruct an asymmetry from T conjugate pairs of triple\nproducts, namely v1 \u00b7(v2 \u00d7v3) > 0 and v1 \u00b7(v2 \u00d7v3) < 0.\nThe choice of T-odd correlations to search for CP viola-\ntion is proposed by many authors (Bensalem, Datta, and\nLondon, 2002a,b; Bensalem and London, 2001; Bigi, 2001;\nKayser, 1990; Valencia, 1989) and studies in D decays fol-\nlow on from similar measurements made for neutral kaon\ndecays.140 One can construct a T-odd observable using\nthe spin or the momentum (vi) of the \ufb01nal state parti-\ncles in the D CM frame. The TP asymmetry observable\nof interest is\nATP = \u0393(v1 \u00b7 (v2 \u00d7 v3) > 0) \u2212\u0393(v1 \u00b7 (v2 \u00d7 v3) < 0)\n\u0393(v1 \u00b7 (v2 \u00d7 v3) > 0) + \u0393(v1 \u00b7 (v2 \u00d7 v3) < 0)\n(19.2.85)\nwhere \u0393 represents the number of signal events and is\nmeasured for D decays only.\nHowever, this is not a true P violating observable, due\nto \ufb01nal state interaction (FSI) e\ufb00ects that can introduce\nasymmetries (Bigi and Li, 2009). In order to remove these\ne\ufb00ects one needs to measure the CP conjugate of this ob-\nservable (ATP ) using the D decays and evaluate the CP\nviolating observable:\naTP \u22611\n2(ATP \u2212ATP ).\n(19.2.86)\nThis can be explained considering that the asymmetry\nATP has a phase that is the sum of a complex CP violating\nweak phase and a real strong phase (introduced by FSI).\nUnder the operation of CP conjugation the weak phase\nchanges its sign, while the strong phase does not. Thus,\nthe di\ufb00erence between ATP and ATP removes the strong\nphase and the factor 1/2 is required for normalization.\nThe exact de\ufb01nition of ATP is given in Eq. (19.2.89).\nThis method requires three independent momentum\nvectors, thus at least four di\ufb00erent particles are recon-\nstructed in the \ufb01nal state unless the spin of the decaying\nparticle is known. In this last case, the spin of the mother\ncan be used in Eq. (19.2.85).\n140 Some of the literature refers to CP violating T-odd observ-\nables as T-violating observables; however, this is not a correct\nnomenclature. T-violation in kaon decays is discussed in the\nPDG (Beringer et al., 2012). Section 17.6 discusses T-violation\nmeasurements by BABAR for B decays, and it has been pointed\nout by Bevan, Inguglia, and Zoccali (2013) that similar mea-\nsurements are possible using pairs of entangled D mesons pro-\nduced at the \u03c8(3770). A recent article discussing TP asymme-\ntries in K, B and D decays has been written by Gronau and\nRosner (2011).\nThe search for CP violation by means of the T-odd\ncorrelations at the B Factories has been performed by\nBABAR in D0 \u2192K+K\u2212\u03c0+\u03c0\u2212, D+ \u2192K+K0\nS\u03c0+\u03c0\u2212and\nD+\ns \u2192K+K0\nS\u03c0+\u03c0\u2212decays. The latter is a Cabibbo fa-\nvored decay and no e\ufb00ect is expected, while the others\nare Cabibbo suppressed decays and the e\ufb00ect could be\nas large as 0.1%, considering Standard Model processes\nonly (Buccella, Lusignoli, Miele, Pugliese, and Santorelli,\n1995). The sensitivity reached at the B Factories for these\nobservables is comparable to the higher SM expectations.\nObserving an asymmetry would be a signal for processes\nbeyond the SM.\nThe variable used to build the T-odd correlation ob-\nservable is de\ufb01ned using the momenta of the \ufb01nal state\nparticles in the D CM frame:\nCTP = pK+ \u00b7 (p\u03c0+ \u00d7 p\u03c0\u2212).\n(19.2.87)\nThe asymmetry parameters to be measured are then:\nATP = \u0393(D, CTP > 0) \u2212\u0393(D, CTP < 0)\n\u0393(D, CTP > 0) + \u0393(D, CTP < 0),\n(19.2.88)\nATP = \u0393(D, \u2212CTP > 0) \u2212\u0393(D, \u2212CTP < 0)\n\u0393(D, \u2212CTP > 0) + \u0393(D, \u2212CTP < 0).\n(19.2.89)\nAll three analyses have measured the asymmetry pa-\nrameters through a simultaneous maximum likelihood \ufb01t\nto the four samples obtained by splitting the data set us-\ning the D \ufb02avor and the CTP (CTP ) value. Furthermore,\na blind analysis has been performed: the asymmetry pa-\nrameters ATP and ATP have been masked adding unknown\nrandom o\ufb00sets, and all the selection criteria and system-\natic e\ufb00ects have been evaluated before unveiling the \ufb01nal\nresult.\nThe D0 \u2192K+K\u2212\u03c0+\u03c0\u2212analysis (del Amo Sanchez,\n2010n) makes use of 471 fb\u22121 data recorded by the BABAR\ndetector at the \u03a5(4S) energy and 40 MeV below. The de-\ncay chain\ne+e\u2212\u2192XD\u2217+; D\u2217+ \u2192\u03c0+\ns D0; D0 \u2192K+K\u2212\u03c0+\u03c0\u2212,\nwhere X indicates any system composed of charged and\nneutral particles, has been reconstructed from the sample\nof events having at least \ufb01ve charged tracks. At \ufb01rst, the\nD0 has been reconstructed, requiring the momentum in\nthe CM frame p\u2217(D0) > 2.5 GeV/c to suppress the back-\nground. Then, the successful D0 candidate has been com-\nbined with any charged track having momentum less than\n0.65 GeV/c (\u03c0+\ns ) to form the D\u2217+ candidate. A contamina-\ntion from D0 \u2192K0\nSK+K\u2212has been removed applying a\nmass veto to the K0\nS \u2192\u03c0+\u03c0\u2212candidates. This procedure\nselects about 50,000 signal events.\nThe two-dimensional distribution of m(K+K\u2212\u03c0+\u03c0\u2212)\nvs. \u2206m = m(K+K\u2212\u03c0+\u03c0\u2212\u03c0+\ns ) \u2212m(K+K\u2212\u03c0+\u03c0\u2212) has\nbeen described by \ufb01ve components: (i) true D0 signal\noriginating from a D\u2217+ decay (signal); and backgrounds\ncomprised of (ii) random \u03c0+\ns\nevents where a true D0\nis combined to an incorrect \u03c0+\ns (D0-peaking); (iii) mis-\nreconstructed D0 decays, where one or more of the D0 de-\ncay products are either not reconstructed or reconstructed\n\n593\nwith the wrong particle hypothesis (\u2206m-peaking); (iv)\ncombinatorial; (v) D+\ns \u2192K+K\u2212\u03c0+\u03c0\u2212\u03c0+ contamination.\nThe functional forms of the probability density functions\nfor the signal and background components are based on\nstudies of the generic e+e\u2212\u2192cc Monte Carlo (MC) sam-\nple. However, all parameters related to these functions\nare determined from a two-dimensional likelihood \ufb01t to\ndata over the full m(K+K\u2212\u03c0+\u03c0\u2212) vs. \u2206m region, shown\nin Fig. 19.2.32. Combinations of Gaussian and Johnson\nSU (Johnson, 1949) lineshapes are used for peaking dis-\ntributions, and polynomials and threshold functions for\nthe non-peaking backgrounds.\nMany possible sources of systematic e\ufb00ect have been\nconsidered in this analysis, for each of them the related\nselection criteria have been varied by a small amount to\nevaluate the deviations with respect to the asymmetries\nobtained applying the nominal criteria. Among them, the\nlargest contributions to systematic error are due to the\nparticle identi\ufb01cation, the selection on p\u2217(D0) and the \ufb01t\nbias.\nThe results are\nATP (D0) = (\u221268.5 \u00b1 7.3(stat) \u00b1 5.8(syst)) \u00d7 10\u22123,\nATP (D0) = (\u221270.5 \u00b1 7.3(stat) \u00b1 3.9(syst)) \u00d7 10\u22123,\naTP (D0) = (1.0 \u00b1 5.1(stat) \u00b1 4.4(syst)) \u00d7 10\u22123.\n(19.2.90)\nNo CP violation is found, even though ATP and ATP are\nsigni\ufb01cantly di\ufb00erent from zero, indicating the e\ufb00ect of\nFSIs.\nThe reconstruction of the D+\n(s) \u2192K+K0\nS\u03c0+\u03c0\u2212de-\ncays in the other BABAR analysis (Lees, 2011i), that used\n520 fb\u22121 recorded around a CM energy of 10.6 GeV, is\nsimilar. After the reconstruction of the K0\nS \u2192\u03c0+\u03c0\u2212de-\ncay, the K0\nS candidates are combined into a vertex with\nthree other charged tracks in the event to reconstruct in-\nclusive D+\n(s) decays. A kinematic selection on p\u2217(D+\n(s)) >\n2.5 GeV/c is required to suppress the background. Possible\nbackground contamination from D+\n(s) \u2192K+K0\nSK0\nS decays\nhave been removed by applying a K0\nS veto.\nThe signal to background ratio has been then opti-\nmized using a likelihood ratio. The probability density\nfunctions used to build the likelihood ratio are taken from\nthe distributions of three kinematic variables: (i) p\u2217(D+\n(s));\n(ii) \u2206p = P1 \u2212P2, the di\ufb00erence between the probability\nof the nominal \ufb01t (P1) and the probability of the \ufb01t ob-\ntained constraining the D+\n(s) vertex into the interaction\nregion (P2); and (iii) LT (D+\n(s)), the \ufb02ight distance of the\nD+\n(s) meson in the transverse plane. The signal distribu-\ntions are obtained from the signal regions of two control\nsamples, the Cabibbo favored D+ \u2192K0\nS\u03c0+\u03c0+\u03c0\u2212and\nD+\ns \u2192K\u2212K0\nS\u03c0+\u03c0+ decays, for D+ and D+\ns , respectively.\nThe background distributions are taken from data side-\nbands.\nA likelihood ratio, optimized on S/\n\u221a\nS + B (see Chap-\nter 4) for the signal region, has been applied to obtain the\nbest signi\ufb01cance of the mass peak. About 20,000 (30,000)\nD+ (D+\ns ) signal events have been reconstructed.\nThe model to \ufb01t the K+K0\nS\u03c0+\u03c0\u2212mass spectrum has\nbeen developed and validated on large samples of inclusive\nMC processed using the same reconstruction and analysis\nchain as that used for real events. The mass spectrum\nhas been separated in two regions centered on D+ and\nD+\ns\npeak, respectively, and the speci\ufb01c requirement on\nlikelihood ratio has been applied.\nThe model used to simultaneously \ufb01t the four samples\nobtained separating the events by charge and CTP (CTP )\nvalue is composed of two Gaussians for the peak and a\nsecond order polynomial for D+ (D+\ns ) background.\nThe simultaneous \ufb01t on the four data subsamples al-\nlows one to measure directly the asymmetries:\nATP (D+) = (+11.2 \u00b1 14.1(stat) \u00b1 5.7(syst)) \u00d7 10\u22123,\nATP (D\u2212) = (+35.1 \u00b1 14.3(stat) \u00b1 7.2(syst)) \u00d7 10\u22123,\nATP (D+\ns ) = (\u221299.2 \u00b1 10.7(stat) \u00b1 8.3(syst)) \u00d7 10\u22123,\nATP (D\u2212\ns ) = (\u221272.1 \u00b1 10.9(stat) \u00b1 10.7(syst)) \u00d7 10\u22123,\n(19.2.91)\nfrom which the CP violation parameters can be obtained\naTP (D+) = (\u221212.0 \u00b1 10.0(stat) \u00b1 4.6(syst)) \u00d7 10\u22123,\naTP (D+\ns ) = (\u221213.6 \u00b1 7.7(stat) \u00b1 3.4(syst)) \u00d7 10\u22123.\n(19.2.92)\nThe sources of systematic error that have been con-\nsidered are the \ufb01t model, the particle identi\ufb01cation, the\n\ufb01t bias measured on MC and the selection based on the\nlikelihood ratio. The procedure to evaluate the system-\natic error follows the same strategy of the D0 analysis.\nA slightly di\ufb00erent behavior is observed for the ATP and\nATP asymmetries in D+ and D+\ns . Even if the \ufb01nal state\nis the same, a di\ufb00erent resonant sub-structure may be re-\nsponsible for this di\ufb00erence (Gronau and Rosner, 2011).\nThe CP violation results obtained at the B Factories in\nfour-body D decays are consistent with zero to a precision\nof 0.5%. These results are in agreement with expectations\nfrom SM predictions. Nevertheless, the relative simplicity\nof the analyses based on T-odd correlations and the re-\nsults that can be obtained allow one to consider this tool\nas fundamental to search for CP violation in four-body de-\ncays. Furthermore, the study of T-odd correlations allows\none to probe FSI in four-body D decays.\n19.2.6.4 Summary\nNumerous t-integrated searches for CP violation in charm\nmeson decays have been performed by the B Factories\nand these show no signi\ufb01cant intrinsic e\ufb00ect at the levels\nof sensitivity achieved. These di\ufb00er from a few percent for\nthe DCS decays to over a few tenths of a percent for SCS\ndecays to 0.1% for CF decays (see Table 19.2.5). Because\nof the various detector induced and physics (forward-\nbackward) asymmetries the measurements require careful\ncalibration of the data using control samples and hence\nrepresent one of the most demanding measurements per-\nformed at the B Factories. BABAR and Belle developed\n\n594\n)\n2\n m (GeV/c\n6\n0.14\n0.145\n0.15\n)\n2\n) (GeV/c\n-/\n+\n/\n-\nK\n+\nm(K\n1.84\n1.86\n1.88\n1.9\n(a)\n)\n2\nEvents/ ( 0.80 MeV/c\n0\n1000\n2000\n3000\n4000\n)\n2\nEvents/ ( 0.80 MeV/c\n0\n1000\n2000\n3000\n4000\ndata\nSignal\n peaking\n0\nD\nm peaking\n6\nCombinatoric\n+\ns\nD\n(b)\n0\n)\n2\nEvents/ ( 0.15 MeV/c\n0\n5000\n10000\n)\n2\nEvents/ ( 0.15 MeV/c\n0\n5000\n10000\n0\ndata\nSignal\n peaking\n0\nD\nm peaking\n6\nCombinatoric\n+\ns\nD\n(c)\n)\n2\n) (GeV/c\n-/\n+\n/\n-\nK\n+\nm(K\n1.84\n1.86\n1.88\n1.9\nPull\n)\n2\n) (GeV/c\n-/\n+\n/\n-\nK\n+\nm(K\n1.84\n1.86\n1.88\n1.9\nPull\n-3\n 0\n+3\n)\n2\n m (GeV/c\n6\n0.14\n0.145\n0.15\nPull\n)\n2\n m (GeV/c\n6\n0.14\n0.145\n0.15\nPull\n-3\n 0\n+3\nFigure 19.2.32. From (del Amo Sanchez, 2010n). The distribution of selected events in the m(K+K\u2212\u03c0+\u03c0\u2212) vs. \u2206m plane (a)\nis shown together with the projections of the events with overlaid the \ufb01t results for m(K+K\u2212\u03c0+\u03c0\u2212) (b) and \u2206m (c), with the\nshaded areas indicating the di\ufb00erent contributions. In the bottom, the distribution of the normalized residuals (Pull), is shown\nfor each \ufb01t projection.\nseveral methods for such calibrations which assure a sat-\nisfactory control of measurement uncertainties that are\napplicable for the next generation of \ufb02avor factories (note\nthat the main systematic uncertainties, arising from lim-\nited statistics of control data samples, will be reduced with\nincreased luminosity). It is a remarkable demonstration\nthat both experiments can measure subtle e\ufb00ects such as\nthe asymmetry arising from the CP violation in the neu-\ntral kaon system in charm meson decays involving K0\nS\u2019s.\nIn combination with t-dependent measurements, CP vio-\nlating asymmetries represent interesting tests of the SM,\nas described further in Section 19.2.7.\n19.2.7 t-dependent CP violating asymmetries\nA general aspect of the possible CP violation e\ufb00ects in\nthe charm sector as well as various parameterizations were\ndiscussed in Section 19.2.1.3. In the time dependence of\nD0 decays one can search for the e\ufb00ects of all three types\nof CP violation.\n19.2.7.1 Decays to CP eigenstates\nLet us start by examining the decays into CP eigenstates,\nlike K+K\u2212. The measurements of the mixing-related pa-\nrameter yCP in this decay mode are described in Sections\n19.2.3.1 and 19.2.3.2. In order to search for CP violating\ne\ufb00ects one has to distinguish between decays of particles\nand anti-particles. Squaring the modulus in Eqs (19.2.11)\nand (19.2.12) (keeping the parameter q/p, i.e. not setting\nq = p = 1/\n\u221a\n2), and using the parameterization as de\ufb01ned\nin Eqs (19.2.17), (19.2.18) and (19.2.20), we arrive at the\ntime evolution of D0 \u2192K+K\u2212decays\n|\u27e8K+K\u2212|D0(\u0393t)\u27e9|2 = e\u2212\u0393t|AKK|2\n[1 \u2212(1 + AM \u2212AKK\nD\n2\n)(x sin \u03c6 \u2212y cos \u03c6) \u0393t],\n(19.2.93)\nand an equivalent expression for |\u27e8K+K\u2212|D0(t)\u27e9|2. It is\nvalid to linear order in the dimensionless decay time \u0393t.\nOne can see that in the above dependence parameters de-\nscribing all three types of CP violation are present: AM\n(CP violation in mixing), AKK\nD\n(CP violation in decay)\nand \u03c6 (CP violation in the interference between decays\nwith and without mixing). If Eq. (19.2.93) is regarded as\nthe \ufb01rst term in the expansion of an exponential func-\ntion,141 we arrive at separate expressions for the inverse\nof the e\ufb00ective lifetime of neutral meson decays in this\nmode:\n1\n\u03c4KK\n= 1\n\u03c4\n\u0002\n1 \u2213\n\u00001 \u00b1 (AM \u2212AKK\nD\n)/2\n\u0001\n(x sin \u03c6 \u2213y cos \u03c6)\n\u0003\n,\n(19.2.94)\nwhere the upper sign corresponds to D0 and the lower one\nto D0 decays. Hence by measuring separately the e\ufb00ective\nlifetimes of neutral D meson decays (using tagging of the\ninitial D meson \ufb02avor with D\u2217mesons, as described in\nSection 19.2.1.5) one can determine the lifetime asymme-\ntry:\nA\u0393 \u2261\u03c4(D0 \u2192KK) \u2212\u03c4(D0 \u2192KK)\n\u03c4(D0 \u2192KK) + \u03c4(D0 \u2192KK) =\n= AM \u2212AKK\nD\n2\ny cos \u03c6 \u2212x sin \u03c6 .\n(19.2.95)\nA non-zero value of the asymmetry A\u0393 would be a sign of\nCP violation in the D0 system - at least one parameter,\n141 This is equivalent to the derivation of the yCP parameter,\nsee Eq. (19.2.30) \u2013 (19.2.34), but now separately for D0 and\nD0 decays.\n\n595\nAKK\nD\n, AM or \u03c6, must be di\ufb00erent from zero. The sensitiv-\nity of A\u0393 to the CP violating parameters is limited by the\nsmall magnitude of the mixing parameters x and y.\nMeasurements of this asymmetry were typically per-\nformed together with the measurements of yCP . The av-\nerage of measurements (Staric, 2012a; Lees, 2013d) using\nthe K+K\u2212and \u03c0+\u03c0\u2212\ufb01nal states is found to be\nA\u0393 = (0.02 \u00b1 0.17)% ,\n(19.2.96)\nwhere the error includes statistical and systematic uncer-\ntainties.142\nThe main contributions to the systematic uncertainty\non A\u0393 arise from similar sources as in the yCP measure-\nments, from possible biases in the acceptance dependence\non the decay time and the assumption of an equal mean\nof the resolution function in both decay modes used (see\nSection 19.2.3.1). From the A\u0393 value one can conclude\nthere is currently no signi\ufb01cant sign of CP violation at\nthe sensitivity level of 0.25%.\nIt should be noted that the decay time integrated CP\nviolating asymmetry, as de\ufb01ned in Eq. (19.2.63) of Sec-\ntion 19.2.6, also receives contributions from all the types of\nCP violation, and the CP violation in decay (Af\nD) appears\nin the linear order. Upon the summation of Eq. (19.2.65)\nand Eq. (19.2.95) we get\nAKK\nCP + A\u0393 = AKK\nD\n(19.2.97)\n(in the above equation the CP violation in decays to K+K\u2212\nis denoted by AKK\nD\n). Hence one can estimate the amount\nof CP violation in decay by summing the two correspond-\ning results. Using the averages of the AKK(\u03c0\u03c0)\nCP\nmeasure-\nments (see Section 19.2.6.2), and assuming the systematic\nuncertainties due to completely di\ufb00erent methods of mea-\nsurements are uncorrelated, one obtains results for the\nK+K\u2212and \u03c0+\u03c0\u2212\ufb01nal states:\nAKK\nD\n= (\u22120.22 \u00b1 0.29)% ,\nA\u03c0\u03c0\nD = (+0.13 \u00b1 0.43)% ,\n(19.2.98)\nincluding both types of uncertainties.\n19.2.7.2 Hadronic wrong-sign decays\nThe measurements of the mixing parameters in this type\nof decay are described in Section 19.2.2. Since the \ufb01t to\nthe decay time dependence of the wrong-sign decays in-\nvolves parameters x\u20322 and y\u2032, a similar \ufb01t is repeated by\n142 Note that A\u0393 can in principle di\ufb00er for various di\ufb00erent\n\ufb01nal states due to the Af\nD term in Eq. (19.2.95). Hence the\naveraging of the A\u0393 values obtained in D meson decays to\nK+K\u2212and \u03c0+\u03c0\u2212\ufb01nal states is not justi\ufb01ed. However, the\ndi\ufb00erence between (1/2)(AM \u2212AKK\nD\n)y cos \u03c6 and (1/2)(AM \u2212\nA\u03c0\u03c0\nD )y cos \u03c6, i.e. (1/2)(A\u03c0\u03c0\nD \u2212AKK\nD\n)y cos \u03c6, is only (1\u00b11)\u00d710\u22125\nusing the average values (Amhis et al., 2012) of parameters\ninvolved. As long as the accuracy of A\u0393 measurement doesn\u2019t\nreach that level the approximation done in the averaging is\njusti\ufb01ed.\napplying Eq. (19.2.22) separately for D0 and D0 decays.\nOne introduces separate parameters x\u20322\u00b1 and y\u2032\u00b1, where\n+ and \u2212denote parameters for D0 and D0 decays, respec-\ntively. Any di\ufb00erence between corresponding parameters\ndenoted by + or \u2212represents a sign of CP violation. Pa-\nrameters x\u20322\u00b1 and y\u2032\u00b1 can of course be related to the CP\nviolating parameters in mixing and in the interference in-\ntroduced in Section 19.2.1.3:\nx\u2032\u00b1 =\n\u00141 \u00b1 AM\n1 \u2213AM\n\u00151/4\n(x\u2032 cos \u03c6 \u00b1 y\u2032 sin \u03c6),\ny\u2032\u00b1 =\n\u00141 \u00b1 AM\n1 \u2213AM\n\u00151/4\n(y\u2032 cos \u03c6 \u2213x\u2032 sin \u03c6).(19.2.99)\nApart from the above parameters, RD is also dupli-\ncated to R\u00b1\nD using an analogous notation. Any di\ufb00erence\nbetween R+\nD and R\u2212\nD is related to CP violation in decay:\nAD = R+\nD \u2212R\u2212\nD\nR+\nD + R\u2212\nD\n.\n(19.2.100)\nInclusion of more free parameters to describe the CP\nviolation leads to a reduced statistical accuracy of the ob-\ntained results. This can be seen in Fig. 19.2.11, comparing\nthe 95% C.L. regions of x\u20322 and y\u2032 as obtained from the\n\ufb01ts allowing or neglecting the CP violation.\nFits allowing for CP violation were performed by Zhang\n(2006) and Aubert (2007j). They are given in Table 19.2.6.\nTable 19.2.6. CP violation results using D0 \u2192K\u03c0 WS decays\nfrom BABAR (Aubert, 2007j) and Belle (Zhang, 2006). When\ntwo uncertainties are given, the \ufb01rst is statistical and the sec-\nond systematic. Results with a single uncertainty have both\nstatistical and systematic components combined. Limits corre-\nspond to 95% C.L.\nParameter\nFit Results (\u00d710\u22123)\nBABAR\nBelle\nAssuming both mixing and CP violation\nRD\n3.03 \u00b1 0.16 \u00b1 0.10\n\u2014\nAD\n\u221221 \u00b1 52 \u00b1 15\n23 \u00b1 47\nAM\n\u2212\n670 \u00b1 1200\nx\u20322+\n\u22120.24 \u00b1 0.43 \u00b1 0.30\n\u2014\ny\u2032+\n9.8 \u00b1 6.4 \u00b1 4.5\n\u2014\nx\u20322\u2212\n\u22120.20 \u00b1 0.41 \u00b1 0.29\n\u2014\ny\u2032\u2212\n9.6 \u00b1 6.1 \u00b1 4.3\n\u2014\nx\u20322\n\u2212\n< 0.72\ny\u2032\n\u2212\n\u221228 < y\u2032 < 21\nTaking the averages of the measurements 143 and as-\nsuming uncorrelated systematic errors one obtains\nx\u20322+ \u2212x\u20322\u2212= (0.011 \u00b1 0.041)%\n143 Also converting the results from Belle to x\u20322\u00b1 and y\u2032\u00b1,\naccording to (Amhis et al., 2012).\n\n596\ny\u2032+ \u2212y\u2032\u2212= (\u22120.19 \u00b1 0.64)% ,\n(19.2.101)\nconsistent with no CP violation.\nIn the study of the D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212decays (see Sec-\ntion 19.2.2.3) BABAR (Aubert, 2006ap) also performs a \ufb01t\nallowing for CP violation. The D0 and D0 decay-time dis-\ntributions are treated separately, by making a substitution\nin Eq. (19.2.26):\n\u03b1ey\u2032 \u2192|p/q|\u00b11(\u03b1ey\u2032 cos e\u03c6 \u00b1 \u03b2ex\u2032 sin e\u03c6)\nx2 + y2 \u2192|p/q|\u00b12(x2 + y2),\n(19.2.102)\nchoosing the \u201c+\u201d (\u201c\u2212\u201d) sign for D0 (D0) candidate de-\ncays, respectively. CP violation in mixing is parameterized\nby |p/q| and a CP-violating phase e\u03c6 is introduced to ac-\ncount for CP violation in the interference between mixing\nand DCS decay. The resulting values of the CP violating\nparameters are consistent with no CP violation:\nRM = [0.017+0.017\n\u22120.016(stat) \u00b1 0.003(syst)]%,\n|p/q| = 1.1+4.0\n\u22120.6(stat) \u00b1 0.1(syst),\n\u03b1ey\u2032 cos e\u03c6 = \u22120.006+0.008\n\u22120.006(stat) \u00b1 0.006(syst),\n\u03b2ex\u2032 cos e\u03c6 = 0.002+0.005\n\u22120.003(stat) \u00b1 0.006(syst).\n(19.2.103)\n19.2.7.3 t-dependent Dalitz Analyses\nViolation of the CP symmetry can also be searched for in\nthe analyses of the decay time dependence of the Dalitz\ndistributions in multi-body \ufb01nal states. As for the hadronic\nwrong-sign decays one can perform a \ufb01t to separate D0\nand D0 samples (see the previous section). Any di\ufb00er-\nence in the resulting mixing parameters can be ascribed\nto CP violation. This is done in the measurement of the\nK+\u03c0\u2212\u03c00 \ufb01nal state (see Section 19.2.4.1) by BABAR (Au-\nbert, 2009u). The resulting x\u2032, y\u2032 parameters are shown\nin Table 19.2.7. Within the uncertainties they are consis-\ntent between the two samples indicating no signi\ufb01cant CP\nviolation.\nTable 19.2.7. CP violation results using separate D0 and D0\nsamples in the analysis of K+\u03c0\u2212\u03c00 \ufb01nal state (Aubert, 2009u).\nD0 only\nx\u2032 = (+2.53+0.54\n\u22120.63 \u00b1 0.39)%\ny\u2032 = (\u22120.05+0.63\n\u22120.67 \u00b1 0.50)%\nD0 only\nx\u2032 = (+3.55+0.73\n\u22120.83 \u00b1 0.65)%\ny\u2032 = (\u22120.54+0.40\n\u22121.16 \u00b1 0.41)%\nIn the Belle search for CP violation in the K0\nS\u03c0+\u03c0\u2212\n\ufb01nal state (Abe, 2007b) the measurement consists of an\nextension of the \ufb01t procedure described in Section 19.2.4.2.\nThe time evolution of the Dalitz distribution as given in\nEq. (19.2.52) is used without setting q = p = 1/\n\u221a\n2. The\npossibility of CP violation in mixing and mixing induced\nCP violation is parameterized by q/p = |q/p|ei\u03c6 with |q/p|\nand \u03c6 as free parameters of the \ufb01t. The CP violation in de-\ncay would be manifest as a di\ufb00erence between the magni-\ntudes or phases of the individual intermediate states con-\ntributing. This type of the CP violation is searched for\n\ufb01rst by allowing these amplitudes to di\ufb00er for D0 and D0\ndecays, while not (yet) introducing additional parameters\ndescribing the other two types of the CP violation. Such\nan approach is used due to possible complications in the\n\ufb01tting procedure.144 In this measurement no signi\ufb01cant\ndeviations between the amplitudes of intermediate-state\ncontributions to D0 and D0 decays were found, and hence\none can conclude that no sign of CP violation in decay\nwas observed. Following this, the individual amplitudes\nare \ufb01xed to be the same for D0 and D0 and the parame-\nters |q/p| and \u03c6 are introduced. The results are listed in\nTable 19.2.8.\nBABAR (del Amo Sanchez, 2010f) uses the same ap-\nproach for the K+\u03c0\u2212\u03c00 \ufb01nal state, \ufb01tting separately D0\nand D0 tagged samples with duplicated mixing parame-\nters denoted as x+, y+ and x\u2212, y\u2212, respectively. The re-\nsults are given in Table 19.2.8.\nTable 19.2.8. Results of search for CP violation in time de-\npendent Dalitz analysis of K0\nSh+h\u2212\ufb01nal state (del Amo San-\nchez, 2010f; Abe, 2007b).\nExperiment\nSample\nResults [\u00d7103]\nBABAR\n486.5 fb\u22121\nCP violation\nPurity: 98.5%\nx+ = 0.0 \u00b1 3.3\ny+ = 5.5 \u00b1 2.7\nx\u2212= 3.3 \u00b1 3.3\ny\u2212= 5.9 \u00b1 2.8\nBelle\n540 fb\u22121\nCP violation\nPurity: 95.0%\nx = 8.1 \u00b1 3.0+1.0+0.9\n\u22120.7\u22121.6\ny = 3.7 \u00b1 2.5+0.7+0.7\n\u22121.3\u22120.8\n|q/p| = 0.86+0.30+0.06\n\u22120.29\u22120.03 \u00b1 0.08\n\u03c6 = (\u221214+16+5+2\n\u221218\u22123\u22124)\u25e6\nThe results show that parameters x+, y+ are consistent\nwith x\u2212, y\u2212, |q/p| is consistent with unity and \u03c6 is consis-\ntent with 0. Hence the measurements show no signi\ufb01cant\nsign of CP violation.\n19.2.8 Summary\nMixing of neutral charm mesons has been established by\nthe B Factories. The \ufb01rst results were reported in 2007 and\npublished as back-to-back articles. Mixing was established\nthrough the study of wrong sign decays by BABAR (Au-\nbert, 2007j) (see Section 19.2.2), and via the measurement\nof yCP by Belle (Staric, 2007) (see Section 19.2.3). The\naccuracy achieved by the B Factories is well beyond the\nexpectations before the start of data taking in 1999. By\n144 Note that by allowing magnitudes and phases of the D0\nand D0 decays to di\ufb00er essentially doubles the number of free\nparameters in the \ufb01t.\n\n597\nthe time data taking was well under way, the full poten-\ntial of B Factories as charm factories was realized and\ninterest in charm physics, especially in the FCNC\u2019s of D\nmesons, was greatly increased. The reason for this was\nthe physics interest in constraints on NP arising from an\nup-type quark (charm) FCNC\u2019s as well as the availability\nof large samples of reconstructed charm hadrons. Mixing\nparameters in the D0 \u2212D0 system are now known to an\naccuracy of O(10\u22123) from measurements done at the B\nFactories. The average of results from B Factories on the\nmixing parameters x and y, shown in the upper part of\nTable 19.2.9, are\nx = (0.59+0.21\n\u22120.22)%\ny = (0.78 \u00b1 0.12)% .\n(19.2.104)\nGraphically they are depicted in Fig. 19.2.33. The no-\nmixing hypothesis is rejected with a signi\ufb01cance of O(10)\u03c3.\nx (%)\n\u00ef0.5\n0\n0.5\n1\n1.5\ny (%)\n\u00ef0.5\n0\n0.5\n1\n1.5\nCPV allowed\nm\n 1 \nm\n 2 \nm\n 3 \nm\n 4 \nm\n 5 \nFigure 19.2.33. Likelihood contours of the HFAG-like \ufb01t to\nvarious measurements of mixing and CP violation parameters\nin the D0 system, in the (x, y) plane.\nThe average is calculated according to the Heavy Fla-\nvor Averaging Group (Amhis et al., 2012) method, using a\n\u03c72 \ufb01t assuming uncorrelated systematic errors, but taking\ninto account statistical correlations among the observables\nas provided by the experiments. Free parameters of the \ufb01t\nare listed in the lower part of Table 19.2.9.\nBecause the long-distance contributions to the D0\u2212D0\nmixing amplitude are di\ufb03cult to calculate, the measured\nvalues are di\ufb03cult to interpret. They may receive some\ncontribution from unknown NP processes, although the\nmeasured values can be accommodated within the SM.\nFor several years observation of CP violating asym-\nmetries in the charm sector at the level of O(10\u22122) was\nconsidered as rather clear signature for NP. Measurements\nperformed at the B Factories achieved the sensitivity level\nof O(10\u22123). They are probably some of the most demand-\ning measurements as far as the systematic uncertainties\nare concerned because one needs to control detector in-\nduced asymmetries using various control data samples.\nSeveral CP violating asymmetries are measured to be at\nthe few per mille level but consistent with no CP violation.\nAverages of the most important CP violation parameters\nare given in Table 19.2.9. In Fig. 19.2.34 the likelihood\ncontours of the average are shown in the (|q/p|, \u03c6) plane.\nNo deviations from CP conservation in the charm sec-\ntor have been observed. Measurements at the B Factories\nhave triggered an increased activity also on the theoretical\nside providing more accurate predictions.\n|q/p|\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\nArg(q/p) [deg.]\n\u00ef60\n\u00ef40\n\u00ef20\n0\n20\n40\n60\nm\n 1 \nm\n 2 \nm\n 3 \nm\n 4 \nm\n 5 \nFigure 19.2.34. Likelihood contours of the HFAG-like \ufb01t to\nvarious measurements of mixing and CP violation parameters\nin the D0 system, in the (|q/p|, \u03c6) plane.\nResults on mixing and especially CP violation in the\ncharm sector have not dried up with the end of the data\ntaking at B Factories. The LHCb collaboration recently\npresented a very precise measurement of the CP violation\nin D0 \u2192h+h\u2212decays (Aaij et al., 2013c). One can hope\nfor more precise (statistically signi\ufb01cant) measurements\nof CP violation in the charm sector from this and future\n\ufb02avor physics experiments.\n\n598\nTable 19.2.9. Results on mixing and CP violation parameters for neutral charm mesons from B Factories. Averages are\ncalculated using the HFAG method assuming uncorrelated systematic errors.\nResults\nDecay mode\nParameter\nReference\nK+K\u2212, \u03c0+\u03c0\u2212\nyCP = (0.72 \u00b1 0.18 \u00b1 0.12)%\n(Lees, 2013d)\nA\u0393 = (0.09 \u00b1 0.26 \u00b1 0.06)%\nyCP = (1.11 \u00b1 0.22 \u00b1 0.11)%\n(Staric, 2012a)\nA\u0393 = (\u22120.03 \u00b1 0.20 \u00b1 0.08)%\nAKK\nCP = (0.00 \u00b1 0.34 \u00b1 0.13)%\n(Aubert, 2008aq)\nA\u03c0\u03c0\nCP = (\u22120.24 \u00b1 0.52 \u00b1 0.22)%\nAKK\nCP = (\u22120.43 \u00b1 0.30 \u00b1 0.11)%\n(Staric, 2008)\nA\u03c0\u03c0\nCP = (0.43 \u00b1 0.52 \u00b1 0.12)%\nK0\nS\u03c6\nyCP = (0.11 \u00b1 0.61 \u00b1 0.52)%\n(Zupanc, 2009)\nK\u00b1\u03c0\u2213\nRK\u03c0\nD\n= (0.303 \u00b1 0.0189)%\n(Aubert, 2007j)\nAK\u03c0\nD\n= (\u22122.1 \u00b1 5.4)%\nx\u20322+ = (\u22120.024 \u00b1 0.052)%\ny\u2032+ = (0.98 \u00b1 0.78)%\nx\u20322\u2212= (\u22120.020 \u00b1 0.050)%\ny\u2032\u2212= (0.96 \u00b1 0.75)%\nRK\u03c0\nD\n= (0.364 \u00b1 0.018)%\n(Zhang, 2006)\nAK\u03c0\nD\n= (2.3 \u00b1 4.7)%\nx\u20322+ = (0.032 \u00b1 0.037)%\ny\u2032+ = (\u22120.12 \u00b1 0.58)%\nx\u20322\u2212= (0.006 \u00b1 0.034)%\ny\u2032\u2212= (0.20 \u00b1 0.54)%\nK\u00b1\u03c0\u2213\u03c00\n\u2020\nx\u2032\u2032 = (2.61+0.57\n\u22120.68 \u00b1 0.39)%\n(Aubert, 2006ap)\ny\u2032\u2032 = (\u22120.06+0.55\n\u22120.64 \u00b1 0.34)%\nK0\nSK+K\u2212, K0\nS\u03c0+\u03c0\u2212\nx = (0.16 \u00b1 0.23 \u00b1 0.12 \u00b1 0.08)%\n(del Amo Sanchez, 2010f)\ny = (0.57 \u00b1 0.20 \u00b1 0.13 \u00b1 0.07)%\nx = (0.81 \u00b1 0.30+0.13\n\u22120.17)%\n(Abe, 2007b)\ny = (0.37 \u00b1 0.25+0.10\n\u22120.15)%\n|q/p| = 0.86 \u00b1 0.30+0.10\n\u22120.09\n\u03c6 = (\u22120.244 \u00b1 0.31 \u00b1 0.09) rad\nD0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212\nRM = (0.017+0.017\n\u22120.016 \u00b1 0.003)%\n(Aubert, 2006ap)\n|p/q| = 1.1+4.0\n\u22120.6 \u00b1 0.1\nAverages\nx = (0.59+0.21\n\u22120.22)%\ny = (0.78 \u00b1 0.12)%\n\u03b4K\u03c0 = (26+13\n\u221214)\u25e6\n\u03b4K\u03c0\u03c00 = (22 \u00b1 23)\u25e6\nRK\u03c0\nD\n= (0.332 \u00b1 0.009)%\nAK\u03c0\nD\n= (\u22121.9 \u00b1 2.4)%\n|q/p| = 0.87+0.18\n\u22120.16\n\u03c6 = (\u221212+10\n\u221212)\u25e6\nAKK\nD\n= (\u22120.23 \u00b1 0.26)%\nA\u03c0\u03c0\nD = (0.12 \u00b1 0.40)%\n\u2020: x\u2032\u2032 = x cos \u03b4K\u03c0\u03c00 + y sin \u03b4K\u03c0\u03c00, y\u2032\u2032 = \u2212x sin \u03b4K\u03c0\u03c00 + y cos \u03b4K\u03c0\u03c00\n\n599\n19.3 Charmed meson spectroscopy\nEditors:\nAntimo Palano (BABAR)\nJolanta Brodzicka (Belle)\nPietro Colangelo (theory)\nAdditional section writers:\nTorsten Schroeder\n19.3.1 Introduction\nIn ordinary conditions of temperature and baryon den-\nsity, quantum chromodynamics (QCD) describes colored\nquarks permanently bound in colorless hadrons. Account-\ning for the non-perturbative strong dynamics producing\nthe outstanding phenomenon of con\ufb01nement represents\na di\ufb03culty which has been faced in several ways, using\nmethods with various degrees of theoretical soundness, re-\nliability and a variety of results. The main approaches to\ndescribe bound states of quarks are the constituent quark\nmodels, QCD sum rules and lattice QCD. Moreover, it\nis possible to formulate e\ufb00ective theories of QCD in lim-\nits in which particular symmetries, not present in the full\nQCD Lagrangian, become apparent and can be exploited.\nComparing the outcome of the various calculations (mass\nspectra, decay rates, etc.) to the measurements has al-\nlowed the interpretation of many experimental results. On\nthe other hand, it has been possible to test the accuracy of\nthe theoretical methods and of the procedures adopted to\nobtain quantitative predictions. The wealth of new infor-\nmation in charm spectroscopy collected at the B Factories\nhas allowed a remarkable progress in the description of the\nstrong dynamics of quarks, as it is brie\ufb02y described below.\nA few puzzling features of the observed states deserve fur-\nther investigations.\n19.3.1.1 Constituent quark models\nQuark models are traditionally a method to compute\nproperties like hadron masses and couplings. In such\napproaches the hadrons are approximately described in\nterms of rest-frame valence quark con\ufb01gurations, the dy-\nnamics of which is governed by a Hamiltonian derived\nfrom (or inspired by) QCD. In particular, quark con-\n\ufb01nement is implemented by a \ufb02avor-independent, linearly\nincreasing Lorentz-scalar interquark interaction at large\ndistances, while the short-distance quark dynamics is de-\nscribed by a one-gluon exchange interaction. For a system\ncomprising a heavy quark Q = c and a light antiquark\n\u00afq = \u00afu, \u00afd, \u00afs, the Hamiltonian is written as (Godfrey and\nIsgur, 1985)\nH = H0 + V,\n(19.3.1)\nwhere\nH0 = (p2 + m2\nQ)1/2 + (p2 + m2\n\u00afq)1/2\n(19.3.2)\nis the kinetic term, with p the modulus of the quark three-\nmomentum in the meson rest frame. The potential V in-\ncludes spin-independent and spin-dependent terms:\nV = V0 + V hyp + V so.\n(19.3.3)\nV0 is the sum of the con\ufb01ning and Coulomb potentials\nV0 = \u22124\n3\n\u03b1s(r)\nr\n+ c + \u03c32r\n(19.3.4)\nwith c and \u03c32 as free parameters. V hyp describes the spin-\nspin interaction\nV hyp = 4\n3\n\u03b1S(r)\nmQm\u00afq\nh8\u03c0\n3 sQ \u00b7 s\u00afq \u03b43(r)\n+ 1\nr3\n\u0012\n3(sQ \u00b7 r)(s\u00afq \u00b7 r)\nr2\n\u2212sQ \u00b7 s\u00afq\n\u0013 i\n(19.3.5)\nwith sQ and s\u00afq the heavy quark and light antiquark spin,\nrespectively. V so describes the spin-orbit interaction, ex-\npressed as a sum of the chromomagnetic and Thomas-\nprecession contributions:\nV so(cm) = 4\n3\n\u03b1S(r)\nr3\n\u0012 1\nmQ\n+ 1\nm\u00afq\n\u0013 \u0012 sQ\nmQ\n+ s\u00afq\nm\u00afq\n\u0013\n\u00b7 L,\n(19.3.6)\nV so(Tp) = \u22121\n2r\n\u0012 \u2202\n\u2202rV0\n\u0013 \nsQ\nm2\nQ\n+ s\u00afq\nm2\n\u00afq\n!\n\u00b7 L.\n(19.3.7)\nL is the orbital angular momentum. The solution of a\nSchr\u00a8odinger-like equation with the Hamiltonian (19.3.1)\nallows to obtain the mass spectrum and the wave func-\ntions for the states n2J+1L2S+1 classi\ufb01ed according to the\norbital angular momentum L, the total spin of the quarks\nS = sQ+s\u00afq, the total angular momentum J = L+S, and\nthe radial quantum number n. From the wave functions,\nother quantities can be computed, e.g. the meson decay\nconstants, form factors, the hadron strong couplings.\nA few remarks are in order.\n\u2013 The (\u201cconstituent\u201d) quark masses in the wave equation\nare input parameters, and do not coincide with the\n(\u201ccurrent\u201d) masses appearing in the QCD Lagrangian.\nFor the light u and d quarks the constituent masses are\n\ufb01xed to values of O(100 MeV), and of O(300 MeV) for\nthe strange quark, well above the values of the current\nmasses in the QCD Lagrangian.\n\u2013 The running of the strong coupling \u03b1S can be imple-\nmented as a dependence on the interquark distance,\n\u03b1S = \u03b1S(r); each model is characterized by its imple-\nmentation of \u03b1S(r).\n\u2013 Spin dependent terms in the potential present singu-\nlarities of the type 1/rn with n > 1, corresponding to\n\u201cillegal\u201d operators in the wave equation. This is a con-\nsequence of reducing the relativistic quark-antiquark\ninteraction to an instantaneous potential. The treat-\nment of such singularities introduces a model depen-\ndence in the calculation of the meson properties.\n\n600\n\u2013 The e\ufb00ect of nearby multi-hadron thresholds (or quark\nunquenching) is not taken into account in the calcu-\nlation of, e.g., the mass spectrum. Although such an\napproximation is legitimate in the limit of large num-\nber of colors, in real QCD it represents a systematic\nuncertainty a\ufb00ecting, in particular, the determination\nof the masses of the orbital and radial excitations.\nIn a quark model approach the c\u00afq spectrum (q = u, d, s)\nwas already computed long ago with results shown in Ta-\nble 19.3.1, namely in (Godfrey and Isgur, 1985). These\nare in rather close agreement (within 20\u201330 MeV) with the\ndata in the case of the lightest S-wave (L = 0) states and\nof two JP = 2+ and JP = 1+ P-wave (L = 1) states, as\none can argue considering the experimental measurements\nreported in Tables 19.3.2 and 19.3.3. As for the state with\nJP = 0+ and the second state with JP = 1+ (both with\nL = 1), in the c\u00afs case the predicted masses are larger\n(by about 100 MeV) than the masses of the scalar and\naxial vector DsJ mesons discussed below in this chapter.\nSeveral modi\ufb01cations and improvements have been im-\nplemented, namely in models based on the expansion of\nthe Hamiltonian (19.3.1) in the inverse mass of the charm\nquark, in the spirit of the heavy quark limit described\nin Section 19.3.1.2 (Di Pierro and Eichten, 2001), and in\ndeterminations of the c\u00afq Regge trajectories (Ebert, Faus-\ntov, and Galkin, 2010), but the resulting masses of the\nscalar and of one of the axial vector DsJ mesons remain\nlarger than in the experiment. A few quark models also\npredict spin-orbit inversion for the excited states (Godfrey\nand Kokoski, 1991; Isgur, 1998), which is not observed in\ndata.\nTo quantitatively assess the accuracy of quark model\npredictions is not an easy task, due to the assumptions\nneeded to formulate a wave equation for quark-antiquark\nbound states starting from the QCD Lagrangian; in par-\nticular, the e\ufb00ect of quark unquenching is poorly known.\nNevertheless, the discrepancy between the predictions of\nvarious models and the mass measurements has prompted\nTable 19.3.1. Masses (in GeV) of charmed mesons computed\nin (Godfrey and Isgur, 1985). The corresponding L = 1 ex-\nperimental \ufb01ndings for DJ and DsJ states are reported in Ta-\nble 19.3.2 and Table 19.3.3 respectively.\ncq (L = 0) Mass cq (L = 1) Mass cq (L = 2) Mass\nD(1S0)\n1.88\nD(3P0)\n2.40\nD(3D1)\n2.82\nD(3S1)\n2.04\nD(3P1)\n2.49\nD(3D3)\n2.83\nD(3P2)\n2.50\nD(1P1)\n2.44\ncs (L = 0) Mass cs (L = 1) Mass cs (L = 2) Mass\nDs(1S0)\n1.98\nDs(3P0)\n2.48\nDs(3D1)\n2.90\nDs(3S1)\n2.13\nDs(3P1)\n2.57\nDs(3D3)\n2.92\nDs(3P2)\n2.59\nDs(1P1)\n2.53\nthe idea that some observed states could not be simple\nquark-antiquark con\ufb01gurations, but more complex struc-\ntures, like bound state (\u201cmolecules\u201d) of other mesons\n(Barnes, Close, and Lipkin, 2003) or mixtures of conven-\ntional quark-antiquark with four-quark components (Vi-\njande, Fernandez, and Valcarce, 2006). A discrimination\nbetween the di\ufb00erent possibilities is feasible considering\nthe results not only for the masses, but also for the widths\nof the various decay modes. Within the quark models the\ncalculation of the latter quantities presents further uncer-\ntainties: in the in\ufb01nite heavy quark mass limit a di\ufb00er-\nent formalism can be developed to study the classi\ufb01ca-\ntion, the spectrum and some decay processes of heavy-\nlight hadrons, as discussed below.\n19.3.1.2 Exploiting symmetries of QCD in particular limits:\nthe Heavy Quark Chiral E\ufb00ective Theory\nIn the limit in which the masses of the heavy quarks (i.e.\nquarks with mQ \u226b\u039bQCD) is sent to in\ufb01nity, two symme-\ntries emerge in the QCD Lagrangian. The \ufb01rst one is a \ufb02a-\nvor symmetry, since the dependence on the \ufb02avor in QCD\nis only encoded in the quark mass, and for mQ \u2192\u221ethe\nheavy \ufb02avors are identically described. The second one is\na spin symmetry, arising from the decoupling of the spin of\na heavy quark from the spin of the light quarks and of the\ngluons (usually denoted as light degrees of freedom) (Neu-\nbert, 1994b). The two symmetries can be recognized at\na simple inspection of the Hamiltonian (19.3.1)-(19.3.7);\nboth spin and \ufb02avor symmetries are commonly denoted\nas the \u201cheavy quark symmetry\u201d.\nA consequence of the heavy quark symmetry is that,\nin the in\ufb01nite heavy quark mass limit, heavy-light Q\u00afq\nmesons can be classi\ufb01ed in doublets labeled by the value\nof the total angular momentum jq of the light degrees of\nfreedom with respect to the heavy quark Q (Isgur and\nWise, 1991). The spin of each member of the doublet is\nobtained combining the spin of the heavy quark with the\njq: J = sQ +jq; in the quark model jq would be given by\njq = s\u00afq + L. Spin symmetry implies that in each doublet\nthe two states are degenerate in mass.\nFor L = 0 the doublet has jq = 1\n2 and consists of two\nstates (P, P \u2217) (P refers to a generic heavy meson) with\nspin-parity JP\njq = (0\u2212, 1\u2212)1/2. P-wave states, with L = 1,\nform two doublets: (P \u2217\n0 , P \u2032\n1) with JP\njq = (0+, 1+)1/2, and\n(P1, P \u2217\n2 ) with JP\njq = (1+, 2+)3/2. D-wave states give rise to\ntwo other doublets: (P \u2217\n1 , P2) with JP\njq = (1\u2212, 2\u2212)3/2, and\n(P \u2032\u2217\n2 , P3) with JP\njq = (2\u2212, 3\u2212)5/2. Notice that the parity\nof the doublets has been identi\ufb01ed with the parity of the\ncorresponding mesons, P = (\u22121)L+1.\nThis construction is applied to both open beauty and\nopen charm mesons. In the case of charm, the (P, P \u2217)\ndoublet is \ufb01lled by the Dq and D\u2217\nq states, with q = u, d and\ns. The \ufb01nite heavy quark mass corrections are responsible\nfor removing the mass degeneracy in each doublet (which\nholds in the light SU(3)F limit), and are larger in the case\nof charm than in the case of beauty mesons.\n\n601\nThe conservation of angular momentum and parity in\nstrong interactions, together with the heavy quark sym-\nmetry, imposes constraints on the transitions between the\nmembers of the various doublets with the emission of a\nlight pseudoscalar meson (Isgur and Wise, 1991). In par-\nticular, the transitions of the excited states with jP\nq = 1\n2\n+\ninto states with jP\nq\n=\n1\n2\n\u2212and a pion or kaon occur in\nS-wave, while the transitions of the states with jP\nq = 3\n2\n+\ninto jP\nq\n=\n1\n2\n\u2212ones and a pion or kaon are in D-wave.\nThe consequence is that, if such transitions are kinemati-\ncally allowed, the jP\nq = 1\n2\n+ resonances are expected to be\nbroader than the jP\nq = 3\n2\n+ ones. At the next-to-leading\norder in the 1/mQ expansion, the axial vector states in\nthe jP\nq = 3\n2\n+ doublet can also decay in S-wave. An exam-\nple is provided by the D2 meson, which decays to D\u03c0 in\nD-wave; at the leading order in the heavy quark expan-\nsion, its spin partner D1 decays to D\u2217\u03c0 also in D-wave,\nand their widths, which depend on the three momentum\nof the emitted pion as |p|5\n\u03c0, are quite narrow.145 On the\nother hand, the scalar D\u2217\n0 meson decays to D\u03c0 in S-wave,\nwhich explains its broad width.\nThe strong transitions between states belonging to the\nvarious doublets or within the same doublet, can be stud-\nied in an e\ufb00ective \ufb01eld theory formalism. An e\ufb00ective QCD\nLagrangian is constructed in the in\ufb01nite heavy quark mass\nlimit, hence exploiting the heavy quark symmetry, and\nin the limit in which the light quark masses (u, d and s)\nvanish and another symmetry holds for QCD, the chiral\nSU(3)L \u00d7 SU(3)R symmetry. The various heavy meson\ndoublets are represented by \ufb01elds of 4 \u00d7 4 matrices. The\ndoublets with jP\nq\n=\n1\n2\n\u2212and jP\nq\n=\n1\n2\n+ are described by\nthe \ufb01elds Ha and Sa, respectively, while the doublets with\njP\nq = 3\n2\n+, jP\nq = 3\n2\n\u2212and jP\nq = 5\n2\n\u2212by the \ufb01elds T \u00b5\na , X\u00b5\na and\nX\u2032\u00b5\u03bd\na\n(a is a light \ufb02avor index):\nHa = 1 + v/\n2\n[P \u2217\na\u00b5\u03b3\u00b5 \u2212Pa\u03b35],\nSa = 1 + v/\n2\n[P \u2032\u00b5\n1a\u03b3\u00b5\u03b35 \u2212P \u2217\n0a],\n(19.3.8)\nT \u00b5\na = 1 + v/\n2\n\u00d7\n(\nP \u2217\u00b5\u03bd\n2a \u03b3\u03bd \u2212P1a\u03bd\nr\n3\n2\u03b35\n\u0014\ng\u00b5\u03bd \u2212\u03b3\u03bd\n3 (\u03b3\u00b5 \u2212v\u00b5)\n\u0015)\n,\nand analogous expressions for X\u00b5\na and X\u2032\u00b5\u03bd\na\n, with v the\nmeson four-velocity. The doublet with jP\nq\n=\n1\n2\n\u2212corre-\nsponding to the \ufb01rst radial excitations is described by H\u2032\na\n145 On very general grounds, the matrix element for the transi-\ntion involving the orbital momentum L depends on the spatial\nintegration of a (kr)L term, where k = p/\u210f, p is the momen-\ntum of the \ufb01nal state particle in the rest frame of the decaying\nparticle, and L is the orbital momentum quantum number.\nHence the matrix element is proportional to pL. Furthermore\nthe phase space of a two-body decay is proportional to p. Hence\nthe decay width is proportional to |M|2 \u221dp2L+1.\nwith structure identical to Ha. The various operators Pi\nin Eq. (19.3.8) annihilate mesons of four-velocity v which\nis conserved in strong interaction processes.\nThe octet of light pseudoscalar mesons is introduced\nthrough the \ufb01elds \u03be = e\niM\nf\u03c0 , with M containing \u03c0, K and\n\u03b7 \ufb01elds:\nM =\n\uf8eb\n\uf8ec\n\uf8ec\n\uf8ec\n\uf8ed\nq\n1\n2\u03c00 +\nq\n1\n6\u03b7\n\u03c0+\nK+\n\u03c0\u2212\n\u2212\nq\n1\n2\u03c00 +\nq\n1\n6\u03b7\nK0\nK\u2212\n\u00afK0\n\u2212\nq\n2\n3\u03b7\n\uf8f6\n\uf8f7\n\uf8f7\n\uf8f7\n\uf8f8\n(19.3.9)\nand f\u03c0 = 132 MeV the pion decay constant. The strong in-\nteraction of the heavy mesons with the octet of light pseu-\ndoscalar mesons is described by an e\ufb00ective Lagrangian\ninvariant under chiral transformations of the light \ufb01elds,\nand under heavy-quark spin-\ufb02avor transformations of the\nheavy \ufb01elds. At the leading order in the heavy quark\nmass and light meson momentum expansion, the transi-\ntion F \u2192HM (F = H, S and T, and M a light pseu-\ndoscalar meson) can be described by the Lagrangian terms\n(Burdman and Donoghue, 1992; Wise, 1992; Yan et al.,\n1992)\nLH = g Tr[ \u00afHaHb\u03b3\u00b5\u03b35A\u00b5\nba],\nLS = h Tr[ \u00afHaSb\u03b3\u00b5\u03b35A\u00b5\nba] + h.c.,\n(19.3.10)\nLT = h\u2032\n\u039b\u03c7\nTr[ \u00afHaT \u00b5\nb (iD\u00b5A/ + iD/A\u00b5)ba\u03b35] + h.c.,\nwith\nA\u00b5ba\n=\ni\n2\n\u0000\u03be\u2020\u2202\u00b5\u03be \u2212\u03be\u2202\u00b5\u03be\u2020\u0001\nba,\nD\nthe\ncovari-\nant derivative D\u00b5ba\n=\n\u2212\u03b4ba\u2202\u00b5 + V\u00b5ba and V\u00b5ba\n=\n1\n2\n\u0000\u03be\u2020\u2202\u00b5\u03be + \u03be\u2202\u00b5\u03be\u2020\u0001\nba. \u039b\u03c7 is a chiral symmetry-breaking\nscale (which can be set to \u039b\u03c7 = 1 GeV), and g , h\nand h\u2032 are e\ufb00ective couplings, which can be determined\nfrom experiment or from theoretical calculations (see Sec-\ntion 19.3.1.4).\nA set of other Lagrangian terms for the strong transi-\ntions among the various heavy quark doublets can be con-\nstructed analogously, including a few O(m\u22121\nQ ) corrections\n(Colangelo, De Fazio, and Ferrandes, 2006), from which\nthe decay widths and ratios of decay branching fractions\ncan be computed and compared to experiment. The re-\nsults are useful to cast light on the Q\u00afq spectrum, providing\nsupport to the classi\ufb01cation of the observed resonances.\nIn the c\u00afq (q = u, d) system, the mesons D+,0 and D\u2217+,0\n\ufb01ll the JP\njq = (0\u2212, 1\u2212)1/2 doublets. The properties of the\npositive parity states, collected in Table 19.3.5, follow the\nexpectations based on the classi\ufb01cation scheme outlined\nabove, with a mixing between the two JP = 1+ states. A\nset of heavier states has been observed in the D\u03c0 and\nD\u2217\u03c0 distributions: D(2550)0, D\u2217(2600)0, D\u2217(2600)0,+,\nD(2750)0 and D\u2217(2760)0,+ (del Amo Sanchez, 2010i); for\nthem, a tentative assignment is proposed in the following.\nAlso the observed c\u00afs mesons \ufb01t in the classi\ufb01cation\nscheme based on the heavy quark expansion. The two\nlightest mesons Ds(1969) and D\u2217\ns(2112) \ufb01ll the JP\njq =\n(0\u2212, 1\u2212)1/2 doublet. There are four positive parity states:\n\n602\nTable 19.3.2. Properties of neutral L = 1 DJ mesons.\nJP\nMass (MeV) Width (MeV) Observed decays\nD\u2217\n0\n0+\n2352 \u00b1 50\n261 \u00b1 50\nD\u03c0\nD\u2032\n1\n1+\n2427 \u00b1 36\n384+130\n\u2212105\nD\u2217\u03c0\nD1\n1+\n2421.3 \u00b1 0.6\n27.1 \u00b1 2.7\nD\u2217\u03c0, D0\u03c0+\u03c0\u2212\nD\u2217\n2\n2+\n2462.6 \u00b1 0.7\n49.0 \u00b1 1.4\nD\u2217\u03c0, D\u03c0\nD\u2217\ns0(2317) and D\u2032\ns1(2460) which can be identi\ufb01ed with\nthe members of the doublet JP\njq\n= (0+, 1+)1/2, and\nDs1(2536) and D\u2217\ns2(2573) \ufb01lling the JP\njq = (1+, 2+)3/2\ndoublet (Becirevic, Fajfer, and Prelovsek, 2004; Colangelo\nand De Fazio, 2003; Colangelo, De Fazio, and Ozpineci,\n2005), with a O(\n1\nmQ ) mixing between the two 1+ states.\nBoth the (0+, 1+)1/2 states have masses below the DK\nand the D\u2217K thresholds, respectively, and this explains\ntheir very narrow width (Swanson, 2006).146 Their prop-\nerties are collected in Tables 19.3.7 and 19.3.8.\nThe meson DsJ(2710) has been observed in the\nDK \ufb01nal state, and its spin-parity JP = 1\u2212has been\ndetermined (Brodzicka, 2008). A resonance DsJ(2860)\nhas also been found in the DK spectrum (Aubert,\n2006ag). Since both resonances also appear in the D\u2217K\nspectrum (Aubert, 2009au), they have natural parity,\nJP = 1\u2212, 2+, 3\u2212, \u00b7 \u00b7 \u00b7 . The decay mode into D\u2217K excludes\nthe assignment JP = 0+ for DsJ(2860), and is compati-\nble with the assignment JP = 3\u2212with radial quantum\nnumber n = 1, so that DsJ(2860) could be a member of\nthe doublet JP\njq = (2\u2212, 3\u2212)5/2 (Colangelo, De Fazio, and\nNicotri, 2006). The rather narrow width of this resonance\nwould be justi\ufb01ed by this assignment, since the two-body\ndecay to DK would occur in F-wave. The classi\ufb01cation of\nthe broad structure DsJ(3040) observed in the D\u2217K mass\nspectrum (Aubert, 2009au), has to be done on the basis\nof the available information on the mass, the width and\nthe decay modes, together with the full set of information\nabout the other doublets (Colangelo and De Fazio, 2010).\nImportant observables are ratios of branching fractions,\nnamely\nB(DsJ(2710) \u2192D\u2217K)/B(DsJ(2710) \u2192DK)\nand B(DsJ(2860) \u2192D\u2217K)/B(DsJ(2860) \u2192DK) (with\nD(\u2217)K the sum over D(\u2217)0K+ and D(\u2217)+K0\nS): the com-\nparison of the measurement (Aubert, 2009au) with the\ntheoretical results favors the interpretation of DsJ(2710)\nas the \ufb01rst radial excitation of D\u2217\ns(2112) and a member\nof the excited doublet JP\njq\n= (0\u2212, 1\u2212)1/2 with radial\nquantum number n = 2 (Colangelo, De Fazio, Nicotri,\nand Rizzi, 2008; Close, Thomas, Lakhina, and Swanson,\n2007). In the case of DsJ(2860) the measured ratio\n146 Other\ninterpretations\nof\nD\u2217\ns0(2317)\nand\nD\u2032\ns1(2460)\n(molecules, multiquarks) are reviewed in (Colangelo, De Fazio,\nand Ferrandes, 2004) and (Swanson, 2006); the dynamical gen-\neration of such states has been proposed in (Guo, Shen, Chiang,\nPing, and Zou, 2006; Guo, Shen, and Chiang, 2007).\nof branching fractions is larger than the theoretical\nprediction, leaving the classi\ufb01cation still an open issue.\nTable 19.3.3. Properties of L = 1 DsJ mesons.\nJP\nMass (MeV)\nWidth (MeV)\nObserved decays\nD\u2217\ns0\n0+\n2317.8 \u00b1 0.6\n< 3.8\nD+\ns \u03c00\nD\u2032\ns1\n1+\n2459.5 \u00b1 0.6\n< 3.5\nD\u2217+\ns\n\u03c00, D+\ns \u03b3, D+\ns \u03c0+\u03c0\u2212\nDs1\n1+\n2535.28 \u00b1 0.20\n< 2.5\nD\u2217+K0, D\u22170K+\nD\u2217\ns2\n2+\n2572.6 \u00b1 0.9\n20 \u00b1 5\nD0K+\nThe classi\ufb01cation of D\u2217\ns0(2317) and D\u2032\ns1(2460) as mem-\nbers of the spin doublet jP\nq = 1\n2\n+, together with the obser-\nvation that the mass splitting M(D\u2032\ns1)\u2212M(D\u2217\ns0) coincides\nwith the mass splitting between Ds(1969) and D\u2217\ns(2112)\nwhich belong to the negative parity jP\nq\n=\n1\n2\n\u2212doublet,\nhas inspired the notion of chiral heavy-light meson dou-\nblets (Bardeen, Eichten, and Hill, 2003; Nowak, Rho, and\nZahed, 2004). The idea is that the hadrons comprising a\nsingle heavy quark can be considered as \u201ctethered\u201d sys-\ntems. In a scenario in which (explicitly and spontaneously\nbroken) chiral symmetry is restored in QCD maintain-\ning con\ufb01nement, the heavy-light hadrons might appear\nin parity-doubled bound states which transform as linear\nrepresentations of the chiral symmetry. An e\ufb00ective \ufb01eld\ntheory, constrained by the heavy quark symmetry, can be\nformulated for such parity-doubled states, and as a conse-\nquence the mass di\ufb00erence \u2206M between the jP\nq = 1\n2\n\u00b1 par-\nity doublets can be related to g\u03c0, the 0+ \u21920\u2212\u03c0 coupling\nconstant, and to the pion decay constant f\u03c0 by a relation\nsimilar to the Goldberger-Treiman formula: \u2206M = g\u03c0f\u03c0\n(Bardeen, Eichten, and Hill, 2003).\nThe notion of heavy parity doublets needs to be further\nexplored and con\ufb01rmed, both in the case of the lightest\ndoublets and for the other excited states. It has various\nconsequences for the strong and radiative decay modes.\nThe radiative E1 transitions (1+, 0+) \u2192(1\u2212, 0\u2212)\u03b3, for ex-\nample, as well as the (1+, 1\u2212) \u2192(0+, 0\u2212)\u03b3 M1 transitions,\nare governed by similar combinations of the quark masses\nand electric charges, so that predictions for the various\nmodes can be elaborated and compared to experiment. In\nTable 19.3.4 a tentative classi\ufb01cation of all the observed\nmesons with open charm in HQ doublets is shown (Colan-\ngelo, De Fazio, Giannuzzi, and Nicotri, 2012).\nAs a last remark, the heavy quark symmetry allows to\nuse the information available in the charm sector to pre-\ndict properties in the beauty sector. For example, a dou-\nblet JP\njq = (0+, 1+)1/2 of narrow positive parity b\u00afs mesons\nis expected with masses M(B\u2217\ns0) = (5.71 \u00b1 0.03) GeV and\nM(B\u2032\ns1) = (5.77 \u00b1 0.03) GeV below the BK and B\u2217K\nthresholds and possible decays into Bs\u03c00 and B\u2217\ns\u03c00, re-\nspectively (Colangelo, De Fazio, and Ferrandes, 2006).\n\n603\nTable 19.3.4. Tentative classi\ufb01cation in HQ doublets of the observed mesons with open charm. States with uncertain assignment\nare indicated with (\u2217).\nDoublet\njP\nq\nJP\nc\u00afq (n = 1)\nc\u00afq (n = 2)\nc\u00afs (n = 1)\nc\u00afs (n = 2)\nH\n1\n2\n\u2212\n0\u2212\n1\u2212\nD(1869)\nD\u2217(2010)\nD(2550) (\u2217)\nD\u2217(2600) (\u2217)\nDs(1968)\nD\u2217\ns(2112)\nD\u2217\ns1(2700)\nS\n1\n2\n+\n0+\n1+\nD\u2217\n0(2400)\nD\u2032\n1(2430)\nD\u2217\ns0(2317)\nD\u2032\ns1(2460)\nDsJ(3040) (\u2217)\nT\n3\n2\n+\n1+\n2+\nD1(2420)\nD\u2217\n2(2460)\nDs1(2536)\nD\u2217\ns2(2573)\nDsJ(3040) (\u2217)\nX\u2032\n5\n2\n\u2212\n2\u2212\n3\u2212\nD(2750) (\u2217)\nD(2760) (\u2217)\nDsJ(2860) (\u2217)\n19.3.1.3 Results from QCD sum rules\nThe masses of the open charm mesons, as well as other\nhadronic quantities like the decay constants, can be com-\nputed in QCD by QCD Sum Rules. Two-point correlation\nfunctions of quark currents with the quantum numbers\nof the mesons of interest (Shifman, Vainshtein, and Za-\nkharov, 1979),\n\u03a0(Q2) = i\nZ\nd4x eiq\u00b7x \u27e8T[J(x)J\u2020(0)]\u27e9\n(19.3.11)\nwith J = Jc\u00afq, are expressed in QCD at short distances\n(Q2 \u2192\u221e) in terms of the quark masses, the strong cou-\npling constant \u03b1S and of the vacuum matrix elements\n\u27e8On\u27e9of gauge-invariant quark and gluon operators (vac-\nuum condensates). The latter parameters appear in the\n1/(Q2)n corrections to the perturbative expression of the\ncorrelation functions \u03a0pert(Q2),\n\u03a0QCD(Q2) = \u03a0pert(Q2) +\nX\nn\ncn\n\u27e8On\u27e9\n(Q2)n .\n(19.3.12)\nThe same correlation functions are represented in terms\nof hadronic states,\n\u03a0(Q2) = \u03a0had(Q2),\n(19.3.13)\nand the contributions of the lowest lying states are iso-\nlated from the excited states and the hadronic continuum.\nMatching the two (QCD and hadronic) representations on\nthe basis of analyticity and of (global) quark-hadron du-\nality, expressions can be worked out for, e.g., the meson\nmasses in terms of QCD parameters (Colangelo and Khod-\njamirian, 2000). The method can be formulated also for\nthe e\ufb00ective theories of QCD, namely the Heavy Quark\nE\ufb00ective Theory (Neubert, 1994b). The same approach\ncan be applied to investigate multiquark con\ufb01gurations,\nusing correlation functions of currents composed by sev-\neral quark \ufb01elds.\nThe accuracy of the QCD Sum Rule predictions is re-\nlated to the separation of the various particle contribu-\ntions in the hadronic representation of the two-point cor-\nrelation functions, to the procedure of exploiting quark-\nhadron duality and to the errors in the parameters, in\nparticular the vacuum condensates. Within the uncertain-\nties, the masses of the lightest c\u00afq and c\u00afs mesons have been\npredicted in agreement with experiment (Reinders, Rubin-\nstein, and Yazaki, 1985). Also the masses of the positive\nparity open charm mesons turn out to be compatible with\nmeasurement, and the main features of the radiative and\nstrong decays are reproduced if they are described as ordi-\nnary quark-antiquark con\ufb01gurations (Colangelo, De Fazio,\nand Ozpineci (2005); Dai, Li, Zhu, and Zuo (2008)).\n19.3.1.4 Lattice QCD results\nThe hadron properties can be computed ab initio from\nthe QCD Lagrangian by lattice calculations, analyzing\ncorrelation functions of quark currents of suitably chosen\nquantum numbers. The resulting c\u00afq and c\u00afs mass spectrum\ncan be compared to the measurement, addressing the is-\nsue of the classi\ufb01cation of the observed resonances. How-\never, the calculation of hadronic quantities for dynamical\nlight quarks with masses close to the QCD values is still\na challenging task. Di\ufb00erent results for the meson masses\nhave been found by di\ufb00erent groups, leading to a di\ufb00erent\nclassi\ufb01cation of, e.g., D\u2217\ns0(2317) and D\u2032\ns1(2460). In (Bali,\n2003) the mass M(D\u2217\ns0) = 2.57(11) GeV is obtained for\nthe scalar c\u00afs state, hence a value larger than the measured\nmass of D\u2217\ns0(2317), suggesting a non quark-antiquark in-\nterpretation for this state. On the other hand, in the cal-\nculations in (Dougall, Kenway, Maynard, and McNeile,\n2003) and (Lin, Ohta, Soni, and Yamada, 2006) the mass\nsplitting M(Ds(0+) \u2212M(Ds(0\u2212) turns out to be compat-\nible with experiment. The results of more recent analyses,\nwith overlap fermions for both light and heavy quarks and\nonly one lattice spacing, are consistent with the experi-\nmental masses, in particular for D\u2217\ns0(2317) described as a\nc\u00afs state (Dong et al., 2009). The same conclusion is drawn\n\n604\nin (Gong et al., 2011), where the tetraquark interpretation\nof D\u2217\ns0(2317) is tested and found to be inconsistent with\ndata.\n19.3.2 Production of charmed mesons at B Factories\nCharmed mesons are copiously produced at B Factories\neither directly in e+e\u2212collisions or as products of B me-\nson decays. Both mechanisms allow for complementary\nmeasurements of the charmed multiplets.\nCharm production in B decays is governed by the\nCKM-favored b \u2192c transition, thus B mesons are an\nabundant source of charmed mesons. The restricted kine-\nmatics of BB production at the \u03a5(4S) enable a selection\nof clean B meson samples, while the zero spin of the par-\nent B constrains possible quantum numbers of the daugh-\nter particles and makes their spin-parity measurements\neasier. Depending on the quantum numbers of charmed\nmesons, theory predicts certain patterns in their produc-\ntion rates in B meson decays (Section 17.3), which is\nhelpful in clarifying the nature of the produced particles.\nCharmed mesons bearing high spin or being highly excited\nare suppressed in B meson decays, thus their studies with\ne+e\u2212\u2192c\u00afc continuum data are more feasible.\nAt the center-of-mass (CM) energy of the B Factories,\nthe cross-section of prompt c\u00afc pair production provides a\nlarge fraction of the total hadronic cross-section, resulting\nin large samples of ground and excited charmed mesons\nfrom the hadronization of the produced c quarks (see Sec-\ntion 24.1). The produced hadrons are usually studied in-\nclusively i.e. without reconstruction of the other parti-\ncles in the event. Such an approach allows high e\ufb03ciency\nbut often su\ufb00ers from large background, while charmed\nhadrons coming from strongly decaying excited states can-\nnot be distinguished from those originating directly from\nthe e+e\u2212annihilation.\n19.3.3 Non-strange charm spectroscopy\n19.3.3.1 Introduction\nCharm spectroscopy to this date has still not been fully\nexplored as there are many D meson states predicted\nin the 1980s, which have not been observed experimen-\ntally. Figure 19.3.1 shows the predicted spectrum for a c\u00afu\nsystem (The spectrum of the c \u00afd system is almost identi-\ncal.). The ground states, D0,+ (Goldhaber et al., 1976; Pe-\nruzzi et al., 1976), and spin excitations, D\u2217(0,+) (Feldman\net al., 1977), were \ufb01rst observed respectively in 1976 and\n1977 by the Mark-I experiment at SLAC. Their properties\nare quite well known, though they are still being studied\nwith increasing precision. Recent measurements of D0 and\nD+ masses come from CLEO (Cawl\ufb01eld et al., 2007) and\nKEDR (Anashin et al., 2010). As for the total widths, only\nthe D\u2217+ width has been measured (96 \u00b1 22 keV), as it is\nenlarged by strong D\u2217+ decays. The widths of the other D\nand D\u2217mesons are consistent with zero, because they de-\ncay either mainly weakly, or in the case of the D\u22170 mainly\n \nPJ\n)\n2\nMass (GeV/c\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\n3.2\nD(1.864)\n(2.023)\n*\nD\n(2.558)\n0\nD\n(2.618)\n1\n*\nD\n(2.419)\n1\nD\n(2.380)\n0\n*\nD\n(2.469)\n1\n*\nD\n(2.479)\n2\n*\nD\n(2.801)\n2\nD\n(2.796)\n1\n*\nD\n(2.806)\n2\n*\nD\n(2.806)\n3\n*\nD\n(3.074)\n3\nD\n(3.074)\n2\n*\nD\n(3.079)\n3\n*\nD\n(3.084)\n4\n*\nD\n-0\n-1\n-2\n-3\n+\n0\n+1\n+\n2\n+\n3\n+\n4\n1S\n}\n1P\n}\n1D\n}\n1F\n}\n2S\n}\nFigure 19.3.1. Modi\ufb01ed Godfrey-Isgur predictions (Godfrey\nand Isgur, 1985). The plot shows the c\u00afu spectrum where the\nmasses have been scaled down so that the ground state matches\nthe D0 mass. Also, the 2\u2212states, not shown in the original\npaper, have been inserted following the splitting structure of\nthe 1P states.\nradiatively. Therefore, experiments set only upper limits\nfor them. Decays of D(\u2217) mesons are described in detail in\nSection 19.1. Spin-parities of D(\u2217) quoted in the PDG are\nassigned based on the quark-model predictions, though\nmany studies performed, especially of D(\u2217) produced in\nB decays, con\ufb01rm these assignments (Sections 17.3 and\n17.6).\nWithin the L = 1 orbital excitations labeled as D\u2217\u2217,\nthe narrow doublet was not observed until 1989 owing to\nits lower production rates and larger widths. Eventually\nneutral D0\n1 and D\u22170\n2 mesons were observed in D\u2217+\u03c0\u2212\ufb01nal\nstates by ARGUS (Albrecht et al., 1989d) and CLEO (Av-\nery et al., 1990). Their widths of about 20\u221230 MeV/c2 and\nmasses around 2.4 GeV/c2, were in agreement with the\nmodel predictions (Rosner (1986); Godfrey and Kokoski\n(1991); Falk and Peskin (1994)). The broad L = 1 states\nhave only recently been observed by Belle and BABAR in\nB decays where they could be separated from the back-\nground, as it will be described in the following.\n19.3.3.2 D\u2217\u2217in B decays\nB decays to the D\u03c0 and D\u2217\u03c0 \ufb01nal states are two of the\ndominant hadronic decays and have been measured quite\nwell (Section 17.3). Similar processes, B \u2192D\u2217\u2217\u03c0, are ex-\npected to be a dominant source of D\u2217\u2217mesons. At the\nquark level such decays proceed through a b \u2192cW \u2212\u2192\nc\u00afud transition for which the underlying diagrams are shown\nin Fig. 19.3.2. As D\u2217\u2217mesons are expected to decay dom-\ninantly in the D(\u2217)\u03c0 modes, processes like B \u2192D(\u2217)\u03c0\u03c0\nprovide the best way to study them.\n\n605\nb\n c\n u\n_\nd\n u\n_\n u\n_\nB-\n\u03c0-\nD\n**0\nb\n d\n u\n_\nc\n u\n_\n u\n_\nB-\n\u03c0-\nD\n**0\nb\n d\n u\n_\nc\n d\n_\n d\n_\nB\n- 0\n\u03c0-\nD\n**+\nFigure 19.3.2. From (Kuzmin, 2007). Quark-line diagrams\nfor charged (left and middle) and neutral (right) B \u2192D\u2217\u2217\u03c0\ndecays.\n19.3.3.3 Neutral D\u2217\u2217via B\u2212\u2192D(\u2217)+\u03c0\u2212\u03c0\u2212Dalitz analysis\nThe production of neutral D\u2217\u2217resonances was studied\nthrough a full Dalitz-plot analysis of the three-body de-\ncay B\u2212\u2192D+\u03c0\u2212\u03c0\u2212(Abe, 2004f; Aubert, 2009g) and\nB\u2212\u2192D\u2217+\u03c0\u2212\u03c0\u2212(Abe, 2004f). Thus, for the \ufb01rst time,\ninterference between intermediate states is taken into ac-\ncount in measuring properties of the D\u2217\u2217mesons. First\nBelle performed such a Dalitz analysis using a data sample\nof about 65\u00d7106 of BB pairs; a BABAR analysis, based on\n383\u00d7106 BB pairs, followed. The D(\u2217)+ are reconstructed\nin the clean decay modes: D+ \u2192K\u2212\u03c0+\u03c0+, D\u2217+ \u2192D0\u03c0+\nwith D0 \u2192K\u2212\u03c0+ and K\u2212\u03c0+\u03c0+\u03c0\u2212, ensuring good purity\nover the Dalitz diagram. Reconstructed B candidates are\nidenti\ufb01ed by their \u2206E and mES. In addition a thrust angle\nrequirement, cos \u03b8T < 0.8, is applied to suppress contin-\nuum background (see Section 9). Signal yields, obtained\nfrom \ufb01ts to the \u2206E distributions, of about 1100 events\n(Belle) and 3500 events (BABAR) for B\u2212\u2192D+\u03c0\u2212\u03c0\u2212and\n560 events for B\u2212\u2192D\u2217+\u03c0\u2212\u03c0\u2212(Belle) have been ob-\ntained.\nThe Dalitz plots for the B\u2212\u2192D+\u03c0\u2212\u03c0\u2212candidates\nwithin the \u2206E-mES signal region are shown in Fig. 19.3.3.\nThe plot from BABAR is symmetric in the D\u03c0 masses be-\ncause of the two identical pions. Belle used as the Dalitz\nvariables the lower and higher values of the two D\u03c0 mass\ncombinations, denoted as m2\nmin(D\u03c0) and m2\nmax(D\u03c0); in-\ntermediate resonances emerge in m2\nmin(D\u03c0). The distribu-\ntions clearly display the structure of nodes characteristic\nof the spin-2 resonance D\u2217(2460)0, while an accumulation\nof events in the threshold mass region are attributed to\nthe scalar D\u22170\n0 .\nPrinciples of Dalitz-plot analysis are described in de-\ntail in Section 13. The signal density of the decay B\u2212\u2192\nD+\u03c0\u2212\u03c0\u2212are parameterized as a coherent sum of ampli-\ntudes corresponding to the following intermediate states\nforming the D+\u03c0\u2212system: D\u22170\n2 , D\u22170\n0\nand o\ufb00-shell vector\nD\u22170 (labeled as D\u22170\nv ). Also a virtual B\u22170, contributing as\nB \u2192B\u22170\nv \u03c0 with B\u22170\nv\n\u2192D\u03c0, and a constant amplitude\nfor a non-resonant component are included. Such virtual\ncontributions are of phenomenological origin and are in-\ntroduced to obtain a better description of the Dalitz dis-\ntributions. Both Belle and BABAR analyses employed an\nisobar model in which resonance amplitudes are param-\neterized with Breit-Wigner (BW) functions with a mass\ndependent width and angular dependence related to res-\nonance decay with given orbital momentum (L = 0, 1, 2\nrespectively for the D\u22170\n0 , D\u22170\nv , D\u22170\n2 ). The latter introduces\n4\n4.5\n5\n5.5\n6\n6.5\n7\n7.5\n8\n15\n20\n25\n M2 D\u03c0 max (GeV/c2)2\n M2 D\u03c0 min (GeV/c2)2\n)\n4 \n/c\n2 \n) (GeV\n 1 \n\u03c0\n(D \n2 \nm\n5\n10\n15\n20\n25\n)\n4 \n/c\n2 \n) (GeV\n 2 \n\u03c0\n(D \n2 \nm\n5\n10\n15\n20\n25\nFigure 19.3.3. Dalitz plot for B\u2212\u2192D+\u03c0\u2212\u03c0\u2212from Abe\n(2004f) (left) and (Aubert, 2009g) (right).\nan amplitude dependence on the helicity angle (\u0398h) de-\n\ufb01ned as the angle between the momentum vectors of the\nbachelor pion from the B decay and the pion of the D\u03c0\nsystem in the D\u03c0 rest frame. The signal parameterization\nis convoluted with the experimental mass resolution, typ-\nically of order of a few MeV/c2. The background shape is\nobtained from a \ufb01t to the Dalitz distribution for the \u2206E\nsideband region.\nWith such models for signal and background densities,\nan unbinned maximum-likelihood \ufb01t to the Dalitz plot is\nperformed. The D\u2217\u2217parameters, all the amplitudes and\nrelative phases are free parameters in the \ufb01t. The \ufb01t like-\nlihood value is signi\ufb01cantly improved by the inclusion of\nthe broad scalar resonance, thus Belle claimed the \ufb01rst\nobservation of the D\u22170\n0\nmeson (Abe, 2004f).\nFigure 19.3.4 shows the m2\nmin(D\u03c0), m2\nmax(D\u03c0) and\nm2(\u03c0\u03c0) projections with the \ufb01t result and contributions\nfrom the intermediate resonances superimposed, as ob-\ntained by BABAR. The D\u22170\n0\nsignal and the re\ufb02ection of\nD\u22170\n2\ncan easily be distinguished in the m2\nmin(D\u03c0) and\nm2\nmax(D\u03c0) projections, respectively. The resonance masses\nand widths as well as branching ratio products measured\nin both analyses are very consistent, and are summarized\nin Table 19.3.5.\nFigure 19.3.5 shows M(D+\u03c0\u2212)min (previously labeled\nalso as mmin(D\u03c0)) for di\ufb00erent helicity angle regions, as\nmeasured by Belle. The D\u22170\n2\nis clearly seen for | cos \u0398h| >\n0.67 where the D-wave component peaks, the D\u22170\n0\nis vis-\nible for 0.33 < | cos \u0398h| < 0.67 where the D-wave is sup-\npressed with respect to the S-wave, the range | cos \u0398h| <\n0.33 demonstrates an interference pattern.\nThe B\u2212\u2192D\u2217+\u03c0\u2212\u03c0\u2212decay contains a vector parti-\ncle in the \ufb01nal state, therefore, assuming a negligible D\u2217\nwidth, there are two more variables needed to specify the\n\ufb01nal state in addition to M 2(D\u2217\u03c0)min and M 2(D\u2217\u03c0)max.\nThe following ones are chosen in the analysis performed\nby Belle (Abe, 2004f): the D\u2217helicity angle (\u03b1) between\nthe momenta of pions from the D\u2217and D\u2217\u2217decays in the\n\n606\nTable 19.3.5. From Abe (2004f) (A4), Kuzmin (2007) (K), (Abe, 2005i) (A5) and Aubert (2009g) (A9). The \ufb01tted parameters\nof the D\u2217\u2217mesons and products of branching ratios B(B \u2192D\u2217\u2217\u03c0) \u00d7 B(D\u2217\u2217\u2192f). The \ufb01rst error is statistical, the second one\nis systematic and the third one is model related. World average (WA) values are taken from (Eidelman et al., 2004). \u201c\ufb01xed\u201d\nindicates parameters which were \ufb01xed to values obtained from other \ufb01ts.\nRef.\nD\u2217\u2217\nf\nMass [ MeV/c2]\nWidth [ MeV]\nB(B) \u00d7 B(D\u2217\u2217) [10\u22124]\nA4\nD\u22170\n0\nD+\u03c0\u2212\n2308 \u00b1 17 \u00b1 15 \u00b1 28\n276 \u00b1 21 \u00b1 18 \u00b1 60\n6.1 \u00b1 0.6 \u00b1 0.9 \u00b1 1.6\nA4\nD0\n1\nD\u22c6+\u03c0\u2212\n2421.4 \u00b1 1.5 \u00b1 0.4 \u00b1 0.8\n23.7 \u00b1 2.7 \u00b1 0.2 \u00b1 4.0\n6.8 \u00b1 0.7 \u00b1 1.3 \u00b1 0.3\nA4\nD\n\u20320\n1\nD\u22c6+\u03c0\u2212\n2427 \u00b1 26 \u00b1 20 \u00b1 15\n384+107\n\u221275 \u00b1 24 \u00b1 70\n5.0 \u00b1 0.4 \u00b1 1.0 \u00b1 0.4\nA4\nD\u22170\n2\nD+\u03c0\u2212\nD\u22c6+\u03c0\u2212\n2461.6 \u00b1 2.1 \u00b1 0.5 \u00b1 3.3\n2461.6(\ufb01xed)\n45.6 \u00b1 4.4 \u00b1 6.5 \u00b1 1.6\n45.6(\ufb01xed)\n3.4 \u00b1 0.3 \u00b1 0.6 \u00b1 0.4\n1.8 \u00b1 0.3 \u00b1 0.3 \u00b1 0.2\nA9\nD\u22170\n2\nD+\u03c0\u2212\n2460.4 \u00b1 1.2 \u00b1 1.2 \u00b1 1.9\n41.8 \u00b1 2.5 \u00b1 2.1 \u00b1 2.0\n3.5 \u00b1 0.2 \u00b1 0.2 \u00b1 0.4\nA9\nD\u22170\n0\nD+\u03c0\u2212\n2297 \u00b1 8 \u00b1 5 \u00b1 19\n273 \u00b1 12 \u00b1 17 \u00b1 45\n6.8 \u00b1 0.3 \u00b1 0.4 \u00b1 2.0\nK\nD\u2217+\n0\nD0\u03c0+\n2308(\ufb01xed)\n276(\ufb01xed)\n0.6 \u00b1 0.1 \u00b1 0.1 \u00b1 0.2\nK\nD+\n1\nD\u22c60\u03c0+\n2428.2 \u00b1 2.9 \u00b1 1.6 \u00b1 0.6\n34.9 \u00b1 6.6+4.1\n\u22120.9 \u00b1 4.1\n3.7 \u00b1 0.6+0.7 +0.6\n\u22120.4 \u22120.3\nK\nD\n\u2032+\n1\nD\u22c60\u03c0+\n2427(\ufb01xed)\n384(\ufb01xed)\n< 0.7 @ 90% C.L.\nK\nD\u2217+\n2\nD0\u03c0+\nD\u22c60\u03c0+\n2465.7 \u00b1 1.8 \u00b1 0.8+1.2\n\u22124.7\n2465.7(\ufb01xed)\n49.7 \u00b1 3.8 \u00b1 4.1 \u00b1 4.9\n49.7(\ufb01xed)\n2.1 \u00b1 0.2 \u00b1 0.3 \u00b1 0.1\n2.4 \u00b1 0.4+0.3 +0.4\n\u22120.4 \u22120.2\nA5\nA5\nD0\n1\nD0\u03c0+\u03c0\u2212\nD\u22c60\u03c0+\u03c0\u2212\n2426 \u00b1 3 \u00b1 1\n2422.2(\ufb01xed to WA)\n24 \u00b1 7 \u00b1 8\n18.9(\ufb01xed to WA)\n1.85 \u00b1 0.29 \u00b1 0.35+0.0\n\u22120.43\n< 0.06 @ 90% C.L.\nA5\nD\u22170\n2\nD\u22c60\u03c0+\u03c0\u2212\n2458.9(\ufb01xed to WA)\n23(\ufb01xed to WA)\n< 0.22 @ 90% C.L.\nA5\nA5\nD+\n1\nD+\u03c0+\u03c0\u2212\nD\u22c6+\u03c0+\u03c0\u2212\n2421 \u00b1 2 \u00b1 1\n2422.2(\ufb01xed to WA)\n21 \u00b1 5 \u00b1 8\n18.9(\ufb01xed to WA)\n0.89 \u00b1 0.15 \u00b1 0.17+0.0\n\u22120.27\n< 0.33 @ 90% C.L.\nA5\nD\u2217+\n2\nD\u22c6+\u03c0+\u03c0\u2212\n2459(\ufb01xed to WA)\n25(\ufb01xed to WA)\n< 0.24 @ 90% C.L.\nD\u2217rest frame and the azimuthal angle (\u03b3) of the pion\nfrom the D\u2217relative to the B \u2192D\u2217\u03c0\u03c0 decay plane.\nFigure\n19.3.6\nshows\nthe\nDalitz\ndistribution,\nM 2(D\u2217\u03c0)min vs. M 2(D\u2217\u03c0)max, for the \u2206E-mES sig-\nnal region B candidates. The signi\ufb01cant increase of\nthe event density in M 2(D\u2217\u03c0)min at about 5.8 GeV2/c4\ncorresponds to the narrow D1 and D\u2217\n2\nstates. The\nbroad D\u2032\n1 meson, unobserved at the time the analysis\nwas performed, can also contribute to the D\u2217\u03c0. The\nB\u2212\n\u2192D\u2217+\u03c0\u2212\u03c0\u2212signal is thus parameterized as a\ncoherent sum of the relativistic Breit-Wigner amplitudes\nof these three intermediate states.\nThe HQET predicts that the two 1+ mesons, with\njq =\n1\n2 and jq =\n3\n2, decay into the D\u2217\u03c0 \ufb01nal state via\nS- and D-wave, respectively. Due to the \ufb01nite c-quark\nmass, the observed (physical) states can be a mixture of\nsuch pure states. The mixing can occur for instance via\nthe common D\u2217\u03c0 decay channel and the resulting D\u20321 and\nD1 amplitudes are superpositions of the S- and D-wave\namplitudes:\n|D\u2032\n1\u27e9= |1S\u27e9cos \u03c9 \u2212e+i\u03c8|1D\u27e9sin \u03c9\n|D1\u27e9= |1S\u27e9sin \u03c9 + e\u2212i\u03c8|1D\u27e9cos \u03c9,\n(19.3.14)\nwhere \u03c9 is a mixing angle and \u03c8 is a complex phase. Such\nan amplitude representation is used in the signal model.\nLike in the B\u2212\u2192D+\u03c0\u2212\u03c0\u2212analysis, virtual D\u22170\nv and B\u22170\nv\ncomponents, as well as the constant term are also included\nin the signal function, while the background is estimated\nwith events from the \u2206E sidebands.\nAmplitudes and phases of the intermediate states are\nextracted through an unbinned maximum-likelihood \ufb01t\nin the four-dimensional (M 2(D\u2217\u03c0)min, M 2(D\u2217\u03c0)max, \u03b1,\n\u03b3) phase space. The broad 1+ meson signi\ufb01cantly im-\nproves the \ufb01t likelihood and, thus, Belle claimed its dis-\ncovery. Figure 19.3.6 shows the background-subtracted\nM(D\u2217+\u03c0\u2212)min distribution with the resonance contribu-\ntions obtained from the \ufb01t. The \ufb01tted parameters of\nthe axial mesons are summarized in Table 19.3.5, along\nwith the branching ratio products. The mixing angle be-\ntween the two 1+ mesons and their relative phase were\nmeasured as \u03c9 = (\u22120.10 \u00b1 0.03 \u00b1 0.02 \u00b1 0.02) rad and\n\u03c8 = (0.05\u00b10.20\u00b10.04\u00b10.06) rad. Such a measurement is\nperformed for the \ufb01rst time for the charmed mesons. De-\ncomposition of the S- and D-waves was before attempted\nfor the D1(2420) \u2192D\u2217\u03c0 by CLEO. They set a limit on\nthe S-wave contribution to the total width as a function\nof the relative phase (Avery et al., 1994b; Bergfeld et al.,\n1994).\nFor better illustration of the \ufb01t results, the measured\nangular distributions along with MC simulations performed\n\n607\n)\n4 \n/c\n2\n) (GeV\n\u03c0\n(D\nmin\n2\nm\n4\n5\n6\n7\n8\n9\n10\n)\n4 \n/c\n2 \nEvents/(0.125 GeV\n0\n100\n200\n300\n400\n500\n(a)\n)\n4 \n/c\n2\n) (GeV\n\u03c0\n(D\nmax\n2\nm\n14\n16\n18\n20\n22\n24\n26\n)\n4 \n/c\n2 \nEvents/(0.125 GeV\n0\n50\n100\n150\n(b)\n)\n4 \n/c\n2\n) (GeV\n\u03c0 \u03c0\n(\n2\nm\n0\n2\n4\n6\n8\n10\n12\n)\n4 \n/c\n2 \nEvents/(0.15 GeV\n0\n50\n100\n150\n200\n(c)\nFigure 19.3.4. From (Aubert, 2009g). Result of the Dalitz\nplot \ufb01t to the B\u2212\u2192D+\u03c0\u2212\u03c0\u2212signal candidates: projections\non (a) m2\nmin(D\u03c0), (b) m2\nmax(D\u03c0) and (c) m2(\u03c0\u03c0). The points\nwith error bars are data, the solid curves represent the nominal\n\ufb01t. The shaded areas show the D\u22170\n2\ncontribution, the dashed\ncurves show the D\u22170\n0\nsignal, the dash-dotted curves show the\nD\u2217\nv and B\u2217\nv signals, and the dotted curves show the background.\nwith the \ufb01tted parameters, are shown in Fig. 19.3.7 for the\nM 2(D\u2217\u03c0)min regions populated by the D\u20320\n1 or D0\n1.\n19.3.3.4 Charged D\u2217\u2217via B0 \u2192D(\u2217)0\u03c0+\u03c0\u2212Dalitz analysis\nThe Dalitz analysis of the B0 \u2192D0\u03c0+\u03c0\u2212decay has been\nperformed by Belle (Kuzmin, 2007) using 388 \u00d7 106 BB\npairs. After excluding a subsample of the B0 \u2192D\u2217+\u03c0\u2212\nwith D\u2217+ \u2192D0\u03c0+, Belle obtains a signal yield of about\n0\n100\n200\n300\n400\n-1 < cos\u03b8h< -0.67\n-0.67 < cos\u03b8h < -0.33\n0\n100\n200\n300\n400\n-0.33 < cos\u03b8h < 0\n0 < cos\u03b8h < 0.33\n0\n100\n200\n300\n400\n2\n2.5\n0.33 < cos\u03b8h < 0.67\n2\n2.5\n0.67 < cos\u03b8h < 1\n0\n100\n200\n300\n400\n0\n100\n200\n300\n400\n0\n100\n200\n300\n400\n2\n2.5\n2\n2.5\n0\n100\n200\n300\n400\n0\n100\n200\n300\n400\n0\n100\n200\n300\n400\n2\n2.5\n2\n2.5\nNevnt/\u03b5\nMD\u03c0 min (GeV/c2)\nFigure\n19.3.5.\nFrom\n(Abe,\n2004f).\nE\ufb03ciency-corrected\nM(D+\u03c0\u2212)min distribution in B\u2212\u2192D+\u03c0\u2212\u03c0\u2212for di\ufb00erent he-\nlicity angle ranges. Curves correspond to the \ufb01t to the total\ndistribution (upper blue) and background (lower black) com-\nponent.\n4\n5\n6\n7\n8\n15\n17.5\n20\n22.5\n25\n M2 D*\u03c0 max (GeV/c2)2\n M2 D*\u03c0 min (GeV/c2)2\n0\n10\n20\n30\n40\n50\n60\n70\n2.2\n2.3\n2.4\n2.5\n2.6\n2.7\nMD*\u03c0 min (GeV/c2)\nD*\n1\nD1\nD2\n*\nEvents/10 MeV/c2\nFigure 19.3.6. From (Abe, 2004f). Left: Dalitz plot for\nthe B\u2212\u2192D\u2217+\u03c0\u2212\u03c0\u2212signal candidates. Right: Background-\nsubtracted M(D\u2217\u03c0)min spectrum. Points with error bars cor-\nrespond to data, hatched histograms show \ufb01tted resonance con-\ntributions and the open histogram is a coherent sum of all the\ncontributions. In the \ufb01gure the D\u2032\n1 is indicated as D\u2217\n1.\n2900 events. As intermediate resonances decaying to D0\u03c0+\nas well as resonances decaying to \u03c0+\u03c0\u2212can contribute to\nthe B0 \u2192D0\u03c0+\u03c0\u2212reaction, its kinematics is described\nwith the M 2(D0\u03c0+) and M 2(\u03c0+\u03c0\u2212) invariant masses.\nThe distribution for the reconstructed \u2206E-mES signal re-\ngion events is shown in Fig. 19.3.8. The p.d.f. is comprised\nof D\u2217+\n0 , D\u2217+\n2 , D\u2217\nv and B\u2217+\nv\ncomponents contributing to\nthe D0\u03c0+ system, whereas \u03c1(770), \u03c9, f2(1270), f0(600),\nf0(980) and f0(1370) states can be present in the \u03c0+\u03c0\u2212\nprojection. Parameters of the D\u2217+\n0\nare \ufb01xed to the one\nfrom the neutral D\u22170\n0 \u2192D\u2212\u03c0+ measurement, while light\nscalar mesons are included in the \ufb01t with their param-\neters \ufb01xed to the PDG values (Beringer et al., 2012).\nAn unbinned \ufb01t to the Dalitz distribution gives signi\ufb01-\n\n608\n0\n20\n40\n-1\n-0.5\n0\n0.5\n1\n0 - 5.76(GeV/c2)2\ncos\u03b8\n0\n10\n20\n30\n40\n-1\n-0.5\n0\n0.5\n1\n0 - 5.76(GeV/c2)2\ncos\u03b1\n0\n10\n20\n30\n-2\n0\n2\n0 - 5.76(GeV/c2)2\n\u03b3\n0\n20\n40\n-1\n-0.5\n0\n0.5\n1\n5.76 - 5.98(GeV/c2)2\ncos\u03b8\n0\n20\n40\n-1\n-0.5\n0\n0.5\n1\n5.76 - 5.98(GeV/c2)2\ncos\u03b1\n0\n10\n20\n30\n-2\n0\n2\n5.76 - 5.98(GeV/c2)2\n\u03b3\nFigure 19.3.7. From (Abe, 2004f): Distributions of the D\u2217\u2217\nhelicity angle (cos \u03b8), cos \u03b1 and \u03b3 in regions of M 2(D\u2217\u03c0)min\nwith\ndominance\nof\nthe\nD\u20320\n1\nin\nB\u2212\n\u2192\nD\u2217+\u03c0\u2212\u03c0\u2212\nde-\ncays: M 2(D\u2217\u03c0)min\n<\n5.76 GeV2/c4 and the D0\n1: 5.76\n<\nM 2(D\u2217\u03c0)min < 5.98 GeV2/c4. Points with error bars corre-\nspond to data, the histogram is from MC simulation based\non the \ufb01tted parameters and the hatched histogram shows the\nbackground contribution.\n0\n10\n20\n30\n0\n2.5\n5\n7.5\n10\n12.5\nM\u03c0\u03c0\n2 (GeV/c2)2\nMD\u03c0\n2 (GeV/c2)2\n0\n25\n50\n75\n100\n2\n2.25\n2.5\n2.75\n3\nMD\u03c0 (GeV/c2)\nFigure 19.3.8. From (Kuzmin, 2007): Dalitz plot for the\nB0 \u2192D0\u03c0+\u03c0\u2212signal candidates (left) and M(D0\u03c0+) pro-\njection (right) of the events with cos \u0398h > 0. Points with error\nbars represent data, the hatched histogram shows background\nestimated from generic MC events normalized to the sideband\ndata and the open histogram represents the \ufb01tted function.\ncant contributions from both the charged D\u2217+\n0 , observed\nfor the \ufb01rst time, as well as the D\u2217+\n2 . Fig. 19.3.8 shows\nthe M(D0\u03c0+) spectrum with the \ufb01tted function superim-\nposed, for the cos \u0398h > 0 helicity angle region, where the\n\u03c0\u03c0 resonance contributions and background are low. Fit-\nted D\u2217\u2217+ parameters and measured branching ratio prod-\nucts are presented in Table 19.3.5. It can be seen that the\nproduction branching fraction for the D\u2217+\n0\nis much smaller\nthan for the D\u2217+\n2 .\n19.3.3.5 The D\u2217\u2217production rates\nMeasurements of the charmed meson production rates in\nB decays provide tests of HQET and QCD sum rules.\nThe measured branching ratio products (Table 19.3.5)\nshow that the narrow mesons comprise (36 \u00b1 6)% of the\nB\u2212\u2192D+\u03c0\u2212\u03c0\u2212and (63 \u00b1 6)% of the B\u2212\u2192D\u2217+\u03c0\u2212\u03c0\u2212\ndecays, thus the production rates of the jq = 1\n2 and jq = 3\n2\nc\u00afu mesons are similar. This is inconsistent with the QCD\nsum rule which predicts the dominance of the narrow,\njq = 3\n2 states. However, if the color-suppressed amplitude\n(left diagram in Fig. 19.3.2) contributes signi\ufb01cantly, it\nwould be enhanced for the jq = 1\n2 states. This seems to be\nsupported by the Belle measurements of the color-allowed\nB0 \u2192D(\u2217)0\u03c0+\u03c0\u2212decays, where production rates of the\njq = 3\n2 states are similar to the ones measured in charged\nB decays, but are much lower for the broad jq = 1\n2 states.\nThe measured production rates (Table 19.3.5) give:\nB(B\u2212\u2192D\u22170\n2 \u03c0\u2212)B(D\u22170\n2 \u2192D+\u03c0\u2212)\nB(B\u2212\u2192D\u22170\n2 \u03c0\u2212)B(D\u22170\n2 \u2192D\u2217+\u03c0\u2212) = B(D\u22170\n2 \u2192D+\u03c0\u2212)\nB(D\u22170\n2 \u2192D\u2217+\u03c0\u2212)\n= 1.9 \u00b1 0.5, (19.3.15)\nwhich is consistent with a value predicted by theoretical\nmodels (Rosner, 1986; Godfrey and Kokoski, 1991; Falk\nand Peskin, 1994). Assuming that D\u2217\n2 decay is saturated\nby the D(\u2217)\u03c0 transitions, whereas the D1 decay is satu-\nrated by the D\u2217\u03c0 mode, one gets:\nB(B\u2212\u2192D\u22170\n2 \u03c0\u2212)B(D\u22170\n2 \u2192D+\u03c0\u2212, D\u2217+\u03c0\u2212)\nB(B\u2212\u2192D0\n1\u03c0\u2212)B(D0\n1\u2192D\u2217+\u03c0\u2212)\n=0.77 \u00b1 0.15,\n(19.3.16)\nwhich is by a factor of two larger than the HQET predic-\ntion calculated in the factorization approximation\n(Lei-\nbovich, Ligeti, Stewart, and Wise, 1998; Neubert, 1998).\nFrom these measurements it is impossible to determine\nthe size of the nonfactorized part for the tensor and axial\nmesons or whether higher order corrections to the leading\nfactorized terms should be taken into account. More accu-\nrate measurements of the semileptonic B \u2192D\u2217\u2217l\u03bd decays\n(Section 17.1), which are free of nonfactorized contribu-\ntions, may help to resolve this problem.\n19.3.3.6 Other D\u2217\u2217decays\nStudies of subleading decay modes of the D\u2217\u2217mesons are\nimportant for understanding heavy-light mesons and to\nfurther test theoretical models. Subleading decays could\nmodify the ratio in Eq. (19.3.16). Belle observed the D1 \u2192\nD\u03c0+\u03c0\u2212decays in B \u2192(D(\u2217)\u03c0+\u03c0\u2212)\u03c0\u2212, where D = D0\nor D+, in a sample of 152 \u00d7 106 BB pairs (Abe, 2005i).\nTo suppress the large continuum background, the analysis\nuses a Fisher discriminant (see Section 9), that is based\non the B production angle, the thrust angle, as well as pa-\nrameters characterizing the momentum \ufb02ow in the event,\noriginally developed by CLEO (Asner et al., 1996). The\nM(D\u03c0+\u03c0\u2212) spectra for the B candidates in the \u2206E-mES\nsignal region, shown in Fig. 19.3.9, demonstrate the promi-\nnent D1 signals. No signi\ufb01cant signals are observed for nei-\nther D1 \u2192D\u2217\u03c0+\u03c0\u2212nor D\u2217\n2 \u2192D(\u2217)\u03c0+\u03c0\u2212. Except for the\nD1 peak, the signal-region data are consistent with the\nmass distributions for the \u2206E sidebands. This suggests\nthat there is no signi\ufb01cant contribution from the broad\nD\u2217\u2217mesons. The results of the \ufb01ts to the M(D(\u2217)\u03c0+\u03c0\u2212)\n\n609\n0\n10\n20\n30\n40\n50\n2.2\n2.325\n2.45\n2.575\n2.7\nM(D0\u03c0+\u03c0-) (GeV/c2)\nEvents/ (10 MeV/c2)\n0\n10\n20\n30\n40\n50\n2.2\n2.325\n2.45\n2.575\n2.7\nM(D+\u03c0+\u03c0-) (GeV/c2)\nEvents/ (10 MeV/c2)\nFigure 19.3.9. From (Abe, 2005i): M(D\u03c0+\u03c0\u2212) distributions\nfor the B \u2192(D\u03c0+\u03c0\u2212)\u03c0\u2212candidates in the signal region (open\nhistogram) and \u2206E sidebands (hatched-yellow).\ndistributions and the measured B products are summa-\nrized in Table 19.3.5. The observed D1 \u2192D\u03c0+\u03c0\u2212decays\nlower the ratio in Eq. (19.3.16) to 0.54 \u00b1 0.18 which, thus,\nbecomes consistent with the HQET predictions (see Sec-\ntion 19.3.3.5).\nThe dynamics of the D1 \u2192D\u03c0+\u03c0\u2212decays are ex-\namined in a simpli\ufb01ed way by studying one-dimensional\nprojections of mass and angular variables. The data, com-\npared with MC simulations of various D1 decays models,\nare found to be well described by the D1 \u2192D\u2217\n0\u03c0\u2212decay.\n19.3.3.7 New excited charmed mesons\nTo search for new excited charmed mesons, labeled as DJ,\nBABAR analyzed the inclusive production of the D+\u03c0\u2212,\nD0\u03c0+, and D\u2217+\u03c0\u2212\ufb01nal states in the reaction e+e\u2212\u2192\nc\u00afc \u2192D(\u2217)\u03c0X, where X is any additional system (del\nAmo Sanchez, 2010i). They use a data sample consisting\nof approximately 590 \u00d7 106 c\u00afc events. In the D\u03c0 system,\nthe D+ \u2192K\u2212\u03c0+\u03c0+ and D0 \u2192K\u2212\u03c0+ decays are recon-\nstructed. The D0 candidates, when being combined with\nany additional pion in the event form a D\u2217, are rejected.\nTo improve the signal purity for D0 \u2192K\u2212\u03c0+, it is re-\nquired that cos \u03b8K > \u22120.9, where \u03b8K is the angle between\nthe K\u2212direction and the direction opposite to the e+e\u2212\nCM system in the D0 rest frame. The D\u2217+\u03c0\u2212system is\nreconstructed using the D\u2217+ \u2192D0\u03c0+, D0 \u2192K\u2212\u03c0+ and\nK\u2212\u03c0+\u03c0\u2212\u03c0+ decay modes. Background from e+e\u2212\u2192BB\nevents and much of the combinatorial background, are re-\nmoved by requiring the CM momentum of the D(\u2217)\u03c0 to\nbe greater than 3.0 GeV/c.\nThe measured D+\u03c0\u2212and D0\u03c0+ mass spectra are pre-\nsented in Fig. 19.3.10 and show similar features:\n\u2013 Prominent D\u2217\n2 peaks.\n\u2013 The M(D+\u03c0\u2212) shows a peaking background at about\n2.3 GeV/c2 due to D0\n1 and D\u22170\n2\ndecays to D\u2217+\u03c0\u2212,\nwith the \u03c00 from the D\u2217+ \u2192D+\u03c00 missing. Simi-\nlarly, M(D0\u03c0+) shows feeddown due to the D+\n1 and\nD\u2217+\n2\ndecaying to D\u22170\u03c0+ where D\u22170 \u2192D0\u03c00.\n\u2013 Both D+\u03c0\u2212and D0\u03c0+ mass distributions show new\nstructures around 2.60 and 2.76 GeV/c2, labeled re-\nspectively as D\u2217(2600) and D\u2217(2760).\n)\n2\nEvents / (0.005 GeV/c\n5\n10\n15\n20\n25\n1000\n\u00d7\n)\n2\nEvents / (0.005 GeV/c\n5\n10\n15\n20\n25\n1000\n\u00d7\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\n3\n4\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\n3\n4\nFit A\n)\n2\n) (GeV/c\n\u03c0\nM(D\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n)\n2\nEvents / (0.005 GeV/c\n0\n5\n10\n15\n20\n25\n)\n2\n) (GeV/c\n\u03c0\nM(D\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n)\n2\nEvents / (0.005 GeV/c\n0\n5\n10\n15\n20\n25\nFit B\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\nFigure 19.3.10. From (del Amo Sanchez, 2010i). Mass dis-\ntribution for D+\u03c0\u2212(top) and D0\u03c0+ (bottom) candidates pro-\nduced in the process e+e\u2212\u2192c\u00afc \u2192D\u03c0X, Points correspond\nto data, with the total \ufb01t overlaid as a solid curve. The dot-\nted curves are the signal components. The lower solid curves\ncorrespond to the smooth combinatoric background and to the\npeaking backgrounds at 2.3 GeV/c2. The inset plots show the\ndistributions after subtraction of the combinatoric background.\nThe M(D\u03c0) spectra are \ufb01tted with contributions from\nthe D\u2217\n2, D\u2217(2600) and D\u2217(2760) described with relativis-\ntic BW distributions. The smooth background is modeled\nusing an exponential function multiplied by a two-body\nphase-space factor dropping toward the D\u03c0 mass thresh-\nold. The feeddown is described by convolving BW func-\ntions with a function describing the resolution and mass\nshift obtained from the MC simulation. The masses and\nwidths of the D1 and D\u2217\n2 feeddowns are \ufb01xed to the values\nobtained respectively from the same M(D\u03c0) distribution\nand from the M(D\u2217+\u03c0\u2212) study described below. Finally,\nalthough not visible in the M(D+\u03c0\u2212) mass distribution,\na BW function is included to account for the broad D\u2217\n0.\nThe D\u2217+\u03c0\u2212mass distribution is shown in Fig. 19.3.11\nand exhibits the following features:\n\u2013 Prominent D0\n1 and D\u22170\n2\npeaks.\n\u2013 Two enhancements at 2.60 GeV/c2 and 2.75 GeV/c2,\nwhich are denoted as D\u2217(2600)0 and D(2750)0.\nThe angular analysis of the M(D\u2217+\u03c0\u2212) \u22482.6 GeV/c2\nregion shows that it could not be described by a single\nresonance, instead two resonances with di\ufb00erent helicity-\nangle distributions could be present. Thus, a new compo-\nnent, labeled as D(2550)0, is included in the M(D\u2217+\u03c0\u2212)\n\ufb01t. The D(2550)0 parameters are obtained by requiring\n| cos \u03b8H| > 0.75 in order to suppress the other resonances\n\n610\nTable 19.3.6. From (del Amo Sanchez, 2010i). Summary of the measurements of the old and newly discovered DJ resonances.\nThe \ufb01rst error is statistical and the second is systematic; \u201c\ufb01xed\u201d indicates parameters which were \ufb01xed to values obtained from\nother \ufb01ts. The signi\ufb01cance is de\ufb01ned as the yield divided by its total error.\nResonance\nChannel\nMass (MeV/c2)\nWidth (MeV)\nSigni\ufb01cance\nD1(2420)0\nD\u2217+\u03c0\u2212\n2420.1\u00b10.1\u00b10.8\n31.4\u00b10.5\u00b11.3\nD\u2217\n2(2460)0\nD+\u03c0\u2212\n2462.2\u00b10.1\u00b10.8\n50.5\u00b10.6\u00b10.7\nD(2550)0\nD\u2217+\u03c0\u2212\n2539.4\u00b14.5\u00b16.8\n130\u00b112\u00b113\n3.0\u03c3\nD\u2217(2600)0\nD+\u03c0\u2212\n2608.7\u00b12.4\u00b12.5\n93\u00b16\u00b113\n3.9\u03c3\nD(2750)0\nD\u2217+\u03c0\u2212\n2752.4\u00b11.7\u00b12.7\n71\u00b16\u00b111\n4.2\u03c3\nD\u2217(2760)0\nD+\u03c0\u2212\n2763.3\u00b12.3\u00b12.3\n60.9\u00b15.1\u00b13.6\n8.9\u03c3\nD\u2217\n2(2460)+\nD0\u03c0+\n2465.4\u00b10.2\u00b11.1\n50.5 (\ufb01xed)\nD\u2217(2600)+\nD0\u03c0+\n2621.3\u00b13.7\u00b14.2\n93 (\ufb01xed)\n2.8\u03c3\nD\u2217(2760)+\nD0\u03c0+\n2769.7\u00b13.8\u00b11.5\n60.9 (\ufb01xed)\n3.5\u03c3\n(Fig. 19.3.11, top), where the helicity angle (\u03b8H) is de-\n\ufb01ned in the rest frame of the D\u2217as the angle between\nthe primary pion and the slow pion from the D\u2217decay.\nIn this \ufb01t, the parameters of the D\u22170\n2\nand D\u2217(2600)0 are\n\ufb01xed to those measured in the D+\u03c0\u2212. This \ufb01t also de-\ntermined the parameters of the D0\n1. A complementary \ufb01t\nwith | cos \u03b8H| < 0.5, shown in Fig. 19.3.11 (middle), is\nperformed to discriminate in favor of the D\u2217(2600)0. To\ndetermine the \ufb01nal parameters of the D(2750)0 signal the\ntotal D\u2217+\u03c0\u2212sample is re\ufb01tted (Fig. 19.3.11 (bottom)),\nwhile \ufb01xing the parameters of all other BW components\nto the values determined in the previous \ufb01ts. The broad\nresonance D\u20320\n1 is known to decay to this \ufb01nal state, how-\never, these \ufb01ts were insensitive to its contribution due to\nits large width and because the background parameters\nare free. The \ufb01t results are summarized in Table 19.3.6.\nThe D\u2217(2760)0 signal observed in its decay to D+\u03c0\u2212\nis very close in mass to the D(2750)0 signal observed in\nD\u2217+\u03c0\u2212.\nTo have information on the spin of the observed res-\nonances, the data are divided into 10 sub-samples corre-\nsponding to cos \u03b8H intervals of 0.2. Each sample is \ufb01t-\nted with all shape parameters \ufb01xed to the values de-\ntermined from the \ufb01ts to the total samples. The yields\nextracted from these \ufb01ts are plotted for each resonance\nin Fig. 19.3.12. The cos \u03b8H distributions of the D\u2217\n2 and\nD\u2217(2600) are consistent with the expectations for natural\nparity, de\ufb01ned by P = (\u22121)J, and leading to a sin2 \u03b8H-\nlike distribution. This observation supports the assump-\ntion that the enhancement assigned to the D\u2217(2600) ob-\nserved in the D+\u03c0\u2212and D\u2217+\u03c0\u2212mass spectra belong to\nthe same state, as only states with natural parity can de-\ncay to both D+\u03c0\u2212and D\u2217+\u03c0\u2212. The cos \u03b8H\ndistribution\nfor the D(2550)0 is consistent with pure cos2 \u03b8H as ex-\npected for a JP = 0\u2212state.\nThe branching fraction ratios,\nB(DJ\u2192D+\u03c0\u2212)\nB(DJ\u2192D\u2217+\u03c0\u2212), may be\nused in the identi\ufb01cation of the new states. Such ratios,\ncomputed using the yields obtained from the \ufb01ts to the to-\ntal samples and corrected for the reconstruction e\ufb03ciency,\nare measured to be:\nB(D\u2217\n2(2460)0 \u2192D+\u03c0\u2212)\nB(D\u2217\n2(2460)0 \u2192D\u2217+\u03c0\u2212) = 1.47 \u00b1 0.03 \u00b1 0.16,\nB(D\u2217(2600)0 \u2192D+\u03c0\u2212)\nB(D\u2217(2600)0 \u2192D\u2217+\u03c0\u2212) = 0.32 \u00b1 0.02 \u00b1 0.09,\nB(D\u2217(2760)0 \u2192D+\u03c0\u2212)\nB(D(2750)0 \u2192D\u2217+\u03c0\u2212) = 0.42 \u00b1 0.05 \u00b1 0.11.\n(19.3.17)\nThe D(2550)0 and the D\u2217(2600)0 have mass values and\ncos \u03b8H distributions that are consistent with the predicted\nradial excitations D1\n0(2S) and D3\n1(2S). The D\u2217(2760)0 and\nthe D(2750)0 (assuming these are two di\ufb00erent states)\ncould be some of the four L = 2 states, predicted to lie in\nthis mass region.\n19.3.4 Charmed-strange mesons\n19.3.4.1 Introduction\nThe\nunexpected\ndiscovery\nof\na\nnarrow\nstate,\nD\u2217\ns0(2317)+\n\u2192\nD+\ns \u03c00,\nby\nthe\nBABAR\nexperiment\n(Aubert, 2003j), and a subsequent discovery of yet\nanother narrow particle, Ds1(2460)+ \u2192D\u2217\ns(2112)+\u03c00\nby CLEO (Besson et al., 2003), Belle (Abe, 2004a) and\nBABAR (Aubert, 2004t) raised considerable interest in the\nspectroscopy of charmed mesons. These discoveries were\na surprise because they contradicted the expectations\nof HQET which, till then, had been a very successful\napproach in describing the spectroscopy of D(s) and\nB(s) mesons. The expected spectrum for the c\u00afs states\nis sketched in Fig. 19.3.13. In this scheme, L = 1 c\u00afs\nexcitations consist of a JP = (0+, 1+) doublet carrying\nthe total light-quark angular momentum jq =\n1\n2 and a\n(1+, 2+) doublet having jq =\n3\n2. Figure 19.3.13 shows\nalso a comparison between HQET calculations and\nexperimental measurements of Ds meson masses. The\ntwo jq =\n3\n2 states are expected to be narrow and are\nidenti\ufb01ed as the 1+ Ds1(2536) and the 2+ D\u2217\ns2(2573) seen\nin D\u2217K and DK decays, respectively. These states were\n\ufb01rst observed in the 1980-90s (Albrecht et al., 1989c;\nAlexander et al., 1993; Kubota et al., 1994).\nBefore the observations reported here became avail-\nable, the two jq = 1\n2 states were predicted to have masses\nabove the DK and D\u2217K thresholds, respectively, and\n\n611\nH\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nSignal Yield / 0.2\n0\n20\n40\n1000\n\u00d7\n0.25)\n\u00b1\n [1+(5.72\n\u221d\nY \nH\n\u03b5\n)]\nH\n\u03b8(\n2\ncos\n\u00d7\n(2420)\n1\nD\nH\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nSignal Yield / 0.2\n0\n10\n20\n1000\n\u00d7\nH\n\u03b5)\nH\n\u03b8(\n2\n sin\n\u221d\nY \n(2460)\n2\n*\nD\nH\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nSignal Yield / 0.2\n0\n10\n20\n1000\n\u00d7\nH\n\u03b5)\nH\n\u03b8(\n2\n cos\n\u221d\nY \nD(2550)\nH\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nSignal Yield / 0.2\n0\n5\n10\n1000\n\u00d7\nH\n\u03b5)\nH\n\u03b8(\n2\n sin\n\u221d\nY \nD (2600)\n*\nH\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\nSignal Yield / 0.2\n0\n1\n2\n3\n1000\n\u00d7\n0.28)\n\u00b1\n [1-(0.33\n\u221d\nY \nH\n\u03b5\n)]\nH\n\u03b8(\n2\ncos\n\u00d7\nD(2750)\nFigure 19.3.12. From (del Amo Sanchez, 2010i). Distribution in cos \u03b8H for each signal observed in the D\u2217+\u03c0\u2212\ufb01nal state. The\nerror bars include statistical and correlated systematic uncertainties. The curve is a \ufb01t using the function Y shown in the plot;\n\u03b5H is the e\ufb03ciency as a function of cos \u03b8H.\nrather large widths of order of a few 100 MeV/c2. The lat-\nter was blamed for making their detection hard.\nAs it can be seen from Fig. 19.3.13, the newly dis-\ncovered states at 2.32 and 2.46 GeV/c2 do not \ufb01t these\npredictions. Their masses are considerably lower and are\nbelow their relative D(\u2217)K thresholds. The observed de-\ncay modes violates isospin conservation and is therefore\nlikely to be of electromagnetic origin. This makes their\nwidths extremely narrow (consistent with zero). Two pos-\nsibilities then arise: the calculations are \ufb02awed, or these\nstates have a parton composition other than the assumed\nconventional heavy-light c\u00afs quark-antiquark pair.\n19.3.4.2 Discovery of D\u2217\ns0(2317)+ and Ds1(2460)+\nBABAR \ufb01rst investigated the D+\ns \u03c00 mass spectrum inclu-\nsively produced from e+e\u2212interactions, with 92 fb\u22121 of\ndata used (Aubert, 2003j). The D+\ns is reconstructed in\nthe K+K\u2212\u03c0+ decay mode, with K+K\u2212mass near the\n\u03c6(1020) mass or K\u2212\u03c0+ mass near the K\u2217(892) mass. The\ndecay products of the \u03c6(1020) and K\u2217(892) vector states\nexhibit a cos2 \u03b8h helicity angle behavior and the signal-to-\nbackground ratio is improved by requiring | cos \u03b8h| > 0.5.\nCandidates for \u03c00 \u2192\u03b3\u03b3 are reconstructed using photons\nwhich do not belong to another acceptable \u03c00 candidate\n(\u201c\u03c00 veto\u201d). Only D+\ns \u03c00 candidates with their CM mo-\nmenta p\u2217> 3.5 GeV/c are retained to eliminate back-\nground from B decays and reduce combinatorial back-\nground.\nThe\nresulting\nD+\ns \u03c00\nmass\nspectrum,\nshown\nin\nFig. 19.3.14a, exhibits a clear, narrow signal at a mass\nnear 2.32 GeV/c2, labeled as D\u2217\ns0(2317)+. No such signal\nis observed in the M(D+\ns \u03c00) distribution obtained using\ncandidates from either the D+\ns or the \u03c00 mass sidebands.\nThe same analysis procedure is applied to MC simulations\nof e+e\u2212\u2192c\u00afc events which include all known charm states\nand decays, and yields no 2.32 GeV/c2 peak. This proves\nthat the D\u2217\ns0(2317)+ is not due to re\ufb02ection from other\ncharmed states.\nThe M(D+\ns \u03c00) spectrum in Fig. 19.3.14a is \ufb01tted us-\ning a Gaussian function describing the D\u2217\ns0(2317)+ sig-\nnal and a polynomial background, and yields about 1300\nsignal events with a mass of (2316.8 \u00b1 0.4) MeV/c2 and\nan experimental resolution of (8.6 \u00b1 0.4) MeV/c2. A clear\nD\u2217\ns0(2317)+ \u2192D+\ns \u03c00 signal is also observed for D+\ns \u2192\nK+K\u2212\u03c0+\u03c00 (see Fig. 19.3.14b).\nUsing 13.5 fb\u22121 of data, the D\u2217\ns0(2317)+ was read-\nily con\ufb01rmed by CLEO\n(Besson et al., 2003); in the\nsame analysis they also claimed the discovery of the\nDs1(2460)+ \u2192D\u2217+\ns \u03c00. In the original paper (Aubert,\n2003j), BABAR also reports a narrow signal of 2.46 GeV/c2\nin the M(D+\ns \u03c00\u03b3) spectrum, with most of the peak events\nhaving D+\ns \u03b3 masses consistent with the D\u2217+\ns . However,\nMC simulations showed a complex kinematic superposi-\ntion of signals and re\ufb02ections between Ds1(2460)+ and\nD\u2217\ns0(2317)+ (see below), and for this reason BABAR did\nnot claim immediately the 2.46 GeV/c2 structure being a\nnew resonance.\nA few months later, Belle con\ufb01rmed both D\u2217\ns0(2317)+\nand Ds1(2460)+ using 70 fb\u22121 of data sample\n(Abe,\n2004a). The DsJ signals are studied in the \u2206M(D(\u2217)+\ns\n\u03c00)\n\u2261\nM(D(\u2217)+\ns\n\u03c00) \u2212M(D(\u2217)+\ns\n) mass di\ufb00erence spectra\n(shown in Fig. 19.3.15) as they have a better resolution\nthan the invariant masses, while the secondary particles\nare reconstructed as D\u2217+\ns\n\u2192D+\ns \u03b3 and D+\ns\n\u2192\u03c6\u03c0+.\nLike in the BABAR study, MC simulation reveals that\nDs1(2460)+ \u2192D\u2217+\ns \u03c00 decays produce a re\ufb02ection in the\n\u2206M(D+\ns \u03c00) distribution slightly below the D\u2217\ns0(2317)+\nsignal. On the other hand, the D\u2217\ns0(2317)+ \u2192D+\ns \u03c00 com-\nbined with a random photon passing the D\u2217+\ns\nselection,\ncauses a peaking background to the Ds1(2460)+. Another\nfeed-down source is the Ds1(2460)+ producing a wide\nstructure at its nominal mass, which is due to a random\n\u03b3 in the D\u2217+\ns\nreconstruction. Both these feed-downs are\nvisible in the \u2206M(D\u2217+\ns \u03c00) distributions for the D\u2217+\ns\nside-\nbands in the right upper plot of Fig. 19.3.15.\nIn the D\u2217\ns0(2317)+ \ufb01t (left bottom plot in Fig. 19.3.15),\nboth the signal and the feed-down are represented as Gaus-\nsian shapes, parameters of the latter are \ufb01xed accord-\ning to MC expectation and normalized by the measured\nDs1(2460)+ signal. A \ufb01t to the Ds1(2460)+ mass distri-\nbution is performed for the data with the D\u2217+\ns\nsideband\nsubtracted bin-by-bin (right bottom plot in Fig. 19.3.15).\nMasses corresponding to the \ufb01tted peak positions and the\nupper limits set on the meson widths are summarized in\nTable 19.3.7.\nBABAR developed a di\ufb00erent method for solving\nan overlap between Ds1(2460)+ and D\u2217\ns0(2317)+ (Au-\nbert, 2004t). Considering the \ufb01nal state D+\ns \u03c00\u03b3, the\n\n612\n )\n2\n Events / ( 0.005 GeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n18 1000\n\u00d7\n )\n2\n Events / ( 0.005 GeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n18 1000\n\u00d7\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n0.5\n1\n1.5\n2\n2.5\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n0.5\n1\n1.5\n2\n2.5\nFit C\n )\n2\n Events / ( 0.005 GeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n18\n )\n2\n Events / ( 0.005 GeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n18\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\n3\n4\n5\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n1\n2\n3\n4\n5\nFit D\n)\n2\n) (GeV/c\n-\u03c0\n*+\nM(D\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n )\n2\n Events / ( 0.005 GeV/c\n5\n10\n15\n20\n25\n30\n35\n40\n45\n)\n2\n) (GeV/c\n-\u03c0\n*+\nM(D\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n )\n2\n Events / ( 0.005 GeV/c\n5\n10\n15\n20\n25\n30\n35\n40\n45\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n2\n4\n6\n8\n10\n2.4\n2.5\n2.6\n2.7\n2.8\n0\n2\n4\n6\n8\n10\nFit E\nFigure 19.3.11. From (del Amo Sanchez, 2010i). Mass distri-\nbutions for D\u2217+\u03c0\u2212candidates produced in the process e+e\u2212\u2192\nc\u00afc \u2192D\u2217\u03c0X. Top: candidates with | cos \u03b8H| > 0.75. Middle:\ncandidates with | cos \u03b8H| < 0.5. Bottom: all candidates. Points\ncorrespond to data, with the total \ufb01t overlaid as a solid curve.\nThe lower solid curve is the combinatoric background, and the\ndotted curves are the signal components. The inset plots show\nthe distributions after subtraction of the combinatoric back-\nground.\nDs1(2460)+\nmay\ndecay\nthrough\neither\nD\u2217+\ns \u03c00\nor\nD\u2217\ns0(2317)+\u03b3. To disentangle these modes and reliably\nextract the parameters of the signal, BABAR applies\nan unbinned maximum likelihood \ufb01t simultaneously to\nthe M(D+\ns \u03c00\u03b3), M(D+\ns \u03c00) and M(D+\ns \u03b3) spectra of all\nthe D+\ns \u03c00\u03b3 combinations, using the channel likelihood\nmethod (Condon and Cowell, 1974). This \ufb01t describes\nthe probability density function of the two Ds1(2460)+\ndecay channels as the product of a Gaussian shape in\nthe M(D+\ns \u03c00\u03b3) distribution and a Gaussian shape pro-\njected into the M(D+\ns \u03c00) or M(D+\ns \u03b3) axes, as appropri-\nate. Background sources included in the \ufb01t are: purely\ncombinatorial background, D\u2217+\ns\n\u2192D+\ns \u03b3 decay combined\nwith an unassociated \u03c00, D\u2217\ns0(2317)+ \u2192D+\ns \u03c00 decay\nFigure 19.3.13. The c\u00afs spectrum according to the HQET\nscheme. The P-wave multiplet is shaded. Expectations on the\nmasses according to HQET calculations (lines) are compared\nwith experimental results (dots).\nFigure 19.3.14. From (Aubert, 2003j). a) D+\ns \u03c00 mass spec-\ntrum for D+\ns \u2192K+K\u2212\u03c0+ superimposed with the \ufb01t described\nin the text. b) D+\ns \u03c00 mass distribution for D+\ns \u2192K+K\u2212\u03c0+\u03c00.\nThe structure at 2.32 GeV is due to the D\u2217\ns0(2317)+ resonance.\nThe narrow peak at threshold is due to the D\u2217+\ns\n\u2192D+\ns \u03c00 de-\ncay. The broad structure is due to re\ufb02ections from other states\n(see Section 19.3.4.3).\n\n613\n0\n50\n100\n150\n200\n250\n300\n350\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nM(Ds \u03c00) - M(Ds) (GeV/c2)\nEvents/5MeV\n0\n20\n40\n60\n80\n100\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n M(Ds* \u03c00) - M(Ds*) (GeV/c2)\nEvents/5MeV\n0\n50\n100\n150\n200\n250\n300\n350\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nM(Ds \u03c00) - M(Ds) (GeV/c2)\nEvents/5MeV\n0\n10\n20\n30\n40\n50\n60\n70\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n M(Ds* \u03c00) - M(Ds*) (GeV/c2)\nEvents/5MeV\nFigure\n19.3.15.\nFrom\n(Abe,\n2004a):\nDistributions\nof\n\u2206M(D+\ns \u03c00) (left) and \u2206M(D\u2217+\ns \u03c00) (right). In the upper\nplots data from mass sidebands are also shown: the D+\ns (left)\nand D\u2217+\ns\n(right) sideband regions (solid lines), \u03c00 sidebands\n(dashed). The bottom plots show \ufb01ts to the \u2206M(D+\ns \u03c00) (left)\nand \u2206M(D\u2217+\ns \u03c00) distributions after subtraction of the D\u2217+\ns\nsidebands.\ncombined with a random \u03b3, and a contribution from\nDs1(2460)+ \u2192D\u2217+\ns \u03c00 decay with a random \u03b3 in D\u2217+\ns\ndecay. The Ds1(2460)+ signal for a particular decay mode\nis extracted by calculating for each D+\ns \u03c00\u03b3 combination a\nweight proportional to the relative likelihood contributed\nby the decay mode of interest. Distributions of events so\nweighted, as well as the unweighted M(D+\ns \u03c00\u03b3) spectrum,\nare compared to the likelihood function in Fig. 19.3.16.\nThe decay Ds1(2460)+ \u2192D\u2217\ns0(2317)+\u03b3 is found to be\nnegligible, whereas the decay Ds1(2460)+ \u2192D\u2217+\ns \u03c00 satu-\nrated the D+\ns \u03c00\u03b3 \ufb01nal state. The results of this study were\nlater superseded by (Aubert, 2006e) described below.\n19.3.4.3 High statistics study of D\u2217\ns0(2317)+ and\nDs1(2460)+\nBABAR performed a complete analysis of the D(\u2217)+\ns\n\u03c00 spec-\ntrum using 232 fb\u22121 of data and with some of the selection\ncriteria from the previous analyses reoptimized (Aubert,\n2006e).\nThe invariant mass distribution of the D+\ns \u03c00 combi-\nnations is shown in Fig. 19.3.17. The \u03c00 momentum re-\nquirement to be greater than 350 MeV/c, removes the\nmajority of the D\u2217+\ns\n\u2192D+\ns \u03c00 decays, while keeping the\nentire D\u2217\ns0(2317)+ signal. The unbinned likelihood \ufb01t ap-\nplied to the M(D+\ns \u03c00) distribution includes the D\u2217+\ns\nand\nD\u2217\ns0(2317)+ signals and the following peaking components:\na re\ufb02ection at 2.17 GeV/c2 from D\u2217+\ns\n\u2192D+\ns \u03b3 in which an\nFigure 19.3.16. From (Aubert, 2004t). Maximum likelihood\n\ufb01t results overlaid on the D+\ns \u03c00\u03b3 mass distribution with a)\nno weights and after applying weights corresponding to b) the\nD\u2217+\ns \u03c00 and c) the D\u2217\ns0(2317)+\u03b3 decays.\nunassociated \u03b3 forms a false \u03c00 candidate, as well as a re-\n\ufb02ection appearing directly under the D\u2217\ns0(2317)+ signal.\nThe latter originates from Ds1(2460)+ \u2192D\u2217+\ns \u03c00 with a\nmissing photon from D\u2217+\ns\ndecay. Parameters used to de-\nscribe the former feed-down are determined directly from\nthe data, while the shape of the latter one is based on\nthe MC simulation of the Ds1(2460)+ \u2192D+\ns \u03c00\u03b3 Dalitz\ndistribution. The D\u2217\ns0(2317)+ line shape used in the \ufb01t\nis derived from MC simulation con\ufb01gured with an intrin-\nsic width (0.1 MeV/c2) nearly indistinguishable from zero.\nLarger intrinsic widths assumed in the MC do not result\nin any signi\ufb01cant improvement of the \ufb01t.\nA study of the D+\ns \u03c00\u03b3 mass (see Fig. 19.3.18) is\nperformed with the D+\ns \u03b3 mass required to be close to\nthe D\u2217+\ns\nmass. Similarly to the Belle analysis, there\nwere two re\ufb02ections peaking near the Ds1(2460)+: from\nD\u2217\ns0(2317)+ \u2192D+\ns \u03c00 decays combined with a random \u03b3,\nand from Ds1(2460)+ \u2192D+\ns \u03c00\u03b3 with a wrong \u03b3 chosen.\nIn the \ufb01t to the M(D+\ns \u03c00\u03b3), these components are com-\nbined and described using MC simulations with the rates\nas measured in the previous analysis. A broad re\ufb02ection at\n2.34 MeV/c2, coming from D\u2217+\ns\n\u2192D+\ns \u03b3 decays combined\nwith an unassociated \u03b3, is also considered in the \ufb01t. The\n\n614\nFigure 19.3.17. From (Aubert, 2006e). The invariant mass\ndistribution for D+\ns \u03c00 candidates (solid points) and the equiv-\nalent using the D+\ns sidebands (open points). The curve rep-\nresents the likelihood \ufb01t described in the text and includes a\ncontribution from combinatorial background (light shade) and\nthe re\ufb02ection from Ds1(2460)+ \u2192D\u2217+\ns \u03c00 decay (dark shade).\nThe insert highlights the details near the D\u2217\ns0(2317)+ mass.\nThe narrow peak at threshold is due to the D\u2217+\ns\n\u2192D+\ns \u03c00\ndecay.\nDs1(2460)+ signal shape is obtained using MC, similarly\nto the D\u2217\ns0(2317)+ case.\nThe resulting D\u2217\ns0(2317)+ and Ds1(2460)+ masses and\nupper limits on their widths are given in Table 19.3.7. The\nDs1(2460)+ mass is the average obtained from the D+\ns \u03c00\u03b3,\nD+\ns \u03b3 and D+\ns \u03c0+\u03c0\u2212\ufb01nal states (see Section 19.3.4.4). The\nlimit on the intrinsic Ds1(2460)+ width is taken as the\nbest limit obtained from these three decay modes.\n19.3.4.4 Other decay modes\nThe Ds1(2460)+ decays to the D+\ns \u03b3 and the D+\ns \u03c0+\u03c0\u2212\ufb01nal\nstates were \ufb01rst observed by Belle (Abe, 2004a) and fur-\nther con\ufb01rmed by BABAR (Aubert, 2006e). Selected pho-\ntons are required to pass the \u03c00 veto, while the \u03c0+\u03c0\u2212pairs\nare taken outside of the K0\nS mass window. The left plot in\nFig. 19.3.19 shows the \u2206M(D+\ns \u03b3) = M(D+\ns \u03b3) \u2212M(D+\ns )\ndistribution measured by Belle. A peak at 490 MeV/c2 cor-\nresponds to the Ds1(2460)+, whereas no peak is present in\nthe D\u2217\ns0(2317)+ region at 350 MeV/c2. The observation of\nthe radiative decay of the Ds1(2460)+ rules out its spin-\nparity of 0\u00b1.\nThe invariant mass distribution of the D+\ns \u03c0+\u03c0\u2212candi-\ndates from BABAR presented in right plot in Fig. 19.3.19,\nshows clear signals from Ds1(2460)+ and Ds1(2536)+ and\nFigure 19.3.18. From (Aubert, 2006e). The M(D+\ns \u03c00\u03b3) in-\nvariant mass distribution of candidates in the (a) upper, (b)\nsignal, and (c) lower D+\ns \u03b3 mass selection windows for (solid\npoints) the D+\ns signal and (open points) D+\ns sideband samples.\nThe curves represent the \ufb01ts described in the text. The gray re-\ngions correspond to the predicted re\ufb02ections from D\u2217\ns0(2317)+\n(dark) and D\u2217\ns(2112)+ (light).\nTable 19.3.7. From (Aubert, 2006e) and (Abe, 2004a). The\n\ufb01rst section summarizes the combined mass and width results\nfrom BABAR. The D\u2217\ns0(2317)+ and Ds1(2536)+ mesons are ob-\nserved in only one decay mode covered by this analysis. The\nDs1(2460)+ mass is the average of that obtained from the D+\ns \u03b3,\nD+\ns \u03c00\u03b3, and D+\ns \u03c0+\u03c0\u2212\ufb01nal states, although the latter mea-\nsurement dominates in the average due to superior systematic\nuncertainties. The second section gives Belle results based on\nthe D(\u2217)+\ns\n\u03c00 modes.\nParticle\nMass (MeV/c2)\n\u0393 (MeV/c2)\nD\u2217\ns0(2317)+\n2319.6 \u00b1 0.2 \u00b1 1.4\n< 3.8 @ 95 % C.L.\nDs1(2460)+\n2460.1 \u00b1 0.2 \u00b1 0.8\n< 3.5 @ 95 % C.L.\nDs1(2536)+\n2534.6 \u00b1 0.3 \u00b1 0.7\n< 2.5 @ 95 % C.L.\nD\u2217\ns0(2317)+\n2317.2 \u00b1 0.5 \u00b1 0.9\n< 4.6 @ 90 % C.L.\nDs1(2460)+\n2456.5 \u00b1 1.3 \u00b1 1.3\n< 5.5 @ 90 % C.L.\nnegligible contribution from D\u2217\ns0(2317)+. Searches for the\ndecays of D\u2217\ns0(2317)+ and Ds1(2460)+ to D+\ns \u03c00\u03c00 and\nD\u2217+\ns \u03b3 give no positive results. The branching fraction ra-\ntios for the studied channels, given in Table 19.3.8, are\nmeasured based on the \ufb01tted yields and detection e\ufb03cien-\ncies estimated with an assumption of the same fragmen-\ntation functions for the DsJ states.\nThe dominant decays observed, D\u2217\ns0(2317)+ \u2192D+\ns \u03c00\nand Ds1(2460)+ \u2192D\u2217+\ns \u03c00, violate isospin conservation;\nthat is often considered as a property of four-quark states,\nwhich have long been proposed (Ja\ufb00e, 1977b; Lipkin, 1977).\nThe most unambiguous signature of a molecular interpre-\ntation of the D\u2217\ns0(2317)+ and the Ds1(2460)+ would be an\n\n615\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8\nM(Ds \u03b3) - M(Ds) (GeV/c2)\nEvents/5MeV\nFigure 19.3.19. Left: The \u2206M(D+\ns \u03b3) distribution from (Abe,\n2004a). Right: The M(D+\ns \u03c0+\u03c0\u2212) spectrum from (Aubert,\n2006e). The insert focuses on the D\u2217\ns0(2317)+ region. The spec-\ntra for the D+\ns sideband candidates are plotted with solid his-\ntogram in the left plot and open points in the right one.\nTable 19.3.8.\nA summary of D\u2217\u2217\ns\nbranching fraction ra-\ntios from Belle (\ufb01rst line) and BABAR (second line). For\nthe D\u2217\ns0(2317)+ meson, only one decay mode has been ob-\nserved; this is used as the denominator when calculating the\nD\u2217\ns0(2317)+ branching ratios. For the Ds1(2460)+ meson, the\nD+\ns \u03c00\u03b3 decay mode (consisting of possible decay through ei-\nther D\u2217\ns(2112)+\u03c00 or D\u2217\ns0(2317)+\u03b3) is chosen for this role.\nRatio\nFraction or Limit\nB(Ds1(2460)+\u2192D+\ns \u03c00)\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03c00)\n< 0.21 @ 90 % C.L.\n< 0.042 @ 95 % C.L.\nB(Ds1(2460)+\u2192D+\ns \u03b3)\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03c00)\n= 0.55 \u00b1 0.13 \u00b1 0.08\n= 0.34 \u00b1 0.04 \u00b1 0.04\nB(Ds1(2460)+\u2192D+\ns \u03c0+\u03c0\u2212)\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03c00)\n= 0.14 \u00b1 0.04 \u00b1 0.02\n= 0.077 \u00b1 0.013 \u00b1 0.008\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03b3)\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03c00)\n< 0.31 @ 90 % C.L.\n< 0.24 @ 95 % C.L.\nB(D\u2217\ns0(2317)+\u2192D+\ns \u03b3)\nB(D\u2217\ns0(2317)+\u2192D+\ns \u03c00)\n< 0.05 @ 90 % C.L.\n< 0.14 @ 95 % C.L.\nB(D\u2217\ns0(2317)+\u2192D+\ns \u03c0+\u03c0\u2212)\nB(D\u2217\ns0(2317)+\u2192D+\ns \u03c00)\n< 0.004 @ 90 % C.L.\n< 0.005 @ 95 % C.L.\nB(D\u2217\ns0(2317)+\u2192D\u2217+\ns\n\u03b3)\nB(D\u2217\ns0(2317)+\u2192D+\ns \u03c00)\n< 0.18 @ 90 % C.L.\n< 0.16 @ 95 % C.L.\nobservation of their neutral and doubly-charged partners\ndecaying to D(\u2217)+\ns\n\u03c0\u00b1. However a search for the D\u2217\ns0(2317)\npartners decaying to D+\ns \u03c0+ and D+\ns \u03c0\u2212resulted in no ev-\nidence (Aubert, 2006e).\nThe observed decay pattern is consistent with the JP\nassignments for the D\u2217\ns0(2317)+ and Ds1(2460)+ of respec-\ntively 0+ and 1+, as expected by the potential models for\nthe P-wave c\u00afs mesons with jq = 1\n2.\n19.3.4.5 DsJ production in B decays\nTo clarify the nature of the D\u2217\ns0(2317)+ and Ds1(2460)+\nstates, Belle and BABAR searched for their production in\nB \u2192DDsJ decays. These reactions proceed via \u00afb \u2192\n\u00afcW + \u2192\u00afcc\u00afs transition and are expected to be the domi-\nnant exclusive c\u00afs production mechanism. QCD sum rules\npredict that P-wave charmed mesons with jq = 1\n2 should\nbe more readily produced in B decays than ones having\njq = 3\n2 (Le Yaouanc, Oliver, P`ene, Raynal, and Morenas,\n2001). Thus observation of the B \u2192DD\u2217\ns0(2317)+ and\nB \u2192DDs1(2460)+ would provide a con\ufb01rmation of the\nP-wave nature of these DsJ states. Moreover, measure-\nments of B decays to the \ufb01nal states including the jq = 3\n2\nDsJ mesons, or higher orbital or radial c\u00afs excitations could\nbe a further test of the theoretical predictions on the c\u00afs\nspectroscopy.\nIn a Belle study of the B \u2192DDsJ decays, with\n124 \u00d7 106 BB pairs used, the D is reconstructed as:\nD0 \u2192K+\u03c0\u2212, K+\u03c0\u2212\u03c0\u2212\u03c0+, K+\u03c0\u2212\u03c00, D\u2212\u2192K+\u03c0\u2212\u03c0\u2212.\nThe DsJ states are studied in the D(\u2217)+\ns\n\u03c00, D(\u2217)+\ns\n\u03b3 and\nD(\u2217)+\ns\n\u03c0+\u03c0\u2212\ufb01nal states, with D\u2217+\ns\n\u2192D+\ns \u03b3 and D+\ns \u2192\n\u03c6\u03c0+, K(\u2217)0K+ reconstructed (Krokovny, 2003b). To re-\nduce background the B candidates are required to have\ntheir mES consistent with the nominal B mass (see Sec-\ntions 9 and 7), while the signal events are identi\ufb01ed in\nthe \u2206E-M(DsJ) space. The left plots in Fig. 19.3.20\nshow invariant mass distributions of the DsJ candidates\nwithin the \u2206E signal region, for all the D modes com-\nbined. The presented spectra are for the DsJ decay \ufb01-\nnal states with signi\ufb01cant signals found: D\u2217\ns0(2317)+ \u2192\nD+\ns \u03c00, Ds1(2460)+ \u2192D\u2217+\ns \u03c00 and Ds1(2460)+ \u2192D+\ns \u03b3.\nUnlike the continuum based DsJ studies, cross-feeds be-\ntween the DsJ decay modes were not found, and thus\nthe M(DsJ) spectra are \ufb01tted with signal and back-\nground described respectively with a Gaussian and linear\nfunction. The measured masses of the D\u2217\ns0(2317)+ and\nDs1(2460)+ are respectively 2319.8\u00b12.1\u00b12.0 MeV/c2 and\n2459.2 \u00b1 1.6 \u00b1 2.0 MeV/c2, while the \ufb01tted widths are con-\nsistent with the experimental resolution.\nThe \u2206E distributions shown in Fig. 19.3.20, are pro-\njections for the B candidates having the M(DsJ) within\nthe observed DsJ signals. Branching fractions given in Ta-\nble 19.3.9, are extracted from the \u2206E \ufb01ts of the com-\nbined B \u2192D0D+\nsJ and B \u2192D\u2212D+\nsJ modes, with\ne\ufb03ciencies of the individual modes taken into account\nand isospin invariance assumed. The determined ratio,\nB(Ds1(2460)+\u2192D+\ns \u03b3)\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03c00) = 0.38 \u00b1 0.11 \u00b1 0.04, is consistent\nwith the one obtained from Ds1(2460)+ produced in the\ncontinuum (see Table 19.3.8).\nA helicity angle (\u03b8Ds\u03b3) study is performed for the\nDs1(2460)+ \u2192D+\ns \u03b3 decay, where \u03b8Ds\u03b3 is de\ufb01ned as the\nangle between the D+\ns momentum and the opposite to the\nB meson momentum in the Ds1(2460)+ rest frame. Fig-\nure 19.3.21 shows the background-subtracted cos(\u03b8Ds\u03b3)\ndistribution, where the data points represent signal yields\nfrom the \u2206E \ufb01ts performed in respective cos(\u03b8Ds\u03b3) bins.\n\n616\n0\n10\n20\n(a)\n0\n10\n20\n(b)\n0\n20\n2.2\n2.3\n2.4\n2.5\n2.6\n(c)\nM(DsJ) (GeV/c2)\nEvents/(0.01 GeV)\n0\n10\n20\n(a)\n0\n10\n(b)\n0\n10\n20\n-0.2\n-0.1\n0\n0.1\n0.2\n(c)\n\u2206E (GeV)\nEvents/(0.01 GeV)\nFigure 19.3.20. From (Krokovny, 2003b): The M(DsJ) dis-\ntribution for the \u2206E signal region (left) and the \u2206E distribu-\ntion for the M(DsJ) signal region (right) for the B \u2192DDsJ\ncandidates with (a) D\u2217\ns0(2317)+ \u2192D+\ns \u03c00, (b) Ds1(2460)+ \u2192\nD\u2217+\ns \u03c00 and (c) Ds1(2460)+ \u2192D+\ns \u03b3 decays observed. Hatched\nhistograms in a given variable distribution show the sidebands\nof the other variable, lines represent the \ufb01t result.\nTable 19.3.9. From (Krokovny, 2003b). Measured branching\nfraction products B(B \u2192DDsJ) \u00d7 B(DsJ \u2192f) or 90 % C.L.\nlimits. f is the label of a given \ufb01nal state.\nDecay mode\nProduct B [10\u22124]\nB\u2192DD\u2217\ns0(2317)+, D\u2217\ns0(2317)+\u2192D+\ns \u03c00\n8.5+2.1\n\u22121.9 \u00b1 2.6\nB\u2192DD\u2217\ns0(2317)+, D\u2217\ns0(2317)+\u2192D\u2217+\ns \u03b3\n2.5+2.0\n\u22121.8(< 7.5)\nB\u2192DDs1(2460)+, Ds1(2460)+\u2192D\u2217+\ns \u03c00\n17.8+4.5\n\u22123.9 \u00b1 5.3\nB\u2192DDs1(2460)+, Ds1(2460)+\u2192D+\ns \u03b3\n6.7+1.3\n\u22121.2 \u00b1 2.0\nB\u2192DDs1(2460)+, Ds1(2460)+\u2192D\u2217+\ns \u03b3\n2.7+1.8\n\u22121.5(< 7.3)\nB\u2192DDs1(2460)+, Ds1(2460)+\u2192D+\ns \u03c0+\u03c0\u2212\n< 1.6\nB\u2192DDs1(2460)+, Ds1(2460)+\u2192D+\ns \u03c00\n< 1.8\nAs it can be seen from the \ufb01gure, the J = 1 hypothesis\n\ufb01ts much better the data than the J = 2 hypothesis.\nIn the BABAR approach to the B \u2192D(\u2217)D+\nsJ study\n(Aubert, 2006aw), the D(\u2217) = D(\u2217)0, D(\u2217)\u2212mesons are\nfully reconstructed (Dmeas), while the invariant mass of\nthe DsJ is inferred from the kinematics of the two-body\nB decay, as well as the kinematics of the accompanying B.\nThe analysis used the \u03a5(4S) \u2192BB events in which the B\nmeson (Brec) decays into fully reconstructed hadronic \ufb01nal\nstate Brec \u2192D(\u2217)Y \u2212, with the system Y \u2212composed of\ncombinations of kaons and pions (see Section 7). The DsJ\ninvariant mass is derived from a missing four-momentum\n(pmiss) as:\nmX \u2261\nq\np2\nmiss =\nq\n(p\u03a5 (4S) \u2212pBrec \u2212pDmeas)2,\n(19.3.18)\nwith all the momenta measured in the laboratory system.\nSuch a method allows measurements of absolute B \u2192\nD(\u2217)D+\nsJ branching fractions, without any assumptions on\nthe D+\nsJ decays, at the cost of full reconstruction e\ufb03-\n0\n2\n4\n6\n8\n10\n12\n-1\n-0.5\n0\n0.5\n1\ncos(\u03b8Ds\u03b3)\nEvents/ (0.25)\nFigure\n19.3.21.\nFrom (Krokovny, 2003b): Background-\nsubtracted helicity distribution for the Ds1(2460)+ \u2192D+\ns \u03b3.\nLines show MC expectations for spin hypotheses J = 1 (solid)\nand J = 2 (dashed); J = 0 is forbidden.\n]\n2\n[GeV/c\nX\nm\n1.8\n2\n2.2\n2.4\n2.6\n2\nevents/33MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n-\n(2460)\nsJ\nD\n0\nD\n-*s\nD\n0\nD\n-s\nD\n0\nD\nX\n0\nother D\ncomb.bkg\ndata\n1.8\n2\n2.2\n2.4\n2.6\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nX\nD\n0\nD\n\u2192\n-\nB\n]\n2\n[GeV/c\nX\nm\n1.8\n2\n2.2\n2.4\n2.6\n2\nevents/33MeV/c\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n-\n(2460)\nsJ\nD\n+\nD\n-*s\nD\n+\nD\n-s\nD\n+\nD\nX\n+\nother D\ncomb.bkg\ndata\n1.8\n2\n2.2\n2.4\n2.6\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nX\nD\n+\nD\n\u2192\n0\nB\n]\n2\n[GeV/c\nX\nm\n1.8\n2\n2.2\n2.4\n2.6\n2\nevents/33MeV/c\n0\n50\n100\n150\n200\n250\n300\n-\n(2460)\nsJ\nD\n0\nD*\n-*s\nD\n0\nD*\n-s\nD\n0\nD*\nX\n0\nother D*\ncomb.bkg\ndata\n1.8\n2\n2.2\n2.4\n2.6\n0\n50\n100\n150\n200\n250\n300\nX\nD\n0\nD*\n\u2192\n-\nB\n]\n2\n[GeV/c\nX\nm\n1.8\n2\n2.2\n2.4\n2.6\n2\nevents/33MeV/c\n0\n20\n40\n60\n80\n100\n120\n-\n(2460)\nsJ\nD\n+\nD*\n-*\ns\nD\n+\nD*\n-s\nD\n+\nD*\nX\n+\nother D*\ncomb.bkg\ndata\n1.8\n2\n2.2\n2.4\n2.6\n0\n20\n40\n60\n80\n100\n120\nX\nD\n+\nD*\n\u2192\n0\nB\nFigure 19.3.22. From (Aubert, 2006aw). Distributions of the\nDsJ invariant mass mX(de\ufb01ned in the text). Fitted B \u2192\nD(\u2217)+,0D(\u2217)\u2212\ns\nand B \u2192D(\u2217)+,0Ds1(2460)\u2212signal contribu-\ntions and background components are overlaid to the data\npoints.\nciency of about 0.3 % for B0B0 and 0.2 % for B+B\u2212,\nand the mX resolution being typically a few times worse\nthan in a direct reconstruction. In the mX spectra, shown\nin Fig. 19.3.22, in addition to the D(\u2217)+\ns\n, BABAR observes\nthe Ds1(2460)+ signal.\nThe measured B \u2192D(\u2217)Ds1(2460)+ branching frac-\ntions, calculated using PDG values of the D(\u2217) decay rates,\n\n617\nTable 19.3.10. From (Aubert, 2006aw). Absolute branching\nfractions of the B \u2192D(\u2217)Ds1(2460)+ decays.\nDecay mode\nB [%]\nB0 \u2192D\u2212Ds1(2460)+\n0.26 \u00b1 0.15 \u00b1 0.07\nB0 \u2192D\u2217\u2212Ds1(2460)+\n0.88 \u00b1 0.20 \u00b1 0.14\nB+ \u2192D0Ds1(2460)+\n0.43 \u00b1 0.16 \u00b1 0.13\nB+ \u2192D\u22170Ds1(2460)+\n1.12 \u00b1 0.26 \u00b1 0.20\nare summarized in Table 19.3.10. BABAR further combined\nthese results with their measurements of the product B of\nthe B \u2192D(\u2217)Ds1(2460)+ decays (Aubert, 2004ad), mea-\nsured similarly to the described Belle analysis. This al-\nlowed a \ufb01rst measurement of the Ds1(2460)+ decay rates:\nB(Ds1(2460)+ \u2192D\u2217+\ns \u03c00) = (56 \u00b1 13 \u00b1 9)%,\nB(Ds1(2460)+ \u2192D+\ns \u03b3) = (16 \u00b1 4 \u00b1 3)%.\n(19.3.19)\nBelle studied the production of the Ds1(2536)+ me-\nson in B \u2192D(\u2217)Ds1(2536)+ decays, with D(\u2217) being ei-\nther D0 or D(\u2217)\u2212, using a data sample of 657 \u00d7 106 BB\npairs (Aushev, 2011). The Ds1(2536)+ is reconstructed\nin its dominant decay modes, D\u2217+K0\nS and D\u22170K+. Fig-\nure 19.3.23 shows the M(Ds1(2536)) spectra for the B\ncandidates satisfying the \u2206E-mES selection, for each D(\u2217)\n\ufb02avor and the Ds1(2536)+ decay mode separately. All\nthese distributions are \ufb01tted simultaneously, with the sig-\nnal Ds1(2536)+ described as a BW function convolved\nwith a double Gaussian function describing the mass res-\nolution. The measured Ds1(2536)+ mass and width were\nrespectively 2534.1 \u00b1 0.6 MeV/c2 and 0.75 \u00b1 0.23 MeV/c2,\nconsistent with their PDG values (Beringer et al., 2012).\nA \ufb01t with the Ds1(2536)+ partial width ratio kept as a\nfree parameter, yields:\nB(Ds1(2536)+ \u2192D\u22170K+)\nB(Ds1(2536)+ \u2192D\u2217+K0) = 0.88 \u00b1 0.24 \u00b1 0.08,\n(19.3.20)\nin agreement with the BABAR study (Aubert, 2008bd).\nTable 19.3.11 summarizes ratios of branching fractions,\ncalculated using the latest measurements of the B \u2192\nD(\u2217)D(\u2217)+\ns(J) branching fractions, as well as the Ds1(2536)+\nmeasurements by Belle (Aushev, 2011) and BABAR (Au-\nbert, 2008bd). In these calculations, 100% branching frac-\ntions are assumed for the D\u2217\ns0(2317)+ \u2192D+\ns \u03c00 and\nDs1(2536)+ \u2192D\u2217K decay modes. Within the factor-\nization model and in the heavy quark limit, these ra-\ntios should be of order unity for the D\u2217\ns0(2317)+ and\nDs1(2460)+, whereas for the Ds1(2536)+ they are pre-\ndicted to be very small (Datta and O\u2019Donnell, 2003b;\nLe Yaouanc, Oliver, P`ene, and Raynal, 1996). The de-\ncay pattern for the Ds1(2536)+ follows these expectations,\nwhereas for the D\u2217\ns0(2317)+ and Ds1(2460)+ the ratios are\nrather di\ufb00erent from unity and therefore such an approach\nTable 19.3.11. Ratios of B decay branching ratios measured\nby Belle (Aushev, 2011) and BABAR (Aubert, 2008bd).\nRatio\nFraction\nB(B \u2192DDs1(2536)+)/B(B \u2192DD\u2217\ns)\n0.05 \u00b1 0.01\nB(B \u2192D\u2217Ds1(2536)+)/B(B \u2192D\u2217D\u2217\ns)\n0.04 \u00b1 0.01\nB(B \u2192DDs1(2460)+)/B(B \u2192DD\u2217\ns)\n0.44 \u00b1 0.11\nB(B \u2192D\u2217Ds1(2460)+)/B(B \u2192D\u2217D\u2217\ns)\n0.58 \u00b1 0.12\nB(B \u2192DD\u2217\ns0(2317)+)/B(B \u2192DDs)\n0.10 \u00b1 0.03\nB(B \u2192D\u2217D\u2217\ns0(2317)+)/B(B \u2192D\u2217Ds)\n0.15 \u00b1 0.06\n0\n10\n0\n10\n0\n10\n0\n10\n0\n10\n0\n10\n0\n10\n2.5\n2.54\n0\n10\n2.5\n2.54\n(a)\nEvents/1 MeV/c2\n(b)\n(c)\n(d)\n(e)\n(f)\n(g)\n(h)\n(i)\nM(Ds1(2536)), GeV/c2\n0\n10\n2.5\n2.54\n2.58\nFigure\n19.3.23.\nFrom (Aushev, 2011): The Ds1(2536)+\nmass distributions for: B+ \u2192D0Ds1(2536)+ (a,b,c), B0 \u2192\nD\u2212Ds1(2536)+ (d,e,f), B0 \u2192D\u2217\u2212Ds1(2536)+ (g,h,i) decays\nfollowed by the Ds1(2536)+ decays to: D\u22170K+ with D\u22170 \u2192\nD0\u03b3 (a,d,g); D\u22170K+ with D\u22170 \u2192D0\u03c00 (b,e,h) and D\u2217+K0\nS\nwith D\u2217+ \u2192D0\u03c0+ (c,f,i). The curves show results of the si-\nmultaneous \ufb01t.\nTable 19.3.12. From (Aushev, 2011). Fitted product B:\nB(B\n\u2192\nD(\u2217)Ds1(2536)+) \u00d7 B(Ds1(2536)+\n\u2192\nD\u2217+K0\nS +\nD\u22170K+).\nDecay mode\nProduct B [10\u22124]\nB+ \u2192D0Ds1(2536)+\n3.97 \u00b1 0.85 \u00b1 0.56\nB0 \u2192D\u2212Ds1(2536)+\n2.75 \u00b1 0.62 \u00b1 0.36\nB0 \u2192D\u2217\u2212Ds1(2536)+\n5.01 \u00b1 1.21 \u00b1 0.70\ndoes not really work. One possibility is that these states\nare not canonical c\u00afs. However, the agreement with theory\nwould be improved for the D\u2217\ns0(2317)+, if other prominent\ndecay modes existed in addition to the D+\ns \u03c00.\n19.3.4.6 Precision measurements of Ds1(2536)+ properties\nBABAR measured the mass of the Ds1(2536)+ with a sig-\nni\ufb01cant improvement compared to the world average, and,\nfor the \ufb01rst time, measured directly its decay width, in-\nstead of reporting an upper limit only (Lees, 2011d).\n\n618\n]\n2\n) [GeV/c\n+\ns1\nm(D\n\u2206\n0.02\n0.03\n0.04\n2\nEntries / 0.3 MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n]\n2\n) [GeV/c\n+\ns1\nm(D\n\u2206\n0.02\n0.03\n0.04\n2\nEntries / 0.3 MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nPull\n-3\n 0\n+3\nPull\n]\n2\n) [GeV/c\n+\ns1\nm(D\n\u2206\n0.02\n0.03\n0.04\n2\nEntries / 0.3 MeV/c\n0\n100\n200\n300\n400\n500\n]\n2\n) [GeV/c\n+\ns1\nm(D\n\u2206\n0.02\n0.03\n0.04\n2\nEntries / 0.3 MeV/c\n0\n100\n200\n300\n400\n500\nPull\n-3\n 0\n+3\nPull\nFigure 19.3.24. From (Lees, 2011d). \u2206m(Ds1(2536)+) dis-\ntribution for (left) the D0 \u2192K\u2212\u03c0+ and (right) the D0 \u2192\nK\u2212\u03c0+\u03c0+\u03c0\u2212decay modes. The solid line is the \ufb01t function as\ndescribed in the text, the dotted line indicates the background\ncontribution. The normalized \ufb01t residuals are shown on top.\nTable 19.3.13. From (Lees, 2011d). Combined results for\nmass and width of the Ds1(2536)+.\nParameter\nValue [ MeV/c2]\nM(Ds1(2536)+)\n2535.08 \u00b1 0.01 \u00b1 0.15\nM(Ds1(2536)+) \u2212M(D\u2217+)\n524.83 \u00b1 0.01 \u00b1 0.04\n\u0393(Ds1(2536)+)\n0.92 \u00b1 0.03 \u00b1 0.04\nThe Ds1(2536)+ is reconstructed in D\u2217+K0\nS, with\nD\u2217+\n\u2192\nD0\u03c0+\nand\nD0\n\u2192\nK\u2212\u03c0+,\nK\u2212\u03c0+\u03c0+\u03c0\u2212.\nTo\nimprove\nthe\nresolution,\nthe\nmass\ndi\ufb00erence\n\u2206m(Ds1(2536)+) = M(Ds1(2536)+)\u2212M(D\u2217+)\u2212M(K0\nS)\nis examined. Combinatorial background and events from\nB decays are suppressed by requiring a CM momentum\np\u2217> 2.7 GeV/c.\nThe samples for the two D0 decays are examined sepa-\nrately, the \u2206m(Ds1(2536)+) spectrum for the K\u2212\u03c0+ and\nD0 \u2192K\u2212\u03c0+\u03c0+\u03c0\u2212modes are shown in Fig. 19.3.24. The\nsignal is described with a convolution of a relativistic BW\nlineshape and a p\u2217dependent, multi-Gaussian detector\nresolution parameterization. The dominant systematic un-\ncertainties are related to track reconstruction, the signal\nlineshape modeling and detector resolution parameteriza-\ntion. Results from the \ufb01ts to the two \u2206m(Ds1(2536)+)\nspectra are combined, and the \ufb01nal numbers are given in\nTable 19.3.13.\nThe large and clean sample of Ds1(2536)+ signal can-\ndidates reconstructed by BABAR, enables a study of the\nspin-parity and decay properties of the Ds1(2536)+. In\nthis analysis the D\u2217+K0\nS system is produced inclusively,\nand therefore the origin of the Ds1(2536)+ is not known.\nThus, for the JP study, the decay angle of the D\u2217+ (\u03b8\u2032)\nis examined. The \u03b8\u2032 is measured between the D0 mo-\nmentum in the D\u2217+ CM system and the D\u2217+ momen-\ntum in the Ds1(2536)+ system; the resulting angular dis-\ntribution is in\ufb02uenced by the spin of the Ds1(2536)+.\nThe cos \u03b8\u2032 distribution for both subsamples combined, is\nshown in Fig. 19.3.25 (left). Fits with several models used,\n\u2019\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\n\u2019\n\u03b8\n)/dcos\n+\ns1\ndN(D\n0\n100\n200\n300\n400\n500\n600\n\u03b8\ncos\n-1\n-0.5\n0\n0.5\n1\n\u03b8\n)/dcos\n+\ns1\ndN(D\n0\n100\n200\n300\n400\n500\nFigure\n19.3.25.\nFrom\n(Lees,\n2011d).\nLeft:\nE\ufb03ciency-\ncorrected Ds1(2536)+ signal yield as function of D\u2217+ decay\nangle \u03b8\u2032. Lines correspond to the following hypotheses \ufb01tted\nto the data: JP = 1+, 2\u2212, 3+, . . . with S- and D-wave (solid);\n1+, 2\u2212, 3+, . . . with S-wave only (dash-dotted); 0\u2212(dashed);\n1\u2212, 2+, 3\u2212, . . . (dotted). 0+ is forbidden. Right: E\ufb03ciency-\ncorrected Ds1(2536)+ signal yield as function of Ds1(2536)+\ndecay angle \u03b8. Assuming JP = 1+, the data are \ufb01tted with\nhypotheses of pure S-wave (dotted line); S- and D-wave (solid\nline) Ds1(2536)+ decays.\nshow a clear preference for unnatural spin-parity values\n(JP = 1+, 2\u2212, 3+, . . .), described by a distribution propor-\ntional to cos2 \u03b8\u2032+\u03b2 sin2 \u03b8\u2032. The parameter \u03b2 is the squared\nratio of the D\u2217+ amplitudes with helicities 0 and \u00b11, and\nits measured value of 0.23\u00b10.02 clearly indicates a D-wave\ncontribution to the decay Ds1(2536)+ \u2192D\u2217+K0\nS (\u03b2 = 1\nis the case of a pure S-wave decay.).\nThe Ds1(2536)+ decay angle (\u03b8), de\ufb01ned as the angle\nbetween the D\u2217+ momentum in the Ds1(2536)+ CM sys-\ntem and the Ds1(2536)+ momentum in the e+e\u2212system,\nis shown in Fig. 19.3.25. It supports the hypothesis with\nboth S- and D-wave contributing to the Ds1(2536)+ de-\ncay amplitude. Assuming JP = 1+ for the Ds1(2536)+,\nthe data are expected to have a distribution proportional\nto 1 + t cos2 \u03b8. The \ufb01tted coe\ufb03cient t in combination with\nthe measured \u03b2, yields \u03c100 = 0.48 \u00b1 0.03, consistent with\nthe Belle result (see below), with \u03c100 giving the probabil-\nity that the Ds1(2536)+ helicity is zero.\nBelle studied the Ds1(2536)+ state, inclusively pro-\nduced in the e+e\u2212\u2192c\u00afc continuum, using 462 fb\u22121 of\ndata (Balagura, 2008). A new decay mode, Ds1(2536)+ \u2192\nD+\u03c0\u2212K+ is observed, with the D+\u03c0\u2212and K+\u03c0\u2212two-\nbody systems consistent with phase-space distributions.\nIts branching fractions is measured with respect to the\nnormalization mode Ds1(2536)+ \u2192D\u2217+K0\nS as:\nB(Ds1(2536)+ \u2192D+\u03c0\u2212K+)\nB(Ds1(2536)+ \u2192D\u2217+K0)\n= (3.27 \u00b1 0.18 \u00b1 0.37)%.\n(19.3.21)\nThis ratio is obtained from the Ds1(2536)+ signal yields\nmeasured from the M(D+\u03c0\u2212K+) and M(D\u2217+K0\nS) mass\nspectra, shown in Figure 19.3.26, with the secondary parti-\ncles reconstructed as: D+ \u2192K\u2212\u03c0+\u03c0+ and K0\nS\u03c0+, D\u2217+ \u2192\nD0\u03c0+, D0 \u2192K\u2212\u03c0+, K\u2212\u03c0+\u03c0+\u03c0\u2212and K0\ns\u03c0+\u03c0\u2212. Instead\nof the common p\u2217cut, the analysts applies a requirement\non the scaled momentum (xp) of the Ds1(2536) candidates\n\n619\n0\n50\n100\n150\n2500\n2510\n2520\n2530\n2540\n2550\n2560\nM(D+\u03c0-K+)\nwrong sign\nD+\u03c0+K-\nMeV/c2\nN/0.3 MeV/c2\nM(D0\u03c0+K0\nS) - M(D0\u03c0+) + M(D*+\n PDG ) MeV/c2\nN/0.3 MeV/c2\n0\n200\n400\n2500\n2510\n2520\n2530\n2540\n2550\n2560\nFigure 19.3.26. From (Balagura, 2008): Mass spectra of\nthe D+\u03c0\u2212K+ (top) and D\u2217+K0\nS (bottom) \ufb01nal states. The\nhatched histogram shows a spectrum of the wrong-sign\nD+\u03c0+K\u2212combinations.\nto be larger than 0.8. The scaled momentum is de\ufb01ned as\nxp \u2261p\u2217/p\u2217\nmax, where p\u2217is the Ds1(2536) momentum in\nthe e+e\u2212CM frame, while p\u2217\nmax indicates the maximum\nkinematically allowed momentum in this frame.\nThe mass distributions in Fig. 19.3.26 are \ufb01tted inde-\npendently with a double Gaussian describing the Ds1(2536)\nsignal. The Ds1(2536) mass, measured with respect to its\nPDG value of 2535.35 \u00b1 0.34 \u00b1 0.50 MeV/c2, is \u22120.57 \u00b1\n0.04 MeV/c2 for the Ds1(2536) \u2192D+\u03c0\u2212K+ and \u22120.43 \u00b1\n0.02 MeV/c2 for the Ds1(2536) \u2192D\u2217+K0\nS. The mass reso-\nlution is about 1.5 MeV/c2, thus too large to measure the\nDs1(2536) width.\nFor the Ds1(2536)+ \u2192D\u2217+K0\nS sample as shown in\nFig. 19.3.26, Belle performed a full three-dimensional an-\ngular analysis. Such an analysis allows to study the partial\nwave structure of the Ds1(2536) decay. Assuming JP = 1+\nfor the Ds1(2536), the kinematics of the Ds1(2536) \u2192\nD\u2217+K0\nS decay can be described by three angles \u03b1, \u03b2 and\n\u03b3, de\ufb01ned as shown in Fig. 19.3.27. Then the angular dis-\ntribution in the helicity formalism is expressed as:\nN(\u03b1, \u03b2, \u03b3) =\n9\n4\u03c0(1+2R\u039b) \u00d7\n\u0010\ncos2\u03b3\n\u0002\n\u03c100 cos2\u03b1 + 1\u2212\u03c100\n2\nsin2\u03b1\n\u0003\n+R\u039b sin2\u03b3\n\u0002 1\u2212\u03c100\n2\nsin2\u03b2 + cos2\u03b2\n\u0000\u03c100 sin2\u03b1 + 1\u2212\u03c100\n2\ncos2\u03b1\n\u0001 \u0003\n+\n\u221aR\u039b(1\u22123\u03c100)\n4\nsin2\u03b1 sin2\u03b3 cos\u03b2 cos\u03be\n\u0011\n,\n(19.3.22)\nwhere \u03c100 is the longitudinal Ds1(2536) polarization, and\n\u221aR\u039bei\u03be \u2261A1,0\nA0,0 denotes the ratio of the D\u2217+ amplitudes\nwith helicities of respectively \u00b11 and 0, which are related\nFigure 19.3.27. De\ufb01nitions of the angles: \u03b1 is the Ds1(2536)\nhelicity angle measured in the Ds1(2536) CM frame as the\nangle between the boost direction in the e+e\u2212CM frame and\nthe K0\nS momentum; \u03b2 is the angle between the plane formed\nby these two vectors and the Ds1(2536) decay plane measured\nalso in the Ds1(2536) rest frame; \u03b3 is the D\u2217+ helicity angle\nbetween the \u03c0+ and K0\nS momenta in the D\u2217+ rest frame.\nto S- and D-wave amplitudes in the Ds1(2536) decay:\nA1,0 = (S + D/\n\u221a\n2)/\n\u221a\n3\nA0,0 = (S \u2212\n\u221a\n2D)/\n\u221a\n3.\n(19.3.23)\nTo measure the phase \u03be and, thus, unambiguously deter-\nmine the partial widths, the full three-dimensional angular\nanalysis is necessary, as after integration over any of the\nangles, the cos \u03be interference term in Eq. (19.3.22) van-\nishes.\nThe probability density function for the Ds1(2536) sig-\nnal is given by Eq. (19.3.22) which includes e\ufb03ciency cor-\nrections obtained in the (cos \u03b1, \u03b2, cos \u03b3) angular space de-\ntermined from MC simulation; the background contribu-\ntion is modeled in that space using the M(D\u2217+K0\nS) side-\nband regions. The three-dimensional unbinned maximum\nlikelihood \ufb01t to the Ds1(2536) \u2192D\u2217+K0\nS signal region\ndata yields:\nA1,0\nA0,0\n\u2261\np\nR\u039bei\u03be = a e\u00b1i\u00b7b\n(19.3.24)\nwhere a = \u221a3.6 \u00b1 0.3 \u00b1 0.1, b = 1.27 \u00b1 0.15 \u00b1 0.05, and\n\u03c100 = 0.490 \u00b1 0.012 \u00b1 0.004, showing that the Ds1(2536)\nspin prefers to align transversely to the momentum in the\nxp > 0.8 region. Figure 19.3.28 shows one-dimensional\nprojections of the \ufb01tted data together with the \ufb01t result.\nThe good agreement of the data with theoretical predic-\ntions for the angular distribution of the axial meson, iden-\nti\ufb01es the spin-parity of the Ds1(2536) to be 1+. The \ufb01t re-\nsults given in Eq. (19.3.24) translate into the partial-wave\namplitude ratio of:\nD\nS = ce\u00b1i\u00b7d,\n(19.3.25)\nwhere c = 0.63 \u00b1 0.07 \u00b1 0.02 and d = 0.76 \u00b1 0.03 \u00b1 0.01.\nThis shows that the S-wave amplitude dominates and its\ncontribution to the total width is\n\u0393S\n\u0393S+\u0393D =\n1\n1+|D/S|2 =\n0.72 \u00b1 0.05 \u00b1 0.01, where \u0393S and \u0393D denote the S- and\nD-wave partial widths.\nThe result in Eq. (19.3.25) disagrees with HQET which\npredicts the pure D-wave decay of the Ds1(2536). How-\never, HQET breaking caused by \ufb01nite c-quark mass, can\nlead to mixing between the axial c\u00afs states having jq = 1\n2\n\n620\n0\n0.02\n0.04\n0.06\n0.08\n-1\n0\n1\n0\n\u03c0/2\n\u03c0\n-1\n0\n1\ncos\u03b1\n\u03b2\ncos\u03b3\nFigure\n19.3.28.\nFrom\n(Balagura,\n2008):\nBackground-\nsubtracted,\ne\ufb03ciency-corrected\nand\nnormalized\none-\ndimensional\nprojections\nof\n(cos \u03b1, \u03b2, cos \u03b3)\ndescribed\nin\nthe text. The solid curves show projections of the three-\ndimensional \ufb01t.\nand jq = 3\n2. Then, similarly to Eq. (19.3.14), the physi-\ncal states, Ds1(2460)+ and Ds1(2536)+, can be expressed\nas linear combinations of S- and D-wave amplitudes. As\na result, the Ds1(2536) can contain an admixture of the\nJP = 1+ state with jq = 1\n2 and decaying in pure S wave.\nSince the energy release in the Ds1(2536)+ \u2192D\u2217+K0\nS\ndecay is small, the D-wave is strongly suppressed by the\ncentrifugal barrier factor (q/q0)5 and the S-wave contribu-\ntion, proportional to q/q0, can be signi\ufb01cantly enhanced\neven if the mixing itself is small. Here q denotes the rel-\native momentum of the Ds1(2536) decay products in the\nDs1(2536) rest frame, while q0 is a characteristic momen-\ntum scale of this reaction. Based on the measured D/S\nand input on the parameter q0, theoretical models can\ncalculate the c\u00afs mixing angle (Godfrey, 2005b).\nSome information on the mixing could be also inferred\nfrom the ratio of branching fractions of the radiative de-\ncays Ds1(2460)+ \u2192D+\ns \u03b3 and Ds1(2460)+ \u2192D\u2217+\ns \u03b3. How-\never, only evidence exists for the Ds1(2460)+ \u2192D\u2217+\ns \u03b3\n(see Section 19.3.4.4), and an average of Belle results\nB(Ds1(2460)+\u2192D\u2217+\ns\n\u03b3)\nB(Ds1(2460)+\u2192D+\ns \u03b3) = 0.31 \u00b1 0.14 (Abe, 2004a; Krokovny,\n2003b), gives a constraint of tan (\u03c9 + \u03c90) = 0.8 \u00b1 0.4,\nwhere \u03c9 is the mixing angle, while \u03c90 is a rotation an-\ngle between the jq and (2S+1)P1 bases, and tan \u03c90 = \u2212\n\u221a\n2.\nThe (2S+1)P1 basis is convenient here, as only the 1P1 state\nin Ds1(2460)+ undergoes an electric dipole transition to\nthe D+\ns , while only the 3P1 one to the D\u2217+\ns\n(Godfrey,\n2005b; Yamada, Suzuki, Kazuyama, and Kimura, 2005).\n19.3.4.7 New D+\nsJ mesons decaying to D(\u2217)K.\nThe potential models predict higher orbitally-excited c\u00afs\nstates, as well as a spectrum of states belonging to the next\nlevel (n = 2) of radial excitations. Within the c\u00afs spectrum\nabove the D(\u2217)K threshold, the radially-excited states\n2 3S1 and 3 2S1 (possibly with admixtures of D-waves)\nare predicted to lie respectively at about 2.73 GeV/c2 and\n3.1 GeV/c2 (Godfrey and Isgur, 1985). One expects a large\ntotal production rate of these 2S and 3S states in B de-\ncays, respectively at a level of about 1% and 0.1% (Close\nand Swanson, 2005). However, since the potential model\n0\n20\n40\n60\n2.4\n2.6\n2.8\n3\n3.2\n3.4\nM(D0K+) (GeV/c2)\nSignal yield / 50 MeV/c2\n0\n20\n40\n60\n-1\n-0.5\n0\n0.5\n1\ncos\u03b8hel\nEff. corrected signal yield\nFigure 19.3.29. From (Brodzicka, 2008). Left: Background-\nsubtracted M(D0K+) distribution for B+\n\u2192\nD0D0K+\nwith contribution from D\u2217\ns1(2710)+ (blue , cross shaded his-\ntogram), re\ufb02ections from \u03c8(3770) (green, horizontal shaded)\nand \u03c8(4160) (yellow, full light) and non-resonant contribu-\ntions (brown (dark) and red (vertical shaded) obtained from\nMC simulations based on the \ufb01t results. Right: Background-\nsubtracted and e\ufb03ciency corrected D\u2217\ns1(2710)+ helicity-angle\ndistribution compared to predictions for J = 0 (green, dashed),\n1 (red, full line) and 2 (blue, large dash).\npredictions for the P-wave c\u00afs states have failed, their eval-\nuations must be revised to provide reliable masses and\nwidths of the higher excitations.\nThe mentioned excitations could appear as intermedi-\nate resonances in B \u2192D(\u2217)D(\u2217)K decays. Belle, in the\nstudy of the decay B+ \u2192D0D0K+, observed a new c\u00afs\nresonance, the D\u2217\ns1(2710)+, decaying to D0K+ (Brodz-\nicka, 2008). The D\u2217\ns1(2710)+ peak is clearly visible in\nFigure 19.3.29, showing the M(D0K+) distribution of\nthe B signal candidates, which is obtained from \ufb01ts to\nthe \u2206E-mES distributions for a given M(D0K+) bin. A\nlimited reconstructed B signal yield does not allow for\na full Dalitz-plot analysis, instead the D\u2217\ns1(2710)+ pa-\nrameters are measured from the \ufb01t to the background-\nsubtracted M(D0K+) spectrum, where re\ufb02ections from\ncharmonia decaying to D0D0, \u03c8(3770) and \u03c8(4160), are\nalso taken into account. The charmonium yields are esti-\nmated from \ufb01ts to the M(D0D0) projection, while their\nshapes are based on B+ \u2192\u03c8K+ MC simulations. The\nD\u2217\ns1(2710)+ mass is measured to be (2708\u00b19+11\n\u221210) MeV/c2,\nits width (108 \u00b1 23+36\n\u221231) MeV/c2. The systematic uncer-\ntainties include e\ufb00ects of possible interference between\nthe D\u2217\ns1(2710)+ and the \u03c8(4160). The spin-parity of the\nD\u2217\ns1(2710)+ is established to be 1\u2212from the helicity-angle\ndistribution presented in Figure 19.3.29.\nBABAR explored the DK mass spectrum \ufb01rst using\n240 fb\u22121 (Aubert, 2006ag) and then, with 470 fb\u22121,\nstudied also the D\u2217K system (Aubert, 2009au). In these\nanalyses \ufb01rst observations of D\u2217\ns1(2710)+, D\u2217\nsJ(2860)+\nand DsJ(3040)+ resonances were reported. The measured\nD\u2217\ns1(2710)+ parameters and properties are in agreement\nwith those obtained for this state in B decays, as reported\nabove. The BABAR study is performed inclusively, with\nthe D(\u2217)K systems separated from the BB background\nby means of the CM momentum p\u2217> 3.5 GeV/c. To re-\n\n621\n0\n5000\n10000\n15000\n20000\n2.5\n3\n0\n2500\n5000\n7500\n10000\n2.5\n3\n0\n1000\n2000\n3000\n2.5\n3\n0\n1000\n2000\n3000\n2.5\n3\nFigure 19.3.30. From (Aubert, 2009au). Sideband-subtracted\nDK invariant mass distributions for (a) D0K+, (c) D+K0\nS; (b)\nand (d) show the background-subtracted mass spectra, respec-\ntively.\nmove combinations of the K and D(\u2217) mesons originating\nfrom opposite-side jets, cos \u03b8K > \u22120.8 is required, with\n\u03b8K de\ufb01ned as the angle between the K direction and the\ndirection opposite to the laboratory frame in the D(\u2217)K\nrest frame.\nIn a study of the D0K+ and D+K0\nS \ufb01nal states,\nD0 \u2192K\u2212\u03c0+ and D+ \u2192K\u2212\u03c0+\u03c0+ are reconstructed. The\nD0K+ and D+K0\nS mass spectra, with D sidebands sub-\ntracted, are shown in Fig. 19.3.30(a,c). A single bin peak\nat 2.4 GeV/c2 is a re\ufb02ection from decays of Ds1(2536)+\nto D\u2217K in which the \u03c00 or \u03b3 from the D\u2217decay is\nmissed; the Ds1(2536)+ decay to DK is forbidden. In\naddition to a prominent D\u2217\ns2(2573)+ signal, there are\nalso broad structures associated with the D\u2217\ns1(2710)+ and\nD\u2217\nsJ(2860)+ mesons. A simultaneous binned \u03c72 \ufb01t was\nperformed to the two mass spectra, with the background\ndescribed by a threshold function and the D\u2217\ns2(2573)+,\nD\u2217\ns1(2710)+ and D\u2217\nsJ(2860)+ peaks parameterized with\nrelativistic BW lineshapes where spin 2 was assumed for\nD\u2217\ns2(2573)+, 1 for D\u2217\ns1(2710)+ and spin 0 for D\u2217\nsJ(2860)+.\nFigures 19.3.30(b,d) show the M(D0K+) and M(D+K0\nS)\nmass distributions with \ufb01tted background subtracted. The\n\ufb01t gives the parameters listed in Table 19.3.14.\nIn a study of the D\u2217K system, D\u2217resonances are re-\nconstructed as D\u22170 \u2192D0\u03c00, D\u2217+ \u2192D+\u03c00 and D\u2217+ \u2192\nD0\u03c0+, with D0 \u2192K\u2212\u03c0+, D0 \u2192K\u2212\u03c0+\u03c0+\u03c0\u2212and D+ \u2192\nK\u2212\u03c0+\u03c0+. The total D\u2217K mass spectrum, D\u2217sideband-\nsubtracted and summed over all the channels, is shown\nin Fig. 19.3.31, where above the Ds1(2536)+ signal (not\nshown because out of scale in the \ufb01gure), there are struc-\ntures present around 2.71, 2.86 and 3.04 GeV/c2. A binned\nTable 19.3.14. From (Aubert, 2009au). Resonance param-\neters obtained from the \ufb01ts to the DK and the D\u2217K mass\nspectra. Masses and widths are given in units of MeV/c2. Un-\ncertainties are statistical only.\nSystem\nD\u2217\ns1(2710)+\nD\u2217\nsJ(2860)+\nDsJ(3040)+\nD K\nm=2710.0 \u00b1 3.3\nm=2860.0 \u00b1 2.3\n\u0393=178 \u00b1 19\n\u0393=53 \u00b1 6\nD\u2217K\nm=2712 \u00b1 3\nm=2865.2 \u00b1 3.5\nm=3042 \u00b1 9\n\u0393=103 \u00b1 8\n\u0393=44 \u00b1 8.3\n\u0393=214 \u00b1 34\n0\n1000\n2000\n3000\n4000\n2.5\n3\n3.5\n0\n200\n400\n600\n800\n3\n3.5\nFigure 19.3.31. From (Aubert, 2009au). (a) Fit to the D\u2217K\ninvariant mass spectrum, (b) residuals after subtraction of the\n\ufb01tted background.\nminimum \u03c72 \ufb01t is performed to the combined D\u2217K mass\nspectrum in the region 2.58-3.48 GeV/c2, with the back-\nground parameterized with an exponential function pro-\nviding a good description of the MC in the same mass\nrange. The D+\nsJ peaks are described with relativistic BW\nlineshapes, with JP = 1\u2212and JP = 3\u2212assumed respec-\ntively for D\u2217\ns1(2710)+ and D\u2217\nsJ(2860)+, and an angular\nmomentum L = 1, L = 3, and L = 0 for D\u2217\ns1(2710)+,\nD\u2217\nsJ(2860)+ and DsJ(3040)+, respectively. Since the width\nvalues for the resonances are much larger than the mass\nresolutions, e\ufb00ects of the latter are ignored in the \ufb01t.\nThe resonance parameters resulting from the \ufb01t are given\nin Table 19.3.14 and the corresponding \ufb01tted curves are\nshown in Fig. 19.3.31. The width of the D\u2217\ns1(2710)+ di\ufb00ers\nsomewhat between the M(DK) and M(D\u2217K) \ufb01ts, while\nthe parameter of the D\u2217\nsJ(2860)+ are consistent for both\ndecay modes.\nThe observation of both D\u2217\ns1(2710)+ and D\u2217\nsJ(2860)+\ndecays to both DK and D\u2217K, implies that they have nat-\nural parity JP = 1\u2212, 2+, 3\u2212, . . . (JP = 0+ is ruled out\nbecause of the D\u2217K decay). A further test of the quan-\ntum numbers was performed through analysis of the helic-\nity angle (\u03b8h), computed as the angle between the \u03c0 from\nthe D\u2217decay and the kaon, in the D\u2217rest frame. The\ne\ufb03ciency-corrected D\u2217\ns1(2710)+ and D\u2217\nsJ(2860)+ yields are\nplotted in Fig. 19.3.32, together with the normalized ex-\npectations for the natural parity i.e. 1\u2212cos2 \u03b8h, which give\n\u03c72/NDF of 18.7/5 and 6.3/5, respectively. The large value\nfor the D\u2217\ns1(2710)+ is related to the large uncertainties in\nthe background parameterization.\n\n622\n0\n1\n2\n3\n-1\n0\n1\n0\n0.25\n0.5\n0.75\n1\n-1\n0\n1\nFigure 19.3.32.\nFrom (Aubert, 2009au). Distributions of\ncos \u03b8h for (a) the D\u2217\ns1(2710)+ and (b) the D\u2217\nsJ(2860)+. The\ncurves are expectations for the natural parity.\nBABAR measures the following branching fraction ra-\ntios:\nB(D\u2217\ns1(2710)+ \u2192D\u2217K)\nB(D\u2217\ns1(2710)+ \u2192DK) = 0.91 \u00b1 0.13 \u00b1 0.12 (19.3.26)\nB(D\u2217\nsJ(2860)+ \u2192D\u2217K)\nB(D\u2217\nsJ(2860)+ \u2192DK) = 1.10 \u00b1 0.15 \u00b1 0.19, (19.3.27)\nusing the selected decay channels: D\u22170K+ with D\u22170 \u2192\nD0\u03c00, D0 \u2192K\u2212\u03c0+, and D\u2217+K0\nS with D\u2217+ \u2192D+\u03c00,\nD+ \u2192K\u2212\u03c0+\u03c0+, to reduce systematic uncertainties.\nThe D\u2217\ns1(2710)+ can be either a radial excitation or\nan L = 2 orbital excitation, which are both predicted\nin this mass region. Observation of the D\u2217\ns1(2710)+ \u2192\nD\u2217K decay with rate comparable to that for the DK,\nsuggests that the D\u2217\ns1(2710)+ is a radial excitation of the\nD\u2217\ns state (Colangelo, De Fazio, Nicotri, and Rizzi, 2008).\nInterpretations of the D\u2217\nsJ(2860)+ and DsJ(3040)+ are\nstill unknown.\n19.3.5 Conclusions\nResults from the B Factories have given an important in-\nput to the experimental status of the charm meson spec-\ntroscopy. The observation of the broad states belonging\nto the L = 1 c\u00afu multiplets has validated outstanding pre-\ndictions of the potential models. Properties of this multi-\nplet need to be re\ufb01ned with higher statistics, while their\nproduction has to be studied in various processes. Find-\ning new decay modes, especially radiative ones, could pro-\nvide further tests of the theory. On the other hand, the\nc\u00afs spectroscopy has revealed some surprises. At the mo-\nment, it is still not completely clear if the Ds1(2460)+ and\nD\u2217\ns0(2317)+ are fully understood in terms of Q\u00afq mesons, or\nif we need to include more complex quark con\ufb01gurations\nto understand their properties. In the simplest scenario,\nwhere the Ds1(2460)+ and D\u2217\ns0(2317)+ are the conven-\ntional L = 1 c\u00afs mesons, the potential models may need\nsome serious modi\ufb01cations.\nThe large data samples collected by Belle and BABAR\nalso allowed for precision measurements of already known\nmesons, like the Ds1(2536)+. The new excited DJ and DsJ\nmesons observed open a spectrum of the higher orbital and\nradial excitations that can be studied. They however need\ncon\ufb01rmation and more studies to allow their \ufb01nal assign-\nment. The LHCb experiment, dedicated charm factories\nlike BES III, and super \ufb02avor factories could shed more\nlight on this sector in the future.\n\n623\n19.4 Charmed baryon spectroscopy and\ndecays\nEditors:\nMatthew Charles (BABAR)\nRuslan Chistov (Belle)\nIn this section we discuss the physics of charmed bary-\nons at the B Factories. We begin with the spectroscopy of\nthese states, then turn to the weak decays of their lowest-\nlying ground states. Finally, we consider the use of these\ndecays to study the properties of light baryons.\nThe data samples analysed include both baryons pro-\nduced in the decays of B mesons (see Section 17.12) and\nfrom the e+e\u2212\u2192cc continuum (see Section 24.1). Both\nproduce large samples of charmed baryons. In practice,\nmost of the inclusive analyses discussed in this section use\nonly the continuum sample, since a cut on the center-of-\nmass momentum of the charmed baryon, p\u2217, of around\nECM/4 is very e\ufb00ective at suppressing combinatoric back-\nground, but also removes the entire B sample in the pro-\ncess. However, there is an important exception: exclusive\nB meson decays provide an initial state with known JP ,\nwhich is extremely helpful for measuring the JP quantum\nnumbers of charmed baryons.\n19.4.1 Spectroscopy\n19.4.1.1 Introduction\nOverview\nThe spectroscopy of charmed baryons is beautiful and in-\ntricate. With three quarks there are numerous degrees\nof freedom, giving rise to many more states than in the\ncharmed meson sector. At the same time, the large dif-\nference in mass between the charm quark and the light\nquarks provides a natural way to classify and understand\nthese states by making use of the symmetries emerging in\nHeavy Quark E\ufb00ective Theory (HQET). The spectrum of\nknown singly-charmed states can be thought of in three\nbroad regimes: the ground states, which are a vindica-\ntion of the constituent quark model; the low-lying excited\nstates, which are described well by heavy quark symme-\ntries; and higher excited states, where the situation is\nmurkier.\nThe naming convention for charmed baryons is to take\na light baryon, replace one or more s quarks with c quarks,\nand add a c subscript for every quark replaced. Isospin is\nunchanged. For example, \u039b denotes an sud baryon with\nisospin zero, and so \u039b+\nc denotes a cud baryon with isospin\nzero. Likewise, \u039e0\nc denotes a csd baryon and \u039e+\ncc denotes a\nccd baryon. A summary of charmed baryon states is given\nin Table 19.4.1. Following this convention, the experimen-\ntally known C = 1 baryon states147 are summarized in\n147 Strongly-decaying states are distinguished by their mass\nfollowing the PDG convention, e.g. \u039ec(2645). The \u039e\u2032\nc and\n\u2126\u2217\nc do not decay strongly and are therefore not labelled by\nFig. 19.4.1. Spin-parity assignments follow the PDG (Be-\nringer et al. (2012)); note that in many cases these are\nassigned based on quark model expectations rather than\nmeasurements.\nTable 19.4.1. Baryon \ufb02avor states, isospin, and quark con-\ntent. The symbol q denotes a u or d quark. Baryons with beauty\nare not included for brevity, but follow a similar pattern.\nSymbol\nI\nContent\nN (p,n)\n1/2\nudq\n\u2206\n3/2\nqqq\n\u039b\n0\nsud\n\u03a3\n1\nsqq\n\u039e\n1/2\nssq\n\u2126\n0\nsss\n\u039bc\n0\ncud\n\u03a3c\n1\ncqq\n\u039ec\n1/2\ncsq\n\u2126c\n0\ncss\n\u039ecc\n1/2\nccq\n\u2126cc\n0\nccs\n\u2126ccc\n0\nccc\nc\n\u039b\nc\n\u03a3\nc\n\u039e\nc\n\u2126\n)\n2\nMass of state (MeV/c\n2200\n2300\n2400\n2500\n2600\n2700\n2800\n2900\n3000\n3100\n3200\nc\n\u039b\n+\n1/2\n(2455)\nc\n\u03a3\n+\n1/2\n(2520)\nc\n\u03a3\n+\n3/2\nc\n\u039e\n+\n1/2\n'\nc\n\u039e\n+\n1/2\n(2645)\nc\n\u039e\n+\n3/2\nc\n\u2126\n+\n1/2\n*\nc\n\u2126\n+\n3/2\n(2595)\nc\n\u039b\n-\n1/2\n(2625)\nc\n\u039b\n-\n3/2\n(2790)\nc\n\u039e\n-\n1/2\n(2815)\nc\n\u039e\n-\n3/2\n(2880)\nc\n\u039b\n+\n5/2\n(2940)\nc\n\u039b\n?\n(2800)\nc\n\u03a3\n?\n(2980)\nc\n\u039e\n?\n(3055)\nc\n\u039e\n?\n(3080)\nc\n\u039e\n?\n(2930)\nc\n\u039e\n?\n(3123)\nc\n\u039e\n?\n(2765)\nc\n\u03a3\n/\nc\n\u039b\n?\nFigure 19.4.1. Summary of the known charmed baryon\nstates. The spin-parity JP is given, or marked \u201c?\u201d if not known.\nStates whose existence is unclear (one-star rating in PDG) are\nmarked with a dashed line.\ntheir mass, although the latter is sometimes referred to as the\n\u2126c(2770) in the literature.\n\n624\nQuark model for ground states\nIn the constituent quark model (Gell-Mann, 1964; Zweig,\n1964a,b), baryons composed of u, d, s, c quarks can be clas-\nsi\ufb01ed into SU(4) multiplets according to the symmetry of\ntheir \ufb02avor, spin, and spatial wavefunctions. All states in a\ngiven SU(4) multiplet have the same angular momentum\nJ, and parity P, but can have di\ufb00erent quark \ufb02avors. For\nexcited states with multiple units of orbital angular mo-\nmentum the number of possible multiplets becomes large,\nbut for the ground states the picture is much simpler.\nThis SU(4) symmetry is badly broken due to the large\ncharm mass. and thus di\ufb00erent states with the same con-\nserved quantum numbers will mix, and baryons are not\npure three-quark objects\u2014but it works remarkably well\nfor the ground states.\nQuarks are fermions, so the baryon wavefunction must\nbe overall antisymmetric under quark interchange.148 Bar-\nyons are color singlets, and so have an antisymmetric color\nwavefunction. In the ground state, the orbital angular mo-\nmentum L is zero (S-wave) and the spatial wavefunction is\nsymmetric. Therefore, the product of the spin and \ufb02avor\nwavefunctions must also be symmetric for ground-state\nbaryons. There are two ways this can be accomplished:\nboth wavefunctions can be fully symmetric, or both can\nhave mixed symmetry with the product being symmetric.\nIn concrete terms, we can consider a singly-charmed\nbaryon to consist of a heavy c quark and a light diquark\nwith spin-parity jp. Assuming isospin symmetry and let-\nting q denote a u or d quark, there are four possibilities\nfor the \ufb02avor content of the diquark:\n\u2013 qq with isospin 0 (\ufb02avor antisymmetric);\n\u2013 qq with isospin 1 (\ufb02avor symmetric);\n\u2013 sq with isospin 1/2 (either);\n\u2013 ss with isospin 0 (\ufb02avor symmetric).\nThese correspond to the \u039bc, \u03a3c, \u039ec, and \u2126c states, respec-\ntively. The diquark wavefunction must be antisymmetric\nunder quark interchange. Its color wavefunction is anti-\nsymmetric and in the ground state its spatial wavefunc-\ntion is symmetric, so it may be either \ufb02avor-symmetric\nand spin-symmetric (jp = 1+) or \ufb02avor-antisymmetric\nand spin-antisymmetric (jp = 0+). Combining the diquark\nwith the charm quark gives rise to the possible states set\nout in Table 19.4.2 and illustrated in Fig. 19.4.2, where the\nmultiplets of the full SU(3) symmetry (formed by the u,\nd, and s quarks) are shown. Those with JP = 1/2+ are all\nmembers of the same multiplet as the proton, and those\nwith JP = 3/2+ are all members of the same multiplet\nas the \u2206and \u2126(Fig. 19.4.3). Note that there is a second\nisospin doublet of \u039ec states with JP = 1/2+, denoted \u039e\u2032\nc.\nThe constituent quark model predicts relations be-\ntween the masses of these states as well as their exis-\ntence and quantum numbers. These were expressed for the\nlight baryons as sum rules (see Gell-Mann (1962); Okubo\n148 Strictly, it only needs to be antisymmetric under inter-\nchange of equal-mass quarks, but in order to build the model\nwe assume SU(4) is a good symmetry.\n\u03a30c\n\u03a3+c\n\u03a3++\nc\n\u039e\u20320c\n\u039e\u2032+\nc\n\u21260c\n\u039e0c\n\u039e+c\n\u039b+c\nj = 0, JP = 1\n2\n+\nj = 1, JP = 1\n2\n+\n\u03a3\u22170\nc\n\u03a3\u2217+\nc\n\u03a3\u2217++\nc\n\u039e\u22170\nc\n\u039e\u2217+\nc\n\u2126\u22170\nc\nj = 1, JP = 3\n2\n+\nFigure 19.4.2. The SU(3) multiplets containing the ground\nstate baryons, grouped according to the spin j of the light\ndiquark and the spin-parity JP of the baryon.\nn\np\n-\n\u03a3\n0\n\u03a3\n/\n\u039b\n0\n\u03a3\n/\n\u039b\n+\n\u03a3\n+\nc\n\u03a3\n/\n+\nc\n\u039b\n+\nc\n\u03a3\n/\n+\nc\n\u039b\n'0\nc\n\u039e\n/\n0\nc\n\u039e\n'0\nc\n\u039e\n/\n0\nc\n\u039e\n'+\nc\n\u039e\n/\n+\nc\n\u039e\n'+\nc\n\u039e\n/\n+\nc\n\u039e\n+\ncc\n\u039e\n++\ncc\n\u039e\n+\ncc\n\u2126\n0\nc\n\u2126\n0\nc\n\u03a3\n++\nc\n\u03a3\n-\n\u039e\n0\n\u039e\nC=0\nC=1\nC=2\n+\n2\n1\n = \nP\nJ\n-\n\u2206\n0\n\u2206\n+\n\u2206\n++\n\u2206\n*-\n\u03a3\n*0\n\u03a3\n*+\n\u03a3\n*-\n\u039e\n*0\n\u039e\n*0\nc\n\u03a3\n*+\nc\n\u03a3\n*++\nc\n\u03a3\n*0\nc\n\u039e\n*+\nc\n\u039e\n*+\ncc\n\u039e\n*++\ncc\n\u039e\n-\n\u2126\n*0\nc\n\u2126\n*+\ncc\n\u2126\n++\nccc\n\u2126\n3I\nS\nC\nC=0\nC=1\nC=2\nC=3\n+\n2\n3\n = \nP\nJ\nFigure 19.4.3. The SU(4) multiplets containing the ground\nstate baryons, arranged by spin-parity (JP ), isospin projection\n(I3), strangeness (S), and charm (C). A double ring indicates\nthat two states have the same JP , I3, S, and C quantum num-\nbers.\n(1962)):\n(mN + m\u039e)/2 = (3m\u039b + m\u03a3)/4,\n(19.4.1)\nm\u03a3\u2217\u2212m\u2206= m\u039e\u2217\u2212m\u03a3\u2217= m\u2126\u2212m\u039e\u2217,(19.4.2)\nm\u03a3\u2217\u2212m\u03a3 = m\u039e\u2217\u2212m\u039e,\n(19.4.3)\nof which the \ufb01rst is the famous Gell-Mann-Okubo rule.\nThese can be thought of as expressing the mass as the sum\nof the valence quark masses plus a hyper\ufb01ne (spin-spin)\ncoupling. This can be parameterized in various ways,149\nsuch as (De Rujula, Georgi, and Glashow (1975)):\nM = A + B\u2032 X\ni\n\u2206mi + C\u2032 X\ni>j\nsi \u00b7 sj (mq \u2212\u2206mi \u2212\u2206mj) ,\n(19.4.4)\nwhere A, B\u2032, and C\u2032 are constants, mq is the mass of a\nlight quark, \u2206mi = mi \u2212mq is the mass di\ufb00erence of\nthe ith quark compared to mq, and si is the spin of the\n149 See also Gasiorowicz and Rosner (1981) for a nice review\nwith a di\ufb00erent hyper\ufb01ne interaction term.\n\n625\nTable 19.4.2. Summary of the ground state singly-charmed baryons. S denotes a wavefunction that is fully symmetric under\ninterchange of any two quarks; MS and MA denote mixed overall symmetry with interchange of the two light quarks being\nsymmetric or antisymmetric, respectively; and A would denote a fully antisymmetric wavefunction.\nBaryon\nDiquark\nDiquark I\nDiquark jp\nBaryon \ufb02avor symmetry\nBaryon spin symmetry\nBaryon JP\n\u039bc\nqq\n0\n0+\nMA\nMA\n1/2+\n\u03a3c\nqq\n1\n1+\nMS\nMS\n1/2+\n\u03a3\u2217\nc\nqq\n1\n1+\nS\nS\n3/2+\n\u039ec\nsq\n1/2\n0+\nMA\nMA\n1/2+\n\u039e\u2032\nc\nsq\n1/2\n1+\nMS\nMS\n1/2+\n\u039e\u2217\nc\nsq\n1/2\n1+\nS\nS\n3/2+\n\u2126c\nss\n0\n1+\nMS\nMS\n1/2+\n\u2126\u2217\nc\nss\n0\n1+\nS\nS\n3/2+\nith quark. When evaluated for the ground state baryons,\nthe sum rules given in Eq. 19.4.1\u201319.4.3 are recovered.\nThis simple model can also be extended to baryons with\nheavy quarks. To illustrate its e\ufb00ectiveness, we note that\nthe spectrum and decay pattern of singly-charmed baryon\nground states was mapped out in an essentially correct\nway within about three months of the discovery of charm\nbut it took three decades before all of the states were\nseen experimentally (Beringer et al., 2012). The last to be\ndiscovered was the \u2126\u2217\nc . The equal-spacing mass rule still\nholds for the singly-charmed J = 3/2+ multiplet:\nm\u2126\u2217\nc \u2212m\u039e\u2217\nc = m\u039e\u2217\nc \u2212m\u03a3\u2217\nc ,\n(19.4.5)\nbut with additional \ufb02avors the hyper\ufb01ne terms become\nmore complicated so the analog of Eq. 19.4.3 is:\nm\u2126\u2217\nc \u2212m\u2126c = 2\n\u0000m\u039e\u2217\nc \u2212m\u039e\u2032c\n\u0001\n\u2212\n\u0000m\u03a3\u2217\nc \u2212m\u03a3c\n\u0001\n. (19.4.6)\nSubstituting in the current world-average experimental\nmasses for states other than the \u2126\u2217\nc (Beringer et al., 2012),\none would calculate m\u2126\u2217\nc to be approximately 2774 MeV/c2\nfrom Eq. 19.4.5 or 2770 MeV/c2 from Eq. 19.4.6. As we will\nshow in Section 19.4.1.4, these simple estimates are in re-\nmarkably good agreement with the observed mass.\nHigher states\nBaryons can be given orbital (l) or radial (k) excitations.\nSince in the simplest quark model they are three-body\nsystems there are two degrees of freedom in each case (de-\nnoted \u03c1, \u03bb). For baryons with one heavy quark (mass M)\nand two light quarks (mass m), a natural way to specify\nthese is to divide the system into a light diquark and the\nheavy quark. Taking a simple potential model based on the\nharmonic oscillator, the energy levels are given by (Klempt\nand Richard (2010)):\nE =\nr\nK\nm (3 + 2l\u03c1 + 4k\u03c1) +\ns\nK\n\u00b5 (3 + 2l\u03bb + 4k\u03bb) ,\n(19.4.7)\nwhere l\u03c1,\u03bb = 0, 1, 2, ... and k\u03c1,\u03bb = 0, 1, 2, ..., and K is\na constant describing the potential and \u00b5 = (2/3M +\n1/3m)\u22121 \u22483m in the heavy quark limit. Thus, the \u03c1 ex-\ncitations (within the diquark) require roughly three times\nas much energy as the corresponding \u03bb excitations (be-\ntween quark and diquark). Therefore the lowest-lying ex-\ncitations are those with l\u03bb = 1 and the other quantum\nnumbers zero, i.e. L = 1. (Within this band there will\nbe further splitting, e.g. due to spin-spin and spin-orbit\ncouplings.) The second band will consist of two groups of\nstates that have comparable energy: those with l\u03bb = 2\n(L = 2) and those with k\u03bb = 1 (L = 0), with the other\nquantum numbers being zero. Beyond the second band the\ndegeneracy grows further, but we lack useful experimental\ndata in this region in any case.\nWe can take this quark-diquark separation one step\nfurther for singly-heavy baryons by considering the heavy\nquark to be essentially a spectator and treating the di-\nquark as a distinct object with its own conserved quan-\ntum numbers jp that is the main actor in decays (in\nHQET, jp is the total angular momentum of all light de-\ngrees of freedom, see Isgur and Wise (1991)). As a con-\nsequence, some transitions that would otherwise be al-\nlowed are now forbidden. For example, consider a heavier\nstate with (JP , jp) = (1/2\u2212, 1\u2212) and a lighter state with\n(1/2+, 0+). If we considered only the overall JP , an S-\nwave (L = 0) strong decay of the heavier state to the\nlighter state plus a pion, (1/2\u2212\u21921/2+ 0\u2212), would be\nallowed. This channel would dominate and, if well above\nthreshold, would lead to a large width for the resonance.\nHowever, conservation of angular momentum forbids the\ncorresponding S-wave diquark transition: (1\u2212\u21920+ 0\u2212).\nA D-wave (L = 2) transition is allowed, but would be kine-\nmatically suppressed. The HQET constraints thus have a\nconcrete e\ufb00ect on the decay pattern of excited states, and\nimply that some will be narrow.\nAll this said, it is important to bear in mind that\nstates which share all conserved, external quantum num-\nbers (J, P, I, C, S) can mix. Therefore we should be\ncareful when interpreting observed resonances as speci\ufb01c\nexpected states, particularly for higher excitations.\n\n626\n19.4.1.2 \u039bc, \u03a3c families\nThe known \u039bc and \u03a3c states are shown in Fig. 19.4.1. The\nlowest-lying is the \u039b+\nc ground state, which decays weakly\n(see next section). The most precise measurement of the\n\u039b+\nc\nmass was made by BABAR (Aubert, 2005a). Since\n\u039b+\nc are produced copiously at the B Factories, the key\nchallenge is control of the systematic uncertainties. These\narise from e\ufb00ects which could change the momentum scale,\nprincipally uncertainties in the magnetic \ufb01eld and energy\nloss in material. By selecting \u039b+\nc decay modes with low\nenergy release (Q value), a large fraction of the recon-\nstructed \u039b+\nc mass comes directly from the rest masses of\nthe \ufb01nal-state daughters, which are known to high pre-\ncision, and only a small fraction from the measured 3-\nmomenta. Thus, the e\ufb00ect of the momentum uncertainty\non the \u039b+\nc is reduced. Using the modes \u039b+\nc \u2192\u039bK0\nSK+\nand \u039b+\nc \u2192\u03a30K0\nSK+, the mass is found to be m(\u039b+\nc ) =\n(2286.46\u00b10.14) MeV/c2. At the time of writing, this is the\nmost precise measurement of an open charm hadron mass\nand has signi\ufb01cantly lower uncertainty than existing the-\noretical calculations based upon lattice QCD or advanced\npotential models.\nIn order of increasing mass, the next states are the\nground states \u03a3c(2455) and \u03a3c(2520). In both cases these\nare isotriplets, and the only kinematically allowed strong\ndecay is \u03a3c \u2192\u039b+\nc \u03c0. The \u03a3c(2455) is one of the few\ncharmed baryons whose angular momentum has been mea-\nsured. This was accomplished with a sample of fully re-\nconstructed B\u2212\u2192\u039b+\nc p\u03c0\u2212decays proceeding via an in-\ntermediate \u03a3c(2455)0 (Aubert, 2008aa). In this exclusive\nproduction environment where the initial state is known to\nhave J = 0, the angular distributions for di\ufb00erent spin hy-\npotheses are fully determined (see Sections 12.1 and 19.4.3\nfor more on the helicity formalism). In this case the helic-\nity angle, \u03b8h, is de\ufb01ned as the angle between the direction\nof the \u039b+\nc in the \u03a3c rest frame and the direction of the \u03a3c\nin the B\u2212rest frame. BABAR found that the \u03a3c(2455)0 is\nconsistent with J = 1/2 and inconsistent with J = 3/2 as\nshown in Fig. 19.4.4, in line with the quark model predic-\ntions (Section 19.4.1.1).\nThe lowest-lying excited states are a pair of \u039b+\nc not far\nabove the \u039b+\nc \u03c0+\u03c0\u2212threshold, the \u039bc(2595) and \u039bc(2625).\nThese are interpreted as a doublet with the light diquark\nin a spin-antisymmetric state and one unit of orbital angu-\nlar momentum between the diquark and the heavy quark\n(L = 1), so that the total jp of the light degrees of freedom\nis 1\u2212. Adding in the spin-1/2 heavy quark, the total JP\nof the baryon is 1/2\u2212for the \u039bc(2595) and 3/2\u2212for the\n\u039bc(2625) as shown in the \ufb01rst two rows of Table 19.4.3.\nThe pattern of decays seen by ARGUS (Albrecht et al.,\n1993b, 1997), E687 (Frabetti et al., 1994a, 1996b), and\nCLEO (Edwards et al., 1995) leads to the following con-\nclusions:\n\u2013 The states decay to \u039b+\nc \u03c0+\u03c0\u2212but not to \u039b+\nc \u03c00, so they\nhave isospin 0 (\u039bc) and not 1 (\u03a3c).\n\u2013 The \u039bc(2595) decays predominantly to \u03a3c(2455)0\u03c0+,\nwhich is a favored S-wave decay:\n(1\u2212, 1/2\u2212) \u2192(1+, 1/2+)(0\u2212).\nh\ne\ncos \n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nEvents / ( 0.4 )\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nh\ne\ncos \n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nEvents / ( 0.4 )\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\nFigure 19.4.4. The helicity angle distribution for \u03a3c(2455)0\ncandidates in B\u2212\u2192\u03a3c(2455)0p at BABAR, corrected for ef-\n\ufb01ciency (Aubert, 2008aa). The distributions expected for the\nspin-1/2 hypothesis (solid, horizontal line) and spin-3/2 hy-\npothesis (dashed curve) are shown. The data are consistent\nwith J = 1/2 and exclude J = 3/2 at the 4\u03c3 level.\n\u2013 The \u039bc(2625) does not decay to the kinematically-\nallowed \u03a3c(2455)0\u03c0+ \ufb01nal state, since this would re-\nquire a D-wave decay: (1\u2212, 3/2\u2212) \u2192(1+, 3/2+)(0\u2212).\nInstead, it decays to the 3-body \ufb01nal state \u039b+\nc \u03c0+\u03c0\u2212via\na P-wave transition: (1\u2212, 3/2\u2212) \u2192(0+, 1/2+)(0\u2212)(0\u2212).\nTable 19.4.3. Possible low-lying excited states in HQET, clas-\nsi\ufb01ed according to the spin-alignment of the two light quarks,\nthe spin-parity of the light degrees of freedom jp, and the spin-\nparity of the baryon JP .\nDiquark spin\njp\nJP\n0\n1\u2212\n1/2\u2212\n0\n1\u2212\n3/2\u2212\n1\n0\u2212\n1/2\u2212\n1\n1\u2212\n1/2\u2212\n1\n1\u2212\n3/2\u2212\n1\n2\u2212\n3/2\u2212\n1\n2\u2212\n5/2\u2212\nFollowing Table 19.4.3, we would then expect to see\na set of \ufb01ve \u039bc states in which the light diquark is in a\nspin-symmetric arrangement. In these con\ufb01gurations the\nunit of orbital angular momentum is between the two light\nquarks (l\u03c1 in the notation of Eq. 19.4.7) and so the energy\nlevels will be higher than those of the \ufb01rst two L = 1 \u039bc\nstates discussed above. These heavier states are often de-\nnoted \u039b\u2032\nc in the literature. We would also expect to see\nseven corresponding \u03a3c states, with an inverted hierarchy\ndue to the di\ufb00erent symmetry of the light \ufb02avor wavefunc-\ntion (i.e. \ufb01ve lower \u03a3c isotriplets with j = 1 followed by\n\n627\ntwo higher \u03a3\u2032\nc isotriplets with j = 0). However, looking at\nFig. 19.4.1 we see only a handful of known states at higher\nmasses. By implication, the unobserved states either have\ntoo small a production cross-section or are too broad to be\nvisible as distinct structures in the current data. Future\n\ufb02avor factories with larger data samples may be able to\nshed light on them.\nOf the remaining known states, two are close in mass:\nthe \u039bc/\u03a3c(2765), seen by CLEO and Belle in the \u039b+\nc \u03c0+\u03c0\u2212\n\ufb01nal state (Artuso et al., 2001; Mizuk, 2007) and the\n\u03a3c(2800) isotriplet, seen in \u039b+\nc \u03c0+,0,\u2212by Belle (Mizuk,\n2005). The isospin of the former state is not known exper-\nimentally: the \u039b+\nc \u03c0+\u03c0\u2212\ufb01nal state is accessible to both\nI = 0 and I = 1, and no results are available for the re-\nlated \u039b+\nc \u03c0\u00b1\u03c00 \ufb01nal states which would be populated for\na \u03a3c state but not a \u039bc. The peak is also rather broad\nand could even be due to multiple overlapping resonances\n(see Fig. 19.4.5). A \u03a3c resonance in this region was also\nobserved by BABAR in the analysis of B\u2212\u2192\u039b+\nc p\u03c0\u2212de-\ncays mentioned previously. However, the \ufb01tted mass was\n(2846\u00b18\u00b110) MeV/c2, higher than the world-average mass\nof the \u03a3c(2800)0, (2802+4\n\u22127) MeV/c2 by about 3\u03c3. If this\ndi\ufb00erence is genuine and the states are distinct, the state\nseen by BABAR would be one of the missing \u03a3c states.\nFinally, we turn to the last states: the \u039bc(2880) and\n\u039bc(2940), which were studied by both BABAR and Belle\nand are shown in Fig. 19.4.5. (Aubert, 2007ai; Mizuk,\n2007). CLEO discovered the \u039bc(2880) in the \u039b+\nc \u03c0+\u03c0\u2212\ufb01-\nnal state (Artuso et al., 2001) but did not establish its\nquantum numbers. BABAR observed both states in the\nD0p channel. This is notable as the \ufb01rst observation of the\nstrong decay of a charmed baryon to a charmed meson and\na light baryon. It also allowed the isospin to be determined\nstraightforwardly: no corresponding resonances were seen\nin the isospin partner channel D+p, thus excluding a \u03a3c\ninterpretation.\nBelle studied the same two resonances in the \u039b+\nc \u03c0\u2212\u03c0+\n\ufb01nal state. The spin of the \u039bc(2880), J, was measured\nby Belle in another application of the helicity formalism\n(Section 12.1)\u2014but this time with an inclusive production\nenvironment. Because the initial state is not \ufb01xed, the el-\nements of the density matrix were not known a priori.\nIn the case that all diagonal elements were equal (unbi-\nased production environment), one would get a \ufb02at dis-\ntribution independent of J. However, if they were not\nequal, the result would be an even polynomial in cos \u03b8h\nof order \u2264(2J \u22121), where \u03b8h is the angle between the\ndirection of the \u039b+\nc in the \u03a3c rest frame and the direc-\ntion of the \u03a3c in the \u039bc(2880)+ rest frame. Thus, a \ufb02at\ndistribution would give no discrimination between spins\nbut a higher-order polynomial would exclude lower spins.\nBelle found that a polynomial of order at least 4 was re-\nquired, excluding J = 1/2 and 3/2 but consistent with\nJ = 5/2 (or higher). They also showed that the rela-\ntive branching fractions of \u039bc(2880) \u2192\u03a3c(2520)\u03c0 and\n\u039bc(2880) \u2192\u03a3c(2455)\u03c0 were more consistent with HQET\npredictions for JP = 5/2+ than 5/2\u2212, favoring even par-\nity. This would make the \u039bc(2880) an L = 2 state from\nthe second excitation band\u2014though, as noted earlier, an\nadmixture of states with the same external quantum num-\nbers cannot be excluded (see Cheng and Chua (2007) for\none example).\n19.4.1.3 \u039ec family\nSince all three quark \ufb02avors are di\ufb00erent for the \u039ec, there\nare many allowed con\ufb01gurations. These may be divided\ninto states for which the light diquark wavefunction is\n\ufb02avor-antisymmetric (analogous to \u039bc) or \ufb02avor-symmetric\n(analogous to \u03a3c)\u2014for the ground states, we saw this divi-\nsion between the j = 0 \u039ec and the j = 1 \u039e\u2032\nc and \u039e\u2217\nc (2645)\nin Table 19.4.2\nThe masses of the weakly-decaying \u039e0\nc and \u039e+\nc were\nmeasured by Belle in several decay modes (Lesiak, 2005),\nand these results now dominate the current world-average.\nSeveral decay modes were considered, and as with the \u039b+\nc\nmass measurement those with smaller energy release (no-\ntably \u039e0\nc \u2192pK\u2212K\u2212\u03c0+) generally had smaller systematic\nuncertainties. Combining the decay modes, the mass val-\nues obtained were m\u039e+\nc = (2468.1 \u00b1 0.4+0.2\n\u22121.4) MeV/c2 and\nm\u039e0c = (2471.0 \u00b1 0.3+0.2\n\u22121.4) MeV/c2, where the \ufb01rst uncer-\ntainty is due to statistical, \ufb01tting, and selection e\ufb00ects\nand the second is due to mass scale uncertainty (evalu-\nated with kinematically similar control modes and with\nMonte Carlo simulation). The mass splitting was mea-\nsured to be m\u039e0c \u2212m\u039e+\nc = (2.9 \u00b1 0.5) MeV/c2. Belle and\nBABAR also performed mass measurements of several of\nthe higher states in a variety of decay modes, summarized\nin Table 19.4.4.\nThe \u039e\u2032\nc and \u039ec(2645) ground states form a doublet\nanalogous to the \u03a3c(2455) and \u03a3c(2520) with expected\n(jp, JP ) of (1+, 1/2+) and (1+, 3/2+), respectively. The\nformer is too light to decay strongly, but the electromag-\nnetic transition \u039e\u2032\nc \u2192\u039ec\u03b3 is allowed. BABAR performed\nan angular analysis of \u039e\u20320\nc \u2192\u039e0\nc (\u039e\u2212\u03c0+)\u03b3 in the helicity\nformalism, similar to the \u039bc(2880) discussed above, and\nfound the data to be consistent with J = 1/2 (Aubert,\n2006ba). However, due to the inclusive production envi-\nronment higher spins could not be ruled out.\nThe low-lying excited states \u039ec(2790) and \u039ec(2815)\nare analogous to the \u039bc(2595) and \u039bc(2625), and their\ndecays follow a corresponding pattern: \u039ec(2790) \u2192\u039e\u2032\nc\u03c0,\n\u039ec(2815) \u2192\u039ec(2645)\u03c0. They were therefore identi\ufb01ed as\nthe 1/2\u2212, 3/2\u2212doublet with jp = 1\u2212and the diquark\nin a \ufb02avor-antisymmetric con\ufb01guration (Alexander et al.,\n1999; Csorna et al., 2001). Following the \u039bc/\u03a3c analogy,\nwe would then expect to see \ufb01ve low-lying L = 1 states\nwith a \ufb02avor-symmetric diquark, followed by a small ex-\nplosion of L = 2 states, radially excited states, and higher\nL = 1 states. We have a number of candidates for these\nstates in Fig. 19.4.1, but less information to classify them\nthis time since we cannot use isospin to distinguish them\nas we do for \u039bc/\u03a3c.\nThe lightest of these, the \u039ec(2930), was seen in B\u2212\u2192\n\u039b+\nc \u039b\u2212\nc K\u2212decays (Aubert, 2008e). The Dalitz plot150 is\nclearly not \ufb02at and the \u039b+\nc K\u2212projection is consistent\n150 See Section 13 for more on Dalitz plots.\n\n628\nEvents / 2.5 MeV/c2\nM(\u039b+\nc \u03c0+\u03c0\u2212), GeV/c2\n0\n50\n100\n150\n200\n2.8\n2.9\n3\n3.1\n3.2\nEvents / 0.2\ncos \u03b8\n0\n500\n1000\n1500\n-1\n-0.5\n0\n0.5\n1\nFigure 19.4.5. The \u039bc(2880)+ and \u039bc(2940)+. The two states are visible in the D0p mass spectrum (left, BABAR) and the\n\u039b+\nc \u03c0\u2212\u03c0+ mass spectrum (center, Belle). The \u039bc/\u03a3c(2765) enhancement is also seen at the lower edge of the m(\u039b+\nc \u03c0\u2212\u03c0+)\nspectrum. The helicity angle distribution for \u039bc(2880) \u2192\u03a3c(2455)\u03c0 (right, Belle) is \ufb01tted assuming di\ufb00erent spin hypotheses\nfor the \u039bc(2880): spin-1/2 (dotted line), spin-3/2 (dashed curve), and spin-5/2 (solid curve). The data are consistent with\nJ = 5/2 and exclude J = 1/2 and J = 3/2 at the 5.5\u03c3 and 4.8\u03c3 levels, respectively. (Aubert, 2007ai; Mizuk, 2007)\nTable 19.4.4. Mass and width measurements for strongly-decaying \u039ec states performed at the B Factories. An asterisk indicates\nthat the measurement has statistical signi\ufb01cance below 5\u03c3, and a double-asterisk that the signi\ufb01cance is below 3\u03c3.\nState\nDecay mode\nMass (MeV/c2)\nWidth (MeV)\nSource\n\u039ec(2645)0\n\u039e+\nc \u03c0\u2212\n2465.7 \u00b1 0.2+0.6\n\u22120.7\nneg.\nLesiak (2008)\n\u039ec(2645)+\n\u039e0\nc \u03c0+\n2465.7 \u00b1 0.2+0.6\n\u22120.7\nneg.\nLesiak (2008)\n\u039ec(2815)+\n\u039ec(2645)0\u03c0+\n2817.0 \u00b1 1.2+0.7\n\u22120.8\nneg.\nLesiak (2008)\n\u039ec(2815)0\n\u039ec(2645)+\u03c0\u2212\n2820.4 \u00b1 1.4+0.9\n\u22121.0\nneg.\nLesiak (2008)\n\u039ec(2930)0\n\u039b+\nc K\u2212\n2931 \u00b1 3 \u00b1 5\n36 \u00b1 7 \u00b1 11\nAubert (2008e)\n\u039ec(2980)0\n\u039b+\nc K0\nS\u03c0\u2212\n2977.1 \u00b1 8.8 \u00b1 3.5\n43.5 (\ufb01xed)\nChistov (2006b)\u2217\u2217\n\u039ec(2980)0\n\u039b+\nc K0\nS\u03c0\u2212\n2972.9 \u00b1 4.4 \u00b1 1.6\n31 \u00b1 7 \u00b1 8\nAubert (2008f)\u2217\u2217\n\u039ec(2980)0\n\u039ec(2645)+\u03c0\u2212\n2965.7 \u00b1 2.4+1.1\n\u22121.2\n15 \u00b1 6 \u00b1 3\nLesiak (2008)\n\u039ec(2980)+\n\u039b+\nc K\u2212\u03c0+\n2978.5 \u00b1 2.1 \u00b1 2.0\n43.5 \u00b1 7.5 \u00b1 7.0\nChistov (2006b)\n\u039ec(2980)+\n\u039b+\nc K\u2212\u03c0+\n2969.3 \u00b1 2.2 \u00b1 1.7\n27 \u00b1 8 \u00b1 2\nAubert (2008f)\n\u039ec(2980)+\n\u039ec(2645)0\u03c0+\n2967.7 \u00b1 2.3+1.1\n\u22121.2\n18 \u00b1 6 \u00b1 3\nLesiak (2008)\n\u039ec(3055)+\n\u039b+\nc K\u2212\u03c0+\n3054.2 \u00b1 1.2 \u00b1 0.5\n17 \u00b1 6 \u00b1 11\nAubert (2008f)\n\u039ec(3077)0\n\u039b+\nc K0\nS\u03c0\u2212\n3082.8 \u00b1 1.8 \u00b1 1.5\n5.2 \u00b1 3.1 \u00b1 1.8\nChistov (2006b)\u2217\n\u039ec(3077)0\n\u039b+\nc K0\nS\u03c0\u2212\n3079.3 \u00b1 1.1 \u00b1 0.2\n5.9 \u00b1 2.3 \u00b1 1.5\nAubert (2008f)\u2217\n\u039ec(3077)+\n\u039b+\nc K\u2212\u03c0+\n3076.7 \u00b1 0.9 \u00b1 0.5\n6.2 \u00b1 1.2 \u00b1 0.8\nChistov (2006b)\n\u039ec(3077)+\n\u039b+\nc K\u2212\u03c0+\n3077.0 \u00b1 0.4 \u00b1 0.2\n5.5 \u00b1 1.3 \u00b1 0.6\nAubert (2008f)\n\u039ec(3123)+\n\u039b+\nc K\u2212\u03c0+\n3122.9 \u00b1 1.3 \u00b1 0.3\n4.4 \u00b1 3.4 \u00b1 1.7\nAubert (2008f)\u2217\nwith a single resonance with the parameters given in Ta-\nble 19.4.4. However, given the small sample size and the\ninability to rule out other explanations (such as two over-\nlapping \u039ec resonances or a complicated interference pat-\ntern between \u039ec and charmonium resonances) this is con-\nsidered uncon\ufb01rmed.\nThe remaining resonances were all seen in the \u039b+\nc K\u03c0+\nisodoublet of \ufb01nal states (and, in the case of the \u039ec(2980),\nin \u039ec(2645)\u03c0). The \u039ec(2980) and \u039ec(3077) were discov-\nered by Belle in \u039b+\nc K\u03c0 (see Fig. 19.4.6) and con\ufb01rmed by\nBABAR. Since this is a three-body decay it could proceed\nvia an intermediate \u03a3c. BABAR tested this by \ufb01tting a two-\ndimensional p.d.f. in m(\u039b+\nc \u03c0), m(\u039b+\nc K\u03c0). It was found\nthat approximately half of the \u039ec(2980) decays to this \ufb01-\nnal state proceed through an intermediate \u03a3c(2455) with\nthe rest non-resonant. By contrast, most if not all of the\n\u039ec(3077) decays to this \ufb01nal state proceed via \u03a3c(2455)\nor \u03a3c(2520) with approximately equal branching fractions\n\n629\nto each. Because the \u039ec(2980) is close to threshold on\nthe scale of its natural width, especially with an interme-\ndiate \u03a3c, the available phase space changes signi\ufb01cantly\nacross the resonance. Di\ufb00erent handling of this threshold\nbehavior is the reason for the mild tension in the \ufb01tted\n\u039ec(2980) masses between (Chistov, 2006b) and (Aubert,\n2008f). The masses measured in the \u039ec(2645)\u03c0+ \ufb01nal state\n(Lesiak, 2008), which is far from threshold, are consis-\ntent with the BABAR treatment, although the widths are\nsmaller than either experiment saw in \u039b+\nc K\u03c0. Requiring\nan intermediate \u03a3c reduces the background levels, and by\ndoing this BABAR was able to identify two further candi-\ndate states, the \u039ec(3055) and \u039ec(3123). The latter had a\nlimited statistical signi\ufb01cance (3\u03c3), and needs con\ufb01rma-\ntion.\n0\n25\n50\n75\n100\n125\n150\n175\n200\n2.9\n2.95\n3\n3.05\n3.1\n3.15\n3.2\n3.25\nM(Rc\n+ K-/+) (GeV/c2)\nEvents / 2.5 MeV/c2\nFigure 19.4.6. The m(\u039b+\nc K\u2212\u03c0+) invariant mass spectrum\nat Belle. The \u039ec(2980) and \u039ec(3077) resonances are visible.\n(Chistov, 2006b)\nNo direct measurements of the JP of any of the ex-\ncited \u039ec states are available. Mild constraints on the quan-\ntum numbers can be inferred from the decay pattern. For\nexample, the observation of the \u039ec(3077) in \u03a3c(2455)K\nand \u03a3c(2455)K excludes states with diquark jp = 0\u2212\n(0\u2212\u0338\u21921+0\u2212for any L). However, many quantum num-\nbers are still allowed for these states and there is a range of\nopinions on the best match to the data\u2014see e.g. (Alexan-\nder et al., 1999; Cheng and Chua, 2007; Rosner, 2007).\n19.4.1.4 \u2126c family\nThe available experimental data on the \u2126c ground states\nwere limited before the B Factories, in contrast to the\n\u039bc, \u03a3c, and \u039ec families. The weakly-decaying J = 1/2+\n\u21260\nc had been seen in a number of di\ufb00erent decay modes\nand production environments but with only limited statis-\ntics (typically samples of order 10 events in a given decay\nmode, and never more than 100) and the J = 3/2+ \u2126\u22170\nc\nhad not been observed.\nBelle carried out a precise measurement of the \u21260\nc mass\nusing a sample of 725 decays to the \u2126\u2212\u03c0+ \ufb01nal state\n(Solovieva, 2009), obtaining (2693.6\u00b10.3+1.8\n\u22121.5) MeV/c2. This\ndecay channel was chosen because it is the most copious\nand cleanest; due to the limited production rate, it was\nnot possible to employ low-rate modes close to threshold\nas was done for the \u039b+\nc in Section 19.4.1.2. As a result,\nthe uncertainty is dominated by the mass scale uncertainty\n(evaluated based on the observed variation of the mass as\na function of kinematic variables).\nThe \u2126\u22170\nc\nis too light to undergo strong decay and so\ndecays purely to \u21260\nc\u03b3 (see Fig. 19.4.7). It was discov-\nered by BABAR and con\ufb01rmed by Belle (Aubert, 2006ah;\nSolovieva, 2009). Both measured the mass di\ufb00erence\nm(\u2126\u22170\nc ) \u2212m(\u21260\nc), and the two results are in excellent\nagreement. The PDG average for the mass di\ufb00erence is\n(70.7+0.8\n\u22121.0) MeV/c2. As we saw in equation 19.4.6, the na\u00a8\u0131ve\nquark model prediction for this is:\nm\u2126\u2217\nc \u2212m\u2126c = 2\n\u0000m\u039e\u2217\nc \u2212m\u039e\u2032c\n\u0001\n\u2212\n\u0000m\u03a3\u2217\nc \u2212m\u03a3c\n\u0001\n,\n(19.4.8)\nwhich we evaluate as (74.0\u00b14.3) MeV/c2 based on current\nworld-average measurements of \u039ec and \u03a3c mass di\ufb00er-\nences (Beringer et al., 2012). This is in beautiful agree-\nment with the experimental result.\n2\n GeV/c\n \nc\n0\n1\nPDG\n + M\nc\n0\n1\n \n - M\na \n0\nc\n1\n \nM\n2.75\n2.8\n2.85\n2.9\n2.95\n3\n2\nCandidates / 5 MeV/c\n0\n20\n40\n60\n80\n100\n120\n2\n GeV/c\n \nc\n0\n1\nPDG\n + M\nc\n0\n1\n \n - M\na \n0\nc\n1\n \nM\n2.75\n2.8\n2.85\n2.9\n2.95\n3\n2\nCandidates / 5 MeV/c\n0\n20\n40\n60\n80\n100\n120\nFigure 19.4.7. The m(\u21260\nc\u03b3) invariant mass spectrum at\nBABAR, combining four decay modes of the \u21260\nc: \u2126\u2212\u03c0+,\n\u2126\u2212\u03c0+\u03c00, \u2126\u2212\u03c0+\u03c0\u2212\u03c0+, \u039e\u2212K\u2212\u03c0+\u03c0+. The \u2126\u2217\nc resonance is\nvisible. The shaded histogram represents the combinatoric\nbackground estimated from the \u21260\nc mass sidebands. (Aubert,\n2006ah)\nNo radially or orbitally excited \u2126c have yet been dis-\ncovered, but we would expect their masses to follow a simi-\nlar pattern to the \u03a3c states discussed previously. However,\nthere are fewer options for their decay: transitions of the\nform \u2126c \u2192\u2126c\u03c0 are isospin-suppressed (whereas \u039ecK and\n\u2126c\u03c0\u03c0 are allowed). This could result in \u2126c states that are\nnarrow but whose \u03a3c analogs are too broad to resolve\u2014\nthis will be an interesting area for future \ufb02avor factories\nto search.\n19.4.1.5 Searches for \u039ecc\nThe quark model also predicts baryons with two charm\nquarks and one lighter quark, as shown in Fig. 19.4.2. Be-\ncause two quark \ufb02avors are identical, fewer distinct con-\n\ufb01gurations are possible than for the C = 1 baryons. We\nexpect three weakly-decaying ground states with JP = 1\n2\n+\n\n630\n(\u039e+\ncc, \u039e++\ncc , \u2126+\ncc) and three further states with JP = 3\n2\n+\n(\u039e\u2217+\ncc , \u039e\u2217++\ncc\n, \u2126\u2217+\ncc ). In the baryon mass parameterization\nof Eq. 19.4.4, the mass splittings between these states can\nbe related to those of singly-charmed baryons:\nm\u039e\u2217\ncc \u2212m\u039ecc = m\u03a3\u2217\nc \u2212m\u03a3c \u224864 MeV/c2 (19.4.9)\nm\u2126\u2217\ncc \u2212m\u2126cc = m\u2126\u2217\nc \u2212m\u2126c \u224871 MeV/c2.(19.4.10)\nThis is well below threshold for strong decay, so the \u039e\u2217\ncc\nand \u2126\u2217\ncc states should decay electromagnetically like the\n\u2126\u2217\nc .\nMore ambitiously, we can attempt to relate the masses\nof the weakly decaying ground states. Applying Eq. 19.4.4\nto the \u039ecc, \u03a3c, \u039bc, and nucleon, we can write:\nm\u039ecc = mN + 2(m\u039bc \u2212mN) + 1\n2(m\u03a3c \u2212m\u039bc), (19.4.11)\nwhere the terms represent the base nucleon mass, the mass\no\ufb00set for two charm quarks, and a hyper\ufb01ne correction.\nEvaluating this we obtain m\u039ecc \u22483720 MeV/c2. However,\nthis estimate should be treated with some skepticism: we\nhave assumed that the coe\ufb03cients A, B\u2032, and C\u2032 are the\nsame for all baryons, but in practice these terms have\nsome scale dependence (e.g. on the spatial extent of the\nwavefunction). There are numerous more rigorous theo-\nretical predictions (see, e.g., Roberts and Pervin (2008)\nand the references therein), including increasingly pre-\ncise estimates from Lattice QCD (Liu, Lin, Orginos, and\nWalker-Loud, 2010). Most estimates lie between 3600 and\n3700 MeV/c2.\nTo date, sightings of \u039ecc states have been reported\nonly at the SELEX experiment, a forward spectrometer\nin which a hyperon151 beam (composed of \u03a3\u2212, p, and\n\u03c0\u2212) struck a \ufb01xed target of copper or diamond. SELEX\nclaimed observation of \u039e+\ncc at a mass of 3519 MeV/c2 in\nthe \u039b+\nc K\u2212\u03c0+ and pD+K\u2212\ufb01nal states (Mattson et al.,\n2002; Ocherashvili et al., 2005). In each case the signa-\nture is a small, narrow signal on top of a smaller back-\nground: an excess of 15.9 events above an estimated back-\nground of 6.1\u00b10.5 for \u039b+\nc K\u2212\u03c0+, and of 5.4 above 1.6\u00b10.4\nfor pD+K\u2212. The observations were controversial (Kiselev\nand Likhoded, 2002), primarily because the lifetime and\nthe production rate of \u039ecc at SELEX were far from ex-\npectations. The theory expectation for the \u039e+\ncc lifetime\nis approximately 200\u2013250 fs across a number of models\n(Chang, Li, Li, and Wang, 2008), compared to a reported\nupper limit of 33 fs. Even more surprising, by comparing\nthe relative yields of \u039b+\nc and \u039e+\ncc and correcting for accep-\ntance and additional decay modes, SELEX estimated that\n20% of its sample of 1,630 \u039b+\nc came from \u039e+\ncc decays (pre-\nsumably with a further contribution of similar order from\n\u039e++\ncc ). This runs counter to expectations: it is much more\ndi\ufb03cult to produce a baryon with more than one unit\nof \ufb02avor because two heavy quark-antiquark pairs need\nto be created within a narrow enough kinematic window\n151 A hyperon is a baryon containing at least one strange\nquark. The term predates the discovery of charm and is not\nnormally used to refer to baryons with heavy \ufb02avor.\nfor them to coalesce into a baryon.152 SELEX also re-\nported preliminary observations of several other peaks in\nthe \u039b+\nc K\u2212\u03c0+ and \u039b+\nc K\u2212\u03c0+\u03c0+ mass spectra, claiming a\nfurther \u039e+\ncc state at 3443 MeV/c2 and \u039e++\ncc\nstates at 3460,\n3540, and 3780 MeV/c2 (Russ, 2002, 2003), but did not\npublish these results.\nBABAR, Belle, and the FOCUS photoproduction exper-\niment carried out searches for \u039ecc in an attempt to repro-\nduce the published SELEX observation (Aubert, 2006ao;\nChistov, 2006b; Ratti, 2003). All three examined \u039b+\nc K\u2212\u03c0+\nalong with a variety of other \ufb01nal states. None found any\nsignal. Since the integrated luminosity and the production\ncross-section vary between experiments, upper limits were\nquoted in the form of a production rate relative to \u039b+\nc . At\nthe B Factories this ratio is de\ufb01ned as\nR\u039e+\ncc/\u039b+\nc \u2261\u03c3(e+e\u2212\u2192\u039e+\nccX) B(\u039e+\ncc \u2192\u039b+\nc K\u2212\u03c0+)\n\u03c3(e+e\u2212\u2192\u039b+\nc X)\n,\n(19.4.12)\nwhere X represents the rest of the event and B the branch-\ning fraction, and the ratio is de\ufb01ned in an analogous way\nfor FOCUS. The limits obtained are shown in Table 19.4.5.\nIn each case, the samples of \u039b+\nc events used were much\nlarger than that of SELEX: yields of 19k for FOCUS, 600k\nfor BABAR, and 840k for Belle. However, because the pro-\nduction environments di\ufb00er from that of SELEX it cannot\nbe excluded that the double-charm baryon cross-section is\ndramatically higher with a hyperon in the initial state for\nreasons that are not understood theoretically.\nTable 19.4.5. Upper limits on the production ratio R\u039e+\ncc/\u039b+\nc\nde\ufb01ned in Eq. 19.4.12. SELEX reported a ratio of 9.6%.\nExperiment\nLimit on R\u039e+\ncc/\u039b+\nc\nKinematic cuts\nBABAR\n6.9 \u00d7 10\u22124 @ 95% C.L.\n\u2014\nBABAR\n2.7 \u00d7 10\u22124 @ 95% C.L.\np\u2217> 2.3 GeV/c\nBelle\n1.5 \u00d7 10\u22124 @ 90% C.L.\np\u2217> 2.5 GeV/c\nFOCUS\n2.3 \u00d7 10\u22123 @ 90% C.L.\n\u2014\nThere is one further twist: several of the excited \u039ec\nstates discussed in Section 19.4.1.3, notably the \u039ec(2980)\nand \u039ec(3077), were discovered in the \u039b+\nc K\u2212\u03c0+ \ufb01nal state.\nNone of these states were reported by SELEX (although\nthey were not speci\ufb01cally excluded either). This poses a\nfurther challenge: if the production cross-section at SE-\nLEX were much larger for these excited \u039ec states than\nfor \u039ecc they should have been seen clearly, so their non-\nobservation raises questions about the \u039ecc signals; con-\nversely, if the cross-section for the excited \u039ec is smaller\nthan for \u039ecc the mechanism must be highly exotic since\nthe \u039ec states are not only lighter than \u039ecc but also closer\nin \ufb02avor content to the initial-state \u03a3\u2212.\nUltimately, the nature of the \u039ecc states will become\nclear only when they are observed with high statistics at a\n152 For example, the production rates of \u039b and \u039b+\nc in e+e\u2212\nannihilation events are typically an order of magnitude larger\nthan that of \u039e\u2212(Beringer et al., 2012).\n\n631\n\ufb02avor factory, either vindicating or excluding the SELEX\nresults.\n19.4.1.6 Conclusions\nThe spectroscopy of the ground state C = 1 baryons is\nnow well established, and the lowest-lying \u039bc, \u03a3c, and \u039ec\nexcitations are reasonably well understood. There are still\nquestion marks about the nature of higher states which\nhave been observed, and about the many states which are\npredicted but have not yet been seen. To extend our un-\nderstanding, we need experimental information from three\nsources: from inclusive production with higher statistics\n(e.g. to be able to see the next \u2126c states, whose produc-\ntion cross-section at the B Factories is bound to be small),\nfrom exclusive production in b-meson decays, and from\nexclusive production in b-baryon decays. The latter will\nopen up angular analyses for some charmed baryon states\nthat are di\ufb03cult to produce in quasi-two-body decays of\nB mesons (see Section 17.12), in much the same way that\ncharmed baryon decays allow light baryons to be stud-\nied (see Section 19.4.3). We can look forward to results\nfrom these studies, as well as searches for doubly-charmed\nbaryons, at LHCb and at future e+e\u2212\ufb02avor factories.\n19.4.2 Weak decays\n19.4.2.1 Introduction\nThe investigation of charmed baryon weak decays is more\ndi\ufb03cult then for charmed mesons due to their shorter life-\ntimes and smaller production rate. The reconstruction ef-\n\ufb01ciency is often lower too, due to the frequent presence of\nhyperons in the \ufb01nal state which are long-lived and com-\nmonly have decay modes with a secondary neutron or \u03c00.\nThe lightest charmed baryon \u039b+\nc was discovered long be-\nfore the B Factory era. Subsequently, many weak decay\nmodes, mostly Cabibbo-favored tree diagrams, were ob-\nserved for the \u039b+\nc and \u039e0,+\nc\nbaryons. By contrast, little\nwas known about Cabibbo-suppressed and W-exchange\ndecays153 measurements with more than a dozen signal\nevents had been made even in the early 2000\u2019s. Due to\nthis lack of statistics, it was di\ufb03cult to make de\ufb01nitive\ntests between theoretical models that predicted charmed\nbaryon decay rates (Korner, Kramer, and Willrodt, 1979;\nKorner and Kramer, 1992; Uppal, Verma, and Khanna,\n1994). Both current data and theoretical models point to\nnon-factorizable amplitudes (e.g. W-exchange diagrams)\nhaving a signi\ufb01cant impact on individual decay rates as\nwell as the total widths and hierarchy of charmed baryon\nlifetimes. It is therefore important to gather as many mea-\nsurements as possible on charmed baryon weak decays.\nIn this section we discuss the many new results on \u039b+\nc ,\n\u039e0,+\nc\n, and \u21260\nc weak decays obtained by Belle and BABAR.\n153 Fig. 17.4.1(E) illustrates the W-exchange decay of a meson;\nthe baryon diagram is the same apart from a second spectator\nquark.\nThese measurements make use of the high statistics and\nthe excellent pion-kaon-proton separation, secondary ver-\ntex reconstruction, and photon energy resolution available\nat the B Factories.\n19.4.2.2 Results and discussion\n\u039b+\nc decays\nBelle and BABAR measured several ratios of branching\nfractions, in many cases Cabibbo-suppressed or W-exchange\n\u039b+\nc decay modes taken relative to topologically similar un-\nsuppressed modes. The numerical results for the analyses\ndiscussed below are given in Table 19.4.6.\nWith the initial 32.6 fb\u22121 of data, Belle observed two\nnew Cabibbo-suppressed decays of \u039b+\nc : \u039b+\nc \u2192\u039bK+ and\n\u039b+\nc\n\u2192\u03a30K+ (Abe, 2002h). The \u039b+\nc\nsignals for these\nmodes are shown in Fig. 19.4.8. BABAR subsequently con-\n\ufb01rmed these observarions with 125 fb\u22121 of data, and set\nlimits on two related four-body modes with the same sam-\nple: \u039b+\nc \u2192\u039bK+\u03c0+\u03c0\u2212and \u039b+\nc \u2192\u03a30K+\u03c0+\u03c0\u2212(Aubert,\n2007ag). Both experiments measured the branching frac-\ntions relative to the Cabibbo-favored decay modes \u039b+\nc \u2192\n\u039b\u03c0+ and \u039b+\nc \u2192\u03a30\u03c0+. The results were broadly consis-\ntent with predictions based on a \ufb02avor symmetry approach\n(Sharma and Verma, 1997):\nB(\u039b+\nc \u2192\u039bK+)\nB(\u039b+\nc \u2192\u039b\u03c0+) = [0.025 \u22120.177],\n(19.4.13)\nB(\u039b+\nc \u2192\u03a30K+)\nB(\u039b+\nc \u2192\u03a30\u03c0+) = [0.069 \u22120.78]\n(19.4.14)\nand on the constituent quark model approach (Uppal,\nVerma, and Khanna, 1994):\nB(\u039b+\nc \u2192\u039bK+)\nB(\u039b+\nc \u2192\u039b\u03c0+) = [0.039 \u22120.056],\n(19.4.15)\nB(\u039b+\nc \u2192\u03a30K+)\nB(\u039b+\nc \u2192\u03a30\u03c0+) = [0.08 \u22120.145]\n(19.4.16)\nalthough both models overshoot the second ratio.\nBelle also made the \ufb01rst observation of the Cabibbo-\nsuppressed mode \u039b+\nc \u2192\u03a3+K+\u03c0\u2212(Abe, 2002h), measur-\ning the branching fraction relative to \u039b+\nc\n\u2192\u03a3+\u03c0+\u03c0\u2212.\nThe invariant mass distribution of the suppressed mode\nis shown in Fig. 19.4.9. Belle also investigated another\nCabibbo-suppressed \ufb01nal state in the same paper: \u039b+\nc \u2192\npK+K\u2212. This was analysed inclusively and also separated\ninto p\u03c6 and p(K+K\u2212)non-\u03c6. Finally, BABAR measured\nthe Cabibbo-favored decays \u039b+\nc \u2192\u03a30\u03c0+, \u039e\u2212K+\u03c0+, and\n\u039b \u00afK0K+ relative to \u039b+\nc \u2192\u039b\u03c0+ (Aubert, 2007ag).\nBelle also investigated Cabibbo-favored, W-exchange\n\u039b+\nc decays to the \ufb01nal state \u03a3+K+K\u2212(Abe, 2002h) which\nhad previously been observed by CLEO (Avery et al.,\n1993). As well as measuring the overall branching fraction,\nthey also extracted the rate of \u039b+\nc \u2192\u03a3+\u03c6. Further, they\nobserved a signi\ufb01cant contribution of \u039b+\nc \u2192\u039e(1690)0K+\n\n632\nwith \u039e(1690)0 \u2192\u03a3+K\u2212, and con\ufb01rmed this with the re-\nlated decay \u039b+\nc \u2192\u039e(1690)0K+, \u039e(1690)0 \u2192\u039bK0\nS. These\ndemonstrate that W-exchange decays of charmed baryons\noccur at a non-negligible rate.\n0\n50\n100\n150\n200\n250\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\nm(\u039bK+) \u2212m(\u039b) + mPDG(\u039b) (GeV/c2)\nEntries/(5 MeV/c2)\n0\n20\n40\n60\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\nm(\u03a30K+) \u2212m(\u03a30) + mPDG(\u03a30) (GeV/c2)\nEntries/(5 MeV/c2)\nFigure 19.4.8. The invariant mass distribution of the selected\n\u039bK+ (upper) and \u03a30K+ (lower) combinations at Belle. The\nbumps to the right of the \u039b+\nc signal are due to the re\ufb02ections\nfrom \u039b+\nc \u2192\u039b\u03c0+ and \u039b+\nc \u2192\u03a30\u03c0+, where \u03c0+ is missidenti\ufb01ed\nas K+. (Abe, 2002h)\n0\n20\n40\n60\n80\n100\n120\n2.2\n2.25\n2.3\n2.35\nm(\u03a3+K+\u03c0\u2212) \u2212m(\u03a3+) + mPDG(\u03a3+) (GeV/c2)\nEntries/(5 MeV/c2)\nFigure 19.4.9. The invariant mass distribution of selected\n\u03a3+K+\u03c0\u2212combinations at Belle, showing the \u039b+\nc signal. The\nshaded histogram presents the contribution from the \u03a3+ side-\nbands. (Abe, 2002h)\n\u039e0\nc and \u039e+\nc decays\nIn the charm strange baryon sector, Belle measured ratios\nof branching fractions for a suite of \ufb01nal states: \u039e+\nc\n\u2192\n\u039e\u2212\u03c0+\u03c0+, \u039bK\u2212\u03c0+\u03c0+, and pK0\nSK0\nS; \u039e0\nc \u2192\u039e\u2212\u03c0+, \u039bK\u2212\u03c0+,\n\u039bK0\nS, and pK\u2212K\u2212\u03c0+ (Lesiak, 2005). The numerical re-\nsults are given in Table 19.4.7. For the four-body de-\ncay \u039e0\nc \u2192pK\u2212K\u2212\u03c0+, Belle found that the 3-body reso-\nnant mode \u039e0\nc \u2192pK\u2212\u00afK\u2217(892)0 was responsible for fully\n0.51 \u00b1 0.03 \u00b1 0.01 of the yield.\n)\n2\n candidate mass (GeV/c\n0\nc\n\u039e\n2.38\n2.4\n2.42\n2.44\n2.46\n2.48\n2.5\n2.52\n2.54\n2.56\n2\nEntries per 2.25 MeV/c\n0\n50\n100\n150\n200\n250\n(b)\n2\nEntries per 2.25 MeV/c\n500\n1000\n1500\n2000\n(a)\n0\nFigure 19.4.10. Invariant mass distribution for the \u039e0\nc candi-\ndates reconstructed in the \u039e\u2212\u03c0+ (upper) and \u2126\u2212K+ (lower)\ndecay modes at BABAR. (Aubert, 2005z)\nBABAR studied the two decay modes \u039e0\nc \u2192\u2126\u2212K+ and\n\u039e0\nc \u2192\u039e\u2212\u03c0+. Both are Cabibbo-favored, but the former\nproceeds through a W-exchange diagram and the latter\nthrough a tree diagram. Fig. 19.4.10 shows the invariant\nmass distribution for \u039e0\nc candidates in these two modes.\nThe ratio B(\u039e0\nc \u2192\u2126\u2212K+)/B(\u039e0\nc \u2192\u039e\u2212\u03c0+) was mea-\nsured to be 0.294 \u00b1 0.018 \u00b1 0.016 (Aubert, 2005z), and is\nconsistent with a quark model prediction of 0.32 (Korner\nand Kramer, 1992). Note that this ratio is large, especially\nwhen considering that the di\ufb00erence in phase space favors\n\u039e0\nc \u2192\u039e\u2212\u03c0+ by a factor of 1.7, showing again that contri-\nbutions from W-exchange processes cannot be neglected.\nUsing these modes BABAR measured the \u039e0\nc produc-\ntion momentum spectrum in two data samples, one at\nthe \u03a5(4S) resonance and one 40 MeV below. From these\nspectra the production rate of \u039e0\nc baryon from B decays\nwas measured to be B(B \u2192\u039e0\nc X) \u00d7 B(\u039e0\nc \u2192\u039e\u2212\u03c0+) =\n(2.11\u00b10.19\u00b10.25)\u00d710\u22124 (see Section 17.12) and the pro-\nduction cross-section from the continuum was measured to\nbe \u03c3(e+e\u2212\u2192\u039e0\nc X)\u00d7B(\u039e0\nc \u2192\u039e\u2212\u03c0+) = (388\u00b139\u00b141) fb\nat \u221as = 10.58 GeV (see Section 24.1.2.2). One practical\n\n633\nconsequence is that the production rates of \u039ec from B de-\ncays and from the cc continuuum are comparable, opening\nup the possibility of studying these states in B decays.\n\u21260\nc decays\n2\nCandidates / 5 MeV/c\n10\n20\n30\n40\n50\n60\n70\n80\n90\n2\nCandidates / 5 MeV/c\n10\n20\n30\n40\n50\n60\n70\n80\n90\n+\n\u03c0\n \n-\n\u2126\n(a)\n2\nCandidates / 10 MeV/c\n5\n10\n15\n20\n25\n30\n35\n40\n45\n2\nCandidates / 10 MeV/c\n5\n10\n15\n20\n25\n30\n35\n40\n45\n0\n\u03c0 \n+\n\u03c0 -\n\u2126\n(b)\n2\nCandidates / 5 MeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n2\nCandidates / 5 MeV/c\n2\n4\n6\n8\n10\n12\n14\n16\n-\u03c0\n \n+\n\u03c0 \n+\n\u03c0\n \n-\n\u2126\n(c)\n)\n2\n candidate (GeV/c\n0\nc\n\u2126\n Mass of \n2.5\n2.55\n2.6\n2.65\n2.7\n2.75\n2.8\n2.85\n2.9\n2\nCandidates / 5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n35\n40\n)\n2\n candidate (GeV/c\n0\nc\n\u2126\n Mass of \n2.5\n2.55\n2.6\n2.65\n2.7\n2.75\n2.8\n2.85\n2.9\n2\nCandidates / 5 MeV/c\n0\n5\n10\n15\n20\n25\n30\n35\n40\n+\n\u03c0 \n+\n\u03c0 -\n K\n-\n\u039e\n(d)\nFigure 19.4.11. The invariant mass distributions of \u21260\nc candi-\ndates with 4 di\ufb00erent decay modes at BABAR. (Aubert, 2007ao)\nA thorough experimental study of the \u2126c, the heaviest\nweakly-decaying C = 1, B = 0 hadron, was long overdue.\nBecause of its heavy mass and triple \ufb02avor content, the\nproduction rate of \u21260\nc is low in comparison with other\nground state charmed baryons.\nBABAR studied four Cabibbo-favored decay modes with\n230.5 fb\u22121 of data: \u21260\nc \u2192\u2126\u2212\u03c0+, \u2126\u2212\u03c0+\u03c00, \u2126\u2212\u03c0+\u03c0+\u03c0\u2212,\nand \u039e\u2212K\u2212\u03c0+\u03c0+ (Aubert, 2007ao). Fig. 19.4.11 shows\nthe \u21260\nc invariant mass distributions. The number of re-\nconstructed events and the branching fractions relative to\n\u2126\u2212\u03c0+ mode are presented in Table 19.4.7. These mea-\nsurements represent a signi\ufb01cant improvement upon the\nprevious values. The \u21260\nc \u2192\u2126\u2212\u03c0+ mode was also used by\nBABAR to study the \u21260\nc momentum spectrum. The pattern\nwas similar to that seen for \u039e0\nc : comparable production\nrates of \u21260\nc baryons in the continuum and in the B me-\nson decays (see Fig. 19.4.12), although with overall yields\na factor of \u223c40 smaller. At the time of writing, this re-\nmains the only observation of \u21260\nc in B decays.\np* (GeV/c)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n per 0.5 GeV/c\n0\nc\n\u2126\n-200\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nFigure 19.4.12. The background-subtracted and e\ufb03ciency-\ncorrected \u21260\nc yield in p\u2217(\u21260\nc) bins at BABAR. The histogram\nshows continuum contribution from Monte Carlo modelling.\nThe double-peak structure in this spectrum signalizing about\ntwo production mechanisms. Lower p\u2217peak is due to \u21260\nc pro-\nduction in B decays. Higher-p\u2217peak is due to \u21260\nc production\nin c\u00afc continuum. (Aubert, 2007ao)\n19.4.2.3 Comments on absolute branching fractions\nIn the preceeding discussion, branching fractions of\ncharmed baryon weak decays were quoted relative to ref-\nerence modes. However, at present, there is limited ex-\nperimental information on the absolute branching frac-\ntions of those reference modes for \u039b+\nc and none at all for\n\u039e0\nc , \u039e+\nc , and \u21260\nc. Determining these branching fractions\nis highly important. At present, this limits many mea-\nsurements involving charmed baryons, such as production\ncross-sections and branching fractions of B decays.\nThe situation for \u039b+\nc is covered in the PDG review (Be-\nringer et al., 2012), which obtains B(\u039b+\nc \u2192pK\u2212\u03c0+) =\n(5.0 \u00b1 1.3)%. This was last updated in 2002 and there has\nbeen little progress since. The techniques outlined in the\nreview are limited by systematic or theory uncertainties\nrather than statistical ones, as are many proposed meth-\nods. However, this is not universally true, and we discuss\na few possibilities below.\nThe most direct method would be to operate an e+e\u2212\ncollider at the \u039b+\nc \u039b\u2212\nc threshold. In this environment, ob-\nserving a \u039b+\nc necessarily implies the existence of a recoil-\ning \u039b\u2212\nc with fully determined kinematics, so the branch-\ning fraction can simply be taken as the fraction of cases\nin which this decays to a particular \ufb01nal state.\n\n634\nTable 19.4.6. Summary of Belle and BABAR results on \u039b+\nc Cabibbo-favored (CF), Cabibbo-suppressed (CS) and W-exchange\n(WE) decays.\n\u039b+\nc mode\nExperiment\nYield\n\u039b+\nc reference mode\nBsignal/Bref.\n\u039bK+ (CS)\nBelle\n265 \u00b1 35\n\u039b\u03c0+\n0.074 \u00b1 0.010 \u00b1 0.012\n\u03a30K+ (CS)\nBelle\n75 \u00b1 18\n\u03a30\u03c0+\n0.056 \u00b1 0.014 \u00b1 0.008\n\u039bK+ (CS)\nBABAR\n1162 \u00b1 101\n\u039b\u03c0+\n0.044 \u00b1 0.004 \u00b1 0.003\n\u03a30K+ (CS)\nBABAR\n366 \u00b1 52\n\u03a30\u03c0+\n0.038 \u00b1 0.005 \u00b1 0.003\n\u039bK+\u03c0+\u03c0\u2212(CS)\nBABAR\n160 \u00b1 62\n\u039b\u03c0+\n< 4.1 \u00d7 10\u22122 @90% CL\n\u03a30K+\u03c0+\u03c0\u2212(CS)\nBABAR\n21 \u00b1 24\n\u03a30\u03c0+\n< 2.0 \u00d7 10\u22122 @90% CL\n\u03a3+K+\u03c0\u2212(CS)\nBelle\n105 \u00b1 24\n\u03a3+\u03c0+\u03c0\u2212\n0.047 \u00b1 0.011 \u00b1 0.008\n\u03a3+K+K\u2212(WE)\nBelle\n246 \u00b1 20\n\u03a3+\u03c0+\u03c0\u2212\n0.076 \u00b1 0.007 \u00b1 0.009\n\u03a3+\u03c6 (WE)\nBelle\n129 \u00b1 17\n\u03a3+\u03c0+\u03c0\u2212\n0.085 \u00b1 0.012 \u00b1 0.012\n\u039e(1690)0K+, \u039e(1690)0 \u2192\u03a3+K\u2212(WE)\nBelle\n75 \u00b1 16\n\u03a3+\u03c0+\u03c0\u2212\n0.023 \u00b1 0.005 \u00b1 0.005\n\u039e(1690)0K+, \u039e(1690)0 \u2192\u039b \u00afK0 (WE)\nBelle\n93 \u00b1 26\n\u039b \u00afK0K+\n0.26 \u00b1 0.08 \u00b1 0.03\n\u03a3+K+K\u2212(non-res) (WE)\nBelle\n11 \u00b1 16\n\u03a3+\u03c0+\u03c0\u2212\n< 0.018 @90% CL\npK+K\u2212(CS)\nBelle\n676 \u00b1 89\npK\u2212\u03c0+\n0.014 \u00b1 0.002 \u00b1 0.002\np\u03c6 (CS)\nBelle\n345 \u00b1 43\npK\u2212\u03c0+\n0.015 \u00b1 0.002 \u00b1 0.002\npK+K\u2212(non-\u03c6)\nBelle\n344 \u00b1 81\npK\u2212\u03c0+\n0.007 \u00b1 0.002 \u00b1 0.002\n\u03a30\u03c0+ (CF)\nBABAR\n32693 \u00b1 324\n\u039b\u03c0+\n0.977 \u00b1 0.015 \u00b1 0.051\n\u039e\u2212K+\u03c0+ (CF)\nBABAR\n2665 \u00b1 84\n\u039b\u03c0+\n0.480 \u00b1 0.016 \u00b1 0.039\n\u039b \u00afK0K+ (CF)\nBABAR\n460 \u00b1 30\n\u039b\u03c0+\n0.395 \u00b1 0.026 \u00b1 0.036\nTable 19.4.7. Summary of Belle and BABAR results on \u039e+,0\nc\nand \u21260\nc decays.\nDecay mode\nExperiment\nYield\nReference mode\nBsignal/Bref.\n\u039e+\nc \u2192\u039bK\u2212\u03c0+\u03c0+\nBelle\n1117 \u00b1 55\n\u039e+\nc \u2192\u039e\u2212\u03c0+\u03c0+\n0.32 \u00b1 0.03 \u00b1 0.02\n\u039e+\nc \u2192pK0\nSK0\nS\nBelle\n168 \u00b1 27\n\u039e+\nc \u2192\u039e\u2212\u03c0+\u03c0+\n0.087 \u00b1 0.016 \u00b1 0.014\n\u039e0\nc \u2192pK\u2212K\u2212\u03c0+\nBelle\n1908 \u00b1 62\n\u039e0\nc \u2192\u039e\u2212\u03c0+\n0.33 \u00b1 0.03 \u00b1 0.03\n\u039e0\nc \u2192\u039bK0\nS\nBelle\n465 \u00b1 37\n\u039e0\nc \u2192\u039e\u2212\u03c0+\n0.21 \u00b1 0.02 \u00b1 0.02\n\u039e0\nc \u2192\u039bK\u2212\u03c0+\nBelle\n3268 \u00b1 276\n\u039e0\nc \u2192\u039e\u2212\u03c0+\n1.07 \u00b1 0.12 \u00b1 0.07\n\u039e0\nc \u2192\u2126\u2212K+\nBABAR\n\u2248650\n\u039e0\nc \u2192\u039e\u2212\u03c0+\n0.294 \u00b1 0.018 \u00b1 0.016\n\u21260\nc \u2192\u2126\u2212\u03c0+\u03c00\nBABAR\n64 \u00b1 15\n\u21260\nc \u2192\u2126\u2212\u03c0+\n1.27 \u00b1 0.31 \u00b1 0.11\n\u21260\nc \u2192\u2126\u2212\u03c0+\u03c0+\u03c0\u2212\nBABAR\n25 \u00b1 8\n\u21260\nc \u2192\u2126\u2212\u03c0+\n0.28 \u00b1 0.09 \u00b1 0.01\n\u21260\nc \u2192\u039e\u2212K\u2212\u03c0+\u03c0\u2212\nBABAR\n45 \u00b1 12\n\u21260\nc \u2192\u2126\u2212\u03c0+\n0.46 \u00b1 0.13 \u00b1 0.03\nA related method, applicable at B Factories operat-\ning at the \u03a5(4S), is to identify events with baryon and\ncharm content and then look for a recoiling \u039b\u2212\nc . This ap-\nproach was used by CLEO, requiring both a D and a p in\nthe event and inferring that a \u039b\u2212\nc is present (Ja\ufb00e et al.,\n2000). However, this comes with two disadvantages: the\nkinematics of the \u039b\u2212\nc are not known, and there is a prob-\nlematic background from other event types with the same\nsignature (e.g. e+e\u2212\u2192DpDNX, Dp\u039ecKX).154 Alter-\nnatively, it is possible to use e+e\u2212\u2192\u039b+\nc \u039b\u2212\nc X events in\n154 While we were \ufb01nalising this book Belle submitted an\nabsolute branching fraction analysis for publication, using\na further development of this approach: reconstruction of\nD(\u2217)\u2212p\u03c0+ events, identi\ufb01cation of inclusive \u039b+\nc decays using\nthe missing mass spectrum (the mass of the system recoiling\nagainst D(\u2217)\u2212p\u03c0+), and reconstruction of the subset decaying\nto pK\u2212\u03c0+ (Zupanc, 2013a). The result, B(\u039b+\nc \u2192pK\u2212\u03c0+) =\n(6.84 \u00b1 0.24+0.21\n\u22120.27)%, represents a signi\ufb01cant advance on the\nwhich the \u039b+\nc and the X system are fully reconstructed\u2014\nthe \u201cpopcorn\u201d sample identi\ufb01ed by BABAR in which X\nconsists of a small number of pions and has zero baryon\nand strangeness content is promising (Aubert, 2010b).\n19.4.2.4 Conclusions\nThe experimental and theoretical investigation of charmed\nbaryon weak decays remains one step behind that of\ncharmed mesons, where both experimental data and theo-\nretical models are more abundant. Nonetheless, the results\non charmed baryon weak decays obtained by BABAR and\nBelle could stimulate the development of theoretical mod-\nels describing charmed baryon weak decays. They could\nalso provide a roadmap for further studies of the charmed\nbaryon sector at future super \ufb02avor factories.\nprecision of this quantity. At the time of writing, this analysis\nhas not yet been published.\n\n635\nTable 19.4.8. Angular distributions for the decay chain Xc \u2192RP, R \u2192HP for di\ufb00erent spin hypotheses JR. It is assumed\nthat Xc and H have spin 1/2, that P has spin 0\u2212, and that there is no polarization in the initial state. (Aubert, 2006z)\nJR\ndN/d cos \u03b8h \u221d\n1/2\n1 + \u03b2 cos \u03b8h\n3/2\n1 + 3 cos2 \u03b8h + \u03b2 cos \u03b8h(5 \u22129 cos2 \u03b8h)\n5/2\n1 \u22122 cos2 \u03b8h + 5 cos4 \u03b8h + \u03b2 cos \u03b8h(5 \u221226 cos2 \u03b8h + 25 cos4 \u03b8h)\n19.4.3 Applications to light baryon spectroscopy\n19.4.3.1 Introduction\nA fully exclusive production environment is very helpful\nfor determining the spin or parity of a resonance. We saw\nthis used in Section 19.4.1.2 to measure the spin of the\n\u03a3c(2455) in quasi-two-body B decays, for example. In the\nsame way, charmed baryons may be used as a laboratory\nto study light baryons that are produced as intermediate\nresonances in their decays. The helicity formalism, dis-\ncussed in Section 12.1, is used here; for more detail the\nreader is referred to Jacob and Wick (1959), Chung (1971),\nRichman (1984), and Ziegler (2007).\nIn the cases considered below, the decay chain is of the\nform Xc \u2192RP, R \u2192HP, where Xc is a weakly decaying\ncharmed baryon with JP = 1/2+, R is the intermediate\nresonance to be studied, H is a hyperon with JP = 1/2+,\nand P are pseudoscalars.155 The decay helicity angle \u03b8h is\nde\ufb01ned as the angle between the direction of H in the rest\nframe of R and the direction of R in the rest frame of Xc,\nas illustrated in Fig. 19.4.13. The angular distributions\nexpected under spin hypotheses JR = 1/2, 3/2, 5/2 are\ngiven in Table 19.4.8. Parity violation is allowed in weak\ndecays and introduces an asymmetry in the distributions,\nexpressed by the parameter \u03b2:\n\u03b2 =\n\"\n\u03c1 1\n2 , 1\n2 \u2212\u03c1\u22121\n2 ,\u22121\n2\n\u03c1 1\n2 , 1\n2 + \u03c1\u22121\n2 ,\u22121\n2\n# \"|AJ\n1\n2 |2 \u2212|AJ\n\u22121\n2 |2\n|AJ\n1\n2 |2 + |AJ\n\u22121\n2 |2\n#\n,\n(19.4.17)\nwhere the transition matrix element AJ\n\u03bbf represents the\ncoupling of R to the \ufb01nal state with net helicity \u03bbf, and \u03c1i,i\nare the diagonal density matrix elements inherited from\nthe charmed baryon. If R \u2192HP is a strong decay then\n|AJ\n1\n2 | = |AJ\n\u22121\n2 | and so \u03b2 vanishes.\nIn addition to the technique outlined above for mea-\nsuring the spin of a resonance, charmed baryon decays can\nbe used more generally to measure properties such as the\nmass and width of intermediate resonances in multi-body\ndecays.\n19.4.3.2 Spin of the \u2126\u2212\nThe method introduced in Section 19.4.3.1 was used by\nBABAR in an elegant way to measure the spin of the \u2126\u2212\n155 Strictly speaking, the spin-parity of the charmed baryons\nthemselves has not been measured\u2014and indeed, some of the\npapers cited in this section allow for spins other than 1/2. But\nwe do not consider that possibility here.\n\u20d7K+\n1\n\u20d7\u039e0\nc = \u20d70\n\u20d7\u2126\u2212\n1\n\u20d7\u039b1\n\u20d7K\u2212\n1\na) All decay products in the \u039e0\nc rest-frame.\n\u20d7\u2126\u2212\n1\n\u20d7\u2126\u2212\n2 = \u20d70\n)\n\u03b8h\n\u20d7\u039b2\n\u20d7K\u2212\n2\nb) All decay products in the \u2126\u2212rest-frame;\nin this frame, \u20d7\u2126\u2212\n1 \u2192\u20d7\u2126\u2212\n2 = \u20d70, \u20d7\u039b1 \u2192\u20d7\u039b2, \u20d7K\u2212\n1 \u2192\u20d7K\u2212\n2 .\nFigure 19.4.13. Illustration of the helicity angle \u03b8h for the\ncase of \u039e0\nc \u2192\u2126\u2212K+, \u2126\u2212\u2192\u039bK\u2212. \u03b8h is de\ufb01ned as the angle\nbetween the \u039b direction in the \u2126\u2212rest frame and the \u2126\u2212in\nthe \u039e0\nc rest frame. (Aubert, 2006z)\n(Aubert, 2006z). J\u2126= 3/2 is a key prediction of the\nquark model and was assumed to be correct, but had\nproved di\ufb03cult to test de\ufb01nitively. A sample of approx-\nimately 770 decays of the form \u039e0\nc \u2192\u2126\u2212K+, \u2126\u2212\u2192\n\u039bK\u2212was selected. The mass distribution of these events\nis shown in Fig. 19.4.14(a), and the helicity angle distri-\nbution of these events after background subtraction and\ne\ufb03ciency correction is shown in Fig. 19.4.14(b) and (c).\nThe data are fully consistent with the J\u2126= 3/2 hypoth-\nesis, and are highly inconsistent with the J\u2126= 1/2 and\n5/2 hypotheses. Higher spins would correspond to an even\nhigher-order polynomial, which would not match the data.\nBABAR therefore concluded that J\u2126= 3/2, as predicted.\nAs part of the analysis, BABAR tested for polarization\nof the \u039e0\nc in the lab frame. Polarization would not di-\nrectly a\ufb00ect the angular distribution, since the angle \u03b8h\nis Lorentz-invariant\u2014but a large polarization could a\ufb00ect\nthe weighted e\ufb03ciency as a function of cos \u03b8h (in particular\nbecause the BABAR detector is forward-backward asym-\nmetric in the collision center-of-mass frame). In practice,\nno measureable polarization was found and this simpli\ufb01ed\n\n636\n)\n2\n) (GeV/c\n+\n K\n-\n1\nm(\n2.38\n2.4\n2.42 2.44 2.46 2.48\n2.5\n2.52 2.54 2.56\n2\nEntries/ 2 MeV/c\n0\n50\n100\n150\n200\n250\n300\n350\n(a)\n)\nR\n(\nh\ne\ncos\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nEntries/0.2\n0\n200\n400\n600\n800\n1000\n(b)\n)\nR\n(\nh\ne\ncos\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nEntries/0.2\n0\n200\n400\n600\n800\n1000\n(c)\nFigure 19.4.14. \u039e0\nc \u2192\u2126\u2212K+, \u2126\u2212\u2192\u039bK\u2212events at BABAR, showing the invariant mass distribution in (a) and the\nbackground-subtracted, e\ufb03ciency-corrected angular distribution in (b) and (c). The curves in (b) show the distribution ex-\npected for J\u2126= 3/2, with the asymmetry parameter \u03b2 \ufb01xed to zero (solid line, p-value 0.69) or \ufb02oated (dashed line, p-value\n0.64). The curves in (c) show other spin hypotheses: J\u2126= 1/2 (solid line, p-value 1 \u00d7 10\u221217), J\u2126= 5/2 (dashed curve, p-value\n3 \u00d7 10\u22127). (Aubert, 2006z)\nthe analysis considerably. However, similar measurements\nat colliders such as the Tevatron and LHC would need to\ntake polarization into account.\n19.4.3.3 Properties of \u039e(1530) and \u039e(1690)\nBABAR also applied the method to study the \u039e(1530) res-\nonance, which is predicted by the quark model to have\nJP\n= 3/2+, in the decay \u039b+\nc\n\u2192\u039e\u2212\u03c0+K+ (Aubert,\n2008w). In the limit that the decay is pure quasi-two-body,\nthe formalism described above applies\u2014and super\ufb01cially\nit is indeed quasi-two-body, as shown in Fig. 19.4.15(a)\nwhere the \u039e(1530)0 is the only visible resonance. How-\never, while the angular distribution is roughly quadratic\nand is clearly inconsistent with spin-1/2 or spin-5/2, it is\nnot fully described by the spin-3/2 hypothesis either, as\nshown in Fig. 19.4.15(b). This implies interference with\nanother resonance, which the paper speculates may be a\nhigh-mass \u039b or \u03a30 in the \u039e\u2212K+ channel. The spin-3/2\nhypothesis is corroborated with studies of the moments of\nthe m(\u039e\u2212\u03c0+) distribution (weighting candidates by the\nnth-order Legendre polynomial in cos \u03b8h).\nA similar study of the \u039e(1690) resonance was made\nin \u039b+\nc \u2192\u039bK0K+ (Aubert, 2006y). As with the \u039e(1530)\nanalysis, interference from other resonances in the Dalitz\nplot was found to be signi\ufb01cant and diluted the power of\nthe angular analysis. Correcting for these e\ufb00ects, it was\nfound that J = 1/2 was favored (p-value 0.30), but that\nhigher spins could not be excluded (p-value 0.02 for 3/2,\n0.01 for 5/2).\n19.4.3.4 Conclusions\nAs illustrated in the previous sections, charmed baryons\ncan be used as a clean, exclusive production environment\nto study the properties of light baryons. This allows angu-\nlar analyses which would be nigh impossible in inclusive\nproduction. When applied to strongly decaying resonances\nin multi-body charmed baryon decays, however, interfer-\nence e\ufb00ects cannot be neglected even for narrow states.\n2)\n2\n) (GeV/c\n+\n/\n -\nU\n(\n2\nm\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n2)\n2\n) (GeV/c\n+\n K\n-\nU\n(\n2\nm\n3.2\n3.4\n3.6\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n(a)\n-\nU\ne\ncos\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n-0\n0.2\n0.4\n0.6\n0.8\n1\nEntries/ 0.1\n0\n500\n1000\n1500\n2000\n2500\n(b)\nFigure 19.4.15. \u039b+\nc \u2192\u039e\u2212\u03c0+K+ events at BABAR, showing\n(a) the Dalitz plot, and (b) the angular distribution in the\n\u039e(1530) region. Curves are superimposed for the \u039e(1530) spin\nhypotheses J = 3/2 (solid, p-value 3 \u00d7 10\u22124) and J = 5/2\n(dashed, p-value 6 \u00d7 10\u221244). The hypothesis J = 1/2 would\ncorrespond to a \ufb02at distribution. Color online. (Aubert, 2008w)\n\n637\nChapter 20\nTau physics\nEditors:\nMike Roney (BABAR)\nHisaki Hayashii (Belle)\nAntonio Pich (theory)\nAdditional section writers:\nSwagato Banerjee, Kiyoshi Hayasaka, George La\ufb00erty, Al-\nberto Lusiani, Boris Shwartz\nThe e+e\u2212B Factories, owing to the large cross sec-\ntion for producing tau lepton pairs, are also de facto \u201ctau\nfactories\u201d. The contributions to our understanding of a\nvariety of sectors of the Standard Model and Beyond-the-\nStandard Model theories from studies of the tau lepton at\nBelle and BABAR are presented here. Following an intro-\nductory section that reviews the history of the tau lep-\nton and some basics of its production and decay, this\nchapter proceeds with discussions of the status of tests\nof CPT and charged current lepton universality involving\nthe tau in Section 20.2 and Section 20.3. We then discuss\nsearches for new physics via lepton \ufb02avor violating pro-\ncesses in Section 20.4 and CP violation in tau production\nand decay in Section 20.5. Section 20.6 presents studies\nof hadronic decays of the tau. That section begins with\na theoretical introduction before proceeding with presen-\ntations of measurements of branching fractions, measure-\nments of hadronic mass spectra and spectral functions,\nand searches for second-class currents. These results are\nthen interpreted in terms of tests of the Conserved Vector\nCurrent(CVC) hypothesis and used to extract the hadron\nvacuum polarization contribution to muonic g \u22122 in Sec-\ntion 20.7. Section 20.8 summarises values of |Vus| extracted\nfrom strange decays of the tau. We close with a brief sum-\nmary.156\n20.1 Introduction\nIn this section, we give a brief history of the tau from\nits discovery to the status before B Factory experiments.\nWe also discuss the cross section of the tau-pair produc-\ntion in the e+e\u2212collisions, e+e\u2212\u2192\u03c4 +\u03c4 \u2212as well as the\ncommonly used techniques to select tau-pair events.\nThe tau lepton discovery was reported in 1974 by Mar-\ntin Perl et al. (1975) using the SPEAR electron-positron\ncollider at SLAC scanning over center-of-mass (CM) en-\nergies of 3 GeV to 7.8 GeV. The group initially observed\n86 e+e\u2212\u2192e\u00b1\u00b5\u2213+ missing energy events above 3.8 GeV\nin CM with an expected background of 22 events from\nknown non-tau sources using the \u201cSLAC-LBL magnetic\ndetector\u201d (later called Mark I), which had a full 2\u03c0 az-\nimuthal angle and 50\u25e6\u2264\u03b8 \u2264130\u25e6polar angle acceptance.\nIt consisted of barrels of \u201ctrigger counters\u201d at two radii,\n156 Through out this section, charge-conjugate \u03c4 decays are\nimplied if it is not speci\ufb01ed explicitly.\ncylindrical wire chambers inside a 0.4 T solenoidal mag-\nnetic \ufb01eld, lead-scintillator shower counters outside the\n3 m\u00d73 m long magnet coil and muon wire chambers sur-\nrounding the iron return-yoke of the magnet. The group\ncollected more data and the following year published the\ncross section and lepton spectra from 105 signal events\n(above 34 background events) with which they demon-\nstrated that the events were most economically described\nby e+e\u2212\u2192U +U \u2212where U \u00b1 is a heavy lepton with a\nmass between 1.6 GeV/c2 and 1.8 GeV/c2 decaying via\nU \u2212\u2192\u03bdU\u2113\u2212\u03bd\u2113(Perl et al., 1976). Under that hypothesis\nthey also reported a value of the leptonic branching frac-\ntion, which was in excellent agreement with Paul Tsai\u2019s\ncalculations for a third generation heavy lepton published\na few years earlier in the classic and \ufb01rst comprehensive\npaper on tau physics (Tsai, 1971). Con\ufb01rmation of the\ndiscovery came over the next two years. The Maryland-\nPrinceton-Pavia magnetic detector group operating a sin-\ngle arm spectrometer at SPEAR reported an anomalous\nmuon event rate (Cavalli-Sforza et al., 1976). (Snow, 1976)\nanalysed the charged multiplicity of their \u201canomalous\u201d\nevents and concluded that a new heavy lepton was the sim-\nplest explanation. In 1977 the PLUTO (Burmester et al.,\n1977a,b) and DASP (Brandelik et al., 1977) groups re-\nported con\ufb01rmations of the discovery with their experi-\nments operating at DESY\u2019s DORIS electron-positron col-\nlider in Hamburg. By early 1977 the new particle was be-\ning considered a sequential lepton and was \ufb01rst named the\n\u03c4: \u201cSince there is now substantial evidence that it is a lep-\nton, we wish to designate it by a lower case Greek letter.\nWe use \u03c4 \u00b1 because it appears to be the third charged lep-\nton to be found and \u03c4\u03c1\u03b9\u03c4\u03bf\u03c2 means third in Greek.\u201d (Perl,\n1977). Martin Perl was awarded the 1995 Nobel Prize in\nphysics for this discovery.\nSince its discovery, properties of the tau have primarily\nbeen determined with precision using the e+e\u2212\u2192\u03c4 +\u03c4 \u2212\nprocess as a source of tau leptons. The cross section for\nthis process at \u221as = 10.58 GeV is 0.919\u00b10.003 nb (Baner-\njee, Pietrzyk, Roney, and W\u00b8as, 2008).\nThe text book (Stahl, 2000) is useful to learn more\nabout the history of tau lepton physics.\n20.2 Mass of the tau lepton\nMasses of quarks and leptons are fundamental parame-\nters of the Standard Model. They cannot be determined\nby the theory and must be measured. High precision mea-\nsurements of the mass of the tau lepton are important for\ntesting lepton universality and for calculating branching\nfractions that depend on the tau mass. Uncertainties in the\ntau mass have important consequences on the accuracy of\nthe calculated leptonic-decay rate of the tau lepton, since\nit is proportional to m5\n\u03c4:\n\u0393(\u03c4 \u2212\u2192\u2113\u2212\u03bd\u03c4\u03bd\u2113) = G2\n\u00b5m5\n\u03c4\n192\u03c03 f\n\u0012m2\n\u2113\nm2\u03c4\n\u0013 \u0012\n1 + 3\n5\nm2\n\u03c4\nm2\nW\n\u0013\n\u0012\n1 + \u03b1(m\u03c4)\n2\u03c0\n\u001425\n4 \u2212\u03c02\n\u0015\u0013\n,\n(20.2.1)\n\n638\nf(x) = 1 \u22128x + 8x3 \u2212x4 \u221212x2 ln x,\n(20.2.2)\nwhere \u2113= e, \u00b5 and \u03b1\u22121(m\u03c4) = 133.3. G\u00b5 is the Fermi cou-\npling constant determined precisely from the muon life-\ntime (Marciano and Sirlin, 1988).\nIn addition to the fundamental importance of the tau\nlepton mass in the Standard Model, separate measure-\nments of the masses of the \u03c4 + and \u03c4 \u2212in B Factory ex-\nperiments allow us to test the CPT theorem. CPT invari-\nance is a fundamental symmetry of any local \ufb01eld theory,\nincluding the Standard Model. Any evidence of CPT vio-\nlation would be evidence of local Lorentz violation and a\nsign of physics beyond the Standard Model.\nAt present the precision of the tau mass is dominated\nby the KEDR (Shamov et al., 2009) and BES (Bai et al.,\n1996a) measurements where the mass value was derived\nfrom the energy dependence of the e+e\u2212\u2192\u03c4 +\u03c4 \u2212cross\nsection near production threshold. However, both B Fac-\ntories performed the tau mass determination using a dif-\nferent technique, the so called pseudomass method origi-\nnally introduced by the ARGUS collaboration (Albrecht\net al., 1992a).\nIn this technique, the pseudomass is de\ufb01ned in terms of\nthe mass, energy and momenta of the tau decay products.\nFor the hadronic decays of the \u03c4 \u2212( \u03c4 \u2212\u2192h\u2212\u03bd\u03c4 and its\ncharge conjugate), the tau mass, m\u03c4, is given by\nm\u03c4 =\nq\nM 2\nh + 2(E\u2217\u03c4 \u2212E\u2217\nh)(E\u2217\nh \u2212P \u2217\nh cos \u03b8\u2217),(20.2.3)\nwhere Mh, E\u2217\nh, P \u2217\nh are the invariant mass, energy and the\nmagnitude of the three-momentum of the hadronic system\nh in the e+e\u2212CM frame, respectively. The energy of the\ntau lepton is given by E\u2217\n\u03c4 = \u221as/2, where \u221as = 10.58 GeV.\n\u03b8\u2217is the angle between the hadronic system and the \u03bd\u03c4\ndirection. Since the neutrino is undetected, one can not\nmeasure the angle \u03b8\u2217; thus one de\ufb01nes the pseudomass\nMmin by setting \u03b8\u2217= 0:\nMmin =\nq\nM 2\nh + 2(Ebeam \u2212E\u2217\nh)(E\u2217\nh \u2212P \u2217\nh), (20.2.4)\nwhich is less than or equal to the tau lepton mass.\nFigure 20.2.1 shows the typical pseudomass distribu-\ntion of the combined \u03c4 + and \u03c4 \u2212samples for \u03c4 \u00b1 \u2192\u03c0\u00b1\u03c0+\u03c0\u2212\n\u03bd\u03c4 candidates. A sharp kinematic cuto\ufb00is seen at Mmin \u223c\nm\u03c4. The smearing of the endpoint is caused by the initial\nand \ufb01nal state radiation and the detector resolution.\nTo determine the endpoint from the pseudomass distri-\nbution, a \ufb01t was performed to the data with an empirical\nfunction of the form\nF(x) = (p3 + p4x) tan\u22121\n\u0012p1 \u2212x\np2\n\u0013\n+ p5 + p6x,\n(20.2.5)\nwhere x is the pseudomass, and the pi are free parameters\nof the \ufb01t. Only the position of the endpoint, p1, is impor-\ntant in determining the tau mass. The relation between\nthe estimator p1 and the true tau lepton mass is obtained\nby using several Monte Carlo (MC) samples with di\ufb00erent\nFigure 20.2.1. Pseudomass Mmin distribution for \u03c4 \u00b1 \u2192\n\u03c0\u00b1\u03c0+\u03c0\u2212\u03bd\u03c4 candidates measured by the Belle, shown sepa-\nrately for positively and negatively charged tau decays. The\nsolid points with error bars correspond to \u03c4 + decays, while the\nopen points with error bars are \u03c4 \u2212decays. The solid curve is\nthe result of the \ufb01t to the \u03c4 + pseudomass distribution (Abe,\n2007c).\nvalues of tau mass. In the absence of initial and \ufb01nal state\nradiation (ISR/FSR) and with perfect detector resolution\none expects the relation between the p1 \ufb01t result and the\ngenerated tau mass to be linear with a slope of unity and\nzero o\ufb00set. With the inclusion of ISR/FSR e\ufb00ects and de-\ntector resolution non-zero o\ufb00set is expected.\nThe current status of the tau mass measurements is\nsummarized in Table 20.2.1 (see also Figure 20.2.2). In\nthis table, we also include the results from the measure-\nments by the BES and KEDR experiments, where the tau\nmass is measured from the \u03c4 +\u03c4 \u2212cross section around the\nproduction threshold. The systematics in the pseudomass\ntechnique and the threshold scan are quite di\ufb00erent. Nev-\nertheless, the results from the two methods are in good\nagreement with similar size of errors. The world average\nof the tau lepton mass is (Asner et al., 2010)\nm\u03c4 = (1776.77 \u00b1 0.15) MeV.\n(20.2.6)\nTable 20.2.1. Summary of recent tau mass measurements.\nExperiment\nm\u03c4,\nMeV\nRef.\nBES\n1776.96+0.18+0.25\n\u22120.21\u22120.17\nBai et al. (1996a)\nKEDR\n1776.69+0.17\n\u22120.19 \u00b1 0.15\nShamov et al. (2009)\nBelle\n1776.61 \u00b1 0.13 \u00b1 0.35\nAbe (2007c)\nBABAR\n1776.68 \u00b1 0.12 \u00b1 0.41\nAubert (2009ac)\nAverage\n1776.77 \u00b1 0.15\nAsner et al. (2010)\n\n639\n]\n2\n [MeV/c\n\u03c4\nm\n1770\n1775\n1780\nHFAG Average\n 0.15 (CL = 57.0%)\n\u00b1\n1776.77 \nPDG\u201910 Average\n 0.16\n\u00b1\n1776.82 \nKEDR 2009\n 0.15\n\u00b1 \n -0.19\n+0.17\n1776.69 \nBaBar 2009\n 0.41\n\u00b1\n 0.12 \n\u00b1\n1776.68 \nBelle 2007\n 0.35\n\u00b1\n 0.13 \n\u00b1\n1776.61 \nOPAL 2000\n 1.00\n\u00b1\n 1.60 \n\u00b1\n1775.10 \nCLEO 1997\n 1.20\n\u00b1\n 0.80 \n\u00b1\n1778.20 \nBES 1996\n -0.17\n+0.25\n \n -0.21\n+0.18\n1776.96 \nARGUS 1992\n 1.40\n\u00b1\n 2.40 \n\u00b1\n1776.30 \nDELCO 1978\n -4.00\n+3.00\n1783.00 \nHFAG-Tau\nSummer 2010\nFigure 20.2.2. Measurements and average value of m\u03c4 (Asner\net al., 2010).\nThe mass di\ufb00erence between \u03c4 + and \u03c4 \u2212, \u25b3m = m\u03c4 + \u2212\nm\u03c4 \u2212, can be measured precisely since many sources of\nsystematic error are common for \u03c4 + and \u03c4 \u2212and cancel\nout in \u25b3m. The values of \u25b3m measured by Belle and\nBABAR collaborations are\n\u25b3m = ( 0.05 \u00b1 0.23(stat) \u00b1 0.14(syst)) MeV (Belle),\n\u25b3m = (\u22120.61 \u00b1 0.23(stat) \u00b1 0.06(syst)) MeV (BABAR).\n(20.2.7)\nThe values of \u25b3m obtained for both experiments are con-\nsistent with zero within the errors, where the precisions are\ndominated by statistical uncertainty. The systematic shift\nin the mass di\ufb00erence has been estimated from the mass\ndi\ufb00erences for charged D and Ds mesons. The BABAR re-\nsult shows some deviation, however this is interpreted as\nhaving a 1.2% chance of obtaining a result as di\ufb00erent\nfrom zero as this under the condition of no CPT viola-\ntion, which has been ascertained using MC simulation.\nCombining both Belle and BABAR results, we obtain a\nmass di\ufb00erence of\n\u25b3m = (\u22120.24 \u00b1 0.18) MeV,\n(20.2.8)\nwhere the error is obtained by adding statistical and sys-\ntematic errors from both experiments in quadrature. The\nmean value is the weighted average of the two experiments.\nFrom these results, we obtain an upper limit on the mass\ndi\ufb00erence,\n|m\u03c4+ \u2212m\u03c4\u2212|/m\u03c4\nAVG < 3.0 \u00d7 10\u22124,\n(20.2.9)\nat 90% C.L. Where m\u03c4\nAVG is the averaged mass of m\u03c4+\nand m\u03c4\u2212. The results improve upon the previous OPAL\nconstraint (Abbiendi et al., 2000a) by one order of mag-\nnitude (see Table 20.2.2).\n(In addition to tau mass, a precise measurement of the\ntau-lepton lifetime is reported recently by the Belle collab-\noration (Belous, 2014). For the measurement, they use an\nTable 20.2.2. Measured upper limit of the \u03c4 + and \u03c4 \u2212mass\ndi\ufb00erence at 90% C.L.\nExperiment\n|m+\n\u03c4 \u2212m\u2212\n\u03c4 |/m\u03c4\nAV G\nRef\nOPAL\n< 3.0 \u00d7 10\u22123\nAbbiendi et al. (2000a)\nBelle\n< 2.8 \u00d7 10\u22124\nAbe (2007c)\nBABAR\n< 5.5 \u00d7 10\u22124\nAubert (2009ac)\nunique method that is only applicable in the asymmetric-\nenergy e+e\u2212colliders.)\n20.3 Tests of lepton universality\n20.3.1 Charged current universality between \u00b5-e\nTests of \u00b5 \u2212e universality can be expressed as\n\u0012g\u00b5\nge\n\u00132\n= B(\u03c4 \u2212\u2192\u00b5\u2212\u03bd\u00b5\u03bd\u03c4)\nB(\u03c4 \u2212\u2192e\u2212\u03bde\u03bd\u03c4)\nf(m2\ne/m2\n\u03c4)\nf(m2\u00b5/m2\u03c4), (20.3.1)\nwhere f(x) is given by Eq. (20.2.2), assuming that the\nneutrino masses are negligible (Tsai, 1971). Also, in this\nequation, small corrections of the order m2\ne,\u00b5/m2\nW and\nthe di\ufb00erence between \u03b1(me) and \u03b1(m\u00b5) are ignored, see\nEq. (20.2.2). The relation between the weak coupling con-\nstant gl and the Fermi coupling constant Gl, for the lepton\nl, is given by\nGl =\ng2\nl\n4\n\u221a\n2M 2\nW\n.\n(20.3.2)\nThe HFAG group has performed a constrained \ufb01t\n(Amhis et al., 2012) using 157 branching fraction measure-\nments and 47 constraint equations that \ufb01t 86 quantities.\nFor example, there are measurements of the total branch-\ning fraction of all decays to three charged pions or kaons\nplus any number of neutrals. In addition, there are sepa-\nrate measurements of exclusive branching fractions to spe-\nci\ufb01c \ufb01nal states that have three identi\ufb01ed charged mesons.\nOne constraint is that the sum of exclusive 3-prong decays,\nthe decays involving three charged particles in their \ufb01nal\nstatess, must equal the inclusive 3-prong measurement.\nThe \ufb01t is statistically consistent with the constraint that\nthe sum of all base modes is equal to one, referred to as\nthe \u201cunitarity constraint\u201d, but the unitarity constraint is\nnot explicitly applied. From that \ufb01t, which uses all avail-\nable data including the recent BABAR\u2019s results (Aubert,\n2010f), we obtain B(\u03c4 \u2212\u2192\u00b5\u2212\u03bd\u00b5\u03bd\u03c4)/B(\u03c4 \u2212\u2192e\u2212\u03bde\u03bd\u03c4) =\n0.9761 \u00b1 0.0028, which includes a correlation coe\ufb03cient of\n23% between the branching fractions. This yields a value\nof\n\u0010\ng\u00b5\nge\n\u0011\n= 1.0018 \u00b1 0.0014, which is consistent with the\nSM value.\nThis prediction from tau decays is more precise than\nthe other determinations:\n\u2013 We\naverage\nthe\nmeasurements\nof\nB(\u03c0\n\u2192\ne\u03bde(\u03b3))/B(\u03c0 \u2192\u00b5\u03bd\u00b5(\u03b3)) = (1.2265 \u00b1 0.0034 (stat) \u00b1\n\n640\n0.0044 (syst)) \u00d7 10\u22124 from TRIUMF (Britton et al.,\n1992) and = (1.2346 \u00b1 0.0035 (stat) \u00b1 0.0036 (syst))\n\u00d7 10\u22124 from PSI (Czapek et al., 1993), to obtain a\nvalue of (1.2310 \u00b1 0.0037) \u00d7 10\u22124. Comparing this\nwith the prediction of (1.2352 \u00b1 0.0001) \u00d7 10\u22124 from\nrecent theoretical calculations (Cirigliano and Rosell,\n2007), we obtain a value of\n\u0010\ng\u00b5\nge\n\u0011\n= 1.0017 \u00b1 0.0015.\n\u2013 The\nratio\nB(K \u2192e\u03bde(\u03b3))/B(K \u2192\u00b5\u03bd\u00b5(\u03b3))\nhas\nrecently\nbeen\nmeasured\nvery\nprecisely\nby\nthe\nKLOE (Ambrosino et al., 2009b) and the NA62 (Goud-\nzovski, 2011) collaborations. Using the new world\naverage\nvalue\nof\n(2.487 \u00b1 0.012) \u00d7 10\u22125\nfrom\nGoudzovski\n(2010),\nand\nthe\npredicted\nvalue\nof\n(2.477 \u00b1 0.001) \u00d7 10\u22125 from Cirigliano and Rosell\n(2007), we obtain\n\u0010\ng\u00b5\nge\n\u0011\n= 0.9980 \u00b1 0.0025.\n\u2013 From the report of the FlaviaNet Working Group on\nKaon Decays (Antonelli et al., 2010b), we obtain\n\u0010\ng\u00b5\nge\n\u0011\n= 1.0010 \u00b1 0.0025 using measurements of\nB(K \u2192\u03c0\u00b5\u03bd)/B(K \u2192\u03c0e\u03bd).\n\u2013 From the report of the LEP Electroweak Work-\ning Group (Alcaraz et al., 2006), we obtain\n\u0010\ng\u00b5\nge\n\u0011\n= 0.997 \u00b1 0.010 using measurements of B(W\n\u2192\n\u00b5\u03bd\u00b5)/B(W \u2192e\u03bde).\n20.3.2 Charged current universality between \u03c4-\u00b5\nTau-muon universality is tested with\n\u0012g\u03c4\ng\u00b5\n\u00132\n= B(\u03c4 \u2212\u2192h\u2212\u03bd\u03c4)\nB(h\u2212\u2192\u00b5\u2212\u03bd\u00b5)\n2mhm2\n\u00b5\u03c4h\n(1 + \u03b4h)m3\u03c4\u03c4\u03c4\n \n1 \u2212m2\n\u00b5/m2\nh\n1 \u2212m2\nh/m2\u03c4\n!2\n(20.3.3)\nwhere h = \u03c0 or K and the radiative corrections are \u03b4\u03c0 =\n(0.16 \u00b1 0.14)% and \u03b4K = (0.90 \u00b1 0.22)% (Decker and\nFinkemeier, 1994, 1995; Marciano and Sirlin, 1993).\nUsing the world average mass and lifetime values and\nmeson decay rates (Nakamura et al., 2010) and our uni-\ntarity constrained \ufb01t including recent BABAR results (Au-\nbert, 2010f), we determine\n\u0010\ng\u03c4\ng\u00b5\n\u0011\n= 0.9966 \u00b1 0.0030 and\n0.9860 \u00b1 0.0073 from the pionic and kaonic branching\nfractions, respectively, where the correlation coe\ufb03cient be-\ntween these values is 13.10%. Combining these results, we\nobtain\n\u0010\ng\u03c4\ng\u00b5\n\u0011\n= 0.9954 \u00b1 0.0029, which is 1.6 \u03c3 below the\nSM expectation.\nWe also test lepton universality between \u03c4 and \u00b5 (e),\nby comparing the average electronic (muonic) branching\nfractions of the tau lepton with the predicted branching\nfractions from measurements of the \u03c4 and \u00b5 lifetimes and\ntheir respective masses (Nakamura et al., 2010), using\nknown electroweak and radiative corrections (Marciano\nand Sirlin, 1993). This gives\n\u0010\ng\u03c4\ng\u00b5\n\u0011\n= 1.0011 \u00b1 0.0021\nand\n\u0010\ng\u03c4\nge\n\u0011\n= 1.0030 \u00b1 0.0021. The correlation coe\ufb03cients\nbetween the determination of\n\u0010\ng\u03c4\ng\u00b5\n\u0011\nfrom the electronic\nbranching fraction with the ones obtained from pionic and\nkaonic branching fractions are 48.16% and 21.82%, respec-\ntively. Averaging these three values, we obtain\n\u0010\ng\u03c4\ng\u00b5\n\u0011\n=\n1.0001 \u00b1 0.0020, which is consistent with the SM value.\nIn Fig. 20.3.1, we compare these above determinations\nwith each other and with the values obtained from W\ndecays (Alcaraz et al., 2006).\n20.4 Search for lepton \ufb02avor violation in tau\ndecays\nIn order to progress beyond the Standard Model it is nec-\nessary to incorporate results from many di\ufb00erent measure-\nments and interpret them within a cohesive theoretical\nframework. This will include results from direct searches\n(and discoveries) of new particles at the energy frontier\nof the LHC, neutrino oscillation measurements, g \u22122 and\nelectric dipole moment measurements, as well as searches\n(and discoveries) of LFV in the decays of leptons and\nmesons. Discoveries at the LHC alone will be insu\ufb03cient\nto determine the underlying theoretical structures respon-\nsible for New Physics. Moreover, a discovery of \u00b5+ \u2192e+\u03b3\nalone will not provide su\ufb03cient information to nail down\nthe underlying LFV mechanism or even to identify an un-\nderlying theory: it is critical to probe all LFV modes and\nsearches for \u00b5+ \u2192e+\u03b3 search need to be augmented by\nstudies of \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3\nas well as \u03c4 \u00b1 \u2192e\u00b1\u03b3 . Even in\nthe presence of the existing and projected \u00b5+ \u2192e+\u03b3\nbounds, \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3\ndecays are predicted to occur at\nrates that are accessible at current experiments in many\nmodels (Aushev et al., 2010; Bona et al., 2007b). In fact,\nthe full set of measurements of \u00b5 and \u03c4 LFV processes\nare required as in many models there are strong correla-\ntions between the expected rates of the di\ufb00erent channels.\nIn a supersymmetric seesaw model describing potential\nLFV (Babu and Kolda, 2002; Sher, 2002), for example,\nthere is an expectation that the speci\ufb01c relative rates of\nB(\u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3) : B(\u03c4 \u00b1 \u2192\u00b5\u00b1\u00b5+\u00b5\u2212) : B(\u03c4 \u2192\u00b5\u03b7) are de-\npendent on the model parameters. In the unconstrained\nminimal supersymmetric model (MSSM), which includes\nvarious correlations between the \u03c4 and \u00b5 LFV rates, \u03c4\nLFV branching fractions can be as high as 10\u22127 (Brig-\nnole and Rossi, 2004; Goto, Okada, Shindou, and Tanaka,\n2008) even with the strong experimental bounds on muon\nLFV.\n20.4.1 Tau lepton data samples and search strategies\nWith 1,550 fb\u22121 of data currently collected between the\nBelle and BABAR experiments and the e+e\u2212\u2192\u03c4 +\u03c4 \u2212cross\nsection of 0.919 nb (Banerjee, Pietrzyk, Roney, and W\u00b8as,\n2008), the world sample of \u03c4-leptons produced at the e+e\u2212\ncolliders now exceeds 109 which allows for experimental\nprobing of LFV processes at the O(10\u22127) to O(10\u22128) lev-\nels.\nThe analyses typically select \u03c4-pair events with the ap-\npropriate charged-particle topology, removing non-\u03c4 events\n\n641\n|e\n/g\n\u00b5\n|g\n0.9\n1\n)\n\u03c4\n\u03bd \ne\n\u03bd\n e \n\u2192\n \u03c4\n)/(\n\u03c4\n\u03bd \n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n \u03c4\nHFAG Fit (\n 0.0014\n\u00b1\n1.0019 \n)\ne\n\u03bd\n e \n\u2192\n \n\u03c0\n)/(\n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n \n\u03c0\nTRIUMF, PSI (\n 0.0015\n\u00b1\n1.0017 \n)\ne\n\u03bd\n e \n\u2192\n)/(K \n\u00b5\n\u03bd \n\u00b5\n \n\u2192\nNA62, KLOE (K \n 0.0025\n\u00b1\n0.9980 \n)\ne\n\u03bd\n e \n\u03c0 \n\u2192\n)/(K \n\u00b5\n\u03bd \n\u00b5\n \n\u03c0 \n\u2192\nFlaviaNet (K \n 0.0025\n\u00b1\n1.0010 \n)\ne\n\u03bd\n e \n\u2192\n)/(W \n\u00b5\n\u03bd \n\u00b5\n \n\u2192\nLEP EW WG (W \n 0.0100\n\u00b1\n0.9970 \nHFAG-Tau\nSummer 2010\n|\n\u00b5\n/g\n\u03c4\n|g\n0.9\n1\n)\n\u03c4\n\u03bd\n, K \n\u03c4\n\u03bd \n\u03c0\n, \n\u03c4\n\u03bd \ne\n\u03bd\n e \n\u2192\n \u03c4\nHFAG Average (\n 0.0020\n\u00b1\n1.0001 \n)\n\u03c4\n\u03bd\n, K \n\u03c4\n\u03bd \n\u03c0 \n\u2192\n \u03c4\nHFAG Average (\n 0.0029\n\u00b1\n0.9954 \n)\n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n)/(K \n\u03c4\n\u03bd\n K \n\u2192\n \u03c4\nHFAG Fit (\n 0.0073\n\u00b1\n0.9860 \n) \n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n \n\u03c0\n)/(\n\u03c4\n\u03bd \n\u03c0 \n\u2192\n \u03c4\nHFAG Fit (\n 0.0030\n\u00b1\n0.9966 \n\u03c4\u03c4/\n\u00b5\n\u03c4 \n\u00d7\n) \n\u03c4\n\u03bd \ne\n\u03bd\n e \n\u2192\n \u03c4\nHFAG Fit (\n 0.0021\n\u00b1\n1.0011 \n)\n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n)/(W \n\u03c4\n\u03bd \u03c4 \n\u2192\nLEP EW WG (W \n 0.0130\n\u00b1\n1.0390 \nHFAG-Tau\nSummer 2010\n|e\n/g\n\u03c4\n|g\n0.9\n1\n \n\u03c4\u03c4/\n\u00b5\n\u03c4 \n\u00d7\n) \n\u03c4\n\u03bd \n\u00b5\n\u03bd \n\u00b5\n \n\u2192\n \u03c4\nHFAG Fit (\n 0.0021\n\u00b1\n1.0030 \n)\ne\n\u03bd\n e \n\u2192\n)/(W \n\u03c4\n\u03bd \u03c4 \n\u2192\nLEP EW WG (W \n 0.0140\n\u00b1\n1.0360 \nHFAG-Tau\nSummer 2010\nFigure 20.3.1. Measurements of lepton universality from W,\nkaon, pion, and tau decays.\nwith an impact as minimal as possible on the signal e\ufb03-\nciency. A candidate event is divided into hemispheres in\nthe center-of-mass frame where each hemisphere contains\neither the \u03c4 + or \u03c4 \u2212decay products. The \u03c4 decay asso-\nciated with each hemisphere is then considered a possi-\nble candidate for the LFV decay under consideration, as\ncan be seen in the BABAR detector display of a simulated\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212; \u03c4 + \u2192e+ \u00af\u03bd\u03c4\u03bde; \u03c4 \u2212\u2192\u00b5\u2212\u03b3 event depicted\nin Figure 20.4.1. Whereas Standard Model \u03c4-decays have\nat least one neutrino, the LFV decay products have a com-\nbined energy, E\u2113X, equal to the energy of the \u03c4 which is\napproximately equal to the beam energy in the center-of-\nmass, \u221as/2, and a mass (m\u2113X) equal to that of the \u03c4.\nUsing a two dimensional signal region in the m\u2113X vs \u2206E\nplane, the signal is separated from the Standard Model \u03c4-\ndecay backgrounds with minimal loss of e\ufb03ciency, where\n\u2206E = E\u2113X \u2212\u221as/2. The distributions for the \u03c4 \u00b1 \u2192e\u00b1\u03b3\nand \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3\ndecays in that plane are shown in Fig-\nure 20.4.2 for the BABAR analysis, where the peaking at\n\u2206E = 0 and m\u2113X = m\u03c4 = 1777 MeV/c2 is evident. For\nthe lepton-photon invariant mass BABAR calculates mEC,\nwhich is obtained from a kinematic \ufb01t that requires the\ncenter-of-mass tau energy to be \u221as/2 after assigning the\norigin of the \u03b3 candidate to the point of closest approach\nof the signal lepton track to the e+e\u2212collision axis. Use\nof a \u201csignal box\u201d in the \u2206E-m\u2113X plane encompassing\nevents within approximately two standard deviations of\n\u2206E = 0 and m\u2113X = m\u03c4 = 1777 MeV/c2 serves as the\nmost powerful requirement in the searches for LFV in \u03c4\ndecay. The signal peaks near zero in the distribution of\n\u2206E = E\u2113X \u2212\u221as/2 and typically has a standard deviation\nof around 50 MeV. Using a beam-energy constrained mass\nand constraining photons to come from the same primary\nvertex as the charged particles in the event enables a res-\nolution on m\u2113X of 9 MeV to be achieved.\nThe analyses are normally optimized to give the best\n\u201cexpected upper limit\u201d using MC simulations of the signal\nand backgrounds. Signal e\ufb03ciency (\u03f5) is initially estimated\nusing simulated events and typically lies between 2% and\n10%, depending on the channel under study. The com-\nponents of a generic \u03c4 LFV decay selection e\ufb03ciency are\nroughly: trigger (90%), acceptance/reconstruction (70%),\ncharged-particle hemisphere topology (1-vs-1 or 1-vs-3:\n70%), particle identi\ufb01cation (50%), requirements apart\nfrom those on \u2206E and m\u2113X (50%), \u2206E vs m\u2113X signal\nbox requirements (50%). Data-driven corrections are ap-\nplied to the simulated signal e\ufb03ciencies using the results\nof comparisons between data and simulated control sam-\nples.\nEstimates of the expected number of background events\n(Nbkd) are usually estimated using the distribution shapes\nfrom the Monte Carlo simulation of backgrounds with the\nnormalization obtained from the data in the regions out-\nside the signal box. These BABAR and Belle analyses are\n\u201cblind\u201d in the sense that the analysts have no knowledge\nof the data in the signal region when optimizing for a best\n\u201cexpected upper limit\u201d and estimating systematic uncer-\ntainties. The data in the signal region is \u201cunblinded\u201d only\nafter these steps are completed, and the analyst learns the\nnumber of events observed in the signal region (Nobs), ei-\nther making a discovery, or - as has been the case to date\n- setting an upper limit on the process (see Chapter 14 for\na general discussion of blind analysis techniques).\nNobs and Nbkd together gives the number of signal\nevents (Nsig). When Nobs-Nbkd is consistent with zero,\n\n642\nFigure 20.4.1. A BABAR event display with a simulated LFV \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3\ndecay opposite a Standard Model \u03c4 + \u2192e+ \u00af\u03bd\u03c4\u03bde\ndecay\n E (GeV)\n6\n-1\n-0.5\n0\n0.5\n)\n2\n (GeV/c\nEC\nm\n1.6\n1.7\n1.8\n1.9\n2\nBABAR\n E (GeV)\n6\n-1\n-0.5\n0\n0.5\n)\n2\n (GeV/c\nEC\nm\n1.6\n1.7\n1.8\n1.9\n2\nBABAR\nFigure 20.4.2. The 2\u03c3 elliptical signal-box for \u03c4 \u00b1 \u2192e\u00b1\u03b3 (Left) and \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3 (Right) decays in the mEC vs. \u2206E plane in\nthe BABAR analysis. mEC is the invariant mass of the lepton-photon pair as discussed in the text. Data are shown as red dots\nand contours containing 90% (50%) of signal MC events are shown as the yellow (green) shaded regions (Aubert, 2010i).\nan upper limit on Nsig (N UL\n90 ) is established. Conceptu-\nally, the 90%C.L. branching ratio upper limit is obtained\nfrom:\nBUL\n90 = N UL\n90\n2N\u03c4\u03c4\u03f5 =\nN UL\n90\n2L\u03c3\u03c4\u03c4\u03f5,\n(20.4.1)\nwhere N\u03c4\u03c4 = L\u03c3\u03c4\u03c4 is the number of \u03c4-pairs produced in\ne+e\u2212collisions obtained from the integrated luminosity,\nL, and \u03c4-pair production cross section, \u03c3\u03c4\u03c4. In practice,\nwhen Nbkd is more than a few events, Nsig and Nbkd are\ndetermined from a \ufb01t.\n20.4.2 Results on LFV decays of the tau from Belle\nand BABAR\nIn performing searches, LFV decays can be conveniently\nclassi\ufb01ed as \u03c4 \u00b1 \u2192\u2113\u00b1\u03b3, \u03c4 \u00b1 \u2192\u2113\u00b1\n1 \u2113+\n2 \u2113\u2212\n3 and \u03c4 \u00b1 \u2192\u2113\u00b1h0\nwhere \u2113is either an electron or muon and h0 represents a\nhadronic system. For the BABAR and Belle searches, the\nh0 has been categorized in three ways: i) a pseudoscalar\nmeson: e.g. \u03c00, \u03b7, \u03b7\u2032, K0\nS; ii) a neutral vector meson: e.g.\n\u03c1, \u03c9, K\u2217(892), \u03c6; and iii) inclusive two charged meson de-\ncays, h0 = h+\n1 h\u2212\n2 where h\u00b1\n1(2) is either \u03c0\u00b1 or K\u00b1.\nThe most recent \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3 and \u03c4 \u00b1 \u2192e\u00b1\u03b3 results re-\nported by Belle (Hayasaka, 2008) use a data sample having\nan integrated luminosity of 535 fb\u22121 which corresponds to\n492\u00d7106 \u03c4-pair events. Figure 20.4.3 shows the distribu-\ntion in the m\u2113\u03b3 vs \u2206E plane for the selected sample in\nthe Belle experiment. The main \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3 backgrounds\nin these searches arise from e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3 events and\ne+e\u2212\u2192\u03c4 +\u03c4 \u2212\u03b3 events where one of the \u03c4\u2019s decays via\n\u03c4 \u2192\u00b5\u03bd\u03bd. In both cases the photon, from initial state\nradiation in the latter and initial or \ufb01nal state radiation\n\n643\nM\ninv\n (GeV/c\n2\n)\n\u2206E (GeV)\n1.65\n1.7\n1.75\n1.85\n1.8\n-0.4\n-0.3\n-0.2\n0.1\n-0.1\n0\n(a)\nM\ninv\n (GeV/c\n2\n)\n\u2206E (GeV)\n1.65\n1.7\n1.75\n1.85\n1.8\n-0.4\n-0.3\n-0.2\n-0.1\n0\n0.1\n(b)\nFigure 20.4.3. The distribution in the m\u2113\u03b3 vs \u2206E plane for (a) \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3 and (b) \u03c4 \u00b1 \u2192e\u00b1\u03b3 for the selected sample in the\nBelle analysis. The solid circles and the shaded boxes show the data and the signal MC, respectively. The outer (inner) ellipse\nshows the 3 (2)\u03c3 signal region (Hayasaka, 2008).\nTable 20.4.1. Summary of 90% C.L. upper limits on B(\u03c4 \u2212\u2192\u2113\u2212\u03b3) and B(\u03c4 \u2212\u2192\u2113\u2212\n1 \u2113+\n2 \u2113\u2212\n3 ) LFV \u03c4\ndecays. Nobs and Nbkg are the number of events observed in the signal region and the estimated\nbackground, respectively. BF is the upper limit (90% C.L.) on the branching fraction.\nChannel\nBelle\nBABAR\n(Hayasaka, 2008, 2010)\n(Aubert, 2010i; Lees, 2010a)\nNobs (Nbkg)\nBF\nNobs (Nbkg)\nBF\nevents\n(10\u22128)\nevents\n(10\u22128)\n\u03c4 \u2212\u2192\u00b5\u2212\u03b3\n10 (13.9+6.0\n\u22124.8)\n4.5\n2 (3.6 \u00b1 0.7)\n4.4\n\u03c4 \u2212\u2192e\u2212\u03b3\n5 (5.14+3.86\n\u22122.81)\n12\n0 (1.6 \u00b1 0.4)\n3.3\n\u03c4 \u2212\u2192\u00b5\u2212e+e\u2212\n0 (0.04\u00b10.04)\n1.8\n0 (0.64\u00b10.19)\n2.2\n\u03c4 \u2212\u2192\u00b5\u2212\u00b5+\u00b5\u2212\n0 (0.13\u00b10.06)\n2.1\n0 (0.44\u00b10.17)\n3.3\n\u03c4 \u2212\u2192e\u2212\u00b5+\u00b5\u2212\n0 (0.10\u00b10.04)\n2.7\n0 (0.54\u00b10.14)\n3.2\n\u03c4 \u2212\u2192e\u2212e+e\u2212\n0 (0.21\u00b10.15)\n2.7\n0 (0.12\u00b10.02)\n2.9\n\u03c4 \u2212\u2192e\u2212\u00b5+e\u2212\n0 (0.01\u00b10.01)\n1.5\n0 (0.34\u00b10.12)\n1.8\n\u03c4 \u2212\u2192\u00b5\u2212e+\u00b5\u2212\n0 (0.02\u00b10.02)\n1.7\n0 (0.03\u00b10.02)\n2.6\nin the former, combines with a muon to accidentally fall\nwithin the signal box. The e+e\u2212\u2192\u03c4 +\u03c4 \u2212\u03b3; \u03c4 \u2212\u2192\u00b5\u2212\u03bd\u03c4\u03bd\u00b5\nevents can be classi\ufb01ed as \u201cirreducible\u201d because the events\nare genuine \u03c4-pair events and the \u00b5 and \u03b3 are correctly\nidenti\ufb01ed and measured. A similar irreducible background\nsource from e+e\u2212\u2192\u03c4 +\u03c4 \u2212\u03b3; \u03c4 \u2212\u2192e\u2212\u03bd\u03c4\u03bde exists. Belle\nset a 90% C.L. upper limit on the number of signal events\nfor \u03c4 \u2192\u00b5\u03b3 (\u03c4 \u2192e\u03b3) of 2.0 (3.34) events. These yield\nupper limits of B(\u03c4 \u2192\u00b5\u03b3) < 4.5 \u00d7 10\u22128 and B(\u03c4 \u2192\ne\u03b3) < 1.2 \u00d7 10\u22127. BABAR\u2019s 2009 published 90% C.L. up-\nper limits using a 534 fb\u22121 data sample are 4.4\u00d710\u22128 and\n3.3\u00d710\u22128 on B(\u03c4 \u2192\u00b5\u03b3) and B(\u03c4 \u2192e\u03b3), respectively (Au-\nbert, 2010i). Both experiments report classical frequentist\ncon\ufb01dence intervals. These are reported in Table 20.4.1.\nBelle (Hayasaka, 2010) and BABAR (Lees, 2010a) also\nsearched for \u03c4 \u2192\u21131\u21132\u21133. Fig. 20.4.4 shows the distribu-\ntions in the m\u2113\u2113\u2113vs \u2206E plane for the \u03c4 \u2192\u21131\u21132\u21133 candi-\ndate events before the \ufb01nal selection. There is essentially\nno background in these samples, since the requirement for\nthree leptons is tight and can reduce the background e\ufb00ec-\ntively. No evidence for a signal is seen by either experiment\nand the 90% C.L. upper limits on the branching fractions\nare presented in Table 20.4.1. Unlike the \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3 and\n\u03c4 \u00b1 \u2192e\u00b1\u03b3 searches, there is no irreducible background\n\n644\nTable 20.4.2. Summary of 90% C.L. upper limit on B(\u03c4 \u2212\u2192\u2113\u2212h0) in units of (10\u22128) where\n\u2113= \u00b5 or e and h0 is either a pseudoscalar (upper half) or vector meson (lower half) from the\nBelle (Hayasaka, 2011; Miyazaki, 2006, 2010, 2011; Nishio, 2008) and BABAR (Aubert, 2007ar,\n2008au, 2009o,ao) experiments.\nChannel\n\u2113= e\n(10\u22128)\n\u2113= \u00b5\n(10\u22128)\nBelle\nBABAR\nBelle\nBABAR\n\u03c4 \u2212\u2192\u2113\u2212\u03c00\n2.2\n13\n2.7\n11\n\u03c4 \u2212\u2192\u2113\u2212\u03b7\n4.4\n16\n2.3\n15\n\u03c4 \u2212\u2192\u2113\u2212\u03b7\u2032\n3.6\n24\n3.8\n14\n\u03c4 \u2212\u2192\u2113\u2212K0\nS\n2.6\n3.3\n2.3\n4.0\n\u03c4 \u2212\u2192\u2113\u2212\u03c6\n3.1\n3.1\n8.4\n19.0\n\u03c4 \u2212\u2192\u2113\u2212\u03c10\n1.8\n4.6\n1.2\n2.6\n\u03c4 \u2212\u2192\u2113\u2212\u03c9\n4.8\n11\n4.7\n10\n\u03c4 \u2212\u2192\u2113\u2212K\u22170\n3.2\n5.9\n7.2\n17.0\n\u03c4 \u2212\u2192\u2113\u2212K\u22170\n3.4\n4.6\n7.0\n7.3\nat the current luminosities. The Belle \u03c4 \u2192\u21131\u21132\u21133 analy-\nsis uses 719\u00d7106 \u03c4-pairs whereas BABAR reports on an\nanalysis using 431\u00d7106 \u03c4-pairs. Note that, in addition\nto the reactions violating \ufb02avor, Table Table 20.4.1 also\nlists bounds of similar magnitude on \u03c4 \u2212\u2192e\u2212\u00b5+e\u2212and\n\u03c4 \u2212\u2192\u00b5\u2212e+\u00b5\u2212, which simultaneously violate the lepton-\n\ufb02avors, Le, L\u00b5 and L\u03c4, but the total lepton number is\nconserved.\nBoth Belle, using 901 fb\u22121 (Hayasaka, 2011), and\nBABAR, using 339 fb\u22121 (Aubert, 2007ar), have published\nbounds on LFV \u03c4 decays involving a lepton and a \u03c00, \u03b7 or\n\u03b7\u2032 pseudoscalar. Belle has also published on searches for\n\u03c4 \u2192\u2113K0\nS and \u03c4 \u2192\u2113K0\nSK0\nS\n(Miyazaki, 2010). Searches\nfor LFV involving the \u03c9 vector meson, \u03c4 \u2192\u2113\u03c9, have been\nreported by both experiments with BABAR employing a\ndata set of 384 fb\u22121(Aubert, 2008au) whereas Belle used\n854 fb\u22121(Miyazaki, 2011). From the same data set Belle\nhas also searched for \u03c4 \u2192\u2113\u03c1, \u03c4 \u2192\u2113\u03c6, \u03c4 \u2192\u2113K\u22170 and\n\u03c4 \u2192\u2113K\u22170. The 90% C.L. upper limits on these processes\nare typically around 5\u00d710\u22128 and are listed in Table 20.4.2.\nBABAR, using a 221 fb\u22121, sets limits on LFV inclusive de-\ncays with two charged mesons, \u03c4 \u00b1 \u2192\u2113\u00b1h+\n1 h\u2212\n2 , where no\nassumptions are made on the resonance structure of the\nhadronic \ufb01nal state (Aubert, 2005ab). These bounds range\nfrom 1 \u00d7 10\u22127 to 5 \u00d7 10\u22127, depending on the \ufb01nal state.\nBelle\u2019s equivalent analysis used 854 fb\u22121 and set bounds\nranging from 2.0 \u00d7 10\u22128 to 8.4 \u00d7 10\u22128 (Miyazaki, 2013).\nThe status of searches for lepton \ufb02avor violation in \u03c4\ndecays is summarized in Figure 20.4.5. A table of these\nresults and the corresponding references are provided by\nthe HFAG report of Amhis et al. (2012).\n20.4.3 Future Prospects\nBy the end of 2010 Belle and BABAR had collected a com-\nbined data sample of roughly 1.5 ab\u22121, corresponding to\nthe production of about 1.4\u00d7109 \u03c4 pairs, and those exper-\niments can be expected to update their analyses with their\ncomplete data sets over the next year or two. However, Su-\nperKEKB, a new signi\ufb01cantly higher luminosity e+e\u2212col-\nlider designed to operate at the \u03a5 resonances, but mainly\non the \u03a5(4S), is on the horizon. It will provide exciting\nnew opportunities for the discovery and potential study\nof LFV decays of the \u03c4 lepton. The physics potential of a\nsuper \ufb02avor factory operating with a luminosity of about\n1036cm\u22122s\u22121 has been discussed extensively in (Aushev\net al., 2010; Bona et al., 2007b) Such a facility is expected\nto probe LFV \u03c4 \u00b1 \u2192\u2113\u00b1\u2113+\u2113\u2212and \u03c4 \u00b1 \u2192\u2113\u00b1h0 decays,\nwhich have no irreducible backgrounds, at the O(10\u221210)\nlevel. However, the initial state photon accidental back-\nground will prevent the \u03c4 \u00b1 \u2192\u2113\u00b1\u03b3 decays from being\nprobed below the level of a few 10\u22129. However it should\nbe noted that this irreducible background can be removed\nif one were to accumulate a large sample of tau leptons\nnear production threshold (below about 4 GeV).\n20.5 CP violation in the tau lepton system\nUnderstanding the origin of CP violation is one of the\nmost important outstanding questions in particle physics.\nTo date CP violation has been observed only in the K and\nB meson system157. In the Standard Model, all observed\nCP violation e\ufb00ects can be accommodated by a single irre-\nducible, complex phase in the CKM quark mixing matrix.\n157 The LHCb collaboration reported in 2011 the 3.5\u03c3 sig-\nni\ufb01cance for the di\ufb00erence of the direct CP\nasymmetry\n\u2206ACP = ACP (K+K\u2212)\u2212ACP (\u03c0+\u03c0\u2212), where ACP (K+K\u2212) and\nACP (\u03c0+\u03c0\u2212) are the CP asymmetry for D0(D0) \u2192K+K\u2212and\nD0(D0) \u2192\u03c0+\u03c0\u2212, respectively (Aaij et al., 2012c). However,\ntheir recent update does not con\ufb01rm this observation (Aaij\net al., 2013e). So more data are needed to establish CP\nviolation in the D meson system.\n\n645\n-0.4\n-0.2\n0\n0.2\n1.7\n1.8\nmeee (GeV/c2)\n\u2206E (GeV)\n(a) \u03c4-\u2192e-e+e-\n-0.2\n0\n0.2\n1.7\n1.75\n1.8\n1.85\nm\u00b5\u00b5\u00b5 (GeV/c2)\n\u2206E (GeV)\n(b) \u03c4-\u2192\u00b5-\u00b5+\u00b5-\n-0.2\n0\n0.2\n1.7\n1.75\n1.8\n1.85\nme\u00b5\u00b5 (GeV/c2)\n\u2206E (GeV)\n(c) \u03c4-\u2192e-\u00b5+\u00b5-\n-0.4\n-0.2\n0\n0.2\n1.65\n1.7\n1.75\n1.8\n1.85\nm\u00b5ee (GeV/c2)\n\u2206E (GeV)\n(d) \u03c4-\u2192\u00b5-e+e-\nFigure 20.4.4. Distributions in the M\u2113\u2113\u2113vs \u2206E plane for the selected events for (a) \u03c4 \u00b1 \u2192e\u00b1e+e\u2212, (b) \u03c4 \u00b1 \u2192\u00b5\u00b1\u00b5+\u00b5\u2212, (c)\n\u03c4 \u00b1 \u2192e\u00b1\u00b5+\u00b5\u2212and (d) \u03c4 \u00b1 \u2192\u00b5\u00b1e+e\u2212modes in the Belle analysis (Hayasaka, 2010). The solid circles are data. The shaded\nboxes show the MC signal distribution with arbitrary normalization. The ellipse is the signal region used for evaluating the\nsignal yield.\nThe CKM mechanism alone is however not su\ufb03cient\nenough to explain the observed matter-antimatter asym-\nmetry in the universe, and thus new sources of CP viola-\ntion are necessary. In this regard, one important area is\nthe lepton sector. In the neutral lepton sector, the 3 \u00d7 3\nneutrino mixing matrix can accommodate CP violation.\nA search for signs of CP violation in the neutrino sector is\nthus a primary task in future neutrino experiments. While\nin the charged lepton sector, there is no such mixing, so\nmixing-induced CP violation is not expected. However,\nphysics beyond the Standard Model could produce CP\nviolation in processes involving charged leptons; we would\nexpect such e\ufb00ects to be enhanced for tau leptons because\nof their large mass.\nIn this section, we \ufb01rst discuss CP violation in tau-\npair production, which is usually parameterized in terms\nof the electric dipole moment (EDM) of the tau lepton.\nWe then describe various searches for the CP violation in\ntau decays.\n20.5.1 Electric dipole moment of the tau lepton\nIf a particle has an EDM value of d, the Hamiltonian H\ndescribing a non-relativistic particle of spin S placed in a\nelectric \ufb01eld E can be given by\nH = \u2212d E \u00b7 S\nS .\n(20.5.1)\nThis interaction violates both parity and time-reversal in-\nvariance. Therefore, a non-zero d can exist if and only if\nboth parity and time-reversal invariance (or CP invariance\nunder the CPT theorem) are broken.\n\n646\nFigure 20.4.5. (color online) Limits on the branching fraction at 90 % C.L., obtained from searches for lepton \ufb02avor violation\nin \u03c4 decays. Results from CLEO (closed circle), BABAR (triangle-down), Belle (triangle-up) and LHCb (square) experiments are\nshown. The LHCb result is taken from Aaij et al. (2013f).\nThere are extensive studies of the EDM for electron,\nmuon, neutron and various nuclei such as 199Hg,205Tl,\nthat provide stringent constraints on new CP-violating\nphysics (Czarnecki and Marciano, 2010; Roberts and Mar-\n\n647\nciano, 2010). The current limit on the tau EDM, d\u03c4, is\nmany orders of magnitude less than that of the electron\nand nucleons, since it is di\ufb03cult to measure its EDM\ndue to the short lifetime. However, its size is interesting\nboth theoretically and experimentally. In the Standard\nModel, the EDM of the tau can arise at the multi-loop\nlevel through CKM type quark mixing and is extremely\nsmall, d\u03c4 < 10\u221234e cm, (Hoogeveen, 1990; Pospelov and\nKhriplovich, 1991). A much larger contribution to the tau\nEDM is however predicted by various SM extensions such\nas supersymmetry (Pospelov and Ritz, 2005), unparticle\nphysics (Moyotl, Rosado, and Tavares-Velasco, 2011), and\nmirror leptons (Ibrahim and Nath, 2010).\nExperimentally, one can measure the tau EDM by us-\ning the momentum correlation of decay products in the\ntau-pair production e+e\u2212\u2192\u03c4 +\u03c4 \u2212as explained below.\nThe relativistic generalization of the interaction dE \u00b7 S\nfor a tau lepton (spin 1/2 particle) \u03a8 can be expressed by\nan e\ufb00ective Lagrangian as\nLCP = \u2212d\u03c4\ni\n2\u03a8\u03c3\u00b5\u03bd\u03b35\u03a8 F\u00b5\u03bd,\n(20.5.2)\nwhere d\u03c4 is the electric dipole moment of the tau lepton.\nFurthermore, F \u00b5\u03bd is the electric \ufb01eld tensor and \u03c3\u00b5\u03bd =\ni\n2(\u03b3\u00b5\u03b3\u03bd \u2212\u03b3\u03bd\u03b3\u00b5). From this Lagrangian and the Standard\nModel one, the squared matrix element, M = MSM +\nd\u03c4MEDM, for the tau-pair production\ne+(p) + e\u2212(\u2212p) \u2192\u03c4 +(k, S+) + \u03c4 \u2212(\u2212k, S\u2212)(20.5.3)\nis given by the sum of the SM term |M|2\nSM, the EDM term\n|d\u03c4|2|M|2\nEDM and the interference between them\n|M|2 = (M\u2020\nSM + d\u2020\n\u03c4M\u2020\nEDM)(MSM + d\u03c4MEDM)\n= |M|2\nSM + Re(d\u03c4)M2\nRe + Im(d\u03c4)M2\nIm\n+|d\u03c4|2|M|2\nEDM,\n(20.5.4)\nwhere Re(d\u03c4) [Im(d\u03c4)] is the real [imaginary] part of the\nEDM. Since these terms vanish for the total integrated\ncross section, one needs to study CP-odd observables. The\ninterference terms MRe/Im, being proportional to real and\nimaginary part of d\u03c4, contain the following combination\nof spin-momentum correlations:158\nM2\nRe : (S+ \u00d7 S\u2212) \u00b7 bk and (S+ \u00d7 S\u2212) \u00b7 bp\n(20.5.5)\nM2\nIm : (S+ \u2212S\u2212) \u00b7 bk and (S+ \u2212S\u2212) \u00b7 bp,\n(20.5.6)\nwhere bp (bk) is the unit momentum vector of e+(\u03c4 +) in\nthe CM frame and S\u00b1 are the spin vectors for \u03c4 \u00b1. To\nmeasure Re(d\u03c4) one needs a CP-odd and T-odd (CPT-\neven) operator, as shown in the \ufb01rst line. To measure\nIm(d\u03c4) one needs a CP-odd and T-even (CPT-odd) oper-\nator, as shown in the second equation (20.5.6).159 These\n158 The complete form is given by Bernreuther, Nachtmann,\nand Overmann (1993).\n159 Even in the absence of CPT violation, a non-zero value of\nIm(d\u03c4) could be generated through absorptive contributions,\ni.e., rescattering corrections from on-shell intermediate states.\nterms change their sign for the CP transformation (i.e.\nCP-odd terms). So if one of these terms is non-zero, the\nprocess violates CP.\nIn order to optimize the sensitivity to d\u03c4, Belle employs\na so-called optimal observable method, \ufb01rst proposed by\nAtwood and Soni (1992). In this method, the optimal ob-\nservables can be de\ufb01ned as\nORe =\nM2\nRe\n|MSM|2 ,\nOIm =\nM2\nIm\n|MSM|2 .\n(20.5.7)\nThe mean value of the observable ORe is given by\n< ORe >\u221d\nZ\nORe|M|2d\u03c6\n=\nZ\nM2\nRed\u03c6 + Re(d\u03c4)\nZ (M2\nRe)2\n|MSM|2 d\u03c6,\n(20.5.8)\nwhere the integration is over the phase space (\u03c6) spanned\nby the relevant kinematic variables. The expression for the\nimaginary part is similar. The \ufb01rst term containing the in-\ntegral of M2\nRe and M2\nIm drops out because of their sym-\nmetry properties. The means of the observables < ORe >\nand < OIm > are therefore linear functions of d\u03c4,\n< ORe >= aRe \u00b7 Re(d\u03c4),\n< ORe >= aIm \u00b7 Im(d\u03c4).\n(20.5.9)\nEight di\ufb00erent \ufb01nal states in the decays of \u03c4-pairs,\n(e+\u03bde\u03bd\u03c4)(\u00b5\u2212\u03bd\u00b5\u03bd\u03c4) , (e+\u03bde\u03bd\u03c4)(\u03c0\u2212\u03bd\u03c4),\n(\u00b5+\u03bd\u00b5\u03bd\u03c4), (\u03c0\u2212\u03bd\u03c4) , (e+\u03bde\u03bd\u03c4)(\u03c1\u2212\u03bd\u03c4),\n(\u00b5+\u03bd\u00b5\u03bd\u03c4)(\u03c1\u2212\u03bd\u03c4) , (\u03c0\u2212\u03bd\u03c4)(\u03c1+\u03bd\u03c4),\n(\u03c1\u2212\u03bd\u03c4)(\u03c1+\u03bd\u03c4) , (\u03c0\u2212\u03bd\u03c4)(\u03c0+\u03bd\u03c4)\n(20.5.10)\nand their charge-conjugate modes are analyzed.\nBecause of the undetectable particles (neutrinos), one\ncan not fully reconstruct the quantities S\u00b1 and bk. There-\nfore, for each event the mean values of |MSM|2, M2\nRe and\nM2\nIm are obtained by averaging over all possible kine-\nmatic con\ufb01gurations. In the case when both tau leptons\ndecay hadronically, the tau \ufb02ight direction can be deter-\nmined with a two-hold ambiguity. In the case of leptonic\ntau decays, there is an additional ambiguity from the ef-\nfective mass of the two daughter neutrinos. A Monte Carlo\ntreatment is adopted to take into account the additional\nambiguity in the e\ufb00ective mass of the \u03bd\u00af\u03bd system. Explicit\nformulae for reconstructing the tau\u2019s \ufb02ight direction and\nthe spin vectors are provided in Posthaus and Overmann\n(1998) and Ackersta\ufb00et al. (1997b).\nThe obtained optimal observable distributions for the\n\u03c4 +\u03c4 \u2212\u2192(\u03c0\u03bd\u03c4)(\u03c1\u03bd\u03c4) mode in the Belle experiment (In-\nami, 2003) are shown in Fig. 20.5.1 (a) and (b) for real\nand imaginary part, respectively. Note that the width of\nthe distribution is proportional to the sensitivity. The dis-\ntributions do not show any apparent asymmetry.\nThe values of the EDM obtained from the mean values\nof the optimal observables are plotted in Figure 20.5.2 (a)\nand (b). All results are consistent with the EDM of zero\n\n648\n0\n0.1\n0.2\n0.3\n-10\n-5\n0\n5\n10\nORe\nORe\nORe\nGeV/e\nN / 0.2 GeV/e\n(a) \u03c0\u03c1\n\u00d7104\n0\n0.2\n0.4\n-20\n-10\n0\n10\n20\nOIm\nOIm\nOIm\nGeV/e\nN / 0.5 GeV/e\n(b) \u03c0\u03c1\n\u00d7104\nFigure 20.5.1. Distribution of optimal observables, (a) ORe\nand (b) OIm, for \u03c0\u03c1 events \u03c4 \u2212\u03c4 + \u2192(\u03c0\u2212\u00af\u03bd\u03c4)(\u03c1+\u03bd\u03c4) (Inami,\n2003). Dots are Belle data and white and shaded histograms\nshow the MC simulation for signal and background, respec-\ntively. If CP is violated, mean values < ORe >, < OIm > are\ndi\ufb00er from zero.\nwithin statistical errors. Taking the weighted average of\neight di\ufb00erent modes, Belle sets the 95% con\ufb01dence level\ninterval for the tau-lepton EDM (Inami, 2003) as\n\u22122.2 \u00d7 10\u221217e cm < Re(d\u03c4) < 4.5 \u00d7 10\u221217e cm\n(20.5.11)\nand\n\u22122.5 \u00d7 10\u221217e cm < Im(d\u03c4) < 0.8 \u00d7 10\u221217e cm.\n(20.5.12)\nThese limits are ten times more stringent than the pre-\nvious results given by L3 Acciarri et al. (1998), OPAL\n(Ackersta\ufb00et al., 1998) and DELPHI (Abdallah et al.,\n2004) experiments:\n|d\u03c4| < 3.1 \u00d7 10\u221216 e cm (L3),\n(20.5.13)\n|d\u03c4| < 3.7 \u00d7 10\u221216 e cm (OPAL),\n(20.5.14)\n|d\u03c4| < 3.7 \u00d7 10\u221216 e cm (DELPHI).\n(20.5.15)\n20.5.2 CP violation in tau decay\nIn the Standard Model, no observable CP violation is ex-\npected in the hadronic decays of tau leptons except for\nthe known CP violation in the neutral kaon system. Ob-\nserving a signal would then be manifestation of some kind\nof new physics. For example, the CP violation could orig-\ninate from the minimal supersymmetric Standard Model\n(MSSM) (Calderon, Delepine, and Castro, 2007; Ibrahim\nand Nath, 2008) or from multi-Higgs doublet models (MH-\nDM) (Grossman, 1994; Kiers, Soni, and Wu, 2000; Wein-\nberg, 1976). The charged Higgs bosons in these models\nRe(d\u03c4) (10-16 ecm)\nIm(d\u03c4) (10-16 ecm)\nFigure 20.5.2. Results of the tau-lepton EDM for eight modes\nand the weighted mean for the (a) real and (b) imaginary parts.\nThe error bars include both statistical and systematic errors.\nThe small ticks on the error bars show the statistical errors\n(Inami, 2003).\nplay an important role in strangeness changing (Cabibbo-\nsuppressed) processes with \u25b3S = 1. In the \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4\nmode, a Standard Model CP asymmetry of 0.3%, due to\nthe CP violation in KL \u2192\u03c0+\u03c0\u2212, is expected in the decay\nrates (Bigi and Sanda, 2005; Calderon, Delepine, and Cas-\ntro, 2007). While in new physics models such as MSSM or\nMHDM, a non-zero CP asymmetry is not expected in the\ndecay rates of \u03c4 \u00b1 even if the intermediate scalar bosons\nhave CP violating couplings, but the bosons in the models\nintroduce a CP asymmetry in the angular distribution of\nthe tau decays.\n\n649\n20.5.2.1 Decay rate asymmetry\nA \ufb01rst search for CP violation in the decay rate of the\ntau lepton is carried out by BABAR. They use a dataset\nof 437 million tau lepton pairs (Lees, 2012q) and measure\nthe decay-rate asymmetry\nACP = \u0393(\u03c4 + \u2192K0\nS\u03c0+\u03bd\u03c4) \u2212\u0393(\u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4)\n\u0393(\u03c4 + \u2192K0\nS\u03c0+\u03bd\u03c4) + \u0393(\u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4)\n(20.5.16)\nfor a \u03c4 \u2212\u2192K0\nS\u03c0\u2212(\u22650\u03c00)\u03bd\u03c4 sample. The signal candidates\nare selected by dividing the event into two hemispheres\nusing the event thrust axis in the e+e\u2212CM system. BABAR\nselects events with a charged track identi\ufb01ed as a pion, a\nK0\nS \u2192\u03c0+\u03c0\u2212and up to three \u03c00 candidates in the \u201csignal\u201d\nhemisphere. To reduce background from q\u00afq continuum,\nBABAR require that the momentum of the charged track\nin the \u201ctag\u201d hemisphere be less than 4 GeV/c in the CM\nsystem and be identi\ufb01ed as an electron or muon and the\nmagnitude of the event thrust be between 0.92 and 0.99.\nAfter all selection criteria are applied, a total of 199,064\n(140,602) candidates are obtained in the e-tag (\u00b5-tag)\nsample, of which there are 99842 (70369) in the \u03c4 \u2212and\n99222 (70233) in the \u03c4 + sample. The background is esti-\nmated to be at the 1% level. After the subtraction of back-\nground composed of qq and non-K0\nS tau decays, the decay-\nrate asymmetry is measured to be (\u22120.32 \u00b1 0.23 \u00b1 0.13)%\nfor the e-tag sample and (\u22120.05 \u00b1 0.27 \u00b1 0.10)% for the\n\u00b5-tag sample, where the \ufb01rst errors are statistical and the\nsecond are systematic.\nTo these measured rate-asymmetries, two corrections\nare applied. One is the correction for the di\ufb00erent nuclear-\ninteraction cross section of the K0 and K0 mesons with\nthe material in the detector. A correction to the asym-\nmetry is calculated using the momentum and polar angle\nof the K0\nS candidate together with the nuclear-interaction\ncross section for the neutral kaons. The correction is found\nto be (0.07\u00b10.01)% for both the e-tag and \u00b5-tag samples.\nThe other is a correction for the dilution e\ufb00ect. The \ufb01-\nnal sample includes other tau decay modes with one K0\nS.\nThe decay-rate asymmetry for \u03c4 \u2212\u2192K\u2212K0\nS\u03bd\u03c4 is oppo-\nsite to that of \u03c4 \u2212\u2192K0\nS\u03c0\u2212(\u22650\u03c00)\u03bd\u03c4 in the Standard\nModel because the K0\nS in the \u03c4 \u2212\u2192K0\nS\u03c0\u2212(\u22650\u03c00)\u03bd\u03c4 is\nproduced via a K0, whereas the K0\nS in \u03c4 \u2212\u2192K\u2212K0\nS\u03bd\u03c4\nis produced via a K0. In addition, the decay asymmetry\nis zero in the Standard Model for the \u03c4 \u2192K0K0\u03bd\u03c4 de-\ncay, because the asymmetries due to the K0 and K0 will\ncancel each other. To obtain the genuine rate asymmetry\nfor \u03c4 \u2212\u2192K0\nS\u03c0\u2212(\u22650\u03c00)\u03bd\u03c4, the measured asymmetry is\ndivided by 0.75 \u00b1 0.04.\nFinally, by applying these corrections and combining\nboth the e-tag and \u00b5-tag samples, BABAR obtain the decay-\nrate asymmetry for the \u03c4 \u2212\u2192K0\nS\u03c0\u2212(\u22650\u03c00)\u03bd\u03c4 decay to\nbe\nACP = (\u22120.36 \u00b1 0.23 \u00b1 0.11)%.\n(20.5.17)\nAs pointed out by Grossman and Nir (2012), the pre-\ndicted decay-rate asymmetry is a\ufb00ected by the K0\nS de-\ncay time dependence of the event selection e\ufb03ciency. By\ntaking into account the e\ufb03ciency correction (1.08 \u00b1 0.01)\ncaused by the \ufb01nite acceptance as a function of K0\nS decay\nin the BABAR detector, the Standard Model decay-rate\nasymmetry is predicted to be (0.36 \u00b1 0.01)% (Bigi and\nSanda, 2005). The sign of the asymmetry is di\ufb00erent be-\ntween experiment and the prediction. The measured value\nis 2.8 standard deviations from the Standard Model pre-\ndiction.\n20.5.2.2 Asymmetry in angular distribution\nA \ufb01rst search for the CP asymmetry in the angular distri-\nbution has been carried out by the CLEO collaboration for\nthe \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4 mode using 13 fb\u22121 data (Bonvicini\net al., 2002). Belle performs a similar search in the same\nmode using a data sample of 699 fb\u22121 (Bischofberger,\n2011).\nIn this section, we \ufb01rst introduce the generic formula\nfor the CP asymmetry in the angular distribution of the\ntau decays and how the CP violating parameters are re-\nlated to the observables. The relevant SM Hamiltonian for\nthe Cabibbo-suppressed decays \u03c4 \u00b1 \u2192X\u00b1\ns \u03bd\u03c4, is given by\nHSM = GF\n\u221a\n2 sin \u03b8c[\u03bd\u03c4\u03b3\u00b5(1 \u2212\u03b35)\u03c4][s\u03b3\u00b5(1 \u2212\u03b35)u] + h.c.,\n(20.5.18)\nwhere the form is determined by the vector-boson W \u00b1 ex-\nchange. On the other hand, the Hamiltonian with scalar-\nor pseudoscalar-boson exchange has a form\nHNP = GF\n\u221a\n2 sin \u03b8c[\u03bd\u03c4(1 + \u03b35)\u03c4][s(\u03b7S + \u03b7P \u03b35)u] + h.c.\n(20.5.19)\nwhere \u03b7P and \u03b7S are the complex parameters, in general,\nrelevant for the pseudoscalar and scalar hadronic system,\nrespectively. If either \u03b7P or \u03b7S has a non-zero imaginary\npart, CP is violated in this process (K\u00a8uhn and Mirkes,\n1997).\nAmong them, the scalar \u03b7S term can be measured in\nthe modes decaying to two pseudoscalars such as \u03c4 \u2212\u2192\nK0\nS\u03c0\u2212\u03bd\u03c4. For \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4, the full di\ufb00erential decay\nwidth, in the hadronic rest frame (q1 + q2 = 0), is given\nby\nd\u0393\u03c4 \u2212= G2\nF\n2m\u03c4\nsin2 \u03b8c\n1\n(4\u03c0)3\n(m2\n\u03c4 \u2212Q2)2\nm2\u03c4\n|q1|\n\u00d7 1\n2\n X\nX\nLXWX\n!\ndQ2\np\nQ2\ndcos \u03b8\n2\ndcos \u03b2\n2\n,\n(20.5.20)\nwhere GF is the Fermi coupling constant, \u03b8c is the Cabibbo\nangle, m\u03c4 is the mass of the tau lepton, q1 and q2 denote\nthe three-momenta of K0\nS and \u03c0\u2212, respectively, and Q2 =\n(q1 + q2)2 is the invariant mass squared of the K0\nS\u03c0\u00b1 sys-\ntem. \u03b2 is the helicity angle of K0\nS in the K0\nS\u03c0\u00b1 rest frame\nwhile \u03b8 is the helicity angle of the KS\u03c0\u00b1 system in the tau\nrest frame. The angular coe\ufb03cients LX with X = 1 to 4\nare known functions related to the leptonic current. The\n\n650\nfour hadronic functions WX are formed from the vector\nand scalar form factors F(Q2) and FS(Q2) and are pro-\nportional to |F|2, |FS|2, Re(FFS), and Im(FFS), respec-\ntively. Among them the last term Im(FFS) is most impor-\ntant for a CP measurement, which involves the CP-odd\nterm proportional to Im(\u03b7S) (K\u00a8uhn and Mirkes, 1997).\nThis term has an angular dependence of cos \u03b2 cos \u03c8, where\n\u03c8 is the helicity angle of the tau lepton in the KS\u03c0\u00b1 rest-\nframe. Note that the angles \u03b8 and \u03c8 are correlated and\ntheir cosine can be determined from the energy of the\nKS\u03c0\u00b1 system without measuring the tau direction (K\u00a8uhn\nand Mirkes, 1997).\nIn order to extract the CP violating term proportional\nto Im(FFS), Belle measure the asymmetry, in bins of Q2,\nde\ufb01ned as the di\ufb00erence of the di\ufb00erential \u03c4 + and \u03c4 \u2212de-\ncay width weighted by cos \u03b2 cos \u03c8:\nACP\ni\n=\nR\ncos \u03b2 cos \u03c8\n\u0010\nd\u0393\u03c4\u2212\nd\u03c9\n\u2212d\u0393\u03c4+\nd\u03c9\n\u0011\nd\u03c9\n1\n2\nR \u0010\nd\u0393\u03c4\u2212\ndQ2 + d\u0393\u03c4+\ndQ2\n\u0011\ndQ2\n\u2243\u27e8cos \u03b2 cos \u03c8\u27e9\u03c4 \u2212\u2212\u27e8cos \u03b2 cos \u03c8\u27e9\u03c4 +\n(20.5.21)\nwith d\u03c9 = dQ2dcos \u03b8dcos \u03b2. The asymmetry ACP\ni\nis just\nthe di\ufb00erence between the mean values \u27e8cos \u03b2 cos \u03c8\u27e9for\n\u03c4 + and \u03c4 \u2212events evaluated in bins of Q2.\nThe measured CP asymmetry ACP\ni\nis related to the\nCP parameter Im(\u03b7S) by\nACP\ni\n= \u27e8cos \u03b2 cos \u03c8\u27e9i\n\u03c4 \u2212\u2212\u27e8cos \u03b2 cos \u03c8\u27e9i\n\u03c4 +\n= Ns\nni\n1\n\u03f5tot\u0393\nZZZ Q2\n2,i\nQ2\n1,i\n\u03f5(Q2, cos \u03b2, cos \u03b8)\n\u00d7 cos \u03b2 cos \u03c8\n\u0014d\u0393(\u03c4 \u2212)\nd\u03c9\n\u2212d\u0393(\u03c4 +)\nd\u03c9\n\u0015\nd\u03c9\n\u2243Im(\u03b7S)Ns\nni\nZ Q2\n2,i\nQ2\n1,i\nC(Q2)Im(FF \u2217\nH)\nm\u03c4\ndQ2,\n(20.5.22)\nwith ni = (n\u2212\ni + n+\ni )/2. Where n\u00b1\ni denotes the observed\nnumber of \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4 events in the i-th Q2 bin,\n(Q2 \u2208[Q2\n1,i, Q2\n2,i]), and Ns = P\ni ni. The function C(Q2)\ncontains model-independent terms and detector e\ufb03ciency\ne\ufb00ects, and is obtained after numerical integration over\ncos \u03b2 and cos \u03b8:\nC(Q2) = \u22121\n\u0393\nG2\nF\n2m\u03c4\nsin2 \u03b8c\n1\n(4\u03c0)3\n(m2\n\u03c4 \u2212Q2)2\nQ2\n|q1|2\n(20.5.23)\n\u00d7\nZZ \u03f5(Q2, cos \u03b2, cos \u03c8)\n\u03f5tot\ncos2 \u03b2 cos2 \u03c8 dcos \u03b8 dcos \u03b2,\nhere the coe\ufb03cients \u03f5tot and \u03f5(Q2, cos \u03b2, cos \u03c8) are the to-\ntal and the three-dimensional detector e\ufb03ciencies and \u0393\nis the total \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4 decay width.\nBelle selects events with a charged track identi\ufb01ed as a\npion, K0\nS \u2192\u03c0+\u03c0\u2212and no additional photons with energy\ngreater than 0.2 GeV in the signal hemisphere, and one\ncharged track with the number of photons above 0.1 GeV\nless than \ufb01ve in the tag hemisphere. After all selection cri-\nteria are applied, a total of 162000 \u00b1 403 \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4\nand 162200 \u00b1 403 \u03c4 + \u2192K0\nS\u03c0+\u03bd\u03c4 candidates are selected\nfrom a 699 fb\u22121 data sample. The background subtracted\nasymmetry as a function of\np\nQ2 is shown in Fig. 20.5.3\n(a) and (b). The asymmetry is within two standard devi-\nations (\u03c3) from zero for all mass bins.\n)\n2\nW (GeV/c\n0.8\n1\n1.2\n1.4\n1.6\ncp\nA\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n \n\u00b1\n\u03c0\nS\n0\nK\n\u03c4\n\u03bd\n \n\u2192\n \n\u00b1\n\u03c4 \ndata\ncontrol sample \n=0.1) \nS\n\u03b7\nMC with Im(\n(a)\n \n\u00b1\n\u03c0\nS\n0\nK\n\u03c4\n\u03bd\n \n\u2192\n \n\u00b1\n\u03c4 \ndata\ncontrol sample \n=0.1) \nS\n\u03b7\nMC with Im(\n)\n2\nW (GeV/c\n0.8\n1\n1.2\n1.4\n1.6\ncp\nA\n-0.03\n-0.02\n-0.01\n0\n0.01\n0.02\n0.03\n \n\u00b1\n\u03c0\nS\n0\nK\n\u03c4\n\u03bd\n \n\u2192\n \n\u00b1\n\u03c4 \ndata\ncontrol sample\n(b)\n \n\u00b1\n\u03c0\nS\n0\nK\n\u03c4\n\u03bd\n \n\u2192\n \n\u00b1\n\u03c4 \ndata\ncontrol sample\nFigure 20.5.3. (a) Measured CP asymmetry as a function of\nthe mass of the hadron system W =\np\nQ2. The closed squares\nare data. The triangles indicate the expected asymmetry for\nIm(\u03b7S) = 0.1 [Re(\u03b7S) = 0]. (b) The same data with a zoomed\nvertical scale (\u00d75) for the higher mass bins. The vertical lines\nindicate statistical and systematic errors added in quadrature\n(Bischofberger, 2011).\nIn the most precisely measured mass region, 0.9 GeV <\np\nQ2 < 1.1 GeV, the asymmetry is measured to be\nACP = (1.8 \u00b1 2.1 \u00b1 1.4) \u00d7 10\u22123.\n(20.5.24)\nFrom the measured values of ACP , the parameter Im(\u03b7S)\ncan be extracted from Eq. (20.5.22), where the results on\nthe KS\u03c0\u00b1 mass spectra obtained by Epifanov (2007) are\nused for the values of the form factors F and FS. The\nresultant upper limit for the parameter Im(\u03b7S) is\n|Im(\u03b7S)| < (0.012 to 0.026)\n(20.5.25)\n\n651\nat 90% C.L., where the range of the upper limit is due to\nthe uncertainty of the parameterization used to describe\nthe hadronic form factors and the unknown relative phase\nbetween the spin-one |F| and the spin-zero |FS| form fac-\ntors. The results improve upon the previous limit from the\nCLEO experiment (Bonvicini et al., 2002) by one order of\nmagnitude.\nTheoretical predictions for Im(\u03b7S) are available in the\ncontext of MHDM with three or more Higgs doublets (Choi,\nHagiwara, and Tanabashi, 1995; Grossman, 1994). In such\nmodels \u03b7S is related to the model parameters as (Choi,\nHagiwara, and Tanabashi, 1995),\n\u03b7S \u2243m\u03c4ms\nM 2\nH\u00b1\n\u00b7 X\u2217Z\n(20.5.26)\nif numerically small terms proportional to mu are ig-\nnored. Here, MH\u00b1 is the mass of the lightest charged Higgs\nboson and X and Z are the complex coupling constants\nshown in Fig. 20.5.4 (a). The limits for the |Im(\u03b7S)| result\nin the exclusion region shown in Fig. 20.5.4 (b). For the\nlimit |Im(\u03b7S)| < 0.026, this is equivalent to |Im(XZ\u2217)| <\n0.15 \u00d7 M 2\nH\u00b1.\nIm(XZ*)\n0\n10\n20 30\n40\n50\n60\n70\n80\n90 100\n)\n2\n (GeV/c\n\u00b1\nH\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\nIm(XZ*)\n0\n10\n20 30\n40\n50\n60\n70\n80\n90\n(b)\n100\n)\n2\n (GeV/c\n\u00b1\nH\nM\n0\n50\n100\n150\n200\n250\n300\n350\n400\n)|<0.012 at 90% c. l.\nS\n\u03b7\n|Im(\n)|<0.026 at 90% c. l.\nS\n\u03b7\n|Im(\nFigure 20.5.4. (a) Feynman diagram for a tau decay via\nexchange of a Higgs boson in Multi-Higgs-Doublet models.\n(b) Excluded region of the parameter space in Multi-Higgs-\nDoublet model from limits for |Im(\u03b7S)| (Bischofberger, 2011).\n20.6 Hadronic tau decays\n20.6.1 Theory\nThe hadronic tau decays turn out to be a beautiful labora-\ntory for studying strong interaction e\ufb00ects at low energies\n(Pich, 1998). The tau is the only known lepton massive\nenough to decay into hadrons. Its semileptonic decays are\nthen ideally suited to investigate the hadronic weak cur-\nrents. The \u03c4 \u2212\u2192\u03bd\u03c4h\u2212decay amplitude,\nM(\u03c4 \u2212\u2192\u03bd\u03c4h\u2212) = GF\n\u221a\n2 H\u00b5\nh [\u03bd\u03c4\u03b3\u00b5(1 \u2212\u03b35)\u03c4] ,\n(20.6.1)\nprobes the matrix element of the left-handed charged cur-\nrent between the vacuum and the \ufb01nal hadronic state h\u2212,\nH\u00b5\nh \u2261\u27e8h\u2212|\n\u0000V \u2217\nud d \u03b3\u00b5(1 \u2212\u03b35)u + V \u2217\nus s \u03b3\u00b5(1 \u2212\u03b35)u\n\u0001\n|0\u27e9.\n(20.6.2)\nFor the decay modes with lowest multiplicity, \u03c4 \u2212\u2192\n\u03bd\u03c4\u03c0\u2212and \u03c4 \u2212\u2192\u03bd\u03c4K\u2212, the relevant hadronic matrix\nelements are already known from the measured decays\n\u03c0\u2212\u2192\u00b5\u2212\u03bd\u00b5 and K\u2212\u2192\u00b5\u2212\u03bd\u00b5:\n\u27e8\u03c0\u2212| d \u03b3\u00b5u |0\u27e9= \u2212i f\u03c0 p\u00b5\n\u03c0 ,\n\u27e8K\u2212| s \u03b3\u00b5u |0\u27e9= \u2212i fK p\u00b5\nK ,\n(20.6.3)\nwhere f\u03c0 = (130.4\u00b10.2) MeV and fK = (156.1\u00b10.8) MeV\nare the so-called pion and kaon decay constants (Berin-\nger et al., 2012). The corresponding tau decay widths can\nthen be accurately predicted. The predictions are in good\nagreement with the measured values and provide a test\nof lepton universality. Assuming universality in the quark\ncouplings, muonic decays of the pion and kaon determine\nthe ratio (Cirigliano, Ecker, Neufeld, Pich, and Portoles,\n2012)\n|Vus| fK\n|Vcd| f\u03c0\n= 0.2763 \u00b1 0.0005\n(20.6.4)\nto a higher precision than is currently obtained with tau\ndecays. The determination of this ratio by tau decays is\npresently limited by the measurement of \u0393(\u03c4 \u2212\u2192\u03bd\u03c4K\u2212),\nbut BABAR has signi\ufb01cantly improved the precision of this\nmode, as discussed in Section 20.8.\nFor the two-pion \ufb01nal state, the hadronic matrix ele-\nment is parameterized in terms of the so-called pion form\nfactor F\u03c0(s), de\ufb01ned through [s \u2261(p\u03c0\u2212+ p\u03c00)2]\n\u27e8\u03c0\u2212\u03c00|d\u03b3\u00b5u|0\u27e9\u2261\n\u221a\n2 F\u03c0(s) (p\u03c0\u2212\u2212p\u03c00)\u00b5 .\n(20.6.5)\nIsospin symmetry relates this quantity to the analogous\nform factor measured in e+e\u2212\u2192\u03c0+\u03c0\u2212. Accurate mea-\nsurements of F\u03c0(s) are a critical ingredient of the Standard\nModel prediction for the anomalous magnetic moment of\nthe muon.\nOwing to the di\ufb00erent quarks involved, two form fac-\ntors are needed to characterize the decays \u03c4 \u2192\u03bd\u03c4K\u03c0,\n\u27e8K0\u03c0\u2212|s\u03b3\u00b5u|0\u27e9\u2261f K\u03c0\n+ (s) (pK \u2212p\u03c0)\u00b5+f K\u03c0\n\u2212(s) (pK + p\u03c0)\u00b5\n(20.6.6)\n\n652\nwith s \u2261(p\u03c0 + pK)2. The form factor f K\u03c0\n+ (s) corresponds\nto a hadronic \ufb01nal state with JP = 1\u2212, while the scalar\n(0+) combination f K\u03c0\n0\n(s) = f K\u03c0\n+ (s)+s f K\u03c0\n\u2212(s)/(m2\nK\u2212m2\n\u03c0)\nvanishes in the SU(3) limit because the vector current\nis conserved for equal quark masses. In K \u2192\u03c0\u2113\u03bd (K\u21133)\ndecays one also measures the form factors in the timelike\nregion. More precisely, in the kinematical region m2\n\u2113<\nq2 < (MK \u2212M\u03c0)2. In tau decays this is extended up to\nthe tau mass.\nHigher-multiplicity modes involve a richer dynamical\nstructure, providing a very valuable experimental window\ninto the non-perturbative hadronization of the QCD cur-\nrents. While e+e\u2212data only test the electromagnetic vec-\ntor current, tau decays are sensitive to the vector and\naxial-vector currents, both in the Cabibbo-allowed and\nCabibbo-suppressed channels.\nA dynamical understanding of the hadronic matrix el-\nements can be achieved using analyticity, unitarity and\nsome general properties of QCD, such as chiral symmetry\n, the short-distance asymptotic behavior and the limit of\na large number of QCD colors (Pich, 2007). The high-\nstatistics B Factory data samples provide very impor-\ntant information on the hadronic structure, allowing one\nto improve theoretical tools and get a better control of\nthe strong interaction in the resonance region. These data\nhave already triggered extensive theoretical activity (Boito,\nEscribano, and Jamin, 2009, 2010; G\u00b4omez Dumm, Pich,\nand Portol\u00b4es, 2004; G\u00b4omez Dumm, Roig, Pich, and Por-\ntol\u00b4es, 2010a,b; Guerrero and Pich, 1997; Guo and Roig,\n2010; Jamin, Pich, and Portol\u00b4es, 2006, 2008; Pich and\nPortol\u00b4es, 2001). As a result, there has been considerable\nprogress towards the development of a quantum \ufb01eld the-\nory description of the resonance dynamics at the energy\nscales accessible through tau decays.\n20.6.1.1 Inclusive tau decay width\nThe inclusive character of the total tau hadronic width\nrenders possible an accurate calculation of the ratio\n(Braaten, 1988, 1989; Braaten, Narison, and Pich, 1992;\nLe Diberder and Pich, 1992b; Narison and Pich, 1988)\nR\u03c4 \u2261\u0393(\u03c4 \u2212\u2192\u03bd\u03c4 hadrons)\n\u0393(\u03c4 \u2212\u2192\u03bd\u03c4e\u2212\u03bde)\n= R\u03c4,V + R\u03c4,A + R\u03c4,S .\n(20.6.7)\nR\u03c4,V (R\u03c4,A) is the Cabibbo-allowed decay width into \ufb01nal\nstates with JP = 1\u2212, 0+ (1+, 0\u2212), while R\u03c4,S accounts for\ndecays into states with strangeness S = \u22121.\nThe inclusive hadronic width,\n\u0393(\u03c4 \u2212\u2192\u03bd\u03c4 hadrons) \u221dL\u00b5\u03bd\nX\nh\nZ\ndQh H\u00b5\nh H\u03bd\u2020\nh ,\n(20.6.8)\ninvolves a sum over all possible \ufb01nal hadronic states h\u2212\nwith the corresponding phase-space integration dQh. Uni-\ntarity and analyticity (optical theorem) relate this spectral\ndistribution with the imaginary parts of the two-point cor-\nrelation functions for the vector V \u00b5\nij = \u03c8j\u03b3\u00b5\u03c8i and axial-\nvector A\u00b5\nij = \u03c8j\u03b3\u00b5\u03b35\u03c8i color-singlet quark currents,\n\u03a0\u00b5\u03bd\nij,J (q) \u2261i\nZ\nd4x eiqx \u27e80|T(J \u00b5\nij(x)J \u03bd\nij(0)\u2020)|0\u27e9, (20.6.9)\nwhich have the Lorentz decomposition (J = V, A),\n\u03a0\u00b5\u03bd\nij,J (q) =\n\u0000\u2212g\u00b5\u03bdq2 + q\u00b5q\u03bd\u0001\n\u03a0(1)\nij,J (q2) + q\u00b5q\u03bd \u03a0(0)\nij,J (q2) .\n(20.6.10)\nThe superscript J = 0, 1 denotes the angular momentum\nin the hadronic rest frame and i, j = u, d, s.\nThe imaginary parts of \u03a0(J)\nij,J (q2) are proportional to\nthe spectral functions for hadrons with the corresponding\nquantum numbers. The hadronic decay rate of the tau can\nbe written as an integral of these spectral functions over\nthe invariant mass s = q2 of the \ufb01nal-state hadrons:\nR\u03c4 = 12\u03c0\nZ m2\n\u03c4\n0\nds\nm2\u03c4\n\u0012\n1 \u2212s\nm2\u03c4\n\u00132\n\u00d7\n\u0014\u0012\n1 + 2 s\nm2\u03c4\n\u0013\nIm\u03a0(1)(s) + Im\u03a0(0)(s)\n\u0015\n,\n(20.6.11)\nwhere\n\u03a0(J)(s) \u2261|Vud|2 \u0010\n\u03a0(J)\nud,V (s) + \u03a0(J)\nud,A(s)\n\u0011\n+ |Vus|2 \u0010\n\u03a0(J)\nus,V (s) + \u03a0(J)\nus,A(s)\n\u0011\n.\n(20.6.12)\nThe contributions coming from the \ufb01rst two terms corre-\nspond to R\u03c4,V and R\u03c4,A, respectively, while R\u03c4,S contains\nthe remaining Cabibbo-suppressed contributions.\nThe integrand in Eq. (20.6.11) cannot be calculated at\npresent from QCD. Nevertheless the integral itself can be\ncalculated systematically by exploiting the analytic prop-\nerties of the correlators \u03a0(J)(s). They are analytic func-\ntions of s except along the positive real s-axis, where their\nimaginary parts have discontinuities. R\u03c4 can then be writ-\nten as a contour integral in the complex s-plane running\ncounter-clockwise around the circle |s| = m2\n\u03c4 (Braaten,\nNarison, and Pich, 1992):\nR\u03c4 = 6\u03c0i\nI\n|s|=m2\u03c4\nds\nm2\u03c4\n\u0012\n1 \u2212s\nm2\u03c4\n\u00132\n\u00d7\n\u0014\u0012\n1 + 2 s\nm2\u03c4\n\u0013\n\u03a0(0+1)(s) \u22122 s\nm2\u03c4\n\u03a0(0)(s)\n\u0015\n.\n(20.6.13)\nCauchy\u2019s theorem guarantees that the integration along\nthe closed contour shown in Fig. 20.6.1 gives zero. Up to\na sign the integral along the circle is then equal to the\nsum of the integrals above and below the real axis, which\nreproduces Eq. (20.6.11) because \u03a0(J)(s + i\u03f5) \u2212\u03a0(J)(s \u2212\ni\u03f5) = 2i Im\u03a0(J)(s).\nTo compute the contour integral Eq. (20.6.13) we only\nneed to know the correlators \u03a0(J)(s) for complex values\n\n653\nIm(s)\nm\nRe(s)\n2\n\u03c4\nFigure\n20.6.1.\nIntegration\ncontour\nused\nto\nderive\nEq. (20.6.13).\nof s, with |s| = m2\n\u03c4 which is larger than the scale associ-\nated with non-perturbative e\ufb00ects. Therefore, the Oper-\nator Product Expansion (OPE) can be used to organize\nthe perturbative and non-perturbative contributions into\na systematic expansion in powers of 1/s:\n\u03a0(J)(s) =\nX\nD=0,2,4,...\nC(J)\nD\n(\u2212s)D/2 .\n(20.6.14)\nC(J)\nD\nparameterizes the contributions from operators with\ndimension D. Since parity is a symmetry of the strong in-\nteractions, only operators with even dimension contribute.\nThe leading D = 0 term is the perturbative contribution,\nwhile the corrections correspond to non-perturbative ef-\nfects from operators with dimension D \u22654. Since there\nare no gauge-invariant operators with D=2, the dominant\nnon-perturbative e\ufb00ects appear at D=4 through the so-\ncalled gluon, \u27e8\u03b1SG\u00b5\u03bdG\u00b5\u03bd\u27e9, and quark, \u27e8mqqq\u27e9, vacuum\ncondensates.\nInserting Eq. (20.6.14) into the contour integral, R\u03c4\ncan be expressed as an expansion in powers of 1/m2\n\u03c4. The\nuncertainties associated with the use of the OPE near the\ntimelike axis are heavily suppressed by the presence of a\ndouble zero at s = m2\n\u03c4 in Eq. (20.6.13).\nIn the chiral limit (mu,d,s = 0), the vector and axial-\nvector currents are conserved. This implies s \u03a0(0)(s) = 0.\nTherefore, only the correlator \u03a0(0+1)(s) contributes to\nEq. (20.6.13). Since (1 \u2212x)2(1 + 2x) = 1 \u22123x2 + 2x3\n[x \u2261s/m2\n\u03c4], up to tiny logarithmic running corrections,\nthe only non-perturbative contributions to the contour\nintegration in Eq. (20.6.13) originate from operators of\ndimensions D = 6 and 8. The usually leading D = 4\noperators can only contribute to R\u03c4 with an additional\nsuppression factor of O(\u03b12\nS), which makes their e\ufb00ect neg-\nligible (Braaten, Narison, and Pich, 1992).\n20.6.1.2 Determination of \u03b1S(m\u03c4)\nThe Cabibbo-allowed combination R\u03c4,V +A can be written\nas (Braaten, Narison, and Pich, 1992)\nR\u03c4,V +A = NC |Vud|2 SEW {1 + \u03b4P + \u03b4NP} ,\n(20.6.15)\nwhere NC = 3 is the number of quark colors and SEW =\n1.0201 \u00b1 0.0003 contains the electroweak radiative correc-\ntions (Braaten and Li, 1990; Erler, 2004; Marciano and\nSirlin, 1988). The dominant correction (\u223c20%) is the per-\nturbative QCD contribution \u03b4P, which is already known\nto O(\u03b14\nS) (Baikov, Chetyrkin, and K\u00a8uhn, 2008; Braaten,\nNarison, and Pich, 1992). Quark mass e\ufb00ects are tiny for\nthe Cabibbo-allowed current and amount to a negligible\ncorrection smaller than 10\u22124.\nNon-perturbative contributions \u03b4NP, are suppressed\nby six powers of the tau mass and, therefore, are very\nsmall. Their numerical size has been determined from the\ninvariant-mass distribution of the \ufb01nal hadrons in tau de-\ncay, through the study of weighted integrals (Le Diberder\nand Pich, 1992a),\nRkl\n\u03c4\n\u2261\nZ m2\n\u03c4\n0\nds\n\u0012\n1 \u2212s\nm2\u03c4\n\u0013k \u0012 s\nm2\u03c4\n\u0013l dR\u03c4\nds ,\n(20.6.16)\nwhich can be calculated theoretically in the same way as\nR\u03c4, but are more sensitive to OPE corrections. The pre-\ndicted suppression of the non-perturbative contribution to\nR\u03c4 has been con\ufb01rmed by ALEPH (Barate et al., 1998;\nBuskulic et al., 1993a; Schael et al., 2005), CLEO (Coan\net al., 1995) and OPAL (Ackersta\ufb00et al., 1999). The most\nrecent analysis gives (Davier, Hoecker, and Zhang, 2006)\n\u03b4NP = \u22120.0059 \u00b1 0.0014 ,\n(20.6.17)\nshowing that non-perturbative corrections are below 1%.\nThe QCD prediction for R\u03c4,V +A is then completely\ndominated by \u03b4P; non-perturbative e\ufb00ects being smaller\nthan the perturbative uncertainties from unknown higher-\norder corrections. Using |Vud| = 0.97425\u00b10.00022 (Hardy\nand Towner, 2009) and Eq. (20.6.17), the present exper-\nimental value R\u03c4,V +A = 3.4671 \u00b1 0.0084 (Amhis et al.,\n2012), determines the purely perturbative contribution to\nR\u03c4 to be\n\u03b4P = 0.1995 \u00b1 0.0033 .\n(20.6.18)\nThe predicted value of \u03b4P turns out to be very sen-\nsitive to \u03b1S(m2\n\u03c4), allowing for an accurate determination\nof the fundamental QCD coupling (Braaten, Narison, and\nPich, 1992; Narison and Pich, 1988). The calculation of\nthe O(\u03b14\nS) contribution (Baikov, Chetyrkin, and K\u00a8uhn,\n2008) has triggered a renewed theoretical interest on the\n\u03b1S(m2\n\u03c4) determination, since it allows one to improve the\naccuracy to the four-loop level (Beneke and Jamin, 2008;\nCaprini and Fischer, 2009, 2011; Cvetic, Loewe, Martinez,\nand Valenzuela, 2010; Davier, Descotes-Genon, H\u00a8ocker,\nMalaescu, and Zhang, 2008; Maltman and Yavin, 2008;\nMenke, 2009; Pich, 2011a). The value of \u03b4P in Eq. (20.6.18)\nimplies (Pich, 2011b)\n\u03b1S(m2\n\u03c4) = 0.329 \u00b1 0.013 ,\n(20.6.19)\nwhich is signi\ufb01cantly larger than the values obtained at\nhigher energies. After evolution up to the scale MZ (Ro-\ndrigo, Pich, and Santamaria, 1998), the strong coupling\ndecreases to\n\u03b1S(M 2\nZ) = 0.1198 \u00b1 0.0015 ,\n(20.6.20)\n\n654\nin excellent agreement with the direct measurements at\nthe Z peak and with a better accuracy. The comparison\nof these two determinations of \u03b1S in two very di\ufb00erent en-\nergy regimes, m\u03c4 and MZ, provides a beautiful test of the\npredicted running of the QCD coupling; i.e., a very sig-\nni\ufb01cant experimental veri\ufb01cation of asymptotic freedom.\n20.6.1.3 |Vus| Determination\nA separate measurement of the |\u2206S| = 0 and |\u2206S| = 1\ntau decay widths provides a very clean determination of\nVus (Gamiz, Jamin, Pich, Prades, and Schwab, 2003, 2005,\n2008). To a \ufb01rst approximation the Cabibbo mixing can be\ndirectly obtained from experimental measurements, with-\nout any theoretical input. Neglecting the small SU(3)-\nbreaking corrections from the ms \u2212md quark-mass di\ufb00er-\nence, the measured ratio R\u03c4,S = 0.1612 \u00b1 0.0028 (Amhis\net al., 2012) implies\n|Vus|SU(3) = |Vud|\n\u0012 R\u03c4,S\nR\u03c4,V +A\n\u00131/2\n= 0.210 \u00b1 0.002 .\n(20.6.21)\nThe new branching ratios measured by BABAR and Belle\nare all smaller than the previous world averages, which\ntranslate into a smaller value of R\u03c4,S and |Vus|. For com-\nparison, the previous value R\u03c4,S = 0.1686\u00b10.0047 (Davier,\nHoecker, and Zhang, 2006) resulted in |Vus|SU(3) = 0.215\u00b1\n0.003.\nThis rather remarkable determination is only slightly\nshifted by the small SU(3)-breaking contributions induced\nby the strange quark mass. These e\ufb00ects can be esti-\nmated through a QCD analysis of the di\ufb00erences (Baikov,\nChetyrkin, and K\u00a8uhn, 2005; Chen et al., 2001a; Chetyrkin,\nK\u00a8uhn, and Pivovarov, 1998; Gamiz, Jamin, Pich, Prades,\nand Schwab, 2003, 2005, 2008; Kambor and Maltman,\n2000; Korner, Krajewski, and Pivovarov, 2001; Maltman\nand Kambor, 2001; Maltman and Wolfe, 2006, 2007; Pich\nand Prades, 1998, 1999)\n\u03b4Rkl\n\u03c4\n\u2261\nRkl\n\u03c4,V +A\n|Vud|2 \u2212\nRkl\n\u03c4,S\n|Vus|2 .\n(20.6.22)\nThe only non-zero contributions are proportional to the\nmass-squared di\ufb00erence m2\ns \u2212m2\nd or to vacuum expecta-\ntion values of SU(3)-breaking operators such as \u03b4O4 \u2261\n\u27e80|msss \u2212mddd|0\u27e9\u2248(\u22121.4 \u00b1 0.4) \u00b7 10\u22123 GeV4 (Gamiz,\nJamin, Pich, Prades, and Schwab, 2003; Pich and Prades,\n1998, 1999). The dimensions of these operators are com-\npensated by corresponding powers of m2\n\u03c4, which implies a\nstrong suppression of \u03b4Rkl\n\u03c4 (Pich and Prades, 1998, 1999),\n\u03b4Rkl\n\u03c4 \u224824 SEW\n\u001am2\ns(m2\n\u03c4)\nm2\u03c4\n\u00001 \u2212\u03f52\nd\n\u0001\n\u2206kl(\u03b1S)\n\u22122\u03c02 \u03b4O4\nm4\u03c4\nQkl(\u03b1S)\n\u001b\n,\n(20.6.23)\nwhere \u03f5d \u2261md/ms = 0.053\u00b10.002 (Leutwyler, 1996). The\nperturbative corrections \u2206kl(\u03b1S) and Qkl(\u03b1S) are known\nto O(\u03b13\nS) and O(\u03b12\nS), respectively (Baikov, Chetyrkin, and\nK\u00a8uhn, 2005; Pich and Prades, 1998, 1999).\nThe J = 0 contribution to \u220600(\u03b1S) shows a rather\npathological behavior, with clear signs of being a non-\nconvergent perturbative series. Fortunately, the corre-\nsponding longitudinal contribution to \u03b4R\u03c4 \u2261\u03b4R00\n\u03c4\ncan\nbe estimated phenomenologically with a much better ac-\ncuracy, \u03b4R\u03c4|L = 0.1544 \u00b1 0.0037 (Gamiz, Jamin, Pich,\nPrades, and Schwab, 2003, 2005, 2008; Jamin, Oller, and\nPich, 2006), because it is dominated by far by the well-\nknown \u03c4 \u2192\u03bd\u03c4\u03c0 and \u03c4 \u2192\u03bd\u03c4K contributions. To estimate\nthe remaining transverse component, one needs an input\nvalue for the strange quark mass. Taking the conservative\nvalue \u03b4R\u03c4,th = 0.239 \u00b1 0.030 (Gamiz, 2013), one obtains\n|Vus| =\n \nR\u03c4,S\nR\u03c4,V +A\n|Vud|2 \u2212\u03b4R\u03c4,th\n!1/2\n= 0.2173 \u00b1 0.0020 exp \u00b1 0.0010 th. (20.6.24)\nA larger central value, |Vus| = 0.2217\u00b10.0032, is obtained\nwith the old world average for R\u03c4,S, i.e. R\u03c4,S = 0.1686 \u00b1\n0.0047 (Davier, Hoecker, and Zhang, 2006).\nSizeable changes on the experimental determination of\nR\u03c4,S could be expected from future analyses. In particu-\nlar, the high-multiplicity decay modes are not well known\nat present. The recent decrease of several experimental tau\nbranching ratios is also worrisome, since it could indicate\nsome uncontrolled systematic e\ufb00ect. As pointed out by the\nPDG (Beringer et al., 2012), 18 of the 20 branching frac-\ntions measured at the B Factories for which older non-B\nFactory measurements exist are smaller than the previous\nnon-B Factory values. The average normalized di\ufb00erence\nbetween the two sets of measurements is \u22121.30 \u03c3. Thus,\nthe result in Eq. (20.6.24) could easily \ufb02uctuate in the\nnear future. In fact, combining the measured Cabibbo-\nsuppressed tau distribution with hadronic e+e\u2212data, a\nslightly larger value of |Vus| is obtained (Maltman, 2009;\nMaltman, Wolfe, Banerjee, Nugent, and Roney, 2009).\nThe \ufb01nal error of the |Vus| determination from tau de-\ncay is dominated by the experimental uncertainties. This\nis in contrast with the standard determination from K\u21133\ndecays, where the achievable precision is limited by the-\noretical errors (Cirigliano, Ecker, Neufeld, Pich, and Por-\ntoles, 2012). If R\u03c4,S is measured with a 1% precision,\nthe resulting |Vus| uncertainty will get reduced to around\n0.6%, i.e. \u00b10.0013, making tau decay the best source of\ninformation on |Vus|.\nAn accurate measurement of the invariant-mass distri-\nbution of the \ufb01nal hadrons could allow one to perform a\nsimultaneous determination of |Vus| and the strange quark\nmass, through a correlated analysis of several weighted dif-\nferences \u03b4Rkl\n\u03c4 . However, the extraction of ms su\ufb00ers from\ntheoretical uncertainties related to the convergence of the\nperturbative series \u2206kl(\u03b1S). A better understanding of\nthese corrections is needed.\n\n655\n20.6.1.4 Spectral Functions\nThe invariant-mass distribution of the \ufb01nal state hadrons\nin tau decay contains very important information on the\nlow-energy dynamics of QCD. While the separate mea-\nsurement of each decay mode allows one to study the res-\nonance structure of hadronic form factors with di\ufb00erent\nJP and strangeness quantum numbers, the inclusive and\nsemi-inclusive distributions associated with the di\ufb00erent\nquark currents provide direct access to relevant perturba-\ntive and non-perturbative QCD parameters.\nThe precise determination of \u03b1S(m2\n\u03c4) requires that one\npins down the small non-perturbative contribution to\nR\u03c4,V +A in Eq. (20.6.17), which can only be done through\nan accurate measurement of the corresponding spectral\ndistribution. Similarly, a precise experimental determina-\ntion of the Cabibbo-suppressed distribution would help to\nimprove the extraction of |Vus|, which at present is mainly\nobtained from the total decay width. The inclusive distri-\nbution of hadrons with JP = 1\u2212provides complementary\ninformation, which is needed to predict the hadronic con-\ntribution to the anomalous magnetic moment of the muon\nand the running of the electromagnetic coupling from low\nenergies to the electroweak scale. While the present dis-\ncrepancies between e+e\u2212and tau data are limiting the\ninterpretation of the measured muon g \u22122, the uncertain-\nties induced by this hadronic distribution on \u03b1(M 2\nZ) are\nthe largest source of error in the Higgs mass value ex-\ntracted from precision electroweak tests, to be compared\nwith its direct measurement at the LHC.\nMoreover, the separate measurement of the vector and\naxial-vector spectral functions allows us to extract valu-\nable information on the dynamical breaking of chiral sym-\nmetry. The chiral invariance of massless QCD guarantees\nthat the two-point correlation function of a left-handed\nand a right-handed quark current vanishes identically to\nall orders in perturbation theory. The spontaneous break-\ning of chiral symmetry by the QCD vacuum generates a\nnon-zero value of \u03a0LR(s) = \u03a0(0+1)\nud,V (s) \u2212\u03a0(0+1)\nud,A (s), which\nat large momenta manifests in its OPE through opera-\ntors with dimension D \u22656. At very low momenta, Chiral\nPerturbation Theory (\u03c7PT) dictates the low-energy ex-\npansion of \u03a0LR(s) in terms of the pion decay constant\nand some \u03c7PT couplings (for a basic review of \u03c7PT, see\nEcker (1995); Pich (1995)). Analyticity relates the short-\nand long-distance regimes through the dispersion relation\n1\n2\u03c0i\nI\n|s|=s0\nds w(s) \u03a0LR(s) = \u2212\nZ s0\nsth\nds w(s) \u03c1(s)\n+ 2f 2\n\u03c0 w(m2\n\u03c0) + Res[w(s)\u03a0LR(s), s = 0] ,\n(20.6.25)\nwhere \u03c1(s) \u22611\n\u03c0 Im\u03a0LR(s) and w(s) is an arbitrary weight\nfunction that is analytic in the whole complex plane except\nat the origin (where it can have poles). The last term\nin Eq. (20.6.25) accounts for the possible residue at the\norigin.\nFor s0 \u2264m2\n\u03c4, the integral along the real axis can\nbe evaluated with the measured tau spectral functions.\nThe residues at zero are determined by the \u03c7PT low-\nenergy couplings and, taking s0 large enough, the OPE\ncan be applied in the entire circle |s| = s0. Therefore,\ntaking di\ufb00erent weight functions one can determine the\n\u03c7PT couplings and the OPE coe\ufb03cients from the tau\nspectral data (Davier, Girlanda, H\u00a8ocker, and Stern, 1998;\nGonzalez-Alonso, Pich, and Prades, 2008, 2010a,b). More-\nover, one can explicitly check the predicted QCD asymp-\ntotic behavior (absence of D < 6 contributions in the\nOPE), which is re\ufb02ected in the celebrated \ufb01rst and second\nWeinberg (1967) sum rules. The absence of perturbative\ncontributions makes Eq. (20.6.25) an ideal tool to also in-\nvestigate possible violations of quark-hadron duality,i.e.\nsmall departures from the OPE behavior at small values\nof s0 (Cata, Golterman, and Peris, 2005; Shifman, 2000).\nIt is worth noting that the information extracted from\n\u03a0LR(s) through Eq. (20.6.25) is needed to calculate the\nelectromagnetic penguin contribution to the CP-violating\nratio \u03b5\u2032\nK/\u03b5K in neutral kaon decays. Moreover, since the\nspontaneous breaking of the Standard Model electroweak\nsymmetry has the same formal pattern as the QCD chiral\nsymmetry breaking, \u03a0LR(s) can also be used to investi-\ngate strongly-coupled scenarios of electroweak symmetry\nbreaking (Peskin and Takeuchi, 1990, 1992).\nSince we lack a B Factory analysis of these spectral dis-\ntributions, the ALEPH (Barate et al., 1999; Schael et al.,\n2005) and OPAL (Abbiendi et al., 2004; Ackersta\ufb00et al.,\n1999) measurements are still being used at present. A\nchange of this unfortunate situation is certainly possible\nand appears to be mandatory. Signi\ufb01cant improvement of\nthe LEP measurements should be possible with the much\nlarger data samples collected at the B Factories .\n20.6.2 Tau lepton branching fractions\nThe B Factories, thanks to the large and clean recorded\ntau pairs sample, provide improved measurements of\nhadronic branching fractions for many modes and also\nprovide \ufb01rst measurements of several modes which have\nsmall branching fractions.\nTable 20.6.1 shows the B Factories results that have\nbeen included in the early 2012 HFAG report (Amhis\net al., 2012), while Table 20.6.2 shows the results from\ntwo recent papers, which have not yet been included in\nthe HFAG averages. The corresponding averages are also\nlisted.\n20.6.3 Hadronic spectral functions: Cabibbo-favored\nmodes\nA separate measurement of the mass distribution for each\ndecay mode allows one to study the resonance structure\nof hadronic form factors with di\ufb00erent JP and strange-\nness quantum numbers. In addition, as discussed in Sec-\ntions 20.6.1.1 to 20.6.1.4, inclusive invariant-mass distri-\nbutions of the \ufb01nal state hadrons in tau decay are very im-\nportant for the determination of fundamental constants,\n\n656\nTable 20.6.1. Hadronic tau lepton branching fractions, B, measured by the B Factory experiments that were used in the\nearly 2012 HFAG report (Amhis et al., 2012). The notation (ex.) K0 means the branching fraction excludes the contribution\nK0\nS \u2192\u03c0+\u03c0\u2212to a \u03c0+\u03c0\u2212contained in its \ufb01nal state.\nDecay mode\nSource\nB\nReference\nB(\u03c4 \u2192\u03c0\u2212\u03bd\u03c4)/B(\u03c4 \u2192e\u2212\u03bde\u03bd\u03c4)\nBABAR\n(59.45 \u00b1 0.57 \u00b1 0.25)%\nAubert (2010f)\nHFAG\n(60.675 \u00b1 0.321)%\nAmhis et al. (2012)\n\u03c4 \u2192h\u2212\u03c00\u03bd\u03c4\nBelle\n(25.67 \u00b1 0.01 \u00b1 0.39)%\nFujikawa (2008)\nHFAG\n(25.93 \u00b1 0.09)%\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212\u03c00\u03bd\u03c4\nBelle\n(25.24 \u00b1 0.01 \u00b1 0.39)%\nFujikawa (2008)\nHFAG\n(25.504 \u00b1 0.092) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212\u03c00\u03bd\u03c4\nBABAR\n(0.416 \u00b1 0.003 \u00b1 0.18)%\nAubert (2007ac)\nHFAG\n(0.432 \u00b1 0.015) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212K0\u03bd\u03c4\nBelle\n(0.808 \u00b1 0.004 \u00b1 0.026)%\nEpifanov (2007)\nBABAR\n(0.840 \u00b1 0.004 \u00b1 0.023)%\nAubert (2009s)\nHFAG\n(0.8206 \u00b1 0.0182) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212K0\u03c00\u03bd\u03c4\nBABAR\n(0.342 \u00b1 0.006 \u00b1 0.015)%\nParamesvaran (2009)\nBelle\n(0.384 \u00b1 0.004 \u00b1 0.016)%\nRyu (2012)\nHFAG\n(0.365 \u00b1 0.011) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212\u03c00K0\u03bd\u03c4\nBelle\n(0.148 \u00b1 0.002 \u00b1 0.008)%\nRyu (2012)\nHFAG\n(0.145 \u00b1 0.007) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212\u03c0\u2212\u03c0+\u03bd\u03c4(ex. K0)\nBABAR\n(8.833 \u00b1 0.007 \u00b1 0.127)%\nAubert (2008k)\nBelle\n(8.420 \u00b1 0.003 \u00b1 0.259)%\nLee (2010)\nHFAG\n(9.002 \u00b1 0.051) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212\u03c0\u2212\u03c0+\u03bd\u03c4(ex. K0)\nBABAR\n(0.272 \u00b1 0.0018 \u00b1 0.0092)%\nAubert (2008k)\nBelle\n(0.330 \u00b1 0.0012 \u00b1 0.017)%\nLee (2010)\nHFAG\n(0.293 \u00b1 0.007) \u00b7 10\u22122\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212K\u2212K+\u03bd\u03c4\nBABAR\n(1.346 \u00b1 0.010 \u00b1 0.036) \u00b7 10\u22123\nAubert (2008k)\nBelle\n(1.550 \u00b1 0.007 \u00b1 0.056) \u00b7 10\u22123\nLee (2010)\nHFAG\n(1.435 \u00b1 0.027) \u00b7 10\u22123\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212K\u2212K+\u03bd\u03c4\nBABAR\n(1.58 \u00b1 0.13 \u00b1 0.12) \u00b7 10\u22125\nAubert (2008k)\nBelle\n(3.29 \u00b1 0.17 \u00b1 0.20) \u00b7 10\u22125\nLee (2010)\nHFAG\n(2.18 \u00b1 0.80) \u00b7 10\u22125\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212\u03c6\u03bd\u03c4\nBABAR\n(3.42 \u00b1 0.55 \u00b1 0.25) \u00b7 10\u22125\nAubert (2008k)\n\u03c4 \u2192K\u2212\u03c6\u03bd\u03c4\nBelle\n(4.05 \u00b1 0.25 \u00b1 0.26) \u00b7 10\u22125\nInami (2006)\nBABAR\n(3.39 \u00b1 0.20 \u00b1 0.28) \u00b7 10\u22125\nAubert (2008k)\n\u03c4 \u21923h\u22122h+\u03bd\u03c4(ex. K0)\nBABAR\n(8.56 \u00b1 0.05 \u00b1 0.42) \u00b7 10\u22124\nAubert (2005ag)\nHFAG\n(8.23 \u00b1 0.31) \u00b7 10\u22124\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212\u03c00\u03b7\u03bd\u03c4\nBelle\n(1.35 \u00b1 0.03 \u00b1 0.07) \u00b7 10\u22123\nInami (2009)\nHFAG\n(1.39 \u00b1 0.07) \u00b7 10\u22123\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212\u03b7\u03bd\u03c4\nBABAR\n(1.42 \u00b1 0.11 \u00b1 0.07) \u00b7 10\u22124\ndel Amo Sanchez (2011m)\nBelle\n(1.58 \u00b1 0.05 \u00b1 0.09) \u00b7 10\u22124\nInami (2009)\nHFAG\n(1.528 \u00b1 0.081) \u00b7 10\u22124\nAmhis et al. (2012)\n\u03c4 \u2192K\u2212\u03c00\u03b7\u03bd\u03c4\nBelle\n(4.6 \u00b1 1.1 \u00b1 0.4) \u00b7 10\u22125\nInami (2009)\nHFAG\n(4.8 \u00b1 1.2) \u00b7 10\u22125\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212K0\u03b7\u03bd\u03c4\nBelle\n(8.8 \u00b1 1.4 \u00b1 0.6) \u00b7 10\u22125\nInami (2009)\nHFAG\n(9.4 \u00b1 1.5) \u00b7 10\u22125\nAmhis et al. (2012)\nsuch as \u03b1S(m\u03c4) and |Vus|. They also contain very impor-\ntant information about the low-energy dynamics of QCD.\nTo measure the inclusive mass distribution experimen-\ntally, one needs to separate vector and axial vector \ufb01nal\nstates based on the number of pions, while the Cabibbo-\n\n657\nTable 20.6.2. Recent hadronic tau lepton branching fractions, B, measured by the BABAR and Belle experiments that are not\nyet used in the early 2012 HFAG report (Amhis et al., 2012). The reported HFAG averages do not use the measurements listed\nhere. The notation (ex.)K0 means the branching fraction excludes the contribution K0\nS \u2192\u03c0+\u03c0\u2212to a \u03c0+\u03c0\u2212contained in its\n\ufb01nal state.\nDecay mode\nSource\nB\nReference\n\u03c4 \u2192\u03c0\u2212K0\u03bd\u03c4\nBelle\n(0.832 \u00b1 0.002 \u00b1 0.016)%\nRyu (2014)\n\u03c4 \u2192K\u2212K0\u03bd\u03c4\nBelle\n(0.148 \u00b1 0.0014 \u00b1 0.0054)%\nRyu (2014)\n\u03c4 \u2192\u03c0\u2212K0\u03c00\u03bd\u03c4\nBelle\n(0.386 \u00b1 0.004 \u00b1 0.014)%\nRyu (2014)\n\u03c4 \u2192K\u2212K0\u03c00\u03bd\u03c4\nBelle\n(0.150 \u00b1 0.002 \u00b1 0.008)%\nRyu (2014)\n\u03c4 \u2192\u03c0\u2212KSKS\u03bd\u03c4\nBABAR\n(2.31 \u00b1 0.04 \u00b1 0.08) \u00b7 10\u22124\nLees (2012ae)\nBelle\n(2.33 \u00b1 0.03 \u00b1 0.09) \u00b7 10\u22124\nRyu (2014)\nHFAG\n(2.4 \u00b1 0.5) \u00b7 10\u22124\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212KSKS\u03c00\u03bd\u03c4\nBABAR\n(1.60 \u00b1 0.20 \u00b1 0.22) \u00b7 10\u22125\nLees (2012ae)\nBelle\n(2.00 \u00b1 0.22 \u00b1 0.20) \u00b7 10\u22125\nRyu (2014)\n\u03c4 \u21923\u03c0\u22122\u03c0+\u03bd\u03c4 (ex. K0)\nBABAR\n(8.33 \u00b1 0.04 \u00b1 0.43) \u00b7 10\u22124\nLees (2012z)\n\u03c4 \u21923\u03c0\u22122\u03c0+\u03c00\u03bd\u03c4 (ex. K0)\nBABAR\n(1.65 \u00b1 0.05 \u00b1 0.09) \u00b7 10\u22124\nLees (2012z)\n\u03c4 \u2192\u03c0\u2212\u03c0\u2212\u03c0+\u03b7\u03bd\u03c4 (ex. K0)\nBABAR\n(2.25 \u00b1 0.07 \u00b1 0.12) \u00b7 10\u22124\nLees (2012z)\nHFAG\n(1.492 \u00b1 0.097) \u00b7 10\u22124\nAmhis et al. (2012)\n\u03c4 \u2192\u03c0\u2212\u03c00\u03c00\u03b7\u03bd\u03c4\nBABAR\n(2.01 \u00b1 0.34 \u00b1 0.22) \u00b7 10\u22124\nLees (2012z)\n\u03c4 \u2192\u03c0\u2212\u03c0\u2212\u03c0+\u03c9\u03bd\u03c4 (ex. K0)\nBABAR\n(8.4 \u00b1 0.4 \u00b1 0.6) \u00b7 10\u22125\nLees (2012z)\n\u03c4 \u2192\u03c0\u2212\u03c00\u03c00\u03c9\u03bd\u03c4\nBABAR\n(7.3 \u00b1 1.2 \u00b1 1.2) \u00b7 10\u22125\nLees (2012z)\nfavored and Cabibbo-suppressed modes with kaons are\ndistinguished by an odd or even number of kaons.\n20.6.3.1 \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\u03c4\nAmong the decay channels of the tau lepton, \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\u03c4\nhas the largest branching fraction. From the CVC theo-\nrem, the \u03c0\u2212\u03c00 mass spectrum can be related to the cross\nsection of the process e+e\u2212\u2192\u03c0+\u03c0\u2212and thus used to\nimprove a theoretical error on the anomalous magnetic\nmoment of the muon a\u00b5 = (g\u00b5 \u22122)/2.\nUsing a sample of 5,430,000 \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\u03c4 decays,\nBelle measures the branching fraction and the \u03c0\u03c00 mass\nspectrum (Fujikawa, 2010). After unfolding performed us-\ning the singular-value-decomposition method (H\u00a8ocker and\nKartvelishvili, 1996), the distribution for the \u03c0\u03c00 mass\nspectrum shown in Fig. 20.6.2(a) is obtained. This pre-\ncisely measured spectrum has a shape formed by \u03c1(770),\n\u03c1(1450) and \u03c1(1700) resonances and their interference.\nFigure 20.6.2(b) shows the pion form factor in the \u03c1(770)\nregion obtained from the \u03c0\u03c00 mass spectrum. The mea-\nsured branching fraction is\nB(\u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\u03c4) = (25.24 \u00b1 0.01(stat) \u00b1 0.39(syst))%.\n(20.6.26)\nThe discussion of the CVC relation and the evaluation\nof a\u00b5 using tau-lepton data including this Belle measure-\nment are provided in Section 20.7.\n20.6.3.2 \u03c4 \u2212\u2192(3\u03c0)\u2212\u03bd\u03c4\nThe three-pion \ufb01nal states form a dominant fraction of\nthe axial-vector current. The unfolded 3\u03c0 mass spectrum\ngiven by (1/\u0393)(d\u0393/dM), measured in \u03c4 \u2212\u2192\u03c0\u2212\u03c0+\u03c0\u2212\u03bd\u03c4\nby Belle (Lee, 2010), is shown in Fig. 20.6.3(a). The solid\nhistogram is the spectrum implemented in the current\nTAUOLA program (G\u00b4omez Dumm, Roig, Pich, and Por-\ntol\u00b4es, 2010a). A systematic di\ufb00erence between data and\nMC is observed at the peak region of the a1(1260) reso-\nnance. Belle (red circle) and ALEPH (solid circles) show\nvery good agreement in this peak region as can be seen in\nFig. 20.6.3(b) and (c). This indicates that the model in\nthe current TAUOLA should be updated. Figure 20.6.3(d)\nshows the ratio ALEPH/Belle\u22121. Both data show very\ngood agreement for M 2 between 0.7 and 2.0 GeV2/c4. Out-\nside this range di\ufb00erences of up to 20% between the ex-\nperiments have been observed. This can be attributed to\nthe imperfect modeling of the background or the detector\ne\ufb00ects. Further studies are needed for the high mass re-\ngion, where the mass spectrum plays an important role as\nthe spectral function of the axial-vector current (see the\ndiscussion in Section 20.6.1.4, and 20.6.5 for the recent\nstatus).\n20.6.3.3 \u03c4 \u2212\u2192(KK\u03c0)\u2212\u03bd\u03c4\nThe KK\u03c0 mode has both vector and axial-vector compo-\nnents. The axial-vector component arises from the Wess-\nZumino-Witten chiral-anomalous term (Wess and Zumino,\n1971; Witten, 1983) and the non-anomalous odd-intrinsic-\nparity amplitude (Ruiz-Femenia, Pich, and Portoles, 2003).\n\n658\n10\n10 2\n10 3\n10 4\n10 5\n10 6\n0\n0.5\n1\n1.5\n2\n2.5\n3\n(M\u03c0\u03c00)2\n(GeV/c2)2\nBelle\n(a) \nNumber of entries /0.05(GeV/c2)2\nData\nG&S Fit\n(\u03c1(770) + \u03c1(1450) + \u03c1(1700))\n5\n10\n15\n20\n25\n30\n35\n40\n45\n0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8\n(M\u03c0\u03c00)2\n(GeV/c2)2\n |F\u03c0|2\n(b)\nBelle\nALEPH\nCLEO\nG&S Fit\nFigure 20.6.2. (a) Unfolded \u03c0\u00b1\u03c00 mass spectrum for \u03c4 \u00b1 \u2192\n\u03c0\u00b1\u03c00\u03bd\u03c4 obtained by the Belle experiment (Fujikawa, 2008).\nSolid circles are the data and the solid line is a \ufb01t based on\nthe Gounaris-Sakurai (G&S) parameterization (Gounaris and\nSakurai, 1968). The error bars include both statistical and sys-\ntematic errors. (b) Pion form factor |F\u03c0(s)|2 in the \u03c1(770) re-\ngion derived from the \u03c0\u00b1\u03c00 mass spectrum.\nSee Shekhovtsova, Przedzinski, Roig, and W\u00b8as (2012) for\nmore details.\nThe unfolded KK\u03c0 mass spectrum measured by Belle\n(Lee, 2010) for the \u03c4 \u2212\u2192K\u2212K+\u03c0\u2212\u03bd\u03c4 is shown in Fig.\n20.6.4 (a). In this process there are contributions from\nboth vector and axial-vector currents. The current TAUOLA\noutput (histogram) does not give a satisfactory description\nof the data. In Fig. 20.6.4 (b), the result is compared with\na model prediction based on resonance chiral perturbation\ntheory (G\u00b4omez Dumm, Roig, Pich, and Portol\u00b4es, 2010a).\nThe comparison indicates that a larger axial-vector com-\nponent than the current prediction is needed to improve\nthe agreement between the data and model.\n]\n2\nc\n) [GeV/\n\u03c0\n\u03c0\n\u03c0\nM(\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n)]\n2\nc\n(a)\n1/N (dN/dM) [/10(MeV/\n0\n0.005\n0.01\n0.015\n0.02\n0.025\n2]\n2\nc\n [GeV/\n2)\n\u03c0\n\u03c0\n\u03c0\nM(\n0.5\n1\n1.5\n2\n2.5\n3\n]\n2\n))\n2\nc\n1/N (dN/ds) [/(10(MeV/\n(b)\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\ng0\ng0\n2]\n2\nc\n [GeV/\n2)\n\u03c0\n\u03c0\n\u03c0\n(c)\nM(\n0.5\n1\n1.5\n2\n2.5\n3\n]\n2\n))\n2\nc\n1/N (dN/ds) [/(10(MeV/\n-4\n10\n-3\n10\n-2\n10\ng0\ng0\n2)\n\u03c0\n\u03c0\n\u03c0\nM(\n0.5\n1\n1.5\n2\n2.5\n(d)\n3\n[y(aleph)-y(belle)]/y(belle)\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nGraph\nGraph\nFigure 20.6.3. (color online) (a) Unfolded mass spectrum\n(1/N)dN/dM for the \u03c0\u2212\u03c0+\u03c0\u2212system in \u03c4 \u2212\u2192\u03c0\u2212\u03c0+\u03c0\u2212\u03bd\u03c4\nmeasured by Belle (Lee, 2010). Solid circles with error bars\nare the data with statistical errors; solid-red histogram is the\nspectra implemented in the current TAUOLA program; the hor-\nizontal green band at the zero entry line shows the size of the\nsystematic uncertainties for data. (b) Comparison of \u03c0\u2212\u03c0\u2212\u03c0+\nmass spectra as a function of mass-squared between Belle (red\ncircle) and ALEPH (black circles). (c) in log-scale, (d) the ratio\nALEPH/Belle\u22121.\n20.6.3.4 \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03b7\u03bd\u03c4\nUsing a data sample of 490 fb\u22121, Belle has studied the\n\u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03b7\u03bd\u03c4 decay where the \u03b7 meson is reconstructed\n\n659\n]\n2\nc\n) [GeV/\n\u03c0\nM(KK\n1.2\n1.3\n1.4\n1.5\n1.6\n1.7\n1.8\n)]\n2\nc\n1/N (dN/dM) [/10(MeV/\n0\n0.01\n0.02\n0.03\n0.04\n(a)\n0.05\n)\n2\n (GeV\n\u03c0\nKK\n2\nM\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\n3.2\n)\n-1\n (GeV\n15\n/ds x 10\n\u0393\nd\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n(b)\n4\n stat.)\n\u2295\nData (Error = sys. \nTAUOLA MC\nPT (Roig, et al.), c4=-0.04,g4=-0.5\n\u03c7\nR\n (Axial vector contribution)\n (Vector contribution)\nFigure 20.6.4. (color online) (a) Unfolded mass spectrum\n(1/N)dN/dM for the K\u2212K+\u03c0\u2212system in \u03c4 \u2212\u2192K\u2212K+\u03c0\u2212\u03bd\u03c4\nmeasured by Belle (Lee, 2010). Solid circles with error bars\nare the data with statistical errors; solid-red histogram is the\nspectra implemented in the current TAUOLA program; the hor-\nizontal green band at the zero entry line shows the size of\nthe systematic uncertainties for data. (b) Comparison of the\nresult with the theoretical model based on resonance chiral-\nperturbation theory. Closed circles are Belle data, red-dashed\nand blue-dashed lines are the axial-vector and vector com-\nponents from the chiral-perturbation theory, respectively. the\npink-solid line is the sum of axial-vector and vector compo-\nnents. While the red-solid line is the model implemented in\nthe TAUOLA progarm (G\u00b4omez Dumm, Roig, Pich, and Portol\u00b4es,\n2010a).\nthrough its decay into \u03b3\u03b3 or \u03c0+\u03c0\u2212\u03c00 (Inami, 2009) and\nobtained the new world-average branching fraction of\n(0.139 \u00b1 0.008)%. The branching fraction and the mass\nspectrum are compared with the prediction from the CVC\ntheorem by Cherepanov and Eidelman (2011), using the\ndata from the process e+e\u2212\u2192\u03b7\u03c0+\u03c0\u2212including the recent\nresults from BABAR (Aubert, 2007bb) and SND (Achasov\net al., 2010) collaborations. Belle found that the expected\nbranching fraction (0.153\u00b10.018)% is compatible with the\ntau result and that the mass spectra of the \u03b7\u03c0+\u03c0\u2212system\nin e+e\u2212annihilation and tau decay are consistent with the\nCVC expectation.\n20.6.4 Hadronic spectral functions:\nCabibbo-suppressed modes\n10\n-1\n1\n10\n10 2\n10 3\n10 4\n0.8\n1\n1.2\n1.4\n1.6\nMINV(KS\u03c0), GeV/c2\nNEVENTS\n(a)\nSignal\nKSKL\u03c0\nKS\u03c0\u03c00\nKSK\n3\u03c0\nnon-\u03c4\u03c4\n(b)\nMass (Gev)\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\nentries\n1\n10\n2\n10\n3\n10\n4\n10\nData\nfit\nBABAR\npreliminary\nFigure 20.6.5. KS\u03c0 mass distribution measured by (a)\nBelle (Epifanov, 2007) and by (b) BABAR (Adametz, 2011).\nPoints with error bars in both \ufb01gures are data, the histogram\nshows the \ufb01tted result for the spectrum expected in the model\nincorporating the K\u2217(892) + K\u2217\n0(800) + K\u2217(1410) model. In\nBelle data, di\ufb00erent types of background are also shown, while\nin the BABAR plot, the background is already subtracted.\n20.6.4.1 \u03c4 \u2212\u2192(K\u03c0)\u2212\u03bd\u03c4\nA data sample of 351 fb\u22121 has been used by Belle to study\nthe KS\u03c0\u2212\u03bd\u03c4 \ufb01nal state (Epifanov, 2007). As a result of\nthe analysis, 53,110 lepton-tagged signal events have been\nselected. The measured branching fraction obtained is\nB(\u03c4 \u2212\u2192KS\u03c0\u2212\u03bd\u03c4) = (0.404 \u00b1 0.002 \u00b1 0.013)%\n\n660\n(20.6.27)\nwhich is the most precise among all the published mea-\nsurements and is somewhat lower than all of them al-\nthough within errors consistent with the other results.\nAn analysis of the KS\u03c0\u2212invariant mass spectrum\nshown in Fig. 20.6.5 (top) reveals the dominant contri-\nbution from the K\u2217(892)\u2212with additional contributions\nof higher-mass states at 1400 MeV. A satisfactory \ufb01t is\nobtained only if the existence of a broad scalar state,\nK\u2217\n0(800), is assumed. For the \ufb01rst time the K\u2217(892)\u2212\nmass and width have been measured in tau decay:\nM(K\u2217(892)\u2212) =(895.47 \u00b1 0.20 \u00b1 0.44 \u00b1 0.59) MeV,\n\u0393(K\u2217(892)\u2212) =(46.2 \u00b1 0.6 \u00b1 1.0 \u00b1 0.7) MeV,\n(20.6.28)\nwhere the \ufb01rst uncertainty is the statistical and the sec-\nond systematic. The third uncertainty is model-based. The\nK\u2217(892)\u2212mass is signi\ufb01cantly higher than the world-\naverage value based on various hadronic experiments and\nis much closer to the world average for the neutral K\u2217(892)\n(Nakamura et al., 2010).\nRecently the BABAR collaboration presented the KS\u03c0\u2212\ninvariant mass spectrum in the KS\u03c0\u2212\u03bd\u03c4 decay\n(Adametz, 2011). Figure 20.6.5 (bottom) shows the KS\u03c0\u2212-\ninvariant mass distribution and the \ufb01t result. The mass\nand width of the K\u2217(892)\u2212resonance determined using a\nK\u2217(892) + K\u2217\n0(800) +K\u2217(1410) model yield\nM(K\u2217(892)\u2212) = (894.57 \u00b1 0.19 \u00b1 0.19) MeV,\n\u0393(K\u2217(892)\u2212) = (45.56 \u00b1 0.43 \u00b1 0.57) MeV.\n(20.6.29)\nThe values of the K\u2217(892)\u2212mass and width obtained by\nthe B Factories are in agreement with each other. How-\never, it should be noted that BABAR did not present an\nuncertainty induced by the ambiguity in the model used\nfor the mass spectrum \ufb01t.\n20.6.4.2 \u03c4 \u2212\u2192(K\u03c0\u03c0)\u2212\u03bd\u03c4\nThe unfolded K\u2212\u03c0+\u03c0\u2212mass spectrum measured by Belle\n(Lee, 2010), shown in Fig. 20.6.6 (a), has a peak at\n1.25 GeV/c2 and shoulder at 1.4 GeV/c2, corresponding to\nK1(1270) and K1(1400), respectively. The model in the\nTAUOLA reproduces the qualitative features of the mass\nspectra but fails to reproduce their detail.\n20.6.5 Inclusive non-strange spectral function\nAs was discussed in Section 20.6.1.2, the inclusive non-\nstrange (Cabibbo-favored) spectral function plays an im-\nportant role for the determination of \u03b1S and various theo-\nretical tests of QCD in the transition region between per-\nturbative QCD and resonances. The results obtained by\n]\n2\nc\n) [GeV/\n\u03c0\n\u03c0\nM(K\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n)]\n2\nc\n1/N (dN/dM) [/10(MeV/\n0\n0.01\n0.02\n0.03\n(a)\n0.04\n2)\n2\nc\n (GeV/\n2)\n\u03c0\n\u03c0\nM(K\n0.5\n1\n1.5\n2\n2.5\n3\n(s)\n1\ns\nSpectral function a\n0\n0.2\n0.4\n(b)\n0.6\nFigure 20.6.6. (color online) (a) Unfolded mass spectrum\n(1/N)dN/dM for the K\u2212\u03c0+\u03c0\u2212system in \u03c4 \u2212\u2192K\u2212\u03c0+\u03c0\u2212\u03bd\u03c4\nmeasured by Belle (Lee, 2010). Solid circles with error bars are\nthe data with statistical errors; solid-red histogram is the spec-\ntra implemented in the current TAUOLA program. (b) K\u2212\u03c0+\u03c0\u2212\nspectral function exstructed from the unfolded mass spectrum.\nThe horizontal green band at the zero entry line shown in the\nboth \ufb01gures indicate the size of the systematic uncertainties\nfor data.\nLEP experiments are shown in Fig. 20.6.7 for the vec-\ntor current, and in Fig. 20.6.8, for the axial-vector cur-\nrent. The statistical errors in the high mass region above\n2 GeV2/c4, where perturbative QCD plays an important\nrole, are large. Mass spectra data can contribute signi\ufb01-\ncantly to the improvement of our knowledge of this region.\nSee Boito et al. (2012) for a recent discussion of the im-\nportance of the new data in this region.\n20.6.6 Inclusive strange spectral functions\nAn accurate measurement of strange (Cabibbo-suppressed)\nspectral function plays an important role in the simulta-\nneous determination of |Vus| and the strange quark mass\nms (see Section 20.6.1.3). The strange spectral function\navailable now is obtained from the ALEPH and OPAL\nexperiments at LEP (see Fig. 20.6.9) and has large er-\nrors with coarse binning. Exclusive spectral functions for\nK\u2212K+\u03c0\u2212(Fig. 20.6.4 (b)) and K\u2212\u03c0+\u03c0\u2212(Fig. 20.6.6 (b))\nmeasured by the Belle, show a signi\ufb01cant improvement\n\n661\n0\n0.5\n1\n1.5\n2\n2.5\n3\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n\u03c4\u2013 \u2192 V\u2013\u03bd\u03c4\n\u03c0\u2013\u03c00\n\u03c0\u20133\u03c00, 2\u03c0\u2013\u03c0+\u03c00, (6\u03c0)\u2013\n\u03c9\u03c0\u2013, \u03b7\u03c0\u2013\u03c00, (KK\n\u2013(\u03c0))\u2013\nQCD prediction\nparton model\ns (GeV2)\nv1(s)\nALEPH\n(a)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n0\n0.5\n1\n1.5\n2\n2.5\n3\ns (GeV2)\nv(s)\nOPAL\n(b)\n\u03c0 \u03c00\n3\u03c0 \u03c00, \u03c0 3\u03c00\nMC corr.\nperturbative QCD (massless)\nna\u00efve parton model\nFigure 20.6.7. Vector spectral functions measured by (a)\nALEPH (Davier, Hoecker, and Zhang, 2006; Schael et al., 2005)\nand (b) OPAL (Ackersta\ufb00et al., 1999) experiments.\nover the previous LEP experiments. The measurements\nfor all Cabibbo-suppressed modes, and their sum, to ob-\ntain the total inclusive spectral function are in progress.\n20.6.7 Search for second-class currents\nStandard Model processes that are mediated by the\ncharged hadronic weak current, such as semihadronic tau\ndecays, produce hadronic systems with a well-de\ufb01ned\nset of allowed quantum numbers for spin, parity and\nG-parity. In tau decays these so-called \ufb01rst-class cur-\nrents (Weinberg, 1958) yield hadronic systems with\nJP G = 0++, 0\u2212\u2212, 1+\u2212or 1\u2212+.\nThe quantum numbers JP G = 0+\u2212, 0\u2212+, 1++ and 1\u2212\u2212\nwould be associated with second-class currents. Small con-\ntributions to second-class currents, at the level of order\n10\u22125 to 10\u22126, are expected from isospin violation (and\nhence G-parity violation) due to the mass di\ufb00erence be-\ntween the up and down quarks (Berger and Lipkin, 1987;\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\nQCD prediction\nParton model\n\u03c4\u2013 \u2192 A\u2013\u03bd\u03c4\n\u03c0\u20132\u03c00, 2\u03c0\u2013\u03c0+\n(5\u03c0)\u2013\n(KK\n\u2013\u03c0)\u2013\ns (GeV2)\na1(s)\nALEPH\n(a)\n0\n0.5\n1\n1.5\n2\n2.5\n3\n0\n0.5\n1\n1.5\n2\n2.5\n3\ns (GeV2)\na(s)\nOPAL\n(b)\n3\u03c0, \u03c0 2\u03c00\n3\u03c0 2\u03c00\nMC corr.\nperturbative QCD (massless)\nna\u00efve parton model\nFigure 20.6.8. Axial Vector spectral functions measured by\n(a) ALEPH (Davier, Hoecker, and Zhang, 2006; Schael et al.,\n2005) and (b) OPAL (Ackersta\ufb00et al., 1999) experiments.\nNussinov and So\ufb00er, 2008, 2009; Pich, 1987). However,\nsecond-class currents have not been seen to date in tau de-\ncays, nor indeed in any processes mediated by the hadronic\nweak current. Observation at a level signi\ufb01cantly above\nthat expected from isospin violation would be a signal for\nnew physics contributions (Langacker, 1977).\nTau decay modes that have the quantum numbers as-\nsociated with second-class currents include: \u03c4 \u2212\u2192\u03b7\u03c0\u2212\u03bd\u03c4\nand \u03c4 \u2212\u2192\u03b7\u2032(958)\u03c0\u2212\u03bd\u03c4, both of which correspond to\nJP G = 0+\u2212or 1\u2212\u2212; and \u03c4 \u2192\u03c9(782)\u03c0\u2212\u03bd\u03c4 with the \u03c9\nand \u03c0\u2212in a relative S-wave or D-wave. However, the\n\u03c9(782)\u03c0\u2212\u03bd\u03c4 mode is dominated by the P-wave JP G =\n1\u2212+ \u03c4 \u2212\u2192\u03c1(770)\u2212\u03bd\u03c4 and \u03c1\u2032\u03bd\u03c4 decays, and an angular\nanalysis is required to search for any S-wave or D-wave\n(second-class) contribution.\nBefore the B Factory experiments, the best upper lim-\nits on second-class currents in tau decays came from CLEO\nfor the \u03b7 and \u03b7\u2032 modes (Bartelt et al., 1996) and from\nALEPH for the \u03c9\u03c0\u2212mode (Buskulic et al., 1997). BABAR\nhas published results for all of the above modes, providing\n\n662\n0\n1\n2\n3\n4\n5\n6\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n\u03c4\u2013 \u2192 S\u2013\u03bd\u03c4\nK\n\u2013\u03c0\nK\n\u2013 2\u03c0\nK\n\u2013 3\u03c0 + K\u2013\u03b7 (MC)\nK\n\u2013 4\u03c0 (MC)\nK\n\u2013 5\u03c0 (MC)\npert QCD / parton model\ns (GeV2)\n(v1 + a1)S(s)\nALEPH\n(a)\nOPAL\n(K) from PDG\n\u2212\n(K\u03c0+K\u03b7)\u2212\n(K\u03c0\u03c0+K\u03b7\u03c0)\u2212\n(K\u03c0\u03c0\u03c0)\u2212\nna\u00efve parton model\ns (GeV2 )\n(v+a)\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n(b)\n0.5\n1\n1.5\n2\n2.5\n3\nFigure\n20.6.9.\nStrange spectral functions measured by\n(a) ALEPH\n(Davier, Hoecker, and Zhang, 2006) and (b)\nOPAL (Abbiendi et al., 2004) experiments.\nsigni\ufb01cant improvements in upper limits for the branching\nfractions, but continues to see no evidence for the existence\nof second-class currents.\nThe \u03c4 \u2212\u2192\u03b7\u03c0\u2212\u03bd\u03c4 channel has been studied by BABAR,\nusing the \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 decay mode (del Amo Sanchez,\n2011m). The basic method is to select a sample of can-\ndidate \u03c4 \u2212\u2192\u03c0\u2212\u03c0\u2212\u03c0+\u03c00\u03bd\u03c4 decays and to \ufb01t the inclu-\nsive \u03c0+\u03c0\u2212\u03c00 mass spectrum for the contribution from \u03b7.\nThe limiting factors in this analysis are the relatively large\ncombinatorial background in the 3\u03c0 spectrum from tau de-\ncays to \u03c9(782)\u03c0\u2212\u03bd\u03c4 and \u03c1\u03c0\u03c0\u03bd\u03c4, and the background from\n\u03c4 \u2212\u2192\u03b7\u03c0\u2212\u03c00\u03bd\u03c4 where the additional \u03c00 is undetected.\nThe former background cannot be removed without pro-\nducing signi\ufb01cant distortions of the phase space, and intro-\nducing a strong model dependence in any limit. For these\nreasons, the limit on the branching fraction obtained by\nBABAR, < 0.9 \u00d7 10\u22124 at 95% C.L., was dominated by sys-\ntematic errors and represented only a small improvement\nover the previously existing limit from CLEO (Bartelt\net al., 1996). It may be possible to improve limits further\nat both BABAR and Belle using the \u03b7 \u2192\u03b3\u03b3 decay mode,\nbut here again large backgrounds may be expected, par-\nticularly from \u03c4 \u2212\u2192\u03b7\u03c0\u2212\u03c00\u03bd\u03c4 and \u03c4 \u2212\u2192\u03c0\u2212\u03c00\u03bd\u03c4.\nBABAR has also looked for the second-class current\nmode \u03c4 \u2212\u2192\u03b7\u2032(958)\u03c0\u2212\u03bd\u03c4, with the decay mode \u03b7\u2032 \u2192\n\u03b7\u03c0+\u03c0\u2212and \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 (Lees, 2012z). A \ufb01t for a possi-\nble \u03b7\u2032 contribution in the inclusive \u03b7\u03c0+\u03c0\u2212mass spectrum\ngave no signi\ufb01cant signal above the expected background,\n/\nt\ne\ncos\n-1\n-0.8 -0.6 -0.4 -0.2\n-0\n0.2\n0.4\n0.6 0.8\n1\nEntries/(0.1)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n6\n10\n\u00d7\nFigure 20.6.10. Distribution of cos \u03b8\u03c9\u03c0 from \u03c4 \u2192\u03c9(782)\u03c0\u2212\u03bd\u03c4\nevents in BABAR (Aubert, 2009ap). Here \u03b8\u03c9\u03c0 is the angle, in\nthe \u03c9\u03c0\u2212rest frame, between the normal to the \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00\ndecay plane and the direction of the pion. The curve shows a\n\ufb01t to determine the relative contributions from \ufb01rst-class and\nsecond-class currents.\nallowing a limit to be set on the branching fraction at\n< 4.0 \u00d7 10\u22126 at a 90% C.L.. This is the lowest limit ob-\ntained for any possible second-class decay mode of the tau\nand is at the level where the e\ufb00ects of isospin violation\nmay be expected to appear.\nFigure 20.6.10 is taken from the BABAR analysis of the\nchannel \u03c4 \u2192\u03c9(782)\u03c0\u2212\u03bd\u03c4 (Aubert, 2009ap), and shows\nthe distribution of cos \u03b8\u03c9\u03c0, where \u03b8\u03c9\u03c0 is the angle, in the\n\u03c9\u03c0\u2212rest frame, between the normal to the \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00\ndecay plane and the direction of the pion. This distribu-\ntion has been corrected for the combinatorial background,\nusing distributions from the \u03c9 mass sidebands. The curve\nis a \ufb01t to a sum of S-wave and P-wave contributions. It\nis apparent that the data correspond to an almost pure\nsin2 \u03b8\u03c9\u03c0 distribution, as expected from a P-wave decay.\nThe \ufb01t allows a limit to be put on an possible S-wave\n(i.e. second-class current) contribution to this mode at\na level of < 0.0069 at a 95% C.L.. This corresponds to\nan absolute limit on the branching fraction for the decay\n\u03c4 \u2192\u03c9(782)\u03c0\u2212\u03bd\u03c4 via a second-class current of < 1.4\u00d710\u22124\nat 95% C.L.\n20.7 Tests of CVC and vacuum hadronic\npolarization determination\nThe hypotheses of the CVC and isospin symmetry relate\nthe isovector part of e+e\u2212\u2192hadrons and correspond-\ning (vector current JP = 1\u2212) hadronic decay of the tau\n\n663\nlepton. This follows from the deep relation between weak\nand electromagnetic interactions. The weak vector cur-\nrent and the isovector part of the electromagnetic vector\ncurrent are di\ufb00erent components of the same vector cur-\nrent, so that the matrix element of these currents must\nbe identical assuming SU(2) symmetry. In this case the\nweak isovector current is assumed to be conserved in anal-\nogy with the electromagnetic current. This assumption is\nthe CVC hypothesis and was \ufb01rst introduced by Feyn-\nman and Gell-Mann into their theory of weak interaction\n(Feynman and Gell-Mann, 1958).\nAs a consequence, hadronic currents describing the\nCabibbo-allowed vector part of the tau hadronic decays,\nsuch as 2\u03c0, 4\u03c0, \u03c0\u03c0\u03b7 and \u03c0\u03c9 channels, and low-energy e+e\u2212\nannihilation are closely related to each other (Gilman and\nRhie, 1985). In fact, this relation was used to predict the\ndecays of a heavy lepton even before the discovery of the\ntau lepton (Thacker and Sakurai, 1971; Tsai, 1971).\n20.7.1 CVC and vacuum hadronic polarization\ncontribution in (g \u22122)\u00b5\nIn addition, the CVC relations allow one to use an in-\ndependent high-statistics data sample from tau decays\nfor increasing accuracy of the prediction of the hadronic\ncontributions to the muon anomalous magnetic moments\na\u00b5 = (g \u22122)/2 (Alemany, Davier, and Hoecker, 1998).\nHere, we brie\ufb02y review the basic formula required for this.\nThe leading-order hadronic contribution ahad,LO\n\u00b5\ncan\nbe obtained by using a combination of experimental data\nand perturbative QCD for the hadronic vacuum polariza-\ntion (HVP) of the photon. At low energies, where QCD\ndoes not provide a reliable calculation, the HVP can be\nobtained as a sum over the production cross section of\neach e+e\u2212\u2192X0 channel (Jegerlehner and Ny\ufb00eler, 2009;\nMiller, de Rafael, and Roberts, 2007).\nahad,LO\n\u00b5\n(e+e\u2212) = \u03b12\n3\u03c02\nZ \u221e\n4m2\u03c0\ndsK(s)\ns\nR(0)\nX0(s),\n(20.7.1)\nwhere s is the CM energy squared of the hadron system\nand R(0)\nX0 is the ratio of hadronic X0 to point-like \u00b5+\u00b5\u2212\nbare cross sections in e+e\u2212annihilation given by\nR(0)\nX0(s) = 3s\u03c3X0(s)\n4\u03c0\u03b12\n= 3v0(s).\n(20.7.2)\nThe behavior of the QED kernel K(s) \u223c1/s enhances\nthe low-energy contributions to ahad,LO\n\u00b5\n(Jegerlehner and\nNy\ufb00eler, 2009).\nIn the limit of isospin invariance (v0 = v1) and taking\ninto account the isospin breaking e\ufb00ects, the spectral func-\ntion of the vector current decay \u03c4 \u2192X\u2212\u03bd\u03c4 is related to\nthe e+e\u2212\u2192X0 cross section of the corresponding isovec-\ntor \ufb01nal sate X0,\n\u03c3X0(s) = 4\u03c0\u03b12\ns\nv1,X\u2212(s),\n(20.7.3)\nwhere s is the invariant mass squared of the tau \ufb01nal state\nX\u2212and \u03b1 is the electromagnetic \ufb01ne structure constant.\nThe term v1,X\u2212(s) is the vector spectral function in the\nCabibbo-allowed decays, which is given by\nv1,X\u2212(s) = 3Im\nh\n\u03a0(1)\nV (s)\ni\n=\nm2\n\u03c4\n6|Vud|2\nBX\u2212\nBe\n1\nNX\ndNx\nds\n(20.7.4)\n\u00d7\n\u0012\n1 \u2212s\nm2\u03c4\n\u0013\u22122 \u0012\n1 + 2s\nm2\u03c4\n\u0013\u22121 RIB(s)\nSEW\n,\nwhere, (1/NX)dNX/ds is the normalized invariant mass\nspectrum of the hadronic \ufb01nal state, BX\u2212denotes the\nbranching fraction of \u03c4 \u2212\u2192X\u2212\u03bd\u03c4. The values of other\nparameters, tau mass m\u03c4, the CKM matrix element |Vud|\nand the electron branching fraction Be are known pre-\ncisely.\nThe last term RIB(s)/SEW represents the correction\nfor the isospin-breaking (IB) e\ufb00ects. Short-distance elec-\ntroweak radiative e\ufb00ects lead to the correction SEW =\n1.0235 \u00b1 0.0003 (Davier, Eidelman, Hoecker, and Zhang,\n2003b). All the s-dependent isospin-breaking corrections\nare included in RIB(s). In the dominant \u03c0+\u03c0\u2212decay chan-\nnel, RIB(s) is given by\nRIB(s) = FSR(s)\nGEM(s)\n\u03b23\n0(s)\n\u03b23\n\u2212(s)\n\f\f\f\f\nF0(s)\nF\u2212(s)\n\f\f\f\f\n2\n,\n(20.7.5)\nwhere the subscripts i = 0, \u2212refer to the electric charge of\nthe 2\u03c0 system produced in e+e\u2212annihilation, and in \u03c4 \u2212\nlepton decay, respectively. FSR(s) refers to the \ufb01nal state\nradiative corrections in the e+e\u2212\u2192\u03c0\u2212\u03c0\u2212channel, and\nGEM(s) denotes the long-distance radiative corrections to\nthe inclusive \u03c0\u2212\u03c00 spectrum in \u03c4 \u2192\u03c0\u2212\u03c00\u03bd\u03c4. The second\ncorrection of the ratio of the pion velocities, \u03b23\n0(s)/\u03b23\n\u2212(s),\narises from \u03c0\u00b1 \u2212\u03c00 mass di\ufb00erence. The third IB correc-\ntion term |F0/F\u2212|2 involves the ratio of electromagnetic\n(F0) to weak (F\u2212) form factors and needs to be considered\ncarefully. This ratio involves two sources of IB: (a) \u03c1 \u2212\u03c9\nmixing e\ufb00ects and (b) the mass and width di\ufb00erence of\nneutral and charged \u03c1 mesons.\nTaking these IB corrections into account, the shift in\nthe lowest order hadronic contribution to the muon g \u22122\nusing tau data in the dominant \u03c0\u03c0 channel can be evalu-\nated as\n\u25b3ahad,LO\n\u00b5\n[\u03c0+\u03c0\u2212, \u03c4] = \u03b12\n3\u03c02\nZ \u221e\n4m2\u03c0\ndsK(s)\ns\n3v\u2212(s)\n\u00d7\n\u0014RIB(s)\nSEW\n\u22121\n\u0015\n.\n(20.7.6)\nThe most recent estimates for these e\ufb00ects are summarized\nin Table 20.7.1 (Castro, 2010; Davier et al., 2010). In the\ntable, the last term, the radiative corrections for photon-\ninclusive \u03c1 \u2192\u03c0\u03c0 is di\ufb00erent from the previous estimate\nin (Davier, Eidelman, Hoecker, and Zhang, 2003b).\nUsing all available \u03c0+\u03c0\u2212data from tau lepton decays,\nALEPH, CLEO, OPAL and Belle, and applying these IB\n\n664\nTable 20.7.1. Contributions to \u25b3ahad,LO\n\u00b5\n[\u03c0\u03c0, \u03c4](\u00d710\u221210) from\nthe isospin-breaking correction RIB(s). Corrections shown in\ntwo separate columns correspond to the results obtained us-\ning the Gounaris and Sakurai (1968)(GS), and Kuhn and\nSantamaria (1990)(KS) parameterization of pion form factors\n(Davier et al., 2010).\nSource\n\u25b3ahad,LO\n\u00b5\n[\u03c0\u03c0, \u03c4](10\u221210)\nGS model\nKS model\nSEW\n\u221212.21 \u00b1 0.15\nGEM\n\u22121.92 \u00b1 0.90\nFSR\n+4.67 \u00b1 0.47\n\u03c1 \u2212\u03c9 interference\n+2.80 \u00b1 0.19\n+2.80 \u00b1 0.15\nm\u03c0\u00b1 \u2212m\u03c00 e\ufb00ect on \u03c3\n\u22127.88\nm\u03c1\u00b1 \u2212m\u03c10\n0.20+0.27\n\u22120.19\n0.11+0.19\n\u22120.11\nm\u03c0\u00b1 \u2212m\u03c00 e\ufb00ect on \u0393\u03c1\n+4.09\n+4.02\n\u03c1 \u2192\u03c0\u03c0\u03b3 corr.\n\u22125.91 \u00b1 0.59\n\u22126.39 \u00b1 0.64\nTotal\n\u221216.07 \u00b1 1.22\n\u221216.70 \u00b1 1.23\n\u221216.07 \u00b1 1.85\ncorrections, the lowest order hadronic contributions ob-\ntained are summarized in the 2nd column of Table 20.7.2.\nThe new tau-based estimate of ahad,LO\n\u00b5\nis found to be 1.9\n\u03c3 lower than the results based on the e+e\u2212data. This up-\ndated estimate makes the di\ufb00erence between tau and e+e\u2212\nbased estimates closer than the previous ones reported by\nDavier, Eidelman, Hoecker, and Zhang (2003b).\nIn addition to these IB corrections, the importance of\nthe other e\ufb00ect that was not discussed is recently demon-\nstrated by Jegerlehner and Szafron (2011). They argue\nthat, in addition to \u03c1 \u2212\u03c9 mixing, \u03c1 \u2212\u03b3 interference ex-\nists in the e+e\u2212reaction and they contribute to ahad,LO\n\u00b5\n,\nbut that e\ufb00ect does not exist in tau-lepton decays. The\nsize of the \u03c1 \u2212\u03b3 interference e\ufb00ects is about 5% to 10%\nin the \u03c1-resonance region and changes the sign in the\nlower and upper side of the \u03c1 mass peak (see Fig.6 in\nJegerlehner and Szafron (2011)). After taking this e\ufb00ect\ninto account, the results of ahad,LO\n\u00b5\nobtained from e+e\u2212-\nbased and tau-based data are summarized in the 3rd col-\numn of Table 20.7.2. The table shows a good agreement\nbetween the e+e\u2212and tau-based results, if the \u03c1 \u2212\u03b3 ef-\nfects are taken into account. A similar estimation based\non a Hidden Local Symmetry model is given by Benayoun,\nDavid, DelBuono, and Jegerlehner (2012). To con\ufb01rm this\ninteresting proposal, further investigation at the higher 2\u03c0\nmass region as well as precise experimental tests of the\nCVC relation for other modes such as 4\u03c0, \u03c9\u03c0 and \u03b7\u03c0\u03c0 are\nimportant.\n20.7.2 CVC and \u03c0\u03c0 branching fraction\nThe CVC relation allows one to predict the branching frac-\ntion of the decay \u03c4 \u2192\u03c0\u03c00\u03bd\u03c4 (B\u03c0\u03c0) in terms of the isovec-\ntor part of the e+e\u2212\u2192\u03c0+\u03c0\u2212cross section after taking\ninto account the IB correction:\nBCV C\n\u03c0\u03c0\n= 3\n2\nBe|Vud|2\n\u03c0\u03b12m2\u03c4\nZ m2\n\u03c4\nsmin\nds s\u03c30\n\u03c0+\u03c0\u2212(s)\nTable 20.7.2. Lowest order hadronic (vacuum polarization)\ncontribution ahad,LO\n\u00b5\n[\u03c0\u03c0, \u03c4](\u00d710\u221210 based on all e+e\u2212data in-\ncluding recent BABAR (Lees, 2012n) and KLOE (Ambrosino\net al., 2009a; Babusci et al., 2013) results, and all tau data in-\ncluding recent Belle data (Fujikawa, 2010), obtained by Davier\net al. (2010) and Jegerlehner and Szafron (2011).\nDavier et al.\nJegerlehner and Szafron\nahad,LO\n\u00b5\n[ee]\n690.9 \u00b1 5.2\n690.8 \u00b1 4.7\nahad,LO\n\u00b5\n[\u03c4, ee]\n705.3 \u00b1 4.5\n691.0 \u00b1 4.7\n\u00d7\n\u0012\n1 \u22122\nm2\u03c4\n\u00132 \u0012\n1 + 2s\nm2\u03c4\n\u0013 SEW\nRIB\n, (20.7.7)\nwhere smin = (m\u03c0\u2212+ m\u03c00)2. The meaning of the other\nparameters is the same as for Eq. (20.7.5). The result us-\ning all e+e\u2212data including recent BABAR (Lees, 2012n)\nand KLOE (Ambrosino et al., 2009a; Babusci et al., 2013)\nresults is\nBCV C\n\u03c0\u03c0\n= (24.78 \u00b1 0.17 \u00b1 0.22)%,\n(20.7.8)\nwhile the average of the measured B\u03c0\u03c0 is (25.42 \u00b1 0.10)%\n(Davier et al., 2010). The di\ufb00erence is (0.64\u00b10.10\u00b10.28)%,\nwhich is still substantial, but less signi\ufb01cant than the\nprevious results (Davier, Eidelman, Hoecker, and Zhang,\n2003b).\nIf the \u03c1 \u2212\u03b3 mixing e\ufb00ect is included, the result is\nBCV C\n\u03c0\u03c0\n= (25.20 \u00b1 0.17 \u00b1 0.28)% (Jegerlehner and Szafron,\n2011), which is in good agreement with the measured\nbranching fraction.\n20.8 Measurement of |Vus|\nHere we describe three ways to determine |Vus| using tau\ndecays : B(\u03c4 \u2212\u2192K\u2212\u03bd\u03c4), B(\u03c4 \u2212\u2192K\u2212\u03bd\u03c4)/B(\u03c4 \u2212\u2192\u03c0\u2212\u03bd\u03c4),\nand the inclusive sum of tau branching fractions having\nnet strangeness of unity in the \ufb01nal state:\n1) We use the lattice QCD value of the kaon decay con-\nstant fK = 157 \u00b1 2 MeV (Follana, Davies, Lepage, and\nShigemitsu, 2008), and our value of\nB(\u03c4 \u2212\u2192K\u2212\u03bd\u03c4) = G2\nF f 2\nK|Vus|2m3\n\u03c4\u03c4\u03c4\n16\u03c0\u210f\n\u00d7\n\u0012\n1 \u2212m2\nK\nm2\u03c4\n\u00132\nSEW , (20.8.1)\nwhere SEW = 1.0201 \u00b1 0.0003 (Erler, 2004), to de-\ntermine |Vus| = 0.2204 \u00b1 0.0032 from results of the\nunitarity constrained \ufb01t. This value is consistent with\nthe estimate of |Vus| = 0.2255 \u00b1 0.0010 obtained using\nthe unitarity constraint on the \ufb01rst row of the CKM\nmatrix.\n2) We use fK/f\u03c0 = 1.189 \u00b1 0.007 from lattice QCD (Fol-\nlana, Davies, Lepage, and Shigemitsu, 2008), |Vud| =\n\n665\n0.97425 \u00b1 0.00022 (Hardy and Towner, 2009), and the\nlong-distance correction \u03b4LD = (0.03 \u00b1 0.44)%, esti-\nmated (Banerjee, 2008) using corrections to \u03c4 \u2192h\u03bd\u03c4\nand h \u2192\u00b5\u03bd\u00b5 (Decker and Finkemeier, 1994, 1995;\nMarciano, 2004; Marciano and Sirlin, 1993), for the\nratio\nB(\u03c4 \u2212\u2192K\u2212\u03bd\u03c4)\nB(\u03c4 \u2212\u2192\u03c0\u2212\u03bd\u03c4) = f 2\nK|Vus|2\nf 2\u03c0|Vud|2\n\u0010\n1 \u2212m2\nK\nm2\u03c4\n\u00112\n\u0010\n1 \u2212m2\u03c0\nm2\u03c4\n\u00112 (1 + \u03b4LD),\n(20.8.2)\nwhere short-distance electroweak corrections cancel in\nthis ratio.\nFrom the unitarity constrained \ufb01t, we obtain\nB(\u03c4 \u2212\u2192K\u2212\u03bd\u03c4)/B(\u03c4 \u2212\u2192\u03c0\u2212\u03bd\u03c4) = 0.0643 \u00b1 0.0009,\nwhich includes a small correlation (coe\ufb03cient of \u22120.5%)\nbetween the branching fractions. This yields |Vus| =\n0.2229 \u00b1 0.0021, which is also consistent with the value\nof |Vus| from the CKM unitarity prediction.\n3) The total hadronic width of the \u03c4 normalized to the\nelectronic branching fraction, Rhad = Bhad/Be, can be\nwritten as Rhad = Rnon\u2212strange+Rstrange. We can then\nmeasure\n|Vus| =\ns\nRstrange/\n\u0014Rnon-strange\n|Vud|2\n\u2212\u03b4Rtheory\n\u0015\n.\n(20.8.3)\nHere, we use |Vud| = 0.97425 \u00b1 0.00022 (Hardy and\nTowner, 2009), and \u03b4Rtheory = 0.240 \u00b1 0.032 (Gamiz,\nJamin, Pich, Prades, and Schwab, 2007) obtained with\nthe updated average value of ms(2 GeV) = 94 \u00b1 6 MeV\n(Jamin, Oller, and Pich, 2006), which contributes to\nan error of 0.0010 on |Vus|. We note that this error is\nequivalent to half the di\ufb00erence between calculations\nof |Vus| obtained using \ufb01xed order perturbation the-\nory and contour improved perturbation theory calcula-\ntions of \u03b4Rtheory (Maltman, 2010), and twice as large as\nthe theoretical error proposed in Gamiz, Jamin, Pich,\nPrades, and Schwab (2008).\nAs in Davier, Hoecker, and Zhang (2006), we improve\nupon the estimate of the electronic branching fraction\nby averaging its direct measurement with its estimates\nof (17.899 \u00b1 0.040)% and (17.794 \u00b1 0.062)% obtained\nfrom the averaged values of muonic branching fractions\nand the averaged value of the lifetime of the tau lepton\n= (290.6 \u00b1 1.0) \u00d7 10\u221215 s (Nakamura et al., 2010), as-\nsuming lepton universality and taking into account the\ncorrelation between the leptonic branching fractions.\nThis gives a more precise estimate for the electronic\nbranching fraction: Buni\ne\n= (17.852 \u00b1 0.027)%.\nAssuming lepton universality, the total hadronic branch-\ning fraction can be written as: Bhad = 1\u22121.972558 Buni\ne\n,\nwhich gives a value for the total \u03c4 hadronic width nor-\nmalized to the electronic branching fraction as Rhad =\n3.6291 \u00b1 0.0086.\nThe non-strange width is Rnon\u2212strange = Rhad\u2212Rstrange,\nwhere the estimate for the strange width Rstrange =\n0.1613 \u00b1 0.0028 is obtained from the sum of the strange\nbranching fractions with the unitarity constrained \ufb01t\nas listed in Table 199 in the HFAG report (Amhis et al.,\n2012). This gives a value of |Vus| = 0.2174 \u00b1 0.0022,\nwhich is 3.3 \u03c3 lower than the CKM unitarity predic-\ntion.\nA similar estimation using results from the uncon-\nstrained \ufb01t to the branching fractions gives |Vus| =\n0.2166 \u00b1 0.0023, which is 3.6 \u03c3 lower than the CKM\nunitarity prediction. Since the sum of base modes from\nour unconstrained \ufb01t is less than unity by 1.6 \u03c3, in-\nstead of using Bnon\u2212strange = 1 \u2212Bleptonic \u2212Bstrange,\nwe also evaluate |Vus| from the sum of the averaged\nnon-strange branching fractions. This gives |Vus| =\n0.2169 \u00b1 0.0023, which is 3.5 \u03c3 lower than the CKM\nunitarity prediction.\n|\nus\n|V\n0.2\n0.21\n0.22\n0.23\nCKM Unitarity\n 0.0010\n\u00b1\n0.2255 \n s inclusive)\n\u2192\n \u03c4\nHFAG Fit (\n 0.0022\n\u00b1\n0.2174 \n)\n\u03c4\u03bd \u03c0 \n\u2192\n \u03c4\n)/(\n\u03c4\u03bd\n K \n\u2192\n \u03c4\nHFAG Fit (\n 0.0022\n\u00b1\n0.2238 \n)\n\u03c4\u03bd\n K \n\u2192\n \u03c4\nHFAG Fit (\n 0.0032\n\u00b1\n0.2204 \nHyperon decays\n 0.0050\n\u00b1\n0.2260 \n decays\nl2\nFlaviaNet K\n 0.0013\n\u00b1\n0.2252 \n decays\nl3\nFlaviaNet K\n 0.0013\n\u00b1\n0.2254 \nHFAG-Tau\nSummer 2010\nFigure 20.8.1. Measurements of |Vus| from kaon, hyperon and\ntau decays (Asner et al., 2010).\nA summary of these |Vus| values is shown in Figure 20.8.1,\nwhere we also include values from kaon decays obtained\nfrom Antonelli et al. (2010b) and from hyperon decays ob-\ntained from Jamin (2007). The |Vus| determination from\nhyperon decays was done in Mateu and Pich (2005).\n20.9 Summary of the tau section\nIn summary, B Factory experiments contribute to various\naspects of physics related to tau leptons: The tau mass\n\n666\nis measured with an accuracy of 0.15 MeV, and the mass\ndi\ufb00erence of \u03c4 + and \u03c4 \u2212is tested at the level of 0.03%. The\ncharged current universality is tested at the level of 0.1\n\u22120.2 %. Two orders of magnitude more stringent limits\nare set for 50 lepton \ufb02avor violating tau-lepton decays.\nMeasurements of the tau-EDM and tau mass-di\ufb00erence\nare improved signi\ufb01cantly. For the CP violation of tau-\nlepton decays, the BABAR result shows a 2.8\u03c3 deviation\nfrom the Standard Model prediction for \u03c4 \u2212\u2192K0\nS\u03c0\u2212\u03bd\u03c4,\nwhile Belle \ufb01nd no indication of CP asymmetry in the\ndecay angular distribution.\nThe hadronic tau decays provide a beautiful labora-\ntory to measure the CKM matrix Vus and to study the\nstrong interactions. The values of Vus have been estimated\nvia various methods. The value derived from the inclu-\nsive strange branching fraction provides a result some-\nwhat smaller than the one obtained from kaon decays. The\nbranching fractions and the precise spectral functions have\nbeen measured for various decay modes. The second-class\ncurrent has been searched for at the level of < 4.0 \u00d7 10\u22126\nin the mode \u03c4 \u2192\u03b7\u2032(958)\u03c0\u2212\u03bd\u03c4.\nYet, there are several on-going analyses, which include\nprecise measurements of the tau-lepton lifetime, Michel\nparameters and Cabibbo-allowed and Cabibbo-suppressed\ninclusive spectral functions.\nIn addition, a set of form factors based on \u201cReso-\nnance Chiral Theory\u201d(R\u03c7T) is recently implemented in\nthe TAUOLA MC program (Shekhovtsova, Przedzinski, Roig,\nand W\u00b8as, 2012). The formulae of R\u03c7T is designed to re-\nproduce chiral perturbation theory at the low energy limit\nand has a smooth transition to the perturbative QCD re-\nsults in the high energy region. They rely on the large-NC\nexpansion of QCD. It is nice since these formulae are de-\nsigned so that one can \ufb01t the data without violating the\nbasic requirements of QCD. Tests of R\u03c7T and the determi-\nnation of the model parameters by the data may provide\na new insight into the resonance region from QCD (see\nreferences in Shekhovtsova, Przedzinski, Roig, and W\u00b8as\n(2012) for detailed discussion).\nIn the near future, an additional two orders of mag-\nnitude increase in available data sets is expected to be\naccumulated by future \ufb02avor factories.\n\n667\nChapter 21\nInitial state radiation studies\nEditors:\nFabio Anulli (BABAR)\nGalina Pakhlova (Belle)\nAdditional section writers:\nMichel Davier, Vladimir P. Druzhinin, Simon I. Eidel-\nman, Bertrand Echenard, Mathew G. Graham, Simone\nPacetti, Antimo Palano, Evgeni P. Solodov, Timofey Uglov,\nShuwei Ye\n21.1 Introduction\nLow energy e+e\u2212annihilation are among the most pow-\nerful ways to study the nature of hadrons, because of the\nvery clean environment \u2014 with the perfectly known initial\nstate and the low multiplicity of the produced \ufb01nal states\n\u2014 as has been shown since the \ufb01rst e+e\u2212accumulation\nring, ADA, was built in Frascati (Bernardini, Corazza,\nGhigo, and Touschek, 1960; Cabibbo and Gatto, 1961).\nAt low energies, the hadrons observed in the \ufb01nal state\ncome from the hadronization of the original quark pair\nproduced by the e+e\u2212annihilation via a single interme-\ndiate virtual photon. The process of hadronization is well\ndescribed by Quantum Chromodynamics (QCD) for a rel-\natively high center-of-mass (CM) energy of the e+e\u2212sys-\ntem. However, QCD fails to describe the low energy re-\ngion, which is characterized by intense \ufb01nal state interac-\ntions and rich production of resonant states. Experimental\ndata in this energy region are of fundamental importance\nboth as an input and as validation for the various QCD-\nbased theoretical models of hadronic interactions.\nThe total cross section of e+e\u2212annihilation into had-\nrons is also the experimental input to the calculation of\nthe hadronic contribution to both the anomalous magnetic\nmoment of the muon and the value of the running \ufb01ne-\nstructure constant at the Z0 pole. Therefore, it provides\nhigh precision tests of the Standard Model and searches\nfor New Physics e\ufb00ects.\nStudies of the nature of known light and heavy vector\nmesons, and searches for new resonant states, can be per-\nformed measuring exclusive \ufb01nal states over a wide energy\nrange.\nA novel method of studying e+e\u2212annihilation using\ninitial state radiation (ISR) has been developed in the last\ndecade at various high-luminosity e+e\u2212colliders. Most\nof the results presented in this chapter rely on the ISR\ntechnique (exceptions include D(\u2217)+D(\u2217)\u2212production far\nfrom threshold, Section 21.4.1, and dark force searches,\nSection 21.6). The experimental method, with its theo-\nretical foundations, is described in the next section. Sec-\ntion 21.3 reports on the measurement of a number of\nlight meson \ufb01nal states, with implications for the value of\n(g\u22122)\u00b5 discussed in Section 21.3.2. Measurements of time-\nlike baryon form factors are presented in Section 21.3.7,\nwhile Sections 21.4 and 21.5 report on the studies of open-\ncharm production via e+e\u2212annihilation and the searches\nfor new, possibly exotic, vector states, respectively. A de-\ntailed discussion of the results of these two sections can\nbe found in sections 18.2 and 18.3. Finally, Section 21.6\npresents a search for e+e\u2212annihilation into multi-lepton\n\ufb01nal states at a CM energy of \u223c10.6 GeV, which could\nbe a manifestation of dark boson decays.\n21.2 The Initial State Radiation method\nThe e+e\u2212annihilation process is described at lowest order\nby the Feynman diagram shown in Fig. 21.2.1. The center-\nof-mass energy squared is given by s = 4E\u22172\nb , for a collider\noperating with beams of CM energy E\u2217\nb . Exclusive and\ntotal hadronic cross sections as a function of s have usually\nbeen obtained by scanning the accessible energy range,\nand collecting a certain amount of data at each value of\nthe beam energies.\ne+\nhadrons\ne-\nFigure 21.2.1. The lowest-order Feynman diagram describing\nthe process of e+e\u2212annihilation into hadrons.\nHowever, the colliding electrons can emit one or se-\nveral photons from the initial state, so that the e\ufb00ective\nCM energy of the e+e\u2212collision can take any value from\nmth, the production threshold of the hadronic system,\nup to \u221as = 2E\u2217\nb . The process e\ufb00ectively studied is thus\ne+e\u2212\u2192f + n\u03b3, n = 0, 1, 2, ..., where f is a given \ufb01nal\nstate; the cross section depends on the Born cross section\nat all energies below \u221as (Kuraev and Fadin, 1985):\n\u03c3(s) =\n1\u2212m2\nth/s\nZ\n0\nW(s, x) \u03c30(s(1 \u2212x)) dx .\n(21.2.1)\nHere, x is the fraction of the beam energy carried by the\nphotons emitted from the initial state, the radiator func-\ntion W(s, x) is the photon emission probability density\nfunction, which is fully calculable in QED (see e.g. Actis\net al. (2010) and references therein), and \u03c30(s(1 \u2212x)) is\nthe Born cross section for the process e+e\u2212\u2192f at the\nreduced center-of-mass energy squared\ns\u2032 = s(1 \u2212x).\n(21.2.2)\n\n668\nIn energy-scan experiments, the contribution of ISR is\nnormally suppressed by requiring energy and momentum\nbalance between the \ufb01nal hadronic state and the initial\ne+e\u2212state. This limits the fraction of energy carried by\nradiated photons within the experimental resolution, and\nEq.(21.2.1) can then be written as\n\u03c3(s) = \u03c30(s) (1 + \u03b4(s)),\n(21.2.3)\nwhere the factor 1 + \u03b4(s) summarizes the QED radiative\ncorrections, which can be as large as 10% for slowly vary-\ning cross sections.\nOn the other hand, the emission of initial state radia-\ntion allows the study of e+e\u2212annihilation for a continu-\nous spectrum of energies below the nominal beam energy,\nwithout changing the operating conditions of the collider,\nas outlined long ago (Baier and Khoze, 1965; Bonneau\nand Martin, 1971). This becomes clear when we write the\ndi\ufb00erential form of the cross section\nd\u03c3(s, x)\ndx\n= W(s, x) \u03c30(s(1 \u2212x)),\n(21.2.4)\nand note that the reduced CM energy after photon emis-\nsion is just the invariant mass of the hadronic system:\nm =\np\ns(1 \u2212x). In terms of m, the di\ufb00erential cross sec-\ntion becomes\nd\u03c3(s, m)\ndm\n= 2m\ns W(s, m) \u03c30(m).\n(21.2.5)\nIt should also be noted that the dominant contribu-\ntion from ISR processes comes from the diagram shown in\nFig. 21.2.2, with a single photon emitted. From the experi-\nmental point of view, the Born di\ufb00erential cross section for\nthe process e+e\u2212\u2192f as a function of m is obtained from\nthe measurement of the cross section for e+e\u2212\u2192\u03b3ISR+f.\ne+\nhadrons\ne-\n!\nFigure 21.2.2. The lowest-order Feynman diagram describing\nthe process of e+e\u2212\u2192\u03b3ISR + hadrons.\nThe experimental method, and the potential for pre-\ncise measurements of the hadronic cross sections and for\nlow-energy spectroscopy at the forthcoming \u03c6- and B Fac-\ntories, were discussed in several papers at the end of the\n90\u2019s: Arbuzov, Kuraev, Merenkov, and Trentadue (1998);\nBenayoun, Eidelman, Ivanchenko, and Silagadze (1999);\nBinner, K\u00a8uhn, and Melnikov (1999); Konchatnij and Me-\nrenkov (1999). The high luminosities reached in these col-\nliders provide substantial datasets despite the suppression\ndue to the additional QED vertex in Fig. 21.2.2.\n21.2.1 Radiator function and Monte Carlo generators\nThe dependence of the radiator function on the polar angle\nof the ISR photon with respect to the beam axis in the CM\nsystem is given at lowest order by (Bonneau and Martin,\n1971)\nW0(s, x, \u03b8) = \u03b1\n\u03c0x\n\uf8ee\n\uf8ef\uf8f0\n(2 \u22122x + x2) sin2 \u03b8 \u2212x2\n2 sin4 \u03b8\n\u0010\nsin2 \u03b8 + 4m2e\ns\ncos2 \u03b8\n\u00112\n\u22124m2\ne\ns\n(1 \u22122x) sin2 \u03b8 \u2212x2 cos4 \u03b8\n\u0010\nsin2 \u03b8 + 4m2e\ns\ncos2 \u03b8\n\u00112\n\uf8f9\n\uf8fa\uf8fb,\n(21.2.6)\nwhere \u03b1 is the \ufb01ne-structure constant, and me is the elec-\ntron mass. The ISR photons are emitted predominantly at\nsmall angles, however a signi\ufb01cant fraction of them have\nlarge angles. In particular, at CM energies \u221as \u223c10 GeV\nmore than 10% of the high-energy ISR photons are emit-\nted within the \ufb01ducial volume of the detector. These fea-\ntures provide the basis for two di\ufb00erent experimental ap-\nproaches to the study of ISR processes: The tagged ap-\nproach, with detection of the ISR photon, and the un-\ntagged one, where the detection of the ISR photon is not\nexplicitly required. These two approaches will be discussed\nin detail in Section 21.2.4.\nThe radiator function at lowest order is obtained by\nintegration of Eq.(21.2.6) over the polar angle in the CM\nframe, in the range appropriate to the experimental sit-\nuation. In the tagged approach, \u03b80 < \u03b8 < \u03c0 \u2212\u03b80, where\n\u03b80 \u226bme/\u221as is chosen to cover the \ufb01ducial volume of\nthe electromagnetic calorimeter. Writing C = cos \u03b80, the\nradiator function becomes\nW0(s, x, \u03b80) = \u03b1\n\u03c0x\n\u0014\n(2\u22122x+x2) ln 1 + C\n1 \u2212C \u2212x2C\n\u0015\n, (21.2.7)\nwhile for an untagged analysis (0<\u03b8<\u03c0)\nW0(s, x) = \u03b1\n\u03c0x(2 \u22122x + x2)\n\u0014\nln s\nm2e\n\u22121\n\u0015\n.\n(21.2.8)\nRadiative corrections to W0 are as large as 15% (Ku-\nraev and Fadin, 1985). It is therefore necessary to include\nhigher-order diagrams to reach the desired level of accu-\nracy in the calculation of W(s, x). The study of radiative\ncorrections to ISR processes has been pursued in several\ntheoretical works, some of which have been used as the ba-\nsis for Monte Carlo (MC) generators to be used in analysis\nof experimental data.\nTwo di\ufb00erent MC generators are used at the B Facto-\nries: AfkQed and PHOKHARA . The AfkQed package is based\non the EVA event generator (Binner, K\u00a8uhn, and Melnikov,\n1999; Czyz and K\u00a8uhn, 2001). It was initially designed to\nsimulate 2\u03c0 and 4\u03c0 production with the ISR photon emit-\nted at large angles. Soft multi-photon emission in the ini-\ntial state is generated with the structure function tech-\nnique (Ca\ufb00o, Czyz, and Remiddi, 1994), while \ufb01nal state\nradiation (FSR) is generated using the PHOTOS simulation\n\n669\npackage (Barberio, van Eijk, and W\u00b8as, 1991). The AfkQed\npackage provides the generation of a number of hadronic\n\ufb01nal states, including \u03c0+\u03c0\u2212, \u03c0+\u03c0\u2212\u03c00, 4\u03c0, 5\u03c0, 6\u03c0, and\nmodes with kaons and light baryons. Additional modes\ncan be easily implemented. It also includes the process\ne+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3, for which both ISR and FSR diagrams\nand their interference are taken into account. This gener-\nator is used by BABAR, for all the analyses where a tagged\nISR photon is required. In order to properly calculate the\nradiator function the ISR photon is generated in an angu-\nlar range slightly larger than the acceptance of the electro-\nmagnetic calorimeter, typically with 20\u25e6< \u03b8 < 160\u25e6. The\nachieved accuracy, of the order of 1%, is su\ufb03cient for all\nthe measured \ufb01nal states, with the exception of the \u03c0+\u03c0\u2212\nchannel, for which sub-percent precision is required. This\nparticular case will be discussed in detail in Section 21.3.3\nThe PHOKHARA event generator is based on theoreti-\ncal work by Rodrigo, Czyz, K\u00a8uhn, and Szopa (2002) and\nCzyz, Grzelinska, K\u00a8uhn, and Rodrigo (2003). The calcu-\nlations include one-loop corrections and next-to-leading\norder (NLO) ISR radiative corrections: that is, up to two\nhard ISR photons are generated. For the processes e+e\u2212\u2192\n\u03c0+\u03c0\u2212\u03b3, e+e\u2212\u2192K+K\u2212\u03b3, and e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3, NLO\nFSR corrections are also implemented, with interference\nbetween ISR and FSR. The accuracy in the determination\nof the radiator function is estimated to be about 0.5%. The\nPHOKHARA generator is used for both tagged and untagged\nISR studies, and it is particularly appropriate for mea-\nsurement of the \u03c0+\u03c0\u2212and K+K\u2212\ufb01nal states. It is used\nin both B Factory experiments, as well as in the KLOE\nexperiment at the \u03c6 factory DA\u03a6NE.\nIn the latest PHOKHARA version, several multi-hadron\n\ufb01nal states are implemented. However it should be noted\nthat for these more complex channels the main theoretical\nuncertainty does not come from the treatment of the ra-\ndiative corrections, but from the dependence of the matrix\nelement on the hadronic model used to describe the pro-\ncess. Detection e\ufb03ciencies estimated via MC simulation\ndepend in fact on the angular and momentum distribu-\ntions generated by the chosen model. In order to deter-\nmine a systematic uncertainty due to the model depen-\ndence, the hadron distributions from MC simulations are\nreweighted with those from data, and the detection ef-\n\ufb01ciencies resulting from di\ufb00erent theoretical models are\ncompared.\n21.2.2 Cross section\nExperimentally, the Born cross section as a function of\nm for the process e+e\u2212\u2192f, \u03c30(m), is obtained from\nthe measured mass spectrum of the corresponding ISR\nprocess e+e\u2212\u2192\u03b3ISRf, taking into account the detection\ne\ufb03ciency \u03b5(s, m), and the integrated luminosity L:\ndN(s, m)\ndm\n= \u03b5(s, m) d\u03c3(s, m)\ndm\nL.\n(21.2.9)\nReplacing the di\ufb00erential cross section by the expres-\nsion in Eq. (21.2.5), we obtain\ndN(s, m)\ndm\n= \u03b5(s, m) (1 + \u03b4r(s, m)) \u03c30(m) dLISR(m)\ndm\n,\n(21.2.10)\nwhere 1 + \u03b4r(s, m) = W(s, m)/W0(s, m) is the radiative\ncorrection factor mentioned in the previous subsection,\nand we have introduced the so-called e\ufb00ective ISR di\ufb00er-\nential luminosity:\ndLISR(m)\ndm\n= 2m\ns W0(s, m) L.\n(21.2.11)\nThe Born radiator function is given by Eq.(21.2.7) or\nEq.(21.2.8) depending on the experimental conditions.\nThe mass spectrum is then subdivided in small mass\nbins of width \u2206m, within which both W and \u03c30 vary little,\nand the cross section is extracted for each bin from the\nnumber of events \u2206N falling in that bin:\n\u03c30(mi) = \u2206N(mi)\n\u2206m\n1\n\u03b5(s, mi) (1 + \u03b4r) dLISR(mi)/dm.\n(21.2.12)\nThe ISR luminosity is the quantity to be compared\nwith the luminosity integrated by previous experiments\nvia conventional energy scan. The solid line in Fig. 21.2.3\nreports the mass dependence of the ISR di\ufb00erential lumi-\nnosity calculated at an e+e\u2212CM energy of 10.58 GeV,\nfor a tagged analysis, assuming a typical acceptance of\n10% and the integrated luminosity of the BABAR data set\nof 470 fb\u22121. The ISR luminosity, calculated considering\nan energy-bin width of 0.02 GeV, increases from about\n0.2 pb\u22121 at the \u03c0+\u03c0\u2212production threshold up to more\nthan 3 pb\u22121 at 3.5 GeV. Only part of this range has been\ncovered by energy scans at previous experiments. In par-\nticular the region below \u221as = 1.4 GeV has been inves-\ntigated with high precision by the SND and CMD-2 ex-\nperiments at the VEPP-2M collider in Novosibirsk. They\nhave collected a sample similar in size to that available\nat BABAR, in particular in the regions around the peaks\nof the vector meson resonances. There is much less data\navailable at energies above 1.4 GeV, most of it collected\nby the experiments DM1 and DM2 at the DCI collider in\nOrsay. The histograms in the \ufb01gure report the luminosity\nintegrated by CMD-2 and DM2. Precise measurements of\nthe e+e\u2212\u2192\u03c0+\u03c0\u2212cross section have also been performed\nby the KLOE experiment by means of both ISR untagged\nand tagged analyses. Information about the data collected\nby energy scan experiments has been extracted from sev-\neral published papers, whose main results are reported in\ncomparison with B Factories results in the following sec-\ntions.\nIn the mass region of charm production the ISR\nluminosity ranges from tens to hundreds of pb\u22121 per\n100 MeV/c2 wide mass bin, signi\ufb01cantly exceeding the in-\ntegrated luminosity collected by direct e+e\u2212experiments.\nBy comparison the recent CLEO-c (Cronin-Hennessy\net al., 2009) energy scan collected a total of 60 pb\u22121 in\ntwelve points between 3.97 and 4.26 GeV, and BESIII ac-\n\n670\n0\n1000\n2000\n3000\n1\n2\n3\nEc.m. (GeV)\ndL/dE (nb-1/0.02 GeV)\nFigure 21.2.3. BABAR ISR luminosity versus equivalent CM\nenergy calculated in energy bins 20 MeV wide, for an inte-\ngrated machine luminosity of 470 fb\u22121 and an angular accep-\ntance for the ISR photon between 0.35 and 2.4 rad. For com-\nparison, the histogram reports the luminosity integrated by the\nCMD-2 and DM2 experiment with a conventional energy scan,\nat energies below and above 1.4 GeV, respectively; these data\nare presented in many separate papers, as discussed in the text.\nThe two high, narrow peaks correspond to the energy regions\naround the mass of the \u03c1 and \u03c6 resonances, where most of the\ndata were collected.\ncumulated 53 pb\u22121 data at 3.900 GeV and 482 pb\u22121 data\nat 4.009 GeV (Ablikim et al., 2013b).\nIn conclusion, the current data samples of ISR events\navailable at the B Factories are larger than those pro-\nduced directly in e+e\u2212collisions for all masses with the\nexceptions of the regions around the narrow resonances\n(\u03c9, \u03c6, J/\u03c8, and \u03c8(2S)). In particular, the data in the\nmass regions above 1.4 GeV/c2 for light quarks, and in\nthe charm region, are unique both in terms of quantity\nand quality.\n21.2.3 Mass resolution and energy scale\nMass resolution and absolute energy scale have to be kept\nunder control in order to assess the accuracy of the cross\nsections measured with the ISR method.\nThe mass resolution is determined by the precision of\nthe measurement of the parameters (angles and momenta)\nof the reconstructed tracks, and of the energy and direc-\ntion of the photons from \u03c00 and \u03b7 decays. It is therefore\nexpected that the mass resolution is best in the vicin-\nity of the production threshold, due to the lower particle\nmomenta, and degrades with increasing mass. The mass\nresolution is measured with simulated events, \ufb01tting the\ndistribution of the di\ufb00erence between the reconstructed\nand generated invariant masses. It is then checked with\nexperimental data by \ufb01tting the line shape of narrow res-\nonances, such as the \u03c6 or the J/\u03c8.\nFor multi-hadron systems with only charged particles,\ntypical values of the invariant mass resolution obtained\nat the B Factories range from 4 up to 7 MeV/c2, when\nthe mass increases from 1.5 to 3 GeV/c2. The presence of\nneutral pions worsens the resolution by a few\nMeV/c2.\nThe width of the mass bin chosen for the majority of the\nanalyses in this energy region is 25 MeV/c2, reducing in\nthis way the e\ufb00ect of the mass resolution on the mea-\nsured mass spectrum. A bin size of only 2 MeV/c2 has\nbeen used by BABAR for the \u03c0+\u03c0\u2212\ufb01nal state close to the\npeak of the \u03c1 meson (Aubert, 2009ah), requiring a spe-\nci\ufb01c procedure for unfolding the resolution e\ufb00ects from\nthe \u03c0+\u03c0\u2212mass-spectrum (Malaescu, 2009). A small bin\nsize of 5 MeV/c2 was also used for the process e+e\u2212\u2192pp\u03b3\nin the pp mass region close to the production threshold,\nwhere the resolution is less than 2 MeV/c2, as shown in\nFig. 21.2.4, allowing the study of the proton electromag-\nnetic form factor with unprecedented accuracy (Aubert,\n2005ah; see also the discussion in Section 21.3.7.3 below).\nIn the charm mass region, the \ufb01nal-state hadrons have\nsmaller momenta, and the mass resolution is of the order\nof 5 MeV/c2, which is much smaller than the typical bin\nsizes used of 20\u201325 MeV/c2.\nMpp (GeV/c2)\nMass resolution (MeV/c2)\n0\n5\n10\n15\n20\n2\n3\n4\nFigure 21.2.4. Mass resolution of the pp system as a function\nof the reconstructed pp mass obtained by BABAR for the process\ne+e\u2212\u2192pp\u03b3ISR. BABAR internal, prepared for (Aubert, 2006d)\nanalysis.\nThe absolute mass scale is calibrated by comparison of\nthe reconstructed mass values for known resonances with\ntheir nominal peak positions. In all cases a relative accu-\nracy signi\ufb01cantly better than 10\u22123 has been measured.\n\n671\n21.2.4 Comparison of tagged and untagged ISR\nmeasurements with direct e+e\u2212measurements\nAs already outlined, analyses of processes with hard pho-\nton emission in the initial state can be performed with or\nwithout detection of the ISR photon. In this section we\ndiscuss the general features of the two approaches, and\ncompare them to direct e+e\u2212measurements.\nOne of the main issues with measurements of exclu-\nsive cross sections at e+e\u2212experiments is that each col-\nlider is able to scan only a limited range of center-of-mass\nenergies. Signi\ufb01cant normalization uncertainties are there-\nfore present when data from di\ufb00erent experiments, or even\ndata from the same experiment at di\ufb00erent energies, are\ncombined. In the ISR technique, by contrast, exclusive\ncross sections are measured simultaneously over a con-\ntinuous and very wide range of energies, with the same\nexperimental conditions.\nThe requirement that the ISR photon is emitted within\nthe detector angular acceptance results in an e\ufb03ciency\nloss of about an order of magnitude relative to the full\nISR production. In some cases, tagging of the ISR pho-\nton allows for analyses with partial reconstruction of the\nhadronic system, increasing the global detection e\ufb03ciency\nwhile keeping the background at an a\ufb00ordable level.\nIn untagged analyses, the detection of the ISR pho-\nton is not required, while the hadronic system must be\nfully reconstructed. The detection e\ufb03ciency is typically\nhigher in this case with respect to the tagged analyses;\nhowever this is not true for all experimental conditions.\nIn particular, for low invariant masses the hadronic sys-\ntem is subject to a strong boost, and the hadrons are\nproduced in a narrow cone centered around the direction\nopposite to the ISR photon momentum. As a consequence,\nmost of the events with the ISR photon emitted roughly\ncollinear with the beam axis are rejected also in the case\nof an untagged analysis, because a fraction of the hadrons\nfalls outside the detector acceptances. The overall detec-\ntion e\ufb03ciencies are therefore very similar for the tagged\nand untagged approach up to an invariant mass of about\n3\u22123.5 GeV/c2, where the \ufb01nal state hadrons are emitted at\nlarge enough angles to be within the angular acceptance of\nthe calorimeter and tracking system, and the small-angle\nISR begins to contribute signi\ufb01cantly.\nThe previous considerations about detection e\ufb03cien-\ncies constitute the main reason why, at the B Factories,\nthe untagged approach is used for measurements of ex-\nclusive cross sections of hadronic \ufb01nal states with an in-\nvariant mass above 3.5 GeV/c2, in particular to study the\nproduction of open charm and charmonium. By contrast,\nall the studies of e+e\u2212annihilation into light hadrons are\nperformed requiring the detection of the ISR photon.\nIn ISR events, the \ufb01nal state hadrons have a measur-\nable momentum even at production threshold, because of\nthe boost of the hadronic system recoiling against the ra-\ndiated high-energy photon. As a consequence, the detec-\ntion e\ufb03ciency di\ufb00ers from zero at threshold and, generally,\nvaries smoothly over the whole measured range of inva-\nriant masses, unlike in direct e+e\u2212measurements where\nthe detection e\ufb03ciency drops to zero close to threshold. As\nan example, Fig. 21.2.5 shows the detection e\ufb03ciency as\na function of the pp mass, obtained at BABAR for the pro-\ncess e+e\u2212\u2192pp\u03b3ISR with the photon detected (Aubert,\n2006d).\nMpp GeV/c2\nDetection efficiency\n0.1\n0.15\n0.2\n0.25\n2\n2.25\n2.5\n2.75\n3\nFigure 21.2.5. The detection e\ufb03ciency, as measured by\nBABAR for the process e+e\u2212\u2192pp\u03b3ISR in a tagged analysis,\nvaries slowly as a function of the reconstructed pp mass (Au-\nbert, 2006d).\nAs we have already observed, for tagged ISR analy-\nses the hadrons, produced in a cone around the direc-\ntion opposite to the tagged photon, generally fall in an\ninstrumented region of the detector. The detection e\ufb03-\nciency is thus only weakly dependent on the \ufb01nal state\nhadrons\u2019 angular distribution in the reference frame where\nthe hadronic system is at rest, and the uncertainties re-\nlated to the theoretical models used for simulation are sig-\nni\ufb01cantly reduced. This is in contrast with both untagged\nISR analyses and direct e+e\u2212measurements, for which\nthe region at small polar angles is largely inaccessible.\nThere are also prices to pay for using the ISR tech-\nnique. As discussed in Section 21.2.3, a good mass reso-\nlution and absolute mass scale are obtained in ISR anal-\nyses, but in direct e+e\u2212measurements these quantities\nare given respectively by the beam energy spread and by\nthe beam energy setting, which are determined far more\nprecisely.\nThe sources of background events for ISR measure-\nments are signi\ufb01cantly larger than those for direct e+e\u2212\nmeasurements. In the latter case, the main backgrounds\nto a given \ufb01nal state come from other e+e\u2212\u2192hadrons\nreactions, due to undetected low momentum particles or\nto wrong particle identi\ufb01cation, but such backgrounds are\nlimited by the requirement of four-momentum conserva-\ntion. For ISR events, a source of background of the same\nkind is due to mis-reconstructed events from other ISR\nprocesses where one or more particles escape detection.\nThe constraint of four-momentum conservation is much\nless e\ufb00ective in this case because of the relatively poor\nresolution on the measurement of the energy of the ISR\n\n672\nphoton and the emission of secondary photons, which de-\ngrade the kinematic \ufb01ts in both the tagged and untagged\nanalyses.\nA background source a\ufb00ecting mainly the tagged anal-\nyses comes from e+e\u2212annihilations at full energy (that\nis, without the emission of an ISR photon) but contain-\ning a high-energy \u03c00. If the \u03c00 is not correctly recon-\nstructed because the two decay-photons are not resolved\nand therefore merged by the reconstruction algorithm, or\none of them is undetected, the process e+e\u2212\u2192X\u03c00 can\nmimic the ISR process e+e\u2212\u2192X\u03b3ISR. The contribution\nof this background to distributions needed in an analy-\nsis is estimated for each process from generic light quark\ncontinuum MC samples using for normalization a sample\nof e+e\u2212\u2192X\u03c00 with a reconstructed \u03c00 selected from\ndata. The background contribution is then subtracted.\nThis is the dominant source of background at masses of\nthe hadronic system higher than about 2 GeV/c2, and lim-\nits the measurable mass range for light hadron \ufb01nal states\nto m < 4.0\u20134.5 GeV/c2.\nFor untagged analyses, the background due to non-\nISR events only partially reconstructed can be suppressed\nby requiring that the missing momentum of the event is\ncollinear with the beam axis. Another signi\ufb01cant source\nof background for untagged analysis is due to two-photon\nprocesses e+e\u2212\u2192e+e\u2212\u03b3\u2217\u03b3\u2217\u2192e+e\u2212X, where the col-\nliding electron and positron are scattered predominantly\nat small angles, and are therefore undetected (see Chap-\nter 22 for a discussion of the two-photon reactions). In such\nevents the missing momentum is roughly along the beam\naxis, but the missing mass is large, so e\ufb00ective suppression\nof this kind of background is obtained requiring a missing\nmass close to zero, as expected if the only missing particle\nis the hard ISR photon.\n21.3 Exclusive hadronic cross-sections\nThe precision of the Standard Model calculation of the\nmuon anomalous magnetic moment is limited by the un-\ncertainty on the hadronic contribution; for many years this\ncontribution was determined using only data from e+e\u2212\nscan experiments (Davier, Eidelman, Hoecker, and Zhang,\n2003b). The discrepancy between (g\u22122)\u00b5 calculations and\nthe direct measurement by the E821 experiment (Bennett\net al., 2006), on the order of three standard deviations,\ncalled for new and more precise measurements of the e+e\u2212\nhadronic cross section.\nThis has been the main physics motivation for the\nintensive BABAR program of measurements of exclusive\ne+e\u2212annihilation to light-quark hadrons, using ISR. In\naddition, the large data sample and good detector per-\nformance enable spectroscopic studies of unprecedented\naccuracy in the energy region below 3 GeV.\nMany \ufb01nal states have already been studied at BABAR:\nfrom \u03c0+\u03c0\u2212(Aubert, 2009ah), the most important chan-\nnel for (g \u22122)\u00b5, to almost all of the possible channels with\nup to six hadrons in the \ufb01nal state. Exclusive production\ne+e\u2212\u2192BB (where B = p, \u039b, \u03a3) has also been measured\nin order to extract the time-like electromagnetic form fac-\ntors of the corresponding baryons. Belle investigated the\n\u03c6\u03c0+\u03c0\u2212(\u03c6 \u2192K+K\u2212) \ufb01nal state (Shen, 2009). A few more\nstates are under study at the time of writing of this book,\nwhich are essential to complete the main part of the pro-\ngram for the estimate of the hadronic contribution to the\nvalue of (g\u22122)\u00b5, namely \u03c0+\u03c0\u2212\u03c00 \u03c00, K+K\u2212, K0\nSK0\nL+n\u03c0,\nand K0\nSK\u00b1\u03c0\u2213+ n\u03c00, with n = 0, 1, 2.\nThis section is organized as follows. The general fea-\ntures common to most of these analyses are described in\nSection 21.3.1. The hadronic contribution to (g \u22122)\u00b5, the\nmeasurement of the \u03c0+\u03c0\u2212cross-section, and the impact of\nthis and other ISR results on (g \u22122)\u00b5 and \u03b1(MZ) are dis-\ncussed in Sections 21.3.2\u201321.3.4 respectively. Light meson\nspectroscopy results from the study of multi-hadron \ufb01nal\nstates are presented in Section 21.3.5; the search for the\nfJ(2220) is discussed separately in Section 21.3.6. Finally,\ntime-like baryon form factor measurements are described\nin Section 21.3.7.\n21.3.1 Common analysis strategy\nAll the aforementioned analyses are performed with the\nISR tagged approach. A loose pre-selection is applied to\n\ufb01lter out ISR candidate events: The ISR event is tagged\nby the detection of a photon of CM energy E\u2217\n\u03b3 > 3 GeV.\nA rough balance between the beam energies and the en-\nergy of the reconstructed event, and a well reconstructed\nprimary vertex from the charged tracks are required. Ad-\nditional photons are considered only if they have an en-\nergy above 0.03 GeV. In any case, the photon with high-\nest energy is assumed to be the ISR photon. The above\npre-selection works for most of the \ufb01nal states with a few\nexceptions, such as processes with long-lived particles or\nwith only neutral particles in the \ufb01nal state, for which a\ndedicated selection has been implemented.\nEach candidate event is then subject to a set of con-\nstrained kinematic \ufb01ts, under di\ufb00erent hypotheses for the\n\ufb01nal state. The \ufb01t results, along with information on char-\nged-particle identi\ufb01cation, are used to both select the \ufb01-\nnal states of interest and measure backgrounds from other\nprocesses. The kinematic \ufb01ts use the ISR photon direc-\ntion and energy along with the four-momenta and covari-\nance matrices of the colliding electrons and of the selected\ntracks and photons in the \ufb01nal state. Masses of narrow\nresonances, such as \u03c00, \u03b7 and \u03c6 mesons, are constrained\nin the \ufb01t to their nominal values.\nIn general, the main background at low invariant mas-\nses comes from other ISR processes; at higher masses the\nbackground is due to continuum qq production, as ex-\nplained in Section 21.2.4 above.\n21.3.2 Hadronic vacuum polarization\nHere we brie\ufb02y describe polarization of the vacuum due to\n\ufb02uctuations (Section 21.3.2.1), and its e\ufb00ects on the run-\nning of the electromagnetic coupling (Section 21.3.2.2) and\non the muon magnetic anomaly (Section 21.3.2.3). The\n\n673\nhadronic cross section in e+e\u2212annihilation is a crucial\ninput to the calculation of both quantities. The measure-\nment of the e+e\u2212\u2192\u03c0+\u03c0\u2212cross section, and the e\ufb00ect\nof this and other ISR exclusive results on (g \u22122)\u00b5 and\n\u03b1(MZ), are then discussed in Sections 21.3.3 and 21.3.4\nrespectively.\n21.3.2.1 Quantum \ufb02uctuations\nA virtual photon exchanged in an electromagnetic pro-\ncess can \ufb02uctuate into particle-antiparticle pairs leading\nto a polarization of the vacuum. While the e\ufb00ect of lepton\npairs can be readily calculated with QED, hadronic e\ufb00ects\ncan be treated with QCD only at large energies (quark-\nantiquark pairs). At low energies perturbative QCD can-\nnot be employed any more, but fortunately hadronic vac-\nuum polarization can still be evaluated with a dispersion\nintegral (Bouchiat and Michel, 1961) involving experimen-\ntal data on the cross section for e+e\u2212\u2192hadrons, usually\nexpressed in terms of its ratio R to the point like cross\nsection. This technique applies to two situations of great\nimportance in particle physics: the running of the elec-\ntromagnetic coupling \u03b1(s), particularly its value at the Z\npole where precision tests of the electroweak physics are\nperformed, and the calculation of the Standard Model pre-\ndiction for the lepton magnetic anomaly, especially in the\ncase of the muon because of its sensitivity to new physics.\nThe conservation of the vector current (CVC) allows\none to use \u03c4 decay data to compute the dispersion inte-\ngral (Alemany, Davier, and Hoecker, 1998), but in this\ncase small corrections must be applied in order to take\ninto account isospin symmetry breaking between the weak\ncharged and electromagnetic hadronic currents. This sub-\nject is discussed in Section 20.7.\n21.3.2.2 The running of the electromagnetic coupling\nThe running of the electromagnetic fine structure constant\n\u03b1(s) is governed by the renormalized vacuum polarization\nfunction, \u03a0\u03b3(s). For the spin 1 photon, \u03a0\u03b3(s) is given by\nthe Fourier transform of the time-ordered product of the\nelectromagnetic currents j\u00b5\nem(s) in the vacuum:\n(q\u00b5q\u03bd\u2212q2g\u00b5\u03bd) \u03a0\u03b3(q2) = i\nZ\nd4x eiqx\u27e80|T(j\u00b5\nem(x)j\u03bd\nem(0))|0\u27e9.\n(21.3.1)\nWith \u2206\u03b1(s) = \u22124\u03c0\u03b1 Re [\u03a0\u03b3(s) \u2212\u03a0\u03b3(0)] and \u2206\u03b1(s) =\n\u2206\u03b1lep(s) + \u2206\u03b1had(s), which subdivides the running con-\ntributions into a leptonic and a hadronic part, one has\n\u03b1(s) =\n\u03b1(0)\n1 \u2212\u2206\u03b1lep(s) \u2212\u2206\u03b1had(s) ,\n(21.3.2)\nwhere 4\u03c0\u03b1(0) is the square of the electron charge in the\nlong-wavelength Thomson limit.\nThe leptonic contribution at s = M 2\nZ is known pre-\ncisely at three-loop order (Steinhauser, 1998): \u2206\u03b1lep(M 2\nZ) =\n314.98\u00d710\u22124. Using analyticity and unitarity, the disper-\nsion integral for the contribution from the hadronic vac-\nuum polarization reads\n\u2206\u03b1had(M 2\nZ) = \u2212\u03b1(0)M 2\nZ\n3\u03c0\nRe\nZ \u221e\n4m2\n\u03c0\nds\nR(s)\ns(s \u2212M 2\nZ) \u2212i\u03f5 ,\n(21.3.3)\nand, employing the identity 1/(x\u2032\u2212x\u2212i\u03f5)\u03f5\u21920 = P{1/(x\u2032\u2212\nx)} + i\u03c0\u03b4(x\u2032 \u2212x), the above integral is evaluated using\nthe principal value integration technique. Here, R(s) \u2261\nR(0)(s), denotes the ratio of the \u2018bare\u2019 cross section for\ne+e\u2212annihilation into hadrons to the point like muon-\npair cross section. The \u2018bare\u2019 cross section, \u03c3(0)(s) = \u03c3(s)\n\u0002\n\u03b1(0)/\u03b1(s)\n\u0003\n, is de\ufb01ned as the measured cross section with\nvacuum polarization e\ufb00ects from the photon propagator\nremoved.\n21.3.2.3 The muon magnetic anomaly\nA prediction from Dirac theory is that charged leptons\nhave a magnetic moment equal to the Bohr magneton\n(e\u210f/2m), corresponding to a gyromagnetic ratio g = 2.\nHowever the magnetic anomaly, de\ufb01ned as a = (g \u22122)/2,\ndeviates from zero because of virtual corrections from higher\norders in QED and from other interactions. It is conve-\nnient to separate the Standard Model prediction for the\nanomalous magnetic moment of the muon aSM\n\u00b5\ninto its\ndifferent contributions,\naSM\n\u00b5\n= aQED\n\u00b5\n+ ahad\n\u00b5\n+ aweak\n\u00b5\n;\n(21.3.4)\nthe hadronic term is dominated by lowest-order (LO) vac-\nuum polarization (VP), whose Feynman diagram is shown\nin Fig. 21.3.1. But ahad\n\u00b5\nreceives further contributions,\nsmaller by a factor \u223c30, from higher-order (HO) vacuum\npolarization (several loops in photon propagators includ-\ning at least one hadronic loop) and the so-called light-\nby-light (LBL) contribution, where the hadronic loop is\nconnected to the QED part by four photon legs.\n\u00b5+\n\u00b5\u2212\n\u03b3\n\u03b3\n\u03b3\nFigure 21.3.1. The Feynman diagram for the lowest-order\ncontribution of hadronic vacuum polarization to the muon\nmagnetic anomaly.\nAs in the case of \u03b1(MZ), by virtue of the analyticity of\nthe vacuum polarization correlator, the LO contribution of\nthe hadronic vacuum polarization to a\u00b5 can be calculated\nvia a dispersion integral\nahad,LO\n\u00b5\n= \u03b12(0)\n3\u03c02\nZ \u221e\n4m2\n\u03c0\nds K(s)\ns\nR(s) .\n(21.3.5)\n\n674\nThe QED kernel, K(s) is given by (Brodsky and De Rafael,\n1968)\nK(s) = x2\n\u0012\n1 \u2212x2\n2\n\u0013\n+ (1 + x)2\n\u0012\n1 + 1\nx2\n\u0013\n\u00d7\n\u0012\nln(1 + x) \u2212x + x2\n2\n\u0013\n+ (1 + x)\n(1 \u2212x)x2 ln x ,\n(21.3.6)\nwith x = (1 \u2212\u03b2\u00b5)/(1 + \u03b2\u00b5) and \u03b2\u00b5 = (1 \u22124m2\n\u00b5/s)1/2. The\nfunction K(s) decreases monotonically with increasing s.\nIt gives a strong weight to the low energy part of the\nintegral (21.3.5). About 92% of the total contribution to\nahad\n\u00b5\nis accumulated at CM energies \u221as below 1.8 GeV,\nand 73% of ahad\n\u00b5\nis covered by the two-pion final state\nwhich is dominated by the \u03c1(770) resonance.\n21.3.3 Measurement of e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3)\nPrecise results on the e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3) cross section\nhave been obtained by BABAR (Aubert, 2009ah), using\n232 fb\u22121 of recorded data. In this analysis, two-body ISR\nprocesses e+e\u2212\u2192\u03b3ISRX with \ufb01nal states X = \u03c0+\u03c0\u2212(\u03b3)\nand X = \u00b5+\u00b5\u2212(\u03b3) are measured, where the charged par-\nticle pair can be accompanied by a \ufb01nal state radiation\n(FSR) photon. The \u03c0\u03c0 cross section is obtained from the\nratio of pion to muon yields, thereby signi\ufb01cantly reduc-\ning the systematic uncertainty. Furthermore the measured\nmuon cross section can be compared to the QED predic-\ntion, providing a powerful cross check of the analysis.\nIn this approach the measurement of the cross sec-\ntion \u03c3\u03c0\u03c0(\u03b3) uses the e\ufb00ective ISR luminosity provided by\nthe measured mass spectrum of \u00b5\u00b5\u03b3ISR(\u03b3) events. For the\nmuon QED test, the measurement of \u03c3\u00b5\u00b5(\u03b3) uses the ISR\nluminosity calculated from the e+e\u2212integrated luminosity\nand the radiator function obtained from PHOKHARA .\nIn addition to the pre-selection requirements, two-body\nISR events are selected requiring exactly two tracks of op-\nposite charge, each with a momentum p > 1 GeV/c and\nwithin the polar angle range 0.40 to 2.45 rad in the labo-\nratory frame. The charged-particle tracks are required to\nhave at least 15 hits in the DCH, to originate within 5 mm\nof the collision axis, and to extrapolate to DIRC and IFR\nactive areas, excluding low-e\ufb03ciency regions.\nMC simulation is used to compute acceptance and\nmass-dependent e\ufb03ciencies for trigger, reconstruction, PID,\nand event selection. Corrections for di\ufb00erences between\ndata and MC e\ufb03ciencies amount to at most a few percent\nand are known to the few permill level or better.\nThe precision aimed for by this analysis requires ded-\nicated studies of the detector performance, particularly\nregarding track reconstruction and particle identi\ufb01cation\ne\ufb03ciencies. These are determined taking advantage of the\nkinematic constraints of pair production. Two-prong ISR\ncandidates are selected on the basis of the ISR photon and\none detected track, and subjected to a kinematic \ufb01t to es-\ntimate the expected parameters of the second track. Com-\nparison with the sample of reconstructed second-track can-\ndidates allows the measurement of the track reconstruc-\ntion e\ufb03ciency.\nPure samples of muon, pion, and kaon pairs are ob-\ntained from two-prong ISR events where one track is se-\nlected as a \u00b5-, \u03c0-, or K-candidate respectively, according\nto the output of cut-based and likelihood selectors (see\nSection 5.2). The other track is used to determine the\ne\ufb03ciency and misidenti\ufb01cation probabilities of the PID\nalgorithm under test, as a function of momentum and po-\nsition in the IFR or the DIRC. The e\ufb03ciencies for \u00b5 are of\nthe order of 90%, with 10% misidenti\ufb01ed as \u03c0. The \u03c0 e\ufb03-\nciency depends strongly on momentum, with the fraction\nof pions misidenti\ufb01ed as K increasing from 1% at 1 GeV/c\nto 20% at 6 GeV/c; the fraction misidenti\ufb01ed as \u00b5 is 5\u20136%,\nand that as e around 2%.\nThe multi-hadronic background from e+e\u2212\u2192qq is es-\ntimated as explained in Section 21.2.4. The background\nfrom other ISR processes is dominated by the e+e\u2212\u2192\n\u03c0+\u03c0\u2212\u03c00\u03b3ISR and e+e\u2212\u2192\u03c0+\u03c0\u22122\u03c00\u03b3ISR reactions, which\nare estimated using MC simulation. Residual background\nsources from the e+e\u2212\u2192\u03b3\u03b3 process with photon conver-\nsion and radiative Bhabha events are studied and taken\ninto account.\nThe analysis allows for one additional ISR or FSR pho-\nton, and is thus e\ufb00ectively performed at NLO in \u03b1. Each\nevent is subjected to two kinematic \ufb01ts to the e+e\u2212\u2192\nX\u03b3ISR hypothesis, where X allows for an additional pho-\nton from the initial or \ufb01nal state, detected or not. The\n\ufb01rst \ufb01t, called the \u2018ISR\u2019 \ufb01t, tests the consistency of the\nreconstructed event with the presence of an undetected\nISR photon collinear with the collision axis. The second\n\ufb01t, called the \u2018FSR\u2019 \ufb01t, is performed only if an additional\nphoton with E\u03b3 > 25 MeV is detected, and tests the hy-\npothesis that this photon is radiated by the \ufb01nal state\ntracks. Misreconstructed events and residual background\ngenerally have large \u03c72 values for both \ufb01ts, and can be sep-\narated from signal events. If the \u2018FSR\u2019 \ufb01t has the smaller\n\u03c72, the mass of the hadronic \ufb01nal state is calculated in-\ncluding the 4-momentum of the additional detected pho-\nton.\nThe computed detector acceptance and the selection\ne\ufb03ciency of the kinematic \ufb01t procedure are sensitive to\nan imperfect description of radiative e\ufb00ects in the gener-\nator. The estimated rates of FSR for data and MC sim-\nulation are found to be consistent at better than the one\npermill level. The AfkQed generator simulates additional\nISR production in the collinear approximation and ap-\nplies an energy cut-o\ufb00for very hard photons. The e\ufb00ects\nof these approximations are estimated by comparing the\nAfkQed generator at four-vector level with the PHOKHARA\ngenerator, which gives a full description of the process\nat next-to-leading order. Corrections to the acceptance of\nthe order of a few percent are found for the individual\n\u03c0+\u03c0\u2212(\u03b3) and \u00b5+\u00b5\u2212(\u03b3) processes, but since photon emis-\nsion from the initial state is common to the two channels,\nthe \u03c0+\u03c0\u2212(\u03b3)/\u00b5+\u00b5\u2212(\u03b3) ratio is a\ufb00ected only at the few\npermill level. Therefore the measurement of the pion cross\nsection is to a large extent insensitive to the description\nof NLO e\ufb00ects in the generator.\n\n675\nA QED test is performed by comparing the \u00b5+\u00b5\u2212(\u03b3)\nmass spectrum in data with that in MC-simulated events.\nIn particular, the distribution of the data is background-\nsubtracted, and the distribution of the AfkQed-based full\nsimulation, normalized to the data luminosity, is corrected\nfor all known data/MC detector and reconstruction di\ufb00er-\nences and for the generator NLO limitations determined\nfrom the comparison between PHOKHARA and AfkQed. The\nratio, shown in Fig. 21.3.2, is rather \ufb02at from threshold to\n3 GeV/c2 and consistent with unity, as found by a \ufb01t to a\nconstant value which returns\n\u03c3data\n\u00b5\u00b5\u03b3(\u03b3)\n\u03c3NLO QED\n\u00b5\u00b5\u03b3(\u03b3)\n\u22121 = (40 \u00b1 20 \u00b1 55 \u00b1 94) \u00d7 10\u22124 , (21.3.7)\nwith \u03c72/ndof = 55.4/54; the errors are statistical, sys-\ntematic from this analysis, and systematic from the in-\ntegrated luminosity respectively. The QED test is thus\nsatis\ufb01ed within an overall accuracy of 1.1%.\n0.9\n0.95\n1\n1.05\n1.1\n0\n1\n2\n3\nm\u00b5\u00b5(GeV/c2)\ndata/QED\nNLO QED test\nFigure 21.3.2. The ratio of the e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3(\u03b3) cross\nsection measured by BABAR to the NLO QED prediction (Au-\nbert, 2009ah). The solid line and the shaded band represent\nthe central value and errors given in Eq. (21.3.7).\nBefore extraction of the \ufb01nal cross section, an un-\nfolding procedure, described in detail in Malaescu (2009),\nis applied to the background-subtracted and e\ufb03ciency-\ncorrected m\u03c0\u03c0 spectrum. A mass-transfer matrix obtained\nusing simulation provides the probability that an event\ngenerated in an interval i of the reduced e+e\u2212CM en-\nergy\n\u221a\ns\u2032 is reconstructed in a m\u03c0\u03c0 interval j. In the en-\nergy region around the \u03c1 peak, where the cross section is\nmeasured in energy intervals 2 MeV wide, the signi\ufb01cant\nelements of the mass-transfer matrix lie near the diagonal\nover a typical range of 6 MeV, which corresponds to the\nenergy resolution.\n [GeV]\ns\u2019\n0.5\n1\n1.5\n2\n2.5\n3\nCross section [nb]\n-3\n10\n-2\n10\n-1\n10\n1\n10\n2\n10\n3\n10\nBABAR\n [GeV]\ns\u2019\n0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95\n1\nCross section [nb]\n0\n200\n400\n600\n800\n1000\n1200\n1400\nBABAR\nFigure 21.3.3. The bare cross section for e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3)\nmeasured by BABAR (Aubert, 2009ah) in the full energy range.\nThe inset shows an enlarged view of the energy region around\nthe \u03c1 and \u03c9 masses. Total uncertainties are shown.\nFigure 21.3.3 shows the e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3) bare cross\nsection including FSR measured by BABAR as a function\nof the CM energy. It is dominated by the \u03c1 resonance,\nand shows the e\ufb00ect of the \u03c1\u2212\u03c9 interference at 0.78 GeV,\na clear dip at 1.6 GeV resulting from interference with a\nheavier \u03c1 state, and additional structure above 2 GeV. The\nsystematic uncertainty ranges from 0.5% in the energy re-\ngion around the \u03c1 mass, up to 5% at the highest measured\nenergies, and is smaller than the statistical error in the cor-\nresponding energy interval over the whole spectrum. The\ncontributions of the various sources to the systematic un-\ncertainties are shown in Table 21.3.1 for the central energy\nregion 0.4 <\n\u221a\ns\u2032 < 1.2 GeV.\nThe square of the pion form factor is de\ufb01ned as usual\nby the ratio of the dressed cross section without FSR, and\nTable 21.3.1.\nRelative systematic uncertainties (in 10\u22123)\nin the e+e\u2212\u2192\u03c0+\u03c0\u2212(\u03b3) cross section by\n\u221a\ns\u2032 intervals up to\n1.2 GeV (Aubert, 2009ah). The statistical part of the e\ufb03ciency\nuncertainties is included in the total statistical uncertainty in\neach interval, and, therefore, it is not reported in the table.\nsource of uncertainty\n\u221a\ns\u2032 ( GeV)\n0.4\u20130.5\n0.5\u20130.6\n0.6\u20130.9\n0.9\u20131.2\ntrigger/ \ufb01lter\n2.7\n1.9\n1.0\n0.5\ntracking\n2.1\n2.1\n1.1\n1.7\n\u03c0-ID\n2.5\n6.2\n2.4\n4.2\nbackground\n4.3\n5.2\n1.0\n3.0\nacceptance\n1.6\n1.0\n1.0\n1.6\nkinematic \ufb01t (\u03c72)\n0.9\n0.3\n0.3\n0.9\ncorrelated \u00b5\u00b5 ID loss\n2.0\n3.0\n1.3\n2.0\n\u03c0\u03c0/\u00b5\u00b5 non-cancel.\n1.4\n1.6\n1.1\n1.3\nunfolding\n2.7\n2.7\n1.0\n1.3\nISR luminosity (\u00b5\u00b5)\n3.4\n3.4\n3.4\n3.4\ntotal uncertainty\n8.1\n10.2\n5.0\n6.5\n\n676\nthe lowest-order cross section for point-like spin 0 charged\nparticles. Thus,\n|F\u03c0|2(s\u2032) =\n3s\u2032\n\u03c0\u03b12(0)\u03b23\u03c0\n\u03c3\u03c0\u03c0(s\u2032) ,\n(21.3.8)\nwith the pion velocity \u03b2\u03c0 =\np\n1 \u22124m2\u03c0/s\u2032. A vector-me-\nson-dominance (VMD) model is used to \ufb01t the BABAR\npion form factor, correlating the observed structures to\nthe e\ufb00ects from higher-mass isovector vector mesons. In\naddition to the \u03c1 and \u03c9 (isoscalar, but interfering with the\n\u03c1 through its isospin-violating \u03c0+\u03c0\u2212decay), three higher\n\u03c1 states at (1493 \u00b1 15) MeV/c2, (1861 \u00b1 17) MeV/c2, and\n(2254 \u00b1 22) MeV/c2 are required to \ufb01t the data. The \ufb01t is\nshown in Fig. 21.3.4.\n [GeV]\ns\u2019\n0.5\n1\n1.5\n2\n2.5\n3\n2|\n!\n|F\n-3\n10\n-2\n10\n-1\n10\n1\n10\nBABAR\n [GeV]\ns\u2019\n0.5\n1\n1.5\n2\n2.5\n3\n2|\n!\n|F\n-3\n10\n-2\n10\n-1\n10\n1\n10\n [GeV]\ns\u2019\n0.72\n0.74\n0.76\n0.78\n0.8\n0.82\n2|\n!\n|F\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nBABAR\n [GeV]\ns\u2019\n0.72\n0.74\n0.76\n0.78\n0.8\n0.82\n2|\n!\n|F\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nFigure 21.3.4. The pion form factor squared measured by\nBABAR (Aubert, 2009ah) as a function of\n\u221a\ns\u2032 in the full range,\nwith details of the \u03c1\u2212\u03c9 interference region shown in the inset.\nThe line represents a VMD \ufb01t with the \u03c1, the \u03c9, and three\nhigher \u03c1 states.\n21.3.4 Impact of ISR results on (g \u22122)\u00b5 and \u03b1(MZ)\n21.3.4.1 The BABAR \u03c0+\u03c0\u2212contribution\nThe BABAR 2\u03c0 results discussed above can be used in a\nstraightforward way to compute the dispersion integral of\nEq. 21.3.5. The errors are computed using the full statis-\ntical and systematic covariance matrices. The systematic\nuncertainties for each source are taken to be fully corre-\nlated over all mass regions. The upper range of integration\n(1.8 GeV) is chosen in accordance with previous evalua-\ntions (Davier, Eidelman, Hoecker, and Zhang, 2003a,b)\nin which the contribution of the higher energy region was\ncomputed using QCD. This procedure was justi\ufb01ed by de-\ntailed studies using \u03c4 decay data (Barate et al., 1998). The\ncontribution to a\u00b5 in the 1.8\u20133 GeV range, obtained with\nthe present BABAR data, is (0.21\u00b10.01)\u00d710\u221210, thus neg-\nligible with respect to the uncertainty in the main region.\nThe contribution from threshold to 1.8 GeV is obtained\nfor the \ufb01rst time from a single experiment:\na\u03c0\u03c0(\u03b3),LO\n\u00b5\n= (514.1 \u00b1 2.2 \u00b1 3.1) \u00d7 10\u221210 ,\n(21.3.9)\nwhere the errors are statistical and systematic.\n21.3.4.2 Comparison to other determinations\nDirect comparison with the results from other experiments\nis complicated by two facts: (i) e+e\u2212scan experiments\nprovide cross section measurements at discrete and un-\nequally spaced energy values, while the ISR method pro-\nvides a continuous spectrum and, (ii) unlike BABAR no\nother experiment covers the complete mass spectrum from\nthreshold up to energies where the contributions become\nnegligible. Wherever gaps remain, they have been \ufb01lled by\nusing the weighted-average cross section values from the\nother experiments. This approach has been followed by\nDavier, Hoecker, Malaescu, Yuan, and Zhang (2010) from\nwhich the relevant integrals are extracted.\nCorrelations between systematic uncertainties have been\ntaken into account, particularly for radiative corrections,\nwhen combining the results from all experiments. The\ncombination is performed in small energy bins at the cross\nsection level, taking into account possible disagreements\nleading to an increased uncertainty of the resulting av-\nerage. The contribution of the \u03c0+\u03c0\u2212channel to a\u00b5 ob-\ntained from the combination of all measurements of the\ne+e\u2212\u2192\u03c0+\u03c0\u2212cross section is (507.8 \u00b1 3.2) \u00d7 10\u221210. It is\ncompared in Fig. 21.3.5 with the determinations of a\u00b5 cal-\nculated using the data form the individual experiments.\nAll determinations are indeed consistent within the un-\ncertainties, BABAR and CMD-2 (Akhmetshin et al., 2006,\n2007; Aulchenko et al., 2005) being almost a factor of two\nmore precise than SND (Achasov et al., 2006) and KLOE\n(Ambrosino et al., 2009a, 2011).\nThe BABAR result is also consistent with determina-\ntions using \u03c4 decay with isospin-breaking corrections from\nDavier et al. (2010), which are also reported in Fig. 21.3.5.\nThis reduces the previous tension between e+e\u2212and \u03c4 val-\nues (Davier, Eidelman, Hoecker, and Zhang, 2003a). Look-\ning at the full picture it is important to note that the four\ninputs (CMD-2/SND, KLOE, BABAR, \u03c4) have completely\nindependent systematic uncertainties.\n21.3.4.3 Other exclusive channels\nRemaining contributions from other exclusive channels up\nto 1.8 GeV amount to about 18% of ahad,LO\n\u00b5\n. Previous re-\nsults were obtained by CMD-2/SND from the \u03c9 and \u03c6\nresonances, and from multihadrons up to 1.4 GeV. Data\nbetween 1.4 GeV and 2 GeV from the DM2 experiment\nwere rather poor. However it was shown by the LEP exper-\niments that perturbative QCD could be used at the \u03c4 mass\nscale with accuracies of about 1% (Ackersta\ufb00et al., 1999;\n\n677\n500\n520\n540\n560\na\u00b52!,LO (10-10)\n\" ALEPH\n\" CLEO\n\" OPAL\n\" Belle\nee BABAR\nee CMD-2\nee SND\nee KLOE\nFigure 21.3.5. Evaluation of LO hadronic vacuum polariza-\ntion 2\u03c0 contributions to the muon magnetic anomaly in the\nenergy range [2m\u03c0, 1.8 GeV] from BABAR, other e+e\u2212exper-\niments (Davier, Hoecker, Malaescu, Yuan, and Zhang, 2010),\nand \u03c4 experiments (Davier et al., 2010); see the text for details.\nThe errors include both statistical and systematic sources.\nFor the \u03c4 values, a common systematic error of 1.9 is in-\ncluded to account for uncertainties in the isospin-breaking cor-\nrections. The vertical bands represent the combined result,\nwhich amount to (507.8 \u00b1 3.2) \u00d7 10\u221210 for the \u03c0\u03c0 value, and\n(515.2\u00b13.0\u00b11.9)\u00d710\u221210 for the \u03c4 value. They are not obtained\nas the weighted average of the di\ufb00erent values, but originate\nfrom a local combination of the respective spectral functions.\nBarate et al., 1998), so it became advantageous (Davier\nand Hoecker, 1998) to use theory above 1.8 GeV.\nThe situation between 1 GeV and 1.8 GeV changed\ndrastically with the advent of ISR BABAR data. In fact\nan almost complete set of precise measurements is avail-\nable and a few remaining channels are being analyzed.\nThese measurements bene\ufb01t from the excellent particle\nidenti\ufb01cation, providing access to many previously unmea-\nsured cross sections. They help to discriminate between\nolder, less precise and sometimes contradictory results.\nFigure 21.3.6 gives a few examples of measured cross sec-\ntions and demonstrates the impact of the BABAR results.\nThe band shown on all these plots represents the combi-\nnation by Davier, Hoecker, Malaescu, and Zhang (2011)\nof all existing data using the HVPTools package (Davier,\nHoecker, Malaescu, Yuan, and Zhang, 2010): it is clearly\ndominated by the BABAR results.\nThe measurement using the full available data set of\nthe production cross section for several \ufb01nal states are in\nprogress at BABAR. Particularly relevant for the calcula-\ntion of the muon anomaly are \u03c0+\u03c0\u2212\u03c00\u03c00, K+K\u2212, KSKL,\nand KSKL\u03c0+\u03c0\u2212. Some channels involving \u03c00 multiplici-\nties larger than 2 will probably remain unmeasured. The\nestimate of the missing channels, obtained using isospin\nrelations or inequalities (Davier, Hoecker, Malaescu, and\nZhang, 2011), is greatly facilitated by the studies of pro-\nduced \ufb01nal states performed by BABAR on the related\nchannels as discussed in the following sections.\n21.3.4.4 The complete muon anomaly prediction\nMeasurements from all experiments have been combined\nin the recent analysis of Davier, Hoecker, Malaescu, and\nZhang (2011). The weight of the ISR BABAR data in\nthe combination is the largest of all experiments: 41%\nfor 2\u03c0 and from 58 to 100% for the other measured ex-\nclusive channels below 1.8 GeV. More recently an in-\ndependent analysis using the same data has been pre-\nsented (Hagiwara, Liao, Martin, Nomura, and Teubner,\n2011) with similar results. Adding all contributions (QED,\nelectroweak, hadronic LO VP, hadronic HO VP, hadronic\nlight-by-light) as given in Davier, Hoecker, Malaescu, and\nZhang (2011), using for hadronic LO VP the combined\nresult, one obtains the predicted value\naSM\n\u00b5\n= (11 659 180.2\u00b14.2\u00b12.6\u00b10.2)\u00d710\u221210 , (21.3.10)\nwhere the three uncertainties come from hadronic VP\n(e+e\u2212data), the LBL calculations, and the sum of QED\nand Weak contributions, respectively, for a total uncer-\ntainty of \u00b14.9\u00d710\u221210. The Standard Model prediction can\nbe compared to the direct measurement (Bennett et al.,\n2006), slightly updated in (Nakamura et al., 2010):\naexp\n\u00b5\n= (11 659 208.9 \u00b1 6.3) \u00d7 10\u221210 .\n(21.3.11)\nThe experimental value exceeds the theory prediction\nby (28.7 \u00b1 8.0) \u00d7 10\u221210, i.e. 3.6 standard deviations. Al-\nthough the deviation is not signi\ufb01cant enough to claim a\ndeparture from the Standard Model, it con\ufb01rms the trend\nof earlier results using previous data (Davier, Eidelman,\nHoecker, and Zhang, 2003b; Hagiwara, Martin, Nomura,\nand Teubner, 2007; Jegerlehner and Ny\ufb00eler, 2009).\nSuch a deviation could originate from new physics be-\nyond the Standard Model. One possibility, much discussed\nin the literature, is the e\ufb00ect of contributions from super-\nsymmetry (SUSY) involving scalar muons or neutrinos,\nand gauginos at a few hundred GeV mass scale. For the\nmoment this explanation is not con\ufb01rmed by the early\nLHC results as no evidence has yet been found for new\nparticles in this mass range. While under tension this sce-\nnario is not yet ruled out as many SUSY versions can still\nbe considered.\nHowever it is clear that the muon (g \u22122) discrep-\nancy should be further explored. The progress will follow\ntwo lines. First, projects are considered at FNAL and J-\nPARC to extend the direct measurement to higher pre-\ncision. Second, more precise measurements of e+e\u2212\u2192\nhadrons are possible with VEPP2000 and in the longer\nterm with the new generation of B Factories using the ISR\nmethod. Combining the two approaches could produce a\nvery signi\ufb01cant deviation which would unambiguously sig-\nnal physics beyond the Standard Model.\n\n678\n [GeV]\ns\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n10\n20\n30\n40\n50\n60\nND\nM3N\nMEA\nCMD\nDM1\nDM2\nOLYA\nCMD2\nSND\nBABAR\nAverage\n-!\n2\n+\n!\n2\n\"\n-e\n+\ne\n [GeV]\ns\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n10\n20\n30\n40\n50\n60\n [GeV]\ns\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n10\n20\n30\n40\n50\n60\nND\nM3N\nDM2\nOLYA\nSND\nBABAR preliminary\nAverage\n0\n\u03c0\n2\n-\u03c0\n+\n\u03c0\n\u2192\n-e\n+\ne\n [GeV]\ns\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n10\n20\n30\n40\n50\n60\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n2\n4\n6\n8\n10\nDM1\nDM2\nBABAR\nAverage\n-!\n+\n!\n-\nK\n+\nK\n\"\n-e\n+\ne\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n2\n4\n6\n8\n10\n [GeV]\ns\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n2\n4\n6\n8\n10\n12\n14\n16\nM3N\nCMD\nDM1\nBABAR\nAverage\n0\n!\n-!\n2\n+\n!\n2\n\"\n-e\n+\ne\n [GeV]\ns\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n2\n4\n6\n8\n10\n12\n14\n16\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n1\n2\n3\n4\n5\nM3N\nDM1\nDM2\nBABAR\nAverage\n-!\n3\n+\n!\n3\n\"\n-e\n+\ne\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n1\n2\n3\n4\n5\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n2\n4\n6\n8\n10\n12\n14\nM3N\nDM2\nBABAR\nAverage\n0\n!\n2\n-!\n2\n+\n!\n2\n\"\n-e\n+\ne\n [GeV]\ns\n1.4\n1.6\n1.8\n2\n2.2\n2.4\nCross section [nb]\n0\n2\n4\n6\n8\n10\n12\n14\nFigure 21.3.6. Cross sections versus center-of-mass energy for e+e\u2212\n\u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212, e+e\u2212\n\u2192\u03c0+\u03c0\u2212\u03c00\u03c00, e+e\u2212\n\u2192\nK+K\u2212\u03c0+\u03c0\u2212, e+e\u2212\u21922\u03c0+2\u03c0\u2212\u03c00, e+e\u2212\u21923\u03c0+3\u03c0\u2212, e+e\u2212\u21922\u03c0+2\u03c0\u22122\u03c00. The open circles show data from BABAR which\ndominate in precision. The references for the earlier results displayed are given in Davier, Hoecker, Malaescu, and Zhang (2011).\nThe error bars show the statistical and systematic uncertainties added in quadrature. The shaded (green online) band is the\ncombined result \u00b11\u03c3 taking all experiments into account using the HVPTools package (Davier, Hoecker, Malaescu, Yuan, and\nZhang, 2010).\n21.3.4.5 The prediction for \u03b1(M 2\nZ)\nAll hadronic contributions considered above are used as\ninput to compute the dispersion relation in Eq. (21.3.3)\nwith the result\n\u2206\u03b1had(M 2\nZ) = (275.0 \u00b1 1.0) \u00d7 10\u22124 ,\n(21.3.12)\nwhich, contrary to the evaluation of ahad,LO\n\u00b5\n, is not dom-\ninated by the uncertainty in the experimental low-energy\ndata, but by contributions from all energy regions, where\nboth experimental and theoretical errors have similar mag-\nnitude. Nevertheless the new ISR data provided by BABAR\npermits a signi\ufb01cant improvement in precision. The result\nin Eq. (21.3.12) can be compared with the value obtained\nin Hagiwara, Liao, Martin, Nomura, and Teubner (2011),\n(276.3 \u00b1 1.4) \u00d7 10\u22124.\nAdding the leptonic contribution \u2206\u03b1lep(M 2\nZ), one \ufb01nds\n\u03b1\u22121(M 2\nZ) = 128.952 \u00b1 0.014 .\n(21.3.13)\nThe running electromagnetic coupling at MZ enters\nat various levels the global SM \ufb01t to electroweak precision\ndata. It contributes to the radiator functions that modify\nthe vector and axial-vector couplings in the partial Z bo-\nson widths to fermions, and also to the SM prediction of\n\n679\nFigure 21.3.7. Overall \u03c72 for the Standard G\ufb01tter elec-\ntroweak \ufb01t (Baak et al., 2012; green shaded band) with the\nresult obtained for the new evaluation of \u2206\u03b1had(M 2\nZ). The\nshaded areas represent the excluded regions at 95% C.L. from\nthe LEP and LHC experiments, leaving only a small window\nnear 126 GeV where a very signi\ufb01cant signal is observed by\nthe ATLAS (Aad et al., 2012) and CMS (Chatrchyan et al.,\n2012b) experiments.\nthe W mass and the e\ufb00ective weak mixing angle. Overall,\nthe \ufb01t exhibits a \u221239% correlation between the Higgs mass\n(MH) and \u2206\u03b1had(M 2\nZ) (Baak et al., 2012), so that the de-\ncrease in the value given in Eq.(21.3.12) and thus in the\nrunning electromagnetic coupling strength, with respect\nto earlier evaluations, leads to an increase in the most\nprobable value of MH returned by the \ufb01t. Figure 21.3.7\nshows the standard G\ufb01tter result (green shaded band;\nBaak et al., 2012), using as the hadronic contribution the\nresult obtained by using Eq. (21.3.12). The \ufb01tted Higgs\nmass shifts from (84 +30\n\u221223) GeV/c2 to (91 +30\n\u221223) GeV/c2. The\nstationary error of the latter value, in spite of the im-\nproved accuracy, is due to the logarithmic MH dependence\nof the \ufb01t observables. The new 95% upper limit on MH is\n163 GeV/c2. A new boson with properties compatible with\nthe Higgs particle has been discovered by the ATLAS (Aad\net al., 2012) and CMS (Chatrchyan et al., 2012b) experi-\nments at the LHC. The fact that its mass of 126 GeV/c2 is\nconsistent with the range allowed above can be considered\nas a triumph for the Standard Model in the so-far hidden\nsector of gauge symmetry breaking.\n21.3.5 Light meson spectroscopy\nMost of the multi-hadron \ufb01nal states feature a variety of\ninternal sub-processes, with formation of several interme-\ndiate states, whose properties can be measured thanks to\nthe large available statistics at the B Factories.\nIn some cases, however, these studies are made di\ufb03cult\nby the presence of broad interfering intermediate states,\nand have been performed only in a qualitative way. As\nan example, the study of the two- and three-pion invari-\nant mass distributions of the process e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c00\u03c00\nshows important contributions from \u03c9(780)\u03c0, a1(1260)\u03c0,\nand \u03c1+\u03c1\u2212intermediate states, which strongly interfere.\nA partial-wave analysis combining the data of e+e\u2212\u2192\n\u03c0+\u03c0\u2212\u03c00\u03c00 and e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212is required in order\nto separate the di\ufb00erent sub-processes and to study the\ntwo excited \u03c1 states, \u03c1(1450) and \u03c1(1700), decaying into\nfour pions.\nIn many other cases, more quantitative results have\nbeen obtained. A non-exhaustive summary of these results\nis presented below.\n21.3.5.1 Study of \u03c9-like resonances\nThe e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c00 cross section is dominated by the\nproduction of the well-known vector states \u03c9, \u03c6, and J/\u03c8.\nBetween 1 and 2 GeV the cross section is generally de-\nscribed as the sum of two \u03c9-like resonances: \u03c9(1420) or \u03c9\u2032,\nand \u03c9(1650) or \u03c9\u2032\u2032, whose parameters are not yet well es-\ntablished. The published BABAR results (Aubert, 2004af)\nare based on an integrated luminosity of only 89.3 fb\u22121.\nTherefore, an update of the study using the full avail-\nable dataset is desirable. The measured cross section in\nthe 1.05\u20133.0 GeV/c2 mass region is shown in Fig. 21.3.8.\nThere is good agreement with previous results by the SND\nexperiment (Achasov et al., 2002) below 1.4 GeV/c2; sig-\nni\ufb01cant disagreement with DM2 results (Antonelli et al.,\n1992) is observed at higher energies.\nM3! (GeV/c2)\nCross section (nb)\n0\n2\n4\n6\n8\n1.5\n2\n2.5\n3\nM3! (GeV/c2)\nEvents/(25 MeV/c2)\n0\n100\n200\n300\n1.2\n1.4\n1.6\n1.8\nFigure 21.3.8. The e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c00 cross section measured\nby the BABAR experiment (Aubert, 2004af; full circles) in the 1-\n3 GeV/c2 range compared with the SND (Achasov et al., 2002;\nopen circles) and DM2 (Antonelli et al., 1992; triangles) data.\nThe inset shows the result of a \ufb01t to the mass distribution as\nexplained in the text.\nThe three pion mass spectrum below 1.8 GeV/c2, ob-\ntained by BABAR, is \ufb01tted as the sum of the four known\nvector resonances \u03c9, \u03c6, \u03c9\u2032, and \u03c9\u2032\u2032. The \ufb01t result in the\n\u03c9\u2032 and \u03c9\u2032\u2032 mass region is shown in the inset to Fig. 21.3.8,\nsuperimposed on the experimental data. The resonance\nparameters from the \ufb01t are reported in the \ufb01rst column of\nTable 21.3.2, together with the corresponding values from\nstudies of ISR processes with \ufb01ve and six hadrons in the\n\ufb01nal state.\nClear \u03b7 \u21923\u03c0 and \u03c9 \u21923\u03c0 signals are observed in\nthe e+e\u2212\u21922(\u03c0+\u03c0\u2212)\u03c00 process. The cross sections for\n\n680\n0\n2\n4\n1\n2\n3\n4\nEc.m. (GeV)\n!(e+e-\"#$+$-) (nb)\n0\n1\n2\n3\n1\n1.5\n2\n2.5\n3\nEc.m. (GeV)\n!(e+e-\"#$+$-) (nb)\nFigure 21.3.9.\nThe e+e\u2212\u2192\u03b7\u03c0+\u03c0\u2212(top) and e+e\u2212\u2192\n\u03c9\u03c0+\u03c0\u2212(bottom) cross sections measured by BABAR (Aubert,\n2007bb) in comparison with direct e+e\u2212measurements.\nproduction of the \u03b7\u03c0+\u03c0\u2212and \u03c9\u03c0+\u03c0\u2212\ufb01nal states, mea-\nsured by BABAR (Aubert, 2007bb), are compared to pre-\nvious, less precise data (Akhmetshin et al., 2000; Antonelli\net al., 1988; Cordier et al., 1981; Druzhinin et al., 1986)\nin Fig. 21.3.9. Several new features are revealed by the\nBABAR data. In particular, the study of the \u03c0+\u03c0\u2212mass\ndistribution shows a clear contribution of the intermediate\nstate \u03c9f0(980) to the \u03c9\u03c0+\u03c0\u2212cross section. In addition,\nthe \u03c9\u03c0+\u03c0\u2212cross section has been \ufb01tted, after removal of\nthe \u03c9f0(980) contribution, with a sum of two BW func-\ntions, referring to the \u03c9\u2032 and \u03c9\u2032\u2032, as in the case of the\n\u03c0+\u03c0\u2212\u03c00 \ufb01nal state. The \ufb01tted parameters are reported in\nthe third column Table 21.3.2.\nFinally, further structure compatible with \u03c9 excita-\ntions has been observed in e+e\u2212\u21922(\u03c0+\u03c0\u2212\u03c00) (Aubert,\n2006az). In fact, in addition to clear \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 and\n\u03c9 \u2192\u03c0+\u03c0\u2212\u03c00 signals, a small associated production of \u03b7\nand \u03c9 is observed in this channel. The cross section for\nthe e+e\u2212\u2192\u03c9\u03b7 reaction, reported in Fig. 21.3.10, shows\na peak in the \u03c9(1650) energy region, which is \ufb01tted with\na Breit-Wigner function.\n0\n2\n4\n1.25\n1.5\n1.75\n2\n2.25\n2.5\n2.75\n3\n3.25\nEc.m. (GeV)\n!(e+e-\"#$) (nb)\nFigure 21.3.10.\nThe e+e\u2212\u2192\u03c9\u03b7 cross section extracted\nfrom the 2(\u03c0+\u03c0\u2212\u03c00) \ufb01nal state measured by BABAR (Aubert,\n2006az). The solid line is the result of the \ufb01t with a Breit-\nWigner function.\nAs can be seen from Table 21.3.2, there is general con-\nsistency among the \u03c9\u2032 and \u03c9\u2032\u2032 parameters measured in the\ndi\ufb00erent channels. An update of the three pion \ufb01nal state\nmeasurement with the full available BABAR data set, and a\ncombined \ufb01t to all channels, could give information on rel-\native decay rates and signi\ufb01cantly improve the knowledge\nof these states.\n21.3.5.2 Study of excited \u03c1 and \u03c6 states in the KK\u03c0 and\nKK\u03b7 \ufb01nal states\nBy studying the Dalitz plots of the e+e\u2212\u2192K0\nSK\u00b1\u03c0\u2213\nand e+e\u2212\u2192K+K\u2212\u03c00 \ufb01nal states, the DM1 and DM2\nexperiments have identi\ufb01ed e+e\u2212\u2192KK\u2217(892) and its\ncharge conjugate as the dominant sub-process, and mea-\nsured the contributions of the di\ufb00erent isospin (I = 0, 1)\ncomponents. They also observed a resonant structure in\nthe isoscalar component, which was interpreted as the\n\ufb01rst excitation of the \u03c6 resonance, thereafter called the\n\u03c6(1680) or \u03c6\u2032 (Bisello et al., 1991; Buon et al., 1982).\nBABAR performs a similar study of the K0\nSK\u00b1\u03c0\u2213and\nK+K\u2212\u03c00 \ufb01nal states, using a \u2243220 fb\u22121 sample (Aubert,\n2008ab). The large amount of data allows the measure-\nment of the cross sections up to a CM energy of 4.5 GeV,\nand a much more accurate study of the Dalitz plots of\nthe two processes, shown in Fig. 21.3.11. It can be seen\nthat in both processes, the main contributions come from\nthe KK\u2217(892) and KK\u2217\n2(1430) intermediate states, and\nthat the Dalitz plot population for the K0\nSK\u00b1\u03c0\u2213channel\nis strongly asymmetric. This is because both the neutral\nK0K\u22170 and charged K\u00b1K\u2217\u2213combinations are involved,\nand these are produced by, respectively, the sum and the\ndi\ufb00erence of the iso-scalar and iso-vector amplitudes. By\nstudying the Dalitz plots, the moduli and relative phase\nof the isospin components for both the KK\u2217(892) and\n\n681\nTable 21.3.2. Summary of the \u03c9(1420) (or \u03c9\u2032) and \u03c9(1650) (or \u03c9\u2032\u2032) resonance parameters obtained from the \ufb01ts described in\nthe text. mi and \u0393i are the mass and the full width of state i, respectively, \u03c30i is the peak cross section, \u0393eeBif the dielectron\nwidth multiplied by the branching fraction for decays into the \ufb01nal state f, and \u03c6i is the phase w.r.t. the \u03c9 amplitude. The\nerrors shown are combination of statistical and systematic uncertainties. The values without errors were \ufb01xed in the \ufb01ts.\nFit\n3\u03c0 (Aubert, 2004af)\n\u03c9\u03b7 (Aubert, 2006az)\n\u03c9\u03c0+\u03c0\u2212(Aubert, 2007bb)\nPDG (Amsler et al., 2008)\n\u03c30\u03c9\u2032 (nb)\n\u2013\n\u2013\n1.01 \u00b1 0.29\n\u2013\n\u0393eeB\u03c9\u2032f(eV)\n369\n\u2013\n17.5 \u00b1 5.4\n\u2013\nm\u03c9\u2032(GeV/c2)\n1.350 \u00b1 0.03\n\u2013\n1.38 \u00b1 0.07\n1.40 \u2013 1.45\n\u0393\u03c9\u2032(GeV)\n0.450 \u00b1 0.10\n\u2013\n0.13 \u00b1 0.05\n0.180 \u2013 0.250\n\u03c6\u03c9\u2032 (rad)\n\u03c0\n\u2013\n\u03c0\n\u2013\n\u03c30\u03c9\u2032\u2032 (nb)\n\u2013\n3.08 \u00b1 0.33\n2.47 \u00b1 0.18\n\u2013\n\u0393eeB\u03c9\u2032\u2032f(eV)\n286\n\u2013\n103.5 \u00b1 8.3\n\u2013\nm\u03c9\u2032\u2032(GeV/c2)\n1.660 \u00b1 0.010\n1.645 \u00b1 0.008\n1.667 \u00b1 0.014\n1.670 \u00b1 0.030\n\u0393\u03c9\u2032\u2032(GeV)\n0.220 \u00b1 0.036\n0.114 \u00b1 0.014\n0.222 \u00b1 0.032\n0.315 \u00b1 0.035\n\u03c6\u03c9\u2032\u2032 (rad)\n0\n0\n0\n\u2013\n1\n2\n3\n4\n1\n2\n3\n4\nM2 (GeV2/c4)\nM2 (GeV2/c4)\nK+!0\nK-!0\n1\n2\n3\n4\n1\n2\n3\n4\nM2 (GeV2/c4)\nM2 (GeV2/c4)\nK\u00b1!\n\u00b1\nKS!\u00b1\nFigure 21.3.11. The Dalitz plot distribution for the K+K\u2212\u03c00 (left) and K0\nSK\u03c0 \ufb01nal state (right) measured by BABAR (Aubert,\n2008ab).\nKK\u2217\n2(1430) cross sections have been obtained as a func-\ntion of the CM energy. The isoscalar \u03c30 and isovector\n\u03c31 cross sections for e+e\u2212\u2192KK\u2217(892) are shown in\nFig. 21.3.12(a,b). The isoscalar component is dominant,\nand shows a clear resonant peak at a CM energy of \u223c\n1.7 GeV, consistent with the \u03c6(1680) meson. The isovector\ncomponent is also incompatible with a pure phase space\nshape, and shows a resonant structure, as can be deduced\nby a study including the information on the relative phase\nbetween \u03c30 and \u03c31.\nA global \ufb01t has been performed using six di\ufb00erent\nsources of information: \u03c30, \u03c31 and their relative phase; the\nK+K\u2212\u03c00 cross section shown in Fig. 21.3.12(c), and the\n\u03c6\u03b7 cross section measured reconstructing two di\ufb00erent \u03b7\ndecay modes: \u03b7 \u2192\u03b3\u03b3 (Aubert, 2008ab), and \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00\n(Aubert, 2007bb). The e+e\u2212\u2192\u03c6\u03b7 reaction is well suited\nto study excited \u03c6 states, because the production of any\n\u03c9-like state, even if allowed by quantum-number conser-\nvation, is strongly suppressed by the OZI rule. The mea-\nsured \u03c6\u03b7 cross section reported in Fig. 21.3.12(d) shows a\nbroad peak at a CM energy of about 1.7 GeV, which can\nbe identi\ufb01ed as a new decay channel of the \u03c6(1680) me-\nson. The same dominant resonance \u03c6\u2032 is therefore assumed\nto \ufb01t both the \u03c6\u03b7 and the isoscalar KK\u2217(892) cross sec-\ntions. An additional resonance, \u03c6\u2032\u2032 is included to account\nfor a small peak seen at a CM energy of about 2.15 GeV\nin the \u03c6\u03b7 cross section. The \ufb01t results are superimposed\non the cross section data in Fig. 21.3.12 and are listed\nin Table 21.3.3. The parameters obtained for the \u03c6\u2032 and\n\u03c1\u2032 are compatible with previous measurements (Amsler\n\n682\n0\n2.5\n5\n7.5\n10\n1.4\n1.6\n1.8\n2\n2.2\nEc.m.(GeV)\n!0(e\n+e\n-\"KK\n*) (nb)\n(a)\n0\n1\n2\n3\n4\n1.4\n1.6\n1.8\n2\n2.2\nEc.m.(GeV)\n!1(e\n+e\n-\"KK\n*) (nb)\n(b)\n0\n2\n4\n6\n1.4\n1.6\n1.8\n2\nEc.m.(GeV)\n!(e\n+e\n-\"K\n\u00b1K\n* (892)) (nb)\n\u00b1\n(c)\n0\n1\n2\n3\n1.5\n2\n2.5\n3\nEc.m.(GeV)\n!(e\n+e\n-\"#$) (nb)\n(d)\nFigure 21.3.12.\nIsoscalar (a) and isovector (b) components of the e+e\u2212\u2192K0\nSK\u03c0 cross section; the e+e\u2212\u2192K\u00b1K\u2217(892)\u2213\ncross section obtained by the BABAR experiment, using e+e\u2212\u2192K+K\u2212\u03c00 events (c), and the e+e\u2212\u2192\u03c6\u03b7 cross section (d). The\npoints with error bars are data and the gray bands represent the \ufb01t and its uncertainty (Aubert, 2008ab).\net al., 2008). Concerning the \u03c6\u2032\u2032 resonance, which is seen\nonly in the \u03c6\u03b7 channel with a signi\ufb01cance of about 2.5\u03c3,\nthe \ufb01tted parameters are close to those for the Y (2175)\nstate observed in the \u03c6f0(980) \ufb01nal state (Aubert, 2006c),\ndiscussed in Section 21.3.5.3.\nAn interesting sub-process of the K+K\u2212\u03b3\u03b3 \ufb01nal state\nmeasured for the \ufb01rst time by BABAR is e+e\u2212\u2192\u03c6\u03c00 (Au-\nbert, 2008ab). The decays of ordinary isovector resonances\nto \u03c6\u03c00 are suppressed by the OZI rule, so structure in this\nchannel could serve as a signal for exotic resonant states.\nTwo possible descriptions are considered to \ufb01t the \u03c6\u03c00\ncross section, assuming respectively the presence of one\nor two radial excitations of the \u03c1 meson (despite being\nOZI suppressed).160 In the \ufb01rst case, the parameters ob-\ntained for the unique isovector state are 1593\u00b132 MeV/c2\nfor the mass and 203 \u00b1 97 MeV for the width, which\nare compatible with those of the \u03c1(1700) (Amsler et al.,\n2008). A slightly better \ufb01t quality is obtained if two reso-\nnances are assumed, as seen from the results shown in Ta-\nble 21.3.3. The parameters obtained for the \ufb01rst resonance\n(indicated by \u03c1\u2032\u2032 in the Table) are consistent with those\nof the C(1480) state observed in \u03c0\u2212p \u2192\u03c6\u03c00n charge-\n160 It should be noted that in the region 1 GeV to 2 GeV\nseveral wide resonances, mixtures of ss, uu and dd states, are\npresent and hence the OZI rule may not be directly applicable.\nexchange reaction (Bityukov et al., 1987). However, a \ufb01rm\nconclusion cannot be drawn, and an OZI-violating decay\nof the \u03c1(1700) is not excluded. The second structure, the\n\u03c1(1900), is compatible with the \u201cdip\u201d already observed in\nother experiments, predominantly in multi-hadron \ufb01nal\nstates (Antonelli et al., 1996; Frabetti et al., 2001), and\nby BABAR in the ISR production of six-pion \ufb01nal states\n(Aubert, 2006az). In the last-cited result, however, a sig-\nni\ufb01cantly larger width has been measured, so the situation\nis still uncertain.\n21.3.5.3 The discovery of the Y (2175) in K+K\u2212\u03c0\u03c0 \ufb01nal\nstates.\nThe e+e\u2212\u2192K+K\u2212\u03c0+\u03c0\u2212and e+e\u2212\u2192K+K\u2212\u03c00\u03c00\nreactions proceed through the production of numer-\nous intermediate states. The invariant mass distribu-\ntions of the two- and three-particle combinations indi-\ncate that the intermediate states K\u2217(892)0K\u00b1\u03c0\u2213and\nK\u2217(892)\u2213K\u00b1\u03c00 dominate in these reactions. A small\nK\u2217\n2(1430)K\u03c0 contribution is also seen, while states with\ntwo K\u2217, namely K\u2217(892)K\u2217(892), K\u2217(892)K\u2217\n2(1430), and\nK\u2217\n2(1430)K\u2217\n2(1430), account for less than 1% of the total\nreaction yield.\n\n683\nTable 21.3.3. Summary of parameters obtained for the \u03c1 and \u03c6 radial excitation from the study of the KK\u03c0 and KK\u03b7 \ufb01nal\nstates (Aubert, 2008ab), including the data on the \u03c6\u03b7 cross section from Aubert (2007bb). The parameters for the \u03c1\u2032\u2032 are taken\nfrom the \ufb01t to the \u03c6\u03c00 cross section with two resonances (see the text).\nIsospin\nR\n\u0393R\neeBR\nKK\u2217(eV)\n\u0393R\neeBR\n\u03c6\u03b7 (eV)\nMR (MeV)\n\u0393R (MeV)\n0\n\u03c6\u2032\n369 \u00b1 53 \u00b1 1\n138 \u00b1 33 \u00b1 28\n1709 \u00b1 20 \u00b1 43\n322 \u00b1 77 \u00b1 160\n0\n\u03c6\u2032\u2032\n\u2212\n1.7 \u00b1 0.7 \u00b1 1.3\n2125 \u00b1 22 \u00b1 10\n61 \u00b1 50 \u00b1 13\n1\n\u03c1\u2032\n127 \u00b1 15 \u00b1 6\n\u2212\n1505 \u00b1 19 \u00b1 7\n418 \u00b1 25 \u00b1 4\n1\n\u03c1\u2032\u2032\n\u2212\n3.5 \u00b1 0.9 \u00b1 0.3\n1570 \u00b1 36 \u00b1 62\n144 \u00b1 75 \u00b1 43\n1\n\u03c1(1900)\n\u2212\n2.0 \u00b1 0.6 \u00b1 0.4\n1909 \u00b1 17 \u00b1 25\n48 \u00b1 17 \u00b1 2\nAmong the most interesting studies of this \ufb01nal state\nperformed by BABAR is the extraction of the relatively\nsmall contributions of the \u03c6\u03c0+\u03c0\u2212and \u03c6\u03c00\u03c00 (\u03c6\n\u2192\nK+K\u2212) intermediate states (Aubert, 2006c, 2007bc). The\noriginal motivation was the search for decays of the then\nrecently-discovered vector meson Y (4260). As discussed\nin Section 18.3, the Y (4260) was discovered by BABAR in\nthe process e+e\u2212\u2192\u03b3ISRY (4260) \u2192\u03b3ISRJ/\u03c8\u03c0+\u03c0\u2212, but\nwas not seen to decay to D(\u2217)D(\u2217), although this was ex-\npected for a wide conventional charmonium state with a\nmass well above the DD production threshold. A certain\nexotic-structure model for the Y (4260) predicted a large\nbranching fraction for the decay into \u03c6\u03c0\u03c0 (Zhu, 2005).\nSince the \u03c6 resonance is relatively narrow, a clean\nsample of \u03c6\u03c0\u03c0 events can be easily separated. The scat-\nter plot of the reconstructed masses, m(\u03c0+\u03c0\u2212) versus\nm(K+K\u2212), for selected events in a data sample corre-\nsponding to 232 fb\u22121 is shown in Fig. 21.3.13(a) (Aubert,\n2006c): a clear \u03c6 \u2192K+K\u2212vertical band is visible, as well\nas an accumulation of events indicating correlated pro-\nduction of the \u03c6 and f0(980) \u2192\u03c0\u03c0 resonances. A wide\nhorizontal band corresponding to \u03c10 \u2192\u03c0+\u03c0\u2212produc-\ntion is also seen. The invariant mass distribution of the\n\u03c0\u03c0 system in \u03c6\u03c0\u03c0 events is obtained using the condition\n|m(K+K\u2212) \u2212m\u03c6| < 10 MeV/c2, where m\u03c6 is the nominal\n\u03c6-mass. The background from true K+K\u2212\u03c0\u03c0 events with\nnon-resonant K+K\u2212pair is subtracted using the \u03c6 mass\nsidebands 10 < |m(K+K\u2212) \u2212m\u03c6| < 20 MeV/c2; other\nbackgrounds are subtracted based on MC simulation. The\n\ufb01nal mass spectrum for \u03c0\u03c0 pairs associated with \u03c6 produc-\ntion is shown in Fig. 21.3.13(b)(Aubert, 2007bc). Besides\nthe clear f0(980) signal, and a concentration consistent\nwith the f2(1270) resonance, a broad bump at lower mass\nvalues is observed, which can be interpreted as the con-\ntroversial f0(600) scalar meson.\nThe e+e\u2212\u2192\u03c6\u03c0\u03c0 mass spectrum is measured in\n25 MeV/c2 wide bins by extracting the number of re-\nconstructed \u03c6 \u2192K+K\u2212decays from a \ufb01t to the K+K\u2212\nmass spectrum. The corresponding cross section is then\nobtained applying Eq. (21.2.12) and taking into account\nthe \u03c6 \u2192K+K\u2212branching fraction. With an analogous\nprocedure, but requiring in addition that 0.85 < m(\u03c0\u03c0) <\n1.1 GeV/c2, a 90% pure sample of \u03c6f0(980) is selected,\nand, assuming a decay rate B(f0(980) \u2192\u03c0+\u03c0\u2212) = 2/3,\nthe cross section is measured. Similar distributions and\nresults are obtained for the \u03c6\u03c00\u03c00 \ufb01nal state.\nThe cross section for the two f0(980) decay modes are\nconsistent with each other; both are shown in Fig. 21.3.14.\nThe data are successfully described by a relatively nar-\nrow resonance, called the Y (2175), interfering with a non-\nresonant term. The result of the \ufb01t is shown as the solid\nline in the \ufb01gure. By contrast, the attempt to \ufb01t the data\nwith only the non-resonant term, accounting for the \ufb01-\nnite width of the \u03c6 and f0(980), and for their spin and\nphase space, is clearly unsatisfactory (see the dashed red\nline). The histogram is the result of a simulation of the\nnon-resonant e+e\u2212\u2192\u03c6(1020)f0(980) reaction, which also\nfails to reproduce the features seen in the data.\nThe Y (2175) was con\ufb01rmed by the BES Collabora-\ntion in the \u03c6f0(980) invariant mass spectrum from J/\u03c8 \u2192\n\u03b7\u03c6f0(980) decays (Ablikim et al., 2008b), as well as in\nsubsequent measurements making use of the full data sets\nnow available to Belle and BABAR.\nThe new analyses at the two B Factories select the\n\u03c6\u03c0\u03c0 and \u03c6f0(980) \ufb01nal states in a way similar to the\nprevious BABAR analysis and measure rather consistent\ncross sections, and, thanks to the larger data samples\n(674 fb\u22121 for Belle, and 475 fb\u22121 for BABAR), a more\nprecise study of the e+e\u2212\u2192\u03c6\u03c0\u03c0 cross section and of\nthe intermediate states involved is possible. In both cases,\nthe e+e\u2212\u2192\u03c6(1020)\u03c0+\u03c0\u2212cross section shows two clear\npeaks: the \ufb01rst, at about 1.7 GeV, can be attributed to the\n\u03c6(1680), and the second, above 2 GeV, to the Y (2175).\nDi\ufb00erent models have been used by the two collaborations\nto \ufb01t the cross section distributions.\nBelle (Shen, 2009) uses an incoherent sum of two Breit-\nWigner functions, one for the \u03c6(1680), which is assumed\nto decay into \u03c6\u03c0+\u03c0\u2212, and the other for the Y (2175) which\ndecays predominantly into \u03c6f0(980). The result of the \ufb01t\nis shown as the solid line in Fig. 21.3.15, while the separate\ncontributions of the two \ufb01tted resonances are given by the\ndotted lines.\nIn the BABAR analysis (Lees, 2012d), it is also noted\nthat the second structure, associated to the Y (2175), com-\npletely disappears if events with a dipion mass under the\nf0(980) peak are removed. Figure 21.3.16 shows the BABAR\ndata and the result of a \ufb01t to a VMD-based model. This as-\nsumes that two vector mesons contribute to the cross sec-\n\n684\n0.5\n1\n1\n1.02\n1.04\n1.06\nm(K-K+) (GeV/c2)\nm(!+!-) (GeV/c2)\n \n(b)\n0\n25\n50\n75\n100\n0.4 0.6 0.8 1 1.2\nm(\u03c0+\u03c0\u2212\nEvents/0.015 GeV/c\n) (GeV/c\n2\n)\n2\nFigure\n21.3.13.\n(a)\nThe\nreconstructed\nm(\u03c0+\u03c0\u2212)\nvs\nm(K+K\u2212) distribution for the e+e\u2212\u2192K+K\u2212\u03c0+\u03c0\u2212reac-\ntion measured by BABAR (Aubert, 2006c). The vertical lines\nidentify the selected region around the \u03c6 mass peak. (b) Back-\nground subtracted m(\u03c0+\u03c0\u2212) distribution of selected e+e\u2212\u2192\n\u03c6(1020)\u03c0+\u03c0\u2212events (Aubert, 2007bc). The solid line is the\nresults of the \ufb01t to the data with a coherent sum of two Breit-\nWigner functions, referring to the f0(600) and f0(980).\ntion: the \u03c6(1680) decaying both to \u03c6f0(600) and \u03c6f0(980),\nand the Y (2175) decaying to \u03c6f0(980) only. Since the nom-\ninal \u03c6(1680) mass lies below the \u03c6f0(980) threshold, the\n\u03c6(1680) \u2192\u03c6f0(980) decay will reveal itself as a smooth\nbump in the energy dependence of the e+e\u2212\u2192\u03c6f0(980)\ncross section above 2 GeV, as shown by the dotted line in\nthe plot. The solid line is the result of the total \ufb01t to the\n\u03c6\u03c0\u03c0 cross section, which clearly indicates the need for an\nadditional resonance centered at about 2.2 GeV, on top\nof the dashed line showing the \u03c6(1680) contribution.\nBoth collaborations also \ufb01tted the selected samples of\n\u03c6f0(980) events, \ufb01nding results consistent with the \ufb01ts to\nthe whole \u03c6\u03c0+\u03c0\u2212sample. The \ufb01nal quoted values for the\n0\n0.2\n0.4\n0.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\nEc.m. (GeV)\n\u03c3(\u03c6 f0) (nb)\nFigure 21.3.14.\nThe e+e\u2212\u2192\u03c6f0(980) cross sections mea-\nsured in the K+K\u2212\u03c0+\u03c0\u2212(circles) and K+K\u2212\u03c00\u03c00 (squares)\n\ufb01nal states using an integrated luminosity of 232 fb\u22121 by\nBABAR (Aubert, 2007bc). The hatched histogram shows the\nsimulated cross section in the no-resonance hypothesis, which\nis consistent with a \ufb01t to the data with only a non-resonant\ncomponent (dashed line). The solid line represents the result\nof the \ufb01t described in the text assuming the presence of the\nY (2175).\n0\n0.2\n0.4\n0.6\n0.8\n1.5\n2\n2.5\n3\nEC.M. (GeV)\n!(\"#+#-) (nb)\nFigure 21.3.15.\nThe e+e\u2212\u2192\u03c6\u03c0+\u03c0\u2212cross section mea-\nsured by Belle (Shen, 2009). The solid line is the result of a\n\ufb01t with two incoherent BW functions, one for the \u03c6(1680) and\nthe other for the Y (2175). The dashed lines show the individual\ncontributions of the two resonances.\nparameters of the \u03c6(1680) and Y (2175) resonances are in\nreasonable agreement between Belle and BABAR (consider-\ning slightly di\ufb00erent modelling, for example (in)coherence\nof contributing amplitudes). In particular, for the mass\nand the width of the Y (2175), Belle \ufb01nds, respectively,\nmY = (2.079 \u00b1 0.013+0.079\n\u22120.028) GeV/c2 and \u0393Y = (192 \u00b1\n23+25\n\u221261) MeV, while BABAR \ufb01nds a higher mass, mY =\n(2.180\u00b10.008\u00b10.008) GeV/c2, and a smaller width, \u0393Y =\n(77 \u00b1 15 \u00b1 10) MeV.\n\n685\n0\n0.25\n0.5\n0.75\n1\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\nEc.m., GeV\n!(\"##), nb\n0\n0.25\n0.5\n0.75\n1\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\nEc.m., GeV\n!(\"##), nb\nFigure 21.3.16. The \ufb01t to the e+e\u2212\u2192\u03c6\u03c0+\u03c0\u2212cross section\nmeasured by BABAR (Lees, 2012d) in the two-resonance model\ndescribed in the text (solid curve). The contribution of the\n\ufb01rst resonance (\u03c6(1680)) is shown by the dashed line. The dot-\nted line shows the \ufb01rst resonance contribution in the \u03c6f0(980)\ndecay mode only.\nThe nature of the Y (2175) is still uncertain. The simi-\nlar width (\u2248200 MeV) measured by Belle for the \u03c6(1680)\nand the Y (2175), even if with large uncertainties, may\nsuggest that the Y (2175) is a radially excited ss vec-\ntor state. On the other hand, the signi\ufb01cantly smaller\nwidth reported by BABAR and BES, and the di\ufb00erent\ndecay modes observed for the \u03c6(1680) and the Y (2175),\ndo not favor this solution (Napsuciale, Oset, Sasaki, and\nVaquera-Araujo, 2007). Several other interpretations have\nbeen proposed, such as a ssss four-quark state, or a gluon\nhybrid ssg. For a review of this and other recently discov-\nered hadrons see (Zhu, 2008) and references therein. The\nstudy of the Y (2175) in other decay modes is needed to\ndistinguish between the di\ufb00erent possibilities.\n21.3.5.4 Summary of studies of J/\u03c8 and \u03c8(2S) decays.\nThe clear J/\u03c8 and \u03c8(2S) signals observed in the cross\nsections for e+e\u2212annihilation to almost all the \ufb01nal states\npresented in the previous sections allowed a systematic\nstudy of the decays of the two charmonium states to light\nhadrons with the BABAR detector.\nThe Born cross section for the production via ISR of\na narrow resonance such as a \u03c8, and its subsequent decay\nto the \ufb01nal state X, is given by\n\u03c3\u03c8 = 12\u03c02\u0393(\u03c8 \u2192e+e\u2212)B(\u03c8 \u2192X)\nsm\u03c8\nW0(s, x\u03c8, \u03b80) ,\n(21.3.14)\nwhere m\u03c8, \u0393(\u03c8 \u2192e+e\u2212), and B(\u03c8 \u2192X) are the mass\nof the \u03c8, its partial width to electrons, and its branch-\ning fraction to the \ufb01nal state X respectively. The radi-\nator function W0 has been introduced in Section 21.2.1,\nand x\u03c8 = 1 \u2212m2\n\u03c8/s is the fraction of the CM energy\ncarried by the photon in the case of radiative return to\nthe \u03c8 mass. Therefore, for a given \ufb01nal state X, the pro-\nduct of the electronic width and the branching fraction\n\u0393(\u03c8 \u2192e+e\u2212)B(\u03c8 \u2192X) can be obtained by measuring\nthe number of \u03c8 decays in the e+e\u2212\u2192X mass spectrum.\nThe samples of J/\u03c8 and \u03c8(2S) available for these stud-\nies are signi\ufb01cantly smaller than those collected at other\nfacilities. The total cross section for e+e\u2212\u2192\u03b3ISRJ/\u03c8 with\na tagged ISR photon is about 3.4 pb, corresponding to 1.7\nmillion J/\u03c8\u2019s for an integrated luminosity of \u223c500 fb\u22121;\nabout 60 million J/\u03c8\u2019s have been produced in the BES\nII experiment at the BEPC e+e\u2212collider. However, sys-\ntematic uncertainties are signi\ufb01cantly smaller at BABAR\n(typically 3\u20135%, compared to 10\u201315% at BES II), due in\nparticular to superior particle identi\ufb01cation.161 As a re-\nsult BABAR measurements are competitive and in many\ncases more accurate than previous data for all decays with\nbranching fractions O(10\u22123) and higher, and many decays\nto \ufb01nal states containing charged kaons have been stud-\nied for the \ufb01rst time. In summary, using the ISR method,\nthe BABAR experiment has improved the precision on the\nmeasurement of a few tens of J/\u03c8 and \u03c8(2S) branching\nfractions, and has observed about 20 new decay modes.\nA complete list of these results is found in the Review of\nParticle Physics (Beringer et al., 2012).\n21.3.6 Search for fJ(2220)\nEvidence for the fJ(2220), a narrow resonance with a mass\naround 2.2 GeV/c2 also known as \u03be(2230), was \ufb01rst pre-\nsented by the Mark III Collaboration (Baltrusaitis et al.,\n1986). The fJ(2220) was seen as a narrow signal above a\nbroad enhancement in both J/\u03c8 \u2192\u03b3fJ(2220), fJ(2220) \u2192\nK+K\u2212and fJ(2220) \u2192K0\nSK0\nS decays with signi\ufb01cance\nof 3.6 and 4.7 standard deviations, respectively. The BES\nCollaboration has also subsequently reported evidence in\nradiative J/\u03c8 decays at a comparable level of signi\ufb01cance\n(Bai et al., 1996b), while searches for direct formation\nin p\u00afp collisions or two-photon processes were inconclusive\n(see for example Crede and Meyer, 2009, for an experi-\nmental review).\nThe unexpectedly narrow width of the fJ(2220), ap-\nproximately 20 MeV, triggered many conjectures about\nits nature (see for example Blundell and Godfrey, 1996).\nThe possibility of a glueball (Ward, 1985), a bound state\nof gluons, is particularly attractive as several lattice QCD\ncalculations predict a mass for the ground state 2++ glue-\nball close to 2.2 GeV/c2 (Chen and Su, 2004; Morningstar\nand Peardon, 1997). No glueball candidate has been un-\nambiguously observed to date.\nBased on a sample of 16 million J/\u03c8 mesons produced\nin ISR events, BABAR performed a search for fJ(2220) pro-\nduction in radiative J/\u03c8 \u2192\u03b3fJ(2220) decays (del Amo San-\n161 In 2009, the upgraded BESIII experiment at BEPCII has\ncollected 225 million J/\u03c8 and 106 million \u03c8(2S) events. The\nsystematic error is signi\ufb01cantly improved over BESII experi-\nment (Ablikim et al., 2012b).\n\n686\nchez, 2010o). The fJ(2220) is identi\ufb01ed through its subse-\nquent decay into a K+K\u2212or K0\nSK0\nS pair. The ISR photon\nis not required to be detected.\nRequirements on particle identi\ufb01cation, secondary ver-\ntex reconstruction, decay angles and global event infor-\nmation are used to improve the signal purity. The J/\u03c8\ncandidates are then \ufb01tted, constraining their mass and\ndecay products to a common vertex. The \ufb01tted K+K\u2212\nand K0\nSK0\nS mass spectra are shown in Fig. 21.3.17, to-\ngether with the expected contributions of the inclusive\ne+e\u2212\u2192qq(\u03b3) (q = u, d, s, c) background as well as J/\u03c8 \u2192\n\u03b3f \u2032\n2(1525) and \u03b3f0(1710) channels. A possible contribu-\ntion from J/\u03c8 \u2192K\u2217\u00b1K\u2213decays was found to be neg-\nligible. Sideband data from the unconstrained J/\u03c8 mass\ndistributions are used to model the non-resonant back-\nground. The sum of these components reproduces the data\nwell at a global level. Remaining events are due mainly\nto generic J/\u03c8 decays producing additional undetected\nparticles, mostly with pions misidenti\ufb01ed as kaons in the\ncharged mode.\nThe number of signal events is determined using an un-\nbinned maximum likelihood \ufb01t in the range 1.9 GeV/c2 <\nmKK < 2.6 GeV/c2, \ufb01xing the mass and width of the\nfJ(2220) to 2.231 GeV/c2 and 23 MeV, respectively. No\nevidence of a fJ(2220) signal is observed. Upper limits\non the J/\u03c8 \u2192\u03b3fJ(2220), fJ(2220) \u2192K+K\u2212and K0\nSK0\nS\nproduct branching fractions are derived at the 90% con\ufb01-\ndence level as a function of the spin and helicity assumed\nfor the fJ(2220). For all hypotheses of spin and helicity,\nthese limits are below the central values reported by Mark\nIII. Only one hypothesis (spin J = 2 and helicity h = 0)\nis compatible with the BES results for both \ufb01nal states,\nwhile all other possibilities are excluded.\n21.3.7 Measurement of time-like baryon form factors\nElectromagnetic form factors (FFs) describe the modi\ufb01ca-\ntions of pointlike photon-hadron vertices due to the struc-\nture of hadrons. The e+e\u2212annihilation in two hadrons or\nthe electron scattering o\ufb00a nucleon are described in QED\nby a product of an electronic and a hadronic electroma-\ngnetic currents. While the coupling of the photon with the\nelectron is exactly calculable in QED, the coupling with\nthe hadron is not. The dynamical content of the hadronic\nvertex can be however described with a set of form factors,\nand can be directly extracted from data.\n21.3.7.1 Nucleon Form Factors\nThe elastic scattering of an electron by a nucleon\ne\u2212N \u2192e\u2212N is represented, in the Born approximation,\nby Fig. 21.3.18, with time \ufb02owing from the bottom to\nthe top of the diagram. In this kinematic region the 4-\nmomentum of the virtual photon is space-like and hence\nits squared value is negative: q2 = \u22122\u03c91\u03c92(1\u2212cos \u03b8e) \u22640,\nwhere \u03c91(2) is the energy of the incoming (outgoing) elec-\ntron and \u03b8e is the scattering angle. The same diagram, but\nwith time \ufb02owing left to right (right to left), represents the\n)\n2\n mass (GeV/c\n-\nK\n+\nK\n1\n1.5\n2\n2.5\n3\n) \n2\nEntries / (0.05 GeV/c\n0\n100\n200\n300\n400\n500\nData\nInclusive bkg\n!\n(1525) \n2\n f\u2019\n\"\n \n#\nJ/\n!\n(1710) \n0\n f\n\"\n \n#\nJ/\n)\n2\n mass (GeV/c\n-\nK\n+\nK\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n) \n2\nEntries / 0.02 (GeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n)\n2\n mass (GeV/c\n-\nK\n+\nK\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n) \n2\nEntries / 0.02 (GeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n)\n2\n mass (GeV/c\nS\n0\nK\nS\n0\nK\n1\n1.5\n2\n2.5\n3\n) \n2\nEntries / (0.075 GeV/c\n0\n5\n10\n15\n20\n25\n30\n35\nData\nInclusive bkg\n!\n(1525) \n2\n f\u2019\n\"\n \n#\nJ/\n!\n(1710) \n0\n f\n\"\n \n#\nJ/\n)\n2\n mass (GeV/c\nS\n0\nK\nS\n0\nK\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n) \n2\nEntries / 0.02 (GeV/c\n0\n1\n2\n3\n4\n5\n6\n)\n2\n mass (GeV/c\nS\n0\nK\nS\n0\nK\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n) \n2\nEntries / 0.02 (GeV/c\n0\n1\n2\n3\n4\n5\n6\nFigure 21.3.17. The K+K\u2212(top) and K0\nSK0\nS (bottom) mass\nspectra obtained by BABAR in selected J/\u03c8 \u2192\u03b3K+K\u2212and\nJ/\u03c8 \u2192\u03b3K0\nSK0\nS decays, together with the expected contribu-\ntions of the non-resonant background, J/\u03c8 \u2192\u03b3f \u2032\n2(1525) and\nJ/\u03c8 \u2192\u03b3f0(1710) reactions. The results of the \ufb01t to the data\nare shown in the inset (del Amo Sanchez, 2010o).\ne\u2212(k1)\ne\u2212(k2)\nN(p1)\nN(p2)\n\u03b3(q)\nAnnihilation\nScattering\nFigure 21.3.18. One-photon exchange Feynman diagram for\nscattering e\u2212N \u2192e\u2212N and annihilation e+e\u2212\u2192NN.\nannihilation e+e\u2212\u2192NN (NN \u2192e+e\u2212). For these pro-\ncesses the 4-momentum q is time-like: q2 = (2\u03c9)2 \u22650,\nwhere \u03c9 \u2261\u03c91 = \u03c92 is the common value of the lepton\nenergy in the e+e\u2212center-of-mass frame.\n\n687\nThe Feynman amplitude for the elastic scattering is\nM = 1\nq2\n\u0002\ne u(k2)\u03b3\u00b5u(k1)\n\u0003\u0002\ne U(p2)\u0393\u00b5(p1, p2)U(p1)\n\u0003\n,\n(21.3.15)\nwhere ki = (\u03c9i, ki) and pi (i = 1, 2) are the electron and\nnucleon four-vectors, u and U are the electron and nucleon\nspinors, and \u0393\u00b5 is a non-constant matrix which describes\nthe nucleon vertex. Using gauge and Lorentz invariance\nthe most general form of such a matrix is (Foldy, 1952)\n\u0393\u00b5 = \u03b3\u00b5F1(q2) + i\u03c3\u00b5\u03bdq\u03bd\n2m\nF2(q2) ,\n(21.3.16)\nwhere m is the nucleon mass. \u0393\u00b5 depends on two Lorentz\nscalar functions of q2, the Dirac (F1(q2)) and Pauli FFs\n(F2(q2)), that describe the helicity-conserving and the heli-\ncity-reversing parts of the hadronic current, respectively.\nNormalizations at q2 = 0 follow from total charge and\nmagnetic moment of the nucleon: F1(0) = QN and F2(0) =\naN respectively, where QN is the electric charge (in units\nof e) and aN the anomalous magnetic moment of the nu-\ncleon N, in units of the nuclear magneton e\u210f/2m.162\nOther pairs of FFs can be de\ufb01ned as combinations of\nF1 and F2: of particular interest are the so-called Sachs\nFFs GE and GM (Hand, 1963), de\ufb01ned as\nGE = F1 + q2\n4m2 F2,\nGM = F1 + F2 .\n(21.3.17)\nThese expressions are obtained by considering the hadronic\ncurrent in the Breit frame: the Fourier transformations of\nGE and GM give the spatial distributions of charge and\nmagnetic moment of the nucleon; the normalizations are\nGE(0) = QN ,\nGM(0) = \u00b5N ,\n(21.3.18)\nwhere \u00b5N is the nucleon magnetic moment in units of the\nnuclear magneton.163\n21.3.7.2 Cross sections and data\nThe di\ufb00erential cross section of the annihilation process\ne+e\u2212\u2192NN, for unpolarized colliding beams, is given in\nthe e+e\u2212CM by (Zichichi, Berman, Cabibbo, and Gatto,\n1962)\nd\u03c3\nd\u2126= \u03b12\u03b2 C\n4 q2\n\u0014\n(1 + cos2 \u03b8)\n\f\fGM(q2)\n\f\f2+ 1\n\u03c4 sin2 \u03b8\n\f\fGE(q2)\n\f\f2\n\u0015\n,\n(21.3.19)\n162 For proton F1(0) = 1, F2(0) = 1.7928, and for neutron\nF1(0) = 0, F2(0) = \u22121.9130.\n163 For proton GM(0) = 2.7928 and for neutron GM(0) =\n\u22121.9130.\nwhere \u03c4 = q2/4m2, \u03b2 =\np\n1 \u22121/\u03c4 is the velocity of the\noutgoing nucleon, and C is the so-called Coulomb fac-\ntor (Sakharov, 1948)\nC =\n\uf8f1\n\uf8f4\n\uf8f2\n\uf8f4\n\uf8f3\n\u03c0\u03b1/\u03b2\n1 \u2212exp(\u2212\u03c0\u03b1/\u03b2)\nfor QN = 1\n1\nfor QN = 0 ,\n(21.3.20)\nwhich accounts for electromagnetic NN \ufb01nal state interac-\ntions; C corresponds to the squared value of the Coulomb\nscattering wave function at the origin. Integration of Eq.\n(21.3.19) over the polar angle gives the total cross section:\n\u03c3(q2) = 4\u03c0\u03b12\u03b2 C\n3 q2\n\u0014\f\fGM(q2)\n\f\f2 + 1\n2\u03c4\n\f\fGE(q2)\n\f\f2\n\u0015\n.\n(21.3.21)\nAt production threshold |GE(4m2)| = |GM(4m2)|, while\nat high q2 the contribution of GE to the cross sec-\ntion becomes negligible because of the suppression from\nthe 1/2\u03c4 term. Experiments usually quote measurements\nof |GM(q2)| under the working hypothesis |GE(q2)| =\n|GM(q2)|, which is exactly true only at threshold. BABAR\nintroduces an e\ufb00ective FF de\ufb01ned as\n|F(q2)|2 = 2\u03c4|GM(q2)|2 + |GE(q2)|2\n2\u03c4 + 1\n,\n(21.3.22)\nwhich can be directly compared to the previous measure-\nments of |GM(q2)|. The total cross section is thus written\nas\n\u03c3(q2) = 4\u03c0\u03b12\u03b2C\n3q2\n\u0012\n1 + 1\n2\u03c4\n\u0013\n|F(q2)|2 .\n(21.3.23)\nSimultaneous extraction of |GE| and |GM| requires precise\ndetermination of the |GE/GM| ratio, which is possible in\nprinciple by measuring the angular distributions of the\noutgoing particles, using Eq. (21.3.19). A |GE/GM| mea-\nsurement for the proton is discussed in Section 21.3.7.4\nbelow.\n21.3.7.3 Measurement of e+e\u2212\u2192pp\nThe BABAR experiment performed an ISR tagged analy-\nsis of e+e\u2212\u2192\u03b3ISRpp based on a sample of 232 fb\u22121 of\ndata, and selected more than 4000 events, measuring the\ne+e\u2212\u2192pp cross section with highest accuracy in the\nrange of pp invariant mass from threshold up to about\nM 2\npp = 4.5 GeV/c2 (Aubert, 2006d). As for the other ISR\nprocesses previously discussed, the reconstructed hadronic\nmass gives the CM energy of the hadronic process: M 2\npp =\nq2. Figure 21.3.19 shows a comparison of the measured\ncross section for Mpp < 2.9 GeV/c2 with previous mea-\nsurements performed with lower precision by Castellano\net al. (1973) and the Fenice experiment (Antonelli et al.,\n1998) at Adone, by DM1 (Delcourt et al., 1979) and DM2\n(Bisello et al., 1990), and more recently by CLEO (Pedlar\net al., 2005) and BES (Ablikim et al., 2005a).\n\n688\nFENICE\nDM2\nDM1\nADONE73\nBES\nBABAR\nMpp (GeV/c2)\nCross section (pb)\n0\n500\n1000\n1500\n2\n2.2\n2.4\n2.6\n2.8\nFigure 21.3.19. The e+e\u2212\u2192pp cross section measured by\nBABAR (Aubert, 2006d) in the energy region from threshold to\nabout 3 GeV. Data from previous experiments are shown for\ncomparison.\nOne interesting feature, now apparent due to the preci-\nsion of the data, is that the pp cross section is nearly con-\nstant at 0.8 nb for energies up to around 200 MeV above\nthe threshold, before falling with increasing energy. The\ncorresponding e\ufb00ective form factor results are presented in\nFig. 21.3.20 as a function of Mpp, together with results ob-\ntained from the pp \u2192e+e\u2212experiments PS170 (Bardin\net al., 1994), E760 (Armstrong et al., 1993), and E835\n(Ambrogiani et al., 1999; Andreotti et al., 2003). General\nconsistency among all these data is observed: in particular\nthe precise data from BABAR and from the PS170 exper-\niment (pp annihilation at LEAR) show a similar rise in\nthe form factor when the energy approaches pp thresh-\nold. Several explanations of this intriguing feature have\nbeen proposed, such as that the sharp rise is due to \ufb01-\nnal state interaction of the proton and antiproton (see\nDmitriev and Milstein, 2007, and references therein); or\nthat it is due to a contribution from a vector-meson reso-\nnance with a mass of about 1.9 GeV/c2, just below the pp\nproduction threshold (such a state is observed as a dip\nin the cross section of the e+e\u2212\u21926\u03c0 processes: Au-\nbert, 2006az; Frabetti et al., 2001). The hypothesis of\nan incorrect evaluation of the Coulomb factor has also\nbeen advanced: see for example Ferroli, Pacetti, and Za-\nllo (2012). The dashed line in Fig. 21.3.20 is the result\nof a \ufb01t of the form factor data according to the function\nFQCD = A/(m4 log2(m2/\u039b2)), which correspond to the\nperturbative QCD prediction for the asymptotic behav-\nior of the baryon form factors (Chernyak and Zhitnitsky,\n1977; Lepage and Brodsky, 1979b). Here, \u039b = 0.3 GeV\nand A is a free parameter of the \ufb01t. It is seen that the\nasymptotic result provides a reasonable description of the\ndata even at these energies.\nFENICE\nDM2\nDM1\nBES\nCLEO\nPS170\nE835\nE760\nBABAR\nMpp (GeV/c2)\nProton form factor\n10\n-2\n10\n-1\n2\n3\n4\nFENICE\nDM2\nDM1\nBES\nPS170\nE835\nE760\nBABAR\nM pp (GeV/c2)\nProton form factor\n0\n0.2\n0.4\n0.6\n2\n2.25\n2.5\n2.75\n3\nFigure 21.3.20. The proton form factor measured by BABAR\n(Aubert, 2006d) compared to data from previous e+e\u2212\u2192pp\n(blue online) and pp \u2192e+e\u2212(red online) experiments. The\ndashed line is the \ufb01t to all available data according to the\nperturbative QCD prediction. The bottom plot shows an ex-\npanded view of the energy region below 3 GeV.\n21.3.7.4 Measurement of |Gp\nE/Gp\nM|\nThe distribution of the proton helicity angle in the pp\nrest frame for e+e\u2212\u2192\u03b3ISRpp events can be written as\na function of the ratio of the electric and magnetic form\nfactors:\ndN\nd cos \u03b8p\n= A\n \nHM(cos \u03b8p, q2) +\n\f\f\f\f\nGE\nGM\n\f\f\f\f\n2\nHE(cos \u03b8p, q2)\n!\n.\n(21.3.24)\nThe functions HE and HM, which are determined us-\ning MC simulation, do not strongly di\ufb00er from the terms\nsin2 \u03b8p and 1 + cos2 \u03b8p that appear in Eq. (21.3.19). The\nmass region from pp threshold up to 3 GeV/c2 is divided\ninto six intervals. The angular distribution in each inter-\nval is then \ufb01tted to Eq. (21.3.24), with A and |GE/GM| as\nfree parameters. The functions HE and HM are modeled\nwith the histograms obtained from MC simulation with\nthe pp selection applied. The values of the ratio |GE/GM|\nobtained by Aubert (2005ah) are signi\ufb01cantly larger than\nunity, as shown in Fig. 21.3.21, in disagreement with pre-\nvious results from PS170 at LEAR (Bardin et al., 1994).\n\n689\nMpp (GeV/c2)\n|GE/GM|\n0\n0.5\n1\n1.5\n2\n2.5\n2\n2.25\n2.5\n2.75\n3\nFigure 21.3.21. The proton |GE/GM| ratio measured by\nBABAR (Aubert, 2006d; solid points) compared with PS170 data\n(Bardin et al., 1994; open circles). The curve is a result of a \ufb01t\nto BABAR data with the function (1 + ax/(1 + bx2)).\nWe should note that the PS170 data were limited by in-\ncomplete angular acceptance (| cos \u03b8p| < 0.8) and were\na\ufb00ected by strong angular dependence of the detection ef-\n\ufb01ciency: this limitation is not present when a tagged ISR\nanalysis is performed.\n21.3.7.5 Measurement of strange baryon form factors.\nThe BABAR Collaboration has also studied the produc-\ntion via ISR of several \ufb01nal states made of strange baryon\npairs, namely e+e\u2212\u2192\u039b\u039b, \u03a3\u03a3, and \u039b\u03a30 (\u03a30\u039b) (Aubert,\n2007az). Only a single measurement of \u039b\u039b production at\n2.386 GeV, by the DM2 Collaboration, and upper lim-\nits on the other process, were previously available. The\n\u039b is reconstructed in the p\u03c0\u2212decay, while for the \u03a3 the\ndecay chain \u03a3 \u2192\u039b\u03c0, \u039b \u2192p\u03c0\u2212is used. The cross sec-\ntion measured for e+e\u2212\u2192\u039b\u039b, based on about 200 se-\nlected events, after background subtraction, is shown in\nFig. 21.3.22. The measured cross section is consistent with\na behavior similar to that in pp production: an almost \ufb02at\ndistribution from threshold over a \u223c200 MeV range, and\nin particular a value di\ufb00erent from zero at threshold. This\nbehavior is contrary to expectations, as the Coulomb fac-\ntor plays no role for neutral \ufb01nal-state particles. However,\nthe large uncertainties due to the limited sample can not\nexclude a vanishing cross section at threshold.\nThe study of the angular distribution of produced \u039b\u2019s\nallows the measurement of |GE/GM|: the ratio is consis-\ntent with unity within the large statistical uncertainty.\nShould the relative phase \u03c6 between GE and GM be\ndi\ufb00erent from zero, polarization of the outgoing bary-\nons, perpendicular to the scattering plane of the process\ne+e\u2212\u2192BB, is expected (see Dubnickova, Dubnicka, and\nRekalo, 1996, and Czyz, Grzelinska, and K\u00a8uhn, 2007, for\nDM2\nBABAR\nM!!\u2013 (GeV/c2)\nCross section (pb)\n0\n100\n200\n300\n2.2\n2.4\n2.6\n2.8\n3\nFigure 21.3.22. The e+e\u2212\u2192\u039b\u039b cross section measured by\nBABAR (Aubert, 2007az) in comparison with the DM2 measure-\nment (Bisello et al., 1990).\nthe speci\ufb01c case of ISR production). While the polariza-\ntion of the outgoing protons in the pp production case\ncannot be measured in BABAR, the \u039b polarization \u03b6 can\nbe extracted from the proton angular distribution in the\n\u039b \u2192p\u03c0\u2212decay,\ndN\nd cos \u03b8p\u03b6\n= A (1 + \u03b1\u039b\u03b6 cos \u03b8p\u03b6) ,\n(21.3.25)\nwhere \u03b8p\u03b6 is the angle between the polarization axis and\nthe proton momentum in the \u039b rest frame, and \u03b1\u039b =\n0.642 \u00b1 0.013 (Yao et al., 2006) the decays asymmetry\nparameter, with \u03b1\u039b = \u2212\u03b1\u039b. For unpolarized events in the\nMC simulation, the distribution is consistent with being\nisotropic (\ufb02at in cos \u03b8p\u03b6), as expected.\nThe \ufb01t to the background subtracted data distribution\nreturns a slope of 0.020 \u00b1 0.097. Under the assumption of\n|GE| = |GM| this measurement can be converted into a\n90% C.L. interval for the relative phase of the two form\nfactors: \u22120.76 < sin \u03c6 < 0.98. The obtained limits are very\nweak, but the method has been proven to work and could\ngive interesting results when signi\ufb01cantly larger samples\nbecome available.\nFig. 21.3.23 shows the strange-baryon e\ufb00ective form\nfactors measured by BABAR. About 20 candidate events\nhave been selected for both e+e\u2212\u2192\u03a3\u03a3 and e+e\u2212\u2192\n\u03a30\u039b. It is seen that the \u039b, \u03a30, and \u03a30\u039b form factors are of\nthe same order. For comparison, the proton FF measured\nby BABAR is also shown: the energy-dependence of the \u039b\nand proton FFs di\ufb00er. A \ufb01t to the \u039b FF with the power-\nlaw function F(Q2) \u223cQ\u2212n returns n \u22439, showing that\nthe asymptotic regime (n = 4) predicted by perturbative-\nQCD is not reached in the measured energy range below\n3 GeV.\n\n690\np\n!0\n\"!0\n\"\nm (GeV/c2)\n|F|\n0\n0.1\n0.2\n0.3\n2.2\n2.4\n2.6\n2.8\n3\nFigure 21.3.23. The baryon form factors measured by BABAR\nversus the dibaryon invariant mass. Data taken from Aubert\n(2005ah, 2007az).\n21.4 Open charm production\nDue to intriguing discoveries of exotic charmonium like\nstates (see Secs. 21.5 and 18.3) with masses at which con-\nventional charmonium states are expected to decay pre-\ndominantly into pairs of open charm mesons it is of great\ninterest to explore the ISR production of these \ufb01nal states.\nExclusive production of open charm has been stud-\nied in two di\ufb00erent regimes at the B Factories: far from\nthreshold, in e+e\u2212annihilation at the CM energy of the\ncollider (Section 21.4.1), and from threshold up to 5\u20136 GeV,\ndepending on the \ufb01nal state, using the ISR technique (Sec-\ntions 21.4.2\u201321.4.6). There is no general approach to these\nmeasurements: the method that yields maximum signi\ufb01-\ncance needs to be determined case-by-case. The measure-\nment of e+e\u2212\u2192D(\u2217)+D(\u2217)\u2212production at the CM en-\nergy (Section 21.4.1) introduced a partial reconstruction\nmethod that exploits the special properties of the D\u2217de-\ncay. Here D(\u2217) denotes a D or D\u2217meson. Measurement\nof DD production in ISR events, on the other hand, was\nperformed by full reconstruction of both charmed mesons\n(Section 21.4.2). Analyses of D(\u2217)+D\u2217\u2212(Section 21.4.3),\ncharmed-strange (Section 21.4.4), and three-body charmed\nmeson cross sections (Section 21.4.5), and a study of charmed\nbaryon production (Section 21.4.6), use variants of these\ntechniques.\nIn ISR events of this type, the continuous spectrum\nof photons emitted from the initial state provides access\nto a range of energies above open charm threshold. This\nallows the measurement of cross sections without the ad-\nditional systematic uncertainties due to variation of the\ndetector and machine conditions from one energy point to\nanother during the relatively long time of the data col-\nlection. However, the electromagnetic suppression of ISR\nprocesses and the reduced reconstruction e\ufb03ciency due\nto the event topology present considerable challenges. Re-\nconstruction of exclusive production at the CM energy\ndoes not face these problems, but in this regime the cross\nsection itself is low. Together with the very high luminosi-\nties available at the B Factories, careful choice of analy-\nsis methods has allowed many exclusive charmed hadron\ncross sections to be measured over a wide energy range,\nwith good accuracy.\n21.4.1 Measurement of exclusive D(\u2217)+D(\u2217)\u2212\nproduction far from threshold\nKnowledge of exclusive charmed meson production in e+e\u2212\nannihilation is rather poor. The only exception is the near-\nthreshold region, where the small phase space limits the\nnumber of particles in the \ufb01nal state. Heavy quark e\ufb00ec-\ntive theory (HQET), based on heavy-quark spin symme-\ntry, provides a description of these processes in terms of a\nuniversal form factor called the Isgur-Wise function. For\nlarge q2, however, the leading-twist contribution, violating\nthis symmetry, becomes dominant. In the intermediate-q2\nregion the contribution of the symmetry-violating terms\nremains signi\ufb01cant. A calculation that takes this e\ufb00ect\ninto account (Grozin and Neubert, 1997) predicts cross\nsections of about 2.5 pb\u22121 for the e+e\u2212\u2192D\u2217\nT D\u2217\nL and\ne+e\u2212\u2192DD\u2217processes, where the subscripts T and L in-\ndicate transverse and longitudinal polarization of the D\u2217,\nrespectively. The cross section of the e+e\u2212\u2192DD process\nis estimated to be at least 1000 times smaller.\nExclusive meson production in e+e\u2212annihilation is\ndi\ufb03cult to study experimentally due to its extremely\nlow cross-section and reconstruction e\ufb03ciency. A partial\nreconstruction method is therefore used: one D(\u2217) me-\nson is fully reconstructed while the other remains unre-\nconstructed. For de\ufb01niteness, suppose the D(\u2217)+ is the\nfully reconstructed meson. The distribution of recoil mass\nMrecoil, where\nM 2\nrecoil(D(\u2217)+) = (ECM \u2212E(D(\u2217)+))2 \u2212p2(D(\u2217)+),\n(21.4.1)\ncan be used for identi\ufb01cation of the process. Signal events\nare expected to cluster around the mass of the unrecon-\nstructed D(\u2217)\u2212meson. This method provides better re-\nconstruction e\ufb03ciency than the exclusive reconstruction\nof the event, but the background level is also much higher.\nIf the unreconstructed meson is a D\u2217, one can recon-\nstruct one of its decay products\u2014usually the pion, \u03c0\u2212\nslow,\nin D\u2217\u2212\u2192D0\u03c0\u2212\nslow\u2014and construct the recoil mass di\ufb00er-\nence\n\u2206Mrecoil = Mrecoil(D(\u2217)+) \u2212Mrecoil(D(\u2217)+\u03c0\u2212\nslow).\n(21.4.2)\nSince most of the uncertainties cancel in the di\ufb00erence,\nthe peak at the nominal mass di\ufb00erence mD\u2217\u2212mD in\nthe \u2206Mrecoil distribution remains narrow (\u223c1 MeV/c2).\nThe width is determined mostly by the slow pion recon-\nstruction accuracy. The use of the recoil mass di\ufb00erence\nas a discriminating or a signal variable is a powerful tool\nfor background suppression. It was used by the Belle col-\nlaboration in ISR analyses (see Section 21.4.3) and in the\n\n691\nstudy of D-meson semileptonic decays (Widhalm, 2006;\nsee Section 19.1.5).\nExclusive e+e\u2212\u2192D(\u2217)+D(\u2217)\u2212processes have been\nstudied by the Belle collaboration using 89 fb\u22121 of data\n(Uglov, 2004). Recoil mass spectra for events with re-\ncoil mass di\ufb00erence lying within 2 MeV/c2 of the nomi-\nnal value are shown in Fig. 21.4.1(a) and (b) for D\u2217+D\u2217\u2212\nand D+D\u2217\u2212\ufb01nal states. The recoil mass spectrum for the\ne+e\u2212\u2192D+D\u2212process is shown in Fig. 21.4.1(c). The\nspectra are \ufb01tted with a sum of signal and background\nfunctions. ISR photon emission produces a tail in Mrecoil,\nwhich must be taken into account. The approach used\nis to divide events in the Monte Carlo into those with\n(EISR > 10 MeV) and without (EISR < 10 MeV) an ISR\nphoton of signi\ufb01cant energy, and to determine separate\nsignal shapes for the two categories. The \ufb01nal measure-\nment is of the Born cross-section, which does not depend\non the ISR photon cuto\ufb00value, although experimental\nestimation of the ISR fraction does contribute to the sys-\ntematic uncertainty.\nThe signal is parameterized as a sum of a signal Gaus-\nsian and a Monte Carlo-based shape for events with sign-\n\ufb01cant ISR. The background is described by a threshold\nfunction \u03b1 \u00b7 (x \u2212mD\u2217\u2212\u2212m\u03c00)\u03b2, where \u03b1 and \u03b2 are \ufb01t pa-\nrameters. Both signal and background contributions are\nconvolved with the detector resolution. In the D\u2217+D\u2217\u2212\nand D+D\u2217\u2212\ufb01nal states, the D\u2217mesons can have either\nlongitudinal or transverse polarization. To distinguish these\ncases the angular distributions of the D\u2217decays are \ufb01tted\nwith the sum of the Monte Carlo shapes for all possible\npolarizations. The \ufb01t results and extracted cross sections\nare summarized in Table 21.4.1.\nSystematic uncertainties for D\u2217+D\u2217\u2212and D+D\u2217\u2212\ufb01-\nnal states, shown in Table 21.4.2, are dominated by the\nuncertainty in the tracking e\ufb03ciency, and the estimation\nof the fraction of events with a hard ISR photon. The main\nuncertainty in the e+e\u2212\u2192D+D\u2212cross-section is due to\nthe non-resonant e+e\u2212\u2192D+D\u03c0 process and cannot be\nreliably estimated.\nThe measured e+e\u2212\u2192D\u2217+\nT D\u2217\u2212\nL\nand D+D\u2217\u2212\nT\ncross\nsections are 3\u20134 times smaller than predicted in Grozin\nand Neubert (1997). The upper limits set for the e+e\u2212\u2192\nD\u2217+\nL D\u2217\u2212\nL\nand D\u2217+\nT D\u2217\u2212\nT\nprocesses are also lower than the\nHQET prediction; the limit on the e+e\u2212\u2192D+D\u2212pro-\ncess does not contradict the prediction. Unlike the abso-\nlute values, the cross-section ratios (on which the theoreti-\ncal uncertainties are much smaller) are in agreement with\nthe measured values. Calculations in the pQCD frame-\nwork (Liu, He, Zhang, and Chao, 2010) are in agreement\nwith the measured e+e\u2212\u2192D\u2217+D\u2217\u2212and D+D\u2217\u2212cross-\nsections, although the predicted D\u2217polarizations are far\nfrom the measured values. Another pQCD calculation tak-\ning into account the hard part of the meson wave function\nonly (Berezhnoy and Likhoded, 2005) represents the data\nwell, but being a rough estimation, requires a more accu-\nrate approach.\nTable 21.4.1. Fit results and Born cross-sections for e+e\u2212\u2192\nD(\u2217)+D(\u2217)\u2212from Uglov (2004). Upper limits are determined at\nthe 90% con\ufb01dence level. HQET predictions, which are approx-\nimate, are taken from Grozin and Neubert (1997); the D\u2217+\nL D\u2212\n\ufb01nal state is forbidden within this scheme. The pQCD predic-\ntion is from Liu, He, Zhang, and Chao (2010).\n\ufb01nal state\nsignal\ncross-section\nHQET\npQCD\nevents\n(pb)\n(pb)\n(pb)\nD\u2217+\nT D\u2217\u2212\nT\n5+15\n\u221213\n< 0.02\n0.05\nD\u2217+\nT D\u2217\u2212\nL\n708 \u00b1 36\n0.55 \u00b1 0.03\n3.0\n0.347\nD\u2217+\nL D\u2217\u2212\nL\n4+18\n\u221217\n< 0.02\n0.1\nD\u2217+\nT D\u2212\n433 \u00b1 24\n0.62 \u00b1 0.03\n3.0\n0.699\nD\u2217+\nL D\u2212\n\u22121.5 \u00b1 2.2\n< 0.006\n\u2013\nD+D\u2212\n\u221213 \u00b1 24\n< 0.04\n0.006\n0.098\nTable 21.4.2. Systematic uncertainty in the D(\u2217)+D\u2217\u2212cross-\nsections. From Uglov (2004).\nSource\nD\u2217+D\u2217\u2212\nD+D\u2217\u2212\nTracking e\ufb03ciency\n9%\n8%\nEstimation of ISR-events fraction\n5%\n5%\nB(D(\u2217))\n4%\n8%\nK/\u03c0 misidenti\ufb01cation\n2%\n2%\nBackground estimation\n+1\n\u22120%\n+1\n\u22120%\nForm-factor energy dependence\n0.8%\n0.8%\nTotal\n11%\n13%\n21.4.2 Measurement of the DD cross section via full\nreconstruction\nThe simplest way to select signal events in the e+e\u2212\u2192\nDD\u03b3ISR process (where D = D0 or D+) is a full recon-\nstruction of the \ufb01nal state, i.e. reconstruction of both D\nand D mesons, and the ISR photon. Although this tagged\nISR method provides almost complete background sup-\npression due to the speci\ufb01c event topology (the \ufb01nal state\ncontains an energetic photon of (4 \u22125) GeV and a pair\nof charmed mesons), the e\ufb03ciency is low as the photon\nescapes detection in \u223c90% of events. To increase the\ne\ufb03ciency the presence of the ISR photon is inferred us-\ning energy-momentum conservation. The \u03b3ISR signature\nin this case is a peak at zero in the spectrum of the square\nof the mass recoiling against the reconstructed DD sys-\ntem:\nM 2\nrecoil(DD) = (ECM \u2212EDD)2 \u2212p2\nDD.\n(21.4.3)\nHere EDD and pDD are the CM energy and momen-\ntum of the DD combination, respectively. Good momen-\ntum resolution of the reconstructed charmed mesons pro-\nvides a narrow peak in the recoil mass squared distribu-\ntion, and a low background level. The remaining back-\nground contribution from e+e\u2212\u2192DD(n)\u03c0\u03b3ISR pro-\ncesses can be strongly suppressed by excluding events\n\n692\n0\n200\n0\n100\nN/50 MeV/c2\nD*+D*-\na)\nD+D*-\nb)\nMrecoil(D(*)+)\nGeV/c2\nD+D-+D+D*-\nc)\n0\n200\n1.6\n1.8\n2\n2.2\n2.4\nFigure 21.4.1. Recoil mass spectra for: a) e+e\u2212\u2192D\u2217+D\u2217\u2212\nand b) e+e\u2212\u2192D+D\u2217\u2212processes with a \u2206Mrecoil require-\nment, respectively; c) e+e\u2212\u2192D+D\u2212. Points with error bars\nrepresent the data. The solid curve corresponds to the \ufb01t de-\nscribed in the text; the hatched histogram shows the back-\nground contribution estimated from the sidebands; the dotted\ncurve stands for the background fraction found by the \ufb01t. The\ndashed curve represents fraction of the events with signi\ufb01cant\nISR correction. From (Uglov, 2004).\ncontaining additional charged tracks not used in the\nD or D reconstruction. To suppress the tail of the\ne+e\u2212\u2192D(\u2217)D(\u2217)(n)\u03c00\u03b3ISR spectrum, a tight require-\nment on |M 2\nrecoil(DD)| is applied.\nBoth BABAR and Belle collaborations use this method.\nThe BABAR analysis is based on a 384 fb\u22121 data sam-\nple (Aubert, 2009n) in which DD candidates are recon-\nstructed in seven combinations of D0 and D+ decay modes.\nAside from \u03c00\u2019s from D0 decays, it is required that there\nbe no more than one other \u03c00 candidate in the event. The\ntracks of each D candidate are geometrically constrained\nto come from a common vertex. Subsequently, each DD\npair is re\ufb01tted to a common vertex with the constraint\nthat they originate from the e+e\u2212interaction region.\nThe distribution of M 2\nrecoil(DD), summed over all DD\nchannels, is shown in Fig. 21.4.2. The large bump to the\nright of the signal peak is due to e+e\u2212\u2192DD\u03c00\u03b3ISR\nevents. The inset shows the distribution of the DD CM\npolar angle \u03b8 for events with |M 2\nrecoil(DD)| < 1 GeV2/c4.\nThe sharp peak at cos(\u03b8DD) = \u22121 is typical for ISR pro-\nduction and agrees with Monte Carlo simulations.\nFigure 21.4.2. From BABAR\n(Aubert, 2009n). Recoil mass\nsquared, summed over all DD channels for e+e\u2212\u2192DD\u03b3ISR\nevent candidates. The shaded (yellow) histogram corresponds\nto combinatorial background estimated from the DD mass\nsidebands. The small inset shows the distribution of the center-\nof-mass polar angle of the DD system in the ISR region,\n|M 2\nrecoil(DD)| < 1 GeV2/c4.\nThe e+e\u2212\u2192DD cross sections (Fig. 21.4.3) are ex-\ntracted from the DD mass distributions after background\nsubtraction, using the method described in Section 21.2.2.\nThe combinatorial background contribution is determin-\ned using DD sideband regions and amounts to 17.5% for\nD0D0, and 7.1% for D+D\u2212, of the signal candidates with\n|M 2\nrecoil(DD)| < 1 GeV2/c4; this is the dominant source\nof background. E\ufb03ciencies and DD mass resolution are\nobtained from Monte Carlo simulation. The mass reso-\nlution determined from the di\ufb00erence between generated\nand reconstructed DD mass is found to be similar for all\nchannels, and increases from 1.5 MeV/c2 at threshold to\n5 MeV/c2 at MDD = 6.0 GeV/c2.\nThe Belle analysis of the e+e\u2212\u2192DD\u03b3ISR process\n(Pakhlova, 2008a), based on a 673.8 fb\u22121 data sample, is\nsimilar. Belle de\ufb01nes a signal region by the requirement\n|M 2\nrecoil(DD)| < 0.7 GeV2/c4. In cases when the ISR pho-\nton falls within the detector acceptance (| cos(\u03b8DD)| <\n0.9), its detection is required and the di\ufb00erence between\nthe CM energy and the invariant mass of the DD\u03b3ISR\ncombination must be smaller than 0.58 GeV/c2.\nThe resulting e+e\u2212\u2192D0D0 and D+D\u2212exclusive\ncross sections, averaged over each bin width, are shown\nin Fig. 21.4.3 with statistical uncertainties only. The total\nsystematic uncertainties are 10% (BABAR obtained 10.9%\n\n693\n0\n1\n2\n3\n4\n5\n6\n7\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n\u221as, GeV\n\u03c3(nb)\ne+e\u2013 \u2192 D0 D\n\u2013 0\n0\n0.5\n1\n3.8\n4\n4.2\n4.4\n0\n1\n2\n3\n4\n5\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n\u221as, GeV\n\u03c3(nb)\ne+e\u2013 \u2192 D+ D\u2013\n0\n0.5\n1\n3.8\n4\n4.2\n4.4\nFigure 21.4.3. Exclusive cross sections vs. \u221as for (upper plot)\ne+e\u2212\u2192D0D0 and (lower plot) e+e\u2212\u2192D+D\u2212, measured\nby Belle (solid squares) and BABAR (open circles). The region\nimmediately above the \u03c8(3770) is shown inset on an expanded\nscale. Prepared from the Pakhlova (2008a) and Aubert (2009n)\ndata.\nfor D0D0 and 8.1% for D+D\u2212) and comparable with the\nstatistical errors in the cross section around the \u03c8(3770)\npeak; elsewhere, statistical errors dominate.\nThe e+e\u2212\u2192DD exclusive cross sections observed by\nthe two collaborations are in a good agreement. Both con-\ntain a clear \u03c8(3770) signal and structures near the \u03c8(4040)\nand \u03c8(4415) masses. A signi\ufb01cant peak at 3.9 GeV/c2,\ncalled G(3900), is in qualitative agreement with predic-\ntions of the coupled-channel model (Eichten, Gottfried,\nKinoshita, Lane, and Yan, 1980).\nThe cross section ratio \u03c3(e+e\u2212\u2192D+D\u2212)/\u03c3(e+e\u2212\u2192\nD0D0) for MDD \u2248M\u03c8(3770) is measured by Belle (in\nthe bin (3.76 \u22123.78) GeV/c2) and by BABAR ((3.74 \u2212\n3.80) GeV/c2) to be 1.39\u00b10.31\u00b10.12 and 1.78\u00b10.33\u00b10.24\nrespectively. These values are in agreement with the world\naverage value of 1.28 \u00b1 0.14 (Beringer et al., 2012).\n21.4.3 Partial reconstruction of D(\u2217)+D\u2217\u2212\ufb01nal states\nIn the case of D(\u2217)+D\u2217\u2212\ufb01nal states,164 the full recon-\nstruction method discussed in the previous section turns\nout to be too ine\ufb03cient. The main reason for this is the\nvery low reconstruction e\ufb03ciency of the D\u2217\u00b1 when the\nISR photon is emitted at small polar angles, due to the\nlow reconstruction e\ufb03ciency for slow pions from D\u2217\u00b1 de-\ncays. If the photon is emitted along the beam axis and the\nD(\u2217)+D\u2217\u2212system is close to threshold, the D(\u2217)+ and D\u2217\u2212\nmeson transverse momenta are low. Because of the small\nenergy release in D\u2217\u2212\u2192D\u03c0\u2212\nslow decay, the \u03c0\u2212\nslow trans-\nverse momentum is also very low, and such pions do not\nreach the instrumented parts of the detector. Therefore,\nreconstructable D\u2217\u00b1 mesons correspond to the \u03b3ISR emit-\nted at large angles, i.e. both the \u03b3ISR and the D(\u2217)+D\u2217\u2212\npair possess large transverse momenta. The reconstruction\ne\ufb03ciency of such isolated energetic photons is high, and\nit is worth requiring the \u03b3ISR to be detected.\nThe signal e\ufb03ciency can be increased further by se-\nlecting events without explicitly reconstructing one of the\ncharm mesons. In particular, full reconstruction of only\nthe D(\u2217)+, together with the \u03b3ISR, allows the D\u2217\u2212meson\nto be identi\ufb01ed using the peak around the D\u2217\u2212mass in\nthe spectrum of masses recoiling against the D(\u2217)+\u03b3ISR\nsystem:\nMrecoil(D(\u2217)+\u03b3ISR) =\nq\n(ECM\u2212ED(\u2217)+\u03b3ISR)2\u2212p2\nD(\u2217)+\u03b3ISR.\n(21.4.4)\nHere ED(\u2217)+\u03b3ISR and pD(\u2217)+\u03b3ISR are the CM energy and\nmomentum, respectively, of the D(\u2217)+\u03b3ISR combination.\nThis peak is expected to be wide and asymmetric due to\nthe \u03b3ISR energy resolution and higher-order corrections\nto ISR cross section. The resolution of this peak (esti-\nmated to be \u223c300 MeV/c2) is not su\ufb03cient to separate\nthe DD\u2217, D\u2217D\u2217, and D(\u2217)D\u2217\u03c0 \ufb01nal states. To disentangle\nthese various contributions and to suppress combinatorial\nbackgrounds, one can use the slow pion from the unrecon-\nstructed D\u2217\u2212. The di\ufb00erence between the masses recoiling\nagainst D(\u2217)+\u03b3ISR and D(\u2217)+\u03c0\u2212\nslow\u03b3ISR (recoil mass di\ufb00er-\nence),\n\u2206Mrecoil = Mrecoil(D(\u2217)+\u03b3ISR)\u2212Mrecoil(D(\u2217)+\u03c0\u2212\nslow\u03b3ISR) ,\n(21.4.5)\nhas a narrow distribution for signal events (\u03c3\u223c1.4 MeV/c2)\naround mD\u2217\u2212\u2212mD0, since the uncertainty in the \u03b3ISR mo-\nmentum partially cancels out.\nThe e\ufb03ciency gain using the described partial recon-\nstruction method over the full reconstruction method is\n\u223c1/\u03f5D0 and \u223c2/\u03f5D0, for D+D\u2217\u2212and D\u2217+D\u2217\u2212\ufb01nal\nstates respectively, where \u03f5D0 is the D0 reconstruction ef-\n\ufb01ciency.\nIn the case of full reconstruction, exclusive cross sec-\ntions are obtained from D(\u2217)+D\u2217\u2212mass spectra. In the\npartial reconstruction case D\u2217\u2212is not reconstructed and\nthe D(\u2217)+D\u2217\u2212mass can not be calculated directly. How-\never, it is equivalent to Mrecoil(\u03b3ISR), the mass recoiling\n164 The notation represents the sum of D+D\u2217\u2212and D\u2217+D\u2217\u2212\n\ufb01nal states.\n\n694\nagainst the ISR photon (ignoring higher-order QED pro-\ncesses). The problem of poor photon energy resolution\n(and, thus poor Mrecoil(\u03b3ISR) resolution) is solved by ap-\nplying a \ufb01t constraining Mrecoil(D(\u2217)+\u03b3ISR) to the D\u2217\u2212\nmass. This re\ufb01t procedure corrects the \u03b3ISR momentum\nand as a result, the Mrecoil(\u03b3ISR) = M(D(\u2217)+D\u2217\u2212) resolu-\ntion is improved by a factor \u223c10: it varies from \u223c6 MeV\nat D(\u2217)+D\u2217\u2212threshold to \u223c12 MeV at M(D(\u2217)+D\u2217\u2212) =\n5 GeV/c2. In addition the resolution of the recoil mass dif-\nference after the re\ufb01t procedure (\u2206M \ufb01t\nrecoil) is improved by\na factor \u223c2.\nThis method, developed by Belle, is applied to the\ne+e\u2212\u2192D(\u2217)+D\u2217\u2212cross section measurement using a\ndata sample of 673.8 fb\u22121 (Abe, 2007d). The signal region\nis de\ufb01ned by the requirement that Mrecoil(D\u2217+\u03b3ISR) lie\nwithin \u00b10.2 GeV/c2 of the D\u2217\u2212mass and that \u2206M \ufb01t\nrecoil be\nwithin \u00b12 MeV/c2 of mD\u2217\u2212\u2212mD0. The e+e\u2212\u2192D(\u2217)+D\u2217\u2212\ncross sections are extracted from the Mrecoil(\u03b3ISR) dis-\ntributions after background subtraction. All background\ncontributions are estimated from the data and the combi-\nnatorial background is found to be the dominant source.\nThe resulting exclusive e+e\u2212\u2192D(\u2217)+D\u2217\u2212cross sec-\ntions are shown in Figs 21.4.4 and 21.4.5 with statistical\nuncertainties only. The total systematic uncertainties are\n11% for D+D\u2217\u2212and 10% for D\u2217+D\u2217\u2212, comparable to the\nstatistical errors in the cross section.\n\u221as , GeV\n\u03c3(nb)\n0\n1\n2\n3\n4\n5\n6\n7\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\nFigure 21.4.4. The exclusive cross sections for e+e\u2212\u2192\nD+D\u2217\u2212measured by Belle (Abe, 2007d; solid squares) and\nBABAR (Aubert, 2009n; open triangles); e+e\u2212\u2192D0D\u22170 mea-\nsured by BABAR (open circles).\nThe results of the BABAR measurements (Aubert, 2009n)\nbased on 384 fb\u22121 of data are shown in the same plots.\nBecause the full reconstruction method was used, the sta-\ntistical uncertainties in these measurements are signi\ufb01-\ncantly larger than those of Belle. The cross sections for\nD0D\u22170, D+D\u2217\u2212, and D\u2217D\u2217(the latter being the sum of\nthe neutral and charged modes, i.e. D\u22170D\u22170 and D\u2217+D\u2217\u2212)\nare presented in Fig. 21.4.4 and Fig. 21.4.5 respectively.\nThe systematic uncertainties in the cross sections are es-\n\u221as, GeV\n\u03c3(nb)\n0\n2\n4\n6\n8\n10\n12\n4\n4.2\n4.4\n4.6\n4.8\n5\nFigure 21.4.5. The exclusive cross sections for e+e\u2212\u2192\nD\u2217+D\u2217\u2212measured by Belle (Abe, 2007d; solid squares) and\ne+e\u2212\u2192D\u2217D\u2217measured by BABAR (Aubert, 2009n; open cir-\ncles).\ntimated to be 10.9% for D0D\u22170, 9.3% for D+D\u2217\u2212, and\n12.4% for D\u2217D\u2217.\nBelle and BABAR measurements are in good agreement,\nand compatible with the DD\u2217and D\u2217D\u2217exclusive cross\nsections measured by CLEO-c (Cronin-Hennessy et al.,\n2009); the CLEO-c measurements are more precise; they\ninclude, however, only the narrow energy range from 3.97\nto 4.26 GeV. Aside from a prominent excess near the\n\u03c8(4040) resonance, the e+e\u2212\u2192D+D\u2217\u2212cross section is\nrelatively featureless. Integrating the cross sections from\nthreshold to 6 GeV/c2, BABAR obtained\n\u03c3(D+D\u2217\u2212)\n\u03c3(D0D\u22170) = 0.95 \u00b1 0.09 \u00b1 0.10,\n(21.4.6)\nconsistent with unity. The shape of the e+e\u2212\u2192D\u2217+D\u2217\u2212\ncross section is complicated, with several local maxima\nand minima. Reliable interpretation will require more data.\n21.4.4 e+e\u2212\u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\nBoth BABAR and Belle use the full reconstruction tech-\nnique to measure e+e\u2212\u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\ncross sections. Par-\ntial reconstruction of D\u2217+\ns\ndecaying to D+\ns \u03b3 is impractical\nbecause of a huge combinatorial background.\nBABAR results based on a 525 fb\u22121 data sample (del\nAmo Sanchez, 2010d) are presented in Fig. 21.4.6. For\neach candidate event BABAR reconstructs a D+\ns D\u2212\ns pair.\nWhile one of the D+\ns is required to decay to K+K\u2212\u03c0+, the\nsecond D\u2212\ns meson is reconstructed in three decay modes:\nK+K\u2212\u03c0\u2212, K+K\u2212\u03c0\u2212\u03c00, and K0\nSK\u2212. Belle measurements\nof the exclusive e+e\u2212\u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\ncross sections (Pakh-\nlova, 2011) based on a 967 fb\u22121 data sample are shown in\nFig. 21.4.7. To increase the sample size Belle reconstructs\nboth D+\ns\n(+ c.c.) mesons in six decay modes: K0\nSK+,\nK\u2212K+\u03c0+, K\u2212K+\u03c0+\u03c00, K0\nSK\u2212\u03c0+\u03c0+, \u03b7\u03c0+ and \u03b7\u2032\u03c0+.\nThe presented cross sections are averaged over the bin\n\n695\n0\n0.2\n0.4\n0.6\n3.8\n4\n4.2 4.4 4.6 4.8\n5\n0\n0.5\n1\n4\n4.2\n4.4\n4.6\n4.8\n5\n\u03c3(nb)\nM(Ds+Ds\u2013), GeV/c2\na)\n\u03c3(nb)\nM(Ds+Ds*\u2013), GeV/c2\nb)\n\u03c3(nb)\nM(Ds*+Ds*\u2013), GeV/c2\nc)\n0\n0.2\n0.4\n0.6\n0.8\n4.2\n4.4\n4.6\n4.8\n5\nFigure 21.4.7. Exclusive cross sections for (a) e+e\u2212\u2192D+\ns D\u2212\ns , (b) e+e\u2212\u2192D+\ns D\u2217\u2212\ns\n(and charge conjugate), and (c) e+e\u2212\u2192\nD\u2217+\ns D\u2217\u2212\ns , from Belle data (Pakhlova, 2011). Error bars show statistical uncertainties only. The dotted lines show the masses of\nthe \u03c8(4040), \u03c8(4160) and \u03c8(4415) states.\nFigure 21.4.6. Exclusive cross sections for (a) e+e\u2212\n\u2192\nD+\ns D\u2212\ns , (b) e+e\u2212\u2192D+\ns D\u2217\u2212\ns\n(and charge conjugate), and (c)\ne+e\u2212\u2192D\u2217+\ns D\u2217\u2212\ns , from BABAR data (del Amo Sanchez, 2010d).\nThe error bars correspond to statistical errors only.\nwidth; error bars show statistical uncertainties only. The\nsystematic uncertainties are evaluated by BABAR (Belle)\nto be 23%(11%) for D+\ns D\u2212\ns , 13%(17%) for D+\ns D\u2217\u2212\ns\nand\n13%(31%) for D\u2217+\ns D\u2217\u2212\ns .\nThe identi\ufb01cation of relatively narrow \u03c8 states in\nBABAR spectra is complicated by the large bin size of\n100 MeV. Nevertheless BABAR results are consistent with\nthe more precise Belle measurements (in 40 MeV bins).\nA clear peak at threshold, around the \u03c8(4040) mass, is\nseen in the e+e\u2212\u2192D+\ns D\u2212\ns cross section. In the e+e\u2212\u2192\nD+\ns D\u2217\u2212\ns\ncross section two peaks are evident, around the\n\u03c8(4160) and the \u03c8(4415) masses. The e+e\u2212\u2192D\u2217+\ns D\u2217\u2212\ns\ndata sample is small, and there is no clear structure in\nthe cross section. Both the e+e\u2212\u2192D+\ns D\u2217\u2212\ns\ncross section\nand the sum of the exclusive e+e\u2212\u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\ncross\nsections exhibit a dip near the Y (4260) mass (see Section\n18.3.5), similar to what is seen in e+e\u2212\u2192D\u2217+D\u2217\u2212and\nin the total cross section for charm production.\n21.4.5 Three-body charm \ufb01nal states\n M(D0D-\u03c0+), GeV/c2\n\u03c3(nb)\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n4\n4.2\n4.4\n4.6\n4.8\n5\nFigure 21.4.8. The exclusive cross section for e+e\u2212\n\u2192\nD0D\u2212\u03c0+ measured by Belle (Pakhlova, 2008c). The dotted\nline corresponds to the mass of the \u03c8(4415).\nThe \ufb01rst measurements of three-body open charm \ufb01nal\nstates in e+e\u2212annihilation have been performed using the\n\n696\nfull reconstruction method by Belle. The cross section for\ne+e\u2212\u2192D0D\u2212\u03c0+ measured using a 673 fb\u22121 data sam-\nple (Pakhlova, 2008c) is shown in Fig. 21.4.8. A prominent\n\u03c8(4415) peak is observed. From a study of the resonant\nstructure in \u03c8(4415) decays (discussed in Section 18.2.2.2)\nBelle concludes that the \u03c8(4415)\n\u2192\nD0D\u2212\u03c0+ pro-\ncess is dominated by \u03c8(4415) \u2192DD\u2217\n2(2460). It was\nfound that B(\u03c8(4415) \u2192D0D\u2212\u03c0+\nnon\u2212res)/B(\u03c8(4415 \u2192\nDD\u2217\n2(2460)\n\u2192\nD0D\u2212\u03c0+)\n<\n0.22 at the 90% C.L.\nThe peak cross section for the e+e\u2212\u2192\u03c8(4415) \u2192\nDD\u2217\n2(2460) process at ECM = m\u03c8(4415)c2 is calculated\nto be \u03c3(e+e\u2212\u2192\u03c8(4415)) \u00d7 B(\u03c8(4415) \u2192DD\u2217\n2(2460)) \u00d7\nB(D\u2217\n2(2460) \u2192D\u03c0+) = (0.74 \u00b1 0.17 \u00b1 0.08) nb.\nThe e+e\u2212\u2192D0D\u2217\u2212\u03c0+ exclusive cross section, based\non a 695 fb\u22121 data sample (Pakhlova, 2009), is shown\nin Fig. 21.4.9. The main motivation of this study is\nthe search for Y (4260) \u2192D0D\u2217\u2212\u03c0+ decays discussed\nin Section 18.3.5. An estimate of the branching fraction\nfor \u03c8(4415) \u2192D0D\u2217\u2212\u03c0+ decay can be found in Sec-\ntion 18.2.2.2.\n\u03c3(nb)\nGeV/c2\nM(D0D*-\u03c0+)\n0\n0.5\n1\n4\n4.2\n4.4\n4.6\n4.8\n5\n5.2\nFigure 21.4.9. The exclusive cross section for e+e\u2212\n\u2192\nD0D\u2217\u2212\u03c0+ averaged over the bin width with statistical un-\ncertainties only from Belle data (Pakhlova, 2009). The total\nsystematic uncertainty is 10%. The \ufb01t function corresponds to\nthe 90% C.L. upper limit on \u03c8(4415) taking into account sys-\ntematic uncertainties. The solid line represents the sum of the\nsignal and threshold contributions. The threshold function is\nshown by the dashed line.\n21.4.6 Charm baryon production in e+e\u2212annihilation\nThe \ufb01rst measurement of the e+e\u2212\u2192\u039b+\nc \u039b\u2212\nc process near\nthreshold has been performed by Belle in ISR events, us-\ning 695 fb\u22121 of data (Pakhlova, 2008b), with the partial\nreconstruction technique. Full reconstruction of both the\n\u039b+\nc and \u039b\u2212\nc baryons su\ufb00ers from the low \u039bc reconstruc-\ntion e\ufb03ciency, and the small branching fractions for de-\ncays to accessible \ufb01nal states; Belle requires reconstruction\nof only one of the \u039bc baryons (using pK0\nS, pK\u03c0 and \u039b\u03c0\n\ufb01nal states) and the ISR photon. The exclusive e+e\u2212\u2192\n\u039b+\nc \u039b\u2212\nc cross section is determined from the recoil mass\nMrecoil(\u03b3ISR). A re\ufb01t constraining Mrecoil(\u039b+\nc \u03b3ISR) to the\nnominal \u039b\u2212\nc mass improves the Mrecoil(\u03b3ISR) resolution:\nthe \ufb01nal resolution varies from \u223c3 MeV/c2 just above\nthreshold to \u223c8 MeV/c2 at M\u039b+\nc \u039b\u2212\nc \u223c5.4 GeV/c2. Com-\nbinatorial background is suppressed by a factor \u223c10 by\nrequiring the presence of at least one p in the event from\nthe decay of the unreconstructed \u039b\u2212\nc ; this requirement re-\nduces the signal e\ufb03ciency by \u223c40%.\nThe resulting cross section is shown in Fig. 21.4.10.\nA signi\ufb01cant enhancement, called X(4630) by Belle, is\nseen at threshold, with a peak cross section \u03c3(e+e\u2212\u2192\nX(4630)) \u00d7 B(X(4630) \u2192\u039b+\nc \u039b\u2212\nc ) = (0.47+0.11\n\u22120.10\n+0.05\n\u22120.08 \u00b1\n0.19) nb. Belle obtains \u0393ee/\u0393tot\u00d7B(X(4630) \u2192\u039b+\nc \u039b\u2212\nc ) =\n(0.68+0.16\n\u22120.15\n+0.07\n\u22120.11 \u00b10.28)\u00d710\u22126. The last error is due to the\nuncertainties of \u039bc branching fractions.\n\u03c3(nb)\nGeV/c2\nM(\u039b+\nc \u039b\u2013\nc)\n0\n0.2\n0.4\n0.6\n4.5\n4.6\n4.7\n4.8\n4.9\n5\n5.1\n5.2\n5.3\n5.4\nFigure 21.4.10. The exclusive cross section for e+e\u2212\u2192\n\u039b+\nc \u039b\u2212\nc measured by Belle (Pakhlova, 2008b).\nThe nature of the observed enhancement remains un-\nclear. More details on its parameters and corresponding\ndiscussion can be found in Section 18.3.5.\n21.4.7 Sum of exclusive vs inclusive cross section\nIn conclusion, using the ISR method allows the measure-\nment of nine cross sections for e+e\u2212annihilation to open\ncharm \ufb01nal states over a wide energy range, beginning at\nthreshold. For the \ufb01rst time the inclusive cross section to\ncharm hadrons is decomposed into the sum of the exclu-\nsive components e+e\u2212\u2192DD, DD\u2217, D\u2217D\u2217, DD\u03c0, DD\u2217\u03c0,\nD+\ns D\u2212\ns , D+\ns D\u2217\u2212\ns , D\u2217+\ns D\u2217\u2212\ns , and \u039b+\nc \u039b\u2212\nc . This sum, shown\nin Fig. 21.4.11, almost saturates the inclusive cross sec-\ntion; the DD\u2217and D\u2217D\u2217\ufb01nal states dominate.\n21.5 Search for exotic charmonium\nInitial state radiation events provide an ideal environment\nto study known vector states as well as search for addi-\ntional such states. Searches for new vector mesons have\n\n697\n\u221as, GeV\n uds\n R \u2013 R\n0\n1\n2\n3\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\nFigure 21.4.11. Inclusive measurements of R \u2212Ruds, where\nR = \u03c3(e+e\u2212\u2192hadrons)/\u03c3(e+e\u2212\u2192\u00b5+\u00b5\u2212) and Ruds =\n2.121 \u00b1 0.023 \u00b1 0.083 by BES II (Ablikim et al., 2007; open\ncircles), compared to the sum of exclusive cross sections (solid\nsquares) measured by Belle.\ncommonly proceeded by looking for their decay to conven-\ntional charmonium states plus additional light hadrons.\nThe study of the \u03c0+\u03c0\u2212J/\u03c8 and \u03c0+\u03c0\u2212\u03c8(2S) \ufb01nal states is\npresented in Sections 21.5.1 and 21.5.2 respectively. Pos-\nsible vector decays to open charm \ufb01nal states are treated\nin Section 21.4 above. A general discussion of the new,\nand possibly exotic vector states is presented elsewhere\n(Section 18.3.5).\n21.5.1 Y family states in ISR \u03c0+\u03c0\u2212J/\u03c8\nAn important exotic charmonium candidate, the Y (4260),\nhas been observed in the \u03c0+\u03c0\u2212J/\u03c8 \ufb01nal state. The discov-\nery and subsequent studies are reported in Sections 21.5.1.1\nand 21.5.1.2 respectively. The claimed broad structure\nY (4008) is discussed in the latter section.\n21.5.1.1 The Y (4260) discovery\nThe discovery by Belle of the surprisingly narrow X(3872)\nresonance from the study of B \u2192J/\u03c8\u03c0+\u03c0\u2212K decays\n(Choi, 2003), discussed in Section 18.3.2, renewed experi-\nmental interest in charmonium spectroscopy. In order to\nunderstand the X(3872) when its quantum numbers were\nhardly known in 2004, BABAR searched for X(3872) \u2192\n\u03c0+\u03c0\u2212J/\u03c8 in the ISR process e+e\u2212\u2192\u03b3ISR\u03c0+\u03c0\u2212J/\u03c8, where\nJ/\u03c8 decays to \u2113+\u2113\u2212, using a data sample corresponding to\n232 fb\u22121 (Aubert, 2005y). The analysis was performed re-\nquiring exclusive reconstruction of the hadronic \ufb01nal state,\nbut not explicit detection of the ISR photon. The large and\nclean ISR \u03c8(2S) \u2192\u03c0+\u03c0\u2212J/\u03c8 sample provides a good\ncontrol sample for validation and selection criteria opti-\nmization. In a subsample of 123 fb\u22121 of data, as shown in\nFig. 21.5.1, no evidence for the X(3872) was found, but\nan enhancement was seen around 4.3 GeV/c2.\n1\n10\n2\n10\n)\n-l\n+l\n-\u03c0\n+\n\u03c0\nm(\n3.4\n3.5\n3.6\n3.7\n3.8\n3.9\n4\n)\n\u03c8\n)-m(J/\n-l\n+\nm(l\n-0.2\n-0.1\n0\n0.1\n0.2\n(a)\n0\n1\n2\n3\n4\n5\n6\n)\n-l\n+l\n-\u03c0\n+\n\u03c0\nm(\n4\n4.5\n5\n5.5\n6\n6.5\n7\n)\n\u03c8\n)-m(J/\n-l\n+\nm(l\n-0.2\n-0.1\n0\n0.1\n0.2\n(b)\nFigure\n21.5.1.\nThe scatter plot of m(\u2113+\u2113\u2212) \u2212m(J/\u03c8)\nvs. m(\u03c0+\u03c0\u2212J/\u03c8) for ISR produced \u03c0+\u03c0\u2212J/\u03c8\nevents col-\nlected by BABAR in 123 fb\u22121. (a) low m(\u03c0+\u03c0\u2212J/\u03c8) range\n[3.4, 4.0] GeV/c2 (log scale): A clean \u03c8(2S) signal is observed\nwhile no evidence of a X(3872) signal is seen. (b) high\nm(\u03c0+\u03c0\u2212J/\u03c8) range [3.8, 7.0] GeV/c2 (linear scale): An en-\nhancement around 4.3 GeV/c2 is found. BABAR internal, from\n(Aubert, 2005y) analysis.\nIn order to avoid any possible bias and to \ufb01rmly es-\ntablish this observation, the BABAR analysis blinds the en-\nhancement region [4.2, 4.4] GeV/c2, and optimizes the se-\nlection criteria by maximizing the quantity N/(3/2+\n\u221a\nB)\n(Punzi, 2003b), where 3/2 corresponds to the search for a\n3\u03c3 signal, N is the total number of \u03b3ISR\u03c8(2S), \u03c8(2S) \u2192\n\u03c0+\u03c0\u2212J/\u03c8 candidates in the 20 MeV/c2 \u03c0+\u03c0\u2212J/\u03c8 mass\nrange that brackets the \u03c8(2S) nominal mass, and B is the\nnumber of (background) events in the \u03c0+\u03c0\u2212J/\u03c8 mass re-\ngions [3.8, 4.2] GeV/c2 and [4.4, 4.8] GeV/c2, scaled to the\nwidth of the excluded region. The selection criteria are op-\ntimized taking advantage of the features of ISR emission,\nthat is, a recoil mass close to zero, and a small transverse\ncomponent of the visible momentum in the e+e\u2212CM, in-\ncluding the ISR photon when it is reconstructed. Exactly\nfour tracks consistent with production at the e+e\u2212inter-\naction point are allowed: two oppositely charged tracks\nidenti\ufb01ed as pions, and a pair of identi\ufb01ed leptons (ei-\nther e+e\u2212or \u00b5+\u00b5\u2212) whose reconstructed invariant mass\nis within an optimized interval around the J/\u03c8 peak. Ad-\nditional cuts on kinematic variables of the hadronic system\nare applied to further reject background sources.\nIn order to improve the mass resolution, the four tracks\nare re\ufb01tted with a constraint to a common vertex, and the\nlepton pair kinematically constrained to the J/\u03c8 mass.\nThe resulting \u03c0+\u03c0\u2212J/\u03c8 mass-resolution function is well-\ndescribed by a Breit-Wigner distribution with a full width\nat half maximum increasing from 4.2 MeV/c2 at the \u03c8(2S)\n\n698\n)\n2\n) (GeV/c\n\u03c8\nJ/\n-\u03c0\n+\n\u03c0\nm(\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n2\nEvents / 20 MeV/c\n0\n10\n20\n30\n40\n)\n2\n) (GeV/c\n\u03c8\nJ/\n-\u03c0\n+\n\u03c0\nm(\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n2\nEvents / 20 MeV/c\n0\n10\n20\n30\n40\n)\n2\n) (GeV/c\n\u03c8\nJ/\n-\u03c0\n+\n\u03c0\nm(\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n2\nEvents / 20 MeV/c\n0\n10\n20\n30\n40\n)\n2\n) (GeV/c\n\u03c8\nJ/\n-\u03c0\n+\n\u03c0\nm(\n3.8\n4\n4.2\n4.4\n4.6\n4.8\n5\n2\nEvents / 20 MeV/c\n0\n10\n20\n30\n40\n sidebands\n\u03c8\nJ/\n3.6 3.8\n4\n4.2 4.4 4.6 4.8\n5\n1\n10\n2\n10\n3\n10\n4\n10\nFigure 21.5.2. The \u03c0+\u03c0\u2212J/\u03c8 invariant mass spectrum in the\nrange 3.8\u22125.0 GeV/c2 and (inset) over a wider range that in-\ncludes the \u03c8(2S), obtained from BABAR with a data sample\nof 232 fb\u22121 (Aubert, 2005y). The points with error bars repre-\nsent the selected data and the shaded histogram represents the\nscaled data from neighboring J/\u03c8 sidebands. A \ufb01t to the mass\nspectrum with a single Breit-Wigner and a polynomial func-\ntion, shown as the solid line, clearly identi\ufb01es the new Y (4260)\nresonance. The dashed curve represents the background poly-\nnomial component.\nto 5.3 MeV/c2 at 4.3 GeV/c2. The \u03c0+\u03c0\u2212J/\u03c8 invariant mass\nspectrum for candidates passing all criteria is shown in\nFig. 21.5.2 as points with error bars. A signal of 11802 \u00b1\n110 \u03c8(2S) events is observed, consistent with the expec-\ntation. An enhancement near 4.26 GeV/c2, now known as\nthe Y (4260), is clearly observed; no other structures are\nevident at the masses of the known JP C = 1\u2212\u2212charmo-\nnium states (i.e. the \u03c8(4040), \u03c8(4160), and \u03c8(4415)), or\nat the X(3872).\nAn unbinned maximum likelihood \ufb01t to the \u03c0+\u03c0\u2212J/\u03c8\nmass spectrum in the range [3.8, 5.0] GeV/c2 is performed\nassuming only one broad resonance is present (Fig. 21.5.2).\nThe \ufb01tting function consists of a relativistic Breit-Wigner\nfunction describing the peak, and a second-order poly-\nnomial background, convolved with a Cauchy resolution\nfunction. The \ufb01t \ufb01nds (125\u00b123) events in the peak, with a\nmass of (4259\u00b18) MeV/c2 and a width of (88\u00b123) MeV/c2.\nthe signi\ufb01cance of the Y (4260) signal is above 8 \u03c3.\nThe ISR photon is reconstructed in (24 \u00b1 8)% of the\nY (4260) events, within the uncertainty the same as 25%\nobserved for ISR \u03c8(2S) events. Kinematic distributions for\na sample of background subtracted data are compared to\nanalogous quantities obtained for simulated ISR events,\nand found in good agreement, con\ufb01rming that the ISR-\nproduction hypothesis \u2013 essential in order to assign the\nJP C = 1\u2212\u2212quantum numbers for the new resonant state\n\u2013 is correct.\n21.5.1.2 Subsequent Y (4260) analyses\nAfter the discovery of the Y (4260), CLEO (Coan et al.,\n2006) performed an energy scan around \u221as = 4.26 GeV,\n0\n20\n40\n60\n80\n4\n4.5\n5\n5.5\nM(\u03c0+\u03c0-J/\u03c8) (GeV/c2)\nEntries/20 MeV/c2\nSolution I\nSolution II\nFigure 21.5.3. (upper) The \u03c0+\u03c0\u2212J/\u03c8 mass spectrum mea-\nsured by Belle (Yuan, 2007). Points with errors show selected\nevents in the J/\u03c8 signal region, while the histogram shows the\nscaled J/\u03c8 sideband distribution. The curves show the best \ufb01t\n(solid line) and the contribution from each component for the\ntwo solutions, as described in the text. (lower) The \u03c0+\u03c0\u2212J/\u03c8\nmass spectrum measured by BABAR in a 454 fb\u22121 data sample\n(Lees, 2012ab). The solid curve shows the result of a simultane-\nous \ufb01t to the data (points with errors) and to the background\ncontrol sample obtained from the J/\u03c8 sidebands (shaded his-\ntogram).\nand were able to con\ufb01rm the process Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8\nand observed also Y (4260) \u2192\u03c00\u03c00J/\u03c8. The measured ra-\ntio, B(Y (4260) \u2192\u03c00\u03c00J/\u03c8)/ B(Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8) \u2248\n0.5, implies that the Y (4260) has isospin zero. They also\nfound the \ufb01rst evidence for Y (4260) \u2192K+K\u2212J/\u03c8, and\nset upper limits on many other decay modes. These re-\nsults are based on measurements at discrete energies, and\ndo not resolve the Y (4260) lineshape; it is assumed that\nthe Y (4260) saturates the \u03c0+\u03c0\u2212J/\u03c8 and related cross-\nsections at the peak.\nThe observation of the Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8 decay in\nISR-untagged studies has been con\ufb01rmed by CLEO (He\net al., 2006), by analysing a data sample of about 13.3\nfb\u22121, and with much more data by Belle (Yuan, 2007)\nand BABAR (Lees, 2012ab) . The selection criteria in the\nBelle and BABAR analyses are similar to those in the orig-\n\n699\ninal BABAR measurement with some exceptions.165 The\nresulting mass spectra shown in Fig. 21.5.3 present a clear\npeak at \u223c4.26 GeV/c2, but have di\ufb00erences elsewhere in\nthe analyzed energy region. The analysts of the two Col-\nlaborations have adopted di\ufb00erent \ufb01t models to describe\nthe data.\nTable 21.5.1. Results of the best \ufb01t to the \u03c0+\u03c0\u2212J/\u03c8 mass\nspectrum obtained by the Belle experiment (Yuan, 2007). M,\n\u0393tot, and B \u00d7 \u0393e+e\u2212are respectively the mass, total width,\nand product of the branching fraction to \u03c0+\u03c0\u2212J/\u03c8 and e+e\u2212\npartial width of the two interfering resonances R1 and R2,\nwhile \u03c6 is their relative phase. The results for both destructive\nand constructive interference solutions are reported.\nParameters\nSolution I\nSolution II\nR1 : M\n(MeV/c2)\n4008 \u00b1 40+114\n\u221228\n\u0393tot\n(MeV)\n226 \u00b1 44 \u00b1 87\nB \u00d7 \u0393e+e\u2212\n(eV)\n5.0 \u00b1 1.4+6.1\n\u22120.9\n12.4 \u00b1 2.4+14.8\n\u22121.1\nR2 : M\n(MeV/c2)\n4247 \u00b1 12+17\n\u221232\n\u0393tot\n(MeV)\n108 \u00b1 19 \u00b1 10\nB \u00d7 \u0393e+e\u2212\n(eV)\n6.0 \u00b1 1.2+4.7\n\u22120.5\n20.6 \u00b1 2.3+9.1\n\u22121.7\n\u03c6\n(\u25e6)\n+12 \u00b1 29+7\n\u221298\n\u2212111 \u00b1 7+28\n\u221231\nIn particular, an accumulation of events at a mass\nof about 4.01 GeV/c2 is observed in about 548 fb\u22121 of\ndata analyzed by Belle. An unbinned maximum likelihood\n\ufb01t is performed to the mass spectrum corrected for the\nmass-dependent e\ufb03ciency and normalized to the e\ufb00ective\nISR luminosity, for masses above 3.8 GeV/c2, as shown\nin Fig. 21.5.3 (top). The \ufb01t model consists of a coherent\nsum of two Breit-Wigner resonance functions (see Section\n13.2.1), and assumes that there is no continuum produc-\ntion of e+e\u2212\u2192\u03c0+\u03c0\u2212J/\u03c8. The background is estimated\nfrom J/\u03c8 sidebands and \ufb01xed in the \ufb01t, while contribu-\ntions from the tail of the \u03c8(2S) and \u03c8(3770) are estimated\nfrom the world average values of their parameters, added\nincoherently, and \ufb01xed. Two solutions with equally good\n\ufb01t quality are found, corresponding to constructive and\ndestructive interference between the two resonances. They\npresent equal masses and widths for the two resonances,\nbut di\ufb00erent partial widths and relative phase. The qual-\nity of the \ufb01t determined from the binned distribution is\n\u03c72/ndof = 81/78.\nThe results are summarized in Table 21.5.1. The sig-\nni\ufb01cance of the resonance at lower mass is larger than 5\u03c3.\nAlthough its mass is close to that of the \u03c8(4040), the \ufb01tted\nwidth is larger than the world average value (80\u00b110 MeV)\nof the latter. The \ufb01t using two interfering resonances yields\na much better description of the observed distribution\nthan a \ufb01t with a single resonance. Using the same func-\ntional form of the \ufb01tted function as in Aubert (2005y) the\n165 For example, Belle did not use the J/\u03c8 mass constraint\nand hence the sideband events can be used to estimate the\nbackground.\nparameters of the state at higher mass are consistent with\nthose reported by BABAR (see Table 21.5.2).\nThe BABAR update on the study of the ISR-produced\n\u03c0+\u03c0\u2212J/\u03c8 \ufb01nal state is based on a data sample cor-\nresponding to 454 fb\u22121 (Lees, 2012ab). An unbinned,\nextended-maximum likelihood \ufb01t is performed in the re-\ngion [3.74, 5.5] GeV/c2 to the \u03c0+\u03c0\u2212J/\u03c8 mass distribution\nfrom the J/\u03c8 signal region, shown in Fig. 21.5.3(bottom),\nand simultaneously to the background distribution from\nthe J/\u03c8 sidebands. The shape of the background mass\ndistribution is described by a third order polynomial func-\ntion. The signal function consists of a coherent sum of a\nBreit-Wigner function for the Y (4260), and an exponen-\ntial function, which provides an empirical description of\nthe \u03c8(2S) tail and possible continuum production of the\n\u03c0+\u03c0\u2212J/\u03c8 \ufb01nal state. Also in this case, the signal function\naccounts for the mass-dependency of the reconstruction\ne\ufb03ciency and e\ufb00ective ISR luminosity, and is convolved\nwith a Gaussian resolution function obtained from MC\nsimulation. The parameters of the Y (4260) resulting from\nthe \ufb01t are in agreement with the previous measurements,\nand are reported in Table 21.5.2, which summarizes the\nISR Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8 analyses from various exper-\niments performed under the single-resonance hypothesis.\nThe BABAR data do not support the Belle observation of\na broad structure at 4.08 GeV/c2.\nThe invariant mass distribution of the dipion system\nfor events with a \u03c0+\u03c0\u2212J/\u03c8 mass close to the Y (4260) is\nfound to deviate signi\ufb01cantly from phase space in both\nBABAR and Belle data samples (see Fig. 18.3.10). It shows\nan accumulation around 0.95 GeV/c2, followed by an abrupt\nfall to near zero at \u223c1 GeV/c2, and then rises again. Such\nbehavior is reproduced by BABAR (Lees, 2012ab) with a\nmodel assuming a coherent sum of a nonresonant \u03c0+\u03c0\u2212S-\nwave amplitude and a resonant amplitude describing the\nf0(980). The \ufb01t to the data sample assuming this simple\nmodel shows that the f0(980) contribution is produced\nin a fraction 0.17 \u00b1 0.13 of Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8 decays,\nwhere only the statistical error is quoted.\nIn another study Belle observes also a signi\ufb01cant ac-\ncumulation of events in the J/\u03c8\u03c0\u00b1 invariant mass of the\nY (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8 decays (Liu, 2013). The state de-\nnoted as Z(3900)\u00b1, which is clearly not a charmonium\nstate (charge), is observed with a signi\ufb01cance larger than\n5 \u03c3, and is in Y (4260) decays produced with a branch-\ning ratio of B(Y (4260) \u2192Z(3900)\u00b1\u03c0\u2213)B(Z(3900)\u00b1 \u2192\n\u03c0\u00b1J/\u03c8)/B(Y (4260) \u2192\u03c0+\u03c0\u2212J/\u03c8) = (29.0 \u00b1 8.9)%, where\nthe uncertainty is statistical only. The properties of the\nstate are consistent with the one observed by BESIII (Ab-\nlikim et al., 2013a).\nBeside the J/\u03c8\u03c0\u03c0\u03b3ISR \ufb01nal state Belle studied also the\nISR process with the production of J/\u03c8KK (Yuan, 2008)\nand J/\u03c8\u03b7 (Wang, Han, Yuan, Shen, and Wang, 2013).\nThe former measurement is the \ufb01rst observation of that\n\ufb01nal state in the ISR process. No evidence for the Y (4260)\nis found and the upper limit on the product of the two-\nelectron width and the branching fraction is determined\nto be \u0393(Y (4260) \u2192e+e\u2212)B(Y (4260) \u2192K+K\u2212J/\u03c8) <\n1.2 eV/ with 90% C.L. In the J/\u03c8\u03b7 \ufb01nal state clear signals\n\n700\nTable 21.5.2. Summary of ISR \u03c0+\u03c0\u2212J/\u03c8 measurements by various experiments under the single-resonance hypothesis, where\nY stands for Y (4260). The \ufb01rst uncertainty is statistical and the second systematic (if only one is given it is the statistical\nuncertainty only).\nExperiments\nL (fb\u22121)\nNY\nmass (MeV/c2)\n\u0393tot (MeV)\nB(Y \u2192\u03c0+\u03c0\u2212J/\u03c8)\u0393Y \u2192e+e\u2212(eV)\nCLEO (He et al., 2006)\n13.3\n37\n4284+17\n\u221216 \u00b1 4\n73+39\n\u221225 \u00b1 5\n8.9+3.9\n\u22123.1 \u00b1 1.8\nBelle (Yuan, 2007)\n548\n324 \u00b1 21\n4263 \u00b1 6\n126 \u00b1 18\n9.7 \u00b1 1.1\nBABAR (Lees, 2012ab)\n454\n344 \u00b1 39\n4244 \u00b1 5 \u00b1 4\n114+16\n\u221215 \u00b1 7\n9.2 \u00b1 0.8 \u00b1 0.7\nof \u03c8(4040) and \u03c8(4160) are observed, and no signal of\nY (4260). For the latter the upper limit is \u0393(Y (4260) \u2192\ne+e\u2212)B(Y (4260) \u2192\u03b7J/\u03c8) < 14.2 eV at 90% C.L.\n21.5.2 Y family states in ISR \u03c0+\u03c0\u2212\u03c8(2S)\nSince the Y (4260) is above the mass threshold for \u03c8(2S)\nplus \u03c0+\u03c0\u2212, it is natural to ask if Y (4260) also decays to\n\u03c0+\u03c0\u2212\u03c8(2S). In order to further clarify the nature of the\nY (4260), and search for similar states, BABAR (Aubert,\n2007m) and Belle (Wang, 2007c) have studied the ISR pro-\ncess e+e\u2212\u2192\u03b3ISR\u03c0+\u03c0\u2212\u03c8(2S). The \u03c8(2S) is reconstructed\nin the \u03c0+\u03c0\u2212J/\u03c8 decay mode, with J/\u03c8 \u2192\u2113+\u2113\u2212. The anal-\nysis procedure is similar to the case of the \u03c0+\u03c0\u2212J/\u03c8 \ufb01-\nnal state. An additional background source, produced by\ndi\ufb00erent combinations within the same 2(\u03c0+\u03c0\u2212)J/\u03c8 sys-\ntem where at least one of the primary pions is combined\nwith the J/\u03c8 to form a \u03c0+\u03c0\u2212J/\u03c8 candidate, must be sub-\ntracted from the selected sample. The clean sample of se-\nlected \u03c8(2S) decays is used for signal estimation, while\nthe sidebands of the \u03c8(2S) mass distribution are used for\nbackground subtraction.\nThe BABAR analysis (Aubert, 2007m) is based on a\nsample of 298 fb\u22121. The \u03c0+\u03c0\u2212\u03c8(2S) mass spectrum of\n78 events selected within the \u03c8(2S) mass window is rep-\nresented by data points in Fig. 21.5.4. The dashed curve\nshows the result of the \ufb01t to the Y (4260) using resonance\nparameters \ufb01xed to those of Aubert (2005y). The \u03c72/ndof\nof 21.3/8 quanti\ufb01es the inconsistency of the data with\nthe decay of Y (4260) to this \ufb01nal state. However, a clear\naccumulation of events is seen at a mass of about 4.35\nGeV/c2, and a \ufb01t to a single resonance with free mass\nand width parameters returns m = (4324 \u00b1 24) MeV/c2\nand \u0393 = (172 \u00b1 33) MeV, with a much better \ufb01t quality:\n\u03c72/ndof = 7.3/7 (the errors are statistical only). A \ufb01t to\nthe known \u03c8(4415) with \ufb01xed parameters is also of poor\nquality, supporting the hypothesis of a new state.\nIn a similar analysis, performed using twice the dataset,\nBelle (Wang, 2007c) con\ufb01rms the state at about 4.35 GeV/c2,\nand observes another structure at higher masses. A \ufb01t\nto the \u03c0+\u03c0\u2212\u03c8(2S) invariant-mass spectrum of selected\nevents with two coherent vector resonances returns for\nthe lower-mass resonance m = (4361 \u00b1 9 \u00b1 9) MeV/c2 and\n\u0393 = (74 \u00b1 15 \u00b1 10) MeV, and for the state at higher mass\nm = (4664 \u00b1 11 \u00b1 5) MeV/c2 and \u0393 = (48 \u00b1 15 \u00b1 3) MeV.\nA small enhancement around 4685 MeV/c2 in a single 50\n)\n2\n) (GeV/c\n\u03c8\n)J/\n-\n\u03c0\n+\n\u03c0\nm(2(\n4\n4.5\n5\n5.5\n2\nEvents / 50MeV/c\n5\n10\n)\n2\n) (GeV/c\n\u03c8\n)J/\n-\n\u03c0\n+\n\u03c0\nm(2(\n4\n4.5\n5\n5.5\n2\nEvents / 50MeV/c\n5\n10\n)\n2\n) (GeV/c\n\u03c8\n)J/\n-\n\u03c0\n+\n\u03c0\nm(2(\n4\n4.5\n5\n5.5\n2\nEvents / 50MeV/c\n5\n10\n)\n2\n) (GeV/c\n\u03c8\n)J/\n-\n\u03c0\n+\n\u03c0\nm(2(\n4\n4.5\n5\n5.5\n2\nEvents / 50MeV/c\n5\n10\nFigure 21.5.4. Invariant mass spectrum up to 5.7 GeV/c2 for\nselected ISR-produced 2(\u03c0+\u03c0\u2212)J/\u03c8 candidates in 298 fb\u22121 of\nBABAR data (Aubert, 2007m). The shaded histogram represents\nthe background estimated from the sidebands of the \u03c8(2S)\nmass spectrum, and the curves represent \ufb01ts to the data (see\nthe text).\nMeV/c2 bin was visible also in the BABAR measurement,\nbut not signi\ufb01cant due to the lower integrated luminos-\nity. A recent analysis performed by BABAR (Lees, 2012ac)\nusing the whole data set con\ufb01rms the state, now named\nY (4660), with parameters consistent with those measured\nby Belle.\n21.6 Dark force searches\nWhile the astrophysical evidence for dark matter is now\noverwhelming, its precise nature and origin remain elu-\nsive. Recent results from terrestrial and satellite exper-\niments have motivated an interesting proposal in which\nWIMP-like dark matter particles carry charge of a new yet\nunknown force (Arkani-Hamed, Finkbeiner, Slatyer, and\nWeiner, 2009; Fayet, 2007; Pospelov, Ritz, and Voloshin,\n2008). The corresponding gauge boson, the so-called dark\nphoton A\u2032, couples to the Standard Model photon through\nmixing between the photon and dark photon \ufb01elds (kinetic\nmixing) with mixing strength \u03f5.\nThis opens the possibility of dark matter annihilation\ninto a pair of dark photons which subsequently decay to\nSM particles. The mass of the dark photon is constrained\nto be at most a few GeV, to be compatible with the\nelectron/positron excess observed by PAMELA (Adriani\n\n701\n0\n5\n10\n15\n4\n4.5\n5\n5.5\nM(\u03c0+\u03c0-\u03c8(2S)) (GeV/c2)\nEntries/25 MeV/c2\nFigure 21.5.5. The \u03c0+\u03c0\u2212\u03c8(2S) invariant mass distribution\nfor events that pass the \u03c8(2S) selection in Belle 673 fb\u22121 data\n(Wang, 2007c). The open histogram is the data while the\nshaded histogram is the normalized \u03c8(2S) sidebands. The solid\ncurve shows the result of the the best \ufb01t with two coherent\nP-wave resonances together with a constant incoherent back-\nground term. The two dashed curves at each peak show the\ntwo solutions for constructive and destructive interference.\net al., 2010, 2009) and FERMI (Abdo et al., 2009; Ack-\nermann et al., 2012), without a comparable anti-proton\nsignal. Dark photons decay almost exclusively to lepton-\npairs if their mass is below \u223c500 MeV, while the contri-\nbution of pion pairs is signi\ufb01cant between \u223c500 MeV and\n\u223c1 GeV, and multi-hadron channels become dominant at\nhigher masses. The dark boson masses are usually gener-\nated via the Higgs mechanism, adding one or more dark\nHiggs bosons (h\u2032) to the theory.\n21.6.1 Searches for a dark photon\nA dark photon can be readily produced in the reaction\ne+e\u2212\u2192\u03b3A\u2032, A\u2032 \u2192\u2113+\u2113\u2212. The signature is similar to that\nof a light CP-odd Higgs boson, A0, in \u03a5(2S, 3S) \u2192\u03b3A0,\nA0 \u2192\u2113+\u2113\u2212(Aubert, 2009an). The \u03a5(2S, 3S) candidates\nare reconstructed by combining two oppositely-charged\ntracks with a photon. At least one track must be iden-\nti\ufb01ed as a muon and the energy of the photon in the CM\nframe is required to be larger than 0.5 GeV. No additional\ntracks or photons must be detected in the event. The sig-\nnal yield is extracted as a function of the A0 mass by a\nseries of unbinned extended maximum likelihood \ufb01ts to\nthe distribution of the dimuon mass. No signi\ufb01cant sig-\nnal is observed, and upper limits on the branching frac-\ntion \u03a5(2S, 3S) \u2192\u03b3A0, A0 \u2192\u2113+\u2113\u2212are derived. These\nresults have been reinterpreted (Bjorken, Essig, Schuster,\nand Toro, 2009) as limits on the mixing strength \u03f5 at the\nlevel 10\u22123 \u221210\u22122 (Fig. 21.6.1).\nAdditional searches have been performed which may\nbe reinterpreted as limits on dark photon production, such\nas e+e\u2212\u2192\u03b3 invisible (Aubert, 2008at), e+e\u2212\u2192\u03b3 hadrons\n(Lees, 2011j), or e+e\u2212\u2192\u03b3\u03c4 +\u03c4 \u2212(see Section 18.4.7.1, and\nAubert, 2009ai).\n0.01\n0.1\n1\n10\n10!7\n10!6\n10!5\n10!4\n10!3\n10!2 0.01\n0.1\n1\n10\n10!7\n10!6\n10!5\n10!4\n10!3\n10!2\nmA'!GeV\n\u0395\nE137\nE141\nE774\na\u039c\nY3S\nKLOE\nAPEX\nMainz\nFigure 21.6.1. Adopted from (Bjorken, Essig, Schuster, and\nToro, 2009). Constraints on the mixing strength, \u03f5, as a func-\ntion of the dark photon mass. The red line shows the value\nof the coupling required to explain the discrepancy between\nthe calculated and measured anomalous magnetic moment of\nthe muon (Pospelov, 2009). The excluded regions obtained\nby reinterpreting the upper limits on the Y (2S, 3S) \u2192A0\u03b3,\nA0 \u2192\u2113+\u2113\u2212(Aubert, 2009an) branching fractions are shown\nas a yellow band.\n21.6.2 A search for dark gauge bosons\nNon-Abelian extensions of dark sectors introduce addi-\ntional dark gauge bosons, generically denoted W \u2032, W \u2032\u2032, ....\nThe detailed phenomenology depends on the structure of\nthe model, but heavy dark bosons decay to lighter states\nif kinematically accessible, while the lightest bosons are\nmetastable and decay to SM fermions via their mixing\nwith the dark photon (Baumgart, Cheung, Ruderman,\nWang, and Yavin, 2009; Essig, Schuster, and Toro, 2009).\nBABAR has performed a search for di-boson produc-\ntion in the four lepton \ufb01nal state, e+e\u2212\u2192A\u2032\u2217\u2192W \u2032W \u2032\u2032,\nW \u2032 \u2192\u2113+\u2113\u2212, W \u2032\u2032 \u2192\u2113\u2032+\u2113\u2032\u2212with \u2113, \u2113\u2032 = e, \u00b5 (Aubert,\n2009aj). The study, based on 513 fb\u22121 of data collected\nmostly at the \u03a5(4S) resonance, has been performed in\nthe context of inelastic dark matter models (Tucker-Smith\nand Weiner, 2001), searching for two bosons with similar\nmasses. Events containing four leptons originating from\nthe interaction point with a total invariant mass greater\nthan 10 GeV are selected. Additional selection criteria on\nthe boson decay angles and the angle between the decay\nplanes of the two bosons are applied to further reject the\nbackground.\nThe signal is extracted as a function of the average\ndileptonic mass in the range 0.24 \u22125.3 GeV in 10 MeV\nsteps. No signi\ufb01cant signal is observed and 90% C.L. up-\nper limits on the mixing strength at the 10\u22123 level have\nbeen set, assuming a dark sector coupling constant \u03b1D =\n\n702\ngD/4\u03c0 = O(10\u22122), and equal branching fractions of a dark\ngauge boson to e+e\u2212and \u00b5+\u00b5\u2212.\n21.6.3 A search for dark Higgs bosons\nThe Higgsstrahlung process, e+e\u2212\u2192A\u2032h\u2032, h\u2032 \u2192A\u2032A\u2032, of-\nfers another gateway to dark sectors, as this process is one\nof the few suppressed by only a single power of the mix-\ning strength, and the background is expected to be almost\nnegligible (Batell, Pospelov, and Ritz, 2009). A search for\ndark Higgs boson production has been performed in the\nrange 0.8 < mh\u2032 < 10.0 GeV and 0.25 < mA\u2032 < 3.0 GeV\nwith the constraint mh\u2032 > 2mA\u2032 (Lees, 2012s). The sig-\nnal events are either fully reconstructed using A\u2032 \u2192\u2113+\u2113\u2212\nand A\u2032 \u2192\u03c0+\u03c0\u2212decays (exclusive mode), or partially re-\nconstructed (inclusive mode). In the latter case, only two\nof the three dark photons are identi\ufb01ed as dilepton res-\nonances, with the four-momentum of the remaining dark\nphoton identi\ufb01ed with that of the recoiling system. The ex-\nclusive modes contain six tracks having an invariant mass\nclose to \u221as, forming three dark photon candidates of sim-\nilar mass. The six pion \ufb01nal state has a signi\ufb01cantly larger\nbackground than the other channels and is excluded from\nthe search. Inclusive modes are \ufb01rst identi\ufb01ed by selecting\ntwo dileptonic resonances with similar mass, and requir-\ning the mass of the recoiling system to be compatible with\nthe dark photon hypothesis.\nNo signi\ufb01cant signal is observed, and 90% C.L. upper\nlimits on the product of the dark sector coupling con-\nstant and the mixing strength, \u03b1D\u03f52, are derived. The\nresults are displayed in Fig. 21.6.2 as a function of the\ndark photon mass for selected values of the dark Higgs\nboson masses. Values as low as 10\u221210 \u221210\u22128 are excluded\nfor a large range of dark photon and dark Higgs masses.\nAssuming \u03b1D = \u03b1EM, these measurements translate into\nlimits on the mixing strength in the range 10\u22124 \u221210\u22123.\n (GeV)\nA\u2019\nm\n-1\n10\n1\n2\n! \nD\n\"\n-10\n10\n-9\n10\n-8\n10\n-7\n10\n-6\n10\n-5\n10\n = 9 GeV\nh\u2019\nm\n = 7 GeV\nh\u2019\nm\n = 5 GeV\nh\u2019\nm\n = 3 GeV\nh\u2019\nm\n = 1 GeV\nh\u2019\nm\nFigure 21.6.2. Upper limit at 90% C.L. set by BABAR (Lees,\n2012s) on the product \u03b1D\u03f52 as a function of the dark photon\nmass for selected values of dark Higgs boson masses. The peak-\ning structure arising near mA\u2032 \u223c0.8 GeV and mA\u2032 \u223c1.0 GeV\nre\ufb02ects the presence of the \u03c9 and \u03c6 resonances. At these\nmasses, dark photons decay predominantly to 3(\u03c0+\u03c0\u2212\u03c00) and\n3(K+K\u2212) \ufb01nal states, not included in the search.\n\n703\nChapter 22\nTwo-photon physics\nEditors:\nVladimir P. Druzhinin (BABAR)\nSadaharu Uehara (Belle)\nAdditional section writers:\nHideyuki Nakazawa, Cheng Ping Shen, Yasushi Watan-\nabe, Chang Chun Zhang\n22.1 Descriptions of two-photon topics to be\ncovered\n22.1.1 Introduction for two-photon physics\nAn electron-positron collider is also a photon-photon col-\nlider. Since the photon couples directly to the electric\ncharge of quarks, we can study hadron structures and\nQCD physics, e\ufb00ectively, in hadron production induced\nby two-photon collisions. The even C-parity of the two-\nphoton system is complementary with the odd C-parity\nin e+e\u2212collisions. In an e+e\u2212collider, a virtual photon\nis emitted from each lepton; a collision of these photons\nproduces \ufb01nal-state particles as shown in Figure 22.1.1.\nThe two-photon center-of-mass (CM) energy, W, which is\nthe same as the invariant mass of the \ufb01nal-state system,\nis continuously distributed between zero and just below\nthe e+e\u2212CM energy. For practical purposes, the usable\nrange is between a few 100 MeV and \u223c4.5 GeV. The\nlower side is limited by experimental trigger conditions\nand the upper by the luminosity and backgrounds from\ne+e\u2212annihilation events.\ne+\ne-\nX\nFigure 22.1.1. A Feynman diagram illustrating hadron pro-\nduction in two-photon collisions e+e\u2212\u2192e+e\u2212X.\nThe study of hadron production in two-photon pro-\ncesses at the B Factories has contributed to better under-\nstanding of non-perturbative QCD and light-quark meson\nspectroscopy at low and intermediate energies. It also con-\ntributes to searches and measurements of charmonium(-\nlike) states as well as a test of perturbative-QCD models\nfor exclusive meson production at high energies (Brodsky\nand Lepage, 1981; Chernyak and Zhitnitsky, 1984).\n22.1.2 Cross section for \u03b3\u03b3 collisions (zero-tag)\nIn hadron production via two-photon collisions,\ne+e\u2212\u2192e+e\u2212X,\n(22.1.1)\nthe cross sections of the processes are given as a function\nof W and the Q2 value of each incident photon, where Q2\nis the negative of the mass squared of the virtual photon\nand is the same as the absolute value of four-momentum\ntransfer squared between the incident (pe,ini) and recoiled\nelectron or positron (pe,rec), Q2 = \u2212(pe,rec \u2212pe.ini)2. Here-\nafter we refer to both electrons and positrons as electrons\nfor brevity.\nRoughly speaking for the B Factory energies, the size\nof the cross section is a comparable order of magnitude\nwith that for e+e\u2212annihilation. The cross section is largest\nin the kinematic regions where the Q2 value is very close\nto zero and W is small when compared with the beam en-\nergy. In contrast, in regions where either W or Q2 is much\nlarger than the typical QCD energy scale (\u223c1 GeV), the\ncross section decreases rapidly so that statistical uncer-\ntainty dominates the measurement errors at the B Facto-\nries.\nWe discuss here the zero-tag method used to measure\nand derive the cross section corresponding to real two-\nphoton collisions, where neither of the recoiling electrons\nare detected. The Q2 of the emitted virtual photons has a\ncontinuous distribution and peaks very close to zero (i.e.\nsmaller than the electron mass squared). Most events have\nQ2 much smaller than the QCD scale or any hadron-mass\nsquared, say (100 MeV)2, so the measured cross section\napproximates that of the collisions of real photons.\nWe approximate a real photon in \u03b3\u03b3 cross-section mea-\nsurements with a virtual photon having a small Q2 and\nextrapolate the cross section measured with \ufb01nite Q2 pho-\ntons to the Q2 = 0 limit, using an appropriate Q2 de-\npendence of the cross section that is interpreted as a\nphoton-hadron form factor e\ufb00ect. In addition, when we\nadopt an equivalent-photon approximation (EPA), the ef-\nfect from each photon is separated and factorized; also,\nthe real two-photon cross section is decoupled from the\nphoton-emission part (Berger and Wagner, 1987; Bud-\nnev, Ginzburg, Meledin, and Serbo, 1975). With these\napproximations, we can de\ufb01ne and calculate a universal\ntwo-photon luminosity function L\u03b3\u03b3 as a function of W:\nL\u03b3\u03b3(W) =\nd\ndW\n\u0012 Z\nN(k1, Eb)N(k2, Eb) 1\nQ2\n1\n1\nQ2\n2\nF(Q2\n1, W)F(Q2\n2, W)dk1dk2dQ2\n1dQ2\n2\n\u0013\n,\n(22.1.2)\nwhere N(ki, Eb) is the probability density function (ob-\ntained from QED) for the virtual photon with index\ni = 1, 2 and energy ki emitted from the incident lepton\nwith energy Eb, and F(Q2\ni , W) is the factorized form fac-\ntor e\ufb00ect for this photon (normalized to the real photon\nF(0, W)= 1). The two-photon luminosity function is used\n\n704\nto translate the e+e\u2212-based cross section \u03c3ee at given W\nto the corresponding \u03b3\u03b3 cross section \u03c3\u03b3\u03b3(W) by the re-\nlation\n\u03c3\u03b3\u03b3(W) =\n1\nL\u03b3\u03b3(W)\nd\u03c3ee\ndW .\n(22.1.3)\nWe also use several di\ufb00erential cross sections in the\nmeasurement of the angular and momentum distributions\nof the \ufb01nal-state particles, accounting for the e\ufb03ciencies\nas a function of the measured variables. For example, the\ndi\ufb00erential cross section for a process with a two-body\n\ufb01nal state is given by the following formula:\nd\u03c3\u03b3\u03b3\nd| cos \u03b8\u2217| =\n\u2206N\n\u2206W\u2206| cos \u03b8\u2217| \u03f5 L\u03b3\u03b3(W)\nR\nLdt,(22.1.4)\nwhere \u03b8\u2217is the scattering angle of a \ufb01nal-state particle in\nthe two-photon CM frame, \u2206N is the number of signal\nevents in a two-dimensional bin with a bin size of \u2206W \u00d7\n\u2206| cos \u03b8\u2217|, \u03f5 is the e\ufb03ciency for the bin and\nR\nLdt is the\nintegrated luminosity for e+e\u2212incident beams.\n22.1.3 Resonance production\nThe single meson formation process \u03b3\u03b3 \u2192R, in which\nonly one meson R is produced from the two-photon col-\nlision, is one of the most important processes in two-\nphoton physics. The quantum numbers of the meson R\nare limited: it must be electrically neutral and have even\nC-parity; the spin-parity of J = 1\u00b1 or JP =(odd)\u2212are\nprohibited in collisions of real photons. There are other\nrestrictions for the helicity for the produced meson R.\nThis process allows us to measure the two-photon par-\ntial width of the \ufb01nal-state meson R. The cross section\ncan be written as:\n\u03c3(W) = 8\u03c0(2J + 1)\u0393\u03b3\u03b3\u0393B(R \u2192\ufb01nal state)\n(W 2 \u2212M 2\nR)2 + M 2\nR\u03932 ,\n(22.1.5)\nwhere MR, \u0393\u03b3\u03b3 and \u0393 are the mass, two-photon decay\nwidth, and total width of the meson resonance R, respec-\ntively. B(R \u2192\ufb01nal state) is the branching fraction for\nthe decay of the meson R. Here we assume that the res-\nonance shape is represented by a conventional relativis-\ntic Breit-Wigner function (see Chapter 13). If we know\nthe branching fraction of the meson\u2019s decay mode used in\nthe measurement, then we can extract the two-photon de-\ncay width; otherwise, we measure the product of the two-\nphoton decay width and the branching fraction. The two-\nphoton partial decay width is a fundamental and direct\nobservable to explore the qq or exotic nature of the neu-\ntral meson. Even for a non-exotic meson, the two-photon\ndecay width is useful to study the quarks\u2019 quantum state\ninside the meson and to test QCD models (Munz, 1996).\nIn a zero-tag measurement, we can make the signal\nevents almost free from other processes by applying a\nrather stringent transverse-momentum balance. This is a\ngreat advantage in searches for new resonances as well as\nnew decay modes of known hadrons. The requirement for\nthe transverse-momentum balance also restricts the Q2 of\nthe incident photon and ensures the processes originates\nfrom real photon collisions. Similar requirements are also\nuseful in the single-tag cases described below to ensure a\nsmall Q2 for the untagged photon.\n22.1.4 Single-tag measurements\nWhen one of the scattered electrons is detected, we re-\nfer to these two-photon processes as single-tag modes. In\nthe single-tag process, we can probe the structure of the\nreal photon or a hadron with a high-Q2 photon; this pro-\ncess is very useful for studies of hadron and QCD physics\nsuch as meson transition form factors (Brodsky and Lep-\nage, 1981). The Q2 of the virtual photon is determined\nby measuring the scattering angle and energy of the recoil\nelectron with the following Lorentz-invariant formula:\nQ2 = 4EbE\u2032 sin2 \u03b8\n2,\n(22.1.6)\nwhere Eb and E\u2032 are the energies of the incident and re-\ncoiling (tagged) electrons and \u03b8 is the scattering angle of\nthe tagged electron.\nThe formation of a resonance in the single-tag process\nis a fertile \ufb01eld of study at the B Factories, especially in\nthe high-Q2 region where the production cross section is\nhighly suppressed. We impose a kinematic requirement on\nthe single-tag mode that all the \ufb01nal state particles be ob-\nserved except for the non-tagged incident electron (which\ncan be inferred from a missing-mass constraint). In the\nB Factory experiments, the pseudoscalar transition form\nfactors have been measured in single-tag modes, and are\ndiscussed in section 22.7. It is also possible to produce\nspin-1 (axial-vector) mesons in the single-tag process, al-\nthough such measurements have not been reported from\nthe B Factories.\n22.1.5 Monte-Carlo Techniques\nNo general-purpose Monte-Carlo (MC) generator for two-\nphoton processes was available during the running of the\nB Factories. For exclusive two-photon processes, we can\nexplicitly specify the combination of the \ufb01nal-state parti-\ncles exclusively as well as the W distribution used in the\nevent generation. In addition, angular distributions must\nbe speci\ufb01ed in the event generation.\nFor these purposes, several MC generators to simu-\nlate a resonance or an exclusive \ufb01nal-state system from\ntwo-photon collisions, such as TREPS (Uehara, 1996),\nGGRESRC (Druzhinin, Kardapoltsev, and Tayursky, 2010),\nGamgam (Aubert, 2010g) etc., are prepared and are used\nin the analysis. In these generators, one can specify func-\ntional shapes of distributions for W, Q2 and angles of\n\ufb01nal-state particles, or they can be generated by built-in\ndefault functions. Usually, an equivalent-photon approx-\nimation is adopted for zero-tag event generation while a\nQ2 distribution not based on EPA is sometimes used for\nthe single-tag cases. Even for the non-EPA cases, we can\n\n705\nobtain the conversion factor to obtain the \u03b3\u03b3\u2217physics vari-\nable, such as the square of a transition form factor, from\nthe e+e\u2212-based cross section through the MC calculations.\nThe Q2 dependence or its maximum limit a\ufb00ects values\nor de\ufb01nitions of the luminosity function, the cross section\non the e+e\u2212-incident basis and the e\ufb03ciency in the mea-\nsurements of the zero-tag mode; hence consistency among\nthese quantities must be considered in the analysis.\nBackground processes are modeled using generators\nwhich take into account the higher-order QED processes,\nparton-distribution functions and/or soft hadrons, such as\nPythia (Sj\u00a8ostrand, Mrenna, and Skands, 2006).\n22.2 Pseudoscalar meson-pair production\nThe energy region of meson-pair production through two-\nphoton processes can be naturally divided into a low en-\nergy region, where resonance production is dominant, and\na high energy region, where cross sections tend to show\nasymptotic behavior and can be compared to QCD pre-\ndictions.\nIn this section, we restrict ourselves to the pair pro-\nduction of pseudoscalar mesons (denoted as P1 and P2).\nBelle has made extensive studies of these processes for\nboth charged-meson pairs,\n(1) \u03b3\u03b3 \u2192\u03c0+\u03c0\u2212(Mori, 2007a,b; Nakazawa, 2005),\n(2) \u03b3\u03b3 \u2192K+K\u2212(Abe, 2003d; Nakazawa, 2005),\nand neutral-meson pairs,\n(3) \u03b3\u03b3 \u2192K0\nSK0\nS (Chen, 2007c; Uehara, 2013),\n(4) \u03b3\u03b3 \u2192\u03c00\u03c00 (Uehara, 2008a, 2009b),\n(5) \u03b3\u03b3 \u2192\u03b7\u03c00 (Uehara, 2009a),\n(6) \u03b3\u03b3 \u2192\u03b7\u03b7 (Uehara, 2010a).\nThe polar angle (\u03b8\u2217) coverage is typically restricted to\n| cos \u03b8\u2217| < 0.6; for neutral pairs decaying into photons this\nrange is extended to | cos \u03b8\u2217| < 0.8 or | cos \u03b8\u2217| < 1.0, be-\ncause small angle photons can be detected by the endcap\ncalorimeters. The wider coverage provides better separa-\ntion of the partial waves as discussed in Section 22.2.1.1.\nAs an example of the high statistics in raw data that\nhave been recorded at the B Factories, we show the W\ndependence of the experimental yields for the \u03b3\u03b3 \u2192\u03c0+\u03c0\u2212\nand \u03b3\u03b3 \u2192\u03b7\u03c00 candidate events in Fig. 22.2.1 (a) and (b),\nrespectively.\n22.2.1 Light-quark meson resonances\nA measurement of a meson resonance (denoted as R) de-\ncaying into two pseudoscalar mesons through two-photon\nproduction allows the determination of its parameters such\nas the mass, total width and, in particular, the product of\nthe two-photon width and the branching fraction to the\nmeson pair, \u0393\u03b3\u03b3B(R \u2192P1P2). If B(R \u2192P1P2) is known,\na two-photon width is derived, which is otherwise di\ufb03cult\nto obtain. The two-photon width of a meson is intimately\nrelated to its charge structure, giving in turn valuable in-\nformation on its quark content and structure.\n1\n10\n100\n1000\n10000\n100000\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\nW (GeV)\nNumber of events/ 20 MeV\nAll candidate events\nEstimated '\nbackground\npt-unbalanced background\n)\n2\nW (GeV/c\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\nevents/(5MeV/c)\n160\n170\n180\n190\n200\n210\n220\n230\n(980)\n0f\n(1270)\n2f\n2\n3\n10\n(a) \u03c0+\u03c0\u2212\n(b) \u03b7\u03c00\nFigure 22.2.1. Invariant mass, W, distribution for (a) \u03b3\u03b3 \u2192\n\u03c0+\u03c0\u2212and (b) \u03b3\u03b3 \u2192\u03b7\u03c00 candidate events. The distribution\nin (a) includes the \u03b3\u03b3 \u2192\u00b5+\u00b5\u2212background. In (b), the solid\ncurve shows the background from other processes; that is deter-\nmined experimentally from the transverse-momentum-balance\ndistribution. Taken from (Mori, 2007a; Uehara, 2009a).\nOne of the longstanding puzzles of QCD is the low\nmass scalar nonet: f0(500), K\u2217\n0(800), f0(980) and a0(980),\nwhose masses must be higher than 1.2 GeV/c2 if they\nare ordinary qq bound states (Close and Tornqvist, 2002;\n\u2019t Hooft, Isidori, Maiani, Polosa, and Riquer, 2008). One\npossible explanation exploits the attractive force between\na quark pair (di-quark) in the color anti-triplet state. In\nthis picture, a di-quark anti-di-quark pair forms a nonet\nwith lower masses for the scalar states. In such a state,\nits two-photon width is expected to be an order of mag-\nnitude smaller compared to that of the qq state (Amsler\nand Tornqvist, 2004). 166\n166 The typical size of the two-photon width for the usual\nqq state is given, for example, for f2(1270) meson; that is\n\u0393\u03b3\u03b3(f2(1270) = 3.03 \u00b1 0.35 keV (Beringer et al., 2012).\n\n706\n22.2.1.1 Di\ufb00erential cross sections and partial wave analysis\nIn this subsection, we present the formalism of the di\ufb00er-\nential cross section for two-photon production of a meson\npair in terms of partial waves and then discuss a possible\nmethod to extract the resonance parameters.\nIn the energy region W \u22643 GeV, the partial waves\nwith spin J > 4 may be neglected so that only S-, D-\nand G- waves need be considered. The di\ufb00erential cross\nsection can be expressed as:\nd\u03c3\nd\u2126(\u03b3\u03b3 \u2192P1P2) =\n(22.2.1)\n\f\fS Y 0\n0 + D0 Y 0\n2 + G0 Y 0\n4\n\f\f2 +\n\f\fD2 Y 2\n2 + G2 Y 2\n4\n\f\f2 ,\nwhere D0 and G0 (D2 and G2) denote the helicity 0 (2)\ncomponents of the D- and G- wave, respectively,167 and\nY \u03bb\nJ are the spherical harmonics in which the helicity \u03bb\nis quantized for the \u03b3\u03b3 axis. The angular dependence of\nthe cross section is governed by the spherical harmonics,\nwhile the energy dependence is determined by the partial\nwaves. Since the absolute value of harmonics |Y \u03bb\nJ | are not\nindependent, the partial waves cannot be separated from\nthe information on the di\ufb00erential cross sections alone.\nWe write Eq. (22.2.1) as\nd\u03c3\n4\u03c0d| cos \u03b8\u2217| ( \u03b3\u03b3 \u2192P1P2) =\n(22.2.2)\nbS2 |Y 0\n0 |2 + bD2\n0 |Y 0\n2 |2 + bD2\n2 |Y 2\n2 |2\n+ bG2\n0 |Y 0\n4 |2 + bG2\n2 |Y 2\n4 |2 .\nThe amplitudes bS2, bD2\n0, bD2\n2, bG2\n0 and bG2\n2 can be expressed\nin terms of S, D0, D2, G0 and G2 (Uehara, 2008a). Since\nthe squares of the spherical harmonics are orthogonal, we\ncan \ufb01t di\ufb00erential cross sections to obtain bS2, bD2\n0, bD2\n2, bG2\n0\nand bG2\n2 for each W bin. Two types of \ufb01t are used: the\n\u201cSD\u201d \ufb01t and \u201cSDG\u201d \ufb01t; G-waves are neglected in the SD\n\ufb01t.\nAs an example of the analysis, we discuss the Belle re-\nsults for \u03b3\u03b3 \u2192\u03b7\u03c00 (Uehara, 2009a). The spectra of bS2, bD2\n0\nand bD2\n2 obtained by the SD \ufb01t for this process are shown\nin Fig. 22.2.2. The spectrum for bS2 shows a clear peak of\nthe spin zero a0(980) with a shoulder that may be due to\nthe a0(1450) while the spectrum for bD2\n2 is dominated by\nthe spin two a2(1320) with a hint of the a2(1700). There\nis no clear structure for the bD2\n0 component. The SDG \ufb01t\nreveals that G-waves are negligible in this energy region.\n22.2.1.2 Resonance parameter extraction by partial wave\nanalysis\nHere, we describe a method to derive information from\nresonances by parameterizing partial wave amplitudes and\nthen \ufb01tting di\ufb00erential cross sections. Note that we do not\n167 In this chapter we denote individual partial waves by Ro-\nman style and parameterized waves by italics.\nf\nFigure 22.2.2. Spectra of (top) bS2, (middle) bD2\n0 and (bottom)\nbD2\n2 for \u03b3\u03b3 \u2192\u03b7\u03c00. The solid lines are the results of the partial-\nwave analysis discussed in Section 22.2.1.2. The error bars show\nthe diagonal components of error matrix for the \ufb01t parameters.\nFrom (Uehara, 2009a).\n\ufb01t the obtained bS2, bD2\n0 and bD2\n2 spectra; instead, we \ufb01t\nthe di\ufb00erential cross sections directly, but the results are\nshown in the bS2, bD2\n0, bD2\n2 spectra. Two to three orders of\nmagnitude higher statistics are available at B Factories\ncompared to pre-B Factory experiments which permits\nsuch a luxury.168\nOnce the functional forms of the amplitudes are pre-\npared, we use Eq. (22.2.1) to \ufb01t the di\ufb00erential cross sec-\ntions. The fundamental di\ufb03culty is the presence of inter-\nference among resonances and non-resonant amplitudes\nthat are basically unknown. A \ufb01t with many free param-\neters often results in multiple solutions corresponding to\nconstructive and destructive interference. Thus, one has\nto minimize the number of parameters to obtain a stable\nand unique solution. The e\ufb00ects of parameterization de-\npendence are incorporated in the systematic uncertainties,\nwhich are typically obtained by changing the parameteri-\nzation.\nIn the partial wave analysis for the low energy region\nW < 1.5 GeV where the J > 2 waves can be neglected\nsafely, the a2(1320) contribution is assumed only in the\n168 See Whalley (2001) for a compilation for pre-B Factory\nexperiments.\n\n707\nD2 wave, since bD2\n2 is dominated by the a2(1320) reso-\nnance and the bD2\n0 component is small. For the S-wave,\nthe shoulder in the bS2 spectrum above the a0(980) peak\nmay be understood due to the a0(1450). However, in the\n\ufb01t Belle introduces a new resonance a0(Y ), since the res-\nonance parameters are found to be quite di\ufb00erent from\nthose of the a0(1450).\nAs a result, Belle uses the following parameterization\nfor the S-, D0 and D2 waves:\nS = Aa0(980)ei\u03c6s0 + Aa0(Y )ei\u03c6s1 + BS ,\nD0 = BD0 ,\nD2 = Aa2(1320)ei\u03c6d2 + BD2 ,\n(22.2.3)\nwhere Aa0(980), Aa0(Y ) and Aa2(1320) are the amplitudes\nof the a0(980), a0(Y ) and a2(1320), respectively; BS, BD0\nand BD2 are non-resonant (hereafter called \u201cbackground\u201d)\namplitudes for S-, D0 and D2 waves; and \u03c6s0, \u03c6s1, and \u03c6d2\nare the phases of resonances relative to background am-\nplitudes. The goal of the analysis is to obtain parameters\nof the a0(980) and a0(Y ) and to check the consistency of\nthe a2(1320) parameters that have been measured well in\nthe past.\nThe background amplitudes are parameterized as sec-\nond order polynomials in W for both the real and imag-\ninary parts of all waves. The arbitrary phases are \ufb01xed\nby choosing \u03c6s0 = \u03c6d2 = 0. for S- and D- waves. We\nconstrain all the background amplitudes to be zero at\nthe threshold in accordance with the expectation that the\ncross section vanishes in the Thomson limit which was\noriginally discussed in the context of low-energy Compton\nscattering. The relativistic Breit-Wigner resonance ampli-\ntude (see Chapter 13) is used for a resonance.\nThe data are \ufb01t using the minimizer Minuit (James\nand Roos, 1975). Many \ufb01ts are done using di\ufb00erent, ran-\ndomly chosen starting parameters. In this way, Belle search\nfor a global minimum and locate ambiguous solutions.\nThe resulting best \ufb01t obtained is displayed in Fig. 22.2.2.\nThe measured spectra, bS2, bD2\n0 and bD2\n2, are reproduced\nfairly well by the \ufb01t.\nTable 22.2.1 summarizes the \ufb01t results for \u03b3\u03b3 \u2192\u03b7\u03c00\nas well as the other processes measured by Belle: \u03b3\u03b3 \u2192\n\u03c0+\u03c0\u2212, \u03b3\u03b3 \u2192K+K\u2212, \u03b3\u03b3 \u2192K0\nSK0\nS, \u03b3\u03b3 \u2192\u03c00\u03c00 and \u03b3\u03b3 \u2192\n\u03b7\u03b7.\nThe main results in this table are as follows. Belle\nmeasures the two-photon widths for the scalar resonances\nf0(980) and a0(980) for the \ufb01rst time with signi\ufb01cant\nstatistics; the f0(980) is observed as a clear peak both\nin the \u03c0+\u03c0\u2212and \u03c00\u03c00 modes; the a0(980) is measured\nclearly in the \u03b7\u03c00 mode. The measured two-photon widths\nare small compared to those of the f2(1270) and a2(1320).\nThis supports the di-quark anti-di-quark hypothesis for\nthese mesons. In addition, Belle \ufb01nds several resonance\nstates in the range 1.3\u20132.4 GeV with substantial cou-\npling to two photons. Belle perform a generic partial wave\nanalysis including possible interferences with non-resonant\nterms. Systematic errors for some resonance parameters\nare large, resulting from a preference for destructive in-\nterference between the resonance and other components.\nFor example see S and D2 in Eq. 22.2.3, which tends to\nenhance variations of parameters. In addition, this generic\nanalysis results in multiple solutions in some cases.\nThe Belle results provide good-quality unfolded data\non the di\ufb00erential cross sections for six pseudoscalar modes,\n\u03b3\u03b3 \u2192\u03c0+\u03c0\u2212, K+K\u2212, \u03c00\u03c00, K0\nSK0\nS, \u03b7\u03c00 and \u03b7\u03b7. These\nhigh-statistics data can be used to update partial wave\nanalyses that employ low energy constraints and incorpo-\nrate all available hadron data (Pennington, Mori, Uehara,\nand Watanabe, 2008). We expect that these high-statistics\ndata will be used to derive more accurate resonance pa-\nrameters.\n22.2.2 Comparison with QCD predictions at high\nenergy\nTwo-photon production of exclusive hadronic \ufb01nal states\nprovides useful information about resonances, perturba-\ntive QCD, and non-perturbative QCD. From the theo-\nretical point of view, a two-photon process is attractive\nbecause of the absence of strong interactions in the initial\nstate.\nBrodsky and Lepage (1981) (BL) numerically calcu-\nlated the amplitude for the hard exclusive \u03b3\u03b3 \u2192M1M 2\nprocesses within the context of the perturbative-QCD\n(pQCD) for the \ufb01rst time. A similar formula is also dis-\ncussed by Chernyak and Zhitnitsky (1984). In this pQCD\nframework, the amplitude for \u03b3\u03b3 \u2192M1M 2 can be de-\nscribed in a factorized form:\nM\u03bb1\u03bb2(s, \u03b8\u2217) =\n(22.2.4)\nZ 1\n0\nZ 1\n0\ndxdy\u03c6M(x, Qx)\u03c6M(y, Qy)T\u03bb1\u03bb2(x, y, \u03b8\u2217),\nwhere s is the squared invariant mass of the di-meson sys-\ntem, \u03c6M(x, Qx) is a single-meson distribution amplitude\nfor a meson M. The squared amplitude |\u03c6M(x, Qx)|2 is\nproportional to a probability for \ufb01nding a valence quark\nand antiquark in the meson, carrying a fraction x and\n1 \u2212x, respectively, of the meson\u2019s momentum. Qx is the\ntypical momentum scale in the process, \u223cmin(x, 1 \u2212\nx)\u221as sin \u03b8\u2217. The term T\u03bb1\u03bb2 is a hard scattering ampli-\ntude for \u03b3\u03bb1\u03b3\u03bb2 \u2192qqqq with photon helicities \u03bb1 and \u03bb2.\nFrom the sum rule, the overall normalization is \ufb01xed as\nZ 1\n0\ndx\u03c6M(x, 0) = fM/2\n\u221a\n3,\n(22.2.5)\nwhere fM is the decay constant for meson M.\nFor mesons with helicity zero the leading-term calcu-\nlation gives the following dependence on s and scattering\nangle \u03b8\u2217:\nd\u03c3\nd| cos \u03b8\u2217| = 16\u03c0\u03b12 |FM(s)|2\ns\n(\n[(e1 \u2212e2)2]2\n(1 \u2212cos2 \u03b8\u2217)2\n+2(e1e2)[(e1 \u2212e2)2]\n1 \u2212cos2 \u03b8\u2217\ng(\u03b8\u2217)\n\n708\nTable 22.2.1. Summary of partial wave analyses in the energy region below 2.4 GeV. If two values are given for the two-photon\npartial decay width \u0393\u03b3\u03b3, the upper value is the one for the spin-helicity assignment (J, \u03bb) = (2, 2) and the lower one for (0, 0).\nB is the branching fraction of the resonance to the corresponding decay mode otherwise explicitly noted. For the \u03c00\u03c00 mode,\nwe provide the value B(f2 \u2192\u03b3\u03b3) instead of \u0393\u03b3\u03b3 since the total width is known for f2(1270). The resonances f0(Y ), a0(X) and\nf2(X) correspond to signals of new or unidenti\ufb01ed resonances found. In the K+K\u2212mode, fJ/f0/a2 and fJ/f2 mean that there\nare ambiguities in the signal assignment. Quoted upper limits are at 90% con\ufb01dence level.\nMode\nResonance\nMass (MeV/c2)\nWidth (MeV)\n\u0393\u03b3\u03b3 (eV), (J, \u03bb)=\n(\n(2, 2)\n(0, 0)\nReference\n\u03c0+\u03c0\u2212\nf0(980)\n985.6+1.2+1.1\n\u22121.5\u22121.6\n34.2+13.9+8.8\n\u221211.8\u22122.5\n205+95+147\n\u221283\u2212117\nMori (2007b)\n\u03b7\u2032(958)\nB(\u03c0+\u03c0\u2212)<2.9\u00d710\u22123 (with interference), 3.3\u00d710\u22124 (without)\nK+K\u2212\nf \u2032\n2(1525)\n1518\u00b11\u00b13\n82\u00b12\u00b13\n28.2\u00b12.4\u00b15.8/B\nAbe (2003d)\nfJ/f0/a2\n1737\u00b15\u00b17\n151\u00b122\u00b124\n(\n10.3\u00b12.1\u00b12.3/B\n76\u00b115\u00b117/B\nf2(2010)\n1980\u00b12\u00b114\n297\u00b112\u00b16\n61\u00b12\u00b13/B\nfJ/f2\n2327\u00b19\u00b16\n275\u00b136\u00b120\n(\n22\u00b13\u00b16/B\n161\u00b122\u00b148/B\nK0\nSK0\nS\nf \u2032\n2(1525)\n1525.3+1.2+3.7\n\u22121.4\u22122.1\n82.9+2.1+3.1\n\u22122.2\u22122.0\n48+67+108\n\u22128\u221212\n/B(KK)\nUehara (2013)\nf0(1710)\n1750+6+29\n\u22127\u221218\n139+11+96\n\u221212\u221250\n12+3+227\n\u22122\u22128\n/B(KK)\nf2(2200)\n2243+7+3\n\u22126\u221229\n145\u00b112+27\n\u221234\n3.2+0.5+1.3\n\u22120.4\u22122.2/B(KK)\nf0(2500)\n2539\u00b114+38\n\u221214\n274+77+126\n\u221261\u2212163\n40+9+17\n\u22127\u221240/B(KK)\n\u03c00\u03c00\nf0(980)\n982.2\u00b11.0+8.1\n\u22128.0\n286\u00b117+211\n\u221270\nUehara (2008a)\nf2(1270)\n\ufb01xed\n\ufb01xed\nB(f2 \u2192\u03b3\u03b3) = (1.57 \u00b1 0.01+1.39\n\u22120.14) \u00d7 10\u22125\nf0(Y )\n1470+6+72\n\u22127\u2212255\n90+2+50\n\u22121\u221222\n11+4+603\n\u22122\u22127\n/B\nf2(1950)\n2038+13\n\u221211\n441+27\n\u221225\n54+23\n\u221214/B\nUehara (2009b)\nf4(2050)\n1884+14+218\n\u221213\u221225\n453\u00b120+31\n\u2212129\n136+24+415\n\u221222\u221291\n\u03b7\u03c00\na0(980)\n982.3+0.6+3.1\n\u22120.7\u22124.7\n75.6\u00b11.6+17.4\n\u221210.0\n128+3+502\n\u22122\u221243 /B\nUehara (2009a)\na0(Y )\n1316.8+0.7+24.7\n\u22121.0\u22124.6\n65.0+2.1+99.1\n\u22125.4\u221232.6\n432\u00b16+1073\n\u2212256 /B\na2(1320)\n\ufb01xed\n\ufb01xed\n145+97\n\u221234/B\n\u03b7\u03b7\nf0(Y )\n1262+51+82\n\u221278\u2212103\n484+246+246\n\u2212170\u2212263\n121+133+169\n\u221253\u2212106 /B\nUehara (2010a)\nf2(1270)\n\ufb01xed\n\ufb01xed\n11.5+1.8+4.5\n\u22122.0\u22123.7/B\nf2(X)\n1737\u00b19+198\n\u221265\n228+21+234\n\u221220\u2212153\n5.2+0.9+37.3\n\u22120.8\u22124.5 /B\n+2(e1e2)2g2(\u03b8\u2217)\n)\n,\n(22.2.6)\nwhere e1 and e2 are the quark charges and FM is the me-\nson\u2019s electromagnetic form factor. Finally, g(\u03b8\u2217) is a func-\ntion of order one expressing the additional \u03b8\u2217dependence.\n169 In principle, both FM and g(\u03b8\u2217) can be obtained from\nthe meson wave function \u03c6M(x, Qx). However, at present\nthey are unknown since the function \u03c6M(x, Qx) is a non-\nperturbative quantity with an unknown x dependence.\n169 See the original paper (Brodsky and Lepage, 1981) for the\nexplicit formula.\n\n709\nUnder the assumption that \u03c6K and \u03c6\u03c0 are similar in\nshape, the di\ufb00erential cross section ratio for production\nof K+K\u2212and \u03c0+\u03c0\u2212depends only on the meson decay\nconstants f 4\nK/f 4\n\u03c0. Benayoun and Chernyak (1990) (BC)\nemploy di\ufb00erent wave functions for \u03c6\u03c0(x) and \u03c6K(x), tak-\ning into account SU(3) symmetry breaking e\ufb00ects. The\nnext-to-leading order calculation is done by Duplancic and\nNizic (2006).\nAs an alternative model for the meson-pair produc-\ntion in the two-photon processes, Diehl, Kroll, and Vogt\n(2002) (DKV) proposed a \u201chandbag model\u201d. In the hand-\nbag model, the di\ufb00erential cross section for the process is\ngiven by\nd\u03c3\nd| cos \u03b8\u2217|(\u03b3\u03b3 \u2192MM) = 8\u03c0\u03b12\ns\n1\nsin4 \u03b8\u2217|RMM(s)|2,\n(22.2.7)\nwhere the transition amplitude is expressed as a hard scat-\ntering \u03b3\u03b3 \u2192qq times a form factor RMM(s) describing the\nsoft transition qq \u2192MM. The main dynamical assump-\ntion of this model is that, at present energies W \u22644 GeV,\nall amplitudes for \u03b3\u03b3 \u2192MM are still dominated by \u201csoft\u201d\ncomponents. In this model, the angular distribution is pro-\nportional to 1/ sin4 \u03b8\u2217for both charged and neutral meson\npairs.\n22.2.2.1 Angular Dependence of Di\ufb00erential Cross Section\nAs can be seen from Eq. (22.2.6), there is distinct dif-\nference for charged and neutral meson pair production in\npQCD. For charged meson pairs, the angular distribution\nis given by 1/ sin4 \u03b8\u2217, since the \ufb01rst (leading) term domi-\nnates. This angular dependence is expected to be realized\nin a certain large |t| region of the Mandelstam variable.\nMeanwhile, for neutral meson pairs, the \ufb01rst and the sec-\nond terms are zero since the quark charges are the same\n(e1 = e2), so the angular dependence is given by the third\n(non-leading) term \u221dg2(\u03b8\u2217). As a result, a complicated\nangular distribution depending on the meson wave ampli-\ntude is expected for the neutral meson pairs. On the other\nhand, the handbag model predicts a 1/ sin4 \u03b8\u2217dependence\nfor large W for both charged and neutral meson pairs.\nThe measured results from Belle are summarized in\nTable 22.2.2. For the charged meson pairs, \u03b3\u03b3 \u2192\u03c0+\u03c0\u2212,\nK+K\u2212, the angular distributions are described by the\n1/ sin4 \u03b8\u2217form quite well. On the other hand, for the neu-\ntral meson pairs, \u03b3\u03b3 \u2192\u03c00\u03c00, K0\nSK0\nS, \u03b7\u03c00 and \u03b7\u03b7, the an-\ngular distributions show more complicated behavior. 170\n22.2.2.2 Energy Dependence of Cross Section and ratio of\nCross Sections\nOther important predictions for the hard exclusive pro-\ncesses in QCD are the power-law dependence of the cross\n170 An update analysis for \u03b3\u03b3 \u2192K0\nSK0\nS using full Belle data\nshows clearly that the angular distribution for this mode can\nnot be described by a 1/ sin4 \u03b8\u2217form. See Uehara (2013).\nsection, \u03c30 \u223cW \u2212n, and the ratio of the cross sections for\nthe di\ufb00erent processes. These results are summarized in\nTable 22.2.3.\nFor the W dependence, pQCD predicts n = 6 for the\ncharged meson pairs, and n = 10 for the neutral meson\npairs in the energy region accessible in the B Factory ex-\nperiments (Benayoun and Chernyak, 1990). The data for\n\u03b3\u03b3 \u2192\u03c0+\u03c0\u2212, K+K\u2212show slightly higher n than the pre-\ndicted value of n = 6 but within the systematic errors as\nshown in Figs 22.2.3(a) and (b).\nOn the other hand, for the neutral meson pairs, the\nprocesses \u03b3\u03b3 \u2192K0\nSK0\nS shows a steeper W dependence\nthan that for the charged meson pairs as can be seen in\nFig. 22.2.3(d). The measured value of the slope n = 11.0\u00b1\n0.4\u00b10.4 (Uehara, 2013) shows a good agreement with the\npQCD prediction by Chernyak (Chernyak, 2006, 2012).\nFor the ratio of the cross sections, pQCD predicts a\nlarge suppression for the neutral mesons compared to the\ncharged mesons. In contrast, in the handbag model, the\nratio is determined by soft dynamics such as the iso-spin,\nSU(3) relation. As can be seen in Fig. 22.2.3(e), the data\nshow a large suppression for the ratio\n\u03c3(\u03b3\u03b3 \u2192K0\nSK0\nS)\n\u03c3(\u03b3\u03b3 \u2192K+K\u2212).\n(22.2.8)\nThis is consistent with the pQCD expectation, but does\nnot agree with the handbag model. In addition, the ratio\n\u03c3(\u03b3\u03b3 \u2192K+K\u2212) over \u03c3(\u03b3\u03b3 \u2192\u03c0+\u03c0\u2212) is consistent with\npQCD prediction by Benayoun and Chernyak (1990) [BC],\nwhere the di\ufb00erence of wave functions for pion and kaon\nis taken into account (see Fig. 22.2.3(c)).\nOne exception is the ratio\n\u03c3(\u03b3\u03b3 \u2192\u03c00\u03c00)\n\u03c3(\u03b3\u03b3 \u2192\u03c0+\u03c0\u2212).\n(22.2.9)\nThis neutral to charged ratio is rather large as shown in\nTable 22.2.3. This result is inconsistent with the pQCD\npredictions where the neutral modes are expected to be\nsuppressed. The result, however, can be explained by the\nhandbag model (Diehl and Kroll, 2010) quite well.\nFurther study of the di\ufb00erential cross section data is\nneeded to clarify these unresolved problems.\n22.3 Vector meson-pair production\nA clear signal for the production of a new state via\nthe \u03b3\u03b3 process, X(3915) \u2192\u03c9J/\u03c8 (Uehara, 2010b),(Lees,\n2012ad), and evidence for another state X(4350) \u2192\n\u03c6J/\u03c8 (Shen, 2010a) have been reported, thereby introduc-\ning new puzzles in charmonium(-like) spectroscopy (see\nalso Sections 18.2 and 18.3). It is natural to extend the\nabove theoretical picture to similar states coupling to \u03c9\u03c6,\n\u03c9\u03c9 or \u03c6\u03c6.\nMeasurements of the cross sections for \u03b3\u03b3 \u2192V V (Liu,\n2012), where V is a vector particle,in particular V V =\n\u03c9\u03c6, \u03c6\u03c6 and \u03c9\u03c9, are based on an analysis of the 870 fb\u22121\n\n710\nTable 22.2.2. Angular dependence of di\ufb00erential cross sections in comparison with 1/ sin4 \u03b8\u2217dependence.\nmode\n1/ sin4 \u03b8\u2217\nenergy range\n| cos \u03b8\u2217| range\nreference\n\u03c0+\u03c0\u2212\nMatch well.\n3.0 - 4.1\n< 0.6\nNakazawa (2005)\nK+K\u2212\nMatch well.\n3.0 - 4.1\n< 0.6\nNakazawa (2005)\nK0\nSK0\nS\n\u03b1 varies from 4\u20138 for 1/ sin\u03b1 \u03b8\u2217\n2.6 - 3.3\n< 0.8\nUehara (2013)\n\u03c00\u03c00\n1/ sin4 \u03b8\u2217+ b cos \u03b8\u2217better.\n2.4 - 4.1\u2020\n< 0.8\nUehara (2008a)\nApproaches 1/ sin4 \u03b8\u2217above 3.1 GeV.\n\u03b7\u03c00\nGood agreement above 2.7 GeV.\n3.1 - 4.1\n< 0.8\nUehara (2009a)\n\u03b7\u03b7\nPoor agreement.\n2.4 - 3.3\n< 0.9\nUehara (2010a)\n1/ sin6 \u03b8\u2217better above 3.0 GeV.\n\u2020 \u03c7cJ region, 3.3 - 3.6 GeV is excluded.\nTable 22.2.3. The value of n of \u03c30 \u221dW \u2212n in various reactions \ufb01tted in the W and | cos \u03b8\u2217| ranges indicated and the ratio of\nthe cross sections in comparison with QCD predictions from Brodsky and Lepage (1981) [BL], Benayoun and Chernyak (1990)\n[BC], and Diehl, Kroll, and Vogt (2002) [DKV]. The \ufb01rst and second errors are statistical and systematic, respectively.\nProcess\nn\nW (GeV)\n| cos \u03b8\u2217|\nBL\nBC\nDKV\n\u03c0+\u03c0\u2212\n7.9 \u00b1 0.4 \u00b1 1.5\n3.0 - 4.1\n< 0.6\n6\n6\nK+K\u2212\n7.3 \u00b1 0.3 \u00b1 1.5\n3.0 - 4.1\n< 0.6\n6\n6\nK0\nSK0\nS\n#\n10.5 \u00b1 0.6 \u00b1 0.5\n2.4 - 4.0\u2020\n< 0.6\n-\n10\nK0\nSK0\nS\n##\n11.0 \u00b1 0.4 \u00b1 0.4\n2.6 - 4.0\u2020\n< 0.8\n-\n10\n\u03c00\u03c00\n8.0 \u00b1 0.5 \u00b1 0.4\n3.1 - 4.1\u2020\n< 0.8\n-\n10\n\u03b7\u03c00\n10.5 \u00b1 1.2 \u00b1 0.5\n3.1 - 4.1\n< 0.8\n-\n10\n\u03b7\u03b7\n7.8 \u00b1 0.6 \u00b1 0.4\n2.4 \u2013 3.3\n< 0.8\n-\n10\nProcess\n\u03c30 ratio\nW (GeV)\n| cos \u03b8\u2217|\nBL\nBC\nDKV\nK+K\u2212/\u03c0+\u03c0\u2212\n0.89 \u00b1 0.04 \u00b1 0.15\n3.0 - 4.1\n< 0.6\n2.3\n1.06\nK0\nSK0\nS/K+K\u2212#\n\u223c0.13 to \u223c0.01\n2.4 - 4.0\n< 0.6\u2020\n0.005\n2/25\n\u03c00\u03c00/\u03c0+\u03c0\u2212\n0.32 \u00b1 0.03 \u00b1 0.06\n3.1 - 4.1\n< 0.6\u2020\n0.04-0.07\n0.5\n\u03b7\u03c00/\u03c00\u03c00\n0.48 \u00b1 0.05 \u00b1 0.04\n3.1 - 4.0\n< 0.8\u2020\n0.24Rf(0.46Rf)\u2021\n\u03b7\u03b7/\u03c00\u03c00\n0.37 \u00b1 0.02 \u00b1 0.03\n2.4 - 3.3\n< 0.8\n0.36R2\nf(0.62R2\nf)\u2021\n\u2020 \u03c7cJ region, 3.3 \u2013 3.6 GeV is excluded.\n\u2021 \u03b7 meson as a pure SU(3) octet (mixture of octet and singlet with \u03b8p = \u221218\u25e6), Rf = f 2\n\u03b7/f 2\n\u03c00.\n# From Chen (2007c).\n## From Uehara (2013).\ndata sample taken at or near the \u03a5(nS) (n = 1, ..., 5)\nresonances with the Belle detector.\nAfter event selections, clear \u03c9 and \u03c6 signals are ob-\nserved. We obtain the number of V V events in each V V\ninvariant mass bin by \ufb01tting the | P P \u2217\nt | distribution be-\ntween zero and 0.9 GeV/c, where | P P \u2217\nt | is the magni-\ntude of the vector sum of the \ufb01nal transverse momenta of\nthe particle in the e+e\u2212CM frame. The resulting V V in-\nvariant mass distributions are shown in Fig. 22.3.1; some\nobvious structures are observed in the low V V invariant\nmass region.\nTwo-dimensional (2D) angular distributions are inves-\ntigated to obtain the JP quantum numbers of the struc-\ntures. In the process \u03b3\u03b3 \u2192V V , \ufb01ve angular variables are\nkinematically independent: z, z\u2217, z\u2217\u2217, \u03c6\u2217, and \u03c6\u2217\u2217. Using\n\u03c9\u03c6 as an example, z is the cosine of the scattering polar\nangle of the \u03c6 meson in the \u03b3\u03b3 CM system; z\u2217and \u03c6\u2217\nare the cosine of the helicity angle of K+ in the \u03c6 decay\nand the azimuthal angle de\ufb01ned in the \u03c6 rest frame with\nrespect to the \u03b3\u03b3 \u2192\u03c9\u03c6 scattering plane; z\u2217\u2217and \u03c6\u2217\u2217are\nthe cosine of the helicity angle of normal direction to the\ndecay plane of the \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00 and the azimuthal angle\nde\ufb01ned in the \u03c9 rest frame. We use the transversity angle\n(\u03c6T ) and polar-angle product (\u03a0\u03b8) to analyze the angu-\nlar distributions. They are de\ufb01ned as \u03c6T = |\u03c6\u2217+ \u03c6\u2217\u2217|/2\u03c0,\n\u03a0\u03b8 = [1 \u2212(z\u2217)2][1 \u2212(z\u2217\u2217)2].\nThe number of signal events is obtained by \ufb01tting the\n| P P \u2217\nt | distribution in each \u03c6T and \u03a0\u03b8 bin in the 2D\nspace. The 2D space is divided into 4\u00d74, 5\u00d75, and 10\u00d710\nbins for \u03c9\u03c6, \u03c6\u03c6, and \u03c9\u03c9, respectively, in several wide V V\nmass bins as shown in Fig. 22.3.2. The resulting 2D an-\ngular distributions are \ufb01tted with the signal shapes from\nMC-simulated samples with di\ufb00erent JP assumptions (0+,\n0\u2212, 2+, 2\u2212). The following features are found: (1) for \u03c9\u03c6:\n0+ (S-wave) or 2+ (S-wave) can describe the data with\n\u03c72/ndf = 1.1 or 1.2, while a mixture of 0+ (S-wave) and\n\n711\n\u03b3\u03b3\u2192\n\u00b1\n\u00b1\n\u03c3\n\u03b8 <\nDKV SU(3) limit\nBL prediction\nBC prediction\nW(GeV)\n(b)\n\u03c30(K0\nSK0\nS)/\u03c30(K+K-)\n(|cos\u03b8*|<0.6)\n0\n0.05\n0.1\n0.15\n2.5\n3\n3.5\n4\nW[GeV]\n2.5\n3\n3.5\n4\n|<0.6 )\n*\n\u03b8\n[nb] ( |cos\n0\n\u03c3\n10\n-2\n10\n-1\n1\n-\nK\n+\n(b)K\nBelle\nALEPH\nW[GeV]\n2.5\n3\n3.5\n4\n|<0.6 )\n*\n\u03b8\n[nb] ( |cos\n0\n\u03c3\n10\n-2\n10\n-1\n1\n-\n\u03c0\n+\n\u03c0\n(a)\nBelle\nALEPH\nW[GeV]\n2.4\n2.6\n2.8\n3\n3.2\n3.4\n3.6\n3.8\n4\n)\n\u03c0\n\u03c0\n(\n0\n\u03c3\n(KK) /\n0\n\u03c3\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6 (c)\n(d)\n(e)\nFigure 22.2.3. Cross section for the processes (a) \u03b3\u03b3 \u2192\n\u03c0+\u03c0\u2212, (b) \u03b3\u03b3 \u2192K+K\u2212and (d) \u03b3\u03b3 \u2192K0\nSK0\nS, integrated\nover | cos(\u03b8\u2217| < 0.6, as a function of W. The solid line in (a)\nand (b) is the prediction n = 6, while that in (d) is the best\n\ufb01t. The \ufb01gures (c) and (e) show the ratio of the cross section\namong these processes. The solid line in (c) is a \ufb01t with a\nconstant. The horizontal lines in (e) show various theoretical\npredictions. From (Chen, 2007c; Nakazawa, 2005).\n2+ (S-wave) describes the data with \u03c72/ndf = 0.9 (ndf\nbeing the number of degrees of freedom); (2) for \u03c6\u03c6: a\nmixture of 0+ (S-wave) and 2\u2212(P-wave) describes the\ndata with \u03c72/ndf = 1.3; and (3) for \u03c9\u03c9: a mixture of\n0+ (S-wave) and 2+ (S-wave) describes the data with\n\u03c72/ndf = 1.3.\nThe \u03b3\u03b3 \u2192V V cross sections are shown in Fig. 22.3.2.\nThe cross sections for di\ufb00erent JP values as a function\nof M(V V ) are also shown in this \ufb01gure. While there are\nsubstantial spin-zero components in all three modes, there\nare also signi\ufb01cant spin-two components, certainly in the\n\u03c6\u03c6 and \u03c9\u03c9 modes.\nThe cross sections for \u03b3\u03b3 \u2192\u03c9\u03c6 are much lower than\nthe prediction of the q2q2 tetraquark model (Achasov and\nShestakov, 1991) of 1 nb. The resonant structure in the\n\u03b3\u03b3 \u2192\u03c6\u03c6 mode is found nearly at the predicted mass\nfrom the model. However, the \u03c6\u03c6 cross section is an or-\nder of magnitude lower than the expectation. On the other\nhand, the t-channel factorization model (Alexander, Levy,\nand Maor, 1986) predicts that the \u03c6\u03c6 cross sections vary\n)\n2\n) (GeV/c\n\u03c6\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 0.03 GeV/c\n0\n50\n100\n150\n200\n250\n300\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 0.03 GeV/c\n0\n50\n100\n150\n200\n250\n300\n)\n2\n) (GeV/c\n\u03c9\n\u03c9\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 0.02 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n2\nEvents / 0.02 GeV/c\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n)\n2\n) (GeV/c\n\u03c6\n\u03c9\nM(\n1.5\n2\n2.5\n3\n3.5\n4\nEvents / 0.04 GeV/c2\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n(a)\n(c)\n(b)\n\u03c6\nFigure 22.3.1. The (a) \u03c9\u03c6, (b) \u03c6\u03c6 and (c) \u03c9\u03c9 invariant mass\ndistributions. The shaded histograms are from the correspond-\ning normalized sidebands. From (Liu, 2012).\nbetween 0.001 nb and 0.05 nb in the mass region of 2.0\nGeV/c2 to 5.0 GeV/c2, which are much lower than the\nexperimental data. For \u03b3\u03b3 \u2192\u03c9\u03c9, the t-channel factoriza-\ntion model predicts a broad structure between 1.8 GeV/c2\nand 3.0 GeV/c2 with a peak cross section of 10-30 nb near\n2.2 GeV/c2, while the one-pion-exchange model (Achasov,\nKarnakov, and Shestakov, 1987) predicts an enhancement\nnear threshold around 1.6 GeV/c2 with a peak cross sec-\ntion of 13 nb using their preferred value of the slope pa-\nrameter. Both the peak position and the peak height pre-\ndictions from these models disagree with the Belle mea-\nsurements. Therefore none of the models discussed here\ncan explain the data (Chernyak, 2012).\n\n712\n)\n2\n) (GeV/c\n\u03c6\n\u03c6\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n) (nb)\n\u03c6\n\u03c6\n\u2192\n\u03b3\n\u03b3(\n\u03c3\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n) (nb)\n(\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\ndata\n+\n0\n-2\n1.5\n2\n2.5\n3\n3.5\n4\n-3\n10\n-2\n10\n-1\n10\n1\n1.5\n2\n2.5\n3\n3.5\n4\n-3\n10\n-2\n10\n-1\n10\n1\n)\n2\n) (GeV/c\n\u03c9\n\u03c9\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n) (nb)\n\u03c9\n\u03c9\n\u2192\n\u03b3\n\u03b3(\n\u03c3\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\ndata\n+\n0\n+\n2\n1.5\n2\n2.5\n3\n3.5\n4\n-3\n10\n-2\n10\n-1\n10\n1\n10\n1.5\n2\n2.5\n3\n3.5\n4\n-3\n10\n-2\n10\n-1\n10\n1\n10\n)\n2\n) (GeV/c\n\u03c6\n\u03c9\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n) (nb)\n\u03c6\n\u03c9\n\u2192\n\u03b3\n\u03b3(\n\u03c3\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n)\n2\n) (GeV/c\nM(\n1.5\n2\n2.5\n3\n3.5\n4\n) (nb)\n(\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\ndata\n+\n0\n+\n2\n1.5\n2\n2.5\n3\n3.5\n4\n-3\n10\n-2\n10\n-1\n10\n(a)\n(b)\n(c)\nFigure 22.3.2. The cross sections of \u03b3\u03b3 \u2192\u03c9\u03c6 (a), \u03c6\u03c6 (b), and\n\u03c9\u03c9 (c) are shown as points with error bars. The cross sections\nfor di\ufb00erent JP values as a function of M(V V ) are shown as\nthe triangles and squares with error bars. The inset also shows\nthe cross section on a semi-logarithmic scale. In the high energy\nregion, the solid curve shows a \ufb01t to a W \u2212n\n\u03b3\u03b3 dependence for the\ncross section after the signi\ufb01cant charmonium contributions\n(\u03b7c, \u03c7c0 and \u03c7c2) were excluded. From (Liu, 2012).\nAs shown Belle \ufb01ts the W dependence of the cross\nsection with a form W \u2212n\n\u03b3\u03b3 . The results are shown, in the\ninset of Fig. 22.3.2 with solid curves. The \ufb01t gives n =\n7.2 \u00b1 0.6, 8.4 \u00b1 1.1, and 9.1 \u00b1 0.6 for the \u03c9\u03c6, \u03c9\u03c9, and \u03c6\u03c6\nmodes, respectively. These results are consistent with the\npredictions from pQCD (Chernyak, 2010).\n22.4 \u03b7\u2032\u03c0+\u03c0\u2212production\nThe invariant mass spectrum of the \u03b7\u2032\u03c0+\u03c0\u2212\ufb01nal state\nproduced in two-photon collisions is obtained using a 673\nfb\u22121 data sample by the Belle experiment. In addition to\nthe prominent \u03b7c signal, an enhanced shoulder is evident\nin the mass region below 2 GeV/c2 in the background-\nsubtracted distribution of Fig. 22.4.1 (Zhang, 2012).\n0\n50\n100\n150\n200\n250\n300\n1.5\n1.75\n2\n2.25\n2.5 2.75\n3\n3.25\nEntries/40MeV/c2\nM(\u03b7,\u03c0+\u03c0\u2212) [GeV/c2]\nFigure 22.4.1. Background subtracted invariant mass distri-\nbution for the \u03b7\u2032\u03c0+\u03c0\u2212candidates from (Zhang, 2012). The\npoints with error bars are the \u03b7\u2032\u03c0+\u03c0\u2212yields extracted from\n\ufb01tting the | P p \u2217\nt | distribution in each sliced mass bin. Here,\n| P p \u2217\nt | is determined by taking the absolute value of the vec-\ntor sum of the transverse momenta of \u03b7\u2032 and the \u03c0+\u03c0\u2212tracks\nin the e+e\u2212CM system.\nThe \ufb01rst evidence for decays of \u03b7(1760) to \u03b7\u2032\u03c0+\u03c0\u2212is\nreported, showing two solutions for its parameters, de-\npending on the inclusion or not of the X(1835) (Ablikim\net al., 2005b, 2011), whose existence is marginal in our\n\ufb01ts. The decay \u03b7(1760) \u2192\u03b7\u2032\u03c0+\u03c0\u2212is found with a sig-\nni\ufb01cance of 4.7\u03c3, with the assumption that the X(1835)\nis not produced; the \u03b7(1760) mass and width are de-\ntermined to be M = (1768+24\n\u221225 \u00b1 10) MeV/c2 and \u0393 =\n(224+62\n\u221256 \u00b1 25) MeV/c2. The \ufb01tted \u03b7(1760) mass is consis-\ntent with the existing measurements (Ablikim et al., 2006;\nBai et al., 1999; Bisello et al., 1987, 1989). The product\nof the two-photon decay width and the branching frac-\ntion for the \u03b7(1760) decay to \u03b7\u2032\u03c0+\u03c0\u2212is determined to be\n\u0393\u03b3\u03b3B(\u03b7(1760) \u2192\u03b7\u2032\u03c0+\u03c0\u2212) = (28.2+7.9\n\u22127.5\u00b13.7) eV/c2. When\nthe mass spectrum is \ufb01tted with two coherent resonances,\nthe \u03b7(1760) and X(1835), the \u03b7(1760) mass and width\nare found to be M = (1703+12\n\u221211 \u00b1 1.8) MeV/c2 and \u0393 =\n(42+36\n\u221222\u00b115) MeV/c2. The signal signi\ufb01cances including the\n\n713\nsystematic error are estimated to be 4.1\u03c3 for the \u03b7(1760)\nand 2.8\u03c3 for the X(1835). Upper limits on the product\n\u0393\u03b3\u03b3B for the X(1835) decay to \u03b7\u2032\u03c0+\u03c0\u2212at the 90% con\ufb01-\ndence level for the two \ufb01t solutions are \u0393\u03b3\u03b3B(X(1835) \u2192\n\u03b7\u2032\u03c0+\u03c0\u2212) < 35.6 eV/c2 with \u03c6 = (287+42\n\u221251)\u25e6for construc-\ntive interference and \u0393\u03b3\u03b3B(X(1835) \u2192\u03b7\u2032\u03c0+\u03c0\u2212) < 83\neV/c2 with \u03c6 = (139+19\n\u22129 )\u25e6for destructive interference.\nHere \u03c6 is the relative phase between X(1835) and \u03b7(1760).\nThe \ufb01t results provide a marginal preference for the in-\nterpretation of the X(1835) as a radial excitation of the\n\u03b7\u2032 (Huang and Zhu, 2006; Klempt and Zaitsev, 2007).\n22.5 Baryon-pair production\nTwo-photon collisions provide a clean environment for\nbaryon pair production, which is a useful laboratory to\nstudy baryon production mechanisms and the perturba-\ntive QCD prediction. A measurement of the simplest pro-\ncess, \u03b3\u03b3 \u2192pp, has been reported by the Belle experi-\nment (Kuo, 2005).\nGeneral theories of hard exclusive processes in QCD\npredict the dimensional counting rule (Sivers, Brodsky,\nand Blankenbecler, 1976) in the two-photon production\nprocesses of both meson and baryon pairs:\nd\u03c3\ndt = s2\u2212ncf(\u03b8\u2217)\n(22.5.1)\nat su\ufb03ciently high energy. Where s is the invariant-mass\nsquare of the \u03b3\u03b3 system and t is the Mandelstam variable\nbetween incident \u03b3 and p in the \ufb01nal state; \u03b8\u2217is the meson\nscattering angle in the two-photon CM system as de\ufb01ned\npreviously. The coe\ufb03cient nc is the number of elementary\nconstituents participating in the hard interaction. For the\ntwo-photonic baryon-pair production, nc is nc = 8, which\nleads171 to \u03c3 \u223cW \u221210 (for meson-pair production, nc =\n6 leads to \u03c3 \u223cW \u22126). The cross section is predicted to\nfall rapidly at high energies, and thus, its measurement is\nuseful to test this behavior.\nAs another approach, the handbag model (Diehl, Kroll,\nand Vogt, 2003) \u2014 discussed earlier for meson-pair pro-\nduction \u2014 also provides a prediction for the baryon pro-\nduction process. Thus, we can apply the same models\nfor both meson and baryon production phenomena from\nthe vacuum. Quasi-elementary diquark (qq) models might\nhave the potential to modify these predictions.\nIn Belle analysis, careful calibration of the trigger ef-\n\ufb01ciency for both track and energy triggers and a base ad-\njustment for time-of-\ufb02ight measurement is needed in order\nto cope with the particular experimental conditions for an\nexclusive \ufb01nal state of a proton and an antiproton.\nThe cross section integrated over the CM angle in the\nrange | cos \u03b8\u2217| < 0.6 has been obtained. The \ufb01t, accord-\ning to the power low (\u03c3 \u223cW \u2212n), provides n = 15.1+0.8\n\u22121.1\nand n = 12.4+2.4\n\u22122.3 in the range of W = 2.5 \u22122.9 GeV and\n3.2\u22124.0 GeV, respectively, as shown in Fig. 22.5.1. These\n171 Note that integration over t results in an additional factor\nof W 2.\nnumbers are signi\ufb01cantly larger than the meson-pair pro-\nduction case, and support the dimensional counting rule.\nThe result for the higher energy region is consistent with\nthe prediction with n = 10. While the measured cross\nsection is more compatible with the calculation based on\nthe diquark model with only helicity conserved ampli-\ntudes (Berger and Schweiger, 2003). Since precise data are\navailable for baryon-pair production in two-photon pro-\ncesses at high energy, improved theoretical understanding\nis needed.\nAs for the angular dependence of the di\ufb00erential cross\nsection, existing models can reproduce the general ten-\ndency, which shows a large-angle enhancement near the\nthreshold (below 2.4 GeV) and a small-angle enhancement\nat the high energies (above 2.7 GeV). However, at the in-\ntermediate and the available highest energies, agreement\nbetween the model predictions and the results remains\nunsatisfactory.\n Belle (|cose*| < 0.6)\n(a)\nfit with floating n\nn=15.1 (r2/ndf=0.36)\nn=12.4 (r2/ndf=0.52)\nWaa (GeV)\nm(aaApp\n<) (nb)\n10\n-3\n10\n-2\n10\n-1\n1\n10\n2\n2.2 2.4 2.6 2.8\n3\n3.2 3.4 3.6 3.8\n4\nFigure 22.5.1. Cross section for \u03b3\u03b3 \u2192p\u00afp. The solid and\ndotted lines show the results of separate \ufb01ts with \u03c3 \u221dW \u2212n\nto the data in the range of W = 2.5 \u22122.9 GeV and 3.2 \u2212\n4.0 GeV, respectively. The error bars include statistical and\nsystematic errors. The \u03c72/ndf values for each \ufb01t are indicated\nin the \ufb01gure. From (Kuo, 2005).\n22.6 Charmonium formation\nIn this section, we discuss only the two-photon decay width\n(\u0393\u03b3\u03b3) measurements of the charmonium(-like) states pro-\nduced by photon-photon formation. Related studies of new\nCharmonia or exotic charmonium-like particles and the\n\n714\nother properties of known or newly discovered states are\ndiscussed in other sections (18.2, 18.3).\nThe two-photon width of a charmonium(-like) parti-\ncle probes the internal structure of the resonance because\nit is sensitive to electric charge of the constituents and\nthe wave function near the central point. As a result,\nsuch measurements test QCD models that describe heavy\nquarkonia and help to identify possible exotic particles.\nMeasurements of production from two-photon collisions\ngive a direct way to measure this quantity in the presence\nof relatively small backgrounds.\nThe cross section for a single-resonance formation is\nproportional to the product of the two-photon decay width\nand the branching fraction to the \ufb01nal state(s) where the\ncharmonium is identi\ufb01ed, \u0393\u03b3\u03b3(R)B(R \u2192\ufb01nal state) (see\nEq. (22.1.5)). This is the direct observable from such mea-\nsurements. Then, knowledge of either \u0393\u03b3\u03b3(R) or B(R \u2192\n\ufb01nal state) with a reasonable accuracy from independent\nmeasurements permits us to extract the other property.\nWe summarize the measurements from the zero-tag\nmodes in Tables 22.6.1 and 22.6.2. The three well known\nCharmonia, \u03b7c, \u03c7c0 and \u03c7c2, have been measured exten-\nsively in various decay modes. According to Beringer et al.\n(2012), the two-photon decay widths of these states, \ufb01t-\nted to these measurements as well as branching fraction\nmeasurements in other processes, are more or less estab-\nlished and are dominated by the contributions from the B\nFactory two-photon measurements. Inconsistencies among\ndi\ufb00erent kinds of measurement remain in some decay modes\nof the \u03b7c. In addition, several new decay modes have been\nmeasured for the \ufb01rst time. For example, a new decay\nmode of \u03b7c(2S) to K+K\u2212\u03c0+\u03c0\u2212\u03c00 was reported by BABAR\nin the production process \u03b3\u03b3 \u2192\u03b7c(2S) (Lees, 2010b).\nThe new states \u03c7c2(2P), also denoted by Z(3930) (Ue-\nhara, 2006; Aubert, 2010g), X(3915) (Uehara, 2010b),(Lees,\n2012ad); and X(4350) (Shen, 2010a) were found in the\ntwo-photon process and thus proved that this test bed\nis useful in searching for new states. Table 22.6.2 shows\nan upper limit for the Y (4140) production (Shen, 2010a),\nwhich was observed in B decays by CDF (Aaltonen et al.,\n2009a). It also shows the \ufb01rst-ever measurement reported\nby CLEO for the \u03b7c(2S) state (Asner et al., 2004a).\nThe measured size of \u0393\u03b3\u03b3B for \u03c7c2(2P) \u2192DD is\nconsistent with the theoretical prediction (Uehara, 2006),\n(Aubert, 2010g). The measured \u0393\u03b3\u03b3B values for the \u03c7c2(2P)\nand \u03b7c(2S) have been cited as evidence of their identi\ufb01ca-\ntion as radially excited states of the sequential Charmo-\nnia. In contrast, the large value of \u0393\u03b3\u03b3B for X(3915) \u2192\n\u03c9J/\u03c8 (Uehara, 2010b),(Lees, 2012ad) has attracted inter-\nest in exploring the true nature of this state.\n22.7 Form factor measurements with\nsingle-tag processes\nTwo-photon production of the pseudoscalar mesons \u03c00 (Au-\nbert, 2009y), \u03b7 (del Amo Sanchez, 2011f), \u03b7\u2032 (del Amo San-\nchez, 2011f), and \u03b7c (Lees, 2010b) in the single-tag mode\nhas been studied by BABAR. Following these publications,\nTable 22.6.1. Measurements of the product of the two-photon\ndecay width and branching fraction (\u0393\u03b3\u03b3B) for charmonium\nstates. Upper limits correspond to a 90% con\ufb01dence level.\nDecay\n\u0393\u03b3\u03b3B (eV)\nReference\n\u03b7c\npp\n7.20 \u00b1 1.53 +0.67\n\u22120.75\nKuo (2005)\nKK\u03c0\n386 \u00b1 8 \u00b1 21\nLees (2010b)\n\u03b7\u2032\u03c0+\u03c0\u2212\n50.5+4.2\n\u22124.1 \u00b1 5.6\nZhang (2012)\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\n40.7 \u00b1 3.7 \u00b1 5.3\nUehara (2008b)\nK+K\u2212\u03c0+\u03c0\u2212\n25.7 \u00b1 3.2 \u00b1 4.9\nUehara (2008b)\nK+K\u2212K+K\u2212\n5.6 \u00b1 1.1 \u00b1 1.6\nUehara (2008b)\n\u03c1\u03c1\n< 39\nUehara (2008b)\nf2f2\n69 \u00b1 17 \u00b1 12\nUehara (2008b)\nK\u2217K\u2217\n32.4 \u00b1 4.2 \u00b1 5.8\nUehara (2008b)\nf2f \u2032\n2\n49 \u00b1 9 \u00b1 13\nUehara (2008b)\n\u03c6\u03c6\n7.75 \u00b1 0.66 \u00b1 0.62\nLiu (2012)\n\u03c9\u03c9\n8.67 \u00b1 2.86 \u00b1 0.96\nLiu (2012)\n\u03c9\u03c6\n< 0.49\nLiu (2012)\nK+K\u2212\u03c0+\u03c0\u2212\u03c00\n190 \u00b1 6 \u00b1 28\ndel Amo Sanchez\u2020\n\u03c7c0\n\u03c0+\u03c0\u2212\n15.1 \u00b1 2.1 \u00b1 2.3\nNakazawa (2005)\n\u03c00\u03c00\n9.7 \u00b1 1.5 \u00b1 1.2\nUehara (2009b)\nK+K\u2212\n14.3 \u00b1 1.6 \u00b1 2.3\nNakazawa (2005)\nK0\nSK0\nS\n5.57 \u00b1 0.56 \u00b1 0.39\nChen (2007c)\n\u03b7\u03b7\n9.4 \u00b1 2.3 \u00b1 1.2\nUehara (2010a)\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\n44.7 \u00b1 3.6 \u00b1 4.9\nUehara (2008b)\nK+K\u2212\u03c0+\u03c0\u2212\n38.8 \u00b1 3.7 \u00b1 4.7\nUehara (2008b)\nK+K\u2212K+K\u2212\n7.9 \u00b1 1.3 \u00b1 1.1\nUehara (2008b)\nK\u22170K\u2212\u03c0+or c.c.\n16.7 \u00b1 6.1 \u00b1 3.0\nUehara (2008b)\n\u03c1\u03c1\n< 12\nUehara (2008b)\nK\u2217K\u2217\n< 18\nUehara (2008b)\n\u03c6\u03c6\n1.72 \u00b1 0.33 \u00b1 0.14\nLiu (2012)\n\u03c9\u03c9\n< 3.9\nLiu (2012)\n\u03c9\u03c6\n< 0.34\nLiu (2012)\nK+K\u2212\u03c0+\u03c0\u2212\u03c00\n26 \u00b1 4 \u00b1 4\ndel Amo Sanchez\u2020\n\u03c7c2\n\u03c0+\u03c0\u2212\n0.76 \u00b1 0.14 \u00b1 0.11\nNakazawa (2005)\n\u03c00\u03c00\n0.18 +0.15\n\u22120.14 \u00b1 0.08\nUehara (2009b)\nK+K\u2212\n0.44 \u00b1 0.11 \u00b1 0.07\nNakazawa (2005)\nK0\nSK0\nS\n0.24 \u00b1 0.05 \u00b1 0.02\nChen (2007c)\n\u03b7\u03b7\n0.53 \u00b1 0.22 \u00b1 0.09\nUehara (2010a)\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\n5.01 \u00b1 0.44 \u00b1 0.55\nUehara (2008b)\nK+K\u2212\u03c0+\u03c0\u2212\n4.42 \u00b1 0.42 \u00b1 0.53\nUehara (2008b)\nK+K\u2212K+K\u2212\n1.10 \u00b1 0.21 \u00b1 0.15\nUehara (2008b)\n\u03c10\u03c0+\u03c0\u2212\n3.2 \u00b1 1.9 \u00b1 0.5\nUehara (2008b)\n\u03c1\u03c1\n< 7.8\nUehara (2008b)\nK\u2217K\u2217\n2.4 \u00b1 0.5 \u00b1 0.8\nUehara (2008b)\n\u03c6\u03c6\n0.62 \u00b1 0.07 \u00b1 0.05\nLiu (2012)\n\u03c9\u03c9\n< 0.64\nLiu (2012)\n\u03c9\u03c6\n< 0.04\nLiu (2012)\nKK\u03c0\n1.8 \u00b1 0.5 \u00b1 0.2\ndel Amo Sanchez\u2020\nK+K\u2212\u03c0+\u03c0\u2212\u03c00\n6.5 \u00b1 0.9 \u00b1 1.5\ndel Amo Sanchez\u2020\n\u2020 del Amo Sanchez (2011h)\n\n715\nTable 22.6.2. Measurements of the product of the two-photon\ndecay width and branching fraction (\u0393\u03b3\u03b3B) for charmonium-\nlike states. Some results depend on the assumption of the\nspin-parity (JP ) assignments shown. Upper limits shown cor-\nrespond to a 90% con\ufb01dence level.\nDecay\n\u0393\u03b3\u03b3B (eV)\nReference\n\u03b7c(2S):\nKK\u03c0\n73 \u00b1 20 \u00b1 8\nCLEO\u2217\n41 \u00b1 4 \u00b1 6\ndel Amo Sanchez\u2020\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212\n< 6.5\nUehara (2008b)\nK+K\u2212\u03c0+\u03c0\u2212\n< 5.0\nUehara (2008b)\nK+K\u2212K+K\u2212\n< 2.9\nUehara (2008b)\nK+K\u2212\u03c0+\u03c0\u2212\u03c00\n30 \u00b1 6 \u00b1 5\ndel Amo Sanchez\u2020\n\u03c7c2(2P)(Z(3930)):\nDD\n180 \u00b1 50 \u00b1 30\nUehara (2006)\n240 \u00b1 50 \u00b1 40\nAubert (2010g)\nKK\u03c0\n< 2.1\ndel Amo Sanchez\u2020\nK+K\u2212\u03c0+\u03c0\u2212\u03c00\n< 3.4\ndel Amo Sanchez\u2020\nothers:\nX(3915) \u2192\u03c9J/\u03c8\n61 \u00b1 17 \u00b1 8 (0+)\nUehara (2010b)\n52 \u00b1 10 \u00b1 3 (0+)\nLees (2012ad)\n18 \u00b1 5 \u00b1 2 (2+)\nUehara (2010b)\n10.5\u00b11.9\u00b10.6 (2+)\nLees (2012ad)\nY (4140) \u2192\u03c6J/\u03c8\n< 36 (0+)\nShen (2010a)\n< 5.3 (2+)\nShen (2010a)\nX(4350) \u2192\u03c6J/\u03c8\n6.7 +3.2\n\u22122.4 (0+)\nShen (2010a)\n1.5 +0.7\n\u22120.6 (2+)\nShen (2010a)\n\u2020 del Amo Sanchez (2011h)\n\u2217derived from Asner et al. (2004a)\nBelle reported their measurement of the \u03c00 production (Ue-\nhara, 2012). The amplitude of two-photon production of\na pseudoscalar meson is written as follows\nA = e2\u03b5\u00b5\u03bd\u03b1\u03b2e\u00b5\n1e\u03bd\n2q\u03b1\n1 q\u03b2\n2 F(q2\n1, q2\n2),\n(22.7.1)\nwhere \u03b5\u00b5\u03bd\u03b1\u03b2 is a Levi-Civita antisymmetric tensor and ei\nand qi are the polarization four-vectors and four-momenta\nof the photons. The e\ufb00ect of strong interactions in this\nprocess is described by the photon-meson transition form\nfactor F(q2\n1, q2\n2), which depends on the photon virtuali-\nties q2\n1 and q2\n2. In the single-tag mode, one of the photons\nis quasi-real, q2\n2 \u22480. The form factor is measured as a\nfunction of the squared momentum transfer to the tagged\n(detected) electron Q2 = \u2212q2\n1.\nIn theory, the\ntransition form factor F(Q2)\n\u2261\nF(\u2212Q2, 0) for the \u03c00 is calculated from \ufb01rst principles only\nin two extreme cases: at Q2 = 0 from the axial anomaly\nin the chiral limit of QCD, F(0) =\n\u221a\n2/(4\u03c02f\u03c0) (Adler,\n1969; Bell and Jackiw, 1969), and at Q2 \u2192\u221efrom per-\nturbative QCD (pQCD), Q2F(Q2) =\n\u221a\n2f\u03c0 (Lepage and\nBrodsky, 1980), where f\u03c0 \u22480.131 GeV is the pion de-\ncay constant. At large Q2 (Q2 \u226b\u039b2\nQCD) in the frame-\nwork of pQCD, the transition form factor can be repre-\nsented as the convolution of a calculable amplitude for\n\u03b3\u03b3\u2217\u2192qq with a non-perturbative meson distribution am-\nplitude (DA) \u03c6\u03c0(x, Q2) (Lepage and Brodsky, 1980). The\nlatter describes the transition of the meson with momen-\ntum P into two quarks with momenta Px and P(1 \u2212x).\nIn lowest order pQCD, the photon-pion transition form\nfactor is given by\nQ2F(Q2) =\n\u221a\n2f\u03c0\n3\nZ 1\n0\ndx\nx \u03c6\u03c0(x, Q2)+O(\u03b1s)+O\n \n\u039b2\nQCD\nQ2\n!\n,\n(22.7.2)\nwhere \u039bQCD is the QCD scale parameter.\nThe meson DA plays an important role in theoretical\ndescriptions of many QCD processes (\u03b3\u2217\u2192\u03c0+\u03c0\u2212, \u03b3\u03b3 \u2192\n\u03c0+\u03c0\u2212, and B \u2192\u03c0l\u03bdl, for example). The shape of DA (i.e.,\nthe x dependence) is unknown, but its evolution with Q2\nis predicted by pQCD. The models for DA\u2019s can be tested\nusing data on the photon meson transition form-factors.\nIt is instructive to estimate the sizes of the NLO\npQCD and power corrections for Eq. (22.7.2). For this,\nwe use results of the form-factor calculation with the\nasymptotic DA \u03c6ASY(x) = 6x(1 \u2212x) (Lepage and Brod-\nsky, 1979a) from Bakulev, Mikhailov, and Stefanis (2003,\n2004). The NLO contribution (Braaten, 1983; del Aguila\nand Chase, 1981) varies from 15% to 10% in the Q2\nrange of 4 to 50 GeV2 in the BABAR measurements. The\npower correction, estimated using the light-cone sum rule\nmethod (Khodjamirian, 1999; Schmedding and Yakovlev,\n2000) (where the twist-4 contribution is also taken into ac-\ncount), is about 15% at 4 GeV2 and falls to about 2% at\nQ2 = 20 GeV2. The calculation of the power correction\nis model-dependent. It is di\ufb03cult to estimate the corre-\nsponding model uncertainty so it is important to perform\nform-factor measurements at the largest possible values\nof Q2. At the center-of-mass energy \u221as = 10.6 GeV, the\ne+e\u2212\u2192e+e\u2212\u03c00 di\ufb00erential cross section d\u03c3/dQ2 is about\n10 fb/ GeV2 at Q2 = 10 GeV2. It falls with increasing Q2\nas Q\u22126. The most precise measurement of the form factors\nprior to BABAR was made by CLEO using data collected\nat \u03a5(4S) with an integrated luminosity of 3 fb\u22121. The\n\u03b3\u03b3\u2217\u03c00 form factor was measured for Q2 up to 8 GeV2.\nThe B Factory measurements have extended the Q2 re-\ngion up to 40 GeV2. These measurements are described\nin the following section.\n22.7.1 The \u03b3\u03b3\u2217\u03c00 transition form factor\nThe process e+e\u2212\u2192e+e\u2212\u03c00 in the single-tag mode has\nspeci\ufb01c features that complicate its experimental study.\nThe event contains only three detectable particles: two\nphotons from \u03c00 decay and an electron. Such events, with\nonly one charged track and low multiplicity, are rejected\nby the standard BABAR trigger and o\ufb04ine \ufb01lters. Fortu-\nnately, a special trigger line was designed at BABAR to\nselect so-called virtual Compton scattering (VCS) events\nfor electromagnetic-calorimeter calibration. VCS is the\n\n716\ne+e\u2212\u2192e+e\u2212\u03b3 process in the speci\ufb01c kinematical con-\n\ufb01guration in which one of the \ufb01nal electrons moves along\nthe collision axis while the other electron and photon are\nemitted at large angles. The VCS trigger selects events\nin which the detected electron plus photon system has a\nsmall transverse momentum and the recoil mass close to\nzero. For most of e+e\u2212\u2192e+e\u2212\u03c00 events, the close pho-\ntons from \u03c00 decay cannot be separated by the trigger\ncluster algorithm and are identi\ufb01ed as a single photon.\nTherefore, the VCS trigger has relatively large e\ufb03ciency\nfor events of the process under study (50\u201380%, depending\non the \u03c00 energy).\nThe second feature is the large QED background. The\nmain background source is VCS. There is also a sizable\nbackground from the e+e\u2212\u2192e+e\u2212\u03b3\u03b3 process in which\none of the \ufb01nal electrons is soft and one of the photons is\nemitted along the beam axis. The photon from the QED\nprocess, together with a soft photon (from beam back-\nground, for example) may give the invariant mass close to\nthe \u03c00 mass. Special selection criteria described in detail in\nAubert (2009y) are applied to suppress QED background.\nAfter QED background suppression, the signal events\nare selected by the requirements that there are electron\nand \u03c00 candidates in an event with energies above 2.0 and\n1.5 GeV, respectively, and that the electron plus \u03c00 sys-\ntem has a small transverse momentum and a recoil mass\nclose to zero. To avoid systematic uncertainty due to pos-\nsible data-simulation di\ufb00erences in detector response near\nthe detector edges, the e+e\u2212\u2192e+e\u2212\u03c00 cross section is\nmeasured in the region Q2 > 4 GeV2, where the detection\ne\ufb03ciency for signal events is greater than 5%. The Q2 re-\ngion from 4 to 40 GeV2 is divided into 17 intervals. For\neach interval, the number of signal events is determined\nfrom the \ufb01t to the two-photon invariant mass spectrum\nwith a sum of a \u03c00 resolution function and a polynomial\nbackground distribution. For Q2 > 40 GeV2, no evidence\nof a signal over background is found in the two-photon\ninvariant mass distribution. The total number of events\nwith a \u03c00 in the Q2 range 4\u201340 GeV2 is about 14000.\nSome events containing a \u03c00 may arise from back-\nground processes such as e+e\u2212annihilation, vector-meson\nbremsstrahlung e+e\u2212\u2192e+e\u2212V , and two-photon pro-\ncesses with higher multiplicity \ufb01nal states such as e+e\u2212\u2192\ne+e\u2212\u03c00\u03c00.\nThe e+e\u2212annihilation background is estimated us-\ning the di\ufb00erence in the distributions of the e\u00b1\u03c00 mo-\nmentum z-component for signal and background. In two-\nphoton events with a tagged positron (electron), the mo-\nmentum z-component is negative (positive), while anni-\nhilation events are produced symmetrically. The annihi-\nlation background is assumed to be equal to the number\nevents with the wrong sign of the e\u00b1\u03c00 momentum z-\ncomponent and is found to be negligible.\nThe largest bremsstrahlung background is expected to\narise from the process e+e\u2212\u2192e+e\u2212\u03c9 with \u03c9 decaying\nto \u03c00\u03b3. The background is estimated from the number of\ndata events with an extra photon, in which the invari-\nant mass of the \u03c00\u03b3 system is close to the \u03c9 mass. This\nbackground is also found to be negligible.\nThe main source of the peaking background is the pro-\ncess e+e\u2212\u2192e+e\u2212\u03c00\u03c00. To estimate this background,\nevents with an extra \u03c00 are selected in data. The number\nof selected e+e\u2212\u2192e+e\u2212\u03c00\u03c00 data events is then scaled\nto the standard selection using a scale factor determined\nfrom MC simulation for the e+e\u2212\u2192e+e\u2212\u03c00\u03c00 process.\nThe fraction of two-photon background events in the e\u03c00\ndata sample is found to be about 13% for Q2 < 10 GeV2\nand decreases to 6\u20137% for Q2 > 10 GeV2.\nThe Q2 dependence of the detection e\ufb03ciency is de-\ntermined from MC simulation. The MC e\ufb03ciency is cor-\nrected for a possible data-MC simulation di\ufb00erence in elec-\ntron identi\ufb01cation, trigger ine\ufb03ciency, \u03c00 detection ef-\n\ufb01ciency, recoil-mass and transverse-momentum distribu-\ntions. The identi\ufb01cation and trigger corrections are de-\ntermined from the control sample of VCS events. The\n\u03c00 e\ufb03ciency is studied by using events of the process\ne+e\u2212\u2192\u03c9\u03b3, \u03c9 \u2192\u03c0+\u03c0\u2212\u03c00, which are selected and re-\nconstructed using measured parameters of only the two\ncharged tracks and the photon. A total e\ufb03ciency correc-\ntion is found to be about 7% and depends weakly on Q2.\nThe systematic uncertainty associated with the e\ufb03ciency\ncorrection is about 2.5%.\nThe transition form factor F(Q2) is extracted by com-\nparing the measured and calculated values of the di\ufb00eren-\ntial cross section d\u03c3/dQ2. The cross-section measurement\nis performed at small (less than 0.18 GeV2) but non-zero\nvalues of the momentum transfer to the untagged elec-\ntron, |q2\n2|. This leads to a model uncertainty in the F(Q2)\nvalues extracted from the experiment due to the unknown\ndependence of the transition form factor on q2\n2. This model\nuncertainty is estimated from comparison of the F(Q2)\nvalues obtained with two di\ufb00erent models for the q2\n2 depen-\ndence: the QCD-inspired model F(q2\n1, q2\n2) \u221d1/(q2\n1 + q2\n2) \u2248\n1/q2\n1 with the form factor practically independent of q2\n2,\nand the vector dominance model F(q2\n2) \u221d1/(1 \u2212q2\n2/m2\n\u03c1),\nwhere m\u03c1 is the \u03c1 meson mass. The model uncertainty in\nthe form factor is estimated to be 1.8%.\nThe Q2 dependence of the scaled \u03b3\u03b3\u2217\u03c00 transition form\nfactor Q2F(Q2) obtained in the BABAR experiment, to-\ngether with the CLEO (Gronberg et al., 1998) and CELLO\n(Behrend et al., 1991) results, is shown in Fig. 22.7.1.\nThe errors shown are statistical and Q2-dependent sys-\ntematic uncertainties combined in quadrature. The Q2-\ndependent systematic uncertainty, which is of the same\norder of magnitude as the statistical one, is dominated\nby the uncertainties from the \ufb01tting procedure and back-\nground subtraction. The Q2-independent systematic un-\ncertainty, not shown in Fig. 22.7.1, is equal to 2.3% and\nincludes uncertainties in the e\ufb03ciency correction, radia-\ntive correction, integrated luminosity, and the model un-\ncertainty discussed above. In the Q2 region 4-9 GeV2 the\nBABAR results are in reasonable agreement with the CLEO\nmeasurements (Gronberg et al., 1998), but have signi\ufb01-\ncantly better precision.\nAt Q2 > 10 GeV2, the measured form factor exceeds\nthe asymptotic limit predicted by pQCD (Lepage and\nBrodsky, 1980), which is indicated in Fig. 22.7.1 by the\nhorizontal line. Such behavior is speci\ufb01c for a \u201cwide\u201d pion\n\n717\nCELLO\nCLEO\nBABAR\nCZ\nASY\nBMS\nQ2 (GeV2)\nQ2|F(Q2)| (GeV)\n0\n0.1\n0.2\n0.3\n0\n10\n20\n30\n40\nFigure 22.7.1. The scaled \u03b3\u03b3\u2217\u03c00 transition form factor. The\ndashed line indicates the asymptotic limit. The solid line, dot-\nted line, and shaded band represent the predictions for the\nform factor (Bakulev, Mikhailov, and Stefanis, 2003, 2004) for\nthe Chernyak and Zhitnitsky (1982) [CZ], asymptotic (Lepage\nand Brodsky, 1979a) [ASY], and Bakulev, Mikhailov, and Ste-\nfanis (2001) [BMS] models for the pion distribution amplitude,\nrespectively.\nDA. The shapes of three selected DA\u2019s [asymptotic (Lep-\nage and Brodsky, 1979a); Chernyak and Zhitnitsky (1982);\nand Bakulev, Mikhailov, and Stefanis (2001)] with dif-\nferent widths are shown in Fig. 22.7.2 for Q2 = 5.76\nGeV2. The values of the Gegenbauer coe\ufb03cients a2 and a4\nused for calculation of the DA\u2019s are taken from Bakulev,\nMikhailov, and Stefanis (2003, 2004). The form factors\ncorresponding to these DA\u2019s (Bakulev, Mikhailov, and\nStefanis, 2003, 2004) are presented in Fig. 22.7.1. None of\nthese models describe the data satisfactorily in the full Q2\nrange of the BABAR measurement. From the three mod-\nels only one \u2014 with the widest Chernyak-Zhitnitsky DA\n\u2014 gives the form factor exceeding the asymptotic limit.\nThe prediction of this model is not inconsistent with the\nBABAR data in the region Q2 > 15 GeV2, where power\ncorrections are expected to be small.\nMany theoretical papers devoted to the \u03b3\u03b3\u2217\u03c00 tran-\nsition form factor appeared after the BABAR publication.\nThere is no consensus on the theoretical description of\nthe BABAR data at the time of writing. Some publications\n\u2014 for example, Bakulev, Mikhailov, Pimikov, and Stefa-\nnis (2011); Roberts, Roberts, Bashir, Gutierrez-Guerrero,\nand Tandy (2010)\u2014argue that the form-factor data can-\nnot be described by theory in the full Q2 region cov-\nered by the CLEO and BABAR experiments, and that\nthe BABAR data are likely to be incorrect for Q2 > 9\nGeV2. Other authors obtain reasonable descriptions of the\ndata using relatively wide DA\u2019s: see, for example, Agaev,\nBraun, O\ufb00en, and Porkert (2011); Kroll (2011). Note\nthat Bakulev, Mikhailov, Pimikov, and Stefanis (2011)\nand Agaev, Braun, O\ufb00en, and Porkert (2011) use the\nsame light-cone sum rule method to estimate power cor-\nx\nq(x)\n0\n0.5\n1\n1.5\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 22.7.2. The pion distribution amplitudes at Q2 =\n5.76 GeV2 for three models: asymptotic (Lepage and Brodsky,\n1979a) [solid line], Chernyak and Zhitnitsky (1982) [dashed\nline], and Bakulev, Mikhailov, and Stefanis (2001) [dotted line].\nrections but draw completely di\ufb00erent conclusions. The\nthird group of theoretical evaluations, Dorokhov (2010);\nPolyakov (2009); Radyushkin (2009), suggests the use of\nan unconventional pion DA, which is non-zero at the end\npoints x = 0, 1. The transition form factor obtained with\nsuch DA increases logarithmically with increasing Q2 and\ndescribes data well.\nThe BABAR measurement (Aubert, 2009y) covers the\nQ2 region above 10 GeV2 for the \ufb01rst time and, in this\nregion, the form factor goes above the prediction of the\nasymptotic QCD value with a rather steep increase. This\nresult has attracted the interest of many theoretical physi-\ncists as described above. An independent measurement of\nthe pion form factor was much desired and was provided\nby Belle (Uehara, 2012) using data corresponding to an in-\ntegrated luminosity of 759 fb\u22121. The selection of the signal\nevents, the background reduction, and the analysis were\nmade using methods similar to those used in the BABAR\nanalysis.\nIn this Belle analysis, event triggers to collect the sig-\nnal events are provided by the electromagnetic calorimeter\nsystem. The main trigger, the total energy trigger with a\nhigh-energy threshold (high-energy trigger), is vetoed by\nthe Bhabha trigger logic (the Bhabha trigger, to detect\nBhabha events) to avoid polluting the high-energy trigger\nwith Bhabha events. This mechanism brings a signi\ufb01cant\nloss of the e\ufb03ciency for the signal process e+e\u2212\u2192e(e)\u03c00\nand has the side e\ufb00ect of reducing a fraction of the ac-\nceptance. Here the symbol (e) indicates the electron scat-\ntered in the forward direction and then is not detected.\nThis condition in Belle is in contrast to the BABAR mea-\nsurement, where a special salvaging mechanism for such\nevents was used. Due to this situation in Belle, a compli-\ncated selection condition for the polar-angle combinations\nof the electron and the two-photon system were imposed\n\n718\nto reduce the uncertainty of the trigger ine\ufb03ciency caused\nby the Bhabha veto.\nRadiative-Bhabha events with a VCS con\ufb01guration\nwere used for the calibration of the trigger system. Com-\nbining event samples collected by the high-energy trig-\nger and by the Bhabha trigger (the latter taken with a\nprescale factor 50) and compensating for the e\ufb00ect from\nthe Bhabha veto statistically, the trigger e\ufb03ciency was\ndetermined as a function of the energy deposit. The MC\nevents, generated by the Rabhat program (Tobimatsu\nand Shimizu, 1989) for the radiative-Bhabha process, are\nfed to the trigger simulator code. The thresholds of the\nBhabha trigger have thus been tuned to reproduce the\nexperimentally determined e\ufb03ciencies. The cross section\nfrom the Rabhat program has also enabled a comparison\nof the absolute experimental yields with those of the MC\nsample after the tuning of the trigger simulation to ver-\nify the e\ufb03ciency determination. This study validates the\ntrigger e\ufb03ciency at the 10% level.\nIn the Belle analysis, background contributions from\nboth e+e\u2212\u2192e(e)\u03c00\u03c00 and e+e\u2212\u2192e(e)\u03c00\u03b3 production\nprocesses are anticipated by studies. Belle actively collect\nthese backgrounds and measures the yield of these pro-\ncesses by requiring the detection of an additional pion or\nphoton. The observed yields are introduced into a MC\ngenerator for the background processes, and the contam-\nination in the signal sample is estimated. The result is\nabout 2% for the e+e\u2212\u2192e(e)\u03c00\u03c00, and is 0.8% \u2013 3% de-\npending on Q2 for e+e\u2212\u2192e(e)\u03c00\u03b3. These contributions\nare subtracted from the measured signal yield.\nAmong systematic uncertainties from di\ufb00erent sources\nthat are assigned to the cross section, the biggest con-\ntributions come from the extraction of the \u03c00 yield with\nthe \ufb01t and the uncertainty of the trigger e\ufb03ciency; they\ndepend largely on the Q2 regions. The total systematic\nuncertainty for the combined cross section is between 8%\nand 14% (and between 4% and 7% for the form factor),\ndepending on the Q2 region.\nThe Belle result for the transition form factor is shown\nin Fig. 22.7.3 together the results of the previous measure-\nments. It is compared with the asymptotic QCD predic-\ntion shown by the dashed line. Belle has applied a \ufb01t to a\nparameterization with an asymptotic limit, Q2|F(Q2)| =\nBQ2/(Q2 + C). The obtained result for the asymptotic\nvalue, B = 0.209 \u00b1 0.016 GeV, is slightly larger than the\nQCD prediction but still consistent with it. The \ufb01t curve\nis shown in the \ufb01gure.\nThe values of Q2|F(Q2)| measured by Belle agree with\nthe previous measurements (Aubert (2009y), Behrend et al.\n(1991); Gronberg et al. (1998)), for Q2 <\n\u223c9 GeV2. The\napparent systematic shift between Belle and BABAR cor-\nresponds to a 2.3\u03c3 di\ufb00erence in the Q2 region between\n9 GeV2 and 20 GeV2, taking into account both statisti-\ncal and systematic uncertainties in the two measurements.\nThe Belle result does not show a rapid growth of the form\nfactor beyond the asymptotic prediction of QCD, in con-\ntrast to the BABAR result, and is closer to the theoretical\npredictions.\nQ\n2\n \n(GeV\n2\n)\nQ \n2\n|F(Q\n2\n)| (GeV)\n0.2\n0.25\n0.3\n0.35\n0\n0.05\n0.1\n0.15\n0\n10\n20\n3 0\n40\nBa Bar\nCL EO\nCELLO\nBe lle\nfit(A)\nfit(A)\nfit(B)\nFigure 22.7.3. Comparison of the results for the product\nQ2|F(Q2)| for the \u03c00 from di\ufb00erent experiments. The curves\nare from the \ufb01ts (A) to \u223c(Q2/10 GeV2)\u03b2 and (B) to \u223c\nQ2/(Q2+C). The dashed line shows the asymptotic prediction\nfrom pQCD (\u223c0.185 GeV).\n22.7.2 The \u03b3\u03b3\u2217\u03b7 and \u03b3\u03b3\u2217\u03b7\u2032 transition form factors\nThe meson-photon transition form factors for \u03b7 and\n\u03b7\u2032 have been measured by BABAR in the e+e\u2212\n\u2192\ne+e\u2212\u03b7(\u2032)\n(del\nAmo\nSanchez,\n2011f)\nand\ne+e\u2212\n\u2192\n\u03b7(\u2032)\u03b3 (Aubert, 2006w) reactions. The decay modes \u03b7\u2032 \u2192\n\u03c0+\u03c0\u2212\u03b7, \u03b7 \u2192\u03b3\u03b3 and \u03b7 \u2192\u03c0+\u03c0+\u03c00 are used to re-\nconstruct \u03b7\u2032 and \u03b7 mesons, respectively. For single-tag\ne+e\u2212\u2192e+e\u2212\u03b7 events, \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00 is the only decay\nmode available for analysis. The events with neutral \u03b7 de-\ncays, to 2\u03b3 and to 3\u03c00, do not pass the BABAR trigger and\nbackground \ufb01lters.\nIn contrast to the e+e\u2212\u2192e+e\u2212\u03c00 process, the QED\nbackground for the processes e+e\u2212\u2192e+e\u2212\u03b7(\u2032) is almost\nfully rejected by the requirement that charged-pion can-\ndidates be identi\ufb01ed as pions. The hadron background\nfrom e+e\u2212annihilation is suppressed by the requirement\nof electron identi\ufb01cation. As a result, after applying the\ntransverse-momentum and recoil-mass conditions e+e\u2212\u2192\ne+e\u2212\u03b7(\u2032) events are selected with low non-peaking back-\nground. The numbers of events containing true \u03b7 and \u03b7\u2032\nare determined from the \ufb01t to the \u03c0+\u03c0+\u03c00 and \u03c0+\u03c0\u2212\u03b7\nmass distributions with a sum of an \u03b7(\u2032) resolution func-\ntion and a linear non-peaking background distribution.\nThe \ufb01t is performed in 11 Q2 intervals from the Q2 range\n4\u201340 GeV2. Above 40 GeV2 all observed \u03b7(\u2032) candidates\nare expected to originate from background. The \ufb01tted\nnumber of \u03b7 and \u03b7\u2032 events in the Q2 range 4\u201340 GeV2\nis about 3000 and 5000, respectively.\nFor \u03b7\u2032 events the only observed source of peaking back-\nground is e+e\u2212annihilation. The contribution of e+e\u2212an-\nnihilation is estimated using events with the wrong sign of\nthe e\u00b1\u03b7\u2032 momentum z-component, and subtracted. This\nbackground is important only in the two highest-Q2 inter-\nvals (Q2 > 25 GeV2), where it reaches about 10%.\nFor \u03b7 events, three sources of peaking background are\nstudied and subtracted. These are the e+e\u2212annihilation\n\n719\nand the two-photon processes e+e\u2212\u2192e+e\u2212\u03b7\u03c00 and e+e\u2212\n\u2192e+e\u2212\u03b7\u2032 with \u03b7\u2032 decaying to \u03c00\u03c00\u03b7. The contributions\nof the e+e\u2212annihilation and the e+e\u2212\u2192e+e\u2212\u03b7\u03c00 back-\nground are estimated using the di\ufb00erence between signal\nand background events in the distribution of the e\u00b1\u03b7 recoil\nmass and are found to be about 15% of signal events.\nThe measured scaled \u03b3\u03b3\u2217\u03b7 and \u03b3\u03b3\u2217\u03b7\u2032 transition form\nfactors are shown in Fig. 22.7.4 as functions of Q2. The\nCLEO* (a\u009ba A d)\nCLEO (e+e- A da)\nBABAR (a\u009ba A d)\nBABAR (e+e- A da)\n(a)\nQ2 (GeV2)\nQ2F(Q2) (GeV)\n0\n0.1\n0.2\n0.3\n10\n10\n2\nCLEO* (a\u009ba A d/)\nCLEO (e+e- A d/a)\nBABAR (a\u009ba A d/)\nBABAR (e+e- A d/a)\n(b)\nQ2 (GeV2)\nQ2F(Q2) (GeV)\n0\n0.1\n0.2\n0.3\n10\n10\n2\nFigure 22.7.4. Scaled (a) \u03b3\u03b3\u2217\u03b7 and (b) \u03b3\u03b3\u2217\u03b7\u2032 transition form\nfactors. The dashed lines indicate the asymptotic limits for\nthe form factors. From (del Amo Sanchez, 2011f) and (Aubert,\n2006w).\nquoted errors are statistical and Q2-dependent system-\natic uncertainty combined in quadrature. The latter in-\nclude the systematic uncertainty in the number of signal\nevents due to the \ufb01tting procedure and background sub-\ntraction as well as the statistical errors on the e\ufb03ciency\ncorrection and MC simulation, and do not exceed 50% of\nthe statistical error. The Q2-independent systematic error\nis about 3% and includes uncertainties in the e\ufb03ciency\ncorrection, radiative correction, integrated luminosity, \u03b7(\u2032)\ndecay branching fractions, and the model uncertainty due\nto the unknown dependence of the transition form fac-\ntor on the momentum transfer to the untagged electron.\nFigure 22.7.4 shows also results of the CLEO measure-\nment (Gronberg et al., 1998). BABAR has improved sig-\nni\ufb01cantly the precision and has extended the Q2 region\nfor form factor measurements relative to CLEO. For \u03b7\u2032,\nthe BABAR and CLEO data are in good agreement. For \u03b7,\nthe agreement is worse. The CLEO point at 7 GeV2 lies\nhigher than the BABAR data by about 3\u03c3.\nThe e+e\u2212\u2192\u03b7(\u2032)\u03b3 reactions can also be used to de-\ntermine the transition form factors in the time-like region\n(q2 > 0). The form factors at Q2 = 14.2 GeV2 are ob-\ntained from the values of the e+e\u2212\u2192\u03b7(\u2032)\u03b3 cross sections\nmeasured by CLEO (Pedlar et al., 2009) near the maxi-\nmum of the \u03c8(3770) resonance. The assumption is used\nthat the contributions of the \u03c8(3770) \u2192\u03b7(\u2032)\u03b3 decays to\nthe cross sections are negligible. The CLEO form factors\nin both the time-like and space-like q2 regions are com-\npared in Fig. 22.7.4; they are expected to be close to each\nother at high Q2. The CLEO measurements support this\nhypothesis. Therefore, the BABAR measurements of the\ne+e\u2212\u2192\u03b7(\u2032)\u03b3 cross sections (Aubert, 2006w) near the\nmaximum of the \u03a5(4S) resonance can be used to extend\nthe Q2 region for the \u03b7 and \u03b7\u2032 form-factor measurements\nup to 112 GeV2. The time-like form-factor values at 112\nGeV2 are shown in Fig. 22.7.4.\nTheoretical interpretation of the results on the \u03b7 and\n\u03b7\u2032 form factors takes into account the \u03b7 \u2212\u03b7\u2032 mixing and\nan admixture of the gluon component in the SU(3)-singlet\nstate. The dashed lines in Fig. 22.7.4 indicate the asymp-\ntotic limits for the scaled \u03b7 and \u03b7\u2032 form factors. They are\ncalculated using mixing parameters from Kroll (2011). It\nis seen that Q2 dependencies of the form factors for \u03b7 and\n\u03b7\u2032 di\ufb00er from those for \u03c00. On the other hand, there is an\nindication that the \u03b7 form factor exceeds the asymptotic\nlimit at large Q2. The theoretical analyses (see, for exam-\nple, Agaev (2010); Brodsky, Cao, and de Teramond (2011);\nKroll (2011); Noguera and Scopetta (2012)) show that the\n\u03b7 and \u03b7\u2032 form-factor data are reasonably well reproduced\nby models with DA\u2019s not very di\ufb00erent from the asymp-\ntotic one. The BABAR results on the meson-photon transi-\ntion form factors for light pseudoscalars indicate that the\npion DA is signi\ufb01cantly wider than the DA\u2019s of \u03b7 and \u03b7\u2032\nmesons. However, Belle results do not exhibit such rapid\ngrowth in the higher Q2 region seen in the BABAR. So fur-\nther investigations are very important for understanding\nof the pion DA.\n22.7.3 The \u03b3\u03b3\u2217\u03b7c transition form factor\nThe meson-photon transition form factor for \u03b7c has been\nmeasured by BABAR (Lees, 2010b) using single-tag events\nof the e+e\u2212\u2192e+e\u2212\u03b7c process. The \u03b7c is reconstructed\nvia its decay to KSK\u2212\u03c0+. Since the branching fraction\nfor \u03b7c \u2192KSK\u2212\u03c0+ is known with low accuracy, it is\nimpossible to perform an absolute measurement of the\n\n720\nform factor. Therefore, the Q2 distribution for selected\n\u03b7c events is divided by the number of no-tag two-photon\n\u03b7c \u2192KSK\u2212\u03c0+ events, and the normalized form factor\nF(Q2)/F(0) is measured.\nThe number of single-tag events containing \u03b7c me-\nson is determined from the \ufb01t to the KSK\u2212\u03c0+ invariant\nmass distributions with a sum of an \u03b7c resolution func-\ntion, a J/\u03c8 resolution function, and a quadratic back-\nground distribution. The J/\u03c8\u2019s are produced in the pro-\ncess e+e\u2212\u2192e+e\u2212J/\u03c8. The \ufb01tted number of \u03b7c events in\nthe Q2 region from 2 to 50 GeV2 is about 500. To obtain\nthe Q2 distribution this region is divided into 11 intervals.\nThe process e+e\u2212\u2192e+e\u2212J/\u03c8 with J/\u03c8 decaying to\n\u03b7c\u03b3 is the dominant source of background peaking at \u03b7c\nmass. The background is estimated from the Q2 distribu-\ntion for e+e\u2212\u2192e+e\u2212J/\u03c8 events with J/\u03c8 \u2192KSK\u2212\u03c0+.\nIts fraction changes from about 1.0% for Q2 < 10 GeV2\nto about 5% at Q2 \u223c30 GeV2.\nQ2 (GeV2)\n|F(Q2)/F(0)|\n0\n0.2\n0.4\n0.6\n0.8\n1\n0\n10\n20\n30\n40\n50\nFigure 22.7.5. The normalized \u03b3\u03b3\u2217\u03b7c transition form factor\nmeasured by BABAR. The curve shows the \ufb01t with a monopole\nfunction. From (Lees, 2010b).\nThe normalized \u03b7c transition form factor is shown in\nFig. 22.7.5. The errors shown are combined statistical and\nQ2-dependent systematic uncertainty. There is also a Q2-\nindependent error equal to 4.3%. The main source of the\nsystematic error is an uncertainty on the detection e\ufb03-\nciency.\nFor the \u03b7c meson, the leading order formula for the\nlight-meson transition form factor is modi\ufb01ed to take into\naccount the large mass of the c-quark. The term 1/x in\nEq. (22.7.2) should be replaced with Q2/[xQ2 + m2\nc(1 +\n4xx)], where x = 1 \u2212x, and mc is the c-quark mass. As a\nconsequence, the \u03b3\u03b3\u2217\u03b7c transition form factor can be pre-\ndicted by pQCD starting from Q2 = 0. However, the Q2\ndependence of the form factor becomes rather insensitive\nto the shape of the \u03b7c DA, and is described by a monopole\nfunction with a pole parameter \u039b \u223c10 GeV2 (Feldmann\nand Kroll, 1997). This value is close to the vector-meson\ndominance model (VDM) prediction \u039b = m2\nJ/\u03c8 = 9.6\nGeV2.\nThe result of the \ufb01t to the BABAR data on the normal-\nized \u03b7c form factor with a monopole function is shown in\nFig. 22.7.5. The extracted pole parameter \u039b = 8.5 \u00b1 0.6 \u00b1\n0.7 GeV2 is in agreement with both VDM and QCD (Feld-\nmann and Kroll, 1997) predictions, and with the result of\nthe lattice QCD calculation \u039b = 8.4 \u00b1 0.4 GeV2 (Dudek\nand Edwards, 2006).\n22.7.4 Summary\nTwo-photon physics has entered a completely new level of\nmaturity as a result of the B Factory experiments. Prior\nto the B Factories, two-photon couplings of resonances\nhave been measured for a limited number of mesons only,\nand many of those were only known approximately. The B\nFactory experiments have provided precise measurements\nand opened a path to the systematic study of spectroscopy\nincluding classi\ufb01cation of mesons and exploration of exotic\nand new states.\nIn addition, the measurements of exclusive processes\nof hadron-pair production and of two-photon meson tran-\nsition form factors have become practical tests of QCD\nusing data from the the B Factory experiments.\nWhile many phenomena have been investigated, some\nsubjects are still left to be clari\ufb01ed because of systematic\nuncertainties in experiments or yet-to-be developed the-\noretical frameworks. In some other subjects, insu\ufb03cient\nstatistics prevent us from obtaining a clear view. It is ex-\npected that future projects will be able to signi\ufb01cantly\nadvance our understanding in this area.\n\n721\nChapter 23\nB0\ns physics at the \u03a5 (5S)\nEditors:\nAlexey Drutskoy (Belle)\nAdditional section writers:\nSevda Esen, Brian Hamilton, Jin Li, Alan Schwartz\n23.1 Introduction\nIn this section we discuss the results of B0\ns meson stud-\nies using BABAR and Belle data collected with a center-of-\nmass (CM) energy in the region of the \u03a5(5S) resonance.172\nThe experimental exploration of this region was started in\n1985 by the CUSB Collaboration (Lovelock et al., 1985)\nand since then much has been learned about B0\ns decays\nusing data from the \u03a5(5S). Future super \ufb02avor factories\ninclude B0\ns studies in their physics proposals as an impor-\ntant part of their research program.\nExperimental determination of the B0\ns meson began\ncirca 1990 at CUSB II (Lee-Franzini et al., 1990). Subse-\nquently B0\ns mesons were studied by the LEP experiments\nin e+e\u2212collisions at the CM energy of the Z0 boson mass,\nhowever the statistical signi\ufb01cance of those results is lim-\nited. Later, B0\ns physics was explored with improved accu-\nracy at the Tevatron experiments using pp collision data\nwith a 1.8 TeV CM energy taken during the \ufb01rst run pe-\nriod, 1990\u20131995, and later with higher statistics during the\nrun II period at 1.96 TeV. The Tevatron experiments CDF\nand D\u00d8 measure several B0\ns decay branching fractions, de-\ntermined for the \ufb01rst time the mixing parameter \u2206ms, as\nopposed to placing lower bounds on this frequency, and\nobtained many other interesting results in this area.\nHistorically, e+e\u2212colliders near open beauty threshold\nwere designed to run at the \u03a5(4S) resonance and focused\non studies of B0\nd and B+ mesons. In particular, Belle and\nBABAR were designed to take data with asymmetric en-\nergy e+e\u2212beam collisions at a CM energy of 10.58 GeV.\nHowever, the new territory of B0\ns physics could also be ex-\nplored at the B Factories. The B0\nsB0\ns production threshold\nlies only about 150 MeV higher than the \u03a5(4S) produc-\ntion energy, and therefore, is reachable by B Factories\nwithout signi\ufb01cant modi\ufb01cation. Fig. 23.1.1 shows the ra-\ntio of hadronic to e+e\u2212\u2192\u00b5+\u00b5\u2212cross-sections as a func-\ntion of the CM energy in the region just above the \u03a5(4S),\nwhere two further resonances are clearly seen. These are\nusually called the \u03a5(5S) and \u03a5(6S). As the \u03a5(5S) has a\nbb quark content, e+e\u2212collisions at the \u03a5(5S) CM energy\nare expected to be an e\ufb00ective source of the B0\ns meson\nproduction. However a very high luminosity must be de-\nlivered by the B Factories to provide a su\ufb03cient number of\nB0\ns mesons, for statistically signi\ufb01cant measurements. The\n172 The \u03a5(5S) resonance is also referred to as the \u03a5(10860) in\nthe literature.\n [GeV]\ns\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\nb\nR\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nFigure 23.1.1. Measured ratio of hadronic to e+e\u2212\u2192\u00b5+\u00b5\u2212\ncross-sections, Rb, as a function of the CM energy, from an\nenergy scan performed by the BABAR collaboration (Aubert,\n2009x). The result of a \ufb01t to a function including background\nand \u03a5(5S) and \u03a5(6S) resonances is shown by the curve. The\nerror bars represent the statistical and the uncorrelated sys-\ntematic uncertainties added in quadrature.\ncross section for B0\ns production at the \u03a5(5S) is measured\nto be (0.340 \u00b1 0.016) nb (see Section 23.2.4).\nThe opportunity to perform detailed studies of the B\nand B0\ns mesons using data collected at the \u03a5(5S) was dis-\ncussed by theorists many years ago (Atwood and Soni,\n2002; Falk and Petrov, 2000; Lee-Franzini, Ono, Sanda,\nand Tornqvist, 1985; Lellouch, Randall, and Sather, 1993).\nThese ideas were explored experimentally from the outset,\nhowever the \ufb01rst signi\ufb01cant tests were made in 2003 when\nthe CLEO collaboration collected a small \u03a5(5S) data sam-\nple of 0.42 fb\u22121. Using these data, CLEO found evidence\nof B0\ns production at the \u03a5(5S) (Artuso et al., 2005a; Bon-\nvicini et al., 2006; Huang et al., 2007). In 2005 the Belle\ncollaboration collected 1.86 fb\u22121 of data at the \u03a5(5S) and\nobtained statistically signi\ufb01cant estimates of the B0\ns pro-\nduction parameters (Drutskoy, 2007a,b) that established\nthe feasibility of physics studies of B0\ns mesons at Belle.\nMotivated by these results Belle started to accumulate\ndata at the \u03a5(5S), collecting \u223c22 fb\u22121 in 2006, \u223c27 fb\u22121\nin 2008 and \u223c71 fb\u22121 in 2009. In the last periods of run-\nning both Belle and BABAR performed energy scans in the\nregion of the \u03a5(5S) and \u03a5(6S) resonances. Details of data\ntaking for these experiments are found in Chapter 3, and\nthe energy scan results are discussed in Section 18.4.3.\nThere are many reasons to develop a comprehensive\nphysics program for the study of B0\ns mesons at Belle. In\n2005 the available information regarding B0\ns decays was\nvery limited, with only a few decay branching fractions\nmeasured. Studies of B0\ns decays are important to build a\nmore complete picture of B physics: any signi\ufb01cant dif-\nference between the behavior of B0\ns decays and the corre-\nsponding decays of B0 and B+ mesons could indicate ad-\nditional SM contributions such as annihilation penguins or\nlarge W-exchange topologies that play an important role.\nFormulae relating B0\ns, B0, and B+ production or decay pa-\nrameters are tested and SU(3) symmetry violating e\ufb00ects\n\n722\nare estimated. B0\ns decays are well suited for precise tests\nof the Standard Model, in particular there are unique fea-\ntures and processes that can be studied, such as the large\nlifetime di\ufb00erence between the short-lived and long-lived\nstates and processes described by a penguin annihilation\ndiagram.\nIn this chapter we discuss measurements of B0\ns decays\nat the \u03a5(5S) that have been performed by the Belle collab-\noration since 2005. Currently the Belle sample comprises\n121 fb\u22121 of data, which is the world\u2019s largest dataset at\nthe \u03a5(5S). At the time of writing most of the published\nBelle results were obtained using only 23.6 fb\u22121 of data.\nHowever, it is worth noting that several measurements\nare in the process of being updated. The BABAR collabo-\nration performed an energy scan in the range 10.54 GeV to\n11.20 GeV, however BABAR did not take a large data sam-\nple of a \ufb01xed energy at the \u03a5(5S) peak. Section 23.3.1\ndiscusses the BABAR measurement of the B0\ns semileptonic\nbranching fraction.\n23.2 Basic \u03a5 (5S) properties and beauty\nhadronization\nIn this section we give a classi\ufb01cation of the basic processes\nwhich take place in e+e\u2212annihilation with CM energy\nclose to the \u03a5(5S) mass peak (Section 23.2.1). The choice\nof the CM energy optimal for B0\ns studies is then explained\n(Section 23.2.2). Then the procedures used to calculate the\nnumber of B0\ns mesons in a data sample (Section 23.2.3)\nand to measure the bb cross section (Section 23.2.4) are\ndiscussed. We describe the method used to reconstruct B\nand B0\ns mesons exclusively in Section 23.2.6. The rates\ndetermined for speci\ufb01c \u03a5(5S) decay channels with the B\nand B0\ns mesons in the \ufb01nal states are summarized in Sec-\ntions 23.2.5 and 23.2.7.\n23.2.1 Event classi\ufb01cation\nThe classi\ufb01cation of hadronic events produced at the \u03a5(5S)\nis shown in Fig. 23.2.1: for simplicity, non-hadronic pro-\ncesses are not included. Final states with B and B0\ns mesons\n(designated as bb events) are formed through both reso-\nnant \u03a5(5S) production and bb continuum production. As\nthese two event classes have the same \ufb01nal states, an indi-\nvidual event cannot be attributed to a speci\ufb01c class. The\nexistence of two possible sources of B and B0\ns event pro-\nduction should always be taken into account in theoretical\ncalculations. The uu, dd, ss, and cc continuum is usually\na signi\ufb01cant source of background, when a speci\ufb01c B or\nB0\ns decay mode is reconstructed.\nThus bb events are divided into three categories:\nevents containing B0\ns mesons, B mesons, and bottomo-\nnium states. A bottomonium state should have allowed\nquantum numbers and is accompanied by a light parti-\ncle or a combination of light particles, such as \u03c00, \u03b7, \u03b3,\n\u03c0+\u03c0\u2212, K+K\u2212, and so on. Taking into account the lim-\nited phase-space, only three \ufb01nal states with B0\ns mesons\nHadronic events at Y(5S)\nY(5S) reson.\nb continuum\nu,d,s,c continuum\nbb events\n_\nBs events\nB0, B+ events\nY X\nBs Bs\n* *\n_\nBs Bs\n*\n_\nBs Bs\n_\nB B\n* *\n_\nB B\n*\n_\nB B\n_\nB B \u03c0\n* *\n_\nB B \u03c0\n*\n_\nB B \u03c0\n_\nB B \u03c0 \u03c0\n_\nISR\nFigure 23.2.1. Classi\ufb01cation of hadronic events produced in\ne+e\u2212collisions at a CM energy close to the \u03a5(5S) peak po-\nsition. As noted in the text it is possible to have initial state\nradiation production of the lower mass states for CM energy\ncollisions in the region of the \u03a5(5S) resonance, signi\ufb01ed by the\nISR term circled twice in this schematic.\nare possible: B0\nsB0\ns, B\u22170\ns B0\ns + B0\nsB\u22170\ns , and B\u22170\ns B\u22170\ns . Here\nthe B\u22170\ns B0\ns and B0\nsB\u22170\ns\nstates have the same mass com-\nbination and are almost indistinguishable experimentally,\nand are therefore counted as a single \ufb01nal state. For B\n\ufb01nal states there is enough energy to produce three two-\nbody \ufb01nal states, three three-body \ufb01nal states, and one\nfour-body \ufb01nal state (see Fig. 23.2.1). Here the neutral\nB0 and charged B+ mesons are treated together as a B.\nResonant states decay with \u223c100% probability via the\nmodes B\u22170\ns\n\u2192B0\ns\u03b3 and B\u22170 \u2192B0\u03b3. Additionally e+e\u2212\ncollisions with a center-of-mass energy corresponding to\nthe \u03a5(5S) resonance undergoing Initial State Radiation\n(ISR) can result in direct production of B or B0\ns mesons\nin association with an ISR photon.\nNon-hadronic processes are not included in the above\nclassi\ufb01cation. Some of these processes have large cross-\nsections, in particular e+e\u2212\n\u2192\ne+e\u2212, \u00b5+\u00b5\u2212, \u03c4 +\u03c4 \u2212,\ne+e+e\u2212e\u2212, \u03b3\u03b3, and \u03b3\u03b3X. However these processes are\nstrongly suppressed by the Belle trigger and HadronBJ\n(see Section 3.5.3) event selections, and therefore their\nresidual contributions are negligible in most studies. The\nproposed classi\ufb01cation re\ufb02ects our best knowledge of pos-\nsible mechanisms, and does not include some rare pro-\ncesses that have very low probabilities. For example, the\nstrongly suppressed transition e+e\u2212\u2192ss \u2192B0\nsB0\ns is due\nto ss continuum production with subsequent bb pair cre-\nation, however here it is classi\ufb01ed as bb continuum. The\nprocess of bb annihilation to lighter quarks also has a very\n\n723\nlow probability and is treated as non-bb continuum in the\nfollowing.\n23.2.2 Choice of CM energy for data taking at the\n\u03a5 (5S)\nTo maximize the bb and B0\ns event production an opti-\nmal CM energy is chosen for taking data in the region of\nthe \u03a5(5S). The suitable CM energy region was approxi-\nmately known from the data collected by CLEO (Besson\net al., 1985) and CUSB (Lovelock et al., 1985). However,\nto optimize the choice of CM energy, an energy scan in\nthe region of the peak position of the \u03a5(5S) resonance\nwas performed by Belle as a precursor to taking data at\nthe \u03a5(5S) resonance. For technical reasons both KEKB\nbeam energies were changed simultaneously, keeping the\nCM boost unchanged with respect to \u03a5(4S) running.\nAn integrated luminosity of \u223c30 pb\u22121 was collected at\n\ufb01ve values with an e+e\u2212CM energy between 10825 MeV\nand 10905 MeV. The ratio of the number of hadronic\nevents with second-to-zeroth Fox-Wolfram moment R2 <\n0.2 (see Chapter 9 for a de\ufb01nition of R2) to the num-\nber of Bhabha events is measured as a function of the\nCM energy (Fig. 23.2.2). This ratio is expected to have\na shape close to that of a Breit-Wigner function in the\nregion of the \u03a5(5S) resonance, above a \ufb02at background.\nAs a systematic check, the mean value of the mass ob-\ntained from the \ufb01t, M = (10868 \u00b1 6 \u00b1 14) MeV/c2, was\nfound to be in good agreement with the PDG 2006 value\nM\u03a5 (5S) = (10865 \u00b1 8) MeV/c2 (Yao et al., 2006). Finally,\nthe energy of 10869 MeV was chosen for subsequent \u03a5(5S)\nruns.\nThe accuracy of the CM energy measurement based\non the collider magnet currents is about \u00b1 6 MeV. Three\nmethods are employed in order to measure the CM en-\nergy more precisely, all of these have an accuracy of about\n1 MeV. The original method applied for data samples of\n10 fb\u22121 or larger measures the energy by reconstructing\ne+e\u2212\u2192\u03a5(1S)\u03c0+\u03c0\u2212and e+e\u2212\u2192\u03a5(2S)\u03c0+\u03c0\u2212decays.\nAs the masses of these \u03a5 resonances are known to a pre-\ncision better that 1 MeV/c2, these mass constraints are\nused to signi\ufb01cantly improve the CM energy resolution\nrelative to the collider measurement. Subsequent methods\nthat are used include reconstructing speci\ufb01c B and B0\ns de-\ncay modes, and using e+e\u2212\u2192\u00b5+\u00b5\u2212. This last method\nrequires that ISR corrections be determined accurately\nusing Monte Carlo (MC) simulation.\nThe \ufb01rst two methods are applied post factum to ob-\ntain the CM energy; however, to keep the same energy\nfrom run to run, we need to know the energy accurately\nbefore taking data. Due to the proximity of the B0\ns pro-\nduction threshold (in particular the B\u22170\ns B\u22170\ns channel opens\nup only \u223c40 MeV below the chosen CM energy) even a\nfew MeV CM energy shift can result in sizable variations\nof production rates of individual channels. Unfortunately,\nhysteresis can a\ufb00ect the CM energy setup process based\non the magnet currents (taking into account the large un-\ncertainty of the energy de\ufb01nition), even when the set-up\nECM (GeV)\nN (Hadron, R2< 0.2) / N (Bhabha)\n0.41\n0.42\n0.43\n0.44\n0.45\n0.46\n10.8\n10.85\n10.9\nFigure 23.2.2. The ratio of the number of hadronic events\n(R2 < 0.2) to the number of Bhabha events as a function of\nthe e+e\u2212CM energy, from Drutskoy (2007a). Only statistical\nerrors are shown. The curve is the result of the \ufb01t to a sum of\na Breit-Wigner function and a constant.\nprocedure used to reach the same CM energy is similar\nfor all data taking periods. To maximize luminosity the\nCM energy must be chosen at the beginning of a run. The\ne+e\u2212\u2192\u00b5+\u00b5\u2212method is expected to provide the most\nrobust and accurate value of the CM energy for future\nexperiments.\n23.2.3 Calculation of the number of B0\ns mesons in a\ndata sample\nIt is important to determine the number of B0\ns mesons\nin a data sample with high precision because the corre-\nsponding uncertainty is usually the dominant systematic\nuncertainty in B0\ns branching fraction measurements. Tak-\ning into account the hadronic event classi\ufb01cation discussed\nabove, the following parameters are required in order to\nobtain the number of B0\ns mesons in a data sample taken\nat a given CM energy:\n1. The integrated luminosity of the data sample Lint.\n2. The bb production cross section \u03c3 (e+e\u2212\u2192bb), also\ndenoted as \u03c3bb.\n3. The fraction of bb events containing a B(\u2217)0\ns\nB(\u2217)0\ns\npair,\nusually referred to as fs.\n4. The fractions of events produced through speci\ufb01c pro-\nduction channels over all B(\u2217)0\ns\nB(\u2217)0\ns\nevents: fB0sB0s,\nfB\u22170\ns B0s, and fB\u22170\ns B\u22170\ns .\nThese parameters are measured experimentally. The\nintegrated luminosity of a data sample is precisely deter-\nmined using the standard Belle procedure brie\ufb02y discussed\nin Section 3.2.1. In the following two subsections we dis-\ncuss the method used for the \u03c3bb cross section measure-\nment and the experimental technique used to obtain fs.\nUsing these parameters the number of B0\ns mesons in a\ndata sample is calculated:\nN(B0\ns) = 2 \u00d7 Lint \u00d7 \u03c3bb \u00d7 fs.\n(23.2.1)\n\n724\nThe number of B0\ns mesons produced through a speci\ufb01c\nproduction channel is obtained by multiplying the num-\nber of B0\ns mesons N(B0\ns) by the corresponding channel\nfractions fB0sB0s, fB\u22170\ns B0s, or fB\u22170\ns B\u22170\ns .\nSimilar to the B0\ns fraction fs, the fractions of events\nwith B mesons (fB) and a bottomonium (fbot) over all bb\nevents is introduced. The sum of these parameters is \ufb01xed\nto unity: fs + fB + fbot = 1. Additionally the fractions\nof charged and neutral B mesons produced per bb event,\nf(B+) and f(B0), is de\ufb01ned. As two B mesons are pro-\nduced per \u03a5(5S) decay and some channels include both\ncharged and neutral B mesons (such as B0B\u2212\u03c0+), a factor\n2 is included in the de\ufb01nition, resulting in the equality\nfB = f(B+) + f(B0)\n2\n.\n(23.2.2)\n23.2.4 bb cross section at the \u03a5 (5S)\nThe bb production cross section at a \ufb01xed CM energy is\nobtained from the formula\n\u03c3bb = N bb\n5S / L5S,\n(23.2.3)\nwhere N bb\n5S is the number of bb events in the \u03a5(5S) data\nsample and L5S is the integrated luminosity of the sample.\nTo obtain the number of bb events in a \u03a5(5S) data sam-\nple the uu, dd, ss, and cc continuum are subtracted from\nthe full number of hadronic events. The uu + dd + ss + cc\ncontinuum contribution is estimated using the data col-\nlected at a CM energy 60 MeV below the \u03a5(4S) resonance\n(so-called \u201co\ufb00-resonance\u201d data). As the continuum cross\nsection decreases with energy as 1/E2\nCM, the correspond-\ning factor has to be applied to correct for the CM energy\ndi\ufb00erence. Belle measured the bb cross section (Drutskoy,\n2007a) using a data sample of 1.86 fb\u22121 taken at the \u03a5(5S)\nenergy of \u223c10869 MeV and a data sample of 3.67 fb\u22121 col-\nlected at the o\ufb00-resonance energy 10520 MeV.\nThe number of bb events is obtained from the formula\nN bb\n5S = 1\n\u03f5bb\n5S\n\u0012\nN had\n5S\n\u2212N had\no\ufb00\u00b7 L5S\nLo\ufb00\n\u00b7 E 2\no\ufb00\nE 2\n5S\n\u00b7 \u03f5con\n5S\n\u03f5con\no\ufb00\n\u0013\n, (23.2.4)\nwhere N had\n5S\nand N had\no\ufb00\nare the numbers of hadronic events\nin the \u03a5(5S) and o\ufb00-resonance continuum data samples,\nrespectively. Here \u03f5bb\n5S is the e\ufb03ciency to select a bb event\nin the \u03a5(5S) data sample, which was estimated from MC\nsimulation and found to be \u03f5bb\n5S = (99 \u00b1 1)%. The ratio of\ne\ufb03ciencies to reconstruct continuum events in the \u03a5(5S)\nand o\ufb00-resonance data samples (each one is around 79 %)\nwas also obtained from MC: \u03f5con\n5S /\u03f5con\no\ufb00\n= 1.007 \u00b1 0.003.\nThe CM energy ratio Eo\ufb00/E5S is known with high ac-\ncuracy, as discussed above. The integrated luminosity ra-\ntio L5S/Lo\ufb00= 0.5061 \u00b1 0.0020 is calculated using the\nstandard Belle luminosity measurement procedure with\nBhabha events (Section 3.2.1).\nThe number of bb events obtained is very sensitive to\nthese ratios of luminosities, energies, and e\ufb03ciencies. The\ncorresponding uncertainties are 0.4% for the luminosity\nratio, 0.3% for the e\ufb03ciency ratio, and less than 0.1% for\nthe energy ratio. The combined uncertainty is about 0.5%\nand it is di\ufb03cult to reduce this systematic uncertainty fur-\nther. As the two terms in the subtraction are of the same\norder and about 10 times larger than the result (since con-\ntinuum is about 10 times larger than bb production), the\nuncertainty of the bb event de\ufb01nition is dominated by the\n0.5% uncertainty multiplied by a factor 10: \u223c5% in total.\nAn improvement in the determination of the luminosity\nratio is required if one is to reduce the total uncertainty\nof this method.\nPotentially a precise luminosity ratio measurement is\ndirectly obtained from the ratio of normalized momentum\ndistributions (for these two datasets) of high momentum\ncharged pions, charged kaons, and D0 mesons (Drutskoy,\n2007a), however non-hadronic backgrounds must be ac-\ncurately subtracted. Here the normalized momentum of a\nparticle h is de\ufb01ned as x(h) = P(h)/Pmax(h), where P(h)\nis the measured momentum of the particle, and Pmax(h)\nis the expected value of its momentum if it were produced\nin the process e+e\u2212\u2192h\u00afh at the same CM energy.\nUsing Eqs (23.2.3) and (23.2.4) Belle obtains the bb\nproduction cross section \u03c3bb = (0.302 \u00b1 0.015) nb using\n1.86 fb\u22121 \u03a5(5S) data sample (Drutskoy, 2007a). This num-\nber is used in the initial Belle B0\ns studies based on the\n23.6 fb\u22121 data sample. Later with the full data sample of\n121.4 fb\u22121 a slightly higher bb production cross section was\nobtained, \u03c3bb = (0.340\u00b10.016) nb, and is used in analyses\nof the full dataset.\n23.2.5 Fraction of bb events with B0\ns mesons\nA method also used in inclusive particle spectra analyses\nis adopted to obtain the fraction of bb events resulting in \ufb01-\nnal states with B0\ns mesons in the \u03a5(5S) data. This method\nwas developed by CLEO and was applied to the analysis\nof inclusive D+\n(s) production (Artuso et al., 2005a), then\nlater for the study of \u03c6 production (Huang et al., 2007).\nBelle measures the D+\n(s) and D0 inclusive spectra (Drut-\nskoy, 2007a) and an estimate for fs is obtained from these\nstudies. The inclusive spectra analysis method is based on\nthe fact that the inclusive production rate of the D+\n(s), D0,\nand \u03c6 mesons is very di\ufb00erent in B0\ns and B decays.\nThe analysis of the D+\n(s) inclusive spectra will be dis-\ncussed below to illustrate the method; the D0 and \u03c6 spec-\ntra analyses are very similar. As Belle combines results of\nD+\n(s) and D0 production spectra to reduce the systematic\nuncertainty obtained for fs, additional detail is given for\nthe D0 spectra analysis. The Belle measurement of fs was\nmade using data samples of 1.86 fb\u22121 taken at the \u03a5(5S)\nand 3.67 fb\u22121 at the o\ufb00-resonance energy of 10520 MeV.\nTo avoid large backgrounds, only the clean decay mode\nD+\n(s) \u2192\u03c6\u03c0+, where \u03c6 \u2192K+K\u2212, is used in this analysis;\nsimilarly in order to select D0, the decay D0 \u2192K\u2212\u03c0+ is\nused.\n\n725\n(a)\nx(Ds)\nEvents / 0.05\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n0\n0.2\n0.4\n0.6\n0.8\n1\n(b)\nx(D0)\nEvents / 0.05\n0\n1000\n2000\n3000\n4000\n5000\n0\n0.2\n0.4\n0.6\n0.8\n1\nFigure 23.2.3. The D+\ns normalized momentum x(D+\ns ) (a) and\nthe D0 normalized momentum x(D0) (b). The points with er-\nror bars are the \u03a5(5S) data, while the histograms show the nor-\nmalized o\ufb00-resonance data. Plots are from Drutskoy (2007a).\nAs the CM energy is di\ufb00erent for the \u03a5(5S) and o\ufb00-\nresonance data samples, a momentum scale normaliza-\ntion is applied when comparing the inclusive spectra. The\nnormalized D+\n(s) momentum distributions (as de\ufb01ned in\nthe previous subsection) obtained for the \u03a5(5S) and o\ufb00-\nresonance data samples are shown in Fig. 23.2.3(a). To\nobtain these distributions the D+\n(s) signal yields were ex-\ntracted from a \ufb01t in each bin of x(D+\ns ). The continuum\ndistribution is normalized to the \u03a5(5S) distribution us-\ning the energy-corrected luminosity ratio. As we can see\nin Fig. 23.2.3(a) the \u03a5(5S) and o\ufb00-resonance distribu-\ntions agree well in the region x(D+\ns ) > 0.5, where bb\nevents cannot contribute. The excess of events in the re-\ngion x(D+\ns ) < 0.5 corresponds to inclusive D+\n(s) produc-\ntion in bb events. Similar behavior is observed for the D0\ninclusive spectra as shown in Fig. 23.2.3(b).\nAfter continuum subtraction and a bin-by-bin e\ufb03ciency\ncorrection, the sum of events over all bins within the in-\nterval x(D+\ns ) < 0.5 is divided by the D+\n(s) and \u03c6 decay\nbranching fractions and by the number of bb events in the\n\u03a5(5S) data sample to obtain the inclusive branching frac-\ntion:\nB(\u03a5(5S) \u2192DsX) =\nP N bb\nbin(Ds)/\u03f5bin\nN bb\n5S \u00b7 B(D+\ns \u2192\u03c6\u03c0+) \u00b7 B(\u03c6 \u2192K+K\u2212)\n.\n(23.2.5)\nFrom this formula Belle obtains the value B(\u03a5(5S) \u2192\nD+\ns X)/2 = (23.6 \u00b1 1.2 \u00b1 3.6)%, which includes a factor of\n1/2 to compare with B(s) branching fractions. This inclu-\nsive branching fraction gives the average number of D+\ns\nmesons produced in bb events at the \u03a5(5S) energy.\nThe value of B(\u03a5(5S) \u2192D+\ns X)/2 is signi\ufb01cantly larger\nthan the branching fraction for D+\ns production in B de-\ncays, which was calculated in Drutskoy (2007a) as B(B \u2192\nD+\ns X) = (8.7\u00b11.2)%. The signi\ufb01cant increase of D+\ns pro-\nduction at the \u03a5(5S) compared to that at the \u03a5(4S) in-\ndicates a sizable B0\ns production rate.\nThe fraction fs of B(\u2217)0\ns\nB(\u2217)0\ns\nevents in all bb events\nproduced at the \u03a5(5S) is extracted from the following\nrelation:\nB(\u03a5(5S) \u2192D+\ns X)/2 = fs \u00b7 B(B0\ns \u2192D+\ns X) +\n(1 \u2212fs) \u00b7 B(B \u2192D+\ns X),\n(23.2.6)\nwhere B(B0\ns \u2192D+\ns X) and B(B \u2192D+\ns X) are the average\nfractions of D+\ns mesons produced in B0\ns and B decays, re-\nspectively. Using the measurement of B(\u03a5(5S) \u2192D+\ns X),\nthe measured value of B(B \u2192D+\ns X) = (8.7 \u00b1 1.2)%,\nand the model-dependent estimate B(B0\ns\n\u2192D+\ns X) =\n(92 \u00b1 11)% (Artuso et al., 2005a), Belle determines fs =\n(17.9 \u00b1 1.4 \u00b1 4.1)%. The systematic uncertainty on fs is\nobtained by propagating the systematic uncertainties on\nthe branching fractions included in Eq. (23.2.6), taking\ninto account the correlation induced by B(D+\n(s) \u2192\u03c6\u03c0+).\nBottomonium production in \u03a5(5S) decays, which occurs\nat the few percent level, is neglected in Eq. (23.2.6).\nA similar procedure is applied to D0 inclusive spectra\nand the inclusive branching fraction\nB(\u03a5(5S) \u2192D0X)/2 = (53.8 \u00b1 2.0 \u00b1 3.4)%\n(23.2.7)\nis determined. Using the inclusive D0 production branch-\ning fractions of the \u03a5(5S), B, and B0\ns decays and replac-\ning D+\ns by D0 in Eq. (23.2.6), the ratio fs = (18.1 \u00b1 3.6 \u00b1\n7.5)% of B(\u2217)0\ns\nB(\u2217)0\ns\nevents to all bb events at the \u03a5(5S)\nis obtained. Combining these two fs measurements and\ntaking into account the anti-correlated systematic uncer-\ntainty due to the number of bb events, an average value\nfs = (18.0 \u00b1 1.3 \u00b1 3.2)% is obtained. This measurement\nis in good agreement with the CLEO measurement fs =\n(16.0 \u00b1 2.6 \u00b1 5.8)% (Artuso et al., 2005a).173 In the Belle\nmeasurements based on 23.6 fb\u22121 of data the value fs =\n(19.5+3.0\n\u22122.3)% is used, which was the PDG average of all fs\nmeasurements obtained at that time. The Belle analyses\n173 Subsequently CLEO used several methods to measure fs\n(Huang et al., 2007); however, all of these measurements have\nlarge uncertainties.\n\n726\nwith the full data sample of 121.4 fb\u22121 use run-dependent\nmeasurements of fs, which are obtained from D+\n(s) inclu-\nsive spectra studies.\nThe uncertainty due to fs is currently the dominant\nsystematic uncertainty on B0\ns decay branching fraction\nmeasurements at the \u03a5(5S). There are several methods\nthat can be used to potentially reduce this uncertainty to\nless than (4\u20135)%, however the choice of the most precise\nmethod requires further study. For the next generation of\nB Factories this uncertainty is expected to be reduced to\n(2\u20133)%, which would result in a total systematic uncer-\ntainty of \u22485% for B0\ns branching fraction measurements.\n23.2.6 Exclusive B0\ns and B decay reconstruction\ntechnique\nThe technique used for exclusive B0\ns and B meson re-\nconstruction at the \u03a5(5S) is similar to the one used at\nthe \u03a5(4S). However additional complexity appears at the\n\u03a5(5S) due to many new intermediate channels that open\nup at the increased CM energy. For a given B0\ns or B decay\nchannel the energy and momenta for all \ufb01nal state parti-\ncles are calculated in the CM system. Usually the low-\nmomentum photons from B\u22170\ns\nand B\u2217decays are not re-\nconstructed because of their low reconstruction e\ufb03ciency.\nTwo kinematic variables are used to reconstruct and iden-\ntify exclusive B (or B0\ns) signals at the \u03a5(5S) using a tech-\nnique similar to that used at the \u03a5(4S) for isolating Bu,d\nmesons (see Chapter 7). The \ufb01rst is the energy di\ufb00erence\n\u2206E given by\n\u2206E = E\u22c6\nB \u2212E\u22c6\nbeam,\n(23.2.8)\nand the second is the beam-energy-substituted mass\nmES =\nq\nE\u22c62\nbeam \u2212p\u22c62\nB ,\n(23.2.9)\ncalled \u201cMbc\u201d in Belle publications, where E\u22c6\nB and p\u22c6\nB are\nthe energy and momentum of the B0\ns or B candidate in\nthe e+e\u2212CM system, and E\u22c6\nbeam is the CM beam energy.\nFigure 23.2.4 shows the B0\ns and B signal distributions\nin the mES and \u2206E plane for di\ufb00erent intermediate \u03a5(5S)\ndecay channels. The events shown are obtained from MC\nsimulation of B0\ns \u2192D\u2212\ns \u03c0+ and B0 \u2192D\u2212\u03c0+ decays.\nThe three ellipsoidal regions on the right side of Figure\n23.2.4 correspond to the intermediate \u03a5(5S) decay chan-\nnels B\u22170\ns B\u22170\ns , B\u22170\ns B0\ns + B0\nsB\u22170\ns , and B0\nsB0\ns. These three\nB0\ns signal regions are well separated, re\ufb02ecting changes in\nkinematics corresponding to the cases where both, only\none, or neither of the B0\ns mesons originate from a B\u22170\ns\ndecay. A MC simulation indicates that the correlation be-\ntween the reconstructed mES and \u2206E variables within the\nellipses is small and can usually be neglected. The central\npoint of each ellipse corresponds to the decay parameters\nM cen\nbc\n= M(B0\ns) and \u2206Ecen = 0 for the channel B0\nsB0\ns,\nand M cen\nbc = M(B\u22170\ns ) and \u2206Ecen = \u2212E(\u03b3) for the channel\nB\u22170\ns B\u22170\ns , with the central value for the B\u22170\ns B0\ns + B0\nsB\u22170\ns\nchannel as the midpoint between the two individual con-\ntributions.\n\u2206E (GeV)\nMbc (GeV/c2)\n5.25\n5.3\n5.35\n5.4\n5.45\n-0.3\n-0.2\n-0.1\n0\n0.1\n0.2\nFigure 23.2.4. The Mbc = mES and \u2206E scatter plot obtained\nfrom MC simulations of di\ufb00erent intermediate \u03a5(5S) decay\nchannels with B0\ns \u2192D\u2212\ns \u03c0+ and B0 \u2192D\u2212\u03c0+ decays. The\nellipses show the signal regions for the intermediate B\u22170\ns B\u22170\ns\n(top, blue), B\u22170\ns B0\ns and B0\nsB\u22170\ns (middle, green), and B0\nsB0\ns (bot-\ntom, red) channels. The band region includes (from bottom to\ntop) the signals from BB (red), B\u2217B and BB\u2217(green), B\u2217B\u2217\n(blue), three-body B(\u2217)B(\u2217)\u03c0 (violet), and four-body BB\u03c0\u03c0\n(turquoise) channels.\nThe band in the center of Fig. 23.2.4 corresponds to\nthe intermediate \u03a5(5S) decay channels with non-strange\nB mesons. The channels are located inside the band in the\nfollowing order with increasing mES: BB, B\u2217B + BB\u2217,\nB\u2217B\u2217, three-body B(\u2217)B(\u2217)\u03c0, and four-body BB\u03c0\u03c0. The\ntwo-body channels are well separated from each other in\nmES (for B decays with only a few reconstructed photons).\nIn contrast, the mES distributions of the three three-body\nchannels overlap signi\ufb01cantly with each other and par-\ntially overlap the distribution for the four-body channel.\nThe numbers of events inside and outside the ellipti-\ncal regions is used to estimate the number of B0\ns signal\nand background events. However, in general an unbinned\nextended maximum likelihood \ufb01t to mES and \u2206E is ap-\nplied to extract the number of signal events. The prob-\nability density functions used for this are adjusted using\nMC simulation and sideband data.\nAs for studies of B mesons at the \u03a5(4S), the B0\ns sig-\nnal shapes at the \u03a5(5S) are usually modeled with a single\nGaussian for mES and a double Gaussian with common\nmean for \u2206E. More complicated shapes have to be used\nto describe an electromagnetic tail, which appears if pho-\ntons or electrons are present in the reconstructed B0\ns \ufb01nal\nstate of interest. Light quark continuum backgrounds are\nusually modeled with an ARGUS function (see Chapter 7)\nfor mES and a polynomial function for \u2206E. Potentially it\n\n727\nis possible to simultaneously \ufb01t all three B0\ns signal regions\n(three intermediate channels, i.e. the three types of \ufb01nal\nstate containing B0\ns mesons introduced in Section 23.2.1).\nHowever, as shown below the rate of the channel B\u22170\ns B\u22170\ns\nis about 90% of all B0\ns channels (if the CM energy is close\nto the \u03a5(5S) peak position), and in many cases it is rea-\nsonable to only include the region corresponding to this\n\ufb01nal state in the \ufb01t.\n23.2.7 Fractions of events with B mesons\nMeasurements of event fractions containing B0\ns mesons in\nthe \ufb01nal state produced at the CM energy of the \u03a5(5S)\nresonance (see Fig. 23.2.1) provide information about b-\nquark dynamics. Moreover, these fractions have to be pre-\ncisely known to build a reliable MC model of \u03a5(5S) de-\ncays, which is required in order to make accurate back-\nground estimates in B(s) decay studies. Several measure-\nments of the B channel fractions at the \u03a5(5S) have been\nperformed by Belle (Drutskoy, 2010). The experimental\ntechniques used in these measurements are described be-\nlow, and \ufb01nally all results obtained are summarized in\nTable 23.2.1 and discussed together with the results of B0\ns\nbranching fraction measurements.\nThe measurements are based on a 23.6 fb\u22121 data sam-\nple. The \ufb01ve decay modes B+ \u2192J/\u03c8K+, B0 \u2192J/\u03c8K\u22170,\nB+ \u2192D0\u03c0+ (with D0 \u2192K+\u03c0\u2212and K+\u03c0+\u03c0\u2212\u03c0\u2212), and\nB0 \u2192D\u2212\u03c0+ (D\u2212\u2192K+\u03c0\u2212\u03c0\u2212) were used to reconstruct\nB mesons. These modes were chosen because they have\nlarge and precisely measured branching fractions and con-\ntain only charged particles in the \ufb01nal state; these char-\nacteristics result in small systematic uncertainties.\nBelle measures the charged and neutral B production\nrates normalized to the number of bb events. To obtain\nthe sum of all possible channels, the \u2206E + mES \u2212mB\nprojections of the two-dimensional scatter plots for all\nevents within the allowed range 5.268 GeV/c2 < mES <\n5.440 GeV/c2 are used. The \u2206E + mES \u2212mB projec-\ntion works as a rotation in the \u2206E and mES plane (see\nFig. 23.2.4 for an illustration). Therefore all signal events\nfrom the inclined band contribute to the \u2206E +mES \u2212mB\ndistribution as a single Gaussian peak. These inclined pro-\njections are \ufb01t to obtain the integrated B decay event\nyields with a function including two terms: a Gaussian to\ndescribe the signal and a \ufb01rst-order polynomial to describe\nbackground.\nUsing the \ufb01t results, the charged and neutral B pro-\nduction rates per bb event are obtained from the formula\nf(B+,0) =\nY \ufb01t\nB\u2192X\n(N bb\n5S \u00d7 \u03f5B\u2192X \u00d7 BB\u2192X)\n,\n(23.2.10)\nwhere Y \ufb01t\nB\u2192X is the event yield obtained from the \ufb01t for a\nspeci\ufb01c mode B \u2192X, N bb\n5S is the full number of bb events\nin the dataset, \u03f5B\u2192X is the reconstruction e\ufb03ciency in-\ncluding all types of strange B meson branching fractions,\nand BB\u2192X is the corresponding B decay branching frac-\ntion taken from the PDG (Beringer et al., 2012). The av-\nerage production rates obtained for charged and neutral B\nTable 23.2.1. The B and B0\ns channel fractions at the CM\nenergy of the \u03a5(5S).\nChannel\n% / bb event\n% / B0\ns event\nAll B0\ns events\n19.5+3.0\n\u22122.3\nB\u22170\ns B\u22170\ns\n90.1+3.8\n\u22124.0 \u00b1 0.2\nB\u22170\ns B0\ns + B0\nsB\u22170\ns\n7.3+3.3\n\u22123.0 \u00b1 0.1\nB0\nsB0\ns\n2.6+2.6\n\u22122.5\nAll B events\n73.7 \u00b1 3.2 \u00b1 5.1\nB+ mesons\n72.1+3.9\n\u22123.8 \u00b1 5.0\nB0 mesons\n77.0+5.8\n\u22125.6 \u00b1 6.1\nBB\n5.5 +1.0\n\u22120.9 \u00b1 0.4\nBB\u2217+B\u2217B\n13.7 \u00b1 1.3 \u00b1 1.1\nB\u2217B\u2217\n37.5 +2.1\n\u22121.9 \u00b1 3.0\nBB \u03c0\n0.0 \u00b1 1.2 \u00b1 0.3\nBB\u2217\u03c0 + B\u2217B\u03c0\n7.3 +2.3\n\u22122.1 \u00b1 0.8\nB\u2217B\u2217\u03c0\n1.0 +1.4\n\u22121.3 \u00b1 0.4\nISR to \ufb01nal B\n9.2 +3.0\n\u22122.8 \u00b1 1.0\nmesons are shown in Table 23.2.1. The f(B+) and f(B0)\nvalues are equal within uncertainties, which is consistent\nwith isospin symmetry. The average of the charged and\nneutral B modes is (73.7 \u00b1 3.2 \u00b1 5.1)%.\nThe two-body channel branching fractions are mea-\nsured; values are averaged over charged and neutral B\nmesons. The mES projections are obtained for events in\nthe signal band (shown in Fig. 23.2.5(a)) and the projec-\ntions are \ufb01t with a function including signal and back-\nground terms (Fig. 23.2.5(b)). The shapes of the signal\ncomponents are taken from MC simulation, and those\nof combinatorial background are modeled using sideband\ndata. The \ufb01t region is restricted to the interval mES \u2208\n[5.268, 5.348] GeV/c2. The three peaks corresponding to\nthe BB, BB\u2217+B\u2217B and B\u2217B\u2217channels (from left to\nright) are clearly seen in Fig. 23.2.5(b). The matrix el-\nements responsible for three- and four-body decays are\nnot known, and the rates of three- and four-body contri-\nbutions cannot be obtained in a model-independent way\nfrom a \ufb01t to these mES distributions. The \ufb01t results are\ngiven in Table 23.2.1.\nIn order to reconstruct the three-body channels, an ad-\nditional charged pion produced directly via B(\u2217)B(\u2217) \u03c0+\nis combined with two B(\u2217) mesons. For each charged pion\nnot included in the reconstructed B candidate, right-sign\nB+\u03c0\u2212, B0\u03c0\u2212, B0\u03c0+, or B\u2212\u03c0+ combinations are formed.\nThe reconstructed B candidates are selected from the\nthree-body signal region given by 5.37 GeV/c2 < mES <\n5.44 GeV/c2 and |\u2206E + mES \u2212mB| < 0.03 GeV. Then a\nspecial variable \u2206X = \u2206Emis +mmis\nES \u2212mB was calculated\nfor all selected B\u03c0 candidates, where the variables mmis\nES\nand \u2206Emis are obtained for the missing B meson using\nthe energy and momentum of the reconstructed B\u03c0 com-\nbination in the CM frame. The \u2206X variable re\ufb02ects the\nmissing mass in the reconstructed B\u03c0 system.\n\n728\n(a)\n\u2206E (GeV)\nMbc (GeV/c2)\n5.25\n5.3\n5.35\n5.4\n5.45\n-0.4\n-0.2\n0\n0.2\n(b)\nMbc (GeV/c2)\nEvents / 4 MeV/c2\n0\n50\n100\n5.3\n5.35\n5.4\nFigure 23.2.5. (a) The Mbc = mES and \u2206E scatter plot for\nthe B+ \u2192J/\u03c8K+ mode (data) from Drutskoy (2010). The\nband indicates the signal region corresponding to the intervals\n5.268 GeV/c2 < mES < 5.440 GeV/c2 and |\u2206E + mES \u2212mB| <\n0.03 GeV. (b) The mES distribution in data after background\nsubtraction. The sum of the \ufb01ve signi\ufb01cant B decays (points\nwith error bars, see Table 23.2.1) and results of the \ufb01t (his-\ntogram) used to extract the two-body channel fractions are\nshown.\nFigure 23.2.6(a) shows the \u2206X distributions obtained\nfor MC simulated BB\u03c0+, BB\u2217\u03c0++B\u2217B\u03c0+, B\u2217B\u2217\u03c0+, and\nBB\u03c0\u03c0 events where the B+ \u2192J/\u03c8K+ mode is generated.\nThe background due to random charged tracks from the\nunobserved B meson is also shown. The studied channel\ncontributions are well separated as seen in Fig. 23.2.6(a).\nThe reconstruction e\ufb03ciency for the four-body channel\n(the small peak on the rightmost part of Fig. 23.2.6(a)) is\nsmall and model dependent.\nFinally, the \u2206X distribution obtained from the data\nis shown in Fig. 23.2.6(b). This distribution is \ufb01tted with\na function including four terms: three Gaussian distribu-\ntions with \ufb01xed shapes in order to describe the BB\u03c0+,\nBB\u2217\u03c0+ + B\u2217B\u03c0+, and B\u2217B\u2217\u03c0+ contributions, and a\nsecond-order polynomial to describe the background. The\nfour-body channel contribution is negligible and is not in-\ncluded in the \ufb01t. The three-body channel fractions ob-\ntained from the \ufb01t are given in Table 23.2.1.\n(a)\n\u2206E mis+ Mbc\nmis - mB (GeV)\nEvents / 8 MeV\n0\n0.1\n0.2\n0.3\n0.4\n-0.1\n0\n0.1\n(b)\n\u2206E mis+ Mbc\nmis - mB (GeV)\nEvents / 8 MeV\n0\n5\n10\n15\n20\n25\n30\n35\n-0.1\n0\n0.1\nFigure 23.2.6. (a) The \u2206X = \u2206Emis+mmis\nES \u2212mB distribution\nnormalized to unity for MC simulated B+ \u2192J/\u03c8K+ decays\nin the (peaks from left to right) BB\u03c0+, BB\u2217\u03c0+ + B\u2217B \u03c0+,\nB\u2217B\u2217\u03c0+, and BB\u03c0\u03c0 channels. (b) The \u2206X = \u2206Emis+mmis\nES \u2212\nmB data distribution for right-sign B\u2212/0 \u03c0+ combinations for\nthe sum of the \ufb01ve studied B modes. Plots are from Drutskoy\n(2010).\nAll results obtained on B and B0\ns channel fraction mea-\nsurements are summarized in Table 23.2.1. The fractions\nfor speci\ufb01c B0\ns channels for all events with B0\ns mesons\nare taken from Louvot (2009). The di\ufb00erence between the\nnumber of B events and the sum of all two-body or three-\nbody channels is assumed to be due to ISR producing\na system of lower CM energy with subsequent BB-pair\nproduction. The ISR rate obtained using this assumption\nagrees with theoretical expectations.\nThe measurement of fractions for speci\ufb01c B0\ns chan-\nnels of all events with B0\ns mesons is discussed in the next\nsection. An unexpected feature of B0\ns production at the\n\u03a5(5S) is the strong dominance of the B\u22170\ns B\u22170\ns\nchannel.\nThe observed value is close to 90%, although initial the-\noretical estimates gives values of about 70%. Taking into\naccount the B event rate of (73.7\u00b13.2\u00b15.1)% and the B0\ns\nevent rate of fs = (19.5+3.0\n\u22122.2)% at the \u03a5(5S), there is still\nroom for unobserved transitions to non-BB \ufb01nal states\nwith a bottomonium meson. The large fraction for the\n\n729\nthree-body BB\u2217\u03c0+B\u2217B\u03c0 channel was not predicted theo-\nretically and is not yet understood. The channel BB\u03c0 was\nnot observed and its production is probably suppressed\ndue to the 0\u2212quantum numbers of all three \ufb01nal particles\nproduced from the 1\u2212initial state, which results in two\nP-wave amplitudes.\n23.3 Measurements of B0\ns decays at \u03a5 (5S)\nBranching fraction measurements discussed here are or-\ndered in terms of decreasing value and cover semi-leptonic\nB0\ns decays (Section 23.3.1); the Cabibbo favored de-\ncays B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+(\u03c1+) and B0\ns \u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\n(Sec-\ntions 23.3.2 and 23.3.3, respectively); color suppressed de-\ncays (Section 23.3.4); charmless two-body decays (Sec-\ntion 23.3.5); and \ufb01nally loop (or penguin) decays (Sec-\ntion 23.3.6).\n23.3.1 B0\ns semileptonic branching fraction\nAlthough BABAR performed no dedicated \u03a5(5S) running,\na scan was performed in 2008 in 5 MeV steps covering the\nCM energy (ECM) range 10.54 GeV \u2264ECM \u226411.2 GeV,\nintegrating a total of 4.25 fb\u22121 of data. These data are\nused to study B0\ns production in this region and to obtain\na measurement of the inclusive B0\ns semileptonic branch-\ning fraction B(B0\ns \u2192\u2113\u03bdX). Semileptonic decays of B0\nd\nmesons have a large branching fraction to \ufb01nal states in-\ncluding a charm meson. Similarly semileptonic decays of\nB0\ns mesons have large transition rates to \ufb01nal states in-\ncluding a Ds meson, which subsequently decays (15.7% of\nthe time (Beringer et al., 2012)) into a \u03c6+anything \ufb01nal\nstate. The BABAR analysis exploits the existence of the\nCabibbo-favored decay chain Bs \u2192Ds \u2192\u03c6.\nIn 15 MeV wide bins of ECM, BABAR measures the\nyields of three inclusive processes in the scan data: the\nyield of multi-hadronic events containing at least three\ncharged tracks and with Fox-Wolfram moment less than\nor equal to 0.2 (the event yield), the inclusive yield of\nevents containing \u03c6 mesons (the \u03c6 yield), and the inclu-\nsive yield of events containing a \u03c6 in coincidence with a\nwell-identi\ufb01ed e or \u00b5 having a CM momentum exceeding\n900 MeV (the \u03c6-lepton yield). The \u03c6 candidates are re-\nconstructed in the decay mode \u03c6 \u2192K+K\u2212from pairs\nof tracks, with the highest probability to be kaons, that\nare \ufb01tted to a common vertex. Yields are determined by\nbinned maximum likelihood \ufb01ts to the K+K\u2212invariant\nmass distribution of the selected candidates in events with\n(\u03c6-lepton) and without (\u03c6) a track passing the lepton se-\nlection. The p.d.f. used to \ufb01t the distribution consists of\na Voigt pro\ufb01le174 signal peak on top of a background con-\nsisting of the product of a threshold function opening at\n2mK\u00b1 and a linear factor. Each yield is normalized to\nthe number of events in the ECM bin which pass criteria\nidentifying them as e+e\u2212\u2192\u00b5+\u00b5\u2212events.\n174 The convolution of a Breit-Wigner with a Gaussian resolu-\ntion function.\nIn order to remove the contribution from continuum\ne+e\u2212\u2192qq events, where q = u, d, s, c, BABAR performs\nthe same measurements in a 7.89 fb\u22121 sample of data\ntaken 40 MeV below the \u03a5(4S) mass and subtracts the o\ufb00-\nresonance yields from the yields obtained in each bin. The\nvalue to be subtracted is corrected as a function of ECM\nfor the variation of the selection e\ufb03ciency with energy as\ndeduced from simulation. With continuum contributions\nto the yields removed, the remaining yield is the sum of\ncontributions from BB and B0\nsB0\ns events as follows:\nCh = RB [fs\u03f5s\nh + (1 \u2212fs)\u03f5h]\n(23.3.1)\nC\u03c6 = RB\n\u0002\nfs\u03f5s\n\u03c6P(BsBs \u2192\u03c6X)\n+(1 \u2212fs)\u03f5\u03c6P(BB \u2192\u03c6X)\n\u0003\n(23.3.2)\nC\u03c6\u2113= RB\n\u0002\nfs\u03f5s\n\u03c6\u2113P(BsBs \u2192\u03c6\u2113X)\n+(1 \u2212fs)\u03f5\u03c6\u2113P(BB \u2192\u03c6\u2113X)\n\u0003\n,\n(23.3.3)\nwhere\nfs \u2261\nNBs\nNBu + NBd + NBs\n(23.3.4)\nis the ratio of B0\ns events to all b hadron events, RB =\n\u03c3(e+e\u2212\u2192B(s)B(s))/\u03c3(e+e\u2212\u2192\u00b5+\u00b5\u2212), and the e\ufb03cien-\ncies \u03f5(s)\nX and probabilities P(B(s)B(s) \u2192\u03c6(\u2113)X) are pre-\nsented schematically. The values of Ch, C\u03c6 and C\u03c6\u2113across\nthe scanned region are shown in Fig. 23.3.1.\nThe ratio fs is obtained from the combination of Eqs\n(23.3.1) and (23.3.2). The probability that a BB pair pro-\nduces a \u03c6 meson scaled by the corresponding e\ufb03ciency,\n\u03f5\u03c6P(BB \u2192\u03c6X), is obtained by direct measurement of\nthe event and \u03c6 yields in an 18.55 fb\u22121 sample of data\ntaken at the \u03a5(4S) resonance, followed by the applica-\ntion of Eqs (23.3.1) and (23.3.2) with fs = 0. The corre-\nsponding probability in B0\ns events is estimated from previ-\nously measured branching fractions plus small corrections\nfrom estimated Bs \u2192cc\u03c6 and Bs \u2192DDsX (followed\nby D \u2192\u03c6) rates. The result, presented in 45 MeV wide\nbins, is seen in Fig. 23.3.2. The ratio, above threshold,\nis observed to peak around the \u03a5(5S) mass and is small\nelsewhere.\nIn order to extract the semileptonic branching frac-\ntion, an estimate of P(B0\nsB0\ns \u2192\u03c6\u2113X) as a function of\nB(Bs \u2192\u2113\u03bdX) is constructed using known branching frac-\ntions plus the estimated ones mentioned earlier. This es-\ntimate separately treats leptons from events with one B0\ns\nsemileptonic decay, events with two B0\ns semileptonic de-\ncays, and events in which neither B0\ns has decayed semi-\nleptonically but instead a lepton from a charmed meson\nhas passed the lepton momentum selection. For the lat-\nter BABAR includes contributions from events with up to\ntwo leptons coming from D\u00b1, D0, or D\u00b1\ns decays. Selec-\ntion e\ufb03ciencies for each case are determined separately\nfrom simulation. Again the \u03a5(4S) data mentioned earlier\nare used to obtain \u03f5\u03c6\u2113P(BB \u2192\u03c6\u2113X). With these esti-\nmates, BABAR constructs a \u03c72 from the expected value of\n\u03f5\u03c6\u2113P(BsBs \u2192\u03c6\u2113X), estimated as a function of B(Bs \u2192\n\u2113\u03bdX), and the value obtained by the measured quanti-\nties and Eqs (23.3.1) and (23.3.3). Minimization of this\n\n730\n (GeV)\nCM\n(a)\nE\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\n/15 MeV\n\u00b5\n\u00b5\nEvents per \n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n (GeV)\nCM\n(b)\nE\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\n/15 MeV\n\u00b5\n\u00b5\n yield per \n\u03c6\n0\n5\n10\n15\n20\n25\n-3\n10\n\u00d7\n (GeV)\nCM\n(c)\nE\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\n/15 MeV\n\u00b5\n\u00b5\n-lepton yield per \n\u03c6\n0\n1\n2\n3\n4\n5\n-3\n10\n\u00d7\nFigure 23.3.1. Relative values of the (a) event, (b) \u03c6, and\n(c) \u03c6-lepton yields after continuum subtraction is performed.\nCorrections for detector e\ufb03ciency have not been applied. The\nB0\ns production threshold is located at the dotted line. From\nLees (2012a).\n (GeV)\nCM\nE\n10.6\n10.7\n10.8\n10.9\n11\n11.1\n11.2\nsf\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\nFigure 23.3.2. fs in 45 MeV wide bins of ECM. The larger\nblue error bars represent the sum in quadrature of statistical\nand systematic uncertainties, while the inner ones show the\nstatistical uncertainty alone. The broken line denotes the B0\ns\nthreshold. From Lees (2012a).\n\u03c72 with respect to the branching fraction yields B(Bs \u2192\n\u2113\u03bdX) = (9.5+2.5\n\u22122.0)%.\nThe dominant contribution to the systematic uncer-\ntainty comes from the poor knowledge of the inclusive rate\nB(Bs \u2192DsX) (+8.72\n\u221213.58 events). Other sources include un-\ncertainties due to biases in the technique found using en-\nsembles of simulated experiments (+0.39\n\u221210.00 events), see Sec-\ntion 11.5.2; the impact of neglecting ISR and two-photon\ncontributions to the event subtraction (+1.57\n\u22127.14 events); es-\ntimated branching fractions used (\u00b13.4 events); uncer-\ntainties due to the use of particle identi\ufb01cation (\u00b13.21\nevents); statistical uncertainties in the quantities deter-\nmined from \u03a5(4S) data and daughter branching fractions\n(\u00b13.1 events); uncertainties in the selection e\ufb03ciency ob-\ntained by variation of the R2 and lepton momentum re-\nquirements (+1.99\n\u22122.85 events); sensitivity to the background\nparameterization and possible presence of scalar contri-\nbutions in the threshold region (\u00b10.93 events); the un-\ncertainty in other world-average branching fractions used\n(+0.52\n\u22120.54 events); and \ufb01xed parameters used in the \ufb01t to the\nK+K\u2212invariant mass distribution (+0.49\n\u22120.15 events).\nWith systematic uncertainties included, the \ufb01nal re-\nsult is found to be B(Bs \u2192\u2113\u03bdX) = (9.5+2.5+1.1\n\u22122.0\u22121.9)%, in\ngood agreement with expectations from spectator pro-\ncesses that would predict a similar branching fraction for\nthe B0 and the B0\ns. A more complete overview may be\nfound in Lees (2012a).\n23.3.2 Cabibbo favored decays B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+(\u03c1+)\nThe B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+ and B0\ns \u2192D(\u2217)\u2212\ns\n\u03c1+ decays were\nthe \ufb01rst processes studied by Belle at the \u03a5(5S). These\ndecays are described by Cabibbo-favored tree diagrams,\nwhich have no suppression factors; therefore, relatively\nlarge branching fractions are expected for these decays.\nThe decay B0\ns \u2192D\u2212\ns \u03c0+ was previously observed and stud-\nied with high statistics at the Tevatron experiments. How-\never to identify the other three modes the neutral parti-\ncles (\u03b3 from D\u2217\u2212\ns\nand \u03c00 from \u03c1) have to be reconstructed,\nwhich was not possible at other experiments; LHCb was\nnot in operation at that time. These decay modes were\nthe primary goals for observation at Belle.\nAlthough the theoretical models used to describe these\ndecays are relatively simple, any experimental results on\nthese modes are welcome because they test the applica-\nbility and accuracy of the basic approaches of B meson\ntheoretical calculations. In particular these decays are well\nsuited to test heavy-quark theories that predict, based on\nSU(3) symmetry, similarities between the decay param-\neters of B0\ns mesons and their corresponding B0 counter-\nparts. These include the unitarized quark model (Torn-\nqvist, 1984), heavy quark e\ufb00ective theory (HQET; De-\nandrea, Di Bartolomeo, Gatto, and Nardulli, 1993), and a\nmore recent approach based on chiral symmetry (Bardeen,\nEichten, and Hill, 2003).\nMoreover, because of their large branching fractions,\nthese decays can be used to measure parameters in \u03a5(5S)\ndecays, such as the masses of the B0\ns and B\u22170\ns\nmesons\n\n731\n)\n2\n (GeV/c\nbc\n(a)\nM\n5.3\n5.32 5.34 5.36 5.38\n5.4\n5.42 5.44\n )\n2\nEvents / ( 5 MeV/c\n0\n20\n40\n60\n80\n5.3\n5.32 5.34 5.36 5.38\n5.4\n5.42 5.44\n20\n40\n60\n80\n E (GeV)\n\u2206\n\u22120.3 \u22120.2 \u22120.1\n(b)\n0\n0.1\n0.2\n0.3\n0.4\nEvents / ( 10 MeV )\n0\n10\n20\n30\n40\n50\n\u22120.3 \u22120.2 \u22120.1\n0\n0.1\n0.2\n0.3\n0.4\n10\n20\n30\n40\n50\nFigure\n23.3.3.\n(a)\nMbc\n=\nmES\ndistribution\nof\nthe\nB0\ns\n\u2192D\u2212\ns \u03c0+ candidates with \u2206E in the B\u22170\ns B\u22170\ns\nsignal\nregion [\u221280, \u221217] MeV. (b) \u2206E distribution of the B0\ns\n\u2192\nD\u2212\ns \u03c0+ candidates with Mbc in the B\u22170\ns B\u22170\ns\nsignal region\n[5.41, 5.43] GeV/c2. The di\ufb00erent \ufb01tted components are shown\nwith dashed curves for the signal, dotted curves for the B0\ns \u2192\nD\u2217\u2212\ns \u03c0+ background, and dash-dotted curves for the contin-\nuum. The total \ufb01t is shown as a solid line. Plots are from\nLouvot (2009).\nand the relative fractions of di\ufb00erent \u03a5(5S) decay chan-\nnels. Precisely measured branching fractions of these de-\ncay modes can also be used as a primary normalization at\nhadron colliders, where the absolute branching fractions\nare di\ufb03cult to measure.\nThe B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+ and B0\ns \u2192D(\u2217)\u2212\ns\n\u03c1+ decays are\nobserved and studied by Belle using 23.6 fb\u22121 of data col-\nlected at the \u03a5(5S) resonance CM energy region (Louvot,\n2009, 2010). Evidence for the B0\ns \u2192D(\u2217)\u2213\ns\nK\u00b1 decay is also\nfound, at the level of 3.5\u03c3, in these studies. The technique\nused to identify B0\ns signals is described in Section 23.2\nand only \ufb01nal results are discussed here. Details of the\nanalyses are found in the original papers.\nTwo-dimensional unbinned extended maximum likeli-\nhood \ufb01ts are applied to obtain the B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+ and\nB0\ns \u2192D(\u2217)\u2212\ns\n\u03c1+ decay branching fractions. The mES and\n\u2206E projections of the two-dimensional distribution for\nthe decay B0\ns \u2192D\u2212\ns \u03c0+ are shown in Fig. 23.3.3 to-\ngether with the \ufb01t projections. Five additional parame-\nters were measured using this decay mode: the fractions\nof the B0\ns pair production modes at the \u03a5(5S) energy,\n0\n5\n10\n20\n25\n30\n15\n35\n0\n5\n10\n20\n25\n15\n0\n5\n10\n20\n15\n5.3\n5.34\n5.38\n5.42\nFigure 23.3.4. Left (right): Mbc = mES (\u2206E) distributions\nfor B0\ns \u2192D\u2217\u2212\ns \u03c0+ (top) and B0\ns \u2192D\u2212\ns \u03c1+ (bottom) candidates\nwith \u2206E (mES) restricted to the \u00b12.5\u03c3 B\u22170\ns B\u22170\ns\nsignal region.\nThe blue solid curve is the total \ufb01tted p.d.f., while the green\n(black) dotted curve is the peaking (continuum) background\nand the red dashed curve is the signal. Plots are from Louvot\n(2010).\n0\n5\n10\n20\n25\n15\n0\n4\n8\n16\n12\n5.3\n5.34\n5.38\n5.42\n-0.2\n-0.1\n0\n0.1\n0.2\n0.3\n0.4\n0\n4\n8\n12\n0\n4\n8\n16\n12\n-0.8\n-0.4\n0\n0.4\n0.8\n-0.8\n-0.4\n0\n0.4\n0.8\nFigure 23.3.5. Distributions for the B0\ns \u2192D\u2217\u2212\ns \u03c1+ candidates.\nTop: Mbc = mES and \u2206E distributions, as in the previous\n\ufb01gure. Bottom: distributions of the cosine of the helicity angles\nof the D\u2217\u2212\ns\n(left) and \u03c1+ (right) with mES and \u2206E restricted\nto the B\u22170\ns B\u22170\ns\nkinematic region. The components of the total\np.d.f. (blue solid line) are shown separately: the black-dotted\ncurve is the background and the two red-dashed curves are the\nsignal. The large (small) signal component corresponds to the\nlongitudinal (transverse) signal. Plots are from Louvot (2010).\nfB\u22170\ns B\u22170\ns =\n\u000090.1+3.8\n\u22124.0 \u00b1 0.2\n\u0001\n%, fB\u22170\ns B0s =\n\u00007.3+3.3\n\u22123.0 \u00b1 0.1\n\u0001\n%,\nfB0sB0s =\n\u00002.6+2.6\n\u22122.5\n\u0001\n%, and the masses mB\u22170\ns\n= (5416.4 \u00b1\n0.4 \u00b1 0.5) MeV/c2 and mB0s = (5364.4 \u00b1 1.3 \u00b1 0.7) MeV/c2.\nThe \u03a5(5S) \u2192B\u22170\ns B\u22170\ns channel fraction is found to be large\nand this channel strongly dominates over other channels.\nA similar method is used to extract the branching frac-\ntions for the other three decay modes. The mES and \u2206E\nprojections of the two-dimensional distributions for the\ndecays B0\ns \u2192D\u2217\u2212\ns \u03c0+ and B0\ns \u2192D\u2212\ns \u03c1+ are shown in\nFig. 23.3.4. The mES and \u2206E projections and helicity dis-\n\n732\nTable 23.3.1. Top: measured branching fractions with sta-\ntistical, systematic (without fs), and fs uncertainties, and\nHQET predictions from the factorization hypothesis (Dean-\ndrea, Di Bartolomeo, Gatto, and Nardulli, 1993). Bottom:\nbranching fraction ratios where several systematic uncertain-\nties cancel out.\nMode\nB (10\u22123)\nBHQET (10\u22123)\nB0\ns \u2192D\u2212\ns \u03c0+\n3.67+0.35\n\u22120.33\n+0.43\n\u22120.42 \u00b1 0.49\n2.8\nB0\ns \u2192D\u2217\u2212\ns \u03c0+\n2.4+0.5\n\u22120.4 \u00b1 0.3 \u00b1 0.4\n2.8\nB0\ns \u2192D\u2212\ns \u03c1+\n8.5+1.3\n\u22121.2 \u00b1 1.1 \u00b1 1.3\n7.5\nB0\ns \u2192D\u2217\u2212\ns \u03c1+\n11.8+2.2\n\u22122.0 \u00b1 1.7 \u00b1 1.8\n8.9\nB0\ns \u2192D\u2213\ns K\u00b1\n0.24+0.12\n\u22120.10 \u00b1 0.03 \u00b1 0.03\nRatios\nB(B0\ns \u2192D\u2217\u2212\ns \u03c0+)/B(B0\ns \u2192D\u2212\ns \u03c0+) = 0.65+0.15\n\u22120.13 \u00b1 0.07\nB(B0\ns \u2192D\u2212\ns \u03c1+)/B(B0\ns \u2192D\u2212\ns \u03c0+) = 2.3 \u00b1 0.4 \u00b1 0.2\nB(B0\ns \u2192D\u2217\u2212\ns \u03c1+)/B(B0\ns \u2192D\u2212\ns \u03c0+) = 3.2 \u00b1 0.6 \u00b1 0.3\nB(B0\ns \u2192D\u2217\u2212\ns \u03c1+)/B(B0\ns \u2192D\u2212\ns \u03c1+) = 1.4 \u00b1 0.3 \u00b1 0.1\ntributions for the D\u2217\u2212\ns\nand \u03c1 are shown in Fig. 23.3.5 for\nthe decay B0\ns \u2192D\u2217\u2212\ns \u03c1+. As the latter decay is that of\na B0\ns meson decaying into a \ufb01nal state with two vector\nparticles, one can perform an angular analysis of the \ufb01nal\nstate in terms of the helicity angles (and angle between\ndecay planes) of the intermediate vector particles as de-\nscribed in Chapter 12. A simpli\ufb01ed angular analysis (in-\ntegrating over the angle between the two decay planes) of\nB0\ns \u2192D\u2217\u2212\ns \u03c1+ indicates strong dominance of the longitudi-\nnal polarization: the obtained fraction of this component\nis fL = 1.05+0.08\n\u22120.10(stat)+0.03\n\u22120.04(syst). This result is compati-\nble with expectations from HQET and na\u00a8\u0131ve factorization\ncomputed for some Bu,d to two-vector particle \ufb01nal states\n(see Sections 17.3 and 17.4 for discussions of such states).\nAll branching fractions measured and their ratios are sum-\nmarized in Table 23.3.1. The results obtained are consis-\ntent with theoretical predictions based on HQET (Dean-\ndrea, Di Bartolomeo, Gatto, and Nardulli, 1993) and are\nsimilar to the corresponding B0 decay branching fractions.\n23.3.3 Cabibbo favored decays B0\ns \u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\nBelle has also used \u03a5(5S) data to measure B0\ns\n\u2192\nD(\u2217)+\ns\nD(\u2217)\u2212\ns\ndecays. An initial study was done using\n23.6 fb\u22121 of data (Esen, 2010), while a subsequent study\nuses the full 121.4 fb\u22121 data set (Esen, 2013). The \ufb01-\nnal states reconstructed consist of D+\n(s)D\u2212\ns , D\u2217+\ns D\u2212\ns +\nD\u2217\u2212\ns D+\n(s) (\u2261D\u2217\u00b1\ns D\u2213\ns ), and D\u2217+\ns D\u2217\u2212\ns . These are expected\nto be mostly CP-even, and their partial widths are ex-\npected to dominate the di\ufb00erence in widths between the\ntwo B0\ns CP eigenstates, \u2206\u0393CP\ns\n(Aleksan, Le Yaouanc,\nOliver, P`ene, and Raynal, 1993). This parameter is equal\nto \u2206\u0393s/ cos \u03c612, where \u2206\u0393s is the decay width di\ufb00er-\nence between the mass eigenstates, and \u03c612 is the CP-\nviolating phase in B0\ns-B0\ns mixing.175 Thus the branch-\ning fraction gives a constraint in the \u2206\u0393s-\u03c612 parame-\nter space. Both parameters can receive contributions from\nnew physics (Buras, Carlucci, Gori, and Isidori, 2010;\nLenz and Nierste, 2011; Ligeti, Papucci, Perez, and Zu-\npan, 2010).\nThe decays B0\ns \u2192D+\n(s)D\u2212\ns , D\u2217\u00b1\ns D\u2213\ns , and D\u2217+\ns D\u2217\u2212\ns\nare\nreconstructed via D+\n(s) \u2192\u03c6\u03c0+, K0\nS K+, K\u22170K+, \u03c6\u03c1+,\nK0\nS K\u2217+, and K\u22170K\u2217+; charge-conjugate modes are im-\nplicitly included. The daughter mesons are reconstructed\nvia K0\nS \u2192\u03c0+\u03c0\u2212, K\u22170 \u2192K+\u03c0\u2212, K\u2217+ \u2192K0\nS\u03c0+, \u03c6 \u2192\nK+K\u2212, \u03c1+ \u2192\u03c0+\u03c00, and \u03c00 \u2192\u03b3\u03b3. For the three vector-\npseudoscalar \ufb01nal states, it is required that | cos \u03b8hel| >\n0.20, where \u03b8hel is the angle between the momentum of\nthe charged daughter of the vector particle and the direc-\ntion opposite the D+\ns momentum, evaluated in the rest\nframe of the vector particle.\nBelle combines D+\n(s) candidates with photon candi-\ndates to reconstruct D\u2217+\ns\n\u2192D+\n(s)\u03b3 decays. The mass dif-\nference MD+\ns \u03b3 \u2212MD+\ns must be within 12.0 MeV/c2 of the\nnominal value. Events are required to satisfy 5.25 GeV/c2 <\nmES < 5.45 GeV/c2 and \u22120.15 GeV < \u2206E < 0.10 GeV.\nOnly small contributions from B0\nsB0\ns and B0\nsB\u22170\ns\nevents\nare expected, and these contributions are \ufb01xed relative\nto B\u22170\ns B\u22170\ns\naccording to the Belle measurement of B0\ns \u2192\nD\u2212\ns \u03c0+ decays (Louvot, 2009). Belle quotes \ufb01tted signal\nyields from B\u22170\ns B\u22170\ns\nonly and uses these to determine the\nbranching fractions. Approximately half of the selected\nevents have multiple B0\ns \u2192D(\u2217)+\ns\nD(\u2217)\u2212\ns\ncandidates. These\ntypically arise from photons produced via \u03c00 \u2192\u03b3\u03b3 that\nare wrongly assigned as D\u2217+\ns\ndaughters. For these events\nthe candidate that minimizes a \u03c72 constructed from the\nreconstructed D+\ns and (if present) D\u2217+\ns\nmasses is selected.\nBackground from e+e\u2212\u2192qq (q = u, d, s, c) is rejected\nby using a Fisher discriminant based on a set of modi-\n\ufb01ed Fox-Wolfram moments (see Section 9.5). The remain-\ning background consists of \u03a5(5S) \u2192B(\u2217)\ns B(\u2217)\ns\n\u2192D+\ns X,\n\u03a5(5S) \u2192BBX (bb hadronizes to B0, B0, or B\u00b1), and\nB0\ns \u2192D\u00b1\nsJ(2317)D(\u2217)\ns , D\u00b1\nsJ(2460)D(\u2217)\ns , or D\u00b1\ns D\u2213\ns \u03c00. The\nlast three processes peak at negative \u2206E, and their yields\nare estimated to be small using analogous B0\nd \u2192D\u00b1\nsJD(\u2217)\nbranching fractions. They are considered only when eval-\nuating the systematic uncertainty due to backgrounds.\nThe signal yields are determined via a two-dimensional\nunbinned maximum-likelihood \ufb01t to the mES-\u2206E dis-\ntributions. The signal p.d.f.s have components for cor-\nrectly reconstructed decays, \u201cwrong combination\u201d decays\nin which a non-signal track or \u03b3 is included, and \u201ccross-\nfeed\u201d decays in which a D\u2217\u00b1\ns D\u2213\ns\n(D\u2217+\ns D\u2217\u2212\ns ) is recon-\nstructed as a D+\ns D\u2212\ns (D+\ns D\u2212\ns or D\u2217\u00b1\ns D\u2213\ns ), or a D+\ns D\u2212\ns\n(D\u2217\u00b1\ns D\u2213\ns ) is reconstructed as a D\u2217\u00b1\ns D\u2213\ns\nor D\u2217+\ns D\u2217\u2212\ns\n(D\u2217+\ns D\u2217\u2212\ns ). All signal shape parameters are taken from the\nMC simulation and calibrated using B0\ns \u2192D(\u2217)\u2212\ns\n\u03c0+ and\n175 Speci\ufb01cally, \u03c612 =arg(\u2212M12/\u039312), where M12 and \u039312 are\nthe o\ufb00-diagonal elements of the B0\ns-B0\ns mass and decay matri-\nces. Also see Chapter 10.\n\n733\nTable 23.3.2. The fractions of B0\ns signal events in % (from\nMC simulation) reconstructed as correctly reconstructed (CR)\nand wrong combination (WC) signal, and cross-feed events.\nCross-feed up and down are denoted by \u2020 and \u2021, respectively.\nMode\nCR\nWC\nCross-feed\nD+\ns D\u2212\ns\n76.1\n6.0\n17.1 (D\u2217\u00b1\ns D\u2213\ns )\u2021; 0.8 (D\u2217+\ns D\u2217\u2212\ns )\u2021\nD\u2217\u00b1\ns D\u2213\ns\n44.4\n38.5\n8.2 (D+\ns D\u2212\ns )\u2020; 8.9 (D\u2217+\ns D\u2217\u2212\ns )\u2021\nD\u2217+\ns D\u2217\u2212\ns\n31.8\n37.6\n2.0 (D+\ns D\u2212\ns )\u2020; 28.6 (D\u2217\u00b1\ns D\u2213\ns )\u2020\nTable 23.3.3. B\u22170\ns B\u22170\ns correctly reconstructed signal yield (Y )\nand e\ufb03ciency (\u03b5), including intermediate branching fractions,\nand resulting branching fraction (B). The \ufb01rst uncertainties\nlisted are statistical; the others are systematic. The last error\nfor the sum is due to external factors (\u03a5(5S) \u2192B\u22170\ns B\u22170\ns\nand\nD+\ns branching fractions).\nMode\nY\n\u03b5\nB\n(events)\n(\u00d710\u22124)\n(%)\nD+\n(s)D\u2212\ns\n33.1+6.0\n\u22125.4\n4.72\n0.58 +0.11\n\u22120.09 \u00b1 0.13\nD\u2217\u00b1\ns D\u2213\ns\n44.5+5.8\n\u22125.5\n2.08\n1.76 +0.23\n\u22120.22 \u00b1 0.40\nD\u2217+\ns D\u2217\u2212\ns\n24.4+4.1\n\u22123.8\n1.01\n1.98 +0.33\n\u22120.31\n+0.52\n\u22120.50\nSum\n102.0+9.3\n\u22128.6\n4.32 +0.42\n\u22120.39\n+0.56\n\u22120.54 \u00b1 0.88\nB0 \u2192D(\u2217)+\ns\nD\u2212decays. The fractions of wrong combina-\ntion signal and cross-feed down events are taken from MC\n(see Table 23.3.2); the fractions of cross-feed up events are\n\ufb02oated as they are di\ufb03cult to simulate accurately (many\nB0\ns partial widths are unmeasured).176 As the cross-feed\ndown fractions are \ufb01xed, the separate D+\ns D\u2212\ns , D\u2217\u00b1\ns D\u2213\ns ,\nand D\u2217+\ns D\u2217\u2212\ns\nsamples are \ufb01tted simultaneously.\nThe projections of the \ufb01t are shown in Fig. 23.3.6. The\n\ufb01tted correctly reconstructed signal yields are listed in Ta-\nble 23.3.3 along with signal e\ufb03ciencies (including interme-\ndiate branching fractions from Nakamura et al., 2010) and\nthe resulting branching fractions. The signi\ufb01cance is cal-\nculated as\np\n2 ln(Lmax/L0), where Lmax and L0 are the\nlikelihood values when the signal yield is \ufb02oated and when\nit is set to zero, respectively. Systematic uncertainties on\nthe yield are included in the signi\ufb01cance by smearing the\nlikelihood function by a Gaussian distribution with width\ncorresponding to the total additive systematic uncertainty.\nThe signi\ufb01cance computed for D+\n(s)D\u2212\ns\n, D\u2217\u00b1\ns D\u2213\ns , and\nD\u2217+\ns D\u2217\u2212\ns , is 11.5\u03c3, 10.1\u03c3 and 7.8\u03c3, respectively.\nThe systematic uncertainties are dominated by fac-\ntors external to the analysis, i.e., fs (18%) and the D+\n(s)\nbranching fractions (8.6%). The uncertainty due to the\nwrong combination and cross-feed fractions, which are taken\nfrom the MC simulation, is \u223c4.6% for D\u2217\u00b1\ns D\u2213\ns and \u223c10%\n176 Cross-feed up/down corresponds to a background event\ntype that is mis-reconstructed so as to move upward/downward\nin \u2206E in order to overlap with signal. For example a D+\ns D\u2212\ns\n\ufb01nal state would have to be mis-reconstructed, including an\nextra photon, in order to be reconstructed under the D\u2217+\ns D\u2212\ns\npeak in \u2206E. This is an example of cross-feed up.\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n5\n10\n15\n20\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n5\n10\n15\n20\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n10\n20\n30\n40\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n10\n20\n30\n40\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n10\n20\n30\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n10\n20\n30\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n20\n40\n60\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n20\n40\n60\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n5\n10\nE (GeV)\n6\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\nEvents/ 12.5 MeV\n0\n5\n10\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n10\n20\n30\n)\n2\n (GeV/c\nbc\nM\n5.25\n5.3\n5.35\n5.4\n5.45\n2\nEvents/ 10 MeV/c\n0\n10\n20\n30\nFigure 23.3.6. (left) \u2206E \ufb01t projections for events satisfy-\ning Mbc = mES \u2208[5.41, 5.43] GeV/c2, and (right) mES \ufb01t\nprojections for events satisfying \u2206E \u2208[\u22120.08, \u22120.02] GeV.\nThe top row shows B0\ns \u2192D+\n(s)D\u2212\ns ; the middle row shows\nB0\ns \u2192D\u2217\u00b1\ns D\u2213\ns ; and the bottom row shows B0\ns \u2192D\u2217+\ns D\u2217\u2212\ns .\nThe red dashed curves show correctly reconstructed and wrong\ncombination signal; the blue dash-dotted curves show cross-\nfeed; the magenta dotted curves show background; and the\nblack solid curves show the total. Plots are from Esen (2013).\nfor D\u2217+\ns D\u2217\u2212\ns . The fraction of longitudinal D\u2217+\ns D\u2217\u2212\ns\npolar-\nization fL for this measurement is taken to be the value\nfrom the analogous decay B0\nd \u2192D\u2217+\ns D\u2217\u2212: 0.52\u00b1 0.05 (Be-\nringer et al., 2012). The systematic error is taken to be the\nchange in signal yield when fL is varied over a wide range:\nfrom 2\u03c3 higher than 0.52 down to the low central value\nmeasured by Belle (see below). This error is less than three\nevents on each of the modes.\nIn the limits of mb,c \u2192\u221ewith (mb\u22122mc) \u21920 and Nc\n(number of colors)\u2192\u221e, the D\u2217\u00b1\ns D\u2213\ns and D\u2217+\ns D\u2217\u2212\ns\nmodes\nare CP-even and (along with D+\ns D\u2212\ns ) saturate the width\ndi\ufb00erence \u2206\u0393CP\ns\n(Aleksan, Le Yaouanc, Oliver, P`ene, and\nRaynal, 1993). Assuming negligible CP violation (\u03c6s \u22480),\nthe branching fraction is related to \u2206\u0393s via \u2206\u0393s/\u0393s =\n\n734\n2B/(1 \u2212B). Inserting the total B from Table 23.3.3 gives\n\u2206\u0393s/\u0393s = 0.090 \u00b1 0.009(stat) \u00b1 0.023(syst), which is con-\nsistent with the HFAG average (Asner et al., 2011). This\nresult has similar precision to that of recent measure-\nments (Aaij et al., 2012h; Aaltonen et al., 2012b). The\ncentral value is consistent with, but lower than, the the-\noretical prediction (Lenz and Nierste, 2011); the di\ufb00er-\nence may be due to the unknown CP-odd component in\nB0\ns \u2192D\u2217+\ns D\u2217\u2212\ns , and contributions from three-body \ufb01nal\nstates. The former is estimated to be only 6% for analo-\ngous B0 \u2192D\u2217+\ns D\u2217\u2212decays (Rosner, 1990), but the latter\nare expected to be signi\ufb01cant: Chua, Hou, and Shen (2011)\ncalculate\n\u2206\u0393(B0\ns \u2192D(\u2217)\ns D(\u2217)K(\u2217))/\u0393s = 0.064 \u00b1 0.047. This cal-\nculation predicts \u2206\u0393s/\u0393s from D(\u2217)+\ns\nD(\u2217)\u2212\ns\nalone to be\n0.102 \u00b1 0.030, which agrees well with the Belle result.\nIn addition to measuring the branching fractions,\nBelle also measures the longitudinal polarization frac-\ntion (fL) of B0\ns \u2192D\u2217+\ns D\u2217\u2212\ns . To measure fL, Belle per-\nforms an unbinned maximum likelihood \ufb01t to the co-\nsine of the helicity angles \u03b81 and \u03b82, where \u03b81,2 are\nthe angles between the daughter \u03b3 momentum and the\ndirection opposite to the B0\ns momentum in the D\u2217+\ns\nand D\u2217\u2212\ns\nrest frames, respectively. The angular dis-\ntribution is\n\u0000|A+|2 + |A\u2212|2\u0001 \u0000cos2 \u03b81 + 1\n\u0001 \u0000cos2 \u03b82 + 1\n\u0001\n+\n|A0|24 sin2 \u03b81 sin2 \u03b82, where A+, A\u2212, and A0 are the three\npolarization amplitudes in the helicity basis (see Chap-\nter 12). The fraction fL equals |A0|2/(|A0|2 + |A+|2 +\n|A\u2212|2). To account for resolution and e\ufb03ciency variation,\nthe signal p.d.f.s are taken from MC. The result is\nfL = 0.06 +0.18\n\u22120.17 \u00b1 0.03 ,\n(23.3.5)\nwhere the systematic errors are dominated by the \ufb01xed\nwrong combination signal fractions (+0.013, \u22120.015) and\nthe \ufb01xed background level (\u00b10.022). The helicity angle\ndistributions and \ufb01t projections are shown in Fig. 23.3.7.\n1\ne\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/ 0.2\n0\n5\n10\n15\n2\ne\ncos\n-1\n-0.5\n0\n0.5\n1\nEvents/ 0.2\n0\n5\n10\n15\nFigure 23.3.7. Helicity angle distributions and projections of\nthe \ufb01t result for B0\ns \u2192D\u2217+\ns D\u2217\u2212\ns . The red dashed (blue dash-\ndotted) curves show the transverse (longitudinal) components;\nthe magenta dotted curves show background; and the black\nsolid curves show the total. Plots are from Esen (2013).\n23.3.4 Color suppressed decays B0\ns \u2192J/\u03c8\u03b7(\u2032) and\nB0\ns \u2192J/\u03c8f0(980)\nBelle uses 121.4 fb\u22121 of data accumulated at the \u03a5(5S)\nresonance to search for, and observe, exclusive color-\nsuppressed B0\ns\ndecays with an underlying b \u2192ccs\nquark transition. Among these, the pure CP-eigenstate\n\ufb01nal state decays B0\ns \u2192J/\u03c8f0(980) and B0\ns \u2192J/\u03c8\u03b7(\u2032)\nare of special interest. These decays, which were not yet\nobserved, could be used in the future to study time-\ndependent CP asymmetries. In addition the ratio of the\nB0\ns \u2192J/\u03c8\u03b7\u2032 and J/\u03c8\u03b7 branching fractions constitutes a\ntest of \u03b7 \u2212\u03b7\u2032 mixing.\nThe study of the B0\ns \u2192J/\u03c8f0(980) decay is described\nin detail in Li (2011). The reconstruction of the decay\nmode B0\ns \u2192J/\u03c8f0(980) includes f0(980) decaying into\ntwo charged pions. The main backgrounds are from the\ninclusive decays B0\ns, B0\nd, and B+ \u2192J/\u03c8X, where the con-\ntributions from B0\ns \u2192J/\u03c8\u03b7\u2032 and B+ \u2192J/\u03c8(K+, \u03c0+) are\nmodeled exclusively and set to their known branching frac-\ntions. Since the f0(980) resonance is wide, \u223c60 MeV/c2,\nwe need to describe the M\u03c0\u03c0 spectrum using the Flatt\u00b4e\nformula with a phase-space factor, and the f0(1370) line-\nshape is described using a relativistic Breit-Wigner. Both\nof these line shapes are described in Section 13.2.1. A two-\ndimensional \ufb01t with the variables \u2206E and M\u03c0\u03c0 is per-\nformed to extract the signal yield, where the mES signal\nregion corresponding to the B\u22170\ns B\u22170\ns\nchannel was chosen.\nThe data surprisingly also show an enhancement around\nM\u03c0\u03c0 \u223c1400 MeV/c2, where the \u2206E distribution is also\nstrongly peaked (see Fig. 23.3.8). Thus Belle includes the\ncontribution from the f0(1370) resonance coherently with\nthe f0(980) resonance in the M\u03c0\u03c0 signal \ufb01t model.\nStudies of the decay modes B0\ns \u2192J/\u03c8\u03b7 and J/\u03c8\u03b7\u2032\nare described in (Li, 2012). Five \u03b7 and \u03b7\u2032 sub-channels are\nreconstructed, \u03b7 \u2192\u03b3\u03b3, \u03b7 \u2192\u03c0+\u03c0\u2212\u03c00, \u03b7\u2032 \u2192\u03b7(\u03b3\u03b3)\u03c0+\u03c0\u2212,\n\u03b7\u2032 \u2192\u03b7(\u03c0+\u03c0\u2212\u03c00)\u03c0+\u03c0\u2212and \u03b7\u2032 \u2192\u03c10\u03b3. To use as much\ninformation as possible, a simultaneous \ufb01t to the two-\ndimensional \u2206E - mES distributions of all \ufb01ve sub-channels\nis performed in order to extract the branching fraction.\nThe signal includes contributions from all three B0\ns pro-\nduction channels \u03a5(5S) \u2192B(\u2217)0\ns\nB(\u2217)0\ns\n. The \ufb01t results are\nshown in Fig. 23.3.8.\nBelle observes the three decay modes and measures\ntheir branching fractions:\nB(B0\ns \u2192J/\u03c8f0(980); f0(980) \u2192\u03c0+\u03c0\u2212)\n= (1.16+0.31\n\u22120.19\n+0.15\n\u22120.17\n+0.26\n\u22120.18) \u00d7 10\u22124,\nB(B0\ns \u2192J/\u03c8\u03b7) = (5.10 \u00b1 0.50 \u00b1 0.25 +1.14\n\u22120.79) \u00d7 10\u22124,\nB(B0\ns \u2192J/\u03c8\u03b7\u2032) = (3.71 \u00b1 0.61 \u00b1 0.18 +0.83\n\u22120.57) \u00d7 10\u22124,\n(23.3.6)\nwhere the three quoted uncertainties are statistical, sys-\ntematic, and from NB(\u2217)0\ns\nB(\u2217)0\ns\n. Evidence for the decay with\nthe f0(1370) is also found and the branching fraction\nB(B0\ns \u2192J/\u03c8f0(1370); f0(1370) \u2192\u03c0+\u03c0\u2212)\n= (0.34+0.11\n\u22120.14\n+0.03\n\u22120.02\n+0.08\n\u22120.05) \u00d7 10\u22124\n(23.3.7)\n\n735\n)\n2\n (GeV/c\n\u03c0\n\u03c0\nM\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n)\n2\nEvents/(20 MeV/c\n0\n2\n4\n6\n8\n10\n12\nE (GeV)\n\u2206\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\nEvents/(6 MeV)\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\n E (GeV)\n\u2206\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.016 GeV )\n0\n5\n10\n15\n20\n25\n E (GeV)\n\u2206\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.016 GeV )\n0\n5\n10\n15\n20\n25\n E (GeV)\n\u2206\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.016 GeV )\n0\n2\n4\n6\n8\n10\n12\n E (GeV)\n\u2206\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.016 GeV )\n0\n2\n4\n6\n8\n10\n12\nFigure 23.3.8. Data \ufb01t projections for B0\ns \u2192J/\u03c8 \u03c0+\u03c0\u2212(top\ntwo plots), B0\ns \u2192J/\u03c8 \u03b7 (\u03b7 \u2192\u03b3\u03b3) and B0\ns \u2192J/\u03c8 \u03b7\u2032 (\u03b7\u2032 \u2192\u03c1\u03b3)\n(bottom two plots, respectively). The J/\u03c8 \u03c0+\u03c0\u2212M\u03c0\u03c0 (\u2206E)\ndistributions are for events in the \u2206E (f0(980)) signal region.\nThe J/\u03c8 \u03b7(\u2032) \u2206E distributions are for events in the mES signal\nregion. The dotted curves show the total background contri-\nbution. Plots are from Li (2011, 2012).\nis measured, where the signi\ufb01cance of the signal is 4.2\u03c3.\nThe quoted uncertainties are statistical, systematic, and\nfrom NB(\u2217)0\ns\nB(\u2217)0\ns\n, respectively. The observed J/\u03c8 helicity\ndistributions corresponding to f0(980) and f0(1370) sig-\nnals are consistent with scalar \u03c0\u03c0 resonances.\nThe ratio obtained for the two branching fractions\nB(B0\ns \u2192J/\u03c8\u03b7\u2032)\nB(B0s \u2192J/\u03c8\u03b7) = 0.73 \u00b1 0.14(stat) \u00b1 0.02(syst)\n(23.3.8)\nis smaller than the expected value 1.04 \u00b1 0.04 calculated\nfrom other \u03b7\u2212\u03b7\u2032 mixing measurements at the level of 2.1\u03c3.\nThe measured production channel fractions fB\u22170\ns B\u22170\ns\nand\nfB\u22170\ns B0s from the Bs \u2192J/\u03c8\u03b7(\u2032) study are consistent with\naverages from other measurements.\n23.3.5 Charmless decays B0\ns \u2192hh, h = \u03c0, K\nBelle uses 23.6 fb\u22121 of data to search for the two-body\ncharmless decays B0\ns \u2192K+K\u2212, B0\ns \u2192K0K0, B0\ns \u2192\nK\u2212\u03c0+, and B0\ns \u2192\u03c0+\u03c0\u2212. The branching fractions for\nthese modes may exhibit direct CP asymmetries, as has\nbeen observed for B0\nd \u2192K\u00b1\u03c0\u2213decays. In addition, mea-\nsurement of the K+K\u2212and \u03c0+\u03c0\u2212time-dependent CP\nasymmetries yields information on the CKM phases \u03c61\nand \u03c63 . While the all-charged \ufb01nal states have also been\nstudied at hadron collider experiments (Aaij et al., 2012d;\nAaltonen et al., 2009b; Abulencia et al., 2006c; Morello,\n2007), the K0K0 \ufb01nal state is di\ufb03cult to reconstruct at a\nhadron collider but is well-suited to an e+e\u2212experiment.\nDetails of the analysis are found in Peng (2010). To\nselect B0\ns decays, events are required to satisfy mES \u2208\n[5.35, 5.45] GeV/c2 and \u2206E \u2208[\u22120.20, 0.20] GeV; this re-\ngion is referred to as the \ufb01tting region. Within this region a\nsmaller signal region is de\ufb01ned: mES \u2208[5.40, 5.43] GeV/c2\nand \u2206E \u2208[\u22120.10, 0.00] GeV. The signal region corresponds\nto e+e\u2212\u2192B\u22170\ns B\u22170\ns\nproduction.\nTo suppress the large backgrounds from e+e\u2212\u2192qq\ncontinuum production, a Fisher discriminant based on a\nset of modi\ufb01ed Fox-Wolfram moments is used. This dis-\ncriminant is used to calculate the likelihood that an event\nis signal (Ls) or background (Lqq). A requirement is then\nmade on the ratio Ls/Lqq. After this requirement, there\nare 300, 444, 188, and 345 candidates remaining in the \ufb01t-\nting regions for K+K\u2212, K\u2212\u03c0+, \u03c0+\u03c0\u2212, and K0K0 modes,\nrespectively.\nThe signal yields are obtained from an unbinned ex-\ntended maximum likelihood \ufb01t to the mES and \u2206E distri-\nbutions. Projections of the \ufb01t are shown in Fig. 23.3.9, and\nthe \ufb01t results along with corresponding branching frac-\ntions or 90% C.L. upper limits are listed in Table 23.3.4.\nA signi\ufb01cant signal is observed for the K+K\u2212\ufb01nal\nstate; the signi\ufb01cance is 5.8\u03c3. Systematic uncertainty is\nincluded in the signi\ufb01cance by convolving the likelihood\nfunction with a Gaussian having a width equal to the total\nsystematic uncertainty associated with the \ufb01tting proce-\ndure. The 90% C.L. upper limits (B90%) in Table 23.3.4\n\n736\n0\n5\n10\n15\n0\n5\n10\n15\nEvents / 20MeV\n0\n2\n4\n6\n8\n10\n0\n5\n10\n-0.2\n0\n0.2\n6E (GeV)\n6E (GeV)\n6E (GeV)\n6E (GeV)\n0\n10\n20\n0\n5\n10\n15\nEvents / 5MeV/c2\n0\n5\n10\n0\n5\n10\n5.35\n5.4\n5.45\nMbc (GeV/c2)\nMbc (GeV/c2)\nMbc (GeV/c2)\nMbc (GeV/c2)\nFigure 23.3.9. Distributions of \u2206E (left) and Mbc = mES\n(right) with \ufb01tted distributions superimposed for K+K\u2212(a,b),\nK+\u03c0\u2212(c,d), \u03c0+\u03c0\u2212(e,f), and K0K0 (g,h) events. The \u2206E\n(mES) distributions are for events within the signal region for\nmES (\u2206E). The red dot-dashed curves show the signal com-\nponent; the grey dashed curves show the qq background; the\ngreen dotted curves in the K\u2212\u03c0+ plots show the K+K\u2212cross-\nfeed; and the blue solid curves show the total. Plots are from\nPeng (2010).\nTable 23.3.4. Signal yields, signi\ufb01cances (\u03a3), reconstruction\ne\ufb03ciencies (\u03f5), and either the branching fraction or 90% C.L.\nupper limit for charmless two-body B0\ns decays. The \ufb01rst error\nlisted is statistical, the second error is systematic, and the third\nerror is due to the B(\u2217)0\ns\nB(\u2217)0\ns\nfraction fs.\nMode\nYield\n\u03a3\n\u03f5(%)\nB (10\u22125)\nK+K\u2212\n23.4+5.5\n\u22126.3\n5.8\n24.5\n3.8+1.0\n\u22120.9 \u00b1 0.5 \u00b1 0.5\nK\u2212\u03c0+\n5.4+5.1\n\u22124.3\n1.2\n21.0\n< 2.6\n\u03c0+\u03c0\u2212\n\u22122.0+2.3\n\u22121.5\n\u2212\n14.4\n< 1.2\nK0K0\n5.2+5.0\n\u22124.3\n1.2\n8.0\n< 6.6\nare obtained by integrating the likelihood function:\nZ B90%\n0\nL(B) dB = 0.9 \u00d7\nZ 1\n0\nL(B) dB .\n(23.3.9)\nThis method assumes a uniform prior distribution for B.\nThe K\u2212\u03c0+ and \u03c0+\u03c0\u2212limits are consistent with, but have\nless sensitivity than, results from CDF (Aaltonen et al.,\n2009b; Morello, 2007). At the time of writing, there were\nno other limits on B0\ns \u2192K0K0.\n23.3.6 Penguin decays B0\ns \u2192\u03c6\u03b3, B0\ns \u2192\u03b3\u03b3\nBelle uses 23.6 fb\u22121 of data to search for the radiative\npenguin decay B0\ns \u2192\u03c6\u03b3 and the penguin annihilation de-\ncay B0\ns \u2192\u03b3\u03b3. The Standard Model predictions for these\nprocesses are (3 \u22126) \u00d7 10\u22125 and (5 \u221210) \u00d7 10\u22127, re-\nspectively (Ali, Pecjak, and Greub, 2008; Ball, Jones, and\nZwicky, 2007; Bosch and Buchalla, 2002a; Chang, Lin, and\nYao, 1997; Reina, Ricciardi, and Soni, 1997). Both decays\nproceed via internal loop diagrams and thus are sensitive\nto new physics at high energy scales occurring within the\nloops. For example, supersymmetric models with broken\nR parity (Gemintern, Bar-Shalom, and Eilam, 2004) and\ntwo-Higgs doublet models (Aliev and Iltan, 1998) can in-\ncrease the B0\ns \u2192\u03b3\u03b3 branching fraction by an order of\nmagnitude over the Standard Model prediction. As dis-\ncussed in Section 17.2, a branching ratio measurement of\nB0\ns \u2192\u03b3\u03b3 could be used in the determination of |Vtd/Vts|.\nDetails of these analyses are found in Wicht (2008).\nNeutral \u03c6 mesons are reconstructed via \u03c6 \u2192K+K\u2212, in\nwhich the K+K\u2212invariant mass is required to be within\n12 MeV/c2 (\u223c2.5\u03c3) of the nominal \u03c6 mass. For the B0\ns \u2192\n\u03b3\u03b3 decay, only photons reconstructed within the barrel re-\ngion of the ECL (33\u25e6< \u03b8 < 128\u25e6) are used. To select B0\ns\ndecays, events are required to satisfy mES > 5.3 GeV/c2,\n\u2206E < 0.40 GeV, and either \u2206E > \u22120.40 GeV for B0\ns \u2192\n\u03c6\u03b3 or \u2206E > \u22120.70 GeV for B0\ns \u2192\u03b3\u03b3. To reject large back-\ngrounds from continuum production, especially e+e\u2212\u2192\nqq\u03b3 in which a high energy \u03b3 is produced, a Fisher dis-\ncriminant based on a set of Fox-Wolfram moments is used.\nThe signal yields are obtained from an unbinned ex-\ntended maximum likelihood \ufb01t to the mES, \u2206E, and, for\nB0\ns \u2192\u03c6\u03b3, cos \u03b8hel distributions. The helicity angle \u03b8hel is\nde\ufb01ned as the angle between the B0\ns and the K+ in the\n\u03c6 rest frame. Signal events should follow a 1 \u2212cos2 \u03b8hel\ndistribution, while qq continuum background events tend\nto be distributed \ufb02at in cos \u03b8hel. The \ufb01t obtains separate\nsignal yields for e+e\u2212\u2192B0\nsB0\ns, B\u2217\nsB0\ns, and B\u2217\nsB\u2217\ns produc-\ntion, but only the last of these is used to determine the\nbranching fractions. The projections of the \ufb01t are shown\nin Figs 23.3.10 and 23.3.11, and the \ufb01t results are listed\nin Table 23.3.5.\nA signi\ufb01cant signal is observed for B0\ns \u2192\u03c6\u03b3. The\nsigni\ufb01cance is calculated as\np\n2 ln(Lmax/L0), where Lmax\nand L0 are the likelihood values when the signal yield is\n\ufb02oated and when it is set to zero, respectively; the result\n\n737\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n0\n2\n4\n6\n8\n10\n12\n14\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n0\n2\n4\n6\n8\n10\n12\n14\nE (GeV)\n6\n-0.4 -0.3 -0.2 -0.1 0\n0.1 0.2 0.3 0.4\nEvents / ( 0.08 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nE (GeV)\n6\n-0.4 -0.3 -0.2 -0.1 0\n0.1 0.2 0.3 0.4\nEvents / ( 0.08 GeV )\n0\n2\n4\n6\n8\n10\n12\n14\nhel\ne\ncos \n-1\n-0.5\n0\n0.5\n1\nEvents / ( 0.25 )\n0\n1\n2\n3\n4\n5\n6\n7\n8\nhel\ne\ncos \n-1\n-0.5\n0\n0.5\n1\nEvents / ( 0.25 )\n0\n1\n2\n3\n4\n5\n6\n7\n8\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\nE (GeV)\n6\n \n-0.3\n-0.2\n-0.1\n 0\n0.1\n0.2\n0.3\n0.4\nFigure 23.3.10. Mbc = mES, \u2206E, and cos \u03b8hel projections for\nB0\ns \u2192\u03c6\u03b3. The points with error bars show the data; the thin\nsolid curves show the signal contribution; the dashed curves\nshow the continuum contribution; and the thick solid curves\nshow the total. The bottom right \ufb01gure shows the (mES, \u2206E)\nplane; the dashed lines denote the signal region used to calcu-\nlate the branching fraction. Plots are from Wicht (2008).\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n-4\n-2\n0\n2\n4\n6\n8\n10\n)\n2\n (GeV/c\nbc\nM\n5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44\n )\n2\nEvents / ( 0.01 GeV/c\n-4\n-2\n0\n2\n4\n6\n8\n10\nE (GeV)\n6\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.11 GeV )\n-2\n0\n2\n4\n6\n8\n10\nE (GeV)\n6\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\nEvents / ( 0.11 GeV )\n-2\n0\n2\n4\n6\n8\n10\nFigure 23.3.11. Mbc = mES and \u2206E projections for B0\ns \u2192\n\u03b3\u03b3. The points with error bars show the data; the thin solid\ncurves show the signal contribution; the dashed curves show\nthe continuum contribution; and the thick solid curves show\nthe total. In the mES \ufb01gure, the signals (negative) from\ne+e\u2212\u2192B0\nsB0\ns, B\u22170\ns B0\ns, and B\u22170\ns B\u22170\ns\nappear from left to right.\nPlots are from Wicht (2008).\nis 5.5\u03c3. Systematic uncertainties are evaluated by vary-\ning \ufb01xed parameters in the \ufb01t by \u00b11\u03c3, re\ufb01tting, and tak-\ning the resulting change in the branching fraction as the\nsystematic uncertainty associated with that parameter.\nThe systematic uncertainty is included in the signi\ufb01cance\nby calculating the signi\ufb01cance using the lowest value of\nLmax obtained when evaluating individual systematic un-\ncertainties. The resulting 5.5\u03c3 signi\ufb01cance constitutes the\nTable 23.3.5. Fitted signal yields, and either the branching\nfraction or 90% C.L. upper limit. The \ufb01rst error listed is sta-\ntistical, and the second is systematic.\nMode\nSB0sB0s\nSB\u22170\ns B0s\nSB\u22170\ns B\u22170\ns\nB (10\u22126)\n\u03c6\u03b3\n\u22120.7+2.5\n\u22121.6\n0.5+2.9\n\u22121.9\n18+6\n\u22125\n57+18\n\u221215\n+12\n\u221211\n\u03b3\u03b3\n\u22124.7+3.9\n\u22122.8\n\u22120.8+4.8\n\u22123.8\n\u22127.3+2.4\n\u22122.0\n< 8.7\nobservation of a radiative decay of the B0\ns meson. The\nmeasured branching fraction is in agreement with theo-\nretical predictions.\nThe 90% C.L. upper limit for the B0\ns \u2192\u03b3\u03b3 branching\nfraction (B90%) is obtained using the same method as for\nthe two-body decays (see Eq. 23.3.9) by integrating the\nlikelihood function assuming a uniform prior in B. Sys-\ntematic uncertainties are included by convolving the like-\nlihood function with Gaussian distributions corresponding\nto each systematic error contribution. The resulting up-\nper limit of 8.7 \u00d7 10\u22126 is a signi\ufb01cant improvement over\nprevious limits and about one order of magnitude above\nthe SM prediction.\n23.4 Conclusion\nB0\ns mesons were studied using data collected in the \u03a5(5S)\nenergy region with an e+e\u2212collider by the B Factories.\nMany new B0\ns decays are observed, and branching frac-\ntions for several B0\ns decays are measured with a precision\ncomparable with that of existing results.\nB0\ns measurements at the \u03a5(5S), when compared with\nthe measurements at hadron-hadron colliders, have the\nfollowing advantages:\n1. Channels with neutral particles, such as photons, \u03c00\u2019s,\nor \u03b7 mesons are precisely measured. The bene\ufb01t is most\nprominent in the case of reconstruction of low energy\nphotons or several neutral particles in an event.\n2. Missing mass methods are used with the partial recon-\nstruction technique, due to the low momenta of the B0\ns\nmesons in the \u03a5(5S) rest frame.\n3. The almost 100% trigger e\ufb03ciency is an advantage of\nthe B Factory experiments. No special procedures have\nto be used to estimate the trigger e\ufb03ciencies.\n4. The full number of B0\ns mesons in a data sample is\ncalculated with a small systematic uncertainty. This\nallows one to measure absolute -rather than relative-\nbranching fractions.\nThe most important disadvantages of B0\ns meson stud-\nies at the \u03a5(5S) are the smaller initial number of B0\ns\nmesons, the lack of ability to resolve B0\ns oscillations (hence\nit is not possible to perform time-dependent CP analyses),\nand the necessity to choose between data taking at the\n\u03a5(5S) and \u03a5(4S). In general B0\ns meson studies with e+e\u2212\ncolliders at the \u03a5(5S) and at hadron-hadron machines are\ncomplementary and together provide the best coverage of\nthe whole spectrum of the most interesting decay chan-\nnels.\n\n738\nTable 23.4.1. Measured B0\ns branching fractions with statistical, systematic (without fs), and fs uncertainties are shown. If\nno signi\ufb01cant signal is observed the 90% C.L. upper limit is given. If the third uncertainty is absent, the second uncertainty\nincludes both systematic uncertainties. The corresponding B0 branching fractions from PDG Beringer et al. (2012) are also\nshown for comparison.\nB0\ns mode\nB\nB0 mode\nB [PDG]\nB0\ns \u2192D\u2212\ns \u03c0+\n(3.67+0.35\n\u22120.33\n+0.43\n\u22120.42 \u00b1 0.49) \u00d7 10\u22123\nB0 \u2192D\u2212\u03c0+\n(2.68 \u00b1 0.13) \u00d7 10\u22123\nB0\ns \u2192D\u2217\u2212\ns \u03c0+\n(2.4+0.5\n\u22120.4 \u00b1 0.3 \u00b1 0.4) \u00d7 10\u22123\nB0 \u2192D\u2217\u2212\u03c0+\n(2.76 \u00b1 0.13) \u00d7 10\u22123\nB0\ns \u2192D\u2212\ns \u03c1+\n(8.5+1.3\n\u22121.2 \u00b1 1.1 \u00b1 1.3) \u00d7 10\u22123\nB0 \u2192D\u2212\u03c1+\n(7.8 \u00b1 1.3) \u00d7 10\u22123\nB0\ns \u2192D\u2217\u2212\ns \u03c1+\n(11.8+2.2\n\u22122.0 \u00b1 1.7 \u00b1 1.8) \u00d7 10\u22123\nB0 \u2192D\u2217\u2212\u03c1+\n(6.8 \u00b1 0.9) \u00d7 10\u22123\nB0\ns \u2192D\u2213\ns K\u00b1\n(2.4+1.2\n\u22121.0 \u00b1 0.3 \u00b1 0.3) \u00d7 10\u22124\nB0 \u2192D\u2212K+\n(1.97 \u00b1 0.21) \u00d7 10\u22124\nB0\ns \u2192D+\ns D\u2212\ns\nB0 \u2192D\u2212D+\ns\n(7.2 \u00b1 0.8) \u00d7 10\u22123\nB0\ns \u2192D\u2217\u00b1\ns D\u2213\ns\nB0 \u2192D\u2217\u00b1D\u2213\ns\n(1.54 \u00b1 0.19) \u00d7 10\u22122\nB0\ns \u2192D\u2217+\ns D\u2217\u2212\ns\nB0 \u2192D\u2217\u2212D\u2217+\ns\n(1.77 \u00b1 0.14) \u00d7 10\u22122\nB0\ns \u2192J/\u03c8\u03b7\n(5.10 \u00b1 0.50 \u00b1 0.25+1.14\n\u22120.79) \u00d7 10\u22124\nB0 \u2192J/\u03c8K0\n(8.74 \u00b1 0.32) \u00d7 10\u22124\nB0\ns \u2192J/\u03c8\u03b7\u2032\n(3.71 \u00b1 0.61 \u00b1 0.18+0.83\n\u22120.57) \u00d7 10\u22124\nB0 \u2192J/\u03c8K0\n(8.74 \u00b1 0.32) \u00d7 10\u22124\nB0\ns \u2192J/\u03c8f0(980),\n(1.16+0.31\n\u22120.19\n+0.15\n\u22120.17\n+0.26\n\u22120.18) \u00d7 10\u22124\nf0(980) \u2192\u03c0+\u03c0\u2212\nB0\ns \u2192K+K\u2212\n(3.8+1.0\n\u22120.9 \u00b1 0.5 \u00b1 0.5) \u00d7 10\u22125\nB0 \u2192K+\u03c0\u2212\n(1.94 \u00b1 0.06) \u00d7 10\u22125\nB0\ns \u2192K\u2212\u03c0+\n< 2.6 \u00d7 10\u22125\nB0\ns \u2192\u03c0+\u03c0\u2212\n< 1.2 \u00d7 10\u22125\nB0\ns \u2192K0 \u00afK0\n< 6.6 \u00d7 10\u22125\nB0\ns \u2192\u03c6\u03b3\n(5.7+1.8\n\u22121.5\n+1.2\n\u22121.1) \u00d7 10\u22125\nB0 \u2192K\u22170\u03b3\n(4.33 \u00b1 0.15) \u00d7 10\u22125\nB0\ns \u2192\u03b3\u03b3\n< 8.7 \u00d7 10\u22126\nThe B0\ns decay branching fractions measured at the\n\u03a5(5S) are summarized in Table 23.4.1. The branching\nfractions of the corresponding B0 decays are also shown\nfor comparison.\nThe results obtained demonstrate that the B0\ns and B0\nmeson branching fractions are consistent within uncertain-\nties. The B0\ns branching fractions with \u03b7 and \u03b7\u2032 mesons in\nthe \ufb01nal state are expected to be about 1/3 of the corre-\nsponding B0 branching fractions with a K0, because the\n\u03b7(\u2032) meson is assumed to be approximately one third s\u00afs.\nThe results indicate that the larger mass of the s-quark,\ncompared with the mass of the d-quark, does not result\nin signi\ufb01cant rearrangement of the intrinsic structure of\nthe B meson, consisting of both heavy and light quarks. It\nshould also be noted that Belle did not \ufb01nd any signi\ufb01cant\ndeviations of the experimentally measured B0\ns branching\nfractions from the corresponding theoretical predictions.\n\n739\nChapter 24\nQCD-related physics\nAlthough the main objective of the B Factories is the\nstudy of \ufb02avor physics and weak decays, some additional\ninsights on QCD-related physics have been gained. From\nthe data of both BABAR and Belle, the functions for the\nfragmentation of light quarks into light hadrons and for\nthe fragmentation of the charm quark into charmed mesons\nand baryons have been extracted with improved precision.\nNot only the unpolarized, but also the spin-dependent\nfragmentation functions have been measured, adding a\ncrucial input to studies of transverse quark polarization\nin the nucleon.\nAnother QCD-related issue is the search for exotic\nstates. While charmonium-like exotic states are discussed\nin Section 18.3, searches for exotic states composed of light\nquarks are described in Section 24.2. Searches for such\nstates have been performed by BABAR and Belle, showing\nno evidence for any of the previously claimed pentaquark\nstates nor for any other member of the pentaquark family.\n24.1 Fragmentation\nEditors:\nFabio Anulli (BABAR)\nRalf Seidl (Belle)\nShunzo Kumano (theory)\nAdditional section writers:\nDave Muller\n24.1.1 Introduction\nA consequence of the con\ufb01ning property of the strong in-\nteraction is that energetic quarks and gluons produced\nin high-energy collisions appear as collimated \u201cjets\u201d of\nhadrons. The process by which this occurs, called frag-\nmentation, is understood qualitatively, but there are few\nquantitative theoretical predictions. A better understand-\ning of this process is desirable as a probe of the strong\ninteraction, and an empirical understanding is essential to\nthe interpretation of much current and future high-energy\ndata, in which the observable products of interactions and\ndecays of heavy particles, known and yet to be discov-\nered, appear as hadronic jets. The intrinsic properties of\njets are best studied in e+e\u2212annihilation, where hadrons\noriginate from primordial quarks and antiquarks, which\nare produced back-to-back in the CM frame. This kind of\nprocess leads to \ufb01nal sates with two jets, in case hard glu-\nons are emitted by the quarks three and more jet events\nemerge.\nJets can be characterized by their overall structure,\ne.g. shape, energy \ufb02ow, etc., and by the number, types\nand momentum spectra of hadrons produced. These prop-\nerties depend on the energy, mass, charge and spin of the\nquark or gluon that initiated the jet. The initial quark is\ncontained in a leading hadron that carries its \ufb02avor, per-\nhaps its spin, and a fraction of its energy that is higher,\non average, for heavier quarks. Additional qq pairs are\nproduced from the vacuum to form the other hadrons in\nthe jet, with probabilities that depend strongly on the\nquark mass, with ss pairs being suppressed with respect\nto uu and dd pairs by a factor of roughly three, and heav-\nier quarks by much larger factors. In this way, c and b\njets generally contain a single D or B hadron with typi-\ncally more than half the jet energy, along with a few softer\nhadrons. However, the leading heavy hadron decays into a\nnumber of softer particles that in\ufb02uence the jet structure.\nLighter \ufb02avor jets contain more primary hadrons with a\nbroader range of momentum.\nHadron-production processes in high-energy reactions\nare also important for investigating properties of quark-\nhadron matter in heavy-ion collisions and for \ufb01nding the\norigin of the nucleon spin in polarized lepton-nucleon and\nnucleon-nucleon reactions. In describing the hadron-pro-\nduction cross sections in high-energy reactions, fragmen-\ntation functions (FFs) are essential quantities. A fragmen-\ntation function quanti\ufb01es the probability of producing a\nparticular hadron h in a jet initiated by a particular par-\nton. They are measured most directly by the hadron pro-\nductions in electron-positron annihilation, e+e\u2212\u2192h X,\nwhere h is the hadron under investigation and X is the\nrest of the hadronic \ufb01nal state.\nIn e+e\u2212annihilation the initial partonic state is rather\nsimple and can be described by a quark-antiquark pair at\nleading order in the strong coupling \u03b1S. In single \u03b3\u22c6ex-\nchange (see Fig. 24.1.1), the relative production of quark\n\ufb02avors is given by the charge squared of the quarks. At en-\nergy scales below the open bottom threshold the produc-\ntion of uu and cc pairs amounts to 40% each, and that of\ndd and ss pairs to 10% each. The cross section for hadron\nproduction e+ + e\u2212\u2192h + X is described by a quark-\nantiquark pair creation by the reaction e+e\u2212\u2192q\u00afq and\nhigher-order corrections such as e+e\u2212\u2192q\u00afqg, and then by\na fragmentation process to create a hadron h from quark\n(q), antiquark (\u00afq), or gluon (g). The hadron multiplicity177\nis de\ufb01ned by the hadron-production cross section and the\ntotal hadronic cross section (Ellis, Stirling, and Webber,\n1996) \u03c3tot = \u03c3e+e\u2212\u2192q\u00afq:\nF h(z, Q2) =\n1\n\u03c3tot\nd\u03c3(e+e\u2212\u2192hX)\ndz\n,\n(24.1.1)\nwhere the variable Q2 is the virtual photon momentum\nsquared in e+e\u2212\u2192\u03b3\u22c6, and it is given by Q2 = s, with \u221as\nbeing the CM energy. The variable z is the hadron energy\nEh scaled to the beam energy \u221as/2:\nz \u2261\nEh\n\u221as/2 = 2Eh\nQ .\n(24.1.2)\n177 The hadron multiplicity is often also called fragmentation\nfunction despite being a di\ufb00erent object.\n\n740\nFigure\n24.1.1.\nTypical\nhadron-production\nprocess\nin\nelectron-positron annihilation (e+ + e\u2212\u2192h + X).\nThe total cross section is described by the q\u00afq-pair creation\nprocesses, e+e\u2212\u2192\u03b3\u22c6\u2192q\u00afq and higher-order corrections:\n\u03c3tot = 4\u03c0\u03b12\ns\nX\nq\ne2\nq\n\u0014\n1 + \u03b1S(Q2)\n\u03c0\n+ \u00b7 \u00b7 \u00b7\n\u0015\n.\n(24.1.3)\nAt CM energies higher than those available at B factories,\nZ0 exchange must be taken into account, as it modi\ufb01es the\ntotal cross section and the \ufb02avor composition, but not the\nFF for a given \ufb02avor.\nThe hadron multiplicities are related to the actual frag-\nmentation functions which are de\ufb01ned as parton densities\nfor inclusively detecting a hadron h with fractional energy\nz from an initial state parton q. Sometimes FFs are also\nobtained as a di\ufb00erential in the fractional energy and the\nhadron transverse momentum Ph,\u22a5relative to the initial\nparton energy and can also depend on the parton and\nhadron spin orientations, d2\u03c3/dzdPh,\u22a5. The fragmenta-\ntion process is described by the sum of hadrons produced\nfrom primary quarks, antiquarks, and gluons (Ellis, Stir-\nling, and Webber, 1996):\nF h(z, Q2) =\nX\ni\nCi(z, \u03b1S) \u2297Dh\ni (z, Q2).\n(24.1.4)\nHere, Dh\ni (z, Q2) is a fragmentation function of the hadron\nh created by a parton i (= u, d, s, \u00b7\u00b7\u00b7, g), and it indicates\nthe probability of producing the hadron h, from the parton\ni with the energy fraction z at the momentum squared\nscale Q2. The convolution integral \u2297is de\ufb01ned by\nf(z) \u2297g(z) =\nZ 1\nz\ndy\ny f(y)g\n\u0012z\ny\n\u0013\n.\n(24.1.5)\nThe simplest FF is this unpolarized FF Dh\ni (z, Q2). Po-\nlarized FFs also exist and are discussed in Section 24.1.3.\nAlthough the FF has the meaning of the production prob-\nability in the leading order (LO) of the running coupling\nconstant \u03b1S, it is a scheme-dependent quantity if higher-\norder corrections are taken into account. The coe\ufb03cient\nfunction Ci(z, \u03b1S) is trivial at leading order. At next-to-\nleading order (NLO), quark-gluon splitting appears, the\ncorresponding coe\ufb03cient functions are needed, and the\ngluon FF appears. The NLO results are listed, for exam-\nple, in Kretzer (2000) and Albino, Kniehl, and Kramer\n(2005, 2008) for the modi\ufb01ed minimal subtraction (MS)\nscheme. The coe\ufb03cient functions are now known to the\nNNLO level for the unpolarized case (Mitov, Moch, and\nVogt, 2006).\nA sum rule exists for the FFs because of energy con-\nservation. As the variable z is the energy fraction for the\nproduced hadron, its sum weighted by the fragmentation\nfunctions should be unity:\nX\nh\nZ 1\n0\ndz z Dh\ni (z, Q2) \u2261\nX\nh\nM h\ni = 1,\n(24.1.6)\nwhere M h\ni is the second moment of Dh\ni (z, Q2). The mean-\ning of this result is that the sum of all \ufb01nal state hadrons\u2019\nfractional energies integrated over the energy fraction has\nto retain the initial parton\u2019s energy. Not all of the hadrons\nare observed experimentally, so that in practice it is not\npossible to con\ufb01rm this sum rule precisely from measure-\nments. However, it is a useful relation in determining the\nFFs when performing a global analysis by providing a con-\nstraint on their magnitude.\nAs\nthis\nhadron\nformation\ntakes\nplace\nat\nsmall\nmasses and low energies it can only be described non-\nperturbatively. In the parton model, the fragmentation\nfunction is de\ufb01ned by (Brock et al., 1995; Collins, 1993)\nDh\ni (x) =\nX\nX\nZ dy\u2212\n24\u03c0 eik+y\u2212Tr\n\u0002\n\u03b3+\n0\n\f\f\u03c8i(0, y\u2212, 0\u22a5)\n\f\f h, X\n\u000b\n\u00d7\n\nh, X\n\f\f \u00af\u03c8i(0)\n\f\f 0\n\u000b\u0003\n,\n(24.1.7)\nwhere k is the parent quark momentum, the light-cone no-\ntation is de\ufb01ned by a\u00b1 = (a0 \u00b1 a3)/\n\u221a\n2, the variable z is\nthen given by z = p+\nh /k+ with the hadron momentum ph,\nand \u22a5is the transverse direction to the third coordinate.\nTo be precise, a gauge link needs to be introduced in Eq.\n(24.1.7) so as to satisfy color gauge invariance. In the par-\nton model, fragmentation functions are generally de\ufb01ned\nin a similar way as the parton distribution functions, how-\never they cannot be calculated by lattice simulations due\nto the hadron in the \ufb01nal state.\nThe Q2 evolution for the fragmentation functions is\ncalculated by perturbative QCD in the same way as the\none for the parton distribution functions. It is given by the\ntime-like DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-\nParisi) evolution equations (Ellis, Stirling, and Webber,\n\n741\n1996; Hirai and Kumano, 2011):\n\u2202\n\u2202ln Q2 Dh\nq+\ni (z, Q2) = \u03b1S(Q2)\n2\u03c0\n\u0014 X\nj\nPqjqi(z) \u2297Dh\nq+\nj (z, Q2)\n+ 2Pgq(z) \u2297Dh\ng (z, Q2)\n\u0015\n,\n\u2202\n\u2202ln Q2 Dh\ng (z, Q2) = \u03b1S(Q2)\n2\u03c0\n\u0014\nPqg(z) \u2297\nX\nj\nDh\nq+\nj (z, Q2)\n+ Pgg(z) \u2297Dh\ng (z, Q2)\n\u0015\n,\n(24.1.8)\nwhere Dh\nq+(x, Q2) denotes the fragmentation-function\ncombination\nDh\nq (x, Q2) + Dh\n\u00afq (x, Q2).\nThe\nfunctions\nPqjqi(z), Pgq(z), Pqg(z), and Pgg(z) are splitting func-\ntions, where the o\ufb00-diagonal elements Pgq(z) and Pqg(z)\nare interchanged in the splitting-function matrix from the\nparton distribution function case (Ellis, Stirling, and Web-\nber, 1996). One should note that the time-like functions\nare slightly di\ufb00erent from the space-like ones in the next-\nto-leading order (Ellis, Stirling, and Webber, 1996).\nThere are measurements of the FFs in electron-positron\nannihilation at various center-of-mass energies. However,\nthey are not accurate enough to determine precise func-\ntional forms. Data were taken mainly in the Z-mass region\nat the SLAC Linear Collider (SLC) and Large Electron-\nPositron Collider (LEP), which means that the scaling vio-\nlation has not been determined precisely for the multiplic-\nities. The FFs still have large uncertainties, particularly\nfor the so-called disfavored functions (such as D\u03c0\u2212\nu (z, Q2),\ni.e. the function describing a \u03c0\u2212creation from an initial\nu quark - as opposed to the favored FF D\u03c0+\nu (x, Q2)), even\nfor the pion, and there are large discrepancies among the\nobtained FFs from di\ufb00erent global analysis groups.\nThe Belle and BABAR data play an important role in\nthe accurate determination of the FFs by extending the\nkinematical region of z due to high-statistics measure-\nments. The Belle and BABAR measurements are performed\nat CM energies around 10 GeV. Together with the ac-\ncurate measurements at the Z mass the scaling behavior\nof FFs can be studied. The knowledge of the energy de-\npendence will improve the physics results of high-energy\nexperiments at LHC and RHIC, and other high-energy\nfacilities.\nGenerally, fragmentation functions can be de\ufb01ned for\nany kind of \ufb01nal state hadron as long as it has been pro-\nduced in strong processes only. Hadrons being produced\nin weak decays should in principle not be included, but\ngiven the di\ufb03culty of determining their relative fractions\nexperimentally they are often included. So far, most of\nthe fragmentation functions were obtained from e+e\u2212an-\nnihilation alone (Albino, Kniehl, and Kramer, 2008; Hirai,\nKumano, Nagai, Oka, and Sudoh, 2007) due to their clean\ninitial state. However, as the unpolarized parton distribu-\ntion functions in the intermediate xBjorken range, where\nxBjorken is the momentum fraction a parton carries rela-\ntive to the nucleon, are relatively well known, recent ex-\ntractions of FFs from the world data also include some\nsemi-inclusive deep inelastic scattering and proton-proton\ncollision data, such as in de Florian, Sassot, and Strat-\nmann (2008). Given its non-perturbative nature and the\nneed for a DGLAP evolution to obtain all components,\nFFs are generally obtained from a global analysis of the\nworld data where available. In such a global analysis the\nfragmentation functions are parameterized at an initial\nscale which is \ufb01t to all existing data. While the e+e\u2212\ndata is usually quite precise, it is generally limited to\nthe sum of quark and antiquark FFs as it is not known\nfrom which side a \ufb01nal state hadron emerged. Also, as\nmentioned above, the gluon FF only appears in NLO and\ntherefore can only be obtained from e+e\u2212data by com-\nparing very di\ufb00erent scales via the evolution. Therefore\nthe data from semi-inclusive DIS and proton-proton scat-\ntering gives some valuable additions to the global analysis,\nbut also the large lever arm between data obtained close\nto the Z0 resonance and the B Factories\u2019 data is quite\nuseful.\nBelle and BABAR have studied the inclusive momen-\ntum spectra of a number of light and charmed hadrons in\ne+e\u2212annihilation. They have also studied spin-induced\ncorrelations between particles in opposite jets. These are\ndescribed in the subsections below.\n24.1.2 Unpolarized fragmentation functions\nThe production rate of a particular type of hadron in jets\nof a particular (set of) \ufb02avor(s) can be quanti\ufb01ed by the\nmultiplicities F h(z, Q2) (see Eq. 24.1.1), which is the av-\nerage number of hadrons of type h produced per unit z\nin a jet, and z is a measure of the fraction of the quark\u2019s\nenergy carried by the hadron. Apart from the normalized\nhadron energy z, a number of other de\ufb01nitions xh related\nto normalized momenta are in use, and the relevant one\nis de\ufb01ned below in each case.\nFFs cannot be calculated perturbatively in QCD, so\nthere are no \ufb01rm theoretical predictions. The ansatz of lo-\ncal parton-hadron duality (LPHD) combined with calcula-\ntions of gluon radiation in the modi\ufb01ed leading logarithm\napproximation (MLLA) (Azimov, Dokshitzer, Khoze, and\nTroyan, 1985) predicts properties of the distributions of\nthe dimensionless variable \u03be =ln(\u221as/2p\u2217) for light hadrons,\nwhere p\u2217is the magnitude of the hadron momentum in\nthe CM system. The parameters depend on the hadron\nmass and the jet energy. There are several phenomeno-\nlogical models of fragmentation, involving three di\ufb00erent\nhadron production methods. Here we consider represen-\ntatives of each, the HERWIG 5.8 (Marchesini et al., 1992),\nJetset 7.4 (Sj\u00a8ostrand, 1994) and UCLA 4.1 (Chun and\nBuchanan, 1998) event generators.\nFor su\ufb03ciently heavy quarks q, the high mass pro-\nvides a convenient cut-o\ufb00point in the perturbative regime\nand the multiplicity F q(xq) of the heavy quark before\nhadronization can be calculated (Braaten, Cheung, Flem-\ning, and Yuan, 1995; Colangelo and Nason, 1992; Collins\nand Spiller, 1986; Dokshitzer, Khoze, and Troian, 1996;\n\n742\nMele and Nason, 1991). The observable heavy hadron mul-\ntiplicity F H(xH) is thought to be related by a simple con-\nvolution or hadronization model. Several phenomenologi-\ncal models of heavy-quark fragmentation have been pro-\nposed (Andersson, Gustafson, Ingelman, and Sj\u00a8ostrand,\n1983; Bowler, 1981; Kartvelishvili, Likhoded, and Petrov,\n1978; Peterson, Schlatter, Schmitt, and Zerwas, 1983).\nPredictions depend on the quark mass, with F H(xp) being\nmuch harder for b hadrons than c hadrons, and in some\ncases on the mass and quantum numbers of H. Hadrons\ncontaining the same heavy quark type are generally pre-\ndicted to have similar F H(xH), although di\ufb00erences be-\ntween mesons and baryons have been suggested (Chun and\nBuchanan, 1998; Kartvelishvili and Likhoded, 1979).\nThe scaling properties, or \u221as dependences, of hadron\nproduction are of particular interest. Since QCD is only\nweakly scale dependent, distributions of xh should be al-\nmost independent of \u221as, except for the e\ufb00ects of hadron\nmasses/phase space and the running of \u03b1S. However, the\nquark \ufb02avor composition varies with \u221as in e+e\u2212annihila-\ntion, and must be modeled for light hadrons. This provides\na nice test of models and MLLA QCD.\nSo far, Belle and BABAR have measured multiplicities\nfor several of the lightest and heaviest particles produced\nat around 10.5 GeV. These include the light, non-strange\nmesons \u03c0\u00b1 and \u03b7, the lightest strange meson K\u00b1, and the\nlightest baryon p/p, which can be used to test MLLA QCD\nand hadronization models. The \ufb01ve charmed mesons D0,\nD+, D+\ns , D\u22170 and D\u2217+, and three charmed baryons \u039b+\nc ,\n\u039e0\nc and \u21260\nc can be used to test models and calculations\nfor heavy quarks. In addition, the correlated production\nof \u039b+\nc and \u039b\n\u2212\nc has been studied, providing a stringent test\nof models in an extreme region. These are discussed in the\nfollowing subsections.\n24.1.2.1 Light hadrons \u03c0\u00b1, K\u00b1, p/p\nBABAR and Belle have measured the inclusive production\ncross sections of charged pions and kaons in e+e\u2212\u2192qq\nevents at the o\ufb00-resonance CM energies of 10.54 GeV and\n10.52 GeV, respectively, while BABAR also measured pro-\ntons and neutral \u03b7 meson at 10.54 GeV. The data sets used\ncontain integrated luminosities of 0.91 fb\u22121 for BABAR\nand 68.0 fb\u22121 for Belle. Uncertainties of inclusive mea-\nsurements of fragmentation are dominated by systematic\nuncertainties even in relatively small samples of data with\ngood running conditions. Hence the data are selected from\nruns with very stable running conditions.\nInclusive measurements such as these require a clean\nsample of multihadron events with low bias against parti-\ncles of any particular type, multiplicity or momentum. All\nresults reported in this Section are displayed as a function\nof the normalized hadron energy z.\nFor the charged \u03c0/K/p analyses, BABAR (Muller, 2004)\nrequires: three or more well reconstructed charged tracks\nthat form a good vertex located within 5 mm of the beam\naxis and within 5 cm of the center of the collision region\nalong the beam axis; a sum of charged plus neutral energy\nEtot in the range 5\u201314 GeV; R2 (see Section 9.3) less than\n0.9; the polar angle \u03b8\u2217\nthrust of the event thrust axis with\nrespect to the electron beam direction in the CM frame\nto satisfy178 | cos \u03b8\u2217\nthrust| < 0.8; the track with the highest\nmomentum in the laboratory frame p, not to be identi\ufb01ed\nas an electron in events with fewer than six good tracks,\nand neither of the two highest-p tracks to be identi\ufb01ed as\nan electron in events with only three tracks.\nThe requirements on Etot and cos \u03b8\u2217\nthrust select events\nwell contained within the sensitive volume of the detector\nwith low bias on the momentum spectra. The e\ufb03ciency\nof this selection is determined on a simulated sample of\nevents, and corrected for di\ufb00erences between data and sim-\nulation. The result is 68% for u\u00afu, d \u00afd and s\u00afs events, and\n73% for c\u00afc events. Similarly, they estimate backgrounds\nof 5.1% and 0.1%, respectively, from \u03c4-pair and radiative\nBhabha events, which contribute up to 20% and 8% of the\ncharged tracks at the highest momenta. The background\nfrom two-photon processes is below 1%, and backgrounds\nfrom \u00b5-pairs, hard initial state radiation (i.e. photon ener-\ngies of more than several 100 MeV), beam-gas and beam-\nwall interactions are negligible.\nHigh quality charged tracks are selected and identi\ufb01ed\nas pions, kaons or protons using the momentum and ion-\nization energy loss measured in the DCH and the velocity\nmeasured via the Cherenkov angle in the DIRC (see Chap-\nter 2). A global likelihood algorithm is used that considers\nthe set of dE/dx values for the reconstructed tracks in\neach event, along with the set of Cherenkov angles mea-\nsured from photons detected in the DIRC (Chapter 5).\nThe likelihood is optimized to keep the misidenti\ufb01cation\nrates as low as reasonably possible, while maintaining high\nidenti\ufb01cation e\ufb03ciencies that vary slowly with both mo-\nmentum and polar angle. It identi\ufb01es pions and kaons\n(protons) with e\ufb03ciencies of over 99% for p below 0.7\n(1.0) GeV/c, over 90% for p below 1.5 (4.5) GeV/c, and\nover 50% for p below 4.0 (6.5) GeV/c. Misidenti\ufb01cation\nrates are below 1%, 6% and 4% in these three regions.\nSince the e+e\u2212system is boosted in the laboratory\nframe of reference, the analysis is performed separately\nfor tracks in six di\ufb00erent polar angle regions. The tracks\nin each region span di\ufb00erent ranges of p, but each is trans-\nformed into the same range of momenta in the CM frame,\np\u2217. This provides a set of powerful cross checks on the de-\ntector performance and material interactions, backgrounds,\nthe true polar angle and p\u2217distributions, and the boost\nvalue itself. In each region, the full matrix of hadron iden-\nti\ufb01cation e\ufb03ciencies (\u03c0\u00b1, K\u00b1, p\u00b1) is calibrated from the\ndata as a function of p using a set of control samples\n(Chapter 5). The corrected e\ufb03ciency matrices are inverted\nand used to convert the numbers of identi\ufb01ed pions, kaons\nand protons into di\ufb00erential production cross sections per\n178 The event thrust axis is calculated using all particles in\nthe event, or all charged tracks in the case of the BABAR light\nhadron analysis; it approximates the back-to-back direction of\nthe two leading jets typically produced in events from contin-\nuum. We note that the thrust de\ufb01ned in Section 9.3, is instead\nbuilt upon the decay products of the reconstructed B meson,\nwith \u03b8T the angle between the thrust of the B decay products\nand the thrust of the rest of the event.\n\n743\nhadronic event per unit momentum in the laboratory frame,\n(1/Nevt)dni/dp, i = \u03c0, K, p. Each corrected cross section\nis then transformed into the e+e\u2212CM frame. Results\nfrom the six regions are compared as a cross check, and\nthen combined to give the \ufb01nal measured cross sections,\n(1/Nevt) dni/dp\u2217. There is a small correction for residual\nlepton contamination, and results are given in two ways,\nincluding or excluding the contributions from decays of\nK0\nS and weakly decaying strange baryons; here we con-\nsider the latter.\nThe total systematic uncertainty on the pion cross sec-\ntion is at the level of a few percent in the full momentum\nrange. It is dominated at low momenta by tracking e\ufb03-\nciencies, by background contamination between 0.75 and\nabout 3 GeV/c, and by particle identi\ufb01cation at the high-\nest momenta. The uncertainties on the kaon and proton\ncross sections have similar patterns, but are signi\ufb01cantly\nlarger, in particular for momenta below 0.2 GeV/c and\nabove 4 GeV/c.\nThe uncertainties all have large point to point corre-\nlations. There is an overall normalization uncertainty of\n0.9% that does not a\ufb00ect the shape of any cross section.\nSeveral uncertainties are fully correlated over the entire\np\u2217range, but vary slowly with p\u2217and can have broad ef-\nfects on the shape. The uncertainties from the calibration\nof the particle ID are correlated over ranges of a few bins,\nand can lead to apparent structures.\nThe Belle analysis (Leitgab, 2012, 2013) similarly re-\nquires events with at least 3 charged tracks, a visible en-\nergy above 7 GeV and either jet mass179 above 1.8 GeV or\nthe jet mass normalized by the visible energy to be above\n0.25. Tracks are selected within the central detector with\n\u22120.511 \u2264cos \u03b8 < 0.842, where the polar angle \u03b8 is calcu-\nlated in the laboratory frame, with a minimum momen-\ntum of a track of 500 MeV and at least three hits in the\nvertex detector. Tracks are also required to originate from\nwithin distances of 1.3 cm radially and 4 cm longitudi-\nnally from the interaction point. The particles were iden-\nti\ufb01ed as pions, kaons, protons, electrons or muons via like-\nlihood ratios obtained from the information of the CDC,\nACC, TOF, ECL, and KLM (see Chapter 2). The charge\nseparated particle identi\ufb01cation e\ufb03ciencies and fake rates\nwere evaluated using a data driven method by relying on\nknown decays of D\u2217, \u039b and J/\u03c8\u2019s (see Chapter 5). These\nmatrices for \u03c0, K, p, \u00b5 and e were obtained in a \ufb01ne 17\n\u00d7 9 (p, cos \u03b8) binning. Where not completely de\ufb01ned by\ndata, an interpolation between adjacent bins or extrapo-\nlation based on MC simulation (Pythia 6.2 for u, d, s, c\nproduction, a dedicated \u03c4 +\u03c4 \u2212and electro-magnetic pro-\ncess generators) was used. The extracted matrices were\ninverted; the uncertainties arising from the limited size\nof the data control samples were assigned as systematic\nuncertainties. Another important uncertainty in the Belle\nanalysis arises from momentum smearing which migrates\nthe contents of a certain z-bin over several, mostly adja-\n179 The jet mass squared is de\ufb01ned as the square of the sum of\nall particle four-momenta in one hemisphere: M 2 =\n\u0000P\ni pi\n\u00012\nwhere the hemisphere is de\ufb01ned by the normal to the thrust\naxis.\ncent bins. Smearing was evaluated using MC and corrected\nfor by inverting the smearing matrix (from generated z\nbin a to reconstructed z bin). The statistical uncertainties\non the matrix elements were converted into systematic\nuncertainties of the multiplicities. Further corrections in-\nclude in-\ufb02ight decays, detector interactions as well as re-\nconstruction e\ufb03ciencies. Furthermore backgrounds from\nnon-QCD processes were estimated using MC and sub-\ntracted. The e\ufb00ects of ISR events were removed by eval-\nuating the fraction of events with center-of-mass energies\nless than 0.5% below the nominal energy in the MC and\nremoving that fraction from the data sample. As the frac-\ntion might depend on how well the MC describes the data\nvarious MC parameter settings were considered and the\nspread obtained was assigned as systematic uncertainty.\nAcceptance e\ufb00ects were corrected by \ufb01tting both, data\nand MC cos \u03b8 distributions within the measured range, to\nestimate the fraction of non-reconstructed tracks.\nThe BABAR analysis of the momentum spectrum of the\n\u03b7 meson begins with a similar hadronic event selection.\nThe \u03b7 mesons are reconstructed in the \u03b3\u03b3 decay mode:\nhigh quality neutral clusters with energy above 0.15 GeV\nare selected, and all pairs of such photon candidates are\nconsidered. If any pair has an invariant mass in the range\n0.11 < M\u03b3\u03b3 < 0.155 GeV/c2, consistent with a \u03c00 decay,\nthen both photon candidates are rejected. A pair is also\nrejected if | cos \u03b8\u03b3| > 0.8, where \u03b8\u03b3 is the angle between\neither photon momentum and the boost direction of the\nlaboratory system in the \u03b7 rest frame.\nSurviving pairs of photons are binned by the pair mo-\nmentum in the CM frame p\u2217, and the invariant mass\ndistribution in each bin is \ufb01tted with a sum of signal\nand background functions over the range 0.35 < M\u03b3\u03b3 <\n0.75 GeV/c2. The signal function is the sum of a Gaussian\ndistribution and Novosibirsk180 distribution whose param-\neters depend on p\u2217in such a way as to reproduce the\nline-shape induced by photon energy loss in front of the\nEMC. The e\ufb03ciency, de\ufb01ned as the ratio of the yield \ufb01tted\nfor the MC sample to the true number of \u03b7 \u2192\u03b3\u03b3 decays\nproduced, ranges between 24% and 34%. The relative sys-\ntematic uncertainty includes a component due to normal-\nization of 6.2%, arising from the single photon e\ufb03ciency,\nthe event selection and the \u03b7\u2192\u03b3\u03b3 branching fraction. Ad-\nditional point-to-point systematic uncertainties arise from\nthe \ufb01tting procedure and signal and background shapes.\nThey are 27% at p\u2217= 0, where backgrounds are very high,\nbut then drop rapidly to well below 6% at 1 GeV/c. Rel-\native statistical uncertainty drops from 15% at low p\u2217to\n2% above 1.5 GeV/c.\nResults\nBoth BABAR (Lees, 2013f) and Belle (Leitgab, 2013) pub-\nlished results of the light hadron fragmentation recently,\n180 The Novosibirsk function is an empirical p.d.f. de\ufb01ned as\nf(M\u03b3\u03b3) =\n1\n\u221a\n2\u03c0\u03c3 exp\n\u0002\n\u22120.5\n\u0000ln2(1 + \u039b \u00b7 (M\u03b3\u03b3 \u2212\u00b5)/\u03c3\u03c4 2) + \u03c4 2\u0001\u0003\n,\nwhere \u039b = sinh(\u03c4\n\u221a\nln 4)/\n\u221a\nln 4, \u00b5 is the peak position, and \u03c4\nis the tail parameter.\n\n744\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n0\n1\n2\n3\n4\n5\nBaBar Preliminary\nBelle Preliminary\nARGUS\n\u00b1\nK\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n0\n10\n20\n30\n40\n50\nBaBar Preliminary\nBelle Preliminary\nARGUS\n\u00b1\n\u03c0\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nBaBar Preliminary\nARGUS\n\u03b7\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nBaBar Preliminary\nARGUS\np\np/\nFigure 24.1.2. Comparison of the multiplicities for \u03c0\u00b1, K\u00b1,\np/p, and \u03b7, measured by BABAR at \u221as = 10.54 GeV (compiled\nfrom Muller, 2004 and Lees, 2013f), Belle at 10.52 GeV (com-\npiled from Leitgab, 2012 and Leitgab, 2013), and ARGUS at\n9.98 GeV (Albrecht et al., 1989a, 1990b).\nin the form of di\ufb00erential particles multiplicities ((1/Nevt)\ndN/dz) and in the form of di\ufb00erential cross sections\n((1/\u03c3had) d\u03c3/dz), respectively. The results presented in\nthis section are compiled from earlier results leading to\nthese publications. The measured particle spectra normal-\nized to the number Nevt of hadronic events are shown as\na function of z in Figs 24.1.2 and 24.1.3 with linear and\nlogarithmic vertical scales, respectively. The measured \u03b7\nspectrum covers almost full kinematic range, and the oth-\ners cover the range of z from around 0.1 for pions and\nkaons and 0.15 for protons to the kinematic limit, which\nincludes the bulk of the kaon and proton spectra, as well\nas the peak and high side of the pion spectrum. The only\nprevious measurements at a nearby energy, from the AR-\nGUS experiment at \u221as=9.98 GeV (Albrecht et al., 1989a,\n1990b), are also shown in Fig. 24.1.2. Only statistical er-\nrors are shown for the BABAR data, as the correlated 3-6%\nsystematic uncertainties are dominated by normalization.\nThe results from the three experiments are in fair agree-\nment within uncertainties, and the B Factory results are\nfar more precise in most ranges and extend the coverage\nsigni\ufb01cantly when compared with previous experiments.\nFor pions, the total uncertainties are comparable and are\ncorrelated over signi\ufb01cant z ranges in the BABAR and AR-\nGUS cases while they are signi\ufb01cantly more precise in the\nBelle case. The ARGUS data extend to lower z values, so\nthat the majority of the spectrum is covered between the\nthree experiments. At low z, BABAR and ARGUS data\nsets di\ufb00er by up to (7 \u00b1 4)%, which might indicate the\nexpected small scaling violation.\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n-2\n10\n-1\n10\n1\n10\nBaBar Preliminary\nBelle Preliminary\nARGUS\n Pythia\n UCLA\n HERWIG\n\u00b1\nK\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n-2\n10\n-1\n10\n1\n10\n2\n10\nBaBar Preliminary\nBelle Preliminary\nARGUS\n Pythia\n UCLA\n HERWIG\n\u00b1\n\u03c0\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n-3\n10\n-2\n10\n-1\n10\n1\n10\nBaBar Preliminary\nARGUS\n Pythia\n UCLA\n HERWIG\n\u03b7\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n-3\n10\n-2\n10\n-1\n10\n1\n10\nBaBar Preliminary\nARGUS\n Pythia\n UCLA\n HERWIG\np\np/\nFigure 24.1.3. Comparison of the BABAR (Muller, 2004; Lees,\n2013f), Belle (Leitgab, 2012, 2013), and ARGUS (Albrecht\net al., 1989a, 1990b) \u03c0\u00b1, K\u00b1, p/p, and \u03b7 multiplicities with\nthe predictions of the UCLA (blue), Jetset/Pythia (red), and\nHERWIG (green) fragmentation models.\nFigure 24.1.3 compares the BABAR, Belle and ARGUS\nmultiplicities with the predictions of the three fragmen-\ntation models discussed above. Default parameter values\nare used, which have been chosen based on previous data,\nmostly at higher energies. The shape of the bulk of the\n\u03c0\u00b1 spectrum is described qualitatively by all three mod-\nels, but no model describes the spectrum well in detail.\nJetset/Pythia\nand UCLA also describe the K\u00b1 cross\nsection reasonably well, whereas HERWIG peaks at lower\nz value. Jetset and UCLA also describe the \u03b7 cross sec-\ntion fairly well, though UCLA\u2019s spectrum is slightly too\nsoft and Jetset\u2019s spectrum predicts higher multiplicity\nthan the data both around the peak and at very high z\nvalues. HERWIG\u2019s spectrum shape does not agree with the\ndata. The proton spectrum is quite problematic: Jetset\ndescribes the shape qualitatively, but is consistently above\nthe data (i.e. predicts higher multiplicity); UCLA describes\nthe shape in the peak region, but then falls much too\nslowly, rising above the data at high z; HERWIG also de-\nscribes the shape in the peak region, but is far too high\noverall and exhibits an experimentally unobserved struc-\nture at high z values.\nSimilar de\ufb01ciencies in these models have been reported\nat higher energies (Abe et al., 1999; Abreu et al., 1998; Ai-\nhara et al., 1988; Akers et al., 1994a; Braunschweig et al.,\n1989; Buskulic et al., 1995; Itoh et al., 1995), although ear-\nlier MC versions were used and parameter values varied.\nOne should note that the deviations of predictions from\nthe data had the same sign at higher energies, suggest-\ning that the scaling properties might be well simulated.\n\n745\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n-2\n10\n-1\n10\n1\n10\nSLD\nTASSO\nBaBar Preliminary\nUCLA 91.2 GeV\nUCLA 30 GeV\nUCLA 10.54 GeV\n\u00b1\nK\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n-2\n10\n-1\n10\n1\n10\n2\n10\nSLD\nTASSO\nBaBar Preliminary\nJetSet 91.2 GeV\nJetSet 30 GeV\nJetSet 10.54 GeV\n\u00b1\n\u03c0\nz\n0 0.10.20.3 0.4 0.50.6 0.7 0.80.9 1\n dN /dz \nevt\n1/N\n-3\n10\n-2\n10\n-1\n10\n1\n10\nALEPH + L3\nBaBar Preliminary\nJetSet 91.2 GeV\nJetSet 30 GeV\nJetSet 10.54 GeV\n\u03b7\nz\n0 0.10.2 0.3 0.40.5 0.6 0.70.8 0.9 1\n dN /dz \nevt\n1/N\n-3\n10\n-2\n10\n-1\n10\n1\n10\nSLD\nTASSO\nBaBar Preliminary\nJetSet 91.2 GeV\nJetSet 30 GeV\nJetSet 10.54 GeV\np\np/\nFigure 24.1.4.\n\u03c0\u00b1, K\u00b1, p/p and \u03b7 multiplicities measured\nat three di\ufb00erent CM energies, compared with the predictions\nof the simulations described in the text. BABAR data are from\nMuller (2004).\nTo test the scaling properties of the models, each was run\nwith its current default parameters at various energies and\ncompared with the available data.\nFigure 24.1.4 shows a scaling test of the Jetset model\nusing \u03c0\u00b1 cross sections from BABAR, TASSO (Braun-\nschweig et al., 1989) and SLD (Abe et al., 1999). The latter\ntwo experiments provide the best precision and/or high-z\ncoverage at \u221as near 30 GeV and at the Z0, respectively.\nData from other experiments are consistent and yield the\nsame conclusions. Strong scaling violations are evident,\nboth at low z due to the pion mass and at high z from the\nrunning of the strong coupling \u03b1S.Jetset provides an ex-\ncellent description of all three data sets, with di\ufb00erences\nof only few percent at very low and very high z values.\nUCLA and HERWIG also describe the scaling violation well,\nalthough they do not reproduce the spectrum as well at\nany energy.\nFigure 24.1.4 also shows a similar test of the UCLA\nmodel for K\u00b1 cross sections. UCLA describes the BABAR\nand Belle results best, and similar scaling is predicted by\nthe other models. Here, the di\ufb00erent \ufb02avor composition of\nthe three samples modi\ufb01es the expected scaling violation.\nCharged kaons from bb events, which are absent from the\nBABAR data, raise the TASSO cross section in the 0.1\u20130.3\nregion, but do not contribute at high z. At the Z0, the\nrelative production of up- and down-type quarks changes\ndramatically, and the larger bb and ss event fractions raise\nthe simulated cross section to nearly the same level as at\n35 GeV for z above about 0.2. The \ufb02avor dependence has\nbeen shown (Abe et al., 1999; Abreu et al., 1998) to be\nmodeled at the Z0 at the level of about 10%. The change\nin the measured cross sections is about 15% less than pre-\ndicted, but this could be due to issues with the \ufb02avor\ndependence.\nSimilar results are obtained for the \u03b7 meson from\nALEPH and L3 data at 91 GeV (Adriani et al., 1992;\nBarate et al., 2000), and compared with the Jetset pre-\ndictions. Again, other data and models give the same con-\nclusions. The \ufb02avor dependence is smaller, and the dis-\ncrepancy at the Z0 is larger than for K\u00b1, perhaps indi-\ncating a failure of the models.\nFor protons, also shown in Fig. 24.1.4, the Jetset\nmodel is tested with one parameter value changed, the\nprobability for a given string break to produce a diquark-\nantidiquark, rather than quark-antiquark, pair, from 0.1\nto 0.085, which provides a good description of the higher-\nenergy data. Here, the simulated high-xp scaling violation\nbetween 10.54 and 34 GeV is about the same as for the\npions, but that between 34 and 91 GeV is slightly larger\nsince fast protons are expected to be produced predomi-\nnantly in uu and dd events. The prediction for 10.54 GeV\nrises well above the BABAR data, exceeding it by as much\nas a factor of 4.5 at z =0.9. Similar behavior is seen for\nJetset with default parameters, HERWIG, and UCLA at high\nxp. This indicates that we do not understand the scaling\nproperties of protons, or perhaps of baryons or heavier\nhadrons in general.\nThese data can be used to test the predictions of MLLA\nQCD combined with the ansatz of LPHD (Azimov, Dok-\nshitzer, Khoze, and Troyan, 1985), by transforming to the\nvariable \u03be = ln(\u221as/2p\u2217). This representation emphasizes\nthe low momentum region (large \u03be). It is predicted that:\nthe \u03be distribution would be approximately Gaussian over a\nrange of \u223c1 unit around it\u2019s peak position \u03be\u2217; a distorted\nGaussian should describe the distribution over a wider\nrange; \u03be\u2217should decrease exponentially with hadron mass\nat a given CM energy \u221as and \u03be\u2217should increase logarith-\nmically with \u221as for a given hadron. Conventionally, \u03be\u2217is\nfound by \ufb01tting a Gaussian distribution to the data over\nsets of points within 0.5\u20131 units of the approximate peak\nposition. Next, the widest roughly symmetric range about\nthis position is found in which a Gaussian \ufb01t gives a good\n\u03c72, and this range is then extended as far as possible in\none direction. Results of such \ufb01ts and the ranges are listed\nin Table 24.1.1. Acceptable \ufb01ts were found over ranges at\nleast 1 unit wide, consistent with the prediction.\nTable 24.1.1. Results of the Gaussian and distorted Gaussian\n(where a skewness term and a kurtosis term are added) \ufb01ts to\nthe \u03be distributions. The \ufb01t ranges and the peak positions \u03be\u2217\nare reported (Muller, 2004).\nParticle\nGaussian\nDistorted Gaussian\nFit range\n\u03be\u2217\nFit range\n\u03be\u2217\n\u03c0\u00b1\n1.7 - 3.0\n2.36\u00b10.01\n0.0 - 3.2\n2.36\u00b10.01\nK\u00b1\n1.0 - 2.2\n1.64\u00b10.01\n0.0 - 3.2\n1.64\u00b10.01\n\u03b7\n0.9 - 2.2\n1.48\u00b10.02\np/\u00afp\n1.0 - 2.2\n1.61\u00b10.01\n0.0 - 2.8\n1.61\u00b10.01\n\n746\nTable 24.1.2. The fraction of each particle\u2019s spectrum covered by the BABAR (Muller, 2004) measurement is given in the second\ncolumn. The total multiplicity per e+e\u2212\u2192qq event at 10.54 GeV measured by BABAR in the third column are compared with\nthe predictions of fragmentation models and previous results from CLEO (at 10.49 GeV; Behrends et al., 1985) and ARGUS (at\n9.98 GeV; Albrecht et al., 1989a). The \ufb01rst error on each BABAR result is experimental and the second is from the extrapolation\nprocedure.\nParticle\nCoverage\nBABAR\nJetset\nUCLA\nHERWIG\nCLEO\nARGUS\n\u03c0\u00b1\n0.878\u00b10.015\n6.405\u00b10.134\u00b10.106\n6.22\n6.44\n6.31\n8.3\u00b10.4\n6.38\u00b10.12\nK\u00b1\n0.985\u00b10.006\n0.910\u00b10.017\u00b10.006\n0.934\n1.010\n1.010\n1.3\u00b10.2\n0.888\u00b10.030\n\u03b7\n1.0\n0.276\u00b10.017\u00b10.000\n0.354\n0.278\n0.233\n\u2013\n0.19\u00b10.06\np/p\n0.966\u00b10.008\n0.235\u00b10.011\u00b10.002\n0.336\n0.217\n0.46\n0.40\u00b10.06\n0.271\u00b10.018\nTable 24.1.1 reports also the results of the \ufb01ts per-\nformed adding small skewness s and kurtosis \u03ba terms to\nthe Gaussian distribution.\nG\u2032(\u03be) =\nN\n\u03c3\n\u221a\n2\u03c0 exp\n\u0012\u03ba\n8 + s\u03b4\n2 \u2212(2 + \u03ba)\u03b42\n4\n+ s\u03b43\n6 + \u03ba\u03b44\n24\n\u0013\n,\n(24.1.9)\nwhere \u03b4=(\u03be \u2212\u03be\u2217)/\u03c3, \u03c3 is the square root of the variance.\nThe \ufb01tted ranges are signi\ufb01cantly larger, consistent with\nthe MLLA QCD prediction. The values of \u03be\u2217measured by\nBABAR and previous experiments at higher energies for\nthe di\ufb00erent particles are shown in Fig. 24.1.5. The lines\nsimply connect the precise points at the Z0 with those\nfrom BABAR. The other data points are consistent with\nthese lines, and hence with the expected logarithmic en-\nergy dependence, but more precise data at other energies\nare needed to test this prediction. There is a clear di\ufb00er-\nence between the pions and kaons that increases slowly\nwith energy; the values for \u03b7 (measured only at BABAR\nand at the Z0), are slightly below those for K\u00b1. However,\nthe proton data are inconsistent with an overall decrease\nwith hadron mass.\n10\n2\n10\n3\n10\n4\nS=ECM\n2 (GeV\n2)\n2.0\n2.5\n3.0\n3.5\nPeak Position \u03be*\n\u03c0\n\u00b1\nK\n\u00b1\np/pbar\nBaBar\nTASSO\nTASSO\nTPC\nTASSO\nTOPAZ\nZ\n0\nFigure 24.1.5.\nPeak position \u03be\u2217vs e+e\u2212CM energy for\ncharged pions, kaons, and protons from various experiments.\nThe lines connect the precise points at the Z0 with those from\nBABAR (Muller, 2004).\nTotal multiplicities of each particle type per event are\ncalculated by integrating the di\ufb00erential rates, taking all\nuncertainties and their correlations into account, and ex-\ntrapolating into any unmeasured regions. The second step\nis model dependent: correction factors are evaluated us-\ning a combination of the three models and a number of\n\ufb01ts to the \u03be distributions, and have large uncertainties\nwhen substantial fractions of the spectrum are not mea-\nsured. The \u03b7 spectrum is measured over the full kinematic\nrange, so this is not an issue. The good coverage for kaons\nand protons makes their corrections and their uncertain-\nties fairly small. The coverage for pions at low momenta\ndoes not extend much below the peak (see Fig. 24.1.2),\nrequiring large correction and giving the dominant uncer-\ntainty. The correction factors and the total rates are listed\nin Table 24.1.2, along with previous results from CLEO\n(Behrends et al., 1985) and ARGUS (Albrecht et al., 1989a)\nand the predictions of the three models. BABAR and AR-\nGUS results are in good agreement, while CLEO measures\nsigni\ufb01cantly higher rates for all particle types.\nDi\ufb00erential production ratios for pairs of particles are\nsensitive to speci\ufb01c features of the hadronization process,\nand many of the systematic uncertainties cancel at least\npartially. It is equivalent and conventional to report the\nfractions f\u03c0, fK and fp of all charged hadrons that are pi-\nons, kaons and protons, respectively. Pions dominate the\ncharged hadron production at low z, as is expected from\ntheir lower mass and the contributions from many decays\nof heavier hadrons. As z increases, the pion fraction drops\nas the kaon and proton fractions rise toward values of\nabout 35% and 8%, respectively. At higher z, the trend\nreverses due to kinematics, especially for protons which\nmust be produced along with an anti-baryon. The three\nmodels describe the general trend of the data, but none\ndescribes either the shape or the magnitude at all mo-\nmenta.\nGlobal analysis for fragmentation functions\nSince there were measurements of the multiplicities given\nby Eq. (24.1.1) at various facilities, global analyses have\nbeen made using the available world data. From the anal-\nyses, the optimum FFs were determined, and even their\nuncertainties were estimated.\n\n747\nIn the same way as global analyses for the parton dis-\ntribution functions are determined, the FFs are expressed\nin terms of a number of parameters at the initial scale Q2\n(\u2261Q2\n0). Usually, a simple polynomial form is used:\nDh\ni (z, Q2\n0) = N h\ni z\u03b1h\ni (1 \u2212z)\u03b2h\ni ,\n(24.1.10)\nbecause the functions should vanish at z = 1. Here, N h\ni ,\n\u03b1h\ni , and \u03b2h\ni are parameters to be determined by a \u03c72 min-\nimization of e+ + e\u2212\u2192h + X data. The initial scale\nQ2\n0 is arbitrary. However, it is, for example, assumed that\nQ2\n0 = 1 GeV2 for light quark and gluon functions, and\nabove the mass thresholds m2\nc and m2\nb for charm and bot-\ntom functions, where mc and mb are charm- and bottom-\nquark masses, respectively. For light hadrons (h), one typ-\nically separates pions (\u03c0+ + \u03c0\u2212), kaons (K+ + K\u2212), and\nprotons/anti-protons (p+\u00afp). Because the second moments\nM h\ni should satisfy the sum rule of Eq. (24.1.6), it is useful\nto take M h\ni as one of the parameters instead of N h\ni . The\nparameters are related with each other by the relation\nN h\ni =\nM h\ni\nB(\u03b1h\ni + 2, \u03b2h\ni + 1),\n(24.1.11)\nwhere B(\u03b1h\ni + 2, \u03b2h\ni + 1) is the beta function.\nIn analyzing the light hadrons, a common function\nis assumed for favored fragmentation functions (see Sec-\ntion 24.1.1) from up and down quarks while di\ufb00erent pa-\nrameters are allowed for a favored FF from a strange quark\nby considering the mass di\ufb00erence. Also di\ufb00erent param-\neters are assigned for disfavored FFs. A \ufb02avor symmetric\nform is assumed for disfavored FFs from light quarks (up,\ndown, and strange quarks) due to lack of experimental in-\nformation, although the light antiquark distributions are\nnot \ufb02avor symmetric in the unpolarized parton distribu-\ntion functions (Kumano, 1998).\nIn Fig. 24.1.6, FFs for (\u03c0+ + \u03c0\u2212)/2 determined by\n\u201cHKNS\u201d (Hirai, Kumano, Nagai, and Sudoh, 2007a,b)\nare shown, together with other parameterizations: \u201cKKP\u201d\n(Kniehl, Kramer, and Potter, 2000), \u201cKretzer\u201d (Kretzer,\n2000), \u201cAKK\u201d (Albino, Kniehl, and Kramer, 2005, 2008),\nand \u201cDSS\u201d (de Florian, Sassot, and Stratmann, 2007a,b;\nEpele, Llubaro\ufb00, Sassot, and Stratmann, 2012). Since nei-\nther BABAR and Belle results have been published at the\ntime of this analysis, they were not yet taken into ac-\ncount. These functions were obtained in the NLO (MS)\nscheme and the uncertainty bands were obtained in the\nHKNS analysis by using the Hessian method (Pumplin,\nStump, and Tung, 2001). The gluon and light-quark func-\ntions are shown at Q2 = 2 GeV2, where the uncertain-\nties are generally large. The charm- and bottom-quark\nfunctions are shown at the scale of their mass thresholds\nQ2 = m2\nc or m2\nb. Disfavored-quark and gluon functions,\nfor example s-quark functions of Kretzer and AKK, are\ncompletely di\ufb00erent between the analysis groups; how-\never, they agree within the uncertainties. One can notice\nthat the disfavored-quark and gluon FFs have large un-\ncertainties, which should be signi\ufb01cantly improved by the\nrecently published Belle and BABAR measurements once\n-0.5\n0\n0.5\n1\n1.5\n-0.5\n0\n0.5\n1\n1.5\n-0.5\n0\n0.5\n1\n1.5\n-0.5\n0\n0.5\n1\n1.5\n0\n0.2\n0.4\n0.6\n0.8\n1\nz\n-0.5\n0\n0.5\n1\n1.5\n0\n0.2\n0.4\n0.6\n0.8\n1\nz\ngluon\nu quark\nc quark\nb quark\nQ2 = 2 GeV2\nQ2 = 2 GeV2\nQ2 = 2 GeV2\nQ2 = 10 GeV2\nQ2 = 100 GeV2\nKKP\nAKK\nKretzer\nHKNS\ns quark\nzD(\u03c0 +\u03c0 )/2 (z)\n+\n-\nDSS\nFigure 24.1.6. Determined fragmentation functions for the\npion and their comparison with other parameterizations (Hi-\nrai, Kumano, Nagai, and Sudoh, 2007a,b). The shaded bands\nindicate estimated uncertainties of the HKNS.\nthey are included. There are available codes from the dif-\nferent analysis groups for calculating the FFs at a given\nkinematical condition of z and Q2. A summary of the sta-\ntus of the various FFs is given by Albino et al. (2008); an\nonline generator is provided by Arleo and Guillet (2008).\nRecent works on the analyses of the FFs can be found in\nChristova and Leader (2009) and Albino and Christova\n(2010).\nThe favored and disfavored FFs re\ufb02ect internal \ufb02avor\ncontent of a hadron, which leads to an interesting sugges-\ntion that exotic hadrons could be found by investigating\ntheir FFs (Hirai, Kumano, Oka, and Sudoh, 2008). As an\nexample, internal structure of the controversial f0(980)\nmeson, which is possibly q\u00afq or tetra-quark (qq\u00afq\u00afq), could\nbe determined if accurate data become available. For ex-\nample, a future super \ufb02avor factory with forty times higher\nluminosity could provide the accurate information needed\nto distinguish the disfavored functions from the favored\nones of the f0 meson.\n24.1.2.2 Charmed hadrons\nBelle and BABAR have measured fragmentation functions\nfor several charmed hadrons, the heaviest particles avail-\n\n748\nable for study below the \u03a5(4S). These are generally ex-\npressed in terms of xp =p\u2217/pmax, where pmax =\np\ns/4 \u2212m2\nh\nis the maximum momentum for production via the e+e\u2212\u2192\nqq process. In this variable, all hadrons have the same\nkinematic range, 0 \u2264xp \u22641. In B Factories where pairs\nof B mesons decay nearly at rest in the CM system the\nxp for hadrons from B decay cannot exceed 0.5 Charmed\nhadrons must be reconstructed in a particular decay mode.\nBy convention, an analysis is described for a particular\nhadron and decay mode, but the inclusion of the charge\nconjugate state and decay mode is always implied.\nBelle (Seuster, 2006) have studied several charmed me-\nsons, the ground state D0, D\u00b1, D\u00b1\ns and the excited D\u22170\nand D\u2217\u00b1, as well as the lowest-mass charmed baryon \u039b\u00b1\nc .\nEvents are selected by requiring at least three charged\ntracks and a calorimeter energy sum between 10% and\n80% of the CM energy. There are also requirements on\nthe average cluster energy, the invariant mass of the par-\nticles in each thrust hemisphere, and the position of the\nevent vertex. This selection is 87% e\ufb03cient for cc events.\nCharged tracks are required to be consistent with orig-\ninating from the event vertex, and are identi\ufb01ed as \u03c0\u00b1,\nK\u00b1 or pp using a combination of information from the\ndrift chamber, time-of-\ufb02ight and Cherenkov systems (see\nChapter 5). A loose selection is used, in which identi\ufb01-\ncation e\ufb03ciencies are above 95% (80% for protons) and\nmisidenti\ufb01cation rates are at most 26% (7%). Candidate\n\u03c00 mesons are formed from pairs of photon candidates\nwith energy above 30 MeV and invariant mass near the\n\u03c00 mass.\nCandidate D0 \u2192K\u2212\u03c0+ decays are formed by com-\nbining an identi\ufb01ed K\u2212with an identi\ufb01ed \u03c0+. Similarly,\nD+ \u2192K\u2212\u03c0+\u03c0+ and \u039b+\nc \u2192pK\u2212\u03c0+ candidates are formed\nby combining three identi\ufb01ed tracks, and D+\ns \u2192K+K\u2212\u03c0+\ncandidates are selected in which the K+K\u2212combination\nhas an invariant mass within 7 MeV/c2 of the nominal \u03c6\nmeson mass. Candidates of each type are binned in xp,\nand the number of true charmed hadrons in each bin is\nestimated by \ufb01tting their invariant mass distribution in\nthe region near the relevant hadron mass.\nCandidate D\u2217+ \u2192D0\u03c0+ decays are formed from those\nD0 candidates with an invariant mass within 15 MeV/c2 of\nthe nominal D0 mass, combined with each slow, positively\ncharged track, assumed to be a \u03c0+. Similarly, D\u2217+ \u2192\nD+\u03c00 and D\u22170 \u2192D0\u03c00 candidates are formed from D\ncandidates with a mass within 15 MeV/c2 of the relevant\nnominal mass, combined with a soft \u03c00 candidate. These\nD\u2217candidates are binned in xp, and the number of true\nD\u2217mesons in each bin is extracted from a \ufb01t to the dis-\ntribution of the mass di\ufb00erence \u2206m between the D\u2217and\nD candidates. Since the true mass di\ufb00erence is close to\nthreshold, \u2206m has better resolution than any individual\ninvariant mass. The yields are divided by the reconstruc-\ntion e\ufb03ciency and the relevant branching fraction(s) to\ngive di\ufb00erential cross sections as functions of xp.\nBABAR have studied the charmed baryons \u039b\u00b1\nc\n(Au-\nbert, 2007p), \u039e0\nc (Aubert, 2005z), \u21260\nc (Aubert, 2007ao),\ncontaining zero, one and two strange valence quarks, re-\nspectively, in addition to the charm quark. Since charmed\nbaryons can only be produced in e+e\u2212\u2192cc events, there\nis no event selection other than the requirement of enough\ntracks in the event to reconstruct the particle in question\nin its target decay mode.\nThe \u039b\u00b1\nc\nstudy uses a sample of 9.5 fb\u22121 of o\ufb00-\nresonance data and reconstructs the 3-body decay mode\n\u039b+\nc \u2192pK\u2212\u03c0+. High quality tracks are selected and identi-\n\ufb01ed as described in Section 24.1.2.1. Each set of an identi-\n\ufb01ed p, K\u2212and \u03c0+ is considered a \u039b+\nc candidate, and each\ntrack\u2019s momentum at its point of closest approach to the\nbeam axis is corrected for energy loss using the correct\nmass. The invariant mass is calculated with a resolution\nthat varies from 3.75 MeV/c2 at low xp to 5.75 MeV/c2\nat high xp.\nThe reconstruction e\ufb03ciency varies rapidly near the\nedges of the detector acceptance, so a tight \ufb01ducial re-\nquirement is made that the polar angle of the \u039b\u00b1\nc candi-\ndate \u03b8\u039b in the e+e\u2212CM frame satis\ufb01es \u22120.7 0.2. The azimuthal asym-\nmetries are observed in a cos(\u03c61 + \u03c62) modulation in the\nnormalized two-hadron yields, R = N(\u03c61 + \u03c62)/\u27e8N12\u27e9,\nwhere \u03c61,2 are the azimuthal angles de\ufb01ned in the CM by\nFigure 24.1.10. Azimuthal angles \u03c61 and \u03c62 de\ufb01ned for the\ntwo hadrons relative to the plane spanned by the lepton and\nthrust axis.\nthe two planes of hadrons relative to the plane contain-\ning both the e+e\u2212pair and the thrust axis as shown in\nFig. 24.1.10. N(\u03c61 + \u03c62) is the number of pion pairs with\nthe sum of the azimuthal angles \u03c61 + \u03c62, and \u27e8N12\u27e9is the\naverage number of pion pairs over the whole \u03c61 +\u03c62 inter-\nval. Similar de\ufb01nitions can be obtained where the refer-\nence axis is de\ufb01ned by the plane containing the e+e\u2212pair\nand the second hadron in which case only one angle \u03c60\nappears and the modulation becomes a cos(2\u03c60) modula-\ntion (and the corresponding normalized yields are denoted\nR0).\nAcceptance e\ufb00ects and gluon radiation can also gen-\nerate fake azimuthal modulations and were found to be\nsubstantial in MC (Pythia 6.2 and GEANT3 ). To isolate\nthe spin dependent fragmentation e\ufb00ect from these back-\nground e\ufb00ects, the method of double ratios was applied us-\ning ratios of di\ufb00erent pion charge combinations. The nor-\nmalized yields for opposite-sign pion pairs as a function of\nthe azimuthal angle RU(cos(\u03c61 + \u03c62)) (or RU\n0 (cos(2\u03c60)))\nwere divided by the normalized yields of like-sign pairs,\nRU\n(0)/RL\n(0) and \ufb01tted. Similar ratios between unlike sign\npion pairs and any charged pion pairs (RU\n(0)/RC\n(0)) were\nalso extracted. As both background e\ufb00ects are expected\nto be proportional to the unpolarized fragmentation func-\ntions, their contributions to the normalized yields are the\nsame for both charge sign combinations and they can-\ncel when building the double ratio. As the Collins func-\ntions are expected to be di\ufb00erent for favored and dis-\nfavored fragmentation, a net asymmetry related to the\nCollins functions should remain. The double ratios as a\nfunction of the azimuthal angles were then \ufb01t with az-\nimuthal modulations RU/RL = AUL\n12 cos(\u03c61 + \u03c62) + B (or\nRU\n0 /RL\n0 = AUL\n0\ncos(2\u03c60) + B0) of which the cos(\u03c61 + \u03c62)\n(or cos(2\u03c60)) part is proportional to the Collins functions.\nIn case of the any charge pion pairs the corresponding\namplitudes are denoted AUC\n12(0). An example of the nor-\nmalized raw yield, double ratio and its modulation can be\nseen in Fig. 24.1.11 using the \u03c60 angle. The normalized\nraw yields are paremetrized similarly as the double ratios\n\n754\n0.9\n1\n1.1\nR0\na\n0\nL=-0.081\u00b10.003\nb\n0\nL=1.000\u00b10.002\n\u03c72/ndf=0.738\na\n0\nU=-0.055\u00b10.003\nb\n0\nU=1.000\u00b10.002\n\u03c72/ndf=1.207\n2\u03c60 [rad]\nRU/RL\nA0=0.025\u00b10.004\nB0=1.001\u00b10.003\n\u03c72/ndf=0.925\n0.96\n1\n1.04\n-3\n-2\n-1\n0\n1\n2\n3\nFigure 24.1.11. From Abe (2006a). Top: Example of uncor-\nrected unlike-sign (open circles) and like-sign (open squares)\ndi-pion normalized rate R0 vs. 2\u03c60 in the bin z1(z2) \u2208[0.5, 0.7],\nz2(z1) \u2208[0.3, 0.5]. Bottom: The di-pion double ratio RU\n0 /RL\n0\nvs. 2\u03c60 in the same z1, z2 bin. Resulting parameters of the \ufb01t\ndescribed in the text (full and dashed lines) are also shown.\nfor like- and unlike-sign pairs. In order to distinguish the\nparameters the latter are labeled by a, b instead of A, B.\nThe double ratio method was tested using a sample of\ngeneric light quark MC production, where all e\ufb00ects ex-\ncept those by the Collins fragmentation were present and\nit was found, that the resulting raw asymmetries canceled\nas expected. Further tests include destroying the correla-\ntion between quark and anti-quark side by mixing pions\nfrom di\ufb00erent events. Those were found to be consistent\nwith zero as expected. Also arti\ufb01cial asymmetries were in-\ntroduced in the MC to study the reconstruction e\ufb03ciency.\nSome underestimation of the reconstructed asymmetries\nwas found to be caused by the resolution smearing of the\nreconstructed thrust axis and the resulting azimuthal an-\ngles. The reason is that experimentally one cannot directly\nobtain the actual quark-antiquark axis, but has to rely on\nobtaining an approximate axis via the event shape variable\nthrust. As this is performed using the thrust algorithm\nsumming over all reconstructed particles this experimen-\ntal approximation reproduces the actual quark-antiquark\naxis with a \ufb01nite accuracy. It is found that even on the\ngenerator level there is some discrepancy, which is fur-\nther enhanced by detector resolutions. In the Belle experi-\nment the average cosine of the angle formed by the recon-\nstructed thrust axis and the generated quark-antiquark\npair axis for light quarks is 0.990 with an RMS of 0.015\n(Seidl, 2008), as obtained from a Pythia (Sj\u00a8ostrand, 1995)\nsimulated sample of events and GEANT (Brun, Bruyant,\nMaire, McPherson, and Zanarini, 1987) detector simula-\ntion. The resulting reduction of the extracted cos(\u03c61 +\u03c62)\nasymmetries was corrected for by scaling them with a fac-\ntor 1.66 \u00b1 0.04 (Seidl, 2008) which was obtained from the\nweighted MC simulation asymmetry studies.\nThe contribution to the asymmetries by light quarks\nand charm quarks (the latter representing background for\nthe light quark fragmentation measurements) were sepa-\nrated using, in addition to the main data sample, a charm\nenhanced data sample. In the latter candidate \u03c0 K pairs\nwith the invariant mass in the range of D meson and D \u03c0s\ncombinations consistent with a D\u2217meson were selected.\nThe initial measurement (Abe, 2006a) was performed on\n29.1 fb\u22121 of data obtained 60 MeV below the \u03a5(4S) reso-\nnance, while the second publication (Seidl, 2008) utilized\n551 fb\u22121 of data including the resonance data. It was\nfound that the thrust selection mentioned above removes\nmost of the B decay events (the remaining pollution of the\nsample with B meson decays is around 2%). The results\nof the latter measurement are shown in Fig. 24.1.12.\nIt can be seen that the asymmetries are of the order\nof several percent and are rising with increasing fractional\nenergy. The direct interpretation is not straightforward\nsince the asymmetries are di\ufb00erences of products of fa-\nvored and disfavored Collins and unpolarized fragmenta-\ntion functions:\nRU\n12\nRC\n12\n= 1 + cos(\u03c61 + \u03c62)AUC\n12 ,\nAUC\n12 =\nsin2 \u03b8\n1 + cos2 \u03b8\n\u00d7\n(f\n\u0010\nH\u22a5,fav\n1\n\u00afH\u22a5,fav\n2\n+ H\u22a5,dis\n1\n\u00afH\u22a5,dis\n2\n\u0011\n\u0000Dfav\n1\n\u00afDfav\n2\n+ Ddis\n1\n\u00afDdis\n2\n\u0001\n\u2212\nf\n\u0010\n(H\u22a5,fav\n1\n+ H\u22a5,dis\n1\n)( \u00afH\u22a5,fav\n2\n+ \u00afH\u22a5,dis\n2\n)\n\u0011\n\u0000(Dfav\n1\n+ Ddis\n1 )( \u00afDfav\n2\n+ \u00afDdis\n2 )\n\u0001\n)\n,\n(24.1.13)\nwhere a shorthand notation was used for the fragmenta-\ntion functions of hemispheres 1 and 2, i.e. H\u22a5\n2 = H\u22a5h\n1,q (z2)\nand similarly for the unpolarized fragmentation functions\nD2 = Dh\n1,q(z2); also the favored and disfavored FF\u2019s are\ndenoted by superscripts fav and dis, respectively. A simi-\nlar notation holds for the AUL\n12 amplitude. Anselmino et al.\n(2007) extracted the corresponding favored and disfavored\nCollins fragmentation functions from the Belle data and\nfound that they are both sizeable and of opposite sign. Us-\ning this they were able to extract the quark transversity\ndistribution from the HERMES (Airapetian et al., 2005)\nand COMPASS (Alexakhin et al., 2005) data for the \ufb01rst\ntime.\nIn this extraction some improvements in the knowledge\nof the Collins function are still needed. For example, the\nintrinsic transverse momentum dependence is not known\nand was only estimated. Recent results have been shown\nby BABAR (Garzia, 2013), with an analysis similar to that\nperformed by Belle and based on a data sample corre-\nsponding to an integrated luminosity of about 468 fb\u22121\ncollected at the \u03a5(4S) and 40 MeV below. A general con-\nsistency between the BABAR and Belle asymmetries mea-\nsured as a function of the fractional energies is observed.\nThe z-range explored by BABAR extends from 0.15 to 0.9.\nIn addition, BABAR performed a study of the azimuthal\nasymmetries as a function of the transverse momentum of\nthe pions with respect to the thrust axis. As an example,\n\n755\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\n0.2\n0.4\n0.6\n0.8\nA12\n0.20.75]\nt1\np\nFigure 24.1.13. Preliminary BABAR results (Garzia, 2013)\non azimuthal asymmetries measured from \ufb01ts to the RU/RL\n(A12,UL), and RU/RC (A12,UC) ratios, as functions of the\ntransverse momentum pt2 for four bins of pt1, from top left\nto bottom right. Statistical and systematic errors are shown as\nerrors bars and shaded bands respectively.\nFig. 24.1.13 shows the azimuthal asymmetries measured in\nthe thrust reference frame. The energy and transverse mo-\nmentum dependence of the Collins asymmetries obtained\nby BABAR can be combined with the Belle data and the\nresults from SIDIS experiments for an improved global\nanalysis as done in Anselmino et al. (2007).\nCollins functions for other \ufb01nal state hadrons still need\nto be extracted to improve the sensitivity for di\ufb00erent\nquark \ufb02avors and to match the extracted asymmetries in\nSIDIS experiments. Also, an important test of the mecha-\nnism which creates this transverse spin e\ufb00ect (Collins ef-\nfect) still needs to be performed. According to a model by\nArtru and Mekh\ufb01(1990) which follows string fragmenta-\ntion, the Collins e\ufb00ect for a transversely polarized vector\nmeson should be of di\ufb00erent sign as that for pseudoscalar\nmesons. Results from those studies are not yet available.\n24.1.3.2 Interference fragmentation function\nThe second chiral-odd fragmentation function is the in-\nterference fragmentation function (IFF), H\u2222\n1 (z, m), which\ndescribes the fragmentation of a transversely polarized\nquark into a pair of hadrons of di\ufb00erent charge with total\nfractional energy z and an invariant mass m. A nonzero\nIFF can be created by the interference of two hadrons in\na relative S- or P-wave state. For charged pion pairs this\ncould therefore be either a simple S-wave (which might\nbe related to the \u03c3 resonance) interfering with the P-wave\nstate related to the \u03c1 meson (which is observed as a di-\npion resonance). This potential interference also governs\nthe invariant mass dependence according to theory pre-\ndictions. Based on pion-pion phase shift analysis of data,\nJa\ufb00e, Jin, and Tang (1998) suggest a sign change of the\ntwo-pion interference fragmentation function is required\nat the invariant mass of the \u03c1 meson. Radici, Jakob, and\nBianconi (2002) suggest no sign change but the maximum\nof the IFF magnitude at the same mass. The di\ufb00erence\nbetween the interference fragmentation function and the\nCollins fragmentation function is that intrinsic transverse\nmomenta of hadrons created in the fragmentation are in-\ntegrated over in the former case, which enables the use\nFigure 24.1.14. Azimuthal angles \u03c61 and \u03c62 de\ufb01ned for the\ntwo hadron pairs\u2019s planes (denoted by the yellow planes) rela-\ntive to plane spanned by the lepton and thrust axis (blue).\n\n756\n < 0.42 \n2\n0.35 < z\n < 0.35 \n2\n0.28 < z\n \n12\n a\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n < 0.28 \n2\n0.20 < z\n < 0.65 \n2\n0.57 < z\n < 0.57 \n2\n0.50 < z\n \n12\n a\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n < 0.50 \n2\n0.42 < z\n1\nz\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n < 1.00 \n2\n0.82 < z\n1\nz\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n < 0.82 \n2\n0.72 < z\n1\nz\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n \n12\n a\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n < 0.72 \n2\n0.65 < z\nFigure 24.1.15. Azimuthal cos(\u03c61+\u03c62) modulations a12 of normalized yield of charged pion pairs as a function of the fractional\nenergy z2 for 9 di\ufb00erent bins of z1 from top left to bottom right as measured by Belle (Vossen, 2011). The \ufb01lled areas represent\nthe systematic uncertainties.\nof collinear factorization. This in turn leads to the QCD\nevolution of the interference fragmentation function being\nknown and makes it easily applicable at various energies\nand in di\ufb00erent processes such as in SIDIS or p p collisions.\nIFF measurements were performed by HERMES\n(Airapetian et al., 2008), Compass (Adolph et al., 2012;\nWollny, 2009), PHENIX (Yang, 2009) and STAR (Vossen,\n2012). These measurements determine the product of two\nunknown quantities: quark transversity and the interfer-\nence fragmentation functions. Therefore the measurement\nof the interference fragmentation function alone in e+e\u2212\nannihilation enable the access to quark transversity, inde-\npendent of the methods using Collins FF. Similar to the\nCollins analysis, the interference fragmentation function\ncan be reconstructed at B Factories using the combination\nof two chiral-odd fragmentation functions in each hemi-\nsphere (Boer, Jakob, and Radici, 2003). Therefore, one\nmeasures inclusively two hadron pairs in opposite hemi-\nspheres in e+e\u2212annihilation. Again the two hemispheres\nare de\ufb01ned by the thrust axis and a thrust > 0.8 ensures\ntwo-jet like topology (Vossen, 2011). All four hadrons are\nrequired to be detected in the central part of the detector\nand to have a minimal fractional energy of 0.1. In ad-\ndition, the invariant mass of each pair is required to be\nin the range of 0.25 to 2 GeV/c2. To avoid acceptance\ne\ufb00ects at the edges of the detector, hadrons were only se-\nlected if they originated in a cone around the thrust axis\nof \u02c6n \u00b7 Ph > 0.8 where the thrust axis was again limited\nto the barrel parts of the detector, identical to the Collins\nanalysis. Two azimuthal angles \u03c61,2 are calculated, de-\n\ufb01ned by the plane of each hadron pair relative to the plane\nspanned by the e+e\u2212pair and the thrust axis, as displayed\nin Fig. 24.1.14.\nAgain the normalized yields as a function of the az-\nimuthal angles are \ufb01tted. The cos(\u03c61 + \u03c62) modulation is\nproportional to the product of the interference fragmen-\ntation functions for the quark and antiquark sides nor-\nmalized by the corresponding unpolarized fragmentation\nfunctions. After the application of the opening angle selec-\ntion around the thrust axis, nearly vanishing acceptance\ne\ufb00ects (< 0.1%) were observed in MC simulations of light\nquark production. Therefore it is possible to directly ob-\ntain the IFFs without the need for double ratios. The azi-\nmuthal modulation is again \ufb01tted by b12+a12 cos(\u03c61+\u03c62)\nof which the cosine modulation can be interpreted as\na12 \u221d\u2212\nsin2 \u03b8\n1 + cos2 \u03b8\nP\nq e2\nqH\u2222,q\n1\n(z1, m1)H\u2222,\u00afq\n1\n(z2, m2) + c.c.\nP\nq e2qDq\n1(z1, m1)D\u00afq\n1(z2, m2) + c.c.\n,\n(24.1.14)\n\n757\n2\n < 0.62 GeV/c\n2\n < m\n2\n0.50 GeV/c\n2\n < 0.50 GeV/c\n2\n < m\n2\n0.40 GeV/c\n \n12\n a\n-0.16\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n2\n < 0.40 GeV/c\n2\n < m\n2\n0.25 GeV/c\n]\n2\n [GeV/c\n1\nm\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n2\n < 1.10 GeV/c\n2\n < m\n2\n0.90 GeV/c\n2\n < 0.90 GeV/c\n2\n < m\n2\n0.77 GeV/c\n \n12\n a\n-0.16\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n2\n < 0.77 GeV/c\n2\n < m\n2\n0.62 GeV/c\n]\n2\n [GeV/c\n1\nm\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n2\n < 2.00 GeV/c\n2\n < m\n2\n1.50 GeV/c\n]\n2\n [GeV/c\n1\nm\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n \n12\n a\n-0.16\n-0.14\n-0.12\n-0.1\n-0.08\n-0.06\n-0.04\n-0.02\n0\n0.02\n2\n < 1.50 GeV/c\n2\n < m\n2\n1.10 GeV/c\nFigure 24.1.16. Azimuthal cos(\u03c61 + \u03c62) modulations a12 of the normalized yield of charged pion pairs as a function of the\ninvariant mass m2 for 8 di\ufb00erent bins of m1 from top left to bottom right as measured by Belle (Vossen, 2011). The \ufb01lled areas\nrepresent the systematic uncertainties.\nwhere \u03b8 is the polar angle between the lepton and the\nthrust axis. Similar systematic studies as in the Collins\nanalysis were performed, such as mixed-event tests where\nthe two hadron pairs were selected from di\ufb00erent events,\nthe zero tests in MC simulations without any spin e\ufb00ects\npresent as well as studies of the bias of the asymmetries for\ncertain opening angle and thrust selections. The stability\nover various data-taking periods for on- and o\ufb00-resonance\ndata were also studied and found to be consistent. Again\nthe thrust axis smearing reduces the magnitude of the\nasymmetries to 92% of the generated value as found in\nsimulations (less than in the case of Collins FF measure-\nment).\nResults have been obtained so far by Belle, for charged\npion pairs, using 672 fb\u22121 (Vossen, 2011). The asymme-\ntries are displayed, for example, as a function of the two\nfractional energies of the two pairs in Fig. 24.1.15. It can\nbe seen that the asymmetries are increasing with frac-\ntional energy. This can again be explained if more of the\nquarks\u2019 spin information is contained at the highest frac-\ntional energies. The overall magnitude of the asymmetries\nis quite remarkable, reaching more than 10%. Given that\nthe asymmetry parameter a12 is proportional to the prod-\nuct of two IFFs (see Eq. 24.1.14) this means that the e\ufb00ect\nof a single IFF can be as large as 30%.\nFigure 24.1.16 shows the asymmetries as a function\nof the invariant mass of the pion pairs. Here one sees\nan increase in the magnitude of asymmetries up to and\nslightly above the \u03c1 mass, where the asymmetries seem\nto level o\ufb00. At the highest invariant masses, the frac-\ntion of charm events according to MC is largest, such\nthat some e\ufb00ect might originate from charm events. How-\never e\ufb00orts to separate charm and uds events showed lit-\ntle di\ufb00erence between the extracted uds and all events.\nThe asymmetries also show clearly that no sign change\nof the interference fragmentation function occurs at the\ninvariant mass of the \u03c1 meson and therefore rules out\nJa\ufb00e\u2019s prediction (Ja\ufb00e, Jin, and Tang, 1998). Theoret-\nical e\ufb00orts to obtain the quark transversity by combining\nthe e+e\u2212IFF results with the corresponding SIDIS re-\nsults performed by Bacchetta, Courtoy, and Radici (2011)\nand Courtoy, Bacchetta, Radici, and Bianconi (2012) show\na quark transversity distribution similar to the one ex-\ntracted using the Collins fragmentation functions, although\nuncertainties are currently still rather large. A recent up-\ndate of that analysis by Courtoy, Bacchetta, and Radici\n(2012) shows excellent agreement when the recent COM-\nPASS data (Adolph et al., 2012) are included. The simi-\nlarity of the extracted transversity distributions suggests\nthat the unknown QCD evolution of the Collins func-\n\n758\ntion is not too di\ufb00erent from the regular DGLAP evo-\nlution, otherwise the magnitudes at as di\ufb00erent scales of\nQ2 = 110 GeV2 (B Factories) and 2.4 GeV2 (HERMES)\nwould also have been rather di\ufb00erent.\nFuture measurements of IFF should include \u03c00\u03c0\u00b1,\n\u03c0\u00b1,0K and KK, as well as combinations of di\ufb00erent pairs\nin di\ufb00erent hemispheres to gain additional information on\nthe two hadron equivalents of favored and disfavored frag-\nmentation.\n24.1.4 Summary on fragmentation functions\nBelle and BABAR have extracted high precision unpolar-\nized fragmentation functions for light and charmed mesons\nand some of the charmed baryons. While light hadrons\ncontain a relatively small energy fraction of the initial par-\ntons the same fraction for charmed hadrons amounts to\nabout 60%. The measured light quark fragmentation func-\ntions will be used to signi\ufb01cantly improve the global QCD\n\ufb01ts on fragmentation and will in turn provide further ac-\ncess to the \ufb02avor structure of the nucleon in semi-inclusive\nDIS and pp experiments. Spin dependent Collins and in-\nterference fragmentation functions were directly obtained\nfor the \ufb01rst time and found to be sizeable. They give ac-\ncess to the transverse spin structure of the nucleon since\nthey act as quark spin analyzers. They have also been used\ntogether with SIDIS world data to obtain the transversity\ndistribution functions of the nucleon.\n\n759\n24.2 Pentaquark searches\nEditors:\nJonathon Coleman (BABAR)\nBruce Yabsley (Belle)\nAdditional section writers:\nRoman Mizuk\nSince the early years of the quark model, there has\nbeen speculation concerning states with unusual valence\nquark content: something other than qqq or qq. Other\ncolor-singlet con\ufb01gurations are allowed by SU(3), so the\nquestion becomes whether the dynamics of the strong in-\nteraction allows such states to form and to be at least\nmetastable. So-called pentaquark states, with valence con-\ntent qqqqq (or charge conjugate), are an important ex-\nample. Theoretical work on pentaquark states is brie\ufb02y\nsummarized in Section 24.2.1.\nThe subject became important for the B Factories due\nto positive claims in 2003, initially from experiments work-\ning at the boundary of particle and nuclear physics. The\noriginal \u0398(1540)+ evidence was from a search in photo-\nproduction by LEPS (Nakano et al., 2003), and an analy-\nsis of kaon interaction data from DIANA (Barmin et al.,\n2003). Many other positive claims for the \u0398(1540)+ and\nother pentaquark states followed. These are summarized\nin Section 24.2.2.\nA programme of searches then followed at both Belle\nand BABAR, which may be roughly divided by production\nmechanism: inclusive production (Section 24.2.3), searches\nin B decays (Section 24.2.4), and interaction of primary\nparticles in the material of the detector (Section 24.2.5).\nThe latter provide the most direct challenge to the original\npentaquark claims. The lessons from B Factory data are\nsummarized in Section 24.2.6.\n24.2.1 Theoretical studies on pentaquarks\nIn the light-quark baryon sector, spin and \ufb02avor are com-\nbined to yield a \ufb02avor-spin SU(6) representation of the\nspectroscopy. The baryon states are composed of three\nquarks, each of which is assumed to be a color triplet, with\nall baryons assumed to be color singlets. The allowed state\nvectors are thus anti-symmetric in color, and symmetric in\nspace-spin-\ufb02avor, and in this way the quark con\ufb01gurations\nsatisfy Fermi statistics. All of the known baryon states up\nto \u223c2 GeV, i.e. those with at least 3 stars in the Parti-\ncle Data Group (PDG) evaluation, are accommodated in\nthis scheme, and the non-relativistic three-quark potential\nmodel of Isgur and Karl can also explain the occurrence\nof \u201cmissing states\u201d on the basis of their highly inelastic\ndecay characteristics (Koniuk and Isgur, 1980). In fact, in\nthe review article by Hey and Kelly (1983) it is pointed out\nthat the successful description of the known baryon states\nin terms of con\ufb01ned triplets of spin-half quarks with a hid-\nden color degree of freedom is perhaps the most signi\ufb01cant\noutcome of all the attempts at describing the spectroscopy\n(and couplings) of the baryonic excitations. However, in\nthe context of QCD, the apparent absence of baryons with\ncomposition qqqqq or qqqg is not understood.\n24.2.1.1 Early partial wave analyses\nThe most obvious way to prove the existence of qqqqq\nstates is to identify resonant structure in the KN sys-\ntem, since an S = +1 baryon must at minimum contain\n\ufb01ve quarks. Since the early days of the quark model, such\nevidence has been sought in the Partial Wave Analysis\n(PWA) of KN elastic, charge exchange, and inelastic scat-\ntering data. The results of these searches for Z\u2217states, as\nthey were called, are summarized brie\ufb02y in Hey and Kelly\n(1983). Only the P01 and P13 amplitudes show hints of\nstructure (in the mass region 1.8\u20131.9 GeV/c2), but it was\nthen concluded that there is no convincing evidence of res-\nonant behavior. In its 1986 review (Aguilar-Benitez et al.,\n1986) the PDG drew a line under these studies with the\nfollowing comment:\n. . . the [PWA] results permit no de\ufb01nite conclusion\n\u2014 the same story heard for 15 years. The stan-\ndards of proof must simply be much more severe\nhere than in a channel in which many resonances\nare already known to exist. The general prejudice\nagainst baryons not made of three quarks and the\nlack of any experimental activity in this area make\nit likely that it will be another 15 years before the\nissue is decided.\nThe Z\u2217listings appeared for the last time in that issue,\nand starting with the following review (Yost et al., 1988),\nonly a reference to the 1986 edition was included. After\nthat, the subject of exotic baryons did not receive much\nattention except from a few theorists motivated by the old\nchiral soliton ideas due to Skyrme (1962).\n24.2.1.2 The pentaquark revival; prediction of the\n\u0398(1540)+\nA decade later Diakonov, Petrov, and Polyakov (1997)\nmade a remarkable prediction concerning the existence of\na positive strangeness baryon state just above KN thresh-\nold in mass (\u223c1.53 GeV/c2) and of extremely narrow\nwidth (\u0393 < 15 MeV). Such a state would be manifestly ex-\notic since it would have a minimal content of four quarks\nand an anti-quark (s). The predictions were based on the\ngeneralization of a chiral soliton model (Skyrme, 1962),\nin which nucleons are viewed as solitons of the pion \ufb01eld.\nQuantization of the rotations of this \ufb01eld in ordinary and\n\ufb02avor SU(3) space leads to a baryon ground state which\nis an octet with spin 1/2, and to a \ufb01rst excited state which\nis a spin 3/2 decuplet, just as happens to be the case in\nnature. In the case of three \ufb02avors, the next excitation\ncorresponds to an anti-decuplet with spin 1/2. The struc-\nture of this anti-decuplet is shown in Fig. 24.2.1, with the\nexotic S = +1 state occupying the apex of the triangle.\nThe states at the extreme edges of the base of the trian-\ngle are also manifestly exotic with minimal quark content\n\n760\nS\nI3\nO+\n5\nududs\nT+\n5\nuud(dd+ss)\nT0\n5\nudd(uu+ss)\nY<\n5 dds(uu+ss)\nY+\n5 uus(dd+ss)\nU\nU <\n<\n+\n5\n5\ndsdsu\nuss(uu+dd)\ndss(uu+dd)\nususd\nFigure 24.2.1. The anti-decuplet (annuli) and octet (\ufb01lled\ncircles) that are generally assumed for the lowest mass pen-\ntaquarks. The vertical axis is the strangeness and the horizon-\ntal axis is the isospin. The quark content of the anti-decuplet\nmembers is shown. (Reproduced from Aubert, 2004aa.)\nas shown. As indicated, the mass splitting between the\nisospin multiplets of di\ufb00erent strangeness is linear; in Di-\nakonov, Petrov, and Polyakov (1997), it is estimated to be\n\u223c180 MeV/c2. The overall mass scale was de\ufb01ned by iden-\ntifying the nucleon member of the anti-decuplet with the\nN(1710) resonance (Eidelman et al., 2004), and this led\nto an estimation of the \u0398(1540)+ mass of \u223c1.53 GeV/c2.\nA subsequent calculation of the width of this state led to\nthe estimate that it should be \u223c15 MeV, which, if correct,\nshould make it amenable to experimental detection pro-\nvided that the cross section for production is large enough.\nOn page 312 of Diakonov, Petrov, and Polyakov (1997),\nthere is a comment that the data from the LASS exper-\niment might be used to look for the \u0398(1540)+. This was\nin fact done in 1997 using data selected for the reaction\nK+p \u2192\u03c0+K+n at an incident momentum 11 GeV/c, but\nno signal was observed. The result shown at the 7th Inter-\nnational Symposium on Meson-Nucleon Physics and the\nStructure of the Nucleon in 1997 can be found in Napoli-\ntano, Cummings, and Witkowski (2004). Old, but high\nquality, bubble chamber data selected for the reaction\nK+p \u2192\u03c0+K0p in the momentum region around 1 GeV/c\n(Berthon et al., 1973) also fail to reveal a signal, and sug-\ngest cross section values less than 10 \u00b5b. Representative\nDalitz plots in the \u0398(1540)+ region reported in the 2004\nPDG review article by George Trilling (Eidelman et al.,\n2004) are quite clear: there is no evidence of \u0398(1540)+\nproduction.\nFor more than \ufb01ve years after the publication of the\nDiakonov et al. paper there was no experimental evidence\nto support the prediction of the \u0398(1540)+ but the situ-\nation changed dramatically in the fall of 2002 when the\nLEPS Collaboration claimed to have observed photopro-\nduction of a \u0398(1540)+ candidate (Nakano et al., 2003).\nThen, during a pentaquark workshop at Je\ufb00erson Lab\n(JLab) in November 2003, K.Kadija, representing the\nNA49 Collaboration, presented evidence for the produc-\ntion of a \u039e5(1860)++ pentaquark candidate and a neutral\npartner in p \u2212p interactions at a CM energy of 17.2 GeV\n(later published in Alt et al., 2004). If this state is inter-\npreted as belonging to the anti-decuplet of Diakonov et\nal., the mass (\u223c1.862 GeV/c2) and width (< 18 MeV) val-\nues are much smaller than those predicted (2.07 GeV/c2\nand > 140 MeV, respectively). In a subsequent paper, Di-\nakonov and Petrov (2004) no longer used the N(1710)\nto set the absolute mass scale for their predictions, but\nused the mass values of the \u0398(1540)+ and \u039e5(1860) to\nde\ufb01ne a new anti-decuplet central mass and mass split-\nting (\u223c108 MeV/c2). The reduction of the splitting from\nthe 180 MeV/c2 value of Diakonov, Petrov, and Polyakov\n(1997) could be reproduced by increasing the value of\nthe nucleon sigma term used in the calculation, and ar-\nguments were given to indicate that the NA49 width limit\nwas reasonable if the true width of the \u0398(1540)+ was\n< 3 MeV, and the two states were members of the same\nanti-decuplet.\n24.2.1.3 Subsequent studies\nStimulated by the \ufb02urry of experimental activity on the\npentaquark front, other models of the \u201cquark cluster\u201d type\nsoon appeared. The \ufb01rst of these, due to Karliner and\nLipkin (2003), divided the pentaquark constituents into a\ndi-quark and a tri-quark cluster with the quarks of iden-\ntical \ufb02avor in di\ufb00erent clusters. Each cluster has isospin\nzero and is a color non-singlet (separating the pairs of\nidentical \ufb02avor); one unit of orbital angular momentum\nthen yields IJP = 0 1\n2\n+ as expected for the lowest anti-\ndecuplet, and the centrifugal barrier keeps the clusters\nbeyond the range of the repulsive color-magnetic force.\nThe individual clusters bind together as a result of color-\nelectric forces. The model yields a \u0398(1540)+ mass esti-\nmate of \u223c1.59 GeV/c2, and an anti-decuplet mass split-\nting which is only \u223c50 MeV/c2. This is a quark-based\nmodel which led to a resonant S = +1 baryon state in the\nvicinity of KN threshold.\nA second model of this type is due to Ja\ufb00e and Wilczek\n(2003). The \u0398(1540)+ is described in terms of two ud di-\nquarks and a bachelor s quark. The ground state diquark-\ndiquark-antiquark con\ufb01guration leads to a degenerate octet\nand anti-decuplet whose symmetry is broken as a result of\nthe strange quark mass, leading to mixing of the two mul-\ntiplets. Incorporating the \u0398(1540)+ as the Y = 2 member\nof the anti-decuplet leads to a somewhat di\ufb00erent spec-\ntroscopy than that of Diakonov, Petrov, and Polyakov\n(1997), and in particular yields a JP = 1/2+ nucleon\nstate at a mass lower than the \u0398(1540)+ which is asso-\nciated with the broad Roper resonance.182 However, the\npredicted mass of the \u039e5(1860) state is more than 100 MeV\nbelow the mass of the state claimed by the NA49 experi-\nment.\n182 A Roper resonance is a broad baryon state with a mass\ncirca 1440 MeV, denoted by P11(1440), see Alvarez-Ruso (2010)\nand references therein for more details.\n\n761\nFinally, it should be possible to employ Lattice Gauge\ntechniques to investigate the hypothetical existence of an\nexotic pentaquark resonant state in the vicinity of KN\nthreshold. Holland and Juge (2006) discussed the status of\nsuch calculations, and concluded that there was as yet no\nevidence favoring the existence of any such state. However\nthe paper cautions that \u201cabsence of evidence\u201d should not\nbe considered to be \u201cevidence of absence\u201d at the present\nearly stage of these e\ufb00orts.\nSince the claim of evidence for \u0398(1540)+ production,\nmany models generating estimates of production cross sec-\ntion rates in photoproduction and hadroproduction reac-\ntions have been presented in the literature. Cross section\nestimates range from a fraction of a nanobarn to sev-\neral hundred nb in photoproduction, and from a fraction\nof a microbarn to several millibarns in hadroproduction,\ndepending on the reaction and details of the model. A\nsampling of such calculations can be found in Oh, Kim,\nand Lee (2004a,b), and in some of the references listed\nin these papers. Some of the calculations yield unaccept-\nable results: e.g. for the reaction K+p \u2192\u03c0+\u0398(1540)+ the\npredicted cross section is \u223c1.5 mb at low beam momen-\ntum, clearly inconsistent with the published data (Berthon\net al., 1973).\n24.2.2 Positive claims in 2003\u20132005\n24.2.2.1 \u0398(1540)+\nTable 24.2.1 is adapted from Dzierba, Meyer, and Szczepa-\nniak (2005), and summarizes the various claims for the\nobservation of the \u0398(1540)+ pentaquark state. The cor-\nresponding collaborations and reactions studied are sum-\nmarized; also listed are the mass and width estimates, and\nclaimed signi\ufb01cance.\nThe \ufb01rst three rows of the table result from photopro-\nduction of the same exclusive \ufb01nal state, with the signal\nappearing in the K+n invariant mass distribution (Nakano\net al., 2003; Stepanyan et al., 2003). The next two rows\nare from photoproduction of di\ufb00erent exclusive \ufb01nal states\non a proton target, with the signal again appearing in\nthe K+n invariant mass distribution (Barth et al., 2003;\nKubarovsky et al., 2004). The quoted mass and width val-\nues appear to be consistent.\nThe remaining measurements are for the K0\nSp system.\nOnly for the exclusive \ufb01nal states of Abdel-Bary et al.\n(2004) and Barmin et al. (2003) is it known with certainty\nthat the K0\nS is produced as a K0. These eight measure-\nments are obtained using a variety of incident particles\n(K+, p, neutrino, and e\u00b1) and targets, and six of them\nare from inclusive production processes. These measure-\nments yield a discrepancy of at least 3\u03c3 between the mass\nvalues from the K+n and K0\nSp systems.\nThe overall mean value of the mass from these mea-\nsurements is 1535.3 \u00b1 2.6 MeV/c2, where the error is esti-\nmated from the spread in the individual values, since this\nis larger than would be expected from the quoted errors\non the measurements.\nIf the \u0398(1540)+ exists, its e\ufb00ects should be seen in\nK+d scattering data for incident K+ laboratory momenta\naround 440 MeV/c, unless its width is very small. Since\nthe CM energy in this region is below pion production\nthreshold, the cross section reaches the unitarity limit at\nresonance, and for spin 1/2 is Bi \u00d7 Bf \u00d7 68 mb, where Bi\nand Bf are the branching fractions to the initial and \ufb01nal\nstates. These branching fractions are equal to 0.5 for the\n\u0398(1540)+. Integrating over the resonance peak, the net\ne\ufb00ect results in a contribution \u0393 \u00d7 (Bi \u00d7 Bf \u00d7 107 mb),\nwhere \u0393 is the width of the resonance. Several studies\nof the rather sparse scattering data in this region (Arndt,\nStrakovsky, and Workman, 2003; Cahn and Trilling, 2004;\nHaidenbauer and Krein, 2003; Nussinov, 2003, 2004) con-\nclude that \u0393 must be less than 5 MeV. In addition, in Cahn\nand Trilling (2004) the Xe bubble chamber data of Barmin\net al. (2003), when interpreted in terms of K+n charge\nexchange scattering, yield the value \u0393 = (0.9 \u00b1 0.3) MeV,\nwith no estimate of systematic uncertainty. The conclu-\nsion therefore is that if the \u0398(1540)+ exists its width must\nbe < 5 MeV, and may even be as small as \u223c1 MeV. The\nwidth estimates in Table 24.2.1 are consistent with such\nvalues.\nSince the mass distributions of the claimed signals were\nobtained in many di\ufb00erent contexts, it is di\ufb03cult to be-\nlieve that the signals might be spurious. However, the fact\nthat the mass value estimates are spread over a range\nwhich seems too large for the uncertainties quoted, and the\nobservation that in all of the distributions, the peak signal\nbin contains only 0\u201350 events above background, indicate\nthe need to exercise caution. This is especially relevant in\nlight of JLab results (DeVita, 2005) in what is essentially\na much higher statistics repetition of the SAPHIR exper-\niment. Cross section estimates for \u0398(1540)+ production\nare either non-existent, unclear, or unreliable.\nThe COSY experiment (Abdel-Bary et al., 2004) quotes\na cross section of (0.4\u00b10.1\u00b10.1) \u00b5b but does not indicate\nclearly whether all branching fraction values and isospin\nClebsch-Gordan coe\ufb03cients have been taken into account.\nThe SAPHIR experiment (Barth et al., 2003) initially\nquoted a cross section for the reaction \u03b3p \u2192K0\u0398(1540)+\nof 300 nb, but this has since been reduced to 50 nb, and\nJLab measurements of the same reaction (DeVita, 2005)\nyield a 95% C.L. upper limit in the range 1\u20134 nb for the\nrelevant region of photon laboratory energy. As of 2005,\nwhen the B Factory studies were being performed, there\nwas no other useful information.\n24.2.2.2 \u039e5(1860)\nThese are the states contributing the base of the anti-\ndecuplet triangle in Fig. 24.2.1. Only one observation has\nbeen claimed to date, from the NA49 Collaboration study-\ning the interactions of a 158 GeV/c proton beam in a liquid\nhydrogen target (Alt et al., 2004). The combined invari-\nant mass distributions for the systems \u039e\u2212\u03c0\u2212, \u039e\u2212\u03c0+, and\ntheir anti-particle counterparts reveal a narrow signal of\n\u223c68 events over a background of \u223c77 events; the width is\nconsistent with the detector resolution (18 MeV/c2). The\n\n762\nTable 24.2.1. Results from experiments reporting the observation of the \u0398(1540)+ in a K+n or K0\nSp invariant mass distri-\nbution, expanded from Table 3 of Dzierba, Meyer, and Szczepaniak (2005). Seven of these experiments involve real or virtual\nphotoproduction (denoted by *), and four more involve hadroproduction on a hydrogen or nuclear target. (Xe)\u2032 denotes a\nrecoiling Xe. The second LEPS result (Nakano, 2004) was a conference presentation that did not include a mass and width.\nExperiment\nReaction\nMass\nWidth\nSigni\ufb01cance\nReference\n(MeV)\n(MeV)\n(\u03c3)\nLEPS(1)*\n\u03b312C \u2192K+K\u2212X\n1540 \u00b1 10\n< 25\n4.6\nNakano et al. (2003)\nLEPS(2)*\n\u03b3d \u2192K+K\u2212X\n\u2013\n\u2212\u2212\n\u2013\nNakano (2004)\nCLAS(d)*\n\u03b3d \u2192K+K\u2212(n)p\n1542 \u00b1 5\n< 21\n5.2\nStepanyan et al. (2003)\nCLAS(p)*\n\u03b3p \u2192K+K\u2212(n)\n1555 \u00b1 10\n< 26\n7.8\nKubarovsky et al. (2004)\nSAPHIR*\n\u03b3p \u2192K0K+(n)\n1540 \u00b1 6\n< 25\n4.8\nBarth et al. (2003)\nCOSY\npp \u2192\u03a3+K0p\n1530 \u00b1 5\n< 18\n4\u20136\nAbdel-Bary et al. (2004)\nJINR\np(C3H8) \u2192K0\nSpX\n1530 \u00b1 5\n9.2 \u00b1 1.8\n5.5\nAslanyan et al. (2005)\u2020\nSVD\npA \u2192K0\nSpX, (A = C, Si, Pb)\n1540 \u00b1 8\n< 24\n5.6\nAleev et al. (2005)\nDIANA\nK+Xe \u2192K0p(Xe)\u2032\n1539 \u00b1 2\n< 9\n4.4\nBarmin et al. (2003)\n\u03bdBC(ITEP)\n\u03bdNe \u2192K0\nSpX\n1533 \u00b1 5\n< 20\n6.7\nAsratyan et al. (2004)\u2021\nNOMAD\n\u03bd\u00b5A \u2192K0\nSpX, (A = Fe, Al, Pb)\n1528.7 \u00b1 2.5\n< 21\n4.4\nCamilleri (2005)\nHERMES*\ne+d \u2192K0\nSpX\n1528 \u00b1 3\n13 \u00b1 9\n\u223c5\nAirapetian et al. (2004)\nZEUS*\ne\u2212p \u2192e\u2212K0\nSpX\n1522 \u00b1 3\n8 \u00b1 4\n\u223c5\nChekanov et al. (2004a)\n\u2020 Aslanyan, Emelyanenko, and Rikhkvitzkaya (2005)\n\u2021 Asratyan, Dolgolenko, and Kubantsev (2004)\n\ufb01tted mass value is (1.862\u00b10.002) GeV/c2. A \u039e5(1860)++\nbaryon is manifestly exotic; it occupies the lower-left ver-\ntex of the anti-decuplet, with the minimal quark compo-\nsition shown. It is troubling that there have been no other\nobservations of this state to date, but even more trou-\nbling that members of the same collaboration have pub-\nlicly questioned the analysis (Fischer and Wenig, 2004).\n24.2.2.3 \u0398c(3100)\nAgain there was only one experiment claiming evidence\nfor this anti-charm baryon state (Aktas et al., 2004). The\nsignal is observed by the H1 Collaboration at HERA in the\nD\u2217\u2212p and D\u2217+p invariant mass distributions; the \ufb01tted\nmass value is (3.099\u00b10.003\u00b10.005) GeV/c2 and the width\nis consistent with detector resolution (\u223c12 MeV/c2). The\nminimal quark content is uuddc, so that the state is a\nmanifestly exotic pentaquark candidate. There has been\nno corroboration of this state to date; in particular, the\nZEUS experiment operating under the same conditions at\nHERA has found no evidence of a signal (Chekanov et al.,\n2004b). The H1 result was later retracted.\n24.2.2.4 Negative searches\nThe experiments which have searched in vain for evidence\nof the three pentaquark states are summarized in Dzierba,\nMeyer, and Szczepaniak (2005). There is a fairly detailed\ndiscussion of the various non-observations in the reference,\nwhich we do not repeat here.\n24.2.3 Inclusive production searches\n24.2.3.1 Strange pentaquark candidates\nA dedicated search for inclusive production of the \u0398(1540)+\nwas performed by BABAR (Aubert, 2005ac); searches for\nthe doubly-strange states \u039e5(1860)0 and \u039e5(1860)++, re-\nported by NA49 (Alt et al., 2004) and supposed to be\npartners of the \u0398(1540)+ within a pentaquark 10 multi-\nplet, were presented in the same paper.\nIn this analysis, the pK0\nS system, with K0\nS \u2192\u03c0+\u03c0\u2212,\nwas investigated for evidence of \u0398(1540)+ production in\ne+e\u2212collisions at a CM energy of 10.58 GeV, and 0.04 GeV\nbelow.\nThe pK0\nS invariant mass distribution showed a large\n(\u223c100,000 events) signal corresponding to the produc-\ntion of the \u039b(2285)+ charmed baryon, and this was used\nto verify that the dependence of mass resolution upon\nCM momentum p\u2217was well reproduced in Monte Carlo\nsimulation. The same simulation in the mass region of\nthe \u0398(1540)+ yields mass resolution values in the range\n1.7\u20132.2 MeV/c2. The excellent agreement obtained for the\n\u039b(2285)+ data demonstrates that these resolution esti-\nmates are reliable. No \u0398(1540)+ signal was observed, nei-\nther when the pK0\nS mass distribution was taken as a whole,\nnor when it was examined as a function of p\u2217. This re-\nmained true for sub-samples of the data for which each\nevent was required to contain an identi\ufb01ed K\u2212(in order\nto bias the K0\nS sample toward K0 rather than K0), and/or\nan anti-proton (in order to bias the sample toward con-\nserved baryon number).\nFor a \ufb01xed \u0398(1540)+ mass value of 1.54 GeV/c2, and\n\ufb01xed total width values of 1 MeV and 8 MeV, resolution-\n\n763\nMass (GeV/c2)\nMean rate per event / (2J+1)\ne+e-AHadrons\n3s=92 GeV\n3s=10 GeV\np\nR\nY\n6++\nU\nY*\nR(1520)\nU*\n1\ne5\nK=1 MeV\nK=8 MeV\nAssume Br(pKs0)=25%\nU5- -\nK=1 MeV\nK=18 MeV\nAssume Br(U-/-)=50%\nBaBar Pq search limits\nFor total particle+antiparticle rate:\n\u00d7(2J+1) where J=total angular momentum\n\u00d72 for particle+antiparticle states\n10\n-7\n10\n-6\n10\n-5\n10\n-4\n10\n-3\n10\n-2\n10\n-1\n1\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\nFigure 24.2.2. From Aubert (2004aa): Compilation of light\n(no c or b quarks) baryon production rates in e+e\u2212to hadrons\nfrom the PDG. Limits from BABAR on pentaquark production\nin e+e\u2212\u2192hadrons are shown, at least an order of magnitude\nbelow the expected trend for \u201cnormal\u201d baryons.\nsmeared P-wave Breit-Wigner lineshapes were used to ob-\ntain 95% C.L. cross section upper limits for each 0.5 GeV/c\nmomentum interval in the range 0\u20135 GeV/c.\nLimits for the integrated cross section values of 80 fb\nand 60 fb were extracted for width values 1 MeV and 8 MeV,\nrespectively. The values obtained for a mass choice of\n1.53 GeV/c2 were virtually identical to these. These upper\nlimit values are signi\ufb01cantly below the cross section values\nwhich would be expected for a particle of mass 1.54 GeV/c2\non the basis of the observed production rates for \u201cordi-\nnary\u201d hadrons (see Fig. 24.2.2). This suggests that, if the\n\u0398(1540)+ pentaquark state does in fact exist, its produc-\ntion is highly suppressed in e+e\u2212interactions at 10.58 GeV\nwith respect to that of well-established hadrons.\nTwo CLAS results testing for the possible existence of\nthe \u0398(1540)+ were found to be in disagreement with each\nother (McKinnon et al., 2006; Stepanyan et al., 2003). The\n2003 result claimed observation of a narrow K+n reso-\nnance in the process \u03b3d \u2192K+K\u2212pn. The 2006 paper is\nthe result of a dedicated high luminosity run by the CLAS\ncollaboration designed speci\ufb01cally to test the validity of\nformer publication in a data sample over 30 times larger\nthan the original one. This subsequent paper found no ev-\nidence for a narrow resonance. In 2007 CLAS re-analysed\ntheir data using a consistent Bayesian methodology (Ire-\nland et al., 2008) in order to understand if those previous\nresults were compatible with each other or not, and to ver-\nify if there was any evidence for a \u0398(1540)+ signal. They\nconclude that the results are indeed compatible, however\nthat there is insu\ufb03cient information in the 2003 data to\nsupport the original claim of the existence of a new state.\n24.2.3.2 The charmed pentaquark candidate \u0398c(3100)\nSearches for the charmed pentaquark candidate \u0398c(3100)0\nwere performed in inclusive production by BABAR (Au-\nbert, 2006ar), and in B decays by Belle (Abe, 2004e).\nIn BABAR, no evidence for the production of the\n\u0398c(3100)0 state in a sample of over 125,000 pD\u2217com-\nbinations was found. Upper limits on the product of the\ninclusive \u0398c(3100)0 production cross section times branch-\ning fraction to this mode for two assumptions of its nat-\nural width, which are valid for any state in the vicin-\nity of 3100 MeV/c2, were set. It would be interesting to\ncompare these limits with the rate expected for an or-\ndinary charmed baryon of mass 3100 MeV/c2. However,\nrates had been measured for only two charmed baryons,\nthe \u039b+\nc (2285) (Seuster, 2006; see also Eidelman et al.,\n2004), and \u03a3c(2455) (Eidelman et al., 2004) at the time\nof publication, with a precision that does not allow a\nmeaningful estimate of the mass dependence. The mass\ndependence observed (Eidelman et al., 2004) for non-\ncharmed baryons in e+e\u2212annihilations predicts a rate\nfor a 3100 MeV/c2 baryon about 1,000 times smaller than\nthat of the \u039b+\nc (2285). Belle limits for a narrow state in\nboth e+e\u2212\u2192cc and \u03a5(4S) events are roughly 1,000 and\n500 times below the \u039b+\nc (2285) and \u03a3c(2455) rates, respec-\ntively.\nAs a result the existence of an ordinary charmed bar-\nyon with this mass and decay mode cannot be excluded.\n24.2.4 Searches in B decays\nParasitic searches were performed at the B Factories for\nthe \u0398(1540)+ and a hypothetical partner \u0398\u2217++ (Wang,\n2005; Aubert, 2005p), through analyses of B \u2192ppK de-\ncays (Section 17.12). These searches failed to provide any\nindication of either of these pentaquark candidates. Belle\nconcludes from their data that a quark fragmentation in-\nterpretation is supported, while a resonant gluonic state\norigin is disfavored.\n24.2.5 Searches using interactions in the detector\nmaterial\nIf they exist, pentaquarks are thought to be produced at\nlow energy, and as a result low energy searches are of\nparamount importance. To access the low energy domain,\nBelle performed a detailed investigation using secondary\ninteractions of hadrons in the detector material. The pro-\ntons and kaons that do not originate from the e+e\u2212inter-\naction point were selected and pK pairs that form high-\nquality vertices with the radial distance R > 1 cm were\nconsidered. The spatial distribution of the pK0\nS pairs for\nthe central part of the Belle detector is shown in Fig. 24.2.3\nfor the two running periods with di\ufb00erent con\ufb01gurations\n\n764\ny (cm)\nSVD1\nSVD2\nx (cm)\nx (cm)\nFigure 24.2.3. Distribution of reconstructed secondary pK0\nS vertices in the Belle detector for both the SVD1 (left) and SVD2\n(right) data samples, from Mizuk, Danilov (2006).\nN/2 MeV/c2\nN/2 MeV/c2\nmpK ( GeV/c2)\nmpK0\nS ( GeV/c2)\n(a)\n(b)\n0\n2000\n4000\n6000\n8000\n1.4\n1.45\n1.5\n1.55\n1.6\n1.65\n1.7\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n550\n1.5\n1.55\n1.6\n1.65\nFigure 24.2.4. (a) Mass spectra of pK\u00b1 (points with error bars) and pK0\nS (histogram) of secondary pairs, and (b) secondary\npK0\nS pairs (small dots with error bars) and expected yield of the charge exchange reaction per 2 MeV/c2 (open dots). The\ndashed line in (b) corresponds to the result of a \ufb01t to a third order polynomial and the \u0398(1540)+ contribution expected from\nthe DIANA result is shown (solid line). Figures are reproduced from Mizuk, Danilov (2006).\nof the inner detectors. The beam pipe, the layers of sili-\ncon vertex detector (three layers for SVD1 and four layers\nfor SVD2) and inner support of the central drift chamber\nare clearly seen, which demonstrates that the secondary\ninteractions are the dominant source of the selected pK0\nS\nvertices. Similar \u201cdetector tomography\u201d pictures were ob-\ntained for the pK\u2212and pK+ vertices.\nBelle performed the search both for inclusive produc-\ntion and for formation of the \u0398(1540)+ (Mizuk, Danilov,\n2006). The invariant mass distributions for the secondary\npK\u2212and pK0\nS vertices are shown in Figure 24.2.4. There\nis a clear \u039b(1520) signal in the pK\u2212distribution while\nthere is no \u0398(1540)+ signal in the K0\nS distribution. Belle\nused the \u039b(1520) signal as a reference and placed a 90%\nC.L. upper limit on the ratio\n\u03c3(KN \u2192\u0398(1540)+X)\n\u03c3(KN \u2192\u039b(1520)X\n< 2.5%.\n(24.2.1)\nBelle \ufb01nds that it is very rarely that there is an addi-\ntional kaon track from the secondary pK vertex. Therefore\nthe interactions are induced by strange particles, primar-\nily kaons, with the contribution of hyperons estimated\nto be negligible. Given that the typical projectile kaon\nmomentum is only 1 GeV, this is a unique null result in\nthe low energy domain. The upper limit is much smaller\n\n765\n1.450\n1.500\n1.550\n1.600\n1.650\n1.700\npKshort Mass (GeV/c\n2)\n0\n10\n20\n30\n40\n50\n60\nCandidates / (8 MeV/c\n2) \nHERMES\nBaBar\nNormalization region\ne\n\u00b1D\ne\n\u00efBe\ncandidates\n1171\n227174\nECM\n10.6 GeV\n9.4\nQ\n2\n~0\n~0\n(a) Comparison with HERMES (Airapetian et al., 2004),\nusing HERMES data above 1.58 GeV/c2 for normaliza-\ntion.\n1.450\n1.500\n1.550\n1.600\n1.650\n1.700\npKshort Mass (GeV/c\n2)\n0\n100\n200\n300\nCandidates / (5 MeV/c\n2) \nZEUS\nBaBar\nNormalization\nregion\ne\n\u00b1p\ne\n\u00efBe\ncandidates\n14622\n227174\nECM\n300 GeV\n9.4\nQ\n2\n>20 GeV\n2\n~0\n(b) Comparison with ZEUS (Chekanov et al., 2004a),\nusing ZEUS data below 1.48 GeV/c2 for normalization.\nFigure 24.2.5. From Coleman (2005): BABAR K0\nS p mass distributions from electroproduction in Be, compared with results\nfrom previous experiments. In each case, the BABAR distribution is normalized to that of the other experiment in the region\nshown.\nthan the corresponding values from experiments with pos-\nitive results, however, its interpretation remains model-\ndependent.\nTo obtain a model-independent constraint on the\n\u0398(1540)+ parameters Belle searched for the formation of\nthe \u0398(1540)+ using the exclusive charge-exchange reac-\ntion K+p \u2192pK0\nS. The yield of \u0398(1540)+ formed in s-\nchannel transitions is directly related to its width. In this\nsearch the projectile K+ was not reconstructed and its\nmomentum was determined from the energy-momentum\nof the secondary pK0\nS pair and from the vertex con-\nstraints. The Fermi momentum of the struck neutron was\nalso determined. The procedure was veri\ufb01ed and cali-\nbrated using D\u2217+ \u2192\u03c0+D0(\u2192\u03c0\u2212K+) decays in which\nthe K+ had interacted in the detector material. To sup-\npress the background from inelastic K+n \u2192pK0\nS X scat-\ntering, Belle applied veto on additional charged tracks\nfrom the secondary vertex and required that the Fermi\nmomentum be in the range 50 to 300 MeV. These re-\nquirements suppress inelastic reactions by a factor of\nfour. The charge exchange reaction accounts for about\n10% of the resulting sample. No \u0398(1540)+ signal is ob-\nserved and an upper limit on the \u0398(1540)+ width is set\n\u0393(K+p \u2192\u0398(1540)+ \u2192pKs) < 0.64 MeV at 90% C.L.\nfor a \u0398(1540)+ mass of 1539 MeV. This upper limit is\nmarginally consistent with the measurement by the DI-\nANA experiment (0.9 \u00b1 0.3) MeV (Barmin et al., 2003)\nand does not support the evidence reported by DIANA.\nLikewise, the search for the \u0398(1540)+ was extended to\nthe interactions of secondary hadrons, background tracks\nof every type, and beam halo electrons and positrons in\nthe material of the inner BABAR detector (Coleman, 2005).\nIt was demonstrated that the candidate (K0\nS, p) vertices\nreproduce the detector geometry very well, however the\ninclusive K0\nSp mass distribution shows no pentaquark sig-\nnal.\nSub-samples of the candidates with at least one associ-\nated charged track, and also those remaining after reject-\ning (K0\nS, p) vertices with at least one associated baryon\nwere examined. The study has been restricted to the re-\ngions which can be interpreted as corresponding to electro-\nproduction in Be (mainly) and Ta, and has been repeated\nincluding in addition a small sample of vertices with an\nassociated electron. Again, no \u0398(1540)+ signal has been\nobserved. Since there is no quantitative information on the\n\ufb02ux of o\ufb00-beam electrons and positrons, it is not possible\nto estimate upper limits for the production cross section\nas was done in Aubert (2004aa, 2005ac).\nThe BABAR electroproduction results have been com-\npared to those of the HERMES (Airapetian et al., 2004)\nand ZEUS (Chekanov et al., 2004a) experiments, the re-\nsults of which are shown in Fig. 24.2.5. These compar-\nisons seem to indicate a signi\ufb01cant loss of acceptance for\nthe HERMES experiment in the K0\nSp mass region below\n\u223c1.52 GeV/c2. There is no evidence for the \u039b(1480) and\n\u0398(1540)+ signals of the ZEUS analysis, and this creates\nserious reservations about the signi\ufb01cance of the \u0398(1540)+\nobservations claimed by HERMES and ZEUS. A subse-\nquent search by H1 for the \u0398(1540)+also found no evi-\ndence for a signal (Aktas et al., 2006).\nFinally, the BABAR results on the electroproduction of\nthe K0\nSpK system have been compared to the SAPHIR\n(Barth et al., 2003) results on the photoproduction of\nthe K+nK0 \ufb01nal state. A crude attempt at normalizing\nthe production of \u039b(1520) observed in both analyses leads\nto the conclusion that a \u0398(1540)+ signal as observed by\nSAPHIR would not be signi\ufb01cant in the corresponding\nBABAR K0\nSp mass distribution. The BABAR results are in\ncomplete accord with those presented by the CLAS Col-\nlaboration (DeVita, 2005).\n\n766\n24.2.6 Summary\nIn summary, the \ufb01nal result of the high statistics searches\nat the B Factories summarized above is that no experi-\nment has yielded any evidence for the production of the\n\u0398(1540)+ or other members of the pentaquark family. Fur-\nthermore, a comparison of the BABAR results on electro-\nproduction in Be to those from the HERMES (e+D) and\nZEUS (e+p) experiments leads to the conclusion that prior\nclaims for the observation of \u0398(1540)+ in electroproduc-\ntion are not convincing. The inclusive and exclusive K+p\ninteraction searches from Belle also result in the conclu-\nsion that claims for the observation of \u0398(1540)+ are un-\nconvincing. In light of these results it would seem clear\nthat the only way to clarify the issue brought about by the\nexperiments which still claim a signal is for those experi-\nments to collect and analyse signi\ufb01cantly more data. How-\never, many of the analyses have been carried out in exper-\niments which are now decommissioned. Nevertheless, for\nthose which can be repeated, there is a clear need for new\nhigh statistics data to be collected with well-calibrated,\nlarge-acceptance detectors. Proof of principle has been\namply provided by the results from CLAS (DeVita, 2005),\nwhich so convincingly refute the earlier claim of \u0398(1540)+\nobservation from SAPHIR (Barth et al., 2003).\nThe whole saga is succinctly summed up by the 2006\nand 2008 PDG reports as given below. The 2006 Review\nof Particle Physics concluded (Yao et al., 2006):\n. . . there has not been a high-statistics con\ufb01rmation\nof any of the original experiments that claimed to\nsee the \u0398(1540)+; there have been two high-statistics\nrepeats from Je\ufb00erson Lab that have clearly shown\nthe original positive claims in those two cases to\nbe wrong; there have been a number of other high-\nstatistics experiments, none of which have found\nany evidence for the \u0398(1540)+; and all attempts\nto con\ufb01rm the two other claimed pentaquark states\nhave led to negative results. The conclusion that\npentaquarks in general, and the \u0398(1540)+, in par-\nticular, do not exist, appears compelling.\nThe 2008 Review of Particle Physics went even fur-\nther (Amsler et al., 2008):\nThere are two or three recent experiments that \ufb01nd\nweak evidence for signals near the nominal masses,\nbut there is simply no point in tabulating them in\nview of the overwhelming evidence that the claimed\npentaquarks do not exist. The only advance in par-\nticle physics thought worthy of mention in the Amer-\nican Institute of Physics \u201cPhysics News in 2003\u201d\nwas a false alarm. The whole story \u2014 the discover-\nies themselves, the tidal wave of papers by theorists\nand phenomenologists that followed, and the even-\ntual \u201cundiscovery\u201d \u2014 is a curious episode in the\nhistory of science.\nDespite these null results, LEPS results as of 2009 con-\ntinue to claim the existence of a narrow state with a mass\nof 1524 \u00b1 4 MeV/c2, with a statistical signi\ufb01cance of 5.1 \u03c3\n(Nakano et al., 2009).\n\n767\nChapter 25\nGlobal interpretation\nThe chapters in this book have described a wide range of\nmeasurements that have been made by the B Factories.\nIt is possible to relate a number of these to either expec-\ntations from Standard Model (SM) based calculations, or\nhypothesized scenarios of physics beyond the SM. This\nchapter describes in detail how key measurements from\nthe B Factories can be combined in order to constrain our\nunderstanding of the CKM matrix, and the role of the KM\nmechanism in the SM (Section 25.1); and how one may be\nable to go beyond the SM and constrain features and parts\nof the parameter space for postulated new physics models\n(Section 25.2).\nPrior to the B Factories there had already been a va-\nriety of results on \ufb02avor physics, which had produced a\nreference point to be improved upon by the B Factories.\nThe measurement of \u03f5K as well as measurements in the\ncharm sector provided indirect constraints on B decays. In\nparticular, the charm physics performed at CLEO-c, run-\nning at the open charm threshold, produced some results\nthat would not be surpassed by BABAR or Belle and gave\nsome tight constraints. ARGUS, CLEO, and the LEP ex-\nperiments investigated bottom hadrons directly and gave\na \ufb01rst picture of what to expect in terms of the SM picture\nof the Unitarity Triangle. However, the question remained:\nwould the SM expectation be borne out experimentally?\nThere are two requirements for an observable to be\nof interest for global \ufb01ts. Firstly the observable must be\nsomething that is \u201ctheoretically clean\u201d, meaning that the\ntheoretical uncertainties in predicting this quantity in the\nSM are negligible or at least small. If this is not satis\ufb01ed,\nthen one will have trouble incorporating theoretical un-\ncertainties into the comparison of data with the model.\nThe result may be apparent deviations from the SM that\nin reality have a more mundane origin, since they are re-\nally a manifestation of an approximate calculation in a\nSM framework. The second requirement is that one can\nmake a signi\ufb01cant measurement of the observable of in-\nterest. When looking for CP violation in order to test the\nKM mechanism this translates into \ufb01nding evidence for a\nnon-zero level of indirect CP violation. While direct CP\nviolation is also of interest, hadronic uncertainties arising\nfrom strong phase di\ufb00erences, which are di\ufb03cult to calcu-\nlate, limit the constraints that can be placed on the SM\nusing direct CP asymmetries.\nIn the context of searching for physics beyond the SM\nthe requirement that an observable be theoretically clean\nis, again, of paramount importance. However, the require-\nment that one can perform a signi\ufb01cant measurement may\nbe relaxed in some circumstances. Broadly speaking there\nare two extremes that one can focus on. The \ufb01rst is to\nsearch for e\ufb00ects of forbidden or rare decays that would\notherwise be absent or unobservable within the SM. If a\nlarge signal were to be found in such a mode, then that\nwould unequivocally point to new physics. The second\ntype of study requires the measurement of a process that\nis sensitive to new physics and in addition has a measur-\nable SM contribution. Here one aims to compare a pre-\ncisely measured observable with the SM expectation to\nsee if there is agreement or not. A signi\ufb01cant deviation\nfrom the SM would indicate new physics, and compatibil-\nity with the SM can be used to infer constraints on new\nphysics models or even exclude them. Any deviation from\nthe SM expectation can be used to constrain the ratio of\nthe complex coupling divided by the square of the energy\nscale of the new physics appearing in the Lagrangian. This\napproach is complementary to direct searches at the LHC\nwhere one constrains the energy scale directly.\nIn recent years the focus on constraining benchmark\nnew physics scenarios has matured with the realization\nthat individual searches have so far failed to produce an\nunambiguous discovery. By combining constraints from a\nnumber of di\ufb00erent modes one can learn about the allowed\nstructure of beyond-SM scenarios \u2014 that is, which pat-\nterns of new physics predictions are compatible with the\ndata. This aspect of the B Factory program remains a\nfocus for the next generation of experiments.\nExperimental guidance is required in order to help the-\norists understand what possible behavior could be allowed\nby new physics, while still being compatible with the exist-\ning constraints on the SM. For this reason it is important\nto understand the SM description of CP violation, which\nis discussed in Section 25.1, and also to explore benchmark\nnew physics models (Section 25.2), until such time as an\nexperimental discovery is made that can be used to guide\nus toward an improved understanding of nature.\n\n768\n25.1 Global CKM \ufb01ts\nEditors:\nGerald Eigen (BABAR)\nRyosuke Itoh (Belle)\nMarcella Bona (theory)\n25.1.1 Introduction\nThe previous sections of this book present a plethora of\nanalyses that provide measurements of various observ-\nables, which in turn can be related to fundamental the-\nory parameters. In particular, some observables are con-\nnected with the elements of the CKM matrix, which for\nthree quark families is speci\ufb01ed by four independent pa-\nrameters as discussed in detail in Section 16.4. One con-\nvenient parameterization of the CKM matrix is the small-\nangle approximation by Wolfenstein, Eq. (16.4.4). In this\napproximation, following the Wolfenstein-Buras rede\ufb01ni-\ntion, there are four parameters, A, \u03bb, \u03c1 and \u03b7, that fully\ndetermine the CKM matrix, see Eqns (16.4.5), (16.4.6),\nand (16.4.8).\nThe parameter A is of order one and is determined\nby Vcb, \u03bb is the expansion parameter and is related to\nthe Cabibbo angle by \u03bb = sin \u03b8c, and \u03c1 and \u03b7 represent\nthe apex of the Unitarity Triangle (see Section 16.5). A\nnon-zero value of \u03b7 indicates CP violation in the Stan-\ndard Model. These four parameters are simultaneously de-\ntermined by combining various experimental results and\ntheory parameters connecting the observables to the CKM\nformulation in a global CKM \ufb01t.\nThis section gives a brief overview of CP violation in\nthe era of the B Factories (Section 25.1.2) before describ-\ning two global \ufb01t strategies that were continually updated\nduring that time (Section 25.1.3). Experimental and theo-\nretical inputs required in order to perform a global \ufb01t are\ndiscussed in Sections 25.1.4 and 25.1.5, respectively. Re-\nsults of SM-based global \ufb01ts are given in Section 25.1.6,\nand concluding remarks can be found in Section 25.1.7.\n25.1.2 CP violation in the era of the B Factories\nOne of the most important results of the B Factory physics\nprogram is the observation that CP violation in quark\n\ufb02avor-changing processes is described by the Kobayashi-\nMaskawa (KM) mechanism. The KM mechanism has been\ntested to \u223cO(10%) by current measurements from the\nB Factories. In the KM mechanism, only one funda-\nmental weak phase (the Kobayashi-Maskawa phase \u03b4 in\nEq. (16.4.3)) is present and \u03b4 is the single source of CP\nviolation in the SM in the quark sector. The consistency of\n\u03b5K with the observed CP violation in Bd decays and mea-\nsurements of sides and angles of the Unitarity Triangle all\npoint to this common origin of CP violation. In addition,\nboth the value of \u2206ms and the recent LHCb measure-\nments of the weak phase describing mixing-induced CP vi-\nolation in Bs decays agree with the KM mechanism within\nerrors. This agreement between b \u2192d, b \u2192s and s \u2192d\ntransitions is nicely illustrated in Fig. 25.1.1. Another im-\nportant con\ufb01rmation of the KM mechanism is the obser-\nvation that a global CKM \ufb01t with only CP-conserving\nobservables and one with only CP-violating observables\nyield the same values of \u03c1 and \u03b7, as shown in Figs 25.1.2\nand 25.1.3.\n25.1.3 Methodology\nTwo main collaborations have performed global CKM \ufb01ts,\nperiodically releasing new results in concert with updated\nmeasurements from the B Factories. Therefore the im-\npact of new measurements from BABAR and Belle were\nconstantly discussed in terms of their constraints on the\nSM, and of possible tensions that could point toward new\nphysics. The methodologies employed by these two groups,\nCKM\ufb01tter and UT\ufb01t, are discussed below. Detailed refer-\nences to the various global \ufb01t analyses performed are given\nin the sections concerned with the experimental and theo-\nretical inputs later in this chapter. For the purpose of this\nbook, the two groups used a uni\ufb01ed set of inputs coming\nfrom the book averages of B Factory data in the context of\nthe Standard Model description of quark \ufb02avor-changing\nprocesses.\nA third approach, called the scan method, has been de-\nscribed in a recent paper (Eigen, Dubois-Felsmann, Hitlin,\nand Porter, 2013). This method makes minimal assump-\ntions as to the distribution of theory errors in \ufb01tting for\nthe Unitarity Triangle parameters, instead scanning over\na large range of theoretical parameters for \ufb01ts found to\nhave an acceptable \u03c72 value. It also extends the global \ufb01t,\nallowing the determination of correlations in the \ufb01t be-\ntween underlying physical parameters that are related to\nmore than one observable, e.g. \u03c61 and \u03c62. The statistical\nprocedure used in the scan method follows the approach\nadopted in the BABAR physics book (Harrison and Quinn,\n1998).\n25.1.3.1 CKM\ufb01tter\nThe CKM\ufb01tter group (Charles et al., 2005), a collabora-\ntion of experimental and theoretical physicists, performs\nphenomenological studies related to \ufb02avor physics and CP\nviolation. To quantify the impact of measurements on the\nSM parameters as well as on some postulated extensions\nof the SM, they developed a global \ufb01t package based on a\nfrequentist statistical approach. They use a speci\ufb01c model\nfor theoretical uncertainties (most often related to the as-\nsessment of hadronic quantities) as biases bounded in a\nrange, R\ufb01t (H\u00a8ocker, Lacker, Laplace, and Le Diberder,\n2001).\nThe CKM\ufb01tter group adopted the following frame-\nwork. They constrain a certain number of parameters in\nthe model such as the Wolfenstein parameters describing\nthe CKM matrix, quark masses, or hadronic quantities\nin order to compare a set of observations xobs with their\n\n769\ntheoretical predictions in a given model. The unknown pa-\nrameters entering the theoretical predictions are split into\ntwo sets, parameters of interest such as (\u03c1, \u03b7) denoted by\n\u00b5, and those of no interest called nuisance parameters,\nsuch as hadronic quantities, which are denoted by \u03bd.\nA general approach to constrain the fundamental pa-\nrameters of interest is a hypothesis test, quantifying the\ncompatibility of the data with the null hypothesis that\nthe true value of a fundamental parameter \u00b5t is equal to a\nparticular value \u00b5. In order to interpret the distribution of\nobservables under the null hypothesis, a test statistic mea-\nsuring whether the data are compatible or not is de\ufb01ned.\nIn analogy with the case of simple hypotheses for which\nall the values of the fundamental parameters are de\ufb01ned,\nthe CKM\ufb01tter framework uses the maximum likelihood\nratio de\ufb01ned as\n\u039b(x, \u00b5) = sup\u03bd Lx(\u00b5, \u03bd)\nsup\u00b5,\u03bd Lx(\u00b5, \u03bd),\n\u2206\u03c72 = \u22122 ln(\u039b),\n(25.1.1)\nwhere Lx(\u00b5, \u03bd) denotes the likelihood built from exper-\nimental data and theoretical inputs x, and sup refers to\nthe supremum, otherwise known as least upper bound.\nNote that the \u2206\u03c72 of the test statistic does not necessar-\nily follow a \u03c72 distribution, especially if the distributions\nof the observables exhibit signi\ufb01cant non-Gaussian prop-\nerties. In the asymptotic regime, however, Wilks\u2019 theorem\nstates that the distribution of \u2206\u03c72 should converge to a \u03c72\ndistribution depending only on the number of parameters\ntested (Wilks, 1938).\nFrom this test statistic, a p-value for the observations\nxobs is built under the null hypothesis \u00b5t = \u00b5 correspond-\ning to the probability that the test statistic is as large as,\nor larger than, that observed\np(xobs; \u00b5) = P[\u2206\u03c72 \u2265\u2206\u03c72(xobs; \u00b5)].\n(25.1.2)\nSmall p-values provide evidence against the null hypoth-\nesis. This p-value can be computed using pseudo experi-\nments with Monte Carlo methods, or directly in terms of\nincomplete \u0393 functions if one assumes that the asymptotic\nregime has been reached. After having computed the p-\nvalue associated with each value of \u00b5, con\ufb01dence intervals\nfor a given con\ufb01dence level can be de\ufb01ned by considering\nthe region where 1 \u2212C.L. \u2264p(x; \u00b5).\nPractically the \ufb01t is performed by scanning \u00b5, min-\nimizing the likelihood Lx with respect to the other pa-\nrameters, and identifying the \u201cbest-\ufb01t\u201d value. Unless ex-\nplicitly provided by the experiments, the likelihoods are\nbuilt assuming the uncertainties in the experimental mea-\nsurements are Gaussian, whereas the theoretical errors are\ntreated in the R\ufb01t scheme as constrained in a strict range.\nThe p-values are extracted from the scan of the test statis-\ntic and are analyzed to provide con\ufb01dence intervals or con-\n\ufb01dence regions for the fundamental parameters of interest.\n25.1.3.2 UT\ufb01t\nThe UT\ufb01t Collaboration is formed of experimental and\ntheoretical physicists performing the Unitarity Triangle\nanalysis following the method described in Ciuchini et al.\n(2001) and Bona et al. (2005). This section summarizes\nthe basic ingredients of the UT\ufb01t analysis method that is\ndeveloped in the framework of a Bayesian approach.\nIn the following sections, several equations are given\nthat relate a constraint cj (where cj stands for one of M\nconstraints such as |Vub/Vcb|, \u2206md, \u2206ms, |\u03b5K| and etc.,\nfor j = 1, . . . , M) to the Unitarity Triangle parameters \u03c1\nand \u03b7, via a set of N ancillary parameters x, where x =\n{x1, x2, . . . , xN} stand for all experimentally determined\nor theoretically calculated quantities on which the various\ncj depend:\ncj \u2261cj(\u03c1, \u03b7; x).\n(25.1.3)\nIn the ideal case of exact knowledge of cj and x, each\nof the constraints provides a curve in the (\u03c1, \u03b7) plane.\nIn such a case, there would be no reason to favor any\nof the points on the curve, unless one has some further\ninformation or physical prejudice, which might exclude\npoints outside a determined physical region, or, in general,\nassign di\ufb00erent weights to di\ufb00erent points. In reality one\nsu\ufb00ers from several uncertainties on the quantities cj and\nx. However, there are values for cj and x which can be\nconsidered as ruled out. For example if one considers the\nmeasurement of \u03c63 = (67 \u00b1 11)\u25e6, the value of this angle\nis currently constrained to lie within some almost certain\nrange, 45\u25e6< \u03c63 < 89\u25e6, and so a value of \u03c63 \u223c20\u25e6is\nexcluded. Moreover, it is much more probable that the\nvalue of \u03c63 lies between 56\u25e6and 78\u25e6rather than in the\nrest of the interval, in spite of the fact that the two sub-\nintervals have the same widths. This means that, instead\nof a single curve in the (\u03c1, \u03b7) plane, one has a family of\ncurves which depends on the distributions of cj and x. As\na result, di\ufb00erent points in the (\u03c1, \u03b7) plane have di\ufb00erent\nweights (even if they were taken to be equally probable a\npriori) and our con\ufb01dence on the values of \u03c1 and \u03b7 clusters\nin a region of the plane.\nThe above considerations can be formalized using the\nBayesian approach: the uncertainty is described in terms\nof a probability density function (p.d.f.) which quanti\ufb01es\nour con\ufb01dence on the values of a given quantity. The in-\nference of \u03c1 and \u03b7 becomes a straightforward application\nof probability theory. In the following, all the p.d.f.s are\ncalled f(. . . ) assuming a di\ufb00erent functional form that de-\npends on the speci\ufb01ed arguments.\nWe can de\ufb01ne the p.d.f. f(\u03c1, \u03b7) that takes into account\nthe uncertainties on cj and x:\nf(\u03c1, \u03b7) \u221d\nZ\n1\n\u221a\n2\u03c0 \u03c3(cj) exp\n\u0014\n\u2212(cj(\u03c1, \u03b7, x) \u2212bcj)2\n2 \u03c32(cj)\n\u0015\n\u00b7\n\u00b7f(x1) \u00b7 f(x2) \u00b7 \u00b7 \u00b7 f(xN) dx ,\n(25.1.4)\nwhere bcj is the experimental best estimate of cj, with un-\ncertainty \u03c3(cj). For simplicity, a Gaussian distribution can\nbe assumed as an individual p.d.f. for each constraint cj.\nIn principle we should consider a joint f(cj, x), but we\nsplit it into the product of the individual p.d.f.s, assum-\ning quantities are independent.\nAlthough the above derivation of Eq. (25.1.4) is proba-\nbly the most intuitive one, UT\ufb01t choose to de\ufb01ne a global\n\n770\ninference relating \u03c1, \u03b7, cj and x, which is the usual way\nof performing Bayesian inference. This method is followed\nby a second step where marginalization is performed over\nthose quantities which are not of interest. In this case\nBayes theorem can be used to give\nf(cj, \u03c1, \u03b7, x | bcj) \u221df(bcj | cj, \u03c1, \u03b7, x) \u00b7 f(cj, \u03c1, \u03b7, x)\n\u221df(bcj | cj) \u00b7 f(cj | \u03c1, \u03b7, x) \u00b7 f(x, \u03c1, \u03b7)\n\u221df(bcj | cj) \u00b7 \u03b4(cj \u2212cj(\u03c1, \u03b7, x)) \u00b7\n\u00b7f(x) \u00b7 f\u25e6(\u03c1, \u03b7) ,\n(25.1.5)\nwhere f\u25e6(\u03c1, \u03b7) denotes the prior probability distribution.\nEquation (25.1.4) can be recovered by i) assuming a Gaus-\nsian error function for bcj around cj; ii) considering the\nvarious xi as independent; iii) taking a \ufb02at a priori dis-\ntribution for \u03c1 and \u03b7; and iv) by integrating Eq. (25.1.5)\nover cj and x.\nAt this point, the extension of the formalism to several\nconstraints is straightforward. One can rewrite Eq. (25.1.5)\nas\nf(\u03c1, \u03b7, x | bc1, ..., bcM) \u221d\nY\nj=1,M\nfj(bcj | \u03c1, \u03b7, x) \u00d7\nY\ni=1,N\nfi(xi) \u00d7\n\u00d7f\u25e6(\u03c1, \u03b7) ,\n(25.1.6)\nwhere the conditioning on fj from the cj have been re-\nmoved, since the cj act as intermediate variables which\nare integrated away to obtain a marginal probability dis-\ntribution.\nIntegrating Eq. (25.1.6) over x, one can rewrite the\nglobal inference in the following way:\nf(\u03c1, \u03b7 |bc, f) \u221dL(bc | \u03c1, \u03b7, f) \u00d7 f\u25e6(\u03c1, \u03b7) ,\n(25.1.7)\nwhere bc stands for the set of measured constraints, f in-\ndicates the dependence from the set of p.d.f.s that can be\nexplicitly written as:\nL(bc | \u03c1, \u03b7, f) =\nZ\nY\nj=1,M\nfj(bcj | \u03c1, \u03b7, x)\nY\ni=1,N\nfi(xi) dxi\n(25.1.8)\nwhich is the e\ufb00ective overall likelihood taking into account\nall possible values of xj, properly weighted. Hence the\noverall likelihood depends on the best knowledge of all\nxi, described by f(x).\nIn conclusion, while a priori all values for \u03c1 and \u03b7\nare considered equally likely, a posteriori the probability\nclusters around the point which maximizes the likelihood.\nThe \ufb01nal (unnormalized) p.d.f. obtained starting from a\n\ufb02at distribution of \u03c1 and \u03b7 is\nf(\u03c1, \u03b7) \u221d\nZ\nY\nj=1,M\nfj(bcj | \u03c1, \u03b7, x)\nY\ni=1,N\nfi(xi) dxi,\n(25.1.9)\nwhere the integration can be performed using Monte Carlo\nmethods.\n25.1.4 Experimental inputs\nThe following sections discuss the observables that are\nused in global \ufb01ts in order to extract CKM parameters.\nThe input values used for these observables are taken from\nthe averages performed for this book and they are sum-\nmarized in Tables 25.1.1 and 25.1.2.\n25.1.4.1 |Vud| and |Vus|\nThe magnitudes of the CKM elements Vud and Vus re-\nquired in the CKM global \ufb01ts are extracted from semi-\nleptonic u \u2192d and u \u2192s transitions that are not mea-\nsured at the B Factories. These two CKM matrix elements\nare the most precisely measured parameters. The deter-\nmination of Vud involves super-allowed 0+ \u21920+ nuclear\nbeta decays and \u03c0+ \u2192\u03c00e+\u03bd decays. The determina-\ntion of Vus is based on semileptonic kaon decays. Results\nare provided by the Flavianet working group (Antonelli\net al., 2010b). For the extraction of Vus, various structure\nconstants are needed, which are calculated using lattice\nQCD analyses by averaging the latest Nf = 2 + 1 calcu-\nlations by BMW (Durr et al., 2010), MILC\u201909 (Bazavov\net al., 2009) and HPQCD/UKQCD (Follana, Davies, Lep-\nage, and Shigemitsu, 2008). The latest results yield (Be-\nringer et al., 2012)\n|Vud| = 0.97425 \u00b1 0.00022,\n(25.1.10)\n|Vus| = 0.2252 \u00b1 0.0009.\n(25.1.11)\n25.1.4.2 B Factory results\nThe experimental inputs from the B Factories are:\nUnitarity Triangle sides (see Section 16.5):\nThe sides of the Unitarity Triangle are:\nRu = |Vud||Vub|\n|Vcd||Vcb| =\nq\n\u03c12 + \u03b72\n(25.1.12)\nand\nRt = |Vtd||Vtb|\n|Vcd||Vcb| =\nq\n(1 \u2212\u03c1)2 + \u03b72.\n(25.1.13)\nSince |Vtb| \u22431 and |Vcd| \u223c|Vus|, we just need to focus\non measurements of |Vcb|, |Vub| and |Vtd|.\n\u2013 |Vcb|:\nthis CKM matrix element is measured in\nsemileptonic b \u2192c transitions as described in Sec-\ntion 17.1. The present average over inclusive and\nexclusive decays yields |Vcb| = [41.67 (1\u00b10.009exp\u00b1\n0.012th)] \u00d7 10\u22123.\n\u2013 |Vub|: this is the CKM matrix element measured in\nsemileptonic b \u2192u transitions as described in Sec-\ntion 17.1. The present average over inclusive and\nexclusive decays yields |Vub| = [3.95 (1\u00b10.096exp \u00b1\n0.099th)] \u00d7 10\u22123.\n\u2013 |Vtd|: this CKM matrix element is extracted from\nthe oscillation frequency \u2206md in B0\ndB0\nd mixing\nas shown in Eq. (17.2.1). The de\ufb01nition of \u2206md\nfrom \ufb01rst principles is given in Section 10.1, while\nits experimental extraction is described in Sec-\ntion 17.5.2. To relate \u2206md to |Vtd|, we need to\n\n771\nknow several other quantities: the Inami-Lim func-\ntion S0(xt) (Buras and Fleischer, 1998; Inami and\nLim, 1981) with xt = m2\nt/M 2\nW , the top mass mt\ntaken in the MS scheme (mt, see below), the per-\nturbative QCD short-distance NLO correction \u03b7B,\nand the non-perturbative QCD parameters fBd and\nBBd. Table 25.1.3 lists the latest lattice QCD cal-\nculations for the latter two parameters (see Sec-\ntion 25.1.5), while mt is listed in Table 25.1.2.\nUnitarity Triangle angles:\n\u2013 \u03c61: this weak phase is de\ufb01ned in terms of CKM ma-\ntrix elements in Eq. (16.5.3). The most precise mea-\nsurements of this quantity are obtained via time-\ndependent CP analyses of b \u2192ccs processes. The\nanalyses contributing to \u03c61 measurements are de-\nscribed in detail in Section 17.6 and yield sin 2\u03c61 =\n0.677 \u00b1 0.020. The ambiguities from the sin 2\u03c61\nmeasurements are resolved via measurements of \ufb01-\nnal states that have an asymmetry dependence on\ncos 2\u03c61 (see Section 17.6.8).\n\u2013 \u03c62: this weak phase is de\ufb01ned in terms of CKM\nmatrix elements in Eq. (16.5.4) and is measured\nin b \u2192uud processes. The analyses contributing\nto \u03c62 measurement are described in detail in Sec-\ntion 17.7. Averaging results from charmless two-\nbody B decays into \u03c0\u03c0, \u03c1\u03c1, and \u03c1\u03c0 \ufb01nal states\nyields \u03c62 = (88 \u00b1 5)\u25e6.\n\u2013 \u03c63: this weak phase is de\ufb01ned in terms of CKM\nmatrix elements in Eq. (16.5.5) and is extracted in\nB \u2192D(\u2217)K and B \u2192DK\u2217decays using various\nmethods. The individual analyses are described in\ndetail in Section 17.8. The present average from the\nB Factories is \u03c63 = (67 \u00b1 11)\u25e6.\nLeptonic decays:\n\u2013 B(B \u2192\u03c4\u03bd\u03c4): this branching fraction is linked to\nthe CKM matrix elements |Vub| and the B decay\nconstant fBd via Eq. (17.10.4). Including the recent\nBelle results as discussed in Section 17.10.2.2, the\npresent world average is (1.15 \u00b1 0.23) \u00d7 10\u22124.\n25.1.4.3 Other measurement inputs\nA number of other experimental inputs are required in or-\nder to perform global \ufb01ts. The values of these experimen-\ntal inputs can be found in the review of particle physics\ncompiled by the PDG (Beringer et al., 2012). The most\nrelevant of these other observables are \u03b5K, \u2206ms and the\nquark masses. They are described in the following:\n\u2013 \u03b5K: this parameter represents indirect CP violation in\nthe mixing in the K0K0 system. De\ufb01ning the ratios of\ndecay amplitudes of KS and KL into two pions as\n\u03b700 \u2261A(KL \u2192\u03c00\u03c00)\nA(KS \u2192\u03c00\u03c00),\n\u03b7+\u2212\u2261A(KL \u2192\u03c0+\u03c0\u2212)\nA(KS \u2192\u03c0+\u03c0\u2212),\n(25.1.14)\nindirect (in the mixing) and direct (in the amplitudes)\nCP violation can be parameterized by\n\u03b5K = \u03b700 + 2\u03b7+\u2212\n3\n,\n\u03b5\u2032\nK = \u2212\u03b700 + \u03b7+\u2212\n3\n,\n(25.1.15)\nrespectively.\nUsing the e\ufb00ective \u2206S = 2 Hamiltonian, \u03b5K is related\nto CKM parameters by\n|\u03b5K| = G2\nF m2\nW mKf 2\nK\n12\n\u221a\n2\u03c02\u2206mK\nbBK\n\u0000\u03b7ccS(xc, xc)Im[(VcsV \u2217\ncd)2]\n+\u03b7ttS(xt, xt)Im[(VtsV \u2217\ntd)2]\n+2\u03b7tcS(xc, xt)Im[VcsV \u2217\ncdVtsV \u2217\ntd]\n\u0001\n,\n(25.1.16)\nwhere \u2206mK is the K0K0 oscillation frequency, fK is\nthe kaon decay constant, mK is the kaon mass, bBK pa-\nrameterizes the value of the hadronic matrix element\n(bag parameter), S(xq, xq\u2032) are Inami-Lim functions\nfor top quark and charm quark contributions that in-\ntroduce QCD correction factors \u03b7tt, \u03b7tc and \u03b7cc and all\nother parameters are the same as those in Eq. (17.2.1).\nAs for \u2206md, the quantity xq = mq(mq)2/m2\nW where\nq = c, t and the quark masses are determined in the\nMS scheme discussed below.\nWhile \u03b5\u2032\nK su\ufb00ers from theory uncertainties that are too\nlarge to provide a useful constraint in the (\u03c1, \u03b7) plane,\n\u03b5K provides a hyperbolic dependence between \u03c1 and\n\u03b7. This can be shown by rearranging the Wolfenstein\nparameters in Eq. (25.1.16):\n|\u03b5K| \u221d\u03b7\n\u0002\u00001 \u2212\u03c1\n\u0001\n+ P(A, \u03bb)\n\u0003\n(25.1.17)\nwhere P is a function of A and \u03bb and it does not depend\non \u03b7 or \u03c1. A \ufb01t to K \u2192\u03c0\u03c0 data yields (Beringer et al.,\n2012)\n|\u03b5K| = (2.228 \u00b1 0.011) \u00d7 10\u22123.\n(25.1.18)\n\u2013 \u2206ms: this parameter is the oscillation frequency mea-\nsured in B0\nsB0\ns mixing and it provides a determination\nof the CKM matrix element |Vts|. It is calculated in\na similar way to \u2206md, using the \u2206B = 2 e\ufb00ective\nHamiltonian, yielding\n\u2206ms = G2\nF\n6\u03c02 \u03b7BM 2\nW mBsf 2\nBs bBBsS0(xt)|VtsV \u2217\ntb|2,\n(25.1.19)\nwhere mBs is the B0\ns mass, fBs is the Bs-decay con-\nstant, bBBs is the bag parameter and all other pa-\nrameters are the same as those for \u2206md listed in\nEq. (17.2.1). The numerical values of the theoretical\ninput parameters are summarized in Table 25.1.3. The\nratio \u2206ms/\u2206md provides a more accurate measure-\nment of the Unitarity Triangle side Rt than \u2206md since\nthe ratios of QCD parameters have smaller theory un-\ncertainties than fBs and BBs themselves. The CDF\nexperiment was the \ufb01rst to measure \u2206ms, obtaining a\nvalue (Abulencia et al., 2006b) of:\n17.77 \u00b1 0.10 \u00b1 0.07 ps\u22121.\n(25.1.20)\nThis result has been subsequently con\ufb01rmed by LHCb\nthat obtains now an improved precision (Aaij et al.,\n2013d). Combining these results yields the present\nworld average of \u2206ms = 17.719 \u00b1 0.043 shown in Ta-\nble 25.1.2.\n\n772\nTable 25.1.1. Input values for the global \ufb01t from B Factory measurements.\nInput\nValue\nReference\nsin 2\u03c61\n0.677 \u00b1 0.020\nSection 17.6.\n\u03c62 [\u25e6]\n88 \u00b1 5\nSection 17.7\n\u03c63 [\u25e6]\n67 \u00b1 11\nSection 17.8\n\u2206md [ps\u22121]\n0.508 \u00b1 0.003 \u00b1 0.003\nSection 17.5.2\n|Vcb| [10\u22123]\n41.67 (1 \u00b1 0.009 \u00b1 0.012)\nSection 17.1.6.1\n|Vub| [10\u22123]\n3.95 (1 \u00b1 0.096 \u00b1 0.099)\nSection 17.1.6.2\nB(B \u2192\u03c4\u03bd\u03c4)\n(1.15 \u00b1 0.23) \u00d7 10\u22124\nSection 17.10.2.2\n\u2013 top mass: the mass of the top quark mt has been mea-\nsured by the Tevatron and the LHC experiments with\na combined precision of about 0.6%, and its current av-\nerage value is mt = (173.18 \u00b1 0.94) GeV/c2 (Aaltonen\net al., 2012a). Whatever the analysis method adopted,\nthe quantity measured in data corresponds to the top\nquark mass scheme assumed in the Monte Carlo sim-\nulation used. As a consequence, there is no immediate\nconnection between this measured value and any other\nmass scheme, such as the pole or MS mass scheme.\nIn QED the position of the pole in the propagator is\nthe de\ufb01nition of the particle mass, while in QCD the\nquark propagator has no pole because the quarks are\ncon\ufb01ned. So the problem of the de\ufb01nition of the quark\nmass can be addressed from two perspectives: the long-\ndistance behavior which corresponds to the pole-mass\nscheme, and the short-distance behavior, which, for ex-\nample, can be represented by the MS mass scheme.\nThe relation between the pole mass and any other mass\nscheme mt(R, \u00b5) is expressed as a perturbative series\nin \u03b1S(mt) and it can be written as mpole\nt\n= mt(R, \u00b5)+\n\u03b4mt(R, \u00b5) (Hoang and Stewart, 2008) where\n\u03b4mt(R, \u00b5) = R\n\u221e\nX\nn=1\nn\nX\nk=0\nank\n\u0014\u03b1S(\u00b5)\n4\u03c0\n\u0015n\nlnk \u0010 \u00b5\nR\n\u0011\n(25.1.21)\nwith R being a dimension-one scale intrinsic to the\nscheme, ank \ufb01nite numerical coe\ufb03cients and \u00b5 is the\nrenormalization scale. An example of this conversion\ncan be found in Beringer et al. (2012).\nThe experimentally measured mt is considered to be\nclose to the pole mass and in some analyses it is as-\nsumed that mt measured is indeed equal to mpole\nt\n(see\nfor example ALEPH, CDF, D0, DELPHI, L3, OPAL,\nSLD and the LEP, Tevatron and SLD Electroweak and\nHeavy Flavour Working Groups, 2010). Conversely,\nthe input value mt used for the global \ufb01ts is the top\nrunning mass calculated in the MS renormalization\nscheme and its value is obtained by pole-to-MS match-\ning. At the 3-loop level with \ufb01ve quark \ufb02avors the re-\nlation is (Broadhurst, Gray, and Schilcher, 1991; Gray,\nBroadhurst, and Schilcher, 1990; Melnikov and van\nRitbergen, 2000)\nmt(mt) = mt\n \n1 \u22124\n3\n\u0012\u03b1S(mt)\n\u03c0\n\u0013\n\u22129.12530\n\u0012\u03b1S(mt)\n\u03c0\n\u00132\n\u221280.4045\n\u0012\u03b1S(mt)\n\u03c0\n\u00133 !\n,\n(25.1.22)\nwhere \u03b1S(mt) = 0.1068 \u00b1 0.0018. This yields an MS\nmass of mt(mt) = 163.3 \u00b1 0.9 GeV/c2. One can com-\npare this result with the top mass obtained using the\nmeasured cross section, which has a similar central\nvalue, but slightly larger uncertainty mt(mt) = 163.3\u00b1\n2.7 GeV/c2, for example see (Moch, 2012).\n\u2013 mb(mb), mc(mc), ms(ms): these are the running quark\nmasses evaluated in the MS scheme and at the scale\nindicated. The values used are given in Table 25.1.2.\n25.1.5 Theoretical inputs: derivation of hadronic\nobservables\nMost of the experimental inputs described above for the\nglobal \ufb01t rely upon knowledge of hadronic matrix ele-\nments that parameterize the non-perturbative QCD con-\ntributions to weak decays and mixing. These contributions\nrepresent the connection between the quark-level funda-\nmental quantities and the hadronic-level experimental ob-\nservables.\nThese hadronic matrix elements are obtained from nu-\nmerical lattice QCD calculations. State-of-the-art lattice\ncomputations now regularly include the e\ufb00ects of the sea\nup, down and strange quarks. They also typically use sim-\nulations at pion masses below 300 MeV/c2, or even below\n200 MeV/c2, in order to control the extrapolation to the\nphysical pion mass. For many hadronic matrix elements\nof interest, there are now at least two or more reliable\nlattice calculation results. In order to use the lattice in-\nputs in a global \ufb01t, it is necessary to average di\ufb00erent\nresults. However as there are potentially signi\ufb01cant corre-\nlations between various lattice uncertainties, averaging is\nnot straightforward, and correlations must be taken into\naccount. Statistical and systematic errors may be corre-\nlated, and one needs to be su\ufb03ciently familiar with the lat-\ntice computational methods used in order to understand\nhow to treat a given result in the averaging procedure.\nA complete review of lattice techniques is beyond the\nscope of this book. We therefore rely on the averaging\nwork of Laiho, Lunghi, and Van de Water (2010). They\naverage the latest LQCD results for leptonic decay con-\nstants, meson mixing parameters, and semileptonic form\n\n773\nTable 25.1.2. Input values for the global \ufb01t from other experimental measurements (non-B Factory). The quark masses are\nthe running MS quark masses as explained in the text.\nInput\nValue\nReference\n\u03b1S(mZ)\n0.1184 \u00b1 0.0007\n(Beringer et al., 2012)\nmt [ GeV/c2 ]\n163.3 \u00b1 0.9\nDetermined for this book\nmb [ GeV/c2 ]\n4.18 \u00b1 0.03\n(Beringer et al., 2012)\nmc [ GeV/c2 ]\n1.275 \u00b1 0.025\n(Beringer et al., 2012)\nms [ GeV/c2 ]\n0.0935 \u00b1 0.0025\n(Beringer et al., 2012)\n\u03c4Bd [ps]\n1.519 \u00b1 0.007\n(Amhis et al., 2012)\n\u03c4B+ [ps]\n1.642 \u00b1 0.008\n(Amhis et al., 2012)\n\u03c4Bs [ps]\n1.503 \u00b1 0.010\n(Amhis et al., 2012)\n\u03b5K\n0.002228 \u00b1 0.000011\n(Beringer et al., 2012)\n\u2206ms\n17.719 \u00b1 0.043\n(Amhis et al., 2012)\nfactors. Only results from simulations with three dynam-\nical quark \ufb02avors are included in the averages if there are\nassociated proceedings or publications that include com-\nprehensive error budgets. When computing averages, they\nassume that all errors are normally distributed and follow\nthe prescription outlined by Schmelling (1995) to take the\ncorrelations into account. Moreover, they assume that any\ncorrelated source of error for two lattice calculations is\n100% correlated. This assumption is conservative and will\nlead to an overestimate of the total error of the lattice av-\nerages; nevertheless, it is the most systematic treatment\npossible without knowledge of the correlation matrices,\nwhich do not exist, between the various calculations. Fi-\nnally, they adopt the PDG prescription to combine several\nmeasurements whose spread is wider than that expected\nfrom the quoted errors: the error on the average is multi-\nplied by the square root of the \u03c72 per degree of freedom.\nThe global \ufb01ts use four inputs that depend on these\nhadronic observables: \u03b5K, \u2206md, \u2206ms, and B(B \u2192\u03c4\u03bd\u03c4).\nThese are related to two decay constants (fBd, fBs) and\nthree hadronic matrix elements (BK, BBd, BBs). The\npreferred choice of minimally correlated inputs is BK,\nfBs/fBd, BBs/BBd, BBs and fBs. In general the quanti-\nties related to B0\nsB0\ns mixing are preferred as current lattice\nQCD calculations can simulate directly at the physical s-\nquark mass, but must extrapolate to the u- and d-quark\nmasses. Therefore the chiral extrapolation error, which is\noften the dominant systematic, is smaller for BBs and fBs\nthan for the lighter B meson parameters. The ratios are\nchosen in order to bene\ufb01t from cancellations of uncertain-\nties done on the lattice. A basic description of the hadronic\nquantities that must be included in the global \ufb01ts follows:\n\u2013 BK is related to the parameter \u03b5K as de\ufb01ned in Sec-\ntion 25.1.4.3. When strong interactions are considered,\n\u2206S = 2 transitions can no longer be discussed at the\nquark level. Instead, an e\ufb00ective Hamiltonian must be\nconsidered between mesonic initial and \ufb01nal states.\nSince the strong coupling constant is large at typical\nhadronic scales, the resulting matrix element cannot be\ncalculated in perturbation theory. However the OPE\ndoes factorize long- and short-distance e\ufb00ects.\nThe dependence on the renormalization scheme and\nscale \u00b5 is canceled by that of the hadronic matrix el-\nement \u27e8K0|Q\u2206S=2\nR\n(\u00b5)|K0\u27e9. The latter corresponds to\nthe long-distance e\ufb00ects of the e\ufb00ective Hamiltonian\nand must be computed non-perturbatively. For histor-\nical, as well as technical reasons, it is convenient to\nexpress it in terms of the parameter BK, de\ufb01ned as:\nBK(\u00b5) = \u27e8K0|Q\u2206S=2\nR\n(\u00b5)|K0\u27e9\n8\n3m2\nKf 2\nK\n.\n(25.1.23)\nThe four-quark operator Q\u2206S=2(\u00b5) is renormalized at\nthe scale \u00b5 in some regularization scheme, usually taken\nto be the na\u00a8\u0131ve dimensional regularization. The renor-\nmalization group independent parameter bBK is related\nto BK(\u00b5) by a function of the renormalized gauge cou-\npling (g(\u00b5)) and perturbative coe\ufb03cients (\u03b20, \u03b21, \u03b30,\nand \u03b31):\nbBK =\n\u0012g(\u00b5)2\n4\u03c0\n\u0013\u2212\u03b30\n2\u03b20 \u0014\n1+ g(\u00b5)2\n(4\u03c0)2\n\u0012\u03b21\u03b30\u2212\u03b20\u03b31\n2\u03b20\n\u0013\u0015\nBK(\u00b5).\n(25.1.24)\nA more detailed discussion can be found in (Colangelo\net al., 2011) and references therein.\n\u2013 for Bs, the parameter of the renormalized operator is\nde\ufb01ned as\nBBs(\u00b5) = \u27e8Bs|Q\u2206B=2\nd\n(\u00b5)|Bs\u27e9\n8\n3m2\nBsf 2\nBs\n,\n(25.1.25)\nwhere Q\u2206B=2\ns\n= (b\u03b3\u00b5(1 \u2212\u03b35)s)(b\u03b3\u00b5(1 \u2212\u03b35)s) and \u00b5 is\nthe renormalization scale. This de\ufb01nition stems from\nthe vacuum saturation approximation in which BBs =\n1. One can de\ufb01ne BBd in a similar way.\nThe renormalization group invariant parameter bBBs of\nEq. (25.1.19) is de\ufb01ned as\nbBBs = \u03b1S(\u00b5)\u2212\u03b30\n2\u03b20\n\u0012\n1 + \u03b1S(\u00b5)\n4\u03c0\nJ\n\u0013\nBBs(\u00b5).\n(25.1.26)\nIn all schemes \u03b30 = 4, whereas J depends on the\nscheme used for renormalizing Q\u2206B=2\ns\n(\u00b5). In the theo-\nretical expressions, the physical amplitudes are always\n\n774\nde\ufb01ned in terms of bBBs. The advantage is that this\nquantity is both renormalization scale and scheme in-\ndependent.\nHowever, the important quantities are not the B pa-\nrameters themselves but the combinations f 2\nxBx (where x\ncan be K or Bd,s) which are simply related to the physical\namplitudes by the factors 8m2\nx/3. In the case of the kaon\nsystem, the decay constant is derived from experiments\nas one measures the product |Vus|fK, while for the Bd,s\nmesons, we rely on lattice QCD determinations.\nThe hadronic parameters from lattice QCD discussed\nabove and used as inputs for the global \ufb01ts can be found\nin Table 25.1.3.\n25.1.6 Results from the global \ufb01ts\nHere we report the results for the global \ufb01ts from the\ntwo main collaborations described in Section 25.1.3. Us-\ning all the inputs described in the previous sections and\nthe statistical techniques speci\ufb01c to the two \ufb01tting groups,\nit is possible to extract the CKM matrix parameters from\nglobal \ufb01ts to the set of relevant measurements. Particular\nattention is paid to the least precisely determined param-\neters \u03c1 and \u03b7, especially in light of their importance with\nregard to CP violation in the SM.\nTable 25.1.4 shows the numerical results obtained from\nthe two global \ufb01ts performed using the inputs given in Ta-\nbles 25.1.1, 25.1.2 and 25.1.3. Fig. 25.1.1 shows the (\u03c1, \u03b7)\nplane illustrating the constraints used along with the re-\nsults from the two global \ufb01ts. These results are consistent,\nindicating that there is su\ufb03cient experimental data to\ndraw meaningful conclusions regarding the CKM matrix\npicture using either frequentist or Bayesian approaches.\nThe combination of all the constraints gives a single pre-\nferred area, illustrating the exceptional agreement of mea-\nsurements with SM predictions.\nTable 25.1.4. Results from the global \ufb01ts.\nParameter\nOutput Value\nCKM\ufb01tter\nUT\ufb01t\n\u03c1\n0.129+0.027\n\u22120.022\n0.130 \u00b1 0.020\n\u03b7\n0.345 \u00b1 0.014\n0.348 \u00b1 0.013\nsin 2\u03c61\n0.684 \u00b1 0.019\n0.689 \u00b1 0.018\n\u03c62 [\u25e6]\n88.8+4.2\n\u22123.6\n88.4 \u00b1 2.8\n\u03c63 [\u25e6]\n68.9+3.5\n\u22124.2\n69.5 \u00b1 3.0\nThe compatibility of the constraints used can be eval-\nuated in each of the two \ufb01t methods by excluding a single\ngiven constraint at a time and evaluating the value for\nthat observable from the global \ufb01t performed using all\nthe other constraints. The comparison between this in-\nferred (or predicted) value and the value of the excluded\nconstraint can be used to test the agreement of each indi-\nvidual constraint with respect to all the others, assuming\nthat the SM is an adequate description of the underlying\nphysics. These predictions are shown in Table 25.1.5.\nA few small tensions are currently present in the global\n\ufb01ts. None of these are statistically signi\ufb01cant, however\nthey should be kept in mind in light of future updates. The\nvalue of sin 2\u03c61 is now obtained with such a small uncer-\ntainty that it is driving the other predictions, thus high-\nlighting some inconsistencies. For example, \u03b5K is showing\nsome tension through the less precise determination of the\nbBK parameter. Moreover, the two determinations of |Vub|\nand |Vcb| still present marginal agreement between the in-\nclusive and exclusive values and in particular the inclusive\nvalues show more signi\ufb01cant discrepancies in the context\nof the global \ufb01t. Future improvements in lattice QCD de-\nterminations will be extremely interesting to assess these\ne\ufb00ects.\nHistorically there has been tension between the B \u2192\n\u03c4\u03bd branching fraction and other constraints on the CKM\nmatrix. For a number of years this tension was interpreted\nby the community as being a possible hint for new physics.\nAt the time of writing, the experimental situation is com-\npatible with the SM, and there is no signi\ufb01cant tension\nevident between the constraints. The results shown in Ta-\nble 25.1.4 include the branching fraction of B \u2192\u03c4\u03bd as an\ninput, however very similar results are obtained when this\ninput is removed from the global \ufb01t. See Section 17.10 for\nmore details regarding the experimental determination of\nthe branching fraction of B \u2192\u03c4\u03bd, and the subsequent\ninterpretation of this observable.\nAs stated at the start of this chapter, it is also pos-\nsible to illustrate the success of the SM in describing the\nmeasurements of the B Factories by comparing the values\nobtained for \u03c1 and \u03b7 for CP-conserving and CP-violating\nquantities. These constraints are shown in Figs 25.1.2 and\n25.1.3. The agreement between these determinations of\nthe apex of the Unitarity Triangle is good, and is taken\nas evidence that the CKM matrix and KM mechanism\ngive the leading order description of quark mixing and\nCP violation in the SM. The dominant CP-violating con-\nstraints come from charmonium decay measurements of\n\u03c61 = \u03b2 (Section 17.6) and charmless B decay measure-\nments of \u03c62 = \u03b1 (Section 17.7). Such a coherent picture is\nof course possible only after more than a decade of precise\nmeasurement by experimentalists and the corresponding\nimprovement in theoretical control and understanding.\n25.1.7 Conclusions\nData from the B Factories have enabled the KM mech-\nanism to be tested in a comprehensive way using direct\nmeasurements of CP-violating observables. The constraints\nfrom CP-violating observables alone is su\ufb03cient to verify\nthat the KM mechanism is the dominant source of CP vi-\nolation in the SM. The level of CP violation measured via\nUnitarity Triangle angles in B decays is consistent with\nthat obtained from other tests of the CKM matrix (sides:\nVub, Vcb, mixing parameters, and \u03b5K). The set of non-\nangle constraints related to the Unitarity Triangle in the\n\n775\nTable 25.1.3. Input values for the global \ufb01t from Lattice QCD.\nInput\nValue\nReference\n|Vud|\n0.97425 \u00b1 0.00022\n(Colangelo et al., 2011)\n|Vus|\n0.2208 \u00b1 0.0039\n(Colangelo et al., 2011)\nfBs [ MeV ]\n227.6 \u00b1 2.2 \u00b1 4.5\n(Laiho, Lunghi, and Van de Water, 2010)\nfBs/fBd\n1.201 \u00b1 0.012 \u00b1 0.012\n(Laiho, Lunghi, and Van de Water, 2010)\nbBBs\n1.33 \u00b1 0.06\n(Laiho, Lunghi, and Van de Water, 2010)\nBBs/BBd\n1.05 \u00b1 0.07\n(Laiho, Lunghi, and Van de Water, 2010)\nbBK\n0.7643 \u00b1 0.0034 \u00b1 0.0091\n(Laiho, Lunghi, and Van de Water, 2010)\n3\nq\n3\nq\n2\nq\n2\nq\nd\nm\n6\nK\n\u00a1\ns\nm\n6\n & \nd\nm\n6\nub\nV\n1\nq\nsin 2\n(e\ns\nexcluded at CL > 0.95\n2\nq\n1\nq\n3\nq\nl\n-1.0\n-0.5\n0.0\n0.5\n1.0\nd\n-1.0\n-0.5\n0.0\n0.5\n1.0\n 95% C.L. areas\nPBF\nCKM\nf i t t e r\n\u03c1\n-1\n-0.5\n0\n0.5\n1\n\u03b7\n-1\n-0.5\n0\n0.5\n1\n\u03b3\n\u03b2\n\u03b1\ns\nm\n\u2206\nd\nm\n\u2206\nd\nm\n\u2206\nK\n\u03b5\ncb\nV\nub\nV\n)\n\u03bd\n\u03c4\n\u2192\nBR(B\nPBF\nSM fit\n95% Prob.\nAreas\nFigure 25.1.1. Results of global \ufb01ts in the (\u03c1, \u03b7) plane, from CKM\ufb01tter and UT\ufb01t, showing the consistency of b \u2192d, b \u2192s\nand s \u2192d \ufb02avor-changing transitions with the Kobayashi-Maskawa mechanism for the common origin of the observed CP\nviolation. The inputs of Tables 25.1.1 through 25.1.3 are used to obtain these plots. The second solution for the value of \u03c61 is\nsuppressed using the measurements of \ufb01nal states that have an asymmetry dependence on cos 2\u03c61. The corresponding numerical\nresults from these \ufb01ts can be found in Table 25.1.4.\nTable 25.1.5. Compatibility of the individual inputs with their prediction from the global \ufb01t.\nInput\nInput value\nPredicted value\nUT\ufb01t [#\u03c3]\nsin 2\u03c61\n0.677 \u00b1 0.020\n0.756 \u00b1 0.041 [1.7\u03c3]\n\u03c62 [\u25e6]\n88 \u00b1 5\n88.7 \u00b1 3.3 [0.1\u03c3]\n\u03c63 [\u25e6]\n67 \u00b1 11\n69.7 \u00b1 3.1 [0.2\u03c3]\n\u2206ms [ ps\u22121]\n17.719 \u00b1 0.043\n17.35 \u00b1 1.05 [0.7\u03c3]\n|Vcb| [10\u22123]\n41.67 \u00b1 0.63\n42.45 \u00b1 0.65 [0.8\u03c3]\n|Vub| [10\u22123]\n3.95 \u00b1 0.54\n3.61 \u00b1 0.11 [0.6\u03c3]\nbBK\n0.7643 \u00b1 0.0034 \u00b1 0.0091\n0.810 \u00b1 0.061 [0.3\u03c3]\nB(B \u2192\u03c4\u03bd\u03c4) 10\u22124\n(1.15 \u00b1 0.23)\n0.818 \u00b1 0.062 [1.4\u03c3]\nSM provides a complementary test of the CKM mecha-\nnism, however those constraints require theoretical input\nin order to translate measurements into a constraint on\nthe apex of the Unitarity Triangle. Hence the B factories\nprovided an experimentally and theoretically clean set of\ntests of the Standard Model in the measurements of the\nangles of the Unitarity Triangle. M. Kobayashi and T.\nMaskawa shared the 2008 Nobel Prize for their model of\nCP violation that inspired several generations of experi-\nmental exploration. During the lifetime of the B Factories\n\n776\nd\nm\n\u2206\ns\nm\n\u2206\n & \nd\nm\n\u2206\nub\nV\n2\n\u03c6\n1\n\u03c6\n3\n\u03c6\n\u03c1\n-0.4\n-0.2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b7\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nexcluded area has CL > 0.95\nPBF\nCKM\nf i t t e r\n3\n\u03c6\n2\n\u03c6\n2\n\u03c6\nK\n\u03b5\nK\n\u03b5\n1\n\u03c6\nsin 2\n2\n\u03c6\n1\n\u03c6\n3\n\u03c6\n\u03c1\n-0.4\n-0.2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n\u03b7\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nexcluded area has CL > 0.95\nPBF\nCKM\nf i t t e r\nFigure 25.1.2. The consistency between the \ufb01t to CP-conserving observables (left) and CP-violating observables (right) from\nthe CKM\ufb01tter group. The CP-conserving observables are the B0\u2212B0 and B0\ns \u2212B0\ns mass di\ufb00erences, \u2206md and \u2206ms, respectively,\nand the measurement of |Vub| from semileptonic b \u2192dl\u03bdl decays. The CP-violating observables are from K (\u03b5K) and B (\u03c61,\n\u03c62, \u03c63) decays.\n\u03c1\n-1\n-0.5\n0\n0.5\n1\n\u03b7\n-1\n-0.5\n0\n0.5\n1\ns\nm\n\u2206\nd\nm\n\u2206\nd\nm\n\u2206\nK\n\u03b5\ncb\nV\nub\nV\nPBF\nSM fit\n95% Prob.\nAreas\n\u03c1\n-1\n-0.5\n0\n0.5\n1\n\u03b7\n-1\n-0.5\n0\n0.5\n1\n\u03b3\n\u03b2\n\u03b1\nPBF\nSM fit\n95% Prob.\nAreas\nFigure 25.1.3. The consistency between the \ufb01t to CP-conserving observables and from K measurements (on the left) and the\nangles (B Factory-dominated on the right) from the UT\ufb01t group. The constraints used in the left plot are the B0 \u2212B0 and\nB0\ns \u2212B0\ns mass di\ufb00erences, \u2206md and \u2206ms, respectively, the measurements of |Vub| and |Vcb| from semileptonic B decays, and\nthe CP-violation parameter \u03b5K. The constraints used in the right plot are the \u201cangles\u201d observables, i.e. measurements of \u03c61\n(= \u03b2), \u03c62 (= \u03b1), and \u03c63 (= \u03b3).\na number of constraints have been found to be in not-so-\ngood agreement, and such tensions in the data have led\nto speculation of possible new physics scenarios, however\nthe Standard Model persists.\nThe Tevatron and LHC experiments (CDF, D\u00d8, AT-\nLAS, CMS, and LHCb) have also produced results that\ncan be used to test the CP-violating \ufb02avor parameters\nrelated to the Standard Model description of B meson\ndecays. While a detailed discussion is beyond the scope\nof this book, it should be noted that measurements from\nthese experiments are compatible with results from the B\nFactories. At the time of writing this book, there is no\nsigni\ufb01cant evidence for a departure from the KM picture\nof CP violation and the CKM matrix description of quark\nmixing.\nIt should be noted that it is still possible for sources\nof new physics to exist. Indeed given our understanding\nof the cosmological model of the Big Bang, it is thought\nthat new sources of CP violation must exist. Any higher\norder contributions to CP violation in the quark sector\nthat might be manifest in a hypothetical new physics sce-\nnario are constrained by the results discussed in this sec-\ntion: i.e. CP violation in the quark sector beyond the SM\ncannot be O(1). In the absence of experimental indica-\ntions of a departure from the CKM picture the particle\nphysics community chooses to explore the space of possi-\nble new physics models. Given the variety of such models,\none has to focus on the predictions and behavior of spe-\nci\ufb01c benchmark models, a number of which are discussed\nin Section 25.2.\n\n777\n25.2 Benchmark new physics models\nEditors:\nEmi Kou, Jure Zupan (theory)\nIn this section we review the impact of the B Factories\non our understanding of the \ufb02avor structure in the Stan-\ndard Model (SM) and on constraining new physics (NP)\nmodels. The most important overall result of the B Fac-\ntories physics program is the fact that the CP violation\nobserved in \ufb02avor changing processes with quarks is due\nto the Kobayashi-Maskawa (KM) mechanism (Kobayashi\nand Maskawa, 1973). For instance, prior to the B Fac-\ntories, the kaon sector was the only system where CP\nviolation was observed (see Section 16.1). The observed\nstrength of the CP violation in mixing, \u03f5K \u22432.3 \u00d7 10\u22123,\nwas consistent with the KM mechanism with an O(1) CP\nphase in the CKM matrix. While encouraging, this by no\nmeans constituted a proof that the KM mechanism was re-\nally the origin of the observed CP violation. The \ufb01rst test\nof the KM mechanism was then done by the measurement\nof sin 2\u03c61 by the B Factories.\nBy now the KM mechanism has been tested at the\nlevel of \u223cO(10%), while deviations from its predictions\nat levels smaller than this are still allowed. In the KM\nmechanism there is only one weak phase, providing a sin-\ngle source of CP violation. The consistency of \u03f5K with the\nobserved CP violation in B0\nd\u2212B0\nd mixing and the measure-\nments of the sides and angles of the standard CKM Uni-\ntarity Triangle all point to this common origin of CP vio-\nlation. In addition, the size of \u2206ms and the recent LHCb\nbound on the size of the weak phase in B0\ns \u2212B0\ns mixing\nboth agree with the KM mechanism within errors. This\nagreement between b \u2192d, b \u2192s and s \u2192d transitions is\nnicely summarized in the CKM \ufb01t plot (see Fig. 25.1.1).\nAnother important indicator that the CP violation we are\nobserving in \ufb02avor changing processes of quarks is due to\nthe KM mechanism, comes from a comparison of a \ufb01t with\nonly CP conserving observables with a \ufb01t with only CP\nviolating observables. Both \ufb01ts point to the same region\nin the \u00af\u03c1 and \u00af\u03b7 plane, which is a strong test of KM nature\nof CP violation (see Fig. 25.1.2).\nThe measurements at the B Factories also had a direct\nimpact on new physics models. For instance, a measure-\nment that sin 2\u03c61 is O(1) immediately excluded approxi-\nmate CP models. In these models all the couplings which\ngovern the low energy phenomena are real or almost real,\nwith imaginary components always much smaller than the\nreal ones. In the SM, the observed \u03f5K and \u03f5\u2032, represent-\ning the CP violation in the kaon sector, are small, which\ncan be explained by the smallness of the CKM matrix ele-\nments entering into the description of these observables. In\nthe approximate CP models it would be small because CP\nsymmetry is only slightly broken and thus all CP violat-\ning phases are small. A set of well motivated realizations\nin the SUSY framework was put forward (Abel and Frere,\n1997; Babu and Barr, 1994; Babu, Dutta, and Mohapa-\ntra, 2000; Eyal, Masiero, Nir, and Silvestrini, 1999; Eyal\nand Nir, 1998). For instance approximate CP conservation\ncould naturally solve the \u201cSUSY CP problem\u201d explaining\nwhy EDMs are so small. All these models were excluded\nonce sin 2\u03c61 was measured and its value turned out to be\nlarge, i.e. O(1).\nAnother set of models that was excluded by the fact\nthat sin 2\u03c61 was found to be bigger than 0.1, were the left-\nright symmetric models with spontaneous CP breaking\n(Ball and Fleischer, 2000; Ball, Frere, and Matias, 2000;\nBergmann and Perez, 2001). In these models Yukawa in-\nteractions are CP conserving, while the CP violation arises\nfrom the complex vacuum expectation values of the Higgs\n\ufb01elds. Because of this the value of the CKM phase \u03b4 can-\nnot take any value, but is found to be restricted to be\nbelow |\u03b4 mod \u03c0| < 0.25 (Ball, Frere, and Matias, 2000).\nThis was experimentally excluded as soon as sin 2\u03c61 was\nmeasured with some precision.\nAfter the measurement of sin 2\u03c61 it was still possible\nthat the observed large sin 2\u03c61 value was due to a new\nsuperweak-like four fermion interaction and that direct\nCP violation is small, just as it is small in kaon decays\n(Wolfenstein, 2002). This (somewhat arti\ufb01cial) possibility\nwas excluded by the discovery of direct CP violation in\nB \u2192K+\u03c0\u2212decays (Aubert, 2004u; Chao, 2005).\nThe constraints on general NP are best illustrated on\nthe case of mixing. The NP contributions to B0\nd,s \u2212B0\nd,s\nmixing can be completely generally parameterized by\nM d,s\n12 =\n\u0000M d,s\n12\n\u0001SM \u00001 + hd,s e2i\u03c3d,s\u0001\n,\n(25.2.1)\nwhere\n\u0000M d,s\n12\n\u0001SM are the matrix elements of the SM e\ufb00ec-\ntive weak Hamiltonian for B0\nd,s \u2212B0\nd,s mixing. The mag-\nnitudes of NP contributions relative to the SM are given\nby hd and hs for B0\nd \u2212B0\nd and B0\ns \u2212B0\ns mixing, respec-\ntively, while \u03c3d,s are the corresponding NP weak phases. If\nNP models do not lead to diagrams which can induce the\nB0\nd \u2212B0\nd and B0\ns \u2212B0\ns mixing, then we have hs = hd = 0.\nFig. 25.2.1 shows the present experimental constraints on\nthe parameters hd,s and \u03c3d,s. One sees that contributions\nat the level of \u223c10%\u221220% are allowed for any weak phase\n(if one includes B \u2192\u03c4\u03bd in the \ufb01t there is a slight pref-\nerence for a nonzero phase), but corrections larger than\n50% are also still possible.\nNote that the SM contributions to the meson mixing\nare both loop and CKM suppressed. The CKM suppres-\nsion for B0\nd \u2212B0\nd mixing is |V \u2217\ntdVtb|2 \u223cO(\u03bb6). The expan-\nsion parameter, \u03bb \u22430.23, in the Wolfenstein parameteri-\nzation of the CKM matrix equals the sine of the Cabibbo\nangle. Similarly, there is a CKM suppression of B0\ns \u2212B0\ns\nmixing of |V \u2217\ntsVtb|2 \u223cO(\u03bb4) and a CKM suppression of\nK0 \u2212K0 mixing proportional to |V \u2217\ntdVts|2 \u223cO(\u03bb10). This\nmeans that, if there is new physics at the TeV scale which\ncontributes to the mixing amplitudes at tree level or at the\nloop level, it has to have a very non-generic \ufb02avor struc-\nture. The upper bounds on the coupling strengths for a 1\nTeV suppression scale are given in Table 25.2.1. The same\ntable also shows the alternative interpretation of the data\n\u2013 giving the lower bounds on NP scale, if the coupling\nstrengths are assumed to be large, O(1).\n\n778\ns\nh\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\ns\n\u03c3\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\np-value\nexcluded area has CL > 0.95\nLP 11\nCKM\nf i t t e r\nd\nh\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nd\n\u03c3\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\n1-CL\nMoriond 09\nCKM\nf i t t e r\n\u03bd\n\u03c4 \n\u2192\nw/o B \nFigure 25.2.1. The present constraints on contributions from NP processes in B0\ns mixing (left) and B0\nd mixing (right), nor-\nmalized to the SM contributions. From (Ligeti, 2011).\nTable 25.2.1. Bounds on \u2206F = 2 operators of the form (C/\u039b2) O, with O given in the \ufb01rst column. The bounds on \u039b assume\nC = 1, and the bounds on C assume \u039b = 1 TeV. From (Hewett et al., 2012).\nOperator\nBounds on \u039b [TeV] (C = 1)\nBounds on C (\u039b = 1 TeV)\nObservables\nRe\nIm\nRe\nIm\n(\u00afsL\u03b3\u00b5dL)2\n9.8 \u00d7 102\n1.6 \u00d7 104\n9.0 \u00d7 10\u22127\n3.4 \u00d7 10\u22129\n\u2206mK; \u03f5K\n(\u00afsR dL)(\u00afsLdR)\n1.8 \u00d7 104\n3.2 \u00d7 105\n6.9 \u00d7 10\u22129\n2.6 \u00d7 10\u221211\n\u2206mK; \u03f5K\n(\u00afcL\u03b3\u00b5uL)2\n1.2 \u00d7 103\n2.9 \u00d7 103\n5.6 \u00d7 10\u22127\n1.0 \u00d7 10\u22127\n\u2206mD; |q/p|, \u03c6D\n(\u00afcR uL)(\u00afcLuR)\n6.2 \u00d7 103\n1.5 \u00d7 104\n5.7 \u00d7 10\u22128\n1.1 \u00d7 10\u22128\n\u2206mD; |q/p|, \u03c6D\n(\u00afbL\u03b3\u00b5dL)2\n5.1 \u00d7 102\n9.3 \u00d7 102\n3.3 \u00d7 10\u22126\n1.0 \u00d7 10\u22126\n\u2206md; S\u03c8K0\nS\n(\u00afbR dL)(\u00afbLdR)\n1.9 \u00d7 103\n3.6 \u00d7 103\n5.6 \u00d7 10\u22127\n1.7 \u00d7 10\u22127\n\u2206md; S\u03c8K0\nS\n(\u00afbL\u03b3\u00b5sL)2\n1.1 \u00d7 102\n2.2 \u00d7 102\n7.6 \u00d7 10\u22125\n1.7 \u00d7 10\u22125\n\u2206ms; S\u03c8\u03c6\n(\u00afbR sL)(\u00afbLsR)\n3.7 \u00d7 102\n7.4 \u00d7 102\n1.3 \u00d7 10\u22125\n3.0 \u00d7 10\u22126\n\u2206ms; S\u03c8\u03c6\n25.2.1 Short description of NP models\nWe \ufb01rst quickly describe the NP models we will consider.\nThese are the models which could induce a signi\ufb01cant\ndeviation from the SM in the various observables mea-\nsured at the B Factories and thus, have been considered\nas benchmark NP models. The expected deviations in B\nmeson observables and the results from the B Factories\nare described in the next section, where one can also \ufb01nd\ndetailed references for further reading.\nFourth generation\nSince the origin of the three generations in the SM is un-\nclear, it is natural to consider a possibility that additional\ngenerations exist. An extension of the SM by a 4th gen-\neration means that in addition to the particles in the SM\nthere is an extra pair of heavy quarks, the t\u2032 (up-type) and\nb\u2032 (down-type), as well as a new heavy charged lepton and\nan additional heavy neutrino. We focus on the e\ufb00ects due\nto additional heavy quarks. The CKM matrix described in\nChapter 16 is now a 4\u00d74 unitary matrix. With three gen-\nerations there are four physical parameters in the CKM\nmatrix: three rotation angles and a single complex phase,\nwhere the phase is responsible for CP violation. In a four\ngeneration model there are 3 extra rotation angles and\n2 new CP violating phases compared to the SM.183 In\nthis model, the CKM elements obey quadrilateral and not\ntriangle unitarity relations as in the SM. The new CP vi-\nolating phases can lead to additional CP violation beyond\nthe SM predictions (e.g. in the penguin b \u2192s transitions).\nThe violation of Unitarity Triangle relations is checked by\nglobal CKM \ufb01ts (see Section 25.1, the \ufb01ts were also ex-\ntended to include the 4th generation).\n183 An n\u00d7n unitary matrix contains 2n2 \u2212(n+(n2 \u2212n)) = n2\nreal parameters while we can absorb 2n \u22121 phases in the de\ufb01-\nnition of the quark \ufb01elds, which results in (n \u22121)2 real param-\neters. Here we assign the n(n \u22121)/2 parameters as rotation\nangles and the rest as phases.\n\n779\nTwo Higgs Doublet Models\nIn the SM, the so-called Higgs \ufb01eld, an SU(2) doublet\nscalar \ufb01eld, is introduced. The electroweak symmetry is\nbroken spontaneously by its non-zero vacuum expectation\nvalue, which leads to the particle masses. This feature is\nretained also, if there is more than one Higgs doublet. The\nTwo Higgs Doublet Model (2HDM) is the simplest ex-\ntension of this kind, introducing one more Higgs doublet.\nIn the particle spectrum we then have three neutral and\none charged scalar. For B physics the form of the Yukawa\ncouplings is especially important. Several interesting lim-\nits are discussed in the literature. Here we mostly focus\non the so-called Type II 2HDM where each of the two\nHiggs doublets only couple to down or up quarks. In this\nway phenomenologically unacceptable FCNCs due to tree\nlevel neutral Higgs exchanges do not arise. As a result,\nthe main e\ufb00ects in \ufb02avor physics are due to the charged\nHiggs contributions. Even though the LHC searches for\nthe charged Higgs directly, the constraints on the proper-\nties of this new particle, its mass and its couplings, come\nmainly indirectly from B decays. Note that Type II 2HDM\nalso describes the Higgs sector of the Minimal Supersym-\nmetric Standard Model at tree level.\nMinimal Flavor Violation\nMinimal Flavor Violation (MFV) is a general hypothesis\nthat can apply to a large class of NP models. The central\nassumption is that the only source of \ufb02avor violation \u2013 also\nin the NP sector \u2013 are the SM Yukawa coupling matrices,\nYU,D. This is the minimal amount of \ufb02avor breaking in\nany NP model. The \ufb02avor breaking due to YU,D will at\nleast through loop corrections then also propagate to other\nsectors of the NP theory.\nFor MFV NP, generically the FCNCs are of the same\norder as in the SM (but can be smaller, if NP particles\ninvolved in the FCNC process are heavy). In MFV the\nform of \ufb02avor violation is \ufb01xed, implying strict correlations\nbetween di\ufb00erent processes. This is especially true for the\nconstrained MFV (cMFV) where CP violation is only due\nto the CKM phase and the e\ufb00ective weak Hamiltonian\nhas exactly the same form as in the SM. For instance, in\nthe cMFV the NP contributions to B0\nd \u2212B0\nd mixing and\nB0\ns \u2212B0\ns mixing, when normalized to the SM, are exactly\nthe same. A sign of cMFV would be a deviation from\nthe SM that can be described without new CP violating\nphases and without enlarging the SM operator basis. A\ndiscrepancy in \u03c61 determined from B \u2192J/\u03c8K0\nS and the\nglobal Unitarity Triangle \ufb01t, on the other hand, would rule\nout the cMFV framework.\nExtensions of MFV\nOne can have viable TeV NP with not too large FCNCs\neven, if the \ufb02avor breaking is not just due to the SM\nYukawa couplings. It su\ufb03ces that all the \ufb02avor breaking\nhas a structure similar to the SM one. The most impor-\ntant feature is that there is a hierarchy similar to the one\nin the quark \ufb02avor sector of the SM. The \ufb01rst two genera-\ntions are much lighter than the third generation. Also, the\nmixing between the third and the \ufb01rst two generations is\nmuch smaller than the one between the \ufb01rst two genera-\ntions (i.e. Vcb, Vub \u226aVus). If this pattern is also present\nin NP with roughly the same hierarchies and directions\nof \ufb02avor breaking as in the SM, then FCNCs generated\nby NP will not be dangerously large. This insight can be\nformalized using symmetries and goes by the name of gen-\neral MFV (GMFV). It is more general than cMFV, but\ncoincides with the most general form of MFV, if Yukawa\ncouplings are perturbative. Since GMFV is more general,\nthere are also less correlations between observables. For in-\nstance, depending on which operators dominate, the new\nCP violating phases in B0\nd \u2212B0\nd and B0\ns \u2212B0\ns mixing are\neither exactly the same or there is a new CP violating\nphase only in B0\ns \u2212B0\ns mixing as we will see below.\nSupersymmetry\nThe supersymmetric (SUSY) extensions of the SM are\nsome of the most popular NP models. SUSY relates fermi-\nons and bosons. For example, the gauge bosons have their\nfermion superpartners and fermions have their scalar su-\nperpartners. SUSY at the TeV scale is motivated by the\nfact that it solves the SM hierarchy problem. The quan-\ntum corrections to the Higgs mass are quadratically di-\nvergent and would drive the Higgs mass to the Planck\nscale \u223c1019 GeV, unless the contributions are canceled.\nIn SUSY models they are canceled by the virtual correc-\ntions from the superpartners. The minimal SUSY exten-\nsion of the SM refers to the scenario where all the SM\n\ufb01elds obtain superpartners but there are no other addi-\ntional \ufb01elds. This is the Minimal Supersymmetric Stan-\ndard Model (MSSM). SUSY cannot be an exact symme-\ntry since in that case superpartners would have the same\nmasses as the SM particles, in clear con\ufb02ict with observa-\ntions. Di\ufb00erent mechanisms of SUSY breaking have very\ndi\ufb00erent consequences for \ufb02avor observables. In complete\ngenerality the MSSM has more than a hundred parame-\nters, most of them coming from the so-called soft SUSY\nbreaking terms (the SUSY breaking terms with dimension-\nful couplings, such as e.g. masses, so that the divergence\nis at most logarithmic). If superpartners exist at the TeV\nscale the most general form with O(1) \ufb02avor breaking co-\ne\ufb03cients is excluded due to \ufb02avor constraints. This has\nbeen dubbed the SUSY \ufb02avor problem (or in general the\nNP \ufb02avor problem).\nMFV SUSY\nA popular solution to the SUSY \ufb02avor problem is to as-\nsume that the SUSY breaking mechanism and the induced\ninteractions are \ufb02avor \u201cuniversal\u201d. The \ufb02avor universal-\nity is often imposed at a very high scale corresponding\n\n780\nto the SUSY breaking mechanism. It could be at, for in-\nstance, the Planck scale (\u223c1019 GeV), the GUT scale\n(\u223c1016 GeV) or some intermediate scale such as the\ngauge mediation scale (\u223c106 GeV). The \ufb02avor breaking\ncan then be transferred only from the SM Yukawa cou-\nplings to the other interactions through renormalization\ngroup running from the higher scale to the weak scale.\nAs a result, the \ufb02avor breaking comes entirely from the\nSM Yukawa couplings (thus, an example of a concrete\nMFV NP scenario). Since the soft SUSY breaking terms\nare \ufb02avor-blind, the squark masses are degenerate at the\nhigh energy scale. The squark mass splitting occurs only\ndue to quark Yukawa couplings, where only top Yukawa\nand potentially bottom Yukawa couplings are large. Thus\nthe \ufb01rst two generation squarks remain degenerate to very\ngood approximation, while the third generation squarks\nare split.\nnonMFV-SUSY\nWhile \ufb02avor blind SUSY breaking is well motivated, it\nis important to keep track of other possibilities \u2013 with\nmore general \ufb02avor breaking patterns. A very useful ap-\nproach is the mass insertion approximation (MIA). The\napproximation is easiest to explain in the basis, where the\nSM fermions have diagonal masses, while the sfermions\nhave undergone exactly the same \ufb02avor transformations\nas their SM fermion partners (this is the so-called super-\nCKM basis). All neutral gauge interactions are still \ufb02a-\nvor diagonal, charged currents are proportional to the\nCKM elements, while the sfermion mass matrices have\nalso o\ufb00-diagonal \ufb02avor violating entries. Phenomenologi-\ncally, the o\ufb00-diagonal entries need to be small. They can\nthus be treated as perturbations, compared to the diago-\nnal ones. The size of the resulting \ufb02avor violation is usually\nparametrized by dimensionless ratios of o\ufb00-diagonal and\n(the average of) diagonal entries in mass matrices, (\u03b4q\nAB)ij,\nwhere A, B are the chiralities (L, R) and q indicates the\n(u, d) type. In principle (\u03b4q\nAB)ij are only bounded by the\nexperiments, but are otherwise completely general.\nSUSY alignment models\nIf the squark mass basis is almost the same as the quark\nmass basis, then the FCNCs due to squarks and gluinos\nrunning in the loops are suppressed. Alignment of squark\nand quark mass matrices is easily achieved in \ufb02avor model\nbuilding and could be a remnant of the underlying sym-\nmetry. The alignment models are very close in spirit to\nMFV models \u2013 that there is a relation between the \ufb02avor\nbreaking in squark and quark sectors \u2013 but di\ufb00er in de-\ntails. For instance, in alignment models the squark matri-\nces can carry arbitrary phases, the relation between squark\nand quark mass eigenstate bases is only approximate and\nmost importantly, the \ufb01rst two generations squarks need\nnot be degenerate but can have O(1) splitting in their\nmass spectra.\nThe bounds on FCNCs in up and down quark sectors\nput strong constraints on alignment models. For instance\nthe measured values of D0 \u2212D0 and K0 \u2212K0 mixing\nrequire that the splitting between the \ufb01rst two generations\nof left-handed squarks is less than O(0.1) for TeV squarks\nmasses.\nRandall-Sundrum models of \ufb02avor\nThe Randall-Sundrum (RS) model introduces a \u201cwarped\u201d\nextra dimension, i.e. a \ufb01fth dimension for which the metric\nof the \ufb01ve dimensional space time contains an exponential\n\u201cwarp\u201d factor. The Higgs of the SM is con\ufb01ned to a four\ndimensional subspace, the \u201cTeV brane\u201d, while the full \ufb01ve\ndimensional space is called the \u201cbulk\u201d. This idea provides\nan interesting solution to the hierarchy problem by gen-\nerating the weak scale from the Planck scale through this\nexponential warp factor. The RS model can also explain\nthe hierarchy of fermion masses. The fermionic wave func-\ntions extend in the bulk with the heavier particles located\ncloser to the TeV brane. Then, the fermion wave func-\ntion pro\ufb01les (locations of di\ufb00erent fermions in the bulk)\ncan also provide the exponential warp factor and an O(1)\nchange in the parameters in the 5 dimensional theory can\nlead to the hierarchical \ufb02avor structure in the 4 dimen-\nsional theory. The existence of an extra dimension results\nin each SM particle to be accompanied by a whole tower of\nexcited \u201cKaluza-Klein\u201d (KK) states. The exchanges of KK\nexcitations of gluons and the distortion of the Z boson\u2019s\n5D pro\ufb01le then generate FCNCs at tree level. These e\ufb00ects\nare naturally suppressed, however, by the same mecha-\nnism that explains the hierarchy of fermion masses. The\nresulting FCNCs are not too large for the light quarks,\nwith the exception of K0 \u2212K0 mixing, where modest can-\ncellations between di\ufb00erent contributions are required if\nthe KK mass scale is 2-3 TeV. In this case large e\ufb00ects in\nseveral B physics observables are also expected. The 5D\nmasses are complex in general, so that there are many new\nsources of CP violation. O(1) NP weak phases in B0\nd \u2212B0\nd\nmixing and B0\ns \u2212B0\ns mixing would thus be expected.\nLittle Higgs Models\nLittle Higgs models are an alternative way to solve the\nhierarchy problem. The mass of a scalar particle is stabi-\nlized, if it is a Goldstone boson of a spontaneously broken\nglobal symmetry. The Goldstone boson is massless, if the\noriginal global symmetry is exact, and has a small nonzero\nmass, if there is already a small explicit breaking of the\nglobal symmetry. Little Higgs models implement this idea\nby constructing an extension of the SM such that the SM\nHiggs particle is the Goldstone mode of an enlarged sym-\nmetry. This symmetry is also explicitly broken in order\nto achieve a small mass for the Goldstone modes. Un-\nlike SUSY, the solution to the hierarchy problem in Little\nHiggs models is only partial \u2013 just for 1-loop corrections\nto the Higgs mass. The models therefore require UV com-\npletion at a scale of a few TeV, i.e. the models are not\n\n781\nvalid to arbitrary high energies but need to be supple-\nmented with extra \ufb01elds and/or interactions. One of the\nmore interesting realizations is the Littlest Higgs model\nwith T parity. In it the SM \ufb01elds are supplemented by a\nnew heavy top quark (T+), a triplet of heavy scalars (\u03a6)\nas well as a new set of heavy gauge bosons W \u00b1\nH , Z0\nH, AH.\nIt has an interesting non-MFV \ufb02avor structure with only\n10 new parameters in the quark sector. As a result there\nare still correlations between FCNC processes in the down\nand up-quark sectors. The constraints from B \u2192Xs\u03b3 are\neasily satis\ufb01ed, while signi\ufb01cant e\ufb00ects would be expected\nin Bs mixing and in K \u2192\u03c0\u03bd\u00af\u03bd and KL \u2192\u03c00\u2113+\u2113\u2212decays.\n25.2.2 Detailed description of NP models\nWe now give a more detailed description of the models, fo-\ncusing especially on the impact the B Factory observables\nhad on constraining the models. We highlight the follow-\ning observables in particular, sin 2\u03c61, B \u2192Xs\u03b3, B \u2192\u03c4\u03bd,\nD0 \u2212D0 mixing, B \u2192\u03c6K0\nS, all of which are listed in Ta-\nble 25.2.2. We also include the anomalous moment of the\nmuon, (g \u22122)\u00b5, as another important observable. Even\nthough it was not measured at the B Factories, the ISR\nresults obtained at the B Factories provide crucial inputs\nto the SM predictions (see Section 21.3.4 for detailed dis-\ncussions on the impact of the B Factories ISR result on\nthe muon g \u22122). For ease of comparison a star system\nis used in Table 25.2.2, where more stars mean that the\ngeneric predictions of the model agree better with the ob-\nservations (from 1 to 3 stars).\n25.2.2.1 Fourth generation\nThere is no compelling theoretical reason for having only\nthree generations of fermions. It is thus important to search\nfor additional heavier quarks. The simplest possibility is\na sequential 4th generation, where new heavy quarks have\nthe same quantum numbers as in the SM \u2013 the left-handed\nt\u2032 and b\u2032 form an SU(2)L doublet, while the right-handed\nt\u2032 and b\u2032 are singlets (for a review see (Frampton, Hung,\nand Sher, 2000)). In this model the 3 \u00d7 3 CKM matrix is\nno longer unitary since it is only a part of the full 4 \u00d7 4\nmatrix\n\uf8eb\n\uf8ec\n\uf8ed\nVud Vus Vub Vub\u2032\nVcd Vcs Vcb Vcb\u2032\nVtd Vts Vtb Vtb\u2032\nVt\u2032d Vt\u2032s Vt\u2032b Vt\u2032b\u2032\n\uf8f6\n\uf8f7\n\uf8f8.\n(25.2.2)\nThis means that the global \ufb01ts of the CKM unitarity must\nbe supplemented with 3 \u00d7 3 unitarity relaxed, see, e.g.,\n(Bobrowski, Lenz, Riedl, and Rohrwild, 2009).\nThe heavy quarks can contribute to any loop type di-\nagrams. In particular, since the loop function of the box\nand the penguin diagrams grow with the mass of the heavy\nquark in the loop, these contributions can be large. There-\nfore, the precise measurements obtained by the B Facto-\nries lead to very strong constraints on the fourth row and\ncolumn of the enlarged 4 \u00d7 4 quark mixing matrix.\nWe \ufb01rst focus on the impact of the sin 2\u03c61 measure-\nment by the B Factories. The B0\nd \u2212B0\nd box diagram now\nalso has a heavy top quark, t\u2032, running in the loop. After\nimposing the 4 \u00d7 4 unitarity the mixing matrix element is\ngiven by\nM12 = G2\nF m2\nW\n6\u03c02\n\u02c6\u03b7BmB \u02c6BBdf 2\nBd\n\u0002\n\u03bb2\ntS0(xt)+\n2\u03bbt\u03bbt\u2032S0(xt, xt\u2032) + \u03bb2\nt\u2032S0(xt\u2032)\n\u0003\n,\n(25.2.3)\nwhere the Inami-Lim functions, S0, describe the t and t\u2032\nquark contributions in the loop in terms of their masses\nxi \u2261m2\ni /m2\nW (Inami and Lim, 1981). The CKM matrix\nelements are included in \u03bbi \u2261V \u2217\nibVid and the NLO QCD\ncorrection \u02c6\u03b7B is taken as \u02c6\u03b7B = 0.55 (Buchalla, Buras, and\nLautenbacher, 1996). The non-perturbative QCD e\ufb00ects\nare absorbed in the bag parameter \u02c6BBd and the decay\nconstant fBd, for which we use ( \u02c6BBd)1/2fBd = (216 \u00b1 16)\nMeV (Nakamura et al., 2010). Introduction of the fourth\ngeneration quarks has two e\ufb00ects. First, the value of the\nCKM element \u03bbt multiplying the top contribution can dif-\nfer from the one obtained from the CKM \ufb01ts where 3 \u00d7 3\nunitarity is assumed. Second, there is an additional con-\ntribution from the t\u2032 in the loop.\nThe two e\ufb00ects are related through the 4 \u00d7 4 unitar-\nity condition, \u03bbu + \u03bbc + \u03bbt + \u03bbt\u2032 = 0 with \u03bbu = (3.8 \u00b1\n0.5) \u00d7 10\u22123ei(\u221268\u00b110)\u25e6and \u03bbc = (\u22129.4 \u00b1 0.5) \u00d7 10\u22123 ex-\ntracted from the processes involving only tree level dia-\ngrams (Nakamura et al., 2010). The predictions\n\u2206md = 2|M 4SM\n12\n|,\nSb\u2192c\u00afcs = \u2212Im\ns\nM \u22174SM\n12\nM 4SM\n12\n,\n(25.2.4)\nthen depend only one complex parameter, \u03bbt\u2032 (or\nequivalently \u03bbt by using the unitarity relation), and the\nmass of t\u2032. The experimental world averages, \u2206md =\n(0.510 \u00b1 0.004) ps\u22121 and Sb\u2192c\u00afcs = 0.677 \u00b1 0.020 (see\nSections 17.5.2 and 17.6 for the experimental extrac-\ntion of these values), are consistent with the SM pre-\ndictions within errors, \u2206mSM\nd\n= (0.51 \u00b1 0.12) ps\u22121 and\nSb\u2192c\u00afcs = 0.74 \u00b1 0.09. Fixing the mass of t\u2032 to 600 GeV\nthe constraints on \u03bbt\u2032 are shown in Fig. 25.2.2. The dashed\nline is the constraint from the mass di\ufb00erence \u2206md, which\nwas known before the B Factories but with much larger\nuncertainty. The sin 2\u03c61 measurement (solid line) gives a\nstrong constraint |\u03bbt\u2032| < 0.005. Combined constraints ex-\nclude the colored regions.\nThe next example is the B \u2192Xs\u03b3 branching ratio,\nwhich also receives a contribution from a t\u2032 quark running\nin the loop. The experimental measurements agree with\nthe SM prediction from up, charm and top quarks running\nin the loop. However, as in the case of B0 \u2212B0 mixing,\nthe top contribution in the 4th generation scenario can\ndi\ufb00er from the SM due to a di\ufb00erent V \u2217\ntbVts obtained from\n4 \u00d7 4 CKM \ufb01ts. This can then leave some more space\nfor the non-zero t\u2032 contribution. The obtained constraint\non V \u2217\nt\u2032bVt\u2032s is not so strong since the branching ratio is\ndominated by the tree level O2 contributions which are\nproportional to V \u2217\ncbVcs. The B \u2192Xs\u03b3 branching ratio\n\n782\nTable 25.2.2. The agreement of NP models and the SM with the experimental results including the measurements from the B\nFactories (more stars means better agreement). See text for further explanations. The \u2212sign means there is no clear expectation.\nObservable\n4th gen.\n2HDM\nMFV\neMFV\nMFV-SUSY\ngenSUSY\naligSUSY\nRS\nLittle H\nSM\nsin 2\u03c61\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\nB \u2192Xs\u03b3\n\u22c6\u22c6\u22c6\n\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\nB \u2192\u03c4\u03bd\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\nD0 \u2212D0 mixing\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\n\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\nB \u2192\u03c6K0\nS\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\u22c6\u22c6\n\u22c6\n\u22c6\u22c6\n(g \u22122)\u00b5\n\u22c6\n\u22c6\n\u2212\n\u2212\n\u22c6\u22c6\n\u22c6\u22c6\n\u2212\n\u22c6\u22c6\n\u22c6\u22c6\n\u22c6\nallows V \u2217\nt\u2032bVt\u2032s \u223cO(\u03bb) which is a much weaker bound\nthan the constraints obtained from other measurements\nsuch as B0\ns \u2212B0\ns oscillation.\nAnother example is D0\u2212D0 mixing where the b\u2032 quark\ncould contribute in the loop diagram in addition to the SM\nparticles. Saturating the experimental value of xD gives\n|V \u2217\ncb\u2032Vub\u2032|2 <\n\u223c10\u22122,\n(25.2.5)\nfor a 600 GeV b\u2032.\nThe other observables receive some contributions from\nthe 4th generation, though so far, the constraints are not\nas strong as from B0 \u2212B0 mixing and D0 \u2212D0 mix-\ning. Namely, the CP asymmetry of B \u2192\u03c6K0\nS, to which\nt\u2032 can contribute both in B0 \u2212B0 oscillations (box di-\nagram) and the b \u2192s decay (gluon penguin diagram).\nThe oscillation part is constrained very strongly by the\nB \u2192J/\u03c8K0\nS channel. The decay part could constrain the\n4th generation parameters although it turns out that the\nobtained constraint is not very strong. Another observ-\nable, the decay B \u2192\u03c4\u03bd is tree dominated. Thus, the 4th\ngeneration contribution appears only through the modi\ufb01-\ncation of the CKM matrix element, namely, Vub, due to\nthe broken unitarity. This can be detected by observing\ndi\ufb00erent values of Vub in the measurements through tree\nand loop processes. So far, the observed di\ufb00erence is not\nstatistically signi\ufb01cant. The muon g \u22122 can receive a con-\ntribution from the 4th generation neutrino (Lynch, 2001).\nHowever, the contribution is not large enough to explain\nthe observed deviation from the SM.\nThe main message of this section is that the CKM ma-\ntrix elements for the heavy fermions can be very strongly\nconstrained from the B Factory observables. A sizable\nmixing of SM quarks with 4th generation quarks is ex-\ncluded. If, on the other hand, one na\u00a8\u0131vely extrapolates the\nWolfenstein structure of the CKM to 4 generations, one\nmay expect that \u03bbt\u2032 \u223c\u03bb4 so that an order of magnitude\nimprovement in precision of \ufb02avor observables would be\nmost welcome. Also, the direct searches at the LHC now\nexclude heavy fermions with masses below \u223c600 GeV.\nThis limit is high enough that the unitarity mass limit\nhas been reached \u2013 the fermion-fermion scattering ampli-\ntude becomes larger than one and the fermions become\nstrongly coupled. This means that the loop corrections we\ndiscussed above must be taken with a grain of salt as they\nwere obtained using perturbative calculations. Finally, the\ndiscovery of the Higgs-like particle with a mass of about\nRe(V \u2217\nt\u2032bVt\u2032d)\nIm(V \u2217\nt\u2032bVt\u2032d)\nPBF\nFigure 25.2.2. Constraints on the real and imaginary parts\nof V \u2217\nt\u2032bVt\u2032d from \u2206md (dashed) and sin 2\u03c61 (solid) are shown\nfor mt\u2032 = 600 GeV. The blue regions are excluded at 1\u03c3, 2\u03c3\nand 3\u03c3 (from lighter to darker) assuming Gaussian errors.\n125 GeV also excludes the perturbative 4th generation,\nsince in that case the production and decays of the Higgs\nwould be modi\ufb01ed signi\ufb01cantly (Eberhardt et al., 2012;\nKu\ufb02ik, Nir, and Volansky, 2012).\n25.2.2.2 Two Higgs Doublet Models\nA simple extension of the Standard Model is to add an ex-\ntra Higgs doublet to the \ufb01eld content. Despite being a very\nsimple modi\ufb01cation, it can lead to drastic changes in low\nenergy \ufb02avor phenomenology. If all Yukawa interactions\nbetween the two Higgs doublets and quarks are allowed,\nthen this leads to FCNCs from neutral Higgs exchanges\nthat are orders of magnitude above the experimentally\nallowed values. No FCNCs arise if only one Higgs dou-\nblet couples to quarks, while the other is inert (this is the\nType I 2HDM). The other option is that one of the Higgs\ndoublets, H1, couples to the right-handed down quarks,\nwhile the other Higgs doublet, H2 couples to the right-\nhanded up quarks only. This is the Type II 2HDM, and\ncorresponds to the Higgs sector of the MSSM when loop\ncorrections from sparticles are neglected. A more general\n\n783\nway to avoid tree-level FCNCs is to require alignment be-\ntween the Yukawa couplings of the two Higgs doublets.\nAlignment is parameterized by three complex parameters\nand covers the above two types of the 2HDM models as\nspecial cases (Pich and Tuzon, 2009).\nFrom now on we focus on the Type II 2HDM for which\nthe expectations regarding \ufb02avor observables are collected\nin Table 25.2.2. In the 2HDM there are 3 real scalars, two\nCP-even and one CP-odd neutral Higgs bosons, and one\ncharged Higgs boson H\u00b1. In Type II 2HDM the interac-\ntions of the neutral Higgses are \ufb02avor diagonal, so that the\n\ufb02avor violation arises only at loop level like in the SM. The\nexchange of a charged Higgs, H\u00b1, can lead to signi\ufb01cant\ncontributions to the B physics observables. The interac-\ntions with quarks are given by\nL =(2\n\u221a\n2GF )1/2\n3\nX\ni,j=1\nui\n\u0000AumuiVijPL\n\u2212AdVijmdiPR\n\u0001\ndjH+ + h.c.,\n(25.2.6)\nwhere PL,R \u2261(1\u2213\u03b35)/2. ui and dj are the mass eigenstate\n\ufb01elds, i, j the generation indices, mu,d the diagonal quark\nmass matrices and Vij the CKM matrix elements. In the\nType II 2HDM the coe\ufb03cients Au,d depend only on the\nratio of the H2 and H1 Higgs vacuum expectation values,\ntan \u03b2 = v2/v1,\nAu = cot \u03b2,\nAd = \u2212tan \u03b2.\n(25.2.7)\nWe expect a signi\ufb01cant contribution from the loop induced\ndiagrams with a charged Higgs and a top quark in the\nloop such as Bd \u2212Bd oscillation and the decay B \u2192Xs\u03b3.\nA large enhancement of the charged Higgs contribution\nis possible because of the \ufb01rst term in Eq. (25.2.6) with\nui = t due to the large top quark mass. While the experi-\nmental measurements of the Bd \u2212Bd oscillation frequency\ncan constrain part of the parameter space, in particular for\nsmall tan \u03b2, the constraint from B \u2192Xs\u03b3 is generically\nmore important. At LO the Wilson coe\ufb03cient relevant for\nB \u2192Xs\u03b3 including the NP contributions is (Ciuchini, De-\ngrassi, Gambino, and Giudice, 1998b; Grinstein, Springer,\nand Wise, 1990; Hou and Willey, 1988)\nC7,8(MW ) = CSM\n7,8\n\u0012 m2\nt\nm2\nW \u00b1\n\u0013\n+ A2\nu\n3 G7,8\n\u0012 m2\nt\nm2\nH\u00b1\n\u0013\n\u2212AuAdF7,8\n\u0012 m2\nt\nm2\nH\u00b1\n\u0013\n.\n(25.2.8)\nThe second and the third terms give charged Higgs contri-\nbutions and are enhanced by m2\nt, as expected. The signs of\nAu and Ad are opposite in Type II 2HDM (see Eq. 25.2.7)\nso that both terms interfere constructively with the SM\nterm. The term proportional to A2\nu is relevant only for\nsmall tan \u03b2, while the term proportional to AuAd is im-\nportant almost independently of tan \u03b2.\nThe SM prediction for the branching ratio of B \u2192\nXs\u03b3 has been drastically improved in the past 10 years.\nThe NNLO predictions are available both for the SM and\nfor the charged Higgs contributions (Misiak et al., 2007).\nThe most recent analysis shows that the SM prediction\nis roughly 1 sigma below the experimental value (see Sec-\ntion 17.9 for more details) and the following lower limit on\nthe charged Higgs mass is obtained for any value of tan \u03b2\nmH\u00b1 > 295 GeV.\n(25.2.9)\nAnother very important constraint on the Type II\n2HDM has been obtained from the B Factory measure-\nments of B(B \u2192\u03c4\u03bd) (see Section 17.10 for more discus-\nsions on this process). This tree level process occurs in the\nSM with a diagram in which the B meson annihilates into\na W boson followed by its decay into \u03c4\u03bd. In the 2HDM,\na similar process is possible but the W is replaced with\nthe charged Higgs. The resulting branching ratio can be\nexpressed as\nB(B \u2192\u03c4\u03bd) = B(B \u2192\u03c4\u03bd)SM\n\u0012\n1 \u2212tan2 \u03b2 m2\nB\nm2\nH\u00b1\n\u00132\n,\n(25.2.10)\nwhere\nB(B \u2192\u03c4\u03bd)SM = G2\nF mBm2\n\u03c4\n8\u03c0\n\u0012\n1 \u2212m2\n\u03c4\nm2\nB\n\u00132\nf 2\nB|Vub|2\u03c4B.\n(25.2.11)\nThe second term in the parenthesis of Eq. (25.2.10) is due\nto the charged Higgs.\nReplacing the left hand side of Eq. (25.2.10) with the\nexperimental bound obtained by the B Factories, a combi-\nnation of the parameters mH\u00b1/ tan \u03b2 can be constrained.\nThe two solutions\nmH\u00b1\nmB tan \u03b2 =\n\u0010\n1 \u00b1\nq\nrB\u2192\u03c4\u03bd\nexp\n\u0011\u22121/2\n,\n(25.2.12)\nwith\nrB\u2192\u03c4\u03bd\nexp\n= B(B \u2192\u03c4\u03bd)exp\nB(B \u2192\u03c4\u03bd)SM\n(25.2.13)\nare plotted, respectively, as grey and black lines in\nFig. 25.2.3. Here we use the SM prediction for the branch-\ning ratio, B(B \u2192\u03c4\u03bd)SM = (1.01\u00b10.29)\u00d710\u22124, as quoted\nin Section 17.10. The vertical lines indicate the current\nworld average (see also Section 17.10)\nB(B \u2192\u03c4\u03bd)exp = (1.15 \u00b1 0.23) \u00d7 10\u22126,\n(25.2.14)\nwith 1\u03c3 (dotted), 2\u03c3 (dashed) and 3\u03c3 (solid) errors. The\ntwo vertical yellow regions are excluded at 95% C.L. Note\nthat the theoretical error to the SM prediction denoted\nabove is indicated in the right top corner of Fig. 25.2.3.\nIt results in additional uncertainties on top of the exper-\nimental ones. The horizontal yellow region is excluded by\nthe B(B \u2192Xs\u03b3) measurement.\nThe \ufb01rst solution (gray lines) are already excluded by\nthe constraints from B \u2192Xs\u03b3 as well as from B \u2192D\u03c4\u03bd.\nThe second solutions (black lines) can give a constraint on\nm\u00b1\nH stronger than B(B \u2192Xs\u03b3). By taking into account\n\n784\nthe 3\u03c3 experimental error, for instance, one obtains a lower\nbound mH\u00b1 \u2265370 (556) GeV for tan \u03b2 = 40 (60). Note\nthat this bound is very sensitive to the theoretical input\nand could be lowered by over 100 (150) GeV by taking\ninto account the theoretical uncertainty discussed above.\nIt is clear that further reduction of both theoretical and\nexperimental errors will shed light on the charged Higgs\nsearches in this model in the future.\nWe discuss next brie\ufb02y the other observables, for\ndetails see (Barger, Hewett, and Phillips, 1990; Gross-\nman, 1994; Krawczyk and Pokorski, 1991; Wahab El Kaf-\nfas, Osland, and Ogreid, 2007). For the \u2206F = 2 (F is\nstrangeness or bottomness) processes, the impact on the\nB0 \u2212B0 mixing frequency and phase is small while the\nD0 \u2212D0 mixing could receive a large contribution, in par-\nticular for large tan \u03b2 (Golowich, Hewett, Pakvasa, and\nPetrov, 2007). However, since the SM value of the D0\u2212D0\nmixing parameter is not well determined it is di\ufb03cult to\nobtain a strict constraint, even though order of magnitude\nestimates are already interesting. Since this model does\nnot include a large CP violating phase in the b \u2192s transi-\ntion part, the CP violation in B \u2192\u03c6K0\nS does not receive a\nsigni\ufb01cant NP contribution. The recent BABAR measure-\nment of the ratio R(D(\u2217)) \u2261B(B \u2192D(\u2217)\u03c4\u03bd)/B(B \u2192\nD(\u2217)l\u03bd) shows some deviation from the SM (Lees, 2012e).\nThe charged Higgs can contribute to this process, however,\nthe deviation in R(D) and R(D\u2217) cannot be explained si-\nmultaneously within Type II 2HDM (Lees, 2012e) (see\nSection 17.10 for more details). It is, however, possible\nto explain the observed pattern using 2HDM with more\ngeneral \ufb02avor structure (Fajfer, Kamenik, Nisandzic, and\nZupan, 2012). The muon magnetic moment, (g \u22122)\u00b5, is\nfound not to provide a signi\ufb01cant contribution after tak-\ning into account the constraints discussed in this Sec-\ntion (Jegerlehner and Ny\ufb00eler, 2009; Krawczyk, 2002; Wa-\nhab El Ka\ufb00as, Osland, and Ogreid, 2007).\n25.2.2.3 Minimal Flavor Violation\nThe MFV hypothesis states that \ufb02avor violation in NP\ncomes from the same source as in the SM, the SM Yukawa\ncouplings (Buras, 2003; Buras, Gambino, Gorbahn, Jager,\nand Silvestrini, 2001; Chivukula and Georgi, 1987; Ciu-\nchini, Degrassi, Gambino, and Giudice, 1998a; D\u2019Ambrosio,\nGiudice, Isidori, and Strumia, 2002; Hall and Randall,\n1990). The reasoning behind this hypothesis on one hand\nis that this is the minimal amount of \ufb02avor breaking that\nneeds to be present, since it is already seen in the SM. On\nthe other hand, it also leads to relatively small deviations\nfrom the SM in \ufb02avor observables and is not excluded ex-\nperimentally. In principle many di\ufb00erent NP models can\nbe of MFV type, but the best known example is low en-\nergy SUSY with gauge mediated SUSY breaking (that we\ndiscuss separately below). Another example are universal\nextra dimensions with universal boundary conditions. In\nboth cases the only source of \ufb02avor violation are the SM\nYukawa couplings.\nAn important bene\ufb01t of the MFV hypothesis is that\nthe e\ufb00ects of NP on \ufb02avor observables can be worked out\nTheory error\n20\n30\n40\n50\n60\n70\n80\n20 30 40 50 60 70 80\n0.0\n0.5\n1.0\n1.5\n2.0\n0\n200\n400\n600\n800\n1000\nmH\u00b1 (GeV)\nrB\u2192\u03c4\u03bd\nexp\n= B(B \u2192\u03c4\u03bd)exp\nB(B \u2192\u03c4\u03bd)SM\nPBF\nFigure 25.2.3. Constraints on the charged Higgs mass in\nthe Type II 2HDM from the B Factory measurements of\nB(B \u2192\u03c4\u03bd) and B(B \u2192Xs\u03b3). The x-axis represents the\npresent experimental value of B(B \u2192\u03c4\u03bd) normalized to the\nSM prediction (see text for details). The vertical yellow re-\ngions are excluded by the current world average experimental\nvalue, B(B \u2192\u03c4\u03bd)exp = (1.15 \u00b1 0.23) \u00d7 10\u22126, at 95% C.L.,\nwhile the 1\u03c3, 2\u03c3, 3\u03c3 errors on the same experimental value are\ndenoted by the dotted, dashed, and solid lines, respectively.\nThe horizontal yellow region is excluded by the B(B \u2192Xs\u03b3)\nmeasurement (see Eq. 25.2.9). The grey and the black lines\ncorrespond to the predictions of the Type II 2HDM given in\nEq. (25.2.12), respectively, with labels denoting the di\ufb00erent\nvalues of tan \u03b2.\nwithout committing to a concrete model. This is done\nusing a so-called spurion analysis (D\u2019Ambrosio, Giudice,\nIsidori, and Strumia, 2002), which we review quickly. The\nSM Yukawa interactions for quarks are\nLY = \u00afQLYDdRH + \u00afQLYUuRHc + h.c., (25.2.15)\nwhere the generation indices i on the left-handed\nquarks Qi\n=\n(uL, dL)i, and on right-handed quarks\n(uR)i, (dR)i were suppressed, while Hc \u2261i\u03c42H\u2217, where \u03c42\nis the SU(2) generator, was used. If the Yukawa coupling\nmatrices YD, YU were zero, it would not be possible to dis-\ntinguish the three generations of quarks. Thus, the theory\nwould have a global symmetry, GF = SU(3)Q\u00d7SU(3)UR\u00d7\nSU(3)DR, since any of the quark \ufb01elds QL, uR, dR can be\nrotated independently. In other words, the global sym-\nmetry GF is explicitly broken by the fact that Yukawa\ncouplings are not zero \u2013 quarks have nonzero masses in\nthe SM. One can then use a formal trick and pretend\nthat Yukawa coupling matrices do transform under GF as\nYU \u223c(3, \u00af3, 1), YD \u223c(3, 1, \u00af3) (The jargon used is that YU,D\nare promoted to be spurions, where the name comes from\nthe fact that these are now \ufb01ctitious or spurious auxiliary\n\ufb01elds.). All the interactions are then formally invariant un-\nder GF . Under the MFV hypothesis also NP is assumed\nto be invariant under GF .\n\n785\nIntegrating out NP particles we obtain corrections to\nthe e\ufb00ective weak Hamiltonian. However, since NP is for-\nmally invariant under GF we know its \ufb02avor structure. We\njust need to construct an e\ufb00ective weak Hamiltonian that\nis GF invariant, and all the breaking comes from YU and\nYD. This then also \ufb01xes the allowed \ufb02avor breaking. The\nYukawa coupling matrices YU and YD are not aligned and\nare diagonal in di\ufb00erent bases for QL. The misalignment\nleads to \ufb02avor changing charged currents, J\u00b5\nC = \u00afuL\u03b3\u00b5V dL,\nwith V being the same as the CKM matrix.\nIn this section we focus on a particular realization of\nMFV \u2013 the so-called constrained minimal \ufb02avor viola-\ntion (cMFV) (Blanke, Buras, Guadagnoli, and Tarantino,\n2006; Buras, Gambino, Gorbahn, Jager, and Silvestrini,\n2001). The assumptions that underlie cMFV are (i) the\nSM \ufb01elds are the only light degrees of freedom in the the-\nory, (ii) there is only one light Higgs and (iii) the SM\nYukawa couplings are the only sources of \ufb02avor violation.\nThe NP e\ufb00ective Hamiltonian for qj \u2192qi processes fol-\nlowing from these assumptions thus has exactly the same\nCKM suppression and form of the e\ufb00ective operators as\nin the SM. This is sometimes taken to be the de\ufb01nition of\ncMFV (Blanke, Buras, Guadagnoli, and Tarantino, 2006;\nBuras, 2003; Buras, Gambino, Gorbahn, Jager, and Sil-\nvestrini, 2001). For instance, the e\ufb00ective Hamiltonian for\nthe \u2206F = 2 transitions is\nHNP\ne\ufb00= CNP\n\u039b2\nNP\n\u0000V \u2217\ntiVtj\n\u00012Qij,\n(25.2.16)\nwhere the Wilson coe\ufb03cient CNP is real, while Qij are\nexactly the same operators as in the SM e\ufb00ective weak\nHamiltonian. For B0\nd \u2212B0\nd this is Qbd = (\u00afbL\u03b3\u00b5dL)2. Note\nthat CNP is universal \u2013 it is the same for K0 \u2212K0, B0\nd \u2212\nB0\nd and B0\ns \u2212B0\ns mixing. The relative sizes of the NP\ncontributions are given entirely by the CKM matrix el-\nements which are the same as in the SM. As a conse-\nquence Eq. (25.2.16) provides a very strong constraint on\nthe scale of NP masses. Note that two-Higgs doublet mod-\nels or MFV MSSM even with small tan \u03b2 does not \ufb01t in\nthe cMFV and sizable contributions from operators with\nnon-SM chiral structures in addition to Eq. (25.2.16) are\npossible.\nBecause cMFV is a very constrained modi\ufb01cation of\nthe weak Hamiltonian, Eq. (25.2.16), one can experimen-\ntally distinguish it from the other BSM scenarios by look-\ning at the correlations between observables in K and B\ndecays. A sign of cMFV would be a deviation from the\nSM predictions that can be described without new CP\nviolating phases and without enlarging the SM operator\nbasis. For instance, in B0\nd \u2212B0\nd and B0\ns \u2212B0\ns mixing ob-\nservables the discrepancy from the SM is possible only\nin the value of \u2206md and \u2206ms and not in the mixing\nphases. Furthermore, the corrections normalized to the\nSM are universal, so that hs = hd in Eq. (25.2.1), while\nthe additional weak phases are zero, i.e. \u03c3s = \u03c3d = 0\nor \u03c3s = \u03c3d = \u03c0/2. A discrepancy in \u03c61 determined from\nB \u2192J/\u03c8K0\nS and the global Unitarity Triangle \ufb01t would\nrule out the cMFV framework. Similarly, a sizable B0\ns \u2212B0\ns\nmixing phase would rule out cMFV NP.\nSince the CKM-like suppression is automatically en-\ncoded in the NP contributions to \ufb02avor transitions, no\nlarge \ufb02avor violations are expected from TeV scale NP.\nThe results from the B Factories are precise enough, how-\never, that the energy scale probed is in the multi-TeV\nregime already. The most stringent constraints are coming\nfrom b \u2192s\u03b3 and b \u2192sl+l\u2212decays. Setting the NP Wilson\ncoe\ufb03cients CNP\ni\n= 1 in Eq. (25.2.16), one has \u039bNP > 6.1\nTeV (Hurth, Isidori, Kamenik, and Mescia, 2009 and up-\ndate by Hurth and Mahmoudi, 2012). If the NP states\nare exchanged at tree level, this would mean that they\nneed to be heavier than about 6 TeV. If they only con-\ntribute through loops, they need to be heavier than about\n\u223c6 TeV/4\u03c0 = 0.5 TeV for O(1) couplings. The precise\nvalue depends on the spin and charge of the exchanged\nparticle.\nSimilarly, one has a bound \u039bNP > 5.9 TeV for contri-\nbutions to meson mixing (Bona et al., 2006, 2008). The\nNP modi\ufb01cations to K0 \u2212K0, D0 \u2212D0, B0\nd \u2212B0\nd and\nB0\ns \u2212B0\ns are rigidly related in cMFV. There is only one\noperator, (\u00afqLj\u03b3\u00b5qLj)2, and the \ufb02avors of quarks \ufb01x the\nCKM suppressions. The bound on \u039bNP is predominantly\ndue to the \u03f5K constraint. This means that no e\ufb00ects in\nD0 \u2212D0, B0\nd \u2212B0\nd and B0\ns \u2212B0\ns mixing are expected in\ncMFV with the present experimental precision. Similarly,\nsince there are no new CP violating phases beyond the\nCKM phase, the \u03c61 phase determined from b \u2192s pen-\nguin transitions B \u2192\u03c6K0\nS is expected to be the same as\nobtained from B \u2192J/\u03c8K0\nS.\nThe MFV also relates the b \u2192u\u03c4\u03bd and b \u2192c\u03c4\u03bd\ncharged current transitions. In the SM the amplitudes for\nthese two transitions are proportional to the Vub and Vcb\nmatrix elements. The same is true for NP contributions.\nNormalized to the SM the deviations in both of these two\ntransitions thus need to be the same, if NP is of MFV\ntype. There are indications of deviations from the SM in\nB\u2212\u2192\u03c4 \u2212\u03bd and in B \u2192D(\u2217)\u03c4\u03bd (Lees, 2012e), which pro-\nceed through b \u2192u\u03c4\u03bd and b \u2192c\u03c4\u03bd quark level transi-\ntions, respectively, (see Sections 17.10 and 25.1). The rel-\native sizes of the two discrepancies, however, di\ufb00er from\nthe universal behavior predicted by the MFV. Therefore\nMFV is not preferred as an explanation of the anomalies\n(Fajfer, Kamenik, Nisandzic, and Zupan, 2012).\nFinally, the minimal incarnation of MFV \u2013 cMFV \u2013 is\na hypothesis about the \ufb02avor violation in the quark sector.\nTherefore there is no clear prediction about the size of the\nmuon anomalous magnetic moment, (g \u22122)\u00b5.\n25.2.2.4 Extensions of MFV\nThe phenomenologically most important extensions of\ncMFV hypothesis are: i) relaxing the assumption that\nthe CP violation is only due to the CKM phase, allow-\ning also for nonzero \ufb02avor diagonal weak phases, and ii)\nto allow for larger higher order terms in the spurion expan-\nsion. This General MFV (GMFV) hypothesis was formal-\nized by Kagan, Perez, Volansky, and Zupan (2009), who\nidenti\ufb01ed the new small spurions: the o\ufb00-diagonal CKM\n\n786\nmatrix elements and the masses of the \ufb01rst two genera-\ntion quarks. For an earlier discussion of \ufb02avor diagonal\nCP phases within the MSSM see (Colangelo, Nikolidakis,\nand Smith, 2009), for a nonlinear realization of MFV see\n(Albrecht, Feldmann, and Mannel, 2010; Feldmann, Jung,\nand Mannel, 2009; Feldmann and Mannel, 2008)\nThe important di\ufb00erence between cMFV and GMFV\nis that in cMFV there are relations between s \u2194d, b \u2194d\nand b \u2194s transitions, in GMFV only b \u2194d and b \u2194s\ntransitions are directly related. There are two classes of\nNP contributions. Class-1 operators do not contain light\nright-handed quarks, and class-2 operators do. An exam-\nple of a class-1 operator is, for instance, (\u00afqL\u03b3\u00b5bL)2, and\nan example of a class-2 operator is (\u00afqLbR)(\u00afqRbL). The dis-\ntinction is phenomenologically important, since the Wil-\nson coe\ufb03cients of the class-2 operators are proportional to\nlight-quark masses. In B0\nd,s \u2212B0\nd,s mixing then the class-2\noperators only contribute to B0\ns\u2212B0\ns mixing (up to md/ms\ncorrections) and would give hd \u226ahs. Thus one would ex-\npect a deviation from the SM in the CP violating phase\nof the Bs oscillation measurements but not in measure-\nments of sin 2\u03c61 from B \u2192J/\u03c8K0\nS. In contrast, class-1\noperators contribute universally to both (relative to the\nSM) and would give hd = hs and \u03c3d = \u03c3s in Eq. (25.2.1).\nIn many realistic models we would expect both class-1\nand class-2 NP contributions, so the predictions would be\nsomewhere in between: smaller e\ufb00ects in B0\nd \u2212B0\nd mixing\nthan in B0\ns \u2212B0\ns mixing, yet still nonzero.\nAn example of such GMFV NP is MSSM with U(2)3\n\ufb02avor symmetry (Barbieri, Isidori, Jones-Perez, Lodone,\nand Straub, 2011), which is broken by the light-quark\nmasses and the o\ufb00-diagonal CKM elements. Gluino medi-\nated amplitudes are the dominant non-standard e\ufb00ect in\n\u2206F = 2 observables and are of class-1. All class-2 contri-\nbutions are suppressed. As a result the size of the correc-\ntion is proportional to the CKM combination of the corre-\nsponding SM amplitude, a signature of class-1 MFV con-\ntributions. The proportionality coe\ufb03cients are the same\nfor the Bd and Bs systems, while it may be di\ufb00erent in\nthe kaon system \u2013 a signature of GMFV. Another GMFV\ncharacteristic is that new CP violating phases can only\nappear in the Bd and Bs systems. Since in the U(2)3\nsymmetric MSSM they would come from class-1 contri-\nbutions, the phase shifts would be universal. From the\nstill allowed deviations in SBd\u2192\u03c8K0\nS from sin 2\u03c61 Barbi-\neri, Isidori, Jones-Perez, Lodone, and Straub (2011) de-\nduce that 0.05 \u2272SBs\u2192\u03c8\u03c6 \u22720.2.\nThe expectation for the B \u2192Xs\u03b3 branching ratio are\nthe same as in cMFV, discussed in Section 25.2.2.3. For\nweak scale NP particles with masses of a few 100 GeV\nwe would thus expect a deviation in B \u2192Xs\u03b3 already\nin the present measurements, even though the particles\nonly enter in loops. On top of this, in GMFV there are\nadditional CP violating phases, which can lead to an en-\nhanced direct CP asymmetry in B \u2192Xd,s\u03b3. The CP\nviolating e\ufb00ects are also expected in D0 \u2212D0 mixing,\nwith arg(M12/\u039312) \u223cO(5%) for \u039bGMFV = 1 TeV (Ka-\ngan, Perez, Volansky, and Zupan, 2009). At present, the\nexperimental error is roughly twice as large as this ex-\npectation. There is also no clear prediction for the \ufb02avor\ndiagonal observable (g \u22122)\u00b5.\nThere are also other extensions of the MFV hypothesis,\nbeside GMFV. At the practical level the GMFV is equiva-\nlent to the Next-to-Minimal Flavor Violation (NMFV) hy-\npothesis, even though the original motivations were di\ufb00er-\nent. NMFV was put forward in (Agashe, Papucci, Perez,\nand Pirjol, 2005) by demanding that NP contributions\nonly roughly obey the CKM hierarchy, and in particu-\nlar can have O(1) new weak phases. The consequences of\nspurions that transform di\ufb00erently under GF than the SM\nYukawa coupling matrices have been worked out by Feld-\nmann and Mannel (2007). The MFV hypothesis has also\nbeen extended to the leptonic sector (MLFV) in (Cirigliano\nand Grinstein, 2006; Cirigliano, Grinstein, Isidori, and\nWise, 2005). In MLFV the most sensitive FCNC probe\nin the leptonic sector is \u00b5 \u2192e\u03b3, while \u03c4 \u2192\u00b5\u03b3 could\nbe suppressed below the sensitivity of future super \ufb02avor\nfactories.\n25.2.2.5 MFV SUSY\nLow energy supersymmetry (SUSY), where the superpart-\nners have \u223cTeV scale masses is one of the most popu-\nlar solutions to the hierarchy problem. Since this model\nis perturbative one can make reliable predictions. This\naids the popularity of SUSY among theorists. Already\nits minimal incarnation \u2013 the Minimal Supersymmetric\nStandard Model \u2013 has the salient features of gauge cou-\npling uni\ufb01cation and contains a viable dark matter can-\ndidate. The \u201cMinimal\u201d in the MSSM refers to the \ufb01eld\ncontent. Each SM particle obtains only one superpartner,\nand also the extension of the Higgs sector is minimal. How-\never, the \ufb02avor structure need not be minimal. The pa-\nrameters that describe the supersymmetry breaking, e.g.,\nthe squark masses and trilinear couplings can in principle\ncarry very di\ufb00erent \ufb02avor structures from the one seen in\nthe quark sector of the SM. In total there are 124 param-\neters in the MSSM, much more than the 19 parameters\nof the SM (Berger and Grossman, 2009; Dimopoulos and\nSutter, 1995; Haber, 2001). Of these parameters, 110 are\nin the \ufb02avor sector: 30 masses, 39 real mixing angles and\n41 phases. If all of the mixing angles and phases were\nO(1) this would lead to FCNCs that are orders of mag-\nnitude larger than the experimental bounds. The SUSY\nbreaking does have to be non-generic and further assump-\ntions about its structure are required in order to have\nan acceptable phenomenology. An attractive hypothesis is\nMFV, which we discussed in general terms in the previ-\nous subsections. The \ufb02avor breaking is assumed to arise\nonly from the Yukawa interactions (in this case from the\nsuperpotential), while the SUSY breaking is \ufb02avor blind.\nThis means that the squark masses can be written as\n\u02dcm2\nqL = \u02dcm2(a11 + b1YUY \u2020\nU + b2YDY \u2020\nD\nb3YDY \u2020\nDYUY \u2020\nU + b4YUY \u2020\nUYDY \u2020\nD + \u00b7 \u00b7 \u00b7 ),\n(25.2.17)\nand similarly for right-handed squarks. The coe\ufb03cients\na1, b1,2 are real from the hermiticity of the Hamiltonian,\n\n787\nwhile b3 and b4 can in general be complex and be sources\nof additional CP violating weak phases. For small tan \u03b2\nthese terms are negligible since YD is much smaller than\nYU. The values of the coe\ufb03cients are \ufb01xed by the model\nof the SUSY breaking. They can be zero at some high\nscale M, but are then generated due to the renormaliza-\ntion group running e\ufb00ect from this high scale to the low\nscale bi \u223c(1/4\u03c02) log(M 2/ \u02dcm2). In gauge-mediated SUSY\nbreaking the scale M would be given by the masses of the\nmessengers particles between the SUSY breaking sector\nand low energy sector.\nSince MFV SUSY is an example of the MFV theory our\ngeneral discussion in the previous two subsections applies.\nThe superpartners can be integrated out and matched\nonto the e\ufb00ective weak Hamiltonian. Because MFV MSSM\nis a concrete model the predictions can in fact be more pre-\ncise (for a review see, e.g., Isidori and Straub, 2012). For\ntan \u03b2 \u226b1 and/or if the \u00b5 parameter, the coupling of bi-\nlinear term of the MSSM Higgs sector, is large enough, the\nresulting low energy operator basis does not contain only\nthe SM operators. This means that in this limit it is not\na cMFV model. In the large tan \u03b2 limit the most sensitive\nobservables are the branching fractions for Bs \u2192\u00b5+\u00b5\u2212\nand B \u2192\u03c4\u03bd. For most of the parameter space B(B \u2192\u03c4\u03bd)\nis reduced by the charged Higgs correction compared to\nthe SM.\nAn interesting prediction of MFV MSSM is that the\ncontributions to \u2206md,s are always positive and increase\nthe oscillation frequency above the SM (Altmannshofer,\nBuras, and Guadagnoli, 2007). However, the NP e\ufb00ects\nin SJ/\u03c8 K0\nS and \u2206md/\u2206ms are very small and thus do\nnot disrupt the Unitarity Triangle of the SM. There are\nalso only small e\ufb00ects in Bs \u2192J/\u03c8\u03c6 expected. Simi-\nlarly, the contributions to D0 \u2212D0 mixing are small (Alt-\nmannshofer, Buras, Gori, Paradisi, and Straub, 2010). If\nthe \ufb02avor blind phases are nonzero, then EDMs and B(b \u2192\ns\u03b3) are the strongest constraints (Altmannshofer, Buras,\nand Paradisi, 2008). The dominant NP source in S\u03c6K0\nS\narises from the chromomagnetic operator CNP\n8g , and the ef-\nfects in S\u03c6K0\nS are expected to be signi\ufb01cantly larger than\nin S\u03b7\u2032K0\nS (both in the same direction), with even O(1)\ncorrections not too hard to achieve. The e\ufb00ect is also\nstrongly correlated with the size of the direct CP asym-\nmetry ACP (b \u2192s\u03b3), with an e\ufb00ect of up to 0.05 typical.\nThere is also a natural explanation of the small devia-\ntion from the SM observed in the muon-magnetic moment\n(g \u22122)\u00b5 as long as sleptons are not much heavier than\nsquarks (see e.g. Jegerlehner and Ny\ufb00eler, 2009).\n25.2.2.6 non-MFV SUSY\nIn investigations of SUSY models, strong assumptions\n(such as the MFV ansatz discussed in the previous section)\nare often imposed in order to reduce the large number of\nparameters introduced by the unknown SUSY breaking\nmechanism. A common motivation behind the assump-\ntions is to avoid an unwanted excess of CP violation and\nFCNC. However, by working within those assumptions,\none could potentially also miss a signal of SUSY particles.\nIn this section we follow a more model independent ap-\nproach \u2013 the mass insertion approximation (MIA) (Hall,\nKosteleck\u00b4y, and Raby, 1986). In this approach the \ufb02avor\no\ufb00-diagonal part of the squark mass matrix in the Super-\nCKM basis is parameterized by the mass insertion param-\neter, (\u03b4q\nAB)ij, where A, B denote the chirality (L, R) and\nq indicates the (u, d) type. Assuming that the o\ufb00-diagonal\nelements are smaller than the diagonal ones, the sfermion\npropagator can be expanded as\n\u27e8\u02dcqAi\u02dcq\u2217\nBj\u27e9= i(k21 \u2212\u02dcm21 \u2212\u02dcm2\u03b4q\nAB)\u22121\nij\n(25.2.18)\n\u2243\ni\u03b4ij\nk2 \u2212\u02dcm2 + i \u02dcm2(\u03b4q\nAB)ij\n(k2 \u2212\u02dcm2)2 + \u00b7 \u00b7 \u00b7 ,\nwhere 1 is the unit matrix and \u02dcm is the averaged squark\nmass, used also to normalize the o\ufb00-diagonal mass matrix\nelements, so that (\u03b4q\nAB)ij are dimensionless. In a general\nanalysis all the mass insertion parameters (\u03b4q\nAB)ij should\nbe taken into account and are then only constrained from\nvarious \ufb02avor experiments.\nThe B Factory observables are particularly sensitive\nto the down type mass insertion elements with ij = 13\n(b \u2192d transitions) and ij = 23 (b \u2192s transitions). We\nalso note that the source of \ufb02avor violation in this frame-\nwork comes from the loop diagrams with gluinos and neu-\ntralinos whereas the former is dominant due to the large\nstrong coupling constant.\nFor a general \ufb02avor structure signi\ufb01cant excesses in\nFCNC and CP violation are possible for various B Factory\nobservables. The non-observation of large deviations from\nthe SM therefore stringently constrains the mass insertion\nparameters. As an example let us take the (\u03b4d\nAB)13 mass\ninsertions. These are constrained by the \u2206md and sin 2\u03c61\nmeasurements. The m\u02dcg \u2243m\u02dcq = 500 GeV gluino contribu-\ntion to \u2206md normalized to the SM is (Gabbiani, Gabrielli,\nMasiero, and Silvestrini, 1996; Gabrielli and Khalil, 2003)\nM SUSY\n12\nM SM\n12\n\u2243\n1\n(VtbV \u2217\ntd)2\nn\n4.0 \u00d7 10\u22123 \u0002\n(\u03b4d\n23)2\nLL + (\u03b4d\n23)2\nRR\n\u0003\n+ 8.1 \u00d7 10\u22122 \u0002\n(\u03b4d\n23)2\nLR + (\u03b4d\n23)2\nRL\n\u0003\n\u22121.3 \u00d7 10\u22121 \u0002\n(\u03b4d\n23)LR(\u03b4d\n23)RL\n\u0003\n\u22125.0 \u00d7 10\u22121 \u0002\n(\u03b4d\n23)LL(\u03b4d\n23)RR\n\u0003 o\n.\n(25.2.19)\nNote that in terms of observables one has\n\u2206md = 2|M SM\n12 + M SUSY\n12\n|,\n(25.2.20)\nSb\u2192c\u00afcs = \u2212Im\n\u0010M \u2217SM\n12\n+ M \u2217SUSY\n12\nM SM\n12 + M SUSY\n12\n\u00111/2\n.\n(25.2.21)\nThe resulting constraints following from the experi-\nmental world averages \u2206md = (0.510 \u00b1 0.004) ps\u22121 and\nSb\u2192c\u00afcs = 0.677 \u00b1 0.020 (see Section 17.5.2 and Sec-\ntion 17.6 for the experimental extraction of these values)\nare shown in Fig. 25.2.4 (top panels). We use VtbV \u2217\ntd =\n(8.7 \u00b1 0.8) \u00d7 10\u22123ei(0.41\u00b10.06), which is obtained in a simi-\nlar way as in Section 25.2.2.1 by using the unitarity condi-\ntion with VcbV \u2217\ncd and VubV \u2217\nud extracted from the tree level\n\n788\nRe(\u03b4d\n13)LL\nIm(\u03b4d\n13)LL\nPBF\nIm(\u03b4d\n13)LR\nRe(\u03b4d\n13)LR\nPBF\nRe(\u03b4d\n23)LR\nIm(\u03b4d\n23)LR\nPBF\nIm(\u03b4d\n23)RL\nRe(\u03b4d\n23)RL\nPBF\nFigure 25.2.4. Top: constraints on the down type ij = 13\nmass insertions from B0\nd \u2212B0\nd oscillation measurements at the\nB Factories. The dashed lines represent 3\u03c3 bounds from \u2206md\nand the solid lines from sin 2\u03c61. Bottom: constraints on the\ndown type ij = 23 mass insertions from the B(B \u2192Xs\u03b3) mea-\nsurement (dashed lines) and the time-dependent CP asymme-\ntry in the penguin-dominated B \u2192\u03c6K0\nS transition (solid line).\nThe colored regions are excluded at 1, 2 and 3 \u03c3 combining the\ncorresponding two measurements.\nprocesses. We assume that only one of four mass inser-\ntions is nonzero, and show the constraints on LL and LR\nmass insertions as representative examples. The RR and\nRL mass insertion have similar constraints, respectively.\nThe dashed lines show the constraints from \u2206md mea-\nsurements, while the solid lines show the constraints from\nthe latest sin 2\u03c61 measurement from the B Factories. One\n\ufb01nds that typically the chirality preserving mass inser-\ntions, (\u03b4d\n13)LL/RR <\n\u223c10\u22121, are less constrained than the\nchirality \ufb02ipping ones, (\u03b4d\n13)LR/RL <\n\u223c10\u22122, (for both their\nreal and imaginary parts).\nIn the lower panels of Fig. 25.2.4 we show the impact\nthat the B Factory measurements of the B \u2192Xs\u03b3 branch-\ning ratio have on the chirality \ufb02ipping (AB = LR/RL)\nmass insertions for b \u2192s transitions. Again, the con-\nstraints are at the O(0.01) level. The (\u03b4d\nAB)23 mass in-\nsertions are also constrained by the B0\ns \u2212B0\ns oscillation\nmeasurement. However, as we show below, for the case\nof AB = LR/RL the chiral enhancement makes the B \u2192\nXs\u03b3 constraints much stronger than the ones from B0\ns\u2212B0\ns\noscillations.\nThe gluino contribution to the b \u2192s (\u2206B = 1)\ntransition is described by the following e\ufb00ective Hamil-\ntonian (Khalil and Kou, 2003)\nH\u2206B=1\ne\ufb00\n= \u2212GF\n\u221a\n2 VtbV \u2217\nts\n\" 6\nX\ni=3\nCiOi\n(25.2.22)\n+ C\u03b3O\u03b3 + CgOg +\n6\nX\ni=3\n\u02dcCi \u02dcOi + \u02dcC\u03b3 \u02dcO\u03b3 + \u02dcCg \u02dcOg\n#\n,\nwith\nO3/4 =\n\u0000s\u03b1/\u03b1b\u03b1/\u03b2\n\u0001\nV \u2212A\n\u0000s\u03b2/\u03b2s\u03b2/\u03b1\n\u0001\nV \u2212A, (25.2.23)\nO5/6 =\n\u0000s\u03b1/\u03b1b\u03b1/\u03b2\n\u0001\nV \u2212A\n\u0000s\u03b2/\u03b2s\u03b2/\u03b1)V +A, (25.2.24)\nO\u03b3 = \u22121\n3\ne\n4\u03c02 mb\n\u0000s\u03b1\u03c3\u00b5\u03bdPRb\u03b1\n\u0001\nF\u00b5\u03bd,\n(25.2.25)\nOg = gs\n4\u03c02 mb\n\u0000s\u03b1\u03c3\u00b5\u03bdPRT A\n\u03b1\u03b2b\u03b2\n\u0001\nGA\n\u00b5\u03bd,\n(25.2.26)\nwhere the Dirac structure of four-fermion operators is\n\u0000sb\n\u0001\nV \u2212A\n\u0000ss\n\u0001\nV \u2213A = 4\n\u0000s\u03b3\u00b5PLb\n\u0001\u0000s\u03b3\u00b5PRs\n\u0001\n, and the sum-\nmation over the color indices \u03b1, \u03b2 is understood. The terms\nwith a tilde are obtained from Ci,g and Oi,g through a\nL \u2194R replacement. The B \u2192Xs\u03b3 branching fraction\nreceives SUSY contributions mainly from O\u03b3, \u02dcO\u03b3, \u02dcOg and\nOg. These dimension 5 operators are chirality \ufb02ipping \u2013\nthe external b and s quark \ufb01elds have di\ufb00erent chiralities.\nIn the SM, the W boson couples only to the left-handed\nfermions (V \u2212A current) so that the chirality \ufb02ip comes\nfrom the quark mass insertion on the external quark \ufb01elds.\nThe O\u03b3 and Og operators are thus suppressed in the SM by\none power of mb/mW . In non-MFV SUSY, on the other\nhand, there are additional interactions that can induce\nthe chirality \ufb02ip inside the loop. The mb factor is then re-\nplaced by the internal heavy particle masses and the chi-\nrality \ufb02ipping coupling (in MIA these will be (\u03b4q\nLR)ij). The\nresulting Wilson coe\ufb03cients from the gluino-squark loop\nare (Gabbiani, Gabrielli, Masiero, and Silvestrini, 1996):\nC\u02dcg\n\u03b3(MS) = \u2212\n\u221a\n2\u03b1S\u03c0\n2GF VtbV \u2217\ntsm2\n\u02dcq\n(25.2.27)\n\u00d7\n(\n(\u03b4d\nLR)23\nm\u02dcg\nmb\n8\n3M1(x) + (\u03b4d\nLL)23\n8\n3M3(x)\n)\n.\nC\u02dcg\ng(MS) = \u2212\n\u221a\n2\u03b1S\u03c0\n2GF VtbV \u2217\ntsm2\n\u02dcq\n(25.2.28)\n\u00d7\n(\n(\u03b4d\nLR)23\nm\u02dcg\nmb\n\u00141\n3M1(x) + 3M2(x)\n\u0015\n+(\u03b4d\nLL)23\n\u00141\n3M3(x) + 3M4(x)\n\u0015 )\n.\nThe \u02dcC\u03b3 and \u02dcCg coe\ufb03cients are obtained by making the\nL \u2194R replacement. One can see that indeed the terms\nwith the chirality-\ufb02ipping LR/RL mass insertions are en-\nhanced by the m\u02dcg/mb factor. This term could potentially\ninduce large contributions to b \u2192s penguin transition\nprocesses. On the bottom panels of Fig 25.2.4, we present\nthe constraints on the LR and RL mass insertions (dashed\nline) from the B(B \u2192Xs\u03b3) measurement. The di\ufb00erence\nbetween the two cases comes from the fact that the LR\ncontribution adds coherently to the SM at the amplitude\nlevel while the RL contribution does not interfere with the\nSM and adds in the amplitudes squared.\n\n789\nThe corrections to the chromo-magnetic operators Og\nand \u02dcOg can also have signi\ufb01cant e\ufb00ects on the hadronic B\ndecays. An important additional constraint on (\u03b4d\nLR/RL)23\nis thus obtained from the penguin-dominated B \u2192\u03c6K0\nS\ndecay. In the SM, the time dependent CP asymmetry for\nthis channel is the same as the one obtained from the\ndecay B \u2192c\u00afcK0\nS (where c\u00afc represents any charmonium\nstate such as J/\u03c8). If S\u03c6K0\nS \u0338= Sc\u00afcK0\nS is found, this would\nbe an indication of new physics. The deviation needs to be\nlarger than the theoretical errors on the di\ufb00erence. A list\nof estimates for the theory errors on S\u03c6K0\nS \u2212Sc\u00afcK0\nS and\nfor other b \u2192s penguin transition dominated channels,\ne.g., S\u03b7\u2032K0\nS, etc., can be found in (Zupan, 2007). Histori-\ncally there was an indication for a deviation from the SM,\nhowever by now, the deviation has diminished and the\ncurrent world averages (see Section 17.6.6 for details of\nexperimental extraction of these values),\nS\u03c6K0\nS \u2212Sc\u00afcK0\nS =\n0.06 \u00b1 0.12,\n(25.2.29)\nS\u03b7\u2032K0\nS \u2212Sc\u00afcK0\nS = \u22120.09 \u00b1 0.07,\n(25.2.30)\nare consistent with the SM, though the experimental er-\nrors are still relatively large. The constraints on the LR\nand RL mass insertions are nontrivial and are comparable\nto the ones following from B \u2192Xs\u03b3, see lower panels in\nFig. 25.2.4. The regions excluded by combining the mea-\nsurements of the B \u2192Xs\u03b3 branching fraction and S\u03c6K0\nS\nare also shown in Fig. 25.2.4 as colored regions.\nFurther constraints on the corresponding mass inser-\ntions can be obtained from the other loop-induced observ-\nables. For instance, D0\u2212D0 mixing constrains the up-type\nmass insertions (\u03b4u\nAB)12, while (g\u22122)\u00b5 constrains the slep-\nton mass insertions (\u03b4l\nAB)22, see, e.g., (Chang, Chang, Ke-\nung, Sinha, and Sinha, 2002; Chankowski, Lebedev, and\nPokorski, 2005; Gabbiani, Gabrielli, Masiero, and Silves-\ntrini, 1996; Hisano and Tobe, 2001).\n25.2.2.7 SUSY Alignment models\nThe measurement of D0 \u2212D0 mixing at Belle and BABAR\nhad important implications for the \ufb02avor structure of the\nMSSM (Ciuchini et al., 2007; Nir, 2007a,b). The squark\ncontributions to \u2206F = 2 processes involving the \ufb01rst two\ngenerations, i.e. to K0\u2212K0 and to D0\u2212D0 mixing, have to\nbe su\ufb03ciently suppressed in order not to generate contri-\nbutions to the mixing larger than what is experimentally\nobserved. The contributions arising from the box diagram\nwith a gluino and the \ufb01rst two generation squark doublets\n\u02dcQL1,2 are given by, see e.g. (Raz, 2002),\nM D\n12 \u221d\n1\nm2\n\u02dcu\n(\u2206m2\n\u02dcu)2\nm4\n\u02dcu\n(Ku\n21Ku\u2217\n11 )2,\n(25.2.31)\nM K\n12 \u221d\n1\nm2\n\u02dcd\n(\u2206m2\n\u02dcd)2\nm4\n\u02dcd\n(Kd\n21\u2217Kd\n11)2.\n(25.2.32)\nHere m\u02dcu, \u02dcd are the averaged squark masses of the \ufb01rst\ntwo up and down generation squarks, \u2206m2\n\u02dcu, \u02dcd are the cor-\nresponding mass squared di\ufb00erences, while Ku(d) is the\nmixing matrix for the gluino coupling to left-handed up\n(down) quarks and the squark partners. The proportion-\nality coe\ufb03cients depend on the D and K decay constants,\nthe bag parameters and a function of m\u02dcq/m\u02dcu, \u02dcd.\nThere are three generic ways how these contributions\ncan be suppressed. The \ufb01rst possibility is that the \ufb01rst\ntwo generation squarks are heavy, m\u02dcq \u226b1 TeV. Since\nthey contribute to dimension 6 operators, these contribu-\ntions scale as \u221d1/m2\n\u02dcq and become irrelevant when squarks\nare much heavier than the weak scale. The second pos-\nsibility is that the squarks are degenerate, i.e. that the\nmass splitting between the \ufb01rst two generations is small,\n\u2206m2\n\u02dcq \u226am2\n\u02dcq. If they were exactly degenerate, one would\nbe free to choose the \ufb02avor basis for squarks anyway one\nwants \u2013 in particular to coincide with the mass basis of\n\ufb01rst two generation quarks. The \ufb02avor breaking e\ufb00ects\nthus need to be proportional to the splitting between the\nsquarks. Finally, the squarks could be aligned with the\nquarks, so that the mass eigenstate basis for squarks al-\nmost coincides with the mass eigenstate basis of quarks\nand thus Kd,u\n21 \u226a1.\nAlignment naturally arises in Froggatt-Nielsen type\n\ufb02avor models of squark masses (Leurer, Nir, and Seiberg,\n1994; Nir and Seiberg, 1993). For left-handed squarks there\nis also a relation between the matrices that diagonalize up\nand down squarks. Up to corrections of m2\nc/m2\n\u02dcq \u223cO(10\u22125)\none has\nKuKd\u2020 = VCKM.\n(25.2.33)\nFor the mixing between the \ufb01rst two generations this means\nthat\nKu\n21 \u2212Kd\n21 \u2243sin \u03b8C = 0.23.\n(25.2.34)\nTherefore the 21 entries in the quark-squark-gluino cou-\npling matrices cannot be smaller than the mixing between\nthe \ufb01rst two generations in the SM. If squarks have masses\nof around 1 TeV and non-degenerate this is at odds with\neither K0 \u2212K0 mixing and D0 \u2212D0 mixing. Barring can-\ncellations there are two possibilities. The \ufb01rst one is that\nsquarks are quasi-degenerate. The level of degeneracy re-\nquired is \u2206m\u02dcq/m\u02dcq \u22720.12 (Gedalia, Grossman, Nir, and\nPerez, 2009; Nir, 2007b). The other option is that squarks\nare heavy. If one sets Ku\n21 = 0.23 and Kd\n12 \u22430 as in the\noriginal alignment model by Nir and Seiberg (1993), then\nm\u02dcq \u22732 TeV, and much heavier, if Kd\n12 is nonzero. We thus,\ncan state model-independently that barring cancellations,\nif the squarks are light enough to be observed at the LHC,\nthen they must be quasi-degenerate. Note that, in order\nto reach this conclusion the experimental information on\nD0 \u2212D0 mixing parameters provided by the B Factories\n(in particular that they are small, x, y \u223cO(1%)), was es-\nsential. In the original alignment model the gluino-squark\nloop induced FCNCs are absent in the down quark sector.\nTherefore among the observables in Table 25.2.2 the only\nplace we would expect deviations is D0 \u2212D0 mixing.\n\n790\n25.2.2.8 Randall-Sundrum models of \ufb02avor\nThe Randall-Sundrum (RS) models of \ufb02avor have an am-\nbitious goal. They strive to simultaneously solve the hi-\nerarchy problem, the \ufb02avor problem of new physics and\nexplain the \ufb02avor structure in the SM. The hierarchy prob-\nlem refers to the Planck scale \u223c1019 GeV being so much\nbigger than the electroweak scale \u223c1 TeV. The \ufb02avor\nproblem of new physics is that new physics at 1 TeV\n(which solves the hierarchy problem) must not enhance\nFCNCs above the SM level. At the same time the RS\nmodels of \ufb02avor also provide an explanation for the \ufb02a-\nvor structure in the Standard Model \u2013 the origin of the\nhierarchy of masses and mixing \u2013 through localization of\nquark \ufb01elds in the 5th dimension (Gherghetta and Po-\nmarol, 2000; Grossman and Neubert, 2000).\nThe RS models are extra dimensional models where a\nslice of 5-dimensional (5D) space-time (bulk) is truncated\nby \ufb02at 4-dimensional boundaries \u2013 the two 4-dimensional\n(4D) branes. The Planck brane is on the UV side of the\nbulk, while the TeV brane is on the IR side of the bulk.\nThis setup results in a warped metric for the bulk (Randall\nand Sundrum, 1999)\nds2 = e\u22122krc|\u03c6|\u03b7\u00b5\u03bddx\u00b5dx\u03bd \u2212r2\ncd\u03c62,\n(25.2.35)\nwhere k is the 5D curvature scale, rc the compacti\ufb01cation\nradius, and \u03c6 \u2208[\u2212\u03c0, \u03c0] the coordinate along the 5th di-\nmension. The hierarchy problem is solved by the presence\nof the warp factor e\u22122krc|\u03c6|, which suppresses the funda-\nmental Planck scale \u223c1019 GeV down to the weak scale\n\u223c1 TeV for krc \u224812.\nIn the initial RS models all the SM \ufb01elds were as-\nsumed to be localized on the IR brane and only gravity\npropagated in the bulk (Davoudiasl, Hewett, and Rizzo,\n2000). This immediately lead to phenomenological prob-\nlems, because the cut-o\ufb00of the e\ufb00ective 4D theory is also\nwarped down to TeV scale. A viable model is obtained, if\nthe fermions and gauge bosons are allowed to propagate\nin the bulk, while only the Higgs boson is localized on the\nIR brane. The 5D pro\ufb01les of the SM fermions (the zero\nmodes) have an exponential form\nf (0)\ni\n\u223ce(1/2\u2212ci)krc\u03c6.\n(25.2.36)\nThe light fermions have bulk mass parameters ci > 1/2,\nand are thus localized near the Planck brane. This has\ntwo bene\ufb01cial consequences. On one hand it suppresses\nFCNCs due to virtual exchanges of Kaluza-Klein (KK)\nstates \u2013 the excitations of the SM \ufb01elds that arise because\nof the compact extra dimension. The suppression is due\nto di\ufb00erent localizations of zero mode fermions, that peak\nnear the UV brane, and KK modes that peak near the\nIR brane. Therefore there is only a small overlap between\nthe two (Gherghetta and Pomarol, 2000). Since the Higgs\nboson is localized on the IR brane this also explains the\nsmallness of the masses of UV localized light fermions \u2013\nit is due to the fact that they have only a small overlap\nwith the Higgs wave function. The 4D Yukawa coupling\nmatrices are given by\n(Y 4D\nu,d )ij = (Y 5D\nu,d )ijfQifuj,dj,\n(25.2.37)\nwith fQi (fuj,dj) the values of wave functions for the left-\nhanded (right-handed) fermions at the IR brane, where\nthe Higgs is situated, cf. Eq. (25.2.36). The hierarchy of\nthe SM quark masses is naturally obtained for O(1) val-\nues of 5D Yukawa parameters (Y 5D\nu,d )ij and values of ci,\nwhere an order unity change in ci results in an exponential\nchange in the value of quark masses (Gherghetta and Po-\nmarol, 2000; Grossman and Neubert, 2000; Huber, 2003).\nThe zero mode (i.e. SM) gluons and photons have\n\ufb02at wave functions in the \u03c6 direction due to unbroken\nSU(3)C \u00d7U(1)EM gauge invariance. The Z and W \u00b1 wave\nfunctions, on the other hand, are distorted near the IR\nbrane, since electroweak symmetry is spontaneously bro-\nken. This generates tree level FCNCs mediated by the Z\nand the KK gauge bosons. This is in contrast to the SM,\nwhere due to the GIM mechanism the FCNCs arise only at\nthe one loop level. Still, the FCNCs in the RS models are\nsuppressed despite the fact that they arise at tree level.\nThe reason is that the light quarks are localized at the UV\nbrane, while both the KK modes and the distortion of the\nZ shape function are all localized near the IR brane. The\nFCNCs are then suppressed by the small wave function\noverlaps. This so-called \u201cRS-GIM mechanism\u201d su\ufb03ces to\navoid disastrously large FCNCs, but with some tension in\nthe kaon sector (Agashe, Perez, and Soni, 2004).\nThe above setup has several phenomenological impli-\ncations. Because the SM gauge bosons and fermions mix\nwith the corresponding KK modes, the CKM matrix is no\nlonger unitary. The corrections to CKM unitarity are of\norder O(v2/m2\nKK). For KK masses in the few TeV range\nthese corrections are thus very small, at percent level or\nsmaller.\nEasier to observe are e\ufb00ects due to additional \ufb02avor\nand CP violating sources in the model. The 5D mass ma-\ntrices CQ, Cu, Cd have 18 new mixing angles and 9 com-\nplex phases beyond the SM Yukawa couplings (Agashe,\nPerez, and Soni, 2005). The new CP violating weak phases\ncan a\ufb00ect low energy CP violating observables. For a low\nKK mass scale, mKK \u22723 TeV, the tree level KK gluon ex-\nchanges lead to contributions to B0\nd\u2212B0\nd and B0\ns \u2212B0\ns mix-\ning that are roughly of the same size as the SM contribu-\ntions, but with arbitrary weak phases (Agashe, Perez, and\nSoni, 2005). The possibility of such large contributions to\nthe B0\nd\u2212B0\nd mixing was excluded by the B Factories, while\nlarge phases in B0\ns \u2212B0\ns mixing are severely constrained by\nthe LHCb results. For K0\u2212K0 mixing by far the most im-\nportant is the generation of operators with the left-right\n(LR) chiral structure from KK gluon exchanges. These\nare enhanced by the renormalization group running and\nby chirally enhanced matrix elements. They give a contri-\nbution that is a factor 140 larger than the SM LL opera-\ntor, if the KK scale is around 3 TeV (Bauer, Casagrande,\nHaisch, and Neubert, 2010; Blanke, Buras, Duling, Gori,\nand Weiler, 2009; Casagrande, Goertz, Haisch, Neubert,\nand Pfoh, 2008; Csaki, Falkowski, and Weiler, 2008).\nThe KK masses below 3 TeV would be allowed by the\nRS models with additional custodial symmetry which can\nsatisfy the electroweak precision data constraints. (Agashe,\nContino, Da Rold, and Pomarol, 2006; Agashe, Delgado,\n\n791\nMay, and Sundrum, 2003; Csaki, Grojean, Pilo, and Tern-\ning, 2004). In contrast the data on \u03f5K imply a generic\nlower bound on MKK of roughly 20 TeV for anarchic 5D\nmasses ci with O(1) coe\ufb03cients (Csaki, Falkowski, and\nWeiler, 2008). With modest \ufb01ne tuning KK mass scales\nof 2 to 3 TeV are still allowed (Blanke, Buras, Duling,\nGori, and Weiler, 2009), or if additional \ufb02avor symme-\ntries are introduced in the 5D Yukawa coupling matrices\n(Cacciapaglia et al., 2008; Csaki, Falkowski, and Weiler,\n2009; Csaki, Perez, Surujon, and Weiler, 2010; Fitzpatrick,\nPerez, and Randall, 2007). Constraints from K0\u2212K0 mix-\ning are also reduced in \u201csoft wall\u201d RS models, where the\nIR brane is removed and the Higgs is free to propagate in\nthe bulk (Archer, Huber, and Jager, 2011).\nIn RS models there are also potential e\ufb00ects in \u2206F = 1\nmodes (Bauer, Casagrande, Haisch, and Neubert, 2010;\nBlanke, Buras, Duling, Gori, and Weiler, 2009). Rare\nBs,d \u2192\u00b5+\u00b5\u2212and Bs,d \u2192Xs,d\u03bd\u00af\u03bd are not a\ufb00ected much\nand remain SM like, with the corrections to the branching\nfractions below 15%. Larger e\ufb00ects in B(B \u2192Xs\u03b3) are in\nprinciple possible from contributions to dipole operators\nfor a somewhat tuned parameter set, which however, are\nexcluded by the data from B Factories. The contributions\nto EDMs are also generically large, about a factor 20 above\nthe present experimental bounds, leading to additional\nconstraints on RS parameter space. The branching frac-\ntions B(K \u2192\u03c00\u03bd\u00af\u03bd) and B(K+ \u2192\u03c0+\u03bd\u00af\u03bd) can be enhanced\nby a factor \u223c2 compared to the SM, however simultane-\nous enhancements of SBs\u2192J/\u03c8 \u03c6 and K \u2192\u03c0\u03bd\u00af\u03bd branching\nratios are not likely. The corrections to the CKM matrix\nare dominated by the e\ufb00ects due to the mixing with the\nKK gauge bosons. The deviations from the SM are small:\neven for the largest e\ufb00ects for the CKM elements involv-\ning third generation quarks, they can be up to 1 \u22122%.\nModest e\ufb00ects at the order of O(5%) are expected on\nSB\u2192\u03c6K0\nS and other b \u2192s penguin transitions (Agashe,\nPerez, and Soni, 2005; Bauer, Casagrande, Haisch, and\nNeubert, 2010). The constraints from Z \u2192b\u00afb, \u03f5K and\nB0 \u2212B0 mixing also su\ufb03ce to predict the mass di\ufb00erence\nin D0 \u2212D0 mixing to be not much larger then what is\nobserved, however a signi\ufb01cant spread in the CP violat-\ning mixing phase is possible, with the bulk of the predic-\ntions on the phase | arg(M D\n12/\u0393D\n12)| \u227290\u25e6. The B Factories\nconstraints from D0 \u2212D0 mixing are thus nontrivial and\nexclude a signi\ufb01cant part of the parameter space (Bauer,\nCasagrande, Haisch, and Neubert, 2010). The corrections\nto B \u2192\u03c4\u03bd can be at most 1% (Bauer, Casagrande, Haisch,\nand Neubert, 2010). The \ufb01rst complete calculation of one\nloop contributions to (g \u22122)\u00b5 was completed recently by\nBeneke, Dey, and Rohrwild (2012), and the result is about\nan order of magnitude below the present experimental er-\nror.\n25.2.2.9 Little Higgs models\nThe Little Higgs models present another direction for a\npotential solution to the hierarchy problem (for a pedagog-\nical review see Schmaltz and Tucker-Smith, 2005). We fo-\ncus on a particular model \u2013 the Littlest Higgs Model with\nT-parity (Cheng and Low, 2003, 2004; Low, 2004) \u2013 whose\n\ufb02avor structure was studied in detail by the Munich group\n(Bigi, Blanke, Buras, and Recksiegel, 2009; Blanke, Buras,\nDuling, Poschenrieder, and Tarantino, 2007; Blanke, Buras,\nDuling, Recksiegel, and Tarantino, 2010; Blanke et al.,\n2007, 2006; Blanke, Buras, Recksiegel, and Tarantino, 2008;\nBlanke, Buras, Recksiegel, Tarantino, and Uhlig, 2007a,b)\nand supplemented by Goto, Okada, and Yamamoto (2009)\nand by del Aguila, Illana, and Jenkins (2009).\nThe Littlest Higgs Model with T-parity (LHT) has a\nrelatively small number of new parameters that describe\nthe \ufb02avor sector \u2013 10 in the quark sector (Blanke, Buras,\nDuling, Recksiegel, and Tarantino, 2010). The relevant op-\nerators in the e\ufb00ective weak Hamiltonian that are gener-\nated by integrating out NP contributions are the same as\nin the SM. The fact that the model has T-parity means\nthat the NP scale f can be quite low, f = 500 GeV. This\nis quite di\ufb00erent from for instance the RS models that\nwere described in the previous section (where even in the\nmodels with custodial protection the KK scale is in the\nrange of 2 \u22123 TeV). Another interesting di\ufb00erence with\nthe RS models is that the constraints from B \u2192Xs\u03b3 and\nneutron electric dipole moment are not very strong and\nare easily satis\ufb01ed.\nIn the LHT there are new \ufb02avor interactions beyond\nthe CKM matrix VCKM. These new interactions involve\nthe heavy gauge bosons W \u00b1\nH , ZH, AH which get emitted\nfrom the SM quarks when they convert to a mirror quark.\nThese interactions of mirror and SM quarks are described\nby the two 3 \u00d7 3 unitary mixing matrices VHd and VHu\nthat are related by V \u2020\nHuVHd = VCKM. This means that the\nFCNCs in down-quark and up-quark sectors are related.\nThe main phenomenological features of LHT contri-\nbutions in the \ufb02avor observables are as follows (Buras,\n2009). The rare B decays are SM-like to a good extend.\nFor instance Bs,d \u2192\u00b5+\u00b5\u2212can be enhanced by O(30%)\ncompared to the SM, where the largest corrections come\nfrom the T-even sector. Typical deviations in SJ/\u03c8\u03c6 are\nat the order of O(5\u221210%), with the details depending on\nthe spectrum of the mirror fermions. They are thus smaller\nthen in RS. Similar e\ufb00ects would be expected in sin 2\u03c61\ndetermination from B \u2192J/\u03c8K0\nS with the corrections to\na large extend uncorrelated with the ones in B0\ns \u2212B0\ns mix-\ning (Blanke, Buras, Recksiegel, and Tarantino, 2008). The\ncontributions to B(B \u2192Xs\u03b3) are relatively small, at the\norder of up to about 3% of the SM value, which is smaller\nthan the theoretical uncertainty on the SM prediction.\nThe corrections to B \u2192\u03c4\u03bd are very small since there are\nno tree level contributions. The e\ufb00ects in S\u03c6K0\nS are also\nexpected to be small, since both b \u2192sg and electroweak\npenguin corrections are not sizable.\nThe B(\u00b5 \u2192e\u03b3) can reach 2 \u00d7 10\u221211 so that some\n\ufb01ne tuning of the parameters is required to satisfy MEG\nbounds (Adam et al., 2013). Also, the contributions in\nthe lepton \ufb02avor violating decays, \u00b5\u2212e conversion, \u00b5\u2212\u2192\ne\u2212e+e\u2212, \u03c4\n\u2192\u00b5\u03b3, \u03c4\n\u21923\u00b5 clearly distinguish LHT\nfrom SUSY. The contributions to (g \u22122)\u00b5 are negligi-\nble (see (Jegerlehner and Ny\ufb00eler, 2009) and references\ntherein). There are CP violating contributions to the\n\n792\nD0 \u2212D0 mixing amplitudes. The weak phase in the mix-\ning can still be large (and would be even much larger if\nthe \u03f5K constraint is omitted). It can lead to e\ufb00ects in\nD0 \u2212D0 mixing that are of several percent, e.g. \u22120.02 \u2272\nSD\u2192K0\nS\u03c6 \u2272+0.01 (Bigi, Blanke, Buras, and Recksiegel,\n2009).\n25.2.3 Summary\nFlavor physics has a signi\ufb01cant potential to discover new\nphysics by its sensitivity to high energy scales through\nvirtual e\ufb00ects. At present, there is no solid experimental\nhint of an e\ufb00ect beyond the SM. Lacking any preferred\ntheoretical foundation for the observed \ufb02avor structure,\nan analysis of the new physics e\ufb00ects in low energy preci-\nsion observables must thus make use of well de\ufb01ned and\ncommonly agreed benchmark models. While clearly it is\nnot possible to cover all the possibilities, a large enough\nset of representative benchmark models gives a picture of\nwhat kind of e\ufb00ects are possible. Many of the currently\ndiscussed scenarios are already highly constrained or can\nbe strongly constrained at the currently planned experi-\nments.\nOne of the main motivations to extend the Standard\nModel with new particles with TeV masses is to solve\nthe hierarchy problem \u2013 to stabilize the electroweak scale\nagainst radiative corrections. The \ufb02avor structure in most\ncases is not \ufb01xed by the rationale behind the model and\nhence remains mostly arbitrary from the theoretical con-\nsiderations. Experimentally, on the other hand, the \ufb02avor\nstructure in the new physics sector is tightly constrained.\nThe legacy of the B Factories program is that in low en-\nergy \ufb02avor violating processes the dominant contributions\nare from the SM. The low energy e\ufb00ects of a viable new\nphysics model have to be minimally \ufb02avor violating, or at\nleast have to be close to this limit. In fact, mainly due to\nthe data of the two B Factories, the corners of phase space\nfor non-MFV e\ufb00ects in low energy processes have become\nvery sparse.\nBoth BABAR and Belle have performed a test of the\n\ufb02avor structure, in many cases at a precision level. In this\nrespect the two experiments have performed a similar task\nin the \ufb02avor sector as LEP did for the gauge couplings;\nstill we do not have any substantial hint for a crack in the\nstructure of the SM, neither in the gauge nor in the \ufb02avor\nsector.\nFuture experiments at both the energy as well as the\nintensity frontier will have an extended reach and a larger\nsensitivity. In particular, super \ufb02avor factories will re-\n\ufb01ne many of the measurements performed at BABAR and\nBelle and thus improve the reach for new physics. Com-\nplementary to this, there will be measurements of leptonic\nprocesses at dedicated experiments, focusing especially\non lepton-number and lepton-\ufb02avor violating processes.\nThese e\ufb00orts will be augmented further by experiments\nat the energy frontier, which will be mainly the LHC ex-\nperiments ATLAS and CMS for the next decade. A direct\ndiscovery of new degrees of freedom at the energy frontier\n\u2013 beyond the discovery of a single Higgs particle \u2013 will\nclearly have a signi\ufb01cant impact on our understanding of\n\ufb02avor physics in the future.\n\n793\nAppendix A\nGlossary of terms\nThis part of the book summarizes commonly used terms,\nabbreviations, quantities, and acronyms found elsewhere\nin the book as a quick reference. References to places\nwhere terms are \ufb01rst introduced have been made. Where\nappropriate the second cross reference is given to sections\nin which a term is described in more details.\nACC : The Belle aerogel Cherenkov counter (1.4.4; 2.2.3).\nAcoplanarity : The acoplanarity of a two-particle \ufb01nal\nstate is de\ufb01ned as \u03c62 \u2212\u03c61 \u2212\u03c0. The azimuthal angles of\nthe \ufb01nal state particles are \u03c6i, where i = 1, 2 (17.4.3).\nAWG : Analysis Working Group; a physics sub-group\nwithin the BABAR Collaboration (2.1).\nbasf : Belle Analysis and Simulation Framework (3.1).\nBDT : Boosted (or bagged) decision tree. This is an MVA\nclassi\ufb01cation algorithm used widely in the latter years of\ndata analysis at the B Factories (5; 4).\nBSM : Beyond the Standard Model (18.1; 25.2).\nCDC : The Belle central drift chamber (1.4.4; 2.2.2).\nCLEO Fisher : The CLEO Fisher discriminant formed\nof nine energy \ufb02ow cones. This has been widely used as\na variable to discriminate between B meson signal-like\nevents and light quark continuum background. Also see\nFisher discriminant (9.3).\nCKM matrix : Cabibbo-Kobayashi Maskawa quark mix-\ning matrix (1; 16).\nCM : Centre of mass (1.2.2).\nContinuum background : This is the term given to\nbackgrounds from e+e\u2212transitions to light fermion anti-\nfermion pairs in collisions. Typically continuum background\nrefers to light-quark pairs qq, where q = u, d, s, and c\n(2.2.5).\ncos \u03b8B : Cosine of the angle between beam axis and B\nmomentum in the \u03a5(4S) rest frame (9.3).\ncos \u03b8S : Cosine of the angle between sphericity axes of\nROE and B candidate (9.3).\ncos \u03b8T : Cosine of the angle between beam and B thrust\naxes (9.3).\nDAQ : Data acquisition (1.4.3.1; 2.2.7).\nDCH : The BABAR drift chamber (2.1; 2.2.2).\nDIRC : The BABAR detector of internally re\ufb02ected Che-\nrenkov light, used for charged particle identi\ufb01cation (in\nparticular the \u03c0/K separation) in the barrel region (1.4;\n2.2.3).\nECOC : Error-correcting output codes (5.2).\nECL : The Belle electromagnetic calorimeter (1.4.4.2; 2.2.4).\nEMC : The BABAR electromagnetic calorimeter (2.1; 2.2.4).\nEML : Extended maximum likelihood (11).\nExperiment : An Experiment, with an upper case \u201cE\u201d,\nis the name given in Belle to the di\ufb00erent data taking peri-\nods. BABAR analogy of an Experiment is a Run. Only odd\nnumbers were used for Experiments, there are 31 Belle\nExperiments. See also Run (3.2).\nF : Generic Fisher discriminant: a linear combination of\nvariables (4).\nFisher discriminant : A linear combination of variables\nwhich is often used to compute a variable to discriminate\nbetween signal-like B meson events and light quark con-\ntinuum background; see also CLEO Fisher (4).\nFPGA : Field-Programmable Gate Array, a con\ufb01gurable\nintegrated circuit (2.2.2).\nFOM : Figure of merit, a test statistic often used dur-\ning optimization (4.3).\nFSR : Final state radiation (17.4.4).\nHi : The ith Fox-Wolfram moments (9).\nhk\nl : Normalized Fox-Wolfram moments given by Eq. (9.5.2).\nHER : High energy ring (1.4.3.1).\nHQET : Heavy Quark E\ufb00ective Theory (17.1; 17.9.1.2).\nIFR : The instrumented \ufb02ux return of BABAR, used for\nK0\nL and muon detection (1.4.3.1; 2.2.5).\nIP : The interaction point (2.1).\nIR : The interaction region (1.3).\nISR : Initial state radiation (15.1.1).\nKLM : The instrumented \ufb02ux return of Belle, used for\nK0\nL and muon detection (1.4.4; 2.2.5).\nKSFW : Fisher discriminant: a linear combination of\nmodi\ufb01ed Fox-Wolfram moments given by Eq. (9.5.3).\n\n794\nLi : The ith \u2018monomial\u2019 corresponding to an angle-weighted\nenergy \ufb02ow variable given by Eq. (9.4.1).\nL1, L3 : The \ufb01rst (hardware-based) and the second (software-\nbased) trigger level, respectively (2.1; 2.2.6).\nLCSR : Light cone sum rule, a formulation of QCD sum\nrules speci\ufb01cally suited for the calculation of heavy-to-\nlight form factors. (17.1).\nLER : Low energy ring (1.4.3.1).\nLocal operator : In quantum \ufb01eld theory local opera-\ntors are the product of \ufb01eld operators evaluated at the\nsame space-time point (17.1.3).\nLQCD : Lattice QCD (17.1).\nLST : Limited Streamer Mode, the technology selected\nby BABAR to replace the whole IFR barrel because of a\ndramatic decrease in performance of the original RPCs\n(1.4; 2.2.5).\nLTDA : BABAR long-term data analysis system (3.7).\nMC : Monte Carlo (3.1).\nMFV : Minimal \ufb02avor violation model (25.2).\nML : Maximum likelihood (11).\nMLP : A multi-layer perceptron is a common type of\narti\ufb01cial neural network used in particle physics. Neural\nnetworks have been used widely at the B Factories, most\nnotably in terms of \ufb02avor tagging (4; 8).\nMSSM : Minimal super-symmetric standard model (25.2).\nMVA : A multi-variate analysis is the study of a multi-\ndimensional problem space in the context of discriminat-\ning between di\ufb00erent types of event. Practical demonstra-\ntions of the use of MVA techniques can be found through-\nout this book, in particular in the context of PID (4; 5; 9).\nNN : Neural Network : multi-layered combination of vari-\nables. See also MLP (4; 9).\nNP : \u201cNew physics\u201d, which is any physics not described\nby the Standard Model (2.2.6; 17.2).\nNRQCD : Non-relativistic QCD (17.1.1).\nOPE : Operator Product Expansion (17.1.1).\np.d.f. : Probability density function (7.4.4; 11.1).\nPenguin : Loop contribution mediating a \ufb02avour chang-\ning neutral current (7.4).\nPenguin pollution : Penguin contributions which carry\na weak phase di\ufb00erent form the tree contribution, thereby\nintroducing a \u201cpollution\u201d (i,e, hadronic uncertainties) into\nthe extraction of CKM phases. (17.4.4; 17.7).\nPID : Charged particle identi\ufb01cation (2.1; 2.2.3).\nPV : Primary Vertex (6.4).\nPlanarity : The planarity (or aplanarity) of the event\nis a measure of the transverse component of momentum\nof of the event plane. This is related ot the smallest eigen-\nvalue of the sphericity tensor \u03bb3, where the aplanarity A\nis 3\u03bb3/2. For a planar event A = 0. For an isotropic event\nA = 1/2 (17.4.3).\nQCDF : QCD Factorization (17.4; 17.9.1).\nQuasi-Two-Body : For a decay to a \ufb01nal state with on\nresonance and a long-lived particle e.g. B0 \u2192\u03c1+\u03c0\u2212, the\nquasi-two-body approximation is sometimes invoked. This\napproximation is the assumption that the resonance can\nbe treated as a particle with de\ufb01nite mass. In practice this\nmeans that any interference between the reconstructed\nresonance of interest and other amplitudes contributing\nto a same body \ufb01nal state is not explicitly accounted for\nin a \ufb01t to data using a Dalitz plot, but is treated as a sys-\ntematic e\ufb00ect, or if deemed appropriate neglected. This\napproximation is commonly used in the study of charm-\nless B decays (17.4).\nR : Signal-to-background likelihood ratio used by Belle\nand given by Eq. (9.5.11).\nRi : Normalized Fox-Wolfram moments (BABAR notation;\n9).\nRs0\nl , R00\nl\n: Modi\ufb01ed Fox-Wolfram moments (9).\nROE : Rest of the event: Particles found in the detec-\ntor that are not associated with the reconstructed signal\ncandidate (6.5).\nRPC : Resistive plate chamber, the technology selected\nby BABAR and Belle to instrument their muon detectors\n(1.4; 2.2.5).\nRun : A Run, with an upper case \u201cR\u201d, is the name given\nin BABAR to the di\ufb00erent data taking periods. An analogy\nof Run at Belle is an Experiment. There are seven BABAR\nRuns, each several month-long. See also Experiment (3.2).\nrun : A run, with a lower case \u201cr\u201d, is the basic unit of\nBABAR and Belle data collection. The full BABAR physics\ndataset contains more than 38,000 such runs (3.2).\nSCET : Soft Collinear E\ufb00ective Theory (17.4; 17.9.1.4).\nSFW : Fisher discriminant : linear combination of Fox-\n\n795\nWolfram moments given by Eq. (9.5.1).\nSM : Standard Model of Particle Physics (1).\nSNNS : Stuttgart Neural Network Simulator, an imple-\nmentation of a neural network algorithm (4).\nSpectator : A quark, which does not change its \ufb02avor\nin a weak decay process (17.4.4; 17.7)\nSOB : The so-called stand o\ufb00box of the BABAR DIRC\n(2.1).\nSphericity : Tensorial representation of energy \ufb02ow, given\nby Eq. 9.3.2,\nsPlot : The sPlot technique is an event re-weighting tech-\nnique that is used in order to project out \ufb01t components,\nsuch as signal or background. The technique was devel-\noped at the B Factories. This technique has often been\nused when presenting results from BABAR (11; 11.2.3).\nSPR : StatPatternRecognition, a ROOT-based package\nwith a number of implemented multivariate methods (4).\nStrong phase : A phase that is invariant under the op-\nerator CP (13.2.4).\nSVT : The BABAR silicon vertex tracker (2.1; 2.2.1).\nSVTRAD : The BABAR silicon vertex radiation moni-\ntoring system (2.2.1).\nSVD : The Belle silicon vertex detector (2.1; 2.2.1).\nThree-Body : Decay to a \ufb01nal state with three long-\nlived particles e.g. B+ \u2192\u03c0+\u03c0+\u03c0\u2212(9.4.2).\nThrust : Vectorial representation of energy \ufb02ow, given\nby Eq. 9.3.1.\nTree : Contribution to a decay which is mediated by Feyn-\nman diagrams without loops. (17.4.4; 17.7)\nTwo-Body : Decay to a \ufb01nal state with two long-lived\nparticles e.g. B0 \u2192\u03c0+\u03c0\u2212(7.1.1).\nTMVA : Toolkit for Multivariate Analysis, a ROOT-\nbased package with a number of implemented multivariate\nmethods (4.4.4; 4.5).\nTOF : The Belle time-of-\ufb02ight detector (1.4.4.1; 2.2.3).\nTwist : In quantum \ufb01eld theory the twist of an opera-\ntor is de\ufb01ned as the di\ufb00erence between its dimension and\nits spin (17.1.4.1).\n2HDM : Two-Higgs doublet model (17.10.2.1; 25.2).\nVM : Virtual Machine (3.7).\nWeak phase : A phase that changes sign under the op-\nerator CP (13.2.4).\n\n796\nAppendix B: The BABAR Collaboration author list\nB. Auberta, R. Baratea, D. Boutignya, F. Couderca, P. del Amo Sancheza, J.-M. Gaillarda, A. Hicheura,\nY. Karyotakisa, J. P. Leesa, V. Poireaua, X. Prudenta, P. Robbea, V. Tisseranda, A. Zghichea, E. Graugesb,\nJ. Garra Ticob, L. Lopezc,d, M. Martinellic,d, A. Palanoc,d, M. Pappagalloc,d, A. Pompilic,d, G. P. Chene, J. C. Chene,\nN. D. Qie, G. Ronge, P. Wange, Y. S. Zhue, G. Eigenf, B. Stuguf, L. Sunf, G. S. Abramsg, M. Battagliag, J. Beringerg,v,\nA. W. Borglandg, A. B. Breong, D. N. Browng, J. Button-Shaferg, R. N. Cahng, E. Charlesg, M. V. Chistiakovag,\nA. R. Clarkg, C. T. Dayg, M. Furmang, M. S. Gillg, Y. Groysmang, B. Hoobermang, R. G. Jacobseng, F. Jenseng,\nR. W. Kadelg, J. A. Kadykg, L. T. Kerthg, Yu. G. Kolomenskyg, J. F. Kralg, G. Kukartsevg, C. LeClercg, M. J. Leeg,\nM. E. Levig, G. Lynchg, A. M. Merchantg, L. M. Mirg, P. J. Oddoneg, T. J. Orimotog, I. L. Osipenkovg, E. Petigurag,\nM. Pripsteing, N. A. Roeg, A. Romosang, M. T. Ronan\u2020g, V. G. Shelkovg, A. Suzukig, K. Tackmanng, T. Tanabeg,\nD. Troostg, W. A. Wenzelg, M. Zismang, P. G. Bright-Thomash, K. E. Fordh, T. J. Harrisonh, A. J. Harth,\nC. M. Hawkesh, A. Kirkh, D. J. Knowlesh, S. E. Morganh, S. W. O\u2019Neale\u2020h, R. C. Pennyh, D. Smithh, N. Sonih,\nA. T. Watsonh, N. K. Watsonh, K. Goetzeni, T. Heldi, H. Kochi, M. Kunzei, B. Lewandowski\u2020i, M. Pelizaeusi,\nK. Petersi, H. Schmueckeri, T. Schroederi, M. Steinkei, A. Fellaj, E. Antoniolij, J. C. Andressk, J. T. Boydk,\nN. Chevalierk, W. N. Cottinghamk, N. Dycek, B. Fosterk, C. Mackayk, A. Massk, J. D. McFallk, D. Walkerk,\nD. Wallomk, K. Abel, D. J. Asgeirssonl, T. Cuhadar-Donszelmannl, C. Heartyl, N. S. Knechtl, T. S. Mattisonl,\nJ. A. McKennal, R. Y. Sol, D. Thiessenl, M. Barrettm, B. Camanzim, S. Jollym, A. Khanm, P. Kyberdm,\nA. K. McKemeym, M. Saleemm, D. J. Sherwoodm, L. Teodorescum, V. E. Blinovn,o,p, A. A. Botovn, A. D. Bukin\u2020n,p,\nA. R. Buzykaevn, V. P. Druzhininn,p, V. B. Golubevn,p, V. N. Ivanchenkon, A. A. Koroln,p, E. A. Kravchenkon,p,\nA. P. Onuchinn,o,p, S. I. Serednyakovn,p, Yu. I. Skovpenn,p, E. P. Solodovn,p, V. I. Telnovn,p, K. Yu. Todyshevn,p,\nA. N. Yushkovn, D. S. Bestq, M. Bondioliq, J. Boothq, M. Bruinsmaq, M. Chaoq, S. Curryq, I. Eschrichq, D. Kirkbyq,\nA. J. Lankfordq, M. Mandelkernq, E. C. Martinq, R. K. Mommsenq, J. Schultzq, D. P. Stokerq, G. Zioulasq, S. Abachir,\nK. Arisakar, C. Buchananr, S. Chunr, B. L. Hart\ufb01elr, H. Atmacans, B. Deys, S. D. Foulkess, J. W. Garys, J. Layters,\nF. Lius, O. Longs, E. Mullins, B. C. Shen\u2020s, G. M. Vitugs, K. Wangs, Z. Yasins, L. Zhangs, H. K. Hadavandt,\nE. J. Hillt, H. P. Paart, S. Rahatlout, U. Schwanket, V. Sharmat, J. W. Berryhillu, C. Campagnariu, A. Cunhau,\nB. Dahmesu, J. M. Flaniganu, M. Franco Sevillau, T. M. Hongu, D. Kovalskyiu, N. Kuznetsovau, S. L. Levyu, A. Luu,\nM. A. Mazuru, J. D. Richmanu, Y. Rozenu, W. Verkerkeu, C. A. Westu, T. W. Beckv, A. M. Eisnerv, C. J. Flaccov,\nA. A. Grillov, M. Grothev, C. A. Heuschv, J. Krosebergv, W. S. Lockmanv, A. J. Martinezv, G. Nesomv, T. Schalkv,\nR. E. Schmitzv, B. A. Schummv, A. Seidenv, E. Spencerv, P. Spradlinv, M. Turriv, W. Walkowiakv, L. Wangv,\nM. Wilderv, D. C. Williamsv, M. G. Wilsonv, L. O. Winstromv, D. S. Chaow, E. Chenw, C. H. Chengw, D. A. Dollw,\nM. P. Dorstenw, A. Dvoretskiiw, B. Echenardw, R. J. Erwinw, F. Fangw, K. T. Floodw, J. E. Hansonw, D. G. Hitlinw,\nS. Metzlerw, J. S. Minamoraw, I. Narskyw, P. Ongmongkolkulw, J. Oyangw, T. Piatenkow, F. C. Porterw,\nA. Y. Rakitinw, A. Rydw, A. Samuelw, S. Yangw, R. Y. Zhuw, R. Andreassenx, S. Devmalx, M. S. Dubrovinx,\nC. Fabbyx, T. L. Geldx, Z. Huardx, S. Jayatillekex, G. Mancinellix, B. T. Meadowsx, K. Mishrax, M. D. Sokolo\ufb00x,\nL. Sunx, T. Abey, E. A. Antillony, T. Barillariy, J. Beckery, F. Blancy, P. C. Bloomy, B. Broomery, S. Cheny,\nZ. C. Cliftony, I. M. Derringtony, J. Destreey, M. O. Dimay, E. Erdosy, S. Faheyy, W. T. Fordy, F. Gaedey, A. Gazy,\nJ. D. Gilmany, J. Hachtely, J. F. Hirschauery, D. R. Johnsony, A. Kreisely, A. K. Michaely, M. Nagely, U. Nauenbergy,\nA. Olivasy, H. Parky, A. Penzkofery, P. Rankiny, D. M. Rodriguezy, J. Royy, W. O. Ruddicky, S. Seny, J. G. Smithy,\nE. W. Thomasy, E. W. Tomassiniy, K. A. Ulmery, W. C. van Hoeky, D. L. Wagnery, S. R. Wagnery, C. G. Westy,\nJ. Zhangy, R. Ayadz, J. Blouwz, A. Chenz, E. A. Eckhartz, J. L. Hartonz, T. Huz, W. H. Tokiz, R. J. Wilsonz,\nF. Winklmeierz, Q. L. Zengz, D. Altenburgaa, A. Haukeaa, H. Jasperaa, T.M. Karbachaa, J. Merkelaa, A. Petzoldaa,\nB. Spaanaa, K. Wackeraa, T. Brandtab, J. Broseab, T. Colbergab, G. Dahlingerab, M. Dickoppab, P. Ecksteinab,\nH. Futterschneiderab, S. Kaiserab, M. J. Kobelab, R. Krauseab, W. F. Maderab, E. Malyab, R. M\u00a8uller-Pfe\ufb00erkornab,\nR. Nogowskiab, S. Ottoab, J. Schubertab, K. R. Schubertab, R. Schwierzab, J. E. Sundermannab, A. Volkab,\nL. Wildenab, L. Behrac, D. Bernardac, F. Brochardac, J. Cohen-Tanugiac, F. Dohouac, S. Ferragac, G. Fouqueac,\nF. Gastaldiac, E. Latourac, A. Mathieuac, P. Matriconac, P. Mora de Freitasac, C. Renardac, E. Roussotac, S. Schrenkac,\nS. T\u2019Jampensac, Ch. Thiebauxac, G. Vasileiadisac, M. Verderiac, A. Anjomshoaaad, R. Bernetad, P. J. Clarkad,\nD. R. Lavinad, F. Muheimad, S. Playferad, A. I. Robertsonad, J. E. Swainad, J. E. Watsonad, Y. Xiead, M. Falboae,\nD. Andreottiaf, M. Andreottiaf,ag, D. Bettoniaf, C. Bozziaf, R. Calabreseaf,ag, V. Carassitiaf, A. Cecchiaf, G. Cibinettoaf,\nA. Cotta Ramusinoaf, F. Evangelistiaf, E. Fioravantiaf, P. Franchiniaf, I. Garziaaf, L. Landiaf,ag, E. Luppiaf,ag,\nR. Malagutiaf, M. Muneratoaf,ag, M. Negriniaf, C. Padoanaf,ag, A. Petrellaaf, L. Piemonteseaf, V. Santoroaf,\nA. Sartiaf,ag, E. Treadwellah, F. Anulliai,ce, R. Baldini-Ferroliai, M. E. Biaginiai, A. Calcaterraai, G. Finocchiaroai,\nS. Martellottiai, P. Patteriai, I. M. Peruzziai,by, M. Piccoloai, M. Ramaai, R. de Sangroai, Y. Xieai, A. Zalloai,\nS. Bagnascoaj,ak, A. Buzzoaj, R. Capraaj,ak, R. Contriaj,ak, G. Crosettiaj,ak, E. Guidoaj,ak, M. Lo Vetereaj,ak,\nM. M. Macriaj, S. Minutoliaj, M. R. Mongeaj,ak, P. Musicoaj, S. Passaggioaj, F. C. Pastoreaj,ak, C. Patrignaniaj,ak,\n\n797\nM. G. Piaaj, E. Robuttiaj, A. Santroniaj,ak, S. Tosiaj,ak, B. Bhuyanal, V. Prasadal, S. Baileyam, G. Brandenburg\u2020am,\nK. S. Chaisanguanthumam, C. L. Leeam, M. Moriiam, E. Wonam, J. Wuam, A. J. Edwardsan, A. Adametzao,\nR. S. Dubitzkyao, U. Langeneggerao, J. Marksao, S. Schenkao, U. Uwerao, V. Kloseap, H. M. Lackerap,\nM. L. Aspinwallaq, W. Bhimjiaq, D. A. Bowermanaq, P. D. Daunceyaq, U. Egedeaq, R. L. Flackaq, J. R. Gaillardaq,\nN. J. W. Gunawardaneaq, G. W. Mortonaq, J .A. Nashaq, M. B. Nikolichaq, W. Panduro Vazquezaq, P. Sandersaq,\nD. Smithaq, G. P. Tayloraq, M. Tibbettsaq, P. K. Beheraar, X. Chaiar, M. J. Charlesar, G. J. Grenierar, R. Hamiltonar,\nS.-J. Leear, U. Mallikar, N. T. Meyerar, C. Chenas, J. Cochranas, H. B. Crawleyas, L. Dongas, V. Eygesas,\nP.-A. Fischeras, J. Lamsaas, W. T. Meyeras, S. Prellas, E. I. Rosenbergas, A. E. Rubinas, Y. Y. Gaoat, A. V. Gritsanat,\nZ. J. Guoat, C. K. Laeat, G. Schottau, J. N. Albertav, N. Arnaudav, C. Beigbederav, M. Benkebilav, D. Bretonav,\nR. Cizeronav, M. Davierav, D. Derkachav, S. D\u02c6uav, J. Firmino da Costaav, G. Grosdidierav, A. H\u00a8ockerav, S. Laplaceav,\nF. Le Diberderav, V. Lepeltier\u2020av, A. M. Lutzav, B. Malaescuav, J. Y. Niefav, T. C. Petersenav, S. Plaszczynskiav,\nS. Pruvotav, S. Rodierav, P. Roudeauav, M. H. Schuneav, J. Serranoav, V. Sordiniav,ce,cf, A. Stocchiav, V. Tocutav,\nS. Trincaz-Duvoidav, A. Valassiav, L. L. Wangav, G. Wormserav, R. M. Biontaaw, V. Brigljevi\u00b4caw, D. J. Langeaw,\nM. Muggeaw, M. C. Simaniaw, K. van Bibberaw, D. M. Wrightaw, I. Binghamax, J. P. Burkeax, M. Carrollax,\nC. A. Chavezax, J. P. Colemanax, P. Cookeax, I. J. Forsterax, J. R. Fryax, E. Gabathulerax, R. Gametax, M. Georgeax,\nD. E. Hutchcroftax, M. Kayax, S. McMahonax, A. Muirax, R. J. Parryax, D. J. Payneax, K. C. Scho\ufb01eldax,\nR. J. Sloaneax, P. Sutcli\ufb00eax, C. Touramanisax, D. E. Azzopardiay, G. Bellodiay, A. J. Bevanay, C. K. Clarkeay,\nC. M. Cormackay, F. Di Lodovicoay, P. Dixonay, K. A. Georgeay, W. Mengesay, D. Newman-Coburn\u2020ay,\nR. J. L. Potteray, R. Saccoay, H. W. Shorthouseay, M. Sigamaniay, P. Strotheray, P. B. Vidalay, M. I. Williamsay,\nC. L. Brownaz, G. Cowanaz, H. U. Flaecheraz, S. Georgeaz, M. G. Greenaz, D. A. Hopkinsaz, P. S. Jacksonaz,\nA. Kurupaz, C. E. Markeraz, P. McGrathaz, T. R. McMahonaz, S. Paramesvaranaz, F. Salvatoreaz, G. Vaitsasaz,\nM. A. Winteraz, A. C. Wrenaz, J. Bougherba, D. N. Brownba, C. L. Davisba, Y. Liba, J. Pavlovichba, A. G. Denigau,bb,\nM. Fritschbb, W. Gradlbb, K. Griessingerbb, A. Hafnerbb, E. Prencipebb, J. Allisonbc, K. E. Alwynbc, D. S. Baileybc,\nN. R. Barlowbc, R. J. Barlowbc, Y. M. Chiabc, C. L. Edgarbc, A. C. Fortibc, J. Fullwoodbc, P. A. Hartbc,\nM. C. Hodgkinsonbc, F. Jacksonbc, G. Jacksonbc, M. P. Kellybc, S. D. Kolyabc, G. D. La\ufb00ertybc, A. J. Lyonbc,\nM. T. Naisbitbc, N. Savvasbc, J. H. Weatherallbc, T. J. Westbc, J. C. Williamsbc, J. I. Yibc, J. Andersonbd, E. Behnbd,\nA. Farbinbd, B. Hamiltonbd, W. D. Hulsbergenbd, A. Jawaherybd, V. Lillardbd, D. A. Robertsbd, J. R. Schieckbd,\nJ. M. Tugglebd, G. Blaylockbe, C. Dallapiccolabe, S. S. Hertzbachbe, R. Ko\ufb02erbe, V. B. Koptchevbe, X. Libe,\nC. S. Linbe, T. B. Moorebe, E. Salvatibe, S. Saremibe, H. Staenglebe, S. Y. Willocqbe, J. Wittlinbe, R. Cowanbf,\nD. Dujmicbf, P. H. Fisherbf, S. W. Hendersonbf, K. Koenekebf, M. I. Langbf, G. Sciollabf, M. Spitznagelbf, F. Taylorbf,\nR. K. Yamamoto\u2020bf, M. Yibf, M. Zhaobf, Y. Zhengbf, D. I. Brittonbg, R. Cheaibbg, M. Klemettibg, D. J. J. Mangeolbg,\nS. E. Mclachlin\u2020bg, M. Milekbg, P. M. Patel\u2020bg, S. H. Robertsonbg, M. Schrambg, P. Biassonibh,bi, G. Cerizzabh,bi,\nP. Gandinibh,bi, F. Lannibh,bi, A. Lazzarobh,bi, V. Lombardobh,bi, N. Neribh, F. Palombobh,bi, R. Pellegrinibh,bi,\nS. Strackabh,bi, J. M. Bauerbj, M. Booke\u2020bj, L. Cremaldibj, V. Eschenburgbj, R. Kroegerbj, M. Reepbj, J. Reidybj,\nD. A. Sandersbj, P. Sonnekbj, D. J. Summersbj, H. W. Zhaobj, R. Godangbk, J. F. Arguinbl, M. Beaulieubl, S. Brunetbl,\nD. Cotebl, J. P. Martinbl, X. Nguyenbl, S. Sabikbl, R. Seitzbl, E. Sicardbl, M. Simardbl, P. Tarasbl, B. Viaudbl,\nA. Wochbl, V. Zacekbl, H. Nicholsonbm, N. Cavallobn, G. De Nardobn,bo, F. Fabozzibn, C. Gattobn, L. Listabn,\nD. Monorchiobn,bo, G. Onoratobn,bo, P. Paoluccibn, D. Piccolobn,bo, C. Sciaccabn,bo, M. A. Baakbp, H. Bultenbp,\nG. Ravenbp, H. L. Snoekbp, N. M. Casonbq, C. P. Jessopbq, K. J. Knoepfelbq, J. M. LoSeccobq, J. R. G. Alsmillerbr,\nT. A. Gabrielbr, T. Allmendingerbs, G. Benellibs, B. Braubs, L. A. Corwinbs, K. K. Ganbs, K. Honscheidbs,\nD. Hufnagelbs, H. Kaganbs, R. Kassbs, J. P. Morrisbs, A. M. Rahimibs, J. J. Regensburgerbs, D. S. Smithbs,\nR. Ter-Antonyanbs, Q. K. Wongbs, N. L. Blountbt, J. Braubt, R. Freybt, O. Igonkinabt, M. Iwasakibt, J. A. Kolbbt,\nM. Lubt, C. T. Potterbt, R. Rahmatbt, N. B. Sinevbt, D. Strombt, J. Strubebt, E. Torrencebt, E. Borsatobu,bv,\nG. Castellibu, F. Colecchiabu,bv, A. Crescentebu, F. Dal Corsobu, A. Dorigobu, C. Faninbu, E. Feltresibu,bv, F. Furanobu,\nN. Gagliardibu,bv, F. Galeazzibu,bv, M. Margonibu,bv, M. Marzollabu, G. Michelonbu,bv, M. Morandinbu, M. Posoccobu,\nM. Rotondobu, G. Simibu, F. Simonettobu,bv, P. Solagnabu, E. Stevanatobu, R. Stroilibu,bv, G. Tiozzobu, E. Torassabu,\nC. Vocibu,bv, S. Akarbw, P. Baillybw, E. Ben-Haimbw, M. Benayounbw, M. Bombenbw, G.R. Bonneaudbw, H. Briandbw,\nL. Del Buonobw, G. Calderinibw, J. Chauveaubw, P. Davidbw, J.-F. Genatbw, O. Hamonbw, M. J. J. Johnbw,\nH. Lebbolobw, Ph. Lerustebw, J. Lorybw, J. Malcl`esbw, G. Marchioribw, L. Martinbw, J. Ocarizbw, M. Pivkbw,\nJ. Prendkibw, L. Roosbw, S. Sittbw, J. Starkbw, G. Th\u00b4erinbw, C. De la Vaissi`erebw, A. Vallereaubw, S. Versill\u00b4ebw,\nB. Zhangbw, M. Biasinibx,by, R. Covarellibx,by, E. Manonibx, S. Pacettibx,by, S. Pennazzibx,by, M. Pioppibx,by, A. Rossibx,\nC. Angelinibz,ca, G. Batignanibz,ca, S. Bettarinibz,ca, F. Bosibz, F. Buccibz,ca, E. Campagnabz,ca, M. Carpinellibz,ca,\nG. Casarosabz,ca, R. Cencibz,ca, A. Cervellibz,ca, V. Del Gambabz,ca, F. Fortibz,ca, M. A. Giorgibz,ca, A. Lusianibz,cb,\nM. Morgantibz,ca, F. Morsanibz, B. Oberhofbz,ca, E. Paolonibz,ca, A. Perezbz, F. Ra\ufb00aellibz, G. Rizzobz,ca,\nF. Sandrellibz,ca, G. Triggianibz,ca, J. J. Walshbz,ca, M. Hairecc, D. Juddcc, K. Paickcc, L. Turnbullcc, D. E. Wagonercc,\nJ. Biesiadacd, N. Danielsoncd, P. Elmercd, R. E. Fernholzcd, Y. P. Laucd, C. Lucd, V. Miftakovcd, J. Olsencd,\n\n798\nD. Lopes Pegnacd, W. R. Sandscd, S. F. Scha\ufb00nercd, A. J. S. Smithcd, A. V. Telnovcd, A. Tumanovcd, E. W. Varnescd,\nE. Baracchinice,cf, F. Bellinice,cf, G. Cavotoce, A. D\u2019Orazioce,cf, E. Di Marcoce,cf, R. Faccinice,cf, F. Ferrarottoce,\nF. Ferronice,cf, K. Fratinice, M. Gasperoce,cf, P. D. Jacksonce,cf, E. Lamannace,cf, E. Leonardice, L. Li Gioice,cf,\nM. A. Mazzonice, S. Morgantice, G. Pireddace, F. Polcice,cf,av, D. del Rece,cf, F. Rengace,cf, F. Safai Tehranice,\nM. Serrace, C. Voenace, C. B\u00a8ungercg, S. Christcg, S. Dittrichcg, O. Gr\u00a8unbergcg, T. Hartmanncg, M. He\u00dfcg, T. Leddigcg,\nH. Schr\u00a8oder\u2020cg, C. Vo\u00dfcg, G. Wagnercg, R. Waldicg, T. Adyech, M. Blych, C. Brewch, B. Claxtonch, C. Condurachech,\nN. De Grootch, J. Dowdellch, B. Franekch, S. Galagederach, N. I. Geddesch, G. P. Gopalch, J. Kaych, J. Lidburych,\nS. Madanich, G. Markeych, E. O. Olaiyach, P. Olleych, S. Ricciardich, W. Roethelch, M. Wattch, F. F. Wilsonch,\nS. M. Xellach, R. Aleksanci, P. Besson\u2020ci, P. Bourgeoisci, P. Convertci, G. De Domenicoci, S. Emeryci, M. Escalierci,\nL. Esteveci, A. Gaidotci, S. F. Ganzhurci, Z. Georgetteci, P.-F. Giraudci, L. Gossetci, P. Gra\ufb03nci, G. Grazianici,\nG. Hamel de Monchenaultci, S. Herv\u00b4eci, M. Karolakci, W. Kozaneckici, M. Langerci, M. Legendreci, A. de Lesquenci,\nG. W. Londonci, V. Marquesci, B. Mayerci, P. Micoutci, J. P. Molsci, J. P. Moulyci, Y. Penichotci, J. Rolquinci,\nB. Serfassci, J. C. Toussaintci, M. Usseglioci, G. Vasseurci, Ch. Y`echeci, M. Zitoci, I. Adamcj, I. J. R. Aitchisoncj,\nM. T. Allencj, R. Akre\u2020cj, P. L. Anthonycj, D. Astoncj, T. Azemooncj, D. J. Bardcj, J. Barteltcj, R. Bartolduscj,\nP. Bechtlecj, J. Beclacj, R. Bell\u2020cj, J. F. Benitezcj, N. Bergercj, K. Bertschecj, E. Bloomcj, C. T. Boeheimcj,\nK. Bouldincj, A. M. Boyarskicj, R. F. Boycecj, M. Brownecj, O. L. Buchmuellercj, W. Burgesscj, Y. Caicj, C. Cartarocj,\nA. Ceseracciucj, R. Clauscj, M. R. Converycj, D. P. Coupalcj, W. W. Craddockcj, G. Cranecj, M. Cristinzianicj,\nS. DeBargercj, F. J. Deckercj, H. DeStaebler\u2020cj, J. C. Dingfeldercj, M. Donaldcj, J. Dorfancj, G. P. Dubois-Felsmanncj,\nW. Dunwoodiecj, M. Ebertcj, S. Ecklundcj, R. Ericksoncj, S. Fancj, R. C. Fieldcj, A. Fishercj, J. Foxcj, B. G. Fulsomcj,\nA. M. Gabareencj, I. Gaponenkocj, T. Glanzmancj, S. J. Gowdycj, M. T. Grahamcj, P. Greniercj, T. Hadigcj, V. Halyocj,\nG. Hallercj, J. Hamiltoncj, A. Hanushevskycj, A. Hasancj, T. Haascj, C. Hastcj, C. Heecj, T. Himelcj, T. Hryn\u2019ovacj,\nM. E. Hu\ufb00ercj, T. Hungcj, W. R. Innescj, R. Iversoncj, J. Kaminskicj, M. H. Kelseycj, H. Kimcj, P. Kimcj, D. Kharakhcj,\nM. L. Kociancj, A. Krasnykhcj, J. Krebscj, W. Kroegercj, A. Kulikovcj, N. Kuritacj, D. W. G. S. Leithcj, P. Lewiscj,\nS. Licj, J. Libbycj, D. Lindemanncj, B. Lindquistcj, V. L\u00a8uthcj, S. Luitzcj, H. L. Lynchcj, D. B. MacFarlanecj,\nH. Marsiskecj, M. McCullochcj, J. McDonaldcj, R. Melencj, S. Menkecj, R. Messner\u2020cj, S. Metcalfecj, L. J. Mosscj,\nR. Mountcj, D. R. Mullercj, H. Nealcj, D. Nelsoncj, S. Nelsoncj, M. Nordbycj, Y. Nosochkovcj, A. Novokhatskicj,\nC. P. O\u2019Gradycj, F. G. O\u2019Neillcj, I. Oftecj, V. E. Ozcancj, T. Pavelcj, A. Perazzocj, M. Perlcj, S. Petrakcj,\nM. Piemontesecj, S. Piersoncj, T. Pulliamcj, H. Quinncj, B. N. Ratcli\ufb00cj, S. Ratkovskycj, R. Reifcj, C. Rivettacj,\nR. Rodriguezcj, A. Roodmancj, A. A. Salnikovcj, O. H. Saxtoncj, T. Schietingercj, R. H. Schindlercj, H. Schwarzcj,\nJ. Schwieningcj, J. Seemancj, V. V. Serbocj, D. Smithcj, A. Snydercj, E. Soderstromcj, A. Sohacj, M. Stanekcj,\nJ. Stelzercj, D. Sucj, M. K. Sullivancj, S. Suncj, K. Suzukicj, S. K. Swaincj, H. A. Tanakacj, D. Teytelmancj,\nJ. M. Thompsoncj, J. S. Tinslaycj, A. Trunovcj, J. Turnercj, N. van Bakelcj, D. van Winklecj, J. Va\u2019vracj,\nA. P. Wagnercj, W. F. Wangcj, M. Weavercj, T. Webercj, A. J. R. Weinsteincj, U. Wienandscj, W. J. Wisniewskicj,\nM. Wittgencj, W. Wittmercj, D. H. Wrightcj, H. W. Wulsincj, Y. Yancj, A. K. Yarritucj, K. Yicj, G. Yockycj,\nC. C. Youngcj, V. Zieglercj, X. R. Chenck, N. Coptyck, H. Liuck, W. Parkck, M. V. Purohitck, H. Singhck,\nA. W. Weidemannck, R. M. Whiteck, J. R. Wilsonck, F. X. Yumicevack, A. Randle-Condecl, S. J. Sekulacl, M. Belliscm,\nP. R. Burchatcm, S. A. Majewskicm, T. I. Meyercm, T. S. Miyashitacm, B. A. Petersencm, E. M. T. Pucciocm, C. Roatcm,\nM. Ahmedcn, S. Ahmedcn, M. S. Alamcn, R. Bulacn, J. A. Ernstcn, V. Jaincn, J. Liucn, B. Pancn, M. A. Saeedcn,\nF. R. Wapplercn, S. B. Zaincn, R. Gorodeiskyco, N. Guttmanco, D. R. Peimerco, A. So\ufb00erco, R. Hendersoncp,\nA. De Silvacp, W. Buggcq, H. Cohncq, P. Lundcq, M. Krishnamurthycq, G. Ragghianticq, S. M. Spaniercq,\nB. J. Wogslandcq, R. Eckmanncr, J. L. Ritchiecr, A. M. Rulandcr, A. Satpathycr, C. J. Schillingcr, R. F. Schwitterscr,\nB. C. Wraycr, B. W. Drummondcs, J. M. Izencs, I. Kitayamacs, X. C. Loucs, G. Williamscs, S. Yecs, F. Bianchict,cu,\nM. Bonact,cu, F. De Morict,cu, A. Filippict,cu, F. Galloct,cu, D. Gambact,cu, M. Pelliccionict,cu, S. Zambitoct,cu,\nF. Daudoct, B. Di Girolamoct, P. Grossoct, A. Smolct, P. P. Trapanict, D. Zaninct, C. Boreancv,cw, L. Bosisiocv,cw,\nF. Cossutticv, G. Della Riccacv,cw, S. Dittongocv,cw, S. Grancagnolocv,cw, L. Lancericv,cw, P. Poropat\u2020cv,cw, M. Prestcv,\nI. Rashevskayacv, E. Vallazzacv, L. Vitalecv,cw, G. Vuagnincv,cw, P. F. Manfredicx, V. Recx, V. Spezialicx, E. D. Frankcy,\nL. Gladneycy, Q. H. Guocy, J. Panettacy, R. S. Panvini\u2020cz, V. Azzolinida, J. Bernabeuda, N. Lopez-Marchda,\nF. Martinez-Vidalda, D. A. Milanesda, A. Oyangurenda, P. Villanueva-Perezda, A. Agarwaldb, H. Ahmeddb, J. Albertdb,\nSw. Banerjeedb, F. U. Bernlochnerdb, C. M. Browndb, H. H. F. Choidb, D. Fortindb, K. B. Franshamdb, K. Hamanodb,\nG. J. Kingdb, R. Kowalewskidb, M. J. Lewczukdb, C. Lindsaydb, C. B. Lockedb, T. Lueckdb, I. M. Nugentdb,\nJ. M. Roneydb, R. J. Sobiedb, N. Tasneemdb, J. J. Backdc, T. J. Gershondc, P. F. Harrisondc, J. Ilicdc, T. E. Lathamdc,\nG. B. Mohantydc, M. R. Penningtondc, H. R. Banddd, X. Chendd, B. Chengdd, S. Dasudd, M. Dattadd,\nA. M. Eichenbaumdd, J. J. Hollardd, H. Hudd, J. R. Johnsondd, P. E. Kutterdd, H. Lidd, R. Liudd, B. Melladodd,\nA. Mihalyidd, A. K. Mohapatradd, Y. Pandd, M. Pierinidd, R. Prepostdd, I. J. Scottdd, P. Tandd, C. O. Vuosalodd,\nJ. H. von Wimmersperg-Toellerdd, S. L. Wudd, Z. Yudd, M. G. Greenede, T. M. B. Kordichde, Y. Rozendf\n\n799\naLaboratoire d\u2019Annecy-le-Vieux de Physique des Particules (LAPP), Universit\u00b4e de Savoie, CNRS/IN2P3, F-74941 Annecy-le-Vieux, France\nbUniversitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain\ncINFN Sezione di Bari, I-70126 Bari, Italy\ndDipartmento di Fisica, Universit`a di Bari, I-70126 Bari, Italy\neInstitute of High Energy Physics, Beijing 100039, China\nfUniversity of Bergen, Institute of Physics, N-5007 Bergen, Norway\ngLawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA\nhUniversity of Birmingham, Birmingham, B15 2TT, United Kingdom\niRuhr Universit\u00a8at Bochum, Institut f\u00a8ur Experimentalphysik 1, D-44780 Bochum, Germany\njINFN CNAF I-40127 Bologna, Italy\nkUniversity of Bristol, Bristol BS8 1TL, United Kingdom\nlUniversity of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1\nmBrunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom\nnBudker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russia\noNovosibirsk State Technical University, Novosibirsk 630092, Russia\npNovosibirsk State University, Novosibirsk 630090, Russia\nqUniversity of California at Irvine, Irvine, California 92697, USA\nrUniversity of California at Los Angeles, Los Angeles, California 90024, USA\nsUniversity of California at Riverside, Riverside, California 92521, USA\ntUniversity of California at San Diego, La Jolla, California 92093, USA\nuUniversity of California at Santa Barbara, Santa Barbara, California 93106, USA\nvUniversity of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA\nwCalifornia Institute of Technology, Pasadena, California 91125, USA\nxUniversity of Cincinnati, Cincinnati, Ohio 45221, USA\nyUniversity of Colorado, Boulder, Colorado 80309, USA\nzColorado State University, Fort Collins, Colorado 80523, USA\naaTechnische Universit\u00a8at Dortmund, Fakult\u00a8at Physik, D-44221 Dortmund, Germany\nabTechnische Universit\u00a8at Dresden, Institut f\u00a8ur Kern- und Teilchenphysik, D-01062 Dresden, Germany\nacLaboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France\nadUniversity of Edinburgh, Edinburgh EH9 3JZ, United Kingdom\naeElon University, Elon University, North Carolina 27244-2010, USA\nafINFN Sezione di Ferrara, I-44100 Ferrara, Italy\nagDipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara, I-44100 Ferrara, Italy\nahFlorida A&M University, Tallahassee, Florida 32307, USA\naiINFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy\najINFN Sezione di Genova, I-16146 Genova, Italy\nakDipartimento di Fisica, Universit`a di Genova, I-16146 Genova, Italy\nalIndian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India\namHarvard University, Cambridge, Massachusetts 02138, USA\nanHarvey Mudd College, Claremont, California 91711, USA\naoUniversit\u00a8at Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany\napHumboldt-Universit\u00a8at zu Berlin, Institut f\u00a8ur Physik, D-12489 Berlin, Germany\naqImperial College London, London, SW7 2AZ, United Kingdom\narUniversity of Iowa, Iowa City, Iowa 52242, USA\nasIowa State University, Ames, Iowa 50011-3160, USA\natJohns Hopkins University, Baltimore, Maryland 21218, USA\nauUniversit\u00a8at Karlsruhe, Institut f\u00a8ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany\navLaboratoire de l\u2019Acc\u00b4el\u00b4erateur Lin\u00b4eaire, IN2P3/CNRS et Universit\u00b4e Paris-Sud 11, Centre Scienti\ufb01que d\u2019Orsay, F-91898 Orsay Cedex,\nFrance\nawLawrence Livermore National Laboratory, Livermore, California 94550, USA\naxUniversity of Liverpool, Liverpool L69 7ZE, United Kingdom\nayQueen Mary, University of London, London, E1 4NS, United Kingdom\nazUniversity of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom\nbaUniversity of Louisville, Louisville, Kentucky 40292, USA\nbbJohannes Gutenberg-Universit\u00a8at Mainz, Institut f\u00a8ur Kernphysik, D-55099 Mainz, Germany\nbcUniversity of Manchester, Manchester M13 9PL, United Kingdom\nbdUniversity of Maryland, College Park, Maryland 20742, USA\nbeUniversity of Massachusetts, Amherst, Massachusetts 01003, USA\nbfMassachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA\nbgMcGill University, Montr\u00b4eal, Qu\u00b4ebec, Canada H3A 2T8\nbhINFN Sezione di Milano, I-20133 Milano, Italy\nbiDipartimento di Fisica, Universit`a di Milano, I-20133 Milano, Italy\nbjUniversity of Mississippi, University, Mississippi 38677, USA\nbkUniversity of South Alabama, Mobile, Alabama 36688, USA\nblUniversit\u00b4e de Montr\u00b4eal, Physique des Particules, Montr\u00b4eal, Qu\u00b4ebec, Canada H3C 3J7\nbmMount Holyoke College, South Hadley, Massachusetts 01075, USA\nbnINFN Sezione di Napoli, I-80126 Napoli, Italy\nboDipartimento di Scienze Fisiche, Universit`a di Napoli Federico II, I-80126 Napoli, Italy\nbpNIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands\nbqUniversity of Notre Dame, Notre Dame, Indiana 46556, USA\nbrOak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA\n\n800\nbsOhio State University, Columbus, Ohio 43210, USA\nbtUniversity of Oregon, Eugene, Oregon 97403, USA\nbuINFN Sezione di Padova, I-35131 Padova, Italy\nbvDipartimento di Fisica, Universit`a di Padova, I-35131 Padova, Italy\nbwLaboratoire de Physique Nucl\u00b4eaire et de Hautes Energies, IN2P3/CNRS, Universit\u00b4e Pierre et Marie Curie-Paris6, Universit\u00b4e Denis\nDiderot-Paris7, F-75252 Paris, France\nbxINFN Sezione di Perugia I-06123 Perugia, Italy\nbyDipartimento di Fisica, Universit`a di Perugia, I-06123 Perugia, Italy\nbzINFN Sezione di Pisa, I-56127 Pisa, Italy\ncaDipartimento di Fisica, Universit`a di Pisa, I-56127 Pisa, Italy\ncbScuola Normale Superiore di Pisa, I-56127 Pisa, Italy\nccPrairie View A&M University, Prairie View, Texas 77446, USA\ncdPrinceton University, Princeton, New Jersey 08544, USA\nceINFN Sezione di Roma, I-00185 Roma, Italy\ncfDipartimento di Fisica, Universit`a di Roma La Sapienza, I-00185 Roma, Italy\ncgUniversit\u00a8at Rostock, D-18051 Rostock, Germany\nchRutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom\nciCEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France\ncjSLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA\nckUniversity of South Carolina, Columbia, South Carolina 29208, USA\nclSouthern Methodist University, Dallas, Texas 75275, USA\ncmStanford University, Stanford, California 94305-4060, USA\ncnState University of New York, Albany, New York 12222, USA\ncoTel Aviv University, Tel Aviv, 69978, Israel\ncpTRIUMF, Vancouver, BC, Canada V6T 2A3\ncqUniversity of Tennessee, Knoxville, Tennessee 37996, USA\ncrUniversity of Texas at Austin, Austin, Texas 78712, USA\ncsUniversity of Texas at Dallas, Richardson, Texas 75083, USA\nctINFN Sezione di Torino, I-10125 Torino, Italy\ncuDipartimento di Fisica Sperimentale, Universit`a di Torino, I-10125 Torino, Italy\ncvINFN Sezione di Trieste, I-34127 Trieste, Italy\ncwDipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\ncxUniversit`a di Pavia, Dipartimento di Elettronica and INFN, I-27100 Pavia, Italy\ncyUniversity of Pennsylvania, Philadelphia, Pennsylvania 19104, USA\nczVanderbilt University, Nashville, Tennessee 37235, USA\ndaIFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain\ndbUniversity of Victoria, Victoria, British Columbia, Canada V8W 3P6\ndcDepartment of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom\nddUniversity of Wisconsin, Madison, Wisconsin 53706, USA\ndeYale University, New Haven, Connecticut 06511, USA\ndfTechnion, Haifa, Israel\n\u2020Deceased\n\n801\nAppendix C: The Belle Collaboration author list\nA. Abashian\u2020g, K. Abeu, K. Abecg, N. Abeci, R. Abebh, T. Abech,u, I. Adachiu, K. Adamczyks, B. S. Ahnar,\nH. S. Ahnby, H. Aiharaj, K. Akaiu, M. Akatsuq, M. Akemotou, R. Akhmetshini,b, J. P. Alexanderu, G. Alimonticq,\nQ. Ancv, D. Anipkob, K. Aokiu, K. Arinsteinb,bj, K. Asaibc, M. Asaiv, Y. Asanocx, D. M. Asnerbn, T. Asocm,\nV. Aulchenkob,bj, T. Aushevl,ah, T. Azizcd, S. Bahinipatico,aa, A. M. Bakichbx, A. Balabo, V. Balaguraah, Y. Banbp,\nE. Banass, S. Banerjeecd, E. Barberiobw, M. Barberocq, M. Barrettcq, W. Bartelk,u, A. Bayl, I. Bednyb,bj, S. Behariu,\nP. K. Beheracy, D. Beilineb, K. Belousaf, V. Bhardwajbo,bc, B. Bhuyany, M. Bischofbergerbc, U. Bitencal, I. Bizjakal,\nS. Blythbd,bg,i, A. Bondarb,bj, G. Bonvicinicz, A. Bozeks, M. Bra\u02c7ckocs,al,u, J. Brodzickas,u, T. E. Browdercq,\nB. C. K. Caseycq, M. C. Changh,i,ch, P. Changi, Y. H. Changbd, Y. W. Changi, Y. Chaoi, V. Chekelianaw, A. Chenbd,\nH. F. Chencv, K. F. Cheni, J. -H. Cheni, P. Cheni, W. T. Chenbd, Y. Q. Cheni, B. G. Cheone,t,cb, C. C. Chiangi,\nS. Chidzikbq, K. Chilikinah, R. Chistovah, I. S. Chodc, K. Choaq, V. Chobanovaaw, K. S. Choidc, S. K. Choir,\nY. K. Choicb, Y. Choicb, P. H. Chui, A. Chuvikovbq, D. Cinabrocz, S. Colebx, J. Crnkoviccr, J. Dalsenobw,u,aw,m,\nM. Danilovah,ay, A. Dascd, M. Dashg, J. Dingfeldercn, L. Dneprovsky\u2020b, Y. Doiu, Z. Dole\u02c7zaln, L. Y. Dongai, R. Dowdbw,\nZ. Dr\u00b4asaln, J. Dragicbw,u, A. Drutskoyco,ah,ay, Y. C. Duhh, Y. T. Duhi, W. Dungelaj, D. Duttay, S. Eidelmanb,bj,\nV. Eygesah, Y. Enariq, R. Enomotou, D. Epifanovb,bj,j, S. Esenco, C. W. Evertonbw, F. Fangcq, H. Farhatcz,\nJ. E. Fastbn, M. Feindtae, T. Ferberk, R. E. Fernholzbq, J. Flanaganu, S. Fratinaal, A. Freyw, M. Friedlaj, H. Fujiiu,\nM. Fujikawabc, Y. Fujitau, Y. Fujiyamaci, C. Fukunagacj, M. Fukushimau, Y. Funahashiu, Y. Funakoshiu,\nK. Furukawau, N. Gabyshevb,bj,u, S. Gangulycz, A. Garmashb,bj,ce,bq, V. Gaurcd, T. J. Gershonu, R. Gillardcz,\nF. Giordanocr, R. Glattaueraj, A. Gobd, Y. M. Goht, G. Gokhroocd, P. Goldenzweigco, B. Golobo,al, A. Gordonbw,\nA. Gori\u02c7sekal, V. I. Goriletskyag, K. Gotowg, B.V. Grinyovag, H. Gulercq,ax, R. S. Guobe, H. C. Haar, H. Haar, J. Habau,\nC. Hagnerg, F. Haitanicg, T. Hajij, H. Hamasakiu, B. Y. Hanar, Y. L. Hanai, H. Hanadach, K. Hanagakibq, F. Handach,\nK. Harau,q,bm, T. Harau,bm, Y. Haradabh, B. Harropbq, T. Haruyamau, Y. Hasegawabz, N. C. Hastingsbw,u,j,\nK. Hasukobu, K. Hayasakaap,q, K. Hayashiu, H. Hayashiibc, M. Hazumiu,bm, E. M. Heenanbw, D. He\ufb00ernanbm,\nY. Higashiu, Y. Higasinoq, I. Higuchich, T. Higuchiao,u, S. Hikitack, L. Hinzl, T. Hiraici, H. Hiranock, N. Hitomiu,\nC. T. Hoii, T. Hojobm, T. Hokuueq, Y. Horiich,ap, Y. Hoshicg, K. Hoshinack, S. Houi,bd, W. S. Houi, Y. B. Hsiungi,\nC. L. Hsui, S. C. Hsui, H. C. Huangi, T. J. Huangi, Y. C. Huangbe, H. J. Hyunat, S. Ichizawaci, T. Igakiq, A. Igarashicx,\nS. Igarashiu, Y. Igarashiu, T. Iijimaap,q, K. Ikadoq, H. Ikedau, H. Ikedau,bc, K. Ikedabc, K. Inamiq, Y. Inouebl,\nA. Ishikawau, A. Ishikawaq,bv,ch,j, H. Ishinoci, K. Itagakich, S. Itamiq, K. Itohj, R. Itohu, M. Iwabuchice,dc,c, G. Iwaibh,\nM. Iwaiu, S. Iwaidacx, M. Iwamotoc, H. Iwasakiu, M. Iwasakij, Y. Iwasakiu, T. Iwashitabc, D. J. Jacksonbm, C. Jacobyl,\nI. Jaeglecq, P. Jalochas, H. K. Jangby, C. M. Jeni, X. B. Jiai, M. Jonescq, K. K. Joou, N. J. Joshicd, N. Joshicd,\nT. Juliusbw, R. Kaganah, D. H. Kahat, H. Kajiq, S. Kajiwarabm, H. Kakunoj,ci,cj, T. Kameshimacx, T. Kamitaniu,\nJ. Kanekoci, J. H. Kangdc, J. S. Kangar, T. Kaniq, P. Kapustas, K. Kasamiu, G. Katanou, S. U. Kataokabc,\nN. Katayamau, E. Katoch, Y. Katoq, H. Kawaic, H. Kawaij, M. Kawaiu, N. Kawamuraa, T. Kawasakibm,bh, N. Kentcq,\nH. R. Khanbv,ci, A. Kibayashiu,ci, H. Kichimiu, C. Kieslingaw, M. Kikuchiu, E. Kikutaniu, B. H. Kimby, C. H. Kimby,\nD. W. Kimcb, H. J. Kimat, H. J. Kimdc, H. O. Kimat,cb, H. W. Kimar, J. B. Kimar, J. H. Kimcb,aq, K. T. Kimar,\nM. J. Kimat, S. K. Kimby, S. M. Kimcb, T. H. Kimdc, Y. I. Kimat, Y. J. Kimce,aq, K. Kinoshitaco, J. Klucaral,\nB. R. Koar, N. Kobayashibt,ci, S. Kobayashibv, T. Kobayashiu, S. Koblitzaw, P. Kody\u02c7sn, S. Koikeu, S. Koishici,\nH. Koisou, Y. Kondou, H. Konishick, P. Koppenburgu, K. Korotushenkobq, S. Korparcs,al, R. T. Kouzesbn, Y. Kozakaiq,\nM. Krepsae, P. Kri\u02c7zano,al, P. Krokovnyb,bj,u, B. Kronenbitterae, T. Kubou, T. Kuhrae, R. Kulasirico, R. Kumarbo,br,\nS. Kumarbo, T. Kumitacj, T. Kuniyabv, C. C. Kuobd, T. -L. Kuoi, H. Kurashiroci, E. Kuriharac,u, Y. Kurokibm,\nA. Kusakaj, A. Kuzminb,bj, P. Kvasni\u02c7ckan, Y. J. Kwondc, S. H. Kyeongdc, J. S. Langecp,bu,am, G. Lederaj, J. S. Leecb,\nJ. Leeby, M. C. Leei, M. H. Leeu, M. J. Leeby, S. E. Leeby, S. H. Leeby,ar, Y. J. Leei, M. Leitgabcr,bu, R. Leitnern,\nC. Leonidopoulosbq, T. Lesiaks,cc, H. B. Liai, J. Licv,cq,by, X. Liby, Y. Lig, J. Libbyz, C. L. Limdc, A. Limosanibw,u,\nJ. Y. Linh, S. W. Lini, Y. S. Lini, C. Liucv, H. M. Liuai, T. Liubq, Y. Liuce,q,co,i, Z. Q. Liuai, D. Liventsevah,u,\nR. Louvotl, R. S. Lui, P. Lukinb,bj, O. Lutzae, V. R. Lyubinskyag, J. MacNaughtonu,aj, G. Majumdercd, Y. Makidau,\nH. Mamadack, A. Manabeu, F. Mandlaj, Z. P. Maoai, D. Marlowbq, M. Masuzawau, T. Matsubaraj, T. Matsudaba,\nTakeshi Matsudau, H. Matsumotobh, S. Matsumotof, T. Matsumotocj,q, H. Matsuo\u2020as, D. Matvienkob,bj, A. Matyjas,\nS. McOniebx, T. Medvedevaah, S. Michizonou, Y. Mikamich, T. Mimashiu, C. Mindasbq, W. Mitaro\ufb00aj,\nK. Miyabayashibc, H. Miyakebm, H. Miyatabh, Y. Miyazakiq, R. Mizukah,ay,az, L. C. Mo\ufb03ttbw, G. B. Mohantycd,\nA. Mohapatracy, D. Mohapatrabn,g, A. Mollaw,m, G. R. Moloneybw, G. F. Moorheadbw, N. Morgang, S. Moricx,\nT. Morif,q,ci, J. Muelleru,cu, A. Murakamibv, T. Murakamiu, N. Muramatsubm,bt,bs, R. Mussaac,ad, I. Nagaiq,\nT. Nagaminech, Y. Nagasakav, Y. Nagashimabm, S. Nagayamau, T. Nakadairaj, Y. Nakahamaj, M. Nakajimach,\nT. Nakajimach, I. Nakamurau, T. T. Nakamurau, T. Nakamuraci, E. Nakanobl, M. Nakaou, H. Nakayamau,\nH. Nakazawaf,ce,bd, J. W. Namcb, S. Naritach, Z. Natkaniecs, M. Nayakz, E. Nedelkovskaaw, K. Neichicg, N. K. Nisarcd,\nS. Neubauerae, C. Ngj, C. Niebuhrk, M. Niiyamaas, S. Nishidau,as, K. Nishimuracq, Y. Nishioq, O. Nitohck,\n\n802\nS. Noguchibc, T. Nomuraas, S. Nozakich, T. Nozakiu, A. Ogawabu, K. Ogawau, S. Ogawacf, Y. Ogawau, R. Ohkubou,\nK. Ohmiu, Y. Ohnishiu, F. Ohnoci, T. Ohshimaq, Y. Ohshimaci, N. Ohuchiu, K. Oideu, N. Oishiq, T. Okabeq,\nN. Okazakick, T. Okazakibc, S. Okunoan, S. L. Olsenby,cq,ai, S. Onoci, Y. Onukibh,bu,ch,j, T. Oobac, T. Oshimaq,\nW. Ostrowiczs, C. Oswaldcn, H. Ozakiu, P. Pakhlovah,ay,az, G. Pakhlovaah, H. Palka\u2020s, A. I. Panovaag,\nE. Panzenb\u00a8ockbc,w, C. S. Parkby, C. W. Parkar,cb, H. K. Parkat, H. Parkat, K. S. Parkcb, N. Parslowbx, L. S. Peakbx,\nT. K. Pedlarav, C. C. Pengi, J. C. Pengi, K. C. Pengi, T. Pengcv, M. Grosse Perdekampcr,bu, M. Pernicka\u2020aj,\nJ.-P. Perroudl, R. Pestotnikal, M. Peterscq, M. Petri\u02c7cal, L. E. Piiloneng, A. Poluektovb,bj, E. Prebysbq, M. Primae,\nK. Prothmannaw,m, M. R\u00a8ohrkenae, J. Raafco, R. Rabbermanbq, B. Reisertaw, M. Ritteraw, J. L. Rodriguezcq,\nL. Romanovb, F. J. Rongal,u, N. Rootb, M. Rosencq, A. Rostomyank, M. Rozanskas, K. Rybickis, S. Ryuby,\nJ. Ryukobm, H. Sagawau, H. Sahoocq, S. Sahui, M. Saigoch, T. Saitoch, S. Saitohc,ce, K. Sakaiu,bh, Y. Sakaiu,\nH. Sakamotoas, H. Sakauebl, S. Sandilyacd, W. Sandsbq, M. Sanpeicg, D. Santelco, L. Santeljal, T. Sanukich,\nT. R. Sarangicy,ce, T. Sasakiu, N. Sasaoas, M. Satapathycy, Noriaki Satoq, Nobuhiko Satou, Y. Satoch, N. Satoyamabz,\nA. Satpathyu,co, V. Savinovcu, K. Sayeedco, P. Sch\u00a8onmeierch, J. Sch\u00a8umannu,bg,i, T. Schietingerl, S. Schmidaj,\nO. Schneiderl, G. Schnellcw,x, S. Schrenkg,co, C. Schwandau,aj, A. J. Schwartzco, R. Seidlcr,bu, T. Sekicj, A.I. Sekiyabc,\nS. Semenovah, D. Semmleram, K. Senyoda,q, O. Seonq, Y. Settaif, R. Seustercq, M. E. Seviorbw, K. V. Shakhovaag,\nL. Shangai, M. Shapkinaf, V. Shebalinb,bj, C. P. Shencq,ai,q, D. Z. Shend, Y. T. Sheni, T. A. Shibatabt,ci, T. Shibatabh,\nH. Shibuyacf, T. Shidarau, K. Shimadabh, M. Shimoyamabc, S. Shinomiyabm, J. G. Shiui, L. I. Shpilinskayaag,\nB. Shwartzb,bj, A. Sibidanovbx, A. Sidorovb, V. Sidorov\u2020b, V. Sieglebu, F. Simonaw,m, J. B. Singhbo, R. Sinhaak,\nP. Smerkolal, Y. S. Sohndc, A. Sokolovaf, E. Solovievaah, A. Somovco, N. Sonibo, R. Stamenu, S. Stani\u02c7cct,u,cx,\nM. Stari\u02c7cal, M. Stederk, H. Steiningeraj, R. Stockcp, H. Stoeckbx, J. Stypulas, R. Sudacj, R. Sugaharau, A. Sugiq,\nT. Sugimurau, A. Sugiyamaq,bv, S. Suitohq, M. Sumihamabt,p, K. Sumisawabm,u, T. Sumiyoshiu,cj, H. F. Sungi,\nY. Susakiq, J. I. Suzukiu, J. Suzukiu, K. Suzukic,u,q, S. Y. Suzukiu, S. Suzukidb,bv,q, S. K. Swaincy,cq, M. Tabatac,\nH. Tajimaj, O. Tajimach,u, K. Takahashici, S. Takahashibh, T. Takahashibl, F. Takasakiu, T. Takayamach, M. Takitabm,\nK. Tamaiu, U. Tamponiac,ad, N. Tamurabk,bh, N. Tancl, K. Tanabej, J. Tanakaj, M. Tanakau, S. Tanakau, Y. Tanakabb,\nK. Tanidaby, N. Taniguchiu,as, G. Tatishvilibn, T. Tatomiu, M. Tawadau, G. N. Taylorbw, Y. Teramotobl, F. Thorneaj,\nX. C. Tianbp, I. Tikhomirovah, M. Tomotou,q, T. Tomuraj, S. N. Toveybw, K. Trabelsiu,cq,bm, W. Trischukbq,\nK. L. Tsaii, Y. T. Tsaii, T. Tsuboyamau, Y. Tsujitacx, K. Tsukadau, T. Tsukamotou, Y. W. Tungi, K. Uchidacq,\nM. Uchidabt,ci, Y. Uchidace, S. Ueharau, M. Uekich, K. Uenou, K. Uenoi, T. Uglovah,ay, N. Ujiieu, Y. Unnoe,c,t,u,\nS. Unou, P. Urquijobw,cn, Y. Ushirodau,as, Y. Usovb,bj, Y. Usukiq, S. E. Vahsenbq,cq, P. Vanhoeferaw, C. Van Hulsecw,\nG. Varnercq, K. E. Varvellbx, Y. S. Velikzhanini, K. Vervinkl, S. Villal, E. L. Vinogradag, A. Vinokurovab,bj,\nV. Vorobyevb,bj, A. Vossenab,cr, M. N. Wagneram, C. C. Wangi,ai, C. H. Wangbf,bg, J. G. Wangg, J. Wangbp,\nM. Z. Wangi, P. Wangai, T. J. Wangai, X. L. Wangai,g, Y. F. Wangcv, M. Watanabebh, Y. Watanabean,ci, R. Weddbw,\nJ. T. Weii, E. Whiteco, J. Wichtl,u, L. Widhalm\u2020aj, J. Wiechczynskis, K. M. Williamsg, R. Wixtedbq, E. Wonar,by,\nC. H. Wui, Q. L. Xieai, Z. Z. Xucv, B. D. Yabsleybx,g, Y. Yamadau, M. Yamagach, A. Yamaguchich, H. Yamaguchiu,\nT. Yamakica, H. Yamamotocq,ch, N. Yamamotou, S. Yamamotocj, T. Yamanakabm, H. Yamaokau, J. Yamaokacq,\nY. Yamaokau, Y. Yamashitabi,j, M. Yamauchiu, D. S. Yand, H. Yanaibh, S. Yanakaci, H. Yangby, R. Yangbq,\nS. Yashchenkok, J. Yashimau, Y. Yasuu, S. W. Yecv, P. Yehi, Z. W. Yind, J. Yingbp, K. Yokoyamau, M. Yokoyamaj,\nT. Yokoyamack, K. Yoshidaq, M. Yoshidau, Y. Yoshimurau, C. X. Yuai, C. Z. Yuanai, Y. Yuanai, Y. Yusabh,ch,g,\nH. Yutaa, D. Z\u00a8urcherl, D. Zanderae, S. L. Zangai, B. G. Zaslavskyag, C. C. Zhangai, J. Zhangu,cx, L. M. Zhangcv,\nS. Q. Zhangai, Z. P. Zhangcv, H. W. Zhaoai,u, Z. G. Zhaocv, Y. H. Zhengcq, Z. P. Zhengai, V. Zhilichb,bj, P. Zhoucz,\nZ. M. Zhubp, V. Zhulanovb,bj, T. Zieglerbq, A. Zupancae,al, N. Zwahlenl, O. Zyukovab,bj, T. \u02c7Zivkoal, D. \u02c7Zontaro,al,u,cx\naAomori University, Aomori 030-0943, Japan\nbBudker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation\ncChiba University, Chiba 263-8522, Japan\ndChinese Academy of Science, Beijing 100864, PR China\neChonnam National University, Gwangju 500-757, South Korea\nfChuo University, Tokyo 192-0393, Japan\ngVirginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA\nhDepartment of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan\niDepartment of Physics, National Taiwan University, Taipei 10617, Taiwan\njDepartment of Physics, University of Tokyo, Tokyo 113-0033, Japan\nkDeutsches Elektronen-Synchrotron, 22607 Hamburg, Germany\nl \u00b4Ecole Polytechnique F\u00b4ed\u00b4erale de Lausanne (EPFL), 1015 Lausanne, Switzerland\nmExcellence Cluster Universe, Technische Universit\u00a8at M\u00a8unchen, 85748 Garching, Germany\nnFaculty of Mathematics and Physics, Charles University, 121 16 Prague, The Czech Republic\noFaculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia\npGifu University, Gifu 501-1193, Japan\nqGraduate School of Science, Nagoya University, Nagoya 464-8602, Japan\nrGyeongsang National University, Chinju 660-701, South Korea\n\n803\nsH. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland\ntHanyang University, Seoul 133-791, South Korea\nuHigh Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan\nvHiroshima Institute of Technology, Hiroshima 731-5193, Japan\nwII. Physikalisches Institut, Georg-August-Universit\u00a8at G\u00a8ottingen, 37073 G\u00a8ottingen, Germany\nxIkerbasque, 48011 Bilbao, Spain\nyIndian Institute of Technology Guwahati, Assam 781039, India\nzIndian Institute of Technology Madras, Chennai 600036, India\naaIndian Institute of Technology Bhubaneswar, SatyaNagar, 751007, India\nabIndiana University, Bloomington, IN 47408, USA\nacINFN - Sezione di Torino, 10125 Torino, Italy\nadDipartimento di Fisica, Universit`a di Torino, I-10125 Torino, Italy\naeInstitut f\u00a8ur Experimentelle Kernphysik, Karlsruher Institut f\u00a8ur Technologie, 76131 Karlsruhe, Germany\nafInstitute for High Energy Physics, Protvino 142281, Russian Federation\nagInstitute for Single Crystals, National Academy of Sciences of Ukraine, Kharkov 61001, Ukraine\nahInstitute for Theoretical and Experimental Physics, Moscow 117218, Russian Federation\naiInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, PR China\najInstitute of High Energy Physics, 1050 Vienna, Austria\nakInstitute of Mathematical Sciences, Chennai 600113, India\nalJ. Stefan Institute, 1000 Ljubljana, Slovenia\namJustus-Liebig-Universit\u00a8at Gie\u00dfen, 35392 Gie\u00dfen, Germany\nanKanagawa University, Yokohama 221-8686, Japan\naoKavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan\napKobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan\naqKorea Institute of Science and Technology Information, Daejeon 305-806, South Korea\narKorea University, Seoul 136-713, South Korea\nasKyoto University, Kyoto 606-8502, Japan\natKyungpook National University, Daegu 702-701, South Korea\nauLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA\navLuther College, Decorah, IA 52101, USA\nawMax-Planck-Institut f\u00a8ur Physik, 80805 M\u00a8unchen, Germany\naxMcGill University, Montr\u00b4eal H3A 0G4, Canada\nayMoscow Institute of Physics and Technology, Moscow Region 141700, Russian Federation\nazMoscow Physical Engineering Institute, Moscow 115409, Russian Federation\nbaUniversity of Miyazaki, Miyazaki 889-2192, Japan\nbbNagasaki Institute of Applied Science, Nagasaki 851-0123, Japan\nbcNara Women\u2019s University, Nara 630-8506, Japan\nbdNational Central University, Chung-li 32054, Taiwan\nbeNational Kaohsiung Normal University, Kaohsiung 80201, Taiwan\nbfNational Lien-Ho Institute of Technology, Miao Li 360, Taiwan\nbgNational United University, Miao Li 36003, Taiwan\nbhNiigata University, Niigata 950-2181, Japan\nbiNippon Dental University, Niigata 951-8580, Japan\nbjNovosibirsk State University, Novosibirsk 630090, Russian Federation\nbk Okayama University, Okayama 700-8530, Japan\nblOsaka City University, Osaka 558-8585, Japan\nbmOsaka University, Osaka 565-0871, Japan\nbnPaci\ufb01c Northwest National Laboratory, Richland, WA 99352, USA\nboPanjab University, Chandigarh 160014, India\nbpPeking University, Beijing 100871, PR China\nbqPrinceton University, Princeton, NJ 08542, USA\nbrPunjab Agricultural University, Ludhiana 141004, India\nbsResearch Center for Electron Photon Science, Tohoku University, Sendai 980-8578, Japan\nbtResearch Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan\nbuRIKEN BNL Research Center, Brookhaven, NY 11973, USA\nbvSaga University, Saga 840-8502, Japan\nbwSchool of Physics, University of Melbourne, Victoria 3010, Australia\nbxSchool of Physics, University of Sydney, NSW 2006, Australia\nbySeoul National University, Seoul 151-742, South Korea\nbzShinshu University, Nagano 390-8621, Japan\ncaSugiyama Jogakuen University, Aichi 470-0131, Japan\ncbSungkyunkwan University, Suwon 440-746, South Korea\nccT. Ko\u00b4sciuszko Cracow University of Technology, Krakow 31-342, Poland\ncdTata Institute of Fundamental Research, Mumbai 400005, India\nceThe Graduate University for Advanced Studies, Hayama 240-0193, Japan\ncfToho University, Funabashi 274-8510, Japan\ncgTohoku Gakuin University, Tagajo 985-8537, Japan\nchTohoku University, Sendai 980-8578, Japan\nciTokyo Institute of Technology, Tokyo 152-8550, Japan\ncjTokyo Metropolitan University, Tokyo 192-0397, Japan\nckTokyo University of Agriculture and Technology, Tokyo 184-8588, Japan\n\n804\nclTokyo University of Science, Chiba 278-8510, Japan\ncmToyama National College of Maritime Technology, Toyama 933-0293, Japan\ncnUniversity of Bonn, 53115 Bonn, Germany\ncoUniversity of Cincinnati, Cincinnati, OH 45221, USA\ncpUniversity of Frankfurt, 60318 Frankfurt am Main, Germany\ncqUniversity of Hawaii, Honolulu, HI 96822, USA\ncrUniversity of Illinois at Urbana-Champaign, Urbana, IL 61801, USA\ncsUniversity of Maribor, 2000 Maribor, Slovenia\nctUniversity of Nova Gorica, 5000 Nova Gorica, Slovenia\ncuUniversity of Pittsburgh, Pittsburgh, PA 15260, USA\ncvUniversity of Science and Technology of China, Hefei 230026, PR China\ncwUniversity of the Basque Country UPV/EHU, 48080 Bilbao, Spain\ncxUniversity of Tsukuba, Tsukuba 305-0801, Japan\ncyUtkal University, Bhubaneswar, India\nczWayne State University, Detroit, MI 48202, USA\ndaYamagata University, Yamagata 990-8560, Japan\ndbYokkaichi University, Yokkaichi 512-8045, Japan\ndcYonsei University, Seoul 120-749, South Korea\n\u2020Deceased\n\n805\nAppendix D\nAcknowledgments\nThe preparation of this book has been directly sup-\nported by the US Department of Energy, MEXT (Japan),\nthe Natural Sciences and Engineering Research Council\n(Canada), and Commissariat `a l\u2019Energie Atomique and\nInstitut National de Physique Nucl\u00b4eaire et de Physique\ndes Particules (France). Individuals have been supported\nby the Royal Society (UK).\nThe authors of this book wish to thank the KEK and\nSLAC laboratories for their support with regard to prepa-\nration of this manuscript, and in particular providing meet-\ning and computing facilities to aid preparation of this\nmanuscript. In addition we wish to thank the following\ninstitutes who have hosted meetings of the book collabora-\ntion and general editors: Johannes Gutenberg Universit\u00a8at,\nMainz; Iowa State University; LAAP; University of Siegen;\nUniversity of Ljubljana; Queen Mary, University of Lon-\ndon, and the University of Melbourne. We would also like\nto thank the reprographics department at Queen Mary,\nUniversity of London for their contribution in preparation\nof the artwork for the cover page of this book. Adrian\nBevan and Soeren Prell would speci\ufb01cally like to thank\nPatricia Burchat, Francois Le Diberder, and A.J. Stew-\nart Smith for their counsel as members of the BABAR\nadvisory committee on preparations for this book and\nJ. Michael Roney and David B. MacFarlane for their sup-\nport as BABAR spokesperson and SLAC director of particle\nphysics and astrophysics during the writing of the book.\nBo\u02c7stjan Golob and Bruce Yabsley would speci\ufb01cally like to\nthank Tom Browder, Hisaki Hayashii, Toru Iijima, Leo Pi-\nilonen, Yoshihide Sakai and Masanori Yamauchi for their\nsupport of the project in the role of Belle spokespersons.\nWe would also like to thank Nittsia Harrison, Donna Her-\nnandez, Chihiro Imai, Homer Neal, and Shinobu Oishi, for\ntheir local support for meetings, Homer Neal and Char-\nlotte Hee for computing support at SLAC and in particu-\nlar Sarodia Vydelingum for her many e\ufb00orts with regard\nto organizing meetings, websites and travel arrangements\nduring this project.\nThe BABAR and Belle authors are grateful for the\ntremendous support they have received from their home\ninstitutions during the operation of the B Factories.\nThe BABAR Collaboration is grateful for the extraor-\ndinary contributions of their PEP-II colleagues in achiev-\ning the excellent luminosity and machine conditions that\nhave made this work possible. The success of this project\nalso relies critically on the expertise and dedication of the\ncomputing organizations that support BABAR. The col-\nlaborating institutions wish to thank SLAC for its sup-\nport and the kind hospitality extended to them. This\nwork is supported by the US Department of Energy\nand National Science Foundation, the Natural Sciences\nand Engineering Research Council (Canada), the Com-\nmissariat `a l\u2019Energie Atomique and Institut National de\nPhysique Nucl\u00b4eaire et de Physique des Particules (France),\nthe Bundesministerium f\u00a8ur Bildung und Forschung and\nDeutsche Forschungsgemeinschaft (Germany), the Isti-\ntuto Nazionale di Fisica Nucleare (Italy), the Foundation\nfor Fundamental Research on Matter (The Netherlands),\nthe Research Council of Norway, the Ministry of Edu-\ncation and Science of the Russian Federation, Ministerio\nde Econom\u00b4\u0131a y Competitividad (Spain), the Science and\nTechnology Facilities Council (United Kingdom), and the\nBinational Science Foundation (U.S.-Israel). Individuals\nhave received support from the Marie-Curie IEF program\n(European Union) and the A. P. Sloan Foundation (USA).\nThe Belle Collaboration wishes to thank the KEKB\ngroup for the excellent operation of the accelerator; the\nKEK cryogenics group for the e\ufb03cient operation of the\nsolenoid; and the KEK computer group, the National\nInstitute of Informatics, and the PNNL/EMSL com-\nputing group for valuable computing and SINET4 net-\nwork support. We acknowledge support from the Min-\nistry of Education, Culture, Sports, Science, and Tech-\nnology (MEXT) of Japan, the Japan Society for the Pro-\nmotion of Science (JSPS), and the Tau-Lepton Physics\nResearch Center of Nagoya University; the Australian Re-\nsearch Council and the Australian Department of Indus-\ntry, Innovation, Science and Research; Austrian Science\nFund under Grant No. P 22742-N16; the National Nat-\nural Science Foundation of China under Contracts No.\n10575109, No. 10775142, No. 10825524, No. 10875115,\nNo. 10935008 and No. 11175187; the Ministry of Edu-\ncation, Youth and Sports of the Czech Republic under\nContract No. LG14034; the Carl Zeiss Foundation, the\nDeutsche Forschungsgemeinschaft and the Volkswagen-\nStiftung; the Department of Science and Technology of\nIndia; the Istituto Nazionale di Fisica Nucleare of Italy;\nthe WCU program of the Ministry of Education, Sci-\nence and Technology, National Research Foundation of\nKorea Grants No. 2011-0029457, No. 2012-0008143, No.\n2012R1A1A2008330, No. 2013R1A1A3007772; the BRL\nprogram under NRF Grant No. KRF-2011-0020333, No.\nKRF-2011-0021196, Center for Korean J-PARC Users,\nNo. NRF-2013K1A3A7A06056592; the BK21 Plus pro-\ngram and the GSDC of the Korea Institute of Science\nand Technology Information; the Polish Ministry of Sci-\nence and Higher Education and the National Science Cen-\nter; the Ministry of Education and Science of the Russian\nFederation and the Russian Federal Agency for Atomic\nEnergy; the Slovenian Research Agency; the Basque Foun-\ndation for Science (IKERBASQUE) and the UPV/EHU\nunder program UFI 11/55; the Swiss National Science\nFoundation; the National Science Council and the Min-\nistry of Education of Taiwan; and the U.S. Department of\nEnergy and the National Science Foundation. This work\nis supported by a Grant-in-Aid from MEXT for Science\nResearch in a Priority Area (\u201cNew Development of Flavor\nPhysics\u201d) and from JSPS for Creative Scienti\ufb01c Research\n(\u201cEvolution of Tau-lepton Physics\u201d).\n\n806\nBaBar publications\nAdam 2005:\nI. Adam et al. \u201cThe DIRC particle identi\ufb01cation sys-\ntem for the BABAR experiment\u201d. Nucl. Instrum. Meth.\nA538, 281\u2013357 (2005).\nAllmendinger 2012:\nT. Allmendinger, B. Bhuyan, D. N. Brown, H. Choi,\nS. Christ et al. \u201cTrack Finding E\ufb03ciency in BABAR\u201d.\nNucl. Instrum. Meth. A704, 44 (2012). 1207.2849.\nAndreotti 2003:\nM. Andreotti et al.\n\u201cA Barrel IFR with Limited\nStreamer Tubes\u201d, 2003.\nBABAR Internal Report, un-\npublished.\nAnulli 2002:\nF. Anulli et al. \u201cThe BABAR Instrumented Flux Return\nPerformance: Lessons Learned\u201d. Nucl. Instrum. Meth.\nA494, 455\u2013463 (2002).\nAnulli 2003:\nF. Anulli et al. \u201cMechanisms A\ufb00ecting Performance of\nthe BABAR Resistive Plate Chambers and Searches for\nRemediation\u201d.\nNucl. Instrum. Meth. A508, 128\u2013132\n(2003).\nAnulli 2005a:\nF. Anulli et al.\n\u201cBABAR Forward Endcap Upgrade\u201d.\nNucl. Instrum. Meth. A539, 155\u2013171 (2005).\nAnulli 2005b:\nF. Anulli et al.\n\u201cPerformance of 2nd Generation\nBABAR Resistive Plate Chambers\u201d.\nNucl. Instrum.\nMeth. A552, 276\u2013291 (2005).\nAubert 2000:\nB. Aubert et al. \u201cA Study of time dependent CP violat-\ning asymmetries in B0 \u2192J/\u03c8K0\nS and B0 \u2192\u03c8(2S)K0\nS\ndecays\u201d hep-ex/0008048.\nAubert 2001a:\nB. Aubert et al. \u201cMeasurement of CP violating asym-\nmetries in B0 decays to CP eigenstates\u201d. Phys. Rev.\nLett. 86, 2515\u20132522 (2001). hep-ex/0102030.\nAubert 2001b:\nB. Aubert et al. \u201cMeasurement of J/\u03c8 production in\ncontinuum e+e\u2212annihilations near \u221as = 10.6 GeV\u201d.\nPhys. Rev. Lett. 87, 162002 (2001). hep-ex/0106044.\nAubert 2001c:\nB. Aubert et al. \u201cMeasurement of the B0 and B+ meson\nlifetimes with fully reconstructed hadronic \ufb01nal states\u201d.\nPhys. Rev. Lett. 87, 201803 (2001). hep-ex/0107019.\nAubert 2001d:\nB. Aubert et al. \u201cMeasurements of the branching frac-\ntions of exclusive charmless B meson decays with \u03b7\u2032\nor \u03c9 mesons\u201d.\nPhys. Rev. Lett. 87, 221802 (2001).\nhep-ex/0108017.\nAubert 2001e:\nB. Aubert et al. \u201cObservation of CP violation in the\nB0 meson system\u201d. Phys. Rev. Lett. 87, 091801 (2001).\nhep-ex/0107013.\nAubert 2002a:\nB. Aubert et al.\n\u201cA study of time dependent CP-\nviolating asymmetries and \ufb02avor oscillations in neu-\ntral B decays at the \u03a5(4S)\u201d. Phys. Rev. D66, 032003\n(2002). hep-ex/0201020.\nAubert 2002b:\nB. Aubert et al. \u201cMeasurement of B0 \u2212B0 \ufb02avor os-\ncillations in hadronic B0 decays\u201d. Phys. Rev. Lett. 88,\n221802 (2002). hep-ex/0112044.\nAubert 2002c:\nB. Aubert et al. \u201cMeasurement of branching fractions\nfor exclusive B decays to charmonium \ufb01nal states\u201d.\nPhys. Rev. D65, 032001 (2002). hep-ex/0107025.\nAubert 2002d:\nB. Aubert et al. \u201cMeasurement of D+\ns and D\u2217+\ns\nproduc-\ntion in B meson decays and from continuum e+e\u2212an-\nnihilation at \u221as = 10.6 GeV\u201d. Phys. Rev. D65, 091104\n(2002). hep-ex/0201041.\nAubert 2002e:\nB. Aubert et al. \u201cMeasurement of the B0\u2212B0 oscillation\nfrequency with inclusive dilepton events\u201d. Phys. Rev.\nLett. 88, 221803 (2002). hep-ex/0112045.\nAubert 2002f:\nB. Aubert et al. \u201cMeasurement of the B0 lifetime with\npartially reconstructed B0 \u2192D\u2217\u2212\u2113+\u03bd\u2113decays\u201d. Phys.\nRev. Lett. 89, 011802 (2002). [Erratum-ibid. 89, 169903\n(2002)], hep-ex/0202005.\nAubert 2002g:\nB. Aubert et al.\n\u201cMeasurement of the CP-violating\nasymmetry amplitude sin 2\u03b2\u201d.\nPhys. Rev. Lett. 89,\n201802 (2002). hep-ex/0207042.\nAubert 2002h:\nB.\nAubert\net\nal.\n\u201cMeasurements\nof\nbranching\nfractions and CP-violating asymmetries in B0\n\u2192\n\u03c0+\u03c0\u2212, K+\u03c0\u2212, K+K\u2212decays\u201d.\nPhys. Rev. Lett. 89,\n281802 (2002). hep-ex/0207055.\nAubert 2002i:\nB. Aubert et al.\n\u201cSearch for T and CP violation in\nB0 \u2212B0 mixing with inclusive dilepton events\u201d. Phys.\nRev. Lett. 88, 231801 (2002). hep-ex/0202041.\nAubert 2002j:\nB. Aubert et al. \u201cThe BABAR detector\u201d. Nucl. Instrum.\nMeth. A479, 1\u2013116 (2002). hep-ex/0105044.\nAubert 2003a:\nB. Aubert et al.\n\u201cA measurement of the B0\n\u2192\nJ/\u03c8\u03c0+\u03c0\u2212branching fraction\u201d.\nPhys. Rev. Lett. 90,\n091801 (2003). hep-ex/0209013.\nAubert 2003b:\nB. Aubert et al. \u201cEvidence for B+ \u2192J/\u03c8p\u039b and search\nfor B0 \u2192J/\u03c8pp\u201d. Phys. Rev. Lett. 90, 231801 (2003).\nhep-ex/0303036.\nAubert 2003c:\nB. Aubert et al.\n\u201cEvidence for the rare decay B \u2192\nK\u2217\u2113+\u2113\u2212and measurement of the B \u2192K\u2113+\u2113\u2212branch-\ning fraction\u201d.\nPhys. Rev. Lett. 91, 221802 (2003).\nhep-ex/0308042.\nAubert 2003d:\nB. Aubert et al.\n\u201cMeasurement of B0 \u2192D(\u2217)+\ns\nD\u2217\u2212\nbranching fractions and B0 \u2192D(\u2217)+\ns\nD\u2217\u2212polarization\nwith a partial reconstruction technique\u201d.\nPhys. Rev.\nD67, 092003 (2003). hep-ex/0302015.\nAubert 2003e:\nB. Aubert et al. \u201cMeasurement of the B0 meson life-\n\n807\ntime with partial reconstruction of B0 \u2192D\u2217\u2212\u03c0+ and\nB0 \u2192D\u2217\u2212\u03c1+ decays\u201d. Phys. Rev. D67, 091101 (2003).\nhep-ex/0212012.\nAubert 2003f:\nB. Aubert et al.\n\u201cMeasurement of the branching\nfractions for the exclusive decays of B0 and B+ to\nD(\u2217)D(\u2217)K\u201d. Phys. Rev. D68, 092001 (2003). hep-ex/\n0305003.\nAubert 2003g:\nB. Aubert et al.\n\u201cMeasurement of time-dependent\nCP asymmetries and the CP-odd fraction in the decay\nB0 \u2192D\u2217+D\u2217\u2212\u201d. Phys. Rev. Lett. 91, 131801 (2003).\nhep-ex/0306052.\nAubert 2003h:\nB. Aubert et al. \u201cMeasurements of branching fractions\nand CP-violating asymmetries in B0 \u2192\u03c1\u00b1h\u2213decays\u201d.\nPhys. Rev. Lett. 91, 201802 (2003). hep-ex/0306030.\nAubert 2003i:\nB. Aubert et al. \u201cMeasurements of CP-violating asym-\nmetries and branching fractions in B meson decays to\n\u03b7\u2032K\u201d.\nPhys. Rev. Lett. 91, 161801 (2003).\nhep-ex/\n0303046.\nAubert 2003j:\nB. Aubert et al. \u201cObservation of a narrow meson de-\ncaying to D+\ns \u03c00 at a mass of 2.32 GeV/c2\u201d. Phys. Rev.\nLett. 90, 242001 (2003). hep-ex/0304021.\nAubert 2003k:\nB. Aubert et al. \u201cObservation of the decay B0 \u2192\u03c00\u03c00\u201d.\nPhys. Rev. Lett. 91, 241801 (2003). hep-ex/0308012.\nAubert 2003l:\nB. Aubert et al. \u201cRare B decays into states containing a\nJ/\u03c8 meson and a meson with ss quark content\u201d. Phys.\nRev. Lett. 91, 071801 (2003). hep-ex/0304014.\nAubert 2003m:\nB. Aubert et al.\n\u201cSimultaneous measurement of the\nB0 meson lifetime and mixing frequency with B0 \u2192\nD\u2217\u2212\u2113+\u03bd\u2113decays\u201d.\nPhys. Rev. D67, 072002 (2003).\nhep-ex/0212017.\nAubert 2003n:\nB. Aubert et al. \u201cStudy of inclusive production of char-\nmonium mesons in B decay\u201d. Phys. Rev. D67, 032002\n(2003). hep-ex/0207097.\nAubert 2004a:\nB. Aubert et al.\n\u201cB meson decays to \u03b7(\u2032)K\u2217, \u03b7(\u2032)\u03c1,\n\u03b7(\u2032)\u03c00, \u03c9\u03c00, and \u03c6\u03c00\u201d. Phys. Rev. D70, 032006 (2004).\nhep-ex/0403025.\nAubert 2004b:\nB. Aubert et al. \u201cBranching fractions and CP asymme-\ntries in B0 \u2192K+K\u2212K0\nS and B+ \u2192K+K0\nSK0\nS\u201d. Phys.\nRev. Lett. 93, 181805 (2004). hep-ex/0406005.\nAubert 2004c:\nB. Aubert et al. \u201cDetermination of the branching frac-\ntion for B \u2192Xc\u2113\u03bd decays and of |Vcb| from hadronic\nmass and lepton energy moments\u201d. Phys. Rev. Lett. 93,\n011803 (2004). hep-ex/0404017.\nAubert 2004d:\nB. Aubert et al. \u201cJ/\u03c8 production via initial state ra-\ndiation in e+e\u2212\u2192\u00b5+\u00b5\u2212\u03b3 at an e+e\u2212center-of-mass\nenergy near 10.6 GeV\u201d. Phys. Rev. D69, 011103 (2004).\nhep-ex/0310027.\nAubert 2004e:\nB. Aubert et al. \u201cLimits on the decay-rate di\ufb00erence of\nneutral B mesons and on CP, T, and CPT violation in\nB0B0 oscillations\u201d. Phys. Rev. Lett. 92, 181801 (2004).\nhep-ex/0311037.\nAubert 2004f:\nB. Aubert et al. \u201cLimits on the decay rate di\ufb00erence\nof neutral B mesons and on CP, T, and CPT violation\nin B0B0 oscillations\u201d. Phys. Rev. D70, 012007 (2004).\nhep-ex/0403002.\nAubert 2004g:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand charge asymmetries in B\u00b1 \u2192\u03c1\u00b1\u03c00 and B\u00b1 \u2192\n\u03c10\u03c0\u00b1 decays, and search for B0 \u2192\u03c10\u03c00\u201d. Phys. Rev.\nLett. 93, 051802 (2004). hep-ex/0311049.\nAubert 2004h:\nB. Aubert et al. \u201cMeasurement of the B \u2192Xs\u2113+\u2113\u2212\nbranching fraction with a sum over exclusive modes\u201d.\nPhys. Rev. Lett. 93, 081802 (2004). hep-ex/0404006.\nAubert 2004i:\nB. Aubert et al.\n\u201cMeasurement of the B0\n\u2192\nK\u2217\n2(1430)0\u03b3 and B+ \u2192K\u2217\n2(1430)+\u03b3 branching frac-\ntions\u201d.\nPhys. Rev. D70, 091105 (2004).\nhep-ex/\n0409035.\nAubert 2004j:\nB. Aubert et al. \u201cMeasurement of the B+/B0 produc-\ntion ratio from the \u03a5(4S) meson using B+ \u2192J/\u03c8K+\nand B0 \u2192J/\u03c8K0\nS decays\u201d. Phys. Rev. D69, 071101\n(2004). hep-ex/0401028.\nAubert 2004k:\nB. Aubert et al. \u201cMeasurement of the branching fraction\nand polarization for the decay B\u2212\u2192D0\u2217K\u2217\u2212\u201d. Phys.\nRev. Lett. 92, 141801 (2004). hep-ex/0308057.\nAubert 2004l:\nB. Aubert et al. \u201cMeasurement of the branching frac-\ntions and CP-asymmetry of B\u2212\u2192D0\nCP K\u2212decays\nwith the BABAR detector\u201d. Phys. Rev. Lett. 92, 202002\n(2004). hep-ex/0311032.\nAubert 2004m:\nB. Aubert et al. \u201cMeasurement of the branching frac-\ntions for inclusive B\u2212and B0 decays to \ufb02avor-tagged\nD, Ds and \u039bc\u201d.\nPhys. Rev. D70, 091106 (2004).\nhep-ex/0408113.\nAubert 2004n:\nB. Aubert et al.\n\u201cMeasurement of the electron en-\nergy spectrum and its moments in inclusive B \u2192Xe\u03bd\ndecays\u201d.\nPhys. Rev. D69, 111104 (2004).\nhep-ex/\n0403030.\nAubert 2004o:\nB. Aubert et al. \u201cMeasurement of the time-dependent\nCP asymmetry in the B0 \u2192\u03c6K0 decay\u201d. Phys. Rev.\nLett. 93, 071801 (2004). hep-ex/0403026.\nAubert 2004p:\nB. Aubert et al. \u201cMeasurement of time-dependent CP\nasymmetries and constraints on sin(2\u03b2 +\u03b3) with partial\nreconstruction of B0 \u2192D\u2217\u2213\u03c0\u00b1 decays\u201d.\nPhys. Rev.\nLett. 92, 251802 (2004). hep-ex/0310037.\n\n808\nAubert 2004q:\nB. Aubert et al. \u201cMeasurements of CP violating asym-\nmetries in B0 \u2192K0\nS\u03c00 decays\u201d. Phys. Rev. Lett. 93,\n131805 (2004). hep-ex/0403001.\nAubert 2004r:\nB. Aubert et al.\n\u201cMeasurements of moments of the\nhadronic mass distribution in semileptonic B decays\u201d.\nPhys. Rev. D69, 111103 (2004). hep-ex/0403031.\nAubert 2004s:\nB. Aubert et al. \u201cMeasurements of the mass and width\nof the \u03b7c meson and of an \u03b7c(2S) candidate\u201d. Phys. Rev.\nLett. 92, 142002 (2004). hep-ex/0311038.\nAubert 2004t:\nB. Aubert et al. \u201cObservation of a narrow meson de-\ncaying to D+\ns \u03c00\u03b3 at a mass of 2.458 GeV/c2\u201d. Phys.\nRev. D69, 031101 (2004). hep-ex/0310050.\nAubert 2004u:\nB. Aubert et al. \u201cObservation of direct CP violation\nin B0 \u2192K+\u03c0\u2212decays\u201d. Phys. Rev. Lett. 93, 131801\n(2004). hep-ex/0407057.\nAubert 2004v:\nB. Aubert et al. \u201cObservation of the decay B \u2192J/\u03c8\u03b7K\nand search for X(3872) \u2192J/\u03c8\u03b7\u201d. Phys. Rev. Lett. 93,\n041801 (2004). hep-ex/0402025.\nAubert 2004w:\nB. Aubert et al. \u201cObservation of the decay B0 \u2192\u03c1+\u03c1\u2212\nand measurement of the branching fraction and polar-\nization\u201d.\nPhys. Rev. D69, 031102 (2004).\nhep-ex/\n0311017.\nAubert 2004x:\nB. Aubert et al. \u201cSearch for B-meson decays to two-\nbody \ufb01nal states with a0(980) mesons\u201d.\nPhys. Rev.\nD70, 111102 (2004). hep-ex/0407013.\nAubert 2004y:\nB. Aubert et al. \u201cSearch for B0 decays to invisible \ufb01nal\nstates and to \u03bd\u03bd\u03b3\u201d. Phys. Rev. Lett. 93, 091802 (2004).\nhep-ex/0405071.\nAubert 2004z:\nB. Aubert et al. \u201cSearch for \ufb02avor-changing neutral cur-\nrent and lepton \ufb02avor violating decays of D0 \u2192\u2113+\u2113\u2212\u201d.\nPhys. Rev. Lett. 93, 191801 (2004). hep-ex/0408023.\nAubert 2004aa:\nB. Aubert et al. \u201cSearch for strange pentaquark pro-\nduction in e+e\u2212annihilations at \u221as = 10.58 GeV and\nin \u03a5(4S) decays\u201d. In \u201cProceedings, 32nd International\nConference on High Energy Physics (ICHEP 2004) :\nBeijing, China, August 16-22, 2004\u201d, 2004, pages 99\u2013\n106. hep-ex/0408064.\nAubert 2004ab:\nB. Aubert et al. \u201cSearch for the decay B0 \u2192pp\u201d. Phys.\nRev. D69, 091503 (2004). hep-ex/0403003.\nAubert 2004ac:\nB. Aubert et al.\n\u201cSearch for the rare leptonic decay\nB+ \u2192\u00b5+\u03bd\u00b5\u201d.\nPhys. Rev. Lett. 92, 221803 (2004).\nhep-ex/0401002.\nAubert 2004ad:\nB. Aubert et al. \u201cStudy of B \u2192D(\u2217)+\nsJ\nD(\u2217) decays\u201d.\nPhys. Rev. Lett. 93, 181801 (2004). hep-ex/0408041.\nAubert 2004ae:\nB. Aubert et al. \u201cStudy of B\u00b1 \u2192J/\u03c8\u03c0\u00b1 and B\u00b1 \u2192\nJ/\u03c8K\u00b1 decays: Measurement of the ratio of branching\nfractions and search for direct CP violation\u201d. Phys. Rev.\nLett. 92, 241802 (2004). hep-ex/0401035.\nAubert 2004af:\nB. Aubert et al. \u201cStudy of e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c00 process\nusing initial state radiation with BABAR\u201d. Phys. Rev.\nD70, 072004 (2004). hep-ex/0408078.\nAubert 2004ag:\nB. Aubert et al. \u201cStudy of the decay B0(B0) \u2192\u03c1+\u03c1\u2212,\nand constraints on the CKM angle \u03b1\u201d. Phys. Rev. Lett.\n93, 231801 (2004). hep-ex/0404029.\nAubert 2005a:\nB. Aubert et al. \u201cA precision measurement of the \u039b+\nc\nbaryon mass\u201d. Phys. Rev. D72, 052006 (2005). hep-ex/\n0507009.\nAubert 2005b:\nB. Aubert et al. \u201cA search for the decay B+ \u2192K+\u03bd\u03bd\u201d.\nPhys. Rev. Lett. 94, 101801 (2005). hep-ex/0411061.\nAubert 2005c:\nB. Aubert et al.\n\u201cAmbiguity-free measurement of\ncos(2\u03b2): Time-integrated and time-dependent angular\nanalyses of B \u2192J/\u03c8K\u03c0\u201d.\nPhys. Rev. D71, 032005\n(2005). hep-ex/0411016.\nAubert 2005d:\nB. Aubert et al.\n\u201cAn amplitude analysis of the de-\ncay B\u00b1 \u2192\u03c0\u00b1\u03c0\u00b1\u03c0\u2213\u201d. Phys. Rev. D72, 052002 (2005).\nhep-ex/0507025.\nAubert 2005e:\nB. Aubert et al. \u201cBranching fraction and CP asymme-\ntries of B0 \u2192K0\nSK0\nSK0\nS\u201d. Phys. Rev. Lett. 95, 011801\n(2005). hep-ex/0502013.\nAubert 2005f:\nB. Aubert et al.\n\u201cDalitz plot analysis of D0\n\u2192\nK0K+K\u2212\u201d. Phys. Rev. D72, 052008 (2005). hep-ex/\n0507026.\nAubert 2005g:\nB. Aubert et al.\n\u201cDalitz-plot analysis of the decays\nB\u00b1 \u2192K\u00b1\u03c0\u2213\u03c0\u00b1\u201d.\nPhys. Rev. D72, 072003 (2005).\n[Erratum-ibid. D74, 099903 (2006)], hep-ex/0507004.\nAubert 2005h:\nB. Aubert et al.\n\u201cDetermination of |Vub| from mea-\nsurements of the electron and neutrino momenta in\ninclusive semileptonic B decays\u201d.\nPhys. Rev. Lett.\n95, 111801 (2005). [Erratum-ibid. 97, 019903 (2006)],\nhep-ex/0506036.\nAubert 2005i:\nB. Aubert et al. \u201cImproved measurement of CP asym-\nmetries in B0 \u2192(cc)K(\u2217)0 decays\u201d. Phys. Rev. Lett.\n94, 161803 (2005). hep-ex/0408127.\nAubert 2005j:\nB. Aubert et al. \u201cImproved measurement of the CKM\nangle \u03b1 using B0 \u2192\u03c1+\u03c1\u2212decays\u201d. Phys. Rev. Lett. 95,\n041805 (2005). hep-ex/0503049.\nAubert 2005k:\nB. Aubert et al.\n\u201cMeasurement of branching frac-\ntions and charge asymmetries for exclusive B decays\nto charmonium\u201d. Phys. Rev. Lett. 94, 141801 (2005).\n\n809\nhep-ex/0412062.\nAubert 2005l:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand charge asymmetries in B+ decays to \u03b7\u03c0+, \u03b7K+, \u03b7\u03c1+\nand \u03b7\u2032\u03c0+, and search for B0 decays to \u03b7K0 and \u03b7\u03c9\u201d.\nPhys. Rev. Lett. 95, 131803 (2005). hep-ex/0503035.\nAubert 2005m:\nB. Aubert et al. \u201cMeasurement of CP asymmetries in\nB0 \u2192\u03c6K0 and B0 \u2192K+K\u2212K0\nS decays\u201d. Phys. Rev.\nD71, 091102 (2005). hep-ex/0502019.\nAubert 2005n:\nB. Aubert et al. \u201cMeasurement of double charmonium\nproduction in e+e\u2212annihilations at \u221as = 10.6 GeV\u201d.\nPhys. Rev. D72, 031101 (2005). hep-ex/0506062.\nAubert 2005o:\nB. Aubert et al. \u201cMeasurement of \u03b3 in B\u2213\u2192D(\u2217)K\u2213\ndecays with a Dalitz analysis of D \u2192K0\nS\u03c0\u2212\u03c0+\u201d. Phys.\nRev. Lett. 95, 121802 (2005). hep-ex/0504039.\nAubert 2005p:\nB. Aubert et al. \u201cMeasurement of the B+ \u2192ppK+\nbranching fraction and study of the decay dynamics\u201d.\nPhys. Rev. D72, 051101 (2005). hep-ex/0507012.\nAubert 2005q:\nB. Aubert et al. \u201cMeasurement of the B0 \u2192D\u2217\u2212D\u2217+\ns\nand D+\ns \u2192\u03c6\u03c0+ branching fractions\u201d. Phys. Rev. D71,\n091104 (2005). hep-ex/0502041.\nAubert 2005r:\nB. Aubert et al. \u201cMeasurement of the branching fraction\nof \u03a5(4S) \u2192B0B0\u201d. Phys. Rev. Lett. 95, 042001 (2005).\nhep-ex/0504001.\nAubert 2005s:\nB. Aubert et al.\n\u201cMeasurement of the branching ra-\ntios \u0393(D\u2217+\ns\n\u2192D+\ns \u03c00)/\u0393(D\u2217+\ns\n\u2192D+\ns \u03b3) and \u0393(D\u22170 \u2192\nD0\u03c00)/\u0393(D\u22170 \u2192D0\u03b3)\u201d.\nPhys. Rev. D72, 091101\n(2005). hep-ex/0508039.\nAubert 2005t:\nB. Aubert et al. \u201cMeasurement of the ratio B(B\u2212\u2192\nD\u22170K\u2212)/B(B\u2212\u2192D\u22170\u03c0\u2212) and of the CP asymmetry\nof B\u2212\u2192D\u22170\nCP +K\u2212decays\u201d. Phys. Rev. D71, 031102\n(2005). hep-ex/0411091.\nAubert 2005u:\nB. Aubert et al.\n\u201cMeasurement of time-dependent\nCP asymmetries and the CP-odd fraction in the decay\nB0 \u2192D\u2217+D\u2217\u2212\u201d. Phys. Rev. Lett. 95, 151804 (2005).\nhep-ex/0506082.\nAubert 2005v:\nB. Aubert et al. \u201cMeasurement of time-dependent CP-\nviolating asymmetries and constraints on sin(2\u03b2 + \u03b3)\nwith partial reconstruction of B \u2192D\u2217\u2213\u03c0\u00b1 decays\u201d.\nPhys. Rev. D71, 112003 (2005). hep-ex/0504035.\nAubert 2005w:\nB. Aubert et al.\n\u201cMeasurements of branching frac-\ntions and time-dependent CP-violating asymmetries in\nB \u2192\u03b7\u2032K decays\u201d. Phys. Rev. Lett. 94, 191802 (2005).\nhep-ex/0502017.\nAubert 2005x:\nB. Aubert et al.\n\u201cMeasurements of the B \u2192Xs\u03b3\nbranching fraction and photon spectrum from a sum of\nexclusive \ufb01nal states\u201d. Phys. Rev. D72, 052004 (2005).\nhep-ex/0508004.\nAubert 2005y:\nB. Aubert et al. \u201cObservation of a broad structure in the\n\u03c0+\u03c0\u2212J/\u03c8 mass spectrum around 4.26 GeV/c2\u201d. Phys.\nRev. Lett. 95, 142001 (2005). hep-ex/0506081.\nAubert 2005z:\nB. Aubert et al.\n\u201cProduction and decay of \u039e0\nc at\nBABAR\u201d. Phys. Rev. Lett. 95, 142003 (2005). hep-ex/\n0504014.\nAubert 2005aa:\nB. Aubert et al. \u201cSearch for a charged partner of the\nX(3872) in the B meson decay B \u2192X\u2212K, X\u2212\u2192\nJ/\u03c8\u03c0\u2212\u03c00\u201d. Phys. Rev. D71, 031501 (2005). hep-ex/\n0412051.\nAubert 2005ab:\nB. Aubert et al. \u201cSearch for lepton-\ufb02avor and lepton-\nnumber violation in the decay \u03c4 \u2212\u2192\u2113\u2213h\u00b1h\u2032\u2212\u201d. Phys.\nRev. Lett. 95, 191801 (2005). hep-ex/0506066.\nAubert 2005ac:\nB. Aubert et al. \u201cSearch for strange-pentaquark produc-\ntion in e+e\u2212annihilation at \u221as = 10.58 GeV\u201d. Phys.\nRev. Lett. 95, 042002 (2005). hep-ex/0502004.\nAubert 2005ad:\nB. Aubert et al. \u201cSearch for the rare decay B0 \u2192D\u22170\u03b3\u201d.\nPhys. Rev. D72, 051106 (2005). hep-ex/0506070.\nAubert 2005ae:\nB. Aubert et al.\n\u201cSearch for the rare leptonic decay\nB\u2212\u2192\u03c4 \u2212\u03bd\u03c4\u201d.\nPhys. Rev. Lett. 95, 041804 (2005).\nhep-ex/0407038.\nAubert 2005af:\nB. Aubert et al. \u201cStudy of the B \u2192J/\u03c8K\u2212\u03c0+\u03c0\u2212decay\nand measurement of the B \u2192X(3872)K\u2212branching\nfraction\u201d.\nPhys. Rev. D71, 071103 (2005).\nhep-ex/\n0406022.\nAubert 2005ag:\nB. Aubert et al. \u201cStudy of the \u03c4 \u2212\u21923h\u22122h+\u03bd\u03c4 decay\u201d.\nPhys. Rev. D72, 072001 (2005). hep-ex/0505004.\nAubert 2005ah:\nB.\nAubert\net\nal.\n\u201cThe\ne+e\u2212\n\u2192\n\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212,\nK+K\u2212\u03c0+\u03c0\u2212, and K+K\u2212K+K\u2212cross sections at\ncenter-of-mass energies 0.5 GeV \u2013 4.5 GeV measured\nwith initial-state radiation\u201d. Phys. Rev. D71, 052001\n(2005). hep-ex/0502025.\nAubert 2006a:\nB. Aubert et al. \u201cA search for the decay B+ \u2192\u03c4 +\u03bd\u03c4\u201d.\nPhys. Rev. D73, 057101 (2006). hep-ex/0507069.\nAubert 2006b:\nB. Aubert et al. \u201cA search for the rare decay B0 \u2192\n\u03c4 +\u03c4 \u2212at BABAR\u201d. Phys. Rev. Lett. 96, 241802 (2006).\nhep-ex/0511015.\nAubert 2006c:\nB. Aubert et al. \u201cA Structure at 2175 MeV in e+e\u2212\u2192\n\u03c6f0(980) Observed via Initial-State Radiation\u201d. Phys.\nRev. D74, 091103 (2006). hep-ex/0610018.\nAubert 2006d:\nB. Aubert et al. \u201cA Study of e+e\u2212\u2192pp using initial\nstate radiation with BABAR\u201d. Phys. Rev. D73, 012005\n(2006). hep-ex/0512023.\n\n810\nAubert 2006e:\nB. Aubert et al.\n\u201cA study of the D\u2217\nsJ(2317)+ and\nDsJ(2460)+ mesons in inclusive cc production near\n\u221as = 10.6 GeV\u201d.\nPhys. Rev. D74, 032007 (2006).\nhep-ex/0604030.\nAubert 2006f:\nB. Aubert et al. \u201cB meson decays to \u03c9K\u2217, \u03c9\u03c1, \u03c9\u03c9, \u03c9\u03c6,\nand \u03c9f0\u201d. Phys. Rev. D74, 051102 (2006). hep-ex/\n0605017.\nAubert 2006g:\nB. Aubert et al. \u201cBranching fraction limits for B0 de-\ncays to \u03b7\u2032\u03b7, \u03b7\u2032\u03c00 and \u03b7\u03c00\u201d. Phys. Rev. D73, 071102\n(2006). hep-ex/0603013.\nAubert 2006h:\nB. Aubert et al.\n\u201cBranching fraction measurements\nof charged B\ndecays to K\u2217+K+K\u2212, K\u2217+\u03c0+K\u2212,\nK\u2217+K+\u03c0\u2212and K\u2217+\u03c0+\u03c0\u2212\ufb01nal states\u201d.\nPhys. Rev.\nD74, 051104 (2006). hep-ex/0607113.\nAubert 2006i:\nB. Aubert et al. \u201cDalitz plot analysis of the decay B\u00b1 \u2192\nK\u00b1K\u00b1K\u2213\u201d. Phys. Rev. D74, 032003 (2006). hep-ex/\n0605003.\nAubert 2006j:\nB. Aubert et al. \u201cImproved measurement of CP asym-\nmetries in B0 \u2192(cc)K(\u2217)0 decays\u201d hep-ex/0607107.\nAubert 2006k:\nB. Aubert et al. \u201cMeasurement of B0 \u2192D(\u2217)0K(\u2217)0\nbranching fractions\u201d. Phys. Rev. D74, 031101 (2006).\nhep-ex/0604016.\nAubert 2006l:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand charge asymmetries in B decays to an \u03b7 meson\nand a K\u2217meson\u201d. Phys. Rev. Lett. 97, 201802 (2006).\nhep-ex/0608005.\nAubert 2006m:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand CP-violating charge asymmetries for B meson de-\ncays to D(\u2217)D(\u2217), and implications for the CKM angle\n\u03b3\u201d. Phys. Rev. D73, 112004 (2006). hep-ex/0604037.\nAubert 2006n:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand resonance contributions for B0 \u2192D0K+\u03c0\u2212and\nsearch for B0 \u2192D0K+\u03c0\u2212decays\u201d. Phys. Rev. Lett.\n96, 011803 (2006). hep-ex/0509036.\nAubert 2006o:\nB. Aubert et al. \u201cMeasurement of branching fractions\nin radiative B decays to \u03b7K\u03b3 and search for B decays\nto \u03b7\u2032K\u03b3\u201d. Phys. Rev. D74, 031102 (2006). hep-ex/\n0603054.\nAubert 2006p:\nB. Aubert et al. \u201cMeasurement of the absolute branch-\ning fractions B \u2192D\u03c0, D\u2217\u03c0, D\u2217\u2217\u03c0 with a missing mass\nmethod\u201d.\nPhys. Rev. D74, 111102 (2006).\nhep-ex/\n0609033.\nAubert 2006q:\nB. Aubert et al. \u201cMeasurement of the B\u2212\u2192D0K\u2217\u2212\nbranching fraction\u201d. Phys. Rev. D73, 111104 (2006).\nhep-ex/0604017.\nAubert 2006r:\nB. Aubert et al.\n\u201cMeasurement of the B \u2192\u03c0\u2113\u03bd\nBranching Fraction and Determination of |Vub| with\nTagged B Mesons\u201d. Phys. Rev. Lett. 97, 211801 (2006).\nhep-ex/0607089.\nAubert 2006s:\nB. Aubert et al. \u201cMeasurement of the B0 lifetime and\nthe B0B0 oscillation frequency using partially recon-\nstructed B0 \u2192D\u2217+\u2113\u2212\u03bd\u2113decays\u201d.\nPhys. Rev. D73,\n012004 (2006). hep-ex/0507054.\nAubert 2006t:\nB. Aubert et al. \u201cMeasurement of the branching fraction\nand photon energy moments of B \u2192Xs\u03b3 and ACP (B \u2192\nXs+d\u03b3)\u201d. Phys. Rev. Lett. 97, 171803 (2006). hep-ex/\n0607071.\nAubert 2006u:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntion and Time-Dependent CP Asymmetry in the Decay\nB0 \u2192D\u2217+D\u2217\u2212K0\ns\u201d. Phys. Rev. D74, 091101 (2006).\nhep-ex/0608016.\nAubert 2006v:\nB. Aubert et al. \u201cMeasurement of the D+ \u2192\u03c0+\u03c00 and\nD+ \u2192K+\u03c00 branching fractions\u201d. Phys. Rev. D74,\n011107 (2006). hep-ex/0605044.\nAubert 2006w:\nB. Aubert et al. \u201cMeasurement of the \u03b7 and \u03b7\u2032 transition\nform factors at q2 = 112 GeV/c2\u201d. Phys. Rev. D74,\n012002 (2006). hep-ex/0605018.\nAubert 2006x:\nB. Aubert et al. \u201cMeasurement of the inclusive electron\nspectrum in charmless semileptonic B decays near the\nkinematic endpoint and determination of |Vub|\u201d. Phys.\nRev. D73, 012006 (2006). hep-ex/0509040.\nAubert 2006y:\nB. Aubert et al. \u201cMeasurement of the Mass and Width\nand Study of the Spin of the \u039e(1690)0 Resonance from\n\u039b+\nc\n\u2192\u039bK0K+ Decay at BABAR\u201d.\nIn \u201cProceedings,\n33rd International Conference on High Energy Physics\n(ICHEP 2006) : Moscow, Russia, July 26-August 2,\n2006\u201d, 2006. hep-ex/0607043.\nAubert 2006z:\nB. Aubert et al. \u201cMeasurement of the spin of the \u2126\u2212\nhyperon at BABAR\u201d. Phys. Rev. Lett. 97, 112001 (2006).\nhep-ex/0606039.\nAubert 2006aa:\nB. Aubert et al. \u201cMeasurement of time-dependent CP\nasymmetries in B0 \u2192D(\u2217)\u00b1\u03c0\u2213and B0 \u2192D\u00b1\u03c1\u2213\ndecays\u201d.\nPhys. Rev. D73, 111101 (2006).\nhep-ex/\n0602049.\nAubert 2006ab:\nB. Aubert et al. \u201cMeasurements of branching fractions,\npolarizations, and direct CP-violation asymmetries in\nB \u2192\u03c1K\u2217and B \u2192f0(980)K\u2217decays\u201d. Phys. Rev.\nLett. 97, 201801 (2006). hep-ex/0607057.\nAubert 2006ac:\nB. Aubert et al. \u201cMeasurements of branching fractions,\nrate asymmetries, and angular distributions in the rare\ndecays B \u2192K\u2113+\u2113\u2212and B \u2192K\u2217\u2113+\u2113\u2212\u201d. Phys. Rev.\nD73, 092001 (2006). hep-ex/0604007.\n\n811\nAubert 2006ad:\nB. Aubert et al. \u201cMeasurements of CP-violating asym-\nmetries and branching fractions in B decays to \u03c9K and\n\u03c9\u03c0\u201d. Phys. Rev. D74, 011106 (2006). hep-ex/0603040.\nAubert 2006ae:\nB. Aubert et al. \u201cMeasurements of the absolute branch-\ning fractions of B\u00b1 \u2192K\u00b1Xcc\u201d. Phys. Rev. Lett. 96,\n052002 (2006). hep-ex/0510070.\nAubert 2006af:\nB. Aubert et al. \u201cMeasurements of the B \u2192D\u2217form-\nfactors using the decay B0 \u2192D\u2217+e\u2212\u00af\u03bde\u201d. Phys. Rev.\nD74, 092004 (2006). hep-ex/0602023.\nAubert 2006ag:\nB. Aubert et al. \u201cObservation of a new Ds meson de-\ncaying to DK at a mass of 2.86 GeV/c2\u201d. Phys. Rev.\nLett. 97, 222001 (2006). hep-ex/0607082.\nAubert 2006ah:\nB. Aubert et al. \u201cObservation of an excited charm bar-\nyon \u2126\u2217\nc decaying to \u21260\nc\u03b3\u201d. Phys. Rev. Lett. 97, 232001\n(2006). hep-ex/0608055.\nAubert 2006ai:\nB. Aubert et al. \u201cObservation of B+ \u2192K0K+ and\nB0 \u2192K0K0\u201d.\nPhys. Rev. Lett. 97, 171805 (2006).\nhep-ex/0608036.\nAubert 2006aj:\nB. Aubert et al. \u201cObservation of B0 meson decay to\na1(1260)\u00b1\u03c0\u2213\u201d.\nPhys. Rev. Lett. 97, 051802 (2006).\nhep-ex/0603050.\nAubert 2006ak:\nB. Aubert et al.\n\u201cPrecise Branching Ratio Measure-\nments of the Decays D0\n\u2192\n\u03c0\u2212\u03c0+\u03c00 and D0\n\u2192\nK\u2212K+\u03c00\u201d. Phys. Rev. D74, 091102 (2006). hep-ex/\n0608009.\nAubert 2006al:\nB. Aubert et al. \u201cSearch for B meson decays to \u03b7\u2032\u03b7\u2032K\u201d.\nPhys. Rev. D74, 031105 (2006). hep-ex/0605008.\nAubert 2006am:\nB. Aubert et al. \u201cSearch for B+ \u2192\u03c6\u03c0+ and B0 \u2192\u03c6\u03c00\nDecays\u201d.\nPhys. Rev. D74, 011102 (2006).\nhep-ex/\n0605037.\nAubert 2006an:\nB. Aubert et al.\n\u201cSearch for B+ \u2192X(3872)K+,\nX(3872) \u2192J/\u03c8\u03b3\u201d. Phys. Rev. D74, 071101 (2006).\nhep-ex/0607050.\nAubert 2006ao:\nB. Aubert et al.\n\u201cSearch for doubly charmed bary-\nons \u039e+\ncc and \u039e++\ncc\nin BABAR\u201d. Phys. Rev. D74, 011103\n(2006). hep-ex/0605075.\nAubert 2006ap:\nB. Aubert et al. \u201cSearch for D0 \u2212D0 mixing in the de-\ncays D0 \u2192K+\u03c0\u2212\u03c0+\u03c0\u2212\u201d. In \u201cProceedings, 33rd Inter-\nnational Conference on High Energy Physics (ICHEP\n2006) : Moscow, Russia, July 26 \u2013 August 2, 2006\u201d,\n2006. hep-ex/0607090.\nAubert 2006aq:\nB. Aubert et al. \u201cSearch for T, CP and CPT violation\nin B0\u2212B0 mixing with inclusive dilepton events\u201d. Phys.\nRev. Lett. 96, 251802 (2006). hep-ex/0603053.\nAubert 2006ar:\nB. Aubert et al. \u201cSearch for the charmed pentaquark\ncandidate \u0398c(3100)0 in e+e\u2212annihilations at \u221as =\n10.58 GeV\u201d. Phys. Rev. D73, 091101 (2006). hep-ex/\n0604006.\nAubert 2006as:\nB. Aubert et al. \u201cSearch for the decay B0 \u2192a\u00b1\n1 \u03c1\u2213\u201d.\nPhys. Rev. D74, 031104 (2006). hep-ex/0605024.\nAubert 2006at:\nB. Aubert et al. \u201cSearch for the decay B0 \u2192K0\nSK0\nSK0\nL\u201d.\nPhys. Rev. D74, 032005 (2006). hep-ex/0606031.\nAubert 2006au:\nB. Aubert et al. \u201cSearch for the decay of a B0 or B0\nmeson to K\u22170K0 or K\u22170K0\u201d. Phys. Rev. D74, 072008\n(2006). hep-ex/0606050.\nAubert 2006av:\nB. Aubert et al. \u201cSearches for B0 decays to \u03b7K0, \u03b7\u03b7,\n\u03b7\u2032\u03b7\u2032, \u03b7\u03c6, and \u03b7\u2032\u03c6\u201d.\nPhys. Rev. D74, 051106 (2006).\nhep-ex/0607063.\nAubert 2006aw:\nB. Aubert et al.\n\u201cStudy of B \u2192D(\u2217)D(\u2217)\ns(J) Decays\nand Measurement of D\u2212\ns\nand DsJ(2460)\u2212Branching\nFractions\u201d. Phys. Rev. D74, 031103 (2006). hep-ex/\n0605036.\nAubert 2006ax:\nB. Aubert et al. \u201cStudy of J/\u03c8\u03c0+\u03c0\u2212states produced in\nB0 \u2192J/\u03c8\u03c0+\u03c0\u2212K0 and B\u2212\u2192J/\u03c8\u03c0+\u03c0\u2212K\u2212\u201d. Phys.\nRev. D73, 011101 (2006). hep-ex/0507090.\nAubert 2006ay:\nB. Aubert et al. \u201cStudy of the decay B0 \u2192D\u2217+\u03c9\u03c0\u2212\u201d.\nPhys. Rev. D74, 012001 (2006). hep-ex/0604009.\nAubert 2006az:\nB. Aubert et al. \u201cThe e+e\u2212\u21923(\u03c0+\u03c0\u2212), 2(\u03c0+\u03c0\u2212\u03c00)\nand K+K\u22122(\u03c0+\u03c0\u2212) cross sections at center-of-mass en-\nergies from production threshold to 4.5 GeV measured\nwith initial-state radiation\u201d. Phys. Rev. D73, 052003\n(2006). hep-ex/0602006.\nAubert 2006ba:\nB. Aubert et al. \u201c\u039e\u2032\nc production at BABAR\u201d Submit-\nted to ICHEP2006, Report-no: BABAR-CONF-06/008,\nSLAC-PUB-12024, hep-ex/0607086.\nAubert 2007a:\nB. Aubert et al. \u201cA Search for B+ \u2192\u03c4 +\u03bd\u201d. Phys. Rev.\nD76, 052002 (2007). 0705.1820.\nAubert 2007b:\nB. Aubert et al. \u201cA Study of B0 \u2192\u03c1+\u03c1\u2212Decays and\nConstraints on the CKM Angle \u03b1\u201d. Phys. Rev. D76,\n052007 (2007). 0705.2157.\nAubert 2007c:\nB. Aubert et al.\n\u201cAmplitude analysis of the B\u00b1 \u2192\n\u03c6K\u2217(892)\u00b1 decay\u201d. Phys. Rev. Lett. 99, 201802 (2007).\n0705.1798.\nAubert 2007d:\nB. Aubert et al.\n\u201cAmplitude Analysis of the decay\nD0 \u2192K\u2212K+\u03c00\u201d.\nPhys. Rev. D76, 011102 (2007).\n0704.3593.\nAubert 2007e:\nB. Aubert et al. \u201cBranching fraction and charge asym-\nmetry measurements in B \u2192J/\u03c8\u03c0\u03c0 decays\u201d.\nPhys.\n\n812\nRev. D76, 031101 (2007). 0704.1266.\nAubert 2007f:\nB. Aubert et al. \u201cBranching fraction and CP-violation\ncharge asymmetry measurements for B-meson decays\nto \u03b7K\u00b1, \u03b7\u03c0\u00b1, \u03b7\u2032K, \u03b7\u2032\u03c0\u00b1, \u03c9K, and \u03c9\u03c0\u00b1\u201d. Phys. Rev.\nD76, 031103 (2007). 0706.3893.\nAubert 2007g:\nB. Aubert et al. \u201cBranching fraction measurement of\nB0 \u2192D(\u2217)+\u03c0\u2212, B\u2212\u2192D(\u2217)0\u03c0\u2212and isospin analysis of\nB \u2192D(\u2217)\u03c0 decays\u201d. Phys. Rev. D75, 031101 (2007).\nhep-ex/0610027.\nAubert 2007h:\nB. Aubert et al. \u201cEvidence for B0 \u2192\u03c10\u03c10 decay and\nimplications for the CKM angle \u03b1\u201d. Phys. Rev. Lett.\n98, 111801 (2007). hep-ex/0612021.\nAubert 2007i:\nB. Aubert et al. \u201cEvidence for charged B meson decays\nto a1(1260)\u00b1\u03c00 and a1(1260)0\u03c0\u00b1\u201d. Phys. Rev. Lett. 99,\n261801 (2007). 0708.0050.\nAubert 2007j:\nB. Aubert et al. \u201cEvidence for D0 \u2212D0 Mixing\u201d. Phys.\nRev. Lett. 98, 211802 (2007). hep-ex/0703020.\nAubert 2007k:\nB. Aubert et al. \u201cEvidence for the B0 \u2192ppK\u22170 and\nB+ \u2192\u03b7cK\u2217+ decays and Study of the Decay Dynamics\nof B Meson Decays into pph Final States\u201d. Phys. Rev.\nD76, 092004 (2007). 0707.1648.\nAubert 2007l:\nB. Aubert et al. \u201cEvidence for the Rare Decay B+ \u2192\nD+\ns \u03c00\u201d. Phys. Rev. Lett. 98, 171801 (2007). hep-ex/\n0611030.\nAubert 2007m:\nB. Aubert et al. \u201cEvidence of a broad structure at an\ninvariant mass of 4.32 GeV/c2 in the reaction e+e\u2212\u2192\n\u03c0+\u03c0\u2212\u03c8(2S) measured at BABAR\u201d. Phys. Rev. Lett. 98,\n212001 (2007). hep-ex/0610057.\nAubert 2007n:\nB. Aubert et al.\n\u201cImproved Measurement of Time-\nDependent CP Asymmetries and the CP-Odd Fraction\nin the Decay B0 \u2192D\u2217+D\u2217\u2212\u201d. Phys. Rev. D76, 111102\n(2007). 0708.1549.\nAubert 2007o:\nB. Aubert et al.\n\u201cImproved Measurements of the\nBranching Fractions for B0 \u2192\u03c0+\u03c0\u2212and B0 \u2192K+\u03c0\u2212,\nand a Search for B0 \u2192K+K\u2212\u201d.\nPhys. Rev. D75,\n012008 (2007). hep-ex/0608003.\nAubert 2007p:\nB. Aubert et al. \u201cInclusive \u039bc production in e+e\u2212an-\nnihilations at \u221as = 10.54 GeV and in \u03a5(4S) decays\u201d.\nPhys. Rev. D75, 012003 (2007). hep-ex/0609004.\nAubert 2007q:\nB. Aubert et al. \u201cMeasurement of B decays to \u03c6K\u03b3\u201d.\nPhys. Rev. D75, 051102 (2007). hep-ex/0611037.\nAubert 2007r:\nB. Aubert et al. \u201cMeasurement of branching fractions\nand mass spectra of B \u2192K\u03c0\u03c0\u03b3\u201d.\nPhys. Rev. Lett.\n98, 211804 (2007). [Erratum-ibid. 100, 189903 (2008);\nErratum-ibid. 100, 199905 (2008)], hep-ex/0507031.\nAubert 2007s:\nB. Aubert et al.\n\u201cMeasurement of cos 2\u03b2 in B0 \u2192\nD(\u2217)h0 Decays with a Time-Dependent Dalitz Plot\nAnalysis of D \u2192K0\nS\u03c0+\u03c0\u2212\u201d.\nPhys. Rev. Lett. 99,\n231802 (2007). 0708.1544.\nAubert 2007t:\nB. Aubert et al.\n\u201cMeasurement of CP Asymmetry\nin B0 \u2192Ks\u03c00\u03c00 Decays\u201d.\nPhys. Rev. D76, 071101\n(2007). hep-ex/0702010.\nAubert 2007u:\nB. Aubert et al. \u201cMeasurement of CP-Violating Asym-\nmetries in B0 \u2192D(\u2217)\u00b1D\u2213\u201d.\nPhys. Rev. Lett. 99,\n071801 (2007). 0705.1190.\nAubert 2007v:\nB. Aubert et al. \u201cMeasurement of CP-violating asym-\nmetries in B0 \u2192(\u03c1\u03c0)0 using a time-dependent Dalitz\nplot analysis\u201d. Phys. Rev. D76, 012004 (2007). hep-ex/\n0703008.\nAubert 2007w:\nB. Aubert et al.\n\u201cMeasurement of CP\nViolation\nParameters with a Dalitz Plot Analysis of B\u00b1\n\u2192\nD\u03c0+\u03c0\u2212\u03c00K\u00b1\u201d.\nPhys. Rev. Lett. 99, 251801 (2007).\nhep-ex/0703037.\nAubert 2007x:\nB. Aubert et al.\n\u201cMeasurement of decay amplitudes\nof B \u2192J/\u03c8K\u2217, \u03c8(2S)K\u2217, and \u03c7c1K\u2217with an angular\nanalysis\u201d. Phys. Rev. D76, 031102 (2007). 0704.0522.\nAubert 2007y:\nB. Aubert et al.\n\u201cMeasurement of the B\u00b1 \u2192\u03c1\u00b1\u03c00\nBranching Fraction and Direct CP Asymmetry\u201d. Phys.\nRev. D75, 091103 (2007). hep-ex/0701035.\nAubert 2007z:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntions of Exclusive B \u2192D/D\u2217/(D(\u2217)\u03c0)\u2113\u2212\u03bd\u2113Decays\nin Events Tagged by a Fully Reconstructed B Me-\nson\u201d.\nIn \u201cLepton and photon interactions at high\nenergies. Proceedings, 23rd International Symposium,\nLP2007, Daegu, South Korea, August 13\u201318, 2007\u201d,\n2007. 0708.1738.\nAubert 2007aa:\nB. Aubert et al. \u201cMeasurement of the CP asymmetry\nand branching fraction of B0 \u2192\u03c10K0\u201d.\nPhys. Rev.\nLett. 98, 051803 (2007). hep-ex/0608051.\nAubert 2007ab:\nB. Aubert et al. \u201cMeasurement of the hadronic form-\nfactor in D0 \u2192K\u2212e+\u03bde Decays\u201d.\nPhys. Rev. D76,\n052005 (2007). 0704.0020.\nAubert 2007ac:\nB. Aubert et al. \u201cMeasurement of the \u03c4 \u2212\u2192K\u2212\u03c00\u03bd\u03c4\nbranching fraction\u201d. Phys. Rev. D76, 051104 (2007).\n0707.2922.\nAubert 2007ad:\nB. Aubert et al. \u201cMeasurement of the time-dependent\nCP asymmetry in B0 \u2192D(\u2217)\nCP h0 decays\u201d. Phys. Rev.\nLett. 99, 081801 (2007). hep-ex/0703019.\nAubert 2007ae:\nB. Aubert et al. \u201cMeasurements of CP-Violating Asym-\nmetries in B0 \u2192a\u00b1\n1 (1260)\u03c0\u2213decays\u201d. Phys. Rev. Lett.\n98, 181803 (2007). hep-ex/0612050.\n\n813\nAubert 2007af:\nB. Aubert et al. \u201cMeasurements of CP-violating asym-\nmetries in the decay B0 \u2192K+K\u2212K0\u201d.\nPhys. Rev.\nLett. 99, 161802 (2007). 0706.3885.\nAubert 2007ag:\nB. Aubert et al. \u201cMeasurements of \u039b+\nc branching frac-\ntions of Cabibbo-suppressed decay modes involving \u039b\nand \u03a30\u201d.\nPhys. Rev. D75, 052002 (2007).\nhep-ex/\n0601017.\nAubert 2007ah:\nB. Aubert et al.\n\u201cMeasurements of the Branching\nFractions of B0 \u2192K\u22170K+K\u2212, B0 \u2192K\u22170\u03c0+K\u2212,\nB0 \u2192K\u22170K+\u03c0\u2212, and B0 \u2192K\u22170\u03c0+\u03c0\u2212\u201d. Phys. Rev.\nD76, 071104 (2007). 0708.2543.\nAubert 2007ai:\nB. Aubert et al.\n\u201cObservation of a charmed baryon\ndecaying to D0p at a mass near 2.94 GeV/c2\u201d. Phys.\nRev. Lett. 98, 012001 (2007). hep-ex/0603052.\nAubert 2007aj:\nB. Aubert et al. \u201cObservation of B-meson decays to b1\u03c0\nand b1K\u201d. Phys. Rev. Lett. 99, 241803 (2007). 0707.\n4561.\nAubert 2007ak:\nB. Aubert et al. \u201cObservation of B \u2192\u03b7\u2032K\u2217and ev-\nidence for B+ \u2192\u03b7\u2032\u03c1+\u201d. Phys. Rev. Lett. 98, 051802\n(2007). hep-ex/0607109.\nAubert 2007al:\nB. Aubert et al. \u201cObservation of B+ to \u03c1+K0 and Mea-\nsurement of its Branching Fraction and Charge Asym-\nmetry\u201d.\nPhys. Rev. D76, 011103 (2007).\nhep-ex/\n0702043.\nAubert 2007am:\nB. Aubert et al.\n\u201cObservation of CP violation in\nB0 \u2192\u03b7\u2032K0 decays\u201d.\nPhys. Rev. Lett. 98, 031801\n(2007). hep-ex/0609052.\nAubert 2007an:\nB. Aubert et al.\n\u201cObservation of the Decay B+ \u2192\nK+K\u2212\u03c0+\u201d. Phys. Rev. Lett. 99, 221801 (2007). 0708.\n0376.\nAubert 2007ao:\nB. Aubert et al. \u201cProduction and decay of \u21260\nc\u201d. Phys.\nRev. Lett. 99, 062001 (2007). hep-ex/0703030.\nAubert 2007ap:\nB. Aubert et al. \u201cSearch for B0 \u2192\u03c6(K+\u03c0\u2212) decays\nwith large K+\u03c0\u2212invariant mass\u201d.\nPhys. Rev. D76,\n051103 (2007). 0705.0398.\nAubert 2007aq:\nB. Aubert et al.\n\u201cSearch for D0 \u2212D0 mixing using\ndoubly \ufb02avor tagged semileptonic decay modes\u201d. Phys.\nRev. D76, 014018 (2007). 0705.0704.\nAubert 2007ar:\nB. Aubert et al. \u201cSearch for Lepton Flavor Violating\nDecays \u03c4 \u00b1 \u2192\u2113\u00b1\u03c00, \u2113\u00b1\u03b7, \u2113\u00b1\u03b7\u2032\u201d. Phys. Rev. Lett. 98,\n061803 (2007). hep-ex/0610067.\nAubert 2007as:\nB. Aubert et al. \u201cSearch for neutral B-meson decays\nto a0\u03c0, a0K, \u03b7\u03c10, and \u03b7f0\u201d. Phys. Rev. D75, 111102\n(2007). hep-ex/0703038.\nAubert 2007at:\nB. Aubert et al. \u201cSearch for Prompt Production of \u03c7c\nand X(3872) in e+e\u2212Annihilations\u201d. Phys. Rev. D76,\n071102 (2007). 0707.1633.\nAubert 2007au:\nB. Aubert et al.\n\u201cSearch for the decay B+\n\u2192\nK+\u03c4 \u2213\u00b5\u00b1\u201d. Phys. Rev. Lett. 99, 201801 (2007). 0708.\n1303.\nAubert 2007av:\nB. Aubert et al.\n\u201cSearch for the decay B+\n\u2192\nK\u22170(892)K+\u201d. Phys. Rev. D76, 071103 (2007). 0706.\n1059.\nAubert 2007aw:\nB. Aubert et al. \u201cSearch for the radiative leptonic decay\nB+ \u2192\u03b3\u2113+\u03bdl\u201d 0704.1478.\nAubert 2007ax:\nB. Aubert et al.\n\u201cSearch for the rare decay B \u2192\n\u03c0\u2113+\u2113\u2212\u201d. Phys. Rev. Lett. 99, 051801 (2007). hep-ex/\n0703018.\nAubert 2007ay:\nB. Aubert et al. \u201cStudy of B0 \u2192\u03c00\u03c00, B\u00b1 \u2192\u03c0\u00b1\u03c00,\nand B\u00b1 \u2192K\u00b1\u03c00 Decays, and Isospin Analysis of B \u2192\n\u03c0\u03c0 Decays\u201d. Phys. Rev. D76, 091102 (2007). 0707.\n2798.\nAubert 2007az:\nB. Aubert et al. \u201cStudy of e+e\u2212\u2192\u039b\u039b, \u039b\u03a30, \u03a30\u03a30\nusing initial state radiation with BABAR\u201d. Phys. Rev.\nD76, 092006 (2007). 0709.1988.\nAubert 2007ba:\nB. Aubert et al. \u201cStudy of inclusive B\u2212and B0 de-\ncays to \ufb02avor-tagged D, Ds and \u039b+\nc \u201d. Phys. Rev. D75,\n072002 (2007). hep-ex/0606026.\nAubert 2007bb:\nB. Aubert et al. \u201cThe e+e\u2212\u21922(\u03c0+\u03c0\u2212)\u03c00, 2(\u03c0+\u03c0\u2212)\u03b7,\nK+K\u2212\u03c0+\u03c0\u2212\u03c00 and K+K\u2212\u03c0+\u03c0\u2212\u03b7 Cross Sections Mea-\nsured with Initial-State Radiation\u201d. Phys. Rev. D76,\n092005 (2007).\n[Erratum-ibid. D77, 119902 (2008)],\n0708.2461.\nAubert 2007bc:\nB. Aubert et al.\n\u201cThe e+e\u2212\n\u2192\nK+K\u2212\u03c0+\u03c0\u2212,\nK+K\u2212\u03c00\u03c00 and K+K\u2212K+K\u2212Cross Sections Mea-\nsured with Initial-State Radiation\u201d. Phys. Rev. D76,\n012008 (2007). 0704.0630.\nAubert 2008a:\nB. Aubert et al. \u201cA Measurement of CP Asymmetry in\nb \u2192s\u03b3 using a Sum of Exclusive Final States\u201d. Phys.\nRev. Lett. 101, 171804 (2008). 0805.4796.\nAubert 2008b:\nB. Aubert et al. \u201cA Measurement of the branching frac-\ntions of exclusive B \u2192D(\u2217)(\u03c0)\u2113\u2212\u03bd\u2113decays in events\nwith a fully reconstructed B meson\u201d. Phys. Rev. Lett.\n100, 151802 (2008). 0712.3503.\nAubert 2008c:\nB. Aubert et al.\n\u201cA Search for B+ \u2192\u03c4 +\u03bd with\nHadronic B tags\u201d.\nPhys. Rev. D77, 011107 (2008).\n0708.2260.\nAubert 2008d:\nB. Aubert et al. \u201cA Study of B \u2192X(3872)K, with\nX(3872) \u2192J/\u03c8\u03c0+\u03c0\u2212\u201d.\nPhys. Rev. D77, 111101\n\n814\n(2008). 0803.2838.\nAubert 2008e:\nB. Aubert et al. \u201cA study of B \u2192\u039ec\u039b\u2212\nc and B \u2192\n\u039b+\nc \u039b\u2212\nc K decays at BABAR\u201d. Phys. Rev. D77, 031101\n(2008). 0710.5775.\nAubert 2008f:\nB. Aubert et al. \u201cA Study of Excited Charm-Strange\nBaryons with Evidence for new Baryons \u039ec(3055)+ and\n\u039ec(3123)+\u201d. Phys. Rev. D77, 012002 (2008). 0710.\n5763.\nAubert 2008g:\nB. Aubert et al.\n\u201cDalitz Plot Analysis of the Decay\nB0(B0) \u2192K\u00b1\u03c0\u2213\u03c00\u201d. Phys. Rev. D78, 052005 (2008).\n0711.4417.\nAubert 2008h:\nB. Aubert et al.\n\u201cDetermination of the form-factors\nfor the decay B0 \u2192D\u2217\u2212\u2113+\u03bdl and of the CKM matrix\nelement |Vcb|\u201d. Phys. Rev. D77, 032002 (2008). 0705.\n4008.\nAubert 2008i:\nB. Aubert et al. \u201cEvidence for CP violation in B0 \u2192\nJ/\u03c8\u03c00 decays\u201d. Phys. Rev. Lett. 101, 021801 (2008).\n0804.0896.\nAubert 2008j:\nB. Aubert et al.\n\u201cEvidence for Direct CP Violation\nfrom Dalitz-plot analysis of B\u00b1 \u2192K\u00b1\u03c0\u2213\u03c0\u00b1\u201d. Phys.\nRev. D78, 012004 (2008). 0803.4451.\nAubert 2008k:\nB. Aubert et al.\n\u201cExclusive branching fraction mea-\nsurements of semileptonic tau decays into three charged\nhadrons, \u03c4 \u2212\u2192\u03c6\u03c0\u2212\u03bd\u03c4 and \u03c4 \u2212\u2192\u03c6K\u2212\u03bd\u03c4\u201d. Phys. Rev.\nLett. 100, 011801 (2008). 0707.2981.\nAubert 2008l:\nB. Aubert et al. \u201cImproved measurement of the CKM\nangle \u03b3 in B\u2213\u2192D(\u2217)K(\u2217\u2213) decays with a Dalitz plot\nanalysis of D decays to K0\nS\u03c0+\u03c0\u2212and K0\nSK+K\u2212\u201d. Phys.\nRev. D78, 034023 (2008). 0804.2089.\nAubert 2008m:\nB. Aubert et al.\n\u201cMeasurement of CP Asymmetries\nand Branching Fractions in B0 \u2192\u03c0+\u03c0\u2212, B0 \u2192K+\u03c0\u2212,\nB0 \u2192\u03c00\u03c00, B0 \u2192K0\u03c00 and Isospin Analysis of\nB \u2192\u03c0\u03c0 Decays\u201d 27 pages, submitted to ICHEP2008\nReport-no: BABAR-CONF-00-014, SLAC-PUB-13326,\n0807.4226.\nAubert 2008n:\nB. Aubert et al.\n\u201cMeasurement of D0 \u2212D0 mixing\nusing the ratio of lifetimes for the decays D0 \u2192K\u2212\u03c0+,\nK\u2212K+, and \u03c0\u2212\u03c0+\u201d. Phys. Rev. D78, 011105 (2008).\n0712.2249.\nAubert 2008o:\nB. Aubert et al. \u201cMeasurement of Ratios of Branch-\ning Fractions and CP Violating Asymmetries of B\u00b1 \u2192\nD\u2217K\u00b1 Decays\u201d. Phys. Rev. D78, 092002 (2008). 0807.\n2408.\nAubert 2008p:\nB. Aubert et al. \u201cMeasurement of the absolute branch-\ning fraction of D0 \u2192K\u2212\u03c0+\u201d. Phys. Rev. Lett. 100,\n051802 (2008). 0704.2080.\nAubert 2008q:\nB. Aubert et al.\n\u201cMeasurement of the B \u2192Xs\u03b3\nBranching Fraction and Photon Energy Spectrum using\nthe Recoil Method\u201d. Phys. Rev. D77, 051103 (2008).\n0711.4889.\nAubert 2008r:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntion, Polarization, and CP Asymmetries in B0 \u2192\u03c10\u03c10\nDecay, and Implications for the CKM Angle \u03b1\u201d. Phys.\nRev. D78, 071104 (2008). 0807.4977.\nAubert 2008s:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntions of B \u2192D\u2217\u2217l\u2212\u03bdl decays in Events Tagged by a\nFully Reconstructed B Meson\u201d. Phys. Rev. Lett. 101,\n261802 (2008). 0808.0528.\nAubert 2008t:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntions of the Radiative Charm Decays D0 \u2192K\u22170\u03b3 and\nD0 \u2192\u03c6\u03b3\u201d. Phys. Rev. D78, 071101 (2008). 0808.1838.\nAubert 2008u:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntions of the Rare Decays B0\n\u2192D(\u2217)+\ns\n\u03c0\u2212, B0\n\u2192\nD(\u2217)+\ns\n\u03c1\u2212, and B0 \u2192D(\u2217)\u2212\ns\nK(\u2217)+\u201d. Phys. Rev. D78,\n032005 (2008). 0803.4296.\nAubert 2008v:\nB. Aubert et al. \u201cMeasurement of the Decay B\u2212\u2192\nD\u22170e\u2212\u03bde\u201d. Phys. Rev. Lett. 100, 231803 (2008). 0712.\n3493.\nAubert 2008w:\nB. Aubert et al.\n\u201cMeasurement of the Spin of the\n\u039e(1530) Resonance\u201d. Phys. Rev. D78, 034008 (2008).\n0803.1863.\nAubert 2008x:\nB. Aubert et al. \u201cMeasurement of Time-Dependent CP\nAsymmetry in B0 \u2192K0\nS\u03c00\u03b3 Decays\u201d. Phys. Rev. D78,\n071102 (2008). 0807.3103.\nAubert 2008y:\nB. Aubert et al. \u201cMeasurements of B \u2192{\u03c0, \u03b7, \u03b7\u2032}\u2113\u03bd\u2113\nBranching Fractions and Determination of |Vub| with\nSemileptonically Tagged B Mesons\u201d. Phys. Rev. Lett.\n101, 081801 (2008). 0805.2408.\nAubert 2008z:\nB. Aubert et al. \u201cMeasurements of Branching Fractions\nfor B+ \u2192\u03c1+\u03b3, B0 \u2192\u03c10\u03b3, and B0 \u2192\u03c9\u03b3\u201d. Phys. Rev.\nD78, 112001 (2008). 0808.1379.\nAubert 2008aa:\nB. Aubert et al. \u201cMeasurements of B(B0 \u2192\u039b+\nc p and\nB(B\u2212\u2192\u039b+\nc p\u03c0\u2212) and Studies of \u039b+\nc \u03c0\u2212Resonances\u201d.\nPhys. Rev. D78, 112003 (2008). 0807.4974.\nAubert 2008ab:\nB. Aubert et al. \u201cMeasurements of e+e\u2212\u2192K+K\u2212\u03b7,\nK+K\u2212\u03c00 and K0\nsK\u00b1\u03c0\u2213cross-sections using initial\nstate radiation events\u201d. Phys. Rev. D77, 092002 (2008).\n0710.4451.\nAubert 2008ac:\nB. Aubert et al. \u201cMeasurements of Partial Branching\nFractions for B \u2192Xu\u2113\u03bd and Determination of |Vub|\u201d.\nPhys. Rev. Lett. 100, 171802 (2008). 0708.3702.\n\n815\nAubert 2008ad:\nB. Aubert et al. \u201cObservation and Polarization Mea-\nsurements of B\u00b1 \u2192\u03c6K\u00b1\n1 and B\u00b1 \u2192\u03c6K\u2217\u00b1\n2 \u201d. Phys.\nRev. Lett. 101, 161801 (2008). 0806.4419.\nAubert 2008ae:\nB. Aubert et al.\n\u201cObservation of B+ Meson Decays\nto a1(1260)+K0 and B0 to a1(1260)\u2212K+\u201d. Phys. Rev.\nLett. 100, 051803 (2008). 0709.4165.\nAubert 2008af:\nB. Aubert et al. \u201cObservation of B+ \u2192\u03b7\u03c1+ and search\nfor B0 decays to \u03b7\u2032\u03b7, \u03b7\u03c00, \u03b7\u2032\u03c00, and \u03c9\u03c00\u201d. Phys. Rev.\nD78, 011107 (2008). 0804.2422.\nAubert 2008ag:\nB. Aubert et al. \u201cObservation of B0 \u2192\u03c7c0K\u22170 and\nevidence for B+ \u2192\u03c7c0K\u2217+\u201d. Phys. Rev. D78, 091101\n(2008). 0808.1487.\nAubert 2008ah:\nB. Aubert et al. \u201cObservation of B0 \u2192K\u22170K\u22170 and\nsearch for B0 \u2192K\u22170K\u22170\u201d. Phys. Rev. Lett. 100, 081801\n(2008). 0708.2248.\nAubert 2008ai:\nB. Aubert et al. \u201cObservation of B\u2212\u2192D(\u2217)+\ns\nK\u2212\u03c0\u2212\nand B0 \u2192D+\ns K0\nS\u03c0\u2212and Search for B0 \u2192D\u2217+\ns K0\nS\u03c0\u2212\nand B\u2212\u2192D(\u2217)+\ns\nK\u2212K\u2212\u201d. Phys. Rev. Lett. 100, 171803\n(2008). 0707.1043.\nAubert 2008aj:\nB. Aubert et al.\n\u201cObservation of B+ \u2192b+\n1 K0 and\nsearch for B-meson decays to b0\n1K0 and b1\u03c00\u201d. Phys.\nRev. D78, 011104 (2008). 0805.1217.\nAubert 2008ak:\nB. Aubert et al.\n\u201cObservation of the bottomonium\nground state in the decay \u03a5(3S) \u2192\u03b3\u03b7b\u201d. Phys. Rev.\nLett. 101, 071801 (2008). [Erratum-ibid. 102, 029901\n(2009)], 0807.1086.\nAubert 2008al:\nB. Aubert et al. \u201cObservation of the semileptonic decays\nB \u2192D\u2217\u03c4 \u2212\u03bd\u03c4 and evidence for B \u2192D\u03c4 \u2212\u03bd\u03c4\u201d. Phys.\nRev. Lett. 100, 021801 (2008). 0709.1698.\nAubert 2008am:\nB. Aubert et al. \u201cObservation of Y (3940) \u2192J/\u03c8\u03c9 in\nB \u2192J/\u03c8\u03c9K at BABAR\u201d. Phys. Rev. Lett. 101, 082001\n(2008). 0711.2047.\nAubert 2008an:\nB. Aubert et al. \u201cSearch for B \u2192K\u2217\u03bd\u03bd decays\u201d. Phys.\nRev. D78, 072007 (2008). 0808.1338.\nAubert 2008ao:\nB. Aubert et al. \u201cSearch for B0 \u2192K\u2217+K\u2217\u2212\u201d. Phys.\nRev. D78, 051103 (2008). 0806.4467.\nAubert 2008ap:\nB. Aubert et al. \u201cSearch for CP Violation in Neutral D\nMeson Cabibbo-suppressed Three-body Decays\u201d. Phys.\nRev. D78, 051102 (2008). 0802.4035.\nAubert 2008aq:\nB. Aubert et al. \u201cSearch for CP violation in the decays\nD0 \u2192K\u2212K+ and D0 \u2192\u03c0\u2212\u03c0+\u201d. Phys. Rev. Lett. 100,\n061803 (2008). 0709.2715.\nAubert 2008ar:\nB. Aubert et al. \u201cSearch for CPT and Lorentz Violation\nin B0 \u2212B0 Oscillations with Dilepton Events\u201d. Phys.\nRev. Lett. 100, 131802 (2008). 0711.2713.\nAubert 2008as:\nB. Aubert et al. \u201cSearch for decays of B0 mesons into\ne+e\u2212, \u00b5+\u00b5\u2212, and e\u00b1\u00b5\u2213\ufb01nal states\u201d. Phys. Rev. D77,\n032007 (2008). 0712.1516.\nAubert 2008at:\nB. Aubert et al. \u201cSearch for Invisible Decays of a Light\nScalar in Radiative Transitions \u03a5(3S) \u2192\u03b3A0\u201d. In \u201cPro-\nceedings, 34th International Conference on High En-\nergy Physics (ICHEP 2008) : Philadelphia, Pennsylva-\nnia, July 30 \u2013 August 5, 2008\u201d, 2008. arXiv:0808.0017.\nAubert 2008au:\nB. Aubert et al. \u201cSearch for Lepton Flavor Violating\nDecays \u03c4 \u00b1 \u2192\u2113\u00b1\u03c9 (\u2113= e, \u00b5)\u201d. Phys. Rev. Lett. 100,\n071802 (2008). 0711.0980.\nAubert 2008av:\nB. Aubert et al. \u201cSearch for the decays B0 \u2192e+e\u2212\u03b3\nand B0 \u2192\u00b5+\u00b5\u2212\u03b3\u201d. Phys. Rev. D77, 011104 (2008).\n0706.2870.\nAubert 2008aw:\nB. Aubert et al. \u201cSearch for the highly suppressed de-\ncays B\u2212\u2192K+\u03c0\u2212\u03c0\u2212and B\u2212\u2192K\u2212K\u2212\u03c0+\u201d. Phys.\nRev. D78, 091102 (2008). 0808.0900.\nAubert 2008ax:\nB. Aubert et al.\n\u201cSearch for the rare charmless\nhadronic decay B+ \u2192a+\n0 \u03c00\u201d. Phys. Rev. D77, 011101\n(2008). [Erratum-ibid. D77, 019904 (2008), Erratum-\nibid. D77, 039903 (2008)], 0708.0963.\nAubert 2008ay:\nB. Aubert et al. \u201cSearches for B meson decays to \u03c6\u03c6,\n\u03c6\u03c1, \u03c6f0(980), and f0(980)f0(980) \ufb01nal states\u201d. Phys.\nRev. Lett. 101, 201801 (2008). 0807.3935.\nAubert 2008az:\nB. Aubert et al. \u201cSearches for the decays B0 \u2192\u2113\u00b1\u03c4 \u2213\nand B+ \u2192\u2113+\u03bd (l = e, \u00b5) using hadronic tag reconstruc-\ntion\u201d. Phys. Rev. D77, 091104 (2008). 0801.0697.\nAubert 2008ba:\nB. Aubert et al.\n\u201cStudy of B-meson decays to\n\u03b7cK(\u2217), \u03b7c(2S)K(\u2217) and \u03b7c\u03b3K(\u2217)\u201d.\nPhys. Rev. D78,\n012006 (2008). 0804.1208.\nAubert 2008bb:\nB. Aubert et al. \u201cStudy of B Meson Decays with Ex-\ncited \u03b7 and \u03b7\u2032 Mesons\u201d. Phys. Rev. Lett. 101, 091801\n(2008). 0804.0411.\nAubert 2008bc:\nB. Aubert et al. \u201cStudy of hadronic transitions between\nUpsilon states and observation of \u03a5(4S) \u2192\u03b7\u03a5(1S) de-\ncay\u201d. Phys. Rev. D78, 112002 (2008). 0807.2014.\nAubert 2008bd:\nB. Aubert et al. \u201cStudy of Resonances in Exclusive B\nDecays to D(\u2217)D(\u2217)K\u201d. Phys. Rev. D77, 011102 (2008).\n0708.1565.\nAubert 2008be:\nB. Aubert et al.\n\u201cStudy of the decay D+\ns\n\u2192\nK+K\u2212e+\u03bde\u201d. Phys. Rev. D78, 051101 (2008). 0807.\n1599.\nAubert 2008bf:\nB. Aubert et al. \u201cTime-dependent and time-integrated\nangular analysis of B \u2192\u03d5K0\nS\u03c00 and \u03d5K\u00b1\u03c0\u2213\u201d. Phys.\n\n816\nRev. D78, 092008 (2008). 0808.3586.\nAubert 2008bg:\nB. Aubert et al. \u201cTime-dependent Dalitz plot analysis\nof B0 \u2192D\u2213K0\u03c0\u00b1 decays\u201d. Phys. Rev. D77, 071102\n(2008). 0712.3469.\nAubert 2009a:\nB. Aubert et al. \u201cA Model-independent search for the\ndecay B+ \u2192\u2113+\u03bd\u2113\u03b3\u201d. Phys. Rev. D80, 111105 (2009).\n0907.1681.\nAubert 2009b:\nB. Aubert et al. \u201cA Search for Invisible Decays of the\n\u03a5(1S)\u201d. Phys. Rev. Lett. 103, 251801 (2009). 0908.\n2840.\nAubert 2009c:\nB. Aubert et al. \u201cAngular Distributions in the Decays\nB \u2192K\u2217\u2113+\u2113\u2212\u201d. Phys. Rev. D79, 031102 (2009). 0804.\n4412.\nAubert 2009d:\nB. Aubert et al.\n\u201cB meson decays to charmless me-\nson pairs containing \u03b7 or \u03b7\u2032 mesons\u201d. Phys. Rev. D80,\n112002 (2009). 0907.1743.\nAubert 2009e:\nB. Aubert et al. \u201cBranching Fractions and CP-Violating\nAsymmetries in Radiative B Decays to \u03b7K\u03b3\u201d. Phys.\nRev. D79, 011102 (2009). 0805.1317.\nAubert 2009f:\nB. Aubert et al.\n\u201cConstraints on the CKM angle \u03b3\nin B0 \u2192D0(D0)K\u22170 with a Dalitz analysis of D0 \u2192\nKS\u03c0+\u03c0\u2212\u201d. Phys. Rev. D79, 072003 (2009). 0805.2001.\nAubert 2009g:\nB. Aubert et al.\n\u201cDalitz Plot Analysis of B\u2212\u2192\nD+\u03c0\u2212\u03c0\u2212\u201d. Phys. Rev. D79, 112004 (2009). 0901.1291.\nAubert 2009h:\nB. Aubert et al.\n\u201cDalitz Plot Analysis of B\u00b1 \u2192\n\u03c0\u00b1\u03c0\u00b1\u03c0\u2213Decays\u201d.\nPhys. Rev. D79, 072006 (2009).\n0902.2051.\nAubert 2009i:\nB. Aubert et al.\n\u201cDalitz Plot Analysis of D+\ns\n\u2192\n\u03c0+\u03c0\u2212\u03c0+\u201d. Phys. Rev. D79, 032003 (2009). 0808.0971.\nAubert 2009j:\nB. Aubert et al. \u201cDirect CP, Lepton Flavor and Isospin\nAsymmetries in the Decays B \u2192K(\u2217)\u2113+\u2113\u2212\u201d. Phys. Rev.\nLett. 102, 091803 (2009). 0807.4119.\nAubert 2009k:\nB. Aubert et al. \u201cEvidence for B+ \u2192K\u22170K\u2217+\u201d. Phys.\nRev. D79, 051102 (2009). 0901.1223.\nAubert 2009l:\nB. Aubert et al.\n\u201cEvidence for the \u03b7b(1S) Meson in\nRadiative \u03a5(2S) Decay\u201d. Phys. Rev. Lett. 103, 161801\n(2009). 0903.1124.\nAubert 2009m:\nB. Aubert et al. \u201cEvidence for X(3872) \u2192\u03c8(2S)\u03b3 in\nB\u00b1 \u2192X(3872)K\u00b1 decays, and a study of B \u2192cc\u03b3K\u201d.\nPhys. Rev. Lett. 102, 132001 (2009). 0809.0042.\nAubert 2009n:\nB. Aubert et al. \u201cExclusive Initial-State-Radiation Pro-\nduction of the DD, DD\u2217, and D\u2217D\u2217Systems\u201d. Phys.\nRev. D79, 092001 (2009). 0903.1597.\nAubert 2009o:\nB. Aubert et al. \u201cImproved limits on lepton \ufb02avor vio-\nlating tau decays to \u2113\u03c6, \u2113\u03c1, \u2113K\u2217and \u2113\u00afK\u2217\u201d. Phys. Rev.\nLett. 103, 021801 (2009). 0904.0339.\nAubert 2009p:\nB. Aubert et al. \u201cImproved Measurement of B+ \u2192\u03c1+\u03c10\nand Determination of the Quark-Mixing Phase Angle\n\u03b1\u201d. Phys. Rev. Lett. 102, 141802 (2009). 0901.3522.\nAubert 2009q:\nB. Aubert et al.\n\u201cMeasurement of B \u2192X\u03b3 Decays\nand Determination of |Vtd/Vts|\u201d. Phys. Rev. Lett. 102,\n161803 (2009). 0807.4975.\nAubert 2009r:\nB. Aubert et al. \u201cMeasurement of Branching Fractions\nand CP and Isospin Asymmetries in B \u2192K\u2217(892)\u03b3\nDecays\u201d. Phys. Rev. Lett. 103, 211802 (2009). 0906.\n2177.\nAubert 2009s:\nB. Aubert et al. \u201cMeasurement of B(\u03c4 \u2212\u2192K0\u03c0\u2212\u03bd\u03c4)\nusing the BABAR detector\u201d. Nucl. Phys. Proc. Suppl.\n189, 193\u2013198 (2009). 0808.1121.\nAubert 2009t:\nB. Aubert et al. \u201cMeasurement of CP violation observ-\nables and parameters for the decays B\u00b1 \u2192DK\u2217\u00b1\u201d.\nPhys. Rev. D80, 092001 (2009). 0909.3981.\nAubert 2009u:\nB. Aubert et al. \u201cMeasurement of D0 \u2212D0 mixing from\na time-dependent amplitude analysis of D0 \u2192K+\u03c0\u2212\u03c00\ndecays\u201d. Phys. Rev. Lett. 103, 211801 (2009). 0807.\n4544.\nAubert 2009v:\nB. Aubert et al. \u201cMeasurement of D0\u2212D0 Mixing using\nthe Ratio of Lifetimes for the Decays D0 to K\u2212\u03c0+ and\nK+K\u2212\u201d. Phys. Rev. D80, 071103 (2009). 0908.0761.\nAubert 2009w:\nB. Aubert et al. \u201cMeasurement of the Branching Frac-\ntion and \u039b Polarization in B0 \u2192\u039bp\u03c0\u2212\u201d. Phys. Rev.\nD79, 112009 (2009). 0904.4724.\nAubert 2009x:\nB. Aubert et al. \u201cMeasurement of the e+e\u2212\u2192bb cross\nsection between \u221as = 10.54 GeV and 11.20 GeV\u201d.\nPhys. Rev. Lett. 102, 012001 (2009). 0809.4120.\nAubert 2009y:\nB. Aubert et al. \u201cMeasurement of the \u03b3\u03b3\u2217\u2192\u03c00 tran-\nsition form factor\u201d.\nPhys. Rev. D80, 052002 (2009).\n0905.4778.\nAubert 2009z:\nB. Aubert et al. \u201cMeasurement of Time-Dependent CP\nAsymmetry in B0 \u2192ccK(\u2217)0 Decays\u201d. Phys. Rev. D79,\n072009 (2009). 0902.1708.\nAubert 2009aa:\nB. Aubert et al. \u201cMeasurement of time dependent CP\nasymmetry parameters in B0 meson decays to \u03c9K0\nS,\n\u03b7\u2032K0, and \u03c00K0\nS\u201d.\nPhys. Rev. D79, 052003 (2009).\n0809.1174.\nAubert 2009ab:\nB. Aubert et al.\n\u201cMeasurements of the Semileptonic\nDecays B \u2192D\u2113\u03bd and B \u2192D\u2217\u2113\u03bd Using a Global Fit to\nDX\u2113\u03bd Final States\u201d. Phys. Rev. D79, 012002 (2009).\n\n817\n0809.0828.\nAubert 2009ac:\nB. Aubert et al.\n\u201cMeasurements of the \u03c4 Mass and\nMass Di\ufb00erence of the \u03c4 + and \u03c4 \u2212at BABAR\u201d. Phys.\nRev. D80, 092005 (2009). 0909.3562.\nAubert 2009ad:\nB. Aubert et al. \u201cMeasurements of time-dependent CP\nasymmetries in B0 \u2192D(\u2217)+D(\u2217)\u2212decays\u201d. Phys. Rev.\nD79, 032002 (2009). 0808.1866.\nAubert 2009ae:\nB. Aubert et al. \u201cObservation and Polarization Mea-\nsurement of B0 \u2192a1(1260)+a1(1260)\u2212Decay\u201d. Phys.\nRev. D80, 092007 (2009). 0907.1776.\nAubert 2009af:\nB. Aubert et al. \u201cObservation of B Meson Decays to\n\u03c9K\u2217and Improved Measurements for \u03c9\u03c1 and \u03c9f0\u201d.\nPhys. Rev. D79, 052005 (2009). 0901.3703.\nAubert 2009ag:\nB. Aubert et al. \u201cObservation of the baryonic B decay\nB0 \u2192\u039b+\nc pK\u2212\u03c0+\u201d.\nPhys. Rev. D80, 051105 (2009).\n0907.4566.\nAubert 2009ah:\nB. Aubert et al.\n\u201cPrecise measurement of the e+e\u2212\nto \u03c0+\u03c0\u2212(\u03b3) cross section with the Initial State Radia-\ntion method at BABAR\u201d. Phys. Rev. Lett. 103, 231801\n(2009). 0908.3589.\nAubert 2009ai:\nB. Aubert et al. \u201cSearch for a low-mass Higgs boson\nin \u03a5(3S) \u2192\u03b3A0, A0 \u2192\u03c4 +\u03c4 \u2212at BABAR\u201d. Phys. Rev.\nLett. 103, 181801 (2009). 0906.2219.\nAubert 2009aj:\nB. Aubert et al. \u201cSearch for a Narrow Resonance in\ne+e\u2212to Four Lepton Final States\u201d. In \u201cProceedings,\n24th International Symposium on Lepton-Photon Inter-\nactions at High Energy (LP09) : Hamburg, Germany,\nAugust 17\u201322, 2009\u201d, 2009. arXiv:0908.2821.\nAubert 2009ak:\nB. Aubert et al. \u201cSearch for B-meson decays to b1\u03c1 and\nb1K\u2217\u201d. Phys. Rev. D80, 051101 (2009). 0907.3485.\nAubert 2009al:\nB. Aubert et al. \u201cSearch for b \u2192u transitions in B0 \u2192\nD0K\u22170 decays\u201d. Phys. Rev. D80, 031102 (2009). 0904.\n2112.\nAubert 2009am:\nB. Aubert et al.\n\u201cSearch for B0 Meson Decays to\n\u03c00K0\nSK0\nS, \u03b7K0\nSK0\nS, and \u03b7\u2032K0\nSK0\nS\u201d.\nPhys. Rev. D80,\n011101 (2009). 0905.0868.\nAubert 2009an:\nB. Aubert et al. \u201cSearch for Dimuon Decays of a Light\nScalar Boson in Radiative Transitions \u03a5 \u2192\u03b3A0\u201d. Phys.\nRev. Lett. 103, 081803 (2009). 0905.4539.\nAubert 2009ao:\nB. Aubert et al. \u201cSearch for Lepton Flavor Violating\nDecays \u03c4 \u2192\u2113K0\nS with the BABAR Experiment\u201d. Phys.\nRev. D79, 012004 (2009). 0812.3804.\nAubert 2009ap:\nB. Aubert et al. \u201cSearch for Second-Class Currents in\n\u03c4 \u2212\u2192\u03c9\u03c0\u2212\u03bd\u03c4\u201d. Phys. Rev. Lett. 103, 041802 (2009).\n0904.3080.\nAubert 2009aq:\nB. Aubert et al. \u201cSearch for the B+ \u2192K+\u03bd\u03bd Decay\nUsing Semi-Leptonic Tags\u201d 0911.1988.\nAubert 2009ar:\nB. Aubert et al.\n\u201cSearch for the decay B+\n\u2192\nK0\nSK0\nS\u03c0+\u201d. Phys. Rev. D79, 051101 (2009). 0811.1979.\nAubert 2009as:\nB. Aubert et al. \u201cSearch for the Rare Leptonic Decays\nB+ \u2192\u2113+\u03bd\u2113(\u2113= e, \u00b5)\u201d. Phys. Rev. D79, 091101 (2009).\n0903.1220.\nAubert 2009at:\nB. Aubert et al. \u201cSearch for the Z(4430)\u2212at BABAR\u201d.\nPhys. Rev. D79, 112001 (2009). 0811.0564.\nAubert 2009au:\nB. Aubert et al. \u201cStudy of DsJ decays to D\u2217K in in-\nclusive e+e\u2212interactions\u201d.\nPhys. Rev. D80, 092003\n(2009). 0908.0806.\nAubert 2009av:\nB. Aubert et al. \u201cTime-dependent amplitude analysis\nof B0 \u2192K0\nS\u03c0+\u03c0\u2212\u201d. Phys. Rev. D80, 112001 (2009).\n0905.3615.\nAubert 2010a:\nB. Aubert et al. \u201cA Search for B+ \u2192\u2113+\u03bd\u2113Recoiling\nAgainst B\u2212\u2192D0\u2113\u2212\u03bdX\u201d.\nPhys. Rev. D81, 051101\n(2010). 0912.2453.\nAubert 2010b:\nB. Aubert et al. \u201cCorrelated leading baryon-antibaryon\nproduction in e+e\u2212\u2192cc \u2192\u039b+\nc \u039b\u2212\nc X\u201d.\nPhys. Rev.\nD82, 091102 (2010). 1006.2216.\nAubert 2010c:\nB. Aubert et al. \u201cMeasurement and interpretation of\nmoments in inclusive semileptonic decays B \u2192Xc\u2113\u2212\u03bd\u201d.\nPhys. Rev. D81, 032003 (2010). 0908.0415.\nAubert 2010d:\nB. Aubert et al. \u201cMeasurement of branching fractions\nof B decays to K1(1270)\u03c0 and K1(1400)\u03c0 and determi-\nnation of the CKM angle \u03b1 from B0 \u2192a1(1260)\u00b1\u03c0\u2213\u201d.\nPhys. Rev. D81, 052009 (2010). 0909.2171.\nAubert 2010e:\nB. Aubert et al. \u201cMeasurement of |Vcb| and the Form-\nFactor Slope in B \u2192D\u2113\u2212\u03bd Decays in Events Tagged\nby a Fully Reconstructed B Meson\u201d. Phys. Rev. Lett.\n104, 011802 (2010). 0904.4063.\nAubert 2010f:\nB. Aubert et al. \u201cMeasurements of Charged Current\nLepton Universality and |Vus| using Tau Lepton Decays\nto e\u2212\u03bde\u03bd\u03c4, \u00b5\u2212\u03bd\u00b5\u03bd\u03c4, \u03c0\u2212\u03bd\u03c4, and K\u2212\u03bd\u03c4\u201d. Phys. Rev. Lett.\n105, 051602 (2010). 0912.0242.\nAubert 2010g:\nB. Aubert et al. \u201cObservation of the \u03c7c2(2P) meson in\nthe reaction \u03b3\u03b3 \u2192DD at BABAR\u201d. Phys. Rev. D81,\n092003 (2010). 1002.0281.\nAubert 2010h:\nB. Aubert et al.\n\u201cObservation of the decay B0 \u2192\n\u039bcp\u03c00\u201d. Phys. Rev. D82, 031102 (2010). 1007.1370.\nAubert 2010i:\nB. Aubert et al. \u201cSearches for Lepton Flavor Violation\nin the Decays \u03c4 \u00b1 \u2192e\u00b1\u03b3 and \u03c4 \u00b1 \u2192\u00b5\u00b1\u03b3\u201d. Phys. Rev.\nLett. 104, 021802 (2010). 0908.2381.\n\n818\nAubert 2013:\nB. Aubert et al. \u201cThe BABAR Detector: Upgrades, Op-\neration and Performance\u201d. Nucl. Instrum. Meth. A729.\n1305.3560.\nBand 2006:\nH. R. Band et al. \u201cPerformance and Aging Studies of\nBABAR Resistive Plate Chambers\u201d. Nucl. Phys. Proc.\nSuppl. 158, 139\u2013142 (2006).\nBrown 1997:\nD. Brown. \u201cAn object-oriented extended Kalman \ufb01lter\ntracking algorithm\u201d, 1997. Talk given at Computing in\nHigh-energy Physics (CHEP 97), Berlin, Germany, 7-11\nApr 1997.\nBrown, Gritsan, Guo, and Roberts 2009:\nD. N. Brown, A. V. Gritsan, Z. J. Guo, and D. Roberts.\n\u201cLocal Alignment of the BABAR Silicon Vertex Tracking\nDetector\u201d. Nucl. Instrum. Meth. A603, 467\u2013484 (2009).\n0809.3823.\nCahn 2000:\nR. Cahn. \u201cTagMixZ and its Application to the Analysis\nof CP Violation\u201d BABAR Analysis Document #17.\ndel Amo Sanchez 2010a:\nP. del Amo Sanchez et al. \u201cDalitz-plot Analysis of B0 \u2192\nD0\u03c0+\u03c0\u2212\u201d. PoS ICHEP2010, 250 (2010). 1007.4464.\ndel Amo Sanchez 2010b:\nP. del Amo Sanchez et al. \u201cEvidence for direct CP vi-\nolation in the measurement of the Cabibbo-Kobayashi-\nMaskawa angle \u03b3 with B\u2213\u2192D(\u2217)K(\u2217)\u2213decays\u201d. Phys.\nRev. Lett. 105, 121801 (2010). 1005.1096.\ndel Amo Sanchez 2010c:\nP. del Amo Sanchez et al.\n\u201cEvidence for the decay\nX(3872) \u2192J/\u03c8\u03c9\u201d. Phys. Rev. D82, 011101 (2010).\n1005.5190.\ndel Amo Sanchez 2010d:\nP. del Amo Sanchez et al.\n\u201cExclusive Production of\nD+\ns D\u2212\ns , D\u2217+\ns D\u2212\ns , and D\u2217+\ns D\u2217\u2212\ns\nvia e+e\u2212Annihilation\nwith Initial-State-Radiation\u201d. Phys. Rev. D82, 052004\n(2010). 1008.0338.\ndel Amo Sanchez 2010e:\nP. del Amo Sanchez et al.\n\u201cMeasurement of CP ob-\nservables in B\u00b1 \u2192DCP K\u00b1 decays and constraints on\nthe CKM angle \u03b3\u201d. Phys. Rev. D82, 072004 (2010).\n1007.0504.\ndel Amo Sanchez 2010f:\nP. del Amo Sanchez et al. \u201cMeasurement of D0 \u2212D0\nmixing parameters using D0 \u2192K0\nS\u03c0+\u03c0\u2212and D0 \u2192\nK0\nSK+K\u2212decays\u201d.\nPhys. Rev. Lett. 105, 081803\n(2010). 1004.5053.\ndel Amo Sanchez 2010g:\nP. del Amo Sanchez et al. \u201cMeasurement of the Abso-\nlute Branching Fractions for D\u2212\ns \u2192\u2113\u2212\u03bd\u2113and Extraction\nof the Decay Constant fDs\u201d. Phys. Rev. D82, 091103\n(2010). 1008.4080.\ndel Amo Sanchez 2010h:\nP. del Amo Sanchez et al. \u201cB-meson decays to \u03b7\u2032\u03c1, \u03b7\u2032f0,\nand \u03b7\u2032K\u2217\u201d. Phys. Rev. D82, 011502 (2010). 1004.0240.\ndel Amo Sanchez 2010i:\nP. del Amo Sanchez et al. \u201cObservation of new reso-\nnances decaying to D\u03c0 and D\u2217\u03c0 in inclusive e+e\u2212col-\nlisions near \u221as =10.58 GeV\u201d. Phys. Rev. D82, 111101\n(2010). 1009.2076.\ndel Amo Sanchez 2010j:\nP. del Amo Sanchez et al. \u201cObservation of the Rare De-\ncay B0 \u2192K0\nSK\u00b1\u03c0\u2213\u201d. Phys. Rev. D82, 031101 (2010).\n1003.0640.\ndel Amo Sanchez 2010k:\nP. del Amo Sanchez et al. \u201cObservation of the \u03a5(13DJ)\nbottomonium state through decays to \u03c0+\u03c0\u2212\u03a5(1S)\u201d.\nPhys. Rev. D82, 111102 (2010). 1004.0175.\ndel Amo Sanchez 2010l:\nP. del Amo Sanchez et al. \u201cSearch for B+ meson decay\nto a+\n1 K\u22170\u201d. Phys. Rev. D82, 091101 (2010). 1007.2732.\ndel Amo Sanchez 2010m:\nP. del Amo Sanchez et al. \u201cSearch for b \u2192u transitions\nin B\u2212\u2192DK\u2212and D\u2217K\u2212Decays\u201d. Phys. Rev. D82,\n072006 (2010). 1006.4241.\ndel Amo Sanchez 2010n:\nP. del Amo Sanchez et al. \u201cSearch for CP violation us-\ning T-odd correlations in D0 \u2192K+K\u2212\u03c0+\u03c0\u2212decays\u201d.\nPhys. Rev. D81, 111103 (2010). 1003.3397.\ndel Amo Sanchez 2010o:\nP. del Amo Sanchez et al. \u201cSearch for fJ(2220) in radia-\ntive J/\u03c8 decays\u201d. Phys. Rev. Lett. 105, 172001 (2010).\n1007.3526.\ndel Amo Sanchez 2010p:\nP. del Amo Sanchez et al. \u201cSearch for the Rare Decay\nB \u2192K\u03bd\u03bd\u201d. Phys. Rev. D82, 112002 (2010). 1009.\n1529.\ndel Amo Sanchez 2010q:\nP. del Amo Sanchez et al.\n\u201cStudy of B \u2192X\u03b3 de-\ncays and determination of |Vtd/Vts|\u201d. Phys. Rev. D82,\n051101 (2010). 1005.4087.\ndel Amo Sanchez 2010r:\nP. del Amo Sanchez et al. \u201cTest of lepton universality in\n\u03a5(1S) decays at BABAR\u201d. Phys. Rev. Lett. 104, 191801\n(2010). 1002.4358.\ndel Amo Sanchez 2011a:\nP. del Amo Sanchez et al.\n\u201cAnalysis of the D+ \u2192\nK\u2212\u03c0+e+\u03bde decay channel\u201d. Phys. Rev. D83, 072001\n(2011). 1012.1810.\ndel Amo Sanchez 2011b:\nP. del Amo Sanchez et al. \u201cDalitz plot analysis of D+\ns \u2192\nK+K\u2212\u03c0+\u201d.\nPhys. Rev. D83, 052001 (2011).\n1011.\n4190.\ndel Amo Sanchez 2011c:\nP. del Amo Sanchez et al.\n\u201cMeasurement of partial\nbranching fractions of inclusive charmless B meson de-\ncays to K+, K0, and \u03c0+\u201d.\nPhys. Rev. D83, 031103\n(2011). 1012.5031.\ndel Amo Sanchez 2011d:\nP. del Amo Sanchez et al. \u201cMeasurement of the B0 \u2192\n\u03c0\u2212\u2113+\u03bd and B+ \u2192\u03b7(\u2032)\u2113+\u03bd Branching Fractions, the\nB0 \u2192\u03c0\u2212\u2113+\u03bd and B+ \u2192\u03b7\u2113+\u03bd Form-Factor Shapes,\nand Determination of |Vub|\u201d. Phys. Rev. D83, 052011\n(2011). 1010.0987.\ndel Amo Sanchez 2011e:\nP. del Amo Sanchez et al.\n\u201cMeasurement of the\nB \u2192D(\u2217)D(\u2217)K branching fractions\u201d. Phys. Rev. D83,\n\n819\n032004 (2011). 1011.3929.\ndel Amo Sanchez 2011f:\nP. del Amo Sanchez et al. \u201cMeasurement of the \u03b3\u03b3\u2217\u2192\u03b7\nand \u03b3\u03b3\u2217\u2192\u03b7\u2032 transition form factors\u201d. Phys. Rev. D84,\n052001 (2011). 1101.1142.\ndel Amo Sanchez 2011g:\nP. del Amo Sanchez et al. \u201cMeasurements of branching\nfractions, polarizations, and direct CP-violation asym-\nmetries in B+ \u2192\u03c10K\u2217+ and B+ \u2192f0(980)K\u2217+ de-\ncays\u201d. Phys. Rev. D83, 051101 (2011). 1012.4044.\ndel Amo Sanchez 2011h:\nP. del Amo Sanchez et al. \u201cObservation of \u03b7c(1S) and\n\u03b7c(2S) decays to K+K\u2212\u03c0+\u03c0\u2212\u03c00 in two-photon inter-\nactions\u201d. Phys. Rev. D84, 012004 (2011). 1103.3971.\ndel Amo Sanchez 2011i:\nP. del Amo Sanchez et al.\n\u201cSearch for CP violation\nin the decay D\u00b1 \u2192K0\nS\u03c0\u00b1\u201d. Phys. Rev. D83, 071103\n(2011). 1011.5477.\ndel Amo Sanchez 2011j:\nP. del Amo Sanchez et al. \u201cSearch for Production of In-\nvisible Final States in Single-Photon Decays of \u03a5(1S)\u201d.\nPhys. Rev. 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D83, 032007 (2011). 1005.3288.\ndel Amo Sanchez 2012:\nP. del Amo Sanchez et al. \u201cObservation and study of the\nbaryonic B-meson decays B \u2192D(\u2217)pp(\u03c0)(\u03c0)\u201d. Phys.\nRev. D85, 092017 (2012). 1111.4387.\nFerroni 2009:\nF. Ferroni. \u201cThe Second Generation BABAR RPCs: Fi-\nnal Evaluation Of Performance\u201d. Nucl. Instrum. Meth.\nA602, 649\u2013652 (2009).\nFord 2000:\nW. T. Ford et al. \u201cBlind Analyses in BABAR \u201d BABAR\nAnalysis Document #91.\nGarzia 2013:\nI. Garzia. \u201cMeasurement of Collins asymmetries in in-\nclusive production of pion pairs in e+e\u2212collisions at\nBABAR\u201d. PoS ICHEP2012, 272 (2013). 1211.5293.\nGr\u00a8unberg 2012:\nO. Gr\u00a8unberg.\n\u201cBaryonic B decays at BABAR\u201d.\nIn\nE. Aug\u00b4e, J. Dumarchez, B. Pietrzyk, and J. T. T.\nV\u02c6an, editors, \u201cProceedings of the 47th Rencontres de\nMoriond 2012, QCD and High Energy Interactions\u201d,\n2012, pages 129\u2013131. 1211.0212.\nHarrison and Quinn 1998:\nP. F. Harrison and H. R. Quinn, editors. The BABAR\nphysics book: Physics at an asymmetric B Factory.\n1998. SLAC-R-0504.\nLe Diberder 1990:\nF. Le Diberder.\n\u201cPrecision on CP-Violation Mea-\nsurements and Requirement on the Vertex Resolution\u201d\nBABAR Analysis Document #34.\nLees 2010a:\nJ. P. Lees et al. \u201cLimits on tau Lepton-Flavor Violat-\ning Decays in three charged leptons\u201d. Phys. Rev. D81,\n111101 (2010). 1002.4550.\nLees 2010b:\nJ. P. Lees et al. \u201cMeasurement of the \u03b3\u03b3\u2217\u2192\u03b7c tran-\nsition form factor\u201d.\nPhys. Rev. D81, 052010 (2010).\n1002.3000.\nLees 2010c:\nJ. P. Lees et al.\n\u201cSearch for Charged Lepton Flavor\nViolation in Narrow \u03a5 Decays\u201d. Phys. Rev. Lett. 104,\n151802 (2010). 1001.1883.\nLees 2011a:\nJ. P. Lees et al. \u201cAmplitude Analysis of B0 \u2192K+\u03c0\u2212\u03c00\nand Evidence of Direct CP Violation in B \u2192K\u2217\u03c0 de-\ncays\u201d. Phys. Rev. D83, 112010 (2011). 1105.0125.\nLees 2011b:\nJ. P. Lees et al. \u201cBranching Fraction Measurements of\nthe Color-Suppressed Decays B0 \u2192D(\u2217)0\u03c00, D(\u2217)0\u03b7,\nD(\u2217)0\u03c9, and D(\u2217)0\u03b7\u2032 and Measurement of the Polariza-\ntion in the Decay B0 \u2192D\u22170\u03c9\u201d. Phys. Rev. D84, 112007\n(2011). 1107.5751.\nLees 2011c:\nJ. P. Lees et al. \u201cEvidence for the hb(1P) meson in the\ndecay \u03a5(3S) \u2192\u03c00hb(1P)\u201d. Phys. Rev. D84, 091101\n(2011). 1102.4565.\nLees 2011d:\nJ. P. Lees et al. \u201cMeasurement of the mass and width\nof the Ds1(2536)+ meson\u201d.\nPhys. Rev. D83, 072003\n(2011). 1103.2675.\nLees 2011e:\nJ. P. Lees et al. \u201cMeasurements of branching fractions\nand CP asymmetries and studies of angular distribu-\ntions for B \u2192\u03c6\u03c6K decays\u201d. Phys. Rev. D84, 012001\n(2011). 1105.5159.\nLees 2011f:\nJ. P. Lees et al. \u201cObservation of the baryonic B decay\nB0 \u2192\u039b+\nc \u039bK\u2212\u201d. Phys. Rev. D84, 071102 (2011). 1108.\n3211.\nLees 2011g:\nJ. P. Lees et al.\n\u201cObservation of the rare decay\nB+ \u2192K+\u03c00\u03c00 and measurement of the quasi-two\nbody contributions B+ \u2192K\u2217+\u03c00, B+ \u2192f0(980)K+\nand B+ \u2192\u03c7c0K+\u201d. Phys. Rev. D84, 092007 (2011).\n1109.0143.\nLees 2011h:\nJ. P. Lees et al.\n\u201cSearch for b \u2192u Transitions in\nB\u00b1 \u2192[K\u2213\u03c0\u00b1\u03c00]DK\u00b1 Decays\u201d.\nPhys. Rev. D84,\n012002 (2011). 1104.4472.\nLees 2011i:\nJ. P. Lees et al.\n\u201cSearch for CP violation using T-\n\n820\nodd correlations in D+ \u2192K+K0\nS\u03c0+\u03c0\u2212and D+\ns\n\u2192\nK+K0\nS\u03c0+\u03c0\u2212decays\u201d. Phys. Rev. D84, 031103 (2011).\n1105.4410.\nLees 2011j:\nJ. P. Lees et al. \u201cSearch for hadronic decays of a light\nHiggs boson in the radiative decay \u03a5 \u2192\u03b3A0\u201d. Phys.\nRev. Lett. 107, 221803 (2011). 1108.3549.\nLees 2011k:\nJ. P. Lees et al. \u201cSearches for Rare or Forbidden Se-\nmileptonic Charm Decays\u201d. Phys. Rev. D84, 072006\n(2011). 1107.4465.\nLees 2011l:\nJ. P. Lees et al. \u201cStudy of di-pion bottomonium transi-\ntions and search for the hb(1P) state\u201d. Phys. Rev. D84,\n011104 (2011). 1105.4234.\nLees 2011m:\nJ. P. Lees et al.\n\u201cStudy of radiative bottomonium\ntransitions using converted photons\u201d. Phys. Rev. D84,\n072002 (2011). 1104.5254.\nLees 2011n:\nJ. P. Lees et al. \u201cStudy of \u03a5(3S, 2S) \u2192\u03b7\u03a5(1S) and\n\u03a5(3S, 2S) \u2192\u03c0+\u03c0\u2212\u03a5(1S) hadronic transitions\u201d. Phys.\nRev. D84, 092003 (2011). 1108.5874.\nLees 2012a:\nJ. P. Lees et al. \u201cA Measurement of the Semileptonic\nBranching Fraction of the B0\ns Meson\u201d. Phys. Rev. D85,\n011101 (2012). 1110.5600.\nLees 2012b:\nJ. P. Lees et al. \u201cA search for the decay modes B\u00b1 \u2192\nh\u00b1\u03c4\u2113\u201d. Phys. Rev. D86, 012004 (2012). 1204.2852.\nLees 2012c:\nJ. P. Lees et al.\n\u201cAmplitude analysis and measure-\nment of the time-dependent CP asymmetry of B0 \u2192\nK0\nSK0\nSK0\nS decays\u201d.\nPhys. Rev. D85, 054023 (2012).\n1111.3636.\nLees 2012d:\nJ. P. Lees et al.\n\u201cCross Sections for the Re-\nactions\ne+e\u2212\n\u2192\nK+K\u2212\u03c0+\u03c0\u2212, K+K\u2212\u03c00\u03c00,\nand\nK+K\u2212K+K\u2212Measured Using Initial-State Radiation\nEvents\u201d. Phys. Rev. D86, 012008 (2012). 1103.3001.\nLees 2012e:\nJ. P. Lees et al.\n\u201cEvidence for an excess of B \u2192\nD(\u2217)\u03c4 \u2212\u03bd\u03c4 decays\u201d. Phys. Rev. Lett. 109, 101802 (2012).\n1205.5442.\nLees 2012f:\nJ. P. Lees et al. \u201cExclusive Measurements of b \u2192s\u03b3\nTransition Rate and Photon Energy Spectrum\u201d. Phys.\nRev. D86, 052012 (2012). 1207.2520.\nLees 2012g:\nJ. P. Lees et al.\n\u201cImproved Limits on B0 Decays to\nInvisible Final States and to \u03bd\u00af\u03bd\u03b3\u201d. Phys. Rev. D86,\n051105 (2012). 1206.2543.\nLees 2012h:\nJ. P. Lees et al. \u201cInitial-State Radiation Measurement\nof the e+e\u2212\u2192\u03c0+\u03c0\u2212\u03c0+\u03c0\u2212Cross Section\u201d. Phys. Rev.\nD85, 112009 (2012). 1201.5677.\nLees 2012i:\nJ. P. Lees et al.\n\u201cMeasurement of Branching Frac-\ntions and Rate Asymmetries in the Rare Decays B \u2192\nK(\u2217)l+l\u2212\u201d. Phys. Rev. D86, 032012 (2012). 1204.3933.\nLees 2012j:\nJ. P. Lees et al. \u201cMeasurement of B(B \u2192Xs\u03b3), the\nB \u2192Xs\u03b3 photon energy spectrum, and the direct CP\nasymmetry in B \u2192Xs+d\u03b3 decays\u201d. Phys. Rev. D86,\n112008 (2012). 1207.5772.\nLees 2012k:\nJ. P. Lees et al. \u201cMeasurement of the Time-Dependent\nCP\nAsymmetry of Partially Reconstructed B0\n\u2192\nD\u2217+D\u2217\u2212Decays\u201d.\nPhys. Rev. D86, 112006 (2012).\n1208.1282.\nLees 2012l:\nJ. P. Lees et al. \u201cB0 meson decays to \u03c10K\u22170, f0K\u22170,\nand \u03c1\u2212K\u2217+, including higher K\u2217resonances\u201d. Phys.\nRev. D85, 072005 (2012). 1112.3896.\nLees 2012m:\nJ. P. Lees et al. \u201cObservation of Time Reversal Viola-\ntion in the B0 Meson System\u201d. Phys. Rev. Lett. 109,\n211801 (2012). 1207.5832.\nLees 2012n:\nJ. P. Lees et al. \u201cPrecise Measurement of the e+e\u2212\u2192\n\u03c0+\u03c0\u2212(\u03b3) Cross Section with the Initial-State Radiation\nMethod at BABAR\u201d. Phys. Rev. D86, 032013 (2012).\n1205.2228.\nLees 2012o:\nJ. P. Lees et al. \u201cPrecision Measurement of the B \u2192\nXs\u03b3 Photon Energy Spectrum, Branching Fraction, and\nDirect CP Asymmetry ACP (B \u2192Xs+d\u03b3)\u201d. Phys. Rev.\nLett. 109, 191801 (2012). 1207.2690.\nLees 2012p:\nJ. P. Lees et al. \u201cSearch for B \u2192\u039b+\nc Xl\u2212\u03bd Decays in\nEvents With a Fully Reconstructed B Meson\u201d. Phys.\nRev. D85, 011102 (2012). 1110.6005.\nLees 2012q:\nJ. P. Lees et al. \u201cSearch for CP Violation in the De-\ncay \u03c4 \u2212\u2192\u03c0\u2212K0\nS(\u22650\u03c00)\u03bd\u03c4\u201d. Phys. Rev. D85, 031102\n(2012). 1109.1527.\nLees 2012r:\nJ. P. Lees et al. \u201cSearch for lepton-number violating\nprocesses in B+ \u2192h\u2212\u2113+\u2113+ decays\u201d. Phys. Rev. D85,\n071103 (2012). 1202.3650.\nLees 2012s:\nJ. P. Lees et al.\n\u201cSearch for Low-Mass Dark-Sector\nHiggs Bosons\u201d. Phys. Rev. Lett. 108, 211801 (2012).\n1202.1313.\nLees 2012t:\nJ. P. Lees et al.\n\u201cSearch for resonances decaying to\n\u03b7c\u03c0+\u03c0\u2212in two-photon interactions\u201d. Phys. Rev. D86,\n092005 (2012). 1206.2008.\nLees 2012u:\nJ. P. Lees et al.\n\u201cSearch for the Decay D0 \u2192\u03b3\u03b3\nand Measurement of the Branching Fraction for D0 \u2192\n\u03c00\u03c00\u201d. Phys. Rev. D85, 091107 (2012). 1110.6480.\nLees 2012v:\nJ. P. Lees et al. \u201cSearch for the decay modes D0 \u2192\ne+e\u2212, D0 \u2192\u00b5+\u00b5\u2212, and D0 \u2192e\u00b5\u201d. Phys. Rev. D86,\n032001 (2012). 1206.5419.\nLees 2012w:\nJ. P. Lees et al.\n\u201cSearch for the Z1(4050)+ and\n\n821\nZ2(4250)+ states in B0\n\u2192\u03c7c1K\u2212\u03c0+ and B+\n\u2192\n\u03c7c1K0\nS\u03c0+\u201d. Phys. Rev. D85, 052003 (2012). 1111.5919.\nLees 2012x:\nJ. P. Lees et al. \u201cStudy of B \u2192Xu\u2113\u03bd decays in BB\nevents tagged by a fully reconstructed B-meson decay\nand determination of |Vub|\u201d. Phys. Rev. D86, 032004\n(2012). 1112.0702.\nLees 2012y:\nJ. P. Lees et al. \u201cStudy of CP violation in Dalitz-plot\nanalyses of B0 \u2192K+K\u2212K0\nS, B+ \u2192K+K\u2212K+, and\nB+ \u2192K0\nSK0\nSK+\u201d.\nPhys. Rev. D85, 112010 (2012).\n1201.5897.\nLees 2012z:\nJ. P. Lees et al. \u201cStudy of high-multiplicity 3-prong and\n5-prong tau decays at BABAR\u201d. Phys. Rev. D86, 092010\n(2012). 1209.2734.\nLees 2012aa:\nJ. P. Lees et al. \u201cStudy of the baryonic B decay B\u2212\u2192\n\u03a3++\nc\np\u03c0\u2212\u03c0\u2212\u201d. Phys. Rev. D86, 091102 (2012). 1208.\n3086.\nLees 2012ab:\nJ. P. Lees et al.\n\u201cStudy of the reaction e+e\u2212\u2192\nJ/\u03c8\u03c0+\u03c0\u2212via initial-state radiation at BABAR\u201d. Phys.\nRev. D86, 051102 (2012). 1204.2158.\nLees 2012ac:\nJ. P. Lees et al.\n\u201cStudy of the reaction e+e\u2212\u2192\n\u03c8(2S)\u03c0+\u03c0\u2212via initial state radiation at BABAR\u201d 1211.\n6271.\nLees 2012ad:\nJ. P. Lees et al. \u201cStudy of X(3915) \u2192J/\u03c8\u03c9 in two-\nphoton collisions\u201d.\nPhys. Rev. D86, 072002 (2012).\n1207.2651.\nLees 2012ae:\nJ. P. Lees et al.\n\u201cThe branching fraction of \u03c4 \u2212\u2192\n\u03c0\u2212K0\nSK0\nS(\u03c00)\u03bd\u03c4 decays\u201d.\nPhys. Rev. D86, 092013\n(2012). 1208.0376.\nLees 2013a:\nJ. P. Lees et al.\n\u201cEvidence of B \u2192\u03c4\u03bd decays with\nhadronic B tags\u201d.\nPhys. Rev. D88, 031102 (2013).\n1207.0698.\nLees 2013b:\nJ. P. Lees et al. \u201cMeasurement of CP Asymmetries and\nBranching Fractions in Charmless Two-Body B-Meson\nDecays to Pions and Kaons\u201d. Phys. Rev. D87, 052009\n(2013). 1206.3525.\nLees 2013c:\nJ. P. Lees et al. \u201cMeasurement of CP-violating asym-\nmetries in B0 \u2192(\u03c1\u03c0)0 decays using a time-dependent\nDalitz plot analysis\u201d. Phys. Rev. D88, 012003 (2013).\n1304.3503.\nLees 2013d:\nJ. P. Lees et al. \u201cMeasurement of D0 \u2212D0 Mixing and\nCP Violation in Two-Body D0 Decays\u201d.\nPhys. Rev.\nD87, 012004 (2013). 1209.3896.\nLees 2013e:\nJ. P. Lees et al. \u201cObservation of direct CP violation in\nthe measurement of the Cabibbo-Kobayashi-Maskawa\nangle \u03b3 with B\u00b1 \u2192D(\u2217)K(\u2217)\u00b1 decays\u201d.\nPhys. Rev.\nD87, 052015 (2013). 1301.1029.\nLees 2013f:\nJ. P. Lees et al. \u201cProduction of charged pions, kaons and\nprotons in e+e\u2212annihilations into hadrons at \u221as =\n10.54 GeV\u201d. Phys. Rev. D88, 032011 (2013). 1306.\n2895.\nLees 2013g:\nJ. P. Lees et al. \u201cSearch for CP Violation in B0 \u2212B0\nMixing using Partial Reconstruction of B0 \u2192D\u2217\u2212Xl+\u03bd\nand a Kaon Tag\u201d. Phys. Rev. Lett. 111, 101802 (2013).\n1305.1575.\nLees 2013h:\nJ. P. Lees et al. \u201cStudy of the decay B0 \u2192\u039b+\nc p\u03c0+\u03c0\u2212\nand its intermediate states\u201d. Phys. Rev. D87, 092004\n(2013). 1302.0191.\nLees 2013i:\nJ. P. Lees et al. \u201cTime-Integrated Luminosity Recorded\nby the BABAR Detector at the PEP-II e+e\u2212Collider\u201d.\nNucl. Instrum. Meth. A726, 203\u2013213 (2013).\n1301.\n2703.\nLees 2014:\nJ. P. Lees et al.\n\u201cMeasurement of the B \u2192Xsl+l\u2212\nbranching fraction from a sum of exclusive \ufb01nal states\u201d.\nPhys. Rev. Lett. 112, 211802 (2014). 1312.5364.\nMcGregor 2008:\nG. D. McGregor. \u201cB Counting at BABAR\u201d 0812.1954.\nMuller 2004:\nD. R. Muller.\n\u201cIdenti\ufb01ed hadron production at SLD\nand BABAR\u201d. Eur. Phys. J. C33, S572\u2013S574 (2004).\nPiccolo 2002:\nD. Piccolo et al.\n\u201cThe RPC Based IFR system at\nthe BABAR experiment: Preliminary results\u201d. Nucl. In-\nstrum. Meth. A477, 435\u2013439 (2002).\nPiccolo 2003:\nD. Piccolo et al. \u201cPerformance of RPCs in the BABAR\nExperiment\u201d.\nNucl. Instrum. Meth. A515, 322\u2013327\n(2003).\nRoodman 2000:\nA. Roodman. \u201cBlind Analysis of sin 2\u03b2\u201d BABAR Anal-\nysis Document #43.\n\n822\nBelle publications\nAbashian 2002a:\nA. Abashian, K. Abe, K. Abe, P. K. Behera, F. Handa\net al. \u201cMuon identi\ufb01cation in the Belle experiment at\nKEKB\u201d. Nucl. Instrum. Meth. A491, 69\u201382 (2002).\nAbashian 2001:\nA. Abashian et al. \u201cMeasurement of the CP violation\nparameter sin 2\u03c61 in B0\nd meson decays\u201d.\nPhys. Rev.\nLett. 86, 2509\u20132514 (2001). hep-ex/0102018.\nAbashian 2002b:\nA. Abashian et al. \u201cThe Belle Detector\u201d. Nucl. Instrum.\nMeth. A479, 117\u2013232 (2002).\nAbe 2001a:\nK. Abe et al. \u201cA measurement of the branching fraction\nfor the inclusive B \u2192Xs\u03b3 decays with Belle\u201d. Phys.\nLett. B511, 151\u2013158 (2001). hep-ex/0103042.\nAbe 2001b:\nK. Abe et al.\n\u201cMeasurement of B0\nd \u2212B0\nd mixing\nrate from the time evolution of dilepton events at\nthe \u03a5(4S)\u201d.\nPhys. Rev. Lett. 86, 3228\u20133232 (2001).\nhep-ex/0011090.\nAbe 2001c:\nK. Abe et al. \u201cMeasurement of branching fractions for\nB \u2192\u03c0\u03c0, K\u03c0 and KK decays\u201d. Phys. Rev. Lett. 87,\n101801 (2001). hep-ex/0104030.\nAbe 2001d:\nK. Abe et al. \u201cMeasurement of the branching fraction\nfor B \u2192\u03b7\u2032K and search for B \u2192\u03b7\u2032\u03c0+\u201d. Phys. Lett.\nB517, 309\u2013318 (2001). hep-ex/0108010.\nAbe 2001e:\nK. Abe et al.\n\u201cObservation of B \u2192J/\u03c8K1(1270)\u201d.\nPhys. Rev. Lett. 87, 161601 (2001). hep-ex/0105014.\nAbe 2001f:\nK. Abe et al. \u201cObservation of Cabibbo suppressed B \u2192\nD(\u2217)K\u2212decays at Belle\u201d. Phys. Rev. Lett. 87, 111801\n(2001). hep-ex/0104051.\nAbe 2001g:\nK. Abe et al. \u201cObservation of large CP violation in the\nneutral B meson system\u201d. Phys. Rev. Lett. 87, 091802\n(2001). hep-ex/0107061.\nAbe 2002a:\nK. Abe et al. \u201cA measurement of lifetime di\ufb00erence in\nD0 meson decays\u201d. Phys. Rev. Lett. 88, 162001 (2002).\nhep-ex/0111026.\nAbe 2002b:\nK. Abe et al. \u201cAn improved measurement of mixing-\ninduced CP violation in the neutral B meson system\u201d.\nPhys. Rev. D66, 071102 (2002). hep-ex/0208025.\nAbe 2002c:\nK. Abe et al. \u201cMeasurement of B(B0 \u2192D+l\u2212\u03bd) and de-\ntermination of |Vcb|\u201d. Phys. Lett. B526, 258\u2013268 (2002).\nhep-ex/0111082.\nAbe 2002d:\nK. Abe et al. \u201cMeasurements of branching fractions and\ndecay amplitudes in B \u2192J/\u03c8K\u2217decays\u201d. Phys. Lett.\nB538, 11\u201320 (2002). hep-ex/0205021.\nAbe 2002e:\nK. Abe et al. \u201cObservation of B+ \u2192\u03c7c0K+\u201d. Phys.\nRev. Lett. 88, 031802 (2002). hep-ex/0111069.\nAbe 2002f:\nK. Abe et al. \u201cObservation of B\u00b1 \u2192ppK\u00b1\u201d. Phys.\nRev. Lett. 88, 181803 (2002). hep-ex/0202017.\nAbe 2002g:\nK. Abe et al. \u201cObservation of B0 \u2192D(\u2217)0pp\u201d. Phys.\nRev. Lett. 89, 151802 (2002). hep-ex/0205083.\nAbe 2002h:\nK. Abe et al. \u201cObservation of Cabibbo-suppressed and\nW-exchange \u039b+\nc baryon decays\u201d. Phys. Lett. B524, 33\u2013\n43 (2002). hep-ex/0111032.\nAbe 2002i:\nK. Abe et al.\n\u201cObservation of \u03c7c2 production in B\nmeson decay\u201d.\nPhys. Rev. Lett. 89, 011803 (2002).\nhep-ex/0202028.\nAbe 2002j:\nK. Abe et al. \u201cObservation of double cc production in\ne+e\u2212annihilation at \u221as \u224810.6 GeV\u201d. Phys. Rev. Lett.\n89, 142001 (2002). hep-ex/0205104.\nAbe 2002k:\nK. Abe et al. \u201cObservation of mixing induced CP viola-\ntion in the neutral B meson system\u201d. Phys. Rev. D66,\n032007 (2002). hep-ex/0202027.\nAbe 2002l:\nK. Abe et al. \u201cObservation of the decay B \u2192K\u2113+\u2113\u2212\u201d.\nPhys. Rev. Lett. 88, 021801 (2002). hep-ex/0109026.\nAbe 2002m:\nK. Abe et al. \u201cPrecise measurement of B meson life-\ntimes with hadronic decay \ufb01nal states\u201d. Phys. Rev. Lett.\n88, 171801 (2002). hep-ex/0202009.\nAbe 2002n:\nK. Abe et al. \u201cProduction of prompt charmonia in e+e\u2212\nannihilation at \u221as = 10.6 GeV\u201d. Phys. Rev. Lett. 88,\n052001 (2002). hep-ex/0110012.\nAbe 2003a:\nK. Abe et al. \u201cEvidence for B0 \u2192\u03c00\u03c00\u201d. Phys. Rev.\nLett. 91, 261801 (2003). hep-ex/0308040.\nAbe 2003b:\nK. Abe et al. \u201cEvidence for CP-violating asymmetries in\nB0 \u2192\u03c0+\u03c0\u2212decays and constraints on the CKM angle\n\u03c62\u201d. Phys. Rev. D68, 012001 (2003). hep-ex/0301032.\nAbe 2003c:\nK. Abe et al. \u201cMeasurement of branching fractions and\ncharge asymmetries for two-body B meson decays with\ncharmonium\u201d. Phys. Rev. D67, 032003 (2003). hep-ex/\n0211047.\nAbe 2003d:\nK. Abe et al. \u201cMeasurement of K+K\u2212production in\ntwo-photon collisions in the resonant-mass region\u201d. Eur.\nPhys. J. C32, 323\u2013336 (2003). hep-ex/0309077.\nAbe 2003e:\nK. Abe et al.\n\u201cMeasurement of time-dependent CP-\nviolating asymmetries in B0 \u2192\u03c6K0\nS, K+K\u2212K0\nS, and\n\u03b7\u2032K0\nS decays\u201d.\nPhys. Rev. Lett. 91, 261602 (2003).\nhep-ex/0308035.\nAbe 2003f:\nK. Abe et al. \u201cStudy of time-dependent CP-violating\nasymmetries in b \u2192sqq decays\u201d.\nPhys. Rev. D67,\n031102 (2003). hep-ex/0212062.\n\n823\nAbe 2004a:\nK. Abe et al. \u201cMeasurements of the DsJ resonance prop-\nerties\u201d. Phys. Rev. Lett. 92, 012002 (2004). hep-ex/\n0307052.\nAbe 2004b:\nK. Abe et al. \u201cObservation of large CP violation and\nevidence for direct CP violation in B0 \u2192\u03c0+\u03c0\u2212decays\u201d.\nPhys. Rev. Lett. 93, 021601 (2004). hep-ex/0401029.\nAbe 2004c:\nK. Abe et al. \u201cObservation of radiative decay D0 \u2192\n\u03c6\u03b3\u201d.\nPhys. Rev. Lett. 92, 101803 (2004).\nhep-ex/\n0308037.\nAbe 2004d:\nK. Abe et al. \u201cSearch for B+ \u2192\u00b5+\u03bd\u00b5 and B+ \u2192\u2113+\u03bd\u2113\u03b3\ndecays\u201d. In \u201cProceedings, 32nd International Confer-\nence on High Energy Physics (ICHEP 2004) : Beijing,\nChina, August 16-22, 2004\u201d, 2004. hep-ex/0408132.\nAbe 2004e:\nK. Abe et al. \u201cSearch for pentaquarks at Belle\u201d. In\n\u201cProceedings, International Workshop, Pentaquark\u201904,\nSPring-8, Nishiharima, Hyogo, Japan, July 20\u201323,\n2004\u201d, 2004, pages 91\u201398. hep-ex/0411005.\nAbe 2004f:\nK. Abe et al.\n\u201cStudy of B\u2212\u2192D\u2217\u22170\u03c0\u2212(D\u2217\u22170 \u2192\nD(\u2217)+\u03c0\u2212) decays\u201d. Phys. Rev. D69. hep-ex/0307021.\nAbe 2004g:\nK. Abe et al. \u201cStudy of double charmonium production\nin e+e\u2212annihilation at \u221as \u224810.6 GeV\u201d. Phys. Rev.\nD70, 071102 (2004). hep-ex/0407009.\nAbe 2005a:\nK. Abe et al. \u201cEvidence for X(3872) \u2192\u03b3J/\u03c8 and the\nsub-threshold decay X(3872) \u2192\u03c9J/\u03c8\u201d.\nIn \u201cLepton\nand photon interactions at high energies. Proceedings,\n22nd International Symposium, LP 2005, Uppsala, Swe-\nden, June 30\u2013July 5, 2005\u201d, 2005. hep-ex/0505037.\nAbe 2005b:\nK. Abe et al. \u201cImproved evidence for direct CP vio-\nlation in B0 \u2192\u03c0+\u03c0\u2212decays and model-independent\nconstraints on \u03c62\u201d. Phys. Rev. Lett. 95, 101801 (2005).\nhep-ex/0502035.\nAbe 2005c:\nK. Abe et al. \u201cImproved measurement of CP-violation\nparameters sin(2\u03c61) and |\u03bb|, B meson lifetimes, and\nB0 \u2212B0 mixing parameter \u2206md\u201d.\nPhys. Rev. D71,\n072003 (2005).\n[Erratum-ibid. D71, 079903 (2005)],\nhep-ex/0408111.\nAbe 2005d:\nK. Abe et al. \u201cMeasurement of the branching fractions\nfor B \u2192D\u03c0\u2113\u2212\u03bd\u2113and B \u2192D\u2217\u03c0\u2113\u2212\u03bdl\u201d. Phys. Rev. D72,\n051109 (2005). hep-ex/0507060.\nAbe 2005e:\nK. Abe et al. \u201cMeasurements of B decays to two kaons\u201d.\nPhys. Rev. Lett. 95, 231802 (2005). hep-ex/0506080.\nAbe 2005f:\nK. Abe et al. \u201cMeasurements of branching fractions and\npolarization in B \u2192K\u2217\u03c1 decays\u201d. Phys. Rev. Lett. 95,\n141801 (2005). hep-ex/0408102.\nAbe 2005g:\nK. Abe et al. \u201cObservation of a near-threshold \u03c9J/\u03c8\nmass enhancement in exclusive B \u2192K\u03c9J/\u03c8 decays\u201d.\nPhys. Rev. Lett. 94, 182002 (2005). hep-ex/0408126.\nAbe 2005h:\nK. Abe et al. \u201cObservation of B0 \u2192\u03c00\u03c00\u201d. Phys. Rev.\nLett. 94, 181803 (2005). hep-ex/0408101.\nAbe 2005i:\nK. Abe et al. \u201cObservation of the D1(2420) \u2192D\u03c0+\u03c0\u2212\ndecays\u201d. Phys. Rev. Lett. 94, 221805 (2005). hep-ex/\n0410091.\nAbe 2005j:\nK. Abe et al. \u201cTime-dependent CP asymmetries in b \u2192\nsqq transitions and sin(2\u03c61) in B0 \u2192J/\u03c8K0 decays\nwith 386 million BB pairs\u201d hep-ex/0507037.\nAbe 2006a:\nK. Abe et al. \u201cMeasurement of azimuthal asymmetries\nin inclusive production of hadron pairs in e+e\u2212anni-\nhilation at Belle\u201d. Phys. Rev. Lett. 96, 232002 (2006).\nhep-ex/0507063.\nAbe 2006b:\nK. Abe et al. \u201cObservation of B+ \u2192\u039b+\nc \u039b\u2212\nc K+ and\nB0 \u2192\u039b+\nc \u039b\u2212\nc K0 decays\u201d. Phys. Rev. Lett. 97, 202003\n(2006). hep-ex/0508015.\nAbe 2007a:\nK. Abe et al. \u201cImproved measurements of branching\nfractions and CP asymmetries in B \u2192\u03b7h decays\u201d.\nPhys. Rev. D75, 071104 (2007). hep-ex/0608033.\nAbe 2007b:\nK. Abe et al.\n\u201cMeasurement of D0 \u2212D0 mixing in\nD0 \u2192K0\nS\u03c0+\u03c0\u2212decays\u201d. Phys. Rev. Lett. 99, 131803\n(2007). 0704.1000.\nAbe 2007c:\nK. Abe et al. \u201cMeasurement of the mass of the \u03c4-lepton\nand an upper limit on the mass di\ufb00erence between \u03c4 +\nand \u03c4 \u2212\u201d. Phys. Rev. Lett. 99, 011801 (2007). hep-ex/\n0608046.\nAbe 2007d:\nK. Abe et al.\n\u201cMeasurement of the near-threshold\ne+e\u2212\u2192D(\u2217)\u00b1D\u2217\u2213cross section using initial-state ra-\ndiation\u201d. Phys. Rev. Lett. 98, 092001 (2007). hep-ex/\n0608018.\nAbe 2007e:\nK. 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D77, 036004 (2007).\n0707.0677.\n\nIndex\nA (Wolfenstein parameter), 181, 768\nA0, 418, 506, 701, see Higgs, low mass\n\u03b1, see \u03c62\nACC, see Aerogel Cherenkov counter\nAcoplanarity, 242\nAction, 203\nActivation function, 63\nADA, 667\nAdler zero, 152, 534\nAerogel Cherenkov counter, 7, 14, 19, 29, 30, 50, 71\nALEPH, 280, 295, 653, 658, 661, 663, 745\nAllEvents, 51\nAngular analysis, 140, 159, 172, 221, 226, 236, 244, 252,\n258, 263, 267, 303, 305, 306, 318, 328, 365, 390,\n391, 450, 452\u2013454, 457, 470, 477, 493, 599, 600,\n605, 606, 609, 610, 618, 627, 635, 661, 732\nAngular basis, 140, 734\nAngular distribution, 88, 109, 113, 140, 141, 143, 146,\n148, 150, 151, 172, 252, 263, 267, 311, 319, 337,\n385, 389, 390, 401, 412, 436, 437, 450, 454, 467,\n471, 549, 586, 590, 606, 618, 619, 626, 635, 636,\n648, 649, 666, 671, 687\u2013689, 691, 734\nAnnihilation, see Weak annihilation\nAnnihilation diagram, 236, 238, 240, 426, 430, 437, 444,\n516\u2013518, 520, 526, 527\nARGUS, 1, 85, 87, 90, 109, 119, 179, 276, 280, 281, 288,\n311, 422, 423, 462, 516, 604, 626, 638, 744, 767\nARGUS function, 87, 93, 171, 424, 513\nAsymptotic freedom, 194, 469, 654\nATLAS, 679, 776, 792\nAxial vector, 140, 190, 234, 239, 241, 260, 329, 332, 366,\n393, 396, 549, 600, 601, 606, 608, 619, 652, 653,\n655\u2013657, 660, 678, 704\nAzimuthal angle, 21, 24, 67, 73, 89, 141, 168, 243, 310,\n606, 637, 710, 753, 754, 756\nBrecoil, see Bsig and Recoil method\nBCP , 122, 125\u2013127, 173, 289, 298, 306\nB\ufb02av, 104, 105, 107, 122, 125, 126, 173, 174, 289, 306\nBrec, 79, 80, 83, 100, 102, 105, 153, 173, 174, 277, 279,\n282, 284, 293, 310\nBsig, 92, 198, 396, 452\nBtag, 79, 81, 91, 93, 95\u201397, 100\u2013102, 106, 122, 123, 153,\n173, 174, 198, 310, 333\u2013335, 395, 452\n\u03b2, see \u03c61\nB-counting, 42, 53, 171\nBack propagation, 63, 105\nBackground frames, 40, 49\nBackground remediation, 11, 20\nBackground suppression, 88, 109, 187, 205, 227, 308\u2013\n310, 340, 348, 353, 371, 372, 374, 377, 396,\n399, 401\u2013403, 405, 406, 412\u2013415, 417, 419, 672,\n690, 691, 693, 696, 716\nBag parameter, 216, 281, 771, 781, 789\nBagged decision tree, 64, 65, 394\nBagging, 64\nBaryogenesis, 180, 420\nBaryon number, 180, 410, 420, 522, 752, 762\nviolation, 180, 410, 420, 422\nBaryonium, 434, 437\nbasf, see Belle analysis and simulation framework\nBeam energy constrained mass, see Mbc\nBeam energy substituted mass, see mES\nBeam halo, 16, 765\nBeam pipe, 6, 12, 14, 16, 19, 26, 29, 34, 41, 44, 45, 83,\n285, 287, 588\nBeam-beam e\ufb00ect, 5, 12\nBeamspot, see Interaction point\nBeamspot constraint, 77, 78, 80, 172, 315, 571\nBEAST, 10, 15\nBell inequality, 290\nBelle analysis and simulation framework, 40, 47, 49\nBenchmark new physics, see New physics\nBEPC, 441, 478, 685\nBEPC2, 441\nBES, 441, 457, 459, 638, 683, 685\u2013687\nBES II, 547, 685, 697\nBES III, 347, 360, 441, 460, 622\nBGRS method, 332, 341, 342\nBhabha events, 12, 31, 34, 42, 45, 47, 48, 52, 53, 56,\n77, 109, 165, 168, 170, 295, 415, 461, 495, 500,\n503, 504, 512, 558, 674, 717, 723, 724, 742\nBias, 17, 26, 47, 59, 79, 80, 105, 125, 126, 128, 138, 146,\n151, 156, 160, 161, 164, 165, 171\u2013174, 212, 232,\n243, 278, 283, 308, 322, 334, 335, 358, 359, 495,\n521, 567, 580, 627, 697, 730, 742, 757, 762, 768\nBig Bang, 180, 776\nBinary classi\ufb01er, 59, 62, 63, 68\nBlatt-Weisskopf form factor, 151, 351, 497, 548\nBlind analysis, 20, 60, 160, 164, 398, 556, 568, 582, 584,\n592, 641, 697\nBNL E787, 160\nBNL E791, 160\nBNL E821, 672\nBNL E888, 160\nBoost factor, 2, 5, 80, 125, 172, 277, 282\nBoosted decision tree, 60\u201363, 212, 242, 406, 419, 510\nBoosting, 63\nBootstrap, 64\nBorn cross section, 461, 667\u2013669, 685, 691\nBose symmetry, 281, 302, 330\nBottomonium, 17, 60, 197, 441, 443, 485, 721, 722\nBox diagram, 119, 120, 184, 216, 280, 288, 304, 328,\n365, 387, 393, 561, 562, 781, 782, 789\nBremsstrahlung, 48, 49, 190, 232, 305, 388, 392, 403,\n411, 418, 421, 439, 503, 716\nBrookhaven, 1, 160, 561\nBTeV, 4\nC, see CP violation, time-dependent\n\u03c72, 68, 73, 75, 78, 94, 103, 128, 130, 137, 138, 172, 193,\n206, 243, 267, 279, 300, 321, 327, 337, 339, 342,\n899\n\n900\n352, 495, 521, 527, 533, 534, 536\u2013538, 547, 568,\n570, 571, 590, 597, 621, 674, 699, 710, 729, 732,\n745, 749, 768, 773\n\u03c7d, 105, 281, 283, 284\nCabibbo allowed, see Cabibbo favored\nCabibbo angle, 178, 274, 649, 768\nCabibbo favored, 194, 345, 357, 412, 438, 516, 525, 554,\n564, 567, 573, 578, 587, 588, 591\u2013593, 631\u2013633,\n655, 657, 660, 666, 729, 730\nCabibbo forbidden, see Cabibbo suppressed\nCabibbo suppressed, 105, 209, 222, 308, 345, 382, 428,\n438, 439, 516, 523, 524, 528, 544, 554, 562,\n564, 565, 573, 578, 587, 588, 592, 631, 648,\n649, 652, 654, 659, 660, 666\nCalibration constant, 25, 28, 30, 31, 35, 40, 46, 47\nCaltech, 561\nCDC, see Drift chamber\nCDF, 216, 217, 276, 277, 280, 281, 288, 441, 470, 471,\n477, 551, 585, 714, 721, 736, 771, 776\nCELLO, 716\nCESR, 1, 3, 185, 441, 478, 516\nCharge symmetry, see CP violation, time-dependent\nCharged current, 178, 181, 637, 639, 640, 651, 661, 666,\n673, 780, 785\nCharged particle identi\ufb01cation, 7, 10, 14, 19, 28, 38, 59,\n67, 94, 164, 168, 227, 244, 381, 567\nalgorithm, see Charged particle identi\ufb01cation, se-\nlector\nselector, 39, 60, 67\u201369\ntweaking, 69, 70\nCharm CP violation, 182, 561, 584, 594\nCharm mixing, 119, 561\nCharm penguin, 240, 367\nCharmless B decay, 20, 21, 52, 84, 93, 109, 112, 114,\n117, 126, 154, 155, 185, 187, 205, 211, 212,\n236, 328, 329, 331, 342, 367, 386, 388, 396,\n419, 425, 431, 440, 735, 774, 789\nquasi-two-body, 52, 110, 248, 303, 312, 328, 335,\n339, 342\nthree-body, 84, 113, 115, 118, 268, 303, 314, 317,\n328, 330, 338, 342\ntwo-body, 115, 117, 245, 328, 333, 342, 425, 440,\n735, 789\nCherenkov photon, 7, 21, 28, 30, 50, 67, 68, 94\n\u03c7PT, see Chiral perturbation theory\nChiral perturbation theory, 191, 201, 203, 600, 652, 655\nChiral soliton model, 759\nChromo magnetic moment, 190, 275, 366, 599, 787\nCKM Matrix, 1, 119, 174, 178, 181, 185, 186, 216, 236,\n250, 272, 274, 280, 288, 302, 326, 328, 344, 360,\n361, 368, 379, 395, 405, 426, 427, 438, 516, 519,\n545, 547, 551, 562, 564, 644, 663, 664, 666, 767,\n768, 777, 778, 781\u2013783, 785, 786, 790, 791\nCLAS, 762, 763\nClebsch-Gordan coe\ufb03cients, 238, 425, 761\nCLEO, 1, 7, 85, 86, 88, 109, 110, 157, 159, 165, 187,\n205, 211, 242, 276, 281, 288, 295, 312, 357\u2013\n360, 374, 402, 422, 423, 425, 452, 460, 462,\n464, 471, 478, 488, 492, 494, 502, 503, 505,\n506, 513, 516, 519, 525, 527, 547, 567, 573,\n590, 604, 606, 608, 610, 611, 626, 627, 631,\n646, 649, 651, 653, 661, 663, 687, 698, 714\u2013\n717, 719, 721, 723, 724, 746, 749\u2013751, 767\nCLEO cones, 110, 242\nCLEO Fisher, 110, 112\nCLEO II, 370, 551\nCLEO III, 441, 547\nCLEO-c, 210, 347, 349, 441, 457, 520, 521, 546, 547,\n551, 553, 767\nCMD-2, 669, 676\nCMS, 679, 776, 792\nCoherence factor, 349, 350\nCollection, 40, 46, 49, 51, 53\nCollimators, 6\nCollins function, see Fragmentation\nColor\nallowed, 221\u2013223, 236, 237, 240, 258, 430, 523, 608\nanti-triplet, 705\noctet, 222, 223, 234, 445, 446, 462\u2013465\noctet operator, 445\nsinglet, 183, 221, 442, 445, 446, 462\u2013464, 624, 652,\n759\nsuppressed, 221\u2013227, 232, 236\u2013238, 240, 241, 248,\n268, 311, 319, 345, 350, 363, 426, 430, 435,\n516, 517, 523, 538, 608, 734\ntransparency, 223\nColumbia, 561\nCombinatorial background, 83, 84, 90, 93, 97, 109, 166,\n167, 170, 171, 187\u2013189, 212, 231, 232, 279,\n284\u2013286, 308, 310, 340, 346, 396, 399, 405,\n450\u2013453, 455, 456, 471, 473, 491, 494, 510, 522,\n525\u2013527, 538, 554, 556, 558, 566, 574, 585, 593,\n609, 611, 612, 662, 692\u2013694, 696, 727\nCOMPASS, 754\nCompton scattering, 48, 49, 707, 715\nConditions database, 46, 48, 49\nConserved vector current, 652, 653\nContinuum background, 34, 83, 86, 90, 94, 95, 97, 98,\n109, 126, 131, 136, 154, 155, 165, 187, 188, 205,\n206, 211, 231, 242\u2013244, 266, 280, 282, 284\u2013287,\n295, 296, 308\u2013310, 333\u2013335, 337, 340, 346, 348,\n371\u2013373, 380, 397, 399, 401, 402, 406, 431, 449,\n457, 478, 486, 487, 489, 507, 511, 544, 547, 550,\n556, 603\u2013605, 608, 632, 633, 649, 672, 735, 736\nContinuum suppression, 84, 94, 95, 109, 187, 308, 309,\n315\u2013317, 340, 346, 371, 372, 397, 399, 424\nCornell, 1, 4, 274\nCosmic ray, 16, 31, 41, 48, 50, 54, 74, 75\nCOSY, 762\nCoulomb potential, 16, 190, 442, 505, 577, 599, 687\nCoupled bunch instabilities, 6\nCovariance matrix, 59, 62, 75, 78, 129, 131, 163, 192,\n231, 458, 574, 578, 672, 676\nCP violation\n\u03c4 decay, 637, 644, 645, 648, 666\nB decay, see \u03c61, \u03c62, \u03c63, CP violation in decay and\nCP violation in mixing\nD decay, 165, 182, 345, 519, 525, 561\n\n901\nin decay, 143, 162, 173, 174, 179, 183, 184, 223, 236,\n237, 239\u2013241, 245, 250, 271, 272, 311, 316, 317,\n320, 321, 323, 327, 329, 330, 345, 346, 356, 371,\n375, 382, 384, 387, 389, 438, 565, 579, 585, 590,\n644, 771, 777, 786, 787\nin mixing, 119, 154, 179, 236, 245, 250, 260, 272,\n274, 292, 323, 370, 561, 585, 771, 774, 777\nmixing induced, 173, 183, 302, 328, 774\nsuper-weak model, 179, 236, 302, 777\ntime-dependent, 2, 3, 17, 18, 79, 80, 100, 134, 140,\n142, 172, 185, 227, 230, 250, 274, 276, 279,\n281, 289, 302, 328, 365, 377, 379, 385, 594,\n735, 771, 788\nCP violation in interference between mixing and decay,\nsee CP violation, mixing induced\nCP violation, direct, see CP violation, in decay\nCP-even, 122, 140, 142, 147, 175, 304\u2013306, 308, 310\u2013\n312, 315, 316, 331, 345, 346, 573, 576, 585,\n732, 733, 783\nCP-odd, 122, 140, 144, 147, 175, 304\u2013306, 310\u2013312, 345,\n346, 506, 513, 573, 576, 585, 647, 650, 734, 783\nCPT, 119, 180, 185, 274, 289, 292, 294, 295, 297\u2013299,\n322, 637\u2013639, 645, 647\nCross feed, 155, 205, 231, 243, 359, 405, 406, 431, 615,\n732, 736\nCross section\ne+e\u2212, 722\n\u03b3\u03b3, 703\n\u00b5+\u00b5\u2212, 55, 486, 721, 722\nqq, 55, 667\n\u03c4 +\u03c4 \u2212, 637, 640, 722\nbb, 486, 722\u2013724\ncc, 690, 696\ntt, 216\nCrossing angle, 6, 18, 21\nCrystal Ball, 93, 449, 453, 463, 489, 507, 508, 513, 524,\n555\nCrystal Barrel, 532\nCUSB, 721, 723\nCUSB II, 721\nCVC, see Conserved vector current\nD-wave, 140, 151, 350, 437, 441, 450, 461, 480, 494, 495,\n533, 534, 547, 548, 600, 601, 605, 606, 618\u2013620,\n625, 626, 661, 706, 707\nDs1(2460), 225, 226, 602, 603, 620, 696, 732\nDs1(2536), 320, 321, 602, 610, 617, 619, 622\nD\u2217\nsJ(2317), 228, 524, 610, 611, 613\u2013615, 622, 732\n\u2206\u0393d, 120, 122, 154, 173, 288, 297, 323\n\u2206\u0393s, 288\n\u2206md, 2, 17, 101, 120, 142, 154, 173, 179, 183, 216, 274,\n276, 279, 281, 288, 290\u2013292, 302, 769\u2013771, 773,\n781, 785, 787, 788\n\u2206ms, 280, 281, 288, 291, 768, 771, 777, 785\n\u2206t, see Proper time di\ufb00erence\ndE/dx, see Speci\ufb01c energy loss\nD\u00d8, 216, 277, 280, 288, 296, 441, 473, 721, 776\nDA\u03a6NE, 669\nDalitz plot, 113, 149, 161, 171, 226, 244, 263, 268, 271,\n272, 303, 315\u2013317, 319, 327\u2013329, 331, 338, 342,\n345, 350, 358, 363, 379, 463, 480, 496, 518, 527,\n528, 530, 536\u2013538, 541, 542, 575, 578, 579, 590,\n605, 607, 613, 636\nmodel, 149, 350, 356, 358, 359, 363, 464, 481, 529,\n533, 534, 576, 578, 579, 590, 593\nmodel independent analysis, 158, 159, 358, 590\nsquare, 154, 155, 317, 533, 534\nDark force, 667, 700\ndark Higgs, 701, 702\ndark photon, 700, 701\nDark gauge boson, see Dark force\nDark matter, 413, 441, 485, 509, 511, 700, 786\nDASP, 637\nData quality, 35, 40, 46, 52, 53\nData summary tape, 47\nDCH, see Drift chamber\nDCI, 669\n\u2206E, 85, 87, 135, 147, 171, 187, 205, 231, 232, 242, 248,\n264, 267, 277, 285, 286, 305, 310, 313, 315\u2013317,\n320, 321, 333, 334, 336, 337, 340, 346, 348, 353,\n359, 374, 375, 377\u2013381, 388, 392, 421, 431, 449,\n457, 463, 473, 642, 726, 727, 731, 732, 734, 736\nDecay chain, 2, 48, 73, 83, 88, 91, 140, 141, 146, 166,\n191, 227, 320, 374, 392, 635, 729\nDecay constant, 204, 216, 222, 223, 238, 239, 281, 333,\n361, 362, 395, 396, 400, 404, 410, 517, 519, 520,\n551, 553, 599, 601\u2013603, 651, 655, 664, 707, 709,\n715, 771\u2013774, 781, 789\nDecay length, see Flight length\nDecay time di\ufb00erence, see Proper time di\ufb00erence\nDeep inelastic scattering, 741, 752\nDELPHI, 15, 280, 648, 753\nDESY, 1, 561, 637\nDetector of internally re\ufb02ected Cherenkov light, 7, 11,\n14, 19, 21, 26, 28, 31, 38, 43, 67, 68, 334, 380,\n421, 674, 742\nDetector resolution, see Resolution\nDGE, see Dressed-gluon exponentiation\nDGLAP evolution, 740, 758\nDIANA, 759, 762\nDi\ufb00erential decay probability, 141, 149, 190, 191, 206,\n209, 215, 389, 432, 436, 440, 545, 547, 548,\n551, 649\nDilepton events, 111, 220, 232, 282, 368, 419, 495, 503\u2013\n505, 701, 702\nDilution, see Tagging, mistag\nDip angle, 73\nDiquark model, 426, 427\nDirac theory, 370, 673\nDIRC, see Detector of internally re\ufb02ected Cherenkov\nlight\nDirect CP violation, see CP violation, in decay\nDIS, see Deep inelastic scattering\nDispersion relation, see Hadronic dispersion relation\nDM1, 669, 680, 687\nDM2, 669, 679, 687\nDONUT, 179\nDORIS, 6, 185, 637\nDORIS-II, 1, 3, 516\n\n902\nDouble tagged event, 97, 505, 581, 584\nDQM, see Data quality monitor\nDressed-gluon exponentiation, 210, 214, 369, 377\nDrift chamber, 7, 10, 11, 14, 19, 21, 23, 26, 34, 43, 45,\n46, 67, 68, 74, 674, 742\nDST, see Data summary tape\nDuality violation, 195, 655\nDunnington, 160\nDuty cycle, 35, 44\nEECL, see Eextra\nEextra, 92, 394, 397, 398, 403, 406, 407, 412, 414, 418,\n522, 552\n\u03f5, 161, 302, 768, 769, 771, 773\n\u03f5\u2032, 161, 302, 771\nE653, see Fermilab E653\nE687, see Fermilab E687\nE691, see Fermilab E691\nE704, see Fermilab E704\nE760, see Fermilab E760\nE787, see BNL E787\nE791, see BNL E791, see Fermilab E791\nE797, see BNL E797\nE821, see BNL E821\nE835, see Fermilab E835\nE888, see BNL 888\nECL, see Electromagnetic calorimeter\nECOC, see Error-correcting output code\nEDM, see Electric dipole moment\nE\ufb00ective phase, 308, 316, 329\nEigenstate\nCP, 1, 2, 122, 140, 175, 250, 281, 289, 294, 296, 298,\n302\u2013305, 311, 312, 314, 315, 319, 320, 323, 324,\n332, 334, 338, 339, 345\u2013348, 358, 359, 377, 384,\n387, 534, 536, 565, 573, 585, 594, 732, 734\n\ufb02avor, 120, 281, 324, 564\nhelicity, 140\nmass, 122, 216, 280, 288, 293, 323, 561, 563, 573,\n578, 783, 789\ntransversity, 140\nElectric dipole moment, 181, 322, 640, 645, 791\nElectromagnetic calorimeter, 7, 11, 15, 18, 19, 30, 96,\n168, 170, 305, 371, 397, 489, 491, 499, 511,\n522, 552, 668, 669, 717\nElectron cloud instability, 6, 12, 16\nElectroweak baryogenesis, 180\nElectroweak penguin, 330, 365, 410, 440\nEMC, see Electromagnetic calorimeter\nEML, see Maximum-likelihood, extended\nEnergy \ufb02ow, 110, 243, 739\nEnergy scan, 17, 34, 42, 54, 55, 457, 461, 486, 491, 669,\n721\u2013723, 729\nEntanglement, see Quantum entanglement\nEPR correlation, see Quantum entanglement\nEquivalent-photon approximation, 703, 704\nError-correcting output code, 64, 67\nEstimator, 59, 64, 75, 101, 128\u2013130, 165, 346, 638\n\u03b7b, 17, 447, 448, 492, 498, 499, 502\n\u03b7b(1S), 60, 485, 488, 490, 500, 504\n\u03b7b(2S), 60, 485, 490\n\u03b7, 182, 183, 768\n\u03b7c, 126, 140, 232, 302, 305, 441, 448, 477, 498, 500, 502,\n714, 719\nEvent migration, 155, 264, 266, 359\nEvent reconstruction, 46, 48, 54, 83, 277, 315, 333, 395,\n397, 480, 520, 567, 585, 588, 593, 674, 690\nEvent shape variable, 55, 94, 109, 114, 187, 205, 242,\n264, 282, 311, 315, 334, 346, 348, 372, 377,\n397, 399, 401, 403, 406, 411, 412, 419, 431,\n449, 457, 514, 581, 754\nExclusive B meson reconstruction, 83, 227, 374, 377,\n387, 405, 424, 520, 722, 726\nExhaustive matrix, 64, 68\nExotic state, 232, 258, 441, 469, 486, 501, 667, 682, 697,\n704, 713, 739, 759\nExperiment, see Run\nExtra dimensions, see New physics\nF-wave, 497, 602\n\u03c61, 2, 10, 17, 123, 172, 175, 182\u2013185, 219, 227, 289, 292,\n298, 302, 326, 328, 330, 344, 345, 735, 768, 771,\n774, 777, 781, 785, 786, 791\n\u03c6e\ufb00\n1 , 308, 310, 316, 317\n\u03c62, 123, 175, 182, 183, 185, 218, 292, 303, 328, 345, 768,\n771, 774\n\u03c6e\ufb00\n2 , 328, 329, 332, 339, 341, 344\n\u03c63, 123, 159, 174, 175, 182\u2013185, 292, 303, 328, 332, 345,\n735, 769, 771\nADS method, 345, 347\nGGSZ method, 345, 350\nGLW method, 345\nModel independent approach, 159, 358\nFactorization, 186, 221, 225, 237, 238, 310, 366, 370,\n438, 462, 608, 617, 711, 756\nna\u00a8\u0131ve, 221, 234, 241, 260, 331, 435, 463, 517, 520,\n732\nQCD, 218, 221, 239, 250, 260, 341, 367, 379, 396,\n444, 446, 448, 502, 517\nFast pion, 88, 103\nFCNC, see Flavor Changing Neutral Current\nFeed-across, 431\nFeed-down, 206, 244, 280, 424, 431, 452, 455, 463, 611,\n613, 733\nFeed-up, 733\nFeldman-Cousins method, 356, 411, 426, 556, 570, 583\nFERMI, 701\nFermi constant, 120, 186, 216, 222, 237, 275, 366, 395,\n410, 519, 545, 562, 638, 639, 649, 651, 771, 781\nFermi motion, 197\nFermilab, 1, 4, 160, 179, 191, 208, 441, 540, 677\nFermilab E653, 551\nFermilab E687, 547, 551, 626\nFermilab E691, 547\nFermilab E704, 753\nFermilab E760, 688\nFermilab E791, 159, 160, 537, 540, 551, 567\nFermilab E835, 688\nFESR, see Finite energy sum rule\nFF, see Fragmentation function\nFierz identity, 222\n\n903\nFigure of merit, 59, 115, 346, 489\nFinal state interaction, 143, 153, 224, 322, 432, 435,\n516, 548, 592, 667, 687, 688\nFinal state radiation, 79, 232, 248, 373, 495, 503, 638,\n642, 668, 674\nFine-tuning, 791\nFinite energy sum rule, 197\nFisher discriminant, 62, 110, 111, 242, 308, 311, 313,\n316, 334, 335, 337, 346, 353, 401, 402, 411,\n457, 510, 544, 545, 547, 548, 608, 732, 735,\n736\nFit fraction, 158, 264, 267, 271, 272, 351, 352, 458, 533,\n534, 536\u2013538\nfL, see Longitudinal, polarization\nFlatt\u00b4e, 150, 734\nFlavianet, 770\nFlavor Changing Neutral Current, 178, 179, 182, 216,\n219, 236, 410, 416, 516, 555\u2013558, 561, 563, 597,\n779\u2013782, 786, 787, 789\u2013791\nFlavor singlet, 250\nFlavor speci\ufb01c \ufb01nal state, 2, 100\u2013102, 116, 122, 126,\n289, 298, 317, 318, 322, 384, 386, 564, 567,\n573\nFlavor tagging, see tagging\nFlight length, 2, 29, 73, 77\u201380, 168, 276, 282, 286, 538,\n556, 558, 566, 567\nFluka, 50\nFNAL, see Fermilab\nFock space, 445\nFOCUS, 525, 545, 550, 551, 573, 630\nFOM, see Figure of merit\nForm factor, 150, 151, 158, 186, 187, 189\u2013192, 194, 201,\n203, 205, 217, 218, 222, 223, 238\u2013240, 260, 267,\n351, 357, 361, 369, 370, 378\u2013382, 390, 391, 395,\n396, 404\u2013406, 430, 437, 440, 460, 517, 520, 538,\n543\u2013549, 551, 599, 650\u2013652, 655, 657, 658, 663,\n666, 667, 670, 672, 675, 686, 689, 703\u2013705, 708,\n709, 714, 715, 718, 719, 773\nForward backward asymmetry, 387, 390\u2013393, 585\u2013587,\n593, 635\nFour-quark operator, 274, 366, 444, 773\nFox-Wolfram moment, 55, 94, 110, 187, 242, 284, 285,\n309, 313, 335, 397, 415, 419, 489, 513, 556,\n723, 729, 732, 735, 736\nFraction of longitudinally polarized events, see Longi-\ntudinal polarization\nFragmentation, 103, 109, 126, 211, 219, 225, 276, 371,\n375, 381, 422, 425, 434, 437\u2013439, 462, 463, 466,\n517, 522, 556, 563, 586, 604, 652, 667, 722, 739,\n741, 746, 749\nCollins function, 753\nfunction, 445, 614, 741, 747, 752\ninterference function, 755\nPeterson function, 467\npolarized function, 752\nunpolarized function, 741\nFSI, see Final state interaction\nFSR, see Final state radiation\nG-wave, 706\nG(3900), 462, 693\nGF , see Fermi constant\n\u03b3, see \u03c63\ng \u22122, 637, 640, 655, 663, 673, 677, 781, 782, 784\u2013787,\n789, 791\nG parity, 236, 258, 260, 272, 497, 661\nGEANT, 40, 49, 50, 753\nGell-Mann-Okubo rule, 624\nGenetic algorithm, 267\nG\ufb01tter, 679\n\u03b3\u03b3, see Two-photon\nGIM mechanism, 120, 178, 179, 383, 516, 555, 557, 561,\n790\nGini index, 60, 63\nGlobal Fit, 147, 183, 196, 200, 289, 298, 319, 341, 396,\n446, 678, 681, 758, 767\nCKM \ufb01tter, 768\nscan method, 768\nUT\ufb01t, 768, 769\nGlueball, 258, 434, 437, 685\nGluonium, 250\nGMFV, see New physics, general minimal \ufb02avor viola-\ntion\nGOF, see Goodness-of-\ufb01t\nGolden mode, 2, 175, 184, 185, 232, 250, 289, 302, 303,\n305, 327\nGoodness-of-\ufb01t, 138, 171, 534, 537, 557\nGounaris-Sakurai lineshape, 150, 351, 357, 658, 664\nGrand uni\ufb01ed theories, 180, 420, 780\nGrid computing, 13, 41, 51\nGSI, 441\nGUT, see New physics, Grand uni\ufb01ed theory\nH\u00b1, see Higgs, charged\nhb(1P), 490, 492, 497\nhb(2P), 490, 492, 497\nH1, 762\nHadron collider, 100, 411, 421, 446, 731, 735, 737\nHadron multiplicity, 52, 53, 489, 739, 740, 742\nHadronBJ, 52, 56, 722\nHadronic B reconstruction, 63, 83, 88, 92, 212, 397,\n412\u2013414, 416, 417, 500\nHadronic dispersion relation, 187, 201, 204\nHadronic mass, 187, 195, 196, 198, 199, 211, 392, 663,\n668, 672, 674, 687\nHadronic mass moment, 195, 196, 198, 199\nHadronic matrix element, 186, 203, 216, 219, 237, 274,\n276, 302, 367, 369, 519, 651, 652, 771\u2013773\nHadronic tag, 92, 100, 174, 189, 303, 374, 394, 397\u2013399,\n402, 405, 408, 412\u2013414, 416, 417, 583\nHadronization, see Fragmentation\nHamiltonian, 119, 186, 222, 223, 237, 238, 281, 322, 365,\n369, 395, 448, 519, 562, 563, 599, 600, 645, 649,\n771, 777, 779, 785, 786, 791\nHamming distance, 64\nHandbag model, 709\nHard kernel, 218, 239, 370\nHard scale, 194, 239, 369, 370, 443, 445, 447\nHard-scattering kernel, see Hard kernel\nHardware trigger, see Trigger, L1\n\n904\nHeavy-quark expansion, 187, 238, 239, 241, 274, 275,\n516, 517, 520\nHeavy-to-light form-factor, 201, 546, 600\nHelicity, 88, 140, 151, 156, 172, 205, 239, 241, 243, 280,\n310, 319, 337, 340, 357, 361, 378, 385, 390, 395,\n410, 426, 453, 465, 467, 517, 531, 549, 551, 555,\n605, 608, 610, 611, 615, 620, 621, 626, 635, 649,\n686, 688, 704, 706\u2013708, 710, 731, 734\u2013736\nHelicity suppression, 395, 410, 413, 518\nHERA, 4, 762\nHERA-B, 4\nHERMES, 753, 756, 758, 762, 765, 766\nHESSE, 129, 131, 134, 137\nHessian method, 747\nHidden local symmetry, 664\nHiggs\nboson, 117, 179, 410, 469, 679, 780, 790\ncharged, 186, 365, 395, 396, 410, 506, 553, 554, 651\ndark, see Dark force\n\ufb01eld, 299, 506, 777, 779\nlow mass, 506, 701, 702, 785\nmass, 377, 395, 508, 679, 779\nvacuum expectation value, 395, 783\nHiggsstrahlung, 702\nHQE, see Heavy-quark expansion\nHQET, see Heavy-quark e\ufb00ective theory\nHybrid state, 97, 98, 211, 442, 469, 477, 501, 685\nHyper\ufb01ne mass splitting, 195, 442, 447, 477, 493, 494,\n624, 630\nIFR, see Instrumented \ufb02ux return\nImpact parameter, 23, 26, 74, 103, 274, 285, 581\nImportance sampling, 191\nIndirect CP violation, see CP violation, mixing-induced\nInfrared divergence, 239, 240, 445\nInitial state radiation, 48, 169, 441, 455, 462, 467, 482,\n667, 722, 742\nInjectable, 27, 35, 44\nInstrumented \ufb02ux return, 11, 12, 14, 19, 28, 34, 38, 43,\n55, 67\u201369, 305, 421, 674\nInteraction length, 33, 152, 534\nInteraction point, 5, 18, 23, 29, 31, 33, 52, 53, 67, 73\u2013\n75, 81, 83, 167, 172, 313, 315, 504, 516, 526,\n581, 582, 697, 701, 743\nInteraction region, see Interaction point\nInterference CP violation, see CP violation, in interfer-\nence\nInterference fragmentation function, see Fragmentation\nInvisible decays, 34, 42, 410, 413, 485, 509, 701\nIP, see Interaction point\nIR, see Interaction point\nIsgur-Wise function, 404, 550, 690\nIsobar model, 150, 151, 153, 158, 263, 320, 350, 359,\n533, 536\u2013538, 576, 578, 579, 605\nIsospin, 178, 192, 202, 217, 223, 250, 258, 260, 333, 361,\n375, 378, 380\u2013383, 388, 406, 425, 437, 438, 470,\n471, 488, 502, 504, 505, 518, 524, 585, 611, 614,\n615, 623, 624, 626, 627, 629, 651, 661\u2013663, 673,\n676, 680, 698, 727, 760, 761\nanalysis, 328, 329, 331, 333, 338, 342, 518, 519, 524,\n585\nbreaking, 250, 260, 344, 382, 390, 470, 488, 502,\n504, 524, 661\u2013663, 673, 676\ntriangle, 330, 342\nIsospin decomposition, see Isospin\nISR, see Initial state radiation\nJacobian, 74, 156, 265\nJarlskog, 182\nJe\ufb00erson Laboratory, 760, 761\nJet, 52, 109, 110, 154, 205, 239, 240, 242, 266, 333, 337,\n422, 431, 558, 621, 739, 741\u2013743, 749, 751, 753,\n756\nJetset, 48, 211, 219, 375, 381, 741, 744, 745, 749, 751,\n752\nJLab, see Je\ufb00erson Laboratory\nK-matrix formalism, 151, 264, 351, 356, 534, 579\nKalman \ufb01lter, 74, 76\nKEDR, 441, 462, 604, 638\nKEK, 3, 4, 9, 10, 15, 21, 25, 36, 58, 441\nKEKB, 1, 4\u20136, 15, 19, 21, 26, 35, 41, 42, 45, 723\nKinematic approximation, 125, 278\nKinetic scheme, 190, 195, 196, 200, 210\nK0\nL and muon detection system, 15, 19, 20, 32, 34, 50,\n67, 68, 305, 743\nKLM, see K0\nL and muon detection system\nKLOE, 640, 664, 669, 676\nKM mechanism, see Kobayashi-Maskawa mechanism\nKobayashi-Maskawa mechanism, 1, 6, 178, 179, 302,\n327, 768, 775, 777\nKTeV, 160\nL0, 111\u2013113, 187, 308, 334, 353\nL2, 112, 113, 187, 205, 308, 334, 353\n\u039b/mb expansion, 218, 237, 239, 241, 367, 368, 370, 382\n\u039bQCD, 366, 367, 369, 389, 390, 516, 519, 688, 703, 715\nL3 (experiment), 280, 648, 745\nLagrange multiplier, 76\nLagrangian, 180, 197, 223, 239, 444, 446, 447, 599\u2013601,\n603, 647\nLamb shift, 443\n\u03bb (Wolfenstein parameter), 181, 219, 518, 563, 564, 768,\n777, 782\nLASS, 153, 537, 538, 549, 760\nLAT, see Lateral moment\nLateral moment, 67, 168, 403, 489\nLattice QCD, 183, 186, 187, 191, 197, 201\u2013203, 208,\n216, 217, 219, 362, 396, 441, 443, 444, 447,\n449, 460, 461, 469, 477, 485, 543, 546, 547,\n551, 553, 599, 603, 626, 630, 664, 685, 720,\n740, 770\u2013774\nLBL, 4, 567, 637\nLCSR, see Light-cone sum rule\nLeaf by leaf \ufb01t, see Vertex, \ufb01t\nLEAR, 688\nLeft-right symmetric models, 777, 790\nLEP, 179, 185, 276, 281, 288, 561, 640, 655, 660, 661,\n676, 721, 741, 767, 792\n\n905\nLEP electroweak working group, 640\nLEPS, 759, 760, 762\nLeptogenesis, 180\nLepton energy moment, 195, 198, 199\nLepton \ufb02avor violation, 410, 416, 512, 640\nLepton number violation, 180, 410\nLepton universality, 388, 485, 513, 637, 651, 665\nLeptonic decays, 186, 395, 413, 422, 426, 494, 512, 637,\n647, 771\nLeptoquark, 411\nLESR, see Low-energy sum rule\nLetter of intent, 4, 6, 8\u201310, 15\nLevel 1 trigger, see Trigger, L1\nLevel 3 trigger, see Trigger, L3\nLFV, see Lepton \ufb02avor violation\nLHC, 4, 13, 216, 219, 292, 411, 441, 484, 636, 640, 655,\n677, 679, 741, 772, 776, 779, 782, 792\nLHCb, 4, 216, 217, 288, 289, 296, 379, 388, 390, 393,\n426, 471, 473, 481, 551, 585, 597, 622, 631,\n644, 730, 734, 768, 771, 776, 777, 790\nLHT, see New physics, Little Higgs with T-parity\nLight-by-light contribution, 673, 677\nLight-cone distribution amplitude, 223, 239, 240, 370\nLight-cone sum rule, 186, 201, 203, 370, 546, 715, 717\nLikelihood, 61, 128\n\ufb01t bias, 164, 171\njoint, 111, 136\nLikelihood ratio, 62, 67, 114, 115, 117, 129, 138\nLikelihood ratio plot, 133\nLimited streamer tube, 7, 14, 15, 19, 32, 43, 44\nLINAC, see Linear accelerator\nLinear accelerator, 5\nLLNL, 4\nLNV, see Lepton number violation\nLocal operator, 120, 194, 209, 210, 367, 369, 444, 519\nLocal parton-hadron duality, 741\nLong distance, 119, 120, 187, 190, 194, 209, 222, 237,\n239, 303, 312, 365, 368, 385, 437, 442, 516, 519,\n520, 525, 555, 557, 562, 655, 663, 665, 772, 773\nLong term data access, 57\nLongitudinal polarization, 140, 143, 146, 147, 227, 236,\n239, 241, 244, 252, 260, 263, 272, 328, 330,\n335, 337, 370, 390, 619, 654, 690, 732, 734\nLorentz boost, 18, 80, 124, 125, 277, 282, 486\nLorentz covariance, 119, 300\nLorentz invariance, 180, 222, 290, 292, 298, 687\nLow-energy sum rule, 197\nLowMult, 52, 53\nLQCD, see Lattice QCD\nLST, see Limited streamer tube\nLTDA, see Long term data access\nLuminosity, 2, 4\u20137, 11\u201314, 16, 18, 25, 26, 30, 32\u201335, 38,\n41\u201345, 48, 171, 723\nmH, 395, 396, 406, 550, 553, 679, 783\nm\u03c4, 637\nmb, 197, 200, 204, 209, 212, 215, 365, 747\nMbc, 85\nmES, 85, 726\nMAC, 274\nMachine detector interface, 11, 20\nMagnetic moment, 190, 275, 366, 599, 651, 655, 663,\n667, 672, 687, 784, 785, 787\nMajorana neutrino, 410, 418, 419\nMandelstam variable, 430\nMARK I, 461\nMARK II, 274\nMARK III, 516, 525\nMasks (movable), 6, 16\nMass constraint, 75, 76, 200, 215, 397, 418, 504, 522,\n704, 723\nMass di\ufb00erence, 77, 84, 120, 142, 179, 216, 286, 292,\n297, 298, 321, 463, 471, 486, 493, 514, 516,\n521, 522, 524, 538, 544, 554, 557, 568, 571,\n581, 582, 602, 611, 618, 629, 639, 661, 663,\n666, 690, 691, 693, 694, 732, 747\u2013749, 781, 791\nMatter-antimatter asymmetry, see CP violation\nMaximum-likelihood, see also Likelihood\nestimator, 101, 128\nextended, 132\n\ufb01t, 62, 80, 87, 111, 113, 118, 128, 147, 154, 155,\n157, 170, 171, 242, 279, 281, 283, 286, 288,\n300, 308, 321, 324, 333, 346, 398, 399, 402,\n405, 406, 411, 424, 425, 457, 463, 489, 495,\n496, 504, 507, 511, 514, 536, 556, 569, 571,\n574, 575, 581, 612, 619, 698, 699, 701, 726,\n729, 731, 735, 736\nmethod, 61, 128\nMeson distribution amplitude, 223, 240\nMFV, see New physics, minimal \ufb02avor violation\nMHDM, see New physics, multi-Higgs doublet model\nMIGRAD, 131\nMINOS, 131\nMinuit, 131, 132, 163, 707\nMirror lepton, 647\nmistag, see Tagging, mistag\nMixed events, 2, 124, 284, 289, 582, 584\nMixing\nB0\nsB0\ns, 288, 771, 773, 777\nB0B0, 1, 17, 18, 100, 119, 154, 179, 216, 236, 260,\n274, 561, 770, 777\nD0D0, 119, 350, 357, 518, 519, 524, 525, 529, 536,\n537, 556, 561\nK0K0, 179, 293, 296, 322, 323, 561, 777, 780, 785,\n789\u2013791\n\u03b7-\u03b7\u2032, 238\nformalism, 119, 561\nneutrino, 410, 416, 512, 645\nnew physics, 777\nparameters, see xd, xs\nquark, 1, 178, 274, 344, 561, 644, 647, 774, 776,\n778, 781\nMixing diagram, see Box diagram\nModel independent analysis, see Dalitz plot, model in-\ndependent analysis\nModi\ufb01ed leading logarithm approximation, 741, 742,\n745, 746\nMolecule, 258, 469, 470, 501, 600, 602\nMonte Carlo event generators\n\n906\nGamgam, 48, 704\nAAFH, 50\nAfkQed, 48, 668, 674\nBHLUMI, 48, 50\nBHWIDE, 48\nCTOY, 50\nDiag36, 48\nEvtGen, 48, 50, 146\nGheisha, 49\nHemiCosm, 48, 50\nHERWIG, 741, 744, 745, 750, 752\nKK, 50\nKK2F, 48\nPHOKHARA, 668, 669, 674, 675\nPHOTOS, 668\nPythia, 48, 705, 743, 744, 753, 754\nqq98, 50\nSingleParticle, 48\nTAUOLA, 48, 50, 657, 658, 660, 666\nDecay Turtle, 48\nTurtleRead, 48\nUCLA, 741, 744, 745, 749, 752\nx Pythia, 744\nBkqed, 48\nGGRESRC, 704\nTREPS, 704\nMonte Carlo production, 7, 47\nMS scheme, 197, 204, 214, 740, 747, 771, 772\nMSSM, see New physics, MSSM\nMultilayer perceptron, 62, 113\nMultiple scattering, 14, 27, 48, 49, 73\u201375, 78, 287, 574,\n577\nMultivariate method, 59, 67, 100, 104, 113\nMultivariate normal, 59, 62\nMVA, see Multivariate method\nNA49, 760\u2013762\nNA62, 640\nNaturalness, 506\nNeural network, 62, 63, 65, 93, 104, 105, 113\u2013115, 205,\n242, 243, 315, 324, 335, 337, 346, 412, 511, 522\nNeuroBayes, 66, 93, 94, 117, 522\nNeutral current, 178, 185, 236, 516, 555, 557, 558, 561,\n780\nNeutrino mixing, 410, 416, 512, 645\nNew physics\n4th generation, 179, 565, 778, 781\nR-parity violating SUSY, 555\nR-parity violating supersymmetry, 311, 565, 736\ncharged, see Higgs, charged\ndark matter, see Dark matter\nextra dimensions, 377, 413, 469, 780, 784, 790\ngeneral minimal \ufb02avor violation, 779, 785, 786\ngrand uni\ufb01ed theory, 180, 420, 780\nin mixing, 290, 565, 790\u2013792\nlittle Higgs, 780, 791\nlittle Higgs with T-parity, 780, 791\nlow mass Higgs, see Higgs, low mass\nminimal \ufb02avor violation, 779, 784\nminimal \ufb02avor violation SUSY, 779, 786\nMSSM, 395, 408, 506, 553, 558, 640, 648, 779, 782,\n785\u2013787, 789\nmulti-Higgs doublet model, 648, 651\nNMSSM, 506, 508\nnon-minimal \ufb02avor violation SUSY, 787\nRandall-Sundrum models of \ufb02avor, 780, 790\nStandard Model Extension, 298, 299, 301\nsupersymmetry, 311, 395, 418, 512, 553, 555, 565,\n647, 651, 677, 736, 777, 779, 780, 784\nsupersymmetry alignment models, 780, 789\nSUSY, see New physics, Supersymmetry\ntechnicolor, 469\ntwo Higgs doublet model, 377, 395, 410, 506, 553,\n648, 736, 779, 782, 785\nNext-to-leading-log, 218, 365\nNLL, see Next-to-leading-log\nNOMAD, 160, 762\nNon-perturbative QCD, 186, 187, 189, 190, 195, 196,\n198, 201, 203, 204, 209, 210, 214, 221, 237,\n239\u2013241, 330, 365, 367\u2013370, 379, 392, 441, 443\u2013\n447, 516, 652, 653, 655, 703, 707, 740, 741,\n771\u2013773, 781\nNon-relativistic QCD, 186, 441, 443, 444, 446, 488, 502,\n752\nNon-relativistic sum rule, 197\nNonresonant, 150, 153, 159, 211, 316, 537, 542, 699\nNRQCD, see Non-relativistic QCD\nNRSR, see Non-relativistic sum rule\nNuisance parameter, 128, 129, 136, 137, 471, 558, 769\nObjectivity, 13, 35, 46\nO\ufb00-resonance, 41, 724\n\u2126\u2212spin measurement, 636\nOn-resonance, 41, 55\nOPAL, 280, 295, 296, 639, 648, 653, 660, 661, 663\nOPE, see Operator product expansion\nOpen charm, 221, 345, 408, 412, 442, 446, 457, 467, 469,\n492, 600, 602, 626, 667, 690, 697\nOperator product expansion, 187, 190, 191, 194, 198,\n204, 209, 210, 365, 367, 369, 519, 562, 563,\n653, 655, 773\nOptical theorem, 190, 367, 652\nOptimize, 59, 101, 105, 113, 116, 160, 162, 164, 641,\n647, 723\nOrthocharmonium, 441\nOrthopositronium, 441\n1S scheme, 199, 200\nOsaka conference, 17, 303\nOscillation, see Mixing\nOver-training, 61\nOZI suppression, 227, 498, 681, 682\nP, 140, 178, 427\nP-wave, 2, 122, 140, 151, 153, 281, 319, 350, 389, 437,\n441, 469, 477, 480, 485, 488, 492, 497, 498, 502,\n531, 532, 534, 538, 541, 543, 547, 548, 551, 600,\n615, 620, 626, 661, 662, 711, 729, 755, 763\n\u03c0f, see Fast pion\n\u03c0s, see Slow pion\nPAMELA, 700\n\n907\nPANDA, 441\nPANTHER, 40, 47\nParapositronium, 441\nParity, see P\nParity violation, 178, 635\nPartial B reconstruction, 83, 88, 99, 166, 167, 280, 284,\n285, 310, 361, 505, 671, 690, 693, 694, 696, 737\nPartial wave analysis, 140, 147, 159, 250, 530, 531, 540,\n541, 590, 619, 679, 706, 707, 759\nPartially conserved axial current, 198\nParticle identi\ufb01cation, see Charged particle identi\ufb01ca-\ntion\nParton-hadron duality, 187, 196, 201, 204, 741\nPati-Salam model, 411\nPattern recognition, 23, 65, 75, 353, 431\nPCAC, see Partially conserved axial current\np.d.f., see Probability density function\nPenguin, 183, 216, 219, 220, 222, 227, 232, 236, 237, 245,\n250, 260, 268, 303\u2013305, 308, 312, 314, 316, 317,\n328, 365, 410, 426, 430, 436\u2013438, 460, 518, 519,\n526, 527, 565, 655, 722, 736, 778, 781, 782, 785,\n788, 789, 791\nPenguin pollution, 248, 328, 338, 519\nPentaquark, 739, 751, 759\nPEP, 48, 274\nPEP-II, 1, 4\u20136, 8, 11\u201313, 16, 18, 21, 23, 27, 35, 38, 41,\n43\u201345, 54\nPerceptron, 62, 113, 335, 511\nPerturbative QCD, 120, 190, 191, 194\u2013196, 198, 203,\n210, 225, 239, 250, 365\u2013367, 369, 389, 462, 464,\n502, 546, 550, 653\u2013655, 660, 663, 666, 673, 676,\n688, 703, 707, 713, 715, 740, 741\nPHENIX, 441, 756\nPID, see Charged particle identi\ufb01cation\nPlanarity, 242\nPLUTO, 637\nPMT, 21, 28\u201330\nPOCA, see Point of closest approach\nPoint of closest approach, 73, 748\nPolar angle, 18, 21, 25, 29\u201331, 47, 53, 71, 80, 102, 103,\n125, 141, 164\u2013168, 205, 243, 297, 335, 415, 419,\n437, 438, 495, 504, 508, 510, 513, 575, 586\u2013588,\n649, 668, 671, 687, 692, 693, 705, 710, 742, 743,\n748, 757\nPolarization, 115, 140, 143, 189, 190, 197, 227, 236, 239,\n241, 243, 244, 252, 260, 263, 272, 290, 311, 328,\n330, 333, 335\u2013337, 379, 390, 405, 438, 467, 555,\n635, 637, 662, 663, 672, 689, 715, 732\u2013734, 752\nPole model, 426, 427, 430, 434, 439, 544, 546, 548\nPOLE program, 411\nPower correction, 194, 196, 218, 239\u2013241, 367, 379, 391,\n715, 717\nPQCD, see Perturbative QCD\nPrimary lepton, 102, 285, 295, 406, 417, 512\nPrimary vertex, see Vertex, primary\nProbability density function, 62, 81, 115, 126, 128, 147,\n171\nPro\ufb01le likelihood ratio, 129\nPrompt calibration, 46, 49\nPrompt reconstruction, 46\nProper time, 276, 325, see Proper time di\ufb00erence\nProper time di\ufb00erence, 2, 119, 122, 123, 142, 153, 172,\n306, 333, 361\nProtractor, 18\nPS170, 688\nPseudomass, 638\nPseudoscalar, 89, 140, 143\u2013146, 150, 165, 181, 189, 225,\n332, 370, 385, 442, 488, 504, 518, 527, 545, 561,\n562, 601, 635, 642, 644, 649, 704, 705, 732, 755\ncurrent, 197\nPull, 138, 243, 244, 557, 574, 593\nPunzi problem, 60, 135, 697\nPurity, 29, 60, 68, 69, 88, 93, 126, 127, 136, 165, 167,\n174, 225, 242, 277, 279, 280, 286\u2013288, 291, 303,\n333, 336, 348, 386, 397, 399, 421, 583, 584, 605,\n609, 686\nQ, see Tagging, e\ufb00ective e\ufb03ciency, Q\nQAM, see Quality assurance monitor\nQCD\nbeta function, 196\ncorrection, 120, 186, 187, 216, 275, 276, 367, 439,\n550, 653, 715, 771, 781\nLagrangian, 197, 223, 444, 446, 599\u2013601, 603\nmultipole expansion model, 502\nvacuum, 181, 222, 447, 655\nQuality assurance, 47\nQuality assurance monitor, 55\nQuantum entanglement, 119, 289, 322\nQuark model, 1, 179, 206, 258, 367, 413, 430, 546, 599,\n600, 623\u2013626, 629, 631, 632, 636, 730, 759\nQuark-gluon spectral density, 204\nQuark-hadron duality, 195, 366, 367, 603, 655\nQuarkonia, 197, 441, 449, 469, 485\nQuartet, 2, 182\nR2, 55, 94, 111, 723\n\u03c1\u03c0 puzzle, 498\nR-parity, 311, 555, 565, 736\nRabhat, 718\nRadiative correction, 48, 239, 240, 304, 487, 502, 640,\n653, 663, 668, 669, 792\nRadiative penguin, 92, 216, 217, 219, 365, 439, 736\nRadiator function, 667, 668, 674, 678, 685\nRandom forest, 64, 242, 510\nRaw data, 27, 34, 40, 46, 47, 49, 54, 705\nReal-time reconstruction farm, 34, 36, 47\nReceiver operating characteristic, 60\nRecoil method, 83, 91, 92, 97, 242, 370, 485, 615, 616,\n726\nRectangular cuts, 61, 93, 402\nRelativistic Breit-Wigner lineshape, 84, 340, 350, 352,\n451, 453, 454, 457, 487, 489, 536, 538, 548,\n578, 579, 606, 609, 618, 621, 698, 704, 707\nResidue theorem, 197, 655\nResolution\nfunction (\u2206t), 80, 81, 124, 126, 325\nmass, 76, 78, 84, 93, 171, 221, 352, 353, 543, 574,\n605, 617, 619, 621, 670, 692, 697, 748, 762\n\n908\ntrack, 73\nvertex, 18, 45, 76, 77, 79, 81, 124, 125, 127, 242,\n281, 322, 334, 571\nResonance, 149\u2013151\nResonance propagator, 150, 151\nRest of the event, 79, 93, 110\u2013112, 114, 154, 172, 187,\n189, 242, 243, 353, 374, 392, 397, 489, 581,\n630, 742\nRFARM, see Real-time reconstruction farm\nRHIC, 441, 741\n\u03c1, 182, 183, 768\nRight sign decay, 102, 522, 537, 567\nROC, see Receiver operating characteristic\nROE, see Rest of the event\nRolling calibration, 25, 46\nRooFit, 130, 139, 163\nRoot, 13, 35, 40, 46, 54, 130, 131, 163\nrootd, 40, 46, 58\nRPV, see R-parity\nRPV SUSY, see New physics, R-parity violating SUSY\nRun, 41\nS, see CP violation, time-dependent\nS-wave, 151\u2013153, 319, 340, 350, 351, 357, 379, 389, 450,\n456, 460, 461, 485, 488, 496, 498, 531, 534,\n536\u2013538, 540\u2013543, 547\u2013551, 578, 579, 600, 601,\n605, 606, 618, 619, 624\u2013626, 661, 662, 706, 707,\n710, 755\nSakharov, 180, 302, 420\nSAPHIR, 762\nScalar\ncurrent, 239\nmeson, 140, 241, 242, 248, 258, 478, 600, 601, 603,\n605, 607, 683\nScaled momentum spectrum, 422, 423, 524, 525, 618\nScattering length, 152, 351, 534\nScattering matrix, 151, 263\nSCET, see Soft-collinear e\ufb00ective theory\nSchr\u00a8odinger equation, 119\nSecond class current, 637, 661, 666\nSecondary lepton, 102\nSELEX, 630\nSemileptonic decays, 87, 95, 96, 100, 102, 174, 186, 228,\n230, 274, 279, 281, 324, 362, 365, 395, 411\u2013413,\n417, 419, 516, 542, 543, 580, 608, 651, 691, 729,\n770\nSense wire, 27, 28\nShape function, 210, 212, 214, 368, 369\nShort distance, 119, 120, 174, 187, 190, 204, 222, 237,\n312, 365, 369, 391, 434, 437, 439, 440, 442, 445,\n516, 562, 599, 603, 652, 655, 663, 665, 771\u2013773\nSidereal time, 299\u2013301\nSIDIS, 752\nSigmoid, 62, 63\nSigni\ufb01cance, 59, 94, 114, 130\nSilicon detector, 7, 14, 15, 19, 23, 41, 42, 44, 45, 166,\n168, 172, 313, 314, 353, 566, 588\nSimulation production, 47, see Monte Carlo production\nSingle event upset (SEU), 26\nSingular value decomposition, 198, 657\nSkim, 40, 46, 47, 49, 51, 54\u201356, 61\nSLAC, 1, 3\u20135, 7, 10\u201313, 16, 17, 20, 41, 49, 54, 274, 561,\n604, 637, 741\nSLC, 3, 11, 741\nSLD, 276, 280, 745\nSlow pion, 88\u201390, 101\u2013104, 165, 170, 296, 310, 566, 568,\n574, 578\u2013581, 583, 586, 589, 610, 690, 693, 748\nSM4, see New physics, 4th generation\nSME, see Standard Model Extension\nSND, 659, 669, 676, 679\nSNNS, see Stuttgart neural network simulator\nSOB, see Stand o\ufb00box\nSoft scale, 194, 369, 443, 446, 447\nSoft-collinear e\ufb00ective theory, 369, 370, 382, 448\nSoftware trigger, see Trigger, L3\nSolenoid, 16, 19, 21, 41, 42, 73, 637\nSPEAR, 516, 567, 637\nSpeci\ufb01c energy loss, 7, 14, 28, 29, 31, 62, 334, 421, 742\nSpectator model, 275\nSpectator quark, 217, 250, 260, 275, 365, 427, 436, 463,\n516, 625, 631\nSpectral function, 637, 652, 655, 659, 660, 663, 666\nSpherical harmonic, 441, 531, 541\nSphericity, 110, 242\nSpherocity, 242\nsPlot, 59, 133, 334, 425\nSquare Dalitz plot, see Dalitz plot, square\nSSC, 4\nStable beams, 45\nStand o\ufb00box, 21, 28, 29\nStandard Model Extension, 298, 299, 301\nSTAR, 441, 756\nStrong CP problem, 181\nStrong phase, 153, 159, 174, 183, 224, 226, 237, 263,\n267, 272, 310, 326, 330, 332, 339, 341, 345,\n349, 350, 353, 358, 359, 361, 383, 565, 568,\n571, 572, 578, 592, 767\nStuttgart neural network simulator, 66, 105\nSU(2), see Isospin\nSU(2) breaking, see Isospin breaking\nSU(3), 178, 226, 227, 237, 238, 250, 252, 260, 329, 332,\n341, 342, 361, 363, 411, 445, 517, 562, 565, 600,\n601, 624, 652, 654, 709, 719, 730, 759, 784, 790\nSU(3) breaking, 517, 519, 562, 563, 654, 709, 721\nSU(4), 411, 624\nSU(6), 759\nSuper \ufb02avor factory, 17, 58, 92, 97, 115, 127, 219, 235,\n280, 289, 296, 298, 301, 329, 330, 341, 344,\n358, 360, 387, 392, 394, 426, 427, 474, 475,\n484, 502, 577, 622, 634, 644, 721, 786, 792\nSuper-weak model, 179, 236, 302, 777\nSuperconducting solenoid, see Solenoid\nSupersymmetry, see New physics, Supersymmetry\nSupervised learning, 62\nSUSY, see New physics, Supersymmetry\nSUSY CP problem, 777\nSVT, see Silicon detector\nSVTRAD, 25, 37\nsWeight, 134, 137, 244\n\n909\nSynchrotron radiation, 6, 14, 16, 41\nSystematic error, 164\n\u039b, 167\n\u03b3, 170\nz scale, 172\nCP violation in background, 173\nK0\nS, 167, 168\n\u03c00, 168\nalignment, 172\nbackground model, 164, 171\nbeam spot, 172\nboost, 172\ncharged particle identi\ufb01cation, 168\ndetector charge asymmetry, 165, 172, 250, 295, 587,\n649\nexternal input, 173\n\ufb01t bias, 164, 171\nresolution function, 173\ntag-side interference, 174, 306\ntagging, 173\ntime-dependent, 172\ntracking, 164\n\u03b8c, see Cabibbo angle\nT, 322, 592, 645\nT violation\nin mixing, 296\nmixing induced, 292, 322, 326\nT-odd correlation, 592\nTagging, 59, 67, 79, 92, 95, 97, 100, 119, 128, 153, 171\u2013\n173, 179, 188, 189, 192, 212, 243, 281, 290, 302,\n333, 361, 371, 373, 374, 413, 455, 566, 671\nB \ufb02avor, 59, 80, 100, 119, 123, 128, 136, 137, 173,\n281, 282, 285, 290, 298, 303, 306, 310, 313,\n315, 316, 320, 333, 334, 337\ncategory, 100, 101, 125, 286, 287, 337\ndilution, see Tagging, mistag\ndouble-tag, 97, 397, 505, 584\ne\ufb00ective e\ufb03ciency, Q, 100, 101, 108\nmistag, 100, 124, 137, 281\u2013283, 286, 287, 303, 310,\n320, 333, 334, 537\nperformance, 100, 104, 106, 127, 136, 173, 306, 334\nsingle-tag, 97, 98, 104, 584, 704, 714, 715, 719\ntag-side interference, 101, 104, 127, 174, 298, 303,\n306, 322\ntan \u03b2, 395, 396, 406, 418, 783\u2013785, 787\nTASSO, 745\n\u03c4B+, 274\n\u03c4B0, 126, 173, 274\nTauSkim, 52, 53\nTDPA, see Time-dependent Dalitz plot analysis\nTechnical design report, 8, 10\nTechnicolor, see New physics, technicolor\nTensor meson, 140, 143, 144, 146, 151, 239, 241, 248,\n260, 504, 533\nTetraquark, 470, 471, 473, 478, 479, 482, 604\nTevatron, 4, 179, 185, 276, 288, 388, 411, 636, 721, 730,\n772, 776\nThreshold enhancement, 422, 428, 431, 477, 541, 711,\n713\nThrust, 94, 103, 110, 187, 242, 286, 489, 649, 748, 754\nThrust axis, 103, 110, 187, 243, 285, 335, 340, 353, 397,\n413, 414, 489, 513, 544, 547, 649, 742, 753,\n754, 756, 757\nTier A, 13\nTime-dependent CP asymmetry, 100, 119, 172, 183,\n302, 328, 385\nTime-dependent Dalitz plot analysis, 150, 153, 267, 303,\n315, 317, 319, 331, 343, 363, 577, 579, 594\nTime-of-\ufb02ight detector, 7, 14, 19, 29, 50, 62, 67, 68, 94,\n567, 713, 743, 748\nTOF, see Time-of-\ufb02ight detector\nTop mass, 179, 280, 365, 561\nTopological discrimination, 109\nTrack\ndetection, 19, 23, 26\ne\ufb03ciency, 27, 164, 165, 167, 169, 170, 296, 588, 591,\n674, 691, 752\nhelix, 73, 75\nparameterization, 73\nreconstruction, 25\u201327, 29, 46, 73, 144, 164\u2013167,\n169, 265, 587, 618, 674\nTraining, 60, 62\u201364, 68, 69, 104, 105, 113\nTransversality, 151\nTransverse polarization, 115, 140, 143, 239, 337, 378,\n555, 752\nTransversity, 140\u2013142, 318, 331, 390, 710, 752, 756, 758\nTree \ufb01tter, see Vertex, \ufb01t\nTrento convention, 753\nTrickle injection, 23, 35, 43, 44\nTrigger, 7, 19, 34, 40, 41, 53\nbackground, 48\nelectromagnetic, 34\nglobal decision logic (GDL), 20, 34\nglobal trigger (GLT), 20\nIFR, 34\nL0, 15\nL1, 15, 19, 27, 34, 44, 54\nL3, 19, 34\u201336, 44, 46\nlow-multiplicity, 510\ntrack, 14, 34\nvirtual Compton scatter, 716\nTrigger scintillation counter, 29\nTriple product asymmetry, 592\nTRIUMF, 640\nTSC, see Trigger scintillation counter\nTwo Higgs doublet model, see New physics, Two Higgs\ndoublet model\nTwo-photon, 34, 46, 52, 53, 71, 148, 441, 451, 453, 454,\n460\u2013462, 672, 685, 703, 730\nzero-tag method, 53, 703\u2013705, 714\n2HDM, see New physics, Two Higgs doublet model\nU-spin, 252, 383\nUCLA, 3\nUniform phase space, see Nonresonant\nUnitarity, 151, 153, 179, 182, 184, 186, 216, 237, 274,\n302, 322, 328, 345, 366, 379, 383, 540, 545, 547,\n562, 639, 640, 652, 664, 761, 768, 778, 781\n\n910\nUnitarity Triangle, 119, 123, 140, 182, 185, 186, 219,\n276, 281, 289, 292, 298, 302, 328, 345, 379,\n385, 396, 768, 777\u2013779, 785, 787\nUnmixed events, 2, 124, 279, 281\u2013285, 287, 581\nUnparticle, 647\nUnquenched lattice QCD, 191, 448, 544, 551, 553\n\u03a5(1S), 42, 446\u2013448, 485, 723\n\u03a5(2S), 17, 34, 41, 42, 44, 54, 56, 448, 485, 701, 723\n\u03a5(3S), 17, 34, 41, 42, 54, 56, 485, 701\n\u03a5(4S), 2, 3, 16, 18, 34, 41, 42, 44, 73, 77, 80, 100, 109,\n115, 143, 153, 183, 185, 464, 466, 471, 476,\n503, 504, 547, 550, 592, 604, 616, 701, 715,\n719, 721, 723\u2013726, 729, 730, 737\n\u03a5(5S), 42, 100, 379, 416, 492, 493, 496, 721\nUS Air Force, 11\nVacuum polarization, 637, 663, 672\nValidation, 60, 61, 105\nVcb, 2, 87, 174, 175, 182, 185, 186, 222, 223, 236, 271,\n274, 275, 304, 311, 345, 379, 395, 543, 545,\n549, 768\u2013770, 779, 785, 787\nVcd, 2, 174, 175, 182, 271, 311, 333, 340, 345, 545, 562,\n651, 770, 771, 787\nVCS, see Compton scattering, virtual\nVcs, 275, 304, 340, 545, 547, 562\nVector meson dominance, 554, 555, 676, 683\nVEPP-2M, 669\nVEPP-4M, 441\nVEPP2000, 677\nVertex\nalgorithm, 73, 75, 76, 78\ndetector, see Silicon detector\n\ufb01t, 73, 75, 76, 80, 135, 167, 172, 283, 284, 313, 334,\n425, 520, 552, 566, 568, 570, 571, 574, 582,\n686, 729, 748\nposition, 36, 56, 73, 75\u201377, 79\u201381, 115, 125, 166,\n172, 264, 277, 279, 280, 282, 286, 313, 315,\n334, 568, 748\nprimary, 19, 52, 53, 73, 77, 103, 283, 527, 566, 641,\n672\nproduction, 78, 80, 276, 522, 527, 528, 566, 582,\n748\nVMD, see Vector meson dominance\nVtb, 2, 120, 182, 216, 218, 236, 271, 304, 366, 367, 770,\n777, 787\nVtd, 2, 120, 182, 185, 216, 274, 280, 281, 288, 379, 380,\n387, 545, 770\nVtd/Vts, 216, 371, 379\u2013381, 387\nVts, 182, 185, 216, 236, 367, 379, 771\nVub, 87, 162, 174, 175, 182, 185, 186, 236, 274, 304, 345,\n366, 376, 395, 396, 405, 543, 769, 770, 779,\n782, 785\nVud, 174, 175, 182, 218, 311, 340, 545, 562, 770\nVus, 182, 304, 340, 545, 562, 637, 651, 654, 664, 770\nWeak annihilation, 210, 214, 217, 218, 227, 236, 238,\n240, 241, 382, 395, 396, 426, 429, 516\u2013518, 563\nWeak interaction, 1, 178\u2013180, 186, 237, 238, 241, 258,\n280, 322, 367, 422, 516, 543, 663\nWeak phase, 1, 153, 174, 183, 227, 236, 250, 263, 264,\n267, 289, 308, 312, 316, 322, 328\u2013330, 339, 341,\n356, 360, 361, 387, 390, 564, 565, 585, 592, 768,\n771, 777, 780, 785\u2013787, 790\nWess-Zumino-Witten chiral-anomalous term, 657\nWilks\u2019 theorem, 129, 769\nWilson coe\ufb03cient, 194, 196, 222, 223, 237, 238, 241,\n366, 369, 370, 389\u2013391, 393, 444, 446, 448, 519,\n520, 783, 785, 786, 788\nWilson-loop operator, 194, 237, 365, 446, 785, 786\nWIMP, 700\nWolfenstein parameterization, 181, 219, 263, 360, 518,\n562, 768, 777\nWolfenstein-Buras parameterization, 182, 768\nWrong sign decay, 287, 529, 544, 563, 567, 580, 584,\n596, 716\nWrong tag fraction, see Tagging, mistag\nX(1835), 434, 712\nX(3872), 448, 470, 471, 473, 474, 501, 697, 698\nX(3880), 456\nX(3915), 501, 709, 714\nX(3940), 455, 476, 477\nX(4160), 456\nX(4350), 478, 501, 709, 714\nX(4630), 435, 478, 696\nxd, 101, 281, 291, 297\nXRootD, 41, 46\nxs, 291\nXTC \ufb01le, see Raw data\nx(\u2032), see Charm mixing\n\u201cXYZ\u201d state, 230, 441, 469, 501\nY (3915), 476, 477\nY (3940), 476\nY (4008), 697\nY (4140), 477, 501, 714\nY (4260), 458, 478, 479, 486, 683, 695, 697, 698, 700\nY (4350), 478, 479, 486\nY (4660), 478, 479, 486, 700\nyCP , 573, 596\nYukawa couplings, 779, 780, 783, 784, 790\nYukawa interactions, 777\ny(\u2032), see Charm mixing\nZ(3900), 482\nZ(3930), 453, 476, 477, 714\nZ(4020), 482\nZ(4050)+, 480, 481\nZ(4250)+, 480, 481\nZ(4430)+, 480, 481, 484\nZ\u2032 boson, 271\nZb(10610), 496, 497\nZb(10650), 496, 497\nZeemach tensor, 357\nZernike moment, 67\nZEUS, 762, 765, 766\nzlib, 47\n", "Supernova Pointing Capabilities of DUNE\nA. Abed Abud,35 B. Abi,156 R. Acciarri,66 M. A. Acero,12 M. R. Adames,194 G. Adamov,72\nM. Adamowski,66 D. Adams,20 M. Adinolfi,19 C. Adriano,30 A. Aduszkiewicz,81 J. Aguilar,126\nB. Aimard,51 F. Akbar,175 K. Allison,43 S. Alonso Monsalve,35 M. Alrashed,119 A. Alton,13 R. Alvarez,39\nT. Alves,88 H. Amar,84 P. Amedo,85, 84 J. Anderson,8 D. A. Andrade,87 C. Andreopoulos,128\nM. Andreotti,94, 67 M. P. Andrews,66 F. Andrianala,5 S. Andringa,127 N. Anfimov\n, A. Ankowski,184\nM. Antoniassi,194 M. Antonova,84 A. Antoshkin , A. Aranda-Fernandez,42 L. Arellano,135 E. Arrieta\nDiaz,180 M. A. Arroyave,66 J. Asaadi,198 A. Ashkenazi,195 D. Asner,20 L. Asquith,192 E. Atkin,88\nD. Auguste,160 A. Aurisano,40 V. Aushev,124 D. Autiero,110 F. Azfar,156 A. Back,91 H. Back,157\nJ. J. Back,210 I. Bagaturia,72 L. Bagby,66 N. Balashov\n, S. Balasubramanian,66 P. Baldi,24\nW. Baldini,94 J. Baldonedo,207 B. Baller,66 B. Bambah,82 R. Banerjee,217 F. Barao,127, 112\nG. Barenboim,84 P. Barham Alz\u00b4as,35 G. J. Barker,210 W. Barkhouse,148 G. Barr,156 J. Barranco\nMonarca,77 A. Barros,194 N. Barros,127, 61 D. Barrow,156 J. L. Barrow,136 A. Basharina-Freshville,204\nA. Bashyal,8 V. Basque,66 C. Batchelor,57 L. Bathe-Peters,156 J.B.R. Battat,211 F. Battisti,156 F. Bay,4\nM. C. Q. Bazetto,30 J. L. L. Bazo Alba,169 J. F. Beacom,154 E. Bechetoille,110 B. Behera,68 E. Belchior,130\nG. Bell,52 L. Bellantoni,66 G. Bellettini,103, 167 V. Bellini,93, 31 O. Beltramello,35 N. Benekos,35\nC. Benitez Montiel,84, 10 D. Benjamin,20 F. Bento Neves,127 J. Berger,44 S. Berkman,139 J. Bernal,10\nP. Bernardini,97, 179 A. Bersani,96 S. Bertolucci,92, 17 M. Betancourt,66 A. Betancur Rodr\u00b4\u0131guez,58\nA. Bevan,172 Y. Bezawada,23 A. T. Bezerra,62 T. J. Bezerra,192 A. Bhat,37 V. Bhatnagar,159 J. Bhatt,204\nM. Bhattacharjee,89 M. Bhattacharya,66 S. Bhuller,19 B. Bhuyan,89 S. Biagi,105 J. Bian,24 K. Biery,66\nB. Bilki,15, 108 M. Bishai,20 A. Bitadze,135 A. Blake,125 F. D. Blaszczyk,66 G. C. Blazey,149\nE. Blucher,37 J. Bogenschuetz,198 J. Boissevain,129 S. Bolognesi,34 T. Bolton,119 L. Bomben,98, 107\nM. Bonesini,98, 140 C. Bonilla-Diaz,32 F. Bonini,20 A. Booth,172 F. Boran,91 S. Bordoni,35 R. Borges\nMerlo,30 A. Borkum,192 N. Bostan,108 J. Bracinik,16 D. Braga,66 B. Brahma,90 D. Brailsford,125\nF. Bramati,98 A. Branca,98 A. Brandt,198 J. Bremer,35 C. Brew,178 S. J. Brice,66 V. Brio,93\nC. Brizzolari,98, 140 C. Bromberg,139 J. Brooke,19 A. Bross,66 G. Brunetti,98, 140 M. Brunetti,210\nN. Buchanan,44 H. Budd,175 J. Buergi,14 D. Burgardt,212 S. Butchart,192 G. Caceres V.,23 I. Cagnoli,92, 17\nT. Cai,217 R. Calabrese,94, 67 J. Calcutt,155 M. Calin,21 L. Calivers,14 E. Calvo,39 A. Caminata,96\nA. F. Camino,168 W. Campanelli,127 A. Campani,96, 71 A. Campos Benitez,208 N. Canci,100 J. Cap\u00b4o,84\nI. Caracas,134 D. Caratelli,27 D. Carber,44 J. M. Carceller,35 G. Carini,20 B. Carlus,110 M. F. Carneiro,20\nP. Carniti,98 I. Caro Terrazas,44 H. Carranza,198 N. Carrara,23 L. Carroll,119 T. Carroll,214 A. Carter,176\nE. Casarejos,207 D. Casazza,94 J. F. Casta\u02dcno Forero,7 F. A. Casta\u02dcno,6 A. Castillo,182 C. Castromonte,106\nE. Catano-Mur,213 C. Cattadori,98 F. Cavalier,160 F. Cavanna,66 S. Centro,158 G. Cerati,66 C. Cerna,131\nA. Cervelli,92 A. Cervera Villanueva,84 K. Chakraborty,166 S. Chakraborty,86 M. Chalifour,35\nA. Chappell,210 N. Charitonidis,35 A. Chatterjee,166 H. Chen,20 M. Chen,24 W. C. Chen,200 Y. Chen,184\nZ. Chen-Wishart,176 D. Cherdack,81 C. Chi,45 F. Chiapponi,92, 17 R. Chirco,87 N. Chitirasreemadam,103, 167\nK. Cho,122 S. Choate,149 D. Chokheli,72 P. S. Chong,164 B. Chowdhury,8 D. Christian,66 A. Chukanov\n,\nM. Chung,203 E. Church,157 M. F. Cicala,204 M. Cicerchia,158 V. Cicero,92, 17 R. Ciolini,103 P. Clarke,57\nG. Cline,126 T. E. Coan,188 A. G. Cocco,100 J. A. B. Coelho,161 A. Cohen,161 J. Collazo,207 J. Collot,76\nE. Conley,55 J. M. Conrad,136 M. Convery,184 S. Copello,96 P. Cova,99, 162 C. Cox,176 L. Cremaldi,144\nL. Cremonesi,172 J. I. Crespo-Anad\u00b4on,39 M. Crisler,66 E. Cristaldo,98, 10 J. Crnkovic,66 G. Crone,204\nR. Cross,210 A. Cudd,43 C. Cuesta,39 Y. Cui,26 F. Curciarello,95 D. Cussans,19 J. Dai,76 O. Dalager,24\nR. Dallavalle,161 W. Dallaway,200 H. da Motta,33 Z. A. Dar,213 R. Darby,192 L. Da Silva Peres,65\nQ. David,110 G. S. Davies,144 S. Davini,96 J. Dawson,161 R. De Aguiar,30 P. De Almeida,30 P. Debbins,108\nI. De Bonis,51 M. P. Decowski,146, 3 A. de Gouv\u02c6ea,150 P. C. De Holanda,30 I. L. De Icaza Astiz,192 P. De\nJong,146, 3 P. Del Amo Sanchez,51 A. De la Torre,39 G. De Lauretis,110 A. Delbart,34 D. Delepine,77\nM. Delgado,98, 140 A. Dell\u2019Acqua,35 G. Delle Monache,95 N. Delmonte,99, 162 P. De Lurgio,8 R. Demario,139\nG. De Matteis,97, 179 J. R. T. de Mello Neto,65 D. M. DeMuth,206 S. Dennis,29 C. Densham,178 P. Denton,20\nG. W. Deptuch,20 A. De Roeck,35 V. De Romeri,84 J. P. Detje,29 J. Devine,35 R. Dharmapalan,79\nM. Dias,202 A. Diaz,28 J. S. D\u00b4\u0131az,91 F. D\u00b4\u0131az,169 F. Di Capua,100, 145 A. Di Domenico,181, 104 S. Di\nDomizio,96, 71 S. Di Falco,103 L. Di Giulio,35 P. Ding,66 L. Di Noto,96, 71 E. Diociaiuti,95 C. Distefano,105\narXiv:2407.10339v1 [hep-ex] 14 Jul 2024\n\n2\nR. Diurba,14 M. Diwan,20 Z. Djurcic,8 D. Doering,184 S. Dolan,35 F. Dolek,208 M. J. Dolinski,54\nD. Domenici,95 L. Domine,184 S. Donati,103, 167 Y. Donon,35 S. Doran,109 D. Douglas,184 T.A. Doyle,189\nA. Dragone,184 F. Drielsma,184 L. Duarte,202 D. Duchesneau,51 K. Duffy,156, 66 K. Dugas,24 P. Dunne,88\nB. Dutta,196 H. Duyang,185 D. A. Dwyer,126 A. S. Dyshkant,149 S. Dytman,168 M. Eads,149 A. Earle,192\nS. Edayath,109 D. Edmunds,139 J. Eisch,66 P. Englezos,177 A. Ereditato,37 T. Erjavec,23 C. O. Escobar,66\nJ. J. Evans,135 E. Ewart,91 A. C. Ezeribe,183 K. Fahey,66 L. Fajt,35 A. Falcone,98, 140 M. Fani\u2019,129\nC. Farnese,101 S. Farrell,174 Y. Farzan,111 D. Fedoseev\n, J. Felix,77 Y. Feng,109 E. Fernandez-Martinez,133\nG. Ferry,160 L. Fields,151 P. Filip,49 A. Filkins,193 F. Filthaut,146, 173 R. Fine,129 G. Fiorillo,100, 145\nM. Fiorini,94, 67 S. Fogarty,44 W. Foreman,87 J. Fowler,55 J. Franc,50 K. Francis,149 D. Franco,37\nJ. Franklin,56 J. Freeman,66 J. Fried,20 A. Friedland,184 S. Fuess,66 I. K. Furic,68 K. Furman,172\nA. P. Furmanski,143 R. Gaba,159 A. Gabrielli,92, 17 A. M Gago,169 F. Galizzi,98 H. Gallagher,201\nA. Gallas,160 N. Gallice,20 V. Galymov,110 E. Gamberini,35 T. Gamble,183 F. Ganacim,194 R. Gandhi,78\nS. Ganguly,66 F. Gao,27 S. Gao,20 D. Garcia-Gamez,73 M. \u00b4A. Garc\u00b4\u0131a-Peris,84 F. Gardim,62 S. Gardiner,66\nD. Gastler,18 A. Gauch,14 J. Gauvreau,153 P. Gauzzi,181, 104 S. Gazzana,95 G. Ge,45 N. Geffroy,51\nB. Gelli,30 S. Gent,187 L. Gerlach,20 Z. Ghorbani-Moghaddam,96 T. Giammaria,94, 67 D. Gibin,158, 101\nI. Gil-Botella,39 S. Gilligan,155 A. Gioiosa,103 S. Giovannella,95 C. Girerd,110 A. K. Giri,90 C. Giugliano,94\nV. Giusti,103 D. Gnani,126 O. Gogota,124 S. Gollapinni,129 K. Gollwitzer,66 R. A. Gomes,63 L. V. Gomez\nBermeo,182 L. S. Gomez Fajardo,182 F. Gonnella,16 D. Gonzalez-Diaz,85 M. Gonzalez-Lopez,133\nM. C. Goodman,8 S. Goswami,166 C. Gotti,98 J. Goudeau,130 E. Goudzovski,16 C. Grace,126\nE. Gramellini,135 R. Gran,142 E. Granados,77 P. Granger,161 C. Grant,18 D. R. Gratieri,70, 30 G. Grauso,100\nP. Green,156 S. Greenberg,22, 126 J. Greer,19 W. C. Griffith,192 F. T. Groetschla,35 K. Grzelak,209\nL. Gu,125 W. Gu,20 V. Guarino,8 M. Guarise,94, 67 R. Guenette,135 E. Guerard,160 M. Guerzoni,92\nD. Guffanti,98, 140 A. Guglielmi,101 B. Guo,185 Y. Guo,189 A. Gupta,184 V. Gupta,146, 3 G. Gurung,198\nD. Gutierrez,170 P. Guzowski,135 M. M. Guzzo,30 S. Gwon,38 A. Habig,142 H. Hadavand,198 L. Haegel,110\nR. Haenni,14 L. Hagaman,215 A. Hahn,66 J. Haiston,186 J. Hakenm\u00a8uller,55 T. Hamernik,66 P. Hamilton,88\nJ. Hancock,16 F. Happacher,95 D. A. Harris,217, 66 J. Hartnell,192 T. Hartnett,178 J. Harton,44\nT. Hasegawa,121 C. Hasnip,156 R. Hatcher,66 K. Hayrapetyan,172 J. Hays,172 E. Hazen,18 M. He,81\nA. Heavey,66 K. M. Heeger,215 J. Heise,191 S. Henry,175 M. A. Hernandez Morquecho,87 K. Herner,66\nV. Hewes,40 A. Higuera,174 C. Hilgenberg,143 S. J. Hillier,16 A. Himmel,66 E. Hinkle,37 L.R. Hirsch,194\nJ. Ho,53 J. Hoff,66 A. Holin,178 T. Holvey,156 E. Hoppe,157 S. Horiuchi,208 G. A. Horton-Smith,119\nM. Hostert,143 T. Houdy,160 B. Howard,66 R. Howell,175 I. Hristova,178 M. S. Hronek,66 J. Huang,23\nR.G. Huang,126 Z. Hulcher,184 M. Ibrahim,60 G. Iles,88 N. Ilic,200 A. M. Iliescu,95 R. Illingworth,66\nG. Ingratta,92, 17 A. Ioannisian,216 B. Irwin,143 L. Isenhower,1 M. Ismerio Oliveira,65 R. Itay,184\nC.M. Jackson,157 V. Jain,2 E. James,66 W. Jang,198 B. Jargowsky,24 D. Jena,66 I. Jentz,214 X. Ji,20\nC. Jiang,115 J. Jiang,189 L. Jiang,208 A. Jipa,21 F. R. Joaquim,127, 112 W. Johnson,186 C. Jollet,131\nB. Jones,198 R. Jones,183 D. Jos\u00b4e Fern\u00b4andez,85 N. Jovancevic,152 M. Judah,168 C. K. Jung,189 T. Junk,66\nY. Jwa,184, 45 M. Kabirnezhad,88 A. C. Kaboth,176, 178 I. Kadenko,124 I. Kakorin\n, A. Kalitkina\n,\nD. Kalra,45 M. Kandemir,59 D. M. Kaplan,87 G. Karagiorgi,45 G. Karaman,108 A. Karcher,126\nY. Karyotakis,51 S. Kasai,123 S. P. Kasetti,130 L. Kashur,44 I. Katsioulas,16 A. Kauther,149\nN. Kazaryan,216 L. Ke,20 E. Kearns,18 P.T. Keener,164 K.J. Kelly,35 E. Kemp,30 O. Kemularia,72\nY. Kermaidic,160 W. Ketchum,66 S. H. Kettell,20 M. Khabibullin\n, N. Khan,88 A. Khvedelidze,72\nD. Kim,196 J. Kim,175 B. King,66 B. Kirby,45 M. Kirby,20 A. Kish,66 J. Klein,164 J. Kleykamp,144\nA. Klustova,88 T. Kobilarcik,66 L. Koch,134 K. Koehler,214 L. W. Koerner,81 D. H. Koh,184\nL. Kolupaeva\n, D. Korablev\n, M. Kordosky,213 T. Kosc,76 U. Kose,35 V. A. Kosteleck\u00b4y,91\nK. Kothekar,19 I. Kotler,54 M. Kovalcuk,49 V. Kozhukalov\n, W. Krah,146 R. Kralik,192 M. Kramer,126\nL. Kreczko,19 F. Krennrich,109 I. Kreslo,14 T. Kroupova,164 S. Kubota,135 M. Kubu,35 Y. Kudenko\n,\nV. A. Kudryavtsev,183 G. Kufatty,69 S. Kuhlmann,8 J. Kumar,79 P. Kumar,183 S. Kumaran,24 P. Kunze,51\nJ. Kunzmann,14 R. Kuravi,126 N. Kurita,184 C. Kuruppu,185 V. Kus,50 T. Kutter,130 J. Kvasnicka,49\nT. Labree,149 T. Lackey,66 A. Lambert,126 B. J. Land,164 C. E. Lane,54 N. Lane,135 K. Lang,199\nT. Langford,215 M. Langstaff,135 F. Lanni,35 O. Lantwin,51 J. Larkin,20 P. Lasorak,88 D. Last,164\nA. Laudrain,134 A. Laundrie,214 G. Laurenti,92 E. Lavaut,160 A. Lawrence,126 P. Laycock,20 I. Lazanu,21\nM. Lazzaroni,99, 141 T. Le,201 S. Leardini,85 J. Learned,79 T. LeCompte,184 C. Lee,66 V. Legin,124\n\n3\nG. Lehmann Miotto,35 R. Lehnert,91 M. A. Leigui de Oliveira,64 M. Leitner,126 D. Leon Silverio,186\nL. M. Lepin,69, 135 J.-Y Li,57 S. W. Li,23 Y. Li,20 H. Liao,119 C. S. Lin,126 D. Lindebaum,19 S. Linden,20\nR. A. Lineros,32 J. Ling,190 A. Lister,214 B. R. Littlejohn,87 H. Liu,20 J. Liu,24 Y. Liu,37 S. Lockwitz,66\nM. Lokajicek,49 I. Lomidze,72 K. Long,88 T. V. Lopes,62 J.Lopez,6 I. L\u00b4opez de Rego,39 N. L\u00b4opez-March,84\nT. Lord,210 J. M. LoSecco,151 W. C. Louis,129 A. Lozano Sanchez,54 X.-G. Lu,210 K.B. Luk,80, 22\nB. Lunday,164 X. Luo,27 E. Luppi,94, 67 J. Maalmi,160 D. MacFarlane,184 A. A. Machado,30 P. Machado,66\nC. T. Macias,91 J. R. Macier,66 M. MacMahon,204 A. Maddalena,75 A. Madera,35 P. Madigan,22, 126\nS. Magill,8 C. Magueur,160 K. Mahn,139 A. Maio,127, 61 A. Major,55 K. Majumdar,128 M. Man,200\nR. C. Mandujano,24 J. Maneira,127, 61 S. Manly,175 A. Mann,201 K. Manolopoulos,178 M. Manrique Plata,91\nS. Manthey Corchado,39 V. N. Manyam,20 M. Marchan,66 A. Marchionni,66 W. Marciano,20 D. Marfatia,79\nC. Mariani,208 J. Maricic,79 F. Marinho,113 A. D. Marino,43 T. Markiewicz,184 F. Das Chagas Marques,30\nC. Marquet,131 D. Marsden,135 M. Marshak,143 C. M. Marshall,175 J. Marshall,210 L. Martina,97, 179\nJ. Mart\u00b4\u0131n-Albo,84 N. Martinez,119 D.A. Martinez Caicedo,186 F. Mart\u00b4\u0131nez L\u00b4opez,172 P. Mart\u00b4\u0131nez Mirav\u00b4e,84\nS. Martynenko,20 V. Mascagna,98 C. Massari,98 A. Mastbaum,177 F. Matichard,126 S. Matsuno,79\nG. Matteucci,100, 145 J. Matthews,130 C. Mauger,164 N. Mauri,92, 17 K. Mavrokoridis,128 I. Mawby,125\nR. Mazza,98 A. Mazzacane,66 T. McAskill,211 N. McConkey,204 K. S. McFarland,175 C. McGrew,189\nA. McNab,135 L. Meazza,98 V. C. N. Meddage,68 B. Mehta,159 P. Mehta,116 P. Melas,11 O. Mena,84\nH. Mendez,170 P. Mendez,35 D. P. M\u00b4endez,20 A. Menegolli,102, 163 G. Meng,101 A. C. E. A. Mercuri,194\nA. Meregaglia,131 M. D. Messier,91 S. Metallo,143 J. Metcalf,201, 136 W. Metcalf,130 M. Mewes,91\nH. Meyer,212 T. Miao,66 A. Miccoli,97 G. Michna,187 V. Mikola,204 R. Milincic,79 F. Miller,214 G. Miller,135\nW. Miller,143 O. Mineev\n, A. Minotti,98, 140 L. Miralles,35 O. G. Miranda,41 C. Mironov,161 S. Miryala,20\nS. Miscetti,95 C. S. Mishra,66 S. R. Mishra,185 A. Mislivec,143 M. Mitchell,130 D. Mladenov,35 I. Mocioiu,165\nA. Mogan,66 N. Moggi,92, 17 R. Mohanta,82 T. A. Mohayai,91 N. Mokhov,66 J. Molina,10 L. Molina\nBueno,84 E. Montagna,92, 17 A. Montanari,92 C. Montanari,102, 66, 163 D. Montanari,66 D. Montanino,97, 179\nL. M. Monta\u02dcno Zetina,41 M. Mooney,44 A. F. Moor,183 Z. Moore,193 D. Moreno,7 O. Moreno-Palacios,213\nL. Morescalchi,103 D. Moretti,98 R. Moretti,98 C. Morris,81 C. Mossey,66 M. Mote,130 C. A. Moura,64\nG. Mouster,125 W. Mu,66 L. Mualem,28 J. Mueller,44 M. Muether,212 F. Muheim,57 A. Muir,52\nM. Mulhearn,23 D. Munford,81 L. J. Munteanu,35 H. Muramatsu,143 J. Muraz,76 M. Murphy,208\nT. Murphy,193 J. Muse,143 A. Mytilinaki,178 J. Nachtman,108 Y. Nagai,60 S. Nagu,132 R. Nandakumar,178\nD. Naples,168 S. Narita,114 A. Nath,89 A. Navrer-Agasson,88 N. Nayak,20 M. Nebot-Guinot,57 A. Nehm,134\nJ. K. Nelson,213 O. Neogi,108 J. Nesbit,214 M. Nessi,66, 35 D. Newbold,178 M. Newcomer,164 R. Nichol,204\nF. Nicolas-Arnaldos,73 A. Nikolica,164 J. Nikolov,152 E. Niner,66 K. Nishimura,79 A. Norman,66\nA. Norrick,66 P. Novella,84 J. A. Nowak,125 M. Oberling,8 J. P. Ochoa-Ricoux,24 S. Oh,55 S.B. Oh,66\nA. Olivier,151 A. Olshevskiy\n, T. Olson,81 Y. Onel,108 Y. Onishchuk,124 A. Oranday,91 M. Osbiston,210\nJ. A. Osorio V\u00b4elez,6 L. Otiniano Ormachea,46, 106 J. Ott,24 L. Pagani,23 G. Palacio,58 O. Palamara,66\nS. Palestini,35 J. M. Paley,66 M. Pallavicini,96, 71 C. Palomares,39 S. Pan,166 P. Panda,82 W. Panduro\nVazquez,176 E. Pantic,23 V. Paolone,168 V. Papadimitriou,66 R. Papaleo,105 A. Papanestis,178\nD. Papoulias,11 S. Paramesvaran,19 A. Paris,170 S. Parke,66 E. Parozzi,98, 140 S. Parsa,14 Z. Parsa,20\nS. Parveen,116 M. Parvu,21 D. Pasciuto,103 S. Pascoli,92, 17 L. Pasqualini,92, 17 J. Pasternak,88\nC. Patrick,57, 204 L. Patrizii,92 R. B. Patterson,28 T. Patzak,161 A. Paudel,66 L. Paulucci,64 Z. Pavlovic,66\nG. Pawloski,143 D. Payne,128 V. Pec,49 E. Pedreschi,103 S. J. M. Peeters,192 W. Pellico,66 A. Pena Perez,184\nE. Pennacchio,110 A. Penzo,108 O. L. G. Peres,30 Y. F. Perez Gonzalez,56 L. P\u00b4erez-Molina,39 C. Pernas,213\nJ. Perry,57 D. Pershey,69 G. Pessina,98 G. Petrillo,184 C. Petta,93, 31 R. Petti,185 M. Pfaff,88 V. Pia,92, 17\nL. Pickering,178, 176 F. Pietropaolo,35, 101 V.L.Pimentel,47, 30 G. Pinaroli,20 J. Pinchault,51 K. Pitts,208\nK. Plows,156 R. Plunkett,66 C. Pollack,170 T. Pollman,146, 3 D. Polo-Toledo,12 F. Pompa,84 X. Pons,35\nN. Poonthottathil,86, 109 V. Popov,195 F. Poppi,92, 17 J. Porter,192 M. Potekhin,20 R. Potenza,93, 31\nJ. Pozimski,88 M. Pozzato,92, 17 T. Prakash,126 C. Pratt,23 M. Prest,98 F. Psihas,66 D. Pugnere,110\nX. Qian,20 J. Queen,55 J. L. Raaf,66 V. Radeka,20 J. Rademacker,19 B. Radics,217 A. Rafique,8\nE. Raguzin,20 M. Rai,210 S. Rajagopalan,20 M. Rajaoalisoa,40 I. Rakhno,66 L. Rakotondravohitra,5\nL. Ralte,90 M. A. Ramirez Delgado,164 B. Ramson,66 A. Rappoldi,102, 163 G. Raselli,102, 163 P. Ratoff,125\nR. Ray,66 H. Razafinime,40 E. M. Rea,143 J. S. Real,76 B. Rebel,214, 66 R. Rechenmacher,66\nM. Reggiani-Guzzo,135 J. Reichenbacher,186 S. D. Reitzner,66 H. Rejeb Sfar,35 E. Renner,129 A. Renshaw,81\n\n4\nS. Rescia,20 F. Resnati,35 Diego Restrepo,6 C. Reynolds,172 M. Ribas,194 S. Riboldi,99 C. Riccio,189\nG. Riccobene,105 J. S. Ricol,76 M. Rigan,192 E. V. Rinc\u00b4on,58 A. Ritchie-Yates,176 S. Ritter,134 D. Rivera,129\nR. Rivera,66 A. Robert,76 J. L. Rocabado Rocha,84 L. Rochester,184 M. Roda,128 P. Rodrigues,156\nM. J. Rodriguez Alonso,35 J. Rodriguez Rondon,186 A. J. Roeth,55 S. Rosauro-Alcaraz,160 P. Rosier,160\nD. Ross,139 M. Rossella,102, 163 M. Rossi,35 M. Ross-Lonergan,129 N. Roy,217 P. Roy,212 C. Rubbia,74\nA. Ruggeri,92, 17 G. Ruiz Ferreira,135 B. Russell,136 D. Ruterbories,175 A. Rybnikov\n, A. Saa-Hernandez,85\nR. Saakyan,204 S. Sacerdoti,161 S. K. Sahoo,90 N. Sahu,90 P. Sala,99, 35 N. Samios,20 O. Samoylov\n,\nM. C. Sanchez,69 A. S\u00b4anchez Bravo,84 P. Sanchez-Lucas,73 V. Sandberg,129 D. A. Sanders,144\nS. Sanfilippo,105 D. Sankey,178 D. Santoro,99 N. Saoulidou,11 P. Sapienza,105 C. Sarasty,40 I. Sarcevic,9\nI. Sarra,95 G. Savage,66 V. Savinov,168 G. Scanavini,215 A. Scaramelli,102 A. Scarff,183 T. Schefke,130\nH. Schellman,155, 66 S. Schifano,94, 67 P. Schlabach,66 D. Schmitz,37 A. W. Schneider,136 K. Scholberg,55\nA. Schukraft,66 B. Schuld,43 A. Segade,207 E. Segreto,30 A. Selyunin\n, C. R. Senise,202 J. Sensenig,164\nM. H. Shaevitz,45 P. Shanahan,66 P. Sharma,159 R. Kumar,171 K. Shaw,192 T. Shaw,66 K. Shchablo,110\nJ. Shen,164 C. Shepherd-Themistocleous,178 A. Sheshukov\n, W. Shi,189 S. Shin,117 S. Shivakoti,212\nI. Shoemaker,208 D. Shooltz,139 R. Shrock,189 B. Siddi,94 M. Siden,44 J. Silber,126 L. Simard,160\nJ. Sinclair,184 G. Sinev,186 Jaydip Singh,132 J. Singh,132 L. Singh,48 P. Singh,172 V. Singh,48 S. Singh\nChauhan,159 R. Sipos,35 C. Sironneau,161 G. Sirri,92 K. Siyeon,38 K. Skarpaas,184 J. Smedley,175\nE. Smith,91 J. Smith,189 P. Smith,91 J. Smolik,50, 49 M. Smy,24 M. Snape,210 E.L. Snider,66 P. Snopok,87\nD. Snowden-Ifft,153 M. Soares Nunes,66 H. Sobel,24 M. Soderberg,193 S. Sokolov\n, C. J. Solano\nSalinas,205, 106 S. S\u00a8oldner-Rembold,88 S.R. Soleti,126 N. Solomey,212 V. Solovov,127 W. E. Sondheim,129\nM. Sorel,84 A. Sotnikov\n, J. Soto-Oton,84 A. Sousa,40 K. Soustruznik,36 F. Spinella,103 J. Spitz,138\nN. J. C. Spooner,183 K. Spurgeon,193 D. Stalder,10 M. Stancari,66 L. Stanco,101, 158 J. Steenis,23 R. Stein,19\nH. M. Steiner,126 A. F. Steklain Lisb\u02c6oa,194 A. Stepanova\n, J. Stewart,20 B. Stillwell,37 J. Stock,186\nF. Stocker,35 T. Stokes,130 M. Strait,143 T. Strauss,66 L. Strigari,196 A. Stuart,42 J. G. Suarez,58\nJ. Subash,16 A. Surdo,97 L. Suter,66 C. M. Sutera,93, 31 K. Sutton,28 Y. Suvorov,100, 145 R. Svoboda,23\nS. K. Swain,147 B. Szczerbinska,197 A. M. Szelc,57 A. Sztuc,204 A. Taffara,103 N. Talukdar,185 J. Tamara,7\nH. A. Tanaka,184 S. Tang,20 N. Taniuchi,29 A. M. Tapia Casanova,137 B. Tapia Oregui,199\nA. Tapper,88 S. Tariq,66 E. Tarpara,20 E. Tatar,83 R. Tayloe,91 D. Tedeschi,185 A. M. Teklu,189\nJ. Tena Vidal,195 P. Tennessen,126, 4 M. Tenti,92 K. Terao,184 F. Terranova,98, 140 G. Testera,96\nT. Thakore,40 A. Thea,178 A. Thiebault,160 S. Thomas,193 A. Thompson,196 C. Thorn,20 S. C. Timm,66\nE. Tiras,59, 108 V. Tishchenko,20 N. Todorovi\u00b4c,152 L. Tomassetti,94, 67 A. Tonazzo,161 D. Torbunov,20\nM. Torti,98 M. Tortola,84 F. Tortorici,93, 31 N. Tosi,92 D. Totani,27 M. Toups,66 C. Touramanis,128\nD. Tran,81 R. Travaglini,92 J. Trevor,28 E. Triller,139 S. Trilov,19 J. Truchon,214 D. Truncali,181, 104\nW. H. Trzaska,118 Y. Tsai,24 Y.-T. Tsai,184 Z. Tsamalaidze,72 K. V. Tsang,184 N. Tsverava,72 S. Z. Tu,115\nS. Tufanli,35 C. Tunnell,174 J. Turner,56 M. Tuzi,84 J. Tyler,119 E. Tyley,183 M. Tzanov,130\nM. A. Uchida,29 J. Ure\u02dcna Gonz\u00b4alez,84 J. Urheim,91 T. Usher,184 H. Utaegbulam,175 S. Uzunyan,149\nM. R. Vagins,120, 24 P. Vahle,213 S. Valder,192 G. A. Valdiviesso,62 E. Valencia,77 R. Valentim,202\nZ. Vallari,28 E. Vallazza,98 J. W. F. Valle,84 R. Van Berg,164 R. G. Van de Water,129 D. V. Forero,137\nA. Vannozzi,95 M. Van Nuland-Troost,146 F. Varanini,101 D. Vargas Oliva,200 S. Vasina\n, N. Vaughan,155\nK. Vaziri,66 A. V\u00b4azquez-Ramos,73 J. Vega,46 S. Ventura,101 A. Verdugo,39 S. Vergani,204 M. Verzocchi,66\nK. Vetter,66 M. Vicenzi,20 H. Vieira de Souza,161 C. Vignoli,75 C. Vilela,127 E. Villa,35 S. Viola,105\nB. Viren,20 A. Vizcaya-Hernandez,44 T. Vrba,50 Q. Vuong,175 A. V. Waldron,172 M. Wallbank,40\nJ. Walsh,139 T. Walton,66 H. Wang,25 J. Wang,186 L. Wang,126 M.H.L.S. Wang,66 X. Wang,66 Y. Wang,25\nK. Warburton,109 D. Warner,44 L. Warsame,88 M.O. Wascko,156 D. Waters,204 A. Watson,16\nK. Wawrowska,178, 192 A. Weber,134, 66 C. M. Weber,143 M. Weber,14 H. Wei,130 A. Weinstein,109\nH. Wenzel,66 S. Westerdale,26 M. Wetstein,109 K. Whalen,178 J. Whilhelmi,215 A. White,198 A. White,215\nL. H. Whitehead,29 D. Whittington,193 M. J. Wilking,143 A. Wilkinson,204 C. Wilkinson,126 F. Wilson,178\nR. J. Wilson,44 P. Winter,8 W. Wisniewski,184 J. Wolcott,201 J. Wolfs,175 T. Wongjirad,201 A. Wood,81\nK. Wood,126 E. Worcester,20 M. Worcester,20 M. Wospakrik,66 K. Wresilo,29 C. Wret,175 S. Wu,143\nW. Wu,66 W. Wu,24 M. Wurm,134 J. Wyenberg,53 Y. Xiao,24 I. Xiotidis,88 B. Yaeggy,40 N. Yahlali,84\nE. Yandel,27 K. Yang,156 T. Yang,66 A. Yankelevich,24 N. Yershov\n, K. Yonehara,66 T. Young,148 B. Yu,20\nH. Yu,20 J. Yu,198 Y. Yu,87 W. Yuan,57 R. Zaki,217 J. Zalesak,49 L. Zambelli,51 B. Zamorano,73\n\n5\nA. Zani,99 O. Zapata,6 L. Zazueta,193 G. P. Zeller,66 J. Zennamo,66 K. Zeug,214 C. Zhang,20 S. Zhang,91\nM. Zhao,20 E. Zhivun,20 E. D. Zimmerman,43 S. Zucchelli,92, 17 J. Zuklin,49 V. Zutshi,149 and R. Zwaska66\n(The DUNE Collaboration)\n1Abilene Christian University, Abilene, TX 79601, USA\n2University of Albany, SUNY, Albany, NY 12222, USA\n3University of Amsterdam, NL-1098 XG Amsterdam, The Netherlands\n4Antalya Bilim University, 07190 D\u00a8o\u00b8semealt\u0131/Antalya, Turkey\n5University of Antananarivo, Antananarivo 101, Madagascar\n6University of Antioquia, Medell\u00b4\u0131n, Colombia\n7Universidad Antonio Nari\u02dcno, Bogot\u00b4a, Colombia\n8Argonne National Laboratory, Argonne, IL 60439, USA\n9University of Arizona, Tucson, AZ 85721, USA\n10Universidad Nacional de Asunci\u00b4on, San Lorenzo, Paraguay\n11University of Athens, Zografou GR 157 84, Greece\n12Universidad del Atl\u00b4antico, Barranquilla, Atl\u00b4antico, Colombia\n13Augustana University, Sioux Falls, SD 57197, USA\n14University of Bern, CH-3012 Bern, Switzerland\n15Beykent University, Istanbul, Turkey\n16University of Birmingham, Birmingham B15 2TT, United Kingdom\n17Universit`a di Bologna, 40127 Bologna, Italy\n18Boston University, Boston, MA 02215, USA\n19University of Bristol, Bristol BS8 1TL, United Kingdom\n20Brookhaven National Laboratory, Upton, NY 11973, USA\n21University of Bucharest, Bucharest, Romania\n22University of California Berkeley, Berkeley, CA 94720, USA\n23University of California Davis, Davis, CA 95616, USA\n24University of California Irvine, Irvine, CA 92697, USA\n25University of California Los Angeles, Los Angeles, CA 90095, USA\n26University of California Riverside, Riverside CA 92521, USA\n27University of California Santa Barbara, Santa Barbara, California 93106 USA\n28California Institute of Technology, Pasadena, CA 91125, USA\n29University of Cambridge, Cambridge CB3 0HE, United Kingdom\n30Universidade Estadual de Campinas, Campinas - SP, 13083-970, Brazil\n31Universit`a di Catania, 2 - 95131 Catania, Italy\n32Universidad Cat\u00b4olica del Norte, Antofagasta, Chile\n33Centro Brasileiro de Pesquisas F\u00b4\u0131sicas, Rio de Janeiro, RJ 22290-180, Brazil\n34IRFU, CEA, Universit\u00b4e Paris-Saclay, F-91191 Gif-sur-Yvette, France\n35CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland\n36Institute of Particle and Nuclear Physics of the Faculty of Mathematics\nand Physics of the Charles University, 180 00 Prague 8, Czech Republic\n37University of Chicago, Chicago, IL 60637, USA\n38Chung-Ang University, Seoul 06974, South Korea\n39CIEMAT, Centro de Investigaciones Energ\u00b4eticas, Medioambientales y Tecnol\u00b4ogicas, E-28040 Madrid, Spain\n40University of Cincinnati, Cincinnati, OH 45221, USA\n41Centro de Investigaci\u00b4on y de Estudios Avanzados del\nInstituto Polit\u00b4ecnico Nacional (Cinvestav), Mexico City, Mexico\n42Universidad de Colima, Colima, Mexico\n43University of Colorado Boulder, Boulder, CO 80309, USA\n44Colorado State University, Fort Collins, CO 80523, USA\n45Columbia University, New York, NY 10027, USA\n46Comisi\u00b4on Nacional de Investigaci\u00b4on y Desarrollo Aeroespacial, Lima, Peru\n47Centro de Tecnologia da Informacao Renato Archer, Amarais - Campinas, SP - CEP 13069-901\n48Central University of South Bihar, Gaya, 824236, India\n49Institute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic\n50Czech Technical University, 115 19 Prague 1, Czech Republic\n51Laboratoire d\u2019Annecy de Physique des Particules, Universit\u00b4e\nSavoie Mont Blanc, CNRS, LAPP-IN2P3, 74000 Annecy, France\n52Daresbury Laboratory, Cheshire WA4 4AD, United Kingdom\n53Dordt University, Sioux Center, IA 51250, USA\n54Drexel University, Philadelphia, PA 19104, USA\n55Duke University, Durham, NC 27708, USA\n\n6\n56Durham University, Durham DH1 3LE, United Kingdom\n57University of Edinburgh, Edinburgh EH8 9YL, United Kingdom\n58Universidad EIA, Envigado, Antioquia, Colombia\n59Erciyes University, Kayseri, Turkey\n60E\u00a8otv\u00a8os Lor\u00b4and University, 1053 Budapest, Hungary\n61Faculdade de Ci\u02c6encias da Universidade de Lisboa - FCUL, 1749-016 Lisboa, Portugal\n62Universidade Federal de Alfenas, Po\u00b8cos de Caldas - MG, 37715-400, Brazil\n63Universidade Federal de Goias, Goiania, GO 74690-900, Brazil\n64Universidade Federal do ABC, Santo Andr\u00b4e - SP, 09210-580, Brazil\n65Universidade Federal do Rio de Janeiro, Rio de Janeiro - RJ, 21941-901, Brazil\n66Fermi National Accelerator Laboratory, Batavia, IL 60510, USA\n67University of Ferrara, Ferrara, Italy\n68University of Florida, Gainesville, FL 32611-8440, USA\n69Florida State University, Tallahassee, FL, 32306 USA\n70Fluminense Federal University, 9 Icara\u00b4\u0131 Niter\u00b4oi - RJ, 24220-900, Brazil\n71Universit`a degli Studi di Genova, Genova, Italy\n72Georgian Technical University, Tbilisi, Georgia\n73University of Granada & CAFPE, 18002 Granada, Spain\n74Gran Sasso Science Institute, L\u2019Aquila, Italy\n75Laboratori Nazionali del Gran Sasso, L\u2019Aquila AQ, Italy\n76University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France\n77Universidad de Guanajuato, Guanajuato, C.P. 37000, Mexico\n78Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India\n79University of Hawaii, Honolulu, HI 96822, USA\n80Hong Kong University of Science and Technology, Kowloon, Hong Kong, China\n81University of Houston, Houston, TX 77204, USA\n82University of Hyderabad, Gachibowli, Hyderabad - 500 046, India\n83Idaho State University, Pocatello, ID 83209, USA\n84Instituto de F\u00b4\u0131sica Corpuscular, CSIC and Universitat de Val`encia, 46980 Paterna, Valencia, Spain\n85Instituto Galego de F\u00b4\u0131sica de Altas Enerx\u00b4\u0131as, University of\nSantiago de Compostela, Santiago de Compostela, 15782, Spain\n86Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India\n87Illinois Institute of Technology, Chicago, IL 60616, USA\n88Imperial College of Science Technology and Medicine, London SW7 2BZ, United Kingdom\n89Indian Institute of Technology Guwahati, Guwahati, 781 039, India\n90Indian Institute of Technology Hyderabad, Hyderabad, 502285, India\n91Indiana University, Bloomington, IN 47405, USA\n92Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna BO, Italy\n93Istituto Nazionale di Fisica Nucleare Sezione di Catania, I-95123 Catania, Italy\n94Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, I-44122 Ferrara, Italy\n95Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Frascati, Frascati, Roma, Italy\n96Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova GE, Italy\n97Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 - Lecce, Italy\n98Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3 - I-20126 Milano, Italy\n99Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milano, Italy\n100Istituto Nazionale di Fisica Nucleare Sezione di Napoli, I-80126 Napoli, Italy\n101Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padova, Italy\n102Istituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy\n103Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa PI, Italy\n104Istituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Roma RM, Italy\n105Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy\n106Universidad Nacional de Ingenier\u00b4\u0131a, Lima 25, Per\u00b4u\n107University of Insubria, Via Ravasi, 2, 21100 Varese VA, Italy\n108University of Iowa, Iowa City, IA 52242, USA\n109Iowa State University, Ames, Iowa 50011, USA\n110Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France\n111Institute for Research in Fundamental Sciences, Tehran, Iran\n112Instituto Superior T\u00b4ecnico - IST, Universidade de Lisboa, Portugal\n113Instituto Tecnol\u00b4ogico de Aeron\u00b4autica, Sao Jose dos Campos, Brazil\n114Iwate University, Morioka, Iwate 020-8551, Japan\n115Jackson State University, Jackson, MS 39217, USA\n\n7\n116Jawaharlal Nehru University, New Delhi 110067, India\n117Jeonbuk National University, Jeonrabuk-do 54896, South Korea\n118Jyv\u00a8askyl\u00a8a University, FI-40014 Jyv\u00a8askyl\u00a8a, Finland\n119Kansas State University, Manhattan, KS 66506, USA\n120Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan\n121High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801, Japan\n122Korea Institute of Science and Technology Information, Daejeon, 34141, South Korea\n123National Institute of Technology, Kure College, Hiroshima, 737-8506, Japan\n124Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine\n125Lancaster University, Lancaster LA1 4YB, United Kingdom\n126Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA\n127Laborat\u00b4orio de Instrumenta\u00b8c\u02dcao e F\u00b4\u0131sica Experimental de\nPart\u00b4\u0131culas, 1649-003 Lisboa and 3004-516 Coimbra, Portugal\n128University of Liverpool, L69 7ZE, Liverpool, United Kingdom\n129Los Alamos National Laboratory, Los Alamos, NM 87545, USA\n130Louisiana State University, Baton Rouge, LA 70803, USA\n131Laboratoire de Physique des Deux Infinis Bordeaux - IN2P3, F-33175 Gradignan, Bordeaux, France,\n132University of Lucknow, Uttar Pradesh 226007, India\n133Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain\n134Johannes Gutenberg-Universit\u00a8at Mainz, 55122 Mainz, Germany\n135University of Manchester, Manchester M13 9PL, United Kingdom\n136Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n137University of Medell\u00b4\u0131n, Medell\u00b4\u0131n, 050026 Colombia\n138University of Michigan, Ann Arbor, MI 48109, USA\n139Michigan State University, East Lansing, MI 48824, USA\n140Universit`a di Milano Bicocca , 20126 Milano, Italy\n141Universit`a degli Studi di Milano, I-20133 Milano, Italy\n142University of Minnesota Duluth, Duluth, MN 55812, USA\n143University of Minnesota Twin Cities, Minneapolis, MN 55455, USA\n144University of Mississippi, University, MS 38677 USA\n145Universit`a degli Studi di Napoli Federico II , 80138 Napoli NA, Italy\n146Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands\n147National Institute of Science Education and Research (NISER), Odisha 752050, India\n148University of North Dakota, Grand Forks, ND 58202-8357, USA\n149Northern Illinois University, DeKalb, IL 60115, USA\n150Northwestern University, Evanston, Il 60208, USA\n151University of Notre Dame, Notre Dame, IN 46556, USA\n152University of Novi Sad, 21102 Novi Sad, Serbia\n153Occidental College, Los Angeles, CA 90041\n154Ohio State University, Columbus, OH 43210, USA\n155Oregon State University, Corvallis, OR 97331, USA\n156University of Oxford, Oxford, OX1 3RH, United Kingdom\n157Pacific Northwest National Laboratory, Richland, WA 99352, USA\n158Universt`a degli Studi di Padova, I-35131 Padova, Italy\n159Panjab University, Chandigarh, 160014, India\n160Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n161Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, Paris, France\n162University of Parma, 43121 Parma PR, Italy\n163Universit`a degli Studi di Pavia, 27100 Pavia PV, Italy\n164University of Pennsylvania, Philadelphia, PA 19104, USA\n165Pennsylvania State University, University Park, PA 16802, USA\n166Physical Research Laboratory, Ahmedabad 380 009, India\n167Universit`a di Pisa, I-56127 Pisa, Italy\n168University of Pittsburgh, Pittsburgh, PA 15260, USA\n169Pontificia Universidad Cat\u00b4olica del Per\u00b4u, Lima, Per\u00b4u\n170University of Puerto Rico, Mayaguez 00681, Puerto Rico, USA\n171Punjab Agricultural University, Ludhiana 141004, India\n172Queen Mary University of London, London E1 4NS, United Kingdom\n173Radboud University, NL-6525 AJ Nijmegen, Netherlands\n174Rice University, Houston, TX 77005\n175University of Rochester, Rochester, NY 14627, USA\n\n8\n176Royal Holloway College London, London, TW20 0EX, United Kingdom\n177Rutgers University, Piscataway, NJ, 08854, USA\n178STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom\n179Universit`a del Salento, 73100 Lecce, Italy\n180Universidad del Magdalena, Santa Marta - Colombia\n181Sapienza University of Rome, 00185 Roma RM, Italy\n182Universidad Sergio Arboleda, 11022 Bogot\u00b4a, Colombia\n183University of Sheffield, Sheffield S3 7RH, United Kingdom\n184SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA\n185University of South Carolina, Columbia, SC 29208, USA\n186South Dakota School of Mines and Technology, Rapid City, SD 57701, USA\n187South Dakota State University, Brookings, SD 57007, USA\n188Southern Methodist University, Dallas, TX 75275, USA\n189Stony Brook University, SUNY, Stony Brook, NY 11794, USA\n190Sun Yat-Sen University, Guangzhou, 510275, China\n191Sanford Underground Research Facility, Lead, SD, 57754, USA\n192University of Sussex, Brighton, BN1 9RH, United Kingdom\n193Syracuse University, Syracuse, NY 13244, USA\n194Universidade Tecnol\u00b4ogica Federal do Paran\u00b4a, Curitiba, Brazil\n195Tel Aviv University, Tel Aviv-Yafo, Israel\n196Texas A&M University, College Station, Texas 77840\n197Texas A&M University - Corpus Christi, Corpus Christi, TX 78412, USA\n198University of Texas at Arlington, Arlington, TX 76019, USA\n199University of Texas at Austin, Austin, TX 78712, USA\n200University of Toronto, Toronto, Ontario M5S 1A1, Canada\n201Tufts University, Medford, MA 02155, USA\n202Universidade Federal de S\u02dcao Paulo, 09913-030, S\u02dcao Paulo, Brazil\n203Ulsan National Institute of Science and Technology, Ulsan 689-798, South Korea\n204University College London, London, WC1E 6BT, United Kingdom\n205Universidad Nacional Mayor de San Marcos, Lima, Peru\n206Valley City State University, Valley City, ND 58072, USA\n207University of Vigo, E- 36310 Vigo Spain\n208Virginia Tech, Blacksburg, VA 24060, USA\n209University of Warsaw, 02-093 Warsaw, Poland\n210University of Warwick, Coventry CV4 7AL, United Kingdom\n211Wellesley College, Wellesley, MA 02481, USA\n212Wichita State University, Wichita, KS 67260, USA\n213William and Mary, Williamsburg, VA 23187, USA\n214University of Wisconsin Madison, Madison, WI 53706, USA\n215Yale University, New Haven, CT 06520, USA\n216Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia\n217York University, Toronto M3J 1P3, Canada\nThe determination of the direction of a stellar core collapse via its neutrino emission is crucial\nfor the identification of the progenitor for a multimessenger follow-up. A highly effective method of\nreconstructing supernova directions within the Deep Underground Neutrino Experiment (DUNE) is\nintroduced. The supernova neutrino pointing resolution is studied by simulating and reconstructing\nelectron-neutrino charged-current absorption on 40Ar and elastic scattering of neutrinos on electrons.\nProcedures to reconstruct individual interactions, including a newly developed technique called\n\u201cbrems flipping\u201d, as well as the burst direction from an ensemble of interactions are described.\nPerformance of the burst direction reconstruction is evaluated for supernovae happening at a distance\nof 10 kpc for a specific supernova burst flux model. The pointing resolution is found to be 3.4 degrees\nat 68% coverage for a perfect interaction-channel classification and a fiducial mass of 40 kton,\nand 6.6 degrees for a 10 kton fiducial mass respectively. Assuming a 4% rate of charged-current\ninteractions being misidentified as elastic scattering, DUNE\u2019s burst pointing resolution is found to\nbe 4.3 degrees (8.7 degrees) at 68% coverage.\nCONTENTS\nI. Introduction\n9\nII. Supernova neutrino emission\n10\nIII. Supernova neutrino detection at DUNE\n11\nA. Neutrino-Electron Elastic Scattering\n11\n\n9\nB. Electron-Neutrino Charged-Current\nAbsorption Interactions\n13\nIV. Simulation and reconstruction of supernova\nevents\n13\nA. Simulation of events in DUNE\n13\nB. Primary track identification and energy\nreconstruction\n15\nC. Direction reconstruction and head-tail\ndisambiguation\n16\nD. Performance of the reconstruction\nalgorithm on single events\n16\nV. Maximum likelihood method for burst\npointing\n17\nVI. Performance of reconstruction algorithm on\nsupernova simulations\n19\nVII. Summary and outlook\n22\nAcknowledgements\n23\nReferences\n24\n. Appendix\n25\nI.\nINTRODUCTION\nDetecting neutrinos from core-collapse supernovae\nopens up the possibility to study the astrophysics\nof stellar collapse and the properties of neutrinos\nand their interactions. The first and only supernova\nneutrino detection on Earth so far was achieved with\nSN1987A, when a few tens of electron-antineutrino\nevents1 were registered [1\u20133]. While it was already\npossible to derive valuable insights from these data\n(e.g., Ref. [4, 5]), a high-statistics, high-resolution\ndetection of various neutrino flavors from a future\nsupernova will bring invaluable advancement in\nparticle physics and astrophysics. Information can\nbe derived from the detected neutrino event rate,\ntiming, energy spectrum, flavor composition, and\nangular distribution.\nAn important characteristic feature of a supernova\nneutrino burst is that it emerges promptly after the\ncore bounce, preceding the related electromagnetic\nphenomena.\nAs neutrinos interact only via the\nweak interaction,\nthey can escape more easily\nin comparison to photons, allowing the neutrino\n1 We note here the use of \u201cevent\u201d to refer to an individual\nrecorded neutrino interaction, as per standard particle\nphysics usage.\nIn this paper, \u201cburst\u201d will refer to the\nensemble of events from a single core collapse.\nsignal to be observed well before the associated\nelectromagnetic\nradiation\n(as\ncan\ngravitational\nradiation). The Supernova Early Warning System\n(SNEWS) [6] is designed such that information\nretrieved from the supernova neutrino signal can\nbe\nmade\navailable\nworldwide\nquickly,\nthereby\nfacilitating the prompt detection of subsequent\nmulti-messenger supernova-related phenomena [7,\n8].\nClearly, it is highly desirable for information\nabout the position of the supernova in the sky to\nbe ascertained as fast as possible. Not only is the\ndirection useful for the localization of the supernova\nto enable prompt measurements, but for the case\nwhen the core collapse fails to produce a bright\nexplosion in electromagnetic radiation (e.g. black\nhole formation), a neutrino burst direction may help\nto locate a missing progenitor using archival data.\nSuch pointing information is available from the\nneutrinos themselves.\nOne possible strategy for\ndetermining the direction to the supernova is via\n\u201ctriangulation\u201d from the relative timing of neutrinos\nobserved at different locations around the globe [9\u2013\n12].\nHowever, the most promising way to achieve\nprecision pointing is to exploit anisotropic neutrino\ninteractions [9] for which information about the\nincoming neutrino direction is preserved in the\nfinal-state particle angular distribution.\nWater\nCherenkov detectors such as Super-Kamiokande and\nHyper-Kamiokande can make use of directional\nCherenkov radiation to determine the supernova\ndirection [13].\nWe note also that for a known source direction,\ndirectional reconstruction of final-state particles can\nimprove the neutrino energy determination, as well\nas statistical classification of interaction channels\nwith known anisotropy. Both of these can improve\nthe extraction of physics and astrophysics from the\nburst.\nThe Deep Underground Neutrino Experiment\n(DUNE) is capable of a supernova burst detection\namong other physics goals [14, 15].\nAn overview\nof DUNE\u2019s supernova detection capability is given\nin Ref. [14].\nIn the several tens of kilotonnes\n(kton) of liquid argon (LAr) volume of DUNE,\ncharged-current interactions of electron neutrinos\n(\u03bdeCC)\non\n40Ar\nand\nneutrinos\nof\nall\nflavors\nscattering elastically on electrons (eES) will result in\ncharge signals in DUNE\u2019s time projection chamber\n(TPC) and scintillation light that is read out\nvia photosensors.\nIn this work, both \u03bdeCC and\neES interactions are discussed.2\nPrimarily eES\ninteractions carry directional information, but the\n2 We focus here on directional information derived from the\n\n10\nnear-isotropic \u03bdeCC interactions have a higher cross\nsection.\nA supernova burst alert from DUNE,\nincluding pointing information, will be a valuable\ninput to SNEWS.\nThe overall ability for DUNE to point to a\nsupernova using the events recorded from a core\ncollapse depends on several factors. Two primary\nfactors affect the direction resolution of individually\nrecorded neutrino events. First, there are intrinsic\nangular spreads between the recoil directions of the\nfinal-state products and the neutrino direction. For\neES interactions, which are the most important for\nthe pointing ability, this energy-dependent spread is\nvery well understood from weak interaction physics;\nfor \u03bdeCC it is less well known.\nSecond,\nthe\ndetector angular resolution smears the reconstructed\ndirection with respect to the final-state electron\ndirection.\nDetector-resolution smearing can in\nprinciple be improved with better reconstruction\nalgorithms,\nalthough there will be an intrinsic\nphysical limit for a given detector configuration. For\nthis study, we use standard DUNE reconstruction\ntechniques (detailed in Sec. IV), with some minor\nimprovements,\nas\nwell\nas\na\nnovel\nadditional\ntechnique we call \u201cbrems flipping,\u201d which provides\nevent-by-event a modest improvement in head-tail\ndirectional disambiguation by looking at the location\nof the secondary particles\u2019 tracks relative to the\nprimary track.\nWhile individual-event resolution on neutrino\ndirection is relatively modest due to both physical\nangular spread and instrumental uncertainty, for\nthe statistical ensemble of events in a burst the\ndirectional determination improves approximately\nby the inverse square root of the number of events\ndetected.\nWe evaluate here the overall supernova\nburst pointing resolution,\nwhich will enable a\nsuccessful contribution from DUNE to a multi-\nmessenger detection of a core-collapse supernova.\nThe scope of this study,\nwhich makes use of\nstandard offline reconstruction software, addresses\nonly intrinsic pointing ability and does not consider\nlatency for dissemination of pointing information.\nSection II introduces the supernova neutrino-\nemission model that we use.\nIn Sec. III, the\nDUNE detector and the expected signatures of\nthe\nneutrino\ninteraction\nchannels\nin\nthe\nLAr\nvolume\nare\ndescribed.\nSec.\nIV\nprovides\na\nexpected prompt burst of tens-of-MeV neutrinos, although\nwe note that higher energy (GeV scale or more) neutrinos\nmay follow a supernova [16, 17].\nThese may provide\nprecision pointing due to both higher intrinsic lepton-\nneutrino collimation and better detector performance at\nhigh energy; however, they likely arrive on a long time scale\n(hours to years) after the supernova.\ndescription of the simulation of supernova neutrino\nevents in DUNE and the subsequently applied\nreconstruction algorithms including the relevant\nsoftware tools.\nThis is followed by Sec. V on the\nmaximum likelihood method for the burst direction\ndetermination. In Sec. VI the overall performance of\nsupernova burst direction reconstruction for DUNE\nis evaluated.\nFinally, Sec. VII summarizes the\nresults of the study and provides a road map for\npotential future studies in this area.\nII.\nSUPERNOVA NEUTRINO EMISSION\nWhen a massive star has depleted all of its\nnuclear fuel, the outgoing radiation pressure ceases\nto counteract the inward gravitational pull of the\nstar, collapsing it into a compact object such as a\nneutron star or a black hole. During this process,\n99% of the gravitational binding energy of the\nremnant is emitted in the form of neutrinos with\nenergies of a few tens of MeV over a few tens of\nseconds. Supernova neutrinos are released in several\nstages during a core collapse. At the beginning of\nthe collapse (over tens of milliseconds), neutrinos are\nprimarily produced via electron capture (p + e\u2212\u2192\nn+\u03bde) as the star undergoes neutronization. During\nthe subsequent accretion phase (which lasts for tens\nto hundreds of milliseconds), more neutrinos of all\nflavors are created, counteracting the shock heating\nof the in-falling matter. Subsequently, \u03bd\u00af\u03bd pairs are\nemitted over the next tens of seconds, such that\nthese neutrino pairs shed most of the gravitational\nbinding energy, thereby cooling the remnant [18].\nThe study of supernova neutrinos is particularly\nuseful in providing insights on varied topics in\nastrophysics and neutrino physics. As neutrinos are\nintimately involved in the collapse and subsequent\nexplosion processes, measurements of the supernova\nneutrino\nsignal\nallow\nfor\nthe\nexamination\nof\nthe complex interactions that occur during the\ncore collapse.\nAdditionally, supernova neutrino\nsignals\nhave\nthe\nimportant\nfeature\nthat\nthe\ninitial luminosity is roughly equally divided among\nflavors.\nThe subsequent flavor transitions provide\ninformation on the neutrino mass ordering, as well\nas insights into exotic flavor transition physics [19\u2013\n22].\nFor this study, the GKVM [23] core-collapse\nsupernova neutrino emission model is used to\ndescribe the neutrino energy spectrum.\nThere\nare known to be fairly large (up to an order\nof\nmagnitude)\nuncertainties\non\nthe\nsupernova\nneutrino flux prediction,\nand result both from\nintrinsic progenitor variance and from theoretical\nuncertainties. These variances will have an impact\n\n11\non the total number of neutrinos detected as well\nas on details of the neutrino flavor composition\nand spectra.\nHowever, the pointing capabilities\nof the DUNE detector are primarily sensitive to\nevent statistics rather than to details of the model\nflux. We therefore do not survey different supernova\nmodels here.\nThe selected model produces an\nintermediate number of eES events among a range\nof models.\nExpected event rates without energy\nsmearing are calculated with SNOwGLoBES [24],\nwhich computes the recoil energy distribution as\ndescribed in the next section. It is assumed that the\nsupernova explosion occurs at a distance of 10 kpc\nfrom Earth, within the Milky Way for our selected\nmodel.\nThe total expected number of events and\nthe events per interaction channel are presented\nin Tab. I. We do not study the effects of flavor\ntransitions3.\nIII.\nSUPERNOVA NEUTRINO DETECTION\nAT DUNE\nDUNE is unique in the sense that it will be able\nto register large numbers of electron neutrinos, while\nall other experiments of similar size, e.g., Hyper-\nK [25] and JUNO [26], primarily detect electron\nantineutrinos via inverse beta decay on free protons.\nImmediately following the core collapse, electron-\nneutrino emission through neutronization dominates\nand insights on the neutrino mass ordering can be\ngained from observed differences in the neutrino\nflavor composition and spectra due to oscillation\ndynamics within the supernova [22].\nWe consider neutrino detection at DUNE\u2019s far\ndetector\nliquid\nargon\ntime\nprojection\nchamber\n(LArTPC). The full planned design consists of\n40 kton of fiducial mass4 of liquid argon placed into\nfour modules. Both single-module (10 kton) and all-\nmodules (40 kton) performance is considered in this\nstudy. We consider DUNE\u2019s first-module design for\nthis study. Each of the active volumes is bound by\nthe cathode plane assembly (CPA) and the anode\nplane assembly (APA) and surrounded by the field\ncage. A uniform electric field is created between the\nCPA and APA, drifting ionization charges toward\nthe APA. Three planes of sensing wires, each with\n3 Flavor transitions may affect the total number of neutrino\nevents, but with uncertainty not exceeding the overall\nflux model uncertainties; spectral modulations will be a\nsubdominant effect on pointing capabilities.\n4 We note this is the fiducial mass for long-baseline physics;\nactive mass for supernova event detection could potentially\nbe larger.\na different orientation, are located at the APA.\nCharge depositions on these readout planes are used\nto reconstruct the location of the particle energy\ndeposition in two dimensions, and the drift timing\ninformation allows for the reconstruction of the third\nspatial coordinate.\nIn addition to the LArTPCs,\nthe Photon Detection System (PDS) is used to\ntag neutrino events. In this study, information on\nthe timing of the interaction is retrieved from the\ndetection of photon flashes to be able to estimate\nthe charge loss during drift. More details about the\nphoton detectors can be found in [27].\nThe two neutrino-interaction channels considered\nin this study are neutrino-electron elastic scattering\ninteractions\nand\n\u03bde\n+\n40Ar\nCC\nabsorption\ninteractions.\nNeutral-current and anti-neutrino\nCC interactions are also expected [14].\nHowever,\nas these channels are known to be subdominant\nand are at present not well understood, they are\nnot included in this study.\nIn the following, the\nnature of the dominant interaction channels is\ndescribed and the simulated energy spectra and\nangular distributions in the detector are discussed.\nFor eES events, the event rates are determined from\nSNOwGLoBES, using the GKVM supernova model.\nIt also provides the recoil energy distribution as\ninput to a LArSoft [28] neutrino-electron scattering\nevent generator. For \u03bdeCC events, MARLEY [29]\nand its LArSoft interface are applied to generate the\nevents with the correct energy distribution.\nOnce\nagain the GKVM supernova model is provided as\ninput to MARLEY in this case.\nAll simulations\nare done in a subset of the full DUNE far detector\ngeometry simulating 1.6 kton of fiducial volume\nto reduce memory,\ndisk,\nand computing time\nrequirements. The simulated workspace features six\nplanes of APAs (two APAs tall) along the beam\ndirection.\nFor the full detector module, there are\n150 APAs proposed in total, stacked two-tall and\n25 along the beam direction.\nBecause the spatial\nextent of the neutrino events under consideration is\nmuch smaller than the simulated workspace size, we\nexpect the scaling down of the simulated geometry\nto have a negligible effect on the conclusions of the\nstudy.\nA.\nNeutrino-Electron Elastic Scattering\nThe most relevant interaction for directional\ninformation is when a neutrino elastically scatters off\nof an electron in the LAr. This interaction applies\nto all flavors but the largest cross section is for \u03bde.\nA visualization of a Geant4 event is shown in Fig. 1.\nThe direction of the scattered electron is highly\ncorrelated to the direction of the neutrino.\nIn\n\n12\nFIG. 1. Geant4 illustration of the energy deposition for examples of two event types: (a) \u03bdeCC: A 25 MeV electron\nneutrino is absorbed by an argon nucleus resulting in the excitation of the nucleus and the emission of an electron.\n(b) eES: An incoming electron neutrino of 12 MeV scatters elastically in the LAr. Charged particles are emitted in\nthe forward direction of the primary electron. The \u03bdeCC primary electron tracks are on average longer than eES\ntracks due to the lower energies of the eES recoils; in contrast, \u03bdeCC electrons tend to retain most of the energy\nof the incoming neutrino. Gamma tracks are not shown in the display, but red blips (representing electrons) from\ngamma interactions with the argon (primarily Compton scatters) can be seen.\nTABLE I. The eES and \u03bdeCC event rates (total for\nthe interaction channel in bold) for DUNE within a\nfiducial volume of 40 kton, and for a core collapse at\na distance of 10 kpc, using the GKVM model.\nNo\ntriggering efficiency or detector resolution effects are\napplied here,\nin contrast to [14].\nNeutrino flavor\ntransition effects beyond those included in the GKVM\nmodel are neglected.\nThe neutrino event rate scales\nlinearly with detector mass and with inverse-square\ndependence on supernova distance.\nChannel\nExpected Event Count\n\u03bd + e\u2212\u2192\u03bd + e\u2212(all flavors)\n325.8\n\u03bde + e\u2212\u2192\u03bde + e\u2212\n155.5\n\u00af\u03bde + e\u2212\u2192\u00af\u03bde + e\u2212\n67.3\n\u03bd\u00b5,\u03c4 + e\u2212\u2192\u03bd\u00b5,\u03c4 + e\u2212\n55.2\n\u00af\u03bd\u00b5,\u03c4 + e\u2212\u2192\u00af\u03bd\u00b5,\u03c4 + e\u2212\n47.8\n\u03bde + 40Ar \u2192e\u2212+ 40K\u2217\n3300.0\nparticular, the scattering angle \u03b8e is described by\n[30]:\ncos \u03b8e = E\u03bd + me\nE\u03bd\nr\nT\nT + 2me\n,\n(1)\nwhere T is the electron kinetic energy, E\u03bd is the\nneutrino energy, and me is the electron mass. The\ndistribution of T is given by the differential cross\nsection:\nd\u03c3(\u03bde)\ndT\n= GF\n2me\n2\u03c0\n\"\n(gV + gA)2\n+(gV \u2212gA)2\n\u0012\n1 \u2212T\nE\u03bd\n\u00132\n+(gA\n2 \u2212gV\n2)meT\nE\u03bd\n2\n#\n,\n(2)\nwhere GF is the Fermi coupling constant, and gA\nand gV are given according to neutrino flavor [30] in\nTab. II.\nTABLE II. Coupling strengths in the cross section of\nneutrino-electron scattering from Ref. [30].\nThe cross\nsection of \u03bde electron scattering is enhanced due to\nthe possibility of both neutral- and charged-current\ninteractions occurring; \u00af\u03bde-electron elastic scattering is\nhelicity-suppressed with respect to \u03bde scattering.\nFlavor\ngA\ngV\n\u03bde\n1/2\n2 sin2 \u03b8W + 1/2\n\u00af\u03bde\n\u22121/2\n2 sin2 \u03b8W + 1/2\n\u03bd\u00b5,\u03c4\n\u22121/2\n2 sin2 \u03b8W \u22121/2\n\u00af\u03bd\u00b5,\u03c4\n1/2\n2 sin2 \u03b8W \u22121/2\nThe event rate split into the different neutrino\nflavors\ncan\nbe\nfound\nin\nTab.\nI.\nThe\nenergy\ndistributions\nof\nthe\ngenerated\nneutrinos\nand\nscattered electrons are shown in Fig. 2(a, blue).\nThe distribution of the scattering angle, computed\nvia the energy distribution and Eq. 1, is depicted\n\n13\nin Fig. 2(b, blue) showing the sensitivity to the\ndirection of the incoming neutrino.\nB.\nElectron-Neutrino Charged-Current\nAbsorption Interactions\nDUNE is particularly sensitive to the charged-\ncurrent absorption of \u03bde on 40Ar (\u03bdeCC):\n\u03bde + 40Ar \u2192e\u2212+ 40K\u2217.\n(3)\nThe primary observable of this interaction is\nthe emitted e\u2212; additional observables are the de-\nexcitation products of the excited potassium nucleus\nin the final state. The output energy and angular\ndistributions of this interaction are also shown in\nFig. 2 in red and Fig. 1 (a) depicts an example from\nGeant4.\nEvents from \u03bdeCC interactions are considerably\nmore abundant than the aforementioned eES events\n(about 3000 events at a core collapse distance of\n10 kpc for DUNE compared to 300 for eES in\nTab. I). Yet, the direction of the electron trajectory\ncorrelates very weakly with the neutrino direction,\ndue to the two competing nuclear transition types,\nFermi and Gamow-Teller. The electrons produced\nby CC-induced interactions governed by Fermi\ntransitions have an angular distribution described\nby 1 +\nv\nc cos \u03b8,\nwhile Gamow-Teller transitions\ncorrespond to 1 \u22121\n3\nv\nc cos \u03b8 [31] with respect to the\nneutrino direction.\nFor our assumed supernova\nneutrino energy spectrum, the angle dependence of\nthe two contributions happen to cancel each other\nout almost exactly, resulting in a nearly isotropic\nangular distribution for \u03bdeCC events, as shown in\nthe red distribution in Fig. 2(b). Figure 3 depicts\nthe contribution of the two matrix elements for\nthe GKVM supernova spectrum.\nThe pointing\nresolution for a supernova burst therefore depends\non a precise classifier between eES and \u03bdeCC events\nas discussed in Sec. V.\nWe\nnote\nthat\nthe\nFermi/Gamow-Teller\ncancellation\nis\nnot\nperfect\nfor\nother\nassumed\nflux\nspectra\n(e.g.\nRef.\n[31]),\nresulting\nin\na\nweak anisotropy of the \u03bdeCC-absorption-induced\nelectrons for many cases.\nFurthermore, forbidden\ntransitions, not currently included in MARLEY,\nhave a backward angular distribution [32] which\nmay have an effect on the overall \u03bdeCC anisotropy.\nCurrently, there are large (and not fully understood)\nuncertainties on the relative components of \u03bdeCC\nnuclear transition type and hence on the \u03bdeCC\nangular distribution (as well as on the total cross\nsection [33].)\nWe note that while the expected\n\u03bdeCC anisotropy is relatively weak, it should be\npossible to extract directional information from the\n\u03bdeCC events, especially if the competing nuclear\ntransition\ntypes\ncan\nbe\ntagged\nand\nexamined\nseparately.\nIn principle, the nuclear transition\ntypes can be distinguished statistically using their\ndifferent nuclear de-excitation product distributions.\nHowever, given the large uncertainties on the \u03bdeCC\nangular\ndistribution5\nand\nthat\nour\nassumed\nspectrum\nproduces\nthe\nmost\nexperimentally\nchallenging situation\u2014 a directional signal on top\nof a uniform \u03bdeCC distribution\u2014 we evaluate the\npointing ability under this simple assumption and\nleave detailed study and use of \u03bdeCC anisotropies\nfor the future.\nIV.\nSIMULATION AND\nRECONSTRUCTION OF SUPERNOVA\nEVENTS\nA.\nSimulation of events in DUNE\nFull-detector Monte Carlo simulations are used\nto determine the statistical distribution of the\nparticles resulting from the neutrino interactions and\nultimately the supernova pointing resolution.\nThe eES and \u03bdeCC event generators in LArSoft\nproduce\nparticles\nuniformly\nin\nthe\nworkspace\ngeometry\nwith\nrandom\nneutrino\ndirections\nsampled from an isotropic angular distribution.\nStandard radioactive and detector noise models\nwere\nused\nduring\nthe\nsimulations\n[15].\nThe\nconsidered radioactive background sources include\ncontaminants of the liquid argon such as 39Ar and\n85Kr,\nradioactive contaminants from the TPC,\nand neutrons from the cavern walls.\nWe expect\nradiological and cosmogenic background to have\na relatively small effect on the pointing quality.\nThe dominant 39Ar background of 1 Bq/kg results\nin only of the order of one background-induced\nblip expected in the spatial vicinity of a supernova\nevent over one drift time [34]. Therefore we expect\nour evaluation to be robust against evolutions of\nthe DUNE background model.\nFurthermore, the\nbackground will be known precisely; it can be fully\ncharacterized from the data taken near in time to\nthe supernova burst, which will enable optimization\nof\nbackground\nmitigation\nfor\nreconstruction\nalgorithms.\nThe\nsimulated\nelectronics\nsignal\nprocess accounts for the charge deposition and drift\nphysics, the field response of the sensing wires,\nelectronics and digitization response of the front-end\nelectronics, as well as the inherent electronics noise\n5 Note that these uncertainties may be addressed directly\nwith independent laboratory measurements.\n\n14\n10\n20\n30\n40\n50\n60\nE (MeV)\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\nNormalized Event Distribution (MeV\n1)\neCC\neCC e\neCC e +\neES\neES e\n(a)\n1.00\n0.75\n0.50\n0.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\ne)\n10\n2\n10\n1\n100\n101\nNormalized Event Distribution\neES\neCC\n(b)\n20\n40\n60\n80\nE (MeV)\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\ncos(\ne)\neES\n10\n5\n10\n4\n10\n3\n10\n2\n10\n1\nNormalized Event Distribution (MeV\n1)\n(c)\n20\n40\n60\n80\nE (MeV)\n1.00\n0.75\n0.50\n0.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\ne)\neCC\n10\n4\n10\n3\n10\n2\nNormalized Event Distribution (MeV\n1)\n(d)\nFIG. 2. Comparison of the cross-section-weighted energy and angular distributions of electrons for the \u03bde + 40Ar\n\u03bdeCC events in red and the eES events in blue. The angular plots are shown as a function of the cosine of the angle\nbetween the neutrino direction and the final-state electron direction. For both types of interactions, the supernova\nenergy spectrum is assumed for the incoming neutrinos. Top left: distribution of the energy of incoming neutrinos\n(continuous line) and outgoing electrons (dashed line). Top right: distribution of the cosine of the scattering angle.\nBottom: two-dimensional distributions showing the relative number of events as a function of both the neutrino\nenergy and the cosine of the scattering angle, for the two types of interactions.\naccording to Ref. [34].\nThe Projection Matching\nAlgorithm [35] is used for 3D track reconstruction.\nAn example eES event display is shown in Fig. 4.\nOf note, the longest track marked by \u201d0\u201d (several\ntens of cm) with high charge deposition corresponds\nto the primary electron and there are as well as\nseveral shorter tracks.\nThese tracks result from\nlower energy final-state particles that were produced\nfrom the interaction (such as the deexcitation\nproducts of \u03bdeCC events), or secondary particles\ncreated as the primary electron travels in the\ndetector.\nNotably, some secondary particles have\ndirections that correlate to the primary electron,\nmaking them useful in determining the starting\ndirection of the primary electron track (discussed\nin Sec. IV B). Additionally, charge may also be\nregistered as a result of background radioactive\ndecay events,\nsuch as the decay of\n39Ar and\nelectronics noise.\nThese signals are very short\ncompared to the primary electron, are far apart from\neach other, and are of low amplitude, which are\nall characteristics that can be used for extracting\nsignals from background.\n\n15\nFIG. 3.\nThe contribution of Fermi and Gamow-\nTeller transitions to the angular distribution for \u03bdeCC\nevents, generated from MARLEY for the GVKM flux\nmodel. For this model\u2019s neutrino spectrum, the angular\ncorrelation cancels out to a good approximation.\nB.\nPrimary track identification and energy\nreconstruction\nThe reconstruction algorithm consists of several\nsteps. First, the energy depositions associated with\nthe supernova neutrinos are identified. The first step\nin reconstructing the event is to determine which\nreconstructed track corresponds to the primary\nelectron\n(marked\nwith\n\u201c0\u201d in\nFig.\n4).\nThe\nDUNE version of the projection matching algorithm\nas\ndescribed\nin\n[36]\nis\napplied\nfor\nthe\ntrack\nreconstruction. We show in the following that the\noverall performance of the low-energy reconstruction\nis sufficient for the task at hand. Specific mitigations\nfor the intrinsic head-tail ambiguity of the track\nwill be described. In a noise- and background-free\nscenario, the track of the primary electron typically\nhas the greatest length (see Fig. 1), as the electron\ndeposits more charge compared to its secondary\nparticles. However, the presence of radioactive decay\nparticles can complicate this, as a highly energetic\nradioactive decay product may deposit more charge\nthan the primary electron and create a longer track.\nThese scenarios are rejected by examining the spatial\ndistance between tracks. Particles associated with\nthe neutrino interactions are clustered together,\nwhile the radioactive particles are spaced out over\nthe total simulated LAr volume.\nTherefore, the\nprimary track is selected by examining the relative\nposition of charge depositions.\nReconstructed 3D\nspace points are sorted by their corresponding hit\ncharges, and for the ten space points with the highest\ncharge depositions, the distances between these\nspace points are calculated. The two space points\n870\n875\n880\n885\n890\n895\n900\n905\n2800\n2900\n3000\n3100\n3200\n3300\n880\n890\n900\n910\n920\n930\n940\n2800\n2900\n3000\n3100\n3200\n3300\n0\n1\n2\n210\n215\n220\n225\n230\n235\n240\n245\n2850\n2900\n2950\n3000\n3050\n3100\n3150\n3200\n3250\nWire ID\nt [ticks]\nX Plane\nV Plane\nU Plane\nWire ID\nWire ID\nt [ticks]\nt [ticks]\n0\n2\n1\n1\n0\n2\nFIG. 4. Example standard DUNE event display of an\neES event. The colors show a heat map of the charge\ndeposited on each wire segment per time tick.\nFrom\ntop to bottom, the three plots show the view of the\nthree wire planes, U, V, and X respectively, for one APA\nof the LArTPC. The trajectories with numerical labels\nare reconstructed tracks, where \u201c0\u201d corresponds to the\nprimary electron track, while \u201d1\u201d and \u201d2\u201d refer to the\nbrems particles.\nwith the closest spatial distance between each other\namong those ten space points are picked and one\nof them is selected as the estimated reconstructed\nvertex position. While this location may not exactly\nbe the true vertex, it allows the rough localization\nof the position inside the detector. The track with\nthe most associated charge in the proximity of this\nreconstructed vertex (within a sphere of radius of\n120 cm) is finally selected to be the primary electron\ntrack.\nNext,\nthe energy of the primary electron is\nevaluated, as the pointing resolution of an event\ndepends on the energy of its electron.\nEnergy\nreconstruction is done by summing the total charge\ndeposited near the identified interaction vertex (with\na distance cut applied at 70 cm, five times the 14 cm\nradiation length of liquid Ar), and mapping charge\nto energy using a linear relationship. This distance\ncut is applied to reject the energy depositions of\nradioactive particles far away from the interaction\nvertex.\nCharge loss due to drift is also corrected\nby examining the time difference between the\ninteraction time provided by the optical detector and\nthe TPC signal collection time. An electron lifetime\nof 3000 \u00b5s in LAr is assumed.\nComparing the\n\n16\nreconstructed primary electron energy after drift-\ntime correction to the true energy of the simulated\nparticles shows a linear relationship.\nC.\nDirection reconstruction and head-tail\ndisambiguation\nMost relevant for the supernova pointing is the\nprimary electron\u2019s direction. The goal is to attain\na accurate \u201creconstruction resolution\u201d, which goes\nalong with minimizing the sky area that must be\nsurveyed to confidently encompass the supernova.\nWe expect a head-tail ambiguity in LArTPC track\ndirections as the charge drift speed towards the\nanode is slow compared to the propagation of\nparticles through the TPC material. Consequently,\nthe track\u2019s head-tail direction cannot be determined\nthrough timing.\nIn other words, it is not known\nthrough timing which side of the track corresponds\nto the origin of the track, causing the reconstructed\ndirection to potentially be opposite of the true\ncharged-particle track direction.\nThis results in\na bimodal distribution of angle between the true\nand reconstructed directon around the true and\nreversed directions of the primary track.\nThe\nreconstruction algorithm aims to enhance the peak\npointing towards the true direction.\nTo evaluate the performance of the reconstruction\nresolution, we consider detection probabilities from\nscanning the sky regions with the highest likelihood\nvalues\nfirst.\nThe\ncosine\nangles\nbetween\nthe\nreconstructed direction and the truth direction are\ncollected into a histogram.\nThe histogram is\nintegrated from both the forward and backward\ndirections inwards, up until the histogram drops\nbelow a certain value.\nThis value is lowered\nuntil the integral equals 68% of the total integral\nof the distribution.\nThe resolution metric \u201csky\nfraction\u201d is defined to be the fraction of the sky\nthat is covered by the integration.\nThe sky\nfraction can be used to define an equivalent angular\nresolution by multiplying with 4\u03c0. If the two sides\nof the distribution are close to fully symmetric,\nthe sky fraction would be twice as large as the\nfully unambigiuous case, corresponding to an equal\nprobability of success for finding the supernova on\neach side of the sky.\nThe\nhead-tail\nambiguity\ncan\nbe\nresolved\nstatistically by looking at the adjacent tracks\ncreated by secondary particles. The bremsstrahlung\ngamma rays from the primary electron subsequently\nrelease electrons in argon atoms via Compton\nscattering.\nThese secondary electrons correlate\nwith the forward direction of the primary electron.\nThe directional correlation is closer when the\nprimary electron is of higher energy. The particular\nprocedure of disambiguating the direction of the\nprimary electron is carried out in a process called\n\u201cbrems flipping\u201d. To apply the method, a starting-\npoint and an end-point of the primary electron\ntrack are assumed arbitrarily.\nThe vectors from\nthe starting point as well as from the end point\nof the primary track to each secondary track are\ndetermined. Subsequently, the cosine value of the\nangle between each vector pointing to the secondary\ntracks and the vector along the primary track is\nevaluated.\nThe average of these cosine values is\ncalculated. In the next step, the assignment of the\nstarting-point and the end-point are switched and\nthe same calculations are carried out. Of the two\nvertices, the one with the larger average cosine value\nis finally selected as the actual starting point of the\nprimary track. Most of the secondary particles are\nemitted towards the end of the primary track in a\nforward direction, leading to a preference for larger\ncosine values (corresponding to smaller angles) as\ncan be understood from Fig. 5. The brems-flipping\nmethod is also described in Algorithm 1 (see\nAppendix).\n \n \n1\n2\n3\n2\n3\n1\nFIG. 5.\nIllustration of brems flipping:\nThe angles\nbetween the brems particles (blue) and the primary track\nmarked in black correspond to the actual direction of the\nprimary electron, while the ones marked in red belong\nto the incorrect opposite direction. The average of the\ncosine of these angles is larger in the case of the correct\nset of angles.\nD.\nPerformance of the reconstruction\nalgorithm on single events\nThe performance of the reconstruction algorithm\nbefore the application of brems flipping is shown in\n\n17\nthe top plot of Fig. 6 in blue. The distribution is\ncentered around both the parallel and anti-parallel\ndirections with respect to the true direction, with\na minor preference for the parallel direction. The\nreason for this preference is that the projection\nmatching algorithm creates many track candidates\nat first and then merges candidates that are close to\neach other and have a small angle between them. If\na secondary track is sufficiently close to the primary\ntrack, the merging process may combine it with\nthe primary track, flipping the primary track to\nthe correct orientation. Brems flipping extends the\nsame principle to the separately detected brems\nparticles, meaning that their location with respect\nto the track indicates the direction of the primary\ntrack. By applying brems flipping, the magnitude\nof the distribution in red in the anti-parallel\ndirection is significantly decreased, confirming that\nthe technique is a valuable tool in resolving the\nambiguity in track directions.\nThe bottom plot of Fig. 6 shows how brems\nflipping reduces the sky fraction for mono-energetic\nelectron energies.\nThe electron energy spectrum\nfrom eES events is given as a reference for the energy\nregime of interest for supernova pointing.\nBrems\nflipping has a higher impact at higher primary\nelectron energies, as those result in more secondary\ntracks. The successful application of brems flipping\non the full supernova neutrino MC is presented in\nSec. V.\nOur studies show that the performance of the\ntracking algorithm as a function of the initial track\ndirection with respect to the detector coordinate\nsystem is not perfectly isotropic, as expected. The\nparticle track\u2019s inclination with respect to the\nreadout wire planes affects the charge deposition\non the wires [35] and therefore influences the\nuncertainty of the reconstructed direction.\nThe\nworst performance is observed along the drift\ndirection (detector coordinate \u00b1\u02c6x).\nFigure 7(a)\ndemonstrates this anisotropy. For this figure, it is\nassumed that there are no directional ambiguities, to\nreveal the full impact of this anisotropy. Figure 7(b)\nis created assuming the actual performance of\nthe\nreconstruction\nalgorithm\nincluding\nbrems\nflipping for the head-tail disambiguation.\nWhile\nthe reconstruction performance varies with track\ndirection, the figures show that the track direction\nambiguity has a stronger detector anisotropy. We\ntherefore first evaluate pointing capability assuming\na uniform performance in directional reconstruction.\nSubsequently, we investigate the performance of the\nmethod as a function of supernova direction in\ndetector coordinates.\n\u22121.00\n\u22120.75\n\u22120.50\n\u22120.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\u03b8\nreco\n)\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\n3.5\n4.0\nNormalized E ent Distribution\nWithout Brems Flipping\nWith Brems Flipping\n10\n20\n30\n40\n50\n60\n70\nElectron Energy (MeV)\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\n0.35\n0.40\nMonoenergetic e\u2212 Sky Fraction\nBrems Flipping\nWithout Brems Flipping\nPerfect Disambiguation\neES Electron\n Energy Spectrum (AU)\nFIG. 6.\nEffectiveness of the brems-flipping algorithm:\nThe top plot shows the bimodal distribution of the\nangular\ndifference\nbetween\ntrue\nand\nreconstructed\nelectron directions using the supernova eES electron\nenergy spectrum, centering around the parallel (cos \u03b8 =\n1) and anti-parallel (cos \u03b8 = \u22121) directions.\nBrems\nflipping significantly decreases the magnitude of the anti-\nparallel peak. The bottom plot shows the relationship\nbetween the covered sky fraction and mono-energetic\nelectron energy.\nThe black curve corresponds to a\nperfect directional disambiguation always resulting the\ntrue direction.\nBrems flipping performs better at\nhigher energies, as there are more secondary tracks\nto reference.\nThe electron energy spectrum from eES\nin gray illustrates the energies relevant to supernova\npointing.\nV.\nMAXIMUM LIKELIHOOD METHOD\nFOR BURST POINTING\nA maximum\nlikelihood\nmethod\n[13]\nis\nused\nto\nreconstruct\nthe\ndirection\nof\na\nsupernova\nburst ensemble of events from the reconstructed\ninformation of individual neutrino events.\nFor an\nevent with a known interaction type, the probability\ndensity function (PDF) has the functional form\n\n18\n-150\u00b0 -120\u00b0 -90\u00b0 -60\u00b0 -30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0\n120\u00b0 150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\nPerfect Head-Tail Disambiguation\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nSky Fraction\n(a)\n-150\u00b0 -120\u00b0 -90\u00b0 -60\u00b0 -30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0\n120\u00b0 150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\nWith Brems Flipping\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nSky Fraction\n(b)\nFIG. 7.\nPointing resolution, defined in terms of \u201csky\nfraction\u201d as described in the text, of individual electron\nevents as a function of the electron\u2019s true direction in\nthe detector coordinate system to study anisotropies\nin the performance.\nThe coordinate system is defined\nwith \u00b1\u02c6x being the drift directions,\nand +\u02c6z being\napproximately the beam direction. \u03b8 (shown vertically)\nand \u03d5 (shown horizontally) are spherical coordinates in\na coordinate system for which \u03b8 = 90\u25e6correspond to\nthe +\u02c6z direction and \u03b8 = 0\u25e6, \u03d5 = 0\u25e6corresponds to\nthe +\u02c6x direction.\nThe supernova eES electron energy\ndistribution is used. (a) shows the pointing resolution\ngiven perfect track head-tail disambiguation (b) depicts\nthe pointing resolution for the actual performance of the\nreconstruction algorithm including the brems-flipping\nalgorithm.\nof pr(Ei, \u02c6di; \u02c6dSN), where the index r indicates the\nneutrino channel: eES or \u03bdeCC. Ei and \u02c6di are the\nreconstructed energy and direction of the specific\nevent, and \u02c6dSN is the direction of the supernova.\nThe PDF is formulated to be a function of the\nreconstructed energy as well as the inner product of\nthe supernova direction and reconstructed electron\ndirection,\n\u02c6di \u00b7 \u02c6dSN = cos \u03b8SN,i, as we make the\naforementioned assumption that the event direction\nreconstruction quality is uniform as a function\nof the true neutrino direction6.\nThe PDFs are\nnormalized by energy bin, as the electron energy\ndistribution does not affect the direction likelihood.\nLArSoft simulations of one million events in each\nchannel are used to determine the PDFs.\nThe\nMonte Carlo samples are divided into energy bins,\nspanning from 0 to 40 MeV with a width of 2 MeV\nper bin, from 40 MeV to 70 MeV at 10 MeV per\nbin, and a final bin spanning from 70 MeV from\n100 MeV. Varying energy bin widths are used to\nensure sufficient counting statistics at high energies,\nwhere the expected numbers of events are low.\nThe generated PDFs are shown in Fig. 8 for\nboth eES and \u03bdeCC events. For the \u03bdeCC channel,\nthe low correlation between electron and neutrino\ndirections renders the PDF mostly flat.\nThe eES\ninteractions demonstrate a high correlation between\nthe\nsupernova\ndirection\nand\nthe\nreconstructed\ndirection.\nA bimodal distribution is seen due to\nthe tracks\u2019 head-tail ambiguity, but the peak for the\ntrue direction (centered around cos \u03b8SN = 1) has a\nmuch higher amplitude than the peak around the\nflipped direction (cos \u03b8SN = \u22121) thanks to brems\nflipping. In particular, at higher electron energies,\nthe pointing of eES events improves both in variance\naround the supernova direction, as well as in track\ndirectional disambiguation (the same effect as can be\nobserved in Figure 6). The improved performance at\nhigh energy is further demonstrated in projections of\nthis PDF for various energy ranges shown in Figure\n9.\nThe supernova direction can be reconstructed\nfrom the PDFs with the maximum likelihood\nmethod.\nGiven a set of reconstructed events, the\nlog-likelihood as a function of supernova direction is\nexpressed as:\n\u2212log L( \u02c6dSN) = \u2212\nX\ni\nlog p(Ei, \u02c6di; \u02c6dSN)\n(4)\nHere,\na perfect classification between eES and\n\u03bdeCC events is assumed, p = peES.\nThe effect\nof imperfect classifications is discussed later.\nBy\nparameterizing \u02c6dSN using the azimuth and zenith\nangles, the supernova direction is reconstructed via\na two-variable minimization. For the minimization,\nevents that have reconstructed electron energies\nof less than 5 MeV are excluded,\nas they are\nfound to reduce pointing performance due to the\nrelatively large uncertainties in their energy and\n6 In principle residual detector response anisotropy can be\ntaken into account in the likelihood PDFs.\n\n19\n1.00\n0.75\n0.50\n0.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\nSN)\n0\n20\n40\n60\n80\n100\nElectron Energy (MeV)\nPeES(Ei, cos(\nSN))\n10\n2\n10\n1\n1.00\n0.75\n0.50\n0.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\nSN)\n0\n20\n40\n60\n80\n100\nElectron Energy (MeV)\nP eCC(Ei, cos(\nSN))\n10\n2\n10\n1\nFIG. 8. PDFs of eES and \u03bdeCC events. The eES PDF\ndemonstrates a high correlation between the supernova\nand primary electrons\u2019 direction increasing towards\nhigher electron energies. The \u03bdeCC PDF is mostly flat,\nas the correlation between primary electron and neutrino\ndirections is weak.\ndirection reconstruction. The minimization is done\nby a grid search.\nThe grid search provides the\nlikelihood function value for all directions in the\nsky, which is illustrated in a directional map. The\nreconstructed neutrino directions associated with a\ntypical supernova burst are shown in Fig. 10, and\nthe output of the reconstruction procedure is shown\nin Fig. 11. Two local minima are 180 degrees away\nfrom each other due to the remaining ambiguity in\ntrack direction.\nVI.\nPERFORMANCE OF\nRECONSTRUCTION ALGORITHM ON\nSUPERNOVA SIMULATIONS\nSupernova bursts are simulated to evaluate the\nperformance of the reconstruction algorithm. The\n1.00\n0.75\n0.50\n0.25\n0.00\n0.25\n0.50\n0.75\n1.00\ncos(\u03b8SN)\n10\n1\n100\np[cos(\u03b8SN)]\n0 MeV < Ee\n10 MeV\n10 MeV < Ee\n20 MeV\n20 MeV < Ee\n50 MeV\nEe > 50 MeV \nFIG. 9. Several bins for the PDF of the eES interaction\nin Figure 8, re-binned to 10 MeV / bin.\nThe relative\nmagnitude of the peak near cos \u03b8SN = 1 (the parallel\ndirection) increases as energy increases because brems\nflipping improves at high energies. The width of the true\ndirection peaks also decreases, indicating a decrease in\ndirectional variance.\nsimulation is carried out by randomly picking eES\nand \u03bdeCC events from a large pool of events with\nuniformly distributed neutrino directions.\nThe\nnumber of events selected per burst is based on\nthe expected number of interactions for a 10 kpc\nsupernova, as calculated by SNOwGLoBES (see\nTab. I). For each selected event, the reconstructed\ndirection is rotated such that all events correspond\nto the same neutrino direction.\nTo account for\nthe effect of the anisotropic direction reconstruction\nperformance,\nevents\nare\nonly\nselected\nif\ntheir\nneutrino direction lies within a cone of a 10 degree\nopening angle of the randomly selected supernova\ndirection.\nIn total, 10,000 supernova bursts are\nsimulated and reconstructed using only eES events,\nand a pointing resolution (as defined in the previous\nsection) of 3.4 degrees for a fiducial mass of 40 kton\n(four modules, full setup) and 6.6 degrees for one\nmodule of 10 kton is achieved.\nThe distribution\nof the truth-to-reconstruction angular difference for\nthe burst is shown in Fig. 12 for two different\nassumptions on event classification quality.\nIt is\nworth noting that only \u223c0.1% of the simulated\nbursts\u2019 reconstructed directions differed more than\n90 degrees from the supernova position thanks to\nthe brems flipping for both classification cases.\nThe reconstructed directions of poorly reconstructed\nbursts are very close to being anti-parallel to the\nsupernova direction.\nIn reality, the capability to distinguish between\neES and \u03bdeCC events, with the latter carrying poor\npointing information, needs to be considered. The\n\n20\n-150\u00b0 -120\u00b0\n-90\u00b0\n-60\u00b0\n-30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0\n120\u00b0\n150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\neCC\neES\nFIG. 10. An example directional map filled with the reconstructed electron directions for a simulated supernova\nburst, eES events carrying the directional information are marked in blue. Event statistics are shown for a core\ncollapse at a distance of 10 kpc, and 40 kton of fiducial mass in the detector.\n-150\u00b0-120\u00b0 -90\u00b0 -60\u00b0 -30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0 120\u00b0 150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\n1650\n1700\n1750\n1800\n1850\n1900\nNegative Log-likelihood\n0.68\n0.90\n0.99\nConfidence level\nFIG. 11. An example directional map filled with the negative log-likelihood values and confidence contours. This map\nis computed from the same burst shown as in Fig. 10. Reconstruction is done assuming the classification parameters\nof ceES\u2192eES = 0.86 and c\u03bdeCC\u2192eES = 0.04 and a successful direction reconstruction is achieved with the actual\nsupernova direction marked with a star in the figure.\nquality of a realistic event classifier can be quantified\nin the form of a confusion matrix:\nC =\n\u0014\nceES\u2192eES\nceES\u2192\u03bdeCC\nc\u03bdeCC\u2192eES c\u03bdeCC\u2192\u03bdeCC\n\u0015\n(5)\nThe elements of this matrix are expressed in\nthe form of cA\u2192B, which describes the portion of\nevents of interaction type A that are classified as\ninteraction type B. The matrix is normalized to be\nindependent of the expected number of events for\neach interaction. Assuming no loss of events due to\ndetector inefficiency, the rows of the matrix will sum\nto one. The worst-case scenario would correspond to\na confusion matrix with all of its elements being 1/2,\nwhich effectively represents a completely random\ngrouping of all events into two groups.\n\n21\n0.9800\n0.9825\n0.9850\n0.9875\n0.9900\n0.9925\n0.9950\n0.9975\n1.0000\ncos(\u03b8\nreco\n\u2212\ntr\u2212e\n)\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\nN)rmalized SN E.ent Distributi)n\nFidu ial Mass: 10 kt\n \nES\n\u2192\nES\n=\n0.86,\nc\nCC\n\u2192\nES\n=\n0.04; \u03c3\n=\n os(8.76\n\u2218\n)\nPerfect Classification, \u03c3\n=\n os(6.55\n\u2218\n)\n0.9800\n0.9825\n0.9850\n0.9875\n0.9900\n0.9925\n0.9950\n0.9975\n1.0000\ncos(\u03b8\nreco\n\u2212\n\u2212r.e\n)\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\n0.35\nNor(alized SN Eve)\u2212 Dis\u2212ri .\u2212io)\nFid.cial Mass: 40 k\u2212\nc\nES\n\u2192\nES\n=\n0.86,\nc\nCC\n\u2192\nES\n=\n0.04; \u03c3\n=\ncos(4.27\n\u2218\n)\nPerfect Classificatio), \u03c3\n=\ncos(3.29\n\u2218\n)\nFIG. 12. Distribution of the angular difference between\nthe reconstructed and true supernova direction, for\n10,000 simulated supernova bursts. The distribution is\nshown for both perfect event classification and for an\nassumed 4% misclassification of \u03bdeCC events as eES\nas described in [37].\nThe ranges to the right of the\nrespective colored dashed lines correspond to the 68%\nconfidence intervals.\nThe few bursts with a flipped\nreconstructed direction are excluded from the figure.\nThe top figure corresponds to 10 kton fiducial mass,\nwhile it is 40 kton for the bottom figure.\nIn adopting a more realistic classifier taking\ninto\naccount\nthe\nmisidentification\nof\nevents,\nthe\naforementioned\nreconstruction\nprocedure\nis\neffectively unchanged, except that the PDF p used\nin (4) no longer corresponds to peES,\nbut is\nrather a sum of peES and p\u03bdeCC, weighted by the\nexpected number of events from each interaction\nin the classification channel,\nwhich should be\nknown ahead of time.\nAs pointing information\nis primarily accessible from eES events, only the\neES classification channel is used for direction\nreconstruction.\nSubsequently, the only elements\nin the confusion matrix C that affect the pointing\nresolution are ceES\u2192eES and c\u03bdeCC\u2192eES. Figure 13\nshows the pointing resolution as a function of these\ntwo matrix elements.\nFor the worst-case scenario\n(where both elements are equal to 0.5), the pointing\nresolution is 102 degrees.\nWhile highly precise\nclassifiers would provide highly accurate pointing\nresults, even a weak classifier can yield a useful\npointing resolution.\nAt ceES\u2192eES\n= 0.6, only\n20% better than random selection, the pointing\nresolution reaches around 40 degrees,\nsignificant\nenough to determine the quadrant of the sky that\nthe supernova belongs to. An optimistic estimate of\na boosted-decision-tree-based classifier is established\nin [37] at ceES\u2192eES\n= 0.86 and c\u03bdeCC\u2192eES\n=\n0.04.\nWith this classifier, the pointing resolution\namounts to 4.3 degrees (8.7 degrees) for a fiducial\nmass of 40 kton (10 kton). The distribution of the\nreconstruction angle is compared to the perfect\nclassification case in Fig. 12.\nWhile this study\nprovides a rough estimation of the classification\ncapabilities,\nfurther validation work is required\nto understand the classification performance in\nthe presence of noise.\nFurthermore,\nbecause\nclassification performance likely depends on the\nenergy of the event, additional improvements in\npointing resolution could be made by leveraging\nenergy regions where the classifier performs best.\nMoreover, in a future fast online pipeline, real-\ntime channel tagging before the comparison of the\nreconstructed events to the PDF will likely improve\nthe overall performance as well.\nThe pointing resolution is shown as a function\nof the number of expected events in Fig. 14,\nalong with the corresponding progenitor distance,\ncalculated assuming the GKVM model.\nThe\npointing resolution is roughly proportional to the\nsupernova distance, and inversely proportional to\nthe square root of the number of expected events,\nas expected.\nThe supernova pointing resolution as a function of\nthe supernova position in the sky is also examined.\nFig. 15 shows the pointing resolution as a function of\nthe detector coordinates. As for the results shown in\nFig. 7, better pointing resolution can be seen closer\nto the \u00b1\u02c6z directions (with +\u02c6z being approximately\nthe beam direction).\nNote that due to the way\nsupernova bursts are simulated (as described at the\nbeginning of this section), the dependence of the\npointing resolution estimate is smeared around the\nincoming neutrino direction by the event selection\nradius of 10 degrees \u2013 but qualitatively, the variation\nin pointing resolution is of the order of a few\ndegrees.\nFig. 16 shows the pointing resolution in\nthe equatorial celestial coordinate system (RA/Dec),\nas a function of declination, averaged over right\nascension.\nThe figure also depicts the expected\ndeclination distribution for galactic supernovae to\n\n22\n0.2\n0.4\n0.6\n0.8\n1.0\nc\neES\n\u2192\neES\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nc\n\u03bd\ne\nCC\n\u2192\neES\nFiducial Mass: 10 kt\n0.005\n0.010\n0.050\n0.250\n0.250\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nSky fraction\n0.2\n0.4\n0.6\n0.8\n1.0\nc\neES\n\u2192\neES\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nc\n\u03bd\ne\nCC\n\u2192\neES\nFiducial Mass: 40 kt\n0.002\n0.005\n0.010\n0.050\n0.250\n0.0\n0.1\n0.2\n0.3\n0.4\nSky fraction\nFIG. 13.\nBurst pointing resolution as a function of\neES true positives (ceES\u2192eES) and \u03bdeCC false negatives\n(c\u03bdeCC\u2192eES). Results assuming the fiducial mass of a\nsingle far detector module (10 kton) and all four planned\nmodules (40 kton) are shown. For each pair of values,\n1000 supernova bursts are simulated to determine the\npointing resolution. Contour lines for various pointing\nresolution angles are also shown.\nillustrate the most likely directions for a supernova\nto occur.\nNotably, because the \u02c6z direction of the\ndetector is positioned at around \u22129\u25e6of declination,\nthe resolution is best around the same angle.\nVII.\nSUMMARY AND OUTLOOK\nAn\nanalysis\nframework\nfor\nreconstructing\nsupernova neutrino burst directions at DUNE is\ndescribed.\nBy reconstructing the eES and \u03bdeCC\nevents during a supernova burst, the supernova\ndirection can be determined from the correlation\nbetween the supernova neutrino and the outgoing\nprimary electron created in the interaction with\nthe LAr.\nThe dominant interaction channels are\n6\n8\n10\n12\n14\nSupernova Distance (kpc)\n1\n150\n1\n175\n1\n200\n1\n225\n1\n250\n1\n300\n1\n350\n1\n400\n1\n500\n1\n600\n1\n800\n1\n1200\n1/\nNeES\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\nSky Fraction\nceES\neES = 1.00, c\neCC\neES = 0.00\nceES\neES = 0.86, c\neCC\neES = 0.04\nFIG. 14.\nBurst pointing resolution as a function of\nthe number of detected eES events (NeES), as well as\nthe corresponding supernova distance. The event rates\nare calculated assuming the GKVM model at a given\ndistance and are for a fiducial volume of 40 kton.\n\u03bdeCC and eES, with only the latter containing\nsignificant accessible information on the neutrino\ndirection, but being an order of magnitude less\nfrequent than the former. Monte Carlo simulations\nin LArSoft were used to generate a data set of\nsupernova\nbursts\nto\nevaluate\nthe\nperformance\nof the reconstruction algorithm for the planned\nDUNE detector setup.\nFrom this data set, the\nenergy and direction of the primary electron were\nreconstructed.\nTo reduce head-tail ambiguities a\nhighly effective technique called brems flipping was\ndeveloped. Finally, the pointing resolution is derived\nfor ensembles of supernova burst events using a\nmaximum likelihood method.\nWith perfect event\nclassification of the two event types considered,\nthe pointing resolution is 3.4 degrees (6.6 degrees)\nwith 68% coverage for supernovae at a distance of\n10 kpc and an effective fiducial volume of 40 kton\n(10 kton). For a moderately optimistic classification\nperformance, incorrect classification of 4% \u03bdeCC\nevents as eES, the estimated pointing resolution is\n4.3 degrees (8.7 degrees) with 68% coverage.\nThe\nresults presented here represent an average over all\nsupernova directions in the sky.\nIn reality, there\nis a minor anisotropy in the burst reconstruction\ncapability of the LAr TPC, resulting in a variation\nof the order of a few degrees in resolution.\nA continued effort should be carried out to further\nimprove the current supernova pointing capabilities\nof DUNE. Prompt dissemination of directional\ninformation will be critical for multi-messenger\nastronomy, and efforts are underway to enable low-\nlatency pointing with DUNE. Furthermore, given\na core collapse at the most frequently expected\n\n23\n-150\u00b0\n-120\u00b0\n-90\u00b0\n-60\u00b0\n-30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0\n120\u00b0\n150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\nFiducial Mass: 10kt\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\n0.014\n0.016\nSky Fraction\n-150\u00b0\n-120\u00b0\n-90\u00b0\n-60\u00b0\n-30\u00b0\n0\u00b0\n30\u00b0\n60\u00b0\n90\u00b0\n120\u00b0\n150\u00b0\n-75\u00b0\n-60\u00b0\n-45\u00b0\n-30\u00b0\n-15\u00b0\n0\u00b0\n15\u00b0\n30\u00b0\n45\u00b0\n60\u00b0\n75\u00b0\nFiducial Mass: 40kt\n0.0005\n0.0010\n0.0015\n0.0020\n0.0025\n0.0030\nSky Fraction\nFIG. 15.\nBurst pointing resolution as a function of\nthe direction of the supernova, given in the detector\ncoordinate system (\u00b1\u02c6x is the drift direction, +\u02c6z is\napproximately the beam direction). \u03b8 (shown vertically)\nand \u03d5 (shown horizontally) are spherical coordinates in a\ncoordinate system for which \u03b8 = 90\u25e6corresponds to the\n+\u02c6z direction and \u03b8 = 0\u25e6, \u03d5 = 0\u25e6correspond to the +\u02c6x\ndirection.\nPointing resolution is given for the fiducial\nvolumes of 10 kton and 40 kton.\nPerfect classification\nbetween eES and \u03bdeCC events is assumed in these plots.\nNote that the local pointing resolution is smeared by the\nevent selection radius of 10 degrees.\ndistance from\nEarth\nfor a galactic supernova,\ndetection of supernova neutrino events can be\nexpected in multiple large-scale neutrino detectors.\nBy combining DUNE\u2019s data with events in other\ndetectors, one may take advantage of greater event\nstatistics as well as the strengths of different detector\ntechnologies, resulting in a noticeable improvement\nto the current pointing resolution.\nFurthermore,\nwe anticipate that steady improvements to pattern\nrecognition technologies, especially via machine-\nlearning techniques, will enhance the performance\nof next-generation particle track reconstruction and\nhead-tail disambiguation algorithms, allowing for\nadditional gains in pointing ability.\nExtended\ninvestigation of the eES/\u03bdeCC classification at\n80\n60\n40\n20\n0\n20\n40\n60\n80\nDeclination (deg)\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\n0.014\n0.016\n0.018\nSky Fraction\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\nSN distribution (A.U.)\nSky Fraction, 40 kton\nSky Fraction, 10 kton\nGalactic SN distribution\nFIG. 16. Burst pointing resolution as a function of the\nsupernova direction, shown as a function of declination.\nThe pointing resolution is averaged over right ascension.\nShown on a separate axis is the expected declination\ndistribution for galactic supernovae [38].\nDUNE is required, as this currently provides the\ngreatest uncertainty in the pointing resolution.\nFurthermore,\nsubdominant\ninteraction\nchannels\nshould be considered as well.\nAs a final note,\nlaboratory investigation of neutrino interactions\nin the few-tens-of-MeV range in argon will be\nessential to fully understand the detector directional\nresponse [39].\nACKNOWLEDGEMENTS\nThe ProtoDUNE-XX detector was constructed\nand operated on the CERN Neutrino Platform.\nWe gratefully acknowledge the support of the\nCERN management, and the CERN EP, BE, TE,\nEN and IT Departments for NP04/ProtoDUNE-\nSP. This document was prepared by the DUNE\ncollaboration using the resources of the Fermi\nNational Accelerator Laboratory (Fermilab), a U.S.\nDepartment of Energy, Office of Science, HEP User\nFacility.\nFermilab is managed by Fermi Research\nAlliance, LLC (FRA), acting under Contract No.\nDE-AC02-07CH11359.\nThis work was supported\nby CNPq, FAPERJ, FAPEG and FAPESP, Brazil;\nCFI, IPP and NSERC, Canada; CERN; M\u02c7SMT,\nCzech Republic;\nERDF, H2020-EU and MSCA,\nEuropean Union; CNRS/IN2P3 and CEA, France;\nINFN, Italy; FCT, Portugal; NRF, South Korea;\nCAM, Fundaci\u00b4on \u201cLa Caixa\u201d, Junta de Andaluc\u00b4\u0131a-\nFEDER, MICINN, and Xunta de Galicia, Spain;\nSERI and SNSF, Switzerland; T\u00a8UB\u02d9ITAK, Turkey;\nThe\nRoyal\nSociety\nand\nUKRI/STFC,\nUnited\nKingdom; DOE and NSF, United States of America.\n\n24\nThis research used resources of the National Energy\nResearch Scientific Computing Center (NERSC), a\nU.S. Department of Energy Office of Science User\nFacility operated under Contract No.\nDE-AC02-\n05CH11231.\n[1] R. 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Gardiner, Nuclear de-excitations in low-energy\ncharged-current \u03bde scattering on\n40Ar, Physical\nReview C 103, 044604 (2021).\n[32] N.\nVan\nDessel,\nA.\nNikolakopoulos,\nand\nN. Jachowicz, Lepton kinematics in low energy\nneutrino-Argon interactions, Phys. Rev. C 101,\n045502 (2020), arXiv:1912.10714 [nucl-th].\n[33] A.\nAbed\nAbud\net\nal.\n(DUNE),\nImpact\nof\ncross-section uncertainties on supernova neutrino\nspectral parameter fitting in the Deep Underground\nNeutrino Experiment, Phys. Rev. D 107, 112012\n(2023), arXiv:2303.17007 [hep-ex].\n[34] B. Abi, R. Acciarri, M. A. Acero, G. Adamov,\nD. Adams, M. Adinolfi, Z. Ahmad, J. Ahmed,\nT. Alion, S. A. Monsalve, et al., Volume IV. The\nDUNE far detector single-phase technology, Journal\nof Instrumentation 15 (08), T08010.\n[35] M. Antonello et al., Precise 3D track reconstruction\nalgorithm for the ICARUS T600 liquid argon\ntime\nprojection\nchamber\ndetector,\nAdv.\nHigh\nEnergy Phys. 2013, 260820 (2013), arXiv:1210.5089\n[physics.ins-det].\n[36] M.\nAntonello,\nB.\nBaibussinov,\nP.\nBenetti,\nE. Calligarich, N. Canci, S. Centro, A. Cesana,\nK. Cieslik, D. Cline, A. Cocco, et al., Precise 3d\ntrack reconstruction algorithm for the icarus t600\nliquid argon time projection chamber detector,\nAdvances in High Energy Physics 2013 (2013).\n[37] E. Conley, Using boosted decision trees to identify\nsupernova\nneutrino\ninteractions\nin\nDUNE,\nin\nNeutrino 2020 (Zenodo, 2020).\n[38] A. Mirizzi, G. Raffelt, and P. D. Serpico, Earth\nmatter effects in supernova neutrinos:\nOptimal\ndetector\nlocations,\nJournal\nof\nCosmology\nand\nAstroparticle Physics 2006 (05), 012.\n[39] J. Asaadi et al., Physics Opportunities in the ORNL\nSpallation Neutron Source Second Target Station\nEra, in 2022 Snowmass Summer Study\n(2022)\narXiv:2209.02883 [hep-ex].\nAppendix: Appendix\nThe details of the code implementation of the\ndescriped brems-flipping algorithm are shown in\nAlgorithm 1.\nAlgorithm 1: Brems Flipping\ninput : Two candidate e\u2212vertices with\npositions \u20d7r1, \u20d7r2 and momentum\ndirections \u02c6d1, \u02c6d2;\nSet of secondary particle vertex\npositions {\u20d7rd}\noutput: Reconstructed e\u2212direction.\nbegin\nSumCos1, SumCos2 \u21900;\nfor i \u21901 to 2 do\nfor \u20d7r \u2208{\u20d7rd} do\nSumCosi \u2190SumCosi +\n\u02c6\ndi\u00b7(\u20d7r\u2212\u20d7ri)\n|\u20d7r\u2212\u20d7ri|\nend\nend\nif SumCos1 > SumCos2 then\nreturn \u02c6d1\nelse\nreturn \u02c6d2\nend\nend\n", "Search for subsolar-mass black hole binaries in the second\npart of Advanced LIGO\u2019s and Advanced Virgo\u2019s third\nobserving run\nR. Abbott1 , H. Abe2 , F. Acernese3,4 , K. Ackley\n5 ,\nS. Adhicary6 , N. Adhikari\n7 , R. X. Adhikari\n1 ,\nV. K. Adkins8 , V. B. Adya9 , C. Affeldt10,11 ,\nD. Agarwal12 , M. Agathos\n13,14 , O. D. Aguiar\n15 ,\nL. Aiello\n16 , A. Ain17 , P. Ajith\n18 ,\nT. Akutsu\n19,20 , S. Albanesi21,22 , R. A. Alfaidi23 ,\nC. All\u00e9n\u00e924 , A. Allocca\n25,4 , P. A. Altin\n9 ,\nA. Amato\n26,27 , S. Anand1 , A. Ananyeva1 ,\nS. B. Anderson\n1 , W. G. Anderson\n1 , M. Ando28,29 ,\nT. Andrade30 , N. Andres\n24 , M. Andr\u00e9s-Carcasona\n31 ,\nT. Andri\u0107\n32 , S. Ansoldi33,34 , J. M. Antelis\n35 ,\nS. Antier\n36,37 , T. Apostolatos38 , E. Z. Appavuravther39,40 ,\nS. Appert1 , S. K. Apple41 , K. Arai\n1 ,\nA. Araya\n42 , M. C. Araya\n1 , J. S. Areeda\n43 ,\nM. Ar\u00e8ne44 , N. Aritomi\n19 , N. Arnaud\n45,46 ,\nM. Arogeti47 , S. M. Aronson8 , K. G. Arun\n48 ,\nH. Asada\n49 , G. Ashton\n50 , Y. Aso\n51,52 ,\nM. Assiduo53,54 , S. Assis de Souza Melo46 , S. M. Aston55 ,\nP. Astone\n56 , F. Aubin\n54 , K. AultONeal\n35 ,\nS. Babak\n44 , F. Badaracco\n57 , C. Badger58 ,\nS. Bae59 , Y. Bae60 , S. Bagnasco\n22 ,\nY. Bai1 , J. G. Baier61 , J. Baird44 ,\nR. Bajpai\n62 , T. Baka63 , M. Ball64 ,\nG. Ballardin46 , S. W. Ballmer65 , G. Baltus\n66 ,\nS. Banagiri\n67 , B. Banerjee\n32 , D. Bankar\n12 ,\nJ. C. Barayoga1 , B. C. Barish1 , D. Barker68 ,\nP. Barneo\n30 , F. Barone\n69,4 , B. Barr\n23 ,\nL. Barsotti\n70 , M. Barsuglia\n44 , D. Barta\n71 ,\nJ. Bartlett68 , M. A. Barton\n23 , I. Bartos72 ,\nS. Basak18 , R. Bassiri\n73 , A. Basti74,17 ,\nM. Bawaj\n39,75 , J. C. Bayley\n23 , M. Bazzan76,77 ,\nB. B\u00e9csy\n78 , V. M. Bedakihale79 , F. Beirnaert\n80 ,\nM. Bejger\n81 , I. Belahcene45 , A. S. Bell\n23 ,\nV. Benedetto82 , D. Beniwal83 , W. Benoit\n84 ,\nJ. D. Bentley\n85 , M. BenYaala86 , S. Bera87 ,\nM. Berbel\n88 , F. Bergamin10,11 , B. K. Berger\n73 ,\nS. Bernuzzi\n14 , M. Beroiz\n1 , C. P. L. Berry\n23 ,\nD. Bersanetti\n89 , A. Bertolini27 , J. Betzwieser\n55 ,\nD. Beveridge\n90 , R. Bhandare91 , A. V. Bhandari12 ,\narXiv:2212.01477v2 [astro-ph.HE] 26 Jan 2024\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL1\nU. Bhardwaj\n37,27 , R. Bhatt1 , D. Bhattacharjee\n61,92 ,\nS. Bhaumik\n72 , A. Bianchi27,93 , I. A. Bilenko94 ,\nM. Bilicki\n95 , G. Billingsley\n1 , S. Bini96,97 ,\nO. Birnholtz\n98 , S. Biscans1,70 , M. Bischi53,54 ,\nS. Biscoveanu\n70 , A. Bisht10,11 , B. Biswas\n12 ,\nM. Bitossi46,17 , M.-A. Bizouard\n36 , J. K. Blackburn\n1 ,\nC. D. Blair90,55 , D. G. Blair90 , R. M. Blair68 ,\nF. Bobba99,100 , N. Bode\n10,11 , M. Bo\u00ebr36 ,\nG. Bogaert36 , M. Boldrini101,56 , G. N. Bolingbroke\n83 ,\nL. D. Bonavena76 , R. Bondarescu\n30 , F. Bondu102 ,\nE. Bonilla\n73 , R. Bonnand\n24 , P. Booker10,11 ,\nR. Bork1 , V. Boschi\n17 , N. Bose103 ,\nS. Bose12 , V. Bossilkov90 , V. Boudart\n66 ,\nY. Bouffanais76,77 , A. Bozzi46 , C. Bradaschia17 ,\nP. R. Brady\n7 , A. Bramley55 , A. Branch55 ,\nM. Branchesi\n32,104 , J. E. Brau\n64 , M. Breschi\n14 ,\nT. Briant\n105 , J. H. Briggs23 , A. Brillet36 ,\nM. Brinkmann10,11 , P. Brockill7 , A. F. Brooks\n1 ,\nJ. Brooks46 , D. D. Brown83 , S. Brunett1 ,\nG. Bruno57 , R. Bruntz\n106 , J. Bryant107 ,\nF. Bucci54 , J. Buchanan106 , T. Bulik108 ,\nH. J. Bulten27 , A. Buonanno\n109,110 , K. Burtnyk68 ,\nR. Buscicchio\n107,111,112 , D. Buskulic24 , C. Buy\n113 ,\nR. L. Byer73 , G. S. Cabourn Davies\n114 , G. Cabras\n33,34 ,\nR. Cabrita\n57 , L. Cadonati\n47 , G. Cagnoli\n115 ,\nC. Cahillane68 , J. Calder\u00f3n Bustillo116 , J. D. Callaghan23 ,\nT. A. Callister117,118 , E. Calloni25,4 , J. B. Camp119 ,\nM. Canepa120,89 , G. Caneva\n31 , M. Cannavacciuolo99 ,\nK. C. Cannon\n29 , H. Cao83 , Z. Cao\n121 ,\nL. A. Capistran122 , E. Capocasa\n44,19 , E. Capote65 ,\nG. Carapella99,100 , F. Carbognani46 , M. Carlassara10,11 ,\nJ. B. Carlin\n123 , M. Carpinelli124,125,46 , G. Carrillo64 ,\nJ. J. Carter\n10,11 , G. Carullo\n74,17 , J. Casanueva Diaz46 ,\nC. Casentini126,127 , G. Castaldi128 , S. Caudill27,63 ,\nM. Cavagli\u00e0\n92 , F. Cavalier\n45 , R. Cavalieri\n46 ,\nG. Cella\n17 , P. Cerd\u00e1-Dur\u00e1n129 , E. Cesarini\n127 ,\nW. Chaibi36 , W. Chakalis117,118 , S. Chalathadka Subrahmanya\n85 ,\nE. Champion\n130 , C.-H. Chan131 , C. Chan29 ,\nC. L. Chan\n132 , K. Chan132 , M. Chan133 ,\nK. Chandra103 , I. P. Chang131 , W. Chang131 ,\nP. Chanial\n46,44 , S. Chao131 , C. Chapman-Bird\n23 ,\nP. Charlton\n134 , E. Chassande-Mottin\n44 , C. Chatterjee\n90 ,\nDebarati Chatterjee\n12 , Deep Chatterjee\n7 , M. Chaturvedi91 ,\nS. Chaty\n44 , K. Chatziioannou\n1 , C. Chen\n135,131 ,\nD. Chen\n51 , H. Y. Chen\n70 , J. Chen\n70 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL2\nLVK\nK. Chen136 , X. Chen90 , Y.-B. Chen137 ,\nY.-R. Chen131 , Y. Chen137 , H. Cheng72 ,\nP. Chessa\n74,17 , H. Y. Cheung132 , H. Y. Chia72 ,\nF. Chiadini\n138,100 , C-Y. Chiang139 , G. Chiarini77 ,\nR. Chierici140 , A. Chincarini\n89 , M. L. Chiofalo74,17 ,\nA. Chiummo\n46 , R. K. Choudhary90 , S. Choudhary\n12 ,\nN. Christensen\n36 , Q. Chu90 , Y-K. Chu139 ,\nS. S. Y. Chua\n9 , K. W. Chung58 , G. Ciani\n76,77 ,\nP. Ciecielag81 , M. Cie\u015blar\n81 , M. Cifaldi126,127 ,\nA. A. Ciobanu83 , R. Ciolfi\n141,77 , F. Clara68 ,\nJ. A. Clark\n1 , T. A. Clarke5 , P. Clearwater142 ,\nS. Clesse143 , F. Cleva36 , E. Coccia32,104 ,\nE. Codazzo\n32 , P.-F. Cohadon\n105 , D. E. Cohen\n45 ,\nM. Colleoni\n87 , C. G. Collette144 , A. Colombo\n111,112 ,\nM. Colpi111,112 , C. M. Compton68 , L. Conti\n77 ,\nS. J. Cooper107 , P. Corban55 , T. R. Corbitt\n8 ,\nI. Cordero-Carri\u00f3n\n145 , S. Corezzi75,39 , N. J. Cornish\n78 ,\nA. Corsi\n146 , S. Cortese\n46 , A. C. Coschizza147 ,\nR. Cotesta110 , R. Cottingham55 , M. W. Coughlin\n84 ,\nJ.-P. Coulon36 , S. T. Countryman148 , B. Cousins\n6 ,\nP. Couvares\n1 , D. M. Coward90 , M. J. Cowart55 ,\nD. C. Coyne\n1 , R. Coyne\n149 , K. Craig86 ,\nJ. D. E. Creighton\n7 , T. D. Creighton150 , A. W. Criswell\n84 ,\nM. Croquette\n105 , S. G. Crowder151 , J. R. Cudell\n66 ,\nT. J. Cullen8 , A. Cumming23 , R. Cummings\n23 ,\nE. Cuoco46,152,17 , M. Cury\u0142o108 , P. Dabadie115 ,\nT. Dal Canton\n45 , S. Dall\u2019Osso\n56 , G. D\u00e1lya\n80,153 ,\nA. Dana73 , B. D\u2019Angelo\n120,89 , S. Danilishin\n26,27 ,\nS. D\u2019Antonio127 , K. Danzmann10,11 , C. Darsow-Fromm\n85 ,\nA. Dasgupta79 , L. E. H. Datrier23 , Sayantani Datta\n48 ,\nV. Dattilo46 , I. Dave91 , M. Davier45 ,\nD. Davis\n1 , M. C. Davis\n154 , E. J. Daw\n155 ,\nM. Dax\n110 , D. DeBra\u221773 , M. Deenadayalan12 ,\nJ. Degallaix\n156 , M. De Laurentis25,4 , S. Del\u00e9glise\n105 ,\nV. Del Favero\n130 , F. De Lillo\n57 , N. De Lillo23 ,\nD. Dell\u2019Aquila\n124,125 , W. Del Pozzo74,17 , F. De Matteis126,127 ,\nV. D\u2019Emilio16 , N. Demos70 , T. Dent\n116 ,\nA. Depasse\n57 , R. De Pietri\n157,158 , R. De Rosa\n25,4 ,\nC. De Rossi46 , R. DeSalvo\n128,159 , R. De Simone138 ,\nS. Dhurandhar12 , R. Diab72 , M. C. D\u00edaz\n150 ,\nN. A. Didio65 , T. Dietrich\n110 , L. Di Fiore4 ,\nC. Di Fronzo107 , C. Di Giorgio\n99,100 , F. Di Giovanni\n129 ,\nM. Di Giovanni32 , T. Di Girolamo\n25,4 , D. Diksha27,26 ,\nA. Di Lieto\n74,17 , A. Di Michele\n75 , S. Di Pace\n101,56 ,\nI. Di Palma\n101,56 , F. Di Renzo\n74,17 , A. K. Divakarla72 ,\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL3\nA. Dmitriev\n107 , Z. Doctor\n67 , P. P. Doleva106 ,\nL. Donahue160 , L. D\u2019Onofrio\n25,4 , F. Donovan70 ,\nK. L. Dooley16 , T. Dooney63 , S. Doravari\n12 ,\nO. Dorosh161 , M. Drago\n101,56 , J. C. Driggers\n68 ,\nY. Drori1 , J.-G. Ducoin162,44 , L. Dunn\n123 ,\nU. Dupletsa32 , O. Durante99,100 , D. D\u2019Urso\n124,125 ,\nP.-A. Duverne45 , S. E. Dwyer68 , C. Eassa68 ,\nP. J. Easter5 , M. Ebersold163 , T. Eckhardt\n85 ,\nG. Eddolls\n23 , B. Edelman\n64 , T. B. Edo1 ,\nO. Edy\n114 , A. Effler\n55 , S. Eguchi\n133 ,\nJ. Eichholz\n9 , S. S. Eikenberry72 , M. Eisenmann24,19 ,\nR. A. Eisenstein70 , A. Ejlli\n16 , E. Engelby43 ,\nY. Enomoto\n28 , L. Errico25,4 , R. C. Essick\n164 ,\nH. Estell\u00e9s87 , D. Estevez\n165 , T. Etzel1 ,\nM. Evans\n70 , T. M. Evans55 , T. Evstafyeva13 ,\nB. E. Ewing6 , F. Fabrizi\n53,54 , F. Faedi54 ,\nV. Fafone\n126,127,32 , H. Fair65 , S. Fairhurst16 ,\nP. C. Fan\n160 , A. M. Farah\n166 , B. Farr\n64 ,\nW. M. Farr\n117,118 , G. Favaro\n76 , M. Favata\n167 ,\nM. Fays\n66 , M. Fazio168 , J. Feicht1 ,\nM. M. Fejer73 , E. Fenyvesi\n71,169 , D. L. Ferguson\n170 ,\nA. Fernandez-Galiana\n70 , I. Ferrante\n74,17 , T. A. Ferreira15 ,\nF. Fidecaro\n74,17 , P. Figura\n108 , A. Fiori\n17,74 ,\nI. Fiori\n46 , M. Fishbach\n67 , R. P. Fisher106 ,\nR. Fittipaldi171,100 , V. Fiumara172,100 , R. Flaminio24,19 ,\nE. Floden84 , H. K. Fong29 , J. A. Font\n129,173 ,\nB. Fornal\n159 , P. W. F. Forsyth9 , A. Franke85 ,\nS. Frasca101,56 , F. Frasconi\n17 , J. P. Freed35 ,\nZ. Frei\n153 , A. Freise\n27,93 , O. Freitas174 ,\nR. Frey\n64 , P. Fritschel70 , V. V. Frolov55 ,\nG. G. Fronz\u00e9\n22 , Y. Fujii175 , Y. Fujikawa176 ,\nY. Fujimoto177 , P. Fulda72 , M. Fyffe55 ,\nH. A. Gabbard23 , W. E. Gabella178 , B. U. Gadre\n110,63 ,\nJ. R. Gair\n110 , J. Gais132 , S. Galaudage5 ,\nR. Gamba14 , D. Ganapathy\n70 , A. Ganguly\n12 ,\nD.-F. Gao\n179 , D. Gao73 , S. G. Gaonkar12 ,\nB. Garaventa\n89,120 , J. Garcia-Bellido\n180 , C. Garc\u00eda-N\u00fa\u00f1ez181 ,\nC. Garc\u00eda-Quir\u00f3s87,10,11 , K. A. Gardner147 , J. Gargiulo 46 ,\nF. Garufi\n25,4 , C. Gasbarra\n126,127 , B. Gateley68 ,\nV. Gayathri\n72 , G.-G. Ge\n179 , G. Gemme\n89 ,\nA. Gennai\n17 , J. George91 , O. Gerberding\n85 ,\nL. Gergely\n182 , S. Ghonge\n47 , Abhirup Ghosh\n110 ,\nArchisman Ghosh\n80 , Shaon Ghosh\n167 , Shrobana Ghosh16 ,\nTathagata Ghosh\n12 , L. Giacoppo101,56 , J. A. Giaime\n8,55 ,\nK. D. Giardina55 , D. R. Gibson181 , C. Gier86 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL4\nLVK\nP. Giri\n17,74 , F. Gissi82 , S. Gkaitatzis\n46 ,\nJ. Glanzer8 , A. E. Gleckl43 , F. G. Godoy47 ,\nP. Godwin6 , E. Goetz\n147 , R. Goetz\n72 ,\nJ. Golomb1 , B. Goncharov\n32 , G. Gonz\u00e1lez\n8 ,\nM. Gosselin46 , R. Gouaty\n24 , D. W. Gould9 ,\nS. Goyal18 , B. Grace9 , A. Grado\n183,4 ,\nV. Graham23 , M. Granata\n156 , V. Granata\n99 ,\nS. Gras70 , P. Grassia1 , C. Gray68 ,\nR. Gray\n184 , G. Greco39 , A. C. Green\n72 ,\nR. Green16 , A. M. Gretarsson35 , E. M. Gretarsson35 ,\nD. Griffith1 , W. L. Griffiths\n16 , H. L. Griggs\n47 ,\nG. Grignani75,39 , A. Grimaldi\n96,97 , S. J. Grimm32,104 ,\nH. Grote\n16 , S. Grunewald110 , A. S. Gruson43 ,\nD. Guerra\n129 , G. M. Guidi\n53,54 , A. R. Guimaraes8 ,\nH. K. Gulati79 , F. Gulminelli185 , A. M. Gunny70 ,\nH.-K. Guo\n159 , Y. Guo27 , Anchal Gupta1 ,\nAnuradha Gupta\n186 , P. Gupta27,63 , S. K. Gupta103 ,\nJ. Gurs85 , R. Gustafson187 , N. Gutierrez156 ,\nF. Guzman\n122 , S. Ha188 , I. P. W. Hadiputrawan136 ,\nL. Haegel\n44 , S. Haino139 , O. Halim\n34 ,\nE. D. Hall\n70 , E. Z. Hamilton163 , G. Hammond23 ,\nW.-B. Han\n189 , M. Haney\n163 , J. Hanks68 ,\nC. Hanna6 , M. D. Hannam16 , O. Hannuksela63,27 ,\nH. Hansen68 , J. Hanson55 , R. Harada190 ,\nT. Harder36 , K. Haris27,63 , J. Harms\n32,104 ,\nG. M. Harry\n41 , I. W. Harry\n114 , D. Hartwig\n85 ,\nK. Hasegawa191 , B. Haskell81 , C.-J. Haster\n70 ,\nJ. S. Hathaway130 , K. Hattori192 , K. Haughian\n23 ,\nH. Hayakawa193 , K. Hayama133 , F. J. Hayes23 ,\nJ. Healy\n130 , A. Heidmann\n105 , A. Heidt10,11 ,\nM. C. Heintze55 , J. Heinze\n10,11 , J. Heinzel70 ,\nH. Heitmann\n36 , F. Hellman\n194 , P. Hello45 ,\nA. F. Helmling-Cornell\n64 , G. Hemming\n46 , M. Hendry\n23 ,\nI. S. Heng23 , E. Hennes\n27 , J.-S. Hennig26,27 ,\nM. Hennig26,27 , C. Henshaw47 , A. G. Hernandez195 ,\nF. Hernandez Vivanco5 , M. Heurs\n10,11 , A. L. Hewitt\n196 ,\nS. Higginbotham16 , S. Hild26,27 , P. Hill86 ,\nY. Himemoto197 , A. S. Hines122 , N. Hirata19 ,\nC. Hirose176 , T-C. Ho136 , S. Hochheim10,11 ,\nD. Hofman156 , J. N. Hohmann85 , D. G. Holcomb\n154 ,\nN. A. Holland27,93 , I. J. Hollows\n155 , Z. J. Holmes\n83 ,\nK. Holt55 , D. E. Holz\n166 , Q. Hong131 ,\nJ. Hough23 , S. Hourihane1 , D. Howell117,118 ,\nE. J. Howell\n90 , C. G. Hoy\n16 , D. Hoyland107 ,\nA. Hreibi10,11 , B-H. Hsieh191 , H-F. Hsieh\n131 ,\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL5\nC. Hsiung135 , H-Y. Huang\n139 , P. Huang\n179 ,\nY-C. Huang\n131 , Y.-J. Huang\n139 , Y. Huang70 ,\nM. T. H\u00fcbner\n5 , A. D. Huddart198 , B. Hughey35 ,\nD. C. Y. Hui\n199 , V. Hui\n24 , S. Husa87 ,\nS. H. Huttner23 , R. Huxford6 , T. Huynh-Dinh55 ,\nJ. Hyland\n23 , G. A. Iandolo26 , S. Ide200 ,\nB. Idzkowski\n108 , A. Iess\n152,17 , K. Inayoshi\n201 ,\nY. Inoue136 , P. Iosif\n202 , J. Irwin\n23 ,\nIsh Gupta\n6 , M. Isi\n117,118 , K. Ito203 ,\nY. Itoh\n177,204 , B. R. Iyer\n18 , V. JaberianHamedan\n90 ,\nT. Jacqmin\n105 , P.-E. Jacquet\n105 , S. J. Jadhav205 ,\nS. P. Jadhav\n12 , T. Jain13 , A. L. James\n16 ,\nA. Z. Jan\n170 , K. Jani\n178 , J. Janquart63,27 ,\nK. Janssens\n206,36 , N. N. Janthalur205 , P. Jaranowski\n207 ,\nD. Jariwala72 , S. Jarov147 , R. Jaume\n87 ,\nA. C. Jenkins\n58 , K. Jenner83 , C. Jeon208 ,\nW. Jia70 , J. Jiang\n72 , H.-B. Jin\n209,210 ,\nG. R. Johns106 , R. Johnston23 , N. Johny10,11 ,\nA. W. Jones\n90 , D. I. Jones211 , P. Jones107 ,\nR. Jones23 , P. Joshi6 , L. Ju\n90 ,\nK. Jung188 , P. Jung\n60 , J. Junker\n10,11 ,\nV. Juste165 , K. Kaihotsu203 , T. Kajita\n212 ,\nM. Kakizaki\n213 , C. Kalaghatgi63,27,214 , V. Kalogera\n67 ,\nB. Kamai1 , M. Kamiizumi\n193 , N. Kanda\n177,204 ,\nS. Kandhasamy\n12 , G. Kang\n215 , J. B. Kanner1 ,\nY. Kao131 , S. J. Kapadia18 , D. P. Kapasi\n9 ,\nS. Karat1 , C. Karathanasis\n31 , S. Karki\n92 ,\nR. Kashyap6 , M. Kasprzack\n1 , W. Kastaun10,11 ,\nT. Kato191 , S. Katsanevas\n46 , E. Katsavounidis70 ,\nW. Katzman55 , T. Kaur90 , K. Kawabe68 ,\nK. Kawaguchi\n191 , F. K\u00e9f\u00e9lian36 , D. Keitel\n87 ,\nJ. S. Key\n216 , S. Khadka73 , F. Y. Khalili\n94 ,\nS. Khan\n16 , T. Khanam146 , E. A. Khazanov217 ,\nN. Khetan32,104 , M. Khursheed91 , N. Kijbunchoo\n9 ,\nC. Kim\n208 , J. C. Kim218 , J. Kim\n219 ,\nK. Kim\n208 , P. Kim220 , W. S. Kim60 ,\nY.-M. Kim\n188 , C. Kimball67 , N. Kimura193 ,\nB. King221 , M. Kinley-Hanlon\n23 , R. Kirchhoff\n10,11 ,\nJ. S. Kissel\n68 , S. Klimenko72 , T. Klinger16 ,\nA. M. Knee\n147 , N. Knust10,11 , Y. Kobayashi177 ,\nP. Koch10,11 , S. M. Koehlenbeck\n10,11 , G. Koekoek27,26 ,\nK. Kohri222 , K. Kokeyama\n16 , S. Koley\n32 ,\nP. Kolitsidou\n16 , M. Kolstein\n31 , V. Kondrashov1 ,\nA. K. H. Kong\n131 , A. Kontos\n221 , M. Korobko\n85 ,\nR. V. Kossak10,11 , M. Kovalam90 , N. Koyama176 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL6\nLVK\nD. B. Kozak1 , C. Kozakai\n51 , L. Kranzhoff10,11 ,\nV. Kringel10,11 , N. V. Krishnendu\n10,11 , A. Kr\u00f3lak\n223,161 ,\nG. Kuehn10,11 , P. Kuijer\n27 , S. Kulkarni\n186 ,\nA. Kumar205 , Praveen Kumar\n116 , Prayush Kumar\n18 ,\nRahul Kumar68 , Rakesh Kumar79 , J. Kume29 ,\nK. Kuns\n70 , Y. Kuromiya203 , S. Kuroyanagi\n224,225 ,\nS. Kuwahara190 , K. Kwak\n188 , G. Lacaille23 ,\nP. Lagabbe24 , D. Laghi\n113 , E. Lalande226 ,\nM. Lalleman206 , A. Lamberts36,227 , M. Landry68 ,\nB. B. Lane70 , R. N. Lang\n70 , J. Lange170 ,\nB. Lantz\n73 , I. La Rosa24 , A. Lartaux-Vollard\n45 ,\nP. D. Lasky\n5 , J. Lawrence146 , M. Laxen\n55 ,\nA. Lazzarini\n1 , C. Lazzaro76,77 , P. Leaci\n101,56 ,\nS. Leavey\n10,11 , S. LeBohec159 , Y. K. Lecoeuche\n147 ,\nE. Lee191 , H. M. Lee\n228 , H. W. Lee\n218 ,\nK. Lee\n220 , R. Lee\n131 , I. N. Legred1 ,\nJ. Lehmann10,11 , A. Lema\u00eetre229 , M. Lenti\n54,230 ,\nM. Leonardi\n19 , E. Leonova\n37 , N. Leroy\n45 ,\nN. Letendre24 , C. Levesque226 , Y. Levin5 ,\nJ. N. Leviton187 , K. Leyde44 , A. K. Y. Li1 ,\nB. Li131 , K. L. Li\n231 , P. Li232 ,\nT. G. F. Li132 , X. Li\n137 , C-Y. Lin\n233 ,\nE. T. Lin\n131 , F-K. Lin139 , F-L. Lin\n234 ,\nH. L. Lin\n136 , L. C.-C. Lin\n231 , F. Linde214,27 ,\nS. D. Linker128,195 , T. B. Littenberg235 , G. C. Liu\n135 ,\nJ. Liu\n90 , X. Liu7 , F. Llamas150 ,\nR. K. L. Lo\n1 , T. Lo131 , L. T. London37,70 ,\nA. Longo\n236 , D. Lopez163 , M. Lopez Portilla63 ,\nM. Lorenzini\n126,127 , V. Loriette237 , M. Lormand55 ,\nG. Losurdo\n17 , T. P. Lott47 , J. D. Lough\n10,11 ,\nC. O. Lousto\n130 , G. Lovelace43 , M. J. Lowry106 ,\nJ. F. Lucaccioni61 , H. L\u00fcck10,11 , D. Lumaca\n126,127 ,\nA. P. Lundgren114 , Y. Lung132 , L.-W. Luo\n139 ,\nA. W. Lussier\n226 , J. E. Lynam106 , M. Ma\u2019arif136 ,\nR. Macas\n114 , M. MacInnis70 , D. M. Macleod\n16 ,\nI. A. O. MacMillan\n1 , A. Macquet\n31,36 , I. Maga\u00f1a Hernandez7 ,\nC. Magazz\u00f9\n17 , R. M. Magee\n1 , R. Maggiore\n107,27,93 ,\nM. Magnozzi\n89,120 , S. Mahesh238 , E. Majorana101,56 ,\nC. N. Makarem1 , I. Maksimovic237 , S. Maliakal1 ,\nA. Malik91 , N. Man36 , V. Mandic\n84 ,\nV. Mangano\n101,56 , B. R. Mannix64 , G. L. Mansell\n65,68,70 ,\nG. Mansingh41 , M. Manske\n7 , M. Mantovani\n46 ,\nM. Mapelli\n76,77 , F. Marchesoni40,39,239 , D. Mar\u00edn Pina\n30 ,\nF. Marion\n24 , Z. Mark137 , S. M\u00e1rka\n148 ,\nZ. M\u00e1rka\n148 , C. Markakis\n184 , A. S. Markosyan73 ,\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL7\nA. Markowitz1 , E. Maros1 , A. Marquina145 ,\nS. Marsat\n113 , F. Martelli53,54 , I. W. Martin\n23 ,\nR. M. Martin167 , M. Martinez31 , V. A. Martinez72 ,\nV. Martinez\n115 , K. Martinovic58 , D. V. Martynov107 ,\nE. J. Marx70 , H. Masalehdan\n85 , K. Mason70 ,\nA. Masserot24 , M. Masso-Reid\n23 , S. Mastrogiovanni\n44,36 ,\nA. Matas110 , M. Mateu-Lucena\n87 , M. Matiushechkina\n10,11 ,\nN. Mavalvala\n70 , J. J. McCann90 , R. McCarthy68 ,\nD. E. McClelland\n9 , P. K. McClincy6 , S. McCormick55 ,\nL. McCuller\n1,70 , G. I. McGhee23 , J. McGinn23 ,\nS. C. McGuire55 , C. McIsaac114 , J. McIver\n147 ,\nA. McLeod\n90 , T. McRae9 , S. T. McWilliams238 ,\nD. Meacher\n7 , M. Mehmet\n10,11 , A. K. Mehta110 ,\nQ. Meijer63 , A. Melatos123 , G. Mendell68 ,\nA. Menendez-Vazquez\n31 , C. S. Menoni\n168 , R. A. Mercer\n7 ,\nL. Mereni156 , K. Merfeld64 , E. L. Merilh55 ,\nJ. D. Merritt64 , M. Merzougui36 , C. Messenger\n23 ,\nC. Messick70 , P. M. Meyers\n137 , F. Meylahn\n10,11 ,\nA. Mhaske12 , A. Miani\n96,97 , H. Miao240 ,\nI. Michaloliakos\n72 , C. Michel\n156 , Y. Michimura\n28 ,\nH. Middleton\n123 , D. P. Mihaylov\n110 , A. Miller195 ,\nA. L. Miller57 , B. Miller37,27 , M. Millhouse123 ,\nJ. C. Mills16 , E. Milotti\n241,34 , Y. Minenkov127 ,\nN. Mio242 , Ll. M. Mir31 , M. Miravet-Ten\u00e9s\n129 ,\nA. Mishkin72 , C. Mishra243 , T. Mishra\n72 ,\nT. Mistry155 , A. L. Mitchell27,93 , S. Mitra\n12 ,\nV. P. Mitrofanov\n94 , G. Mitselmakher\n72 , R. Mittleman70 ,\nO. Miyakawa\n193 , K. Miyo\n193 , S. Miyoki\n193 ,\nGeoffrey Mo\n70 , L. M. Modafferi\n87 , E. Moguel61 ,\nK. Mogushi92 , S. R. P. Mohapatra70 , S. R. Mohite\n7 ,\nM. Molina-Ruiz\n194 , C. Mondal185 , M. Mondin195 ,\nM. Montani53,54 , C. J. Moore107 , J. Moragues\n87 ,\nD. Moraru68 , F. Morawski81 , A. More\n12 ,\nS. More\n12 , C. Moreno\n35 , G. Moreno68 ,\nY. Mori203 , S. Morisaki\n7 , N. Morisue177 ,\nY. Moriwaki213 , G. Morras\n180 , B. Mours\n165 ,\nC. M. Mow-Lowry\n27,93 , S. Mozzon\n114 , F. Muciaccia101,56 ,\nD. Mukherjee\n235 , Soma Mukherjee150 , Subroto Mukherjee79 ,\nSuvodip Mukherjee\n164,37 , N. Mukund\n10,11 , A. Mullavey55 ,\nJ. Munch83 , E. A. Mu\u00f1iz\n65 , P. G. Murray\n23 ,\nS. Muusse83 , S. L. Nadji10,11 , K. Nagano\n244 ,\nA. Nagar22,245 , T. Nagar5 , K. Nakamura\n19 ,\nH. Nakano\n246 , M. Nakano55,191 , Y. Nakayama203 ,\nV. Napolano46 , I. Nardecchia\n126,127 , T. Narikawa191 ,\nH. Narola63 , L. Naticchioni\n56 , R. K. Nayak\n247 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL8\nLVK\nB. F. Neil90 , J. Neilson82,100 , A. Nelson122 ,\nT. J. N. Nelson55 , M. Nery10,11 , P. Neubauer61 ,\nA. Neunzert216 , K. Y. Ng70 , S. W. S. Ng\n83 ,\nC. Nguyen\n44,248 , P. Nguyen64 , T. Nguyen70 ,\nL. Nguyen Quynh\n249 , J. Ni84 , W.-T. Ni\n209,179,131 ,\nS. A. Nichols8 , G. Nieradka81 , T. Nishimoto191 ,\nA. Nishizawa\n29 , S. Nissanke37,27 , E. Nitoglia\n140 ,\nW. Niu6 , F. Nocera46 , M. Norman16 ,\nC. North16 , J. Notte167 , J. Novak\n250,251,252,248,253 ,\nJ. F. Nu\u00f1o Siles\n180 , S. Nozaki192 , G. Nurbek150 ,\nL. K. Nuttall\n114 , Y. Obayashi\n191 , J. Oberling68 ,\nB. D. O\u2019Brien72 , J. O\u2019Dell198 , E. Oelker\n23 ,\nM. Oertel\n250,251,252,248,253 , W. Ogaki191 , G. Oganesyan32,104 ,\nJ. J. Oh\n60 , K. Oh\n199 , S. H. Oh\n60 ,\nT. O\u2019Hanlon55 , M. Ohashi\n193 , T. Ohashi177 ,\nM. Ohkawa\n176 , F. Ohme\n10,11 , H. Ohta29 ,\nY. Okutani200 , R. Oliveri\n254 , C. Olivetto250 ,\nK. Oohara\n191,255 , R. Oram55 , B. O\u2019Reilly\n55 ,\nR. G. Ormiston84 , N. D. Ormsby106 , M. Orselli\n39,75 ,\nR. O\u2019Shaughnessy\n130 , E. O\u2019Shea\n256 , S. Oshino\n193 ,\nS. Ossokine\n110 , C. Osthelder1 , S. Otabe2 ,\nD. J. Ottaway\n83 , H. Overmier55 , A. E. Pace6 ,\nG. Pagano74,17 , R. Pagano8 , G. Pagliaroli32,104 ,\nA. Pai103 , S. A. Pai91 , S. Pal247 ,\nJ. R. Palamos64 , O. Palashov217 , C. Palomba\n56 ,\nK.-C. Pan\n131 , P. K. Panda205 , P. T. H. Pang27,63 ,\nF. Pannarale\n101,56 , B. C. Pant91 , F. H. Panther90 ,\nF. Paoletti\n17 , A. Paoli46 , A. Paolone56,257 ,\nG. Pappas202 , A. Parisi\n17,152,135 , J. Park\n258 ,\nW. Parker\n55 , D. Pascucci\n80 , A. Pasqualetti46 ,\nR. Passaquieti\n74,17 , D. Passuello17 , M. Patel106 ,\nN. R. Patel68 , M. Pathak83 , B. Patricelli\n74,17 ,\nA. S. Patron8 , S. Paul\n64 , E. Payne\n1 ,\nM. Pedraza1 , R. Pedurand100 , R. Pegna\n17,74 ,\nM. Pegoraro77 , A. Pele55 , F. E. Pe\u00f1a Arellano\n193 ,\nS. Penano73 , S. Penn\n259 , A. Perego96,97 ,\nA. Pereira115 , T. Pereira\n260 , C. J. Perez68 ,\nC. P\u00e9rigois\n141 , C. C. Perkins72 , A. Perreca\n96,97 ,\nS. Perri\u00e8s140 , J. W. Perry27,93 , D. Pesios202 ,\nJ. Petermann\n85 , H. P. Pfeiffer\n110 , H. Pham55 ,\nK. A. Pham\n84 , K. S. Phukon\n27,214 , H. Phurailatpam132 ,\nO. J. Piccinni\n56,31 , M. Pichot\n36 , M. Piendibene74,17 ,\nF. Piergiovanni53,54 , L. Pierini\n101,56 , G. Pierra140 ,\nV. Pierro\n82,100 , G. Pillant46 , M. Pillas45 ,\nF. Pilo\n17 , L. Pinard156 , C. Pineda-Bosque195 ,\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL9\nI. M. Pinto\n82,100,261,25 , M. Pinto46 , B. J. Piotrzkowski7 ,\nK. Piotrzkowski57 , M. Pirello68 , M. D. Pitkin\n196 ,\nA. Placidi\n39,75 , E. Placidi101,56 , M. L. Planas\n87 ,\nW. Plastino\n262,236 , R. Poggiani\n74,17 , E. Polini\n24 ,\nD. Y. T. Pong132 , S. Ponrathnam12 , E. K. Porter44 ,\nC. Posnansky6 , R. Poulton\n46 , J. Powell142 ,\nM. Pracchia24 , T. Pradier165 , A. K. Prajapati79 ,\nK. Prasai73 , R. Prasanna205 , G. Pratten\n107 ,\nM. Principe82,261,100 , G. A. Prodi\n263,97 , L. Prokhorov107 ,\nP. Prosposito126,127 , L. Prudenzi110 , A. Puecher27,63 ,\nM. Punturo\n39 , F. Puosi17,74 , P. Puppo56 ,\nM. P\u00fcrrer\n110 , H. Qi\n16 , N. Quartey106 ,\nV. Quetschke150 , P. J. Quinonez35 , R. Quitzow-James92 ,\nF. J. Raab68 , G. Raaijmakers37,27 , H. Radkins68 ,\nN. Radulesco36 , P. Raffai\n153 , S. X. Rail226 ,\nS. Raja91 , C. Rajan91 , K. E. Ramirez\n55 ,\nT. D. Ramirez43 , A. Ramos-Buades\n110 , D. Rana12 ,\nJ. Rana6 , P. R. Rangnekar73 , P. Rapagnani101,56 ,\nA. Ray\n7 , V. Raymond\n16 , N. Raza\n147 ,\nM. Razzano\n74,17 , J. Read43 , T. Regimbau24 ,\nL. Rei\n89 , S. Reid86 , S. W. Reid106 ,\nM. Reinhard72 , D. H. Reitze1 , P. Relton\n16 ,\nA. Renzini1 , P. Rettegno\n21,22 , B. Revenu\n44 ,\nJ. Reyes167 , A. Reza27 , M. Rezac43 ,\nA. S. Rezaei56,101 , F. Ricci101,56 , D. Richards198 ,\nJ. W. Richardson\n264 , L. Richardson122 , K. Riles\n187 ,\nS. Rinaldi\n74,17 , C. Robertson198 , N. A. Robertson1 ,\nR. Robie1 , F. Robinet45 , A. Rocchi\n127 ,\nS. Rodriguez43 , L. Rolland\n24 , J. G. Rollins\n1 ,\nM. Romanelli102 , R. Romano3,4 , C. L. Romel68 ,\nA. Romero\n31 , I. M. Romero-Shaw5 , J. H. Romie55 ,\nS. Ronchini\n32,104 , T. J. Roocke\n83 , L. Rosa4,25 ,\nC. A. Rose7 , D. Rosi\u0144ska108 , M. P. Ross\n265 ,\nM. Rossello87 , S. Rowan23 , S. J. Rowlinson107 ,\nSantosh Roy12 , Soumen Roy63 , A. Royzman159 ,\nD. Rozza\n124,125 , P. Ruggi46 , E. Ruiz Morales\n180 ,\nK. Ruiz-Rocha178 , K. Ryan68 , S. Sachdev\n7 ,\nT. Sadecki68 , J. Sadiq\n116 , P. Saffarieh27,93 ,\nS. Saha\n131 , Y. Saito193 , K. Sakai266 ,\nM. Sakellariadou\n58 , S. Sakon6 , O. S. Salafia\n267,112,111 ,\nF. Salces-Carcoba\n1 , L. Salconi46 , M. Saleem\n84 ,\nF. Salemi\n96,97 , M. Sall\u00e9\n27 , A. Samajdar\n112 ,\nE. J. Sanchez1 , J. H. Sanchez43 , L. E. Sanchez1 ,\nN. Sanchis-Gual\n268,129 , J. R. Sanders269 , A. Sanuy\n30 ,\nT. R. Saravanan12 , N. Sarin5 , A. Sasli\n202 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL10\nLVK\nB. Sassolas156 , H. Satari90 , B. S. Sathyaprakash\n6,16 ,\nO. Sauter\n72 , R. L. Savage\n68 , V. Savant\n12 ,\nT. Sawada\n177 , H. L. Sawant12 , S. Sayah156 ,\nD. Schaetzl1 , M. Scheel137 , J. Scheuer67 ,\nM. G. Schiworski\n83 , P. Schmidt\n107 , S. Schmidt63 ,\nR. Schnabel\n85 , M. Schneewind10,11 , R. M. S. Schofield64 ,\nA. Sch\u00f6nbeck85 , B. W. Schulte10,11 , B. F. Schutz16,10,11 ,\nE. Schwartz\n16 , J. Scott\n23 , S. M. Scott\n9 ,\nM. Seglar-Arroyo\n24 , Y. Sekiguchi\n270 , D. Sellers55 ,\nA. S. Sengupta271 , D. Sentenac46 , E. G. Seo132 ,\nV. Sequino25,4 , A. Sergeev217 , G. Servignat251 ,\nY. Setyawati\n63 , T. Shaffer68 , M. S. Shahriar\n67 ,\nM. A. Shaikh\n18 , B. Shams159 , L. Shao\n201 ,\nA. Sharma32,104 , P. Sharma91 , P. Shawhan\n109 ,\nN. S. Shcheblanov\n229 , A. Sheela243 , E. Sheridan178 ,\nY. Shikano\n272,273 , M. Shikauchi29 , H. Shimizu\n274 ,\nK. Shimode\n193 , H. Shinkai\n275 , T. Shishido52 ,\nA. Shoda\n19 , D. H. Shoemaker\n70 , D. M. Shoemaker\n170 ,\nS. ShyamSundar91 , M. Sieniawska57 , D. Sigg\n68 ,\nL. Silenzi\n39,40 , L. P. Singer\n119 , D. Singh\n6 ,\nM. K. Singh\n18 , N. Singh\n108 , A. Singha\n26,27 ,\nA. M. Sintes\n87 , V. Sipala124,125 , V. Skliris16 ,\nB. J. J. Slagmolen\n9 , T. J. Slaven-Blair90 , J. Smetana107 ,\nJ. R. Smith\n43 , L. Smith23 , R. J. E. Smith\n5 ,\nJ. Soldateschi\n230,276,54 , S. N. Somala\n277 , K. Somiya\n2 ,\nI. Song\n131 , K. Soni\n12 , S. Soni\n70 ,\nV. Sordini140 , F. Sorrentino89 , N. Sorrentino\n74,17 ,\nR. Soulard36 , T. Souradeep278,12 , V. Spagnuolo26,27 ,\nA. P. Spencer\n23 , M. Spera\n76,77 , P. Spinicelli46 ,\nA. K. Srivastava79 , V. Srivastava65 , C. Stachie36 ,\nF. Stachurski23 , D. A. Steer\n44 , J. Steinlechner26,27 ,\nS. Steinlechner\n26,27 , N. Stergioulas202 , S. Stevenson142 ,\nD. J. Stops107 , K. A. Strain\n23 , L. C. Strang123 ,\nG. Stratta\n279,56 , M. D. Strong8 , A. Strunk68 ,\nR. Sturani260 , A. L. Stuver\n154 , M. Suchenek81 ,\nS. Sudhagar\n12 , R. Sugimoto\n280,244 , H. G. Suh\n7 ,\nA. G. Sullivan\n148 , T. Z. Summerscales\n281 , L. Sun\n9 ,\nS. Sunil79 , A. Sur\n81 , J. Suresh\n29,57 ,\nP. J. Sutton\n16 , Takamasa Suzuki\n176 , Takanori Suzuki2 ,\nToshikazu Suzuki191 , B. L. Swinkels\n27 , A. Syx165 ,\nM. J. Szczepa\u0144czyk\n72 , P. Szewczyk\n108 , M. Tacca\n27 ,\nH. Tagoshi191 , S. C. Tait\n23 , H. Takahashi\n282 ,\nR. Takahashi\n19 , S. Takano28 , H. Takeda\n28 ,\nM. Takeda177 , C. J. Talbot86 , C. Talbot70 ,\nN. Tamanini\n113 , K. Tanaka283 , Taiki Tanaka191 ,\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL11\nTakahiro Tanaka\n284 , A. J. Tanasijczuk57 , S. Tanioka\n193 ,\nD. B. Tanner72 , D. Tao1 , L. Tao\n72 ,\nR. D. Tapia6 , E. N. Tapia San Mart\u00edn\n27 , C. Taranto126 ,\nA. Taruya\n285 , J. D. Tasson\n160 , R. Tenorio\n87 ,\nJ. E. S. Terhune\n154 , L. Terkowski\n85 , H. Themann195 ,\nM. P. Thirugnanasambandam12 , M. Thomas55 , P. Thomas68 ,\nS. Thomas43 , D. Thompson160 , E. E. Thompson47 ,\nJ. E. Thompson\n16 , S. R. Thondapu91 , K. A. Thorne55 ,\nE. Thrane5 , Shubhanshu Tiwari\n163 , Srishti Tiwari\n12 ,\nV. Tiwari\n16 , A. M. Toivonen84 , A. E. Tolley\n114 ,\nT. Tomaru\n19 , T. Tomura\n193 , M. Tonelli74,17 ,\nA. Torres-Forn\u00e9\n129 , C. I. Torrie1 , I. Tosta e Melo\n125 ,\nE. Tournefier\n24 , D. T\u00f6yr\u00e49 , A. Trapananti\n40,39 ,\nF. Travasso\n39,40 , G. Traylor55 , J. Trenado\n30 ,\nM. Trevor109 , M. C. Tringali\n46 , A. Tripathee\n187 ,\nL. Troiano286,100 , A. Trovato\n34,241 , L. Trozzo\n4,193 ,\nR. J. Trudeau1 , D. Tsai131 , K. W. Tsang27,287,63 ,\nT. Tsang\n288 , J-S. Tsao234 , M. Tse\n70 ,\nR. Tso137 , S. Tsuchida177 , L. Tsukada6 ,\nD. Tsuna29 , T. Tsutsui\n29 , K. Turbang\n289,206 ,\nM. Turconi36 , C. Turski80 , D. Tuyenbayev\n177 ,\nH. Ubach\n30 , A. S. Ubhi\n107 , N. Uchikata\n191 ,\nT. Uchiyama\n193 , R. P. Udall\n1 , A. Ueda290 ,\nT. Uehara\n291,292 , K. Ueno\n29 , G. Ueshima293 ,\nC. S. Unnikrishnan294 , A. L. Urban8 , T. Ushiba\n193 ,\nA. Utina\n26,27 , H. Vahlbruch\n10,11 , N. Vaidya\n1 ,\nG. Vajente\n1 , A. Vajpeyi5 , G. Valdes\n122 ,\nM. Valentini\n186,96,97 , S. Vallero22 , V. Valsan\n7 ,\nN. van Bakel27 , M. van Beuzekom\n27 , M. van Dael\n27,295 ,\nJ. F. J. van den Brand\n26,93,27 , C. Van Den Broeck63,27 , D. C. Vander-Hyde65 ,\nA. Van de Walle45 , J. van Dongen27,93 , H. van Haevermaet\n206 ,\nJ. V. van Heijningen\n57 , J. Vanosky1 , M. H. P. M. van Putten296 ,\nZ. van Ranst\n26 , N. van Remortel\n206 , M. Vardaro214,27 ,\nA. F. Vargas123 , V. Varma\n110 , M. Vas\u00fath\n71 ,\nA. Vecchio\n107 , G. Vedovato77 , J. Veitch\n23 ,\nP. J. Veitch\n83 , J. Venneberg\n10,11 , G. Venugopalan\n1 ,\nP. Verdier\n140 , D. Verkindt\n24 , P. Verma161 ,\nY. Verma\n91 , S. M. Vermeulen\n16 , D. Veske\n148 ,\nF. Vetrano53 , A. Vicer\u00e9\n53,54 , S. Vidyant65 ,\nA. D. Viets\n297 , A. Vijaykumar\n18 , V. Villa-Ortega\n116 ,\nJ.-Y. Vinet36 , A. Virtuoso241,34 , S. Vitale\n70 ,\nH. Vocca75,39 , E. R. G. von Reis68 , J. S. A. von Wrangel10,11 ,\nC. Vorvick\n68 , S. P. Vyatchanin\n94 , L. E. Wade61 ,\nM. Wade\n61 , K. J. Wagner\n130 , R. C. Walet27 ,\nM. Walker106 , G. S. Wallace86 , L. Wallace1 ,\nMNRAS 000, 000\u2013000 (2022)\n\nL12\nLVK\nJ. Wang\n179 , J. Z. Wang187 , W. H. Wang150 ,\nR. L. Ward9 , J. Warner68 , M. Was\n24 ,\nT. Washimi\n19 , N. Y. Washington1 , K. Watada106 ,\nD. Watarai190 , J. Watchi\n144 , K. E. Wayt61 ,\nB. Weaver68 , C. R. Weaving114 , S. A. Webster23 ,\nM. Weinert10,11 , A. J. Weinstein\n1 , R. Weiss70 ,\nC. M. Weller265 , R. A. Weller\n178 , F. Wellmann10,11 ,\nL. Wen90 , P. We\u00dfels10,11 , K. Wette\n9 ,\nJ. T. Whelan\n130 , D. D. White43 , B. F. Whiting\n72 ,\nC. Whittle\n70 , O. S. Wilk61 , D. Wilken\n10,11,11 ,\nC. E. Williams160 , D. Williams\n23 , M. J. Williams\n23 ,\nA. R. Williamson\n114 , J. L. Willis\n1 , B. Willke\n10,11 ,\nC. C. Wipf1 , G. Woan\n23 , J. Woehler10,11 ,\nJ. K. Wofford\n130 , I. A. Wojtowicz160 , D. Wong147 ,\nI. C. F. Wong\n132 , M. Wright23 , C. Wu\n131 ,\nD. S. Wu\n10,11 , H. Wu131 , D. M. Wysocki\n7 ,\nL. Xiao\n1 , N. Yadav81 , T. Yamada274 ,\nH. Yamamoto\n1 , K. Yamamoto\n213 , T. Yamamoto\n193 ,\nK. Yamashita203 , R. Yamazaki200 , F. W. Yang\n159 ,\nK. Z. Yang\n84 , L. Yang\n168 , Y.-C. Yang131 ,\nY. Yang\n298 , Yang Yang72 , M. J. Yap9 ,\nD. W. Yeeles16 , S.-W. Yeh131 , A. B. Yelikar\n130 ,\nJ. Yokoyama\n29,28 , T. Yokozawa193 , J. Yoo\n256 ,\nT. Yoshioka203 , Hang Yu\n137 , Haocun Yu\n70 ,\nH. Yuzurihara191 , A. Zadro\u017cny161 , M. Zanolin35 ,\nS. Zeidler\n299 , T. Zelenova46 , J.-P. Zendri77 ,\nM. Zevin\n166 , M. Zhan179 , H. Zhang234 ,\nJ. Zhang\n9 , L. Zhang1 , R. Zhang\n72 ,\nT. Zhang107 , Y. Zhang122 , C. Zhao\n90 ,\nG. Zhao144 , Y. Zhao\n191,19 , Yue Zhao159 ,\nY. Zheng\n92 , R. Zhou194 , X. J. Zhu\n5 ,\nZ.-H. Zhu\n121,232 , A. B. Zimmerman\n170 , M. E. Zucker1,70 , and J. Zweizig\n1\n(The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration)\nand\nS. Shandera6 and D. Jeong6\n\u2217Deceased, December 2021.\n1LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n2Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan\n3Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n6The Pennsylvania State University, University Park, PA 16802, USA\n7University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n8Louisiana State University, Baton Rouge, LA 70803, USA\n9OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n10Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n11Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n12Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL13\n13University of Cambridge, Cambridge CB2 1TN, United Kingdom\n14Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n15Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n16Cardiff University, Cardiff CF24 3AA, United Kingdom\n17INFN, Sezione di Pisa, I-56127 Pisa, Italy\n18International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n19Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n20Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n21Dipartimento di Fisica, Universit\u00e0 degli Studi di Torino, I-10125 Torino, Italy\n22INFN Sezione di Torino, I-10125 Torino, Italy\n23SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n24Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n25Universit\u00e0 di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n26Maastricht University, 6200 MD Maastricht, Netherlands\n27Nikhef, 1098 XG Amsterdam, Netherlands\n28Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n29Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n30Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, 08028, Spain\n31Institut de F\u00edsica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n32Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n33Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n34INFN, Sezione di Trieste, I-34127 Trieste, Italy\n35Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n36Artemis, Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, F-06304 Nice, France\n37GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH\nAmsterdam, Netherlands\n38Department of Physics, National and Kapodistrian University of Athens, 15771 Ilissia, Greece\n39INFN, Sezione di Perugia, I-06123 Perugia, Italy\n40Universit\u00e0 di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n41American University, Washington, D.C. 20016, USA\n42Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan\n43California State University Fullerton, Fullerton, CA 92831, USA\n44Universit\u00e9 de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France\n45Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n46European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n47Georgia Institute of Technology, Atlanta, GA 30332, USA\n48Chennai Mathematical Institute, Chennai 603103, India\n49Department of Mathematics and Physics, Graduate School of Science and Technology, Hirosaki University, Hirosaki, Aomori 036-8561,\nJapan\n50Royal Holloway, University of London, London TW20 0EX, United Kingdom\n51Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan\n52The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan\n53Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n54INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n55LIGO Livingston Observatory, Livingston, LA 70754, USA\n56INFN, Sezione di Roma, I-00185 Roma, Italy\n57Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n58King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n59Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n60National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n61Kenyon College, Gambier, OH 43022, USA\n62School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki\n305-0801, Japan\n63Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n64University of Oregon, Eugene, OR 97403, USA\n65Syracuse University, Syracuse, NY 13244, USA\n66Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n67Northwestern University, Evanston, IL 60208, USA\n68LIGO Hanford Observatory, Richland, WA 99352, USA\n69Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno,\nItaly\n70LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n71Wigner RCP, RMKI, H-1121 Budapest, Hungary\n72University of Florida, Gainesville, FL 32611, USA\n73Stanford University, Stanford, CA 94305, USA\n74Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n75Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n76Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\nMNRAS 000, 000\u2013000 (2022)\n\nL14\nLVK\n77INFN, Sezione di Padova, I-35131 Padova, Italy\n78Montana State University, Bozeman, MT 59717, USA\n79Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n80Universiteit Gent, B-9000 Gent, Belgium\n81Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n82Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n83OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n84University of Minnesota, Minneapolis, MN 55455, USA\n85Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n86SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n87IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n88Departamento de Matem\u00e1ticas, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n89INFN, Sezione di Genova, I-16146 Genova, Italy\n90OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n91RRCAT, Indore, Madhya Pradesh 452013, India\n92Missouri University of Science and Technology, Rolla, MO 65409, USA\n93Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n94Lomonosov Moscow State University, Moscow 119991, Russia\n95Center for Theoretical Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland\n96Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n97INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n98Bar-Ilan University, Ramat Gan, 5290002, Israel\n99Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n100INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n101Universit\u00e0 di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n102Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-3500 Rennes, France\n103Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n104INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n105Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n106Christopher Newport University, Newport News, VA 23606, USA\n107University of Birmingham, Birmingham B15 2TT, United Kingdom\n108Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n109University of Maryland, College Park, MD 20742, USA\n110Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n111Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n112INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n113L2IT, Laboratoire des 2 Infinis - Toulouse, Universit\u00e9 de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n114University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n115Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n116IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n117Stony Brook University, Stony Brook, NY 11794, USA\n118Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n119NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n120Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n121Department of Astronomy, Beijing Normal University, Beijing 100875, China\n122Texas A&M University, College Station, TX 77843, USA\n123OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n124Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n125INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n126Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n127INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n128University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n129Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n130Rochester Institute of Technology, Rochester, NY 14623, USA\n131National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China\n132The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n133Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n134OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n135Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan\n136Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City\n32001, Taiwan\n137CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n138Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n139Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan\n140Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n141INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n142OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n143Universit\u00e9 libre de Bruxelles, 1050 Bruxelles, Belgium\nMNRAS 000, 000\u2013000 (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL15\n144Universit\u00e9 Libre de Bruxelles, Brussels 1050, Belgium\n145Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n146Texas Tech University, Lubbock, TX 79409, USA\n147University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n148Columbia University, New York, NY 10027, USA\n149University of Rhode Island, Kingston, RI 02881, USA\n150The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n151Bellevue College, Bellevue, WA 98007, USA\n152Scuola Normale Superiore, I-56126 Pisa, Italy\n153E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n154Villanova University, Villanova, PA 19085, USA\n155The University of Sheffield, Sheffield S10 2TN, United Kingdom\n156Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n157Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n158INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n159The University of Utah, Salt Lake City, UT 84112, USA\n160Carleton College, Northfield, MN 55057, USA\n161National Center for Nuclear Research, 05-400 \u015awierk-Otwock, Poland\n162Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00e9, CNRS, UMR 7095, 75014 Paris, France\n163University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n164Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n165Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n166University of Chicago, Chicago, IL 60637, USA\n167Montclair State University, Montclair, NJ 07043, USA\n168Colorado State University, Fort Collins, CO 80523, USA\n169Institute for Nuclear Research, H-4026 Debrecen, Hungary\n170University of Texas, Austin, TX 78712, USA\n171CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n172Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n173Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n174Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n175Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan\n176Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n177Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n178Vanderbilt University, Nashville, TN 37235, USA\n179State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement\nScience and Technology (APM), Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, China\n180\n181SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n182University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n183INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n184Queen Mary University of London, London E1 4NS, United Kingdom\n185Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n186The University of Mississippi, University, MS 38677, USA\n187University of Michigan, Ann Arbor, MI 48109, USA\n188Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n189Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China\n190University of Tokyo, Tokyo, 113-0033, Japan.\n191Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n192Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n193Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205,\nJapan\n194University of California, Berkeley, CA 94720, USA\n195California State University, Los Angeles, Los Angeles, CA 90032, USA\n196Lancaster University, Lancaster LA1 4YW, United Kingdom\n197College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan\n198Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n199Department of Astronomy & Space Science, Chungnam National University, Yuseong-gu, Daejeon 34134, Republic of Korea\n200Department of Physical Sciences, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan\n201Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian District, Beijing 100871, China\n202Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n203Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan\n204Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sumiyoshi-ku, Osaka City, Osaka\n558-8585, Japan\n205Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n206Universiteit Antwerpen, 2000 Antwerpen, Belgium\n207University of Bia\u0142ystok, 15-424 Bia\u0142ystok, Poland\nMNRAS 000, 000\u2013000 (2022)\n\nL16\nLVK\n208Ewha Womans University, Seoul 03760, Republic of Korea\n209National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, China\n210School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, China\n211University of Southampton, Southampton SO17 1BJ, United Kingdom\n212Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n213Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n214Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n215\n216University of Washington Bothell, Bothell, WA 98011, USA\n217Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n218Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n219Department of Physics, Myongji University, Yongin 17058, Republic of Korea\n220Sungkyunkwan University, Seoul 03063, Republic of Korea\n221Bard College, Annandale-On-Hudson, NY 12504, USA\n222Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki\n305-0801, Japan\n223Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n224Instituto de Fisica Teorica, 28049 Madrid, Spain\n225Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n226Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n227Laboratoire Lagrange, Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire C\u00f4te d\u2019Azur, CNRS, F-06304 Nice, France\n228Seoul National University, Seoul 08826, Republic of Korea\n229NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n230Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n231Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan\n232School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China\n233National Center for High-performance computing, National Applied Research Laboratories, Hsinchu Science Park, Hsinchu City\n30076, Taiwan\n234Department of Physics, National Taiwan Normal University, sec. 4, Taipei 116, Taiwan\n235NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n236INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n237ESPCI, CNRS, F-75005 Paris, France\n238West Virginia University, Morgantown, WV 26506, USA\n239School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n240\n241Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n242Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan\n243Indian Institute of Technology Madras, Chennai 600036, India\n244Institute of Space and Astronautical Science (JAXA), Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan\n245Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France\n246Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n247Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n248Universit\u00e9 de Paris, 75006 Paris, France\n249Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA\n250Centre national de la recherche scientifique, 75016 Paris, France\n251Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, 92190 Meudon, France\n252Observatoire de Paris, 75014 Paris, France\n253Universit\u00e9 PSL, 75006 Paris, France\n254Institute of Physics of the Czech Academy of Sciences, 182 00 Praha 8, Czechia\n255Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n256Cornell University, Ithaca, NY 14850, USA\n257Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n258Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea\n259Hobart and William Smith Colleges, Geneva, NY 14456, USA\n260International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n261Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n262Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n263Universit\u00e0 di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n264University of California, Riverside, Riverside, CA 92521, USA\n265University of Washington, Seattle, WA 98195, USA\n266Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, Nagaoka City, Niigata 940-8532,\nJapan\n267INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n268Departamento de Matem\u00e1tica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\n3810-183 Aveiro, Portugal\n269Marquette University, Milwaukee, WI 53233, USA\n270Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan\n271Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\nMNRAS 000, 000\u2013000 (2022)\n\nMNRAS 000, 000\u2013000 (2022)\nPreprint 29 January 2024\nCompiled using MNRAS LATEX style file v3.0\n272Graduate School of Science and Technology, Gunma University, Maebashi, Gunma 371-8510, Japan\n273Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA\n274Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n275Faculty of Information Science and Technology, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan\n276INAF, Osservatorio Astrofisico di Arcetri, I-50125 Firenze, Italy\n277Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n278Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n279Istituto di Astrofisica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n280Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City,\nKanagawa 252-5210, Japan\n281Andrews University, Berrien Springs, MI 49104, USA\n282Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, Setagaya, Tokyo 158-0082, Japan\n283Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo, Kashiwa City,\nChiba 277-8582, Japan\n284Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n285Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n286Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit\u00e0 di Salerno, I-84084 Fisciano,\nSalerno, Italy\n287Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG Groningen, Netherlands\n288Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n289Vrije Universiteit Brussel, 1050 Brussel, Belgium\n290Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n291Department of Communications Engineering, National Defense Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan\n292Department of Physics, University of Florida, Gainesville, FL 32611, USA\n293Department of Information and Management Systems Engineering, Nagaoka University of Technology, Nagaoka City, Niigata 940-2188,\nJapan\n294Tata Institute of Fundamental Research, Mumbai 400005, India\n295Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n296Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea\n297Concordia University Wisconsin, Mequon, WI 53097, USA\n298Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan\n299Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan\n\u00a9 2022 The Authors\n\nL18\nLVK\nABSTRACT\nWe describe a search for gravitational waves from compact binaries with at least one component with mass\n0.2 M\u2299\u20131.0 M\u2299and mass ratio q \u22650.1 in Advanced LIGO and Advanced Virgo data collected between 1 November\n2019, 15:00 UTC and 27 March 2020, 17:00 UTC. No signals were detected. The most significant candidate has\na false alarm rate of 0.2 yr\u22121. We estimate the sensitivity of our search over the entirety of Advanced LIGO\u2019s\nand Advanced Virgo\u2019s third observing run, and present the most stringent limits to date on the merger rate of\nbinary black holes with at least one subsolar-mass component. We use the upper limits to constrain two fiducial\nscenarios that could produce subsolar-mass black holes: primordial black holes (PBH) and a model of dissipative\ndark matter. The PBH model uses recent prescriptions for the merger rate of PBH binaries that include a rate\nsuppression factor to effectively account for PBH early binary disruptions. If the PBHs are monochromatically\ndistributed, we can exclude a dark matter fraction in PBHs fPBH \u22730.6 (at 90% confidence) in the probed\nsubsolar-mass range. However, if we allow for broad PBH mass distributions we are unable to rule out fPBH = 1.\nFor the dissipative model, where the dark matter has chemistry that allows a small fraction to cool and collapse\ninto black holes, we find an upper bound fDBH < 10\u22125 on the fraction of atomic dark matter collapsed into black holes.\nKey words: (transients:) black hole mergers \u2013 black hole physics \u2013 (cosmology:) dark matter\n1 INTRODUCTION\nThe Advanced LIGO (Aasi et al. 2015) and Advanced\nVirgo (Acernese et al. 2015) detectors have completed three\nobserving runs, O1, O2, and O3 (split into O3a and O3b),\nsince the first observation of gravitational waves from a bi-\nnary black hole (BBH) coalescence (Abbott et al. 2016b).\nThe collected data have been analyzed by the LIGO\u2013Virgo\u2013\nKAGRA (LVK) Collaboration (Abbott et al. 2020a) in suc-\ncessive versions of the Gravitational Wave Transient Cata-\nlog (GWTC; Abbott et al. 2016a, 2019a, 2021d,a,b), which\nreport a total of 90 candidate gravitational-wave (GW) events\nfrom the coalescence of compact binary systems with a prob-\nability of astrophysical origin > 0.5. Several additional can-\ndidates of compact binary signals have also been included in\nindependent catalogs (Nitz et al. 2019a; Magee et al. 2019;\nVenumadhav et al. 2019, 2020; Nitz et al. 2019b, 2021b,a;\nOlsen et al. 2022) after analyzing the publicly released strain\ndata (Abbott et al. 2021e). These detections have revealed\nfeatures in the population of coalescing objects that revolu-\ntionize our previous understanding of astrophysics and stel-\nlar evolution (Mandel & Farmer 2022; Spera et al. 2022).\nThe masses of many black holes (BHs) detected in GWs\nare much larger than those of the BHs observed in X\u2013ray\nbinaries (Bailyn et al. 1998; Ozel et al. 2010; Farr et al.\n2011; Fishbach & Kalogera 2022) and some signals, such\nas GW190521 (Abbott et al. 2020c,f), have primary com-\nponent masses within the predicted pair-instability mass\ngap (Woosley 2017; Farmer et al. 2019). On the other side\nof the mass range are events like GW190425 (Abbott et al.\n2020d), whose total mass is substantially larger than any\nknown Galactic neutron star binary (Farrow et al. 2019; Ab-\nbott et al. 2020b), and events like GW190814 (Abbott et al.\n2020e, 2021f) and GW200210\u2212092254 (Abbott et al. 2021b)\nthat are also atypical due to their highly asymmetric masses\nand the properties of their light components (Zevin et al.\n2020). While open questions remain, GWs have provided a\nunique census of the population of black holes in binaries in\nour Universe (Abbott et al. 2021c).\nCurrent models of stellar evolution predict that white\ndwarfs that end their thermonuclear burning with a mass\ngreater than the Chandrasekhar limit (Chandrasekhar 1931;\nChandrasekhar 1935; Suwa et al. 2018; M\u00fcller et al. 2019; Ertl\net al. 2019) will collapse to form either a neutron star or a\nsupersolar-mass black hole. Since there are no standard astro-\nphysical channels that produce subsolar-mass objects more\ncompact than white dwarfs, the detection of a subsolar-mass\n(SSM) compact object would indicate the presence of a new\nformation mechanism alternative to usual stellar evolution.\nGiven the still-unknown nature of 84% of the matter in\nthe Universe (Aghanim et al. 2020), it is reasonable to con-\nsider whether the DM might be composed of, or produce, dis-\ntinct populations of compact objects. Primordial black holes\n(PBHs), postulated to form from the collapse of large over-\ndensities in the early Universe (Zel\u2019dovich & Novikov 1967;\nHawking 1971; Carr & Hawking 1974; Chapline 1975), are\ncandidates to form at least a fraction of the dark matter\n(DM) while providing an explanation to several open prob-\nlems in astrophysics and cosmology (Barrow et al. 1991; Bean\n& Magueijo 2002; Kashlinsky 2016; Clesse & Garc\u00eda-Bellido\n2018). Soon after the first BBH coalescence was observed,\nit was suggested (Bird et al. 2016; Clesse & Garc\u00eda-Bellido\n2017; Sasaki et al. 2016) that the detected BHs could have\na primordial origin. Large primordial fluctuations at small\nscales generated during inflation can produce PBHs (Carr &\nLidsey 1993; Ivanov et al. 1994; Kim & Lee 1996; Garc\u00eda-\nBellido et al. 1996), though other processes in the early\nUniverse, like bubble nucleation and domain walls (Garriga\net al. 2016), cosmic string loops, and scalar field instabili-\nties (Khlopov et al. 1985; Cotner & Kusenko 2017) can also\nbe sources of overdensities that eventually collapse to pro-\nduce PBHs (Khlopov 2010; Carr et al. 2021b; Carr & Kuhnel\n2020; Villanueva-Domingo et al. 2021). The thermal history\nof the Universe can further enhance the formation of PBH at\ndifferent scales (Carr et al. 2021a). For example, the quark\u2013\nhadron (QCD) transition significantly reduces the radiation\npressure of the plasma, so that a uniform primordial enhance-\nMNRAS 000, 18\u2013?? (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL19\nment stretching across the QCD scale will generate a distri-\nbution of PBH masses that is sharply peaked around a solar\nmass (Byrnes et al. 2018) as well as a broader mass distri-\nbution at both larger and smaller masses that could explain\nsome of the GW observations (Clesse & Garcia-Bellido 2022;\nJedamzik 2021, 2020; Chen et al. 2022; Juan et al. 2022; Fran-\nciolini & Urbano 2022). In particular, GW events in the SSM\nrange could be used to probe mergers involving PBH black\nholes from a QCD enhanced peak.\nModels of particle dark matter can also produce compact\nobjects either from an interaction of dark matter with Stan-\ndard Model particles, such as boson stars or neutron stars\ntransmuted into black holes due to DM accretion (Dasgupta\net al. 2021; Kouvaris et al. 2018; Kouvaris & Tinyakov 2011;\nde Lavallaz & Fairbairn 2010; Goldman & Nussinov 1989;\nBramante & Elahi 2015; Bramante & Linden 2014; Bramante\net al. 2018; Takhistov 2018; Takhistov et al. 2021), or directly\nfrom the gravitational collapse of dissipative DM (Ryan et al.\n2022; Chang et al. 2019; Shandera et al. 2018; Choquette\net al. 2019; Latif et al. 2019; D\u2019Amico et al. 2018; Essig et al.\n2019; Hippert et al. 2022). DM black holes (DBHs) may form\nin the late universe if DM has a sufficiently rich particle con-\ntent to allow dissipation and collapse of DM into compact\nstructures. While these mechanisms generically produce black\nholes that overlap the standard astrophysical population, un-\nder specific assumptions they may also be able to create SSM\ncompact objects.\nSearches for compact binaries with at least one compo-\nnent below 1 M\u2299have been carried out using both Initial\nLIGO (Abbott et al. 2005, 2008), and Advanced LIGO and\nAdvanced Virgo data (Abbott et al. 2018a, 2019b, 2022; Nitz\n& Wang 2021c, 2022, 2021b; Phukon et al. 2021; Nitz & Wang\n2021a). No firm detections were reported in any of these anal-\nyses. We describe and present the results of the search for the\nGWs from binary systems with at least one SSM component\ndown to 0.2M\u2299, using data from the second part of the third\nobserving run (O3b) in Sec. 2. We find no unambiguous GW\ncandidates. The null result, combined with our previous anal-\nysis of the first part of the third observing run (O3a; Abbott\net al. 2022), allows us to set in Sec. 3 upper limits on the\nmerger rate of binaries with one SSM component, as func-\ntion of the chirp mass and in the m1\u2013m2 plane.\nThese new upper limits on the merger rate can be used to\nconstrain any model that might generate compact objects in\nthe SSM range. As illustrative examples, we derive in Sec. 4\nnew constraints on two particular scenarios, PBHs and a\nmodel of DBHs. For PBH models, we calculate the merger\nrate of SSM binaries taking into account the early (H\u00fctsi\net al. 2021) and late binary formation scenarios (Clesse &\nGarcia-Bellido 2022; Phukon et al. 2021), and we reevalu-\nate the constraints on PBH DM models with monochromatic\n(delta-function) and extended mass distributions. We update\nthe PBH merger rate model of previous LVK works (Ab-\nbott et al. 2018b, 2019c, 2022) with additional physics to\nallow for binary disruption and find that the constraints on\nmonochromatically distributed PBHs are weakened. We also\nconsider broad PBH mass functions such as those of ther-\nmal history scenarios of PBHs and find that they are not\nsignificantly constrained in the SSM range by the present\nLVK data. For DBHs, we constrain a simple atomic dark\nmatter model where DM consists of two oppositely charged\ndark fermions interacting via a dark photon (Shandera et al.\n2018). This model has been estimated to produce a sizeable\npopulation of SSM black holes if the heavier of the fermions,\nX, is more massive than the Standard Model proton (Shan-\ndera et al. 2018); the fermion mass range previously probed\nwas 0.66 GeV/c2 < mX < 8.8 GeV/c2 (Abbott et al. 2022;\nSingh et al. 2021). We obtain improved constraints on the\nfraction of DM in DBHs as a function of the minimum mass\nof the DBHs. In Sec. 5 we summarize our findings and discuss\nprospects for Advanced LIGO and Advanced Virgo\u2019s fourth\nobserving run.\n2 SEARCH\nThe SSM search analyzes data collected during O3b, covering\nthe period from 1 November 2019 1500 UTC to 27 March\n2020 1700 UTC. The characterization and calibration of data\nand the non-linear removal of spectral lines follow the same\nmethods as in our O3a analyses (Abbott et al. 2021a,d, 2022).\nThe analysis is performed by using three matched-filtering\npipelines: GstLAL (Messick et al. 2017; Sachdev et al. 2019;\nHanna et al. 2020), MBTA (Aubin et al. 2021) and PyCBC (Allen\net al. 2012; Allen 2005; Dal Canton et al. 2014; Usman\net al. 2016; Nitz et al. 2017; Davies et al. 2020). These\nanalyses correlate the data with a bank of templates that\nmodel the gravitational-wave signals expected from binaries\nin quasi-circular orbit. All search pipelines use the same\ntemplate banks and the same setup as for the O3a SSM\nanalysis (Abbott et al. 2022). Templates are generated us-\ning the TaylorF2 waveform (Sathyaprakash & Dhurandhar\n1991; Blanchet et al. 1995; Poisson 1998; Damour et al. 2001;\nMik\u00f3czi et al. 2005; Blanchet et al. 2005; Arun et al. 2009;\nBuonanno et al. 2009; Boh\u00e9 et al. 2013, 2015; Mishra et al.\n2016) and include phase terms up to 3.5 post-Newtonian\norder, but no amplitude corrections. We estimate the GW\nemission starting at a frequency of 45 Hz to limit the com-\nputational cost of the search; we estimate that this reduces\nthe network average signal-to-noise ratio (SNR) by 7%. The\ntemplate bank was constructed using a geometric placement\nalgorithm (Harry et al. 2014). The bank is designed to re-\ncover binaries with (redshifted) primary mass m1 \u2208[0.2, 10 ]\nM\u2299and secondary mass m2 \u2208[0.2, 1.0 ] M\u2299. The lower mass\nbound is set for consistency with previous searches (Abbott\net al. 2018b, 2019c, 2022) and to limit the computational\ncost of the search. We additionally limit the binary mass ra-\ntio, q \u2261m2/m1, with m2 \u2264m1, to range from 0.1 < q < 1.0.\nWe include the effect of spins aligned with the orbital an-\ngular momentum. For masses of a binary component larger\nthan 0.5 M\u2299we allow for a dimensionless component spin\n(\u03c71,2 = |S1,2|/m2\n1,2, with S1,2 the angular momentum of\nthe compact objects) up to 0.9, while for compact objects\nwith masses less than or equal to 0.5 M\u2299, we limit the maxi-\nmum dimensionless spin to 0.1. The restriction on component\nspins is chosen to reduce the computational cost of the anal-\nyses (Abbott et al. 2022). We set a minimum match (Owen\n1996) of 0.97 to ensure that no more than 10% of astrophys-\nical signals can be missed due to the discrete sampling of the\nparameter space.\nWe report in Table 1 the most significant candidates down\nto the threshold false alarm rate (FAR) of FAR < 2 yr\u22121. We\ndo not apply a trials factor to our analysis. We identify only\nthree triggers that pass this threshold in at least one pipeline.\nMNRAS 000, 18\u2013?? (2022)\n\nL20\nLVK\nTable 1. The triggers with a FAR < 2 yr\u22121 in at least one search pipeline. We include the search-measured parameters associated with\neach candidate: m1 and m2, the redshifted component masses, and \u03c71 and \u03c72, the dimensionless component spin. The parameters shown\nin the table are the ones reported by the search where the trigger is identified with the lowest FAR. H, L, and V denote the Hanford,\nLivingston, and Virgo interferometers, respectively. The dashes in the \u201cV SNR\u201d column mean that no single-detector trigger was found in\nAdvanced Virgo. The network SNR is computed by adding the SNR of single detector triggers in quadrature.\nFAR [yr\u22121]\nPipeline\nGPS time\nm1 [M\u2299]\nm2 [M\u2299]\n\u03c71\n\u03c72\nH SNR\nL SNR\nV SNR\nNetwork SNR\n0.20\nGstLAL\n1267725971.02\n0.78\n0.23\n0.57\n0.02\n6.31\n6.28\n-\n8.90\n1.37\nMBTA\n1259157749.53\n0.40\n0.24\n0.10\n\u22120.05\n6.57\n5.31\n5.81\n10.25\n1.56\nGstLAL\n1264750045.02\n1.52\n0.37\n0.49\n0.10\n6.74\n6.10\n-\n9.10\nVisual inspection of the data around the time of the triggers\nindicate no data quality issues that would point to a definitive\ninstrumental origin of the candidates. However, the number\nof triggers with their estimated FAR is consistent with what\nwe would expect if no astrophysical signal was present in the\ndata, given that the duration of O3b is 0.34 yr and that three\npipelines are being used. The most significant candidate has\na FAR of 0.2 yr\u22121, which assuming a Poisson distribution for\nthe background triggers and an observing time of 0.34 yr,\ncorresponds to a p-value of 6.6%. We conclude that there is\nno statistically significant evidence for the detection of a GW\nfrom a SSM source.\n3 SENSITIVITY AND RATE LIMITS\nThe absence of significant candidates in O3b allows us to\ncharacterize the sensitivity of our search and to set upper\nlimits on the merger rate of such binary systems. We es-\ntimate the sensitive volume\u2013time \u27e8V T\u27e9over all of O3. We\nfind the sensitivity of each of the three pipelines introduced\nin Sec. 2 with a common set of simulated signals in real\ndata, generated using the precessing post-Newtonian wave-\nform model SpinTaylorT5 (Ajith 2011), with source compo-\nnent masses sampled from log-uniform distributions with pri-\nmary masses in range (0.19, 11.0) M\u2299and secondary masses\nin range (0.19, 1.1) M\u2299. The injection\u2019s component spins are\ndistributed isotropically with dimensionless spin magnitudes\ngoing up to 0.1. The injections are distributed uniformly in\ncomoving volume up to a maximum redshift of z = 0.2, at\nwhich the sensitivity of the search has been checked to be\nnegligible. We injected a total of approximately 2 million sim-\nulated signals, spaced 15 s apart, spanning all O3.\nThe sensitivity of each search pipeline is estimated by com-\nputing the sensitive volume\u2013time of the search:\n\u27e8V T\u27e9= \u03f5 Vinj T ,\n(1)\nwhere \u03f5 is the efficiency, defined as the ratio of recovered\nto total injections in the data in the source frame mass bin\nof interest, T is the analyzed time, and Vinj is the comov-\ning volume at the farthest injected simulation. Each pipeline\nuses all injections with q > 0.05. We evaluate the uncertain-\nties at 90% confidence interval on the sensitive volume\u2013time\nestimate (Tiwari 2018) and consider binomial errors on the\nefficiency \u03f5, given by\n\u03b4 (V T) = 1.645\ns\n\u03f5 (1 \u2212\u03f5)\nNinj\nVinj T ,\n(2)\nwhere Ninj are the total injections in the considered mass\nrange.\nWe use the FAR of the most significant candidate in O3 for\neach pipeline to estimate the upper limit on the merger rate in\naccordance with the loudest event statistic formalism (Biswas\net al. 2009). The FAR thresholds used were 0.2 yr\u22121, 1.4 yr\u22121\nand 0.14 yr\u22121 (Abbott et al. 2022) for GstLAL, MBTA and\nPyCBC, respectively. By omitting a trials factor in our anal-\nysis, we obtain a conservative upper limit on the sensitive\n\u27e8V T\u27e9of the searches. Though MBTA and PyCBC results use the\nfull injection set, GstLAL analyzed a subset; the uncertainties\nin \u27e8V T\u27e9shown in Fig. 1 are therefore larger for GstLAL.\nTo lowest order, the inspiral of a binary depends sensitively\non the chirp mass of the system (Blanchet 2014), which is de-\nfined as M \u2261(m1m2)3/5/(m1 + m2)1/5. Therefore, we split\nthe population into nine equally spaced chirp mass bins in the\nrange 0.16M\u2299\u2264M \u22642.72M\u2299to determine the \u27e8V T\u27e9as a\nfunction of the chirp mass, shown in Fig. 1. The highest chirp\nmass bin of this search exhibits a drop in sensitivity as the\ncomponent masses contained within this bin are beyond the\nredshifted component masses covered by the template bank\n(Sec. 2). As a consequence, there is a drop in efficiency and\nsmaller \u27e8V T\u27e9values in that region. The sensitivity estimates\nobtained from the analysis of O3a data with the common\ninjection set are consistent with the ones reported in our pre-\nvious work (Abbott et al. 2022).\nThe null result from O3 yields \u27e8V T\u27e9values approximately\n2 times larger than those obtained for O3a, in agreement\nwith the expected increase in observing time. The sensitive\nhypervolumes of the searches presented in GWTC-3 (Abbott\net al. 2021b) for chirp masses of 1.3 M\u2299and 2.3 M\u2299are\ncomparable to those in Fig. 1 even though the mass ratio\nbounds of the two populations are different.\nGiven the obtained sensitive volume and the absence of sig-\nnificant detection, one can infer merger rate limits. Treating\neach bin, i, as a different population, we computed an upper\nlimit on the binary merger rate to 90% confidence (Biswas\net al. 2009):\nR90,i =\n2.3\n\u27e8V T\u27e9i .\n(3)\nWe show in Fig. 2 and in Fig. 3 the upper limits on the binary\nmerger rate as function of the chirp mass and in the source\nm1\u2013m2 plane, respectively.\n4 CONSTRAINTS ON DARK MATTER MODELS\nThe upper limits that we infer from our null result can gener-\nically be used to constrain models that predict an observable\npopulation of binaries with at least one SSM component.\nWe connect our results to two possible sources of SSM black\nholes: PBHs and DBHs. We parameterize our constraints in\nMNRAS 000, 18\u2013?? (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL21\n0.5\n1.0\n1.5\n2.0\n2.5\nM (M\u2299)\n10\u22124\n10\u22123\n10\u22122\n\u27e8V T\u27e9(Gpc3 yr)\nGstLAL O3\nMBTA O3\nPyCBC O3\nFigure 1. Sensitive volume\u2013time as a function of the source frame\nchirp mass in data from O3, obtained through the analysis of the\nset of common injections (blue triangles with dotted lines, orange\ncircles with dashed lines, and green squares with continuous lines).\nThe statistical errors are evaluated at 90% confidence interval,\nfollowing Eq. (2) and represented by the shaded areas.\n0.5\n1.0\n1.5\n2.0\n2.5\nM (M\u2299)\n102\n103\n104\nR90 (Gpc\u22123 yr\u22121)\nGstLAL\nMBTA\nPyCBC\nFigure 2. Merger rate limits as function of the source frame chirp\nmass of the binary system, in data from the full O3. The dotted,\ndashed and solid lines represent the 90% confidence limits obtained\nby GstLAL, MBTA and PyCBC, respectively.\nterms of the fraction of the dark matter that can be com-\nprised of compact objects under each model.\n4.1 Primordial Black Holes\nThe abundance and mass distribution of PBHs depend on\nthe details of their particular formation mechanism. The pri-\n100\n101\nR90 (Gpc\u22123 yr\u22121)\n\u00d7102\n0.19\n0.43\n0.62\n0.78\n0.94\n1.10\nm2 (M\u2299)\n(48.30 \u00b1 2.09)\n(17.02 \u00b1 0.76)\n(9.35 \u00b1 0.43)\n(6.74 \u00b1 0.32)\n(4.83 \u00b1 0.23)\n(13.36 \u00b1 0.64)\n(5.98 \u00b1 0.28)\n(3.70 \u00b1 0.17)\n(2.77 \u00b1 0.12)\n(2.15 \u00b1 0.09)\n(7.32 \u00b1 0.41)\n(3.86 \u00b1 0.18)\n(2.27 \u00b1 0.10)\n(1.75 \u00b1 0.07)\n(1.42 \u00b1 0.06)\n(4.96 \u00b1 0.46)\n(2.91 \u00b1 0.13)\n(1.95 \u00b1 0.09)\n(1.41 \u00b1 0.06)\n(1.15 \u00b1 0.05)\n(2.44 \u00b1 0.13)\n(1.69 \u00b1 0.08)\n(1.29 \u00b1 0.06)\n(3.53 \u00b1 0.27)\nGstLAL\n0.19\n0.43\n0.62\n0.78\n0.94\n1.10\nm2 (M\u2299)\n(41.09 \u00b1 1.11)\n(14.84 \u00b1 0.41)\n(8.81 \u00b1 0.27)\n(6.17 \u00b1 0.19)\n(4.57 \u00b1 0.14)\n(11.93 \u00b1 0.37)\n(5.39 \u00b1 0.16)\n(3.56 \u00b1 0.11)\n(2.64 \u00b1 0.08)\n(2.14 \u00b1 0.06)\n(7.10 \u00b1 0.26)\n(3.70 \u00b1 0.11)\n(2.34 \u00b1 0.07)\n(1.81 \u00b1 0.05)\n(1.37 \u00b1 0.04)\n(5.17 \u00b1 0.33)\n(3.26 \u00b1 0.10)\n(2.00 \u00b1 0.06)\n(1.37 \u00b1 0.04)\n(1.12 \u00b1 0.03)\n(3.17 \u00b1 0.13)\n(1.81 \u00b1 0.06)\n(1.31 \u00b1 0.04)\n(2.77 \u00b1 0.13)\nMBTA\n0.19\n2.68\n4.53\n6.49\n8.63\n11.00\nm1 (M\u2299)\n0.19\n0.43\n0.62\n0.78\n0.94\n1.10\nm2 (M\u2299)\n(45.77 \u00b1 1.30)\n(16.70 \u00b1 0.50)\n(9.91 \u00b1 0.32)\n(7.16 \u00b1 0.23)\n(5.33 \u00b1 0.18)\n(14.03 \u00b1 0.46)\n(6.32 \u00b1 0.20)\n(4.13 \u00b1 0.14)\n(3.04 \u00b1 0.10)\n(2.48 \u00b1 0.08)\n(8.14 \u00b1 0.32)\n(4.43 \u00b1 0.14)\n(2.78 \u00b1 0.09)\n(2.10 \u00b1 0.07)\n(1.64 \u00b1 0.05)\n(5.38 \u00b1 0.35)\n(3.43 \u00b1 0.11)\n(2.28 \u00b1 0.08)\n(1.63 \u00b1 0.05)\n(1.34 \u00b1 0.04)\n(2.70 \u00b1 0.10)\n(1.85 \u00b1 0.06)\n(1.47 \u00b1 0.05)\n(2.89 \u00b1 0.14)\nPyCBC\nFigure 3. Merger rate limits in the source frame m1\u2013m2 plane,\nin data from the full O3 for the three pipelines. The error bars\nin each panel are given at the 90% confidence interval, following\nEq. 2.\nmordial power spectrum generated during inflation must have\nsufficiently large fluctuations on small scales for PBHs forma-\ntion, while keeping the fluctuations small at the scale of the\nobserved cosmic microwave background anisotropies (Cole\net al. 2022). This is possible in several two-field models of\ninflation (Clesse & Garc\u00eda-Bellido 2015; Braglia et al. 2020;\nZhou et al. 2020; De Luca et al. 2021), single-field models\nwith a non slow-roll regime due to specific features in the\ninflation dynamics\n(Garc\u00eda-Bellido & Ruiz Morales 2017;\nEzquiaga et al. 2018), and by the enhancement of fluctua-\ntions at small scales due to quantum diffusion (Pattison et al.\n2017; Ezquiaga et al. 2020), which provide recent examples\nof inflationary scenarios that can produce PBHs in the SSM\nrange.\nThe probability of matter fluctuations to collapse into\nPBHs is enhanced by the decrease of the radiation pres-\nsure as different particles become non-relativistic along the\nthermal history of the Universe (Carr et al. 2021a). In par-\nticular, a peak around a solar mass is expected due to the\nQCD transition, although its exact position and height de-\npend on the characteristics of the matter fluctuations at those\nscales (Byrnes et al. 2018). Furthermore, the probability of bi-\nMNRAS 000, 18\u2013?? (2022)\n\nL22\nLVK\nnary formation and thus estimates of the event rates depends\non the clustering of PBHs and the cluster dynamics. This re-\nmains an area of active study (Raidal et al. 2019; Trashorras\net al. 2021; Jedamzik 2020). All these uncertainties make our\npredictions on the DM fraction of PBHs very sensitive to\nthe particular choice of the model parameters (Escriv\u00e0 et al.\n2022; Franciolini et al. 2022).\nWe update the theoretical merger rate of PBHs used in pre-\nvious LVK searches (Abbott et al. 2018b, 2019c, 2022). We\napproximate the merger rates of early PBH binaries (EBs)\nformed in the radiation-dominated era with the approxima-\ntions provided by H\u00fctsi et al. (2021); Chen & Huang (2018);\nAli-Ha\u00efmoud et al. (2017) and numerically validated with N-\nbody simulations in Raidal et al. (2019),\ndRPBH\nd ln m1d ln m2 = 1.6 \u00d7 106 Gpc\u22123 yr\u22121 \u00d7 fsupf 53/37\nPBH f(m1)\u00d7\nf(m2)\n\u0012m1 + m2\nM\u2299\n\u0013\u221232/37 \u0014\nm1m2\n(m1 + m2)2\n\u0015\u221234/37\n,\n(4)\nwhere fPBH denotes the DM density fraction made of PBHs\nand f(m) is the normalized PBH density distribution. We ne-\nglect the redshift dependence in the merger rates, since the\ncurrent generation of ground-based interferometers is only\nsensitive to BBHs with at least one SSM component at low\nredshifts. The main difference, compared to the theoretical\nrates predicted by Sasaki et al. (2016) that were used in pre-\nvious LVK searches, comes from a rate suppression factor fsup\nthat effectively accounts for PBH binary disruptions by early\nforming clusters due to Poisson fluctuations in the initial\nPBH separation, by matter inhomogeneities, and by nearby\nPBHs (Suyama & Yokoyama 2019; Matsubara et al. 2019).\nFor instance, if PBHs have all the same mass or a strongly\npeaked mass function and significantly contribute to the dark\nmatter, one gets fsup \u22482.3\u00d710\u22123f \u22120.65\nPBH , so the merger rates\nare highly suppressed (H\u00fctsi et al. 2021). As a result, the lim-\nits on fPBH are much less stringent than previously estimated.\nData from O2 still allow for fPBH = 1 in a scenario where\nall the PBHs have the same mass. Though monochromati-\ncally distributed PBHs are unrealistic, they provide a useful\napproximation for models with a highly peaked distribution,\ne.g., as predicted from PBH scenarios with sharp QCD tran-\nsitions (Carr et al. 2021a). Given the still large uncertainties\nand possible caveats for the merger rate prescriptions of early\nbinaries, we also considered the case where merger rates en-\ntirely come from late PBH binaries (LBs) formed dynamically\ninside PBH clusters seeded by the above-mentioned Poisson\nfluctuations that grow in the matter-dominated era and lead\nto the formation of PBH clusters, following Clesse & Garcia-\nBellido (2022); Phukon et al. (2021). This allows us to illus-\ntrate the important variations in the PBH limits obtained for\ndifferent binary formation scenarios.\nFor a monochromatic PBH mass distribution, we derive\nnew limits on fPBH in the SSM range, shown in Fig. 4, for\nboth EBs and LBs. While the scenario of DM entirely made\nof PBHs with the same mass was not totally excluded by\nprevious searches, after O3 it becomes strongly disfavored up\nto 1M\u2299, with fPBH < 0.6 around 0.3M\u2299and fPBH < 0.09\nat 1M\u2299. For LBs only, we do not find yet significant limits,\nsince we do not restrict fPBH to be lower than one.\nFor unequal mass BBH, the merger rates are more uncer-\ntain and model dependent, but one can obtain a limit on an\nFigure 4.\nConstraints on DM fraction of PBHs, fPBH, for a\nmonochromatic mass function and assuming the merger rates for\nearly PBH binaries from H\u00fctsi et al. (2021) (orange) and late PBH\nbinaries from Phukon et al. (2021) (blue). Shown in black are re-\nsults for SSM searches in O2 (Abbott et al. 2019b) with and with-\nout the rate suppression factor fsup. For the first time, fPBH = 1\nfor early binaries is excluded in the whole SSM range probed by\nthis search.\neffective parameter\nFPBH \u2261\n\u0012\nfsup\n2.3 \u00d7 10\u22123\n\u0013\nf(m1)f(m2)f 53/37\nPBH\n,\n(5)\nin such a way that it corresponds to the product of f(m2)\nand f(m1) in a scenario where fPBH \u22481. This allows us to\nestablish model-independent limits on PBHs since FPBH en-\ncompasses all the uncertainties on the mass distribution and\nrate suppression, by using the limits shown in Fig. 3 and the\nrates of Eq. (4) but neglecting their variations in individual\nmass bins. We find that the limits on FPBH is sensitive to the\nlocation in the m1\u2013m2 plane. These can be used to constrain\nfPBH for arbitrary mass functions. For models with fPBH = 1\nand a peak above 1M\u2299, these restrict the possible distribu-\ntion of BHs in the SSM range. We find that some repre-\nsentative distributions with QCD-enhanced features (Byrnes\net al. 2018; Carr et al. 2021a; De Luca et al. 2021; Jedamzik\n2021) become constrained in the range fPBH \u2248(0.1\u20131). SSM\nsearches are therefore complementary to searches in the solar\nmass range in order to distinguish PBH mass functions that\nare viable from those that are more constrained.\n4.2 Dark black holes\nIf all or some of the DM has rich enough particle content\nto dissipate kinetic energy and cool, then compact objects\nmade from DM may form through gravitational collapse of\nthe dark gas (Shandera et al. 2018). The particle content\nof the DM allows SSM black holes if, for example, there is\nMNRAS 000, 18\u2013?? (2022)\n\nSearch for SSM BBHs in aLIGO and AdV in O3\nL23\na cosmologically dominant heavy fermion analogous to the\nproton but with mass greater than 938 MeV/c2. In that case,\nthe Chandrasekhar limit for DM black holes is lower than\nthat for Standard Model matter. Constraints on SSM black\nholes in mergers then constrain formation channels for DM\nblack holes in the detectable mass range, bounding the total\ncooling rate (total dissipation) of the dark sector (Singh et al.\n2021).\nHere we consider a population of DBHs formed within a\nparticular dissipative scenario, the atomic DM model (Ack-\nerman et al. 2009; Kaplan et al. 2010; Feng et al. 2009),\nwith a power-law distribution of masses modeled after ob-\nservations and simulations of Population III stars (Stacy &\nBromm 2013; Greif et al. 2011; Hartwig et al. 2016). We de-\nrive the posterior probability for the fraction of dissipative\nDM that can be in black holes, the lower and upper limits of\nthe DBH mass distribution, and the power-law slope, using\nthe sensitive volume from the SSM search and modelled rates\nfor DBH mergers (Shandera et al. 2018; Singh et al. 2021).\nThe posterior is marginalized over the parameters that char-\nacterize the distribution, including the power-law slope and\nthe upper limit of the distribution to obtain the constraints\non the fraction of dissipative DM that can be in black holes,\nfDBH, together with the lower limit of the DBH distribution\nM DBH\nmin , as done in Singh et al. (2021); Abbott et al. (2021a)\npreviously.\nThe upper limits on fDBH are shown as a function of M DBH\nmin\nin Fig. 5. Compared to the results obtained from the SSM\nsearch in O3a (Abbott et al. 2022), where the most strin-\ngent constraint on fDBH \u22720.003%, the limit improves by\nroughly a factor of 2, which can be directly attributed to\nthe increase in the observing time. We derive the strictest\nlimit on fDBH \u22720.0012 \u2212\u22120.0014% at M DBH\nmin\n= 1M\u2299\nacross the 3 pipelines. The range of heavy dark fermion\nmasses, mX probed by this search inferred from the Chan-\ndrasekhar limit of the fermionic particle progenitors of DBHs,\nis 1.1 GeV/c2 < mX < 8.9 GeV/c2.\nA non-detection provides no information for the model pa-\nrameter M DBH\nmin\n< 2 \u00d7 10\u22122M\u2299because the searches are not\nsensitive enough to support distributions with M DBH\nmin\nin that\nmass range since we only consider M DBH\nmax\n= rM DBH\nmin\nwith\n2 \u2264r \u22641000. We also exclude limits where M DBH\nmin\n> 1M\u2299\nbecause the detection of a SSM DBH would require a mass\ndistribution with M DBH\nmin\n\u22641M\u2299. If these limits survive with\nsubsequent searches, the detection of a SSM compact ob-\nject would directly constrain the particle properties of atomic\ndark matter. Future searches could potentially rule out re-\ngions of the DM parameter space associated with dissipative\ndark matter.\n5 CONCLUSIONS AND OUTLOOK\nWe have presented a search for compact binary coalescences\nwith at least one SSM component in data from the second\nhalf of the third LVK observing run, O3b. The search did not\nyield any significant candidates.\nThe absence of significant candidates enables us to set im-\nproved merger-rate limits based on the full O3 dataset. We\nobtain consistent results with each of the three considered\nsearch pipelines. We demonstrate how the new upper limits\nFigure 5.\nConstraints on the abundance of DBHs, fDBH, as a\nfunction of the lower limit of the DBH mass distribution, MDBH\nmin\nfrom O3 data for the 3 search pipelines: GstLAL (dotted), MBTA\n(dashed) and PyCBC (solid). Constraints from the search for SSM\ncompact objects in O3a data (Abbott et al. 2022) are shown for\ncomparison.\ncan be used to constrain two illustrative models: SSM PBHs\nand DBHs.\nWe have considered PBH merger rate models that incorpo-\nrate additional physics relative to previous LVK works and\nobtained new limits that are less stringent than previous LVK\nsearches for SSM objects. Using these upper limits, the data\nallow us to exclude equal mass PBHs with a DM fraction\nsmaller than one, in the entire subsolar range probed by the\nsearch. More general PBH distributions with extended mass\nfunctions remain viable, even for fPBH \u22481. Our SSM search\ntherefore provides limits that are complementary to other\ntypes of observations such as pulsar timing arrays (De Luca\net al. 2021; Chen et al. 2020; Dom\u00e8nech & Pi 2022; Kohri\n& Terada 2021) and microlensing surveys (Allsman et al.\n2001; Tisserand et al. 2007; Wyrzykowski et al. 2011) that\ncan probe or constrain the GW background induced by the\ndensity fluctuations at the origin of the formation of SSM\nPBHs.\nFor the dissipative dark matter model we consider, bounds\non dark matter self-interactions on large scales (Markevitch\net al. 2004) already weakly constrain the amount of dark\nmatter that can be efficiently cooling, so only some of the\ndark matter can have cooled sufficiently to form compact\nobjects (Buckley & DiFranzo 2018; Shandera et al. 2018).\nOur analysis here provides the strongest constraint on this\nfraction so far from a SSM search, finding that no more than\nfDBH \u224810\u22125 of atomic dark matter can be collapsed into\nblack holes for distributions that include DBHs in the 0.2\u2013\n1M\u2299range where the sensitive volume is determined from\nthis search alone.\nGiven the fundamental physics implications of observing a\nMNRAS 000, 18\u2013?? (2022)\n\nL24\nLVK\nSSM black hole, it will be important to continue this type of\nsearch in the next LVK observing runs (Abbott et al. 2020a).\nEach of the upcoming observing runs will be preceded by de-\ntector upgrades, designed to enhance the sensitivity of our\nground-based interferometer network and our reach into the\nUniverse. These developments will facilitate either the detec-\ntion of a SSM compact object or provide tighter constraints\non their abundance.\nACKNOWLEDGMENTS\nAnalyses in this catalog relied upon the LALSuite software\nlibrary (LIGO Scientific Collaboration 2018). The detection\nof the signals and subsequent significance evaluations in this\ncatalog were performed with the GstLAL-based inspiral soft-\nware pipeline (Messick et al. 2017; Sachdev et al. 2019;\nHanna et al. 2020; Cannon et al. 2021), with the MBTA\npipeline (Adams et al. 2016; Aubin et al. 2021), and with the\nPyCBC (Usman et al. 2016; Nitz et al. 2017; Davies et al.\n2020) package. Plots were prepared with Matplotlib (Hunter\n2007). Numpy (Harris et al. 2020) and Scipy (Virtanen et al.\n2020) were used in the preparation of the manuscript.\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded by\nthe National Science Foundation. The authors also grate-\nfully acknowledge the support of the Science and Technol-\nogy Facilities Council (STFC) of the United Kingdom, the\nMax-Planck-Society (MPS), and the State of Niedersach-\nsen/Germany for support of the construction of Advanced\nLIGO and construction and operation of the GEO 600 de-\ntector. Additional support for Advanced LIGO was provided\nby the Australian Research Council. The authors gratefully\nacknowledge the Italian Istituto Nazionale di Fisica Nucleare\n(INFN), the French Centre National de la Recherche Scien-\ntifique (CNRS) and the Netherlands Organization for Sci-\nentific Research (NWO), for the construction and operation\nof the Virgo detector and the creation and support of the\nEGO consortium. The authors also gratefully acknowledge\nresearch support from these agencies as well as by the Council\nof Scientific and Industrial Research of India, the Department\nof Science and Technology, India, the Science & Engineer-\ning Research Board (SERB), India, the Ministry of Human\nResource Development, India, the Spanish Agencia Estatal\nde Investigaci\u00f3n (AEI), the Spanish Ministerio de Ciencia e\nInnovaci\u00f3n and Ministerio de Universidades, the Conselleria\nde Fons Europeus, Universitat i Cultura and the Direcci\u00f3\nGeneral de Pol\u00edtica Universitaria i Recerca del Govern de les\nIlles Balears, the Conselleria d\u2019Innovaci\u00f3, Universitats, Ci\u00e8n-\ncia i Societat Digital de la Generalitat Valenciana and the\nCERCA Programme Generalitat de Catalunya, Spain, the\nNational Science Centre of Poland and the European Union\n\u2014 European Regional Development Fund; Foundation for\nPolish Science (FNP), the Swiss National Science Founda-\ntion (SNSF), the Russian Foundation for Basic Research, the\nRussian Science Foundation, the European Commission, the\nEuropean Social Funds (ESF), the European Regional De-\nvelopment Funds (ERDF), the Royal Society, the Scottish\nFunding Council, the Scottish Universities Physics Alliance,\nthe Hungarian Scientific Research Fund (OTKA), the French\nLyon Institute of Origins (LIO), the Belgian Fonds de la\nRecherche Scientifique (FRS-FNRS), Actions de Recherche\nConcert\u00e9es (ARC) and Fonds Wetenschappelijk Onderzoek\n\u2014 Vlaanderen (FWO), Belgium, the Paris \u00cele-de-France Re-\ngion, the National Research, Development and Innovation Of-\nfice Hungary (NKFIH), the National Research Foundation of\nKorea, the Natural Science and Engineering Research Coun-\ncil Canada, Canadian Foundation for Innovation (CFI), the\nBrazilian Ministry of Science, Technology, and Innovations,\nthe International Center for Theoretical Physics South Amer-\nican Institute for Fundamental Research (ICTP-SAIFR), the\nResearch Grants Council of Hong Kong, the National Natural\nScience Foundation of China (NSFC), the Leverhulme Trust,\nthe Research Corporation, the Ministry of Science and Tech-\nnology (MOST), Taiwan, the United States Department of\nEnergy, and the Kavli Foundation. The authors gratefully ac-\nknowledge the support of the NSF, STFC, INFN and CNRS\nfor provision of computational resources. Funding for this\nproject was provided by the Charles E. Kaufman Foundation\nof The Pittsburgh Foundation and the Institute for Compu-\ntational and Data Sciences at Penn State.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-Aid\nfor Specially Promoted Research 26000005, JSPS Grant-\nin-Aid for Scientific Research on Innovative Areas 2905:\nJP17H06358, JP17H06361 and JP17H06364, JSPS Core-to-\nCore Program A. Advanced Research Networks, JSPS Grant-\nin-Aid for Scientific Research (S) 17H06133 and 20H05639 ,\nJSPS Grant-in-Aid for Transformative Research Areas (A)\n20A203: JP20H05854, the joint research program of the In-\nstitute for Cosmic Ray Research, University of Tokyo, Na-\ntional Research Foundation (NRF), Computing Infrastruc-\nture Project of KISTI-GSDC, Korea Astronomy and Space\nScience Institute (KASI), and Ministry of Science and ICT\n(MSIT) in Korea, Academia Sinica (AS), AS Grid Center\n(ASGC) and the Ministry of Science and Technology (MoST)\nin Taiwan under grants including AS-CDA-105-M06, Ad-\nvanced Technology Center (ATC) of NAOJ, and Mechanical\nEngineering Center of KEK.\nWe would like to thank all of the essential workers who put\ntheir health at risk during the COVID-19 pandemic, without\nwhom we would not have been able to complete this work.\nDATA AVAILABILITY\nThe raw data used in the analyses are available via the Grav-\nitational Wave Open Science Center. 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Barros5, N. Barros28,51,\nD. Barrow2, J. L. Barrow52, A. Basharina-Freshville53, A. Bashyal22, V. Basque3,\nC. Batchelor54, L. Bathe-Peters2, J.B.R. Battat55, F. Battisti2, F. Bay56, M. C. Q. Bazetto9,\nJ. L. L. Bazo Alba57, J. F. Beacom58, E. Bechetoille40, B. Behera59, E. Belchior60,\nG. Bell61, L. Bellantoni3, G. Bellettini62,63, V. Bellini64,65, O. Beltramello1, N. Benekos1,\nC. Benitez Montiel20,66, D. Benjamin7, F. Bento Neves28, J. Berger67, S. Berkman68,\nJ. Bernal66, P. Bernardini69,70, A. Bersani71, S. Bertolucci72,73, M. Betancourt3, A. Betancur\nRodr\u00edguez74, A. Bevan75, Y. Bezawada76, A. T. Bezerra77, T. J. Bezerra36, A. Bhat78,\nV. Bhatnagar79, J. Bhatt53, M. Bhattacharjee80, M. Bhattacharya3, S. Bhuller8, B. Bhuyan80,\nS. Biagi81, J. Bian44, K. Biery3, B. Bilki82,83, M. Bishai7, A. Bitadze32, A. Blake84,\nF. D. Blaszczyk3, G. C. Blazey85, E. Blucher78, J. Bogenschuetz34, J. Boissevain86,\nS. Bolognesi87, T. Bolton16, L. Bomben88,89, M. Bonesini88,90, C. Bonilla-Diaz91, F. Bonini7,\nA. Booth75, F. Boran41, S. Bordoni1, R. Borges Merlo9, A. Borkum36, N. Bostan83,\nJ. Bracinik92, D. Braga3, B. Brahma93, D. Brailsford84, F. Bramati88, A. Branca88,\nA. Brandt34, J. Bremer1, C. Brew94, S. J. Brice3, V. Brio64, C. Brizzolari88,90, C. Bromberg68,\nJ. Brooke8, A. Bross3, G. Brunetti88,90, M. Brunetti43, N. Buchanan67, H. Budd13,\nJ. Buergi95, D. Burgardt96, S. Butchart36, G. Caceres V.76, I. Cagnoli72,73, T. Cai47,\nR. Calabrese25,26, J. Calcutt97, M. Calin98, L. Calivers95, E. Calvo18, A. Caminata71,\nA. F. Camino99, W. Campanelli28, A. Campani71,100, A. Campos Benitez101, N. Canci102,\nJ. Cap\u00f320, I. Caracas103, D. Caratelli104, D. Carber67, J. M. Carceller1, G. Carini7,\nB. Carlus40, M. F. Carneiro7, P. Carniti88, I. Caro Terrazas67, H. Carranza34, N. Carrara76,\nL. Carroll16, T. Carroll105, A. Carter106, E. Casarejos45, D. Casazza25, J. F. Casta\u00f1o Forero107,\nF. A. Casta\u00f1o108, A. Castillo109, C. Castromonte110, E. Catano-Mur111, C. Cattadori88,\nF. Cavalier37, F. Cavanna3, S. Centro112, G. Cerati3, C. Cerna113, A. Cervelli72, A. Cervera\nVillanueva20, K. Chakraborty114, S. Chakraborty115, M. Chalifour1, A. Chappell43,\nN. Charitonidis1, A. Chatterjee114, H. Chen7, M. Chen44, W. C. Chen116, Y. Chen30,\nZ. Chen-Wishart106, D. Cherdack10, C. Chi117, R. Chirco23, N. Chitirasreemadam62,63,\nK. Cho118, S. Choate85, D. Chokheli6, P. S. Chong119, B. Chowdhury22, D. Christian3,\nA. Chukanov29, M. Chung120, E. Church42, M. F. Cicala53, M. Cicerchia112, V. Cicero72,73,\nR. Ciolini62, P. Clarke54, G. Cline11, T. E. Coan121, A. G. Cocco102, J. A. B. Coelho122,\nA. Cohen122, J. Collazo45, J. Collot123, E. Conley124, J. M. Conrad52, M. Convery30,\nS. Copello71, P. Cova125,126, C. Cox106, L. Cremaldi127, L. Cremonesi75, J. I. Crespo-\nAnad\u00f3n18, M. Crisler3, E. Cristaldo88,66, J. Crnkovic3, G. Crone53, R. Cross43, A. Cudd14,\nC. Cuesta18, Y. Cui128, F. Curciarello129, D. Cussans8, J. Dai123, O. Dalager44, R. Dallavalle122,\nW. Dallaway116, H. da Motta130, Z. A. Dar111, R. Darby36, L. Da Silva Peres131, Q. David40,\nG. S. Davies127, S. Davini71, J. Dawson122, R. De Aguiar9, P. De Almeida9, P. Debbins83,\nI. De Bonis12, M. P. Decowski132,133, A. de Gouv\u00eaa134, P. C. De Holanda9, I. L. De Icaza\nAstiz36, P. De Jong132,133, P. Del Amo Sanchez12, A. De la Torre18, G. De Lauretis40,\narXiv:2403.03212v1 [physics.ins-det] 5 Mar 2024\n\nVersion March 6, 2024 submitted to Instruments\n2 of 47\nA. Delbart87, D. Delepine50, M. Delgado88,90, A. Dell\u2019Acqua1, G. Delle Monache129,\nN. Delmonte125,126, P. De Lurgio22, R. Demario68, G. De Matteis69, J. R. T. de Mello\nNeto131, D. M. DeMuth135, S. Dennis136, C. Densham94, P. Denton7, G. W. Deptuch7,\nA. De Roeck1, V. De Romeri20, J. P. Detje136, J. Devine1, R. Dharmapalan137, M. Dias138,\nA. Diaz139, J. S. D\u00edaz41, F. D\u00edaz57, F. Di Capua102,140, A. Di Domenico141,142, S. Di\nDomizio71,100, S. Di Falco62, L. Di Giulio1, P. Ding3, L. Di Noto71,100, E. Diociaiuti129,\nC. Distefano81, R. Diurba95, M. Diwan7, Z. Djurcic22, D. Doering30, S. Dolan1,\nF. Dolek101, M. J. Dolinski143, D. Domenici129, L. Domine30, S. Donati62,63, Y. Donon1,\nS. Doran144, D. Douglas30, T.A. Doyle145, A. Dragone30, F. Drielsma30, L. Duarte138,\nD. Duchesneau12, K. Duffy2,3, K. Dugas44, P. Dunne19, B. Dutta146, H. Duyang147,\nD. A. Dwyer11, A. S. Dyshkant85, S. Dytman99, M. Eads85, A. Earle36, S. Edayath144,\nD. Edmunds68, J. Eisch3, P. Englezos148, A. Ereditato78, T. Erjavec76, C. O. Escobar3,\nJ. J. Evans32, E. Ewart41, A. C. Ezeribe149, K. Fahey3, L. Fajt1, A. Falcone88,90, M. Fani\u201986,\nC. Farnese150, S. Farrell151, Y. Farzan152, D. Fedoseev29, J. Felix50, Y. Feng144, E. Fernandez-\nMartinez153, G. Ferry37, L. Fields154, P. Filip155, A. Filkins156, F. Filthaut132,157, R. Fine86,\nG. Fiorillo102,140, M. Fiorini25,26, S. Fogarty67, W. Foreman23, J. Fowler124, J. Franc158,\nK. Francis85, D. Franco78, J. Franklin159, J. Freeman3, J. Fried7, A. Friedland30, S. Fuess3,\nI. K. Furic59, K. Furman75, A. P. Furmanski160, R. Gaba79, A. Gabrielli72,73, A. M. Gago57,\nF. Galizzi88, H. Gallagher161, A. Gallas37, N. Gallice7, V. Galymov40, E. Gamberini1,\nT. Gamble149, F. Ganacim5, R. Gandhi162, S. Ganguly3, F. Gao104, S. Gao7, D. Garcia-\nGamez163, M. \u00c1. Garc\u00eda-Peris20, F. Gardim77, S. Gardiner3, D. Gastler164, A. Gauch95,\nJ. Gauvreau165, P. Gauzzi141,142, S. Gazzana129, G. Ge117, N. Geffroy12, B. Gelli9,\nS. Gent166, L. Gerlach7, Z. Ghorbani-Moghaddam71, T. Giammaria25,26, D. Gibin112,150,\nI. Gil-Botella18, S. Gilligan97, A. Gioiosa62, S. Giovannella129, C. Girerd40, A. K. Giri93,\nC. Giugliano25, V. Giusti62, D. Gnani11, O. Gogota39, S. Gollapinni86, K. Gollwitzer3,\nR. A. Gomes167, L. V. Gomez Bermeo109, L. S. Gomez Fajardo109, F. Gonnella92,\nD. Gonzalez-Diaz21, M. Gonzalez-Lopez153, M. C. Goodman22, S. Goswami114, C. Gotti88,\nJ. Goudeau60, E. Goudzovski92, C. Grace11, E. Gramellini32, R. Gran168, E. Granados50,\nP. Granger122, C. Grant164, D. R. Gratieri169,9, G. Grauso102, P. Green2, S. Greenberg170,11,\nJ. Greer8, W. C. Griffith36, F. T. Groetschla1, K. Grzelak171, L. Gu84, W. Gu7, V. Guarino22,\nM. Guarise25,26, R. Guenette32, E. Guerard37, M. Guerzoni72, D. Guffanti88,90, A. Guglielmi150,\nB. Guo147, Y. Guo145, A. Gupta30, V. Gupta132,133, G. Gurung34, D. Gutierrez172,\nP. Guzowski32, M. M. Guzzo9, S. Gwon173, A. Habig168, H. Hadavand34, L. Haegel40,\nR. Haenni95, L. Hagaman174, A. Hahn3, J. Haiston175, J. Hakenmueller124, T. Hamernik3,\nP. Hamilton19, J. Hancock92, F. Happacher129, D. A. Harris47,3, J. Hartnell36, T. Hartnett94,\nJ. Harton67, T. Hasegawa176, C. Hasnip2, R. Hatcher3, K. Hayrapetyan75, J. Hays75,\nE. Hazen164, M. He10, A. Heavey3, K. M. Heeger174, J. Heise177, S. Henry13, M. A. Hernandez\nMorquecho23, K. Herner3, V. Hewes38, A. Higuera151, C. Hilgenberg160, S. J. Hillier92,\nA. Himmel3, E. Hinkle78, L.R. Hirsch5, J. Ho178, J. Hoff3, A. Holin94, T. Holvey2,\nE. Hoppe42, S. Horiuchi101, G. A. Horton-Smith16, M. Hostert160, T. Houdy37, B. Howard3,\nR. Howell13, I. Hristova94, M. S. Hronek3, J. Huang76, R.G. Huang11, Z. Hulcher30,\nM. Ibrahim179, G. Iles19, N. Ilic116, A. M. Iliescu129, R. Illingworth3, G. Ingratta72,73,\nA. Ioannisian180, B. Irwin160, L. Isenhower181, M. Ismerio Oliveira131, R. Itay30,\nC.M. Jackson42, V. Jain182, E. James3, W. Jang34, B. Jargowsky44, D. Jena3, I. Jentz105, X. Ji7,\nC. Jiang183, J. Jiang145, L. Jiang101, A. Jipa98, F. R. Joaquim28,48, W. Johnson175, C. Jollet113,\nB. Jones34, R. Jones149, D. Jos\u00e9 Fern\u00e1ndez21, N. Jovancevic184, M. Judah99, C. K. Jung145,\nT. Junk3, Y. Jwa30,117, M. Kabirnezhad19, A. C. Kaboth106,94, I. Kadenko39, I. Kakorin29,\nA. Kalitkina29, D. Kalra117, M. Kandemir185, D. M. Kaplan23, G. Karagiorgi117, G. Karaman83,\nA. Karcher11, Y. Karyotakis12, S. Kasai186, S. P. Kasetti60, L. Kashur67, I. Katsioulas92,\nA. Kauther85, N. Kazaryan180, L. Ke7, E. Kearns164, P.T. Keener119, K.J. Kelly1, E. Kemp9,\nO. Kemularia6, Y. Kermaidic37, W. Ketchum3, S. H. Kettell7, M. Khabibullin187,\nN. Khan19, A. Khotjantsev187, A. Khvedelidze6, D. Kim146, J. Kim13, B. King3, B. Kirby117,\nM. Kirby7, A. Kish3, J. Klein119, J. Kleykamp127, A. Klustova19, T. Kobilarcik3,\nL. Koch103, K. Koehler105, L. W. Koerner10, D. H. Koh30, L. Kolupaeva29, D. Korablev29,\n\nVersion March 6, 2024 submitted to Instruments\n3 of 47\nM. Kordosky111, T. Kosc123, U. Kose1, V. A. Kosteleck\u00fd41, K. Kothekar8, I. Kotler143,\nM. Kovalcuk155, V. Kozhukalov29, W. Krah132, R. Kralik36, M. Kramer11, L. Kreczko8,\nF. Krennrich144, I. Kreslo95, T. Kroupova119, S. Kubota32, M. Kubu1, Y. Kudenko187,\nV. A. Kudryavtsev149, G. Kufatty188, S. Kuhlmann22, S. Kulagin187, J. Kumar137,\nP. Kumar149, S. Kumaran44, P. Kunze12, J. Kunzmann95, R. Kuravi11, N. Kurita30,\nC. Kuruppu147, V. Kus158, T. Kutter60, J. Kvasnicka155, T. Labree85, T. Lackey3, A. Lambert11,\nB. J. Land119, C. E. Lane143, N. Lane32, K. Lang189, T. Langford174, M. Langstaff32,\nF. Lanni1, O. Lantwin12, J. Larkin7, P. Lasorak19, D. Last119, A. Laudrain103, A. Laundrie105,\nG. Laurenti72, E. Lavaut37, A. Lawrence11, P. Laycock7, I. Lazanu98, M. Lazzaroni125,190,\nT. Le161, S. Leardini21, J. Learned137, T. LeCompte30, C. Lee3, V. Legin39, G. Lehmann\nMiotto1, R. Lehnert41, M. A. Leigui de Oliveira191, M. Leitner11, D. Leon Silverio175,\nL. M. Lepin188,32, J.-Y Li54, S. W. Li76, Y. Li7, H. Liao16, C. S. Lin11, D. Lindebaum8,\nS. Linden7, R. A. Lineros91, J. Ling192, A. Lister105, B. R. Littlejohn23, H. Liu7, J. Liu44,\nY. Liu78, S. Lockwitz3, M. Lokajicek155, I. Lomidze6, K. Long19, T. V. Lopes77, J.Lopez108,\nI. L\u00f3pez de Rego18, N. L\u00f3pez-March20, T. Lord43, J. M. LoSecco154, W. C. Louis86,\nA. Lozano Sanchez143, X.-G. Lu43, K.B. Luk193,170, B. Lunday119, X. Luo104, E. Luppi25,26,\nJ. Maalmi37, D. MacFarlane30, A. A. Machado9, P. Machado3, C. T. Macias41, J. R. Macier3,\nM. MacMahon53, A. Maddalena194, A. Madera1, P. Madigan170,11, S. Magill22, C. Magueur37,\nK. Mahn68, A. Maio28,51, A. Major124, K. Majumdar24, M. Man116, R. C. Mandujano44,\nJ. Maneira28,51, S. Manly13, A. Mann161, K. Manolopoulos94, M. Manrique Plata41,\nS. Manthey Corchado18, V. N. Manyam7, M. Marchan3, A. Marchionni3, W. Marciano7,\nD. Marfatia137, C. Mariani101, J. Maricic137, F. Marinho195, A. D. Marino14, T. Markiewicz30,\nF. Das Chagas Marques9, C. Marquet113, D. Marsden32, M. Marshak160, C. M. Marshall13,\nJ. Marshall43, L. Martina69, J. Mart\u00edn-Albo20, N. Martinez16, D.A. Martinez Caicedo 175,\nF. Mart\u00ednez L\u00f3pez75, P. Mart\u00ednez Mirav\u00e920, S. Martynenko7, V. Mascagna88, C. Massari88,\nA. Mastbaum148, F. Matichard11, S. Matsuno137, G. Matteucci102,140, J. Matthews60,\nC. Mauger119, N. Mauri72,73, K. Mavrokoridis24, I. Mawby84, R. Mazza88, A. Mazzacane3,\nT. McAskill55, N. McConkey53, K. S. McFarland13, C. McGrew145, A. McNab32,\nL. Meazza88, V. C. N. Meddage59, A. Mefodiev187, B. Mehta79, P. Mehta196, P. Melas197,\nO. Mena20, H. Mendez172, P. Mendez1, D. P. M\u00e9ndez7, A. Menegolli198,199, G. Meng150,\nA. C. E. A. Mercuri5, A. Meregaglia113, M. D. Messier41, S. Metallo160, J. Metcalf161,52,\nW. Metcalf60, M. Mewes41, H. Meyer96, T. Miao3, A. Miccoli69, G. Michna166, V. Mikola53,\nR. Milincic137, F. Miller105, G. Miller32, W. Miller160, O. Mineev187, A. Minotti88,90,\nL. Miralles1, O. G. Miranda200, C. Mironov122, S. Miryala7, S. Miscetti129, C. S. Mishra3,\nS. R. Mishra147, A. Mislivec160, M. Mitchell60, D. Mladenov1, I. Mocioiu201, A. Mogan3,\nN. Moggi72,73, R. Mohanta46, T. A. Mohayai41, N. Mokhov3, J. Molina66, L. Molina\nBueno20, E. Montagna72,73, A. Montanari72, C. Montanari198,3,199, D. Montanari3,\nD. Montanino69,70, L. M. Monta\u00f1o Zetina200, M. Mooney67, A. F. Moor149, Z. Moore156,\nD. Moreno107, O. Moreno-Palacios111, L. Morescalchi62, D. Moretti88, R. Moretti88,\nC. Morris10, C. Mossey3, M. Mote60, C. A. Moura191, G. Mouster84, W. Mu3, L. Mualem139,\nJ. Mueller67, M. Muether96, F. Muheim54, A. Muir61, M. Mulhearn76, D. Munford10,\nL. J. Munteanu1, H. Muramatsu160, J. Muraz123, M. Murphy101, T. Murphy156, J. Muse160,\nA. Mytilinaki94, J. Nachtman83, Y. Nagai179, S. Nagu202, R. Nandakumar94, D. Naples99,\nS. Narita203, A. Nath80, A. Navrer-Agasson32, N. Nayak7, M. Nebot-Guinot54, A. Nehm103,\nJ. K. Nelson111, O. Neogi83, J. Nesbit105, M. Nessi3,1, D. Newbold94, M. Newcomer119,\nR. Nichol53, F. Nicolas-Arnaldos163, A. Nikolica119, J. Nikolov184, E. Niner3, K. Nishimura137,\nA. Norman3, A. Norrick3, P. Novella20, J. A. Nowak84, M. Oberling22, J. P. Ochoa-Ricoux44,\nS. Oh124, S.B. Oh3, A. Olivier154, A. Olshevskiy29, T. Olson10, Y. Onel83, Y. Onishchuk39,\nA. Oranday41, M. Osbiston43, J. A. Osorio V\u00e9lez108, L. Otiniano Ormachea204,110, J. Ott44,\nL. Pagani76, G. Palacio74, O. Palamara3, S. Palestini1, J. M. Paley3, M. Pallavicini71,100,\nC. Palomares18, S. Pan114, P. Panda46, W. Panduro Vazquez106, E. Pantic76, V. Paolone99,\nV. Papadimitriou3, R. Papaleo81, A. Papanestis94, D. Papoulias197, S. Paramesvaran8,\nA. Paris172, S. Parke3, E. Parozzi88,90, S. Parsa95, Z. Parsa7, S. Parveen196, M. Parvu98,\nD. Pasciuto62, S. Pascoli72,73, L. Pasqualini72,73, J. Pasternak19, C. Patrick54,53, L. Patrizii72,\n\nVersion March 6, 2024 submitted to Instruments\n4 of 47\nR. B. Patterson139, T. Patzak122, A. Paudel3, L. Paulucci191, Z. Pavlovic3, G. Pawloski160,\nD. Payne24, V. Pec155, E. Pedreschi62, S. J. M. Peeters36, W. Pellico3, A. Pena Perez30,\nE. Pennacchio40, A. Penzo83, O. L. G. Peres9, Y. F. Perez Gonzalez159, L. P\u00e9rez-Molina18,\nC. Pernas111, J. Perry54, D. Pershey188, G. Pessina88, G. Petrillo30, C. Petta64,65, R. Petti147,\nM. Pfaff19, V. Pia72,73, L. Pickering94,106, F. Pietropaolo1,150, V.L.Pimentel205,9, G. Pinaroli7,\nJ. Pinchault12, K. Pitts101, K. Plows2, R. Plunkett3, C. Pollack172, T. Pollman132,133,\nD. Polo-Toledo4, F. Pompa20, X. Pons1, N. Poonthottathil115,144, V. Popov35, F. Poppi72,73,\nJ. Porter36, M. Potekhin7, R. Potenza64,65, J. Pozimski19, M. Pozzato72,73, T. Prakash11,\nC. Pratt76, M. Prest88, F. Psihas3, D. Pugnere40, X. Qian7, J. L. Raaf3, V. Radeka7,\nJ. Rademacker8, B. Radics47, A. Rafique22, E. Raguzin7, M. Rai43, S. Rajagopalan7,\nM. Rajaoalisoa38, I. Rakhno3, L. Rakotondravohitra27, L. Ralte93, M. A. Ramirez\nDelgado119, B. Ramson3, A. Rappoldi198,199, G. Raselli198,199, P. Ratoff84, R. Ray3,\nH. Razafinime38, E. M. Rea160, J. S. Real123, B. Rebel105,3, R. Rechenmacher3, M. Reggiani-\nGuzzo32, J. Reichenbacher175, S. D. Reitzner3, H. Rejeb Sfar1, E. Renner86, A. Renshaw10,\nS. Rescia7, F. Resnati1, D. Restrepo108, C. Reynolds75, M. Ribas5, S. Riboldi125,\nC. Riccio145, G. Riccobene81, J. S. Ricol123, M. Rigan36, E. V. Rinc\u00f3n74, A. Ritchie-Yates106,\nS. Ritter103, D. Rivera86, R. Rivera3, A. Robert123, J. L. Rocabado Rocha20, L. Rochester30,\nM. Roda24, P. Rodrigues2, M. J. Rodriguez Alonso1, J. Rodriguez Rondon175, S. Rosauro-\nAlcaraz37, P. Rosier37, D. Ross68, M. Rossella198,199, M. Rossi1, M. Ross-Lonergan86,\nN. Roy47, P. Roy96, C. Rubbia206, A. Ruggeri72, G. Ruiz Ferreira32, B. Russell52,\nD. Ruterbories13, A. Rybnikov29, A. Saa-Hernandez21, R. Saakyan53, S. Sacerdoti122,\nS. K. Sahoo93, N. Sahu93, P. Sala125,1, N. Samios7, O. Samoylov29, M. C. Sanchez188,\nA. S\u00e1nchez Bravo20, P. Sanchez-Lucas163, V. Sandberg86, D. A. Sanders127, S. Sanfilippo81,\nD. Sankey94, D. Santoro125, N. Saoulidou197, P. Sapienza81, C. Sarasty38, I. Sarcevic207,\nI. Sarra129, G. Savage3, V. Savinov99, G. Scanavini174, A. Scaramelli198, A. Scarff149,\nT. Schefke60, H. Schellman97,3, S. Schifano25,26, P. Schlabach3, D. Schmitz78, A. W. Schneider52,\nK. Scholberg124, A. Schukraft3, B. Schuld14, A. Segade45, E. Segreto9, A. Selyunin29,\nC. R. Senise138, J. Sensenig119, M. H. Shaevitz117, P. Shanahan3, P. Sharma79, R. Kumar208,\nK. Shaw36, T. Shaw3, K. Shchablo40, J. Shen119, C. Shepherd-Themistocleous94,\nA. Sheshukov29, W. Shi145, S. Shin209, S. Shivakoti96, I. Shoemaker101, D. Shooltz68,\nR. Shrock145, B. Siddi25, M. Siden67, J. Silber11, L. Simard37, J. Sinclair30, G. Sinev175,\nJaydip Singh202, J. Singh202, L. Singh210, P. Singh75, V. Singh210, S. Singh Chauhan79,\nR. Sipos1, C. Sironneau122, G. Sirri72, K. Siyeon173, K. Skarpaas30, J. Smedley13,\nE. Smith41, J. Smith145, P. Smith41, J. Smolik158,155, M. Smy44, M. Snape43, E.L. Snider3,\nP. Snopok23, D. Snowden-Ifft165, M. Soares Nunes3, H. Sobel44, M. Soderberg156,\nS. Sokolov29, C. J. Solano Salinas211,110, S. S\u00f6ldner-Rembold32, S.R. Soleti11, N. Solomey96,\nV. Solovov28, W. E. Sondheim86, M. Sorel20, A. Sotnikov29, J. Soto-Oton20, A. Sousa38,\nK. Soustruznik212, F. Spinella62, J. Spitz213, N. J. C. Spooner149, K. Spurgeon156,\nD. Stalder66, M. Stancari3, L. Stanco150,112, J. Steenis76, R. Stein8, H. M. Steiner11,\nA. F. Steklain Lisb\u00f4a5, A. Stepanova29, J. Stewart7, B. Stillwell78, J. Stock175, F. Stocker1,\nT. Stokes60, M. Strait160, T. Strauss3, L. Strigari146, A. Stuart31, J. G. Suarez74, J. Subash92,\nA. Surdo69, L. Suter3, C. M. Sutera64,65, K. Sutton139, Y. Suvorov102,140, R. Svoboda76,\nS. K. Swain214, B. Szczerbinska215, A. M. Szelc54, A. Sztuc53, A. Taffara62, N. Talukdar147,\nJ. Tamara107, H. A. Tanaka30, S. Tang7, N. Taniuchi136, A. M. Tapia Casanova216,\nB. Tapia Oregui189, A. Tapper19, S. Tariq3, E. Tarpara7, E. Tatar217, R. Tayloe41,\nD. Tedeschi147, A. M. Teklu145, J. Tena Vidal35, P. Tennessen11,56, M. Tenti72, K. Terao30,\nF. Terranova88,90, G. Testera71, T. Thakore38, A. Thea94, A. Thiebault37, S. Thomas156,\nA. Thompson146, C. Thorn7, S. C. Timm3, E. Tiras185,83, V. Tishchenko7, N. Todorovi\u00b4c184,\nL. Tomassetti25,26, A. Tonazzo122, D. Torbunov7, M. Torti88, M. Tortola20, F. Tortorici64,65,\nN. Tosi72, D. Totani104, M. Toups3, C. Touramanis24, D. Tran10, R. Travaglini72,\nJ. Trevor139, E. Triller68, S. Trilov8, J. Truchon105, D. Truncali141,142, W. H. Trzaska218,\nY. Tsai44, Y.-T. Tsai30, Z. Tsamalaidze6, K. V. Tsang30, N. Tsverava6, S. Z. Tu183,\nS. Tufanli1, C. Tunnell151, J. Turner159, M. Tuzi20, J. Tyler16, E. Tyley149, M. Tzanov60,\nM. A. Uchida136, J. Ure\u00f1a Gonz\u00e1lez20, J. Urheim41, T. Usher30, H. Utaegbulam13,\n\nS. Uzunyan85, M. R. Vagins219,44, P. Vahle111, S. Valder36, G. A. Valdiviesso77, E. Valencia50,\nR. Valentim138, Z. Vallari139, E. Vallazza88, J. W. F. Valle20, R. Van Berg119, R. G. Van\nde Water86, D. V. Forero216, A. Vannozzi129, M. Van Nuland-Troost132, F. Varanini150,\nD. Vargas Oliva116, S. Vasina29, N. Vaughan97, K. Vaziri3, A. V\u00e1zquez-Ramos163,\nJ. Vega204, S. Ventura150, A. Verdugo18, S. Vergani53, M. Verzocchi3, K. Vetter3,\nM. Vicenzi7, H. Vieira de Souza122, C. Vignoli194, C. Vilela28, E. Villa1, S. Viola81,\nB. Viren7, A. Vizcaya-Hernandez67, T. Vrba158, Q. Vuong13, A. V. Waldron75, M. Wallbank38,\nJ. Walsh68, T. Walton3, H. Wang220, J. Wang175, L. Wang11, M.H.L.S. Wang3, X. Wang3,\nY. Wang220, K. Warburton144, D. Warner67, L. Warsame19, M.O. Wascko2, D. Waters53,\nA. Watson92, K. Wawrowska94,36, A. Weber103,3, C. M. Weber160, M. Weber95, H. Wei60,\nA. Weinstein144, H. Wenzel3, S. Westerdale128, M. Wetstein144, K. Whalen94, J. Whilhelmi174,\nA. White34, A. White174, L. H. Whitehead136, D. Whittington156, M. J. Wilking160,\nA. Wilkinson53, C. Wilkinson11, F. Wilson94, R. J. Wilson67, P. Winter22, W. Wisniewski30,\nJ. Wolcott161, J. Wolfs13, T. Wongjirad161, A. Wood10, K. Wood11, E. Worcester7,\nM. Worcester7, M. Wospakrik3, K. Wresilo136, C. Wret13, S. Wu160, W. Wu3, W. Wu44,\nM. Wurm103, J. Wyenberg178, Y. Xiao44, I. Xiotidis19, B. Yaeggy38, N. Yahlali20, E. Yandel104,\nK. Yang2, T. Yang3, A. Yankelevich44, N. Yershov187, K. Yonehara3, T. Young49, B. Yu7,\nH. Yu7, J. Yu34, Y. Yu23, W. Yuan54, R. Zaki47, J. Zalesak155, L. Zambelli12, B. Zamorano163,\nA. Zani125, O. Zapata108, L. Zazueta156, G. P. Zeller3, J. Zennamo3, K. Zeug105, C. Zhang7,\nS. Zhang41, M. Zhao7, E. Zhivun7, E. D. Zimmerman14, S. Zucchelli72,73, J. Zuklin155,\nV. Zutshi85, R. Zwaska3, and On behalf of the DUNE Collaboration\n1\nCERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland\n2\nUniversity of Oxford, Oxford, OX1 3RH, United Kingdom\n3\nFermi National Accelerator Laboratory, Batavia, IL 60510, USA\n4\nUniversidad del Atl\u00e1ntico, Barranquilla, Atl\u00e1ntico, Colombia\n5\nUniversidade Tecnol\u00f3gica Federal do Paran\u00e1, Curitiba, Brazil\n6\nGeorgian Technical University, Tbilisi, Georgia\n7\nBrookhaven National Laboratory, Upton, NY 11973, USA\n8\nUniversity of Bristol, Bristol BS8 1TL, United Kingdom\n9\nUniversidade Estadual de Campinas, Campinas - SP, 13083-970, Brazil\n10\nUniversity of Houston, Houston, TX 77204, USA\n11\nLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA\n12\nLaboratoire d\u2019Annecy de Physique des Particules, Universit\u00e9 Savoie Mont Blanc, CNRS, LAPP-IN2P3, 74000\nAnnecy, France\n13\nUniversity of Rochester, Rochester, NY 14627, USA\n14\nUniversity of Colorado Boulder, Boulder, CO 80309, USA\n15\nETH Zurich, Zurich, Switzerland\n16\nKansas State University, Manhattan, KS 66506, USA\n17\nAugustana University, Sioux Falls, SD 57197, USA\n18\nCIEMAT, Centro de Investigaciones Energ\u00e9ticas, Medioambientales y Tecnol\u00f3gicas, E-28040 Madrid, Spain\n19\nImperial College of Science Technology and Medicine, London SW7 2BZ, United Kingdom\n20\nInstituto de F\u00edsica Corpuscular, CSIC and Universitat de Val\u00e8ncia, 46980 Paterna, Valencia, Spain\n21\nInstituto Galego de F\u00edsica de Altas Enerx\u00edas, University of Santiago de Compostela, Santiago de Compostela,\n15782, Spain\n22\nArgonne National Laboratory, Argonne, IL 60439, USA\n23\nIllinois Institute of Technology, Chicago, IL 60616, USA\n24\nUniversity of Liverpool, L69 7ZE, Liverpool, United Kingdom\n25\nIstituto Nazionale di Fisica Nucleare Sezione di Ferrara, I-44122 Ferrara, Italy\n26\nUniversity of Ferrara, Ferrara, Italy\n27\nUniversity of Antananarivo, Antananarivo 101, Madagascar\n28\nLaborat\u00f3rio de Instrumenta\u00e7\u00e3o e F\u00edsica Experimental de Part\u00edculas, 1649-003 Lisboa and 3004-516 Coimbra,\nPortugal\n29\nJoint Institute for Nuclear Research, Dzhelepov Laboratory of Nuclear Problems 6 Joliot-Curie, Dubna,\nMoscow Region, 141980 RU\n30\nSLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA\n31\nUniversidad de Colima, Colima, Mexico\n32\nUniversity of Manchester, Manchester M13 9PL, United Kingdom\n33\nUniversidad del Magdalena, Santa Marta - Colombia\nVersion March 6, 2024 submitted to Instruments\nhttps://www.mdpi.com/journal/instruments\n\nVersion March 6, 2024 submitted to Instruments\n6 of 47\n34\nUniversity of Texas at Arlington, Arlington, TX 76019, USA\n35\nTel Aviv University, Tel Aviv-Yafo, Israel\n36\nUniversity of Sussex, Brighton, BN1 9RH, United Kingdom\n37\nUniversit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n38\nUniversity of Cincinnati, Cincinnati, OH 45221, USA\n39\nTaras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine\n40\nInstitut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France\n41\nIndiana University, Bloomington, IN 47405, USA\n42\nPacific Northwest National Laboratory, Richland, WA 99352, USA\n43\nUniversity of Warwick, Coventry CV4 7AL, United Kingdom\n44\nUniversity of California Irvine, Irvine, CA 92697, USA\n45\nUniversity of Vigo, E- 36310 Vigo Spain\n46\nUniversity of Hyderabad, Gachibowli, Hyderabad - 500 046, India\n47\nYork University, Toronto M3J 1P3, Canada\n48\nInstituto Superior T\u00e9cnico - IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal\n49\nUniversity of North Dakota, Grand Forks, ND 58202-8357, USA\n50\nUniversidad de Guanajuato, Guanajuato, C.P. 37000, Mexico\n51\nFaculdade de Ci\u00eancias da Universidade de Lisboa - FCUL, 1749-016 Lisboa, Portugal\n52\nMassachusetts Institute of Technology, Cambridge, MA 02139, USA\n53\nUniversity College London, London, WC1E 6BT, United Kingdom\n54\nUniversity of Edinburgh, Edinburgh EH8 9YL, United Kingdom\n55\nWellesley College, Wellesley, MA 02481, USA\n56\nAntalya Bilim University, 07190 D\u00f6\u00b8semealt\u0131/Antalya, Turkey\n57\nPontificia Universidad Cat\u00f3lica del Per\u00fa, Lima, Per\u00fa\n58\nOhio State University, Columbus, OH 43210, USA\n59\nUniversity of Florida, Gainesville, FL 32611-8440, USA\n60\nLouisiana State University, Baton Rouge, LA 70803, USA\n61\nDaresbury Laboratory, Cheshire WA4 4AD, United Kingdom\n62\nIstituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa PI, Italy\n63\nUniversit\u00e0 di Pisa, I-56127 Pisa, Italy\n64\nIstituto Nazionale di Fisica Nucleare Sezione di Catania, I-95123 Catania, Italy\n65\nUniversit\u00e0 di Catania, 2 - 95131 Catania, Italy\n66\nUniversidad Nacional de Asunci\u00f3n, San Lorenzo, Paraguay\n67\nColorado State University, Fort Collins, CO 80523, USA\n68\nMichigan State University, East Lansing, MI 48824, USA\n69\nIstituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 - Lecce, Italy\n70\nUniversit\u00e0 del Salento, 73100 Lecce, Italy\n71\nIstituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova GE, Italy\n72\nIstituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna BO, Italy\n73\nUniversit\u00e0 di Bologna, 40127 Bologna, Italy\n74\nUniversidad EIA, Envigado, Antioquia, Colombia\n75\nQueen Mary University of London, London E1 4NS, United Kingdom\n76\nUniversity of California Davis, Davis, CA 95616, USA\n77\nUniversidade Federal de Alfenas, Po\u00e7os de Caldas - MG, 37715-400, Brazil\n78\nUniversity of Chicago, Chicago, IL 60637, USA\n79\nPanjab University, Chandigarh, 160014, India\n80\nIndian Institute of Technology Guwahati, Guwahati, 781 039, India\n81\nIstituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy\n82\nBeykent University, Istanbul, Turkey\n83\nUniversity of Iowa, Iowa City, IA 52242, USA\n84\nLancaster University, Lancaster LA1 4YB, United Kingdom\n85\nNorthern Illinois University, DeKalb, IL 60115, USA\n86\nLos Alamos National Laboratory, Los Alamos, NM 87545, USA\n87\nIRFU, CEA, Universit\u00e9 Paris-Saclay, F-91191 Gif-sur-Yvette, France\n88\nIstituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3 - I-20126 Milano, Italy\n89\nUniversity of Insubria, Via Ravasi, 2, 21100 Varese VA, Italy\n90\nUniversit\u00e0 di Milano Bicocca , 20126 Milano, Italy\n91\nUniversidad Cat\u00f3lica del Norte, Antofagasta, Chile\n92\nUniversity of Birmingham, Birmingham B15 2TT, United Kingdom\n93\nIndian Institute of Technology Hyderabad, Hyderabad, 502285, India\n94\nSTFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom\n95\nUniversity of Bern, CH-3012 Bern, Switzerland\n96\nWichita State University, Wichita, KS 67260, USA\n\nVersion March 6, 2024 submitted to Instruments\n7 of 47\n97\nOregon State University, Corvallis, OR 97331, USA\n98\nUniversity of Bucharest, Bucharest, Romania\n99\nUniversity of Pittsburgh, Pittsburgh, PA 15260, USA\n100\nUniversit\u00e0 degli Studi di Genova, Genova, Italy\n101\nVirginia Tech, Blacksburg, VA 24060, USA\n102\nIstituto Nazionale di Fisica Nucleare Sezione di Napoli, I-80126 Napoli, Italy\n103\nJohannes Gutenberg-Universit\u00e4t Mainz, 55122 Mainz, Germany\n104\nUniversity of California Santa Barbara, Santa Barbara, CA 93106, USA\n105\nUniversity of Wisconsin Madison, Madison, WI 53706, USA\n106\nRoyal Holloway College London, London, TW20 0EX, United Kingdom\n107\nUniversidad Antonio Nari\u00f1o, Bogot\u00e1, Colombia\n108\nUniversity of Antioquia, Medell\u00edn, Colombia\n109\nUniversidad Sergio Arboleda, 11022 Bogot\u00e1, Colombia\n110\nUniversidad Nacional de Ingenier\u00eda, Lima 25, Per\u00fa\n111\nWilliam and Mary, Williamsburg, VA 23187, USA\n112\nUniverst\u00e0 degli Studi di Padova, I-35131 Padova, Italy\n113\nLaboratoire de Physique des Deux Infinis Bordeaux - IN2P3, F-33175 Gradignan, Bordeaux, France,\n114\nPhysical Research Laboratory, Ahmedabad 380 009, India\n115\nIndian Institute of Technology Kanpur, Uttar Pradesh 208016, India\n116\nUniversity of Toronto, Toronto, Ontario M5S 1A1, Canada\n117\nColumbia University, New York, NY 10027, USA\n118\nKorea Institute of Science and Technology Information, Daejeon, 34141, South Korea\n119\nUniversity of Pennsylvania, Philadelphia, PA 19104, USA\n120\nUlsan National Institute of Science and Technology, Ulsan 689-798, South Korea\n121\nSouthern Methodist University, Dallas, TX 75275, USA\n122\nUniversit\u00e9 Paris Cit\u00e9, CNRS, Astroparticule et Cosmologie, Paris, France\n123\nUniversity Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France\n124\nDuke University, Durham, NC 27708, USA\n125\nIstituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milano, Italy\n126\nUniversity of Parma, 43121 Parma PR, Italy\n127\nUniversity of Mississippi, University, MS 38677 USA\n128\nUniversity of California Riverside, Riverside CA 92521, USA\n129\nIstituto Nazionale di Fisica Nucleare Laboratori Nazionali di Frascati, Frascati, Roma, Italy\n130\nCentro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro, RJ 22290-180, Brazil\n131\nUniversidade Federal do Rio de Janeiro, Rio de Janeiro - RJ, 21941-901, Brazil\n132\nNikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands\n133\nUniversity of Amsterdam, NL-1098 XG Amsterdam, The Netherlands\n134\nNorthwestern University, Evanston, Il 60208, USA\n135\nValley City State University, Valley City, ND 58072, USA\n136\nUniversity of Cambridge, Cambridge CB3 0HE, United Kingdom\n137\nUniversity of Hawaii, Honolulu, HI 96822, USA\n138\nUniversidade Federal de S\u00e3o Paulo, 09913-030, S\u00e3o Paulo, Brazil\n139\nCalifornia Institute of Technology, Pasadena, CA 91125, USA\n140\nUniversit\u00e0 degli Studi di Napoli Federico II , 80138 Napoli NA, Italy\n141\nSapienza University of Rome, 00185 Roma RM, Italy\n142\nIstituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Roma RM, Italy\n143\nDrexel University, Philadelphia, PA 19104, USA\n144\nIowa State University, Ames, Iowa 50011, USA\n145\nStony Brook University, SUNY, Stony Brook, NY 11794, USA\n146\nTexas A&M University, College Station, Texas 77840\n147\nUniversity of South Carolina, Columbia, SC 29208, USA\n148\nRutgers University, Piscataway, NJ, 08854, USA\n149\nUniversity of Sheffield, Sheffield S3 7RH, United Kingdom\n150\nIstituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padova, Italy\n151\nRice University, Houston, TX 77005\n152\nInstitute for Research in Fundamental Sciences, Tehran, Iran\n153\nMadrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain\n154\nUniversity of Notre Dame, Notre Dame, IN 46556, USA\n155\nInstitute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic\n156\nSyracuse University, Syracuse, NY 13244, USA\n157\nRadboud University, NL-6525 AJ Nijmegen, Netherlands\n158\nCzech Technical University, 115 19 Prague 1, Czech Republic\n159\nDurham University, Durham DH1 3LE, United Kingdom\n\nVersion March 6, 2024 submitted to Instruments\n8 of 47\n160\nUniversity of Minnesota Twin Cities, Minneapolis, MN 55455, USA\n161\nTufts University, Medford, MA 02155, USA\n162\nHarish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India\n163\nUniversity of Granada CAFPE, 18002 Granada, Spain\n164\nBoston University, Boston, MA 02215, USA\n165\nOccidental College, Los Angeles, CA 90041\n166\nSouth Dakota State University, Brookings, SD 57007, USA\n167\nUniversidade Federal de Goias, Goiania, GO 74690-900, Brazil\n168\nUniversity of Minnesota Duluth, Duluth, MN 55812, USA\n169\nFluminense Federal University, 9 Icara\u00ed Niter\u00f3i - RJ, 24220-900, Brazil\n170\nUniversity of California Berkeley, Berkeley, CA 94720, USA\n171\nUniversity of Warsaw, 02-093 Warsaw, Poland\n172\nUniversity of Puerto Rico, Mayaguez 00681, Puerto Rico, USA\n173\nChung-Ang University, Seoul 06974, South Korea\n174\nYale University, New Haven, CT 06520, USA\n175\nSouth Dakota School of Mines and Technology, Rapid City, SD 57701, USA\n176\nHigh Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801, Japan\n177\nSanford Underground Research Facility, Lead, SD, 57754, USA\n178\nDordt University, Sioux Center, IA 51250, USA\n179\nE\u00f6tv\u00f6s Lor\u00e1nd University, 1053 Budapest, Hungary\n180\nYerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia\n181\nAbilene Christian University, Abilene, TX 79601, USA\n182\nUniversity of Albany, SUNY, Albany, NY 12222, USA\n183\nJackson State University, Jackson, MS 39217, USA\n184\nUniversity of Novi Sad, 21102 Novi Sad, Serbia\n185\nErciyes University, Kayseri, Turkey\n186\nNational Institute of Technology, Kure College, Hiroshima, 737-8506, Japan\n187\nInstitute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia\n188\nFlorida State University, Tallahassee, FL, 32306 USA\n189\nUniversity of Texas at Austin, Austin, TX 78712, USA\n190\nUniversit\u00e0 degli Studi di Milano, I-20133 Milano, Italy\n191\nUniversidade Federal do ABC, Santo Andr\u00e9 - SP, 09210-580, Brazil\n192\nSun Yat-Sen University, Guangzhou, 510275, China\n193\nHong Kong University of Science and Technology, Kowloon, Hong Kong, China\n194\nLaboratori Nazionali del Gran Sasso, L\u2019Aquila AQ, Italy\n195\nInstituto Tecnol\u00f3gico de Aeron\u00e1utica, Sao Jose dos Campos, Brazil\n196\nJawaharlal Nehru University, New Delhi 110067, India\n197\nUniversity of Athens, Zografou GR 157 84, Greece\n198\nIstituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy\n199\nUniversit\u00e0 degli Studi di Pavia, 27100 Pavia PV, Italy\n200\nCentro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional (Cinvestav), Mexico\nCity, Mexico\n201\nPennsylvania State University, University Park, PA 16802, USA\n202\nUniversity of Lucknow, Uttar Pradesh 226007, India\n203\nIwate University, Morioka, Iwate 020-8551, Japan\n204\nComisi\u00f3n Nacional de Investigaci\u00f3n y Desarrollo Aeroespacial, Lima, Peru\n205\nCentro de Tecnologia da Informacao Renato Archer, Amarais - Campinas, SP - CEP 13069-901\n206\nGran Sasso Science Institute, L\u2019Aquila, Italy\n207\nUniversity of Arizona, Tucson, AZ 85721, USA\n208\nPunjab Agricultural University, Ludhiana 141004, India\n209\nJeonbuk National University, Jeonrabuk-do 54896, South Korea\n210\nCentral University of South Bihar, Gaya, 824236, India\n211\nUniversidad Nacional Mayor de San Marcos, Lima, Peru\n212\nInstitute of Particle and Nuclear Physics of the Faculty of Mathematics and Physics of the Charles\nUniversity, 180 00 Prague 8, Czech Republic\n213\nUniversity of Michigan, Ann Arbor, MI 48109, USA\n214\nNational Institute of Science Education and Research (NISER), Odisha 752050, India\n215\nTexas AM University - Corpus Christi, Corpus Christi, TX 78412, USA\n216\nUniversity of Medell\u00edn, Medell\u00edn, 050026 Colombia\n217\nIdaho State University, Pocatello, ID 83209, USA\n218\nJyv\u00e4skyl\u00e4 University, FI-40014 Jyv\u00e4skyl\u00e4, Finland\n219\nKavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan\n220\nUniversity of California Los Angeles, Los Angeles, CA 90095, USA\n\nVersion March 6, 2024 submitted to Instruments\n9 of 47\n\u2020\nIn memory of our colleague, Dr. Davide Salvatore Porzio, who is no longer with us.\nAbstract: The Module-0 Demonstrator is a single-phase 600 kg liquid argon time projection cham-\nber operated as a prototype for the DUNE liquid argon near detector. Based on the ArgonCube\ndesign concept, Module-0 features a novel 80k-channel pixelated charge readout and advanced\nhigh-coverage photon detection system. In this paper, we present an analysis of an eight-day data\nset consisting of 25 million cosmic ray events collected in the spring of 2021. We use this sample to\ndemonstrate the imaging performance of the charge and light readout systems as well as the signal\ncorrelations between the two. We also report argon purity and detector uniformity measurements,\nand provide comparisons to detector simulations.\n1. Introduction\nCharge readout in liquid argon time projection chambers (LArTPCs) has traditionally\nbeen accomplished via a set of projective wire planes, as successfully demonstrated e.g.\nin the ICARUS [1], ArgoNeuT [2], MicroBooNE [3] and ProtoDUNE-SP [4,5] experiments,\nand as planned for the first large detector module of the DUNE experiment currently in\npreparation at the Sanford Underground Research Facility (SURF) underground laboratory\nin South Dakota [6]. However, this approach leads to inherent ambiguities in the 3D\nreconstruction of charge information that present serious challenges for LArTPC-based\nnear detectors, where a high rate of neutrino interactions and an associated high-intensity\nmuon flux cannot be avoided. In particular, 3D reconstruction becomes limited by overlap\nof charge clusters in one or more projections, and the unique association of deposited\ncharge to single interactions becomes intractable.\nTo overcome event pile-up, a novel approach has been proposed and is being devel-\noped for the LArTPC of the Near Detector (ND) complex of the DUNE experiment, close\nto the neutrino source at Fermilab. This technology implements three main innovations\ncompared to traditional wire-based LArTPCs: a pixelated charge readout enabling true\n3D reconstruction, a high-performance light readout system providing fast and efficient\ndetection of scintillation light, and segmentation into optically isolated regions. By achiev-\ning a low signal occupancy in both readout systems, the segmentation enables efficient\nreconstruction and unambiguous matching of charge and light signals.\nThis paper describes the first tonne-scale prototype of this technology, referred to\nas Module-0, and its performance as evaluated with a large cosmic ray data set acquired\nover a period of several days at the University of Bern. Section 2 provides an overview\nof the detector, as well as of its charge and light readout systems. Section 3 discusses the\nperformance of the charge readout system in detail, and Section 4 does the same for the\nlight readout system. Section 5 then reviews several analyses performed with reconstructed\ntracks from the cosmic ray data set collected during the Module-0 that allow to assess the\nperformance of the fully-integrated system. Important metrics for successful operation\nare addressed, such as electron lifetime, electric field uniformity, and the ability to match\ncharge and light signals, among others. Section 6 offers some concluding thoughts.\n2. The Module-0 Demonstrator\n2.1. Detector Description\nThe Module-0 demonstrator is the first fully integrated, tonne-scale prototype of the\nDUNE Liquid Argon Near Detector (ND-LAr) design. That detector will consist of a 7 \u00d7 5\narray of 1 \u00d7 1 \u00d7 3 m3 detector modules [7] based on the ArgonCube detector concept [8],\neach housing two 50 cm\u2013drift TPC volumes with 24.9% optical detector coverage of the\ninterior area. Module-0 has dimensions of 0.7 m \u00d7 0.7 m \u00d7 1.4 m, and brings together the\ninnovative features of LArPix [9,10] pixelated 3D charge readout, advanced ArCLight [11]\nand Light Collection Module (LCM) [12] optical detectors, and field shaping provided by\na low-profile resistive shell [13]. This integrated prototype also tests the charge and light\n\nVersion March 6, 2024 submitted to Instruments\n10 of 47\nsystem control interfaces, data acquisition, triggering, and timing. Module-0 is the first of\nfour functionally-identical modules that together will comprise an upcoming 2 \u00d7 2 ND-LAr\nprototype, known as ProtoDUNE-ND. Following construction and initial tests with cosmic\nray event samples, this larger detector will be deployed underground in the NuMI neutrino\nbeam at Fermilab [14] to demonstrate the physics performance of the technology in a\nsimilar neutrino beam environment to the DUNE ND. The work presented here describes\nthe analysis of a data set of cosmic ray events obtained with the Module-0 detector, installed\nin a liquid argon cryostat at the Laboratory for High-Energy Physics of the University of\nBern. Over a period of eight days, the detector collected a sample of approximately\n25 million self-triggered cosmic ray\u2013induced events along with sets of diagnostic and\ncalibration data. The data collection period included an array of characterization tests and\ndata collection with changes to detector trigger conditions, thresholds, and with the TPC\ndrift field as high as 1 kV/cm. For a brief second running period, the cryostat was emptied\nand refilled following a series of gas purges rather than complete evacuation, to assess the\npurity impact; this is discussed further in Section 5.1. A gallery of events of different types\nis shown in Fig. 1. These images illustrate the rich 3D raw data from the pixelated charge\nreadout system, the imaging capabilities for complex event topologies, and the low noise\nlevels.\nA schematic showing an exploded view of Module-0 with annotations of the key\ncomponents is provided in Fig. 2, and a photograph of the interior of the Module-0 detector\nas seen from the bottom prior to final assembly in Fig. 3. The module is divided into two\nidentical TPC drift regions sharing a central high-voltage cathode that provides the drift\nelectric field. Opposite the cathode at a distance of 30 cm are the anode planes, pixelated\nwith charge-sensitive gold-plated pads where drifting ionization electrons are collected.\nThe sides of the module are covered with photon detectors \u2014 alternating ArCLight and\nLCM tiles. The TPC drift region is surrounded by a resistive field shell made of carbon-\nloaded Kapton films. This low-profile field cage provides field shaping to ensure a uniform\nelectric field throughout the TPC volumes.\n2.2. The Charge Readout System\nThe charge readout is accomplished using a two-dimensional array of charge-sensitive\npads on the two anode planes parallel to the cathode. While pixel-based charge readout\nhas already been implemented in gaseous TPCs, LArTPCs have additional challenges due\nto restrictions on power dissipation. A proof of principle for pixelated charge readout in a\nsingle-phase LArTPC is described in Ref. [15], where a test device was exposed to cosmic\nray muons. Readout electronics were also developed [9,16] and successfully applied in a\npixel-readout LArTPC. Each of the anode planes on opposite sides of the central cathode\nis comprised of a 2 \u00d7 4 array of anode tiles. Each tile is a large-area printed circuit board\n(PCB) containing a 70 \u00d7 70 grid of 4,900 charge-sensitive pixel pads with a 4.43 mm pitch.\nOn the back of each PCB is a 10 \u00d7 10 grid of custom low-power, low-noise cryogenic-\ncompatible LArPix-v2 application-specific integrated circuits (ASICs) [10], as shown in\nFig. 4. Each ASIC is a mixed-signal chip consisting of 64 analog front-end amplifiers, 64\nanalog-to-digital converters, and a shared digital core that manages configuration and data\nI/O. Each pixel channel functions as an independent self-triggering detector with nearly\n100% uptime, and is only unresponsive to charge for 100 ns while the frontend resets. The\nLArPix ASIC leverages the sparsity of LArTPC signals. The chip is in a quiescent mode\nwhen not self-triggering on ionization activity higher than O(100) keV. Thus, it avoids\ndigitization and readout of mostly-quiescent data. At liquid argon temperatures, the rate\nof accumulation of spurious charge (leakage current) is about 500 electrons/second. Each\nchannel periodically resets to discard spurious charge that has collected at the input. In\ntotal, Module-0 comprises 78,400 instrumented LArTPC pixels.\nPower and data I/O is provided to each tile by a single 34-pin twisted-pair ribbon cable.\nThese cables are connected at the cryostat flange to a custom feedthrough PCB mounted on\nthe cryostat lid. Data acquisition is controlled by the Pixel Array Controller and Network\n\nVersion March 6, 2024 submitted to Instruments\n11 of 47\n(b) EM Shower\n(d) \u201cNeutrino-like\u201d\n(c) Multi-Prong Shower\n(a) Stopping Muon + Michel e-\nCharge [103 e\u2013]\nFigure 1.\nGallery of four representative cosmic ray-induced events collected with Module-0, as\nrecorded in the raw event data, with collected charge converted to units of thousands of electrons.\nIn all cases, the central plane in grey denotes the cathode, and the color scale denotes the collected\ncharge. (a) shows a stopping muon and the subsequent Michel electron decay, (b) denotes an\nelectromagnetic (EM) shower, (c) is a multi-prong shower, and (d) is \u201cneutrino-like\u201d in that the vertex\nof this interaction appears to be inside the active volume.\n\nVersion March 6, 2024 submitted to Instruments\n12 of 47\nPixelated \nAnode Tile \n(70\u2a0970 pixels)\nArCLight Tile\nLCM Tiles\nResistive Field Sheet\nCathode\n0.7 m\n0.7 m\n1.40 m\n0.63 m\nFigure 2. Schematic of the 0.7 m \u00d7 0.7 m \u00d7 1.4 m Module-0 detector with annotations of the key\ncomponents.\n(PACMAN) card (Fig. 5), which provides filtered power and noise-isolated data I/O to\neight tiles. Two PACMAN controllers are mounted in metal enclosures attached to the\nouter surface of each feedthrough. During Module-0 operation, the PACMAN controller\nreceived a pulse-per-second timing signal for data synchronization between charge readout\nand light readout systems, and external trigger signals from the light readout system were\nembedded as markers into the charge readout data stream. Data are carried over a standard\ncopper ethernet cable connected at each PACMAN to a network switch. Subsequently, data\nare transferred to and from the DAQ system via an optical fiber connection.\nFor the LArTPC ionization charge measurement, LArPix ASICs mainly operate in\nself-trigger mode, where a trigger is initiated on a per-channel basis when a channel-level\ncharge threshold is exceeded. In this mode of operation LArPix incurs negligible dead time\nand produces only modest data volumes, due to the sparsity of ionization signals in 3D,\neven for high-energy events. Serial data packets stream out of the system continuously via\nthe PACMAN boards and are processed offline for analysis. A programmable channel-level\nthreshold is set using internal digital to analog converters (DACs), which are tuned so\nthat the spurious (i.e. noise-related) trigger rate is less than 2 Hz for each channel. For\nModule-0, channel thresholds were operated in two regimes: low and high threshold (see\nFig. 6). Low threshold (\u223c5.8 ke\u2212/pixel or \u223c1\n4 MIP/pixel) operation optimized charge\nsignal sensitivity at the expense of incurring additional triggers due to e.g. digital pickup,\nwhereas high threshold (\u223c10.7 ke\u2212/pixel or \u223c1\n2 MIP/pixel) operation benefited from\nimproved trigger stability at the expense of charge sensitivity. Updated revisions of the\nLArPix ASIC include additional pickup mitigation that will allow channel thresholds to\nbe lowered further. Also, a slight rising trend in event rate can be seen over some of the\n\nVersion March 6, 2024 submitted to Instruments\n13 of 47\nCathode\nArCLight tile\nLCM tile\nCarbon-loaded Kapton \nfield cage sheet\nLArPix pixelated anode\nFigure 3. Photograph of the Module-0 detector interior as seen from the bottom, with annotations of\nthe key components.\nFigure 4. Front (left) and back (right) of a TPC anode tile. The front contains 4,900 charge-sensitive\npixels with 4.43 mm pitch that face the cathode, and the back contains a 10 \u00d7 10 array of LArPix\nASICs. The dimensions are 31 cm \u00d7 32 cm, with the extra centimeter providing space for the light\nsystem attachment points.\ndifferent periods, most likely due to the emergence during data taking of pixels with a\nhigh data rate. It is believed that this small effect, which has no impact on the physics\nperformance, can be mitigated by improving the procedure used to set the thresholds.\nASICs within an anode tile are routed out to the DAQ through a configurable \u201chydra\u201d\nnetwork, wherein each ASIC has the ability to pass data packets to and from any adjacent\nneighbor. The scheme allows for system robustness in the event that an ASIC along the\nsignal path becomes nonfunctional, though none of the 1600 ASICs failed during Module-0\noperation. A few-millisecond delay is incurred for data packets produced deeper in the\nnetwork to reach the PACMAN controller relative to data packets produced closer to it. This\nis accounted for during hit digitization: each data packet carries a timestamp at creation\nwhen the hit signal is digitized, and when packets reach the PACMAN controller, a receipt\ntimestamp is also assigned. Time ordering and filtering on packet trigger type is performed\noffline. In order to monitor the integrity of the data in near\u2013real time, a dedicated nearline\nmonitoring system was developed and operated during the Module-0 run. An automated\nanalysis was performed on each run\u2019s raw data once the run ended and provided metrics\nincluding system trigger rates, trigger timing and offsets, channel occupancy and trigger\n\nVersion March 6, 2024 submitted to Instruments\n14 of 47\nFigure 5. The Pixel Array Controller and Network card (PACMAN), which controls the data acquisi-\ntion and power for the charge readout system.\n2021-04-02\n2021-04-03\n2021-04-04\n2021-04-05\n2021-04-06\n2021-04-07\n2021-04-08\n2021-04-09\n2021-04-10\n0\n20\n40\n60\n80\nEvent Rate [Hz]\nCommissioning\nHigh Threshold\nLow Threshold\nPedestal\nDiagnostics\nDrift HV Ramp\nEvent Rate\nCumulative\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\nCumulative Event Count\n1e7\nDUNE:ND-LAr 2x2\nFigure 6. Run event rate and cumulative events as a function of time with respect to charge readout\noperating condition.\nrates, and data corruption checks. Cosmic rays produced a self-trigger rate of \u223c0.25 Hz\nper pixel. This resulted in a total pixel hit rate of \u223c20 kHz for the entire Module-0 detector,\nyielding a modest data rate of 2.5 Mb/s.\n2.3. The Light Readout System\nThe Light Readout System (LRS) provides fast timing information using the prompt\n\u223c128 nm scintillation light induced by charged particles in LAr. The detection of scin-\ntillation photons provides absolute reference for event timing (t0) and, when operated\nin an intense neutrino beam, will allow for unambiguous association of charge signals\nfrom the specific neutrino interactions of interest (i.e. pile-up mitigation). The LRS uses a\nnovel dielectric light detection technique capable of being placed inside the field-shaping\nstructure to increase light yield and localization of light signals. The LRS consists of two\nfunctionally-similar silicon photomultiplier (SiPM)-based detectors for efficient collection\nof single UV photons with large surface coverage: the Light Collection Module (LCM)\nand the ArCLight module. The full LRS system includes these modules together with\nthe ancillary readout, front-end electronics, DAQ (ADCs, synchronization, and trigger),\n\nVersion March 6, 2024 submitted to Instruments\n15 of 47\nfeedthrough flanges, SiPM power supply subsystem, and slow controls, as well as cabling\nand interconnection between different elements. LCM and ArCLight modules share the\nsame basic operation principle. The vacuum ultraviolet (VUV) scintillation light produced\nby LAr is shifted from 128 nm to visible light by a wavelength shifter (WLS). Tetraphenyl\nbutadiene (TPB) coated on the surface of the light collection systems provides an efficient\nWLS, and the emission spectrum of TPB is quite broad with a peak intensity of around\n425 nm (violet light). Part of the light emitted at the surface of the light detection system\neventually enters the bulk structure of the detector and is shifted to green light by a dopant\n(coumarin) in a bulk material, which also acts as a light trap (see Fig. 7).\n73%\n73%\n:/6\u0003)LEHU\n\u0014\u0003PP\n6L30\u00033&%\n6L30\n\u0019\u0013\u0013\u0003PP\n\u0014\u0011\u0018\u0003PP\n\u0003\u0003\u0003\u0016\u0003PP\n\u0016\u0003\u021dP\n6L30\u00033&%\n6L30\n\u0003\u0003\u0003\u0016\u0003PP\n\u0014\u0011\u0018\u0003PP\n73%\n'LFKURLF\u00030LUURU\n:/6\u00033ODVWLF\n\u0014\u0013\u0003PP\n6L30\u00033&%\n6L30\n\u0015\u001b\u0013\u0003PP\n\u0014\u0011\u0018\u0003PP\n\u0003\u0003\u0003\u0016\u0003PP\n\u0019\u0003PP\n\u0014\u0014\u0015\u0003\u021dP\n\u0016\u0003\u021dP\nFigure 7. Detection principle of the two types of modules comprising the LRS: a segment of an\nArCLight tile (top) and a single LCM optical fiber (bottom). The wave-like lines indicate example\nphoton trajectories, where the white points indicate interactions. Drawings are not to scale.\nThe ArCLight module has been developed by Bern University [11] and uses the\nARAPUCA [17] principle of light trapping. The general concept, illustrated in Fig. 7 (top),\nis that violet light enters a bulk WLS volume and is re-emitted as green light, and the\nvolume has a coating reflective to green light on all sides except on the SiPM photosensor\nwindow. A dichroic filter transparent to the violet light and reflective for the green is\nused on the WLS (tetraphenyl butadiene, TPB) side. The overall module dimensions are\n300 mm \u00d7 300 mm \u00d7 10 mm. A photograph of an ArCLight module is shown in Fig. 8\n(left).\nThe LCM prototype is a frame cantilevered by a PVC plate that holds 25 WLS fibers\nbent into a bundle whose both ends are readout by a SiPM light sensor. Fibers are grouped\nand held by spacer bars with holes fixed on the PVC plate by means of polycarbonate\nscrews to provide matching of thermal contraction. The PVC plate with the WLS fibers is\ncoated with TPB, which re-emits the absorbed VUV light to the violet (\u223c425 nm). This light\n\nVersion March 6, 2024 submitted to Instruments\n16 of 47\nis then shifted inside multi-cladding \u2205=1.2 mm Kuraray Y-11 fibers to green (\u223c510 nm),\nand hence is trapped by total internal reflection guiding it to the SiPM readout at the\nfiber end, as depicted in Fig. 7 (bottom). For each group of LCMs, the center module\nuses bis-MSB as a WLS rather than TPB to evaluate this alternative option; the photon\ndetection efficiency performance is discussed in Section 4 and the relative performance can\nbe observed in Fig. 26. The LCM dimensions are 100 mm \u00d7 300 mm \u00d7 10 mm. Fig. 8 (right)\nshows three LCMs.\nFigure 8. An ArCLight tile (left) and three LCM tiles (right), as assembled within the Module-0\nstructure.\nIn order to digitize analog signals from SiPMs, a 100 MHz, 10-bit, 64-channel (dif-\nferential signals, full range \u00b11.6 V) ADC prototype module in VME standard produced\nat the Joint Institute for Nuclear Research (JINR) was used (see Fig. 9 left). This ADC\nmodule streams UDP/TCP data packets via M-link MStream protocol using a 10 Gbps\noptical link. The ADC boards have the capability to be synchronized via a White Rabbit\nsystem [18]. This was not available for Module-0 run, for which timing synchronization\nbetween the charge light systems was provided by a dedicated system shown in Fig. 9\n(right). To merge data between light and charge systems, a trigger signal generated by\nthe LRS is written out to the charge readout data stream. This trigger signal is also fed to\nthe analog input of both ADCs to allow for precise time matching between ADC boards\nfor further LRS data analysis. Additionally, a pulse-per-second from a stable GPS source\nwas used for both detection systems to provide accurate synchronization. For the LRS, the\npulse-per-second signal was fed to the analog input of each ADC. During the Module-0\nrun, the LRS operated in a self-triggered mode with adjustable threshold settings. The\nthresholds for the LCMs are approximately 30 photoelectrons, as discussed in Section 4.\nFigure 9. LRS data acquisition components: JINR ADC board (left), synchronization and trigger\nscheme (right).\n\nVersion March 6, 2024 submitted to Instruments\n17 of 47\n3. Charge Readout Performance\n3.1. System Overview\nModule-0 operation represents the first demonstration of the LArPix-v2 pixelated\ncharge readout system in a tonne-scale LArTPC. Continuous acquisition and imaging of\nself-triggered cosmic ray data were successfully exercised, demonstrating the excellent\nperformance of this technology. This section presents an array of studies of the charge\nreadout system performance, including: pixel channel signal baselines and time stability,\ncharge response as a function of track position and angle relative to the pixel plane, re-\nsponse uniformity across the instrumented area, ADC saturation, and overall calorimetric\nmeasurement performance.\nIn parallel to this successful series of technological achievements, this first large-scale\nintegrated test highlighted areas for continued improvement in future iterations of the\nmodule design. This includes improved anode tile grounding and optimization of the\npixel pad geometry. In the former case, enhancements to the grounding scheme will\nenable improved system-wide per-channel charge threshold sensitivity and system trigger\nstability, specifically allowing readout of the pixels on the edge of neighboring tiles, and\nmitigating the effects of triggering induced by system synchronization signals observed in\nthe Module-0 data. In the latter case, modifications to the pixel pad geometry will further\nminimize far-field current induction in the pixels, reducing the sensitivity of the readout\nsystem to drifting charge that is far from the anode plane. Additional improvements to\nthe ASIC-related noise budget are planned for the next-generation LArPix design. Of the\ntotal 78,400 instrumented pixel channels in Module-0, 92.2% were enabled for LArTPC\noperation. The channels were disabled mainly due to limitations noted above \u2014 grounding\nnear tile edges (4.2%), elevated noise levels due to signal pickup (3.1%), high noise or\nleakage current (0.5%) \u2014 and their locations are illustrated in Fig. 10. As noted above, no\nASICs failed during Module-0 operations.\n3.2. Noise and Stability\nPeriodic diagnostics (pedestal) runs were taken to monitor the stability of the charge\nreadout system. These diagnostic runs entailed issuing a periodic trigger on a per-channel\nbasis in a round-robin fashion among channels on a single ASIC. In this way, sub-threshold\ncharge was digitized to monitor channel pedestal and the AC noise stability in time, with\nthe ADC value returned by each digitization reflecting the sum of the quiescent pedestal\nvoltage of the front-end amplifier and the integrated charge. The distributions of ADC\nvalues collected during pedestal runs were in agreement with the design expectations, with\na median value of \u223c78 counts per channel, and pedestal voltage varied by approximately\n30 mV between channels. To determine the integrated charge, a correction for this pedestal\nvalue must be applied. We computed the channel-by-channel pedestal ADC value by using\nthe truncated mean around the peak of the ADC value distribution of each channel. The\nsignal amplitude in mV was inferred based on the internal reference DAC values and the\nASIC analog voltage, and a global gain value of 245 e\u2212/mV was then used to convert the\nsignal amplitude to charge.\nAdditionally, the stability of the charge readout over time was verified using cosmic\nray data samples, by measuring the most probable value (MPV) and the full width at half\nmaximum (FWHM) of the dQ/dx distribution of minimum ionising particle (MIP) tracks\nfor each data run, as shown in Fig. 11. To make these track-based measurements, 3D hits\nregistered by the charge system are clustered together using the DBSCAN algorithm [19].\nA principal component analysis of hits within each cluster then provides three-dimensional\nsegments that we define as reconstructed tracks. The charge dQ corresponds to the sum\nof the hits associated to the reconstructed track and the 3D reconstructed track length dx.\nThe dQ/dx distribution is then fitted with a Gaussian-convolved Moyal distribution [20],\nwhich is used to extract the MPV and the FWHM. Total system noise contributes \u223c950 e\u2212\nequivalent noise charge (ENC) to each pixel hit, as assessed using periodic forced triggering\nof pixel channels in the absence of actual signals (Fig. 12). To put this metric in context, the\n\nVersion March 6, 2024 submitted to Instruments\n18 of 47\nintrinsic energy loss fluctuations associated with the charge from a 4 GeV MIP would be\n\u223c1800 e\u2212in ND-LAr\u2019s 3.7 mm pixel pitch. Therefore, the charge resolution is smaller than\nthe intrinsic physical fluctuations for particle kinematics relevant to ND-LAr.\nFigure 10.\nSelf-trigger active pixel channels (in blue) and inactive channels (in black). In these\ncoordinates, x is horizontal and y is vertical, both parallel to the anode plane, and z is the drift\ndirection, perpendicular to the anode plane, completing a right-handed system. The origin is the\ncenter of the module.\nExamining the corresponding charge in each pixel that has triggered (Fig. 13), we\nidentify a sharp rising edge corresponding to the self-trigger threshold at approximately\n5.8 \u00d7 103 electrons (low threshold) and 11 \u00d7 103 electrons (high threshold). Above the\nself-trigger threshold, a peak at roughly 24 \u00d7 103 electrons corresponds to the typical charge\ndeposited by a MIP crossing the full pixel pitch of 4.43 mm. Of note are the markedly\ndifferent charge distributions of the high\u2013 and low-threshold data. We find that for the\nlow-threshold data, the average number of triggers per single channel for MIP energy\ndeposition is substantially larger than for the high-threshold data, with mean values of 1.53\nand 1.14 respectively. These numbers are well-reproduced by the Monte Carlo simulation\n(MC) described in Section 5, with values of 1.52 and 1.12 respectively for a similar set\nof reconstructed MIP tracks. Summing the charge of all digitizations on each specific\nchannel for a given event increases the similarity between the low-threshold data with\nthe high-threshold data (Fig. 14). This is indicative of a \u201cpre-triggering\u201d effect, in which\na channel is triggered by the induced signal generated by the drifting charge in advance\nof the charge signal arrival at the anode plane, thus motivating the reduction of far-field\neffects discussed above.\n\nVersion March 6, 2024 submitted to Instruments\n19 of 47\n2021-04-02\n2021-04-03\n2021-04-04\n2021-04-05\n2021-04-06\n2021-04-07\n2021-04-08\n2021-04-09\n2021-04-10\n2\n3\n4\n5\n6\n7\nCommissioning\nDiagnostics\nDrift HV ramp\nPedestal\nHigh threshold\nLow threshold\nMPV\nFWHM\ndQ/dx [103 e\u2013/mm]\nDUNE:ND-LAr 2x2\nFigure 11. Most probable value (black circles) and full width at half maximum (white circles) of the\ndQ/dx distribution for each data run. The system shows a good charge readout stability during data\ntaking periods, both for high threshold (yellow bands) and low threshold (purple bands) runs.\n0\n500\n1000\n1500\n2000\n2500\n3000\nEquivalent noise charge (ENC) [e-]\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\nChannel count / (25 ENC [e-])\nDUNE:ND-LAr 2x2\nFigure 12. LArPix channel noise in units of electron charge signal, as observed using periodic forced\ntriggers. The total system noise is \u223c950 e\u2212, compared to a signal amplitude of \u223c1800 e\u2212for a 4\nGeV MIP track in ND-LAr\u2019s 3.7 mm pixel pitch.\n\nVersion March 6, 2024 submitted to Instruments\n20 of 47\n0\n10\n40\n50\n20 \n30 \n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nHits per mm\ndata (low threshold) [50% of rising edge = 5.8ke]\nsimulation (low threshold) [50% of rising edge = 5.9ke]\ndata (high threshold) [50% of rising edge = 10.7ke]\nsimulation (high threshold) [50% of rising edge = 10.5ke]\nHit charge [ke-]\nDUNE:ND-LAr 2x2\nFigure 13. Self-trigger charge distribution for MIP tracks measured in thousands of electrons (ke\u2212);\n50% of the rising edge are shown as indicators of the charge readout self-trigger thresholds. The low-\nand high-threshold curves are obtained from runs with the same 20 minute exposure. Each entry\nis normalized by hit charge over fitted track length. The MC simulation shown in comparison is\ndescribed in Section 5.\n0\n20\n40\n60\n80\n100\nEvent charge [ke-]\n0.0000\n0.0025\n0.0050\n0.0075\n0.0100\n0.0125\n0.0150\n0.0175\n0.0200\nHits per mm\ndata (low threshold)\nsimulation (low threshold)\ndata (high threshold)\nsimulation (high threshold)\nDUNE:ND-LAr 2x2\nFigure 14. Total event charge per channel for MIP tracks measured in thousands of electrons (ke\u2212).\nThe MC simulation shown in comparison is described in Section 5.\n\nVersion March 6, 2024 submitted to Instruments\n21 of 47\n0\n2\n4\n6\n8\nr [mm]\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\n0.014\nHits per mm\ndata (low threshold)\nsimulation (low threshold)\ndata (high threshold)\nsimulation (high threshold)\npixel boundaries\nDUNE:ND-LAr 2x2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n [radian]\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\nHits per mm\ndata (low threshold)\nsimulation (low threshold)\ndata (high threshold)\nsimulation (high threshold)\nDUNE:ND-LAr 2x2\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\n| | [radian]\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\nHits per mm\ndata (low threshold)\nsimulation (low threshold)\ndata (high threshold)\nsimulation (high threshold)\nDUNE:ND-LAr 2x2\nFigure 15. Comparisons of response variation in the radial distance from the pixel center to the point\nof closest approach of the track projected onto the anode plane (r, top), the track inclination relative\nto the anode plane (polar angle \u03b8, middle), and the orientation angle of the track projected onto the\nanode plane (azimuthal angle \u03d5, bottom). The MC shown in comparison is described in Section 5.\n\nVersion March 6, 2024 submitted to Instruments\n22 of 47\n3.3. Pixel Charge Response\nTo study the individual pixel charge response, we examine the variation in response\nbased on the track inclination relative to the anode plane (polar angle \u03b8), the orientation\nangle of the track projected onto the anode plane (azimuthal angle \u03d5), and the radial\ndistance from the pixel center to the point of closest approach of the track projected onto\nthe anode plane (r). Fig. 15 shows the distribution of these three quantities, normalized by\nthe total track length. Generally, the \u03b8 and \u03d5 distributions are comparable between data and\nsimulations. The r distribution shows significantly more triggers to peripheral tracks than\nsimulated events. An overall normalization difference between high- and low-threshold\ndata reflects the decreased sensitivity to tracks that clip the corners of the pixel.\nA similar finding resulted from studying the distance between the MIP ionization axis\nand the center of the pixel. This ionization axis can be inferred by performing a Hough\ntransform algorithm (HTA) on the x, y, and estimated z dimensions of the hit cloud. A\nprojection of the HTA line onto the pixel plane provides the minimum array of pixels\nalong the axis that could have recorded some charge. This line is then divided into 0.1 mm\nsegments longitudinally. Each individual segment\u2019s center then falls into a specific pixel,\nwhich is used to determine the distance between the segment center and the pixel center\nin x and y. The segments are split into three categories: (1) all segments as mentioned\nabove independent of the recorded charge on that particular pixel, (2) those that fell into a\npixel which did give a response, and (3) those in pixels that did not trigger. Prior to this\ncategorization, all segments contained by pixels known to be inactive are excluded. In\nFig. 16, the ratios of the number of segments in the latter two categories to the first one are\nshown. The four corners are over-represented for pixels that did not give a response but\nhad the main ionization line crossing their pad. This quantifies the sensitivity of individual\npixels to tracks clipping the corners. This difference in sensitivity is characterized by only a\n3% drop from pixel center to pixel edge where the minimum response is 85.5%.\n2.0 \n0.1300 \n1.5 \n0.1275 \n1.0 \n0.5 \n0.1250 \n0.0 \n0.1225 \n-0.5\n0.1200 \n-1.0\n0.1175 \n-1.5\n0.1150 \n-2.0\n-2.0\n-1.5\n-1.0\n-0.5\n0.0 \n0.5 \n1.0 \n1.5 \n2.0 \nx distance to pixel center [mm]\ny distance to pixel center [mm]\nDUNE:ND-LAr 2x2\n2.0 \n0.8850 \n1.5 \n0.8825 \n1.0 \n0.5 \n0.8800 \n0.0 \n0.8775 \n-0.5\n0.8750 \n-1.0\n0.8725 \n-1.5\n0.8700 \n-2.0\n-2.0\n-1.5\n-1.0\n-0.5\n0.0 \n0.5 \n1.0 \n1.5 \n2.0 \nx distance to pixel center [mm]\ny distance to pixel center [mm]\nDUNE:ND-LAr 2x2\nFigure 16. Relative rate of pixel response as a function of the distance between Hough line segments\nand segment containing pixel\u2019s center for pixels on gaps, i.e. no charge response (left), and on tracks,\ni.e. with charge response (right) to the total.\nFigs. 17 and 18 show the charge distribution with respect to the track orientation\nfor low- and high-threshold data, respectively. Overall, similar features appear in each\npanel: a prominent peak corresponding to the charge deposited by a MIP across a single\npixel width. In the r distribution, a secondary distribution of low-charge hits is present,\ncorresponding to tracks that clip the corners of the pixel. This feature is also present in the \u03d5\ndistribution as an increase in the spread of the charge as \u03d5 \u2192\u03c0/4. The \u03b8 distribution shows\na characteristic increase in the charge as \u03b8 \u21920, which corresponds to tracks perpendicular\nto the anode plane, where each pixel can see a contribution from a relatively long track\nlength. A flattening of the observed charge near \u03b8 = 0.8 is a threshold effect and is not\npresent in the low-threshold data. To test the responsiveness of individual pixels and\nidentify potentially malfunctioning channels beyond those known to be inactive, a MIP\nresponse map of the entire pixel plane was constructed. This map is the ratio of recorded\n\nVersion March 6, 2024 submitted to Instruments\n23 of 47\nDUNE:ND-LAr 2x2\nFigure 17.\nSelf-trigger charge distribution for MIP tracks with different track orientations with\nrespect to the pixel, normalized to number of triggered channels per reconstructed track length.\nLow-threshold data are used. The MC simulation shown in comparison in the second column is\ndescribed in Section 5.\n\nVersion March 6, 2024 submitted to Instruments\n24 of 47\nDUNE:ND-LAr 2x2\nFigure 18. Same as Fig. 17 but for high threshold data.\n\nVersion March 6, 2024 submitted to Instruments\n25 of 47\nover expected hits, and identifies regions on the pixel plane which are less responsive than\nothers. Both components start off with the same principle of performing an HTA on the\nx, y, and inferred z dimensions of the hit cloud to obtain the MIP\u2019s central ionization axis\nin 3D. This axis is then projected onto the pixel plane to result in a 2D line. Next, all hits\nwithin 8 mm of the line are selected and the maximum track width is set equal to the most\ndistant point within this radius. To then obtain the first map, all pixels that recorded hits\nwithin a radius equal to the maximum track width of the projected line receive an entry. To\nconstruct the second map, all existing pixels within that same radius receive an entry. If a\npixel is unresponsive, it will not show up in the first but will appear in the second, leading\nto a low ratio in that specific area. Selection cuts place requirements on the straightness\nof tracks relative to the fit Hough lines as well as the consistency with a roughly constant\nenergy deposition profile, to ensure that the events analyzed consist primarily of MIP-like\ntracks. Fig. 19 shows the resulting MIP response maps for both anode planes.\n200\n0\n200\nPixel plane X [mm]\n600\n400\n200\n0\n200\n400\n600\nPixel plane Y [mm]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nDUNE:ND-LAr 2x2\n200\n0\n200\nPixel plane X [mm]\n600\n400\n200\n0\n200\n400\n600\nPixel plane Y [mm]\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nDUNE:ND-LAr 2x2\nFigure 19. MIP response maps for anode plane 1 (left) and anode plane 2 (right), showing the\nfraction of triggered hits on each pixel relative to the expected number based on reconstructed track\ntrajectories.\n3.4. Saturation\nAn additional consideration is saturation in the LArPix-v2 ASIC\u2019s 8-bit successive-\napproximation ADC, which is expected to occur when the charge on a given channel\nexceeds 200 ke\u2212within a 2.6 \u00b5s time window. A scan for events including saturated\npackets was performed over eight hours of cosmic ray data acquired at high gain and\nlow threshold. Packets within 1 s of a time synchronization pulse were found to include\nadditional noise and saturation effects, and were excluded. After accounting for this, a\nsmall fraction (2.9 \u00d7 10\u22126) of events with matching charge and light information contained\na saturated ADC measurement. These events were manually inspected, and the saturation\nwas clearly uncorrelated in space and time with the physical interactions, but rather they\nleaked into the event due to their proximity with a sync pulse. With low thresholds,\n< 0.002% of triggers resulted in ADC saturation, again driven by the pulse-per-second sync\nsignal; channels 35-37 on all chips, which are located physically adjacent to the sync pulse\n\nVersion March 6, 2024 submitted to Instruments\n26 of 47\npin, saturated most often and together accounted for 15% of these saturated packets. The\nADC count distribution for events with deposited energy between 2 and 10 GeV is shown\nin Fig. 20. These energies are of interest as they are representative of neutrino interactions\nat ND-LAr, and the distribution falls well within the dynamic range of the ADC.\n0\n50\n100\n150\n200\n250\nADC Counts\n100\n101\n102\n103\nCounts per bin\nDUNE:ND-LAr 2x2\nFigure 20. Per-pixel ADC value distribution for cosmic ray events between 2 and 10 GeV. All signals\nare well within the ADC dynamic range of 0\u2013256 counts.\n3.5. Calorimetric Response\nFinally, the calorimetric response of Module-0 charge readout was also studied. Figs. 21\nand 22 show the variation of the dQ/dx for segments of different lengths relative to the\ntrack orientation, defined by the azimuth angle \u03d5 and the \u03b8 angle between the track and\na vector normal to the anode plane. The reconstructed tracks used for this analysis come\nfrom the low threshold runs (see Section 1). Events with more than 20 reconstructed tracks\nwere excluded, since they often correspond to large showers or non-cosmic triggers. Tracks\nwere required to be longer than 10 cm and to have at least 20 associated hits. They were\nthen subdivided into segments of variable length from 10 to 400 mm and the distributions\nwere fit with a Gaussian-convolved Moyal function. The MPV shows a slight dependence\non cos \u03b8, with tracks that impinge perpendicularly to the anode plane tending to have a\nlarger amount of deposited charge per unit length. These data provide insight into subtle\neffects in the pixel charge response, such as those related to induction effects and electric\nfield uniformity, and enable a data-driven calibration.\n4. Light Readout Performance\n4.1. Overview\nThe Module-0 detector also provided a large-scale, fully integrated test of the light\nreadout system, enabling a detailed performance characterization of the ArCLight and\nLCM modules, readout, DAQ, triggering, and timing with a large set of events. Using\ncosmic ray data and dedicated diagnostic runs under a variety of detector configurations, a\nsuite of tests was performed to assess the charge spectrum, inter\u2013 and intra-event timing\naccuracy, and photon detection efficiency. The subsequent matching of events between the\ncharge and light system is considered in Section 5.3.\n\nVersion March 6, 2024 submitted to Instruments\n27 of 47\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n400 mm\n5.72 103e /mm\nFWHM\nMPV\n300 mm\n5.70 103e /mm\n200 mm\n5.73 103e /mm\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n150 mm\n5.77 103e /mm\n100 mm\n5.76 103e /mm\n50 mm\n5.70 103e /mm\n1.0\n0.5\n0.0\n0.5\n1.0\nAnode plane cos\u03b8\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n30 mm\n5.61 103e /mm\n1.0\n0.5\n0.0\n0.5\n1.0\nAnode plane cos\u03b8\n20 mm\n5.57 103e /mm\n1.0\n0.5\n0.0\n0.5\n1.0\nAnode plane cos\u03b8\n10 mm\n5.52 103e /mm\nDUNE:ND-LAr 2x2\nFigure 21. dQ/dx measured for segments of different lengths as a function of the orientation relative\nto the anode planes. A value of cos \u03b8 = 0 corresponds to segments parallel to the anode plane. The\ndistributions in each bin have been fitted with a Gaussian-convolved Moyal function. The red points\ncorrespond to the most probable value of the fitted distribution and the dashed rectangles correspond\nto the full width at half maximum. The dashed black line represents the average MPV.\n\nVersion March 6, 2024 submitted to Instruments\n28 of 47\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n400 mm\n5.50 103e /mm\nFWHM\nMPV\n300 mm\n5.65 103e /mm\n200 mm\n5.74 103e /mm\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n150 mm\n5.65 103e /mm\n100 mm\n5.70 103e /mm\n50 mm\n5.64 103e /mm\n/2\n0\nAnode plane \n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e /mm]\n30 mm\n5.57 103e /mm\n/2\n0\nAnode plane \n20 mm\n5.48 103e /mm\n/2\n0\nAnode plane \n10 mm\n5.42 103e /mm\nDUNE:ND-LAr 2x2\nFigure 22. dQ/dx measured for segments of different lengths as a function of the azimuthal angle\n\u03d5 = atan2(y, x), where y and x are the components of the segment along the anode plane axes.\nThe distributions in each bin are fitted with a Gaussian-convolved Moyal function. The red points\ncorrespond to the most probable value of the fitted distribution and the dashed rectangles correspond\nto the FWHM. The dashed black line represents the average MPV.\n\nVersion March 6, 2024 submitted to Instruments\n29 of 47\n4.2. Calibration\nBefore collecting cosmic data, a SiPM gain calibration was performed using an LED\nsource, where the bias voltage for each SiPM channel was adjusted to obtain a uniform\ngain distribution across the channels, as shown in Fig. 23. The amplification factors for\nthe variable gain amplifiers used in the SiPM readout chain were also tuned, and set to\nmaximum (31 dB) except for LCM channels (21 dB) during cosmic ray data taking, to adjust\nsignals to the input dynamic range of the ADC. LCMs were used to provide an external\ntrigger to the charge readout system, with an effective threshold of about 30 photoelectrons\n(p.e.). The trigger message, written into the continuous self-triggered data stream of the\ncharge readout system, provides a precise timestamped flag for identifying coincidences\nbetween charge and light readout.\nEntries \n 10000\nMean \n 164.2\nStd Dev \n 132.2\nIntegral \n 9999\n / ndf\n2\n\u03c7\n 26.6 / 26\np0 \n 5.9\n\u00b1\n 192.2 \np1 \n 0.350\n\u00b1\n1.467 \n\u2212\np2 \n 0.24\n\u00b1\n12.79 \np3 \n 6.6\n\u00b1\n 228.6 \np4 \n 0.50\n\u00b1\n 68.87 \np5 \n 0.42\n\u00b1\n 14.62 \n100\n\u2212\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\nCharge [ADC counts]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\nNumber of events, N\nEntries \n 10000\nMean \n 164.2\nStd Dev \n 132.2\nIntegral \n 9999\n / ndf\n2\n\u03c7\n 26.6 / 26\np0 \n 5.9\n\u00b1\n 192.2 \np1 \n 0.350\n\u00b1\n1.467 \n\u2212\np2 \n 0.24\n\u00b1\n12.79 \np3 \n 6.6\n\u00b1\n 228.6 \np4 \n 0.50\n\u00b1\n 68.87 \np5 \n 0.42\n\u00b1\n 14.62 \nGate ~ 200 ns\nVGA@maximum gain of 31dB\nDUNE:ND-LAr 2x2\nEntries \n 87\nMean \n 89.29\nStd Dev \n 9.143\nIntegral \n 87\n / ndf \n2\n\u03c7\n 34.84 / 97\nConstant \n 0.499\n\u00b1\n 3.796 \nMean \n 0.98\n\u00b1\n 89.29 \nSigma \n 0.694\n\u00b1\n 9.143 \n0\n50\n100\n150\n200\n250\nCharge [ADC counts]\n0\n1\n2\n3\n4\n5\n6\nNumber of events, N\nEntries \n 87\nMean \n 89.29\nStd Dev \n 9.143\nIntegral \n 87\n / ndf \n2\n\u03c7\n 34.84 / 97\nConstant \n 0.499\n\u00b1\n 3.796 \nMean \n 0.98\n\u00b1\n 89.29 \nSigma \n 0.694\n\u00b1\n 9.143 \nDUNE:ND-LAr 2x2\nFigure 23. Typical charge spectrum obtained during SiPM gain calibration (left); SiPM gain distribu-\ntion (right).\n4.3. Time Resolution\nEvents induced by cosmic muons traversing the TPC volume were used to extract the\ntime resolution of the light detectors. The time measurement proceeds as follows: each\nwaveform is oversampled through a Fourier transform to increase the number of points on\nthe rising edge, enabling a good linear fit of it. Then, a linear fit to the baseline is performed,\nand the crossing point of the rising edge of the signal with the baseline is calculated,\nproviding a robust single-channel event time. This process is illustrated in Fig. 24 (left). The\nextracted time resolution for a pair of neighboring LCM channels is shown in Fig. 24 (right)\nas a function of the signal amplitude. This quantity is obtained by taking the standard\ndeviation of the time difference recorded between the two channels over multiple events\nwithout any time-of-flight corrections. For large signals, this resolution approaches \u223c2 ns.\nAn example application of the excellent timing resolution for the LCMs is the identification\nof Michel electrons from stopping muon decays, where the relative timing between the\nmuon and electron signals is dominated by the mean lifetime of the muon, \u03c4 \u223c2.2 \u00b5s.\nTwo examples of signals from a stopping muon and a delayed Michel electron detected\nby the LCM are shown in Fig. 25. Since the muon decay time is variable but follows a\nwell-understood exponential distribution, such events may be used, for example, to study\nevent pile-up in neutrino interactions.\n4.4. Efficiency\nTo assess the efficiency of the LRS, the scintillation light induced by tracks recon-\nstructed from the TPC charge readout data is used. In particular, cosmic muon tracks\ncrossing the entire detector vertically are considered. In a 3D simulation, the charge of a\ntrack is discretized to single points with a 1 mm resolution along the track, assuming an\ninfinitely thin true trajectory. For each point in this voxelized event, the solid angle to the\nlight detector in the detector module is then calculated. Next, assuming isotropic scintil-\nlation light emission, the solid angle can be used to compute the geometrical acceptance\n\nVersion March 6, 2024 submitted to Instruments\n30 of 47\n80\n85\n90\n95\n100\n105\n110\nTime, ADC samples\n14000\n\u2212\n12000\n\u2212\n10000\n\u2212\n8000\n\u2212\n6000\n\u2212\n4000\n\u2212\n2000\n\u2212\n0\n2000\nAmplitude, V\nOversampled signal (\u00d710)\nBaseline\nFront edge\nCrosspoint\nDUNE:ND-LAr 2x2\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\n220\n240\n Light intensity, ph.e.\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n5.5\n6\nStd.Dev., ns\n / ndf\n2\n\u03c7\n 2.016 / 3\na\n 1.999\n\u00b1\n 27.426 \nb\n 0.368\n\u00b1\n 1.661 \n / ndf\n2\n\u03c7\n 2.016 / 3\na\n 1.999\n\u00b1\n 27.426 \nb\n 0.368\n\u00b1\n 1.661 \nDUNE:ND-LAr 2x2\nFigure 24. Oversampled signal using Fourier transformation. Red lines show the linear approxima-\ntions of the rising edge and the baseline (left). The time resolution between two LCMs (LCM-011,\nLCM-017) as a function of the signal response (right).\n0\n200\n400\n600\n800\n1000\nSample number, N\n14\n\u2212\n12\n\u2212\n10\n\u2212\n8\n\u2212\n6\n\u2212\n4\n\u2212\n2\n\u2212\n0\n3\n10\n\u00d7\nAmplitude, channels\nDUNE:ND-LAr 2x2\n0\n200\n400\n600\n800\n1000\nSample number, N\n6\n\u2212\n5\n\u2212\n4\n\u2212\n3\n\u2212\n2\n\u2212\n1\n\u2212\n0\n3\n10\n\u00d7\nAmplitude, channels\nDUNE:ND-LAr 2x2\nFigure 25.\nTwo examples showing signals of the stopping muon and delayed Michel electron\ndetected by the LCM. The waveforms were digitized at 10 ns intervals.\n\nVersion March 6, 2024 submitted to Instruments\n31 of 47\nof the light for each detector tile. The number of photons hitting the detector surface is\nestimated by multiplying the geometrical acceptance by the number of emitted photons per\nunit track length and integrating over the full track length. Here, the number of emitted\nphotons per unit track length has been calculated for the nominal electric field intensity\nof 0.5 kV cm\u22121 [21]. Rayleigh scattering, a small effect over the relevant distance scales, is\nneglected in this calculation.\nThe photon detection efficiency (PDE) of the light detection system can be estimated\nby comparing the measured number of p.e. and the estimated number of photons hitting\nthe detector surface, as obtained from the simulation described above. Since the waveforms\nobtained with the light detectors have been integrated using a limited gate length, the actual\nscintillation light might be underestimated. This was corrected by multiplying the number\nof reconstructed photons by an integration gate acceptance factor, which is calculated based\non the detector response and the scintillation timing characteristics. Fig. 26 shows the\nmeasured PDE for all ArCLight and LCM modules used in the Module-0 detector. The\nLCM shows an average PDE of 0.6%, which enables a light trigger for events depositing\nMeV-scale energies, with an accurate scintillation amplitude and energy reconstruction.\nThe PDE of the ArCLight modules is about a factor of 10 lower than the corresponding\nvalue obtained with the LCMs, which allows for a larger dynamic range. The ArCLight\ntechnology additionally enables a high position sensitivity, which can be used to accurately\ntriangulate the origin of the scintillation light emission point [11]. For the LCM it can be\nobserved that tiles placed at the top (see Fig. 26 (right), LCM groups 4\u20136, 10\u201312, 16\u201318,\nand 22\u201324) of the TPC show a systematically lower PDE with respect to tiles placed in the\nmiddle of the TPC. This can be explained by an anisotropy of light collection of LCM with\nrespect to the angle of incoming photons, driven by structural non-uniformity of fibers\nand spaces. The absence of non-uniform effects in the ArCLight tiles due to reflections on\nthe TPC structure or Rayleigh scattering, meanwhile, further indicates that these effects\nare negligible within the experimental uncertainties. In Module-0, a Hamamatsu MPPC\nS13360-6025 [22] is used. By replacing the SiPM for future modules with the MPPC S13360-\n6050 with higher efficiency, the overall PDE would improve by a factor of 1.6 to yield a\nLCM efficiency of about 1%.\n1\n2\n3\n4\n5\n6\n7\n8\nArCLight tile number\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\nPDE [%]\nDUNE:ND-LAr 2x2\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\nLCM tile number\n0\n0.5\n1\n1.5\n2\n2.5\n3\nPDE [%]\nDUNE:ND-LAr 2x2\nFigure 26.\nAbsolute PDE for each ArCLight (left) and LCM (right) tile (arbitrary numbering).\nArCLight tile 7 was disabled during Module-0 data taking. The LCM tiles are placed in sets of 3 to\ncover the same area as one ArCLight tile.\n5. Measurements with Cosmic Ray Data Samples\nThe following sections discuss the analyses performed using reconstructed tracks from\nthe large cosmic ray data set collected during the Module-0 run. As discussed in Section 1,\nthe Module-0 detector incorporates several novel technologies for the first time in a LArTPC\nof this scale. These studies assess the performance of the fully-integrated system, including\nthe LArPix charge readout with a very large channel count, the high-coverage hybrid LCM\nand ArCLight photon detection systems, and their matching; the capability to achieve the\n\nVersion March 6, 2024 submitted to Instruments\n32 of 47\nnecessary levels of LAr purity for physics measurements without prior evacuation of the\ncryostat; and the degree of drift field uniformity achievable with the low-profile resistive\nshell field cage. Detailed studies of each of these key detector parameters demonstrate\nexcellent performance of the integrated system relative to the requirements in view of the\noperation for the DUNE ND-LAr.\nIn support of these studies, a sample of cosmic rays has been simulated using COR-\nSIKA [23], a program for detailed simulation of extended air showers. The passage of the\nparticles through matter has been simulated using a Geant4-based Monte Carlo [24]. The\ndetector simulation has been performed with larnd-sim [25,26], a set of highly-parallelized\nGPU algorithms for the simulation of pixelated LArTPCs. A track-fitting algorithm is\napplied to provide an estimate of the particle track angle and location. First, a 3D point\ncloud is reconstructed using the unique channel index to determine the position transverse\nto the anode and the drift time. DBSCAN (k = 5, \u03f5 = 2.5 cm) [19] is used to find the hit\nclusters. The cluster radius (\u03f5) was tuned using the k = 5th-neighbor distance of 3D points\nfrom a typical run. Each cluster is then passed through a RANSAC line fit [27] with an\noutlier radius of \u03c1 = 8 mm and 100 random samples. This provides a set of highly-collinear\npoints which constitute the reconstructed track.\n5.1. Electron lifetime\nThe amount of charge collected by the readout system depends heavily on the electron\nlifetime, \u03c4, in the argon of the TPC volume. The electron lifetime parameterizes (in units of\ntime) how much charge is lost due to attachment to electronegative impurities in the argon,\nsuch as oxygen or water, during the drift of the deposited ionization charge toward the\nanode. The charge measured at the anode, Q, is given by\nQ = e\u2212t/\u03c4 \u00b7 R \u00b7 Q0,\n(1)\nwhere Q0 is the amount of the primary ionization charge deposited by a particle in the\nliquid argon, R is the recombination factor that describes the fraction of charge that survives\nprompt recombination of the ionization with argon ions prior to drift, and t is the drift time\nfrom the point of original charge deposition to detection in the anode plane. Measuring\nsignals originating across the entire TPC via the charge readout system requires a sufficient\nelectron lifetime in the detector. For the DUNE ND-LAr detector this requirement is\n> 0.5 ms at a drift electric field of 500 V/cm; this relatively low value compared to other\nlarge LArTPC detectors [4,28,29] is due to the relatively short maximum drift length of\nDUNE ND-LAr (\u223c50 cm) and allows ND-LAr to meet the charge attenuation performance\nof the far detector, which specifies a 3 ms lifetime in a detector with a 3.5 m drift length\nat a 500 V/cm drift field [30]. A measurement of the electron lifetime with Module-0 has\nbeen carried out to confirm that the materials used in the detector, which will be similar to\nthose of DUNE ND-LAr, are compatible with the argon purity requirement. Additionally,\ntracking this parameter as a function of time is necessary to provide a calibration of charge\nscale for other measurements carried out using the Module-0 charge data.\nAs seen in Eq. 1, charge measurements at the anode depend both on the electron life-\ntime and the recombination factor. However, by measuring Q as a function of the drift time\nfor a collection of cosmic muon tracks that span the entire drift distance, the dependence\non R, which is independent of drift time, can be ignored as an overall normalization factor.\nAdditionally, a more fitting quantity to use in this study is dQ/dx, the measured charge per\nunit length along the cosmic muon track, given the dependence of the amount of charge\nseen by a single pixel channel on the orientation of each track. The electron lifetime for\neach Module-0 data run at a drift electric field of 500 V/cm is measured by applying an\nexponential fit to the mean dQ/dx of muon track segments as a function of drift time to the\nanode, assuming a uniform dQ/dx. A sample of anode-cathode-crossing tracks is used for\nthis measurement; these tracks span the entire drift distance and the absolute drift time\nassociated with each part of the track is known for this track sample. The electron lifetime\nvalues measured in Module-0 were consistently above 2 ms for the duration of the run,\n\nVersion March 6, 2024 submitted to Instruments\n33 of 47\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nDrift time [\u00b5s]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n/cm]\n-\ndQ/dx [ke\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\nDUNE:ND-LAr 2x2\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nDrift time [\u00b5s]\n0\n20\n40\n60\n80\n100\n120\n140\n160\n/cm]\n-\nMean dQ/dx [ke\nms\n-0.13\nElectron lifetime: 2.64+0.15\nDUNE:ND-LAr 2x2\nFigure 27. Measured dQ/dx versus drift time for ionization associated with anode-cathode-crossing\nmuon tracks (left); mean dQ/dx versus drift time, along with exponential fit, for the same track\nsample (right).\n2021-04-02\n2021-04-03\n2021-04-04\n2021-04-05\n2021-04-06\n2021-04-07\n2021-04-08\n2021-04-09\n2021-04-10\nDate\n0\n1\n2\n3\n4\n5\nElectron lifetime [ms]\nDUNE:ND-LAr 2x2\n2021-06-23 12\n2021-06-24 00\n2021-06-24 12\n2021-06-25 00\n2021-06-25 12\n2021-06-26 00\nDate and hour\n0\n1\n2\n3\n4\n5\nElectron lifetime [ms]\nDUNE:ND-LAr 2x2\nFigure 28. Extracted electron lifetime as a function of time during Module-0 Run 1 (top) and Run 2\n(bottom), with the average uniformly exceeding 2 ms in both cases.\nthus satisfying the \u03c4 > 0.5 ms requirement. This trend continued in the second run (Run 2)\nof Module-0, where cryogenic operations differed from those in Run 1. Run 1 achieved LAr\npurity through cryostat evacuation before cooldown and LAr filling, while Run 2 made\nuse of a piston purge procedure (repeatedly purging the volume with clean gas), as this is\nthe anticipated approach for the full-scale cryostat of ND-LAr. A recirculation system with\nfiltration was operational during both runs. Results are shown in Fig. 28.\n5.2. Electric field uniformity\nThe magnitude of electric field distortions due to space charge effects for Module-0 are\nexpected to be much smaller than other, larger LArTPC detectors running near the surface,\nsuch as MicroBooNE [31] and ProtoDUNE-SP [32]. This is due to the relatively small\nmaximum drift length of \u223c30 cm of Module-0, compared to \u223c2.5 m for MicroBooNE and\n\u223c3.6 m for ProtoDUNE-SP. Even for a maximum drift length of \u223c50 cm that is anticipated\nfor DUNE ND-LAr, the impact from space charge effects is expected to be negligible; the\nfact that ND-LAr will operate 65 m underground will reduce this effect further due to the\nsmaller flux of cosmic muons. However, it is possible that electric field inhomogeneities\n\nVersion March 6, 2024 submitted to Instruments\n34 of 47\narise in the Module-0 detector from other sources. In particular, it is important to determine\nwhether or not the field cage design causes significant distortions of the electric field, which\ncan alter the trajectories ionization electrons take while drifting to the anode plane. Such\ndistortions could lead to incorrect reconstruction of the true position of original energy\ndepositions in the detector due to primary particles ionizing the argon, consequently\nimpacting their trajectory and energy reconstruction. Furthermore, associated modification\nto the electric field intensity throughout the detector can lead to significant impact on\nthe amount of electron-ion recombination experienced by ionization electrons, leading to\nbias in reconstructed particle energy scale or degradation of reconstructed particle energy\nresolution. The use of the novel resistive field cage technology in Module-0, as is anticipated\nfor DUNE ND-LAr, provides an important opportunity to study the impact on electric field\nhomogeneity.\nFollowing the methodology developed by the MicroBooNE experiment for analysis of\nspace charge effects [31], electric field distortions are probed using end points of through-\ngoing cosmic muon tracks in Module-0 data. Tracks passing through an anode plane and\nanother face of the detector that is not the other anode plane are selected for this study,\nproviding a known absolute drift time associated with each part of the track via subtracting\nthe time associated with the anode side of the track. The track end point associated with the\nnon-anode side of the anode-crossing track is then probed by measuring the transverse (i.e.,\nperpendicular to the drift direction) displacement from the edge of the TPC active volume,\nas measured from the y value (TPC top and bottom) or x value (TPC front and back sides,\nperpendicular to the drift direction) of the pixel channels at the edge of the detector. The\naverage transverse displacement is recorded as a function of the two directions within the\nTPC face for all four non-anode faces of the Module-0 TPC. If there are no electric field\ndistortions in the detector, there would be no inward migration of ionization electrons\nduring drift, leading to zero transverse displacement of ionization charge with respect to\nthe TPC face for this sample of through-going muon tracks (contamination from stopping\nmuons is expected to be less than 1%). The result of the average transverse displacement\nmeasurement is shown for the TPC top and bottom in Fig. 29 and for the TPC front and back\nin Fig. 30. A few features not associated with electric field distortions in the detector should\nbe pointed out. First, there are gaps in coverage near the anode planes (z values of roughly\n\u00b130 cm) due to a requirement in the track selection that the non-anode side of the track is at\nleast 5 cm away from both anode planes, and near the pixel plane edges (edges of the TPC\nface) due to a requirement that the non-anode side of the track is not located within 1 cm\n(2 cm) of these features. These selection criteria were introduced to minimize contamination\nof the sample from poorly-reconstructed muon tracks. Some residual contamination is seen\nnear the edges of the pixel planes, where the measured average transverse spatial offset is\nartificially large due to edge channels of the pixel planes being turned off for data-taking,\nleading to the ends of tracks being clipped off near the edges of pixel planes. Second, the\ntwo horizontal bands in the bottom right corner of the right side of Fig. 30 are associated\nwith a known grounding issue of an ArCLight unit in this part of the detector. The vertical\ngap in the right panel of Fig. 29 is due to inactive channels in this region of the anode plane\n(see Fig. 10).\nAfter accounting for these two artifacts, non-negligible transverse spatial offsets are\nobserved near the cathode (central horizontal lines in Fig. 29, central vertical lines in Fig. 30),\nroughly 1 cm on average but as large as 2.5 cm in some places in the TPC. After adding an\nadditional \u223c1 cm to these measurements to account for the separation between the edge\npixel channels and the field cage (or light detectors in the case of the front and back of the\nTPC), the average (maximum) transverse spatial offset experienced by drifting ionization\ncharge originating near the cathode is roughly 2 cm (3.5 cm). Ascribing this transverse\ndrift to an additional electric field component strictly in the direction transverse to the\nTPC faces, the average (maximum) transverse electric field magnitude leading to this\namount of inward drift of ionization charge is roughly 30 V/cm (60 V/cm). The associated\naverage (maximum) impact to the electric field magnitude in the detector is 0.2% (0.7%).\n\nVersion March 6, 2024 submitted to Instruments\n35 of 47\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nX\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nZ\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nCalib. \u2206Y [cm]: Top Face\nDUNE:ND-LAr 2x2\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nX\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nZ\n5\n\u2212\n4.5\n\u2212\n4\n\u2212\n3.5\n\u2212\n3\n\u2212\n2.5\n\u2212\n2\n\u2212\n1.5\n\u2212\n1\n\u2212\n0.5\n\u2212\n0\nCalib. \u2206Y [cm]: Bottom Face\nDUNE:ND-LAr 2x2\nFigure 29. Average spatial offsets measured at the top (left) and bottom (right) of the Module-0\ndetector. These offsets in cm are measured with respect to the location of the pixel channels at the\nedge of the detector.\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nZ\n60\n\u2212\n40\n\u2212\n20\n\u2212\n0\n20\n40\n60\n [cm]\nreco\nY\n5\n\u2212\n4.5\n\u2212\n4\n\u2212\n3.5\n\u2212\n3\n\u2212\n2.5\n\u2212\n2\n\u2212\n1.5\n\u2212\n1\n\u2212\n0.5\n\u2212\n0\nCalib. \u2206X [cm]: Upstream Face\nDUNE:ND-LAr 2x2\n30\n\u2212\n20\n\u2212\n10\n\u2212\n0\n10\n20\n30\n [cm]\nreco\nZ\n60\n\u2212\n40\n\u2212\n20\n\u2212\n0\n20\n40\n60\n [cm]\nreco\nY\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\nCalib. \u2206X [cm]: Downstream Face\nDUNE:ND-LAr 2x2\nFigure 30. Average spatial offsets measured at the front (left) and back (right) of the Module-0\ndetector. These offsets in cm are measured with respect to the location of the pixel channels at the\nedge of the detector.\n\nVersion March 6, 2024 submitted to Instruments\n36 of 47\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nTime since 4/2/2021 00:00:00 [h]\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\nTransverse spatial offset [cm]\n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [-25, -5] cm, \n\u2208\n \nreco\nX\nBottom: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [5, 25] cm, \n\u2208\n \nreco\nX\nBottom: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [-25, -5] cm, \n\u2208\n \nreco\nX\nTop: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [5, 25] cm, \n\u2208\n \nreco\nX\nTop: \nDUNE:ND-LAr 2x2\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\nTime since 4/2/2021 00:00:00 [h]\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\nTransverse spatial offset [cm]\n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [-25, -5] cm, \n\u2208\n \nreco\nX\nBottom: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [5, 25] cm, \n\u2208\n \nreco\nX\nBottom: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [-25, -5] cm, \n\u2208\n \nreco\nX\nTop: \n [3, 10] cm\n\u2208\n| \nreco\n|Z\n [5, 25] cm, \n\u2208\n \nreco\nX\nTop: \nDUNE:ND-LAr 2x2\nFigure 31. Time dependence of spatial offsets in the \u2212z (top) and +z (bottom) drift volumes. These\noffsets are measured with respect to the location of the pixel channels at the edge of the detector.\nThis is below the conservative physics requirement of 1% maximum allowed deviation\nof the electric field magnitude within 95% of the detector volume, indicating that the\ndesign of the field cage is adequate for the physics goals of DUNE ND-LAr. It is worth\npointing out that this physics requirement for electric field distortions corresponds to after\ndetector calibrations have been carried out, while the measurements presented here have\nno calibration applied. It is thus expected that the calibrated electric field map would\nbe even more homogeneous at DUNE ND-LAr. An additional study is carried out to\ndetermine if the small electric field distortions in the Module-0 detector vary substantially\nover time. A substantial time dependence of the electric field distortions may complicate\nefforts to obtain a calibrated electric field map in the DUNE ND-LAr detector using cosmic\nmuons, neutrino-induced muons, or dedicated calibration hardware. Average transverse\nspatial offsets were measured at four different places on each side of the Module-0 cathode\nas a function of time, spanning two full days of data-taking. The results of the study\nare shown in Fig. 31. No substantial time dependence of transverse spatial offsets is\nobserved (< 0.2 cm), indicating that calibration of the underlying electric field distortions is\nachievable by averaging measured spatial offsets over at least a few days of data-taking. A\nstudy of electric field stability over longer periods of time is planned in future prototyping\nof the DUNE ND-LAr detector concept.\n5.3. Charge-light matching\nEfficient matching between signals in the charge and light readout systems is essential,\nas this enables the use of light to disambiguate pile-up of separate neutrino interactions\n\nVersion March 6, 2024 submitted to Instruments\n37 of 47\n0\n5\n10\n15\n20\n25\n30\nCharge-light matching time window (\u00b1N \u00b5s)\n0.2\n0.4\n0.6\n0.8\n1\nCharge-light matching efficiency\nDUNE:ND-LAr 2x2\n0\n5\n10\n15\n20\n25\n30\nCharge-light matching time window (\u00b1N \u00b5s)\n3\n\u2212\n10\n2\n\u2212\n10\n1\n\u2212\n10\n1\nCharge-light matching inefficiency\nDUNE:ND-LAr 2x2\nFigure 32. Charge-light matching efficiency in linear scale (left) and inefficiency in logarithmic\nscale (right) for light detector triggers matched to the arrival time of charge at the anode side of\nanode-cathode-crossing tracks.\n1\n\u2212\n0\n1\n2\n3\n4\n5\n6\nCharge/light time offset [\u00b5s]\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nEntries/bin\nData\nCrystal ball fit\nGaussian component\nDUNE:ND-LAr 2x2\nFigure 33. Time offset distribution for light detector triggers matched to the arrival time of charge at\nthe anode side of anode-cathode-crossing tracks (charge minus light).\nwithin a single beam spill. The unique association between charge and light signals is a\nnontrivial problem in a large-volume LArTPC, especially in an environment with a high\nrate of neutrino event pile-up, such as DUNE ND-LAr. This motivates the modular design,\nwhere the full active volume is composed of an array of optically-isolated TPC volumes,\neach with high coverage of optical detectors with fast timing and good spatial resolution.\nCharge-light matching in Module-0 has been accomplished via association of precision\nGPS-synchronized timestamps in the two systems. Here, two performance metrics are\nconsidered: the efficiency of matching for a selection of tracks as a function of the allowed\ncoincidence time window and the resolution in terms of the offset between the two systems\u2019\ntimestamps. Fig. 32 shows the matching efficiency for varying definitions of the allowed\ntime window for coincidence formation, for a selection of anode-cathode-crossing muon\ntracks. The overwhelming majority of these are single tracks, as the probability of having\nanother event in the same \u223c200 \u00b5s window is very small. For conservative matching\nparameters, an efficiency of \u226599.7% is found. In this study, the timing resolution is\nlimited by the spatial resolution of the tracking from the charge readout, not by the intrinsic\nlight detector timing resolution, which is discussed in Section 4. Next, Fig. 33 illustrates\nthe relative time offset between the two systems for the Module-0 prototype, again for a\nselection of anode-cathode-crossing tracks. The distribution exhibits a Gaussian core and a\ntail. The asymmetric tail of the distribution, captured by a Crystal Ball fit [33], is due to\ntrack truncation near the boundaries of the pixel planes. The Gaussian component of the\nCrystal Ball fit is also shown; the standard deviation of the Gaussian, 0.4\u00b5s, is identified\nas the charge readout timing resolution. The physics requirements for ND-LAr require\nthat the resolution in the drift dimension be at least as precise as that across the anode\nplane, i.e. the pixel pitch divided by\n\u221a\n12, or 1.3 mm. The resolution extracted in Module-0\ncorresponds to 0.6 mm at a drift electric field of 500 V/cm, thus meeting the requirement.\n\nVersion March 6, 2024 submitted to Instruments\n38 of 47\n\u2212300 \u2212200 \u2212100\n0\n100\n200\n300\nz [mm]\n\u2212600\n\u2212400\n\u2212200\n0\n200\n400\n600\ny [mm]\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nx [mm]\n\u2212600\n\u2212400\n\u2212200\n0\n200\n400\n600\ny [mm]\n20\n40\n60\n80\n100\n120\n140\n160\n180\n200\nz [mm]\n\u2212600\n\u2212400\n\u2212200\n0\n200\n400\n600\ny [mm]\n0\n10\n20\n30\n40\n50\nz [mm]\n\u2212600\n\u2212400\n\u2212200\n0\n200\n400\n600\ny [mm]\n0\n10\n20\n30\n40\n50\nDUNE:ND-LAr 2x2\n\u2212300 \u2212200 \u2212100\n0\n100\n200\n300\n\u2212300 \u2212200 \u2212100\n0\n100\n200\n300\n\u2212300 \u2212200 \u2212100\n0\n100\n200\n300\nFigure 34. Charge-light matched event display of a cosmic muon track. The left two panels show the\nTPC charge readout, in a z \u2212y project (left) and x \u2212y projection (center left). The right two panels\nshow the light detector responses for the arrays at \u2212x (center right) and +x (right), with each bin\nalong the vertical axis representing the strength of signal read by individual SiPMs.\n5.4. Correlation of the charge and light yield\nMatched charge and light events as shown in Figure 34 provide another data sample\nwhich may be used to study the correlation in the relative charge and light yields in the\ndetector. These yields are related to electric-field dependent recombination effects.\nTo describe the recombination mechanism in LAr we formalize the ionization and\nexcitation states generated by the deposited energy of a traversing particle as follows:\nNi + Nex = QY + LY,\n(2)\nwhere the sum of available ionization (Ni) and excitation (Nex) states determines the total\nnumber of electrons (QY) and photons (LY) generated in LAr. The number of ionization\nstates Ni is given by\nNi =\nEdep\nWi\n, Wi = 23.6 eV,\n(3)\nwhere Wi is the ionization work function [34] and Edep is the deposited energy. In the\nabsence of charge attenuation and impurities, the total charge Q arriving at the anode\ndepends only on the initially-produced ionization charge Q0 = Nie as\nQY = Ni \u00b7 Rc,\n(4)\nLY = Ni\n\u0012\n1 + Nex\nNi\n\u2212Rc\n\u0013\n,\n(5)\nwhere the charge recombination factor Rc is dependent on the electric field \u03f5, and e is the\nelectron charge. In the presence of impurities, the electron lifetime correction is applied\nfirst; see Eq. 1. Increasing \u03f5 leads to less recombination between argon ions and ionization\nelectrons, and thus more free charge carriers are present in the TPC drift field, increasing the\ntotal detected charge at the anode plane. At the same time, a reduced charge recombination\nfactor corresponds to less scintillation light produced within the TPC, leading to a decrease\nof the light yield at higher electric fields, as expressed by Eq. 4. Hence, the amount of\ncharge yield and the amount of light yield observed in the detector are expected to be\nanti-correlated. To describe the recombination of electron-ion pairs, we focus on the most\ncommonly used models, namely the Box [35] and the Birks\u2019 models [36], and compare\nthe results of Module-0 measurements with those of the ICARUS [37] and ArgoNeuT [38]\n\nVersion March 6, 2024 submitted to Instruments\n39 of 47\nexperiments. The Box model assumes zero electron diffusion, zero ion mobility, and a\ndistribution of ionization electrons that are uniformly produced within a 3D box along the\npath of the ionizing particle. The collected charge Q is given by\nQ = Q0 \u00b7 ABox\n\u03be\n\u00b7 ln(\u03be),\n(6)\nwhere Q0 denotes the primary ionization charge and \u03be is\n\u03be = N0Kr\n4a2\u00b5\u03f5,\n(7)\nwhere a is the linear size of the charge \u2018box\u2019, N0 denotes the number of electrons in the\nbox and Kr is the recombination rate constant. \u00b5 and \u03f5 define the electron mobility and the\nelectric field, respectively. Note that in the limit of an infinite electric field intensity \u03f5, the\ncollected charge at the anode plane corresponds to the initially produced charge, Q0. Birks\u2019\nmodel describes the collected charge QY as\nQY = Ni \u00b7\nABirks\n1 + kB\n\u03f5 \u00b7 dE\ndx\n= Q0\ne Rc,\n(8)\nwhere ABirks and kB are fitting constants. In this formulation of the Birks\u2019 model, for infinite\nelectric field intensities \u03f5 \u2192\u221e, the recombination factor does not go to 1 and is limited to\nRc \u2192A. We can now express the light yield as\nLY = Ni\n \n1 + Nex\nNi\n\u2212\nABirks\n1 + kB\n\u03f5 \u00b7 dE\ndx\n!\n.\n(9)\nHowever, since the fraction of excited states Nex\nNi is not precisely known, the commonly\nused model for description of the light yield in scintillating materials uses the following\nformulation:\nLY = L0(1 \u2212\u03b1Rc) = L0RL,\n(10)\nL0 =\nEdep\nWL\n, WL = 19.5 eV,\n(11)\nwhere L0 denotes the number of scintillation photons at zero electric field intensity, \u03b1 is a\nconstant fitted to the data and WL is the scintillation work function [39]. This formulation\nis used in this analysis to evaluate the parameters in the Birks\u2019 model for the light yield.\nTo study the charge and light correlation in Module-0, data samples at different electric\nfield intensities ranging from 0.05 kV cm\u22121 to 1.00 kV cm\u22121 were acquired and analysed.\nThese events contain information about the collected charge and scintillation light. A\nselection of vertical through-going tracks, as expected from MIP muons, was used to extract\nthe collected charge and light per unit length of the track. For the measurement of the\ncollected charge per unit track length, the track was divided into 2 cm segments and the\ntotal charge collected each the segment was divided by the segment length. Then, the light\nyield per unit track length is extracted as:\ndL\ndx =\nLdetected\nR\n\u2126dl \u00d7 PDE \u00d7 G.\n(12)\nThe factors in this expression include the geometrical acceptance R\n\u2126dl, the readout gate\nacceptance G, and the overall PDE of each tile reported in Section 4. The geometrical\nacceptance was computed based on the charge data and the track segment position with\nrespect to a light detection tile, integrated over the track length. The readout gate acceptance\nis an estimation of the fraction of photons which reach the SiPM within the readout\n\nVersion March 6, 2024 submitted to Instruments\n40 of 47\n0\n0.2\n0.4\n0.6\n0.8\n1\nE field [kV/cm]\n0\n20\n40\n60\n80\n100\n3\n10\n\u00d7\n/cm]\ne-\nCharge [N\n / ndf\n2\n\u03c7\n 0.935 / 18\nBirks\nA\n 0.01171\n\u00b1\n 0.8203 \nBirks\nk\n 0.005411\n\u00b1\n 0.05787 \n / ndf\n2\n\u03c7\n 0.935 / 18\nBirks\nA\n 0.01171\n\u00b1\n 0.8203 \nBirks\nk\n 0.005411\n\u00b1\n 0.05787 \nFit Comparison\nBirks' fit to data\nBox fit to data\nICARUS results\nDUNE:ND-LAr 2x2\n0.2\n0.4\n0.6\n0.8\n1\nE field [kV/cm]\n0\n20\n40\n60\n80\n100\n3\n10\n\u00d7\n/cm]\nph\nLight [N\n / ndf\n2\n\u03c7\n 19.86 / 16\nBirks\nA\n 0.4457\n\u00b1\n 0.7875 \nBirks\nk\n 0.00406\n\u00b1\n 0.03722 \nlight\n\u03b1\n 0.457\n\u00b1\n 0.8075 \n / ndf\n2\n\u03c7\n 19.86 / 16\nBirks\nA\n 0.4457\n\u00b1\n 0.7875 \nBirks\nk\n 0.00406\n\u00b1\n 0.03722 \nlight\n\u03b1\n 0.457\n\u00b1\n 0.8075 \nDUNE:ND-LAr 2x2\nFigure 35. Charge yield as a function of the electric field intensity fitted with the Box and Birks\u2019\nmodels, and compared to ICARUS results (left); Light yield as a function of the electric field intensity\nfitted separately with the Birks\u2019 model (right).\nFit parameters\nABirks [kV g cm\u22123 MeV\u22121]\nkBirks [kV g cm\u22123 MeV\u22121]\nCharge only fit\n(0.820 \u00b1 0.011)\n(0.058 \u00b1 0.005)\nLight only fit\n(0.79 \u00b1 0.45)\n(0.037 \u00b1 0.004)\nCombined fit\n(0.794 \u00b1 0.008)\n(0.045 \u00b1 0.003)\nTable 1. The fitted parameters of the Birks\u2019 model using the Module-0 data.\nintegration gate of 500 ns. The gate acceptance was measured using the average waveform\nof the light signals in Module-0 data to be \u223c64% for both the LCM and ArCLight modules.\nThe dQ/dx and dL/dx distributions are well-described by a Landau-convolved Gaus-\nsian function, which is used to extract the most probable value (MPV). We note that the fits\nare performed on raw data, i.e. without additional calibration of the track dE/dx. Due to\nuncorrected charge losses, the extracted MPV values for charge measurements should be\ncompared with an effective value of \u223c1.8 MeV/cm, while MPVs corresponding to light\nmeasurements correspond to an effective dE/dx \u223c2.1 MeV/cm. The dependence of the\ncharge yield and the light yield MPV values with respect to the electric field density is\nillustrated in Fig. 35.\nThe charge yield and light yield data points were fitted separately to the Birks\u2019 model,\nwith results shown in Fig. 35 and Tab. 1. We note that for the light yield fit (Fig. 35, right),\nper Eq. 10, the ABirks and \u03b1light parameters are totally correlated and cannot be extracted\nindependently. The left panel of Fig. 35 also shows a comparison of the charge yield data\n(red points) to fits using a Birks\u2019 model (red curve) and Box model (green curve), alongside\nthe results from the ICARUS experiment (blue curve), demonstrating good agreement\nbetween the results.\nNext, a combined fit of the Birks\u2019 model to both charge and light yield data sets was\nperformed. Fig. 36 shows the final result of the correlation study. The best fit results\nfor the Birks\u2019 model parameters are ABirks = 0.794 \u00b1 0.008 and kBirks = 0.045 \u00b1 0.003,\nwith a \u03c72/ndf of 23.2/35, where the number of degrees of freedom calculated based on\n19 fit points per dataset (charge and light) included in the fit and three fit parameters.\nTable 2 summarizes the Birks\u2019 model parameters obtained with the Module-0 detector and\ncompares them with the parameters found in the ICARUS and the ArgoNeuT experiments.\nThe results of the simultaneous fit of the Birks\u2019 model to the light and charge distributions\nshow reasonable agreement with previous experiments.\n5.5. Michel electrons\nMichel electrons, i.e. electrons from stopped muon decay, constitute a readily available\nand versatile tool for the study and characterisation of the performance of a LArTPC. They\nare abundant for surface-level detectors exposed to a large cosmic ray muon flux, and\nwith \u00b5 \u2192e\u03bde\u03bd\u00b5 as the almost exclusive decay channel, the number of events is given by\n\nVersion March 6, 2024 submitted to Instruments\n41 of 47\n0\n0.2\n0.4\n0.6\n0.8\n1\nE field [kV/cm]\n0\n20\n40\n60\n80\n100\n3\n10\n\u00d7\n/cm]\nph\n/cm] or [N\ne-\n[N\n / ndf\n2\n\u03c7\np0 \np1 \n / ndf\n2\n\u03c7\np0 \np1 \n / ndf\n2\n\u03c7\nBirks\nA\nBirks\nk\nlight\n\u03b1\n / ndf\n2\n\u03c7\nBirks\nA\nBirks\nk\nlight\n\u03b1\n23.22 / 35\n0.7938 \u00b1 0.008069\n0.04517 \u00b1 0.003313\n0.8139 \u00b1 0.004672 \nDUNE:ND-LAr 2x2\nFigure 36. Light yield (blue) and charge yield (red) extracted from a simultaneous fit with the Birks\u2019\nmodel.\nExperiment\nABirks [kV g cm\u22123 MeV\u22121]\nkBirks [kV g cm\u22123 MeV\u22121]\nReference\nICARUS\n(0.800 \u00b1 0.003)\n(0.0486 \u00b1 0.0006)\n[37]\nArgoNeuT\n(0.806 \u00b1 0.010)\n(0.052 \u00b1 0.001)\n[38]\nModule-0\n(0.794 \u00b1 0.008)\n(0.045 \u00b1 0.003)\nThis work\nTable 2. Comparison of the ICARUS and ArgoNeuT results with the current study.\nthe probability of the muon to come to rest in the detector. The electrons produced by\nthe decay have a well-characterised energy spectrum with a cutoff at \u223c50 MeV and their\ntopology is relatively easy to tag: a long muon track ending with a Bragg peak followed\nby a short ionization track from the electron at a different angle with respect to the muon\ndirection. Fig. 1 includes one example of a stopping muon decaying with a Michel electron\nin Module-0. The effective muon lifetime of \u223c2 \u00b5s is short relative to the TPC drift speed,\nleading to minimal displacement of the muon track endpoint and electron track start.\nHowever, it is large relative to the time resolution of the light readout system, allowing\nthe two signals to be tagged separately: the first light pulse corresponding to the muon\nionization, and the second to the electron, can be easily separated for a large majority of\nevents due to the excellent timing resolution of ArCLight and LCM detectors. Fig. 37 shows\nthe event display of a selected Michel electron candidate, with the two peaks showing the\nwaveforms of the light detectors located in one of the two half-TPCs.\nThe Michel electron candidates\u2019 topology is mainly characterised by a long ionisation\ntrail left over by the crossing muon. An automatic selection algorithm based on the event\ntopology and the presence of the Bragg peak at the end of the muon track was developed\nand applied to the subset of cosmic data. Visual event validation was performed on selected\nevents to validate the analysis. The final distribution of the reconstructed Michel electron\nenergy based on the automated charge reconstruction is shown in Fig. 38. The end point is\nnear the expected true end point of 53 MeV. The spectrum peaks at lower energies mainly\nas a consequence of partial containment, imperfect clustering, and charge below threshold,\nparticularly from electrons Compton-scattered by Bremmstrahlung photons radiated from\nthe primary electron [40\u201342].\n5.6. Detector simulation validation with cosmic ray tracks\nFinally, selected samples of cosmic ray tracks are compared in detail to a cosmic ray\nsimulation based on the CORSIKA event generator and the detailed microphysical detector\n\nVersion March 6, 2024 submitted to Instruments\n42 of 47\nx [mm]\n250\n0\n250\nz [mm]\n250\n0\n250\ny [mm]\n600\n400\n200\n0\n200\n400\n600\n0\n5000\nTime [ns]\n0\n0\n5000\nTime [ns]\n0\n0\n-10000\n0\n-10000\n-10000\n-10000\nDUNE:ND-LAr 2x2\nFigure 37. Event display of a Michel electron candidate shown in a 3D view (left) and with associated\nwaveforms from photon detectors (right). In the right panel, orange and blue indicate the two\noptically isolated semi-TPCs. The red circles highlight an example the two pulses on the photon\ndetectors correspond to the entering muon and the electron resulting from its decay.\n0\n10\n20\n30\n40\n50\n60\n70\n80\nMichel electron energy (charge reconstruction) [MeV]\n0\n100\n200\n300\n400\n500\n600\nEntries/bin\nDUNE:ND-LAr 2x2\nFigure 38. Charge-based energy spectrum of Michel electron candidates from a sample of recon-\nstructed muon decays, using the full data set and automated event reconstruction.\nsimulation introduced in Section 5. Starting from the cosmic ray track reconstruction\ndescribed there, the track\u2019s start and end points are found by projecting the 3D points onto\nthe cluster\u2019s principal components. The DBSCAN+RANSAC fit is applied on outlying\nhits until all are placed within a cluster or no hits remain. This is sufficient for studies of\nlow-level detector response, as it provides a local approximation of the track trajectory with\nminimal impact from \u03b4-rays and hard scatters. Reconstructed tracks may show artificial\ngaps due to the presence of disabled channels. Also, cathode-piercing tracks will usually\nbe reconstructed as separated tracks, due to the non-zero cathode thickness. Thus, tracks\n\nVersion March 6, 2024 submitted to Instruments\n43 of 47\nwith an angle smaller than 20\u25e6and closer than 10 cm are stitched together for the following\nstudies. A comparison between the spatial coordinates of the stitched tracks in data and\nsimulation is shown in Fig. 39.\nProbability/bin\nDUNE:ND-LAr 2x2\nProbability/bin\nDUNE:ND-LAr 2x2\nFigure 39. Start and end coordinates of stitched tracks in data (high and low threshold runs) and\nsimulation.\nFig. 40 shows a comparison of the dQ/dx for low threshold and high threshold runs\nwith a sample of simulated cosmic rays. The dQ/dx has been measured for segments of\ndifferent lengths, following the procedure described in Section 5.6. The simulation assumes\nthe Birks model for electron recombination and a gain of 4 mV/103 e\u2212[36]. In the data,\nthe amount of charge that reaches the anode is corrected by the electron lifetime factor\ncalculated in Section 5.1.\nNext, the dQ/dx as a function of the reconstructed track residual range is considered.\nAs noted in Section 5.5, for a muon that stops in the detector the amount of deposited\ncharge per unit length will increase as it approaches the end point, forming a Bragg peak.\nFig. 41 shows an example of a stopping muon and the subsequent Michel electron. The\ndQ/dx has been measured by subdividing the reconstructed track in 10 mm segments\n(our dx) and summing the charge contained in each segment (the dQ). The data show a\nBragg peak near the end of the reconstructed track, where the residual range is close to\nzero. The theoretical prediction is obtained by taking the \u27e8dE\ndx \u27e9values tabulated in Ref. [43]\nfor muons in LAr, divided by the argon ionization energy (23.6 eV) and multiplied by the\nrecombination factor RICARUS\nBirks\n, calculated in Ref. [37].\nThe observed distributions indicate good overall agreement between data and sim-\nulations, in particular with the ability to correctly reproduce the position of the dQ/dx\npeak. Module-0 data provide input that can be used to further tune the detector simulation,\nincluding modeling of additional noise sources and details of the anode response. Mean-\nwhile, the strong overall agreement in the vertex positioning and calorimetry indicates that\nthe initial detector response model is able to capture the main features of the cosmic ray\ntrack samples.\n\nVersion March 6, 2024 submitted to Instruments\n44 of 47\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\n1.4\n1.6\nN. entries / (0.4 103e\n/mm)\n400 mm\nSimulation\nSim. MPV 4.50 103 e /mm\nData low MPV 4.54 103 e /mm\nData high MPV 4.56 103 e /mm\nModule-0 data - low threshold\nModule-0 data - high threshold\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n300 mm\nSim. MPV 4.48 103 e /mm\nData low MPV 4.54 103 e /mm\nData high MPV 4.54 103 e /mm\n0.0\n0.2\n0.4\n0.6\n0.8\n200 mm\nSim. MPV 4.60 103 e /mm\nData low MPV 4.60 103 e /mm\nData high MPV 4.62 103 e /mm\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nN. entries / (0.4 103e\n/mm)\n150 mm\nSim. MPV 4.60 103 e /mm\nData low MPV 4.62 103 e /mm\nData high MPV 4.62 103 e /mm\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n100 mm\nSim. MPV 4.62 103 e /mm\nData low MPV 4.62 103 e /mm\nData high MPV 4.62 103 e /mm\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n50 mm\nSim. MPV 4.54 103 e /mm\nData low MPV 4.52 103 e /mm\nData high MPV 4.54 103 e /mm\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e\n/mm]\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\nN. entries / (0.4 103e\n/mm)\n30 mm\nSim. MPV 4.50 103 e /mm\nData low MPV 4.46 103 e /mm\nData high MPV 4.56 103 e /mm\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e\n/mm]\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n20 mm\nSim. MPV 4.44 103 e /mm\nData low MPV 4.40 103 e /mm\nData high MPV 4.58 103 e /mm\n0\n2\n4\n6\n8\n10\n12\n14\ndQ/dx [103e\n/mm]\n0.0\n0.1\n0.2\n0.3\n0.4\n10 mm\nSim. MPV 4.44 103 e /mm\nData low MPV 4.34 103 e /mm\nData high MPV 4.66 103 e /mm\nDUNE:ND-LAr 2x2\nFigure 40. dQ/dx measured for segments of different lengths for low threshold runs (black dots),\nhigh threshold runs (white dots) and a sample of simulated cosmic rays (red line). The distributions\nhave been fitted with a Gaussian-convolved Moyal function (dashed lines).\n200\n250\n300\n350\n400\n450\n500\n550\n600\ny [mm]\n100\n150\n200\nx [mm]\nMuon\nElectron\n0\n50\n100\n150\n200\n250\n300\n350\n400\nMuon residual range [mm]\n0\n10\n20\ndQ/dx [103 e\n/mm]\nData\ndE\ndx PDG / WLAr\nICARUS\nBirks\n0\n20\n40\nCharge [103 e\n]\nDUNE:ND-LAr 2x2\nFigure 41. Top: event display of the anode plane for a selected stopping muon (blue) and subsequent\nMichel electron (orange). Bottom: dQ/dx for the reconstructed muon track as a function of the\nresidual range dQ/dx and the theoretical curve for muons stopping in liquid argon (red line).\n\nVersion March 6, 2024 submitted to Instruments\n45 of 47\n6. Conclusions\nWe have reported here the experimental results of exposing the Module-0 demonstra-\ntor, a tonne-scale LArTPC with pixel-based charge readout, to cosmic rays. This new type\nof neutrino detector is designed to meet the challenges of the near detector complex of\nthe forthcoming DUNE experiment, which will be exposed to a very intense beam-related\nflux of particles. These challenges are expected to severely hamper the performance of\na conventional, wire-readout, monolithic LArTPC, where reconstruction of complex 3D\nevent topologies using a small number of 2D projections can lead to unsolvable ambiguities,\nparticularly when multiple events overlap in the drift direction. The novel Module-0 design\nfeatures a combination of new technological solutions: a pixelated anode to read out the\nionization electron signal that provides native three-dimensional charge imaging, a modu-\nlar structure with relatively short drift length, high-performance scintillation light detection\nsystems, and an innovative approach to field shaping using a low-profile resistive shell.\nModule-0 is one of four units that will comprise the 2 \u00d7 2 demonstrator (ProtoDUNE-ND)\nbeing installed at Fermilab to be exposed to the NuMI neutrino beam.\nA detailed assessment of this technology has been performed by operating Module-0,\nas well as the associated cryogenics, data acquisition, trigger, and timing infrastructure,\nat the University of Bern. A large sample of 25 million self-triggered cosmic ray-induced\nevents was collected and analyzed, along with an array of dedicated diagnostic data runs.\nThe response of the 78,400-pixel readout system was studied, as well as the performance\nof the two independent and complementary light detection systems. The data analysis\ndemonstrated key physics requirements of this technology, such as the electron lifetime,\nthe uniformity of the electric field, and the matching/correlation between the charge and\nlight signals. The reconstruction of particle tracks and Michel electrons illustrates the\nphysics capabilities, and the comparison with detailed, microphysical simulations has\ndemonstrated a robust understanding of the workings of this new type of LArTPC detector.\nOverall, these results demonstrate the key design features of the technique and provide\na confirmation of the outstanding imaging capabilities of this next-generation LArTPC\ndesign.\n7. Acknowledgments\nThis document was prepared by the DUNE collaboration using the resources of the\nFermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of\nScience, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA),\nacting under Contract No. DE-AC02-07CH11359. This work was supported by CNPq,\nFAPERJ, FAPEG and FAPESP, Brazil; CFI, IPP and NSERC, Canada; CERN; M\u0160MT, Czech\nRepublic; ERDF, H2020-EU and MSCA, European Union; CNRS/IN2P3 and CEA, France;\nINFN, Italy; FCT, Portugal; NRF, South Korea; CAM, Fundaci\u00f3n \u201cLa Caixa\u201d, Junta de\nAndaluc\u00eda-FEDER, MICINN, and Xunta de Galicia, Spain; SERI and SNSF, Switzerland;\nT\u00dcB\u02d9ITAK, Turkey; The Royal Society and UKRI/STFC, United Kingdom; DOE and NSF,\nUnited States of America. 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Random Sample Consensus: A Paradigm for Model Fitting with\nApplications to Image Analysis and Automated Cartography. Commun. ACM 1981, 24, 381\u2013395.\nhttps://doi.org/10.1145/358669.358692.\n\nVersion March 6, 2024 submitted to Instruments\n47 of 47\n28.\nAdams, C.; Alrashed, M.; An, R.; Anthony, J.; Asaadi, J.; Ashkenazi, A.; Balasubramanian, S.;\nBaller, B.; Barnes, C.; Barr, G.; et al. Calibration of the charge and energy loss per unit length of\nthe MicroBooNE liquid argon time projection chamber using muons and protons. Journal of\nInstrumentation 2020, 15, P03022\u2013P03022. https://doi.org/10.1088/1748-0221/15/03/p03022.\n29.\nBettini, A.; Braggiotti, A.; Casagrande, F.; Casoli, P.; Cennini, P.; Centro, S.; Cheng, M.; Ciocio,\nA.; Cittolin, S.; Cline, D.; et al. A study of the factors affecting the electron lifetime in ultra-\npure liquid argon. 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Skwarnicki, Ph.D Thesis, DESY F31-86-02(1986), Appendix E; M.J. Oreglia, Ph.D Thesis,\nSLAC-236(1980), Appendix D; J. E. Gaiser, Ph.D Thesis, SLAC-255(1982), Appendix F.\n34.\nShibamura, E.; Hitachi, A.; Doke, T.; Takahashi, T.; Kubota, S.; Miyajima, M. Drift velocities of\nelectrons, saturation characteristics of ionization and W-values for conversion electrons in liquid\nargon, liquid argon-gas mixtures and liquid xenon. Nucl. Instrum. Meth. 1975, 131, 249\u2013258.\nhttps://doi.org/10.1016/0029-554X(75)90327-4.\n35.\nThomas, J.; Imel, D.A. Recombination of electron-ion pairs in liquid argon and liquid xenon.\nPhys. Rev. A 1987, 36, 614\u2013616. https://doi.org/10.1103/PhysRevA.36.614.\n36.\nBirks, J.B. Scintillations from Organic Crystals: Specific Fluorescence and Relative Response to\nDifferent Radiations. Proc. Phys. Soc. A 1951, 64, 874\u2013877. https://doi.org/10.1088/0370-1298/\n64/10/303.\n37.\nAmoruso, S.; et al. Study of electron recombination in liquid argon with the ICARUS TPC. Nucl.\nInstrum. Meth. A 2004, 523, 275\u2013286. https://doi.org/10.1016/j.nima.2003.11.423.\n38.\nAcciarri, R.; et al. A study of electron recombination using highly ionizing particles in the\nArgoNeuT Liquid Argon TPC.\nJournal of Instrumentation 2013, 8, P08005\u2013P08005.\nhttps:\n//doi.org/10.1088/1748-0221/8/08/p08005.\n39.\nDoke, T.; Hitachi, A.; Kikuchi, J.; Masuda, K.; Okada, H.; Shibamura, E. Absolute Scintillation\nYields in Liquid Argon and Xenon for Various Particles. Japanese Journal of Applied Physics 2002,\n41, 1538. https://doi.org/10.1143/JJAP.41.1538.\n40.\nAbed Abud, A.; et al.\nIdentification and reconstruction of low-energy electrons in the\nProtoDUNE-SP detector. Phys. Rev. D 2023, 107, 092012, [arXiv:hep-ex/2211.01166]. https:\n//doi.org/10.1103/PhysRevD.107.092012.\n41.\nForeman, W.; et al. Calorimetry for low-energy electrons using charge and light in liquid argon.\nPhys. Rev. D 2020, 101, 012010, [arXiv:physics.ins-det/1909.07920]. https://doi.org/10.1103/\nPhysRevD.101.012010.\n42.\nAcciarri, R.; et al. Michel Electron Reconstruction Using Cosmic-Ray Data from the MicroBooNE\nLArTPC. JINST 2017, 12, P09014, [arXiv:physics.ins-det/1704.02927]. https://doi.org/10.1088/\n1748-0221/12/09/P09014.\n43.\nGroom, D.E.; Mokhov, N.V.; Striganov, S.I. Muon stopping power and range tables 10-MeV to\n100-TeV. Atom. Data Nucl. Data Tabl. 2001, 78, 183\u2013356. https://doi.org/10.1006/adnd.2001.086\n1.\n", "Draft version 18 April 2023\nTypeset using LATEX twocolumn style in AASTeX62\nSearch for gravitational-lensing signatures in the full third observing run of the LIGO\u2013Virgo network\nThe LIGO Scientific Collaboration, the Virgo Collaboration and the KAGRA Collaboration\nABSTRACT\nGravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational\nwave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics.\nIn this work, we have extended the search for lensing signatures to all binary black hole events from the third\nobserving run of the LIGO\u2013Virgo network. We search for repeated signals from strong lensing by 1) performing\ntargeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters\nand sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals,\nand 4) performing dual-signal Bayesian analysis that takes into account selection e\ufb00ects and astrophysical\nknowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent\nphase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to\npoint masses. None of these searches yields signi\ufb01cant evidence for lensing. Finally, we use the non-detection of\ngravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction\nof dark matter composed of compact objects.\n1. INTRODUCTION\nGravitational lensing occurs when a massive object bends\nspacetime in a way that alters the path or properties of a\npropagating wave. Gravitational lensing is expected to a\ufb00ect\ngravitational waves (GWs), resulting, for example, in repeated\nsignals, (de-)magni\ufb01cation of the amplitude, phase shifts, and\nbeating patterns (Ohanian 1974; Thorne 1982; Deguchi &\nWatson 1986; Wang et al. 1996; Nakamura 1998; Takahashi\n& Nakamura 2003). The exact alteration of the gravitational\nwaveform depends on the nature of the lens system.\nFor massive lenses, gravitational lensing changes the GW\namplitude without a\ufb00ecting the frequency evolution (Wang\net al. 1996; Dai & Venumadhav 2017; Ezquiaga et al. 2021).\nMoreover, such systems may also produce multiple signals\nobserved as repeated events separated by a time delay of\nminutes to months for galaxies (Ng et al. 2018; Li et al. 2018;\nOguri 2018), and up to years for galaxy clusters (Smith et al.\n2018, 2017, 2019; Robertson et al. 2020; Ryczanowski et al.\n2020). The current-generation GW detector network has a\nrealistic chance of detecting the \ufb01rst lensed signal within its\noperation period (Ng et al. 2018; Li et al. 2018; Oguri 2018).\nFor low-mass lenses, such as stars or compact objects,\nmicrolensing introduces beating patterns in the wave-\nform (Deguchi & Watson 1986; Nakamura 1998; Takahashi\n& Nakamura 2003; Cao et al. 2014; Jung & Shin 2019; Lai\net al. 2018; Christian et al. 2018; Dai et al. 2018; Diego 2020).\nMore generally, a \ufb01eld of light lenses may produce even more\ncomplex patterns on the gravitational waveform (Diego et al.\n2019; Pagano et al. 2020; Cheung et al. 2021). Under the right\nconditions and with su\ufb03cient knowledge about the lens, these\nbeating patterns may be observable with current-generation\nGW detectors.\nThe detection of lensed GWs paves the way for numerous\nscienti\ufb01c pursuits, including source localization (Hannuksela\net al. 2020) and characterization (Lai et al. 2018; Diego 2020;\nOguri & Takahashi 2020), precision cosmology (Sereno et al.\n2011; Liao et al. 2017; Cao et al. 2019; Li et al. 2019b; Han-\nnuksela et al. 2020), and tests of general relativity (Baker &\nTrodden 2017; Collett & Bacon 2017; Fan et al. 2017; Goyal\net al. 2021b; Ezquiaga & Zumalac\u00b4arregui 2020). Indeed,\nthe prospects for fundamental physics and astrophysics have\nsparked a wide interest in searching for lensed GWs. Previ-\nous work from the LIGO\u2013Virgo Collaboration has considered\na range of strong and microlensing signatures for events in\nthe \ufb01rst half of the third observing run (O3a) (Abbott et al.\n2021a). Nevertheless, these studies have yielded no con\ufb01dent\nevidence for GW lensing.\nIn this work, we search for a variety of lensing signatures in\nthe third LIGO Scienti\ufb01c, Virgo, and KAGRA (LVK) Collabo-\nration Gravitational-Wave Transient Catalog (GWTC-3) (Ab-\nbott et al. 2021b) and study its implications for GW lensing.\nIn particular, we expand on the lensing results presented for\nthe \ufb01rst half of the third observing run of the LIGO\u2013Virgo\nnetwork (O3a) (Abbott et al. 2021a) by including the signals\nfound in the second half of the third observing run (O3b) and\nby including additional analyses to further test the lensing\nhypothesis and interpret their outcomes. First, we search for\nthe e\ufb00ects of strong lensing by studying the similarity and\nlensing evidence for pairs of binary black hole (BBH) mergers.\nWe consider both pairs of detected mergers (super-threshold)\nand pairs formed by detected mergers and candidates that\nnominally fall below the detection threshold (sub-threshold)\narXiv:2304.08393v1 [gr-qc] 17 Apr 2023\n\n2\nwith consistent waveform morphologies. Second, we search\nfor evidence of microlensing induced by point-mass lenses.\nFinally, we constrain the expected rate of lensed signals, black\nhole (BH) merger-rate density, and the fraction of dark matter\ncomposed of compact objects.\nIt is important to note that GWTC-3 is a cumulative catalog\ndescribing all the GW transients found in all observing runs to\ndate: O1, O2, O3a, and O3b. O1 made observations between\n2015 September 12 00:00 UTC to 2016 January 19 16:00\nUTC, O2 between 2016 November 30 16:00 UTC to 2017\nAugust 25 22:00 UTC, O3a between 2019 April 1 15:00\nUTC to 2019 October 1 15:00 UTC, and O3b between 2019\nNovember 1 15:00 UTC to 2020 March 27 17:00 UTC.\nResults of all analyses in this paper and associated data\nproducts can be found in Abbott et al. (2021c). GW strain\ndata (GWOSC 2021) and posterior samples (Abbott et al.\n2021d) for all events from GWTC-3 are available from the\nZenodo platform or the Gravitational Wave Open Science\nCenter (Abbott et al. 2021e).\n2. DATA AND EVENTS\nThe analyses presented here expand on the lensing re-\nsults from the \ufb01rst half of O3 (also referred to as O3a) by\ndocumenting new results from the second half of O3 (also\nreferred to as O3b) using GWTC-3 (Abbott et al. 2021f).\nThe O3a lensing results paper (Abbott et al. 2021a) used the\nGWTC-2 catalog (Abbott et al. 2021g). Since then, GWTC-\n2.1 (Abbott et al. 2021h) has reclassi\ufb01ed 2 of the candidates\nused in the O3a lensing paper as having a probability of\nastrophysical origin of less than 0.5 and are not included in\nthe results described here, speci\ufb01cally GW190424 180648\nand GW190909 114149. GWTC-3 also includes 5 events\nthat were identi\ufb01ed by the O3a lensing sub-threshold\ncounterpart image search,\nnamely GW190925 233845,\nGW190426 190642, GW190725 184728, GW190805 211137,\nand GW190916 200658.\nVarious instrumental upgrades have led to more sensitive\ndata in O3b, with a median binary neutron star (BNS) inspiral\nranges (Finn & Cherno\ufb001993; Allen et al. 2012a) of 115 Mpc\nin O3b compared to 108 Mpc in O3a for LIGO Hanford, 133\nMpc in O3b compared to 135 Mpc O3a for LIGO Livingston,\nand 51 Mpc in O3b compared to 45 Mpc in O3a for Virgo (Ab-\nbott et al. 2021f). The duty factor for at least one detector\nbeing online was 96.6%; for any two detectors being online at\nthe same time was 85.3%; and for all three detectors together\nwas 51%. Further details regarding instrument performance\nand data quality for O3b are available in Abbott et al. (2021f);\nDavis et al. (2021a); Acernese et al. (2022).\nThe LIGO and Virgo detectors used a photon recoil-based\ncalibration (Karki et al. 2016; Cahillane et al. 2017; Viets et al.\n2018) resulting in a complex-valued, frequency-dependent\ndetector response. Previous studies have documented the sys-\ntematic error and uncertainty bounds for O3b strain calibration\nin LIGO (Sun et al. 2020, 2021) and Virgo (Acernese et al.\n2021).\nTransient noise sources, referred to as glitches, contaminate\nthe data and can a\ufb00ect the con\ufb01dence of candidate detections.\nTimes a\ufb00ected by glitches and other data quality issues are\nidenti\ufb01ed so that searches for GW events can exclude (veto)\nthese periods of poor data quality (Abbott et al. 2016a, 2020a;\nDavis et al. 2021b; Nguyen et al. 2021; Fiori et al. 2020).\nIn addition, several known persistent noise sources are sub-\ntracted from the data using information from witness auxiliary\nsensors (Driggers et al. 2019; Davis et al. 2019).\nCandidate events, including those reported in Abbott et al.\n(2021f) and the new candidates found by the search for sub-\nthreshold counterpart images in Sec. 3.1 of this paper, have\nundergone a validation process to evaluate if instrumental\nartifacts could a\ufb00ect the analysis; this process is described in\ndetail in Sec. 5.5 of Davis et al. (2021b). This process can\nalso identify data quality issues that need further mitigation\nfor individual events, such as the subtraction of glitches (Cor-\nnish et al. 2021; Davis et al. 2022) and non-stationary noise\ncouplings (Vajente et al. 2020), before executing parameter\nestimation (PE) algorithms. See Table XIV of Abbott et al.\n(2021f) for the list of events requiring such mitigation.\nThe GWTC-3 catalog (Abbott et al. 2021f) contains 35\nevents from O3b in addition to the 55 previous events from\nprevious observing runs (Abbott et al. 2021h) with a false-\nalarm rate (FAR) below two per year, and an expected rate\nof contamination from detector noise less than 10\u201315% (Ab-\nbott et al. 2021f). We neglect the potential contamination\nin this analysis. These events were identi\ufb01ed by four search\npipelines: one minimally modeled transient search cWB (Kli-\nmenko et al. 2004, 2005, 2006, 2011, 2016) and three matched-\n\ufb01lter searches GstLAL (Sachdev et al. 2019; Hanna et al.\n2020; Messick et al. 2017), Multi-Band Template Analy-\nsis (MBTA) (Adams et al. 2016; Aubin et al. 2021), and Py-\nCBC (Allen et al. 2012b; Allen 2005; Dal Canton et al. 2014;\nUsman et al. 2016; Nitz et al. 2017). Their parameters were es-\ntimated through Bayesian inference using the bilby (Ashton\net al. 2019; Smith et al. 2020; Romero-Shaw et al. 2020) and\nRIFT (Pankow et al. 2015; Lange et al. 2017; Wysocki et al.\n2019) packages. Both the matched-\ufb01lter searches and PE use\na variety of BBH waveform models which generally combine\nknowledge from post-Newtonian theory, the e\ufb00ective-one-\nbody formalism, and numerical relativity (for general intro-\nductions to these approaches, see Blanchet 2014; Damour &\nNagar 2016; Palenzuela 2020; Schmidt 2020 and references\ntherein). The analyses in this paper rely on the same methods,\nand the speci\ufb01c waveform models and analysis packages used\nare described in each section.\nOf the 35 events from O3b, 31 are likely BBHs, while\nfour have component masses consistent with being below\n\n3\n3 M\u2299(Abbott et al. 2021i,f), thus potentially containing a\nneutron star. We consider these 35 events in the analyses doc-\numented in this paper. Speci\ufb01cally, we use the following input\ndata sets for each analysis. The searches for sub-threshold\ncounterpart images in Sec. 3.1 cover the whole O3 strain data\nset, using the same data quality veto choices as in Abbott et al.\n(2021f) but a strain data set consistent with the PE analyses:\nthe \ufb01nal calibration version of LIGO data (Sun et al. 2021)\nwith additional noise subtraction (Vajente et al. 2020). The\nposterior-overlap analysis in Sec. 3.2 starts from the poste-\nrior samples released with GWTC-3 (GWOSC 2021). The\njoint-PE analyses in Sec. 3.3 and microlensing analysis in\nSec. 4 reanalyze the strain data in short segments around the\nevent times, available from the same data release, with data\nselection and noise mitigation choices matching those of the\nPE analyses in Abbott et al. (2021f).\n3. STRONG LENSING\nIf a GW travels close enough to a massive lens, it will pro-\nduce multiple images, with the number of images depending\non the lens pro\ufb01le and source lens geometry. This regime\nis known as the strong-lensing limit. Each of these lensed\nimages hL\nj will have a change in its amplitude, arrival time\nand phase compared to the emitted signal h (Schneider et al.\n1992):\nhL\nj ( f) =\nq\n|\u00b5j| exp\nh\ni2\u03c0f\u2206tj \u2212isign(f)nj\u03c0\ni\nh( f) ,\n(1)\nfor n j = 0, 1/2, 1 for type I, II and III images, which cor-\nrespond to di\ufb00erent minima of the lensing potential. While\nthe magni\ufb01cation \u00b5j and time delay \u2206t j do not a\ufb00ect the\nwaveform morphology (they are completely degenerate with\nthe luminosity distance and coalescence time) the frequency-\nindependent lensing phase shift n j\u03c0 could induce distortions\nwhen the signal has multiple frequency components (Dai &\nVenumadhav 2017; Ezquiaga et al. 2021). In particular, this\noccurs for type II images since type I does not have a phase\nshift, and type III only \ufb02ips the overall sign, which is degener-\nate with shifting the polarization angle by \u03c0/2. The sign(f)\nterm is only there to ensure that the time domain waveform is\nreal.\nMaking a distinction between e\ufb00ects that do and do not\nchange the waveform morphology, we divide our search into\ntwo parts. First, we search for pairs of events consistent with\nthe strong-lensing hypothesis. Some of these pairs will have\nsu\ufb03ciently strong amplitudes that can be identi\ufb01ed as con\ufb01-\ndent detections (super-threshold) by the search pipelines used\nin Abbott et al. (2021g,h,f), while others may have not been\nidenti\ufb01ed as signals (sub-threshold) because of the relative\nde-magni\ufb01cation. Our searches will include both sub- and\nsuper-threshold pairs. A pair is the minimum association, but\nhigher multiplicities are also possible. Then, we search for\nstrong lensing focusing on the distortion of type II images.\n3.1. Sub-threshold Search\nIn this section, we describe the search for possible sub-\nthreshold counterparts of super-threshold detections from O3.\nWe perform searches over all O3 strain data following the\nrules for data selection described in Abbott et al. (2021h) and\nAbbott et al. (2021f). A general search for GWs uses a large\ntemplate bank covering a broad parameter space as we have\nno prior information about the signal subspace, resulting in a\nhigh trials factor and hence incurring a high noise background.\nSub-threshold (lensed) GWs with smaller amplitudes will\ntherefore be easily buried in the noise without being identi\ufb01ed\nas detections as they cannot pass the usual detection threshold.\nTo uncover these sub-threshold (lensed) signals, we have\nto e\ufb00ectively reduce the noise background while keeping the\ntargeted foreground (i.e. the signals) constant (Li et al. 2019a;\nMcIsaac et al. 2020; Dai et al. 2020). The strong lensing\nhypothesis asserts that lensed GWs, super-threshold or sub-\nthreshold, coming from the same origin have identical wave-\nforms apart from an overall scaling factor and a Morse phase\nfactor as described in Eq. 1, and hence should have consistent\ninferred intrinsic masses and spins. 1 Therefore, we can con-\nstruct a reduced template bank with only templates that have\nmasses and spins similar to those of a target super-threshold\ndetection. Using the reduced bank lowers the trials factors\nand noise background and e\ufb00ectively searches for previously\nunidenti\ufb01ed possible sub-threshold lensed counterparts to the\ntarget detection. For each known candidate from O3 with\na probability of astrophysical origin pastro > 0.5, we create\na reduced template bank using their respective public poste-\nrior mass and spin samples released with GWTC-3 (GWOSC\n2021), ensuring that the templates will match well with their\nrespective target events while improving the ranking statistics\nof the search for similar events, and hence potentially return-\ning new candidates that previously did not reach the threshold\npastro > 0.5 in GWTC-3. Details of how the reduced banks\nare constructed can be found in Li et al. (2019a).\nGiven these template banks, we proceed with con\ufb01gurations\nand procedures as outlined in Abbott et al. (2021a) to produce\na priority list of potential lensed candidates matching each\ntarget event, using GstLAL (Messick et al. 2016; Sachdev\net al. 2019) as the search pipeline. The list of candidates ob-\ntained is again further vetted using a sky location consistency\ncheck detailed in Wong et al. (2021); Abbott et al. (2021a) to\nensure the candidates have consistent sky location with the\ntarget event. To avoid false dismissal at this step, we only\nveto candidates with an overlap in 90% credible region of the\nsky location O90%CR = 0. All candidates with non-vanishing\n1 The Morse phase factor for di\ufb00erent image types has not been considered\nin the search described here. Should a GW include detectable higher-order\nmultipole moments, then the Morse phase factor will cause complicated\nchanges to the waveforms, inducing a loss in the search sensitivity.\n\n4\nlocalization overlap are kept for further follow-up with data\nquality checks as discussed in Sec. 2.\nIn Table 1, we list the top \ufb01ve candidates from the indi-\nvidual targeted searches for counterparts of the detections\nreported in O3. As in the O3a lensing paper (Abbott et al.\n2021a), we do not assess in detail the probability of astro-\nphysical origin for each of these. It is also important to note\nthat the reported false-alarm rates (FARs) do not indicate how\nlikely each trigger is a lensed counterpart of the target event,\nbut only how likely noise produces a trigger with a ranking\nstatistic higher or equal to that of the candidate under con-\nsideration using these reduced template banks. Similar to\nAbbott et al. (2021a), we account for the fact that we have\nanalyzed \u223c332 days of data multiple times for a total of 76\nevents, and set the FAR threshold to be 1 in 69 years (i.e.\n4.59 \u00d7 10\u221210 Hz). We followed up on the top two candidates\nlisted that passed the FAR threshold through golum\u2019s joint PE\nanalysis (Janquart et al. 2021, discussed in 3.3). The results\nare included in Table 1. Since both pairs of candidates have\nmildly negative log10 coherence ratios, showing that there is\nno evidence supporting the lensing hypothesis for either of\nthese pairs, we did not further follow them up with the more\ncomputationally intensive hanabi analysis (Lo & Maga\u02dcna\nHernandez 2021, discussed in 3.3).\n3.2. Preliminary Identi\ufb01cation of Lensed Pair Candidates\nMultiple, non-overlapping images produced by strongly\nlensed GW signals have identical phase evolution, and there-\nfore their intrinsic parameters (as well as their orbit\u2019s incli-\nnation with respect to the line of sight) are expected to have\noverlapping posteriors. In addition, the angular separations of\nimages (produced by galaxies or galaxy clusters) are several\norders of magnitude smaller than the uncertainties associated\nwith their GW sky location. As a result, their sky localisations\nwill also overlap. (As in the previous section, the Morse phase\nfor di\ufb00erent image types is not considered here.)\nUnder these assumptions, a Bayes-factor statistic (BL\nU) that\nassesses the consistency between a lensed candidate pair\u2019s\nposterior distributions of intrinsic parameters, sky location,\nand inclination angle (and thus acts as a discriminator be-\ntween the lensed and unlensed hypotheses) can be constructed\n(Haris et al. 2018). To convert this statistic to a false-positive\nprobability (FPP),2 a background distribution of unlensed BL\nU\nneeds to be estimated.\nTo that end, we conduct an injection campaign involving\nBBHs only, in which we sample component masses m1,2 from\na power-law distribution (Abbott et al. 2016b) in the range\n2 FAR and FPP, while conceptually similar, pertain to di\ufb00erent contexts in\nthis work. In particular, we use FPP exclusively for signi\ufb01cances associated\nwith candidate lensed pairs to discriminate them from unlensed pairs. On the\nother hand, a FAR is associated with the signi\ufb01cance assigned to individual\ncandidate GW signal events.\n(10\u201350M\u2299). We assume that the redshift distribution of BBHs\nis similar to population synthesis simulations of isolated bi-\nnary evolution (Belczynski et al. 2008, 2010; Dominik et al.\n2013; Eldridge et al. 2019; Bou\ufb00anais et al. 2021; Zevin et al.\n2021). All other parameters are sampled from uninformative\nprior distributions (Haris et al. 2018). We inject the simulated\nsignals into Gaussian noise with O3a representative power\nspectral density (PSD) for a LIGO\u2013Virgo detector network.\nWe compute BL\nU for all possible pairs in this injection set, and\nfollowing Abbott et al. (2021a), we assign an FPP to a candi-\ndate pair using its BL\nU. Candidate lensed pairs involving BNS\nor neutron star-black hole (NSBH) events are not analyzed\nand ranked.\nWe additionally employ a machine learning (ML)-based\nbinary classi\ufb01cation scheme to rapidly provide a probability of\nclass membership (lensed or unlensed) for a given candidate\nBBH pair (Goyal et al. 2021a). Such an analysis not only\nserves as an independent method to rank candidate pairs but\nalso provides a quantitative signi\ufb01cance to pairs for which\nsource-parameter inference samples are unavailable.\nQ-transform-based (Chatterji et al. 2004) time\u2013frequency\nmaps of strongly lensed BBHs are expected to have similar\nshapes, although the signal energy in each time-frequency tile\nwill di\ufb00er between images. Furthermore, as mentioned earlier,\ntheir sky localisations will overlap. Exploiting these facts, ML\nmodels that take Q-transforms and Bayestar (Singer & Price\n2016) sky localisations as inputs, are built. These models use\na DenseNet (Huang et al. 2016) architecture (with several\nlayers pre-trained on the ImageNet dataset; Deng et al. 2009),\nand XGBoost (Chen & Guestrin 2016) algorithms, trained on\nlensed and unlensed BBH signals injected in Gaussian noise\n(for details on the ML training set, see Goyal et al. (2021a))\nThe outputs of the individual models are then combined to\nprovide a probability that a candidate pair is lensed or un-\nlensed.\nTo convert this probability to an FPP, we construct a back-\nground distribution of ML probabilities using a population of\nunlensed BBH events injected in Gaussian noise character-\nized by the O3a representative PSD \u2013 the same as was used\nfor the posterior overlap statistic. This PSD is found to be\nsu\ufb03ciently similar to the averaged O3 PSD for the estimation\nof the background distribution so as not to change the pre-\nliminary selection of candidate pairs. The BBH population\nis identical to the one used by the posterior overlap statistic\nanalysis to construct its corresponding background distribu-\ntion. Furthermore, the sky localisations used to rank candidate\npairs come from the same PE analysis used to estimate the\nposterior overlap statistic 3.\n3 Note that Bayestar, which is used to assign ML probabilities to real-\nevent candidate pairs, is expected to provide sky localisations that are similar\nto those provided by this PE analysis.\n\n5\nTable 1. Top 5 candidates from individual sub-threshold searches for strongly-lensed counterpart images of O3 events from GWTC-3.\nTarget event\nLensed candidate (UTC)\n\u2206t [days]\n(1 + z)M(M\u2299)\n(1 + z)Mtarget(M\u2299)\nFAR\nh\nyr\u22121i\nO90%CR [%]\nlog10(CL\nU)\nGW190930 133541\n19-08-05 13:43:48\n\u221256.0\n10.2\n9.86\n0.002\n61.00%\n\u22126.4\nGW191204 171526\n19-08-05 13:43:48\n\u2212121.1\n10.2\n9.66\n0.006\n25.40%\n\u221212.2\nGW190828 065509\n19-11-12 12:13:18\n76.2\n45.5\n17.3\n0.023\n18.00%\n-\nGW190725 174728\n19-08-05 13:43:48\n10.8\n10.2\n8.88\n0.038\n39.50%\n-\nGW190828 065509\n20-02-06 07:24:59\n162.0\n15.1\n17.3\n0.154\n36.00%\n-\nNote\u2014 The \ufb01rst column lists the target event from O3. The second column shows the time (YY-MM-DD HH-MM-SS) in UTC of the found\nsub-threshold candidate. The third column shows the time di\ufb00erence (in days) between the candidate and the target event. The fourth column\nshows the redshifted chirp mass of the template that found the trigger. The \ufb01fth column shows the redshifted chirp mass of the target event.\nThe sixth column shows the FARs from the individual search for the new candidate from the second column. The seventh column shows the\npercentage overlap of the 90% sky localization regions between the candidate and the target event. The eighth column shows the log10 coherence\nratio obtained from golum\u2019s joint PE analysis.\nA plot comparing the FPPs assigned by the posterior over-\nlap and ML analyses is shown in Fig. 1. Candidates that have\neither a posterior-overlap-assigned FPP or ML-assigned-FPP,\n(or both), that are smaller than 1%, are selected for more\ncomprehensive Bayesian analyses.\n10\u22123\n10\u22122\n10\u22121\n100\nML FPP\n10\u22123\n10\u22122\n10\u22121\n100\nPosterior Overlap FPP\n100\n200\n300\nNo. of pairs\n200\n400\n600\n800\nNo. of pairs\nO3a-O3a\nO3a-O3b\nO3b-O3b\nFigure 1. The FPPs of each lensed candidate pair constructed from\nthe set of GW events that exceed an astrophysical probability (Farr\net al. 2015; Kapadia et al. 2020) threshold of 0.5, as evaluated using\nthe BL\nU and ML classi\ufb01cation statistics. Orange dashed lines that\ncorrespond to an FPP threshold of 10\u22122, are also placed. Pairs whose\nBL\nU-based or ML-based FPPs fall below this threshold are selected\nfor additional joint parameter estimation analyses. BL\nU < 10\u22126 has\nbeen mapped to an FPP of 1, which is re\ufb02ected in the gap along the\nvertical axis between 0.4 and 1.\n3.3. Joint Parameter Estimation\nSimilar to the analysis of O3a data (Abbott et al. 2021a),\nwe perform a joint PE analysis for the most relevant candidate\nlensing pairs. We follow up on the pairs that display low FPP\nin their posterior overlap or ML classi\ufb01cation scheme. These\nare pairs within the whole of O3, but we only consider here\nthose with at least one event in O3b since pairs in O3a were\nstudied in Abbott et al. (2021a). We use two complementary\npipelines: golum (Janquart et al. 2021) and hanabi (Lo &\nMaga\u02dcna Hernandez 2021). Both pipelines use the nested\nsampling algorithm dynesty (Speagle 2020), and implement\nthe joint PE with the help of bilby (Ashton et al. 2019;\nRomero-Shaw et al. 2020).\ngolum (Janquart et al. 2021) is a joint PE tool where the\nworkload is reduced by analyzing the two images, under the\nlensed hypothesis, in two successive stages. The \ufb01rst image\nis characterized by the same parameters of the unlensed case\n(where the time of coalescence and the luminosity distance\nare the observed ones) with an additional Morse factor. The\nsecond image is then analyzed using (samples of) the posterior\nfrom the \ufb01rst image as the prior and linking the parameters\nmodi\ufb01ed by lensing through three lensing parameters: a time\ndi\ufb00erence, a relative magni\ufb01cation, and a Morse factor di\ufb00er-\nence. The \ufb01nal coherence ratio CL\nU is the ratio of the product\nof the evidences for the two runs under the lensed hypothesis\nand the product of evidences for the two images analyzed\nunder the unlensed hypothesis.\nhanabi (Lo & Maga\u02dcna Hernandez 2021) \ufb01rst performs a\njoint inference on a signal pair by constructing a joint likeli-\nhood function that is a product of the likelihood function for\neach individual event, with a joint prior distribution. The latter\nis de\ufb01ned for a set of joint parameters that can simultaneously\ndescribe both signals if they are truly lensed, for example, the\nmasses and the spins, as well as a set of parameters that are\ndi\ufb00erent for each of the signals such as the time of arrival,\nthe apparent luminosity distance, and the Morse phase factor\nassociated to each of the lensed signals. The joint parameter\nspace is explored with the package hanabi.inference (Lo\n& Maga\u02dcna Hernandez 2021). The inference result is then\nreweighted with an astrophysically motivated prior distribu-\ntion; for example, the astrophysical prior distribution for the\n\n6\nredshifted component masses would be dependent on both\nthe population model for the intrinsic BBH masses and the\nredshift distribution of the sources. However, the true source\nredshift cannot be determined from GW observations alone\nsince the true source redshift is degenerate with the magni\ufb01-\ncation from strong lensing. To compute the Bayes factor BL\nU,\nthe source redshift, which serves as a hyper-parameter for the\nsignal pair, must be marginalized over. Selection e\ufb00ects enter\nas a normalization constant to the marginal data likelihood.\nThis procedure is implemented in hanabi.hierarchical\nwith the help of gwpopulation (Talbot et al. 2019). The ratio\nof unnormalized evidences calculated under the lensed hy-\npothesis and the unlensed hypothesis using this astrophysical\nprior is referred to as the population-weighted coherence ratio\nCL\nU\n\f\f\fpop, while the ratio of normalized evidences that accounts\nfor both population prior and selection e\ufb00ects is referred to as\nthe Bayes factor BL\nU in this analysis. We follow our \ufb01ducial\nsingular isothermal sphere (SIS) lensing model when com-\nputing the magni\ufb01cation prior (Abbott et al. 2021a). This\nanalysis however does not impose any informative prior on\nthe time delay or the image types from the lensing model.\nBoth pipelines use IMRPhenomXPHM (Pratten et al. 2021)\nas the waveform model, with an additional Morse phase ap-\nplied to each of the waveform polarizations in the frequency\ndomain. Other inputs, such as the power spectral density es-\ntimates and the calibration envelopes, are chosen to match\nthe analyses done in the GWTC-3 catalog paper (Abbott et al.\n2021b). Following the same prescriptions of the other anal-\nyses, we \ufb01x the BBH population model to the Power-Law +\nPeak model for the primary masses and the merger rate history\nto Madau\u2013Dickinson star-formation rate (Madau & Dickinson\n2014) normalized by the median GWTC-3 rate (Abbott et al.\n2021j).\nTaking advantage of golum\u2019s rapid joint PE, we analyze the\n75 pairs of candidates highlighted by posterior overlap and\nML. For each of them, we compute the coherence ratio, which\naccounts for the probability ratio of the lensed and unlensed\nhypotheses without including selection e\ufb00ects and population\npriors. We \ufb01nd that there is a wide range of log10(CL\nU) values,\nwith a peak slightly above zero. This comes from the fact\nthat this analysis considers only triggers already \ufb02agged by\nthe posterior overlap and ML analyses. As a consequence,\nthe analysis is biased towards the higher values. Neverthe-\nless, a signi\ufb01cant proportion of events \ufb02agged with the ML\npipeline and the posterior overlap pipeline are disfavored, hav-\ning log10(CL\nU) < 0. When comparing the highest coherence\nratio found in the data, log10(CL\nU) = 2.5, with a background\nof unlensed events, we \ufb01nd that it is well within the expected\nvalues, with 1% of the background events having larger CL\nU.\nThis background is computed for a population of compact\nbinaries that follows the mass, spin and redshift distribution\nof GWTC-3 (Abbott et al. 2021j). This large number of posi-\ntive log10(CL\nU) is consistent with the high number of expected\nfalse alarms (Wierda et al. 2021; C\u00b8 al\u0131s\u00b8kan et al. 2022a). For\nthose pairs with the highest coherence ratio, we follow up\nwith the hanabi pipeline for a total of 17 pairs. Our main\nresults are presented in Fig. 2, where the left column indicates\nthe event pairs and the horizontal axis their BL\nU. There we\ncan observe that none of the event pairs shows support for\nthe lensing hypothesis, i.e. all BL\nU < 1. The pair with highest\nBL\nU is GW190620 030421 \u2013 GW200216 220804, for an evi-\ndence against lensing of \u223c1/100 with the \ufb01ducial merger rate\ndensity model following the Madau-Dickinson star-formation\nrate. As a robustness check of how using di\ufb00erent merger rate\ndensity models would change the results, we repeat the cal-\nculations using two more models, namely Rmin(z) and Rmax(z)\nfrom our previous O3a analysis (Abbott et al. 2021a) that\nminimally and maximally bracket many existing population-\nsynthesis results (Belczynski et al. 2008, 2010; Dominik et al.\n2013; Eldridge et al. 2019). We see that while the exact values\nfor the Bayes factor change with the use of di\ufb00erent merger\nrate density models, the conclusion remains that there is no\nsupport for the lensing hypothesis in any of the event pairs\nanalyzed. To further assess the signi\ufb01cance of these pairs\nwe also include a color code to indicate the probability of\nhaving an astrophysical origin ppair\nastro, de\ufb01ned as the product\nof the highest pastro of each event reported in the GWTC-3\ncatalog paper (Abbott et al. 2021b) by di\ufb00erent pipelines. In\nconclusion, we \ufb01nd no evidence of multiply imaged events.\n3.4. Type II image search\nIn addition to the search for strong-lensing identifying mul-\ntiple images, we also look for the distortions that lensing\nintroduces in type II images (Ezquiaga et al. 2021). This is be-\ncause the frequency-independent phase shift that each image\nacquires becomes a frequency-dependent time delay for di\ufb00er-\nent frequency components. Therefore, for signals containing\ndi\ufb00erent measurable spherical harmonic modes, as recently\ndetected in GW190412 (Abbott et al. 2020c), GW190814 (Ab-\nbott et al. 2020d), and other events (Abbott et al. 2021b),\nthe overall lensed waveform can be distorted. The extent of\nthe distortion is subject to the power in modes beyond the\nquadrupole radiation. As a consequence, we do not expect to\nsee these distortions in the majority of the lensed events with\ncurrent sensitivities. However, if not searched for, they might\nbe mistaken with deviations from general relativity (Ezquiaga\net al. 2022).\nTo look for these distortions, we use golum (Janquart et al.\n2021). Within GWTC-3 we identify 10 events whose poste-\nrior has some information about the Morse phase, either by\nfavoring or disfavoring the distortions of the type II image by\nmore than 4% with respect to normality, i.e. the probability\nof each image type p(nj) is p(n j) > 0.37 or p(n j) < 0.29. We\nsummarize the evidence of one image type versus another in\n\n7\n1 : 1\n1 : 10\n1 : 100\n1 : 1000\n1 : 10000\nBL\nU\nGW190413 13 \u2212GW191109 01\nGW190413 05 \u2212GW200209 08\nGW190413 05 \u2212GW200219 09\nGW190421 21 \u2212GW191222 03\nGW190527 09 \u2212GW190719 21\nGW190602 17 \u2212GW191230 18\nGW190620 03 \u2212GW200216 22\nGW190701 20 \u2212GW200220 12\nGW190803 02 \u2212GW200219 09\nGW190805 21 \u2212GW190916 20\nGW190929 01 \u2212GW200216 22\nGW190930 13 \u2212GW191105 14\nGW191103 01 \u2212GW191105 14\nGW191222 03 \u2212GW200128 02\nMadau \u2212Dickinson\nRmax(z)\nRmin(z)\n0.80\n0.85\n0.90\n0.95\n1.00\nppair\nastro\nFigure 2. Bayes factors BL\nU from hanabi for the highest-ranked multiple-image candidate pairs. As a check on the robustness of our results, we\nshow the Bayes factors calculated using three di\ufb00erent merger rate density models, namely the \ufb01ducial model tracking the Madau\u2013Dickinson\nstar-formation rate (Madau & Dickinson 2014), and also the Rmin(z) and Rmax(z) model introduced in Abbott et al. (2021a). The color for each\nmarker represents the value of ppair\nastro for each pair, which is the probability that both of the signals from a pair are of astrophysical origins and not\nfrom terrestrial sources.\nFig. 3. Since only type II images display waveform distortions,\nwe only compute the Bayes factors of the type-II-vs-I and the\ntype-II-vs-III hypotheses. As can be seen in Fig. 3, only a few\nevents display a preference for one image type versus the other\none. This is expected given the signal-to-noise ratio (SNR)\nof these events and their power in higher multipole moments.\nHowever, GW190412 and GW200129 065458 present higher\nevidence for type II images. For GW190412 we \ufb01nd a log10\nBayes factor for type II vs. I of 0.60 \u00b1 0.16 and for type II vs.\nIII of 0.22\u00b10.16. For GW200129 065458 we \ufb01nd 0.38\u00b10.14\nand 0.24 \u00b1 0.14 for type II vs. I and type II vs. III respectively.\nThese events have possible super-threshold counterparts but\nthose were discarded by the golum analysis. In addition, we\nhave also searched for sub-threshold triggers associated with\nthese events, but found none.\nTo assess the signi\ufb01cance of the type II images, we follow\nup on GW190412 and GW200129 065458 performing a sim-\nulation campaign of type I and type II images. GW190412\nsimulations show that indeed this event has enough power\nin higher multipole moments to favor the type II hypothesis\nso that it could meaningfully test that hypothesis and would\nfavor it if it were true. For GW200129 065458, however, that\nis not the case. Moreover, GW200129 065458 might have a\nsigni\ufb01cant glitch under subtraction (Payne et al. 2022). The\npreference of GW190412 for a type II image could be just a\nsystematic e\ufb00ect due to the waveform modeling, especially\nsince this event falls in challenging parts of the parameter\nspace (Abbott et al. 2020c; Colleoni et al. 2021; Hannam et al.\nGW200129_065458\nGW190412\nFigure 3. Distribution of Bayes factors comparing di\ufb00erent image\ntype hypotheses for the 10 most relevant events. We compare the\nprobability of being type II vs. type I (blue-solid histogram) and of\nbeing type II vs. type III (orange-dashed histogram). Only type II\nimages display waveform distortions and for that reason, we do not\ncompare type III vs. type I.\n2021). For this reason, we repeat the analysis with di\ufb00er-\nent waveform families from our \ufb01ducial IMRPhenomXPHM\nmodel (Pratten et al. 2021). We \ufb01nd that the preference for\na type II image remains when using SEOBNRv4PHM (Os-\nsokine et al. 2020) or IMRPhenomPv3HM (Khan et al. 2020).\nThe same conclusion holds when using di\ufb00erent noise re-\nalizations for the simulations. Details on these simulation\ncampaigns can be found in Appendix A.\n\n8\nAlthough we \ufb01nd a mild preference for the type II image\nhypothesis in GW190412, we \ufb01nd that this analysis cannot\nprovide conclusive evidence of strong lensing. However, our\ntechniques and pipeline will be relevant for future observ-\ning runs when high-SNR events display stronger evidence of\nhigher-order modes.\n4. MICROLENSING EFFECTS\nWhen the characteristic wavelengths of GWs are compa-\nrable to the Schwarzschild radius of a lens (\u03bbGW \u223cRlens\nSch),\nwe may observe frequency-dependent magni\ufb01cation of the\nwaveform that can inform us about the lens model (Taka-\nhashi & Nakamura 2003; Cao et al. 2014; Jung & Shin 2019;\nLai et al. 2018; Christian et al. 2018; Dai et al. 2018; Diego\net al. 2019; Diego 2020; Pagano et al. 2020; Cheung et al.\n2021; Cremonese et al. 2021; C\u00b8 al\u0131s\u00b8kan et al. 2022b). Since\nthe GWs of sources such as BBHs sweeps through a wide\nrange of frequencies, these beating patterns can reveal the\npresence of intervening microlenses. In the sensitive range\nof ground-based detectors, these e\ufb00ects are expected for ob-\njects up to \u223c105M\u2299, which includes stellar-mass objects and\nintermediate-mass BHs.\nObjects that can cause these microlensing e\ufb00ects are pre-\ndominantly found in larger structures. Therefore we expect\nthat realistic microlensing due to a \ufb01eld of microlenses em-\nbedded in an external macromodel potential such as galaxies\nand galaxy clusters causes complex e\ufb00ects on the unlensed\nwaveforms (Diego et al. 2019). While the e\ufb00ects of these\nsystems on GW signals have been studied (Diego 2020; Che-\nung et al. 2021; Mishra et al. 2021; Yeung et al. 2021), the\nresulting waveforms are computationally costly to evaluate.\nNevertheless, in the absence of speci\ufb01c knowledge of the mat-\nter distribution along the travel path and to keep the problem\ncomputationally tractable, we assume that the beating patterns\nare caused by isolated point masses as a \ufb01rst approximation.\nIn this case, the microlensed waveform hMicro can be related\nto the unlensed waveform hU according to\nhMicro( f; \u03b8, Mz\nL, y) = hU( f; \u03b8) F( f; Mz\nL, y) ,\n(2)\nwhere \u03b8 represents the set of parameters de\ufb01ning an unlensed\nGW signal, Mz\nL = ML(1 + zl) is the redshifted lens mass, y\nis the dimensionless impact parameter, and F(f; Mz\nL, y) is\nthe frequency-dependent lensing magni\ufb01cation factor (e.g.,\nTakahashi & Nakamura 2003).\nSimilar to Abbott et al. (2021a), we perform Bayesian infer-\nence on all events from O3b using the unlensed signal model\nhU and the microlensing signal model hMicro. In particular,\nwe use bilby (Ashton et al. 2019; Romero-Shaw et al. 2020)\nand the nested sampling algorithm dynesty (Speagle 2020).\nData products such as strain data and PSDs are the same as\nfor GWTC-3 and between the two signal models (Abbott et al.\n2021b) For the GW parameters, we use the same priors as\nGWTC-3, while the prior on the lens mass Mz\nL is log uniform\nin the range [1\u2013105 M\u2299] and the prior on the impact parameter\nis p(y) \u221dy between [0.1, 3]. All events were analyzed using\nIMRPhenomXPHM (Pratten et al. 2021).\nThe process yields posterior probability distributions of\n\u03b8 or\nn\n\u03b8, Mz\nL, y\no\nfor the unlensed and lensed signal models,\nrespectively. Moreover, we compute the evidence ratio be-\ntween the microlensed and unlensed signal models, better\nknown as the Bayes factor BMicro\nU\n. Fig. 4 shows the distri-\n\u22122\n\u22121\n0\n1\n2\nlog10 BMicro\nU\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\nP\n\u0000log10 BMicro\nU\n\u0001\nO3 Events\nBackground\nFigure 4. Distribution of microlensing log10 Bayes factors BMicro\nU\nfor all events in O3 (blue, solid line) and simulated unlensed signals\n(orange, dashed line) from Abbott et al. (2021a).\nbution of log10 BMicro\nU\nfor all the events in O3 and simulated\nunlensed signals from Abbott et al. (2021a). The distribu-\ntion of log10 BMicro\nU\nis primarily clustered around 0 and the\ndistribution for O3 events does not extend to signi\ufb01cantly\nhigher values than the distribution for simulated signals. The\nmarginalized posteriors of the microlensing parameters are\nshown in Appendix B. We conclude that there is no com-\npelling evidence for the presence of microlensing signatures.\n5. IMPLICATIONS\nIn this section, we consider some of the implications that\nderive from the search for lensing signatures. We \ufb01rst forecast\nthe number of detectable strongly lensed events based on the\nlatest knowledge on the merger-rate density (Sec. 5.1). Next,\nwe infer upper limits on the strong lensing rate using the non-\ndetection of resolvable strongly lensed BBH events (Sec. 5.2).\nFinally, we use the non-detection of microlensing to infer the\ncompact dark matter fraction in the Universe (Sec. 5.3).\n5.1. Strong lensing rate\nWe predict the rate of lensing using the standard methods\noutlined in the literature (Ng et al. 2018; Li et al. 2018; Oguri\n2018; Xu et al. 2021; Mukherjee et al. 2021a; Wierda et al.\n2021), at galaxy and galaxy-cluster lens mass scales. To\nmodel the lens population, we need to choose a density pro\ufb01le\n\n9\nand a mass function. We adopt the SIS density pro\ufb01le for both\ngalaxies and galaxy clusters. Moreover, we use the velocity\ndispersion function from the Sloan Digital Sky Survey (Choi\net al. 2007) for galaxies and the halo mass function from\nTinker et al. (2008) for clusters which have also been used in\nother lensing studies (e.g., Oguri & Marshall 2010; Robertson\net al. 2020). The SIS pro\ufb01le can accurately describe lensing\nby galaxies, but the mass distribution of clusters tends to be\nmore complicated. Nevertheless, Robertson et al. (2020) have\ndemonstrated that the SIS model can reproduce the lensing\nrate predictions from a study of numerically simulated cluster\nlenses. Thus, we adopt the same model for both galaxies and\ngalaxy clusters.\nUnder the SIS model, we obtain two images with di\ufb00erent\nmagni\ufb01cations and arrival times. The rate of strong lensing is\ngiven by\nRlens =\nZ dN(Mh, zl)\ndMh\ndDc\ndzl\nRm(zm)\n1 + zm\ndVc\ndzm\n\u03c3(Mh, zl, zm, \u03c1, \u03c1c)\n\u00d7 p(\u03c1|zm) d\u03c1 dzm dzl dMh ,\n(3)\nwhere dN(Mh, zl)/dMh is the di\ufb00erential comoving number\ndensity of lensing halos in a halo mass shell at lens redshift zl,\nDc and Vc are the comoving distance and volume, respectively,\nat a given redshift, Rm(zm) is the total comoving merger rate\ndensity at redshift zm, (1+zm) accounts for the cosmological\ntime dilation, p(\u03c1 | zm) is the distribution of SNR at a given\nredshift, \u03c1c is the network SNR threshold, and \u03c3 is the lensing\ncross-section which indicates, as a function of its various argu-\nments, how e\ufb03ciently strong lensing will occur. We model the\nmass distribution of BBHs following the results for the Power\nLaw + Peak model of Abbott et al. (2021j). We consider a\nmerger rate density model that assumes the Madau\u2013Dickinson\nansatz (Madau & Dickinson 2014) that is consistent with\nrecent results from GWTC-3. Moreover, we make use of\nthe absence of a detected stochastic gravitational-wave back-\nground (SGWB) to further constrain the merger rate density\n(Abbott et al. 2021j). For consistency with previous analyses\n(e.g., Abbott et al. 2021k), we take the Hubble constant from\nPlanck 2015 observations to be H0 = 67.9 km s\u22121 Mpc\u22121\n(Ade et al. 2016). Furthermore, we choose \u03c1c = 8 as a point\nestimator of the detectability of GW signals. We \ufb01nd this\nchoice to be consistent with the search results in Abbott et al.\n(2021g) and Sec. 3.1, and we estimate its impact to be sub-\ndominant compared to other sources of uncertainty.\nIn Table 2, we show our estimates for the relative rate of\nlensing expected to be observed by the LIGO\u2013Virgo network\nof detectors. The results are shown separately for galaxy-\nscale and cluster-scale lenses. Furthermore, these rates are\ncalculated for events that are doubly lensed and for two cases:\nwhen only a single event (i.e., the brighter one) is detected\n(S), and when both of the doubly lensed events are detected\n(D). The expected fractional rate of lensing (i.e. the lensed to\nunlensed rate) spans the range O(10\u22124\u201310\u22123), depending on\nthe merger rate density assumed. We estimate the fractional\nrate of observed double (single) events for galaxy-scale lenses\nto lie in the range 1.9\u221211.0 \u00d710\u22124 (5.0\u221219.5 \u00d710\u22124 ). Simi-\nlarly, for cluster-scale lenses, the fractional rate is estimated to\nbe in the range of 0.8\u22124.4 \u00d710\u22124 (2.0\u22127.6 \u00d710\u22124), typically\nlower than the rates on galaxy scales. These estimates sug-\ngest that observing a lensed double image is unlikely at the\ncurrent sensitivity of the LIGO\u2013Virgo network of detectors.\nNevertheless, at design sensitivity and with future upgrades,\nstandard forecasts suggest that the possibility of observing\nsuch events might become signi\ufb01cant (Ng et al. 2018; Li et al.\n2018; Oguri 2018; Xu et al. 2021; Mukherjee et al. 2021a;\nWierda et al. 2021). Compared with other lens models, our\nlensing rates are consistent with those predicted for singular\nisothermal ellipsoid (SIE) models (e.g., Oguri 2018; Xu et al.\n2021; Wierda et al. 2021).\n5.2. Implications from the non-observation of strongly lensed\nevents\nThe absence of any detections of strongly lensed GW events\nbefore and during O3 provides a complementary way to con-\nstrain the merger rates of compact objects at high redshift. The\ndetection of individual GW events has enabled measurement\nof the low redshift (z < 1) merger rate (Abbott et al. 2021j).\nHowever, the high redshift merger rate of GW sources is not\nyet measured directly, and we have only been able to place\nan upper limit on it from the absence of a detection of the\nSGWB (Abbott et al. 2021l). The absence of such a detection\nnaturally leads to a bound on the lensing rate expected from\nGWTC-3 (Mukherjee et al. 2021b; Buscicchio et al. 2020).\nBy using the same power-law form for the merger rate as\nthat used in Sec. 5.1, but extended up to z = 2, we obtain\nlimits on the merger rate at redshift z > 1 from the absence\nof detections of strongly lensed events. The corresponding\nconstraints (90% credible intervals) are shown in Fig. 5 as\nthe cross-hatched region bounded by the dash-dotted curves.\nThe changes in the upper bound of the merger rates are driven\nby the absence of detected lensing events, whereas the lower\nbound is driven by the low-redshift constraints on the merger\nrate. For comparison, the current limits on the merger rate\nfrom GWTC-3 up to redshift z = 1 (Abbott et al. 2021j), with\nthe bounding curves extrapolated to higher redshifts z > 1, are\nshown as the grey shaded region bounded by the dotted curves.\nFor further comparison, we have also plotted the solid black\ncurves which show the current constraints from the absence\nof detection of the SGWB (Abbott et al. 2021l). The upper\nbounds on the merger rate from lensing are more stringent\nthan the bounds from GWTC-3 at high redshift (Abbott et al.\n2021j), and are also comparable with the bounds from the\nSGWB for redshifts z < 1.2. The slight di\ufb00erence between\n\n10\nTable 2. Expected fractional rates of observable lensed double events at current LIGO\u2013Virgo sensitivity.\nMerger Rate Density\nGalaxies\nGalaxy Clusters\nModel\nRD\nRS\nRD\nRS\nGWTC-3+Stochastic\n1.9\u221211.0 \u00d710\u22124\n5.0\u221219.5 \u00d710\u22124\n0.8\u22124.4 \u00d710\u22124\n2.0\u22127.6 \u00d710\u22124\nNote\u2014 This table lists the relative rates of lensed double events expected to be observed by LIGO\u2013Virgo at the current sensitivity where both of\nthe lensed events are detected (RD) and only one of the lensed events is detected (RS) above the SNR threshold. The rates encompass a 90 percent\ncredible interval. We show the rate of lensing by galaxies (\u03c3vd = 10\u2013300 km s\u22121) and galaxy clusters (log10(Mhalo/M\u2299) \u223c14\u201316) separately.\n0.0\n0.5\n1.0\n1.5\n2.0\nzm\n100\n101\n102\n103\nRm(zm) [Gpc\u22123 yr\u22121]\nSGWB\nNo lensing\nLensing\nFigure 5. Merger rate density as a function of redshift based on the\nGWTC-3 results without lensing constraints (grey) and with lensing\nconstraints (cross-hatching) included. For clarity, we show only the\nresults for galaxy-scale lenses. Because lensed detections may occur\nat higher redshifts than unlensed events, their non-observation can\nbe used to constrain the rate of mergers at higher redshifts. The \u2018No\nlensing\u2019 results shown here do not include constraints derived from\nthe absence of an SGWB. The latter constraints are shown separately\nby the solid black curves.\nthe constraints on the merger rates at low redshift derived from\nthe SGWB (Abbott et al. 2021l) and from GWTC-3 (Abbott\net al. 2021j) arise because the bounds from the SGWB are\nobtained here using the previous constraints on the merger rate\nat low redshift derived using GWTC-2 (Abbott et al. 2021m).\n5.3. Constraints on compact dark matter from\ngravitational-wave microlensing\nObjects whose size is comparable to their gravitational\nradius, and that cause microlensing e\ufb00ects on GW signals,\ncould be candidates for dark matter. Although their abun-\ndance is heavily constrained by several astronomical observa-\ntions (Carr & Kuhnel 2020; Carr et al. 2020), the possibility of\ntheir contributing to dark matter cannot be ruled out in several\nmass windows.\nHere we use the non-observation of microlensing e\ufb00ects\non the GW signals detected by LIGO and Virgo to constrain\nthe fraction of dark matter contributed by compact objects in\nthe mass range \u223c102\u2013105 M\u2299(Jung & Shin 2019; Urrutia &\nVaskonen 2021; Basak et al. 2021). The essential idea is that\nif a signi\ufb01cant fraction of dark matter is in the form of com-\npact objects, they would introduce detectable microlensing\nsignatures on the GW signals that we observe.\nAssuming that lensed and unlensed events occur as Poisson\nprocesses, we compute the posterior distribution on the lens-\ning fraction (u \u2261\u039b\u2113/\u039b), de\ufb01ned as the ratio of Poisson means\nof lensed events to the total number of detected events. This is\nthen used to compute the posterior of the fraction of compact\ndark matter (fDM \u2261\u2126CO/\u2126DM) (Basak et al. 2021). We take\nthat a total of N = 67 BBH mergers are detected during the\nO3 run 4, and none of them is lensed (i.e., N\u2113= 0). We then\nestimate the posterior distribution of the lensing fraction u.\nFinally, the posterior of fDM can be computed as\np( fDM | {N\u2113= 0, N}) = p(u | {N\u2113= 0, N})\n\f\f\f\f\f\ndu\nd fDM\n\f\f\f\f\f ,\n(4)\nwhere du/d fDM is the Jacobian that relates the observed frac-\ntion u of lensed events to the compact dark matter fraction\nfDM in the Universe.\nWe determine this Jacobian by simulating astrophysical\npopulations of BBH mergers lensed by point mass lenses\n(Basak et al. 2021).5 The constraints we obtain depend upon\nthe assumed distributions of the component masses, spins and\nthe redshifts of the mergers, which have considerable uncer-\ntainties. We assume that the masses are distributed according\nto the Power-law + Peak model of Abbott et al. (2021j) while\nspins are assumed to be aligned/antialigned with the orbital\nangular momentum with magnitudes distributed uniformly\nin (0, 0.99). We use the approximant IMRPhenomD (Khan\net al. 2016) to produce the waveforms. We consider di\ufb00er-\nent redshift distributions of the mergers: uniform distribution\nin comoving volume, the power-law model of Abbott et al.\n(2021j), the Madau-Dickinson model (Madau & Dickinson\n2014), as well as some representative population-synthesis\nmodels given by Dominik et al. (2013) and Belczynski et al.\n(2016). In our simulations, compact objects are approximated\nby point mass lenses and distributed uniformly in comoving\n4 These are the events cataloged in GWTC-3 that do not contain a neutron\nstar component.\n5 The simulations are done assuming the O3b representative PSD and\nGaussian noise. The Jacobian is not expected to change signi\ufb01cantly if real\nnoise is used instead.\n\n11\nvolume. Binaries producing a network SNR of 8 or above in\nthe LIGO\u2013Virgo detectors are deemed detectable. In order to\nreduce the computational cost of performing the simulations,\nwe estimate BMicro\nU\nusing an approximation to the Bayes factor\nthat is expected to be accurate in the high-SNR regime (Cor-\nnish et al. 2011; Vallisneri 2012). We then compute the frac-\ntion of detected events that produce a BMicro\nU\nlarger than the\nhighest BMicro\nU\nobtained from real LIGO\u2013Virgo events. This\nlensing fraction is computed as a function of the fDM, which\nis used to compute the Jacobian du/dfDM.\n102\n103\n104\n105\nM\u2113[M\u2299]\n0.2\n0.4\n0.6\n0.8\n1.0\nfDM\nSpread in fDM using 5 redshift distributions\n\ufb02at prior\nJe\ufb00reys prior\nFigure 6. The spread in the 90% upper limits on fDM obtained from\nthe O3 events using 5 di\ufb00erent redshift distribution models for BBH\nmergers: Belczynski et al. (2016),Dominik et al. (2013), Madau &\nDickinson (2014), Abbott et al. (2021j) and uniform in comoving 4-\nvolume, assuming a monochromatic mass spectrum for the compact\nobjects forming dark matter. The lens mass is shown on the horizon-\ntal axis. The grey (black) shaded regions correspond to the spread in\nfDM upper bounds computed assuming \ufb02at (Je\ufb00reys) prior on \u039b and\n\u039b\u2113. The upper and lower curves bounding the spreads correspond\nto the most pessimistic (weakest) and optimistic (strongest) upper\nlimits, as determined from the set of assumed redshift distributions,\nin each mass bin.\nThe largest value of the microlensing likelihood ratio ob-\ntained from GWTC-3 events is log10 BMicro\nU\n= 0.799. We\ncompute the fraction of simulated events with log10 BMicro\nU\n\u2265\n0.799, for di\ufb00erent lens masses. This allows us to compute\nthe Jacobian du/dfDM and thus the posterior on fDM. The 90%\nupper limits are shown as a function of the lens mass (assum-\ning a monochromatic spectrum) in Fig. 6. The bounds we\nobtain are weaker than some of the existing constraints (Carr\n& Kuhnel 2020; Carr et al. 2020). The GW lensing bounds\nwill improve signi\ufb01cantly in the next few years as the sensitiv-\nity of GW detectors improve (Abbott et al. 2018). Assuming\n\u223c300 BBH detections in O4 and O(1000) detections in O5,\nthe constraints on fDM will improve to \u223c10\u22121 and \u223c10\u22122,\nrespectively.\n6. CONCLUDING REMARKS\nWe have extended the search for lensing signatures to all\nBBH candidates with a probability of astrophysical origin\nhigher than 0.5 from O3b (Abbott et al. 2021b). While we\nhave not observed any signi\ufb01cant candidates for strongly\nlensed events, we updated the constraints on the rate of such\nevents from several di\ufb00erent analyses. First, we searched for\nsub-threshold repeated signals associated with super-threshold\nevents using reduced template banks produced from the poste-\nrior probability distributions of the super-threshold events. In-\nteresting sub-threshold/super-threshold pairs and pairs formed\nfrom two super-threshold events were further analyzed for\ntheir probability of being from a single, strongly lensed source.\nFor super-threshold/super-threshold pairs, we calculated the\ndegree of overlap between the posteriors of the intrinsic param-\neters and sky location, which were obtained from Bayesian\ninference. Moreover, we analyzed these pairs using a new\nanalysis based on the comparison of spectrograms through\nmachine learning. Finally, pairs with false-positive probability\nfrom either analysis smaller than 10\u22122 were further studied\nby conducting full joint Bayesian inference analyses that take\npopulation priors and selection e\ufb00ects into account. We found\nno pairs that show signi\ufb01cant evidence for strong lensing.\nThe events from O3b were also analyzed for distortions\ncaused by the lens on the gravitational waveform. First, we\nsearched for the distortions that lensing introduces on type\nII signals, which are in the form of a frequency-independent\nphase shift (Morse phase). The Bayes factors for all events\nshow no evidence for type II signal distortions. Similarly, we\nsearched for the frequency-dependent distortions caused by\npoint masses. None of the computed Bayes factors show any\nsigni\ufb01cant signs of microlensing. For both analyses, some\nevents show interesting features in the posteriors for the Morse\nphase or lens mass. However, follow-up analyses using sim-\nulated signals show no further signs of the lensing nature\nof these features. Altogether, we found no signi\ufb01cant evi-\ndence for distortions of the gravitational waveforms that can\nbe attributed to lensing.\nThe lack of evidence for lensing is then used to infer prop-\nerties of the lensing rates and to set constraints on the dark\nmatter fraction of (dark) compact objects.\nFinally, we note that our conclusions are based on estimates\nand assumptions that are in line with other analyses from the\nLIGO\u2013Virgo\u2013KAGRA Collaboration (Abbott et al. 2021f,j).\nIt is possible to arrive at di\ufb00erent conclusions and interpreta-\ntions if assumptions are chosen di\ufb00erently. Examples include\nclaims that almost all detections are strongly lensed if one\nassumes that heavy BHs do not exist (Broadhurst et al. 2018,\n2020a,b). Data from the upcoming observing runs are ex-\n\n12\npected to further expand the catalog of GW detections that\ncan further shed light on the lensing of GWs (Abbott et al.\n2020b). Moreover, multi-messenger astronomy may provide\nsigni\ufb01cant input in con\ufb01rming and interpreting possible lensed\nGW signals (Wempe et al. 2022).\nThis material is based upon work supported by NSF\u2019s LIGO\nLaboratory which is a major facility fully funded by the Na-\ntional Science Foundation. The authors also gratefully ac-\nknowledge the support of the Science and Technology Facili-\nties Council (STFC) of the United Kingdom, the Max-Planck-\nSociety (MPS), and the State of Niedersachsen/Germany for\nsupport of the construction of Advanced LIGO and construc-\ntion and operation of the GEO 600 detector. Additional sup-\nport for Advanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the Ital-\nian Istituto Nazionale di Fisica Nucleare (INFN), the French\nCentre National de la Recherche Scienti\ufb01que (CNRS) and the\nNetherlands Organization for Scienti\ufb01c Research (NWO), for\nthe construction and operation of the Virgo detector and the\ncreation and support of the EGO consortium. The authors also\ngratefully acknowledge research support from these agencies\nas well as by the Council of Scienti\ufb01c and Industrial Research\nof India, the Department of Science and Technology, India,\nthe Science & Engineering Research Board (SERB), India,\nthe Ministry of Human Resource Development, India, the\nSpanish Agencia Estatal de Investigaci\u00b4on (AEI), the Spanish\nMinisterio de Ciencia e Innovaci\u00b4on and Ministerio de Uni-\nversidades, the Conselleria de Fons Europeus, Universitat i\nCultura and the Direcci\u00b4o General de Pol\u00b4\u0131tica Universitaria\ni Recerca del Govern de les Illes Balears, the Conselleria\nd\u2019Innovaci\u00b4o, Universitats, Ci`encia i Societat Digital de la Gen-\neralitat Valenciana and the CERCA Programme Generalitat\nde Catalunya, Spain, the National Science Centre of Poland\nand the European Union \u2013 European Regional Development\nFund; Foundation for Polish Science (FNP), the Swiss Na-\ntional Science Foundation (SNSF), the Russian Foundation\nfor Basic Research, the Russian Science Foundation, the Eu-\nropean Commission, the European Social Funds (ESF), the\nEuropean Regional Development Funds (ERDF), the Royal\nSociety, the Scottish Funding Council, the Scottish Univer-\nsities Physics Alliance, the Hungarian Scienti\ufb01c Research\nFund (OTKA), the French Lyon Institute of Origins (LIO),\nthe Belgian Fonds de la Recherche Scienti\ufb01que (FRS-FNRS),\nActions de Recherche Concert\u00b4ees (ARC) and Fonds Weten-\nschappelijk Onderzoek \u2013 Vlaanderen (FWO), Belgium, the\nParis \u02c6Ile-de-France Region, the National Research, Develop-\nment and Innovation O\ufb03ce Hungary (NKFIH), the National\nResearch Foundation of Korea, the Natural Science and Engi-\nneering Research Council Canada, Canadian Foundation for\nInnovation (CFI), the Brazilian Ministry of Science, Technol-\nogy, and Innovations, the International Center for Theoretical\nPhysics South American Institute for Fundamental Research\n(ICTP-SAIFR), the Research Grants Council of Hong Kong,\nthe National Natural Science Foundation of China (NSFC),\nthe Leverhulme Trust, the Research Corporation, the National\nScience and Technology Council (NSTC), Taiwan, the United\nStates Department of Energy, and the Kavli Foundation. The\nauthors gratefully acknowledge the support of the NSF, STFC,\nINFN and CNRS for provision of computational resources.\nThis work was supported by MEXT, JSPS Leading-edge\nResearch Infrastructure Program, JSPS Grant-in-Aid for Spe-\ncially Promoted Research 26000005, JSPS Grant-inAid for\nScienti\ufb01c Research on Innovative Areas 2905: JP17H06358,\nJP17H06361 and JP17H06364, JSPS Core-to-Core Program\nA. Advanced Research Networks, JSPS Grantin-Aid for\nScienti\ufb01c Research (S) 17H06133 and 20H05639 , JSPS\nGrant-in-Aid for Transformative Research Areas (A) 20A203:\nJP20H05854, the joint research program of the Institute for\nCosmic Ray Research, University of Tokyo, National Re-\nsearch Foundation (NRF), Computing Infrastructure Project\nof Global Science experimental Data hub Center (GSDC) at\nKISTI, Korea Astronomy and Space Science Institute (KASI),\nand Ministry of Science and ICT (MSIT) in Korea, Academia\nSinica (AS), AS Grid Center (ASGC) and the National Sci-\nence and Technology Council (NSTC) in Taiwan under grants\nincluding the Rising Star Program and Science Vanguard\nResearch Program, Advanced Technology Center (ATC) of\nNAOJ, and Mechanical Engineering Center of KEK.\nSoftware:\nAnalyses in this paper made use of\nLALSuite (LIGO Scienti\ufb01c Collaboration and Virgo Col-\nlaboration 2018), the GstLAL (Cannon et al. 2012; Messick\net al. 2017; Hanna et al. 2020; Sachdev et al. 2019) pipeline;\nBayesian inference with bilby (Ashton et al. 2019; Smith\net al. 2020; Romero-Shaw et al. 2020); as well as the pack-\nages NumPy (Harris et al. 2020), SciPy (Virtanen et al. 2020),\nAstropy (Robitaille et al. 2013; Price-Whelan et al. 2018),\nIPython (Perez & Granger 2007), and ligo.skymap (Singer\n2019). Plots were produced with Matplotlib (Hunter 2007),\nand Seaborn (Waskom et al. 2020).\nAPPENDIX\nA. TYPE II SIMULATION CAMPAIGNS\nGiven the mild evidence of GW190412 and GW200129 065458 towards being a type II strongly lensed image presented in Sec.\n3.4, we follow up on these events by doing an injection campaign where we simulate type I and type II images similar to the events,\n\n13\nand verify whether the posteriors recovered are compatible with the distribution observed for the real events. These injections are\nperformed in di\ufb00erent noise realizations and with di\ufb00erent waveform models. The observed feature could be caused by two main\nother e\ufb00ects than a type II image: noise artifacts or systematic e\ufb00ects in the waveform modeling. In the former, non-Gaussianities\nin the noise could be such that they lead to the observation of spurious features, while in the latter case, the speci\ufb01c combination of\nobserved parameters could lead to some systematic issues in \ufb01tting with the waveform model. Waveform systematics might be\nespecially important for these events since they lie in challenging parts of the parameter space (Abbott et al. 2020c; Colleoni et al.\n2021; Hannam et al. 2021). Moreover, for GW200129 065458 Payne et al. (2022) reports that there could be a signi\ufb01cant glitch\nunder subtraction.\nTo test for the noise-related features, we generate colored Gaussian noise from the PSD around the time of the candidate and\nthen inject the maximum likelihood parameters coming from the parameter estimation and take the Morse factor to be either the\nvalue for a type I or a type II image. In the \ufb01rst step, we do this for only one noise realization for each event to see whether we can\nreproduce similar features or not. For GW200129 065458, the injection shows that the e\ufb00ect is too weak to be distinguishable from\none image type to the other, as can be seen in the uninformative posteriors of Fig. 7. As a consequence, no further investigation is\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nn1\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n1.2\nP(n1)\nReal event\nType I injected\nType II injected\nFigure 7. Posterior distribution of the Morse phase for GW200129 065458. We compare the real event posterior (solid-blue) with an injection\ncampaign of type I (dashed-orange) and type II (dotted-green) images. Type II images correspond to n1 = 1/2. For this event, the di\ufb00erences\nbetween the distribution are small and make it di\ufb03cult to learn anything additional about the event. The Kolmogorov\u2013Smirnov statistic is 0.07\nfor type I vs real, and 0.08 for type II vs real.\ndone into this event. On the other hand, for GW190412, the feature seen in the real data is compatible with the one seen in the\ninjection (see Fig. 8).\nGiven that the real-data results are compatible with the type II injection for GW190412, we investigate further the noise\nhypothesis. For this purpose, we take the maximum likelihood parameters and a Morse factor of 0 or 1/2 and inject the signal\ngenerated with the IMRPhenomXPHM (Pratten et al. 2021) model in ten di\ufb00erent noise realizations. We then repeat the analysis in\nthe same way as for the real signal and verify if we retrieve the same preference for a type II image. For all the noise realizations\nused here, we see the same behavior as in Fig. 8.\nWe perform an extra test by injecting the maximum likelihood parameters with a given image type in the generated noise for\ndi\ufb00erent waveform models. We use the IMRPhenomPv3HM (Khan et al. 2020) and the SEOBNRv4PHM (Ossokine et al. 2020)\nmodel to generate the signal and use the IMRPhenomXPHM (Pratten et al. 2021) model to recover it. This enables us to combine\nthe two possible sources of systematics. This way, we can verify whether a di\ufb00erent noise combined with a di\ufb00erent model also\nleads to a preference for type II images. For all the noise realizations and the two models used for the injections, we \ufb01nd that the\ninjections always recover the correct hypothesis, and the fact that the real event supports type II is unlikely to be a result of noise\nor waveform artifacts, as shown in Fig. 9.\nAlthough these tests do not discard the type II image hypothesis, they cannot conclusively con\ufb01rm it. To con\ufb01rm the presence of\nlensing for this event with a mild preference for a type II image, we would need additional evidence. Therefore, we search for\npossible sub-threshold counterparts with the methodology explained in Sec. 3.1. However, we \ufb01nd only marginal triggers.\n\n14\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nn1\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\nP(n1)\nReal event\nType I injected\nType II injected\nFigure 8. Posterior distribution of the Morse phase for GW190412. We compare the real event posterior (solid-blue) with an injection campaign\nof type I (dashed-orange) and type II (dotted-green) images. Type II images correspond to n1 = 1/2. For this event, the peak seen in the real data\nand the one seen for the type II image are compatible, hinting at a possible type II image. In this case, the Kolmogorov\u2013Smirnov statistic is 0.20\nfor type I vs real, and 0.13 for type II vs real.\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nn1\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\n3.0\nP(n1)\nIMRPhenomPv3HM, Type I\nIMRPhenomPv3HM, Type II\nSEOBNRv4PHM, Type I\nSEOBNRv4PHM, Type II\nReal event\nFigure 9.\nComparison of the Morse factor distribution for the real event (solid-purple) with the recovered posterior distribution for an\ninjection made with IMRPhenomPv3HM for a type I image (dashed-blue) and a type II image (dotted-orange), and with an injection made with\nSEOBNRv4PHM for a type I image (dashed-green) and a type II image (dotted-red). In all the cases, the posterior distributions agree with the\ninjected data, with the real event resembling a type II image.\nIn the end, these additional searches did not enable us to \ufb01nd any extra evidence for lensing, while still not ruling out the\npossibility for GW190412 to be a type II image.\nB. MARGINALIZED POSTERIORS OF MICROLENSING PARAMETERS\nAs a supplement to the distribution of log10 Bayes factors BMicro\nU\nshown in Fig. 4, we show the individual marginalized posterior\ndistributions of redshifted lens mass Mz\nL and log10 BMicro\nU\n(right vertical axis) in Fig. 10. The Bayes factors individually do not\nshow clear evidence for microlensing by point-mass lenses. However, several events show a narrow posterior distribution of the\nredshifted lens mass. An example is GW200208 130117 (with log10 BMicro\nU\n= 0.8), for which the waveform corresponding to the\nmaximum posterior for this event, with and without lensing, is shown in Fig. 11. The beating pattern introduced by the point-mass\nlens is most visible as a reduction of the amplitude for two cycles in the middle of the signal and an increase in the amplitude\n\n15\n0\n1\n2\n3\n4\n5\nlog10(M z\nL/M\u2299)\nGW200322_091133\nGW200316_215756\nGW200311_115853\nGW200308_173609\nGW200306_093714\nGW200302_015811\nGW200225_060421\nGW200224_030524\nGW200220_124850\nGW200220_061928\nGW200219_094415\nGW200216_220804\nGW200209_085452\nGW200208_222618\nGW200208_130117\nGW200202_154313\nGW200129_065458\nGW200128_022011\nGW200112_155838\nGW191230_180458\nGW191222_033537\nGW191216_213338\nGW191215_223052\nGW191204_171526\nGW191204_110529\nGW191129_134029\nGW191127_050227\nGW191126_115259\nGW191109_010717\nGW191105_143521\nGW191103_012549\n0.1\n0.19\n0.3\n0.19\n0.12\n\u22120.02\n0.25\n0.2\n0.26\n\u22120.14\n0.22\n0.05\n0.05\n\u22120.07\n0.8\n0.62\n0.58\n\u22120.01\n\u22120.02\n0.12\n0.14\n0.3\n0.05\n\u22120.01\n0.1\n0.15\n0.08\n\u22120.01\n0.55\n0.03\n0.05\nlog10BMicro\nU\nFigure 10. Marginalized posterior distributions of redshifted lens mass Mz\nL and log10 BMicro\nU\nbetween microlensed and unlensed hypotheses.\nbefore and after this reduction. We hypothesize that short-duration noise \ufb02uctuations may have caused an apparent dip in the\nsignal, which in turn may have led to a distortion similar to a point-mass lens beating pattern. This is corroborated by a low Bayes\nfactor BMicro\nU\n, which concludes the data is inconclusive about the microlensing hypothesis.\nREFERENCES\nAbbott, B. P., et al. 2016a, Class. Quant. Grav., 33, 134001,\ndoi: 10.1088/0264-9381/33/13/134001\n\u2014. 2016b, Astrophys. J., 833, L1, doi: 10.3847/2041-8205/833/1/L1\n\u2014. 2018, Living Rev. Rel., 21, 3, doi: 10.1007/s41114-020-00026-9\n\u2014. 2020a, Class. Quant. Grav., 37, 055002,\ndoi: 10.1088/1361-6382/ab685e\n\u2014. 2020b, Living Rev. Relativity, 23, 3,\ndoi: 10.1007/s41114-020-00026-9\nAbbott, R., et al. 2020c, Phys. Rev. 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J.,\n910, 152, doi: 10.3847/1538-4357/abe40e\n\nThe LIGO Scientific Collaboration, the Virgo Collaboration and the KAGRA Collaboration, R. Abbott,1 H. Abe,2 F. Acernese,3, 4\nK. Ackley,5 S. Adhicary,6 N. Adhikari,7 R. X. Adhikari,1 V. K. Adkins,8 V. B. Adya,9 C. Affeldt,10, 11 D. Agarwal,12 M. Agathos,13, 14\nO. D. Aguiar,15 L. Aiello,16 A. Ain,17 P. Ajith,18 T. Akutsu,19, 20 S. Albanesi,21, 22 R. A. Alfaidi,23 C. All\u00b4en\u00b4e,24 A. Allocca,25, 4 P. A. Altin,9\nA. Amato,26, 27 S. Anand,1 A. Ananyeva,1 S. B. Anderson,1 W. G. Anderson,1 M. Ando,28, 29 T. Andrade,30 N. Andres,24\nM. Andr\u00b4es-Carcasona,31 T. Andri\u00b4c,32 S. Ansoldi,33, 34 J. M. Antelis,35 S. Antier,36, 37 T. Apostolatos,38 E. Z. Appavuravther,39, 40 S. Appert,1\nS. K. Apple,41 K. Arai,1 A. Araya,42 M. C. Araya,1 J. S. Areeda,43 M. Ar`ene,44 N. Aritomi,19 N. Arnaud,45, 46 M. Arogeti,47 S. M. Aronson,8\nH. Asada,48 G. Ashton,49 Y. Aso,50, 51 M. Assiduo,52, 53 S. Assis de Souza Melo,46 S. M. Aston,54 P. Astone,55 F. Aubin,53 K. AultONeal,35\nS. Babak,44 F. Badaracco,56 C. Badger,57 S. Bae,58 Y. Bae,59 S. Bagnasco,22 Y. Bai,1 J. G. Baier,60 J. Baird,44 R. Bajpai,61 T. Baka,62\nM. Ball,63 G. Ballardin,46 S. W. Ballmer,64 G. Baltus,65 S. Banagiri,66 B. Banerjee,32 D. Bankar,12 J. C. Barayoga,1 B. C. Barish,1\nD. Barker,67 P. Barneo,30 F. Barone,68, 4 B. Barr,23 L. Barsotti,69 M. Barsuglia,44 D. Barta,70 J. Bartlett,67 M. A. Barton,23 I. Bartos,71\nS. Basak,18 R. Bassiri,72 A. Basti,73, 17 M. Bawaj,39, 74 J. C. Bayley,23 M. Bazzan,75, 76 B. B\u00b4ecsy,77 V. M. Bedakihale,78 F. Beirnaert,79\nM. Bejger,80 I. Belahcene,45 A. S. Bell,23 V. Benedetto,81 D. Beniwal,82 W. Benoit,83 J. D. Bentley,84 M. BenYaala,85 S. Bera,86\nM. Berbel,87 F. Bergamin,10, 11 B. K. Berger,72 S. Bernuzzi,14 M. Beroiz,1 C. P. L. Berry,23 D. Bersanetti,88 A. Bertolini,27 J. Betzwieser,54\nD. Beveridge,89 R. Bhandare,90 A. V. Bhandari,12 U. Bhardwaj,37, 27 R. Bhatt,1 D. Bhattacharjee,60, 91 S. Bhaumik,71 A. Bianchi,27, 92\nI. A. Bilenko,93 M. Bilicki,94 G. Billingsley,1 S. Bini,95, 96 O. Birnholtz,97 S. Biscans,1, 69 M. Bischi,52, 53 S. Biscoveanu,69 A. Bisht,10, 11\nB. Biswas,12 M. Bitossi,46, 17 M.-A. Bizouard,36 J. K. Blackburn,1 C. D. Blair,89, 54 D. G. Blair,89 R. M. Blair,67 F. Bobba,98, 99 N. Bode,10, 11\nM. Bo\u00a8er,36 G. Bogaert,36 M. Boldrini,100, 55 G. N. Bolingbroke,82 L. D. Bonavena,75 R. Bondarescu,30 F. Bondu,101 E. Bonilla,72\nR. Bonnand,24 P. Booker,10, 11 R. Bork,1 V. Boschi,17 N. Bose,102 S. Bose,12 V. Bossilkov,89 V. Boudart,65 Y. Bouffanais,75, 76 A. Bozzi,46\nC. Bradaschia,17 P. R. Brady,7 A. Bramley,54 A. Branch,54 M. Branchesi,32, 103 J. E. Brau,63 M. Breschi,14 T. Briant,104 J. H. Briggs,23\nA. Brillet,36 M. Brinkmann,10, 11 P. Brockill,7 A. F. Brooks,1 J. Brooks,46 D. D. Brown,82 S. Brunett,1 G. Bruno,56 R. Bruntz,105\nJ. Bryant,106 F. Bucci,53 J. Buchanan,105 T. Bulik,107 H. J. Bulten,27 A. Buonanno,108, 109 K. Burtnyk,67 R. Buscicchio,106, 110, 111\nD. Buskulic,24 C. Buy,112 R. L. Byer,72 G. S. Cabourn Davies,113 G. Cabras,33, 34 R. Cabrita,56 L. Cadonati,47 G. Cagnoli,114 C. Cahillane,67\nJ. Calder\u00b4on Bustillo,115 J. D. Callaghan,23 T. A. Callister,116, 117 E. Calloni,25, 4 J. B. Camp,118 M. Canepa,119, 88 G. Caneva,31\nM. Cannavacciuolo,98 K. C. Cannon,29 H. Cao,82 Z. Cao,120 L. A. Capistran,121 E. Capocasa,44, 19 E. Capote,64 G. Carapella,98, 99\nF. Carbognani,46 M. Carlassara,10, 11 J. B. Carlin,122 M. Carpinelli,123, 124, 46 G. Carrillo,63 J. J. Carter,10, 11 G. Carullo,73, 17\nJ. Casanueva Diaz,46 C. Casentini,125, 126 G. Castaldi,127 S. Caudill,27, 62 M. Cavagli`a,91 F. Cavalier,45 R. Cavalieri,46 G. Cella,17\nP. Cerd\u00b4a-Dur\u00b4an,128 E. Cesarini,126 W. Chaibi,36 W. Chakalis,116, 117 S. Chalathadka Subrahmanya,84 E. Champion,129 C.-H. Chan,130\nC. Chan,29 C. L. Chan,131 K. Chan,131 M. Chan,132 K. Chandra,102 I. P. Chang,130 W. Chang,130 P. Chanial,46, 44 S. Chao,130\nC. Chapman-Bird,23 P. Charlton,133 E. Chassande-Mottin,44 C. Chatterjee,89 Debarati Chatterjee,12 Deep Chatterjee,7 M. Chaturvedi,90\nS. Chaty,44 K. Chatziioannou,1 C. Chen,134, 130 D. Chen,50 H. Y. Chen,69 J. Chen,69 K. Chen,135 X. Chen,89 Y.-B. Chen,136 Y.-R. Chen,130\nY. Chen,136 H. Cheng,71 P. Chessa,73, 17 H. Y. Cheung,131 H. Y. Chia,71 F. Chiadini,137, 99 C-Y. Chiang,138 G. Chiarini,76 R. Chierici,139\nA. Chincarini,88 M. L. Chiofalo,73, 17 A. Chiummo,46 R. K. Choudhary,89 S. Choudhary,12 N. Christensen,36 Q. Chu,89 Y-K. Chu,138\nS. S. Y. Chua,9 K. W. Chung,57 G. Ciani,75, 76 P. Ciecielag,80 M. Cie\u00b4slar,80 M. Cifaldi,125, 126 A. A. Ciobanu,82 R. Ciolfi,140, 76 F. Clara,67\nJ. A. Clark,1 T. A. Clarke,5 P. Clearwater,141 S. Clesse,142 F. Cleva,36 E. Coccia,32, 103 E. Codazzo,32 P.-F. Cohadon,104 D. E. Cohen,45\nM. Colleoni,86 C. G. Collette,143 A. Colombo,110, 111 M. Colpi,110, 111 C. M. Compton,67 L. Conti,76 S. J. Cooper,106 P. Corban,54\nT. R. Corbitt,8 I. Cordero-Carri\u00b4on,144 S. Corezzi,74, 39 N. J. Cornish,77 A. Corsi,145 S. Cortese,46 A. C. Coschizza,146 R. Cotesta,109\nR. Cottingham,54 M. W. Coughlin,83 J.-P. Coulon,36 S. T. Countryman,147 B. Cousins,6 P. Couvares,1 D. M. Coward,89 M. J. Cowart,54\nD. C. Coyne,1 R. Coyne,148 K. Craig,85 J. D. E. Creighton,7 T. D. Creighton,149 A. W. Criswell,83 M. Croquette,104 S. G. Crowder,150\nJ. R. Cudell,65 T. J. Cullen,8 A. Cumming,23 R. Cummings,23 E. Cuoco,46, 151, 17 M. Cury\u0142o,107 P. Dabadie,114 T. Dal Canton,45 S. Dall\u2019Osso,55\nG. D\u00b4alya,79, 152 A. Dana,72 B. D\u2019Angelo,119, 88 S. Danilishin,26, 27 S. D\u2019Antonio,126 K. Danzmann,10, 11 C. Darsow-Fromm,84 A. Dasgupta,78\nL. E. H. Datrier,23 Sayak Datta,12 Sayantani Datta,153 V. Dattilo,46 I. Dave,90 M. Davier,45 D. Davis,1 M. C. Davis,154 E. J. Daw,155\nM. Dax,109 D. DeBra,72, \u2217M. Deenadayalan,12 J. Degallaix,156 M. De Laurentis,25, 4 S. Del\u00b4eglise,104 V. Del Favero,129 F. De Lillo,56\nN. De Lillo,23 D. Dell\u2019Aquila,123, 124 W. Del Pozzo,73, 17 F. De Matteis,125, 126 V. D\u2019Emilio,16 N. Demos,69 T. Dent,115 A. Depasse,56\nR. De Pietri,157, 158 R. De Rosa,25, 4 C. De Rossi,46 R. DeSalvo,127, 159 R. De Simone,137 S. Dhurandhar,12 R. Diab,71 M. C. D\u00b4\u0131az,149\nN. A. Didio,64 T. Dietrich,109 L. Di Fiore,4 C. Di Fronzo,106 C. Di Giorgio,98, 99 F. Di Giovanni,128 M. Di Giovanni,32 T. Di Girolamo,25, 4\nD. Diksha,27, 26 A. Di Lieto,73, 17 A. Di Michele,74 S. Di Pace,100, 55 I. Di Palma,100, 55 F. Di Renzo,73, 17 A. K. Divakarla,71 A. Dmitriev,106\nZ. Doctor,66 P. P. Doleva,105 L. Donahue,160 L. D\u2019Onofrio,25, 4 F. Donovan,69 K. L. Dooley,16 T. Dooney,62 S. Doravari,12 O. Dorosh,161\nM. Drago,100, 55 J. C. Driggers,67 Y. Drori,1 J.-G. Ducoin,162, 44 L. Dunn,122 U. Dupletsa,32 O. Durante,98, 99 D. D\u2019Urso,123, 124\nP.-A. Duverne,45 S. E. Dwyer,67 C. Eassa,67 P. J. Easter,5 M. Ebersold,163 T. Eckhardt,84 G. Eddolls,23 B. Edelman,63 T. B. Edo,1 O. Edy,113\nA. Effler,54 S. Eguchi,132 J. Eichholz,9 S. S. Eikenberry,71 M. Eisenmann,24, 19 R. A. Eisenstein,69 A. Ejlli,16 E. Engelby,43 Y. Enomoto,28\nL. Errico,25, 4 R. C. Essick,164 H. Estell\u00b4es,86 D. Estevez,165 T. Etzel,1 M. Evans,69 T. M. Evans,54 T. Evstafyeva,13 B. E. Ewing,6\nJ. M. Ezquiaga,166 F. Fabrizi,52, 53 F. Faedi,53 V. Fafone,125, 126, 32 H. Fair,64 S. Fairhurst,16 P. C. Fan,160 A. M. Farah,166 B. Farr,63\nW. M. Farr,116, 117 G. Favaro,75 M. Favata,167 M. Fays,65 M. Fazio,168 J. Feicht,1 M. M. Fejer,72 E. Fenyvesi,70, 169 D. L. Ferguson,170\nA. Fernandez-Galiana,69 I. Ferrante,73, 17 T. A. Ferreira,15 F. Fidecaro,73, 17 P. Figura,107 A. Fiori,17, 73 I. Fiori,46 M. Fishbach,66\nR. P. Fisher,105 R. Fittipaldi,171, 99 V. Fiumara,172, 99 R. Flaminio,24, 19 E. Floden,83 H. K. Fong,29 J. A. Font,128, 173 B. Fornal,159\nP. W. F. Forsyth,9 A. Franke,84 S. Frasca,100, 55 F. Frasconi,17 J. P. Freed,35 Z. Frei,152 A. Freise,27, 92 O. Freitas,174 R. Frey,63 P. Fritschel,69\nV. V. Frolov,54 G. G. Fronz\u00b4e,22 Y. Fujii,175 Y. Fujikawa,176 Y. Fujimoto,177 P. Fulda,71 M. Fyffe,54 H. A. Gabbard,23 W. E. Gabella,178\nB. U. Gadre,109, 62 J. R. Gair,109 J. Gais,131 S. Galaudage,5 R. Gamba,14 D. Ganapathy,69 A. Ganguly,12 D.-F. Gao,179 D. Gao,72\nS. G. Gaonkar,12 B. Garaventa,88, 119 C. Garc\u00b4\u0131a-N\u00b4u\u02dcnez,180 C. Garc\u00b4\u0131a-Quir\u00b4os,86, 10, 11 K. A. Gardner,146 J. Gargiulo,46 F. Garufi,25, 4\nC. Gasbarra,125, 126 B. Gateley,67 V. Gayathri,71 G.-G. Ge,179 G. Gemme,88 A. Gennai,17 J. George,90 O. Gerberding,84 L. Gergely,181\nS. Ghonge,47 Abhirup Ghosh,109 Archisman Ghosh,79 Shaon Ghosh,167 Shrobana Ghosh,16 Tathagata Ghosh,12 L. Giacoppo,100, 55\nJ. A. Giaime,8, 54 K. D. Giardina,54 D. R. Gibson,180 C. Gier,85 P. Giri,17, 73 F. Gissi,81 S. Gkaitatzis,46 J. Glanzer,8 A. E. Gleckl,43\nF. G. Godoy,47 P. Godwin,6 E. Goetz,146 R. Goetz,71 J. Golomb,1 B. Goncharov,32 G. Gonz\u00b4alez,8 M. Gosselin,46 R. Gouaty,24 D. W. Gould,9\nS. Goyal,18 B. Grace,9 A. Grado,182, 4 V. Graham,23 M. Granata,156 V. Granata,98 S. Gras,69 P. Grassia,1 C. Gray,67 R. Gray,183 G. Greco,39\nA. C. Green,71 R. Green,16 A. M. Gretarsson,35 E. M. Gretarsson,35 D. Griffith,1 W. L. Griffiths,16 H. L. Griggs,47 G. Grignani,74, 39\nA. Grimaldi,95, 96 S. J. Grimm,32, 103 H. Grote,16 S. Grunewald,109 A. S. Gruson,43 D. Guerra,128 G. M. Guidi,52, 53 A. R. Guimaraes,8\nH. K. Gulati,78 F. Gulminelli,184 A. M. Gunny,69 H.-K. Guo,159 Y. Guo,27 Anchal Gupta,1 Anuradha Gupta,185 P. Gupta,27, 62 S. K. Gupta,102\n\n21\nJ. Gurs,84 R. Gustafson,186 N. Gutierrez,156 F. Guzman,121 S. Ha,187 I. P. W. Hadiputrawan,135 L. Haegel,44 S. Haino,138 O. Halim,34\nE. D. Hall,69 E. Z. Hamilton,163 G. Hammond,23 W.-B. Han,188 M. Haney,163 J. Hanks,67 C. Hanna,6 M. D. Hannam,16 O. Hannuksela,62, 27\nH. Hansen,67 J. Hanson,54 R. Harada,189 T. Harder,36 K. Haris,27, 62 J. Harms,32, 103 G. M. Harry,41 I. W. Harry,113 D. Hartwig,84\nK. Hasegawa,190 B. Haskell,80 C.-J. Haster,69 J. S. Hathaway,129 K. Hattori,191 K. Haughian,23 H. Hayakawa,192 K. Hayama,132 F. J. Hayes,23\nJ. Healy,129 A. Heidmann,104 A. Heidt,10, 11 M. C. Heintze,54 J. Heinze,10, 11 J. Heinzel,69 H. Heitmann,36 F. Hellman,193 P. Hello,45\nA. F. Helmling-Cornell,63 G. Hemming,46 M. Hendry,23 I. S. Heng,23 E. Hennes,27 J.-S. Hennig,26, 27 M. Hennig,26, 27 C. Henshaw,47\nA. G. Hernandez,194 F. Hernandez Vivanco,5 M. Heurs,10, 11 A. L. Hewitt,195 S. Higginbotham,16 S. Hild,26, 27 P. Hill,85 Y. Himemoto,196\nA. S. Hines,121 N. Hirata,19 C. Hirose,176 T-C. Ho,135 S. Hochheim,10, 11 D. Hofman,156 J. N. Hohmann,84 D. G. Holcomb,154\nN. A. Holland,27, 92 I. J. Hollows,155 Z. J. Holmes,82 K. Holt,54 D. E. Holz,166 Q. Hong,130 J. Hough,23 S. Hourihane,1 D. Howell,116, 117\nE. J. Howell,89 C. G. Hoy,16 D. Hoyland,106 A. Hreibi,10, 11 B-H. Hsieh,190 H-F. Hsieh,130 C. Hsiung,134 H-Y. Huang,138 P. Huang,179\nY-C. Huang,130 Y.-J. Huang,138 Y. Huang,69 M. T. H\u00a8ubner,5 A. D. Huddart,197 B. Hughey,35 D. C. Y. Hui,198 V. Hui,24 S. Husa,86\nS. H. Huttner,23 R. Huxford,6 T. Huynh-Dinh,54 J. Hyland,23 G. A. Iandolo,26 S. Ide,199 B. Idzkowski,107 A. Iess,151, 17 K. Inayoshi,200\nY. Inoue,135 P. Iosif,201 J. Irwin,23 Ish Gupta,6 M. Isi,116, 117 K. Ito,202 Y. Itoh,177, 203 B. R. Iyer,18 V. JaberianHamedan,89 T. Jacqmin,104\nP.-E. Jacquet,104 S. J. Jadhav,204 S. P. Jadhav,12 T. Jain,13 A. L. James,16 A. Z. Jan,170 K. Jani,178 J. Janquart,62, 27 K. Janssens,205, 36\nN. N. Janthalur,204 P. Jaranowski,206 D. Jariwala,71 S. Jarov,146 R. Jaume,86 A. C. Jenkins,57 K. Jenner,82 C. Jeon,207 W. Jia,69 J. Jiang,71\nH.-B. Jin,208, 209 G. R. Johns,105 R. Johnston,23 N. Johny,10, 11 A. W. Jones,89 D. I. Jones,210 P. Jones,106 R. Jones,23 P. Joshi,6 L. Ju,89 K. Jung,187\nP. Jung,59 J. Junker,10, 11 V. Juste,165 K. Kaihotsu,202 T. Kajita,211 M. Kakizaki,191 C. Kalaghatgi,62, 27, 212 V. Kalogera,66 B. Kamai,1\nM. Kamiizumi,192 N. Kanda,177, 203 S. Kandhasamy,12 G. Kang,213 J. B. Kanner,1 Y. Kao,130 S. J. Kapadia,18 D. P. Kapasi,9 S. Karat,1\nC. Karathanasis,31 S. Karki,91 R. Kashyap,6 M. Kasprzack,1 W. Kastaun,10, 11 T. Kato,190 S. Katsanevas,46 E. Katsavounidis,69 W. Katzman,54\nT. Kaur,89 K. Kawabe,67 K. Kawaguchi,190 F. K\u00b4ef\u00b4elian,36 D. Keitel,86 J. S. Key,214 S. Khadka,72 F. Y. Khalili,93 S. Khan,16 T. Khanam,145\nE. A. Khazanov,215 N. Khetan,32, 103 M. Khursheed,90 N. Kijbunchoo,9 C. Kim,207 J. C. Kim,216 J. Kim,217 K. Kim,207 P. Kim,218 W. S. Kim,59\nY.-M. Kim,187 C. Kimball,66 N. Kimura,192 B. King,219 M. Kinley-Hanlon,23 R. Kirchhoff,10, 11 J. S. Kissel,67 S. Klimenko,71 T. Klinger,16\nA. M. Knee,146 N. Knust,10, 11 Y. Kobayashi,177 P. Koch,10, 11 S. M. Koehlenbeck,10, 11 G. Koekoek,27, 26 K. Kohri,220 K. Kokeyama,16\nS. Koley,32 P. Kolitsidou,16 M. Kolstein,31 V. Kondrashov,1 A. K. H. Kong,130 A. Kontos,219 M. Korobko,84 R. V. Kossak,10, 11\nM. Kovalam,89 N. Koyama,176 D. B. Kozak,1 C. Kozakai,50 L. Kranzhoff,10, 11 V. Kringel,10, 11 N. V. Krishnendu,10, 11 A. Kr\u00b4olak,221, 161\nG. Kuehn,10, 11 P. Kuijer,27 S. Kulkarni,185 A. Kumar,204 Praveen Kumar,115 Prayush Kumar,18 Rahul Kumar,67 Rakesh Kumar,78 J. Kume,29\nK. Kuns,69 Y. Kuromiya,202 S. Kuroyanagi,222, 223 S. Kuwahara,189 K. Kwak,187 G. Lacaille,23 P. Lagabbe,24 D. Laghi,112 E. Lalande,224\nM. Lalleman,205 A. Lamberts,36, 225 M. Landry,67 B. B. Lane,69 R. N. Lang,69 J. Lange,170 B. Lantz,72 I. La Rosa,24 A. Lartaux-Vollard,45\nP. D. Lasky,5 J. Lawrence,145 M. Laxen,54 A. Lazzarini,1 C. Lazzaro,75, 76 P. Leaci,100, 55 S. Leavey,10, 11 S. LeBohec,159 Y. K. Lecoeuche,146\nE. Lee,190 H. M. Lee,226 K. Lee,218 R. Lee,130 I. N. Legred,1 J. Lehmann,10, 11 A. Lema\u02c6\u0131tre,227 M. Lenti,53, 228 M. Leonardi,19 E. Leonova,37\nN. Leroy,45 N. Letendre,24 C. Levesque,224 Y. Levin,5 J. N. Leviton,186 K. Leyde,44 A. K. Y. Li,1 B. Li,130 K. L. Li,229 P. Li,230 T. G. F. Li,131\nX. Li,136 C-Y. Lin,231 E. T. Lin,130 F-K. Lin,138 F-L. Lin,232 H. L. Lin,135 L. C.-C. Lin,229 F. Linde,212, 27 S. D. Linker,127, 194 T. B. Littenberg,233\nG. C. Liu,134 J. Liu,89 X. Liu,7 F. Llamas,149 R. K. L. Lo,1 T. Lo,130 L. T. London,37, 69 A. Longo,234 D. Lopez,163 M. Lopez Portilla,62\nM. Lorenzini,125, 126 V. Loriette,235 M. Lormand,54 G. Losurdo,17 T. P. Lott,47 J. D. Lough,10, 11 C. O. Lousto,129 G. Lovelace,43\nM. J. Lowry,105 J. F. Lucaccioni,60 H. L\u00a8uck,10, 11 D. Lumaca,125, 126 A. P. Lundgren,113 Y. Lung,131 L.-W. Luo,138 A. W. Lussier,224\nJ. E. Lynam,105 M. Ma\u2019arif,135 R. Macas,113 M. MacInnis,69 D. M. Macleod,16 I. A. O. MacMillan,1 A. Macquet,31, 36 I. Maga\u02dcna Hernandez,7\nC. Magazz`u,17 R. M. Magee,1 R. Maggiore,106, 27, 92 M. Magnozzi,88, 119 S. Mahesh,236 E. Majorana,100, 55 C. N. Makarem,1 I. Maksimovic,235\nS. Maliakal,1 A. Malik,90 N. Man,36 V. Mandic,83 V. Mangano,100, 55 B. R. Mannix,63 G. L. Mansell,64, 67, 69 G. Mansingh,41 M. Manske,7\nM. Mantovani,46 M. Mapelli,75, 76 F. Marchesoni,40, 39, 237 D. Mar\u00b4\u0131n Pina,30 F. Marion,24 Z. Mark,136 S. M\u00b4arka,147 Z. M\u00b4arka,147\nC. Markakis,183 A. S. Markosyan,72 A. Markowitz,1 E. Maros,1 A. Marquina,144 S. Marsat,112 F. Martelli,52, 53 I. W. Martin,23\nR. M. Martin,167 M. Martinez,31 V. A. Martinez,71 V. Martinez,114 K. Martinovic,57 D. V. Martynov,106 E. J. Marx,69 H. Masalehdan,84\nK. Mason,69 A. Masserot,24 M. Masso-Reid,23 S. Mastrogiovanni,44, 36 A. Matas,109 M. Mateu-Lucena,86 M. Matiushechkina,10, 11\nN. Mavalvala,69 J. J. McCann,89 R. McCarthy,67 D. E. McClelland,9 P. K. McClincy,6 S. McCormick,54 L. McCuller,1, 69 G. I. McGhee,23\nJ. McGinn,23 S. C. McGuire,54 C. McIsaac,113 J. McIver,146 A. McLeod,89 T. McRae,9 S. T. McWilliams,236 D. Meacher,7 M. Mehmet,10, 11\nA. K. Mehta,109 Q. Meijer,62 A. Melatos,122 G. Mendell,67 A. Menendez-Vazquez,31 C. S. Menoni,168 R. A. Mercer,7 L. Mereni,156\nK. Merfeld,63 E. L. Merilh,54 J. D. Merritt,63 M. Merzougui,36 C. Messenger,23 C. Messick,69 P. M. Meyers,136 F. Meylahn,10, 11\nA. Mhaske,12 A. Miani,95, 96 H. Miao,213 I. Michaloliakos,71 C. Michel,156 Y. Michimura,28 H. Middleton,122 D. P. Mihaylov,109 A. Miller,194\nA. L. Miller,56 B. Miller,37, 27 M. Millhouse,122 J. C. Mills,16 E. Milotti,238, 34 Y. Minenkov,126 N. Mio,239 Ll. M. Mir,31\nM. Miravet-Ten\u00b4es,128 A. Mishkin,71 C. Mishra,240 T. Mishra,71 T. Mistry,155 A. L. Mitchell,27, 92 S. Mitra,12 V. P. Mitrofanov,93\nG. Mitselmakher,71 R. Mittleman,69 O. Miyakawa,192 K. Miyo,192 S. Miyoki,192 Geoffrey Mo,69 L. M. Modafferi,86 E. Moguel,60\nK. Mogushi,91 S. R. P. Mohapatra,69 S. R. Mohite,7 M. Molina-Ruiz,193 C. Mondal,184 M. Mondin,194 M. Montani,52, 53 C. J. Moore,106\nJ. Moragues,86 D. Moraru,67 F. Morawski,80 A. More,12 S. More,12 C. Moreno,35 G. Moreno,67 Y. Mori,202 S. Morisaki,7 N. Morisue,177\nY. Moriwaki,191 B. Mours,165 C. M. Mow-Lowry,27, 92 S. Mozzon,113 F. Muciaccia,100, 55 D. Mukherjee,233 Soma Mukherjee,149\nSubroto Mukherjee,78 Suvodip Mukherjee,164, 37 N. Mukund,10, 11 A. Mullavey,54 J. Munch,82 E. A. Mu\u02dcniz,64 P. G. Murray,23 S. Muusse,82\nS. L. Nadji,10, 11 K. Nagano,241 A. Nagar,22, 242 T. Nagar,5 K. Nakamura,19 H. Nakano,243 M. Nakano,54, 190 Y. Nakayama,202 V. Napolano,46\nI. Nardecchia,125, 126 H. Narola,62 L. Naticchioni,55 R. K. Nayak,244 B. F. Neil,89 J. Neilson,81, 99 A. Nelson,121 T. J. N. Nelson,54 M. Nery,10, 11\nP. Neubauer,60 A. Neunzert,214 K. Y. Ng,69 S. W. S. Ng,82 C. Nguyen,44, 245 P. Nguyen,63 T. Nguyen,69 L. Nguyen Quynh,246 J. Ni,83\nW.-T. Ni,208, 179, 130 S. A. Nichols,8 G. Nieradka,80 T. Nishimoto,190 A. Nishizawa,29 S. Nissanke,37, 27 E. Nitoglia,139 W. Niu,6 F. Nocera,46\nM. Norman,16 C. North,16 J. Notte,167 J. Novak,247, 248, 249, 245, 250 S. Nozaki,191 G. Nurbek,149 L. K. Nuttall,113 Y. Obayashi,190 J. Oberling,67\nB. D. O\u2019Brien,71 J. O\u2019Dell,197 E. Oelker,23 M. Oertel,247, 248, 249, 245, 250 W. Ogaki,190 G. Oganesyan,32, 103 J. J. Oh,59 K. Oh,198 S. H. Oh,59\nT. O\u2019Hanlon,54 M. Ohashi,192 T. Ohashi,177 M. Ohkawa,176 F. Ohme,10, 11 H. Ohta,29 Y. Okutani,199 R. Oliveri,251 C. Olivetto,247\nK. Oohara,190, 252 R. Oram,54 B. O\u2019Reilly,54 R. G. Ormiston,83 N. D. Ormsby,105 M. Orselli,39, 74 R. O\u2019Shaughnessy,129 E. O\u2019Shea,253\nS. Oshino,192 S. Ossokine,109 C. Osthelder,1 S. Otabe,2 D. J. Ottaway,82 H. Overmier,54 A. E. Pace,6 G. Pagano,73, 17 R. Pagano,8\nG. Pagliaroli,32, 103 A. Pai,102 S. A. Pai,90 S. Pal,244 J. R. Palamos,63 O. Palashov,215 C. Palomba,55 K.-C. Pan,130 P. K. Panda,204\nP. T. H. Pang,27, 62 F. Pannarale,100, 55 B. C. Pant,90 F. H. Panther,89 F. Paoletti,17 A. Paoli,46 A. Paolone,55, 254 G. Pappas,201 A. Parisi,17, 151, 134\nJ. Park,255 W. Parker,54 D. Pascucci,79 A. Pasqualetti,46 R. Passaquieti,73, 17 D. Passuello,17 M. Patel,105 N. R. Patel,67 M. Pathak,82\nB. Patricelli,73, 17 A. S. Patron,8 S. Paul,63 E. Payne,1 M. Pedraza,1 R. Pedurand,99 R. Pegna,17, 73 M. Pegoraro,76 A. Pele,54\n\n22\nF. E. Pe\u02dcna Arellano,192 S. Penano,72 S. Penn,256 A. Perego,95, 96 A. Pereira,114 T. Pereira,257 C. J. Perez,67 C. P\u00b4erigois,140 C. C. Perkins,71\nA. Perreca,95, 96 S. Perri`es,139 J. W. Perry,27, 92 D. Pesios,201 J. Petermann,84 H. P. Pfeiffer,109 H. Pham,54 K. A. Pham,83 K. S. Phukon,27, 212\nH. Phurailatpam,131 O. J. Piccinni,55, 31 M. Pichot,36 M. Piendibene,73, 17 F. Piergiovanni,52, 53 L. Pierini,100, 55 G. Pierra,139 V. Pierro,81, 99\nG. Pillant,46 M. Pillas,45 F. Pilo,17 L. Pinard,156 C. Pineda-Bosque,194 I. M. Pinto,81, 99, 258, 25 M. Pinto,46 B. J. Piotrzkowski,7\nK. Piotrzkowski,56 M. Pirello,67 M. D. Pitkin,195 A. Placidi,39, 74 E. Placidi,100, 55 M. L. Planas,86 W. Plastino,259, 234 R. Poggiani,73, 17\nE. Polini,24 D. Y. T. Pong,131 S. Ponrathnam,12 E. K. Porter,44 C. Posnansky,6 R. Poulton,46 J. Powell,141 M. Pracchia,24 T. Pradier,165\nA. K. Prajapati,78 K. Prasai,72 R. Prasanna,204 G. Pratten,106 M. Principe,81, 258, 99 G. A. Prodi,260, 96 L. Prokhorov,106 P. Prosposito,125, 126\nL. Prudenzi,109 A. Puecher,27, 62 M. Punturo,39 F. Puosi,17, 73 P. Puppo,55 M. P\u00a8urrer,109 H. Qi,16 N. Quartey,105 V. Quetschke,149\nP. J. Quinonez,35 R. Quitzow-James,91 F. J. Raab,67 G. Raaijmakers,37, 27 H. Radkins,67 N. Radulesco,36 P. Raffai,152 S. X. Rail,224 S. Raja,90\nC. Rajan,90 K. E. Ramirez,54 T. D. Ramirez,43 A. Ramos-Buades,109 D. Rana,12 J. Rana,6 P. R. Rangnekar,72 P. Rapagnani,100, 55 A. Ray,7\nV. Raymond,16 N. Raza,146 M. Razzano,73, 17 J. Read,43 T. Regimbau,24 L. Rei,88 S. Reid,85 S. W. Reid,105 M. Reinhard,71 D. H. Reitze,1\nP. Relton,16 A. Renzini,1 P. Rettegno,21, 22 B. Revenu,44 J. Reyes,167 A. Reza,27 M. Rezac,43 A. S. Rezaei,55, 100 F. Ricci,100, 55 D. Richards,197\nJ. W. Richardson,261 L. Richardson,121 K. Riles,186 S. Rinaldi,73, 17 C. Robertson,197 N. A. Robertson,1 R. Robie,1 F. Robinet,45 A. Rocchi,126\nS. Rodriguez,43 L. Rolland,24 J. G. Rollins,1 M. Romanelli,101 R. Romano,3, 4 C. L. Romel,67 A. Romero,31 I. M. Romero-Shaw,5\nJ. H. Romie,54 S. Ronchini,32, 103 T. J. Roocke,82 L. Rosa,4, 25 C. A. Rose,7 D. Rosi\u00b4nska,107 M. P. Ross,262 M. Rossello,86 S. Rowan,23\nS. J. Rowlinson,106 Santosh Roy,12 Soumen Roy,62 A. Royzman,159 D. Rozza,123, 124 P. Ruggi,46 K. Ruiz-Rocha,178 K. Ryan,67 S. Sachdev,7\nT. Sadecki,67 J. Sadiq,115 P. Saffarieh,27, 92 S. Saha,130 Y. Saito,192 K. Sakai,263 M. Sakellariadou,57 S. Sakon,6 F. Salces-Carcoba,1\nL. Salconi,46 M. Saleem,83 F. Salemi,95, 96 M. Sall\u00b4e,27 A. Samajdar,111 E. J. Sanchez,1 J. H. Sanchez,43 L. E. Sanchez,1 N. Sanchis-Gual,264, 128\nJ. R. Sanders,265 A. Sanuy,30 T. R. Saravanan,12 N. Sarin,5 A. Sasli,201 B. Sassolas,156 H. Satari,89 B. S. Sathyaprakash,6, 16 O. Sauter,71\nR. L. Savage,67 V. Savant,12 T. Sawada,177 H. L. Sawant,12 S. Sayah,156 D. Schaetzl,1 M. Scheel,136 J. Scheuer,66 M. G. Schiworski,82\nP. Schmidt,106 S. Schmidt,62 R. Schnabel,84 M. Schneewind,10, 11 R. M. S. Schofield,63 A. Sch\u00a8onbeck,84 B. W. Schulte,10, 11 B. F. Schutz,16, 10, 11\nE. Schwartz,16 J. Scott,23 S. M. Scott,9 M. Seglar-Arroyo,24 Y. Sekiguchi,266 D. Sellers,54 A. S. Sengupta,267 D. Sentenac,46 E. G. Seo,131\nV. Sequino,25, 4 A. Sergeev,215 G. Servignat,248 Y. Setyawati,62 T. Shaffer,67 M. S. Shahriar,66 M. A. Shaikh,18 B. Shams,159 L. Shao,200\nA. Sharma,32, 103 P. Sharma,90 P. Shawhan,108 N. S. Shcheblanov,227 A. Sheela,240 E. Sheridan,178 Y. Shikano,268, 269 M. Shikauchi,29\nH. Shimizu,270 K. Shimode,192 H. Shinkai,271 T. Shishido,51 A. Shoda,19 D. H. Shoemaker,69 D. M. Shoemaker,170 S. ShyamSundar,90\nM. Sieniawska,56 D. Sigg,67 L. Silenzi,39, 40 L. P. Singer,118 D. Singh,6 M. K. Singh,18 N. Singh,107 A. Singha,26, 27 A. M. Sintes,86\nV. Sipala,123, 124 V. Skliris,16 B. J. J. Slagmolen,9 T. J. Slaven-Blair,89 J. Smetana,106 J. R. Smith,43 L. Smith,23 R. J. E. Smith,5\nJ. Soldateschi,228, 272, 53 S. N. Somala,273 K. Somiya,2 I. Song,130 K. Soni,12 S. Soni,69 V. Sordini,139 F. Sorrentino,88 N. Sorrentino,73, 17\nR. Soulard,36 T. Souradeep,274, 12 V. Spagnuolo,26, 27 A. P. Spencer,23 M. Spera,75, 76 P. Spinicelli,46 A. K. Srivastava,78 V. Srivastava,64\nC. Stachie,36 F. Stachurski,23 D. A. Steer,44 J. Steinlechner,26, 27 S. Steinlechner,26, 27 N. Stergioulas,201 D. J. Stops,106 K. A. Strain,23\nL. C. Strang,122 G. Stratta,275, 55 M. D. Strong,8 A. Strunk,67 R. Sturani,257 A. L. Stuver,154 M. Suchenek,80 S. Sudhagar,12\nR. Sugimoto,276, 241 H. G. Suh,7 A. G. Sullivan,147 T. Z. Summerscales,277 L. Sun,9 S. Sunil,78 A. Sur,80 J. Suresh,29, 56 P. J. Sutton,16\nTakamasa Suzuki,176 Takanori Suzuki,2 Toshikazu Suzuki,190 B. L. Swinkels,27 A. Syx,165 M. J. Szczepa\u00b4nczyk,71 P. Szewczyk,107 M. Tacca,27\nH. Tagoshi,190 S. C. Tait,23 H. Takahashi,278 R. Takahashi,19 S. Takano,28 H. Takeda,28 M. Takeda,177 C. J. Talbot,85 C. Talbot,69\nN. Tamanini,112 K. Tanaka,279 Taiki Tanaka,190 Takahiro Tanaka,280 A. J. Tanasijczuk,56 S. Tanioka,192 D. B. Tanner,71 D. Tao,1 L. Tao,71\nR. D. Tapia,6 E. N. Tapia San Mart\u00b4\u0131n,27 C. Taranto,125 A. Taruya,281 J. D. Tasson,160 R. Tenorio,86 J. E. S. Terhune,154 L. Terkowski,84\nH. Themann,194 M. P. Thirugnanasambandam,12 M. Thomas,54 P. Thomas,67 S. Thomas,43 D. Thompson,160 E. E. Thompson,47 J. E. Thompson,16\nS. R. Thondapu,90 K. A. Thorne,54 E. Thrane,5 Shubhanshu Tiwari,163 Srishti Tiwari,12 V. Tiwari,16 A. M. Toivonen,83 A. E. Tolley,113\nT. Tomaru,19 T. Tomura,192 M. Tonelli,73, 17 A. Torres-Forn\u00b4e,128 C. I. Torrie,1 I. Tosta e Melo,124 E. Tournefier,24 D. T\u00a8oyr\u00a8a,9\nA. Trapananti,40, 39 F. Travasso,39, 40 G. Traylor,54 J. Trenado,30 M. Trevor,108 M. C. Tringali,46 A. Tripathee,186 L. Troiano,282, 99\nA. Trovato,34, 238 L. Trozzo,4, 192 R. J. Trudeau,1 D. Tsai,130 K. W. Tsang,27, 283, 62 T. Tsang,284 J-S. Tsao,232 M. Tse,69 R. Tso,136 S. Tsuchida,177\nL. Tsukada,6 D. Tsuna,29 T. Tsutsui,29 K. Turbang,285, 205 M. Turconi,36 C. Turski,79 D. Tuyenbayev,177 H. Ubach,30 A. S. Ubhi,106\nT. Uchiyama,192 R. P. Udall,1 A. Ueda,286 T. Uehara,287, 288 K. Ueno,29 G. Ueshima,289 C. S. Unnikrishnan,290 A. L. Urban,8 T. Ushiba,192\nA. Utina,26, 27 H. Vahlbruch,10, 11 N. Vaidya,1 G. Vajente,1 A. Vajpeyi,5 G. Valdes,121 M. Valentini,185, 95, 96 S. Vallero,22 V. Valsan,7\nN. van Bakel,27 M. van Beuzekom,27 M. van Dael,27, 291 J. F. J. van den Brand,26, 92, 27 C. Van Den Broeck,62, 27 D. C. Vander-Hyde,64\nA. Van de Walle,45 J. van Dongen,27, 92 H. van Haevermaet,205 J. V. van Heijningen,56 J. Vanosky,1 M. H. P. M. van Putten,292 Z. van Ranst,26\nN. van Remortel,205 M. Vardaro,212, 27 A. F. Vargas,122 V. Varma,109 M. Vas\u00b4uth,70 A. Vecchio,106 G. Vedovato,76 J. Veitch,23 P. J. Veitch,82\nJ. Venneberg,10, 11 G. Venugopalan,1 P. Verdier,139 D. Verkindt,24 P. Verma,161 Y. Verma,90 S. M. Vermeulen,16 D. Veske,147 F. Vetrano,52\nA. Vicer\u00b4e,52, 53 S. Vidyant,64 A. D. Viets,293 A. Vijaykumar,18 V. Villa-Ortega,115 J.-Y. Vinet,36 A. Virtuoso,238, 34 S. Vitale,69 H. Vocca,74, 39\nE. R. G. von Reis,67 J. S. A. von Wrangel,10, 11 C. Vorvick,67 S. P. Vyatchanin,93 L. E. Wade,60 M. Wade,60 K. J. Wagner,129 R. C. Walet,27\nM. Walker,105 G. S. Wallace,85 L. Wallace,1 J. Wang,179 J. Z. Wang,186 W. H. Wang,149 R. L. Ward,9 J. Warner,67 M. Was,24 T. Washimi,19\nN. Y. Washington,1 K. Watada,105 D. Watarai,189 J. Watchi,143 K. E. Wayt,60 B. Weaver,67 C. R. Weaving,113 S. A. Webster,23\nM. Weinert,10, 11 A. J. Weinstein,1 R. Weiss,69 C. M. Weller,262 R. A. Weller,178 F. Wellmann,10, 11 L. Wen,89 P. We\u00dfels,10, 11 K. Wette,9\nJ. T. Whelan,129 D. D. White,43 B. F. Whiting,71 C. Whittle,69 O. S. Wilk,60 D. Wilken,10, 11, 11 C. E. Williams,160 D. Williams,23\nM. J. Williams,23 A. R. Williamson,113 J. L. Willis,1 B. Willke,10, 11 C. C. Wipf,1 G. Woan,23 J. Woehler,10, 11 J. K. Wofford,129\nI. A. Wojtowicz,160 D. Wong,146 I. C. F. Wong,131 M. Wright,23 C. Wu,130 D. S. Wu,10, 11 H. Wu,130 D. M. Wysocki,7 L. Xiao,1 N. Yadav,80\nT. Yamada,270 H. Yamamoto,1 K. Yamamoto,191 T. Yamamoto,192 K. Yamashita,202 R. Yamazaki,199 F. W. Yang,159 K. Z. Yang,83 L. Yang,168\nY.-C. Yang,130 Y. Yang,294 Yang Yang,71 M. J. Yap,9 D. W. Yeeles,16 S.-W. Yeh,130 A. B. Yelikar,129 J. Yokoyama,29, 28 T. Yokozawa,192\nJ. Yoo,253 T. Yoshioka,202 Hang Yu,136 Haocun Yu,69 H. Yuzurihara,190 A. Zadro\u02d9zny,161 M. Zanolin,35 S. Zeidler,295 T. Zelenova,46\nJ.-P. Zendri,76 M. Zevin,166 M. Zhan,179 H. Zhang,232 J. Zhang,9 L. Zhang,1 R. Zhang,71 T. Zhang,106 Y. Zhang,121 C. Zhao,89 G. Zhao,143\nY. Zhao,190, 19 Yue Zhao,159 Y. Zheng,91 R. Zhou,193 X. J. Zhu,5 Z.-H. Zhu,120, 230 A. B. Zimmerman,170 M. E. Zucker,1, 69 and J. Zweizig1\n1LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n2Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n\n23\n6The Pennsylvania State University, University Park, PA 16802, USA\n7University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n8Louisiana State University, Baton Rouge, LA 70803, USA\n9OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n10Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n11Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n12Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n13University of Cambridge, Cambridge CB2 1TN, United Kingdom\n14Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n15Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n16Cardi\ufb00University, Cardi\ufb00CF24 3AA, United Kingdom\n17INFN, Sezione di Pisa, I-56127 Pisa, Italy\n18International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n19Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n20Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n21Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n22INFN Sezione di Torino, I-10125 Torino, Italy\n23SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n24Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n25Universit`a di Napoli \u201cFederico II\u201d, I-80126 Napoli, Italy\n26Maastricht University, 6200 MD Maastricht, Netherlands\n27Nikhef, 1098 XG Amsterdam, Netherlands\n28Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n29Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n30Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, 08028, Spain\n31Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n32Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n33Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n34INFN, Sezione di Trieste, I-34127 Trieste, Italy\n35Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n36Artemis, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n37GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n38Department of Physics, National and Kapodistrian University of Athens, 15771 Ilissia, Greece\n39INFN, Sezione di Perugia, I-06123 Perugia, Italy\n40Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n41American University, Washington, D.C. 20016, USA\n42Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan\n43California State University Fullerton, Fullerton, CA 92831, USA\n44Universit\u00b4e de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France\n45Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n46European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n47Georgia Institute of Technology, Atlanta, GA 30332, USA\n48Department of Mathematics and Physics, Graduate School of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan\n49Royal Holloway, University of London, London TW20 0EX, United Kingdom\n50Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan\n52Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n53INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n54LIGO Livingston Observatory, Livingston, LA 70754, USA\n55INFN, Sezione di Roma, I-00185 Roma, Italy\n56Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n57King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n58Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n59National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n60Kenyon College, Gambier, OH 43022, USA\n61School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki 305-0801, Japan\n62Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, Netherlands\n\n24\n63University of Oregon, Eugene, OR 97403, USA\n64Syracuse University, Syracuse, NY 13244, USA\n65Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n66Northwestern University, Evanston, IL 60208, USA\n67LIGO Hanford Observatory, Richland, WA 99352, USA\n68Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno, Italy\n69LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n70Wigner RCP, RMKI, H-1121 Budapest, Hungary\n71University of Florida, Gainesville, FL 32611, USA\n72Stanford University, Stanford, CA 94305, USA\n73Universit`a di Pisa, I-56127 Pisa, Italy\n74Universit`a di Perugia, I-06123 Perugia, Italy\n75Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n76INFN, Sezione di Padova, I-35131 Padova, Italy\n77Montana State University, Bozeman, MT 59717, USA\n78Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n79Universiteit Gent, B-9000 Gent, Belgium\n80Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n81Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n82OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n83University of Minnesota, Minneapolis, MN 55455, USA\n84Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n85SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n86IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n87Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain\n88INFN, Sezione di Genova, I-16146 Genova, Italy\n89OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n90RRCAT, Indore, Madhya Pradesh 452013, India\n91Missouri University of Science and Technology, Rolla, MO 65409, USA\n92Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n93Lomonosov Moscow State University, Moscow 119991, Russia\n94Center for Theoretical Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland\n95Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n96INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n97Bar-Ilan University, Ramat Gan, 5290002, Israel\n98Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n99INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n100Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n101Univ Rennes, CNRS, Institut FOTON - UMR 6082, F-3500 Rennes, France\n102Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n103INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n104Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n105Christopher Newport University, Newport News, VA 23606, USA\n106University of Birmingham, Birmingham B15 2TT, United Kingdom\n107Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n108University of Maryland, College Park, MD 20742, USA\n109Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n110Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n111INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n112L2IT, Laboratoire des 2 In\ufb01nis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n113University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n114Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n115IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n116Stony Brook University, Stony Brook, NY 11794, USA\n117Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n118NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n119Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n\n25\n120Department of Astronomy, Beijing Normal University, Beijing 100875, China\n121Texas A&M University, College Station, TX 77843, USA\n122OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n123Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n124INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n125Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n126INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n127University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n128Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n129Rochester Institute of Technology, Rochester, NY 14623, USA\n130National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China\n131The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n132Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n133OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n134Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan\n135Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City 32001, Taiwan\n136CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n137Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n138Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan\n139Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n140INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n141OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n142Universit\u00b4e libre de Bruxelles, 1050 Bruxelles, Belgium\n143Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n144Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n145Texas Tech University, Lubbock, TX 79409, USA\n146University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n147Columbia University, New York, NY 10027, USA\n148University of Rhode Island, Kingston, RI 02881, USA\n149The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n150Bellevue College, Bellevue, WA 98007, USA\n151Scuola Normale Superiore, I-56126 Pisa, Italy\n152E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n153Chennai Mathematical Institute, Chennai 603103, India\n154Villanova University, Villanova, PA 19085, USA\n155The University of She\ufb03eld, She\ufb03eld S10 2TN, United Kingdom\n156Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne,\nFrance\n157Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n158INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n159The University of Utah, Salt Lake City, UT 84112, USA\n160Carleton College, North\ufb01eld, MN 55057, USA\n161National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n162Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00b4e, CNRS, UMR 7095, 75014 Paris, France\n163University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n164Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n165Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n166University of Chicago, Chicago, IL 60637, USA\n167Montclair State University, Montclair, NJ 07043, USA\n168Colorado State University, Fort Collins, CO 80523, USA\n169Institute for Nuclear Research, H-4026 Debrecen, Hungary\n170University of Texas, Austin, TX 78712, USA\n171CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n172Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n173Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n174Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n175Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan\n\n26\n176Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n177Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n178Vanderbilt University, Nashville, TN 37235, USA\n179State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology\n(APM), Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, China\n180SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n181University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n182INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n183Queen Mary, University of London, London E1 4NS, United Kingdom\n184Universit\u00b4e de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n185The University of Mississippi, University, MS 38677, USA\n186University of Michigan, Ann Arbor, MI 48109, USA\n187Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n188Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China\n189University of Tokyo, Tokyo, 113-0033, Japan.\n190Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n191Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n192Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n193University of California, Berkeley, CA 94720, USA\n194California State University, Los Angeles, Los Angeles, CA 90032, USA\n195Lancaster University, Lancaster LA1 4YW, United Kingdom\n196College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan\n197Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n198Department of Astronomy & Space Science, Chungnam National University, Yuseong-gu, Daejeon 34134, Republic of Korea\n199Department of Physical Sciences, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan\n200Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian District, Beijing 100871, China\n201Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n202Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan\n203Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n204Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n205Universiteit Antwerpen, 2000 Antwerpen, Belgium\n206University of Bia\u0142ystok, 15-424 Bia\u0142ystok, Poland\n207Ewha Womans University, Seoul 03760, Republic of Korea\n208National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, China\n209School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, China\n210University of Southampton, Southampton SO17 1BJ, United Kingdom\n211Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n212Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, Netherlands\n213\n214University of Washington Bothell, Bothell, WA 98011, USA\n215Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n216Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n217Department of Physics, Myongji University, Yongin 17058, Republic of Korea\n218Sungkyunkwan University, Seoul 03063, Republic of Korea\n219Bard College, Annandale-On-Hudson, NY 12504, USA\n220Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n221Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n222Instituto de Fisica Teorica, 28049 Madrid, Spain\n223Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n224Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n225Laboratoire Lagrange, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n226Seoul National University, Seoul 08826, Republic of Korea\n227NAVIER, \u00b4Ecole des Ponts, Univ Gustave Ei\ufb00el, CNRS, Marne-la-Vall\u00b4ee, France\n228Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n229Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan\n230School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China\n231National Center for High-performance computing, National Applied Research Laboratories, Hsinchu Science Park, Hsinchu City 30076, Taiwan\n\n27\n232Department of Physics, National Taiwan Normal University, sec. 4, Taipei 116, Taiwan\n233NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n234INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n235ESPCI, CNRS, F-75005 Paris, France\n236West Virginia University, Morgantown, WV 26506, USA\n237School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n238Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n239Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan\n240Indian Institute of Technology Madras, Chennai 600036, India\n241Institute of Space and Astronautical Science (JAXA), Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan\n242Institut des Hautes Etudes Scienti\ufb01ques, F-91440 Bures-sur-Yvette, France\n243Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n244Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n245Universit\u00b4e de Paris, 75006 Paris, France\n246Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA\n247Centre national de la recherche scienti\ufb01que, 75016 Paris, France\n248Laboratoire Univers et Th\u00b4eories, Observatoire de Paris, 92190 Meudon, France\n249Observatoire de Paris, 75014 Paris, France\n250Universit\u00b4e PSL, 75006 Paris, France\n251Institute of Physics of the Czech Academy of Sciences, 182 00 Praha 8, Czechia\n252Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n253Cornell University, Ithaca, NY 14850, USA\n254Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n255Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea\n256Hobart and William Smith Colleges, Geneva, NY 14456, USA\n257International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n258Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n259Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n260Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n261University of California, Riverside, Riverside, CA 92521, USA\n262University of Washington, Seattle, WA 98195, USA\n263Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, Nagaoka City, Niigata 940-8532, Japan\n264Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications, 3810-183 Aveiro, Portugal\n265Marquette University, Milwaukee, WI 53233, USA\n266Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan\n267Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n268Graduate School of Science and Technology, Gunma University, Maebashi, Gunma 371-8510, Japan\n269Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA\n270Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n271Faculty of Information Science and Technology, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan\n272INAF, Osservatorio Astro\ufb01sico di Arcetri, I-50125 Firenze, Italy\n273Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n274Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n275Istituto di Astro\ufb01sica e Planetologia Spaziali di Roma, 00133 Roma, Italy\n276Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City, Kanagawa 252-5210, Japan\n277Andrews University, Berrien Springs, MI 49104, USA\n278Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, Setagaya, Tokyo 158-0082, Japan\n279Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n280Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n281Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n282Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n283Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG Groningen, Netherlands\n284Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n285Vrije Universiteit Brussel, 1050 Brussel, Belgium\n286Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n287Department of Communications Engineering, National Defense Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan\n288Department of Physics, University of Florida, Gainesville, FL 32611, USA\n\n28\n289Department of Information and Management Systems Engineering, Nagaoka University of Technology, Nagaoka City, Niigata 940-2188, Japan\n290Tata Institute of Fundamental Research, Mumbai 400005, India\n291Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands\n292Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea\n293Concordia University Wisconsin, Mequon, WI 53097, USA\n294Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan\n295Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan\n\u2217Deceased, December 2021.\n", "Model-based Cross-correlation Search for Gravitational Waves from the Low-mass\nX-Ray Binary Scorpius X-1 in LIGO O3 Data\nR. Abbott1, H. Abe2, F. Acernese3,4, K. Ackley5\n, S. Adhicary6, N. Adhikari7\n, R. X. Adhikari1\n, V. K. Adkins8, V. B. Adya9,\nC. Affeldt10,11, D. Agarwal12, M. Agathos13,14\n, O. D. Aguiar15\n, L. Aiello16\n, A. Ain17, P. Ajith18\n, T. Akutsu19,20\n,\nS. Albanesi21,22, R. A. Alfaidi23, C. All\u00e9n\u00e924, A. Allocca4,25\n, P. A. Altin9\n, A. Amato26,27\n, S. Anand1, A. Ananyeva1,\nS. B. Anderson1\n, W. G. Anderson1\n, M. Ando28,29, T. Andrade30, N. Andres24\n, M. Andr\u00e9s-Carcasona31\n, T. Andri\u010732\n,\nS. Ansoldi33,34, J. M. Antelis35\n, S. Antier36,37\n, T. Apostolatos38, E. Z. Appavuravther39,40, S. Appert1, S. K. Apple41,\nK. Arai1\n, A. Araya42\n, M. C. Araya1\n, J. S. Areeda43\n, M. Ar\u00e8ne44, N. Aritomi19\n, N. Arnaud45,46\n, M. Arogeti47,\nS. M. Aronson8, H. Asada48\n, G. Ashton49\n, Y. Aso50,51\n, M. Assiduo52,53, S. Assis de Souza Melo46, S. M. Aston54,\nP. Astone55\n, F. Aubin53\n, K. AultONeal35\n, S. Babak44\n, F. Badaracco56\n, C. Badger57, S. Bae58, Y. Bae59,\nS. Bagnasco22\n, Y. Bai1, J. G. Baier60, J. Baird44, R. Bajpai61\n, T. Baka62, M. Ball63, G. Ballardin46, S. W. Ballmer64,\nG. Baltus65\n, S. Banagiri66\n, B. Banerjee32\n, D. Bankar12\n, J. C. Barayoga1, B. C. Barish1, D. Barker67, P. Barneo30\n,\nF. Barone4,68\n, B. Barr23\n, L. Barsotti69\n, M. Barsuglia44\n, D. Barta70\n, J. Bartlett67, M. A. Barton23\n, I. Bartos71,\nS. Basak18, R. Bassiri72\n, A. Basti17,73, M. Bawaj39,74\n, J. C. Bayley23\n, M. Bazzan75,76, B. B\u00e9csy77\n, V. M. Bedakihale78,\nF. Beirnaert79\n, M. Bejger80\n, I. Belahcene45, A. S. Bell23\n, V. Benedetto81, D. Beniwal82, W. Benoit83\n, J. D. Bentley84\n,\nM. BenYaala85, S. Bera86, M. Berbel87\n, F. Bergamin10,11, B. K. Berger72\n, S. Bernuzzi14\n, M. Beroiz1\n, D. Bersanetti88\n,\nA. Bertolini27, J. Betzwieser54\n, D. Beveridge89\n, R. Bhandare90, A. V. Bhandari12, U. Bhardwaj27,37\n, R. Bhatt1,\nD. Bhattacharjee60,91\n, S. Bhaumik71\n, A. Bianchi27,92, I. A. Bilenko93, M. Bilicki94\n, G. Billingsley1\n, S. Bini95,96,\nO. Birnholtz97\n, S. Biscans1,69, M. Bischi52,53, S. Biscoveanu69\n, A. Bisht10,11, B. Biswas12\n, M. Bitossi17,46,\nM.-A. Bizouard36\n, J. K. Blackburn1\n, C. D. Blair54,89, D. G. Blair89, R. M. Blair67, F. Bobba98,99, N. Bode10,11\n, M. Bo\u00ebr36,\nG. Bogaert36, M. Boldrini55,100, G. N. Bolingbroke82\n, L. D. Bonavena75, R. Bondarescu30\n, F. Bondu101, E. Bonilla72\n,\nR. Bonnand24\n, P. Booker10,11, R. Bork1, V. Boschi17\n, N. Bose102, S. Bose12, V. Bossilkov89, V. Boudart65\n,\nY. Bouffanais75,76, A. Bozzi46, C. Bradaschia17, P. R. Brady7,298\n, A. Bramley54, A. Branch54, M. Branchesi32,103\n,\nJ. E. Brau63\n, M. Breschi14\n, T. Briant104\n, J. H. Briggs23, A. Brillet36, M. Brinkmann10,11, P. Brockill7, A. F. Brooks1\n,\nJ. Brooks46, D. D. Brown82, S. Brunett1, G. Bruno56, R. Bruntz105\n, J. Bryant106, F. Bucci53, J. Buchanan105, T. Bulik107,\nH. J. Bulten27, A. Buonanno108,109\n, K. Burtnyk67, R. Buscicchio106,110,111\n, D. Buskulic24, C. Buy112\n, R. L. Byer72,\nG. S. Cabourn Davies113\n, G. Cabras33,34\n, R. Cabrita56\n, L. Cadonati47\n, G. Cagnoli114\n, C. Cahillane67,\nJ. Calder\u00f3n Bustillo115, J. D. Callaghan23, T. A. Callister116,117, E. Calloni4,25, J. B. Camp118, M. Canepa88,119, G. Caneva31\n,\nM. Cannavacciuolo98, K. C. Cannon29\n, H. Cao82, Z. Cao120\n, L. A. Capistran121, E. Capocasa19,44\n, E. Capote64,\nG. Carapella98,99, F. Carbognani46, M. Carlassara10,11, J. B. Carlin122\n, M. Carpinelli46,123,124, G. Carrillo63, J. J. Carter10,11\n,\nG. Carullo17,73\n, J. Casanueva Diaz46, C. Casentini125,126, G. Castaldi127, S. Caudill27,62, M. Cavagli\u00e091\n, F. Cavalier45\n,\nR. Cavalieri46\n, G. Cella17\n, P. Cerd\u00e1-Dur\u00e1n128, E. Cesarini126\n, W. Chaibi36, W. Chakalis116,117,\nS. Chalathadka Subrahmanya84\n, E. Champion129\n, C.-H. Chan130, C. Chan29, C. L. Chan131\n, K. Chan131, M. Chan132,\nK. Chandra102, I. P. Chang130, W. Chang130, P. Chanial44,46\n, S. Chao130, C. Chapman-Bird23\n, P. Charlton133\n,\nE. Chassande-Mottin44\n, C. Chatterjee89\n, Debarati Chatterjee12\n, Deep Chatterjee7\n, M. Chaturvedi90, S. Chaty44\n,\nC. Chen130,134\n, D. Chen50\n, H. Y. Chen69\n, J. Chen69\n, K. Chen135, X. Chen89, Y.-B. Chen136, Y.-R. Chen130, Y. Chen136,\nH. Cheng71, P. Chessa17,73\n, H. Y. Cheung131, H. Y. Chia71, F. Chiadini99,137\n, C-Y. Chiang138, G. Chiarini76, R. Chierici139,\nA. Chincarini88\n, M. L. Chiofalo17,73, A. Chiummo46\n, R. K. Choudhary89, S. Choudhary12\n, N. Christensen36\n, Q. Chu89,\nY-K. Chu138, S. S. Y. Chua9\n, K. W. Chung57, G. Ciani75,76\n, P. Ciecielag80, M. Cie\u015blar80\n, M. Cifaldi125,126, A. A. Ciobanu82,\nR. Ciol\ufb0176,140\n, F. Clara67, J. A. Clark1\n, T. A. Clarke5, P. Clearwater141, S. Clesse142, F. Cleva36, E. Coccia32,103,\nE. Codazzo32\n, P.-F. Cohadon104\n, D. E. Cohen45\n, M. Colleoni86\n, C. G. Collette143, A. Colombo110,111\n, M. Colpi110,111,\nC. M. Compton67, L. Conti76\n, S. J. Cooper106, P. Corban54, T. R. Corbitt8\n, I. Cordero-Carri\u00f3n144\n, S. Corezzi39,74,\nN. J. Cornish77\n, A. Corsi145\n, S. Cortese46\n, A. C. Coschizza146, R. Cotesta109, R. Cottingham54, M. W. Coughlin83\n,\nJ.-P. Coulon36, S. T. Countryman147, B. Cousins6\n, P. Couvares1\n, D. M. Coward89, M. J. Cowart54, D. C. Coyne1\n,\nR. Coyne148\n, K. Craig85, J. D. E. Creighton7\n, T. D. Creighton149, A. W. Criswell83\n, M. Croquette104\n, S. G. Crowder150,\nJ. R. Cudell65\n, T. J. Cullen8, A. Cumming23, R. Cummings23\n, E. Cuoco17,46,151, M. Cury\u0142o107, P. Dabadie114,\nT. Dal Canton45\n, S. Dall\u2019Osso55\n, G. D\u00e1lya79,152\n, A. Dana72, B. D\u2019Angelo88,119\n, S. Danilishin26,27\n, S. D\u2019Antonio126,\nK. Danzmann10,11, C. Darsow-Fromm84\n, A. Dasgupta78, L. E. H. Datrier23, Sayantani Datta153\n, V. Dattilo46, I. Dave90,\nM. Davier45, D. Davis1\n, M. C. Davis154\n, E. J. Daw155\n, M. Dax109\n, D. De Bra72,299, M. Deenadayalan12, J. Degallaix156\n,\nM. De Laurentis4,25, S. Del\u00e9glise104\n, V. Del Favero129\n, F. De Lillo56\n, N. De Lillo23, D. Dell\u2019Aquila123,124\n,\nW. Del Pozzo17,73, F. De Matteis125,126, V. D\u2019Emilio16, N. Demos69, T. Dent115\n, A. Depasse56\n, R. De Pietri157,158\n,\nR. De Rosa4,25\n, C. De Rossi46, R. DeSalvo127,159\n, R. De Simone137, S. Dhurandhar12, R. Diab71, M. C. D\u00edaz149\n,\nN. A. Didio64, T. Dietrich109\n, L. Di Fiore4, C. Di Fronzo106, C. Di Giorgio98,99\n, F. Di Giovanni128\n, M. Di Giovanni32,\nT. Di Girolamo4,25\n, D. Diksha26,27, A. Di Lieto17,73\n, A. Di Michele74\n, S. Di Pace55,100\n, I. Di Palma55,100\n,\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nhttps://doi.org/10.3847/2041-8213/aca1b0\n\u00a9 2022. The Author(s). Published by the American Astronomical Society.\n1\n\nF. Di Renzo17,73\n, A. K. Divakarla71, A. Dmitriev106\n, Z. Doctor66\n, P. P. Doleva105, L. Donahue160, L. D\u2019Onofrio4,25\n,\nF. Donovan69, K. L. Dooley16, T. Dooney62, S. Doravari12\n, O. Dorosh161, M. Drago55,100\n, J. C. Driggers67\n, Y. Drori1,\nJ.-G. Ducoin44,162, L. Dunn122\n, U. Dupletsa32, O. Durante98,99, D. D\u2019Urso123,124\n, P.-A. Duverne45, S. E. Dwyer67, C. Eassa67,\nP. J. Easter5, M. Ebersold163, T. Eckhardt84\n, G. Eddolls23\n, B. Edelman63\n, T. B. Edo1, O. Edy113\n, A. Ef\ufb02er54\n,\nS. Eguchi132\n, J. Eichholz9\n, S. S. Eikenberry71, M. Eisenmann19,24, R. A. Eisenstein69, A. Ejlli16\n, E. Engelby43,\nY. Enomoto28\n, L. Errico4,25, R. C. Essick164\n, H. Estell\u00e9s86, D. Estevez165\n, T. Etzel1, M. Evans69\n, T. M. Evans54,\nT. Evstafyeva13, B. E. Ewing6, F. Fabrizi52,53\n, F. Faedi53, V. Fafone32,125,126\n, H. Fair64, S. Fairhurst16, P. C. Fan160\n,\nA. M. Farah166\n, B. Farr63\n, W. M. Farr116,117\n, G. Favaro75\n, M. Favata167\n, M. Fays65\n, M. Fazio168, J. Feicht1,\nM. M. Fejer72, E. Fenyvesi70,169\n, D. L. Ferguson170\n, A. Fernandez-Galiana69\n, I. Ferrante17,73\n, T. A. Ferreira15,\nF. Fidecaro17,73\n, P. Figura107\n, A. Fiori17,73\n, I. Fiori46\n, M. Fishbach66\n, R. P. Fisher105, R. Fittipaldi99,171,\nV. Fiumara99,172, R. Flaminio19,24, E. Floden83, H. K. Fong29, J. A. Font128,173\n, B. Fornal159\n, P. W. F. Forsyth9, A. Franke84,\nS. Frasca55,100, F. Frasconi17\n, J. P. Freed35, Z. Frei152\n, A. Freise27,92\n, O. Freitas174, R. Frey63\n, P. Fritschel69,\nV. V. Frolov54, G. G. Fronz\u00e922\n, Y. Fujii175, Y. Fujikawa176, Y. Fujimoto177, P. Fulda71, M. Fyffe54, H. A. Gabbard23,\nW. E. Gabella178, B. U. Gadre62,109\n, J. R. Gair109\n, J. Gais131, S. Galaudage5, R. Gamba14, D. Ganapathy69\n, A. Ganguly12\n,\nD.-F. Gao179\n, D. Gao72, S. G. Gaonkar12, B. Garaventa88,119\n, C. Garc\u00eda-N\u00fa\u00f1ez180, C. Garc\u00eda-Quir\u00f3s10,11,86, K. A. Gardner146,\nJ. Gargiulo46, F. Garu\ufb014,25\n, C. Gasbarra125,126\n, B. Gateley67, V. Gayathri71\n, G.-G. Ge179\n, G. Gemme88\n, A. Gennai17\n,\nJ. George90, O. Gerberding84\n, L. Gergely181\n, S. Ghonge47\n, Abhirup Ghosh109\n, Archisman Ghosh79\n, Shaon Ghosh167\n,\nShrobana Ghosh16, Tathagata Ghosh12\n, L. Giacoppo55,100, J. A. Giaime8,54\n, K. D. Giardina54, D. R. Gibson180, C. Gier85,\nP. Giri17,73\n, F. Gissi81, S. Gkaitatzis46\n, J. Glanzer8, A. E. Gleckl43, F. G. Godoy47, P. Godwin6, E. Goetz146\n, R. Goetz71\n,\nJ. Golomb1, B. Goncharov32\n, G. Gonz\u00e1lez8\n, M. Gosselin46, R. Gouaty24\n, D. W. Gould9, S. Goyal18, B. Grace9,\nA. Grado4,182\n, V. Graham23, M. Granata156\n, V. Granata98\n, S. Gras69, P. Grassia1, C. Gray67, R. Gray183\n, G. Greco39,\nA. C. Green71\n, R. Green16, A. M. Gretarsson35, E. M. Gretarsson35, D. Grif\ufb01th1, W. L. Grif\ufb01ths16\n, H. L. Griggs47\n,\nG. Grignani39,74, A. Grimaldi95,96\n, S. J. Grimm32,103, H. Grote16\n, S. Grunewald109, A. S. Gruson43, D. Guerra128\n,\nG. M. Guidi52,53\n, A. R. Guimaraes8, H. K. Gulati78, F. Gulminelli184, A. M. Gunny69, H.-K. Guo159\n, Y. Guo27, Anchal Gupta1,\nAnuradha Gupta185\n, P. Gupta27,62, S. K. Gupta102, J. Gurs84, R. Gustafson186, N. Gutierrez156, F. Guzman121\n, S. Ha187,\nI. P. W. Hadiputrawan135, L. Haegel44\n, S. Haino138, O. Halim34\n, E. D. Hall69\n, E. Z. Hamilton163, G. Hammond23,\nW.-B. Han188\n, M. Haney163\n, J. Hanks67, C. Hanna6, M. D. Hannam16, O. Hannuksela27,62, H. Hansen67, J. Hanson54,\nR. Harada189, T. Harder36, K. Haris27,62, J. Harms32,103\n, G. M. Harry41\n, I. W. Harry113\n, D. Hartwig84\n, K. Hasegawa190,\nB. Haskell80, C.-J. Haster69\n, J. S. Hathaway129, K. Hattori191, K. Haughian23\n, H. Hayakawa192, K. Hayama132, F. J. Hayes23,\nJ. Healy129\n, A. Heidmann104\n, A. Heidt10,11, M. C. Heintze54, J. Heinze10,11\n, J. Heinzel69, H. Heitmann36\n,\nF. Hellman193\n, P. Hello45, A. F. Helmling-Cornell63\n, G. Hemming46\n, M. Hendry23\n, I. S. Heng23, E. Hennes27\n,\nJ.-S. Hennig26,27, M. Hennig26,27, C. Henshaw47, A. G. Hernandez194, F. Hernandez Vivanco5, M. Heurs10,11\n, A. L. Hewitt195\n,\nS. Higginbotham16, S. Hild26,27, P. Hill85, Y. Himemoto196, A. S. Hines121, N. Hirata19, C. Hirose176, T-C. Ho135, S. Hochheim10,11,\nD. Hofman156, J. N. Hohmann84, D. G. Holcomb154\n, N. A. Holland27,92, I. J. Hollows155\n, Z. J. Holmes82\n, K. Holt54,\nD. E. Holz166\n, Q. Hong130, J. Hough23, S. Hourihane1, D. Howell116,117, E. J. Howell89\n, C. G. Hoy16\n, D. Hoyland106,\nA. Hreibi10,11, B-H. Hsieh190, H-F. Hsieh130\n, C. Hsiung134, H-Y. Huang138\n, P. Huang179\n, Y-C. Huang130\n,\nY.-J. Huang138\n, Y. Huang69, M. T. H\u00fcbner5\n, A. D. Huddart197, B. Hughey35, D. C. Y. Hui198\n, V. Hui24\n, S. Husa86,\nS. H. Huttner23, R. Huxford6, T. Huynh-Dinh54, J. Hyland23\n, G. A. Iandolo26, S. Ide199, B. Idzkowski107\n, A. Iess17,151\n,\nK. Inayoshi200\n, Y. Inoue135, P. Iosif201\n, J. Irwin23\n, Ish Gupta6\n, M. Isi116,117\n, K. Ito202, Y. Itoh177,203\n, B. R. Iyer18\n,\nV. JaberianHamedan89\n, T. Jacqmin104\n, P.-E. Jacquet104\n, S. J. Jadhav204, S. P. Jadhav12\n, T. Jain13, A. L. James16\n,\nA. Z. Jan170\n, K. Jani178\n, J. Janquart27,62, K. Janssens36,205\n, N. N. Janthalur204, P. Jaranowski206\n, D. Jariwala71, S. Jarov146,\nR. Jaume86\n, A. C. Jenkins57\n, K. Jenner82, C. Jeon207, W. Jia69, J. Jiang71\n, H.-B. Jin208,209\n, G. R. Johns105, R. Johnston23,\nN. Johny10,11, A. W. Jones89\n, D. I. Jones210, P. Jones106, R. Jones23, P. Joshi6, L. Ju89\n, K. Jung187, P. Jung59\n,\nJ. Junker10,11\n, V. Juste165, K. Kaihotsu202, T. Kajita211\n, M. Kakizaki191\n, C. Kalaghatgi27,62,212, V. Kalogera66\n, B. Kamai1,\nM. Kamiizumi192\n, N. Kanda177,203\n, S. Kandhasamy12\n, G. Kang213\n, J. B. Kanner1, Y. Kao130, S. J. Kapadia18,\nD. P. Kapasi9\n, S. Karat1, C. Karathanasis31\n, S. Karki91\n, R. Kashyap6, M. Kasprzack1\n, W. Kastaun10,11, T. Kato190,\nS. Katsanevas46,300\n, E. Katsavounidis69, W. Katzman54, T. Kaur89, K. Kawabe67, K. Kawaguchi190\n, F. K\u00e9f\u00e9lian36,\nD. Keitel86\n, J. S. Key214\n, S. Khadka72, F. Y. Khalili93\n, S. Khan16\n, T. Khanam145, E. A. Khazanov215, N. Khetan32,103,\nM. Khursheed90, N. Kijbunchoo9\n, C. Kim207\n, J. C. Kim216, J. Kim217\n, K. Kim207\n, P. Kim218, W. S. Kim59,\nY.-M. Kim187\n, C. Kimball66, N. Kimura192, B. King219, M. Kinley-Hanlon23\n, R. Kirchhoff10,11\n, J. S. Kissel67\n,\nS. Klimenko71, T. Klinger16, A. M. Knee146\n, N. Knust10,11, Y. Kobayashi177, P. Koch10,11, S. M. Koehlenbeck10,11\n,\nG. Koekoek26,27, K. Kohri220, K. Kokeyama16\n, S. Koley32\n, P. Kolitsidou16\n, M. Kolstein31\n, V. Kondrashov1,\nA. K. H. Kong130\n, A. Kontos219\n, M. Korobko84\n, R. V. Kossak10,11, M. Kovalam89, N. Koyama176, D. B. Kozak1,\nC. Kozakai50\n, L. Kranzhoff10,11, V. Kringel10,11, N. V. Krishnendu10,11\n, A. Kr\u00f3lak161,221\n, G. Kuehn10,11, P. Kuijer27\n,\nS. Kulkarni185\n, A. Kumar204, Praveen Kumar115\n, Prayush Kumar18\n, Rahul Kumar67, Rakesh Kumar78, J. Kume29,\nK. Kuns69\n, Y. Kuromiya202, S. Kuroyanagi222,223\n, S. Kuwahara189, K. Kwak187\n, G. Lacaille23, P. Lagabbe24, D. Laghi112\n,\nE. Lalande224, M. Lalleman205, A. Lamberts36,225, M. Landry67, B. B. Lane69, R. N. Lang69\n, J. Lange170, B. Lantz72\n,\n2\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nI. La Rosa24, A. Lartaux-Vollard45\n, P. D. Lasky5\n, J. Lawrence145, M. Laxen54\n, A. Lazzarini1\n, C. Lazzaro75,76,\nP. Leaci55,100\n, S. Leavey10,11\n, S. LeBohec159, Y. K. Lecoeuche146\n, E. Lee190, H. M. Lee226\n, H. W. Lee216\n, K. Lee218\n,\nR. Lee130\n, I. N. Legred1, J. Lehmann10,11, A. Lemai\u0302tre227, M. Lenti53,228\n, M. Leonardi19\n, E. Leonova37\n, N. Leroy45\n,\nN. Letendre24, C. Levesque224, Y. Levin5, J. N. Leviton186, K. Leyde44, A. K. Y. Li1, B. Li130, K. L. Li229\n, P. Li230,\nT. G. F. Li131, X. Li136\n, C-Y. Lin231\n, E. T. Lin130\n, F-K. Lin138, F-L. Lin232\n, H. L. Lin135\n, L. C.-C. Lin229\n,\nF. Linde27,212, S. D. Linker127,194, T. B. Littenberg233, G. C. Liu134\n, J. Liu89\n, X. Liu7, F. Llamas149, R. K. L. Lo1\n, T. Lo130,\nL. T. London37,69, A. Longo234\n, D. Lopez163, M. Lopez Portilla62, M. Lorenzini125,126\n, V. Loriette235, M. Lormand54,\nG. Losurdo17,301\n, T. P. Lott47, J. D. Lough10,11\n, C. O. Lousto129\n, G. Lovelace43, M. J. Lowry105, J. F. Lucaccioni60,\nH. L\u00fcck10,11, D. Lumaca125,126\n, A. P. Lundgren113, Y. Lung131, L.-W. Luo138\n, A. W. Lussier224\n, J. E. Lynam105,\nM. Ma\u2019arif135, R. Macas113\n, M. MacInnis69, D. M. Macleod16\n, I. A. O. MacMillan1\n, A. Macquet31,36\n,\nI. Maga na Hernandez7, C. Magazz\u00f917\n, R. M. Magee1\n, R. Maggiore27,92,106\n, M. Magnozzi88,119\n, S. Mahesh236,\nE. Majorana55,100, C. N. Makarem1, I. Maksimovic235, S. Maliakal1, A. Malik90, N. Man36, V. Mandic83\n, V. Mangano55,100\n,\nB. R. Mannix63, G. L. Mansell64,67,69\n, G. Mansingh41, M. Manske7\n, M. Mantovani46\n, M. Mapelli75,76\n,\nF. Marchesoni39,40,237, D. Mar\u00edn Pina30\n, F. Marion24\n, Z. Mark136, S. M\u00e1rka147\n, Z. M\u00e1rka147\n, C. Markakis183\n,\nA. S. Markosyan72, A. Markowitz1, E. Maros1, A. Marquina144, S. Marsat112\n, F. Martelli52,53, I. W. Martin23\n, R. M. Martin167,\nM. Martinez31, V. A. Martinez71, V. Martinez114\n, K. Martinovic57, D. V. Martynov106, E. J. Marx69, H. Masalehdan84\n,\nK. Mason69, A. Masserot24, M. Masso-Reid23\n, S. Mastrogiovanni36,44\n, A. Matas109, M. Mateu-Lucena86\n,\nM. Matiushechkina10,11\n, N. Mavalvala69\n, J. J. McCann89, R. McCarthy67, D. E. McClelland9\n, P. K. McClincy6,\nS. McCormick54, L. McCuller1,69\n, G. I. McGhee23, J. McGinn23, S. C. McGuire54, C. McIsaac113, J. McIver146\n,\nA. McLeod89\n, T. McRae9, S. T. McWilliams236, D. Meacher7\n, M. Mehmet10,11\n, A. K. Mehta109, Q. Meijer62, A. Melatos122,\nG. Mendell67, A. Menendez-Vazquez31\n, C. S. Menoni168\n, R. A. Mercer7\n, L. Mereni156, K. Merfeld63, E. L. Merilh54,\nJ. D. Merritt63, M. Merzougui36, C. Messenger23\n, C. Messick69, P. M. Meyers136\n, F. Meylahn10,11\n, A. Mhaske12,\nA. Miani95,96\n, H. Miao238, I. Michaloliakos71\n, C. Michel156\n, Y. Michimura28\n, H. Middleton122\n, D. P. Mihaylov109\n,\nA. Miller194, A. L. Miller56, B. Miller27,37, M. Millhouse122, J. C. Mills16, E. Milotti34,239\n, Y. Minenkov126, N. Mio240,\nLl. M. Mir31, M. Miravet-Ten\u00e9s128\n, A. Mishkin71, C. Mishra241, T. Mishra71\n, T. Mistry155, A. L. Mitchell27,92, S. Mitra12\n,\nV. P. Mitrofanov93\n, G. Mitselmakher71\n, R. Mittleman69, O. Miyakawa192\n, K. Miyo192\n, S. Miyoki192\n, Geoffrey Mo69\n,\nL. M. Modafferi86\n, E. Moguel60, K. Mogushi91, S. R. P. Mohapatra69, S. R. Mohite7\n, M. Molina-Ruiz193\n, C. Mondal184,\nM. Mondin194, M. Montani52,53, C. J. Moore106, J. Moragues86\n, D. Moraru67, F. Morawski80, A. More12\n, S. More12\n,\nC. Moreno35\n, G. Moreno67, Y. Mori202, S. Morisaki7\n, N. Morisue177, Y. Moriwaki191, B. Mours165\n,\nC. M. Mow-Lowry27,92\n, S. Mozzon113\n, F. Muciaccia55,100, D. Mukherjee233\n, Soma Mukherjee149, Subroto Mukherjee78,\nSuvodip Mukherjee37,164\n, N. Mukund10,11\n, A. Mullavey54, J. Munch82, E. A. Mu niz64\n, P. G. Murray23\n, S. Muusse82,\nS. L. Nadji10,11, K. Nagano242\n, A. Nagar22,243, T. Nagar5, K. Nakamura19\n, H. Nakano244\n, M. Nakano54,190, Y. Nakayama202,\nV. Napolano46, I. Nardecchia125,126\n, T. Narikawa190, H. Narola62, L. Naticchioni55\n, R. K. Nayak245\n, B. F. Neil89,\nJ. Neilson81,99, A. Nelson121, T. J. N. Nelson54, M. Nery10,11, P. Neubauer60, A. Neunzert214, K. Y. Ng69, S. W. S. Ng82\n,\nC. Nguyen44,246\n, P. Nguyen63, T. Nguyen69, L. Nguyen Quynh247\n, J. Ni83, W.-T. Ni130,179,208\n, S. A. Nichols8,\nG. Nieradka80, T. Nishimoto190, A. Nishizawa29\n, S. Nissanke27,37, E. Nitoglia139\n, W. Niu6, F. Nocera46, M. Norman16,\nC. North16, J. Notte167, J. Novak246,248,249,250,251\n, S. Nozaki191, G. Nurbek149, L. K. Nuttall113\n, Y. Obayashi190\n,\nJ. Oberling67, B. D. O\u2019Brien71, J. O\u2019Dell197, E. Oelker23\n, M. Oertel246,248,249,250,251\n, W. Ogaki190, G. Oganesyan32,103,\nJ. J. Oh59\n, K. Oh198\n, S. H. Oh59\n, T. O\u2019Hanlon54, M. Ohashi192\n, T. Ohashi177, M. Ohkawa176\n, F. Ohme10,11\n,\nH. Ohta29, Y. Okutani199, R. Oliveri252\n, C. Olivetto248, K. Oohara190,253\n, R. Oram54, B. O\u2019Reilly54\n, R. G. Ormiston83,\nN. D. Ormsby105, M. Orselli39,74\n, R. O\u2019Shaughnessy129\n, E. O\u2019Shea254\n, S. Oshino192\n, S. Ossokine109\n, C. Osthelder1,\nS. Otabe2, D. J. Ottaway82\n, H. Overmier54, A. E. Pace6, G. Pagano17,73, R. Pagano8, G. Pagliaroli32,103, A. Pai102, S. A. Pai90,\nS. Pal245, J. R. Palamos63, O. Palashov215, C. Palomba55\n, K.-C. Pan130\n, P. K. Panda204, P. T. H. Pang27,62, F. Pannarale55,100\n,\nB. C. Pant90, F. H. Panther89, F. Paoletti17\n, A. Paoli46, A. Paolone55,255, G. Pappas201, A. Parisi17,134,151\n, J. Park256\n,\nW. Parker54\n, D. Pascucci79\n, A. Pasqualetti46, R. Passaquieti17,73\n, D. Passuello17, M. Patel105, N. R. Patel67, M. Pathak82,\nB. Patricelli17,73\n, A. S. Patron8, S. Paul63\n, E. Payne1\n, M. Pedraza1, R. Pedurand99, R. Pegna17,73\n, M. Pegoraro76, A. Pele54,\nF. E. Pe na Arellano192\n, S. Penano72, S. Penn257\n, A. Perego95,96, A. Pereira114, T. Pereira258\n, C. J. Perez67, C. P\u00e9rigois140\n,\nC. C. 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P\u00fcrrer109\n, H. Qi16\n, N. Quartey105,\nV. Quetschke149, P. J. Quinonez35, R. Quitzow-James91, F. J. Raab67, G. Raaijmakers27,37, H. Radkins67, N. Radulesco36,\nP. Raffai152\n, S. X. Rail224, S. Raja90, C. Rajan90, K. E. Ramirez54\n, T. D. Ramirez43, A. Ramos-Buades109\n, D. Rana12,\n3\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nJ. Rana6, P. R. Rangnekar72, P. Rapagnani55,100, A. Ray7\n, V. Raymond16\n, N. Raza146\n, M. Razzano17,73\n, J. Read43,\nT. Regimbau24, L. Rei88\n, S. Reid85, S. W. Reid105, M. Reinhard71, D. H. Reitze1, P. Relton16\n, A. Renzini1, P. Rettegno21,22\n,\nB. Revenu44\n, J. Reyes167, A. Reza27, M. Rezac43, A. S. Rezaei55,100, F. Ricci55,100, D. Richards197, J. W. Richardson262\n,\nL. Richardson121, K. Riles186\n, S. Rinaldi17,73\n, C. Robertson197, N. A. Robertson1, R. Robie1, F. Robinet45, A. Rocchi126\n,\nS. Rodriguez43, L. Rolland24\n, J. G. Rollins1\n, M. Romanelli101, R. Romano3,4, C. L. Romel67, A. Romero31\n,\nI. M. Romero-Shaw5, J. H. Romie54, S. Ronchini32,103\n, T. J. Roocke82\n, L. Rosa4,25, C. A. Rose7, D. Rosi\u0144ska107,\nM. P. Ross263\n, M. Rossello86, S. Rowan23, S. J. Rowlinson106, Santosh Roy12, Soumen Roy62, A. Royzman159,\nD. Rozza123,124\n, P. Ruggi46, K. Ruiz-Rocha178, K. Ryan67, S. Sachdev7\n, T. Sadecki67, J. Sadiq115\n, P. Saffarieh27,92,\nS. Saha130\n, Y. Saito192, K. Sakai264, M. Sakellariadou57\n, S. Sakon6, O. S. Sala\ufb01a110,111,265\n, F. Salces-Carcoba1\n,\nL. Salconi46, M. Saleem83\n, F. Salemi95,96\n, M. Sall\u00e927\n, A. Samajdar111\n, E. J. Sanchez1, J. H. Sanchez43, L. E. Sanchez1,\nN. Sanchis-Gual128,266\n, J. R. Sanders267, A. Sanuy30\n, T. R. Saravanan12, N. Sarin5, A. Sasli201\n, B. Sassolas156, H. Satari89,\nB. S. Sathyaprakash6,16\n, O. Sauter71\n, R. L. Savage67\n, V. Savant12\n, T. Sawada177\n, H. L. Sawant12, S. Sayah156,\nD. Schaetzl1, M. Scheel136, J. Scheuer66, M. G. Schiworski82\n, P. Schmidt106\n, S. Schmidt62, R. Schnabel84\n,\nM. 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Tsang27,62,285, T. Tsang286\n, J-S. Tsao232, M. Tse69\n, R. Tso136,\nS. Tsuchida177, L. Tsukada6, D. Tsuna29\n, T. Tsutsui29\n, K. Turbang205,287\n, M. Turconi36, C. Turski79, D. Tuyenbayev177\n,\nH. Ubach30\n, A. S. Ubhi106\n, N. Uchikata190\n, T. Uchiyama192\n, R. P. Udall1\n, A. Ueda288, T. Uehara289,290\n,\nK. Ueno29\n, G. Ueshima291, C. S. Unnikrishnan292, A. L. Urban8, T. Ushiba192\n, A. Utina26,27\n, H. Vahlbruch10,11\n,\nN. Vaidya1\n, G. Vajente1\n, A. Vajpeyi5, G. Valdes121\n, M. Valentini95,96,185\n, S. Vallero22, V. Valsan7\n, N. van Bakel27,\nM. van Beuzekom27\n, M. van Dael27,293\n, J. F. J. van den Brand26,27,92\n, C. Van Den Broeck27,62, D. C. Vander-Hyde64,\nA. Van de Walle45, J. van Dongen27,92, H. van Haevermaet205\n, J. V. van Heijningen56\n, J. Vanosky1, M. H. P. M. van Putten294,\nZ. van Ranst26\n, N. van Remortel205\n, M. Vardaro27,212, A. F. Vargas122, V. Varma109\n, M. Vas\u00fath70\n, A. Vecchio106\n,\nG. Vedovato76, J. Veitch23\n, P. J. Veitch82\n, J. Venneberg10,11\n, G. Venugopalan1\n, P. Verdier139\n, D. Verkindt24\n,\nP. Verma161, Y. Verma90\n, S. M. Vermeulen16\n, D. Veske147\n, F. Vetrano52, A. Vicer\u00e952,53\n, S. Vidyant64, A. D. Viets295\n,\nA. Vijaykumar18\n, V. Villa-Ortega115\n, J.-Y. Vinet36, A. Virtuoso34,239, S. Vitale69\n, H. Vocca39,74, E. R. G. von Reis67,\nJ. S. A. von Wrangel10,11, C. Vorvick67\n, S. P. Vyatchanin93\n, L. E. Wade60, M. Wade60\n, K. J. Wagner129\n, R. C. Walet27,\nM. Walker105, G. S. Wallace85, L. Wallace1, J. Wang179\n, J. Z. Wang186, W. H. Wang149, R. L. Ward9, J. Warner67, M. Was24\n,\nT. Washimi19\n, N. Y. Washington1, K. Watada105, D. Watarai189, J. Watchi143\n, K. E. Wayt60, B. Weaver67, C. R. Weaving113,\nS. A. Webster23, M. Weinert10,11, A. J. Weinstein1\n, R. Weiss69, C. M. Weller263, R. A. Weller178\n, F. Wellmann10,11, L. Wen89,\nP. We\u00dfels10,11, K. Wette9\n, J. T. Whelan129\n, D. D. White43, B. F. Whiting71\n, C. Whittle69\n, O. S. Wilk60,\nD. Wilken10,11,11\n, C. E. Williams160, D. Williams23\n, M. J. Williams23\n, A. R. Williamson113\n, J. L. Willis1\n,\nB. Willke10,11\n, C. C. Wipf1, G. Woan23\n, J. Woehler10,11, J. K. Wofford129\n, I. A. Wojtowicz160, D. Wong146,\nI. C. F. Wong131\n, M. Wright23, C. Wu130\n, D. S. Wu10,11\n, H. Wu130, D. M. Wysocki7\n, L. Xiao1\n, N. Yadav80,\nT. Yamada272, H. Yamamoto1\n, K. Yamamoto191\n, T. Yamamoto192\n, K. Yamashita202, R. Yamazaki199, F. W. Yang159\n,\nK. Z. Yang83\n, L. Yang168\n, Y.-C. Yang130, Y. Yang296\n, Yang Yang71, M. J. Yap9, D. W. Yeeles16, S.-W. Yeh130,\n4\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nA. B. Yelikar129\n, J. Yokoyama28,29,303\n, T. Yokozawa192, J. Yoo254\n, T. Yoshioka202, Hang Yu136\n, Haocun Yu69\n,\nH. Yuzurihara190, A. Zadro\u017cny161, M. Zanolin35, S. Zeidler297\n, T. Zelenova46, J.-P. Zendri76, M. Zevin166\n, M. Zhan179,\nH. Zhang232, J. Zhang9\n, L. Zhang1, R. Zhang71\n, T. Zhang106, Y. Zhang121, C. Zhao89\n, G. Zhao143, Y. Zhao19,190\n,\nYue Zhao159, Y. Zheng91\n, R. Zhou193, X. J. Zhu5\n, Z.-H. Zhu120,230\n, A. B. Zimmerman170\n, M. E. Zucker1,69, and\nJ. Zweizig1\nThe LIGO Scienti\ufb01c Collaboration, the Virgo Collaboration, and the KAGRA Collaboration\n1 LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n2 Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan\n3 Dipartimento di Farmacia, Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n4 INFN, Sezione di Napoli, I-80126 Napoli, Italy\n5 OzGrav, School of Physics & Astronomy, Monash University, Clayton, VIC 3800, Australia\n6 The Pennsylvania State University, University Park, PA 16802, USA\n7 University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n8 Louisiana State University, Baton Rouge, LA 70803, USA\n9 OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n10 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n11 Leibniz Universit\u00e4t Hannover, D-30167 Hannover, Germany\n12 Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n13 University of Cambridge, Cambridge CB2 1TN, UK\n14 Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00e4t Jena, D-07743 Jena, Germany\n15 Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil\n16 Cardiff University, Cardiff CF24 3AA, UK\n17 INFN, Sezione di Pisa, I-56127 Pisa, Italy\n18 International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n19 Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n20 Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n21 Dipartimento di Fisica, Universit\u00e0 degli Studi di Torino, I-10125 Torino, Italy\n22 INFN Sezione di Torino, I-10125 Torino, Italy\n23 SUPA, University of Glasgow, Glasgow G12 8QQ, UK\n24 Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules\u2014IN2P3, F-74000 Annecy, France\n25 Universit\u00e0 di Napoli \u201cFederico II,\u201d I-80126 Napoli, Italy\n26 Maastricht University, 6200 MD Maastricht, The Netherlands\n27 Nikhef, 1098 XG Amsterdam, The Netherlands\n28 Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n29 Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n30 Institut de Ci\u00e8ncies del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, E-08028, Spain\n31 Institut de F\u00edsica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n32 Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n33 Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit\u00e0 di Udine, I-33100 Udine, Italy\n34 INFN, Sezione di Trieste, I-34127 Trieste, Italy\n35 Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n36 Artemis, Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire de la C\u00f4te d\u2019Azur, CNRS, F-06304 Nice, France\n37 GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands\n38 Department of Physics, National and Kapodistrian University of Athens, 15771 Ilissia, Greece\n39 INFN, Sezione di Perugia, I-06123 Perugia, Italy\n40 Universit\u00e0 di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n41 American University, Washington, DC 20016, USA\n42 Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan\n43 California State University Fullerton, Fullerton, CA 92831, USA\n44 Universit\u00e9 de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France\n45 Universit\u00e9 Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France\n46 European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n47 Georgia Institute of Technology, Atlanta, GA 30332, USA\n48 Department of Mathematics and Physics, Graduate School of Science and Technology, Hirosaki University, Hirosaki, Aomori 036-8561, Japan\n49 Royal Holloway, University of London, London TW20 0EX, UK\n50 Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan\n51 The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan\n52 Universit\u00e0 degli Studi di Urbino \u201cCarlo Bo,\u201d I-61029 Urbino, Italy\n53 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n54 LIGO Livingston Observatory, Livingston, LA 70754, USA\n55 INFN, Sezione di Roma, I-00185 Roma, Italy\n56 Universit\u00e9 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n57 King\u2019s College London, University of London, London WC2R 2LS, UK\n58 Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n59 National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n60 Kenyon College, Gambier, OH 43022, USA\n61 School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki 305-0801, Japan\n62 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, 3584 CC Utrecht, The Netherlands\n63 University of Oregon, Eugene, OR 97403, USA\n64 Syracuse University, Syracuse, NY 13244, USA\n65 Universit\u00e9 de Li\u00e8ge, B-4000 Li\u00e8ge, Belgium\n66 Northwestern University, Evanston, IL 60208, USA\n67 LIGO Hanford Observatory, Richland, WA 99352, USA\n68 Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana,\u201d Universit\u00e0 di Salerno, I-84081 Baronissi, Salerno, Italy\n5\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n69 LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n70 Wigner RCP, RMKI, H-1121 Budapest, Hungary\n71 University of Florida, Gainesville, FL 32611, USA\n72 Stanford University, Stanford, CA 94305, USA\n73 Universit\u00e0 di Pisa, I-56127 Pisa, Italy\n74 Universit\u00e0 di Perugia, I-06123 Perugia, Italy\n75 Universit\u00e0 di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n76 INFN, Sezione di Padova, I-35131 Padova, Italy\n77 Montana State University, Bozeman, MT 59717, USA\n78 Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n79 Universiteit Gent, B-9000 Gent, Belgium\n80 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n81 Dipartimento di Ingegneria, Universit\u00e0 del Sannio, I-82100 Benevento, Italy\n82 OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n83 University of Minnesota, Minneapolis, MN 55455, USA\n84 Universit\u00e4t Hamburg, D-22761 Hamburg, Germany\n85 SUPA, University of Strathclyde, Glasgow G1 1XQ, UK\n86 IAC3\u2013IEEC, Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n87 Departamento de Matem\u00e1ticas, Universitat Aut\u00f2noma de Barcelona, E-08193 Bellaterra (Barcelona), Spain\n88 INFN, Sezione di Genova, I-16146 Genova, Italy\n89 OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n90 RRCAT, Indore, Madhya Pradesh 452013, India\n91 Missouri University of Science and Technology, Rolla, MO 65409, USA\n92 Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands\n93 Lomonosov Moscow State University, Moscow 119991, Russia\n94 Center for Theoretical Physics, Polish Academy of Sciences, 02-668, Warsaw, Poland\n95 Universit\u00e0 di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n96 INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n97 Bar-Ilan University, Ramat Gan, 5290002, Israel\n98 Dipartimento di Fisica \u201cE.R. Caianiello,\u201d Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n99 INFN, Sezione di Napoli, Gruppo Collegato di Salerno, I-80126 Napoli, Italy\n100 Universit\u00e0 di Roma \u201cLa Sapienza,\u201d I-00185 Roma, Italy\n101 Univ Rennes, CNRS, Institut FOTON\u2014UMR 6082, F-3500 Rennes, France\n102 Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n103 INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n104 Laboratoire Kastler Brossel, Sorbonne Universit\u00e9, CNRS, ENS-Universit\u00e9 PSL, Coll\u00e8ge de France, F-75005 Paris, France\n105 Christopher Newport University, Newport News, VA 23606, USA\n106 University of Birmingham, Birmingham B15 2TT, UK\n107 Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n108 University of Maryland, College Park, MD 20742, USA\n109 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n110 Universit\u00e0 degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n111 INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n112 L2IT, Laboratoire des 2 In\ufb01nis\u2014Toulouse, Universit\u00e9 de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n113 University of Portsmouth, Portsmouth, PO1 3FX, UK\n114 Universit\u00e9 de Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Institut Lumi\u00e8re Mati\u00e8re, F-69622 Villeurbanne, France\n115 IGFAE, Universidade de Santiago de Compostela, E-15782 Spain\n116 Stony Brook University, Stony Brook, NY 11794, USA\n117 Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n118 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n119 Dipartimento di Fisica, Universit\u00e0 degli Studi di Genova, I-16146 Genova, Italy\n120 Department of Astronomy, Beijing Normal University, Beijing 100875, People\u02bcs Republic of China\n121 Texas A&M University, College Station, TX 77843, USA\n122 OzGrav, University of Melbourne, Parkville, VIC 3010, Australia\n123 Universit\u00e0 degli Studi di Sassari, I-07100 Sassari, Italy\n124 INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n125 Universit\u00e0 di Roma Tor Vergata, I-00133 Roma, Italy\n126 INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n127 University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n128 Departamento de Astronom\u00eda y Astrof\u00edsica, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n129 Rochester Institute of Technology, Rochester, NY 14623, USA\n130 National Tsing Hua University, Hsinchu City, 30013, Taiwan\n131 The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n132 Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n133 OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n134 Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan\n135 Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City 32001, Taiwan\n136 CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n137 Dipartimento di Ingegneria Industriale (DIIN), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n138 Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan\n139 Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n140 INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n141 OzGrav, Swinburne University of Technology, Hawthorn, VIC 3122, Australia\n142 Universit\u00e9 libre de Bruxelles, B-1050 Bruxelles, Belgium\n143 Universit\u00e9 Libre de Bruxelles, B-1050 Brussels, Belgium\n144 Departamento de Matem\u00e1ticas, Universitat de Val\u00e8ncia, E-46100 Burjassot, Val\u00e8ncia, Spain\n6\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n145 Texas Tech University, Lubbock, TX 79409, USA\n146 University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n147 Columbia University, New York, NY 10027, USA\n148 University of Rhode Island, Kingston, RI 02881, USA\n149 The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n150 Bellevue College, Bellevue, WA 98007, USA\n151 Scuola Normale Superiore, I-56126 Pisa, Italy\n152 E\u00f6tv\u00f6s University, Budapest 1117, Hungary\n153 Chennai Mathematical Institute, Chennai 603103, India\n154 Villanova University, Villanova, PA 19085, USA\n155 The University of Shef\ufb01eld, Shef\ufb01eld S10 2TN, UK\n156 Universit\u00e9 Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00e9riaux Avanc\u00e9s (LMA), IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne,\nFrance\n157 Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit\u00e0 di Parma, I-43124 Parma, Italy\n158 INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n159 The University of Utah, Salt Lake City, UT 84112, USA\n160 Carleton College, North\ufb01eld, MN 55057, USA\n161 National Center for Nuclear Research, 05-400 \u015awierk-Otwock, Poland\n162 Institut d\u2019Astrophysique de Paris, Sorbonne Universit\u00e9, CNRS, UMR 7095, F-75014 Paris, France\n163 University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n164 Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n165 Universit\u00e9 de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n166 University of Chicago, Chicago, IL 60637, USA\n167 Montclair State University, Montclair, NJ 07043, USA\n168 Colorado State University, Fort Collins, CO 80523, USA\n169 Institute for Nuclear Research, H-4026 Debrecen, Hungary\n170 University of Texas, Austin, TX 78712, USA\n171 CNR-SPIN, I-84084 Fisciano, Salerno, Italy\n172 Scuola di Ingegneria, Universit\u00e0 della Basilicata, I-85100 Potenza, Italy\n173 Observatori Astron\u00f2mic, Universitat de Val\u00e8ncia, E-46980 Paterna, Val\u00e8ncia, Spain\n174 Centro de F\u00edsica das Universidades do Minho e do Porto, Universidade do Minho, PT-4710-057 Braga, Portugal\n175 Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan\n176 Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n177 Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n178 Vanderbilt University, Nashville, TN 37235, USA\n179 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology\n(APM), Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, People\u02bcs Republic of China\n180 SUPA, University of the West of Scotland, Paisley PA1 2BE, UK\n181 University of Szeged, D\u00f3m t\u00e9r 9, Szeged 6720, Hungary\n182 INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n183 Queen Mary University of London, London E1 4NS, UK\n184 Universit\u00e9 de Normandie, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, F-14000 Caen, France\n185 The University of Mississippi, University, MS 38677, USA\n186 University of Michigan, Ann Arbor, MI 48109, USA\n187 Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n188 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, People\u02bcs Republic of China\n189 University of Tokyo, Tokyo, 113-0033, Japan\n190 Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n191 Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n192 Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205, Japan\n193 University of California, Berkeley, CA 94720, USA\n194 California State University, Los Angeles, Los Angeles, CA 90032, USA\n195 Lancaster University, Lancaster LA1 4YW, UK\n196 College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan\n197 Rutherford Appleton Laboratory, Didcot OX11 0DE, UK\n198 Department of Astronomy & Space Science, Chungnam National University, Yuseong-gu, Daejeon 34134, Republic of Korea\n199 Department of Physical Sciences, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan\n200 Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian District, Beijing 100871, People\u02bcs Republic of China\n201 Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece\n202 Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan\n203 Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n204 Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n205 Universiteit Antwerpen, B-2000 Antwerpen, Belgium\n206 University of Bia\u0142ystok, 15-424 Bia\u0142ystok, Poland\n207 Ewha Womans University, Seoul 03760, Republic of Korea\n208 National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, People\u02bcs Republic of China\n209 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, People\u02bcs Republic of China\n210 University of Southampton, Southampton SO17 1BJ, UK\n211 Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n212 Institute for High-Energy Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands\n213 Chung-Ang University, Seoul 06974, Republic of Korea\n214 University of Washington Bothell, Bothell, WA 98011, USA\n215 Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n216 Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n217 Department of Physics, Myongji University, Yongin 17058, Republic of Korea\n218 Sungkyunkwan University, Seoul 03063, Republic of Korea\n7\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n219 Bard College, Annandale-On-Hudson, NY 12504, USA\n220 Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n221 Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n222 Instituto de Fisica Teorica, E-28049 Madrid, Spain\n223 Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n224 Universit\u00e9 de Montr\u00e9al/Polytechnique, Montreal, QC H3T 1J4, Canada\n225 Laboratoire Lagrange, Universit\u00e9 C\u00f4te d\u2019Azur, Observatoire C\u00f4te d\u2019Azur, CNRS, F-06304 Nice, France\n226 Seoul National University, Seoul 08826, Republic of Korea\n227 NAVIER, \u00c9cole des Ponts, Univ Gustave Eiffel, CNRS, Marne-la-Vall\u00e9e, France\n228 Universit\u00e0 di Firenze, Sesto Fiorentino I-50019, Italy\n229 Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan\n230 School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, People\u02bcs Republic of China\n231 National Center for High-performance Computing, National Applied Research Laboratories, Hsinchu Science Park, Hsinchu City 30076, Taiwan\n232 Department of Physics, National Taiwan Normal University, Section 4, Taipei 116, Taiwan\n233 NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n234 INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n235 ESPCI, CNRS, F-75005 Paris, France\n236 West Virginia University, Morgantown, WV 26506, USA\n237 School of Physics Science and Engineering, Tongji University, Shanghai 200092, People\u02bcs Republic of China\n238 Tsinghua University, Beijing 100084, People\u2019s Republic of China\n239 Dipartimento di Fisica, Universit\u00e0 di Trieste, I-34127 Trieste, Italy\n240 Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan\n241 Indian Institute of Technology Madras, Chennai 600036, India\n242 Institute of Space and Astronautical Science (JAXA), Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan\n243 Institut des Hautes Etudes Scienti\ufb01ques, F-91440 Bures-sur-Yvette, France\n244 Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n245 Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n246 Universit\u00e9 de Paris, F-75006 Paris, France\n247 Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA\n248 Centre national de la recherche scienti\ufb01que, F-75016 Paris, France\n249 Laboratoire Univers et Th\u00e9ories, Observatoire de Paris, F-92190 Meudon, France\n250 Observatoire de Paris, F-75014 Paris, France\n251 Universit\u00e9 PSL, F-75006 Paris, France\n252 Institute of Physics of the Czech Academy of Sciences, 182 00 Praha 8, Czechia\n253 Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n254 Cornell University, Ithaca, NY 14850, USA\n255 Consiglio Nazionale delle Ricerche\u2014Istituto dei Sistemi Complessi, I-00185 Roma, Italy\n256 Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea\n257 Hobart and William Smith Colleges, Geneva, NY 14456, USA\n258 International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n259 Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi,\u201d I-00184 Roma, Italy\n260 Dipartimento di Matematica e Fisica, Universit\u00e0 degli Studi Roma Tre, I-00146 Roma, Italy\n261 Universit\u00e0 di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n262 University of California, Riverside, Riverside, CA 92521, USA\n263 University of Washington, Seattle, WA 98195, USA\n264 Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, Nagaoka City, Niigata 940-8532, Japan\n265 INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n266 Departamento de Matem\u00e1tica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications, 3810-183 Aveiro, Portugal\n267 Marquette University, Milwaukee, WI 53233, USA\n268 Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan\n269 Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n270 Graduate School of Science and Technology, Gunma University, Maebashi, Gunma 371-8510, Japan\n271 Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA\n272 Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n273 Faculty of Information Science and Technology, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan\n274 INAF, Osservatorio Astro\ufb01sico di Arcetri, I-50125 Firenze, Italy\n275 Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n276 Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n277 Istituto di Astro\ufb01sica e Planetologia Spaziali di Roma, I-00133 Roma, Italy\n278 Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City, Kanagawa 252-5210, Japan\n279 Andrews University, Berrien Springs, MI 49104, USA\n280 Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, Setagaya, Tokyo 158-0082, Japan\n281 Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n282 Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n283 Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n284 Dipartimento di Scienze Aziendali\u2014Management and Innovation Systems (DISA-MIS), Universit\u00e0 di Salerno, I-84084 Fisciano, Salerno, Italy\n285 Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747 AG Groningen, The Netherlands\n286 Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n287 Vrije Universiteit Brussel, B-1050 Brussel, Belgium\n288 Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n289 Department of Communications Engineering, National Defense Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan\n290 Department of Physics, University of Florida, Gainesville, FL 32611, USA\n291 Department of Information and Management Systems Engineering, Nagaoka University of Technology, Nagaoka City, Niigata 940-2188, Japan\n292 Tata Institute of Fundamental Research, Mumbai 400005, India\n293 Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands\n294 Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea\n8\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n295 Concordia University Wisconsin, Mequon, WI 53097, USA\n296 Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan\n297 Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan\nReceived 2022 September 2; revised 2022 October 7; accepted 2022 October 8; published 2022 December 16\nAbstract\nWe present the results of a model-based search for continuous gravitational waves from the low-mass X-ray binary\nScorpius X-1 using LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo. This\nis a semicoherent search that uses details of the signal model to coherently combine data separated by less than a\nspeci\ufb01ed coherence time, which can be adjusted to balance sensitivity with computing cost. The search covered a\nrange of gravitational-wave frequencies from 25 to 1600 Hz, as well as ranges in orbital speed, frequency, and\nphase determined from observational constraints. No signi\ufb01cant detection candidates were found, and upper limits\nwere set as a function of frequency. The most stringent limits, between 100 and 200 Hz, correspond to an\namplitude h0 of about 10\u221225 when marginalized isotropically over the unknown inclination angle of the neutron\nstar\u2019s rotation axis, or less than 4 \u00d7 10\u221226 assuming the optimal orientation. The sensitivity of this search is now\nprobing amplitudes predicted by models of torque balance equilibrium. For the usual conservative model assuming\naccretion at the surface of the neutron star, our isotropically marginalized upper limits are close to the predicted\namplitude from about 70 to 100 Hz; the limits assuming that the neutron star spin is aligned with the most likely\norbital angular momentum are below the conservative torque balance predictions from 40 to 200 Hz. Assuming a\nbroader range of accretion models, our direct limits on gravitational-wave amplitude delve into the relevant\nparameter space over a wide range of frequencies, to 500 Hz or more.\nUni\ufb01ed Astronomy Thesaurus concepts: Gravitational waves (678); Gravitational wave astronomy (675); Low-\nmass x-ray binary stars (939); Neutron stars (1108)\n1. Introduction\nRapidly rotating neutron stars (NSs) are primary targets for\ncontinuous gravitational-wave (GW) searches with the current\nnetwork\nof\nground-based\ndetectors,\nLIGO,\nVirgo,\nand\nKAGRA. In these stars a deformation, or \u201cmountain,\u201d\nsustained by elastic or magnetic strains, may result in a time-\nvarying quadrupole from rotation, leading to the emission of\nGWs. Similarly, modes of oscillation may also lead to GW\nemission (see Lasky 2015 for a review).\nIn particular, NSs in low-mass X-ray binaries (LMXBs) are\nsome of the most promising sources. In these systems\nmagnetically channeled accretion from the companion onto\nthe NS provides a mechanism to create a \u201cmountain\u201d\n(Ushomirsky et al. 2000; Melatos & Payne 2005; Osborne &\nJones 2020; Singh et al. 2020), and the resulting GW torque\nmay provide the solution to an astrophysical conundrum. There\nappears to be a sharp observed cutoff in the spin frequency (\u03bds)\ndistribution of NSs in LMXBs at \u03bds \u2248750 Hz (Chakrabarty\net al. 2003; Patruno et al. 2017), well below the theoretical\nbreakup frequency for an NS (Haskell et al. 2018).\nAlthough there are still several uncertainties in the modeling\nof the spin-up accretion torques (Patruno & Watts 2021;\nGlampedakis & Suvorov 2021), which may explain this\nobservation (Patruno et al. 2012; Ertan & Alpar 2021), it has\nbeen suggested that the spin-down GW torques due to\nmountains can lead to an equilibrium at high frequencies that\nnaturally explains the observed spins of NSs in LMXBs\n(Papaloizou & Pringle 1978; Wagoner 1984; Bildsten 1998)\nand the clustering of systems above \u03bds \u2248500 Hz and close to\nthe maximum frequency (Patruno et al. 2017; Gittins &\nAndersson 2019). In such a scenario there is a natural\ncorrelation between the observed X-ray \ufb02ux and the expected\nstrength of the GWs, as a higher accretion rate leads to a\nstronger spin-up torque and thus requires a stronger GW torque\nfor equilibrium (note that even if this equilibrium holds on\naverage, there is expected to be some slight \ufb02uctuation in\nfrequency or \u201cspin wandering\u201d; Bildsten et al. 1997; Mukherjee\net al. 2018). Scorpius X-1 (Sco X-1), the most luminous\nLMXB, which is presumed to consist of an NS of mass\n\u22481.4Me in a binary orbit with a companion star of mass\n\u22480.4Me (Steeghs & Casares 2002), is therefore a very\npromising potential source of GWs. Some of the parameters\ninferred from electromagnetic observations of the system are\nsummarized in Table 1. Note that the orbital eccentricity of Sco\nX-1 is believed to be small (Steeghs & Casares 2002; Wang\net al. 2018) and is ignored in this search. Inclusion of eccentric\norbits would add two search parameters that are determined by\nthe eccentricity and the argument of periapse (Messenger 2011;\nLeaci & Prix 2015).\nGiven its promise as a source for potentially detectable\ncontinuous gravitational waves, Sco X-1 has been the subject\nof numerous GW searches and search methods to date, starting\nwith a fully coherent search (Jaranowski et al. 1998) of 6 hr\nfrom initial LIGO\u2019s second science run (Abbott et al. 2007a).\nBeginning with the fourth science run, results for Sco X-1 have\nbeen reported (Abbott et al. 2007b; Abadie et al. 2011) as part\nof a search for stochastic signals from isolated sky positions,\nalso known as the radiometer search (Ballmer 2006), which has\ncontinued in Advanced LIGO\u2019s \ufb01rst three observing runs\n(Abbott et al. 2017a, 2019, 2021a). Sco X-1 has also been\nincluded in a search principally designed for unknown binary\nsystems (Goetz & Riles 2011) and subsequently improved to\nsearch directly for Sco X-1 (Meadors et al. 2016); these\n298 lsc-spokesperson@ligo.org\n299 Deceased, December 2021.\n300 Deceased, November 2022.\n301 virgo-spokesperson@ego-gw.it\n302 Deceased, March 2022.\n303 kscboard-chair@icrr.u-tokyo.ac.jp\nOriginal content from this work may be used under the terms\nof the Creative Commons Attribution 4.0 licence. Any further\ndistribution of this work must maintain attribution to the author(s) and the title\nof the work, journal citation and DOI.\n9\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nsearches were applied to data from initial LIGO\u2019s \ufb01fth and sixth\nscience runs (Aasi et al. 2014; Meadors et al. 2017). A search\nmethod connected to Doppler-modulated sidebands (Messenger\n& Woan 2007; Sammut et al. 2014) was developed and applied\nto data from initial LIGO\u2019s sixth science run (Aasi et al. 2015a).\nThis was further adopted into the so-called Viterbi search\n(Suvorova et al. 2016, 2017), which uses a hidden Markov\nmodel to track possible spin wandering; the Viterbi search has\nbeen applied to data from Advanced LIGO\u2019s \ufb01rst three\nobserving runs (Abbott et al. 2017b, 2022a). The cross-\ncorrelation method (Dhurandhar et al. 2008; Whelan et al.\n2015) used in the present work is an extension of the radiometer\nsearch that uses the signal model of GWs from an LMXB such\nas Sco X-1 to look for correlations between data at different\ntimes. It has been applied to data from Advanced LIGO\u2019s \ufb01rst\nand second science runs to set the strongest limits so far on GWs\nfrom Sco X-1 (Abbott et al. 2017c; Zhang et al. 2021).\nThe Advanced LIGO Gravitational-Wave Observatory (Aasi\net al. 2015b) has conducted three observing runs, the last two in\ncoordination with Advanced Virgo (Acernese et al. 2015). In\nthese three runs, transient GWs were detected from over 90\ncoalescences of binary systems of black holes and/or NSs\n(Abbott et al. 2021b). The LIGO-Virgo O3 observing run\n(Buikema 2020; Abbott et al. 2020) began on 2019 April 01\n15:00:00 UTC (GPS 1238166018), continued until a commis-\nsioning break at 2019 October 01 15:00:00 UTC (GPS\n1253977218), resumed on 2019 November 01 15:00:00 UTC\n(GPS\n1256655618),\nand\nended\non\n2020\nMarch\n27\n17:00:00 UTC (GPS 1269363618). In 2020 April, immediately\nfollowing the LIGO-Virgo run, the KAGRA detector (Aso\net al. 2013; Akutsu et al. 2021) and the GEO 600 detector\n(L\u00fcck et al. 2010; Affeldt et al. 2014; Dooley et al. 2016)\nconducted joint observations (Abbott et al. 2022b). In this\nanalysis, we use data from the two LIGO detectors, as Virgo\nand KAGRA data were signi\ufb01cantly less sensitive.\nWe use the calibrated data that are limited to times when a\ndetector was in scienti\ufb01c observing mode (Davis et al. 2021).\nDue to the presence of transient instrumental glitches that\ndegrade the sensitivity by raising the overall noise spectrum,\nwe apply the \u201cself-gating\u201d procedure (Zweizig & Riles 2021) to\nremove these glitches when analyzing data below 600 Hz. This\nreduces the total volume of data included in the analysis below\n600 Hz from 243\u2013244 days to 231\u2013240 days for the LIGO\nHanford detector and from 250\u2013251 days to 216\u2013248 days for\nthe LIGO Livingston detector. (The ranges are due to\ndifferences in the time baseline used in producing Fourier\ntransforms at different frequencies; see Section 3.)\nIn addition, as in Abbott et al. (2017c), we exclude from our\nanalysis frequencies at which the data are known to be\nin\ufb02uenced by instrumental disturbances of narrow frequency\nextent, known as \u201clines.\u201d In practice, this procedure removes\ndata from times at which the signal model has Doppler-shifted\nthe GW signal frequency f0 of the search template into the\ninstrumental line, reducing the sensitivity of the search near\nknown lines.\nThe remainder of the paper is laid out as follows: In\nSection 2 we describe the properties of Sco X-1 and the\nmodeled GW signal from it. In Section 3 we describe the\nspeci\ufb01cs of the cross-correlation search as implemented for this\nanalysis. In Section 4 we describe the identi\ufb01cation and follow-\nup of potential signals. Section 5 sets upper limits on the\nstrength of GWs from Sco X-1 from the sensitivity and result\nof the search on Advanced LIGO data and simulated signals\nand considers their implications on various torque balance\nmodels. Finally, Section 6 contains the conclusions.\n2. Model of Gravitational Waves from Sco X-1\nThe modeled GW signal from a rotating NS consists of a \u201cplus\u201d\npolarization component h\nt\nA\nt\ncos\n=\nF\n+\n+\n( )\n[ ( )] and a \u201ccross\u201d\npolarization component h t\nA\nt\nsin\n=\nF\n\u00b4\n\u00b4\n( )\n[ ( )].304 The signal\nrecorded in a particular detector will be a linear combination of\nh+ and h\u00d7 determined by the detector\u2019s orientation as a\nfunction of time. The two polarization amplitudes are\nA\nh\nA\nh\n1\ncos\n2\nand\ncos ,\n1\n0\n2\n0\ni\ni\n=\n+\n=\n+\n\u00b4\n( )\nwhere h0 is an intrinsic amplitude describing the strength of the\nsignal when it reaches the solar system and \u03b9 is the inclination\nof the NS\u2019s spin to the line of sight. (For an NS in a binary, the\nspin inclination \u03b9 is not necessarily equal to the inclination i of\nthe\nbinary\norbit.)\nIf\n\u03b9 = 0\u00b0\nor\n180\u00b0,\nA\u00d7 = \u00b1 A+,\nand\nTable 1\nObserved Parameters of the LMXB Sco X-1\nParameter\nValue\nRight ascensiona\n16h19m55.0850s\nDecl.a\n15\n38 24.9\n-\n\uf0b0\n\u00a2\n\uf0b2\n}\n{\nDistance (kpc)\n2.8 \u00b1 0.3\nOrbital inclination ib\n44(deg) \u00b1 6(deg)\nK1 (km s\u22121)c\n[40, 90]\ntasc (GPS s)d\n974,416,624 \u00b1 50\nPorb (s)e\n68,023.86 \u00b1 0.043\nNotes. Uncertainties are 1\u03c3 unless otherwise stated. There are uncertainties\n(relevant to the present search) in the projected velocity amplitude K1 of the\nNS, the orbital period Porb, and the time tasc at which the NS crosses the\nascending node (moving away from the observer), measured in the solar system\nbarycenter.\na The sky position (as quoted in Abbott et al. 2007a, derived from Bradshaw\net al. 1999) is determined to the microarcsecond and therefore can be treated as\nknown in the present search.\nb The inclination i of the orbit to the line of sight, from observation of radio jets\nin Fomalont et al. (2001), is not necessarily the same as the inclination angle \u03b9\nof the NS\u2019s spin axis, which determines the degree of polarization of the GW in\nEquation (1).\nc The projected orbital velocity K1 as estimated by Doppler tomography\nmeasurements and Monte Carlo simulations in Wang et al. (2018), which show\nK1 to be weakly determined beyond the constraint that 40 km s\u22121 \uf088\nK1 \uf08890 km s\u22121.\nd The time of ascension tasc, at which the NS crosses the ascending node\n(moving away from the observer), measured in the solar system barycenter, is\nderived from the time of inferior conjunction of the companion given in Wang\net al. (2018) by subtracting Porb/4. It corresponds to a time of 2010 November\n21 23:16:49 UTC and can be propagated to other epochs by adding an integer\nmultiple of Porb, which results in increased uncertainty in tasc and correlations\nbetween Porb and tasc; see Figure 2.\ne The orbital period reported in Wang et al. (2018). Note that this differs from\nthe previous estimate in Galloway et al. (2014) by 2.6\u03c3.\nReferences. Bradshaw et al. (1999); Fomalont et al. (2001); Wang et al.\n(2018).\n304 The preferred (spin-2) polarization basis is constructed from orthonormal\nunit vectors in the plane of the sky: one along the projection of the NS spin\naxis, and the other along the intersection of the NS equatorial plane with the\nplane of the sky. This basis is rotated relative to a \ufb01ducial north-and-east-on-\nthe-sky basis by an (unknown) polarization angle \u03c8, equivalent to the position\nangle of the NS\u2019s polarization axis (Jaranowski et al. 1998; Prix &\nWhelan 2007).\n10\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\ngravitational radiation is circularly polarized. If \u03b9 = 90\u00b0,\nA\u00d7 = 0, and it is linearly polarized. The general case, elliptical\npolarization, has\nA\nA\n0 <\n<\n\u00b4\n+\n\u2223\n\u2223\n. Many search methods are\nsensitive to the combination\nh\nA\nA\nh\n2\n1\ncos\n2\ncos\n2\n,\n2\n0\neff 2\n2\n2\n0\n2\n2\n2\n2\ni\ni\n=\n+\n=\n+\n+\n+\n\u00b4\n(\n)\n[(\n)\n]\n[\n]\n( )\nwhich is equal to h0\n2 for circular polarization and h\n8\n0\n2\nfor\nlinear polarization (Messenger et al. 2015; this was the\nconvention used in Abbott et al. 2017c but differs by a factor\nof 2.5 from the de\ufb01nition of h0\neff 2\n(\n) in Whelan et al. 2015).\nIn order to understand the astrophysical relevance of the GW\nstrengths we are probing, a useful benchmark is the so-called\ntorque balance level. As already mentioned, it has been\nsuggested that an LMXB, such as Sco X-1, may be in an\nequilibrium state where the spin-up torque due to accretion is\nbalanced by a spin-down torque due to GW emission\n(Papaloizou & Pringle 1978; Wagoner 1984; Bildsten 1998).\nIn order to obtain an estimate of the GW amplitude, we start by\ntaking a simple spin-up torque of the form (Pringle &\nRees 1972)\n\uf026\nN\nM GMr ,\n3\nA =\n( )\nwhere \uf026M is the mass accretion rate onto the NS, which we infer\nfrom the X-ray \ufb02ux FX; M is the mass of the star; G is the\ngravitational constant; and r is the lever arm, i.e., the radius at\nwhich the accretion torque is applied. By balancing the spin-up\ntorque with the GW torque, i.e., imposing\n\uf026\nN\nE\n2\nA\nGW\ns\npn\n=\n, we\ncan obtain the GW amplitude (Watts et al. 2008):\n\uf065\n*\nh\nF\nR\nr\nM\nM\n5.48\n10\n10\nerg cm\ns\n300 Hz\n10 km\n10 km\n1.4\n.\n4\nX\ns\n0\n27\n8\n2\n1\n1 2\n1 2\n1 2\n1 4\n1 4\nn\n\u00bb\n\u00b4\n\u00b4\n-\n-\n-\n-\n-\n\u239c\n\u239f\n\u239c\n\u239f\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n( )\nNote that the usual torque balance benchmark assumes that\naccretion occurs at the surface of the NS, r = R* = 10 km. (If\nthe magnetic \ufb01eld is strong enough to truncate the accretion\ndisk above the surface, the lever arm will instead be the Alfv\u00e9n\nradius, r = rA, and the GW amplitude implied by Equation (4)\nwill be larger, as given in, e.g., Zhang et al. (2021) and Abbott\net al. (2022a).) For Sco X-1, using the observed X-ray \ufb02ux\nFX = 3.9 \u00d7 10\u22127 erg cm\u22122 s\u22121 from Watts et al. (2008) and\nassuming that the GW frequency f0 is twice the spin frequency\n\u03bds (as would be the case for GWs generated by triaxiality in the\nNS), the torque balance value is\nh\nf\n3.4\n10\n600 Hz\n.\n5\n0\n26\n0\n1 2\n\u00bb\n\u00b4\n-\n-\n\u239b\n\u239d\n\u239e\n\u23a0\n( )\nIt is important to note that this amplitude is simply an order-\nof-magnitude estimate, which we use as a benchmark to\nunderstand whether our searches are probing astrophysically\nsigni\ufb01cant portions of parameter space. Much of the physics\nentering the accretion torque is, in fact, highly uncertain and\ndepends on unknown physical parameters, such as the topology\nof the stellar magnetic \ufb01eld, the disk\u2212\ufb01eld coupling, viscous\nheating in the disk, ef\ufb01ciency of X-ray emission, or radiation\npressure in the disk. All these effects can strongly in\ufb02uence the\nspin-up torque, leading not only to a large rescaling (of up to an\norder\nof\nmagnitude) of\nthe\nstrength\nof\nthe\ntorque\nin\nEquation (3) but in general also to different scalings with the\nparameters of the system (Patruno et al. 2012; Haskell et al.\n2015; Glampedakis & Suvorov 2021). For example, Andersson\net al. (2005) have even suggested that, for high accretion\nluminosities, radiation pressure will lead to a sub-Keplerian\ndisk and a strongly reduced spin-up torque. In this case Sco\nX-1 would host a slowly rotating NS, which does not emit\nGWs in our current search band. In light of the various\nuncertainties, we will retain the standard simplifying assump-\ntions in the derivation of Equation (5) for most of our torque\nbalance comparisons, but keep in mind that the torque balance\nlevel is uncertain and model dependent and should not be\ninterpreted too strictly.\n3. Setup of Cross-correlation Search\nThe cross-correlation (CrossCorr) search method (Dhurandhar\net al. 2008; Whelan et al. 2015) has been used to search for\nGWs from Sco X-1 in LIGO data from the \ufb01rst two observing\nruns of Advanced LIGO and Advanced Virgo (Abbott et al.\n2017c; Zhang et al. 2021). It uses the signal model described in\nSection 2 to construct an appropriately weighted statistic \u03c1\nincluding correlations between data separated by up to a\ncoherence time Tmax. The statistic is constructed using short\nFourier transforms (SFTs) of length Tsft. If the SFTs are labeled\nby an index K, L, etc., which encodes the detector and time of\nthe SFT, and zK is an appropriately normalized combination of\nthe Fourier data at the frequency of interest, we can write the\nstatistic \u03c1 as\n*\n*\n*\nW\nz z\nW\nz z\n,\n6\nKL\nKL K L\nKL K L\n\uf050\n\u00e5\nr =\n+\n\u00ce\n(\n)\n( )\nwhere \uf050is the set of all pairs of SFTs whose start times differ\nby Tmax or less and WKL is a complex weighting factor\nconstructed using the signal model. Since the choice of\nfrequency bin(s) in the construction of zK and the amplitude\nand phase of the weighting factor WKL for each SFT pair\ndepend on the unknown parameters of the signal, we must\nconduct the search at a set of points in parameter space, each of\nwhich de\ufb01nes a \u201csearch template.\u201d\nThe maximum separation Tmax can be chosen to \u201ctune\u201d the\nsearch: higher Tmax values produce a more sensitive search but\ncan signi\ufb01cantly increase computing cost, both due to the\nincreased number of correlation terms in the statistic and\nespecially due to the increased density of search templates\nneeded in the parameter space. As detailed in Abbott et al.\n(2017c), the Tsft and Tmax values were chosen as a function of\nGW frequency and orbital parameters in order to optimize the\nsearch at a given computing cost. For the present search, we\nused the same Tmax values as in O1 rather than re-optimizing.305\nThe one exception is for the GW frequency range 400\u2013600 Hz,\nfor which the achievable sensitivity is closer in O3 than it was\nin O1 to the signal strength nominally expected from the torque\nbalance model Equation (5); for those frequencies, we used\ndouble the Tmax of the O1 search. Note that, even with the same\ncoherence times, the O3 search would require more computing\n305 The O2 analysis of Zhang et al. (2021), which was limited to GW\nfrequencies between 40 and 180 Hz, used a longer coherence time of \u223c19 hr by\nleveraging the resampling techniques described in Meadors et al. (2017).\n11\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nresources than the O1 search, due to the increased observing\ntime. However, by using a more ef\ufb01cient template lattice and\nconvenient coordinate choices as described in Wagner et al.\n(2022), we are able to offset the increase in observing time and\nmaintain a manageable computing time.\nIn addition to the GW signal frequency, f0, we search over\nthe orbital parameters of the system, as summarized in Table 2.\nThe projected semimajor axis of the orbit is assumed to lie in\nthe range a\ni\nsin\n1.44, 3.25\n\u00ce [\n] lt-s, corresponding to a range in\nprojected orbital velocity of [40, 90] km s\u22121. The search region\nin orbital period Porb and time of ascension tasc is constructed\nusing the method of Wagner et al. (2022): the time of ascension\ntasc is propagated 4125 orbits to de\ufb01ne\nt\nt\n4125\n68023.86 s,\n7\nasc\nasc\n\u00a2\n=\n+\n\u00b4\n( )\nand the \u201csheared\u201d orbital period is de\ufb01ned as\nP\nP\nt\n2.42\n10\n1255015049 .\n8\norb\n4\nasc\n=\n-\n\u00b4\n\u00a2\n-\n-\n\u02dc\n(\n)\n( )\nThe most likely tasc\u00a2\nis 2019 October 13 15:17:11 UTC (GPS\n1255015049). The coordinates tasc\u00a2\nand P\u02dc are approximately\nuncorrelated both in the parameter space metric of the search\nand in the astrophysical prior distribution.306 Note that the\nincluded prior probability is an underestimate of the ef\ufb01ciency\nin covering parameter space, since the \u201csheared\u201d period\ncoordinate P\u02dc was unresolved in many search jobs, i.e., the\nmismatch associated with an offset of 3.3 \u00d7 0.011 s from the\nmost likely value 68023.86 s (the dashed rectangular bound-\naries in Figure 1) was less than 0.0625.\nThe search was done over a range of t\n1255015049\nasc\u00a2\n=\n\uf0b1\n3\n185 s\n\u00b4\nand with P\u02dc constrained to lie in an elliptical region\ncentered on 68,023.86 s with semiaxes of 3.3 \u00d7 0.011 s for P\u02dc\nand 3.3 \u00d7 185 s for tasc\u00a2 , as illustrated in Figure 1. For reference,\nin Figure 2 we show this region in the coordinates t\nP\n,\nasc\norb\n\u00a2\n(\n),\nalong with the search regions used in Abbott et al. (2017c) and\nZhang et al. (2021), propagated forward in time to the epoch\nconsidered in this analysis.\nTo perform the analysis, the parameter space was divided\ninto small jobs that could be run in parallel. Each 5 Hz GW\nfrequency band was divided into between 100 and 4000 sub-\nbands, and the orbital parameter space was divided into 9 or 20\ncells, as illustrated in Figure 3. These subdivisions of parameter\nspace were chosen so that each analysis job would run in a\nreasonable amount of time (\uf08810 hr), allowing the analysis to be\ndone quickly via distributed computing.\nSearch templates were placed in the parameter space using\nan\n*\nAn lattice with a maximum mismatch of 0.25 as described in\nWagner et al. (2022) and Wette (2014). Because the use of the\nsheared coordinate P\u02dc reduces the 1\u03c3 prior uncertainty from\n0.043 to 0.011 s, the period was unresolved for most search\njobs. We computed the maximum mismatch\nP\nmax\nm \u02dc\nassociated\nwith an offset of 3.3 \u00d7 0.011 s. For jobs in which\n\uf084\nP\nmax\nm \u02dc\n0.0625, the initial search was done with P\n68023.86 s\n=\n\u02dc\nand\nan\n*\nA3 lattice in the other three parameters\nf\na\ni t\n,\nsin ,\n0\nasc\u00a2\n(\n).\nTo account for the nonzero mismatch contribution from\nthe possible P\u02dc offset, the maximum mismatch of the\n*\nA3 lattice\nwas set to 0.25\nP\nmax\nm\n\u2013\n\u02dc\n. (Note that this actually guarantees\ncoverage at the speci\ufb01ed maximum mismatch over a rectangle\nin t\nP\n,\nasc\u00a2\n\u02dc rather than just the ellipse shown in Figure 1.) If, on\nthe other hand, the P\u02dc coordinate was resolved in a particular\nsearch job, an\n*\nA4\nlattice in all of the coordinates with\nmaximum mismatch of 0.25 was used.\nAs noted in Section 1, even in approximate equilibrium, Sco\nX-1 may undergo stochastic variation of the GW frequency f0,\nalso known as \u201cspin wandering.\u201d As in Abbott et al. (2017c), we\ncan apply the estimates in Whelan et al. (2015) to set bounds on\nthe loss of signal-to-noise ratio (S/N) under a simplistic model in\nwhich the GW frequency undergoes a net spin-up or spin-down\nof magnitude\n\uf026f drift\n\u2223\u2223\n, changing on a timescale Tdrift. For O3,\nin which the duration of the run from start to end is\nTrun = 3.12 \u00d7 107 and the coherence times used for the initial\nsearch are\n\uf084\nT\n18720 s\nmax\n, the expected loss of S/N is\n\uf026\nE\nE\nE\nT\nf\nT\n0.018 10 s\n10\nHz s\n18720 s\n,\n9\nideal\nideal\ndrift\n6\ndrift\n12\n1\n2\nmax\n2\nr\nr\nr\n-\n\u00bb\n-\n-\n\u239c\n\u239f\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n[ ]\n[ ]\n[ ]\n\u2223\u2223\n( )\nwhich indicates that spin wandering is not likely to be an\nimportant effect for this search. In addition, as noted in Zhang\net al. (2021), the predictions of Mukherjee et al. (2018) based\non the time variation of the X-ray \ufb02ux from Sco X-1 imply\nconsiderably less spin wandering than the naive\n\uf026f drift\n\u2223\u2223\n\u2212Tdrift\nmodel, whose \ufb01ducial parameters are taken from Messenger\net al. (2015).\n4. Candidates, Outliers, and Follow-up\nThe detection statistic \u03c1 is normalized to have zero mean and\nunit variance in Gaussian noise. As in Abbott et al. (2017c), we\nmake a naive estimate of the expected background by assuming\nthat each search template represents an independent Gaussian\nrandom number, and we use this value to set the threshold at an\napproximate level of one expected false-alarm level per 50 Hz.\nAs shown in Figure 4, the threshold for follow-up for this\nsearch was set at 6.3 for 25 Hz < f0 < 400 Hz, 6.2 for\nTable 2\nParameters Used for the Cross-correlation Search\nParameter\nRange\nf0 (Hz)\n[25, 1600]\na\ni\nsin\n(lt-s)a\n[1.44, 3.25]\ntasc\u00a2\n(GPS s)b\n1,255,015,049 \u00b1 3 \u00d7 185\nP\u02dc (s)c\n68,023.86 \u00b1 3.3 \u00d7 0.011\nNotes.\na The range for the projected semimajor axis a\ni\nK P\nsin\n2\n1 orb\np\n=\n(\n) in lt-s was\ntaken from the constraint K1 \u00e4 [40, 90] km s\u22121.\nb This value for the time of ascension tasc\u00a2 , de\ufb01ned in Equation (7), has been\npropagated forward by 4125 orbits from the value of tasc in Table 1 and\ncorresponds to a time of 2019 October 13 15:17:11 UTC, near the middle of\nthe O3 run. The increase in uncertainty is due to the uncertainty in Porb.\nc This is the \u201csheared\u201d period de\ufb01ned in Equation (8); note that the uncertainty\nin P\u02dc has been reduced compared to the marginal uncertainty in Porb by the same\nfactor by which the uncertainty in tasc\u00a2\nhas been increased relative to that for tasc,\nas described in Wagner et al. (2022). The search region in P\u02dc is given by the\nelliptical boundary shown in Figure 1, but it is de\ufb01ned as \u201cunresolved\u201d if only\none template is needed to cover 68,023.86 \u00b1 3.3 \u00d7 0.011 at a maximum\nmismatch of 0.0625.\n306 The correlations would have been even smaller had the optimal coef\ufb01cient\n2.25 \u00d7 10\u22124 been used in Equation (8), but a software bug led to the use of the\ncoef\ufb01cient 2.42 \u00d7 10\u22124. The impact of this error is negligible, however,\nreducing the prior probability covered by the search region from 99.4%\nto 99.2%.\n12\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n400 Hz < f0 < 600 Hz, and 5.8 for 600 Hz < f0 < 1600 Hz. Due\nin part to our more ef\ufb01cient template placement, we were able\nto use a lower follow-up threshold than in Abbott et al. (2017c),\nexcept for 400 Hz < f0 < 600 Hz, where we used the same\nthreshold, despite having a search with twice the coherence\ntime. Table 3 shows the resulting expected numbers of false\nalarms in each GW frequency range.\nFor candidates exceeding the follow-up threshold, we\napplied the procedure detailed in Abbott et al. (2017c). Here\nwe highlight the basic steps, as well as details that were\nchanged for this analysis:\n1. Candidates were \u201cclustered\u201d together in GW frequency,\nwith all templates within 0.01 Hz of a peak in S/N above\nthe threshold being represented by the parameters of the\npeak. These are known as the \u201clevel 0\u201d results.\n2. A \u201cre\ufb01nement\u201d search was performed on each level 0\ncandidate, with the same Tmax as the original search and a\nresolution \u223c3\u00d7 as \ufb01ne as the original lattice. This and\nlater stages of follow-up were run on a rectangular grid in\nthe \u201csheared\u201d parameters\nf\na\ni t\nP\n,\nsin ,\n,\n0\nasc\u00a2\n(\n\u02dc). For the\nre\ufb01nement stage, a grid of 13 \u00d7 13 \u00d7 13 \u00d7 5 points was\nused, centered on the\nf\na\ni t\n,\nsin ,\n0\nasc\u00a2\n(\n) values of the\ncandidate, and covering the full prior range in the initially\nunresolved P\u02dc. To deal with the effects of unknown\nnarrowband features (\u201clines\u201d) present in a single detector,\nwe computed a detection statistic using only data from\nthe LIGO Livingston Observatory (LLO) detector and\nanother using only LIGO Hanford Observatory (LHO)\ndata. If either of these exceeded the detection statistic\nconstructed from all the data, we vetoed the candidate as\na likely instrumental artifact. Candidates from the\nFigure 1. Search region in terms of parameters tasc\u00a2\nand P\u02dc de\ufb01ned in\nEquations (7) and (8), respectively. The lattice is constructed to completely\ncover, with maximum mismatch 0.25, the solid black truncated ellipse. The\nsolid black ellipse has semiaxes 3.3 \u00d7 185 s in tasc\u00a2\nand 3.3 \u00d7 0.011 s in P\u02dc, and\nthe truncating boundaries are at \u00b13 \u00d7 185 s of the most likely tasc\u00a2\nvalue. For\ncomparison, the thin colored ellipses show curves of constant prior probability\ncorresponding to 1\u03c3, 2\u03c3, and 3\u03c3 (containing 39.3%, 86.5%, and 98.9% of the\nprior probability, respectively), including the effects of changing coordinates\nfrom tasc and Porb appearing in Table 1 to tasc\u00a2\nand P\u02dc. The inner search region, in\nwhich we choose a longer Tmax to do a deeper search, is within \u00b1185 s of the\nmost likely value of tasc\u00a2\nand contains 68.1% of the prior probability, while the\nfull search region, within \u00b13 \u00d7 185 s of the most likely tasc\u00a2\nvalue, contains\n99.2% of the prior probability. The slight misalignment of the prior and search\nellipses is due to a software bug, which led to a de\ufb01nition of P\u02dc that differed\nslightly from the optimal one, as described in Section 3. The dashed rectangular\nboundaries show the region effectively covered by the majority of search jobs\nfor which the \u201csheared\u201d period coordinate P\u02dc was unresolved in many search\njobs, i.e., the mismatch associated with an offset of 3.3 \u00d7 0.011 s from the most\nlikely value 68023.86 s was less than 0.0625.\nFigure 2. The search regions and prior uncertainties shown in Figure 1,\nexpressed in terms of the system parameters tasc\u00a2\nand Porb. For reference, we also\nshow the regions used for the O1 analysis in Abbott et al. (2017c; gray dashed\nlines) and reported for the O2 analysis in Zhang et al. (2021; orange dotted\nlines), propagated to the epoch of this search (which transforms the rectangular\nsearch regions into parallelograms). Note that the search region for Abbott et al.\n(2017c) is offset in both Porb and tasc\u00a2\nbecause it used the Porb estimate in\nGalloway et al. (2014), while the others used the updated estimate in Wang\net al. (2018). The analysis of Abbott et al. (2017c) is still believed to have\ncovered the plausible signal space because of the underresolution of the period\ndirection and the fact that the offset in tasc\u00a2\ninduced by the inaccurate Porb value\nwas less for the epoch of the search (2015 rather than 2019).\nFigure 3. Illustration of parameter space cells in tasc\u00a2\nand a\ni\nsin and example of\ncoherence times Tmax, in seconds, chosen as a function of the orbital parameters\nof the NS. Increasing coherence time improves the sensitivity but increases the\ncomputational cost of the search. The values used are the same as in Abbott\net al. (2017c), except between 400 and 600 Hz, where they have been doubled;\nsee Table 3 for details.\n13\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nre\ufb01nement search that survive this veto are known as the\n\u201clevel 1\u201d results.\n3. Two successive rounds of follow-up were performed,\nstarting with the level 1 candidates. At each stage, the\ncoherence time Tmax was quadrupled from the previous\nstage, and the density of templates in each direction was\nincreased\nby\na\nfactor\nof\n3.\nThe\ngrid\nused\nwas\n13 \u00d7 13 \u00d7 13 \u00d7 13 in\nf\na\ni t\nP\n,\nsin ,\n,\n0\nasc\u00a2\n(\n\u02dc), centered on\nthe peak of the previous level\u2019s results. Candidates that\nincreased their S/N from the previous level were known\nas the \u201clevel 2\u201d (4\u00d7 the original Tmax) and \u201clevel 3\u201d\n(16\u00d7 the original Tmax) results.\nA total of 22 candidates survive level 3 of follow-up. Two\nchecks were done to determine whether any of them represent\nconvincing detection candidates: one using the results of the\ncross-correlation\nsearch,\nand\none\nusing\nan\nindependent\npipeline.\nFor the \ufb01rst check, in Figure 5 we plot the ratio by which the\nS/N increases from level 1 to level 2 and from level 2 to\nlevel 3. We also plot the corresponding ratios for all of the\ncandidates surviving level 2 (the 16\u00d7 original Tmax follow-up is\nnot available for candidates that fail level 2), as well as for the\nsimulated signal injections described in Section 5. We would\nnaively expect a real signal to double its S/N between level 1\nand level 2, and again between level 2 and level 3, but none of\nthe candidates from the search come close to this. As in Abbott\net al. (2017c), none of the candidates double their S/N from\nlevel 1 to level 3, let alone in a single follow-up stage. On the\nother hand, all but one of the injections, while not doubling\ntheir S/N with each stage of follow-up, increase their S/N\nnoticeably more than any of the candidates from the search.\nFigure 4. Selection of follow-up threshold as a function of GW frequency. If\nthe data contained no signal and only Gaussian noise, each template in the\nparameter space would have some chance of producing a statistic value\nexceeding a given threshold. Within each 5 Hz frequency band, the total\nnumber of templates was computed and used to \ufb01nd the threshold at which the\nexpected number of Gaussian outliers above that value would be 0.1. This is\nshown with short blue lines for the templates in the present search (see\nTable 3); for reference, the thresholds calculated from the numbers of templates\nin the O1 search of Abbott et al. (2017c) are shown in orange. Because of the\nmore ef\ufb01cient template placement of algorithm from Wagner et al. (2022), the\nO3 search has fewer templates, and therefore a lower implied threshold, than\nthe O1 search, which used the same coherence times. The exception is for\n400 Hz < f0 < 600 Hz, where the same threshold of 6.2 was used for the O1\nand O3 searches, and the latter used twice the coherence time (and therefore a\ndenser parameter space lattice) as the former. The present search uses a\nthreshold of 6.3 for 25 Hz < f0 < 400 Hz and 5.8 for 600 Hz < f0 < 1600 Hz\n(black dashed line), which are lower than in the O1 search (magenta dashed\nline). Note that the large number of non-Gaussian outliers (see Table 3) makes\nthe Gaussian follow-up level an imprecise tool in any event.\nTable 3\nSummary of Numbers of Templates and Candidates\nf0 (Hz)\nTsft\nTmax (s)\n\u03c1\nNumber of\nExpected Gauss\nFollow-up Level\nMin\nMax\n(s)\nMin\nMax\nThresha\nTemplates\nFalse Alarmsb\n0c\n1d\n2e\n3f\n25\n50\n1440\n10080\n18720\n6.3\n5.68 \u00d7 109\n0.8\n63\n31\n10\n1\n50\n100\n1020\n8160\n14280\n6.3\n2.88 \u00d7 1010\n4.3\n131\n114\n40\n2\n100\n150\n840\n6720\n10920\n6.3\n6.13 \u00d7 1010\n9.1\n169\n166\n73\n3\n150\n200\n720\n5040\n8640\n6.3\n6.69 \u00d7 1010\n10.0\n171\n170\n68\n2\n200\n300\n600\n2400\n4800\n6.3\n4.54 \u00d7 1010\n6.7\n66\n66\n14\n4\n300\n400\n510\n1530\n3060\n6.3\n2.09 \u00d7 1010\n3.1\n19\n19\n1\n1\n400\n600\n360\n720\n2160\n6.2\n3.46 \u00d7 1010\n9.8\n343\n226\n20\n9\n600\n800\n360\n360\n360\n5.8\n1.80 \u00d7 109\n6.0\n15\n15\n0\n0\n800\n1200\n300\n300\n300\n5.8\n4.36 \u00d7 109\n14.5\n226\n70\n2\n0\n1200\n1600\n240\n240\n240\n5.8\n4.36 \u00d7 109\n14.5\n346\n55\n2\n0\nNotes. For each range of GW frequencies, this table shows the SFT duration Tsft; the minimum and maximum coherence time Tmax used for the search, across the\ndifferent orbital parameter space cells (see Figure 3); the threshold in S/N \u03c1 used for follow-up; the total number of templates; and the number of candidates at various\nstages of the process. (See Section 4 for detailed description of the follow-up procedure.)\na This is the threshold for initiating follow-up, i.e., to produce a level 0 candidate.\nb This is the number of candidates that would be expected in Gaussian noise, given the number of templates and the follow-up threshold.\nc This is the actual number of candidates (after clustering) that crossed the S/N threshold and were followed up.\nd This is the number of candidates remaining after re\ufb01nement. All of the candidates \u201cmissing\u201d at this stage have been removed by the single-detector veto for unknown\nlines, de\ufb01ned in Section 4.\ne This is the number of candidates remaining after each has been followed up with a Tmax equal to 4\u00d7 the original Tmax for that candidate. (True signals should\napproximately double their S/N; any candidates whose S/N goes down have been dropped.) All of the signals present at this stage are shown in Figure 5, which also\nshows the behavior of the search on simulated signals injected in software.\nf This is the number of candidates remaining after Tmax has been increased to 16\u00d7 its original value.\n14\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nNote that, at some GW signal frequencies, known instru-\nmental lines lead us to omit all the data from one of the two\nLIGO detectors from the search. This produces a single-\ndetector search for which the unknown-line veto is not\napplicable. Of the 22 search outliers that survived our veto\nprocess, 6 were in this category, as well as 4 of the injections,\nincluding the one injection that increased its S/N negligibly\nunder the follow-up procedure. Also note that of the 821\ninjected signals (out of 918) that produced \u03c1 values above their\nrespective thresholds, 817 survived all the levels of follow-up.\n(There were three vetoed at level 1, one at level 2, and zero at\nlevel 3, all because of the single-detector unknown-line veto.)\nWe thus conclude that our follow-up procedure is relatively\nrobust and that there are no convincing detection candidates\nfrom the search.\nAn additional, complementary, multistage MCMC follow-up\nusing the method described in Tenorio et al. (2021) using the\nPyFstat package (Ashton & Prix 2018; Keitel et al. 2021;\nAshton et al. 2022) was applied to the 22 outliers using the\nsame con\ufb01guration as in Abbott et al. (2022c). This method\nplaces templates adaptively to compute the semicoherent\n\uf046-statistic (Jaranowski et al. 1998; Cutler & Schutz 2005)\naround the candidate of interest using a diminishing number of\ncoherent segments (660, 330, 92, 24, 4, and 1). The coherence\ntimes of the corresponding segments range from half a day to\nthe full observing run. A Bayes factor is computed using the\n\uf046-statistic values from subsequent coherence stages corresp-\nonding to the loudest template. The signal hypothesis assesses\nthe consistency of these values, whereas the noise hypothesis\nstates the (in)consistency of the \ufb01nal value with the background\ndistribution, taking the \ufb01nal-stage factor into account.\nThe resulting Bayes factor values are signi\ufb01cantly lower than\nwhat would be expected for a signal detectable by this search,\nas con\ufb01rmed by an analogous follow-up of a similar number of\ninjected signals.\n5. Upper Limits and Implications\nSince our search produced no convincing detection candi-\ndates, we set upper limits on the strength of GWs from Sco X-1\nas a function of GW frequency, using the method described in\ndetail in Abbott et al. (2017c). First, naive Bayesian upper\nlimits were set within each 0.05 Hz band, using the 95th\npercentile of the posterior on h0\n2 or h0\neff 2\n(\n) deduced from the\nhighest S/N seen in each band.307 Then, a series of simulated\nsignals were added to the data at a variety of amplitudes, and a\nBayesian logistic regression analysis was performed to estimate\nthe factor by which to multiply the naive 95% Bayesian upper\nlimit on amplitude in order to reach the threshold of 95% signal\nrecovery. (As in Abbott et al. (2017c), \u201crecovery\u201d was de\ufb01ned\nas an increase in the maximum S/N seen in a band, over the\nvalue with no injection present.) We performed a total of 918\ninjections308 between 25 and 500 Hz, of which 863 were\nrecovered, with a resulting adjustment factor of 1.19 to the\namplitude of the h0\neff upper limit. As described in Abbott et al.\n(2017c), to set the adjustment factor for the h0 limit, we limit\nattention to injections that were generated with a speci\ufb01ed h0\nrather than h0\neff, of which we recovered 546 of 575, with a\nresulting adjustment factor of 1.17.309 The upper limits\nincluding these adjustment factors are shown in Figure 6.\nThe upper limits placed by this search improve on those from\nprevious observing runs and are now probing a theoretically\nsigni\ufb01cant portion of parameter space. This is usually quanti\ufb01ed\nin terms of the torque balance amplitude, i.e., the GW amplitude\nthat would be required for GW spin-down torques to balance the\naccretion torque. As discussed in Section 1, this limit is a useful\nbenchmark but is highly uncertain, re\ufb02ecting the high level of\nuncertainty in the theoretical modeling of accretion torques. We\nillustrate this in Figure 7 by comparing the upper limits from our\nsearch not only to the standard limit of Equation (5), obtained\nby assuming the lever arm to be the radius of the NS,\nr = R* = 10 km, in Equation (4), but also to an example of the\nrange of torque balance amplitudes allowed by current models\nfor accretion onto a magnetized star. First, we consider a model\nof the same form as in Equations (3) and (5), but we do not\nassume accretion to occur on the surface, but rather take the\ntorque arm to be the Alfv\u00e9n radius rA, at which the disk is\ntruncated by the magnetic \ufb01eld (Pringle & Rees 1972):\n\uf026\n\uf065\n\uf065\nr\nX\nM\nM\nM\nM\nR\nB\n35\n10\nyr\n1.4\n10 km\n10 G\nkm,\n10\nA\n10\n1\n2 7\n1 7\n12 7\n8\n4 7\n=\n\u00b4\n-\n-\n-\n-\n\u239c\n\u239f\n\u239c\n\u239f\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n\u239b\n\u239d\n\u239e\n\u23a0\n(\n)\nFigure 5. Ratios of follow-up statistics for search candidates and simulated\nsignals. This plot shows all of the candidates that survived level 2 of follow-up\n(see Section 4 and Table 3), both from the main search and from the analysis of\nthe simulated signal injections described in Section 5. It shows the ratios of the\nS/N \u03c1 after follow-up level 1 (at the original coherence time Tmax), level 2 (at\n4\u00d7 the original coherence time), and level 3 (at 16\u00d7 the original coherence\ntime). (The boxes labeled \u201csingle detector\u201d are outliers or injections at GW\nfrequencies where only one detector\u2019s data were included in the analysis\nbecause of known instrumental artifacts in the other detector.) The green\ndashed lines are at constant values of \u03c1level 3/\u03c1level 1 equal to 2 and 4. There are\nno points with \u03c1level 2/\u03c1level 1 < 1 because those candidates do not survive\nlevel 2 follow-up and are therefore not subjected to level 3 follow-up. From the\nconstruction of the statistic in Whelan et al. (2015), the naive expectation is that\nthe S/N will roughly double each time Tmax is quadrupled. Empirically, the\nfollow-ups of injections do not show exactly that relationship, but all but one\n(which was injected at a frequency contaminated by instrumental artifacts)\nshow signi\ufb01cant increases in S/N that are not seen in any of the follow-ups of\nsearch candidates. We thus conclude that no convincing detection candidates\nare present.\n307 We used a simple extreme value likelihood assuming independent\nGaussian distributions for the detection statistics from the templates in the\ninitial bank. Future work may leverage more sophisticated methods of\nestimating this distribution, such as those of Tenorio et al. (2022).\n308 These are the same injections that were used to validate the follow-up\nprocedure, as described in Section 4.\n309 For comparison, the adjustment factors in Abbott et al. (2017c) were 1.44\nfor h0 and 1.21 for h0\neff. The fact that the factors derived from the current search\nare comparable is evidence that the template bank modi\ufb01cations of Wagner\net al. (2022) do not signi\ufb01cantly reduce the sensitivity of the search.\n15\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nwhere 0.1 \uf088X \uf0881 is a phenomenological parameter that\nencodes the uncertainty in the truncation radius of the disk.\nUsing the mass accretion rate of Sco X-1 inferred from X-ray\nobservations (Watts et al. 2008), along with B = 108 G\nand X = 1, gives an Alfv\u00e9n radius of rA \u224849 km, which\nis used to generate the curve in Figure 7. We also consider one\nof the parameterized models of Glampedakis & Suvorov\n(2021), which encompass a wide range of physics and can\nsuccessfully \ufb01t spin-up episodes in a number of observed\nLMXBs. In particular, for illustrative purposes, we use their\nFigure 6. Upper limits from directed searches in advanced LIGO data. Top: upper limit on h0, after marginalizing over NS spin inclination \u03b9, assuming an isotropic\nprior. The dashed line shows the nominal expected level assuming torque balance (Equation (5)) as a function of GW frequency. Bottom: upper limit on h0\neff, de\ufb01ned\nin Equation (2). This is equivalent to the upper limit on h0 assuming circular polarization. (Note that the marginalized upper limit in the top panel is dominated by\nlinear polarization and so is a factor of almost\n8 higher). The blue dotted\u2013dashed line (labeled as \u201ctb w/\u03b9 = 44\u00b0\u201d) corresponds to the assumption that the NS spin is\naligned to the most likely orbital angular momentum and \u03b9 \u2248i \u224844\u00b0 (see Table 1). The blue diagonal bands show h0\neff levels corresponding to the torque balance h0 in\nthe top panel. The darker-shaded band corresponds (5th to 95th percentiles) to a Gaussian distribution with mean and standard deviation corresponding to\n\u03b9 = 44\u00b0 \u00b1 6\u00b0, as used in Zhang et al. (2021). Finally, the lighter-shaded band shows the full range of possible h0\neff values corresponding to torque balance, with\ncircular polarization at the top and linear polarization on the bottom. For comparison with the \u201cCrossCorr O3\u201d results presented in this paper, we show in the top panel\nthe isotropic marginalized limits from the previous cross-correlation searches in Abbott et al. (2017c) (\u201cCrossCorr O1\u201d) and Zhang et al. (2021) (\u201cCrossCorr O2\u201d). In\nthe bottom panel we include the limits assuming circular polarization from other searches of O3 data: \u201cRadiometer O3\u201d is the narrowband radiometer analysis of\nAbbott et al. (2021a), which used data from Advanced LIGO\u2019s \ufb01rst three observing runs, and \u201cViterbi O3\u201d is the analysis of Abbott et al. (2022a) using a hidden\nMarkov model.\n16\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n\u201cnew\u201d\nmodel\n2,\nfor\nwhich\nthe\ntorque\nhas\nthe\nform\nN\nN 1\n3\n2\n3\nA\nA\nA\n2\n7 2\n7 2\nx\nx\nw\n=\n+\n-\n-\n(\n)\n( )\n, with the fastness para-\nmeter\nR\nR\nA\nA\nC\n3 2\nw = (\n)(\n)\nand the\ncorotation\nradius\nRc=\n\uf065\nM\nM\n27\n1.4\nkm\n1 3\n500\n2 3\nsn\n-\n(\n)(\n)(\n)(\n)\n. We consider two values\nfor the magnetic \ufb01eld strength at the surface of the star, B = 108\nand 109 G, and consider values of \u03be between 0.3 (which sets the\nupper limit in our plots) and 0.5.\nAs can be clearly seen, there is a wide portion of parameter\nspace allowed by theoretical models. Furthermore, at higher\nfrequencies the theory is intrinsically uncertain; it is in fact\nunclear whether one should expect the source to be rapidly\nrotating, as some of the models of Glampedakis & Suvorov\n(2021) predict spin equilibrium due to accretion alone below\nGW frequencies of roughly 1 kHz, without any need for\ngravitational radiation\u2013in fact, it is also possible that the NS\nmay not be in the frequency range we are searching. This\n\u201cfuzziness\u201d in the torque balance limit (which may be even\nfurther enhanced by additional effects not considered in the\nmodels of Glampedakis & Suvorov (2021), such as viscous\nheating in the disk or the ef\ufb01ciency of X-ray emission) makes it\ntherefore impossible to draw \ufb01rm conclusions on the equation\nof state (EOS) of the NS, or magnetic \ufb01eld strength, directly\nfrom our upper limits, without committing to a particular\naccretion model. It is therefore important to remember, when\nanalyzing our results, that torque balance may not be active in\nthis system, or that even if it is, the GW torques may only be\nactive for a fraction of the time, with a low duty cycle for GW\nemission (Haskell et al. 2015).\nNevertheless, it is clear from Figure 7 that in the range we\nare most sensitive to, approximately between 30 and 400 Hz,\nour upper limits are probing below even the more stringent\nlimit set by accretion onto the surface, thus searching a\nphysically signi\ufb01cant portion of parameter space. Furthermore,\nour results are probing the parameter space predicted by the\nmodels of Glampedakis & Suvorov (2021) up to f0 \u223c500 Hz.\nSearching at these higher GW frequencies is important;\nalthough the frequency of Sco X-1 is not known, the\ndistribution of spin frequencies of the observed AMXPs\nappears to be bimodal (Patruno et al. 2017), with a \u201cfast\u201d\npopulation of pulsars, for which Patruno et al. (2017) make\nthe hypothesis that GW emission may play a role, centered\naround \u03bds \u2248550 Hz (i.e., f0 \u22481100 Hz for triaxial emission),\nand a slower population centered around \u03bds \u2248300 Hz (i.e.,\nf0 \u2248600 Hz).\nTo give an illustration of how our results can constrain\npossible torque balance models, consider in more detail the\nsimplest accretion model, i.e., that obtained by setting r = R* in\nEquation (3). In this case we may ask whether, by comparing\nthe upper limits from our searches to the theoretical value for\nthe h0 in Equation (3), it is possible to put constraints on the\nphysical parameters of the star for which the torque balance\nscenario is still viable. To answer this question, we consider\ntwo parameters: the mass of the star and the inclination angle \u03b9,\nfor two EOSs taken from the CompOSE database (Typel et al.\n2015; Oertel et al. 2017; Typel et al. 2022) both for a softer\nEOS, GR15 (Gulminelli & Raduta 2015), and for a stiffer EOS,\nGPPVA (Grill et al. 2014). The results can be seen in Figure 8\nfor the mass of the NSs. We see that, for the range of GW\nfrequencies in which our search is most sensitive, we can\nexclude the torque balance scenario for higher-mass NSs,\nespecially in the case of a stiffer EOS. The GW amplitude is,\nhowever, clearly very strongly affected by the inclination\nangle, so in Figure 8 we also plot our constraints in terms of the\ninclination\nangle\n\u03b9,\nholding\nthe\nstellar\nmass\n\ufb01xed\nat\nM = 1.4Me. In this case we also see that we can rule out\ntorque balance models with nearly circular polarization (small\n\u03b9) over a wide range of frequencies for both choices of EOS.\n6. Conclusions and Outlook\nWe have presented the results of the most sensitive search to\ndate for GWs from Sco X-1, using LIGO detector data from the\nthird observing run of Advanced LIGO and Advanced Virgo.\nWe have set upper limits across a range of GW signal\nfrequencies 25 Hz < f0 < 1600 Hz, corresponding to NS spin\nfrequencies of 12.5 Hz < \u03bds < 800 Hz. The sensitivity of our\nsearch is now probing possible models of torque balance\nequilibrium over a range of GW frequencies spanning hundreds\nof hertz and, for the \ufb01rst time, approaches the standard\nconservative torque balance prediction even under pessimistic\nassumptions about NS inclination angle. We expect to see a\nfurther improvement in sensitivity from upcoming LIGO-\nVirgo-KAGRA observing runs (Abbott et al. 2020).\nThis material is based on work supported by NSF\u02bcs LIGO\nLaboratory, which is a major facility fully funded by the\nNational Science Foundation. The authors also gratefully\nacknowledge the support of the Science and Technology\nFacilities Council (STFC) of the United Kingdom, the Max-\nPlanck-Society (MPS), and the State of Niedersachsen/\nGermany for support of the construction of Advanced LIGO\nand construction and operation of the GEO 600 detector.\nAdditional support for Advanced LIGO was provided by the\nAustralian Research Council. The authors gratefully acknowl-\nedge the Italian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scienti\ufb01que\n(CNRS), and the Netherlands Organization for Scienti\ufb01c\nResearch (NWO) for the construction and operation of the\nVirgo detector and the creation and support of the EGO\nFigure 7. Comparison of upper limits to predictions of torque balance models.\nThe gray band indicates the h0 upper limit implied by the h0\neff upper limit in the\nbottom panel of Figure 6, assuming the range of possible inclinations from\n\uf084\n\uf084\n0\ncos\n1\ni\n\u2223\n\u2223\n. (Linear polarization (cos\n0\ni =\n) is at the top, and circular\npolarization (cos\n1\ni = \uf0b1) is at the bottom.) The dashed blue line is the usual\nconservative torque balance estimate assuming accretion at the surface of the\nNS, r = R* = 10 km. The dotted\u2013dashed red line is the same model assuming a\nlever arm of r = rA \u224849 km, which is the value of the Alfv\u00e9n radius given by\nEquation (10) for \u03be = 1 and B = 108 G. Note that this is slightly larger than the\nvalue of 35 km used in, e.g., Zhang et al. (2021) and Abbott et al. (2022a),\nsince we use the inferred mass accretion rate of Sco X-1. The colored bands\nshow the range of predictions for the models of Glampedakis & Suvorov\n(2021), in particular model 2, for the range of 0.3 < \u03be < 0.5, assuming a\nmagnetic \ufb01eld of 108 G (GS8) or 109 G (GS9).\n17\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\nconsortium. The authors also gratefully acknowledge research\nsupport from these agencies, as well as by the Council of\nScienti\ufb01c and Industrial Research of India, the Department of\nScience and Technology, India, the Science & Engineering\nResearch Board (SERB), India, the Ministry of Human\nResource Development, India, the Spanish Agencia Estatal de\nInvestigaci\u00f3n (AEI), the Spanish Ministerio de Ciencia e\nInnovaci\u00f3n and Ministerio de Universidades, the Conselleria de\nFons Europeus, Universitat i Cultura and the Direcci\u00f3 General\nde Pol\u00edtica Universitaria i Recerca del Govern de les Illes\nBalears, the Conselleria d\u2019Innovaci\u00f3 Universitats, Ci\u00e8ncia i\nSocietat Digital de la Generalitat Valenciana and the CERCA\nProgramme Generalitat de Catalunya, Spain, the National\nScience Centre of Poland and the European Union\u2014European\nRegional Development Fund, Foundation for Polish Science\n(FNP), the Swiss National Science Foundation (SNSF), the\nRussian Foundation for Basic Research, the Russian Science\nFoundation, the European Commission, the European Social\nFunds (ESF), the European Regional Development Funds\n(ERDF), the Royal Society, the Scottish Funding Council, the\nScottish Universities Physics Alliance, the Hungarian Scienti\ufb01c\nResearch Fund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scienti\ufb01que (FRS-\nFNRS), Actions de Recherche Concert\u00e9es (ARC) and Fonds\nWetenschappelijk Onderzoek\u2014Vlaanderen (FWO), Belgium,\nthe\nParis\nI\u0302le-de-France\nRegion,\nthe\nNational\nResearch,\nDevelopment and Innovation Of\ufb01ce Hungary (NKFIH), the\nNational Research Foundation of Korea, the Natural Science\nand Engineering Research Council Canada, Canadian Founda-\ntion for Innovation (CFI), the Brazilian Ministry of Science,\nTechnology, and Innovations, the International Center for\nTheoretical Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council of Hong\nKong, the National Natural Science Foundation of China\n(NSFC), the Leverhulme Trust, the Research Corporation, the\nMinistry of Science and Technology (MOST), Taiwan, the\nUnited States Department of Energy, and the Kavli Foundation.\nThe authors gratefully acknowledge the support of the NSF,\nSTFC, INFN, and CNRS for provision of computational\nresources.\nThis work was supported by MEXT, JSPS Leading-edge\nResearch\nInfrastructure\nProgram,\nJSPS\nGrant-in-Aid\nfor\nSpecially\nPromoted\nResearch\n26000005,\nJSPS\nGrant-in-\nAid for Scienti\ufb01c Research on Innovative Areas 2905:\nJP17H06358, JP17H06361, and JP17H06364, JSPS Core-to-\nCore Program A. Advanced Research Networks, JSPS Grant-\nin-Aid for Scienti\ufb01c Research (S) 17H06133 and 20H05639,\nJSPS Grant-in-Aid for Transformative Research Areas (A)\nFigure 8. Illustration of how the upper limits shown in Figure 6 can constrain models for Sco X-1 that include torque balance due to gravitational waves. In the top\nrow, we show constraints on the NS mass, assuming torque balance due to GW at the speci\ufb01ed frequency, in the simple model where r = R*. We consider two EOSs,\na softer model, GR15 (Gulminelli & Raduta 2015), and a stiffer model, GPPVA (Grill et al. 2014). The largest exclusion region is for an NS inclination angle \u03b9 = 0\u00b0\n(or 180\u00b0), where the GWs would be circularly polarized. Assuming the worst-case scenario of linear polarization \u03b9 = 90\u00b0 gives constraints that hold for any\ninclination, and the most likely value of \u03b9 = 44\u00b0 (aligned with the binary orbit) gives an intermediate case. We see that for both EOSs (and especially for the stiffer\nEOS) the torque balance scenario can be excluded for higher-mass NSs for the GW frequency range in which our searches are more sensitive. Since the inclination\nangle plays a strong role in the constraints, we present in the bottom row, for the same EOSs but for a \ufb01xed mass of M = 1.4Me, the limits that can be set on \u03b9. We see\nthat, for both EOSs, our observations can exclude nearly circular polarized (small \u03b9) GW emission at the torque balance level for a wide range of frequencies.\n18\nThe Astrophysical Journal Letters, 941:L30 (19pp), 2022 December 20\nAbbott et al.\n\n20A203: JP20H05854, the joint research program of the\nInstitute for Cosmic Ray Research, University of Tokyo,\nNational Research Foundation (NRF), Computing Infrastruc-\nture Project of KISTI-GSDC, Korea Astronomy and Space\nScience Institute (KASI), and Ministry of Science and ICT\n(MSIT) in Korea, Academia Sinica (AS), AS Grid Center\n(ASGC) and the Ministry of Science and Technology (MoST)\nin\nTaiwan\nunder\ngrants\nincluding\nAS-CDA-105-M06,\nAdvanced Technology Center (ATC) of NAOJ, and Mechan-\nical Engineering Center of KEK.\nThis paper has been assigned LIGO Document No. LIGO-\nP2100110-v13.\nSoftware: LALSuite (LIGO Scienti\ufb01c Collaboration 2018),\nLatticeTiling (Wette 2014), PyFstat (Ashton & Prix\n2018; Keitel et al. 2021; Ashton et al. 2022) numpy (Harris\net al. 2020), matplotlib (Hunter 2007), scipy (Virtanen\net al. 2020).\nReferences\nAasi, J., Abbott, B. 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Adamowski,66\nD. Adams,20 M. Adinolfi,19 C. Adriano,30 A. Aduszkiewicz,81 J. Aguilar,126 F. Akbar,175 K. Allison,43 S. Alonso\nMonsalve,35 M. Alrashed,119 A. Alton,13 R. Alvarez,39 T. Alves,88 H. Amar,84 P. Amedo,85, 84 J. Anderson,8\nC. Andreopoulos,128 M. Andreotti,94, 67 M. P. Andrews,66 F. Andrianala,5 S. Andringa,127 N. Anfimov\n,\nA. Ankowski,184 D. Antic,19 M. Antoniassi,193 M. Antonova,84 A. Antoshkin\n, A. Aranda-Fernandez,42\nL. Arellano,135 E. Arrieta Diaz,180 M. A. Arroyave,66 J. Asaadi,197 A. Ashkenazi,194 D. M. Asner,20 L. Asquith,191\nE. Atkin,88 D. Auguste,160 A. Aurisano,40 V. Aushev,124 D. Autiero,110 M. B. Azam,87 F. Azfar,156 A. Back,91\nH. Back,157 J. J. Back,209 I. Bagaturia,72 L. Bagby,66 N. Balashov\n, S. Balasubramanian,66 P. Baldi,24\nW. Baldini,94 J. Baldonedo,206 B. Baller,66 B. Bambah,82 R. Banerjee,216 F. Barao,127, 112 D. Barbu,21\nG. Barenboim,84 P. Barham Alz\u00b4as,35 G. J. Barker,209 W. Barkhouse,148 G. Barr,156 J. Barranco Monarca,77\nA. Barros,193 N. Barros,127, 61 D. Barrow,156 J. L. Barrow,143 A. Basharina-Freshville,203 A. Bashyal,8 V. Basque,66\nC. Batchelor,57 L. Bathe-Peters,156 J.B.R. Battat,210 F. Battisti,156 F. Bay,4 M. C. Q. Bazetto,30 J. L. L. Bazo\nAlba,169 J. F. Beacom,154 E. Bechetoille,110 B. Behera,186 E. Belchior,130 G. Bell,52 L. Bellantoni,66\nG. Bellettini,103, 167 V. Bellini,93, 31 O. Beltramello,35 N. Benekos,35 C. Benitez Montiel,84, 10 D. Benjamin,20\nF. Bento Neves,127 J. Berger,44 S. Berkman,139 J. Bernal,10 P. Bernardini,97, 179 A. Bersani,96 S. Bertolucci,92, 17\nM. Betancourt,66 A. Betancur Rodr\u00b4\u0131guez,58 A. Bevan,172 Y. Bezawada,23 A. T. Bezerra,62 T. J. Bezerra,191\nA. Bhat,37 V. Bhatnagar,159 J. Bhatt,203 M. Bhattacharjee,89 M. Bhattacharya,66 S. Bhuller,19 B. Bhuyan,89\nS. Biagi,105 J. Bian,24 K. Biery,66 B. Bilki,15, 108 M. Bishai,20 A. Bitadze,135 A. Blake,125 F. D. Blaszczyk,66\nG. C. Blazey,149 E. Blucher,37 A. Bodek,175 J. Bogenschuetz,197 J. Boissevain,129 S. Bolognesi,34 T. Bolton,119\nL. Bomben,98, 107 M. Bonesini,98, 140 C. Bonilla-Diaz,32 F. Bonini,20 A. Booth,172 F. Boran,91 S. Bordoni,35\nR. Borges Merlo,30 A. Borkum,191 N. Bostan,108 R. Bouet,131 J. Boza,44 J. Bracinik,16 B. Brahma,90\nD. Brailsford,125 F. Bramati,98 A. Branca,98 A. Brandt,197 J. Bremer,35 C. Brew,178 S. J. Brice,66 V. Brio,93\nC. Brizzolari,98, 140 C. Bromberg,139 J. Brooke,19 A. Bross,66 G. Brunetti,98, 140 M. Brunetti,209 N. Buchanan,44\nH. Budd,175 J. Buergi,14 A. Bundock,19 D. Burgardt,211 S. Butchart,191 G. Caceres V.,23 I. Cagnoli,92, 17 T. Cai,216\nR. Calabrese,100 R. Calabrese,94, 67 J. Calcutt,155 L. Calivers,14 E. Calvo,39 A. Caminata,96 A. F. Camino,168\nW. Campanelli,127 A. Campani,96, 71 A. Campos Benitez,207 N. Canci,100 J. Cap\u00b4o,84 I. Caracas,134 D. Caratelli,27\nD. Carber,44 J. M. Carceller,35 G. Carini,20 B. Carlus,110 M. F. Carneiro,20 P. Carniti,98 I. Caro Terrazas,44\nH. Carranza,197 N. Carrara,23 L. Carroll,119 T. Carroll,213 A. Carter,176 E. Casarejos,206 D. Casazza,94\nJ. F. Casta\u02dcno Forero,7 F. A. Casta\u02dcno,6 A. Castillo,182 C. Castromonte,106 E. Catano-Mur,212 C. Cattadori,98\nF. Cavalier,160 F. Cavanna,66 S. Centro,158 G. Cerati,66 C. Cerna,131 A. Cervelli,92 A. Cervera Villanueva,84\nK. Chakraborty,166 S. Chakraborty,86 M. Chalifour,35 A. Chappell,209 N. Charitonidis,35 A. Chatterjee,166\nH. Chen,20 M. Chen,24 W. C. Chen,199 Y. Chen,184 Z. Chen-Wishart,176 D. Cherdack,81 C. Chi,45 F. Chiapponi,92\nR. Chirco,87 N. Chitirasreemadam,103, 167 K. Cho,122 S. Choate,108 D. Chokheli,72 P. S. Chong,164 B. Chowdhury,8\nD. Christian,66 A. Chukanov\n, M. Chung,202 E. Church,157 M. F. Cicala,203 M. Cicerchia,158 V. Cicero,92, 17\nR. Ciolini,103 P. Clarke,57 G. Cline,126 T. E. Coan,188 A. G. Cocco,100 J. A. B. Coelho,161 A. Cohen,161\nJ. Collazo,206 J. Collot,76 E. Conley,55 J. M. Conrad,136 M. Convery,184 S. Copello,96 A. F. V. Cortez,217\nP. Cova,99, 162 C. Cox,176 L. Cremaldi,144 L. Cremonesi,172 J. I. Crespo-Anad\u00b4on,39 M. Crisler,66 E. Cristaldo,98, 10\nJ. Crnkovic,66 G. Crone,203 R. Cross,209 A. Cudd,43 C. Cuesta,39 Y. Cui,26 F. Curciarello,95 D. Cussans,19\nJ. Dai,76 O. Dalager,66 R. Dallavalle,161 W. Dallaway,199 R. D\u2019Amico,94, 67 H. da Motta,33 Z. A. Dar,212\nR. Darby,191 L. Da Silva Peres,65 Q. David,110 G. S. Davies,144 S. Davini,96 J. Dawson,161 R. De Aguiar,30 P. De\nAlmeida,30 P. Debbins,108 I. De Bonis,51 M. P. Decowski,146, 3 A. de Gouv\u02c6ea,150 P. C. De Holanda,30 I. L. De\nIcaza Astiz,191 P. De Jong,146, 3 P. Del Amo Sanchez,51 A. De la Torre,39 G. De Lauretis,110 A. Delbart,34\nD. Delepine,77 M. Delgado,98, 140 A. Dell\u2019Acqua,35 G. Delle Monache,95 N. Delmonte,99, 162 P. De Lurgio,8\nR. Demario,139 G. De Matteis,97, 179 J. R. T. de Mello Neto,65 D. M. DeMuth,205 S. Dennis,29 C. Densham,178\nP. Denton,20 G. W. Deptuch,20 A. De Roeck,35 V. De Romeri,84 J. P. Detje,29 J. Devine,35 R. Dharmapalan,79\nM. Dias,201 A. Diaz,28 J. S. D\u00b4\u0131az,91 F. D\u00b4\u0131az,169 F. Di Capua,100, 145 A. Di Domenico,181, 104 S. Di Domizio,96, 71\nS. Di Falco,103 L. Di Giulio,35 P. Ding,66 L. Di Noto,96, 71 E. Diociaiuti,95 C. Distefano,105 R. Diurba,14\nM. Diwan,20 Z. Djurcic,8 D. Doering,184 S. Dolan,35 F. Dolek,207 M. J. Dolinski,54 D. Domenici,95 L. Domine,184\nS. Donati,103, 167 Y. Donon,35 S. Doran,109 D. Douglas,184 T.A. Doyle,189 A. Dragone,184 F. Drielsma,184\nL. Duarte,201 D. Duchesneau,51 K. Duffy,156 K. Dugas,24 P. Dunne,88 B. Dutta,195 H. Duyang,185 D. A. Dwyer,126\nA. S. Dyshkant,149 S. Dytman,168 M. Eads,149 A. Earle,191 S. Edayath,109 D. Edmunds,139 J. Eisch,66 P. Englezos,177\nA. Ereditato,37 T. Erjavec,23 C. O. Escobar,66 J. J. Evans,135 E. Ewart,91 A. C. Ezeribe,183 K. Fahey,66 L. Fajt,35\n\n2\nA. Falcone,98, 140 M. Fani\u2019,143, 129 C. Farnese,101 S. Farrell,174 Y. Farzan,111 D. Fedoseev\n, J. Felix,77 Y. Feng,109\nE. Fernandez-Martinez,133 D. Fern\u00b4andez-Posada,85 G. Ferry,160 E. Fialova,50 L. Fields,151 P. Filip,49 A. Filkins,192\nF. Filthaut,146, 173 R. Fine,129 G. Fiorillo,100, 145 M. Fiorini,94, 67 S. Fogarty,44 W. Foreman,87 J. Fowler,55\nJ. Franc,50 K. Francis,149 D. Franco,37 J. Franklin,56 J. Freeman,66 J. Fried,20 A. Friedland,184 S. Fuess,66\nI. K. Furic,68 K. Furman,172 A. P. Furmanski,143 R. Gaba,159 A. Gabrielli,92, 17 A. M Gago,169 F. Galizzi,98\nH. Gallagher,200 N. Gallice,20 V. Galymov,110 E. Gamberini,35 T. Gamble,183 F. Ganacim,193 R. Gandhi,78\nS. Ganguly,66 F. Gao,27 S. Gao,20 D. Garcia-Gamez,73 M. \u00b4A. Garc\u00b4\u0131a-Peris,84 F. Gardim,62 S. Gardiner,66\nD. Gastler,18 A. Gauch,14 J. Gauvreau,153 P. Gauzzi,181, 104 S. Gazzana,95 G. Ge,45 N. Geffroy,51 B. Gelli,30\nS. Gent,187 L. Gerlach,20 Z. Ghorbani-Moghaddam,96 T. Giammaria,94, 67 D. Gibin,158, 101 I. Gil-Botella,39\nS. Gilligan,155 A. Gioiosa,103 S. Giovannella,95 C. Girerd,110 A. K. Giri,90 C. Giugliano,94 V. Giusti,103 D. Gnani,126\nO. Gogota,124 S. Gollapinni,129 K. Gollwitzer,66 R. A. Gomes,63 L. V. Gomez Bermeo,182 L. S. Gomez Fajardo,182\nF. Gonnella,16 D. Gonzalez-Diaz,85 M. Gonzalez-Lopez,133 M. C. Goodman,8 S. Goswami,166 C. Gotti,98\nJ. Goudeau,130 E. Goudzovski,16 C. Grace,126 E. Gramellini,135 R. Gran,142 E. Granados,77 P. Granger,161\nC. Grant,18 D. R. Gratieri,70, 30 G. Grauso,100 P. Green,156 S. Greenberg,126, 22 J. Greer,19 W. C. Griffith,191\nF. T. Groetschla,35 K. Grzelak,208 L. Gu,125 W. Gu,20 V. Guarino,8 M. Guarise,94, 67 R. Guenette,135 M. Guerzoni,92\nD. Guffanti,98, 140 A. Guglielmi,101 B. Guo,185 F. Y. Guo,189 A. Gupta,184 V. Gupta,146, 3 G. Gurung,197\nD. Gutierrez,170 P. Guzowski,135 M. M. Guzzo,30 S. Gwon,38 A. Habig,142 H. Hadavand,197 L. Haegel,110\nR. Haenni,14 L. Hagaman,214 A. Hahn,66 J. Haiston,186 J. Hakenm\u00a8uller,55 T. Hamernik,66 P. Hamilton,88\nJ. Hancock,16 F. Happacher,95 D. A. Harris,216, 66 A. Hart,172 J. Hartnell,191 T. Hartnett,178 J. Harton,44\nT. Hasegawa,121 C. M. Hasnip,35 R. Hatcher,66 K. Hayrapetyan,172 J. Hays,172 E. Hazen,18 M. He,81 A. Heavey,66\nK. M. Heeger,214 J. Heise,190 P. Hellmuth,131 S. Henry,175 J. Hern\u00b4andez-Gar\u00b4\u0131a,84 K. Herner,66 V. Hewes,40\nA. Higuera,174 C. Hilgenberg,143 S. J. Hillier,16 A. Himmel,66 E. Hinkle,37 L.R. Hirsch,193 J. Ho,53 J. Hoff,66\nA. Holin,178 T. Holvey,156 E. Hoppe,157 S. Horiuchi,207 G. A. Horton-Smith,119 T. Houdy,160 B. Howard,216\nR. Howell,175 I. Hristova,178 M. S. Hronek,66 J. Huang,23 R.G. Huang,126 Z. Hulcher,184 M. Ibrahim,59 G. Iles,88\nN. Ilic,199 A. M. Iliescu,95 R. Illingworth,66 G. Ingratta,92, 17 A. Ioannisian,215 B. Irwin,143 L. Isenhower,1\nM. Ismerio Oliveira,65 R. Itay,184 C.M. Jackson,157 V. Jain,2 E. James,66 W. Jang,197 B. Jargowsky,24 D. Jena,66\nI. Jentz,213 X. Ji,20 C. Jiang,115 J. Jiang,189 L. Jiang,207 A. Jipa,21 J. H. Jo,20 F. R. Joaquim,127, 112 W. Johnson,186\nC. Jollet,131 B. Jones,197 R. Jones,183 N. Jovancevic,152 M. Judah,168 C. K. Jung,189 T. Junk,66 Y. Jwa,184, 45\nM. Kabirnezhad,88 A. C. Kaboth,176, 178 I. Kadenko,124 I. Kakorin\n, A. Kalitkina\n, D. Kalra,45 M. Kandemir,60\nD. M. Kaplan,87 G. Karagiorgi,45 G. Karaman,108 A. Karcher,126 Y. Karyotakis,51 S. Kasai,123 S. P. Kasetti,130\nL. Kashur,44 I. Katsioulas,16 A. Kauther,149 N. Kazaryan,215 L. Ke,20 E. Kearns,18 P.T. Keener,164 K.J. Kelly,195\nE. Kemp,30 O. Kemularia,72 Y. Kermaidic,160 W. Ketchum,66 S. H. Kettell,20 M. Khabibullin\n, N. Khan,88\nA. Khvedelidze,72 D. Kim,195 J. Kim,175 M. J. Kim,66 B. King,66 B. Kirby,45 M. Kirby,20 A. Kish,66 J. Klein,164\nJ. Kleykamp,144 A. Klustova,88 T. Kobilarcik,66 L. Koch,134 K. Koehler,213 L. W. Koerner,81 D. H. Koh,184\nL. Kolupaeva\n, D. Korablev\n, M. Kordosky,212 T. Kosc,76 U. Kose,35 V. A. Kosteleck\u00b4y,91 K. Kothekar,19\nI. Kotler,54 M. Kovalcuk,49 V. Kozhukalov\n, W. Krah,146 R. Kralik,191 M. Kramer,126 L. Kreczko,19\nF. Krennrich,109 I. Kreslo,14 T. Kroupova,164 S. Kubota,135 M. Kubu,35 Y. Kudenko\n, V. A. Kudryavtsev,183\nG. Kufatty,69 S. Kuhlmann,8 S. Kulagin\n, J. Kumar,79 P. Kumar,183 S. Kumaran,24 J. Kunzmann,14 R. Kuravi,126\nN. Kurita,184 C. Kuruppu,185 V. Kus,50 T. Kutter,130 M. Ku\u00b4zniak,217 J. Kvasnicka,49 T. Labree,149 T. Lackey,66\nI. Lal\u02d8au,21 A. Lambert,126 B. J. Land,164 C. E. Lane,54 N. Lane,135 K. Lang,198 T. Langford,214 M. Langstaff,135\nF. Lanni,35 O. Lantwin,51 J. Larkin,20 P. Lasorak,88 D. Last,164 A. Laudrain,134 A. Laundrie,213 G. Laurenti,92\nE. Lavaut,160 P. Laycock,20 I. Lazanu,21 R. LaZur,44 M. Lazzaroni,99, 141 T. Le,200 S. Leardini,85 J. Learned,79\nT. LeCompte,184 V. Legin,124 G. Lehmann Miotto,35 R. Lehnert,91 M. A. Leigui de Oliveira,64 M. Leitner,126\nD. Leon Silverio,186 L. M. Lepin,69 J.-Y Li,57 S. W. Li,24 Y. Li,20 H. Liao,119 C. S. Lin,126 D. Lindebaum,19\nS. Linden,20 R. A. Lineros,32 A. Lister,213 B. R. Littlejohn,87 H. Liu,20 J. Liu,24 Y. Liu,37 S. Lockwitz,66\nM. Lokajicek,49 I. Lomidze,72 K. Long,88 T. V. Lopes,62 J.Lopez,6 I. L\u00b4opez de Rego,39 N. L\u00b4opez-March,84\nT. Lord,209 J. M. LoSecco,151 W. C. Louis,129 A. Lozano Sanchez,54 X.-G. Lu,209 K.B. Luk,80, 126, 22 B. Lunday,164\nX. Luo,27 E. Luppi,94, 67 D. MacFarlane,184 A. A. Machado,30 P. Machado,66 C. T. Macias,91 J. R. Macier,66\nM. MacMahon,203 A. Maddalena,75 A. Madera,35 P. Madigan,22, 126 S. Magill,8 C. Magueur,160 K. Mahn,139\nA. Maio,127, 61 A. Major,55 K. Majumdar,128 S. Mameli,103 M. Man,199 R. C. Mandujano,24 J. Maneira,127, 61\nS. Manly,175 A. Mann,200 K. Manolopoulos,178 M. Manrique Plata,91 S. Manthey Corchado,39 V. N. Manyam,20\nM. Marchan,66 A. Marchionni,66 W. Marciano,20 D. Marfatia,79 C. Mariani,207 J. Maricic,79 F. Marinho,113\nA. D. Marino,43 T. Markiewicz,184 F. Das Chagas Marques,30 C. Marquet,131 M. Marshak,143 C. M. Marshall,175\n\n3\nJ. Marshall,209 L. Martina,97, 179 J. Mart\u00b4\u0131n-Albo,84 N. Martinez,119 D.A. Martinez Caicedo,186 F. Mart\u00b4\u0131nez\nL\u00b4opez,172 P. Mart\u00b4\u0131nez Mirav\u00b4e,84 S. Martynenko,20 V. Mascagna,98 C. Massari,98 A. Mastbaum,177 F. Matichard,126\nS. Matsuno,79 G. Matteucci,100, 145 J. Matthews,130 C. Mauger,164 N. Mauri,92, 17 K. Mavrokoridis,128 I. Mawby,125\nR. Mazza,98 T. McAskill,210 N. McConkey,172, 203 K. S. McFarland,175 C. McGrew,189 A. McNab,135 L. Meazza,98\nV. C. N. Meddage,68 A. Mefodiev\n, B. Mehta,159 P. Mehta,116 P. Melas,11 O. Mena,84 H. Mendez,170 P. Mendez,35\nD. P. M\u00b4endez,20 A. Menegolli,102, 163 G. Meng,101 A. C. E. A. Mercuri,193 A. Meregaglia,131 M. D. Messier,91\nS. Metallo,143 W. Metcalf,130 M. Mewes,91 H. Meyer,211 T. Miao,66 J. Micallef,200, 136 A. Miccoli,97 G. Michna,187\nR. Milincic,79 F. Miller,213 G. Miller,135 W. Miller,143 O. Mineev\n, A. Minotti,98, 140 L. Miralles,35 O. G. Miranda,41\nC. Mironov,161 S. Miryala,20 S. Miscetti,95 C. S. Mishra,66 P. Mishra,82 S. R. Mishra,185 A. Mislivec,143\nM. Mitchell,130 D. Mladenov,35 I. Mocioiu,165 A. Mogan,66 N. Moggi,92, 17 R. Mohanta,82 T. A. Mohayai,91\nN. Mokhov,66 J. Molina,10 L. Molina Bueno,84 E. Montagna,92, 17 A. Montanari,92 C. Montanari,102, 66, 163\nD. Montanari,66 D. Montanino,97, 179 L. M. Monta\u02dcno Zetina,41 M. Mooney,44 A. F. Moor,183 Z. Moore,192\nD. Moreno,7 O. Moreno-Palacios,212 L. Morescalchi,103 D. Moretti,98 R. Moretti,98 C. Morris,81 C. Mossey,66\nC. A. Moura,64 G. Mouster,125 W. Mu,66 L. Mualem,28 J. Mueller,44 M. Muether,211 F. Muheim,57 A. Muir,52\nM. Mulhearn,23 D. Munford,81 L. J. Munteanu,35 H. Muramatsu,143 J. Muraz,76 M. Murphy,207 T. Murphy,192\nJ. Muse,143 A. Mytilinaki,178 J. Nachtman,108 Y. Nagai,59 S. Nagu,132 R. Nandakumar,178 D. Naples,168\nS. Narita,114 A. Navrer-Agasson,88, 135 N. Nayak,20 M. Nebot-Guinot,57 A. Nehm,134 J. K. Nelson,212 O. Neogi,108\nJ. Nesbit,213 M. Nessi,66, 35 D. Newbold,178 M. Newcomer,164 R. Nichol,203 F. Nicolas-Arnaldos,73 A. Nikolica,164\nJ. Nikolov,152 E. Niner,66 K. Nishimura,79 A. Norman,66 A. Norrick,66 P. Novella,84 A. Nowak,125 J. A. Nowak,125\nM. Oberling,8 J. P. Ochoa-Ricoux,24 S. Oh,55 S.B. Oh,66 A. Olivier,151 A. Olshevskiy\n, T. Olson,81 Y. Onel,108\nY. Onishchuk,124 A. Oranday,91 G. D. Orebi Gann,22, 126 M. Osbiston,209 J. A. Osorio V\u00b4elez,6 L. O\u2019Sullivan,134\nL. Otiniano Ormachea,46, 106 J. Ott,24 L. Pagani,23 G. Palacio,58 O. Palamara,66 S. Palestini,35 J. M. Paley,66\nM. Pallavicini,96, 71 C. Palomares,39 S. Pan,166 P. Panda,82 W. Panduro Vazquez,176 E. Pantic,23 V. Paolone,168\nR. Papaleo,105 A. Papanestis,178 D. Papoulias,11 S. Paramesvaran,19 A. Paris,170 S. Parke,66 E. Parozzi,98, 140\nS. Parsa,14 Z. Parsa,20 S. Parveen,116 M. Parvu,21 D. Pasciuto,103 S. Pascoli,92, 17 L. Pasqualini,92, 17 J. Pasternak,88\nC. Patrick,57, 203 L. Patrizii,92 R. B. Patterson,28 T. Patzak,161 A. Paudel,66 L. Paulucci,64 Z. Pavlovic,66\nG. Pawloski,143 D. Payne,128 V. Pec,49 E. Pedreschi,103 S. J. M. Peeters,191 W. Pellico,66 A. Pena Perez,184\nE. Pennacchio,110 A. Penzo,108 O. L. G. Peres,30 Y. F. Perez Gonzalez,56 L. P\u00b4erez-Molina,39 C. Pernas,212\nJ. Perry,57 D. Pershey,69 G. Pessina,98 G. Petrillo,184 C. Petta,93, 31 R. Petti,185 M. Pfaff,88 V. Pia,92, 17\nL. Pickering,178, 176 F. Pietropaolo,35, 101 V.L.Pimentel,47, 30 G. Pinaroli,20 S. Pincha,89 J. Pinchault,51 K. Pitts,207\nK. Plows,156 C. Pollack,170 T. Pollman,146, 3 F. Pompa,84 X. Pons,35 N. Poonthottathil,86, 109 V. Popov,194\nF. Poppi,92, 17 J. Porter,191 L. G. Porto Paix\u02dcao,30 M. Potekhin,20 R. Potenza,93, 31 J. Pozimski,88 M. Pozzato,92, 17\nT. Prakash,126 C. Pratt,23 M. Prest,98 F. Psihas,66 D. Pugnere,110 X. Qian,20 J. Queen,55 J. L. Raaf,66 V. Radeka,20\nJ. Rademacker,19 B. Radics,216 F. Raffaelli,103 A. Rafique,8 E. Raguzin,20 M. Rai,209 S. Rajagopalan,20\nM. Rajaoalisoa,40 I. Rakhno,66 L. Rakotondravohitra,5 L. Ralte,90 M. A. Ramirez Delgado,164 B. Ramson,66\nA. Rappoldi,102, 163 G. Raselli,102, 163 P. Ratoff,125 R. Ray,66 H. Razafinime,40 E. M. Rea,143 J. S. Real,76\nB. Rebel,213, 66 R. Rechenmacher,66 J. Reichenbacher,186 S. D. Reitzner,66 H. Rejeb Sfar,35 E. Renner,129\nA. Renshaw,81 S. Rescia,20 F. Resnati,35 Diego Restrepo,6 C. Reynolds,172 M. Ribas,193 S. Riboldi,99 C. Riccio,189\nG. Riccobene,105 J. S. Ricol,76 M. Rigan,191 E. V. Rinc\u00b4on,58 A. Ritchie-Yates,176 S. Ritter,134 D. Rivera,129\nR. Rivera,66 A. Robert,76 J. L. Rocabado Rocha,84 L. Rochester,184 M. Roda,128 P. Rodrigues,156 M. J. Rodriguez\nAlonso,35 J. Rodriguez Rondon,186 S. Rosauro-Alcaraz,160 P. Rosier,160 D. Ross,139 M. Rossella,102, 163 M. Rossi,35\nM. Ross-Lonergan,129 N. Roy,216 P. Roy,211 C. Rubbia,74 A. Ruggeri,92 G. Ruiz,135 B. Russell,136\nD. Ruterbories,175 A. Rybnikov\n, S. Sacerdoti,161 S. Saha,168 S. K. Sahoo,90 N. Sahu,90 P. Sala,66 N. Samios,20\nO. Samoylov\n, M. C. Sanchez,69 A. S\u00b4anchez Bravo,84 A. S\u00b4anchez-Castillo,73 P. Sanchez-Lucas,73 V. Sandberg,129\nD. A. Sanders,144 S. Sanfilippo,105 D. Sankey,178 D. Santoro,99, 162 N. Saoulidou,11 P. Sapienza,105 C. Sarasty,40\nI. Sarcevic,9 I. Sarra,95 G. Savage,66 V. Savinov,168 G. Scanavini,214 A. Scaramelli,102 A. Scarff,183 T. Schefke,130\nH. Schellman,155, 66 S. Schifano,94, 67 P. Schlabach,66 D. Schmitz,37 A. W. Schneider,136 K. Scholberg,55\nA. Schukraft,66 B. Schuld,43 A. Segade,206 E. Segreto,30 A. Selyunin\n, D. Senadheera,168 S. H. Seo,66\nC. R. Senise,201 J. Sensenig,164 M. H. Shaevitz,45 P. Shanahan,66 P. Sharma,159 R. Kumar,171 S. Sharma\nPoudel,186 K. Shaw,191 T. Shaw,66 K. Shchablo,110 J. Shen,164 C. Shepherd-Themistocleous,178 A. Sheshukov\n,\nJ. Shi,29 W. Shi,189 S. Shin,117 S. Shivakoti,211 I. Shoemaker,207 D. Shooltz,139 R. Shrock,189 B. Siddi,94\nM. Siden,44 J. Silber,126 L. Simard,160 J. Sinclair,184 G. Sinev,186 J. Singh,23 L. Singh,48 P. Singh,172 V. Singh,48\nS. Singh Chauhan,159 R. Sipos,35 C. Sironneau,161 G. Sirri,92 K. Siyeon,38 K. Skarpaas,184 J. Smedley,175\n\n4\nE. Smith,91 J. Smith,189 P. Smith,91 J. Smolik,50, 49 M. Smy,24 M. Snape,209 E.L. Snider,66 P. Snopok,87\nD. Snowden-Ifft,153 M. Soares Nunes,66 H. Sobel,24 M. Soderberg,192 S. Sokolov\n, C. J. Solano Salinas,204, 106\nS. S\u00a8oldner-Rembold,88, 135 N. Solomey,211 V. Solovov,127 W. E. Sondheim,129 M. Sorel,84 A. Sotnikov\n,\nJ. Soto-Oton,84 A. Sousa,40 K. Soustruznik,36 F. Spinella,103 J. Spitz,138 N. J. C. Spooner,183 K. Spurgeon,192\nD. Stalder,10 M. Stancari,66 L. Stanco,158, 101 J. Steenis,23 R. Stein,19 H. M. Steiner,126 A. F. Steklain Lisb\u02c6oa,193\nA. Stepanova\n, J. Stewart,20 B. Stillwell,37 J. Stock,186 F. Stocker,35 T. Stokes,130 M. Strait,143 T. Strauss,66\nL. Strigari,195 A. Stuart,42 J. G. Suarez,58 J. Subash,16 A. Surdo,97 L. Suter,66 C. M. Sutera,93, 31 K. Sutton,28\nY. Suvorov,100, 145 R. Svoboda,23 S. K. Swain,147 B. Szczerbinska,196 A. M. Szelc,57 A. Sztuc,203 A. Taffara,103\nN. Talukdar,185 J. Tamara,7 H. A. Tanaka,184 S. Tang,20 N. Taniuchi,29 A. M. Tapia Casanova,137 B. Tapia\nOregui,198 A. Tapper,88 S. Tariq,66 E. Tarpara,20 E. Tatar,83 R. Tayloe,91 D. Tedeschi,185 A. M. Teklu,189 J. Tena\nVidal,194 P. Tennessen,126, 4 M. Tenti,92 K. Terao,184 F. Terranova,98, 140 G. Testera,96 T. Thakore,40 A. Thea,178\nS. Thomas,192 A. Thompson,195 C. Thorn,20 S. C. Timm,66 E. Tiras,60, 108 V. Tishchenko,20 N. Todorovi\u00b4c,152\nL. Tomassetti,94, 67 A. Tonazzo,161 D. Torbunov,20 M. Torti,98, 140 M. Tortola,84 F. Tortorici,93, 31 N. Tosi,92\nD. Totani,27 M. Toups,66 C. Touramanis,128 D. Tran,81 R. Travaglini,92 J. Trevor,28 E. Triller,139 S. Trilov,19\nJ. Truchon,213 D. Truncali,181, 104 W. H. Trzaska,118 Y. Tsai,24 Y.-T. Tsai,184 Z. Tsamalaidze,72 K. V. Tsang,184\nN. Tsverava,72 S. Z. Tu,115 S. Tufanli,35 C. Tunnell,174 S. Turnberg,87 J. Turner,56 M. Tuzi,84 J. Tyler,119\nE. Tyley,183 M. Tzanov,130 M. A. Uchida,29 J. Ure\u02dcna Gonz\u00b4alez,84 J. Urheim,91 T. Usher,184 H. Utaegbulam,175\nS. Uzunyan,149 M. R. Vagins,120, 24 P. Vahle,212 S. Valder,191 G. A. Valdiviesso,62 E. Valencia,77 R. Valentim,201\nZ. Vallari,28 E. Vallazza,98 J. W. F. Valle,84 R. Van Berg,164 R. G. Van de Water,129 D. V. Forero,137\nA. Vannozzi,95 M. Van Nuland-Troost,146 F. Varanini,101 D. Vargas Oliva,199 S. Vasina\n, N. Vaughan,155\nK. Vaziri,66 A. V\u00b4azquez-Ramos,73 J. Vega,46 S. Ventura,101 A. Verdugo,39 S. Vergani,203 M. Verzocchi,66\nK. Vetter,66 M. Vicenzi,20 H. Vieira de Souza,161 C. Vignoli,75 C. Vilela,127 E. Villa,35 S. Viola,105 B. Viren,20\nA. P. Vizcaya Hernandez,44 Q. Vuong,175 A. V. Waldron,172 M. Wallbank,40 J. Walsh,139 T. Walton,66 H. Wang,25\nJ. Wang,186 L. Wang,126 M.H.L.S. Wang,66 X. Wang,66 Y. Wang,25 K. Warburton,109 D. Warner,44 L. Warsame,88\nM.O. Wascko,156, 178 D. Waters,203 A. Watson,16 K. Wawrowska,178, 191 A. Weber,134, 66 C. M. Weber,143\nM. Weber,14 H. Wei,130 A. Weinstein,109 S. Westerdale,26 M. Wetstein,109 K. Whalen,178 A. White,197 A. White,214\nL. H. Whitehead,29 D. Whittington,192 J. Wilhlemi,214 M. J. Wilking,143 A. Wilkinson,203 C. Wilkinson,126\nF. Wilson,178 R. J. Wilson,44 P. Winter,8 W. Wisniewski,184 J. Wolcott,200 J. Wolfs,175 T. Wongjirad,200\nA. Wood,81 K. Wood,126 E. Worcester,20 M. Worcester,20 M. Wospakrik,66 K. Wresilo,29 C. Wret,175 S. Wu,143\nW. Wu,66 W. Wu,24 M. Wurm,134 J. Wyenberg,53 Y. Xiao,24 I. Xiotidis,88 B. Yaeggy,40 N. Yahlali,84\nE. Yandel,27 J. Yang,80 K. Yang,156 T. Yang,66 A. Yankelevich,24 N. Yershov\n, K. Yonehara,66 T. Young,148\nB. Yu,20 H. Yu,20 J. Yu,197 Y. Yu,87 W. Yuan,57 R. Zaki,216 J. Zalesak,49 L. Zambelli,51 B. Zamorano,73\nA. Zani,99 O. Zapata,6 L. Zazueta,192 G. P. Zeller,66 J. Zennamo,66 K. Zeug,213 C. Zhang,20 S. Zhang,91\nM. Zhao,20 E. Zhivun,20 E. D. Zimmerman,43 S. Zucchelli,92, 17 J. Zuklin,49 V. Zutshi,149 and R. Zwaska66\n(The DUNE Collaboration)\n1Abilene Christian University, Abilene, TX 79601, USA\n2University at Albany, SUNY, Albany, NY 12222, USA\n3University of Amsterdam, NL-1098 XG Amsterdam, The Netherlands\n4Antalya Bilim University, 07190 D\u00a8o\u00b8semealt\u0131/Antalya, Turkey\n5University of Antananarivo, Antananarivo 101, Madagascar\n6University of Antioquia, Medell\u00b4\u0131n, Colombia\n7Universidad Antonio Nari\u02dcno, Bogot\u00b4a, Colombia\n8Argonne National Laboratory, Argonne, IL 60439, USA\n9University of Arizona, Tucson, AZ 85721, USA\n10Universidad Nacional de Asunci\u00b4on, San Lorenzo, Paraguay\n11University of Athens, Zografou GR 157 84, Greece\n12Universidad del Atl\u00b4antico, Barranquilla, Atl\u00b4antico, Colombia\n13Augustana University, Sioux Falls, SD 57197, USA\n14University of Bern, CH-3012 Bern, Switzerland\n15Beykent University, Istanbul, Turkey\n16University of Birmingham, Birmingham B15 2TT, United Kingdom\n17Universit`a di Bologna, 40127 Bologna, Italy\n18Boston University, Boston, MA 02215, USA\n19University of Bristol, Bristol BS8 1TL, United Kingdom\n20Brookhaven National Laboratory, Upton, NY 11973, USA\n21University of Bucharest, Bucharest, Romania\n22University of California Berkeley, Berkeley, CA 94720, USA\n\n5\n23University of California Davis, Davis, CA 95616, USA\n24University of California Irvine, Irvine, CA 92697, USA\n25University of California Los Angeles, Los Angeles, CA 90095, USA\n26University of California Riverside, Riverside CA 92521, USA\n27University of California Santa Barbara, Santa Barbara, CA 93106, USA\n28California Institute of Technology, Pasadena, CA 91125, USA\n29University of Cambridge, Cambridge CB3 0HE, United Kingdom\n30Universidade Estadual de Campinas, Campinas - SP, 13083-970, Brazil\n31Universit`a di Catania, 2 - 95131 Catania, Italy\n32Universidad Cat\u00b4olica del Norte, Antofagasta, Chile\n33Centro Brasileiro de Pesquisas F\u00b4\u0131sicas, Rio de Janeiro, RJ 22290-180, Brazil\n34IRFU, CEA, Universit\u00b4e Paris-Saclay, F-91191 Gif-sur-Yvette, France\n35CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland\n36Institute of Particle and Nuclear Physics of the Faculty of Mathematics\nand Physics of the Charles University, 180 00 Prague 8, Czech Republic\n37University of Chicago, Chicago, IL 60637, USA\n38Chung-Ang University, Seoul 06974, South Korea\n39CIEMAT, Centro de Investigaciones Energ\u00b4eticas, Medioambientales y Tecnol\u00b4ogicas, E-28040 Madrid, Spain\n40University of Cincinnati, Cincinnati, OH 45221, USA\n41Centro de Investigaci\u00b4on y de Estudios Avanzados del Instituto Polit\u00b4ecnico Nacional (Cinvestav), Mexico City, Mexico\n42Universidad de Colima, Colima, Mexico\n43University of Colorado Boulder, Boulder, CO 80309, USA\n44Colorado State University, Fort Collins, CO 80523, USA\n45Columbia University, New York, NY 10027, USA\n46Comisi\u00b4on Nacional de Investigaci\u00b4on y Desarrollo Aeroespacial, Lima, Peru\n47Centro de Tecnologia da Informacao Renato Archer, Amarais - Campinas, SP - CEP 13069-901\n48Central University of South Bihar, Gaya, 824236, India\n49Institute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic\n50Czech Technical University, 115 19 Prague 1, Czech Republic\n51Laboratoire d\u2019Annecy de Physique des Particules, Universit\u00b4e Savoie Mont Blanc, CNRS, LAPP-IN2P3, 74000 Annecy, France\n52Daresbury Laboratory, Cheshire WA4 4AD, United Kingdom\n53Dordt University, Sioux Center, IA 51250, USA\n54Drexel University, Philadelphia, PA 19104, USA\n55Duke University, Durham, NC 27708, USA\n56Durham University, Durham DH1 3LE, United Kingdom\n57University of Edinburgh, Edinburgh EH8 9YL, United Kingdom\n58Universidad EIA, Envigado, Antioquia, Colombia\n59E\u00a8otv\u00a8os Lor\u00b4and University, 1053 Budapest, Hungary\n60Erciyes University, Kayseri, Turkey\n61Faculdade de Ci\u02c6encias da Universidade de Lisboa - FCUL, 1749-016 Lisboa, Portugal\n62Universidade Federal de Alfenas, Po\u00b8cos de Caldas - MG, 37715-400, Brazil\n63Universidade Federal de Goias, Goiania, GO 74690-900, Brazil\n64Universidade Federal do ABC, Santo Andr\u00b4e - SP, 09210-580, Brazil\n65Universidade Federal do Rio de Janeiro, Rio de Janeiro - RJ, 21941-901, Brazil\n66Fermi National Accelerator Laboratory, Batavia, IL 60510, USA\n67University of Ferrara, Ferrara, Italy\n68University of Florida, Gainesville, FL 32611-8440, USA\n69Florida State University, Tallahassee, FL, 32306 USA\n70Fluminense Federal University, 9 Icara\u00b4\u0131 Niter\u00b4oi - RJ, 24220-900, Brazil\n71Universit`a degli Studi di Genova, Genova, Italy\n72Georgian Technical University, Tbilisi, Georgia\n73University of Granada & CAFPE, 18002 Granada, Spain\n74Gran Sasso Science Institute, L\u2019Aquila, Italy\n75Laboratori Nazionali del Gran Sasso, L\u2019Aquila AQ, Italy\n76University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France\n77Universidad de Guanajuato, Guanajuato, C.P. 37000, Mexico\n78Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India\n79University of Hawaii, Honolulu, HI 96822, USA\n80Hong Kong University of Science and Technology, Kowloon, Hong Kong, China\n81University of Houston, Houston, TX 77204, USA\n82University of Hyderabad, Gachibowli, Hyderabad - 500 046, India\n83Idaho State University, Pocatello, ID 83209, USA\n84Instituto de F\u00b4\u0131sica Corpuscular, CSIC and Universitat de Val`encia, 46980 Paterna, Valencia, Spain\n85Instituto Galego de F\u00b4\u0131sica de Altas Enerx\u00b4\u0131as, University of Santiago de Compostela, Santiago de Compostela, 15782, Spain\n\n6\n86Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India\n87Illinois Institute of Technology, Chicago, IL 60616, USA\n88Imperial College of Science, Technology and Medicine, London SW7 2BZ, United Kingdom\n89Indian Institute of Technology Guwahati, Guwahati, 781 039, India\n90Indian Institute of Technology Hyderabad, Hyderabad, 502285, India\n91Indiana University, Bloomington, IN 47405, USA\n92Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna BO, Italy\n93Istituto Nazionale di Fisica Nucleare Sezione di Catania, I-95123 Catania, Italy\n94Istituto Nazionale di Fisica Nucleare Sezione di Ferrara, I-44122 Ferrara, Italy\n95Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Frascati, Frascati, Roma, Italy\n96Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genova GE, Italy\n97Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 - Lecce, Italy\n98Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3 - I-20126 Milano, Italy\n99Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milano, Italy\n100Istituto Nazionale di Fisica Nucleare Sezione di Napoli, I-80126 Napoli, Italy\n101Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padova, Italy\n102Istituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy\n103Istituto Nazionale di Fisica Nucleare Laboratori Nazionali di Pisa, Pisa PI, Italy\n104Istituto Nazionale di Fisica Nucleare Sezione di Roma, 00185 Roma RM, Italy\n105Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy\n106Universidad Nacional de Ingenier\u00b4\u0131a, Lima 25, Per\u00b4u\n107University of Insubria, Via Ravasi, 2, 21100 Varese VA, Italy\n108University of Iowa, Iowa City, IA 52242, USA\n109Iowa State University, Ames, Iowa 50011, USA\n110Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France\n111Institute for Research in Fundamental Sciences, Tehran, Iran\n112Instituto Superior T\u00b4ecnico - IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal\n113Instituto Tecnol\u00b4ogico de Aeron\u00b4autica, Sao Jose dos Campos, Brazil\n114Iwate University, Morioka, Iwate 020-8551, Japan\n115Jackson State University, Jackson, MS 39217, USA\n116Jawaharlal Nehru University, New Delhi 110067, India\n117Jeonbuk National University, Jeonrabuk-do 54896, South Korea\n118Jyv\u00a8askyl\u00a8a University, FI-40014 Jyv\u00a8askyl\u00a8a, Finland\n119Kansas State University, Manhattan, KS 66506, USA\n120Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan\n121High Energy Accelerator Research Organization (KEK), Ibaraki, 305-0801, Japan\n122Korea Institute of Science and Technology Information, Daejeon, 34141, South Korea\n123National Institute of Technology, Kure College, Hiroshima, 737-8506, Japan\n124Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine\n125Lancaster University, Lancaster LA1 4YB, United Kingdom\n126Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA\n127Laborat\u00b4orio de Instrumenta\u00b8c\u02dcao e F\u00b4\u0131sica Experimental de Part\u00b4\u0131culas, 1649-003 Lisboa and 3004-516 Coimbra, Portugal\n128University of Liverpool, L69 7ZE, Liverpool, United Kingdom\n129Los Alamos National Laboratory, Los Alamos, NM 87545, USA\n130Louisiana State University, Baton Rouge, LA 70803, USA\n131Laboratoire de Physique des Deux Infinis Bordeaux - IN2P3, F-33175 Gradignan, Bordeaux, France,\n132University of Lucknow, Uttar Pradesh 226007, India\n133Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain\n134Johannes Gutenberg-Universit\u00a8at Mainz, 55122 Mainz, Germany\n135University of Manchester, Manchester M13 9PL, United Kingdom\n136Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n137University of Medell\u00b4\u0131n, Medell\u00b4\u0131n, 050026 Colombia\n138University of Michigan, Ann Arbor, MI 48109, USA\n139Michigan State University, East Lansing, MI 48824, USA\n140Universit`a di Milano Bicocca , 20126 Milano, Italy\n141Universit`a degli Studi di Milano, I-20133 Milano, Italy\n142University of Minnesota Duluth, Duluth, MN 55812, USA\n143University of Minnesota Twin Cities, Minneapolis, MN 55455, USA\n144University of Mississippi, University, MS 38677 USA\n145Universit`a degli Studi di Napoli Federico II , 80138 Napoli NA, Italy\n146Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, Netherlands\n147National Institute of Science Education and Research (NISER), Odisha 752050, India\n148University of North Dakota, Grand Forks, ND 58202-8357, USA\n149Northern Illinois University, DeKalb, IL 60115, USA\n\n7\n150Northwestern University, Evanston, Il 60208, USA\n151University of Notre Dame, Notre Dame, IN 46556, USA\n152University of Novi Sad, 21102 Novi Sad, Serbia\n153Occidental College, Los Angeles, CA 90041\n154Ohio State University, Columbus, OH 43210, USA\n155Oregon State University, Corvallis, OR 97331, USA\n156University of Oxford, Oxford, OX1 3RH, United Kingdom\n157Pacific Northwest National Laboratory, Richland, WA 99352, USA\n158Universt`a degli Studi di Padova, I-35131 Padova, Italy\n159Panjab University, Chandigarh, 160014, India\n160Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n161Universit\u00b4e Paris Cit\u00b4e, CNRS, Astroparticule et Cosmologie, Paris, France\n162University of Parma, 43121 Parma PR, Italy\n163Universit`a degli Studi di Pavia, 27100 Pavia PV, Italy\n164University of Pennsylvania, Philadelphia, PA 19104, USA\n165Pennsylvania State University, University Park, PA 16802, USA\n166Physical Research Laboratory, Ahmedabad 380 009, India\n167Universit`a di Pisa, I-56127 Pisa, Italy\n168University of Pittsburgh, Pittsburgh, PA 15260, USA\n169Pontificia Universidad Cat\u00b4olica del Per\u00b4u, Lima, Per\u00b4u\n170University of Puerto Rico, Mayaguez 00681, Puerto Rico, USA\n171Punjab Agricultural University, Ludhiana 141004, India\n172Queen Mary University of London, London E1 4NS, United Kingdom\n173Radboud University, NL-6525 AJ Nijmegen, Netherlands\n174Rice University, Houston, TX 77005\n175University of Rochester, Rochester, NY 14627, USA\n176Royal Holloway College London, London, TW20 0EX, United Kingdom\n177Rutgers University, Piscataway, NJ, 08854, USA\n178STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom\n179Universit`a del Salento, 73100 Lecce, Italy\n180Universidad del Magdalena, Santa Marta - Colombia\n181Sapienza University of Rome, 00185 Roma RM, Italy\n182Universidad Sergio Arboleda, 11022 Bogot\u00b4a, Colombia\n183University of Sheffield, Sheffield S3 7RH, United Kingdom\n184SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA\n185University of South Carolina, Columbia, SC 29208, USA\n186South Dakota School of Mines and Technology, Rapid City, SD 57701, USA\n187South Dakota State University, Brookings, SD 57007, USA\n188Southern Methodist University, Dallas, TX 75275, USA\n189Stony Brook University, SUNY, Stony Brook, NY 11794, USA\n190Sanford Underground Research Facility, Lead, SD, 57754, USA\n191University of Sussex, Brighton, BN1 9RH, United Kingdom\n192Syracuse University, Syracuse, NY 13244, USA\n193Universidade Tecnol\u00b4ogica Federal do Paran\u00b4a, Curitiba, Brazil\n194Tel Aviv University, Tel Aviv-Yafo, Israel\n195Texas A&M University, College Station, Texas 77840\n196Texas A&M University - Corpus Christi, Corpus Christi, TX 78412, USA\n197University of Texas at Arlington, Arlington, TX 76019, USA\n198University of Texas at Austin, Austin, TX 78712, USA\n199University of Toronto, Toronto, Ontario M5S 1A1, Canada\n200Tufts University, Medford, MA 02155, USA\n201Universidade Federal de S\u02dcao Paulo, 09913-030, S\u02dcao Paulo, Brazil\n202Ulsan National Institute of Science and Technology, Ulsan 689-798, South Korea\n203University College London, London, WC1E 6BT, United Kingdom\n204Universidad Nacional Mayor de San Marcos, Lima, Peru\n205Valley City State University, Valley City, ND 58072, USA\n206University of Vigo, E- 36310 Vigo Spain\n207Virginia Tech, Blacksburg, VA 24060, USA\n208University of Warsaw, 02-093 Warsaw, Poland\n209University of Warwick, Coventry CV4 7AL, United Kingdom\n210Wellesley College, Wellesley, MA 02481, USA\n211Wichita State University, Wichita, KS 67260, USA\n212William and Mary, Williamsburg, VA 23187, USA\n213University of Wisconsin Madison, Madison, WI 53706, USA\n\n8\n214Yale University, New Haven, CT 06520, USA\n215Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia\n216York University, Toronto M3J 1P3, Canada\n217Astrocent, Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences, Warsaw 00-614, Poland\n\nDUNE Phase II\nAbstract\nThe international collaboration designing and constructing the Deep Underground\nNeutrino Experiment (DUNE) at the Long-Baseline Neutrino Facility (LBNF) has de-\nveloped a two-phase strategy toward the implementation of this leading-edge, large-scale\nscience project. The 2023 report of the US Particle Physics Project Prioritization Panel\n(P5) reaffirmed this vision and strongly endorsed DUNE Phase I and Phase II, as did the\nEuropean Strategy for Particle Physics. While the construction of the DUNE Phase I is\nwell underway, this White Paper focuses on DUNE Phase II planning. DUNE Phase-II\nconsists of a third and fourth far detector (FD) module, an upgraded near detector com-\nplex, and an enhanced 2.1 MW beam. The fourth FD module is conceived as a \u201cModule\nof Opportunity\u201d, aimed at expanding the physics opportunities, in addition to support-\ning the core DUNE science program, with more advanced technologies. This document\nhighlights the increased science opportunities offered by the DUNE Phase II near and far\ndetectors, including long-baseline neutrino oscillation physics, neutrino astrophysics, and\nphysics beyond the standard model. It describes the DUNE Phase II near and far detector\ntechnologies and detector design concepts that are currently under consideration. A sum-\nmary of key R&D goals and prototyping phases needed to realize the Phase II detector\ntechnical designs is also provided. DUNE\u2019s Phase II detectors, along with the increased\nbeam power, will complete the full scope of DUNE, enabling a multi-decadal program of\ngroundbreaking science with neutrinos.\n10\n\nDUNE Phase II\nContents\nExecutive summary\n13\n1\nThe elements of DUNE Phase II\n15\n2\nDUNE Phase II physics\n17\n2.1\nLong-baseline neutrino oscillation physics . . . . . . . . . . . . . . . . . . . . . .\n18\n2.1.1\nGoals of the oscillation physics program of Phase II . . . . . . . . . . . .\n18\n2.1.2\nThe role of Phase II detectors . . . . . . . . . . . . . . . . . . . . . . . .\n20\n2.2\nNeutrino astrophysics and other low-energy physics opportunities\n. . . . . . . .\n21\n2.2.1\nSNB neutrinos\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n22\n2.2.2\nSolar neutrinos\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n25\n2.2.3\nOther low-energy physics opportunities . . . . . . . . . . . . . . . . . . .\n26\n2.3\nPhysics beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . .\n27\n2.3.1\nRare event searches at the near detector\n. . . . . . . . . . . . . . . . . .\n27\n2.3.2\nRare event searches at the far detector . . . . . . . . . . . . . . . . . . .\n29\n2.3.3\nNon-standard neutrino oscillation phenomena\n. . . . . . . . . . . . . . .\n29\n3\nThe DUNE phase II far detector\n30\n3.1\nIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n30\n3.2\nThe vertical drift detector design\n. . . . . . . . . . . . . . . . . . . . . . . . . .\n30\n3.2.1\nCharge readout planes (anodes) . . . . . . . . . . . . . . . . . . . . . . .\n32\n3.2.2\nHigh-voltage system\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n33\n3.2.3\nPhoton detection system . . . . . . . . . . . . . . . . . . . . . . . . . . .\n35\n3.3\nOptimized charge and photon readouts for Phase II vertical drift FD modules\n.\n35\n3.3.1\nOptimized photon readout with APEX . . . . . . . . . . . . . . . . . . .\n36\n3.3.2\nStrip-based charge readout . . . . . . . . . . . . . . . . . . . . . . . . . .\n40\n3.3.3\nPixel-based charge readout . . . . . . . . . . . . . . . . . . . . . . . . . .\n41\n3.3.4\nOptical-based charge readout\n. . . . . . . . . . . . . . . . . . . . . . . .\n46\n3.3.5\nIntegrated charge and light readout on anode\n. . . . . . . . . . . . . . .\n48\n3.4\nLiquid-argon doping\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n51\n3.4.1\nLiquid xenon\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n52\n3.4.2\nPhotosensitive dopants . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n53\n3.5\nHybrid Cherenkov plus scintillation detection\n. . . . . . . . . . . . . . . . . . .\n54\n3.5.1\nHybrid detection concept . . . . . . . . . . . . . . . . . . . . . . . . . . .\n54\n3.5.2\nTheia physics program\n. . . . . . . . . . . . . . . . . . . . . . . . . . .\n55\n3.5.3\nTechnology readiness levels . . . . . . . . . . . . . . . . . . . . . . . . . .\n56\n3.6\nBackground control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n57\n3.6.1\nExternal neutrons and photons\n. . . . . . . . . . . . . . . . . . . . . . .\n58\n3.6.2\nInternal backgrounds from detector materials\n. . . . . . . . . . . . . . .\n58\n3.6.3\nIntrinsic backgrounds from unstable isotopes in the target\n. . . . . . . .\n59\n3.6.4\nRadon background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n59\n3.6.5\nThe SLoMo concept\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n59\n11\n\nDUNE Phase II\n3.6.6\nResearch and development requirements\n. . . . . . . . . . . . . . . . . .\n60\n3.7\nToward detector concepts for Phase II FD modules\n. . . . . . . . . . . . . . . .\n61\n4\nThe DUNE Phase II near detector\n65\n4.1\nDesign motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n65\n4.2\nPhase II improved tracker concept . . . . . . . . . . . . . . . . . . . . . . . . . .\n67\n4.2.1\nCharge readout of TPC\n. . . . . . . . . . . . . . . . . . . . . . . . . . .\n68\n4.2.2\nCalorimeter concept\n. . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n72\n4.2.3\nMagnet concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n73\n4.2.4\nMuon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n76\n4.2.5\nLight detection options . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n76\n4.2.6\nR&D and engineering road map . . . . . . . . . . . . . . . . . . . . . . .\n77\n4.3\nImprovements to Phase I near detector components . . . . . . . . . . . . . . . .\n78\n4.3.1\nPhase II ND-LAr detector . . . . . . . . . . . . . . . . . . . . . . . . . .\n79\n4.3.2\nPhase II SAND detector . . . . . . . . . . . . . . . . . . . . . . . . . . .\n80\n4.4\nNear-detector options for non-argon far detector modules . . . . . . . . . . . . .\n80\n4.4.1\nOxygen and water targets in SAND . . . . . . . . . . . . . . . . . . . . .\n80\n4.4.2\nLiquid scintillator targets in the ND-GAr calorimeter . . . . . . . . . . .\n82\n4.4.3\nWater-based near detector . . . . . . . . . . . . . . . . . . . . . . . . . .\n83\nGlossary\n85\n12\n\nDUNE Phase II\nExecutive summary\nThe preponderance of matter over antimatter in the early universe, the dynamics of the super-\nnova neutrino bursts (SNBs) that produced the heavy elements necessary for life, the nature of\ndark matter, and whether protons eventually decay \u2013 these mysteries at the forefront of particle\nphysics and astrophysics are key to understanding the evolution of our universe.\nThe Deep Underground Neutrino Experiment (DUNE) will address these questions in a\nmultidecadal science program with its world-leading liquid argon (LAr) detector technology.\nThe international DUNE experiment, hosted by the Fermi National Accelerator Laboratory\n(Fermilab), is designing, developing, and constructing a near detector (ND) complex at Fermilab\n(the near site) and a suite of four large detector modules 1300 km downstream at the Sanford\nUnderground Research Facility (SURF) in South Dakota (the far site). These detectors will\nrecord neutrinos over a wide energy range, originating from a new high-intensity neutrino\nbeamline at Fermilab. The modular far detector (FD) will also detect neutrinos produced by\ncosmic rays in the atmosphere and from astrophysical sources. The ND and FD will also be\nsensitive to a broad range of phenomena beyond the standard model (). The beamline as well as\nthe excavations, infrastructure, and facilities for housing and supporting the DUNE detectors\nare provided by the Long-Baseline Neutrino Facility (LBNF).\nThe DUNE Collaboration was launched in 2015, following the recommendations of the 2013\nupdate of the European Strategy for Particle Physics [1] and of the 2014 Report of the US\nParticle Physics Project Prioritization Panel (P5) [2]. DUNE and LBNF will complete this\nproject in two phases, based on the availability of resources and the ability to reach science\nmilestones. The latest P5 report released in December 2023 reaffirmed this vision [3].\nThe construction of the first project phase (Phase I), funded through commitments by a\ncoalition of international funding agencies, is well underway. Its successful completion is cur-\nrently the Collaboration\u2019s main priority. Excavation at the far site is complete, and fabrication\nof various beamline and detector components for Phase I is progressing well. The facilities\ncurrently being constructed by LBNF at both the near and far sites are designed to host the\nfull scope (Phase I and Phase II) of the DUNE experiment.\nThe Phase II of DUNE that encompasses an enhanced 2.1 MW beam, a third and fourth far\ndetector (FD) module, and an upgraded ND complex, is the subject of this paper. The primary\nobjective of DUNE Phase II is a set of precise measurements of the parameters of the neutrino\nmixing matrix, \u03b823, \u03b813, \u2206m2\n32, and \u03b4CP, to establish Charge Conjugation-Parity Symmetry\nViolation (CPV) over a broad range of possible values of \u03b4CP, and to search for new physics\nin neutrino oscillations. DUNE also seeks to detect neutrinos from low-energy astrophysical\nsources. The additional mass brought by the Phase II FD modules would increase the statistics\nof a supernova burst signal and extend DUNE\u2019s reach beyond the Milky Way. The Phase II\nFD module design concepts would also perform sensitive searches for new physics with solar\nneutrinos by lowering the detection threshold in the relevant MeV-scale energy range and by\nreducing the background rates in this energy regime. Finally, Phase II will expand DUNE\u2019s\nnew physics discovery reach via more sensitive searches for rare processes at the ND and FD\nsites, and for non-standard neutrino oscillation phenomena.\nThis world-class physics program requires an increase in the statistical power of the de-\n13\n\nDUNE Phase II\ntectors, which will be achieved by increasing the FD target mass with the additional modules\nand by exceeding 2 MW beam power, as recommended by the 2023 P5 committee in the US.\nIn addition, an upgraded ND will be required to control systematic uncertainties of neutrino\ninteractions on argon (or other selected FD target nuclei). The design of the Phase II FD\nmodules will incorporate lessons learned from the construction of the Phase I modules, with\nthe goal of optimizing physics performance, reliability, and cost.\nThe design of the third FD module will build on that of the second, the single-phase\ntechnology used for far detector module 2 (FD2), optimizing for performance and cost. This\ndesign implements -based horizontal anode planes at the top and bottom of the liquid-argon\ntime-projection chamber (LArTPC) drift volume with a cathode plane in the middle, and a\nthat hangs from the cryostat roof on which photon detectors will be mounted.\nThe fourth FD module is conceived as a \u201cModule of Opportunity\u201d, which would allow to\naddress new physics questions, in addition to the primary science program, with more advanced\ntechnologies. R&D for the design of the fourth module focuses primarily on optimization of\nreadout techniques for both charge and scintillation light. It also considers the possibility of LAr\ndoping. A possible improvement of the LAr charge-readout technology is the replacement of\nthe PCB-readout by pixels or by an optical-based charge readout. A hybrid approach to detect\nCherenkov and scintillation light is also under investigation, motivated by a complementary\nprogram of low-energy physics. All technologies proposed for the Module of Opportunity are\nexpected to provide additional and complementary CPV sensitivity. In addition, background\ncontrol is an essential ingredient of all FD module designs.\nThe Phase II ND will ensure that DUNE\u2019s sensitivity to oscillation parameters is not lim-\nited by systematic uncertainties. It is optimized for highly performing particle ID (PID), low\ntracking thresholds for protons and pions, and acceptance over a wide range of momenta. A\nmagnetized gaseous argon time-projection chamber (GArTPC) at the near site, which will\nreplace the Muon Spectrometer (TMS), will provide these constraints by measuring the inter-\naction of neutrinos on argon with unprecedented precision due to its low thresholds. It offers\nsuperior discrimination between neutrinos and antineutrinos, as well as momentum determina-\ntion of particles exiting the detector.\nThese plans fully align with the recommendations of the 2023 P5 report [3], which proposes\na \u201csecond phase of DUNE (Phase II) with an early implementation of an enhanced 2.1 MW\nbeam, a third far detector (module), and an upgraded near detector complex as the definitive\nlong-baseline neutrino oscillation experiment of its kind,\u201d as well as \u201cresearch and development\n(R&D) towards an advanced fourth detector.\u201d\nThe Phase II R&D program is a global effort with contributions from all DUNE partners.\nNew collaborators are also invited to participate in the development and design of the new\ndetector technologies. Part of the R&D described in this document is carried out within the\nframework of the European Committee for Future Accelerators (ECFA) detector R&D col-\nlaborations hosted by the European Laboratory for Particle Physics (CERN) and those being\nformed under the umbrella of the Coordinating Panel for Advanced Detectors (CPAD) in the\nUS. DUNE has been designed to become the \u201cbest-in-class\u201d global neutrino observatory. The\nPhase II far and near detector components, and the increased beam power, will enable a new\nera of precision and discovery in neutrino physics.\n14\n\nDUNE Phase II\n1\nThe elements of DUNE Phase II\nThe DUNE experiment at the LBNF was conceived in 2015, following the recommendations of\nthe 2013 update of the European Strategy for Particle Physics [1] and of the 2014 Report of the\nUS Particle Physics Project Prioritization Panel (P5) [2]. The 2014 P5 Report recommended\ndeveloping, in collaboration with international partners, a coherent long-baseline neutrino pro-\ngram hosted by Fermilab, with a mean sensitivity to leptonic CPV of better than three standard\ndeviations (\u03c3) over more than 75% of the range of possible values of the CP-violating phase \u03b4CP.\nThe 2014 P5 Report also recommended a broad program of neutrino astrophysics and physics\nBeyond the Standard Model (BSM) as part of DUNE, including demonstrated capability to\nsearch for SNBs and for proton decay. Likewise, the 2013 Update of the European Strategy\nfor Particle Physics and its 2020 update [4] recommended that Europe and CERN (through its\nNeutrino Platform) continue to collaborate towards the successful completion of the .\nThe DUNE Collaboration and the Project have made substantial progress toward the re-\nalization of this enterprise, with the aim to start the scientific exploitation in 2029. Based\non recent estimates, including a flux prediction using a fully-engineered neutrino beamline, the\nultimate CPV measurement goal put forward by the 2014 P5 Report can be reached with an ex-\nposure of about 1000 kt\u00b7MW\u00b7yr. This can be achieved in about 15 years of physics data-taking\n(see Sec. 2.1), assuming that Phase II elements as described in this document are pursued.\nDUNE\u2019s neutrino astrophysics and BSM physics programs also benefit from multidecadal op-\nerations, to realize DUNE\u2019s full physics potential and achieve its scientific goals.\nFor the successful implementation of DUNE and LBNF, we need to consider the full extent\nof the available resources and funding profiles, provide a realistic estimate of the project costs,\nand achieve a clear understanding of the experimental configurations and exposures that are\nnecessary to reach various physics milestones. As a result of this exercise, the DUNE Collabo-\nration and the LBNF/DUNE-US Project have decided to pursue the experiment in two phases,\nas summarized in Table 1.\nParameter\nPhase I\nPhase II\nImpact\nFD mass\n2 FD modules (20 kt fidu-\ncial)\n4 FD modules (40 kt fidu-\ncial LAr equivalent)\nFD statistics\nBeam power\n1.2 MW\nUp to 2.3 MW\nFD statistics\nND configuration\nND-LAr+TMS, SAND\nND-LAr, ND-GAr, SAND\nSystematics\nTable 1: A high-level description of the two-phased approach to DUNE. The ND-LAr detector,\nincluding its capability to move sideways (DUNE Precision Reaction-Independent Spectrum\nMeasurement (DUNE-PRISM)), and the System for on-Axis Neutrino Detection (SAND) are\npresent in both phases of the ND. Note that the non-argon options currently under consideration\nfor Phase II near and far detectors are not shown.\nIn developing this two-phase strategy, we are guided by the original recommendations for\nthe DUNE program, which remain valid and timely. The latest P5 report released in December\n2023 reaffirmed this vision and strongly endorsed DUNE Phase I and II. In its report [3], the\n15\n\nDUNE Phase II\nP5 panel reaffirmed that the highest priority in the coming decade, independent of budget\nscenarios, is the completion of construction of existing projects which includes LBNF and\nDUNE Phase I, and the Proton Improvement Plan II (PIP-II).\nThe panel also strongly recommended constructing a portfolio of major projects, of which\nthe second-highest priority was a \u201cre-envisioned second phase of DUNE (Phase II) with an\nearly implementation of an enhanced 2.1 MW beam (aka ), a far detector module 3 (FD3),\nand an upgraded ND complex as the definitive long-baseline neutrino oscillation experiment of\nits kind.\u201d The panel also endorsed DUNE\u2019s fourth FD module (far detector module 4 (FD4))\nconcept as a \u201cModule of Opportunity\u201d and recommended exploring a range of alternative\ntargets, including low-radioactivity argon, xenon-doped argon, and novel organic or water-\nbased liquid scintillators, to maximize the science reach, particularly in the low-energy regime.\nAn accelerated and expanded R&D program in the next decade is recommended for FD4 and\nif budget scenarios are favorable, initiation of construction is also recommended.\nThe overall project design for Phase I is complete, and this project phase is funded through\ncommitments by several international funding agencies and CERN. LBNF excavation at the\nfar site is complete, and fabrication of various beamline and detector components for Phase I\nare well underway. An important component of the DUNE strategy is that the facilities con-\nstructed by LBNF at both the near and far sites are designed to support the full scope of the\nDUNE experiment from the beginning. During Phase I, the facilities at the near site are thus\nconstructed to support a >2 MW primary beamline and neutrino beamline, as well as a hybrid\nND for all DUNE experimental phases. Likewise, the far site design includes underground halls\nfor four FD modules.\nThe Phase I beamline will produce a wide-band neutrino beam with up to 1.2 MW beam\npower, designed to be upgradable to 2.4 MW. The Phase I ND includes a moveable LArTPC\nwith pixel readout called ND-LAr, integrated with a downstream muon spectrometer called\nTMS [5], and an on-axis magnetized neutrino detector called SAND further downstream. The\nND-LAr+TMS detector can be moved sideways over a range of off-axis angles and neutrino\nenergies (DUNE-PRISM concept), for an optimal characterization of the neutrino-argon inter-\nactions.\nThe Phase I FD includes two LArTPC modules, each containing 17 kt of liquid argon\n(LAr). The far detector module 1 (FD1) is a horizontal drift time projection chamber (TPC),\nas developed and operated in at the CERN Neutrino Platform and similar in concept to the , ,\nand detectors [6]. The FD2 is a vertical drift TPC. Its design capitalizes on the experience with\nthe demonstrator at CERN. For the cryogenic infrastructure in support of the two LArTPC\nmodules, Phase I will include two large cryostats (one per FD module), 35 kt of LAr, and three\nnitrogen refrigeration units.\nWhile several options are under consideration for the Phase II components of the far and\nnear site detectors, key elements have already been defined:\n\u2022 A core component of Phase II is a More Capable Near Detector (). The main improvement\nto the ND is the addition of a magnetized high-pressure gaseous argon TPC (HPgTPC),\nsurrounded by an electromagnetic calorimeter and by a muon detector called . ND-GAr\nwill serve both as a new muon spectrometer for ND-LAr, replacing the TMS in this\ncapacity, and as a new neutrino detector to study neutrino-argon interactions occurring\n16\n\nDUNE Phase II\nin the HPgTPC. In addition, upgrades to the ND-LAr and SAND systems are considered,\nas well as potential ND options in the case of a non-argon technology for FD4.\n\u2022 Two additional FD modules, FD3 and FD4, will be added at the far site, for a total of\nfour. The DUNE FD2 vertical drift technology forms the basis for the envisioned designs\nfor FD3 and FD4. A non-argon option such as liquid scintillator (e.g., ) is also under\nconsideration as an alternative technology for FD4. The cryogenic infrastructure at the\nfar site will be upgraded for Phase II with a fourth nitrogen refrigeration unit to provide\ncapacity for up to an additional 35 kt of LAr.\n\u2022 A beam upgrade to increase the intensity to >2 MW. This is achieved by ACE-MIRT,\nwhich increases the frequency of beam spills by nearly a factor of two. While this is part\nof Phase II, it is possible to implement the upgrades that comprise ACE-MIRT before\nDUNE beam data taking begins.\nThe R&D underpinning the Phase II concepts is performed as part of a global program.\nThe Detector R&D () collaborations hosted by CERN, which have been established as part of\nthe European Committee for Future Accelerators (ECFA) roadmap, cover many of the detector\nconcepts under study for DUNE Phase II. The DRD1 collaboration focuses on gaseous detectors\nand the DRD2 focuses on liquid detectors. Both collaborations have been formed recently. They\nare expected to grow with collaborators from within and outside Europe. Both the DRD1 and\nDRD2 collaborations were approved in December 2023 as official CERN experiments and held\ntheir first collaboration meetings in February 2024 at CERN. The ECFA DRD collaborations are\nstrongly aligned with the Detector R&D collaborations (s) being formed under the Coordinating\nPanel for Advanced Detectors (CPAD) umbrella in the US. There is an active effort underway\nto coordinate activities across the CERN-hosted and US-based collaborations on synergistic\nareas of R&D toward achieving common scientific and technological goals.\nThis document is organized as follows. Section 2 covers the science that DUNE will pursue\nwith Phase II, covering long-baseline neutrino oscillation physics, neutrino astrophysics, and\nBSM physics. A progress report on DUNE\u2019s Phase II far and near neutrino detectors is given\nin Sections 3 and 4, respectively. These two sections cover our current understanding of the\ndetector requirements to carry out the Phase II physics goals, and a current snapshot of the\nmain detector design options that are under consideration. These sections also summarize the\ncritical R&D elements that remain to be addressed and the prototyping phases to be realized\nbefore Phase II detector technical designs can be finalized.\n2\nDUNE Phase II physics\nThis section discusses selected DUNE science drivers in the areas of long-baseline physics, neu-\ntrino astrophysics, and BSM physics that uniquely benefit from an improved performance of\nPhase II beam and detectors. The physics sensitivities are typically shown as functions of\nhigh-level figures of merit, such as exposure time, detector mass, background levels or detec-\ntor acceptance, mostly without entering into the detector technology details. Specific benefits\n17\n\nDUNE Phase II\nbrought by certain technologies are highlighted in Sections 3 and 4, together with the descrip-\ntions of such technologies.\n2.1\nLong-baseline neutrino oscillation physics\nThe DUNE experiment is designed to measure the rate of appearance of electron (anti)neutrinos\n(\u03bde or \u00af\u03bde) and the rate of disappearance of muon (anti)neutrinos (\u03bd\u00b5 or \u00af\u03bd\u00b5), as functions of\nneutrino energy in a wide-band beam.\nDUNE is sensitive to all the parameters governing\n\u03bd1 \u2212\u03bd3 and \u03bd2 \u2212\u03bd3 mixing in the three-flavor model: \u03b823, \u03b813, \u2206m2\n32 (including its sign, which\nis given by the neutrino mass ordering), and the phase \u03b4CP.\nDuring Phase I, DUNE can accumulate approximately 100 kt\u00b7MW\u00b7yr of data in five years.\nThis corresponds to \u2248400 \u03bde and 150 \u00af\u03bde candidates in the FD, depending on the value of\nthe oscillation parameters and assuming equal fractions of neutrino and antineutrino running.\nWhile these data sets will still be statistically limited once Phase I ND systematic constraints\nare accounted for, they are sufficient to conclusively determine the neutrino mass ordering at\n> 5\u03c3 significance, regardless of the true parameter values. If CPV is nearly maximal (\u03b4CP\n\u2248\u00b1\u03c0/2), DUNE can establish CPV at 3\u03c3 in Phase I. DUNE will also make measurements\nof the disappearance parameters \u2206m2\n32 and sin2 2\u03b823 that improve upon current uncertainties.\nHowever, the statistics of Phase I are too low to determine the octant of \u03b823 or to establish\nCPV except in the most favorable scenarios.\n2.1.1\nGoals of the oscillation physics program of Phase II\nThe goals of the oscillation physics program of Phase II are high-precision measurements of all\nfour parameters: \u03b823, \u03b813, \u2206m2\n32 and \u03b4CP, to establish CPV at high significance over a broad\nrange of possible values of \u03b4CP, and to test the three-flavor paradigm as a way to search for\nnew physics in neutrino oscillations. Achieving these goals requires 600 \u22121000 kt\u00b7MW\u00b7yr of\ndata statistics, depending on the measurement. This can be achieved by operating for 6 \u221210\nadditional calendar years with a greater than 2 MW beam and a FD of 40 kt LAr equivalent\nfiducial mass. Without doubling the FD mass and the beam intensity, the additional time\nrequired would be 24 \u221240 years.\nIn particular, the long-baseline sensitivities presented below make the following assumptions\nconcerning the time evolution of the protons on target (POT) delivery, the fiducial FD mass and\nthe ND systematic constraints. The beam power evolution is based on the assumptions of the\nFermilab Proton Intensity Upgrade Central Design Group [7]. The average beam power during\nthe first year of beam operations is 1.1 MW, increasing to 1.6 MW during year 2, thanks to ACE-\nMIRT upgrades [7]. Further beam optimizations are assumed in subsequent years, yielding a\nbeam power of 2.3 MW after approximately 15 years. The assumed POT delivery also includes\na 57% average uptime [8]. As regards the fiducial FD mass, the experiment is assumed to take\ndata with two FD modules (20 kt fiducial mass) during the first three years. The FD3 and FD4\nmodules are assumed to become fully operational in years 4 and 6, respectively, to provide a\nnominal fiducial FD mass of 40 kt. Figure 1 shows how the accumulated exposure, expressed in\nkt\u00b7MW\u00b7yr units, varies as a function of time with this assumed staging scenario. The 600 and\n18\n\nDUNE Phase II\nFigure 1: DUNE integrated exposure, in kt\u00b7MW\u00b7yr units, as a function of time assumed for\nthe long-baseline (LBL) sensitivity results presented in this section. The integrated exposure\nis built from the beam power and FD mass staging assumptions discussed in the text.\n1000 kt\u00b7MW\u00b7yr integrated exposure milestones of DUNE Phase II appear within reach after\napproximately 10 and 15 years of beam plus detector operations, respectively. Finally, it is\nassumed that the Phase I ND systematic constraints will be in effect up to year 6, with the\nimprovements from Phase II ND starting in year 7. The new constraints, as they gradually\nimprove over the course of two years to their final values, will be applied to all past FD data.\nThe precision of the high-statistics measurements is ultimately limited by the systematic\nuncertainties. To achieve DUNE\u2019s science goals will therefore require unprecedented control of\nsystematic uncertainties. The significance for DUNE to establish CPV is shown as a function\nof time in Figure 2. Phase II, with its full 1000 kt\u00b7MW\u00b7yr exposure, will enable DUNE to\nestablish CPV at > 3\u03c3 over 75% of possible \u03b4CP values, and measure it at a precision of\n6\u25e6\u221216\u25e6, depending on the true value.\nDUNE can also measure the angle \u03b823 with world-leading precision and determine the octant\nif it is sufficiently non-maximal. The measurements of \u03b813 and \u2206m2\n32 will approach the precision\nof the current measurement from Daya Bay [9] and the planned measurement from JUNO [10],\nrespectively, which are all performed with a different neutrino flavor, over a different baseline,\nand at a different energy. Comparing the results obtained over this wide range of conditions\nwill provide a more complete and robust test of the three-flavor model. The resolutions to \u03b4CP,\nsin2 2\u03b813, and sin2 \u03b823 are shown as a function of exposure in Figure 3.\nDUNE is also sensitive to BSM physics that impacts neutrino oscillations, including non-\nunitary mixing, non-standard interactions, violation of charge, parity, and time reversal sym-\n19\n\nDUNE Phase II\nFigure 2: The significance for DUNE to establish CPV for 50% (left panel) and 75% (right)\nof \u03b4CP values as a function of running time. See text for details about the assumed staging\nscenario.\nmetry (CPT), and the possible existence of additional neutrino species (see Section 2.3).\n2.1.2\nThe role of Phase II detectors\nThe two additional modules, FD3 and FD4, will provide the additional exposure and improved\nstatistical precision that is critical to achieve the full \u03b4CP sensitivity (Figure 2). They also offer\nthe opportunity to improve the neutrino energy reconstruction and the neutrino interaction\nclassification with enhanced detector technology, for example through optimized charge and\nphoton readout systems (Sec. 3.3). It is crucial that the data from these modules be combined\nwith data from FD1 and FD2, with the systematic constraints from the ND applied to all\nFD modules. For this reason, the most straightforward approach is for FD3 and FD4 to be\nLArTPCs, so that DUNE would immediately benefit from the \u03bd-Ar measurement program of\nthe ND. The oscillation sensitivities presented in Figures 2 and 3 assume the performance of the\nHorizontal Drift module using an end-to-end simulation and reconstruction. The alternative\nLArTPC concepts being considered for FD3 and FD4 are expected to have similar, and perhaps\nslightly improved performance for GeV-scale beam neutrinos, so the existing simulations serve\nas a conservative estimate of the eventual sensitivity.\nIf FD4 is not a LArTPC, the impact on the long-baseline oscillation program is less straight-\nforward. For the Theia concept discussed in Section 3.5, the performance is estimated using\na reconstruction based on the fiTQun package [11], and a boosted decision tree (BDT) [12].\nThe analysis is less sophisticated than the DUNE TDR sensitivities [8], using the GLOBeS\npackage to implement systematics as normalization shifts, but suggests that the sensitivity is\ncomparable to what can be achieved in a single LArTPC module. It does not yet make use of\nthe additional information potentially offered by the scintillation component, which can provide\ntagging of neutrons and other sub-Cherenkov threshold particles, for improved event identifi-\ncation and enhanced calorimetry. Combining a non-LArTPC module with LAr measurements\n20\n\nDUNE Phase II\nFigure 3: The resolutions to \u03b4CP (left), sin2 2\u03b813 (center), and sin2 \u03b823 (right), shown as a function\nof exposure in kt-MW-yrs, assuming the full constraint from the ND, including MCND. The\nultimate precision of DUNE requires an exposure greater than 600 kt-MW-yrs, which requires\nFD3 and FD4 to be built in a reasonable timescale.\ncould potentially provide a cross-check of extracted oscillation parameter values with different\ndetector systematics. A non-LAr FD4 would require a dedicated ND to constrain neutrino cross\nsection uncertainties and detector response on the FD4 nuclear target to a similar precision\nas the LArTPC constraints. Near detector options for non-LAr FD modules are discussed in\nSec. 4.4.\nThe role of MCND (Section 4.2) is to ensure that DUNE can achieve the required level\nof systematic uncertainties for Phase II and to ensure that the results are not systematically\nlimited. It would replace the TMS with a detector that has its own standalone physics capabil-\nities, including constraining neutrino-argon cross section uncertainties and expanding the BSM\nreach of the ND, while also measuring muons exiting the ND-LAr detector. Further study of\nthe ultimate performance of the Phase I ND is important for scoping the Phase II ND.\n2.2\nNeutrino astrophysics and other low-energy physics opportuni-\nties\nDUNE\u2019s broad physics program includes the detection of neutrinos from astrophysical sources\nin the MeV energy range [13], primarily neutrinos from the sun and a SNB. With argon as\nactive material, DUNE will be primarily sensitive to the astroparticle \u03bde flux for energies below\n100 MeV and above 5 MeV due to the relatively large \u03bde charged current (CC) cross section for\nthe process: \u03bde+40Ar \u2192e\u2212+40K\u2217. DUNE will be unique in this regard, making the experiment\nhighly complementary to existing and proposed experiments for the next decades aiming for\nsimilar astrophysical neutrino measurements in the 10s of MeV regime: JUNO [14], Hyper-\nKamiokande [15], and dark matter detectors [16, 17]. This section highlights the improvements\na LArTPC FD module from Phase II would bring. It also includes a summary of the advantages\nof a water-based liquid scintillator, that would be sensitive primarily to the \u00af\u03bde flux, within the\nPhase II program.\n21\n\nDUNE Phase II\nDUNE Phase I will be sensitive to solar and SNB neutrinos, achieving an energy resolution of\n(10\u221220)%. The visible energy threshold will be > 5 MeV for SNB neutrinos and higher for solar\nneutrinos, which do not arrive in a short pulse. Large LArTPC detectors have demonstrated\nmuch lower charge thresholds, \u223c100 keV [18], but Phase I sensitivity will be limited to > 5 MeV\ndue to light collection performance and radiological backgrounds. Thus, innovation on these\nfronts can lower visible energy thresholds for astrophysical neutrinos by as much as two orders of\nmagnitude while also improving energy resolution. Lower thresholds would also fundamentally\nexpand the low-energy physics opportunities with DUNE Phase II. Figure 4 shows a selection\nof potential signatures of astrophysical or other beam-unrelated origin with DUNE Phase II,\ntogether with relevant backgrounds.\nFigure 4: Detectable energy ranges in DUNE LArTPC FD modules for potential < 20 MeV\nsignatures of astrophysical or other non-beam-related origin (blue), and for relevant, overlapping\nbackgrounds (orange). The DM signature refers to weakly-interacting massive particle (WIMP)\ndirect dark matter searches. Adapted from [19].\n2.2.1\nSNB neutrinos\nDUNE will be part of a collaborative, multi-messenger network of neutrino and optical tele-\nscopes studying the next galactic core-collapse supernova (CCSN). With different flavor sen-\nsitivity from other large experiments, DUNE will provide complementary information about\nthe collapse. DUNE\u2019s \u03bde sensitivity is most striking at the earliest times of the SNB, which is\ndominated by \u03bde emission from neutronization in the stellar core, as shown in the top panel of\nFigure 5. During Phase I, DUNE will already be able to detect neutrinos from a CCSN with\nenergies > 5 MeV [20], albeit with lower statistics. The larger mass of Phase II represents a\nsignificant step in extending the detector\u2019s sensitivity to a SNB signal, since the burst trig-\nger efficiency, reconstruction of the supernova direction (bottom right panel of Figure 5), and\nprecise measurement of the supernova spectral parameters (bottom left panel of Figure 5))are\ndominated by the number of neutrino interactions in the detectors. While the expected event\nrate varies significantly among supernova models, the 40 kt (fiducial) DUNE detector would be\n22\n\nDUNE Phase II\nexpected to observe \u22483000 neutrinos from an SNB at a distance of 10 kpc, just beyond the\ncenter of the Milky Way [20].\n6\n8\n10\n12\n14\nSupernova Distance (kpc)\n1\n150\n1\n175\n1\n200\n1\n225\n1\n250\n1\n300\n1\n350\n1\n400\n1\n500\n1\n600\n1\n800\n1\n1200\n1/\nNeES\n0.001\n0.002\n0.003\n0.004\n0.005\n0.006\nSky Fraction\nceES\neES = 1.00, c\neCC\neES = 0.00\nceES\neES = 0.86, c\neCC\neES = 0.04\nFigure 5: The total luminosity of neutrinos released during CCSN from [21] (top). Sensitiv-\nity regions in mean neutrino energy (related to the temperature of supernovae) and neutrino\nluminosity space for three different supernova distances from [22] (bottom left). DUNE\u2019s recon-\nstruction of the direction of a SNB in terms of the fraction of sky allowed at 68% confidence, as\na function of recorded number of neutrino-electron scattering events as well as the correspond-\ning supernova distance from [23] (bottom right).\nThe modular nature of DUNE\u2019s FD makes the experiment ideal for SNB triggering and\ncontributing to SuperNova Early Warning System (SNEWS) [24]. Each FD module will inde-\npendently forward a CCSN alert to SNEWS which will be made available to optical astronomers.\nDeployment of additional detectors in Phase II will effectively ensure that at least one FD mod-\nule is operational whenever a SNB arrives at the detector. With all modules taken together,\nthe increased mass from Phase II will allow DUNE to trigger on further supernovae, increasing\ncoverage in the neighborhood beyond the Milky Way (e.g., in the Large and Small Magellanic\nClouds).\nAs the neutrino signal escapes a core-collapse supernova hours before the first optical signal,\npin-pointing the source of the SNB is fundamentally important to facilitate optical observation\nof the initial stages of the supernova. The electron tracks from neutrino-electron elastic scatter-\n23\n\nDUNE Phase II\ning, a sub-dominant interaction channel for SNB detection, are nearly parallel to the incoming\nneutrino flux and can thus be used to reconstruct the neutrino direction. Supernova pointing\nleverages the excellent tracking capabilities of a LArTPC to identify neutrino-electron scatter-\ning events yielding a pure sample of this low-rate channel. The increased mass from Phase II is\ncritical for realizing DUNE\u2019s full potential. Using a typical flux model, the full 40 kt detector\nwould expect 326 neutrino-electron scattering events compared to 163 in Phase I [23]. This\nreduces the field-of-view for optical follow-up searches following a SNB signal from 0.26% to\n0.14% of the total sky at 1 \u03c3 as shown in the bottom right panel of Figure 5. A Phase II module\nwith pixelated charge readout would also improve SNB pointing resolution by improving the\n3D reconstruction of low-energy electron tracks.\nThe neutrino mass ordering has a strong impact on the expected signal at early times\n(neutronization burst) when electron-type neutrinos dominate the neutrino flux at production\n(see Figure 6 for expected event rates in DUNE). Neutrino flavor transformations can be in-\nduced by neutrino-neutrino scattering and collective modes of oscillation [25]. These effects\nwill leave imprints on the neutrino signal and can be used to study these phenomena exper-\nimentally. These effects will test fundamental neutrino properties by measuring the neutrino\nself-interaction strength [26]. DUNE will also provide competitive constraints on the absolute\nneutrino mass via measurements of the time of flight from the supernova to Earth [27].\nWith argon\u2019s \u03bde flavor sensitivity, DUNE will uniquely probe the neutrino component of\nthe diffuse supernova neutrino background (DSNB) [28] \u2013 Phase II will be critical for such a\nlow-rate search by increasing argon mass.\n40 kton argon, 10 kpc\n Time (seconds) \n0.05\n0.1\n0.15\n0.2\n0.25\nEvents per bin\n10\n20\n30\n40\n50\n60\n70\n80\nInfall\nNeutronization\nAccretion\nCooling\nNo oscillations\nNormal ordering\nInverted ordering\n40 kton argon, 10 kpc\nFigure 6: Expected event rates from [20] as a function of time for the electron-capture supernova\nmodel in [29] and for 40 kt of argon during early stages of the burst. Shown are the event rate\nfor the unrealistic case of no flavor transitions (blue) and the event rates including the effect\nof matter transitions for the normal (red) and inverted (green) mass orderings. Error bars are\nthe expected statistical uncertainty in each (varying) time bin.\nWith significant increase of the photodetector area, e.g., 10% coverage with silicon photo-\nmultipliers (SiPMs) [19], and use of 39Ar-depleted argon, a DUNE Phase II LArTPC module\n24\n\nDUNE Phase II\nwould be sensitive to faint light flashes from Coherent Elastic Neutrino-Nucleus Scattering\n(CE\u03bdNS) interactions on argon during a SNB. The \u201cCEvNS glow\u201d from a supernova would be\nobserved as an increase of low-PE flashes observed through the duration of the burst. As a neu-\ntral current (NC) process, this channel is sensitive to all neutrino flavors, thus giving orthogonal\ninformation to the MeV-scale \u03bde CC interactions. Importantly, CEvNS glow allows DUNE to\ndetermine the supernova neutrino fluence independent of neutrino oscillation uncertainties.\nA water-based liquid scintillator module (e.g., Theia) would sacrifice part of the SNB\n\u03bde statistics for a significant increase in \u00af\u03bde events through inverse \u03b2 decay, with a threshold of\n\u223c2 MeV. Such a module would detect approximately 5000 \u00af\u03bde interactions from a SNB at 10 kpc\ndistance. The scintillation light would provide a tag for neutrons to allow separation between\ninverse \u03b2 decay events and directionally-sensitive elastic scattering reactions. Using the high\nlight output from the scintillation, such a module would also be sensitive to pre-supernova\nneutrinos [30], alerting neutrino experiments to an upcoming SNB.\n2.2.2\nSolar neutrinos\nAfter more than a half century of study, there remain important open questions in particle and\nastrophysics that solar neutrino measurements can potentially resolve. This is due in large part\nto the precision tracking capabilities of the DUNE LArTPC detectors. In addition, because of\nargon\u2019s dominant \u03bde CC interaction channel, the detected energy will correlate strongly with\nthe incoming neutrino energy. With these advantages, DUNE promises excellent potential for\nimproved measurements [31]. Initial studies suggest DUNE Phase I can select a sample of\n8B solar neutrinos that would improve upon current solar measurements of \u2206m2\n21 [32] via the\nprecise measurement of the day-night flux asymmetry induced by Earth matter effects. DUNE\nPhase I can also make the first observation at >5\u03c3 of the \u201chep\u201d flux produced via the 3He +\np \u21924He + e+ + \u03bde nuclear fusion.\nThe energy resolution of DUNE Phase I, (10 \u221220)%, could be improved down to \u22482%\nthrough improvements to the Phase II photon detection system (PDS). This radically improves\ndetermination of solar neutrino parameters. The measurement of the solar mass splitting \u2206m2\n21\nrequires precisely measuring the energy dependence of the neutrino oscillation pattern. A single\nmodule with 2% resolution would make this measurement better than four modules with Phase I\nenergy reconstruction performance.\nFor beam-unrelated FD events, reconstructed photon flashes are used to select events within\nthe detector fiducial volume and to correct ionization charge loss along drift, greatly suppressing\nbackgrounds and improving energy reconstruction, respectively.\nIn Phase I, DUNE\u2019s solar\nneutrino reach will be limited by non-perfect light flash reconstruction and by radiological\nbackgrounds, primarily neutron capture on argon, which can also confuse light-charge matching.\nAs described in Section 3, upgrades to the photon detection can increase DUNE light yield in\nPhase II by a factor of five or more. This will make light flashes from solar neutrino signals\nmore apparent and improve vertex reconstruction from the flash to simplify the light-charge\nmatching algorithm. Neutron capture on 40Ar could be vetoed by rejecting optical flashes that\nreconstruct near the 6.1 MeV Q-value and further mitigated by installation of passive shielding.\nTogether, these would reduce the solar neutrino detection threshold for a Phase II FD module.\n25\n\nDUNE Phase II\nDUNE\u2019s \u03bde CC signal makes it ideal for measuring the energy dependence of the solar electron-\nneutrino survival probability, Pee. With a visible energy threshold at or below 5 MeV for solar\nneutrinos, possible with some technology choices outlined in Section 3, DUNE will probe the\nupturn in Pee. This is the transition region between the low-energy regime where vacuum solar\noscillations dominate and the high-energy regime where the oscillation probability is determined\nby Mikheyev-Smirnov-Wolfenstein effect (MSW) matter effects [33] inside the sun. The same\nMSW matter effects, but in the earth, are central to DUNE\u2019s measurements of neutrino mixing\nparameters with long-baseline oscillation measurements. A significant increase in photodetector\ncoverage would allow measurements of carbon nitrogen oxygen (CNO) solar neutrinos that could\ndistinguish between solar metallicity models [19].\nA FD module based on Theia would also be sensitive to solar neutrinos, through the\nneutrino-electron scattering channel. The Theia technology is sensitive to both scintillation\nand Cherenkov light from low-energy neutrinos \u2013 thus simultaneously providing low thresholds\nand event directionality. Such a module could possibly probe the solar neutrino transition\nregion to even lower energies, near 2 MeV.\n2.2.3\nOther low-energy physics opportunities\nThrough heavy fiducialization and improved energy resolution from increased photodetector\ncoverage, DUNE\u2019s low-energy physics can reach beyond astrophysical neutrinos in Phase II.\nPlanning is underway for future WIMP dark matter experiments. These liquid noble de-\ntectors will scale up the current technologies active target masses with the goal to reach the\nso-called \u201cneutrino fog\u201d, that is the cross-section below which the potential discovery of a dark\nmatter signal is slowed due to the uncertainty in the irreducible background from the coher-\nent elastic scattering of astrophysical neutrinos with nuclei [34]. Leading upcoming projects\ninclude the xenon-based XLZD experiment [35], and the argon-based DarkSide-20k [36] and\nARGO experiments. A DUNE FD module could perform a competitive WIMP dark matter\nsearch complementary to future argon dark matter experiments [37]. Particularly interesting\nwould be the sensitivity to the annual modulation of the WIMP signal, which due to DUNE\u2019s\nlarge target mass would allow a rapid confirmation of any observed signal in the current so-\ncalled generation-2 experiments [19]. A 10% photodetector coverage with SiPMs could give the\nnecessary threshold of \u223c100 keV. Such low thresholds would also require operating the detector\nmodule with underground argon depleted in the 39Ar isotope, for background mitigation.\nBy introducing a large mass fraction of 136Xe or 130Te to a Phase II FD module based on\nLArTPC or Theia technology, respectively, DUNE could also perform neutrinoless double-\u03b2\ndecay (0\u03bd\u03b2\u03b2) searches. The neutrinoless double \u03b2 decay community has laid out a strategic\nplan [38] that calls for a diverse R&D program with sensitivity beyond next-generation ton-scale\nexperiments. DUNE Phase II can contribute toward this long-term 0\u03bd\u03b2\u03b2 effort, in connection\nwith, and as a possible evolution of, the existing 0\u03bd\u03b2\u03b2 program. A DUNE Theia module loaded\nwith 130Te could be a natural evolution of the loaded liquid scintillator technique currently\npursued by SNO+ [39] and KamLAND-Zen [40]. Similarly, a 136Xe-doped DUNE LArTPC\nmodule with sufficiently good energy resolution (\u03c3) of order 2% [41] could expand on liquid\nxenon TPC strategies currently employed by nEXO [42]. Such a LArTPC 0\u03bd\u03b2\u03b2 module would\n26\n\nDUNE Phase II\nalso require sourcing very large amounts of underground argon, in order to mitigate 42Ar-\ninduced backgrounds.\nFinally, thanks to its \u00af\u03bde sensitivity, a Theia module would also observe geo-neutrinos and\nreactor neutrinos [12].\n2.3\nPhysics beyond the Standard Model\nDUNE has discovery sensitivity to a diverse range of physics Beyond the Standard Model\n(BSM), which is complementary to those at collider experiments and other precision experi-\nments. BSM physics accessible at DUNE may be divided into three major areas of research:\nrare processes in the beam observed at the ND (for example heavy neutrinos, light dark mat-\nter, or new physics that could enhance neutrino trident production), rare event BSM particle\nsearches at the FD (for example inelastic boosted dark matter, nucleon decays), and non-\nstandard neutrino oscillation phenomena (for example sterile neutrino mixing, non-standard\ninteractions). In the following, we give examples where DUNE Phase II will bring additional\nunique sensitivity with respect to Phase I and to the performance of current experiments [43].\n2.3.1\nRare event searches at the near detector\nThe high intensity and high energy of the LBNF proton beam enables DUNE to search for\na wide variety of long-lived, exotic particles that are produced in the target and decay in\nthe ND. Heavy neutral leptons (HNLs) and Axion-like particles (ALPs) are examples of well-\nmotivated searches that can be carried out in DUNE. Low density detectors are best suited\nfor such a search, because the signal scales with the detector volume while the background\n(predominantly due to Standard Model neutrino interactions) scales with detector mass. In\nPhase I, SAND can perform such searches with a density of \u223c0.2 g/cm2. In Phase II, the ND-\nGAr substantially improves the reach for these searches with even lower density and a larger\nvolume.\nSignal efficiencies and background rates after selection cuts are found to improve\nsignificantly in Phase II, thanks to ND-GAr [46]. Background rates generally depend on the\ndecay final state.\nIn some cases background-free searches appear possible, for example for\nchannels involving pairs of muons in the final state.\nFor HNLs, the decay rates are proportional to |U\u03b1N|2 in the case of single dominant mixing,\nwhere \u03b1 = e, \u00b5, \u03c4 and the matrix U\u03b1N specifies the mixing between the active SM neutrinos \u03b1\nand the new heavy states N. Figure 7 shows the combined sensitivity for HNL decay channels\nprobing each individual mixing matrix element |U\u03b1N|2, as a function of the HNL mass and under\nthe assumption of no background (result adapted from [44]). As can be seen from the figure,\nDUNE is world-leading at masses below m\u03c4, complementary to the LHC heavier mass searches.\nIn addition, DUNE may have the potential to explore further the portion of parameter space\npredicted by Type I seesaw models. Other phenomenological studies [47, 48, 49, 50] confirm\nthe potential of the DUNE Phase II ND for HNL searches.\nND-GAr is also sensitive to ALPs with masses between 20 MeV and 2 GeV [51, 46]. DUNE\nis expected to improve over present constraints on ALP particles particularly for ALP masses\nbelow the kaon mass. For a wide range of ALP lifetimes, the sensitivity improvement would\n27\n\nDUNE Phase II\nFigure 7: Expected DUNE ND sensitivity at 90% CL to the mixing |U\u03b1N|2 as a function of the\nmass MN, for a total of 7.7 \u00b7 1021 POT, and combining all the possible HNL decay channels\nleading to visible states in the detector. Backgrounds are assumed to be negligible. Results\nare shown for a HNL coupled exclusively to: e (left panel), \u00b5 (middle panel), and \u03c4 (right\npanel). The dotted gray lines enclose the region of parameter space where a Type I seesaw\nmodel could generate light neutrino masses in agreement with oscillation experiments and upper\nbounds coming from the latest KATRIN results on \u03b2-decay searches. A negligible background\nlevel after cuts and a signal selection efficiency of 20% was assumed for this analysis. Figure\nadapted from [44] to include the latest excluded areas from existing results; obtained with\nthe HNLimits [45] package. All sensitivity curves and currently excluded areas assume Dirac\nneutrinos, and that the HNL only couples to one of the charged leptons as indicated by the\nflavor index of the panel, while the other two mixings are set to zero.\nspan many orders of magnitude.\nAnother rare event search at the ND is neutrino trident production, that is, the production\nof a pair of oppositely-charged leptons through the scattering of a neutrino on a heavy nucleus.\nNeutrino trident production is a powerful probe of BSM physics in the leptonic sector [52, 53].\nThe Standard Model (SM) expectation is that the ND will collect approximately a dozen of\nthese rare events per ton of argon per year [54, 55]. To date, only the dimuon final-state has\nbeen observed, although with considerable uncertainties. The main challenge in obtaining a\nprecise measurement of the dimuon trident cross-sections (\u03bd\u00b5 \u2192\u03bd\u00b5\u00b5+\u00b5\u2212and \u00af\u03bd\u00b5 \u2192\u00af\u03bd\u00b5\u00b5+\u00b5\u2212)\nat DUNE will be the copious backgrounds, mainly consisting of CC single-pion production\nevents (\u03bd\u00b5N \u2192\u00b5\u03c0N \u2032), as muon and pion tracks can be easily confused. ND-GAr will tackle\nthis search by improving muon-pion separation through dE/dx measurements in the HPgTPC\nand the calorimeter system, and ND-GAr\u2019s magnetic field will significantly improve signal-\nbackground separation by tagging the opposite charges of the two muons in the final state.\n28\n\nDUNE Phase II\n2.3.2\nRare event searches at the far detector\nPhase II will also enhance BSM searches at the FD, and in particular searches that are expected\nto be nearly background-free at the scale of the experiment\u2019s full exposure. In such cases,\nthe decay or scattering rate sensitivity will be inversely proportional to the FD exposure (in\nkt\u00b7yr), and added exposure in Phase II FD modules will be significant. Background-free (or\nquasi-background-free) searches at the FD may include baryon-number-violating processes.\nFor example, current estimates [43] for the p \u2192K+\u00af\u03bd search yield a mean background rate\nexpectation of 0.4 events for a 400 kt\u00b7yr exposure at the FD.\n2.3.3\nNon-standard neutrino oscillation phenomena\nDUNE is sensitive to neutrino oscillation scenarios beyond the standard three-flavor picture,\nincluding sterile neutrinos, non-standard interactions, and PMNS non-unitarity. These searches\nrely on both the ND and FD, and require high precision and very large exposures, such that\nboth the Phase II ND and FD are important.\nIn addition to searching for BSM modifications to the muon and electron neutrino signals,\nDUNE also has a unique capability to search for tau neutrino appearance because the broadband\nLBNF beam has significant flux above the \u223c3.5 GeV tau charged-current threshold. Searches\nfor tau appearance would enable DUNE to directly constrain the tau elements of the PMNS\nmatrix, and also to search for anomalous \u03bd\u03c4 appearance, which may point to mixing with HNLs\nor non-standard interactions [56, 57]. This would become particularly interesting if hints of\nnon-unitarity are observed in the muon and electron channels. The \u03c4 lepton from beam \u03bd\u03c4\nCC interactions is not directly observable in the DUNE detectors due to its short 2.9 \u00d7 10\u221213 s\nlifetime. However, the final states of \u03c4 decays (\u223c65% into hadrons, \u223c18% into \u03bd\u03c4 + e\u2212+ \u00af\u03bde,\nand \u223c17% into \u03bd\u03c4 + \u00b5\u2212+ \u00af\u03bd\u00b5) can be detected.\nThe LBNF beamline is designed such that the target and the horn focusing system can\nbe replaced. The LBNF/DUNE Construction Project will provide targets and horns designed\nfor 1.2 MW operation, in the standard low-energy beam tune configuration optimized for CPV\nmeasurements. New ACE-MIRT upgrades designed for >1.2 MW operation will be needed, and\ncould provide the capability to run with a higher-energy beam tune optimized for detection\nabove the \u03c4 production threshold. Studies indicate that the \u03bd\u03c4 charged-current interaction rate\nwill more than double at the FD in this case, compared to the standard LBNF beam optimized\nfor CPV [58]. Running with the high-energy tune is not currently planned, but could provide\nfurther physics reach for DUNE in Phase II.\nAt the ND, the baseline is far too short for \u03bd\u00b5 \u2192\u03bd\u03c4 oscillations to occur within a three-\nflavor scenario. However, \u03bd\u03c4 originating in rapid oscillations driven by sterile neutrinos could be\ndetected. A challenge is that for the tau decay to muon channel, a large fraction of the signal\nis at very high energy. In Phase I, the TMS cannot reconstruct momentum by curvature, and\nis limited to measuring T\u00b5 <\u223c6 GeV by range. It may be possible to search for anomalous tau\nappearance in SAND, which is sensitive to higher energy muons by curvature but has much\nsmaller target mass. In Phase II, ND-GAr provides a magnetized spectrometer for ND-LAr\nwhich can reconstruct very high-energy muons by curvature. With one year of data with the\nPhase II ND, preliminary studies show that DUNE\u2019s reach in this channel extends beyond the\n29\n\nDUNE Phase II\npresent strongest limits from NOMAD [59].\n3\nThe DUNE phase II far detector\n3.1\nIntroduction\nThe primary objective of the DUNE Phase II FD is to increase the fiducial mass of DUNE to at\nleast the originally planned 40 kt LAr-equivalent mass. For long-baseline neutrino oscillations,\nit is critical that all four FD modules be compatible with the systematic constraints of the ND.\nNon-LAr options for the Phase II FD would require corresponding additions or changes to the\nND complex in order to achieve a comparable level of systematic uncertainty. These options\nare described in Section 4.4. For MeV-scale physics, the additional mass would double the\nnumber of expected neutrino interactions in a SNB and extend the reach to supernovae beyond\nthe Milky Way. An exposure of hundreds of kt-yrs is required to improve upon oscillation\nparameter measurements with solar neutrinos.\nMost BSM searches also require very long\nexposures to be competitive.\nEnhancements to the detector design have the potential to improve the DUNE program\nby lowering the threshold for MeV-scale neutrinos or by reducing the background rates in this\nenergy regime. Phase II also presents opportunities to expand the DUNE science program\nto new areas while preserving the essential core measurement capabilities. The design of the\nPhase II FD modules will also incorporate lessons learned from the construction of Phase I, in\nparticular the vertical drift FD2, optimizing performance and cost.\n3.2\nThe vertical drift detector design\nThe single-phase vertical drift technology as implemented in ProtoDUNE-VD and planned\nfor FD2 [60] (Figures 8 and 9) draws from the strengths of the DUNE prototypes\n[61] and\nProtoDUNE-SP [62] as well as the previous detectors ICARUS and MicroBooNE. Relative to\nthe well-established single-phase (SP) horizontal drift design that is based on large wire plane\nassemblies, the vertical drift design simplifies detector construction and installation, reducing\noverall detector costs. The vertical drift module uses most of the same structural elements as\nthe ProtoDUNE-DP design (e.g., charge-readout planes (CRPs) to form the anode planes, and\nthe field cage that hangs from the cryostat roof), and is constructed of modular elements that\nare much easier to produce, transport, and install.\nThe cathode at the vertical mid-plane of the detector is suspended from the top CRP support\nstructure and subdivides the detector into two vertically stacked, 6.5 m high drift volumes, with\nCRP readout for both the top and bottom drift volumes. The top CRPs are suspended from\nports on the cryostat roof whereas the bottom CRPs are supported by feet on the cryostat\nfloor.\nThe important features of the vertical drift design, particularly in comparison with the FD1\nhorizontal drift design, are:\n30\n\nDUNE Phase II\nFigure 8: Schematic of the vertical drift FD2 concept with PCB-based charge readout. Corru-\ngations on cryostat wall shown in yellow; PCB-based CRPs (brown, at top and bottom with\nsuperstructure in gray for top CRPs); cathode (violet, at mid-height with openings for photon\ndetectors); field cage modules (white) hung vertically around the perimeter (the portions near\nthe anode planes are 70% optically transparent); photon detectors (light green at right), placed\nin the openings on the cathode and on the cryostat walls, around the perimeter in the vertical\nregions near the anode planes. Updated from [60].\nFigure 9: Perspective view of the vertical drift FD2 detector. From [60].\n31\n\nDUNE Phase II\n\u2022 maximizing the active volume1;\n\u2022 high modularity of detector components;\n\u2022 simplified anode structure based on standard industrial techniques;\n\u2022 simplified cold testing of instrumented anode modules in modest size cryogenic vessels;\n\u2022 field cage structure independent of the other detector components;\n\u2022 extended drift distance;\n\u2022 reduction of dead material in the active volume;\n\u2022 allowance for improved light detection coverage;\n\u2022 simplified and faster installation and quality assurance (QA)/quality control (QC) pro-\ncedures; and\n\u2022 cost-effectiveness.\n3.2.1\nCharge readout planes (anodes)\nThe baseline design FD2 anodes, illustrated in Figure 10, provide three-view charge readout via\ntwo induction planes and one collection plane. The anodes are fabricated from two double-sided,\nperforated, 3.2 mm thick printed circuit boards (PCBs), that are connected mechanically, with\ntheir perforations aligned, to form charge-readout units (CRUs). A pair of CRUs is attached\nto a composite frame to form a CRP; the frame provides mechanical support and planarity.\nThe holes allow the electrons to pass through to reach the collection strips. Each anode plane\nconsists of 80 CRPs in the same layout. The CRPs in the top drift volume, operating completely\nimmersed in the LAr, are suspended from the cryostat roof using a set of superstructures, and\nthe bottom CRPs are supported by posts positioned on the cryostat floor. The superstructures\nhold either two or six CRPs, and allow adjustment, via an externally accessible suspension\nsystem, to compensate for possible deformations in the cryostat roof geometry.\nThe FD2 top and bottom drift volumes implement different charge readout (CRO) elec-\ntronics. The top anode is read out via the top drift electronics (), based on the design used in\nProtoDUNE-DP, that comprises both cold and warm components housed in signal feedthrough\nchimneys (SFT chimneys). These chimneys penetrate the cryostat roof, allowing the compo-\nnents to be fully accessible for repair or upgrade. The bottom detector electronics (), on the\nother hand, implements the same cold electronics (CE) used in the horizontal drift FD1, which\nfeatures local amplification and digitization on the CRP in the LAr, thereby maximizing the\nsignal-to-noise.\n1For reference, the FD2 detector model yields an active volume of 10,586 m3, a 5.6% increase over the\nestimated FD1 active volume of 10,021 m3.\n32\n\nDUNE Phase II\nFigure 10: A top superstructure (green structure on top) that holds a set of six CRPs, and\nbelow it an exploded view of a CRP showing its components: the PCBs (brown), adapter\nboards (green) and edge connectors that together form a CRU, and composite frame (black\nand orange). From [60].\n3.2.2\nHigh-voltage system\nThe FD2 has a horizontal cathode plane placed at detector mid-height, held at a negative\nvoltage, and horizontal s (biased at near-ground potentials) at the top and bottom of the\ndetector, which together provide a nominal uniform E field of 450 V/cm.\nThe main high\nvoltage system (HVS) components are illustrated in Figure 11.\nThe HVS is divided into two systems: (1) supply and delivery, and (2) distribution. The\nsupply and delivery system consists of a negative high voltage power supply (), high voltage\n(HV) cables with integrated resistors to form a low-pass filter network, a HV feedthrough (),\nand a 6 m long extender inside the cryostat to deliver \u2212294 kV to the cathode. The distribution\nsystem consists of the cathode plane, the field cage, and the field cage termination supplies.\nThe cathode plane is an array of 80 cathode modules, each with the same footprint as a CRP,\nformed by highly resistive top and bottom panels mounted on fiber-reinforced plastic () frames.\nThe modular field cage consists of horizontal extruded aluminum electrode profiles stacked\nvertically at a 6 cm pitch. A resistive chain for voltage division between the profiles provides\nthe voltage gradient between the cathode and the top-most and bottom-most field-shaping\nprofiles.\nIn addition to the primary function of providing uniform E fields in the two drift volumes,\nboth the cathode and the field cage designs are tailored to accommodate PDS modules (Sec-\ntion 3.2.3) since it is not possible to place them behind the anode plane, as in the FD1-HD\ndesign. Each cathode module is designed to hold four double-sided X-ARAPUCA PDS modules\nthat are exposed to the top and bottom drift volumes through highly transparent wire mesh\nwindows. Along the walls, the field cage is designed with narrow (15 mm width) profiles in\nthe region within 4 m of the anode plane to provide 70% optical transparency to single-sided\nPDS modules mounted on the cryostat membrane walls behind them, and conventional (46 mm\nwidth) profiles within 2.5 m of the cathode plane.\n33\n\nDUNE Phase II\nFigure 11: A bird\u2019s-eye view of the field cage, with one full-height field cage column (highlighted\nin cyan) that extends the entire height, the HV feedthrough and extender (in the foreground),\nand the cathode (with one cathode module highlighted in cyan and\nmodules installed on\ncathode). From [60].\n34\n\nDUNE Phase II\n3.2.3\nPhoton detection system\nThe FD2 module will implement X-ARAPUCA [63, 64] PDS modules. Functionally, an X-\nARAPUCA module is a light trap that captures wavelength-shifted photons inside boxes\nwith highly reflective internal surfaces until they are eventually detected by SiPMs. An X-\nARAPUCA module has a light collecting area of approximately 600 \u00d7 600 mm2 and a light\ncollection window on either one face (for wall-mount modules) or on two faces (for cathode-\nmount modules). The wavelength-shifted photons are converted to electrical signals by 160\nSiPMs distributed evenly around the perimeter of the photon detector (PD) module. Groups\nof SiPMs are electrically connected to form just two output signals, each corresponding to the\nsum of the response of 80 SiPMs.\nSince their primary components are almost identical to those of FD1-HD, only modest R&D\nwas required for the FD2 PDS modules. The primary differences were to optimize the module\ngeometry and the proximity of the SiPMs to the wavelength-shifting (WLS) plates. Both of\nthese are more favorable in FD2, leading to more efficient light collection onto the SiPMs. As\ndiscussed in Section 3.2.2, the design has the PDs mounted on the four cryostat membrane walls\nand on the cathode structure, facing both top and bottom drift volumes. This configuration\nproduces approximately uniform light measurement across the entire TPC active volume.\nCathode-mount PDs are electrically referenced to the cathode voltage, avoiding any direct\npath to ground. While membrane-mount PDs adopt the same copper-based sensor biasing\nand readout techniques as in FD1-HD, cathode-mount PDs required new solutions to meet the\nchallenging constraint imposed by HVS operation. The cathode-mount PDS are powered using\nnon-conductive power-over-fiber (PoF) technology [65], and the output signals are transmitted\nthrough non-conductive optical fibers, signal-over-fiber (SoF), thus providing voltage isolation\nin both signal reception and transmission.\n3.3\nOptimized charge and photon readouts for Phase II vertical drift\nFD modules\nSeveral variations on the vertical drift design are under consideration to improve the perfor-\nmance and/or reduce the cost. Potential improvements can be broadly grouped into two classes,\nthe charge readout and the photon readout systems.\nOptimizations of the charge readout system include options to improve the production\nprocesses and reduce the cost of the CRPs, possible optimizations of strip pitch and length,\nand channel count (Section 3.3.2). Other options are to replace the strip-based CRP with\na pixel based CRP (Section 3.3.3) or with an optical readout based on electroluminescence\n(Section 3.3.4).\nThe leading criteria for selecting an optimized technology for a Phase II photon readout\nsystem are performance enhancement at low incremental costs, and the ability to leverage\nminimum-risk development of solutions already demonstrated and adopted for Phase I. One of\nthe most attractive options is the proposed concept (Section 3.3.1), in which PDs are integrated\ninto the field cage. The APEX concept makes use of the PoF and SoF technologies developed for\nFD2 and opens up the opportunity to greatly extend the optical coverage. Another optimization\n35\n\nDUNE Phase II\nunder consideration is the addition of photon detection to a pixel-based CRP (Section 3.3.5).\n3.3.1\nOptimized photon readout with APEX\nThe APEX concept (Aluminum profiles with embedded X-ARAPUCA) integrates a large-\narea photon detection system into the detector module\u2019s field cage. APEX is a simplified,\nlightweight, and low(er)-cost photodetector solution for optimizing photon readout that in-\ncreases the active optical coverage of the LAr target volume. This solution is derived from the\nwell-established X-ARAPUCA technology with SiPM photosensors developed for FD2. Con-\ncrete examples of physics topics enabled by an improved light detection system are given in\nSec. 2.2, in the context of the neutrino astrophysics program of DUNE.\nFigure 12: A bird\u2019s-eye view of the field cage with integrated large-area photon detection\nsystem, APEX. The field cage structure is constructed of modules vertically stacked in groups\nof four hanging around the LAr drift volume perimeter from the top.\nThe field cage covers the four vertical sides of the VD LArTPC active volume between the\ntop anode and bottom anode planes, and thus offers the largest available surface for extended\noptical coverage, i.e., APEX can provide up to \u223c60% coverage of the surface enclosing the\nLArTPC active volume if the field cage walls are fully instrumented, as shown in Fig. 12. In\nthe APEX concept, no PD modules are installed on the cathode. The PD readout electronics\nwould need to be referenced to the (high) voltage level of the field cage electrode profile on\nwhich the PD module is installed, and therefore would require electrical isolation. Power and\nsignal transmission can be established via non-conductive optical fibers by using the PoF and\nSoF technologies developed for the FD2 photon detectors that are integrated into that FD\nmodule\u2019s HV cathode plane. These technologies are described in Section 3.2.3. They have\nbeen demonstrated to work reliably for electrical isolation with noise immunity and long-term\nstability in LAr.\nAPEX keeps the same field cage structure as designed for FD2 (see Figure 11), which\nincludes 24 field cage supermodules, each made up of eight 3.0 \u00d7 3.2 m2 field cage modules, for\n36\n\nDUNE Phase II\nFigure 13: An APEX panel. Top left: one PD module installed on field cage profiles. Bottom\nleft: a PD module equipped with a SiPM strip at the center. Center: front view of an APEX\npanel showing the 6 \u00d7 6 array of PD modules mounted on an field cage module. Right: a back\nview of the field cage module showing its aluminum profile structure.\n37\n\nDUNE Phase II\na total of 192 modules. A field cage module consists of horizontal extruded aluminum C-shaped\nelectrode profiles (3 m long and 6 cm wide) stacked vertically at a 6 cm pitch and mounted on\nvertical FR4 I-beams. An APEX panel, illustrated in Figure 13, is a standard vertical drift\nfield cage module instrumented with a 6 \u00d7 6 array of thin, large-area (\u223c50 \u00d7 50 cm2) X-\nARAPUCA-type PD modules installed onto the field cage structure and fully covering it, as\nshown in Figure 13.\nHydrodynamic simulations are under development to understand the\npotential impact of APEX panels on the LAr recirculation.\nSix PD modules constitute a horizontal row of the APEX panel. Each PD module vertically\nspans about nine field cage profiles and is mechanically fastened and electrically referenced to\nthe profile at its mid-height (the fifth of nine). The cavity of this profile houses and provides\nFaraday shielding for the cold electronics readout boards for all six of the PD modules in that\nrow of the array, providing signal conditioning and digitization in cold. Several PoF receivers\nand an SoF transmitter (driver and laser diode) at the center of the \u223c3 m long profile receive\npower and transmit signal, respectively, for the PD modules in the row via optical fibers. The\nsignals from the six PD modules are multiplexed and transmitted over a single optical fiber\nto the (warm) receivers and data acquisition (DAQ), as schematically represented in the block\ndiagram of Figure 14. The fibers are routed through the penetration at the top of the cryostat\nusing the central vertical I-beam of the field cage structure as conduit. Each row of six PD\nmodules in an APEX panel thus forms an electrically isolated system.\nFigure 14: APEX cold readout concept: a row of six PD modules (three of the six are not shown\nin order to display the readout elements) in an APEX panel forming an electrically isolated\nsingle readout system.\nThe PD module, the basic unit of the APEX array, is a simplified version of the light trap\nX-ARAPUCA concept used in the FD1 and FD2 PDS, designed to be a lightweight (\u223c1.8 kg),\ncompact object suitable for efficient mass production. Two WLS stages, #1 and #2 \u2013 with a\ndichroic filter (DF) between them \u2013 convert, transmit, and trap incident LAr scintillation light\nunder the dichroic filter layer. These components are contained in solid PMMA (transparent\nacrylic) slabs that are 6 mm thick, with a surface area of \u223c50\u00d750 cm2, illustrated in Figure 13,\nbottom left. The DF layer is deposited directly on the front plane of the acrylic substrate, and\n38\n\nDUNE Phase II\nthe WLS #1 coating on top of the DF. Chromophore molecules embedded in the substrate\nPMMA (WLS #2) matrix shift transmitted light to a wavelength above the DF cutoff. Light\ntrapping is optimized by ultra-high reflectivity non-metallic thin film lamination (e.g., Vikuiti\nESR) of the acrylic slab edges and backplane. An array of SiPMs mounted on a flex PCB are\noptically bonded to the acrylic surface, as shown in Figure 13, bottom left. Photons trapped by\nreflection in the slab are eventually absorbed by the photosensors, producing electronic signals.\nWe estimate that 80 large-area SiPMs per module, with high photon detection efficiency (),\nganged together into one readout channel, will be sufficient to reach an overall detector efficiency\nof \u03f5D \u22432%.\nAssembly of APEX panels is expected to be simple. To assemble one, aluminum field cage\nprofiles are first assembled to form a field cage module, electronics boards are positioned in the\nprofiles, and PD modules are connected to the boards then fastened to the profiles to complete\nthe APEX panel. An APEX assembly can be built out of bulk materials (aluminum profiles and\nacrylic plates) with low-radioactive content. For this reason, even an extended PDS coverage\ncompared to Phase I modules is not expected to be a dominant contributor to the internal\nbackground budget discussed in Sec. 3.6.\nFigure 15: Map showing the expected in the central (x, y) transverse plane at z = 0 for the\nfield cage-extended coverage APEX photon detection system. Dimmer regions are present near\nthe anode planes (with no PDs on them) and at mid-height (near the non-instrumented cathode\nplane).\nA simulation was performed for a Phase II FD module with APEX, assuming 55% optical\ncoverage of the LAr volume. The light yield LY (x, y, z) of the system was evaluated, i.e., the\nnumber of photoelectrons (PEs) collected per unit of deposited energy anywhere in the LAr\nvolume, assuming 2% detection efficiency of the X-ARAPUCA module and standard LAr scin-\ntillation light emission and propagation parameters. The simulation resulted in an average value\n39\n\nDUNE Phase II\n\u27e8LY \u27e9= 180 PE/MeV across the detector volume, with a minimum of LYmin = 109 PE/MeV\nnear the anode planes, thanks to the extended optical coverage of the APEX system. Such a\nlight yield would be about a factor of 5 higher than the FD2 one, where simulations indicate\nan average light yield of 39 PE/MeV and a minimum light yield of 16 PE/MeV [60]. Figure 15\nshows the light yield map in the transverse plane at the center of the FD module long axis.\nAPEX-specific studies on light-only and charge+light calorimetric performance, impact of non-\nuniform light collection, and achievable PDS thresholds in the presence of background flashes,\nare in progress.\nA series of prototypes are planned to fully develop the APEX concept. A first round of\nprototyping, carried out at CERN, has studied the impact on the drift field uniformity of\nplacing insulating material between field cage electrodes.\nThe (expected) observation of a\nslow buildup of static charge on the surface of the insulating material may, counter-intuitively,\nallow reduction of the number of field cage electrodes, with a larger pitch. The current (2024)\nfocus is on a second (ton-scale) TPC prototype at CERN that will be instrumented with up\nto eight full-size PD modules, primarily for mechanical and cryogenic tests. Additionally, a\nPD module prototype with a full electronic chain, including PoF and SoF systems, will be\nconstructed and tested in parallel before being integrated into this prototype. A larger-sized\nAPEX demonstrator in a several cubic meter LAr cryostat, with O(100) SoF and PoF in/out\nfibers, will be a third-stage prototyping goal in 2024-2025, likely at Fermilab. Finally, a full-\nsized APEX PD-instrumented field cage will be deployed in the VD cryostat at CERN, along\nwith the proposed optical readout (Section 3.3.4).\n3.3.2\nStrip-based charge readout\nThe PCB-based vertical drift anodes, called CRPs, are made up of two stacked PCBs, providing\nthree projective views. The PCB face directly opposite the cathode has a copper guard plane to\nabsorb any unexpected discharges. The reverse side of this PCB is etched with strips that form\nthe first induction plane. The other PCB has strips on the side facing the inner PCB forming\nthe second induction plane, and has the collection plane strips on its reverse side [60]. The\nPCBs are supported by composite frames and mechanically connected using spacers. CRPs\nhave been successfully demonstrated in the 50 L test stand and at full scale in the vertical drift\ncold box. They have been installed in ProtoDUNE-VD in the NP02 cryostat at CERN and will\nbe deployed in the FD2 cryostat at SURF (see Figure 10).\nThis system has already been optimized for deployment in FD2, and as such forms a ref-\nerence solution also for FD3. Additional optimizations should be explored for FD3 to reduce\ncost or to improve performance further. There are various ways in which the strip-based charge\nreadout might be re-optimized that would impact the strip pitch, length, and orientation. A\nmore concrete optimization plan will be developed after assessing ProtoDUNE-VD performance\nin 2025.\nAdditional considerations to be explored include the CRP fabrication techniques, including\nfaster production of the PCB itself and simpler quality control. Some of these ideas have been\ntested in the 50 L test stand at CERN, particularly techniques to reduce PCB hole misalign-\nments.\n40\n\nDUNE Phase II\nIn addition to the CRP, the readout electronics need some re-optimization. Depending on\nthe timescale for construction of FD3, some of the existing electronics production lines may\nno longer be available. This may require re-design of components associated with readout of\nthe top and/or bottom CRPs. For example, a potential optimization of the FD2 BDE includes\nporting the , a custom pre-amplifier and shaping , from the 180 nm to the 65 nm production\nprocess2 to mitigate the risk of losing access to the 180 nm process. The two other BDE custom\nASICs, and , are already using the 65 nm process. Other potential optimizations for the FD2\nBDE design include reducing the cable length for signal and power (it is 27 m for the current\nFD2 design), simplifying detector installation.\n3.3.3\nPixel-based charge readout\nA pixel-based readout would replace the multi-layer strip-based readout with a single-layer\ngrid of charge-sensitive pixels at mm-scale granularity. Instrumenting each pixel with a ded-\nicated electronics channel would achieve a LArTPC with true and unambiguous 3D readout,\nwhere information on the third spatial dimension is provided by the LArTPC drift time. This\nis advantageous compared to conventional wire-based two-dimensional readout, especially for\nhigher-multiplicity interactions of O(GeV) neutrinos. In interactions with several charged par-\nticles in the final state, it is possible for tracks to overlap in one 2D projection, making it more\ndifficult to reconstruct. Similarly, straight-line tracks in strip-based readout have pathological\nangles where the track is recorded entirely along a single strip. Given channel densities of\nO(105) pixels per m2 of anode, pixel readout would require operation at O(100) \u00b5W power\nconsumption per channel, including amplification, digitization and multiplexing. This is nec-\nessary in order to avoid excessive heating of the LArTPC detector, operating near LAr boiling\npoint. Significant progress has been made in recent years in the development of pixel readout\nfor LArTPCs, overcoming issues with excessive waste heat, as well as demonstrating cryo-\ncompatibility, O(104) digital multiplexing, and cost-effective, scalable production. Two options\nfor readout are discussed below, and .\nLArPix Readout\nLArPix [66] is a complete pixel readout system for LArTPCs, consisting of 6400-channel pixel\nanode tiles, cryogenic-compatible data and power cabling, and a multi-tile digital controller\nwith an integrated operating system.\nIt has been developed as the baseline technology of\nPhase I ND-LAr. The system relies on the LArPix ASIC, a 64-channel detector system-on-a-\nchip that includes analog amplification, self-triggering, digitization, digital multiplexing, and a\nconfiguration controller.\nThe LArPix-v1 ASIC demonstrated that waste heat could be controlled through a custom\nlow-power amplifier and channel self-triggering, where the digitization and digital readout are\ndormant until a signal is detected on the pixel. The LArPix-v2 ASIC incorporated a variety\nof improvements to facilitate large-scale production of pixel anodes, including Hydra-IO, a\n2The 180 nm and 65 nm processes are advanced lithographic techniques used in semiconductor fabrication;\nthe dimension refers to feature size.\n41\n\nDUNE Phase II\nnovel programmable chip-to-chip data routing technique to improve system reliability in the\ninaccessible cryogenic detector environment.\nThe current 32\u00d732 cm2 LArPix pixel tile (Figure 16) has 6400 charge-sensitive pixels at\n3.8 mm pitch and can be configured and read out via a single set of differential digital input\nand output wires. The design leverages standard commercial techniques for PCB production to\nrealize a LArTPC anode, achieving 800 e\u2212equivalent noise charge per channel on the sensitive\nTPC-facing side of the tile, while powering and communicating with 100 LArPix ASICs on the\nback side. The power consumption achieved by the current LArPix tile is 14 W/m2, ensuring\nthat the heat flux from the anode is lower than the one from the cryostat walls.\nData acquisition is controlled by the Pixel Array Controller and Network (PACMAN) card,\nresponsible for delivering power and communication to the tiles. A single compact controller\nis currently capable of driving O(10) pixel tiles (e.g., O(105) pixels). It includes a CPU with\nintegrated operating system and programmable logic similar to a field programmable gate array\n(FPGA). The controller is designed to mount on the room-temperature side of a LArTPC cryo-\nstat feedthrough, and incorporates power filtering and ground isolation to ensure the integrity\nof the low-noise environment within the detector.\nFigure 16: Left: Prototype LArPix-v2 anode tile 32 cm in length by 32 cm in height, with\n6400 gold-plated charge sensitive pixel pads at 3.8 mm pitch driven by (right) 100 LArPix-v2\nASICs.\nApproximately 80 LArPix-v2 pixel tiles have been produced as part of the current proto-\ntyping program for the DUNE ND. Sets of 16 pixel tiles have been used to instrument each of\nthe four ton-scale LArTPC modules of the 2\u00d72 Demonstrator (Figure 17), a prototype of the\nmodular LArTPC design planned for the ND. Each module has been operated at the University\nof Bern, and has been used to image over 100 million cosmic ray events.\nThe LArPix-v2 development program has achieved its goal of a scalable design. All compo-\nnents are produced via commercial vendors using traditional electronics production techniques,\nand are ready for integrated testing; no additional assembly is required. LArPix-v2 system\nproduction costs, including all cabling, controllers, and power supplies, are approximately $10k\n42\n\nDUNE Phase II\nper square meter.\nOperation of prototype LArPix anodes, in either vertical or horizontal orientations, show\nthat natural convection provides sufficient heat dissipation to mitigate argon phase transition\n(bubble formation or boiling). In particular, the 2x2 Demonstrator [67], a prototype of the\nDUNE ND, is constructed of multiple fiberglass boxes with a very low perforation, approxi-\nmately 1% of the surface, and rather limited spaces for convective heat dissipation, yet it shows\nno issues with thermal management and has achieved purity in excess of 2 ms. Future work\nincludes a demonstration of LArPix anode heat dissipation in a configuration similar to the\nFD2 design.\nAssuming completion of the development program of LArPix for the DUNE ND, LArPix\nwould already meet most of the requirements for deployment in a future FD module. The\ndevelopment and integration of a high-speed, O(1) GHz, 16-to-1 digital multiplexer would sig-\nnificantly reduce the number of cables and feedthroughs, making deployment in a FD much\nmore feasible. Tests of a large-scale LArPix prototype in the ProtoDUNE-VD system at the\nCERN Neutrino Platform are important to validate the integration and interfaces with the\nother aspects of the vertical drift design.\nQ-Pix Readout\nQ-Pix is a novel pixel-based technology for low-threshold, high-granularity readout that is\nexpected to improve reconstruction relative to projective-based readout, at a much reduced\ndata throughput. It is ideally suited to the low data rate readout environment of the DUNE\nFD modules. The basic concepts of the Q-Pix circuit [68] are shown in Figure 18 (A). The\ninput pixel is envisioned to be a simple circular trace connected to the Q-Pix circuit via a PCB.\nThe circuit begins with the \u201cCharge-Integrate/Reset\u201d (CIR) circuit.\nThis charge-sensitive\namplifier continuously integrates incoming signals on a feedback capacitor until a threshold on\na Schmitt trigger (regenerative comparator) is met. When this threshold is met, the Schmitt\ntrigger starts a rapid \u201creset\u201d enabled by a Metal\u2013oxide\u2013semiconductor field-effect transistor\n(MOSFET) switch, which drains the feedback capacitor and returns the circuit to a stable\nbaseline, at which point the cycle is free to begin again. To mitigate any potential charge\nloss, an alternative design known as the \u201creplenishment\u201d scheme has also been evaluated. In\ncontrast to the reset architecture, the MOSFET now functions as a controlled current source\nsuch that when the Schmitt trigger undergoes a transition, the MOSFET replenishes a charge\nof \u2206Q = I \u00b7 \u2206t, where \u2206t is the reset pulse width or discharge time.\nBoth the \u201creset\u201d and \u201creplenishment\u201d schemes capture and store the present time of a local\nclock within one ASIC. This changes the basic quantum of information for each pixel from the\ntraditional \u201ccharge per unit of time\u201d to the difference between one clock capture and the next\nsequential capture, the Reset Time Difference (RTD). This new unit of information measures\nthe time to integrate a pre-defined charge. Physics signals will produce a sequence of short,\nO(\u00b5s), RTDs.\nOn the other hand, in the absence of a signal, the quiescent input current\nfrom 39Ar and other radiogenic or cosmogenic backgrounds would be small, producing long,\nO(s), RTDs. Signal waveforms can be reconstructed from RTDs by exploiting the fact that the\naverage input current and the RTD are inversely correlated.\n43\n\nDUNE Phase II\nFigure 17: Left: A photograph of one of the four ton-scale LArTPC modules for the 2x2\nDemonstrator, a prototype of the DUNE ND. Right: an example cosmic ray imaged in true 3D\nusing a 102,400-channel LArPix-v2 system in this module (right).\nQ-Pix has shown that this architecture can enhance the physics capabilities of a large-scale\nLArTPC through its ability to provide full 3D information of the events, as opposed to the three\n2D projections provided by FD1/FD2 readout. The first of these demonstrations shows the im-\nproved reconstruction enabled by a pixel based detector when compared to a projective-based\nreadout for DUNE multi-GeV neutrino interactions [70]. This analysis showed enhanced effi-\nciency and purity across all neutrino interaction types analyzed and the ability to reconstruct\nthe topology and content of the hadronic system (including number of final state protons,\ncharged, and neutral pions). Moreover, through an analysis of supernova neutrino interactions\nand a simulation of the Q-Pix architecture, it was shown that Q-Pix can significantly enhance\nthe low-energy neutrino capabilities for kiloton-scale LArTPCs.\nSpecifically, Q-Pix: i) en-\nhances the efficiency of reconstructing low-energy supernova neutrino events over the nominal\nwire based readout, ii) allows for a high-purity and high-efficiency identification of supernova\nneutrino candidates, and iii) affords these enhancements at data rates 106 times less for the\nsame energy threshold [71].\n44\n\nDUNE Phase II\n(A)\n(B)\n(C)\n.\n.\n.\nOutput\nInput\nCharge sensitive\nAmplifier\n.\n+\nSchmitt\nTrigger\nMOSFET\n.\n.\n.\n.\nOutput\nInput\nCharge sensitive\nAmplifier\n.\n+\nSchmitt\nTrigger\nMOSFET\nf\nC\nf\nC\n\u201cReset scheme\u201d\nCharge Input \nReconstructed (Method 1) \nReconstructed (Method 2)\n\u201cReplenishment scheme\u201d\nFigure 18: A) Schematic of the basic concepts of the Q-Pix circuits for the reset and replenish-\nment schemes. B) Left: Schematic of the 16-channel analog front-end and Right: schematic of\nthe 16-channel digital design. C) Current waveform reconstructed using a discrete-component\nimplementation of the Q-Pix replenishment scheme at a charge threshold of 0.46 fC (\u223c2875e\u2212)\nand reconstructed using different digital filtering based on analysis. Images A and C are adapted\nfrom [69].\n45\n\nDUNE Phase II\nA number of prototypes are currently under construction and evaluation to demonstrate the\nQ-Pix readout architecture. These include designs in both 180 nm and 130 nm, evaluation of the\narchitecture using discrete commercial off-the-shelf (COTS) components, as well as extensive\ndigital prototyping using FPGAs.\nThe 180 nm design is shown schematically in Figure 18\n(B). It consists of a 16 channel analog chip implemented with the replenishment architecture,\nand a 16 channel digital chip. On the other hand, Figure 18 (C) shows the implementation\nof the replenishment architecture for the Q-Pix readout using COTS discrete components.\nThis prototype was able to demonstrate the fidelity of reconstructing input from an arbitrary\nwaveform generator with a replenishment threshold of 0.46 fC with replenishment pulse widths\n\u223c300 \u2212600 ns and linear responses to replenishment up to 2 MHz rates. This demonstration\nprovides confidence that the architecture proposed will be capable of meeting the performance\nneeds of future large scale LArTPCs. The consortium of universities and labs working on this\nproject expect both small and large scale demonstrator (O(1000 \u2212100, 000) pixel) LArTPCs\nin the coming next few years.\n3.3.4\nOptical-based charge readout\nThe optical-based readout shares the same physics benefit as the pixel-based charge readout\nsolutions (Sec. 3.3.3) in providing a native 3D readout. This technology has also demonstrated\nthe best spatial resolution of any LArTPC readout option so far, with \u22431.1 mm per pixel [72].\nThe data-driven readout with native zero suppression yields a very efficient raw data storage,\nof relevance for SNB physics. The overall optical gain and the low-noise readout environment\nenable low-threshold (\u2243500 e\u2212per pixel) operation, supporting DUNE\u2019s MeV-scale neutrino\nastrophysics program. From the technical point of view, the (off-cryostat) optical readout also\nbenefits from simplicity of access, greatly simplifying maintenance and upgrade operations.\nFinally, depending on the granularity versus cost trade-off chosen, significant cost savings com-\npared to other readout technologies may also be present.\nThe optical charge readout with fast cameras was developed within the ARIADNE program\nand represents a cost-effective and powerful alternative approach to the existing charge read-\nout methodology. As first demonstrated in the one-ton dual-phase ARIADNE detector, the\nsecondary scintillation (S2) light produced in Thick GEM (THGEM) holes can be captured by\nfast Timepix3 (TPX3) cameras to reconstruct the primary ionization track in 3D.\nThe operation principle of a dual-phase optical TPC readout with a TPX3 system is shown\nin Figure 19a. When a charged particle enters the LAr volume, it causes prompt scintillation\nlight (S1) and ionization. The free ionization electrons are drifted in a uniform electric field to\nthe surface of the liquid. A higher field induced between an extraction grid and the bottom\nelectrode of the THGEM extracts the electrons to the gas phase. Once in gas, the electrons are\naccelerated within the 500 \u00b5m holes of the THGEM at a field set between 22 and 31 kV/cm. As\nwell as charge amplification, secondary scintillation (S2) light is produced. The light is shifted\nwith a tetra-phenyl butadiene (TPB) coated sheet to 430 nm and then detected by cameras\nmounted on optical viewports above the THGEM plane.\nOriginally, the optical readout was tested with EMCCD cameras within the one-ton ARI-\nADNE detector at the T9 charged-particle beamline at CERN [72], and later was upgraded\n46\n\nDUNE Phase II\nFigure 19: (a) Detection principle of dual-phase optical TPC readout with TPX3 camera, first\ndemonstrated in the one-ton ARIADNE detector. (b) LAr interactions from cosmic-ray muons.\nFigures taken from [73].\nwith fast TPX3. The TPX3 camera assembly boosts the S2 light signal and simultaneously\nmeasures Time over Threshold (ToT) and Time of Arrival (ToA) information with 10-bit reso-\nlution. ToT allows accurate calorimetry and ToA gives accurate timing (1.6 ns resolution). The\nTPX3 chip then sends a packet containing information that allows for full 3D reconstruction\nusing a single device. The high readout rate (up to 80 Mhits/s), natively 3D raw data, and low\nstorage due to zero suppression make TPX3 ideal for optical TPC readout.\nThe TPX3 camera system was first tested in low-pressure CF4 gas within the ARIADNE 40 l\nTPC prototype [74]; following this demonstration, a TPX3 camera was mounted on ARIADNE\nand particle tracks from cosmic-ray showers were successfully imaged in 3D for the first time\n(Figure 19b) [73]. The cameras are shown to be sensitive even to pure electroluminescence\nlight generated at the lower end of the THGEM field; this mitigates difficulties often faced\nwhen trying to operate THGEMs at a higher field, where there can be issues with stability.\nUse of cameras has additional benefits, such as ease of upgrade as they are externally mounted.\nThus, they are decoupled from TPC and acoustic noise, and large areas can be covered with\none camera, bringing both cost and operational benefits.\nTo demonstrate this technology further and at a scale relevant to the 10 kt (fiducial) FD\nmodules, a larger-scale test (ARIADNE+) was recently performed [75] at CERN. Four cameras,\neach imaging a 1\u00d71 m2 field of view, were employed. One camera utilized a novel VUV image\nintensifier, eliminating the need for a wavelength shifter.\nThe test also showcased a light\nreadout plane (LRP) comprising sixteen, 50\u00d750 cm2 surface area, glass THGEMs. The novel\n47\n\nDUNE Phase II\nFigure 20: (a) The light readout plane under the cryostat lid; (b) the ARIADNE+ team on top\nof the cryostat; (c) a recorded image of an interaction in LAr.\nmanufacturing process for the glass THGEMs allows for mass production at large scale [76].\nStable operation was achieved, and cosmic-ray muon data from both the visible and VUV\nintensifiers were collected. An image of the detector setup is shown in Figure 20 and results\nare published in [77].\nThe TPX3Cam camera and image intensifiers are commercially available, and a proposal to\ninstrument the ProtoDUNE cryostat with optical readout is underway, with testing anticipated\nto take place in 2025/2026. Further R&D into custom optics and characterization of the next\ngeneration Timepix4 (TPX4) cameras, which are anticipated to become commercially available\nby the end of 2025, can offer further benefits. Another promising ongoing R&D effort is a TPX4\ncamera with an integrated image intensifier [78]. One of these devices will be tested in the near\nfuture within the ARIADNE one-ton detector. Given the current progress of the TPX4 camera\nsystem, partial TPX4 instrumentation in NP02 is anticipated.\n3.3.5\nIntegrated charge and light readout on anode\nDUNE is also pursuing the integration of both light and charge detection modes on the anode\ninto a single detector element. If such a device could be made sensitive both to VUV photons at\nreasonable quantum efficiency and to ionization electrons, this would transform the way noble\nelement detectors collect and process both the charge and light signals. A detection element of\nthis kind would offer: i) intrinsic fine-grained information for both charge and light, providing\naccurate matching between charge and light information; ii) a significant enhancement in the\namount of light collected near the anode and much improved uniformity of response, through\nincreased surface area coverage; and iii) simplification in the design and operation of noble\nelement detectors. The technologies under investigation are described in this section, Solar\nneutrinos in Liquid Argon (SoLAr), , and Q-Pix Light Imaging in Liquid Argon (Q-Pix-LILAr).\n48\n\nDUNE Phase II\nSoLAr\nThe SoLAr technology [79] is based on the concept of a monolithic, light-charge,\npixel-based readout to achieve a low energy threshold with excellent energy resolution (\u22487% at\nfew-MeV neutrino energies [31]) and background rejection through pulse-shape discrimination.\nThe SoLAr readout unit (SRU) under development is a pixel tile based on PCB technology\nthat embeds charge readout pads located at the focal point of the LArTPC field-shaping system\nto collect drifting charges, and highly efficient VUV SiPMs to collect photons in thousands\nof microcells operated in Geiger mode. In order to maintain a uniform electric field, novel\nmonolithic VUV SiPM sensors need to be developed with these features that have charge\nreadout pads and highly efficient UV-light sensitive microcells.\nIn 2020, a joint research program between LAr detector scientists and an industrial partner\n(Hamamatsu Photonics) delivered a SiPM that reached a record efficiency (15% PDE) for\n128 nm light at the argon boiling point (87 K). Nearly at the same time, the first integrated\nsystem for multiplexing the SiPM signal was commissioned and operated inside strong electric\nfields. In 2021 a further development with Hamamatsu Photonics produced a new SiPM with\nthrough-silicon vias that will enable the combination of light detection with the charge readout\nrequired for SoLAr.\nFigure 21: The small-scale SoLAr prototype PCB tested at the University of Bern, front and\nback sides. The anode consists of a 7\u00d77 cm2 readout area with 16 VUV SiPMs (the LAr-facing\nside, at right) and four LArPix-v2a chips on the backplane, at left. The charge pixel pads are\n3 mm in size and are placed at a 3.5 mm pitch. The SiPMs have a 6\u00d76 mm2 sensitive area and\nare placed at a 17.5 mm pitch.\nIn the SoLAr preparatory phase (2021-2022), combined light-charge collection was demon-\nstrated using small-size prototypes [80]. The prototypes were operated successfully and have\ndemonstrated that the principle of combining charge and light readout is possible (Figure 21).\nSimulations accounting for light propagation effects have shown that a 7% energy resolution\ncan be achieved at typical solar neutrino energies (5\u201320 MeV) and using the scintillation sig-\nnal only by replacing anode planes with a pixelated readout integrating a light-sensitive area\ncovering \u223c10% of the surface. This system would enhance the amount of collected light by a\nfactor of five compared with FD1, reducing the frequency at which low-energy background gets\nincorrectly reconstructed to the (higher) energy region of interest of the signal. The authors\n49\n\nDUNE Phase II\nof [31] have studied this remarkable impact of energy resolution in the background budget of a\nLArTPC using conventional readout in a membrane cryostat.\nThe combination of shielding and a 7% energy resolution gives access to the 5\u201310 MeV\nregion, where most of the 8B neutrinos (8B \u21928Be\u2217+ e+ + \u03bde) reside, by greatly reducing the\ndominant background from neutrons and 42K above 5 MeV visible energies. The energy resolu-\ntion is instrumental for sharpening the 17 MeV cutoff of the 8B neutrino spectrum, which lies\njust below the \u201chep\u201d cutoff of 18.8 MeV, and opens a 1.8 MeV window that allows observation\nof a pure sample of hep neutrinos (3He + p \u21924He + e+ + \u03bde) [81]. Light collection outside\nthe anode is ensured by X-ARAPUCA tiles, for a total coverage of (8 \u221210)%.\nThe latter provide the appropriate light yield without resorting to xenon doping, thus\npreserving the pulse-shape discrimination power of liquid argon. Pulse-shape discrimination\nis further enhanced with respect to any existing LArTPC by the unique performance of the\nSRU and the increase of collected light.\nFinally, SoLAr will implement neutron shielding embedded directly in the cryostat walls,\ndelivering a novel membrane-based cryogenic system that also suppresses environmental back-\nground to the limit where the only residual background is generated inside the LArTPC. This\nwill provide a radiopure environment and reduce external neutron background in the 1-4 MeV\nregion by three orders of magnitude.\nLightPix\nA variant of the LArPix ASIC has been designed for scalable readout of very large\narrays of SiPMs. Called LightPix, this ASIC reuses much of the LArPix system design to\nprovide a system that can read out >105 individual SiPMs in a cryogenic environment at costs\nfar below $1 per channel. LightPix may be useful for instrumenting a future far detector PDS\nwith higher quantities of SiPMs than the FD1/FD2 PDS design. This could be used as a\nreadout unit in conjunction with an anode-based light pixel solution, e.g., SoLAr.\nLightPix prototypying in combination with VUV-sensitive SiPMs is underway. The first-\ngeneration 64-channel LightPix-v1 ASIC includes a custom low-power time-to-digital converter\n(TDC) with sub-ns resolution to enable precise measurement of photon arrival times. It also\nimplements programmable digital coincidence logic for the suppression of dark counts, par-\nticularly useful for room-temperature detector applications. The LightPix-v1 ASIC was used\nto demonstrate particle detection in two small-scale prototype VUV-scintillation detectors: a\n16-channel system integrated into a LArPix pixel tile LArTPC detector at LBNL, and a 300-\nchannel system for readout of a high-pressure gaseous helium detector at UC-Berkeley/LBNL.\nA second-generation ASIC, LightPix-v2, is in fabrication. Changes include a new front-end am-\nplifier optimized for use with larger (higher-capacitance) SiPMs, as well as a charge-integrator\nfor use in higher-occupancy environments.\nQ-Pix-LILAr\nThe Q-Pix consortium is pursuing a different integrated charge and light read-\nout system on the anode, by coating a charge readout pixel with a type of photo-conductive\nmaterial that, when struck by a VUV photon, would generate a signal (charge) that could be\ndetected by the same charge readout scheme considered for the ionization charge. The Q-Pix-\nLILAr concept is shown schematically in Figure 22 (A). Moreover, with the proper choice of\n50\n\nDUNE Phase II\nphotoconductor, such a device could have a broad photon wavelength response, thus offering\ndetection of the full spectrum of light produced in noble element TPCs.\nFigure 22: A) Schematic design for the Q-Pix-LILAr integrated charge and light readout,\nfrom [82]. B) Example design for a multimodal (charge and light) pixel where interdigitated\nelectrodes (IDE, not shown) are deposited around the central ionization collection pixel. Once\nthe photoconductor creates single electrons from photon conversion, IDEs define a region of\nhigh electric field where avalanche multiplication of those single electrons occurs, producing\ndetectable signals.\nThree such photo-conductive materials have been explored in recent R&D: Amorphous\nselenium (aSe), zinc oxide (ZnO), and organic photodiodes (OPDs). Their application in a\nliquid argon environment is currently under investigation.\nInitial studies of constructing a\nmultimodal pixel detector have recently focused on utilizing aSe, as the ability to prototype\nand test it was the simplest. The first study on aSe in cold used commercially manufactured\nPCBs to demonstrate that these aSe-based interdigitated electrodes (IDE) are sensitive to VUV\nlight at cryogenic temperatures, are cryo-resistant, and are able to maintain argon purity [82].\nDesigns for a multimodal pixel are shown in Figure 22 (B) where an IDE is deposited around\nthe central ionization collection pixel. This design provides a straightforward way to apply a\nlocal electric field to the aSe, to enable charge gain, and to instrument the area between the\ncharge collection pixels.\nMore recent studies have pushed this capability further to characterize the performance of\nsuch a design to a low photon flux (O(100) photons), at high electric fields (> 70 V/\u00b5m) and at\ncryogenic temperatures. These results continue to show promise. Further R&D into aSe-based\ndevices, as well as other photoconductors, is anticipated to be an area of active research in the\nnear future.\n3.4\nLiquid-argon doping\nA promising direction for expanding DUNE capabilities in a Phase II FD module is to in-\ntroduce dopants to the LAr, creating a detector medium other than pure argon. Generically,\n51\n\nDUNE Phase II\nthese LAr \u201cdoping\u201d techniques may be used to modify the detector response in a desirable\nway or to introduce new target materials of interest into the bulk detector volume. These\napproaches are analogous to widely-used strategies in e.g., scintillator or solid state detectors,\nwhere secondary fluors are sometimes added to scintillators to shift photon wavelengths, or\nelements like gadolinium or lithium are added to increase neutron or neutrino cross sections,\nrespectively. A key constraint for LAr dopants is that they must not interfere with the op-\neration of the LArTPC by introducing electronegative impurities that non-negligibly degrade\nthe LAr transparency to electrons. Furthermore, as for any large-scale detector with complex\nphysics of signal generation, the relevant microphysics (including radiative and non-radiative\nmolecular energy transfer, electron-ion recombination, and scintillation-light production) must\nbe well understood through a robust R&D program to adequately assess the scalability to the\nDUNE FD scale. Several such avenues are being explored that would enhance the charge or\nlight detection capabilities, or introduce new signals of interest. This section discusses two\npromising potential additives that have been previously demonstrated in large-scale LArTPCs.\nThe first category is liquid xenon, which is of interest at low concentrations for impact on the\nscintillation light signal, and at higher concentrations as a signal source. The second includes\nphotosensitive dopants that convert scintillation light to ionization charge.\nThese LAr dopants can be particularly impactful for DUNE Phase II prospects to broaden\nthe low-energy physics program, targeting signals in the MeV to keV energy range. Detection of\nsignals in this regime can enhance the GeV-scale neutrino oscillation physics program through\nenhanced neutrino energy reconstruction [83]. In combination with techniques that lower ra-\ndioactive and external backgrounds, the detection of keV\u2013MeV signals also provide sensitivity\nto a broad array of previously inaccessible signals spanning BSM physics and low-energy neu-\ntrino astrophysics. Examples include low-energy solar and SNB neutrinos, searches for rare\ndecays such as 0\u03bd\u03b2\u03b2, exotic physics such as fractionally-charged particles, and dark matter\nscattering. A more complete list can be found in [84]. An expanded program in these areas\nwould complement DUNE\u2019s program while leveraging the large mass and deep-underground\nlocation.\n3.4.1\nLiquid xenon\nLiquid xenon is a potential additive to the LAr in DUNE Phase II, either at a low (parts per\nmillion (ppm)) or high (up to the percent level) concentration. The loading techniques [85] and\nstability conditions [86] of LAr+LXe mixtures have been explored across this broad range of\nconcentrations.\nAt low concentrations, the presence of xenon impacts the production of scintillation light in\nLAr, acting as a highly efficient wavelength shifter that converts the 128 nm primary scintillation\nwavelength in argon to a longer 178 nm wavelength. This has several advantages, including\nreduced Rayleigh scattering, improved light detection uniformity, a narrowing of the scintillation\ntiming distribution, and a reduction in energy losses to impurities such as nitrogen. Such losses\nwould result from non-radiative energy transfers involving the long-lived triplet state of Ar,\ntransfers that are suppressed with the introduction of xenon. This leads to a much improved\nrobustness of the scintillation light yield against LAr impurities, without appreciable impact on\n52\n\nDUNE Phase II\nthe charge signal. In ProtoDUNE-SP xenon doping up to \u223c20 ppm verified the enhancements\nto optical response and the recovery of light yield in the presence of impurities [85]. Xenon\ndoping at a 10 ppm level is already assumed in the FD2 Phase I module [60].\nAt higher concentrations, up to the percent level, xenon may also be of interest as a signal\nsource. 136Xe is a candidate isotope for 0\u03bd\u03b2\u03b2 which, if observed, would establish the Majorana\nnature of the neutrino and demonstrate a violation of lepton number conservation [87]. The\nintroduction of xenon, either in its natural form (8.9% 136Xe) or enriched to 136Xe, into a large-\nscale, deep-underground LArTPC detector could provide an opportunity to search for this\nimportant decay mode [41]. Mitigation of important backgrounds (39Ar, 42Ar, neutrons) near\nthe 2.458 MeV Q-value for this decay are consistent with the requirements of other potential\nlow-energy physics goals considered for DUNE Phase II, as described in Section 3.6. A key\nchallenge for a competitive search is the massive procurement of xenon, at a level exceeding\nthe world\u2019s current production by more than one order of magnitude, and possibly xenon\nenrichment at the same scale [88]. Another crucial challenge is achieving an energy resolution\nat the percent level for MeV-scale electrons; photosensitive dopants, discussed in the following,\nprovide one avenue toward achieving this.\n3.4.2\nPhotosensitive dopants\nIn a typical pure-LAr TPC, the energy deposited by charged particles is ultimately divided\nbetween ionization electrons, drifted in the electric field and detected at the anode plane, and\nscintillation light, detected by a photon detection system. The photon signal, which is produced\npromptly with ns-scale timing, is used for 3D event position reconstruction as well as triggering\nand absolute timing of neutrino interactions. In a LArTPC doped with a photosensitive dopant,\nthe scintillation signal would be converted to ionization charge, effectively transferring the full\ndeposited energy into that channel. Potential photosensitive dopants under consideration are\na class of hydrocarbons with work functions on the order of the LAr (or Xe-doped LAr) VUV\nprimary scintillation photon energy (7\u20139 eV). A dopant of this kind would convert scintillation\nlight into ionization electrons very efficiently with minimal loss of spatial resolution.\nThe use of such dopants in LArTPCs can offer benefits to both the GeV- and MeV-scale\nphysics programs of DUNE Phase II. In general, the transfer of deposited energy into the\nionization channel leads to an enhancement of the ionization charge, which is measured with\nexcellent efficiency in a LArTPC. This enhancement is particularly pronounced in regions of\nhigh energy deposition, improving prospects for particle identification using charge calorimetry.\nFurthermore, LAr with photosensitive dopants exhibits a significantly more linear relationship\nbetween deposited and visible charge, reducing the scale and uncertainties of corrections related\nto electron-ion recombination effects.\nThe general impact of such dopants in large-scale LArTPCs in practice was studied by the\nICARUS Collaboration. ICARUS performed a long-term test of the Tetra-methyl-germanium\n(TMG) dopant in a three-ton LArTPC exposed to cosmic rays and \u03b3 sources, observing a\nclear enhancement in the ionization charge signal, and a significantly more linear response in\nreconstructed to deposited charge [89].\nImportantly, this test also demonstrated long-term\nstability in realistic LArTPC operating conditions.\nA complete and detailed model of the\n53\n\nDUNE Phase II\nmicrophysics of energy transfer between LAr and candidate photosensitive dopants will require\na comprehensive assessment of potential dopants and their ionization response across a broad\nrange of signal energies for the Phase II program.\nThe enhancements provided by photosensitive dopants are particularly notable for improv-\ning energy resolution at low energies, e.g., to capture point-like signals at or below the MeV\nscale. A significant challenge with measuring such signals is the efficient collection of small\namounts of scintillation light. In the Phase I design, a limited photon detection efficiency of\norder O(0.1%) may limit the capabilities of DUNE to extract spectral information regarding\nMeV-scale signals, and thus to perform energy-based background mitigations. Ideally, a de-\ntector would measure both the ionization and scintillation anti-correlated signals to measure a\nprecise total energy, as in the case of the EXO-200 experiment [90] and as also investigated in\n[91].\nIn principle, a large LArTPC can achieve percent-level energy resolution for MeV-scale sig-\nnals of interest, but this would require detection of tens of percent of the scintillation photons,\na level of efficiency impractical with current and near-future designs. Meanwhile, by convert-\ning the isotropic scintillation light into directional ionization charge, photosensitive dopants\nat the ppm level could allow the full energy to be measured with high efficiency by the TPC\ncharge detection system. In this sense, charge alone would provide a precise energy measure-\nment, analogous to a correlated charge/light measurement. Previous work in the context of\nLAr calorimeters has also considered the impact of several candidate dopants on MeV-scale \u03b1\nparticles, demonstrating substantial charge enhancements for low-energy events with relatively\nlarge scintillation signals [92]. Straightforward future R&D using \u03b2 or \u03b3 sources to study the\nlow-energy electromagnetic response can further clarify the impact and achievable energy res-\nolution for MeV-scale signals of interest for beam neutrino energy measurements, low-energy\nneutrino astrophysics, and keV- to MeV-scale BSM signatures. To fully realize the potential\nof photosensitive dopants in LArTPCs, studies to explore the microphysics involved, and R&D\nto determine the optimal dopant types and concentrations, will also be needed.\n3.5\nHybrid Cherenkov plus scintillation detection\nThe Theia hybrid Cherenkov+scintillation detection concept is motivated by a science pro-\ngram of low-energy astroparticle, rare event, and precision physics (Section 3.5.2).\nIt also\ncontributes to the overall CPV sensitivity (Sec. 2.1). The envisioned 25 kt Theia detector of-\nfers good particle and event identification at both low and high energies, coupled with a target\nof high radio-purity, no inherent radio isotopes, and excellent neutron shielding. This allows\nthe detector to probe physics that requires low threshold and low background.\n3.5.1\nHybrid detection concept\nA detector of the envisioned hybrid design would separate Cherenkov and scintillation light by\nthe use of a novel liquid scintillator [93], fast timing, and spectral sorting. Cherenkov light\noffers electron/muon discrimination at high energy via ring imaging and sensitivity to particle\ndirection at low energy. The scintillation signature offers improved energy and vertex resolution,\n54\n\nDUNE Phase II\nPID capability via species-dependent quenching effects on the time profile, and low-threshold\n(sub-Cherenkov-threshold) particle detection. The combination boasts an additional handle on\nPID from the relative intensity of the two signals.\nThis detector design, being developed as Theia, would offer excellent energy resolution for\nhigh-energy neutrino interactions (better than 10% neutrino energy resolution has been achieved\nwith preliminary algorithms), along with access to a rich program of low-energy, rare-event,\nand precision physics.\nThis is likely a cost-effective option, particularly among those designed to broaden the\nphysics program, thanks to the relatively simple and well-understood detector design that\nomits both cryostat and field cage. The Theia detector concept is shown in Figure 23.\nFigure 23: Illustration of sited in a DUNE FD cavern, with an interior view of the Theia-25\nconcept modeled using the Chroma optical simulation package [94]. Taken from [12].\n3.5.2\nTheia physics program\nTheia will seek to make leading measurements over as broad a range of neutrino physics and\nastrophysics as possible. The scientific program includes:\n\u2022 observations of solar neutrinos \u2013 both a precision measurement of the CNO flux, and a\nprobe of the MSW transition region;\n\u2022 determination of neutrino mass ordering and measurement of the neutrino charge conju-\ngation and parity (CP)-violating phase \u03b4CP;\n55\n\nDUNE Phase II\n\u2022 observations of diffuse supernova neutrinos, and sensitivity to neutrinos from an SNB\nwith directional sensitivity;\n\u2022 sensitive searches for nucleon decay in modes complementary to LAr; and, ultimately,\n\u2022 a search for 0\u03bd\u03b2\u03b2, with sensitivity reaching the normal ordering regime of neutrino mass\nphase space (m\u03b2\u03b2 \u22436 meV).\nTable 2 summarizes the physics reach of Theia-25. The full description of the analysis in\neach case can be found in [12].\nTable 2: Projected Theia physics reach, from Ref. [12]. Exposure is listed in terms of the\nfiducial volume assumed for each analysis. The total detector volume assumed is 70\u00d720\u00d718 m3.\nFor 0\u03bd\u03b2\u03b2, the target mass assumed is the mass of the candidate isotope within the fiducial\nvolume (assumed to be housed within an inner containment vessel). Limits are given at the\n90% CL.\nPhysics Goal\nReach\nExposure (Assumptions)\nLong-baseline oscillations\nEquivalent to 10-kt\n127 kt-MW-yr\nLAr module\nSupernova burst\n< 2\u25e6pointing accuracy\n25-kt detector, 10 kpc distance\n5,000 events\nDSNB\n5\u03c3 discovery\n125 kt-yr (5 yr)\nCNO neutrino flux\n< 10%\n62.5 kt-yr (5 yr, 50% fid. vol.)\nReactor neutrino detection\n2000 events\n100 kt-yr (5 yr, 80% fid. vol.)\nGeo neutrino detection\n2650 events\n100 kt-yr (5 yrs, 80% fid. vol.)\n0\u03bd\u03b2\u03b2\nT1/2 > 1.1 \u00d7 1028 yr\n211 ton-yr 130Te\nNucleon decay p \u2192\u03bdK+\n\u03c4/B > 1.11 \u00d7 1034 yr\n170 kt-yr (10 yr, 17-kt fid. vol.)\nNucleon decay p \u21923\u03bd\n\u03c4/B > 1.21 \u00d7 1032 yr\n170 kt-yr (10 yr, 17-kt fid. vol.)\n3.5.3\nTechnology readiness levels\nThe Theia reference design makes use of a number of novel technologies to achieve successful\nhybrid event detection. This design would be used to enhance the Cherenkov signal by reducing\nand potentially delaying the scintillation component. The use of angular, timing, and spec-\ntral information offers discrimination between Cherenkov and scintillation light for both low-\nand high-energy events. Fast photon detectors \u2013 such as the 8\u201d PMTs now manufactured by\nHamamatsu, which have better than 500 ps transit time spread \u2013 will be coupled with spectral\nsorting achieved via use of dichroic filters [95].\nSuccessful separation of Cherenkov and scintillation light has been demonstrated even in a\nstandard scintillator like LAB-PPO [96] with the use of sufficiently fast photon detectors, and\nwill be even more powerful when coupled with the spectral sorting capabilities envisioned for\nTheia.\n56\n\nDUNE Phase II\nRadiopurity levels exceeding the requirements for the Theia low-energy program have been\nsuccessfully demonstrated by water Cherenkov experiments (SNO) and scintillator experiments\n(Borexino).\nFurther optimization of the design could be achieved by considering deployment of Large\nArea Picosecond Photo-Detectors (LAPPDs) [97, 98], for improved vertex resolution, or slow\nscintillators [99, 100] to provide further separation of the prompt Cherenkov component from\nthe slower scintillation. A more complete discussion of the relevant technology is provided\nin [101].\nThe R&D for Theia will be completed with the successful operation of a number of tech-\nnology demonstrators currently under construction: (i) a one-ton test tank and a 30-ton Water-\nbased Liquid Scintillator (WbLS) deployment demonstrator at Brookhaven National Labora-\ntory (BNL) will demonstrate the required properties and handling of the scintillator; (ii) a low-\nenergy performance demonstrator, , at Lawrence Berkeley National Laboratory (LBNL) [102]\nwill demonstrate the performance capabilities of the scintillator, fast photon detectors, and\nspectral sorting; and (iii) a high-energy demonstration at ANNIE, at Fermilab, will validate\nGeV-scale neutrino detection using hybrid technology [103]. These detectors are all currently\noperational or under commissioning.\n3.6\nBackground control\nThe potential to enhance the physics scope of DUNE Phase II with lower energy thresholds\nhas been attracting significant attention within the wider community [84]. The proposed ideas\ntend to rely on two enhancements over the Phase I program: greater control of radioactive\nbackgrounds and improved energy resolution at lower energies. DUNE is well placed to improve\nthe lower-energy physics scope, first because of the depth of the FD, which is well shielded\nfrom cosmic-induced backgrounds. Secondly, the sheer size of the detector volumes allows for\nsignificant fiducialization to reduce external backgrounds originating within the SURF cavern\nrock and shotcrete. Phase II designs that minimize material in the active regions, such as the\nFD2 or dual-phase (DP) designs, are most favorable for low-background physics due to reduced\nrisk of radioactive backgrounds.\nWe can define two natural physics target energy regions. While these targets are motivated\nby the intrinsic backgrounds in argon-based detector modules (Sections 3.2 through 3.4), most\nof this background control discussion also applies to water-based detectors (Section 3.5), as\ndetailed in the following.\nThe first background target extends the energy threshold down to about 5 MeV. With careful\ncontrol of neutron, \u03b3, and radon related backgrounds, combined with improvements in the low-\nenergy readout, an extended SNB neutrino program can be envisaged, with improved reach\nin terms of supernova distance sensitivity (to the Magellanic Clouds), for elastic scatters with\nimproved directionality, and to the (softer energy) early or late parts of the supernova neutrino\nflux. A low-energy threshold could also allow a precision solar neutrino program to explore\nsolar-reactor oscillation tensions and non-standard interactions. In an argon-based detector,\nthis 5 MeV threshold is set by the intrinsic 42Ar-42K decay chain, as shown in Figure 4.\nThe second background target would extend the energy threshold to even lower values of\n57\n\nDUNE Phase II\n\u223c1 MeV or less. With such a low threshold, ambitious but high-reward physics measurements\nwould include: solar CNO measurements; searches for 0\u03bd\u03b2\u03b2 with xenon loading; and even high-\nmass weakly interacting massive particle dark matter detection could be possible [37]. In an\nargon-based detector, this could be accomplished only by using underground sources of argon,\nthus largely suppressing the intrinsic 42Ar activity.\nThis section outlines some of the most significant radioactive backgrounds and identifies\npaths to reduce them in Phase II detector modules.\n3.6.1\nExternal neutrons and photons\nIn DUNE Phase I, the dominant background to low-energy SNB neutrinos will be from exter-\nnal neutrons, that is neutrons originating from outside the detector (SURF cavern rock and\nshotcrete). These neutrons are primarily of radiogenic origin. When captured in the LAr, they\ncan produce 6.1 MeV or 8.8 MeV \u03b3 cascades which Compton scatter or pair produce electrons\nthat directly mimic the CC neutrino signals. On the other hand, in a water-based detector,\nneutron captures on free hydrogen would result in lower-energy gammas of 2.2 MeV.\nTo remove external neutrons in argon-based detectors, passive shielding can be deployed,\nas first suggested in [31].\nA layer of 40 cm of water, or 30 cm of polyethylene or borated\npolyethylene, is sufficient to attenuate the neutron flux from spontaneous fission or (\u03b1, n)\nreactions in the rock by 3 orders of magnitude, making it subdominant. A shield of this size\nfits within the warm support structure of the cryostat. Alternative approaches would involve\nmodifications to the cryostat design, for example, layering the insulating foam with neutron-\ncapturing materials such as gadolinium-doped acrylic. These same measures will ameliorate\nthe cavern \u03b3 background originating from 238U and 232Th natural decay chains.\nIn a water-based detector, no passive neutron shield around the detector would be necessary.\nExcellent neutron shielding via detector fiducialization would be reached in this case thanks to\nthe plentiful free hydrogen available as part of the detector target.\nSpallation-induced neutron and cosmogenic background events are also possible, though\nthey are primarily short-lived and expected to be orders of magnitude less than the radiogenic\nbackgrounds. A full study of these backgrounds in [104] show that these can be further reduced\nby tagged-muon-proximity event selections.\n3.6.2\nInternal backgrounds from detector materials\nAfter the external cavern neutrons, the most significant source of neutron background comes\nfrom contaminants in materials within the detector, from (\u03b1, n)-induced reactions within the\ncryostat and other components. Photons produced in these events can also distort reconstructed\nquantities due to light flash or charge blip backgrounds, particularly when close to the readout,\nsuch as the cryostat-mounted light sensors. Dark matter experiments have successfully managed\nsuch backgrounds with careful material selection programs, using radioactive assay techniques\nto select favorable materials for detector construction, and to ensure quality assurance during\nproduction and installation processes. The world-leading argon-based dark matter detectors\nhave lowered backgrounds by five orders of magnitude below the DUNE Phase I target. To\nmaintain the sub-dominance of these internal backgrounds relative to externals removed by\n58\n\nDUNE Phase II\nshielding, a DUNE Phase II argon-based detector module will require a less stringent reduction\ntarget of three orders of magnitude on detector components such as cryostat stainless steel [19].\nFor a Theia-type module, internal backgrounds within the fiducial volume are driven by\nthe cleanliness of the target itself. The chemical purity of the water-based liquid scintillator\ntarget is 10\u221217 g/g in both uranium and thorium contaminants, which is considered achievable\nby improving target material purification techniques [12].\n3.6.3\nIntrinsic backgrounds from unstable isotopes in the target\nArgon extracted from the atmosphere contains two background isotopes that can limit sensi-\ntivity at the lowest energy for any argon-based detector: 39Ar, with a decay Q-value of 565 keV;\nand 42Ar, with a decay Q-value of 599 keV and its daughter isotope 42K, which decays with\na Q-value of 3525 keV. The 42Ar-42K chain sets a lower limit of about 5 MeV, dependent on\nthe ultimate low-energy resolution, for low-threshold physics with atmospheric argon. Dark\nmatter experiments have successfully extracted argon from underground sources, which are\ndepleted in both 42Ar and 39Ar [105]. These experiments show reduction factors of order 1400\nfor 39Ar and have seen no 42Ar. The currently only known source of underground argon is\ntoo small to fill a detector the scale of DUNE, but work is ongoing to identify new, larger\nsources which can be used cost-effectively. Recent estimates of the potential reduction of 42Ar\nin underground-sourced argon is expected to be eight orders of magnitude [106].\nIntrinsic argon background contributions would be absent in a Theia-type module. The\nmost abundant radioactive isotope in this target material would be 14C. With a decay Q-\nvalue of 156 keV, 14C would not be a relevant background for any of the low-energy physics\nmeasurements and searches discussed in Section 2.2 in connection with a Theia module.\n3.6.4\nRadon background\nRadon gas has high mobility, emanates from all detector materials, and can diffuse easily\nthroughout the entire detector volume. This background can mimic directly low-energy neu-\ntrinos, through (\u03b1, \u03b3) reactions and misidentified \u03b1 events in the detector. It also produces\ndaughter products which can plateout on internal components such as the photon detector\nsystem, distorting the low-energy reconstruction. Several approaches should be adopted to\ncontrol this background, including: direct removal of radon in the purification system using an\ninline radon trap; selection of detector materials for low radon emanation; surface treatments\nto contain or remove radon sources; removal of a significant emanation source from dust by\ncontrolling and cleaning to higher cleanliness standards than in Phase I; removal of radon from\nair during installation to lower the risk of plateout backgrounds when the detector is open; and\nanalysis techniques such as \u03b1 tagging by pulse shape discrimination.\n3.6.5\nThe SLoMo concept\nOne proposed design for a low-background, argon-based, Phase II far detector is the Sanford\nUnderground Low background Module (SLoMo). This design, shown in Figure 24 provides a\npath to lower background levels using the techniques outlined above, reducing most background\n59\n\nDUNE Phase II\nsources by three orders of magnitude below the expected Phase I levels. This is combined\nwith a significant increase in light coverage within the detector using high quantum efficiency,\nDarkSide-style, SiPM tiles [107] to increase the energy resolution and pulse shape discrimination\npower at lower energies.\nFigure 24: Design for SLoMo, highlighting background control methods required to achieve\ngoals.\nTo get this light coverage, SLoMo aims to densely instrument an interior 1\u20132 kt of highly\nfiducialized underground argon (UAr) in the center of a vertical drift-like detector. The struc-\nture on which to mount the DarkSide SiPM modules is not fixed in this design, though we\npropose light-tight acrylic walls covered in wavelength-shifting foils. Reference [19] shows that\na 20% SiPM coverage, combined with charge detection by existing VD CRPs and viewing an\ninner volume, should easily lead to a sub-2% energy resolution (sigma) at 2 MeV. This feature,\nalong with the negligibly low amount of 42Ar in UAr, makes possible 0\u03bd\u03b2\u03b2 studies with xenon\nloading, should this be a program DUNE wishes to pursue. Reducing 42Ar to very low levels\nalso allows detectable energy spectra from a supernova to reach well into the region where \u03bde\u2212e\nelastic scattering dominates and thus pointing, in principle, is improved. A 20% SiPM module\ncoverage would come at an affordable cost and would detect enough photons to allow pulse\nshape discrimination. The combination of high SiPM coverage, low neutron background, fidu-\ncialization and radon control would allow competitive WIMP dark matter searches in SLoMo.\nSolar CNO investigations would also become possible, as would observation of further phenom-\nena, such as the \u201csupernova glow\u201d [108]. This design is outlined in [19], where the significant\nphysics gains are further explained.\n3.6.6\nResearch and development requirements\nAll the Phase II options to lower the energy threshold require a radioactive background budget\nto be specified and low-background techniques to be deployed to ensure it is achieved. The\n60\n\nDUNE Phase II\nR&D required to achieve these goals includes:\n\u2022 Large-scale materials and assay campaigns, scaling up material selection techniques used\nby low-background fundamental physics experiments to the kt scale.\n\u2022 Cleanliness requirements and approaches for the kt scale.\n\u2022 Radon control in detector liquids, including emanation assay and control at the FD scale.\n\u2022 Low-background photon detection systems, developing new designs that can increase the\nlight detection efficiency without overwhelming a background budget.\n\u2022 Background model and simulation campaign for physics sensitivity analyses.\n\u2022 Novel analysis techniques, such as pulse shape discrimination, to remove background\nevents.\n\u2022 Compact shield designs for argon-based modules, that can fit in the limited DUNE cavern\nspace or within the cryostat structure.\n\u2022 New sources of underground argon, capable of filling an argon-based DUNE FD module\ncost-effectively.\n3.7\nToward detector concepts for Phase II FD modules\nThe DUNE FD2 vertical drift technology forms the basis for the reference design for FD3 and\nFD4. As such, the R&D for FD3 and FD4 is primarily focused on upgraded photon detector\nand charge readout systems for the vertical drift layout. Most of these candidate systems are\neither further developments of the current systems or replacements based on technologies that\nare already under active R&D or in early prototyping phases. A non-LAr option such as Theia\nis also under consideration as an alternative technology for FD4. A summary of technologies\nunder consideration, both LAr and non-LAr options, for these FD modules, along with R&D\nstatus and plans, is provided in Table 3.\nThe detector technologies described in the previous sections (Section 3.2 through 3.6) will\nform the building blocks to define full detector designs for both FD3 and FD4. These technolo-\ngies are not standalone, and most of them can be combined or integrated together, as shown in\nTable 4. It is important to note that the check marks in the table for FD3 are not solely driven\nby Technology Readiness Level (TRL) since several other technologies listed (e.g., ARIADNE,\nLArPix) are also technically mature.\nThe choices for FD3 are primarily motivated by how straightforward the proposed upgrades\nare to implement without requiring major modifications to the baseline FD2 design on which\nFD3 will be based. This is an important consideration since in the case of FD3, the DUNE\ncollaboration is aiming to meet the technically limited schedule, which calls for FD3 installation\nto start no later than 2029. However, as the other technologies listed in Table 3 evolve, they\nmay demonstrate that they meet our FD3 requirements. If so, and if timelines can be met,\n61\n\nDUNE Phase II\nTechnology\nPrototyping Plans\nKey R&D Goals\nCRP\n(Sec. 3.3.2)\n2024: Cold Box tests at CERN.\n2025-2026: ProtoDUNE-VD at CERN.\nPort LArASIC to 65 nm\nprocess\nAPEX\n(Sec. 3.3.1)\n2024: 50 L & 1-ton prototypes at CERN.\n2024-2025: O(100)-channel\ndemonstrator at Fermilab.\n2025-2028: ProtoDUNE-VD at CERN.\nMechanical\nintegration\nof\nAPEX PD in field cage\nSignal conditioning, digiti-\nzation and multiplexing in\ncold\nLArPix,\nLightPix\n(Secs.\n3.3.3\nand 3.3.5)\n2024: 2x2 ND demonstrator at Fermilab.\n2024-2025: Cold Box tests at CERN.\n2026-2028: ProtoDUNE at CERN.\nMicropower,\ncryo-\ncompatible,\ndetector-\non-a-chip ASIC\nScalable integrated 3D pixel\nanode tile\nDigital\naggregator\nASIC\nand PCB\nQ-Pix,\nQ-\nPix-LILAr\n(Secs.\n3.3.3\nand 3.3.5)\n2024: Prototype chips in small-scale\ndemonstrator.\n2025-2026: 16 channels/chip prototypes\nin ton-scale demonstrator at ORNL.\n2026-2027: Full 32-64 channel \u201cphysics\nchip\u201d.\nCharge replenishment and\nmeasurement of reset time\nPower consumption\nR&D on aSe-based devices\nand other photoconductors\nARIADNE\n(Sec. 3.3.4)\n2024: Glass THGEM production at\nLiverpool.\n2025-2026: ProtoDUNE-VD at CERN.\nCustom optics for TPX3\ncamera\nLight Readout Plane design\nwith glass-THGEMs\nCharacterization\nof\nnext-\ngeneration TPX4 camera\nSoLAr\n(Sec. 3.3.5)\n2024: Small-size prototypes at Bern.\n2025-2028: Mid-scale demonstrator at\nBoulby.\nDevelopment\nof\nVUV-\nsensitive SiPMs\nASIC-based\nreadout\nelec-\ntronics\nHybrid\nCherenkov+\nscintilla-\ntion\n(Sec-\ntion 3.5.1)\n2024-2025: Prototypes at BNL (1- &\n30-ton), LBNL (Eos), Fermilab\n(ANNIE).\n2025-26: BUTTON at Boulby.\nTheia organic component\nmanufacturing\nTheia in situ purification\nSpectral photon sorting (di-\nchoicons)\nTable 3: Prototyping plans and key R&D goals for the main Phase II FD technologies under\nconsideration.\n62\n\nDUNE Phase II\nthey will remain under consideration for FD3 (with the exception of Theia). Therefore, their\ncontinued R&D in view of FD3 is encouraged.\nWhile full detector solutions will be defined in the forthcoming years through dedicated\ndesign reports, the following outlines the high-level detector concepts currently under consid-\neration by the DUNE collaboration.\nTechnology\nOption for\nCan integrate with\nFD3\nFD4\nCRP (strip-based charge readout)\n\u2713\n\u2713\nAPEX\nAPEX (X-ARAPUCA light read-\nout on field cage with SiPMs)\n\u2713\n\u2713\nCRP, LArPix, Q-Pix, ARI-\nADNE, SoLAr\nLArPix, LightPix (pixel charge\nand light readout)\n\u2713\nAPEX, SoLAr\nQ-Pix, Q-Pix-LILAr (pixel charge\nand light readout)\n\u2713\nAPEX, SoLAr\nARIADNE (dual-phase with opti-\ncal readout of ionization signal)\n\u2713\nAPEX\nSoLAr (integrated charge and light\npixel readout)\n\u2713\nAPEX, LArPix, Q-Pix\nHybrid Cherenkov + scintilla-\ntion\n\u2713\nN.A.\nTable 4: LArTPC integration of the detector technologies currently being considered for the\nPhase II FD modules. Here, \u201cFD3\u201d refers to the FD3 reference design requiring only minimal\nmodification to the FD2 vertical drift design. The \u201cFD4\u201d options could also become options\nfor FD3 over time.\nFor FD3, we envisage a vertical drift LArTPC that is similar in concept to FD2 (Section 3.2).\nWe do not anticipate any changes to the FD2 high voltage system, with two drift volumes of\n6.5 m drift length each. The CRPs at both anodes would feature three 2D projective views\nof the events, obtained from two double-sided perforated PCBs stacked together, similar to\nFD2. Continued R&D beyond the current CRP design for FD2 will focus on optimizations\nof strip pitch, length and orientation, as well as on streamlining CRP construction techniques\n(Section 3.3.2). Upgrades to FD2 charge readout electronics are possible, such as the adoption\nof the 65 nm process for the fabrication of all FD3 ASICs.\nThe FD3 PDS would be composed of X-ARAPUCA-based PD modules read by SiPMs\nusing PoF and SoF, similar to FD1 and FD2. The installation location (field cage, cathode\nand/or membrane wall), optical coverage, and PD module design of the FD3 PDS will be\ndetermined through APEX technology R&D (Section 3.3.1). This R&D will also determine the\nreference solution for PDS readout electronics, particularly whether analog optical signals will\nbe transmitted outside the cryostat as in FD2, or a digital optical transmission solution will be\nadopted. Background control could include incremental improvements over FD2 protocols, but\nno dedicated passive shields (beyond the cryostat itself) nor underground argon (Section 3.6)\n63\n\nDUNE Phase II\nwould be deployed. We envisage LAr doping as for FD2, via the addition of trace (ppm-level)\namounts of liquid xenon (Section 3.4).\nThe concepts for FD4 introduce further improvements. The concept for the reference design\nis a vertical drift LArTPC with a central cathode and two anodes with pixel-based readouts.\nThe projective readout of CRPs would be replaced by a native 3D charge readout system, either\nemploying charge pixels (see LArPix and Q-Pix technologies in Section 3.3.3) or through an\noptical-based charge readout (see ARIADNE technology in Section 3.3.4). The anode pixels\nmay also serve as scintillation light detection units (see the SoLAr, LightPix and Q-Pix-LILAr\noptions in Section 3.3.5). The symmetric TPC configuration may in principle allow for imple-\nmentation of different pixel-based solutions at the top and bottom anodes, depending on the\nR&D outcome and available resources, as is the case for the different top and bottom electronics\nadopted in FD2.\nA single-drift LArTPC solution for FD4 with a unique ARIADNE-based anode plane on\ntop and the cathode placed at the bottom of the detector is also possible.\nThis solution\nwould require upgrades to the HV system to accommodate a longer (13 m) drift. Commercial\n600 kV power supplies with fluctuations in the output voltage that are sufficiently small for\nthis application already exist.\nOn the other hand, R&D would be needed to scale up the\nhigh-voltage feedthrough design currently being used in the ProtoDUNE-VD demonstrator,\nin order to adapt to the larger diameter high-voltage cable and to the higher voltage values.\nScintillation light detection away from the anodes would be performed with X-ARAPUCA\nmodules further improved from FD3 (see Section 3.3.1). Compact shield designs and greater\ncontrol of radioactive backgrounds would be explored for FD4, given that an important goal\nfor this module would be to extend the physics scope to lower energy thresholds.\nA hybrid detector module capable of separately measuring scintillation and Cherenkov light\n(see Theia technology in Section 3.5) would provide a fully complementary detection technol-\nogy for FD4 compared to FD1-3, and currently forms the basis of the alternative FD4 concept\nbeing explored by the DUNE Collaboration. This module would be designed for both high-\nprecision Cherenkov ring imaging and long-baseline neutrino oscillation sensitivity, and a rich\nprogram across a broad spectrum of physics topics in the MeV-scale energy regime, see Table 2.\nThis can be achieved via either a phased approach, with both the light yield of a water-based\nliquid scintillator target and the coverage of fast-timing photosensors increasing over time in\norder to broaden the physics program, or with a high light-yield liquid scintillator and sufficient\nCherenkov separation to preserve the Cherenkov purity from the start. Near detector options\nfor non-LAr FD modules are discussed in Section 4.4.\nThe DAQ system for FD3 and FD4 will be based on the same architecture designed for\nthe first two FD modules.\nThe DUNE timing system will be extended to these modules,\nfacilitating inter-module synchronization and triggering. Most likely, the DAQ will pursue the\nuse of Ethernet and standard protocols for the readout interface to the detector electronics. Raw\ndata will be stored using the same file format, easing the integration with offline computing.\nThe configuration, control, and monitoring system will be re-used, with customizations as\nneeded. Use of the existing DAQ software will allow us to focus efforts on the aspects that may\nbe implemented differently, and to take advantage of advances in computing technologies. For\nexample, the trigger and data filter may evolve to rely on more sophisticated data processing\n64\n\nDUNE Phase II\ntechniques and technologies, such as Artificial Intelligence (AI), particularly at low energies.\nDecisions on the technology choices for FD3 and FD4 are expected to come no later than\n2027 and 2028, respectively. As noted earlier in this section, the reference designs for FD3 and\nFD4 are upgraded versions of the vertical drift LArTPC technology, with Theia serving as an\nalternative technology choice only in the case of FD4.\nThe final design milestones for Phase II FD modules are driven by the number and extent of\nthe upgrades planned. For example, in the case of an FD2-like module where the only upgrades\nare optimization of CRPs and the APEX light system, one can envision being ready for by\n2028 in a technically limited schedule. In this scenario, the earliest start for installation of FD3\ncan be anticipated in 2029 with completion of installation and filling in 2034. Alternatively,\nif one were to implement pixel-based upgrades such as LArPix, Q-Pix, SoLAr, or ARIADNE\n(top anode plane only), the FDR milestone would likely be delayed until at least 2030.\nAn asymmetric DP vertical drift LArTPC for FD4, with a single drift volume instrumented\nvia a single ARIADNE readout plane, would require significant changes to the HV system. It\nis possible to reach the FDR milestone for this option by 2031-32. In the case of the Theia\noption, a FDR milestone no earlier than 2033 is anticipated. The ProtoDUNEs at CERN will\ncontinue to serve as important platforms to demonstrate several of these technologies and their\npotential for integration.\n4\nThe DUNE Phase II near detector\nIn Phase II, DUNE will have accumulated FD statistics of several thousand oscillated electron\nneutrinos, resulting in statistical uncertainties at the few-percent level on the number of electron\nappearance events. To reach the physics goals of DUNE, a similar level of systematic uncertainty\nmust be achieved, which requires precise constraints from the ND. To understand the needs of\nthe Phase II ND, we must first understand the expected performance of the Phase I ND, which\nconsists of two measurement systems, ND-LAr+TMS, and SAND. In Section 4.1, we describe\nwhy the Phase I ND is critical for DUNE physics, discuss limitations inherent to its design,\nand outline the Phase II requirements that are needed to provide improved constraints on the\nargon-based FD data sample. This is a difficult challenge as the ultimate performance of the\nPhase I ND is not yet understood, and will depend on analysis techniques developed over the\ncoming decade. Section 4.2 describes a detector concept that meets the design motivations of\nSection 4.1. Further improvements may come from upgrades to the Phase I ND components,\nsee Section 4.3. Near-detector options to constrain possible non-argon FD data samples are\ndiscussed in Section 4.4.\n4.1\nDesign motivations\nThe Phase I ND-LAr+TMS detector is designed to measure neutrino interactions on the same\nnuclear target as the FD, and with a detector response similar to the FD. Neutrino energy in\nthe FD is estimated by summing the lepton energy with the hadronic energy. The FD measures\nthe muon energy by range, and the energies of all other particles calorimetrically, in both cases\n65\n\nDUNE Phase II\nexploiting energy deposits occurring in LAr. The ND-LAr+TMS detector also measures muons\nby range, and other particles calorimetrically. It is able to reconstruct the same observables\nas the FD, and measures them with essentially the same resolutions, in an unoscillated beam.\nThis capability is the core requirement of the DUNE ND, and will be a critically important\nconstraint for all DUNE long-baseline measurements. The ND-LAr+TMS system moves off-\naxis (via DUNE-PRISM) to collect data at different fluxes, and directly constrains the energy\ndependence of neutrino cross sections. SAND is permanently on-axis, and measures neutrino\ncross sections on various nuclear targets while also monitoring the beam. SAND has a LAr\ntarget, so that it can also measure cross section ratios, including on argon.\nThe dimensions of Phase I ND-LAr are driven by containment of electrons and hadrons,\nrather than by event rate, so that they can be measured calorimetrically in the same way as\nin the FD. To minimize cost, the dimensions have been chosen to be as small as possible while\nmaintaining full coverage of the neutrino-argon phase space. However, this means that the\nacceptance is non-uniform and depends on the event kinematics, complicating the calorimet-\nric energy measurement. Beam-induced muons will be reconstructed by the ND-LAr+TMS\ncombined system. TMS is able to provide sign selection of muons, which is especially impor-\ntant to reject wrong-sign backgrounds in antineutrino mode. However, ND-LAr itself is not\nmagnetized, so the sign selection is only possible for the muons that enter TMS (\u2273800 MeV\nkinetic energy), and there is no sign selection for other particles. While TMS will provide muon\nmomentum and sign reconstruction for the energy region relevant for long-baseline oscillation\nphysics, the design is such that muons above 6 GeV kinetic energy will not be ranged out nor\nsign-selected.\nThe main purpose of the SAND detector will be to monitor the neutrino beam, but it will\nalso be capable of making independent measurements of the neutrino flux and flavor content.\nThis additional capability adds robustness to the ND complex, enabling better control over\nsystematics and background. Phase I SAND will be able to measure the sign of all charged\nparticles in its low-density CH2 tracker, but not generally for hadrons produced in the argon\ntarget. The SAND tracker will also measure neutrino cross sections on carbon and hydrogen\ntargets.\nTo constrain neutrino-argon interaction modeling, it is useful to identify specific exclusive\nprocesses. Of those, about two thirds of neutrino interactions in DUNE will have pions in\nthe final state. ND-LAr is an excellent detector for identifying pions and protons when they\nare above threshold, and do not undergo strong interactions inside the detector. However,\nmany events in the DUNE energy range have pions with hundreds of MeV kinetic energy,\nwhich travel several interaction lengths and frequently scatter, transferring some energy to\nthe atomic nuclei that is then not seen in a calorimetric energy reconstruction. On the other\nhand, below threshold pions decay to final state particles, including neutrinos, leading to large\nfractions of their rest mass not being visible calorimetrically. Also, protons below 300 MeV/c\nare impossible to detect in ND-LAr because they deposit all of their energy over a range of only\na few mm, producing highly saturated ionization charges recorded on a single pixel. Predictions\non the multiplicity of such low-momentum protons from neutrino-argon interaction models are\nparticularly uncertain.\nThese Phase I limitations motivate the design of the Phase II ND. Specifically, the Phase II\n66\n\nDUNE Phase II\nND should have, when compared to the Phase I ND:\n\u2022 argon as the primary target nucleus,\n\u2022 improved PID across a broad range of energies and angles,\n\u2022 lower tracking thresholds for protons and pions,\n\u2022 minimal secondary interactions in the tracker volume,\n\u2022 4\u03c0 acceptance over a wide range of momenta, and\n\u2022 magnetization to achieve sign selection over a broader muon momentum range.\nEmploying an argon target will ensure that constraints from the Phase II ND can be applied\ndirectly to the argon-based FD without any extrapolation in atomic number.\nA broad acceptance and high PID efficiency will enable exclusive final states to be identified,\nwhich will improve the constraints on neutrino interaction modeling. Low thresholds will make\nthe Phase II ND highly sensitive to nuclear effects. Magnetization will ensure sign selection at\nall energies and angles, for both charged leptons and charged pions.\nIn the event that one of the Phase II FD modules consists of a neutrino target material\nthat is not argon-based and of a detector technology other than LArTPC, such as the Theia\ndetector concept described in Section 3.5, the requirements for the Phase II ND complex will\nneed to be expanded to account for the additional target material(s) and the different neutrino\ndetection method.\n4.2\nPhase II improved tracker concept\nFor Phase II, an improved tracker concept based on a GArTPC would replace TMS downstream\nof ND-LAr. Drawings for the envisaged layouts of the Phase I and Phase II detector suites are\nshown in Figure 25. A GArTPC can reconstruct pions, protons and nuclear fragments with\nlower detection thresholds than a LArTPC can. Figure 26, which compares the same simulated\nevent in each, shows this. The protons travel a much longer distance and can be more clearly\nseparated in gaseous argon.\nThe GArTPC is also less susceptible to confusion of primary\nand secondary interactions, since secondary interactions occur infrequently in the lower-density\ngas detector. If the TPC is inside a magnetic field, it can better distinguish neutrinos and\nantineutrinos and can determine the momenta of particles whose trajectories are not contained\nin the detector. It can also measure neutrino interactions over all directions, unlike the ND-\nLAr, which loses acceptance at high angles with respect to the beam direction. Therefore, a\nGArTPC detector system at the near site, called ND-GAr in the following, provides a valuable\nand complementary data sample to better understand neutrino-argon interactions.\nHowever, a drawback of a GArTPC is the lower neutrino event rate in a given volume\ndue to the lower density.\nOne way to improve this is to use high-pressure argon gas.\nA\ncylindrical volume with a diameter and length both of roughly 5 m, and gas at 10 bar, would\nhave a fiducial mass of nearly one ton of argon, yielding approximately one million neutrino\n67\n\nDUNE Phase II\nFigure 25: Layout of the envisaged Phase I (left) and Phase II (right) ND suite. The neutrino\nbeam enters from the bottom-right corner, and exits at the top-left corner, of the drawings. The\nSAND detector is shown at its permanent on-axis location, while all other detectors upstream\nare shown at their maximum off-axis location.\ninteractions per year. The trade-off between sufficient target mass and low detector density\nhas not been optimized, but would nonetheless be adjustable during operations by setting the\ndetector pressure.\nAs illustrated in Figure 27, the reference design concept for the ND-GAr detector comprises:\n1. a pressurized GArTPC,\n2. a surrounding calorimeter,\n3. a magnet, and\n4. a muon-tagging system.\nA PDS may also prove necessary to reduce pileup and to provide the event t0 for the drift\ntime determination in events that do not reach the calorimeter. It would also help improve\nthe track matching between the TPC and the external calorimeter and muon systems [110].\nAll these subsystems are described in the following. The entire ND-GAr system will move\nperpendicularly to the beam direction together with ND-LAr, as part of the DUNE-PRISM\nconcept.\nThis detector concept is motivated by the considerations in Section 4.1. It also affords\nsignificant opportunities to study BSM physics, as discussed in Section 2.3.\n4.2.1\nCharge readout of TPC\nA variety of techniques can be used to amplify and collect the ionization electrons after their\ndrift to the TPC anode, and the options currently under consideration for ND-GAr are briefly\n68\n\nDUNE Phase II\n680\n690\n700\n710\n720\n730\n900\n1000\n1100\n1200\n1300\n1400\n1500\n930\n940\n950\n960\n970\n980\n1000\n1100\n1200\n1300\n1400\n75\n80\n85\n90\n95\n100\n105\n1000\n1100\n1200\n1300\n1400\n1500\nFigure 26: The same CC \u03bd\u00b5 event with seven low energy protons (kinetic energies ranging\nfrom 7 to 51 MeV) simulated in a LArTPC (left) and a GArTPC (right). The LArTPC event\ndisplay shows time ticks versus channel number for the three projective views of the event. The\nGArTPC reconstruction algorithm finds all eight tracks in the event (seven proton tracks and\none muon track), although only six are visible by eye in this view. All proton tracks travel\n2.4 cm or less in LArTPC. From [109].\npresented here. In all cases, a high-pressure gas mixture with high argon content (>90% mo-\nlar fraction) is envisaged.\nA 96:4 Ar:CH4 mixture was tested successfully during ND-GAr\nR&D [111, 112]. Therefore, non-Ar components in the ND-GAr target will contribute at the\nfew percent level at most to the overall event rate in the TPC. In order to extract pure \u03bd-Ar\ninteractions, such percent-level corrections can be made with high accuracy using Transverse\nKinematic Imbalance techniques [113], joint ND-GAr-SAND fits, and Monte Carlo-based es-\ntimates. High-pressure argon gas mixtures have been used in the past, such as in the PEP-4\ndetector at SLAC [114], which used a (flammable) gas mixture of 80:20 Ar:CH4, operated at\n8.5 atm. A known challenge for high-pressure gas detectors is that the gas amplification gain\ndecreases as the gas pressure increases. For the DUNE ND-GAr, R&D to ensure adequate\nstability and gain in a non-flammable gas is underway.\nMulti-Wire Proportional Chambers\nTo collect sufficient event statistics, the HPgTPC,\nat the core of ND-GAr, must be both large and capable of functioning under high pressures.\nA TPC of the size used in the ALICE experiment at CERN [115] may be adequate in terms of\nsize, but only if the gas inside is pressurized to approximately 10 atm. As a result of the recent\nupgrade of ALICE\u2019s readout system to gaseous electron multipliers (s), the previously operated\nALICE multi-wire proportional chambers have become available. They were previously oper-\nated in ALICE at 1 atm, hence their operation needed to be assessed within a high-pressure\nargon gas environment.\nTwo test stands, one each in the UK and the US, called the Gas-argon Operation of ALICE\nTPC (GOAT) and the Test stand of an Overpressure Argon Detector (TOAD), respectively, are\n69\n\nDUNE Phase II\nFigure 27: Cutaway view of the full ND-GAr detector system, showing the HPgTPC, the\ncalorimeter, the magnet, and the iron yoke. The detectors for the muon-tagging system are not\nshown.\nbeing used to test the ALICE chambers under high pressure. GOAT used a pressure vessel rated\nto 10 atm. It tested an ALICE inner chamber for its achievable gas gain at various pressure set\npoints, amplification voltages, and gas mixtures [111]. TOAD had previously tested an ALICE\nouter chamber for its achievable gas gain up to 5 atm. Currently, it is being commissioned in\nthe Fermilab for data-taking in a test beam and for performing a full detector slice test of the\nelectronics and DAQ. In both test stands, wire-based readout chambers have been tested in\nhigh-pressure environments, demonstrating that they can provide reasonable gas gains when\nthey operate at or above the high voltage values they were subject to in ALICE. Despite this,\nthe long-term operation and stability of these chambers at such high voltages remain to be\ninvestigated. There are also plans to test charge readout systems based on micro-pattern gas\ndetectors, such as GEMs, as described below.\nTPC Readout with GEMs\nIn a TPC using GEMs or \u201cthick GEMs\u201d (THGEMs), the\nionization drift electrons enter the THGEM holes and are accelerated in a high electric field.\nAt sufficiently high fields, this acceleration causes the electrons to further ionize the gas medium,\n70\n\nDUNE Phase II\nresulting in a Townsend avalanche. This exponentially increases the number of electrons and\ntherefore the signal size.\nTypically, GEMs and THGEMs are produced starting from double copper-clad substrates,\neither by photolithography of kapton in the case of the former, or Computer Numerical Con-\ntrol (CNC) drilling of epoxy laminates/FR-4 in the latter. We propose to use a new type of\nTHGEM made out of glass, as also proposed in the context of the optical-based charge readout\noption for the Phase II FD (Section 3.3.4). These glass THGEMs developed at Liverpool (UK)\nare fabricated using a new masked abrasive machining process. The innovation allows for cus-\ntomization of glass THGEMs, where both substrate and electrode materials can be tailored to\nour requirements, which include high stiffness, low outgassing, and resilience to damage from\ndischarges.\nThe amplified electrons from the THGEMs would be read out on a segmented anode to\nallow for tracking reconstruction. Borosilicate glass and fused silica are isotropic and homoge-\nneous substrate materials that can be machined to typical THGEM thicknesses while remain-\ning sturdy and potentially providing better surface finishes than FR-4-based THGEMs. Their\ntransparency, made possible by indium tin oxide (ITO) electrodes, makes them suitable for\noptical imaging of primary ionization, as demonstrated up to 1.5 bar with cosmic ray imaging\nat estimated optical gains up to 106 [116].\nFuture optimization of glass GEMs may include enhancements in light collection with\nwavelength-shifting substrates [117], wavelength-shifting coatings [118], or diamond-like car-\nbon (DLC) coatings for stability [119, 120]. R&D toward a THGEM-based readout is ongoing\nin Spain, where a 10-bar full 3D Optical TPC (Gaseous Argon T0 (GAT0)) is under commis-\nsioning. In addition, R&D toward a GEM-based readout for ND-GAr is currently underway in\nthe US with the GEM Over-pressurized with Reference Gases (GORG) test stand, currently\ntesting a triple-GEM stack.\nTPC Readout electronics\nDue to the high-pressure nature of this detector, readout elec-\ntronics must be developed that can operate inside the pressure vessel to minimize the analog\nsignal path. The electronics must also be zero-suppressed and compatible with the existing\nDUNE DAQ infrastructure for the Phase I ND. Readout electronics has traditionally been one\nof the cost drivers of TPCs. While the pixel size to be used in the final detector module has\nnot been determined, detectors like ALICE had 700k channels. With this number of channels,\nwork is needed to ensure that the electronics system is cost-effective.\nR&D work is underway in the UK and US to deliver such electronics. A prototype system\nusing the SAMPA ASIC, developed for the ALICE TPC upgrade and the sPHENIX detector,\nplus FPGA-based control and aggregation, is already in hand. This solution, scaled up to the\nfull ND-GAr detector, is expected to be much cheaper than the ones adopted for ALICE and\nsPHENIX, thanks to the much lower data rates. If full 3D optical tracking is ultimately adopted,\nthe readout electronics would align with the technical proposal described in Section 3.3.4 for\nFD3 and FD4.\n71\n\nDUNE Phase II\nFigure 28: Possible structure of a combined tile and strip layer sampling calorimeter. The\n(yellow) tile/absorber layers are oriented towards the TPC; they are followed by (green)\nstrip/absorber layers. Dimensions are in mm.\n4.2.2\nCalorimeter concept\nThe GArTPC will excel in measuring charged particle tracks, but to first order is blind to\nneutral particles. As such, it is important to have a system that can detect them. At neutrino\nenergies of a few GeV, these are mostly photons (for example from \u03c00-decays) and neutrons\n(from nuclear break-up) in the kinetic energy range from \u2272100 MeV to \u223cGeV. The photon\nenergy will be determined calorimetrically, while the neutron energy can be determined by\nmeasuring the time of flight between the production vertex and a nuclear re-scatter in the\ncalorimeter [121]. Both photons and neutrons will be key to measuring nuclear effects that will\ninfluence the relationship between true and reconstructed neutrino energy, and the dynamics\nof the neutrino interactions.\nIt is also the case that the HPgTPC should occupy the largest possible volume, and the\ncalorimeter has to surround the TPC. As such, it has a rather large surface area even for\nmodern particle physics detectors. Optimizing this detector to achieve the physics goals while\nstill being affordable is a key task of the gaseous argon detector group.\nA possible affordable technology with the required performance is based on a plastic scin-\ntillator sampling calorimeter that is constructed from active tile layers using a combination of\nthe technology developed by the CALICE R&D Collaboration [122] and the more traditional\nscintillator strip, WLS fiber, and SiPM readout combination, used in neutrino experiments such\nas the near detector. A preliminary structure of the calorimeter is illustrated in Figure 27.\nFurther details of the potential layout of the barrel detector are shown in Figure 28.\nA potential barrel geometry consists of 60 layers with the following layout:\n\u2022 eight inner layers of 2 mm copper + 5 mm of 2.5 \u00d7 2.5 cm2 tiles + 1 mm FR-4, and\n\u2022 52 layers of 2 mm copper + 5 mm of cross-strips 4 cm wide\nA possible barrel calorimeter depth is about 44 cm. The initial performance evaluation for\nphotons, based on a preliminary design that was investigated, is summarized in Figure 29.\n72\n\nDUNE Phase II\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\nPhoton Energy [GeV]\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nmean\n / E\nE\n\u03c3\nBaseline Cu\n2 mm Pb\n1 mm Pb\n0.7 mm Pb\n/ndf 51.9/11\n2\n\u03c7\nA 5.7%\nB 1.6%\nC 4.8%\n/ndf 9.643/11\n2\n\u03c7\nA 8.1%\nB 2.1%\nC 0.5%\n/ndf 36.98/11\n2\n\u03c7\nA 5.4%\nB 1.4%\nC 1.5%\n/ndf 113.7/11\n2\n\u03c7\nA 5.0%\nB 0.7%\nC 3.1%\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n1.6\n1.8\nPhoton Energy [GeV]\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\nRatio Energy Resolution\nBaseline Cu\n2 mm Pb\n1 mm Pb\n0.7 mm Pb\nFigure 29: Left: energy resolution as a function of photon energy for different absorber config-\nurations. The function \u03c3E\nE =\nA\n\u221a\nE \u2295B\nE \u2295C has been fitted to the simulated data, where the \u2295\nsymbols refer to a quadrature sum of the three terms. Right: Ratio of the energy resolution for\nthe different absorber configurations. The best resolution is achieved using thin lead absorber.\nThe overall depth of the electromagnetic calorimeter (ECAL) has been kept constant. More\ndetails can be found in [5].\nFor the present study, copper has been chosen as the absorber material, as initial studies\nhave shown that this material provides a good compromise between calorimeter compactness,\nenergy, and angular resolution. It also allows for the removal of heat generated by the electronics\nin the tile layer. There are several possible readout ASICs on the market to determine the time\nand charge of the SiPM signals, one possibility being the KLauS ASIC [123].\n4.2.3\nMagnet concept\nTo achieve the physics goals, the TPC volume of the ND must be magnetized in order to\nmeasure the momenta of muons and other particles, and to determine the sign of their charge.\nThe magnetized system will analyze both the tracks originating from ND-LAr and penetrating\nfrom upstream, and the tracks produced within the magnetic volume by neutrino interactions.\nThe need to make the magnet as compact as possible, thus minimizing the material at the\ndownstream end of the TPC and in front of the calorimeter, suggests an integrated design\nin which the magnet structure serves also as a pressure vessel for the TPC gas volume. The\nmagnetic design described in [124], and summarized here, fulfills these requirements and is\ncost-effective.\nThe magnet system consists of a superconducting solenoid surrounded by an iron return\nyoke.\nThe superconducting solenoid cryostat serves not only as a pressure vessel body for\nthe HPgTPC, but also as support for it and the calorimeter elements located in its bore.\nAdditionally, the design of the iron magnet yoke uses the mechanical strength of the yoke\u2019s\npole faces to eliminate the large domed heads that would normally be required for a large-\ndiameter pressure vessel.\n73\n\nDUNE Phase II\nAnother important design requirement for ND-GAr is the ability to accurately measure the\nmomentum of muons that originate in ND-LAr. This requirement limits the amount of material\nallowed on the upstream side of ND-GAr and motivates an unconventional and asymmetrical\niron yoke design. An iron yoke that eliminates a portion of the iron along the upstream face has\nbeen developed and designed, and is called Solenoid with Partial return Yoke (SPY). Figure 30\nillustrates the SPY magnet system.\nFigure 30: The SPY magnet system. The hole in the yokes is on the upstream side, to minimize\nmaterial traversed by tracks originating from neutrino interactions in ND-LAr.\nThe following lists the main requirements and technological features of this design in more\ndetail:\n\u2022 The momentum analyzing power of the ND-GAr assembly (magnet + TPC) must provide\nat least 3% momentum resolution for the muons originating within ND-LAr. Additionally,\nfor particles produced as a result of neutrino interactions in the HPgTPC, the resolution\nin neutrino energy reconstruction must be at least as good as that of the DUNE FD.\n\u2022 The magnetic field uniformity, thanks to recent and relevant improvements in the capa-\nbility of event reconstruction, is not required to be very high. A \u00b110% tolerance within\nthe magnetic volume is expected to be sufficient, provided that a very accurate map for\nthe magnet \u201cas built\u201d is measured. However, it is worth emphasizing that the magnet\ndesign fully described in [124] greatly exceeds the \u00b110% requirement, and should offer\na \u00b12% variation over the whole volume. Careful studies were also done to evaluate and\nminimize the magnetic forces between ND-GAr and SAND.\n74\n\nDUNE Phase II\n\u2022 The superconductor will be co-extruded in high-purity aluminum to provide quench pro-\ntection. The current reference solution for cable material is one based on niobium tita-\nnium. Higher temperature superconductors such as MgB2 will also be considered as part\nof an R&D program currently in progress.\n\u2022 The ND-GAr assembly must provide good acceptance for muons exiting ND-LAr and must\nfit within the space constraints imposed by the ND hall design and by DUNE-PRISM.\n\u2022 The ND-GAr\u2019s magnet system must present as little material as possible in the path of\nthe muons exiting from ND-LAr. A similar requirement holds in the downstream face of\nthe yoke, to assist in the discrimination of muons from pions.\n\u2022 The vacuum cryostat must be capable of providing mechanical support and a cryogenic\nenvironment for the superconducting coils. The inner wall of the vacuum cryostat must\nbe sufficiently strong to serve as the outer wall of the pressure vessel for the HPgTPC,\nand to support the weight of the calorimeter.\n\u2022 The carbon steel of the return yoke must provide a uniform 0.5 T magnetic field over the\nfull length of the solenoid, and limit fringe fields to the \u22640.01 T levels required by the\nexperiment and by the co-existence with SAND. It must also provide flat carbon steel\npole tips for the magnet return yoke that match the magnetic field boundary conditions\nat the ends of the solenoid, and provide the mechanical support for the pressure vessel\nend flanges.\nThe main parameters achieved in the current design [124] are summarized in Table 5.\nParameter\nRequirement Notes\nCentral field\n0.5 T\nField uniformity\n\u00b110%\nCurrent design achieves \u00b12%\nRamp time to full field\n30 min\nStray field\n\u22640.01 T\nStray field in SAND negligible, in LAr fiducial vol-\nume (FV) \u224310 G\nBore diameter\n6.73 m\nReduction possible with TPC and ECAL opti-\nmizations\nCoils diameter\n7.85 m\nCryostat diameter at stiffening rings\nSolenoid length\n\u22437.8 m\nSolenoid weight\n\u2243150 t\nYoke total weight\n\u2243757 t\nTable 5: List of SPY parameters according to the current reference design.\n75\n\nDUNE Phase II\n4.2.4\nMuon system\nA GArTPC ND system will need to be outside the calorimeter to improve pion/muon separa-\ntion. The muon tagger would likely implement a well established technology, such as a coarsely\ninstrumented scintillator detector. It is not likely to require substantial R&D, but will need\nengineering effort.\n4.2.5\nLight detection options\nEnabling time-tagging by the TPC would provide an absolute determination of the vertex po-\nsition and interaction time, thus simplifying the matching with external detectors and enabling\nreconstruction of interactions whose by-products range out before reaching them. The only\ndemonstrated technique to accomplish this in TPCs relates to primary scintillation, which due\nto the complexity of the system would require significant R&D, primarily to study the level\nof localization needed in order to associate time information with a given interaction. The\nchoice of gas mixture for the detector will also be key, as different mixtures have very different\nscintillation properties [125, 126].\nAlthough pure argon gas emits scintillation light copiously at a level of 20000 photons/MeV,\ngases employed historically in TPCs for accurate tracking in magnetic fields do not [127]. The\nrecent demonstration of strong (and fast) wavelength shifting in the Ar/CF4 system, with yields\nin the range 700\u20131400 photons/MeV [128, 129], opens up the possibility of ns-level time tagging\nfor energy deposits down to at least 5 MeV [110]. A mere 1% CF4 addition (per volume) seems\nsufficient to achieve this performance while keeping the electron diffusion at 3.6 mm for a 5 m\ndrift (compared to 20 mm for pure argon) for a 200 kV cathode bias. These values are even\nbelow those expected for a conventional Ar/CH4 (90/10) mixture.\nIn view of the requirements for single-photon detection and magnetic field compatibility,\nand given the spectral range of the scintillation, two technologies are of particular interest, as\ndescribed below. A third, light readout of secondary scintillation at the amplification stage, is\nalso an option that could be explored, based on an Ar/CH4 (99/1) mixture (Section 4.2.1).\nSiPMs\nSiPMs are well suited for detection in the visible range, and several ganging schemes\nare currently available for large area coverage (e.g., [130]). Silicon suffers from high dark rate\nat room temperature and, in fact, simulations point to the need for cryogenic operation (-25 C)\nto reach MeV-thresholds in ND-GAr. Methods to do this are under study. A comprehensive\nR&D program has been laid out and is led by Spain. A conceptual description of the ganging\nscheme and active-cryostat concept proposed, along with proof-of-principle demonstrations for\nboth, can be found in [110].\nLAPPDs\nLarge-Area Picosecond Photo-Detectors (LAPPDs) are novel photosensors based\non microchannel plate technology. With sensitive regions of order 20\u00d720 cm and sub-cm po-\nsition resolution, this type of detector is a good candidate for covering large areas. LAPPDs\nare tolerant of magnetic fields and handle sub-ns timing with an excellent signal-to-noise ratio,\nand without any cooling requirements.\nThey were recently demonstrated to work for neu-\ntrino detection by the ANNIE experiment. Ideal coverage could be achieved with about 100\n76\n\nDUNE Phase II\nLAPPDs, which could be delivered within a few years at current production rates. Depending\non the choice of quencher/wavelength shifter, modifying the photocathode composition or a\nwavelength shifter coating might be required.\nStudies to optimize this system are required, and include determining optimal coverage, the\nbest photocathode design, and enclosures to allow the LAPPDs to operate at high pressure.\n4.2.6\nR&D and engineering road map\nR&D will be necessary for this Phase II improved tracker concept, starting in 2024 and lasting\nfor several years. It will be important to fully define the detector requirements, then aim for a\ntechnical design report in the late 2020s, and be ready to begin construction in the early 2030s.\nThe essential R&D and design work needed for ND-GAr includes, but is not limited to, the\nfollowing items:\nND-GAr magnet\nINFN Genova is pursuing R&D on using magnesium diboride (MgB2)\nsuperconducting cables, which have a higher critical temperature and do not face some of the\nchallenges of co-extruding NbTi superconducting cables with high-purity aluminum.\nND-GAr TPC charge readout and electronics test stands\nSeveral R&D efforts are\nalready underway, as described in Section 4.2.1. Examples include the GOAT, TOAD, GORG,\nand GAT0 test stands. Charge readout TPCs are a mature technology, with gas mixtures\nidentified that give sufficient gain. The current R&D priority is to test the full readout chain,\nfrom amplification technology to readout electronics, in a high-pressure test stand, using a\nnon-flammable gas with a high argon fraction, to ensure adequate stability and gain. Electron\ndiffusion measurements will also be performed for the same gas mixtures.\nConcerning the amplification stage, current testing has been done with wire chambers.\nHowever, modern TPCs such as those for ALICE and sPHENIX use GEMs to achieve better\nstability of operation and higher gains.\nFor this reason, R&D for a GEM/THGEM-based\namplification stage has started in the context of the DUNE Phase II ND, as well. The stability\nof proposed wavelength-shifting gases such as Ar/CF4 (99/1) must be studied, as they are low-\nquenched.\nConventional GEM, THGEM, glass-GEMs, glass-Micromegas and wire chamber\namplification stages are all currently under evaluation in Spain, the UK, and the US.\nOnce detailed requirements on tracking performance are established, further R&D on read-\nout electronics and on the segmentation of the charge readout pads/strips will be pursued\naccordingly. The TPC charge readout R&D work is currently ongoing in the UK (GEM work\nand readout electronics), Spain (glass-GEM, SiPMs + TPX3 cameras), and the US (readout\nelectronics and test stands) using sources and test beams.\nLight detection in ND-GAr TPC\nThe realization of light readout at the scale of the ND-\nGAr TPC poses important engineering challenges in relation to photosensor technology, HV\nintegration, and good light collection. Dedicated physics studies are needed to establish the best\ndesign path towards the optimization of the detection thresholds, time-tagging performance,\nand photosensor coverage. Both light readout options discussed above have R&D needs, for\n77\n\nDUNE Phase II\nexample cooling control for SiPMs and operation at high pressure for LAPPDs. Groups in\nSpain are performing R&D on the optimization of the SiPM-based optical readout concept:\nrequired coverage, use of reflectors and light collectors, SiPM channel ganging and cooling\nschemes. R&D on LAPPDs is also underway in the US.\nAlso, the outstanding tracking performance of ND-GAr needs to be guaranteed while en-\nsuring that the photosensor plane not be blinded during the avalanche multiplication process\nin the anode region. This will require an additional R&D step targeting the minimization of\nphoton-feedback, as it is customary for instance in ring-imaging Cherenkov detector applica-\ntions [131].\nND-GAr calorimeter\nR&D was underway in Germany on coupling fibers to SiPMs to\nmaximize light collection and uniformly illuminate the SiPM face. Studies must also be done\nto optimize the calorimeter design, including the number of strip and tile layers, and their\ngranularity. A cost-effective readout electronics system must also be developed.\nND-GAr calibration systems, field cage, and gas systems\nEngineering work is also\nrequired to design the infrastructure and support services for the ND-GAr detector.\nThe\nALICE detector featured a high-performance TPC of similar size [115], therefore that design\ncan potentially be used as a starting point. For example, a laser calibration system that can\nuniformly illuminate the drift volume could provide the required accurate monitoring of drift\nvelocity variations and inhomogeneities within the volume. Such a system must be designed\nin close connection with the HV field cage. The movable ND-GAr will require design of a\nmechanically robust field cage with mechanical end-cap structures. A buffer region in between\nthe field cage and pressure vessel will be needed to degrade the high voltage, and this may\nrequire the use of an additional insulating gas.\nThe detector performance depends crucially on the stability and quality of the gas in the\ndrift region, therefore it will be necessary to develop a system to control and monitor the gas\nmixture in the drift volume. Control operations include pressurization, recirculation, purifica-\ntion, and evacuation of the gas. The current design of the magnet system does not incorporate\na method for evacuation [132]. However, modifying it to function under both pressure and vac-\nuum conditions is well understood. Generally, achieving vacuum is desirable to facilitate the\nreduction and monitoring of O2 and H2O impurities (as well as other unforeseen contaminants).\nIt is also worth considering purifying argon gas in the gas handling system \u2013 which might yield\nsimilar results \u2013 although evacuation could potentially be faster.\n4.3\nImprovements to Phase I near detector components\nAs part of the Phase II program, possible enhancements and improvements to the exisiting\nPhase I components of the ND are being considered.\nThis section discusses such possible\nimprovements to the Phase I detector components ND-LAr and SAND.\n78\n\nDUNE Phase II\n4.3.1\nPhase II ND-LAr detector\nND-LAr is the LAr component of the DUNE ND complex. With the intense neutrino flux and\nhigh event rate at the ND, traditional, monolithic, projective wire readout LArTPCs would be\nstretched beyond their performance limits. To overcome this hurdle, ND-LAr will be fabricated\nout of a matrix of smaller, optically isolated TPCs, read out individually via a pixelated readout.\nThe subdivision of the volume into many smaller TPCs allows for shorter drift distances and\ntimes. This and the optical isolation lead to fewer problems with overlapping interactions.\nThe ND-LAr design consists of 35 optically separated LArTPC modules, which allows for\nindependent identification of \u03bd-Ar interactions in an intense beam environment using optical\ntiming. Each TPC consists of a HV cathode, a low-profile field cage that minimizes the amount\nof inactive material between modules, a light collection system, and a pixel-based charge read-\nout.\nOne key aspect of ND-LAr operation is the ability to cope with many neutrino interactions\nin each spill. The LBNF neutrino beam consists of a 10 \u00b5s wide spill, which leads to O(50) \u03bd\ninteractions per spill in Phase I and O(100) in Phase II. Given the relatively low expected cosmic\nray rate while the beam is on (estimated to be \u223c0.3/spill at 60 m depth), this beam-related\npile-up is the primary challenge confronting the reconstruction of the ND-LAr events. The 3D\npixel charge signal will be read out continuously. The slow drifting electrons (with charge from\nthe cathode taking \u223c300 \u00b5s to travel the 50 cm drift distance) will be read out with an arrival\ntime accuracy of 200 ns and a corresponding charge amplitude within a \u223c2 \u00b5s-wide bin. This\ncoupled with the beam spill width gives a position accuracy of 16 mm. While this is already\ngood spatial positioning, the ND-LAr light system will provide an even more accurate time\ntag of the charge as well as the ability to tag subclusters and spatially disassociated charge\ndepositions resulting from neutral particles, such as neutrons, that come from the neutrino\ninteraction. Thus, the ND-LAr light system has a different role from that in the FD, as it must\ntime-tag charge signal subclusters to enable accurate association of all charge to the proper\nneutrino event, and to reject pile-up of charge from other neutrino signals.\nThe current ND-LAr design being implemented for Phase I satisfies the general requirements\nof DUNE for Phase II in terms of increased beam power and lifetime of detector components.\nNonetheless, additional potential modifications to ND-LAr that might enhance its capabilities\nare under consideration. Given that the ND-LAr uptime during DUNE operations is an impor-\ntant factor to take into consideration, those modifications can be divided into two categories:\nND-LAr upgrades that imply modifications to the inner detector hardware and thus require\nemptying the LAr, and those that do not. In the former, more disruptive, category, current\nideas under exploration include: improvements to neutron detection methods by upgrading op-\ntical detectors with 6Li-glass scintillator, replacement of charge tiles of a module with smaller\npixels and lower threshold, use of photosensitive dopants, and use of radiopure underground\nargon. In the latter (less disruptive) category, possible upgrade options span the following:\ndoping of argon with xenon, upgrade of the off-detector electronics, addition of a rock muon\ntracker in front of ND-LAr, and use of an additional calibration system based on 222Rn injec-\ntion. A decision on these possible ND-LAr upgrade paths will come after the Phase I ND-LAr\ndetector is commissioned.\n79\n\nDUNE Phase II\n4.3.2\nPhase II SAND detector\nSAND is a multipurpose detector composed of a superconducting solenoid, a high-performance\nECAL, a light tracker, and an active LAr target called . The magnet and the ECAL were part\nof the\ndetector at INFN Frascati and will be refurbished for Phase I, without the need for\nupgrades during Phase II. The tracker, based on straw tubes, will be a completely new detector\ncapable of reconstructing charged particle tracks in the magnetic field. Major upgrades for the\ntracker are not foreseen for Phase II.\nGRAIN is an innovative LAr detector that will employ a completely new readout technique,\nusing only scintillation light for track reconstruction. This task is accomplished by cameras with\nlight sensors made of a matrix of SiPMs and optical elements, such as special lenses or Coded\nAperture Masks. The GRAIN project is very challenging because, due to the low efficiency\nof light sensors to VUV scintillation light, the number of photons detected and used by the\nreconstruction algorithms is low.\nFor Phase II GRAIN, the goal is to enhance light collection by improving the SiPM PDE in\nthe VUV range. For this purpose, we are developing with \u201cFondazione Bruno Kessler\u201d (FBK-\nTrento) Backside Illuminated SiPMs (BSI SiPMs).\nIn this architecture, the light entrance\nwindow is on the back of the silicon, while all the metallic contacts are on the front side. This\nwill allow us to improve the fill factor and optimize the anti-reflective coating on the entrance\nwindow. It is planned to substitute all the GRAIN matrices of traditional Front Side SiPMs\nwith the BSI ones for Phase II, if they will be available and mature in time.\n4.4\nNear-detector options for non-argon far detector modules\nIn the event that one of the Phase II FD modules consists of a neutrino target material that is\nnot argon-based, such as the Theia detector concept described in Section 3.5, the Phase II ND\ncomplex will need to provide measurements of neutrino interactions on those same target nuclei.\nSeveral options are under consideration for modifying the Phase I suite of ND sub-detectors\nto make such measurements, including modifying the Phase I SAND to incorporate oxygen\nand water targets, embedding liquid scintillator targets within the ECAL of the GArTPC, and\nconstructing a new, dedicated, water-based near detector. While they introduce identical or\nsimilar nuclear targets, these particular options do not establish a functionally similar detector\nat the near site that would also mitigate detector-related uncertainties at the far detector,\nanalogous to ND-LAr for the argon-based FD modules.\n4.4.1\nOxygen and water targets in SAND\nThe SAND detector is equipped with a modular Straw Tube Tracker (STT) with target layers\nthat are designed to be individually replaceable with different materials. A total of 78 thin\nplanes, each about 1.6% of a radiation length X0, of various passive materials are alternated\nand dispersed throughout active layers, which are made of four straw planes, to guarantee the\nsame acceptance to final state particles produced in (anti)neutrino interactions. The STT allows\nminimizing the thickness of individual active layers and to approximate the ideal case of a pure\ntarget detector \u2013 the targets constitute about 97% of the mass \u2013 while keeping the total thickness\n80\n\nDUNE Phase II\nof the stack comparable to one radiation length and an average density of about 0.17 g/cm3.\nThe lightness of the tracking straws and the chemical purity of the targets, together with the\nphysical spacing among the individual target planes, make the vertex resolution (\u226a1 mm) less\ncritical in associating the interactions to the correct target material. The average momentum\nresolution expected for muons is \u03b4p/p \u223c3.5% and the average angular resolution better than\n2 mrad. The momentum scale can be calibrated to about 0.2% using reconstructed K0 \u2192\u03c0+\u03c0\u2212\ndecays.\nThe STT is optimized for the \u201csolid\u201d hydrogen technique, in which \u03bd(\u00af\u03bd) interactions on free\nprotons are obtained by subtracting measurements on dedicated graphite (C) targets from those\non polypropylene (CH2) targets [133, 134, 135]. The default target configuration in Phase I\nincludes 70 CH2 targets and eight C targets. The use of a distributed target mass within a\nlow-density tracker results in an approximately uniform acceptance over the full 4\u03c0 angle, as\nshown in Figure 31. The acceptance disparity between different targets can be kept within\n10\u22123 for all particles (Figure 31) due to their thinness and their alternation throughout the\ndetector volume. The subtraction procedure between different materials can then be considered\nmodel-independent within these uncertainties. Furthermore, the detector acceptance effectively\ncancels in comparisons between the selected interactions on different target nuclei.\nFigure 31: Left: Muon acceptance for \u03bd\u00b5 CC interactions in a forward horn current () beam in\nSAND. Right: Discrepancy in acceptance between the CH2 and C targets in SAND.\nThe ND can operate with both oxygen and water targets concurrently by replacing some of\nthe initial CH2 targets with polyoxymethylene (CH2O, acetal) planes with equivalent thickness,\ni.e., in terms of radiation length and nuclear interaction length \u03bbI. Interactions on oxygen are\nobtained from a subtraction between CH2O and CH2 targets, while interactions on water are\nobtained from a subtraction between CH2O and C targets [136].\nTo this end, 4.5 mm thick acetal slabs can be used, corresponding to about 0.016 X0 and\n0.008 \u03bbI. The oxygen content by mass within acetal dominates at 53.3%. By replacing only\n20 polypropylene targets (out of 70) with the equivalent CH2O targets, we obtain an oxygen\ntarget mass of about 760 kg and a water target mass of about 850 kg. Assuming an exposure of\n81\n\nDUNE Phase II\n3 \u00d7 1021 POT, corresponding to about two years with the Phase I beam intensity and to about\none year with the Phase II beam, we expect to collect 3\u00d7106 \u03bd\u00b5 CC events with the FHC beam\nand 1 \u00d7 106 \u00af\u03bd\u00b5 CC events with the beam on oxygen. The subtraction procedure introduces an\nincrease of about 40% in the statistical uncertainties with respect to the use of ideal targets. For\n3\u00d71021 POT, the resulting statistical bin-to-bin uncertainties in the \u03bd-nucleus cross-sections as a\nfunction of neutrino energy are comparable to the expected systematic uncertainties introduced\nby the STT momentum scale uncertainty of 0.2% [136].\n4.4.2\nLiquid scintillator targets in the ND-GAr calorimeter\nThe GArTPC described in Section 4.2 is capable of supporting active Theia-type targets\nwithin the downstream portion of the upstream ECAL, as shown in Figure 32. The Theia\nlayers consist of X and Y bars (similar to the NOvA configuration discussed in the next section),\nand interactions in these layers produce particles that enter the high-pressure gas TPC where\nthey are precisely tracked. Neutral particles are measured by the surrounding ECAL, and the\nactive Theia layers provide an additional measure of low-energy particles near the interaction\nvertex (\u201cvertex activity\u201d). For neutrino interactions within the GArTPC, the Theia layers\nwill form an initial low-density section of the ECAL that can provide fast timing for particles\nexiting the TPC.\nWbLS Layers\nHPgTPC\nFigure 32: An upstream segment of the GArTPC ECAL, with the beam is pointing downward.\nThe Theia layers constitute the most downstream portion of the ECAL, and particles produced\nin these layers via neutrino interactions are tracked in the downstream HPgTPC.\nThere is sufficient space within the ECAL to include Theia layers with a thickness of\nat least 10 cm, which would provide more than a ton of target mass.\nThis would produce\nO(1M) charged current \u03bd\u00b5 interactions in a 14 week run on-axis, and O(10k) charged current\n\u03bd\u00b5 interactions in a two week run at the furthest off-axis position, both of which would be\nexpected to occur within a nominal DUNE yearly run.\n82\n\nDUNE Phase II\n4.4.3\nWater-based near detector\nIt is possible to install a detector specifically designed to make measurements for a water-\nbased FD module in the DUNE ND hall.\nIf a new GArTPC is built, it will serve as the\ndownstream spectrometer for ND-LAr, allowing TMS to be used as a downstream spectrometer\nfor a dedicated Water-based Near Detector (WbND). Any configuration of the ND suite will\nbe subject to the space limitations imposed by the near site infrastructure, as completed before\nthe beginning of beam operations. Two possible options for a WbND are a NOvA-style ND,\nor a LiquidO ND, both discussed below.\nNOvA-style near detector\nThe NOvA ND consists of individual cells, as shown in Fig-\nure 33, arranged in horizontal and vertical layers. The cells consist of PVC extrusions filled\nwith liquid scintillator, and a wavelength-shifting fiber collects the light and guides it to the\navalanche photodiode (APD) for readout [137].\n \n \n \nTypical charged particle path \nTo one \nAPD pixel \nL = 15.5 m \n3.5 cm \n5.6 cm \nScintillation Light \nWavelength-shifting \nFiber Loop \nFigure 33: The fundamental unit cell of the detector of the NOvA near detector; the cells are\narranged in horizontal and vertical layers.\nThe NOvA near detector design could be used to construct a WbND by replacing the NOvA\nscintillator with Theia WbLS. Its cell size and scintillator fraction would have to be tuned to\nensure a high muon reconstruction efficiency. This type of detector would also be capable of a\ncalorimetric measurement of the hadronic energy in the neutrino final state, including better\nsensitivity to neutrons than a LAr detector, due to the presence of free hydrogen in the target\nmaterial. This detector technology is well established and would require minimal additional\nR&D.\nLiquidO near detector\nA promising new detector concept for the DUNE ND is based on\nusing opaque scintillators with millimeter-scale scattering length to produce high-resolution\nimages of neutrino interactions [138, 139]. The scintillation photons are stochastically confined\nclose to the point of production via scattering, and a lattice of wavelength-shifting fibers at\n\u22431 cm pitch is used to extract the light. This technology, called LiquidO, removes the need for\nmanual segmentation: the lattice of fibers is constructed first, and then the opaque scintillator\npoured in around the fibers.\nSubstantially better spatial resolution per readout channel is\nachieved by using the profile of the light detected across multiple fibers. Figure 34 shows a CC\n83\n\nDUNE Phase II\nmuon neutrino event as imaged with a LiquidO technology ND. Furthermore, and importantly\nfor a potential Theia DUNE Phase II FD module, the scintillator isotopic composition can\nbe varied by exchanging the scintillator material, e.g., oil-based scintillators can be swapped\nwith water-based ones.\nA design analogous to the T2K Super-FGD detector is envisaged\nfor DUNE with the fibers running in all three perpendicular directions, allowing fine-grained\nprecision tracking and excellent calorimetry. The hydrogen-rich nature of organic or water-\nbased scintillators, together with their fast timing, is advantageous for neutron time-of-flight\nmeasurements and for particle detection in high-rate environments.\nFigure 34: Illustration of a simulated 2 GeV electron neutrino interaction in a LiquidO-style\nND with a 1 cm fiber pitch. The image shows sub-cm spatial resolution and excellent particle\nID can be achieved.\nAcknowledgements\nThis document was prepared by the DUNE collaboration using the resources of the Fermi\nNational Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science,\nHEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under\nContract No. DE-AC02-07CH11359. This work was supported by CNPq, FAPERJ, FAPEG\nand FAPESP, Brazil; CFI, IPP and NSERC, Canada; CERN; M\u02c7SMT, Czech Republic; ERDF,\nH2020-EU and MSCA, European Union; CNRS/IN2P3 and CEA, France; INFN, Italy; FCT,\nPortugal; NRF, South Korea; CAM, Fundaci\u00b4on \u201cLa Caixa\u201d, Junta de Andaluc\u00b4\u0131a-FEDER,\nMICINN, and Xunta de Galicia, Spain; SERI and SNSF, Switzerland; T\u00a8UB\u02d9ITAK, Turkey; The\nRoyal Society and UKRI/STFC, United Kingdom; DOE and NSF, United States of America.\nFermilab Report Number: FERMILAB-TM-2833-LBNF\n84\n\nDUNE Phase II\nGlossary\nEos The XRootD-based distributed file system developed by CERN. 56, 61\nTheia-25 A 25 kt version of the Theia detector concept that could serve as DUNE\u2019s fourth\nfar detector module.. 54, 55\nTheia Proposed hybrid detector with both Cherenkov and scintillation detection capabilities.\n16, 19, 24\u201326, 53\u201358, 60, 61, 63, 64, 66, 79, 81, 82\nneutrinoless double-\u03b2 decay (0\u03bd\u03b2\u03b2) A hypothetical nuclear transition in which a nucleus\nwith with Z protons decays into a nucleus with Z+2 protons and the same mass number,\ntogether with the emission of two electrons and no neutrinos.. 25, 51, 52, 55, 56, 59\nACE-MIRT The Accelerator Complex Evolution with Main Injector Ramp and Target up-\ngrade is a proposed set of major upgrades to the Fermilab accelerator complex aimed at\nan early implementation of an enhanced 2.1 MW beam for DUNE.. 15, 17, 28\nArtificial Intelligence (AI) A field of study in computer science which develops and studies\nintelligent machines.. 63\nAxion-like particle (ALP) A hypothetical pseudoscalar particle that appears in the spon-\ntaneous breaking of a global symmetry.. 26\nanode plane a planar array of charge readout devices covering an entire face of a detector\nmodule. 32\nAPEX Aluminum Profiles with Embedded X-arapuca. 34\u201339, 61, 62, 64\nARIADNE Charge readout technology for LArTPC dual-phase detectors based on gaseous\nelectron multipliers and fast optical cameras.. 39, 45\u201347, 60\u201364\nAmorphous selenium (aSe) A type of photoconductive material.. 50, 61\nASIC application-specific integrated circuit. 40\u201342, 49, 61, 62, 70, 71\nBDE bottom detector electronics. 31, 40\nboosted decision tree (BDT) A method of multivariate analysis. 19\nBrookhaven National Laboratory (BNL) US national laboratory in Upton, NY. 56\nBSM beyond the Standard Model. 12, 14, 16, 18, 20, 26\u201329, 51, 53, 68\ncharged current (CC) Refers to an interaction between elementary particles where a charged\nweak force carrier (W + or W \u2212) is exchanged. 20, 24, 27, 28, 57, 67, 80, 82\n85\n\nDUNE Phase II\ncore-collapse supernova (CCSN) The collapse of stars more than 8\u00d7 as massive as the sun\nwhich produces an intense burst of neutrinos at the end of its fusion cycle in a matter\nof seconds which ejects the outermost stellar gas leaving behind a neutron star remnant..\n21, 22\ncold electronics (CE) Analog and digital readout electronics that operate at cryogenic tem-\nperatures. 31\nCoherent Elastic Neutrino-Nucleus Scattering (CE\u03bdNS) A type of neutrino interac-\ntion with matter.. 24\nEuropean Laboratory for Particle Physics (CERN) The leading particle physics labo-\nratory in Europe and home to the ProtoDUNEs and other prototypes and demonstrators,\nincluding the s. 13\u201315, 39, 42, 61\nCMOS Complementary metal-oxide-semiconductor. 43\nComputer Numerical Control (CNC) A precise drilling method that utilizes a rotating\ncutting tool to produce round holes in a stationary work piece. 69\ncarbon nitrogen oxygen (CNO) The CNO cycle (for carbon-nitrogen-oxygen) is one of the\ntwo known sets of fusion reactions by which stars convert hydrogen to helium, the other\nbeing the proton-proton chain reaction (pp-chain reaction).\nIn the CNO cycle, four\nprotons fuse, using carbon, nitrogen, and oxygen isotopes as catalysts, to produce one\nalpha particle, two positrons and two electron neutrinos. 25, 54, 56, 59\nColdADC A newly developed 16-channels ASIC providing analog to digital conversion. 40\nCOLDATA A 64-channel control and communications ASIC. 40\ncommercial off-the-shelf (COTS) Items, typically hardware such as computers, that may\nbe purchased whole, without any custom design or fabrication and thus at normal con-\nsumer prices and availability. 45\ncharge conjugation and parity (CP) Product of charge conjugation and parity transfor-\nmations. 54\nCoordinating Panel for Advanced Detectors (CPAD) US panel that seeks to promote,\ncoordinate and assist in the research and development of instrumentation and detectors\nfor high-energy physics experiments.. 13, 16\ncharge, parity, and time reversal symmetry (CPT) product of charge, parity and time-\nreversal transformations. 18\nCharge Conjugation-Parity Symmetry Violation (CPV) Lack of symmetry in a system\nbefore and after charge conjugation and parity transformations are applied.\nFor CP\nsymmetry to hold, a particle turns into its corresponding antiparticle under a charge\n86\n\nDUNE Phase II\ntransformation, and a parity transformation inverts its space coordinates, i.e. produces\nthe mirror image. 12\u201314, 17, 18, 28, 53\ncharge readout (CRO) The system for detecting ionization charge distributions in a detector\nmodule. 31\ncharge-readout plane (CRP) An anode technology using a stack of perforated PCBs with\netched electrode strips to provide CRO in 3D; it has two induction layers and one collection\nlayer; it is used in the SP vertical drift FD and DP designs. 29, 31, 32, 34, 35, 39, 40, 59,\n61, 62, 64\ncharge-readout unit (CRU) In the SP vertical drift design an assembly of the s plus adapter\nboards; two to a CRP. 31\ndata acquisition (DAQ) The data acquisition system accepts data from the detector front-\nend (FE) electronics, buffers the data, performs a , builds events from the selected data\nand delivers the result to the offline . 37, 63, 69, 70\ndichroic filter (DF) Optical filter that reflects some wavelengths of light and transmits oth-\ners, with almost no absorption for all wavelengths of interest. 37, 38\ndual-phase (DP) Distinguishes a LArTPC technology by the fact that it operates using argon\nin both gas and liquid phases; sometimes called double-phase. 56, 64\nDRD ECFA Detector R&D. 16\ndiffuse supernova neutrino background (DSNB) The term describing the pervasive, con-\nstant flux of neutrinos due to all past supernova neutrino bursts. 23\nDeep Underground Neutrino Experiment (DUNE) A leading-edge, international exper-\niment for neutrino science and proton decay studies; refers to the entire international\nexperiment and collaboration. 12, 14\nDUNE Precision Reaction-Independent Spectrum Measurement (DUNE-PRISM)\na mobile near detector that can perform measurements over a range of angles off-axis from\nthe neutrino beam direction in order to sample many different neutrino energy distribu-\ntions. 14, 15, 64, 68, 73\nelectromagnetic calorimeter (ECAL) A detector component that measures energy depo-\nsition of traversing particles (in the DUNE near detector design). 72, 74, 78, 79, 81\nEuropean Committee for Future Accelerators (ECFA) Committee charged with the long-\nrange planning of European high-energy facilities: accelerators, large-scale facilities and\nequipment.. 13, 16\n87\n\nDUNE Phase II\nfar detector (FD) The 70 kt total (40 kt fiducial) mass LArTPC DUNE detector, composed\nof four 17.5 kt total (10 kt fiducial) mass modules, to be installed at the far site at SURF\nin Lead, SD, USA. 12, 13, 15\u201322, 24\u201326, 28, 29, 42, 46, 50, 51, 56, 62\u201364, 66, 69, 73, 78,\n79, 81, 82\nfar detector module 1 (FD1) The first DUNE far detector module to be built at SURF.\n15, 19, 29, 31, 37, 43, 48, 49, 62\nfar detector module 2 (FD2) The second DUNE far detector module to be built at SURF.\n13, 15, 16, 19, 29\u201332, 34, 35, 37, 39, 42, 43, 49, 52, 56, 60, 62\u201364\nfar detector module 3 (FD3) The third DUNE far detector module to be built at SURF.\n15\u201317, 19, 20, 39, 60, 62, 63, 70\nfar detector module 4 (FD4) The fourth DUNE far detector module to be built at SURF.\n15\u201317, 19, 20, 60, 62, 63, 70\nFDR Depending on context, either \u201cfinal design report,\u201d a formal project document that\ndescribes the experiment at a final level, or \u201cfinal design review,\u201d a formal review of the\nfinal design of the experiment or of a component. 64\nFermi National Accelerator Laboratory (Fermilab) U.S. national laboratory in Batavia,\nIL. It is the laboratory that hosts LBNF and DUNE, and serves as the experiment\u2019s near\nsite. 12, 14, 56, 61, 69\nFHC forward horn current (\u03bd\u00b5 mode). 80\nfield cage The component of a LArTPC that contains and shapes the applied E field. 13,\n29\u201332, 34, 35, 37\u201339, 54, 61, 62, 77\nfield programmable gate array (FPGA) An integrated circuit technology that allows the\nhardware to be reconfigured to execute different algorithms after its manufacture and\ndeployment. 41, 45, 70\nFRP fiber-reinforced plastic. 32\nFTBF Fermilab Test Beam Facility. 69\nfiducial volume (FV) The detector volume within the TPC that is selected for physics anal-\nysis through cuts on reconstructed event position. 74\ngaseous argon time-projection chamber (GArTPC) A TPC filled with gaseous argon.\n13, 66, 67, 70, 74, 79, 81\nGaseous Argon T0 (GAT0) An Optical TPC demonstrator in Spain. A test stand for ND-\nGAr R&D. 70, 76\n88\n\nDUNE Phase II\nGeant4 A software toolkit for the simulation of the passage of particles through matter using\nMonte Carlo (MC) methods. 38\nGEM Gaseous electron multiplier. 69, 70, 76\nGas-argon Operation of ALICE TPC (GOAT) A test stand for ND-GAr R&D.. 69, 76\nGEM Over-pressurized with Reference Gases (GORG) A test stand for ND-GAr R&D.\n70, 76\nGRAIN In the SAND detector, a small cryostat containing LAr installed upstream of the\nstraw-tube tracker inside the ECAL. 78, 79\nHNL heavy neutral lepton. 26\u201328\nhorizontal drift single-phase, horizontal drift LArTPC technology. 29, 31\nhigh-pressure gaseous argon TPC (HPgTPC) A TPC filled with gaseous argon; a pos-\nsible component of the DUNE ND. 15, 16, 27, 68, 69, 71\u201374, 81\nhigh voltage (HV) Generally describes a voltage applied to drive the motion of free electrons\nthrough some media, e.g., LAr. 32, 35, 63, 64, 76, 77\nHVFT HV feedthrough. 32\nHVPS HV power supply. 32\nhigh voltage system (HVS) The detector subsystem that provides the TPC drift field. 32,\n34\nICARUS A neutrino experiment that was located at the Laboratori Nazionali del Gran Sasso\n(LNGS) in Italy, then refurbished at CERN for re-use in the same neutrino beam from\nFermilab used by the , MicroBooNE and SBND experiments at Fermilab. 15, 29, 52\nKLOE KLOE is a e+e\u2212collider detector spectrometer operated at DAFNE, the \u03d5-meson\nfactory at Frascati, Rome. In DUNE it will consist of a 26 cm Pb+scintillating fiber\nECAL surrounding a cylindrical open detector region that is 4.00 m in diameter and\n4.30 m long.\nThe ECAL and detector region are embedded in a 0.6 T magnetic field\ncreated by a 4.86 m diameter superconducting coil and a 475 tonne iron yoke. 78\nLarge Area Picosecond Photo-Detector (LAPPD) A kind of imaging photodetector de-\nsigned to provide exquisite time resolution.. 56, 75, 76\nliquid argon (LAr) Argon in its liquid phase; it is a cryogenic liquid with a boiling point\nof 87 K and density of 1.4 g/ml. 12\u201317, 19, 20, 29, 35, 37\u201340, 45\u201348, 50\u201353, 55, 57, 60,\n62\u201365, 74, 77, 78, 82\n89\n\nDUNE Phase II\nLArASIC A 16-channel FE ASIC that provides signal amplification and pulse shaping. 40\nLArIAT The repurposed ArgoNeuT LArTPC, modified for use in a charged particle beam,\ndedicated to the calibration and precise characterization of the output response of these\ndetectors. 53\nLArPix ASIC pixelated charge readout for a TPC. 40\u201343, 49, 60\u201362, 64\nliquid-argon time-projection chamber (LArTPC) A TPC filled with liquid argon; the\nbasis for the DUNE FD modules. 13, 15, 19\u201321, 23\u201325, 35, 40\u201343, 45, 48, 49, 51\u201353,\n62\u201364, 66, 67, 77\nlong-baseline (LBL) Refers to the distance between the neutrino source and the FD. It can\nalso refer to the distance between the near and far detectors. The \u201clong\u201d designation is\nan approximate and relative distinction. For DUNE, this distance (between Fermilab and\nSURF) is approximately 1300 km. 18\nLong-Baseline Neutrino Facility (LBNF) Long-Baseline Neutrino Facility; refers to the\nfacilities that support the experiment including in-kind contributions under the line-item\nproject. The portion of LBNF/DUNE-US responsible for developing the neutrino beam,\nthe far site cryostats, and far and near site cryogenics systems, and the conventional\nfacilities, including the excavations. 12, 14, 15, 26, 28, 78\nLBNF/DUNE Construction Project The international project to design and build the fa-\ncilities and detectors for the LBNF and DUNE enterprise (LBNF/DUNE); it includes the\nLBNF/DUNE-US and projects at multiple international partners to manage the contri-\nbutions from non-US institutions and funding agencies to design, build, and install the\ndetector components. 14, 28\nLBNF/DUNE-US Long-Baseline Neutrino Facility/Deep Underground Neutrino Experiment\n- United States; project to design and build the conventional and beamline facilities and\nthe contributions to the detectors. It is organized as a DOE/Fermilab project and in-\ncorporates contributions to the facilities from international partners. It also acts as host\nfor the installation and integration of the DUNE detectors. 14\nLawrence Berkeley National Laboratory (LBNL) US national laboratory in Berkeley,\nCA. 56\nlight yield detected photons per unit deposited energy. 38, 39\nLightPix Low-power, cryogenic-compatible and scalable SiPM readout electronics based on\nthe LArPix ASIC. 47, 49, 61\u201363\nMCND More Capable Near Detector. 15, 20\nMicroBooNE A LArTPC neutrino oscillation experiment at Fermilab. 15, 29\n90\n\nDUNE Phase II\nMetal\u2013oxide\u2013semiconductor field-effect transistor (MOSFET) A type of field-effect tran-\nsistor. 42\nMikheyev-Smirnov-Wolfenstein effect (MSW) Explains the oscillatory behavior of neu-\ntrinos produced inside the sun as they traverse the solar matter. 25, 54\nneutral current (NC) Refers to an interaction between elementary particles where a neu-\ntrally charged weak force carrier (Z0) is exchanged. 24\nnear detector (ND) Refers to the collection of DUNE detector components installed close\nto the neutrino source at Fermilab; also a subproject of LBNF/DUNE-US that includes\ninstallation, infrastructure, and the cryogenics systems for this detector. 12, 13, 15, 17\u201320,\n26, 27, 29, 41\u201343, 64\u201366, 70, 72\u201374, 76, 77, 79, 81\u201383\nND-GAr component of the near detector with a core gaseous argon TPC surrounded by an\nECAL and a magnet. 15, 26\u201328, 67\u201370, 72\u201377\nND-LAr LArTPC component of the near detector based on technology. 13\u201316, 20, 28, 40,\n64\u201368, 72\u201374, 77\u201379, 81\nNP02 The CERN North Area in Experiment Hall North One (EHN1) intersected by the\nhadron beamline, the location of the 800 t cryostat used for ProtoDUNE-DP and for SP\nvertical drift tests and prototypes; also used to refer to the 800 t cryostat in this area. 47\nPCB printed circuit board. 13, 30\u201332, 38, 39, 41, 42, 48, 50, 61, 62\nphoton detector (PD) The detector elements involved in measurement of the number and\narrival times of optical photons produced in a detector module. 34\u201339, 61, 62\nPDE photon detection efficiency. 38, 48, 79\nphoton detection system (PDS) The detector subsystem sensitive to light produced in the\nLAr. 24, 32, 34, 37\u201339, 49, 62, 68\nphotoelectron (PE) An electron ejected from the surface of a material by the photoelectric\neffect. 38\nPEEK Polyether ether ketone, a colorless organic thermoplastic polymer. 39\nparticle ID (PID) Particle identification. 13, 53, 54, 65, 66\nProton Improvement Plan II (PIP-II) A Fermilab project for improving the protons on\ntarget delivered delivered by the LBNF neutrino production beam. This is version two of\nthis plan and it is planned to be followed by a PIP-III. 15\n91\n\nDUNE Phase II\npower-over-fiber (PoF) a technology in which a fiber optic cable carries optical power, which\nis used as an energy source rather than, or as well as, carrying data; this allows a device\nto be remotely powered, while providing electrical isolation between the device and the\npower supply. 34, 35, 37, 39, 62\nprotons on target (POT) Typically used as a unit of normalization for the number of pro-\ntons striking the neutrino production target. 17, 27, 80\nparts per million (ppm) A concentration equal to one part in 106. 51\u201353, 62\nProtoDUNE Either of the two initial DUNE prototype detectors constructed at CERN. One\nprototype implemented SP technology and the other DP. 39\nProtoDUNE-DP The DP ProtoDUNE detector constructed at CERN in NP02. 29\nProtoDUNE-SP The horizontal drift detector module (FD1-HD) ProtoDUNE detector con-\nstructed at CERN in . 15, 29, 51\nProtoDUNE-VD ProtoDUNE with vertical drift technology. This refers to the CRP-based\nprototype to run in NP02 (in the phase). 15, 29, 39, 61, 63\nQ-Pix A pixel-based, 3D, readout technology based on a continuously integrating low-power\ncharge-sensitive amplifier viewed by a Schmitt trigger. 40, 42\u201345, 49, 61, 62, 64\nQ-Pix Light Imaging in Liquid Argon (Q-Pix-LILAr) A Q-Pix pixel coated with a type\nof photoconductive material, to perform integrated charge/light readout on the anode..\n47, 49, 50, 61\u201363\nquality assurance (QA) The process of ensuring that the quality of each element meets\nrequirements during design and development, and to detect and correct poor results prior\nto production. 31\nquality control (QC) The process (e.g., inspection, testing, measurements) of ensuring that\neach manufactured element meets its quality requirements prior to assembly or installa-\ntion. 31\nRDC Detector R&D collaborations. 16\nRHC reverse horn current ( \u03bd\u00b5 \u2192\u03bd\u00b5 mode). 80\nSystem for on-Axis Neutrino Detection (SAND) The beam monitor component of the\nnear detector that remains on-axis at all times and serves as a dedicated neutrino spectrum\nmonitor. 14\u201316, 64\u201366, 69, 73, 74, 77\u201380\nSBND The Short-Baseline Near Detector experiment at Fermilab. 15\n92\n\nDUNE Phase II\nsignal feedthrough chimney (SFT chimney) A volume above the cryostat penetration\nused for a signal feedthrough. 31\nsilicon photomultiplier (SiPM) A solid-state avalanche photodiode sensitive to single pho-\ntoelectron signals. 23, 25, 34\u201336, 38, 48, 49, 58, 59, 61, 62, 71, 75\u201377, 79\nSanford Underground Low background Module (SLoMo) A dedicated low background\nfar detector module that would enhance the physics program of DUNE.. 58, 59\nStandard Model (SM) Refers to a theory describing the interaction of elementary particles.\n27\nsupernova neutrino burst (SNB) A prompt increase in the flux of low-energy neutrinos\nemitted in the first few seconds of a CCSN. It can also refer to a trigger command type\nthat may be due to this phenomenon, or detector conditions that mimic its interaction\nsignature. 12, 14, 20\u201324, 29, 45, 51, 54, 56, 57\nSuperNova Early Warning System (SNEWS) A global supernova neutrino burst trigger\nformed by a coincidence of SNB triggers collected from participating experiments. 22\nsignal-over-fiber (SoF) a technology in which a fiber optic cable carries detector output that\nhas been converted from an electrical to an optical pulse. 34, 35, 37, 39, 62\nSolar neutrinos in Liquid Argon (SoLAr) A new concept for a liquid-argon neutrino de-\ntector technology to extend the sensitivities of these devices to the MeV energy range.\n47\u201349, 61\u201364\nsingle-phase (SP) Distinguishes a LArTPC technology by the fact that it operates using\nargon in its liquid phase only; a legacy DUNE term now replaced by horizontal drift and\nvertical drift. 29\nSolenoid with Partial return Yoke (SPY) Magnet concept currently envisaged to mag-\nnetize ND-GAr.. 72\u201374\nStraw Tube Tracker (STT) Target/tracker system that is part of the SAND near detector..\n79, 80\nSanford Underground Research Facility (SURF) SURF is an underground laboratory\nin Lead, South Dakota, where the DUNE FD will be installed and operated. It is the\ndeepest underground laboratory in the United States.. 12, 39, 57\nT2K T2K (Tokai to Kamioka) is a long-baseline neutrino experiment in Japan studying neu-\ntrino oscillations. 71, 82\nTDE top detector electronics. 31\nThick GEM (THGEM) High-gain gaseous electron multiplier. 45, 46, 61, 69, 70, 76\n93\n\nDUNE Phase II\nTetra-methyl-germanium (TMG) A photosensitive hydrocarbon capable of converting VUV\nscintillation light into ionization charge in a LAr detector.. 52\nMuon Spectrometer (TMS) A muon spectrometer for the Near Detector that will be in-\nstalled for the initial running period of DUNE, before the multi-purpose detector (MPD)\ndetector component is ready. 13, 15, 16, 20, 28, 64\u201366, 81\nTest stand of an Overpressure Argon Detector (TOAD) A test of a high-pressure gaseous\nargon TPC in the Fermilab Test Beam Facility FTBF. 69, 76\ntetra-phenyl butadiene (TPB) A WLS material. 45\ntime projection chamber (TPC) Depending on context: (1) A type of particle detector\nthat uses an E field together with a sensitive volume of gas or liquid, e.g., LAr, to perform\na 3D reconstruction of a particle trajectory or interaction. The activity is recorded by\ndigitizing the waveforms of current induced on the anode as the distribution of ionization\ncharge passes by or is collected on the electrode. (2) TPC is also used in LBNF/DUNE-US\nfor \u201ctotal project cost\u201d. 15, 49, 52, 63\nTechnology Readiness Level (TRL) A method for estimating the maturity of technolo-\ngies.. 60\nvertical drift single-phase, vertical drift LArTPC technology. 13, 16, 29, 30, 37, 39, 42, 59,\n62, 64\nVUV vacuum ultra-violet. 45\u201349, 52, 61, 79\nWater-based Liquid Scintillator (WbLS) A scintillating material consisting of water loaded\nwith liquid scintillator.. 56, 82\nWater-based Near Detector (WbND) A possible DUNE Phase II near detector sub-system\nemploying water as neutrino target.. 81, 82\nweakly-interacting massive particle (WIMP) A hypothesized particle that may be a com-\nponent of dark matter. 21, 25, 59\nwavelength-shifting (WLS) A material or process by which incident photons are absorbed\nby a material and photons are emitted at a different, typically longer, wavelength. 34,\n37, 38, 71\nX-ARAPUCA Extended design with WLS coating on only the external face of the dichroic\nfilter window(s) but with a WLS doped plate inside the cell. 32\u201335, 37, 38, 49, 62, 63\n94\n\nDUNE Phase II\nReferences\n[1] T. 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Antier,37, 38 T. Apostolatos,39 E. Z. Appavuravther,40, 41 S. Appert,1 S. K. Apple,42 K. Arai,1 A. Araya,43\nM. C. Araya,1 J. S. Areeda,44 M. Ar`ene,45 N. Aritomi,20 N. Arnaud,46, 47 M. Arogeti,48 S. M. Aronson,7\nK. G. Arun,49 H. Asada,50 Y. Asali,51 G. Ashton,52 Y. Aso,53, 54 M. Assiduo,55, 56 S. Assis de Souza Melo,47\nS. M. Aston,57 P. Astone,58 F. Aubin,56 K. AultONeal,36 C. Austin,7 S. Babak,45 F. Badaracco,59\nM. K. M. Bader,60 C. Badger,61 S. Bae,62 Y. Bae,63 A. M. Baer,64 S. Bagnasco,23 Y. Bai,1 J. Baird,45 R. Bajpai,65\nT. Baka,66 M. Ball,67 G. Ballardin,47 S. W. Ballmer,68 A. Balsamo,64 G. Baltus,69 S. Banagiri,15 B. Banerjee,32\nD. Bankar,11 J. C. Barayoga,1 C. Barbieri,70, 71, 72 R. Barbieri,73 B. C. Barish,1 D. Barker,74 P. Barneo,29\nF. Barone,75, 4 B. Barr,24 L. Barsotti,76 M. Barsuglia,45 D. Barta,77 J. Bartlett,74 M. A. Barton,24 I. Bartos,78\nS. Basak,19 R. Bassiri,79 A. Basti,80, 18 M. Bawaj,40, 81 J. C. Bayley,24 M. Bazzan,82, 83 B. R. Becher,84 B. B\u00b4ecsy,85\nV. M. Bedakihale,86 F. Beirnaert,87 M. Bejger,88 I. Belahcene,46 V. Benedetto,89 D. Beniwal,90\nM. G. Benjamin,91 T. F. Bennett,92 J. D. Bentley,14 M. BenYaala,33 S. Bera,11 M. Berbel,93 F. Bergamin,9, 10\nB. K. Berger,79 S. Bernuzzi,13 C. P. L. Berry,24 D. Bersanetti,94 A. Bertolini,60 J. Betzwieser,57\nD. Beveridge,95 R. Bhandare,96 A. V. Bhandari,11 U. Bhardwaj,38, 60 R. Bhatt,1 D. Bhattacharjee,97\nS. Bhaumik,78 A. Bianchi,60, 98 I. A. Bilenko,99 G. Billingsley,1 M. Bilicki,100 S. Bini,101, 102 R. Birney,103\nO. Birnholtz,104 S. Biscans,1, 76 M. Bischi,55, 56 S. Biscoveanu,76 A. Bisht,9, 10 B. Biswas,11 M. Bitossi,47, 18\nM.-A. Bizouard,37 J. K. Blackburn,1 C. D. Blair,95 D. G. Blair,95 R. M. Blair,74 F. Bobba,105, 106 N. Bode,9, 10\nM. Bo\u00a8er,37 G. Bogaert,37 M. Boldrini,107, 58 G. N. Bolingbroke,90 L. D. Bonavena,82 F. Bondu,108 E. Bonilla,79\nR. Bonnand,30 P. Booker,9, 10 B. A. Boom,60 R. Bork,1 V. Boschi,18 N. Bose,109 S. Bose,11 V. Bossilkov,95\nV. Boudart,69 Y. Bouffanais,82, 83 A. Bozzi,47 C. Bradaschia,18 P. R. Brady,6 A. Bramley,57 A. Branch,57\nM. Branchesi,32, 110 J. E. Brau,67 M. Breschi,13 T. Briant,111 J. H. Briggs,24 A. Brillet,37 M. Brinkmann,9, 10\nP. Brockill,6 A. F. Brooks,1 J. Brooks,47 D. D. Brown,90 S. Brunett,1 G. Bruno,59 R. Bruntz,64 J. Bryant,14\nF. Bucci,56 T. Bulik,112 H. J. Bulten,60 A. Buonanno,113, 73 K. Burtnyk,74 R. Buscicchio,14 D. Buskulic,30\nC. Buy,114 R. L. Byer,79 G. S. Cabourn Davies,52 G. Cabras,34, 35 R. Cabrita,59 L. Cadonati,48 M. Caesar,115\nG. Cagnoli,26 C. Cahillane,74 J. Calder\u00b4on Bustillo,116 J. D. Callaghan,24 T. A. Callister,117, 118 E. Calloni,25, 4\nJ. Cameron,95 J. B. Camp,119 M. Canepa,120, 94 S. Canevarolo,66 M. Cannavacciuolo,105 K. C. Cannon,28 H. Cao,90\nZ. Cao,121 E. Capocasa,45, 20 E. Capote,68 G. Carapella,105, 106 F. Carbognani,47 M. Carlassara,9, 10\nJ. B. Carlin,122 M. F. Carney,15 M. Carpinelli,123, 124, 47 G. Carrillo,67 G. Carullo,80, 18 T. L. Carver,17\nJ. Casanueva Diaz,47 C. Casentini,125, 126 G. Castaldi,127 S. Caudill,60, 66 M. Cavagli`a,97 F. Cavalier,46\nR. Cavalieri,47 G. Cella,18 P. Cerd\u00b4a-Dur\u00b4an,128 E. Cesarini,126 W. Chaibi,37 S. Chalathadka Subrahmanya,129\nE. Champion,130 C.-H. Chan,131 C. Chan,28 C. L. Chan,132 K. Chan,132 M. Chan,133 K. Chandra,109 I. P. Chang,131\nP. Chanial,47 S. Chao,131 C. Chapman-Bird,24 P. Charlton,134 E. A. Chase,15 E. Chassande-Mottin,45\nC. Chatterjee,95 Debarati Chatterjee,11 Deep Chatterjee,6 M. Chaturvedi,96 S. Chaty,45 K. Chatziioannou,1\nC. Chen,135, 136 D. Chen,53 H. Y. Chen,76 J. Chen,131 K. Chen,137 X. Chen,95 Y.-B. Chen,138 Y.-R. Chen,139 Z. Chen,17\nH. Cheng,78 C. K. Cheong,132 H. Y. Cheung,132 H. Y. Chia,78 F. Chiadini,140, 106 C-Y. Chiang,141 G. Chiarini,83\nR. Chierici,142 A. Chincarini,94 M. L. Chiofalo,80, 18 A. Chiummo,47 R. K. Choudhary,95 S. Choudhary,11\nN. Christensen,37 Q. Chu,95 Y-K. Chu,141 S. S. Y. Chua,8 K. W. Chung,61 G. Ciani,82, 83 P. Ciecielag,88\nM. Cie\u00b4slar,88 M. Cifaldi,125, 126 A. A. Ciobanu,90 R. Ciolfi,143, 83 F. Cipriano,37 F. Clara,74 J. A. Clark,1, 48\nP. Clearwater,144 S. Clesse,145 F. Cleva,37 E. Coccia,32, 110 E. Codazzo,32 P.-F. Cohadon,111 D. E. Cohen,46\nM. Colleoni,146 C. G. Collette,147 A. Colombo,70, 71 M. Colpi,70, 71 C. M. Compton,74 M. Constancio Jr.,16\nL. Conti,83 S. J. Cooper,14 P. Corban,57 T. R. Corbitt,7 I. Cordero-Carri\u00b4on,148 S. Corezzi,81, 40 K. R. Corley,51\nN. J. Cornish,85 D. Corre,46 A. Corsi,149 S. Cortese,47 C. A. Costa,16 R. Cotesta,73 R. Cottingham,57\nM. W. Coughlin,150 J.-P. Coulon,37 S. T. Countryman,51 B. Cousins,151 P. Couvares,1 D. M. Coward,95\nM. J. Cowart,57 D. C. Coyne,1 R. Coyne,152 J. D. E. Creighton,6 T. D. Creighton,91 A. W. Criswell,150\nM. Croquette,111 S. G. Crowder,153 J. R. Cudell,69 T. J. Cullen,7 A. Cumming,24 R. Cummings,24\nL. Cunningham,24 E. Cuoco,47, 154, 18 M. Cury lo,112 P. Dabadie,26 T. Dal Canton,46 S. Dall\u2019Osso,32 G. D\u00b4alya,87, 155\nA. Dana,79 B. D\u2019Angelo,120, 94 S. Danilishin,156, 60 S. D\u2019Antonio,126 K. Danzmann,9, 10 C. Darsow-Fromm,129\nA. Dasgupta,86 L. E. H. Datrier,24 Sayak Datta,11 Sayantani Datta,49 V. Dattilo,47 I. Dave,96 M. Davier,46\nD. Davis,1 M. C. Davis,115 E. J. Daw,157 P. F. De Alarc\u2019on,158 R. Dean,115 D. DeBra,79 M. Deenadayalan,11\nJ. Degallaix,159 M. De Laurentis,25, 4 S. Del\u00b4eglise,111 V. Del Favero,130 F. De Lillo,59 N. De Lillo,24\nD. Dell\u2019Aquila,123 W. Del Pozzo,80, 18 L. M. DeMarchi,15 F. De Matteis,125, 126 V. D\u2019Emilio,17 N. Demos,76\narXiv:2111.03604v2 [astro-ph.CO] 19 Nov 2021\n\n2\nAbbott et al.\nT. Dent,116 A. Depasse,59 R. De Pietri,160, 161 R. De Rosa,25, 4 C. De Rossi,47 R. DeSalvo,127, 162 R. De Simone,140\nS. Dhurandhar,11 M. C. D\u00b4\u0131az,91 N. A. Didio,68 T. Dietrich,73 L. Di Fiore,4 C. Di Fronzo,14 C. Di Giorgio,105, 106\nF. Di Giovanni,128 M. Di Giovanni,32 T. Di Girolamo,25, 4 A. Di Lieto,80, 18 A. Di Michele,81 B. Ding,147\nS. Di Pace,107, 58 I. Di Palma,107, 58 F. Di Renzo,80, 18 A. K. Divakarla,78 A. Dmitriev,14 Z. Doctor,15 L. Donahue,163\nL. D\u2019Onofrio,25, 4 F. Donovan,76 K. L. Dooley,17 S. Doravari,11 M. Drago,107, 58 J. C. Driggers,74 Y. Drori,1\nJ.-G. Ducoin,46 P. Dupej,24 U. Dupletsa,32 O. Durante,105, 106 D. D\u2019Urso,123, 124 P.-A. Duverne,46 S. E. Dwyer,74\nC. Eassa,74 P. J. Easter,5 M. Ebersold,164 T. Eckhardt,129 G. Eddolls,24 B. Edelman,67 T. B. Edo,1 O. Edy,52\nA. Effler,57 S. Eguchi,133 J. Eichholz,8 S. S. Eikenberry,78 M. Eisenmann,30, 20 R. A. Eisenstein,76 A. Ejlli,17\nE. Engelby,44 Y. Enomoto,27 L. Errico,25, 4 R. C. Essick,165 H. Estell\u00b4es,146 D. Estevez,166 Z. Etienne,167\nT. Etzel,1 M. Evans,76 T. M. Evans,57 T. Evstafyeva,12 B. E. Ewing,151 F. Fabrizi,55, 56 F. Faedi,56\nV. Fafone,125, 126, 32 H. Fair,68 S. Fairhurst,17 P. C. Fan,163 A. M. Farah,168 S. Farinon,94 B. Farr,67\nW. M. Farr,117, 118 E. J. Fauchon-Jones,17 G. Favaro,82 M. Favata,169 M. Fays,69 M. Fazio,170 J. Feicht,1\nM. M. Fejer,79 E. Fenyvesi,77, 171 D. L. Ferguson,172 A. Fernandez-Galiana,76 I. Ferrante,80, 18 T. A. Ferreira,16\nF. Fidecaro,80, 18 P. Figura,112 A. Fiori,18, 80 I. Fiori,47 M. Fishbach,15 R. P. Fisher,64 R. Fittipaldi,173, 106\nV. Fiumara,174, 106 R. Flaminio,30, 20 E. Floden,150 H. K. Fong,28 J. A. Font,128, 175 B. Fornal,162 P. W. F. Forsyth,8\nA. Franke,129 S. Frasca,107, 58 F. Frasconi,18 J. P. Freed,36 Z. Frei,155 A. Freise,60, 98 O. Freitas,176 R. Frey,67\nP. Fritschel,76 V. V. Frolov,57 G. G. Fronz\u00b4e,23 Y. Fujii,177 Y. Fujikawa,178 Y. Fujimoto,179 P. Fulda,78\nM. Fyffe,57 H. A. Gabbard,24 B. U. Gadre,73 J. R. Gair,73 J. Gais,132 S. Galaudage,5 R. Gamba,13\nD. Ganapathy,76 A. Ganguly,11 D. Gao,180 S. G. Gaonkar,11 B. Garaventa,94, 120 C. Garc\u00b4\u0131a N\u00b4u\u02dcnez,103\nC. Garc\u00b4\u0131a-Quir\u00b4os,146 F. Garufi,25, 4 B. Gateley,74 V. Gayathri,78 G.-G. Ge,180 G. Gemme,94 A. Gennai,18\nJ. George,96 O. Gerberding,129 L. Gergely,181 P. Gewecke,129 S. Ghonge,48 Abhirup Ghosh,73 Archisman Ghosh,87\nShaon Ghosh,169 Shrobana Ghosh,17 Tathagata Ghosh,11 B. Giacomazzo,70, 71, 72 L. Giacoppo,107, 58 J. A. Giaime,7, 57\nK. D. Giardina,57 D. R. Gibson,103 C. Gier,33 M. Giesler,182 P. Giri,18, 80 F. Gissi,89 S. Gkaitatzis,18, 80 J. Glanzer,7\nA. E. Gleckl,44 P. Godwin,151 E. Goetz,183 R. Goetz,78 N. Gohlke,9, 10 J. Golomb,1 B. Goncharov,32\nG. Gonz\u00b4alez,7 M. Gosselin,47 R. Gouaty,30 D. W. Gould,8 S. Goyal,19 B. Grace,8 A. Grado,184, 4 V. Graham,24\nM. Granata,159 V. Granata,105 A. Grant,24 S. Gras,76 P. Grassia,1 C. Gray,74 R. Gray,24 G. Greco,40\nA. C. Green,78 R. Green,17 A. M. Gretarsson,36 E. M. Gretarsson,36 D. Griffith,1 W. L. Griffiths,17\nH. L. Griggs,48 G. Grignani,81, 40 A. Grimaldi,101, 102 E. Grimes,36 S. J. Grimm,32, 110 H. Grote,17 S. Grunewald,73\nP. Gruning,46 A. S. Gruson,44 D. Guerra,128 G. M. Guidi,55, 56 A. R. Guimaraes,7 G. Guix\u00b4e,29 H. K. Gulati,86\nA. M. Gunny,76 H.-K. Guo,162 Y. Guo,60 Anchal Gupta,1 Anuradha Gupta,185 I. M. Gupta,151 P. Gupta,60, 66\nS. K. Gupta,109 R. Gustafson,186 F. Guzman,187 S. Ha,188 I. P. W. Hadiputrawan,137 L. Haegel,45 S. Haino,141\nO. Halim,35 E. D. Hall,76 E. Z. Hamilton,164 G. Hammond,24 W.-B. Han,189 M. Haney,164 J. Hanks,74 C. Hanna,151\nM. D. Hannam,17 O. Hannuksela,66, 60 H. Hansen,74 T. J. Hansen,36 J. Hanson,57 T. Harder,37 K. Haris,60, 66\nJ. Harms,32, 110 G. M. Harry,42 I. W. Harry,52 D. Hartwig,129 K. Hasegawa,190 B. Haskell,88 C.-J. Haster,76\nJ. S. Hathaway,130 K. Hattori,191 K. Haughian,24 H. Hayakawa,192 K. Hayama,133 F. J. Hayes,24 J. Healy,130\nA. Heidmann,111 A. Heidt,9, 10 M. C. Heintze,57 J. Heinze,9, 10 J. Heinzel,76 H. Heitmann,37 F. Hellman,193\nP. Hello,46 A. F. Helmling-Cornell,67 G. Hemming,47 M. Hendry,24 I. S. Heng,24 E. Hennes,60 J. Hennig,194\nM. H. Hennig,194 C. Henshaw,48 A. G. Hernandez,92 F. Hernandez Vivanco,5 M. Heurs,9, 10 A. L. Hewitt,195\nS. Higginbotham,17 S. Hild,156, 60 P. Hill,33 Y. Himemoto,196 A. S. Hines,187 N. Hirata,20 C. Hirose,178 T-C. Ho,137\nS. Hochheim,9, 10 D. Hofman,159 J. N. Hohmann,129 D. G. Holcomb,115 N. A. Holland,8 I. J. Hollows,157\nZ. J. Holmes,90 K. Holt,57 D. E. Holz,168 Q. Hong,131 J. Hough,24 S. Hourihane,1 E. J. Howell,95 C. G. Hoy,17\nD. Hoyland,14 A. Hreibi,9, 10 B-H. Hsieh,190 H-F. Hsieh,197 C. Hsiung,135 Y. Hsu,131 H-Y. Huang,141 P. Huang,180\nY-C. Huang,139 Y.-J. Huang,141 Yiting Huang,153 Yiwen Huang,76 M. T. H\u00a8ubner,5 A. D. Huddart,198 B. Hughey,36\nD. C. Y. Hui,199 V. Hui,30 S. Husa,146 S. H. Huttner,24 R. Huxford,151 T. Huynh-Dinh,57 S. Ide,200 B. Idzkowski,112\nA. Iess,125, 126 K. Inayoshi,201 Y. Inoue,137 P. Iosif,202 M. Isi,76 K. Isleif,129 K. Ito,203 Y. Itoh,179, 204 B. R. Iyer,19\nV. JaberianHamedan,95 T. Jacqmin,111 P.-E. Jacquet,111 S. J. Jadhav,205 S. P. Jadhav,11 T. Jain,12 A. L. James,17\nA. Z. Jan,172 K. Jani,206 J. Janquart,66, 60 K. Janssens,207, 37 N. N. Janthalur,205 P. Jaranowski,208 D. Jariwala,78\nR. Jaume,146 A. C. Jenkins,61 K. Jenner,90 C. Jeon,209 W. Jia,76 J. Jiang,78 H.-B. Jin,210, 211 G. R. Johns,64\nR. Johnston,24 A. W. Jones,95 D. I. Jones,212 P. Jones,14 R. Jones,24 P. Joshi,151 L. Ju,95 A. Jue,162 P. Jung,63\nK. Jung,188 J. Junker,9, 10 V. Juste,166 K. Kaihotsu,203 T. Kajita,213 M. Kakizaki,191 C. V. Kalaghatgi,17, 66, 60, 214\nV. Kalogera,15 B. Kamai,1 M. Kamiizumi,192 N. Kanda,179, 204 S. Kandhasamy,11 G. Kang,215 J. B. Kanner,1\nY. Kao,131 S. J. Kapadia,19 D. P. Kapasi,8 C. Karathanasis,31 S. Karki,97 R. Kashyap,151 M. Kasprzack,1\nW. Kastaun,9, 10 T. Kato,190 S. Katsanevas,47 E. Katsavounidis,76 W. Katzman,57 T. Kaur,95 K. Kawabe,74\nK. Kawaguchi,190 F. K\u00b4ef\u00b4elian,37 D. Keitel,146 J. S. Key,216 S. Khadka,79 F. Y. Khalili,99 S. Khan,17 T. Khanam,149\nE. A. Khazanov,217 N. Khetan,32, 110 M. Khursheed,96 N. Kijbunchoo,8 A. Kim,15 C. Kim,209 J. C. Kim,218 J. Kim,219\nK. Kim,209 W. S. Kim,63 Y.-M. Kim,188 C. Kimball,15 N. Kimura,192 M. Kinley-Hanlon,24 R. Kirchhoff,9, 10\nJ. S. Kissel,74 S. Klimenko,78 T. Klinger,12 A. M. Knee,183 T. D. Knowles,167 N. Knust,9, 10 E. Knyazev,76\nY. Kobayashi,179 P. Koch,9, 10 G. Koekoek,60, 156 K. Kohri,220 K. Kokeyama,221 S. Koley,32 P. Kolitsidou,17\nM. Kolstein,31 K. Komori,76 V. Kondrashov,1 A. K. H. Kong,197 A. Kontos,84 N. Koper,9, 10 M. Korobko,129\nM. Kovalam,95 N. Koyama,178 D. B. Kozak,1 C. Kozakai,53 V. Kringel,9, 10 A. Kr\u00b4olak,222, 223 G. Kuehn,9, 10\nF. Kuei,131 P. Kuijer,60 S. Kulkarni,185 A. Kumar,205 Prayush Kumar,19 Rahul Kumar,74 Rakesh Kumar,86\nJ. Kume,28 K. Kuns,76 Y. Kuromiya,203 S. Kuroyanagi,224, 225 K. Kwak,188 G. Lacaille,24 P. Lagabbe,30 D. Laghi,114\n\nConstraints on the cosmic expansion history from GWTC\u20133\n3\nE. Lalande,226 M. Lalleman,207 T. L. Lam,132 A. Lamberts,37, 227 M. Landry,74 B. B. Lane,76 R. N. Lang,76\nJ. Lange,172 B. Lantz,79 I. La Rosa,30 A. Lartaux-Vollard,46 P. D. Lasky,5 M. Laxen,57 A. Lazzarini,1\nC. Lazzaro,82, 83 P. Leaci,107, 58 S. Leavey,9, 10 S. LeBohec,162 Y. K. Lecoeuche,183 E. Lee,190 H. M. Lee,228\nH. W. Lee,218 K. Lee,229 R. Lee,139 I. N. Legred,1 J. Lehmann,9, 10 A. Lema\u02c6\u0131tre,230 M. Lenti,56, 231 M. Leonardi,20\nE. Leonova,38 N. Leroy,46 N. Letendre,30 C. Levesque,226 Y. Levin,5 J. N. Leviton,186 K. Leyde,45 A. K. Y. Li,1\nB. Li,131 J. Li,15 K. L. Li,232 P. Li,233 T. G. F. Li,132 X. Li,138 C-Y. Lin,234 E. T. Lin,197 F-K. Lin,141 F-L. Lin,235\nH. L. Lin,137 L. C.-C. Lin,232 F. Linde,214, 60 S. D. Linker,127, 92 J. N. Linley,24 T. B. Littenberg,236 G. C. Liu,135\nJ. Liu,95 K. Liu,131 X. Liu,6 F. Llamas,91 R. K. L. Lo,1 T. Lo,131 L. T. London,38, 76 A. Longo,237 D. Lopez,164\nM. Lopez Portilla,66 M. Lorenzini,125, 126 V. Loriette,238 M. Lormand,57 G. Losurdo,18 T. P. Lott,48\nJ. D. Lough,9, 10 C. O. Lousto,130 G. Lovelace,44 J. F. Lucaccioni,239 H. L\u00a8uck,9, 10 D. Lumaca,125, 126\nA. P. Lundgren,52 L.-W. Luo,141 J. E. Lynam,64 M. Ma\u2019arif,137 R. Macas,52 J. B. Machtinger,15 M. MacInnis,76\nD. M. Macleod,17 I. A. O. MacMillan,1 A. Macquet,37 I. Maga\u02dcna Hernandez,6 C. Magazz`u,18 R. M. Magee,1\nR. Maggiore,14 M. Magnozzi,94, 120 S. Mahesh,167 E. Majorana,107, 58 I. Maksimovic,238 S. Maliakal,1 A. Malik,96\nN. Man,37 V. Mandic,150 V. Mangano,107, 58 G. L. Mansell,74, 76 M. Manske,6 M. Mantovani,47 M. Mapelli,82, 83\nF. Marchesoni,41, 40, 240 D. Mar\u00b4\u0131n Pina,29 F. Marion,30 Z. Mark,138 S. M\u00b4arka,51 Z. M\u00b4arka,51 C. Markakis,12\nA. S. Markosyan,79 A. Markowitz,1 E. Maros,1 A. Marquina,148 S. Marsat,45 F. Martelli,55, 56 I. W. Martin,24\nR. M. Martin,169 M. Martinez,31 V. A. Martinez,78 V. Martinez,26 K. Martinovic,61 D. V. Martynov,14\nE. J. Marx,76 H. Masalehdan,129 K. Mason,76 E. Massera,157 A. Masserot,30 M. Masso-Reid,24\nS. Mastrogiovanni,45 A. Matas,73 M. Mateu-Lucena,146 F. Matichard,1, 76 M. Matiushechkina,9, 10 N. Mavalvala,76\nJ. J. McCann,95 R. McCarthy,74 D. E. McClelland,8 P. K. McClincy,151 S. McCormick,57 L. McCuller,76\nG. I. McGhee,24 S. C. McGuire,57 C. McIsaac,52 J. McIver,183 T. McRae,8 S. T. McWilliams,167 D. Meacher,6\nM. Mehmet,9, 10 A. K. Mehta,73 Q. Meijer,66 A. Melatos,122 D. A. Melchor,44 G. Mendell,74\nA. Menendez-Vazquez,31 C. S. Menoni,170 R. A. Mercer,6 L. Mereni,159 K. Merfeld,67 E. L. Merilh,57\nJ. D. Merritt,67 M. Merzougui,37 S. Meshkov,1, \u2217C. Messenger,24 C. Messick,76 P. M. Meyers,122 F. Meylahn,9, 10\nA. Mhaske,11 A. Miani,101, 102 H. Miao,14 I. Michaloliakos,78 C. Michel,159 Y. Michimura,27 H. Middleton,122\nD. P. Mihaylov,73 L. Milano,25, \u2020 A. L. Miller,59 A. Miller,92 B. Miller,38, 60 M. Millhouse,122 J. C. Mills,17\nE. Milotti,241, 35 Y. Minenkov,126 N. Mio,242 Ll. M. Mir,31 M. Miravet-Ten\u00b4es,128 A. Mishkin,78 C. Mishra,243\nT. Mishra,78 T. Mistry,157 S. Mitra,11 V. P. Mitrofanov,99 G. Mitselmakher,78 R. Mittleman,76 O. Miyakawa,192\nK. Miyo,192 S. Miyoki,192 Geoffrey Mo,76 L. M. Modafferi,146 E. Moguel,239 K. Mogushi,97 S. R. P. Mohapatra,76\nS. R. Mohite,6 I. Molina,44 M. Molina-Ruiz,193 M. Mondin,92 M. Montani,55, 56 C. J. Moore,14 J. Moragues,146\nD. Moraru,74 F. Morawski,88 A. More,11 S. More,11, 244 C. Moreno,36 G. Moreno,74 Y. Mori,203 S. Morisaki,6\nN. Morisue,179 Y. Moriwaki,191 B. Mours,166 C. M. Mow-Lowry,60, 98 S. Mozzon,52 F. Muciaccia,107, 58\nArunava Mukherjee,245 D. Mukherjee,151 Soma Mukherjee,91 Subroto Mukherjee,86 Suvodip Mukherjee,165, 38\nN. Mukund,9, 10 A. Mullavey,57 J. Munch,90 E. A. Mu\u02dcniz,68 P. G. Murray,24 R. Musenich,94, 120 S. Muusse,90\nS. L. Nadji,9, 10 K. Nagano,246 A. Nagar,23, 247 K. Nakamura,20 H. Nakano,248 M. Nakano,190 Y. Nakayama,203\nV. Napolano,47 I. Nardecchia,125, 126 T. Narikawa,190 H. Narola,66 L. Naticchioni,58 B. Nayak,92 R. K. Nayak,249\nB. F. Neil,95 J. Neilson,89, 106 A. Nelson,187 T. J. N. Nelson,57 M. Nery,9, 10 P. Neubauer,239 A. Neunzert,216\nK. Y. Ng,76 S. W. S. Ng,90 C. Nguyen,45 P. Nguyen,67 T. Nguyen,76 L. Nguyen Quynh,250 J. Ni,150\nW.-T. Ni,210, 180, 139 S. A. Nichols,7 T. Nishimoto,190 A. Nishizawa,28 S. Nissanke,38, 60 E. Nitoglia,142 F. Nocera,47\nM. Norman,17 C. North,17 S. Nozaki,191 G. Nurbek,91 L. K. Nuttall,52 Y. Obayashi,190 J. Oberling,74\nB. D. O\u2019Brien,78 J. O\u2019Dell,198 E. Oelker,24 W. Ogaki,190 G. Oganesyan,32, 110 J. J. Oh,63 K. Oh,199 S. H. Oh,63\nM. Ohashi,192 T. Ohashi,179 M. Ohkawa,178 F. Ohme,9, 10 H. Ohta,28 M. A. Okada,16 Y. Okutani,200 C. Olivetto,47\nK. Oohara,190, 251 R. Oram,57 B. O\u2019Reilly,57 R. G. Ormiston,150 N. D. Ormsby,64 R. O\u2019Shaughnessy,130\nE. O\u2019Shea,182 S. Oshino,192 S. Ossokine,73 C. Osthelder,1 S. Otabe,2 D. J. Ottaway,90 H. Overmier,57\nA. E. Pace,151 G. Pagano,80, 18 R. Pagano,7 M. A. Page,95 G. Pagliaroli,32, 110 A. Pai,109 S. A. Pai,96 S. Pal,249\nJ. R. Palamos,67 O. Palashov,217 C. Palomba,58 H. Pan,131 K.-C. Pan,139, 197 P. K. Panda,205 P. T. H. Pang,60, 66\nC. Pankow,15 F. Pannarale,107, 58 B. C. Pant,96 F. H. Panther,95 F. Paoletti,18 A. Paoli,47 A. Paolone,58, 252\nG. Pappas,202 A. Parisi,135 H. Park,6 J. Park,253 W. Parker,57 D. Pascucci,60, 87 A. Pasqualetti,47\nR. Passaquieti,80, 18 D. Passuello,18 M. Patel,64 M. Pathak,90 B. Patricelli,47, 18 A. S. Patron,7 S. Paul,67\nE. Payne,5 M. Pedraza,1 R. Pedurand,106 M. Pegoraro,83 A. Pele,57 F. E. Pe\u02dcna Arellano,192 S. Penano,79\nS. Penn,254 A. Perego,101, 102 A. Pereira,26 T. Pereira,255 C. J. Perez,74 C. P\u00b4erigois,30 C. C. Perkins,78\nA. Perreca,101, 102 S. Perri`es,142 D. Pesios,202 J. Petermann,129 D. Petterson,1 H. P. Pfeiffer,73 H. Pham,57\nK. A. Pham,150 K. S. Phukon,60, 214 H. Phurailatpam,132 O. J. Piccinni,58 M. Pichot,37 M. Piendibene,80, 18\nF. Piergiovanni,55, 56 L. Pierini,107, 58 V. Pierro,89, 106 G. Pillant,47 M. Pillas,46 F. Pilo,18 L. Pinard,159\nC. Pineda-Bosque,92 I. M. Pinto,89, 106, 256 M. Pinto,47 B. J. Piotrzkowski,6 K. Piotrzkowski,59 M. Pirello,74\nM. D. Pitkin,195 A. Placidi,40, 81 E. Placidi,107, 58 M. L. Planas,146 W. Plastino,257, 237 C. Pluchar,258\nR. Poggiani,80, 18 E. Polini,30 D. Y. T. Pong,132 S. Ponrathnam,11 E. K. Porter,45 R. Poulton,47 A. Poverman,84\nJ. Powell,144 M. Pracchia,30 T. Pradier,166 A. K. Prajapati,86 K. Prasai,79 R. Prasanna,205 G. Pratten,14\nM. Principe,89, 256, 106 G. A. Prodi,259, 102 L. Prokhorov,14 P. Prosposito,125, 126 L. Prudenzi,73 A. Puecher,60, 66\nM. Punturo,40 F. Puosi,18, 80 P. Puppo,58 M. P\u00a8urrer,73 H. Qi,17 N. Quartey,64 V. Quetschke,91 P. J. Quinonez,36\nR. Quitzow-James,97 F. J. Raab,74 G. Raaijmakers,38, 60 H. Radkins,74 N. Radulesco,37 P. Raffai,155 S. X. Rail,226\nS. Raja,96 C. Rajan,96 K. E. Ramirez,57 T. D. Ramirez,44 A. Ramos-Buades,73 J. Rana,151 P. Rapagnani,107, 58\n\n4\nAbbott et al.\nA. Ray,6 V. Raymond,17 N. Raza,183 M. Razzano,80, 18 J. Read,44 L. A. Rees,42 T. Regimbau,30 L. Rei,94 S. Reid,33\nS. W. Reid,64 D. H. Reitze,1, 78 P. Relton,17 A. Renzini,1 P. Rettegno,22, 23 B. Revenu,260 A. Reza,60 M. Rezac,44\nF. Ricci,107, 58 D. Richards,198 J. W. Richardson,261 L. Richardson,187 G. Riemenschneider,22, 23 K. Riles,186\nS. Rinaldi,80, 18 K. Rink,183 N. A. Robertson,1 R. Robie,1 F. Robinet,46 A. Rocchi,126 S. Rodriguez,44 L. Rolland,30\nJ. G. Rollins,1 M. Romanelli,108 R. Romano,3, 4 C. L. Romel,74 A. Romero,31 I. M. Romero-Shaw,5 J. H. Romie,57\nS. Ronchini,32, 110 L. Rosa,4, 25 C. A. Rose,6 D. Rosi\u00b4nska,112 M. P. Ross,262 S. Rowan,24 S. J. Rowlinson,14 S. Roy,66\nSantosh Roy,11 Soumen Roy,263 D. Rozza,123, 124 P. Ruggi,47 K. Ruiz-Rocha,206 K. Ryan,74 S. Sachdev,151\nT. Sadecki,74 J. Sadiq,116 S. Saha,197 Y. Saito,192 K. Sakai,264 M. Sakellariadou,61 S. Sakon,151\nO. S. Salafia,72, 71, 70 F. Salces-Carcoba,1 L. Salconi,47 M. Saleem,150 F. Salemi,101, 102 A. Samajdar,71\nE. J. Sanchez,1 J. H. Sanchez,44 L. E. Sanchez,1 N. Sanchis-Gual,265 J. R. Sanders,266 A. Sanuy,29\nT. R. Saravanan,11 N. Sarin,5 B. Sassolas,159 H. Satari,95 B. S. Sathyaprakash,151, 17 O. Sauter,78 R. L. Savage,74\nV. Savant,11 T. Sawada,179 H. L. Sawant,11 S. Sayah,159 D. Schaetzl,1 M. Scheel,138 J. Scheuer,15\nM. G. Schiworski,90 P. Schmidt,14 S. Schmidt,66 R. Schnabel,129 M. Schneewind,9, 10 R. M. S. Schofield,67\nA. Sch\u00a8onbeck,129 B. W. Schulte,9, 10 B. F. Schutz,17, 9, 10 E. Schwartz,17 J. Scott,24 S. M. Scott,8\nM. Seglar-Arroyo,30 Y. Sekiguchi,267 D. Sellers,57 A. S. Sengupta,263 D. Sentenac,47 E. G. Seo,132 V. Sequino,25, 4\nA. Sergeev,217 Y. Setyawati,9, 10, 66 T. Shaffer,74 M. S. Shahriar,15 M. A. Shaikh,19 B. Shams,162 L. Shao,201\nA. Sharma,32, 110 P. Sharma,96 P. Shawhan,113 N. S. Shcheblanov,230 A. Sheela,243 Y. Shikano,268, 269\nM. Shikauchi,28 H. Shimizu,270 K. Shimode,192 H. Shinkai,271 T. Shishido,54 A. Shoda,20 D. H. Shoemaker,76\nD. M. Shoemaker,172 S. ShyamSundar,96 M. Sieniawska,59 D. Sigg,74 L. Silenzi,40, 41 L. P. Singer,119 D. Singh,151\nM. K. Singh,19 N. Singh,112 A. Singha,156, 60 A. M. Sintes,146 V. Sipala,123, 124 V. Skliris,17 B. J. J. Slagmolen,8\nT. J. Slaven-Blair,95 J. Smetana,14 J. R. Smith,44 L. Smith,24 R. J. E. Smith,5 J. Soldateschi,231, 272, 56\nS. N. Somala,273 K. Somiya,2 I. Song,197 K. Soni,11 V. Sordini,142 F. Sorrentino,94 N. Sorrentino,80, 18\nR. Soulard,37 T. Souradeep,274, 11 E. Sowell,149 V. Spagnuolo,156, 60 A. P. Spencer,24 M. Spera,82, 83 P. Spinicelli,47\nA. K. Srivastava,86 V. Srivastava,68 K. Staats,15 C. Stachie,37 F. Stachurski,24 D. A. Steer,45\nJ. Steinlechner,156, 60 S. Steinlechner,156, 60 N. Stergioulas,202 D. J. Stops,14 M. Stover,239 K. A. Strain,24\nL. C. Strang,122 G. Stratta,275, 58 M. D. Strong,7 A. Strunk,74 R. Sturani,255 A. L. Stuver,115 M. Suchenek,88\nS. Sudhagar,11 V. Sudhir,76 R. Sugimoto,276, 246 H. G. Suh,6 A. G. Sullivan,51 T. Z. Summerscales,277 L. Sun,8\nS. Sunil,86 A. Sur,88 J. Suresh,28 P. J. Sutton,17 Takamasa Suzuki,178 Takanori Suzuki,2 Toshikazu Suzuki,190\nB. L. Swinkels,60 M. J. Szczepa\u00b4nczyk,78 P. Szewczyk,112 M. Tacca,60 H. Tagoshi,190 S. C. Tait,24 H. Takahashi,278\nR. Takahashi,20 S. Takano,27 H. Takeda,27 M. Takeda,179 C. J. Talbot,33 C. Talbot,1 N. Tamanini,279\nK. Tanaka,280 Taiki Tanaka,190 Takahiro Tanaka,281 A. J. Tanasijczuk,59 S. Tanioka,192 D. B. Tanner,78 D. Tao,1\nL. Tao,78 R. D. Tapia,151 E. N. Tapia San Mart\u00b4\u0131n,60 C. Taranto,125 A. Taruya,282 J. D. Tasson,163 R. Tenorio,146\nJ. E. S. Terhune,115 L. Terkowski,129 M. P. Thirugnanasambandam,11 M. Thomas,57 P. Thomas,74\nE. E. Thompson,48 J. E. Thompson,17 S. R. Thondapu,96 K. A. Thorne,57 E. Thrane,5 Shubhanshu Tiwari,164\nSrishti Tiwari,11 V. Tiwari,17 A. M. Toivonen,150 A. E. Tolley,52 T. Tomaru,20 T. Tomura,192 M. Tonelli,80, 18\nZ. Tornasi,24 A. Torres-Forn\u00b4e,128 C. I. Torrie,1 I. Tosta e Melo,124 D. T\u00a8oyr\u00a8a,8 A. Trapananti,41, 40\nF. Travasso,40, 41 G. Traylor,57 M. Trevor,113 M. C. Tringali,47 A. Tripathee,186 L. Troiano,283, 106 A. Trovato,45\nL. Trozzo,4, 192 R. J. Trudeau,1 D. Tsai,131 K. W. Tsang,60, 284, 66 T. Tsang,285 J-S. Tsao,235 M. Tse,76 R. Tso,138\nS. Tsuchida,179 L. Tsukada,151 D. Tsuna,28 T. Tsutsui,28 K. Turbang,286, 207 M. Turconi,287 C. Turski,100, 288, 289\nD. Tuyenbayev,179 A. S. Ubhi,14 N. Uchikata,190 T. Uchiyama,192 R. P. Udall,1 A. Ueda,290 T. Uehara,291, 292\nK. Ueno,28 G. Ueshima,293 C. S. Unnikrishnan,294 A. L. Urban,7 T. Ushiba,192 A. Utina,156, 60 G. Vajente,1\nA. Vajpeyi,5 G. Valdes,187 M. Valentini,185, 101, 102 V. Valsan,6 N. van Bakel,60 M. van Beuzekom,60\nM. van Dael,60, 295 J. F. J. van den Brand,156, 98, 60 C. Van Den Broeck,66, 60 D. C. Vander-Hyde,68\nH. van Haevermaet,207 J. V. van Heijningen,59 M. H. P. M. van Putten,296 N. van Remortel,207 M. Vardaro,214, 60\nA. F. Vargas,122 V. Varma,73 M. Vas\u00b4uth,77 A. Vecchio,14 G. Vedovato,83 J. Veitch,24 P. J. Veitch,90\nJ. Venneberg,9, 10 G. Venugopalan,1 D. Verkindt,30 P. Verma,223 Y. Verma,96 S. M. Vermeulen,17 D. Veske,51\nF. Vetrano,55 A. Vicer\u00b4e,55, 56 S. Vidyant,68 A. D. Viets,297 A. Vijaykumar,19 V. Villa-Ortega,116 J.-Y. Vinet,37\nA. Virtuoso,241, 35 S. Vitale,76 H. Vocca,81, 40 E. R. G. von Reis,74 J. S. A. von Wrangel,9, 10 C. Vorvick,74\nS. P. Vyatchanin,99 L. E. Wade,239 M. Wade,239 K. J. Wagner,130 R. C. Walet,60 M. Walker,64 G. S. Wallace,33\nL. Wallace,1 J. Wang,180 J. Z. Wang,186 W. H. Wang,91 R. L. Ward,8 J. Warner,74 M. Was,30 T. Washimi,20\nN. Y. Washington,1 J. Watchi,147 B. Weaver,74 C. R. Weaving,52 S. A. Webster,24 M. Weinert,9, 10\nA. J. Weinstein,1 R. Weiss,76 C. M. Weller,262 R. A. Weller,206 F. Wellmann,9, 10 L. Wen,95 P. We\u00dfels,9, 10\nK. Wette,8 J. T. Whelan,130 D. D. White,44 B. F. Whiting,78 C. Whittle,76 D. Wilken,9, 10 D. Williams,24\nM. J. Williams,24 A. R. Williamson,52 J. L. Willis,1 B. Willke,9, 10 D. J. Wilson,258 C. C. Wipf,1\nT. Wlodarczyk,73 G. Woan,24 J. Woehler,9, 10 J. K. Wofford,130 D. Wong,183 I. C. F. Wong,132 M. Wright,24\nC. Wu,139 D. S. Wu,9, 10 H. Wu,139 D. M. Wysocki,6 L. Xiao,1 T. Yamada,270 H. Yamamoto,1 K. Yamamoto,191\nT. Yamamoto,192 K. Yamashita,203 R. Yamazaki,200 F. W. Yang,162 K. Z. Yang,150 L. Yang,170 Y.-C. Yang,131\nY. Yang,298 Yang Yang,78 M. J. Yap,8 D. W. Yeeles,17 S.-W. Yeh,139 A. B. Yelikar,130 M. Ying,131\nJ. Yokoyama,28, 27 T. Yokozawa,192 J. Yoo,182 T. Yoshioka,203 Hang Yu,138 Haocun Yu,76 H. Yuzurihara,190\nA. Zadro\u02d9zny,223 M. Zanolin,36 S. Zeidler,299 T. Zelenova,47 J.-P. Zendri,83 M. Zevin,168 M. Zhan,180 H. Zhang,235\nJ. Zhang,95 L. Zhang,1 R. Zhang,78 T. Zhang,14 Y. Zhang,187 C. Zhao,95 G. Zhao,147 Y. Zhao,190, 20 Yue Zhao,162\nR. Zhou,193 Z. Zhou,15 X. J. Zhu,5 Z.-H. Zhu,121, 233 A. B. Zimmerman,172 M. E. Zucker,1, 76 and J. Zweizig1\n\nConstraints on the cosmic expansion history from GWTC\u20133\n5\n3000\n1LIGO Laboratory, California Institute of Technology, Pasadena, CA 91125, USA\n2Graduate School of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan\n3Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n4INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n5OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia\n6University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA\n7Louisiana State University, Baton Rouge, LA 70803, USA\n8OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia\n9Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany\n10Leibniz Universit\u00a8at Hannover, D-30167 Hannover, Germany\n11Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India\n12University of Cambridge, Cambridge CB2 1TN, United Kingdom\n13Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit\u00a8at Jena, D-07743 Jena, Germany\n14University of Birmingham, Birmingham B15 2TT, United Kingdom\n15Northwestern University, Evanston, IL 60208, USA\n16Instituto Nacional de Pesquisas Espaciais, 12227-010 S\u02dcao Jos\u00b4e dos Campos, S\u02dcao Paulo, Brazil\n17Cardi\ufb00University, Cardi\ufb00CF24 3AA, United Kingdom\n18INFN, Sezione di Pisa, I-56127 Pisa, Italy\n19International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India\n20Gravitational Wave Science Project, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n21Advanced Technology Center, National Astronomical Observatory of Japan (NAOJ), Mitaka City, Tokyo 181-8588, Japan\n22Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy\n23INFN Sezione di Torino, I-10125 Torino, Italy\n24SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom\n25Universit`a di Napoli \u201cFederico II\u201d, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n26Universit\u00b4e de Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France\n27Department of Physics, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n28Research Center for the Early Universe (RESCEU), The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan\n29Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona, C/ Mart\u00b4\u0131 i Franqu`es 1, Barcelona, 08028, Spain\n30Univ. Savoie Mont Blanc, CNRS, Laboratoire d\u2019Annecy de Physique des Particules - IN2P3, F-74000 Annecy, France\n31Institut de F\u00b4\u0131sica d\u2019Altes Energies (IFAE), Barcelona Institute of Science and Technology, and ICREA, E-08193 Barcelona, Spain\n32Gran Sasso Science Institute (GSSI), I-67100 L\u2019Aquila, Italy\n33SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom\n34Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Universit`a di Udine, I-33100 Udine, Italy\n35INFN, Sezione di Trieste, I-34127 Trieste, Italy\n36Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA\n37Artemis, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n38GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics, University of Amsterdam, Science Park\n904, 1098 XH Amsterdam, Netherlands\n39National and Kapodistrian University of Athens, School of Science Building, 2nd \ufb02oor, Panepistimiopolis, 15771 Ilissia, Greece\n40INFN, Sezione di Perugia, I-06123 Perugia, Italy\n41Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy\n42American University, Washington, D.C. 20016, USA\n43Earthquake Research Institute, The University of Tokyo, Bunkyo-ku, Tokyo 113-0032, Japan\n44California State University Fullerton, Fullerton, CA 92831, USA\n45Universit\u00b4e de Paris, CNRS, Astroparticule et Cosmologie, F-75006 Paris, France\n46Universit\u00b4e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France\n47European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy\n48Georgia Institute of Technology, Atlanta, GA 30332, USA\n49Chennai Mathematical Institute, Chennai 603103, India\n50Department of Mathematics and Physics,\n51Columbia University, New York, NY 10027, USA\n52University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom\n53Kamioka Branch, National Astronomical Observatory of Japan (NAOJ), Kamioka-cho, Hida City, Gifu 506-1205, Japan\n\n6\nAbbott et al.\n54The Graduate University for Advanced Studies (SOKENDAI), Mitaka City, Tokyo 181-8588, Japan\n55Universit`a degli Studi di Urbino \u201cCarlo Bo\u201d, I-61029 Urbino, Italy\n56INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy\n57LIGO Livingston Observatory, Livingston, LA 70754, USA\n58INFN, Sezione di Roma, I-00185 Roma, Italy\n59Universit\u00b4e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium\n60Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands\n61King\u2019s College London, University of London, London WC2R 2LS, United Kingdom\n62Korea Institute of Science and Technology Information, Daejeon 34141, Republic of Korea\n63National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea\n64Christopher Newport University, Newport News, VA 23606, USA\n65School of High Energy Accelerator Science, The Graduate University for Advanced Studies (SOKENDAI), Tsukuba City, Ibaraki\n305-0801, Japan\n66Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands\n67University of Oregon, Eugene, OR 97403, USA\n68Syracuse University, Syracuse, NY 13244, USA\n69Universit\u00b4e de Li`ege, B-4000 Li`ege, Belgium\n70Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy\n71INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy\n72INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy\n73Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany\n74LIGO Hanford Observatory, Richland, WA 99352, USA\n75Dipartimento di Medicina, Chirurgia e Odontoiatria \u201cScuola Medica Salernitana\u201d, Universit`a di Salerno, I-84081 Baronissi, Salerno,\nItaly\n76LIGO Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA\n77Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl\u00b4os \u00b4ut 29-33, Hungary\n78University of Florida, Gainesville, FL 32611, USA\n79Stanford University, Stanford, CA 94305, USA\n80Universit`a di Pisa, I-56127 Pisa, Italy\n81Universit`a di Perugia, I-06123 Perugia, Italy\n82Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy\n83INFN, Sezione di Padova, I-35131 Padova, Italy\n84Bard College, Annandale-On-Hudson, NY 12504, USA\n85Montana State University, Bozeman, MT 59717, USA\n86Institute for Plasma Research, Bhat, Gandhinagar 382428, India\n87Universiteit Gent, B-9000 Gent, Belgium\n88Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland\n89Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy\n90OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia\n91The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA\n92California State University, Los Angeles, Los Angeles, CA 90032, USA\n93Departamento de Matem\u00b4aticas, Universitat Aut`onoma de Barcelona, Edi\ufb01cio C Facultad de Ciencias 08193 Bellaterra (Barcelona),\nSpain\n94INFN, Sezione di Genova, I-16146 Genova, Italy\n95OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia\n96RRCAT, Indore, Madhya Pradesh 452013, India\n97Missouri University of Science and Technology, Rolla, MO 65409, USA\n98Vrije Universiteit Amsterdam, 1081 HV Amsterdam, Netherlands\n99Lomonosov Moscow State University, Moscow 119991, Russia\n100Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u2019ow 32/46, 02-668 Warsaw, Poland\n101Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy\n102INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy\n103SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom\n104Bar-Ilan University, Ramat Gan, 5290002, Israel\n105Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n106INFN, Sezione di Napoli, Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy\n107Universit`a di Roma \u201cLa Sapienza\u201d, I-00185 Roma, Italy\n\nConstraints on the cosmic expansion history from GWTC\u20133\n7\n108Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France\n109Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India\n110INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy\n111Laboratoire Kastler Brossel, Sorbonne Universit\u00b4e, CNRS, ENS-Universit\u00b4e PSL, Coll`ege de France, F-75005 Paris, France\n112Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n113University of Maryland, College Park, MD 20742, USA\n114L2IT, Laboratoire des 2 In\ufb01nis - Toulouse, Universit\u00b4e de Toulouse, CNRS/IN2P3, UPS, F-31062 Toulouse Cedex 9, France\n115Villanova University, Villanova, PA 19085, USA\n116IGFAE, Universidade de Santiago de Compostela, 15782 Spain\n117Stony Brook University, Stony Brook, NY 11794, USA\n118Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA\n119NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\n120Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy\n121Department of Astronomy, Beijing Normal University, Beijing 100875, China\n122OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia\n123Universit`a degli Studi di Sassari, I-07100 Sassari, Italy\n124INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy\n125Universit`a di Roma Tor Vergata, I-00133 Roma, Italy\n126INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy\n127University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy\n128Departamento de Astronom\u00b4\u0131a y Astrof\u00b4\u0131sica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n129Universit\u00a8at Hamburg, D-22761 Hamburg, Germany\n130Rochester Institute of Technology, Rochester, NY 14623, USA\n131National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China\n132The Chinese University of Hong Kong, Shatin, NT, Hong Kong\n133Department of Applied Physics, Fukuoka University, Jonan, Fukuoka City, Fukuoka 814-0180, Japan\n134OzGrav, Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia\n135Department of Physics, Tamkang University, Danshui Dist., New Taipei City 25137, Taiwan\n136Department of Physics and Institute of Astronomy, National Tsing Hua University, Hsinchu 30013, Taiwan\n137Department of Physics, Center for High Energy and High Field Physics, National Central University, Zhongli District, Taoyuan City\n32001, Taiwan\n138CaRT, California Institute of Technology, Pasadena, CA 91125, USA\n139Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan\n140Dipartimento di Ingegneria Industriale (DIIN), Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n141Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan\n142Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, IP2I Lyon / IN2P3, UMR 5822, F-69622 Villeurbanne, France\n143INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy\n144OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia\n145Universit\u00b4e libre de Bruxelles, Avenue Franklin Roosevelt 50 - 1050 Bruxelles, Belgium\n146Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain\n147Universit\u00b4e Libre de Bruxelles, Brussels 1050, Belgium\n148Departamento de Matem\u00b4aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain\n149Texas Tech University, Lubbock, TX 79409, USA\n150University of Minnesota, Minneapolis, MN 55455, USA\n151The Pennsylvania State University, University Park, PA 16802, USA\n152University of Rhode Island, Kingston, RI 02881, USA\n153Bellevue College, Bellevue, WA 98007, USA\n154Scuola Normale Superiore, Piazza dei Cavalieri, 7 - 56126 Pisa, Italy\n155E\u00a8otv\u00a8os University, Budapest 1117, Hungary\n156Maastricht University, P.O. Box 616, 6200 MD Maastricht, Netherlands\n157The University of She\ufb03eld, She\ufb03eld S10 2TN, United Kingdom\n158Universitat de les Illes Balears, IAC3\u2013IEEC, E-07122 Palma de Mallorca, Spain\n159Universit\u00b4e Lyon, Universit\u00b4e Claude Bernard Lyon 1, CNRS, Laboratoire des Mat\u00b4eriaux Avanc\u00b4es (LMA), IP2I Lyon / IN2P3, UMR\n5822, F-69622 Villeurbanne, France\n160Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy\n161INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy\n162The University of Utah, Salt Lake City, UT 84112, USA\n\n8\nAbbott et al.\n163Carleton College, North\ufb01eld, MN 55057, USA\n164University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland\n165Perimeter Institute, Waterloo, ON N2L 2Y5, Canada\n166Universit\u00b4e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France\n167West Virginia University, Morgantown, WV 26506, USA\n168University of Chicago, Chicago, IL 60637, USA\n169Montclair State University, Montclair, NJ 07043, USA\n170Colorado State University, Fort Collins, CO 80523, USA\n171Institute for Nuclear Research, Bem t\u2019er 18/c, H-4026 Debrecen, Hungary\n172University of Texas, Austin, TX 78712, USA\n173CNR-SPIN, c/o Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy\n174Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy\n175Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain\n176Centro de F\u00b4\u0131sica das Universidades do Minho e do Porto, Universidade do Minho, Campus de Gualtar, PT-4710 - 057 Braga, Portugal\n177Department of Astronomy, The University of Tokyo, Mitaka City, Tokyo 181-8588, Japan\n178Faculty of Engineering, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n179Department of Physics, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka City, Osaka 558-8585, Japan\n180State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement\nScience and Technology (APM), Chinese Academy of Sciences, Xiao Hong Shan, Wuhan 430071, China\n181University of Szeged, D\u00b4om t\u00b4er 9, Szeged 6720, Hungary\n182Cornell University, Ithaca, NY 14850, USA\n183University of British Columbia, Vancouver, BC V6T 1Z4, Canada\n184INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy\n185The University of Mississippi, University, MS 38677, USA\n186University of Michigan, Ann Arbor, MI 48109, USA\n187Texas A&M University, College Station, TX 77843, USA\n188Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea\n189Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China\n190Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n191Faculty of Science, University of Toyama, Toyama City, Toyama 930-8555, Japan\n192Institute for Cosmic Ray Research (ICRR), KAGRA Observatory, The University of Tokyo, Kamioka-cho, Hida City, Gifu 506-1205,\nJapan\n193University of California, Berkeley, CA 94720, USA\n194Maastricht University, 6200 MD, Maastricht, Netherlands\n195Lancaster University, Lancaster LA1 4YW, United Kingdom\n196College of Industrial Technology, Nihon University, Narashino City, Chiba 275-8575, Japan\n197Institute of Astronomy, National Tsing Hua University, Hsinchu 30013, Taiwan\n198Rutherford Appleton Laboratory, Didcot OX11 0DE, United Kingdom\n199Department of Astronomy & Space Science, Chungnam National University, Yuseong-gu, Daejeon 34134, Republic of Korea\n200Department of Physical Sciences, Aoyama Gakuin University, Sagamihara City, Kanagawa 252-5258, Japan\n201Kavli Institute for Astronomy and Astrophysics, Peking University, Haidian District, Beijing 100871, China\n202Aristotle University of Thessaloniki, University Campus, 54124 Thessaloniki, Greece\n203Graduate School of Science and Engineering, University of Toyama, Toyama City, Toyama 930-8555, Japan\n204Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Sumiyoshi-ku, Osaka City, Osaka\n558-8585, Japan\n205Directorate of Construction, Services & Estate Management, Mumbai 400094, India\n206Vanderbilt University, Nashville, TN 37235, USA\n207Universiteit Antwerpen, Prinsstraat 13, 2000 Antwerpen, Belgium\n208University of Bia lystok, 15-424 Bia lystok, Poland\n209Ewha Womans University, Seoul 03760, Republic of Korea\n210National Astronomical Observatories, Chinese Academic of Sciences, Chaoyang District, Beijing, China\n211School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chaoyang District, Beijing, China\n212University of Southampton, Southampton SO17 1BJ, United Kingdom\n213Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City, Chiba 277-8582, Japan\n214Institute for High-Energy Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands\n215Chung-Ang University, Seoul 06974, Republic of Korea\n216University of Washington Bothell, Bothell, WA 98011, USA\n\nConstraints on the cosmic expansion history from GWTC\u20133\n9\n217Institute of Applied Physics, Nizhny Novgorod, 603950, Russia\n218Inje University Gimhae, South Gyeongsang 50834, Republic of Korea\n219Department of Physics, Myongji University, Yongin 17058, Republic of Korea\n220Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki\n305-0801, Japan\n221School of Physics and Astronomy, Cardi\ufb00University, Cardi\ufb00, CF24 3AA, UK\n222Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland\n223National Center for Nuclear Research, 05-400 \u00b4Swierk-Otwock, Poland\n224Instituto de Fisica Teorica, 28049 Madrid, Spain\n225Department of Physics, Nagoya University, Chikusa-ku, Nagoya, Aichi 464-8602, Japan\n226Universit\u00b4e de Montr\u00b4eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada\n227Laboratoire Lagrange, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n228Seoul National University, Seoul 08826, Republic of Korea\n229Sungkyunkwan University, Seoul 03063, Republic of Korea\n230NAVIER, \u00b4Ecole des Ponts, Univ Gustave Ei\ufb00el, CNRS, Marne-la-Vall\u00b4ee, France\n231Universit`a di Firenze, Sesto Fiorentino I-50019, Italy\n232Department of Physics, National Cheng Kung University, Tainan City 701, Taiwan\n233School of Physics and Technology, Wuhan University, Wuhan, Hubei, 430072, China\n234National Center for High-performance computing, National Applied Research Laboratories, Hsinchu Science Park, Hsinchu City\n30076, Taiwan\n235Department of Physics, National Taiwan Normal University, sec. 4, Taipei 116, Taiwan\n236NASA Marshall Space Flight Center, Huntsville, AL 35811, USA\n237INFN, Sezione di Roma Tre, I-00146 Roma, Italy\n238ESPCI, CNRS, F-75005 Paris, France\n239Kenyon College, Gambier, OH 43022, USA\n240School of Physics Science and Engineering, Tongji University, Shanghai 200092, China\n241Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy\n242Institute for Photon Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan\n243Indian Institute of Technology Madras, Chennai 600036, India\n244Kavli Institute for the Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Chiba 2778583, Japan\n245Saha Institute of Nuclear Physics, Bidhannagar, West Bengal 700064, India\n246Institute of Space and Astronautical Science (JAXA), Chuo-ku, Sagamihara City, Kanagawa 252-0222, Japan\n247Institut des Hautes Etudes Scienti\ufb01ques, F-91440 Bures-sur-Yvette, France\n248Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto City, Kyoto 612-8577, Japan\n249Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal 741252, India\n250Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA\n251Graduate School of Science and Technology, Niigata University, Nishi-ku, Niigata City, Niigata 950-2181, Japan\n252Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, Piazzale Aldo Moro 5, I-00185 Roma, Italy\n253Korea Astronomy and Space Science Institute (KASI), Yuseong-gu, Daejeon 34055, Republic of Korea\n254Hobart and William Smith Colleges, Geneva, NY 14456, USA\n255International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil\n256Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, I-00184 Roma, Italy\n257Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy\n258University of Arizona, Tucson, AZ 85721, USA\n259Universit`a di Trento, Dipartimento di Matematica, I-38123 Povo, Trento, Italy\n260Subatech, CNRS/IN2P3, IMT Atlantique, Universit\u00b4e de Nantes, Nantes, France\n261University of California, Riverside, Riverside, CA 92521, USA\n262University of Washington, Seattle, WA 98195, USA\n263Indian Institute of Technology, Palaj, Gandhinagar, Gujarat 382355, India\n264Department of Electronic Control Engineering, National Institute of Technology, Nagaoka College, Nagaoka City, Niigata 940-8532,\nJapan\n265Departamento de Matem\u00b4atica da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications,\nCampus de Santiago, 3810-183 Aveiro, Portugal\n266Marquette University, Milwaukee, WI 53233, USA\n267Faculty of Science, Toho University, Funabashi City, Chiba 274-8510, Japan\n268Graduate School of Science and Technology, Gunma University, Maebashi, Gunma 371-8510, Japan\n269Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA\n\n10\nAbbott et al.\n270Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n271Faculty of Information Science and Technology, Osaka Institute of Technology, Hirakata City, Osaka 573-0196, Japan\n272INAF, Osservatorio Astro\ufb01sico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy\n273Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India\n274Indian Institute of Science Education and Research, Pune, Maharashtra 411008, India\n275Istituto di Astro\ufb01sica e Planetologia Spaziali di Roma, Via del Fosso del Cavaliere, 100, 00133 Roma RM, Italy\n276Department of Space and Astronautical Science, The Graduate University for Advanced Studies (SOKENDAI), Sagamihara City,\nKanagawa 252-5210, Japan\n277Andrews University, Berrien Springs, MI 49104, USA\n278Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, Setagaya, Tokyo 158-0082, Japan\n279Laboratoire des 2 In\ufb01nis - Toulouse (L2IT-IN2P3), Universit\u00b4e de Toulouse, CNRS, UPS, F-31062 Toulouse Cedex 9, France\n280Institute for Cosmic Ray Research (ICRR), Research Center for Cosmic Neutrinos (RCCN), The University of Tokyo, Kashiwa City,\nChiba 277-8582, Japan\n281Department of Physics, Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n282Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Sakyou-ku, Kyoto City, Kyoto 606-8502, Japan\n283Dipartimento di Scienze Aziendali - Management and Innovation Systems (DISA-MIS), Universit`a di Salerno, I-84084 Fisciano,\nSalerno, Italy\n284Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, Netherlands\n285Faculty of Science, Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong\n286Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium\n287Artemis, Universit\u00b4e C\u02c6ote d\u2019Azur, Observatoire de la C\u02c6ote d\u2019Azur, CNRS, F-06304 Nice, France\n288Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland\n289Universiteit Gent, B-9000 Gent, Belgium\n290Applied Research Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba City, Ibaraki 305-0801, Japan\n291Department of Communications Engineering, National Defense Academy of Japan, Yokosuka City, Kanagawa 239-8686, Japan\n292Department of Physics, University of Florida, Gainesville, FL 32611, USA\n293Department of Information and Management Systems Engineering, Nagaoka University of Technology, Nagaoka City, Niigata\n940-2188, Japan\n294Tata Institute of Fundamental Research, Mumbai 400005, India\n295Eindhoven University of Technology, Postbus 513, 5600 MB Eindhoven, Netherlands\n296Department of Physics and Astronomy, Sejong University, Gwangjin-gu, Seoul 143-747, Republic of Korea\n297Concordia University Wisconsin, Mequon, WI 53097, USA\n298Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan\n299Department of Physics, Rikkyo University, Toshima-ku, Tokyo 171-8501, Japan\n(Dated: November 22, 2021)\nABSTRACT\nWe use 47 gravitational-wave sources from the Third LIGO\u2013Virgo\u2013KAGRA Gravitational-Wave\nTransient Catalog (GWTC\u20133) to estimate the Hubble parameter H(z), including its current value,\nthe Hubble constant H0. Each gravitational-wave (GW) signal provides the luminosity distance to\nthe source and we estimate the corresponding redshift using two methods: the redshifted masses and\na galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the\nsource mass distribution and H(z).\nThe source mass distribution displays a peak around 34 M\u2299,\nfollowed by a drop-o\ufb00.\nAssuming this mass scale does not evolve with redshift results in a H(z)\nmeasurement, yielding H0 = 68+12\n\u22128 km s\u22121 Mpc\u22121 (68% credible interval) when combined with the H0\nmeasurement from GW170817 and its electromagnetic counterpart. This represents an improvement\nof 17% with respect to the H0 estimate from GWTC\u20131. The second method associates each GW\nevent with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts\nof each event\u2019s potential hosts.\nAssuming a \ufb01xed BBH population, we estimate a value of H0 =\n68+8\n\u22126 km s\u22121 Mpc\u22121 with the galaxy catalog method, an improvement of 42% with respect to our\nGWTC\u20131 result and 20% with respect to recent H0 studies using GWTC\u20132 events. However, we show\nthat this result is strongly impacted by assumptions about the BBH source mass distribution; the only\nevent which is not strongly impacted by such assumptions (and is thus informative about H0) is the\nwell-localized event GW190814.\n\nConstraints on the cosmic expansion history from GWTC\u20133\n11\nKeywords: gravitational waves, cosmology: observations, cosmological parameters\n1. INTRODUCTION\nThe discovery of a gravitational wave (GW) signal\nfrom a binary neutron star (BNS) merger (Abbott\net al. 2017a) and the kilonova emission from its rem-\nnant (Coulter et al. 2017; Abbott et al. 2017b) provided\nthe \ufb01rst GW standard siren measurement of the cosmic\nexpansion history (Abbott et al. 2017c). As pointed out\nby Schutz (1986), the GW signal from a compact binary\ncoalescence directly measures the luminosity distance to\nthe source without any additional distance calibrator,\nearning these sources the name \u201cstandard sirens\u201d (Holz\n& Hughes 2005).\nMeasuring the cosmic expansion as\na function of cosmological redshift is one of the key\navenues with which to explore the constituents of the\nUniverse, along with the other canonical probes such\nas the cosmic microwave background (CMB; Spergel\net al. 2003, 2007; Komatsu et al. 2011; Ade et al. 2014,\n2016; Aghanim et al. 2020), baryon acoustic oscillations\n(Eisenstein & Hu 1998, 1997; Dawson et al. 2013; Alam\net al. 2017), type Ia supernovae (Riess et al. 1996; Perl-\nmutter et al. 1999; Riess et al. 2016; Freedman 2017;\nRiess et al. 2019), strong gravitational lensing (Suyu\net al. 2010; Wong et al. 2020), and cosmic chronometers\n(Jimenez et al. 2019).\nEven though GW sources are excellent distance trac-\ners, using them to study the expansion history also re-\nquires measurement of their redshift. The redshift in-\nformation is usually degenerate with the source masses\nin the GW signal, as the redshifted masses a\ufb00ect the\nGW frequency evolution. However, several techniques\nare proposed to infer the redshift of GW sources and\nbreak the mass-redshift degeneracy.\nFor sources with\ncon\ufb01rmed electromagnetic counterparts, the host galaxy\nand its redshift can be determined directly (Holz &\nHughes 2005; Dalal et al. 2006; MacLeod & Hogan 2008;\nNissanke et al. 2010; Abbott et al. 2017c; Chen et al.\n2018; Feeney et al. 2019). For sources without an elec-\ntromagnetic counterpart, alternative techniques to in-\nfer the source redshift include comparing the redshifted\nmass distribution to an astrophysically-motivated source\nmass distribution (Cherno\ufb00& Finn 1993; Taylor & Gair\n2012; Farr et al. 2019; You et al. 2021; Mastrogiovanni\net al. 2021), obtaining statistical redshift information\nfrom galaxy catalogs (Schutz 1986; MacLeod & Hogan\n2008; Del Pozzo 2012; Nishizawa 2017; Chen et al. 2018;\n\u2217Deceased, August 2020.\n\u2020 Deceased, April 2021.\nNair et al. 2018; Fishbach et al. 2019; Soares-Santos\net al. 2019; Gray et al. 2020; Yu et al. 2020; Palmese\net al. 2020; Borhanian et al. 2020; Finke et al. 2021),\ncomparing the spatial clustering between GW sources\nand galaxies (Oguri 2016; Mukherjee et al. 2020; Bera\net al. 2020; Mukherjee et al. 2021), leveraging exter-\nnal knowledge of the source redshift distribution (Ding\net al. 2019; Ye & Fishbach 2021), and exploiting the\ntidal distortions of neutron stars (Messenger & Read\n2012; Chatterjee et al. 2021).\nThe third LIGO\u2013Virgo\u2013KAGRA GW transient cat-\nalog (GWTC\u20133) (Abbott et al. 2021b) contains 90\ncompact binary coalescence candidate events with at\nleast a 50% probability of being astrophysical in ori-\ngin. Out of the events from the third observing run, a\nnotable electromagnetic counterpart has been claimed\nonly for the high-mass binary black hole (BBH) event\nGW190521 (Graham et al. 2020). However, the signif-\nicance of this association has been re-assessed by sev-\neral authors, who found insu\ufb03cient evidence to claim\na con\ufb01dent association (Ashton et al. 2020; De Paolis\net al. 2020; Palmese et al. 2021). In this work, we do\nnot include the redshift information from this putative\nelectromagnetic counterpart signal. The only standard\nsiren with an electromagnetic counterpart in GWTC\u20133\nremains the BNS GW170817.\nThe remainder of this paper is organized as follows.\nIn Sec. 2 we discuss the statistical methods used to infer\nthe cosmological parameters with and without galaxy\ncatalog information. In Sec. 3 we discuss the proper-\nties of the GW events and galaxy catalogs used in this\npaper. In Sec. 4 we present the results of our analyses\nand in Sec. 5 we discuss their implications for the cos-\nmological parameters. Finally, in Sec. 6 we present our\nconclusions.\n2. METHOD\nWe use two analysis methods: (i) jointly \ufb01tting the\ncosmological parameters and the source population\nproperties of BBHs, without using galaxy catalog in-\nformation (Mastrogiovanni et al. 2021; Sec. 2.1), and\n(ii) \ufb01xing the source population properties, and infer-\nring the cosmological parameters using statistical galaxy\ncatalog information (Gray et al. 2020; Sec. 2.2).\n2.1. Hierarchical inference without galaxy surveys\nThe GW event catalog can be described by two sets of\nparameters: a set of population hyper-parameters \u03a6 that\nare common to the entire population of GW sources, and\na set of intrinsic parameters that are unique for each\n\n12\nAbbott et al.\nevent. The cosmological population hyper-parameters\nin this work are the cosmological parameters for a \ufb02at\nUniverse. For the redshift range considered in the anal-\nysis, the contribution to the total energy density from\nradiation and neutrinos is negligible. Hence, we consider\nthe dark energy density today as \u2126DE(z) = 1\u2212\u2126m. The\ncosmological parameters considered are, therefore, the\nHubble constant H0, the matter density \u2126m and dark\nenergy equation of state (EOS) parameter w(z) = w0.\n(Chevallier & Polarski 2001). The dark energy EOS is\nde\ufb01ned by w = p/\u03c1, where for the standard \u039bCDM we\nhave w = \u22121. Additionally, the set of hyper-parameters\n\u03a6 includes parameters describing the source mass dis-\ntribution and the merger rate density as a function of\nredshift.\nGiven a set of Nobs GW detections associated with\nthe data {x} = (x1, ..., xNobs), the posterior on \u03a6 can\nbe expressed as (Mandel et al. 2019; Thrane & Talbot\n2019; Vitale et al. 2020)\np(\u03a6|{x}, Nobs) = p(\u03a6)\nNobs\nY\ni=1\nR\np(xi|\u03a6, \u03b8)ppop(\u03b8|\u03a6)d\u03b8\nR\npdet(\u03b8, \u03a6)ppop(\u03b8|\u03a6)d\u03b8 , (1)\nwhere p(\u03a6) is a prior on the population parameters, \u03b8\nis the set of parameters intrinsic to each GW event,\nsuch as spins, masses, redshift etc, p(xi|\u03a6, \u03b8) is the GW\nlikelihood, pdet(\u03b8, \u03a6) is the probability of detecting a\nGW event with intrinsic parameters \u03b8 and for popula-\ntion hyper-parameters \u03a6, and ppop(\u03b8|\u03a6) is a population\nmodelled prior. The denominator in Eq. (1) correctly\nnormalizes the posterior and takes into account selection\ne\ufb00ects (Mandel et al. 2019). We use the hierarchical sta-\ntistical framework to infer the population parameters \u03a6\nand the prior that they induce on the distributions of\nthe GW parameters.\nThe intrinsic GW parameters that are interesting for\ncosmology are those which provide information about\nthe redshift z of the source. For sources which are de-\ntected at cosmological distances, GWs provide a mea-\nsurement of the redshifted masses mdet\n1 , mdet\n2\nand lumi-\nnosity distance DL, rather than the redshift and source\nmasses m1, m2, where\nmi =\nmdet\ni\n1 + z(DL; H0, \u2126m, w0).\n(2)\nThe relation between source mass and redshifted mass\ncan then be used to probe cosmology even in the absence\nof an explicit electromagnetic (EM) counterpart (Taylor\net al. 2012; Taylor & Gair 2012) provided source mass\nscale can be well characterized. This approach is more\ne\ufb00ective if the source mass distribution displays sharp\nfeatures (Farr et al. 2019; Ezquiaga & Holz 2021; You\net al. 2021; Mastrogiovanni et al. 2021).\n2.1.1. Population models\nWe model the BBH population since BBHs represent\nthe majority of the detected sources.\nWe now give a\ngeneral overview of the source mass and redshift models\nused in this paper; see App. A for a complete description\nof the population models.\nWe describe the underlying distribution in redshift\nand source masses as\nppop(\u03b8|\u03a6m, H0, \u2126m, w0)=C p(m1, m2|\u03a6m)\u03c8(z|\u03b3, k, zp)\n\u00d7p(z|H0, w0, \u2126m)\n1 + z\n,\n(3)\nwhere C is a normalization factor, p(m1, m2|\u03a6m) is the\nsource frame mass distribution, \u03a6m refers to all the pop-\nulation parameters not related to cosmology, the (1+z)\nterm encodes the clock di\ufb00erence between the source\nframe and detector frame, and p(z|H0, w0, \u2126m) is the\nredshift prior which is taken to be uniform in comoving\nvolume.\nThe term \u03c8(z|\u03b3, k, zp) describes the redshift\nevolution of the merger rate with a parameterization\nsimilar to that of Madau & Dickinson (2014), charac-\nterized by a low-redshift power-law slope \u03b3, a peak at\nredshift zp, and a high-redshift power-law slope k after\nthe peak, or\n\u03c8(z|\u03b3, k, zp) = [1+(1+zp)\u2212\u03b3\u2212k]\n(1 + z)\u03b3\n1 + [(1 + z)/(1 + zp)]\u03b3+k .\n(4)\nThe above rate evolution model is more complex than\nthat in Fishbach et al. (2018); Abbott et al. (2021c,d);\nthis is because when we vary the cosmological param-\neters, the GW observations may be pushed to higher\nredshift z > 2, past the peak of the star formation rate\n(Madau & Dickinson 2014).\nThe source mass models are factorized as\np(m1, m2|\u03a6m) = p(m1|\u03a6m)p(m2|m1, \u03a6m),\n(5)\nwhere the secondary mass is modeled by a power-law\ndistribution between a minimum mass mmin and maxi-\nmum mass m1. For the primary mass, we implement\nthree phenomenological mass models used in Abbott\net al. (2019a, 2021c).\nThe \ufb01rst phenomenological model, is the Truncated\nmodel, describes the mass distribution as a power law\n(PL) between a minimum mass mmin and a maximum\nmass mmax (Fishbach & Holz 2017).\nThe BBH mass\n\nConstraints on the cosmic expansion history from GWTC\u20133\n13\ndistribution inferred from GWTC\u20132 was more compli-\ncated than a Truncated PL, and the second and third\nmodels are extensions of the Truncated model that\ncontain more complex structures to better \ufb01t the mass\ndistribution (Abbott et al. 2021c). The second model,\nBroken Power Law, consists of two PLs attached at a\nbreak\u2013point (Abbott et al. 2021c). The third model is a\nsuperposition of a Truncated and a Gaussian compo-\nnent referred to as Power Law + Peak, in which the\nprimary mass distribution is described by a PL with the\naddition of a Gaussian peak with mean \u00b5g and variance\n\u03c32\ng (Talbot & Thrane 2018). Using the Broken Power\nLaw and Power Law + Peak models, GWTC\u20132 re-\nvealed an excess of BBH systems with primary masses\nin the range \u223c30\u201340 M\u2299, followed by a drop-o\ufb00in the\nmerger rate at high masses (Abbott et al. 2021c). This\nstructure in the PL, modeled either as a break or a Gaus-\nsian peak, may represent the imprint of (pulsational)\npair-instability supernovae (Fryer et al. 2001; Heger &\nWoosley 2002; Farmer et al. 2019; Renzo et al. 2020;\nUmeda et al. 2020).\nIn a companion paper investigating the GWTC\u20133 pop-\nulation (Abbott et al. 2021d) we show the evidence\nfor sub-structures in the BHs primary mass spectrum\naround \u223c10M\u2299. However we also \ufb01nd that the simpler\nPower Law + Peak model is still one of the models\npreferred by the GWTC\u20133 data. For this reason, and\nfor simplicity in this paper, we only adopt models which\nare characterized by a single structure (Broken Power\nLaw and Power Law + Peak) to describe the excess\nof BHs observed around 35M\u2299; this also corresponds to\nthe binaries that we can observe at higher redshifts and\nfor which source mass assumptions could be important.\nIn order to infer H(z) from the BBH population, a\ncrucial assumption is that the source mass distribution\nis independent of redshift (Fishbach et al. 2021). In most\nBBH formation scenarios, we expect some evolution of\nthe mass distribution with redshift, due to factors such\nas the metallicity evolution of the Universe (Kudritzki &\nPuls 2000; Belczynski et al. 2010) and the dependence of\nthe delay time between BBH formation and merger on\nBBH properties (Kushnir et al. 2016; Gallegos-Garcia\net al. 2021; van Son et al. 2021). Nevertheless, if mass\nfeatures, such as the break in the Broken Power\nLaw model or the peak in the Power Law + Peak\nmodel, are caused by the pair-instability supernova pro-\ncess, their location is thought to stay constant within a\nfew solar masses across cosmic time (Farmer et al. 2019).\nThe presence of these sharp mass features drives our cos-\nmological constraints (Farr et al. 2019; Mastrogiovanni\net al. 2021). Moreover, the BBH mass distribution is\nexpected to evolve only weakly over the range of red-\nshift accessible to current observations, at a level below\ncurrent statistical uncertainties (Fishbach & Kalogera\n2021; van Son et al. 2021). Although the BH mass spec-\ntrum at formation may vary with cosmic time, BBH\nchannels typically predict a wide distribution of delay\ntimes between formation and merger, which tends to\nwash out any dependence of BBH mass on merger red-\nshift (Mapelli et al. 2019).\nIn the following we will neglect the selection e\ufb00ect\nof spin distribution as the detection probability due to\ntheir inclusion should not vary by more than a factor of\ntwo (Ng et al. 2018b). This is indeed a negligible term\nwith respect to the statistical uncertainties on our pos-\nteriors (see Sec. 5) and the dependence of the selection\nbias with respect to other parameters such as H0 and \u03b3,\nfor which it nearly follows a power-law.\n2.2. Statistical galaxy catalog method\nWe also use the gwcosmo code (Gray et al. 2020) in\nthe pixelated sky scheme (Gray et al. 2021), i.e. using\nthe HEALPix pixelization algorithm (G\u00b4orski et al. 2005;\nZonca et al. 2019), to infer H0 using information from\ngalaxy surveys.\nThis method assumes a \ufb01xed source\nmass distribution, as well as a \ufb01xed-rate evolution for\nthe binaries, and estimates H0 from the GW data using\ngalaxy catalogs to provide statistical information about\nthe GW source redshifts.\nWhen including galaxy catalog information, the prior\non redshift can be replaced by the distribution of galax-\nies in the survey. However, Eq. (1) needs to be modi\ufb01ed\nin order to take into account completeness corrections.\nThese extra terms account for the impact of incomplete-\nness, i.e. missing galaxies, due to the limited sensitivity\nof the catalog, in the GW localization volume. In this\ncase, the posterior is given by\np(H0|x, Nobs, \u03a6m) = p(H0)p(Nobs|H0, \u03a6m) \u00d7\nNobs\nQ\ni=1\nP\ng\u2208[G, \u00af\nG]\np(xi| \u02c6d, H0, \u03a6m, g)p(g|H0, \u03a6m, \u02c6d),\n(6)\nwhere G is the hypothesis that the GW host galaxy\nis included in the catalog and \u00afG that it is not and\np(g|H0, \u03a6m, \u02c6d) expresses their probabilities for g\n\u2208\n[G, \u00afG].\nThe term p(Nobs|H0, \u03a6m) is the probability\nof having Nobs detections. We analytically marginalize\nover this by assuming a uniform in log rate prior. The\nnotation \u02c6d indicates the hypothesis that an event has\nbeen detected.\nThe likelihoods p(xi| \u02c6d, H0, \u03a6m, g) are\nbuilt from the GW data and corrected for the selection\ne\ufb00ects in the case that the host galaxy is, and is not,\ninside the catalogue; see Gray et al. (2020).\nWe implement an improved version of the analysis pre-\nsented in Abbott et al. (2021a) that can estimate H0\n\n14\nAbbott et al.\nfor any given sky direction covered by the GW local-\nization by dividing the sky into equal-area pixels.\nIn\neach pixel, the apparent magnitude threshold (mthr) is\ntaken to be the median of the apparent magnitudes of\nall the galaxies inside that pixel.\nThis assumption is\na conservative choice for approximating the impact of\ncatalog completeness: all galaxies with apparent mag-\nnitude fainter than the de\ufb01ned threshold are excluded\nfrom the analysis. Using this mthr the completeness is\nassessed and the H0 likelihoods are calculated in each\npixel. In the end, all the pixel likelihoods are combined\nusing weights proportional to the GW posterior proba-\nbility in each pixel to give the \ufb01nal H0 posterior of each\nGW event. Pixels with no GW support make zero con-\ntribution, so only the pixels within the 99.9% sky area\nare used.\nThese improvements are necessary to correct for\ngalaxy catalog incompleteness in the case that the\ngalaxy surveys contained within the catalog are less\nsensitive in particular sky areas, such as the directions\nof the galactic plane. Moreover, the analysis can take\ninto account the fact that the GW luminosity distance\nposterior conditioned on the sky position might sig-\nni\ufb01cantly change between di\ufb00erent sky positions. The\ncombination of galaxy redshift information and lumi-\nnosity distance estimation change from pixel to pixel,\nleading to a more robust estimation of H0.\n3. EVENTS AND CATALOGS SELECTION\n3.1. GW events\nFor our main result, we select 47 GW events with net-\nwork matched \ufb01lter signal-to-noise ratio (SNR) > 11 and\nInverse False Alarm Rate (IFAR) higher than 4 yr, tak-\ning their maximum across the di\ufb00erent search pipelines\nfrom GWTC\u20133 (Abbott et al. 2021b), and no plausible\ninstrumental origin.\nWe also consider events identi\ufb01ed by di\ufb00erent SNR\nchoices to explore possible systematics in the computa-\ntion of selection e\ufb00ects, see App. B. In the remainder\nof the paper we will shortly refer to these di\ufb00erent en-\nsembles by quoting the threshold SNR choices. Of the\n47 events with SNR > 11, 42\nare BBH detections, 2\nare the BNS events GW170817 (Abbott et al. 2017a)\nand GW190425 (Abbott et al. 2020a), 2 are the NSBH\nevents GW200105 and GW200115 (Abbott et al. 2021)\nand one is the asymmetric mass binary GW190814 (Ab-\nbott et al. 2020b). A visual representation of the pop-\nulation of BBHs that we detected is provided in Fig. 1,\nwhere we show the distribution of detector frame masses\nand luminosity distance of the BBHs. We have tabu-\nlated all the GW sources used in this analysis in Table\n1, mentioning their source properties, sky localization\nerror, the 3D localization volume, number of galaxies\nin the catalog within the localization volume and the\nprobability that the GW host is present in the GLADE+\ncatalog (D\u00b4alya et al. 2018, 2021). Note that di\ufb00erently\nfrom (Abbott et al. 2021b), the estimation of masses\nand distances are reported using a prior \u221dD2\nL and not\nuniform in comoving volume since we are interested to\nshow these values using cosmology-agnostic priors. For\nthe events detected during O1, O2 and O3 we use com-\nbined posterior samples from the IMRPhenom (Thompson\net al. 2020; Pratten et al. 2021) and SEOBNR (Ossokine\net al. 2020; Matas et al. 2020) families, while for the two\nNSBH events GW200105 and GW200115 we use pos-\nterior samples generated with low spin priors (Abbott\net al. 2021).1\n1\nEvents in the analysis showing di\ufb00erences in posterior\nsamples with di\ufb00erent waveforms are GW191109 010717 and\nGW200129 065458 (Abbott et al. 2021b). These di\ufb00erences are\nmostly related to the e\ufb00ective and precession spin parameters\nwhich are not considered in this analysis.\n\nConstraints on the cosmic expansion history from GWTC\u20133\n15\n1.0\n1.5\n2.0\n2.5\nlog10(m1/M )\n0.0\n0.5\n1.0\n1.5\n2.0\n2.5\nDensity\nRedshifted masses\nSource masses\n0.5\n1.0\n1.5\n2.0\nlog10(m2/M )\n0.00\n0.25\n0.50\n0.75\n1.00\n1.25\n1.50\n1.75\n2.00\nDensity\nRedshifted masses\nSource masses\n0\n2\n4\n6\nDL[Gpc]\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nDensity [Gpc\n1]\n0.0\n0.3\n0.6\n0.9\n1.1\nz\nFigure 1. Distribution of the mass and luminosity distance parameters for the 42 BBH events with SNR > 11. The \ufb01gure is\ngenerated using a Planck cosmology with H0 = 67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065 with a D2\nL prior and a uniform prior on\nthe detector frame masses ad stacking posterior samples for each event. This \ufb01gure is only representative of the events reported\nin Tab. 4 and does not indicate the population reconstruction. Left: Distribution of the primary detector frame masses (blue\nsolid line) and source frame masses (orange dashed line). Middle: Same but for the secondary source mass. Right: Distribution\nof the luminosity distance (bottom axis) and redshift (top axis).\n\n16\nAbbott et al.\n[!p]\nTable 1. This table reports all of the GW events considered in this paper and summarizes some of their properties reported with their median values and 90% symmetric\ncredible intervals. First, second and third columns: GW event label, detected SNR (highest among the di\ufb00erent pipelines, see (Abbott et al. 2021b)) and inverse false alarm\nrate. Fourth, \ufb01fth, sixth columns: estimated primary and secondary detector frame masses, luminosity distance. Seventh, eighth and ninth columns: primary and secondary\nsource frame masses, and redshift assuming a reference cosmology. Tenth and eleventh columns: sky localization area, and 3D localization comoving volume. The twelfth\ncolumn lists the number of galaxies in GLADE+ inside the localization volume for each event with observed K\u2013band (BJ\u2013band in parenthesis), while the thirteenth column\nreports the probability p(G|z, H0) that GLADE+ detected the GW event host galaxy using the K\u2013band (BJ in parenthesis) luminosity function calculated for a \ufb01ducial \ufb02at\n\u039bCDM cosmology with H0 = 67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065. The lower and upper bounds on these probabilities are derived from the completeness fractions at the\nboundaries of the 90% localization volume. We report these values using a distance prior proportional to D2\nL and a uniform in detector frame masses prior. The events in\nbold are the ones with SNR> 11 entering all the analyses while the others are the ones used only for the systematic studies in App. B.\nName\nSNR\nIFAR\nmdet\n1\nmdet\n2\nDL\nm1\nm2\nz\n\u2206\u2126\n\u2206Vc\nNgal\np(G|z, H0)\n[yr]\n[M\u2299]\n[M\u2299]\n[Mpc]\n[M\u2299]\n[M\u2299]\n[deg2]\n[Gpc3]\nGW150914\n24.4\n1 \u00d7 107\n39+5\n\u22123\n33+3\n\u22125\n400+100\n\u2212200\n35+5\n\u22123\n30+3\n\u22124\n0.09+0.03\n\u22120.03\n200\n3 \u00d7 10\u22124\n3000(3 \u00d7 104)\n50-5(99-72)\nGW151012\n10.0\n100\n27+16\n\u22126\n17+4\n\u22126\n1100+500\n\u2212500\n23+14\n\u22125\n14+4\n\u22125\n0.21+0.09\n\u22120.09\n2000\n0.05\n6000(5 \u00d7 105)\n5-0(73-10)\nGW151226\n13.1\n1 \u00d7 107\n15+8\n\u22124\n8+2\n\u22122\n400+200\n\u2212200\n14+8\n\u22123\n8+2\n\u22122\n0.09+0.04\n\u22120.04\n1000\n0.003\n1 \u00d7 104(1 \u00d7 105)\n58-4(100-70)\nGW170104\n13.0\n1 \u00d7 107\n37+8\n\u22126\n24+6\n\u22126\n1000+400\n\u2212400\n31+7\n\u22126\n20+5\n\u22125\n0.20+0.07\n\u22120.08\n900\n0.02\n8000(4 \u00d7 105)\n8-0(76-17)\nGW170608\n15.4\n1 \u00d7 107\n12+6\n\u22122\n8+1\n\u22122\n300+100\n\u2212100\n11+5\n\u22122\n8+1\n\u22122\n0.07+0.02\n\u22120.02\n400\n4 \u00d7 10\u22124\n4000(2 \u00d7 104)\n69-19(100-87)\nGW170729\n10.8\n6\n80+20\n\u221210\n50+10\n\u221220\n3000+1000\n\u22121000\n50+20\n\u221210\n32+10\n\u22129\n0.5+0.2\n\u22120.2\n1000\n0.3\n60(8 \u00d7 104)\n0-0(12-0)\nGW170809\n12.4\n1 \u00d7 107\n42+10\n\u22127\n28+6\n\u22126\n1000+300\n\u2212400\n35+9\n\u22126\n24+5\n\u22125\n0.20+0.05\n\u22120.07\n300\n0.004\n2000(1 \u00d7 105)\n4-0(70-21)\nGW170814\n16.3\n1 \u00d7 107\n34+6\n\u22123\n29+3\n\u22125\n600+100\n\u2212200\n30+6\n\u22123\n25+3\n\u22124\n0.12+0.03\n\u22120.04\n90\n2 \u00d7 10\u22124\n1000(1 \u00d7 104)\n27-1(91-60)\nGW170817\n33.0\n1 \u00d7 107\n1.48+0.15\n\u22120.09\n1.28+0.09\n\u22120.12\n40+7\n\u221215\n1.47+0.15\n\u22120.09\n1.27+0.09\n\u22120.11\n0.009+0.002\n\u22120.003\n20\n2 \u00d7 10\u22128\n10(6)\n100-100(100-100)\nGW170818\n11.3\n2 \u00d7 104\n43+9\n\u22125\n32+5\n\u22127\n1000+400\n\u2212300\n35+7\n\u22125\n27+4\n\u22125\n0.21+0.07\n\u22120.06\n40\n6 \u00d7 10\u22124\n80(1 \u00d7 104)\n2-0(55-9)\nGW170823\n11.5\n1 \u00d7 107\n53+13\n\u22128\n39+8\n\u221210\n1900+800\n\u2212900\n39+11\n\u22127\n29+6\n\u22127\n0.4+0.1\n\u22120.1\n2000\n0.2\n700(3 \u00d7 105)\n0-0(35-0)\nGW190408 181802\n14.8\n1 \u00d7 105\n32+6\n\u22124\n24+4\n\u22125\n1600+400\n\u2212600\n24+5\n\u22123\n18+3\n\u22124\n0.30+0.06\n\u22120.10\n100\n0.003\n80(2 \u00d7 104)\n0-0(39-3)\nGW190412\n19.7\n1 \u00d7 105\n35+5\n\u22126\n10+2\n\u22121\n700+100\n\u2212200\n30+5\n\u22125\n8.3+1.6\n\u22120.9\n0.15+0.03\n\u22120.03\n20\n3 \u00d7 10\u22125\n100(4000)\n7-0(76-51)\nGW190413 134308\n10.3\n6\n80+20\n\u221210\n60+20\n\u221220\n5000+2000\n\u22122000\n45+13\n\u221210\n31+10\n\u221210\n0.8+0.3\n\u22120.3\n500\n0.2\n0(70)\n0-0(0-0)\nGW190421 213856\n10.5\n400\n62+15\n\u22129\n48+10\n\u221213\n3000+1000\n\u22121000\n41+10\n\u22127\n31+7\n\u22128\n0.5+0.2\n\u22120.2\n1000\n0.2\n1(2 \u00d7 104)\n0-0(5-0)\nGW190425\n12.9\n30\n2.1+0.6\n\u22120.4\n1.4+0.3\n\u22120.3\n160+70\n\u221270\n2.0+0.6\n\u22120.3\n1.4+0.3\n\u22120.3\n0.03+0.01\n\u22120.02\n8000\n0.002\n3 \u00d7 104(6 \u00d7 104)\n95-63(100-100)\nGW190503 185404\n12.8\n1 \u00d7 105\n55+11\n\u221210\n40+10\n\u221210\n1500+700\n\u2212700\n43+9\n\u22128\n29+7\n\u22128\n0.3+0.1\n\u22120.1\n90\n0.005\n100(4 \u00d7 104)\n0-0(46-1)\nGW190512 180714\n12.4\n1 \u00d7 105\n29+7\n\u22127\n16+5\n\u22123\n1500+500\n\u2212600\n23+5\n\u22126\n13+4\n\u22122\n0.29+0.08\n\u22120.10\n200\n0.008\n100(3 \u00d7 104)\n0-0(41-2)\nGW190513 205428\n12.9\n8 \u00d7 104\n50+10\n\u221210\n25+10\n\u22126\n2200+900\n\u2212800\n35+10\n\u22129\n18+7\n\u22124\n0.4+0.1\n\u22120.1\n500\n0.04\n20(3 \u00d7 104)\n0-0(18-0)\nGW190517 055101\n11.3\n3000\n51+15\n\u22128\n35+8\n\u221210\n2000+2000\n\u22121000\n36+12\n\u22128\n25+7\n\u22127\n0.4+0.3\n\u22120.2\n400\n0.1\n90(7 \u00d7 104)\n0-0(28-0)\nGW190519 153544\n13.9\n1 \u00d7 105\n100+20\n\u221210\n60+20\n\u221220\n3000+2000\n\u22121000\n60+10\n\u221210\n40+10\n\u221210\n0.5+0.3\n\u22120.2\n700\n0.2\n9(2 \u00d7 104)\n0-0(7-0)\nGW190521\n14.4\n5000\n150+50\n\u221220\n120+30\n\u221240\n5000+2000\n\u22122000\n90+30\n\u221220\n70+20\n\u221220\n0.7+0.3\n\u22120.3\n900\n0.4\n4(900)\n0-0(0-0)\nGW190521 074359\n24.7\n1 \u00d7 105\n52+7\n\u22126\n41+6\n\u22128\n1300+400\n\u2212600\n42+6\n\u22125\n33+5\n\u22126\n0.25+0.06\n\u22120.10\n500\n0.01\n700(3 \u00d7 104)\n1-0(59-8)\nGW190602 175927\n12.6\n1 \u00d7 105\n100+20\n\u221220\n70+20\n\u221230\n3000+2000\n\u22121000\n70+20\n\u221210\n50+10\n\u221220\n0.5+0.3\n\u22120.2\n700\n0.2\n2(2 \u00d7 104)\n0-0(6-0)\nGW190620 030421\n10.9\n90\n80+20\n\u221220\n50+20\n\u221220\n3000+2000\n\u22121000\n60+20\n\u221210\n30+10\n\u221210\n0.5+0.2\n\u22120.2\n6000\n2\n200(1 \u00d7 105)\n0-0(6-0)\nGW190630 185205\n15.2\n1 \u00d7 105\n42+8\n\u22127\n28+6\n\u22125\n1000+500\n\u2212400\n35+7\n\u22126\n23+5\n\u22125\n0.19+0.09\n\u22120.08\n1000\n0.03\n9000(5 \u00d7 105)\n8-0(76-12)\nGW190701 203306\n11.9\n200\n70+20\n\u221210\n60+10\n\u221220\n2200+800\n\u2212700\n54+12\n\u22128\n41+8\n\u221211\n0.4+0.1\n\u22120.1\n40\n0.003\n9(6000)\n0-0(17-0)\nGW190706 222641\n12.7\n2 \u00d7 104\n110+20\n\u221220\n70+20\n\u221230\n5000+3000\n\u22122000\n60+20\n\u221220\n40+10\n\u221210\n0.8+0.3\n\u22120.3\n600\n0.3\n0(10)\n0-0(0-0)\nGW190707 093326\n13.2\n1 \u00d7 105\n13+4\n\u22122\n10+1\n\u22122\n800+400\n\u2212400\n12+3\n\u22122\n8+1\n\u22122\n0.17+0.06\n\u22120.07\n1000\n0.02\n6000(2 \u00d7 105)\n20-0(86-26)\nGW190708 232457\n13.1\n3000\n21+6\n\u22122\n15+2\n\u22123\n900+300\n\u2212400\n17+5\n\u22122\n13+2\n\u22123\n0.18+0.06\n\u22120.07\n1 \u00d7 104\n0.2\n1 \u00d7 105(4 \u00d7 106)\n10-0(79-24)\nGW190720 000836\n11.6\n1 \u00d7 105\n16+7\n\u22123\n9+2\n\u22123\n800+700\n\u2212300\n13+7\n\u22123\n8+2\n\u22122\n0.17+0.12\n\u22120.06\n500\n0.02\n5000(2 \u00d7 105)\n12-0(81-11)\nGW190727 060333\n12.1\n1 \u00d7 105\n59+13\n\u22128\n46+8\n\u221213\n4000+2000\n\u22121000\n37+9\n\u22126\n29+7\n\u22128\n0.6+0.2\n\u22120.2\n700\n0.2\n0(5000)\n0-0(2-0)\nGW190728 064510\n13.4\n1 \u00d7 105\n14+8\n\u22122\n9+2\n\u22123\n900+200\n\u2212400\n12+7\n\u22122\n8+2\n\u22123\n0.18+0.04\n\u22120.07\n400\n0.004\n2000(1 \u00d7 105)\n10-0(79-30)\nTable 1 continued\n\nConstraints on the cosmic expansion history from GWTC\u20133\n17\nTable 1 (continued)\nName\nSNR\nIFAR\nmdet\n1\nmdet\n2\nDL\nm1\nm2\nz\n\u2206\u2126\n\u2206Vc\nNgal\np(G|z, H0)\n[yr]\n[M\u2299]\n[M\u2299]\n[Mpc]\n[M\u2299]\n[M\u2299]\n[deg2]\n[Gpc3]\nGW190814\n22.2\n1 \u00d7 105\n24+1\n\u22121\n2.72+0.08\n\u22120.09\n240+40\n\u221250\n23+1\n\u22121\n2.59+0.08\n\u22120.09\n0.053+0.009\n\u22120.010\n20\n9 \u00d7 10\u22127\n90(200)\n76-57(100-100)\nGW190828 063405\n16.6\n1 \u00d7 105\n44+7\n\u22125\n36+5\n\u22126\n2200+600\n\u2212900\n32+6\n\u22124\n26+4\n\u22125\n0.40+0.09\n\u22120.15\n500\n0.03\n30(6 \u00d7 104)\n0-0(19-0)\nGW190828 065509\n11.1\n3 \u00d7 104\n31+9\n\u22129\n13+5\n\u22123\n1700+600\n\u2212600\n24+7\n\u22127\n10+4\n\u22122\n0.31+0.10\n\u22120.10\n600\n0.03\n100(5 \u00d7 104)\n0-0(32-1)\nGW190910 112807\n13.4\n300\n57+9\n\u22126\n46+7\n\u22129\n1600+1100\n\u2212700\n43+8\n\u22126\n35+6\n\u22127\n0.3+0.2\n\u22120.1\n9000\n0.9\n6000(1 \u00d7 106)\n0-0(41-0)\nGW190915 235702\n13.1\n1 \u00d7 105\n46+12\n\u22128\n32+7\n\u22128\n1700+700\n\u2212700\n35+9\n\u22126\n24+5\n\u22126\n0.3+0.1\n\u22120.1\n300\n0.02\n700(1 \u00d7 105)\n0-0(35-1)\nGW190924 021846\n13.0\n1 \u00d7 105\n10+8\n\u22122\n6+1\n\u22122\n600+200\n\u2212200\n9+7\n\u22122\n5+1\n\u22122\n0.12+0.04\n\u22120.04\n400\n0.002\n5000(6 \u00d7 104)\n34-1(93-55)\nGW190929 012149\n10.3\n6\n100+30\n\u221220\n40+30\n\u221220\n4000+3000\n\u22122000\n60+20\n\u221220\n26+14\n\u221210\n0.6+0.4\n\u22120.2\n2000\n1\n0(1 \u00d7 104)\n0-0(2-0)\nGW190930 133541\n10.1\n80\n14+14\n\u22123\n9+2\n\u22124\n800+400\n\u2212300\n12+12\n\u22122\n8+2\n\u22123\n0.16+0.07\n\u22120.06\n2000\n0.02\n7000(2 \u00d7 105)\n18-0(85-31)\nGW191105 143521\n10.7\n80\n13+5\n\u22122\n9+2\n\u22122\n1200+400\n\u2212500\n11+4\n\u22122\n7+1\n\u22122\n0.23+0.07\n\u22120.08\n800\n0.02\n3000(3 \u00d7 105)\n1-0(61-10)\nGW191109 010717\n15.8\n6000\n80+10\n\u22128\n60+20\n\u221220\n1300+1400\n\u2212700\n60+10\n\u221210\n50+20\n\u221210\n0.3+0.2\n\u22120.1\n1000\n0.3\n5000(5 \u00d7 105)\n3-0(66-0)\nGW191127 050227\n10.3\n4\n100+60\n\u221230\n40+30\n\u221230\n5000+3000\n\u22123000\n50+40\n\u221220\n20+20\n\u221210\n0.7+0.4\n\u22120.4\n1000\n1\n2(10000)\n0-0(3-0)\nGW191129 134029\n13.3\n1 \u00d7 105\n13+5\n\u22123\n8+2\n\u22122\n800+200\n\u2212300\n11+4\n\u22122\n7+2\n\u22122\n0.16+0.04\n\u22120.06\n800\n0.006\n9000(2 \u00d7 105)\n13-0(82-35)\nGW191204 171526\n17.1\n1 \u00d7 105\n14+4\n\u22122\n9+2\n\u22122\n600+200\n\u2212200\n12+3\n\u22122\n8+2\n\u22122\n0.13+0.03\n\u22120.04\n300\n0.001\n3000(5 \u00d7 104)\n21-0(87-52)\nGW191215 223052\n10.9\n1 \u00d7 105\n33+9\n\u22125\n25+4\n\u22125\n2100+900\n\u2212900\n24+7\n\u22124\n18+4\n\u22124\n0.4+0.1\n\u22120.2\n600\n0.07\n100(8 \u00d7 104)\n0-0(28-0)\nGW191216 213338\n18.6\n1 \u00d7 105\n14+4\n\u22123\n8+2\n\u22122\n300+100\n\u2212100\n13+4\n\u22123\n7+2\n\u22122\n0.07+0.02\n\u22120.03\n500\n4 \u00d7 10\u22124\n4000(3 \u00d7 104)\n67-19(100-86)\nGW191222 033537\n12.0\n1 \u00d7 105\n70+10\n\u221210\n50+10\n\u221220\n3000+2000\n\u22122000\n44+11\n\u22128\n33+9\n\u221210\n0.6+0.2\n\u22120.3\n2000\n0.7\n20(8 \u00d7 104)\n0-0(9-0)\nGW191230 180458\n10.3\n20\n80+20\n\u221210\n60+10\n\u221220\n5000+2000\n\u22122000\n48+13\n\u22129\n36+10\n\u221210\n0.8+0.2\n\u22120.3\n800\n0.2\n0(40)\n0-0(0-0)\nGW200105 162426\n13.9\n5\n9+3\n\u22122\n2.1+0.5\n\u22120.4\n300+100\n\u2212100\n9+3\n\u22122\n1.9+0.5\n\u22120.4\n0.06+0.02\n\u22120.03\n7000\n0.007\n8 \u00d7 104(3 \u00d7 105)\n80-26(100-90)\nGW200112 155838\n17.6\n1 \u00d7 105\n45+8\n\u22126\n34+6\n\u22127\n1300+400\n\u2212500\n36+7\n\u22125\n27+5\n\u22126\n0.25+0.07\n\u22120.08\n4000\n0.09\n8000(1 \u00d7 106)\n0-0(51-7)\nGW200115 042309\n11.5\n1 \u00d7 105\n7+2\n\u22122\n1.4+0.4\n\u22120.2\n300+200\n\u2212100\n7+2\n\u22122\n1.3+0.4\n\u22120.2\n0.06+0.03\n\u22120.03\n700\n0.001\n7000(2 \u00d7 104)\n77-17(100-85)\nGW200128 022011\n10.1\n200\n65+14\n\u22129\n50+10\n\u221213\n4000+2000\n\u22122000\n40+11\n\u22127\n31+9\n\u22128\n0.6+0.3\n\u22120.3\n2000\n1\n7(3 \u00d7 104)\n0-0(4-0)\nGW200129 065458\n26.5\n1 \u00d7 105\n44+10\n\u22126\n31+6\n\u22129\n1000+200\n\u2212300\n37+9\n\u22125\n26+5\n\u22127\n0.19+0.04\n\u22120.06\n80\n5 \u00d7 10\u22124\n400(2 \u00d7 104)\n5-0(70-27)\nGW200202 154313\n11.3\n1 \u00d7 105\n11+4\n\u22122\n8+1\n\u22122\n400+100\n\u2212200\n10+4\n\u22122\n7+1\n\u22122\n0.09+0.03\n\u22120.03\n200\n3 \u00d7 10\u22124\n2000(1 \u00d7 104)\n57-8(69-17)\nGW200208 130117\n10.8\n3000\n53+12\n\u22128\n39+9\n\u221211\n2400+1000\n\u2212900\n37+9\n\u22126\n27+6\n\u22127\n0.4+0.1\n\u22120.1\n40\n0.004\n0(2000)\n0-0(11-0)\nGW200209 085452\n10.0\n20\n56+14\n\u221210\n40+10\n\u221210\n4000+2000\n\u22122000\n34+9\n\u22126\n26+7\n\u22127\n0.6+0.3\n\u22120.3\n900\n0.4\n4(7000)\n0-0(3-0)\nGW200219 094415\n10.8\n1000\n59+13\n\u22129\n44+9\n\u221213\n4000+2000\n\u22122000\n36+10\n\u22126\n27+7\n\u22127\n0.6+0.2\n\u22120.2\n700\n0.2\n7(3000)\n0-0(2-0)\nGW200224 222234\n19.2\n1 \u00d7 105\n53+9\n\u22126\n42+6\n\u221210\n1800+500\n\u2212700\n40+7\n\u22125\n32+5\n\u22127\n0.33+0.07\n\u22120.11\n50\n0.002\n30(1 \u00d7 104)\n0-0(32-1)\nGW200225 060421\n13.1\n9 \u00d7 104\n24+5\n\u22123\n17+3\n\u22125\n1200+500\n\u2212500\n19+5\n\u22123\n14+3\n\u22123\n0.23+0.08\n\u22120.09\n500\n0.01\n2000(2 \u00d7 105)\n3-0(68-9)\nGW200302 015811\n10.6\n9\n49+9\n\u221210\n25+12\n\u22127\n1600+1000\n\u2212700\n38+8\n\u22129\n19+8\n\u22125\n0.3+0.2\n\u22120.1\n7000\n0.8\n7000(1 \u00d7 106)\n0-0(50-0)\nGW200311 115853\n17.6\n1 \u00d7 105\n42+9\n\u22125\n33+5\n\u22128\n1200+300\n\u2212400\n34+7\n\u22124\n27+4\n\u22126\n0.23+0.05\n\u22120.07\n40\n3 \u00d7 10\u22124\n90(1 \u00d7 104)\n0-0(56-16)\nGW200316 215756\n10.1\n1 \u00d7 105\n17+14\n\u22124\n9+3\n\u22123\n1100+400\n\u2212400\n14+11\n\u22124\n7+2\n\u22123\n0.22+0.07\n\u22120.08\n200\n0.005\n500(2 \u00d7 104)\n2-0(59-8)\n\n18\nAbbott et al.\n3.2. Description of the GLADE+ galaxy catalog\nIn one of the analyses that we perform, the red-\nshift information is taken from galaxy surveys for all\nof the events apart from GW170817, for which we as-\nsume the redshift information from its EM counter-\npart. For the analysis taking into account galaxy sur-\nveys we use the GLADE+ (D\u00b4alya et al. 2018, 2021) all-sky\ngalaxy catalog that is a revised version of the \ufb01rst GLADE\ncatalog (D\u00b4alya et al. 2018) containing about 22 mil-\nlion galaxies. GLADE+ incorporates six di\ufb00erent galaxy\ncatalogs and surveys, namely the Gravitational Wave\nGalaxy Catalogue (GWGC, White et al. 2011), Hyper-\nLEDA (Makarov et al. 2014), the 2 Micron All-Sky Sur-\nvey Extended Source Catalog (2MASS XSC, Skrutskie\net al. 2006), the 2MASS Photometric Redshift Catalog\n(2MPZ, Bilicki et al. 2014), the WISExSCOS Photomet-\nric Redshift Catalogue (WISExSCOSPZ, Bilicki et al.\n2016), and the Sloan Digital Sky Survey quasar cata-\nlogue from the 16th data release (SDSS-DR16Q, Lyke\net al. 2020) and covers the full sky with a completeness\nof about 20% up to 800 Mpc.2\nMost of the galaxies\nin the GLADE+ catalog have a redshift measurement ob-\ntained photometrically using an arti\ufb01cial neural network\nalgorithm (Collister & Lahav 2004) with a relative error\n\u03c3zph \u223c0.033(1 + zph) (Bilicki et al. 2016). The peculiar\nvelocity corrections are implemented for galaxies up to\nredshift z < 0.05 using a Bayesian technique (Mukherjee\net al. 2021c) that can capture both linear and non-linear\ncomponents of the velocity \ufb01eld.\nFor our main results, we use all galaxies with measured\nKs\u2013band (denoted as K\u2013band henceforth) luminosity re-\nported in the Vega system and we assign a probability\nfor each galaxy to be the host of a GW event that is\nproportional to this luminosity (luminosity weighting).\nWe also explore possible systematics in our results by\nnot using luminosity weighting and by using BJ\u2013band\nobservations; see Sec. 5.2 for more details. We choose\nthese two bands since we have found that there is a good\nmatch between the galaxy luminosity functions and the\ngalaxy number density of the GLADE+ catalog, in partic-\nular for the K\u2013band, see App. C for more details. The\nK\u2013band galaxies in the GLADE+ catalog are the same as\nthe one in GLADE catalog. The galaxies in the BJ\u2013band\nare present only in the GLADE+ catalog.\n2\nLinks to the di\ufb00erent constituent galaxy catalogs and\nsurveys\nin\nGLADE+\nare\nas\nfollows:\nGWGC-\nhttp://vizier.\nu-strasbg.fr/viz-bin/VizieR?-source=GWGC,\nHyperLEDA-\nhttp://leda.univ-lyon1.fr/, 2MASS XSC-https://old.ipac.caltech.\nedu/2mass/,\n2MPZ-http://ssa.roe.ac.uk/TWOMPZ.html,\nWISExSCOS-http://ssa.roe.ac.uk/WISExSCOS.html,\nSDSS-\nDR16Q-https://www.sdss.org/dr16/algorithms/qso catalog/.\nFig. 2 presents a series of skymaps showing the direc-\ntional dependence of the K\u2013band apparent magnitude\nthreshold for the GLADE+ galaxies, in superposition with\nthe sky localizations of the GW events included in our\nanalysis. Outside of the galactic plane, mthr \u223c13.5 on\naverage for the K\u2013band while within the galactic plane\nregion the apparent magnitude threshold is signi\ufb01cantly\nlower (i.e. brighter).\nWe assume that the K\u2013band absolute magnitude dis-\ntribution for GLADE+ galaxies is well described by a\nSchechter function with parameters (reported for H0 =\n100 km s\u22121 Mpc\u22121) M\u2217,K = \u221223.39 and \u03b1K = \u22121.09\n(Kochanek et al. 2001), while for the BJ\u2013band we use\nM\u2217,BJ = \u221219.66 and \u03b1BJ = \u22121.21 (Norberg et al.\n2002).\nWe set a bright cut-o\ufb00high enough to in-\nclude all the bright galaxies supported by the Schechter\nfunction: Mmin,K = \u221227.00 and Mmin,BJ = \u221222.00.\nFurther, we consider all the galaxies no fainter than\nMmax,K = \u221219.0, Mmax,BJ = \u221216.5. These choices cor-\nrespond to all galaxies with luminosity L > 0.017L\u2217,K\nand L > 0.054L\u2217,BJ, where L\u2217is the characteristic\ngalaxy luminosity of the Schechter luminosity function.\nTo calculate the rest-frame absolute magnitudes of the\ngalaxies, for a given cosmology, we apply color and evo-\nlution corrections as reported in Kochanek et al. (2001)\nfor the K\u2013band and Norberg et al. (2002) for the BJ\u2013\nband.\nFor all events, apart from GW190814, we carry out\nthe analysis using a pixel size of 3.35 deg2, while for\nGW190814 we use a pixel size of 0.2 deg2 since the\nsky localization for this event was 10 times smaller\nthan most of the others. These values have been cho-\nsen taking into account the average number of galax-\nies per square degree reported in GLADE+.\nConsider-\ning the bright and faint limits of the Schechter function\nassumed with a median apparent magnitude threshold\nmthr,K = 13.5 for the K\u2013band and mthr,BJ = 19.7 for\nthe BJ\u2013band, we \ufb01nd that there are \u223c25 galaxies per\nsquare degree in GLADE+ reported in the K\u2013band and\n500 galaxies per square degree reported in the BJ band\nconsidered in the analysis. Note that the actual galaxy\ndensity per square degree is higher outside the galactic\nplane and in the region of GW190814.\nFor any given redshift, the completeness fraction,\nwhich is the probability that the galaxy catalog con-\ntains the host galaxy of the GW event, P(G|z, H0), is\nde\ufb01ned as the fraction of galaxies with absolute mag-\nnitudes brighter than the absolute magnitude threshold\n(calculated from mthr), namely\nP(G|z, H0) =\nR Lmax\nLthr(mthr,z,H0) \u03c6(L)LdL\nR Lmax\nLmin \u03c6(L)LdL\n.\n(7)\n\nConstraints on the cosmic expansion history from GWTC\u20133\n19\nFigure 2. Skymaps showing the GLADE+ K\u2013band apparent magnitude threshold, mthr, generated by dividing the sky into 3.35\ndeg2 pixels, this is the resolution used for all the events but GW190814. A mask is applied that removes from the \ufb01gures all\npixels with mthr < 12.5 in order to improve the \ufb01gure readability. Also shown are the 90% CL sky localizations for the GW\nevents considered in this paper.\nHere \u03c6(L) is the assumed galaxy luminosity function,\nLmin and Lmax are the minimum and maximum lumi-\nnosity corresponding to Mmax and Mmin and Lthr is the\nthreshold luminosity for detection, calculated from mthr.\nFig. 3 shows the completeness fraction of the GLADE+\ncatalog, in the K\u2013band and BJ\u2013band respectively,\nas a function of redshift and for di\ufb00erent values\nof mthr, assuming a \ufb01ducial cosmology with H0 =\n67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065 (Ade et al. 2016).\nAs can be seen from the \ufb01gure, the GLADE+ catalog is\nless complete in the K\u2013band than in the BJ\u2013band, but\nwe decide to use the K\u2013band data for our main results\nas they are better described by the Schechter function\nassumed in our analysis; see App. C.\nFor GLADE+ systematic uncertainties of the photomet-\nric redshift reconstruction are inside the statistical errors\n\n20\nAbbott et al.\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nz\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\np(G|z, H0)\nK-band\n10% sky with mthr\n 13.0\n23% sky with mthr\n 13.3\n53% sky with mthr\n 13.5\n83% sky with mthr\n 13.7\n95% sky with mthr\n 13.9\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\nz\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\np(G|z, H0)\nBJ-band\n11% sky with mthr\n 16.7\n23% sky with mthr\n 18.1\n53% sky with mthr\n 19.7\n83% sky with mthr\n 19.9\n95% sky with mthr\n 20.0\nFigure 3. Top: Completeness fraction of GLADE+ in the K\u2013\nband, indicating the probability that the catalog contains the\nhost galaxy of a GW event, as a function of redshift for H0 =\n67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065.\nThe di\ufb00erent lines\nare calculated for a given K\u2013band apparent magnitude mthr\nthreshold indicated in the legend. The legend also indicates\nthe fraction of the sky, computed by dividing the sky in equal\nsized pixels of 3.35 deg2, for which the apparent magnitude\nthreshold is brighter than the one reported in the legend.\nThe fraction of pixels with no galaxies is \u223c5% for the Bj\nand K bands. Bottom: Same as the top panel but for the\nBJ\u2013band.\n.\nassociated to each galaxy (Bilicki et al. 2014) with a very\nsmall percentage of outliers. We do not consider deeper\ngalaxy surveys with a restricted sky area footprint, such\nas the DES Y1 survey (Drlica-Wagner et al. 2018) or\nDESI Legacy Imaging Survey (Zou et al. 2019) that\nare supposed to be complete up to redshift z \u223c1, since\nwe decide to employ the same all-sky galaxy catalog for\nall of our events. Moreover, color corrections and pho-\ntometric redshift reconstruction might need particular\nattention with deeper galaxy surveys.\n4. RESULTS\nThe \ufb01rst analysis that we present in Sec. 4.1 will fo-\ncus on the impact of the BBH population source masses\non inference of the cosmological parameters, using the\nformalism discussed in Sec. 2.1. This analysis uses no\ngalaxy catalog information; instead constraints on the\ncosmological parameters will be inferred from the mass\nscale set by the source mass distribution. We use only\nthe BBHs detections as they are the majority of the\nsources entering in our cosmological analysis and be-\ncause a joint description of NSBH, BNS and BBHs is\nuncertain.\nThe second analysis in Sec. 4.2 \ufb01xes the source mass\ndistribution and uses redshift information derived from\ngalaxy catalogs, based on the formalism discussed in Sec.\n2.2. Unless stated otherwise, all the \ufb01gures are gener-\nated with a uniform prior on H0, credible intervals are\nreported as maximum posterior and 68.3% highest den-\nsity intervals. We use a \ufb02at-in-log prior on H0 only when\nquoting results combined with GW170817 and its EM\ncounterpart.\n4.1. Implications of population assumptions for\ncosmology\nWe jointly estimate population-related GW param-\neters and cosmological parameters using BBH events,\nsince these are the majority of the GW events observed\nto date. We use the 42 BBH detected events with SNR\n> 11. We exclude from this analysis GW190814 (Ab-\nbott et al. 2021c) given the current uncertainty on the\nnature of the secondary object in this system.\nWe consider two cosmological models:\n(i) a \ufb02at\nw0CDM model with wide priors on the Hubble con-\nstant H0, matter density \u2126m and dark energy equation\nof state (EoS) w0 parameter, and (ii) a \ufb02at \u039bCDM\nUniverse with a \ufb01xed value of \u2126m = 0.3065 (Ade\net al. 2016) and dark energy EoS parameter w0 = \u22121\nand with a restricted prior in the H0 tension region\n(H0 \u2208[65, 77] km s\u22121 Mpc\u22121). We refer to model (i)\nas the w0CDM model, and to model (ii) as the H0-\ntension model. We also adopt wide priors on the hyper-\nparameters of the GW source mass distribution and its\nmerger rate evolution as described in App. A. For all\nthe phenomenological mass models assumed we obtain\nposteriors on the source mass distribution and merger\nrate parameters which are compatible with previous\npopulation studies (Abbott et al. 2021c,d) and the lat-\nest studies with O3b data (Abbott et al. 2021b). See\nApp. B for more details.\nAs evident from values of Bayes factor reported in\nTable 2, we do not \ufb01nd any preference of the data in\nsupporting any one of the cosmological models (w0CDM\nmodel or the H0-tension model) considered in the analy-\nsis. As we will see later, this is because the posteriors on\n\u2126m and w0 are not constrained by the GW observations\nand the error on the H0 estimation extends beyond the\nH0 tension region.\nIn Table 3 we report the Bayes factors computed be-\ntween di\ufb00erent mass models, for the case of wide pri-\n\nConstraints on the cosmic expansion history from GWTC\u20133\n21\nMass model\nlog10 B\nTruncated\n0.2\nPower Law + Peak\n\u22120.3\nBroken Power Law\n\u22120.4\nTable 2. Logarithm of the Bayes factor comparing runs that\nadopt the same source mass model but di\ufb00erent cosmolo-\ngies: wide priors (for a general w0CDM cosmology) versus\nrestricted priors (in the H0 tension region).\nors on the w0CDM cosmological parameters.\nConsis-\ntent with Abbott et al. (2021c,d), we \ufb01nd that, even\nif we allow the cosmological parameters to vary with\nwide priors, the Truncated model is still strongly dis-\nfavored with respect to the Power Law + Peak and\nBroken Power Law models, by a factor \u223c100. This\nresult is consistent with the fact that, as indicated in\nFig. 1, the source mass distribution contains more struc-\nture than a simple Truncated model. As motivated in\nAbbott et al. (2021c), this comparatively poor \ufb01t for\nthe Truncated model is due to the inability of this\nmodel to capture a moderate fraction of detected events\nwith high masses, while predicting a large fraction of de-\ntected events with lower masses. Using the reduced set\nof signals with SNR > 11, we do not \ufb01nd any compelling\nevidence to prefer the Power Law + Peak model over\nthe Broken Power Law model.\nMass model\nlog10 B\nTruncated\n\u22121.9\nPower Law + Peak\n0.0\nBroken Power Law\n\u22120.5\nTable 3. Logarithm of the Bayes factor between the dif-\nferent mass models and the Power Law + Peak model\npreferred by the data, for the case of a w0CDM cosmology\nwith wide priors.\nThe marginal posterior distributions that we obtain\nfor the cosmological parameters H0, \u2126m and w0 are\nshown in Fig. 4 for each phenomenological mass model.\nAs anticipated by our Bayes factor results, we \ufb01nd that\nwith the current BBH GW events we cannot constrain\nthe values of these three cosmological parameters, as we\nobtain broad and uninformative posteriors.\nWith the Power Law + Peak we estimate H0 =\n50+37\n\u221230 km s\u22121 Mpc\u22121, while for the Broken Power\nLaw model we estimate H0 = 44+52\n\u221224 km s\u22121 Mpc\u22121.\nThese constraints on H0, as we will see later, arise from\nthe ability of these models to \ufb01t an excess of BBHs with\nmasses around 35 M\u2299which sets a scale for the redshift\ndistribution of BBHs.\n25\n50\n75\n100\n125\n150\n175\n200\nH0[km s\n1 Mpc\n1]\n0.000\n0.002\n0.004\n0.006\n0.008\n0.010\n0.012\np(H0|x) [km\n1 s Mpc]\nprior\nBroken Power Law\nPower Law + Peak\nTruncated\nPlanck\nSH0ES\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\nm\n0.0\n0.5\n1.0\n1.5\n2.0\np(\nm|x)\n3.0\n2.5\n2.0\n1.5\n1.0\n0.5\n0.0\nw0\n0.0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\np(w0|x)\nFigure 4. Top panel: Marginal posterior distribution for\nH0. Middle panel: Marginal posterior distribution for \u2126m.\nBottom panel: Marginal posterior distribution for w0.\nIn\neach panel the di\ufb00erent lines indicate the 3 phenomenological\nmass models. The solid orange line identi\ufb01es the preferred\nPower Law + Peak model. The pink shaded areas identify\nthe 68% CI of the cosmological parameters inferred from\nmeasurements from the CMB (Ade et al. 2016) (apart for w0\nthat is reported at 95% CI) and the green shaded area in the\ntop panel shows the value of the Hubble constant measured\nin the local Universe (Riess et al. 2019).\nWe discuss this e\ufb00ect further using the Power Law\n+ Peak model. Fig. 5 shows the joint posterior dis-\ntribution between the cosmological parameters and the\nparameters \u00b5g and mmax de\ufb01ned in Eq. (A11), which\ngovern the position of the BBH Gaussian excess and the\n\n22\nAbbott et al.\n30\n40\ng[M ]\n100\n150\nmmax[M ]\n50\n100\n150\nH0[km s\n1 Mpc\n1]\n2.5\n5.0\n7.5\n10.0\n30\n40\ng[M ]\n100\n150\nmmax[M ]\n5\n10\nFigure 5. Posterior probability density for H0 and the population parameters \u00b5g, mmax and \u03b3, governing the position of the\nGaussian peak, the upper end of the mass distribution and the merger rate evolution in the Power Law + Peak mass model.\nThe solid and dashed black lines indicate the 50% and 90% CL contours.\nupper end of the source primary mass distribution re-\nspectively.\nThe presence of a peak in the BBH source mass distri-\nbution allows us to set a characteristic source mass scale,\nwhich informs H(z) and allows us to exclude higher val-\nues of H0. Marginalizing over the cosmological param-\neters, we obtain a central value of \u00b5g = 32+6\n\u22128 M\u2299for\nthe peak position of the Gaussian BBH excess. On the\nother hand, the disfavoured Truncated model shows\nsupport at higher H0. This result is due to the fact that\nthe Truncated model is not able to adequately \ufb01t the\npresence of massive binaries while producing an excess\nof BBHs with masses \u223c40 M\u2299in the detector frame.\nFor this reason, higher H0 values are more supported\nsince those values place events at higher redshifts, thus\nreducing their source masses.\nWhen we combine the H0 posteriors from the three\nmass models with the H0 inferred from the bright stan-\ndard siren GW170817 (see Fig. 6), we \ufb01nd a value\nof H0 = 68+12\n\u22128\nkm s\u22121 Mpc\u22121 for the Power Law\n+ Peak model and H0 = 68+13\n\u22128\nkm s\u22121 Mpc\u22121 for\nthe Broken Power Law model. These results rep-\nresent an improvement of 17% and 12 % respectively\ncompared with the H0 value reported in Abbott et al.\n(2021a) that made use of GW170817 and six BBH detec-\ntions from O2, with redshift information inferred from\ngalaxy catalogs.\nFor the Truncated model, we ob-\ntain H0 = 69+21\n\u22128\nkm s\u22121 Mpc\u22121. These results are ob-\ntained assuming a redshift independent mass distribu-\ntion.\nConsidering a redshift dependence of the mass\ndistribution, can degrade the constraints.\n4.2. Results using galaxy catalog information\n\nConstraints on the cosmic expansion history from GWTC\u20133\n23\n25\n50\n75\n100\n125\n150\n175\n200\nH0[km s\n1 Mpc\n1]\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\np(H0|x) [km\n1 s Mpc]\nBroken Power Law\nPower Law + Peak\nTruncated\nGW170817\nPlanck\nSH0ES\nFigure 6. Posterior distributions for H0 obtained by com-\nbining the H0 posteriors from the 42\nBBH detections\nand the H0 posterior inferred from the bright standard\nsiren GW170817.\nThe pink and green shaded areas iden-\ntify the 68% CI constraints on H0 inferred from the CMB\nanisotropies (Ade et al. 2016) and in the local Universe from\nSH0ES (Riess et al. 2019) respectively.\nWe now discuss constraints on H0 when we \ufb01x the\nsource population model but employ galaxy surveys to\ninfer statistical redshift information using the pixelated\ngwcosmo code (Gray et al. 2020).\nOur analysis in-\ncorporates 47 GW events, comprising 42 BBH detec-\ntions, GW190814, the two BNS events GW170817 and\nGW190425, and the two NSBH events GW200105 and\nGW200115. We include all galaxies of the GLADE+ cata-\nlog that lie inside the 99.9% estimated sky area of each\nevent. We use the GLADE+ K\u2013band data in this analysis,\nadopting luminosity weights for each galaxy. For a more\nin-depth discussion about the impact of our BH popula-\ntion assumptions and choice of photometric bands, see\nSec. 5.2.\nTo describe the distribution of BH primary masses, we\nuse a Power Law + Peak source mass model where\nwe \ufb01x population parameters to the median values ob-\ntained in the joint cosmological and population anal-\nysis described in Sec. 4.1.\nFor the rate evolution we\nadopt \u03b3 = 4.59, k = 2.86 and zp = 2.47, while for the\nPower Law + Peak model we use \u03b1 = 3.78, \u03b2 = 0.81,\nmmax = 112.5 M\u2299, mmin = 4.98 M\u2299, \u03b4m = 4.8 M\u2299\n\u00b5g = 32.27 M\u2299, \u03c3g = 3.88 M\u2299and \u03bbg = 0.03. For the\nNS source mass model we consider a uniform distribu-\ntion between mmin1M\u2299and mmax = 3M\u2299consistently\nwith (Abbott et al. 2021d). We evaluate GW selection\ne\ufb00ects using LIGO and Virgo sensitivities during the\nO1, O2, and O3 runs.\nIn Fig. 7 (page 24) we show the posteriors for all of\nthe GW events considered in this analysis for the K\u2013\nband.\nFor many of the O3 events, the H0 inference\nis dominated by the likelihood based on the hypothe-\nsis that the host galaxy is not in the catalog (referred\nto as out-of-catalog).\nThe out-of-catalog term domi-\nnates for sources that are localized at redshifts at which\nthe GLADE+ galaxy catalog has low completeness fraction\n(see Fig. 3). This is the case for most of the GW sources\nwhich are BBHs observed at large luminosity distances.\nAnother interesting trend observed in Fig. 7 is that, for\nlower values of H0, the in-catalog likelihood terms tend\nto dominate because for low H0 values the GW events\nare placed at smaller redshifts where the galaxy catalog\nis more complete, as shown in Fig. 3.\nFor most of these events, the number of galaxies\npresent in the sky localization volume is large enough\nthat the redshift information is still dominated by pop-\nulation assumptions (Section 5.2).\nGW190814 is the\nonly event for which there is a su\ufb03ciently small num-\nber of galaxies in its sky localization area of about 18\ndeg2.\nIts small area makes this event partially more\ninformative on the value of H0 in comparison to the\nother GW events. We can see in Fig. 7 that, out of all\nthe GW events, the most informative posterior on H0\n(compared to the zero galaxy catalog completeness pos-\nterior) is from GW190814, provided that the luminos-\nity weighting scheme is applied. We have veri\ufb01ed that\nthe H0 posterior with the K\u2013band and using luminos-\nity weights does not depend on the faint end magnitude\nlimit used for the analysis. For this event, we infer an H0\nconstraint of 67+46\n\u221228 km s\u22121 Mpc\u22121 (MAP and HDI). We\nquote the maximum a posteriori probability (MAP) and\nthe corresponding highest density interval (HDI) values\nin the analysis.\nFig. 8 shows the redshift distribution of galaxies in\nthe 90% CI sky area of GW190814 (top panel) and the\ngalaxy catalog completeness (bottom panel), compared\nto the predicted distribution for a prior that is uniform\nin comoving volume. We observe that for the K\u2013band\nthe H0 support results from an excess of galaxies, with\nrespect to the uniform in comoving volume prior, around\nz \u223c0.051. Switching o\ufb00the luminosity weighting as-\nsumption decreases the contribution of this excess of\ngalaxies since the completeness is estimated to be lower.\nThe same excess is not visible in the BJ\u2013band as more\ngalaxies are reported in this band and some luminous\ngalaxies with measured K\u2013band apparent magnitudes\ndo not have measured apparent magnitudes for the BJ\u2013\nband.\nDespite the cases where there is a signi\ufb01cant in-\ncatalog contribution, the \ufb01nal H0 result is nevertheless\ndominated by the BBHs population assumptions which\nare contributing to the out-of-catalog likelihood terms\n\n24\nAbbott et al.\nLikelihood\nGW150914\nPosterior\nGW151226\nGW170104\nGW170608\nGW170809\nGW170814\nLikelihood\nGW170818\nPosterior\nGW170823\nGW190408_181802\nGW190412\nGW190425\nGW190503_185404 GW190512_180714 GW190513_205428\nLikelihood\nGW190517_055101\nPosterior\nGW190519_153544\nGW190521\nGW190521_074359 GW190602_175927 GW190630_185205 GW190701_203306 GW190706_222641\nLikelihood\nGW190707_093326\nPosterior\nGW190708_232457 GW190720_000836 GW190727_060333 GW190728_064510\nGW190814\nGW190828_063405 GW190828_065509\nLikelihood\nGW190910_112807\nPosterior\nGW190915_235702 GW190924_021846 GW191109_010717 GW191129_134029 GW191204_171526 GW191216_213338 GW191222_033537\nLikelihood\nGW200105_162426\n50\n100\nH0[km s\n1 Mpc\n1]\nPosterior\nGW200112_155838\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200115_042309\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200129_065458\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200202_154313\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200224_222234\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200225_060421\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200311_115853\n50\n100\nH0[km s\n1 Mpc\n1]\nFigure 7. Plots reporting the results on the H0 inference for each event using the GLADE+ K band and luminosity weighting.\nTwo panels are shown for each event. Top panels: Hierarchical likelihood under the hypothesis, G, that the host galaxy is in\nthe catalog (blue solid lines) and under the hypothesis, \u00afG, that the host galaxy is not in the catalog (pink dashed lines). The\ndi\ufb00erent lines shown in each panel correspond to the di\ufb00erent pixels within the sky localization area for each event. Bottom\npanels: The blue solid line shows the posterior obtained by summing the terms corresponding to the in-catalog and out-of-catalog\nhypotheses. The orange dashed line shows the posterior obtained by assuming a galaxy catalog with null completeness. In this\ncase the H0 inference comes entirely from the population assumptions. This plot is intended to show which event is informative\non the H0 value and whether the information is coming from population assumptions or galaxy catalog contribution.\n(when the galaxy catalog is not complete) and in the in-\ncatalog terms when a large number of galaxies is present\nin the GW sky localization volume.\nIn Fig. 9 we show the combined H0 posterior inferred\nfrom all of the GW events and for several di\ufb00erent sce-\nnarios. By using all of the dark sirens, together with\nK\u2013band galaxy information from GLADE+, we obtain a\nvalue of H0 = 67+13\n\u221212 km s\u22121 Mpc\u22121.\nThis value is\nstrongly dominated by the BH population assumptions,\nas can be seen in Fig. 9. The H0 value obtained from\npopulation assumptions alone (Empty catalog case in\nFig. 9) is H0 = 67+14\n\u221213 km s\u22121 Mpc\u22121. When we com-\nbine the galaxy catalog measurement with the result\nfrom the bright standard siren GW170817, we obtain\nH0 = 68+8\n\u22126 km s\u22121 Mpc\u22121.\nThis value represents an\nimprovement of 42% with respect to the corresponding\n\nConstraints on the cosmic expansion history from GWTC\u20133\n25\n0\n25\n50\n75\n100\n125\n150\nRedshift distribution\nK-band, 90% CI GW area (mthr = 13.72)\nUniform comoving volume\nGalaxies distribution (weighted)\nGW localization\nGalaxies distribution (unweighted)\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nz\n0.00\n0.25\n0.50\n0.75\n1.00\n1.25\n1.50\nP(G|z, H0)\nweighted\nunweighted\nGW190814 90% CI\n0\n25\n50\n75\n100\n125\n150\nRedshift distribution\nBJ-band, 90% CI GW area (mthr = 19.82)\nUniform comoving volume\nGalaxies distribution (weighted)\nGW localization\nGalaxies distribution (unweighted)\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\n0.08\nz\n0.00\n0.25\n0.50\n0.75\n1.00\n1.25\n1.50\nP(G|z, H0)\nweighted\nunweighted\nGW190814 90% CI\nFigure 8.\nTop panels: Distribution of galaxies observed in the GLADE+ K(left panels) and BJ (right panels) bands as a\nfunction of redshift z with and without galaxy luminosity weights, compared with the GW190814 redshift localization in its\n90% CI sky area, assuming a cosmology with H0 = 67.9 km s\u22121 Mpc\u22121 and \u2126m = 0.3065 (green line) and the predicted redshift\ndistribution for a prior that is uniform in comoving volume (blue dashed line). The redshift distribution is not intended as\nrepresentative of the reconstructed galaxy distribution since it is calculated by stacking each galaxy redshift localization assumed\nas a normal distribution. This procedure only serves to give a rough idea where the H0 contribution is coming from. Bottom\npanels: Completeness calculated using the K and BJ band with and without application of the luminosity weighing scheme.\nresult obtained with GWTC\u20131 (Abbott et al. 2021a),\nand an improvement of 44% with respect to the result\nof H0 = 69+17\n\u22128\nkm s\u22121 Mpc\u22121 obtained using only the\nGW170817 event (Abbott et al. 2021a) .\n5. DISCUSSION\n5.1. Considerations for the BBH-based population\nanalysis\nWe have shown how population assumptions on BBH\nformation dominate the inference on cosmological pa-\nrameters and, in particular, we have seen how the pres-\nence of an excess of BBHs with primary masses between\n30 M\u2299and 40 M\u2299(Farr et al. 2019) sets a scale for the\nBBH redshifts, thus allowing for a weak constraint on\nH0.\nIn\nthe\nBBH-based\npopulation\nanalysis\nwithout\nGW170817, the (H0, \u2126m, w0) parameters are not con-\nstrained.\nIn Fig. 10 we portray these constraints on\nthe expansion rate of the Universe, H(z).\nThe best\nconstraint that we obtain on the expansion rate of the\nUniverse has a value, and uncertainty (median and\nsymmetric 90% CI), of 74+34\n\u221213 km s\u22121 Mpc\u22121 at redshift\nz = 0 if we include the bright siren GW170817, and\n62+87\n\u221241 km s\u22121 Mpc\u22121 at redshift z \u223c0.01 without it.\n5.2. Considerations on the catalog analysis\nAs already discussed in Sec. 4.2, the H0 inference is\ndominated by the population assumptions of the under-\nlying BH mass distribution. In particular, as shown in\nFig. 5, the population parameter that is most strongly\ncorrelated with the value of H0 is the position of the\nBHs excess \u00b5g.\nIn Fig. 11 we show the H0 posterior computed with\ndi\ufb00erent choices of \u00b5g and \ufb01xing the remaining param-\neters. The values of \u00b5g are spaced by \u223c2.5M\u2299, which\nis roughly the uncertainty identi\ufb01ed in Sec. 2.1. It can\nbe seen that the value of \u00b5g has a strong impact on the\ninference of H0. For values of \u00b5g higher than the me-\ndian value of 32.55M\u2299, the posterior supports low H0\nvalues as we need GW events to be at a lower redshift\nto explain the excess of BHs at higher masses. On the\nother hand, for \u00b5g < 32.55 M\u2299, the posterior supports\nhigher H0 value in order to place events at higher red-\nshift compatible with an excess of BHs at lower masses.\nWe also explored the e\ufb00ect of raising the maximum\nmass of the black holes to mmax = 150 M\u2299. As can be\nseen in Fig. 11, raising mmax does not have a signi\ufb01-\ncant e\ufb00ect on the H0 posterior since only few events are\npresent at these masses. One more parameter for which\n\n26\nAbbott et al.\n20\n40\n60\n80\n100\n120\n140\nH0[km s\n1 Mpc\n1]\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\np(H0|x)[km\n1 s Mpc]\nGW170817\nEmpty catalog\nK-band with GW170817\nK-band\nPlanck\nSH0ES\nFigure 9. Hubble constant posterior for several cases. Gray\ndotted line: posterior obtained using all dark standard sirens\nwithout any galaxy catalog information and \ufb01xing the BBH\npopulation model. Orange dashed line: posterior using all\ndark standard sirens with GLADE+ K\u2013band galaxy catalog in-\nformation and \ufb01xed population assumptions.\nBlack solid\nline:\nposterior from GW170817 and its EM counterpart.\nBlue solid line: posterior combining dark standard sirens\nand GLADE+ K\u2013band catalog information (orange dashed line)\nwith GW170817 and its EM counterpart (black solid line).\nThe pink and green shaded areas identify the 68% CI con-\nstraints on H0 inferred from the CMB anisotropies (Ade et al.\n2016) and in the local Universe from SH0ES (Riess et al.\n2019) respectively.\n0.00\n0.25\n0.50\n0.75\n1.00\n1.25\n1.50\n1.75\n2.00\nz\n0\n100\n200\n300\n400\n500\n600\n700\n800\nH(z)[km s\n1 Mpc\n1]\nPrior\nPosterior\nPosterior+GW170817\nFigure 10. Evolution of the Hubble parameter predicted\nfrom the most preferred mass model Power Law + Peak\n(blue lines). The yellow shaded area indicates the 90% CL\ncontours identi\ufb01ed by the uniform priors on H0, \u2126m and w0\nwhile the blue shaded area indicates the 90% CL contours\nfrom the posterior of the preferred mass model. The dashed\nlines indicate the median of the prior and posterior for H(z)\nrespectively.\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\np(H0|x)[km\n1 s Mpc]\nK-band, \ng = 30M\nK-band, = 2.59\nK-band, mmax = 150M\nK-band, \ng = 35M\nK-band\nEmpty catalog\nPlanck\nSH0ES\n20\n40\n60\n80\n100\n120\n140\nH0[km s\n1 Mpc\n1]\n0.00\n0.01\n0.02\n0.03\n0.04\n0.05\np(H0|x)[km\n1 s Mpc]\nBJ-band\nK-band, unweighted\nK-band\nEmpty catalog\nPlanck\nSH0ES\nFigure 11. Systematic e\ufb00ects on the inference of the Hubble\nconstant due to the choice of di\ufb00erent values for the mean \u00b5g\nof the Gaussian component in the source mass model, and\nother population model parameters (upper panel) and dif-\nferent choices for the luminosity band and weighting scheme\nadopted for the GLADE+ galaxy catalog (lower panel). The\npink and green shaded areas identify the 68% CI constraints\non H0 inferred from the CMB anisotropies (Ade et al. 2016)\nand in the local Universe from SH0ES (Riess et al. 2019)\nrespectively.\nwe explored the e\ufb00ect of its variation is the \u03b3 parameter\nin the rate evolution model. In the same plot one can\nsee the H0 posterior for \u03b3 = 2.59. This parameter has a\nstronger e\ufb00ect on the H0 posterior, making the posterior\nless informative and at the same time moving its peak\nto higher values.\nThe galaxy catalog brings additional information only\nfor GW190814, due to the much better sky localization\n(\u223c18 deg2) for this event; this has the e\ufb00ect of providing\nmore support for the H0 tension region.\nIn Fig. 12, we show how population assumptions im-\npact the hierarchical likelihood calculation as a func-\ntion of H0, for the hypotheses that the host galaxy is\n\nConstraints on the cosmic expansion history from GWTC\u20133\n27\n(or is not) inside the catalog. Population assumptions\nstrongly impact the out-of-catalog term of the likeli-\nhood, which is the dominant contribution to the H0 pos-\nterior when the event is localized in an area where the\ngalaxy catalog has a low completeness fraction which\nhappens for most of the GW events that we consider in\nthis analysis. On the other hand, population assump-\ntions are less important for events with a small localiza-\ntion in a region of the galaxy catalog that is complete.\nIn these cases (for example GW190814), the posterior is\ndominated by the in-catalog likelihood terms and hence\nexhibit a weak dependence on the population assump-\ntions.\nThe aforementioned discussion also explains the di\ufb00er-\nence between our results and those found in Finke et al.\n(2021) using GWTC\u20132 events.\nIn that work the au-\nthors found a weak dependence of their posterior on the\nsource population parameters. However, in their case\nonly a few events, above a given completeness threshold\nof 70% for the main result, were used to explore system-\natic e\ufb00ects due to the source population. Moreover, in\nexploring these systematics they varied the population\nassumptions only within the range of uncertainties re-\nported in Abbott et al. (2021c), which already assumes\na \ufb01xed cosmological model with a value of H0 consistent\nwith the Planck results (Ade et al. 2016). Consequently,\nthe results obtained by them are primarily driven by the\nPlanck cosmological parameters.\nFinally, we also explore the systematics introduced by\nchoices related to the galaxy catalog data. In Fig. 11 we\nalso show the H0 posteriors obtained with the GLADE+\ncatalog, but using K\u2013band galaxies without luminosity\nweighting and BJ\u2013band galaxies with luminosity weight-\ning. In both cases, the H0 posterior is not signi\ufb01cantly\na\ufb00ected by this choice and it is, again, dominated by the\npopulation assumptions.\nHowever, the impact of using luminosity weights is\nnot negligible. For instance, in the case of GW190814\n(see Fig. 12), removing the extra luminosity weight sup-\npresses the H0 posterior peak around 70 km s\u22121 Mpc\u22121.\nThis arises because the luminous galaxies shown in\nFig. 8, observed in the K\u2013band, are now contributing to\nthe GW event redshift localization with the same prob-\nability as the other 200+ galaxies included in the GW\nlocalization volume. We have veri\ufb01ed that the H0 poste-\nrior with the K\u2013band and using luminosity weights does\nnot depend on the faint end magnitude limit used for\nthe analysis.\n5.3. Additional systematic uncertainties\nAs we have seen, the presence of a known source mass\nscale can be used to measure cosmological parameters\n(Farr et al. 2019; Mastrogiovanni et al. 2021). However,\nif the source mass distribution is mismodeled, then the\ncosmological inference will be biased. With the current\nset of events, this e\ufb00ect contributes the dominant source\nof systematic uncertainty in the measurement of H(z).\nIn the population-based method, a key assumption is\nthat the source mass distribution does not evolve with\nredshift (Fishbach et al. 2021); any evolution is degen-\nerate with the cosmological inference. Many BBH for-\nmation scenarios predict mild evolution in the mass dis-\ntribution (Mapelli et al. 2019; Weatherford et al. 2021;\nGallegos-Garcia et al. 2021; Mapelli et al. 2021; van Son\net al. 2021), but given our broad statistical uncertainties,\nwe expect this evolution to only weakly a\ufb00ect our re-\nsults, and we do not attempt to calibrate the mass mod-\nels to theory. In the galaxy-catalog based method, we\n\ufb01x the source mass distribution. In this case, the choice\nof the peak location \u00b5g, associated with excess BHs in\nthe distribution of source masses, is a main source of\nsystematic uncertainty. If the \u00b5g parameter is assumed\nto be lower (or higher) than its true value, this can lead\nto a higher (or lower) inferred value of H0. The impact\nof this bias can be reduced if the support from the in-\ncatalog part of the statistical galaxy catalog method is in-\nformative, which is mainly possible for sources with bet-\nter three-dimensional localization error and with a more\ncomplete galaxy catalog. In the future, as more GW de-\ntectors join the network, resulting in more events with\nbetter sky localizations, and galaxy catalogs which are\nmore complete at high redshift, the impact of the source\npopulation on galaxy catalog method can be mitigated.\nOne of the additional sources of contamination, when\nseeking to infer the true luminosity distance DL (and\nhence the true source masses) of a GW source in the\nabsence of an EM counterpart, is the possible lensing of\nthe GW signal due to the intervening matter distribu-\ntion (Schneider et al. 1992; Bartelmann 2010; Nakamura\n1998; Wang et al. 1996; Takahashi & Nakamura 2003;\nDai et al. 2017; Broadhurst et al. 2018; Diego 2019). In\nthe geometric optics limit, lensing modi\ufb01es the GW sig-\nnal by a magni\ufb01cation factor \u00b5 that only changes the\namplitude of the GW strain, leading to a measured lu-\nminosity distance given by \u02dcDL = DL/\u00b5. In the strong\nlensing limit, when the value of \u00b5 is large, the inferred\nluminosity distance to the source \u02dcdL may be substan-\ntially lower than the true luminosity distance, i.e. in-\ntroducing a bias in the measurement of the luminosity\ndistance. However, for the GW detections considered\nhere, the probability of observing such a strongly-lensed\nevent is less than one percent (Ng et al. 2018a; Oguri\n2018; Mukherjee et al. 2021a), even for a broad range\nof astrophysical time-delay scenarios (Mukherjee et al.\n\n28\nAbbott et al.\nOut-cat.\nGW150914\nIn-cat.\nGW151226\nGW170104\nGW170608\nGW170809\nGW170814\nOut-cat.\nGW170818\nIn-cat.\nGW170823\nGW190408_181802\nGW190412\nGW190425\nGW190503_185404 GW190512_180714 GW190513_205428\nOut-cat.\nGW190517_055101\nIn-cat.\nGW190519_153544\nGW190521\nGW190521_074359 GW190602_175927 GW190630_185205 GW190701_203306 GW190706_222641\nOut-cat.\nGW190707_093326\nIn-cat.\nGW190708_232457 GW190720_000836 GW190727_060333 GW190728_064510\nGW190814\nGW190828_063405 GW190828_065509\nOut-cat.\nGW190910_112807\nIn-cat.\nGW190915_235702 GW190924_021846 GW191109_010717 GW191129_134029 GW191204_171526 GW191216_213338 GW191222_033537\nOut-cat.\nGW200105_162426\n50\n100\nH0[km s\n1 Mpc\n1]\nIn-cat.\nGW200112_155838\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200115_042309\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200129_065458\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200202_154313\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200224_222234\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200225_060421\n50\n100\nH0[km s\n1 Mpc\n1]\nGW200311_115853\n50\n100\nH0[km s\n1 Mpc\n1]\nK-band, \ng = 30M\nBJ-band\nK-band, = 2.59\nK-band\nK-band, unweighted\nK-band, mmax = 150M\nK-band, \ng = 35M\nFigure 12. Plots showing, for each event, the hierarchical likelihood as a function of H0 marginalized over sky localization\nas a function of di\ufb00erent population assumptions and using the GLADE+ K-band. The y-axes of each panel start from zero and\nhave the same normalization. Two panels are shown for each event. Top panels: Hierarchical likelihood under the hypothesis\nthat the host galaxy is not in the catalog, for several di\ufb00erent population assumptions. Bottom panels: Hierarchical likelihood\nunder the hypothesis that the host galaxy is in the catalog, again for several di\ufb00erent population assumptions. This plots how\npopulation and galaxy catalog treatment a\ufb00ect the information on the H0 value for each event.\n2021b). Moreover, searches from O1+O2 (Hannuksela\net al. 2019), and more recent LIGO-Virgo analysis of the\nO3a data did not reveal any signs of strong lensing (Ab-\nbott et al. 2021). Furthermore, searches for a stochas-\ntic GW background also provide a model-independent\nbound on the lensing event rate of BBHs (Mukherjee\net al. 2021a; Buscicchio et al. 2020; Abbott et al. 2021),\nwhich is again consistent with a low probability of con-\ntamination due to strong lensing in the GW sources con-\nsidered here.\nIn this paper we, therefore, ignore any\npossible impact of strong lensing on our cosmological\nparameter estimates.\nApart from strong lensing, weak lensing of GW\nsources can also be a potential source of contamina-\ntion. However, due to the e\ufb00ects of sky averaging, weak\nlensing should not produce a bias in the inferred values\n\nConstraints on the cosmic expansion history from GWTC\u20133\n29\nof the cosmological parameters, but will introduce addi-\ntional variance on the luminosity distance of individual\nsirens at the level of a few percent (Holz & Wald 1998;\nHirata et al. 2010) and it is sub-dominant in comparison\nto the intrinsic measurement error (of about 20%) on\nthe luminosity distance even for the best source in our\ncurrent GW catalog. Hence, we also ignore the uncer-\ntainty due to weak lensing in this paper. However, in a\nfuture analysis, we could include the contribution from\nweak lensing and its impact on the distance measure-\nment (Holz & Wald 1998; Cutler & Holz 2009; Hirata\net al. 2010; Namikawa et al. 2016; Mukherjee et al.\n2020).\n6. CONCLUSIONS\nUsing the 47 GW events with detected SNR > 11 re-\nported in the third LIGO-Virgo-KAGRA Gravitational-\nWave Transient Catalog (Abbott et al. 2021b), we have\ninferred constraints on the cosmological parameters\nadopting two di\ufb00erent approaches: hierarchical infer-\nence without galaxy surveys and the statistical galaxy\ncatalog method. We present for the \ufb01rst time analysis\nthat constrains jointly the properties of the population\nof BBHs and the parameters of the cosmological model,\nand we have shown the crucial correlation that exists\nbetween the two sectors.\nWe have shown that an excess population of BHs in\nthe mass range 30 \u2013 40 M\u2299, pointed out by Abbott et al.\n(2021c), is robust to the choice of assumed cosmolog-\nical model parameters.\nWhile our constraints on the\npresent-day matter density, \u2126m, and dark energy EoS,\nw0, parameters are weak, we have measured the Hubble\nconstant to be H0 = 68+12\n\u22128\nkm s\u22121 Mpc\u22121 at 68% CL\nfrom combining dark sirens with information from the\nbright siren GW170817 and its electromagnetic coun-\nterpart (Abbott et al. 2019b). This result represents an\nimprovement of 17% with respect to the H0 value re-\nported from analysis of O1 and O2 data (Abbott et al.\n2021a) that made use of galaxy catalogs alone to infer\nstatistical redshift information. In our analysis we also\nobtain weak constraints on the expansion history as a\nfunction of redshift.\nIn addition we provide a constraint on the value of\nH0 adopting a \ufb01xed Power Law + Peak population\nmodel of BBHs and using statistical redshift information\ninferred from the GLADE+ galaxy catalog. This analysis\nobtained, for the K\u2013band, H0 = 67+13\n\u221212 km s\u22121 Mpc\u22121,\nwhich represents an improvement of 42% with respect to\nAbbott et al. (2021a) alone, and an improvement of 20%\nwith respect to recent H0 studies using GWTC\u20132 events\n(Finke et al. 2021).\nMost of the constraining power\nin our H0 inference comes from the event GW170817\nusing its electromagnetic counterpart. Combining the\nabove result with information from GW170817 we ob-\ntain 68+8\n\u22126 km s\u22121 Mpc\u22121.\nThe most informative dark\nsiren in the GWTC\u20133 catalog is GW190814, which alone\nprovides an estimate of H0 = 67+46\n\u221228 km s\u22121 Mpc\u22121, pro-\nvided that the luminosity weighting scheme is applied.\nA summary of the di\ufb00erent H0 values obtained using\ndi\ufb00erent data sets and model assumptions can be seen\nin Table\n4. The table is divided into two parts. The\n\ufb01rst part summarises the values that we infer for H0\nwhen \ufb01xing the population model to the most favorable\none and then varying the luminosity band from GLADE+\nused in our analysis. We used both the BJ band and\nthe K band and the results are very similar (see also\nFig. 11). The second part of the table summarises the\nresults obtained by marginalizing over the population\nparameters and using no galaxy catalog information.\nAlthough we have improved our previously reported\nconstraints on the value of H0 using these 47 GW events,\nour results are still dominated by the systematic e\ufb00ects\ninduced by the assumptions made about the GW source\npopulation. The choice of mass scale set by \u00b5g, the mass\nat which the excess of BHs is centered, plays a crucial\nrole in constraining the value of H0.\nIn the future, with signi\ufb01cantly more both bright and\ndark sirens it will be possible to make robust measure-\nments of H0 and other cosmological parameters. On the\none hand, measurement of bright sirens will help greatly\nwith inferring the redshift from direct observations of\nEM counterparts (Holz & Hughes 2005; Dalal et al. 2006;\nNissanke et al. 2010; Chen et al. 2018; Feeney et al.\n2019). On the other hand, for dark sirens, the applica-\ntion of cross-correlation techniques to infer the cluster-\ning redshift of GW sources (Mukherjee et al. 2021; Bera\net al. 2020) using spectroscopic galaxy surveys (Diaz &\nMukherjee 2021), the PISN mass scale of black holes\n(Farr et al. 2019; Mastrogiovanni et al. 2021), the red-\nshift distribution of the GW sources (Ding et al. 2019;\nYe & Fishbach 2021), and the tidal distortion of neutron\nstars (Messenger & Read 2012; Chatterjee et al. 2021)\nwill enable robust measurement of the cosmic expansion\nhistory. With the aid of more observations and further\ndevelopment of analysis techniques, we will be able to\nreduce the current systematics and proceed towards ac-\ncurate and precision gravitational-wave cosmology.\nACKNOWLEDGMENTS\nThis material is based upon work supported by NSF\u2019s\nLIGO Laboratory which is a major facility fully funded\nby the National Science Foundation. The authors also\ngratefully acknowledge the support of the Science and\nTechnology Facilities Council (STFC) of the United\n\n30\nAbbott et al.\nDescription\nGalaxy catalog\nBBH mass model\nHHDI\n0\nHsym\n0\n[km s\u22121 Mpc\u22121]\n[km s\u22121 Mpc\u22121]\nNo galaxy catalog, Marginaliz-\ning over population model, 42\nevents\n-\nTruncated\n109+43\n\u221254 (69+21\n\u22128 )\n104+74\n\u221277 (79+44\n\u221219)\n-\nPower Law + Peak\n50+37\n\u221230 (68+12\n\u22128 )\n62+90\n\u221242 (72+30\n\u221213)\n-\nBroken Power Law\n44+52\n\u221224 (68+13\n\u22128 )\n66+98\n\u221247 (73+34\n\u221214)\nUsing\ngalaxy\ncatalog,\nFixed\npopulation model, 47 events\nGLADE+ K\u2013band\nPower Law + Peak\n67+13\n\u221212 (68+8\n\u22126)\n68+25\n\u221221 (70+17\n\u221213)\nGLADE+ BJ\u2013band\nPower Law + Peak\n67+14\n\u221212 (68+9\n\u22126)\n69+25\n\u221223 (71+18\n\u221212)\nTable 4. Values of the Hubble constant obtained in this study using di\ufb00erent data sets and analysis methods. The columns\nare in order: short description of the sources used in the study with SNR> 11; galaxy catalog used (where appropriate); BBH\nmass model used and the 68.3% CL H0 value. The last two columns report the median and symmetric 90% CI H0 values. The\nvalues in the parenthesis is that obtained after combining with the GW170817 EM counterpart posterior.\nKingdom, the Max-Planck-Society (MPS), and the State\nof Niedersachsen/Germany for support of the construc-\ntion of Advanced LIGO and construction and opera-\ntion of the GEO600 detector.\nAdditional support for\nAdvanced LIGO was provided by the Australian Re-\nsearch Council. The authors gratefully acknowledge the\nItalian Istituto Nazionale di Fisica Nucleare (INFN),\nthe French Centre National de la Recherche Scienti\ufb01que\n(CNRS) and the Netherlands Organization for Scien-\nti\ufb01c Research (NWO), for the construction and oper-\nation of the Virgo detector and the creation and sup-\nport of the EGO consortium. The authors also grate-\nfully acknowledge research support from these agencies\nas well as by the Council of Scienti\ufb01c and Industrial Re-\nsearch of India, the Department of Science and Technol-\nogy, India, the Science & Engineering Research Board\n(SERB), India, the Ministry of Human Resource De-\nvelopment, India, the Spanish Agencia Estatal de In-\nvestigaci\u00b4on (AEI), the Spanish Ministerio de Ciencia e\nInnovaci\u00b4on and Ministerio de Universidades, the Con-\nselleria de Fons Europeus, Universitat i Cultura and the\nDirecci\u00b4o General de Pol\u00b4\u0131tica Universitaria i Recerca del\nGovern de les Illes Balears, the Conselleria d\u2019Innovaci\u00b4o,\nUniversitats, Ci`encia i Societat Digital de la General-\nitat Valenciana and the CERCA Programme General-\nitat de Catalunya, Spain, the National Science Centre\nof Poland and the European Union \u2013 European Re-\ngional Development Fund; Foundation for Polish Science\n(FNP), the Swiss National Science Foundation (SNSF),\nthe Russian Foundation for Basic Research, the Rus-\nsian Science Foundation, the European Commission,\nthe European Social Funds (ESF), the European Re-\ngional Development Funds (ERDF), the Royal Society,\nthe Scottish Funding Council, the Scottish Universi-\nties Physics Alliance, the Hungarian Scienti\ufb01c Research\nFund (OTKA), the French Lyon Institute of Origins\n(LIO), the Belgian Fonds de la Recherche Scienti\ufb01que\n(FRS-FNRS), Actions de Recherche Concert\u00b4ees (ARC)\nand Fonds Wetenschappelijk Onderzoek \u2013 Vlaanderen\n(FWO), Belgium, the Paris \u02c6Ile-de-France Region, the\nNational Research, Development and Innovation O\ufb03ce\nHungary (NKFIH), the National Research Foundation\nof Korea, the Natural Science and Engineering Research\nCouncil Canada, Canadian Foundation for Innovation\n(CFI), the Brazilian Ministry of Science, Technology,\nand Innovations, the International Center for Theoreti-\ncal Physics South American Institute for Fundamental\nResearch (ICTP-SAIFR), the Research Grants Council\nof Hong Kong, the National Natural Science Foundation\nof China (NSFC), the Leverhulme Trust, the Research\nCorporation, the Ministry of Science and Technology\n(MOST), Taiwan, the United States Department of En-\nergy, and the Kavli Foundation. The authors gratefully\nacknowledge the support of the NSF, STFC, INFN and\nCNRS for provision of computational resources.\nThis work was supported by MEXT, JSPS Leading-\nedge Research Infrastructure Program, JSPS Grant-in-\nAid for Specially Promoted Research 26000005, JSPS\nGrant-in-Aid for Scienti\ufb01c Research on Innovative Ar-\neas 2905: JP17H06358, JP17H06361 and JP17H06364,\nJSPS Core-to-Core Program A. Advanced Research Net-\nworks, JSPS Grant-in-Aid for Scienti\ufb01c Research (S)\n17H06133 and 20H05639 , JSPS Grant-in-Aid for Trans-\nformative Research Areas (A) 20A203: JP20H05854, the\njoint research program of the Institute for Cosmic Ray\nResearch, University of Tokyo, National Research Foun-\ndation (NRF) and Computing Infrastructure Project of\nKISTI-GSDC in Korea, Academia Sinica (AS), AS Grid\nCenter (ASGC) and the Ministry of Science and Tech-\nnology (MoST) in Taiwan under grants including AS-\nCDA-105-M06, Advanced Technology Center (ATC) of\nNAOJ, Mechanical Engineering Center of KEK.\nWe would like to thank all of the essential workers who\nput their health at risk during the COVID-19 pandemic,\nwithout whom we would not have been able to complete\nthis work.\n\nConstraints on the cosmic expansion history from GWTC\u20133\n31\nREFERENCES\nAbbott, B. P., et al. 2017a, Phys. Rev. Lett., 119, 161101,\ndoi: 10.1103/PhysRevLett.119.161101\n\u2014. 2017b, Astrophys. J. 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Models for background cosmologies\nWe use a \ufb02at \u039bCDM cosmological model with dark energy density as a function of redshift z described by Linder\n(2003)\n\u03c1\u039b(z) = \u03c1\u039b,0(1 + z)3(1+w0),\n(A1)\nwhere \u03c1\u039b is the dark energy density and w0 is a phenomenological parameter. If the dark energy density is constant\nduring the cosmic expansion, as it is in the standard cosmological model, then w0 = \u22121. The luminosity distance is\ncalculated as\nDL(z) = c(1 + z)\nH0\nZ z\n0\ndz\u2032\np\n\u2126m(1 + z\u2032)3 + \u2126\u039b,0(1 + z\u2032)3(1+w0) ,\n(A2)\nwhere \u2126m and \u2126\u039b,0 are the present-day dimensionless matter and dark energy densities respectively and \u2126\u039b,0 = 1\u2212\u2126m.\nWe consider two sets of priors for the cosmological background model which are indicated in Table 5. For the \ufb01rst\nset of priors, we adopt a \ufb02at \u039bCDM cosmology that restricts the Hubble constant to only the range compatible with\nthe H0 tension, while for the second set we adopt more general, wide priors.\nRestricted priors (H0-tension)\nParameter\nDescription\nPrior\nH0\nHubble constant expressed in km s\u22121 Mpc\u22121 in the H0-tension region.\nU(65, 77)\n\u2126m\nPresent-day matter density of the Universe \ufb01xed to the mean value inferred\nfrom measurements of the CMB in Ade et al. (2016)\n0.3065\nw0\nDark energy equation of state parameter \ufb01xed to the value that corresponds\nto a constant density.\n-1\nWide priors\nParameter\nDescription\nPrior\nH0\nHubble constant expressed in km s\u22121 Mpc\u22121\nU(10.0, 200.0)\n\u2126m\nPresent-day matter density of the Universe.\nU(0.0,1.0)\nw0\nDark energy equation of state parameter.\nU(\u22123.0,0.0)\nTable 5.\nSummary of the priors on the cosmological parameters, for the two sets of priors considered.\nA.2. Merger rate and redshift distribution priors\nWe model the binary merger rate using a phenomenological model introduced with the form of Madau & Dickinson\n(2014), motivated by the fact that the binary formation rate might follow the star formation rate. The parameterization\nthat we use Callister et al. (2020) for the merger rate in the detector frame is\ndN\ndtddz = R0[1 + (1 + zp)\u2212\u03b3\u2212k]\u2202Vc\n\u2202z (\u039bc)\n1\n1 + z\n(1 + z)\u03b3\n1 + [(1 + z)/(1 + zp)]\u03b3+k ,\n(A3)\nwhere R0 is the binary merger rate today, Vc is the comoving volume, \u03b3 and k are the slopes of the two power-law\nregimes before and after a turning point zp and \u039bc are a set of parameters describing the cosmological expansion. The\n\n36\nAbbott et al.\nextra 1/(1 + z) factor encodes the clock di\ufb00erence in the source and detector, while the factor (1 + zp) ensures that\ntoday the merger rate is R(z = 0) = R0. The redshift prior, normalized over the redshift, can be expressed as\n\u03c0(z|\u03b3, \u03ba, zp, \u039bc) = 1\nC\ndN\ndtddz ,\n(A4)\nwhere C is the normalization factor calculated from Eq. (A3).\nThe priors that we use on the merger rate hyper-parameters are indicated in Table 6. The prior ranges that we\nmodel are wide enough to include the e\ufb00ect of a possible time delay between the formation and the merger of the\nbinary.\nParameter\nDescription\nPrior\nR0\nBBH merger rate today in Gpc\u22123 yr\u22121\nU(0.0, 100.0)\n\u03b3\nSlope of the powerlaw regime for the rate evolution before the point zp\nU(0.0, 12.0)\nk\nSlope of the powerlaw regime for the rate evolution after the point zp\nU(0.0, 6.0)\nzp\nRedshift turning point between the powerlaw regimes with \u03b3 and k\nU(0.0, 4.0)\nTable 6.\nSummary of the prior hyper-parameters used for the merger rate evolution models adopted in this paper.\nA.3. Phenomenological Mass priors\nThe three phenomenological mass models that we implement are a superposition of two probability density dis-\ntributions and are compatible with the phenomenological priors used for BBHs in Abbott et al. (2021c,d), although\nthe prior ranges on the population parameters are di\ufb00erent. The \ufb01rst is a truncated power law P(x|xmin, xmax, \u03b1)\ndescribed by slope \u03b1, and lower and upper bounds xmin, xmax at which there is a hard cut-o\ufb00\nP(x|xmin, xmax, \u03b1) \u221d\n\uf8f1\n\uf8f2\n\uf8f3\nx\u03b1\n(xmin \u2a7dx \u2a7dxmax)\n0\nOtherwise.\n(A5)\nThe second is a Gaussian distribution with mean \u00b5 and standard deviation \u03c3,\nG(x|\u00b5, \u03c3, a, b) =\n1\n\u03c3\n\u221a\n2\u03c0 exp\n\u0014\n\u2212(x \u2212\u00b5)2\n2\u03c32\n\u0015\n.\n(A6)\nThe source mass priors for the BBHs population that we consider are factorized as\n\u03c0(m1, m2|\u03a6m) = \u03c0(m1|\u03a6m)\u03c0(m2|m1, \u03a6m),\n(A7)\nwhere \u03c0(m1|\u03a6m) is the distribution of the primary mass component while \u03c0(m2|m1, \u03a6m) is the distribution of the\nsecondary mass component given the primary. For all of the mass models, the secondary mass component m2 is\ndescribed with a truncated power-law with slope \u03b2 between a minimum mass mmin and a maximum mass m1\n\u03c0(m2|m1, mmin, \u03b1) = P(m2|mmin, m1, \u03b2),\n(A8)\nwhile the primary mass is described with several models discussed in the following paragraphs.\nFor some of the phenomenological models, we also apply a smoothing factor to the lower end of the mass distribution\n\u03c0(m1, m2|\u03a6m) = [\u03c0(m1|\u03a6m)\u03c0(m2|m1, \u03a6m)]S(m1|\u03b4m, mmin)S(m2|\u03b4m, mmin),\n(A9)\nwhere S is a sigmoid-like window function that adds a tapering of the lower end of the mass distribution. See Eq. (B6)\nand Eq. (B7) of Abbott et al. (2021c) for the explicit expression for the window function.\nThe three phenomenological mass models are highlighted in the following list. In Table 7, we report the prior ranges\nused for the population hyper-parameters.\n\nConstraints on the cosmic expansion history from GWTC\u20133\n37\n\u2022 Truncated model: It describes the distribution of the primary mass m1 with a truncated power law with slope\n\u2212\u03b1 between a minimum mass mmin and a maximum mass mmax.\n\u03c0(m1|mmin, mmax, \u03b1) = P(m1|mmin, mmax, \u2212\u03b1).\n(A10)\n\u2022 Power Law + Peak model: It describes the primary mass component as a superposition of a truncated PL,\nwith slope \u2212\u03b1 between a minimum mass mmin and a maximum mass mmax, plus a Gaussian component with\nmean \u00b5g and standard deviation \u03c3g,\n\u03c0(m1|mmin, mmax, \u03b1, \u03bbg, \u00b5g, \u03c3g) = [(1 \u2212\u03bbg)P(m1|mmin, mmax, \u2212\u03b1) + \u03bbgG(m1|\u00b5g, \u03c3g)].\n(A11)\n\u2022 Broken Power Law model: It describes the distribution of m1 as a PL between a minimum mass mmin and a\nmaximum mass mmax. The Broken Power Law model is characterized by two PL slopes \u03b11 and \u03b12 and by a\nbreaking point between the two regimes at mbreak = b(mmax \u2212mmin), where b is a number \u2208[0, 1]. The broken\nPL model is\n\u03c0(m1|mmin, mmax, \u03b11, \u03b12) = P(m1|mmin, mbreak, \u2212\u03b11) + P(mbreak|mmin, mbreak, \u2212\u03b11)\nP(mbreak|mbreak, mmax, \u2212\u03b12)P(m1|b, mmax, \u2212\u03b12).\n(A12)\nB. FULL RESULTS FROM THE POPULATION ANALYSIS AND EFFECT OF DIFFERENT SNR CUTS\nWe provide extra details on the joint inference of cosmological and population parameters using BBHs.\nIn Fig. 13 we show the corner plots for the posterior associated with the Power Law + Peak model (the one im-\nplemented for the galaxy catalog analysis) adopting wide priors on the cosmological parameters and for the population\nof BBHs. As was also shown in Fig. 5, the main mass-related population parameters correlating with the cosmological\nparameters, and in particular H0, are the position of the Gaussian component (BBH excess in the mass distribution)\nand the higher end of the source mass distribution.\nThe other parameter that correlates with the estimation of H0 is the rate evolution parameter \u03b3. This parameter\nmodels a power-law increasing merger rate with the redshift. We \ufb01nd that higher values of \u03b3 support lower values of\nH0, which is due to the fact that lowering H0 will place events at lower redshifts, which are incompatible with the\nobserved mass distribution; therefore \u03b3 tries to correct this by supporting higher redshifts. However, the posterior on\nthe rate evolution is well within the statistical uncertainties given in (Abbott et al. 2021d).\nWe run additional systematic studies using di\ufb00erent SNR cuts for the selection of the BBHs to include in our\nanalysis. We explore a higher SNR cut of 12 (more pure) that selects a sample of 35 events. We also explore a lower\nSNR cut of 10, allowing 60 events with a IFAR> 0.5 yr and no plausible instrumental origin. For this set of events,\nGW190426 152155 and GW190531 023648 are excluded as their secondary mass extends to lower masses in the NS\nregion.\nThe marginal H0 posterior for all the mass models is shown in Fig. 14, where we show that including more events\nalways produces a posterior on the H0 within the statistical uncertainties of other selection criteria. In all of these\ncases, the excess of BBHs around 35M\u2299is present for all the SNR cuts and it is responsible for the preference observed\nin the H0 posterior.\nC. SCHECHTER LUMINOSITY FUNCTION STUDIES\nIn this Appendix we show comparisons of the Schechter luminosity function (LF) for the galaxies with the K and\nBJ bands galaxies reported in GLADE+. Wrong assumptions on the LF, or incorrect description of the selection biases,\ncould potentially introduce a bias in the inferred H0. Indeed, one of the key assumptions that we have made to\nconstruct our completeness corrections is that the galaxy catalog is magnitude limited, i.e. galaxies are not detected\nonly because they are too faint. This cannot be the case if another selection bias (based on e.g., colors or spectral\nfeatures) were present, or if color and evolution corrections are not implemented properly.\nIn Fig. 15 we show a comparison of the assumed LF and the number density of galaxies per comoving volume present\nin GLADE+. In the case that the galaxy catalog can be correctly described as magnitude-limited, we expect that the\n\n38\nAbbott et al.\nTruncated\nParameter\nDescription\nPrior\n\u03b1\nSpectral index for the PL of the primary mass distribution.\nU(1.5, 12.0)\n\u03b2\nSpectral index for the PL of the mass ratio distribution.\nU(\u22124.0, 12.0)\nmmin\nMinimum mass of the PL component of the primary mass distribution.\nU(2.0 M\u2299, 10.0 M\u2299)\nmmax\nMaximum mass of the PL component of the primary mass distribution.\nU(50.0 M\u2299, 200.0 M\u2299)\nPower Law + Peak\nParameter\nDescription\nPrior\n\u03b1\nSpectral index for the PL of the primary mass distribution.\nU(1.5, 12.0)\n\u03b2\nSpectral index for the PL of the mass ratio distribution.\nU(\u22124.0, 12.0)\nmmin\nMinimum mass of the PL component of the primary mass distribution.\nU(2.0 M\u2299, 10.0 M\u2299)\nmmax\nMaximum mass of the PL component of the primary mass distribution.\nU(50.0 M\u2299, 200.0 M\u2299)\n\u03bbg\nFraction of the model in the Gaussian component.\nU(0.0, 1.0)\n\u00b5g\nMean of the Gaussian component in the primary mass distribution.\nU(20.0 M\u2299, 50.0 M\u2299)\n\u03c3g\nWidth of the Gaussian component in the primary mass distribution.\nU(0.4 M\u2299, 10.0 M\u2299)\n\u03b4m\nRange of mass tapering at the lower end of the mass distribution.\nU(0.0 M\u2299, 10.0 M\u2299)\nBroken Power Law\nParameter\nDescription\nPrior\n\u03b11\nPL slope of the primary mass distribution for masses below mbreak.\nU(1.5, 12.0)\n\u03b12\nPL slope for the primary mass distribution for masses above mbreak.\nU(1.5, 12.0)\n\u03b2\nSpectral index for the PL of the mass ratio distribution.\nU(\u22124.0, 12.0)\nmmin\nMinimum mass of the PL component of the primary mass distribution.\nU(2.0 M\u2299, 50.0 M\u2299)\nmmax\nMaximum mass of the primary mass distribution.\nU(50.0 M\u2299, 200.0 M\u2299)\nb\nThe fraction of the way between mmin and mmax at which the primary\nmass distribution breaks.\nU(0.0,1.0)\n\u03b4m\nRange of mass tapering on the lower end of the mass distribution.\nU(0.0 M\u2299, 10.0 M\u2299)\nTable 7.\nSummary of the priors used for the population hyper-parameters for the three phenomenological mass models.\ndistribution of the GLADE+ galaxies distribution will match the assumed LF at its bright end, and then will start to\ndecrease when we reach (and exceed) the corresponding absolute magnitude threshold. Galaxies in the K\u2013band are\nwell described by this behaviour and missing galaxies can be explained by the impact of the apparent magnitude\nthreshold, while for the BJ\u2013band there seems to be some additional missing galaxies at low redshift. This observed\nbehaviour motivated our decision to present our main results using the K\u2013band magnitudes compiled in the GLADE+\ncatalog.\n\nConstraints on the cosmic expansion history from GWTC\u20133\n39\n2\n1\nw0\n0.25\n0.50\n0.75\nm\n50\n100\n150\nH0\n[km s\n1 Mpc\n1]\n4\n6\n8\n0\n5\n100\n150\nmmax\n[M ]\n4\n6\nmmin\n[M ]\n5\n10\n2\n4\nk\n1\n2\n3\nzp\n2.5\n5.0\n7.5\nm\n2.5\n5.0\n7.5\ng\n0.1\n0.2\n0.3\ng\n25\n50\n75\nR0[Gpc\n3yr\n1]\n30\n40\ng\n[M ]\n2\n1\nw0\n0.250.500.75\nm\n50 100 150\nH0\n[km s\n1 Mpc\n1]\n2.5\n5.0\n7.5\n0\n5\n100\n150\nmmax\n[M ]\n2.5\n5.0\nmmin\n[M ]\n5\n10\n2.5\n5.0\nk\n1\n2\n3\nzp\n2.5 5.0 7.5\nm\n2.5 5.0 7.5\ng\n0.1\n0.2\n0.3\ng\n30\n40\ng\n[M ]\nFigure 13. Corner plots for the preferred Power Law + Peak model parameters and cosmological parameters, \ufb01tted to\nBBHs with SNR > 11.\n\n40\nAbbott et al.\n100\n200\nH0[km s\n1 Mpc\n1]\n0.000\n0.005\n0.010\n0.015\n0.020\np(H0|x) [km\n1 s Mpc]\nBroken Power Law\nSNR>10\nSNR>11\nSNR>12\nPlanck\nSH0ES\n100\n200\nH0[km s\n1 Mpc\n1]\np(H0|x) [km\n1 s Mpc]\nPower Law + Peak\nSNR>10\nSNR>11\nSNR>12\nPlanck\nSH0ES\n100\n200\nH0[km s\n1 Mpc\n1]\np(H0|x) [km\n1 s Mpc]\nTruncated\nSNR>10\nSNR>11\nSNR>12\nPlanck\nSH0ES\nFigure 14. Marginal posterior probability distributions for H0 with using BBH events with three di\ufb00erent SNR cuts and the\nthree mass models.\n22\n21\n20\n19\n18\n17\nM\n5log10h0.7\n10\n5\n10\n4\n10\n3\n10\n2\ndn\ndM[h3\n0.7Mpc\n3]\nBJ-band\n0.00